diff --git a/-Pg11JHzUTo.txt b/-Pg11JHzUTo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c992c083abaa15f21276c7f8694a80badb5cf8d
--- /dev/null
+++ b/-Pg11JHzUTo.txt
@@ -0,0 +1,14459 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so last time we ended on one of these
+
+ align:start position:0%
+so last time we ended on one of these
+ 
+
+ align:start position:0%
+so last time we ended on one of these
+Cliffhangers uh and uh so I rushed you
+
+ align:start position:0%
+Cliffhangers uh and uh so I rushed you
+ 
+
+ align:start position:0%
+Cliffhangers uh and uh so I rushed you
+through a bunch of Japanese data and
+
+ align:start position:0%
+through a bunch of Japanese data and
+ 
+
+ align:start position:0%
+through a bunch of Japanese data and
+then we got to
+
+ align:start position:0%
+then we got to
+ 
+
+ align:start position:0%
+then we got to
+um this new bit of linguistic technology
+
+ align:start position:0%
+um this new bit of linguistic technology
+ 
+
+ align:start position:0%
+um this new bit of linguistic technology
+that's going to be annoying
+
+ align:start position:0%
+that's going to be annoying
+ 
+
+ align:start position:0%
+that's going to be annoying
+um this new bit of linguistic technology
+
+ align:start position:0%
+um this new bit of linguistic technology
+ 
+
+ align:start position:0%
+um this new bit of linguistic technology
+and uh sort of went through it pretty
+
+ align:start position:0%
+and uh sort of went through it pretty
+ 
+
+ align:start position:0%
+and uh sort of went through it pretty
+fast so what I want to do is do the
+
+ align:start position:0%
+fast so what I want to do is do the
+ 
+
+ align:start position:0%
+fast so what I want to do is do the
+run-up to that again a little more
+
+ align:start position:0%
+run-up to that again a little more
+ 
+
+ align:start position:0%
+run-up to that again a little more
+carefully and show you what it is that
+
+ align:start position:0%
+carefully and show you what it is that
+ 
+
+ align:start position:0%
+carefully and show you what it is that
+we're talking about what we were talking
+
+ align:start position:0%
+we're talking about what we were talking
+ 
+
+ align:start position:0%
+we're talking about what we were talking
+about at the end was the position of
+
+ align:start position:0%
+about at the end was the position of
+ 
+
+ align:start position:0%
+about at the end was the position of
+accent and Japanese compounds so here
+
+ align:start position:0%
+accent and Japanese compounds so here
+ 
+
+ align:start position:0%
+accent and Japanese compounds so here
+are a bunch of compound nouns uh in
+
+ align:start position:0%
+are a bunch of compound nouns uh in
+ 
+
+ align:start position:0%
+are a bunch of compound nouns uh in
+Japanese and the observation was that
+
+ align:start position:0%
+Japanese and the observation was that
+ 
+
+ align:start position:0%
+Japanese and the observation was that
+when you have two compound consisting of
+
+ align:start position:0%
+when you have two compound consisting of
+ 
+
+ align:start position:0%
+when you have two compound consisting of
+two parts uh you the result always has
+
+ align:start position:0%
+two parts uh you the result always has
+ 
+
+ align:start position:0%
+two parts uh you the result always has
+one accent it has Accent on one
+
+ align:start position:0%
+one accent it has Accent on one
+ 
+
+ align:start position:0%
+one accent it has Accent on one
+particular syllable
+
+ align:start position:0%
+particular syllable
+ 
+
+ align:start position:0%
+particular syllable
+um the accented syllable doesn't have to
+
+ align:start position:0%
+um the accented syllable doesn't have to
+ 
+
+ align:start position:0%
+um the accented syllable doesn't have to
+be the accented syllable in either of
+
+ align:start position:0%
+be the accented syllable in either of
+ 
+
+ align:start position:0%
+be the accented syllable in either of
+the original you know parts of the
+
+ align:start position:0%
+the original you know parts of the
+ 
+
+ align:start position:0%
+the original you know parts of the
+compounds so like raw egg which is the
+
+ align:start position:0%
+compounds so like raw egg which is the
+ 
+
+ align:start position:0%
+compounds so like raw egg which is the
+first example on this slide
+
+ align:start position:0%
+first example on this slide
+ 
+
+ align:start position:0%
+first example on this slide
+raw and egg uh you know they have
+
+ align:start position:0%
+raw and egg uh you know they have
+ 
+
+ align:start position:0%
+raw and egg uh you know they have
+accents where they have accents raw has
+
+ align:start position:0%
+accents where they have accents raw has
+ 
+
+ align:start position:0%
+accents where they have accents raw has
+an accent on the first syllable egg has
+
+ align:start position:0%
+an accent on the first syllable egg has
+ 
+
+ align:start position:0%
+an accent on the first syllable egg has
+snacks in on the second syllable but raw
+
+ align:start position:0%
+snacks in on the second syllable but raw
+ 
+
+ align:start position:0%
+snacks in on the second syllable but raw
+egg has an accent on the syllable which
+
+ align:start position:0%
+egg has an accent on the syllable which
+ 
+
+ align:start position:0%
+egg has an accent on the syllable which
+is not normally accented in a
+
+ align:start position:0%
+is not normally accented in a
+ 
+
+ align:start position:0%
+is not normally accented in a
+um what we said was you know there is a
+
+ align:start position:0%
+um what we said was you know there is a
+ 
+
+ align:start position:0%
+um what we said was you know there is a
+set of rules for where accent goes in
+
+ align:start position:0%
+set of rules for where accent goes in
+ 
+
+ align:start position:0%
+set of rules for where accent goes in
+these compounds
+
+ align:start position:0%
+these compounds
+ 
+
+ align:start position:0%
+these compounds
+and the rules go something like this uh
+
+ align:start position:0%
+and the rules go something like this uh
+ 
+
+ align:start position:0%
+and the rules go something like this uh
+there's only going to be one accent it
+
+ align:start position:0%
+there's only going to be one accent it
+ 
+
+ align:start position:0%
+there's only going to be one accent it
+needs to be next to the boundary between
+
+ align:start position:0%
+needs to be next to the boundary between
+ 
+
+ align:start position:0%
+needs to be next to the boundary between
+the words
+
+ align:start position:0%
+the words
+ 
+
+ align:start position:0%
+the words
+um and if possible it should be on the
+
+ align:start position:0%
+um and if possible it should be on the
+ 
+
+ align:start position:0%
+um and if possible it should be on the
+second word that is it should be after
+
+ align:start position:0%
+second word that is it should be after
+ 
+
+ align:start position:0%
+second word that is it should be after
+the boundary between the words
+
+ align:start position:0%
+the boundary between the words
+ 
+
+ align:start position:0%
+the boundary between the words
+but you don't do that if that would
+
+ align:start position:0%
+but you don't do that if that would
+ 
+
+ align:start position:0%
+but you don't do that if that would
+result in the accident being on the last
+
+ align:start position:0%
+result in the accident being on the last
+ 
+
+ align:start position:0%
+result in the accident being on the last
+syllable so the sort of General pattern
+
+ align:start position:0%
+syllable so the sort of General pattern
+ 
+
+ align:start position:0%
+syllable so the sort of General pattern
+is the one you're getting in french
+
+ align:start position:0%
+is the one you're getting in french
+ 
+
+ align:start position:0%
+is the one you're getting in french
+fries
+
+ align:start position:0%
+fries
+ 
+
+ align:start position:0%
+fries
+where you get accent at the beginning of
+
+ align:start position:0%
+where you get accent at the beginning of
+ 
+
+ align:start position:0%
+where you get accent at the beginning of
+the second half of the compound potato
+
+ align:start position:0%
+the second half of the compound potato
+ 
+
+ align:start position:0%
+the second half of the compound potato
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um that's what you get in most of the
+
+ align:start position:0%
+um that's what you get in most of the
+ 
+
+ align:start position:0%
+um that's what you get in most of the
+examples on the preceding slide if we go
+
+ align:start position:0%
+examples on the preceding slide if we go
+ 
+
+ align:start position:0%
+examples on the preceding slide if we go
+back to the preceding slide you can see
+
+ align:start position:0%
+back to the preceding slide you can see
+ 
+
+ align:start position:0%
+back to the preceding slide you can see
+that in raw egg right it's at the
+
+ align:start position:0%
+that in raw egg right it's at the
+ 
+
+ align:start position:0%
+that in raw egg right it's at the
+beginning of egg you can see it in field
+
+ align:start position:0%
+beginning of egg you can see it in field
+ 
+
+ align:start position:0%
+beginning of egg you can see it in field
+mouse it's at the beginning of mouse and
+
+ align:start position:0%
+mouse it's at the beginning of mouse and
+ 
+
+ align:start position:0%
+mouse it's at the beginning of mouse and
+uh you're also getting it in French fry
+
+ align:start position:0%
+uh you're also getting it in French fry
+ 
+
+ align:start position:0%
+uh you're also getting it in French fry
+but there's this class sort of coherent
+
+ align:start position:0%
+but there's this class sort of coherent
+ 
+
+ align:start position:0%
+but there's this class sort of coherent
+class of exceptions if the second half
+
+ align:start position:0%
+class of exceptions if the second half
+ 
+
+ align:start position:0%
+class of exceptions if the second half
+of the compound is only one syllable
+
+ align:start position:0%
+of the compound is only one syllable
+ 
+
+ align:start position:0%
+of the compound is only one syllable
+long then you don't put accent on the
+
+ align:start position:0%
+long then you don't put accent on the
+ 
+
+ align:start position:0%
+long then you don't put accent on the
+second half you put it at the end of the
+
+ align:start position:0%
+second half you put it at the end of the
+ 
+
+ align:start position:0%
+second half you put it at the end of the
+first half so Kagawa prefecture uh
+
+ align:start position:0%
+first half so Kagawa prefecture uh
+ 
+
+ align:start position:0%
+first half so Kagawa prefecture uh
+Kagawa is uh its name of a place and
+
+ align:start position:0%
+Kagawa is uh its name of a place and
+ 
+
+ align:start position:0%
+Kagawa is uh its name of a place and
+it's got Accent on its first syllable
+
+ align:start position:0%
+it's got Accent on its first syllable
+ 
+
+ align:start position:0%
+it's got Accent on its first syllable
+but the expression for Kagawa prefecture
+
+ align:start position:0%
+but the expression for Kagawa prefecture
+ 
+
+ align:start position:0%
+but the expression for Kagawa prefecture
+has accent at almost at the boundary
+
+ align:start position:0%
+has accent at almost at the boundary
+ 
+
+ align:start position:0%
+has accent at almost at the boundary
+it's right before the boundary between
+
+ align:start position:0%
+it's right before the boundary between
+ 
+
+ align:start position:0%
+it's right before the boundary between
+them not on the second half of the
+
+ align:start position:0%
+them not on the second half of the
+ 
+
+ align:start position:0%
+them not on the second half of the
+compound unusually because the second
+
+ align:start position:0%
+compound unusually because the second
+ 
+
+ align:start position:0%
+compound unusually because the second
+half of the compound is only one
+
+ align:start position:0%
+half of the compound is only one
+ 
+
+ align:start position:0%
+half of the compound is only one
+syllable longs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm telling you all this not just to
+
+ align:start position:0%
+I'm telling you all this not just to
+ 
+
+ align:start position:0%
+I'm telling you all this not just to
+educate you in what a cool and
+
+ align:start position:0%
+educate you in what a cool and
+ 
+
+ align:start position:0%
+educate you in what a cool and
+complicated language Japanese is uh but
+
+ align:start position:0%
+complicated language Japanese is uh but
+ 
+
+ align:start position:0%
+complicated language Japanese is uh but
+to show you that there are cases of cool
+
+ align:start position:0%
+to show you that there are cases of cool
+ 
+
+ align:start position:0%
+to show you that there are cases of cool
+and complicated phenomena uh that can be
+
+ align:start position:0%
+and complicated phenomena uh that can be
+ 
+
+ align:start position:0%
+and complicated phenomena uh that can be
+fruitfully thought of as a series of
+
+ align:start position:0%
+fruitfully thought of as a series of
+ 
+
+ align:start position:0%
+fruitfully thought of as a series of
+things that you're trying to do which
+
+ align:start position:0%
+things that you're trying to do which
+ 
+
+ align:start position:0%
+things that you're trying to do which
+are in conflict with each other
+
+ align:start position:0%
+are in conflict with each other
+ 
+
+ align:start position:0%
+are in conflict with each other
+sometimes so Japanese wants the accent
+
+ align:start position:0%
+sometimes so Japanese wants the accent
+ 
+
+ align:start position:0%
+sometimes so Japanese wants the accent
+to be on the second word right and next
+
+ align:start position:0%
+to be on the second word right and next
+ 
+
+ align:start position:0%
+to be on the second word right and next
+to the boundary between the words but it
+
+ align:start position:0%
+to the boundary between the words but it
+ 
+
+ align:start position:0%
+to the boundary between the words but it
+also wants it not to be final
+
+ align:start position:0%
+also wants it not to be final
+ 
+
+ align:start position:0%
+also wants it not to be final
+and if it can't have all of those things
+
+ align:start position:0%
+and if it can't have all of those things
+ 
+
+ align:start position:0%
+and if it can't have all of those things
+at once like in gagawa prefecture it has
+
+ align:start position:0%
+at once like in gagawa prefecture it has
+ 
+
+ align:start position:0%
+at once like in gagawa prefecture it has
+to decide do I care more about it not
+
+ align:start position:0%
+to decide do I care more about it not
+ 
+
+ align:start position:0%
+to decide do I care more about it not
+being final or do I care more about it
+
+ align:start position:0%
+being final or do I care more about it
+ 
+
+ align:start position:0%
+being final or do I care more about it
+being on the second word and Japanese
+
+ align:start position:0%
+being on the second word and Japanese
+ 
+
+ align:start position:0%
+being on the second word and Japanese
+cares more about it not about it uh not
+
+ align:start position:0%
+cares more about it not about it uh not
+ 
+
+ align:start position:0%
+cares more about it not about it uh not
+being final right so it retracts it from
+
+ align:start position:0%
+being final right so it retracts it from
+ 
+
+ align:start position:0%
+being final right so it retracts it from
+the second word to the end of the first
+
+ align:start position:0%
+the second word to the end of the first
+ 
+
+ align:start position:0%
+the second word to the end of the first
+word so this is this case does anybody
+
+ align:start position:0%
+word so this is this case does anybody
+ 
+
+ align:start position:0%
+word so this is this case does anybody
+still read Isaac Asimov had these
+
+ align:start position:0%
+still read Isaac Asimov had these
+ 
+
+ align:start position:0%
+still read Isaac Asimov had these
+stories the robot stories uh I had a
+
+ align:start position:0%
+stories the robot stories uh I had a
+ 
+
+ align:start position:0%
+stories the robot stories uh I had a
+book I Robot it was a series of stories
+
+ align:start position:0%
+book I Robot it was a series of stories
+ 
+
+ align:start position:0%
+book I Robot it was a series of stories
+some of you have heard of them at least
+
+ align:start position:0%
+some of you have heard of them at least
+ 
+
+ align:start position:0%
+some of you have heard of them at least
+yeah so they feature uh robots that uh
+
+ align:start position:0%
+yeah so they feature uh robots that uh
+ 
+
+ align:start position:0%
+yeah so they feature uh robots that uh
+have these laws governing how they work
+
+ align:start position:0%
+have these laws governing how they work
+ 
+
+ align:start position:0%
+have these laws governing how they work
+and the laws act like these kinds of
+
+ align:start position:0%
+and the laws act like these kinds of
+ 
+
+ align:start position:0%
+and the laws act like these kinds of
+laws so there's the first law uh and
+
+ align:start position:0%
+laws so there's the first law uh and
+ 
+
+ align:start position:0%
+laws so there's the first law uh and
+then there's the second law and the rule
+
+ align:start position:0%
+then there's the second law and the rule
+ 
+
+ align:start position:0%
+then there's the second law and the rule
+for the second law is you must obey the
+
+ align:start position:0%
+for the second law is you must obey the
+ 
+
+ align:start position:0%
+for the second law is you must obey the
+second law unless it comes in conflict
+
+ align:start position:0%
+second law unless it comes in conflict
+ 
+
+ align:start position:0%
+second law unless it comes in conflict
+with the first law then you disobey the
+
+ align:start position:0%
+with the first law then you disobey the
+ 
+
+ align:start position:0%
+with the first law then you disobey the
+second law and do the first law right
+
+ align:start position:0%
+second law and do the first law right
+ 
+
+ align:start position:0%
+second law and do the first law right
+and there's a third law which you should
+
+ align:start position:0%
+and there's a third law which you should
+ 
+
+ align:start position:0%
+and there's a third law which you should
+do unless it conflicts with the first or
+
+ align:start position:0%
+do unless it conflicts with the first or
+ 
+
+ align:start position:0%
+do unless it conflicts with the first or
+the second laws uh this is like that
+
+ align:start position:0%
+the second laws uh this is like that
+ 
+
+ align:start position:0%
+the second laws uh this is like that
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+um Japanese wants the accent to be on
+
+ align:start position:0%
+um Japanese wants the accent to be on
+ 
+
+ align:start position:0%
+um Japanese wants the accent to be on
+the second word oh unless that's going
+
+ align:start position:0%
+the second word oh unless that's going
+ 
+
+ align:start position:0%
+the second word oh unless that's going
+to make the accent final then you don't
+
+ align:start position:0%
+to make the accent final then you don't
+ 
+
+ align:start position:0%
+to make the accent final then you don't
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+uh that's a way
+
+ align:start position:0%
+uh that's a way
+ 
+
+ align:start position:0%
+uh that's a way
+or to put that another way don't put the
+
+ align:start position:0%
+or to put that another way don't put the
+ 
+
+ align:start position:0%
+or to put that another way don't put the
+accent on the last syllable is more
+
+ align:start position:0%
+accent on the last syllable is more
+ 
+
+ align:start position:0%
+accent on the last syllable is more
+important than put the accent on the
+
+ align:start position:0%
+important than put the accent on the
+ 
+
+ align:start position:0%
+important than put the accent on the
+second word that's the picture so you
+
+ align:start position:0%
+second word that's the picture so you
+ 
+
+ align:start position:0%
+second word that's the picture so you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+um uh Kagawa can with the accent at the
+
+ align:start position:0%
+um uh Kagawa can with the accent at the
+ 
+
+ align:start position:0%
+um uh Kagawa can with the accent at the
+end of Kagawa uh uh and not Kagawa King
+
+ align:start position:0%
+end of Kagawa uh uh and not Kagawa King
+ 
+
+ align:start position:0%
+end of Kagawa uh uh and not Kagawa King
+you know put accent on the at the end
+
+ align:start position:0%
+you know put accent on the at the end
+ 
+
+ align:start position:0%
+you know put accent on the at the end
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's a standard way of representing
+
+ align:start position:0%
+there's a standard way of representing
+ 
+
+ align:start position:0%
+there's a standard way of representing
+these kinds of facts these bodies of
+
+ align:start position:0%
+these kinds of facts these bodies of
+ 
+
+ align:start position:0%
+these kinds of facts these bodies of
+facts which involves this table that
+
+ align:start position:0%
+facts which involves this table that
+ 
+
+ align:start position:0%
+facts which involves this table that
+I've got here at the bottom of the uh
+
+ align:start position:0%
+I've got here at the bottom of the uh
+ 
+
+ align:start position:0%
+I've got here at the bottom of the uh
+the slide this was uh is an approach to
+
+ align:start position:0%
+the slide this was uh is an approach to
+ 
+
+ align:start position:0%
+the slide this was uh is an approach to
+phonology that was invented by people uh
+
+ align:start position:0%
+phonology that was invented by people uh
+ 
+
+ align:start position:0%
+phonology that was invented by people uh
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+um one of them in particular Ellen
+
+ align:start position:0%
+um one of them in particular Ellen
+ 
+
+ align:start position:0%
+um one of them in particular Ellen
+Prince is uh brilliant brilliant men but
+
+ align:start position:0%
+Prince is uh brilliant brilliant men but
+ 
+
+ align:start position:0%
+Prince is uh brilliant brilliant men but
+he enjoys intimidating people and so
+
+ align:start position:0%
+he enjoys intimidating people and so
+ 
+
+ align:start position:0%
+he enjoys intimidating people and so
+instead of calling this a table uh he
+
+ align:start position:0%
+instead of calling this a table uh he
+ 
+
+ align:start position:0%
+instead of calling this a table uh he
+decided to call it a tableau so he gives
+
+ align:start position:0%
+decided to call it a tableau so he gives
+ 
+
+ align:start position:0%
+decided to call it a tableau so he gives
+it a French name uh in order to be as
+
+ align:start position:0%
+it a French name uh in order to be as
+ 
+
+ align:start position:0%
+it a French name uh in order to be as
+intimidating as possible
+
+ align:start position:0%
+intimidating as possible
+ 
+
+ align:start position:0%
+intimidating as possible
+um so I'll I'll adopt that because
+
+ align:start position:0%
+um so I'll I'll adopt that because
+ 
+
+ align:start position:0%
+um so I'll I'll adopt that because
+that's what the tactician standard
+
+ align:start position:0%
+that's what the tactician standard
+ 
+
+ align:start position:0%
+that's what the tactician standard
+phonologists uh linguists standardly
+
+ align:start position:0%
+phonologists uh linguists standardly
+ 
+
+ align:start position:0%
+phonologists uh linguists standardly
+call these objects this is a tableau
+
+ align:start position:0%
+call these objects this is a tableau
+ 
+
+ align:start position:0%
+call these objects this is a tableau
+um and what the Tableau represents is
+
+ align:start position:0%
+um and what the Tableau represents is
+ 
+
+ align:start position:0%
+um and what the Tableau represents is
+this kind of interplay between the
+
+ align:start position:0%
+this kind of interplay between the
+ 
+
+ align:start position:0%
+this kind of interplay between the
+different laws that are governing uh
+
+ align:start position:0%
+different laws that are governing uh
+ 
+
+ align:start position:0%
+different laws that are governing uh
+where the accent goes the idea is the
+
+ align:start position:0%
+where the accent goes the idea is the
+ 
+
+ align:start position:0%
+where the accent goes the idea is the
+most important laws are toward the left
+
+ align:start position:0%
+most important laws are toward the left
+ 
+
+ align:start position:0%
+most important laws are toward the left
+and the least important laws are toward
+
+ align:start position:0%
+and the least important laws are toward
+ 
+
+ align:start position:0%
+and the least important laws are toward
+the right and what you do is Imagine
+
+ align:start position:0%
+the right and what you do is Imagine
+ 
+
+ align:start position:0%
+the right and what you do is Imagine
+imagine all of the places where you
+
+ align:start position:0%
+imagine all of the places where you
+ 
+
+ align:start position:0%
+imagine all of the places where you
+could put the accent and you ask
+
+ align:start position:0%
+could put the accent and you ask
+ 
+
+ align:start position:0%
+could put the accent and you ask
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+how does that placement of the accent
+
+ align:start position:0%
+how does that placement of the accent
+ 
+
+ align:start position:0%
+how does that placement of the accent
+you know square with the various
+
+ align:start position:0%
+you know square with the various
+ 
+
+ align:start position:0%
+you know square with the various
+different laws the little asterisks Mark
+
+ align:start position:0%
+different laws the little asterisks Mark
+ 
+
+ align:start position:0%
+different laws the little asterisks Mark
+places where one of the candidates one
+
+ align:start position:0%
+places where one of the candidates one
+ 
+
+ align:start position:0%
+places where one of the candidates one
+of the sort of options you're
+
+ align:start position:0%
+of the sort of options you're
+ 
+
+ align:start position:0%
+of the sort of options you're
+considering violates one of the laws so
+
+ align:start position:0%
+considering violates one of the laws so
+ 
+
+ align:start position:0%
+considering violates one of the laws so
+for example the first one which kept
+
+ align:start position:0%
+for example the first one which kept
+ 
+
+ align:start position:0%
+for example the first one which kept
+both of the Accents in in the parts of
+
+ align:start position:0%
+both of the Accents in in the parts of
+ 
+
+ align:start position:0%
+both of the Accents in in the parts of
+the compound just kept them both
+
+ align:start position:0%
+the compound just kept them both
+ 
+
+ align:start position:0%
+the compound just kept them both
+violates the most important law which is
+
+ align:start position:0%
+violates the most important law which is
+ 
+
+ align:start position:0%
+violates the most important law which is
+you may only have one accent so it gets
+
+ align:start position:0%
+you may only have one accent so it gets
+ 
+
+ align:start position:0%
+you may only have one accent so it gets
+a star right there yeah and that
+
+ align:start position:0%
+a star right there yeah and that
+ 
+
+ align:start position:0%
+a star right there yeah and that
+eliminates that one from competition
+
+ align:start position:0%
+eliminates that one from competition
+ 
+
+ align:start position:0%
+eliminates that one from competition
+because you know it's violated the most
+
+ align:start position:0%
+because you know it's violated the most
+ 
+
+ align:start position:0%
+because you know it's violated the most
+important law the one that's furthest on
+
+ align:start position:0%
+important law the one that's furthest on
+ 
+
+ align:start position:0%
+important law the one that's furthest on
+the left uh and then what what I've done
+
+ align:start position:0%
+the left uh and then what what I've done
+ 
+
+ align:start position:0%
+the left uh and then what what I've done
+is consider examples where the accent is
+
+ align:start position:0%
+is consider examples where the accent is
+ 
+
+ align:start position:0%
+is consider examples where the accent is
+a four-syllable word so we're
+
+ align:start position:0%
+a four-syllable word so we're
+ 
+
+ align:start position:0%
+a four-syllable word so we're
+considering putting the single accent in
+
+ align:start position:0%
+considering putting the single accent in
+ 
+
+ align:start position:0%
+considering putting the single accent in
+on any of the four syllables the first
+
+ align:start position:0%
+on any of the four syllables the first
+ 
+
+ align:start position:0%
+on any of the four syllables the first
+two uh which have the accent on the
+
+ align:start position:0%
+two uh which have the accent on the
+ 
+
+ align:start position:0%
+two uh which have the accent on the
+first or the second syllable violate the
+
+ align:start position:0%
+first or the second syllable violate the
+ 
+
+ align:start position:0%
+first or the second syllable violate the
+second law which says put the accent
+
+ align:start position:0%
+second law which says put the accent
+ 
+
+ align:start position:0%
+second law which says put the accent
+near the boundary between the two halves
+
+ align:start position:0%
+near the boundary between the two halves
+ 
+
+ align:start position:0%
+near the boundary between the two halves
+of the compound so uh those are ones in
+
+ align:start position:0%
+of the compound so uh those are ones in
+ 
+
+ align:start position:0%
+of the compound so uh those are ones in
+which uh the accent is not on a syllable
+
+ align:start position:0%
+which uh the accent is not on a syllable
+ 
+
+ align:start position:0%
+which uh the accent is not on a syllable
+that's next to the boundary
+
+ align:start position:0%
+that's next to the boundary
+ 
+
+ align:start position:0%
+that's next to the boundary
+um and then uh the the next last one
+
+ align:start position:0%
+um and then uh the the next last one
+ 
+
+ align:start position:0%
+um and then uh the the next last one
+which is the one that wins that's the
+
+ align:start position:0%
+which is the one that wins that's the
+ 
+
+ align:start position:0%
+which is the one that wins that's the
+one that obeys all of the conditions
+
+ align:start position:0%
+one that obeys all of the conditions
+ 
+
+ align:start position:0%
+one that obeys all of the conditions
+except for the least important one which
+
+ align:start position:0%
+except for the least important one which
+ 
+
+ align:start position:0%
+except for the least important one which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um uh it's best to put your accent on
+
+ align:start position:0%
+um uh it's best to put your accent on
+ 
+
+ align:start position:0%
+um uh it's best to put your accent on
+the last word right right that's not
+
+ align:start position:0%
+the last word right right that's not
+ 
+
+ align:start position:0%
+the last word right right that's not
+there there is no you notice there is no
+
+ align:start position:0%
+there there is no you notice there is no
+ 
+
+ align:start position:0%
+there there is no you notice there is no
+perfect candidate there isn't anything
+
+ align:start position:0%
+perfect candidate there isn't anything
+ 
+
+ align:start position:0%
+perfect candidate there isn't anything
+that doesn't have any stars
+
+ align:start position:0%
+that doesn't have any stars
+ 
+
+ align:start position:0%
+that doesn't have any stars
+um what the Tableau does is allow us to
+
+ align:start position:0%
+um what the Tableau does is allow us to
+ 
+
+ align:start position:0%
+um what the Tableau does is allow us to
+think in a you know formal kind of way
+
+ align:start position:0%
+think in a you know formal kind of way
+ 
+
+ align:start position:0%
+think in a you know formal kind of way
+about uh how you satisfy conditions that
+
+ align:start position:0%
+about uh how you satisfy conditions that
+ 
+
+ align:start position:0%
+about uh how you satisfy conditions that
+are not compatible with each other and I
+
+ align:start position:0%
+are not compatible with each other and I
+ 
+
+ align:start position:0%
+are not compatible with each other and I
+just realized I get to take this off I
+
+ align:start position:0%
+just realized I get to take this off I
+ 
+
+ align:start position:0%
+just realized I get to take this off I
+keep forgetting that
+
+ align:start position:0%
+keep forgetting that
+ 
+
+ align:start position:0%
+keep forgetting that
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so that's what the tip low is meant to
+
+ align:start position:0%
+so that's what the tip low is meant to
+ 
+
+ align:start position:0%
+so that's what the tip low is meant to
+represent are there questions about the
+
+ align:start position:0%
+represent are there questions about the
+ 
+
+ align:start position:0%
+represent are there questions about the
+tableau
+
+ align:start position:0%
+tableau
+ 
+
+ align:start position:0%
+tableau
+there's a standard way to represent the
+
+ align:start position:0%
+there's a standard way to represent the
+ 
+
+ align:start position:0%
+there's a standard way to represent the
+fact that the winner is that next last
+
+ align:start position:0%
+fact that the winner is that next last
+ 
+
+ align:start position:0%
+fact that the winner is that next last
+one there where the stress is on the
+
+ align:start position:0%
+one there where the stress is on the
+ 
+
+ align:start position:0%
+one there where the stress is on the
+next last syllable the accent is on the
+
+ align:start position:0%
+next last syllable the accent is on the
+ 
+
+ align:start position:0%
+next last syllable the accent is on the
+next last syllable which is to put a
+
+ align:start position:0%
+next last syllable which is to put a
+ 
+
+ align:start position:0%
+next last syllable which is to put a
+pointing finger next to it like that
+
+ align:start position:0%
+pointing finger next to it like that
+ 
+
+ align:start position:0%
+pointing finger next to it like that
+this is the one that wins
+
+ align:start position:0%
+this is the one that wins
+ 
+
+ align:start position:0%
+this is the one that wins
+optimality Theory this approach to to
+
+ align:start position:0%
+optimality Theory this approach to to
+ 
+
+ align:start position:0%
+optimality Theory this approach to to
+phonology is called optimality Theory
+
+ align:start position:0%
+phonology is called optimality Theory
+ 
+
+ align:start position:0%
+phonology is called optimality Theory
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+um I don't know I guess they just liked
+
+ align:start position:0%
+um I don't know I guess they just liked
+ 
+
+ align:start position:0%
+um I don't know I guess they just liked
+the font that had the pointing finger in
+
+ align:start position:0%
+the font that had the pointing finger in
+ 
+
+ align:start position:0%
+the font that had the pointing finger in
+it so they decided to use it
+
+ align:start position:0%
+it so they decided to use it
+ 
+
+ align:start position:0%
+it so they decided to use it
+okay this is an approach yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh you mean why am I putting an accent
+
+ align:start position:0%
+Oh you mean why am I putting an accent
+ 
+
+ align:start position:0%
+Oh you mean why am I putting an accent
+on Ken over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's a very good point
+
+ align:start position:0%
+yeah that's a very good point
+ 
+
+ align:start position:0%
+yeah that's a very good point
+um it is possible to pronounce Ken by
+
+ align:start position:0%
+um it is possible to pronounce Ken by
+ 
+
+ align:start position:0%
+um it is possible to pronounce Ken by
+itself not as part of a compound so if
+
+ align:start position:0%
+itself not as part of a compound so if
+ 
+
+ align:start position:0%
+itself not as part of a compound so if
+you want to talk about the prefecture
+
+ align:start position:0%
+you want to talk about the prefecture
+ 
+
+ align:start position:0%
+you want to talk about the prefecture
+it's a word it means prefecture so it's
+
+ align:start position:0%
+it's a word it means prefecture so it's
+ 
+
+ align:start position:0%
+it's a word it means prefecture so it's
+which is a sort of kind of like a state
+
+ align:start position:0%
+which is a sort of kind of like a state
+ 
+
+ align:start position:0%
+which is a sort of kind of like a state
+it's an administrative subdivision of
+
+ align:start position:0%
+it's an administrative subdivision of
+ 
+
+ align:start position:0%
+it's an administrative subdivision of
+Japan
+
+ align:start position:0%
+Japan
+ 
+
+ align:start position:0%
+Japan
+um and it's possible to say that word by
+
+ align:start position:0%
+um and it's possible to say that word by
+ 
+
+ align:start position:0%
+um and it's possible to say that word by
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+um Ken is
+
+ align:start position:0%
+um Ken is
+ 
+
+ align:start position:0%
+um Ken is
+unbounded I don't think I know what you
+
+ align:start position:0%
+unbounded I don't think I know what you
+ 
+
+ align:start position:0%
+unbounded I don't think I know what you
+mean you could you oh it's not a bound
+
+ align:start position:0%
+mean you could you oh it's not a bound
+ 
+
+ align:start position:0%
+mean you could you oh it's not a bound
+morpheme that's right it can be it can
+
+ align:start position:0%
+morpheme that's right it can be it can
+ 
+
+ align:start position:0%
+morpheme that's right it can be it can
+be a free morphine yes yes that's right
+
+ align:start position:0%
+be a free morphine yes yes that's right
+ 
+
+ align:start position:0%
+be a free morphine yes yes that's right
+so so uh you can say in Japanese you
+
+ align:start position:0%
+so so uh you can say in Japanese you
+ 
+
+ align:start position:0%
+so so uh you can say in Japanese you
+know the the prefecture is large or
+
+ align:start position:0%
+know the the prefecture is large or
+ 
+
+ align:start position:0%
+know the the prefecture is large or
+whatever uh and then you can show that
+
+ align:start position:0%
+whatever uh and then you can show that
+ 
+
+ align:start position:0%
+whatever uh and then you can show that
+it's accented yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good question there are other
+
+ align:start position:0%
+yeah good question there are other
+ 
+
+ align:start position:0%
+yeah good question there are other
+questions people have about this
+
+ align:start position:0%
+questions people have about this
+ 
+
+ align:start position:0%
+questions people have about this
+okay so this is just meant to illustrate
+
+ align:start position:0%
+okay so this is just meant to illustrate
+ 
+
+ align:start position:0%
+okay so this is just meant to illustrate
+um the workings of optimality theory
+
+ align:start position:0%
+um the workings of optimality theory
+ 
+
+ align:start position:0%
+um the workings of optimality theory
+um why am i showing you this one
+
+ align:start position:0%
+um why am i showing you this one
+ 
+
+ align:start position:0%
+um why am i showing you this one
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+okay oh I I see this is a similar
+
+ align:start position:0%
+okay oh I I see this is a similar
+ 
+
+ align:start position:0%
+okay oh I I see this is a similar
+Tableau for french fry
+
+ align:start position:0%
+Tableau for french fry
+ 
+
+ align:start position:0%
+Tableau for french fry
+so it says the same uh the same
+
+ align:start position:0%
+so it says the same uh the same
+ 
+
+ align:start position:0%
+so it says the same uh the same
+constraints these things that I put in
+
+ align:start position:0%
+constraints these things that I put in
+ 
+
+ align:start position:0%
+constraints these things that I put in
+in all caps up at the top uh in this
+
+ align:start position:0%
+in all caps up at the top uh in this
+ 
+
+ align:start position:0%
+in all caps up at the top uh in this
+case you do end up with Accent on the at
+
+ align:start position:0%
+case you do end up with Accent on the at
+ 
+
+ align:start position:0%
+case you do end up with Accent on the at
+the beginning of potato on the second
+
+ align:start position:0%
+the beginning of potato on the second
+ 
+
+ align:start position:0%
+the beginning of potato on the second
+word that actually is a perfect
+
+ align:start position:0%
+word that actually is a perfect
+ 
+
+ align:start position:0%
+word that actually is a perfect
+candidate so this is an example in which
+
+ align:start position:0%
+candidate so this is an example in which
+ 
+
+ align:start position:0%
+candidate so this is an example in which
+none of the laws are violated by uh by
+
+ align:start position:0%
+none of the laws are violated by uh by
+ 
+
+ align:start position:0%
+none of the laws are violated by uh by
+the best candidate the laws aren't doing
+
+ align:start position:0%
+the best candidate the laws aren't doing
+ 
+
+ align:start position:0%
+the best candidate the laws aren't doing
+conflict with each other so you can put
+
+ align:start position:0%
+conflict with each other so you can put
+ 
+
+ align:start position:0%
+conflict with each other so you can put
+accent at the beginning of the last word
+
+ align:start position:0%
+accent at the beginning of the last word
+ 
+
+ align:start position:0%
+accent at the beginning of the last word
+and potato and it won't be final yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's absolutely right so if for some
+
+ align:start position:0%
+that's absolutely right so if for some
+ 
+
+ align:start position:0%
+that's absolutely right so if for some
+reason that fourth candidate were
+
+ align:start position:0%
+reason that fourth candidate were
+ 
+
+ align:start position:0%
+reason that fourth candidate were
+impossible say there was another very
+
+ align:start position:0%
+impossible say there was another very
+ 
+
+ align:start position:0%
+impossible say there was another very
+high ranking constraint don't uh don't
+
+ align:start position:0%
+high ranking constraint don't uh don't
+ 
+
+ align:start position:0%
+high ranking constraint don't uh don't
+stress the first don't put accent on
+
+ align:start position:0%
+stress the first don't put accent on
+ 
+
+ align:start position:0%
+stress the first don't put accent on
+potato
+
+ align:start position:0%
+potato
+ 
+
+ align:start position:0%
+potato
+um then yes the third would win that's
+
+ align:start position:0%
+um then yes the third would win that's
+ 
+
+ align:start position:0%
+um then yes the third would win that's
+right and uh actually we can kind of see
+
+ align:start position:0%
+right and uh actually we can kind of see
+ 
+
+ align:start position:0%
+right and uh actually we can kind of see
+that by looking at the behavior of
+
+ align:start position:0%
+that by looking at the behavior of
+ 
+
+ align:start position:0%
+that by looking at the behavior of
+kagawaken so if we eliminate
+
+ align:start position:0%
+kagawaken so if we eliminate
+ 
+
+ align:start position:0%
+kagawaken so if we eliminate
+the option of putting Accent on the last
+
+ align:start position:0%
+the option of putting Accent on the last
+ 
+
+ align:start position:0%
+the option of putting Accent on the last
+word that's where the accent goes It
+
+ align:start position:0%
+word that's where the accent goes It
+ 
+
+ align:start position:0%
+word that's where the accent goes It
+goes at the end of the first word
+
+ align:start position:0%
+goes at the end of the first word
+ 
+
+ align:start position:0%
+goes at the end of the first word
+and so it's the best you can do right uh
+
+ align:start position:0%
+and so it's the best you can do right uh
+ 
+
+ align:start position:0%
+and so it's the best you can do right uh
+still near the boundary still only one
+
+ align:start position:0%
+still near the boundary still only one
+ 
+
+ align:start position:0%
+still near the boundary still only one
+accent uh just didn't manage to Accent
+
+ align:start position:0%
+accent uh just didn't manage to Accent
+ 
+
+ align:start position:0%
+accent uh just didn't manage to Accent
+the last word which is what you'd like
+
+ align:start position:0%
+the last word which is what you'd like
+ 
+
+ align:start position:0%
+the last word which is what you'd like
+to do but it's not high on your list of
+
+ align:start position:0%
+to do but it's not high on your list of
+ 
+
+ align:start position:0%
+to do but it's not high on your list of
+list of constraints yep
+
+ align:start position:0%
+list of constraints yep
+ 
+
+ align:start position:0%
+list of constraints yep
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+so this is an approach to thinking about
+
+ align:start position:0%
+so this is an approach to thinking about
+ 
+
+ align:start position:0%
+so this is an approach to thinking about
+phenology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um optimality theory is the name for it
+
+ align:start position:0%
+um optimality theory is the name for it
+ 
+
+ align:start position:0%
+um optimality theory is the name for it
+it says you know in a way it's a kind of
+
+ align:start position:0%
+it says you know in a way it's a kind of
+ 
+
+ align:start position:0%
+it says you know in a way it's a kind of
+comforting Theory it says do the best
+
+ align:start position:0%
+comforting Theory it says do the best
+ 
+
+ align:start position:0%
+comforting Theory it says do the best
+you can you know you have all of these
+
+ align:start position:0%
+you can you know you have all of these
+ 
+
+ align:start position:0%
+you can you know you have all of these
+things probably all of you have
+
+ align:start position:0%
+things probably all of you have
+ 
+
+ align:start position:0%
+things probably all of you have
+encountered things like this in other
+
+ align:start position:0%
+encountered things like this in other
+ 
+
+ align:start position:0%
+encountered things like this in other
+domains at MIT if you've ever dealt with
+
+ align:start position:0%
+domains at MIT if you've ever dealt with
+ 
+
+ align:start position:0%
+domains at MIT if you've ever dealt with
+engineering problems there are probably
+
+ align:start position:0%
+engineering problems there are probably
+ 
+
+ align:start position:0%
+engineering problems there are probably
+cases where you know you have various
+
+ align:start position:0%
+cases where you know you have various
+ 
+
+ align:start position:0%
+cases where you know you have various
+things that you want to achieve and you
+
+ align:start position:0%
+things that you want to achieve and you
+ 
+
+ align:start position:0%
+things that you want to achieve and you
+can't optimize all of them you have to
+
+ align:start position:0%
+can't optimize all of them you have to
+ 
+
+ align:start position:0%
+can't optimize all of them you have to
+decide which ones are the most important
+
+ align:start position:0%
+decide which ones are the most important
+ 
+
+ align:start position:0%
+decide which ones are the most important
+and the idea here is that language is
+
+ align:start position:0%
+and the idea here is that language is
+ 
+
+ align:start position:0%
+and the idea here is that language is
+like that there are cases where
+
+ align:start position:0%
+like that there are cases where
+ 
+
+ align:start position:0%
+like that there are cases where
+you have to decide among your various uh
+
+ align:start position:0%
+you have to decide among your various uh
+ 
+
+ align:start position:0%
+you have to decide among your various uh
+your various desiderata which ones you
+
+ align:start position:0%
+your various desiderata which ones you
+ 
+
+ align:start position:0%
+your various desiderata which ones you
+care about the most
+
+ align:start position:0%
+care about the most
+ 
+
+ align:start position:0%
+care about the most
+The Hope in optimality theory is that
+
+ align:start position:0%
+The Hope in optimality theory is that
+ 
+
+ align:start position:0%
+The Hope in optimality theory is that
+we'll end up with a list of these
+
+ align:start position:0%
+we'll end up with a list of these
+ 
+
+ align:start position:0%
+we'll end up with a list of these
+constraints these laws these rules uh
+
+ align:start position:0%
+constraints these laws these rules uh
+ 
+
+ align:start position:0%
+constraints these laws these rules uh
+that'll be Universal and the differences
+
+ align:start position:0%
+that'll be Universal and the differences
+ 
+
+ align:start position:0%
+that'll be Universal and the differences
+between languages are just a matter of
+
+ align:start position:0%
+between languages are just a matter of
+ 
+
+ align:start position:0%
+between languages are just a matter of
+deciding what order the different
+
+ align:start position:0%
+deciding what order the different
+ 
+
+ align:start position:0%
+deciding what order the different
+constraints are in you know so that
+
+ align:start position:0%
+constraints are in you know so that
+ 
+
+ align:start position:0%
+constraints are in you know so that
+there could be uh uh languages in which
+
+ align:start position:0%
+there could be uh uh languages in which
+ 
+
+ align:start position:0%
+there could be uh uh languages in which
+you know uh the one accent rule is very
+
+ align:start position:0%
+you know uh the one accent rule is very
+ 
+
+ align:start position:0%
+you know uh the one accent rule is very
+low rank and the first uh the first
+
+ align:start position:0%
+low rank and the first uh the first
+ 
+
+ align:start position:0%
+low rank and the first uh the first
+candidate maybe wins right you could
+
+ align:start position:0%
+candidate maybe wins right you could
+ 
+
+ align:start position:0%
+candidate maybe wins right you could
+imagine a language like that uh Tokyo
+
+ align:start position:0%
+imagine a language like that uh Tokyo
+ 
+
+ align:start position:0%
+imagine a language like that uh Tokyo
+Japanese doesn't work that way yeah so
+
+ align:start position:0%
+Japanese doesn't work that way yeah so
+ 
+
+ align:start position:0%
+Japanese doesn't work that way yeah so
+differences between languages are all a
+
+ align:start position:0%
+differences between languages are all a
+ 
+
+ align:start position:0%
+differences between languages are all a
+matter of re-ranking the constraints
+
+ align:start position:0%
+matter of re-ranking the constraints
+ 
+
+ align:start position:0%
+matter of re-ranking the constraints
+that's sort of the the mission statement
+
+ align:start position:0%
+that's sort of the the mission statement
+ 
+
+ align:start position:0%
+that's sort of the the mission statement
+of optimality theories try to figure out
+
+ align:start position:0%
+of optimality theories try to figure out
+ 
+
+ align:start position:0%
+of optimality theories try to figure out
+how the world could work that way
+
+ align:start position:0%
+how the world could work that way
+ 
+
+ align:start position:0%
+how the world could work that way
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+optimality theory was partly inspired by
+
+ align:start position:0%
+optimality theory was partly inspired by
+ 
+
+ align:start position:0%
+optimality theory was partly inspired by
+the discovery of these kinds of
+
+ align:start position:0%
+the discovery of these kinds of
+ 
+
+ align:start position:0%
+the discovery of these kinds of
+conspiracies that we started talking
+
+ align:start position:0%
+conspiracies that we started talking
+ 
+
+ align:start position:0%
+conspiracies that we started talking
+about when I was showing you some stuff
+
+ align:start position:0%
+about when I was showing you some stuff
+ 
+
+ align:start position:0%
+about when I was showing you some stuff
+about yellow money and now we've seen
+
+ align:start position:0%
+about yellow money and now we've seen
+ 
+
+ align:start position:0%
+about yellow money and now we've seen
+another example from Japanese for yellow
+
+ align:start position:0%
+another example from Japanese for yellow
+ 
+
+ align:start position:0%
+another example from Japanese for yellow
+money the conspiracy was uh I don't want
+
+ align:start position:0%
+money the conspiracy was uh I don't want
+ 
+
+ align:start position:0%
+money the conspiracy was uh I don't want
+three consonants in a row and I'll do
+
+ align:start position:0%
+three consonants in a row and I'll do
+ 
+
+ align:start position:0%
+three consonants in a row and I'll do
+various things to achieve that we said
+
+ align:start position:0%
+various things to achieve that we said
+ 
+
+ align:start position:0%
+various things to achieve that we said
+you know you could State rules governing
+
+ align:start position:0%
+you know you could State rules governing
+ 
+
+ align:start position:0%
+you know you could State rules governing
+the various things and maybe in a sense
+
+ align:start position:0%
+the various things and maybe in a sense
+ 
+
+ align:start position:0%
+the various things and maybe in a sense
+you should uh but you sort of the idea
+
+ align:start position:0%
+you should uh but you sort of the idea
+ 
+
+ align:start position:0%
+you should uh but you sort of the idea
+is let's try to keep sight of the fact
+
+ align:start position:0%
+is let's try to keep sight of the fact
+ 
+
+ align:start position:0%
+is let's try to keep sight of the fact
+that all of these rules are trying to
+
+ align:start position:0%
+that all of these rules are trying to
+ 
+
+ align:start position:0%
+that all of these rules are trying to
+achieve the same thing that's we want to
+
+ align:start position:0%
+achieve the same thing that's we want to
+ 
+
+ align:start position:0%
+achieve the same thing that's we want to
+also capture that kind of a fact and
+
+ align:start position:0%
+also capture that kind of a fact and
+ 
+
+ align:start position:0%
+also capture that kind of a fact and
+there's something similar going on here
+
+ align:start position:0%
+there's something similar going on here
+ 
+
+ align:start position:0%
+there's something similar going on here
+in Japanese uh one of the rules the
+
+ align:start position:0%
+in Japanese uh one of the rules the
+ 
+
+ align:start position:0%
+in Japanese uh one of the rules the
+highest ranking rule uh was uh don't
+
+ align:start position:0%
+highest ranking rule uh was uh don't
+ 
+
+ align:start position:0%
+highest ranking rule uh was uh don't
+have more than one accent in word yeah
+
+ align:start position:0%
+have more than one accent in word yeah
+ 
+
+ align:start position:0%
+have more than one accent in word yeah
+and what we saw last time was that there
+
+ align:start position:0%
+and what we saw last time was that there
+ 
+
+ align:start position:0%
+and what we saw last time was that there
+are various things that Japanese does to
+
+ align:start position:0%
+are various things that Japanese does to
+ 
+
+ align:start position:0%
+are various things that Japanese does to
+achieve this depending on the situation
+
+ align:start position:0%
+achieve this depending on the situation
+ 
+
+ align:start position:0%
+achieve this depending on the situation
+so there are
+
+ align:start position:0%
+so there are
+ 
+
+ align:start position:0%
+so there are
+words uh uh like gurai which I think I
+
+ align:start position:0%
+words uh uh like gurai which I think I
+ 
+
+ align:start position:0%
+words uh uh like gurai which I think I
+translated last time is even which are
+
+ align:start position:0%
+translated last time is even which are
+ 
+
+ align:start position:0%
+translated last time is even which are
+accented and if you attach them to
+
+ align:start position:0%
+accented and if you attach them to
+ 
+
+ align:start position:0%
+accented and if you attach them to
+another word that's also accented you
+
+ align:start position:0%
+another word that's also accented you
+ 
+
+ align:start position:0%
+another word that's also accented you
+delete the accent on the first word on
+
+ align:start position:0%
+delete the accent on the first word on
+ 
+
+ align:start position:0%
+delete the accent on the first word on
+the word you're attaching good eye to
+
+ align:start position:0%
+the word you're attaching good eye to
+ 
+
+ align:start position:0%
+the word you're attaching good eye to
+and there are other words like made
+
+ align:start position:0%
+and there are other words like made
+ 
+
+ align:start position:0%
+and there are other words like made
+which means to up to as far as uh which
+
+ align:start position:0%
+which means to up to as far as uh which
+ 
+
+ align:start position:0%
+which means to up to as far as uh which
+are accented but only if they are
+
+ align:start position:0%
+are accented but only if they are
+ 
+
+ align:start position:0%
+are accented but only if they are
+attached to unaccented words
+
+ align:start position:0%
+attached to unaccented words
+ 
+
+ align:start position:0%
+attached to unaccented words
+and then we've done all this talking
+
+ align:start position:0%
+and then we've done all this talking
+ 
+
+ align:start position:0%
+and then we've done all this talking
+about compounds uh these are all
+
+ align:start position:0%
+about compounds uh these are all
+ 
+
+ align:start position:0%
+about compounds uh these are all
+different kinds of examples in which
+
+ align:start position:0%
+different kinds of examples in which
+ 
+
+ align:start position:0%
+different kinds of examples in which
+different things happen there are
+
+ align:start position:0%
+different things happen there are
+ 
+
+ align:start position:0%
+different things happen there are
+different strategies right so for good I
+
+ align:start position:0%
+different strategies right so for good I
+ 
+
+ align:start position:0%
+different strategies right so for good I
+it's delete the accent on the word
+
+ align:start position:0%
+it's delete the accent on the word
+ 
+
+ align:start position:0%
+it's delete the accent on the word
+you've attached good eye to uh for a mad
+
+ align:start position:0%
+you've attached good eye to uh for a mad
+ 
+
+ align:start position:0%
+you've attached good eye to uh for a mad
+it's delete the accent on Monday for the
+
+ align:start position:0%
+it's delete the accent on Monday for the
+ 
+
+ align:start position:0%
+it's delete the accent on Monday for the
+compounds we've now talked about this
+
+ align:start position:0%
+compounds we've now talked about this
+ 
+
+ align:start position:0%
+compounds we've now talked about this
+computation that you go through to try
+
+ align:start position:0%
+computation that you go through to try
+ 
+
+ align:start position:0%
+computation that you go through to try
+to figure out where the single accent
+
+ align:start position:0%
+to figure out where the single accent
+ 
+
+ align:start position:0%
+to figure out where the single accent
+should go but what all of these things
+
+ align:start position:0%
+should go but what all of these things
+ 
+
+ align:start position:0%
+should go but what all of these things
+are doing is trying to arrange for there
+
+ align:start position:0%
+are doing is trying to arrange for there
+ 
+
+ align:start position:0%
+are doing is trying to arrange for there
+to just be a single accent and one of
+
+ align:start position:0%
+to just be a single accent and one of
+ 
+
+ align:start position:0%
+to just be a single accent and one of
+the virtues of optimality theory is that
+
+ align:start position:0%
+the virtues of optimality theory is that
+ 
+
+ align:start position:0%
+the virtues of optimality theory is that
+it allows us to sort of make that part
+
+ align:start position:0%
+it allows us to sort of make that part
+ 
+
+ align:start position:0%
+it allows us to sort of make that part
+of our analysis uh we don't if we just
+
+ align:start position:0%
+of our analysis uh we don't if we just
+ 
+
+ align:start position:0%
+of our analysis uh we don't if we just
+stated these rules we'd be sort of
+
+ align:start position:0%
+stated these rules we'd be sort of
+ 
+
+ align:start position:0%
+stated these rules we'd be sort of
+losing sight of the fact that these
+
+ align:start position:0%
+losing sight of the fact that these
+ 
+
+ align:start position:0%
+losing sight of the fact that these
+rules all seem to be trying to achieve
+
+ align:start position:0%
+rules all seem to be trying to achieve
+ 
+
+ align:start position:0%
+rules all seem to be trying to achieve
+the same thing
+
+ align:start position:0%
+the same thing
+ 
+
+ align:start position:0%
+the same thing
+things people who work on optimality
+
+ align:start position:0%
+things people who work on optimality
+ 
+
+ align:start position:0%
+things people who work on optimality
+Theory are trying to get and then of
+
+ align:start position:0%
+Theory are trying to get and then of
+ 
+
+ align:start position:0%
+Theory are trying to get and then of
+course the goal is to try to understand
+
+ align:start position:0%
+course the goal is to try to understand
+ 
+
+ align:start position:0%
+course the goal is to try to understand
+why we have the constraints that we have
+
+ align:start position:0%
+why we have the constraints that we have
+ 
+
+ align:start position:0%
+why we have the constraints that we have
+and not others it's another kind of
+
+ align:start position:0%
+and not others it's another kind of
+ 
+
+ align:start position:0%
+and not others it's another kind of
+thing people who work on this try to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yes I just said that
+
+ align:start position:0%
+uh yes I just said that
+ 
+
+ align:start position:0%
+uh yes I just said that
+and that so remember yellow money which
+
+ align:start position:0%
+and that so remember yellow money which
+ 
+
+ align:start position:0%
+and that so remember yellow money which
+was avoid strings of three consonants
+
+ align:start position:0%
+was avoid strings of three consonants
+ 
+
+ align:start position:0%
+was avoid strings of three consonants
+either by inserting vowels or by
+
+ align:start position:0%
+either by inserting vowels or by
+ 
+
+ align:start position:0%
+either by inserting vowels or by
+deleting H if you have an H
+
+ align:start position:0%
+deleting H if you have an H
+ 
+
+ align:start position:0%
+deleting H if you have an H
+um so uh
+
+ align:start position:0%
+um so uh
+ 
+
+ align:start position:0%
+um so uh
+I've been saying we could just State
+
+ align:start position:0%
+I've been saying we could just State
+ 
+
+ align:start position:0%
+I've been saying we could just State
+these rules but we'd be missing a
+
+ align:start position:0%
+these rules but we'd be missing a
+ 
+
+ align:start position:0%
+these rules but we'd be missing a
+generalization yellow money is trying to
+
+ align:start position:0%
+generalization yellow money is trying to
+ 
+
+ align:start position:0%
+generalization yellow money is trying to
+avoid three constants in a row Japanese
+
+ align:start position:0%
+avoid three constants in a row Japanese
+ 
+
+ align:start position:0%
+avoid three constants in a row Japanese
+is trying to avoid two Accents in a
+
+ align:start position:0%
+is trying to avoid two Accents in a
+ 
+
+ align:start position:0%
+is trying to avoid two Accents in a
+single word
+
+ align:start position:0%
+single word
+ 
+
+ align:start position:0%
+single word
+um uh maybe it's obvious we don't want
+
+ align:start position:0%
+um uh maybe it's obvious we don't want
+ 
+
+ align:start position:0%
+um uh maybe it's obvious we don't want
+to miss generalizations like that we
+
+ align:start position:0%
+to miss generalizations like that we
+ 
+
+ align:start position:0%
+to miss generalizations like that we
+want to find them and understand them
+
+ align:start position:0%
+want to find them and understand them
+ 
+
+ align:start position:0%
+want to find them and understand them
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so similar kind of thing that we could
+
+ align:start position:0%
+so similar kind of thing that we could
+ 
+
+ align:start position:0%
+so similar kind of thing that we could
+think about here uh we've talked now a
+
+ align:start position:0%
+think about here uh we've talked now a
+ 
+
+ align:start position:0%
+think about here uh we've talked now a
+couple of times about Polish Polish is
+
+ align:start position:0%
+couple of times about Polish Polish is
+ 
+
+ align:start position:0%
+couple of times about Polish Polish is
+one of a number of languages in which uh
+
+ align:start position:0%
+one of a number of languages in which uh
+ 
+
+ align:start position:0%
+one of a number of languages in which uh
+if you have certain kinds of consonants
+
+ align:start position:0%
+if you have certain kinds of consonants
+ 
+
+ align:start position:0%
+if you have certain kinds of consonants
+at the ends of words uh consonants like
+
+ align:start position:0%
+at the ends of words uh consonants like
+ 
+
+ align:start position:0%
+at the ends of words uh consonants like
+B and D and G and Z we convinced
+
+ align:start position:0%
+B and D and G and Z we convinced
+ 
+
+ align:start position:0%
+B and D and G and Z we convinced
+ourselves that they devoice they become
+
+ align:start position:0%
+ourselves that they devoice they become
+ 
+
+ align:start position:0%
+ourselves that they devoice they become
+voiceless at the ends of words that
+
+ align:start position:0%
+voiceless at the ends of words that
+ 
+
+ align:start position:0%
+voiceless at the ends of words that
+allows us to capture various kinds of
+
+ align:start position:0%
+allows us to capture various kinds of
+ 
+
+ align:start position:0%
+allows us to capture various kinds of
+facts about what happens to polish words
+
+ align:start position:0%
+facts about what happens to polish words
+ 
+
+ align:start position:0%
+facts about what happens to polish words
+when they become plural namely but words
+
+ align:start position:0%
+when they become plural namely but words
+ 
+
+ align:start position:0%
+when they become plural namely but words
+that sound voiceless sound consonants
+
+ align:start position:0%
+that sound voiceless sound consonants
+ 
+
+ align:start position:0%
+that sound voiceless sound consonants
+that sound voiceless when they're at the
+
+ align:start position:0%
+that sound voiceless when they're at the
+ 
+
+ align:start position:0%
+that sound voiceless when they're at the
+ends of words uh become voiced sometimes
+
+ align:start position:0%
+ends of words uh become voiced sometimes
+ 
+
+ align:start position:0%
+ends of words uh become voiced sometimes
+when they're no longer at the end of
+
+ align:start position:0%
+when they're no longer at the end of
+ 
+
+ align:start position:0%
+when they're no longer at the end of
+words we decided that's because they're
+
+ align:start position:0%
+words we decided that's because they're
+ 
+
+ align:start position:0%
+words we decided that's because they're
+underlying the uh voiced and they they
+
+ align:start position:0%
+underlying the uh voiced and they they
+ 
+
+ align:start position:0%
+underlying the uh voiced and they they
+devoice when they're at the ends of
+
+ align:start position:0%
+devoice when they're at the ends of
+ 
+
+ align:start position:0%
+devoice when they're at the ends of
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+now so right this is all kind of
+
+ align:start position:0%
+now so right this is all kind of
+ 
+
+ align:start position:0%
+now so right this is all kind of
+familiar you all remember polish yeah
+
+ align:start position:0%
+familiar you all remember polish yeah
+ 
+
+ align:start position:0%
+familiar you all remember polish yeah
+it's not just polish there are lots of
+
+ align:start position:0%
+it's not just polish there are lots of
+ 
+
+ align:start position:0%
+it's not just polish there are lots of
+languages that do this
+
+ align:start position:0%
+languages that do this
+ 
+
+ align:start position:0%
+languages that do this
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh and so what I'm inviting you to do at
+
+ align:start position:0%
+uh and so what I'm inviting you to do at
+ 
+
+ align:start position:0%
+uh and so what I'm inviting you to do at
+the end of this slide is to imagine two
+
+ align:start position:0%
+the end of this slide is to imagine two
+ 
+
+ align:start position:0%
+the end of this slide is to imagine two
+kinds of stories about polish one that
+
+ align:start position:0%
+kinds of stories about polish one that
+ 
+
+ align:start position:0%
+kinds of stories about polish one that
+would say yeah final consonants the
+
+ align:start position:0%
+would say yeah final consonants the
+ 
+
+ align:start position:0%
+would say yeah final consonants the
+voice in Polish and another that would
+
+ align:start position:0%
+voice in Polish and another that would
+ 
+
+ align:start position:0%
+voice in Polish and another that would
+say well there are four rules actually
+
+ align:start position:0%
+say well there are four rules actually
+ 
+
+ align:start position:0%
+say well there are four rules actually
+there's a rule that says b d voices when
+
+ align:start position:0%
+there's a rule that says b d voices when
+ 
+
+ align:start position:0%
+there's a rule that says b d voices when
+it's final and a rule that says d d
+
+ align:start position:0%
+it's final and a rule that says d d
+ 
+
+ align:start position:0%
+it's final and a rule that says d d
+voices when it's final and a rule that
+
+ align:start position:0%
+voices when it's final and a rule that
+ 
+
+ align:start position:0%
+voices when it's final and a rule that
+says G devices yeah
+
+ align:start position:0%
+says G devices yeah
+ 
+
+ align:start position:0%
+says G devices yeah
+both of those would capture all of the
+
+ align:start position:0%
+both of those would capture all of the
+ 
+
+ align:start position:0%
+both of those would capture all of the
+Polish facts one of them is clearly
+
+ align:start position:0%
+Polish facts one of them is clearly
+ 
+
+ align:start position:0%
+Polish facts one of them is clearly
+better yeah uh so we want to understand
+
+ align:start position:0%
+better yeah uh so we want to understand
+ 
+
+ align:start position:0%
+better yeah uh so we want to understand
+why we get the particular phenomena that
+
+ align:start position:0%
+why we get the particular phenomena that
+ 
+
+ align:start position:0%
+why we get the particular phenomena that
+we do in Polish is it clear to everybody
+
+ align:start position:0%
+we do in Polish is it clear to everybody
+ 
+
+ align:start position:0%
+we do in Polish is it clear to everybody
+that that's that it would be better to
+
+ align:start position:0%
+that that's that it would be better to
+ 
+
+ align:start position:0%
+that that's that it would be better to
+do things that way
+
+ align:start position:0%
+do things that way
+ 
+
+ align:start position:0%
+do things that way
+and what we're doing here is uh sort of
+
+ align:start position:0%
+and what we're doing here is uh sort of
+ 
+
+ align:start position:0%
+and what we're doing here is uh sort of
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+why would it be better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would be wrong why why is it better
+
+ align:start position:0%
+what would be wrong why why is it better
+ 
+
+ align:start position:0%
+what would be wrong why why is it better
+to be able to say final continent is The
+
+ align:start position:0%
+to be able to say final continent is The
+ 
+
+ align:start position:0%
+to be able to say final continent is The
+Voice
+
+ align:start position:0%
+Voice
+ 
+
+ align:start position:0%
+Voice
+than to say
+
+ align:start position:0%
+than to say
+ 
+
+ align:start position:0%
+than to say
+well we have these four rules yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it might make it easier to make
+
+ align:start position:0%
+yeah so it might make it easier to make
+ 
+
+ align:start position:0%
+yeah so it might make it easier to make
+cross-linguistic comparisons so yeah
+
+ align:start position:0%
+cross-linguistic comparisons so yeah
+ 
+
+ align:start position:0%
+cross-linguistic comparisons so yeah
+that's a very good point yeah
+
+ align:start position:0%
+that's a very good point yeah
+ 
+
+ align:start position:0%
+that's a very good point yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we also maybe
+
+ align:start position:0%
+we also maybe
+ 
+
+ align:start position:0%
+we also maybe
+I don't know if this is a good way to
+
+ align:start position:0%
+I don't know if this is a good way to
+ 
+
+ align:start position:0%
+I don't know if this is a good way to
+say it maybe it is
+
+ align:start position:0%
+say it maybe it is
+ 
+
+ align:start position:0%
+say it maybe it is
+we want to understand why
+
+ align:start position:0%
+we want to understand why
+ 
+
+ align:start position:0%
+we want to understand why
+the sounds that become voiceless at the
+
+ align:start position:0%
+the sounds that become voiceless at the
+ 
+
+ align:start position:0%
+the sounds that become voiceless at the
+ends of words in Polish are bdg and z
+
+ align:start position:0%
+ends of words in Polish are bdg and z
+ 
+
+ align:start position:0%
+ends of words in Polish are bdg and z
+and not b d a and o right
+
+ align:start position:0%
+and not b d a and o right
+ 
+
+ align:start position:0%
+and not b d a and o right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if we're just making four rules for
+
+ align:start position:0%
+if we're just making four rules for
+ 
+
+ align:start position:0%
+if we're just making four rules for
+those four letters then uh it's not
+
+ align:start position:0%
+those four letters then uh it's not
+ 
+
+ align:start position:0%
+those four letters then uh it's not
+clear there's no reason why one of those
+
+ align:start position:0%
+clear there's no reason why one of those
+ 
+
+ align:start position:0%
+clear there's no reason why one of those
+rules is more natural than the other but
+
+ align:start position:0%
+rules is more natural than the other but
+ 
+
+ align:start position:0%
+rules is more natural than the other but
+as I keep saying
+
+ align:start position:0%
+as I keep saying
+ 
+
+ align:start position:0%
+as I keep saying
+What's Happening Here in Polish is
+
+ align:start position:0%
+What's Happening Here in Polish is
+ 
+
+ align:start position:0%
+What's Happening Here in Polish is
+extremely common uh so you get it in
+
+ align:start position:0%
+extremely common uh so you get it in
+ 
+
+ align:start position:0%
+extremely common uh so you get it in
+Turkish you get it in Russian you get it
+
+ align:start position:0%
+Turkish you get it in Russian you get it
+ 
+
+ align:start position:0%
+Turkish you get it in Russian you get it
+in a bunch of different languages German
+
+ align:start position:0%
+in a bunch of different languages German
+ 
+
+ align:start position:0%
+in a bunch of different languages German
+um and so we want to understand why it's
+
+ align:start position:0%
+um and so we want to understand why it's
+ 
+
+ align:start position:0%
+um and so we want to understand why it's
+common and part of understanding why
+
+ align:start position:0%
+common and part of understanding why
+ 
+
+ align:start position:0%
+common and part of understanding why
+it's common is being able to say that
+
+ align:start position:0%
+it's common is being able to say that
+ 
+
+ align:start position:0%
+it's common is being able to say that
+that's a common rule a standard rule
+
+ align:start position:0%
+that's a common rule a standard rule
+ 
+
+ align:start position:0%
+that's a common rule a standard rule
+that we see all over the place and then
+
+ align:start position:0%
+that we see all over the place and then
+ 
+
+ align:start position:0%
+that we see all over the place and then
+we can get to work on understanding it
+
+ align:start position:0%
+we can get to work on understanding it
+ 
+
+ align:start position:0%
+we can get to work on understanding it
+if we just have these four rules then
+
+ align:start position:0%
+if we just have these four rules then
+ 
+
+ align:start position:0%
+if we just have these four rules then
+it's unclear why those four rules are so
+
+ align:start position:0%
+it's unclear why those four rules are so
+ 
+
+ align:start position:0%
+it's unclear why those four rules are so
+common whereas uh b d a and o d voice at
+
+ align:start position:0%
+common whereas uh b d a and o d voice at
+ 
+
+ align:start position:0%
+common whereas uh b d a and o d voice at
+the ends of words is not at all common I
+
+ align:start position:0%
+the ends of words is not at all common I
+ 
+
+ align:start position:0%
+the ends of words is not at all common I
+don't know of any languages that do that
+
+ align:start position:0%
+don't know of any languages that do that
+ 
+
+ align:start position:0%
+don't know of any languages that do that
+that makes sense that's another sense in
+
+ align:start position:0%
+that makes sense that's another sense in
+ 
+
+ align:start position:0%
+that makes sense that's another sense in
+which yeah making generalizations is
+
+ align:start position:0%
+which yeah making generalizations is
+ 
+
+ align:start position:0%
+which yeah making generalizations is
+good this is this is becoming a
+
+ align:start position:0%
+good this is this is becoming a
+ 
+
+ align:start position:0%
+good this is this is becoming a
+philosophy of science question yeah it's
+
+ align:start position:0%
+philosophy of science question yeah it's
+ 
+
+ align:start position:0%
+philosophy of science question yeah it's
+like you know why why is science good
+
+ align:start position:0%
+like you know why why is science good
+ 
+
+ align:start position:0%
+like you know why why is science good
+why is it good to make generalizations
+
+ align:start position:0%
+why is it good to make generalizations
+ 
+
+ align:start position:0%
+why is it good to make generalizations
+um because it helps us to understand the
+
+ align:start position:0%
+um because it helps us to understand the
+ 
+
+ align:start position:0%
+um because it helps us to understand the
+world we're all better for Faith's
+
+ align:start position:0%
+world we're all better for Faith's
+ 
+
+ align:start position:0%
+world we're all better for Faith's
+reason as well as the reason I just
+
+ align:start position:0%
+reason as well as the reason I just
+ 
+
+ align:start position:0%
+reason as well as the reason I just
+offered yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's um yeah
+
+ align:start position:0%
+it's um yeah
+ 
+
+ align:start position:0%
+it's um yeah
+yes arguably so there are languages that
+
+ align:start position:0%
+yes arguably so there are languages that
+ 
+
+ align:start position:0%
+yes arguably so there are languages that
+D voice vowels
+
+ align:start position:0%
+D voice vowels
+ 
+
+ align:start position:0%
+D voice vowels
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh mokalis is one no Japanese is another
+
+ align:start position:0%
+uh mokalis is one no Japanese is another
+ 
+
+ align:start position:0%
+uh mokalis is one no Japanese is another
+um so Japanese has a general rule
+
+ align:start position:0%
+um so Japanese has a general rule
+ 
+
+ align:start position:0%
+um so Japanese has a general rule
+devoicing
+
+ align:start position:0%
+devoicing
+ 
+
+ align:start position:0%
+devoicing
+um it's High vowels
+
+ align:start position:0%
+um it's High vowels
+ 
+
+ align:start position:0%
+um it's High vowels
+when they are
+
+ align:start position:0%
+when they are
+ 
+
+ align:start position:0%
+when they are
+between voiceless consonants I guess so
+
+ align:start position:0%
+between voiceless consonants I guess so
+ 
+
+ align:start position:0%
+between voiceless consonants I guess so
+uh here's the Japanese word for like and
+
+ align:start position:0%
+uh here's the Japanese word for like and
+ 
+
+ align:start position:0%
+uh here's the Japanese word for like and
+it's pronounced ski ski so the uh isn't
+
+ align:start position:0%
+it's pronounced ski ski so the uh isn't
+ 
+
+ align:start position:0%
+it's pronounced ski ski so the uh isn't
+proud you can't you don't say Suki
+
+ align:start position:0%
+proud you can't you don't say Suki
+ 
+
+ align:start position:0%
+proud you can't you don't say Suki
+unless you're being very slow and
+
+ align:start position:0%
+unless you're being very slow and
+ 
+
+ align:start position:0%
+unless you're being very slow and
+careful
+
+ align:start position:0%
+careful
+ 
+
+ align:start position:0%
+careful
+and uh it's still a vowel in the sense
+
+ align:start position:0%
+and uh it's still a vowel in the sense
+ 
+
+ align:start position:0%
+and uh it's still a vowel in the sense
+that your tongue and the rest of your
+
+ align:start position:0%
+that your tongue and the rest of your
+ 
+
+ align:start position:0%
+that your tongue and the rest of your
+vocal tract is still in the
+
+ align:start position:0%
+vocal tract is still in the
+ 
+
+ align:start position:0%
+vocal tract is still in the
+configuration that it would be if your
+
+ align:start position:0%
+configuration that it would be if your
+ 
+
+ align:start position:0%
+configuration that it would be if your
+vocal cords were vibrating but they
+
+ align:start position:0%
+vocal cords were vibrating but they
+ 
+
+ align:start position:0%
+vocal cords were vibrating but they
+aren't yeah so so yeah they're arguably
+
+ align:start position:0%
+aren't yeah so so yeah they're arguably
+ 
+
+ align:start position:0%
+aren't yeah so so yeah they're arguably
+are voiceless vaults yeah yes Joseph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+um so in this particular example there
+
+ align:start position:0%
+um so in this particular example there
+ 
+
+ align:start position:0%
+um so in this particular example there
+aren't any affixes you can add to ski to
+
+ align:start position:0%
+aren't any affixes you can add to ski to
+ 
+
+ align:start position:0%
+aren't any affixes you can add to ski to
+to devoice the vowel
+
+ align:start position:0%
+to devoice the vowel
+ 
+
+ align:start position:0%
+to devoice the vowel
+um but uh
+
+ align:start position:0%
+um but uh
+ 
+
+ align:start position:0%
+um but uh
+um let me think of a of an example
+
+ align:start position:0%
+um let me think of a of an example
+ 
+
+ align:start position:0%
+um let me think of a of an example
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+Tatsu
+
+ align:start position:0%
+Tatsu
+ 
+
+ align:start position:0%
+Tatsu
+um so this is not high so it doesn't
+
+ align:start position:0%
+um so this is not high so it doesn't
+ 
+
+ align:start position:0%
+um so this is not high so it doesn't
+devoice this is the verb to stand
+
+ align:start position:0%
+devoice this is the verb to stand
+ 
+
+ align:start position:0%
+devoice this is the verb to stand
+um the more polite version of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me try to think of an example let me
+
+ align:start position:0%
+let me try to think of an example let me
+ 
+
+ align:start position:0%
+let me try to think of an example let me
+try to think of an example that does
+
+ align:start position:0%
+try to think of an example that does
+ 
+
+ align:start position:0%
+try to think of an example that does
+what you want but there aren't any
+
+ align:start position:0%
+what you want but there aren't any
+ 
+
+ align:start position:0%
+what you want but there aren't any
+examples that will work with ski yeah
+
+ align:start position:0%
+examples that will work with ski yeah
+ 
+
+ align:start position:0%
+examples that will work with ski yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay so when I think of an example at
+
+ align:start position:0%
+okay so when I think of an example at
+ 
+
+ align:start position:0%
+okay so when I think of an example at
+three in the morning I'll give you a
+
+ align:start position:0%
+three in the morning I'll give you a
+ 
+
+ align:start position:0%
+three in the morning I'll give you a
+call leave me your phone number and uh
+
+ align:start position:0%
+call leave me your phone number and uh
+ 
+
+ align:start position:0%
+call leave me your phone number and uh
+think of that
+
+ align:start position:0%
+think of that
+ 
+
+ align:start position:0%
+think of that
+it's got to be a straightforward way to
+
+ align:start position:0%
+it's got to be a straightforward way to
+ 
+
+ align:start position:0%
+it's got to be a straightforward way to
+do this it's going to bother me now uh
+
+ align:start position:0%
+do this it's going to bother me now uh
+ 
+
+ align:start position:0%
+do this it's going to bother me now uh
+yeah other questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+try to think of questions while I tried
+
+ align:start position:0%
+try to think of questions while I tried
+ 
+
+ align:start position:0%
+try to think of questions while I tried
+to think of examples that do what Joseph
+
+ align:start position:0%
+to think of examples that do what Joseph
+ 
+
+ align:start position:0%
+to think of examples that do what Joseph
+wants because the past tense suffix in
+
+ align:start position:0%
+wants because the past tense suffix in
+ 
+
+ align:start position:0%
+wants because the past tense suffix in
+Japanese oh oh
+
+ align:start position:0%
+Japanese oh oh
+ 
+
+ align:start position:0%
+Japanese oh oh
+yeah yeah okay here's one
+
+ align:start position:0%
+yeah yeah okay here's one
+ 
+
+ align:start position:0%
+yeah yeah okay here's one
+um uh uh adjectives in Japanese
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the the word for new
+
+ align:start position:0%
+so this is the the word for new
+ 
+
+ align:start position:0%
+so this is the the word for new
+atarashi
+
+ align:start position:0%
+atarashi
+ 
+
+ align:start position:0%
+atarashi
+um and uh
+
+ align:start position:0%
+um and uh
+ 
+
+ align:start position:0%
+um and uh
+negative of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I
+
+ align:start position:0%
+and I
+ 
+
+ align:start position:0%
+and I
+uh and so there's a coup that you add to
+
+ align:start position:0%
+uh and so there's a coup that you add to
+ 
+
+ align:start position:0%
+uh and so there's a coup that you add to
+make the negative form
+
+ align:start position:0%
+make the negative form
+ 
+
+ align:start position:0%
+make the negative form
+um and it ends up putting this vowel
+
+ align:start position:0%
+um and it ends up putting this vowel
+ 
+
+ align:start position:0%
+um and it ends up putting this vowel
+between bracelets between voiceless
+
+ align:start position:0%
+between bracelets between voiceless
+ 
+
+ align:start position:0%
+between bracelets between voiceless
+sounds and then yeah City voices so it
+
+ align:start position:0%
+sounds and then yeah City voices so it
+ 
+
+ align:start position:0%
+sounds and then yeah City voices so it
+goes from atarashi to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh or the past tense actually so it was
+
+ align:start position:0%
+uh or the past tense actually so it was
+ 
+
+ align:start position:0%
+uh or the past tense actually so it was
+if you want to say something was new
+
+ align:start position:0%
+if you want to say something was new
+ 
+
+ align:start position:0%
+if you want to say something was new
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again the e that's after the voices
+
+ align:start position:0%
+again the e that's after the voices
+ 
+
+ align:start position:0%
+again the e that's after the voices
+because there's a voiceless sound good
+
+ align:start position:0%
+because there's a voiceless sound good
+ 
+
+ align:start position:0%
+because there's a voiceless sound good
+now I won't call you at two in the
+
+ align:start position:0%
+now I won't call you at two in the
+ 
+
+ align:start position:0%
+now I won't call you at two in the
+morning
+
+ align:start position:0%
+morning
+ 
+
+ align:start position:0%
+morning
+any other questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay
+
+ align:start position:0%
+uh okay
+ 
+
+ align:start position:0%
+uh okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's go back now to the English plural
+
+ align:start position:0%
+let's go back now to the English plural
+ 
+
+ align:start position:0%
+let's go back now to the English plural
+suffix
+
+ align:start position:0%
+suffix
+ 
+
+ align:start position:0%
+suffix
+um and kind of uh review something that
+
+ align:start position:0%
+um and kind of uh review something that
+ 
+
+ align:start position:0%
+um and kind of uh review something that
+we have talked about but in the in the
+
+ align:start position:0%
+we have talked about but in the in the
+ 
+
+ align:start position:0%
+we have talked about but in the in the
+light of all of the things that we've
+
+ align:start position:0%
+light of all of the things that we've
+ 
+
+ align:start position:0%
+light of all of the things that we've
+talked about since then I hope
+
+ align:start position:0%
+talked about since then I hope
+ 
+
+ align:start position:0%
+talked about since then I hope
+it'll become a little clearer so again
+
+ align:start position:0%
+it'll become a little clearer so again
+ 
+
+ align:start position:0%
+it'll become a little clearer so again
+we're talking about the regular English
+
+ align:start position:0%
+we're talking about the regular English
+ 
+
+ align:start position:0%
+we're talking about the regular English
+plural suffix stop thinking about oxen
+
+ align:start position:0%
+plural suffix stop thinking about oxen
+ 
+
+ align:start position:0%
+plural suffix stop thinking about oxen
+and fish and sheep
+
+ align:start position:0%
+and fish and sheep
+ 
+
+ align:start position:0%
+and fish and sheep
+um cats and dogs and bushes we decided
+
+ align:start position:0%
+um cats and dogs and bushes we decided
+ 
+
+ align:start position:0%
+um cats and dogs and bushes we decided
+the underlying form of the plural suffix
+
+ align:start position:0%
+the underlying form of the plural suffix
+ 
+
+ align:start position:0%
+the underlying form of the plural suffix
+is a z right and it undergoes various
+
+ align:start position:0%
+is a z right and it undergoes various
+ 
+
+ align:start position:0%
+is a z right and it undergoes various
+kinds of sound changes depending on
+
+ align:start position:0%
+kinds of sound changes depending on
+ 
+
+ align:start position:0%
+kinds of sound changes depending on
+what's before it so you add Z to all
+
+ align:start position:0%
+what's before it so you add Z to all
+ 
+
+ align:start position:0%
+what's before it so you add Z to all
+three of these underlyingly and then
+
+ align:start position:0%
+three of these underlyingly and then
+ 
+
+ align:start position:0%
+three of these underlyingly and then
+there are generalizations like English
+
+ align:start position:0%
+there are generalizations like English
+ 
+
+ align:start position:0%
+there are generalizations like English
+doesn't like words that end in a z
+
+ align:start position:0%
+doesn't like words that end in a z
+ 
+
+ align:start position:0%
+doesn't like words that end in a z
+that's preceded by a voiceless sound
+
+ align:start position:0%
+that's preceded by a voiceless sound
+ 
+
+ align:start position:0%
+that's preceded by a voiceless sound
+and words don't get to end in two
+
+ align:start position:0%
+and words don't get to end in two
+ 
+
+ align:start position:0%
+and words don't get to end in two
+strident consonants right where
+
+ align:start position:0%
+strident consonants right where
+ 
+
+ align:start position:0%
+strident consonants right where
+stridents or things like the Shu and the
+
+ align:start position:0%
+stridents or things like the Shu and the
+ 
+
+ align:start position:0%
+stridents or things like the Shu and the
+Z that's at the end of bushes yeah
+
+ align:start position:0%
+Z that's at the end of bushes yeah
+ 
+
+ align:start position:0%
+Z that's at the end of bushes yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so those are generalizations but we said
+
+ align:start position:0%
+so those are generalizations but we said
+ 
+
+ align:start position:0%
+so those are generalizations but we said
+one of the attractive things about this
+
+ align:start position:0%
+one of the attractive things about this
+ 
+
+ align:start position:0%
+one of the attractive things about this
+way of thinking about the English plural
+
+ align:start position:0%
+way of thinking about the English plural
+ 
+
+ align:start position:0%
+way of thinking about the English plural
+is that these are generalizations that
+
+ align:start position:0%
+is that these are generalizations that
+ 
+
+ align:start position:0%
+is that these are generalizations that
+just seem to hold about English
+
+ align:start position:0%
+just seem to hold about English
+ 
+
+ align:start position:0%
+just seem to hold about English
+generally English doesn't have any words
+
+ align:start position:0%
+generally English doesn't have any words
+ 
+
+ align:start position:0%
+generally English doesn't have any words
+that end in a z preceded by a voiceless
+
+ align:start position:0%
+that end in a z preceded by a voiceless
+ 
+
+ align:start position:0%
+that end in a z preceded by a voiceless
+sound and we can kind of rely on English
+
+ align:start position:0%
+sound and we can kind of rely on English
+ 
+
+ align:start position:0%
+sound and we can kind of rely on English
+phonology to demand that you do
+
+ align:start position:0%
+phonology to demand that you do
+ 
+
+ align:start position:0%
+phonology to demand that you do
+something if you add Z to cat yeah
+
+ align:start position:0%
+something if you add Z to cat yeah
+ 
+
+ align:start position:0%
+something if you add Z to cat yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+again we've said this before I just want
+
+ align:start position:0%
+again we've said this before I just want
+ 
+
+ align:start position:0%
+again we've said this before I just want
+to say it again a little more clearly
+
+ align:start position:0%
+to say it again a little more clearly
+ 
+
+ align:start position:0%
+to say it again a little more clearly
+there are these conditions and then
+
+ align:start position:0%
+there are these conditions and then
+ 
+
+ align:start position:0%
+there are these conditions and then
+there are also these procedures for
+
+ align:start position:0%
+there are also these procedures for
+ 
+
+ align:start position:0%
+there are also these procedures for
+repairing these violations so you know
+
+ align:start position:0%
+repairing these violations so you know
+ 
+
+ align:start position:0%
+repairing these violations so you know
+what do you do about the fact that you
+
+ align:start position:0%
+what do you do about the fact that you
+ 
+
+ align:start position:0%
+what do you do about the fact that you
+added Z to cat well you D voice the Z
+
+ align:start position:0%
+added Z to cat well you D voice the Z
+ 
+
+ align:start position:0%
+added Z to cat well you D voice the Z
+if the condition just says you can't
+
+ align:start position:0%
+if the condition just says you can't
+ 
+
+ align:start position:0%
+if the condition just says you can't
+have a z preceded by something voiceless
+
+ align:start position:0%
+have a z preceded by something voiceless
+ 
+
+ align:start position:0%
+have a z preceded by something voiceless
+there are various things you could have
+
+ align:start position:0%
+there are various things you could have
+ 
+
+ align:start position:0%
+there are various things you could have
+done to fix that problem you could have
+
+ align:start position:0%
+done to fix that problem you could have
+ 
+
+ align:start position:0%
+done to fix that problem you could have
+voiced the D right so the plural of cat
+
+ align:start position:0%
+voiced the D right so the plural of cat
+ 
+
+ align:start position:0%
+voiced the D right so the plural of cat
+could be cads right that would be a good
+
+ align:start position:0%
+could be cads right that would be a good
+ 
+
+ align:start position:0%
+could be cads right that would be a good
+English word or you could add a vowel
+
+ align:start position:0%
+English word or you could add a vowel
+ 
+
+ align:start position:0%
+English word or you could add a vowel
+like you do in bushes right the plural
+
+ align:start position:0%
+like you do in bushes right the plural
+ 
+
+ align:start position:0%
+like you do in bushes right the plural
+of cat could be catas you know there are
+
+ align:start position:0%
+of cat could be catas you know there are
+ 
+
+ align:start position:0%
+of cat could be catas you know there are
+various things that would fix that
+
+ align:start position:0%
+various things that would fix that
+ 
+
+ align:start position:0%
+various things that would fix that
+problem if that's the problem but this
+
+ align:start position:0%
+problem if that's the problem but this
+ 
+
+ align:start position:0%
+problem if that's the problem but this
+is the thing that you do yeah it's kind
+
+ align:start position:0%
+is the thing that you do yeah it's kind
+ 
+
+ align:start position:0%
+is the thing that you do yeah it's kind
+of like when we were talking about yeah
+
+ align:start position:0%
+of like when we were talking about yeah
+ 
+
+ align:start position:0%
+of like when we were talking about yeah
+well money we said you can't have three
+
+ align:start position:0%
+well money we said you can't have three
+ 
+
+ align:start position:0%
+well money we said you can't have three
+consonants in a row what do you do about
+
+ align:start position:0%
+consonants in a row what do you do about
+ 
+
+ align:start position:0%
+consonants in a row what do you do about
+it well it depends on the situation
+
+ align:start position:0%
+it well it depends on the situation
+ 
+
+ align:start position:0%
+it well it depends on the situation
+right so if one of them is an H you get
+
+ align:start position:0%
+right so if one of them is an H you get
+ 
+
+ align:start position:0%
+right so if one of them is an H you get
+rid of the H if not then you insert a
+
+ align:start position:0%
+rid of the H if not then you insert a
+ 
+
+ align:start position:0%
+rid of the H if not then you insert a
+vowel in this position and not that
+
+ align:start position:0%
+vowel in this position and not that
+ 
+
+ align:start position:0%
+vowel in this position and not that
+position so a similar kind of thing
+
+ align:start position:0%
+position so a similar kind of thing
+ 
+
+ align:start position:0%
+position so a similar kind of thing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is all a way of saying what we
+
+ align:start position:0%
+so this is all a way of saying what we
+ 
+
+ align:start position:0%
+so this is all a way of saying what we
+it's it's uh worthwhile maybe to
+
+ align:start position:0%
+it's it's uh worthwhile maybe to
+ 
+
+ align:start position:0%
+it's it's uh worthwhile maybe to
+distinguish between uh the phonotactic
+
+ align:start position:0%
+distinguish between uh the phonotactic
+ 
+
+ align:start position:0%
+distinguish between uh the phonotactic
+considerations or the the well informed
+
+ align:start position:0%
+considerations or the the well informed
+ 
+
+ align:start position:0%
+considerations or the the well informed
+in this considerations that tell you
+
+ align:start position:0%
+in this considerations that tell you
+ 
+
+ align:start position:0%
+in this considerations that tell you
+this language doesn't like uh three
+
+ align:start position:0%
+this language doesn't like uh three
+ 
+
+ align:start position:0%
+this language doesn't like uh three
+consonants in a row or two accented
+
+ align:start position:0%
+consonants in a row or two accented
+ 
+
+ align:start position:0%
+consonants in a row or two accented
+syllables in your word or uh words
+
+ align:start position:0%
+syllables in your word or uh words
+ 
+
+ align:start position:0%
+syllables in your word or uh words
+ending in a z preceded by a voiceless
+
+ align:start position:0%
+ending in a z preceded by a voiceless
+ 
+
+ align:start position:0%
+ending in a z preceded by a voiceless
+sound there's that kind of condition and
+
+ align:start position:0%
+sound there's that kind of condition and
+ 
+
+ align:start position:0%
+sound there's that kind of condition and
+then there's how do you repair it what
+
+ align:start position:0%
+then there's how do you repair it what
+ 
+
+ align:start position:0%
+then there's how do you repair it what
+kind of a repair do you use
+
+ align:start position:0%
+kind of a repair do you use
+ 
+
+ align:start position:0%
+kind of a repair do you use
+um so there's the well-formed in this
+
+ align:start position:0%
+um so there's the well-formed in this
+ 
+
+ align:start position:0%
+um so there's the well-formed in this
+condition and then there's the repair
+
+ align:start position:0%
+condition and then there's the repair
+ 
+
+ align:start position:0%
+condition and then there's the repair
+yeah so in this particular case the
+
+ align:start position:0%
+yeah so in this particular case the
+ 
+
+ align:start position:0%
+yeah so in this particular case the
+procedures are devoice and insert schwa
+
+ align:start position:0%
+procedures are devoice and insert schwa
+ 
+
+ align:start position:0%
+procedures are devoice and insert schwa
+um there's a particularly sort of
+
+ align:start position:0%
+um there's a particularly sort of
+ 
+
+ align:start position:0%
+um there's a particularly sort of
+striking bit of evidence for this way of
+
+ align:start position:0%
+striking bit of evidence for this way of
+ 
+
+ align:start position:0%
+striking bit of evidence for this way of
+dividing things up uh this distinction
+
+ align:start position:0%
+dividing things up uh this distinction
+ 
+
+ align:start position:0%
+dividing things up uh this distinction
+that I'm drawing between well-formedness
+
+ align:start position:0%
+that I'm drawing between well-formedness
+ 
+
+ align:start position:0%
+that I'm drawing between well-formedness
+conditions on words on the one hand and
+
+ align:start position:0%
+conditions on words on the one hand and
+ 
+
+ align:start position:0%
+conditions on words on the one hand and
+uh types of possible repair on the other
+
+ align:start position:0%
+uh types of possible repair on the other
+ 
+
+ align:start position:0%
+uh types of possible repair on the other
+that we need to think about both of
+
+ align:start position:0%
+that we need to think about both of
+ 
+
+ align:start position:0%
+that we need to think about both of
+those things if we're going to describe
+
+ align:start position:0%
+those things if we're going to describe
+ 
+
+ align:start position:0%
+those things if we're going to describe
+what the language is doing
+
+ align:start position:0%
+what the language is doing
+ 
+
+ align:start position:0%
+what the language is doing
+this is a classic test in 1957 I
+
+ align:start position:0%
+this is a classic test in 1957 I
+ 
+
+ align:start position:0%
+this is a classic test in 1957 I
+mentioned it in class before but I
+
+ align:start position:0%
+mentioned it in class before but I
+ 
+
+ align:start position:0%
+mentioned it in class before but I
+wanted to talk about it a little more
+
+ align:start position:0%
+wanted to talk about it a little more
+ 
+
+ align:start position:0%
+wanted to talk about it a little more
+now that we've drawn this distinction uh
+
+ align:start position:0%
+now that we've drawn this distinction uh
+ 
+
+ align:start position:0%
+now that we've drawn this distinction uh
+so uh Gene burco later Jean burko
+
+ align:start position:0%
+so uh Gene burco later Jean burko
+ 
+
+ align:start position:0%
+so uh Gene burco later Jean burko
+Gleason uh did this work in 1957 with
+
+ align:start position:0%
+Gleason uh did this work in 1957 with
+ 
+
+ align:start position:0%
+Gleason uh did this work in 1957 with
+children she was demonstrating that they
+
+ align:start position:0%
+children she was demonstrating that they
+ 
+
+ align:start position:0%
+children she was demonstrating that they
+know these generalizations about plurals
+
+ align:start position:0%
+know these generalizations about plurals
+ 
+
+ align:start position:0%
+know these generalizations about plurals
+uh even with words they've never heard
+
+ align:start position:0%
+uh even with words they've never heard
+ 
+
+ align:start position:0%
+uh even with words they've never heard
+before so she would show them pictures
+
+ align:start position:0%
+before so she would show them pictures
+ 
+
+ align:start position:0%
+before so she would show them pictures
+like this one this is one of her
+
+ align:start position:0%
+like this one this is one of her
+ 
+
+ align:start position:0%
+like this one this is one of her
+pictures she said this is a wug
+
+ align:start position:0%
+pictures she said this is a wug
+ 
+
+ align:start position:0%
+pictures she said this is a wug
+um and then she would show them
+
+ align:start position:0%
+um and then she would show them
+ 
+
+ align:start position:0%
+um and then she would show them
+two pictures of the same thing and she
+
+ align:start position:0%
+two pictures of the same thing and she
+ 
+
+ align:start position:0%
+two pictures of the same thing and she
+would say now there are two of them
+
+ align:start position:0%
+would say now there are two of them
+ 
+
+ align:start position:0%
+would say now there are two of them
+there are two and children were supposed
+
+ align:start position:0%
+there are two and children were supposed
+ 
+
+ align:start position:0%
+there are two and children were supposed
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+bugs yeah uh even though they'd never
+
+ align:start position:0%
+bugs yeah uh even though they'd never
+ 
+
+ align:start position:0%
+bugs yeah uh even though they'd never
+heard anybody say well before right so
+
+ align:start position:0%
+heard anybody say well before right so
+ 
+
+ align:start position:0%
+heard anybody say well before right so
+Jean Virgo Gleason Gene burko uh made up
+
+ align:start position:0%
+Jean Virgo Gleason Gene burko uh made up
+ 
+
+ align:start position:0%
+Jean Virgo Gleason Gene burko uh made up
+a bunch of words she worked hard to make
+
+ align:start position:0%
+a bunch of words she worked hard to make
+ 
+
+ align:start position:0%
+a bunch of words she worked hard to make
+sure they were not real words and then
+
+ align:start position:0%
+sure they were not real words and then
+ 
+
+ align:start position:0%
+sure they were not real words and then
+she Drew many cute pictures uh and
+
+ align:start position:0%
+she Drew many cute pictures uh and
+ 
+
+ align:start position:0%
+she Drew many cute pictures uh and
+showed children singulars and plurals
+
+ align:start position:0%
+showed children singulars and plurals
+ 
+
+ align:start position:0%
+showed children singulars and plurals
+and said okay here's the singular what's
+
+ align:start position:0%
+and said okay here's the singular what's
+ 
+
+ align:start position:0%
+and said okay here's the singular what's
+the plural right and the kids
+
+ align:start position:0%
+the plural right and the kids
+ 
+
+ align:start position:0%
+the plural right and the kids
+um responded and she wrote down their
+
+ align:start position:0%
+um responded and she wrote down their
+ 
+
+ align:start position:0%
+um responded and she wrote down their
+responses and their responses
+
+ align:start position:0%
+responses and their responses
+ 
+
+ align:start position:0%
+responses and their responses
+interestingly were accurate uh in one
+
+ align:start position:0%
+interestingly were accurate uh in one
+ 
+
+ align:start position:0%
+interestingly were accurate uh in one
+way and sometimes inaccurate in another
+
+ align:start position:0%
+way and sometimes inaccurate in another
+ 
+
+ align:start position:0%
+way and sometimes inaccurate in another
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+interesting to think about so she was
+
+ align:start position:0%
+interesting to think about so she was
+ 
+
+ align:start position:0%
+interesting to think about so she was
+working with children who were five
+
+ align:start position:0%
+working with children who were five
+ 
+
+ align:start position:0%
+working with children who were five
+years old and children who were seven
+
+ align:start position:0%
+years old and children who were seven
+ 
+
+ align:start position:0%
+years old and children who were seven
+years old uh what she discovered was
+
+ align:start position:0%
+years old uh what she discovered was
+ 
+
+ align:start position:0%
+years old uh what she discovered was
+that by the time they're five years old
+
+ align:start position:0%
+that by the time they're five years old
+ 
+
+ align:start position:0%
+that by the time they're five years old
+they are in a sense perfect uh in the
+
+ align:start position:0%
+they are in a sense perfect uh in the
+ 
+
+ align:start position:0%
+they are in a sense perfect uh in the
+sense that all of the words that they
+
+ align:start position:0%
+sense that all of the words that they
+ 
+
+ align:start position:0%
+sense that all of the words that they
+came up with were phonatactically
+
+ align:start position:0%
+came up with were phonatactically
+ 
+
+ align:start position:0%
+came up with were phonatactically
+well-formed English words uh so here are
+
+ align:start position:0%
+well-formed English words uh so here are
+ 
+
+ align:start position:0%
+well-formed English words uh so here are
+three of uh burko's words heaths and
+
+ align:start position:0%
+three of uh burko's words heaths and
+ 
+
+ align:start position:0%
+three of uh burko's words heaths and
+Muzz yeah and uh well I think everybody
+
+ align:start position:0%
+Muzz yeah and uh well I think everybody
+ 
+
+ align:start position:0%
+Muzz yeah and uh well I think everybody
+did well perfectly everybody said the
+
+ align:start position:0%
+did well perfectly everybody said the
+ 
+
+ align:start position:0%
+did well perfectly everybody said the
+plural bug is wugs
+
+ align:start position:0%
+plural bug is wugs
+ 
+
+ align:start position:0%
+plural bug is wugs
+um but there were other cases where you
+
+ align:start position:0%
+um but there were other cases where you
+ 
+
+ align:start position:0%
+um but there were other cases where you
+know uh children would say sometimes
+
+ align:start position:0%
+know uh children would say sometimes
+ 
+
+ align:start position:0%
+know uh children would say sometimes
+things like the plural Thief is heifas
+
+ align:start position:0%
+things like the plural Thief is heifas
+ 
+
+ align:start position:0%
+things like the plural Thief is heifas
+or the plural of fast is fast or the
+
+ align:start position:0%
+or the plural of fast is fast or the
+ 
+
+ align:start position:0%
+or the plural of fast is fast or the
+plural of Moses Muzz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are all words where
+
+ align:start position:0%
+these are all words where
+ 
+
+ align:start position:0%
+these are all words where
+um and then there were other kinds of
+
+ align:start position:0%
+um and then there were other kinds of
+ 
+
+ align:start position:0%
+um and then there were other kinds of
+mistakes that children didn't make so um
+
+ align:start position:0%
+mistakes that children didn't make so um
+ 
+
+ align:start position:0%
+mistakes that children didn't make so um
+nobody said that the plural of wug was
+
+ align:start position:0%
+nobody said that the plural of wug was
+ 
+
+ align:start position:0%
+nobody said that the plural of wug was
+wugs you know or that the plural of wook
+
+ align:start position:0%
+wugs you know or that the plural of wook
+ 
+
+ align:start position:0%
+wugs you know or that the plural of wook
+is right or that the plural fast as fast
+
+ align:start position:0%
+is right or that the plural fast as fast
+ 
+
+ align:start position:0%
+is right or that the plural fast as fast
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what were children doing well children
+
+ align:start position:0%
+what were children doing well children
+ 
+
+ align:start position:0%
+what were children doing well children
+know if you show them something that's
+
+ align:start position:0%
+know if you show them something that's
+ 
+
+ align:start position:0%
+know if you show them something that's
+underlyingly you know you give them
+
+ align:start position:0%
+underlyingly you know you give them
+ 
+
+ align:start position:0%
+underlyingly you know you give them
+Heath
+
+ align:start position:0%
+Heath
+ 
+
+ align:start position:0%
+Heath
+for some reason I'm spelling backwards
+
+ align:start position:0%
+for some reason I'm spelling backwards
+ 
+
+ align:start position:0%
+for some reason I'm spelling backwards
+you give them Heath and you ask them the
+
+ align:start position:0%
+you give them Heath and you ask them the
+ 
+
+ align:start position:0%
+you give them Heath and you ask them the
+plural they know that you're supposed to
+
+ align:start position:0%
+plural they know that you're supposed to
+ 
+
+ align:start position:0%
+plural they know that you're supposed to
+add a z and they know that English
+
+ align:start position:0%
+add a z and they know that English
+ 
+
+ align:start position:0%
+add a z and they know that English
+doesn't allow words that end in a z
+
+ align:start position:0%
+doesn't allow words that end in a z
+ 
+
+ align:start position:0%
+doesn't allow words that end in a z
+preceded by a voiceless sound
+
+ align:start position:0%
+preceded by a voiceless sound
+ 
+
+ align:start position:0%
+preceded by a voiceless sound
+but some of these five and
+
+ align:start position:0%
+but some of these five and
+ 
+
+ align:start position:0%
+but some of these five and
+seven-year-olds were a little fuzzy on
+
+ align:start position:0%
+seven-year-olds were a little fuzzy on
+ 
+
+ align:start position:0%
+seven-year-olds were a little fuzzy on
+on the possible repairs
+
+ align:start position:0%
+on the possible repairs
+ 
+
+ align:start position:0%
+on the possible repairs
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um they none of them said oh yeah it's
+
+ align:start position:0%
+um they none of them said oh yeah it's
+ 
+
+ align:start position:0%
+um they none of them said oh yeah it's
+he right
+
+ align:start position:0%
+he right
+ 
+
+ align:start position:0%
+he right
+but I just said this if the only problem
+
+ align:start position:0%
+but I just said this if the only problem
+ 
+
+ align:start position:0%
+but I just said this if the only problem
+is well this word ends in the voiceless
+
+ align:start position:0%
+is well this word ends in the voiceless
+ 
+
+ align:start position:0%
+is well this word ends in the voiceless
+sound followed by a z in fact what
+
+ align:start position:0%
+sound followed by a z in fact what
+ 
+
+ align:start position:0%
+sound followed by a z in fact what
+you're supposed to do is devoice the Z
+
+ align:start position:0%
+you're supposed to do is devoice the Z
+ 
+
+ align:start position:0%
+you're supposed to do is devoice the Z
+that's what an adult would do it's a
+
+ align:start position:0%
+that's what an adult would do it's a
+ 
+
+ align:start position:0%
+that's what an adult would do it's a
+plural Thief is heafs yeah but if you
+
+ align:start position:0%
+plural Thief is heafs yeah but if you
+ 
+
+ align:start position:0%
+plural Thief is heafs yeah but if you
+were instead to insert a schwa well that
+
+ align:start position:0%
+were instead to insert a schwa well that
+ 
+
+ align:start position:0%
+were instead to insert a schwa well that
+would fix it too right so uh now the Z
+
+ align:start position:0%
+would fix it too right so uh now the Z
+ 
+
+ align:start position:0%
+would fix it too right so uh now the Z
+is preceded by a voiced sound the plural
+
+ align:start position:0%
+is preceded by a voiced sound the plural
+ 
+
+ align:start position:0%
+is preceded by a voiced sound the plural
+Thief is yeah and there were some kids
+
+ align:start position:0%
+Thief is yeah and there were some kids
+ 
+
+ align:start position:0%
+Thief is yeah and there were some kids
+who were going through a stage who were
+
+ align:start position:0%
+who were going through a stage who were
+ 
+
+ align:start position:0%
+who were going through a stage who were
+entertaining that possibility you know
+
+ align:start position:0%
+entertaining that possibility you know
+ 
+
+ align:start position:0%
+entertaining that possibility you know
+that that was the correct repair for
+
+ align:start position:0%
+that that was the correct repair for
+ 
+
+ align:start position:0%
+that that was the correct repair for
+that so what what uh berko found was
+
+ align:start position:0%
+that so what what uh berko found was
+ 
+
+ align:start position:0%
+that so what what uh berko found was
+that children uh universally knew the
+
+ align:start position:0%
+that children uh universally knew the
+ 
+
+ align:start position:0%
+that children uh universally knew the
+phono tactics right they they knew that
+
+ align:start position:0%
+phono tactics right they they knew that
+ 
+
+ align:start position:0%
+phono tactics right they they knew that
+English doesn't allow words that end in
+
+ align:start position:0%
+English doesn't allow words that end in
+ 
+
+ align:start position:0%
+English doesn't allow words that end in
+the Z preceded by a voiceless sound but
+
+ align:start position:0%
+the Z preceded by a voiceless sound but
+ 
+
+ align:start position:0%
+the Z preceded by a voiceless sound but
+they made sort of uh intriguing mistakes
+
+ align:start position:0%
+they made sort of uh intriguing mistakes
+ 
+
+ align:start position:0%
+they made sort of uh intriguing mistakes
+of various kinds not very often most of
+
+ align:start position:0%
+of various kinds not very often most of
+ 
+
+ align:start position:0%
+of various kinds not very often most of
+the kids just did everything perfectly
+
+ align:start position:0%
+the kids just did everything perfectly
+ 
+
+ align:start position:0%
+the kids just did everything perfectly
+but every so often she would get kids
+
+ align:start position:0%
+but every so often she would get kids
+ 
+
+ align:start position:0%
+but every so often she would get kids
+who made some mistakes and the mistakes
+
+ align:start position:0%
+who made some mistakes and the mistakes
+ 
+
+ align:start position:0%
+who made some mistakes and the mistakes
+were of this class that is mistakes
+
+ align:start position:0%
+were of this class that is mistakes
+ 
+
+ align:start position:0%
+were of this class that is mistakes
+where they knew that there needed to be
+
+ align:start position:0%
+where they knew that there needed to be
+ 
+
+ align:start position:0%
+where they knew that there needed to be
+a repair but got the repair wrong
+
+ align:start position:0%
+a repair but got the repair wrong
+ 
+
+ align:start position:0%
+a repair but got the repair wrong
+similarly for Muzz this was a kid who
+
+ align:start position:0%
+similarly for Muzz this was a kid who
+ 
+
+ align:start position:0%
+similarly for Muzz this was a kid who
+you know the singular is Muzz and the
+
+ align:start position:0%
+you know the singular is Muzz and the
+ 
+
+ align:start position:0%
+you know the singular is Muzz and the
+kid knows that you need to add a z and
+
+ align:start position:0%
+kid knows that you need to add a z and
+ 
+
+ align:start position:0%
+kid knows that you need to add a z and
+the kid knows that you can't have two
+
+ align:start position:0%
+the kid knows that you can't have two
+ 
+
+ align:start position:0%
+the kid knows that you can't have two
+stridents at the end of a word the
+
+ align:start position:0%
+stridents at the end of a word the
+ 
+
+ align:start position:0%
+stridents at the end of a word the
+correct answer the adult's answer is to
+
+ align:start position:0%
+correct answer the adult's answer is to
+ 
+
+ align:start position:0%
+correct answer the adult's answer is to
+insert a schwa so the plural of Muzz
+
+ align:start position:0%
+insert a schwa so the plural of Muzz
+ 
+
+ align:start position:0%
+insert a schwa so the plural of Muzz
+will be muzzes but uh deleting the Z one
+
+ align:start position:0%
+will be muzzes but uh deleting the Z one
+ 
+
+ align:start position:0%
+will be muzzes but uh deleting the Z one
+of the Z is hard to know which one uh
+
+ align:start position:0%
+of the Z is hard to know which one uh
+ 
+
+ align:start position:0%
+of the Z is hard to know which one uh
+also fixes that problem and so uh that
+
+ align:start position:0%
+also fixes that problem and so uh that
+ 
+
+ align:start position:0%
+also fixes that problem and so uh that
+was a kid who thought yeah I'll delete a
+
+ align:start position:0%
+was a kid who thought yeah I'll delete a
+ 
+
+ align:start position:0%
+was a kid who thought yeah I'll delete a
+z yeah yeah Joseph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as something that English does yeah no
+
+ align:start position:0%
+as something that English does yeah no
+ 
+
+ align:start position:0%
+as something that English does yeah no
+so English there aren't I don't think
+
+ align:start position:0%
+so English there aren't I don't think
+ 
+
+ align:start position:0%
+so English there aren't I don't think
+any English nouns
+
+ align:start position:0%
+any English nouns
+ 
+
+ align:start position:0%
+any English nouns
+that form their plural by adding a z and
+
+ align:start position:0%
+that form their plural by adding a z and
+ 
+
+ align:start position:0%
+that form their plural by adding a z and
+deleting something before the Z don't
+
+ align:start position:0%
+deleting something before the Z don't
+ 
+
+ align:start position:0%
+deleting something before the Z don't
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+that ever happens yeah this is me
+
+ align:start position:0%
+that ever happens yeah this is me
+ 
+
+ align:start position:0%
+that ever happens yeah this is me
+slowing down while I tried to think of
+
+ align:start position:0%
+slowing down while I tried to think of
+ 
+
+ align:start position:0%
+slowing down while I tried to think of
+English nouns of which I know several
+
+ align:start position:0%
+English nouns of which I know several
+ 
+
+ align:start position:0%
+English nouns of which I know several
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um I can't think of any of it I can't
+
+ align:start position:0%
+um I can't think of any of it I can't
+ 
+
+ align:start position:0%
+um I can't think of any of it I can't
+think of any to do that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so is this clear another reason
+
+ align:start position:0%
+um yeah so is this clear another reason
+ 
+
+ align:start position:0%
+um yeah so is this clear another reason
+to draw this distinction between on the
+
+ align:start position:0%
+to draw this distinction between on the
+ 
+
+ align:start position:0%
+to draw this distinction between on the
+one hand
+
+ align:start position:0%
+one hand
+ 
+
+ align:start position:0%
+one hand
+what I was calling phonotactics these
+
+ align:start position:0%
+what I was calling phonotactics these
+ 
+
+ align:start position:0%
+what I was calling phonotactics these
+rules for which kinds of sounds can be
+
+ align:start position:0%
+rules for which kinds of sounds can be
+ 
+
+ align:start position:0%
+rules for which kinds of sounds can be
+where uh and on the other hand the
+
+ align:start position:0%
+where uh and on the other hand the
+ 
+
+ align:start position:0%
+where uh and on the other hand the
+repairs so uh uh the kids that burka was
+
+ align:start position:0%
+repairs so uh uh the kids that burka was
+ 
+
+ align:start position:0%
+repairs so uh uh the kids that burka was
+working with uh knew the founder tactics
+
+ align:start position:0%
+working with uh knew the founder tactics
+ 
+
+ align:start position:0%
+working with uh knew the founder tactics
+but were sometimes fuzzy on what the
+
+ align:start position:0%
+but were sometimes fuzzy on what the
+ 
+
+ align:start position:0%
+but were sometimes fuzzy on what the
+correct repairs were um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so moral yet again needed to distinguish
+
+ align:start position:0%
+so moral yet again needed to distinguish
+ 
+
+ align:start position:0%
+so moral yet again needed to distinguish
+between on the one hand the phony
+
+ align:start position:0%
+between on the one hand the phony
+ 
+
+ align:start position:0%
+between on the one hand the phony
+tactics and on the other hand the
+
+ align:start position:0%
+tactics and on the other hand the
+ 
+
+ align:start position:0%
+tactics and on the other hand the
+particular sound changes the repairs
+
+ align:start position:0%
+particular sound changes the repairs
+ 
+
+ align:start position:0%
+particular sound changes the repairs
+that enforce the phonotactics it's
+
+ align:start position:0%
+that enforce the phonotactics it's
+ 
+
+ align:start position:0%
+that enforce the phonotactics it's
+apparently possible to know one of those
+
+ align:start position:0%
+apparently possible to know one of those
+ 
+
+ align:start position:0%
+apparently possible to know one of those
+but not the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay that
+
+ align:start position:0%
+um okay that
+ 
+
+ align:start position:0%
+um okay that
+ends a chapter yeah now we're going to
+
+ align:start position:0%
+ends a chapter yeah now we're going to
+ 
+
+ align:start position:0%
+ends a chapter yeah now we're going to
+talk about something else
+
+ align:start position:0%
+talk about something else
+ 
+
+ align:start position:0%
+talk about something else
+so are there any questions about that is
+
+ align:start position:0%
+so are there any questions about that is
+ 
+
+ align:start position:0%
+so are there any questions about that is
+that clear
+
+ align:start position:0%
+that clear
+ 
+
+ align:start position:0%
+that clear
+um we've already done some of this but I
+
+ align:start position:0%
+um we've already done some of this but I
+ 
+
+ align:start position:0%
+um we've already done some of this but I
+want to do more
+
+ align:start position:0%
+want to do more
+ 
+
+ align:start position:0%
+want to do more
+we've been talking about how uh there
+
+ align:start position:0%
+we've been talking about how uh there
+ 
+
+ align:start position:0%
+we've been talking about how uh there
+are some kinds of sound changes that are
+
+ align:start position:0%
+are some kinds of sound changes that are
+ 
+
+ align:start position:0%
+are some kinds of sound changes that are
+natural because they apply to Natural
+
+ align:start position:0%
+natural because they apply to Natural
+ 
+
+ align:start position:0%
+natural because they apply to Natural
+classes of things uh sort of can be
+
+ align:start position:0%
+classes of things uh sort of can be
+ 
+
+ align:start position:0%
+classes of things uh sort of can be
+almost circular uh so you know I quickly
+
+ align:start position:0%
+almost circular uh so you know I quickly
+ 
+
+ align:start position:0%
+almost circular uh so you know I quickly
+introduced you to the word strivons
+
+ align:start position:0%
+introduced you to the word strivons
+ 
+
+ align:start position:0%
+introduced you to the word strivons
+because the generalization about English
+
+ align:start position:0%
+because the generalization about English
+ 
+
+ align:start position:0%
+because the generalization about English
+plurals is that two stridents can't end
+
+ align:start position:0%
+plurals is that two stridents can't end
+ 
+
+ align:start position:0%
+plurals is that two stridents can't end
+the word in English and that's why you
+
+ align:start position:0%
+the word in English and that's why you
+ 
+
+ align:start position:0%
+the word in English and that's why you
+introduce a schwa just in case you're in
+
+ align:start position:0%
+introduce a schwa just in case you're in
+ 
+
+ align:start position:0%
+introduce a schwa just in case you're in
+danger of having two stridents at the
+
+ align:start position:0%
+danger of having two stridents at the
+ 
+
+ align:start position:0%
+danger of having two stridents at the
+end of your word
+
+ align:start position:0%
+end of your word
+ 
+
+ align:start position:0%
+end of your word
+um uh straight in the word strident uh
+
+ align:start position:0%
+um uh straight in the word strident uh
+ 
+
+ align:start position:0%
+um uh straight in the word strident uh
+has an acoustic definition they are
+
+ align:start position:0%
+has an acoustic definition they are
+ 
+
+ align:start position:0%
+has an acoustic definition they are
+fricatives that have lots of high
+
+ align:start position:0%
+fricatives that have lots of high
+ 
+
+ align:start position:0%
+fricatives that have lots of high
+frequency noise uh but uh it's kind of
+
+ align:start position:0%
+frequency noise uh but uh it's kind of
+ 
+
+ align:start position:0%
+frequency noise uh but uh it's kind of
+of interest that there are phenomena
+
+ align:start position:0%
+of interest that there are phenomena
+ 
+
+ align:start position:0%
+of interest that there are phenomena
+like the alamorphy and English plurals
+
+ align:start position:0%
+like the alamorphy and English plurals
+ 
+
+ align:start position:0%
+like the alamorphy and English plurals
+that make reference to That acoustic
+
+ align:start position:0%
+that make reference to That acoustic
+ 
+
+ align:start position:0%
+that make reference to That acoustic
+fact that's apparently something that a
+
+ align:start position:0%
+fact that's apparently something that a
+ 
+
+ align:start position:0%
+fact that's apparently something that a
+language can care about uh how much high
+
+ align:start position:0%
+language can care about uh how much high
+ 
+
+ align:start position:0%
+language can care about uh how much high
+frequency noise you have at once
+
+ align:start position:0%
+frequency noise you have at once
+ 
+
+ align:start position:0%
+frequency noise you have at once
+um it's also something that varies from
+
+ align:start position:0%
+um it's also something that varies from
+ 
+
+ align:start position:0%
+um it's also something that varies from
+language to language there are certain
+
+ align:start position:0%
+language to language there are certain
+ 
+
+ align:start position:0%
+language to language there are certain
+languages that are perfectly happy to
+
+ align:start position:0%
+languages that are perfectly happy to
+ 
+
+ align:start position:0%
+languages that are perfectly happy to
+have long strings of stridents uh
+
+ align:start position:0%
+have long strings of stridents uh
+ 
+
+ align:start position:0%
+have long strings of stridents uh
+English just isn't one of them
+
+ align:start position:0%
+English just isn't one of them
+ 
+
+ align:start position:0%
+English just isn't one of them
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we've already done as I said some
+
+ align:start position:0%
+we've already done as I said some
+ 
+
+ align:start position:0%
+we've already done as I said some
+talking about this so when I was first
+
+ align:start position:0%
+talking about this so when I was first
+ 
+
+ align:start position:0%
+talking about this so when I was first
+introducing you to consonants or
+
+ align:start position:0%
+introducing you to consonants or
+ 
+
+ align:start position:0%
+introducing you to consonants or
+introducing you to vowels I mean you'd
+
+ align:start position:0%
+introducing you to vowels I mean you'd
+ 
+
+ align:start position:0%
+introducing you to vowels I mean you'd
+already met Constance at some point in
+
+ align:start position:0%
+already met Constance at some point in
+ 
+
+ align:start position:0%
+already met Constance at some point in
+your life but we were talking about them
+
+ align:start position:0%
+your life but we were talking about them
+ 
+
+ align:start position:0%
+your life but we were talking about them
+in a particular systematic way uh we
+
+ align:start position:0%
+in a particular systematic way uh we
+ 
+
+ align:start position:0%
+in a particular systematic way uh we
+talked about various ways of classifying
+
+ align:start position:0%
+talked about various ways of classifying
+ 
+
+ align:start position:0%
+talked about various ways of classifying
+them uh saying you know there are some
+
+ align:start position:0%
+them uh saying you know there are some
+ 
+
+ align:start position:0%
+them uh saying you know there are some
+consonants that are fricatives and some
+
+ align:start position:0%
+consonants that are fricatives and some
+ 
+
+ align:start position:0%
+consonants that are fricatives and some
+consonants that are stops or saying
+
+ align:start position:0%
+consonants that are stops or saying
+ 
+
+ align:start position:0%
+consonants that are stops or saying
+there are some consonants that are
+
+ align:start position:0%
+there are some consonants that are
+ 
+
+ align:start position:0%
+there are some consonants that are
+voiced and some consonants that are
+
+ align:start position:0%
+voiced and some consonants that are
+ 
+
+ align:start position:0%
+voiced and some consonants that are
+voiceless so what I want to do today is
+
+ align:start position:0%
+voiceless so what I want to do today is
+ 
+
+ align:start position:0%
+voiceless so what I want to do today is
+to introduce you to some other kinds of
+
+ align:start position:0%
+to introduce you to some other kinds of
+ 
+
+ align:start position:0%
+to introduce you to some other kinds of
+classification and they'll as much as
+
+ align:start position:0%
+classification and they'll as much as
+ 
+
+ align:start position:0%
+classification and they'll as much as
+possible try to show you places where
+
+ align:start position:0%
+possible try to show you places where
+ 
+
+ align:start position:0%
+possible try to show you places where
+languages care about a particular class
+
+ align:start position:0%
+languages care about a particular class
+ 
+
+ align:start position:0%
+languages care about a particular class
+of sounds again this is all in the
+
+ align:start position:0%
+of sounds again this is all in the
+ 
+
+ align:start position:0%
+of sounds again this is all in the
+service of making it easier easier for
+
+ align:start position:0%
+service of making it easier easier for
+ 
+
+ align:start position:0%
+service of making it easier easier for
+us to understand why certain kinds of
+
+ align:start position:0%
+us to understand why certain kinds of
+ 
+
+ align:start position:0%
+us to understand why certain kinds of
+sound changes are natural and others uh
+
+ align:start position:0%
+sound changes are natural and others uh
+ 
+
+ align:start position:0%
+sound changes are natural and others uh
+are are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's one that we've already seen there
+
+ align:start position:0%
+here's one that we've already seen there
+ 
+
+ align:start position:0%
+here's one that we've already seen there
+are sounds that are nasal
+
+ align:start position:0%
+are sounds that are nasal
+ 
+
+ align:start position:0%
+are sounds that are nasal
+this is a contrast that I believe I have
+
+ align:start position:0%
+this is a contrast that I believe I have
+ 
+
+ align:start position:0%
+this is a contrast that I believe I have
+introduced you to before but let me
+
+ align:start position:0%
+introduced you to before but let me
+ 
+
+ align:start position:0%
+introduced you to before but let me
+introduce you to it again there's a
+
+ align:start position:0%
+introduce you to it again there's a
+ 
+
+ align:start position:0%
+introduce you to it again there's a
+distinction
+
+ align:start position:0%
+distinction
+ 
+
+ align:start position:0%
+distinction
+um I think I brought this up last time
+
+ align:start position:0%
+um I think I brought this up last time
+ 
+
+ align:start position:0%
+um I think I brought this up last time
+actually there's a distinction when we
+
+ align:start position:0%
+actually there's a distinction when we
+ 
+
+ align:start position:0%
+actually there's a distinction when we
+talk about consonants between what are
+
+ align:start position:0%
+talk about consonants between what are
+ 
+
+ align:start position:0%
+talk about consonants between what are
+called sonorants
+
+ align:start position:0%
+called sonorants
+ 
+
+ align:start position:0%
+called sonorants
+and what are called obstructs so these
+
+ align:start position:0%
+and what are called obstructs so these
+ 
+
+ align:start position:0%
+and what are called obstructs so these
+are opposites of each other I hope I
+
+ align:start position:0%
+are opposites of each other I hope I
+ 
+
+ align:start position:0%
+are opposites of each other I hope I
+have the word obstrand on a later slide
+
+ align:start position:0%
+have the word obstrand on a later slide
+ 
+
+ align:start position:0%
+have the word obstrand on a later slide
+but just in case I don't there are these
+
+ align:start position:0%
+but just in case I don't there are these
+ 
+
+ align:start position:0%
+but just in case I don't there are these
+two kinds of sounds obstruents
+
+ align:start position:0%
+two kinds of sounds obstruents
+ 
+
+ align:start position:0%
+two kinds of sounds obstruents
+and sonorants
+
+ align:start position:0%
+and sonorants
+ 
+
+ align:start position:0%
+and sonorants
+and the distinction between them has to
+
+ align:start position:0%
+and the distinction between them has to
+ 
+
+ align:start position:0%
+and the distinction between them has to
+do with whether you are building up
+
+ align:start position:0%
+do with whether you are building up
+ 
+
+ align:start position:0%
+do with whether you are building up
+pressure in the oral cavity so uh the
+
+ align:start position:0%
+pressure in the oral cavity so uh the
+ 
+
+ align:start position:0%
+pressure in the oral cavity so uh the
+sonorants are the nasals and the liquids
+
+ align:start position:0%
+sonorants are the nasals and the liquids
+ 
+
+ align:start position:0%
+sonorants are the nasals and the liquids
+and the Glides the the consonants in
+
+ align:start position:0%
+and the Glides the the consonants in
+ 
+
+ align:start position:0%
+and the Glides the the consonants in
+which there's no pressure building up in
+
+ align:start position:0%
+which there's no pressure building up in
+ 
+
+ align:start position:0%
+which there's no pressure building up in
+the oral cavity
+
+ align:start position:0%
+the oral cavity
+ 
+
+ align:start position:0%
+the oral cavity
+whereas the obstruents those are the
+
+ align:start position:0%
+whereas the obstruents those are the
+ 
+
+ align:start position:0%
+whereas the obstruents those are the
+stops and the fricatives the oral stops
+
+ align:start position:0%
+stops and the fricatives the oral stops
+ 
+
+ align:start position:0%
+stops and the fricatives the oral stops
+the fricatives those are the sounds in
+
+ align:start position:0%
+the fricatives those are the sounds in
+ 
+
+ align:start position:0%
+the fricatives those are the sounds in
+which there is pressure building up in
+
+ align:start position:0%
+which there is pressure building up in
+ 
+
+ align:start position:0%
+which there is pressure building up in
+the oral cavity for a stop it's because
+
+ align:start position:0%
+the oral cavity for a stop it's because
+ 
+
+ align:start position:0%
+the oral cavity for a stop it's because
+well you've stopped the flow there at
+
+ align:start position:0%
+well you've stopped the flow there at
+ 
+
+ align:start position:0%
+well you've stopped the flow there at
+the mouth and so pressure is building up
+
+ align:start position:0%
+the mouth and so pressure is building up
+ 
+
+ align:start position:0%
+the mouth and so pressure is building up
+and for a fricative uh well you haven't
+
+ align:start position:0%
+and for a fricative uh well you haven't
+ 
+
+ align:start position:0%
+and for a fricative uh well you haven't
+stopped the flow of air but you're
+
+ align:start position:0%
+stopped the flow of air but you're
+ 
+
+ align:start position:0%
+stopped the flow of air but you're
+constricting it that's how you make a
+
+ align:start position:0%
+constricting it that's how you make a
+ 
+
+ align:start position:0%
+constricting it that's how you make a
+fricative and so pressure is building up
+
+ align:start position:0%
+fricative and so pressure is building up
+ 
+
+ align:start position:0%
+fricative and so pressure is building up
+in the oral cavity and when I say
+
+ align:start position:0%
+in the oral cavity and when I say
+ 
+
+ align:start position:0%
+in the oral cavity and when I say
+pressure is building up in the oral
+
+ align:start position:0%
+pressure is building up in the oral
+ 
+
+ align:start position:0%
+pressure is building up in the oral
+cavity what I mean is that phoneticists
+
+ align:start position:0%
+cavity what I mean is that phoneticists
+ 
+
+ align:start position:0%
+cavity what I mean is that phoneticists
+have put instruments inside people's
+
+ align:start position:0%
+have put instruments inside people's
+ 
+
+ align:start position:0%
+have put instruments inside people's
+mouths to measure air pressure to find
+
+ align:start position:0%
+mouths to measure air pressure to find
+ 
+
+ align:start position:0%
+mouths to measure air pressure to find
+out what happens and they've discovered
+
+ align:start position:0%
+out what happens and they've discovered
+ 
+
+ align:start position:0%
+out what happens and they've discovered
+that this is true yeah so
+
+ align:start position:0%
+that this is true yeah so
+ 
+
+ align:start position:0%
+that this is true yeah so
+um I I try not to lie to you in this
+
+ align:start position:0%
+um I I try not to lie to you in this
+ 
+
+ align:start position:0%
+um I I try not to lie to you in this
+class any more than I can help it but in
+
+ align:start position:0%
+class any more than I can help it but in
+ 
+
+ align:start position:0%
+class any more than I can help it but in
+this particular case what I'm saying is
+
+ align:start position:0%
+this particular case what I'm saying is
+ 
+
+ align:start position:0%
+this particular case what I'm saying is
+absolutely true yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so there's honorance and there
+
+ align:start position:0%
+um okay so there's honorance and there
+ 
+
+ align:start position:0%
+um okay so there's honorance and there
+are obstrands uh we have already talked
+
+ align:start position:0%
+are obstrands uh we have already talked
+ 
+
+ align:start position:0%
+are obstrands uh we have already talked
+about the classification of sounds into
+
+ align:start position:0%
+about the classification of sounds into
+ 
+
+ align:start position:0%
+about the classification of sounds into
+voiced and voiceless sounds so the red
+
+ align:start position:0%
+voiced and voiceless sounds so the red
+ 
+
+ align:start position:0%
+voiced and voiceless sounds so the red
+sounds on this slide are voiced uh and
+
+ align:start position:0%
+sounds on this slide are voiced uh and
+ 
+
+ align:start position:0%
+sounds on this slide are voiced uh and
+as you can see this crosscuts some of
+
+ align:start position:0%
+as you can see this crosscuts some of
+ 
+
+ align:start position:0%
+as you can see this crosscuts some of
+the other classifications so you know
+
+ align:start position:0%
+the other classifications so you know
+ 
+
+ align:start position:0%
+the other classifications so you know
+you can be uh you can be an obstruent
+
+ align:start position:0%
+you can be uh you can be an obstruent
+ 
+
+ align:start position:0%
+you can be uh you can be an obstruent
+like a stop or a fricative and you can
+
+ align:start position:0%
+like a stop or a fricative and you can
+ 
+
+ align:start position:0%
+like a stop or a fricative and you can
+be either voiced or voiceless yeah so uh
+
+ align:start position:0%
+be either voiced or voiceless yeah so uh
+ 
+
+ align:start position:0%
+be either voiced or voiceless yeah so uh
+English stops can be voiced or voiceless
+
+ align:start position:0%
+English stops can be voiced or voiceless
+ 
+
+ align:start position:0%
+English stops can be voiced or voiceless
+English fricatives can be voiced or
+
+ align:start position:0%
+English fricatives can be voiced or
+ 
+
+ align:start position:0%
+English fricatives can be voiced or
+voiceless
+
+ align:start position:0%
+voiceless
+ 
+
+ align:start position:0%
+voiceless
+English sonorants interestingly can only
+
+ align:start position:0%
+English sonorants interestingly can only
+ 
+
+ align:start position:0%
+English sonorants interestingly can only
+be voiced they cannot be voiceless we
+
+ align:start position:0%
+be voiced they cannot be voiceless we
+ 
+
+ align:start position:0%
+be voiced they cannot be voiceless we
+have sonderance like like L like little
+
+ align:start position:0%
+have sonderance like like L like little
+ 
+
+ align:start position:0%
+have sonderance like like L like little
+but we don't have a voiceless version of
+
+ align:start position:0%
+but we don't have a voiceless version of
+ 
+
+ align:start position:0%
+but we don't have a voiceless version of
+L we talked about this when we were
+
+ align:start position:0%
+L we talked about this when we were
+ 
+
+ align:start position:0%
+L we talked about this when we were
+first going through uh sounds there are
+
+ align:start position:0%
+first going through uh sounds there are
+ 
+
+ align:start position:0%
+first going through uh sounds there are
+languages out there that have a
+
+ align:start position:0%
+languages out there that have a
+ 
+
+ align:start position:0%
+languages out there that have a
+voiceless version of L that have a sound
+
+ align:start position:0%
+voiceless version of L that have a sound
+ 
+
+ align:start position:0%
+voiceless version of L that have a sound
+uh Tibetan has one for example uh so if
+
+ align:start position:0%
+uh Tibetan has one for example uh so if
+ 
+
+ align:start position:0%
+uh Tibetan has one for example uh so if
+you go to Casa the capital of Tibet you
+
+ align:start position:0%
+you go to Casa the capital of Tibet you
+ 
+
+ align:start position:0%
+you go to Casa the capital of Tibet you
+must learn to make voiceless cells uh uh
+
+ align:start position:0%
+must learn to make voiceless cells uh uh
+ 
+
+ align:start position:0%
+must learn to make voiceless cells uh uh
+Welsh
+
+ align:start position:0%
+Welsh
+ 
+
+ align:start position:0%
+Welsh
+um has a voiceless L it's they spell it
+
+ align:start position:0%
+um has a voiceless L it's they spell it
+ 
+
+ align:start position:0%
+um has a voiceless L it's they spell it
+with two L's so if you look at Welsh
+
+ align:start position:0%
+with two L's so if you look at Welsh
+ 
+
+ align:start position:0%
+with two L's so if you look at Welsh
+words you'll see pairs of L's that's
+
+ align:start position:0%
+words you'll see pairs of L's that's
+ 
+
+ align:start position:0%
+words you'll see pairs of L's that's
+their way of spelling of voiceless a
+
+ align:start position:0%
+their way of spelling of voiceless a
+ 
+
+ align:start position:0%
+their way of spelling of voiceless a
+voiceless cell so there's a traditional
+
+ align:start position:0%
+voiceless cell so there's a traditional
+ 
+
+ align:start position:0%
+voiceless cell so there's a traditional
+Welsh name spelled like this and
+
+ align:start position:0%
+Welsh name spelled like this and
+ 
+
+ align:start position:0%
+Welsh name spelled like this and
+pronounced Floyd
+
+ align:start position:0%
+pronounced Floyd
+ 
+
+ align:start position:0%
+pronounced Floyd
+uh which has been borrowed into English
+
+ align:start position:0%
+uh which has been borrowed into English
+ 
+
+ align:start position:0%
+uh which has been borrowed into English
+twice as the name Lloyd and the name
+
+ align:start position:0%
+twice as the name Lloyd and the name
+ 
+
+ align:start position:0%
+twice as the name Lloyd and the name
+Floyd
+
+ align:start position:0%
+Floyd
+ 
+
+ align:start position:0%
+Floyd
+these are both attempts to pronounce
+
+ align:start position:0%
+these are both attempts to pronounce
+ 
+
+ align:start position:0%
+these are both attempts to pronounce
+Floyd which we can't pronounce because
+
+ align:start position:0%
+Floyd which we can't pronounce because
+ 
+
+ align:start position:0%
+Floyd which we can't pronounce because
+we don't have that sound
+
+ align:start position:0%
+we don't have that sound
+ 
+
+ align:start position:0%
+we don't have that sound
+um uh yeah so uh English has uh voiced
+
+ align:start position:0%
+um uh yeah so uh English has uh voiced
+ 
+
+ align:start position:0%
+um uh yeah so uh English has uh voiced
+and voiceless obstruents stops and
+
+ align:start position:0%
+and voiceless obstruents stops and
+ 
+
+ align:start position:0%
+and voiceless obstruents stops and
+fricatives but it only has voiced
+
+ align:start position:0%
+fricatives but it only has voiced
+ 
+
+ align:start position:0%
+fricatives but it only has voiced
+dishonorance that's a very common state
+
+ align:start position:0%
+dishonorance that's a very common state
+ 
+
+ align:start position:0%
+dishonorance that's a very common state
+of affairs uh if you're gonna have a
+
+ align:start position:0%
+of affairs uh if you're gonna have a
+ 
+
+ align:start position:0%
+of affairs uh if you're gonna have a
+voicing distinction in only one of these
+
+ align:start position:0%
+voicing distinction in only one of these
+ 
+
+ align:start position:0%
+voicing distinction in only one of these
+places it's in the obstrands uh language
+
+ align:start position:0%
+places it's in the obstrands uh language
+ 
+
+ align:start position:0%
+places it's in the obstrands uh language
+is only having voiced sonorants that's
+
+ align:start position:0%
+is only having voiced sonorants that's
+ 
+
+ align:start position:0%
+is only having voiced sonorants that's
+very common yeah
+
+ align:start position:0%
+very common yeah
+ 
+
+ align:start position:0%
+very common yeah
+though not Universal as we've said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um quick interlude
+
+ align:start position:0%
+um quick interlude
+ 
+
+ align:start position:0%
+um quick interlude
+to use one of these features here are a
+
+ align:start position:0%
+to use one of these features here are a
+ 
+
+ align:start position:0%
+to use one of these features here are a
+bunch of uh verbs that you can make out
+
+ align:start position:0%
+bunch of uh verbs that you can make out
+ 
+
+ align:start position:0%
+bunch of uh verbs that you can make out
+of adjectives so you can take an
+
+ align:start position:0%
+of adjectives so you can take an
+ 
+
+ align:start position:0%
+of adjectives so you can take an
+adjective like black
+
+ align:start position:0%
+adjective like black
+ 
+
+ align:start position:0%
+adjective like black
+and you can make a verb blackened which
+
+ align:start position:0%
+and you can make a verb blackened which
+ 
+
+ align:start position:0%
+and you can make a verb blackened which
+can be either a transitive verb or an
+
+ align:start position:0%
+can be either a transitive verb or an
+ 
+
+ align:start position:0%
+can be either a transitive verb or an
+intrinsic verb I guess so uh you can you
+
+ align:start position:0%
+intrinsic verb I guess so uh you can you
+ 
+
+ align:start position:0%
+intrinsic verb I guess so uh you can you
+can blacken
+
+ align:start position:0%
+can blacken
+ 
+
+ align:start position:0%
+can blacken
+um the paper or blacken the fish I guess
+
+ align:start position:0%
+um the paper or blacken the fish I guess
+ 
+
+ align:start position:0%
+um the paper or blacken the fish I guess
+it means to make it black yeah
+
+ align:start position:0%
+it means to make it black yeah
+ 
+
+ align:start position:0%
+it means to make it black yeah
+similarly something can whiten or lessen
+
+ align:start position:0%
+similarly something can whiten or lessen
+ 
+
+ align:start position:0%
+similarly something can whiten or lessen
+or freshen or darkening you can offer to
+
+ align:start position:0%
+or freshen or darkening you can offer to
+ 
+
+ align:start position:0%
+or freshen or darkening you can offer to
+freshen a drink say yeah it means to
+
+ align:start position:0%
+freshen a drink say yeah it means to
+ 
+
+ align:start position:0%
+freshen a drink say yeah it means to
+make it fresh right so this is there's
+
+ align:start position:0%
+make it fresh right so this is there's
+ 
+
+ align:start position:0%
+make it fresh right so this is there's
+this um that you can add to adjectives
+
+ align:start position:0%
+this um that you can add to adjectives
+ 
+
+ align:start position:0%
+this um that you can add to adjectives
+to make verbs
+
+ align:start position:0%
+to make verbs
+ 
+
+ align:start position:0%
+to make verbs
+sound right
+
+ align:start position:0%
+sound right
+ 
+
+ align:start position:0%
+sound right
+on the other hand there are these other
+
+ align:start position:0%
+on the other hand there are these other
+ 
+
+ align:start position:0%
+on the other hand there are these other
+adjectives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which can't happen yeah so
+
+ align:start position:0%
+which can't happen yeah so
+ 
+
+ align:start position:0%
+which can't happen yeah so
+um the the screen of a computer can
+
+ align:start position:0%
+um the the screen of a computer can
+ 
+
+ align:start position:0%
+um the the screen of a computer can
+darken but it cannot yellow in yeah a
+
+ align:start position:0%
+darken but it cannot yellow in yeah a
+ 
+
+ align:start position:0%
+darken but it cannot yellow in yeah a
+piece of paper uh that gets old uh you
+
+ align:start position:0%
+piece of paper uh that gets old uh you
+ 
+
+ align:start position:0%
+piece of paper uh that gets old uh you
+what you say is that it yellows it
+
+ align:start position:0%
+what you say is that it yellows it
+ 
+
+ align:start position:0%
+what you say is that it yellows it
+yellowed with age you don't say that it
+
+ align:start position:0%
+yellowed with age you don't say that it
+ 
+
+ align:start position:0%
+yellowed with age you don't say that it
+yellow end yeah similarly you can't
+
+ align:start position:0%
+yellow end yeah similarly you can't
+ 
+
+ align:start position:0%
+yellow end yeah similarly you can't
+demon or gray in or clearing or Browning
+
+ align:start position:0%
+demon or gray in or clearing or Browning
+ 
+
+ align:start position:0%
+demon or gray in or clearing or Browning
+yeah all of those things if you want to
+
+ align:start position:0%
+yeah all of those things if you want to
+ 
+
+ align:start position:0%
+yeah all of those things if you want to
+make them into verbs you just they're
+
+ align:start position:0%
+make them into verbs you just they're
+ 
+
+ align:start position:0%
+make them into verbs you just they're
+verbs yeah
+
+ align:start position:0%
+verbs yeah
+ 
+
+ align:start position:0%
+verbs yeah
+yeah does that sound right
+
+ align:start position:0%
+yeah does that sound right
+ 
+
+ align:start position:0%
+yeah does that sound right
+what's the difference between black
+
+ align:start position:0%
+what's the difference between black
+ 
+
+ align:start position:0%
+what's the difference between black
+white less fresh and dark on the one
+
+ align:start position:0%
+white less fresh and dark on the one
+ 
+
+ align:start position:0%
+white less fresh and dark on the one
+hand and yellow dim gray clear and brown
+
+ align:start position:0%
+hand and yellow dim gray clear and brown
+ 
+
+ align:start position:0%
+hand and yellow dim gray clear and brown
+on the other
+
+ align:start position:0%
+on the other
+ 
+
+ align:start position:0%
+on the other
+the endless voiceless
+
+ align:start position:0%
+the endless voiceless
+ 
+
+ align:start position:0%
+the endless voiceless
+stops on the first line in the first
+
+ align:start position:0%
+stops on the first line in the first
+ 
+
+ align:start position:0%
+stops on the first line in the first
+line black white and dark end with
+
+ align:start position:0%
+line black white and dark end with
+ 
+
+ align:start position:0%
+line black white and dark end with
+voiceless stops and less and fresh
+
+ align:start position:0%
+voiceless stops and less and fresh
+ 
+
+ align:start position:0%
+voiceless stops and less and fresh
+and with voiceless fricatives yeah yeah
+
+ align:start position:0%
+and with voiceless fricatives yeah yeah
+ 
+
+ align:start position:0%
+and with voiceless fricatives yeah yeah
+yeah yeah nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yellow dim gray clear and brown
+
+ align:start position:0%
+and yellow dim gray clear and brown
+ 
+
+ align:start position:0%
+and yellow dim gray clear and brown
+and in voiced sounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the cover term for uh stops and
+
+ align:start position:0%
+what's the cover term for uh stops and
+ 
+
+ align:start position:0%
+what's the cover term for uh stops and
+fricatives
+
+ align:start position:0%
+fricatives
+ 
+
+ align:start position:0%
+fricatives
+obstreams yeah so um can be added to
+
+ align:start position:0%
+obstreams yeah so um can be added to
+ 
+
+ align:start position:0%
+obstreams yeah so um can be added to
+words ending and obstruents uh and it
+
+ align:start position:0%
+words ending and obstruents uh and it
+ 
+
+ align:start position:0%
+words ending and obstruents uh and it
+can't be added to two adjectives ending
+
+ align:start position:0%
+can't be added to two adjectives ending
+ 
+
+ align:start position:0%
+can't be added to two adjectives ending
+in sonorance yeah
+
+ align:start position:0%
+in sonorance yeah
+ 
+
+ align:start position:0%
+in sonorance yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+another place where it's useful to
+
+ align:start position:0%
+another place where it's useful to
+ 
+
+ align:start position:0%
+another place where it's useful to
+distinguish uh sonorants from uh
+
+ align:start position:0%
+distinguish uh sonorants from uh
+ 
+
+ align:start position:0%
+distinguish uh sonorants from uh
+obstruents polish plurals I think this
+
+ align:start position:0%
+obstruents polish plurals I think this
+ 
+
+ align:start position:0%
+obstruents polish plurals I think this
+is the last time I will say anything
+
+ align:start position:0%
+is the last time I will say anything
+ 
+
+ align:start position:0%
+is the last time I will say anything
+about polish plurals I can't promise
+
+ align:start position:0%
+about polish plurals I can't promise
+ 
+
+ align:start position:0%
+about polish plurals I can't promise
+because you know it's a very useful
+
+ align:start position:0%
+because you know it's a very useful
+ 
+
+ align:start position:0%
+because you know it's a very useful
+example but if you're getting tired of
+
+ align:start position:0%
+example but if you're getting tired of
+ 
+
+ align:start position:0%
+example but if you're getting tired of
+Polish plurals I apologize I think we're
+
+ align:start position:0%
+Polish plurals I apologize I think we're
+ 
+
+ align:start position:0%
+Polish plurals I apologize I think we're
+just about to the end on the other hand
+
+ align:start position:0%
+just about to the end on the other hand
+ 
+
+ align:start position:0%
+just about to the end on the other hand
+if you've become fond of Polish plurals
+
+ align:start position:0%
+if you've become fond of Polish plurals
+ 
+
+ align:start position:0%
+if you've become fond of Polish plurals
+please gaze at this this slide for a
+
+ align:start position:0%
+please gaze at this this slide for a
+ 
+
+ align:start position:0%
+please gaze at this this slide for a
+while you know because this is your last
+
+ align:start position:0%
+while you know because this is your last
+ 
+
+ align:start position:0%
+while you know because this is your last
+big chance
+
+ align:start position:0%
+big chance
+ 
+
+ align:start position:0%
+big chance
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what we said about polish florals was
+
+ align:start position:0%
+what we said about polish florals was
+ 
+
+ align:start position:0%
+what we said about polish florals was
+that it's useful to say that there are
+
+ align:start position:0%
+that it's useful to say that there are
+ 
+
+ align:start position:0%
+that it's useful to say that there are
+words that end underlyingly in sounds
+
+ align:start position:0%
+words that end underlyingly in sounds
+ 
+
+ align:start position:0%
+words that end underlyingly in sounds
+like G and B and z and that those final
+
+ align:start position:0%
+like G and B and z and that those final
+ 
+
+ align:start position:0%
+like G and B and z and that those final
+sounds G and B and Z devoice when
+
+ align:start position:0%
+sounds G and B and Z devoice when
+ 
+
+ align:start position:0%
+sounds G and B and Z devoice when
+they're at the ends of words so
+
+ align:start position:0%
+they're at the ends of words so
+ 
+
+ align:start position:0%
+they're at the ends of words so
+underlying the word for lie becomes if
+
+ align:start position:0%
+underlying the word for lie becomes if
+ 
+
+ align:start position:0%
+underlying the word for lie becomes if
+you don't add anything to after it all
+
+ align:start position:0%
+you don't add anything to after it all
+ 
+
+ align:start position:0%
+you don't add anything to after it all
+right and same with the word for club
+
+ align:start position:0%
+right and same with the word for club
+ 
+
+ align:start position:0%
+right and same with the word for club
+and the word for Rubble and I have been
+
+ align:start position:0%
+and the word for Rubble and I have been
+ 
+
+ align:start position:0%
+and the word for Rubble and I have been
+in cautiously saying things like polish
+
+ align:start position:0%
+in cautiously saying things like polish
+ 
+
+ align:start position:0%
+in cautiously saying things like polish
+devoices its final consonants
+
+ align:start position:0%
+devoices its final consonants
+ 
+
+ align:start position:0%
+devoices its final consonants
+which was a lie I think I told you just
+
+ align:start position:0%
+which was a lie I think I told you just
+ 
+
+ align:start position:0%
+which was a lie I think I told you just
+now that I try not to lie to you any
+
+ align:start position:0%
+now that I try not to lie to you any
+ 
+
+ align:start position:0%
+now that I try not to lie to you any
+more than I have to
+
+ align:start position:0%
+more than I have to
+ 
+
+ align:start position:0%
+more than I have to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it doesn't devoice its final consonants
+
+ align:start position:0%
+it doesn't devoice its final consonants
+ 
+
+ align:start position:0%
+it doesn't devoice its final consonants
+right because uh polish has words like
+
+ align:start position:0%
+right because uh polish has words like
+ 
+
+ align:start position:0%
+right because uh polish has words like
+Dom which is the word for house and that
+
+ align:start position:0%
+Dom which is the word for house and that
+ 
+
+ align:start position:0%
+Dom which is the word for house and that
+ends in a voiced sound right Dom doesn't
+
+ align:start position:0%
+ends in a voiced sound right Dom doesn't
+ 
+
+ align:start position:0%
+ends in a voiced sound right Dom doesn't
+become Dom yeah
+
+ align:start position:0%
+become Dom yeah
+ 
+
+ align:start position:0%
+become Dom yeah
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so it's not the case that final
+
+ align:start position:0%
+so it's not the case that final
+ 
+
+ align:start position:0%
+so it's not the case that final
+consonants become voiceless in Polish
+
+ align:start position:0%
+consonants become voiceless in Polish
+ 
+
+ align:start position:0%
+consonants become voiceless in Polish
+what are the things that become
+
+ align:start position:0%
+what are the things that become
+ 
+
+ align:start position:0%
+what are the things that become
+voiceless in Polish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obstrands yeah stop centricatives yeah
+
+ align:start position:0%
+obstrands yeah stop centricatives yeah
+ 
+
+ align:start position:0%
+obstrands yeah stop centricatives yeah
+those are the things that become
+
+ align:start position:0%
+those are the things that become
+ 
+
+ align:start position:0%
+those are the things that become
+voiceless in Polish relatedly polish is
+
+ align:start position:0%
+voiceless in Polish relatedly polish is
+ 
+
+ align:start position:0%
+voiceless in Polish relatedly polish is
+like English in having voiced and
+
+ align:start position:0%
+like English in having voiced and
+ 
+
+ align:start position:0%
+like English in having voiced and
+voiceless obstruents but not in having
+
+ align:start position:0%
+voiceless obstruents but not in having
+ 
+
+ align:start position:0%
+voiceless obstruents but not in having
+voiced and not having voiced and
+
+ align:start position:0%
+voiced and not having voiced and
+ 
+
+ align:start position:0%
+voiced and not having voiced and
+voiceless honorings uh polish you know
+
+ align:start position:0%
+voiceless honorings uh polish you know
+ 
+
+ align:start position:0%
+voiceless honorings uh polish you know
+the m in a sense doesn't have anywhere
+
+ align:start position:0%
+the m in a sense doesn't have anywhere
+ 
+
+ align:start position:0%
+the m in a sense doesn't have anywhere
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+polish doesn't have that sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+common situation so it's really final
+
+ align:start position:0%
+common situation so it's really final
+ 
+
+ align:start position:0%
+common situation so it's really final
+obstruents that are becoming voiceless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so that's that's that's a
+
+ align:start position:0%
+okay all right so that's that's that's a
+ 
+
+ align:start position:0%
+okay all right so that's that's that's a
+reason to want to care about the
+
+ align:start position:0%
+reason to want to care about the
+ 
+
+ align:start position:0%
+reason to want to care about the
+distinction between sunrings and
+
+ align:start position:0%
+distinction between sunrings and
+ 
+
+ align:start position:0%
+distinction between sunrings and
+obstrids uh not just because you want to
+
+ align:start position:0%
+obstrids uh not just because you want to
+ 
+
+ align:start position:0%
+obstrids uh not just because you want to
+understand why it's white and darkened
+
+ align:start position:0%
+understand why it's white and darkened
+ 
+
+ align:start position:0%
+understand why it's white and darkened
+and lessened but not yellowing yeah
+
+ align:start position:0%
+and lessened but not yellowing yeah
+ 
+
+ align:start position:0%
+and lessened but not yellowing yeah
+uh it seems to be a distinction that
+
+ align:start position:0%
+uh it seems to be a distinction that
+ 
+
+ align:start position:0%
+uh it seems to be a distinction that
+cares about sonorants and obstruents
+
+ align:start position:0%
+cares about sonorants and obstruents
+ 
+
+ align:start position:0%
+cares about sonorants and obstruents
+here's another one uh polish which as
+
+ align:start position:0%
+here's another one uh polish which as
+ 
+
+ align:start position:0%
+here's another one uh polish which as
+I've said now several times and I think
+
+ align:start position:0%
+I've said now several times and I think
+ 
+
+ align:start position:0%
+I've said now several times and I think
+this might be the last time uh polish is
+
+ align:start position:0%
+this might be the last time uh polish is
+ 
+
+ align:start position:0%
+this might be the last time uh polish is
+doing something that is very common in
+
+ align:start position:0%
+doing something that is very common in
+ 
+
+ align:start position:0%
+doing something that is very common in
+languages of the world it's devoicing
+
+ align:start position:0%
+languages of the world it's devoicing
+ 
+
+ align:start position:0%
+languages of the world it's devoicing
+final obstrands
+
+ align:start position:0%
+final obstrands
+ 
+
+ align:start position:0%
+final obstrands
+um uh uh that's a that's a thing that
+
+ align:start position:0%
+um uh uh that's a that's a thing that
+ 
+
+ align:start position:0%
+um uh uh that's a that's a thing that
+happens a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um phonology so far we've been doing
+
+ align:start position:0%
+um phonology so far we've been doing
+ 
+
+ align:start position:0%
+um phonology so far we've been doing
+phenology for a couple days now uh it's
+
+ align:start position:0%
+phenology for a couple days now uh it's
+ 
+
+ align:start position:0%
+phenology for a couple days now uh it's
+useful to think of sounds as undergoing
+
+ align:start position:0%
+useful to think of sounds as undergoing
+ 
+
+ align:start position:0%
+useful to think of sounds as undergoing
+changes uh sometimes uh driven by sounds
+
+ align:start position:0%
+changes uh sometimes uh driven by sounds
+ 
+
+ align:start position:0%
+changes uh sometimes uh driven by sounds
+coming in contact with each other
+
+ align:start position:0%
+coming in contact with each other
+ 
+
+ align:start position:0%
+coming in contact with each other
+um and we can describe these changes in
+
+ align:start position:0%
+um and we can describe these changes in
+ 
+
+ align:start position:0%
+um and we can describe these changes in
+terms of rules here's the formalism for
+
+ align:start position:0%
+terms of rules here's the formalism for
+ 
+
+ align:start position:0%
+terms of rules here's the formalism for
+rules that I've been showing you uh so
+
+ align:start position:0%
+rules that I've been showing you uh so
+ 
+
+ align:start position:0%
+rules that I've been showing you uh so
+we'll say you know sound a changes into
+
+ align:start position:0%
+we'll say you know sound a changes into
+ 
+
+ align:start position:0%
+we'll say you know sound a changes into
+sound B the slash introduces you to the
+
+ align:start position:0%
+sound B the slash introduces you to the
+ 
+
+ align:start position:0%
+sound B the slash introduces you to the
+environment this is a description of
+
+ align:start position:0%
+environment this is a description of
+ 
+
+ align:start position:0%
+environment this is a description of
+what's happening in Polish and Turkish
+
+ align:start position:0%
+what's happening in Polish and Turkish
+ 
+
+ align:start position:0%
+what's happening in Polish and Turkish
+and German Russian lots of other
+
+ align:start position:0%
+and German Russian lots of other
+ 
+
+ align:start position:0%
+and German Russian lots of other
+languages uh final obstruents so if you
+
+ align:start position:0%
+languages uh final obstruents so if you
+ 
+
+ align:start position:0%
+languages uh final obstruents so if you
+are an obstrom that is something which
+
+ align:start position:0%
+are an obstrom that is something which
+ 
+
+ align:start position:0%
+are an obstrom that is something which
+is now the sonorant you become something
+
+ align:start position:0%
+is now the sonorant you become something
+ 
+
+ align:start position:0%
+is now the sonorant you become something
+which is not voiced if you are at the
+
+ align:start position:0%
+which is not voiced if you are at the
+ 
+
+ align:start position:0%
+which is not voiced if you are at the
+end of a word that environment
+
+ align:start position:0%
+end of a word that environment
+ 
+
+ align:start position:0%
+end of a word that environment
+description is the way to write at the
+
+ align:start position:0%
+description is the way to write at the
+ 
+
+ align:start position:0%
+description is the way to write at the
+end of a word that hash symbol is the
+
+ align:start position:0%
+end of a word that hash symbol is the
+ 
+
+ align:start position:0%
+end of a word that hash symbol is the
+symbol for a boundary between words and
+
+ align:start position:0%
+symbol for a boundary between words and
+ 
+
+ align:start position:0%
+symbol for a boundary between words and
+and the underscore is where the change
+
+ align:start position:0%
+and the underscore is where the change
+ 
+
+ align:start position:0%
+and the underscore is where the change
+takes place so this rule says this
+
+ align:start position:0%
+takes place so this rule says this
+ 
+
+ align:start position:0%
+takes place so this rule says this
+change happens uh when the sound is
+
+ align:start position:0%
+change happens uh when the sound is
+ 
+
+ align:start position:0%
+change happens uh when the sound is
+before a word boundary or if there's
+
+ align:start position:0%
+before a word boundary or if there's
+ 
+
+ align:start position:0%
+before a word boundary or if there's
+another way when it is at the end of a
+
+ align:start position:0%
+another way when it is at the end of a
+ 
+
+ align:start position:0%
+another way when it is at the end of a
+word
+
+ align:start position:0%
+word
+ 
+
+ align:start position:0%
+word
+does that make sense this is a way of
+
+ align:start position:0%
+does that make sense this is a way of
+ 
+
+ align:start position:0%
+does that make sense this is a way of
+writing rules
+
+ align:start position:0%
+writing rules
+ 
+
+ align:start position:0%
+writing rules
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+these rules are part of our knowledge of
+
+ align:start position:0%
+these rules are part of our knowledge of
+ 
+
+ align:start position:0%
+these rules are part of our knowledge of
+a language so you know we've talked
+
+ align:start position:0%
+a language so you know we've talked
+ 
+
+ align:start position:0%
+a language so you know we've talked
+about this uh
+
+ align:start position:0%
+about this uh
+ 
+
+ align:start position:0%
+about this uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+as adults uh all of anybody who is a
+
+ align:start position:0%
+as adults uh all of anybody who is a
+ 
+
+ align:start position:0%
+as adults uh all of anybody who is a
+native speaker of English knows how to
+
+ align:start position:0%
+native speaker of English knows how to
+ 
+
+ align:start position:0%
+native speaker of English knows how to
+make the plural of wug or how to make
+
+ align:start position:0%
+make the plural of wug or how to make
+ 
+
+ align:start position:0%
+make the plural of wug or how to make
+the plural of Bach even so uh how to
+
+ align:start position:0%
+the plural of Bach even so uh how to
+ 
+
+ align:start position:0%
+the plural of Bach even so uh how to
+make plurals of words you've never heard
+
+ align:start position:0%
+make plurals of words you've never heard
+ 
+
+ align:start position:0%
+make plurals of words you've never heard
+before and even words that end in sounds
+
+ align:start position:0%
+before and even words that end in sounds
+ 
+
+ align:start position:0%
+before and even words that end in sounds
+that your language doesn't have right
+
+ align:start position:0%
+that your language doesn't have right
+ 
+
+ align:start position:0%
+that your language doesn't have right
+so if I insist on calling the composer
+
+ align:start position:0%
+so if I insist on calling the composer
+ 
+
+ align:start position:0%
+so if I insist on calling the composer
+Bach if I insist on the original
+
+ align:start position:0%
+Bach if I insist on the original
+ 
+
+ align:start position:0%
+Bach if I insist on the original
+pronunciation of the word kayak which is
+
+ align:start position:0%
+pronunciation of the word kayak which is
+ 
+
+ align:start position:0%
+pronunciation of the word kayak which is
+you know kayaka a single-person vote
+
+ align:start position:0%
+you know kayaka a single-person vote
+ 
+
+ align:start position:0%
+you know kayaka a single-person vote
+which in in yupiak begins and ends with
+
+ align:start position:0%
+which in in yupiak begins and ends with
+ 
+
+ align:start position:0%
+which in in yupiak begins and ends with
+a uvular stop so if I'm trying to
+
+ align:start position:0%
+a uvular stop so if I'm trying to
+ 
+
+ align:start position:0%
+a uvular stop so if I'm trying to
+impress you with my ability to make
+
+ align:start position:0%
+impress you with my ability to make
+ 
+
+ align:start position:0%
+impress you with my ability to make
+uvular stops and I insist on calling a
+
+ align:start position:0%
+uvular stops and I insist on calling a
+ 
+
+ align:start position:0%
+uvular stops and I insist on calling a
+kayak a kayak then my plural for it is
+
+ align:start position:0%
+kayak a kayak then my plural for it is
+ 
+
+ align:start position:0%
+kayak a kayak then my plural for it is
+going to be kayaks right so I'm going to
+
+ align:start position:0%
+going to be kayaks right so I'm going to
+ 
+
+ align:start position:0%
+going to be kayaks right so I'm going to
+add an S sound I'm going to devoice it
+
+ align:start position:0%
+add an S sound I'm going to devoice it
+ 
+
+ align:start position:0%
+add an S sound I'm going to devoice it
+because that uvular stop although it's a
+
+ align:start position:0%
+because that uvular stop although it's a
+ 
+
+ align:start position:0%
+because that uvular stop although it's a
+sound we don't have in English it's
+
+ align:start position:0%
+sound we don't have in English it's
+ 
+
+ align:start position:0%
+sound we don't have in English it's
+voiceless and so we're going to devoice
+
+ align:start position:0%
+voiceless and so we're going to devoice
+ 
+
+ align:start position:0%
+voiceless and so we're going to devoice
+uh do voice after it yeah uh so these
+
+ align:start position:0%
+uh do voice after it yeah uh so these
+ 
+
+ align:start position:0%
+uh do voice after it yeah uh so these
+rules are part of our knowledge of a
+
+ align:start position:0%
+rules are part of our knowledge of a
+ 
+
+ align:start position:0%
+rules are part of our knowledge of a
+language and we can apply them to uh
+
+ align:start position:0%
+language and we can apply them to uh
+ 
+
+ align:start position:0%
+language and we can apply them to uh
+unfamiliar problems unfamiliar words and
+
+ align:start position:0%
+unfamiliar problems unfamiliar words and
+ 
+
+ align:start position:0%
+unfamiliar problems unfamiliar words and
+even unfamiliar sounds
+
+ align:start position:0%
+even unfamiliar sounds
+ 
+
+ align:start position:0%
+even unfamiliar sounds
+um and I've now tried to convince you
+
+ align:start position:0%
+um and I've now tried to convince you
+ 
+
+ align:start position:0%
+um and I've now tried to convince you
+the best way to State these rules
+
+ align:start position:0%
+the best way to State these rules
+ 
+
+ align:start position:0%
+the best way to State these rules
+sometimes at least is in terms of
+
+ align:start position:0%
+sometimes at least is in terms of
+ 
+
+ align:start position:0%
+sometimes at least is in terms of
+features that is
+
+ align:start position:0%
+features that is
+ 
+
+ align:start position:0%
+features that is
+um we don't just want to list the sounds
+
+ align:start position:0%
+um we don't just want to list the sounds
+ 
+
+ align:start position:0%
+um we don't just want to list the sounds
+that undergo a change we want to have
+
+ align:start position:0%
+that undergo a change we want to have
+ 
+
+ align:start position:0%
+that undergo a change we want to have
+these features which are ways of
+
+ align:start position:0%
+these features which are ways of
+ 
+
+ align:start position:0%
+these features which are ways of
+capturing sets of sounds we we think
+
+ align:start position:0%
+capturing sets of sounds we we think
+ 
+
+ align:start position:0%
+capturing sets of sounds we we think
+that there are natural classes of sounds
+
+ align:start position:0%
+that there are natural classes of sounds
+ 
+
+ align:start position:0%
+that there are natural classes of sounds
+that undergo particular changes so there
+
+ align:start position:0%
+that undergo particular changes so there
+ 
+
+ align:start position:0%
+that undergo particular changes so there
+are sound changes that apply say to
+
+ align:start position:0%
+are sound changes that apply say to
+ 
+
+ align:start position:0%
+are sound changes that apply say to
+obstruents to tolerance or to vowels or
+
+ align:start position:0%
+obstruents to tolerance or to vowels or
+ 
+
+ align:start position:0%
+obstruents to tolerance or to vowels or
+to voice sounds or to voiceless sounds
+
+ align:start position:0%
+to voice sounds or to voiceless sounds
+ 
+
+ align:start position:0%
+to voice sounds or to voiceless sounds
+we're not just going to list the sounds
+
+ align:start position:0%
+we're not just going to list the sounds
+ 
+
+ align:start position:0%
+we're not just going to list the sounds
+that undergo sound changes we're gonna
+
+ align:start position:0%
+that undergo sound changes we're gonna
+ 
+
+ align:start position:0%
+that undergo sound changes we're gonna
+we're gonna State these uh in terms of
+
+ align:start position:0%
+we're gonna State these uh in terms of
+ 
+
+ align:start position:0%
+we're gonna State these uh in terms of
+features okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and then the other thing that I've
+
+ align:start position:0%
+and then the other thing that I've
+ 
+
+ align:start position:0%
+and then the other thing that I've
+introduced you to is the idea that at
+
+ align:start position:0%
+introduced you to is the idea that at
+ 
+
+ align:start position:0%
+introduced you to is the idea that at
+least sometimes
+
+ align:start position:0%
+least sometimes
+ 
+
+ align:start position:0%
+least sometimes
+it's fruitful to model these as these
+
+ align:start position:0%
+it's fruitful to model these as these
+ 
+
+ align:start position:0%
+it's fruitful to model these as these
+kinds of sound changes as involving uh
+
+ align:start position:0%
+kinds of sound changes as involving uh
+ 
+
+ align:start position:0%
+kinds of sound changes as involving uh
+ranked constraints this was the the
+
+ align:start position:0%
+ranked constraints this was the the
+ 
+
+ align:start position:0%
+ranked constraints this was the the
+optimality theory tableaus uh that is to
+
+ align:start position:0%
+optimality theory tableaus uh that is to
+ 
+
+ align:start position:0%
+optimality theory tableaus uh that is to
+imagine that languages have a list of
+
+ align:start position:0%
+imagine that languages have a list of
+ 
+
+ align:start position:0%
+imagine that languages have a list of
+things that they are trying to achieve
+
+ align:start position:0%
+things that they are trying to achieve
+ 
+
+ align:start position:0%
+things that they are trying to achieve
+and it's a list that's ranked in order
+
+ align:start position:0%
+and it's a list that's ranked in order
+ 
+
+ align:start position:0%
+and it's a list that's ranked in order
+of priority
+
+ align:start position:0%
+of priority
+ 
+
+ align:start position:0%
+of priority
+and you get to observe the interplay
+
+ align:start position:0%
+and you get to observe the interplay
+ 
+
+ align:start position:0%
+and you get to observe the interplay
+between these different priorities uh in
+
+ align:start position:0%
+between these different priorities uh in
+ 
+
+ align:start position:0%
+between these different priorities uh in
+certain kinds of complicated cases uh
+
+ align:start position:0%
+certain kinds of complicated cases uh
+ 
+
+ align:start position:0%
+certain kinds of complicated cases uh
+the the Japanese accent case was one of
+
+ align:start position:0%
+the the Japanese accent case was one of
+ 
+
+ align:start position:0%
+the the Japanese accent case was one of
+the ones that we looked at
+
+ align:start position:0%
+the ones that we looked at
+ 
+
+ align:start position:0%
+the ones that we looked at
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think that's it for this review
+
+ align:start position:0%
+and I think that's it for this review
+ 
+
+ align:start position:0%
+and I think that's it for this review
+slide is there something else oh okay is
+
+ align:start position:0%
+slide is there something else oh okay is
+ 
+
+ align:start position:0%
+slide is there something else oh okay is
+everyone happy with all of this is there
+
+ align:start position:0%
+everyone happy with all of this is there
+ 
+
+ align:start position:0%
+everyone happy with all of this is there
+any of this that people are looking at
+
+ align:start position:0%
+any of this that people are looking at
+ 
+
+ align:start position:0%
+any of this that people are looking at
+and going no wait how did how did we see
+
+ align:start position:0%
+and going no wait how did how did we see
+ 
+
+ align:start position:0%
+and going no wait how did how did we see
+that or what does that mean or anything
+
+ align:start position:0%
+that or what does that mean or anything
+ 
+
+ align:start position:0%
+that or what does that mean or anything
+like that it's an attempt to make sure
+
+ align:start position:0%
+like that it's an attempt to make sure
+ 
+
+ align:start position:0%
+like that it's an attempt to make sure
+we're all
+
+ align:start position:0%
+we're all
+ 
+
+ align:start position:0%
+we're all
+in the same ballpark here yeah
+
+ align:start position:0%
+in the same ballpark here yeah
+ 
+
+ align:start position:0%
+in the same ballpark here yeah
+oh all I mean by feature are uh things
+
+ align:start position:0%
+oh all I mean by feature are uh things
+ 
+
+ align:start position:0%
+oh all I mean by feature are uh things
+like voiced or sonorant or you know
+
+ align:start position:0%
+like voiced or sonorant or you know
+ 
+
+ align:start position:0%
+like voiced or sonorant or you know
+those kinds of things yeah good question
+
+ align:start position:0%
+those kinds of things yeah good question
+ 
+
+ align:start position:0%
+those kinds of things yeah good question
+um and a standard way to write rules
+
+ align:start position:0%
+um and a standard way to write rules
+ 
+
+ align:start position:0%
+um and a standard way to write rules
+involves putting features in Brackets
+
+ align:start position:0%
+involves putting features in Brackets
+ 
+
+ align:start position:0%
+involves putting features in Brackets
+like that so you know the fancy way to
+
+ align:start position:0%
+like that so you know the fancy way to
+ 
+
+ align:start position:0%
+like that so you know the fancy way to
+say something is voiceless is to say
+
+ align:start position:0%
+say something is voiceless is to say
+ 
+
+ align:start position:0%
+say something is voiceless is to say
+that it's its value for the feature
+
+ align:start position:0%
+that it's its value for the feature
+ 
+
+ align:start position:0%
+that it's its value for the feature
+voice is minus right so it is not voiced
+
+ align:start position:0%
+voice is minus right so it is not voiced
+ 
+
+ align:start position:0%
+voice is minus right so it is not voiced
+yeah that's all that means
+
+ align:start position:0%
+yeah that's all that means
+ 
+
+ align:start position:0%
+yeah that's all that means
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+okay when we ask you to do phonology we
+
+ align:start position:0%
+okay when we ask you to do phonology we
+ 
+
+ align:start position:0%
+okay when we ask you to do phonology we
+will tell you whether we want you to
+
+ align:start position:0%
+will tell you whether we want you to
+ 
+
+ align:start position:0%
+will tell you whether we want you to
+what extent we want you to be formal
+
+ align:start position:0%
+what extent we want you to be formal
+ 
+
+ align:start position:0%
+what extent we want you to be formal
+about how you write your rules yeah so I
+
+ align:start position:0%
+about how you write your rules yeah so I
+ 
+
+ align:start position:0%
+about how you write your rules yeah so I
+think the problem set that I just send
+
+ align:start position:0%
+think the problem set that I just send
+ 
+
+ align:start position:0%
+think the problem set that I just send
+out uh asks you to look around for
+
+ align:start position:0%
+out uh asks you to look around for
+ 
+
+ align:start position:0%
+out uh asks you to look around for
+possible rules in your in the
+
+ align:start position:0%
+possible rules in your in the
+ 
+
+ align:start position:0%
+possible rules in your in the
+what is it it's a green Landing data I
+
+ align:start position:0%
+what is it it's a green Landing data I
+ 
+
+ align:start position:0%
+what is it it's a green Landing data I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+um uh you don't have to sweat this level
+
+ align:start position:0%
+um uh you don't have to sweat this level
+ 
+
+ align:start position:0%
+um uh you don't have to sweat this level
+of formality in your rules so if your
+
+ align:start position:0%
+of formality in your rules so if your
+ 
+
+ align:start position:0%
+of formality in your rules so if your
+rule for that problem said so if you
+
+ align:start position:0%
+rule for that problem said so if you
+ 
+
+ align:start position:0%
+rule for that problem said so if you
+think you've figured out what's going on
+
+ align:start position:0%
+think you've figured out what's going on
+ 
+
+ align:start position:0%
+think you've figured out what's going on
+you can just tell us more or less
+
+ align:start position:0%
+you can just tell us more or less
+ 
+
+ align:start position:0%
+you can just tell us more or less
+don't feel like we're going to count off
+
+ align:start position:0%
+don't feel like we're going to count off
+ 
+
+ align:start position:0%
+don't feel like we're going to count off
+for not using features or not not
+
+ align:start position:0%
+for not using features or not not
+ 
+
+ align:start position:0%
+for not using features or not not
+writing your rules this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right then
+
+ align:start position:0%
+all right then
+ 
+
+ align:start position:0%
+all right then
+now I told you just now
+
+ align:start position:0%
+now I told you just now
+ 
+
+ align:start position:0%
+now I told you just now
+tried to convince you earlier that there
+
+ align:start position:0%
+tried to convince you earlier that there
+ 
+
+ align:start position:0%
+tried to convince you earlier that there
+are cases where uh the Japanese accent
+
+ align:start position:0%
+are cases where uh the Japanese accent
+ 
+
+ align:start position:0%
+are cases where uh the Japanese accent
+case was the one that we spent the most
+
+ align:start position:0%
+case was the one that we spent the most
+ 
+
+ align:start position:0%
+case was the one that we spent the most
+time on where uh it's sort of fruitful
+
+ align:start position:0%
+time on where uh it's sort of fruitful
+ 
+
+ align:start position:0%
+time on where uh it's sort of fruitful
+to think of the phenomenon as involving
+
+ align:start position:0%
+to think of the phenomenon as involving
+ 
+
+ align:start position:0%
+to think of the phenomenon as involving
+a bunch of ranked priorities a bunch of
+
+ align:start position:0%
+a bunch of ranked priorities a bunch of
+ 
+
+ align:start position:0%
+a bunch of ranked priorities a bunch of
+constraints that are all pulling in
+
+ align:start position:0%
+constraints that are all pulling in
+ 
+
+ align:start position:0%
+constraints that are all pulling in
+different directions and you sort of
+
+ align:start position:0%
+different directions and you sort of
+ 
+
+ align:start position:0%
+different directions and you sort of
+solve that problem by deciding which is
+
+ align:start position:0%
+solve that problem by deciding which is
+ 
+
+ align:start position:0%
+solve that problem by deciding which is
+the most important one
+
+ align:start position:0%
+the most important one
+ 
+
+ align:start position:0%
+the most important one
+uh which ones are more important than
+
+ align:start position:0%
+uh which ones are more important than
+ 
+
+ align:start position:0%
+uh which ones are more important than
+which other ones ranking your various
+
+ align:start position:0%
+which other ones ranking your various
+ 
+
+ align:start position:0%
+which other ones ranking your various
+constraints with respect to each other
+
+ align:start position:0%
+constraints with respect to each other
+ 
+
+ align:start position:0%
+constraints with respect to each other
+there are other cases though uh that are
+
+ align:start position:0%
+there are other cases though uh that are
+ 
+
+ align:start position:0%
+there are other cases though uh that are
+uh problematic for that way of thinking
+
+ align:start position:0%
+uh problematic for that way of thinking
+ 
+
+ align:start position:0%
+uh problematic for that way of thinking
+about things uh and there's a sort of
+
+ align:start position:0%
+about things uh and there's a sort of
+ 
+
+ align:start position:0%
+about things uh and there's a sort of
+big literature on trying to reconcile
+
+ align:start position:0%
+big literature on trying to reconcile
+ 
+
+ align:start position:0%
+big literature on trying to reconcile
+these kinds of observations on the one
+
+ align:start position:0%
+these kinds of observations on the one
+ 
+
+ align:start position:0%
+these kinds of observations on the one
+hand uh the observation that there do
+
+ align:start position:0%
+hand uh the observation that there do
+ 
+
+ align:start position:0%
+hand uh the observation that there do
+seem to be these conspiracies where a
+
+ align:start position:0%
+seem to be these conspiracies where a
+ 
+
+ align:start position:0%
+seem to be these conspiracies where a
+language is doing the same thing in a
+
+ align:start position:0%
+language is doing the same thing in a
+ 
+
+ align:start position:0%
+language is doing the same thing in a
+variety of ways which is the kind of
+
+ align:start position:0%
+variety of ways which is the kind of
+ 
+
+ align:start position:0%
+variety of ways which is the kind of
+thing that makes people want to think in
+
+ align:start position:0%
+thing that makes people want to think in
+ 
+
+ align:start position:0%
+thing that makes people want to think in
+terms of running to constraints and on
+
+ align:start position:0%
+terms of running to constraints and on
+ 
+
+ align:start position:0%
+terms of running to constraints and on
+the other hand the kinds of cases which
+
+ align:start position:0%
+the other hand the kinds of cases which
+ 
+
+ align:start position:0%
+the other hand the kinds of cases which
+we've talked about before where it looks
+
+ align:start position:0%
+we've talked about before where it looks
+ 
+
+ align:start position:0%
+we've talked about before where it looks
+more like what's happening is that you
+
+ align:start position:0%
+more like what's happening is that you
+ 
+
+ align:start position:0%
+more like what's happening is that you
+have a bunch of rules and they're
+
+ align:start position:0%
+have a bunch of rules and they're
+ 
+
+ align:start position:0%
+have a bunch of rules and they're
+applying in an order uh and you they
+
+ align:start position:0%
+applying in an order uh and you they
+ 
+
+ align:start position:0%
+applying in an order uh and you they
+they don't necessarily all get
+
+ align:start position:0%
+they don't necessarily all get
+ 
+
+ align:start position:0%
+they don't necessarily all get
+um get obeyed we did this on the board
+
+ align:start position:0%
+um get obeyed we did this on the board
+ 
+
+ align:start position:0%
+um get obeyed we did this on the board
+um when was it last time I think but
+
+ align:start position:0%
+um when was it last time I think but
+ 
+
+ align:start position:0%
+um when was it last time I think but
+let's let's do it on the slide a little
+
+ align:start position:0%
+let's let's do it on the slide a little
+ 
+
+ align:start position:0%
+let's let's do it on the slide a little
+more carefully so cast your minds back
+
+ align:start position:0%
+more carefully so cast your minds back
+ 
+
+ align:start position:0%
+more carefully so cast your minds back
+to when we were talking about Lardo I
+
+ align:start position:0%
+to when we were talking about Lardo I
+ 
+
+ align:start position:0%
+to when we were talking about Lardo I
+tried to convince you we worked out an
+
+ align:start position:0%
+tried to convince you we worked out an
+ 
+
+ align:start position:0%
+tried to convince you we worked out an
+analysis of Lardo
+
+ align:start position:0%
+analysis of Lardo
+ 
+
+ align:start position:0%
+analysis of Lardo
+in which again uh Bearer nominative
+
+ align:start position:0%
+in which again uh Bearer nominative
+ 
+
+ align:start position:0%
+in which again uh Bearer nominative
+singular lardol doesn't Mark number but
+
+ align:start position:0%
+singular lardol doesn't Mark number but
+ 
+
+ align:start position:0%
+singular lardol doesn't Mark number but
+uh bare nominative forms of uh nouns
+
+ align:start position:0%
+uh bare nominative forms of uh nouns
+ 
+
+ align:start position:0%
+uh bare nominative forms of uh nouns
+um undergo various kinds of sound
+
+ align:start position:0%
+um undergo various kinds of sound
+ 
+
+ align:start position:0%
+um undergo various kinds of sound
+changes so lardel has words that
+
+ align:start position:0%
+changes so lardel has words that
+ 
+
+ align:start position:0%
+changes so lardel has words that
+underlyingly end in a k for example and
+
+ align:start position:0%
+underlyingly end in a k for example and
+ 
+
+ align:start position:0%
+underlyingly end in a k for example and
+there was a a general rule in lardel
+
+ align:start position:0%
+there was a a general rule in lardel
+ 
+
+ align:start position:0%
+there was a a general rule in lardel
+that said uh if you have a word that
+
+ align:start position:0%
+that said uh if you have a word that
+ 
+
+ align:start position:0%
+that said uh if you have a word that
+ends in a k get rid of the K you know so
+
+ align:start position:0%
+ends in a k get rid of the K you know so
+ 
+
+ align:start position:0%
+ends in a k get rid of the K you know so
+I'll start writing these down uh some
+
+ align:start position:0%
+I'll start writing these down uh some
+ 
+
+ align:start position:0%
+I'll start writing these down uh some
+marital rules one of them was uh
+
+ align:start position:0%
+marital rules one of them was uh
+ 
+
+ align:start position:0%
+marital rules one of them was uh
+eliminate and I won't try to write them
+
+ align:start position:0%
+eliminate and I won't try to write them
+ 
+
+ align:start position:0%
+eliminate and I won't try to write them
+formally eliminate finally
+
+ align:start position:0%
+formally eliminate finally
+ 
+
+ align:start position:0%
+formally eliminate finally
+okay so the word that we think is
+
+ align:start position:0%
+okay so the word that we think is
+ 
+
+ align:start position:0%
+okay so the word that we think is
+underlying out the word for Boomerang uh
+
+ align:start position:0%
+underlying out the word for Boomerang uh
+ 
+
+ align:start position:0%
+underlying out the word for Boomerang uh
+in Islam and the form is the reason we
+
+ align:start position:0%
+in Islam and the form is the reason we
+ 
+
+ align:start position:0%
+in Islam and the form is the reason we
+think that it's underlying liuang is
+
+ align:start position:0%
+think that it's underlying liuang is
+ 
+
+ align:start position:0%
+think that it's underlying liuang is
+that if you add any suffixes to it you
+
+ align:start position:0%
+that if you add any suffixes to it you
+ 
+
+ align:start position:0%
+that if you add any suffixes to it you
+you get to see that K so the accusative
+
+ align:start position:0%
+you get to see that K so the accusative
+ 
+
+ align:start position:0%
+you get to see that K so the accusative
+I think I told you was
+
+ align:start position:0%
+I think I told you was
+ 
+
+ align:start position:0%
+I think I told you was
+um uh so you know the K shows up uh in
+
+ align:start position:0%
+um uh so you know the K shows up uh in
+ 
+
+ align:start position:0%
+um uh so you know the K shows up uh in
+and in other forms as well
+
+ align:start position:0%
+and in other forms as well
+ 
+
+ align:start position:0%
+and in other forms as well
+we thought there was another rule that
+
+ align:start position:0%
+we thought there was another rule that
+ 
+
+ align:start position:0%
+we thought there was another rule that
+said uh final
+
+ align:start position:0%
+said uh final
+ 
+
+ align:start position:0%
+said uh final
+U becomes ah
+
+ align:start position:0%
+U becomes ah
+ 
+
+ align:start position:0%
+U becomes ah
+uh and that was why uh gandu which is
+
+ align:start position:0%
+uh and that was why uh gandu which is
+ 
+
+ align:start position:0%
+uh and that was why uh gandu which is
+the word for blood uh underlyingly
+
+ align:start position:0%
+the word for blood uh underlyingly
+ 
+
+ align:start position:0%
+the word for blood uh underlyingly
+becomes Kanda uh in the nominative and
+
+ align:start position:0%
+becomes Kanda uh in the nominative and
+ 
+
+ align:start position:0%
+becomes Kanda uh in the nominative and
+in the excuse
+
+ align:start position:0%
+in the excuse
+ 
+
+ align:start position:0%
+in the excuse
+why we think it starts out as gandu
+
+ align:start position:0%
+why we think it starts out as gandu
+ 
+
+ align:start position:0%
+why we think it starts out as gandu
+um so we have these two rules and what
+
+ align:start position:0%
+um so we have these two rules and what
+ 
+
+ align:start position:0%
+um so we have these two rules and what
+we said when we were doing Laredo before
+
+ align:start position:0%
+we said when we were doing Laredo before
+ 
+
+ align:start position:0%
+we said when we were doing Laredo before
+was something like uh we might want
+
+ align:start position:0%
+was something like uh we might want
+ 
+
+ align:start position:0%
+was something like uh we might want
+these rules to apply in a particular
+
+ align:start position:0%
+these rules to apply in a particular
+ 
+
+ align:start position:0%
+these rules to apply in a particular
+order uh in fact I see that I have
+
+ align:start position:0%
+order uh in fact I see that I have
+ 
+
+ align:start position:0%
+order uh in fact I see that I have
+written them in the wrong order
+
+ align:start position:0%
+written them in the wrong order
+ 
+
+ align:start position:0%
+written them in the wrong order
+um if you were to uh take the word nalok
+
+ align:start position:0%
+um if you were to uh take the word nalok
+ 
+
+ align:start position:0%
+um if you were to uh take the word nalok
+which is the underlying form for story
+
+ align:start position:0%
+which is the underlying form for story
+ 
+
+ align:start position:0%
+which is the underlying form for story
+and apply this Rule and then this rule
+
+ align:start position:0%
+and apply this Rule and then this rule
+ 
+
+ align:start position:0%
+and apply this Rule and then this rule
+well then you know you would eliminate
+
+ align:start position:0%
+well then you know you would eliminate
+ 
+
+ align:start position:0%
+well then you know you would eliminate
+the final K that would get you Malu and
+
+ align:start position:0%
+the final K that would get you Malu and
+ 
+
+ align:start position:0%
+the final K that would get you Malu and
+then you would change the final uh
+
+ align:start position:0%
+then you would change the final uh
+ 
+
+ align:start position:0%
+then you would change the final uh
+but that's not in fact the nominative
+
+ align:start position:0%
+but that's not in fact the nominative
+ 
+
+ align:start position:0%
+but that's not in fact the nominative
+form for story The nominative form for
+
+ align:start position:0%
+form for story The nominative form for
+ 
+
+ align:start position:0%
+form for story The nominative form for
+story is yeah and so what I said at the
+
+ align:start position:0%
+story is yeah and so what I said at the
+ 
+
+ align:start position:0%
+story is yeah and so what I said at the
+time was one way of thinking about this
+
+ align:start position:0%
+time was one way of thinking about this
+ 
+
+ align:start position:0%
+time was one way of thinking about this
+a popular way of thinking about this is
+
+ align:start position:0%
+a popular way of thinking about this is
+ 
+
+ align:start position:0%
+a popular way of thinking about this is
+to think there are these rules and it's
+
+ align:start position:0%
+to think there are these rules and it's
+ 
+
+ align:start position:0%
+to think there are these rules and it's
+like an assembly line you know there's
+
+ align:start position:0%
+like an assembly line you know there's
+ 
+
+ align:start position:0%
+like an assembly line you know there's
+first the first station is the one where
+
+ align:start position:0%
+first the first station is the one where
+ 
+
+ align:start position:0%
+first the first station is the one where
+you do this where you get rid of final
+
+ align:start position:0%
+you do this where you get rid of final
+ 
+
+ align:start position:0%
+you do this where you get rid of final
+ooh and then after you're done with that
+
+ align:start position:0%
+ooh and then after you're done with that
+ 
+
+ align:start position:0%
+ooh and then after you're done with that
+you get handed off to another another
+
+ align:start position:0%
+you get handed off to another another
+ 
+
+ align:start position:0%
+you get handed off to another another
+place in the assembly line where they
+
+ align:start position:0%
+place in the assembly line where they
+ 
+
+ align:start position:0%
+place in the assembly line where they
+eliminate final K and what's happened
+
+ align:start position:0%
+eliminate final K and what's happened
+ 
+
+ align:start position:0%
+eliminate final K and what's happened
+with underlying is that it got handed to
+
+ align:start position:0%
+with underlying is that it got handed to
+ 
+
+ align:start position:0%
+with underlying is that it got handed to
+the first station first first station
+
+ align:start position:0%
+the first station first first station
+ 
+
+ align:start position:0%
+the first station first first station
+said well this word and I look it
+
+ align:start position:0%
+said well this word and I look it
+ 
+
+ align:start position:0%
+said well this word and I look it
+doesn't end in ooh I'm not going to do
+
+ align:start position:0%
+doesn't end in ooh I'm not going to do
+ 
+
+ align:start position:0%
+doesn't end in ooh I'm not going to do
+anything and then it gets handed to the
+
+ align:start position:0%
+anything and then it gets handed to the
+ 
+
+ align:start position:0%
+anything and then it gets handed to the
+second station the second station says
+
+ align:start position:0%
+second station the second station says
+ 
+
+ align:start position:0%
+second station the second station says
+oh I need to get rid of the final K
+
+ align:start position:0%
+oh I need to get rid of the final K
+ 
+
+ align:start position:0%
+oh I need to get rid of the final K
+it'll be Yeah by which point the people
+
+ align:start position:0%
+it'll be Yeah by which point the people
+ 
+
+ align:start position:0%
+it'll be Yeah by which point the people
+in the first station might have been
+
+ align:start position:0%
+in the first station might have been
+ 
+
+ align:start position:0%
+in the first station might have been
+saying wait wait let us have that back
+
+ align:start position:0%
+saying wait wait let us have that back
+ 
+
+ align:start position:0%
+saying wait wait let us have that back
+but it's too late it was the idea yes
+
+ align:start position:0%
+but it's too late it was the idea yes
+ 
+
+ align:start position:0%
+but it's too late it was the idea yes
+these are rules that apply in a
+
+ align:start position:0%
+these are rules that apply in a
+ 
+
+ align:start position:0%
+these are rules that apply in a
+particular order that's the way we were
+
+ align:start position:0%
+particular order that's the way we were
+ 
+
+ align:start position:0%
+particular order that's the way we were
+talking about lairdo
+
+ align:start position:0%
+talking about lairdo
+ 
+
+ align:start position:0%
+talking about lairdo
+does that all sound Vaguely Familiar no
+
+ align:start position:0%
+does that all sound Vaguely Familiar no
+ 
+
+ align:start position:0%
+does that all sound Vaguely Familiar no
+that there are these procedures and the
+
+ align:start position:0%
+that there are these procedures and the
+ 
+
+ align:start position:0%
+that there are these procedures and the
+procedures happen in an order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if we imagine thinking about things
+
+ align:start position:0%
+but if we imagine thinking about things
+ 
+
+ align:start position:0%
+but if we imagine thinking about things
+in an optimality theoretic kind of way
+
+ align:start position:0%
+in an optimality theoretic kind of way
+ 
+
+ align:start position:0%
+in an optimality theoretic kind of way
+well it's not hard to come up with
+
+ align:start position:0%
+well it's not hard to come up with
+ 
+
+ align:start position:0%
+well it's not hard to come up with
+constraints right that say this you know
+
+ align:start position:0%
+constraints right that say this you know
+ 
+
+ align:start position:0%
+constraints right that say this you know
+uh star final
+
+ align:start position:0%
+uh star final
+ 
+
+ align:start position:0%
+uh star final
+I have to write it in capital letters
+
+ align:start position:0%
+I have to write it in capital letters
+ 
+
+ align:start position:0%
+I have to write it in capital letters
+because that's what you do in optimality
+
+ align:start position:0%
+because that's what you do in optimality
+ 
+
+ align:start position:0%
+because that's what you do in optimality
+theory uh no final k no final
+
+ align:start position:0%
+theory uh no final k no final
+ 
+
+ align:start position:0%
+theory uh no final k no final
+oh yeah
+
+ align:start position:0%
+oh yeah
+ 
+
+ align:start position:0%
+oh yeah
+um and those constraints would look at
+
+ align:start position:0%
+um and those constraints would look at
+ 
+
+ align:start position:0%
+um and those constraints would look at
+and I look uh sorry it went out and they
+
+ align:start position:0%
+and I look uh sorry it went out and they
+ 
+
+ align:start position:0%
+and I look uh sorry it went out and they
+would say no we can't have the final K
+
+ align:start position:0%
+would say no we can't have the final K
+ 
+
+ align:start position:0%
+would say no we can't have the final K
+it'll be one now and they would look at
+
+ align:start position:0%
+it'll be one now and they would look at
+ 
+
+ align:start position:0%
+it'll be one now and they would look at
+gandu and they would say no can't have
+
+ align:start position:0%
+gandu and they would say no can't have
+ 
+
+ align:start position:0%
+gandu and they would say no can't have
+the final ooh it'll be uh it's got to be
+
+ align:start position:0%
+the final ooh it'll be uh it's got to be
+ 
+
+ align:start position:0%
+the final ooh it'll be uh it's got to be
+Kanda uh it might have other constraints
+
+ align:start position:0%
+Kanda uh it might have other constraints
+ 
+
+ align:start position:0%
+Kanda uh it might have other constraints
+that are responsible for helping you
+
+ align:start position:0%
+that are responsible for helping you
+ 
+
+ align:start position:0%
+that are responsible for helping you
+decide you know the best thing to do
+
+ align:start position:0%
+decide you know the best thing to do
+ 
+
+ align:start position:0%
+decide you know the best thing to do
+with kandu is to change it to Kanda
+
+ align:start position:0%
+with kandu is to change it to Kanda
+ 
+
+ align:start position:0%
+with kandu is to change it to Kanda
+instead of you know Kandi or kand or any
+
+ align:start position:0%
+instead of you know Kandi or kand or any
+ 
+
+ align:start position:0%
+instead of you know Kandi or kand or any
+of the variety of other things you could
+
+ align:start position:0%
+of the variety of other things you could
+ 
+
+ align:start position:0%
+of the variety of other things you could
+have done so it's not all that hard to
+
+ align:start position:0%
+have done so it's not all that hard to
+ 
+
+ align:start position:0%
+have done so it's not all that hard to
+have constraints that say there's
+
+ align:start position:0%
+have constraints that say there's
+ 
+
+ align:start position:0%
+have constraints that say there's
+something wrong with one Oak there's
+
+ align:start position:0%
+something wrong with one Oak there's
+ 
+
+ align:start position:0%
+something wrong with one Oak there's
+something wrong with kandu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's not easy to figure out what to
+
+ align:start position:0%
+but it's not easy to figure out what to
+ 
+
+ align:start position:0%
+but it's not easy to figure out what to
+do next and so if you have those
+
+ align:start position:0%
+do next and so if you have those
+ 
+
+ align:start position:0%
+do next and so if you have those
+conditions that say that adult cannot
+
+ align:start position:0%
+conditions that say that adult cannot
+ 
+
+ align:start position:0%
+conditions that say that adult cannot
+stand words that end in K or words that
+
+ align:start position:0%
+stand words that end in K or words that
+ 
+
+ align:start position:0%
+stand words that end in K or words that
+end in you
+
+ align:start position:0%
+end in you
+ 
+
+ align:start position:0%
+end in you
+um that's the kind of thing we were
+
+ align:start position:0%
+um that's the kind of thing we were
+ 
+
+ align:start position:0%
+um that's the kind of thing we were
+saying about you know Japanese accent
+
+ align:start position:0%
+saying about you know Japanese accent
+ 
+
+ align:start position:0%
+saying about you know Japanese accent
+Japanese doesn't like Accent on the last
+
+ align:start position:0%
+Japanese doesn't like Accent on the last
+ 
+
+ align:start position:0%
+Japanese doesn't like Accent on the last
+syllable so avoid it if you're making a
+
+ align:start position:0%
+syllable so avoid it if you're making a
+ 
+
+ align:start position:0%
+syllable so avoid it if you're making a
+compound
+
+ align:start position:0%
+compound
+ 
+
+ align:start position:0%
+compound
+those generalizations hold for
+
+ align:start position:0%
+those generalizations hold for
+ 
+
+ align:start position:0%
+those generalizations hold for
+boomeranging for blood but they don't
+
+ align:start position:0%
+boomeranging for blood but they don't
+ 
+
+ align:start position:0%
+boomeranging for blood but they don't
+hold for story the one about not having
+
+ align:start position:0%
+hold for story the one about not having
+ 
+
+ align:start position:0%
+hold for story the one about not having
+a word ending in ooh doesn't hold yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are optimality Theory yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both like
+
+ align:start position:0%
+both like
+ 
+
+ align:start position:0%
+both like
+like if it were to do not a lot
+
+ align:start position:0%
+like if it were to do not a lot
+ 
+
+ align:start position:0%
+like if it were to do not a lot
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory like
+
+ align:start position:0%
+Theory like
+ 
+
+ align:start position:0%
+Theory like
+certain words each
+
+ align:start position:0%
+certain words each
+ 
+
+ align:start position:0%
+certain words each
+so that's just it it doesn't right so
+
+ align:start position:0%
+so that's just it it doesn't right so
+ 
+
+ align:start position:0%
+so that's just it it doesn't right so
+the conditions
+
+ align:start position:0%
+the conditions
+ 
+
+ align:start position:0%
+the conditions
+um the sense in which it has something
+
+ align:start position:0%
+um the sense in which it has something
+ 
+
+ align:start position:0%
+um the sense in which it has something
+like an order is that the conditions are
+
+ align:start position:0%
+like an order is that the conditions are
+ 
+
+ align:start position:0%
+like an order is that the conditions are
+ranked with respect to each other
+
+ align:start position:0%
+ranked with respect to each other
+ 
+
+ align:start position:0%
+ranked with respect to each other
+there's the one that's most important
+
+ align:start position:0%
+there's the one that's most important
+ 
+
+ align:start position:0%
+there's the one that's most important
+and the one that's next most important
+
+ align:start position:0%
+and the one that's next most important
+ 
+
+ align:start position:0%
+and the one that's next most important
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+um but if we were to build a tableau
+
+ align:start position:0%
+um but if we were to build a tableau
+ 
+
+ align:start position:0%
+um but if we were to build a tableau
+right we would have these two conditions
+
+ align:start position:0%
+right we would have these two conditions
+ 
+
+ align:start position:0%
+right we would have these two conditions
+don't have final k
+
+ align:start position:0%
+don't have final k
+ 
+
+ align:start position:0%
+don't have final k
+don't have
+
+ align:start position:0%
+don't have
+ 
+
+ align:start position:0%
+don't have
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+um and we would start off with the look
+
+ align:start position:0%
+um and we would start off with the look
+ 
+
+ align:start position:0%
+um and we would start off with the look
+and we'd consider keeping a look
+
+ align:start position:0%
+and we'd consider keeping a look
+ 
+
+ align:start position:0%
+and we'd consider keeping a look
+and we'd consider getting rid of
+
+ align:start position:0%
+and we'd consider getting rid of
+ 
+
+ align:start position:0%
+and we'd consider getting rid of
+the K at the end and maybe we consider
+
+ align:start position:0%
+the K at the end and maybe we consider
+ 
+
+ align:start position:0%
+the K at the end and maybe we consider
+right and this one would get knocked out
+
+ align:start position:0%
+right and this one would get knocked out
+ 
+
+ align:start position:0%
+right and this one would get knocked out
+by star final K right because it would
+
+ align:start position:0%
+by star final K right because it would
+ 
+
+ align:start position:0%
+by star final K right because it would
+end in K and this one would get knocked
+
+ align:start position:0%
+end in K and this one would get knocked
+ 
+
+ align:start position:0%
+end in K and this one would get knocked
+out by star final ooh yeah and this one
+
+ align:start position:0%
+out by star final ooh yeah and this one
+ 
+
+ align:start position:0%
+out by star final ooh yeah and this one
+would pass both of those conditions
+
+ align:start position:0%
+would pass both of those conditions
+ 
+
+ align:start position:0%
+would pass both of those conditions
+so if we just did a tableau like this if
+
+ align:start position:0%
+so if we just did a tableau like this if
+ 
+
+ align:start position:0%
+so if we just did a tableau like this if
+we said you know lardel seems to not
+
+ align:start position:0%
+we said you know lardel seems to not
+ 
+
+ align:start position:0%
+we said you know lardel seems to not
+like this and not like that and we have
+
+ align:start position:0%
+like this and not like that and we have
+ 
+
+ align:start position:0%
+like this and not like that and we have
+evidence for that in these other cases
+
+ align:start position:0%
+evidence for that in these other cases
+ 
+
+ align:start position:0%
+evidence for that in these other cases
+it seems as though
+
+ align:start position:0%
+it seems as though
+ 
+
+ align:start position:0%
+it seems as though
+but that's wrong yeah so the fact is
+
+ align:start position:0%
+but that's wrong yeah so the fact is
+ 
+
+ align:start position:0%
+but that's wrong yeah so the fact is
+this is the one we want to win and it's
+
+ align:start position:0%
+this is the one we want to win and it's
+ 
+
+ align:start position:0%
+this is the one we want to win and it's
+hard to see how once we've posited these
+
+ align:start position:0%
+hard to see how once we've posited these
+ 
+
+ align:start position:0%
+hard to see how once we've posited these
+conditions how we can get this to win
+
+ align:start position:0%
+conditions how we can get this to win
+ 
+
+ align:start position:0%
+conditions how we can get this to win
+this seems like it ought to be better
+
+ align:start position:0%
+this seems like it ought to be better
+ 
+
+ align:start position:0%
+this seems like it ought to be better
+once we posited these conditions so the
+
+ align:start position:0%
+once we posited these conditions so the
+ 
+
+ align:start position:0%
+once we posited these conditions so the
+puzzle and there's something people work
+
+ align:start position:0%
+puzzle and there's something people work
+ 
+
+ align:start position:0%
+puzzle and there's something people work
+on just try to figure out why why is
+
+ align:start position:0%
+on just try to figure out why why is
+ 
+
+ align:start position:0%
+on just try to figure out why why is
+that second one better than the third
+
+ align:start position:0%
+that second one better than the third
+ 
+
+ align:start position:0%
+that second one better than the third
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+yeah how about we rephrase yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we could have a rule that says
+
+ align:start position:0%
+okay so we could have a rule that says
+ 
+
+ align:start position:0%
+okay so we could have a rule that says
+that's nice we could say no final oh
+
+ align:start position:0%
+that's nice we could say no final oh
+ 
+
+ align:start position:0%
+that's nice we could say no final oh
+this is another way of saying what you
+
+ align:start position:0%
+this is another way of saying what you
+ 
+
+ align:start position:0%
+this is another way of saying what you
+just said uh no final ooh that was final
+
+ align:start position:0%
+just said uh no final ooh that was final
+ 
+
+ align:start position:0%
+just said uh no final ooh that was final
+in original form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so we need more capital letters but
+
+ align:start position:0%
+yep so we need more capital letters but
+ 
+
+ align:start position:0%
+yep so we need more capital letters but
+it's okay so yes if we if we state it
+
+ align:start position:0%
+it's okay so yes if we if we state it
+ 
+
+ align:start position:0%
+it's okay so yes if we if we state it
+that way
+
+ align:start position:0%
+that way
+ 
+
+ align:start position:0%
+that way
+um then uh
+
+ align:start position:0%
+um then uh
+ 
+
+ align:start position:0%
+um then uh
+um this passes that version of it
+
+ align:start position:0%
+um this passes that version of it
+ 
+
+ align:start position:0%
+um this passes that version of it
+and as long as we have some other
+
+ align:start position:0%
+and as long as we have some other
+ 
+
+ align:start position:0%
+and as long as we have some other
+condition that says Don't Change vowels
+
+ align:start position:0%
+condition that says Don't Change vowels
+ 
+
+ align:start position:0%
+condition that says Don't Change vowels
+just for the fun of it don't change ooh
+
+ align:start position:0%
+just for the fun of it don't change ooh
+ 
+
+ align:start position:0%
+just for the fun of it don't change ooh
+because you you want to uh which we
+
+ align:start position:0%
+because you you want to uh which we
+ 
+
+ align:start position:0%
+because you you want to uh which we
+surely need right if you give lerdal uh
+
+ align:start position:0%
+surely need right if you give lerdal uh
+ 
+
+ align:start position:0%
+surely need right if you give lerdal uh
+a word that has an ooh in it that's not
+
+ align:start position:0%
+a word that has an ooh in it that's not
+ 
+
+ align:start position:0%
+a word that has an ooh in it that's not
+at the end uh it's not going to change
+
+ align:start position:0%
+at the end uh it's not going to change
+ 
+
+ align:start position:0%
+at the end uh it's not going to change
+um then yes uh then this would win
+
+ align:start position:0%
+um then yes uh then this would win
+ 
+
+ align:start position:0%
+um then yes uh then this would win
+that's right that is indeed one of the
+
+ align:start position:0%
+that's right that is indeed one of the
+ 
+
+ align:start position:0%
+that's right that is indeed one of the
+kinds of things people do in order to
+
+ align:start position:0%
+kinds of things people do in order to
+ 
+
+ align:start position:0%
+kinds of things people do in order to
+handle this kind of problem they make
+
+ align:start position:0%
+handle this kind of problem they make
+ 
+
+ align:start position:0%
+handle this kind of problem they make
+these conditions
+
+ align:start position:0%
+these conditions
+ 
+
+ align:start position:0%
+these conditions
+more complicated yeah because now the
+
+ align:start position:0%
+more complicated yeah because now the
+ 
+
+ align:start position:0%
+more complicated yeah because now the
+conditions the conditions we've had so
+
+ align:start position:0%
+conditions the conditions we've had so
+ 
+
+ align:start position:0%
+conditions the conditions we've had so
+far are all about the form that gets
+
+ align:start position:0%
+far are all about the form that gets
+ 
+
+ align:start position:0%
+far are all about the form that gets
+pronounced they say things like the form
+
+ align:start position:0%
+pronounced they say things like the form
+ 
+
+ align:start position:0%
+pronounced they say things like the form
+that gets pronounced had better not end
+
+ align:start position:0%
+that gets pronounced had better not end
+ 
+
+ align:start position:0%
+that gets pronounced had better not end
+in a k or the form that gets pronounced
+
+ align:start position:0%
+in a k or the form that gets pronounced
+ 
+
+ align:start position:0%
+in a k or the form that gets pronounced
+it better not end in a voiced obstrand
+
+ align:start position:0%
+it better not end in a voiced obstrand
+ 
+
+ align:start position:0%
+it better not end in a voiced obstrand
+if we're doing polish sure you know uh
+
+ align:start position:0%
+if we're doing polish sure you know uh
+ 
+
+ align:start position:0%
+if we're doing polish sure you know uh
+better not have two stridents at the end
+
+ align:start position:0%
+better not have two stridents at the end
+ 
+
+ align:start position:0%
+better not have two stridents at the end
+of the word in a language like English
+
+ align:start position:0%
+of the word in a language like English
+ 
+
+ align:start position:0%
+of the word in a language like English
+this is a more complicated constraint it
+
+ align:start position:0%
+this is a more complicated constraint it
+ 
+
+ align:start position:0%
+this is a more complicated constraint it
+says it had better not end in this kind
+
+ align:start position:0%
+says it had better not end in this kind
+ 
+
+ align:start position:0%
+says it had better not end in this kind
+of sound if it ended in this kind of
+
+ align:start position:0%
+of sound if it ended in this kind of
+ 
+
+ align:start position:0%
+of sound if it ended in this kind of
+sound if it originally you know before
+
+ align:start position:0%
+sound if it originally you know before
+ 
+
+ align:start position:0%
+sound if it originally you know before
+before we started so being so there's a
+
+ align:start position:0%
+before we started so being so there's a
+ 
+
+ align:start position:0%
+before we started so being so there's a
+a an actual debate going on an
+
+ align:start position:0%
+a an actual debate going on an
+ 
+
+ align:start position:0%
+a an actual debate going on an
+optimality theory about whether we want
+
+ align:start position:0%
+optimality theory about whether we want
+ 
+
+ align:start position:0%
+optimality theory about whether we want
+to allow ourselves that kind of power
+
+ align:start position:0%
+to allow ourselves that kind of power
+ 
+
+ align:start position:0%
+to allow ourselves that kind of power
+allowing constraints to make reference
+
+ align:start position:0%
+allowing constraints to make reference
+ 
+
+ align:start position:0%
+allowing constraints to make reference
+not just to the pronounced version but
+
+ align:start position:0%
+not just to the pronounced version but
+ 
+
+ align:start position:0%
+not just to the pronounced version but
+to an earlier version but you're
+
+ align:start position:0%
+to an earlier version but you're
+ 
+
+ align:start position:0%
+to an earlier version but you're
+absolutely right that's the kind of move
+
+ align:start position:0%
+absolutely right that's the kind of move
+ 
+
+ align:start position:0%
+absolutely right that's the kind of move
+people people make people argue for
+
+ align:start position:0%
+people people make people argue for
+ 
+
+ align:start position:0%
+people people make people argue for
+I'm bringing this up just to show you
+
+ align:start position:0%
+I'm bringing this up just to show you
+ 
+
+ align:start position:0%
+I'm bringing this up just to show you
+there's this tension between these two
+
+ align:start position:0%
+there's this tension between these two
+ 
+
+ align:start position:0%
+there's this tension between these two
+ways of thinking about uh phonology and
+
+ align:start position:0%
+ways of thinking about uh phonology and
+ 
+
+ align:start position:0%
+ways of thinking about uh phonology and
+you've just raised one of the ways one
+
+ align:start position:0%
+you've just raised one of the ways one
+ 
+
+ align:start position:0%
+you've just raised one of the ways one
+of the ways in that indeed is has been
+
+ align:start position:0%
+of the ways in that indeed is has been
+ 
+
+ align:start position:0%
+of the ways in that indeed is has been
+taken in the literature to try to figure
+
+ align:start position:0%
+taken in the literature to try to figure
+ 
+
+ align:start position:0%
+taken in the literature to try to figure
+out uh how to deal with this tension but
+
+ align:start position:0%
+out uh how to deal with this tension but
+ 
+
+ align:start position:0%
+out uh how to deal with this tension but
+if you thought that Linguistics was like
+
+ align:start position:0%
+if you thought that Linguistics was like
+ 
+
+ align:start position:0%
+if you thought that Linguistics was like
+finished like we understood everything
+
+ align:start position:0%
+finished like we understood everything
+ 
+
+ align:start position:0%
+finished like we understood everything
+no yeah so this is one of the kinds of
+
+ align:start position:0%
+no yeah so this is one of the kinds of
+ 
+
+ align:start position:0%
+no yeah so this is one of the kinds of
+things that linguists still fight about
+
+ align:start position:0%
+things that linguists still fight about
+ 
+
+ align:start position:0%
+things that linguists still fight about
+like how to how to deal with these kinds
+
+ align:start position:0%
+like how to how to deal with these kinds
+ 
+
+ align:start position:0%
+like how to how to deal with these kinds
+of tensions yes
+
+ align:start position:0%
+of tensions yes
+ 
+
+ align:start position:0%
+of tensions yes
+I think we can still think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can you know make it like Assembly
+
+ align:start position:0%
+we can you know make it like Assembly
+ 
+
+ align:start position:0%
+we can you know make it like Assembly
+Language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+so that is another kind of move that
+
+ align:start position:0%
+so that is another kind of move that
+ 
+
+ align:start position:0%
+so that is another kind of move that
+people make sorry this uh slide has gone
+
+ align:start position:0%
+people make sorry this uh slide has gone
+ 
+
+ align:start position:0%
+people make sorry this uh slide has gone
+away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that isn't another kind of move that
+
+ align:start position:0%
+um that isn't another kind of move that
+ 
+
+ align:start position:0%
+um that isn't another kind of move that
+people make where they say
+
+ align:start position:0%
+people make where they say
+ 
+
+ align:start position:0%
+people make where they say
+um well there are various ways of
+
+ align:start position:0%
+um well there are various ways of
+ 
+
+ align:start position:0%
+um well there are various ways of
+interpreting what you just said uh one
+
+ align:start position:0%
+interpreting what you just said uh one
+ 
+
+ align:start position:0%
+interpreting what you just said uh one
+thing that one move that people made
+
+ align:start position:0%
+thing that one move that people made
+ 
+
+ align:start position:0%
+thing that one move that people made
+especially early on when people were
+
+ align:start position:0%
+especially early on when people were
+ 
+
+ align:start position:0%
+especially early on when people were
+worried about this problem in optimality
+
+ align:start position:0%
+worried about this problem in optimality
+ 
+
+ align:start position:0%
+worried about this problem in optimality
+theory was to say uh we're going to do
+
+ align:start position:0%
+theory was to say uh we're going to do
+ 
+
+ align:start position:0%
+theory was to say uh we're going to do
+something an optimality theory that
+
+ align:start position:0%
+something an optimality theory that
+ 
+
+ align:start position:0%
+something an optimality theory that
+allows us to simulate having rules in
+
+ align:start position:0%
+allows us to simulate having rules in
+ 
+
+ align:start position:0%
+allows us to simulate having rules in
+order so what we'll do is we'll have a
+
+ align:start position:0%
+order so what we'll do is we'll have a
+ 
+
+ align:start position:0%
+order so what we'll do is we'll have a
+word go through the tableaus more than
+
+ align:start position:0%
+word go through the tableaus more than
+ 
+
+ align:start position:0%
+word go through the tableaus more than
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+and the or the conditions can be in
+
+ align:start position:0%
+and the or the conditions can be in
+ 
+
+ align:start position:0%
+and the or the conditions can be in
+different orders in the different
+
+ align:start position:0%
+different orders in the different
+ 
+
+ align:start position:0%
+different orders in the different
+tableaus so we'll have a tableau first
+
+ align:start position:0%
+tableaus so we'll have a tableau first
+ 
+
+ align:start position:0%
+tableaus so we'll have a tableau first
+that says uh you know final K is very
+
+ align:start position:0%
+that says uh you know final K is very
+ 
+
+ align:start position:0%
+that says uh you know final K is very
+bad let's say and it doesn't have
+
+ align:start position:0%
+bad let's say and it doesn't have
+ 
+
+ align:start position:0%
+bad let's say and it doesn't have
+final ooh is bad right and then we'll
+
+ align:start position:0%
+final ooh is bad right and then we'll
+ 
+
+ align:start position:0%
+final ooh is bad right and then we'll
+have another Tableau that maybe doesn't
+
+ align:start position:0%
+have another Tableau that maybe doesn't
+ 
+
+ align:start position:0%
+have another Tableau that maybe doesn't
+have final K is very bad but has final
+
+ align:start position:0%
+have final K is very bad but has final
+ 
+
+ align:start position:0%
+have final K is very bad but has final
+ooh is bad right and that's a way to
+
+ align:start position:0%
+ooh is bad right and that's a way to
+ 
+
+ align:start position:0%
+ooh is bad right and that's a way to
+simulate ordered rules basically is to
+
+ align:start position:0%
+simulate ordered rules basically is to
+ 
+
+ align:start position:0%
+simulate ordered rules basically is to
+say we go through tableaus multiple
+
+ align:start position:0%
+say we go through tableaus multiple
+ 
+
+ align:start position:0%
+say we go through tableaus multiple
+times and the the tableaus look
+
+ align:start position:0%
+times and the the tableaus look
+ 
+
+ align:start position:0%
+times and the the tableaus look
+different from each other they have
+
+ align:start position:0%
+different from each other they have
+ 
+
+ align:start position:0%
+different from each other they have
+different conditions in them or they
+
+ align:start position:0%
+different conditions in them or they
+ 
+
+ align:start position:0%
+different conditions in them or they
+have the conditions in different orders
+
+ align:start position:0%
+have the conditions in different orders
+ 
+
+ align:start position:0%
+have the conditions in different orders
+that's one way one way to talk about it
+
+ align:start position:0%
+that's one way one way to talk about it
+ 
+
+ align:start position:0%
+that's one way one way to talk about it
+you might have had a more clever idea
+
+ align:start position:0%
+you might have had a more clever idea
+ 
+
+ align:start position:0%
+you might have had a more clever idea
+though which was the tableaus I was
+
+ align:start position:0%
+though which was the tableaus I was
+ 
+
+ align:start position:0%
+though which was the tableaus I was
+talking as though these rules are uh
+
+ align:start position:0%
+talking as though these rules are uh
+ 
+
+ align:start position:0%
+talking as though these rules are uh
+ranked with respect to each other you
+
+ align:start position:0%
+ranked with respect to each other you
+ 
+
+ align:start position:0%
+ranked with respect to each other you
+know which ones are more important than
+
+ align:start position:0%
+know which ones are more important than
+ 
+
+ align:start position:0%
+know which ones are more important than
+which other ones but optimality Theory
+
+ align:start position:0%
+which other ones but optimality Theory
+ 
+
+ align:start position:0%
+which other ones but optimality Theory
+people are generally talking novice
+
+ align:start position:0%
+people are generally talking novice
+ 
+
+ align:start position:0%
+people are generally talking novice
+though those happen one at a time uh
+
+ align:start position:0%
+though those happen one at a time uh
+ 
+
+ align:start position:0%
+though those happen one at a time uh
+it's just you're considering all these
+
+ align:start position:0%
+it's just you're considering all these
+ 
+
+ align:start position:0%
+it's just you're considering all these
+possibilities and you decide which one
+
+ align:start position:0%
+possibilities and you decide which one
+ 
+
+ align:start position:0%
+possibilities and you decide which one
+is best by all of these conditions you
+
+ align:start position:0%
+is best by all of these conditions you
+ 
+
+ align:start position:0%
+is best by all of these conditions you
+sound like you're thinking about
+
+ align:start position:0%
+sound like you're thinking about
+ 
+
+ align:start position:0%
+sound like you're thinking about
+something different where you would say
+
+ align:start position:0%
+something different where you would say
+ 
+
+ align:start position:0%
+something different where you would say
+you'd go back to the simple one
+
+ align:start position:0%
+you'd go back to the simple one
+ 
+
+ align:start position:0%
+you'd go back to the simple one
+and you'd say we start with LA look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and uh what we want is something that
+
+ align:start position:0%
+um and uh what we want is something that
+ 
+
+ align:start position:0%
+um and uh what we want is something that
+says something like well I should have
+
+ align:start position:0%
+says something like well I should have
+ 
+
+ align:start position:0%
+says something like well I should have
+put star final ooh first
+
+ align:start position:0%
+put star final ooh first
+ 
+
+ align:start position:0%
+put star final ooh first
+maybe I'll just reverse these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh we have all of our all of our
+
+ align:start position:0%
+uh we have all of our all of our
+ 
+
+ align:start position:0%
+uh we have all of our all of our
+candidates here and we first consider
+
+ align:start position:0%
+candidates here and we first consider
+ 
+
+ align:start position:0%
+candidates here and we first consider
+star final ooh uh-oh but if we consider
+
+ align:start position:0%
+star final ooh uh-oh but if we consider
+ 
+
+ align:start position:0%
+star final ooh uh-oh but if we consider
+a star final ooh star final ooh we'll
+
+ align:start position:0%
+a star final ooh star final ooh we'll
+ 
+
+ align:start position:0%
+a star final ooh star final ooh we'll
+look at nalu and it will it will knock
+
+ align:start position:0%
+look at nalu and it will it will knock
+ 
+
+ align:start position:0%
+look at nalu and it will it will knock
+it out right right so that that will be
+
+ align:start position:0%
+it out right right so that that will be
+ 
+
+ align:start position:0%
+it out right right so that that will be
+bad right there and and we won't ever
+
+ align:start position:0%
+bad right there and and we won't ever
+ 
+
+ align:start position:0%
+bad right there and and we won't ever
+get it back if we do that so what we
+
+ align:start position:0%
+get it back if we do that so what we
+ 
+
+ align:start position:0%
+get it back if we do that so what we
+want is something more like using the
+
+ align:start position:0%
+want is something more like using the
+ 
+
+ align:start position:0%
+want is something more like using the
+teplo to to do something like ordered
+
+ align:start position:0%
+teplo to to do something like ordered
+ 
+
+ align:start position:0%
+teplo to to do something like ordered
+rules you know something that says
+
+ align:start position:0%
+rules you know something that says
+ 
+
+ align:start position:0%
+rules you know something that says
+um we look at this first thing and we we
+
+ align:start position:0%
+um we look at this first thing and we we
+ 
+
+ align:start position:0%
+um we look at this first thing and we we
+are now basically doing rules in an
+
+ align:start position:0%
+are now basically doing rules in an
+ 
+
+ align:start position:0%
+are now basically doing rules in an
+order uh we look at this first thing and
+
+ align:start position:0%
+order uh we look at this first thing and
+ 
+
+ align:start position:0%
+order uh we look at this first thing and
+we ask ourselves what's not look well uh
+
+ align:start position:0%
+we ask ourselves what's not look well uh
+ 
+
+ align:start position:0%
+we ask ourselves what's not look well uh
+it doesn't it doesn't violate this first
+
+ align:start position:0%
+it doesn't it doesn't violate this first
+ 
+
+ align:start position:0%
+it doesn't it doesn't violate this first
+rule and so we'll keep it
+
+ align:start position:0%
+rule and so we'll keep it
+ 
+
+ align:start position:0%
+rule and so we'll keep it
+and then we'll consider the next rule it
+
+ align:start position:0%
+and then we'll consider the next rule it
+ 
+
+ align:start position:0%
+and then we'll consider the next rule it
+does violate that rule and so we'll
+
+ align:start position:0%
+does violate that rule and so we'll
+ 
+
+ align:start position:0%
+does violate that rule and so we'll
+change it we'll make a minimal change to
+
+ align:start position:0%
+change it we'll make a minimal change to
+ 
+
+ align:start position:0%
+change it we'll make a minimal change to
+it this is a way of converting tableaus
+
+ align:start position:0%
+it this is a way of converting tableaus
+ 
+
+ align:start position:0%
+it this is a way of converting tableaus
+into ordered rules I think that's what
+
+ align:start position:0%
+into ordered rules I think that's what
+ 
+
+ align:start position:0%
+into ordered rules I think that's what
+we're now doing
+
+ align:start position:0%
+we're now doing
+ 
+
+ align:start position:0%
+we're now doing
+um and uh it could be yeah after all
+
+ align:start position:0%
+um and uh it could be yeah after all
+ 
+
+ align:start position:0%
+um and uh it could be yeah after all
+things things to think about open
+
+ align:start position:0%
+things things to think about open
+ 
+
+ align:start position:0%
+things things to think about open
+research questions
+
+ align:start position:0%
+research questions
+ 
+
+ align:start position:0%
+research questions
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+okay so the goal here was to get all of
+
+ align:start position:0%
+okay so the goal here was to get all of
+ 
+
+ align:start position:0%
+okay so the goal here was to get all of
+you to try to do better than Linguistics
+
+ align:start position:0%
+you to try to do better than Linguistics
+ 
+
+ align:start position:0%
+you to try to do better than Linguistics
+is so far done so right now we have
+
+ align:start position:0%
+is so far done so right now we have
+ 
+
+ align:start position:0%
+is so far done so right now we have
+these two ways of thinking about
+
+ align:start position:0%
+these two ways of thinking about
+ 
+
+ align:start position:0%
+these two ways of thinking about
+phonology and there are in some kind of
+
+ align:start position:0%
+phonology and there are in some kind of
+ 
+
+ align:start position:0%
+phonology and there are in some kind of
+conflict with each other and there's
+
+ align:start position:0%
+conflict with each other and there's
+ 
+
+ align:start position:0%
+conflict with each other and there's
+active work on trying to figure out how
+
+ align:start position:0%
+active work on trying to figure out how
+ 
+
+ align:start position:0%
+active work on trying to figure out how
+to get them to mesh
+
+ align:start position:0%
+to get them to mesh
+ 
+
+ align:start position:0%
+to get them to mesh
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+where are we
+
+ align:start position:0%
+where are we
+ 
+
+ align:start position:0%
+where are we
+here we are Center and some obstruents
+
+ align:start position:0%
+here we are Center and some obstruents
+ 
+
+ align:start position:0%
+here we are Center and some obstruents
+we did that we did that
+
+ align:start position:0%
+we did that we did that
+ 
+
+ align:start position:0%
+we did that we did that
+okay so um let me introduce you we're
+
+ align:start position:0%
+okay so um let me introduce you we're
+ 
+
+ align:start position:0%
+okay so um let me introduce you we're
+running yeah yeah let me introduce you
+
+ align:start position:0%
+running yeah yeah let me introduce you
+ 
+
+ align:start position:0%
+running yeah yeah let me introduce you
+to another
+
+ align:start position:0%
+to another
+ 
+
+ align:start position:0%
+to another
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh another class of sounds uh again the
+
+ align:start position:0%
+uh another class of sounds uh again the
+ 
+
+ align:start position:0%
+uh another class of sounds uh again the
+the point is to show you uh ways in
+
+ align:start position:0%
+the point is to show you uh ways in
+ 
+
+ align:start position:0%
+the point is to show you uh ways in
+which it's useful to categorize sounds
+
+ align:start position:0%
+which it's useful to categorize sounds
+ 
+
+ align:start position:0%
+which it's useful to categorize sounds
+and the way to try to convince you of
+
+ align:start position:0%
+and the way to try to convince you of
+ 
+
+ align:start position:0%
+and the way to try to convince you of
+that is to show you phenomena that care
+
+ align:start position:0%
+that is to show you phenomena that care
+ 
+
+ align:start position:0%
+that is to show you phenomena that care
+about certain classes of sounds and not
+
+ align:start position:0%
+about certain classes of sounds and not
+ 
+
+ align:start position:0%
+about certain classes of sounds and not
+others uh here are a bunch of Arabic
+
+ align:start position:0%
+others uh here are a bunch of Arabic
+ 
+
+ align:start position:0%
+others uh here are a bunch of Arabic
+nouns together with their definite
+
+ align:start position:0%
+nouns together with their definite
+ 
+
+ align:start position:0%
+nouns together with their definite
+article which you can see is of uh
+
+ align:start position:0%
+article which you can see is of uh
+ 
+
+ align:start position:0%
+article which you can see is of uh
+English is borrowed a bunch of Arabic
+
+ align:start position:0%
+English is borrowed a bunch of Arabic
+ 
+
+ align:start position:0%
+English is borrowed a bunch of Arabic
+words uh that have kept this all so we
+
+ align:start position:0%
+words uh that have kept this all so we
+ 
+
+ align:start position:0%
+words uh that have kept this all so we
+have words like algebra for example or
+
+ align:start position:0%
+have words like algebra for example or
+ 
+
+ align:start position:0%
+have words like algebra for example or
+algorithm where the owl at the end is
+
+ align:start position:0%
+algorithm where the owl at the end is
+ 
+
+ align:start position:0%
+algorithm where the owl at the end is
+this word for the yeah
+
+ align:start position:0%
+this word for the yeah
+ 
+
+ align:start position:0%
+this word for the yeah
+uh so here are some Arabic nouns with
+
+ align:start position:0%
+uh so here are some Arabic nouns with
+ 
+
+ align:start position:0%
+uh so here are some Arabic nouns with
+the word for the in front of them
+
+ align:start position:0%
+the word for the in front of them
+ 
+
+ align:start position:0%
+the word for the in front of them
+but there's this other class of nouns
+
+ align:start position:0%
+but there's this other class of nouns
+ 
+
+ align:start position:0%
+but there's this other class of nouns
+where the word for the changes it's no
+
+ align:start position:0%
+where the word for the changes it's no
+ 
+
+ align:start position:0%
+where the word for the changes it's no
+longer Al
+
+ align:start position:0%
+longer Al
+ 
+
+ align:start position:0%
+longer Al
+um what it gets it still starts with ah
+
+ align:start position:0%
+um what it gets it still starts with ah
+ 
+
+ align:start position:0%
+um what it gets it still starts with ah
+that the consonant in it becomes a copy
+
+ align:start position:0%
+that the consonant in it becomes a copy
+ 
+
+ align:start position:0%
+that the consonant in it becomes a copy
+of the consonant that's after it
+
+ align:start position:0%
+of the consonant that's after it
+ 
+
+ align:start position:0%
+of the consonant that's after it
+so the word for sun which is Shams uh
+
+ align:start position:0%
+so the word for sun which is Shams uh
+ 
+
+ align:start position:0%
+so the word for sun which is Shams uh
+the sun is Ash it's not al-shams
+
+ align:start position:0%
+the sun is Ash it's not al-shams
+ 
+
+ align:start position:0%
+the sun is Ash it's not al-shams
+here I am pretending to speak Arabic is
+
+ align:start position:0%
+here I am pretending to speak Arabic is
+ 
+
+ align:start position:0%
+here I am pretending to speak Arabic is
+there anyone here who actually speaks
+
+ align:start position:0%
+there anyone here who actually speaks
+ 
+
+ align:start position:0%
+there anyone here who actually speaks
+Arabic
+
+ align:start position:0%
+Arabic
+ 
+
+ align:start position:0%
+Arabic
+okay cool I'll just keep pretending
+
+ align:start position:0%
+okay cool I'll just keep pretending
+ 
+
+ align:start position:0%
+okay cool I'll just keep pretending
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay uh this is a classic observation
+
+ align:start position:0%
+okay uh this is a classic observation
+ 
+
+ align:start position:0%
+okay uh this is a classic observation
+Arabic linguists noticed this about
+
+ align:start position:0%
+Arabic linguists noticed this about
+ 
+
+ align:start position:0%
+Arabic linguists noticed this about
+their language uh um they name uh and
+
+ align:start position:0%
+their language uh um they name uh and
+ 
+
+ align:start position:0%
+their language uh um they name uh and
+and noticed the relevant condition is
+
+ align:start position:0%
+and noticed the relevant condition is
+ 
+
+ align:start position:0%
+and noticed the relevant condition is
+that there are certain kinds of sounds
+
+ align:start position:0%
+that there are certain kinds of sounds
+ 
+
+ align:start position:0%
+that there are certain kinds of sounds
+that get the phenomenon on the right
+
+ align:start position:0%
+that get the phenomenon on the right
+ 
+
+ align:start position:0%
+that get the phenomenon on the right
+where the definite article ends in a
+
+ align:start position:0%
+where the definite article ends in a
+ 
+
+ align:start position:0%
+where the definite article ends in a
+copy of the first consonant of the uh
+
+ align:start position:0%
+copy of the first consonant of the uh
+ 
+
+ align:start position:0%
+copy of the first consonant of the uh
+the following noun and other consonants
+
+ align:start position:0%
+the following noun and other consonants
+ 
+
+ align:start position:0%
+the following noun and other consonants
+that don't do that they're they're
+
+ align:start position:0%
+that don't do that they're they're
+ 
+
+ align:start position:0%
+that don't do that they're they're
+called Moon letters and Sun letters
+
+ align:start position:0%
+called Moon letters and Sun letters
+ 
+
+ align:start position:0%
+called Moon letters and Sun letters
+um in the in the Arabic tradition
+
+ align:start position:0%
+um in the in the Arabic tradition
+ 
+
+ align:start position:0%
+um in the in the Arabic tradition
+because well moon is one of the words in
+
+ align:start position:0%
+because well moon is one of the words in
+ 
+
+ align:start position:0%
+because well moon is one of the words in
+the column on the left and sun is one of
+
+ align:start position:0%
+the column on the left and sun is one of
+ 
+
+ align:start position:0%
+the column on the left and sun is one of
+the words in the column on the right
+
+ align:start position:0%
+the words in the column on the right
+ 
+
+ align:start position:0%
+the words in the column on the right
+mnemonic these classes of sounds so the
+
+ align:start position:0%
+mnemonic these classes of sounds so the
+ 
+
+ align:start position:0%
+mnemonic these classes of sounds so the
+moon letters are letters like and K and
+
+ align:start position:0%
+moon letters are letters like and K and
+ 
+
+ align:start position:0%
+moon letters are letters like and K and
+H and Global stop
+
+ align:start position:0%
+H and Global stop
+ 
+
+ align:start position:0%
+H and Global stop
+and the sun letters are sounds like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the moon letters
+
+ align:start position:0%
+the moon letters
+ 
+
+ align:start position:0%
+the moon letters
+no the sun letters yes the sun letters
+
+ align:start position:0%
+no the sun letters yes the sun letters
+ 
+
+ align:start position:0%
+no the sun letters yes the sun letters
+uh are the ones that I've got in the box
+
+ align:start position:0%
+uh are the ones that I've got in the box
+ 
+
+ align:start position:0%
+uh are the ones that I've got in the box
+there they are what are called coronals
+
+ align:start position:0%
+there they are what are called coronals
+ 
+
+ align:start position:0%
+there they are what are called coronals
+so coronals are the interdentals and the
+
+ align:start position:0%
+so coronals are the interdentals and the
+ 
+
+ align:start position:0%
+so coronals are the interdentals and the
+alveolars and the post alveolars if you
+
+ align:start position:0%
+alveolars and the post alveolars if you
+ 
+
+ align:start position:0%
+alveolars and the post alveolars if you
+think about them so you know feel free
+
+ align:start position:0%
+think about them so you know feel free
+ 
+
+ align:start position:0%
+think about them so you know feel free
+to sit there making those noises to
+
+ align:start position:0%
+to sit there making those noises to
+ 
+
+ align:start position:0%
+to sit there making those noises to
+yourself if you want to
+
+ align:start position:0%
+yourself if you want to
+ 
+
+ align:start position:0%
+yourself if you want to
+um what what all of them do is make a
+
+ align:start position:0%
+um what what all of them do is make a
+ 
+
+ align:start position:0%
+um what what all of them do is make a
+consonant sound that's articulated with
+
+ align:start position:0%
+consonant sound that's articulated with
+ 
+
+ align:start position:0%
+consonant sound that's articulated with
+the tip or the blade of your tongue sort
+
+ align:start position:0%
+the tip or the blade of your tongue sort
+ 
+
+ align:start position:0%
+the tip or the blade of your tongue sort
+of the front of your tongue is touching
+
+ align:start position:0%
+of the front of your tongue is touching
+ 
+
+ align:start position:0%
+of the front of your tongue is touching
+some part of the top of your mouth or or
+
+ align:start position:0%
+some part of the top of your mouth or or
+ 
+
+ align:start position:0%
+some part of the top of your mouth or or
+other places so the interdentals your
+
+ align:start position:0%
+other places so the interdentals your
+ 
+
+ align:start position:0%
+other places so the interdentals your
+tongue is sticking out between your
+
+ align:start position:0%
+tongue is sticking out between your
+ 
+
+ align:start position:0%
+tongue is sticking out between your
+teeth are the alveolars or the post
+
+ align:start position:0%
+teeth are the alveolars or the post
+ 
+
+ align:start position:0%
+teeth are the alveolars or the post
+alveolars the tip of your tongue or the
+
+ align:start position:0%
+alveolars the tip of your tongue or the
+ 
+
+ align:start position:0%
+alveolars the tip of your tongue or the
+blade of your tongue is coming into
+
+ align:start position:0%
+blade of your tongue is coming into
+ 
+
+ align:start position:0%
+blade of your tongue is coming into
+contact almost with the top of your
+
+ align:start position:0%
+contact almost with the top of your
+ 
+
+ align:start position:0%
+contact almost with the top of your
+mouth yeah
+
+ align:start position:0%
+mouth yeah
+ 
+
+ align:start position:0%
+mouth yeah
+as opposed to say bilabials where your
+
+ align:start position:0%
+as opposed to say bilabials where your
+ 
+
+ align:start position:0%
+as opposed to say bilabials where your
+tongue can do whatever the heck it feels
+
+ align:start position:0%
+tongue can do whatever the heck it feels
+ 
+
+ align:start position:0%
+tongue can do whatever the heck it feels
+like or veelers which involve your
+
+ align:start position:0%
+like or veelers which involve your
+ 
+
+ align:start position:0%
+like or veelers which involve your
+tongue or uvulus which involve your
+
+ align:start position:0%
+tongue or uvulus which involve your
+ 
+
+ align:start position:0%
+tongue or uvulus which involve your
+tongue but it's the back of your tongue
+
+ align:start position:0%
+tongue but it's the back of your tongue
+ 
+
+ align:start position:0%
+tongue but it's the back of your tongue
+as opposed to the front of your tongue
+
+ align:start position:0%
+as opposed to the front of your tongue
+ 
+
+ align:start position:0%
+as opposed to the front of your tongue
+which is what you're using for things
+
+ align:start position:0%
+which is what you're using for things
+ 
+
+ align:start position:0%
+which is what you're using for things
+like and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that clear the distinction clear and
+
+ align:start position:0%
+is that clear the distinction clear and
+ 
+
+ align:start position:0%
+is that clear the distinction clear and
+uh Arabic gives us a nice
+
+ align:start position:0%
+uh Arabic gives us a nice
+ 
+
+ align:start position:0%
+uh Arabic gives us a nice
+um uh sort of illustration of this the
+
+ align:start position:0%
+um uh sort of illustration of this the
+ 
+
+ align:start position:0%
+um uh sort of illustration of this the
+coronal sounds are the ones that are the
+
+ align:start position:0%
+coronal sounds are the ones that are the
+ 
+
+ align:start position:0%
+coronal sounds are the ones that are the
+the sun letters they're the ones where
+
+ align:start position:0%
+the sun letters they're the ones where
+ 
+
+ align:start position:0%
+the sun letters they're the ones where
+you uh the the last consonant of the
+
+ align:start position:0%
+you uh the the last consonant of the
+ 
+
+ align:start position:0%
+you uh the the last consonant of the
+definite article just becomes a copy of
+
+ align:start position:0%
+definite article just becomes a copy of
+ 
+
+ align:start position:0%
+definite article just becomes a copy of
+the following consonant notice that the
+
+ align:start position:0%
+the following consonant notice that the
+ 
+
+ align:start position:0%
+the following consonant notice that the
+last consonant of the indefinite article
+
+ align:start position:0%
+last consonant of the indefinite article
+ 
+
+ align:start position:0%
+last consonant of the indefinite article
+underlyingly is L which is itself
+
+ align:start position:0%
+underlyingly is L which is itself
+ 
+
+ align:start position:0%
+underlyingly is L which is itself
+coronal so uh it's like the end of the
+
+ align:start position:0%
+coronal so uh it's like the end of the
+ 
+
+ align:start position:0%
+coronal so uh it's like the end of the
+definite article is going to be coronal
+
+ align:start position:0%
+definite article is going to be coronal
+ 
+
+ align:start position:0%
+definite article is going to be coronal
+uh if nothing else happens it's going to
+
+ align:start position:0%
+uh if nothing else happens it's going to
+ 
+
+ align:start position:0%
+uh if nothing else happens it's going to
+be L but if there's a cardinal right
+
+ align:start position:0%
+be L but if there's a cardinal right
+ 
+
+ align:start position:0%
+be L but if there's a cardinal right
+after it it just becomes a copy of the
+
+ align:start position:0%
+after it it just becomes a copy of the
+ 
+
+ align:start position:0%
+after it it just becomes a copy of the
+following chordal does that make sense
+
+ align:start position:0%
+following chordal does that make sense
+ 
+
+ align:start position:0%
+following chordal does that make sense
+that's what's going on in all of these
+
+ align:start position:0%
+that's what's going on in all of these
+ 
+
+ align:start position:0%
+that's what's going on in all of these
+examples so with moon and Mare and book
+
+ align:start position:0%
+examples so with moon and Mare and book
+ 
+
+ align:start position:0%
+examples so with moon and Mare and book
+and more and father the L of the
+
+ align:start position:0%
+and more and father the L of the
+ 
+
+ align:start position:0%
+and more and father the L of the
+definite article can't become a copy of
+
+ align:start position:0%
+definite article can't become a copy of
+ 
+
+ align:start position:0%
+definite article can't become a copy of
+the following consonant and remain
+
+ align:start position:0%
+the following consonant and remain
+ 
+
+ align:start position:0%
+the following consonant and remain
+coronal yeah whereas in the sun letters
+
+ align:start position:0%
+coronal yeah whereas in the sun letters
+ 
+
+ align:start position:0%
+coronal yeah whereas in the sun letters
+the ones on the right by copying the
+
+ align:start position:0%
+the ones on the right by copying the
+ 
+
+ align:start position:0%
+the ones on the right by copying the
+following consonant the the L of the
+
+ align:start position:0%
+following consonant the the L of the
+ 
+
+ align:start position:0%
+following consonant the the L of the
+definite article is still a coronal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+somebody had a great idea about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so that's what's going on in these uh
+
+ align:start position:0%
+uh so that's what's going on in these uh
+ 
+
+ align:start position:0%
+uh so that's what's going on in these uh
+in these Arabic examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay a rule that we could have for
+
+ align:start position:0%
+um okay a rule that we could have for
+ 
+
+ align:start position:0%
+um okay a rule that we could have for
+the Arabic definite article yes I just
+
+ align:start position:0%
+the Arabic definite article yes I just
+ 
+
+ align:start position:0%
+the Arabic definite article yes I just
+said this thank you L is also Cardinal
+
+ align:start position:0%
+said this thank you L is also Cardinal
+ 
+
+ align:start position:0%
+said this thank you L is also Cardinal
+uh a rule we could have for the Arabic
+
+ align:start position:0%
+uh a rule we could have for the Arabic
+ 
+
+ align:start position:0%
+uh a rule we could have for the Arabic
+definite article would say you know in
+
+ align:start position:0%
+definite article would say you know in
+ 
+
+ align:start position:0%
+definite article would say you know in
+the definite article and L becomes a
+
+ align:start position:0%
+the definite article and L becomes a
+ 
+
+ align:start position:0%
+the definite article and L becomes a
+copy of a following coronal consonant so
+
+ align:start position:0%
+copy of a following coronal consonant so
+ 
+
+ align:start position:0%
+copy of a following coronal consonant so
+you know we have sort of a variable
+
+ align:start position:0%
+you know we have sort of a variable
+ 
+
+ align:start position:0%
+you know we have sort of a variable
+consonants uh subscript I which says
+
+ align:start position:0%
+consonants uh subscript I which says
+ 
+
+ align:start position:0%
+consonants uh subscript I which says
+whatever the con following consonant is
+
+ align:start position:0%
+whatever the con following consonant is
+ 
+
+ align:start position:0%
+whatever the con following consonant is
+if it's coronal uh the L will also get
+
+ align:start position:0%
+if it's coronal uh the L will also get
+ 
+
+ align:start position:0%
+if it's coronal uh the L will also get
+the value consonant sub I but it'll
+
+ align:start position:0%
+the value consonant sub I but it'll
+ 
+
+ align:start position:0%
+the value consonant sub I but it'll
+it'll it'll have the same form as the
+
+ align:start position:0%
+it'll it'll have the same form as the
+ 
+
+ align:start position:0%
+it'll it'll have the same form as the
+following consonant yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+or like uh which means home yeah
+
+ align:start position:0%
+or like uh which means home yeah
+ 
+
+ align:start position:0%
+or like uh which means home yeah
+and uh Arabic actually has
+
+ align:start position:0%
+and uh Arabic actually has
+ 
+
+ align:start position:0%
+and uh Arabic actually has
+like which like duplicates uh one letter
+
+ align:start position:0%
+like which like duplicates uh one letter
+ 
+
+ align:start position:0%
+like which like duplicates uh one letter
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+so I think is that when you can
+
+ align:start position:0%
+so I think is that when you can
+ 
+
+ align:start position:0%
+so I think is that when you can
+duplicate the letter you just duplicate
+
+ align:start position:0%
+duplicate the letter you just duplicate
+ 
+
+ align:start position:0%
+duplicate the letter you just duplicate
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+there's like the the moon yeah you can
+
+ align:start position:0%
+there's like the the moon yeah you can
+ 
+
+ align:start position:0%
+there's like the the moon yeah you can
+do that so yeah so but there are I see
+
+ align:start position:0%
+do that so yeah so but there are I see
+ 
+
+ align:start position:0%
+do that so yeah so but there are I see
+what you mean but look there there are
+
+ align:start position:0%
+what you mean but look there there are
+ 
+
+ align:start position:0%
+what you mean but look there there are
+uh consonants like uh p and t and K
+
+ align:start position:0%
+uh consonants like uh p and t and K
+ 
+
+ align:start position:0%
+uh consonants like uh p and t and K
+which are all stops but T is coronal and
+
+ align:start position:0%
+which are all stops but T is coronal and
+ 
+
+ align:start position:0%
+which are all stops but T is coronal and
+P and K are not right and so all of
+
+ align:start position:0%
+P and K are not right and so all of
+ 
+
+ align:start position:0%
+P and K are not right and so all of
+those are equally hard to maintain for a
+
+ align:start position:0%
+those are equally hard to maintain for a
+ 
+
+ align:start position:0%
+those are equally hard to maintain for a
+long time I think or similarly I think
+
+ align:start position:0%
+long time I think or similarly I think
+ 
+
+ align:start position:0%
+long time I think or similarly I think
+what we're hoping you can stop me if
+
+ align:start position:0%
+what we're hoping you can stop me if
+ 
+
+ align:start position:0%
+what we're hoping you can stop me if
+this is not true is that if there are
+
+ align:start position:0%
+this is not true is that if there are
+ 
+
+ align:start position:0%
+this is not true is that if there are
+Arabic words that start with M uh those
+
+ align:start position:0%
+Arabic words that start with M uh those
+ 
+
+ align:start position:0%
+Arabic words that start with M uh those
+you'll get Al before that before in M
+
+ align:start position:0%
+you'll get Al before that before in M
+ 
+
+ align:start position:0%
+you'll get Al before that before in M
+yeah but for Arabic words that start
+
+ align:start position:0%
+yeah but for Arabic words that start
+ 
+
+ align:start position:0%
+yeah but for Arabic words that start
+with n you get a copy of the N yeah and
+
+ align:start position:0%
+with n you get a copy of the N yeah and
+ 
+
+ align:start position:0%
+with n you get a copy of the N yeah and
+again those are all sort of equally easy
+
+ align:start position:0%
+again those are all sort of equally easy
+ 
+
+ align:start position:0%
+again those are all sort of equally easy
+to hold on for a long time so that's a
+
+ align:start position:0%
+to hold on for a long time so that's a
+ 
+
+ align:start position:0%
+to hold on for a long time so that's a
+good this is a good example of science
+
+ align:start position:0%
+good this is a good example of science
+ 
+
+ align:start position:0%
+good this is a good example of science
+you know you had a good hypothesis and
+
+ align:start position:0%
+you know you had a good hypothesis and
+ 
+
+ align:start position:0%
+you know you had a good hypothesis and
+now we're finding data yeah and you
+
+ align:start position:0%
+now we're finding data yeah and you
+ 
+
+ align:start position:0%
+now we're finding data yeah and you
+speak I should have called on you to do
+
+ align:start position:0%
+speak I should have called on you to do
+ 
+
+ align:start position:0%
+speak I should have called on you to do
+to to say these Arabic words yeah Joseph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+at least the English pronunciation
+
+ align:start position:0%
+at least the English pronunciation
+ 
+
+ align:start position:0%
+at least the English pronunciation
+starts really oh yeah but in Arabic I
+
+ align:start position:0%
+starts really oh yeah but in Arabic I
+ 
+
+ align:start position:0%
+starts really oh yeah but in Arabic I
+think it doesn't so uh so the baby maybe
+
+ align:start position:0%
+think it doesn't so uh so the baby maybe
+ 
+
+ align:start position:0%
+think it doesn't so uh so the baby maybe
+you know do you know what algebra is in
+
+ align:start position:0%
+you know do you know what algebra is in
+ 
+
+ align:start position:0%
+you know do you know what algebra is in
+in Arabic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay
+
+ align:start position:0%
+oh okay
+ 
+
+ align:start position:0%
+oh okay
+so I got it backwards yeah so we we uh
+
+ align:start position:0%
+so I got it backwards yeah so we we uh
+ 
+
+ align:start position:0%
+so I got it backwards yeah so we we uh
+we kept the L we didn't do the change so
+
+ align:start position:0%
+we kept the L we didn't do the change so
+ 
+
+ align:start position:0%
+we kept the L we didn't do the change so
+it starts it starts with a J uh starts
+
+ align:start position:0%
+it starts it starts with a J uh starts
+ 
+
+ align:start position:0%
+it starts it starts with a J uh starts
+with a chord and I'll but it didn't do
+
+ align:start position:0%
+with a chord and I'll but it didn't do
+ 
+
+ align:start position:0%
+with a chord and I'll but it didn't do
+the change I wonder whether we borrowed
+
+ align:start position:0%
+the change I wonder whether we borrowed
+ 
+
+ align:start position:0%
+the change I wonder whether we borrowed
+it before Arabic did this sound change
+
+ align:start position:0%
+it before Arabic did this sound change
+ 
+
+ align:start position:0%
+it before Arabic did this sound change
+uh I have no idea I don't know enough
+
+ align:start position:0%
+uh I have no idea I don't know enough
+ 
+
+ align:start position:0%
+uh I have no idea I don't know enough
+about the history of Arabic
+
+ align:start position:0%
+about the history of Arabic
+ 
+
+ align:start position:0%
+about the history of Arabic
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is one kind of rule uh it's a
+
+ align:start position:0%
+so this is one kind of rule uh it's a
+ 
+
+ align:start position:0%
+so this is one kind of rule uh it's a
+very common kind of rule where one sound
+
+ align:start position:0%
+very common kind of rule where one sound
+ 
+
+ align:start position:0%
+very common kind of rule where one sound
+becomes more like another sound it's
+
+ align:start position:0%
+becomes more like another sound it's
+ 
+
+ align:start position:0%
+becomes more like another sound it's
+called the simulation
+
+ align:start position:0%
+called the simulation
+ 
+
+ align:start position:0%
+called the simulation
+um and uh this particular case it's
+
+ align:start position:0%
+um and uh this particular case it's
+ 
+
+ align:start position:0%
+um and uh this particular case it's
+what's sometimes called total
+
+ align:start position:0%
+what's sometimes called total
+ 
+
+ align:start position:0%
+what's sometimes called total
+assimilation where uh one sound just
+
+ align:start position:0%
+assimilation where uh one sound just
+ 
+
+ align:start position:0%
+assimilation where uh one sound just
+becomes a complete copy of another sound
+
+ align:start position:0%
+becomes a complete copy of another sound
+ 
+
+ align:start position:0%
+becomes a complete copy of another sound
+we'll see other cases where one sound
+
+ align:start position:0%
+we'll see other cases where one sound
+ 
+
+ align:start position:0%
+we'll see other cases where one sound
+just kind of changes in ways that
+
+ align:start position:0%
+just kind of changes in ways that
+ 
+
+ align:start position:0%
+just kind of changes in ways that
+resemble a nearby sound
+
+ align:start position:0%
+resemble a nearby sound
+ 
+
+ align:start position:0%
+resemble a nearby sound
+um uh why do you do assimilation
+
+ align:start position:0%
+um uh why do you do assimilation
+ 
+
+ align:start position:0%
+um uh why do you do assimilation
+languages do assimilation all the time
+
+ align:start position:0%
+languages do assimilation all the time
+ 
+
+ align:start position:0%
+languages do assimilation all the time
+and you sort of not hard to have
+
+ align:start position:0%
+and you sort of not hard to have
+ 
+
+ align:start position:0%
+and you sort of not hard to have
+pre-theoretical Notions about why right
+
+ align:start position:0%
+pre-theoretical Notions about why right
+ 
+
+ align:start position:0%
+pre-theoretical Notions about why right
+that you're saving wear and tear on your
+
+ align:start position:0%
+that you're saving wear and tear on your
+ 
+
+ align:start position:0%
+that you're saving wear and tear on your
+articulators uh so you know making it so
+
+ align:start position:0%
+articulators uh so you know making it so
+ 
+
+ align:start position:0%
+articulators uh so you know making it so
+that your articulators your tongue your
+
+ align:start position:0%
+that your articulators your tongue your
+ 
+
+ align:start position:0%
+that your articulators your tongue your
+lips you know uh uh velum don't have to
+
+ align:start position:0%
+lips you know uh uh velum don't have to
+ 
+
+ align:start position:0%
+lips you know uh uh velum don't have to
+do as much moving around uh things uh
+
+ align:start position:0%
+do as much moving around uh things uh
+ 
+
+ align:start position:0%
+do as much moving around uh things uh
+don't move as far or don't move at all
+
+ align:start position:0%
+don't move as far or don't move at all
+ 
+
+ align:start position:0%
+don't move as far or don't move at all
+it probably also makes perception easier
+
+ align:start position:0%
+it probably also makes perception easier
+ 
+
+ align:start position:0%
+it probably also makes perception easier
+in the sense that
+
+ align:start position:0%
+in the sense that
+ 
+
+ align:start position:0%
+in the sense that
+um if you're speaking Arabic and you uh
+
+ align:start position:0%
+um if you're speaking Arabic and you uh
+ 
+
+ align:start position:0%
+um if you're speaking Arabic and you uh
+instead of an L so for uh let's take the
+
+ align:start position:0%
+instead of an L so for uh let's take the
+ 
+
+ align:start position:0%
+instead of an L so for uh let's take the
+Sun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh you know if you know that the word
+
+ align:start position:0%
+um uh you know if you know that the word
+ 
+
+ align:start position:0%
+um uh you know if you know that the word
+for sun is shem's uh and you've got this
+
+ align:start position:0%
+for sun is shem's uh and you've got this
+ 
+
+ align:start position:0%
+for sun is shem's uh and you've got this
+thing before it
+
+ align:start position:0%
+thing before it
+ 
+
+ align:start position:0%
+thing before it
+um basically it's as though you only
+
+ align:start position:0%
+um basically it's as though you only
+ 
+
+ align:start position:0%
+um basically it's as though you only
+need to give your hearer enough
+
+ align:start position:0%
+need to give your hearer enough
+ 
+
+ align:start position:0%
+need to give your hearer enough
+information to help them to know that
+
+ align:start position:0%
+information to help them to know that
+ 
+
+ align:start position:0%
+information to help them to know that
+they're hearing a definite article
+
+ align:start position:0%
+they're hearing a definite article
+ 
+
+ align:start position:0%
+they're hearing a definite article
+before the word for sun
+
+ align:start position:0%
+before the word for sun
+ 
+
+ align:start position:0%
+before the word for sun
+um and Arabic has decided uh it's enough
+
+ align:start position:0%
+um and Arabic has decided uh it's enough
+ 
+
+ align:start position:0%
+um and Arabic has decided uh it's enough
+if you hear the glottal stop and the
+
+ align:start position:0%
+if you hear the glottal stop and the
+ 
+
+ align:start position:0%
+if you hear the glottal stop and the
+vowel and then a coronal yeah
+
+ align:start position:0%
+vowel and then a coronal yeah
+ 
+
+ align:start position:0%
+vowel and then a coronal yeah
+underlyingly that Cardinal maybe is an L
+
+ align:start position:0%
+underlyingly that Cardinal maybe is an L
+ 
+
+ align:start position:0%
+underlyingly that Cardinal maybe is an L
+but as long as we keep it coronal we've
+
+ align:start position:0%
+but as long as we keep it coronal we've
+ 
+
+ align:start position:0%
+but as long as we keep it coronal we've
+given the hearer enough uh that they get
+
+ align:start position:0%
+given the hearer enough uh that they get
+ 
+
+ align:start position:0%
+given the hearer enough uh that they get
+to hear it and in fact we give the
+
+ align:start position:0%
+to hear it and in fact we give the
+ 
+
+ align:start position:0%
+to hear it and in fact we give the
+hearer in a sense two shots of hearing
+
+ align:start position:0%
+hearer in a sense two shots of hearing
+ 
+
+ align:start position:0%
+hearer in a sense two shots of hearing
+the beginning of the word for sun you
+
+ align:start position:0%
+the beginning of the word for sun you
+ 
+
+ align:start position:0%
+the beginning of the word for sun you
+know so we'll have we'll we'll and we'll
+
+ align:start position:0%
+know so we'll have we'll we'll and we'll
+ 
+
+ align:start position:0%
+know so we'll have we'll we'll and we'll
+lengthen that sound right so we'll we'll
+
+ align:start position:0%
+lengthen that sound right so we'll we'll
+ 
+
+ align:start position:0%
+lengthen that sound right so we'll we'll
+pronounce it twice
+
+ align:start position:0%
+pronounce it twice
+ 
+
+ align:start position:0%
+pronounce it twice
+um so we're sort of redistributing the
+
+ align:start position:0%
+um so we're sort of redistributing the
+ 
+
+ align:start position:0%
+um so we're sort of redistributing the
+signal in a way uh to the hearer to make
+
+ align:start position:0%
+signal in a way uh to the hearer to make
+ 
+
+ align:start position:0%
+signal in a way uh to the hearer to make
+to make their life arguably easier
+
+ align:start position:0%
+to make their life arguably easier
+ 
+
+ align:start position:0%
+to make their life arguably easier
+giving up some of what makes the
+
+ align:start position:0%
+giving up some of what makes the
+ 
+
+ align:start position:0%
+giving up some of what makes the
+definite article distinctive in order to
+
+ align:start position:0%
+definite article distinctive in order to
+ 
+
+ align:start position:0%
+definite article distinctive in order to
+emphasize some of some the beginning of
+
+ align:start position:0%
+emphasize some of some the beginning of
+ 
+
+ align:start position:0%
+emphasize some of some the beginning of
+the word for sun no
+
+ align:start position:0%
+the word for sun no
+ 
+
+ align:start position:0%
+the word for sun no
+questions about any of this yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I I was I was trying to to sort of
+
+ align:start position:0%
+so I I was I was trying to to sort of
+ 
+
+ align:start position:0%
+so I I was I was trying to to sort of
+float the idea that it's partly to make
+
+ align:start position:0%
+float the idea that it's partly to make
+ 
+
+ align:start position:0%
+float the idea that it's partly to make
+the pronunciation easier it's so that uh
+
+ align:start position:0%
+the pronunciation easier it's so that uh
+ 
+
+ align:start position:0%
+the pronunciation easier it's so that uh
+your articulators are not having to move
+
+ align:start position:0%
+your articulators are not having to move
+ 
+
+ align:start position:0%
+your articulators are not having to move
+as fast or as far
+
+ align:start position:0%
+as fast or as far
+ 
+
+ align:start position:0%
+as fast or as far
+um but it might also uh make perception
+
+ align:start position:0%
+um but it might also uh make perception
+ 
+
+ align:start position:0%
+um but it might also uh make perception
+in some ways easier in a case like this
+
+ align:start position:0%
+in some ways easier in a case like this
+ 
+
+ align:start position:0%
+in some ways easier in a case like this
+so uh the idea is we'll give up some of
+
+ align:start position:0%
+so uh the idea is we'll give up some of
+ 
+
+ align:start position:0%
+so uh the idea is we'll give up some of
+the special properties of the definite
+
+ align:start position:0%
+the special properties of the definite
+ 
+
+ align:start position:0%
+the special properties of the definite
+article in favor of emphasizing or
+
+ align:start position:0%
+article in favor of emphasizing or
+ 
+
+ align:start position:0%
+article in favor of emphasizing or
+holding for longer the special
+
+ align:start position:0%
+holding for longer the special
+ 
+
+ align:start position:0%
+holding for longer the special
+properties of the word for sun
+
+ align:start position:0%
+properties of the word for sun
+ 
+
+ align:start position:0%
+properties of the word for sun
+or whatever you know the consonant
+
+ align:start position:0%
+or whatever you know the consonant
+ 
+
+ align:start position:0%
+or whatever you know the consonant
+that's at the beginning of the of the
+
+ align:start position:0%
+that's at the beginning of the of the
+ 
+
+ align:start position:0%
+that's at the beginning of the of the
+following now
+
+ align:start position:0%
+following now
+ 
+
+ align:start position:0%
+following now
+um so we'll emphasize some parts of the
+
+ align:start position:0%
+um so we'll emphasize some parts of the
+ 
+
+ align:start position:0%
+um so we'll emphasize some parts of the
+in some ways least predictable part of
+
+ align:start position:0%
+in some ways least predictable part of
+ 
+
+ align:start position:0%
+in some ways least predictable part of
+this you presumably hear definite
+
+ align:start position:0%
+this you presumably hear definite
+ 
+
+ align:start position:0%
+this you presumably hear definite
+articles all the time it's not so
+
+ align:start position:0%
+articles all the time it's not so
+ 
+
+ align:start position:0%
+articles all the time it's not so
+important that you you know get lots of
+
+ align:start position:0%
+important that you you know get lots of
+ 
+
+ align:start position:0%
+important that you you know get lots of
+Clues to the fact that this is an
+
+ align:start position:0%
+Clues to the fact that this is an
+ 
+
+ align:start position:0%
+Clues to the fact that this is an
+infinite article the nouns are going to
+
+ align:start position:0%
+infinite article the nouns are going to
+ 
+
+ align:start position:0%
+infinite article the nouns are going to
+vary you know here are more different
+
+ align:start position:0%
+vary you know here are more different
+ 
+
+ align:start position:0%
+vary you know here are more different
+kinds of nouns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep okay cool uh this is probably a good
+
+ align:start position:0%
+yep okay cool uh this is probably a good
+ 
+
+ align:start position:0%
+yep okay cool uh this is probably a good
+place to stop so let's stop here and uh
+
+ align:start position:0%
+place to stop so let's stop here and uh
+ 
+
+ align:start position:0%
+place to stop so let's stop here and uh
+have a good weekend and I'll see you
+
+ align:start position:0%
+have a good weekend and I'll see you
+ 
+
+ align:start position:0%
+have a good weekend and I'll see you
+guys uh see you guys next week
\ No newline at end of file
diff --git a/-dAgY_AMqGk.txt b/-dAgY_AMqGk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b7d126160fdbc44e3f218276eae22af198e67508
--- /dev/null
+++ b/-dAgY_AMqGk.txt
@@ -0,0 +1,14739 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and say look i'm writing a term paper
+
+ align:start position:0%
+and say look i'm writing a term paper
+ 
+
+ align:start position:0%
+and say look i'm writing a term paper
+on your article you know
+
+ align:start position:0%
+on your article you know
+ 
+
+ align:start position:0%
+on your article you know
+like to ask you a few questions
+
+ align:start position:0%
+like to ask you a few questions
+ 
+
+ align:start position:0%
+like to ask you a few questions
+uh because if when it comes to
+
+ align:start position:0%
+uh because if when it comes to
+ 
+
+ align:start position:0%
+uh because if when it comes to
+engineering ethics there's about a uh if
+
+ align:start position:0%
+engineering ethics there's about a uh if
+ 
+
+ align:start position:0%
+engineering ethics there's about a uh if
+it's strictly engineering ethics as
+
+ align:start position:0%
+it's strictly engineering ethics as
+ 
+
+ align:start position:0%
+it's strictly engineering ethics as
+opposed to
+
+ align:start position:0%
+opposed to
+ 
+
+ align:start position:0%
+opposed to
+other kinds of i mean the more general
+
+ align:start position:0%
+other kinds of i mean the more general
+ 
+
+ align:start position:0%
+other kinds of i mean the more general
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+there's a 90 chance that i will know who
+
+ align:start position:0%
+there's a 90 chance that i will know who
+ 
+
+ align:start position:0%
+there's a 90 chance that i will know who
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+or the author of who you're talking
+
+ align:start position:0%
+or the author of who you're talking
+ 
+
+ align:start position:0%
+or the author of who you're talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+tell you a little bit where they're
+
+ align:start position:0%
+tell you a little bit where they're
+ 
+
+ align:start position:0%
+tell you a little bit where they're
+coming from and invite you to call them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well uh we got a good day today
+
+ align:start position:0%
+okay well uh we got a good day today
+ 
+
+ align:start position:0%
+okay well uh we got a good day today
+uh what i'd like to do is to i'm giving
+
+ align:start position:0%
+uh what i'd like to do is to i'm giving
+ 
+
+ align:start position:0%
+uh what i'd like to do is to i'm giving
+your papers back what i'd like to do is
+
+ align:start position:0%
+your papers back what i'd like to do is
+ 
+
+ align:start position:0%
+your papers back what i'd like to do is
+to review the papers but i want your
+
+ align:start position:0%
+to review the papers but i want your
+ 
+
+ align:start position:0%
+to review the papers but i want your
+permission
+
+ align:start position:0%
+permission
+ 
+
+ align:start position:0%
+permission
+what i want to do is to make an
+
+ align:start position:0%
+what i want to do is to make an
+ 
+
+ align:start position:0%
+what i want to do is to make an
+anonymous review but i want to make it
+
+ align:start position:0%
+anonymous review but i want to make it
+ 
+
+ align:start position:0%
+anonymous review but i want to make it
+public i want to read it out to
+
+ align:start position:0%
+public i want to read it out to
+ 
+
+ align:start position:0%
+public i want to read it out to
+everybody nobody will know who said what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's only two of us
+
+ align:start position:0%
+there's only two of us
+ 
+
+ align:start position:0%
+there's only two of us
+well they don't know which one of you
+
+ align:start position:0%
+well they don't know which one of you
+ 
+
+ align:start position:0%
+well they don't know which one of you
+i'll tell you what it's not it doesn't i
+
+ align:start position:0%
+i'll tell you what it's not it doesn't i
+ 
+
+ align:start position:0%
+i'll tell you what it's not it doesn't i
+don't care
+
+ align:start position:0%
+don't care
+ 
+
+ align:start position:0%
+don't care
+well let's see let's see how it goes i i
+
+ align:start position:0%
+well let's see let's see how it goes i i
+ 
+
+ align:start position:0%
+well let's see let's see how it goes i i
+there's nothing in here that's gonna
+
+ align:start position:0%
+there's nothing in here that's gonna
+ 
+
+ align:start position:0%
+there's nothing in here that's gonna
+that i have to say that's gonna be you
+
+ align:start position:0%
+that i have to say that's gonna be you
+ 
+
+ align:start position:0%
+that i have to say that's gonna be you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+anything that's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let me use some judgment and see
+
+ align:start position:0%
+well let me use some judgment and see
+ 
+
+ align:start position:0%
+well let me use some judgment and see
+how it goes
+
+ align:start position:0%
+how it goes
+ 
+
+ align:start position:0%
+how it goes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what i want you to do is i'm gonna
+
+ align:start position:0%
+now what i want you to do is i'm gonna
+ 
+
+ align:start position:0%
+now what i want you to do is i'm gonna
+the grade that i have put down here
+
+ align:start position:0%
+the grade that i have put down here
+ 
+
+ align:start position:0%
+the grade that i have put down here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is not the grade for the paper you gave
+
+ align:start position:0%
+is not the grade for the paper you gave
+ 
+
+ align:start position:0%
+is not the grade for the paper you gave
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+the grade that i put down here is for
+
+ align:start position:0%
+the grade that i put down here is for
+ 
+
+ align:start position:0%
+the grade that i put down here is for
+your second draft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that will respond to my comments
+
+ align:start position:0%
+that will respond to my comments
+ 
+
+ align:start position:0%
+that will respond to my comments
+and that you can save you don't give
+
+ align:start position:0%
+and that you can save you don't give
+ 
+
+ align:start position:0%
+and that you can save you don't give
+back to me but you can say but you can
+
+ align:start position:0%
+back to me but you can say but you can
+ 
+
+ align:start position:0%
+back to me but you can say but you can
+talk to me about it
+
+ align:start position:0%
+talk to me about it
+ 
+
+ align:start position:0%
+talk to me about it
+okay uh as we go along in other words i
+
+ align:start position:0%
+okay uh as we go along in other words i
+ 
+
+ align:start position:0%
+okay uh as we go along in other words i
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+i said the beginning of class i want to
+
+ align:start position:0%
+i said the beginning of class i want to
+ 
+
+ align:start position:0%
+i said the beginning of class i want to
+see improve
+
+ align:start position:0%
+see improve
+ 
+
+ align:start position:0%
+see improve
+all right so i want you to feel like you
+
+ align:start position:0%
+all right so i want you to feel like you
+ 
+
+ align:start position:0%
+all right so i want you to feel like you
+can doctor this thing up a little bit
+
+ align:start position:0%
+can doctor this thing up a little bit
+ 
+
+ align:start position:0%
+can doctor this thing up a little bit
+okay uh i marked good in several cases
+
+ align:start position:0%
+okay uh i marked good in several cases
+ 
+
+ align:start position:0%
+okay uh i marked good in several cases
+on both papers because mainly because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not because you made good uh
+
+ align:start position:0%
+not because you made good uh
+ 
+
+ align:start position:0%
+not because you made good uh
+observations which you did
+
+ align:start position:0%
+observations which you did
+ 
+
+ align:start position:0%
+observations which you did
+and good thoughts gave me some good
+
+ align:start position:0%
+and good thoughts gave me some good
+ 
+
+ align:start position:0%
+and good thoughts gave me some good
+thoughts but i was actually surprised
+
+ align:start position:0%
+thoughts but i was actually surprised
+ 
+
+ align:start position:0%
+thoughts but i was actually surprised
+positively surprised by the good
+
+ align:start position:0%
+positively surprised by the good
+ 
+
+ align:start position:0%
+positively surprised by the good
+thoughts that both of you had put in
+
+ align:start position:0%
+thoughts that both of you had put in
+ 
+
+ align:start position:0%
+thoughts that both of you had put in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+but it was little things like
+
+ align:start position:0%
+but it was little things like
+ 
+
+ align:start position:0%
+but it was little things like
+that you did get a reference that i had
+
+ align:start position:0%
+that you did get a reference that i had
+ 
+
+ align:start position:0%
+that you did get a reference that i had
+not brought in and you did it on your
+
+ align:start position:0%
+not brought in and you did it on your
+ 
+
+ align:start position:0%
+not brought in and you did it on your
+own that was good okay and for example
+
+ align:start position:0%
+own that was good okay and for example
+ 
+
+ align:start position:0%
+own that was good okay and for example
+um i didn't make a distinction
+
+ align:start position:0%
+um i didn't make a distinction
+ 
+
+ align:start position:0%
+um i didn't make a distinction
+uh between um
+
+ align:start position:0%
+uh between um
+ 
+
+ align:start position:0%
+uh between um
+act and rule utilitarianism
+
+ align:start position:0%
+act and rule utilitarianism
+ 
+
+ align:start position:0%
+act and rule utilitarianism
+and you all figure that out
+
+ align:start position:0%
+and you all figure that out
+ 
+
+ align:start position:0%
+and you all figure that out
+that's the kind of stuff i'm looking for
+
+ align:start position:0%
+that's the kind of stuff i'm looking for
+ 
+
+ align:start position:0%
+that's the kind of stuff i'm looking for
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+another one is an anomaly uh that's just
+
+ align:start position:0%
+another one is an anomaly uh that's just
+ 
+
+ align:start position:0%
+another one is an anomaly uh that's just
+in the field let me tell you let me give
+
+ align:start position:0%
+in the field let me tell you let me give
+ 
+
+ align:start position:0%
+in the field let me tell you let me give
+you something to remember that we that
+
+ align:start position:0%
+you something to remember that we that
+ 
+
+ align:start position:0%
+you something to remember that we that
+will cause you to remember it
+
+ align:start position:0%
+will cause you to remember it
+ 
+
+ align:start position:0%
+will cause you to remember it
+it's a little game that you can play
+
+ align:start position:0%
+it's a little game that you can play
+ 
+
+ align:start position:0%
+it's a little game that you can play
+with three-year-olds
+
+ align:start position:0%
+with three-year-olds
+ 
+
+ align:start position:0%
+with three-year-olds
+you ever play y'all play around with
+
+ align:start position:0%
+you ever play y'all play around with
+ 
+
+ align:start position:0%
+you ever play y'all play around with
+kids
+
+ align:start position:0%
+kids
+ 
+
+ align:start position:0%
+kids
+three-year-olds four-year-olds it's a
+
+ align:start position:0%
+three-year-olds four-year-olds it's a
+ 
+
+ align:start position:0%
+three-year-olds four-year-olds it's a
+little game but it is very my experience
+
+ align:start position:0%
+little game but it is very my experience
+ 
+
+ align:start position:0%
+little game but it is very my experience
+with telling it we're playing this game
+
+ align:start position:0%
+with telling it we're playing this game
+ 
+
+ align:start position:0%
+with telling it we're playing this game
+with these little kids is very
+
+ align:start position:0%
+with these little kids is very
+ 
+
+ align:start position:0%
+with these little kids is very
+very interesting
+
+ align:start position:0%
+very interesting
+ 
+
+ align:start position:0%
+very interesting
+and that is you sit you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what has a big head
+
+ align:start position:0%
+what has a big head
+ 
+
+ align:start position:0%
+what has a big head
+red eyes and each rocks
+
+ align:start position:0%
+red eyes and each rocks
+ 
+
+ align:start position:0%
+red eyes and each rocks
+kisses i don't know
+
+ align:start position:0%
+kisses i don't know
+ 
+
+ align:start position:0%
+kisses i don't know
+you say a big headed red eyed rock eater
+
+ align:start position:0%
+you say a big headed red eyed rock eater
+ 
+
+ align:start position:0%
+you say a big headed red eyed rock eater
+because it's okay
+
+ align:start position:0%
+because it's okay
+ 
+
+ align:start position:0%
+because it's okay
+then you say what has a big a big head
+
+ align:start position:0%
+then you say what has a big a big head
+ 
+
+ align:start position:0%
+then you say what has a big a big head
+yellow eyes at these rocks
+
+ align:start position:0%
+yellow eyes at these rocks
+ 
+
+ align:start position:0%
+yellow eyes at these rocks
+and the kid says a big-headed
+
+ align:start position:0%
+and the kid says a big-headed
+ 
+
+ align:start position:0%
+and the kid says a big-headed
+yellow-eyed
+
+ align:start position:0%
+yellow-eyed
+ 
+
+ align:start position:0%
+yellow-eyed
+rock eater
+
+ align:start position:0%
+rock eater
+ 
+
+ align:start position:0%
+rock eater
+you say no
+
+ align:start position:0%
+you say no
+ 
+
+ align:start position:0%
+you say no
+they only come in red
+
+ align:start position:0%
+they only come in red
+ 
+
+ align:start position:0%
+they only come in red
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+my experience is that four-year-olds see
+
+ align:start position:0%
+my experience is that four-year-olds see
+ 
+
+ align:start position:0%
+my experience is that four-year-olds see
+the point to that that's just the way
+
+ align:start position:0%
+the point to that that's just the way
+ 
+
+ align:start position:0%
+the point to that that's just the way
+life is
+
+ align:start position:0%
+life is
+ 
+
+ align:start position:0%
+life is
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in ethics you'll find a lot of this
+
+ align:start position:0%
+now in ethics you'll find a lot of this
+ 
+
+ align:start position:0%
+now in ethics you'll find a lot of this
+you'll find deontological ethics
+
+ align:start position:0%
+you'll find deontological ethics
+ 
+
+ align:start position:0%
+you'll find deontological ethics
+but nobody very few people not a lot of
+
+ align:start position:0%
+but nobody very few people not a lot of
+ 
+
+ align:start position:0%
+but nobody very few people not a lot of
+people talk about ontological ethics
+
+ align:start position:0%
+people talk about ontological ethics
+ 
+
+ align:start position:0%
+people talk about ontological ethics
+don't be bothered by that
+
+ align:start position:0%
+don't be bothered by that
+ 
+
+ align:start position:0%
+don't be bothered by that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and there'll be a lot of those
+
+ align:start position:0%
+and there'll be a lot of those
+ 
+
+ align:start position:0%
+and there'll be a lot of those
+there'll be a lot of uh let me see if i
+
+ align:start position:0%
+there'll be a lot of uh let me see if i
+ 
+
+ align:start position:0%
+there'll be a lot of uh let me see if i
+can think of another one um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they'll talk about consequentialist and
+
+ align:start position:0%
+they'll talk about consequentialist and
+ 
+
+ align:start position:0%
+they'll talk about consequentialist and
+non-consequentials
+
+ align:start position:0%
+non-consequentials
+ 
+
+ align:start position:0%
+non-consequentials
+but there's another one i'll think of it
+
+ align:start position:0%
+but there's another one i'll think of it
+ 
+
+ align:start position:0%
+but there's another one i'll think of it
+before the class is over but there are a
+
+ align:start position:0%
+before the class is over but there are a
+ 
+
+ align:start position:0%
+before the class is over but there are a
+lot of these little anomaly anomalies
+
+ align:start position:0%
+lot of these little anomaly anomalies
+ 
+
+ align:start position:0%
+lot of these little anomaly anomalies
+just don't let them bother you but pick
+
+ align:start position:0%
+just don't let them bother you but pick
+ 
+
+ align:start position:0%
+just don't let them bother you but pick
+them up pick them up
+
+ align:start position:0%
+them up pick them up
+ 
+
+ align:start position:0%
+them up pick them up
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+another thing is um
+
+ align:start position:0%
+another thing is um
+ 
+
+ align:start position:0%
+another thing is um
+that this case is more properly called
+
+ align:start position:0%
+that this case is more properly called
+ 
+
+ align:start position:0%
+that this case is more properly called
+the a7d case
+
+ align:start position:0%
+the a7d case
+ 
+
+ align:start position:0%
+the a7d case
+than the a7 case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the nomenclature
+
+ align:start position:0%
+it's the nomenclature
+ 
+
+ align:start position:0%
+it's the nomenclature
+for the for the uh for the break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+now here's here's one here's a very
+
+ align:start position:0%
+now here's here's one here's a very
+ 
+
+ align:start position:0%
+now here's here's one here's a very
+significant teaching point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very significant
+
+ align:start position:0%
+very significant
+ 
+
+ align:start position:0%
+very significant
+teaching point for this kind of class
+
+ align:start position:0%
+teaching point for this kind of class
+ 
+
+ align:start position:0%
+teaching point for this kind of class
+on the one hand
+
+ align:start position:0%
+on the one hand
+ 
+
+ align:start position:0%
+on the one hand
+a prescription for behavior
+
+ align:start position:0%
+a prescription for behavior
+ 
+
+ align:start position:0%
+a prescription for behavior
+is made more compelling
+
+ align:start position:0%
+is made more compelling
+ 
+
+ align:start position:0%
+is made more compelling
+i agree
+
+ align:start position:0%
+i agree
+ 
+
+ align:start position:0%
+i agree
+if you use two very different approaches
+
+ align:start position:0%
+if you use two very different approaches
+ 
+
+ align:start position:0%
+if you use two very different approaches
+and come up with the same prescription
+
+ align:start position:0%
+and come up with the same prescription
+ 
+
+ align:start position:0%
+and come up with the same prescription
+that's very compelling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in ethics there's no reason
+
+ align:start position:0%
+but in ethics there's no reason
+ 
+
+ align:start position:0%
+but in ethics there's no reason
+that two prescriptions should be the
+
+ align:start position:0%
+that two prescriptions should be the
+ 
+
+ align:start position:0%
+that two prescriptions should be the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you get different prescriptions you
+
+ align:start position:0%
+if you get different prescriptions you
+ 
+
+ align:start position:0%
+if you get different prescriptions you
+don't have to say you need more work
+
+ align:start position:0%
+don't have to say you need more work
+ 
+
+ align:start position:0%
+don't have to say you need more work
+that's that's the way it can end
+
+ align:start position:0%
+that's that's the way it can end
+ 
+
+ align:start position:0%
+that's that's the way it can end
+okay what you're really looking for is
+
+ align:start position:0%
+okay what you're really looking for is
+ 
+
+ align:start position:0%
+okay what you're really looking for is
+the defensibility of it
+
+ align:start position:0%
+the defensibility of it
+ 
+
+ align:start position:0%
+the defensibility of it
+so um i could give you a classic case
+
+ align:start position:0%
+so um i could give you a classic case
+ 
+
+ align:start position:0%
+so um i could give you a classic case
+one that i think you should think over
+
+ align:start position:0%
+one that i think you should think over
+ 
+
+ align:start position:0%
+one that i think you should think over
+if you had probably one that you thought
+
+ align:start position:0%
+if you had probably one that you thought
+ 
+
+ align:start position:0%
+if you had probably one that you thought
+of before
+
+ align:start position:0%
+of before
+ 
+
+ align:start position:0%
+of before
+it doesn't have a name but uh you've
+
+ align:start position:0%
+it doesn't have a name but uh you've
+ 
+
+ align:start position:0%
+it doesn't have a name but uh you've
+seen it in movies uh
+
+ align:start position:0%
+seen it in movies uh
+ 
+
+ align:start position:0%
+seen it in movies uh
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+ship sinks
+
+ align:start position:0%
+ship sinks
+ 
+
+ align:start position:0%
+ship sinks
+some people escape in a lifeboat
+
+ align:start position:0%
+some people escape in a lifeboat
+ 
+
+ align:start position:0%
+some people escape in a lifeboat
+there are 10 people in the lifeboat
+
+ align:start position:0%
+there are 10 people in the lifeboat
+ 
+
+ align:start position:0%
+there are 10 people in the lifeboat
+there's food enough
+
+ align:start position:0%
+there's food enough
+ 
+
+ align:start position:0%
+there's food enough
+for 10 people for a week but they don't
+
+ align:start position:0%
+for 10 people for a week but they don't
+ 
+
+ align:start position:0%
+for 10 people for a week but they don't
+expect to be picked up for a month
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you can come up come up with a
+
+ align:start position:0%
+well you can come up come up with a
+ 
+
+ align:start position:0%
+well you can come up come up with a
+whole lot of solutions
+
+ align:start position:0%
+whole lot of solutions
+ 
+
+ align:start position:0%
+whole lot of solutions
+that are very different even opposite
+
+ align:start position:0%
+that are very different even opposite
+ 
+
+ align:start position:0%
+that are very different even opposite
+and all of them are equally defensible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can come up with some solutions you
+
+ align:start position:0%
+you can come up with some solutions you
+ 
+
+ align:start position:0%
+you can come up with some solutions you
+can come up
+
+ align:start position:0%
+can come up
+ 
+
+ align:start position:0%
+can come up
+you can come up with a solution
+
+ align:start position:0%
+you can come up with a solution
+ 
+
+ align:start position:0%
+you can come up with a solution
+that is defensible i can come up with
+
+ align:start position:0%
+that is defensible i can come up with
+ 
+
+ align:start position:0%
+that is defensible i can come up with
+the same solution that is not defensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so i
+
+ align:start position:0%
+all right so i
+ 
+
+ align:start position:0%
+all right so i
+in an engineering class we
+
+ align:start position:0%
+in an engineering class we
+ 
+
+ align:start position:0%
+in an engineering class we
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+well let's put it this way in
+
+ align:start position:0%
+well let's put it this way in
+ 
+
+ align:start position:0%
+well let's put it this way in
+undergraduate engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is such a thing as the answer in
+
+ align:start position:0%
+there is such a thing as the answer in
+ 
+
+ align:start position:0%
+there is such a thing as the answer in
+the back of the book
+
+ align:start position:0%
+the back of the book
+ 
+
+ align:start position:0%
+the back of the book
+the operative word is the
+
+ align:start position:0%
+the operative word is the
+ 
+
+ align:start position:0%
+the operative word is the
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in graduate
+
+ align:start position:0%
+in graduate
+ 
+
+ align:start position:0%
+in graduate
+you're going to find you can get more
+
+ align:start position:0%
+you're going to find you can get more
+ 
+
+ align:start position:0%
+you're going to find you can get more
+than one answer
+
+ align:start position:0%
+than one answer
+ 
+
+ align:start position:0%
+than one answer
+and there's cost and benefits
+
+ align:start position:0%
+and there's cost and benefits
+ 
+
+ align:start position:0%
+and there's cost and benefits
+on either side
+
+ align:start position:0%
+on either side
+ 
+
+ align:start position:0%
+on either side
+out there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of good answers a lot of bad
+
+ align:start position:0%
+a lot of good answers a lot of bad
+ 
+
+ align:start position:0%
+a lot of good answers a lot of bad
+answers
+
+ align:start position:0%
+answers
+ 
+
+ align:start position:0%
+answers
+and what is going to count most in many
+
+ align:start position:0%
+and what is going to count most in many
+ 
+
+ align:start position:0%
+and what is going to count most in many
+situations
+
+ align:start position:0%
+situations
+ 
+
+ align:start position:0%
+situations
+is like it is here
+
+ align:start position:0%
+is like it is here
+ 
+
+ align:start position:0%
+is like it is here
+it's your argument
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and that's going to be because and
+
+ align:start position:0%
+uh and that's going to be because and
+ 
+
+ align:start position:0%
+uh and that's going to be because and
+and this is one thing that i try to
+
+ align:start position:0%
+and this is one thing that i try to
+ 
+
+ align:start position:0%
+and this is one thing that i try to
+direct my class to
+
+ align:start position:0%
+direct my class to
+ 
+
+ align:start position:0%
+direct my class to
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people just will not know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no matter what you say
+
+ align:start position:0%
+no matter what you say
+ 
+
+ align:start position:0%
+no matter what you say
+what the right answer is
+
+ align:start position:0%
+what the right answer is
+ 
+
+ align:start position:0%
+what the right answer is
+the question let me tell you a story i
+
+ align:start position:0%
+the question let me tell you a story i
+ 
+
+ align:start position:0%
+the question let me tell you a story i
+got another story let me just tell this
+
+ align:start position:0%
+got another story let me just tell this
+ 
+
+ align:start position:0%
+got another story let me just tell this
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+uh i'm a young assistant professor
+
+ align:start position:0%
+uh i'm a young assistant professor
+ 
+
+ align:start position:0%
+uh i'm a young assistant professor
+and i'm down there and i go down to um
+
+ align:start position:0%
+and i'm down there and i go down to um
+ 
+
+ align:start position:0%
+and i'm down there and i go down to um
+nasa langley research center this is in
+
+ align:start position:0%
+nasa langley research center this is in
+ 
+
+ align:start position:0%
+nasa langley research center this is in
+hampton virginia
+
+ align:start position:0%
+hampton virginia
+ 
+
+ align:start position:0%
+hampton virginia
+know about it
+
+ align:start position:0%
+know about it
+ 
+
+ align:start position:0%
+know about it
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+two summer internships really what
+
+ align:start position:0%
+two summer internships really what
+ 
+
+ align:start position:0%
+two summer internships really what
+division
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+branch uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah in the building where the mercury
+
+ align:start position:0%
+yeah in the building where the mercury
+ 
+
+ align:start position:0%
+yeah in the building where the mercury
+astronauts were trained whoa
+
+ align:start position:0%
+astronauts were trained whoa
+ 
+
+ align:start position:0%
+astronauts were trained whoa
+i was down there in the late 70s and
+
+ align:start position:0%
+i was down there in the late 70s and
+ 
+
+ align:start position:0%
+i was down there in the late 70s and
+almost all through the 80s
+
+ align:start position:0%
+almost all through the 80s
+ 
+
+ align:start position:0%
+almost all through the 80s
+i had grants with them for about 12
+
+ align:start position:0%
+i had grants with them for about 12
+ 
+
+ align:start position:0%
+i had grants with them for about 12
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and i and i had a relationship down
+
+ align:start position:0%
+and i and i had a relationship down
+ 
+
+ align:start position:0%
+and i and i had a relationship down
+there where
+
+ align:start position:0%
+there where
+ 
+
+ align:start position:0%
+there where
+i was going down there so often that
+
+ align:start position:0%
+i was going down there so often that
+ 
+
+ align:start position:0%
+i was going down there so often that
+what i do is rent a house i take
+
+ align:start position:0%
+what i do is rent a house i take
+ 
+
+ align:start position:0%
+what i do is rent a house i take
+students with me
+
+ align:start position:0%
+students with me
+ 
+
+ align:start position:0%
+students with me
+we live in the house
+
+ align:start position:0%
+we live in the house
+ 
+
+ align:start position:0%
+we live in the house
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+and um i did that uh
+
+ align:start position:0%
+and um i did that uh
+ 
+
+ align:start position:0%
+and um i did that uh
+eight or nine years i guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we would all get in the car
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ride down there and
+
+ align:start position:0%
+and ride down there and
+ 
+
+ align:start position:0%
+and ride down there and
+i had this little speech i'd give
+
+ align:start position:0%
+i had this little speech i'd give
+ 
+
+ align:start position:0%
+i had this little speech i'd give
+and i was unmarried at the time
+
+ align:start position:0%
+and i was unmarried at the time
+ 
+
+ align:start position:0%
+and i was unmarried at the time
+and i would tell them
+
+ align:start position:0%
+and i would tell them
+ 
+
+ align:start position:0%
+and i would tell them
+whatever happens in hampton
+
+ align:start position:0%
+whatever happens in hampton
+ 
+
+ align:start position:0%
+whatever happens in hampton
+stays in him
+
+ align:start position:0%
+stays in him
+ 
+
+ align:start position:0%
+stays in him
+okay i don't want any students coming
+
+ align:start position:0%
+okay i don't want any students coming
+ 
+
+ align:start position:0%
+okay i don't want any students coming
+back to howard saying i saw dr broome
+
+ align:start position:0%
+back to howard saying i saw dr broome
+ 
+
+ align:start position:0%
+back to howard saying i saw dr broome
+i said whatever happens down there stays
+
+ align:start position:0%
+i said whatever happens down there stays
+ 
+
+ align:start position:0%
+i said whatever happens down there stays
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so one year we were riding down there
+
+ align:start position:0%
+so one year we were riding down there
+ 
+
+ align:start position:0%
+so one year we were riding down there
+i was riding down there with four three
+
+ align:start position:0%
+i was riding down there with four three
+ 
+
+ align:start position:0%
+i was riding down there with four three
+students four students
+
+ align:start position:0%
+students four students
+ 
+
+ align:start position:0%
+students four students
+three students
+
+ align:start position:0%
+three students
+ 
+
+ align:start position:0%
+three students
+and uh i made my little speech
+
+ align:start position:0%
+and uh i made my little speech
+ 
+
+ align:start position:0%
+and uh i made my little speech
+they agreed with it
+
+ align:start position:0%
+they agreed with it
+ 
+
+ align:start position:0%
+they agreed with it
+and then one of them said does that go
+
+ align:start position:0%
+and then one of them said does that go
+ 
+
+ align:start position:0%
+and then one of them said does that go
+for us too
+
+ align:start position:0%
+for us too
+ 
+
+ align:start position:0%
+for us too
+and i thought there's never a case where
+
+ align:start position:0%
+and i thought there's never a case where
+ 
+
+ align:start position:0%
+and i thought there's never a case where
+i go back to howard deal with students
+
+ align:start position:0%
+i go back to howard deal with students
+ 
+
+ align:start position:0%
+i go back to howard deal with students
+you know i don't care what they did i
+
+ align:start position:0%
+you know i don't care what they did i
+ 
+
+ align:start position:0%
+you know i don't care what they did i
+just don't
+
+ align:start position:0%
+just don't
+ 
+
+ align:start position:0%
+just don't
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i said yeah i guess it goes for you too
+
+ align:start position:0%
+i said yeah i guess it goes for you too
+ 
+
+ align:start position:0%
+i said yeah i guess it goes for you too
+so they started lighting up these reefs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i said oh my god what have i got myself
+
+ align:start position:0%
+i said oh my god what have i got myself
+ 
+
+ align:start position:0%
+i said oh my god what have i got myself
+into then the police came
+
+ align:start position:0%
+into then the police came
+ 
+
+ align:start position:0%
+into then the police came
+it was because they were speaking
+
+ align:start position:0%
+it was because they were speaking
+ 
+
+ align:start position:0%
+it was because they were speaking
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we had they and there's a place in
+
+ align:start position:0%
+we had they and there's a place in
+ 
+
+ align:start position:0%
+we had they and there's a place in
+virginia i'm gonna tell you right now
+
+ align:start position:0%
+virginia i'm gonna tell you right now
+ 
+
+ align:start position:0%
+virginia i'm gonna tell you right now
+it's called uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's called uh
+
+ align:start position:0%
+it's called uh
+ 
+
+ align:start position:0%
+it's called uh
+what's it called
+
+ align:start position:0%
+what's it called
+ 
+
+ align:start position:0%
+what's it called
+i can't think of anybody but there's a
+
+ align:start position:0%
+i can't think of anybody but there's a
+ 
+
+ align:start position:0%
+i can't think of anybody but there's a
+place in virginia where if the police
+
+ align:start position:0%
+place in virginia where if the police
+ 
+
+ align:start position:0%
+place in virginia where if the police
+get you for speeding they don't give you
+
+ align:start position:0%
+get you for speeding they don't give you
+ 
+
+ align:start position:0%
+get you for speeding they don't give you
+a ticket on the spot
+
+ align:start position:0%
+a ticket on the spot
+ 
+
+ align:start position:0%
+a ticket on the spot
+they take you about 10 miles off the
+
+ align:start position:0%
+they take you about 10 miles off the
+ 
+
+ align:start position:0%
+they take you about 10 miles off the
+road to a special place
+
+ align:start position:0%
+road to a special place
+ 
+
+ align:start position:0%
+road to a special place
+where you have to fill out a form
+
+ align:start position:0%
+where you have to fill out a form
+ 
+
+ align:start position:0%
+where you have to fill out a form
+and you have to pay in cash
+
+ align:start position:0%
+and you have to pay in cash
+ 
+
+ align:start position:0%
+and you have to pay in cash
+he took us off and i said i know i'm
+
+ align:start position:0%
+he took us off and i said i know i'm
+ 
+
+ align:start position:0%
+he took us off and i said i know i'm
+going to jail
+
+ align:start position:0%
+going to jail
+ 
+
+ align:start position:0%
+going to jail
+that was 30 years ago
+
+ align:start position:0%
+that was 30 years ago
+ 
+
+ align:start position:0%
+that was 30 years ago
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+we got that the story is that that one
+
+ align:start position:0%
+we got that the story is that that one
+ 
+
+ align:start position:0%
+we got that the story is that that one
+day i went to what's called a division
+
+ align:start position:0%
+day i went to what's called a division
+ 
+
+ align:start position:0%
+day i went to what's called a division
+meeting this was the structures and
+
+ align:start position:0%
+meeting this was the structures and
+ 
+
+ align:start position:0%
+meeting this was the structures and
+dynamics division
+
+ align:start position:0%
+dynamics division
+ 
+
+ align:start position:0%
+dynamics division
+and i had to go to all of the division
+
+ align:start position:0%
+and i had to go to all of the division
+ 
+
+ align:start position:0%
+and i had to go to all of the division
+meetings
+
+ align:start position:0%
+meetings
+ 
+
+ align:start position:0%
+meetings
+and it got mean
+
+ align:start position:0%
+and it got mean
+ 
+
+ align:start position:0%
+and it got mean
+spirited in there that day so you
+
+ align:start position:0%
+spirited in there that day so you
+ 
+
+ align:start position:0%
+spirited in there that day so you
+imagine a room
+
+ align:start position:0%
+imagine a room
+ 
+
+ align:start position:0%
+imagine a room
+there's about 100 engineers
+
+ align:start position:0%
+there's about 100 engineers
+ 
+
+ align:start position:0%
+there's about 100 engineers
+95 of them have phd
+
+ align:start position:0%
+95 of them have phd
+ 
+
+ align:start position:0%
+95 of them have phd
+they call a place a campus when i was
+
+ align:start position:0%
+they call a place a campus when i was
+ 
+
+ align:start position:0%
+they call a place a campus when i was
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and these engineers were up making a
+
+ align:start position:0%
+and these engineers were up making a
+ 
+
+ align:start position:0%
+and these engineers were up making a
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+and the chief was sitting on the side
+
+ align:start position:0%
+and the chief was sitting on the side
+ 
+
+ align:start position:0%
+and the chief was sitting on the side
+and started quizzing them about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it got mean in there
+
+ align:start position:0%
+and it got mean in there
+ 
+
+ align:start position:0%
+and it got mean in there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he hit his hand fist on the table
+
+ align:start position:0%
+he hit his hand fist on the table
+ 
+
+ align:start position:0%
+he hit his hand fist on the table
+and it kept going round and round
+
+ align:start position:0%
+and it kept going round and round
+ 
+
+ align:start position:0%
+and it kept going round and round
+and so uh that was my first meeting i
+
+ align:start position:0%
+and so uh that was my first meeting i
+ 
+
+ align:start position:0%
+and so uh that was my first meeting i
+think and i said my god
+
+ align:start position:0%
+think and i said my god
+ 
+
+ align:start position:0%
+think and i said my god
+if i have to make a presentation in here
+
+ align:start position:0%
+if i have to make a presentation in here
+ 
+
+ align:start position:0%
+if i have to make a presentation in here
+i'm just going to have it ready because
+
+ align:start position:0%
+i'm just going to have it ready because
+ 
+
+ align:start position:0%
+i'm just going to have it ready because
+that was it was awful
+
+ align:start position:0%
+that was it was awful
+ 
+
+ align:start position:0%
+that was it was awful
+awful is the word
+
+ align:start position:0%
+awful is the word
+ 
+
+ align:start position:0%
+awful is the word
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so after that it was lunch time
+
+ align:start position:0%
+so after that it was lunch time
+ 
+
+ align:start position:0%
+so after that it was lunch time
+went to the cafeteria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this man
+
+ align:start position:0%
+and this man
+ 
+
+ align:start position:0%
+and this man
+sat at this long table
+
+ align:start position:0%
+sat at this long table
+ 
+
+ align:start position:0%
+sat at this long table
+after he got his tray set at this long
+
+ align:start position:0%
+after he got his tray set at this long
+ 
+
+ align:start position:0%
+after he got his tray set at this long
+table and nobody
+
+ align:start position:0%
+table and nobody
+ 
+
+ align:start position:0%
+table and nobody
+sat with him at that table not from the
+
+ align:start position:0%
+sat with him at that table not from the
+ 
+
+ align:start position:0%
+sat with him at that table not from the
+division
+
+ align:start position:0%
+division
+ 
+
+ align:start position:0%
+division
+not from anyplace else everybody went
+
+ align:start position:0%
+not from anyplace else everybody went
+ 
+
+ align:start position:0%
+not from anyplace else everybody went
+someplace else and said he's sitting
+
+ align:start position:0%
+someplace else and said he's sitting
+ 
+
+ align:start position:0%
+someplace else and said he's sitting
+over there by himself
+
+ align:start position:0%
+over there by himself
+ 
+
+ align:start position:0%
+over there by himself
+so i came up with my tray and i said i
+
+ align:start position:0%
+so i came up with my tray and i said i
+ 
+
+ align:start position:0%
+so i came up with my tray and i said i
+said look um
+
+ align:start position:0%
+said look um
+ 
+
+ align:start position:0%
+said look um
+i said would you mind some company
+
+ align:start position:0%
+i said would you mind some company
+ 
+
+ align:start position:0%
+i said would you mind some company
+no he said
+
+ align:start position:0%
+no he said
+ 
+
+ align:start position:0%
+no he said
+and so i said well i'm down here just
+
+ align:start position:0%
+and so i said well i'm down here just
+ 
+
+ align:start position:0%
+and so i said well i'm down here just
+for as you know just for the summer
+
+ align:start position:0%
+for as you know just for the summer
+ 
+
+ align:start position:0%
+for as you know just for the summer
+maybe next summer too but
+
+ align:start position:0%
+maybe next summer too but
+ 
+
+ align:start position:0%
+maybe next summer too but
+i said this is an opportunity for me to
+
+ align:start position:0%
+i said this is an opportunity for me to
+ 
+
+ align:start position:0%
+i said this is an opportunity for me to
+learn something
+
+ align:start position:0%
+learn something
+ 
+
+ align:start position:0%
+learn something
+i said it was a pretty
+
+ align:start position:0%
+i said it was a pretty
+ 
+
+ align:start position:0%
+i said it was a pretty
+pretty mean meeting you just had
+
+ align:start position:0%
+pretty mean meeting you just had
+ 
+
+ align:start position:0%
+pretty mean meeting you just had
+and i said to him i said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not only that
+
+ align:start position:0%
+not only that
+ 
+
+ align:start position:0%
+not only that
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it's called a state of space i said
+
+ align:start position:0%
+it's called a state of space i said
+ 
+
+ align:start position:0%
+it's called a state of space i said
+all those phds in there that you're
+
+ align:start position:0%
+all those phds in there that you're
+ 
+
+ align:start position:0%
+all those phds in there that you're
+tearing up and you don't even call the
+
+ align:start position:0%
+tearing up and you don't even call the
+ 
+
+ align:start position:0%
+tearing up and you don't even call the
+phd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masters
+
+ align:start position:0%
+masters
+ 
+
+ align:start position:0%
+masters
+from mit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i said how do you know when they're
+
+ align:start position:0%
+i said how do you know when they're
+ 
+
+ align:start position:0%
+i said how do you know when they're
+right or when they're wrong
+
+ align:start position:0%
+right or when they're wrong
+ 
+
+ align:start position:0%
+right or when they're wrong
+and he said being right or wrong is not
+
+ align:start position:0%
+and he said being right or wrong is not
+ 
+
+ align:start position:0%
+and he said being right or wrong is not
+the issue
+
+ align:start position:0%
+the issue
+ 
+
+ align:start position:0%
+the issue
+he said it's a question of commitment
+
+ align:start position:0%
+he said it's a question of commitment
+ 
+
+ align:start position:0%
+he said it's a question of commitment
+what are they willing to put their
+
+ align:start position:0%
+what are they willing to put their
+ 
+
+ align:start position:0%
+what are they willing to put their
+careers on
+
+ align:start position:0%
+careers on
+ 
+
+ align:start position:0%
+careers on
+he said so i put the heat on them
+
+ align:start position:0%
+he said so i put the heat on them
+ 
+
+ align:start position:0%
+he said so i put the heat on them
+and what i'm looking for is number one
+
+ align:start position:0%
+and what i'm looking for is number one
+ 
+
+ align:start position:0%
+and what i'm looking for is number one
+whether or not they're going to stand by
+
+ align:start position:0%
+whether or not they're going to stand by
+ 
+
+ align:start position:0%
+whether or not they're going to stand by
+what they said or whether they're going
+
+ align:start position:0%
+what they said or whether they're going
+ 
+
+ align:start position:0%
+what they said or whether they're going
+to start back back peddling
+
+ align:start position:0%
+to start back back peddling
+ 
+
+ align:start position:0%
+to start back back peddling
+and number two whether anybody sitting
+
+ align:start position:0%
+and number two whether anybody sitting
+ 
+
+ align:start position:0%
+and number two whether anybody sitting
+out there is going to join them or be
+
+ align:start position:0%
+out there is going to join them or be
+ 
+
+ align:start position:0%
+out there is going to join them or be
+glad it's not them
+
+ align:start position:0%
+glad it's not them
+ 
+
+ align:start position:0%
+glad it's not them
+he said you watched he said i put him
+
+ align:start position:0%
+he said you watched he said i put him
+ 
+
+ align:start position:0%
+he said you watched he said i put him
+under pressure
+
+ align:start position:0%
+under pressure
+ 
+
+ align:start position:0%
+under pressure
+after a while they started back peddling
+
+ align:start position:0%
+after a while they started back peddling
+ 
+
+ align:start position:0%
+after a while they started back peddling
+and nobody came to their aid so we're
+
+ align:start position:0%
+and nobody came to their aid so we're
+ 
+
+ align:start position:0%
+and nobody came to their aid so we're
+not going with those results
+
+ align:start position:0%
+not going with those results
+ 
+
+ align:start position:0%
+not going with those results
+they're probably right
+
+ align:start position:0%
+they're probably right
+ 
+
+ align:start position:0%
+they're probably right
+but we're not going with that
+
+ align:start position:0%
+but we're not going with that
+ 
+
+ align:start position:0%
+but we're not going with that
+he said if they stood up stood up to me
+
+ align:start position:0%
+he said if they stood up stood up to me
+ 
+
+ align:start position:0%
+he said if they stood up stood up to me
+he said he said this is government
+
+ align:start position:0%
+he said he said this is government
+ 
+
+ align:start position:0%
+he said he said this is government
+they know they're going to have there's
+
+ align:start position:0%
+they know they're going to have there's
+ 
+
+ align:start position:0%
+they know they're going to have there's
+going to be a rift coming around in a
+
+ align:start position:0%
+going to be a rift coming around in a
+ 
+
+ align:start position:0%
+going to be a rift coming around in a
+year or so
+
+ align:start position:0%
+year or so
+ 
+
+ align:start position:0%
+year or so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+these guys he's having fire now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he said but look
+
+ align:start position:0%
+he said but look
+ 
+
+ align:start position:0%
+he said but look
+he said if they had stood up to me
+
+ align:start position:0%
+he said if they had stood up to me
+ 
+
+ align:start position:0%
+he said if they had stood up to me
+and if a couple of them out of the
+
+ align:start position:0%
+and if a couple of them out of the
+ 
+
+ align:start position:0%
+and if a couple of them out of the
+audience stood up and stood with them
+
+ align:start position:0%
+audience stood up and stood with them
+ 
+
+ align:start position:0%
+audience stood up and stood with them
+he said that's what we're going to go
+
+ align:start position:0%
+he said that's what we're going to go
+ 
+
+ align:start position:0%
+he said that's what we're going to go
+with the thing might go up and come back
+
+ align:start position:0%
+with the thing might go up and come back
+ 
+
+ align:start position:0%
+with the thing might go up and come back
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+explode he said but that's the business
+
+ align:start position:0%
+explode he said but that's the business
+ 
+
+ align:start position:0%
+explode he said but that's the business
+we're in this is the real world of
+
+ align:start position:0%
+we're in this is the real world of
+ 
+
+ align:start position:0%
+we're in this is the real world of
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+it's the commitment that counts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we got good people out here
+
+ align:start position:0%
+and we got good people out here
+ 
+
+ align:start position:0%
+and we got good people out here
+and if they are willing to commit
+
+ align:start position:0%
+and if they are willing to commit
+ 
+
+ align:start position:0%
+and if they are willing to commit
+then the united states will say
+
+ align:start position:0%
+then the united states will say
+ 
+
+ align:start position:0%
+then the united states will say
+when the thing goes up and explodes they
+
+ align:start position:0%
+when the thing goes up and explodes they
+ 
+
+ align:start position:0%
+when the thing goes up and explodes they
+will say here's some more money try it
+
+ align:start position:0%
+will say here's some more money try it
+ 
+
+ align:start position:0%
+will say here's some more money try it
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if we
+
+ align:start position:0%
+but if we
+ 
+
+ align:start position:0%
+but if we
+having the right answers is not the
+
+ align:start position:0%
+having the right answers is not the
+ 
+
+ align:start position:0%
+having the right answers is not the
+whole story not even the main story when
+
+ align:start position:0%
+whole story not even the main story when
+ 
+
+ align:start position:0%
+whole story not even the main story when
+you particularly talk about space
+
+ align:start position:0%
+you particularly talk about space
+ 
+
+ align:start position:0%
+you particularly talk about space
+where you don't have a tradition
+
+ align:start position:0%
+where you don't have a tradition
+ 
+
+ align:start position:0%
+where you don't have a tradition
+everything you're doing this for the
+
+ align:start position:0%
+everything you're doing this for the
+ 
+
+ align:start position:0%
+everything you're doing this for the
+first time
+
+ align:start position:0%
+first time
+ 
+
+ align:start position:0%
+first time
+okay so that's the real world
+
+ align:start position:0%
+okay so that's the real world
+ 
+
+ align:start position:0%
+okay so that's the real world
+now the good news is
+
+ align:start position:0%
+now the good news is
+ 
+
+ align:start position:0%
+now the good news is
+the bad news is that undergraduate
+
+ align:start position:0%
+the bad news is that undergraduate
+ 
+
+ align:start position:0%
+the bad news is that undergraduate
+education is not like that
+
+ align:start position:0%
+education is not like that
+ 
+
+ align:start position:0%
+education is not like that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+semi depends on who your major professor
+
+ align:start position:0%
+semi depends on who your major professor
+ 
+
+ align:start position:0%
+semi depends on who your major professor
+is graduate education is not like that
+
+ align:start position:0%
+is graduate education is not like that
+ 
+
+ align:start position:0%
+is graduate education is not like that
+in engineering
+
+ align:start position:0%
+in engineering
+ 
+
+ align:start position:0%
+in engineering
+but from day one ethics education is
+
+ align:start position:0%
+but from day one ethics education is
+ 
+
+ align:start position:0%
+but from day one ethics education is
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+because we want we want a good answer
+
+ align:start position:0%
+because we want we want a good answer
+ 
+
+ align:start position:0%
+because we want we want a good answer
+now don't get to get me wrong okay
+
+ align:start position:0%
+now don't get to get me wrong okay
+ 
+
+ align:start position:0%
+now don't get to get me wrong okay
+but it's that i he made up to it and
+
+ align:start position:0%
+but it's that i he made up to it and
+ 
+
+ align:start position:0%
+but it's that i he made up to it and
+whether or not as i'm grading it and as
+
+ align:start position:0%
+whether or not as i'm grading it and as
+ 
+
+ align:start position:0%
+whether or not as i'm grading it and as
+any other professor with greater whether
+
+ align:start position:0%
+any other professor with greater whether
+ 
+
+ align:start position:0%
+any other professor with greater whether
+or not i would commit me
+
+ align:start position:0%
+or not i would commit me
+ 
+
+ align:start position:0%
+or not i would commit me
+and my kids
+
+ align:start position:0%
+and my kids
+ 
+
+ align:start position:0%
+and my kids
+to your answers
+
+ align:start position:0%
+to your answers
+ 
+
+ align:start position:0%
+to your answers
+to your analysis
+
+ align:start position:0%
+to your analysis
+ 
+
+ align:start position:0%
+to your analysis
+because my kids are going to have to
+
+ align:start position:0%
+because my kids are going to have to
+ 
+
+ align:start position:0%
+because my kids are going to have to
+cross that bridge
+
+ align:start position:0%
+cross that bridge
+ 
+
+ align:start position:0%
+cross that bridge
+okay and so uh now
+
+ align:start position:0%
+okay and so uh now
+ 
+
+ align:start position:0%
+okay and so uh now
+i'm interested that you got everything
+
+ align:start position:0%
+i'm interested that you got everything
+ 
+
+ align:start position:0%
+i'm interested that you got everything
+written down
+
+ align:start position:0%
+written down
+ 
+
+ align:start position:0%
+written down
+but there's got to be something under it
+
+ align:start position:0%
+but there's got to be something under it
+ 
+
+ align:start position:0%
+but there's got to be something under it
+that's compelling
+
+ align:start position:0%
+that's compelling
+ 
+
+ align:start position:0%
+that's compelling
+and that is impossible to grade
+
+ align:start position:0%
+and that is impossible to grade
+ 
+
+ align:start position:0%
+and that is impossible to grade
+but i can tell you whether or not it's
+
+ align:start position:0%
+but i can tell you whether or not it's
+ 
+
+ align:start position:0%
+but i can tell you whether or not it's
+there i can tell you whether or not i
+
+ align:start position:0%
+there i can tell you whether or not i
+ 
+
+ align:start position:0%
+there i can tell you whether or not i
+feel it
+
+ align:start position:0%
+feel it
+ 
+
+ align:start position:0%
+feel it
+and i and most importantly
+
+ align:start position:0%
+and i and most importantly
+ 
+
+ align:start position:0%
+and i and most importantly
+even if i don't feel it i've been out
+
+ align:start position:0%
+even if i don't feel it i've been out
+ 
+
+ align:start position:0%
+even if i don't feel it i've been out
+here long enough to know whether
+
+ align:start position:0%
+here long enough to know whether
+ 
+
+ align:start position:0%
+here long enough to know whether
+somebody else will
+
+ align:start position:0%
+somebody else will
+ 
+
+ align:start position:0%
+somebody else will
+i would say yeah there's some people out
+
+ align:start position:0%
+i would say yeah there's some people out
+ 
+
+ align:start position:0%
+i would say yeah there's some people out
+here that would really feel this
+
+ align:start position:0%
+here that would really feel this
+ 
+
+ align:start position:0%
+here that would really feel this
+but that takes time
+
+ align:start position:0%
+but that takes time
+ 
+
+ align:start position:0%
+but that takes time
+my objective in this class is not to
+
+ align:start position:0%
+my objective in this class is not to
+ 
+
+ align:start position:0%
+my objective in this class is not to
+meet that objective
+
+ align:start position:0%
+meet that objective
+ 
+
+ align:start position:0%
+meet that objective
+it's the first time you've had a
+
+ align:start position:0%
+it's the first time you've had a
+ 
+
+ align:start position:0%
+it's the first time you've had a
+engineering ethics course
+
+ align:start position:0%
+engineering ethics course
+ 
+
+ align:start position:0%
+engineering ethics course
+and if this was a sequence then i would
+
+ align:start position:0%
+and if this was a sequence then i would
+ 
+
+ align:start position:0%
+and if this was a sequence then i would
+expect it the next time
+
+ align:start position:0%
+expect it the next time
+ 
+
+ align:start position:0%
+expect it the next time
+it's my objective in this class to talk
+
+ align:start position:0%
+it's my objective in this class to talk
+ 
+
+ align:start position:0%
+it's my objective in this class to talk
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes a few comments um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emmanuel kant takes his
+
+ align:start position:0%
+emmanuel kant takes his
+ 
+
+ align:start position:0%
+emmanuel kant takes his
+uh categorical uh imperative
+
+ align:start position:0%
+uh categorical uh imperative
+ 
+
+ align:start position:0%
+uh categorical uh imperative
+and states it three or four different
+
+ align:start position:0%
+and states it three or four different
+ 
+
+ align:start position:0%
+and states it three or four different
+ways now i think you all picked that up
+
+ align:start position:0%
+ways now i think you all picked that up
+ 
+
+ align:start position:0%
+ways now i think you all picked that up
+there's a subtlety in one of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the golden rule is one of those
+
+ align:start position:0%
+the golden rule is one of those
+ 
+
+ align:start position:0%
+the golden rule is one of those
+statements
+
+ align:start position:0%
+statements
+ 
+
+ align:start position:0%
+statements
+so tie that in to comp
+
+ align:start position:0%
+so tie that in to comp
+ 
+
+ align:start position:0%
+so tie that in to comp
+go he explicitly says that the golden
+
+ align:start position:0%
+go he explicitly says that the golden
+ 
+
+ align:start position:0%
+go he explicitly says that the golden
+rule
+
+ align:start position:0%
+rule
+ 
+
+ align:start position:0%
+rule
+is a legitimate statement of the
+
+ align:start position:0%
+is a legitimate statement of the
+ 
+
+ align:start position:0%
+is a legitimate statement of the
+categorical imperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so what that means is that out of
+
+ align:start position:0%
+now so what that means is that out of
+ 
+
+ align:start position:0%
+now so what that means is that out of
+the different
+
+ align:start position:0%
+the different
+ 
+
+ align:start position:0%
+the different
+formulations of his categorical
+
+ align:start position:0%
+formulations of his categorical
+ 
+
+ align:start position:0%
+formulations of his categorical
+imperative you can pick any one of them
+
+ align:start position:0%
+imperative you can pick any one of them
+ 
+
+ align:start position:0%
+imperative you can pick any one of them
+i'm not too sure that a philosopher
+
+ align:start position:0%
+i'm not too sure that a philosopher
+ 
+
+ align:start position:0%
+i'm not too sure that a philosopher
+would say that one is better than the
+
+ align:start position:0%
+would say that one is better than the
+ 
+
+ align:start position:0%
+would say that one is better than the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+just different ways of stating the thing
+
+ align:start position:0%
+just different ways of stating the thing
+ 
+
+ align:start position:0%
+just different ways of stating the thing
+properly because it's a complicated sort
+
+ align:start position:0%
+properly because it's a complicated sort
+ 
+
+ align:start position:0%
+properly because it's a complicated sort
+of thing
+
+ align:start position:0%
+of thing
+ 
+
+ align:start position:0%
+of thing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+my i guess you all know which which one
+
+ align:start position:0%
+my i guess you all know which which one
+ 
+
+ align:start position:0%
+my i guess you all know which which one
+is my preference treating people is
+
+ align:start position:0%
+is my preference treating people is
+ 
+
+ align:start position:0%
+is my preference treating people is
+means to end
+
+ align:start position:0%
+means to end
+ 
+
+ align:start position:0%
+means to end
+that's my that's my preference um the
+
+ align:start position:0%
+that's my that's my preference um the
+ 
+
+ align:start position:0%
+that's my that's my preference um the
+first one
+
+ align:start position:0%
+first one
+ 
+
+ align:start position:0%
+first one
+uh is a little bit convoluted
+
+ align:start position:0%
+uh is a little bit convoluted
+ 
+
+ align:start position:0%
+uh is a little bit convoluted
+frankly i like it because he's really
+
+ align:start position:0%
+frankly i like it because he's really
+ 
+
+ align:start position:0%
+frankly i like it because he's really
+trying he's really saying what i think
+
+ align:start position:0%
+trying he's really saying what i think
+ 
+
+ align:start position:0%
+trying he's really saying what i think
+he really means and that is he's trying
+
+ align:start position:0%
+he really means and that is he's trying
+ 
+
+ align:start position:0%
+he really means and that is he's trying
+to connect
+
+ align:start position:0%
+to connect
+ 
+
+ align:start position:0%
+to connect
+his categorical imperative
+
+ align:start position:0%
+his categorical imperative
+ 
+
+ align:start position:0%
+his categorical imperative
+to first principles of logic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's important to you
+
+ align:start position:0%
+that's important to you
+ 
+
+ align:start position:0%
+that's important to you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's that i think the main importance
+
+ align:start position:0%
+that's that i think the main importance
+ 
+
+ align:start position:0%
+that's that i think the main importance
+of that to you
+
+ align:start position:0%
+of that to you
+ 
+
+ align:start position:0%
+of that to you
+is that now you can see what counts
+
+ align:start position:0%
+is that now you can see what counts
+ 
+
+ align:start position:0%
+is that now you can see what counts
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+fundamental idea
+
+ align:start position:0%
+fundamental idea
+ 
+
+ align:start position:0%
+fundamental idea
+as opposed to a theory that's
+
+ align:start position:0%
+as opposed to a theory that's
+ 
+
+ align:start position:0%
+as opposed to a theory that's
+incremental
+
+ align:start position:0%
+incremental
+ 
+
+ align:start position:0%
+incremental
+uh you can now say that well now now i
+
+ align:start position:0%
+uh you can now say that well now now i
+ 
+
+ align:start position:0%
+uh you can now say that well now now i
+know what the nobel if there was a nobel
+
+ align:start position:0%
+know what the nobel if there was a nobel
+ 
+
+ align:start position:0%
+know what the nobel if there was a nobel
+prize for
+
+ align:start position:0%
+prize for
+ 
+
+ align:start position:0%
+prize for
+philosophy which there isn't
+
+ align:start position:0%
+philosophy which there isn't
+ 
+
+ align:start position:0%
+philosophy which there isn't
+even though philosophers have got nobel
+
+ align:start position:0%
+even though philosophers have got nobel
+ 
+
+ align:start position:0%
+even though philosophers have got nobel
+prizes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for what for peace uh i think maybe
+
+ align:start position:0%
+for what for peace uh i think maybe
+ 
+
+ align:start position:0%
+for what for peace uh i think maybe
+you can count uh uh some of them all of
+
+ align:start position:0%
+you can count uh uh some of them all of
+ 
+
+ align:start position:0%
+you can count uh uh some of them all of
+them all of them who got it for peace
+
+ align:start position:0%
+them all of them who got it for peace
+ 
+
+ align:start position:0%
+them all of them who got it for peace
+were philosophers or doing philosophy
+
+ align:start position:0%
+were philosophers or doing philosophy
+ 
+
+ align:start position:0%
+were philosophers or doing philosophy
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+some of the chemists
+
+ align:start position:0%
+some of the chemists
+ 
+
+ align:start position:0%
+some of the chemists
+who did it
+
+ align:start position:0%
+who did it
+ 
+
+ align:start position:0%
+who did it
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+sartre
+
+ align:start position:0%
+sartre
+ 
+
+ align:start position:0%
+sartre
+jean-paul
+
+ align:start position:0%
+jean-paul
+ 
+
+ align:start position:0%
+jean-paul
+from versace was a philosophy he got it
+
+ align:start position:0%
+from versace was a philosophy he got it
+ 
+
+ align:start position:0%
+from versace was a philosophy he got it
+he got it and some others but they got
+
+ align:start position:0%
+he got it and some others but they got
+ 
+
+ align:start position:0%
+he got it and some others but they got
+it for literature right
+
+ align:start position:0%
+it for literature right
+ 
+
+ align:start position:0%
+it for literature right
+but they were doing philosophy in the
+
+ align:start position:0%
+but they were doing philosophy in the
+ 
+
+ align:start position:0%
+but they were doing philosophy in the
+literature
+
+ align:start position:0%
+literature
+ 
+
+ align:start position:0%
+literature
+and sartre i think is where frenchmen
+
+ align:start position:0%
+and sartre i think is where frenchmen
+ 
+
+ align:start position:0%
+and sartre i think is where frenchmen
+can pronounce it i think i can get away
+
+ align:start position:0%
+can pronounce it i think i can get away
+ 
+
+ align:start position:0%
+can pronounce it i think i can get away
+with saying a song
+
+ align:start position:0%
+with saying a song
+ 
+
+ align:start position:0%
+with saying a song
+uh is uh someone that i would like to
+
+ align:start position:0%
+uh is uh someone that i would like to
+ 
+
+ align:start position:0%
+uh is uh someone that i would like to
+cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and uh we can read
+
+ align:start position:0%
+and uh we can read
+ 
+
+ align:start position:0%
+and uh we can read
+the good thing about doing sarc is that
+
+ align:start position:0%
+the good thing about doing sarc is that
+ 
+
+ align:start position:0%
+the good thing about doing sarc is that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+his plays you can read these plays
+
+ align:start position:0%
+his plays you can read these plays
+ 
+
+ align:start position:0%
+his plays you can read these plays
+overnight they're real short
+
+ align:start position:0%
+overnight they're real short
+ 
+
+ align:start position:0%
+overnight they're real short
+and we can talk about one or two of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but he is
+
+ align:start position:0%
+but he is
+ 
+
+ align:start position:0%
+but he is
+started is a frenchman he's in a
+
+ align:start position:0%
+started is a frenchman he's in a
+ 
+
+ align:start position:0%
+started is a frenchman he's in a
+different category
+
+ align:start position:0%
+different category
+ 
+
+ align:start position:0%
+different category
+he's going to tell you things just by
+
+ align:start position:0%
+he's going to tell you things just by
+ 
+
+ align:start position:0%
+he's going to tell you things just by
+what i just did he's going to tell a
+
+ align:start position:0%
+what i just did he's going to tell a
+ 
+
+ align:start position:0%
+what i just did he's going to tell a
+story out of that you've got to
+
+ align:start position:0%
+story out of that you've got to
+ 
+
+ align:start position:0%
+story out of that you've got to
+synthesize what the message is
+
+ align:start position:0%
+synthesize what the message is
+ 
+
+ align:start position:0%
+synthesize what the message is
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's see if i can make some more um
+
+ align:start position:0%
+let's see if i can make some more um
+ 
+
+ align:start position:0%
+let's see if i can make some more um
+so there are three ways to look at it
+
+ align:start position:0%
+so there are three ways to look at it
+ 
+
+ align:start position:0%
+so there are three ways to look at it
+if we're doing an analysis
+
+ align:start position:0%
+if we're doing an analysis
+ 
+
+ align:start position:0%
+if we're doing an analysis
+um i know we probably won't have an
+
+ align:start position:0%
+um i know we probably won't have an
+ 
+
+ align:start position:0%
+um i know we probably won't have an
+assignment like we do where we're
+
+ align:start position:0%
+assignment like we do where we're
+ 
+
+ align:start position:0%
+assignment like we do where we're
+specifically told to take this approach
+
+ align:start position:0%
+specifically told to take this approach
+ 
+
+ align:start position:0%
+specifically told to take this approach
+but is it okay just to choose our
+
+ align:start position:0%
+but is it okay just to choose our
+ 
+
+ align:start position:0%
+but is it okay just to choose our
+favorite and pick one and in theory
+
+ align:start position:0%
+favorite and pick one and in theory
+ 
+
+ align:start position:0%
+favorite and pick one and in theory
+should they all come to the same
+
+ align:start position:0%
+should they all come to the same
+ 
+
+ align:start position:0%
+should they all come to the same
+conclusion
+
+ align:start position:0%
+conclusion
+ 
+
+ align:start position:0%
+conclusion
+there's no reason that they should all
+
+ align:start position:0%
+there's no reason that they should all
+ 
+
+ align:start position:0%
+there's no reason that they should all
+come to the same conclusion okay so we
+
+ align:start position:0%
+come to the same conclusion okay so we
+ 
+
+ align:start position:0%
+come to the same conclusion okay so we
+could phrase it in a different way
+
+ align:start position:0%
+could phrase it in a different way
+ 
+
+ align:start position:0%
+could phrase it in a different way
+and come up with something completely
+
+ align:start position:0%
+and come up with something completely
+ 
+
+ align:start position:0%
+and come up with something completely
+different depending on which
+
+ align:start position:0%
+different depending on which
+ 
+
+ align:start position:0%
+different depending on which
+interpretation we'd like our jews to use
+
+ align:start position:0%
+interpretation we'd like our jews to use
+ 
+
+ align:start position:0%
+interpretation we'd like our jews to use
+or think is most appropriate what i hope
+
+ align:start position:0%
+or think is most appropriate what i hope
+ 
+
+ align:start position:0%
+or think is most appropriate what i hope
+is that you have enough experiences in
+
+ align:start position:0%
+is that you have enough experiences in
+ 
+
+ align:start position:0%
+is that you have enough experiences in
+this class that you will find
+
+ align:start position:0%
+this class that you will find
+ 
+
+ align:start position:0%
+this class that you will find
+that you can come up uh with two
+
+ align:start position:0%
+that you can come up uh with two
+ 
+
+ align:start position:0%
+that you can come up uh with two
+opposites even inclusions uh that are
+
+ align:start position:0%
+opposites even inclusions uh that are
+ 
+
+ align:start position:0%
+opposites even inclusions uh that are
+well grounded
+
+ align:start position:0%
+well grounded
+ 
+
+ align:start position:0%
+well grounded
+so and we should write about both of
+
+ align:start position:0%
+so and we should write about both of
+ 
+
+ align:start position:0%
+so and we should write about both of
+them and
+
+ align:start position:0%
+them and
+ 
+
+ align:start position:0%
+them and
+have the same defensibility for both of
+
+ align:start position:0%
+have the same defensibility for both of
+ 
+
+ align:start position:0%
+have the same defensibility for both of
+them okay you're putting me in
+
+ align:start position:0%
+them okay you're putting me in
+ 
+
+ align:start position:0%
+them okay you're putting me in
+my question is
+
+ align:start position:0%
+my question is
+ 
+
+ align:start position:0%
+my question is
+you know because you talked about
+
+ align:start position:0%
+you know because you talked about
+ 
+
+ align:start position:0%
+you know because you talked about
+wanting to have the passion behind the
+
+ align:start position:0%
+wanting to have the passion behind the
+ 
+
+ align:start position:0%
+wanting to have the passion behind the
+argue the conclusion yeah
+
+ align:start position:0%
+argue the conclusion yeah
+ 
+
+ align:start position:0%
+argue the conclusion yeah
+should we
+
+ align:start position:0%
+should we
+ 
+
+ align:start position:0%
+should we
+does that mean we should only write
+
+ align:start position:0%
+does that mean we should only write
+ 
+
+ align:start position:0%
+does that mean we should only write
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the approach that gives us that passion
+
+ align:start position:0%
+the approach that gives us that passion
+ 
+
+ align:start position:0%
+the approach that gives us that passion
+no guys this thing takes time okay
+
+ align:start position:0%
+no guys this thing takes time okay
+ 
+
+ align:start position:0%
+no guys this thing takes time okay
+okay it takes time this is going to be
+
+ align:start position:0%
+okay it takes time this is going to be
+ 
+
+ align:start position:0%
+okay it takes time this is going to be
+an assignment that i'm going to make
+
+ align:start position:0%
+an assignment that i'm going to make
+ 
+
+ align:start position:0%
+an assignment that i'm going to make
+before the class is over
+
+ align:start position:0%
+before the class is over
+ 
+
+ align:start position:0%
+before the class is over
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh the most important thing um not the
+
+ align:start position:0%
+uh the most important thing um not the
+ 
+
+ align:start position:0%
+uh the most important thing um not the
+most important thing but what i'm going
+
+ align:start position:0%
+most important thing but what i'm going
+ 
+
+ align:start position:0%
+most important thing but what i'm going
+to take out of it today
+
+ align:start position:0%
+to take out of it today
+ 
+
+ align:start position:0%
+to take out of it today
+um is something that the office says uh
+
+ align:start position:0%
+um is something that the office says uh
+ 
+
+ align:start position:0%
+um is something that the office says uh
+early on
+
+ align:start position:0%
+early on
+ 
+
+ align:start position:0%
+early on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right at the end of his uh
+
+ align:start position:0%
+right at the end of his uh
+ 
+
+ align:start position:0%
+right at the end of his uh
+preface now he calls it forward rather
+
+ align:start position:0%
+preface now he calls it forward rather
+ 
+
+ align:start position:0%
+preface now he calls it forward rather
+damage forward
+
+ align:start position:0%
+damage forward
+ 
+
+ align:start position:0%
+damage forward
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is a wolfram from the ocean box
+
+ align:start position:0%
+this is a wolfram from the ocean box
+ 
+
+ align:start position:0%
+this is a wolfram from the ocean box
+parcel
+
+ align:start position:0%
+parcel
+ 
+
+ align:start position:0%
+parcel
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um it's part of the ethereum mythology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but this is a german
+
+ align:start position:0%
+uh but this is a german
+ 
+
+ align:start position:0%
+uh but this is a german
+uh who's writing it and um
+
+ align:start position:0%
+uh who's writing it and um
+ 
+
+ align:start position:0%
+uh who's writing it and um
+you're you're probably
+
+ align:start position:0%
+you're you're probably
+ 
+
+ align:start position:0%
+you're you're probably
+most familiar with thomas mallory's
+
+ align:start position:0%
+most familiar with thomas mallory's
+ 
+
+ align:start position:0%
+most familiar with thomas mallory's
+what's called mort arthur king arthur's
+
+ align:start position:0%
+what's called mort arthur king arthur's
+ 
+
+ align:start position:0%
+what's called mort arthur king arthur's
+story you know
+
+ align:start position:0%
+story you know
+ 
+
+ align:start position:0%
+story you know
+gwynevere and all of that you're
+
+ align:start position:0%
+gwynevere and all of that you're
+ 
+
+ align:start position:0%
+gwynevere and all of that you're
+probably most familiar with that
+
+ align:start position:0%
+probably most familiar with that
+ 
+
+ align:start position:0%
+probably most familiar with that
+they are pretty much different versions
+
+ align:start position:0%
+they are pretty much different versions
+ 
+
+ align:start position:0%
+they are pretty much different versions
+of the same story
+
+ align:start position:0%
+of the same story
+ 
+
+ align:start position:0%
+of the same story
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+they're different and you'll find many
+
+ align:start position:0%
+they're different and you'll find many
+ 
+
+ align:start position:0%
+they're different and you'll find many
+of the same characters
+
+ align:start position:0%
+of the same characters
+ 
+
+ align:start position:0%
+of the same characters
+in in these stories
+
+ align:start position:0%
+in in these stories
+ 
+
+ align:start position:0%
+in in these stories
+uh but what this what these what what
+
+ align:start position:0%
+uh but what this what these what what
+ 
+
+ align:start position:0%
+uh but what this what these what what
+what the uh
+
+ align:start position:0%
+what the uh
+ 
+
+ align:start position:0%
+what the uh
+both the translators
+
+ align:start position:0%
+both the translators
+ 
+
+ align:start position:0%
+both the translators
+of both of the ones that i have this one
+
+ align:start position:0%
+of both of the ones that i have this one
+ 
+
+ align:start position:0%
+of both of the ones that i have this one
+and the one of mort arthur
+
+ align:start position:0%
+and the one of mort arthur
+ 
+
+ align:start position:0%
+and the one of mort arthur
+uh start out by telling you
+
+ align:start position:0%
+uh start out by telling you
+ 
+
+ align:start position:0%
+uh start out by telling you
+that well i could translate this thing
+
+ align:start position:0%
+that well i could translate this thing
+ 
+
+ align:start position:0%
+that well i could translate this thing
+back into
+
+ align:start position:0%
+back into
+ 
+
+ align:start position:0%
+back into
+plain english
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i won't
+
+ align:start position:0%
+but i won't
+ 
+
+ align:start position:0%
+but i won't
+be just a few there
+
+ align:start position:0%
+be just a few there
+ 
+
+ align:start position:0%
+be just a few there
+says because if you just read it in
+
+ align:start position:0%
+says because if you just read it in
+ 
+
+ align:start position:0%
+says because if you just read it in
+the vernacular of the time
+
+ align:start position:0%
+the vernacular of the time
+ 
+
+ align:start position:0%
+the vernacular of the time
+that after why
+
+ align:start position:0%
+that after why
+ 
+
+ align:start position:0%
+that after why
+maybe page 30
+
+ align:start position:0%
+maybe page 30
+ 
+
+ align:start position:0%
+maybe page 30
+maybe page 15.
+
+ align:start position:0%
+maybe page 15.
+ 
+
+ align:start position:0%
+maybe page 15.
+it'll sound right
+
+ align:start position:0%
+it'll sound right
+ 
+
+ align:start position:0%
+it'll sound right
+and you've already had that experience
+
+ align:start position:0%
+and you've already had that experience
+ 
+
+ align:start position:0%
+and you've already had that experience
+shakespeare
+
+ align:start position:0%
+shakespeare
+ 
+
+ align:start position:0%
+shakespeare
+you read shakespeare's and uh
+
+ align:start position:0%
+you read shakespeare's and uh
+ 
+
+ align:start position:0%
+you read shakespeare's and uh
+but you would like them you wouldn't
+
+ align:start position:0%
+but you would like them you wouldn't
+ 
+
+ align:start position:0%
+but you would like them you wouldn't
+the first time you read it you would say
+
+ align:start position:0%
+the first time you read it you would say
+ 
+
+ align:start position:0%
+the first time you read it you would say
+good god why didn't why didn't the
+
+ align:start position:0%
+good god why didn't why didn't the
+ 
+
+ align:start position:0%
+good god why didn't why didn't the
+teacher give me plain english
+
+ align:start position:0%
+teacher give me plain english
+ 
+
+ align:start position:0%
+teacher give me plain english
+shakespeare well if they gave me
+
+ align:start position:0%
+shakespeare well if they gave me
+ 
+
+ align:start position:0%
+shakespeare well if they gave me
+shakespeare then after a while
+
+ align:start position:0%
+shakespeare then after a while
+ 
+
+ align:start position:0%
+shakespeare then after a while
+something magic happens this stuff
+
+ align:start position:0%
+something magic happens this stuff
+ 
+
+ align:start position:0%
+something magic happens this stuff
+sounds like
+
+ align:start position:0%
+sounds like
+ 
+
+ align:start position:0%
+sounds like
+you know you feel like you've learned
+
+ align:start position:0%
+you know you feel like you've learned
+ 
+
+ align:start position:0%
+you know you feel like you've learned
+the language right
+
+ align:start position:0%
+the language right
+ 
+
+ align:start position:0%
+the language right
+something happens and that's what
+
+ align:start position:0%
+something happens and that's what
+ 
+
+ align:start position:0%
+something happens and that's what
+happened that's what happens if god took
+
+ align:start position:0%
+happened that's what happens if god took
+ 
+
+ align:start position:0%
+happened that's what happens if god took
+that long explanation to come back to
+
+ align:start position:0%
+that long explanation to come back to
+ 
+
+ align:start position:0%
+that long explanation to come back to
+tell you that that's what happens in
+
+ align:start position:0%
+tell you that that's what happens in
+ 
+
+ align:start position:0%
+tell you that that's what happens in
+this kind of course you're learning
+
+ align:start position:0%
+this kind of course you're learning
+ 
+
+ align:start position:0%
+this kind of course you're learning
+something very new
+
+ align:start position:0%
+something very new
+ 
+
+ align:start position:0%
+something very new
+and it'll take you a while to get in the
+
+ align:start position:0%
+and it'll take you a while to get in the
+ 
+
+ align:start position:0%
+and it'll take you a while to get in the
+rhythm of it
+
+ align:start position:0%
+rhythm of it
+ 
+
+ align:start position:0%
+rhythm of it
+right particularly with complexities
+
+ align:start position:0%
+right particularly with complexities
+ 
+
+ align:start position:0%
+right particularly with complexities
+after a while you'll say well yeah it is
+
+ align:start position:0%
+after a while you'll say well yeah it is
+ 
+
+ align:start position:0%
+after a while you'll say well yeah it is
+complex complex but i sort of see your
+
+ align:start position:0%
+complex complex but i sort of see your
+ 
+
+ align:start position:0%
+complex complex but i sort of see your
+way through this
+
+ align:start position:0%
+way through this
+ 
+
+ align:start position:0%
+way through this
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+let's see many of the comments i have
+
+ align:start position:0%
+let's see many of the comments i have
+ 
+
+ align:start position:0%
+let's see many of the comments i have
+were pretty much the same um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh another another issue is uh with the
+
+ align:start position:0%
+oh another another issue is uh with the
+ 
+
+ align:start position:0%
+oh another another issue is uh with the
+utilitarian approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a little bit forgiving in terms of
+
+ align:start position:0%
+it's a little bit forgiving in terms of
+ 
+
+ align:start position:0%
+it's a little bit forgiving in terms of
+your being able to predict consequences
+
+ align:start position:0%
+your being able to predict consequences
+ 
+
+ align:start position:0%
+your being able to predict consequences
+you don't have to be exact in this even
+
+ align:start position:0%
+you don't have to be exact in this even
+ 
+
+ align:start position:0%
+you don't have to be exact in this even
+if you read stuart milner what they're
+
+ align:start position:0%
+if you read stuart milner what they're
+ 
+
+ align:start position:0%
+if you read stuart milner what they're
+saying is your best judgment at the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you make your judgment at the time
+
+ align:start position:0%
+so you make your judgment at the time
+ 
+
+ align:start position:0%
+so you make your judgment at the time
+you don't have to take into you know see
+
+ align:start position:0%
+you don't have to take into you know see
+ 
+
+ align:start position:0%
+you don't have to take into you know see
+that's what really
+
+ align:start position:0%
+that's what really
+ 
+
+ align:start position:0%
+that's what really
+comes into account
+
+ align:start position:0%
+comes into account
+ 
+
+ align:start position:0%
+comes into account
+with engineering
+
+ align:start position:0%
+with engineering
+ 
+
+ align:start position:0%
+with engineering
+you're gonna build a bridge
+
+ align:start position:0%
+you're gonna build a bridge
+ 
+
+ align:start position:0%
+you're gonna build a bridge
+you're gonna build that bridge for a
+
+ align:start position:0%
+you're gonna build that bridge for a
+ 
+
+ align:start position:0%
+you're gonna build that bridge for a
+life of a hundred years
+
+ align:start position:0%
+life of a hundred years
+ 
+
+ align:start position:0%
+life of a hundred years
+now you're supposed to exp tell me what
+
+ align:start position:0%
+now you're supposed to exp tell me what
+ 
+
+ align:start position:0%
+now you're supposed to exp tell me what
+the consequences are to everybody who
+
+ align:start position:0%
+the consequences are to everybody who
+ 
+
+ align:start position:0%
+the consequences are to everybody who
+crosses that bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got to make some kind of judgment
+
+ align:start position:0%
+you got to make some kind of judgment
+ 
+
+ align:start position:0%
+you got to make some kind of judgment
+reasonable judgment
+
+ align:start position:0%
+reasonable judgment
+ 
+
+ align:start position:0%
+reasonable judgment
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is not so much defensible
+
+ align:start position:0%
+is not so much defensible
+ 
+
+ align:start position:0%
+is not so much defensible
+as it is i'm a user term committable
+
+ align:start position:0%
+as it is i'm a user term committable
+ 
+
+ align:start position:0%
+as it is i'm a user term committable
+you think that other people will say
+
+ align:start position:0%
+you think that other people will say
+ 
+
+ align:start position:0%
+you think that other people will say
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+we'll go along with this
+
+ align:start position:0%
+we'll go along with this
+ 
+
+ align:start position:0%
+we'll go along with this
+and that's why there's a there now when
+
+ align:start position:0%
+and that's why there's a there now when
+ 
+
+ align:start position:0%
+and that's why there's a there now when
+it comes to engineering i'll you won't
+
+ align:start position:0%
+it comes to engineering i'll you won't
+ 
+
+ align:start position:0%
+it comes to engineering i'll you won't
+find this in many of the texts i don't
+
+ align:start position:0%
+find this in many of the texts i don't
+ 
+
+ align:start position:0%
+find this in many of the texts i don't
+think you'll find it in any of them
+
+ align:start position:0%
+think you'll find it in any of them
+ 
+
+ align:start position:0%
+think you'll find it in any of them
+but i'll tell you right now which is one
+
+ align:start position:0%
+but i'll tell you right now which is one
+ 
+
+ align:start position:0%
+but i'll tell you right now which is one
+of the most compelling
+
+ align:start position:0%
+of the most compelling
+ 
+
+ align:start position:0%
+of the most compelling
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rationales an engineer can give for
+
+ align:start position:0%
+rationales an engineer can give for
+ 
+
+ align:start position:0%
+rationales an engineer can give for
+doing x as opposed to y
+
+ align:start position:0%
+doing x as opposed to y
+ 
+
+ align:start position:0%
+doing x as opposed to y
+that works almost if if if it applies
+
+ align:start position:0%
+that works almost if if if it applies
+ 
+
+ align:start position:0%
+that works almost if if if it applies
+works almost all the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we always do it that way
+
+ align:start position:0%
+we always do it that way
+ 
+
+ align:start position:0%
+we always do it that way
+tradition
+
+ align:start position:0%
+tradition
+ 
+
+ align:start position:0%
+tradition
+okay so you got a citizen group in here
+
+ align:start position:0%
+okay so you got a citizen group in here
+ 
+
+ align:start position:0%
+okay so you got a citizen group in here
+and they want to know why you want to
+
+ align:start position:0%
+and they want to know why you want to
+ 
+
+ align:start position:0%
+and they want to know why you want to
+put the nuclear waste dump over there as
+
+ align:start position:0%
+put the nuclear waste dump over there as
+ 
+
+ align:start position:0%
+put the nuclear waste dump over there as
+opposed to over there
+
+ align:start position:0%
+opposed to over there
+ 
+
+ align:start position:0%
+opposed to over there
+and then you come up with some kind of a
+
+ align:start position:0%
+and then you come up with some kind of a
+ 
+
+ align:start position:0%
+and then you come up with some kind of a
+formula and they don't understand the
+
+ align:start position:0%
+formula and they don't understand the
+ 
+
+ align:start position:0%
+formula and they don't understand the
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+and they're mad about it
+
+ align:start position:0%
+and they're mad about it
+ 
+
+ align:start position:0%
+and they're mad about it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if you are able to tell them rightly and
+
+ align:start position:0%
+if you are able to tell them rightly and
+ 
+
+ align:start position:0%
+if you are able to tell them rightly and
+all the other engineers in the room go
+
+ align:start position:0%
+all the other engineers in the room go
+ 
+
+ align:start position:0%
+all the other engineers in the room go
+along with it that that formula is what
+
+ align:start position:0%
+along with it that that formula is what
+ 
+
+ align:start position:0%
+along with it that that formula is what
+we always use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to go a long way with that
+
+ align:start position:0%
+you're going to go a long way with that
+ 
+
+ align:start position:0%
+you're going to go a long way with that
+scientists can't get away with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's always the formulas better than
+
+ align:start position:0%
+there's always the formulas better than
+ 
+
+ align:start position:0%
+there's always the formulas better than
+the old ones
+
+ align:start position:0%
+the old ones
+ 
+
+ align:start position:0%
+the old ones
+but engineers tradition is a good one
+
+ align:start position:0%
+but engineers tradition is a good one
+ 
+
+ align:start position:0%
+but engineers tradition is a good one
+and you can use that in ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+let's see oh uh lastly um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+story terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh i'm gonna leave that one to
+
+ align:start position:0%
+uh i'm gonna leave that one to
+ 
+
+ align:start position:0%
+uh i'm gonna leave that one to
+more discussion as we go along the class
+
+ align:start position:0%
+more discussion as we go along the class
+ 
+
+ align:start position:0%
+more discussion as we go along the class
+because i plan to do more of that
+
+ align:start position:0%
+because i plan to do more of that
+ 
+
+ align:start position:0%
+because i plan to do more of that
+so when you do your draft two
+
+ align:start position:0%
+so when you do your draft two
+ 
+
+ align:start position:0%
+so when you do your draft two
+and i'm going to ask you to make draft
+
+ align:start position:0%
+and i'm going to ask you to make draft
+ 
+
+ align:start position:0%
+and i'm going to ask you to make draft
+to a copy
+
+ align:start position:0%
+to a copy
+ 
+
+ align:start position:0%
+to a copy
+of draft one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that you can look back and see your
+
+ align:start position:0%
+so that you can look back and see your
+ 
+
+ align:start position:0%
+so that you can look back and see your
+progress
+
+ align:start position:0%
+progress
+ 
+
+ align:start position:0%
+progress
+don't amend
+
+ align:start position:0%
+don't amend
+ 
+
+ align:start position:0%
+don't amend
+don't edit draft one
+
+ align:start position:0%
+don't edit draft one
+ 
+
+ align:start position:0%
+don't edit draft one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so as time goes along see if you will
+
+ align:start position:0%
+um so as time goes along see if you will
+ 
+
+ align:start position:0%
+um so as time goes along see if you will
+go back and change anything you said
+
+ align:start position:0%
+go back and change anything you said
+ 
+
+ align:start position:0%
+go back and change anything you said
+about the story terms
+
+ align:start position:0%
+about the story terms
+ 
+
+ align:start position:0%
+about the story terms
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay did i step on anybody's toes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any comments questions
+
+ align:start position:0%
+any comments questions
+ 
+
+ align:start position:0%
+any comments questions
+this was their homework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's do some unfinished well let
+
+ align:start position:0%
+okay let's do some unfinished well let
+ 
+
+ align:start position:0%
+okay let's do some unfinished well let
+me give you more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh unfinished business and then new
+
+ align:start position:0%
+uh unfinished business and then new
+ 
+
+ align:start position:0%
+uh unfinished business and then new
+business
+
+ align:start position:0%
+business
+ 
+
+ align:start position:0%
+business
+uh better stated since you all uh love
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parliamentary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+procedures so much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you ever you have experience with
+
+ align:start position:0%
+you ever you have experience with
+ 
+
+ align:start position:0%
+you ever you have experience with
+parliamentary
+
+ align:start position:0%
+parliamentary
+ 
+
+ align:start position:0%
+parliamentary
+bodies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe we should do more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was chair of the faculty senate at
+
+ align:start position:0%
+i was chair of the faculty senate at
+ 
+
+ align:start position:0%
+i was chair of the faculty senate at
+howard for six years now
+
+ align:start position:0%
+howard for six years now
+ 
+
+ align:start position:0%
+howard for six years now
+senates are usually
+
+ align:start position:0%
+senates are usually
+ 
+
+ align:start position:0%
+senates are usually
+if at universities either a senate
+
+ align:start position:0%
+if at universities either a senate
+ 
+
+ align:start position:0%
+if at universities either a senate
+a committee of the faculty that does
+
+ align:start position:0%
+a committee of the faculty that does
+ 
+
+ align:start position:0%
+a committee of the faculty that does
+certain things
+
+ align:start position:0%
+certain things
+ 
+
+ align:start position:0%
+certain things
+and represents the faculty to the
+
+ align:start position:0%
+and represents the faculty to the
+ 
+
+ align:start position:0%
+and represents the faculty to the
+president
+
+ align:start position:0%
+president
+ 
+
+ align:start position:0%
+president
+uh at howard the senate uh
+
+ align:start position:0%
+uh at howard the senate uh
+ 
+
+ align:start position:0%
+uh at howard the senate uh
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+a um
+
+ align:start position:0%
+a um
+ 
+
+ align:start position:0%
+a um
+consists of all of the fact all the
+
+ align:start position:0%
+consists of all of the fact all the
+ 
+
+ align:start position:0%
+consists of all of the fact all the
+full-time faculty
+
+ align:start position:0%
+full-time faculty
+ 
+
+ align:start position:0%
+full-time faculty
+and it also consists of the president
+
+ align:start position:0%
+and it also consists of the president
+ 
+
+ align:start position:0%
+and it also consists of the president
+and the jesus ex-official members
+
+ align:start position:0%
+and the jesus ex-official members
+ 
+
+ align:start position:0%
+and the jesus ex-official members
+without vote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it the senate all of its committees
+
+ align:start position:0%
+and it the senate all of its committees
+ 
+
+ align:start position:0%
+and it the senate all of its committees
+and all of its meetings are presided
+
+ align:start position:0%
+and all of its meetings are presided
+ 
+
+ align:start position:0%
+and all of its meetings are presided
+over by a faculty person
+
+ align:start position:0%
+over by a faculty person
+ 
+
+ align:start position:0%
+over by a faculty person
+and the senate reports to the board of
+
+ align:start position:0%
+and the senate reports to the board of
+ 
+
+ align:start position:0%
+and the senate reports to the board of
+trustees
+
+ align:start position:0%
+trustees
+ 
+
+ align:start position:0%
+trustees
+through the president
+
+ align:start position:0%
+through the president
+ 
+
+ align:start position:0%
+through the president
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+they give the document to the president
+
+ align:start position:0%
+they give the document to the president
+ 
+
+ align:start position:0%
+they give the document to the president
+and the president is compelled to give
+
+ align:start position:0%
+and the president is compelled to give
+ 
+
+ align:start position:0%
+and the president is compelled to give
+it to the board
+
+ align:start position:0%
+it to the board
+ 
+
+ align:start position:0%
+it to the board
+now the president decide how to give it
+
+ align:start position:0%
+now the president decide how to give it
+ 
+
+ align:start position:0%
+now the president decide how to give it
+to the board
+
+ align:start position:0%
+to the board
+ 
+
+ align:start position:0%
+to the board
+okay but nevertheless that's the way it
+
+ align:start position:0%
+okay but nevertheless that's the way it
+ 
+
+ align:start position:0%
+okay but nevertheless that's the way it
+operates the point i'm trying to make is
+
+ align:start position:0%
+operates the point i'm trying to make is
+ 
+
+ align:start position:0%
+operates the point i'm trying to make is
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+try to imagine an engineer with the
+
+ align:start position:0%
+try to imagine an engineer with the
+ 
+
+ align:start position:0%
+try to imagine an engineer with the
+gavel
+
+ align:start position:0%
+gavel
+ 
+
+ align:start position:0%
+gavel
+parliamentary procedure
+
+ align:start position:0%
+parliamentary procedure
+ 
+
+ align:start position:0%
+parliamentary procedure
+at a university where you got a law
+
+ align:start position:0%
+at a university where you got a law
+ 
+
+ align:start position:0%
+at a university where you got a law
+school
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+department of business
+
+ align:start position:0%
+department of business
+ 
+
+ align:start position:0%
+department of business
+and i'll tell you the hardest ones to
+
+ align:start position:0%
+and i'll tell you the hardest ones to
+ 
+
+ align:start position:0%
+and i'll tell you the hardest ones to
+present over
+
+ align:start position:0%
+present over
+ 
+
+ align:start position:0%
+present over
+we got a medical school surgeons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every surgeon knows exactly
+
+ align:start position:0%
+every surgeon knows exactly
+ 
+
+ align:start position:0%
+every surgeon knows exactly
+the way he or she
+
+ align:start position:0%
+the way he or she
+ 
+
+ align:start position:0%
+the way he or she
+knows it's got to go
+
+ align:start position:0%
+knows it's got to go
+ 
+
+ align:start position:0%
+knows it's got to go
+and you can't tell
+
+ align:start position:0%
+and you can't tell
+ 
+
+ align:start position:0%
+and you can't tell
+one way
+
+ align:start position:0%
+one way
+ 
+
+ align:start position:0%
+one way
+the the lawyers there's a way to deal
+
+ align:start position:0%
+the the lawyers there's a way to deal
+ 
+
+ align:start position:0%
+the the lawyers there's a way to deal
+with them
+
+ align:start position:0%
+with them
+ 
+
+ align:start position:0%
+with them
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+they they they operate with the law just
+
+ align:start position:0%
+they they they operate with the law just
+ 
+
+ align:start position:0%
+they they they operate with the law just
+a lot like they do with ethics if one
+
+ align:start position:0%
+a lot like they do with ethics if one
+ 
+
+ align:start position:0%
+a lot like they do with ethics if one
+lawyer believes a another one believes b
+
+ align:start position:0%
+lawyer believes a another one believes b
+ 
+
+ align:start position:0%
+lawyer believes a another one believes b
+so when the one is believing a is
+
+ align:start position:0%
+so when the one is believing a is
+ 
+
+ align:start position:0%
+so when the one is believing a is
+tearing you up find one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that will use approach b
+
+ align:start position:0%
+that will use approach b
+ 
+
+ align:start position:0%
+that will use approach b
+right so now you're beginning to see
+
+ align:start position:0%
+right so now you're beginning to see
+ 
+
+ align:start position:0%
+right so now you're beginning to see
+what the connection that i am going to
+
+ align:start position:0%
+what the connection that i am going to
+ 
+
+ align:start position:0%
+what the connection that i am going to
+make that is between law and ethics that
+
+ align:start position:0%
+make that is between law and ethics that
+ 
+
+ align:start position:0%
+make that is between law and ethics that
+there's a whole lot of connection and
+
+ align:start position:0%
+there's a whole lot of connection and
+ 
+
+ align:start position:0%
+there's a whole lot of connection and
+depending on what country you're in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competing uh on what country you're in
+
+ align:start position:0%
+competing uh on what country you're in
+ 
+
+ align:start position:0%
+competing uh on what country you're in
+you may find that there's no difference
+
+ align:start position:0%
+you may find that there's no difference
+ 
+
+ align:start position:0%
+you may find that there's no difference
+between law and entities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may go to the middle
+
+ align:start position:0%
+you may go to the middle
+ 
+
+ align:start position:0%
+you may go to the middle
+east and the judges
+
+ align:start position:0%
+east and the judges
+ 
+
+ align:start position:0%
+east and the judges
+have on clerical
+
+ align:start position:0%
+have on clerical
+ 
+
+ align:start position:0%
+have on clerical
+uh outfits
+
+ align:start position:0%
+uh outfits
+ 
+
+ align:start position:0%
+uh outfits
+with the koran in front of them
+
+ align:start position:0%
+with the koran in front of them
+ 
+
+ align:start position:0%
+with the koran in front of them
+and they're doing
+
+ align:start position:0%
+and they're doing
+ 
+
+ align:start position:0%
+and they're doing
+they don't see any difference between
+
+ align:start position:0%
+they don't see any difference between
+ 
+
+ align:start position:0%
+they don't see any difference between
+law ethics and religion no difference
+
+ align:start position:0%
+law ethics and religion no difference
+ 
+
+ align:start position:0%
+law ethics and religion no difference
+it's all the same thing
+
+ align:start position:0%
+it's all the same thing
+ 
+
+ align:start position:0%
+it's all the same thing
+okay uh so where was i
+
+ align:start position:0%
+okay uh so where was i
+ 
+
+ align:start position:0%
+okay uh so where was i
+oh we don't want to do old business
+
+ align:start position:0%
+oh we don't want to do old business
+ 
+
+ align:start position:0%
+oh we don't want to do old business
+unfinished business uh what were we
+
+ align:start position:0%
+unfinished business uh what were we
+ 
+
+ align:start position:0%
+unfinished business uh what were we
+doing last i don't think we finished it
+
+ align:start position:0%
+doing last i don't think we finished it
+ 
+
+ align:start position:0%
+doing last i don't think we finished it
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+there's something i think is unfinished
+
+ align:start position:0%
+there's something i think is unfinished
+ 
+
+ align:start position:0%
+there's something i think is unfinished
+about that uh
+
+ align:start position:0%
+about that uh
+ 
+
+ align:start position:0%
+about that uh
+about our discussion on that
+
+ align:start position:0%
+about our discussion on that
+ 
+
+ align:start position:0%
+about our discussion on that
+we talked about ford
+
+ align:start position:0%
+we talked about ford
+ 
+
+ align:start position:0%
+we talked about ford
+but we didn't talk about any persons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i want to put the question to you
+
+ align:start position:0%
+now i want to put the question to you
+ 
+
+ align:start position:0%
+now i want to put the question to you
+uh first let me put a an observation to
+
+ align:start position:0%
+uh first let me put a an observation to
+ 
+
+ align:start position:0%
+uh first let me put a an observation to
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+a corporation has the status of a person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means a corporation can commit a
+
+ align:start position:0%
+so that means a corporation can commit a
+ 
+
+ align:start position:0%
+so that means a corporation can commit a
+crime
+
+ align:start position:0%
+crime
+ 
+
+ align:start position:0%
+crime
+a corporation can be punished for the
+
+ align:start position:0%
+a corporation can be punished for the
+ 
+
+ align:start position:0%
+a corporation can be punished for the
+prime crime
+
+ align:start position:0%
+prime crime
+ 
+
+ align:start position:0%
+prime crime
+even though nobody in the corporation
+
+ align:start position:0%
+even though nobody in the corporation
+ 
+
+ align:start position:0%
+even though nobody in the corporation
+has been found guilty of committing
+
+ align:start position:0%
+has been found guilty of committing
+ 
+
+ align:start position:0%
+has been found guilty of committing
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+okay we agree on that
+
+ align:start position:0%
+okay we agree on that
+ 
+
+ align:start position:0%
+okay we agree on that
+if you find a better sharper statement
+
+ align:start position:0%
+if you find a better sharper statement
+ 
+
+ align:start position:0%
+if you find a better sharper statement
+and bring it in next class and we'll
+
+ align:start position:0%
+and bring it in next class and we'll
+ 
+
+ align:start position:0%
+and bring it in next class and we'll
+amend it what i just said
+
+ align:start position:0%
+amend it what i just said
+ 
+
+ align:start position:0%
+amend it what i just said
+okay uh when engineering ethics was um
+
+ align:start position:0%
+okay uh when engineering ethics was um
+ 
+
+ align:start position:0%
+okay uh when engineering ethics was um
+really invented back in the early early
+
+ align:start position:0%
+really invented back in the early early
+ 
+
+ align:start position:0%
+really invented back in the early early
+70s
+
+ align:start position:0%
+70s
+ 
+
+ align:start position:0%
+70s
+did i give you a history of engineering
+
+ align:start position:0%
+did i give you a history of engineering
+ 
+
+ align:start position:0%
+did i give you a history of engineering
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+or the sts movement yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there were two great hopes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the scholars mainly the philosophers
+
+ align:start position:0%
+of the scholars mainly the philosophers
+ 
+
+ align:start position:0%
+of the scholars mainly the philosophers
+in in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one great hope was that they someone
+
+ align:start position:0%
+one great hope was that they someone
+ 
+
+ align:start position:0%
+one great hope was that they someone
+would be able to discover a new ethic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe from a utilitarian
+
+ align:start position:0%
+maybe from a utilitarian
+ 
+
+ align:start position:0%
+maybe from a utilitarian
+variety maybe from
+
+ align:start position:0%
+variety maybe from
+ 
+
+ align:start position:0%
+variety maybe from
+a um
+
+ align:start position:0%
+a um
+ 
+
+ align:start position:0%
+a um
+categorical or
+
+ align:start position:0%
+categorical or
+ 
+
+ align:start position:0%
+categorical or
+deontological variety maybe a new
+
+ align:start position:0%
+deontological variety maybe a new
+ 
+
+ align:start position:0%
+deontological variety maybe a new
+variety but a lot of people thought they
+
+ align:start position:0%
+variety but a lot of people thought they
+ 
+
+ align:start position:0%
+variety but a lot of people thought they
+would be able to find a new ethic i'm
+
+ align:start position:0%
+would be able to find a new ethic i'm
+ 
+
+ align:start position:0%
+would be able to find a new ethic i'm
+not so sure that they did meaning a new
+
+ align:start position:0%
+not so sure that they did meaning a new
+ 
+
+ align:start position:0%
+not so sure that they did meaning a new
+moral
+
+ align:start position:0%
+moral
+ 
+
+ align:start position:0%
+moral
+standard on which to face
+
+ align:start position:0%
+standard on which to face
+ 
+
+ align:start position:0%
+standard on which to face
+decisions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+actually they did i'll tell you about
+
+ align:start position:0%
+actually they did i'll tell you about
+ 
+
+ align:start position:0%
+actually they did i'll tell you about
+one or two two that i think they might
+
+ align:start position:0%
+one or two two that i think they might
+ 
+
+ align:start position:0%
+one or two two that i think they might
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+done or we might have done
+
+ align:start position:0%
+done or we might have done
+ 
+
+ align:start position:0%
+done or we might have done
+um so that was one of the great hopes
+
+ align:start position:0%
+um so that was one of the great hopes
+ 
+
+ align:start position:0%
+um so that was one of the great hopes
+another great hope
+
+ align:start position:0%
+another great hope
+ 
+
+ align:start position:0%
+another great hope
+was to be able to
+
+ align:start position:0%
+was to be able to
+ 
+
+ align:start position:0%
+was to be able to
+give a corporation
+
+ align:start position:0%
+give a corporation
+ 
+
+ align:start position:0%
+give a corporation
+moral agency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the hope was to be able to say that
+
+ align:start position:0%
+that the hope was to be able to say that
+ 
+
+ align:start position:0%
+that the hope was to be able to say that
+a corporation did the wrong thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh there was this paper that was
+
+ align:start position:0%
+and uh there was this paper that was
+ 
+
+ align:start position:0%
+and uh there was this paper that was
+written
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+uh one of the i'll call him out one of
+
+ align:start position:0%
+uh one of the i'll call him out one of
+ 
+
+ align:start position:0%
+uh one of the i'll call him out one of
+the giants in the field his name is john
+
+ align:start position:0%
+the giants in the field his name is john
+ 
+
+ align:start position:0%
+the giants in the field his name is john
+ladd l-a-d-d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+john ladd is uh
+
+ align:start position:0%
+john ladd is uh
+ 
+
+ align:start position:0%
+john ladd is uh
+in semi retirement he's uh i guess he's
+
+ align:start position:0%
+in semi retirement he's uh i guess he's
+ 
+
+ align:start position:0%
+in semi retirement he's uh i guess he's
+about 80 now
+
+ align:start position:0%
+about 80 now
+ 
+
+ align:start position:0%
+about 80 now
+but he's still active still writes still
+
+ align:start position:0%
+but he's still active still writes still
+ 
+
+ align:start position:0%
+but he's still active still writes still
+comes to meetings
+
+ align:start position:0%
+comes to meetings
+ 
+
+ align:start position:0%
+comes to meetings
+um john ladd wrote this paper
+
+ align:start position:0%
+um john ladd wrote this paper
+ 
+
+ align:start position:0%
+um john ladd wrote this paper
+and what it said was that there's
+
+ align:start position:0%
+and what it said was that there's
+ 
+
+ align:start position:0%
+and what it said was that there's
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh any moral tradition that would allow
+
+ align:start position:0%
+uh any moral tradition that would allow
+ 
+
+ align:start position:0%
+uh any moral tradition that would allow
+the assignment of moral agency to a
+
+ align:start position:0%
+the assignment of moral agency to a
+ 
+
+ align:start position:0%
+the assignment of moral agency to a
+corporation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a matter of fact he said there's only
+
+ align:start position:0%
+as a matter of fact he said there's only
+ 
+
+ align:start position:0%
+as a matter of fact he said there's only
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+assignment that you can make
+
+ align:start position:0%
+assignment that you can make
+ 
+
+ align:start position:0%
+assignment that you can make
+to a group as opposed to an individual
+
+ align:start position:0%
+to a group as opposed to an individual
+ 
+
+ align:start position:0%
+to a group as opposed to an individual
+you want to take a wild guess as to what
+
+ align:start position:0%
+you want to take a wild guess as to what
+ 
+
+ align:start position:0%
+you want to take a wild guess as to what
+group that is
+
+ align:start position:0%
+group that is
+ 
+
+ align:start position:0%
+group that is
+a collection of persons that has moral
+
+ align:start position:0%
+a collection of persons that has moral
+ 
+
+ align:start position:0%
+a collection of persons that has moral
+that has a
+
+ align:start position:0%
+that has a
+ 
+
+ align:start position:0%
+that has a
+moral agency a collection as opposed to
+
+ align:start position:0%
+moral agency a collection as opposed to
+ 
+
+ align:start position:0%
+moral agency a collection as opposed to
+an individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you make a wild guess you'll probably
+
+ align:start position:0%
+if you make a wild guess you'll probably
+ 
+
+ align:start position:0%
+if you make a wild guess you'll probably
+be right
+
+ align:start position:0%
+be right
+ 
+
+ align:start position:0%
+be right
+a religion
+
+ align:start position:0%
+a religion
+ 
+
+ align:start position:0%
+a religion
+nope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nope
+
+ align:start position:0%
+nope
+ 
+
+ align:start position:0%
+nope
+that's a good one because you would
+
+ align:start position:0%
+that's a good one because you would
+ 
+
+ align:start position:0%
+that's a good one because you would
+think that because of the hierarchical
+
+ align:start position:0%
+think that because of the hierarchical
+ 
+
+ align:start position:0%
+think that because of the hierarchical
+arrangement that no
+
+ align:start position:0%
+arrangement that no
+ 
+
+ align:start position:0%
+arrangement that no
+family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the kids
+
+ align:start position:0%
+because the kids
+ 
+
+ align:start position:0%
+because the kids
+their parents are responsible for what
+
+ align:start position:0%
+their parents are responsible for what
+ 
+
+ align:start position:0%
+their parents are responsible for what
+morally responsible for the kids moral
+
+ align:start position:0%
+morally responsible for the kids moral
+ 
+
+ align:start position:0%
+morally responsible for the kids moral
+behavior he argued and i don't remember
+
+ align:start position:0%
+behavior he argued and i don't remember
+ 
+
+ align:start position:0%
+behavior he argued and i don't remember
+anybody arguing back on it now this is
+
+ align:start position:0%
+anybody arguing back on it now this is
+ 
+
+ align:start position:0%
+anybody arguing back on it now this is
+john ladd talking
+
+ align:start position:0%
+john ladd talking
+ 
+
+ align:start position:0%
+john ladd talking
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if you ever decide to do anything with
+
+ align:start position:0%
+if you ever decide to do anything with
+ 
+
+ align:start position:0%
+if you ever decide to do anything with
+john ladd uh i'll give you a phone
+
+ align:start position:0%
+john ladd uh i'll give you a phone
+ 
+
+ align:start position:0%
+john ladd uh i'll give you a phone
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+i have to look at that but i got it and
+
+ align:start position:0%
+i have to look at that but i got it and
+ 
+
+ align:start position:0%
+i have to look at that but i got it and
+i got his home phone number
+
+ align:start position:0%
+i got his home phone number
+ 
+
+ align:start position:0%
+i got his home phone number
+he'd really like to talk to you
+
+ align:start position:0%
+he'd really like to talk to you
+ 
+
+ align:start position:0%
+he'd really like to talk to you
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that pretty much killed it that uh
+
+ align:start position:0%
+so that pretty much killed it that uh
+ 
+
+ align:start position:0%
+so that pretty much killed it that uh
+corporations could not have moral agency
+
+ align:start position:0%
+corporations could not have moral agency
+ 
+
+ align:start position:0%
+corporations could not have moral agency
+now i'm going to talk about a way to
+
+ align:start position:0%
+now i'm going to talk about a way to
+ 
+
+ align:start position:0%
+now i'm going to talk about a way to
+make a corporation have moral agency but
+
+ align:start position:0%
+make a corporation have moral agency but
+ 
+
+ align:start position:0%
+make a corporation have moral agency but
+it's going to be new but i'm going to
+
+ align:start position:0%
+it's going to be new but i'm going to
+ 
+
+ align:start position:0%
+it's going to be new but i'm going to
+put that towards the end of the course
+
+ align:start position:0%
+put that towards the end of the course
+ 
+
+ align:start position:0%
+put that towards the end of the course
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when we talked about the ford pinto case
+
+ align:start position:0%
+when we talked about the ford pinto case
+ 
+
+ align:start position:0%
+when we talked about the ford pinto case
+i remember us talking a lot about ford
+
+ align:start position:0%
+i remember us talking a lot about ford
+ 
+
+ align:start position:0%
+i remember us talking a lot about ford
+and the ford pinto
+
+ align:start position:0%
+and the ford pinto
+ 
+
+ align:start position:0%
+and the ford pinto
+but i don't remember us talking about
+
+ align:start position:0%
+but i don't remember us talking about
+ 
+
+ align:start position:0%
+but i don't remember us talking about
+individuals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+were there any individual behaviors in
+
+ align:start position:0%
+were there any individual behaviors in
+ 
+
+ align:start position:0%
+were there any individual behaviors in
+there that we should discuss
+
+ align:start position:0%
+there that we should discuss
+ 
+
+ align:start position:0%
+there that we should discuss
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+characterize that behavior as either
+
+ align:start position:0%
+characterize that behavior as either
+ 
+
+ align:start position:0%
+characterize that behavior as either
+morally moral ethical or unethical
+
+ align:start position:0%
+morally moral ethical or unethical
+ 
+
+ align:start position:0%
+morally moral ethical or unethical
+any difference between moral and morals
+
+ align:start position:0%
+any difference between moral and morals
+ 
+
+ align:start position:0%
+any difference between moral and morals
+and ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see that's one thing that uh is typical
+
+ align:start position:0%
+see that's one thing that uh is typical
+ 
+
+ align:start position:0%
+see that's one thing that uh is typical
+of this course
+
+ align:start position:0%
+of this course
+ 
+
+ align:start position:0%
+of this course
+typically you get halfway through the
+
+ align:start position:0%
+typically you get halfway through the
+ 
+
+ align:start position:0%
+typically you get halfway through the
+course before somebody will define what
+
+ align:start position:0%
+course before somebody will define what
+ 
+
+ align:start position:0%
+course before somebody will define what
+the course means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's not unusual at all but but
+
+ align:start position:0%
+okay that's not unusual at all but but
+ 
+
+ align:start position:0%
+okay that's not unusual at all but but
+it's about time for us to get a little
+
+ align:start position:0%
+it's about time for us to get a little
+ 
+
+ align:start position:0%
+it's about time for us to get a little
+sophisticated about
+
+ align:start position:0%
+sophisticated about
+ 
+
+ align:start position:0%
+sophisticated about
+those two words
+
+ align:start position:0%
+those two words
+ 
+
+ align:start position:0%
+those two words
+okay so i'll give you a chance to look
+
+ align:start position:0%
+okay so i'll give you a chance to look
+ 
+
+ align:start position:0%
+okay so i'll give you a chance to look
+them up first and then i'll tell you
+
+ align:start position:0%
+them up first and then i'll tell you
+ 
+
+ align:start position:0%
+them up first and then i'll tell you
+what's going on uh
+
+ align:start position:0%
+what's going on uh
+ 
+
+ align:start position:0%
+what's going on uh
+yeah uh
+
+ align:start position:0%
+yeah uh
+ 
+
+ align:start position:0%
+yeah uh
+are there any individuals that we need
+
+ align:start position:0%
+are there any individuals that we need
+ 
+
+ align:start position:0%
+are there any individuals that we need
+to talk about in this fourth pinto case
+
+ align:start position:0%
+to talk about in this fourth pinto case
+ 
+
+ align:start position:0%
+to talk about in this fourth pinto case
+do they name any or they just talk about
+
+ align:start position:0%
+do they name any or they just talk about
+ 
+
+ align:start position:0%
+do they name any or they just talk about
+engineers
+
+ align:start position:0%
+engineers
+ 
+
+ align:start position:0%
+engineers
+generally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in our little blurb they name one they
+
+ align:start position:0%
+in our little blurb they name one they
+ 
+
+ align:start position:0%
+in our little blurb they name one they
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+echoed the director of automotive safety
+
+ align:start position:0%
+echoed the director of automotive safety
+ 
+
+ align:start position:0%
+echoed the director of automotive safety
+yeah what did they say about it he is
+
+ align:start position:0%
+yeah what did they say about it he is
+ 
+
+ align:start position:0%
+yeah what did they say about it he is
+the one who actually issued the study
+
+ align:start position:0%
+the one who actually issued the study
+ 
+
+ align:start position:0%
+the one who actually issued the study
+with the cost benefit analysis
+
+ align:start position:0%
+with the cost benefit analysis
+ 
+
+ align:start position:0%
+with the cost benefit analysis
+including that
+
+ align:start position:0%
+including that
+ 
+
+ align:start position:0%
+including that
+it was more costly to
+
+ align:start position:0%
+it was more costly to
+ 
+
+ align:start position:0%
+it was more costly to
+add in the safety feature okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he's one character yeah i would say
+
+ align:start position:0%
+so he's one character yeah i would say
+ 
+
+ align:start position:0%
+so he's one character yeah i would say
+another one that's not mentioned in the
+
+ align:start position:0%
+another one that's not mentioned in the
+ 
+
+ align:start position:0%
+another one that's not mentioned in the
+article
+
+ align:start position:0%
+article
+ 
+
+ align:start position:0%
+article
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+iacocca right here
+
+ align:start position:0%
+iacocca right here
+ 
+
+ align:start position:0%
+iacocca right here
+who said we need to make a vehicle
+
+ align:start position:0%
+who said we need to make a vehicle
+ 
+
+ align:start position:0%
+who said we need to make a vehicle
+that's less than two thousand dollars
+
+ align:start position:0%
+that's less than two thousand dollars
+ 
+
+ align:start position:0%
+that's less than two thousand dollars
+you gotta do it
+
+ align:start position:0%
+you gotta do it
+ 
+
+ align:start position:0%
+you gotta do it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh lee iacocca
+
+ align:start position:0%
+uh lee iacocca
+ 
+
+ align:start position:0%
+uh lee iacocca
+interestingly enough after that
+
+ align:start position:0%
+interestingly enough after that
+ 
+
+ align:start position:0%
+interestingly enough after that
+i think you all probably know better
+
+ align:start position:0%
+i think you all probably know better
+ 
+
+ align:start position:0%
+i think you all probably know better
+than i became quite a corporate hero in
+
+ align:start position:0%
+than i became quite a corporate hero in
+ 
+
+ align:start position:0%
+than i became quite a corporate hero in
+america
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well uh echols
+
+ align:start position:0%
+well uh echols
+ 
+
+ align:start position:0%
+well uh echols
+now what do you think echols would say
+
+ align:start position:0%
+now what do you think echols would say
+ 
+
+ align:start position:0%
+now what do you think echols would say
+if eccles came in here what do you think
+
+ align:start position:0%
+if eccles came in here what do you think
+ 
+
+ align:start position:0%
+if eccles came in here what do you think
+eccles
+
+ align:start position:0%
+eccles
+ 
+
+ align:start position:0%
+eccles
+would say how he would say would he
+
+ align:start position:0%
+would say how he would say would he
+ 
+
+ align:start position:0%
+would say how he would say would he
+defend what he did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and could you defend what he did
+
+ align:start position:0%
+and could you defend what he did
+ 
+
+ align:start position:0%
+and could you defend what he did
+and could you consider uh criticize what
+
+ align:start position:0%
+and could you consider uh criticize what
+ 
+
+ align:start position:0%
+and could you consider uh criticize what
+he did
+
+ align:start position:0%
+he did
+ 
+
+ align:start position:0%
+he did
+and you can play devil's advocate you
+
+ align:start position:0%
+and you can play devil's advocate you
+ 
+
+ align:start position:0%
+and you can play devil's advocate you
+can give me both arguments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i assume he would defend what he did
+
+ align:start position:0%
+so i assume he would defend what he did
+ 
+
+ align:start position:0%
+so i assume he would defend what he did
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+that it was that cost-benefit analysis
+
+ align:start position:0%
+that it was that cost-benefit analysis
+ 
+
+ align:start position:0%
+that it was that cost-benefit analysis
+which assigns the cost
+
+ align:start position:0%
+which assigns the cost
+ 
+
+ align:start position:0%
+which assigns the cost
+to human life
+
+ align:start position:0%
+to human life
+ 
+
+ align:start position:0%
+to human life
+is legitimate and it's a practice used
+
+ align:start position:0%
+is legitimate and it's a practice used
+ 
+
+ align:start position:0%
+is legitimate and it's a practice used
+is tradition
+
+ align:start position:0%
+is tradition
+ 
+
+ align:start position:0%
+is tradition
+yeah by
+
+ align:start position:0%
+yeah by
+ 
+
+ align:start position:0%
+yeah by
+engineers
+
+ align:start position:0%
+engineers
+ 
+
+ align:start position:0%
+engineers
+and engineering managers in deciding
+
+ align:start position:0%
+and engineering managers in deciding
+ 
+
+ align:start position:0%
+and engineering managers in deciding
+whether a risk is acceptable
+
+ align:start position:0%
+whether a risk is acceptable
+ 
+
+ align:start position:0%
+whether a risk is acceptable
+all right let's play a game suppose i
+
+ align:start position:0%
+all right let's play a game suppose i
+ 
+
+ align:start position:0%
+all right let's play a game suppose i
+have echoes and i hire you not as my
+
+ align:start position:0%
+have echoes and i hire you not as my
+ 
+
+ align:start position:0%
+have echoes and i hire you not as my
+lawyer but as my ethicist
+
+ align:start position:0%
+lawyer but as my ethicist
+ 
+
+ align:start position:0%
+lawyer but as my ethicist
+and i'm going before it before an
+
+ align:start position:0%
+and i'm going before it before an
+ 
+
+ align:start position:0%
+and i'm going before it before an
+ethical review and you've got to present
+
+ align:start position:0%
+ethical review and you've got to present
+ 
+
+ align:start position:0%
+ethical review and you've got to present
+my case
+
+ align:start position:0%
+my case
+ 
+
+ align:start position:0%
+my case
+to y'all
+
+ align:start position:0%
+to y'all
+ 
+
+ align:start position:0%
+to y'all
+uh and you got to ground us
+
+ align:start position:0%
+uh and you got to ground us
+ 
+
+ align:start position:0%
+uh and you got to ground us
+just can't say give me an opinion how
+
+ align:start position:0%
+just can't say give me an opinion how
+ 
+
+ align:start position:0%
+just can't say give me an opinion how
+would you ground it how can we ground it
+
+ align:start position:0%
+would you ground it how can we ground it
+ 
+
+ align:start position:0%
+would you ground it how can we ground it
+in the fact that
+
+ align:start position:0%
+in the fact that
+ 
+
+ align:start position:0%
+in the fact that
+managers that is their responsibility
+
+ align:start position:0%
+managers that is their responsibility
+ 
+
+ align:start position:0%
+managers that is their responsibility
+like i think we discussed this a little
+
+ align:start position:0%
+like i think we discussed this a little
+ 
+
+ align:start position:0%
+like i think we discussed this a little
+bit last time to worry about money as a
+
+ align:start position:0%
+bit last time to worry about money as a
+ 
+
+ align:start position:0%
+bit last time to worry about money as a
+manager
+
+ align:start position:0%
+manager
+ 
+
+ align:start position:0%
+manager
+that's my ethical responsibility
+
+ align:start position:0%
+that's my ethical responsibility
+ 
+
+ align:start position:0%
+that's my ethical responsibility
+to conduct a study that is going to
+
+ align:start position:0%
+to conduct a study that is going to
+ 
+
+ align:start position:0%
+to conduct a study that is going to
+accurately
+
+ align:start position:0%
+accurately
+ 
+
+ align:start position:0%
+accurately
+tell you how this is going to affect the
+
+ align:start position:0%
+tell you how this is going to affect the
+ 
+
+ align:start position:0%
+tell you how this is going to affect the
+company's finances okay so how can you
+
+ align:start position:0%
+company's finances okay so how can you
+ 
+
+ align:start position:0%
+company's finances okay so how can you
+justify what is that your personal
+
+ align:start position:0%
+justify what is that your personal
+ 
+
+ align:start position:0%
+justify what is that your personal
+theory or is there some out some theory
+
+ align:start position:0%
+theory or is there some out some theory
+ 
+
+ align:start position:0%
+theory or is there some out some theory
+out you can reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you can probably use something of a
+
+ align:start position:0%
+well you can probably use something of a
+ 
+
+ align:start position:0%
+well you can probably use something of a
+content nature not exactly cons but talk
+
+ align:start position:0%
+content nature not exactly cons but talk
+ 
+
+ align:start position:0%
+content nature not exactly cons but talk
+about a contract do you have an
+
+ align:start position:0%
+about a contract do you have an
+ 
+
+ align:start position:0%
+about a contract do you have an
+obligation that's a principle is there a
+
+ align:start position:0%
+obligation that's a principle is there a
+ 
+
+ align:start position:0%
+obligation that's a principle is there a
+principle that you have to live up your
+
+ align:start position:0%
+principle that you have to live up your
+ 
+
+ align:start position:0%
+principle that you have to live up your
+to your contract right
+
+ align:start position:0%
+to your contract right
+ 
+
+ align:start position:0%
+to your contract right
+that is the contract that i have with
+
+ align:start position:0%
+that is the contract that i have with
+ 
+
+ align:start position:0%
+that is the contract that i have with
+the country with the company when i took
+
+ align:start position:0%
+the country with the company when i took
+ 
+
+ align:start position:0%
+the country with the company when i took
+this job
+
+ align:start position:0%
+this job
+ 
+
+ align:start position:0%
+this job
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that was the contract i'm worrying about
+
+ align:start position:0%
+that was the contract i'm worrying about
+ 
+
+ align:start position:0%
+that was the contract i'm worrying about
+money bottom line making this thing work
+
+ align:start position:0%
+money bottom line making this thing work
+ 
+
+ align:start position:0%
+money bottom line making this thing work
+and that is my
+
+ align:start position:0%
+and that is my
+ 
+
+ align:start position:0%
+and that is my
+my confidence
+
+ align:start position:0%
+my confidence
+ 
+
+ align:start position:0%
+my confidence
+okay now we have to worry that after
+
+ align:start position:0%
+okay now we have to worry that after
+ 
+
+ align:start position:0%
+okay now we have to worry that after
+you've said that
+
+ align:start position:0%
+you've said that
+ 
+
+ align:start position:0%
+you've said that
+that there's a an opposing point of view
+
+ align:start position:0%
+that there's a an opposing point of view
+ 
+
+ align:start position:0%
+that there's a an opposing point of view
+that's going to give a different answer
+
+ align:start position:0%
+that's going to give a different answer
+ 
+
+ align:start position:0%
+that's going to give a different answer
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+and that the interesting part about that
+
+ align:start position:0%
+and that the interesting part about that
+ 
+
+ align:start position:0%
+and that the interesting part about that
+is that your customers are most likely
+
+ align:start position:0%
+is that your customers are most likely
+ 
+
+ align:start position:0%
+is that your customers are most likely
+going to use your utilitarian because
+
+ align:start position:0%
+going to use your utilitarian because
+ 
+
+ align:start position:0%
+going to use your utilitarian because
+that affects them
+
+ align:start position:0%
+that affects them
+ 
+
+ align:start position:0%
+that affects them
+that's where they're going gonna see it
+
+ align:start position:0%
+that's where they're going gonna see it
+ 
+
+ align:start position:0%
+that's where they're going gonna see it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+probably uh echoes or somebody in eccles
+
+ align:start position:0%
+probably uh echoes or somebody in eccles
+ 
+
+ align:start position:0%
+probably uh echoes or somebody in eccles
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+would typically say what you just said
+
+ align:start position:0%
+would typically say what you just said
+ 
+
+ align:start position:0%
+would typically say what you just said
+but would say add something to it we've
+
+ align:start position:0%
+but would say add something to it we've
+ 
+
+ align:start position:0%
+but would say add something to it we've
+already said this in the class
+
+ align:start position:0%
+already said this in the class
+ 
+
+ align:start position:0%
+already said this in the class
+we've already seen it and that is
+
+ align:start position:0%
+we've already seen it and that is
+ 
+
+ align:start position:0%
+we've already seen it and that is
+that the ethical responsibility beyond
+
+ align:start position:0%
+that the ethical responsibility beyond
+ 
+
+ align:start position:0%
+that the ethical responsibility beyond
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is at a higher level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now let me give you something
+
+ align:start position:0%
+now let me give you something
+ 
+
+ align:start position:0%
+now let me give you something
+that will come into play once you say
+
+ align:start position:0%
+that will come into play once you say
+ 
+
+ align:start position:0%
+that will come into play once you say
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that i've done my job
+
+ align:start position:0%
+that i've done my job
+ 
+
+ align:start position:0%
+that i've done my job
+the utilitarian responsibility
+
+ align:start position:0%
+the utilitarian responsibility
+ 
+
+ align:start position:0%
+the utilitarian responsibility
+is at the higher level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's play that again
+
+ align:start position:0%
+okay let's play that again
+ 
+
+ align:start position:0%
+okay let's play that again
+my job
+
+ align:start position:0%
+my job
+ 
+
+ align:start position:0%
+my job
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the ontology
+
+ align:start position:0%
+the ontology
+ 
+
+ align:start position:0%
+the ontology
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+a principal
+
+ align:start position:0%
+a principal
+ 
+
+ align:start position:0%
+a principal
+live up to my contracts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i made a deal
+
+ align:start position:0%
+i made a deal
+ 
+
+ align:start position:0%
+i made a deal
+the the contract was legal
+
+ align:start position:0%
+the the contract was legal
+ 
+
+ align:start position:0%
+the the contract was legal
+wait what's the
+
+ align:start position:0%
+wait what's the
+ 
+
+ align:start position:0%
+wait what's the
+what role are you playing now i don't
+
+ align:start position:0%
+what role are you playing now i don't
+ 
+
+ align:start position:0%
+what role are you playing now i don't
+know which world i'm i'm playing eckel's
+
+ align:start position:0%
+know which world i'm i'm playing eckel's
+ 
+
+ align:start position:0%
+know which world i'm i'm playing eckel's
+role okay and
+
+ align:start position:0%
+role okay and
+ 
+
+ align:start position:0%
+role okay and
+then what's the contract
+
+ align:start position:0%
+then what's the contract
+ 
+
+ align:start position:0%
+then what's the contract
+the contract is my job description
+
+ align:start position:0%
+the contract is my job description
+ 
+
+ align:start position:0%
+the contract is my job description
+uh which has legal force because the
+
+ align:start position:0%
+uh which has legal force because the
+ 
+
+ align:start position:0%
+uh which has legal force because the
+corporation
+
+ align:start position:0%
+corporation
+ 
+
+ align:start position:0%
+corporation
+is incorporated that is that it had that
+
+ align:start position:0%
+is incorporated that is that it had that
+ 
+
+ align:start position:0%
+is incorporated that is that it had that
+there is exists a contract between
+
+ align:start position:0%
+there is exists a contract between
+ 
+
+ align:start position:0%
+there is exists a contract between
+the entity and society
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh you can play that game straight
+
+ align:start position:0%
+so uh you can play that game straight
+ 
+
+ align:start position:0%
+so uh you can play that game straight
+down the line there's a contract between
+
+ align:start position:0%
+down the line there's a contract between
+ 
+
+ align:start position:0%
+down the line there's a contract between
+the entity and society in the articles
+
+ align:start position:0%
+the entity and society in the articles
+ 
+
+ align:start position:0%
+the entity and society in the articles
+of incorporation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is a hierarchical
+
+ align:start position:0%
+and that is a hierarchical
+ 
+
+ align:start position:0%
+and that is a hierarchical
+organization
+
+ align:start position:0%
+organization
+ 
+
+ align:start position:0%
+organization
+and my position in the hierarchy has a
+
+ align:start position:0%
+and my position in the hierarchy has a
+ 
+
+ align:start position:0%
+and my position in the hierarchy has a
+name and a responsibility
+
+ align:start position:0%
+name and a responsibility
+ 
+
+ align:start position:0%
+name and a responsibility
+or mission
+
+ align:start position:0%
+or mission
+ 
+
+ align:start position:0%
+or mission
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to live up to that principle i have to
+
+ align:start position:0%
+to live up to that principle i have to
+ 
+
+ align:start position:0%
+to live up to that principle i have to
+live up to that
+
+ align:start position:0%
+live up to that
+ 
+
+ align:start position:0%
+live up to that
+uh mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now to break a contract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the tip
+
+ align:start position:0%
+here's the tip
+ 
+
+ align:start position:0%
+here's the tip
+now we're we're in the gray area between
+
+ align:start position:0%
+now we're we're in the gray area between
+ 
+
+ align:start position:0%
+now we're we're in the gray area between
+ethics and law
+
+ align:start position:0%
+ethics and law
+ 
+
+ align:start position:0%
+ethics and law
+and if we shift too much to the law area
+
+ align:start position:0%
+and if we shift too much to the law area
+ 
+
+ align:start position:0%
+and if we shift too much to the law area
+you'll know it because i won't know what
+
+ align:start position:0%
+you'll know it because i won't know what
+ 
+
+ align:start position:0%
+you'll know it because i won't know what
+i'm talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh but i
+
+ align:start position:0%
+uh but i
+ 
+
+ align:start position:0%
+uh but i
+do know that uh to break a contract both
+
+ align:start position:0%
+do know that uh to break a contract both
+ 
+
+ align:start position:0%
+do know that uh to break a contract both
+parties to the contract have to agree to
+
+ align:start position:0%
+parties to the contract have to agree to
+ 
+
+ align:start position:0%
+parties to the contract have to agree to
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+unless you
+
+ align:start position:0%
+unless you
+ 
+
+ align:start position:0%
+unless you
+break a leg or something like that but
+
+ align:start position:0%
+break a leg or something like that but
+ 
+
+ align:start position:0%
+break a leg or something like that but
+it takes a it takes some agreement
+
+ align:start position:0%
+it takes a it takes some agreement
+ 
+
+ align:start position:0%
+it takes a it takes some agreement
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so your point is going to your point is
+
+ align:start position:0%
+so your point is going to your point is
+ 
+
+ align:start position:0%
+so your point is going to your point is
+going to be included in what i'm about
+
+ align:start position:0%
+going to be included in what i'm about
+ 
+
+ align:start position:0%
+going to be included in what i'm about
+to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know if this is in this
+
+ align:start position:0%
+i don't know if this is in this
+ 
+
+ align:start position:0%
+i don't know if this is in this
+particular textbook or not but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's uh something that's in
+
+ align:start position:0%
+it's uh something that's in
+ 
+
+ align:start position:0%
+it's uh something that's in
+probably um
+
+ align:start position:0%
+probably um
+ 
+
+ align:start position:0%
+probably um
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+engineering ethics textbooks or in
+
+ align:start position:0%
+engineering ethics textbooks or in
+ 
+
+ align:start position:0%
+engineering ethics textbooks or in
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+ethics textbooks
+
+ align:start position:0%
+ethics textbooks
+ 
+
+ align:start position:0%
+ethics textbooks
+or in enough
+
+ align:start position:0%
+or in enough
+ 
+
+ align:start position:0%
+or in enough
+textbooks on science
+
+ align:start position:0%
+textbooks on science
+ 
+
+ align:start position:0%
+textbooks on science
+uh scientific ethics which is mostly
+
+ align:start position:0%
+uh scientific ethics which is mostly
+ 
+
+ align:start position:0%
+uh scientific ethics which is mostly
+research ethics
+
+ align:start position:0%
+research ethics
+ 
+
+ align:start position:0%
+research ethics
+that this is so this is something you
+
+ align:start position:0%
+that this is so this is something you
+ 
+
+ align:start position:0%
+that this is so this is something you
+have to know it's called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the nuremberg principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody want to give a lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+nuremberg the nuremberg trials that's
+
+ align:start position:0%
+nuremberg the nuremberg trials that's
+ 
+
+ align:start position:0%
+nuremberg the nuremberg trials that's
+where it comes from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+now this is interesting
+
+ align:start position:0%
+now this is interesting
+ 
+
+ align:start position:0%
+now this is interesting
+try to read some law i try to read law
+
+ align:start position:0%
+try to read some law i try to read law
+ 
+
+ align:start position:0%
+try to read some law i try to read law
+because i have to argue with lawyers at
+
+ align:start position:0%
+because i have to argue with lawyers at
+ 
+
+ align:start position:0%
+because i have to argue with lawyers at
+dinner all the time on weekends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i just found
+
+ align:start position:0%
+i just found
+ 
+
+ align:start position:0%
+i just found
+when my wife and i go out with friends
+
+ align:start position:0%
+when my wife and i go out with friends
+ 
+
+ align:start position:0%
+when my wife and i go out with friends
+a third of them are lawyers and a third
+
+ align:start position:0%
+a third of them are lawyers and a third
+ 
+
+ align:start position:0%
+a third of them are lawyers and a third
+of them are psychiatrists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other third very
+
+ align:start position:0%
+the other third very
+ 
+
+ align:start position:0%
+the other third very
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i don't defend myself against the
+
+ align:start position:0%
+i don't defend myself against the
+ 
+
+ align:start position:0%
+i don't defend myself against the
+psychiatrist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it just was
+
+ align:start position:0%
+and it just was
+ 
+
+ align:start position:0%
+and it just was
+very strange that uh my wife's first
+
+ align:start position:0%
+very strange that uh my wife's first
+ 
+
+ align:start position:0%
+very strange that uh my wife's first
+husband is the second
+
+ align:start position:0%
+husband is the second
+ 
+
+ align:start position:0%
+husband is the second
+but all of these other psychiatrists are
+
+ align:start position:0%
+but all of these other psychiatrists are
+ 
+
+ align:start position:0%
+but all of these other psychiatrists are
+friends that i had before i met him
+
+ align:start position:0%
+friends that i had before i met him
+ 
+
+ align:start position:0%
+friends that i had before i met him
+and i guess they like practicing on me
+
+ align:start position:0%
+and i guess they like practicing on me
+ 
+
+ align:start position:0%
+and i guess they like practicing on me
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+but this that's significant because
+
+ align:start position:0%
+but this that's significant because
+ 
+
+ align:start position:0%
+but this that's significant because
+uh when we talk about the nuremberg
+
+ align:start position:0%
+uh when we talk about the nuremberg
+ 
+
+ align:start position:0%
+uh when we talk about the nuremberg
+principle there's a there's some really
+
+ align:start position:0%
+principle there's a there's some really
+ 
+
+ align:start position:0%
+principle there's a there's some really
+fundamental stuff fundamental stuff in
+
+ align:start position:0%
+fundamental stuff fundamental stuff in
+ 
+
+ align:start position:0%
+fundamental stuff fundamental stuff in
+there about the law
+
+ align:start position:0%
+there about the law
+ 
+
+ align:start position:0%
+there about the law
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh is taken directly from ethics so
+
+ align:start position:0%
+uh is taken directly from ethics so
+ 
+
+ align:start position:0%
+uh is taken directly from ethics so
+there's two kinds of there's two kinds
+
+ align:start position:0%
+there's two kinds of there's two kinds
+ 
+
+ align:start position:0%
+there's two kinds of there's two kinds
+of law
+
+ align:start position:0%
+of law
+ 
+
+ align:start position:0%
+of law
+anybody know lawyers hang out with
+
+ align:start position:0%
+anybody know lawyers hang out with
+ 
+
+ align:start position:0%
+anybody know lawyers hang out with
+lawyers
+
+ align:start position:0%
+lawyers
+ 
+
+ align:start position:0%
+lawyers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+ sometimes
+
+ align:start position:0%
+ sometimes
+ 
+
+ align:start position:0%
+ sometimes
+you get them to talk i mean if you can
+
+ align:start position:0%
+you get them to talk i mean if you can
+ 
+
+ align:start position:0%
+you get them to talk i mean if you can
+stop them from talking but uh
+
+ align:start position:0%
+stop them from talking but uh
+ 
+
+ align:start position:0%
+stop them from talking but uh
+the two kinds of law um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is called natural law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other one is i'm trying to think
+
+ align:start position:0%
+and the other one is i'm trying to think
+ 
+
+ align:start position:0%
+and the other one is i'm trying to think
+of the name it's not exactly scientific
+
+ align:start position:0%
+of the name it's not exactly scientific
+ 
+
+ align:start position:0%
+of the name it's not exactly scientific
+law what's what's the other one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i get these names i wouldn't prepare to
+
+ align:start position:0%
+i get these names i wouldn't prepare to
+ 
+
+ align:start position:0%
+i get these names i wouldn't prepare to
+talk about this today but now that this
+
+ align:start position:0%
+talk about this today but now that this
+ 
+
+ align:start position:0%
+talk about this today but now that this
+come up i'm gonna go through it and then
+
+ align:start position:0%
+come up i'm gonna go through it and then
+ 
+
+ align:start position:0%
+come up i'm gonna go through it and then
+we'll amend it next class or add to it
+
+ align:start position:0%
+we'll amend it next class or add to it
+ 
+
+ align:start position:0%
+we'll amend it next class or add to it
+or whatever we need to but look up the
+
+ align:start position:0%
+or whatever we need to but look up the
+ 
+
+ align:start position:0%
+or whatever we need to but look up the
+other kind
+
+ align:start position:0%
+other kind
+ 
+
+ align:start position:0%
+other kind
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
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+natural law basically says that law and
+
+ align:start position:0%
+natural law basically says that law and
+ 
+
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+ethics law should never disobey ethical
+
+ align:start position:0%
+ethics law should never disobey ethical
+ 
+
+ align:start position:0%
+ethics law should never disobey ethical
+prisons
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+should always be
+ 
+
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+should always be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+supported by ethical principles
+
+ align:start position:0%
+supported by ethical principles
+ 
+
+ align:start position:0%
+supported by ethical principles
+uh most most law that's done in the
+
+ align:start position:0%
+uh most most law that's done in the
+ 
+
+ align:start position:0%
+uh most most law that's done in the
+united states is not
+
+ align:start position:0%
+united states is not
+ 
+
+ align:start position:0%
+united states is not
+natural law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but both came up in the nuremberg
+
+ align:start position:0%
+but both came up in the nuremberg
+ 
+
+ align:start position:0%
+but both came up in the nuremberg
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+now what happened in the nuremberg
+
+ align:start position:0%
+now what happened in the nuremberg
+ 
+
+ align:start position:0%
+now what happened in the nuremberg
+principle was that the defendants
+
+ align:start position:0%
+principle was that the defendants
+ 
+
+ align:start position:0%
+principle was that the defendants
+uh were nazis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big nazis
+
+ align:start position:0%
+big nazis
+ 
+
+ align:start position:0%
+big nazis
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+their basic defense was
+
+ align:start position:0%
+their basic defense was
+ 
+
+ align:start position:0%
+their basic defense was
+that they were following orders
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that in their country
+
+ align:start position:0%
+that in their country
+ 
+
+ align:start position:0%
+that in their country
+they it's almost the same thing we're
+
+ align:start position:0%
+they it's almost the same thing we're
+ 
+
+ align:start position:0%
+they it's almost the same thing we're
+talking about now with the with with
+
+ align:start position:0%
+talking about now with the with with
+ 
+
+ align:start position:0%
+talking about now with the with with
+ford
+
+ align:start position:0%
+ford
+ 
+
+ align:start position:0%
+ford
+that the government
+
+ align:start position:0%
+that the government
+ 
+
+ align:start position:0%
+that the government
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+
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+had a
+ 
+
+ align:start position:0%
+had a
+but a responsibility to the people
+
+ align:start position:0%
+but a responsibility to the people
+ 
+
+ align:start position:0%
+but a responsibility to the people
+and that there was a hierarchy
+
+ align:start position:0%
+and that there was a hierarchy
+ 
+
+ align:start position:0%
+and that there was a hierarchy
+and that if anybody at the top did
+
+ align:start position:0%
+and that if anybody at the top did
+ 
+
+ align:start position:0%
+and that if anybody at the top did
+something that was morally wrong
+
+ align:start position:0%
+something that was morally wrong
+ 
+
+ align:start position:0%
+something that was morally wrong
+then punish him
+
+ align:start position:0%
+then punish him
+ 
+
+ align:start position:0%
+then punish him
+the rest of us were doing what we were
+
+ align:start position:0%
+the rest of us were doing what we were
+ 
+
+ align:start position:0%
+the rest of us were doing what we were
+legally
+
+ align:start position:0%
+legally
+ 
+
+ align:start position:0%
+legally
+required to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what they said again and what happened
+
+ align:start position:0%
+what they said again and what happened
+ 
+
+ align:start position:0%
+what they said again and what happened
+was in the end what happened was
+
+ align:start position:0%
+was in the end what happened was
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+
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+was in the end what happened was
+that they wound up into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+a
+
+ align:start position:0%
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+
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+a
+quantry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the west
+
+ align:start position:0%
+the west
+ 
+
+ align:start position:0%
+the west
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+say that what they had done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was to commit a crime against humanity
+
+ align:start position:0%
+was to commit a crime against humanity
+ 
+
+ align:start position:0%
+was to commit a crime against humanity
+of which each person in the hierarchy
+
+ align:start position:0%
+of which each person in the hierarchy
+ 
+
+ align:start position:0%
+of which each person in the hierarchy
+was responsible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
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+
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+and
+defense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
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+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+not all of the defendants had the same
+
+ align:start position:0%
+not all of the defendants had the same
+ 
+
+ align:start position:0%
+not all of the defendants had the same
+lawyer
+
+ align:start position:0%
+lawyer
+ 
+
+ align:start position:0%
+lawyer
+there was this one lawyer
+
+ align:start position:0%
+there was this one lawyer
+ 
+
+ align:start position:0%
+there was this one lawyer
+as a matter of fact if you see this
+
+ align:start position:0%
+as a matter of fact if you see this
+ 
+
+ align:start position:0%
+as a matter of fact if you see this
+movement this movie called judgment at
+
+ align:start position:0%
+movement this movie called judgment at
+ 
+
+ align:start position:0%
+movement this movie called judgment at
+nuremberg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lawyer was played
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+by max
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+
+ align:start position:0%
+by max
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+anybody remember his last name
+
+ align:start position:0%
+anybody remember his last name
+ 
+
+ align:start position:0%
+anybody remember his last name
+lawyer
+
+ align:start position:0%
+lawyer
+ 
+
+ align:start position:0%
+lawyer
+god he got the academy award that year
+
+ align:start position:0%
+god he got the academy award that year
+ 
+
+ align:start position:0%
+god he got the academy award that year
+for best supporting actor okay
+
+ align:start position:0%
+for best supporting actor okay
+ 
+
+ align:start position:0%
+for best supporting actor okay
+the lawyer that said
+
+ align:start position:0%
+the lawyer that said
+ 
+
+ align:start position:0%
+the lawyer that said
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they committed they were not only
+
+ align:start position:0%
+they committed they were not only
+ 
+
+ align:start position:0%
+they committed they were not only
+following their orders but yes they
+
+ align:start position:0%
+following their orders but yes they
+ 
+
+ align:start position:0%
+following their orders but yes they
+committed each one of them a crime
+
+ align:start position:0%
+committed each one of them a crime
+ 
+
+ align:start position:0%
+committed each one of them a crime
+against humanity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then he came up with a brilliant remark
+
+ align:start position:0%
+then he came up with a brilliant remark
+ 
+
+ align:start position:0%
+then he came up with a brilliant remark
+to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can't punish a person
+
+ align:start position:0%
+you can't punish a person
+ 
+
+ align:start position:0%
+you can't punish a person
+for breaking a law
+
+ align:start position:0%
+for breaking a law
+ 
+
+ align:start position:0%
+for breaking a law
+that you just made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the time they did it there was no law
+
+ align:start position:0%
+at the time they did it there was no law
+ 
+
+ align:start position:0%
+at the time they did it there was no law
+called crime against humanity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what the west finally did was
+
+ align:start position:0%
+so what the west finally did was
+ 
+
+ align:start position:0%
+so what the west finally did was
+they came up with all of these films
+
+ align:start position:0%
+they came up with all of these films
+ 
+
+ align:start position:0%
+they came up with all of these films
+from the concentration camps
+
+ align:start position:0%
+from the concentration camps
+ 
+
+ align:start position:0%
+from the concentration camps
+and used those films
+
+ align:start position:0%
+and used those films
+ 
+
+ align:start position:0%
+and used those films
+pretty much like the oj case
+
+ align:start position:0%
+pretty much like the oj case
+ 
+
+ align:start position:0%
+pretty much like the oj case
+to just bear down on public opinion
+
+ align:start position:0%
+to just bear down on public opinion
+ 
+
+ align:start position:0%
+to just bear down on public opinion
+so that what it what they did in the end
+
+ align:start position:0%
+so that what it what they did in the end
+ 
+
+ align:start position:0%
+so that what it what they did in the end
+they got pretty much support from
+
+ align:start position:0%
+they got pretty much support from
+ 
+
+ align:start position:0%
+they got pretty much support from
+from the rest of the world
+
+ align:start position:0%
+from the rest of the world
+ 
+
+ align:start position:0%
+from the rest of the world
+that's the way that thing came down
+
+ align:start position:0%
+that's the way that thing came down
+ 
+
+ align:start position:0%
+that's the way that thing came down
+it came down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check the spelling on this i had not uh
+
+ align:start position:0%
+check the spelling on this i had not uh
+ 
+
+ align:start position:0%
+check the spelling on this i had not uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+prepared for this but it's called me lie
+
+ align:start position:0%
+prepared for this but it's called me lie
+ 
+
+ align:start position:0%
+prepared for this but it's called me lie
+uh it was in vietnam it was a vietnam
+
+ align:start position:0%
+uh it was in vietnam it was a vietnam
+ 
+
+ align:start position:0%
+uh it was in vietnam it was a vietnam
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+where an american where american
+
+ align:start position:0%
+where an american where american
+ 
+
+ align:start position:0%
+where an american where american
+soldiers killed these civilians
+
+ align:start position:0%
+soldiers killed these civilians
+ 
+
+ align:start position:0%
+soldiers killed these civilians
+men women and children
+
+ align:start position:0%
+men women and children
+ 
+
+ align:start position:0%
+men women and children
+and lieutenant cali
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said that he
+
+ align:start position:0%
+said that he
+ 
+
+ align:start position:0%
+said that he
+was merely following orders
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what the scholars did i'm not going
+
+ align:start position:0%
+and what the scholars did i'm not going
+ 
+
+ align:start position:0%
+and what the scholars did i'm not going
+to talk about the law anymore
+
+ align:start position:0%
+to talk about the law anymore
+ 
+
+ align:start position:0%
+to talk about the law anymore
+what the scholars did was they came back
+
+ align:start position:0%
+what the scholars did was they came back
+ 
+
+ align:start position:0%
+what the scholars did was they came back
+to the nuremberg principle and said
+
+ align:start position:0%
+to the nuremberg principle and said
+ 
+
+ align:start position:0%
+to the nuremberg principle and said
+that an officer
+
+ align:start position:0%
+that an officer
+ 
+
+ align:start position:0%
+that an officer
+is responsible for what he or she does
+
+ align:start position:0%
+is responsible for what he or she does
+ 
+
+ align:start position:0%
+is responsible for what he or she does
+regardless of the orders
+
+ align:start position:0%
+regardless of the orders
+ 
+
+ align:start position:0%
+regardless of the orders
+the sergeant and the rest of the men
+
+ align:start position:0%
+the sergeant and the rest of the men
+ 
+
+ align:start position:0%
+the sergeant and the rest of the men
+should follow orders
+
+ align:start position:0%
+should follow orders
+ 
+
+ align:start position:0%
+should follow orders
+they divided the house
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if we apply this thinking to ford
+
+ align:start position:0%
+so now if we apply this thinking to ford
+ 
+
+ align:start position:0%
+so now if we apply this thinking to ford
+what we would tell eccles
+
+ align:start position:0%
+what we would tell eccles
+ 
+
+ align:start position:0%
+what we would tell eccles
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+being and a professional employee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as opposed to a technical or other kind
+
+ align:start position:0%
+as opposed to a technical or other kind
+ 
+
+ align:start position:0%
+as opposed to a technical or other kind
+of an employee
+
+ align:start position:0%
+of an employee
+ 
+
+ align:start position:0%
+of an employee
+you are responsible for what you do
+
+ align:start position:0%
+you are responsible for what you do
+ 
+
+ align:start position:0%
+you are responsible for what you do
+orders notwithstanding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now what i'm going to do is
+
+ align:start position:0%
+all right so now what i'm going to do is
+ 
+
+ align:start position:0%
+all right so now what i'm going to do is
+i just thought rather than
+
+ align:start position:0%
+i just thought rather than
+ 
+
+ align:start position:0%
+i just thought rather than
+all of us just uh saying we'll revisit
+
+ align:start position:0%
+all of us just uh saying we'll revisit
+ 
+
+ align:start position:0%
+all of us just uh saying we'll revisit
+this the next time um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to
+
+ align:start position:0%
+i'm going to
+ 
+
+ align:start position:0%
+i'm going to
+make a a lighthearted assignment and
+
+ align:start position:0%
+make a a lighthearted assignment and
+ 
+
+ align:start position:0%
+make a a lighthearted assignment and
+that is that you become familiar with
+
+ align:start position:0%
+that is that you become familiar with
+ 
+
+ align:start position:0%
+that is that you become familiar with
+the new nuremberg principle
+
+ align:start position:0%
+the new nuremberg principle
+ 
+
+ align:start position:0%
+the new nuremberg principle
+uh the cali case
+
+ align:start position:0%
+uh the cali case
+ 
+
+ align:start position:0%
+uh the cali case
+and see if you can apply it to the fort
+
+ align:start position:0%
+and see if you can apply it to the fort
+ 
+
+ align:start position:0%
+and see if you can apply it to the fort
+pinto case
+
+ align:start position:0%
+pinto case
+ 
+
+ align:start position:0%
+pinto case
+and whatever corrections need to be made
+
+ align:start position:0%
+and whatever corrections need to be made
+ 
+
+ align:start position:0%
+and whatever corrections need to be made
+at the next
+
+ align:start position:0%
+at the next
+ 
+
+ align:start position:0%
+at the next
+class uh on anything that i said in this
+
+ align:start position:0%
+class uh on anything that i said in this
+ 
+
+ align:start position:0%
+class uh on anything that i said in this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+or that
+
+ align:start position:0%
+or that
+ 
+
+ align:start position:0%
+or that
+or even the following class that will
+
+ align:start position:0%
+or even the following class that will
+ 
+
+ align:start position:0%
+or even the following class that will
+make that that it will be everybody's
+
+ align:start position:0%
+make that that it will be everybody's
+ 
+
+ align:start position:0%
+make that that it will be everybody's
+responsibility to get it right
+
+ align:start position:0%
+responsibility to get it right
+ 
+
+ align:start position:0%
+responsibility to get it right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh but i think that i'm 99
+
+ align:start position:0%
+uh but i think that i'm 99
+ 
+
+ align:start position:0%
+uh but i think that i'm 99
+on all of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+which one this one
+
+ align:start position:0%
+which one this one
+ 
+
+ align:start position:0%
+which one this one
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one it's in a lot of movies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the name of it
+
+ align:start position:0%
+what's the name of it
+ 
+
+ align:start position:0%
+what's the name of it
+a few good man
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh and guantanamo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there was another one that i didn't
+
+ align:start position:0%
+uh there was another one that i didn't
+ 
+
+ align:start position:0%
+uh there was another one that i didn't
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+uh starring gene hackman
+
+ align:start position:0%
+uh starring gene hackman
+ 
+
+ align:start position:0%
+uh starring gene hackman
+and denzel washington where denzel is
+
+ align:start position:0%
+and denzel washington where denzel is
+ 
+
+ align:start position:0%
+and denzel washington where denzel is
+captain of this nuclear sub
+
+ align:start position:0%
+captain of this nuclear sub
+ 
+
+ align:start position:0%
+captain of this nuclear sub
+and hackman gives him the order to fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh i don't know the name of that film
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+i um i guess you know i'm susceptible to
+
+ align:start position:0%
+i um i guess you know i'm susceptible to
+ 
+
+ align:start position:0%
+i um i guess you know i'm susceptible to
+talking about films in class
+
+ align:start position:0%
+talking about films in class
+ 
+
+ align:start position:0%
+talking about films in class
+if you see any of these films and you
+
+ align:start position:0%
+if you see any of these films and you
+ 
+
+ align:start position:0%
+if you see any of these films and you
+want to make a five minute report on the
+
+ align:start position:0%
+want to make a five minute report on the
+ 
+
+ align:start position:0%
+want to make a five minute report on the
+film that is legitimate for this class
+
+ align:start position:0%
+film that is legitimate for this class
+ 
+
+ align:start position:0%
+film that is legitimate for this class
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that was another one um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you another one that goes
+
+ align:start position:0%
+i'll tell you another one that goes
+ 
+
+ align:start position:0%
+i'll tell you another one that goes
+back a little early for you all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+ronald reagan was president
+
+ align:start position:0%
+ronald reagan was president
+ 
+
+ align:start position:0%
+ronald reagan was president
+there was a
+
+ align:start position:0%
+there was a
+ 
+
+ align:start position:0%
+there was a
+military event
+
+ align:start position:0%
+military event
+ 
+
+ align:start position:0%
+military event
+in the red sea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and reagan came on national television
+
+ align:start position:0%
+and reagan came on national television
+ 
+
+ align:start position:0%
+and reagan came on national television
+and said that
+
+ align:start position:0%
+and said that
+ 
+
+ align:start position:0%
+and said that
+only he as president
+
+ align:start position:0%
+only he as president
+ 
+
+ align:start position:0%
+only he as president
+had the authority
+
+ align:start position:0%
+had the authority
+ 
+
+ align:start position:0%
+had the authority
+to order
+
+ align:start position:0%
+to order
+ 
+
+ align:start position:0%
+to order
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+person a military person in combat to
+
+ align:start position:0%
+person a military person in combat to
+ 
+
+ align:start position:0%
+person a military person in combat to
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+nuclear weapons
+
+ align:start position:0%
+nuclear weapons
+ 
+
+ align:start position:0%
+nuclear weapons
+but he was delegating his authority
+
+ align:start position:0%
+but he was delegating his authority
+ 
+
+ align:start position:0%
+but he was delegating his authority
+authority in the red sea
+
+ align:start position:0%
+authority in the red sea
+ 
+
+ align:start position:0%
+authority in the red sea
+to ship captains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i'll tell you why i remember that so
+
+ align:start position:0%
+now i'll tell you why i remember that so
+ 
+
+ align:start position:0%
+now i'll tell you why i remember that so
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because when i saw him come on
+
+ align:start position:0%
+because when i saw him come on
+ 
+
+ align:start position:0%
+because when i saw him come on
+television and say that
+
+ align:start position:0%
+television and say that
+ 
+
+ align:start position:0%
+television and say that
+i was in an airplane that was getting
+
+ align:start position:0%
+i was in an airplane that was getting
+ 
+
+ align:start position:0%
+i was in an airplane that was getting
+ready to land at
+
+ align:start position:0%
+ready to land at
+ 
+
+ align:start position:0%
+ready to land at
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+iran
+
+ align:start position:0%
+iran
+ 
+
+ align:start position:0%
+iran
+which is on in the red honduras
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was on my way to china and we were
+
+ align:start position:0%
+i was on my way to china and we were
+ 
+
+ align:start position:0%
+i was on my way to china and we were
+actually it was dahren that's where i
+
+ align:start position:0%
+actually it was dahren that's where i
+ 
+
+ align:start position:0%
+actually it was dahren that's where i
+was going dahr rains
+
+ align:start position:0%
+was going dahr rains
+ 
+
+ align:start position:0%
+was going dahr rains
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we were we were just about
+
+ align:start position:0%
+we were we were just about
+ 
+
+ align:start position:0%
+we were we were just about
+20 minutes out
+
+ align:start position:0%
+20 minutes out
+ 
+
+ align:start position:0%
+20 minutes out
+before they said prepare to land and
+
+ align:start position:0%
+before they said prepare to land and
+ 
+
+ align:start position:0%
+before they said prepare to land and
+we're getting laid out looking over
+
+ align:start position:0%
+we're getting laid out looking over
+ 
+
+ align:start position:0%
+we're getting laid out looking over
+there looking at the red sea my goddess
+
+ align:start position:0%
+there looking at the red sea my goddess
+ 
+
+ align:start position:0%
+there looking at the red sea my goddess
+am i gonna be in a nuclear war
+
+ align:start position:0%
+am i gonna be in a nuclear war
+ 
+
+ align:start position:0%
+am i gonna be in a nuclear war
+oh but i remember that um
+
+ align:start position:0%
+oh but i remember that um
+ 
+
+ align:start position:0%
+oh but i remember that um
+so uh yes uh
+
+ align:start position:0%
+so uh yes uh
+ 
+
+ align:start position:0%
+so uh yes uh
+these situations
+
+ align:start position:0%
+these situations
+ 
+
+ align:start position:0%
+these situations
+uh now
+
+ align:start position:0%
+uh now
+ 
+
+ align:start position:0%
+uh now
+i i i i i would like to call them real
+
+ align:start position:0%
+i i i i i would like to call them real
+ 
+
+ align:start position:0%
+i i i i i would like to call them real
+but uh i think that they are real more
+
+ align:start position:0%
+but uh i think that they are real more
+ 
+
+ align:start position:0%
+but uh i think that they are real more
+than realistic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you can follow my meaning in that
+
+ align:start position:0%
+if you can follow my meaning in that
+ 
+
+ align:start position:0%
+if you can follow my meaning in that
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+what do you do when the delegation of
+
+ align:start position:0%
+what do you do when the delegation of
+ 
+
+ align:start position:0%
+what do you do when the delegation of
+authority
+
+ align:start position:0%
+authority
+ 
+
+ align:start position:0%
+authority
+goes down to ship commanders
+
+ align:start position:0%
+goes down to ship commanders
+ 
+
+ align:start position:0%
+goes down to ship commanders
+for a nuclear war to launch a nuclear
+
+ align:start position:0%
+for a nuclear war to launch a nuclear
+ 
+
+ align:start position:0%
+for a nuclear war to launch a nuclear
+weapon in defense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you begin to talk about these issues
+
+ align:start position:0%
+now you begin to talk about these issues
+ 
+
+ align:start position:0%
+now you begin to talk about these issues
+somebody is responsible no matter who
+
+ align:start position:0%
+somebody is responsible no matter who
+ 
+
+ align:start position:0%
+somebody is responsible no matter who
+gave them the authority
+
+ align:start position:0%
+gave them the authority
+ 
+
+ align:start position:0%
+gave them the authority
+well uh so um
+
+ align:start position:0%
+well uh so um
+ 
+
+ align:start position:0%
+well uh so um
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think i'm happy with this discussion
+
+ align:start position:0%
+i think i'm happy with this discussion
+ 
+
+ align:start position:0%
+i think i'm happy with this discussion
+on the ford pinto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can i bring up one topic
+
+ align:start position:0%
+can i bring up one topic
+ 
+
+ align:start position:0%
+can i bring up one topic
+i'm going to bring up i just thought of
+
+ align:start position:0%
+i'm going to bring up i just thought of
+ 
+
+ align:start position:0%
+i'm going to bring up i just thought of
+another topic i'm going to bring up on
+
+ align:start position:0%
+another topic i'm going to bring up on
+ 
+
+ align:start position:0%
+another topic i'm going to bring up on
+it go ahead actually it's a story
+
+ align:start position:0%
+it go ahead actually it's a story
+ 
+
+ align:start position:0%
+it go ahead actually it's a story
+another time well
+
+ align:start position:0%
+another time well
+ 
+
+ align:start position:0%
+another time well
+so i've been trying to find a way to say
+
+ align:start position:0%
+so i've been trying to find a way to say
+ 
+
+ align:start position:0%
+so i've been trying to find a way to say
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+actions of ford and producing and
+
+ align:start position:0%
+actions of ford and producing and
+ 
+
+ align:start position:0%
+actions of ford and producing and
+selling the pintos is not morally
+
+ align:start position:0%
+selling the pintos is not morally
+ 
+
+ align:start position:0%
+selling the pintos is not morally
+defensible
+
+ align:start position:0%
+defensible
+ 
+
+ align:start position:0%
+defensible
+and what i came up with was to say that
+
+ align:start position:0%
+and what i came up with was to say that
+ 
+
+ align:start position:0%
+and what i came up with was to say that
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+the utilitarian cost benefit analysis
+
+ align:start position:0%
+the utilitarian cost benefit analysis
+ 
+
+ align:start position:0%
+the utilitarian cost benefit analysis
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+it was
+
+ align:start position:0%
+it was
+ 
+
+ align:start position:0%
+it was
+not worth it to add the safety feature
+
+ align:start position:0%
+not worth it to add the safety feature
+ 
+
+ align:start position:0%
+not worth it to add the safety feature
+and to sell the car what they didn't
+
+ align:start position:0%
+and to sell the car what they didn't
+ 
+
+ align:start position:0%
+and to sell the car what they didn't
+think about was informant was informed
+
+ align:start position:0%
+think about was informant was informed
+ 
+
+ align:start position:0%
+think about was informant was informed
+consent so like they didn't respect the
+
+ align:start position:0%
+consent so like they didn't respect the
+ 
+
+ align:start position:0%
+consent so like they didn't respect the
+moral agency of the public
+
+ align:start position:0%
+moral agency of the public
+ 
+
+ align:start position:0%
+moral agency of the public
+to decide about their best they were
+
+ align:start position:0%
+to decide about their best they were
+ 
+
+ align:start position:0%
+to decide about their best they were
+getting into it is that an appropriate
+
+ align:start position:0%
+getting into it is that an appropriate
+ 
+
+ align:start position:0%
+getting into it is that an appropriate
+issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+uh now
+
+ align:start position:0%
+uh now
+ 
+
+ align:start position:0%
+uh now
+informed consent i want y'all to know
+
+ align:start position:0%
+informed consent i want y'all to know
+ 
+
+ align:start position:0%
+informed consent i want y'all to know
+that term
+
+ align:start position:0%
+that term
+ 
+
+ align:start position:0%
+that term
+uh informed consent
+
+ align:start position:0%
+uh informed consent
+ 
+
+ align:start position:0%
+uh informed consent
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+comes out of medical ethics
+
+ align:start position:0%
+comes out of medical ethics
+ 
+
+ align:start position:0%
+comes out of medical ethics
+because now you're talking about
+
+ align:start position:0%
+because now you're talking about
+ 
+
+ align:start position:0%
+because now you're talking about
+your physician
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not only getting your consent
+
+ align:start position:0%
+not only getting your consent
+ 
+
+ align:start position:0%
+not only getting your consent
+for some kind of uh
+
+ align:start position:0%
+for some kind of uh
+ 
+
+ align:start position:0%
+for some kind of uh
+uh procedure
+
+ align:start position:0%
+uh procedure
+ 
+
+ align:start position:0%
+uh procedure
+but the physician giving you some
+
+ align:start position:0%
+but the physician giving you some
+ 
+
+ align:start position:0%
+but the physician giving you some
+lessons on what you're doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a little bit of u.s history
+
+ align:start position:0%
+now a little bit of u.s history
+ 
+
+ align:start position:0%
+now a little bit of u.s history
+uh when i was a kid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just did not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just did not criticize what a doctor
+
+ align:start position:0%
+you just did not criticize what a doctor
+ 
+
+ align:start position:0%
+you just did not criticize what a doctor
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+just totally unheard of it was almost uh
+
+ align:start position:0%
+just totally unheard of it was almost uh
+ 
+
+ align:start position:0%
+just totally unheard of it was almost uh
+bordering on the religious you just did
+
+ align:start position:0%
+bordering on the religious you just did
+ 
+
+ align:start position:0%
+bordering on the religious you just did
+not question your doctor and getting a
+
+ align:start position:0%
+not question your doctor and getting a
+ 
+
+ align:start position:0%
+not question your doctor and getting a
+second opinion would have been
+
+ align:start position:0%
+second opinion would have been
+ 
+
+ align:start position:0%
+second opinion would have been
+would have been unthinkable
+
+ align:start position:0%
+would have been unthinkable
+ 
+
+ align:start position:0%
+would have been unthinkable
+uh during the late 60s
+
+ align:start position:0%
+uh during the late 60s
+ 
+
+ align:start position:0%
+uh during the late 60s
+uh that began to turn around
+
+ align:start position:0%
+uh that began to turn around
+ 
+
+ align:start position:0%
+uh that began to turn around
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+mainly because now uh now that
+
+ align:start position:0%
+mainly because now uh now that
+ 
+
+ align:start position:0%
+mainly because now uh now that
+everything i've said is empirically
+
+ align:start position:0%
+everything i've said is empirically
+ 
+
+ align:start position:0%
+everything i've said is empirically
+testable i doubt if anybody would
+
+ align:start position:0%
+testable i doubt if anybody would
+ 
+
+ align:start position:0%
+testable i doubt if anybody would
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+dispute what i just said
+
+ align:start position:0%
+dispute what i just said
+ 
+
+ align:start position:0%
+dispute what i just said
+now you might get a little dispute but
+
+ align:start position:0%
+now you might get a little dispute but
+ 
+
+ align:start position:0%
+now you might get a little dispute but
+anybody who would dispute what i'm about
+
+ align:start position:0%
+anybody who would dispute what i'm about
+ 
+
+ align:start position:0%
+anybody who would dispute what i'm about
+to say would understand clearly what i'm
+
+ align:start position:0%
+to say would understand clearly what i'm
+ 
+
+ align:start position:0%
+to say would understand clearly what i'm
+saying and why i said it
+
+ align:start position:0%
+saying and why i said it
+ 
+
+ align:start position:0%
+saying and why i said it
+and that is that things began to turn
+
+ align:start position:0%
+and that is that things began to turn
+ 
+
+ align:start position:0%
+and that is that things began to turn
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+uh when the women's movement
+
+ align:start position:0%
+uh when the women's movement
+ 
+
+ align:start position:0%
+uh when the women's movement
+began to give women more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recognition
+
+ align:start position:0%
+recognition
+ 
+
+ align:start position:0%
+recognition
+for their um
+
+ align:start position:0%
+for their um
+ 
+
+ align:start position:0%
+for their um
+for their uh
+
+ align:start position:0%
+for their uh
+ 
+
+ align:start position:0%
+for their uh
+responsibilities and
+
+ align:start position:0%
+responsibilities and
+ 
+
+ align:start position:0%
+responsibilities and
+thoughts and abilities
+
+ align:start position:0%
+thoughts and abilities
+ 
+
+ align:start position:0%
+thoughts and abilities
+which meant that you now have women who
+
+ align:start position:0%
+which meant that you now have women who
+ 
+
+ align:start position:0%
+which meant that you now have women who
+had children and who were reading books
+
+ align:start position:0%
+had children and who were reading books
+ 
+
+ align:start position:0%
+had children and who were reading books
+about how to care for their children
+
+ align:start position:0%
+about how to care for their children
+ 
+
+ align:start position:0%
+about how to care for their children
+they just weren't
+
+ align:start position:0%
+they just weren't
+ 
+
+ align:start position:0%
+they just weren't
+consulting the doctors and if the doctor
+
+ align:start position:0%
+consulting the doctors and if the doctor
+ 
+
+ align:start position:0%
+consulting the doctors and if the doctor
+said something that they didn't believe
+
+ align:start position:0%
+said something that they didn't believe
+ 
+
+ align:start position:0%
+said something that they didn't believe
+they'd consult another one so out of
+
+ align:start position:0%
+they'd consult another one so out of
+ 
+
+ align:start position:0%
+they'd consult another one so out of
+that you get the sts movement
+
+ align:start position:0%
+that you get the sts movement
+ 
+
+ align:start position:0%
+that you get the sts movement
+and medical ethics then began to stop
+
+ align:start position:0%
+and medical ethics then began to stop
+ 
+
+ align:start position:0%
+and medical ethics then began to stop
+start talking about informed consent
+
+ align:start position:0%
+start talking about informed consent
+ 
+
+ align:start position:0%
+start talking about informed consent
+being a moral
+
+ align:start position:0%
+being a moral
+ 
+
+ align:start position:0%
+being a moral
+dimension to the relationship between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physician and patient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if you apply informed consent to
+
+ align:start position:0%
+if you apply informed consent to
+ 
+
+ align:start position:0%
+if you apply informed consent to
+engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you run into an not a theoretical but an
+
+ align:start position:0%
+you run into an not a theoretical but an
+ 
+
+ align:start position:0%
+you run into an not a theoretical but an
+applications problem
+
+ align:start position:0%
+applications problem
+ 
+
+ align:start position:0%
+applications problem
+that in most cases in utilitarianism
+
+ align:start position:0%
+that in most cases in utilitarianism
+ 
+
+ align:start position:0%
+that in most cases in utilitarianism
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+you can't find
+
+ align:start position:0%
+you can't find
+ 
+
+ align:start position:0%
+you can't find
+all of the affected parties
+
+ align:start position:0%
+all of the affected parties
+ 
+
+ align:start position:0%
+all of the affected parties
+and informed consent is so easy because
+
+ align:start position:0%
+and informed consent is so easy because
+ 
+
+ align:start position:0%
+and informed consent is so easy because
+it's the it's the patient
+
+ align:start position:0%
+it's the it's the patient
+ 
+
+ align:start position:0%
+it's the it's the patient
+or the patient's mother
+
+ align:start position:0%
+or the patient's mother
+ 
+
+ align:start position:0%
+or the patient's mother
+could be the patient's father too but
+
+ align:start position:0%
+could be the patient's father too but
+ 
+
+ align:start position:0%
+could be the patient's father too but
+you see what i'm saying that we're
+
+ align:start position:0%
+you see what i'm saying that we're
+ 
+
+ align:start position:0%
+you see what i'm saying that we're
+talking about a role in the family they
+
+ align:start position:0%
+talking about a role in the family they
+ 
+
+ align:start position:0%
+talking about a role in the family they
+can play be played by the male 1
+
+ align:start position:0%
+can play be played by the male 1
+ 
+
+ align:start position:0%
+can play be played by the male 1
+all right so uh informed consent then
+
+ align:start position:0%
+all right so uh informed consent then
+ 
+
+ align:start position:0%
+all right so uh informed consent then
+all uh
+
+ align:start position:0%
+all uh
+ 
+
+ align:start position:0%
+all uh
+except for one case but not one case but
+
+ align:start position:0%
+except for one case but not one case but
+ 
+
+ align:start position:0%
+except for one case but not one case but
+one case that i'm going to bring in the
+
+ align:start position:0%
+one case that i'm going to bring in the
+ 
+
+ align:start position:0%
+one case that i'm going to bring in the
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+and i'm going to i'm not going to tell
+
+ align:start position:0%
+and i'm going to i'm not going to tell
+ 
+
+ align:start position:0%
+and i'm going to i'm not going to tell
+you which one it is
+
+ align:start position:0%
+you which one it is
+ 
+
+ align:start position:0%
+you which one it is
+but i'm going to bring one in the class
+
+ align:start position:0%
+but i'm going to bring one in the class
+ 
+
+ align:start position:0%
+but i'm going to bring one in the class
+informed consent in engineering usually
+
+ align:start position:0%
+informed consent in engineering usually
+ 
+
+ align:start position:0%
+informed consent in engineering usually
+gets defused
+
+ align:start position:0%
+gets defused
+ 
+
+ align:start position:0%
+gets defused
+now in this case that you
+
+ align:start position:0%
+now in this case that you
+ 
+
+ align:start position:0%
+now in this case that you
+inform consent
+
+ align:start position:0%
+inform consent
+ 
+
+ align:start position:0%
+inform consent
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you apply it to the ford pinto
+
+ align:start position:0%
+how would you apply it to the ford pinto
+ 
+
+ align:start position:0%
+how would you apply it to the ford pinto
+kit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean one
+
+ align:start position:0%
+i mean one
+ 
+
+ align:start position:0%
+i mean one
+option is that one of the engineers who
+
+ align:start position:0%
+option is that one of the engineers who
+ 
+
+ align:start position:0%
+option is that one of the engineers who
+knew of the test results knew that the
+
+ align:start position:0%
+knew of the test results knew that the
+ 
+
+ align:start position:0%
+knew of the test results knew that the
+car would explode
+
+ align:start position:0%
+car would explode
+ 
+
+ align:start position:0%
+car would explode
+hit in a certain way
+
+ align:start position:0%
+hit in a certain way
+ 
+
+ align:start position:0%
+hit in a certain way
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+at least write a memo to
+
+ align:start position:0%
+at least write a memo to
+ 
+
+ align:start position:0%
+at least write a memo to
+an authority that maybe wasn't being
+
+ align:start position:0%
+an authority that maybe wasn't being
+ 
+
+ align:start position:0%
+an authority that maybe wasn't being
+told about
+
+ align:start position:0%
+told about
+ 
+
+ align:start position:0%
+told about
+like a higher manager
+
+ align:start position:0%
+like a higher manager
+ 
+
+ align:start position:0%
+like a higher manager
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+hope that an action would be taken and
+
+ align:start position:0%
+hope that an action would be taken and
+ 
+
+ align:start position:0%
+hope that an action would be taken and
+then if that didn't do anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know contact the new a news agency
+
+ align:start position:0%
+you know contact the new a news agency
+ 
+
+ align:start position:0%
+you know contact the new a news agency
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now um
+
+ align:start position:0%
+all right now um
+ 
+
+ align:start position:0%
+all right now um
+i don't i've never heard that argument
+
+ align:start position:0%
+i don't i've never heard that argument
+ 
+
+ align:start position:0%
+i don't i've never heard that argument
+applied to the fourth pencil
+
+ align:start position:0%
+applied to the fourth pencil
+ 
+
+ align:start position:0%
+applied to the fourth pencil
+but what i'm saying is you're bringing
+
+ align:start position:0%
+but what i'm saying is you're bringing
+ 
+
+ align:start position:0%
+but what i'm saying is you're bringing
+up something that's causing me causing
+
+ align:start position:0%
+up something that's causing me causing
+ 
+
+ align:start position:0%
+up something that's causing me causing
+my my mind to turn around maybe this is
+
+ align:start position:0%
+my my mind to turn around maybe this is
+ 
+
+ align:start position:0%
+my my mind to turn around maybe this is
+a good project
+
+ align:start position:0%
+a good project
+ 
+
+ align:start position:0%
+a good project
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+whether or not there is
+
+ align:start position:0%
+whether or not there is
+ 
+
+ align:start position:0%
+whether or not there is
+some action
+
+ align:start position:0%
+some action
+ 
+
+ align:start position:0%
+some action
+that is short of whistleblower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that gets in gets the consent of the
+
+ align:start position:0%
+uh that gets in gets the consent of the
+ 
+
+ align:start position:0%
+uh that gets in gets the consent of the
+affected parties
+
+ align:start position:0%
+affected parties
+ 
+
+ align:start position:0%
+affected parties
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is appropriate to this case
+
+ align:start position:0%
+is appropriate to this case
+ 
+
+ align:start position:0%
+is appropriate to this case
+and my instincts tell me it is i mean
+
+ align:start position:0%
+and my instincts tell me it is i mean
+ 
+
+ align:start position:0%
+and my instincts tell me it is i mean
+now we have like the consumer reports so
+
+ align:start position:0%
+now we have like the consumer reports so
+ 
+
+ align:start position:0%
+now we have like the consumer reports so
+if a car is produced and really unsafe
+
+ align:start position:0%
+if a car is produced and really unsafe
+ 
+
+ align:start position:0%
+if a car is produced and really unsafe
+that word gets out and when people buy
+
+ align:start position:0%
+that word gets out and when people buy
+ 
+
+ align:start position:0%
+that word gets out and when people buy
+cars they can consult them
+
+ align:start position:0%
+cars they can consult them
+ 
+
+ align:start position:0%
+cars they can consult them
+and see how it is so maybe that's the
+
+ align:start position:0%
+and see how it is so maybe that's the
+ 
+
+ align:start position:0%
+and see how it is so maybe that's the
+correction on something like this why
+
+ align:start position:0%
+correction on something like this why
+ 
+
+ align:start position:0%
+correction on something like this why
+don't you give us some thought
+
+ align:start position:0%
+don't you give us some thought
+ 
+
+ align:start position:0%
+don't you give us some thought
+everybody give us some fun i think this
+
+ align:start position:0%
+everybody give us some fun i think this
+ 
+
+ align:start position:0%
+everybody give us some fun i think this
+requires a little thought i don't know
+
+ align:start position:0%
+requires a little thought i don't know
+ 
+
+ align:start position:0%
+requires a little thought i don't know
+that anybody has thought of that one
+
+ align:start position:0%
+that anybody has thought of that one
+ 
+
+ align:start position:0%
+that anybody has thought of that one
+i've not seen anything on it
+
+ align:start position:0%
+i've not seen anything on it
+ 
+
+ align:start position:0%
+i've not seen anything on it
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i do know that let's put it this way
+
+ align:start position:0%
+i do know that let's put it this way
+ 
+
+ align:start position:0%
+i do know that let's put it this way
+there is what you're really bringing up
+
+ align:start position:0%
+there is what you're really bringing up
+ 
+
+ align:start position:0%
+there is what you're really bringing up
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're suggesting that there is a
+
+ align:start position:0%
+you're suggesting that there is a
+ 
+
+ align:start position:0%
+you're suggesting that there is a
+continuum somewhere between
+
+ align:start position:0%
+continuum somewhere between
+ 
+
+ align:start position:0%
+continuum somewhere between
+whistleblowing and what they call public
+
+ align:start position:0%
+whistleblowing and what they call public
+ 
+
+ align:start position:0%
+whistleblowing and what they call public
+understanding of engineering
+
+ align:start position:0%
+understanding of engineering
+ 
+
+ align:start position:0%
+understanding of engineering
+and that's a formal term there's an
+
+ align:start position:0%
+and that's a formal term there's an
+ 
+
+ align:start position:0%
+and that's a formal term there's an
+office at the national academy of
+
+ align:start position:0%
+office at the national academy of
+ 
+
+ align:start position:0%
+office at the national academy of
+engineering called public understanding
+
+ align:start position:0%
+engineering called public understanding
+ 
+
+ align:start position:0%
+engineering called public understanding
+of engineering there's a office at the
+
+ align:start position:0%
+of engineering there's a office at the
+ 
+
+ align:start position:0%
+of engineering there's a office at the
+national academy of sciences called
+
+ align:start position:0%
+national academy of sciences called
+ 
+
+ align:start position:0%
+national academy of sciences called
+public understanding of science
+
+ align:start position:0%
+public understanding of science
+ 
+
+ align:start position:0%
+public understanding of science
+uh and so
+
+ align:start position:0%
+uh and so
+ 
+
+ align:start position:0%
+uh and so
+a person could inform them
+
+ align:start position:0%
+a person could inform them
+ 
+
+ align:start position:0%
+a person could inform them
+you might say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh which is not i don't know if this is
+
+ align:start position:0%
+uh which is not i don't know if this is
+ 
+
+ align:start position:0%
+uh which is not i don't know if this is
+the same thing as blowing i haven't
+
+ align:start position:0%
+the same thing as blowing i haven't
+ 
+
+ align:start position:0%
+the same thing as blowing i haven't
+given this thought
+
+ align:start position:0%
+given this thought
+ 
+
+ align:start position:0%
+given this thought
+i don't know who has given a thought my
+
+ align:start position:0%
+i don't know who has given a thought my
+ 
+
+ align:start position:0%
+i don't know who has given a thought my
+instincts tell me nobody's giving a
+
+ align:start position:0%
+instincts tell me nobody's giving a
+ 
+
+ align:start position:0%
+instincts tell me nobody's giving a
+thought
+
+ align:start position:0%
+thought
+ 
+
+ align:start position:0%
+thought
+because i would have read it by now
+
+ align:start position:0%
+because i would have read it by now
+ 
+
+ align:start position:0%
+because i would have read it by now
+so give it some fun
+
+ align:start position:0%
+so give it some fun
+ 
+
+ align:start position:0%
+so give it some fun
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+even if you don't come up with a
+
+ align:start position:0%
+even if you don't come up with a
+ 
+
+ align:start position:0%
+even if you don't come up with a
+conclusion uh if you come up with some
+
+ align:start position:0%
+conclusion uh if you come up with some
+ 
+
+ align:start position:0%
+conclusion uh if you come up with some
+more questions or comments as the as the
+
+ align:start position:0%
+more questions or comments as the as the
+ 
+
+ align:start position:0%
+more questions or comments as the as the
+course goes along
+
+ align:start position:0%
+course goes along
+ 
+
+ align:start position:0%
+course goes along
+throw them in
+
+ align:start position:0%
+throw them in
+ 
+
+ align:start position:0%
+throw them in
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they passed the 20 mile per hour test
+
+ align:start position:0%
+they passed the 20 mile per hour test
+ 
+
+ align:start position:0%
+they passed the 20 mile per hour test
+but in two years there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was a federal standard right yeah
+
+ align:start position:0%
+that was a federal standard right yeah
+ 
+
+ align:start position:0%
+that was a federal standard right yeah
+that was not a professional
+
+ align:start position:0%
+that was not a professional
+ 
+
+ align:start position:0%
+that was not a professional
+engineering standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh now there are two things i can say on
+
+ align:start position:0%
+uh now there are two things i can say on
+ 
+
+ align:start position:0%
+uh now there are two things i can say on
+it and probably what
+
+ align:start position:0%
+it and probably what
+ 
+
+ align:start position:0%
+it and probably what
+ever you have in mind if you if you have
+
+ align:start position:0%
+ever you have in mind if you if you have
+ 
+
+ align:start position:0%
+ever you have in mind if you if you have
+a thought on this
+
+ align:start position:0%
+a thought on this
+ 
+
+ align:start position:0%
+a thought on this
+put it on the table we'll properly buy
+
+ align:start position:0%
+put it on the table we'll properly buy
+ 
+
+ align:start position:0%
+put it on the table we'll properly buy
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+that well you you're in a case almost
+
+ align:start position:0%
+that well you you're in a case almost
+ 
+
+ align:start position:0%
+that well you you're in a case almost
+like this nuremberg case you know
+
+ align:start position:0%
+like this nuremberg case you know
+ 
+
+ align:start position:0%
+like this nuremberg case you know
+somebody's supposed to somebody guilty
+
+ align:start position:0%
+somebody's supposed to somebody guilty
+ 
+
+ align:start position:0%
+somebody's supposed to somebody guilty
+of a crime before
+
+ align:start position:0%
+of a crime before
+ 
+
+ align:start position:0%
+of a crime before
+the act was made a crime
+
+ align:start position:0%
+the act was made a crime
+ 
+
+ align:start position:0%
+the act was made a crime
+if they performed the act before it was
+
+ align:start position:0%
+if they performed the act before it was
+ 
+
+ align:start position:0%
+if they performed the act before it was
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+that's one
+
+ align:start position:0%
+that's one
+ 
+
+ align:start position:0%
+that's one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then there's another one that i want to
+
+ align:start position:0%
+then there's another one that i want to
+ 
+
+ align:start position:0%
+then there's another one that i want to
+bring up in this class i was talking
+
+ align:start position:0%
+bring up in this class i was talking
+ 
+
+ align:start position:0%
+bring up in this class i was talking
+we got to get out of here but i was
+
+ align:start position:0%
+we got to get out of here but i was
+ 
+
+ align:start position:0%
+we got to get out of here but i was
+talking to somebody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me give you do we have an assignment
+
+ align:start position:0%
+let me give you do we have an assignment
+ 
+
+ align:start position:0%
+let me give you do we have an assignment
+we still have to do the two nuclear
+
+ align:start position:0%
+we still have to do the two nuclear
+ 
+
+ align:start position:0%
+we still have to do the two nuclear
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+so that's your assignment we still have
+
+ align:start position:0%
+so that's your assignment we still have
+ 
+
+ align:start position:0%
+so that's your assignment we still have
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+chernobyl and uh three mile hour
+
+ align:start position:0%
+chernobyl and uh three mile hour
+ 
+
+ align:start position:0%
+chernobyl and uh three mile hour
+okay so that's next time this is
+
+ align:start position:0%
+okay so that's next time this is
+ 
+
+ align:start position:0%
+okay so that's next time this is
+thursday
+
+ align:start position:0%
+thursday
+ 
+
+ align:start position:0%
+thursday
+all right um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah now let me do that and then let me
+
+ align:start position:0%
+ah now let me do that and then let me
+ 
+
+ align:start position:0%
+ah now let me do that and then let me
+put this if i have time to put this
+
+ align:start position:0%
+put this if i have time to put this
+ 
+
+ align:start position:0%
+put this if i have time to put this
+other issue on the board
+
+ align:start position:0%
+other issue on the board
+ 
+
+ align:start position:0%
+other issue on the board
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+i want everybody to read this book now
+
+ align:start position:0%
+i want everybody to read this book now
+ 
+
+ align:start position:0%
+i want everybody to read this book now
+i'm going to give you a month to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me see a month a month a month
+
+ align:start position:0%
+um let me see a month a month a month
+ 
+
+ align:start position:0%
+um let me see a month a month a month
+where would a month put us
+
+ align:start position:0%
+where would a month put us
+ 
+
+ align:start position:0%
+where would a month put us
+how about three weeks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the first 50 pages is going to
+
+ align:start position:0%
+because the first 50 pages is going to
+ 
+
+ align:start position:0%
+because the first 50 pages is going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+like reading shakespeare it's going to
+
+ align:start position:0%
+like reading shakespeare it's going to
+ 
+
+ align:start position:0%
+like reading shakespeare it's going to
+be a little laborious that's why i'm
+
+ align:start position:0%
+be a little laborious that's why i'm
+ 
+
+ align:start position:0%
+be a little laborious that's why i'm
+giving you a lot of time
+
+ align:start position:0%
+giving you a lot of time
+ 
+
+ align:start position:0%
+giving you a lot of time
+but after that it rolls right on up
+
+ align:start position:0%
+but after that it rolls right on up
+ 
+
+ align:start position:0%
+but after that it rolls right on up
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+today is the 9th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about uh april 1st
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+april
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay why not the first class after
+
+ align:start position:0%
+oh okay why not the first class after
+ 
+
+ align:start position:0%
+oh okay why not the first class after
+spring break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that april first is saturday so that
+
+ align:start position:0%
+so that april first is saturday so that
+ 
+
+ align:start position:0%
+so that april first is saturday so that
+will be uh
+
+ align:start position:0%
+will be uh
+ 
+
+ align:start position:0%
+will be uh
+april 4th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i'm gonna give you i'm gonna give you
+
+ align:start position:0%
+i'm gonna give you i'm gonna give you
+ 
+
+ align:start position:0%
+i'm gonna give you i'm gonna give you
+the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's important to get the spelling right
+
+ align:start position:0%
+it's important to get the spelling right
+ 
+
+ align:start position:0%
+it's important to get the spelling right
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+there is
+
+ align:start position:0%
+there is
+ 
+
+ align:start position:0%
+there is
+parzival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wolf in front eshenbach
+
+ align:start position:0%
+wolf in front eshenbach
+ 
+
+ align:start position:0%
+wolf in front eshenbach
+and i would like for you to get there's
+
+ align:start position:0%
+and i would like for you to get there's
+ 
+
+ align:start position:0%
+and i would like for you to get there's
+more than one uh
+
+ align:start position:0%
+more than one uh
+ 
+
+ align:start position:0%
+more than one uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+and the translations are different
+
+ align:start position:0%
+and the translations are different
+ 
+
+ align:start position:0%
+and the translations are different
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i would like for you to get the one
+
+ align:start position:0%
+but i would like for you to get the one
+ 
+
+ align:start position:0%
+but i would like for you to get the one
+that's uh penguin classic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is one of the penguin classics
+
+ align:start position:0%
+is one of the penguin classics
+ 
+
+ align:start position:0%
+is one of the penguin classics
+and this particular
+
+ align:start position:0%
+and this particular
+ 
+
+ align:start position:0%
+and this particular
+translator is named hatto
+
+ align:start position:0%
+translator is named hatto
+ 
+
+ align:start position:0%
+translator is named hatto
+attao
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the main reason for choosing hato is to
+
+ align:start position:0%
+the main reason for choosing hato is to
+ 
+
+ align:start position:0%
+the main reason for choosing hato is to
+choose one so that we have the same one
+
+ align:start position:0%
+choose one so that we have the same one
+ 
+
+ align:start position:0%
+choose one so that we have the same one
+because the because the translations
+
+ align:start position:0%
+because the because the translations
+ 
+
+ align:start position:0%
+because the because the translations
+will vary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so get that one and we'll discuss
+
+ align:start position:0%
+okay so get that one and we'll discuss
+ 
+
+ align:start position:0%
+okay so get that one and we'll discuss
+it first class after the spring break
+
+ align:start position:0%
+it first class after the spring break
+ 
+
+ align:start position:0%
+it first class after the spring break
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+don't like i said the first 50 pages
+
+ align:start position:0%
+don't like i said the first 50 pages
+ 
+
+ align:start position:0%
+don't like i said the first 50 pages
+don't be put off
+
+ align:start position:0%
+don't be put off
+ 
+
+ align:start position:0%
+don't be put off
+it's like reading shakespeare the first
+
+ align:start position:0%
+it's like reading shakespeare the first
+ 
+
+ align:start position:0%
+it's like reading shakespeare the first
+time it's a little bit
+
+ align:start position:0%
+time it's a little bit
+ 
+
+ align:start position:0%
+time it's a little bit
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+let me just open a page up man
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there was a heathen named
+
+ align:start position:0%
+there was a heathen named
+ 
+
+ align:start position:0%
+there was a heathen named
+flagetman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who was highly renowned for his
+
+ align:start position:0%
+who was highly renowned for his
+ 
+
+ align:start position:0%
+who was highly renowned for his
+requirements
+
+ align:start position:0%
+requirements
+ 
+
+ align:start position:0%
+requirements
+requirements
+
+ align:start position:0%
+requirements
+ 
+
+ align:start position:0%
+requirements
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+physicist
+
+ align:start position:0%
+physicist
+ 
+
+ align:start position:0%
+physicist
+was descended from solomon
+
+ align:start position:0%
+was descended from solomon
+ 
+
+ align:start position:0%
+was descended from solomon
+don't worry about physics you'll get it
+
+ align:start position:0%
+don't worry about physics you'll get it
+ 
+
+ align:start position:0%
+don't worry about physics you'll get it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in other words uh don't even look for a
+
+ align:start position:0%
+in other words uh don't even look for a
+ 
+
+ align:start position:0%
+in other words uh don't even look for a
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for dictionary i mean a you know
+
+ align:start position:0%
+for dictionary i mean a you know
+ 
+
+ align:start position:0%
+for dictionary i mean a you know
+dictionary
+
+ align:start position:0%
+dictionary
+ 
+
+ align:start position:0%
+dictionary
+just read
+
+ align:start position:0%
+just read
+ 
+
+ align:start position:0%
+just read
+this author's forward
+
+ align:start position:0%
+this author's forward
+ 
+
+ align:start position:0%
+this author's forward
+he'll tell you how to get through this
+
+ align:start position:0%
+he'll tell you how to get through this
+ 
+
+ align:start position:0%
+he'll tell you how to get through this
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+and after this it'll knock your socks
+
+ align:start position:0%
+and after this it'll knock your socks
+ 
+
+ align:start position:0%
+and after this it'll knock your socks
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+don't get part
+
+ align:start position:0%
+don't get part
+ 
+
+ align:start position:0%
+don't get part
+if you get personable mixed up with
+
+ align:start position:0%
+if you get personable mixed up with
+ 
+
+ align:start position:0%
+if you get personable mixed up with
+parsifal p-a-r-s-i-f-a-l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the same mythical character
+
+ align:start position:0%
+it's the same mythical character
+ 
+
+ align:start position:0%
+it's the same mythical character
+pretty much the same story
+
+ align:start position:0%
+pretty much the same story
+ 
+
+ align:start position:0%
+pretty much the same story
+but different
+
+ align:start position:0%
+but different
+ 
+
+ align:start position:0%
+but different
+very different uh which is part and
+
+ align:start position:0%
+very different uh which is part and
+ 
+
+ align:start position:0%
+very different uh which is part and
+parceval is um
+
+ align:start position:0%
+parceval is um
+ 
+
+ align:start position:0%
+parceval is um
+it's another time to go just about time
+
+ align:start position:0%
+it's another time to go just about time
+ 
+
+ align:start position:0%
+it's another time to go just about time
+ago parseval is
+
+ align:start position:0%
+ago parseval is
+ 
+
+ align:start position:0%
+ago parseval is
+the name of the great um
+
+ align:start position:0%
+the name of the great um
+ 
+
+ align:start position:0%
+the name of the great um
+german opera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+he's one of the characters and lauren
+
+ align:start position:0%
+he's one of the characters and lauren
+ 
+
+ align:start position:0%
+he's one of the characters and lauren
+grin is his son
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh this that's a whole different
+
+ align:start position:0%
+and uh this that's a whole different
+ 
+
+ align:start position:0%
+and uh this that's a whole different
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+it's been turned around
+
+ align:start position:0%
+it's been turned around
+ 
+
+ align:start position:0%
+it's been turned around
+then there's percival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+at night
+
+ align:start position:0%
+at night
+ 
+
+ align:start position:0%
+at night
+pretty much you know there's a venn
+
+ align:start position:0%
+pretty much you know there's a venn
+ 
+
+ align:start position:0%
+pretty much you know there's a venn
+diagram there's overlapping stories a
+
+ align:start position:0%
+diagram there's overlapping stories a
+ 
+
+ align:start position:0%
+diagram there's overlapping stories a
+lot in the middle is the same but
+
+ align:start position:0%
+lot in the middle is the same but
+ 
+
+ align:start position:0%
+lot in the middle is the same but
+there's a lot on the edges that are
+
+ align:start position:0%
+there's a lot on the edges that are
+ 
+
+ align:start position:0%
+there's a lot on the edges that are
+different uh percival is the same night
+
+ align:start position:0%
+different uh percival is the same night
+ 
+
+ align:start position:0%
+different uh percival is the same night
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+king arthur's round tape
+
+ align:start position:0%
+king arthur's round tape
+ 
+
+ align:start position:0%
+king arthur's round tape
+that's partial
+
+ align:start position:0%
+that's partial
+ 
+
+ align:start position:0%
+that's partial
+but the stories tell it
+
+ align:start position:0%
+but the stories tell it
+ 
+
+ align:start position:0%
+but the stories tell it
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but i want you to read that one
+
+ align:start position:0%
+but i want you to read that one
+ 
+
+ align:start position:0%
+but i want you to read that one
+and by the time you finished it you will
+
+ align:start position:0%
+and by the time you finished it you will
+ 
+
+ align:start position:0%
+and by the time you finished it you will
+we will start
+
+ align:start position:0%
+we will start
+ 
+
+ align:start position:0%
+we will start
+and i do have time to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that what we have
+
+ align:start position:0%
+that what we have
+ 
+
+ align:start position:0%
+that what we have
+done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far is that we've looked at um in the
+
+ align:start position:0%
+so far is that we've looked at um in the
+ 
+
+ align:start position:0%
+so far is that we've looked at um in the
+greek tradition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've looked at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consequentialist approaches
+
+ align:start position:0%
+consequentialist approaches
+ 
+
+ align:start position:0%
+consequentialist approaches
+we've at least one consequence of
+
+ align:start position:0%
+we've at least one consequence of
+ 
+
+ align:start position:0%
+we've at least one consequence of
+approach one non-consequentialist
+
+ align:start position:0%
+approach one non-consequentialist
+ 
+
+ align:start position:0%
+approach one non-consequentialist
+approach or principled approach or
+
+ align:start position:0%
+approach or principled approach or
+ 
+
+ align:start position:0%
+approach or principled approach or
+deontological approach
+
+ align:start position:0%
+deontological approach
+ 
+
+ align:start position:0%
+deontological approach
+uh then we're going to
+
+ align:start position:0%
+uh then we're going to
+ 
+
+ align:start position:0%
+uh then we're going to
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+virtue
+
+ align:start position:0%
+virtue
+ 
+
+ align:start position:0%
+virtue
+ethics and under that we're going to
+
+ align:start position:0%
+ethics and under that we're going to
+ 
+
+ align:start position:0%
+ethics and under that we're going to
+look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+narrative ethics
+
+ align:start position:0%
+narrative ethics
+ 
+
+ align:start position:0%
+narrative ethics
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+actually what i'm going to do this gets
+
+ align:start position:0%
+actually what i'm going to do this gets
+ 
+
+ align:start position:0%
+actually what i'm going to do this gets
+a little complicated this narrative
+
+ align:start position:0%
+a little complicated this narrative
+ 
+
+ align:start position:0%
+a little complicated this narrative
+ethics is going to be non-greek
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then we're going to remember the two
+
+ align:start position:0%
+and then we're going to remember the two
+ 
+
+ align:start position:0%
+and then we're going to remember the two
+paintings
+
+ align:start position:0%
+paintings
+ 
+
+ align:start position:0%
+paintings
+we have the school at athens all of this
+
+ align:start position:0%
+we have the school at athens all of this
+ 
+
+ align:start position:0%
+we have the school at athens all of this
+is in the school of athens
+
+ align:start position:0%
+is in the school of athens
+ 
+
+ align:start position:0%
+is in the school of athens
+except this one this one goes out and
+
+ align:start position:0%
+except this one this one goes out and
+ 
+
+ align:start position:0%
+except this one this one goes out and
+does something else
+
+ align:start position:0%
+does something else
+ 
+
+ align:start position:0%
+does something else
+then we're going to go look at the
+
+ align:start position:0%
+then we're going to go look at the
+ 
+
+ align:start position:0%
+then we're going to go look at the
+painting
+
+ align:start position:0%
+painting
+ 
+
+ align:start position:0%
+painting
+which is the massive bolsina
+
+ align:start position:0%
+which is the massive bolsina
+ 
+
+ align:start position:0%
+which is the massive bolsina
+and we're going to look at roman point
+
+ align:start position:0%
+and we're going to look at roman point
+ 
+
+ align:start position:0%
+and we're going to look at roman point
+of view
+
+ align:start position:0%
+of view
+ 
+
+ align:start position:0%
+of view
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're going to look at all of these
+
+ align:start position:0%
+we're going to look at all of these
+ 
+
+ align:start position:0%
+we're going to look at all of these
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+through the lens
+
+ align:start position:0%
+through the lens
+ 
+
+ align:start position:0%
+through the lens
+of codes
+
+ align:start position:0%
+of codes
+ 
+
+ align:start position:0%
+of codes
+of ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to go back to each one of
+
+ align:start position:0%
+we're going to go back to each one of
+ 
+
+ align:start position:0%
+we're going to go back to each one of
+these cases and see what the code has
+
+ align:start position:0%
+these cases and see what the code has
+ 
+
+ align:start position:0%
+these cases and see what the code has
+what a some code has to say about it
+
+ align:start position:0%
+what a some code has to say about it
+ 
+
+ align:start position:0%
+what a some code has to say about it
+so that will be towards the end and i do
+
+ align:start position:0%
+so that will be towards the end and i do
+ 
+
+ align:start position:0%
+so that will be towards the end and i do
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+plan to spend a whole lot of time on
+
+ align:start position:0%
+plan to spend a whole lot of time on
+ 
+
+ align:start position:0%
+plan to spend a whole lot of time on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+but i plan to spend a whole lot of time
+
+ align:start position:0%
+but i plan to spend a whole lot of time
+ 
+
+ align:start position:0%
+but i plan to spend a whole lot of time
+on this a whole lot of time on this
+
+ align:start position:0%
+on this a whole lot of time on this
+ 
+
+ align:start position:0%
+on this a whole lot of time on this
+not so much on this not so much on that
+
+ align:start position:0%
+not so much on this not so much on that
+ 
+
+ align:start position:0%
+not so much on this not so much on that
+but a whole lot of time on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when we start doing the narrative
+
+ align:start position:0%
+and when we start doing the narrative
+ 
+
+ align:start position:0%
+and when we start doing the narrative
+ethics
+
+ align:start position:0%
+ethics
+ 
+
+ align:start position:0%
+ethics
+we will need characters
+
+ align:start position:0%
+we will need characters
+ 
+
+ align:start position:0%
+we will need characters
+from mythology and we'll have at least
+
+ align:start position:0%
+from mythology and we'll have at least
+ 
+
+ align:start position:0%
+from mythology and we'll have at least
+one mythology that we can all anchor
+
+ align:start position:0%
+one mythology that we can all anchor
+ 
+
+ align:start position:0%
+one mythology that we can all anchor
+ourselves on
+
+ align:start position:0%
+ourselves on
+ 
+
+ align:start position:0%
+ourselves on
+and i would like to have some other
+
+ align:start position:0%
+and i would like to have some other
+ 
+
+ align:start position:0%
+and i would like to have some other
+mythologies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it would be fun for you
+
+ align:start position:0%
+and it would be fun for you
+ 
+
+ align:start position:0%
+and it would be fun for you
+to read some mythologies from some
+
+ align:start position:0%
+to read some mythologies from some
+ 
+
+ align:start position:0%
+to read some mythologies from some
+cultures that
+
+ align:start position:0%
+cultures that
+ 
+
+ align:start position:0%
+cultures that
+you don't know anything about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or if you know something about them
+
+ align:start position:0%
+or if you know something about them
+ 
+
+ align:start position:0%
+or if you know something about them
+let's make sure they're not west
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well that's it for today thank you
\ No newline at end of file
diff --git a/0cD-tcITuck.txt b/0cD-tcITuck.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b26e94470e3585d95c60bda1f619f7d333be1b34
--- /dev/null
+++ b/0cD-tcITuck.txt
@@ -0,0 +1,803 @@
+align:start position:0%
+ 
+conditional PDFs share most of the
+
+ align:start position:0%
+conditional PDFs share most of the
+ 
+
+ align:start position:0%
+conditional PDFs share most of the
+properties of conditional pmfs all facts
+
+ align:start position:0%
+properties of conditional pmfs all facts
+ 
+
+ align:start position:0%
+properties of conditional pmfs all facts
+for the discrete case have continuous
+
+ align:start position:0%
+for the discrete case have continuous
+ 
+
+ align:start position:0%
+for the discrete case have continuous
+analogs the intuition is more or less
+
+ align:start position:0%
+analogs the intuition is more or less
+ 
+
+ align:start position:0%
+analogs the intuition is more or less
+the same although it is much easier to
+
+ align:start position:0%
+the same although it is much easier to
+ 
+
+ align:start position:0%
+the same although it is much easier to
+grasp in the discrete case for example
+
+ align:start position:0%
+grasp in the discrete case for example
+ 
+
+ align:start position:0%
+grasp in the discrete case for example
+we have seen this version of the total
+
+ align:start position:0%
+we have seen this version of the total
+ 
+
+ align:start position:0%
+we have seen this version of the total
+probability theorem there is a
+
+ align:start position:0%
+probability theorem there is a
+ 
+
+ align:start position:0%
+probability theorem there is a
+continuous analogue in which we replace
+
+ align:start position:0%
+continuous analogue in which we replace
+ 
+
+ align:start position:0%
+continuous analogue in which we replace
+sums by integrals and we replace pmf's
+
+ align:start position:0%
+sums by integrals and we replace pmf's
+ 
+
+ align:start position:0%
+sums by integrals and we replace pmf's
+by pdfs the proof of this fact is
+
+ align:start position:0%
+by pdfs the proof of this fact is
+ 
+
+ align:start position:0%
+by pdfs the proof of this fact is
+actually pretty simple by the
+
+ align:start position:0%
+actually pretty simple by the
+ 
+
+ align:start position:0%
+actually pretty simple by the
+multiplication rule the integrand here
+
+ align:start position:0%
+multiplication rule the integrand here
+ 
+
+ align:start position:0%
+multiplication rule the integrand here
+is just the joint PDF of x and y and we
+
+ align:start position:0%
+is just the joint PDF of x and y and we
+ 
+
+ align:start position:0%
+is just the joint PDF of x and y and we
+know that if we take the joint PDF and
+
+ align:start position:0%
+know that if we take the joint PDF and
+ 
+
+ align:start position:0%
+know that if we take the joint PDF and
+integrate with respect to one variable
+
+ align:start position:0%
+integrate with respect to one variable
+ 
+
+ align:start position:0%
+integrate with respect to one variable
+then we recover the PDF the marginal PDF
+
+ align:start position:0%
+then we recover the PDF the marginal PDF
+ 
+
+ align:start position:0%
+then we recover the PDF the marginal PDF
+of the other random variable so this is
+
+ align:start position:0%
+of the other random variable so this is
+ 
+
+ align:start position:0%
+of the other random variable so this is
+one theorem that extends to the
+
+ align:start position:0%
+one theorem that extends to the
+ 
+
+ align:start position:0%
+one theorem that extends to the
+continuous case moving along we have
+
+ align:start position:0%
+continuous case moving along we have
+ 
+
+ align:start position:0%
+continuous case moving along we have
+defined the conditional expectation in
+
+ align:start position:0%
+defined the conditional expectation in
+ 
+
+ align:start position:0%
+defined the conditional expectation in
+this manner in the discrete case and we
+
+ align:start position:0%
+this manner in the discrete case and we
+ 
+
+ align:start position:0%
+this manner in the discrete case and we
+define it similarly for the continuous
+
+ align:start position:0%
+define it similarly for the continuous
+ 
+
+ align:start position:0%
+define it similarly for the continuous
+case so actually here we now have a new
+
+ align:start position:0%
+case so actually here we now have a new
+ 
+
+ align:start position:0%
+case so actually here we now have a new
+definition this definition is also
+
+ align:start position:0%
+definition this definition is also
+ 
+
+ align:start position:0%
+definition this definition is also
+consistent with the definition of the
+
+ align:start position:0%
+consistent with the definition of the
+ 
+
+ align:start position:0%
+consistent with the definition of the
+expectation of a continuous random
+
+ align:start position:0%
+expectation of a continuous random
+ 
+
+ align:start position:0%
+expectation of a continuous random
+variable the expected value of a
+
+ align:start position:0%
+variable the expected value of a
+ 
+
+ align:start position:0%
+variable the expected value of a
+continuous random variable is the
+
+ align:start position:0%
+continuous random variable is the
+ 
+
+ align:start position:0%
+continuous random variable is the
+integral of x times a density except
+
+ align:start position:0%
+integral of x times a density except
+ 
+
+ align:start position:0%
+integral of x times a density except
+that here we live in a conditional
+
+ align:start position:0%
+that here we live in a conditional
+ 
+
+ align:start position:0%
+that here we live in a conditional
+universe where we're conditioning on
+
+ align:start position:0%
+universe where we're conditioning on
+ 
+
+ align:start position:0%
+universe where we're conditioning on
+this event and therefore we need to use
+
+ align:start position:0%
+this event and therefore we need to use
+ 
+
+ align:start position:0%
+this event and therefore we need to use
+the corresponding conditional PDF
+
+ align:start position:0%
+the corresponding conditional PDF
+ 
+
+ align:start position:0%
+the corresponding conditional PDF
+finally we have the total expectation
+
+ align:start position:0%
+finally we have the total expectation
+ 
+
+ align:start position:0%
+finally we have the total expectation
+theorem in the discrete case and there
+
+ align:start position:0%
+theorem in the discrete case and there
+ 
+
+ align:start position:0%
+theorem in the discrete case and there
+is the obvious analogue in the
+
+ align:start position:0%
+is the obvious analogue in the
+ 
+
+ align:start position:0%
+is the obvious analogue in the
+continuous case where we are using an
+
+ align:start position:0%
+continuous case where we are using an
+ 
+
+ align:start position:0%
+continuous case where we are using an
+integral and a density the
+
+ align:start position:0%
+integral and a density the
+ 
+
+ align:start position:0%
+integral and a density the
+interpretation is that we consider all
+
+ align:start position:0%
+interpretation is that we consider all
+ 
+
+ align:start position:0%
+interpretation is that we consider all
+possibilities for Y under each
+
+ align:start position:0%
+possibilities for Y under each
+ 
+
+ align:start position:0%
+possibilities for Y under each
+possibility of Y we find the expected
+
+ align:start position:0%
+possibility of Y we find the expected
+ 
+
+ align:start position:0%
+possibility of Y we find the expected
+value of x and then we weigh those
+
+ align:start position:0%
+value of x and then we weigh those
+ 
+
+ align:start position:0%
+value of x and then we weigh those
+different possibilities according to the
+
+ align:start position:0%
+different possibilities according to the
+ 
+
+ align:start position:0%
+different possibilities according to the
+corresponding values of the density so
+
+ align:start position:0%
+corresponding values of the density so
+ 
+
+ align:start position:0%
+corresponding values of the density so
+we're taking a weighted average of these
+
+ align:start position:0%
+we're taking a weighted average of these
+ 
+
+ align:start position:0%
+we're taking a weighted average of these
+conditional expectations to obtain the
+
+ align:start position:0%
+conditional expectations to obtain the
+ 
+
+ align:start position:0%
+conditional expectations to obtain the
+overall expectation of the random
+
+ align:start position:0%
+overall expectation of the random
+ 
+
+ align:start position:0%
+overall expectation of the random
+variable X
+
+ align:start position:0%
+variable X
+ 
+
+ align:start position:0%
+variable X
+the derivation of this fact is maybe a
+
+ align:start position:0%
+the derivation of this fact is maybe a
+ 
+
+ align:start position:0%
+the derivation of this fact is maybe a
+little instructive because it uses
+
+ align:start position:0%
+little instructive because it uses
+ 
+
+ align:start position:0%
+little instructive because it uses
+various facts that we have in our hands
+
+ align:start position:0%
+various facts that we have in our hands
+ 
+
+ align:start position:0%
+various facts that we have in our hands
+so let's see how to derive it we start
+
+ align:start position:0%
+so let's see how to derive it we start
+ 
+
+ align:start position:0%
+so let's see how to derive it we start
+from this expression in the right hand
+
+ align:start position:0%
+from this expression in the right hand
+ 
+
+ align:start position:0%
+from this expression in the right hand
+side and we will show that it is equal
+
+ align:start position:0%
+side and we will show that it is equal
+ 
+
+ align:start position:0%
+side and we will show that it is equal
+to the expected value of X the
+
+ align:start position:0%
+to the expected value of X the
+ 
+
+ align:start position:0%
+to the expected value of X the
+expression on the right hand side is
+
+ align:start position:0%
+expression on the right hand side is
+ 
+
+ align:start position:0%
+expression on the right hand side is
+equal to the following it's the integral
+
+ align:start position:0%
+equal to the following it's the integral
+ 
+
+ align:start position:0%
+equal to the following it's the integral
+of the density of Y and then inside here
+
+ align:start position:0%
+of the density of Y and then inside here
+ 
+
+ align:start position:0%
+of the density of Y and then inside here
+we have the conditional expectation
+
+ align:start position:0%
+we have the conditional expectation
+ 
+
+ align:start position:0%
+we have the conditional expectation
+which is defined this way so we just
+
+ align:start position:0%
+which is defined this way so we just
+ 
+
+ align:start position:0%
+which is defined this way so we just
+plug in the definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then what we do is we take this term
+
+ align:start position:0%
+and then what we do is we take this term
+ 
+
+ align:start position:0%
+and then what we do is we take this term
+and move it inside the integral which we
+
+ align:start position:0%
+and move it inside the integral which we
+ 
+
+ align:start position:0%
+and move it inside the integral which we
+can do because this integral is with
+
+ align:start position:0%
+can do because this integral is with
+ 
+
+ align:start position:0%
+can do because this integral is with
+respect to X and therefore this is like
+
+ align:start position:0%
+respect to X and therefore this is like
+ 
+
+ align:start position:0%
+respect to X and therefore this is like
+a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we also interchange the order of
+
+ align:start position:0%
+and we also interchange the order of
+ 
+
+ align:start position:0%
+and we also interchange the order of
+integration now the inner integration is
+
+ align:start position:0%
+integration now the inner integration is
+ 
+
+ align:start position:0%
+integration now the inner integration is
+with respect to Y as far as Y is
+
+ align:start position:0%
+with respect to Y as far as Y is
+ 
+
+ align:start position:0%
+with respect to Y as far as Y is
+concerned this term X is a constant so
+
+ align:start position:0%
+concerned this term X is a constant so
+ 
+
+ align:start position:0%
+concerned this term X is a constant so
+we can take it and move it outside this
+
+ align:start position:0%
+we can take it and move it outside this
+ 
+
+ align:start position:0%
+we can take it and move it outside this
+first integral and place it out there so
+
+ align:start position:0%
+first integral and place it out there so
+ 
+
+ align:start position:0%
+first integral and place it out there so
+this term disappears and goes out there
+
+ align:start position:0%
+this term disappears and goes out there
+ 
+
+ align:start position:0%
+this term disappears and goes out there
+what do we have here
+
+ align:start position:0%
+what do we have here
+ 
+
+ align:start position:0%
+what do we have here
+this part by the previous fact the total
+
+ align:start position:0%
+this part by the previous fact the total
+ 
+
+ align:start position:0%
+this part by the previous fact the total
+probability theorem is just the density
+
+ align:start position:0%
+probability theorem is just the density
+ 
+
+ align:start position:0%
+probability theorem is just the density
+of X so we're left with the integral of
+
+ align:start position:0%
+of X so we're left with the integral of
+ 
+
+ align:start position:0%
+of X so we're left with the integral of
+x times the density of X DX and this is
+
+ align:start position:0%
+x times the density of X DX and this is
+ 
+
+ align:start position:0%
+x times the density of X DX and this is
+the expected value of X finally we have
+
+ align:start position:0%
+the expected value of X finally we have
+ 
+
+ align:start position:0%
+the expected value of X finally we have
+various forms of the expected value rule
+
+ align:start position:0%
+various forms of the expected value rule
+ 
+
+ align:start position:0%
+various forms of the expected value rule
+which barely deserve writing down
+
+ align:start position:0%
+which barely deserve writing down
+ 
+
+ align:start position:0%
+which barely deserve writing down
+because they're exactly what you might
+
+ align:start position:0%
+because they're exactly what you might
+ 
+
+ align:start position:0%
+because they're exactly what you might
+expect consider for example an
+
+ align:start position:0%
+expect consider for example an
+ 
+
+ align:start position:0%
+expect consider for example an
+expression such as this one the expected
+
+ align:start position:0%
+expression such as this one the expected
+ 
+
+ align:start position:0%
+expression such as this one the expected
+value of a function of the random
+
+ align:start position:0%
+value of a function of the random
+ 
+
+ align:start position:0%
+value of a function of the random
+variable X but conditioned on the value
+
+ align:start position:0%
+variable X but conditioned on the value
+ 
+
+ align:start position:0%
+variable X but conditioned on the value
+of the random variable Y how do we
+
+ align:start position:0%
+of the random variable Y how do we
+ 
+
+ align:start position:0%
+of the random variable Y how do we
+calculate this quantity
+
+ align:start position:0%
+calculate this quantity
+ 
+
+ align:start position:0%
+calculate this quantity
+well the expected value rule tells us
+
+ align:start position:0%
+well the expected value rule tells us
+ 
+
+ align:start position:0%
+well the expected value rule tells us
+that we should integrate G of x times
+
+ align:start position:0%
+that we should integrate G of x times
+ 
+
+ align:start position:0%
+that we should integrate G of x times
+the density of X but because here we
+
+ align:start position:0%
+the density of X but because here we
+ 
+
+ align:start position:0%
+the density of X but because here we
+live in a conditional universe we should
+
+ align:start position:0%
+live in a conditional universe we should
+ 
+
+ align:start position:0%
+live in a conditional universe we should
+actually use the corresponding
+
+ align:start position:0%
+actually use the corresponding
+ 
+
+ align:start position:0%
+actually use the corresponding
+conditional PDF of X and there are many
+
+ align:start position:0%
+conditional PDF of X and there are many
+ 
+
+ align:start position:0%
+conditional PDF of X and there are many
+other versions of the expected value
+
+ align:start position:0%
+other versions of the expected value
+ 
+
+ align:start position:0%
+other versions of the expected value
+rule any version that we have seen for
+
+ align:start position:0%
+rule any version that we have seen for
+ 
+
+ align:start position:0%
+rule any version that we have seen for
+the discrete case has also a continuous
+
+ align:start position:0%
+the discrete case has also a continuous
+ 
+
+ align:start position:0%
+the discrete case has also a continuous
+analogue which looks about the same
+
+ align:start position:0%
+analogue which looks about the same
+ 
+
+ align:start position:0%
+analogue which looks about the same
+except that we integrate and that we use
+
+ align:start position:0%
+except that we integrate and that we use
+ 
+
+ align:start position:0%
+except that we integrate and that we use
+densities
\ No newline at end of file
diff --git a/0jljZRnHwOI.txt b/0jljZRnHwOI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a77875a5b948f6a48da0dc32f94b2b3dae730d46
--- /dev/null
+++ b/0jljZRnHwOI.txt
@@ -0,0 +1,8027 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right let's get started everyone so good
+
+ align:start position:0%
+right let's get started everyone so good
+ 
+
+ align:start position:0%
+right let's get started everyone so good
+afternoon welcome to the second lecture
+
+ align:start position:0%
+afternoon welcome to the second lecture
+ 
+
+ align:start position:0%
+afternoon welcome to the second lecture
+of 601 and also of 600 so as always if
+
+ align:start position:0%
+of 601 and also of 600 so as always if
+ 
+
+ align:start position:0%
+of 601 and also of 600 so as always if
+you'd like to follow along with the
+
+ align:start position:0%
+you'd like to follow along with the
+ 
+
+ align:start position:0%
+you'd like to follow along with the
+lecture with the lectures please go
+
+ align:start position:0%
+lecture with the lectures please go
+ 
+
+ align:start position:0%
+lecture with the lectures please go
+ahead and download the slides and the
+
+ align:start position:0%
+ahead and download the slides and the
+ 
+
+ align:start position:0%
+ahead and download the slides and the
+code that um that I'll provide uh at
+
+ align:start position:0%
+code that um that I'll provide uh at
+ 
+
+ align:start position:0%
+code that um that I'll provide uh at
+least an hour before class every day all
+
+ align:start position:0%
+least an hour before class every day all
+ 
+
+ align:start position:0%
+least an hour before class every day all
+right so quick recap of what we did last
+
+ align:start position:0%
+right so quick recap of what we did last
+ 
+
+ align:start position:0%
+right so quick recap of what we did last
+time so last time we talked a little bit
+
+ align:start position:0%
+time so last time we talked a little bit
+ 
+
+ align:start position:0%
+time so last time we talked a little bit
+about um what a computer is
+
+ align:start position:0%
+about um what a computer is
+ 
+
+ align:start position:0%
+about um what a computer is
+and I think the main takeaway from the
+
+ align:start position:0%
+and I think the main takeaway from the
+ 
+
+ align:start position:0%
+and I think the main takeaway from the
+last lecture is really that a computer
+
+ align:start position:0%
+last lecture is really that a computer
+ 
+
+ align:start position:0%
+last lecture is really that a computer
+only does what it is told right so it's
+
+ align:start position:0%
+only does what it is told right so it's
+ 
+
+ align:start position:0%
+only does what it is told right so it's
+not going to spontaneous spontaneously
+
+ align:start position:0%
+not going to spontaneous spontaneously
+ 
+
+ align:start position:0%
+not going to spontaneous spontaneously
+make decisions on its own you as the
+
+ align:start position:0%
+make decisions on its own you as the
+ 
+
+ align:start position:0%
+make decisions on its own you as the
+programmer have to tell it what you want
+
+ align:start position:0%
+programmer have to tell it what you want
+ 
+
+ align:start position:0%
+programmer have to tell it what you want
+it to do by writing programs okay so we
+
+ align:start position:0%
+it to do by writing programs okay so we
+ 
+
+ align:start position:0%
+it to do by writing programs okay so we
+talked about uh simple objects and um
+
+ align:start position:0%
+talked about uh simple objects and um
+ 
+
+ align:start position:0%
+talked about uh simple objects and um
+these objects were of different types so
+
+ align:start position:0%
+these objects were of different types so
+ 
+
+ align:start position:0%
+these objects were of different types so
+we saw integers floats and booleans and
+
+ align:start position:0%
+we saw integers floats and booleans and
+ 
+
+ align:start position:0%
+we saw integers floats and booleans and
+then we did a couple simple operations
+
+ align:start position:0%
+then we did a couple simple operations
+ 
+
+ align:start position:0%
+then we did a couple simple operations
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+them today we're going to look at a
+
+ align:start position:0%
+them today we're going to look at a
+ 
+
+ align:start position:0%
+them today we're going to look at a
+different a new a new type of object
+
+ align:start position:0%
+different a new a new type of object
+ 
+
+ align:start position:0%
+different a new a new type of object
+called a string and then we're going to
+
+ align:start position:0%
+called a string and then we're going to
+ 
+
+ align:start position:0%
+called a string and then we're going to
+introduce some um more powerful uh um
+
+ align:start position:0%
+introduce some um more powerful uh um
+ 
+
+ align:start position:0%
+introduce some um more powerful uh um
+things in our programming toolbox so
+
+ align:start position:0%
+things in our programming toolbox so
+ 
+
+ align:start position:0%
+things in our programming toolbox so
+we're going to look at how to how to
+
+ align:start position:0%
+we're going to look at how to how to
+ 
+
+ align:start position:0%
+we're going to look at how to how to
+Branch within a program and how to make
+
+ align:start position:0%
+Branch within a program and how to make
+ 
+
+ align:start position:0%
+Branch within a program and how to make
+things how to make the computer repeat
+
+ align:start position:0%
+things how to make the computer repeat
+ 
+
+ align:start position:0%
+things how to make the computer repeat
+certain tasks within our program all
+
+ align:start position:0%
+certain tasks within our program all
+ 
+
+ align:start position:0%
+certain tasks within our program all
+right so let's begin by looking at
+
+ align:start position:0%
+right so let's begin by looking at
+ 
+
+ align:start position:0%
+right so let's begin by looking at
+strings so strings are a new object type
+
+ align:start position:0%
+strings so strings are a new object type
+ 
+
+ align:start position:0%
+strings so strings are a new object type
+we've seen so far integers which were
+
+ align:start position:0%
+we've seen so far integers which were
+ 
+
+ align:start position:0%
+we've seen so far integers which were
+whole numbers floats
+
+ align:start position:0%
+whole numbers floats
+ 
+
+ align:start position:0%
+whole numbers floats
+which were decimal numbers and we have
+
+ align:start position:0%
+which were decimal numbers and we have
+ 
+
+ align:start position:0%
+which were decimal numbers and we have
+seen uh we've seen booleans which were
+
+ align:start position:0%
+seen uh we've seen booleans which were
+ 
+
+ align:start position:0%
+seen uh we've seen booleans which were
+true and false so strings are going to
+
+ align:start position:0%
+true and false so strings are going to
+ 
+
+ align:start position:0%
+true and false so strings are going to
+be uh sequences of characters and these
+
+ align:start position:0%
+be uh sequences of characters and these
+ 
+
+ align:start position:0%
+be uh sequences of characters and these
+characters can be anything they could be
+
+ align:start position:0%
+characters can be anything they could be
+ 
+
+ align:start position:0%
+characters can be anything they could be
+letters digits uh special characters and
+
+ align:start position:0%
+letters digits uh special characters and
+ 
+
+ align:start position:0%
+letters digits uh special characters and
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+spaces and you tell python that you're
+
+ align:start position:0%
+spaces and you tell python that you're
+ 
+
+ align:start position:0%
+spaces and you tell python that you're
+um you're talking about a string object
+
+ align:start position:0%
+um you're talking about a string object
+ 
+
+ align:start position:0%
+um you're talking about a string object
+by enclosing it in quotation marks so in
+
+ align:start position:0%
+by enclosing it in quotation marks so in
+ 
+
+ align:start position:0%
+by enclosing it in quotation marks so in
+this case I'm creating an object um
+
+ align:start position:0%
+this case I'm creating an object um
+ 
+
+ align:start position:0%
+this case I'm creating an object um
+whose value is h e l l space t h
+
+ align:start position:0%
+whose value is h e l l space t h
+ 
+
+ align:start position:0%
+whose value is h e l l space t h
+re and python knows it's a string object
+
+ align:start position:0%
+re and python knows it's a string object
+ 
+
+ align:start position:0%
+re and python knows it's a string object
+because we're enclosing it in quotations
+
+ align:start position:0%
+because we're enclosing it in quotations
+ 
+
+ align:start position:0%
+because we're enclosing it in quotations
+they could be either double quotes or
+
+ align:start position:0%
+they could be either double quotes or
+ 
+
+ align:start position:0%
+they could be either double quotes or
+single quotes but as long as you're
+
+ align:start position:0%
+single quotes but as long as you're
+ 
+
+ align:start position:0%
+single quotes but as long as you're
+consistent it doesn't matter and this
+
+ align:start position:0%
+consistent it doesn't matter and this
+ 
+
+ align:start position:0%
+consistent it doesn't matter and this
+object we're we're um we're binding it
+
+ align:start position:0%
+object we're we're um we're binding it
+ 
+
+ align:start position:0%
+object we're we're um we're binding it
+to this variable named high and we're
+
+ align:start position:0%
+to this variable named high and we're
+ 
+
+ align:start position:0%
+to this variable named high and we're
+using that using the equal sign which is
+
+ align:start position:0%
+using that using the equal sign which is
+ 
+
+ align:start position:0%
+using that using the equal sign which is
+the assignment
+
+ align:start position:0%
+the assignment
+ 
+
+ align:start position:0%
+the assignment
+operator okay so from now on whenever we
+
+ align:start position:0%
+operator okay so from now on whenever we
+ 
+
+ align:start position:0%
+operator okay so from now on whenever we
+refer to this variable High Python's
+
+ align:start position:0%
+refer to this variable High Python's
+ 
+
+ align:start position:0%
+refer to this variable High Python's
+going to say oh I know what the value is
+
+ align:start position:0%
+going to say oh I know what the value is
+ 
+
+ align:start position:0%
+going to say oh I know what the value is
+and it's that string of characters
+
+ align:start position:0%
+and it's that string of characters
+ 
+
+ align:start position:0%
+and it's that string of characters
+so we're going to learn about two things
+
+ align:start position:0%
+so we're going to learn about two things
+ 
+
+ align:start position:0%
+so we're going to learn about two things
+that you can do on strings today two
+
+ align:start position:0%
+that you can do on strings today two
+ 
+
+ align:start position:0%
+that you can do on strings today two
+operations one is to concatenate them
+
+ align:start position:0%
+operations one is to concatenate them
+ 
+
+ align:start position:0%
+operations one is to concatenate them
+and concatenation is really just a fancy
+
+ align:start position:0%
+and concatenation is really just a fancy
+ 
+
+ align:start position:0%
+and concatenation is really just a fancy
+word for using this plus operator which
+
+ align:start position:0%
+word for using this plus operator which
+ 
+
+ align:start position:0%
+word for using this plus operator which
+means put the strings
+
+ align:start position:0%
+means put the strings
+ 
+
+ align:start position:0%
+means put the strings
+together so I have this original um
+
+ align:start position:0%
+together so I have this original um
+ 
+
+ align:start position:0%
+together so I have this original um
+variable named high and I create a new
+
+ align:start position:0%
+variable named high and I create a new
+ 
+
+ align:start position:0%
+variable named high and I create a new
+variable called name and in it I'm going
+
+ align:start position:0%
+variable called name and in it I'm going
+ 
+
+ align:start position:0%
+variable called name and in it I'm going
+to assign I'm going to assign the string
+
+ align:start position:0%
+to assign I'm going to assign the string
+ 
+
+ align:start position:0%
+to assign I'm going to assign the string
+a Ana to the variable name and when I
+
+ align:start position:0%
+a Ana to the variable name and when I
+ 
+
+ align:start position:0%
+a Ana to the variable name and when I
+use the plus operator in between high
+
+ align:start position:0%
+use the plus operator in between high
+ 
+
+ align:start position:0%
+use the plus operator in between high
+and name those two variables python is
+
+ align:start position:0%
+and name those two variables python is
+ 
+
+ align:start position:0%
+and name those two variables python is
+going to look at the values of those two
+
+ align:start position:0%
+going to look at the values of those two
+ 
+
+ align:start position:0%
+going to look at the values of those two
+and it's going to just put them
+
+ align:start position:0%
+and it's going to just put them
+ 
+
+ align:start position:0%
+and it's going to just put them
+together okay I'm going to switch to Sky
+
+ align:start position:0%
+together okay I'm going to switch to Sky
+ 
+
+ align:start position:0%
+together okay I'm going to switch to Sky
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+spider and this is just that example
+
+ align:start position:0%
+spider and this is just that example
+ 
+
+ align:start position:0%
+spider and this is just that example
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+the uh from the slides so let's see what
+
+ align:start position:0%
+the uh from the slides so let's see what
+ 
+
+ align:start position:0%
+the uh from the slides so let's see what
+happens so I have the variable um High
+
+ align:start position:0%
+happens so I have the variable um High
+ 
+
+ align:start position:0%
+happens so I have the variable um High
+the variable name and I'm just
+
+ align:start position:0%
+the variable name and I'm just
+ 
+
+ align:start position:0%
+the variable name and I'm just
+concatenating those two together and
+
+ align:start position:0%
+concatenating those two together and
+ 
+
+ align:start position:0%
+concatenating those two together and
+then I'm going to print that out so if I
+
+ align:start position:0%
+then I'm going to print that out so if I
+ 
+
+ align:start position:0%
+then I'm going to print that out so if I
+I run the
+
+ align:start position:0%
+I run the
+ 
+
+ align:start position:0%
+I run the
+code notice it prints out hello there
+
+ align:start position:0%
+code notice it prints out hello there
+ 
+
+ align:start position:0%
+code notice it prints out hello there
+Anna right there's no space and there's
+
+ align:start position:0%
+Anna right there's no space and there's
+ 
+
+ align:start position:0%
+Anna right there's no space and there's
+no space because the concatenation
+
+ align:start position:0%
+no space because the concatenation
+ 
+
+ align:start position:0%
+no space because the concatenation
+operator the plus uh doesn't add any
+
+ align:start position:0%
+operator the plus uh doesn't add any
+ 
+
+ align:start position:0%
+operator the plus uh doesn't add any
+spaces implicitly so again another
+
+ align:start position:0%
+spaces implicitly so again another
+ 
+
+ align:start position:0%
+spaces implicitly so again another
+example of just computer just doing what
+
+ align:start position:0%
+example of just computer just doing what
+ 
+
+ align:start position:0%
+example of just computer just doing what
+it's told if we want to add a space we'd
+
+ align:start position:0%
+it's told if we want to add a space we'd
+ 
+
+ align:start position:0%
+it's told if we want to add a space we'd
+have to actually insert the space
+
+ align:start position:0%
+have to actually insert the space
+ 
+
+ align:start position:0%
+have to actually insert the space
+manually so that's this line here line
+
+ align:start position:0%
+manually so that's this line here line
+ 
+
+ align:start position:0%
+manually so that's this line here line
+eight and in this line we're
+
+ align:start position:0%
+eight and in this line we're
+ 
+
+ align:start position:0%
+eight and in this line we're
+concatenating the VAR the the value of
+
+ align:start position:0%
+concatenating the VAR the the value of
+ 
+
+ align:start position:0%
+concatenating the VAR the the value of
+the variable High with a space notice
+
+ align:start position:0%
+the variable High with a space notice
+ 
+
+ align:start position:0%
+the variable High with a space notice
+we're putting it in quotation marks just
+
+ align:start position:0%
+we're putting it in quotation marks just
+ 
+
+ align:start position:0%
+we're putting it in quotation marks just
+a space and then with
+
+ align:start position:0%
+a space and then with
+ 
+
+ align:start position:0%
+a space and then with
+name so if we go ahead and print that
+
+ align:start position:0%
+name so if we go ahead and print that
+ 
+
+ align:start position:0%
+name so if we go ahead and print that
+value notice this was
+
+ align:start position:0%
+value notice this was
+ 
+
+ align:start position:0%
+value notice this was
+that garbage greeting there and now we
+
+ align:start position:0%
+that garbage greeting there and now we
+ 
+
+ align:start position:0%
+that garbage greeting there and now we
+have a proper greeting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right another so that's the
+
+ align:start position:0%
+right another so that's the
+ 
+
+ align:start position:0%
+right another so that's the
+concatenation um between strings and
+
+ align:start position:0%
+concatenation um between strings and
+ 
+
+ align:start position:0%
+concatenation um between strings and
+then the other thing we're going to look
+
+ align:start position:0%
+then the other thing we're going to look
+ 
+
+ align:start position:0%
+then the other thing we're going to look
+at uh related to Strings is the star
+
+ align:start position:0%
+at uh related to Strings is the star
+ 
+
+ align:start position:0%
+at uh related to Strings is the star
+operator so that's this one here on line
+
+ align:start position:0%
+operator so that's this one here on line
+ 
+
+ align:start position:0%
+operator so that's this one here on line
+10 so python allows you to use the star
+
+ align:start position:0%
+10 so python allows you to use the star
+ 
+
+ align:start position:0%
+10 so python allows you to use the star
+operator which is stands for
+
+ align:start position:0%
+operator which is stands for
+ 
+
+ align:start position:0%
+operator which is stands for
+multiplication between a string and a
+
+ align:start position:0%
+multiplication between a string and a
+ 
+
+ align:start position:0%
+multiplication between a string and a
+number and when you do that python
+
+ align:start position:0%
+number and when you do that python
+ 
+
+ align:start position:0%
+number and when you do that python
+interpret interprets it
+
+ align:start position:0%
+interpret interprets it
+ 
+
+ align:start position:0%
+interpret interprets it
+as repeat that string that many number
+
+ align:start position:0%
+as repeat that string that many number
+ 
+
+ align:start position:0%
+as repeat that string that many number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+times so in this case I'm creating a
+
+ align:start position:0%
+times so in this case I'm creating a
+ 
+
+ align:start position:0%
+times so in this case I'm creating a
+silly greeting and I'm concatenating the
+
+ align:start position:0%
+silly greeting and I'm concatenating the
+ 
+
+ align:start position:0%
+silly greeting and I'm concatenating the
+value of high which is hello there with
+
+ align:start position:0%
+value of high which is hello there with
+ 
+
+ align:start position:0%
+value of high which is hello there with
+the space plus the name so notice here
+
+ align:start position:0%
+the space plus the name so notice here
+ 
+
+ align:start position:0%
+the space plus the name so notice here
+I'm using parentheses to tell python do
+
+ align:start position:0%
+I'm using parentheses to tell python do
+ 
+
+ align:start position:0%
+I'm using parentheses to tell python do
+this operation first and then multiply
+
+ align:start position:0%
+this operation first and then multiply
+ 
+
+ align:start position:0%
+this operation first and then multiply
+whatever the result of this is by
+
+ align:start position:0%
+whatever the result of this is by
+ 
+
+ align:start position:0%
+whatever the result of this is by
+three okay so if I print that
+
+ align:start position:0%
+three okay so if I print that
+ 
+
+ align:start position:0%
+three okay so if I print that
+out it's going to multiply the space
+
+ align:start position:0%
+out it's going to multiply the space
+ 
+
+ align:start position:0%
+out it's going to multiply the space
+with my name three times and it's going
+
+ align:start position:0%
+with my name three times and it's going
+ 
+
+ align:start position:0%
+with my name three times and it's going
+to concatenate that with hello there so
+
+ align:start position:0%
+to concatenate that with hello there so
+ 
+
+ align:start position:0%
+to concatenate that with hello there so
+that's exactly what it printed out
+
+ align:start position:0%
+that's exactly what it printed out
+ 
+
+ align:start position:0%
+that's exactly what it printed out
+there last lecture we talked a little
+
+ align:start position:0%
+there last lecture we talked a little
+ 
+
+ align:start position:0%
+there last lecture we talked a little
+bit about about print today I'm going to
+
+ align:start position:0%
+bit about about print today I'm going to
+ 
+
+ align:start position:0%
+bit about about print today I'm going to
+talk uh about some nuances related to
+
+ align:start position:0%
+talk uh about some nuances related to
+ 
+
+ align:start position:0%
+talk uh about some nuances related to
+print so you use print to interact with
+
+ align:start position:0%
+print so you use print to interact with
+ 
+
+ align:start position:0%
+print so you use print to interact with
+the user um it's cool to write programs
+
+ align:start position:0%
+the user um it's cool to write programs
+ 
+
+ align:start position:0%
+the user um it's cool to write programs
+that print things out to the user so the
+
+ align:start position:0%
+that print things out to the user so the
+ 
+
+ align:start position:0%
+that print things out to the user so the
+keyword here being print and then you
+
+ align:start position:0%
+keyword here being print and then you
+ 
+
+ align:start position:0%
+keyword here being print and then you
+put parentheses after print and in the
+
+ align:start position:0%
+put parentheses after print and in the
+ 
+
+ align:start position:0%
+put parentheses after print and in the
+parentheses you put in whatever you want
+
+ align:start position:0%
+parentheses you put in whatever you want
+ 
+
+ align:start position:0%
+parentheses you put in whatever you want
+to show the
+
+ align:start position:0%
+to show the
+ 
+
+ align:start position:0%
+to show the
+user so in this little program I have
+
+ align:start position:0%
+user so in this little program I have
+ 
+
+ align:start position:0%
+user so in this little program I have
+I create a variable named X I assign it
+
+ align:start position:0%
+I create a variable named X I assign it
+ 
+
+ align:start position:0%
+I create a variable named X I assign it
+the value one and then I print
+
+ align:start position:0%
+the value one and then I print
+ 
+
+ align:start position:0%
+the value one and then I print
+one here I'm
+
+ align:start position:0%
+one here I'm
+ 
+
+ align:start position:0%
+one here I'm
+casting so I'm taking the number one the
+
+ align:start position:0%
+casting so I'm taking the number one the
+ 
+
+ align:start position:0%
+casting so I'm taking the number one the
+integer one and I'm casting it to a
+
+ align:start position:0%
+integer one and I'm casting it to a
+ 
+
+ align:start position:0%
+integer one and I'm casting it to a
+string and you'll see why in a
+
+ align:start position:0%
+string and you'll see why in a
+ 
+
+ align:start position:0%
+string and you'll see why in a
+moment so I want to bring to your
+
+ align:start position:0%
+moment so I want to bring to your
+ 
+
+ align:start position:0%
+moment so I want to bring to your
+attention a couple things here so in the
+
+ align:start position:0%
+attention a couple things here so in the
+ 
+
+ align:start position:0%
+attention a couple things here so in the
+first print I'm using commas everywhere
+
+ align:start position:0%
+first print I'm using commas everywhere
+ 
+
+ align:start position:0%
+first print I'm using commas everywhere
+here and then the second print I'm using
+
+ align:start position:0%
+here and then the second print I'm using
+ 
+
+ align:start position:0%
+here and then the second print I'm using
+plus okay
+
+ align:start position:0%
+plus okay
+ 
+
+ align:start position:0%
+plus okay
+so by definition if you you can use
+
+ align:start position:0%
+so by definition if you you can use
+ 
+
+ align:start position:0%
+so by definition if you you can use
+print you can use commas inside a print
+
+ align:start position:0%
+print you can use commas inside a print
+ 
+
+ align:start position:0%
+print you can use commas inside a print
+inside the parenthesis of
+
+ align:start position:0%
+inside the parenthesis of
+ 
+
+ align:start position:0%
+inside the parenthesis of
+print and if you use a comma Python's
+
+ align:start position:0%
+print and if you use a comma Python's
+ 
+
+ align:start position:0%
+print and if you use a comma Python's
+going to automatically add a space in
+
+ align:start position:0%
+going to automatically add a space in
+ 
+
+ align:start position:0%
+going to automatically add a space in
+between the two things that the comma is
+
+ align:start position:0%
+between the two things that the comma is
+ 
+
+ align:start position:0%
+between the two things that the comma is
+in in between the values so my fav num
+
+ align:start position:0%
+in in between the values so my fav num
+ 
+
+ align:start position:0%
+in in between the values so my fav num
+is is the first thing and the second
+
+ align:start position:0%
+is is the first thing and the second
+ 
+
+ align:start position:0%
+is is the first thing and the second
+thing is whatever is after the
+
+ align:start position:0%
+thing is whatever is after the
+ 
+
+ align:start position:0%
+thing is whatever is after the
+comma let's take X so if you use a comma
+
+ align:start position:0%
+comma let's take X so if you use a comma
+ 
+
+ align:start position:0%
+comma let's take X so if you use a comma
+Python's going to automatically insert a
+
+ align:start position:0%
+Python's going to automatically insert a
+ 
+
+ align:start position:0%
+Python's going to automatically insert a
+space for you okay sometimes you might
+
+ align:start position:0%
+space for you okay sometimes you might
+ 
+
+ align:start position:0%
+space for you okay sometimes you might
+want that sometimes you might not if you
+
+ align:start position:0%
+want that sometimes you might not if you
+ 
+
+ align:start position:0%
+want that sometimes you might not if you
+don't want that you can use the
+
+ align:start position:0%
+don't want that you can use the
+ 
+
+ align:start position:0%
+don't want that you can use the
+concatenation operation the plus and you
+
+ align:start position:0%
+concatenation operation the plus and you
+ 
+
+ align:start position:0%
+concatenation operation the plus and you
+can add all of your little bits together
+
+ align:start position:0%
+can add all of your little bits together
+ 
+
+ align:start position:0%
+can add all of your little bits together
+to create one big
+
+ align:start position:0%
+to create one big
+ 
+
+ align:start position:0%
+to create one big
+string if you're using commas the the
+
+ align:start position:0%
+string if you're using commas the the
+ 
+
+ align:start position:0%
+string if you're using commas the the
+items the objects in between the commas
+
+ align:start position:0%
+items the objects in between the commas
+ 
+
+ align:start position:0%
+items the objects in between the commas
+do not all have to be strings that's the
+
+ align:start position:0%
+do not all have to be strings that's the
+ 
+
+ align:start position:0%
+do not all have to be strings that's the
+plus side of using commas but the noun
+
+ align:start position:0%
+plus side of using commas but the noun
+ 
+
+ align:start position:0%
+plus side of using commas but the noun
+side is you get spaces everywhere
+
+ align:start position:0%
+side is you get spaces everywhere
+ 
+
+ align:start position:0%
+side is you get spaces everywhere
+if you use
+
+ align:start position:0%
+if you use
+ 
+
+ align:start position:0%
+if you use
+plus operator the plus side is python
+
+ align:start position:0%
+plus operator the plus side is python
+ 
+
+ align:start position:0%
+plus operator the plus side is python
+does exactly what you tell it to do but
+
+ align:start position:0%
+does exactly what you tell it to do but
+ 
+
+ align:start position:0%
+does exactly what you tell it to do but
+everything has to be a string object so
+
+ align:start position:0%
+everything has to be a string object so
+ 
+
+ align:start position:0%
+everything has to be a string object so
+my fave num is is a string object you
+
+ align:start position:0%
+my fave num is is a string object you
+ 
+
+ align:start position:0%
+my fave num is is a string object you
+have to convert all of your numbers to
+
+ align:start position:0%
+have to convert all of your numbers to
+ 
+
+ align:start position:0%
+have to convert all of your numbers to
+string objects and so
+
+ align:start position:0%
+string objects and so
+ 
+
+ align:start position:0%
+string objects and so
+on so if we look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spider this is the same almost the same
+
+ align:start position:0%
+spider this is the same almost the same
+ 
+
+ align:start position:0%
+spider this is the same almost the same
+code so here I don't have spaces
+
+ align:start position:0%
+code so here I don't have spaces
+ 
+
+ align:start position:0%
+code so here I don't have spaces
+anywhere so you can see that the first
+
+ align:start position:0%
+anywhere so you can see that the first
+ 
+
+ align:start position:0%
+anywhere so you can see that the first
+line here has commas everywhere so I'm
+
+ align:start position:0%
+line here has commas everywhere so I'm
+ 
+
+ align:start position:0%
+line here has commas everywhere so I'm
+going to have spaces in between every
+
+ align:start position:0%
+going to have spaces in between every
+ 
+
+ align:start position:0%
+going to have spaces in between every
+one of the things that I'm um that I'm
+
+ align:start position:0%
+one of the things that I'm um that I'm
+ 
+
+ align:start position:0%
+one of the things that I'm um that I'm
+printing
+
+ align:start position:0%
+printing
+ 
+
+ align:start position:0%
+printing
+out this line here is sort of a
+
+ align:start position:0%
+out this line here is sort of a
+ 
+
+ align:start position:0%
+out this line here is sort of a
+combination between Comm commas and
+
+ align:start position:0%
+combination between Comm commas and
+ 
+
+ align:start position:0%
+combination between Comm commas and
+concatenation so depending on where I
+
+ align:start position:0%
+concatenation so depending on where I
+ 
+
+ align:start position:0%
+concatenation so depending on where I
+use the comma I'm going to have an extra
+
+ align:start position:0%
+use the comma I'm going to have an extra
+ 
+
+ align:start position:0%
+use the comma I'm going to have an extra
+space and this line here just has
+
+ align:start position:0%
+space and this line here just has
+ 
+
+ align:start position:0%
+space and this line here just has
+concatenation everywhere okay so if I
+
+ align:start position:0%
+concatenation everywhere okay so if I
+ 
+
+ align:start position:0%
+concatenation everywhere okay so if I
+run
+
+ align:start position:0%
+run
+ 
+
+ align:start position:0%
+run
+this notice this very first line added
+
+ align:start position:0%
+this notice this very first line added
+ 
+
+ align:start position:0%
+this notice this very first line added
+spaces everywhere in between all my
+
+ align:start position:0%
+spaces everywhere in between all my
+ 
+
+ align:start position:0%
+spaces everywhere in between all my
+objects the second one added spaces
+
+ align:start position:0%
+objects the second one added spaces
+ 
+
+ align:start position:0%
+objects the second one added spaces
+somewhere and you can sort of Trace
+
+ align:start position:0%
+somewhere and you can sort of Trace
+ 
+
+ align:start position:0%
+somewhere and you can sort of Trace
+through and see exactly where the spaces
+
+ align:start position:0%
+through and see exactly where the spaces
+ 
+
+ align:start position:0%
+through and see exactly where the spaces
+were added and the last line
+
+ align:start position:0%
+were added and the last line
+ 
+
+ align:start position:0%
+were added and the last line
+here didn't add spaces anywhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so printing things out to the console is
+
+ align:start position:0%
+so printing things out to the console is
+ 
+
+ align:start position:0%
+so printing things out to the console is
+nice but the second part of sort of
+
+ align:start position:0%
+nice but the second part of sort of
+ 
+
+ align:start position:0%
+nice but the second part of sort of
+writing an interactive program is
+
+ align:start position:0%
+writing an interactive program is
+ 
+
+ align:start position:0%
+writing an interactive program is
+getting input from the user and that's
+
+ align:start position:0%
+getting input from the user and that's
+ 
+
+ align:start position:0%
+getting input from the user and that's
+that's a more interesting part so if
+
+ align:start position:0%
+that's a more interesting part so if
+ 
+
+ align:start position:0%
+that's a more interesting part so if
+you've done problem set zero you might
+
+ align:start position:0%
+you've done problem set zero you might
+ 
+
+ align:start position:0%
+you've done problem set zero you might
+have sort of already tried to understand
+
+ align:start position:0%
+have sort of already tried to understand
+ 
+
+ align:start position:0%
+have sort of already tried to understand
+this on your own but here we are
+
+ align:start position:0%
+this on your own but here we are
+ 
+
+ align:start position:0%
+this on your own but here we are
+so the way you get input from the user
+
+ align:start position:0%
+so the way you get input from the user
+ 
+
+ align:start position:0%
+so the way you get input from the user
+is using this command function called
+
+ align:start position:0%
+is using this command function called
+ 
+
+ align:start position:0%
+is using this command function called
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+and inside the
+
+ align:start position:0%
+and inside the
+ 
+
+ align:start position:0%
+and inside the
+parentheses you type in whatever you'd
+
+ align:start position:0%
+parentheses you type in whatever you'd
+ 
+
+ align:start position:0%
+parentheses you type in whatever you'd
+like to prompt the user with so in this
+
+ align:start position:0%
+like to prompt the user with so in this
+ 
+
+ align:start position:0%
+like to prompt the user with so in this
+case in my example here I have input and
+
+ align:start position:0%
+case in my example here I have input and
+ 
+
+ align:start position:0%
+case in my example here I have input and
+then here I said type anything so the
+
+ align:start position:0%
+then here I said type anything so the
+ 
+
+ align:start position:0%
+then here I said type anything so the
+user is going to see this text here and
+
+ align:start position:0%
+user is going to see this text here and
+ 
+
+ align:start position:0%
+user is going to see this text here and
+then the program is just going to stop
+
+ align:start position:0%
+then the program is just going to stop
+ 
+
+ align:start position:0%
+then the program is just going to stop
+and it's going to wait for the user to
+
+ align:start position:0%
+and it's going to wait for the user to
+ 
+
+ align:start position:0%
+and it's going to wait for the user to
+type in something and hit
+
+ align:start position:0%
+type in something and hit
+ 
+
+ align:start position:0%
+type in something and hit
+enter as soon as the user types in
+
+ align:start position:0%
+enter as soon as the user types in
+ 
+
+ align:start position:0%
+enter as soon as the user types in
+enter whatever the user types in becomes
+
+ align:start position:0%
+enter whatever the user types in becomes
+ 
+
+ align:start position:0%
+enter whatever the user types in becomes
+a string okay if the user types in a
+
+ align:start position:0%
+a string okay if the user types in a
+ 
+
+ align:start position:0%
+a string okay if the user types in a
+number for example that becomes the
+
+ align:start position:0%
+number for example that becomes the
+ 
+
+ align:start position:0%
+number for example that becomes the
+string that number okay so everything
+
+ align:start position:0%
+string that number okay so everything
+ 
+
+ align:start position:0%
+string that number okay so everything
+that user types in is going to be made
+
+ align:start position:0%
+that user types in is going to be made
+ 
+
+ align:start position:0%
+that user types in is going to be made
+as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string in this line right here whatever
+
+ align:start position:0%
+string in this line right here whatever
+ 
+
+ align:start position:0%
+string in this line right here whatever
+the user types in becomes a string and
+
+ align:start position:0%
+the user types in becomes a string and
+ 
+
+ align:start position:0%
+the user types in becomes a string and
+we're going to bind that string object
+
+ align:start position:0%
+we're going to bind that string object
+ 
+
+ align:start position:0%
+we're going to bind that string object
+to this variable named uh called text
+
+ align:start position:0%
+to this variable named uh called text
+ 
+
+ align:start position:0%
+to this variable named uh called text
+okay so now further in my program I can
+
+ align:start position:0%
+okay so now further in my program I can
+ 
+
+ align:start position:0%
+okay so now further in my program I can
+do whatever I want with this variable
+
+ align:start position:0%
+do whatever I want with this variable
+ 
+
+ align:start position:0%
+do whatever I want with this variable
+text in this case I'm going to print
+
+ align:start position:0%
+text in this case I'm going to print
+ 
+
+ align:start position:0%
+text in this case I'm going to print
+five star
+
+ align:start position:0%
+five star
+ 
+
+ align:start position:0%
+five star
+text okay so if the user for example
+
+ align:start position:0%
+text okay so if the user for example
+ 
+
+ align:start position:0%
+text okay so if the user for example
+gave me ha I'm going to print ha five
+
+ align:start position:0%
+gave me ha I'm going to print ha five
+ 
+
+ align:start position:0%
+gave me ha I'm going to print ha five
+times if the user gave me
+
+ align:start position:0%
+times if the user gave me
+ 
+
+ align:start position:0%
+times if the user gave me
+five what do you think the user what do
+
+ align:start position:0%
+five what do you think the user what do
+ 
+
+ align:start position:0%
+five what do you think the user what do
+you think is going to be printed
+
+ align:start position:0%
+you think is going to be printed
+ 
+
+ align:start position:0%
+you think is going to be printed
+out 25 or five five
+
+ align:start position:0%
+out 25 or five five
+ 
+
+ align:start position:0%
+out 25 or five five
+times great yes exactly five five times
+
+ align:start position:0%
+times great yes exactly five five times
+ 
+
+ align:start position:0%
+times great yes exactly five five times
+okay often times you don't want to work
+
+ align:start position:0%
+okay often times you don't want to work
+ 
+
+ align:start position:0%
+okay often times you don't want to work
+with numbers as strings right you want
+
+ align:start position:0%
+with numbers as strings right you want
+ 
+
+ align:start position:0%
+with numbers as strings right you want
+to work with numbers as numbers right so
+
+ align:start position:0%
+to work with numbers as numbers right so
+ 
+
+ align:start position:0%
+to work with numbers as numbers right so
+you have to cast and we learned that
+
+ align:start position:0%
+you have to cast and we learned that
+ 
+
+ align:start position:0%
+you have to cast and we learned that
+last lecture you cast by just putting in
+
+ align:start position:0%
+last lecture you cast by just putting in
+ 
+
+ align:start position:0%
+last lecture you cast by just putting in
+this little bit right in front of the
+
+ align:start position:0%
+this little bit right in front of the
+ 
+
+ align:start position:0%
+this little bit right in front of the
+input and you can cast it to whatever
+
+ align:start position:0%
+input and you can cast it to whatever
+ 
+
+ align:start position:0%
+input and you can cast it to whatever
+type you want here I cast it to an INT
+
+ align:start position:0%
+type you want here I cast it to an INT
+ 
+
+ align:start position:0%
+type you want here I cast it to an INT
+but you can also cast to a float if you
+
+ align:start position:0%
+but you can also cast to a float if you
+ 
+
+ align:start position:0%
+but you can also cast to a float if you
+want to work with
+
+ align:start position:0%
+want to work with
+ 
+
+ align:start position:0%
+want to work with
+floats and that converts whatever the
+
+ align:start position:0%
+floats and that converts whatever the
+ 
+
+ align:start position:0%
+floats and that converts whatever the
+user typed in as long as it's some
+
+ align:start position:0%
+user typed in as long as it's some
+ 
+
+ align:start position:0%
+user typed in as long as it's some
+number that python knows how to how to
+
+ align:start position:0%
+number that python knows how to how to
+ 
+
+ align:start position:0%
+number that python knows how to how to
+convert into the number itself so in
+
+ align:start position:0%
+convert into the number itself so in
+ 
+
+ align:start position:0%
+convert into the number itself so in
+this case if the user gives me five I'm
+
+ align:start position:0%
+this case if the user gives me five I'm
+ 
+
+ align:start position:0%
+this case if the user gives me five I'm
+going to print out 5 * 5 instead of five
+
+ align:start position:0%
+going to print out 5 * 5 instead of five
+ 
+
+ align:start position:0%
+going to print out 5 * 5 instead of five
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the code
+
+ align:start position:0%
+so that's the code
+ 
+
+ align:start position:0%
+so that's the code
+here so the first bit is I'm going to
+
+ align:start position:0%
+here so the first bit is I'm going to
+ 
+
+ align:start position:0%
+here so the first bit is I'm going to
+get the user to type in anything and I'm
+
+ align:start position:0%
+get the user to type in anything and I'm
+ 
+
+ align:start position:0%
+get the user to type in anything and I'm
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to put 555 and then when I type in the
+
+ align:start position:0%
+to put 555 and then when I type in the
+ 
+
+ align:start position:0%
+to put 555 and then when I type in the
+number since I'm casting it I'm going to
+
+ align:start position:0%
+number since I'm casting it I'm going to
+ 
+
+ align:start position:0%
+number since I'm casting it I'm going to
+do operations with the number okay yeah
+
+ align:start position:0%
+do operations with the number okay yeah
+ 
+
+ align:start position:0%
+do operations with the number okay yeah
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in why do you want to cast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to oh uh the question is why do you want
+
+ align:start position:0%
+to oh uh the question is why do you want
+ 
+
+ align:start position:0%
+to oh uh the question is why do you want
+to cast to a
+
+ align:start position:0%
+to cast to a
+ 
+
+ align:start position:0%
+to cast to a
+string why do you want to cast a string
+
+ align:start position:0%
+string why do you want to cast a string
+ 
+
+ align:start position:0%
+string why do you want to cast a string
+to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number oh so python always whatever you
+
+ align:start position:0%
+number oh so python always whatever you
+ 
+
+ align:start position:0%
+number oh so python always whatever you
+whatever you type in just by default by
+
+ align:start position:0%
+whatever you type in just by default by
+ 
+
+ align:start position:0%
+whatever you type in just by default by
+definition of the input command python
+
+ align:start position:0%
+definition of the input command python
+ 
+
+ align:start position:0%
+definition of the input command python
+always makes it a
+
+ align:start position:0%
+always makes it a
+ 
+
+ align:start position:0%
+always makes it a
+string so if you want to work with
+
+ align:start position:0%
+string so if you want to work with
+ 
+
+ align:start position:0%
+string so if you want to work with
+numbers you have to explicitly tell it
+
+ align:start position:0%
+numbers you have to explicitly tell it
+ 
+
+ align:start position:0%
+numbers you have to explicitly tell it
+I'm going to work with a number so even
+
+ align:start position:0%
+I'm going to work with a number so even
+ 
+
+ align:start position:0%
+I'm going to work with a number so even
+if you give it the number five it's
+
+ align:start position:0%
+if you give it the number five it's
+ 
+
+ align:start position:0%
+if you give it the number five it's
+going to think it's the string
+
+ align:start position:0%
+going to think it's the string
+ 
+
+ align:start position:0%
+going to think it's the string
+five yeah that's just how input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works the next thing it we're going to
+
+ align:start position:0%
+works the next thing it we're going to
+ 
+
+ align:start position:0%
+works the next thing it we're going to
+look at is ways that you can um start
+
+ align:start position:0%
+look at is ways that you can um start
+ 
+
+ align:start position:0%
+look at is ways that you can um start
+adding tests in your code and before you
+
+ align:start position:0%
+adding tests in your code and before you
+ 
+
+ align:start position:0%
+adding tests in your code and before you
+can start adding tests before you can
+
+ align:start position:0%
+can start adding tests before you can
+ 
+
+ align:start position:0%
+can start adding tests before you can
+start adding tests in your code you need
+
+ align:start position:0%
+start adding tests in your code you need
+ 
+
+ align:start position:0%
+start adding tests in your code you need
+to be able to do the actual tests
+
+ align:start position:0%
+to be able to do the actual tests
+ 
+
+ align:start position:0%
+to be able to do the actual tests
+so this is where comparison operators
+
+ align:start position:0%
+so this is where comparison operators
+ 
+
+ align:start position:0%
+so this is where comparison operators
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+in okay so here let's assume that I and
+
+ align:start position:0%
+in okay so here let's assume that I and
+ 
+
+ align:start position:0%
+in okay so here let's assume that I and
+J are variables okay the following
+
+ align:start position:0%
+J are variables okay the following
+ 
+
+ align:start position:0%
+J are variables okay the following
+comparisons are going to give you a
+
+ align:start position:0%
+comparisons are going to give you a
+ 
+
+ align:start position:0%
+comparisons are going to give you a
+Boolean so it's either going to say this
+
+ align:start position:0%
+Boolean so it's either going to say this
+ 
+
+ align:start position:0%
+Boolean so it's either going to say this
+is true or this is false so that's going
+
+ align:start position:0%
+is true or this is false so that's going
+ 
+
+ align:start position:0%
+is true or this is false so that's going
+to be your
+
+ align:start position:0%
+to be your
+ 
+
+ align:start position:0%
+to be your
+test so if I and J are variables you're
+
+ align:start position:0%
+test so if I and J are variables you're
+ 
+
+ align:start position:0%
+test so if I and J are variables you're
+allowed to compare ins with ins floats
+
+ align:start position:0%
+allowed to compare ins with ins floats
+ 
+
+ align:start position:0%
+allowed to compare ins with ins floats
+with floats strings with strings and
+
+ align:start position:0%
+with floats strings with strings and
+ 
+
+ align:start position:0%
+with floats strings with strings and
+you're allowed to compare ins and floats
+
+ align:start position:0%
+you're allowed to compare ins and floats
+ 
+
+ align:start position:0%
+you're allowed to compare ins and floats
+between themselves but you're not
+
+ align:start position:0%
+between themselves but you're not
+ 
+
+ align:start position:0%
+between themselves but you're not
+allowed to compare a string with a
+
+ align:start position:0%
+allowed to compare a string with a
+ 
+
+ align:start position:0%
+allowed to compare a string with a
+number in fact if you even try to do
+
+ align:start position:0%
+number in fact if you even try to do
+ 
+
+ align:start position:0%
+number in fact if you even try to do
+that in Python in spyer here if I try to
+
+ align:start position:0%
+that in Python in spyer here if I try to
+ 
+
+ align:start position:0%
+that in Python in spyer here if I try to
+say is the letter a greater than
+
+ align:start position:0%
+say is the letter a greater than
+ 
+
+ align:start position:0%
+say is the letter a greater than
+five I get some angry
+
+ align:start position:0%
+five I get some angry
+ 
+
+ align:start position:0%
+five I get some angry
+text right right here and this just
+
+ align:start position:0%
+text right right here and this just
+ 
+
+ align:start position:0%
+text right right here and this just
+tells me python doesn't understand the
+
+ align:start position:0%
+tells me python doesn't understand the
+ 
+
+ align:start position:0%
+tells me python doesn't understand the
+meaning of what how do I compare a
+
+ align:start position:0%
+meaning of what how do I compare a
+ 
+
+ align:start position:0%
+meaning of what how do I compare a
+string with a number right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so just like in math we can do these
+
+ align:start position:0%
+so just like in math we can do these
+ 
+
+ align:start position:0%
+so just like in math we can do these
+usual comparisons we can say something's
+
+ align:start position:0%
+usual comparisons we can say something's
+ 
+
+ align:start position:0%
+usual comparisons we can say something's
+greater than something greater or equal
+
+ align:start position:0%
+greater than something greater or equal
+ 
+
+ align:start position:0%
+greater than something greater or equal
+to less than less than or equal to I'd
+
+ align:start position:0%
+to less than less than or equal to I'd
+ 
+
+ align:start position:0%
+to less than less than or equal to I'd
+like to bring to your attention the
+
+ align:start position:0%
+like to bring to your attention the
+ 
+
+ align:start position:0%
+like to bring to your attention the
+equality so the single equal sign is an
+
+ align:start position:0%
+equality so the single equal sign is an
+ 
+
+ align:start position:0%
+equality so the single equal sign is an
+assignment so you're taking a value and
+
+ align:start position:0%
+assignment so you're taking a value and
+ 
+
+ align:start position:0%
+assignment so you're taking a value and
+you're signing it to a variable but when
+
+ align:start position:0%
+you're signing it to a variable but when
+ 
+
+ align:start position:0%
+you're signing it to a variable but when
+you're doing the double equal sign this
+
+ align:start position:0%
+you're doing the double equal sign this
+ 
+
+ align:start position:0%
+you're doing the double equal sign this
+is the test for equality is the value of
+
+ align:start position:0%
+is the test for equality is the value of
+ 
+
+ align:start position:0%
+is the test for equality is the value of
+variable I the same as the value of the
+
+ align:start position:0%
+variable I the same as the value of the
+ 
+
+ align:start position:0%
+variable I the same as the value of the
+variable J okay and that's that's again
+
+ align:start position:0%
+variable J okay and that's that's again
+ 
+
+ align:start position:0%
+variable J okay and that's that's again
+also going to give you a Boolean either
+
+ align:start position:0%
+also going to give you a Boolean either
+ 
+
+ align:start position:0%
+also going to give you a Boolean either
+true or false and you can also test for
+
+ align:start position:0%
+true or false and you can also test for
+ 
+
+ align:start position:0%
+true or false and you can also test for
+inequality with the exclamation equal so
+
+ align:start position:0%
+inequality with the exclamation equal so
+ 
+
+ align:start position:0%
+inequality with the exclamation equal so
+that means is the V value of the
+
+ align:start position:0%
+that means is the V value of the
+ 
+
+ align:start position:0%
+that means is the V value of the
+variable I not equal to the value of the
+
+ align:start position:0%
+variable I not equal to the value of the
+ 
+
+ align:start position:0%
+variable I not equal to the value of the
+variable J true if yes false if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay so those are comparison
+
+ align:start position:0%
+no okay so those are comparison
+ 
+
+ align:start position:0%
+no okay so those are comparison
+operators on Integer floats and strings
+
+ align:start position:0%
+operators on Integer floats and strings
+ 
+
+ align:start position:0%
+operators on Integer floats and strings
+on booleans you can do some logic
+
+ align:start position:0%
+on booleans you can do some logic
+ 
+
+ align:start position:0%
+on booleans you can do some logic
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+and the simplest is just inverting so if
+
+ align:start position:0%
+and the simplest is just inverting so if
+ 
+
+ align:start position:0%
+and the simplest is just inverting so if
+a is a v if a is a variable that can
+
+ align:start position:0%
+a is a v if a is a variable that can
+ 
+
+ align:start position:0%
+a is a v if a is a variable that can
+that has a Boolean value not a is just
+
+ align:start position:0%
+that has a Boolean value not a is just
+ 
+
+ align:start position:0%
+that has a Boolean value not a is just
+going to invert it so if a is true then
+
+ align:start position:0%
+going to invert it so if a is true then
+ 
+
+ align:start position:0%
+going to invert it so if a is true then
+not a is false and vice
+
+ align:start position:0%
+not a is false and vice
+ 
+
+ align:start position:0%
+not a is false and vice
+versa this is a table that sort of
+
+ align:start position:0%
+versa this is a table that sort of
+ 
+
+ align:start position:0%
+versa this is a table that sort of
+represents what I've said here so you
+
+ align:start position:0%
+represents what I've said here so you
+ 
+
+ align:start position:0%
+represents what I've said here so you
+can do you can use and and or these are
+
+ align:start position:0%
+can do you can use and and or these are
+ 
+
+ align:start position:0%
+can do you can use and and or these are
+keywords in Python you can use those two
+
+ align:start position:0%
+keywords in Python you can use those two
+ 
+
+ align:start position:0%
+keywords in Python you can use those two
+keywords on variables on Boolean
+
+ align:start position:0%
+keywords on variables on Boolean
+ 
+
+ align:start position:0%
+keywords on variables on Boolean
+variables and you get the
+
+ align:start position:0%
+variables and you get the
+ 
+
+ align:start position:0%
+variables and you get the
+result A and B is only true if both A
+
+ align:start position:0%
+result A and B is only true if both A
+ 
+
+ align:start position:0%
+result A and B is only true if both A
+and B are
+
+ align:start position:0%
+and B are
+ 
+
+ align:start position:0%
+and B are
+true and A or B is only false if a and b
+
+ align:start position:0%
+true and A or B is only false if a and b
+ 
+
+ align:start position:0%
+true and A or B is only false if a and b
+are false okay and this is the complete
+
+ align:start position:0%
+are false okay and this is the complete
+ 
+
+ align:start position:0%
+are false okay and this is the complete
+table just in case you need to reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it all right so now that we have ways to
+
+ align:start position:0%
+it all right so now that we have ways to
+ 
+
+ align:start position:0%
+it all right so now that we have ways to
+do logical te Yeah question right there
+
+ align:start position:0%
+do logical te Yeah question right there
+ 
+
+ align:start position:0%
+do logical te Yeah question right there
+what does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah great question so what does it
+
+ align:start position:0%
+it yeah great question so what does it
+ 
+
+ align:start position:0%
+it yeah great question so what does it
+mean to compare string with a string
+
+ align:start position:0%
+mean to compare string with a string
+ 
+
+ align:start position:0%
+mean to compare string with a string
+with the greater than so that's just
+
+ align:start position:0%
+with the greater than so that's just
+ 
+
+ align:start position:0%
+with the greater than so that's just
+going to compare them uh
+
+ align:start position:0%
+going to compare them uh
+ 
+
+ align:start position:0%
+going to compare them uh
+lexicographically so does it come first
+
+ align:start position:0%
+lexicographically so does it come first
+ 
+
+ align:start position:0%
+lexicographically so does it come first
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+alphabet so we can even test that out we
+
+ align:start position:0%
+alphabet so we can even test that out we
+ 
+
+ align:start position:0%
+alphabet so we can even test that out we
+can say is a greater than
+
+ align:start position:0%
+can say is a greater than
+ 
+
+ align:start position:0%
+can say is a greater than
+b and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+false so b b comes later in the alphabet
+
+ align:start position:0%
+false so b b comes later in the alphabet
+ 
+
+ align:start position:0%
+false so b b comes later in the alphabet
+than a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so now we have ways to do the
+
+ align:start position:0%
+right okay so now we have ways to do the
+ 
+
+ align:start position:0%
+right okay so now we have ways to do the
+tests so we can add
+
+ align:start position:0%
+tests so we can add
+ 
+
+ align:start position:0%
+tests so we can add
+um some branching to our programming
+
+ align:start position:0%
+um some branching to our programming
+ 
+
+ align:start position:0%
+um some branching to our programming
+toolbox now that we have ways to do
+
+ align:start position:0%
+toolbox now that we have ways to do
+ 
+
+ align:start position:0%
+toolbox now that we have ways to do
+tests okay this is a map of MIT I'm
+
+ align:start position:0%
+tests okay this is a map of MIT I'm
+ 
+
+ align:start position:0%
+tests okay this is a map of MIT I'm
+going to go through sort of a little
+
+ align:start position:0%
+going to go through sort of a little
+ 
+
+ align:start position:0%
+going to go through sort of a little
+example to motivate why we want to do
+
+ align:start position:0%
+example to motivate why we want to do
+ 
+
+ align:start position:0%
+example to motivate why we want to do
+branching in our in our um in our code
+
+ align:start position:0%
+branching in our in our um in our code
+ 
+
+ align:start position:0%
+branching in our in our um in our code
+and I think after this lecture you'll be
+
+ align:start position:0%
+and I think after this lecture you'll be
+ 
+
+ align:start position:0%
+and I think after this lecture you'll be
+able to sort of code up this algorithm
+
+ align:start position:0%
+able to sort of code up this algorithm
+ 
+
+ align:start position:0%
+able to sort of code up this algorithm
+that I'm going to explain so most of us
+
+ align:start position:0%
+that I'm going to explain so most of us
+ 
+
+ align:start position:0%
+that I'm going to explain so most of us
+see MIT as a maze I first did when I
+
+ align:start position:0%
+see MIT as a maze I first did when I
+ 
+
+ align:start position:0%
+see MIT as a maze I first did when I
+came
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here when I first came here obviously I
+
+ align:start position:0%
+here when I first came here obviously I
+ 
+
+ align:start position:0%
+here when I first came here obviously I
+signed up for the free food mailing list
+
+ align:start position:0%
+signed up for the free food mailing list
+ 
+
+ align:start position:0%
+signed up for the free food mailing list
+and MIT MIT being am maaz I had no idea
+
+ align:start position:0%
+and MIT MIT being am maaz I had no idea
+ 
+
+ align:start position:0%
+and MIT MIT being am maaz I had no idea
+where to go right what the shortest path
+
+ align:start position:0%
+where to go right what the shortest path
+ 
+
+ align:start position:0%
+where to go right what the shortest path
+was to free food so one way to to think
+
+ align:start position:0%
+was to free food so one way to to think
+ 
+
+ align:start position:0%
+was to free food so one way to to think
+about it is all I wanted to do was get
+
+ align:start position:0%
+about it is all I wanted to do was get
+ 
+
+ align:start position:0%
+about it is all I wanted to do was get
+to the free
+
+ align:start position:0%
+to the free
+ 
+
+ align:start position:0%
+to the free
+food a very simple algorithm to get
+
+ align:start position:0%
+food a very simple algorithm to get
+ 
+
+ align:start position:0%
+food a very simple algorithm to get
+there would be to say okay I'm going to
+
+ align:start position:0%
+there would be to say okay I'm going to
+ 
+
+ align:start position:0%
+there would be to say okay I'm going to
+take my right hand and I'm going to make
+
+ align:start position:0%
+take my right hand and I'm going to make
+ 
+
+ align:start position:0%
+take my right hand and I'm going to make
+sure that my right hand is always on a
+
+ align:start position:0%
+sure that my right hand is always on a
+ 
+
+ align:start position:0%
+sure that my right hand is always on a
+wall okay and I'm going to go around
+
+ align:start position:0%
+wall okay and I'm going to go around
+ 
+
+ align:start position:0%
+wall okay and I'm going to go around
+campus with my right hand always being
+
+ align:start position:0%
+campus with my right hand always being
+ 
+
+ align:start position:0%
+campus with my right hand always being
+at a wall and eventually I'll get to the
+
+ align:start position:0%
+at a wall and eventually I'll get to the
+ 
+
+ align:start position:0%
+at a wall and eventually I'll get to the
+where the free food is I might not there
+
+ align:start position:0%
+where the free food is I might not there
+ 
+
+ align:start position:0%
+where the free food is I might not there
+might not be any left right but I'll be
+
+ align:start position:0%
+might not be any left right but I'll be
+ 
+
+ align:start position:0%
+might not be any left right but I'll be
+there okay so the algorithm is as
+
+ align:start position:0%
+there okay so the algorithm is as
+ 
+
+ align:start position:0%
+there okay so the algorithm is as
+follows okay if my right hand always has
+
+ align:start position:0%
+follows okay if my right hand always has
+ 
+
+ align:start position:0%
+follows okay if my right hand always has
+to be on a wall then I'm going to say if
+
+ align:start position:0%
+to be on a wall then I'm going to say if
+ 
+
+ align:start position:0%
+to be on a wall then I'm going to say if
+there's no wall to my right side then
+
+ align:start position:0%
+there's no wall to my right side then
+ 
+
+ align:start position:0%
+there's no wall to my right side then
+I'm going to go right until I get to a
+
+ align:start position:0%
+I'm going to go right until I get to a
+ 
+
+ align:start position:0%
+I'm going to go right until I get to a
+wall
+
+ align:start position:0%
+wall
+ 
+
+ align:start position:0%
+wall
+Okay
+
+ align:start position:0%
+Okay
+ 
+
+ align:start position:0%
+Okay
+then if there's a wall to my right and I
+
+ align:start position:0%
+then if there's a wall to my right and I
+ 
+
+ align:start position:0%
+then if there's a wall to my right and I
+can go forward I'm just going to keep
+
+ align:start position:0%
+can go forward I'm just going to keep
+ 
+
+ align:start position:0%
+can go forward I'm just going to keep
+going forward
+
+ align:start position:0%
+going forward
+ 
+
+ align:start position:0%
+going forward
+okay if I keep going forward and there's
+
+ align:start position:0%
+okay if I keep going forward and there's
+ 
+
+ align:start position:0%
+okay if I keep going forward and there's
+a wall to my right in front of me I'm
+
+ align:start position:0%
+a wall to my right in front of me I'm
+ 
+
+ align:start position:0%
+a wall to my right in front of me I'm
+going to turn around and go left okay
+
+ align:start position:0%
+going to turn around and go left okay
+ 
+
+ align:start position:0%
+going to turn around and go left okay
+and then if there's a wall to my right
+
+ align:start position:0%
+and then if there's a wall to my right
+ 
+
+ align:start position:0%
+and then if there's a wall to my right
+in front of me and to the left then I'm
+
+ align:start position:0%
+in front of me and to the left then I'm
+ 
+
+ align:start position:0%
+in front of me and to the left then I'm
+going to turn around and go back so with
+
+ align:start position:0%
+going to turn around and go back so with
+ 
+
+ align:start position:0%
+going to turn around and go back so with
+this fairly simple
+
+ align:start position:0%
+this fairly simple
+ 
+
+ align:start position:0%
+this fairly simple
+algorithm I just follow the the path
+
+ align:start position:0%
+algorithm I just follow the the path
+ 
+
+ align:start position:0%
+algorithm I just follow the the path
+always keeping the wall to my
+
+ align:start position:0%
+always keeping the wall to my
+ 
+
+ align:start position:0%
+always keeping the wall to my
+right and eventually I end up where I
+
+ align:start position:0%
+right and eventually I end up where I
+ 
+
+ align:start position:0%
+right and eventually I end up where I
+need to be okay so notice I used just in
+
+ align:start position:0%
+need to be okay so notice I used just in
+ 
+
+ align:start position:0%
+need to be okay so notice I used just in
+plain English a few keywords okay if
+
+ align:start position:0%
+plain English a few keywords okay if
+ 
+
+ align:start position:0%
+plain English a few keywords okay if
+otherwise things like that so in program
+
+ align:start position:0%
+otherwise things like that so in program
+ 
+
+ align:start position:0%
+otherwise things like that so in program
+in we have those same
+
+ align:start position:0%
+in we have those same
+ 
+
+ align:start position:0%
+in we have those same
+constructs and those same sort of
+
+ align:start position:0%
+constructs and those same sort of
+ 
+
+ align:start position:0%
+constructs and those same sort of
+intuitive words can be used to tell
+
+ align:start position:0%
+intuitive words can be used to tell
+ 
+
+ align:start position:0%
+intuitive words can be used to tell
+python to do something or to do
+
+ align:start position:0%
+python to do something or to do
+ 
+
+ align:start position:0%
+python to do something or to do
+something else or to choose from a
+
+ align:start position:0%
+something else or to choose from a
+ 
+
+ align:start position:0%
+something else or to choose from a
+different um set of possibilities
+
+ align:start position:0%
+different um set of possibilities
+ 
+
+ align:start position:0%
+different um set of possibilities
+okay and this way we can get the
+
+ align:start position:0%
+okay and this way we can get the
+ 
+
+ align:start position:0%
+okay and this way we can get the
+computer to make decisions for us now
+
+ align:start position:0%
+computer to make decisions for us now
+ 
+
+ align:start position:0%
+computer to make decisions for us now
+you might be thinking well you said that
+
+ align:start position:0%
+you might be thinking well you said that
+ 
+
+ align:start position:0%
+you might be thinking well you said that
+computers can't make decisions on their
+
+ align:start position:0%
+computers can't make decisions on their
+ 
+
+ align:start position:0%
+computers can't make decisions on their
+own it's not us programmers are going to
+
+ align:start position:0%
+own it's not us programmers are going to
+ 
+
+ align:start position:0%
+own it's not us programmers are going to
+build these decisions into the program
+
+ align:start position:0%
+build these decisions into the program
+ 
+
+ align:start position:0%
+build these decisions into the program
+and all the computer is going to do is
+
+ align:start position:0%
+and all the computer is going to do is
+ 
+
+ align:start position:0%
+and all the computer is going to do is
+going to say is going to reach the
+
+ align:start position:0%
+going to say is going to reach the
+ 
+
+ align:start position:0%
+going to say is going to reach the
+decision point and say okay this is a
+
+ align:start position:0%
+decision point and say okay this is a
+ 
+
+ align:start position:0%
+decision point and say okay this is a
+decision point should I go left or
+
+ align:start position:0%
+decision point should I go left or
+ 
+
+ align:start position:0%
+decision point should I go left or
+should I go right or which one do I pick
+
+ align:start position:0%
+should I go right or which one do I pick
+ 
+
+ align:start position:0%
+should I go right or which one do I pick
+and these sort of decisions are created
+
+ align:start position:0%
+and these sort of decisions are created
+ 
+
+ align:start position:0%
+and these sort of decisions are created
+by you as a programmer and the computer
+
+ align:start position:0%
+by you as a programmer and the computer
+ 
+
+ align:start position:0%
+by you as a programmer and the computer
+just has to make make the decision and
+
+ align:start position:0%
+just has to make make the decision and
+ 
+
+ align:start position:0%
+just has to make make the decision and
+choose a path okay so in programming
+
+ align:start position:0%
+choose a path okay so in programming
+ 
+
+ align:start position:0%
+choose a path okay so in programming
+there's three sort of simple ways that
+
+ align:start position:0%
+there's three sort of simple ways that
+ 
+
+ align:start position:0%
+there's three sort of simple ways that
+you can add um control flow to your
+
+ align:start position:0%
+you can add um control flow to your
+ 
+
+ align:start position:0%
+you can add um control flow to your
+programs and that's making one decision
+
+ align:start position:0%
+programs and that's making one decision
+ 
+
+ align:start position:0%
+programs and that's making one decision
+and choosing whether to execute
+
+ align:start position:0%
+and choosing whether to execute
+ 
+
+ align:start position:0%
+and choosing whether to execute
+something or execute something
+
+ align:start position:0%
+something or execute something
+ 
+
+ align:start position:0%
+something or execute something
+else the first is the simple if
+
+ align:start position:0%
+else the first is the simple if
+ 
+
+ align:start position:0%
+else the first is the simple if
+okay and given a program that just
+
+ align:start position:0%
+okay and given a program that just
+ 
+
+ align:start position:0%
+okay and given a program that just
+linearly has statements that get
+
+ align:start position:0%
+linearly has statements that get
+ 
+
+ align:start position:0%
+linearly has statements that get
+executed whenever I reach an if
+
+ align:start position:0%
+executed whenever I reach an if
+ 
+
+ align:start position:0%
+executed whenever I reach an if
+statement you're going to check the
+
+ align:start position:0%
+statement you're going to check the
+ 
+
+ align:start position:0%
+statement you're going to check the
+condition the condition is going to be
+
+ align:start position:0%
+condition the condition is going to be
+ 
+
+ align:start position:0%
+condition the condition is going to be
+something that's going to get evaluated
+
+ align:start position:0%
+something that's going to get evaluated
+ 
+
+ align:start position:0%
+something that's going to get evaluated
+to either true or
+
+ align:start position:0%
+to either true or
+ 
+
+ align:start position:0%
+to either true or
+false okay so I've reached the condition
+
+ align:start position:0%
+false okay so I've reached the condition
+ 
+
+ align:start position:0%
+false okay so I've reached the condition
+here and if the condition's true then
+
+ align:start position:0%
+here and if the condition's true then
+ 
+
+ align:start position:0%
+here and if the condition's true then
+I'm going to additionally execute this
+
+ align:start position:0%
+I'm going to additionally execute this
+ 
+
+ align:start position:0%
+I'm going to additionally execute this
+extra set of
+
+ align:start position:0%
+extra set of
+ 
+
+ align:start position:0%
+extra set of
+Expressions but if the condition's false
+
+ align:start position:0%
+Expressions but if the condition's false
+ 
+
+ align:start position:0%
+Expressions but if the condition's false
+then I'm just going to keep going
+
+ align:start position:0%
+then I'm just going to keep going
+ 
+
+ align:start position:0%
+then I'm just going to keep going
+through the program and not execute that
+
+ align:start position:0%
+through the program and not execute that
+ 
+
+ align:start position:0%
+through the program and not execute that
+extra set of instructions
+
+ align:start position:0%
+extra set of instructions
+ 
+
+ align:start position:0%
+extra set of instructions
+okay how does python know which
+
+ align:start position:0%
+okay how does python know which
+ 
+
+ align:start position:0%
+okay how does python know which
+instructions to execute they're going to
+
+ align:start position:0%
+instructions to execute they're going to
+ 
+
+ align:start position:0%
+instructions to execute they're going to
+be inside this what we call code
+
+ align:start position:0%
+be inside this what we call code
+ 
+
+ align:start position:0%
+be inside this what we call code
+block and the code block is denoted by
+
+ align:start position:0%
+block and the code block is denoted by
+ 
+
+ align:start position:0%
+block and the code block is denoted by
+indentation so it's going to be
+
+ align:start position:0%
+indentation so it's going to be
+ 
+
+ align:start position:0%
+indentation so it's going to be
+everything that's indented is part of
+
+ align:start position:0%
+everything that's indented is part of
+ 
+
+ align:start position:0%
+everything that's indented is part of
+that if code
+
+ align:start position:0%
+that if code
+ 
+
+ align:start position:0%
+that if code
+block typic typically four spaces of
+
+ align:start position:0%
+block typic typically four spaces of
+ 
+
+ align:start position:0%
+block typic typically four spaces of
+dentation okay so
+
+ align:start position:0%
+dentation okay so
+ 
+
+ align:start position:0%
+dentation okay so
+that's that's how you'd write code that
+
+ align:start position:0%
+that's that's how you'd write code that
+ 
+
+ align:start position:0%
+that's that's how you'd write code that
+decides whether to execute this extra
+
+ align:start position:0%
+decides whether to execute this extra
+ 
+
+ align:start position:0%
+decides whether to execute this extra
+thing or
+
+ align:start position:0%
+thing or
+ 
+
+ align:start position:0%
+thing or
+not now let's say I don't just want to
+
+ align:start position:0%
+not now let's say I don't just want to
+ 
+
+ align:start position:0%
+not now let's say I don't just want to
+execute an extra thing I want to reach a
+
+ align:start position:0%
+execute an extra thing I want to reach a
+ 
+
+ align:start position:0%
+execute an extra thing I want to reach a
+condition I want to reach a point where
+
+ align:start position:0%
+condition I want to reach a point where
+ 
+
+ align:start position:0%
+condition I want to reach a point where
+I say I'll either go down this path or
+
+ align:start position:0%
+I say I'll either go down this path or
+ 
+
+ align:start position:0%
+I say I'll either go down this path or
+I'll do something else okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's this right
+
+ align:start position:0%
+that's this right
+ 
+
+ align:start position:0%
+that's this right
+here so this if
+
+ align:start position:0%
+here so this if
+ 
+
+ align:start position:0%
+here so this if
+else construct says this is my code I've
+
+ align:start position:0%
+else construct says this is my code I've
+ 
+
+ align:start position:0%
+else construct says this is my code I've
+reached my decision Point here if the
+
+ align:start position:0%
+reached my decision Point here if the
+ 
+
+ align:start position:0%
+reached my decision Point here if the
+condition inside this if is
+
+ align:start position:0%
+condition inside this if is
+ 
+
+ align:start position:0%
+condition inside this if is
+true then I'm going to execute maybe
+
+ align:start position:0%
+true then I'm going to execute maybe
+ 
+
+ align:start position:0%
+true then I'm going to execute maybe
+this set of statements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay but if the condition is not
+
+ align:start position:0%
+here okay but if the condition is not
+ 
+
+ align:start position:0%
+here okay but if the condition is not
+true then I'm not going to execute that
+
+ align:start position:0%
+true then I'm not going to execute that
+ 
+
+ align:start position:0%
+true then I'm not going to execute that
+set of statements and instead I'm going
+
+ align:start position:0%
+set of statements and instead I'm going
+ 
+
+ align:start position:0%
+set of statements and instead I'm going
+to execute under whatever
+
+ align:start position:0%
+to execute under whatever
+ 
+
+ align:start position:0%
+to execute under whatever
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+is so using this construct I'm either
+
+ align:start position:0%
+is so using this construct I'm either
+ 
+
+ align:start position:0%
+is so using this construct I'm either
+going to do one set of expressions or
+
+ align:start position:0%
+going to do one set of expressions or
+ 
+
+ align:start position:0%
+going to do one set of expressions or
+the other but never both okay and after
+
+ align:start position:0%
+the other but never both okay and after
+ 
+
+ align:start position:0%
+the other but never both okay and after
+I've executed one or the other I'm going
+
+ align:start position:0%
+I've executed one or the other I'm going
+ 
+
+ align:start position:0%
+I've executed one or the other I'm going
+to continue on with just the regular
+
+ align:start position:0%
+to continue on with just the regular
+ 
+
+ align:start position:0%
+to continue on with just the regular
+execution of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+program all
+
+ align:start position:0%
+program all
+ 
+
+ align:start position:0%
+program all
+right okay so we're able to either
+
+ align:start position:0%
+right okay so we're able to either
+ 
+
+ align:start position:0%
+right okay so we're able to either
+choose one thing choose one thing or
+
+ align:start position:0%
+choose one thing choose one thing or
+ 
+
+ align:start position:0%
+choose one thing choose one thing or
+another but what if we want to have uh
+
+ align:start position:0%
+another but what if we want to have uh
+ 
+
+ align:start position:0%
+another but what if we want to have uh
+more than one choice so
+
+ align:start position:0%
+more than one choice so
+ 
+
+ align:start position:0%
+more than one choice so
+if some number is equal to zero I want
+
+ align:start position:0%
+if some number is equal to zero I want
+ 
+
+ align:start position:0%
+if some number is equal to zero I want
+to do this if it's equal to one I want
+
+ align:start position:0%
+to do this if it's equal to one I want
+ 
+
+ align:start position:0%
+to do this if it's equal to one I want
+to do this otherwi if it's equal to two
+
+ align:start position:0%
+to do this otherwi if it's equal to two
+ 
+
+ align:start position:0%
+to do this otherwi if it's equal to two
+I want to do this and so on that's where
+
+ align:start position:0%
+I want to do this and so on that's where
+ 
+
+ align:start position:0%
+I want to do this and so on that's where
+this last one comes in and we introduce
+
+ align:start position:0%
+this last one comes in and we introduce
+ 
+
+ align:start position:0%
+this last one comes in and we introduce
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+other keyword here called L
+
+ align:start position:0%
+other keyword here called L
+ 
+
+ align:start position:0%
+other keyword here called L
+if so that stands for short form for
+
+ align:start position:0%
+if so that stands for short form for
+ 
+
+ align:start position:0%
+if so that stands for short form for
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+if so first we check if this condition
+
+ align:start position:0%
+if so first we check if this condition
+ 
+
+ align:start position:0%
+if so first we check if this condition
+is true so we're going through our
+
+ align:start position:0%
+is true so we're going through our
+ 
+
+ align:start position:0%
+is true so we're going through our
+program we've reached our decision point
+
+ align:start position:0%
+program we've reached our decision point
+ 
+
+ align:start position:0%
+program we've reached our decision point
+if the condition is true we're going to
+
+ align:start position:0%
+if the condition is true we're going to
+ 
+
+ align:start position:0%
+if the condition is true we're going to
+execute maybe this set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructions if the condition is not
+
+ align:start position:0%
+instructions if the condition is not
+ 
+
+ align:start position:0%
+instructions if the condition is not
+true maybe we'll
+
+ align:start position:0%
+true maybe we'll
+ 
+
+ align:start position:0%
+true maybe we'll
+check if the condition is not true we
+
+ align:start position:0%
+check if the condition is not true we
+ 
+
+ align:start position:0%
+check if the condition is not true we
+will check this next condition that's
+
+ align:start position:0%
+will check this next condition that's
+ 
+
+ align:start position:0%
+will check this next condition that's
+part of the L if right here and if that
+
+ align:start position:0%
+part of the L if right here and if that
+ 
+
+ align:start position:0%
+part of the L if right here and if that
+one's true we're going to execute a
+
+ align:start position:0%
+one's true we're going to execute a
+ 
+
+ align:start position:0%
+one's true we're going to execute a
+different set of instructions you can
+
+ align:start position:0%
+different set of instructions you can
+ 
+
+ align:start position:0%
+different set of instructions you can
+have more than one L if and depending on
+
+ align:start position:0%
+have more than one L if and depending on
+ 
+
+ align:start position:0%
+have more than one L if and depending on
+which one's true you're going to execute
+
+ align:start position:0%
+which one's true you're going to execute
+ 
+
+ align:start position:0%
+which one's true you're going to execute
+a different set of
+
+ align:start position:0%
+a different set of
+ 
+
+ align:start position:0%
+a different set of
+instructions and then this last else is
+
+ align:start position:0%
+instructions and then this last else is
+ 
+
+ align:start position:0%
+instructions and then this last else is
+sort of a c all where if none of the
+
+ align:start position:0%
+sort of a c all where if none of the
+ 
+
+ align:start position:0%
+sort of a c all where if none of the
+previous conditions were true then just
+
+ align:start position:0%
+previous conditions were true then just
+ 
+
+ align:start position:0%
+previous conditions were true then just
+do this this last set of Expressions so
+
+ align:start position:0%
+do this this last set of Expressions so
+ 
+
+ align:start position:0%
+do this this last set of Expressions so
+in this case you're going to choose
+
+ align:start position:0%
+in this case you're going to choose
+ 
+
+ align:start position:0%
+in this case you're going to choose
+between one of these three one of these
+
+ align:start position:0%
+between one of these three one of these
+ 
+
+ align:start position:0%
+between one of these three one of these
+four roots or however many you
+
+ align:start position:0%
+four roots or however many you
+ 
+
+ align:start position:0%
+four roots or however many you
+have and then when you're done making
+
+ align:start position:0%
+have and then when you're done making
+ 
+
+ align:start position:0%
+have and then when you're done making
+your choice you're going to execute the
+
+ align:start position:0%
+your choice you're going to execute the
+ 
+
+ align:start position:0%
+your choice you're going to execute the
+remaining set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructions so the way this works is if
+
+ align:start position:0%
+instructions so the way this works is if
+ 
+
+ align:start position:0%
+instructions so the way this works is if
+more than one condition is true you're
+
+ align:start position:0%
+more than one condition is true you're
+ 
+
+ align:start position:0%
+more than one condition is true you're
+actually just going to enter one of them
+
+ align:start position:0%
+actually just going to enter one of them
+ 
+
+ align:start position:0%
+actually just going to enter one of them
+and you're going to enter the very first
+
+ align:start position:0%
+and you're going to enter the very first
+ 
+
+ align:start position:0%
+and you're going to enter the very first
+one that's true so you're never going to
+
+ align:start position:0%
+one that's true so you're never going to
+ 
+
+ align:start position:0%
+one that's true so you're never going to
+enter more than one of these code blocks
+
+ align:start position:0%
+enter more than one of these code blocks
+ 
+
+ align:start position:0%
+enter more than one of these code blocks
+you're always enter one and you enter
+
+ align:start position:0%
+you're always enter one and you enter
+ 
+
+ align:start position:0%
+you're always enter one and you enter
+the very the first one that's that
+
+ align:start position:0%
+the very the first one that's that
+ 
+
+ align:start position:0%
+the very the first one that's that
+evaluates to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true so notice that we denoted code
+
+ align:start position:0%
+true so notice that we denoted code
+ 
+
+ align:start position:0%
+true so notice that we denoted code
+blocks using indentation and that's
+
+ align:start position:0%
+blocks using indentation and that's
+ 
+
+ align:start position:0%
+blocks using indentation and that's
+actually one of the things that I really
+
+ align:start position:0%
+actually one of the things that I really
+ 
+
+ align:start position:0%
+actually one of the things that I really
+like about python it sort of forces you
+
+ align:start position:0%
+like about python it sort of forces you
+ 
+
+ align:start position:0%
+like about python it sort of forces you
+to write pretty code and nice looking
+
+ align:start position:0%
+to write pretty code and nice looking
+ 
+
+ align:start position:0%
+to write pretty code and nice looking
+code um and just code that's very
+
+ align:start position:0%
+code um and just code that's very
+ 
+
+ align:start position:0%
+code um and just code that's very
+readable um and that forces you to
+
+ align:start position:0%
+readable um and that forces you to
+ 
+
+ align:start position:0%
+readable um and that forces you to
+indent everything that's a code block
+
+ align:start position:0%
+indent everything that's a code block
+ 
+
+ align:start position:0%
+indent everything that's a code block
+okay so you can easily see sort of where
+
+ align:start position:0%
+okay so you can easily see sort of where
+ 
+
+ align:start position:0%
+okay so you can easily see sort of where
+the flow of control is and where
+
+ align:start position:0%
+the flow of control is and where
+ 
+
+ align:start position:0%
+the flow of control is and where
+decision- making points are and and
+
+ align:start position:0%
+decision- making points are and and
+ 
+
+ align:start position:0%
+decision- making points are and and
+things like
+
+ align:start position:0%
+things like
+ 
+
+ align:start position:0%
+things like
+that okay so in this particular example
+
+ align:start position:0%
+that okay so in this particular example
+ 
+
+ align:start position:0%
+that okay so in this particular example
+we have one if statement here and it
+
+ align:start position:0%
+we have one if statement here and it
+ 
+
+ align:start position:0%
+we have one if statement here and it
+checks if two variables are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal and we have an if L if else
+
+ align:start position:0%
+equal and we have an if L if else
+ 
+
+ align:start position:0%
+equal and we have an if L if else
+and in this example we're going to enter
+
+ align:start position:0%
+and in this example we're going to enter
+ 
+
+ align:start position:0%
+and in this example we're going to enter
+either this code block or this one or
+
+ align:start position:0%
+either this code block or this one or
+ 
+
+ align:start position:0%
+either this code block or this one or
+this one depending on the variables of X
+
+ align:start position:0%
+this one depending on the variables of X
+ 
+
+ align:start position:0%
+this one depending on the variables of X
+and Y and we're only going to enter one
+
+ align:start position:0%
+and Y and we're only going to enter one
+ 
+
+ align:start position:0%
+and Y and we're only going to enter one
+code block and we'll enter the first one
+
+ align:start position:0%
+code block and we'll enter the first one
+ 
+
+ align:start position:0%
+code block and we'll enter the first one
+that that's
+
+ align:start position:0%
+that that's
+ 
+
+ align:start position:0%
+that that's
+true notice you can have nested
+
+ align:start position:0%
+true notice you can have nested
+ 
+
+ align:start position:0%
+true notice you can have nested
+conditionals so inside this first if we
+
+ align:start position:0%
+conditionals so inside this first if we
+ 
+
+ align:start position:0%
+conditionals so inside this first if we
+have another if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and this inner if is only going to
+
+ align:start position:0%
+here and this inner if is only going to
+ 
+
+ align:start position:0%
+here and this inner if is only going to
+be checked when
+
+ align:start position:0%
+be checked when
+ 
+
+ align:start position:0%
+be checked when
+we enter the first this outer
+
+ align:start position:0%
+we enter the first this outer
+ 
+
+ align:start position:0%
+we enter the first this outer
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I do want to make one point though
+
+ align:start position:0%
+okay I do want to make one point though
+ 
+
+ align:start position:0%
+okay I do want to make one point though
+so sometimes you might forget to do the
+
+ align:start position:0%
+so sometimes you might forget to do the
+ 
+
+ align:start position:0%
+so sometimes you might forget to do the
+double equal sign when you do when you
+
+ align:start position:0%
+double equal sign when you do when you
+ 
+
+ align:start position:0%
+double equal sign when you do when you
+check when you're checking for equality
+
+ align:start position:0%
+check when you're checking for equality
+ 
+
+ align:start position:0%
+check when you're checking for equality
+and that's okay if you just use one
+
+ align:start position:0%
+and that's okay if you just use one
+ 
+
+ align:start position:0%
+and that's okay if you just use one
+equal sign Python's going to give you an
+
+ align:start position:0%
+equal sign Python's going to give you an
+ 
+
+ align:start position:0%
+equal sign Python's going to give you an
+error and it's going to say syntax error
+
+ align:start position:0%
+error and it's going to say syntax error
+ 
+
+ align:start position:0%
+error and it's going to say syntax error
+and it's going to highlight this line
+
+ align:start position:0%
+and it's going to highlight this line
+ 
+
+ align:start position:0%
+and it's going to highlight this line
+and then you're going to know that
+
+ align:start position:0%
+and then you're going to know that
+ 
+
+ align:start position:0%
+and then you're going to know that
+there's there's a there's a mistake
+
+ align:start position:0%
+there's there's a there's a mistake
+ 
+
+ align:start position:0%
+there's there's a there's a mistake
+there you should be using equality
+
+ align:start position:0%
+there you should be using equality
+ 
+
+ align:start position:0%
+there you should be using equality
+because it doesn't make sense to be
+
+ align:start position:0%
+because it doesn't make sense to be
+ 
+
+ align:start position:0%
+because it doesn't make sense to be
+using to to assign to be making an
+
+ align:start position:0%
+using to to assign to be making an
+ 
+
+ align:start position:0%
+using to to assign to be making an
+assignment inside the
+
+ align:start position:0%
+assignment inside the
+ 
+
+ align:start position:0%
+assignment inside the
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right so we've learned about branching
+
+ align:start position:0%
+right so we've learned about branching
+ 
+
+ align:start position:0%
+right so we've learned about branching
+and we know about
+
+ align:start position:0%
+and we know about
+ 
+
+ align:start position:0%
+and we know about
+conditionals let's try to apply this
+
+ align:start position:0%
+conditionals let's try to apply this
+ 
+
+ align:start position:0%
+conditionals let's try to apply this
+to uh to a little
+
+ align:start position:0%
+to uh to a little
+ 
+
+ align:start position:0%
+to uh to a little
+game and spoiler we won't be able to
+
+ align:start position:0%
+game and spoiler we won't be able to
+ 
+
+ align:start position:0%
+game and spoiler we won't be able to
+we'll have to learn about a new thing
+
+ align:start position:0%
+we'll have to learn about a new thing
+ 
+
+ align:start position:0%
+we'll have to learn about a new thing
+but back 1980s there was The Legend of
+
+ align:start position:0%
+but back 1980s there was The Legend of
+ 
+
+ align:start position:0%
+but back 1980s there was The Legend of
+Zelda cool
+
+ align:start position:0%
+Zelda cool
+ 
+
+ align:start position:0%
+Zelda cool
+graphics um where there was a scene with
+
+ align:start position:0%
+graphics um where there was a scene with
+ 
+
+ align:start position:0%
+graphics um where there was a scene with
+the Lost Woods okay oversimplification
+
+ align:start position:0%
+the Lost Woods okay oversimplification
+ 
+
+ align:start position:0%
+the Lost Woods okay oversimplification
+if anyone's a Zelda know D die hard fan
+
+ align:start position:0%
+if anyone's a Zelda know D die hard fan
+ 
+
+ align:start position:0%
+if anyone's a Zelda know D die hard fan
+but the basic idea was if you entered
+
+ align:start position:0%
+but the basic idea was if you entered
+ 
+
+ align:start position:0%
+but the basic idea was if you entered
+the woods you know you entered from the
+
+ align:start position:0%
+the woods you know you entered from the
+ 
+
+ align:start position:0%
+the woods you know you entered from the
+left to the right and then as long as
+
+ align:start position:0%
+left to the right and then as long as
+ 
+
+ align:start position:0%
+left to the right and then as long as
+you kept going right it would show you
+
+ align:start position:0%
+you kept going right it would show you
+ 
+
+ align:start position:0%
+you kept going right it would show you
+the same screen over and over again okay
+
+ align:start position:0%
+the same screen over and over again okay
+ 
+
+ align:start position:0%
+the same screen over and over again okay
+and the trick was you just had to go
+
+ align:start position:0%
+and the trick was you just had to go
+ 
+
+ align:start position:0%
+and the trick was you just had to go
+backward and then you'd exit exit the
+
+ align:start position:0%
+backward and then you'd exit exit the
+ 
+
+ align:start position:0%
+backward and then you'd exit exit the
+wood
+
+ align:start position:0%
+wood
+ 
+
+ align:start position:0%
+wood
+okay so very simple using what we know
+
+ align:start position:0%
+okay so very simple using what we know
+ 
+
+ align:start position:0%
+okay so very simple using what we know
+so far we could sort of code this
+
+ align:start position:0%
+so far we could sort of code this
+ 
+
+ align:start position:0%
+so far we could sort of code this
+up and we'd say something like this if
+
+ align:start position:0%
+up and we'd say something like this if
+ 
+
+ align:start position:0%
+up and we'd say something like this if
+the user exits right then set the
+
+ align:start position:0%
+the user exits right then set the
+ 
+
+ align:start position:0%
+the user exits right then set the
+background to the woods
+
+ align:start position:0%
+background to the woods
+ 
+
+ align:start position:0%
+background to the woods
+background otherwise set the background
+
+ align:start position:0%
+background otherwise set the background
+ 
+
+ align:start position:0%
+background otherwise set the background
+to the exit
+
+ align:start position:0%
+to the exit
+ 
+
+ align:start position:0%
+to the exit
+background okay now let's say the user
+
+ align:start position:0%
+background okay now let's say the user
+ 
+
+ align:start position:0%
+background okay now let's say the user
+and then and then in the else we're done
+
+ align:start position:0%
+and then and then in the else we're done
+ 
+
+ align:start position:0%
+and then and then in the else we're done
+let's say the user went right well you'd
+
+ align:start position:0%
+let's say the user went right well you'd
+ 
+
+ align:start position:0%
+let's say the user went right well you'd
+show them the woods background and now
+
+ align:start position:0%
+show them the woods background and now
+ 
+
+ align:start position:0%
+show them the woods background and now
+ask them again where do they want to go
+
+ align:start position:0%
+ask them again where do they want to go
+ 
+
+ align:start position:0%
+ask them again where do they want to go
+if they exit right set the background to
+
+ align:start position:0%
+if they exit right set the background to
+ 
+
+ align:start position:0%
+if they exit right set the background to
+the woods backgr otherwise set the
+
+ align:start position:0%
+the woods backgr otherwise set the
+ 
+
+ align:start position:0%
+the woods backgr otherwise set the
+background to the exit background and so
+
+ align:start position:0%
+background to the exit background and so
+ 
+
+ align:start position:0%
+background to the exit background and so
+on so you notice that there's sort of no
+
+ align:start position:0%
+on so you notice that there's sort of no
+ 
+
+ align:start position:0%
+on so you notice that there's sort of no
+end to this right how many time do you
+
+ align:start position:0%
+end to this right how many time do you
+ 
+
+ align:start position:0%
+end to this right how many time do you
+know do you know how many times the user
+
+ align:start position:0%
+know do you know how many times the user
+ 
+
+ align:start position:0%
+know do you know how many times the user
+might keep going right they might be
+
+ align:start position:0%
+might keep going right they might be
+ 
+
+ align:start position:0%
+might keep going right they might be
+really persistent right and they'll be
+
+ align:start position:0%
+really persistent right and they'll be
+ 
+
+ align:start position:0%
+really persistent right and they'll be
+like maybe maybe if I go a thousand
+
+ align:start position:0%
+like maybe maybe if I go a thousand
+ 
+
+ align:start position:0%
+like maybe maybe if I go a thousand
+times I'll get out of the woods you know
+
+ align:start position:0%
+times I'll get out of the woods you know
+ 
+
+ align:start position:0%
+times I'll get out of the woods you know
+or maybe a thousand one maybe so
+
+ align:start position:0%
+or maybe a thousand one maybe so
+ 
+
+ align:start position:0%
+or maybe a thousand one maybe so
+this this would probably be who knows
+
+ align:start position:0%
+this this would probably be who knows
+ 
+
+ align:start position:0%
+this this would probably be who knows
+how how deep this this nested these
+
+ align:start position:0%
+how how deep this this nested these
+ 
+
+ align:start position:0%
+how how deep this this nested these
+nested ifs okay okay so we don't
+
+ align:start position:0%
+nested ifs okay okay so we don't
+ 
+
+ align:start position:0%
+nested ifs okay okay so we don't
+know so with what we know so far we
+
+ align:start position:0%
+know so with what we know so far we
+ 
+
+ align:start position:0%
+know so with what we know so far we
+can't really code this this cute little
+
+ align:start position:0%
+can't really code this this cute little
+ 
+
+ align:start position:0%
+can't really code this this cute little
+game but enter loops and specifically a
+
+ align:start position:0%
+game but enter loops and specifically a
+ 
+
+ align:start position:0%
+game but enter loops and specifically a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+loop so this code here that could be you
+
+ align:start position:0%
+loop so this code here that could be you
+ 
+
+ align:start position:0%
+loop so this code here that could be you
+know infinitely number of nested if
+
+ align:start position:0%
+know infinitely number of nested if
+ 
+
+ align:start position:0%
+know infinitely number of nested if
+statements deep can be Rewritten using
+
+ align:start position:0%
+statements deep can be Rewritten using
+ 
+
+ align:start position:0%
+statements deep can be Rewritten using
+these three
+
+ align:start position:0%
+these three
+ 
+
+ align:start position:0%
+these three
+lines so we say while the user exits
+
+ align:start position:0%
+lines so we say while the user exits
+ 
+
+ align:start position:0%
+lines so we say while the user exits
+right set the background to the woods
+
+ align:start position:0%
+right set the background to the woods
+ 
+
+ align:start position:0%
+right set the background to the woods
+background and with a while loop it's
+
+ align:start position:0%
+background and with a while loop it's
+ 
+
+ align:start position:0%
+background and with a while loop it's
+going to do what we tell it to do inside
+
+ align:start position:0%
+going to do what we tell it to do inside
+ 
+
+ align:start position:0%
+going to do what we tell it to do inside
+the loop and then it's going to check
+
+ align:start position:0%
+the loop and then it's going to check
+ 
+
+ align:start position:0%
+the loop and then it's going to check
+the condition again and then it's going
+
+ align:start position:0%
+the condition again and then it's going
+ 
+
+ align:start position:0%
+the condition again and then it's going
+to do what we what we say it should do
+
+ align:start position:0%
+to do what we what we say it should do
+ 
+
+ align:start position:0%
+to do what we what we say it should do
+inside the code block and then it's
+
+ align:start position:0%
+inside the code block and then it's
+ 
+
+ align:start position:0%
+inside the code block and then it's
+going to set the check the condition
+
+ align:start position:0%
+going to set the check the condition
+ 
+
+ align:start position:0%
+going to set the check the condition
+again and then when the condition as
+
+ align:start position:0%
+again and then when the condition as
+ 
+
+ align:start position:0%
+again and then when the condition as
+long as the condition is true it's going
+
+ align:start position:0%
+long as the condition is true it's going
+ 
+
+ align:start position:0%
+long as the condition is true it's going
+to keep doing that little Loop there and
+
+ align:start position:0%
+to keep doing that little Loop there and
+ 
+
+ align:start position:0%
+to keep doing that little Loop there and
+as soon as the condition becomes false
+
+ align:start position:0%
+as soon as the condition becomes false
+ 
+
+ align:start position:0%
+as soon as the condition becomes false
+it's going to stop doing the loop and do
+
+ align:start position:0%
+it's going to stop doing the loop and do
+ 
+
+ align:start position:0%
+it's going to stop doing the loop and do
+whatever is right after the
+
+ align:start position:0%
+whatever is right after the
+ 
+
+ align:start position:0%
+whatever is right after the
+while okay so that's basically how a
+
+ align:start position:0%
+while okay so that's basically how a
+ 
+
+ align:start position:0%
+while okay so that's basically how a
+while loop works we have while that's
+
+ align:start position:0%
+while loop works we have while that's
+ 
+
+ align:start position:0%
+while loop works we have while that's
+the keyword the condition is something
+
+ align:start position:0%
+the keyword the condition is something
+ 
+
+ align:start position:0%
+the keyword the condition is something
+that gets evaluated to true or false and
+
+ align:start position:0%
+that gets evaluated to true or false and
+ 
+
+ align:start position:0%
+that gets evaluated to true or false and
+once again we have a code block that's
+
+ align:start position:0%
+once again we have a code block that's
+ 
+
+ align:start position:0%
+once again we have a code block that's
+indented and it tells python these are
+
+ align:start position:0%
+indented and it tells python these are
+ 
+
+ align:start position:0%
+indented and it tells python these are
+the Expressions I want to do as long as
+
+ align:start position:0%
+the Expressions I want to do as long as
+ 
+
+ align:start position:0%
+the Expressions I want to do as long as
+the condition is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true so the condition is true you
+
+ align:start position:0%
+true so the condition is true you
+ 
+
+ align:start position:0%
+true so the condition is true you
+evaluate every expression in the code
+
+ align:start position:0%
+evaluate every expression in the code
+ 
+
+ align:start position:0%
+evaluate every expression in the code
+block when you reach the end of the
+
+ align:start position:0%
+block when you reach the end of the
+ 
+
+ align:start position:0%
+block when you reach the end of the
+expression end of the code block you
+
+ align:start position:0%
+expression end of the code block you
+ 
+
+ align:start position:0%
+expression end of the code block you
+check the condition again if it's true
+
+ align:start position:0%
+check the condition again if it's true
+ 
+
+ align:start position:0%
+check the condition again if it's true
+still you keep doing the Expressions
+
+ align:start position:0%
+still you keep doing the Expressions
+ 
+
+ align:start position:0%
+still you keep doing the Expressions
+check again and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on so here's a little
+
+ align:start position:0%
+on so here's a little
+ 
+
+ align:start position:0%
+on so here's a little
+game and with these lines of code we
+
+ align:start position:0%
+game and with these lines of code we
+ 
+
+ align:start position:0%
+game and with these lines of code we
+were able you know we can code up the
+
+ align:start position:0%
+were able you know we can code up the
+ 
+
+ align:start position:0%
+were able you know we can code up the
+the Lost lwoods of uh of Zelda even
+
+ align:start position:0%
+the Lost lwoods of uh of Zelda even
+ 
+
+ align:start position:0%
+the Lost lwoods of uh of Zelda even
+worse Graphics by the way than the
+
+ align:start position:0%
+worse Graphics by the way than the
+ 
+
+ align:start position:0%
+worse Graphics by the way than the
+original Zelda is this one that I coated
+
+ align:start position:0%
+original Zelda is this one that I coated
+ 
+
+ align:start position:0%
+original Zelda is this one that I coated
+up here so I print out the following
+
+ align:start position:0%
+up here so I print out the following
+ 
+
+ align:start position:0%
+up here so I print out the following
+things you're in the L Forest go left or
+
+ align:start position:0%
+things you're in the L Forest go left or
+ 
+
+ align:start position:0%
+things you're in the L Forest go left or
+right and my program is going to say you
+
+ align:start position:0%
+right and my program is going to say you
+ 
+
+ align:start position:0%
+right and my program is going to say you
+know you're in the lost forest go left
+
+ align:start position:0%
+know you're in the lost forest go left
+ 
+
+ align:start position:0%
+know you're in the lost forest go left
+left or right it's going to get user
+
+ align:start position:0%
+left or right it's going to get user
+ 
+
+ align:start position:0%
+left or right it's going to get user
+input it's going to say while the user
+
+ align:start position:0%
+input it's going to say while the user
+ 
+
+ align:start position:0%
+input it's going to say while the user
+keeps typing in right show them this
+
+ align:start position:0%
+keeps typing in right show them this
+ 
+
+ align:start position:0%
+keeps typing in right show them this
+text and ask them again right so I'm
+
+ align:start position:0%
+text and ask them again right so I'm
+ 
+
+ align:start position:0%
+text and ask them again right so I'm
+asking them again by just saying input
+
+ align:start position:0%
+asking them again by just saying input
+ 
+
+ align:start position:0%
+asking them again by just saying input
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+again and that's it that's going to just
+
+ align:start position:0%
+again and that's it that's going to just
+ 
+
+ align:start position:0%
+again and that's it that's going to just
+keep getting input from the user and if
+
+ align:start position:0%
+keep getting input from the user and if
+ 
+
+ align:start position:0%
+keep getting input from the user and if
+the user doesn't type in right and maybe
+
+ align:start position:0%
+the user doesn't type in right and maybe
+ 
+
+ align:start position:0%
+the user doesn't type in right and maybe
+types in left you're going to exit out
+
+ align:start position:0%
+types in left you're going to exit out
+ 
+
+ align:start position:0%
+types in left you're going to exit out
+of this Loop and print out you got out
+
+ align:start position:0%
+of this Loop and print out you got out
+ 
+
+ align:start position:0%
+of this Loop and print out you got out
+of the last
+
+ align:start position:0%
+of the last
+ 
+
+ align:start position:0%
+of the last
+Force so I have to show you this because
+
+ align:start position:0%
+Force so I have to show you this because
+ 
+
+ align:start position:0%
+Force so I have to show you this because
+I spent
+
+ align:start position:0%
+I spent
+ 
+
+ align:start position:0%
+I spent
+too much time on
+
+ align:start position:0%
+too much time on
+ 
+
+ align:start position:0%
+too much time on
+it but I decided
+
+ align:start position:0%
+it but I decided
+ 
+
+ align:start position:0%
+it but I decided
+to improve on the code that's in the
+
+ align:start position:0%
+to improve on the code that's in the
+ 
+
+ align:start position:0%
+to improve on the code that's in the
+slides and I've written here ways that
+
+ align:start position:0%
+slides and I've written here ways that
+ 
+
+ align:start position:0%
+slides and I've written here ways that
+you guys can also improve it so if I run
+
+ align:start position:0%
+you guys can also improve it so if I run
+ 
+
+ align:start position:0%
+you guys can also improve it so if I run
+my code you you're in the lost forest go
+
+ align:start position:0%
+my code you you're in the lost forest go
+ 
+
+ align:start position:0%
+my code you you're in the lost forest go
+left or right so if I say left then yay
+
+ align:start position:0%
+left or right so if I say left then yay
+ 
+
+ align:start position:0%
+left or right so if I say left then yay
+I got out of the lost
+
+ align:start position:0%
+I got out of the lost
+ 
+
+ align:start position:0%
+I got out of the lost
+forest but if I go right then I'm stuck
+
+ align:start position:0%
+forest but if I go right then I'm stuck
+ 
+
+ align:start position:0%
+forest but if I go right then I'm stuck
+right I took down some trees you can see
+
+ align:start position:0%
+right I took down some trees you can see
+ 
+
+ align:start position:0%
+right I took down some trees you can see
+there's no more trees here I made a
+
+ align:start position:0%
+there's no more trees here I made a
+ 
+
+ align:start position:0%
+there's no more trees here I made a
+table and then I flipped it
+
+ align:start position:0%
+table and then I flipped it
+ 
+
+ align:start position:0%
+table and then I flipped it
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+okay so the expansion to this if you
+
+ align:start position:0%
+okay so the expansion to this if you
+ 
+
+ align:start position:0%
+okay so the expansion to this if you
+want to try it out I I put this in the
+
+ align:start position:0%
+want to try it out I I put this in the
+ 
+
+ align:start position:0%
+want to try it out I I put this in the
+comments here is try to use a counter
+
+ align:start position:0%
+comments here is try to use a counter
+ 
+
+ align:start position:0%
+comments here is try to use a counter
+okay if the user types in write the
+
+ align:start position:0%
+okay if the user types in write the
+ 
+
+ align:start position:0%
+okay if the user types in write the
+first two times just make that a sad
+
+ align:start position:0%
+first two times just make that a sad
+ 
+
+ align:start position:0%
+first two times just make that a sad
+face but if the user types in more than
+
+ align:start position:0%
+face but if the user types in more than
+ 
+
+ align:start position:0%
+face but if the user types in more than
+two times make them cut down some trees
+
+ align:start position:0%
+two times make them cut down some trees
+ 
+
+ align:start position:0%
+two times make them cut down some trees
+and build a table and flip it
+
+ align:start position:0%
+and build a table and flip it
+ 
+
+ align:start position:0%
+and build a table and flip it
+okay that's a cute little expansion if
+
+ align:start position:0%
+okay that's a cute little expansion if
+ 
+
+ align:start position:0%
+okay that's a cute little expansion if
+you want to test yourself to make sure
+
+ align:start position:0%
+you want to test yourself to make sure
+ 
+
+ align:start position:0%
+you want to test yourself to make sure
+you you're getting Loops
+
+ align:start position:0%
+you you're getting Loops
+ 
+
+ align:start position:0%
+you you're getting Loops
+okay so so far we've used while Loops to
+
+ align:start position:0%
+okay so so far we've used while Loops to
+ 
+
+ align:start position:0%
+okay so so far we've used while Loops to
+ask for user input and that's actually
+
+ align:start position:0%
+ask for user input and that's actually
+ 
+
+ align:start position:0%
+ask for user input and that's actually
+somewhere where it makes sense to use
+
+ align:start position:0%
+somewhere where it makes sense to use
+ 
+
+ align:start position:0%
+somewhere where it makes sense to use
+while Loops because you don't actually
+
+ align:start position:0%
+while Loops because you don't actually
+ 
+
+ align:start position:0%
+while Loops because you don't actually
+know how many times the user is going to
+
+ align:start position:0%
+know how many times the user is going to
+ 
+
+ align:start position:0%
+know how many times the user is going to
+type in
+
+ align:start position:0%
+type in
+ 
+
+ align:start position:0%
+type in
+something you can use y Loops to keep
+
+ align:start position:0%
+something you can use y Loops to keep
+ 
+
+ align:start position:0%
+something you can use y Loops to keep
+sort of a counter and to write code that
+
+ align:start position:0%
+sort of a counter and to write code that
+ 
+
+ align:start position:0%
+sort of a counter and to write code that
+counts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something if you do that though there's
+
+ align:start position:0%
+something if you do that though there's
+ 
+
+ align:start position:0%
+something if you do that though there's
+two there's two things you need to take
+
+ align:start position:0%
+two there's two things you need to take
+ 
+
+ align:start position:0%
+two there's two things you need to take
+care of the first is this first line
+
+ align:start position:0%
+care of the first is this first line
+ 
+
+ align:start position:0%
+care of the first is this first line
+here which is sort of an initialization
+
+ align:start position:0%
+here which is sort of an initialization
+ 
+
+ align:start position:0%
+here which is sort of an initialization
+of this Loop
+
+ align:start position:0%
+of this Loop
+ 
+
+ align:start position:0%
+of this Loop
+counter and the second is this line here
+
+ align:start position:0%
+counter and the second is this line here
+ 
+
+ align:start position:0%
+counter and the second is this line here
+which is incrementing your Loop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counter the reason why the second one's
+
+ align:start position:0%
+counter the reason why the second one's
+ 
+
+ align:start position:0%
+counter the reason why the second one's
+important is because let's look at our
+
+ align:start position:0%
+important is because let's look at our
+ 
+
+ align:start position:0%
+important is because let's look at our
+condition here so while n is less than
+
+ align:start position:0%
+condition here so while n is less than
+ 
+
+ align:start position:0%
+condition here so while n is less than
+five if you didn't have this line here
+
+ align:start position:0%
+five if you didn't have this line here
+ 
+
+ align:start position:0%
+five if you didn't have this line here
+you never increment n so every time
+
+ align:start position:0%
+you never increment n so every time
+ 
+
+ align:start position:0%
+you never increment n so every time
+through the loop you just keep printing
+
+ align:start position:0%
+through the loop you just keep printing
+ 
+
+ align:start position:0%
+through the loop you just keep printing
+zeros okay and you'd have an infinite
+
+ align:start position:0%
+zeros okay and you'd have an infinite
+ 
+
+ align:start position:0%
+zeros okay and you'd have an infinite
+loop I do want to show though what if
+
+ align:start position:0%
+loop I do want to show though what if
+ 
+
+ align:start position:0%
+loop I do want to show though what if
+you do have an infinite loop it's not
+
+ align:start position:0%
+you do have an infinite loop it's not
+ 
+
+ align:start position:0%
+you do have an infinite loop it's not
+the end of the world so I can say
+
+ align:start position:0%
+the end of the world so I can say
+ 
+
+ align:start position:0%
+the end of the world so I can say
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+like uh
+
+ align:start position:0%
+like uh
+ 
+
+ align:start position:0%
+like uh
+okay so while
+
+ align:start position:0%
+okay so while
+ 
+
+ align:start position:0%
+okay so while
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+print zero okay so this is going to give
+
+ align:start position:0%
+print zero okay so this is going to give
+ 
+
+ align:start position:0%
+print zero okay so this is going to give
+me an infinite Loop in my
+
+ align:start position:0%
+me an infinite Loop in my
+ 
+
+ align:start position:0%
+me an infinite Loop in my
+program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay so notice it's just printing
+
+ align:start position:0%
+and okay so notice it's just printing
+ 
+
+ align:start position:0%
+and okay so notice it's just printing
+the letter P over and over again and if
+
+ align:start position:0%
+the letter P over and over again and if
+ 
+
+ align:start position:0%
+the letter P over and over again and if
+I let it go any longer it's going to
+
+ align:start position:0%
+I let it go any longer it's going to
+ 
+
+ align:start position:0%
+I let it go any longer it's going to
+slow down the computer so I'm going to
+
+ align:start position:0%
+slow down the computer so I'm going to
+ 
+
+ align:start position:0%
+slow down the computer so I'm going to
+hit control C or command C maybe and
+
+ align:start position:0%
+hit control C or command C maybe and
+ 
+
+ align:start position:0%
+hit control C or command C maybe and
+it's going to stop the program from
+
+ align:start position:0%
+it's going to stop the program from
+ 
+
+ align:start position:0%
+it's going to stop the program from
+printing okay so just in case you ever
+
+ align:start position:0%
+printing okay so just in case you ever
+ 
+
+ align:start position:0%
+printing okay so just in case you ever
+enter infinite Loops in your programs
+
+ align:start position:0%
+enter infinite Loops in your programs
+ 
+
+ align:start position:0%
+enter infinite Loops in your programs
+just go to the console and hit contrl C
+
+ align:start position:0%
+just go to the console and hit contrl C
+ 
+
+ align:start position:0%
+just go to the console and hit contrl C
+and that's going to stop it from sort of
+
+ align:start position:0%
+and that's going to stop it from sort of
+ 
+
+ align:start position:0%
+and that's going to stop it from sort of
+slowing down the
+
+ align:start position:0%
+slowing down the
+ 
+
+ align:start position:0%
+slowing down the
+computer okay so going back to this
+
+ align:start position:0%
+computer okay so going back to this
+ 
+
+ align:start position:0%
+computer okay so going back to this
+example I was saying that if you're
+
+ align:start position:0%
+example I was saying that if you're
+ 
+
+ align:start position:0%
+example I was saying that if you're
+using counters or variables in order to
+
+ align:start position:0%
+using counters or variables in order to
+ 
+
+ align:start position:0%
+using counters or variables in order to
+sort of count up inside the Y Loop you
+
+ align:start position:0%
+sort of count up inside the Y Loop you
+ 
+
+ align:start position:0%
+sort of count up inside the Y Loop you
+have to take care to initialize a count
+
+ align:start position:0%
+have to take care to initialize a count
+ 
+
+ align:start position:0%
+have to take care to initialize a count
+counter variable first and then to
+
+ align:start position:0%
+counter variable first and then to
+ 
+
+ align:start position:0%
+counter variable first and then to
+increment it otherwise you'll enter an
+
+ align:start position:0%
+increment it otherwise you'll enter an
+ 
+
+ align:start position:0%
+increment it otherwise you'll enter an
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+Loop that feels a little bit tedious and
+
+ align:start position:0%
+Loop that feels a little bit tedious and
+ 
+
+ align:start position:0%
+Loop that feels a little bit tedious and
+so there's a
+
+ align:start position:0%
+so there's a
+ 
+
+ align:start position:0%
+so there's a
+shortcut for doing that EX exact same
+
+ align:start position:0%
+shortcut for doing that EX exact same
+ 
+
+ align:start position:0%
+shortcut for doing that EX exact same
+thing so these four lines you can
+
+ align:start position:0%
+thing so these four lines you can
+ 
+
+ align:start position:0%
+thing so these four lines you can
+rewrite those into these two lines right
+
+ align:start position:0%
+rewrite those into these two lines right
+ 
+
+ align:start position:0%
+rewrite those into these two lines right
+here using this new type of loop called
+
+ align:start position:0%
+here using this new type of loop called
+ 
+
+ align:start position:0%
+here using this new type of loop called
+a four
+
+ align:start position:0%
+a four
+ 
+
+ align:start position:0%
+a four
+Loop so the for Loop says for some Loop
+
+ align:start position:0%
+Loop so the for Loop says for some Loop
+ 
+
+ align:start position:0%
+Loop so the for Loop says for some Loop
+variable in this case I named it n you
+
+ align:start position:0%
+variable in this case I named it n you
+ 
+
+ align:start position:0%
+variable in this case I named it n you
+can name it whatever you want in range
+
+ align:start position:0%
+can name it whatever you want in range
+ 
+
+ align:start position:0%
+can name it whatever you want in range
+five we're going to come back to what
+
+ align:start position:0%
+five we're going to come back to what
+ 
+
+ align:start position:0%
+five we're going to come back to what
+range means in a little bit print
+
+ align:start position:0%
+range means in a little bit print
+ 
+
+ align:start position:0%
+range means in a little bit print
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay so every time through the loop
+
+ align:start position:0%
+okay so every time through the loop
+ 
+
+ align:start position:0%
+okay so every time through the loop
+you're going to print out what the value
+
+ align:start position:0%
+you're going to print out what the value
+ 
+
+ align:start position:0%
+you're going to print out what the value
+of n
+
+ align:start position:0%
+of n
+ 
+
+ align:start position:0%
+of n
+is range five
+
+ align:start position:0%
+is range five
+ 
+
+ align:start position:0%
+is range five
+actually creates internally a sequence
+
+ align:start position:0%
+actually creates internally a sequence
+ 
+
+ align:start position:0%
+actually creates internally a sequence
+of numbers starting from zero and going
+
+ align:start position:0%
+of numbers starting from zero and going
+ 
+
+ align:start position:0%
+of numbers starting from zero and going
+to that number 5 - one so the sequence
+
+ align:start position:0%
+to that number 5 - one so the sequence
+ 
+
+ align:start position:0%
+to that number 5 - one so the sequence
+is going to be 0 1 2 3 and
+
+ align:start position:0%
+is going to be 0 1 2 3 and
+ 
+
+ align:start position:0%
+is going to be 0 1 2 3 and
+four the first time through the loop
+
+ align:start position:0%
+four the first time through the loop
+ 
+
+ align:start position:0%
+four the first time through the loop
+you're going to say n is equal to zero
+
+ align:start position:0%
+you're going to say n is equal to zero
+ 
+
+ align:start position:0%
+you're going to say n is equal to zero
+or internally this is what happens n
+
+ align:start position:0%
+or internally this is what happens n
+ 
+
+ align:start position:0%
+or internally this is what happens n
+gets the value zero you're going to
+
+ align:start position:0%
+gets the value zero you're going to
+ 
+
+ align:start position:0%
+gets the value zero you're going to
+print
+
+ align:start position:0%
+print
+ 
+
+ align:start position:0%
+print
+n then you're going to back go back to
+
+ align:start position:0%
+n then you're going to back go back to
+ 
+
+ align:start position:0%
+n then you're going to back go back to
+the to the top n gets the value one then
+
+ align:start position:0%
+the to the top n gets the value one then
+ 
+
+ align:start position:0%
+the to the top n gets the value one then
+you're going to go execute whatever
+
+ align:start position:0%
+you're going to go execute whatever
+ 
+
+ align:start position:0%
+you're going to go execute whatever
+inside so you're going to print
+
+ align:start position:0%
+inside so you're going to print
+ 
+
+ align:start position:0%
+inside so you're going to print
+one then you're going to increment that
+
+ align:start position:0%
+one then you're going to increment that
+ 
+
+ align:start position:0%
+one then you're going to increment that
+to the next value in the sequence you're
+
+ align:start position:0%
+to the next value in the sequence you're
+ 
+
+ align:start position:0%
+to the next value in the sequence you're
+going to print out two and so
+
+ align:start position:0%
+going to print out two and so
+ 
+
+ align:start position:0%
+going to print out two and so
+on so this is the
+
+ align:start position:0%
+on so this is the
+ 
+
+ align:start position:0%
+on so this is the
+general um look of a for Loop so we have
+
+ align:start position:0%
+general um look of a for Loop so we have
+ 
+
+ align:start position:0%
+general um look of a for Loop so we have
+four some uh loop variable again can be
+
+ align:start position:0%
+four some uh loop variable again can be
+ 
+
+ align:start position:0%
+four some uh loop variable again can be
+named whatever you want in range some
+
+ align:start position:0%
+named whatever you want in range some
+ 
+
+ align:start position:0%
+named whatever you want in range some
+number do a bunch of
+
+ align:start position:0%
+number do a bunch of
+ 
+
+ align:start position:0%
+number do a bunch of
+stuff and again these are part of this
+
+ align:start position:0%
+stuff and again these are part of this
+ 
+
+ align:start position:0%
+stuff and again these are part of this
+four Loop code block so you should
+
+ align:start position:0%
+four Loop code block so you should
+ 
+
+ align:start position:0%
+four Loop code block so you should
+indent them to tell python that these
+
+ align:start position:0%
+indent them to tell python that these
+ 
+
+ align:start position:0%
+indent them to tell python that these
+are the things that you should do okay
+
+ align:start position:0%
+are the things that you should do okay
+ 
+
+ align:start position:0%
+are the things that you should do okay
+so when you're using range some number
+
+ align:start position:0%
+so when you're using range some number
+ 
+
+ align:start position:0%
+so when you're using range some number
+you start
+
+ align:start position:0%
+you start
+ 
+
+ align:start position:0%
+you start
+out with variable getting the value
+
+ align:start position:0%
+out with variable getting the value
+ 
+
+ align:start position:0%
+out with variable getting the value
+zero okay with with variable having
+
+ align:start position:0%
+zero okay with with variable having
+ 
+
+ align:start position:0%
+zero okay with with variable having
+value zero you're going to execute all
+
+ align:start position:0%
+value zero you're going to execute all
+ 
+
+ align:start position:0%
+value zero you're going to execute all
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+Expressions after all the expressions in
+
+ align:start position:0%
+Expressions after all the expressions in
+ 
+
+ align:start position:0%
+Expressions after all the expressions in
+the code block are done you're going to
+
+ align:start position:0%
+the code block are done you're going to
+ 
+
+ align:start position:0%
+the code block are done you're going to
+go on to the next value so
+
+ align:start position:0%
+go on to the next value so
+ 
+
+ align:start position:0%
+go on to the next value so
+one you're going to execute all these
+
+ align:start position:0%
+one you're going to execute all these
+ 
+
+ align:start position:0%
+one you're going to execute all these
+expressions with the variable being
+
+ align:start position:0%
+expressions with the variable being
+ 
+
+ align:start position:0%
+expressions with the variable being
+value one and then so on and so on until
+
+ align:start position:0%
+value one and then so on and so on until
+ 
+
+ align:start position:0%
+value one and then so on and so on until
+you go to Su num minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that it so so using range in that
+
+ align:start position:0%
+one that it so so using range in that
+ 
+
+ align:start position:0%
+one that it so so using range in that
+way is a little bit con constraining
+
+ align:start position:0%
+way is a little bit con constraining
+ 
+
+ align:start position:0%
+way is a little bit con constraining
+because you're always going to get
+
+ align:start position:0%
+because you're always going to get
+ 
+
+ align:start position:0%
+because you're always going to get
+values starting from zero and ending at
+
+ align:start position:0%
+values starting from zero and ending at
+ 
+
+ align:start position:0%
+values starting from zero and ending at
+some num minus one okay whatever is in
+
+ align:start position:0%
+some num minus one okay whatever is in
+ 
+
+ align:start position:0%
+some num minus one okay whatever is in
+in the parentheses and range sometimes
+
+ align:start position:0%
+in the parentheses and range sometimes
+ 
+
+ align:start position:0%
+in the parentheses and range sometimes
+you might want to write programs that
+
+ align:start position:0%
+you might want to write programs that
+ 
+
+ align:start position:0%
+you might want to write programs that
+maybe start at a custom some value don't
+
+ align:start position:0%
+maybe start at a custom some value don't
+ 
+
+ align:start position:0%
+maybe start at a custom some value don't
+start at zero maybe they start at five
+
+ align:start position:0%
+start at zero maybe they start at five
+ 
+
+ align:start position:0%
+start at zero maybe they start at five
+maybe they start at minus
+
+ align:start position:0%
+maybe they start at minus
+ 
+
+ align:start position:0%
+maybe they start at minus
+10 and sometimes you might want to write
+
+ align:start position:0%
+10 and sometimes you might want to write
+ 
+
+ align:start position:0%
+10 and sometimes you might want to write
+programs that don't go with uh don't
+
+ align:start position:0%
+programs that don't go with uh don't
+ 
+
+ align:start position:0%
+programs that don't go with uh don't
+increment the numbers by one but maybe
+
+ align:start position:0%
+increment the numbers by one but maybe
+ 
+
+ align:start position:0%
+increment the numbers by one but maybe
+skip every other number or go every two
+
+ align:start position:0%
+skip every other number or go every two
+ 
+
+ align:start position:0%
+skip every other number or go every two
+numbers every three numbers and so on so
+
+ align:start position:0%
+numbers every three numbers and so on so
+ 
+
+ align:start position:0%
+numbers every three numbers and so on so
+you can customize range to your
+
+ align:start position:0%
+you can customize range to your
+ 
+
+ align:start position:0%
+you can customize range to your
+needs the one thing you do need to give
+
+ align:start position:0%
+needs the one thing you do need to give
+ 
+
+ align:start position:0%
+needs the one thing you do need to give
+it is this stop so if you give it only
+
+ align:start position:0%
+it is this stop so if you give it only
+ 
+
+ align:start position:0%
+it is this stop so if you give it only
+one value in the parenthesis that stands
+
+ align:start position:0%
+one value in the parenthesis that stands
+ 
+
+ align:start position:0%
+one value in the parenthesis that stands
+for stop and by default start is going
+
+ align:start position:0%
+for stop and by default start is going
+ 
+
+ align:start position:0%
+for stop and by default start is going
+to have value zero and step is going to
+
+ align:start position:0%
+to have value zero and step is going to
+ 
+
+ align:start position:0%
+to have value zero and step is going to
+have the value
+
+ align:start position:0%
+have the value
+ 
+
+ align:start position:0%
+have the value
+one if you give it two things in the
+
+ align:start position:0%
+one if you give it two things in the
+ 
+
+ align:start position:0%
+one if you give it two things in the
+parentheses you're giving it start and
+
+ align:start position:0%
+parentheses you're giving it start and
+ 
+
+ align:start position:0%
+parentheses you're giving it start and
+stop so the first being start the second
+
+ align:start position:0%
+stop so the first being start the second
+ 
+
+ align:start position:0%
+stop so the first being start the second
+being stop and step gets this value of
+
+ align:start position:0%
+being stop and step gets this value of
+ 
+
+ align:start position:0%
+being stop and step gets this value of
+one by default and if you give it three
+
+ align:start position:0%
+one by default and if you give it three
+ 
+
+ align:start position:0%
+one by default and if you give it three
+things in the parentheses you're giving
+
+ align:start position:0%
+things in the parentheses you're giving
+ 
+
+ align:start position:0%
+things in the parentheses you're giving
+it start stop and step in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order and you're always going to start
+
+ align:start position:0%
+order and you're always going to start
+ 
+
+ align:start position:0%
+order and you're always going to start
+at the start value and stop
+
+ align:start position:0%
+at the start value and stop
+ 
+
+ align:start position:0%
+at the start value and stop
+at or so you're going to start at the
+
+ align:start position:0%
+at or so you're going to start at the
+ 
+
+ align:start position:0%
+at or so you're going to start at the
+start value and you're going to go until
+
+ align:start position:0%
+start value and you're going to go until
+ 
+
+ align:start position:0%
+start value and you're going to go until
+stop minus one so those are the the
+
+ align:start position:0%
+stop minus one so those are the the
+ 
+
+ align:start position:0%
+stop minus one so those are the the
+sequences of
+
+ align:start position:0%
+sequences of
+ 
+
+ align:start position:0%
+sequences of
+numbers so in this first code right here
+
+ align:start position:0%
+numbers so in this first code right here
+ 
+
+ align:start position:0%
+numbers so in this first code right here
+my sum is going to get the value zero
+
+ align:start position:0%
+my sum is going to get the value zero
+ 
+
+ align:start position:0%
+my sum is going to get the value zero
+and you're going to have a for
+
+ align:start position:0%
+and you're going to have a for
+ 
+
+ align:start position:0%
+and you're going to have a for
+loop we're going to start from Seven
+
+ align:start position:0%
+loop we're going to start from Seven
+ 
+
+ align:start position:0%
+loop we're going to start from Seven
+right because we're giving it two
+
+ align:start position:0%
+right because we're giving it two
+ 
+
+ align:start position:0%
+right because we're giving it two
+numbers and when you give it two numbers
+
+ align:start position:0%
+numbers and when you give it two numbers
+ 
+
+ align:start position:0%
+numbers and when you give it two numbers
+it represents start and stop with step
+
+ align:start position:0%
+it represents start and stop with step
+ 
+
+ align:start position:0%
+it represents start and stop with step
+being one so you're starting at seven if
+
+ align:start position:0%
+being one so you're starting at seven if
+ 
+
+ align:start position:0%
+being one so you're starting at seven if
+step is one the next value is
+
+ align:start position:0%
+step is one the next value is
+ 
+
+ align:start position:0%
+step is one the next value is
+eight what's the value after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if we're incrementing by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nine and since we're going until stop
+
+ align:start position:0%
+nine and since we're going until stop
+ 
+
+ align:start position:0%
+nine and since we're going until stop
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one we're not actually going to pick up
+
+ align:start position:0%
+one we're not actually going to pick up
+ 
+
+ align:start position:0%
+one we're not actually going to pick up
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+10 okay so this Loop variable I the very
+
+ align:start position:0%
+10 okay so this Loop variable I the very
+ 
+
+ align:start position:0%
+10 okay so this Loop variable I the very
+first time through the loop is going to
+
+ align:start position:0%
+first time through the loop is going to
+ 
+
+ align:start position:0%
+first time through the loop is going to
+have the value seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my sum is going to be 0 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7 that's everything that's inside the
+
+ align:start position:0%
+7 that's everything that's inside the
+ 
+
+ align:start position:0%
+7 that's everything that's inside the
+code
+
+ align:start position:0%
+code
+ 
+
+ align:start position:0%
+code
+block the next time through the loop I
+
+ align:start position:0%
+block the next time through the loop I
+ 
+
+ align:start position:0%
+block the next time through the loop I
+gets the value
+
+ align:start position:0%
+gets the value
+ 
+
+ align:start position:0%
+gets the value
+eight so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside inside the for Loop my sum gets
+
+ align:start position:0%
+inside inside the for Loop my sum gets
+ 
+
+ align:start position:0%
+inside inside the for Loop my sum gets
+whatever the previous value was which
+
+ align:start position:0%
+whatever the previous value was which
+ 
+
+ align:start position:0%
+whatever the previous value was which
+was 7 + 8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the next time through the loop my
+
+ align:start position:0%
+okay the next time through the loop my
+ 
+
+ align:start position:0%
+okay the next time through the loop my
+sum gets the value 7 + 8 + 9 obviously
+
+ align:start position:0%
+sum gets the value 7 + 8 + 9 obviously
+ 
+
+ align:start position:0%
+sum gets the value 7 + 8 + 9 obviously
+replacing that with the previous value
+
+ align:start position:0%
+replacing that with the previous value
+ 
+
+ align:start position:0%
+replacing that with the previous value
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+15 okay since we're not going through 10
+
+ align:start position:0%
+15 okay since we're not going through 10
+ 
+
+ align:start position:0%
+15 okay since we're not going through 10
+that's where we stop and we're going to
+
+ align:start position:0%
+that's where we stop and we're going to
+ 
+
+ align:start position:0%
+that's where we stop and we're going to
+print out my sum which is going to be
+
+ align:start position:0%
+print out my sum which is going to be
+ 
+
+ align:start position:0%
+print out my sum which is going to be
+the value of 7 + 8 +
+
+ align:start position:0%
+the value of 7 + 8 +
+ 
+
+ align:start position:0%
+the value of 7 + 8 +
+9 oh
+
+ align:start position:0%
+9 oh
+ 
+
+ align:start position:0%
+9 oh
+yeah oh okay yeah start
+
+ align:start position:0%
+yeah oh okay yeah start
+ 
+
+ align:start position:0%
+yeah oh okay yeah start
+do they have to be integers
+
+ align:start position:0%
+do they have to be integers
+ 
+
+ align:start position:0%
+do they have to be integers
+um that's a great question we can try
+
+ align:start position:0%
+um that's a great question we can try
+ 
+
+ align:start position:0%
+um that's a great question we can try
+that out I'm not actually sure right off
+
+ align:start position:0%
+that out I'm not actually sure right off
+ 
+
+ align:start position:0%
+that out I'm not actually sure right off
+just off the top of my head so you can
+
+ align:start position:0%
+just off the top of my head so you can
+ 
+
+ align:start position:0%
+just off the top of my head so you can
+go in spider and
+
+ align:start position:0%
+go in spider and
+ 
+
+ align:start position:0%
+go in spider and
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um let's say in this example here in
+
+ align:start position:0%
+um let's say in this example here in
+ 
+
+ align:start position:0%
+um let's say in this example here in
+this example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so we can say 7.1
+
+ align:start position:0%
+here so we can say 7.1
+ 
+
+ align:start position:0%
+here so we can say 7.1
+10.3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so they have to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers okay so that's that's that
+
+ align:start position:0%
+integers okay so that's that's that
+ 
+
+ align:start position:0%
+integers okay so that's that's that
+example and let's erase that in this
+
+ align:start position:0%
+example and let's erase that in this
+ 
+
+ align:start position:0%
+example and let's erase that in this
+particular example we have start stop
+
+ align:start position:0%
+particular example we have start stop
+ 
+
+ align:start position:0%
+particular example we have start stop
+and step and here we're going going
+
+ align:start position:0%
+and step and here we're going going
+ 
+
+ align:start position:0%
+and step and here we're going going
+every other value so we're starting at
+
+ align:start position:0%
+every other value so we're starting at
+ 
+
+ align:start position:0%
+every other value so we're starting at
+five tell me what the next value is
+
+ align:start position:0%
+five tell me what the next value is
+ 
+
+ align:start position:0%
+five tell me what the next value is
+supposed to
+
+ align:start position:0%
+supposed to
+ 
+
+ align:start position:0%
+supposed to
+be if we're taking every other one seven
+
+ align:start position:0%
+be if we're taking every other one seven
+ 
+
+ align:start position:0%
+be if we're taking every other one seven
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then nine and
+
+ align:start position:0%
+then nine and
+ 
+
+ align:start position:0%
+then nine and
+then are we doing 11 or not excellent
+
+ align:start position:0%
+then are we doing 11 or not excellent
+ 
+
+ align:start position:0%
+then are we doing 11 or not excellent
+nice yeah so we're going to the end
+
+ align:start position:0%
+nice yeah so we're going to the end
+ 
+
+ align:start position:0%
+nice yeah so we're going to the end
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one okay so it's possible that sometimes
+
+ align:start position:0%
+one okay so it's possible that sometimes
+ 
+
+ align:start position:0%
+one okay so it's possible that sometimes
+you write code where you might want to
+
+ align:start position:0%
+you write code where you might want to
+ 
+
+ align:start position:0%
+you write code where you might want to
+exit out of the loop early okay you
+
+ align:start position:0%
+exit out of the loop early okay you
+ 
+
+ align:start position:0%
+exit out of the loop early okay you
+don't want to go through all of the
+
+ align:start position:0%
+don't want to go through all of the
+ 
+
+ align:start position:0%
+don't want to go through all of the
+sequences of your numbers maybe there's
+
+ align:start position:0%
+sequences of your numbers maybe there's
+ 
+
+ align:start position:0%
+sequences of your numbers maybe there's
+a condition inside there where you just
+
+ align:start position:0%
+a condition inside there where you just
+ 
+
+ align:start position:0%
+a condition inside there where you just
+want to exit the loop early inside the Y
+
+ align:start position:0%
+want to exit the loop early inside the Y
+ 
+
+ align:start position:0%
+want to exit the loop early inside the Y
+Loop maybe you want to exit the loop
+
+ align:start position:0%
+Loop maybe you want to exit the loop
+ 
+
+ align:start position:0%
+Loop maybe you want to exit the loop
+before the condition becomes false so
+
+ align:start position:0%
+before the condition becomes false so
+ 
+
+ align:start position:0%
+before the condition becomes false so
+that's where the break statement comes
+
+ align:start position:0%
+that's where the break statement comes
+ 
+
+ align:start position:0%
+that's where the break statement comes
+in so the break works like this it's
+
+ align:start position:0%
+in so the break works like this it's
+ 
+
+ align:start position:0%
+in so the break works like this it's
+going to as soon as python sees this
+
+ align:start position:0%
+going to as soon as python sees this
+ 
+
+ align:start position:0%
+going to as soon as python sees this
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+statement it's going to say okay I'm
+
+ align:start position:0%
+statement it's going to say okay I'm
+ 
+
+ align:start position:0%
+statement it's going to say okay I'm
+going to look at whatever Loop I'm
+
+ align:start position:0%
+going to look at whatever Loop I'm
+ 
+
+ align:start position:0%
+going to look at whatever Loop I'm
+currently
+
+ align:start position:0%
+currently
+ 
+
+ align:start position:0%
+currently
+in I'm not evaluating any expression
+
+ align:start position:0%
+in I'm not evaluating any expression
+ 
+
+ align:start position:0%
+in I'm not evaluating any expression
+after it that comes within my
+
+ align:start position:0%
+after it that comes within my
+ 
+
+ align:start position:0%
+after it that comes within my
+Loop and I'm going to immediately exit
+
+ align:start position:0%
+Loop and I'm going to immediately exit
+ 
+
+ align:start position:0%
+Loop and I'm going to immediately exit
+the loop so I'm going inside this while
+
+ align:start position:0%
+the loop so I'm going inside this while
+ 
+
+ align:start position:0%
+the loop so I'm going inside this while
+this while I'm evaluating this one
+
+ align:start position:0%
+this while I'm evaluating this one
+ 
+
+ align:start position:0%
+this while I'm evaluating this one
+expression and then I suddenly see a
+
+ align:start position:0%
+expression and then I suddenly see a
+ 
+
+ align:start position:0%
+expression and then I suddenly see a
+break expression B does not get
+
+ align:start position:0%
+break expression B does not get
+ 
+
+ align:start position:0%
+break expression B does not get
+evaluated and break is going to
+
+ align:start position:0%
+evaluated and break is going to
+ 
+
+ align:start position:0%
+evaluated and break is going to
+immediately exit out of the innermost
+
+ align:start position:0%
+immediately exit out of the innermost
+ 
+
+ align:start position:0%
+immediately exit out of the innermost
+Loop that it's in so this y Loop that
+
+ align:start position:0%
+Loop that it's in so this y Loop that
+ 
+
+ align:start position:0%
+Loop that it's in so this y Loop that
+has condition two that's the innermost
+
+ align:start position:0%
+has condition two that's the innermost
+ 
+
+ align:start position:0%
+has condition two that's the innermost
+Loop that the brake is found found
+
+ align:start position:0%
+Loop that the brake is found found
+ 
+
+ align:start position:0%
+Loop that the brake is found found
+in so we're going to exit out of this
+
+ align:start position:0%
+in so we're going to exit out of this
+ 
+
+ align:start position:0%
+in so we're going to exit out of this
+innermost Loop here and we're evaluating
+
+ align:start position:0%
+innermost Loop here and we're evaluating
+ 
+
+ align:start position:0%
+innermost Loop here and we're evaluating
+expression C and notice we're evaluating
+
+ align:start position:0%
+expression C and notice we're evaluating
+ 
+
+ align:start position:0%
+expression C and notice we're evaluating
+expression C because it's expression C
+
+ align:start position:0%
+expression C because it's expression C
+ 
+
+ align:start position:0%
+expression C because it's expression C
+is part of the outer while
+
+ align:start position:0%
+is part of the outer while
+ 
+
+ align:start position:0%
+is part of the outer while
+loop it's at the same level as this one
+
+ align:start position:0%
+loop it's at the same level as this one
+ 
+
+ align:start position:0%
+loop it's at the same level as this one
+and these ones are part of the inner
+
+ align:start position:0%
+and these ones are part of the inner
+ 
+
+ align:start position:0%
+and these ones are part of the inner
+while loop
+
+ align:start position:0%
+while loop
+ 
+
+ align:start position:0%
+while loop
+okay okay last thing I want to say is
+
+ align:start position:0%
+okay okay last thing I want to say is
+ 
+
+ align:start position:0%
+okay okay last thing I want to say is
+just a little bit of a comparison
+
+ align:start position:0%
+just a little bit of a comparison
+ 
+
+ align:start position:0%
+just a little bit of a comparison
+between four and while Loops so when
+
+ align:start position:0%
+between four and while Loops so when
+ 
+
+ align:start position:0%
+between four and while Loops so when
+would you use one or the other um this
+
+ align:start position:0%
+would you use one or the other um this
+ 
+
+ align:start position:0%
+would you use one or the other um this
+might be useful in your problem sets so
+
+ align:start position:0%
+might be useful in your problem sets so
+ 
+
+ align:start position:0%
+might be useful in your problem sets so
+for Loops you usually use when you know
+
+ align:start position:0%
+for Loops you usually use when you know
+ 
+
+ align:start position:0%
+for Loops you usually use when you know
+the number of iterations
+
+ align:start position:0%
+the number of iterations
+ 
+
+ align:start position:0%
+the number of iterations
+okay y Loops are very useful when for
+
+ align:start position:0%
+okay y Loops are very useful when for
+ 
+
+ align:start position:0%
+okay y Loops are very useful when for
+example you're getting user input and
+
+ align:start position:0%
+example you're getting user input and
+ 
+
+ align:start position:0%
+example you're getting user input and
+user input is unpredictable right you
+
+ align:start position:0%
+user input is unpredictable right you
+ 
+
+ align:start position:0%
+user input is unpredictable right you
+don't know how many times they're going
+
+ align:start position:0%
+don't know how many times they're going
+ 
+
+ align:start position:0%
+don't know how many times they're going
+to do certain task for both four and Y
+
+ align:start position:0%
+to do certain task for both four and Y
+ 
+
+ align:start position:0%
+to do certain task for both four and Y
+Loops you can end out of the loop early
+
+ align:start position:0%
+Loops you can end out of the loop early
+ 
+
+ align:start position:0%
+Loops you can end out of the loop early
+using the break the four Loop uses this
+
+ align:start position:0%
+using the break the four Loop uses this
+ 
+
+ align:start position:0%
+using the break the four Loop uses this
+counter it's inherent inside the for
+
+ align:start position:0%
+counter it's inherent inside the for
+ 
+
+ align:start position:0%
+counter it's inherent inside the for
+Loop a while loop you can use a counter
+
+ align:start position:0%
+Loop a while loop you can use a counter
+ 
+
+ align:start position:0%
+Loop a while loop you can use a counter
+in order you can use a while loop to
+
+ align:start position:0%
+in order you can use a while loop to
+ 
+
+ align:start position:0%
+in order you can use a while loop to
+count things but you must initialize the
+
+ align:start position:0%
+count things but you must initialize the
+ 
+
+ align:start position:0%
+count things but you must initialize the
+counter before the Y Loop and you have
+
+ align:start position:0%
+counter before the Y Loop and you have
+ 
+
+ align:start position:0%
+counter before the Y Loop and you have
+to remember to increment it within the
+
+ align:start position:0%
+to remember to increment it within the
+ 
+
+ align:start position:0%
+to remember to increment it within the
+loop otherwise wise you'll you maybe
+
+ align:start position:0%
+loop otherwise wise you'll you maybe
+ 
+
+ align:start position:0%
+loop otherwise wise you'll you maybe
+lead to an infinite
+
+ align:start position:0%
+lead to an infinite
+ 
+
+ align:start position:0%
+lead to an infinite
+Loop we've seen in uh as the very first
+
+ align:start position:0%
+Loop we've seen in uh as the very first
+ 
+
+ align:start position:0%
+Loop we've seen in uh as the very first
+example of of a for Loop that the while
+
+ align:start position:0%
+example of of a for Loop that the while
+ 
+
+ align:start position:0%
+example of of a for Loop that the while
+loop the for Loop could be Rewritten as
+
+ align:start position:0%
+loop the for Loop could be Rewritten as
+ 
+
+ align:start position:0%
+loop the for Loop could be Rewritten as
+a while loop but the vice versa is not
+
+ align:start position:0%
+a while loop but the vice versa is not
+ 
+
+ align:start position:0%
+a while loop but the vice versa is not
+necessarily true and the counter example
+
+ align:start position:0%
+necessarily true and the counter example
+ 
+
+ align:start position:0%
+necessarily true and the counter example
+to that is just user input so you might
+
+ align:start position:0%
+to that is just user input so you might
+ 
+
+ align:start position:0%
+to that is just user input so you might
+not know how many times you might do a
+
+ align:start position:0%
+not know how many times you might do a
+ 
+
+ align:start position:0%
+not know how many times you might do a
+certain task all right great that's uh
+
+ align:start position:0%
+certain task all right great that's uh
+ 
+
+ align:start position:0%
+certain task all right great that's uh
+that's all for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today
\ No newline at end of file
diff --git a/2f8CoFvB8uk.txt b/2f8CoFvB8uk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c31124f8bdcf6a0449d1415fc93efaad877d8e2
--- /dev/null
+++ b/2f8CoFvB8uk.txt
@@ -0,0 +1,1856 @@
+ANNOUNCER: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Hi.
+
+Our lecture for today I've
+entitled 'Logarithms Without
+
+Exponents'.
+
+And before I try to clarify
+that, let me make a couple of
+
+general remarks.
+
+First of all, we have now
+completed the rudiments, the
+
+basics so to speak, of
+both differential
+
+and integral calculus.
+
+Consequently, what our next
+ambition will be is to take
+
+these principles and apply
+them to special functions
+
+which are worthy of
+investigation.
+
+And you see, in connection with
+this, the first function
+
+that I've chosen to talk about
+is called the logarithm.
+
+Now the other interesting thing
+is that we are used to
+
+logarithms from high school
+where they were viewed as
+
+being a different kind
+of notation for
+
+talking about exponents.
+
+Now, in the same way when
+we treated the circular
+
+functions, we mentioned that
+one did not have to invent
+
+triangles to talk about
+trigonometry.
+
+The interesting point is that
+one does not have to talk
+
+about exponents to invent
+the logarithm function.
+
+This is why I have entitled
+the lesson, as I say,
+
+'Logarithms without
+Exponents'.
+
+You see, what I would like to do
+is try to mimic, especially
+
+from an engineering point of
+view, how many of these
+
+mathematical topics
+originated.
+
+Let's look at a rather
+straightforward physical
+
+principle, a principle that I'm
+sure we believe permeates
+
+many real life situations.
+
+It's what I call the rule
+of compound interest.
+
+Namely, let's suppose we have a
+physical situation in which
+
+the quantity that
+we're measuring,
+
+which we'll call 'm'.
+
+In other words, the rate of
+change of the quantity is
+
+proportional to the amount
+present, 'dm/ dt' equals 'km'.
+
+Now notice that this is a pretty
+harmless statement.
+
+The rate of change
+is proportional
+
+to the amount present.
+
+We certainly would expect that
+many experiments would run
+
+this way, and there seems to be
+nothing at all supernatural
+
+about this kind of
+an assumption.
+
+At any rate, let's apply our
+previous principles, and see
+
+if we can't, from this
+differential equation, figure
+
+out what 'm' has to be.
+
+Separating the variables, we
+get that 'dm' over 'm' is
+
+equal to 'kdt'.
+
+And now integrating, meaning
+taking the inverse derivative,
+
+we have what?
+
+That the integral of 'dm'
+over 'm' is equal
+
+to 'kt' plus a constant.
+
+Now you see, the interesting
+point is at this stage of the
+
+game, we do not know explicitly
+how to find a
+
+function whose derivative with
+respect to 'm' is '1 over m'.
+
+In fact, that's the
+problem that
+
+underlies today's lecture.
+
+And we will try to answer this
+question, showing how once we
+
+tackle this from a philosophic
+point of view, the rest of the
+
+details follow from material
+that we've already learned.
+
+At any rate, focusing our
+attention on the problem, the
+
+question is this: to determine
+a function, which I'll call
+
+capital 'L of x'--
+
+the 'L' sort of to forewarn us
+of the fact that we will
+
+somehow get a logarithm
+out of this--
+
+such that 'L prime of
+x' is '1 over x'.
+
+And you see, what I want you to
+notice is that if you write
+
+'1 over x' in exponential form,
+in other words, if you
+
+try to write '1 over x' as 'x
+to the n', notice that to
+
+solve this problem, 'L
+of x' would be what?
+
+The integral of 'x' to
+the 'minus 1 dx'.
+
+In other words, this is the case
+of integral ''x to the n'
+
+dx', with 'n' equal
+to minus 1.
+
+And you'll recall that when
+we studied the recipe--
+
+let me just write that over
+here-- when we studied the
+
+recipe of how you integrate 'x
+to the n', we saw that that
+
+was 'x to the 'n + 1'' over
+'n + 1' plus a constant.
+
+And we then observed that this
+doesn't even make sense when
+
+'n' is equal to minus 1,
+because we have a 0
+
+denominator.
+
+From the other point of view,
+the way to look at
+
+this is we said what?
+
+That when you differentiate, you
+lower the exponent by 1.
+
+Notice that to wind up with an
+exponent of minus 1, we would
+
+have had to start with
+an exponent of 0.
+
+But when you differentiate 'x'
+to the 0, that being a
+
+constant, the derivative
+of 'x' to the 0 is 0.
+
+It's not '1 over x'.
+
+You see, in other words, this
+particular recipe that we're
+
+talking about, we don't
+have working for us.
+
+In other words, this is an
+interesting point again.
+
+You say gee whiz, if the recipe
+for the integral ''x to
+
+the n' dx' works for everything
+except 'n' equals
+
+minus 1, nothing's perfect.
+
+Let's be content.
+
+Since it works for every
+number except
+
+that one, why worry?
+
+This is analogous to when
+we talked about taking
+
+derivatives and saw that
+we get a 0 over
+
+0 form every time.
+
+You see, if you pick a function
+at random, the
+
+likelihood that the limit of
+'f of x' as 'x' approaches
+
+'a', the likelihood of that
+being 0 over 0 is very small,
+
+except when you form
+the derivative, you
+
+always get 0 over 0.
+
+And in a similar way, granted
+that integral ''x' to the
+
+minus 1 dx' is one very
+special case.
+
+What we have seen is that this
+comes up every single time
+
+that we want to solve a problem
+of the form 'dm/ dt'
+
+equals 'km'.
+
+In other words then, what it
+really boils down to is that
+
+unless we can come up with
+a function 'L of x' whose
+
+derivative is '1 over x', we
+cannot solve the problem that
+
+we started off today's
+lesson with.
+
+In other words, we must leave
+it in the form integral 'dm
+
+over m' equals 'kt'
+plus a constant.
+
+Well at any rate, let's see what
+such a function capital
+
+'L of x' must look like.
+
+I'm going to utilize both the
+differential calculus approach
+
+and the integral calculus
+approach.
+
+By differential calculus,
+assuming that 'y' equals 'L of
+
+x', what do we know about
+the function 'y'?
+
+By definition, we've defined it
+to be that function whose
+
+derivative is '1 over x'.
+
+So we know its derivative
+is '1 over x'.
+
+The next point is that knowing
+that 'y prime' is '1 over x',
+
+and even though we can't
+integrate '1 over x', we can
+
+certainly differentiate
+'1 over x'.
+
+We can now differentiate
+'1 over x'.
+
+The derivative of '1 over x' is
+minus '1 over 'x squared'',
+
+and we find that 'y
+double prime' is
+
+minus '1 over 'x squared''.
+
+By the way, we should observe
+that we must shy away from 'x'
+
+equaling 0, because you see, we
+would have a 0 denominator
+
+in that case.
+
+If we think of most physical
+situations, notice that we
+
+talk about the amount--
+
+the rate of change
+is proportional
+
+to the amount present.
+
+From a physical point of view,
+the amount present can't be
+
+negative, so let's put the
+restriction on here that the
+
+domain of 'L' will be all
+positive numbers.
+
+Now here's the interesting
+thing.
+
+Intuitively, I can now visualize
+how the function 'L
+
+of x' must look.
+
+Namely, since its first
+derivative is '1 over x' and
+
+'x' is greater than 0, that
+tells me that the curve is
+
+always rising.
+
+And secondly, since '1 over 'x
+squared'' is always positive,
+
+minus '1 over 'x squared'' is
+always negative, that tells me
+
+that my curve is always
+spilling water.
+
+In essence then, what
+must the curve do?
+
+The curve must be rising
+but spilling water.
+
+In other words, the curve
+'L of x' belongs to this
+
+particular family.
+
+Notice that once we have one
+curve which we call 'y' equals
+
+'L of x', by any displacement
+parallel--
+
+vertical displacement,
+we get what?
+
+A member called 'y' equals
+'L of x' plus 'c'.
+
+All that changes is what?
+
+The point at which the curve
+crosses the x-axis, but
+
+whichever member of the
+family we pick, what
+
+typifies 'L of x'?
+
+Its derivative is '1 over x'.
+
+In other words, somehow or
+other, we visualize that 'L of
+
+x' exists, and its graph
+is something like this.
+
+Now suppose we want a more
+tangible form, namely how do
+
+you compute 'L of x'
+for a given 'x'?
+
+I thought what might be a nice
+review now is to see how we
+
+can use our integral calculus
+approach, and in particular
+
+the second fundamental theorem
+of interval calculus.
+
+By the integral calculus
+approach, we do is is we pick
+
+any positive number 'a', and
+once picked, we fix it.
+
+You see, we have a great deal
+of freedom in how we choose
+
+the positive number a.
+
+But let's pick one and
+leave it here.
+
+Now what we'll do is in the
+'y-t' plane, we'll draw the
+
+curve 'y' equals '1 over t'.
+
+And what we'll do now, we'll
+study the area of the region
+
+'R' where 'R' is bounded above
+by 'y' equals '1 over t', on
+
+the left by 't' equals 'a', on
+the right by 't' equals 'x',
+
+and below by the t-axis.
+
+Now we've already seen that the
+function that we get by
+
+taking the definite integral
+from 'a' 'to x', 'dt over t',
+
+has the property that its
+derivative is '1 over x'.
+
+In other words, recall from the
+fundamental theorem, this
+
+is just a generalization of the
+fact that if 'f of t' is a
+
+continuous function, then the
+integral from 'a' to 'x', ''f
+
+of t' dt', is a function
+of 'x'.
+
+And its derivative with
+respect to 'x'
+
+is just 'f of x'.
+
+You see, in other words, I can
+now view capital 'L of x' as
+
+being an area under the curve
+'y' equals '1 over t'.
+
+Notice that I have a degree of
+freedom here, namely what that
+
+area is depends on where
+I choose 'a'.
+
+Notice that if I choose a
+differently, changing 'a'--
+
+let's call this 'a
+prime', say--
+
+changing 'a' changes the area
+under the curve, but notice it
+
+changes it by a fixed amount.
+
+In other words, notice that
+shifting 'a' just changes 'L
+
+of x' by a constant,
+just like the
+
+ordinary in definite integral.
+
+At any rate, these are the two
+approaches that we have.
+
+And if we superimpose them,
+all we're saying is what?
+
+If you start with the
+differential calculus
+
+approach, 'y' equals capital 'L
+of x' must be a member of
+
+this family, crossing the axis
+at some point (a,0) .
+
+And from the integral calculus
+point of view, if you take the
+
+curve 'y' equals '1 over t'
+and compute the area under
+
+that curve from 'a'
+to 'x', that area
+
+function is 'L of x'.
+
+Now we'll let that rest for the
+time being, and now have a
+
+brief digression.
+
+You see, sooner or later, I've
+got to get to what a logarithm
+
+is, and we might just
+as well do that now.
+
+So let's now take a look and
+see what we mean by a
+
+logarithmic function.
+
+You see, quite frequently in
+mathematics, what one does is
+
+one deals with a particular
+special case in which one is
+
+interested.
+
+And having deduced very nice
+results, he looks at this
+
+thing and says, you know, all
+of these results came from a
+
+particular recipe, a particular
+structure that this
+
+system obeyed.
+
+What he then does is he takes
+this recipe or structure,
+
+gives it a general name, and
+now is able to extend this
+
+property to a larger
+class of objects.
+
+For example, let's
+look at this way.
+
+What is the nice thing about
+logarithms in the traditional
+
+sense of the word?
+
+Remember when we learned
+logarithms in high school, by
+
+use of logarithms, we were able
+to replace multiplication
+
+problems by addition problems,
+et cetera.
+
+In other words, remember the
+key structural property was
+
+that the logarithm of a product
+was the sum of the
+
+logarithms.
+
+That was the structural thing
+that we used over and over and
+
+over again.
+
+In fact, it's rather interesting
+to point out that
+
+in many cases where we used the
+properties of logarithms,
+
+we never really had to know
+what a logarithm was.
+
+All we had to know was what?
+
+What properties did it obey,
+and did we have a book of
+
+tables so we could look up the
+logarithm when we had to.
+
+Well at any rate, using this as
+motivation, we now define a
+
+logarithmic function,
+specifically a function f is
+
+called logarithmic if for all
+'x1', 'x2' in the domain of
+
+'f', 'f' of the product of 'x1'
+and 'x2' is 'f of x1'
+
+plus 'f of x2'.
+
+In other words, since we know
+what nice properties a
+
+logarithm has, let's define
+any function 'f' to be
+
+logarithmic if 'f' of a
+product is equal to
+
+the sum of the 'f's.
+
+Now you see, this may sound
+like a pretty simple
+
+statement, but it's
+quite demanding.
+
+In other words, notice--
+
+by the way, somebody says,
+I wonder if there are any
+
+logarithmic functions?
+
+You see, notice that by the way
+we began, there must be at
+
+least one logarithmic function,
+
+namely the usual logarithm.
+
+We know there's at least one
+function which has these
+
+properties.
+
+So the set of all logarithmic
+functions is certainly
+
+not the empty set.
+
+At any rate, let's see what
+we can deduce about any
+
+logarithmic function.
+
+Well for example, I claim that
+if 'f' is logarithmic, 'f of
+
+1' must be 0.
+
+Why is that?
+
+Well, notice that 1 can be
+written as 1 times 1.
+
+And since 'f of 1' times
+1 is 'f of 1' plus 'f
+
+of 1', we have what?
+
+That 'f of 1' is equal to 'f of
+1' plus 'f of 1', therefore
+
+twice 'f of 1' is 'f of 1',
+and therefore by algebraic
+
+manipulation, 'f of 1' is 0.
+
+Which, by the way, does check
+out with the usual logarithm,
+
+the logarithm of 1 to
+any base 'b' is 0.
+
+Secondly, if 'f of '1 over x''
+is defined, you see in other
+
+words, I'm not sure whether '1
+over x' is in the domain of
+
+'f' just because 'x' is, but
+suppose '1 over x' is in the
+
+domain of 'f'.
+
+Then 'f of '1 over x'' is
+equal to minus 'f of x'.
+
+In other words, 'f' of a number
+is minus 'f' of the
+
+reciprocal of that number.
+
+Again, a familiar logarithmic
+property, why does it follow
+
+from our basic definition?
+
+Well notice that we already
+know that 'f of 1' is 0.
+
+We also know that 1 is equal
+to 'x' times '1 over x',
+
+provided 'x' is not 0.
+
+By the way, if 'x' were 0, 1
+over 0 wouldn't be defined, so
+
+we wouldn't be worrying
+about that anyway.
+
+But notice now we have what?
+
+If 'x' is not 0, 'f of 'x times
+'1 over x'' is 0, but by
+
+the logarithmic property, that's
+also 'f of x' plus 'f
+
+of '1 over x''.
+
+Since these two together add up
+to 0, 'f of '1 over x' must
+
+just be minus 'f of x'.
+
+And we'll just take a few more
+properties like this just to
+
+make sure that you see what
+properties logarithmic
+
+functions have.
+
+Remember again the ordinary
+logarithm, the logarithm of a
+
+quotient was the difference
+of the logarithms.
+
+Again, 'f of 'x over y''
+is equal to 'f of
+
+x' minus 'f of y'.
+
+Why is that the case?
+
+Well, look at 'f
+of 'x over y''.
+
+That says 'f of x'
+times '1 over y'.
+
+But again, by logarithmic
+properties, 'f' of a product
+
+is the sum of the 'f's.
+
+Therefore 'f of 'x times '1 over
+y''' is 'f of x' plus 'f
+
+of '1 over y''.
+
+But we just saw that 'f of '1
+over y' is minus 'f of y'.
+
+So we have this familiar
+result now.
+
+And finally, by mathematical
+induction, if 'n' is any
+
+positive integer, 'f of x' to
+the n-th power is just 'n'
+
+times 'f of x'.
+
+And the proof is rather clear.
+
+Namely, 'f of x' to the n-th
+power when 'n' is a positive
+
+integer means 'f of 'x'
+times 'x' times 'x'
+
+times 'x'', 'n' times.
+
+And since the logarithmic
+property says that 'f' of a
+
+product is a sum of the 'f's,
+that's equal to 'f of x' plus
+
+'f of x' plus et cetera plus 'f
+of x', 'n' times, and that
+
+precisely is just 'n'
+times 'f of x'.
+
+In other words, notice that
+our definition of a
+
+logarithmic function, simply
+that 'f of 'x1 times x2'' is
+
+equal to 'f of x1' plus 'f of
+x2' allows us to deduce all of
+
+the familiar properties that
+were known to us in terms of
+
+the traditional meaning
+of logarithm.
+
+And now we come to the most
+important question of today's
+
+lecture, and that is what does
+all of this discussion have to
+
+do with the function that we've
+called capital 'L of x'?
+
+And that's what will
+tackle next.
+
+Let's take a look and see
+whether capital 'L of x' is
+
+indeed a logarithmic function.
+
+Well, if 'L' is to be a
+logarithmic function, if 'b'
+
+is any constant, in particular
+'L of 'b times x'' had better
+
+be equal to 'L of b'
+plus 'L of x'.
+
+That's the definition
+of logarithmic.
+
+Now we don't know
+if that's true.
+
+What do we have at our disposal
+to be able to see
+
+whether we can solve this
+problem or not?
+
+How do we, using calculus,
+check to see whether two
+
+functions are equal?
+
+Remember the standard
+approach is what?
+
+Take the derivative
+of both sides.
+
+If the derivatives are
+equal, then the
+
+functions differ by a constant.
+
+And if we can show that that
+constant is 0, then the two
+
+functions are equal.
+
+So let's take a look and see
+how that works over here.
+
+First of all, let's see what the
+derivative of 'L of bx' is
+
+with respect to 'x'.
+
+And by the way, here again is
+the beauty of what we mean
+
+when we say that all of the
+study that we're making allows
+
+us to utilize every fundamental
+result that we've
+
+learned before.
+
+We've learned that the basic
+definition of 'L' is what?
+
+That if you differentiate 'L'
+with respect to the given
+
+variable, you get 1 over
+that variable.
+
+We want the derivative of 'L
+of bx' with respect to 'x'.
+
+Now, you see the idea is the
+derivative of 'L of u' with
+
+respect to 'u' is '1 over u'.
+
+You see by the chain rule, if we
+were differentiating 'L of
+
+bx' with respect to 'bx', that
+would be '1 over bx'.
+
+I shouldn't say by the
+chain rule yet.
+
+What I'm saying is if we
+differentiate 'L of bx' with
+
+respect to 'bx', we would
+have '1 over bx'.
+
+But we're not differentiating
+with respect to 'bx', we're
+
+differentiating with
+respect to 'x'.
+
+And this is where the
+chain rule comes in.
+
+Namely, we rewrite the
+derivative of 'L of bx' with
+
+respect to 'x' as the derivative
+'L of bx' with
+
+respect to 'bx' times the
+derivative of 'bx' with
+
+respect to 'b'.
+
+And in this way we get what?
+
+The first factor
+is '1 over bx'.
+
+The second factor
+is 'b' itself--
+
+remember 'b' is a constant--
+
+and therefore the derivative
+of 'L of bx' is '1 over x'.
+
+On the other hand, what is
+the derivative of 'L of
+
+b' plus 'L of x'?
+
+Since 'b' is a constant, the
+derivative 'L of b' is 0.
+
+And by definition, the
+derivative of 'L of x' with
+
+respect to 'x' is '1 over x'.
+
+And now you see, comparing these
+two results, we see that
+
+'L of bx' and 'L of b' plus 'L
+of x have the same derivative,
+
+hence they differ by a constant
+which I'll call 'c'.
+
+In other words, notice that
+capital 'L' is what I call
+
+almost logarithmic.
+
+If it weren't for this factor
+constant 'c' in here, it would
+
+be a logarithmic function.
+
+Well at any rate,
+what do we have?
+
+We know that capital 'L of bx'
+is equal to capital 'L of b'
+
+plus capital 'L of x' plus
+some constant 'c'.
+
+To evaluate the constant, we
+only have to evaluate it at
+
+one element in the domain, let's
+pick 'x' equal to 1.
+
+The motif being that if 'x' is
+1, notice that on the left
+
+hand side you have an 'L of b'
+term, on the right hand side
+
+you have an 'L of b' term,
+and they will cancel.
+
+In other words, if 'x' is 1,
+this equation becomes 'L of b'
+
+equals 'L of b' plus 'L of 1'
+plus 'c', from which it
+
+follows that 'c' is
+minus 'L of 1'.
+
+'c' is minus 'L of 1'.
+
+Now what do we want to 'c' to
+be if 'c' were equal to 0?
+
+If 'c' where equal to 0, this
+would be logarithmic, and all
+
+we need to make 'c' equal to 0
+is to set 'L of 1' equal to 0.
+
+In other words, summarizing this
+result, capital 'L of x'
+
+is logarithmic if capital
+'L of 1' is 0.
+
+Now remember, we have a whole
+family of 'L's that work.
+
+What we're saying now is let's
+pick the member of the family
+
+of 'L's that passes through
+the point (1,0) .
+
+And because that's logarithmic,
+let's give that a
+
+special name.
+
+In essence, we will define
+this symbol.
+
+It's written 'ln of x'.
+
+It will later be called the
+natural logarithm of 'x'.
+
+I'm trying to avoid the word
+logarithm here as much as
+
+possible, because I want you to
+see that we haven't had to
+
+use exponents at all in making
+this kind of a definition.
+
+But let's define 'ln of x' to
+be the member of the family
+
+capital 'L of x' plus
+'c' which passes
+
+through the point (1,0).
+
+In essence then, what
+is 'ln of x'?
+
+I'll call it natural log, it's
+easier for me to say.
+
+The natural 'log of x' is that
+function whose derivative with
+
+respect to 'x' is '1 over
+x', and characterized by
+
+the fact that what?
+
+If the input is 1,
+the output is 0.
+
+In other words, the graph
+passes through
+
+the point (1 , 0).
+
+Again, notice that in terms
+of what we said earlier in
+
+today's lesson, we talked about
+the functions 'L of x',
+
+and talked about, in the
+differential calculus
+
+approach, the curve could
+go through any
+
+point on the x-axis.
+
+What we're saying is now if the
+point on the x-axis that
+
+the curve crosses at is (1 ,
+0), that's what 'lnx' will
+
+mean, the natural
+log function.
+
+In terms of the integral
+calculus approach, if the
+
+particular 'a' value that we
+choose, the fixed value that
+
+we're going to study the area
+under, notice that all we're
+
+saying is pick 'a' to be 1.
+
+And by the way, as a
+quick check, all
+
+we're saying is what?
+
+The 'natural log of x' is
+defined to be the area under
+
+this curve as a function
+of 'x'.
+
+In terms of the definite
+integral, that's the integral
+
+from '1 to x,' 'dt over t'.
+
+And notice that if you pick 'x'
+to be 1, the natural log
+
+of 1 is the integral from 1 to
+1 'dt over t', and that's 0,
+
+just as it should be.
+
+So at any rate now, that
+tells me how to
+
+define the natural log.
+
+Am I doing this in terms
+of exponents?
+
+No.
+
+I am trying to do what?
+
+Find a function whose derivative
+with respect to 'x'
+
+is '1 over x', and I'd also like
+that function, since it's
+
+that close to being a
+logarithmic function, to be a
+
+logarithmic function.
+
+In other words, this is how I
+invented the function 'ln of
+
+x', the 'natural log of x'.
+
+It's derivative with respect to
+'x' is '1 over x', and the
+
+natural log of a product is the
+sum of the natural logs.
+
+And by the way, that's exactly
+how we use this material.
+
+Let me just take a few minutes
+and go over something that we
+
+already had an answer
+for, just to show
+
+you how this works.
+
+Let me try to rederive the
+product rule using logarithms.
+
+Suppose 'u' and 'v' are
+differentiable functions of
+
+'x', and I want to find the
+derivative of 'u' times 'v'
+
+with respect to 'x'.
+
+In other words, I'd like
+to find 'dy dx'.
+
+OK, I take the natural
+log of both sides.
+
+In other words, I say if 'y'
+equals 'u' times 'v', the
+
+natural log 'y' equals natural
+log 'u times v'.
+
+Now what is the property that
+the natural log function has?
+
+I deliberately chose it to be
+that member of the l family
+
+that was logarithmic.
+
+The natural log of 'u times
+v' is 'natural log u' plus
+
+'natural log v'.
+
+Now, can I differentiate
+this implicitly
+
+with respect to 'x'?
+
+You see how all of our
+old stuff keeps
+
+coming up in new context.
+
+I take this equation and I
+differentiate it implicitly
+
+with respect to 'x'.
+
+The derivative of the
+left hand side is '1
+
+over y', 'dy dx'.
+
+The derivative of the right
+hand side is what?
+
+Well, the derivative of 'log u'
+with respect to 'u' is '1
+
+over u', but I'm differentiating
+it with
+
+respect to 'x', so I must use
+the correction factor by the
+
+chain rule 'du dx'.
+
+And similarly, the derivative of
+'log v' with respect to 'x'
+
+is '1 over v', 'dv dx'.
+
+And now multiplying through by
+'y', I have obtained that 'dy
+
+dx' is ''y over u' du dx'
+plus ''y over v' dv dx'.
+
+But remembering that 'y' is
+equal to 'u' times 'v', this
+
+becomes 'v 'du dx'' plus 'u 'dv
+dx', and we have arrived
+
+at the familiar product
+rule using logarithmic
+
+differentiation.
+
+You see the point that's really
+important to stress
+
+here it that it wasn't important
+whether the natural
+
+log was an exponent or not.
+
+The important thing that we used
+about logarithms, whether
+
+it was our high school course,
+whether it's going to be in
+
+our college calculus course, the
+important thing was what?
+
+That when we wanted to write the
+log of a product, it was
+
+the sum of the logs.
+
+And now the only additional
+fact that we have from the
+
+calculus approach is that the
+derivative of 'log x' with
+
+respect to 'x' was defined
+to be '1 over x'.
+
+By the way, since there is
+a tendency to think of
+
+traditional logarithms when one
+uses the word logarithm,
+
+if we so wanted--
+
+and there's no reason why
+we have to do this--
+
+if we wanted to associate
+a base with
+
+the natural log system--
+
+this is just a little aside, and
+we'll talk about this more
+
+perhaps in the learning
+exercises or in the
+
+supplementary notes
+as need be--
+
+but the idea is this.
+
+Notice that in a traditional
+logarithm system, if the base
+
+is 'b', the base is
+characterized by the fact that
+
+the 'log of 'b to the
+base b'' is 1.
+
+Thus, if we use 'e' to denote
+the base for the natural log,
+
+whatever 'e' is, it must be
+characterized by the fact that
+
+the 'natural log of e' is 1.
+
+And the reason that I put the
+word base in quotation marks
+
+here is that I would like you
+to observe that again, if I
+
+have never heard of the word
+exponent, it still makes sense
+
+to say find the number e
+such that the 'natural
+
+log of e' is 1.
+
+In fact, I can give you two
+interpretations for that
+
+number 'e', and as a byproduct,
+even show you why
+
+the second fundamental theorem
+of integral calculus is as
+
+powerful as it really is.
+
+See, the idea is this.
+
+To find what 'e' is, all we're
+saying is take the curve 'y'
+
+equals 'natural log x'.
+
+Look to see where the
+y-coordinate is 1.
+
+In other words, draw the
+line 'y' equals 1.
+
+Where that line intercepts the
+curve 'y' equals 'log x', that
+
+x-coordinate is 'e'.
+
+In other words, the 'natural log
+of e' must be 1, so this
+
+is geometrically how I would
+locate 'e' using
+
+differential calculus.
+
+If I wanted to use integral
+calculus, notice that the 'log
+
+of e' by definition is what?
+
+The integral from 1 to
+'e', 'dt over t'.
+
+That's the area of
+this region 'R'.
+
+Now what do I want 'e' to be?
+
+I want 'e' to be that number
+that makes this area 1.
+
+In other words, I want the
+'natural log of e' to be 1.
+
+So again, in the same way that
+one can think of pi as being
+
+geometrically constructed,
+notice I can construct 'e'
+
+geometrically, namely
+again what?
+
+I take the curve 'y' equals '1
+over t' from 't' equals 1,
+
+bounded below by the t-axis,
+and I keep shifting over to
+
+the right until the area of this
+region 'R' is exactly 1.
+
+The 't' value that makes this
+area 1 is called 'e'.
+
+And by the way, notice again
+the power of what I mean by
+
+the area approach.
+
+Notice I can start now to
+get estimates on what
+
+'e' must look like.
+
+Let me show you what I'm
+driving at over here.
+
+Let's suppose we take the curve
+'y' equals '1 over t'
+
+from 1 to 2.
+
+Now what do we mean
+by natural log 2?
+
+Natural log 2 is by definition
+the area of this region here.
+
+Now notice that the smallest
+height of this region, since
+
+the curve is 'y' equals '1 over
+t', the smallest height
+
+of this region is 1/2, and the
+tallest height, the highest
+
+height in this region is 1.
+
+Consequently, whatever the area
+of this region is, it's
+
+less than the area of the
+inscribed rectangle--
+
+it's greater than the area of
+the inscribed rectangle, and
+
+less than the area of the
+circumscribed rectangle.
+
+Now notice that both of these
+rectangles have base 1, and
+
+we're going from 1 to 2.
+
+The height of the inscribed
+rectangle is 1/2, therefore
+
+the area of the small
+rectangle is 1/2.
+
+The area of the big rectangle,
+it's a 1 by 1 rectangle, is 1.
+
+And now what we have is that
+whatever the natural log of 2
+
+is, it being the area of this
+region, it must be what?
+
+Less than 1 but greater
+than 1/2.
+
+We also know that whatever
+'e' is, the 'log of
+
+e' is equal to 1.
+
+Well, let's go on a little
+bit further.
+
+What about the log of 4?
+
+The log of 4, natural log of
+4, is the log of 2 squared.
+
+But we've already seen that
+one of the properties of a
+
+logarithmic function is that
+you can bring the exponent
+
+down as a multiplier.
+
+See, 'f of 'x to the n''
+is 'n 'f of x''.
+
+This becomes 2 log 2, and
+because the natural log of 2
+
+is greater than 1/2, twice
+the natural log of 2
+
+is more than 1.
+
+In other words, if log 2 is more
+than 1/2, twice log 2 is
+
+more than 1.
+
+In other words, if we put these
+three lines together, we
+
+have that the natural log of 2
+is less than the 'natural log
+
+of e', which in turn is less
+than the natural log of 4.
+
+By the way, notice that since
+the derivative of 'log x' with
+
+respect to 'x' is '1 over x',
+and that's positive, 'log x'
+
+is a one to one function.
+
+Therefore, if the log of 2 is
+less than the 'log of e' is
+
+less than the log of 4, it
+follows that 2 must be less
+
+than 'e', which in turn
+must be less than 4.
+
+In other words, even with this
+crude approximation of just
+
+inscribing and circumscribing
+rectangles, I can show again
+
+without reference to exponents
+that whatever the number 'e'
+
+is, the number e defined by the
+fact that 'ln of e' is 1,
+
+that number 'e' is some number
+between 2 and 4.
+
+But again, we won't dwell
+on this too long.
+
+What I want to do now is to come
+back to a summary point,
+
+and at the same time,
+lead into the
+
+lecture for next time.
+
+Recall that we began this
+lecture with the problem of
+
+solving the situation where
+the rate of change was
+
+proportional to the
+amount present.
+
+Given 'dm/ dt' equals 'km', we
+separated variables and got
+
+down to the stage where the
+integral of 'dm over m' was
+
+'kt' plus a constant.
+
+And all we did in the rest of
+today's lecture that was at
+
+all different, was we invented
+and constructed the particular
+
+function whose derivative would
+be '1 over m', and which
+
+had the logarithmic property.
+
+In other words, we can now
+say that this is the
+
+answer to the problem.
+
+This problem is explicitly
+solved because the natural log
+
+function can be viewed as
+an area under a curve.
+
+We can construct it
+for each 'm'.
+
+This is then what we
+managed to do.
+
+And by the way, all I'm saying
+now is that since the log is a
+
+one to one function--
+
+see, its derivative is
+always positive--
+
+can't we talk about the
+inverse function?
+
+In other words, notice that
+another way of writing this is
+
+that id 'natural log m' is 'kt'
+plus 'c', 'm' itself must
+
+be the 'inverse log
+of kt' plus 'c'.
+
+And you see, next time what
+we're going to do is to
+
+explore what we mean
+by the inverse log.
+
+At any rate, in summarizing
+today's lecture, to make sure
+
+that we didn't fall victim to
+all the computational details,
+
+notice that all we did was
+physically motivated the
+
+necessity for inventing a
+function whose derivative with
+
+respect to 'x' was '1 over x'.
+
+And from that point on,
+everything else that we did
+
+followed as applications of
+material that came before.
+
+It's in this sense that the
+course now picks up in tempo.
+
+That as we go on now, we're
+going to be able to cover
+
+larger globs of material in one
+sitting, because we will
+
+find, at least for the next
+several lectures, that every
+
+new topic is basically one new
+idea together with all of the
+
+old recipes.
+
+At any rate, until next
+time, goodbye.
+
+ANNOUNCER: Funding for the
+publication of this video was
+
+provided by the Gabriella and
+Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/2jHK2MxGoio.txt b/2jHK2MxGoio.txt
new file mode 100644
index 0000000000000000000000000000000000000000..80760b36f0864dacfc14d643c0978b0ef31d055d
--- /dev/null
+++ b/2jHK2MxGoio.txt
@@ -0,0 +1,1475 @@
+align:start position:0%
+ 
+welcome back to special relativity 820.
+
+ align:start position:0%
+welcome back to special relativity 820.
+ 
+
+ align:start position:0%
+welcome back to special relativity 820.
+after discussing energy and momentum um
+
+ align:start position:0%
+after discussing energy and momentum um
+ 
+
+ align:start position:0%
+after discussing energy and momentum um
+and examples with collisions we now want
+
+ align:start position:0%
+and examples with collisions we now want
+ 
+
+ align:start position:0%
+and examples with collisions we now want
+to talk about forces
+
+ align:start position:0%
+to talk about forces
+ 
+
+ align:start position:0%
+to talk about forces
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we get back to the example of alice
+
+ align:start position:0%
+we get back to the example of alice
+ 
+
+ align:start position:0%
+we get back to the example of alice
+traveling to the center of the galaxy
+
+ align:start position:0%
+traveling to the center of the galaxy
+ 
+
+ align:start position:0%
+traveling to the center of the galaxy
+and asking what does it mean in terms of
+
+ align:start position:0%
+and asking what does it mean in terms of
+ 
+
+ align:start position:0%
+and asking what does it mean in terms of
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we start from newton's second law we
+
+ align:start position:0%
+we start from newton's second law we
+ 
+
+ align:start position:0%
+we start from newton's second law we
+know that a force is a change in
+
+ align:start position:0%
+know that a force is a change in
+ 
+
+ align:start position:0%
+know that a force is a change in
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+we can write this down as
+
+ align:start position:0%
+we can write this down as
+ 
+
+ align:start position:0%
+we can write this down as
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+d dt uh m naught
+
+ align:start position:0%
+d dt uh m naught
+ 
+
+ align:start position:0%
+d dt uh m naught
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+times u over square root 1 minus u
+
+ align:start position:0%
+times u over square root 1 minus u
+ 
+
+ align:start position:0%
+times u over square root 1 minus u
+square over c square
+
+ align:start position:0%
+square over c square
+ 
+
+ align:start position:0%
+square over c square
+or just with a gamma vector
+
+ align:start position:0%
+or just with a gamma vector
+ 
+
+ align:start position:0%
+or just with a gamma vector
+and the thing to consider here is that
+
+ align:start position:0%
+and the thing to consider here is that
+ 
+
+ align:start position:0%
+and the thing to consider here is that
+now the gamma factor
+
+ align:start position:0%
+now the gamma factor
+ 
+
+ align:start position:0%
+now the gamma factor
+and the velocity are actually time
+
+ align:start position:0%
+and the velocity are actually time
+ 
+
+ align:start position:0%
+and the velocity are actually time
+dependent so there's two components to
+
+ align:start position:0%
+dependent so there's two components to
+ 
+
+ align:start position:0%
+dependent so there's two components to
+this we'll come back to this
+
+ align:start position:0%
+this we'll come back to this
+ 
+
+ align:start position:0%
+this we'll come back to this
+the kinetic energy
+
+ align:start position:0%
+the kinetic energy
+ 
+
+ align:start position:0%
+the kinetic energy
+is the work done by an external force
+
+ align:start position:0%
+is the work done by an external force
+ 
+
+ align:start position:0%
+is the work done by an external force
+and you can get to the kinetic energy by
+
+ align:start position:0%
+and you can get to the kinetic energy by
+ 
+
+ align:start position:0%
+and you can get to the kinetic energy by
+just integrating let's say from a
+
+ align:start position:0%
+just integrating let's say from a
+ 
+
+ align:start position:0%
+just integrating let's say from a
+particle which is accelerated by an
+
+ align:start position:0%
+particle which is accelerated by an
+ 
+
+ align:start position:0%
+particle which is accelerated by an
+external force from a velocity zero to
+
+ align:start position:0%
+external force from a velocity zero to
+ 
+
+ align:start position:0%
+external force from a velocity zero to
+some velocity v
+
+ align:start position:0%
+some velocity v
+ 
+
+ align:start position:0%
+some velocity v
+that's the integral um over this over
+
+ align:start position:0%
+that's the integral um over this over
+ 
+
+ align:start position:0%
+that's the integral um over this over
+the path of the particle
+
+ align:start position:0%
+the path of the particle
+ 
+
+ align:start position:0%
+the path of the particle
+of the path of this object times the
+
+ align:start position:0%
+of the path of this object times the
+ 
+
+ align:start position:0%
+of the path of this object times the
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+if you just
+
+ align:start position:0%
+if you just
+ 
+
+ align:start position:0%
+if you just
+assume here uniform
+
+ align:start position:0%
+assume here uniform
+ 
+
+ align:start position:0%
+assume here uniform
+motion in x direction then this
+
+ align:start position:0%
+motion in x direction then this
+ 
+
+ align:start position:0%
+motion in x direction then this
+simplifies to just an f dx
+
+ align:start position:0%
+simplifies to just an f dx
+ 
+
+ align:start position:0%
+simplifies to just an f dx
+okay so as a first activity i want you
+
+ align:start position:0%
+okay so as a first activity i want you
+ 
+
+ align:start position:0%
+okay so as a first activity i want you
+to find the kinetic energy of an object
+
+ align:start position:0%
+to find the kinetic energy of an object
+ 
+
+ align:start position:0%
+to find the kinetic energy of an object
+with velocity v
+
+ align:start position:0%
+with velocity v
+ 
+
+ align:start position:0%
+with velocity v
+and the mass and mass m naught
+
+ align:start position:0%
+and the mass and mass m naught
+ 
+
+ align:start position:0%
+and the mass and mass m naught
+and as a second part i want you to test
+
+ align:start position:0%
+and as a second part i want you to test
+ 
+
+ align:start position:0%
+and as a second part i want you to test
+this result
+
+ align:start position:0%
+this result
+ 
+
+ align:start position:0%
+this result
+for velocities much much smaller than
+
+ align:start position:0%
+for velocities much much smaller than
+ 
+
+ align:start position:0%
+for velocities much much smaller than
+the speed of light where you used to
+
+ align:start position:0%
+the speed of light where you used to
+ 
+
+ align:start position:0%
+the speed of light where you used to
+doing this kind of calculation and
+
+ align:start position:0%
+doing this kind of calculation and
+ 
+
+ align:start position:0%
+doing this kind of calculation and
+you're familiar with the outcome
+
+ align:start position:0%
+you're familiar with the outcome
+ 
+
+ align:start position:0%
+you're familiar with the outcome
+so we just have to integrate just have
+
+ align:start position:0%
+so we just have to integrate just have
+ 
+
+ align:start position:0%
+so we just have to integrate just have
+to integrate so this is a little bit
+
+ align:start position:0%
+to integrate so this is a little bit
+ 
+
+ align:start position:0%
+to integrate so this is a little bit
+involved here
+
+ align:start position:0%
+involved here
+ 
+
+ align:start position:0%
+involved here
+so we have to integrate from zero to v m
+
+ align:start position:0%
+so we have to integrate from zero to v m
+ 
+
+ align:start position:0%
+so we have to integrate from zero to v m
+naught that's our constant you can take
+
+ align:start position:0%
+naught that's our constant you can take
+ 
+
+ align:start position:0%
+naught that's our constant you can take
+that out d dt of this u um
+
+ align:start position:0%
+that out d dt of this u um
+ 
+
+ align:start position:0%
+that out d dt of this u um
+u times gamma dx okay so you find those
+
+ align:start position:0%
+u times gamma dx okay so you find those
+ 
+
+ align:start position:0%
+u times gamma dx okay so you find those
+two components here
+
+ align:start position:0%
+two components here
+ 
+
+ align:start position:0%
+two components here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then we do a trick where you know we
+
+ align:start position:0%
+and then we do a trick where you know we
+ 
+
+ align:start position:0%
+and then we do a trick where you know we
+introduce this du the x
+
+ align:start position:0%
+introduce this du the x
+ 
+
+ align:start position:0%
+introduce this du the x
+the x
+
+ align:start position:0%
+the x
+ 
+
+ align:start position:0%
+the x
+um and then the integral becomes an m
+
+ align:start position:0%
+um and then the integral becomes an m
+ 
+
+ align:start position:0%
+um and then the integral becomes an m
+times udu
+
+ align:start position:0%
+times udu
+ 
+
+ align:start position:0%
+times udu
+over one minus u square over c square
+
+ align:start position:0%
+over one minus u square over c square
+ 
+
+ align:start position:0%
+over one minus u square over c square
+third
+
+ align:start position:0%
+third
+ 
+
+ align:start position:0%
+third
+to the third
+
+ align:start position:0%
+to the third
+ 
+
+ align:start position:0%
+to the third
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+third power half
+
+ align:start position:0%
+third power half
+ 
+
+ align:start position:0%
+third power half
+okay and then you can just look up the
+
+ align:start position:0%
+okay and then you can just look up the
+ 
+
+ align:start position:0%
+okay and then you can just look up the
+integral or work it out not that
+
+ align:start position:0%
+integral or work it out not that
+ 
+
+ align:start position:0%
+integral or work it out not that
+difficult actually but you find that
+
+ align:start position:0%
+difficult actually but you find that
+ 
+
+ align:start position:0%
+difficult actually but you find that
+this is equal to m naught times c square
+
+ align:start position:0%
+this is equal to m naught times c square
+ 
+
+ align:start position:0%
+this is equal to m naught times c square
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+square root 1 minus u square over c
+
+ align:start position:0%
+square root 1 minus u square over c
+ 
+
+ align:start position:0%
+square root 1 minus u square over c
+square which you have to evaluate for
+
+ align:start position:0%
+square which you have to evaluate for
+ 
+
+ align:start position:0%
+square which you have to evaluate for
+velocities v and 0.
+
+ align:start position:0%
+velocities v and 0.
+ 
+
+ align:start position:0%
+velocities v and 0.
+and when you do that you find those two
+
+ align:start position:0%
+and when you do that you find those two
+ 
+
+ align:start position:0%
+and when you do that you find those two
+components here okay the first one is m
+
+ align:start position:0%
+components here okay the first one is m
+ 
+
+ align:start position:0%
+components here okay the first one is m
+naught c square
+
+ align:start position:0%
+naught c square
+ 
+
+ align:start position:0%
+naught c square
+times gamma and the second one is m
+
+ align:start position:0%
+times gamma and the second one is m
+ 
+
+ align:start position:0%
+times gamma and the second one is m
+naught c square
+
+ align:start position:0%
+naught c square
+ 
+
+ align:start position:0%
+naught c square
+so that result is actually not too
+
+ align:start position:0%
+so that result is actually not too
+ 
+
+ align:start position:0%
+so that result is actually not too
+surprising as we saw
+
+ align:start position:0%
+surprising as we saw
+ 
+
+ align:start position:0%
+surprising as we saw
+that we can write the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+m naught c square
+
+ align:start position:0%
+m naught c square
+ 
+
+ align:start position:0%
+m naught c square
+plus k
+
+ align:start position:0%
+plus k
+ 
+
+ align:start position:0%
+plus k
+and what we just calculated here from
+
+ align:start position:0%
+and what we just calculated here from
+ 
+
+ align:start position:0%
+and what we just calculated here from
+this example
+
+ align:start position:0%
+this example
+ 
+
+ align:start position:0%
+this example
+is k
+
+ align:start position:0%
+is k
+ 
+
+ align:start position:0%
+is k
+is equal to energy
+
+ align:start position:0%
+is equal to energy
+ 
+
+ align:start position:0%
+is equal to energy
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+m naught c square
+
+ align:start position:0%
+m naught c square
+ 
+
+ align:start position:0%
+m naught c square
+okay so that result already makes sense
+
+ align:start position:0%
+okay so that result already makes sense
+ 
+
+ align:start position:0%
+okay so that result already makes sense
+in with respect to the discussion we had
+
+ align:start position:0%
+in with respect to the discussion we had
+ 
+
+ align:start position:0%
+in with respect to the discussion we had
+at this point
+
+ align:start position:0%
+at this point
+ 
+
+ align:start position:0%
+at this point
+okay or you can simplify this by saying
+
+ align:start position:0%
+okay or you can simplify this by saying
+ 
+
+ align:start position:0%
+okay or you can simplify this by saying
+the kinetic energy is gamma minus 1
+
+ align:start position:0%
+the kinetic energy is gamma minus 1
+ 
+
+ align:start position:0%
+the kinetic energy is gamma minus 1
+times m naught c square
+
+ align:start position:0%
+times m naught c square
+ 
+
+ align:start position:0%
+times m naught c square
+okay so if we now evaluate this for
+
+ align:start position:0%
+okay so if we now evaluate this for
+ 
+
+ align:start position:0%
+okay so if we now evaluate this for
+small values of of v
+
+ align:start position:0%
+small values of of v
+ 
+
+ align:start position:0%
+small values of of v
+as we did before we find that the
+
+ align:start position:0%
+as we did before we find that the
+ 
+
+ align:start position:0%
+as we did before we find that the
+kinetic energy is one half m naught v
+
+ align:start position:0%
+kinetic energy is one half m naught v
+ 
+
+ align:start position:0%
+kinetic energy is one half m naught v
+square and
+
+ align:start position:0%
+square and
+ 
+
+ align:start position:0%
+square and
+i find it interesting illustrated what
+
+ align:start position:0%
+i find it interesting illustrated what
+ 
+
+ align:start position:0%
+i find it interesting illustrated what
+this means now so if you plot the
+
+ align:start position:0%
+this means now so if you plot the
+ 
+
+ align:start position:0%
+this means now so if you plot the
+kinetic energy of a particle as a
+
+ align:start position:0%
+kinetic energy of a particle as a
+ 
+
+ align:start position:0%
+kinetic energy of a particle as a
+function of its velocity we find that
+
+ align:start position:0%
+function of its velocity we find that
+ 
+
+ align:start position:0%
+function of its velocity we find that
+you know at for small values
+
+ align:start position:0%
+you know at for small values
+ 
+
+ align:start position:0%
+you know at for small values
+those two curves you know basically
+
+ align:start position:0%
+those two curves you know basically
+ 
+
+ align:start position:0%
+those two curves you know basically
+overlap because more values
+
+ align:start position:0%
+overlap because more values
+ 
+
+ align:start position:0%
+overlap because more values
+m naught c squared
+
+ align:start position:0%
+m naught c squared
+ 
+
+ align:start position:0%
+m naught c squared
+times gamma minus one is basically the
+
+ align:start position:0%
+times gamma minus one is basically the
+ 
+
+ align:start position:0%
+times gamma minus one is basically the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+as one half mv square which is
+
+ align:start position:0%
+as one half mv square which is
+ 
+
+ align:start position:0%
+as one half mv square which is
+just derived here from the taylor
+
+ align:start position:0%
+just derived here from the taylor
+ 
+
+ align:start position:0%
+just derived here from the taylor
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+but for larger values this diverges and
+
+ align:start position:0%
+but for larger values this diverges and
+ 
+
+ align:start position:0%
+but for larger values this diverges and
+especially when you get closer to the
+
+ align:start position:0%
+especially when you get closer to the
+ 
+
+ align:start position:0%
+especially when you get closer to the
+speed of light
+
+ align:start position:0%
+speed of light
+ 
+
+ align:start position:0%
+speed of light
+um you know just to get a quantitative
+
+ align:start position:0%
+um you know just to get a quantitative
+ 
+
+ align:start position:0%
+um you know just to get a quantitative
+example i ask you to do another
+
+ align:start position:0%
+example i ask you to do another
+ 
+
+ align:start position:0%
+example i ask you to do another
+calculation here i want you to
+
+ align:start position:0%
+calculation here i want you to
+ 
+
+ align:start position:0%
+calculation here i want you to
+reinvestigate alice's journey to the
+
+ align:start position:0%
+reinvestigate alice's journey to the
+ 
+
+ align:start position:0%
+reinvestigate alice's journey to the
+center of the galaxy where she has a
+
+ align:start position:0%
+center of the galaxy where she has a
+ 
+
+ align:start position:0%
+center of the galaxy where she has a
+spacecraft which moves with a gamma
+
+ align:start position:0%
+spacecraft which moves with a gamma
+ 
+
+ align:start position:0%
+spacecraft which moves with a gamma
+factor of 15 000
+
+ align:start position:0%
+factor of 15 000
+ 
+
+ align:start position:0%
+factor of 15 000
+an acceleration of 10 meters per second
+
+ align:start position:0%
+an acceleration of 10 meters per second
+ 
+
+ align:start position:0%
+an acceleration of 10 meters per second
+square and the mass of the spacecraft
+
+ align:start position:0%
+square and the mass of the spacecraft
+ 
+
+ align:start position:0%
+square and the mass of the spacecraft
+that says 10 000 metric tons or 10 000
+
+ align:start position:0%
+that says 10 000 metric tons or 10 000
+ 
+
+ align:start position:0%
+that says 10 000 metric tons or 10 000
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+sorry 100 metric tons or 100 000
+
+ align:start position:0%
+sorry 100 metric tons or 100 000
+ 
+
+ align:start position:0%
+sorry 100 metric tons or 100 000
+kilograms so compare the kinetic energy
+
+ align:start position:0%
+kilograms so compare the kinetic energy
+ 
+
+ align:start position:0%
+kilograms so compare the kinetic energy
+using newtonian mechanics or special
+
+ align:start position:0%
+using newtonian mechanics or special
+ 
+
+ align:start position:0%
+using newtonian mechanics or special
+military and you find that the
+
+ align:start position:0%
+military and you find that the
+ 
+
+ align:start position:0%
+military and you find that the
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+is astonishingly large so if you just
+
+ align:start position:0%
+is astonishingly large so if you just
+ 
+
+ align:start position:0%
+is astonishingly large so if you just
+work this out one half m
+
+ align:start position:0%
+work this out one half m
+ 
+
+ align:start position:0%
+work this out one half m
+c square we can just use c square here
+
+ align:start position:0%
+c square we can just use c square here
+ 
+
+ align:start position:0%
+c square we can just use c square here
+because the velocity is basically
+
+ align:start position:0%
+because the velocity is basically
+ 
+
+ align:start position:0%
+because the velocity is basically
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+5 times 10 to the
+
+ align:start position:0%
+5 times 10 to the
+ 
+
+ align:start position:0%
+5 times 10 to the
+22 kilograms meter square over second
+
+ align:start position:0%
+22 kilograms meter square over second
+ 
+
+ align:start position:0%
+22 kilograms meter square over second
+second square
+
+ align:start position:0%
+second square
+ 
+
+ align:start position:0%
+second square
+and in the relativistic terms
+
+ align:start position:0%
+and in the relativistic terms
+ 
+
+ align:start position:0%
+and in the relativistic terms
+the answer is 30 000 times larger
+
+ align:start position:0%
+the answer is 30 000 times larger
+ 
+
+ align:start position:0%
+the answer is 30 000 times larger
+so 30 000 times larger than the
+
+ align:start position:0%
+so 30 000 times larger than the
+ 
+
+ align:start position:0%
+so 30 000 times larger than the
+classical k so the huge difference
+
+ align:start position:0%
+classical k so the huge difference
+ 
+
+ align:start position:0%
+classical k so the huge difference
+between the classical evaluation and the
+
+ align:start position:0%
+between the classical evaluation and the
+ 
+
+ align:start position:0%
+between the classical evaluation and the
+evaluation and the special relativity
+
+ align:start position:0%
+evaluation and the special relativity
+ 
+
+ align:start position:0%
+evaluation and the special relativity
+one more uh word on m
+
+ align:start position:0%
+one more uh word on m
+ 
+
+ align:start position:0%
+one more uh word on m
+f equal m a
+
+ align:start position:0%
+f equal m a
+ 
+
+ align:start position:0%
+f equal m a
+uh the question is how does this
+
+ align:start position:0%
+uh the question is how does this
+ 
+
+ align:start position:0%
+uh the question is how does this
+transform on a learner's transformation
+
+ align:start position:0%
+transform on a learner's transformation
+ 
+
+ align:start position:0%
+transform on a learner's transformation
+is something we already halfway figured
+
+ align:start position:0%
+is something we already halfway figured
+ 
+
+ align:start position:0%
+is something we already halfway figured
+out so here you basically want to see
+
+ align:start position:0%
+out so here you basically want to see
+ 
+
+ align:start position:0%
+out so here you basically want to see
+how a
+
+ align:start position:0%
+how a
+ 
+
+ align:start position:0%
+how a
+uh transforms under loans transformation
+
+ align:start position:0%
+uh transforms under loans transformation
+ 
+
+ align:start position:0%
+uh transforms under loans transformation
+we have started the discussion by saying
+
+ align:start position:0%
+we have started the discussion by saying
+ 
+
+ align:start position:0%
+we have started the discussion by saying
+you know in galilean transformations
+
+ align:start position:0%
+you know in galilean transformations
+ 
+
+ align:start position:0%
+you know in galilean transformations
+acceleration is invariant
+
+ align:start position:0%
+acceleration is invariant
+ 
+
+ align:start position:0%
+acceleration is invariant
+while endurance transformation that's
+
+ align:start position:0%
+while endurance transformation that's
+ 
+
+ align:start position:0%
+while endurance transformation that's
+not the case but if you investigate
+
+ align:start position:0%
+not the case but if you investigate
+ 
+
+ align:start position:0%
+not the case but if you investigate
+again the second law of uh of physics
+
+ align:start position:0%
+again the second law of uh of physics
+ 
+
+ align:start position:0%
+again the second law of uh of physics
+and the force is a change in momentum
+
+ align:start position:0%
+and the force is a change in momentum
+ 
+
+ align:start position:0%
+and the force is a change in momentum
+you find that you get those two
+
+ align:start position:0%
+you find that you get those two
+ 
+
+ align:start position:0%
+you find that you get those two
+components here
+
+ align:start position:0%
+components here
+ 
+
+ align:start position:0%
+components here
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+parallel to the acceleration so m times
+
+ align:start position:0%
+parallel to the acceleration so m times
+ 
+
+ align:start position:0%
+parallel to the acceleration so m times
+gamma a
+
+ align:start position:0%
+gamma a
+ 
+
+ align:start position:0%
+gamma a
+but the second one is not the second one
+
+ align:start position:0%
+but the second one is not the second one
+ 
+
+ align:start position:0%
+but the second one is not the second one
+is m naught times u
+
+ align:start position:0%
+is m naught times u
+ 
+
+ align:start position:0%
+is m naught times u
+times the change in time of the gamma
+
+ align:start position:0%
+times the change in time of the gamma
+ 
+
+ align:start position:0%
+times the change in time of the gamma
+factor and that's not parallel
+
+ align:start position:0%
+factor and that's not parallel
+ 
+
+ align:start position:0%
+factor and that's not parallel
+to f or to a
+
+ align:start position:0%
+to f or to a
+ 
+
+ align:start position:0%
+to f or to a
+and so you find that
+
+ align:start position:0%
+and so you find that
+ 
+
+ align:start position:0%
+and so you find that
+there's two the new vector the new force
+
+ align:start position:0%
+there's two the new vector the new force
+ 
+
+ align:start position:0%
+there's two the new vector the new force
+of a particle is not parallel to the
+
+ align:start position:0%
+of a particle is not parallel to the
+ 
+
+ align:start position:0%
+of a particle is not parallel to the
+acceleration anymore that's kind of
+
+ align:start position:0%
+acceleration anymore that's kind of
+ 
+
+ align:start position:0%
+acceleration anymore that's kind of
+content to
+
+ align:start position:0%
+content to
+ 
+
+ align:start position:0%
+content to
+content
\ No newline at end of file
diff --git a/3gxNrc_EEN8.txt b/3gxNrc_EEN8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2832b17b47503818fe8e338769203b91e204a04a
--- /dev/null
+++ b/3gxNrc_EEN8.txt
@@ -0,0 +1,3128 @@
+align:start position:0%
+ 
+on the evening of August 5th 2012
+
+ align:start position:0%
+on the evening of August 5th 2012
+ 
+
+ align:start position:0%
+on the evening of August 5th 2012
+Pacific Daylight Time NASA's Mars Rover
+
+ align:start position:0%
+Pacific Daylight Time NASA's Mars Rover
+ 
+
+ align:start position:0%
+Pacific Daylight Time NASA's Mars Rover
+named curiosity entered Mars atmosphere
+
+ align:start position:0%
+named curiosity entered Mars atmosphere
+ 
+
+ align:start position:0%
+named curiosity entered Mars atmosphere
+at 20,000 km per hour drag slowed it
+
+ align:start position:0%
+at 20,000 km per hour drag slowed it
+ 
+
+ align:start position:0%
+at 20,000 km per hour drag slowed it
+down to around 1,600 km hour at which
+
+ align:start position:0%
+down to around 1,600 km hour at which
+ 
+
+ align:start position:0%
+down to around 1,600 km hour at which
+point a parachute opened this parachute
+
+ align:start position:0%
+point a parachute opened this parachute
+ 
+
+ align:start position:0%
+point a parachute opened this parachute
+slowed the Rover more to about 320 kmph
+
+ align:start position:0%
+slowed the Rover more to about 320 kmph
+ 
+
+ align:start position:0%
+slowed the Rover more to about 320 kmph
+or 90
+
+ align:start position:0%
+or 90
+ 
+
+ align:start position:0%
+or 90
+m/s finally after Rockets decelerated it
+
+ align:start position:0%
+m/s finally after Rockets decelerated it
+ 
+
+ align:start position:0%
+m/s finally after Rockets decelerated it
+completely the Rover was lower to the
+
+ align:start position:0%
+completely the Rover was lower to the
+ 
+
+ align:start position:0%
+completely the Rover was lower to the
+surface of Mars every step of this dance
+
+ align:start position:0%
+surface of Mars every step of this dance
+ 
+
+ align:start position:0%
+surface of Mars every step of this dance
+was carefully choreographed and
+
+ align:start position:0%
+was carefully choreographed and
+ 
+
+ align:start position:0%
+was carefully choreographed and
+rehearsed in many experiments here on
+
+ align:start position:0%
+rehearsed in many experiments here on
+ 
+
+ align:start position:0%
+rehearsed in many experiments here on
+Earth but how could NASA Engineers be
+
+ align:start position:0%
+Earth but how could NASA Engineers be
+ 
+
+ align:start position:0%
+Earth but how could NASA Engineers be
+sure that their designs would work on a
+
+ align:start position:0%
+sure that their designs would work on a
+ 
+
+ align:start position:0%
+sure that their designs would work on a
+totally different planet the answer is a
+
+ align:start position:0%
+totally different planet the answer is a
+ 
+
+ align:start position:0%
+totally different planet the answer is a
+problem solving method called
+
+ align:start position:0%
+problem solving method called
+ 
+
+ align:start position:0%
+problem solving method called
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis this video is part of the
+
+ align:start position:0%
+analysis this video is part of the
+ 
+
+ align:start position:0%
+analysis this video is part of the
+problem solving video
+
+ align:start position:0%
+problem solving video
+ 
+
+ align:start position:0%
+problem solving video
+series problem solving skills in in
+
+ align:start position:0%
+series problem solving skills in in
+ 
+
+ align:start position:0%
+series problem solving skills in in
+combination with an understanding of the
+
+ align:start position:0%
+combination with an understanding of the
+ 
+
+ align:start position:0%
+combination with an understanding of the
+natural and human-made world are
+
+ align:start position:0%
+natural and human-made world are
+ 
+
+ align:start position:0%
+natural and human-made world are
+critical to the design and optimization
+
+ align:start position:0%
+critical to the design and optimization
+ 
+
+ align:start position:0%
+critical to the design and optimization
+of systems and
+
+ align:start position:0%
+of systems and
+ 
+
+ align:start position:0%
+of systems and
+processes hi my name is Ken Cameron and
+
+ align:start position:0%
+processes hi my name is Ken Cameron and
+ 
+
+ align:start position:0%
+processes hi my name is Ken Cameron and
+I'm a professor of mechanical
+
+ align:start position:0%
+I'm a professor of mechanical
+ 
+
+ align:start position:0%
+I'm a professor of mechanical
+engineering at
+
+ align:start position:0%
+engineering at
+ 
+
+ align:start position:0%
+engineering at
+MIT dimensional analysis is a powerful
+
+ align:start position:0%
+MIT dimensional analysis is a powerful
+ 
+
+ align:start position:0%
+MIT dimensional analysis is a powerful
+tool I use it Nasa uses it and you will
+
+ align:start position:0%
+tool I use it Nasa uses it and you will
+ 
+
+ align:start position:0%
+tool I use it Nasa uses it and you will
+too before watching this video you
+
+ align:start position:0%
+too before watching this video you
+ 
+
+ align:start position:0%
+too before watching this video you
+should be familiar with unit analysis
+
+ align:start position:0%
+should be familiar with unit analysis
+ 
+
+ align:start position:0%
+should be familiar with unit analysis
+and understand the difference between
+
+ align:start position:0%
+and understand the difference between
+ 
+
+ align:start position:0%
+and understand the difference between
+dependent and independent variables by
+
+ align:start position:0%
+dependent and independent variables by
+ 
+
+ align:start position:0%
+dependent and independent variables by
+the end of this video you will be able
+
+ align:start position:0%
+the end of this video you will be able
+ 
+
+ align:start position:0%
+the end of this video you will be able
+to use dimensional analysis to estimate
+
+ align:start position:0%
+to use dimensional analysis to estimate
+ 
+
+ align:start position:0%
+to use dimensional analysis to estimate
+the size of a parachute canopy that can
+
+ align:start position:0%
+the size of a parachute canopy that can
+ 
+
+ align:start position:0%
+the size of a parachute canopy that can
+slow the Rover down to 90 m/s on its
+
+ align:start position:0%
+slow the Rover down to 90 m/s on its
+ 
+
+ align:start position:0%
+slow the Rover down to 90 m/s on its
+descent to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mars before we talk about dimensional
+
+ align:start position:0%
+Mars before we talk about dimensional
+ 
+
+ align:start position:0%
+Mars before we talk about dimensional
+analysis we need to know what dimension
+
+ align:start position:0%
+analysis we need to know what dimension
+ 
+
+ align:start position:0%
+analysis we need to know what dimension
+is dimensions and units are related but
+
+ align:start position:0%
+is dimensions and units are related but
+ 
+
+ align:start position:0%
+is dimensions and units are related but
+different concepts physical quantities
+
+ align:start position:0%
+different concepts physical quantities
+ 
+
+ align:start position:0%
+different concepts physical quantities
+are measured in units the dimension of
+
+ align:start position:0%
+are measured in units the dimension of
+ 
+
+ align:start position:0%
+are measured in units the dimension of
+the physical quantity is independent of
+
+ align:start position:0%
+the physical quantity is independent of
+ 
+
+ align:start position:0%
+the physical quantity is independent of
+the particular unit chosen for example
+
+ align:start position:0%
+the particular unit chosen for example
+ 
+
+ align:start position:0%
+the particular unit chosen for example
+both gr and kilograms are units but they
+
+ align:start position:0%
+both gr and kilograms are units but they
+ 
+
+ align:start position:0%
+both gr and kilograms are units but they
+are units of mass and mass is what we'll
+
+ align:start position:0%
+are units of mass and mass is what we'll
+ 
+
+ align:start position:0%
+are units of mass and mass is what we'll
+call the dimension there are five
+
+ align:start position:0%
+call the dimension there are five
+ 
+
+ align:start position:0%
+call the dimension there are five
+fundamental Dimensions that we commonly
+
+ align:start position:0%
+fundamental Dimensions that we commonly
+ 
+
+ align:start position:0%
+fundamental Dimensions that we commonly
+deal with length mass time temperature
+
+ align:start position:0%
+deal with length mass time temperature
+ 
+
+ align:start position:0%
+deal with length mass time temperature
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+charge all other dimensions are obtained
+
+ align:start position:0%
+charge all other dimensions are obtained
+ 
+
+ align:start position:0%
+charge all other dimensions are obtained
+by taking products and powers of these
+
+ align:start position:0%
+by taking products and powers of these
+ 
+
+ align:start position:0%
+by taking products and powers of these
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+dimensions in this video we'll be
+
+ align:start position:0%
+dimensions in this video we'll be
+ 
+
+ align:start position:0%
+dimensions in this video we'll be
+dealing with length which we denote by
+
+ align:start position:0%
+dealing with length which we denote by
+ 
+
+ align:start position:0%
+dealing with length which we denote by
+the letter L Mass denoted by m and time
+
+ align:start position:0%
+the letter L Mass denoted by m and time
+ 
+
+ align:start position:0%
+the letter L Mass denoted by m and time
+T for example no matter how you measure
+
+ align:start position:0%
+T for example no matter how you measure
+ 
+
+ align:start position:0%
+T for example no matter how you measure
+the physical quantity velocity it has
+
+ align:start position:0%
+the physical quantity velocity it has
+ 
+
+ align:start position:0%
+the physical quantity velocity it has
+the dimension which we denote with
+
+ align:start position:0%
+the dimension which we denote with
+ 
+
+ align:start position:0%
+the dimension which we denote with
+square brackets of length ID time or
+
+ align:start position:0%
+square brackets of length ID time or
+ 
+
+ align:start position:0%
+square brackets of length ID time or
+length time time to the 1
+
+ align:start position:0%
+length time time to the 1
+ 
+
+ align:start position:0%
+length time time to the 1
+Power Pause the video here and determine
+
+ align:start position:0%
+Power Pause the video here and determine
+ 
+
+ align:start position:0%
+Power Pause the video here and determine
+the dimension of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy has Dimension mass time length
+
+ align:start position:0%
+energy has Dimension mass time length
+ 
+
+ align:start position:0%
+energy has Dimension mass time length
+squared over time
+
+ align:start position:0%
+squared over time
+ 
+
+ align:start position:0%
+squared over time
+squared okay great so what's the big
+
+ align:start position:0%
+squared okay great so what's the big
+ 
+
+ align:start position:0%
+squared okay great so what's the big
+deal how is this
+
+ align:start position:0%
+deal how is this
+ 
+
+ align:start position:0%
+deal how is this
+useful remember NASA's
+
+ align:start position:0%
+useful remember NASA's
+ 
+
+ align:start position:0%
+useful remember NASA's
+rover part of the landing sequence calls
+
+ align:start position:0%
+rover part of the landing sequence calls
+ 
+
+ align:start position:0%
+rover part of the landing sequence calls
+for a parachute to slow the vehicle down
+
+ align:start position:0%
+for a parachute to slow the vehicle down
+ 
+
+ align:start position:0%
+for a parachute to slow the vehicle down
+suppose it is our job to design the
+
+ align:start position:0%
+suppose it is our job to design the
+ 
+
+ align:start position:0%
+suppose it is our job to design the
+parachute to slow the Rover to exactly
+
+ align:start position:0%
+parachute to slow the Rover to exactly
+ 
+
+ align:start position:0%
+parachute to slow the Rover to exactly
+90 m/ second
+
+ align:start position:0%
+90 m/ second
+ 
+
+ align:start position:0%
+90 m/ second
+the terminal velocity of the Rover
+
+ align:start position:0%
+the terminal velocity of the Rover
+ 
+
+ align:start position:0%
+the terminal velocity of the Rover
+depends on the mass of the Rover itself
+
+ align:start position:0%
+depends on the mass of the Rover itself
+ 
+
+ align:start position:0%
+depends on the mass of the Rover itself
+and its heat shield and several
+
+ align:start position:0%
+and its heat shield and several
+ 
+
+ align:start position:0%
+and its heat shield and several
+different variables related to the
+
+ align:start position:0%
+different variables related to the
+ 
+
+ align:start position:0%
+different variables related to the
+parachute design the material of the
+
+ align:start position:0%
+parachute design the material of the
+ 
+
+ align:start position:0%
+parachute design the material of the
+canopy the diameter of the hemispherical
+
+ align:start position:0%
+canopy the diameter of the hemispherical
+ 
+
+ align:start position:0%
+canopy the diameter of the hemispherical
+parachute canopy the number of
+
+ align:start position:0%
+parachute canopy the number of
+ 
+
+ align:start position:0%
+parachute canopy the number of
+suspension lines
+
+ align:start position:0%
+suspension lines
+ 
+
+ align:start position:0%
+suspension lines
+etc for Simplicity let's suppose that
+
+ align:start position:0%
+etc for Simplicity let's suppose that
+ 
+
+ align:start position:0%
+etc for Simplicity let's suppose that
+all parachute parameters other than the
+
+ align:start position:0%
+all parachute parameters other than the
+ 
+
+ align:start position:0%
+all parachute parameters other than the
+diameter of the canopy have already been
+
+ align:start position:0%
+diameter of the canopy have already been
+ 
+
+ align:start position:0%
+diameter of the canopy have already been
+determined our goal is to find the
+
+ align:start position:0%
+determined our goal is to find the
+ 
+
+ align:start position:0%
+determined our goal is to find the
+canopy diameter that is as small as
+
+ align:start position:0%
+canopy diameter that is as small as
+ 
+
+ align:start position:0%
+canopy diameter that is as small as
+possible but will correspond to the
+
+ align:start position:0%
+possible but will correspond to the
+ 
+
+ align:start position:0%
+possible but will correspond to the
+desired terminal velocity of 90
+
+ align:start position:0%
+desired terminal velocity of 90
+ 
+
+ align:start position:0%
+desired terminal velocity of 90
+m/s clearly we can't test our designs on
+
+ align:start position:0%
+m/s clearly we can't test our designs on
+ 
+
+ align:start position:0%
+m/s clearly we can't test our designs on
+Mars the question is how can we get
+
+ align:start position:0%
+Mars the question is how can we get
+ 
+
+ align:start position:0%
+Mars the question is how can we get
+meaningful data here on Earth that will
+
+ align:start position:0%
+meaningful data here on Earth that will
+ 
+
+ align:start position:0%
+meaningful data here on Earth that will
+allow us to appropriately size the
+
+ align:start position:0%
+allow us to appropriately size the
+ 
+
+ align:start position:0%
+allow us to appropriately size the
+parachute for use on
+
+ align:start position:0%
+parachute for use on
+ 
+
+ align:start position:0%
+parachute for use on
+Mars how do we predict the behavior of a
+
+ align:start position:0%
+Mars how do we predict the behavior of a
+ 
+
+ align:start position:0%
+Mars how do we predict the behavior of a
+parachute on Mars based on an earth
+
+ align:start position:0%
+parachute on Mars based on an earth
+ 
+
+ align:start position:0%
+parachute on Mars based on an earth
+experiment and what variables do we need
+
+ align:start position:0%
+experiment and what variables do we need
+ 
+
+ align:start position:0%
+experiment and what variables do we need
+to consider in designing our experiment
+
+ align:start position:0%
+to consider in designing our experiment
+ 
+
+ align:start position:0%
+to consider in designing our experiment
+on Earth
+
+ align:start position:0%
+on Earth
+ 
+
+ align:start position:0%
+on Earth
+this is where a problemsolving method
+
+ align:start position:0%
+this is where a problemsolving method
+ 
+
+ align:start position:0%
+this is where a problemsolving method
+called dimensional analysis can help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us before we get started we must first
+
+ align:start position:0%
+us before we get started we must first
+ 
+
+ align:start position:0%
+us before we get started we must first
+determine what the dependent and
+
+ align:start position:0%
+determine what the dependent and
+ 
+
+ align:start position:0%
+determine what the dependent and
+independent variables are in our
+
+ align:start position:0%
+independent variables are in our
+ 
+
+ align:start position:0%
+independent variables are in our
+system the dependent variable is
+
+ align:start position:0%
+system the dependent variable is
+ 
+
+ align:start position:0%
+system the dependent variable is
+terminal velocity this is the quantity
+
+ align:start position:0%
+terminal velocity this is the quantity
+ 
+
+ align:start position:0%
+terminal velocity this is the quantity
+that we wish to constrain by our
+
+ align:start position:0%
+that we wish to constrain by our
+ 
+
+ align:start position:0%
+that we wish to constrain by our
+parachute
+
+ align:start position:0%
+parachute
+ 
+
+ align:start position:0%
+parachute
+design so what variables affect the
+
+ align:start position:0%
+design so what variables affect the
+ 
+
+ align:start position:0%
+design so what variables affect the
+terminal velocity of the parachute in
+
+ align:start position:0%
+terminal velocity of the parachute in
+ 
+
+ align:start position:0%
+terminal velocity of the parachute in
+the Rover
+
+ align:start position:0%
+the Rover
+ 
+
+ align:start position:0%
+the Rover
+system the diameter of the parachute
+
+ align:start position:0%
+system the diameter of the parachute
+ 
+
+ align:start position:0%
+system the diameter of the parachute
+canopy is one such independent variable
+
+ align:start position:0%
+canopy is one such independent variable
+ 
+
+ align:start position:0%
+canopy is one such independent variable
+take a moment to pause the video and
+
+ align:start position:0%
+take a moment to pause the video and
+ 
+
+ align:start position:0%
+take a moment to pause the video and
+identify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+others okay here's our list canopy
+
+ align:start position:0%
+others okay here's our list canopy
+ 
+
+ align:start position:0%
+others okay here's our list canopy
+diameter mass of the Rover we assume the
+
+ align:start position:0%
+diameter mass of the Rover we assume the
+ 
+
+ align:start position:0%
+diameter mass of the Rover we assume the
+mass of the parachute to be
+
+ align:start position:0%
+mass of the parachute to be
+ 
+
+ align:start position:0%
+mass of the parachute to be
+negligible acceleration due to gravity
+
+ align:start position:0%
+negligible acceleration due to gravity
+ 
+
+ align:start position:0%
+negligible acceleration due to gravity
+and the density and viscosity of the
+
+ align:start position:0%
+and the density and viscosity of the
+ 
+
+ align:start position:0%
+and the density and viscosity of the
+atmosphere for this problem we can
+
+ align:start position:0%
+atmosphere for this problem we can
+ 
+
+ align:start position:0%
+atmosphere for this problem we can
+assume that the dependence of the
+
+ align:start position:0%
+assume that the dependence of the
+ 
+
+ align:start position:0%
+assume that the dependence of the
+terminal velocity on atmospheric
+
+ align:start position:0%
+terminal velocity on atmospheric
+ 
+
+ align:start position:0%
+terminal velocity on atmospheric
+viscosity is negligible because the
+
+ align:start position:0%
+viscosity is negligible because the
+ 
+
+ align:start position:0%
+viscosity is negligible because the
+atmosphere on Mars like the atmosphere
+
+ align:start position:0%
+atmosphere on Mars like the atmosphere
+ 
+
+ align:start position:0%
+atmosphere on Mars like the atmosphere
+on Earth is not very
+
+ align:start position:0%
+on Earth is not very
+ 
+
+ align:start position:0%
+on Earth is not very
+viscous if we wanted to derive a
+
+ align:start position:0%
+viscous if we wanted to derive a
+ 
+
+ align:start position:0%
+viscous if we wanted to derive a
+functional relationship that would work
+
+ align:start position:0%
+functional relationship that would work
+ 
+
+ align:start position:0%
+functional relationship that would work
+for example underwater it would be
+
+ align:start position:0%
+for example underwater it would be
+ 
+
+ align:start position:0%
+for example underwater it would be
+important that we include viscosity as
+
+ align:start position:0%
+important that we include viscosity as
+ 
+
+ align:start position:0%
+important that we include viscosity as
+an independent
+
+ align:start position:0%
+an independent
+ 
+
+ align:start position:0%
+an independent
+variable why didn't we include the
+
+ align:start position:0%
+variable why didn't we include the
+ 
+
+ align:start position:0%
+variable why didn't we include the
+surface area of the parachute canopy in
+
+ align:start position:0%
+surface area of the parachute canopy in
+ 
+
+ align:start position:0%
+surface area of the parachute canopy in
+our list of independent
+
+ align:start position:0%
+our list of independent
+ 
+
+ align:start position:0%
+our list of independent
+variables pause the video and take a
+
+ align:start position:0%
+variables pause the video and take a
+ 
+
+ align:start position:0%
+variables pause the video and take a
+moment to discuss with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classmate we didn't include the surface
+
+ align:start position:0%
+classmate we didn't include the surface
+ 
+
+ align:start position:0%
+classmate we didn't include the surface
+area of the canopy because it is not
+
+ align:start position:0%
+area of the canopy because it is not
+ 
+
+ align:start position:0%
+area of the canopy because it is not
+independent from the diameter of the
+
+ align:start position:0%
+independent from the diameter of the
+ 
+
+ align:start position:0%
+independent from the diameter of the
+canopy in fact we can determine the area
+
+ align:start position:0%
+canopy in fact we can determine the area
+ 
+
+ align:start position:0%
+canopy in fact we can determine the area
+as a function of diameter so we don't
+
+ align:start position:0%
+as a function of diameter so we don't
+ 
+
+ align:start position:0%
+as a function of diameter so we don't
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+both question could we use the surface
+
+ align:start position:0%
+both question could we use the surface
+ 
+
+ align:start position:0%
+both question could we use the surface
+area instead of the diameter absolutely
+
+ align:start position:0%
+area instead of the diameter absolutely
+ 
+
+ align:start position:0%
+area instead of the diameter absolutely
+we need the variables to be independent
+
+ align:start position:0%
+we need the variables to be independent
+ 
+
+ align:start position:0%
+we need the variables to be independent
+but it doesn't matter which variables we
+
+ align:start position:0%
+but it doesn't matter which variables we
+ 
+
+ align:start position:0%
+but it doesn't matter which variables we
+use the key is to have identified all of
+
+ align:start position:0%
+use the key is to have identified all of
+ 
+
+ align:start position:0%
+use the key is to have identified all of
+the correct variables to begin with this
+
+ align:start position:0%
+the correct variables to begin with this
+ 
+
+ align:start position:0%
+the correct variables to begin with this
+is where human error can come into play
+
+ align:start position:0%
+is where human error can come into play
+ 
+
+ align:start position:0%
+is where human error can come into play
+if our list of variables isn't
+
+ align:start position:0%
+if our list of variables isn't
+ 
+
+ align:start position:0%
+if our list of variables isn't
+exhaustive the relationship we develop
+
+ align:start position:0%
+exhaustive the relationship we develop
+ 
+
+ align:start position:0%
+exhaustive the relationship we develop
+through dimensional analysis may not be
+
+ align:start position:0%
+through dimensional analysis may not be
+ 
+
+ align:start position:0%
+through dimensional analysis may not be
+correct once we have the full list of
+
+ align:start position:0%
+correct once we have the full list of
+ 
+
+ align:start position:0%
+correct once we have the full list of
+independent variables we can express the
+
+ align:start position:0%
+independent variables we can express the
+ 
+
+ align:start position:0%
+independent variables we can express the
+terminal velocity as some function of
+
+ align:start position:0%
+terminal velocity as some function of
+ 
+
+ align:start position:0%
+terminal velocity as some function of
+these independent variables
+
+ align:start position:0%
+these independent variables
+ 
+
+ align:start position:0%
+these independent variables
+in order to find the function that
+
+ align:start position:0%
+in order to find the function that
+ 
+
+ align:start position:0%
+in order to find the function that
+describes the relationship we need to do
+
+ align:start position:0%
+describes the relationship we need to do
+ 
+
+ align:start position:0%
+describes the relationship we need to do
+several experiments involving four
+
+ align:start position:0%
+several experiments involving four
+ 
+
+ align:start position:0%
+several experiments involving four
+independent variables and fit the
+
+ align:start position:0%
+independent variables and fit the
+ 
+
+ align:start position:0%
+independent variables and fit the
+data that's a lot of work especially
+
+ align:start position:0%
+data that's a lot of work especially
+ 
+
+ align:start position:0%
+data that's a lot of work especially
+because we don't know what the function
+
+ align:start position:0%
+because we don't know what the function
+ 
+
+ align:start position:0%
+because we don't know what the function
+might look
+
+ align:start position:0%
+might look
+ 
+
+ align:start position:0%
+might look
+like but whenever you have an equation
+
+ align:start position:0%
+like but whenever you have an equation
+ 
+
+ align:start position:0%
+like but whenever you have an equation
+all terms in the equations must have the
+
+ align:start position:0%
+all terms in the equations must have the
+ 
+
+ align:start position:0%
+all terms in the equations must have the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+Dimension multiplying two terms
+
+ align:start position:0%
+Dimension multiplying two terms
+ 
+
+ align:start position:0%
+Dimension multiplying two terms
+multiplies the
+
+ align:start position:0%
+multiplies the
+ 
+
+ align:start position:0%
+multiplies the
+dimensions this restricts the possible
+
+ align:start position:0%
+dimensions this restricts the possible
+ 
+
+ align:start position:0%
+dimensions this restricts the possible
+form that a function describing the
+
+ align:start position:0%
+form that a function describing the
+ 
+
+ align:start position:0%
+form that a function describing the
+terminal velocity in terms of our four
+
+ align:start position:0%
+terminal velocity in terms of our four
+ 
+
+ align:start position:0%
+terminal velocity in terms of our four
+other variables can take because the
+
+ align:start position:0%
+other variables can take because the
+ 
+
+ align:start position:0%
+other variables can take because the
+function must combine the variables in
+
+ align:start position:0%
+function must combine the variables in
+ 
+
+ align:start position:0%
+function must combine the variables in
+some way that has the same Dimension as
+
+ align:start position:0%
+some way that has the same Dimension as
+ 
+
+ align:start position:0%
+some way that has the same Dimension as
+velocity and many functions exponential
+
+ align:start position:0%
+velocity and many functions exponential
+ 
+
+ align:start position:0%
+velocity and many functions exponential
+logarithmic
+
+ align:start position:0%
+logarithmic
+ 
+
+ align:start position:0%
+logarithmic
+trigonometric cannot have input
+
+ align:start position:0%
+trigonometric cannot have input
+ 
+
+ align:start position:0%
+trigonometric cannot have input
+variables that have Dimension what would
+
+ align:start position:0%
+variables that have Dimension what would
+ 
+
+ align:start position:0%
+variables that have Dimension what would
+e to the 1 kilogram mean what units
+
+ align:start position:0%
+e to the 1 kilogram mean what units
+ 
+
+ align:start position:0%
+e to the 1 kilogram mean what units
+could it possibly
+
+ align:start position:0%
+could it possibly
+ 
+
+ align:start position:0%
+could it possibly
+have where we're going to show you a
+
+ align:start position:0%
+have where we're going to show you a
+ 
+
+ align:start position:0%
+have where we're going to show you a
+problem solving method that will allow
+
+ align:start position:0%
+problem solving method that will allow
+ 
+
+ align:start position:0%
+problem solving method that will allow
+you to find the most general form of
+
+ align:start position:0%
+you to find the most general form of
+ 
+
+ align:start position:0%
+you to find the most general form of
+such a function this method is called
+
+ align:start position:0%
+such a function this method is called
+ 
+
+ align:start position:0%
+such a function this method is called
+dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis We Begin this process by
+
+ align:start position:0%
+analysis We Begin this process by
+ 
+
+ align:start position:0%
+analysis We Begin this process by
+creating dimensionless versions of the
+
+ align:start position:0%
+creating dimensionless versions of the
+ 
+
+ align:start position:0%
+creating dimensionless versions of the
+variables in our
+
+ align:start position:0%
+variables in our
+ 
+
+ align:start position:0%
+variables in our
+system we create these dimensionless
+
+ align:start position:0%
+system we create these dimensionless
+ 
+
+ align:start position:0%
+system we create these dimensionless
+Expressions out of the variables in our
+
+ align:start position:0%
+Expressions out of the variables in our
+ 
+
+ align:start position:0%
+Expressions out of the variables in our
+system so we don't introduce any new
+
+ align:start position:0%
+system so we don't introduce any new
+ 
+
+ align:start position:0%
+system so we don't introduce any new
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+parameters the first step is to take our
+
+ align:start position:0%
+parameters the first step is to take our
+ 
+
+ align:start position:0%
+parameters the first step is to take our
+list of variables and distill them down
+
+ align:start position:0%
+list of variables and distill them down
+ 
+
+ align:start position:0%
+list of variables and distill them down
+to their fundamental Dimensions remember
+
+ align:start position:0%
+to their fundamental Dimensions remember
+ 
+
+ align:start position:0%
+to their fundamental Dimensions remember
+our fundamental dimensions are length
+
+ align:start position:0%
+our fundamental dimensions are length
+ 
+
+ align:start position:0%
+our fundamental dimensions are length
+mass and time distilling gravity to its
+
+ align:start position:0%
+mass and time distilling gravity to its
+ 
+
+ align:start position:0%
+mass and time distilling gravity to its
+fundamental Dimension we get length per
+
+ align:start position:0%
+fundamental Dimension we get length per
+ 
+
+ align:start position:0%
+fundamental Dimension we get length per
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+squared now you distill the remaining
+
+ align:start position:0%
+squared now you distill the remaining
+ 
+
+ align:start position:0%
+squared now you distill the remaining
+variables of velocity diameter mass and
+
+ align:start position:0%
+variables of velocity diameter mass and
+ 
+
+ align:start position:0%
+variables of velocity diameter mass and
+density into their fundamental
+
+ align:start position:0%
+density into their fundamental
+ 
+
+ align:start position:0%
+density into their fundamental
+Dimensions pause the video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity is length per time diameter is
+
+ align:start position:0%
+velocity is length per time diameter is
+ 
+
+ align:start position:0%
+velocity is length per time diameter is
+length mass is mass and density is mass
+
+ align:start position:0%
+length mass is mass and density is mass
+ 
+
+ align:start position:0%
+length mass is mass and density is mass
+per length
+
+ align:start position:0%
+per length
+ 
+
+ align:start position:0%
+per length
+cubed the second step is to express the
+
+ align:start position:0%
+cubed the second step is to express the
+ 
+
+ align:start position:0%
+cubed the second step is to express the
+fundamental dimensions of mass length
+
+ align:start position:0%
+fundamental dimensions of mass length
+ 
+
+ align:start position:0%
+fundamental dimensions of mass length
+and time in terms of our
+
+ align:start position:0%
+and time in terms of our
+ 
+
+ align:start position:0%
+and time in terms of our
+variables we can write M as Little M we
+
+ align:start position:0%
+variables we can write M as Little M we
+ 
+
+ align:start position:0%
+variables we can write M as Little M we
+can write L as mass / density to the 1/3
+
+ align:start position:0%
+can write L as mass / density to the 1/3
+ 
+
+ align:start position:0%
+can write L as mass / density to the 1/3
+power we can write t as velocity div by
+
+ align:start position:0%
+power we can write t as velocity div by
+ 
+
+ align:start position:0%
+power we can write t as velocity div by
+gravity we had many choices as to how to
+
+ align:start position:0%
+gravity we had many choices as to how to
+ 
+
+ align:start position:0%
+gravity we had many choices as to how to
+write these fundamental dimensions in
+
+ align:start position:0%
+write these fundamental dimensions in
+ 
+
+ align:start position:0%
+write these fundamental dimensions in
+terms of our variables in the end it
+
+ align:start position:0%
+terms of our variables in the end it
+ 
+
+ align:start position:0%
+terms of our variables in the end it
+doesn't matter which Expressions you
+
+ align:start position:0%
+doesn't matter which Expressions you
+ 
+
+ align:start position:0%
+doesn't matter which Expressions you
+choose the third step is to use these
+
+ align:start position:0%
+choose the third step is to use these
+ 
+
+ align:start position:0%
+choose the third step is to use these
+fundamental Dimensions to turn all of
+
+ align:start position:0%
+fundamental Dimensions to turn all of
+ 
+
+ align:start position:0%
+fundamental Dimensions to turn all of
+the variables involved into
+
+ align:start position:0%
+the variables involved into
+ 
+
+ align:start position:0%
+the variables involved into
+dimensionless quantities for example the
+
+ align:start position:0%
+dimensionless quantities for example the
+ 
+
+ align:start position:0%
+dimensionless quantities for example the
+terminal velocity V has dimension of
+
+ align:start position:0%
+terminal velocity V has dimension of
+ 
+
+ align:start position:0%
+terminal velocity V has dimension of
+length over
+
+ align:start position:0%
+length over
+ 
+
+ align:start position:0%
+length over
+time so we multiply V
+
+ align:start position:0%
+time so we multiply V
+ 
+
+ align:start position:0%
+time so we multiply V
+by the dimension of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and divide by the dimension of
+
+ align:start position:0%
+time and divide by the dimension of
+ 
+
+ align:start position:0%
+time and divide by the dimension of
+length to get a dimension of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one we Define a new dimensionless
+
+ align:start position:0%
+one we Define a new dimensionless
+ 
+
+ align:start position:0%
+one we Define a new dimensionless
+variable V bar as this dimensionless
+
+ align:start position:0%
+variable V bar as this dimensionless
+ 
+
+ align:start position:0%
+variable V bar as this dimensionless
+version of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V now you try find D
+
+ align:start position:0%
+V now you try find D
+ 
+
+ align:start position:0%
+V now you try find D
+M Bar G bar and
+
+ align:start position:0%
+M Bar G bar and
+ 
+
+ align:start position:0%
+M Bar G bar and
+rowar pause the video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you should have found that D is D *
+
+ align:start position:0%
+here you should have found that D is D *
+ 
+
+ align:start position:0%
+here you should have found that D is D *
+row over m to the
+
+ align:start position:0%
+row over m to the
+ 
+
+ align:start position:0%
+row over m to the
+1/3 m is
+
+ align:start position:0%
+1/3 m is
+ 
+
+ align:start position:0%
+1/3 m is
+1 G bar is V ^2 over G * row over M the
+
+ align:start position:0%
+1 G bar is V ^2 over G * row over M the
+ 
+
+ align:start position:0%
+1 G bar is V ^2 over G * row over M the
+1/3 and rowar is
+
+ align:start position:0%
+1/3 and rowar is
+ 
+
+ align:start position:0%
+1/3 and rowar is
+one now we can rewrite the equation for
+
+ align:start position:0%
+one now we can rewrite the equation for
+ 
+
+ align:start position:0%
+one now we can rewrite the equation for
+velocity in terms of the new
+
+ align:start position:0%
+velocity in terms of the new
+ 
+
+ align:start position:0%
+velocity in terms of the new
+dimensionless variables it is a new
+
+ align:start position:0%
+dimensionless variables it is a new
+ 
+
+ align:start position:0%
+dimensionless variables it is a new
+function because the variables have been
+
+ align:start position:0%
+function because the variables have been
+ 
+
+ align:start position:0%
+function because the variables have been
+modified notice that V is equal to
+
+ align:start position:0%
+modified notice that V is equal to
+ 
+
+ align:start position:0%
+modified notice that V is equal to
+G this means that V bar and gar are not
+
+ align:start position:0%
+G this means that V bar and gar are not
+ 
+
+ align:start position:0%
+G this means that V bar and gar are not
+independent so our function for V bar
+
+ align:start position:0%
+independent so our function for V bar
+ 
+
+ align:start position:0%
+independent so our function for V bar
+cannot depend on G
+
+ align:start position:0%
+cannot depend on G
+ 
+
+ align:start position:0%
+cannot depend on G
+bar also notice that mbar and rowar are
+
+ align:start position:0%
+bar also notice that mbar and rowar are
+ 
+
+ align:start position:0%
+bar also notice that mbar and rowar are
+both equal to one so our function
+
+ align:start position:0%
+both equal to one so our function
+ 
+
+ align:start position:0%
+both equal to one so our function
+doesn't depend on them
+
+ align:start position:0%
+doesn't depend on them
+ 
+
+ align:start position:0%
+doesn't depend on them
+either this has simplified our
+
+ align:start position:0%
+either this has simplified our
+ 
+
+ align:start position:0%
+either this has simplified our
+relationship V bar is a function of only
+
+ align:start position:0%
+relationship V bar is a function of only
+ 
+
+ align:start position:0%
+relationship V bar is a function of only
+one variable
+
+ align:start position:0%
+one variable
+ 
+
+ align:start position:0%
+one variable
+dbar and remember that dbar is
+
+ align:start position:0%
+dbar and remember that dbar is
+ 
+
+ align:start position:0%
+dbar and remember that dbar is
+dimensionless so it's just a real number
+
+ align:start position:0%
+dimensionless so it's just a real number
+ 
+
+ align:start position:0%
+dimensionless so it's just a real number
+this means that Fe can be any
+
+ align:start position:0%
+this means that Fe can be any
+ 
+
+ align:start position:0%
+this means that Fe can be any
+function the fourth and final step is to
+
+ align:start position:0%
+function the fourth and final step is to
+ 
+
+ align:start position:0%
+function the fourth and final step is to
+rearrange to find a formula for the
+
+ align:start position:0%
+rearrange to find a formula for the
+ 
+
+ align:start position:0%
+rearrange to find a formula for the
+terminal
+
+ align:start position:0%
+terminal
+ 
+
+ align:start position:0%
+terminal
+velocity the key here is that the
+
+ align:start position:0%
+velocity the key here is that the
+ 
+
+ align:start position:0%
+velocity the key here is that the
+equation for the the terminal velocity
+
+ align:start position:0%
+equation for the the terminal velocity
+ 
+
+ align:start position:0%
+equation for the the terminal velocity
+has the correct
+
+ align:start position:0%
+has the correct
+ 
+
+ align:start position:0%
+has the correct
+Dimension and this formula is so General
+
+ align:start position:0%
+Dimension and this formula is so General
+ 
+
+ align:start position:0%
+Dimension and this formula is so General
+that any expression with dimension of
+
+ align:start position:0%
+that any expression with dimension of
+ 
+
+ align:start position:0%
+that any expression with dimension of
+length over time can be written in terms
+
+ align:start position:0%
+length over time can be written in terms
+ 
+
+ align:start position:0%
+length over time can be written in terms
+of this formula by defining fee in
+
+ align:start position:0%
+of this formula by defining fee in
+ 
+
+ align:start position:0%
+of this formula by defining fee in
+different ways let's see
+
+ align:start position:0%
+different ways let's see
+ 
+
+ align:start position:0%
+different ways let's see
+how first create an expression from the
+
+ align:start position:0%
+how first create an expression from the
+ 
+
+ align:start position:0%
+how first create an expression from the
+independent variables that has the same
+
+ align:start position:0%
+independent variables that has the same
+ 
+
+ align:start position:0%
+independent variables that has the same
+Dimension as velocity uh one such
+
+ align:start position:0%
+Dimension as velocity uh one such
+ 
+
+ align:start position:0%
+Dimension as velocity uh one such
+expression is the square root of G *
+
+ align:start position:0%
+expression is the square root of G *
+ 
+
+ align:start position:0%
+expression is the square root of G *
+d by setting the form formula for V
+
+ align:start position:0%
+d by setting the form formula for V
+ 
+
+ align:start position:0%
+d by setting the form formula for V
+equal to theare root of GD we see that
+
+ align:start position:0%
+equal to theare root of GD we see that
+ 
+
+ align:start position:0%
+equal to theare root of GD we see that
+by setting F equal to the identity
+
+ align:start position:0%
+by setting F equal to the identity
+ 
+
+ align:start position:0%
+by setting F equal to the identity
+function f of xals x the two sides of
+
+ align:start position:0%
+function f of xals x the two sides of
+ 
+
+ align:start position:0%
+function f of xals x the two sides of
+the equation can be made
+
+ align:start position:0%
+the equation can be made
+ 
+
+ align:start position:0%
+the equation can be made
+equal and in fact we claim that any
+
+ align:start position:0%
+equal and in fact we claim that any
+ 
+
+ align:start position:0%
+equal and in fact we claim that any
+expression with the correct dimension of
+
+ align:start position:0%
+expression with the correct dimension of
+ 
+
+ align:start position:0%
+expression with the correct dimension of
+length over time created using these
+
+ align:start position:0%
+length over time created using these
+ 
+
+ align:start position:0%
+length over time created using these
+variables can be written in terms of
+
+ align:start position:0%
+variables can be written in terms of
+ 
+
+ align:start position:0%
+variables can be written in terms of
+this formula simply by changing the
+
+ align:start position:0%
+this formula simply by changing the
+ 
+
+ align:start position:0%
+this formula simply by changing the
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+Fe it can be fun to try this this come
+
+ align:start position:0%
+Fe it can be fun to try this this come
+ 
+
+ align:start position:0%
+Fe it can be fun to try this this come
+up with different formulas that have the
+
+ align:start position:0%
+up with different formulas that have the
+ 
+
+ align:start position:0%
+up with different formulas that have the
+correct Dimension you can even add them
+
+ align:start position:0%
+correct Dimension you can even add them
+ 
+
+ align:start position:0%
+correct Dimension you can even add them
+together when you're done then see if
+
+ align:start position:0%
+together when you're done then see if
+ 
+
+ align:start position:0%
+together when you're done then see if
+you can find a way to define fee so that
+
+ align:start position:0%
+you can find a way to define fee so that
+ 
+
+ align:start position:0%
+you can find a way to define fee so that
+our formula is equal to the expression
+
+ align:start position:0%
+our formula is equal to the expression
+ 
+
+ align:start position:0%
+our formula is equal to the expression
+you wrote pause the video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now you may be concerned because
+
+ align:start position:0%
+here now you may be concerned because
+ 
+
+ align:start position:0%
+here now you may be concerned because
+this formula is not unique we made some
+
+ align:start position:0%
+this formula is not unique we made some
+ 
+
+ align:start position:0%
+this formula is not unique we made some
+choices about how to represent our
+
+ align:start position:0%
+choices about how to represent our
+ 
+
+ align:start position:0%
+choices about how to represent our
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+Dimensions what happens if we make
+
+ align:start position:0%
+Dimensions what happens if we make
+ 
+
+ align:start position:0%
+Dimensions what happens if we make
+different choices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we chose M L and T this way M was
+
+ align:start position:0%
+here we chose M L and T this way M was
+ 
+
+ align:start position:0%
+here we chose M L and T this way M was
+Little M L was Little D and T was V over
+
+ align:start position:0%
+Little M L was Little D and T was V over
+ 
+
+ align:start position:0%
+Little M L was Little D and T was V over
+G running through the dimensional
+
+ align:start position:0%
+G running through the dimensional
+ 
+
+ align:start position:0%
+G running through the dimensional
+analysis process with this choice of
+
+ align:start position:0%
+analysis process with this choice of
+ 
+
+ align:start position:0%
+analysis process with this choice of
+fundamental Dimensions we obtain an
+
+ align:start position:0%
+fundamental Dimensions we obtain an
+ 
+
+ align:start position:0%
+fundamental Dimensions we obtain an
+equation for v that looks like
+
+ align:start position:0%
+equation for v that looks like
+ 
+
+ align:start position:0%
+equation for v that looks like
+this to see that these two formulas are
+
+ align:start position:0%
+this to see that these two formulas are
+ 
+
+ align:start position:0%
+this to see that these two formulas are
+equivalent we set the arguments under
+
+ align:start position:0%
+equivalent we set the arguments under
+ 
+
+ align:start position:0%
+equivalent we set the arguments under
+the square root equal and find that we
+
+ align:start position:0%
+the square root equal and find that we
+ 
+
+ align:start position:0%
+the square root equal and find that we
+can express f as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s so any formula with the correct
+
+ align:start position:0%
+s so any formula with the correct
+ 
+
+ align:start position:0%
+s so any formula with the correct
+Dimension can be expressed by this
+
+ align:start position:0%
+Dimension can be expressed by this
+ 
+
+ align:start position:0%
+Dimension can be expressed by this
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+formula and this general formula works
+
+ align:start position:0%
+formula and this general formula works
+ 
+
+ align:start position:0%
+formula and this general formula works
+for any Rover on any Planet whose
+
+ align:start position:0%
+for any Rover on any Planet whose
+ 
+
+ align:start position:0%
+for any Rover on any Planet whose
+terminal velocity through the atmosphere
+
+ align:start position:0%
+terminal velocity through the atmosphere
+ 
+
+ align:start position:0%
+terminal velocity through the atmosphere
+depends on the same variables because
+
+ align:start position:0%
+depends on the same variables because
+ 
+
+ align:start position:0%
+depends on the same variables because
+it's a general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law of course we still don't know what
+
+ align:start position:0%
+law of course we still don't know what
+ 
+
+ align:start position:0%
+law of course we still don't know what
+this function fee is in order to find
+
+ align:start position:0%
+this function fee is in order to find
+ 
+
+ align:start position:0%
+this function fee is in order to find
+fee we can fit experimental data from
+
+ align:start position:0%
+fee we can fit experimental data from
+ 
+
+ align:start position:0%
+fee we can fit experimental data from
+any planet for example
+
+ align:start position:0%
+any planet for example
+ 
+
+ align:start position:0%
+any planet for example
+Earth on Earth we know the gravity and
+
+ align:start position:0%
+Earth on Earth we know the gravity and
+ 
+
+ align:start position:0%
+Earth on Earth we know the gravity and
+Atmospheric density we can specify the
+
+ align:start position:0%
+Atmospheric density we can specify the
+ 
+
+ align:start position:0%
+Atmospheric density we can specify the
+mass of a test Rover to be
+
+ align:start position:0%
+mass of a test Rover to be
+ 
+
+ align:start position:0%
+mass of a test Rover to be
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+kg then we might set up Earthbound
+
+ align:start position:0%
+kg then we might set up Earthbound
+ 
+
+ align:start position:0%
+kg then we might set up Earthbound
+experiments by varying the canopy
+
+ align:start position:0%
+experiments by varying the canopy
+ 
+
+ align:start position:0%
+experiments by varying the canopy
+diameter of a parachute between 1 M to
+
+ align:start position:0%
+diameter of a parachute between 1 M to
+ 
+
+ align:start position:0%
+diameter of a parachute between 1 M to
+20 M and measuring the terminal
+
+ align:start position:0%
+20 M and measuring the terminal
+ 
+
+ align:start position:0%
+20 M and measuring the terminal
+velocity for example suppose we obtain
+
+ align:start position:0%
+velocity for example suppose we obtain
+ 
+
+ align:start position:0%
+velocity for example suppose we obtain
+the following data on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Earth then we could convert this data to
+
+ align:start position:0%
+Earth then we could convert this data to
+ 
+
+ align:start position:0%
+Earth then we could convert this data to
+the dbar V bar axes by scaling the
+
+ align:start position:0%
+the dbar V bar axes by scaling the
+ 
+
+ align:start position:0%
+the dbar V bar axes by scaling the
+variables V and D according to the Earth
+
+ align:start position:0%
+variables V and D according to the Earth
+ 
+
+ align:start position:0%
+variables V and D according to the Earth
+values for the mass gravity and at
+
+ align:start position:0%
+values for the mass gravity and at
+ 
+
+ align:start position:0%
+values for the mass gravity and at
+atmospheric
+
+ align:start position:0%
+atmospheric
+ 
+
+ align:start position:0%
+atmospheric
+density we can fit this data to some
+
+ align:start position:0%
+density we can fit this data to some
+ 
+
+ align:start position:0%
+density we can fit this data to some
+best fit curve and this best fit curve
+
+ align:start position:0%
+best fit curve and this best fit curve
+ 
+
+ align:start position:0%
+best fit curve and this best fit curve
+is our best approximation to that
+
+ align:start position:0%
+is our best approximation to that
+ 
+
+ align:start position:0%
+is our best approximation to that
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+Fe now that we have Fe we can transform
+
+ align:start position:0%
+Fe now that we have Fe we can transform
+ 
+
+ align:start position:0%
+Fe now that we have Fe we can transform
+the axes again to represent the canopy
+
+ align:start position:0%
+the axes again to represent the canopy
+ 
+
+ align:start position:0%
+the axes again to represent the canopy
+diameter and terminal velocity on
+
+ align:start position:0%
+diameter and terminal velocity on
+ 
+
+ align:start position:0%
+diameter and terminal velocity on
+Mars This is done by converting V bar
+
+ align:start position:0%
+Mars This is done by converting V bar
+ 
+
+ align:start position:0%
+Mars This is done by converting V bar
+and D Bar to V and D by scaling
+
+ align:start position:0%
+and D Bar to V and D by scaling
+ 
+
+ align:start position:0%
+and D Bar to V and D by scaling
+according to known values of the gravity
+
+ align:start position:0%
+according to known values of the gravity
+ 
+
+ align:start position:0%
+according to known values of the gravity
+atmospheric density and mass of the
+
+ align:start position:0%
+atmospheric density and mass of the
+ 
+
+ align:start position:0%
+atmospheric density and mass of the
+Rover on
+
+ align:start position:0%
+Rover on
+ 
+
+ align:start position:0%
+Rover on
+Mars to find the diameter we find the
+
+ align:start position:0%
+Mars to find the diameter we find the
+ 
+
+ align:start position:0%
+Mars to find the diameter we find the
+point on the V axis that corresponds to
+
+ align:start position:0%
+point on the V axis that corresponds to
+ 
+
+ align:start position:0%
+point on the V axis that corresponds to
+a terminal velocity of 90
+
+ align:start position:0%
+a terminal velocity of 90
+ 
+
+ align:start position:0%
+a terminal velocity of 90
+m/s and use our curve to determine the
+
+ align:start position:0%
+m/s and use our curve to determine the
+ 
+
+ align:start position:0%
+m/s and use our curve to determine the
+diameter that corresponds to this
+
+ align:start position:0%
+diameter that corresponds to this
+ 
+
+ align:start position:0%
+diameter that corresponds to this
+terminal
+
+ align:start position:0%
+terminal
+ 
+
+ align:start position:0%
+terminal
+velocity now we have the specification
+
+ align:start position:0%
+velocity now we have the specification
+ 
+
+ align:start position:0%
+velocity now we have the specification
+we need to design the size of our
+
+ align:start position:0%
+we need to design the size of our
+ 
+
+ align:start position:0%
+we need to design the size of our
+parachute to be used on The Descent to
+
+ align:start position:0%
+parachute to be used on The Descent to
+ 
+
+ align:start position:0%
+parachute to be used on The Descent to
+Mars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this example we use dimensional
+
+ align:start position:0%
+in this example we use dimensional
+ 
+
+ align:start position:0%
+in this example we use dimensional
+analysis to restrict the possible form
+
+ align:start position:0%
+analysis to restrict the possible form
+ 
+
+ align:start position:0%
+analysis to restrict the possible form
+of a function describing the terminal
+
+ align:start position:0%
+of a function describing the terminal
+ 
+
+ align:start position:0%
+of a function describing the terminal
+velocity of the Mars rover as a function
+
+ align:start position:0%
+velocity of the Mars rover as a function
+ 
+
+ align:start position:0%
+velocity of the Mars rover as a function
+of the parachute canopy diameter
+
+ align:start position:0%
+of the parachute canopy diameter
+ 
+
+ align:start position:0%
+of the parachute canopy diameter
+gravitational acceleration atmospheric
+
+ align:start position:0%
+gravitational acceleration atmospheric
+ 
+
+ align:start position:0%
+gravitational acceleration atmospheric
+density and the mass of the
+
+ align:start position:0%
+density and the mass of the
+ 
+
+ align:start position:0%
+density and the mass of the
+Rover this allowed us to design a
+
+ align:start position:0%
+Rover this allowed us to design a
+ 
+
+ align:start position:0%
+Rover this allowed us to design a
+parachute for use on Mars based on
+
+ align:start position:0%
+parachute for use on Mars based on
+ 
+
+ align:start position:0%
+parachute for use on Mars based on
+Earthbound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiments in general the process of
+
+ align:start position:0%
+experiments in general the process of
+ 
+
+ align:start position:0%
+experiments in general the process of
+dimensional analysis involves
+
+ align:start position:0%
+dimensional analysis involves
+ 
+
+ align:start position:0%
+dimensional analysis involves
+one identifying the dependent variable
+
+ align:start position:0%
+one identifying the dependent variable
+ 
+
+ align:start position:0%
+one identifying the dependent variable
+and independent
+
+ align:start position:0%
+and independent
+ 
+
+ align:start position:0%
+and independent
+variables two expressing the relevant
+
+ align:start position:0%
+variables two expressing the relevant
+ 
+
+ align:start position:0%
+variables two expressing the relevant
+fundamental dimensions in terms of the
+
+ align:start position:0%
+fundamental dimensions in terms of the
+ 
+
+ align:start position:0%
+fundamental dimensions in terms of the
+variables found in step
+
+ align:start position:0%
+variables found in step
+ 
+
+ align:start position:0%
+variables found in step
+one three generating dimensionless
+
+ align:start position:0%
+one three generating dimensionless
+ 
+
+ align:start position:0%
+one three generating dimensionless
+expressions for all the variables using
+
+ align:start position:0%
+expressions for all the variables using
+ 
+
+ align:start position:0%
+expressions for all the variables using
+expressions from step two four producing
+
+ align:start position:0%
+expressions from step two four producing
+ 
+
+ align:start position:0%
+expressions from step two four producing
+a functional relationship between the
+
+ align:start position:0%
+a functional relationship between the
+ 
+
+ align:start position:0%
+a functional relationship between the
+dimensionless dependent variable in
+
+ align:start position:0%
+dimensionless dependent variable in
+ 
+
+ align:start position:0%
+dimensionless dependent variable in
+terms of the remaining independent
+
+ align:start position:0%
+terms of the remaining independent
+ 
+
+ align:start position:0%
+terms of the remaining independent
+dimensionless
+
+ align:start position:0%
+dimensionless
+ 
+
+ align:start position:0%
+dimensionless
+expressions five rearranging to
+
+ align:start position:0%
+expressions five rearranging to
+ 
+
+ align:start position:0%
+expressions five rearranging to
+determine a formula for the variable of
+
+ align:start position:0%
+determine a formula for the variable of
+ 
+
+ align:start position:0%
+determine a formula for the variable of
+interest and six performing experiments
+
+ align:start position:0%
+interest and six performing experiments
+ 
+
+ align:start position:0%
+interest and six performing experiments
+to determine the form of the general
+
+ align:start position:0%
+to determine the form of the general
+ 
+
+ align:start position:0%
+to determine the form of the general
+real valued function that appears in
+
+ align:start position:0%
+real valued function that appears in
+ 
+
+ align:start position:0%
+real valued function that appears in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+formula we've just shown you a very
+
+ align:start position:0%
+formula we've just shown you a very
+ 
+
+ align:start position:0%
+formula we've just shown you a very
+powerful tool which can save you a lot
+
+ align:start position:0%
+powerful tool which can save you a lot
+ 
+
+ align:start position:0%
+powerful tool which can save you a lot
+of time so the next time you're faced
+
+ align:start position:0%
+of time so the next time you're faced
+ 
+
+ align:start position:0%
+of time so the next time you're faced
+with a difficult challenge you might
+
+ align:start position:0%
+with a difficult challenge you might
+ 
+
+ align:start position:0%
+with a difficult challenge you might
+just want to try dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/58B5dEJReQ8.txt b/58B5dEJReQ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ac311d7e7025c5bd67e52e5399bd69ce1f07d2c8
--- /dev/null
+++ b/58B5dEJReQ8.txt
@@ -0,0 +1,10748 @@
+align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's continue our discussion of
+
+ align:start position:0%
+so let's continue our discussion of
+ 
+
+ align:start position:0%
+so let's continue our discussion of
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+norm spaces and bonnet spaces so last
+
+ align:start position:0%
+norm spaces and bonnet spaces so last
+ 
+
+ align:start position:0%
+norm spaces and bonnet spaces so last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+i introduced the space of bounded linear
+
+ align:start position:0%
+i introduced the space of bounded linear
+ 
+
+ align:start position:0%
+i introduced the space of bounded linear
+operators from one
+
+ align:start position:0%
+operators from one
+ 
+
+ align:start position:0%
+operators from one
+uh norm space from another and we saw
+
+ align:start position:0%
+uh norm space from another and we saw
+ 
+
+ align:start position:0%
+uh norm space from another and we saw
+that when
+
+ align:start position:0%
+that when
+ 
+
+ align:start position:0%
+that when
+the target is a bonus base
+
+ align:start position:0%
+the target is a bonus base
+ 
+
+ align:start position:0%
+the target is a bonus base
+then this space of bounded linear
+
+ align:start position:0%
+then this space of bounded linear
+ 
+
+ align:start position:0%
+then this space of bounded linear
+operators is also a bonus space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+we'll look at another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example of a way to obtain a norm space
+
+ align:start position:0%
+example of a way to obtain a norm space
+ 
+
+ align:start position:0%
+example of a way to obtain a norm space
+from a given norm space so
+
+ align:start position:0%
+from a given norm space so
+ 
+
+ align:start position:0%
+from a given norm space so
+i'll be talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subspaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and quotients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just recall
+
+ align:start position:0%
+so let me just recall
+ 
+
+ align:start position:0%
+so let me just recall
+briefly what a subspace is you should
+
+ align:start position:0%
+briefly what a subspace is you should
+ 
+
+ align:start position:0%
+briefly what a subspace is you should
+remember this from linear algebra v will
+
+ align:start position:0%
+remember this from linear algebra v will
+ 
+
+ align:start position:0%
+remember this from linear algebra v will
+always be
+
+ align:start position:0%
+always be
+ 
+
+ align:start position:0%
+always be
+at least a vector space
+
+ align:start position:0%
+at least a vector space
+ 
+
+ align:start position:0%
+at least a vector space
+usually a norm's
+
+ align:start position:0%
+usually a norm's
+ 
+
+ align:start position:0%
+usually a norm's
+space so we say
+
+ align:start position:0%
+space so we say
+ 
+
+ align:start position:0%
+space so we say
+a subset and i've been using this
+
+ align:start position:0%
+a subset and i've been using this
+ 
+
+ align:start position:0%
+a subset and i've been using this
+notation it doesn't mean strict
+
+ align:start position:0%
+notation it doesn't mean strict
+ 
+
+ align:start position:0%
+notation it doesn't mean strict
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a strict subset i'm just kind of used to
+
+ align:start position:0%
+a strict subset i'm just kind of used to
+ 
+
+ align:start position:0%
+a strict subset i'm just kind of used to
+using this notation from
+
+ align:start position:0%
+using this notation from
+ 
+
+ align:start position:0%
+using this notation from
+18 100 a in the textbook use this
+
+ align:start position:0%
+18 100 a in the textbook use this
+ 
+
+ align:start position:0%
+18 100 a in the textbook use this
+notation for
+
+ align:start position:0%
+notation for
+ 
+
+ align:start position:0%
+notation for
+just being a subset not necessarily a
+
+ align:start position:0%
+just being a subset not necessarily a
+ 
+
+ align:start position:0%
+just being a subset not necessarily a
+strict subset so
+
+ align:start position:0%
+strict subset so
+ 
+
+ align:start position:0%
+strict subset so
+quick uh
+
+ align:start position:0%
+quick uh
+ 
+
+ align:start position:0%
+quick uh
+note about that so
+
+ align:start position:0%
+note about that so
+ 
+
+ align:start position:0%
+note about that so
+a subset of v is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subspace if
+
+ align:start position:0%
+a subspace if
+ 
+
+ align:start position:0%
+a subspace if
+raw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements two elements in the
+
+ align:start position:0%
+elements two elements in the
+ 
+
+ align:start position:0%
+elements two elements in the
+field of scalars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and elements in w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+their linear combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is also in w okay so w is closed
+
+ align:start position:0%
+is also in w okay so w is closed
+ 
+
+ align:start position:0%
+is also in w okay so w is closed
+undertaking linear combinations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so it's
+
+ align:start position:0%
+and so it's
+ 
+
+ align:start position:0%
+and so it's
+quite easy to prove and i'll leave this
+
+ align:start position:0%
+quite easy to prove and i'll leave this
+ 
+
+ align:start position:0%
+quite easy to prove and i'll leave this
+to you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subspace
+
+ align:start position:0%
+a subspace
+ 
+
+ align:start position:0%
+a subspace
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+normed uh
+
+ align:start position:0%
+normed uh
+ 
+
+ align:start position:0%
+normed uh
+space of a of a bonus base sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is itself a bonus space
+
+ align:start position:0%
+is itself a bonus space
+ 
+
+ align:start position:0%
+is itself a bonus space
+meaning it's complete with respect to
+
+ align:start position:0%
+meaning it's complete with respect to
+ 
+
+ align:start position:0%
+meaning it's complete with respect to
+the norm
+
+ align:start position:0%
+the norm
+ 
+
+ align:start position:0%
+the norm
+it inherits from v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a bonus base if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a closed subset of v with respect
+
+ align:start position:0%
+it's a closed subset of v with respect
+ 
+
+ align:start position:0%
+it's a closed subset of v with respect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh this metric we have induced by the
+
+ align:start position:0%
+uh this metric we have induced by the
+ 
+
+ align:start position:0%
+uh this metric we have induced by the
+norm
+
+ align:start position:0%
+norm
+ 
+
+ align:start position:0%
+norm
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean you know you can let me talk your
+
+ align:start position:0%
+i mean you know you can let me talk your
+ 
+
+ align:start position:0%
+i mean you know you can let me talk your
+our way through it real quick
+
+ align:start position:0%
+our way through it real quick
+ 
+
+ align:start position:0%
+our way through it real quick
+uh assuming w is a bonus space we want
+
+ align:start position:0%
+uh assuming w is a bonus space we want
+ 
+
+ align:start position:0%
+uh assuming w is a bonus space we want
+to show w is also a
+
+ align:start position:0%
+to show w is also a
+ 
+
+ align:start position:0%
+to show w is also a
+closed subset of v so that means you
+
+ align:start position:0%
+closed subset of v so that means you
+ 
+
+ align:start position:0%
+closed subset of v so that means you
+need to show for example that
+
+ align:start position:0%
+need to show for example that
+ 
+
+ align:start position:0%
+need to show for example that
+one equivalent way of showing this is
+
+ align:start position:0%
+one equivalent way of showing this is
+ 
+
+ align:start position:0%
+one equivalent way of showing this is
+that every sequence that converges
+
+ align:start position:0%
+that every sequence that converges
+ 
+
+ align:start position:0%
+that every sequence that converges
+every sequence of elements from w that
+
+ align:start position:0%
+every sequence of elements from w that
+ 
+
+ align:start position:0%
+every sequence of elements from w that
+converges converges to an element of w
+
+ align:start position:0%
+converges converges to an element of w
+ 
+
+ align:start position:0%
+converges converges to an element of w
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh take a sequence in w that converges
+
+ align:start position:0%
+uh take a sequence in w that converges
+ 
+
+ align:start position:0%
+uh take a sequence in w that converges
+to some element in v
+
+ align:start position:0%
+to some element in v
+ 
+
+ align:start position:0%
+to some element in v
+we now want to show that elements in w
+
+ align:start position:0%
+we now want to show that elements in w
+ 
+
+ align:start position:0%
+we now want to show that elements in w
+then that sequence converges
+
+ align:start position:0%
+then that sequence converges
+ 
+
+ align:start position:0%
+then that sequence converges
+in w or is cauchy in w
+
+ align:start position:0%
+in w or is cauchy in w
+ 
+
+ align:start position:0%
+in w or is cauchy in w
+and since w is a bonus space there must
+
+ align:start position:0%
+and since w is a bonus space there must
+ 
+
+ align:start position:0%
+and since w is a bonus space there must
+be an element in w which it converges to
+
+ align:start position:0%
+be an element in w which it converges to
+ 
+
+ align:start position:0%
+be an element in w which it converges to
+and therefore by uniqueness of limits
+
+ align:start position:0%
+and therefore by uniqueness of limits
+ 
+
+ align:start position:0%
+and therefore by uniqueness of limits
+that limit
+
+ align:start position:0%
+that limit
+ 
+
+ align:start position:0%
+that limit
+of that original sequence must lie in w
+
+ align:start position:0%
+of that original sequence must lie in w
+ 
+
+ align:start position:0%
+of that original sequence must lie in w
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now going the opposite direction
+
+ align:start position:0%
+and now going the opposite direction
+ 
+
+ align:start position:0%
+and now going the opposite direction
+assuming
+
+ align:start position:0%
+assuming
+ 
+
+ align:start position:0%
+assuming
+the subset the subspace is closed
+
+ align:start position:0%
+the subset the subspace is closed
+ 
+
+ align:start position:0%
+the subset the subspace is closed
+you want to show that
+
+ align:start position:0%
+you want to show that
+ 
+
+ align:start position:0%
+you want to show that
+now this subspace is a banach space
+
+ align:start position:0%
+now this subspace is a banach space
+ 
+
+ align:start position:0%
+now this subspace is a banach space
+meaning it's complete
+
+ align:start position:0%
+meaning it's complete
+ 
+
+ align:start position:0%
+meaning it's complete
+well let's take a koshy sequence in w
+
+ align:start position:0%
+well let's take a koshy sequence in w
+ 
+
+ align:start position:0%
+well let's take a koshy sequence in w
+this is also a koshi sequence in v
+
+ align:start position:0%
+this is also a koshi sequence in v
+ 
+
+ align:start position:0%
+this is also a koshi sequence in v
+therefore it has a limit
+
+ align:start position:0%
+therefore it has a limit
+ 
+
+ align:start position:0%
+therefore it has a limit
+this limit has to be in w since w is
+
+ align:start position:0%
+this limit has to be in w since w is
+ 
+
+ align:start position:0%
+this limit has to be in w since w is
+closed and therefore every cochise
+
+ align:start position:0%
+closed and therefore every cochise
+ 
+
+ align:start position:0%
+closed and therefore every cochise
+sequence in w has a limit in w and
+
+ align:start position:0%
+sequence in w has a limit in w and
+ 
+
+ align:start position:0%
+sequence in w has a limit in w and
+therefore w is a bonus face
+
+ align:start position:0%
+therefore w is a bonus face
+ 
+
+ align:start position:0%
+therefore w is a bonus face
+okay so i didn't write out what uh i
+
+ align:start position:0%
+okay so i didn't write out what uh i
+ 
+
+ align:start position:0%
+okay so i didn't write out what uh i
+didn't write out the details but we
+
+ align:start position:0%
+didn't write out the details but we
+ 
+
+ align:start position:0%
+didn't write out the details but we
+talked our way through it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me uh since we're taking a trip
+
+ align:start position:0%
+so let me uh since we're taking a trip
+ 
+
+ align:start position:0%
+so let me uh since we're taking a trip
+down memory lane
+
+ align:start position:0%
+down memory lane
+ 
+
+ align:start position:0%
+down memory lane
+i just recalled what a subspace is now
+
+ align:start position:0%
+i just recalled what a subspace is now
+ 
+
+ align:start position:0%
+i just recalled what a subspace is now
+given a subspace we can
+
+ align:start position:0%
+given a subspace we can
+ 
+
+ align:start position:0%
+given a subspace we can
+obtain a another vector space uh
+
+ align:start position:0%
+obtain a another vector space uh
+ 
+
+ align:start position:0%
+obtain a another vector space uh
+with the data of the the space and the
+
+ align:start position:0%
+with the data of the the space and the
+ 
+
+ align:start position:0%
+with the data of the the space and the
+subspace called the quotient so let me
+
+ align:start position:0%
+subspace called the quotient so let me
+ 
+
+ align:start position:0%
+subspace called the quotient so let me
+recall the quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+briefly recalling what the quotient is
+
+ align:start position:0%
+briefly recalling what the quotient is
+ 
+
+ align:start position:0%
+briefly recalling what the quotient is
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a subspace of v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we define
+
+ align:start position:0%
+we define
+ 
+
+ align:start position:0%
+we define
+an equivalence relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on b
+
+ align:start position:0%
+on b
+ 
+
+ align:start position:0%
+on b
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+saying that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v is
+
+ align:start position:0%
+v is
+ 
+
+ align:start position:0%
+v is
+related to v prime
+
+ align:start position:0%
+related to v prime
+ 
+
+ align:start position:0%
+related to v prime
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+v minus v prime
+
+ align:start position:0%
+v minus v prime
+ 
+
+ align:start position:0%
+v minus v prime
+is in
+
+ align:start position:0%
+is in
+ 
+
+ align:start position:0%
+is in
+w okay
+
+ align:start position:0%
+w okay
+ 
+
+ align:start position:0%
+w okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do i mean by equivalence relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v is always related to v because the
+
+ align:start position:0%
+v is always related to v because the
+ 
+
+ align:start position:0%
+v is always related to v because the
+difference of v is equal to 0 which is
+
+ align:start position:0%
+difference of v is equal to 0 which is
+ 
+
+ align:start position:0%
+difference of v is equal to 0 which is
+an element of w because w is a subspace
+
+ align:start position:0%
+an element of w because w is a subspace
+ 
+
+ align:start position:0%
+an element of w because w is a subspace
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+vector space in its own right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if v is related to v prime then this
+
+ align:start position:0%
+if v is related to v prime then this
+ 
+
+ align:start position:0%
+if v is related to v prime then this
+impr implies v prime is related to v
+
+ align:start position:0%
+impr implies v prime is related to v
+ 
+
+ align:start position:0%
+impr implies v prime is related to v
+simply because we again if this is in w
+
+ align:start position:0%
+simply because we again if this is in w
+ 
+
+ align:start position:0%
+simply because we again if this is in w
+then its minus is also in w
+
+ align:start position:0%
+then its minus is also in w
+ 
+
+ align:start position:0%
+then its minus is also in w
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this is reflexivity
+
+ align:start position:0%
+this is reflexivity
+ 
+
+ align:start position:0%
+this is reflexivity
+and then we also have
+
+ align:start position:0%
+and then we also have
+ 
+
+ align:start position:0%
+and then we also have
+transitivity that if v is related
+
+ align:start position:0%
+transitivity that if v is related
+ 
+
+ align:start position:0%
+transitivity that if v is related
+to v prime and v is related v prime is
+
+ align:start position:0%
+to v prime and v is related v prime is
+ 
+
+ align:start position:0%
+to v prime and v is related v prime is
+related to v double prime
+
+ align:start position:0%
+related to v double prime
+ 
+
+ align:start position:0%
+related to v double prime
+then v is related to v
+
+ align:start position:0%
+then v is related to v
+ 
+
+ align:start position:0%
+then v is related to v
+double prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just simply take v minus v double
+
+ align:start position:0%
+okay just simply take v minus v double
+ 
+
+ align:start position:0%
+okay just simply take v minus v double
+prime and add and subtract v prime
+
+ align:start position:0%
+prime and add and subtract v prime
+ 
+
+ align:start position:0%
+prime and add and subtract v prime
+then you obtain the sum of two elements
+
+ align:start position:0%
+then you obtain the sum of two elements
+ 
+
+ align:start position:0%
+then you obtain the sum of two elements
+in w which must be in w so this is an
+
+ align:start position:0%
+in w which must be in w so this is an
+ 
+
+ align:start position:0%
+in w which must be in w so this is an
+equivalence relation
+
+ align:start position:0%
+equivalence relation
+ 
+
+ align:start position:0%
+equivalence relation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to find the equivalence class of v
+
+ align:start position:0%
+to find the equivalence class of v
+ 
+
+ align:start position:0%
+to find the equivalence class of v
+this is the set of all v prime and v
+
+ align:start position:0%
+this is the set of all v prime and v
+ 
+
+ align:start position:0%
+this is the set of all v prime and v
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+uh v is
+
+ align:start position:0%
+uh v is
+ 
+
+ align:start position:0%
+uh v is
+v prime is related to v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we define a new set v
+
+ align:start position:0%
+and then we define a new set v
+ 
+
+ align:start position:0%
+and then we define a new set v
+mod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+to be the set of all equivalence classes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and instead of writing the equivalence
+
+ align:start position:0%
+and instead of writing the equivalence
+ 
+
+ align:start position:0%
+and instead of writing the equivalence
+class of v we typically write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the plus w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead of the equivalence class of v
+
+ align:start position:0%
+instead of the equivalence class of v
+ 
+
+ align:start position:0%
+instead of the equivalence class of v
+okay so you think of these
+
+ align:start position:0%
+okay so you think of these
+ 
+
+ align:start position:0%
+okay so you think of these
+of the equivalence class of v as being v
+
+ align:start position:0%
+of the equivalence class of v as being v
+ 
+
+ align:start position:0%
+of the equivalence class of v as being v
+plus kind of all elements of w
+
+ align:start position:0%
+plus kind of all elements of w
+ 
+
+ align:start position:0%
+plus kind of all elements of w
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or two
+
+ align:start position:0%
+or two
+ 
+
+ align:start position:0%
+or two
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+are the same if they differ by an
+
+ align:start position:0%
+are the same if they differ by an
+ 
+
+ align:start position:0%
+are the same if they differ by an
+element of w
+
+ align:start position:0%
+element of w
+ 
+
+ align:start position:0%
+element of w
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a set but we it becomes a
+
+ align:start position:0%
+so this is a set but we it becomes a
+ 
+
+ align:start position:0%
+so this is a set but we it becomes a
+vector space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the skate with the uh
+
+ align:start position:0%
+with the skate with the uh
+ 
+
+ align:start position:0%
+with the skate with the uh
+addition and scalar multiplication
+
+ align:start position:0%
+addition and scalar multiplication
+ 
+
+ align:start position:0%
+addition and scalar multiplication
+operations defined in a kind of natural
+
+ align:start position:0%
+operations defined in a kind of natural
+ 
+
+ align:start position:0%
+operations defined in a kind of natural
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+with v1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scalar multiplication is just
+
+ align:start position:0%
+scalar multiplication is just
+ 
+
+ align:start position:0%
+scalar multiplication is just
+the equivalence class
+
+ align:start position:0%
+the equivalence class
+ 
+
+ align:start position:0%
+the equivalence class
+given by lambda times v okay
+
+ align:start position:0%
+given by lambda times v okay
+ 
+
+ align:start position:0%
+given by lambda times v okay
+now you know
+
+ align:start position:0%
+now you know
+ 
+
+ align:start position:0%
+now you know
+you have to take a second and make sure
+
+ align:start position:0%
+you have to take a second and make sure
+ 
+
+ align:start position:0%
+you have to take a second and make sure
+that these operations are well defined
+
+ align:start position:0%
+that these operations are well defined
+ 
+
+ align:start position:0%
+that these operations are well defined
+which i'm sure you did in linear algebra
+
+ align:start position:0%
+which i'm sure you did in linear algebra
+ 
+
+ align:start position:0%
+which i'm sure you did in linear algebra
+what do i mean by well-defined well
+
+ align:start position:0%
+what do i mean by well-defined well
+ 
+
+ align:start position:0%
+what do i mean by well-defined well
+these are two equivalence classes so if
+
+ align:start position:0%
+these are two equivalence classes so if
+ 
+
+ align:start position:0%
+these are two equivalence classes so if
+i take two other representatives say v
+
+ align:start position:0%
+i take two other representatives say v
+ 
+
+ align:start position:0%
+i take two other representatives say v
+one prime and v two prime do i get the
+
+ align:start position:0%
+one prime and v two prime do i get the
+ 
+
+ align:start position:0%
+one prime and v two prime do i get the
+same equivalence class
+
+ align:start position:0%
+same equivalence class
+ 
+
+ align:start position:0%
+same equivalence class
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+as i did with the un prime meaning does
+
+ align:start position:0%
+as i did with the un prime meaning does
+ 
+
+ align:start position:0%
+as i did with the un prime meaning does
+v one prime plus v two prime plus w
+
+ align:start position:0%
+v one prime plus v two prime plus w
+ 
+
+ align:start position:0%
+v one prime plus v two prime plus w
+uh the same equivalence class as v one
+
+ align:start position:0%
+uh the same equivalence class as v one
+ 
+
+ align:start position:0%
+uh the same equivalence class as v one
+plus v two
+
+ align:start position:0%
+plus v two
+ 
+
+ align:start position:0%
+plus v two
+plus w and uh this is not too hard to
+
+ align:start position:0%
+plus w and uh this is not too hard to
+ 
+
+ align:start position:0%
+plus w and uh this is not too hard to
+say or to see
+
+ align:start position:0%
+say or to see
+ 
+
+ align:start position:0%
+say or to see
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so v mod w which is typically uh how you
+
+ align:start position:0%
+so v mod w which is typically uh how you
+ 
+
+ align:start position:0%
+so v mod w which is typically uh how you
+pronounce this v slash w v mod w is a
+
+ align:start position:0%
+pronounce this v slash w v mod w is a
+ 
+
+ align:start position:0%
+pronounce this v slash w v mod w is a
+vector space
+
+ align:start position:0%
+vector space
+ 
+
+ align:start position:0%
+vector space
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note uh we can identify w
+
+ align:start position:0%
+note uh we can identify w
+ 
+
+ align:start position:0%
+note uh we can identify w
+so just the
+
+ align:start position:0%
+so just the
+ 
+
+ align:start position:0%
+so just the
+set w
+
+ align:start position:0%
+set w
+ 
+
+ align:start position:0%
+set w
+uh with the equivalence class zero plus
+
+ align:start position:0%
+uh with the equivalence class zero plus
+ 
+
+ align:start position:0%
+uh with the equivalence class zero plus
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is also equal to w plus little w plus
+
+ align:start position:0%
+is also equal to w plus little w plus
+ 
+
+ align:start position:0%
+is also equal to w plus little w plus
+capital w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we first started talking about
+
+ align:start position:0%
+when we first started talking about
+ 
+
+ align:start position:0%
+when we first started talking about
+norms we
+
+ align:start position:0%
+norms we
+ 
+
+ align:start position:0%
+norms we
+i also introduced what was called a
+
+ align:start position:0%
+i also introduced what was called a
+ 
+
+ align:start position:0%
+i also introduced what was called a
+seminorm now a semi norm recall
+
+ align:start position:0%
+seminorm now a semi norm recall
+ 
+
+ align:start position:0%
+seminorm now a semi norm recall
+satisfied
+
+ align:start position:0%
+satisfied
+ 
+
+ align:start position:0%
+satisfied
+not all three properties of norm
+
+ align:start position:0%
+not all three properties of norm
+ 
+
+ align:start position:0%
+not all three properties of norm
+satisfied it satisfies
+
+ align:start position:0%
+satisfied it satisfies
+ 
+
+ align:start position:0%
+satisfied it satisfies
+homogeneity meaning how scalars pull out
+
+ align:start position:0%
+homogeneity meaning how scalars pull out
+ 
+
+ align:start position:0%
+homogeneity meaning how scalars pull out
+and also the triangle
+
+ align:start position:0%
+and also the triangle
+ 
+
+ align:start position:0%
+and also the triangle
+inequality but it didn't satisfy
+
+ align:start position:0%
+inequality but it didn't satisfy
+ 
+
+ align:start position:0%
+inequality but it didn't satisfy
+positive definiteness meaning
+
+ align:start position:0%
+positive definiteness meaning
+ 
+
+ align:start position:0%
+positive definiteness meaning
+uh the semi norm
+
+ align:start position:0%
+uh the semi norm
+ 
+
+ align:start position:0%
+uh the semi norm
+could be zero for certain non-zero
+
+ align:start position:0%
+could be zero for certain non-zero
+ 
+
+ align:start position:0%
+could be zero for certain non-zero
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know how
+
+ align:start position:0%
+you know how
+ 
+
+ align:start position:0%
+you know how
+how could that arise how could a
+
+ align:start position:0%
+how could that arise how could a
+ 
+
+ align:start position:0%
+how could that arise how could a
+semi-normal rise well think of taking
+
+ align:start position:0%
+semi-normal rise well think of taking
+ 
+
+ align:start position:0%
+semi-normal rise well think of taking
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the maximum of the derivative of a
+
+ align:start position:0%
+the maximum of the derivative of a
+ 
+
+ align:start position:0%
+the maximum of the derivative of a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+right as being a norm
+
+ align:start position:0%
+right as being a norm
+ 
+
+ align:start position:0%
+right as being a norm
+or as being a potential norm
+
+ align:start position:0%
+or as being a potential norm
+ 
+
+ align:start position:0%
+or as being a potential norm
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh it satisfies um homogeneity and a
+
+ align:start position:0%
+uh it satisfies um homogeneity and a
+ 
+
+ align:start position:0%
+uh it satisfies um homogeneity and a
+triangle inequality
+
+ align:start position:0%
+triangle inequality
+ 
+
+ align:start position:0%
+triangle inequality
+um but it is not
+
+ align:start position:0%
+um but it is not
+ 
+
+ align:start position:0%
+um but it is not
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a norm because the derivative of
+
+ align:start position:0%
+a norm because the derivative of
+ 
+
+ align:start position:0%
+a norm because the derivative of
+constant functions
+
+ align:start position:0%
+constant functions
+ 
+
+ align:start position:0%
+constant functions
+is zero
+
+ align:start position:0%
+is zero
+ 
+
+ align:start position:0%
+is zero
+but constant functions aren't
+
+ align:start position:0%
+but constant functions aren't
+ 
+
+ align:start position:0%
+but constant functions aren't
+identically zero if you think of them as
+
+ align:start position:0%
+identically zero if you think of them as
+ 
+
+ align:start position:0%
+identically zero if you think of them as
+elements of say the space of
+
+ align:start position:0%
+elements of say the space of
+ 
+
+ align:start position:0%
+elements of say the space of
+continuously differentiable functions
+
+ align:start position:0%
+continuously differentiable functions
+ 
+
+ align:start position:0%
+continuously differentiable functions
+okay um but this next theorem says that
+
+ align:start position:0%
+okay um but this next theorem says that
+ 
+
+ align:start position:0%
+okay um but this next theorem says that
+if you mod out by
+
+ align:start position:0%
+if you mod out by
+ 
+
+ align:start position:0%
+if you mod out by
+the elements in a vector space
+
+ align:start position:0%
+the elements in a vector space
+ 
+
+ align:start position:0%
+the elements in a vector space
+on which the semi norm is zero
+
+ align:start position:0%
+on which the semi norm is zero
+ 
+
+ align:start position:0%
+on which the semi norm is zero
+then you get
+
+ align:start position:0%
+then you get
+ 
+
+ align:start position:0%
+then you get
+essentially a norm space where the norm
+
+ align:start position:0%
+essentially a norm space where the norm
+ 
+
+ align:start position:0%
+essentially a norm space where the norm
+is given by the semi-norm so if you mod
+
+ align:start position:0%
+is given by the semi-norm so if you mod
+ 
+
+ align:start position:0%
+is given by the semi-norm so if you mod
+out by
+
+ align:start position:0%
+out by
+ 
+
+ align:start position:0%
+out by
+you know the elements with zero semi
+
+ align:start position:0%
+you know the elements with zero semi
+ 
+
+ align:start position:0%
+you know the elements with zero semi
+norm you get a actual norm space
+
+ align:start position:0%
+norm you get a actual norm space
+ 
+
+ align:start position:0%
+norm you get a actual norm space
+the statement is let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a semi-norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a vector space v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we define e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be the set of all v and capital v
+
+ align:start position:0%
+to be the set of all v and capital v
+ 
+
+ align:start position:0%
+to be the set of all v and capital v
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+semi-norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of these vectors is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subspace of v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if i define
+
+ align:start position:0%
+and if i define
+ 
+
+ align:start position:0%
+and if i define
+the following function on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v mod e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what is it
+
+ align:start position:0%
+what is it
+ 
+
+ align:start position:0%
+what is it
+this is simply
+
+ align:start position:0%
+this is simply
+ 
+
+ align:start position:0%
+this is simply
+the norm of
+
+ align:start position:0%
+the norm of
+ 
+
+ align:start position:0%
+the norm of
+the representative v
+
+ align:start position:0%
+the representative v
+ 
+
+ align:start position:0%
+the representative v
+of this equivalence
+
+ align:start position:0%
+of this equivalence
+ 
+
+ align:start position:0%
+of this equivalence
+class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if i define a function like this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this function
+
+ align:start position:0%
+this function
+ 
+
+ align:start position:0%
+this function
+finds
+
+ align:start position:0%
+finds
+ 
+
+ align:start position:0%
+finds
+a norm
+
+ align:start position:0%
+a norm
+ 
+
+ align:start position:0%
+a norm
+on the space v mod e
+
+ align:start position:0%
+on the space v mod e
+ 
+
+ align:start position:0%
+on the space v mod e
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+in short if i have a semi norm and i mod
+
+ align:start position:0%
+in short if i have a semi norm and i mod
+ 
+
+ align:start position:0%
+in short if i have a semi norm and i mod
+out by all the elements
+
+ align:start position:0%
+out by all the elements
+ 
+
+ align:start position:0%
+out by all the elements
+uh with semi norm
+
+ align:start position:0%
+uh with semi norm
+ 
+
+ align:start position:0%
+uh with semi norm
+equal to zero then i get an actual norm
+
+ align:start position:0%
+equal to zero then i get an actual norm
+ 
+
+ align:start position:0%
+equal to zero then i get an actual norm
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+where this norm is
+
+ align:start position:0%
+where this norm is
+ 
+
+ align:start position:0%
+where this norm is
+you know essentially the semi-norm okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's prove this
+
+ align:start position:0%
+okay so let's prove this
+ 
+
+ align:start position:0%
+okay so let's prove this
+so why is
+
+ align:start position:0%
+so why is
+ 
+
+ align:start position:0%
+so why is
+why is this a subspace well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i take two elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+this space of
+
+ align:start position:0%
+this space of
+ 
+
+ align:start position:0%
+this space of
+elements that have zero semi norm
+
+ align:start position:0%
+elements that have zero semi norm
+ 
+
+ align:start position:0%
+elements that have zero semi norm
+and two scalars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if i take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the semi-norm of its linear com the
+
+ align:start position:0%
+the semi-norm of its linear com the
+ 
+
+ align:start position:0%
+the semi-norm of its linear com the
+linear combination formed i want to show
+
+ align:start position:0%
+linear combination formed i want to show
+ 
+
+ align:start position:0%
+linear combination formed i want to show
+this is equal to zero and this follows
+
+ align:start position:0%
+this is equal to zero and this follows
+ 
+
+ align:start position:0%
+this is equal to zero and this follows
+essentially by
+
+ align:start position:0%
+essentially by
+ 
+
+ align:start position:0%
+essentially by
+uh homogeneity and the triangle
+
+ align:start position:0%
+uh homogeneity and the triangle
+ 
+
+ align:start position:0%
+uh homogeneity and the triangle
+inequality this is less than or equal to
+
+ align:start position:0%
+inequality this is less than or equal to
+ 
+
+ align:start position:0%
+inequality this is less than or equal to
+um if i apply the triangle inequality
+
+ align:start position:0%
+um if i apply the triangle inequality
+ 
+
+ align:start position:0%
+um if i apply the triangle inequality
+and then pull the scalars out this is
+
+ align:start position:0%
+and then pull the scalars out this is
+ 
+
+ align:start position:0%
+and then pull the scalars out this is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if these both have norm semi norm
+
+ align:start position:0%
+and if these both have norm semi norm
+ 
+
+ align:start position:0%
+and if these both have norm semi norm
+equal to zero this is equal to zero and
+
+ align:start position:0%
+equal to zero this is equal to zero and
+ 
+
+ align:start position:0%
+equal to zero this is equal to zero and
+now remember a semi norm is always
+
+ align:start position:0%
+now remember a semi norm is always
+ 
+
+ align:start position:0%
+now remember a semi norm is always
+non-negative so if i show something is
+
+ align:start position:0%
+non-negative so if i show something is
+ 
+
+ align:start position:0%
+non-negative so if i show something is
+less than or equal to zero it's also
+
+ align:start position:0%
+less than or equal to zero it's also
+ 
+
+ align:start position:0%
+less than or equal to zero it's also
+then it must be equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first off
+
+ align:start position:0%
+so first off
+ 
+
+ align:start position:0%
+so first off
+we define this function
+
+ align:start position:0%
+we define this function
+ 
+
+ align:start position:0%
+we define this function
+so now let's show that this uh defines a
+
+ align:start position:0%
+so now let's show that this uh defines a
+ 
+
+ align:start position:0%
+so now let's show that this uh defines a
+norm on
+
+ align:start position:0%
+norm on
+ 
+
+ align:start position:0%
+norm on
+v mod e
+
+ align:start position:0%
+v mod e
+ 
+
+ align:start position:0%
+v mod e
+we need to first show it's well defined
+
+ align:start position:0%
+we need to first show it's well defined
+ 
+
+ align:start position:0%
+we need to first show it's well defined
+because you know i'm defining it in
+
+ align:start position:0%
+because you know i'm defining it in
+ 
+
+ align:start position:0%
+because you know i'm defining it in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know a representative of this
+
+ align:start position:0%
+you know a representative of this
+ 
+
+ align:start position:0%
+you know a representative of this
+equivalence class all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what does this mean i.e
+
+ align:start position:0%
+and what does this mean i.e
+ 
+
+ align:start position:0%
+and what does this mean i.e
+if uh
+
+ align:start position:0%
+if uh
+ 
+
+ align:start position:0%
+if uh
+b plus
+
+ align:start position:0%
+b plus
+ 
+
+ align:start position:0%
+b plus
+if i have two equivalence classes
+
+ align:start position:0%
+if i have two equivalence classes
+ 
+
+ align:start position:0%
+if i have two equivalence classes
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+or if i have the same equivalence class
+
+ align:start position:0%
+or if i have the same equivalence class
+ 
+
+ align:start position:0%
+or if i have the same equivalence class
+with two different representatives v and
+
+ align:start position:0%
+with two different representatives v and
+ 
+
+ align:start position:0%
+with two different representatives v and
+v prime
+
+ align:start position:0%
+v prime
+ 
+
+ align:start position:0%
+v prime
+then and i should write
+
+ align:start position:0%
+then and i should write
+ 
+
+ align:start position:0%
+then and i should write
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+not w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the norm of v
+
+ align:start position:0%
+the norm of v
+ 
+
+ align:start position:0%
+the norm of v
+equals the norm of v prime
+
+ align:start position:0%
+equals the norm of v prime
+ 
+
+ align:start position:0%
+equals the norm of v prime
+okay and therefore this function is well
+
+ align:start position:0%
+okay and therefore this function is well
+ 
+
+ align:start position:0%
+okay and therefore this function is well
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we do that again it's going to be
+
+ align:start position:0%
+how do we do that again it's going to be
+ 
+
+ align:start position:0%
+how do we do that again it's going to be
+essentially the triangle inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b plus e
+
+ align:start position:0%
+b plus e
+ 
+
+ align:start position:0%
+b plus e
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+equals v prime plus e meaning i have two
+
+ align:start position:0%
+equals v prime plus e meaning i have two
+ 
+
+ align:start position:0%
+equals v prime plus e meaning i have two
+representatives for the same equivalence
+
+ align:start position:0%
+representatives for the same equivalence
+ 
+
+ align:start position:0%
+representatives for the same equivalence
+class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that means there exists a little e
+
+ align:start position:0%
+and that means there exists a little e
+ 
+
+ align:start position:0%
+and that means there exists a little e
+capital e such that
+
+ align:start position:0%
+capital e such that
+ 
+
+ align:start position:0%
+capital e such that
+v is equal to v prime plus e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if i take the norm of v
+
+ align:start position:0%
+if i take the norm of v
+ 
+
+ align:start position:0%
+if i take the norm of v
+this is equal to norm of v prime plus e
+
+ align:start position:0%
+this is equal to norm of v prime plus e
+ 
+
+ align:start position:0%
+this is equal to norm of v prime plus e
+and by the triangle inequality this is
+
+ align:start position:0%
+and by the triangle inequality this is
+ 
+
+ align:start position:0%
+and by the triangle inequality this is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+norm of v prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus norm of semi norm of e
+
+ align:start position:0%
+plus norm of semi norm of e
+ 
+
+ align:start position:0%
+plus norm of semi norm of e
+and now since e is coming from this set
+
+ align:start position:0%
+and now since e is coming from this set
+ 
+
+ align:start position:0%
+and now since e is coming from this set
+of all vectors with semi norm equal to 0
+
+ align:start position:0%
+of all vectors with semi norm equal to 0
+ 
+
+ align:start position:0%
+of all vectors with semi norm equal to 0
+this is equal to 0 and therefore i get
+
+ align:start position:0%
+this is equal to 0 and therefore i get
+ 
+
+ align:start position:0%
+this is equal to 0 and therefore i get
+the semi norm of v prime
+
+ align:start position:0%
+the semi norm of v prime
+ 
+
+ align:start position:0%
+the semi norm of v prime
+so i've shown that the
+
+ align:start position:0%
+so i've shown that the
+ 
+
+ align:start position:0%
+so i've shown that the
+semi norm of v is less than or equal to
+
+ align:start position:0%
+semi norm of v is less than or equal to
+ 
+
+ align:start position:0%
+semi norm of v is less than or equal to
+the semi norm of v prime
+
+ align:start position:0%
+the semi norm of v prime
+ 
+
+ align:start position:0%
+the semi norm of v prime
+now there was nothing this argument is
+
+ align:start position:0%
+now there was nothing this argument is
+ 
+
+ align:start position:0%
+now there was nothing this argument is
+symmetric in v and v prime all right if
+
+ align:start position:0%
+symmetric in v and v prime all right if
+ 
+
+ align:start position:0%
+symmetric in v and v prime all right if
+v is equal to v prime plus e for some
+
+ align:start position:0%
+v is equal to v prime plus e for some
+ 
+
+ align:start position:0%
+v is equal to v prime plus e for some
+element in capital e so is v prime so i
+
+ align:start position:0%
+element in capital e so is v prime so i
+ 
+
+ align:start position:0%
+element in capital e so is v prime so i
+can also switch
+
+ align:start position:0%
+can also switch
+ 
+
+ align:start position:0%
+can also switch
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+i can also switch v and v prime meaning
+
+ align:start position:0%
+i can also switch v and v prime meaning
+ 
+
+ align:start position:0%
+i can also switch v and v prime meaning
+i've shown that
+
+ align:start position:0%
+i've shown that
+ 
+
+ align:start position:0%
+i've shown that
+p is less than or equal to v prime
+
+ align:start position:0%
+p is less than or equal to v prime
+ 
+
+ align:start position:0%
+p is less than or equal to v prime
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the norm of v prime is less than or
+
+ align:start position:0%
+the norm of v prime is less than or
+ 
+
+ align:start position:0%
+the norm of v prime is less than or
+equal to v
+
+ align:start position:0%
+equal to v
+ 
+
+ align:start position:0%
+equal to v
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are two norms agree
+
+ align:start position:0%
+there are two norms agree
+ 
+
+ align:start position:0%
+there are two norms agree
+so this function here is
+
+ align:start position:0%
+so this function here is
+ 
+
+ align:start position:0%
+so this function here is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well-defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+i'm going to leave it to you now to
+
+ align:start position:0%
+i'm going to leave it to you now to
+ 
+
+ align:start position:0%
+i'm going to leave it to you now to
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this function now which is well-defined
+
+ align:start position:0%
+this function now which is well-defined
+ 
+
+ align:start position:0%
+this function now which is well-defined
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+mod e is in fact does in fact satisfy
+
+ align:start position:0%
+mod e is in fact does in fact satisfy
+ 
+
+ align:start position:0%
+mod e is in fact does in fact satisfy
+all the the properties of a semi norm i
+
+ align:start position:0%
+all the the properties of a semi norm i
+ 
+
+ align:start position:0%
+all the the properties of a semi norm i
+mean it's non-negative
+
+ align:start position:0%
+mean it's non-negative
+ 
+
+ align:start position:0%
+mean it's non-negative
+uh so in
+
+ align:start position:0%
+uh so in
+ 
+
+ align:start position:0%
+uh so in
+from essentially
+
+ align:start position:0%
+from essentially
+ 
+
+ align:start position:0%
+from essentially
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the homogeneity and triangle inequality
+
+ align:start position:0%
+the homogeneity and triangle inequality
+ 
+
+ align:start position:0%
+the homogeneity and triangle inequality
+property of
+
+ align:start position:0%
+property of
+ 
+
+ align:start position:0%
+property of
+the semi norm the triangle inequality
+
+ align:start position:0%
+the semi norm the triangle inequality
+ 
+
+ align:start position:0%
+the semi norm the triangle inequality
+and homogeneity of this function then
+
+ align:start position:0%
+and homogeneity of this function then
+ 
+
+ align:start position:0%
+and homogeneity of this function then
+follow
+
+ align:start position:0%
+follow
+ 
+
+ align:start position:0%
+follow
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know we've essentially
+
+ align:start position:0%
+you know we've essentially
+ 
+
+ align:start position:0%
+you know we've essentially
+equated all elements with semi norm
+
+ align:start position:0%
+equated all elements with semi norm
+ 
+
+ align:start position:0%
+equated all elements with semi norm
+equal to zero to zero so this is why
+
+ align:start position:0%
+equal to zero to zero so this is why
+ 
+
+ align:start position:0%
+equal to zero to zero so this is why
+it's also positive definite so i'm going
+
+ align:start position:0%
+it's also positive definite so i'm going
+ 
+
+ align:start position:0%
+it's also positive definite so i'm going
+to leave that to you
+
+ align:start position:0%
+to leave that to you
+ 
+
+ align:start position:0%
+to leave that to you
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now there's one other way
+
+ align:start position:0%
+okay now there's one other way
+ 
+
+ align:start position:0%
+okay now there's one other way
+uh if we're given
+
+ align:start position:0%
+uh if we're given
+ 
+
+ align:start position:0%
+uh if we're given
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+in this process we started with a semi
+
+ align:start position:0%
+in this process we started with a semi
+ 
+
+ align:start position:0%
+in this process we started with a semi
+norm on the space
+
+ align:start position:0%
+norm on the space
+ 
+
+ align:start position:0%
+norm on the space
+identified the subspace of all
+
+ align:start position:0%
+identified the subspace of all
+ 
+
+ align:start position:0%
+identified the subspace of all
+you know if you'd like zero norm
+
+ align:start position:0%
+you know if you'd like zero norm
+ 
+
+ align:start position:0%
+you know if you'd like zero norm
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+and obtained a new uh
+
+ align:start position:0%
+and obtained a new uh
+ 
+
+ align:start position:0%
+and obtained a new uh
+norm space
+
+ align:start position:0%
+norm space
+ 
+
+ align:start position:0%
+norm space
+but you could start off with a norm
+
+ align:start position:0%
+but you could start off with a norm
+ 
+
+ align:start position:0%
+but you could start off with a norm
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+a closed subspace of that norm space
+
+ align:start position:0%
+a closed subspace of that norm space
+ 
+
+ align:start position:0%
+a closed subspace of that norm space
+and obtain a new
+
+ align:start position:0%
+and obtain a new
+ 
+
+ align:start position:0%
+and obtain a new
+norm space
+
+ align:start position:0%
+norm space
+ 
+
+ align:start position:0%
+norm space
+uh on v
+
+ align:start position:0%
+uh on v
+ 
+
+ align:start position:0%
+uh on v
+mod w if w is at close space
+
+ align:start position:0%
+mod w if w is at close space
+ 
+
+ align:start position:0%
+mod w if w is at close space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know in sort of similar fashion
+
+ align:start position:0%
+you know in sort of similar fashion
+ 
+
+ align:start position:0%
+you know in sort of similar fashion
+where i define this norm this way
+
+ align:start position:0%
+where i define this norm this way
+ 
+
+ align:start position:0%
+where i define this norm this way
+and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the norm on that space won't be the
+
+ align:start position:0%
+well the norm on that space won't be the
+ 
+
+ align:start position:0%
+well the norm on that space won't be the
+same as this one but that'll be in the
+
+ align:start position:0%
+same as this one but that'll be in the
+ 
+
+ align:start position:0%
+same as this one but that'll be in the
+exercises okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's about
+
+ align:start position:0%
+that's about
+ 
+
+ align:start position:0%
+that's about
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is kind of concluding the
+
+ align:start position:0%
+this is kind of concluding the
+ 
+
+ align:start position:0%
+this is kind of concluding the
+elementary section of functional
+
+ align:start position:0%
+elementary section of functional
+ 
+
+ align:start position:0%
+elementary section of functional
+analysis meaning uh the bare bones of
+
+ align:start position:0%
+analysis meaning uh the bare bones of
+ 
+
+ align:start position:0%
+analysis meaning uh the bare bones of
+of bonus spaces and norm spaces
+
+ align:start position:0%
+of bonus spaces and norm spaces
+ 
+
+ align:start position:0%
+of bonus spaces and norm spaces
+and now with the rest of this lecture
+
+ align:start position:0%
+and now with the rest of this lecture
+ 
+
+ align:start position:0%
+and now with the rest of this lecture
+and then uh next lecture we're going to
+
+ align:start position:0%
+and then uh next lecture we're going to
+ 
+
+ align:start position:0%
+and then uh next lecture we're going to
+get into
+
+ align:start position:0%
+get into
+ 
+
+ align:start position:0%
+get into
+you know kind of the fundamental
+
+ align:start position:0%
+you know kind of the fundamental
+ 
+
+ align:start position:0%
+you know kind of the fundamental
+results of functional analysis
+
+ align:start position:0%
+results of functional analysis
+ 
+
+ align:start position:0%
+results of functional analysis
+related to
+
+ align:start position:0%
+related to
+ 
+
+ align:start position:0%
+related to
+bonus spaces
+
+ align:start position:0%
+bonus spaces
+ 
+
+ align:start position:0%
+bonus spaces
+so these theorems that i'll now be
+
+ align:start position:0%
+so these theorems that i'll now be
+ 
+
+ align:start position:0%
+so these theorems that i'll now be
+stating and proving in the in the
+
+ align:start position:0%
+stating and proving in the in the
+ 
+
+ align:start position:0%
+stating and proving in the in the
+coming couple of lectures have names
+
+ align:start position:0%
+coming couple of lectures have names
+ 
+
+ align:start position:0%
+coming couple of lectures have names
+attached to them so
+
+ align:start position:0%
+attached to them so
+ 
+
+ align:start position:0%
+attached to them so
+you should definitely know what they are
+
+ align:start position:0%
+you should definitely know what they are
+ 
+
+ align:start position:0%
+you should definitely know what they are
+what they state what they don't state
+
+ align:start position:0%
+what they state what they don't state
+ 
+
+ align:start position:0%
+what they state what they don't state
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but to prove them i first need a result
+
+ align:start position:0%
+but to prove them i first need a result
+ 
+
+ align:start position:0%
+but to prove them i first need a result
+from metric spaces
+
+ align:start position:0%
+from metric spaces
+ 
+
+ align:start position:0%
+from metric spaces
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i did teach last semester
+
+ align:start position:0%
+i did teach last semester
+ 
+
+ align:start position:0%
+i did teach last semester
+but we didn't cover this theorem i can't
+
+ align:start position:0%
+but we didn't cover this theorem i can't
+ 
+
+ align:start position:0%
+but we didn't cover this theorem i can't
+remember if i covered it in when i
+
+ align:start position:0%
+remember if i covered it in when i
+ 
+
+ align:start position:0%
+remember if i covered it in when i
+taught 18 100 b
+
+ align:start position:0%
+taught 18 100 b
+ 
+
+ align:start position:0%
+taught 18 100 b
+i don't think i did
+
+ align:start position:0%
+i don't think i did
+ 
+
+ align:start position:0%
+i don't think i did
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is about
+
+ align:start position:0%
+so this is about
+ 
+
+ align:start position:0%
+so this is about
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when can you write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or in what way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me let me
+
+ align:start position:0%
+okay so let me let me
+ 
+
+ align:start position:0%
+okay so let me let me
+let me just state the theorem and then
+
+ align:start position:0%
+let me just state the theorem and then
+ 
+
+ align:start position:0%
+let me just state the theorem and then
+i'll interpret it for you
+
+ align:start position:0%
+i'll interpret it for you
+ 
+
+ align:start position:0%
+i'll interpret it for you
+so this is bear's theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it also goes by the name of bears uh the
+
+ align:start position:0%
+it also goes by the name of bears uh the
+ 
+
+ align:start position:0%
+it also goes by the name of bears uh the
+bear category theorem although it has
+
+ align:start position:0%
+bear category theorem although it has
+ 
+
+ align:start position:0%
+bear category theorem although it has
+nothing to do with you know category
+
+ align:start position:0%
+nothing to do with you know category
+ 
+
+ align:start position:0%
+nothing to do with you know category
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+as is
+
+ align:start position:0%
+as is
+ 
+
+ align:start position:0%
+as is
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+i guess used today i don't know if
+
+ align:start position:0%
+i guess used today i don't know if
+ 
+
+ align:start position:0%
+i guess used today i don't know if
+category theory gets used
+
+ align:start position:0%
+category theory gets used
+ 
+
+ align:start position:0%
+category theory gets used
+or if it just is created for itself
+
+ align:start position:0%
+or if it just is created for itself
+ 
+
+ align:start position:0%
+or if it just is created for itself
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you know bears
+
+ align:start position:0%
+you know bears
+ 
+
+ align:start position:0%
+you know bears
+bears category theorem is the only
+
+ align:start position:0%
+bears category theorem is the only
+ 
+
+ align:start position:0%
+bears category theorem is the only
+category
+
+ align:start position:0%
+category
+ 
+
+ align:start position:0%
+category
+theorem that i know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what does it state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if m
+
+ align:start position:0%
+if m
+ 
+
+ align:start position:0%
+if m
+so this is again this is a theorem about
+
+ align:start position:0%
+so this is again this is a theorem about
+ 
+
+ align:start position:0%
+so this is again this is a theorem about
+metric spaces so
+
+ align:start position:0%
+metric spaces so
+ 
+
+ align:start position:0%
+metric spaces so
+uh not
+
+ align:start position:0%
+uh not
+ 
+
+ align:start position:0%
+uh not
+you know necessarily norm spaces so let
+
+ align:start position:0%
+you know necessarily norm spaces so let
+ 
+
+ align:start position:0%
+you know necessarily norm spaces so let
+if m is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+cn
+
+ align:start position:0%
+cn
+ 
+
+ align:start position:0%
+cn
+is a collection of closed subsets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of m
+
+ align:start position:0%
+of m
+ 
+
+ align:start position:0%
+of m
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+m is their union
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i have it in here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i should specify this is n is a natural
+
+ align:start position:0%
+i should specify this is n is a natural
+ 
+
+ align:start position:0%
+i should specify this is n is a natural
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at least one c in uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contains
+
+ align:start position:0%
+contains
+ 
+
+ align:start position:0%
+contains
+an open ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bxr which i'll recall this is
+
+ align:start position:0%
+bxr which i'll recall this is
+ 
+
+ align:start position:0%
+bxr which i'll recall this is
+uh instead of all y and m such that the
+
+ align:start position:0%
+uh instead of all y and m such that the
+ 
+
+ align:start position:0%
+uh instead of all y and m such that the
+distance from x to y
+
+ align:start position:0%
+distance from x to y
+ 
+
+ align:start position:0%
+distance from x to y
+is less than r
+
+ align:start position:0%
+is less than r
+ 
+
+ align:start position:0%
+is less than r
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+at least one c n contains an open ball
+
+ align:start position:0%
+at least one c n contains an open ball
+ 
+
+ align:start position:0%
+at least one c n contains an open ball
+could be stated uh you know more
+
+ align:start position:0%
+could be stated uh you know more
+ 
+
+ align:start position:0%
+could be stated uh you know more
+succinctly
+
+ align:start position:0%
+succinctly
+ 
+
+ align:start position:0%
+succinctly
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+at least one cn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an interior point
+
+ align:start position:0%
+an interior point
+ 
+
+ align:start position:0%
+an interior point
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sometimes in applications these cns
+
+ align:start position:0%
+so sometimes in applications these cns
+ 
+
+ align:start position:0%
+so sometimes in applications these cns
+are not necessarily closed but you know
+
+ align:start position:0%
+are not necessarily closed but you know
+ 
+
+ align:start position:0%
+are not necessarily closed but you know
+if m is equal to the union of these sets
+
+ align:start position:0%
+if m is equal to the union of these sets
+ 
+
+ align:start position:0%
+if m is equal to the union of these sets
+and it's also equal to the union of
+
+ align:start position:0%
+and it's also equal to the union of
+ 
+
+ align:start position:0%
+and it's also equal to the union of
+their closures and so what this theorem
+
+ align:start position:0%
+their closures and so what this theorem
+ 
+
+ align:start position:0%
+their closures and so what this theorem
+says is that if you can write a metric
+
+ align:start position:0%
+says is that if you can write a metric
+ 
+
+ align:start position:0%
+says is that if you can write a metric
+space as a union of sets
+
+ align:start position:0%
+space as a union of sets
+ 
+
+ align:start position:0%
+space as a union of sets
+then the closure of one of those sets
+
+ align:start position:0%
+then the closure of one of those sets
+ 
+
+ align:start position:0%
+then the closure of one of those sets
+has to contain an open ball
+
+ align:start position:0%
+has to contain an open ball
+ 
+
+ align:start position:0%
+has to contain an open ball
+and this um
+
+ align:start position:0%
+and this um
+ 
+
+ align:start position:0%
+and this um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+let's think a little bit of what it
+
+ align:start position:0%
+let's think a little bit of what it
+ 
+
+ align:start position:0%
+let's think a little bit of what it
+means for
+
+ align:start position:0%
+means for
+ 
+
+ align:start position:0%
+means for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or there's a specific terminology for
+
+ align:start position:0%
+or there's a specific terminology for
+ 
+
+ align:start position:0%
+or there's a specific terminology for
+when a closed
+
+ align:start position:0%
+when a closed
+ 
+
+ align:start position:0%
+when a closed
+when the closure of a set does not
+
+ align:start position:0%
+when the closure of a set does not
+ 
+
+ align:start position:0%
+when the closure of a set does not
+contain an open ball that means it's
+
+ align:start position:0%
+contain an open ball that means it's
+ 
+
+ align:start position:0%
+contain an open ball that means it's
+nowhere dense
+
+ align:start position:0%
+nowhere dense
+ 
+
+ align:start position:0%
+nowhere dense
+or that's
+
+ align:start position:0%
+or that's
+ 
+
+ align:start position:0%
+or that's
+the phrase we usually use for that is
+
+ align:start position:0%
+the phrase we usually use for that is
+ 
+
+ align:start position:0%
+the phrase we usually use for that is
+that it's nowhere dense
+
+ align:start position:0%
+that it's nowhere dense
+ 
+
+ align:start position:0%
+that it's nowhere dense
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+bears theorem says that if you have
+
+ align:start position:0%
+bears theorem says that if you have
+ 
+
+ align:start position:0%
+bears theorem says that if you have
+m equal to the union of
+
+ align:start position:0%
+m equal to the union of
+ 
+
+ align:start position:0%
+m equal to the union of
+a collection of sets then the closure of
+
+ align:start position:0%
+a collection of sets then the closure of
+ 
+
+ align:start position:0%
+a collection of sets then the closure of
+one of those sets has to be dense
+
+ align:start position:0%
+one of those sets has to be dense
+ 
+
+ align:start position:0%
+one of those sets has to be dense
+somewhere okay
+
+ align:start position:0%
+somewhere okay
+ 
+
+ align:start position:0%
+somewhere okay
+or you can't write m a complete metric
+
+ align:start position:0%
+or you can't write m a complete metric
+ 
+
+ align:start position:0%
+or you can't write m a complete metric
+space as the union of nowhere dense
+
+ align:start position:0%
+space as the union of nowhere dense
+ 
+
+ align:start position:0%
+space as the union of nowhere dense
+uh subsets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right um
+
+ align:start position:0%
+all right um
+ 
+
+ align:start position:0%
+all right um
+and so this theorem is quite simple to
+
+ align:start position:0%
+and so this theorem is quite simple to
+ 
+
+ align:start position:0%
+and so this theorem is quite simple to
+state it's quite
+
+ align:start position:0%
+state it's quite
+ 
+
+ align:start position:0%
+state it's quite
+very useful and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean quite powerful in applications in
+
+ align:start position:0%
+i mean quite powerful in applications in
+ 
+
+ align:start position:0%
+i mean quite powerful in applications in
+fact you can use this theorem to give an
+
+ align:start position:0%
+fact you can use this theorem to give an
+ 
+
+ align:start position:0%
+fact you can use this theorem to give an
+alternative proof to
+
+ align:start position:0%
+alternative proof to
+ 
+
+ align:start position:0%
+alternative proof to
+something that hopefully you saw in your
+
+ align:start position:0%
+something that hopefully you saw in your
+ 
+
+ align:start position:0%
+something that hopefully you saw in your
+analysis class which is that there
+
+ align:start position:0%
+analysis class which is that there
+ 
+
+ align:start position:0%
+analysis class which is that there
+exists a continuous function which is
+
+ align:start position:0%
+exists a continuous function which is
+ 
+
+ align:start position:0%
+exists a continuous function which is
+nowhere differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe i'll put that in the exercises
+
+ align:start position:0%
+maybe i'll put that in the exercises
+ 
+
+ align:start position:0%
+maybe i'll put that in the exercises
+maybe i'll just point you to it
+
+ align:start position:0%
+maybe i'll just point you to it
+ 
+
+ align:start position:0%
+maybe i'll just point you to it
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+we'll see
+
+ align:start position:0%
+we'll see
+ 
+
+ align:start position:0%
+we'll see
+all right so the proof is by
+
+ align:start position:0%
+all right so the proof is by
+ 
+
+ align:start position:0%
+all right so the proof is by
+contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i believe this is the first
+
+ align:start position:0%
+i believe this is the first
+ 
+
+ align:start position:0%
+i believe this is the first
+contradiction proof that we've done in
+
+ align:start position:0%
+contradiction proof that we've done in
+ 
+
+ align:start position:0%
+contradiction proof that we've done in
+the class
+
+ align:start position:0%
+the class
+ 
+
+ align:start position:0%
+the class
+so in 18100 a and b i mean
+
+ align:start position:0%
+so in 18100 a and b i mean
+ 
+
+ align:start position:0%
+so in 18100 a and b i mean
+you start off everything is by
+
+ align:start position:0%
+you start off everything is by
+ 
+
+ align:start position:0%
+you start off everything is by
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um let's suppose not
+
+ align:start position:0%
+um let's suppose not
+ 
+
+ align:start position:0%
+um let's suppose not
+i.e you can find there is a
+
+ align:start position:0%
+i.e you can find there is a
+ 
+
+ align:start position:0%
+i.e you can find there is a
+collection of closed
+
+ align:start position:0%
+collection of closed
+ 
+
+ align:start position:0%
+collection of closed
+subsets of m such that m is equal to
+
+ align:start position:0%
+subsets of m such that m is equal to
+ 
+
+ align:start position:0%
+subsets of m such that m is equal to
+this union and what we're going to do is
+
+ align:start position:0%
+this union and what we're going to do is
+ 
+
+ align:start position:0%
+this union and what we're going to do is
+we're going to find a point that's not
+
+ align:start position:0%
+we're going to find a point that's not
+ 
+
+ align:start position:0%
+we're going to find a point that's not
+in this union and therefore not an m and
+
+ align:start position:0%
+in this union and therefore not an m and
+ 
+
+ align:start position:0%
+in this union and therefore not an m and
+that'll be our contradiction
+
+ align:start position:0%
+that'll be our contradiction
+ 
+
+ align:start position:0%
+that'll be our contradiction
+we'll use uh
+
+ align:start position:0%
+we'll use uh
+ 
+
+ align:start position:0%
+we'll use uh
+the completeness of m to obtain this
+
+ align:start position:0%
+the completeness of m to obtain this
+ 
+
+ align:start position:0%
+the completeness of m to obtain this
+point because this how we're going to
+
+ align:start position:0%
+point because this how we're going to
+ 
+
+ align:start position:0%
+point because this how we're going to
+obtain this point is
+
+ align:start position:0%
+obtain this point is
+ 
+
+ align:start position:0%
+obtain this point is
+as a limit of a certain sequence
+
+ align:start position:0%
+as a limit of a certain sequence
+ 
+
+ align:start position:0%
+as a limit of a certain sequence
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to uh to be able to say that this limit
+
+ align:start position:0%
+to uh to be able to say that this limit
+ 
+
+ align:start position:0%
+to uh to be able to say that this limit
+exists we're going to show the sequences
+
+ align:start position:0%
+exists we're going to show the sequences
+ 
+
+ align:start position:0%
+exists we're going to show the sequences
+koshi
+
+ align:start position:0%
+koshi
+ 
+
+ align:start position:0%
+koshi
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so we're going to build up this sequence
+
+ align:start position:0%
+so we're going to build up this sequence
+ 
+
+ align:start position:0%
+so we're going to build up this sequence
+uh inductively
+
+ align:start position:0%
+uh inductively
+ 
+
+ align:start position:0%
+uh inductively
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i will write this inductive proof kind
+
+ align:start position:0%
+i will write this inductive proof kind
+ 
+
+ align:start position:0%
+i will write this inductive proof kind
+of carefully this first time
+
+ align:start position:0%
+of carefully this first time
+ 
+
+ align:start position:0%
+of carefully this first time
+and then in the future i'm just going to
+
+ align:start position:0%
+and then in the future i'm just going to
+ 
+
+ align:start position:0%
+and then in the future i'm just going to
+say okay
+
+ align:start position:0%
+say okay
+ 
+
+ align:start position:0%
+say okay
+choose p1 this way choose p2 this way
+
+ align:start position:0%
+choose p1 this way choose p2 this way
+ 
+
+ align:start position:0%
+choose p1 this way choose p2 this way
+continuing in this manner we obtain a
+
+ align:start position:0%
+continuing in this manner we obtain a
+ 
+
+ align:start position:0%
+continuing in this manner we obtain a
+sequence of points this blah blah blah
+
+ align:start position:0%
+sequence of points this blah blah blah
+ 
+
+ align:start position:0%
+sequence of points this blah blah blah
+but this point at this stage i'll write
+
+ align:start position:0%
+but this point at this stage i'll write
+ 
+
+ align:start position:0%
+but this point at this stage i'll write
+this uh inductive proof kind of
+
+ align:start position:0%
+this uh inductive proof kind of
+ 
+
+ align:start position:0%
+this uh inductive proof kind of
+carefully
+
+ align:start position:0%
+carefully
+ 
+
+ align:start position:0%
+carefully
+okay so suppose
+
+ align:start position:0%
+okay so suppose
+ 
+
+ align:start position:0%
+okay so suppose
+not um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certainly contains an open ball
+
+ align:start position:0%
+certainly contains an open ball
+ 
+
+ align:start position:0%
+certainly contains an open ball
+and c1 cannot
+
+ align:start position:0%
+and c1 cannot
+ 
+
+ align:start position:0%
+and c1 cannot
+contain an open ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies m does not equal to the
+
+ align:start position:0%
+this implies m does not equal to the
+ 
+
+ align:start position:0%
+this implies m does not equal to the
+first closed set otherwise the first
+
+ align:start position:0%
+first closed set otherwise the first
+ 
+
+ align:start position:0%
+first closed set otherwise the first
+closed set would contain an open ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus there exists an element p1
+
+ align:start position:0%
+thus there exists an element p1
+ 
+
+ align:start position:0%
+thus there exists an element p1
+and m take away c1
+
+ align:start position:0%
+and m take away c1
+ 
+
+ align:start position:0%
+and m take away c1
+now c1 is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that its complement is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore i can find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a small epsilon 1
+
+ align:start position:0%
+a small epsilon 1
+ 
+
+ align:start position:0%
+a small epsilon 1
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+the ball centered at
+
+ align:start position:0%
+the ball centered at
+ 
+
+ align:start position:0%
+the ball centered at
+p1
+
+ align:start position:0%
+p1
+ 
+
+ align:start position:0%
+p1
+of radius epsilon 1
+
+ align:start position:0%
+of radius epsilon 1
+ 
+
+ align:start position:0%
+of radius epsilon 1
+intersects c1 uh
+
+ align:start position:0%
+intersects c1 uh
+ 
+
+ align:start position:0%
+intersects c1 uh
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+the empty set
+
+ align:start position:0%
+the empty set
+ 
+
+ align:start position:0%
+the empty set
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i'm going to pick c2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+centered at p1 of radius
+
+ align:start position:0%
+centered at p1 of radius
+ 
+
+ align:start position:0%
+centered at p1 of radius
+epsilon 1 over
+
+ align:start position:0%
+epsilon 1 over
+ 
+
+ align:start position:0%
+epsilon 1 over
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+this is not contained in c2 because
+
+ align:start position:0%
+this is not contained in c2 because
+ 
+
+ align:start position:0%
+this is not contained in c2 because
+again this is by contradiction so we're
+
+ align:start position:0%
+again this is by contradiction so we're
+ 
+
+ align:start position:0%
+again this is by contradiction so we're
+assuming that m is written as a union of
+
+ align:start position:0%
+assuming that m is written as a union of
+ 
+
+ align:start position:0%
+assuming that m is written as a union of
+close sets and none of these close sets
+
+ align:start position:0%
+close sets and none of these close sets
+ 
+
+ align:start position:0%
+close sets and none of these close sets
+contain an open ball so this open ball
+
+ align:start position:0%
+contain an open ball so this open ball
+ 
+
+ align:start position:0%
+contain an open ball so this open ball
+cannot be contained in c2
+
+ align:start position:0%
+cannot be contained in c2
+ 
+
+ align:start position:0%
+cannot be contained in c2
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some point p2 in this open ball
+
+ align:start position:0%
+some point p2 in this open ball
+ 
+
+ align:start position:0%
+some point p2 in this open ball
+centered at p1 of radius epsilon 1 over
+
+ align:start position:0%
+centered at p1 of radius epsilon 1 over
+ 
+
+ align:start position:0%
+centered at p1 of radius epsilon 1 over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+p2
+
+ align:start position:0%
+p2
+ 
+
+ align:start position:0%
+p2
+is not in c2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now again
+
+ align:start position:0%
+now again
+ 
+
+ align:start position:0%
+now again
+c2 closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies that
+
+ align:start position:0%
+implies that
+ 
+
+ align:start position:0%
+implies that
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+an epsilon
+
+ align:start position:0%
+an epsilon
+ 
+
+ align:start position:0%
+an epsilon
+2 less than
+
+ align:start position:0%
+2 less than
+ 
+
+ align:start position:0%
+2 less than
+epsilon over 3 so we can make it very
+
+ align:start position:0%
+epsilon over 3 so we can make it very
+ 
+
+ align:start position:0%
+epsilon over 3 so we can make it very
+small if we wish
+
+ align:start position:0%
+small if we wish
+ 
+
+ align:start position:0%
+small if we wish
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ball
+
+ align:start position:0%
+the ball
+ 
+
+ align:start position:0%
+the ball
+centered at p2 of radius epsilon 2
+
+ align:start position:0%
+centered at p2 of radius epsilon 2
+ 
+
+ align:start position:0%
+centered at p2 of radius epsilon 2
+intersects c2 equals
+
+ align:start position:0%
+intersects c2 equals
+ 
+
+ align:start position:0%
+intersects c2 equals
+the empty set
+
+ align:start position:0%
+the empty set
+ 
+
+ align:start position:0%
+the empty set
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now i've picked uh p2
+
+ align:start position:0%
+so now i've picked uh p2
+ 
+
+ align:start position:0%
+so now i've picked uh p2
+p1 and p2 now
+
+ align:start position:0%
+p1 and p2 now
+ 
+
+ align:start position:0%
+p1 and p2 now
+at this point i would usually say
+
+ align:start position:0%
+at this point i would usually say
+ 
+
+ align:start position:0%
+at this point i would usually say
+continuing in this manner we obtain a
+
+ align:start position:0%
+continuing in this manner we obtain a
+ 
+
+ align:start position:0%
+continuing in this manner we obtain a
+sequence of points but let me write out
+
+ align:start position:0%
+sequence of points but let me write out
+ 
+
+ align:start position:0%
+sequence of points but let me write out
+the argument carefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k points
+
+ align:start position:0%
+k points
+ 
+
+ align:start position:0%
+k points
+p1
+
+ align:start position:0%
+p1
+ 
+
+ align:start position:0%
+p1
+pk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1
+
+ align:start position:0%
+epsilon 1
+ 
+
+ align:start position:0%
+epsilon 1
+epsilon k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+two things occur
+
+ align:start position:0%
+two things occur
+ 
+
+ align:start position:0%
+two things occur
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+epsilon k is less than
+
+ align:start position:0%
+epsilon k is less than
+ 
+
+ align:start position:0%
+epsilon k is less than
+epsilon k minus one over three
+
+ align:start position:0%
+epsilon k minus one over three
+ 
+
+ align:start position:0%
+epsilon k minus one over three
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+less than epsilon k minus uh two over
+
+ align:start position:0%
+less than epsilon k minus uh two over
+ 
+
+ align:start position:0%
+less than epsilon k minus uh two over
+three and so on all the way down to
+
+ align:start position:0%
+three and so on all the way down to
+ 
+
+ align:start position:0%
+three and so on all the way down to
+epsilon 1 over
+
+ align:start position:0%
+epsilon 1 over
+ 
+
+ align:start position:0%
+epsilon 1 over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+k minus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you like
+
+ align:start position:0%
+so if you like
+ 
+
+ align:start position:0%
+so if you like
+k here is bigger than or equal to 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh pj
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfy
+
+ align:start position:0%
+satisfy
+ 
+
+ align:start position:0%
+satisfy
+pj is in the ball centered at p j minus
+
+ align:start position:0%
+pj is in the ball centered at p j minus
+ 
+
+ align:start position:0%
+pj is in the ball centered at p j minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+of radius epsilon j minus one over three
+
+ align:start position:0%
+of radius epsilon j minus one over three
+ 
+
+ align:start position:0%
+of radius epsilon j minus one over three
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the ball
+
+ align:start position:0%
+the ball
+ 
+
+ align:start position:0%
+the ball
+of centered at p j
+
+ align:start position:0%
+of centered at p j
+ 
+
+ align:start position:0%
+of centered at p j
+epsilon j intersect c
+
+ align:start position:0%
+epsilon j intersect c
+ 
+
+ align:start position:0%
+epsilon j intersect c
+j equals
+
+ align:start position:0%
+j equals
+ 
+
+ align:start position:0%
+j equals
+the empty set
+
+ align:start position:0%
+the empty set
+ 
+
+ align:start position:0%
+the empty set
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me start those uh
+
+ align:start position:0%
+let me start those uh
+ 
+
+ align:start position:0%
+let me start those uh
+two properties right there
+
+ align:start position:0%
+two properties right there
+ 
+
+ align:start position:0%
+two properties right there
+we're gonna obtain
+
+ align:start position:0%
+we're gonna obtain
+ 
+
+ align:start position:0%
+we're gonna obtain
+another point
+
+ align:start position:0%
+another point
+ 
+
+ align:start position:0%
+another point
+satisfying those two properties
+
+ align:start position:0%
+satisfying those two properties
+ 
+
+ align:start position:0%
+satisfying those two properties
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know why i'm being a stickler it
+
+ align:start position:0%
+i don't know why i'm being a stickler it
+ 
+
+ align:start position:0%
+i don't know why i'm being a stickler it
+doesn't really matter but let me put a
+
+ align:start position:0%
+doesn't really matter but let me put a
+ 
+
+ align:start position:0%
+doesn't really matter but let me put a
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because that's not necessarily satisfied
+
+ align:start position:0%
+because that's not necessarily satisfied
+ 
+
+ align:start position:0%
+because that's not necessarily satisfied
+for p1 but okay
+
+ align:start position:0%
+for p1 but okay
+ 
+
+ align:start position:0%
+for p1 but okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now i want to show there exist i can
+
+ align:start position:0%
+now i want to show there exist i can
+ 
+
+ align:start position:0%
+now i want to show there exist i can
+obtain
+
+ align:start position:0%
+obtain
+ 
+
+ align:start position:0%
+obtain
+a k plus first point satisfying
+
+ align:start position:0%
+a k plus first point satisfying
+ 
+
+ align:start position:0%
+a k plus first point satisfying
+those two properties okay
+
+ align:start position:0%
+those two properties okay
+ 
+
+ align:start position:0%
+those two properties okay
+again this is just formally saying that
+
+ align:start position:0%
+again this is just formally saying that
+ 
+
+ align:start position:0%
+again this is just formally saying that
+once i've chosen p2 then i can choose a
+
+ align:start position:0%
+once i've chosen p2 then i can choose a
+ 
+
+ align:start position:0%
+once i've chosen p2 then i can choose a
+p3
+
+ align:start position:0%
+p3
+ 
+
+ align:start position:0%
+p3
+doing this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argument again and it'll satisfy
+
+ align:start position:0%
+argument again and it'll satisfy
+ 
+
+ align:start position:0%
+argument again and it'll satisfy
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+p2 satisfied with epsilon one except now
+
+ align:start position:0%
+p2 satisfied with epsilon one except now
+ 
+
+ align:start position:0%
+p2 satisfied with epsilon one except now
+with epsilon two but now i'm just making
+
+ align:start position:0%
+with epsilon two but now i'm just making
+ 
+
+ align:start position:0%
+with epsilon two but now i'm just making
+it more formal so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now again m is the union of all these
+
+ align:start position:0%
+now again m is the union of all these
+ 
+
+ align:start position:0%
+now again m is the union of all these
+closed sets none of which contain an
+
+ align:start position:0%
+closed sets none of which contain an
+ 
+
+ align:start position:0%
+closed sets none of which contain an
+open ball
+
+ align:start position:0%
+open ball
+ 
+
+ align:start position:0%
+open ball
+so since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ball
+
+ align:start position:0%
+the ball
+ 
+
+ align:start position:0%
+the ball
+of radius p k
+
+ align:start position:0%
+of radius p k
+ 
+
+ align:start position:0%
+of radius p k
+epsilon k over 3
+
+ align:start position:0%
+epsilon k over 3
+ 
+
+ align:start position:0%
+epsilon k over 3
+is not contained
+
+ align:start position:0%
+is not contained
+ 
+
+ align:start position:0%
+is not contained
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+k plus 1.
+
+ align:start position:0%
+k plus 1.
+ 
+
+ align:start position:0%
+k plus 1.
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+element pk plus one
+
+ align:start position:0%
+element pk plus one
+ 
+
+ align:start position:0%
+element pk plus one
+not in
+
+ align:start position:0%
+not in
+ 
+
+ align:start position:0%
+not in
+ck plus one or i should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p k plus 1 is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ck plus one
+
+ align:start position:0%
+ck plus one
+ 
+
+ align:start position:0%
+ck plus one
+okay so let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's pk
+
+ align:start position:0%
+there's pk
+ 
+
+ align:start position:0%
+there's pk
+epsilon k
+
+ align:start position:0%
+epsilon k
+ 
+
+ align:start position:0%
+epsilon k
+over three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c k plus one
+
+ align:start position:0%
+c k plus one
+ 
+
+ align:start position:0%
+c k plus one
+so maybe they're not disjoint maybe
+
+ align:start position:0%
+so maybe they're not disjoint maybe
+ 
+
+ align:start position:0%
+so maybe they're not disjoint maybe
+there's some overlap but then i can find
+
+ align:start position:0%
+there's some overlap but then i can find
+ 
+
+ align:start position:0%
+there's some overlap but then i can find
+a point p k plus one um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in there that's not in ck plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists an epsilon k plus one which
+
+ align:start position:0%
+there exists an epsilon k plus one which
+ 
+
+ align:start position:0%
+there exists an epsilon k plus one which
+i can choose very small say smaller than
+
+ align:start position:0%
+i can choose very small say smaller than
+ 
+
+ align:start position:0%
+i can choose very small say smaller than
+epsilon k over 3
+
+ align:start position:0%
+epsilon k over 3
+ 
+
+ align:start position:0%
+epsilon k over 3
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+again because ck plus 1 is closed
+
+ align:start position:0%
+again because ck plus 1 is closed
+ 
+
+ align:start position:0%
+again because ck plus 1 is closed
+pk plus 1 is not in ck plus 1. so i can
+
+ align:start position:0%
+pk plus 1 is not in ck plus 1. so i can
+ 
+
+ align:start position:0%
+pk plus 1 is not in ck plus 1. so i can
+find a small
+
+ align:start position:0%
+find a small
+ 
+
+ align:start position:0%
+find a small
+ball around pk plus 1 disjoint from ck
+
+ align:start position:0%
+ball around pk plus 1 disjoint from ck
+ 
+
+ align:start position:0%
+ball around pk plus 1 disjoint from ck
+plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersect ck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+the empty set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then
+
+ align:start position:0%
+okay so then
+ 
+
+ align:start position:0%
+okay so then
+uh given k points i can then choose a k
+
+ align:start position:0%
+uh given k points i can then choose a k
+ 
+
+ align:start position:0%
+uh given k points i can then choose a k
+plus first point
+
+ align:start position:0%
+plus first point
+ 
+
+ align:start position:0%
+plus first point
+uh satisfying these two bullet points
+
+ align:start position:0%
+uh satisfying these two bullet points
+ 
+
+ align:start position:0%
+uh satisfying these two bullet points
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by induction we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found a sequence of points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and m
+
+ align:start position:0%
+and m
+ 
+
+ align:start position:0%
+and m
+such that and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon k so if you like k starts at 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon k and 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that for all k
+
+ align:start position:0%
+such that for all k
+ 
+
+ align:start position:0%
+such that for all k
+those two bullet points hold such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which i denoted which i put a little
+
+ align:start position:0%
+which i denoted which i put a little
+ 
+
+ align:start position:0%
+which i denoted which i put a little
+star by star hold so i'm talking about
+
+ align:start position:0%
+star by star hold so i'm talking about
+ 
+
+ align:start position:0%
+star by star hold so i'm talking about
+these two points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when i say star i mean
+
+ align:start position:0%
+so when i say star i mean
+ 
+
+ align:start position:0%
+so when i say star i mean
+these two statements here
+
+ align:start position:0%
+these two statements here
+ 
+
+ align:start position:0%
+these two statements here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's show that this sequence is
+
+ align:start position:0%
+now let's show that this sequence is
+ 
+
+ align:start position:0%
+now let's show that this sequence is
+koshy so now i claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+follows so i'm not going to write out
+
+ align:start position:0%
+follows so i'm not going to write out
+ 
+
+ align:start position:0%
+follows so i'm not going to write out
+the full epsilon m argument but i'm just
+
+ align:start position:0%
+the full epsilon m argument but i'm just
+ 
+
+ align:start position:0%
+the full epsilon m argument but i'm just
+going to write down the crucial estimate
+
+ align:start position:0%
+going to write down the crucial estimate
+ 
+
+ align:start position:0%
+going to write down the crucial estimate
+that proves this this follows from
+
+ align:start position:0%
+that proves this this follows from
+ 
+
+ align:start position:0%
+that proves this this follows from
+the fact that for all
+
+ align:start position:0%
+the fact that for all
+ 
+
+ align:start position:0%
+the fact that for all
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all l
+
+ align:start position:0%
+for all l
+ 
+
+ align:start position:0%
+for all l
+if i look at the distance between p k
+
+ align:start position:0%
+if i look at the distance between p k
+ 
+
+ align:start position:0%
+if i look at the distance between p k
+and p k a plus l because you know in the
+
+ align:start position:0%
+and p k a plus l because you know in the
+ 
+
+ align:start position:0%
+and p k a plus l because you know in the
+end when i look at um if i want to show
+
+ align:start position:0%
+end when i look at um if i want to show
+ 
+
+ align:start position:0%
+end when i look at um if i want to show
+something's koshy i need to take the
+
+ align:start position:0%
+something's koshy i need to take the
+ 
+
+ align:start position:0%
+something's koshy i need to take the
+difference of two or the distance
+
+ align:start position:0%
+difference of two or the distance
+ 
+
+ align:start position:0%
+difference of two or the distance
+between two points um
+
+ align:start position:0%
+between two points um
+ 
+
+ align:start position:0%
+between two points um
+one you know i can choose as uh the
+
+ align:start position:0%
+one you know i can choose as uh the
+ 
+
+ align:start position:0%
+one you know i can choose as uh the
+point occurring earlier in the sequence
+
+ align:start position:0%
+point occurring earlier in the sequence
+ 
+
+ align:start position:0%
+point occurring earlier in the sequence
+and then one occurring later
+
+ align:start position:0%
+and then one occurring later
+ 
+
+ align:start position:0%
+and then one occurring later
+anyways
+
+ align:start position:0%
+anyways
+ 
+
+ align:start position:0%
+anyways
+then by the triangle inequality repeated
+
+ align:start position:0%
+then by the triangle inequality repeated
+ 
+
+ align:start position:0%
+then by the triangle inequality repeated
+i can write that this is less than or
+
+ align:start position:0%
+i can write that this is less than or
+ 
+
+ align:start position:0%
+i can write that this is less than or
+equal to the distance from p k
+
+ align:start position:0%
+equal to the distance from p k
+ 
+
+ align:start position:0%
+equal to the distance from p k
+p k plus one
+
+ align:start position:0%
+p k plus one
+ 
+
+ align:start position:0%
+p k plus one
+plus the distance from p
+
+ align:start position:0%
+plus the distance from p
+ 
+
+ align:start position:0%
+plus the distance from p
+k plus one p k plus l
+
+ align:start position:0%
+k plus one p k plus l
+ 
+
+ align:start position:0%
+k plus one p k plus l
+and now i could do the triangle
+
+ align:start position:0%
+and now i could do the triangle
+ 
+
+ align:start position:0%
+and now i could do the triangle
+inequality again
+
+ align:start position:0%
+inequality again
+ 
+
+ align:start position:0%
+inequality again
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so i get that this is less than or equal
+
+ align:start position:0%
+so i get that this is less than or equal
+ 
+
+ align:start position:0%
+so i get that this is less than or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the distance from p k to p k plus 1 plus
+
+ align:start position:0%
+the distance from p k to p k plus 1 plus
+ 
+
+ align:start position:0%
+the distance from p k to p k plus 1 plus
+the distance from p k
+
+ align:start position:0%
+the distance from p k
+ 
+
+ align:start position:0%
+the distance from p k
+plus 1 to p k plus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on until i get to the distance
+
+ align:start position:0%
+and so on until i get to the distance
+ 
+
+ align:start position:0%
+and so on until i get to the distance
+between p
+
+ align:start position:0%
+between p
+ 
+
+ align:start position:0%
+between p
+k plus l minus 1
+
+ align:start position:0%
+k plus l minus 1
+ 
+
+ align:start position:0%
+k plus l minus 1
+and p k plus l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh by star what's in yellow
+
+ align:start position:0%
+uh by star what's in yellow
+ 
+
+ align:start position:0%
+uh by star what's in yellow
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+p k plus one is in the epsilon k over
+
+ align:start position:0%
+p k plus one is in the epsilon k over
+ 
+
+ align:start position:0%
+p k plus one is in the epsilon k over
+three ball
+
+ align:start position:0%
+three ball
+ 
+
+ align:start position:0%
+three ball
+uh centered at p k
+
+ align:start position:0%
+uh centered at p k
+ 
+
+ align:start position:0%
+uh centered at p k
+so this is less than epsilon k
+
+ align:start position:0%
+so this is less than epsilon k
+ 
+
+ align:start position:0%
+so this is less than epsilon k
+over three and the same thing here less
+
+ align:start position:0%
+over three and the same thing here less
+ 
+
+ align:start position:0%
+over three and the same thing here less
+than epsilon k plus one
+
+ align:start position:0%
+than epsilon k plus one
+ 
+
+ align:start position:0%
+than epsilon k plus one
+over three
+
+ align:start position:0%
+over three
+ 
+
+ align:start position:0%
+over three
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+k plus l minus 1
+
+ align:start position:0%
+k plus l minus 1
+ 
+
+ align:start position:0%
+k plus l minus 1
+over 3.
+
+ align:start position:0%
+over 3.
+ 
+
+ align:start position:0%
+over 3.
+and now all of those are less than uh
+
+ align:start position:0%
+and now all of those are less than uh
+ 
+
+ align:start position:0%
+and now all of those are less than uh
+if you go to the first one is less than
+
+ align:start position:0%
+if you go to the first one is less than
+ 
+
+ align:start position:0%
+if you go to the first one is less than
+epsilon 1 over 3k minus of 1 so then
+
+ align:start position:0%
+epsilon 1 over 3k minus of 1 so then
+ 
+
+ align:start position:0%
+epsilon 1 over 3k minus of 1 so then
+this is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1 over
+
+ align:start position:0%
+epsilon 1 over
+ 
+
+ align:start position:0%
+epsilon 1 over
+3 k plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1 over 3
+
+ align:start position:0%
+epsilon 1 over 3
+ 
+
+ align:start position:0%
+epsilon 1 over 3
+k plus l
+
+ align:start position:0%
+k plus l
+ 
+
+ align:start position:0%
+k plus l
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i can actually sum this up right
+
+ align:start position:0%
+and now i can actually sum this up right
+ 
+
+ align:start position:0%
+and now i can actually sum this up right
+this is equal to and this is
+
+ align:start position:0%
+this is equal to and this is
+ 
+
+ align:start position:0%
+this is equal to and this is
+strictly less than uh
+
+ align:start position:0%
+strictly less than uh
+ 
+
+ align:start position:0%
+strictly less than uh
+epsilon one and if i summed now from
+
+ align:start position:0%
+epsilon one and if i summed now from
+ 
+
+ align:start position:0%
+epsilon one and if i summed now from
+l equals k to infinity one over
+
+ align:start position:0%
+l equals k to infinity one over
+ 
+
+ align:start position:0%
+l equals k to infinity one over
+three k this is equal to
+
+ align:start position:0%
+three k this is equal to
+ 
+
+ align:start position:0%
+three k this is equal to
+one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1 3 k
+
+ align:start position:0%
+epsilon 1 3 k
+ 
+
+ align:start position:0%
+epsilon 1 3 k
+1 over 1 minus 1 3
+
+ align:start position:0%
+1 over 1 minus 1 3
+ 
+
+ align:start position:0%
+1 over 1 minus 1 3
+which equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1 over 2
+
+ align:start position:0%
+epsilon 1 over 2
+ 
+
+ align:start position:0%
+epsilon 1 over 2
+3 to the minus k
+
+ align:start position:0%
+3 to the minus k
+ 
+
+ align:start position:0%
+3 to the minus k
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+okay so the distance between a point p k
+
+ align:start position:0%
+okay so the distance between a point p k
+ 
+
+ align:start position:0%
+okay so the distance between a point p k
+and p k plus l
+
+ align:start position:0%
+and p k plus l
+ 
+
+ align:start position:0%
+and p k plus l
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+some constant times three to the minus k
+
+ align:start position:0%
+some constant times three to the minus k
+ 
+
+ align:start position:0%
+some constant times three to the minus k
+uh plus one so if k is very large this
+
+ align:start position:0%
+uh plus one so if k is very large this
+ 
+
+ align:start position:0%
+uh plus one so if k is very large this
+is very small independent of l okay so i
+
+ align:start position:0%
+is very small independent of l okay so i
+ 
+
+ align:start position:0%
+is very small independent of l okay so i
+shouldn't have used l here
+
+ align:start position:0%
+shouldn't have used l here
+ 
+
+ align:start position:0%
+shouldn't have used l here
+and that's uh
+
+ align:start position:0%
+and that's uh
+ 
+
+ align:start position:0%
+and that's uh
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this shows that the sequence is koshy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since m is complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+p and m
+
+ align:start position:0%
+p and m
+ 
+
+ align:start position:0%
+p and m
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+these elements p k
+
+ align:start position:0%
+these elements p k
+ 
+
+ align:start position:0%
+these elements p k
+converge to p
+
+ align:start position:0%
+converge to p
+ 
+
+ align:start position:0%
+converge to p
+and now we're going to show this point p
+
+ align:start position:0%
+and now we're going to show this point p
+ 
+
+ align:start position:0%
+and now we're going to show this point p
+does not lie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in any of the cj's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll do it by showing it's
+
+ align:start position:0%
+and we'll do it by showing it's
+ 
+
+ align:start position:0%
+and we'll do it by showing it's
+essentially in all of these
+
+ align:start position:0%
+essentially in all of these
+ 
+
+ align:start position:0%
+essentially in all of these
+balls pj epsilon j
+
+ align:start position:0%
+balls pj epsilon j
+ 
+
+ align:start position:0%
+balls pj epsilon j
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and it's kind of a similar
+
+ align:start position:0%
+all right and it's kind of a similar
+ 
+
+ align:start position:0%
+all right and it's kind of a similar
+computation to what we just did
+
+ align:start position:0%
+computation to what we just did
+ 
+
+ align:start position:0%
+computation to what we just did
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all k
+
+ align:start position:0%
+for all k
+ 
+
+ align:start position:0%
+for all k
+natural number if we look at the
+
+ align:start position:0%
+natural number if we look at the
+ 
+
+ align:start position:0%
+natural number if we look at the
+distance between
+
+ align:start position:0%
+distance between
+ 
+
+ align:start position:0%
+distance between
+pk
+
+ align:start position:0%
+pk
+ 
+
+ align:start position:0%
+pk
+plus 1
+
+ align:start position:0%
+plus 1
+ 
+
+ align:start position:0%
+plus 1
+pk plus 1 plus l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again if i
+
+ align:start position:0%
+again if i
+ 
+
+ align:start position:0%
+again if i
+so if i just go back to
+
+ align:start position:0%
+so if i just go back to
+ 
+
+ align:start position:0%
+so if i just go back to
+this computation right here
+
+ align:start position:0%
+this computation right here
+ 
+
+ align:start position:0%
+this computation right here
+right this we proved was less than
+
+ align:start position:0%
+right this we proved was less than
+ 
+
+ align:start position:0%
+right this we proved was less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+k plus one
+
+ align:start position:0%
+k plus one
+ 
+
+ align:start position:0%
+k plus one
+times one over three
+
+ align:start position:0%
+times one over three
+ 
+
+ align:start position:0%
+times one over three
+k plus one
+
+ align:start position:0%
+k plus one
+ 
+
+ align:start position:0%
+k plus one
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+uh actually one over three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus one over three squared plus
+
+ align:start position:0%
+plus one over three squared plus
+ 
+
+ align:start position:0%
+plus one over three squared plus
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+one over
+
+ align:start position:0%
+one over
+ 
+
+ align:start position:0%
+one over
+three k plus one um
+
+ align:start position:0%
+three k plus one um
+ 
+
+ align:start position:0%
+three k plus one um
+no k plus l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or i'm sorry i think that's just l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+this thing is less than if i replace it
+
+ align:start position:0%
+this thing is less than if i replace it
+ 
+
+ align:start position:0%
+this thing is less than if i replace it
+by the infinite sum so this is less than
+
+ align:start position:0%
+by the infinite sum so this is less than
+ 
+
+ align:start position:0%
+by the infinite sum so this is less than
+epsilon k plus 1
+
+ align:start position:0%
+epsilon k plus 1
+ 
+
+ align:start position:0%
+epsilon k plus 1
+times the infinite sum again
+
+ align:start position:0%
+times the infinite sum again
+ 
+
+ align:start position:0%
+times the infinite sum again
+m equals 0 to infinity
+
+ align:start position:0%
+m equals 0 to infinity
+ 
+
+ align:start position:0%
+m equals 0 to infinity
+3 to the minus m
+
+ align:start position:0%
+3 to the minus m
+ 
+
+ align:start position:0%
+3 to the minus m
+which equals
+
+ align:start position:0%
+which equals
+ 
+
+ align:start position:0%
+which equals
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is again equal to
+
+ align:start position:0%
+so this is again equal to
+ 
+
+ align:start position:0%
+so this is again equal to
+epsilon k plus one times
+
+ align:start position:0%
+epsilon k plus one times
+ 
+
+ align:start position:0%
+epsilon k plus one times
+three halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we've proven that uh the distance
+
+ align:start position:0%
+we've proven that uh the distance
+ 
+
+ align:start position:0%
+we've proven that uh the distance
+between pk plus one pk plus one plus l
+
+ align:start position:0%
+between pk plus one pk plus one plus l
+ 
+
+ align:start position:0%
+between pk plus one pk plus one plus l
+is less than uh epsilon
+
+ align:start position:0%
+is less than uh epsilon
+ 
+
+ align:start position:0%
+is less than uh epsilon
+k plus one um
+
+ align:start position:0%
+k plus one um
+ 
+
+ align:start position:0%
+k plus one um
+times three over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me take the limit as l goes to
+
+ align:start position:0%
+let me take the limit as l goes to
+ 
+
+ align:start position:0%
+let me take the limit as l goes to
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pk plus 1 plus l converges to the point
+
+ align:start position:0%
+pk plus 1 plus l converges to the point
+ 
+
+ align:start position:0%
+pk plus 1 plus l converges to the point
+p so i get that the distance
+
+ align:start position:0%
+p so i get that the distance
+ 
+
+ align:start position:0%
+p so i get that the distance
+between p k plus 1
+
+ align:start position:0%
+between p k plus 1
+ 
+
+ align:start position:0%
+between p k plus 1
+and the point p
+
+ align:start position:0%
+and the point p
+ 
+
+ align:start position:0%
+and the point p
+is less than or equal to um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three halves
+
+ align:start position:0%
+three halves
+ 
+
+ align:start position:0%
+three halves
+epsilon k plus one and remember epsilon
+
+ align:start position:0%
+epsilon k plus one and remember epsilon
+ 
+
+ align:start position:0%
+epsilon k plus one and remember epsilon
+k plus one is less than
+
+ align:start position:0%
+k plus one is less than
+ 
+
+ align:start position:0%
+k plus one is less than
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a third epsilon k so this is
+
+ align:start position:0%
+a third epsilon k so this is
+ 
+
+ align:start position:0%
+a third epsilon k so this is
+less than one half epsilon k
+
+ align:start position:0%
+less than one half epsilon k
+ 
+
+ align:start position:0%
+less than one half epsilon k
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and since pk plus one remember this is
+
+ align:start position:0%
+and since pk plus one remember this is
+ 
+
+ align:start position:0%
+and since pk plus one remember this is
+in the ball of radius one third epsilon
+
+ align:start position:0%
+in the ball of radius one third epsilon
+ 
+
+ align:start position:0%
+in the ball of radius one third epsilon
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+so i get that the distance between pk
+
+ align:start position:0%
+so i get that the distance between pk
+ 
+
+ align:start position:0%
+so i get that the distance between pk
+and p
+
+ align:start position:0%
+and p
+ 
+
+ align:start position:0%
+and p
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+the distance between pk and pk plus one
+
+ align:start position:0%
+the distance between pk and pk plus one
+ 
+
+ align:start position:0%
+the distance between pk and pk plus one
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+and p
+
+ align:start position:0%
+and p
+ 
+
+ align:start position:0%
+and p
+we get this is less than or equal to a
+
+ align:start position:0%
+we get this is less than or equal to a
+ 
+
+ align:start position:0%
+we get this is less than or equal to a
+third epsilon k
+
+ align:start position:0%
+third epsilon k
+ 
+
+ align:start position:0%
+third epsilon k
+plus a half epsilon k and this is less
+
+ align:start position:0%
+plus a half epsilon k and this is less
+ 
+
+ align:start position:0%
+plus a half epsilon k and this is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+epsilon k which means that
+
+ align:start position:0%
+epsilon k which means that
+ 
+
+ align:start position:0%
+epsilon k which means that
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+is in the ball of radius p k of radius
+
+ align:start position:0%
+is in the ball of radius p k of radius
+ 
+
+ align:start position:0%
+is in the ball of radius p k of radius
+epsilon k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+by the second property up in star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fact that all these balls are
+
+ align:start position:0%
+the fact that all these balls are
+ 
+
+ align:start position:0%
+the fact that all these balls are
+disjoint from
+
+ align:start position:0%
+disjoint from
+ 
+
+ align:start position:0%
+disjoint from
+each of the balls that's disjoint from
+
+ align:start position:0%
+each of the balls that's disjoint from
+ 
+
+ align:start position:0%
+each of the balls that's disjoint from
+ck means p is not
+
+ align:start position:0%
+ck means p is not
+ 
+
+ align:start position:0%
+ck means p is not
+in ck now k was arbitrary here
+
+ align:start position:0%
+in ck now k was arbitrary here
+ 
+
+ align:start position:0%
+in ck now k was arbitrary here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we conclude that p
+
+ align:start position:0%
+we conclude that p
+ 
+
+ align:start position:0%
+we conclude that p
+is not in
+
+ align:start position:0%
+is not in
+ 
+
+ align:start position:0%
+is not in
+this union
+
+ align:start position:0%
+this union
+ 
+
+ align:start position:0%
+this union
+which gives me which is equal to m
+
+ align:start position:0%
+which gives me which is equal to m
+ 
+
+ align:start position:0%
+which gives me which is equal to m
+and that's a contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i mean you know i said the strategy
+
+ align:start position:0%
+so i mean you know i said the strategy
+ 
+
+ align:start position:0%
+so i mean you know i said the strategy
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+top of the proof
+
+ align:start position:0%
+top of the proof
+ 
+
+ align:start position:0%
+top of the proof
+you know we the technical argument maybe
+
+ align:start position:0%
+you know we the technical argument maybe
+ 
+
+ align:start position:0%
+you know we the technical argument maybe
+muddled what was going on but again the
+
+ align:start position:0%
+muddled what was going on but again the
+ 
+
+ align:start position:0%
+muddled what was going on but again the
+point is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know you can build
+
+ align:start position:0%
+you know you can build
+ 
+
+ align:start position:0%
+you know you can build
+if this conclusion does not hold you can
+
+ align:start position:0%
+if this conclusion does not hold you can
+ 
+
+ align:start position:0%
+if this conclusion does not hold you can
+build
+
+ align:start position:0%
+build
+ 
+
+ align:start position:0%
+build
+a sequence which has this uh
+
+ align:start position:0%
+a sequence which has this uh
+ 
+
+ align:start position:0%
+a sequence which has this uh
+disjointness property from this
+
+ align:start position:0%
+disjointness property from this
+ 
+
+ align:start position:0%
+disjointness property from this
+collection of open sets
+
+ align:start position:0%
+collection of open sets
+ 
+
+ align:start position:0%
+collection of open sets
+uh such that the sequence is koshi
+
+ align:start position:0%
+uh such that the sequence is koshi
+ 
+
+ align:start position:0%
+uh such that the sequence is koshi
+and because m is a complete metric space
+
+ align:start position:0%
+and because m is a complete metric space
+ 
+
+ align:start position:0%
+and because m is a complete metric space
+you can then extract a limit p this
+
+ align:start position:0%
+you can then extract a limit p this
+ 
+
+ align:start position:0%
+you can then extract a limit p this
+limit p will have all the properties
+
+ align:start position:0%
+limit p will have all the properties
+ 
+
+ align:start position:0%
+limit p will have all the properties
+that these pk's had namely that they're
+
+ align:start position:0%
+that these pk's had namely that they're
+ 
+
+ align:start position:0%
+that these pk's had namely that they're
+not in any of the c
+
+ align:start position:0%
+not in any of the c
+ 
+
+ align:start position:0%
+not in any of the c
+k's
+
+ align:start position:0%
+k's
+ 
+
+ align:start position:0%
+k's
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+this point p does not lie in
+
+ align:start position:0%
+this point p does not lie in
+ 
+
+ align:start position:0%
+this point p does not lie in
+the metric space which is nonsense so we
+
+ align:start position:0%
+the metric space which is nonsense so we
+ 
+
+ align:start position:0%
+the metric space which is nonsense so we
+arrived at our contradiction and
+
+ align:start position:0%
+arrived at our contradiction and
+ 
+
+ align:start position:0%
+arrived at our contradiction and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+bears category theorem is proven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's bear categories theorem
+
+ align:start position:0%
+let's bear categories theorem
+ 
+
+ align:start position:0%
+let's bear categories theorem
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's now use this to prove some some
+
+ align:start position:0%
+let's now use this to prove some some
+ 
+
+ align:start position:0%
+let's now use this to prove some some
+fundamental results of functional
+
+ align:start position:0%
+fundamental results of functional
+ 
+
+ align:start position:0%
+fundamental results of functional
+analysis so the first result we'll prove
+
+ align:start position:0%
+analysis so the first result we'll prove
+ 
+
+ align:start position:0%
+analysis so the first result we'll prove
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+what's called the uniform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundedness theorem
+
+ align:start position:0%
+boundedness theorem
+ 
+
+ align:start position:0%
+boundedness theorem
+which says that if you have a
+
+ align:start position:0%
+which says that if you have a
+ 
+
+ align:start position:0%
+which says that if you have a
+a sequence of linear bounded linear
+
+ align:start position:0%
+a sequence of linear bounded linear
+ 
+
+ align:start position:0%
+a sequence of linear bounded linear
+operators on a bonnet space
+
+ align:start position:0%
+operators on a bonnet space
+ 
+
+ align:start position:0%
+operators on a bonnet space
+then point wise boundedness implies sort
+
+ align:start position:0%
+then point wise boundedness implies sort
+ 
+
+ align:start position:0%
+then point wise boundedness implies sort
+of uniform boundedness
+
+ align:start position:0%
+of uniform boundedness
+ 
+
+ align:start position:0%
+of uniform boundedness
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or boundedness and a uniform boundedness
+
+ align:start position:0%
+or boundedness and a uniform boundedness
+ 
+
+ align:start position:0%
+or boundedness and a uniform boundedness
+in the operator norm
+
+ align:start position:0%
+in the operator norm
+ 
+
+ align:start position:0%
+in the operator norm
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let b be
+
+ align:start position:0%
+let b be
+ 
+
+ align:start position:0%
+let b be
+bonux base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let t n
+
+ align:start position:0%
+and let t n
+ 
+
+ align:start position:0%
+and let t n
+be a sequence of bounded linear
+
+ align:start position:0%
+be a sequence of bounded linear
+ 
+
+ align:start position:0%
+be a sequence of bounded linear
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we denoted last time by this
+
+ align:start position:0%
+which we denoted last time by this
+ 
+
+ align:start position:0%
+which we denoted last time by this
+script b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to some other norm space v
+
+ align:start position:0%
+to some other norm space v
+ 
+
+ align:start position:0%
+to some other norm space v
+okay so i didn't write that but
+
+ align:start position:0%
+okay so i didn't write that but
+ 
+
+ align:start position:0%
+okay so i didn't write that but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+v is a norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+for all b and capital b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup
+
+ align:start position:0%
+soup
+ 
+
+ align:start position:0%
+soup
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+t n b
+
+ align:start position:0%
+t n b
+ 
+
+ align:start position:0%
+t n b
+norm
+
+ align:start position:0%
+norm
+ 
+
+ align:start position:0%
+norm
+is less than infinity so if i assume
+
+ align:start position:0%
+is less than infinity so if i assume
+ 
+
+ align:start position:0%
+is less than infinity so if i assume
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this sequence is point wise bounded
+
+ align:start position:0%
+this sequence is point wise bounded
+ 
+
+ align:start position:0%
+this sequence is point wise bounded
+point-wise bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then i can conclude that they're
+
+ align:start position:0%
+then i can conclude that they're
+ 
+
+ align:start position:0%
+then i can conclude that they're
+uniformly bounded namely the soup of the
+
+ align:start position:0%
+uniformly bounded namely the soup of the
+ 
+
+ align:start position:0%
+uniformly bounded namely the soup of the
+operator norms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to use the bear category
+
+ align:start position:0%
+so we're going to use the bear category
+ 
+
+ align:start position:0%
+so we're going to use the bear category
+theorem so we're going to write
+
+ align:start position:0%
+theorem so we're going to write
+ 
+
+ align:start position:0%
+theorem so we're going to write
+the binocular space b as a union of
+
+ align:start position:0%
+the binocular space b as a union of
+ 
+
+ align:start position:0%
+the binocular space b as a union of
+closed subsets what will be these closed
+
+ align:start position:0%
+closed subsets what will be these closed
+ 
+
+ align:start position:0%
+closed subsets what will be these closed
+subsets remember we're trying to find
+
+ align:start position:0%
+subsets remember we're trying to find
+ 
+
+ align:start position:0%
+subsets remember we're trying to find
+kind of a uniform
+
+ align:start position:0%
+kind of a uniform
+ 
+
+ align:start position:0%
+kind of a uniform
+bound on
+
+ align:start position:0%
+bound on
+ 
+
+ align:start position:0%
+bound on
+on the t end so
+
+ align:start position:0%
+on the t end so
+ 
+
+ align:start position:0%
+on the t end so
+kind of just playing around so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define
+
+ align:start position:0%
+define
+ 
+
+ align:start position:0%
+define
+subset of b to be ck this is a set of
+
+ align:start position:0%
+subset of b to be ck this is a set of
+ 
+
+ align:start position:0%
+subset of b to be ck this is a set of
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+elements b and b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that the norm of b
+
+ align:start position:0%
+such that the norm of b
+ 
+
+ align:start position:0%
+such that the norm of b
+is less than or equal to 1
+
+ align:start position:0%
+is less than or equal to 1
+ 
+
+ align:start position:0%
+is less than or equal to 1
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+soup n
+
+ align:start position:0%
+soup n
+ 
+
+ align:start position:0%
+soup n
+t n of b
+
+ align:start position:0%
+t n of b
+ 
+
+ align:start position:0%
+t n of b
+is less than or equal to k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so first off
+
+ align:start position:0%
+so first off
+ 
+
+ align:start position:0%
+so first off
+uh these are closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i should say what is k k here is a
+
+ align:start position:0%
+so i should say what is k k here is a
+ 
+
+ align:start position:0%
+so i should say what is k k here is a
+natural number
+
+ align:start position:0%
+natural number
+ 
+
+ align:start position:0%
+natural number
+ck is closed why is this well we need to
+
+ align:start position:0%
+ck is closed why is this well we need to
+ 
+
+ align:start position:0%
+ck is closed why is this well we need to
+show that a sequence converging a
+
+ align:start position:0%
+show that a sequence converging a
+ 
+
+ align:start position:0%
+show that a sequence converging a
+sequence of elements from ck that
+
+ align:start position:0%
+sequence of elements from ck that
+ 
+
+ align:start position:0%
+sequence of elements from ck that
+converges converges to an element of ck
+
+ align:start position:0%
+converges converges to an element of ck
+ 
+
+ align:start position:0%
+converges converges to an element of ck
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+bn
+
+ align:start position:0%
+bn
+ 
+
+ align:start position:0%
+bn
+this is a sequence of elements in ck
+
+ align:start position:0%
+this is a sequence of elements in ck
+ 
+
+ align:start position:0%
+this is a sequence of elements in ck
+and b n converges to b
+
+ align:start position:0%
+and b n converges to b
+ 
+
+ align:start position:0%
+and b n converges to b
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm
+
+ align:start position:0%
+the norm
+ 
+
+ align:start position:0%
+the norm
+of b is equal to limit as n goes to
+
+ align:start position:0%
+of b is equal to limit as n goes to
+ 
+
+ align:start position:0%
+of b is equal to limit as n goes to
+infinity of the norm of b n
+
+ align:start position:0%
+infinity of the norm of b n
+ 
+
+ align:start position:0%
+infinity of the norm of b n
+um and each of these is less than or
+
+ align:start position:0%
+um and each of these is less than or
+ 
+
+ align:start position:0%
+um and each of these is less than or
+equal to one so
+
+ align:start position:0%
+equal to one so
+ 
+
+ align:start position:0%
+equal to one so
+the limit has to be less than or equal
+
+ align:start position:0%
+the limit has to be less than or equal
+ 
+
+ align:start position:0%
+the limit has to be less than or equal
+to one
+
+ align:start position:0%
+to one
+ 
+
+ align:start position:0%
+to one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i shouldn't
+
+ align:start position:0%
+so i shouldn't
+ 
+
+ align:start position:0%
+so i shouldn't
+maybe i'll use a
+
+ align:start position:0%
+maybe i'll use a
+ 
+
+ align:start position:0%
+maybe i'll use a
+and the tns i have the b n so let me uh
+
+ align:start position:0%
+and the tns i have the b n so let me uh
+ 
+
+ align:start position:0%
+and the tns i have the b n so let me uh
+use m
+
+ align:start position:0%
+use m
+ 
+
+ align:start position:0%
+use m
+and for all
+
+ align:start position:0%
+and for all
+ 
+
+ align:start position:0%
+and for all
+m a natural number
+
+ align:start position:0%
+m a natural number
+ 
+
+ align:start position:0%
+m a natural number
+t m
+
+ align:start position:0%
+t m
+ 
+
+ align:start position:0%
+t m
+applied to b and norm
+
+ align:start position:0%
+applied to b and norm
+ 
+
+ align:start position:0%
+applied to b and norm
+this is equal to the limit
+
+ align:start position:0%
+this is equal to the limit
+ 
+
+ align:start position:0%
+this is equal to the limit
+as n goes to infinity of
+
+ align:start position:0%
+as n goes to infinity of
+ 
+
+ align:start position:0%
+as n goes to infinity of
+t m
+
+ align:start position:0%
+t m
+ 
+
+ align:start position:0%
+t m
+b n
+
+ align:start position:0%
+b n
+ 
+
+ align:start position:0%
+b n
+in norm because these are bounded linear
+
+ align:start position:0%
+in norm because these are bounded linear
+ 
+
+ align:start position:0%
+in norm because these are bounded linear
+operators and therefore
+
+ align:start position:0%
+operators and therefore
+ 
+
+ align:start position:0%
+operators and therefore
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tm of b is equal to the limit as n goes
+
+ align:start position:0%
+tm of b is equal to the limit as n goes
+ 
+
+ align:start position:0%
+tm of b is equal to the limit as n goes
+to infinity of t m of b
+
+ align:start position:0%
+to infinity of t m of b
+ 
+
+ align:start position:0%
+to infinity of t m of b
+n okay
+
+ align:start position:0%
+n okay
+ 
+
+ align:start position:0%
+n okay
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+the norm of tm
+
+ align:start position:0%
+the norm of tm
+ 
+
+ align:start position:0%
+the norm of tm
+of bn is always well this is always less
+
+ align:start position:0%
+of bn is always well this is always less
+ 
+
+ align:start position:0%
+of bn is always well this is always less
+than or equal to k
+
+ align:start position:0%
+than or equal to k
+ 
+
+ align:start position:0%
+than or equal to k
+because the b ends are in c k
+
+ align:start position:0%
+because the b ends are in c k
+ 
+
+ align:start position:0%
+because the b ends are in c k
+and soup of all these guys is less than
+
+ align:start position:0%
+and soup of all these guys is less than
+ 
+
+ align:start position:0%
+and soup of all these guys is less than
+or equal to k so
+
+ align:start position:0%
+or equal to k so
+ 
+
+ align:start position:0%
+or equal to k so
+that's also less than or equal to k
+
+ align:start position:0%
+that's also less than or equal to k
+ 
+
+ align:start position:0%
+that's also less than or equal to k
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e is in ck which implies ck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is closed
+
+ align:start position:0%
+is closed
+ 
+
+ align:start position:0%
+is closed
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the closed ball
+
+ align:start position:0%
+the closed ball
+ 
+
+ align:start position:0%
+the closed ball
+or i shouldn't say it's not the closure
+
+ align:start position:0%
+or i shouldn't say it's not the closure
+ 
+
+ align:start position:0%
+or i shouldn't say it's not the closure
+of the open ball but the closed ball
+
+ align:start position:0%
+of the open ball but the closed ball
+ 
+
+ align:start position:0%
+of the open ball but the closed ball
+b in capital b such that
+
+ align:start position:0%
+b in capital b such that
+ 
+
+ align:start position:0%
+b in capital b such that
+b is less than or equal to one this is
+
+ align:start position:0%
+b is less than or equal to one this is
+ 
+
+ align:start position:0%
+b is less than or equal to one this is
+equal to the union
+
+ align:start position:0%
+equal to the union
+ 
+
+ align:start position:0%
+equal to the union
+over all k of c k y
+
+ align:start position:0%
+over all k of c k y
+ 
+
+ align:start position:0%
+over all k of c k y
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so first off each of these is contained
+
+ align:start position:0%
+so first off each of these is contained
+ 
+
+ align:start position:0%
+so first off each of these is contained
+in this close ball but i'm assuming by
+
+ align:start position:0%
+in this close ball but i'm assuming by
+ 
+
+ align:start position:0%
+in this close ball but i'm assuming by
+star that
+
+ align:start position:0%
+star that
+ 
+
+ align:start position:0%
+star that
+uh no matter what b is in the bonnet
+
+ align:start position:0%
+uh no matter what b is in the bonnet
+ 
+
+ align:start position:0%
+uh no matter what b is in the bonnet
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+soup over n of these is less than
+
+ align:start position:0%
+soup over n of these is less than
+ 
+
+ align:start position:0%
+soup over n of these is less than
+infinity so there's always
+
+ align:start position:0%
+infinity so there's always
+ 
+
+ align:start position:0%
+infinity so there's always
+some integer k
+
+ align:start position:0%
+some integer k
+ 
+
+ align:start position:0%
+some integer k
+given a b so given a certain b in this
+
+ align:start position:0%
+given a b so given a certain b in this
+ 
+
+ align:start position:0%
+given a b so given a certain b in this
+set i can always find a large enough
+
+ align:start position:0%
+set i can always find a large enough
+ 
+
+ align:start position:0%
+set i can always find a large enough
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+such that this
+
+ align:start position:0%
+such that this
+ 
+
+ align:start position:0%
+such that this
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+uh that integer so it has to
+
+ align:start position:0%
+uh that integer so it has to
+ 
+
+ align:start position:0%
+uh that integer so it has to
+every element in here has to lie in one
+
+ align:start position:0%
+every element in here has to lie in one
+ 
+
+ align:start position:0%
+every element in here has to lie in one
+of these sets c sub k so
+
+ align:start position:0%
+of these sets c sub k so
+ 
+
+ align:start position:0%
+of these sets c sub k so
+this is equal to the union
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+is a complete metric space because it's
+
+ align:start position:0%
+is a complete metric space because it's
+ 
+
+ align:start position:0%
+is a complete metric space because it's
+a closed subset of m so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+metric space
+
+ align:start position:0%
+metric space
+ 
+
+ align:start position:0%
+metric space
+written as the union of
+
+ align:start position:0%
+written as the union of
+ 
+
+ align:start position:0%
+written as the union of
+a sub uh union of closed subsets so by
+
+ align:start position:0%
+a sub uh union of closed subsets so by
+ 
+
+ align:start position:0%
+a sub uh union of closed subsets so by
+bears
+
+ align:start position:0%
+bears
+ 
+
+ align:start position:0%
+bears
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+one of these sets containing an open
+
+ align:start position:0%
+one of these sets containing an open
+ 
+
+ align:start position:0%
+one of these sets containing an open
+ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the form b naught
+
+ align:start position:0%
+of the form b naught
+ 
+
+ align:start position:0%
+of the form b naught
+delta naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of these c k's uh
+
+ align:start position:0%
+so one of these c k's uh
+ 
+
+ align:start position:0%
+so one of these c k's uh
+contains an open ball now we're going to
+
+ align:start position:0%
+contains an open ball now we're going to
+ 
+
+ align:start position:0%
+contains an open ball now we're going to
+show we're going to use this k and to
+
+ align:start position:0%
+show we're going to use this k and to
+ 
+
+ align:start position:0%
+show we're going to use this k and to
+derive a uniform bound
+
+ align:start position:0%
+derive a uniform bound
+ 
+
+ align:start position:0%
+derive a uniform bound
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+e is in b
+
+ align:start position:0%
+e is in b
+ 
+
+ align:start position:0%
+e is in b
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's write it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if b is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the open ball
+
+ align:start position:0%
+the open ball
+ 
+
+ align:start position:0%
+the open ball
+of radius delta 0 centered at 0. so this
+
+ align:start position:0%
+of radius delta 0 centered at 0. so this
+ 
+
+ align:start position:0%
+of radius delta 0 centered at 0. so this
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+ie the
+
+ align:start position:0%
+ie the
+ 
+
+ align:start position:0%
+ie the
+norm of b is less than delta 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+b naught plus b
+
+ align:start position:0%
+b naught plus b
+ 
+
+ align:start position:0%
+b naught plus b
+is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this open ball uh
+
+ align:start position:0%
+this open ball uh
+ 
+
+ align:start position:0%
+this open ball uh
+centered at b naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup n of
+
+ align:start position:0%
+soup n of
+ 
+
+ align:start position:0%
+soup n of
+t n
+
+ align:start position:0%
+t n
+ 
+
+ align:start position:0%
+t n
+of b naught plus b
+
+ align:start position:0%
+of b naught plus b
+ 
+
+ align:start position:0%
+of b naught plus b
+norm is less than or equal to
+
+ align:start position:0%
+norm is less than or equal to
+ 
+
+ align:start position:0%
+norm is less than or equal to
+k all right so this ball is contained in
+
+ align:start position:0%
+k all right so this ball is contained in
+ 
+
+ align:start position:0%
+k all right so this ball is contained in
+c k and therefore if i take the soup
+
+ align:start position:0%
+c k and therefore if i take the soup
+ 
+
+ align:start position:0%
+c k and therefore if i take the soup
+over n of t sub n applied to this thing
+
+ align:start position:0%
+over n of t sub n applied to this thing
+ 
+
+ align:start position:0%
+over n of t sub n applied to this thing
+this is less than or equal to k
+
+ align:start position:0%
+this is less than or equal to k
+ 
+
+ align:start position:0%
+this is less than or equal to k
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then i conclude that
+
+ align:start position:0%
+but then i conclude that
+ 
+
+ align:start position:0%
+but then i conclude that
+soup over n
+
+ align:start position:0%
+soup over n
+ 
+
+ align:start position:0%
+soup over n
+of tn applied to b
+
+ align:start position:0%
+of tn applied to b
+ 
+
+ align:start position:0%
+of tn applied to b
+which is less than or equal to soup n
+
+ align:start position:0%
+which is less than or equal to soup n
+ 
+
+ align:start position:0%
+which is less than or equal to soup n
+so i'm gonna add and subtract b zero
+
+ align:start position:0%
+so i'm gonna add and subtract b zero
+ 
+
+ align:start position:0%
+so i'm gonna add and subtract b zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me actually write this as soup
+
+ align:start position:0%
+let me actually write this as soup
+ 
+
+ align:start position:0%
+let me actually write this as soup
+of t and
+
+ align:start position:0%
+of t and
+ 
+
+ align:start position:0%
+of t and
+b zero plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t n
+
+ align:start position:0%
+t n
+ 
+
+ align:start position:0%
+t n
+b 0 plus b
+
+ align:start position:0%
+b 0 plus b
+ 
+
+ align:start position:0%
+b 0 plus b
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+less than or equal to by the triangle
+
+ align:start position:0%
+less than or equal to by the triangle
+ 
+
+ align:start position:0%
+less than or equal to by the triangle
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+and then carrying the soup through this
+
+ align:start position:0%
+and then carrying the soup through this
+ 
+
+ align:start position:0%
+and then carrying the soup through this
+is less than or equal to soup n
+
+ align:start position:0%
+is less than or equal to soup n
+ 
+
+ align:start position:0%
+is less than or equal to soup n
+t n b 0
+
+ align:start position:0%
+t n b 0
+ 
+
+ align:start position:0%
+t n b 0
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+soup n
+
+ align:start position:0%
+soup n
+ 
+
+ align:start position:0%
+soup n
+t n
+
+ align:start position:0%
+t n
+ 
+
+ align:start position:0%
+t n
+d 0 plus b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so b0
+
+ align:start position:0%
+so b0
+ 
+
+ align:start position:0%
+so b0
+is certainly in this ball which is
+
+ align:start position:0%
+is certainly in this ball which is
+ 
+
+ align:start position:0%
+is certainly in this ball which is
+contained in ck
+
+ align:start position:0%
+contained in ck
+ 
+
+ align:start position:0%
+contained in ck
+so this is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is still in that ball um
+
+ align:start position:0%
+okay and this is still in that ball um
+ 
+
+ align:start position:0%
+okay and this is still in that ball um
+of radius delta 0 centered at b0 so it
+
+ align:start position:0%
+of radius delta 0 centered at b0 so it
+ 
+
+ align:start position:0%
+of radius delta 0 centered at b0 so it
+lies in ck
+
+ align:start position:0%
+lies in ck
+ 
+
+ align:start position:0%
+lies in ck
+and therefore this soup is also less
+
+ align:start position:0%
+and therefore this soup is also less
+ 
+
+ align:start position:0%
+and therefore this soup is also less
+than or equal to k equals 2k
+
+ align:start position:0%
+than or equal to k equals 2k
+ 
+
+ align:start position:0%
+than or equal to k equals 2k
+so i've shown
+
+ align:start position:0%
+so i've shown
+ 
+
+ align:start position:0%
+so i've shown
+that if i take any element in the open
+
+ align:start position:0%
+that if i take any element in the open
+ 
+
+ align:start position:0%
+that if i take any element in the open
+ball
+
+ align:start position:0%
+ball
+ 
+
+ align:start position:0%
+ball
+of radius delta 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the soup over n of t n of b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than or equal to 2k
+
+ align:start position:0%
+is less than or equal to 2k
+ 
+
+ align:start position:0%
+is less than or equal to 2k
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and now it's just a simple rescaling
+
+ align:start position:0%
+and now it's just a simple rescaling
+ 
+
+ align:start position:0%
+and now it's just a simple rescaling
+argument to show that the soup of the
+
+ align:start position:0%
+argument to show that the soup of the
+ 
+
+ align:start position:0%
+argument to show that the soup of the
+norms are now bounded so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose norm of b
+
+ align:start position:0%
+suppose norm of b
+ 
+
+ align:start position:0%
+suppose norm of b
+equals 1
+
+ align:start position:0%
+equals 1
+ 
+
+ align:start position:0%
+equals 1
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the norm of
+
+ align:start position:0%
+the norm of
+ 
+
+ align:start position:0%
+the norm of
+tn of
+
+ align:start position:0%
+tn of
+ 
+
+ align:start position:0%
+tn of
+delta 0 over 2
+
+ align:start position:0%
+delta 0 over 2
+ 
+
+ align:start position:0%
+delta 0 over 2
+applied to b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for all n
+
+ align:start position:0%
+so for all n
+ 
+
+ align:start position:0%
+so for all n
+certainly less than or equal to the soup
+
+ align:start position:0%
+certainly less than or equal to the soup
+ 
+
+ align:start position:0%
+certainly less than or equal to the soup
+over n of all of these which is less
+
+ align:start position:0%
+over n of all of these which is less
+ 
+
+ align:start position:0%
+over n of all of these which is less
+than or equal to 2k because this is an
+
+ align:start position:0%
+than or equal to 2k because this is an
+ 
+
+ align:start position:0%
+than or equal to 2k because this is an
+element with norm delta 0 over 2 which
+
+ align:start position:0%
+element with norm delta 0 over 2 which
+ 
+
+ align:start position:0%
+element with norm delta 0 over 2 which
+is less than delta 0 so this is less
+
+ align:start position:0%
+is less than delta 0 so this is less
+ 
+
+ align:start position:0%
+is less than delta 0 so this is less
+than or equal to 2k
+
+ align:start position:0%
+than or equal to 2k
+ 
+
+ align:start position:0%
+than or equal to 2k
+which implies
+
+ align:start position:0%
+which implies
+ 
+
+ align:start position:0%
+which implies
+so again tn is linear so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i should have reversed this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let n be a natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let b
+
+ align:start position:0%
+let b
+ 
+
+ align:start position:0%
+let b
+equal to one
+
+ align:start position:0%
+equal to one
+ 
+
+ align:start position:0%
+equal to one
+then okay
+
+ align:start position:0%
+then okay
+ 
+
+ align:start position:0%
+then okay
+so then t n applied to b is less than or
+
+ align:start position:0%
+so then t n applied to b is less than or
+ 
+
+ align:start position:0%
+so then t n applied to b is less than or
+equal to uh four k over delta zero
+
+ align:start position:0%
+equal to uh four k over delta zero
+ 
+
+ align:start position:0%
+equal to uh four k over delta zero
+now this holds for all b with uh length
+
+ align:start position:0%
+now this holds for all b with uh length
+ 
+
+ align:start position:0%
+now this holds for all b with uh length
+equal to one
+
+ align:start position:0%
+equal to one
+ 
+
+ align:start position:0%
+equal to one
+and therefore the operator norm which is
+
+ align:start position:0%
+and therefore the operator norm which is
+ 
+
+ align:start position:0%
+and therefore the operator norm which is
+the soup over all b
+
+ align:start position:0%
+the soup over all b
+ 
+
+ align:start position:0%
+the soup over all b
+with norm equal to one is less than or
+
+ align:start position:0%
+with norm equal to one is less than or
+ 
+
+ align:start position:0%
+with norm equal to one is less than or
+equal to four k
+
+ align:start position:0%
+equal to four k
+ 
+
+ align:start position:0%
+equal to four k
+over delta zero this holds for all n and
+
+ align:start position:0%
+over delta zero this holds for all n and
+ 
+
+ align:start position:0%
+over delta zero this holds for all n and
+therefore the soup
+
+ align:start position:0%
+therefore the soup
+ 
+
+ align:start position:0%
+therefore the soup
+over n
+
+ align:start position:0%
+over n
+ 
+
+ align:start position:0%
+over n
+of the operator norm is less than or
+
+ align:start position:0%
+of the operator norm is less than or
+ 
+
+ align:start position:0%
+of the operator norm is less than or
+equal to 4k
+
+ align:start position:0%
+equal to 4k
+ 
+
+ align:start position:0%
+equal to 4k
+over delta 0 and therefore
+
+ align:start position:0%
+over delta 0 and therefore
+ 
+
+ align:start position:0%
+over delta 0 and therefore
+giving us the uniform bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i have time for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay i don't think i have time for
+
+ align:start position:0%
+okay i don't think i have time for
+ 
+
+ align:start position:0%
+okay i don't think i have time for
+the entire proof of what's uh what's to
+
+ align:start position:0%
+the entire proof of what's uh what's to
+ 
+
+ align:start position:0%
+the entire proof of what's uh what's to
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+so i think we'll just stop there for now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/5Pw5k0z1L4Q.txt b/5Pw5k0z1L4Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e22cbc8adee88805ecceb633e75f6818221cb5c
--- /dev/null
+++ b/5Pw5k0z1L4Q.txt
@@ -0,0 +1,8395 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so uh this is I could
+
+ align:start position:0%
+ocw.mit.edu okay so uh this is I could
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so uh this is I could
+say Delta function day uh break from
+
+ align:start position:0%
+say Delta function day uh break from
+ 
+
+ align:start position:0%
+say Delta function day uh break from
+linear algebra mostly uh uh so it's
+
+ align:start position:0%
+linear algebra mostly uh uh so it's
+ 
+
+ align:start position:0%
+linear algebra mostly uh uh so it's
+we're looking at another type of right
+
+ align:start position:0%
+we're looking at another type of right
+ 
+
+ align:start position:0%
+we're looking at another type of right
+hand side before in the differential
+
+ align:start position:0%
+hand side before in the differential
+ 
+
+ align:start position:0%
+hand side before in the differential
+equation and in the difference equation
+
+ align:start position:0%
+equation and in the difference equation
+ 
+
+ align:start position:0%
+equation and in the difference equation
+so the right hand sides up to now uh the
+
+ align:start position:0%
+so the right hand sides up to now uh the
+ 
+
+ align:start position:0%
+so the right hand sides up to now uh the
+one we looked at was a
+
+ align:start position:0%
+one we looked at was a
+ 
+
+ align:start position:0%
+one we looked at was a
+uniform uh constant load second
+
+ align:start position:0%
+uniform uh constant load second
+ 
+
+ align:start position:0%
+uniform uh constant load second
+derivative equal one now uh a point
+
+ align:start position:0%
+derivative equal one now uh a point
+ 
+
+ align:start position:0%
+derivative equal one now uh a point
+load well in a way we're now solving a
+
+ align:start position:0%
+load well in a way we're now solving a
+ 
+
+ align:start position:0%
+load well in a way we're now solving a
+whole bunch of problems because the
+
+ align:start position:0%
+whole bunch of problems because the
+ 
+
+ align:start position:0%
+whole bunch of problems because the
+point load
+
+ align:start position:0%
+point load
+ 
+
+ align:start position:0%
+point load
+can be in different places so instead of
+
+ align:start position:0%
+can be in different places so instead of
+ 
+
+ align:start position:0%
+can be in different places so instead of
+solving one problem with with one on the
+
+ align:start position:0%
+solving one problem with with one on the
+ 
+
+ align:start position:0%
+solving one problem with with one on the
+right hand side we're solving with a
+
+ align:start position:0%
+right hand side we're solving with a
+ 
+
+ align:start position:0%
+right hand side we're solving with a
+Delta function okay now a Delta function
+
+ align:start position:0%
+Delta function okay now a Delta function
+ 
+
+ align:start position:0%
+Delta function okay now a Delta function
+is you you probably have seen the and
+
+ align:start position:0%
+is you you probably have seen the and
+ 
+
+ align:start position:0%
+is you you probably have seen the and
+heard the words and seen the symbol but
+
+ align:start position:0%
+heard the words and seen the symbol but
+ 
+
+ align:start position:0%
+heard the words and seen the symbol but
+uh maybe not done much with a Delta
+
+ align:start position:0%
+uh maybe not done much with a Delta
+ 
+
+ align:start position:0%
+uh maybe not done much with a Delta
+function so let's uh it takes a little
+
+ align:start position:0%
+function so let's uh it takes a little
+ 
+
+ align:start position:0%
+function so let's uh it takes a little
+practice but it's really worth it uh
+
+ align:start position:0%
+practice but it's really worth it uh
+ 
+
+ align:start position:0%
+practice but it's really worth it uh
+it's a great model of uh maybe what
+
+ align:start position:0%
+it's a great model of uh maybe what
+ 
+
+ align:start position:0%
+it's a great model of uh maybe what
+can't quite happen physically to have a
+
+ align:start position:0%
+can't quite happen physically to have a
+ 
+
+ align:start position:0%
+can't quite happen physically to have a
+load acting exactly at a point and
+
+ align:start position:0%
+load acting exactly at a point and
+ 
+
+ align:start position:0%
+load acting exactly at a point and
+nowhere else so the Delta function is
+
+ align:start position:0%
+nowhere else so the Delta function is
+ 
+
+ align:start position:0%
+nowhere else so the Delta function is
+let's I drew its picture the Delta
+
+ align:start position:0%
+let's I drew its picture the Delta
+ 
+
+ align:start position:0%
+let's I drew its picture the Delta
+function is zero this is Delta of X is
+
+ align:start position:0%
+function is zero this is Delta of X is
+ 
+
+ align:start position:0%
+function is zero this is Delta of X is
+zero except at that one point the origin
+
+ align:start position:0%
+zero except at that one point the origin
+ 
+
+ align:start position:0%
+zero except at that one point the origin
+x equals z and then along and back to
+
+ align:start position:0%
+x equals z and then along and back to
+ 
+
+ align:start position:0%
+x equals z and then along and back to
+zero again so nothing's happening no
+
+ align:start position:0%
+zero again so nothing's happening no
+ 
+
+ align:start position:0%
+zero again so nothing's happening no
+load uh except at that one point
+
+ align:start position:0%
+load uh except at that one point
+ 
+
+ align:start position:0%
+load uh except at that one point
+and let me just uh so there's no uh
+
+ align:start position:0%
+and let me just uh so there's no uh
+ 
+
+ align:start position:0%
+and let me just uh so there's no uh
+hesitation in when I change the from X
+
+ align:start position:0%
+hesitation in when I change the from X
+ 
+
+ align:start position:0%
+hesitation in when I change the from X
+to x minus a what does that do to a
+
+ align:start position:0%
+to x minus a what does that do to a
+ 
+
+ align:start position:0%
+to x minus a what does that do to a
+graph if I have a function of X and I
+
+ align:start position:0%
+graph if I have a function of X and I
+ 
+
+ align:start position:0%
+graph if I have a function of X and I
+instead think look at the shift the
+
+ align:start position:0%
+instead think look at the shift the
+ 
+
+ align:start position:0%
+instead think look at the shift the
+function to f of x minus a I shift X to
+
+ align:start position:0%
+function to f of x minus a I shift X to
+ 
+
+ align:start position:0%
+function to f of x minus a I shift X to
+x - a well in this case and in all cases
+
+ align:start position:0%
+x - a well in this case and in all cases
+ 
+
+ align:start position:0%
+x - a well in this case and in all cases
+it will just shift the graph so if I
+
+ align:start position:0%
+it will just shift the graph so if I
+ 
+
+ align:start position:0%
+it will just shift the graph so if I
+drew a picture of Delta of xus
+
+ align:start position:0%
+drew a picture of Delta of xus
+ 
+
+ align:start position:0%
+drew a picture of Delta of xus
+a the load now would happen when this is
+
+ align:start position:0%
+a the load now would happen when this is
+ 
+
+ align:start position:0%
+a the load now would happen when this is
+zero because it's Delta at zero is the
+
+ align:start position:0%
+zero because it's Delta at zero is the
+ 
+
+ align:start position:0%
+zero because it's Delta at zero is the
+impulse and now this is zero at x equal
+
+ align:start position:0%
+impulse and now this is zero at x equal
+ 
+
+ align:start position:0%
+impulse and now this is zero at x equal
+a in other words the load moved to the
+
+ align:start position:0%
+a in other words the load moved to the
+ 
+
+ align:start position:0%
+a in other words the load moved to the
+point a so there's a there's the the
+
+ align:start position:0%
+point a so there's a there's the the
+ 
+
+ align:start position:0%
+point a so there's a there's the the
+shifting load but the load could fall
+
+ align:start position:0%
+shifting load but the load could fall
+ 
+
+ align:start position:0%
+shifting load but the load could fall
+anywhere between 0 and
+
+ align:start position:0%
+anywhere between 0 and
+ 
+
+ align:start position:0%
+anywhere between 0 and
+one okay so Delta of X the load actually
+
+ align:start position:0%
+one okay so Delta of X the load actually
+ 
+
+ align:start position:0%
+one okay so Delta of X the load actually
+falls at zero well we don't quite want
+
+ align:start position:0%
+falls at zero well we don't quite want
+ 
+
+ align:start position:0%
+falls at zero well we don't quite want
+that load at the boundary so let's think
+
+ align:start position:0%
+that load at the boundary so let's think
+ 
+
+ align:start position:0%
+that load at the boundary so let's think
+of the point a the load point is
+
+ align:start position:0%
+of the point a the load point is
+ 
+
+ align:start position:0%
+of the point a the load point is
+somewhere between Zer and one okay can I
+
+ align:start position:0%
+somewhere between Zer and one okay can I
+ 
+
+ align:start position:0%
+somewhere between Zer and one okay can I
+just take a little time to recall the
+
+ align:start position:0%
+just take a little time to recall the
+ 
+
+ align:start position:0%
+just take a little time to recall the
+main facts about Delta functions well
+
+ align:start position:0%
+main facts about Delta functions well
+ 
+
+ align:start position:0%
+main facts about Delta functions well
+when I say recall I it could very well
+
+ align:start position:0%
+when I say recall I it could very well
+ 
+
+ align:start position:0%
+when I say recall I it could very well
+be new to you okay so that's what the
+
+ align:start position:0%
+be new to you okay so that's what the
+ 
+
+ align:start position:0%
+be new to you okay so that's what the
+Delta function that's my best graph of
+
+ align:start position:0%
+Delta function that's my best graph of
+ 
+
+ align:start position:0%
+Delta function that's my best graph of
+the Delta function but of course I'm in
+
+ align:start position:0%
+the Delta function but of course I'm in
+ 
+
+ align:start position:0%
+the Delta function but of course I'm in
+using the word function I'm kind of
+
+ align:start position:0%
+using the word function I'm kind of
+ 
+
+ align:start position:0%
+using the word function I'm kind of
+breaking the rules because no function I
+
+ align:start position:0%
+breaking the rules because no function I
+ 
+
+ align:start position:0%
+breaking the rules because no function I
+mean the function is functions can be
+
+ align:start position:0%
+mean the function is functions can be
+ 
+
+ align:start position:0%
+mean the function is functions can be
+zero there can be zero there but they're
+
+ align:start position:0%
+zero there can be zero there but they're
+ 
+
+ align:start position:0%
+zero there can be zero there but they're
+not supposed to be
+
+ align:start position:0%
+not supposed to be
+ 
+
+ align:start position:0%
+not supposed to be
+infinite at a single point in between
+
+ align:start position:0%
+infinite at a single point in between
+ 
+
+ align:start position:0%
+infinite at a single point in between
+but this one is let me go back to Delta
+
+ align:start position:0%
+but this one is let me go back to Delta
+ 
+
+ align:start position:0%
+but this one is let me go back to Delta
+of x to match the uh these figures
+
+ align:start position:0%
+of x to match the uh these figures
+ 
+
+ align:start position:0%
+of x to match the uh these figures
+of course they would also just shift
+
+ align:start position:0%
+of course they would also just shift
+ 
+
+ align:start position:0%
+of course they would also just shift
+Along by a Maybe yeah maybe no harm in
+
+ align:start position:0%
+Along by a Maybe yeah maybe no harm in
+ 
+
+ align:start position:0%
+Along by a Maybe yeah maybe no harm in
+that I I'll I'll sorry
+
+ align:start position:0%
+that I I'll I'll sorry
+ 
+
+ align:start position:0%
+that I I'll I'll sorry
+I'll I'll stay there and now I want to
+
+ align:start position:0%
+I'll I'll stay there and now I want to
+ 
+
+ align:start position:0%
+I'll I'll stay there and now I want to
+integrate it and that's when a Delta
+
+ align:start position:0%
+integrate it and that's when a Delta
+ 
+
+ align:start position:0%
+integrate it and that's when a Delta
+function comes to into its own it's it's
+
+ align:start position:0%
+function comes to into its own it's it's
+ 
+
+ align:start position:0%
+function comes to into its own it's it's
+it's its value of infinity is a little
+
+ align:start position:0%
+it's its value of infinity is a little
+ 
+
+ align:start position:0%
+it's its value of infinity is a little
+bit uncertain what does that mean but
+
+ align:start position:0%
+bit uncertain what does that mean but
+ 
+
+ align:start position:0%
+bit uncertain what does that mean but
+when we integrate it what's the key fact
+
+ align:start position:0%
+when we integrate it what's the key fact
+ 
+
+ align:start position:0%
+when we integrate it what's the key fact
+about Delta function that the integral
+
+ align:start position:0%
+about Delta function that the integral
+ 
+
+ align:start position:0%
+about Delta function that the integral
+of a Delta
+
+ align:start position:0%
+of a Delta
+ 
+
+ align:start position:0%
+of a Delta
+function from let's say let's integrate
+
+ align:start position:0%
+function from let's say let's integrate
+ 
+
+ align:start position:0%
+function from let's say let's integrate
+the whole thing we can safely start way
+
+ align:start position:0%
+the whole thing we can safely start way
+ 
+
+ align:start position:0%
+the whole thing we can safely start way
+at the far left and go way to the far
+
+ align:start position:0%
+at the far left and go way to the far
+ 
+
+ align:start position:0%
+at the far left and go way to the far
+right because it's zero all the time
+
+ align:start position:0%
+right because it's zero all the time
+ 
+
+ align:start position:0%
+right because it's zero all the time
+there except at one point and you know
+
+ align:start position:0%
+there except at one point and you know
+ 
+
+ align:start position:0%
+there except at one point and you know
+so what's the area under that spike it
+
+ align:start position:0%
+so what's the area under that spike it
+ 
+
+ align:start position:0%
+so what's the area under that spike it
+is one that's right so that's the fact
+
+ align:start position:0%
+is one that's right so that's the fact
+ 
+
+ align:start position:0%
+is one that's right so that's the fact
+the sort of central fact about a Delta
+
+ align:start position:0%
+the sort of central fact about a Delta
+ 
+
+ align:start position:0%
+the sort of central fact about a Delta
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+that the area is one oh well let me
+
+ align:start position:0%
+that the area is one oh well let me
+ 
+
+ align:start position:0%
+that the area is one oh well let me
+while I'm really writing down the
+
+ align:start position:0%
+while I'm really writing down the
+ 
+
+ align:start position:0%
+while I'm really writing down the
+central fact let me write let me write
+
+ align:start position:0%
+central fact let me write let me write
+ 
+
+ align:start position:0%
+central fact let me write let me write
+it more specifically more more yeah more
+
+ align:start position:0%
+it more specifically more more yeah more
+ 
+
+ align:start position:0%
+it more specifically more more yeah more
+more uh generally suppose I integrate
+
+ align:start position:0%
+more uh generally suppose I integrate
+ 
+
+ align:start position:0%
+more uh generally suppose I integrate
+and this is Delta functions now really
+
+ align:start position:0%
+and this is Delta functions now really
+ 
+
+ align:start position:0%
+and this is Delta functions now really
+showing up if I integrate a Delta
+
+ align:start position:0%
+showing up if I integrate a Delta
+ 
+
+ align:start position:0%
+showing up if I integrate a Delta
+function against some times some nice
+
+ align:start position:0%
+function against some times some nice
+ 
+
+ align:start position:0%
+function against some times some nice
+function now have you ever thought about
+
+ align:start position:0%
+function now have you ever thought about
+ 
+
+ align:start position:0%
+function now have you ever thought about
+that what will be the answer if I
+
+ align:start position:0%
+that what will be the answer if I
+ 
+
+ align:start position:0%
+that what will be the answer if I
+integrate the Delta function against
+
+ align:start position:0%
+integrate the Delta function against
+ 
+
+ align:start position:0%
+integrate the Delta function against
+some nice function okay so I'm still
+
+ align:start position:0%
+some nice function okay so I'm still
+ 
+
+ align:start position:0%
+some nice function okay so I'm still
+getting Zero from this
+
+ align:start position:0%
+getting Zero from this
+ 
+
+ align:start position:0%
+getting Zero from this
+term all the way along until I hit the
+
+ align:start position:0%
+term all the way along until I hit the
+ 
+
+ align:start position:0%
+term all the way along until I hit the
+spike and then after it goes back to
+
+ align:start position:0%
+spike and then after it goes back to
+ 
+
+ align:start position:0%
+spike and then after it goes back to
+zero again so
+
+ align:start position:0%
+zero again so
+ 
+
+ align:start position:0%
+zero again so
+whatever it's got to be at the spike at
+
+ align:start position:0%
+whatever it's got to be at the spike at
+ 
+
+ align:start position:0%
+whatever it's got to be at the spike at
+x equals zero because I'm put the spike
+
+ align:start position:0%
+x equals zero because I'm put the spike
+ 
+
+ align:start position:0%
+x equals zero because I'm put the spike
+here at zero the impulse so what do you
+
+ align:start position:0%
+here at zero the impulse so what do you
+ 
+
+ align:start position:0%
+here at zero the impulse so what do you
+think's the answer for that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one yeah it's the function so the yeah
+
+ align:start position:0%
+one yeah it's the function so the yeah
+ 
+
+ align:start position:0%
+one yeah it's the function so the yeah
+tell me again and I'll write it down G
+
+ align:start position:0%
+tell me again and I'll write it down G
+ 
+
+ align:start position:0%
+tell me again and I'll write it down G
+is zero g it's the it's a value of this
+
+ align:start position:0%
+is zero g it's the it's a value of this
+ 
+
+ align:start position:0%
+is zero g it's the it's a value of this
+function G we don't care what it is to
+
+ align:start position:0%
+function G we don't care what it is to
+ 
+
+ align:start position:0%
+function G we don't care what it is to
+the left and to the right at zero
+
+ align:start position:0%
+the left and to the right at zero
+ 
+
+ align:start position:0%
+the left and to the right at zero
+because it's really at zero that this
+
+ align:start position:0%
+because it's really at zero that this
+ 
+
+ align:start position:0%
+because it's really at zero that this
+thing turns on and that its value at
+
+ align:start position:0%
+thing turns on and that its value at
+ 
+
+ align:start position:0%
+thing turns on and that its value at
+that point is just uh gives us the
+
+ align:start position:0%
+that point is just uh gives us the
+ 
+
+ align:start position:0%
+that point is just uh gives us the
+amplitude of the impulse which is G of0
+
+ align:start position:0%
+amplitude of the impulse which is G of0
+ 
+
+ align:start position:0%
+amplitude of the impulse which is G of0
+okay and of course if G is the constant
+
+ align:start position:0%
+okay and of course if G is the constant
+ 
+
+ align:start position:0%
+okay and of course if G is the constant
+function one I'm back to that formula
+
+ align:start position:0%
+function one I'm back to that formula
+ 
+
+ align:start position:0%
+function one I'm back to that formula
+but this is maybe the thing to watch for
+
+ align:start position:0%
+but this is maybe the thing to watch for
+ 
+
+ align:start position:0%
+but this is maybe the thing to watch for
+okay actually there's there's a lot
+
+ align:start position:0%
+okay actually there's there's a lot
+ 
+
+ align:start position:0%
+okay actually there's there's a lot
+built into that little thing we'll come
+
+ align:start position:0%
+built into that little thing we'll come
+ 
+
+ align:start position:0%
+built into that little thing we'll come
+back to that okay now so that's Delta
+
+ align:start position:0%
+back to that okay now so that's Delta
+ 
+
+ align:start position:0%
+back to that okay now so that's Delta
+functions uh integrated and now here are
+
+ align:start position:0%
+functions uh integrated and now here are
+ 
+
+ align:start position:0%
+functions uh integrated and now here are
+some pictures these are the good
+
+ align:start position:0%
+some pictures these are the good
+ 
+
+ align:start position:0%
+some pictures these are the good
+pictures
+
+ align:start position:0%
+pictures
+ 
+
+ align:start position:0%
+pictures
+okay so here is one integral of the
+
+ align:start position:0%
+okay so here is one integral of the
+ 
+
+ align:start position:0%
+okay so here is one integral of the
+delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function it's a step function okay and
+
+ align:start position:0%
+function it's a step function okay and
+ 
+
+ align:start position:0%
+function it's a step function okay and
+the step of course will occur at the
+
+ align:start position:0%
+the step of course will occur at the
+ 
+
+ align:start position:0%
+the step of course will occur at the
+point a if I the the integral of the
+
+ align:start position:0%
+point a if I the the integral of the
+ 
+
+ align:start position:0%
+point a if I the the integral of the
+Delta function at a point a will be the
+
+ align:start position:0%
+Delta function at a point a will be the
+ 
+
+ align:start position:0%
+Delta function at a point a will be the
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+function that where the action happens
+
+ align:start position:0%
+function that where the action happens
+ 
+
+ align:start position:0%
+function that where the action happens
+the jump happens I could call it a jump
+
+ align:start position:0%
+the jump happens I could call it a jump
+ 
+
+ align:start position:0%
+the jump happens I could call it a jump
+function at that point a because just
+
+ align:start position:0%
+function at that point a because just
+ 
+
+ align:start position:0%
+function at that point a because just
+for the reason we said that if we end
+
+ align:start position:0%
+for the reason we said that if we end
+ 
+
+ align:start position:0%
+for the reason we said that if we end
+integrate the integral is zero and then
+
+ align:start position:0%
+integrate the integral is zero and then
+ 
+
+ align:start position:0%
+integrate the integral is zero and then
+as soon as our integral passes this
+
+ align:start position:0%
+as soon as our integral passes this
+ 
+
+ align:start position:0%
+as soon as our integral passes this
+point so this is the integral of the
+
+ align:start position:0%
+point so this is the integral of the
+ 
+
+ align:start position:0%
+point so this is the integral of the
+this is I integrated it I I I
+
+ align:start position:0%
+this is I integrated it I I I
+ 
+
+ align:start position:0%
+this is I integrated it I I I
+integrate to get to this picture I start
+
+ align:start position:0%
+integrate to get to this picture I start
+ 
+
+ align:start position:0%
+integrate to get to this picture I start
+with that Delta function and I integrate
+
+ align:start position:0%
+with that Delta function and I integrate
+ 
+
+ align:start position:0%
+with that Delta function and I integrate
+and it suddenly jumps to one as soon as
+
+ align:start position:0%
+and it suddenly jumps to one as soon as
+ 
+
+ align:start position:0%
+and it suddenly jumps to one as soon as
+the integral goes past the spike the
+
+ align:start position:0%
+the integral goes past the spike the
+ 
+
+ align:start position:0%
+the integral goes past the spike the
+impulse okay so a step function very
+
+ align:start position:0%
+impulse okay so a step function very
+ 
+
+ align:start position:0%
+impulse okay so a step function very
+handy function step function
+
+ align:start position:0%
+handy function step function
+ 
+
+ align:start position:0%
+handy function step function
+sometimes called a heavys side function
+
+ align:start position:0%
+sometimes called a heavys side function
+ 
+
+ align:start position:0%
+sometimes called a heavys side function
+named after the guy who uh the
+
+ align:start position:0%
+named after the guy who uh the
+ 
+
+ align:start position:0%
+named after the guy who uh the
+electrical engineer I think who who
+
+ align:start position:0%
+electrical engineer I think who who
+ 
+
+ align:start position:0%
+electrical engineer I think who who
+started who first sort of worked out the
+
+ align:start position:0%
+started who first sort of worked out the
+ 
+
+ align:start position:0%
+started who first sort of worked out the
+rules for using these okay let's
+
+ align:start position:0%
+rules for using these okay let's
+ 
+
+ align:start position:0%
+rules for using these okay let's
+integrate one more time because we have
+
+ align:start position:0%
+integrate one more time because we have
+ 
+
+ align:start position:0%
+integrate one more time because we have
+second order equation second derivative
+
+ align:start position:0%
+second order equation second derivative
+ 
+
+ align:start position:0%
+second order equation second derivative
+so we better integrate twice to to to
+
+ align:start position:0%
+so we better integrate twice to to to
+ 
+
+ align:start position:0%
+so we better integrate twice to to to
+see what sort of answer we get Now
+
+ align:start position:0%
+see what sort of answer we get Now
+ 
+
+ align:start position:0%
+see what sort of answer we get Now
+integrate a step function so again the
+
+ align:start position:0%
+integrate a step function so again the
+ 
+
+ align:start position:0%
+integrate a step function so again the
+integral is zero all the way to the left
+
+ align:start position:0%
+integral is zero all the way to the left
+ 
+
+ align:start position:0%
+integral is zero all the way to the left
+so I'm still getting zero but now Beyond
+
+ align:start position:0%
+so I'm still getting zero but now Beyond
+ 
+
+ align:start position:0%
+so I'm still getting zero but now Beyond
+this point I'm integrating one and the
+
+ align:start position:0%
+this point I'm integrating one and the
+ 
+
+ align:start position:0%
+this point I'm integrating one and the
+integral of one is
+
+ align:start position:0%
+integral of one is
+ 
+
+ align:start position:0%
+integral of one is
+X so now that I would call a ramp
+
+ align:start position:0%
+X so now that I would call a ramp
+ 
+
+ align:start position:0%
+X so now that I would call a ramp
+function that's that's a nice short word
+
+ align:start position:0%
+function that's that's a nice short word
+ 
+
+ align:start position:0%
+function that's that's a nice short word
+for for this valuable function the ramp
+
+ align:start position:0%
+for for this valuable function the ramp
+ 
+
+ align:start position:0%
+for for this valuable function the ramp
+function is the function that's zero and
+
+ align:start position:0%
+function is the function that's zero and
+ 
+
+ align:start position:0%
+function is the function that's zero and
+then X so what oh now so what derivative
+
+ align:start position:0%
+then X so what oh now so what derivative
+ 
+
+ align:start position:0%
+then X so what oh now so what derivative
+of the tell me about about that ramp
+
+ align:start position:0%
+of the tell me about about that ramp
+ 
+
+ align:start position:0%
+of the tell me about about that ramp
+function just think
+
+ align:start position:0%
+function just think
+ 
+
+ align:start position:0%
+function just think
+about what happens to its derivative at
+
+ align:start position:0%
+about what happens to its derivative at
+ 
+
+ align:start position:0%
+about what happens to its derivative at
+the point a as I run along and I hit
+
+ align:start position:0%
+the point a as I run along and I hit
+ 
+
+ align:start position:0%
+the point a as I run along and I hit
+this key Point what happens to the
+
+ align:start position:0%
+this key Point what happens to the
+ 
+
+ align:start position:0%
+this key Point what happens to the
+derivative of the
+
+ align:start position:0%
+derivative of the
+ 
+
+ align:start position:0%
+derivative of the
+ramp
+
+ align:start position:0%
+ramp
+ 
+
+ align:start position:0%
+ramp
+it is does the what does the derivative
+
+ align:start position:0%
+it is does the what does the derivative
+ 
+
+ align:start position:0%
+it is does the what does the derivative
+do I'm look focus on that ramp now what
+
+ align:start position:0%
+do I'm look focus on that ramp now what
+ 
+
+ align:start position:0%
+do I'm look focus on that ramp now what
+does the derivative do at that
+
+ align:start position:0%
+does the derivative do at that
+ 
+
+ align:start position:0%
+does the derivative do at that
+point it jumps the derivative jumps the
+
+ align:start position:0%
+point it jumps the derivative jumps the
+ 
+
+ align:start position:0%
+point it jumps the derivative jumps the
+slope is the derivative the slope jumps
+
+ align:start position:0%
+slope is the derivative the slope jumps
+ 
+
+ align:start position:0%
+slope is the derivative the slope jumps
+from zero and here the slope is one and
+
+ align:start position:0%
+from zero and here the slope is one and
+ 
+
+ align:start position:0%
+from zero and here the slope is one and
+of course that's what that's telling us
+
+ align:start position:0%
+of course that's what that's telling us
+ 
+
+ align:start position:0%
+of course that's what that's telling us
+here's the picture of the derivative
+
+ align:start position:0%
+here's the picture of the derivative
+ 
+
+ align:start position:0%
+here's the picture of the derivative
+what does the second derivative
+
+ align:start position:0%
+what does the second derivative
+ 
+
+ align:start position:0%
+what does the second derivative
+do well since I integrate twice I
+
+ align:start position:0%
+do well since I integrate twice I
+ 
+
+ align:start position:0%
+do well since I integrate twice I
+guess going back two steps I'll find out
+
+ align:start position:0%
+guess going back two steps I'll find out
+ 
+
+ align:start position:0%
+guess going back two steps I'll find out
+what the second derivative is so the
+
+ align:start position:0%
+what the second derivative is so the
+ 
+
+ align:start position:0%
+what the second derivative is so the
+first derivative go it takes a
+
+ align:start position:0%
+first derivative go it takes a
+ 
+
+ align:start position:0%
+first derivative go it takes a
+jump the second derivative is the
+
+ align:start position:0%
+jump the second derivative is the
+ 
+
+ align:start position:0%
+jump the second derivative is the
+derivative of that jump
+
+ align:start position:0%
+derivative of that jump
+ 
+
+ align:start position:0%
+derivative of that jump
+so it's got the impulse so the second
+
+ align:start position:0%
+so it's got the impulse so the second
+ 
+
+ align:start position:0%
+so it's got the impulse so the second
+derivative this is straight line here
+
+ align:start position:0%
+derivative this is straight line here
+ 
+
+ align:start position:0%
+derivative this is straight line here
+second derivative straight line This is
+
+ align:start position:0%
+second derivative straight line This is
+ 
+
+ align:start position:0%
+second derivative straight line This is
+straight line here second derivative of
+
+ align:start position:0%
+straight line here second derivative of
+ 
+
+ align:start position:0%
+straight line here second derivative of
+a straight line is a straight line but
+
+ align:start position:0%
+a straight line is a straight line but
+ 
+
+ align:start position:0%
+a straight line is a straight line but
+at the at that point the first
+
+ align:start position:0%
+at the at that point the first
+ 
+
+ align:start position:0%
+at the at that point the first
+derivative jumps the second derivative
+
+ align:start position:0%
+derivative jumps the second derivative
+ 
+
+ align:start position:0%
+derivative jumps the second derivative
+has that Delta function in other words
+
+ align:start position:0%
+has that Delta function in other words
+ 
+
+ align:start position:0%
+has that Delta function in other words
+that's that that's the okay if I keep
+
+ align:start position:0%
+that's that that's the okay if I keep
+ 
+
+ align:start position:0%
+that's that that's the okay if I keep
+integrating and I don't need higher
+
+ align:start position:0%
+integrating and I don't need higher
+ 
+
+ align:start position:0%
+integrating and I don't need higher
+integrals in this in today lecture uh
+
+ align:start position:0%
+integrals in this in today lecture uh
+ 
+
+ align:start position:0%
+integrals in this in today lecture uh
+another integral would be what if I
+
+ align:start position:0%
+another integral would be what if I
+ 
+
+ align:start position:0%
+another integral would be what if I
+integrate this function then it's
+
+ align:start position:0%
+integrate this function then it's
+ 
+
+ align:start position:0%
+integrate this function then it's
+running along to zero what's the
+
+ align:start position:0%
+running along to zero what's the
+ 
+
+ align:start position:0%
+running along to zero what's the
+integral of this uh doesn't quite turn
+
+ align:start position:0%
+integral of this uh doesn't quite turn
+ 
+
+ align:start position:0%
+integral of this uh doesn't quite turn
+that steeply um what's that curve
+
+ align:start position:0%
+that steeply um what's that curve
+ 
+
+ align:start position:0%
+that steeply um what's that curve
+there if i' if I've integrated the ramp
+
+ align:start position:0%
+there if i' if I've integrated the ramp
+ 
+
+ align:start position:0%
+there if i' if I've integrated the ramp
+here's the integral first The Next Step
+
+ align:start position:0%
+here's the integral first The Next Step
+ 
+
+ align:start position:0%
+here's the integral first The Next Step
+Up the integral of the ramp would
+
+ align:start position:0%
+Up the integral of the ramp would
+ 
+
+ align:start position:0%
+Up the integral of the ramp would
+be it'll be x s yeah it'll be a parabola
+
+ align:start position:0%
+be it'll be x s yeah it'll be a parabola
+ 
+
+ align:start position:0%
+be it'll be x s yeah it'll be a parabola
+X2 over two the integral of that and now
+
+ align:start position:0%
+X2 over two the integral of that and now
+ 
+
+ align:start position:0%
+X2 over two the integral of that and now
+what do I get when I integrate this one
+
+ align:start position:0%
+what do I get when I integrate this one
+ 
+
+ align:start position:0%
+what do I get when I integrate this one
+I get something very important not
+
+ align:start position:0%
+I get something very important not
+ 
+
+ align:start position:0%
+I get something very important not
+important today but important in a few
+
+ align:start position:0%
+important today but important in a few
+ 
+
+ align:start position:0%
+important today but important in a few
+weeks it's it's and very useful in
+
+ align:start position:0%
+weeks it's it's and very useful in
+ 
+
+ align:start position:0%
+weeks it's it's and very useful in
+Computing these have turned out to be uh
+
+ align:start position:0%
+Computing these have turned out to be uh
+ 
+
+ align:start position:0%
+Computing these have turned out to be uh
+just the right thing so again now I'm
+
+ align:start position:0%
+just the right thing so again now I'm
+ 
+
+ align:start position:0%
+just the right thing so again now I'm
+integrating that everybody can tell me
+
+ align:start position:0%
+integrating that everybody can tell me
+ 
+
+ align:start position:0%
+integrating that everybody can tell me
+what is that what's that curve
+
+ align:start position:0%
+what is that what's that curve
+ 
+
+ align:start position:0%
+what is that what's that curve
+now it's the next integral of course the
+
+ align:start position:0%
+now it's the next integral of course the
+ 
+
+ align:start position:0%
+now it's the next integral of course the
+area under that will be X Cub over
+
+ align:start position:0%
+area under that will be X Cub over
+ 
+
+ align:start position:0%
+area under that will be X Cub over
+6 okay so now that is a function yeah
+
+ align:start position:0%
+6 okay so now that is a function yeah
+ 
+
+ align:start position:0%
+6 okay so now that is a function yeah
+it's worth maybe just for practice
+
+ align:start position:0%
+it's worth maybe just for practice
+ 
+
+ align:start position:0%
+it's worth maybe just for practice
+what's the deal with that
+
+ align:start position:0%
+what's the deal with that
+ 
+
+ align:start position:0%
+what's the deal with that
+function that's pretty smooth
+
+ align:start position:0%
+function that's pretty smooth
+ 
+
+ align:start position:0%
+function that's pretty smooth
+function because it certainly passes
+
+ align:start position:0%
+function because it certainly passes
+ 
+
+ align:start position:0%
+function because it certainly passes
+right it it meets at that point the
+
+ align:start position:0%
+right it it meets at that point the
+ 
+
+ align:start position:0%
+right it it meets at that point the
+first derivative meets at that point the
+
+ align:start position:0%
+first derivative meets at that point the
+ 
+
+ align:start position:0%
+first derivative meets at that point the
+second derivative meets at that point
+
+ align:start position:0%
+second derivative meets at that point
+ 
+
+ align:start position:0%
+second derivative meets at that point
+the third derivative does what of this
+
+ align:start position:0%
+the third derivative does what of this
+ 
+
+ align:start position:0%
+the third derivative does what of this
+blind the third derivative take three
+
+ align:start position:0%
+blind the third derivative take three
+ 
+
+ align:start position:0%
+blind the third derivative take three
+steps back down the line and you see
+
+ align:start position:0%
+steps back down the line and you see
+ 
+
+ align:start position:0%
+steps back down the line and you see
+that the third derivative jumps right
+
+ align:start position:0%
+that the third derivative jumps right
+ 
+
+ align:start position:0%
+that the third derivative jumps right
+the third derivative of that is the
+
+ align:start position:0%
+the third derivative of that is the
+ 
+
+ align:start position:0%
+the third derivative of that is the
+third derivative would be shall I for c
+
+ align:start position:0%
+third derivative would be shall I for c
+ 
+
+ align:start position:0%
+third derivative would be shall I for c
+for cubic spline or something the third
+
+ align:start position:0%
+for cubic spline or something the third
+ 
+
+ align:start position:0%
+for cubic spline or something the third
+derivative will be zero there and the
+
+ align:start position:0%
+derivative will be zero there and the
+ 
+
+ align:start position:0%
+derivative will be zero there and the
+third derivative of that is exactly like
+
+ align:start position:0%
+third derivative of that is exactly like
+ 
+
+ align:start position:0%
+third derivative of that is exactly like
+back to that back to that back to one is
+
+ align:start position:0%
+back to that back to that back to one is
+ 
+
+ align:start position:0%
+back to that back to that back to one is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so the third derivative so the cubic
+
+ align:start position:0%
+so the third derivative so the cubic
+ 
+
+ align:start position:0%
+so the third derivative so the cubic
+blinds so smooth your eye doesn't see
+
+ align:start position:0%
+blinds so smooth your eye doesn't see
+ 
+
+ align:start position:0%
+blinds so smooth your eye doesn't see
+that that that that they're very useful
+
+ align:start position:0%
+that that that that they're very useful
+ 
+
+ align:start position:0%
+that that that that they're very useful
+for drawing many many purposes uh CAD
+
+ align:start position:0%
+for drawing many many purposes uh CAD
+ 
+
+ align:start position:0%
+for drawing many many purposes uh CAD
+programs would use such things
+
+ align:start position:0%
+programs would use such things
+ 
+
+ align:start position:0%
+programs would use such things
+constantly because they're they're
+
+ align:start position:0%
+constantly because they're they're
+ 
+
+ align:start position:0%
+constantly because they're they're
+convenient they're piece they have nice
+
+ align:start position:0%
+convenient they're piece they have nice
+ 
+
+ align:start position:0%
+convenient they're piece they have nice
+pieces that you can fit together and
+
+ align:start position:0%
+pieces that you can fit together and
+ 
+
+ align:start position:0%
+pieces that you can fit together and
+they fit together very smoothly uh but
+
+ align:start position:0%
+they fit together very smoothly uh but
+ 
+
+ align:start position:0%
+they fit together very smoothly uh but
+they really are two separate functions
+
+ align:start position:0%
+they really are two separate functions
+ 
+
+ align:start position:0%
+they really are two separate functions
+okay so that's up to cubic spine but we
+
+ align:start position:0%
+okay so that's up to cubic spine but we
+ 
+
+ align:start position:0%
+okay so that's up to cubic spine but we
+our focus is these would solve what
+
+ align:start position:0%
+our focus is these would solve what
+ 
+
+ align:start position:0%
+our focus is these would solve what
+equations would those
+
+ align:start position:0%
+equations would those
+ 
+
+ align:start position:0%
+equations would those
+solve well that takes how many
+
+ align:start position:0%
+solve well that takes how many
+ 
+
+ align:start position:0%
+solve well that takes how many
+derivatives to get to a Delta so what
+
+ align:start position:0%
+derivatives to get to a Delta so what
+ 
+
+ align:start position:0%
+derivatives to get to a Delta so what
+what would be the equation uh what would
+
+ align:start position:0%
+what would be the equation uh what would
+ 
+
+ align:start position:0%
+what would be the equation uh what would
+be the the what would be the right hand
+
+ align:start position:0%
+be the the what would be the right hand
+ 
+
+ align:start position:0%
+be the the what would be the right hand
+side yeah let me take the fourth
+
+ align:start position:0%
+side yeah let me take the fourth
+ 
+
+ align:start position:0%
+side yeah let me take the fourth
+derivative yeah I just ask the question
+
+ align:start position:0%
+derivative yeah I just ask the question
+ 
+
+ align:start position:0%
+derivative yeah I just ask the question
+that way what would be the fourth
+
+ align:start position:0%
+that way what would be the fourth
+ 
+
+ align:start position:0%
+that way what would be the fourth
+derivative of that cubic
+
+ align:start position:0%
+derivative of that cubic
+ 
+
+ align:start position:0%
+derivative of that cubic
+spine a Delta right four steps back so
+
+ align:start position:0%
+spine a Delta right four steps back so
+ 
+
+ align:start position:0%
+spine a Delta right four steps back so
+what is physically what what are we
+
+ align:start position:0%
+what is physically what what are we
+ 
+
+ align:start position:0%
+what is physically what what are we
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+here do you do you recognize what what
+
+ align:start position:0%
+here do you do you recognize what what
+ 
+
+ align:start position:0%
+here do you do you recognize what what
+kind in if I ask now people in mechanics
+
+ align:start position:0%
+kind in if I ask now people in mechanics
+ 
+
+ align:start position:0%
+kind in if I ask now people in mechanics
+when will we meet a fourth order
+
+ align:start position:0%
+when will we meet a fourth order
+ 
+
+ align:start position:0%
+when will we meet a fourth order
+equation fourth derivative equals a
+
+ align:start position:0%
+equation fourth derivative equals a
+ 
+
+ align:start position:0%
+equation fourth derivative equals a
+load anybody know the the the physical
+
+ align:start position:0%
+load anybody know the the the physical
+ 
+
+ align:start position:0%
+load anybody know the the the physical
+situation where fourth der
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where beams yeah it's the equation for a
+
+ align:start position:0%
+where beams yeah it's the equation for a
+ 
+
+ align:start position:0%
+where beams yeah it's the equation for a
+beam a beam uh has uh the bending of a
+
+ align:start position:0%
+beam a beam uh has uh the bending of a
+ 
+
+ align:start position:0%
+beam a beam uh has uh the bending of a
+beam so it's a beam this eraser isn't
+
+ align:start position:0%
+beam so it's a beam this eraser isn't
+ 
+
+ align:start position:0%
+beam so it's a beam this eraser isn't
+too very much like a beam but anyway I
+
+ align:start position:0%
+too very much like a beam but anyway I
+ 
+
+ align:start position:0%
+too very much like a beam but anyway I
+put the chalk on well nothing happened
+
+ align:start position:0%
+put the chalk on well nothing happened
+ 
+
+ align:start position:0%
+put the chalk on well nothing happened
+um sit on it whatever uh it'll Bend and
+
+ align:start position:0%
+um sit on it whatever uh it'll Bend and
+ 
+
+ align:start position:0%
+um sit on it whatever uh it'll Bend and
+that bending will be given by a beam
+
+ align:start position:0%
+that bending will be given by a beam
+ 
+
+ align:start position:0%
+that bending will be given by a beam
+equation okay so let will meet the beam
+
+ align:start position:0%
+equation okay so let will meet the beam
+ 
+
+ align:start position:0%
+equation okay so let will meet the beam
+equation so it's the most most equations
+
+ align:start position:0%
+equation so it's the most most equations
+ 
+
+ align:start position:0%
+equation so it's the most most equations
+of uh physics
+
+ align:start position:0%
+of uh physics
+ 
+
+ align:start position:0%
+of uh physics
+mechanics uh biology everything are
+
+ align:start position:0%
+mechanics uh biology everything are
+ 
+
+ align:start position:0%
+mechanics uh biology everything are
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+order Newton's law is often the reason
+
+ align:start position:0%
+order Newton's law is often the reason
+ 
+
+ align:start position:0%
+order Newton's law is often the reason
+but uh we get up to fourth order
+
+ align:start position:0%
+but uh we get up to fourth order
+ 
+
+ align:start position:0%
+but uh we get up to fourth order
+sometimes okay and very seldom get
+
+ align:start position:0%
+sometimes okay and very seldom get
+ 
+
+ align:start position:0%
+sometimes okay and very seldom get
+higher hopefully yeah beams or plates
+
+ align:start position:0%
+higher hopefully yeah beams or plates
+ 
+
+ align:start position:0%
+higher hopefully yeah beams or plates
+that table would that that table would
+
+ align:start position:0%
+that table would that that table would
+ 
+
+ align:start position:0%
+that table would that that table would
+be a plate and it would have a fourth
+
+ align:start position:0%
+be a plate and it would have a fourth
+ 
+
+ align:start position:0%
+be a plate and it would have a fourth
+order equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let let's start solving this
+
+ align:start position:0%
+okay let let's start solving this
+ 
+
+ align:start position:0%
+okay let let's start solving this
+problem what's the solution what's the
+
+ align:start position:0%
+problem what's the solution what's the
+ 
+
+ align:start position:0%
+problem what's the solution what's the
+general solution to that equation minus
+
+ align:start position:0%
+general solution to that equation minus
+ 
+
+ align:start position:0%
+general solution to that equation minus
+the second derivative so notice the
+
+ align:start position:0%
+the second derivative so notice the
+ 
+
+ align:start position:0%
+the second derivative so notice the
+minus that I like and the load is now
+
+ align:start position:0%
+minus that I like and the load is now
+ 
+
+ align:start position:0%
+minus that I like and the load is now
+moved to the point a so the solution U
+
+ align:start position:0%
+moved to the point a so the solution U
+ 
+
+ align:start position:0%
+moved to the point a so the solution U
+of X let let's let's write down all
+
+ align:start position:0%
+of X let let's let's write down all
+ 
+
+ align:start position:0%
+of X let let's let's write down all
+solutions well tell me one solution
+
+ align:start position:0%
+solutions well tell me one solution
+ 
+
+ align:start position:0%
+solutions well tell me one solution
+first one particular solution what is
+
+ align:start position:0%
+first one particular solution what is
+ 
+
+ align:start position:0%
+first one particular solution what is
+one function for which minus the second
+
+ align:start position:0%
+one function for which minus the second
+ 
+
+ align:start position:0%
+one function for which minus the second
+derivative would be the
+
+ align:start position:0%
+derivative would be the
+ 
+
+ align:start position:0%
+derivative would be the
+Delta that's what we got over there so
+
+ align:start position:0%
+Delta that's what we got over there so
+ 
+
+ align:start position:0%
+Delta that's what we got over there so
+just bring that Blackboard over
+
+ align:start position:0%
+just bring that Blackboard over
+ 
+
+ align:start position:0%
+just bring that Blackboard over
+here change its sign because that minus
+
+ align:start position:0%
+here change its sign because that minus
+ 
+
+ align:start position:0%
+here change its sign because that minus
+and what are you going to tell me
+
+ align:start position:0%
+and what are you going to tell me
+ 
+
+ align:start position:0%
+and what are you going to tell me
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+a ramp minus a ramp and the ramp of
+
+ align:start position:0%
+a ramp minus a ramp and the ramp of
+ 
+
+ align:start position:0%
+a ramp minus a ramp and the ramp of
+course will ramp up at the point a in
+
+ align:start position:0%
+course will ramp up at the point a in
+ 
+
+ align:start position:0%
+course will ramp up at the point a in
+order to match where the so that it's
+
+ align:start position:0%
+order to match where the so that it's
+ 
+
+ align:start position:0%
+order to match where the so that it's
+second the second derivative of that the
+
+ align:start position:0%
+second the second derivative of that the
+ 
+
+ align:start position:0%
+second the second derivative of that the
+second derivative of R will be Delta the
+
+ align:start position:0%
+second derivative of R will be Delta the
+ 
+
+ align:start position:0%
+second derivative of R will be Delta the
+minus is correct and the point is
+
+ align:start position:0%
+minus is correct and the point is
+ 
+
+ align:start position:0%
+minus is correct and the point is
+correct okay now does that solve our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+no no the ramp is going upwards it's not
+
+ align:start position:0%
+no no the ramp is going upwards it's not
+ 
+
+ align:start position:0%
+no no the ramp is going upwards it's not
+zero what am I
+
+ align:start position:0%
+zero what am I
+ 
+
+ align:start position:0%
+zero what am I
+forgetting what do I not yet have
+
+ align:start position:0%
+forgetting what do I not yet have
+ 
+
+ align:start position:0%
+forgetting what do I not yet have
+there's more to be more to this solution
+
+ align:start position:0%
+there's more to be more to this solution
+ 
+
+ align:start position:0%
+there's more to be more to this solution
+just as there was for a uniform load
+
+ align:start position:0%
+just as there was for a uniform load
+ 
+
+ align:start position:0%
+just as there was for a uniform load
+what what was the
+
+ align:start position:0%
+what what was the
+ 
+
+ align:start position:0%
+what what was the
+more constant
+
+ align:start position:0%
+more constant
+ 
+
+ align:start position:0%
+more constant
+and and I I want two two
+
+ align:start position:0%
+and and I I want two two
+ 
+
+ align:start position:0%
+and and I I want two two
+uh homogeneous Solutions null Solutions
+
+ align:start position:0%
+uh homogeneous Solutions null Solutions
+ 
+
+ align:start position:0%
+uh homogeneous Solutions null Solutions
+two solutions with derivative equ second
+
+ align:start position:0%
+two solutions with derivative equ second
+ 
+
+ align:start position:0%
+two solutions with derivative equ second
+derivative equals zero one of them is C
+
+ align:start position:0%
+derivative equals zero one of them is C
+ 
+
+ align:start position:0%
+derivative equals zero one of them is C
+and the other one is DX thanks okay
+
+ align:start position:0%
+and the other one is DX thanks okay
+ 
+
+ align:start position:0%
+and the other one is DX thanks okay
+that's the whole solution okay okay so
+
+ align:start position:0%
+that's the whole solution okay okay so
+ 
+
+ align:start position:0%
+that's the whole solution okay okay so
+what I want to I mean my we need that C+
+
+ align:start position:0%
+what I want to I mean my we need that C+
+ 
+
+ align:start position:0%
+what I want to I mean my we need that C+
+DX we got two boundary conditions to
+
+ align:start position:0%
+DX we got two boundary conditions to
+ 
+
+ align:start position:0%
+DX we got two boundary conditions to
+satisfy just as before so I need two
+
+ align:start position:0%
+satisfy just as before so I need two
+ 
+
+ align:start position:0%
+satisfy just as before so I need two
+constants that'll do it perfectly and
+
+ align:start position:0%
+constants that'll do it perfectly and
+ 
+
+ align:start position:0%
+constants that'll do it perfectly and
+I'll get an exact answer okay and it it
+
+ align:start position:0%
+I'll get an exact answer okay and it it
+ 
+
+ align:start position:0%
+I'll get an exact answer okay and it it
+it well so this is a ramp
+
+ align:start position:0%
+it well so this is a ramp
+ 
+
+ align:start position:0%
+it well so this is a ramp
+what oh yeah before I go further let me
+
+ align:start position:0%
+what oh yeah before I go further let me
+ 
+
+ align:start position:0%
+what oh yeah before I go further let me
+just let's let's just how what I think
+
+ align:start position:0%
+just let's let's just how what I think
+ 
+
+ align:start position:0%
+just let's let's just how what I think
+about this this is a ramp that that
+
+ align:start position:0%
+about this this is a ramp that that
+ 
+
+ align:start position:0%
+about this this is a ramp that that
+turns which way down right this is a
+
+ align:start position:0%
+turns which way down right this is a
+ 
+
+ align:start position:0%
+turns which way down right this is a
+with that minus sign that ramp turns
+
+ align:start position:0%
+with that minus sign that ramp turns
+ 
+
+ align:start position:0%
+with that minus sign that ramp turns
+down at the point x equal a right it and
+
+ align:start position:0%
+down at the point x equal a right it and
+ 
+
+ align:start position:0%
+down at the point x equal a right it and
+it's its derivative goes from 0 to minus
+
+ align:start position:0%
+it's its derivative goes from 0 to minus
+ 
+
+ align:start position:0%
+it's its derivative goes from 0 to minus
+one the the derivative the slope of this
+
+ align:start position:0%
+one the the derivative the slope of this
+ 
+
+ align:start position:0%
+one the the derivative the slope of this
+guy drops by one because of the minus
+
+ align:start position:0%
+guy drops by one because of the minus
+ 
+
+ align:start position:0%
+guy drops by one because of the minus
+sign of sorry the slope yeah the slope
+
+ align:start position:0%
+sign of sorry the slope yeah the slope
+ 
+
+ align:start position:0%
+sign of sorry the slope yeah the slope
+of the of
+
+ align:start position:0%
+of the of
+ 
+
+ align:start position:0%
+of the of
+the sorry the slope of the yeah the
+
+ align:start position:0%
+the sorry the slope of the yeah the
+ 
+
+ align:start position:0%
+the sorry the slope of the yeah the
+slope of the ramp function of minus the
+
+ align:start position:0%
+slope of the ramp function of minus the
+ 
+
+ align:start position:0%
+slope of the ramp function of minus the
+ramp it goes at zero drops by one and
+
+ align:start position:0%
+ramp it goes at zero drops by one and
+ 
+
+ align:start position:0%
+ramp it goes at zero drops by one and
+and what this is going to do is take
+
+ align:start position:0%
+and what this is going to do is take
+ 
+
+ align:start position:0%
+and what this is going to do is take
+that ramp and adjust
+
+ align:start position:0%
+that ramp and adjust
+ 
+
+ align:start position:0%
+that ramp and adjust
+it to the to go through the fixed ends
+
+ align:start position:0%
+it to the to go through the fixed ends
+ 
+
+ align:start position:0%
+it to the to go through the fixed ends
+so let's just do it let's just do it
+
+ align:start position:0%
+so let's just do it let's just do it
+ 
+
+ align:start position:0%
+so let's just do it let's just do it
+what are C and D what are C and D my
+
+ align:start position:0%
+what are C and D what are C and D my
+ 
+
+ align:start position:0%
+what are C and D what are C and D my
+point a let let me draw a graph that's
+
+ align:start position:0%
+point a let let me draw a graph that's
+ 
+
+ align:start position:0%
+point a let let me draw a graph that's
+always the best thing always draw a
+
+ align:start position:0%
+always the best thing always draw a
+ 
+
+ align:start position:0%
+always the best thing always draw a
+graph of your of these Solutions
+
+ align:start position:0%
+graph of your of these Solutions
+ 
+
+ align:start position:0%
+graph of your of these Solutions
+okay so let me put in the point a okay
+
+ align:start position:0%
+okay so let me put in the point a okay
+ 
+
+ align:start position:0%
+okay so let me put in the point a okay
+so I'm drawing now a picture of the
+
+ align:start position:0%
+so I'm drawing now a picture of the
+ 
+
+ align:start position:0%
+so I'm drawing now a picture of the
+solution from zero to one I'll graph it
+
+ align:start position:0%
+solution from zero to one I'll graph it
+ 
+
+ align:start position:0%
+solution from zero to one I'll graph it
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+got okay what what what do I have here
+
+ align:start position:0%
+got okay what what what do I have here
+ 
+
+ align:start position:0%
+got okay what what what do I have here
+well let should we just plug in plug in
+
+ align:start position:0%
+well let should we just plug in plug in
+ 
+
+ align:start position:0%
+well let should we just plug in plug in
+uh the boundary conditions and find c
+
+ align:start position:0%
+uh the boundary conditions and find c
+ 
+
+ align:start position:0%
+uh the boundary conditions and find c
+and d That's the direct way what is
+
+ align:start position:0%
+and d That's the direct way what is
+ 
+
+ align:start position:0%
+and d That's the direct way what is
+C see I'm going to plug in hopefully I
+
+ align:start position:0%
+C see I'm going to plug in hopefully I
+ 
+
+ align:start position:0%
+C see I'm going to plug in hopefully I
+might find it from just the first
+
+ align:start position:0%
+might find it from just the first
+ 
+
+ align:start position:0%
+might find it from just the first
+boundary condition if I if I'm starting
+
+ align:start position:0%
+boundary condition if I if I'm starting
+ 
+
+ align:start position:0%
+boundary condition if I if I'm starting
+from zero well this guy certainly starts
+
+ align:start position:0%
+from zero well this guy certainly starts
+ 
+
+ align:start position:0%
+from zero well this guy certainly starts
+at zero right it it the ramp hasn't done
+
+ align:start position:0%
+at zero right it it the ramp hasn't done
+ 
+
+ align:start position:0%
+at zero right it it the ramp hasn't done
+anything until it gets to a and this guy
+
+ align:start position:0%
+anything until it gets to a and this guy
+ 
+
+ align:start position:0%
+anything until it gets to a and this guy
+is certainly zero so what is C gone
+
+ align:start position:0%
+is certainly zero so what is C gone
+ 
+
+ align:start position:0%
+is certainly zero so what is C gone
+right okay good now what is
+
+ align:start position:0%
+right okay good now what is
+ 
+
+ align:start position:0%
+right okay good now what is
+D okay well all right what's
+
+ align:start position:0%
+D okay well all right what's
+ 
+
+ align:start position:0%
+D okay well all right what's
+d uh let's see let me draw the
+
+ align:start position:0%
+d uh let's see let me draw the
+ 
+
+ align:start position:0%
+d uh let's see let me draw the
+so there's a there's a DX and D D won't
+
+ align:start position:0%
+so there's a there's a DX and D D won't
+ 
+
+ align:start position:0%
+so there's a there's a DX and D D won't
+be zero I want that thing to be one to
+
+ align:start position:0%
+be zero I want that thing to be one to
+ 
+
+ align:start position:0%
+be zero I want that thing to be one to
+be zero at 0.1 so I I want to determine
+
+ align:start position:0%
+be zero at 0.1 so I I want to determine
+ 
+
+ align:start position:0%
+be zero at 0.1 so I I want to determine
+D okay let me let me determine D so what
+
+ align:start position:0%
+D okay let me let me determine D so what
+ 
+
+ align:start position:0%
+D okay let me let me determine D so what
+is the minus the ramp at x equal 1 I'm
+
+ align:start position:0%
+is the minus the ramp at x equal 1 I'm
+ 
+
+ align:start position:0%
+is the minus the ramp at x equal 1 I'm
+plugging in x equal 1 is that right I'm
+
+ align:start position:0%
+plugging in x equal 1 is that right I'm
+ 
+
+ align:start position:0%
+plugging in x equal 1 is that right I'm
+going straight forward here plugging in
+
+ align:start position:0%
+going straight forward here plugging in
+ 
+
+ align:start position:0%
+going straight forward here plugging in
+x equal one into this boundary condition
+
+ align:start position:0%
+x equal one into this boundary condition
+ 
+
+ align:start position:0%
+x equal one into this boundary condition
+ready for this guy okay what's the ramp
+
+ align:start position:0%
+ready for this guy okay what's the ramp
+ 
+
+ align:start position:0%
+ready for this guy okay what's the ramp
+so it's minus and the ramp
+
+ align:start position:0%
+so it's minus and the ramp
+ 
+
+ align:start position:0%
+so it's minus and the ramp
+is well if this ramp is if if a ramp is
+
+ align:start position:0%
+is well if this ramp is if if a ramp is
+ 
+
+ align:start position:0%
+is well if this ramp is if if a ramp is
+shifted over then that shifted over so
+
+ align:start position:0%
+shifted over then that shifted over so
+ 
+
+ align:start position:0%
+shifted over then that shifted over so
+at x equal to one what's the ramp how
+
+ align:start position:0%
+at x equal to one what's the ramp how
+ 
+
+ align:start position:0%
+at x equal to one what's the ramp how
+how high has that ramp gone one minus a
+
+ align:start position:0%
+how high has that ramp gone one minus a
+ 
+
+ align:start position:0%
+how high has that ramp gone one minus a
+right the ramp is xus a at that point x
+
+ align:start position:0%
+right the ramp is xus a at that point x
+ 
+
+ align:start position:0%
+right the ramp is xus a at that point x
+at at the point x = 1 it will be 1 - A
+
+ align:start position:0%
+at at the point x = 1 it will be 1 - A
+ 
+
+ align:start position:0%
+at at the point x = 1 it will be 1 - A
+so I think I get 1 - 1 - A
+
+ align:start position:0%
+so I think I get 1 - 1 - A
+ 
+
+ align:start position:0%
+so I think I get 1 - 1 - A
+minus the ramp plus d *
+
+ align:start position:0%
+minus the ramp plus d *
+ 
+
+ align:start position:0%
+minus the ramp plus d *
+what one I'm plugging in xal 1 and
+
+ align:start position:0%
+what one I'm plugging in xal 1 and
+ 
+
+ align:start position:0%
+what one I'm plugging in xal 1 and
+that's supposed to
+
+ align:start position:0%
+that's supposed to
+ 
+
+ align:start position:0%
+that's supposed to
+equal zero
+
+ align:start position:0%
+equal zero
+ 
+
+ align:start position:0%
+equal zero
+good so I'm doing I'm doing this the
+
+ align:start position:0%
+good so I'm doing I'm doing this the
+ 
+
+ align:start position:0%
+good so I'm doing I'm doing this the
+sort of the systematic way of writing
+
+ align:start position:0%
+sort of the systematic way of writing
+ 
+
+ align:start position:0%
+sort of the systematic way of writing
+down the general solution discovering
+
+ align:start position:0%
+down the general solution discovering
+ 
+
+ align:start position:0%
+down the general solution discovering
+that D what do I discover D is put it on
+
+ align:start position:0%
+that D what do I discover D is put it on
+ 
+
+ align:start position:0%
+that D what do I discover D is put it on
+the other side D is 1 - A and of course
+
+ align:start position:0%
+the other side D is 1 - A and of course
+ 
+
+ align:start position:0%
+the other side D is 1 - A and of course
+don't forget that it's multiplying the X
+
+ align:start position:0%
+don't forget that it's multiplying the X
+ 
+
+ align:start position:0%
+don't forget that it's multiplying the X
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right let me just draw the
+
+ align:start position:0%
+okay all right let me just draw the
+ 
+
+ align:start position:0%
+okay all right let me just draw the
+picture it's uh yeah here's how I think
+
+ align:start position:0%
+picture it's uh yeah here's how I think
+ 
+
+ align:start position:0%
+picture it's uh yeah here's how I think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+it the solution is away from x equal a
+
+ align:start position:0%
+it the solution is away from x equal a
+ 
+
+ align:start position:0%
+it the solution is away from x equal a
+what does the solution look
+
+ align:start position:0%
+what does the solution look
+ 
+
+ align:start position:0%
+what does the solution look
+like to the left of x equal a What's My
+
+ align:start position:0%
+like to the left of x equal a What's My
+ 
+
+ align:start position:0%
+like to the left of x equal a What's My
+Graph going to be it's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a straight line right to the left of
+
+ align:start position:0%
+be a straight line right to the left of
+ 
+
+ align:start position:0%
+be a straight line right to the left of
+here there is no
+
+ align:start position:0%
+here there is no
+ 
+
+ align:start position:0%
+here there is no
+load the the equation is second
+
+ align:start position:0%
+load the the equation is second
+ 
+
+ align:start position:0%
+load the the equation is second
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+equals zero the solution to that is the
+
+ align:start position:0%
+equals zero the solution to that is the
+ 
+
+ align:start position:0%
+equals zero the solution to that is the
+straight line in other words until I get
+
+ align:start position:0%
+straight line in other words until I get
+ 
+
+ align:start position:0%
+straight line in other words until I get
+to a this thing hasn't started it's only
+
+ align:start position:0%
+to a this thing hasn't started it's only
+ 
+
+ align:start position:0%
+to a this thing hasn't started it's only
+this straight line it the solution does
+
+ align:start position:0%
+this straight line it the solution does
+ 
+
+ align:start position:0%
+this straight line it the solution does
+something like that it's a straight line
+
+ align:start position:0%
+something like that it's a straight line
+ 
+
+ align:start position:0%
+something like that it's a straight line
+and I guess actually that's what it is
+
+ align:start position:0%
+and I guess actually that's what it is
+ 
+
+ align:start position:0%
+and I guess actually that's what it is
+because the C isn't here and that's all
+
+ align:start position:0%
+because the C isn't here and that's all
+ 
+
+ align:start position:0%
+because the C isn't here and that's all
+we've got left so that's that's that
+
+ align:start position:0%
+we've got left so that's that's that
+ 
+
+ align:start position:0%
+we've got left so that's that's that
+straight
+
+ align:start position:0%
+straight
+ 
+
+ align:start position:0%
+straight
+line what happens what is it for the
+
+ align:start position:0%
+line what happens what is it for the
+ 
+
+ align:start position:0%
+line what happens what is it for the
+second half tell me what the solution
+
+ align:start position:0%
+second half tell me what the solution
+ 
+
+ align:start position:0%
+second half tell me what the solution
+looks like in the second half in between
+
+ align:start position:0%
+looks like in the second half in between
+ 
+
+ align:start position:0%
+looks like in the second half in between
+a and
+
+ align:start position:0%
+a and
+ 
+
+ align:start position:0%
+a and
+one it's going downhill
+
+ align:start position:0%
+one it's going downhill
+ 
+
+ align:start position:0%
+one it's going downhill
+why because it got to get back to
+
+ align:start position:0%
+why because it got to get back to
+ 
+
+ align:start position:0%
+why because it got to get back to
+zero and it's how is it going
+
+ align:start position:0%
+zero and it's how is it going
+ 
+
+ align:start position:0%
+zero and it's how is it going
+downhills it has to be
+
+ align:start position:0%
+downhills it has to be
+ 
+
+ align:start position:0%
+downhills it has to be
+linear in this region has to be linear
+
+ align:start position:0%
+linear in this region has to be linear
+ 
+
+ align:start position:0%
+linear in this region has to be linear
+why how do I know it's linear here
+
+ align:start position:0%
+why how do I know it's linear here
+ 
+
+ align:start position:0%
+why how do I know it's linear here
+because one way is to say the equation
+
+ align:start position:0%
+because one way is to say the equation
+ 
+
+ align:start position:0%
+because one way is to say the equation
+in that region is second derivative
+
+ align:start position:0%
+in that region is second derivative
+ 
+
+ align:start position:0%
+in that region is second derivative
+equals z second derivative equals z
+
+ align:start position:0%
+equals z second derivative equals z
+ 
+
+ align:start position:0%
+equals z second derivative equals z
+straight line This is my solution it's 1
+
+ align:start position:0%
+straight line This is my solution it's 1
+ 
+
+ align:start position:0%
+straight line This is my solution it's 1
+- ax here and it's whatever it is to get
+
+ align:start position:0%
+- ax here and it's whatever it is to get
+ 
+
+ align:start position:0%
+- ax here and it's whatever it is to get
+back to
+
+ align:start position:0%
+back to
+ 
+
+ align:start position:0%
+back to
+zero what what what what will it take to
+
+ align:start position:0%
+zero what what what what will it take to
+ 
+
+ align:start position:0%
+zero what what what what will it take to
+get back to
+
+ align:start position:0%
+get back to
+ 
+
+ align:start position:0%
+get back to
+zero let's see well we could plug in
+
+ align:start position:0%
+zero let's see well we could plug in
+ 
+
+ align:start position:0%
+zero let's see well we could plug in
+we've got one expression here or I could
+
+ align:start position:0%
+we've got one expression here or I could
+ 
+
+ align:start position:0%
+we've got one expression here or I could
+just look at that I could say okay
+
+ align:start position:0%
+just look at that I could say okay
+ 
+
+ align:start position:0%
+just look at that I could say okay
+what's the equation for the straight
+
+ align:start position:0%
+what's the equation for the straight
+ 
+
+ align:start position:0%
+what's the equation for the straight
+line that's at at this point what is the
+
+ align:start position:0%
+line that's at at this point what is the
+ 
+
+ align:start position:0%
+line that's at at this point what is the
+yeah it's 1 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ax
+
+ align:start position:0%
+ax
+ 
+
+ align:start position:0%
+ax
+H I want it to be
+
+ align:start position:0%
+H I want it to be
+ 
+
+ align:start position:0%
+H I want it to be
+linear I want it to
+
+ align:start position:0%
+linear I want it to
+ 
+
+ align:start position:0%
+linear I want it to
+get to
+
+ align:start position:0%
+get to
+ 
+
+ align:start position:0%
+get to
+zero let's see if I if I want that it
+
+ align:start position:0%
+zero let's see if I if I want that it
+ 
+
+ align:start position:0%
+zero let's see if I if I want that it
+would be great to have 1 - x * something
+
+ align:start position:0%
+would be great to have 1 - x * something
+ 
+
+ align:start position:0%
+would be great to have 1 - x * something
+I have to figure out
+
+ align:start position:0%
+I have to figure out
+ 
+
+ align:start position:0%
+I have to figure out
+what because with the one minus X at xal
+
+ align:start position:0%
+what because with the one minus X at xal
+ 
+
+ align:start position:0%
+what because with the one minus X at xal
+one that'll drop off that's linear what
+
+ align:start position:0%
+one that'll drop off that's linear what
+ 
+
+ align:start position:0%
+one that'll drop off that's linear what
+number what's the key here that that
+
+ align:start position:0%
+number what's the key here that that
+ 
+
+ align:start position:0%
+number what's the key here that that
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+slope I want to match them up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there think at at and that's the point x
+
+ align:start position:0%
+there think at at and that's the point x
+ 
+
+ align:start position:0%
+there think at at and that's the point x
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+a this is supposed to match that at x
+
+ align:start position:0%
+a this is supposed to match that at x
+ 
+
+ align:start position:0%
+a this is supposed to match that at x
+equal a do you have an idea for what I
+
+ align:start position:0%
+equal a do you have an idea for what I
+ 
+
+ align:start position:0%
+equal a do you have an idea for what I
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+take what what what what do I put right
+
+ align:start position:0%
+take what what what what do I put right
+ 
+
+ align:start position:0%
+take what what what what do I put right
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a look at the Symmetry in those two
+
+ align:start position:0%
+a look at the Symmetry in those two
+ 
+
+ align:start position:0%
+a look at the Symmetry in those two
+sides 1 - A * X going up 1 - x * a going
+
+ align:start position:0%
+sides 1 - A * X going up 1 - x * a going
+ 
+
+ align:start position:0%
+sides 1 - A * X going up 1 - x * a going
+down at x equal a it hits that point
+
+ align:start position:0%
+down at x equal a it hits that point
+ 
+
+ align:start position:0%
+down at x equal a it hits that point
+right that so we've solved it we could
+
+ align:start position:0%
+right that so we've solved it we could
+ 
+
+ align:start position:0%
+right that so we've solved it we could
+think about this different ways I could
+
+ align:start position:0%
+think about this different ways I could
+ 
+
+ align:start position:0%
+think about this different ways I could
+have got that one - x
+
+ align:start position:0%
+have got that one - x
+ 
+
+ align:start position:0%
+have got that one - x
+uh let's see I could have got it from
+
+ align:start position:0%
+uh let's see I could have got it from
+ 
+
+ align:start position:0%
+uh let's see I could have got it from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+formula in a way I like to get it from
+
+ align:start position:0%
+formula in a way I like to get it from
+ 
+
+ align:start position:0%
+formula in a way I like to get it from
+the picture I see it sort of I see the
+
+ align:start position:0%
+the picture I see it sort of I see the
+ 
+
+ align:start position:0%
+the picture I see it sort of I see the
+point what what happened at that point
+
+ align:start position:0%
+point what what happened at that point
+ 
+
+ align:start position:0%
+point what what happened at that point
+what what are the jump conditions this
+
+ align:start position:0%
+what what are the jump conditions this
+ 
+
+ align:start position:0%
+what what are the jump conditions this
+is another way to ask the see how the
+
+ align:start position:0%
+is another way to ask the see how the
+ 
+
+ align:start position:0%
+is another way to ask the see how the
+Delta function works what are the jump
+
+ align:start position:0%
+Delta function works what are the jump
+ 
+
+ align:start position:0%
+Delta function works what are the jump
+conditions I want to know when I ask
+
+ align:start position:0%
+conditions I want to know when I ask
+ 
+
+ align:start position:0%
+conditions I want to know when I ask
+about jump conditions I want to know
+
+ align:start position:0%
+about jump conditions I want to know
+ 
+
+ align:start position:0%
+about jump conditions I want to know
+what are the conditions on U of X the
+
+ align:start position:0%
+what are the conditions on U of X the
+ 
+
+ align:start position:0%
+what are the conditions on U of X the
+displacement what are the conditions on
+
+ align:start position:0%
+displacement what are the conditions on
+ 
+
+ align:start position:0%
+displacement what are the conditions on
+the slope U Prime of X that would be
+
+ align:start position:0%
+the slope U Prime of X that would be
+ 
+
+ align:start position:0%
+the slope U Prime of X that would be
+that'll be the strain when we're
+
+ align:start position:0%
+that'll be the strain when we're
+ 
+
+ align:start position:0%
+that'll be the strain when we're
+speaking about
+
+ align:start position:0%
+speaking about
+ 
+
+ align:start position:0%
+speaking about
+elasticity uh what's just for U of X
+
+ align:start position:0%
+elasticity uh what's just for U of X
+ 
+
+ align:start position:0%
+elasticity uh what's just for U of X
+what are what what's the statement about
+
+ align:start position:0%
+what are what what's the statement about
+ 
+
+ align:start position:0%
+what are what what's the statement about
+U of x from the left and from the right
+
+ align:start position:0%
+U of x from the left and from the right
+ 
+
+ align:start position:0%
+U of x from the left and from the right
+at that at that point of
+
+ align:start position:0%
+at that at that point of
+ 
+
+ align:start position:0%
+at that at that point of
+at that c critical point the point of
+
+ align:start position:0%
+at that c critical point the point of
+ 
+
+ align:start position:0%
+at that c critical point the point of
+the load from the left and from the
+
+ align:start position:0%
+the load from the left and from the
+ 
+
+ align:start position:0%
+the load from the left and from the
+right U of X
+
+ align:start position:0%
+right U of X
+ 
+
+ align:start position:0%
+right U of X
+is the same U of X matches up U of x
+
+ align:start position:0%
+is the same U of X matches up U of x
+ 
+
+ align:start position:0%
+is the same U of X matches up U of x
+from the left is that height U of x from
+
+ align:start position:0%
+from the left is that height U of x from
+ 
+
+ align:start position:0%
+from the left is that height U of x from
+the right is that I I want to write down
+
+ align:start position:0%
+the right is that I I want to write down
+ 
+
+ align:start position:0%
+the right is that I I want to write down
+those jump
+
+ align:start position:0%
+those jump
+ 
+
+ align:start position:0%
+those jump
+conditions because that's another way to
+
+ align:start position:0%
+conditions because that's another way to
+ 
+
+ align:start position:0%
+conditions because that's another way to
+see this U of X youu at
+
+ align:start position:0%
+see this U of X youu at
+ 
+
+ align:start position:0%
+see this U of X youu at
+a from
+
+ align:start position:0%
+a from
+ 
+
+ align:start position:0%
+a from
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+should equal
+
+ align:start position:0%
+should equal
+ 
+
+ align:start position:0%
+should equal
+U how do you want me to just say U is
+
+ align:start position:0%
+U how do you want me to just say U is
+ 
+
+ align:start position:0%
+U how do you want me to just say U is
+continuous yeah I'll just say it in
+
+ align:start position:0%
+continuous yeah I'll just say it in
+ 
+
+ align:start position:0%
+continuous yeah I'll just say it in
+words U is U of X is
+
+ align:start position:0%
+words U is U of X is
+ 
+
+ align:start position:0%
+words U is U of X is
+continuous at that just means it doesn't
+
+ align:start position:0%
+continuous at that just means it doesn't
+ 
+
+ align:start position:0%
+continuous at that just means it doesn't
+jump at x equal
+
+ align:start position:0%
+jump at x equal
+ 
+
+ align:start position:0%
+jump at x equal
+a so that's you could say that's a non-
+
+ align:start position:0%
+a so that's you could say that's a non-
+ 
+
+ align:start position:0%
+a so that's you could say that's a non-
+jump condition the function itself
+
+ align:start position:0%
+jump condition the function itself
+ 
+
+ align:start position:0%
+jump condition the function itself
+doesn't jump why not because we're
+
+ align:start position:0%
+doesn't jump why not because we're
+ 
+
+ align:start position:0%
+doesn't jump why not because we're
+talking about some elastic bar on which
+
+ align:start position:0%
+talking about some elastic bar on which
+ 
+
+ align:start position:0%
+talking about some elastic bar on which
+we put a point load the thing isn't
+
+ align:start position:0%
+we put a point load the thing isn't
+ 
+
+ align:start position:0%
+we put a point load the thing isn't
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+break the bar is going the displacement
+
+ align:start position:0%
+break the bar is going the displacement
+ 
+
+ align:start position:0%
+break the bar is going the displacement
+is going to be continuous but what's the
+
+ align:start position:0%
+is going to be continuous but what's the
+ 
+
+ align:start position:0%
+is going to be continuous but what's the
+condition on U Prime of X the the
+
+ align:start position:0%
+condition on U Prime of X the the
+ 
+
+ align:start position:0%
+condition on U Prime of X the the
+derivative the slope so that's the
+
+ align:start position:0%
+derivative the slope so that's the
+ 
+
+ align:start position:0%
+derivative the slope so that's the
+function and now tell me what's the deal
+
+ align:start position:0%
+function and now tell me what's the deal
+ 
+
+ align:start position:0%
+function and now tell me what's the deal
+on the slope what's the comparison
+
+ align:start position:0%
+on the slope what's the comparison
+ 
+
+ align:start position:0%
+on the slope what's the comparison
+between the I I have a slope of whatever
+
+ align:start position:0%
+between the I I have a slope of whatever
+ 
+
+ align:start position:0%
+between the I I have a slope of whatever
+it is going along here and I have a
+
+ align:start position:0%
+it is going along here and I have a
+ 
+
+ align:start position:0%
+it is going along here and I have a
+slope of a new slope so U Prime of x the
+
+ align:start position:0%
+slope of a new slope so U Prime of x the
+ 
+
+ align:start position:0%
+slope of a new slope so U Prime of x the
+slope jumps
+
+ align:start position:0%
+slope jumps
+ 
+
+ align:start position:0%
+slope jumps
+right and how much does it
+
+ align:start position:0%
+right and how much does it
+ 
+
+ align:start position:0%
+right and how much does it
+jump minus one it drops by one the slope
+
+ align:start position:0%
+jump minus one it drops by one the slope
+ 
+
+ align:start position:0%
+jump minus one it drops by one the slope
+because of because of my minus sign so
+
+ align:start position:0%
+because of because of my minus sign so
+ 
+
+ align:start position:0%
+because of because of my minus sign so
+this tells me that the yeah let me write
+
+ align:start position:0%
+this tells me that the yeah let me write
+ 
+
+ align:start position:0%
+this tells me that the yeah let me write
+that down the slope U Prime of X drops
+
+ align:start position:0%
+that down the slope U Prime of X drops
+ 
+
+ align:start position:0%
+that down the slope U Prime of X drops
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that would give me this is a
+
+ align:start position:0%
+one that would give me this is a
+ 
+
+ align:start position:0%
+one that would give me this is a
+different another way to say what the
+
+ align:start position:0%
+different another way to say what the
+ 
+
+ align:start position:0%
+different another way to say what the
+equation is
+
+ align:start position:0%
+equation is
+ 
+
+ align:start position:0%
+equation is
+asking the equation is looking for two
+
+ align:start position:0%
+asking the equation is looking for two
+ 
+
+ align:start position:0%
+asking the equation is looking for two
+pieces of straight lines that meet at a
+
+ align:start position:0%
+pieces of straight lines that meet at a
+ 
+
+ align:start position:0%
+pieces of straight lines that meet at a
+but their slope drops by one by the way
+
+ align:start position:0%
+but their slope drops by one by the way
+ 
+
+ align:start position:0%
+but their slope drops by one by the way
+what were the slopes it's good to graph
+
+ align:start position:0%
+what were the slopes it's good to graph
+ 
+
+ align:start position:0%
+what were the slopes it's good to graph
+the slopes too uh let me take out the
+
+ align:start position:0%
+the slopes too uh let me take out the
+ 
+
+ align:start position:0%
+the slopes too uh let me take out the
+let me graph the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slopes the slope U Prime the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX okay what what's the slope here slope
+
+ align:start position:0%
+DX okay what what's the slope here slope
+ 
+
+ align:start position:0%
+DX okay what what's the slope here slope
+is 1 - A in this point right the
+
+ align:start position:0%
+is 1 - A in this point right the
+ 
+
+ align:start position:0%
+is 1 - A in this point right the
+derivative is 1 - A along to here so
+
+ align:start position:0%
+derivative is 1 - A along to here so
+ 
+
+ align:start position:0%
+derivative is 1 - A along to here so
+slope is 1 minus a d d d d and now at x
+
+ align:start position:0%
+slope is 1 minus a d d d d and now at x
+ 
+
+ align:start position:0%
+slope is 1 minus a d d d d and now at x
+equal a the slope changes to this one
+
+ align:start position:0%
+equal a the slope changes to this one
+ 
+
+ align:start position:0%
+equal a the slope changes to this one
+and what's the slope of that second
+
+ align:start position:0%
+and what's the slope of that second
+ 
+
+ align:start position:0%
+and what's the slope of that second
+part minus a look it did it right minus
+
+ align:start position:0%
+part minus a look it did it right minus
+ 
+
+ align:start position:0%
+part minus a look it did it right minus
+a is the slope along
+
+ align:start position:0%
+a is the slope along
+ 
+
+ align:start position:0%
+a is the slope along
+here you see one minus a it dropped by
+
+ align:start position:0%
+here you see one minus a it dropped by
+ 
+
+ align:start position:0%
+here you see one minus a it dropped by
+one the one disappeared to leave a slope
+
+ align:start position:0%
+one the one disappeared to leave a slope
+ 
+
+ align:start position:0%
+one the one disappeared to leave a slope
+of minus a that's what the
+
+ align:start position:0%
+of minus a that's what the
+ 
+
+ align:start position:0%
+of minus a that's what the
+the you know I guess if I just imagine a
+
+ align:start position:0%
+the you know I guess if I just imagine a
+ 
+
+ align:start position:0%
+the you know I guess if I just imagine a
+imagine a bar I'm fixing it at both
+
+ align:start position:0%
+imagine a bar I'm fixing it at both
+ 
+
+ align:start position:0%
+imagine a bar I'm fixing it at both
+ends okay there's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar and
+
+ align:start position:0%
+bar and
+ 
+
+ align:start position:0%
+bar and
+we'll I'm just thinking for people who
+
+ align:start position:0%
+we'll I'm just thinking for people who
+ 
+
+ align:start position:0%
+we'll I'm just thinking for people who
+like to see a physical picture of what's
+
+ align:start position:0%
+like to see a physical picture of what's
+ 
+
+ align:start position:0%
+like to see a physical picture of what's
+Happening that's what this is we'll do
+
+ align:start position:0%
+Happening that's what this is we'll do
+ 
+
+ align:start position:0%
+Happening that's what this is we'll do
+it properly very very soon okay I've got
+
+ align:start position:0%
+it properly very very soon okay I've got
+ 
+
+ align:start position:0%
+it properly very very soon okay I've got
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+bar it's a very light bar it's it's its
+
+ align:start position:0%
+bar it's a very light bar it's it's its
+ 
+
+ align:start position:0%
+bar it's a very light bar it's it's its
+weight is not a a problem here but it's
+
+ align:start position:0%
+weight is not a a problem here but it's
+ 
+
+ align:start position:0%
+weight is not a a problem here but it's
+got a load at the point so I'll measure
+
+ align:start position:0%
+got a load at the point so I'll measure
+ 
+
+ align:start position:0%
+got a load at the point so I'll measure
+X going downwards and at the point x
+
+ align:start position:0%
+X going downwards and at the point x
+ 
+
+ align:start position:0%
+X going downwards and at the point x
+equal a I'm hanging a heavy load
+
+ align:start position:0%
+equal a I'm hanging a heavy load
+ 
+
+ align:start position:0%
+equal a I'm hanging a heavy load
+okay a load how do I draw a
+
+ align:start position:0%
+okay a load how do I draw a
+ 
+
+ align:start position:0%
+okay a load how do I draw a
+load
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe a like a big weight or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something okay that's a it's a
+
+ align:start position:0%
+something okay that's a it's a
+ 
+
+ align:start position:0%
+something okay that's a it's a
+he what what's going to happen to this
+
+ align:start position:0%
+he what what's going to happen to this
+ 
+
+ align:start position:0%
+he what what's going to happen to this
+dumb bar uh when when uh when I when I
+
+ align:start position:0%
+dumb bar uh when when uh when I when I
+ 
+
+ align:start position:0%
+dumb bar uh when when uh when I when I
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+that just tell me physically what's
+
+ align:start position:0%
+that just tell me physically what's
+ 
+
+ align:start position:0%
+that just tell me physically what's
+going to happen what's going to happen
+
+ align:start position:0%
+going to happen what's going to happen
+ 
+
+ align:start position:0%
+going to happen what's going to happen
+above the
+
+ align:start position:0%
+above the
+ 
+
+ align:start position:0%
+above the
+load it's going to stretch right tension
+
+ align:start position:0%
+load it's going to stretch right tension
+ 
+
+ align:start position:0%
+load it's going to stretch right tension
+the the the bar is going
+
+ align:start position:0%
+the the the bar is going
+ 
+
+ align:start position:0%
+the the the bar is going
+to the load is going to pull the bar
+
+ align:start position:0%
+to the load is going to pull the bar
+ 
+
+ align:start position:0%
+to the load is going to pull the bar
+down it's going to stretch this part and
+
+ align:start position:0%
+down it's going to stretch this part and
+ 
+
+ align:start position:0%
+down it's going to stretch this part and
+because nothing special is happening
+
+ align:start position:0%
+because nothing special is happening
+ 
+
+ align:start position:0%
+because nothing special is happening
+it's going to stretch it
+
+ align:start position:0%
+it's going to stretch it
+ 
+
+ align:start position:0%
+it's going to stretch it
+linearly and then what's going to happen
+
+ align:start position:0%
+linearly and then what's going to happen
+ 
+
+ align:start position:0%
+linearly and then what's going to happen
+below the
+
+ align:start position:0%
+below the
+ 
+
+ align:start position:0%
+below the
+load
+
+ align:start position:0%
+load
+ 
+
+ align:start position:0%
+load
+compression so the slope will go
+
+ align:start position:0%
+compression so the slope will go
+ 
+
+ align:start position:0%
+compression so the slope will go
+negative and nothing special happens so
+
+ align:start position:0%
+negative and nothing special happens so
+ 
+
+ align:start position:0%
+negative and nothing special happens so
+it the slope will be negative but it'll
+
+ align:start position:0%
+it the slope will be negative but it'll
+ 
+
+ align:start position:0%
+it the slope will be negative but it'll
+be constant the slope will drop from
+
+ align:start position:0%
+be constant the slope will drop from
+ 
+
+ align:start position:0%
+be constant the slope will drop from
+this to this the displacement the the
+
+ align:start position:0%
+this to this the displacement the the
+ 
+
+ align:start position:0%
+this to this the displacement the the
+that point will go down a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit that little bit it goes down is
+
+ align:start position:0%
+bit that little bit it goes down is
+ 
+
+ align:start position:0%
+bit that little bit it goes down is
+actually the height of this is is that
+
+ align:start position:0%
+actually the height of this is is that
+ 
+
+ align:start position:0%
+actually the height of this is is that
+because that's the displacement that
+
+ align:start position:0%
+because that's the displacement that
+ 
+
+ align:start position:0%
+because that's the displacement that
+it'll go down a little bit it'll stretch
+
+ align:start position:0%
+it'll go down a little bit it'll stretch
+ 
+
+ align:start position:0%
+it'll go down a little bit it'll stretch
+above it'll compress below and we see
+
+ align:start position:0%
+above it'll compress below and we see
+ 
+
+ align:start position:0%
+above it'll compress below and we see
+that in that picture of the displacement
+
+ align:start position:0%
+that in that picture of the displacement
+ 
+
+ align:start position:0%
+that in that picture of the displacement
+displacements it the displacement is all
+
+ align:start position:0%
+displacements it the displacement is all
+ 
+
+ align:start position:0%
+displacements it the displacement is all
+down right displacement you know nature
+
+ align:start position:0%
+down right displacement you know nature
+ 
+
+ align:start position:0%
+down right displacement you know nature
+is still going to all the the bar is
+
+ align:start position:0%
+is still going to all the the bar is
+ 
+
+ align:start position:0%
+is still going to all the the bar is
+going to move down that's why this uh
+
+ align:start position:0%
+going to move down that's why this uh
+ 
+
+ align:start position:0%
+going to move down that's why this uh
+function doesn't this function the
+
+ align:start position:0%
+function doesn't this function the
+ 
+
+ align:start position:0%
+function doesn't this function the
+displacement function is positive it
+
+ align:start position:0%
+displacement function is positive it
+ 
+
+ align:start position:0%
+displacement function is positive it
+goes all down but the slope function is
+
+ align:start position:0%
+goes all down but the slope function is
+ 
+
+ align:start position:0%
+goes all down but the slope function is
+positive here so so tension is positive
+
+ align:start position:0%
+positive here so so tension is positive
+ 
+
+ align:start position:0%
+positive here so so tension is positive
+slope stretch a and compression is
+
+ align:start position:0%
+slope stretch a and compression is
+ 
+
+ align:start position:0%
+slope stretch a and compression is
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+okay well all that to solve um this
+
+ align:start position:0%
+okay well all that to solve um this
+ 
+
+ align:start position:0%
+okay well all that to solve um this
+equation maybe while we're on a roll
+
+ align:start position:0%
+equation maybe while we're on a roll
+ 
+
+ align:start position:0%
+equation maybe while we're on a roll
+let's solve
+
+ align:start position:0%
+let's solve
+ 
+
+ align:start position:0%
+let's solve
+the free fixed guy so this is our we're
+
+ align:start position:0%
+the free fixed guy so this is our we're
+ 
+
+ align:start position:0%
+the free fixed guy so this is our we're
+might as well be systematic this was the
+
+ align:start position:0%
+might as well be systematic this was the
+ 
+
+ align:start position:0%
+might as well be systematic this was the
+fixed fixed problem let me below it
+
+ align:start position:0%
+fixed fixed problem let me below it
+ 
+
+ align:start position:0%
+fixed fixed problem let me below it
+solve the freef fix problem so it'll be
+
+ align:start position:0%
+solve the freef fix problem so it'll be
+ 
+
+ align:start position:0%
+solve the freef fix problem so it'll be
+minus U Prime that's the second
+
+ align:start position:0%
+minus U Prime that's the second
+ 
+
+ align:start position:0%
+minus U Prime that's the second
+derivative equals Delta at x minus a
+
+ align:start position:0%
+derivative equals Delta at x minus a
+ 
+
+ align:start position:0%
+derivative equals Delta at x minus a
+same same setup but now the top end
+
+ align:start position:0%
+same same setup but now the top end
+ 
+
+ align:start position:0%
+same same setup but now the top end
+is what's so it's free at the top what
+
+ align:start position:0%
+is what's so it's free at the top what
+ 
+
+ align:start position:0%
+is what's so it's free at the top what
+does that
+
+ align:start position:0%
+does that
+ 
+
+ align:start position:0%
+does that
+mean slope is
+
+ align:start position:0%
+mean slope is
+ 
+
+ align:start position:0%
+mean slope is
+zero at the top and the but it's still
+
+ align:start position:0%
+zero at the top and the but it's still
+ 
+
+ align:start position:0%
+zero at the top and the but it's still
+fixed at the bottom okay so this will be
+
+ align:start position:0%
+fixed at the bottom okay so this will be
+ 
+
+ align:start position:0%
+fixed at the bottom okay so this will be
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed let let me go straight to the
+
+ align:start position:0%
+fixed let let me go straight to the
+ 
+
+ align:start position:0%
+fixed let let me go straight to the
+picture let me go straight to the
+
+ align:start position:0%
+picture let me go straight to the
+ 
+
+ align:start position:0%
+picture let me go straight to the
+picture of U of
+
+ align:start position:0%
+picture of U of
+ 
+
+ align:start position:0%
+picture of U of
+X so there is x equal 0 there's xal 1
+
+ align:start position:0%
+X so there is x equal 0 there's xal 1
+ 
+
+ align:start position:0%
+X so there is x equal 0 there's xal 1
+here's the load at a what's
+
+ align:start position:0%
+here's the load at a what's
+ 
+
+ align:start position:0%
+here's the load at a what's
+up and I can I I'll while you're
+
+ align:start position:0%
+up and I can I I'll while you're
+ 
+
+ align:start position:0%
+up and I can I I'll while you're
+thinking about that let me draw a
+
+ align:start position:0%
+thinking about that let me draw a
+ 
+
+ align:start position:0%
+thinking about that let me draw a
+picture to match this picture a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar fixed at the
+
+ align:start position:0%
+bar fixed at the
+ 
+
+ align:start position:0%
+bar fixed at the
+bottom but not at the top okay and it's
+
+ align:start position:0%
+bottom but not at the top okay and it's
+ 
+
+ align:start position:0%
+bottom but not at the top okay and it's
+got its load here hanging
+
+ align:start position:0%
+got its load here hanging
+ 
+
+ align:start position:0%
+got its load here hanging
+down okay but let's do it math first and
+
+ align:start position:0%
+down okay but let's do it math first and
+ 
+
+ align:start position:0%
+down okay but let's do it math first and
+then check with the
+
+ align:start position:0%
+then check with the
+ 
+
+ align:start position:0%
+then check with the
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what we got two or three ways now
+
+ align:start position:0%
+okay what we got two or three ways now
+ 
+
+ align:start position:0%
+okay what we got two or three ways now
+to try to get the answer the systematic
+
+ align:start position:0%
+to try to get the answer the systematic
+ 
+
+ align:start position:0%
+to try to get the answer the systematic
+way would be to write down this
+
+ align:start position:0%
+way would be to write down this
+ 
+
+ align:start position:0%
+way would be to write down this
+solution and plug in the two boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions that'd be that'd be a
+
+ align:start position:0%
+conditions that'd be that'd be a
+ 
+
+ align:start position:0%
+conditions that'd be that'd be a
+straightforward way yeah let's we could
+
+ align:start position:0%
+straightforward way yeah let's we could
+ 
+
+ align:start position:0%
+straightforward way yeah let's we could
+even start by so u u of X
+
+ align:start position:0%
+even start by so u u of X
+ 
+
+ align:start position:0%
+even start by so u u of X
+is the particular solution the the ramp
+
+ align:start position:0%
+is the particular solution the the ramp
+ 
+
+ align:start position:0%
+is the particular solution the the ramp
+plus NE CX plus
+
+ align:start position:0%
+plus NE CX plus
+ 
+
+ align:start position:0%
+plus NE CX plus
+d and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just plug in x equals z that shouldn't
+
+ align:start position:0%
+just plug in x equals z that shouldn't
+ 
+
+ align:start position:0%
+just plug in x equals z that shouldn't
+be that'll be easy if I plug in x equals
+
+ align:start position:0%
+be that'll be easy if I plug in x equals
+ 
+
+ align:start position:0%
+be that'll be easy if I plug in x equals
+0 in in the in the free condition what
+
+ align:start position:0%
+0 in in the in the free condition what
+ 
+
+ align:start position:0%
+0 in in the in the free condition what
+does that tell me at x equals z this
+
+ align:start position:0%
+does that tell me at x equals z this
+ 
+
+ align:start position:0%
+does that tell me at x equals z this
+corner this ramp hasn't started so the
+
+ align:start position:0%
+corner this ramp hasn't started so the
+ 
+
+ align:start position:0%
+corner this ramp hasn't started so the
+slope is zero the slope of the constant
+
+ align:start position:0%
+slope is zero the slope of the constant
+ 
+
+ align:start position:0%
+slope is zero the slope of the constant
+is zero what do I learn from this
+
+ align:start position:0%
+is zero what do I learn from this
+ 
+
+ align:start position:0%
+is zero what do I learn from this
+boundary condition U Prime of Z equals
+
+ align:start position:0%
+boundary condition U Prime of Z equals
+ 
+
+ align:start position:0%
+boundary condition U Prime of Z equals
+z that c is zero before I learned that D
+
+ align:start position:0%
+z that c is zero before I learned that D
+ 
+
+ align:start position:0%
+z that c is zero before I learned that D
+was Zero but now from that condition I'm
+
+ align:start position:0%
+was Zero but now from that condition I'm
+ 
+
+ align:start position:0%
+was Zero but now from that condition I'm
+going to learn C is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero do the picture for
+
+ align:start position:0%
+zero do the picture for
+ 
+
+ align:start position:0%
+zero do the picture for
+me do the picture for me the what's the
+
+ align:start position:0%
+me do the picture for me the what's the
+ 
+
+ align:start position:0%
+me do the picture for me the what's the
+graph of the this is a graph of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X remember now it starts from zero
+
+ align:start position:0%
+X remember now it starts from zero
+ 
+
+ align:start position:0%
+X remember now it starts from zero
+slope because it's free at the top what
+
+ align:start position:0%
+slope because it's free at the top what
+ 
+
+ align:start position:0%
+slope because it's free at the top what
+does the graph look like in the first
+
+ align:start position:0%
+does the graph look like in the first
+ 
+
+ align:start position:0%
+does the graph look like in the first
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+yep it's a straight line has to be a
+
+ align:start position:0%
+yep it's a straight line has to be a
+ 
+
+ align:start position:0%
+yep it's a straight line has to be a
+straight line because there's no
+
+ align:start position:0%
+straight line because there's no
+ 
+
+ align:start position:0%
+straight line because there's no
+force and what kind of a
+
+ align:start position:0%
+force and what kind of a
+ 
+
+ align:start position:0%
+force and what kind of a
+line it's going to be
+
+ align:start position:0%
+line it's going to be
+ 
+
+ align:start position:0%
+line it's going to be
+horizontal because it starts out
+
+ align:start position:0%
+horizontal because it starts out
+ 
+
+ align:start position:0%
+horizontal because it starts out
+horizontal the the slope has to be zero
+
+ align:start position:0%
+horizontal the the slope has to be zero
+ 
+
+ align:start position:0%
+horizontal the the slope has to be zero
+at zero and nothing changes until a so
+
+ align:start position:0%
+at zero and nothing changes until a so
+ 
+
+ align:start position:0%
+at zero and nothing changes until a so
+it comes along
+
+ align:start position:0%
+it comes along
+ 
+
+ align:start position:0%
+it comes along
+there right okay so that's now I've
+
+ align:start position:0%
+there right okay so that's now I've
+ 
+
+ align:start position:0%
+there right okay so that's now I've
+started out with the right left the
+
+ align:start position:0%
+started out with the right left the
+ 
+
+ align:start position:0%
+started out with the right left the
+correct boundary condition at zero which
+
+ align:start position:0%
+correct boundary condition at zero which
+ 
+
+ align:start position:0%
+correct boundary condition at zero which
+was no slope and now what's it going to
+
+ align:start position:0%
+was no slope and now what's it going to
+ 
+
+ align:start position:0%
+was no slope and now what's it going to
+do the other half from a to
+
+ align:start position:0%
+do the other half from a to
+ 
+
+ align:start position:0%
+do the other half from a to
+one it's going to be again it'll be a
+
+ align:start position:0%
+one it's going to be again it'll be a
+ 
+
+ align:start position:0%
+one it's going to be again it'll be a
+straight line right because there's no
+
+ align:start position:0%
+straight line right because there's no
+ 
+
+ align:start position:0%
+straight line right because there's no
+Force there and what happens at the all
+
+ align:start position:0%
+Force there and what happens at the all
+ 
+
+ align:start position:0%
+Force there and what happens at the all
+the action of course is at this point a
+
+ align:start position:0%
+the action of course is at this point a
+ 
+
+ align:start position:0%
+the action of course is at this point a
+and what action is it tell me what sort
+
+ align:start position:0%
+and what action is it tell me what sort
+ 
+
+ align:start position:0%
+and what action is it tell me what sort
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+line how do I finish the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture what do I
+
+ align:start position:0%
+picture what do I
+ 
+
+ align:start position:0%
+picture what do I
+do I I start here right because the the
+
+ align:start position:0%
+do I I start here right because the the
+ 
+
+ align:start position:0%
+do I I start here right because the the
+bar the bar is not coming falling apart
+
+ align:start position:0%
+bar the bar is not coming falling apart
+ 
+
+ align:start position:0%
+bar the bar is not coming falling apart
+u u is continuous I don't get a gap
+
+ align:start position:0%
+u u is continuous I don't get a gap
+ 
+
+ align:start position:0%
+u u is continuous I don't get a gap
+suddenly and now what do I do from
+
+ align:start position:0%
+suddenly and now what do I do from
+ 
+
+ align:start position:0%
+suddenly and now what do I do from
+there only thing I can possibly do is I
+
+ align:start position:0%
+there only thing I can possibly do is I
+ 
+
+ align:start position:0%
+there only thing I can possibly do is I
+have to end up here and it has to be a
+
+ align:start position:0%
+have to end up here and it has to be a
+ 
+
+ align:start position:0%
+have to end up here and it has to be a
+straight line that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it that's what the picture will have to
+
+ align:start position:0%
+it that's what the picture will have to
+ 
+
+ align:start position:0%
+it that's what the picture will have to
+look like and what does that correspond
+
+ align:start position:0%
+look like and what does that correspond
+ 
+
+ align:start position:0%
+look like and what does that correspond
+to in the in the in the uh picture in
+
+ align:start position:0%
+to in the in the in the uh picture in
+ 
+
+ align:start position:0%
+to in the in the in the uh picture in
+the in the for the bar
+
+ align:start position:0%
+the in the for the bar
+ 
+
+ align:start position:0%
+the in the for the bar
+so well what happens with this bar the
+
+ align:start position:0%
+so well what happens with this bar the
+ 
+
+ align:start position:0%
+so well what happens with this bar the
+above the
+
+ align:start position:0%
+above the
+ 
+
+ align:start position:0%
+above the
+weight what's what happens to this top
+
+ align:start position:0%
+weight what's what happens to this top
+ 
+
+ align:start position:0%
+weight what's what happens to this top
+part of the bar in that
+
+ align:start position:0%
+part of the bar in that
+ 
+
+ align:start position:0%
+part of the bar in that
+picture and what happens to the lower
+
+ align:start position:0%
+picture and what happens to the lower
+ 
+
+ align:start position:0%
+picture and what happens to the lower
+part of the bar so this is this was at
+
+ align:start position:0%
+part of the bar so this is this was at
+ 
+
+ align:start position:0%
+part of the bar so this is this was at
+the point x equal a this is x equal Zer
+
+ align:start position:0%
+the point x equal a this is x equal Zer
+ 
+
+ align:start position:0%
+the point x equal a this is x equal Zer
+this is xal 1 what happens above the bar
+
+ align:start position:0%
+this is xal 1 what happens above the bar
+ 
+
+ align:start position:0%
+this is xal 1 what happens above the bar
+above the
+
+ align:start position:0%
+above the
+ 
+
+ align:start position:0%
+above the
+weight it just it just a rigid motion
+
+ align:start position:0%
+weight it just it just a rigid motion
+ 
+
+ align:start position:0%
+weight it just it just a rigid motion
+just goes down but because what happens
+
+ align:start position:0%
+just goes down but because what happens
+ 
+
+ align:start position:0%
+just goes down but because what happens
+below the weight is same compression or
+
+ align:start position:0%
+below the weight is same compression or
+ 
+
+ align:start position:0%
+below the weight is same compression or
+compression still happening this is
+
+ align:start position:0%
+compression still happening this is
+ 
+
+ align:start position:0%
+compression still happening this is
+still squeezed shall I try to draw
+
+ align:start position:0%
+still squeezed shall I try to draw
+ 
+
+ align:start position:0%
+still squeezed shall I try to draw
+it so this is after after the weight
+
+ align:start position:0%
+it so this is after after the weight
+ 
+
+ align:start position:0%
+it so this is after after the weight
+this is this got squeezed but this part
+
+ align:start position:0%
+this is this got squeezed but this part
+ 
+
+ align:start position:0%
+this is this got squeezed but this part
+did not get squeezed and that's what
+
+ align:start position:0%
+did not get squeezed and that's what
+ 
+
+ align:start position:0%
+did not get squeezed and that's what
+we're seeing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here uh no fixed this displacement so
+
+ align:start position:0%
+here uh no fixed this displacement so
+ 
+
+ align:start position:0%
+here uh no fixed this displacement so
+this is this means that that picture
+
+ align:start position:0%
+this is this means that that picture
+ 
+
+ align:start position:0%
+this is this means that that picture
+means that all the all
+
+ align:start position:0%
+means that all the all
+ 
+
+ align:start position:0%
+means that all the all
+the pieces of the bar here got moved
+
+ align:start position:0%
+the pieces of the bar here got moved
+ 
+
+ align:start position:0%
+the pieces of the bar here got moved
+down by the same amount whatever this we
+
+ align:start position:0%
+down by the same amount whatever this we
+ 
+
+ align:start position:0%
+down by the same amount whatever this we
+don't know that number
+
+ align:start position:0%
+don't know that number
+ 
+
+ align:start position:0%
+don't know that number
+yet and then
+
+ align:start position:0%
+yet and then
+ 
+
+ align:start position:0%
+yet and then
+uh below it they got
+
+ align:start position:0%
+uh below it they got
+ 
+
+ align:start position:0%
+uh below it they got
+compressed well we're almost there but
+
+ align:start position:0%
+compressed well we're almost there but
+ 
+
+ align:start position:0%
+compressed well we're almost there but
+we don't get have that solution what's
+
+ align:start position:0%
+we don't get have that solution what's
+ 
+
+ align:start position:0%
+we don't get have that solution what's
+the how come back to this picture U of
+
+ align:start position:0%
+the how come back to this picture U of
+ 
+
+ align:start position:0%
+the how come back to this picture U of
+AIS is continuous got it and what's the
+
+ align:start position:0%
+AIS is continuous got it and what's the
+ 
+
+ align:start position:0%
+AIS is continuous got it and what's the
+what's the real condition that's going
+
+ align:start position:0%
+what's the real condition that's going
+ 
+
+ align:start position:0%
+what's the real condition that's going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+determine where we are what that what
+
+ align:start position:0%
+determine where we are what that what
+ 
+
+ align:start position:0%
+determine where we are what that what
+those Heights are the the numbers in
+
+ align:start position:0%
+those Heights are the the numbers in
+ 
+
+ align:start position:0%
+those Heights are the the numbers in
+there it it's got to look like that but
+
+ align:start position:0%
+there it it's got to look like that but
+ 
+
+ align:start position:0%
+there it it's got to look like that but
+what what we got more than that we got
+
+ align:start position:0%
+what what we got more than that we got
+ 
+
+ align:start position:0%
+what what we got more than that we got
+to know what are the actual what is that
+
+ align:start position:0%
+to know what are the actual what is that
+ 
+
+ align:start position:0%
+to know what are the actual what is that
+height what is this what's the slope
+
+ align:start position:0%
+height what is this what's the slope
+ 
+
+ align:start position:0%
+height what is this what's the slope
+here the slope is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero here the slope is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what's the slope in the second part
+
+ align:start position:0%
+what what's the slope in the second part
+ 
+
+ align:start position:0%
+what what's the slope in the second part
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+key and you know what it has to be
+
+ align:start position:0%
+key and you know what it has to be
+ 
+
+ align:start position:0%
+key and you know what it has to be
+because what happens to the slope if if
+
+ align:start position:0%
+because what happens to the slope if if
+ 
+
+ align:start position:0%
+because what happens to the slope if if
+I have the second derivative as a Delta
+
+ align:start position:0%
+I have the second derivative as a Delta
+ 
+
+ align:start position:0%
+I have the second derivative as a Delta
+function with that minus sign the
+
+ align:start position:0%
+function with that minus sign the
+ 
+
+ align:start position:0%
+function with that minus sign the
+slope drops
+
+ align:start position:0%
+slope drops
+ 
+
+ align:start position:0%
+slope drops
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+one and the slope here is zero so the
+
+ align:start position:0%
+one and the slope here is zero so the
+ 
+
+ align:start position:0%
+one and the slope here is zero so the
+slope here
+
+ align:start position:0%
+slope here
+ 
+
+ align:start position:0%
+slope here
+isus one and now and it has to get
+
+ align:start position:0%
+isus one and now and it has to get
+ 
+
+ align:start position:0%
+isus one and now and it has to get
+through there so what is the
+
+ align:start position:0%
+through there so what is the
+ 
+
+ align:start position:0%
+through there so what is the
+function what's the function that has a
+
+ align:start position:0%
+function what's the function that has a
+ 
+
+ align:start position:0%
+function what's the function that has a
+slope of minus1 and comes down to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's it's it's got to have a minus X in
+
+ align:start position:0%
+it's it's it's got to have a minus X in
+ 
+
+ align:start position:0%
+it's it's it's got to have a minus X in
+it and what's the constant to make it
+
+ align:start position:0%
+it and what's the constant to make it
+ 
+
+ align:start position:0%
+it and what's the constant to make it
+come out right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what do I write now here for U of
+
+ align:start position:0%
+yeah what do I write now here for U of
+ 
+
+ align:start position:0%
+yeah what do I write now here for U of
+x- x 1 - x that has a slope of minus one
+
+ align:start position:0%
+x- x 1 - x that has a slope of minus one
+ 
+
+ align:start position:0%
+x- x 1 - x that has a slope of minus one
+the derivative is minus1 at x equal 1 it
+
+ align:start position:0%
+the derivative is minus1 at x equal 1 it
+ 
+
+ align:start position:0%
+the derivative is minus1 at x equal 1 it
+comes to zero that's it and what do I
+
+ align:start position:0%
+comes to zero that's it and what do I
+ 
+
+ align:start position:0%
+comes to zero that's it and what do I
+write what's U of X up
+
+ align:start position:0%
+write what's U of X up
+ 
+
+ align:start position:0%
+write what's U of X up
+here and therefore right there what
+
+ align:start position:0%
+here and therefore right there what
+ 
+
+ align:start position:0%
+here and therefore right there what
+what's what's the yeah what what's the
+
+ align:start position:0%
+what's what's the yeah what what's the
+ 
+
+ align:start position:0%
+what's what's the yeah what what's the
+displacement there of all this bit that
+
+ align:start position:0%
+displacement there of all this bit that
+ 
+
+ align:start position:0%
+displacement there of all this bit that
+moves down how much does it move
+
+ align:start position:0%
+moves down how much does it move
+ 
+
+ align:start position:0%
+moves down how much does it move
+down one minus a why one minus a that's
+
+ align:start position:0%
+down one minus a why one minus a that's
+ 
+
+ align:start position:0%
+down one minus a why one minus a that's
+the right answer one minus
+
+ align:start position:0%
+the right answer one minus
+ 
+
+ align:start position:0%
+the right answer one minus
+a why is
+
+ align:start position:0%
+a why is
+ 
+
+ align:start position:0%
+a why is
+that because it had to match up at x
+
+ align:start position:0%
+that because it had to match up at x
+ 
+
+ align:start position:0%
+that because it had to match up at x
+equal a at x equal a this and that match
+
+ align:start position:0%
+equal a at x equal a this and that match
+ 
+
+ align:start position:0%
+equal a at x equal a this and that match
+up at x equal a that slope that function
+
+ align:start position:0%
+up at x equal a that slope that function
+ 
+
+ align:start position:0%
+up at x equal a that slope that function
+and that function match up so the the
+
+ align:start position:0%
+and that function match up so the the
+ 
+
+ align:start position:0%
+and that function match up so the the
+slope the the slope picture is zero and
+
+ align:start position:0%
+slope the the slope picture is zero and
+ 
+
+ align:start position:0%
+slope the the slope picture is zero and
+oh I'm sorry this can't draw it because
+
+ align:start position:0%
+oh I'm sorry this can't draw it because
+ 
+
+ align:start position:0%
+oh I'm sorry this can't draw it because
+I got I'm at the bottom of the board the
+
+ align:start position:0%
+I got I'm at the bottom of the board the
+ 
+
+ align:start position:0%
+I got I'm at the bottom of the board the
+slope picture maybe I can draw it here
+
+ align:start position:0%
+slope picture maybe I can draw it here
+ 
+
+ align:start position:0%
+slope picture maybe I can draw it here
+the slope picture is zero along to here
+
+ align:start position:0%
+the slope picture is zero along to here
+ 
+
+ align:start position:0%
+the slope picture is zero along to here
+and then it drops by one to one minus a
+
+ align:start position:0%
+and then it drops by one to one minus a
+ 
+
+ align:start position:0%
+and then it drops by one to one minus a
+so that's a picture of U Prime zero and
+
+ align:start position:0%
+so that's a picture of U Prime zero and
+ 
+
+ align:start position:0%
+so that's a picture of U Prime zero and
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one this this is the thing to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at okay
+
+ align:start position:0%
+at okay
+ 
+
+ align:start position:0%
+at okay
+that's uh that's hard work when you were
+
+ align:start position:0%
+that's uh that's hard work when you were
+ 
+
+ align:start position:0%
+that's uh that's hard work when you were
+seeing Delta functions the first time
+
+ align:start position:0%
+seeing Delta functions the first time
+ 
+
+ align:start position:0%
+seeing Delta functions the first time
+but of course the functions did not get
+
+ align:start position:0%
+but of course the functions did not get
+ 
+
+ align:start position:0%
+but of course the functions did not get
+complicated we kept a clean uh uh
+
+ align:start position:0%
+complicated we kept a clean uh uh
+ 
+
+ align:start position:0%
+complicated we kept a clean uh uh
+example and from which which we man
+
+ align:start position:0%
+example and from which which we man
+ 
+
+ align:start position:0%
+example and from which which we man
+which we matched up with a figure and
+
+ align:start position:0%
+which we matched up with a figure and
+ 
+
+ align:start position:0%
+which we matched up with a figure and
+we've got the answer and we've got a
+
+ align:start position:0%
+we've got the answer and we've got a
+ 
+
+ align:start position:0%
+we've got the answer and we've got a
+couple of ways to do it one is this uh
+
+ align:start position:0%
+couple of ways to do it one is this uh
+ 
+
+ align:start position:0%
+couple of ways to do it one is this uh
+uh standard systematic plug-in boundary
+
+ align:start position:0%
+uh standard systematic plug-in boundary
+ 
+
+ align:start position:0%
+uh standard systematic plug-in boundary
+condition way the other way is
+
+ align:start position:0%
+condition way the other way is
+ 
+
+ align:start position:0%
+condition way the other way is
+this U of X does something here then the
+
+ align:start position:0%
+this U of X does something here then the
+ 
+
+ align:start position:0%
+this U of X does something here then the
+slope has to drop by one and that that's
+
+ align:start position:0%
+slope has to drop by one and that that's
+ 
+
+ align:start position:0%
+slope has to drop by one and that that's
+the that's the key to everything with
+
+ align:start position:0%
+the that's the key to everything with
+ 
+
+ align:start position:0%
+the that's the key to everything with
+the boundary condition so in a way we
+
+ align:start position:0%
+the boundary condition so in a way we
+ 
+
+ align:start position:0%
+the boundary condition so in a way we
+have a piece to the left and a piece to
+
+ align:start position:0%
+have a piece to the left and a piece to
+ 
+
+ align:start position:0%
+have a piece to the left and a piece to
+the right two constants here two
+
+ align:start position:0%
+the right two constants here two
+ 
+
+ align:start position:0%
+the right two constants here two
+constants here and somewhere there are
+
+ align:start position:0%
+constants here and somewhere there are
+ 
+
+ align:start position:0%
+constants here and somewhere there are
+four conditions that settle those four
+
+ align:start position:0%
+four conditions that settle those four
+ 
+
+ align:start position:0%
+four conditions that settle those four
+constants you know we could have a
+
+ align:start position:0%
+constants you know we could have a
+ 
+
+ align:start position:0%
+constants you know we could have a
+straight line here a straight line here
+
+ align:start position:0%
+straight line here a straight line here
+ 
+
+ align:start position:0%
+straight line here a straight line here
+that's two and two two but what are the
+
+ align:start position:0%
+that's two and two two but what are the
+ 
+
+ align:start position:0%
+that's two and two two but what are the
+four conditions that that settle those
+
+ align:start position:0%
+four conditions that that settle those
+ 
+
+ align:start position:0%
+four conditions that that settle those
+four constants well we have a boundary
+
+ align:start position:0%
+four constants well we have a boundary
+ 
+
+ align:start position:0%
+four constants well we have a boundary
+condition here that's one boundary
+
+ align:start position:0%
+condition here that's one boundary
+ 
+
+ align:start position:0%
+condition here that's one boundary
+condition here is two we need two more
+
+ align:start position:0%
+condition here is two we need two more
+ 
+
+ align:start position:0%
+condition here is two we need two more
+conditions to settle the the two pairs
+
+ align:start position:0%
+conditions to settle the the two pairs
+ 
+
+ align:start position:0%
+conditions to settle the the two pairs
+of constants and there they are that's
+
+ align:start position:0%
+of constants and there they are that's
+ 
+
+ align:start position:0%
+of constants and there they are that's
+the condition at the and that two two
+
+ align:start position:0%
+the condition at the and that two two
+ 
+
+ align:start position:0%
+the condition at the and that two two
+more two conditions at the at the uh
+
+ align:start position:0%
+more two conditions at the at the uh
+ 
+
+ align:start position:0%
+more two conditions at the at the uh
+jump at the at the uh discontinuity okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I've got to do the discrete
+
+ align:start position:0%
+now I've got to do the discrete
+ 
+
+ align:start position:0%
+now I've got to do the discrete
+case are you up for the discrete
+
+ align:start position:0%
+case are you up for the discrete
+ 
+
+ align:start position:0%
+case are you up for the discrete
+case the case where uh we're doing we
+
+ align:start position:0%
+case the case where uh we're doing we
+ 
+
+ align:start position:0%
+case the case where uh we're doing we
+have a difference
+
+ align:start position:0%
+have a difference
+ 
+
+ align:start position:0%
+have a difference
+equation so we're doing KU equal a
+
+ align:start position:0%
+equation so we're doing KU equal a
+ 
+
+ align:start position:0%
+equation so we're doing KU equal a
+column of the identity column of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+let let me just take it to be let me
+
+ align:start position:0%
+let let me just take it to be let me
+ 
+
+ align:start position:0%
+let let me just take it to be let me
+take a
+
+ align:start position:0%
+take a
+ 
+
+ align:start position:0%
+take a
+specific column say 0 1 Z Zer Zer let
+
+ align:start position:0%
+specific column say 0 1 Z Zer Zer let
+ 
+
+ align:start position:0%
+specific column say 0 1 Z Zer Zer let
+let let's suppose we have
+
+ align:start position:0%
+let let's suppose we have
+ 
+
+ align:start position:0%
+let let's suppose we have
+five I'm going to draw a picture
+
+ align:start position:0%
+five I'm going to draw a picture
+ 
+
+ align:start position:0%
+five I'm going to draw a picture
+now we have five because I made it five
+
+ align:start position:0%
+now we have five because I made it five
+ 
+
+ align:start position:0%
+now we have five because I made it five
+by five 1 two three four five here is
+
+ align:start position:0%
+by five 1 two three four five here is
+ 
+
+ align:start position:0%
+by five 1 two three four five here is
+zero and here is six so H is 1 over 5 +
+
+ align:start position:0%
+zero and here is six so H is 1 over 5 +
+ 
+
+ align:start position:0%
+zero and here is six so H is 1 over 5 +
+1 1 16 that's the Delta X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now and my equation says so what is my
+
+ align:start position:0%
+now and my equation says so what is my
+ 
+
+ align:start position:0%
+now and my equation says so what is my
+equation say remember what K is K
+
+ align:start position:0%
+equation say remember what K is K
+ 
+
+ align:start position:0%
+equation say remember what K is K
+is U is then U1 U2 u3 u4 and u5 the
+
+ align:start position:0%
+is U is then U1 U2 u3 u4 and u5 the
+ 
+
+ align:start position:0%
+is U is then U1 U2 u3 u4 and u5 the
+unknowns K is our old friend with
+
+ align:start position:0%
+unknowns K is our old friend with
+ 
+
+ align:start position:0%
+unknowns K is our old friend with
+twos and minus
+
+ align:start position:0%
+twos and minus
+ 
+
+ align:start position:0%
+twos and minus
+On's and minus
+
+ align:start position:0%
+On's and minus
+ 
+
+ align:start position:0%
+On's and minus
+On's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm going to find the solution and
+
+ align:start position:0%
+okay I'm going to find the solution and
+ 
+
+ align:start position:0%
+okay I'm going to find the solution and
+this will be a partic this will be the
+
+ align:start position:0%
+this will be a partic this will be the
+ 
+
+ align:start position:0%
+this will be a partic this will be the
+solution that has a load at this point
+
+ align:start position:0%
+solution that has a load at this point
+ 
+
+ align:start position:0%
+solution that has a load at this point
+this is like my point a right here the
+
+ align:start position:0%
+this is like my point a right here the
+ 
+
+ align:start position:0%
+this is like my point a right here the
+point in the continuous case a could run
+
+ align:start position:0%
+point in the continuous case a could run
+ 
+
+ align:start position:0%
+point in the continuous case a could run
+anywhere between zero and one in the
+
+ align:start position:0%
+anywhere between zero and one in the
+ 
+
+ align:start position:0%
+anywhere between zero and one in the
+discrete case I've got five possible
+
+ align:start position:0%
+discrete case I've got five possible
+ 
+
+ align:start position:0%
+discrete case I've got five possible
+load points and I picked the second one
+
+ align:start position:0%
+load points and I picked the second one
+ 
+
+ align:start position:0%
+load points and I picked the second one
+five columns of the identity Matrix five
+
+ align:start position:0%
+five columns of the identity Matrix five
+ 
+
+ align:start position:0%
+five columns of the identity Matrix five
+places to put that one I put it there
+
+ align:start position:0%
+places to put that one I put it there
+ 
+
+ align:start position:0%
+places to put that one I put it there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now can I draw the picture here should
+
+ align:start position:0%
+now can I draw the picture here should
+ 
+
+ align:start position:0%
+now can I draw the picture here should
+we do
+
+ align:start position:0%
+we do
+ 
+
+ align:start position:0%
+we do
+the which should we do first should we
+
+ align:start position:0%
+the which should we do first should we
+ 
+
+ align:start position:0%
+the which should we do first should we
+do freef fixed because that came
+
+ align:start position:0%
+do freef fixed because that came
+ 
+
+ align:start position:0%
+do freef fixed because that came
+out even easier than fixed fixed notice
+
+ align:start position:0%
+out even easier than fixed fixed notice
+ 
+
+ align:start position:0%
+out even easier than fixed fixed notice
+the the solution here had two parts this
+
+ align:start position:0%
+the the solution here had two parts this
+ 
+
+ align:start position:0%
+the the solution here had two parts this
+is the way I would write that
+
+ align:start position:0%
+is the way I would write that
+ 
+
+ align:start position:0%
+is the way I would write that
+answer because you could draw a picture
+
+ align:start position:0%
+answer because you could draw a picture
+ 
+
+ align:start position:0%
+answer because you could draw a picture
+but if you want to write the
+
+ align:start position:0%
+but if you want to write the
+ 
+
+ align:start position:0%
+but if you want to write the
+formula uh what would I do I would break
+
+ align:start position:0%
+formula uh what would I do I would break
+ 
+
+ align:start position:0%
+formula uh what would I do I would break
+it into two
+
+ align:start position:0%
+it into two
+ 
+
+ align:start position:0%
+it into two
+pieces uh 1 minus a up to the point
+
+ align:start position:0%
+pieces uh 1 minus a up to the point
+ 
+
+ align:start position:0%
+pieces uh 1 minus a up to the point
+a and because that's what it was running
+
+ align:start position:0%
+a and because that's what it was running
+ 
+
+ align:start position:0%
+a and because that's what it was running
+along here and then down here it was 1
+
+ align:start position:0%
+along here and then down here it was 1
+ 
+
+ align:start position:0%
+along here and then down here it was 1
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+x x greater or equal
+
+ align:start position:0%
+x x greater or equal
+ 
+
+ align:start position:0%
+x x greater or equal
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's important to mention you you
+
+ align:start position:0%
+yeah that's important to mention you you
+ 
+
+ align:start position:0%
+yeah that's important to mention you you
+have to have some guidance on how to
+
+ align:start position:0%
+have to have some guidance on how to
+ 
+
+ align:start position:0%
+have to have some guidance on how to
+write the answer and when the answer has
+
+ align:start position:0%
+write the answer and when the answer has
+ 
+
+ align:start position:0%
+write the answer and when the answer has
+two parts this is a good way to write it
+
+ align:start position:0%
+two parts this is a good way to write it
+ 
+
+ align:start position:0%
+two parts this is a good way to write it
+in two parts it's a little too you're
+
+ align:start position:0%
+in two parts it's a little too you're
+ 
+
+ align:start position:0%
+in two parts it's a little too you're
+compressing it too much to write to use
+
+ align:start position:0%
+compressing it too much to write to use
+ 
+
+ align:start position:0%
+compressing it too much to write to use
+that ramp function you can better to
+
+ align:start position:0%
+that ramp function you can better to
+ 
+
+ align:start position:0%
+that ramp function you can better to
+split it apart into the into before a
+
+ align:start position:0%
+split it apart into the into before a
+ 
+
+ align:start position:0%
+split it apart into the into before a
+and above and after a what's going to
+
+ align:start position:0%
+and above and after a what's going to
+ 
+
+ align:start position:0%
+and above and after a what's going to
+happen happen
+
+ align:start position:0%
+happen happen
+ 
+
+ align:start position:0%
+happen happen
+over here oh yeah all right let let's
+
+ align:start position:0%
+over here oh yeah all right let let's
+ 
+
+ align:start position:0%
+over here oh yeah all right let let's
+just can we take a shot shot at this
+
+ align:start position:0%
+just can we take a shot shot at this
+ 
+
+ align:start position:0%
+just can we take a shot shot at this
+problem and let
+
+ align:start position:0%
+problem and let
+ 
+
+ align:start position:0%
+problem and let
+me mention again in the
+
+ align:start position:0%
+me mention again in the
+ 
+
+ align:start position:0%
+me mention again in the
+review this that'll be in here this
+
+ align:start position:0%
+review this that'll be in here this
+ 
+
+ align:start position:0%
+review this that'll be in here this
+afternoon and every Wednesday afternoon
+
+ align:start position:0%
+afternoon and every Wednesday afternoon
+ 
+
+ align:start position:0%
+afternoon and every Wednesday afternoon
+um I'll just be ready for questions
+
+ align:start position:0%
+um I'll just be ready for questions
+ 
+
+ align:start position:0%
+um I'll just be ready for questions
+please bring
+
+ align:start position:0%
+please bring
+ 
+
+ align:start position:0%
+please bring
+questions uh they can be questions on
+
+ align:start position:0%
+questions uh they can be questions on
+ 
+
+ align:start position:0%
+questions uh they can be questions on
+the homework even better if they're
+
+ align:start position:0%
+the homework even better if they're
+ 
+
+ align:start position:0%
+the homework even better if they're
+questions on on other problems questions
+
+ align:start position:0%
+questions on on other problems questions
+ 
+
+ align:start position:0%
+questions on on other problems questions
+on the lecture questions
+
+ align:start position:0%
+on the lecture questions
+ 
+
+ align:start position:0%
+on the lecture questions
+yeah questions are essential to make
+
+ align:start position:0%
+yeah questions are essential to make
+ 
+
+ align:start position:0%
+yeah questions are essential to make
+that help session um helpful okay all
+
+ align:start position:0%
+that help session um helpful okay all
+ 
+
+ align:start position:0%
+that help session um helpful okay all
+right what do you think's cooking
+
+ align:start position:0%
+right what do you think's cooking
+ 
+
+ align:start position:0%
+right what do you think's cooking
+here what at a typical a typical uh
+
+ align:start position:0%
+here what at a typical a typical uh
+ 
+
+ align:start position:0%
+here what at a typical a typical uh
+somewhere in the middle
+
+ align:start position:0%
+somewhere in the middle
+ 
+
+ align:start position:0%
+somewhere in the middle
+here I'm I'm going to draw the use I'm
+
+ align:start position:0%
+here I'm I'm going to draw the use I'm
+ 
+
+ align:start position:0%
+here I'm I'm going to draw the use I'm
+going to shall I just draw
+
+ align:start position:0%
+going to shall I just draw
+ 
+
+ align:start position:0%
+going to shall I just draw
+them and and now what's my condition
+
+ align:start position:0%
+them and and now what's my condition
+ 
+
+ align:start position:0%
+them and and now what's my condition
+going my I got to put the boundary
+
+ align:start position:0%
+going my I got to put the boundary
+ 
+
+ align:start position:0%
+going my I got to put the boundary
+conditions on oh I have put the boundary
+
+ align:start position:0%
+conditions on oh I have put the boundary
+ 
+
+ align:start position:0%
+conditions on oh I have put the boundary
+conditions on by by putting that two
+
+ align:start position:0%
+conditions on by by putting that two
+ 
+
+ align:start position:0%
+conditions on by by putting that two
+there I did the I I'm up to here okay
+
+ align:start position:0%
+there I did the I I'm up to here okay
+ 
+
+ align:start position:0%
+there I did the I I'm up to here okay
+let's let's do that
+
+ align:start position:0%
+let's let's do that
+ 
+
+ align:start position:0%
+let's let's do that
+one when I put when I chose
+
+ align:start position:0%
+one when I put when I chose
+ 
+
+ align:start position:0%
+one when I put when I chose
+K and put a two in there I was picking
+
+ align:start position:0%
+K and put a two in there I was picking
+ 
+
+ align:start position:0%
+K and put a two in there I was picking
+the fixed fixed boundary conditions
+
+ align:start position:0%
+the fixed fixed boundary conditions
+ 
+
+ align:start position:0%
+the fixed fixed boundary conditions
+so can can I just say it's going to be
+
+ align:start position:0%
+so can can I just say it's going to be
+ 
+
+ align:start position:0%
+so can can I just say it's going to be
+beautiful the solution over there is
+
+ align:start position:0%
+beautiful the solution over there is
+ 
+
+ align:start position:0%
+beautiful the solution over there is
+going to look like this the solution
+
+ align:start position:0%
+going to look like this the solution
+ 
+
+ align:start position:0%
+going to look like this the solution
+over here is going to be up up up it's
+
+ align:start position:0%
+over here is going to be up up up it's
+ 
+
+ align:start position:0%
+over here is going to be up up up it's
+going to be a straight line but only
+
+ align:start position:0%
+going to be a straight line but only
+ 
+
+ align:start position:0%
+going to be a straight line but only
+points in a line and it'll be straight
+
+ align:start position:0%
+points in a line and it'll be straight
+ 
+
+ align:start position:0%
+points in a line and it'll be straight
+line down that value that value that
+
+ align:start position:0%
+line down that value that value that
+ 
+
+ align:start position:0%
+line down that value that value that
+value those will be U1 U2 u3 u4 and
+
+ align:start position:0%
+value those will be U1 U2 u3 u4 and
+ 
+
+ align:start position:0%
+value those will be U1 U2 u3 u4 and
+u5 okay
+
+ align:start position:0%
+u5 okay
+ 
+
+ align:start position:0%
+u5 okay
+and what's more
+
+ align:start position:0%
+and what's more
+ 
+
+ align:start position:0%
+and what's more
+the this is going to drop by one
+
+ align:start position:0%
+the this is going to drop by one
+ 
+
+ align:start position:0%
+the this is going to drop by one
+again actually I didn't have to redraw
+
+ align:start position:0%
+again actually I didn't have to redraw
+ 
+
+ align:start position:0%
+again actually I didn't have to redraw
+the picture it falls right on I in case
+
+ align:start position:0%
+the picture it falls right on I in case
+ 
+
+ align:start position:0%
+the picture it falls right on I in case
+X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+26 so that it fits that picture the I'm
+
+ align:start position:0%
+26 so that it fits that picture the I'm
+ 
+
+ align:start position:0%
+26 so that it fits that picture the I'm
+claiming we have another
+
+ align:start position:0%
+claiming we have another
+ 
+
+ align:start position:0%
+claiming we have another
+extremely lucky
+
+ align:start position:0%
+extremely lucky
+ 
+
+ align:start position:0%
+extremely lucky
+case if we can use the word lucky for
+
+ align:start position:0%
+case if we can use the word lucky for
+ 
+
+ align:start position:0%
+case if we can use the word lucky for
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+math uh that I'm claiming that the way
+
+ align:start position:0%
+math uh that I'm claiming that the way
+ 
+
+ align:start position:0%
+math uh that I'm claiming that the way
+the you remember for the uniform load
+
+ align:start position:0%
+the you remember for the uniform load
+ 
+
+ align:start position:0%
+the you remember for the uniform load
+with a one with when the when we had
+
+ align:start position:0%
+with a one with when the when we had
+ 
+
+ align:start position:0%
+with a one with when the when we had
+second derivative equal one the solution
+
+ align:start position:0%
+second derivative equal one the solution
+ 
+
+ align:start position:0%
+second derivative equal one the solution
+was a perfect
+
+ align:start position:0%
+was a perfect
+ 
+
+ align:start position:0%
+was a perfect
+Parabola and the discrete solution the
+
+ align:start position:0%
+Parabola and the discrete solution the
+ 
+
+ align:start position:0%
+Parabola and the discrete solution the
+difference equation was right on the
+
+ align:start position:0%
+difference equation was right on the
+ 
+
+ align:start position:0%
+difference equation was right on the
+parabola for this fixed fixed case it's
+
+ align:start position:0%
+parabola for this fixed fixed case it's
+ 
+
+ align:start position:0%
+parabola for this fixed fixed case it's
+going to happen again so it won't always
+
+ align:start position:0%
+going to happen again so it won't always
+ 
+
+ align:start position:0%
+going to happen again so it won't always
+happen those are the only two important
+
+ align:start position:0%
+happen those are the only two important
+ 
+
+ align:start position:0%
+happen those are the only two important
+right hand sides I know that there the
+
+ align:start position:0%
+right hand sides I know that there the
+ 
+
+ align:start position:0%
+right hand sides I know that there the
+two most important right hand sides and
+
+ align:start position:0%
+two most important right hand sides and
+ 
+
+ align:start position:0%
+two most important right hand sides and
+those are the two lucky
+
+ align:start position:0%
+those are the two lucky
+ 
+
+ align:start position:0%
+those are the two lucky
+ones if we have a constant that lies
+
+ align:start position:0%
+ones if we have a constant that lies
+ 
+
+ align:start position:0%
+ones if we have a constant that lies
+right on a parabola if if we have a
+
+ align:start position:0%
+right on a parabola if if we have a
+ 
+
+ align:start position:0%
+right on a parabola if if we have a
+Delta function it lies right on
+
+ align:start position:0%
+Delta function it lies right on
+ 
+
+ align:start position:0%
+Delta function it lies right on
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+ramp and there it is so that's the
+
+ align:start position:0%
+ramp and there it is so that's the
+ 
+
+ align:start position:0%
+ramp and there it is so that's the
+that's what the solution looks like now
+
+ align:start position:0%
+that's what the solution looks like now
+ 
+
+ align:start position:0%
+that's what the solution looks like now
+I have to figure out what these numbers
+
+ align:start position:0%
+I have to figure out what these numbers
+ 
+
+ align:start position:0%
+I have to figure out what these numbers
+are I
+
+ align:start position:0%
+are I
+ 
+
+ align:start position:0%
+are I
+guess yes what are those numbers oh well
+
+ align:start position:0%
+guess yes what are those numbers oh well
+ 
+
+ align:start position:0%
+guess yes what are those numbers oh well
+actually if it falls right on I know the
+
+ align:start position:0%
+actually if it falls right on I know the
+ 
+
+ align:start position:0%
+actually if it falls right on I know the
+numbers yeah so a
+
+ align:start position:0%
+numbers yeah so a
+ 
+
+ align:start position:0%
+numbers yeah so a
+is 2 six one 2 six yeah so let me let me
+
+ align:start position:0%
+is 2 six one 2 six yeah so let me let me
+ 
+
+ align:start position:0%
+is 2 six one 2 six yeah so let me let me
+keep 2 six okay so a is 26 that that's
+
+ align:start position:0%
+keep 2 six okay so a is 26 that that's
+ 
+
+ align:start position:0%
+keep 2 six okay so a is 26 that that's
+that's that value
+
+ align:start position:0%
+that's that value
+ 
+
+ align:start position:0%
+that's that value
+so I let me say what I think U
+
+ align:start position:0%
+so I let me say what I think U
+ 
+
+ align:start position:0%
+so I let me say what I think U
+is so this was a picture of U that's u 1
+
+ align:start position:0%
+is so this was a picture of U that's u 1
+ 
+
+ align:start position:0%
+is so this was a picture of U that's u 1
+2 3 4 and five and now the I think it
+
+ align:start position:0%
+2 3 4 and five and now the I think it
+ 
+
+ align:start position:0%
+2 3 4 and five and now the I think it
+lies right on that so it's going to be 1
+
+ align:start position:0%
+lies right on that so it's going to be 1
+ 
+
+ align:start position:0%
+lies right on that so it's going to be 1
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+26 of X going up and 1 - x * 26 going
+
+ align:start position:0%
+26 of X going up and 1 - x * 26 going
+ 
+
+ align:start position:0%
+26 of X going up and 1 - x * 26 going
+down my my point is that I'll be able to
+
+ align:start position:0%
+down my my point is that I'll be able to
+ 
+
+ align:start position:0%
+down my my point is that I'll be able to
+figure out what that
+
+ align:start position:0%
+figure out what that
+ 
+
+ align:start position:0%
+figure out what that
+uh this is U then this is the U
+
+ align:start position:0%
+uh this is U then this is the U
+ 
+
+ align:start position:0%
+uh this is U then this is the U
+okay you're going to say
+
+ align:start position:0%
+okay you're going to say
+ 
+
+ align:start position:0%
+okay you're going to say
+why before I let me pause before putting
+
+ align:start position:0%
+why before I let me pause before putting
+ 
+
+ align:start position:0%
+why before I let me pause before putting
+in numbers and say why is it how do why
+
+ align:start position:0%
+in numbers and say why is it how do why
+ 
+
+ align:start position:0%
+in numbers and say why is it how do why
+how do I know that the solution is right
+
+ align:start position:0%
+how do I know that the solution is right
+ 
+
+ align:start position:0%
+how do I know that the solution is right
+on the function the the the continuous
+
+ align:start position:0%
+on the function the the the continuous
+ 
+
+ align:start position:0%
+on the function the the the continuous
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+well can I draw a set of pictures just
+
+ align:start position:0%
+well can I draw a set of pictures just
+ 
+
+ align:start position:0%
+well can I draw a set of pictures just
+like those
+
+ align:start position:0%
+like those
+ 
+
+ align:start position:0%
+like those
+guys for discreet yeah let me just draw
+
+ align:start position:0%
+guys for discreet yeah let me just draw
+ 
+
+ align:start position:0%
+guys for discreet yeah let me just draw
+those for a discreete here that that's
+
+ align:start position:0%
+those for a discreete here that that's
+ 
+
+ align:start position:0%
+those for a discreete here that that's
+that's shows you the the magic okay so
+
+ align:start position:0%
+that's shows you the the magic okay so
+ 
+
+ align:start position:0%
+that's shows you the the magic okay so
+so there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a I'm going to draw a vector now so I'm
+
+ align:start position:0%
+a I'm going to draw a vector now so I'm
+ 
+
+ align:start position:0%
+a I'm going to draw a vector now so I'm
+not it's I'm going to have to lift the
+
+ align:start position:0%
+not it's I'm going to have to lift the
+ 
+
+ align:start position:0%
+not it's I'm going to have to lift the
+chalk it won't a function and it'll be
+
+ align:start position:0%
+chalk it won't a function and it'll be
+ 
+
+ align:start position:0%
+chalk it won't a function and it'll be
+the Delta Vector so it'll be the Delta
+
+ align:start position:0%
+the Delta Vector so it'll be the Delta
+ 
+
+ align:start position:0%
+the Delta Vector so it'll be the Delta
+Vector Delta with so there's 0.1 012 up
+
+ align:start position:0%
+Vector Delta with so there's 0.1 012 up
+ 
+
+ align:start position:0%
+Vector Delta with so there's 0.1 012 up
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+six it'll be the Delta
+
+ align:start position:0%
+six it'll be the Delta
+ 
+
+ align:start position:0%
+six it'll be the Delta
+Vector well if I just draw the Delta
+
+ align:start position:0%
+Vector well if I just draw the Delta
+ 
+
+ align:start position:0%
+Vector well if I just draw the Delta
+Vector the Delta Vector has a one there
+
+ align:start position:0%
+Vector the Delta Vector has a one there
+ 
+
+ align:start position:0%
+Vector the Delta Vector has a one there
+so the this is the Delta Vector do I
+
+ align:start position:0%
+so the this is the Delta Vector do I
+ 
+
+ align:start position:0%
+so the this is the Delta Vector do I
+need well you can see that it's it's the
+
+ align:start position:0%
+need well you can see that it's it's the
+ 
+
+ align:start position:0%
+need well you can see that it's it's the
+delta the vector is now going to be the
+
+ align:start position:0%
+delta the vector is now going to be the
+ 
+
+ align:start position:0%
+delta the vector is now going to be the
+the vector of all zeros and it's got a
+
+ align:start position:0%
+the vector of all zeros and it's got a
+ 
+
+ align:start position:0%
+the vector of all zeros and it's got a
+one at the key at the impulse and and
+
+ align:start position:0%
+one at the key at the impulse and and
+ 
+
+ align:start position:0%
+one at the key at the impulse and and
+then zero so it's a discrete impulse
+
+ align:start position:0%
+then zero so it's a discrete impulse
+ 
+
+ align:start position:0%
+then zero so it's a discrete impulse
+that would be a better word discrete
+
+ align:start position:0%
+that would be a better word discrete
+ 
+
+ align:start position:0%
+that would be a better word discrete
+impulse impulse at zero okay yeah so
+
+ align:start position:0%
+impulse impulse at zero okay yeah so
+ 
+
+ align:start position:0%
+impulse impulse at zero okay yeah so
+let's let's stay with an Impulse at zero
+
+ align:start position:0%
+let's let's stay with an Impulse at zero
+ 
+
+ align:start position:0%
+let's let's stay with an Impulse at zero
+all right what is
+
+ align:start position:0%
+all right what is
+ 
+
+ align:start position:0%
+all right what is
+the what's the next guy what's my next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture again let me put put in
+
+ align:start position:0%
+picture again let me put put in
+ 
+
+ align:start position:0%
+picture again let me put put in
+zero one two 3 onwards okay minus one so
+
+ align:start position:0%
+zero one two 3 onwards okay minus one so
+ 
+
+ align:start position:0%
+zero one two 3 onwards okay minus one so
+on um what do I want to do now what do I
+
+ align:start position:0%
+on um what do I want to do now what do I
+ 
+
+ align:start position:0%
+on um what do I want to do now what do I
+draw a second I always look over here
+
+ align:start position:0%
+draw a second I always look over here
+ 
+
+ align:start position:0%
+draw a second I always look over here
+what did I draw a second over
+
+ align:start position:0%
+what did I draw a second over
+ 
+
+ align:start position:0%
+what did I draw a second over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+the step now what what why did I draw a
+
+ align:start position:0%
+the step now what what why did I draw a
+ 
+
+ align:start position:0%
+the step now what what why did I draw a
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+function what how did I get from here to
+
+ align:start position:0%
+function what how did I get from here to
+ 
+
+ align:start position:0%
+function what how did I get from here to
+here I integrated I took the integral
+
+ align:start position:0%
+here I integrated I took the integral
+ 
+
+ align:start position:0%
+here I integrated I took the integral
+okay so how will I get from here to this
+
+ align:start position:0%
+okay so how will I get from here to this
+ 
+
+ align:start position:0%
+okay so how will I get from here to this
+picture I don't integrate
+
+ align:start position:0%
+picture I don't integrate
+ 
+
+ align:start position:0%
+picture I don't integrate
+I add sum okay so coming along from the
+
+ align:start position:0%
+I add sum okay so coming along from the
+ 
+
+ align:start position:0%
+I add sum okay so coming along from the
+left all these all along here this sum
+
+ align:start position:0%
+left all these all along here this sum
+ 
+
+ align:start position:0%
+left all these all along here this sum
+is all zero because it was always zero
+
+ align:start position:0%
+is all zero because it was always zero
+ 
+
+ align:start position:0%
+is all zero because it was always zero
+so it's z0 Z
+
+ align:start position:0%
+so it's z0 Z
+ 
+
+ align:start position:0%
+so it's z0 Z
+zero and then oops wait a minute it's is
+
+ align:start position:0%
+zero and then oops wait a minute it's is
+ 
+
+ align:start position:0%
+zero and then oops wait a minute it's is
+it a one
+
+ align:start position:0%
+it a one
+ 
+
+ align:start position:0%
+it a one
+there yeah I think it must be so here it
+
+ align:start position:0%
+there yeah I think it must be so here it
+ 
+
+ align:start position:0%
+there yeah I think it must be so here it
+wasn't a zero
+
+ align:start position:0%
+wasn't a zero
+ 
+
+ align:start position:0%
+wasn't a zero
+wrong here it's a one and what is it
+
+ align:start position:0%
+wrong here it's a one and what is it
+ 
+
+ align:start position:0%
+wrong here it's a one and what is it
+next what's next to it one because I'm
+
+ align:start position:0%
+next what's next to it one because I'm
+ 
+
+ align:start position:0%
+next what's next to it one because I'm
+I'm adding more and more zeros but I
+
+ align:start position:0%
+I'm adding more and more zeros but I
+ 
+
+ align:start position:0%
+I'm adding more and more zeros but I
+have that one now okay a
+
+ align:start position:0%
+have that one now okay a
+ 
+
+ align:start position:0%
+have that one now okay a
+discrete step it's a discrete step zeros
+
+ align:start position:0%
+discrete step it's a discrete step zeros
+ 
+
+ align:start position:0%
+discrete step it's a discrete step zeros
+and then ones okay now comes the SE so
+
+ align:start position:0%
+and then ones okay now comes the SE so
+ 
+
+ align:start position:0%
+and then ones okay now comes the SE so
+what am I going to call that well a uh
+
+ align:start position:0%
+what am I going to call that well a uh
+ 
+
+ align:start position:0%
+what am I going to call that well a uh
+no a step right it'll be a step function
+
+ align:start position:0%
+no a step right it'll be a step function
+ 
+
+ align:start position:0%
+no a step right it'll be a step function
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+vector and the oh yeah if the sums of
+
+ align:start position:0%
+vector and the oh yeah if the sums of
+ 
+
+ align:start position:0%
+vector and the oh yeah if the sums of
+the Delta Vector gave me the step Vector
+
+ align:start position:0%
+the Delta Vector gave me the step Vector
+ 
+
+ align:start position:0%
+the Delta Vector gave me the step Vector
+how do I go the other
+
+ align:start position:0%
+how do I go the other
+ 
+
+ align:start position:0%
+how do I go the other
+way the what do I do with the step
+
+ align:start position:0%
+way the what do I do with the step
+ 
+
+ align:start position:0%
+way the what do I do with the step
+Vector to get back to the Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector differences right sums in One
+
+ align:start position:0%
+Vector differences right sums in One
+ 
+
+ align:start position:0%
+Vector differences right sums in One
+Direction differences in the other so
+
+ align:start position:0%
+Direction differences in the other so
+ 
+
+ align:start position:0%
+Direction differences in the other so
+the D differences of the step Factor are
+
+ align:start position:0%
+the D differences of the step Factor are
+ 
+
+ align:start position:0%
+the D differences of the step Factor are
+the Delta Factor okay the step is the
+
+ align:start position:0%
+the Delta Factor okay the step is the
+ 
+
+ align:start position:0%
+the Delta Factor okay the step is the
+sum of the Deltas and the Delta is the
+
+ align:start position:0%
+sum of the Deltas and the Delta is the
+ 
+
+ align:start position:0%
+sum of the Deltas and the Delta is the
+differences of the step okay now for the
+
+ align:start position:0%
+differences of the step okay now for the
+ 
+
+ align:start position:0%
+differences of the step okay now for the
+crucial next guy what's it going to
+
+ align:start position:0%
+crucial next guy what's it going to
+ 
+
+ align:start position:0%
+crucial next guy what's it going to
+be I
+
+ align:start position:0%
+be I
+ 
+
+ align:start position:0%
+be I
+add wait a minute what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up I'm looking for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture do I get it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah I hope
+
+ align:start position:0%
+uh yeah I hope
+ 
+
+ align:start position:0%
+uh yeah I hope
+so or we oh look we ran out of time I
+
+ align:start position:0%
+so or we oh look we ran out of time I
+ 
+
+ align:start position:0%
+so or we oh look we ran out of time I
+don't have to do this but I will okay so
+
+ align:start position:0%
+don't have to do this but I will okay so
+ 
+
+ align:start position:0%
+don't have to do this but I will okay so
+uh so I'm get as I add I get zeros and
+
+ align:start position:0%
+uh so I'm get as I add I get zeros and
+ 
+
+ align:start position:0%
+uh so I'm get as I add I get zeros and
+then it's
+
+ align:start position:0%
+then it's
+ 
+
+ align:start position:0%
+then it's
+one and then I add on one more one
+
+ align:start position:0%
+one and then I add on one more one
+ 
+
+ align:start position:0%
+one and then I add on one more one
+look you see what's happening I I run
+
+ align:start position:0%
+look you see what's happening I I run
+ 
+
+ align:start position:0%
+look you see what's happening I I run
+along at zero but I I I'm going to look
+
+ align:start position:0%
+along at zero but I I I'm going to look
+ 
+
+ align:start position:0%
+along at zero but I I I'm going to look
+at the book to see
+
+ align:start position:0%
+at the book to see
+ 
+
+ align:start position:0%
+at the book to see
+um whether that jump should come here or
+
+ align:start position:0%
+um whether that jump should come here or
+ 
+
+ align:start position:0%
+um whether that jump should come here or
+here so I've got a little bit of this to
+
+ align:start position:0%
+here so I've got a little bit of this to
+ 
+
+ align:start position:0%
+here so I've got a little bit of this to
+finish next time and I'm open for any
+
+ align:start position:0%
+finish next time and I'm open for any
+ 
+
+ align:start position:0%
+finish next time and I'm open for any
+questions this afternoon okay thanks and
+
+ align:start position:0%
+questions this afternoon okay thanks and
+ 
+
+ align:start position:0%
+questions this afternoon okay thanks and
+sorry to keep you late
\ No newline at end of file
diff --git a/5s6rUYpVYjg.txt b/5s6rUYpVYjg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1c0721598e9a7df694fa8473332b1d89d9ff2d2c
--- /dev/null
+++ b/5s6rUYpVYjg.txt
@@ -0,0 +1,1947 @@
+align:start position:0%
+ 
+today we're going to finish our
+
+ align:start position:0%
+today we're going to finish our
+ 
+
+ align:start position:0%
+today we're going to finish our
+discussion of atoms and light in
+
+ align:start position:0%
+discussion of atoms and light in
+ 
+
+ align:start position:0%
+discussion of atoms and light in
+interaction and finally get some of
+
+ align:start position:0%
+interaction and finally get some of
+ 
+
+ align:start position:0%
+interaction and finally get some of
+those rates last time we reviewed the
+
+ align:start position:0%
+those rates last time we reviewed the
+ 
+
+ align:start position:0%
+those rates last time we reviewed the
+Einstein's argument I instead use his
+
+ align:start position:0%
+Einstein's argument I instead use his
+ 
+
+ align:start position:0%
+Einstein's argument I instead use his
+argument to discover spontaneous
+
+ align:start position:0%
+argument to discover spontaneous
+ 
+
+ align:start position:0%
+argument to discover spontaneous
+stimulated emission of radiation and how
+
+ align:start position:0%
+stimulated emission of radiation and how
+ 
+
+ align:start position:0%
+stimulated emission of radiation and how
+it accompanies the process of absorption
+
+ align:start position:0%
+it accompanies the process of absorption
+ 
+
+ align:start position:0%
+it accompanies the process of absorption
+all the time and there was also of
+
+ align:start position:0%
+all the time and there was also of
+ 
+
+ align:start position:0%
+all the time and there was also of
+course this process of spontaneous
+
+ align:start position:0%
+course this process of spontaneous
+ 
+
+ align:start position:0%
+course this process of spontaneous
+radiation that we found the formula for
+
+ align:start position:0%
+radiation that we found the formula for
+ 
+
+ align:start position:0%
+radiation that we found the formula for
+that transition rate in terms of the
+
+ align:start position:0%
+that transition rate in terms of the
+ 
+
+ align:start position:0%
+that transition rate in terms of the
+transition rate for stimulated radiation
+
+ align:start position:0%
+transition rate for stimulated radiation
+ 
+
+ align:start position:0%
+transition rate for stimulated radiation
+so let me review a couple of things that
+
+ align:start position:0%
+so let me review a couple of things that
+ 
+
+ align:start position:0%
+so let me review a couple of things that
+we had so we have an electric field that
+
+ align:start position:0%
+we had so we have an electric field that
+ 
+
+ align:start position:0%
+we had so we have an electric field that
+interacts with the atom there's a
+
+ align:start position:0%
+interacts with the atom there's a
+ 
+
+ align:start position:0%
+interacts with the atom there's a
+position vector that points to the
+
+ align:start position:0%
+position vector that points to the
+ 
+
+ align:start position:0%
+position vector that points to the
+charge Q and we have two levels level B
+
+ align:start position:0%
+charge Q and we have two levels level B
+ 
+
+ align:start position:0%
+charge Q and we have two levels level B
+with energy EB and level a with energy
+
+ align:start position:0%
+with energy EB and level a with energy
+ 
+
+ align:start position:0%
+with energy EB and level a with energy
+EA we introduce a dipole moment operator
+
+ align:start position:0%
+EA we introduce a dipole moment operator
+ 
+
+ align:start position:0%
+EA we introduce a dipole moment operator
+which was defined as Q times R and it's
+
+ align:start position:0%
+which was defined as Q times R and it's
+ 
+
+ align:start position:0%
+which was defined as Q times R and it's
+an operator because R is an operator the
+
+ align:start position:0%
+an operator because R is an operator the
+ 
+
+ align:start position:0%
+an operator because R is an operator the
+position is an operator in quantum
+
+ align:start position:0%
+position is an operator in quantum
+ 
+
+ align:start position:0%
+position is an operator in quantum
+mechanics so we observed and we've
+
+ align:start position:0%
+mechanics so we observed and we've
+ 
+
+ align:start position:0%
+mechanics so we observed and we've
+observed several times that the
+
+ align:start position:0%
+observed several times that the
+ 
+
+ align:start position:0%
+observed several times that the
+processes be going to a of stimulated
+
+ align:start position:0%
+processes be going to a of stimulated
+ 
+
+ align:start position:0%
+processes be going to a of stimulated
+emission and the process of a going to
+
+ align:start position:0%
+emission and the process of a going to
+ 
+
+ align:start position:0%
+emission and the process of a going to
+be of absorption are the same same to
+
+ align:start position:0%
+be of absorption are the same same to
+ 
+
+ align:start position:0%
+be of absorption are the same same to
+first order in perturbation theory and
+
+ align:start position:0%
+first order in perturbation theory and
+ 
+
+ align:start position:0%
+first order in perturbation theory and
+we wrote last time the formula for it
+
+ align:start position:0%
+we wrote last time the formula for it
+ 
+
+ align:start position:0%
+we wrote last time the formula for it
+using our general formula for harmonic
+
+ align:start position:0%
+using our general formula for harmonic
+ 
+
+ align:start position:0%
+using our general formula for harmonic
+transitions not Fermi's golden rule
+
+ align:start position:0%
+transitions not Fermi's golden rule
+ 
+
+ align:start position:0%
+transitions not Fermi's golden rule
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+this was a discrete transition
+
+ align:start position:0%
+this was a discrete transition
+ 
+
+ align:start position:0%
+this was a discrete transition
+apparently between these two levels so
+
+ align:start position:0%
+apparently between these two levels so
+ 
+
+ align:start position:0%
+apparently between these two levels so
+here is the formula let me remind you
+
+ align:start position:0%
+here is the formula let me remind you
+ 
+
+ align:start position:0%
+here is the formula let me remind you
+what it was there was an electric field
+
+ align:start position:0%
+what it was there was an electric field
+ 
+
+ align:start position:0%
+what it was there was an electric field
+was both of the farm to naught cosine
+
+ align:start position:0%
+was both of the farm to naught cosine
+ 
+
+ align:start position:0%
+was both of the farm to naught cosine
+Omega T times a vector n okay all our
+
+ align:start position:0%
+Omega T times a vector n okay all our
+ 
+
+ align:start position:0%
+Omega T times a vector n okay all our
+results from the discussion of light and
+
+ align:start position:0%
+results from the discussion of light and
+ 
+
+ align:start position:0%
+results from the discussion of light and
+atoms from previous lecture so here we
+
+ align:start position:0%
+atoms from previous lecture so here we
+ 
+
+ align:start position:0%
+atoms from previous lecture so here we
+go the transition probability as a
+
+ align:start position:0%
+go the transition probability as a
+ 
+
+ align:start position:0%
+go the transition probability as a
+function of time is given by this
+
+ align:start position:0%
+function of time is given by this
+ 
+
+ align:start position:0%
+function of time is given by this
+quantity in naught is half the peak
+
+ align:start position:0%
+quantity in naught is half the peak
+ 
+
+ align:start position:0%
+quantity in naught is half the peak
+amplitude of the electric field we
+
+ align:start position:0%
+amplitude of the electric field we
+ 
+
+ align:start position:0%
+amplitude of the electric field we
+always have this extra two here the a B
+
+ align:start position:0%
+always have this extra two here the a B
+ 
+
+ align:start position:0%
+always have this extra two here the a B
+is our the matrix elements of the
+
+ align:start position:0%
+is our the matrix elements of the
+ 
+
+ align:start position:0%
+is our the matrix elements of the
+operator D between the states here a and
+
+ align:start position:0%
+operator D between the states here a and
+ 
+
+ align:start position:0%
+operator D between the states here a and
+B so that's an inner product this is
+
+ align:start position:0%
+B so that's an inner product this is
+ 
+
+ align:start position:0%
+B so that's an inner product this is
+dotted with the vector n that refers to
+
+ align:start position:0%
+dotted with the vector n that refers to
+ 
+
+ align:start position:0%
+dotted with the vector n that refers to
+the polarization of the electric field
+
+ align:start position:0%
+the polarization of the electric field
+ 
+
+ align:start position:0%
+the polarization of the electric field
+that whole number is squared and then we
+
+ align:start position:0%
+that whole number is squared and then we
+ 
+
+ align:start position:0%
+that whole number is squared and then we
+have the sine squared over x squared
+
+ align:start position:0%
+have the sine squared over x squared
+ 
+
+ align:start position:0%
+have the sine squared over x squared
+function that we've usually had so this
+
+ align:start position:0%
+function that we've usually had so this
+ 
+
+ align:start position:0%
+function that we've usually had so this
+is our situation but what's gonna happen
+
+ align:start position:0%
+is our situation but what's gonna happen
+ 
+
+ align:start position:0%
+is our situation but what's gonna happen
+but we're interested and the situation
+
+ align:start position:0%
+but we're interested and the situation
+ 
+
+ align:start position:0%
+but we're interested and the situation
+that Einstein was considering was when
+
+ align:start position:0%
+that Einstein was considering was when
+ 
+
+ align:start position:0%
+that Einstein was considering was when
+you had a box
+
+ align:start position:0%
+you had a box
+ 
+
+ align:start position:0%
+you had a box
+you had thermal radiation and those
+
+ align:start position:0%
+you had thermal radiation and those
+ 
+
+ align:start position:0%
+you had thermal radiation and those
+atoms were there here we have a discrete
+
+ align:start position:0%
+atoms were there here we have a discrete
+ 
+
+ align:start position:0%
+atoms were there here we have a discrete
+process of transition from one state to
+
+ align:start position:0%
+process of transition from one state to
+ 
+
+ align:start position:0%
+process of transition from one state to
+another state neither one is a continuum
+
+ align:start position:0%
+another state neither one is a continuum
+ 
+
+ align:start position:0%
+another state neither one is a continuum
+when we had the ionization we were going
+
+ align:start position:0%
+when we had the ionization we were going
+ 
+
+ align:start position:0%
+when we had the ionization we were going
+from one state bound the continuum of
+
+ align:start position:0%
+from one state bound the continuum of
+ 
+
+ align:start position:0%
+from one state bound the continuum of
+flying electro
+
+ align:start position:0%
+flying electro
+ 
+
+ align:start position:0%
+flying electro
+and therefore a Fermi golden rule arose
+
+ align:start position:0%
+and therefore a Fermi golden rule arose
+ 
+
+ align:start position:0%
+and therefore a Fermi golden rule arose
+by integration here what are we to
+
+ align:start position:0%
+by integration here what are we to
+ 
+
+ align:start position:0%
+by integration here what are we to
+integrate well there is something to
+
+ align:start position:0%
+integrate well there is something to
+ 
+
+ align:start position:0%
+integrate well there is something to
+integrate the fact of the matter is that
+
+ align:start position:0%
+integrate the fact of the matter is that
+ 
+
+ align:start position:0%
+integrate the fact of the matter is that
+when you have this blood body radiation
+
+ align:start position:0%
+when you have this blood body radiation
+ 
+
+ align:start position:0%
+when you have this blood body radiation
+you will have a spectrum Omega of
+
+ align:start position:0%
+you will have a spectrum Omega of
+ 
+
+ align:start position:0%
+you will have a spectrum Omega of
+electric fields you don't just have one
+
+ align:start position:0%
+electric fields you don't just have one
+ 
+
+ align:start position:0%
+electric fields you don't just have one
+electric field at one specific frequency
+
+ align:start position:0%
+electric field at one specific frequency
+ 
+
+ align:start position:0%
+electric field at one specific frequency
+you will have many components of the
+
+ align:start position:0%
+you will have many components of the
+ 
+
+ align:start position:0%
+you will have many components of the
+electric field at different frequencies
+
+ align:start position:0%
+electric field at different frequencies
+ 
+
+ align:start position:0%
+electric field at different frequencies
+at different directions so in particular
+
+ align:start position:0%
+at different directions so in particular
+ 
+
+ align:start position:0%
+at different directions so in particular
+when you have blackbody radiation you
+
+ align:start position:0%
+when you have blackbody radiation you
+ 
+
+ align:start position:0%
+when you have blackbody radiation you
+will have in the spectrum here is omega
+
+ align:start position:0%
+will have in the spectrum here is omega
+ 
+
+ align:start position:0%
+will have in the spectrum here is omega
+be a that is the frequency for which the
+
+ align:start position:0%
+be a that is the frequency for which the
+ 
+
+ align:start position:0%
+be a that is the frequency for which the
+transitions tend to be more important
+
+ align:start position:0%
+transitions tend to be more important
+ 
+
+ align:start position:0%
+transitions tend to be more important
+remember when your Omega your frequency
+
+ align:start position:0%
+remember when your Omega your frequency
+ 
+
+ align:start position:0%
+remember when your Omega your frequency
+Omega is the frequency of the external
+
+ align:start position:0%
+Omega is the frequency of the external
+ 
+
+ align:start position:0%
+Omega is the frequency of the external
+light when your frequency Omega
+
+ align:start position:0%
+light when your frequency Omega
+ 
+
+ align:start position:0%
+light when your frequency Omega
+coincides with the Omega of this
+
+ align:start position:0%
+coincides with the Omega of this
+ 
+
+ align:start position:0%
+coincides with the Omega of this
+transition this stimulated emission or
+
+ align:start position:0%
+transition this stimulated emission or
+ 
+
+ align:start position:0%
+transition this stimulated emission or
+the absorption get enhanced so here is
+
+ align:start position:0%
+the absorption get enhanced so here is
+ 
+
+ align:start position:0%
+the absorption get enhanced so here is
+Omega be a that's one of the frequencies
+
+ align:start position:0%
+Omega be a that's one of the frequencies
+ 
+
+ align:start position:0%
+Omega be a that's one of the frequencies
+in the blackbody radiation but there are
+
+ align:start position:0%
+in the blackbody radiation but there are
+ 
+
+ align:start position:0%
+in the blackbody radiation but there are
+many many more nearby so and they are
+
+ align:start position:0%
+many many more nearby so and they are
+ 
+
+ align:start position:0%
+many many more nearby so and they are
+incoherent that is in the blackbody
+
+ align:start position:0%
+incoherent that is in the blackbody
+ 
+
+ align:start position:0%
+incoherent that is in the blackbody
+radiation
+
+ align:start position:0%
+radiation
+ 
+
+ align:start position:0%
+radiation
+each amplitude for a different frequency
+
+ align:start position:0%
+each amplitude for a different frequency
+ 
+
+ align:start position:0%
+each amplitude for a different frequency
+is independent of the other ones or like
+
+ align:start position:0%
+is independent of the other ones or like
+ 
+
+ align:start position:0%
+is independent of the other ones or like
+random so here is our sum therefore we
+
+ align:start position:0%
+random so here is our sum therefore we
+ 
+
+ align:start position:0%
+random so here is our sum therefore we
+must we know that when we have several
+
+ align:start position:0%
+must we know that when we have several
+ 
+
+ align:start position:0%
+must we know that when we have several
+inputs not just one electric field but
+
+ align:start position:0%
+inputs not just one electric field but
+ 
+
+ align:start position:0%
+inputs not just one electric field but
+many electric fields we will have to add
+
+ align:start position:0%
+many electric fields we will have to add
+ 
+
+ align:start position:0%
+many electric fields we will have to add
+the transition probability caused by the
+
+ align:start position:0%
+the transition probability caused by the
+ 
+
+ align:start position:0%
+the transition probability caused by the
+different electric fields and in this
+
+ align:start position:0%
+different electric fields and in this
+ 
+
+ align:start position:0%
+different electric fields and in this
+case we will have to sum the effects of
+
+ align:start position:0%
+case we will have to sum the effects of
+ 
+
+ align:start position:0%
+case we will have to sum the effects of
+the electric field squares of the main
+
+ align:start position:0%
+the electric field squares of the main
+ 
+
+ align:start position:0%
+the electric field squares of the main
+components of the blackbody radiation
+
+ align:start position:0%
+components of the blackbody radiation
+ 
+
+ align:start position:0%
+components of the blackbody radiation
+that lie near this Omega ba that is the
+
+ align:start position:0%
+that lie near this Omega ba that is the
+ 
+
+ align:start position:0%
+that lie near this Omega ba that is the
+one that would trigger a transition so
+
+ align:start position:0%
+one that would trigger a transition so
+ 
+
+ align:start position:0%
+one that would trigger a transition so
+this is how we're going to obtain
+
+ align:start position:0%
+this is how we're going to obtain
+ 
+
+ align:start position:0%
+this is how we're going to obtain
+something that will look like a Fermi
+
+ align:start position:0%
+something that will look like a Fermi
+ 
+
+ align:start position:0%
+something that will look like a Fermi
+golden rule as well here there's a
+
+ align:start position:0%
+golden rule as well here there's a
+ 
+
+ align:start position:0%
+golden rule as well here there's a
+transition the transition is between
+
+ align:start position:0%
+transition the transition is between
+ 
+
+ align:start position:0%
+transition the transition is between
+this great state but the trigger for the
+
+ align:start position:0%
+this great state but the trigger for the
+ 
+
+ align:start position:0%
+this great state but the trigger for the
+transition is a superposition of
+
+ align:start position:0%
+transition is a superposition of
+ 
+
+ align:start position:0%
+transition is a superposition of
+electromagnetic waves that we have to
+
+ align:start position:0%
+electromagnetic waves that we have to
+ 
+
+ align:start position:0%
+electromagnetic waves that we have to
+integrate over so one can say that the
+
+ align:start position:0%
+integrate over so one can say that the
+ 
+
+ align:start position:0%
+integrate over so one can say that the
+electric field electric field is a
+
+ align:start position:0%
+electric field electric field is a
+ 
+
+ align:start position:0%
+electric field electric field is a
+superposition of incoherent waves with
+
+ align:start position:0%
+superposition of incoherent waves with
+ 
+
+ align:start position:0%
+superposition of incoherent waves with
+different Omega
+
+ align:start position:0%
+different Omega
+ 
+
+ align:start position:0%
+different Omega
+eyes different frequencies different yz0
+
+ align:start position:0%
+eyes different frequencies different yz0
+ 
+
+ align:start position:0%
+eyes different frequencies different yz0
+of omega i different amplitudes and
+
+ align:start position:0%
+of omega i different amplitudes and
+ 
+
+ align:start position:0%
+of omega i different amplitudes and
+different vectors unit vector so each
+
+ align:start position:0%
+different vectors unit vector so each
+ 
+
+ align:start position:0%
+different vectors unit vector so each
+mode of this blood body radiation has a
+
+ align:start position:0%
+mode of this blood body radiation has a
+ 
+
+ align:start position:0%
+mode of this blood body radiation has a
+different amplitude and a different
+
+ align:start position:0%
+different amplitude and a different
+ 
+
+ align:start position:0%
+different amplitude and a different
+Omega and a different polarization and
+
+ align:start position:0%
+Omega and a different polarization and
+ 
+
+ align:start position:0%
+Omega and a different polarization and
+we have to sum over those that are near
+
+ align:start position:0%
+we have to sum over those that are near
+ 
+
+ align:start position:0%
+we have to sum over those that are near
+Omega ba and we know the only over near
+
+ align:start position:0%
+Omega ba and we know the only over near
+ 
+
+ align:start position:0%
+Omega ba and we know the only over near
+ones because this function doesn't allow
+
+ align:start position:0%
+ones because this function doesn't allow
+ 
+
+ align:start position:0%
+ones because this function doesn't allow
+you to or it becomes too small when you
+
+ align:start position:0%
+you to or it becomes too small when you
+ 
+
+ align:start position:0%
+you to or it becomes too small when you
+get far away from that central frequency
+
+ align:start position:0%
+get far away from that central frequency
+ 
+
+ align:start position:0%
+get far away from that central frequency
+so as a first step I can rewrite this
+
+ align:start position:0%
+so as a first step I can rewrite this
+ 
+
+ align:start position:0%
+so as a first step I can rewrite this
+transition probability to make it a
+
+ align:start position:0%
+transition probability to make it a
+ 
+
+ align:start position:0%
+transition probability to make it a
+little clearer I would say here it is
+
+ align:start position:0%
+little clearer I would say here it is
+ 
+
+ align:start position:0%
+little clearer I would say here it is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+transition probability for spontaneous
+
+ align:start position:0%
+transition probability for spontaneous
+ 
+
+ align:start position:0%
+transition probability for spontaneous
+emission of radiation associated to a
+
+ align:start position:0%
+emission of radiation associated to a
+ 
+
+ align:start position:0%
+emission of radiation associated to a
+particular mode of the radiation field
+
+ align:start position:0%
+particular mode of the radiation field
+ 
+
+ align:start position:0%
+particular mode of the radiation field
+would be given by four is zero of Omega
+
+ align:start position:0%
+would be given by four is zero of Omega
+ 
+
+ align:start position:0%
+would be given by four is zero of Omega
+I squared H squared
+
+ align:start position:0%
+I squared H squared
+ 
+
+ align:start position:0%
+I squared H squared
+Bab that is some matrix element in of
+
+ align:start position:0%
+Bab that is some matrix element in of
+ 
+
+ align:start position:0%
+Bab that is some matrix element in of
+the dipole operator in the atom that
+
+ align:start position:0%
+the dipole operator in the atom that
+ 
+
+ align:start position:0%
+the dipole operator in the atom that
+doesn't depend on anything having to do
+
+ align:start position:0%
+doesn't depend on anything having to do
+ 
+
+ align:start position:0%
+doesn't depend on anything having to do
+with the radiation M is possibly
+
+ align:start position:0%
+with the radiation M is possibly
+ 
+
+ align:start position:0%
+with the radiation M is possibly
+dependent on the radiation sine squared
+
+ align:start position:0%
+dependent on the radiation sine squared
+ 
+
+ align:start position:0%
+dependent on the radiation sine squared
+of 1/2 Omega B a minus Omega I the Omega
+
+ align:start position:0%
+of 1/2 Omega B a minus Omega I the Omega
+ 
+
+ align:start position:0%
+of 1/2 Omega B a minus Omega I the Omega
+I is the arming of the electric field so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've put all these things to
+
+ align:start position:0%
+so I've put all these things to
+ 
+
+ align:start position:0%
+so I've put all these things to
+represent the contribution from the 8th
+
+ align:start position:0%
+represent the contribution from the 8th
+ 
+
+ align:start position:0%
+represent the contribution from the 8th
+mode of the radiation field to the
+
+ align:start position:0%
+mode of the radiation field to the
+ 
+
+ align:start position:0%
+mode of the radiation field to the
+transition amplitude that's what it does
+
+ align:start position:0%
+transition amplitude that's what it does
+ 
+
+ align:start position:0%
+transition amplitude that's what it does
+so you could say oh the eighth mode is
+
+ align:start position:0%
+so you could say oh the eighth mode is
+ 
+
+ align:start position:0%
+so you could say oh the eighth mode is
+one in which I would write to me not of
+
+ align:start position:0%
+one in which I would write to me not of
+ 
+
+ align:start position:0%
+one in which I would write to me not of
+I so here would be 2 e not of Omega I
+
+ align:start position:0%
+I so here would be 2 e not of Omega I
+ 
+
+ align:start position:0%
+I so here would be 2 e not of Omega I
+cosine of Omega I T times the vector n
+
+ align:start position:0%
+cosine of Omega I T times the vector n
+ 
+
+ align:start position:0%
+cosine of Omega I T times the vector n
+Omega I that's the ithe mode of the
+
+ align:start position:0%
+Omega I that's the ithe mode of the
+ 
+
+ align:start position:0%
+Omega I that's the ithe mode of the
+electric field and that ice mode of the
+
+ align:start position:0%
+electric field and that ice mode of the
+ 
+
+ align:start position:0%
+electric field and that ice mode of the
+electric field does this transition and
+
+ align:start position:0%
+electric field does this transition and
+ 
+
+ align:start position:0%
+electric field does this transition and
+we have to sum over all this modes that
+
+ align:start position:0%
+we have to sum over all this modes that
+ 
+
+ align:start position:0%
+we have to sum over all this modes that
+are nearby here ok this is a low non
+
+ align:start position:0%
+are nearby here ok this is a low non
+ 
+
+ align:start position:0%
+are nearby here ok this is a low non
+trivial things that we have to do now
+
+ align:start position:0%
+trivial things that we have to do now
+ 
+
+ align:start position:0%
+trivial things that we have to do now
+but the way to think about it is that
+
+ align:start position:0%
+but the way to think about it is that
+ 
+
+ align:start position:0%
+but the way to think about it is that
+we've seen from the einstein arguments
+
+ align:start position:0%
+we've seen from the einstein arguments
+ 
+
+ align:start position:0%
+we've seen from the einstein arguments
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's a function U of Omega which is
+
+ align:start position:0%
+there's a function U of Omega which is
+ 
+
+ align:start position:0%
+there's a function U of Omega which is
+the energy density per unit frequency so
+
+ align:start position:0%
+the energy density per unit frequency so
+ 
+
+ align:start position:0%
+the energy density per unit frequency so
+that when you multiply by the Omega this
+
+ align:start position:0%
+that when you multiply by the Omega this
+ 
+
+ align:start position:0%
+that when you multiply by the Omega this
+is the energy density contained in the
+
+ align:start position:0%
+is the energy density contained in the
+ 
+
+ align:start position:0%
+is the energy density contained in the
+part of the spectrum with a range the
+
+ align:start position:0%
+part of the spectrum with a range the
+ 
+
+ align:start position:0%
+part of the spectrum with a range the
+Amida that's your energy density so
+
+ align:start position:0%
+Amida that's your energy density so
+ 
+
+ align:start position:0%
+Amida that's your energy density so
+that's an important quantity because it
+
+ align:start position:0%
+that's an important quantity because it
+ 
+
+ align:start position:0%
+that's an important quantity because it
+represents a number of photons and
+
+ align:start position:0%
+represents a number of photons and
+ 
+
+ align:start position:0%
+represents a number of photons and
+that's how Einstein argued that that
+
+ align:start position:0%
+that's how Einstein argued that that
+ 
+
+ align:start position:0%
+that's how Einstein argued that that
+defines or is a part of the ingredients
+
+ align:start position:0%
+defines or is a part of the ingredients
+ 
+
+ align:start position:0%
+defines or is a part of the ingredients
+of constructing the rate at which
+
+ align:start position:0%
+of constructing the rate at which
+ 
+
+ align:start position:0%
+of constructing the rate at which
+transitions will be happening so we have
+
+ align:start position:0%
+transitions will be happening so we have
+ 
+
+ align:start position:0%
+transitions will be happening so we have
+to relay this to energy so let's try to
+
+ align:start position:0%
+to relay this to energy so let's try to
+ 
+
+ align:start position:0%
+to relay this to energy so let's try to
+relate it to energy so we use things
+
+ align:start position:0%
+relate it to energy so we use things
+ 
+
+ align:start position:0%
+relate it to energy so we use things
+from electromagnetism some basic facts
+
+ align:start position:0%
+from electromagnetism some basic facts
+ 
+
+ align:start position:0%
+from electromagnetism some basic facts
+from electromagnetism if you have so
+
+ align:start position:0%
+from electromagnetism if you have so
+ 
+
+ align:start position:0%
+from electromagnetism if you have so
+I'll go here if you have a wave in
+
+ align:start position:0%
+I'll go here if you have a wave in
+ 
+
+ align:start position:0%
+I'll go here if you have a wave in
+general for a wave you have an e field
+
+ align:start position:0%
+general for a wave you have an e field
+ 
+
+ align:start position:0%
+general for a wave you have an e field
+and a B field and you have energies you
+
+ align:start position:0%
+and a B field and you have energies you
+ 
+
+ align:start position:0%
+and a B field and you have energies you
+electric a new magnetic these are energy
+
+ align:start position:0%
+electric a new magnetic these are energy
+ 
+
+ align:start position:0%
+electric a new magnetic these are energy
+densities and there's a simple formula
+
+ align:start position:0%
+densities and there's a simple formula
+ 
+
+ align:start position:0%
+densities and there's a simple formula
+for them the electric energy is equal to
+
+ align:start position:0%
+for them the electric energy is equal to
+ 
+
+ align:start position:0%
+for them the electric energy is equal to
+the magnitude of the electric field
+
+ align:start position:0%
+the magnitude of the electric field
+ 
+
+ align:start position:0%
+the magnitude of the electric field
+squared over 8 pi and in our case the
+
+ align:start position:0%
+squared over 8 pi and in our case the
+ 
+
+ align:start position:0%
+squared over 8 pi and in our case the
+magnitude of the electric field is the
+
+ align:start position:0%
+magnitude of the electric field is the
+ 
+
+ align:start position:0%
+magnitude of the electric field is the
+electric field in our convention is to e
+
+ align:start position:0%
+electric field in our convention is to e
+ 
+
+ align:start position:0%
+electric field in our convention is to e
+naught cosine Omega T so what do we get
+
+ align:start position:0%
+naught cosine Omega T so what do we get
+ 
+
+ align:start position:0%
+naught cosine Omega T so what do we get
+here for a naught squared cosine squared
+
+ align:start position:0%
+here for a naught squared cosine squared
+ 
+
+ align:start position:0%
+here for a naught squared cosine squared
+Omega T over 8 pi so this is 1 over 2 pi
+
+ align:start position:0%
+Omega T over 8 pi so this is 1 over 2 pi
+ 
+
+ align:start position:0%
+Omega T over 8 pi so this is 1 over 2 pi
+e naught squared cosine squared of Omega
+
+ align:start position:0%
+e naught squared cosine squared of Omega
+ 
+
+ align:start position:0%
+e naught squared cosine squared of Omega
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+but nobody really cares about the
+
+ align:start position:0%
+but nobody really cares about the
+ 
+
+ align:start position:0%
+but nobody really cares about the
+fluctuation of the energy you need the
+
+ align:start position:0%
+fluctuation of the energy you need the
+ 
+
+ align:start position:0%
+fluctuation of the energy you need the
+average energy at the volume so the time
+
+ align:start position:0%
+average energy at the volume so the time
+ 
+
+ align:start position:0%
+average energy at the volume so the time
+dependence must be averaged so from here
+
+ align:start position:0%
+dependence must be averaged so from here
+ 
+
+ align:start position:0%
+dependence must be averaged so from here
+the average over time of the electric
+
+ align:start position:0%
+the average over time of the electric
+ 
+
+ align:start position:0%
+the average over time of the electric
+field energy density is the average over
+
+ align:start position:0%
+field energy density is the average over
+ 
+
+ align:start position:0%
+field energy density is the average over
+time of closing squared which is one
+
+ align:start position:0%
+time of closing squared which is one
+ 
+
+ align:start position:0%
+time of closing squared which is one
+half so we have 1 over 4 pi is zero
+
+ align:start position:0%
+half so we have 1 over 4 pi is zero
+ 
+
+ align:start position:0%
+half so we have 1 over 4 pi is zero
+squared so that's the average electric
+
+ align:start position:0%
+squared so that's the average electric
+ 
+
+ align:start position:0%
+squared so that's the average electric
+field energy for a wave and that's the
+
+ align:start position:0%
+field energy for a wave and that's the
+ 
+
+ align:start position:0%
+field energy for a wave and that's the
+average over time but in a
+
+ align:start position:0%
+average over time but in a
+ 
+
+ align:start position:0%
+average over time but in a
+electromagnetic wave the average
+
+ align:start position:0%
+electromagnetic wave the average
+ 
+
+ align:start position:0%
+electromagnetic wave the average
+electric energy and the average magnetic
+
+ align:start position:0%
+electric energy and the average magnetic
+ 
+
+ align:start position:0%
+electric energy and the average magnetic
+energy are the same so you be or um
+
+ align:start position:0%
+energy are the same so you be or um
+ 
+
+ align:start position:0%
+energy are the same so you be or um
+magnetic is equal to UE the averages are
+
+ align:start position:0%
+magnetic is equal to UE the averages are
+ 
+
+ align:start position:0%
+magnetic is equal to UE the averages are
+identical and then of the total energy
+
+ align:start position:0%
+identical and then of the total energy
+ 
+
+ align:start position:0%
+identical and then of the total energy
+density therefore is perfect total you
+
+ align:start position:0%
+density therefore is perfect total you
+ 
+
+ align:start position:0%
+density therefore is perfect total you
+it's already average energy density
+
+ align:start position:0%
+it's already average energy density
+ 
+
+ align:start position:0%
+it's already average energy density
+would be u e+ u m which is 2 you eat and
+
+ align:start position:0%
+would be u e+ u m which is 2 you eat and
+ 
+
+ align:start position:0%
+would be u e+ u m which is 2 you eat and
+it's therefore 1 over 2 pi e naught
+
+ align:start position:0%
+it's therefore 1 over 2 pi e naught
+ 
+
+ align:start position:0%
+it's therefore 1 over 2 pi e naught
+squared so our end result is that the
+
+ align:start position:0%
+squared so our end result is that the
+ 
+
+ align:start position:0%
+squared so our end result is that the
+energy density u is 1 over 2 pi e naught
+
+ align:start position:0%
+energy density u is 1 over 2 pi e naught
+ 
+
+ align:start position:0%
+energy density u is 1 over 2 pi e naught
+squared ok usually thing here that is
+
+ align:start position:0%
+squared ok usually thing here that is
+ 
+
+ align:start position:0%
+squared ok usually thing here that is
+important is that there's lots of
+
+ align:start position:0%
+important is that there's lots of
+ 
+
+ align:start position:0%
+important is that there's lots of
+factors of 2 as factors of 2 in defining
+
+ align:start position:0%
+factors of 2 as factors of 2 in defining
+ 
+
+ align:start position:0%
+factors of 2 as factors of 2 in defining
+the energy density in our
+
+ align:start position:0%
+the energy density in our
+ 
+
+ align:start position:0%
+the energy density in our
+in overtime in adding electric and
+
+ align:start position:0%
+in overtime in adding electric and
+ 
+
+ align:start position:0%
+in overtime in adding electric and
+magnetic contributions of this is
+
+ align:start position:0%
+magnetic contributions of this is
+ 
+
+ align:start position:0%
+magnetic contributions of this is
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+it's important to get those factors of 2
+
+ align:start position:0%
+it's important to get those factors of 2
+ 
+
+ align:start position:0%
+it's important to get those factors of 2
+right otherwise your final formulas will
+
+ align:start position:0%
+right otherwise your final formulas will
+ 
+
+ align:start position:0%
+right otherwise your final formulas will
+be off so here is a the end result is a
+
+ align:start position:0%
+be off so here is a the end result is a
+ 
+
+ align:start position:0%
+be off so here is a the end result is a
+nice formula that rep allows you to
+
+ align:start position:0%
+nice formula that rep allows you to
+ 
+
+ align:start position:0%
+nice formula that rep allows you to
+rewrite the amplitude of your
+
+ align:start position:0%
+rewrite the amplitude of your
+ 
+
+ align:start position:0%
+rewrite the amplitude of your
+oscillation in terms of its contribution
+
+ align:start position:0%
+oscillation in terms of its contribution
+ 
+
+ align:start position:0%
+oscillation in terms of its contribution
+to the energy density so here it goes we
+
+ align:start position:0%
+to the energy density so here it goes we
+ 
+
+ align:start position:0%
+to the energy density so here it goes we
+can now think of this by saying if I
+
+ align:start position:0%
+can now think of this by saying if I
+ 
+
+ align:start position:0%
+can now think of this by saying if I
+have an electric field squared at some
+
+ align:start position:0%
+have an electric field squared at some
+ 
+
+ align:start position:0%
+have an electric field squared at some
+frequency well that's 2 pi times the
+
+ align:start position:0%
+frequency well that's 2 pi times the
+ 
+
+ align:start position:0%
+frequency well that's 2 pi times the
+energy density contributing at that
+
+ align:start position:0%
+energy density contributing at that
+ 
+
+ align:start position:0%
+energy density contributing at that
+frequency that's just the specialization
+
+ align:start position:0%
+frequency that's just the specialization
+ 
+
+ align:start position:0%
+frequency that's just the specialization
+of this to an arbitrary frequency and
+
+ align:start position:0%
+of this to an arbitrary frequency and
+ 
+
+ align:start position:0%
+of this to an arbitrary frequency and
+Omega I and an Omega I here so with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can now rewrite this transition
+
+ align:start position:0%
+we can now rewrite this transition
+ 
+
+ align:start position:0%
+we can now rewrite this transition
+amplitude the transition rebel can be
+
+ align:start position:0%
+amplitude the transition rebel can be
+ 
+
+ align:start position:0%
+amplitude the transition rebel can be
+now expressed in terms of energy
+
+ align:start position:0%
+now expressed in terms of energy
+ 
+
+ align:start position:0%
+now expressed in terms of energy
+densities so what do we have we have P B
+
+ align:start position:0%
+densities so what do we have we have P B
+ 
+
+ align:start position:0%
+densities so what do we have we have P B
+to a of P I would be equal to for that
+
+ align:start position:0%
+to a of P I would be equal to for that
+ 
+
+ align:start position:0%
+to a of P I would be equal to for that
+for remains there and then instead of
+
+ align:start position:0%
+for remains there and then instead of
+ 
+
+ align:start position:0%
+for remains there and then instead of
+Enochs squared we put two pi u of Omega
+
+ align:start position:0%
+Enochs squared we put two pi u of Omega
+ 
+
+ align:start position:0%
+Enochs squared we put two pi u of Omega
+I over H squared and not much changes
+
+ align:start position:0%
+I over H squared and not much changes
+ 
+
+ align:start position:0%
+I over H squared and not much changes
+anymore VAB and Omega I squared sine
+
+ align:start position:0%
+anymore VAB and Omega I squared sine
+ 
+
+ align:start position:0%
+anymore VAB and Omega I squared sine
+squared of 1/2 Omega B a minus Omega I P
+
+ align:start position:0%
+squared of 1/2 Omega B a minus Omega I P
+ 
+
+ align:start position:0%
+squared of 1/2 Omega B a minus Omega I P
+over Omega B a minus Omega I squared
\ No newline at end of file
diff --git a/6PxncdxIXNE.txt b/6PxncdxIXNE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1a59441809cd7680765d17d1ad9aa527fe898c9
--- /dev/null
+++ b/6PxncdxIXNE.txt
@@ -0,0 +1,13996 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I.E when multiple uh
+
+ align:start position:0%
+ocw.mit.edu I.E when multiple uh
+ 
+
+ align:start position:0%
+ocw.mit.edu I.E when multiple uh
+lineages of beneficial uh mutants are
+
+ align:start position:0%
+lineages of beneficial uh mutants are
+ 
+
+ align:start position:0%
+lineages of beneficial uh mutants are
+kind of spreading in the population at
+
+ align:start position:0%
+kind of spreading in the population at
+ 
+
+ align:start position:0%
+kind of spreading in the population at
+the same time right so when these clones
+
+ align:start position:0%
+the same time right so when these clones
+ 
+
+ align:start position:0%
+the same time right so when these clones
+are somehow interfering with each other
+
+ align:start position:0%
+are somehow interfering with each other
+ 
+
+ align:start position:0%
+are somehow interfering with each other
+in the population you know how is it
+
+ align:start position:0%
+in the population you know how is it
+ 
+
+ align:start position:0%
+in the population you know how is it
+that that clonal interference effect
+
+ align:start position:0%
+that that clonal interference effect
+ 
+
+ align:start position:0%
+that that clonal interference effect
+kind of plays out in the context of
+
+ align:start position:0%
+kind of plays out in the context of
+ 
+
+ align:start position:0%
+kind of plays out in the context of
+these microbial asexual populations and
+
+ align:start position:0%
+these microbial asexual populations and
+ 
+
+ align:start position:0%
+these microbial asexual populations and
+in particular in this uh in this paper
+
+ align:start position:0%
+in particular in this uh in this paper
+ 
+
+ align:start position:0%
+in particular in this uh in this paper
+what they were trying to measure was the
+
+ align:start position:0%
+what they were trying to measure was the
+ 
+
+ align:start position:0%
+what they were trying to measure was the
+distribution of effects of beneficial
+
+ align:start position:0%
+distribution of effects of beneficial
+ 
+
+ align:start position:0%
+distribution of effects of beneficial
+mutations right so you put a population
+
+ align:start position:0%
+mutations right so you put a population
+ 
+
+ align:start position:0%
+mutations right so you put a population
+into some new environment there may be
+
+ align:start position:0%
+into some new environment there may be
+ 
+
+ align:start position:0%
+into some new environment there may be
+some beneficial mutations that are
+
+ align:start position:0%
+some beneficial mutations that are
+ 
+
+ align:start position:0%
+some beneficial mutations that are
+possible the question is what is the
+
+ align:start position:0%
+possible the question is what is the
+ 
+
+ align:start position:0%
+possible the question is what is the
+probability distribution of effects of
+
+ align:start position:0%
+probability distribution of effects of
+ 
+
+ align:start position:0%
+probability distribution of effects of
+those benef beneficial mutations and
+
+ align:start position:0%
+those benef beneficial mutations and
+ 
+
+ align:start position:0%
+those benef beneficial mutations and
+this is uh as you might imagine a very
+
+ align:start position:0%
+this is uh as you might imagine a very
+ 
+
+ align:start position:0%
+this is uh as you might imagine a very
+basic quantity that we'd like to
+
+ align:start position:0%
+basic quantity that we'd like to
+ 
+
+ align:start position:0%
+basic quantity that we'd like to
+understand uh just to understand how
+
+ align:start position:0%
+understand uh just to understand how
+ 
+
+ align:start position:0%
+understand uh just to understand how
+Evolution Works in sort of new
+
+ align:start position:0%
+Evolution Works in sort of new
+ 
+
+ align:start position:0%
+Evolution Works in sort of new
+environments but it's actually something
+
+ align:start position:0%
+environments but it's actually something
+ 
+
+ align:start position:0%
+environments but it's actually something
+that's rather difficult to measure and
+
+ align:start position:0%
+that's rather difficult to measure and
+ 
+
+ align:start position:0%
+that's rather difficult to measure and
+and it's uh what's interesting here is
+
+ align:start position:0%
+and it's uh what's interesting here is
+ 
+
+ align:start position:0%
+and it's uh what's interesting here is
+it's difficult to measure in in kind of
+
+ align:start position:0%
+it's difficult to measure in in kind of
+ 
+
+ align:start position:0%
+it's difficult to measure in in kind of
+for for maybe a surprising reason um but
+
+ align:start position:0%
+for for maybe a surprising reason um but
+ 
+
+ align:start position:0%
+for for maybe a surprising reason um but
+I think that this is a wonderful example
+
+ align:start position:0%
+I think that this is a wonderful example
+ 
+
+ align:start position:0%
+I think that this is a wonderful example
+of how you you know if life gives you
+
+ align:start position:0%
+of how you you know if life gives you
+ 
+
+ align:start position:0%
+of how you you know if life gives you
+lemons that you make lemonade is that is
+
+ align:start position:0%
+lemons that you make lemonade is that is
+ 
+
+ align:start position:0%
+lemons that you make lemonade is that is
+that the expression
+
+ align:start position:0%
+that the expression
+ 
+
+ align:start position:0%
+that the expression
+okay right so in this paper they set out
+
+ align:start position:0%
+okay right so in this paper they set out
+ 
+
+ align:start position:0%
+okay right so in this paper they set out
+to try and measure the distribution of
+
+ align:start position:0%
+to try and measure the distribution of
+ 
+
+ align:start position:0%
+to try and measure the distribution of
+effects of beneficial limitations they
+
+ align:start position:0%
+effects of beneficial limitations they
+ 
+
+ align:start position:0%
+effects of beneficial limitations they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+unsuccessful right but they were
+
+ align:start position:0%
+unsuccessful right but they were
+ 
+
+ align:start position:0%
+unsuccessful right but they were
+unsuccessful for an interesting reason
+
+ align:start position:0%
+unsuccessful for an interesting reason
+ 
+
+ align:start position:0%
+unsuccessful for an interesting reason
+so then they were able to write but I
+
+ align:start position:0%
+so then they were able to write but I
+ 
+
+ align:start position:0%
+so then they were able to write but I
+think it's a very nice uh s
+
+ align:start position:0%
+think it's a very nice uh s
+ 
+
+ align:start position:0%
+think it's a very nice uh s
+okay um are there any questions about uh
+
+ align:start position:0%
+okay um are there any questions about uh
+ 
+
+ align:start position:0%
+okay um are there any questions about uh
+where we are or administrative things
+
+ align:start position:0%
+where we are or administrative things
+ 
+
+ align:start position:0%
+where we are or administrative things
+before we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going all right all right so just to
+
+ align:start position:0%
+going all right all right so just to
+ 
+
+ align:start position:0%
+going all right all right so just to
+recap where we were from from last time
+
+ align:start position:0%
+recap where we were from from last time
+ 
+
+ align:start position:0%
+recap where we were from from last time
+right we introduced this Moran model in
+
+ align:start position:0%
+right we introduced this Moran model in
+ 
+
+ align:start position:0%
+right we introduced this Moran model in
+which there's a fixed population size n
+
+ align:start position:0%
+which there's a fixed population size n
+ 
+
+ align:start position:0%
+which there's a fixed population size n
+right then each of these sort of uh
+
+ align:start position:0%
+right then each of these sort of uh
+ 
+
+ align:start position:0%
+right then each of these sort of uh
+Cycles what we do is we uh we choose one
+
+ align:start position:0%
+Cycles what we do is we uh we choose one
+ 
+
+ align:start position:0%
+Cycles what we do is we uh we choose one
+individual to uh to divide and we choose
+
+ align:start position:0%
+individual to uh to divide and we choose
+ 
+
+ align:start position:0%
+individual to uh to divide and we choose
+uh one individual to be replaced and we
+
+ align:start position:0%
+uh one individual to be replaced and we
+ 
+
+ align:start position:0%
+uh one individual to be replaced and we
+have the daughter say cell replace the
+
+ align:start position:0%
+have the daughter say cell replace the
+ 
+
+ align:start position:0%
+have the daughter say cell replace the
+um replace the the cell that was chosen
+
+ align:start position:0%
+um replace the the cell that was chosen
+ 
+
+ align:start position:0%
+um replace the the cell that was chosen
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+replacement right now in that model uh
+
+ align:start position:0%
+replacement right now in that model uh
+ 
+
+ align:start position:0%
+replacement right now in that model uh
+what we found was that there's some
+
+ align:start position:0%
+what we found was that there's some
+ 
+
+ align:start position:0%
+what we found was that there's some
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+X1 for a new Mutant with relative inness
+
+ align:start position:0%
+X1 for a new Mutant with relative inness
+ 
+
+ align:start position:0%
+X1 for a new Mutant with relative inness
+R to actually fix in the
+
+ align:start position:0%
+R to actually fix in the
+ 
+
+ align:start position:0%
+R to actually fix in the
+population and this uh this is in the
+
+ align:start position:0%
+population and this uh this is in the
+ 
+
+ align:start position:0%
+population and this uh this is in the
+case of no clonal
+
+ align:start position:0%
+case of no clonal
+ 
+
+ align:start position:0%
+case of no clonal
+interference okay so CI will in general
+
+ align:start position:0%
+interference okay so CI will in general
+ 
+
+ align:start position:0%
+interference okay so CI will in general
+be clonal interference today right so
+
+ align:start position:0%
+be clonal interference today right so
+ 
+
+ align:start position:0%
+be clonal interference today right so
+this is this is uh if there's just this
+
+ align:start position:0%
+this is this is uh if there's just this
+ 
+
+ align:start position:0%
+this is this is uh if there's just this
+one mutation that we're considering then
+
+ align:start position:0%
+one mutation that we're considering then
+ 
+
+ align:start position:0%
+one mutation that we're considering then
+the the question of surviving stochastic
+
+ align:start position:0%
+the the question of surviving stochastic
+ 
+
+ align:start position:0%
+the the question of surviving stochastic
+Extinction kind of at the beginning is
+
+ align:start position:0%
+Extinction kind of at the beginning is
+ 
+
+ align:start position:0%
+Extinction kind of at the beginning is
+equivalent to the question of um being
+
+ align:start position:0%
+equivalent to the question of um being
+ 
+
+ align:start position:0%
+equivalent to the question of um being
+able to fix in the population for uh for
+
+ align:start position:0%
+able to fix in the population for uh for
+ 
+
+ align:start position:0%
+able to fix in the population for uh for
+certainly for for a beneficial mutation
+
+ align:start position:0%
+certainly for for a beneficial mutation
+ 
+
+ align:start position:0%
+certainly for for a beneficial mutation
+with r greater than one okay so what we
+
+ align:start position:0%
+with r greater than one okay so what we
+ 
+
+ align:start position:0%
+with r greater than one okay so what we
+want to do today to just start is to try
+
+ align:start position:0%
+want to do today to just start is to try
+ 
+
+ align:start position:0%
+want to do today to just start is to try
+to think about how we can use this model
+
+ align:start position:0%
+to think about how we can use this model
+ 
+
+ align:start position:0%
+to think about how we can use this model
+and and and this equation uh in order to
+
+ align:start position:0%
+and and and this equation uh in order to
+ 
+
+ align:start position:0%
+and and and this equation uh in order to
+understand the probability of uh of
+
+ align:start position:0%
+understand the probability of uh of
+ 
+
+ align:start position:0%
+understand the probability of uh of
+fixation when there's more than one
+
+ align:start position:0%
+fixation when there's more than one
+ 
+
+ align:start position:0%
+fixation when there's more than one
+mutant in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population right so here what we found
+
+ align:start position:0%
+population right so here what we found
+ 
+
+ align:start position:0%
+population right so here what we found
+is that this thing there are two uh two
+
+ align:start position:0%
+is that this thing there are two uh two
+ 
+
+ align:start position:0%
+is that this thing there are two uh two
+limits that we might want to keep track
+
+ align:start position:0%
+limits that we might want to keep track
+ 
+
+ align:start position:0%
+limits that we might want to keep track
+of right so this thing goes to 1/ n for
+
+ align:start position:0%
+of right so this thing goes to 1/ n for
+ 
+
+ align:start position:0%
+of right so this thing goes to 1/ n for
+neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mutations and it goes to uh s uh for um
+
+ align:start position:0%
+mutations and it goes to uh s uh for um
+ 
+
+ align:start position:0%
+mutations and it goes to uh s uh for um
+for moderately beneficial mutations okay
+
+ align:start position:0%
+for moderately beneficial mutations okay
+ 
+
+ align:start position:0%
+for moderately beneficial mutations okay
+for um so s is defined as R minus one
+
+ align:start position:0%
+for um so s is defined as R minus one
+ 
+
+ align:start position:0%
+for um so s is defined as R minus one
+okay so this it's this for S kind of
+
+ align:start position:0%
+okay so this it's this for S kind of
+ 
+
+ align:start position:0%
+okay so this it's this for S kind of
+greater than zero but for uh and for S *
+
+ align:start position:0%
+greater than zero but for uh and for S *
+ 
+
+ align:start position:0%
+greater than zero but for uh and for S *
+n uh much larger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay so I guess this already says that s
+
+ align:start position:0%
+okay so I guess this already says that s
+ 
+
+ align:start position:0%
+okay so I guess this already says that s
+is greater than zero so we could ignore
+
+ align:start position:0%
+is greater than zero so we could ignore
+ 
+
+ align:start position:0%
+is greater than zero so we could ignore
+that okay are there any questions about
+
+ align:start position:0%
+that okay are there any questions about
+ 
+
+ align:start position:0%
+that okay are there any questions about
+uh about this before we get going
+
+ align:start position:0%
+uh about this before we get going
+ 
+
+ align:start position:0%
+uh about this before we get going
+to practice using
+
+ align:start position:0%
+to practice using
+ 
+
+ align:start position:0%
+to practice using
+it all right so I just wanted to have us
+
+ align:start position:0%
+it all right so I just wanted to have us
+ 
+
+ align:start position:0%
+it all right so I just wanted to have us
+consider a few two possible
+
+ align:start position:0%
+consider a few two possible
+ 
+
+ align:start position:0%
+consider a few two possible
+situations
+
+ align:start position:0%
+situations
+ 
+
+ align:start position:0%
+situations
+right all right population size 10 what
+
+ align:start position:0%
+right all right population size 10 what
+ 
+
+ align:start position:0%
+right all right population size 10 what
+we want to do is consider a situation
+
+ align:start position:0%
+we want to do is consider a situation
+ 
+
+ align:start position:0%
+we want to do is consider a situation
+where there are uh two
+
+ align:start position:0%
+where there are uh two
+ 
+
+ align:start position:0%
+where there are uh two
+mutants
+
+ align:start position:0%
+mutants
+ 
+
+ align:start position:0%
+mutants
+uh and we're going to call them A and B
+
+ align:start position:0%
+uh and we're going to call them A and B
+ 
+
+ align:start position:0%
+uh and we're going to call them A and B
+all right with uh relative Fitness R A
+
+ align:start position:0%
+all right with uh relative Fitness R A
+ 
+
+ align:start position:0%
+all right with uh relative Fitness R A
+1.01 and
+
+ align:start position:0%
+1.01 and
+ 
+
+ align:start position:0%
+1.01 and
+RB
+
+ align:start position:0%
+RB
+ 
+
+ align:start position:0%
+RB
+099 so a is a beneficial mutant and B is
+
+ align:start position:0%
+099 so a is a beneficial mutant and B is
+ 
+
+ align:start position:0%
+099 so a is a beneficial mutant and B is
+a delerious mutant right uh and in all
+
+ align:start position:0%
+a delerious mutant right uh and in all
+ 
+
+ align:start position:0%
+a delerious mutant right uh and in all
+these problems we're going to assume
+
+ align:start position:0%
+these problems we're going to assume
+ 
+
+ align:start position:0%
+these problems we're going to assume
+that the rest of the population has uh
+
+ align:start position:0%
+that the rest of the population has uh
+ 
+
+ align:start position:0%
+that the rest of the population has uh
+has Fitness one right so these fitnesses
+
+ align:start position:0%
+has Fitness one right so these fitnesses
+ 
+
+ align:start position:0%
+has Fitness one right so these fitnesses
+of A and B they're uh as compared to the
+
+ align:start position:0%
+of A and B they're uh as compared to the
+ 
+
+ align:start position:0%
+of A and B they're uh as compared to the
+rest of population so in this case there
+
+ align:start position:0%
+rest of population so in this case there
+ 
+
+ align:start position:0%
+rest of population so in this case there
+are eight other individuals with
+
+ align:start position:0%
+are eight other individuals with
+ 
+
+ align:start position:0%
+are eight other individuals with
+relative Fitness
+
+ align:start position:0%
+relative Fitness
+ 
+
+ align:start position:0%
+relative Fitness
+one and so uh the question is what is
+
+ align:start position:0%
+one and so uh the question is what is
+ 
+
+ align:start position:0%
+one and so uh the question is what is
+the probability that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixes all right takes over the
+
+ align:start position:0%
+fixes all right takes over the
+ 
+
+ align:start position:0%
+fixes all right takes over the
+population reaches uh
+
+ align:start position:0%
+population reaches uh
+ 
+
+ align:start position:0%
+population reaches uh
+number of a individuals equal to 10
+
+ align:start position:0%
+number of a individuals equal to 10
+ 
+
+ align:start position:0%
+number of a individuals equal to 10
+right at that stage we're not allowing
+
+ align:start position:0%
+right at that stage we're not allowing
+ 
+
+ align:start position:0%
+right at that stage we're not allowing
+for any new mutations here so then
+
+ align:start position:0%
+for any new mutations here so then
+ 
+
+ align:start position:0%
+for any new mutations here so then
+that's the end of the Dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you can start thinking about it
+
+ align:start position:0%
+yeah so you can start thinking about it
+ 
+
+ align:start position:0%
+yeah so you can start thinking about it
+and I will give some options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this is in the Moran model
+
+ align:start position:0%
+all right so this is in the Moran model
+ 
+
+ align:start position:0%
+all right so this is in the Moran model
+what is the probability that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixes I'll give you 20 seconds to think
+
+ align:start position:0%
+fixes I'll give you 20 seconds to think
+ 
+
+ align:start position:0%
+fixes I'll give you 20 seconds to think
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+all right do you need more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time all right let's go ahead and P and
+
+ align:start position:0%
+time all right let's go ahead and P and
+ 
+
+ align:start position:0%
+time all right let's go ahead and P and
+see where we are ready 3 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+all right we got some uh I'd say B's C's
+
+ align:start position:0%
+all right we got some uh I'd say B's C's
+ 
+
+ align:start position:0%
+all right we got some uh I'd say B's C's
+is kind of the dominant all right so
+
+ align:start position:0%
+is kind of the dominant all right so
+ 
+
+ align:start position:0%
+is kind of the dominant all right so
+there there's there's generally a
+
+ align:start position:0%
+there there's there's generally a
+ 
+
+ align:start position:0%
+there there's there's generally a
+disagreement uh between B and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C interesting okay uh yeah I think that
+
+ align:start position:0%
+C interesting okay uh yeah I think that
+ 
+
+ align:start position:0%
+C interesting okay uh yeah I think that
+there's I mean it's almost 50/50 uh it
+
+ align:start position:0%
+there's I mean it's almost 50/50 uh it
+ 
+
+ align:start position:0%
+there's I mean it's almost 50/50 uh it
+is a bit splotchy somehow you may need
+
+ align:start position:0%
+is a bit splotchy somehow you may need
+ 
+
+ align:start position:0%
+is a bit splotchy somehow you may need
+to uh make some effort to find something
+
+ align:start position:0%
+to uh make some effort to find something
+ 
+
+ align:start position:0%
+to uh make some effort to find something
+that disagrees with you but please do so
+
+ align:start position:0%
+that disagrees with you but please do so
+ 
+
+ align:start position:0%
+that disagrees with you but please do so
+all right turn to a neighbor and try to
+
+ align:start position:0%
+all right turn to a neighbor and try to
+ 
+
+ align:start position:0%
+all right turn to a neighbor and try to
+convince them that you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 something else yeah so yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's let's go ahead and Recon and see
+
+ align:start position:0%
+let's let's go ahead and Recon and see
+ 
+
+ align:start position:0%
+let's let's go ahead and Recon and see
+if uh see if
+
+ align:start position:0%
+if uh see if
+ 
+
+ align:start position:0%
+if uh see if
+anybody ready three two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right okay so I'd say that
+
+ align:start position:0%
+one all right okay so I'd say that
+ 
+
+ align:start position:0%
+one all right okay so I'd say that
+there's some migration towards C but
+
+ align:start position:0%
+there's some migration towards C but
+ 
+
+ align:start position:0%
+there's some migration towards C but
+it's not U not not all the way okay can
+
+ align:start position:0%
+it's not U not not all the way okay can
+ 
+
+ align:start position:0%
+it's not U not not all the way okay can
+um all right different uh different
+
+ align:start position:0%
+um all right different uh different
+ 
+
+ align:start position:0%
+um all right different uh different
+arguments and uh you you may want to D
+
+ align:start position:0%
+arguments and uh you you may want to D
+ 
+
+ align:start position:0%
+arguments and uh you you may want to D
+is the is the argument being made over
+
+ align:start position:0%
+is the is the argument being made over
+ 
+
+ align:start position:0%
+is the is the argument being made over
+here D so if there's one individual from
+
+ align:start position:0%
+here D so if there's one individual from
+ 
+
+ align:start position:0%
+here D so if there's one individual from
+a and one individual from B and
+
+ align:start position:0%
+a and one individual from B and
+ 
+
+ align:start position:0%
+a and one individual from B and
+basically the they're about the same
+
+ align:start position:0%
+basically the they're about the same
+ 
+
+ align:start position:0%
+basically the they're about the same
+Fitness then the probability that they
+
+ align:start position:0%
+Fitness then the probability that they
+ 
+
+ align:start position:0%
+Fitness then the probability that they
+should I guess take over is 50% that
+
+ align:start position:0%
+should I guess take over is 50% that
+ 
+
+ align:start position:0%
+should I guess take over is 50% that
+assumes that one of them will take over
+
+ align:start position:0%
+assumes that one of them will take over
+ 
+
+ align:start position:0%
+assumes that one of them will take over
+yeah is there any reason to assume that
+
+ align:start position:0%
+yeah is there any reason to assume that
+ 
+
+ align:start position:0%
+yeah is there any reason to assume that
+one of them should take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over I think that uh we may agree that
+
+ align:start position:0%
+over I think that uh we may agree that
+ 
+
+ align:start position:0%
+over I think that uh we may agree that
+the probability that a fixes is going to
+
+ align:start position:0%
+the probability that a fixes is going to
+ 
+
+ align:start position:0%
+the probability that a fixes is going to
+be approximately equal to the
+
+ align:start position:0%
+be approximately equal to the
+ 
+
+ align:start position:0%
+be approximately equal to the
+probability that b fixes that's going to
+
+ align:start position:0%
+probability that b fixes that's going to
+ 
+
+ align:start position:0%
+probability that b fixes that's going to
+be a useful Insight but but it may be
+
+ align:start position:0%
+be a useful Insight but but it may be
+ 
+
+ align:start position:0%
+be a useful Insight but but it may be
+that both F exct right so we have to
+
+ align:start position:0%
+that both F exct right so we have to
+ 
+
+ align:start position:0%
+that both F exct right so we have to
+keep track of that so that's the
+
+ align:start position:0%
+keep track of that so that's the
+ 
+
+ align:start position:0%
+keep track of that so that's the
+argument for why it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deep you're welcome anytime we try all
+
+ align:start position:0%
+deep you're welcome anytime we try all
+ 
+
+ align:start position:0%
+deep you're welcome anytime we try all
+right yeah so between B and C where uh
+
+ align:start position:0%
+right yeah so between B and C where uh
+ 
+
+ align:start position:0%
+right yeah so between B and C where uh
+how to how can we think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this you can tell once again what your
+
+ align:start position:0%
+this you can tell once again what your
+ 
+
+ align:start position:0%
+this you can tell once again what your
+neighbor said that's fine yes um uh well
+
+ align:start position:0%
+neighbor said that's fine yes um uh well
+ 
+
+ align:start position:0%
+neighbor said that's fine yes um uh well
+my neigh as opposed to me made the made
+
+ align:start position:0%
+my neigh as opposed to me made the made
+ 
+
+ align:start position:0%
+my neigh as opposed to me made the made
+the um decision to try to think about it
+
+ align:start position:0%
+the um decision to try to think about it
+ 
+
+ align:start position:0%
+the um decision to try to think about it
+intuitively instead of trying to get
+
+ align:start position:0%
+intuitively instead of trying to get
+ 
+
+ align:start position:0%
+intuitively instead of trying to get
+through all the math yes always good to
+
+ align:start position:0%
+through all the math yes always good to
+ 
+
+ align:start position:0%
+through all the math yes always good to
+think about things intuitively rather
+
+ align:start position:0%
+think about things intuitively rather
+ 
+
+ align:start position:0%
+think about things intuitively rather
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+that's so a is very slightly beneficial
+
+ align:start position:0%
+that's so a is very slightly beneficial
+ 
+
+ align:start position:0%
+that's so a is very slightly beneficial
+and so it it's just a little bit uh more
+
+ align:start position:0%
+and so it it's just a little bit uh more
+ 
+
+ align:start position:0%
+and so it it's just a little bit uh more
+likely to fix than a neutral commutation
+
+ align:start position:0%
+likely to fix than a neutral commutation
+ 
+
+ align:start position:0%
+likely to fix than a neutral commutation
+okay and how can we quantify this
+
+ align:start position:0%
+okay and how can we quantify this
+ 
+
+ align:start position:0%
+okay and how can we quantify this
+statement right that that I know I said
+
+ align:start position:0%
+statement right that that I know I said
+ 
+
+ align:start position:0%
+statement right that that I know I said
+that I didn't like math but you know
+
+ align:start position:0%
+that I didn't like math but you know
+ 
+
+ align:start position:0%
+that I didn't like math but you know
+every now and then we should look at it
+
+ align:start position:0%
+every now and then we should look at it
+ 
+
+ align:start position:0%
+every now and then we should look at it
+all right so yeah so the statement that
+
+ align:start position:0%
+all right so yeah so the statement that
+ 
+
+ align:start position:0%
+all right so yeah so the statement that
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+approximately a neutral mutation how how
+
+ align:start position:0%
+approximately a neutral mutation how how
+ 
+
+ align:start position:0%
+approximately a neutral mutation how how
+is it that we can how do we know that I
+
+ align:start position:0%
+is it that we can how do we know that I
+ 
+
+ align:start position:0%
+is it that we can how do we know that I
+mean did we have a criteria for nearly
+
+ align:start position:0%
+mean did we have a criteria for nearly
+ 
+
+ align:start position:0%
+mean did we have a criteria for nearly
+neutral yes we have a criteria for
+
+ align:start position:0%
+neutral yes we have a criteria for
+ 
+
+ align:start position:0%
+neutral yes we have a criteria for
+nearly neutral right what what is that
+
+ align:start position:0%
+nearly neutral right what what is that
+ 
+
+ align:start position:0%
+nearly neutral right what what is that
+what does it mean to be nearly neutral
+
+ align:start position:0%
+what does it mean to be nearly neutral
+ 
+
+ align:start position:0%
+what does it mean to be nearly neutral
+uh the magnitude of s n is that's right
+
+ align:start position:0%
+uh the magnitude of s n is that's right
+ 
+
+ align:start position:0%
+uh the magnitude of s n is that's right
+s * n is much less than one means that
+
+ align:start position:0%
+s * n is much less than one means that
+ 
+
+ align:start position:0%
+s * n is much less than one means that
+it's nearly neutral and what that means
+
+ align:start position:0%
+it's nearly neutral and what that means
+ 
+
+ align:start position:0%
+it's nearly neutral and what that means
+is that the probability of fixing is the
+
+ align:start position:0%
+is that the probability of fixing is the
+ 
+
+ align:start position:0%
+is that the probability of fixing is the
+same as if it were a neutral
+
+ align:start position:0%
+same as if it were a neutral
+ 
+
+ align:start position:0%
+same as if it were a neutral
+mutation or approximately same and is
+
+ align:start position:0%
+mutation or approximately same and is
+ 
+
+ align:start position:0%
+mutation or approximately same and is
+that is that the case here yes yes s is
+
+ align:start position:0%
+that is that the case here yes yes s is
+ 
+
+ align:start position:0%
+that is that the case here yes yes s is
+0.01 so 1 100 and is 10 so s * n is
+
+ align:start position:0%
+0.01 so 1 100 and is 10 so s * n is
+ 
+
+ align:start position:0%
+0.01 so 1 100 and is 10 so s * n is
+equal to 0.1
+
+ align:start position:0%
+equal to 0.1
+ 
+
+ align:start position:0%
+equal to 0.1
+right which means that both you know so
+
+ align:start position:0%
+right which means that both you know so
+ 
+
+ align:start position:0%
+right which means that both you know so
+a is maybe nearly neutral is B nearly
+
+ align:start position:0%
+a is maybe nearly neutral is B nearly
+ 
+
+ align:start position:0%
+a is maybe nearly neutral is B nearly
+neutral yes yes so both A and B are
+
+ align:start position:0%
+neutral yes yes so both A and B are
+ 
+
+ align:start position:0%
+neutral yes yes so both A and B are
+nearly neutral right one of them is an
+
+ align:start position:0%
+nearly neutral right one of them is an
+ 
+
+ align:start position:0%
+nearly neutral right one of them is an
+advantageous M one's aerious but in this
+
+ align:start position:0%
+advantageous M one's aerious but in this
+ 
+
+ align:start position:0%
+advantageous M one's aerious but in this
+population size they both behave as if
+
+ align:start position:0%
+population size they both behave as if
+ 
+
+ align:start position:0%
+population size they both behave as if
+they're nearly neutral right but in a
+
+ align:start position:0%
+they're nearly neutral right but in a
+ 
+
+ align:start position:0%
+they're nearly neutral right but in a
+larger population right so if we had a
+
+ align:start position:0%
+larger population right so if we had a
+ 
+
+ align:start position:0%
+larger population right so if we had a
+million individuals would these be
+
+ align:start position:0%
+million individuals would these be
+ 
+
+ align:start position:0%
+million individuals would these be
+neutral
+
+ align:start position:0%
+neutral
+ 
+
+ align:start position:0%
+neutral
+mutations no okay right so the question
+
+ align:start position:0%
+mutations no okay right so the question
+ 
+
+ align:start position:0%
+mutations no okay right so the question
+of whether something behaves as a
+
+ align:start position:0%
+of whether something behaves as a
+ 
+
+ align:start position:0%
+of whether something behaves as a
+neutral mutation depends upon the
+
+ align:start position:0%
+neutral mutation depends upon the
+ 
+
+ align:start position:0%
+neutral mutation depends upon the
+population size via this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation all right so then okay so
+
+ align:start position:0%
+relation all right so then okay so
+ 
+
+ align:start position:0%
+relation all right so then okay so
+that's that's and then and then how do
+
+ align:start position:0%
+that's that's and then and then how do
+ 
+
+ align:start position:0%
+that's that's and then and then how do
+we go from there well the the um the
+
+ align:start position:0%
+we go from there well the the um the
+ 
+
+ align:start position:0%
+we go from there well the the um the
+probability of a neutral mutation
+
+ align:start position:0%
+probability of a neutral mutation
+ 
+
+ align:start position:0%
+probability of a neutral mutation
+population that's right a neutral
+
+ align:start position:0%
+population that's right a neutral
+ 
+
+ align:start position:0%
+population that's right a neutral
+mutation will fix probability of one 10
+
+ align:start position:0%
+mutation will fix probability of one 10
+ 
+
+ align:start position:0%
+mutation will fix probability of one 10
+right so indeed we're going to get this
+
+ align:start position:0%
+right so indeed we're going to get this
+ 
+
+ align:start position:0%
+right so indeed we're going to get this
+and and and you know and we need to
+
+ align:start position:0%
+and and and you know and we need to
+ 
+
+ align:start position:0%
+and and and you know and we need to
+highlight that we can you have to be
+
+ align:start position:0%
+highlight that we can you have to be
+ 
+
+ align:start position:0%
+highlight that we can you have to be
+very careful about just sticking things
+
+ align:start position:0%
+very careful about just sticking things
+ 
+
+ align:start position:0%
+very careful about just sticking things
+into formulas right so even though you
+
+ align:start position:0%
+into formulas right so even though you
+ 
+
+ align:start position:0%
+into formulas right so even though you
+know you may remember that the
+
+ align:start position:0%
+know you may remember that the
+ 
+
+ align:start position:0%
+know you may remember that the
+probability of a beneficial mutant
+
+ align:start position:0%
+probability of a beneficial mutant
+ 
+
+ align:start position:0%
+probability of a beneficial mutant
+fixing um in a population is is s but
+
+ align:start position:0%
+fixing um in a population is is s but
+ 
+
+ align:start position:0%
+fixing um in a population is is s but
+that's only for S * n being much larger
+
+ align:start position:0%
+that's only for S * n being much larger
+ 
+
+ align:start position:0%
+that's only for S * n being much larger
+than one and that's only when there's no
+
+ align:start position:0%
+than one and that's only when there's no
+ 
+
+ align:start position:0%
+than one and that's only when there's no
+clonal interference when there when
+
+ align:start position:0%
+clonal interference when there when
+ 
+
+ align:start position:0%
+clonal interference when there when
+you're when you don't have to compete
+
+ align:start position:0%
+you're when you don't have to compete
+ 
+
+ align:start position:0%
+you're when you don't have to compete
+with other beneficial mutants in the
+
+ align:start position:0%
+with other beneficial mutants in the
+ 
+
+ align:start position:0%
+with other beneficial mutants in the
+lineage right we're going to see an
+
+ align:start position:0%
+lineage right we're going to see an
+ 
+
+ align:start position:0%
+lineage right we're going to see an
+example of this in a moment okay but if
+
+ align:start position:0%
+example of this in a moment okay but if
+ 
+
+ align:start position:0%
+example of this in a moment okay but if
+you just have a single mutant in the
+
+ align:start position:0%
+you just have a single mutant in the
+ 
+
+ align:start position:0%
+you just have a single mutant in the
+population that's beneficial in the
+
+ align:start position:0%
+population that's beneficial in the
+ 
+
+ align:start position:0%
+population that's beneficial in the
+sense of it's not it's not neutral right
+
+ align:start position:0%
+sense of it's not it's not neutral right
+ 
+
+ align:start position:0%
+sense of it's not it's not neutral right
+then probably a fixation is s you know
+
+ align:start position:0%
+then probably a fixation is s you know
+ 
+
+ align:start position:0%
+then probably a fixation is s you know
+and of course this this is nonsensical
+
+ align:start position:0%
+and of course this this is nonsensical
+ 
+
+ align:start position:0%
+and of course this this is nonsensical
+right because you can't I it wouldn't
+
+ align:start position:0%
+right because you can't I it wouldn't
+ 
+
+ align:start position:0%
+right because you can't I it wouldn't
+make any it would certainly it would you
+
+ align:start position:0%
+make any it would certainly it would you
+ 
+
+ align:start position:0%
+make any it would certainly it would you
+know given that you say oh well if it
+
+ align:start position:0%
+know given that you say oh well if it
+ 
+
+ align:start position:0%
+know given that you say oh well if it
+were neutral it would fix with a
+
+ align:start position:0%
+were neutral it would fix with a
+ 
+
+ align:start position:0%
+were neutral it would fix with a
+probability of 10% and then you say oh
+
+ align:start position:0%
+probability of 10% and then you say oh
+ 
+
+ align:start position:0%
+probability of 10% and then you say oh
+but if it's advantageous mutant you know
+
+ align:start position:0%
+but if it's advantageous mutant you know
+ 
+
+ align:start position:0%
+but if it's advantageous mutant you know
+it can't fix with a probability less
+
+ align:start position:0%
+it can't fix with a probability less
+ 
+
+ align:start position:0%
+it can't fix with a probability less
+than that
+
+ align:start position:0%
+than that
+ 
+
+ align:start position:0%
+than that
+right so so this is NE neutral fixation
+
+ align:start position:0%
+right so so this is NE neutral fixation
+ 
+
+ align:start position:0%
+right so so this is NE neutral fixation
+probability is 10% are there any
+
+ align:start position:0%
+probability is 10% are there any
+ 
+
+ align:start position:0%
+probability is 10% are there any
+questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argument all right so let's consider a
+
+ align:start position:0%
+argument all right so let's consider a
+ 
+
+ align:start position:0%
+argument all right so let's consider a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+problem all right all right so now we're
+
+ align:start position:0%
+problem all right all right so now we're
+ 
+
+ align:start position:0%
+problem all right all right so now we're
+going to consider a
+
+ align:start position:0%
+going to consider a
+ 
+
+ align:start position:0%
+going to consider a
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+larger so it's going to be the same
+
+ align:start position:0%
+larger so it's going to be the same
+ 
+
+ align:start position:0%
+larger so it's going to be the same
+situation where we have these two
+
+ align:start position:0%
+situation where we have these two
+ 
+
+ align:start position:0%
+situation where we have these two
+mutants present uh as as single single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+individuals so what we want to know now
+
+ align:start position:0%
+individuals so what we want to know now
+ 
+
+ align:start position:0%
+individuals so what we want to know now
+is the probability that b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixes once again you should start
+
+ align:start position:0%
+fixes once again you should start
+ 
+
+ align:start position:0%
+fixes once again you should start
+thinking about this while I type
+
+ align:start position:0%
+thinking about this while I type
+ 
+
+ align:start position:0%
+thinking about this while I type
+in okay oh but there was one other thing
+
+ align:start position:0%
+in okay oh but there was one other thing
+ 
+
+ align:start position:0%
+in okay oh but there was one other thing
+I wanted to say actually over here um if
+
+ align:start position:0%
+I wanted to say actually over here um if
+ 
+
+ align:start position:0%
+I wanted to say actually over here um if
+we modeled this these population
+
+ align:start position:0%
+we modeled this these population
+ 
+
+ align:start position:0%
+we modeled this these population
+Dynamics using differential
+
+ align:start position:0%
+Dynamics using differential
+ 
+
+ align:start position:0%
+Dynamics using differential
+equations right so instead of doing the
+
+ align:start position:0%
+equations right so instead of doing the
+ 
+
+ align:start position:0%
+equations right so instead of doing the
+Moran process where we have stochastic
+
+ align:start position:0%
+Moran process where we have stochastic
+ 
+
+ align:start position:0%
+Moran process where we have stochastic
+dynamics of of division replacement and
+
+ align:start position:0%
+dynamics of of division replacement and
+ 
+
+ align:start position:0%
+dynamics of of division replacement and
+so forth if you write down a
+
+ align:start position:0%
+so forth if you write down a
+ 
+
+ align:start position:0%
+so forth if you write down a
+differential equation describing this
+
+ align:start position:0%
+differential equation describing this
+ 
+
+ align:start position:0%
+differential equation describing this
+situation okay what is the probability
+
+ align:start position:0%
+situation okay what is the probability
+ 
+
+ align:start position:0%
+situation okay what is the probability
+that a fixes I'm going to give you five
+
+ align:start position:0%
+that a fixes I'm going to give you five
+ 
+
+ align:start position:0%
+that a fixes I'm going to give you five
+seconds one all right one
+
+ align:start position:0%
+seconds one all right one
+ 
+
+ align:start position:0%
+seconds one all right one
+okay okay so you don't get to vote
+
+ align:start position:0%
+okay okay so you don't get to vote
+ 
+
+ align:start position:0%
+okay okay so you don't get to vote
+indeed one
+
+ align:start position:0%
+indeed one
+ 
+
+ align:start position:0%
+indeed one
+okay right so if you had written down
+
+ align:start position:0%
+okay right so if you had written down
+ 
+
+ align:start position:0%
+okay right so if you had written down
+differential equation then there's no
+
+ align:start position:0%
+differential equation then there's no
+ 
+
+ align:start position:0%
+differential equation then there's no
+Randomness there whichever mutant has
+
+ align:start position:0%
+Randomness there whichever mutant has
+ 
+
+ align:start position:0%
+Randomness there whichever mutant has
+the largest Fitness will fix probability
+
+ align:start position:0%
+the largest Fitness will fix probability
+ 
+
+ align:start position:0%
+the largest Fitness will fix probability
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay probability D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this you show me both
+
+ align:start position:0%
+so this you show me both
+ 
+
+ align:start position:0%
+so this you show me both
+cards yeah I'll give you uh I'll give
+
+ align:start position:0%
+cards yeah I'll give you uh I'll give
+ 
+
+ align:start position:0%
+cards yeah I'll give you uh I'll give
+you 20 30 seconds to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take yes is there just one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes all right so this is kind that's why
+
+ align:start position:0%
+yes all right so this is kind that's why
+ 
+
+ align:start position:0%
+yes all right so this is kind that's why
+yeah so it's just the same thing so
+
+ align:start position:0%
+yeah so it's just the same thing so
+ 
+
+ align:start position:0%
+yeah so it's just the same thing so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+a yeah a single a mutant and a single B
+
+ align:start position:0%
+a yeah a single a mutant and a single B
+ 
+
+ align:start position:0%
+a yeah a single a mutant and a single B
+mutant yeah single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a single B but you should know how to
+
+ align:start position:0%
+a single B but you should know how to
+ 
+
+ align:start position:0%
+a single B but you should know how to
+calculate these things if I tell you
+
+ align:start position:0%
+calculate these things if I tell you
+ 
+
+ align:start position:0%
+calculate these things if I tell you
+that they were other some other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right do you need more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so in general if you don't look at
+
+ align:start position:0%
+time so in general if you don't look at
+ 
+
+ align:start position:0%
+time so in general if you don't look at
+me when I ask that question I'm going to
+
+ align:start position:0%
+me when I ask that question I'm going to
+ 
+
+ align:start position:0%
+me when I ask that question I'm going to
+take that as meaning that you're still
+
+ align:start position:0%
+take that as meaning that you're still
+ 
+
+ align:start position:0%
+take that as meaning that you're still
+thinking about it is that is that is
+
+ align:start position:0%
+thinking about it is that is that is
+ 
+
+ align:start position:0%
+thinking about it is that is that is
+that how I should interpret that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go ahead and vote just so that we
+
+ align:start position:0%
+let's go ahead and vote just so that we
+ 
+
+ align:start position:0%
+let's go ahead and vote just so that we
+can uh see where we are okay ready three
+
+ align:start position:0%
+can uh see where we are okay ready three
+ 
+
+ align:start position:0%
+can uh see where we are okay ready three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one oh right uh okay yeah we're we're
+
+ align:start position:0%
+one oh right uh okay yeah we're we're
+ 
+
+ align:start position:0%
+one oh right uh okay yeah we're we're
+all over the place that's great um
+
+ align:start position:0%
+all over the place that's great um
+ 
+
+ align:start position:0%
+all over the place that's great um
+because that that's that's that means
+
+ align:start position:0%
+because that that's that's that means
+ 
+
+ align:start position:0%
+because that that's that's that means
+your neighbor will either be able to
+
+ align:start position:0%
+your neighbor will either be able to
+ 
+
+ align:start position:0%
+your neighbor will either be able to
+help you or confuse you or do something
+
+ align:start position:0%
+help you or confuse you or do something
+ 
+
+ align:start position:0%
+help you or confuse you or do something
+all right so let's um let's go ahead all
+
+ align:start position:0%
+all right so let's um let's go ahead all
+ 
+
+ align:start position:0%
+all right so let's um let's go ahead all
+right so right there's a million yeah
+
+ align:start position:0%
+right so right there's a million yeah
+ 
+
+ align:start position:0%
+right so right there's a million yeah
+population size a million we have two
+
+ align:start position:0%
+population size a million we have two
+ 
+
+ align:start position:0%
+population size a million we have two
+mutants in the population one has
+
+ align:start position:0%
+mutants in the population one has
+ 
+
+ align:start position:0%
+mutants in the population one has
+relative Fitness to one has relative
+
+ align:start position:0%
+relative Fitness to one has relative
+ 
+
+ align:start position:0%
+relative Fitness to one has relative
+Fitness of um an advantage of of um
+
+ align:start position:0%
+Fitness of um an advantage of of um
+ 
+
+ align:start position:0%
+Fitness of um an advantage of of um
+1% okay uh one thing to be careful of
+
+ align:start position:0%
+1% okay uh one thing to be careful of
+ 
+
+ align:start position:0%
+1% okay uh one thing to be careful of
+here is uh
+
+ align:start position:0%
+here is uh
+ 
+
+ align:start position:0%
+here is uh
+the equation that we have for uh
+
+ align:start position:0%
+the equation that we have for uh
+ 
+
+ align:start position:0%
+the equation that we have for uh
+probability of fixation fixation
+
+ align:start position:0%
+probability of fixation fixation
+ 
+
+ align:start position:0%
+probability of fixation fixation
+here ah there's there's one more thing
+
+ align:start position:0%
+here ah there's there's one more thing
+ 
+
+ align:start position:0%
+here ah there's there's one more thing
+that I should say it's for um s well
+
+ align:start position:0%
+that I should say it's for um s well
+ 
+
+ align:start position:0%
+that I should say it's for um s well
+it's an S much less than
+
+ align:start position:0%
+it's an S much less than
+ 
+
+ align:start position:0%
+it's an S much less than
+one okay just
+
+ align:start position:0%
+one okay just
+ 
+
+ align:start position:0%
+one okay just
+for right so this is for a moderately
+
+ align:start position:0%
+for right so this is for a moderately
+ 
+
+ align:start position:0%
+for right so this is for a moderately
+beneficial mutation otherwise you have
+
+ align:start position:0%
+beneficial mutation otherwise you have
+ 
+
+ align:start position:0%
+beneficial mutation otherwise you have
+to use the full
+
+ align:start position:0%
+to use the full
+ 
+
+ align:start position:0%
+to use the full
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+yes all right go ahead and turn to your
+
+ align:start position:0%
+yes all right go ahead and turn to your
+ 
+
+ align:start position:0%
+yes all right go ahead and turn to your
+neighbor and uh try to convince them
+
+ align:start position:0%
+neighbor and uh try to convince them
+ 
+
+ align:start position:0%
+neighbor and uh try to convince them
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+go RB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so everybody should be talking to
+
+ align:start position:0%
+so everybody should be talking to
+ 
+
+ align:start position:0%
+so everybody should be talking to
+somebody what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think um well it's okay to not know but
+
+ align:start position:0%
+think um well it's okay to not know but
+ 
+
+ align:start position:0%
+think um well it's okay to not know but
+that's why you uh that's why you you can
+
+ align:start position:0%
+that's why you uh that's why you you can
+ 
+
+ align:start position:0%
+that's why you uh that's why you you can
+you uh you should either join them or um
+
+ align:start position:0%
+you uh you should either join them or um
+ 
+
+ align:start position:0%
+you uh you should either join them or um
+you know or if you look behind you
+
+ align:start position:0%
+you know or if you look behind you
+ 
+
+ align:start position:0%
+you know or if you look behind you
+there's someone else that looks very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh all right why don't let's okay let's
+
+ align:start position:0%
+uh all right why don't let's okay let's
+ 
+
+ align:start position:0%
+uh all right why don't let's okay let's
+what that my reasons are always that's
+
+ align:start position:0%
+what that my reasons are always that's
+ 
+
+ align:start position:0%
+what that my reasons are always that's
+always good reasons you it'll be they'll
+
+ align:start position:0%
+always good reasons you it'll be they'll
+ 
+
+ align:start position:0%
+always good reasons you it'll be they'll
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+educational all right let uh let's let's
+
+ align:start position:0%
+educational all right let uh let's let's
+ 
+
+ align:start position:0%
+educational all right let uh let's let's
+go ahead and reconvene okay I know that
+
+ align:start position:0%
+go ahead and reconvene okay I know that
+ 
+
+ align:start position:0%
+go ahead and reconvene okay I know that
+there there were a lot of different uh
+
+ align:start position:0%
+there there were a lot of different uh
+ 
+
+ align:start position:0%
+there there were a lot of different uh
+different guesses on this problem which
+
+ align:start position:0%
+different guesses on this problem which
+ 
+
+ align:start position:0%
+different guesses on this problem which
+means that it may be that the
+
+ align:start position:0%
+means that it may be that the
+ 
+
+ align:start position:0%
+means that it may be that the
+conversations were uh were scattered or
+
+ align:start position:0%
+conversations were uh were scattered or
+ 
+
+ align:start position:0%
+conversations were uh were scattered or
+difficult or it was difficult to uh
+
+ align:start position:0%
+difficult or it was difficult to uh
+ 
+
+ align:start position:0%
+difficult or it was difficult to uh
+converge but I I still let's see let's
+
+ align:start position:0%
+converge but I I still let's see let's
+ 
+
+ align:start position:0%
+converge but I I still let's see let's
+see if uh it made any difference ready
+
+ align:start position:0%
+see if uh it made any difference ready
+ 
+
+ align:start position:0%
+see if uh it made any difference ready
+three two
+
+ align:start position:0%
+three two
+ 
+
+ align:start position:0%
+three two
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+all right yeah so I'd say that the the
+
+ align:start position:0%
+all right yeah so I'd say that the the
+ 
+
+ align:start position:0%
+all right yeah so I'd say that the the
+conversations have helped uh but we but
+
+ align:start position:0%
+conversations have helped uh but we but
+ 
+
+ align:start position:0%
+conversations have helped uh but we but
+we're still you know a fair distribution
+
+ align:start position:0%
+we're still you know a fair distribution
+ 
+
+ align:start position:0%
+we're still you know a fair distribution
+between maybe a c and d still okay um
+
+ align:start position:0%
+between maybe a c and d still okay um
+ 
+
+ align:start position:0%
+between maybe a c and d still okay um
+but uh yeah somebody want to give an
+
+ align:start position:0%
+but uh yeah somebody want to give an
+ 
+
+ align:start position:0%
+but uh yeah somebody want to give an
+explanation for one of those three or
+
+ align:start position:0%
+explanation for one of those three or
+ 
+
+ align:start position:0%
+explanation for one of those three or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+John right
+
+ align:start position:0%
+John right
+ 
+
+ align:start position:0%
+John right
+perfect okay I just want to make sure
+
+ align:start position:0%
+perfect okay I just want to make sure
+ 
+
+ align:start position:0%
+perfect okay I just want to make sure
+that we all agree on this logic all
+
+ align:start position:0%
+that we all agree on this logic all
+ 
+
+ align:start position:0%
+that we all agree on this logic all
+right so if the only thing we had was
+
+ align:start position:0%
+right so if the only thing we had was
+ 
+
+ align:start position:0%
+right so if the only thing we had was
+mutation B yeah then the probability
+
+ align:start position:0%
+mutation B yeah then the probability
+ 
+
+ align:start position:0%
+mutation B yeah then the probability
+fixation would be 1% because um in that
+
+ align:start position:0%
+fixation would be 1% because um in that
+ 
+
+ align:start position:0%
+fixation would be 1% because um in that
+case is this a nearly neutral mutation
+
+ align:start position:0%
+case is this a nearly neutral mutation
+ 
+
+ align:start position:0%
+case is this a nearly neutral mutation
+no right so that means that uh it's
+
+ align:start position:0%
+no right so that means that uh it's
+ 
+
+ align:start position:0%
+no right so that means that uh it's
+probability of fixation is going to be
+
+ align:start position:0%
+probability of fixation is going to be
+ 
+
+ align:start position:0%
+probability of fixation is going to be
+around s in this case one uh 01 okay but
+
+ align:start position:0%
+around s in this case one uh 01 okay but
+ 
+
+ align:start position:0%
+around s in this case one uh 01 okay but
+but now a is there so you like first you
+
+ align:start position:0%
+but now a is there so you like first you
+ 
+
+ align:start position:0%
+but now a is there so you like first you
+expect you expect the
+
+ align:start position:0%
+expect you expect the
+ 
+
+ align:start position:0%
+expect you expect the
+probility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+exactly a yeah no no I mean it's uh uh
+
+ align:start position:0%
+exactly a yeah no no I mean it's uh uh
+ 
+
+ align:start position:0%
+exactly a yeah no no I mean it's uh uh
+no but that's that's that's precisely
+
+ align:start position:0%
+no but that's that's that's precisely
+ 
+
+ align:start position:0%
+no but that's that's that's precisely
+what's happening so the for B to fix it
+
+ align:start position:0%
+what's happening so the for B to fix it
+ 
+
+ align:start position:0%
+what's happening so the for B to fix it
+requires two things to happen right
+
+ align:start position:0%
+requires two things to happen right
+ 
+
+ align:start position:0%
+requires two things to happen right
+first B has to survive stochastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Extinction
+
+ align:start position:0%
+Extinction
+ 
+
+ align:start position:0%
+Extinction
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+you know and okay so we're going to
+
+ align:start position:0%
+you know and okay so we're going to
+ 
+
+ align:start position:0%
+you know and okay so we're going to
+multiply these probabilities um
+
+ align:start position:0%
+multiply these probabilities um
+ 
+
+ align:start position:0%
+multiply these probabilities um
+a doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survive we're going to discuss in a
+
+ align:start position:0%
+survive we're going to discuss in a
+ 
+
+ align:start position:0%
+survive we're going to discuss in a
+moment what this really means in terms
+
+ align:start position:0%
+moment what this really means in terms
+ 
+
+ align:start position:0%
+moment what this really means in terms
+of surviving stochast Extinction but the
+
+ align:start position:0%
+of surviving stochast Extinction but the
+ 
+
+ align:start position:0%
+of surviving stochast Extinction but the
+when a new mutation appears in the
+
+ align:start position:0%
+when a new mutation appears in the
+ 
+
+ align:start position:0%
+when a new mutation appears in the
+population it will either relatively
+
+ align:start position:0%
+population it will either relatively
+ 
+
+ align:start position:0%
+population it will either relatively
+quickly go extinct or it will relatively
+
+ align:start position:0%
+quickly go extinct or it will relatively
+ 
+
+ align:start position:0%
+quickly go extinct or it will relatively
+quickly become established that's what
+
+ align:start position:0%
+quickly become established that's what
+ 
+
+ align:start position:0%
+quickly become established that's what
+we call that what that means is that it
+
+ align:start position:0%
+we call that what that means is that it
+ 
+
+ align:start position:0%
+we call that what that means is that it
+will if it's a beneficial mutation it
+
+ align:start position:0%
+will if it's a beneficial mutation it
+ 
+
+ align:start position:0%
+will if it's a beneficial mutation it
+will take over unless it's Al by someone
+
+ align:start position:0%
+will take over unless it's Al by someone
+ 
+
+ align:start position:0%
+will take over unless it's Al by someone
+else okay so it has to be that b
+
+ align:start position:0%
+else okay so it has to be that b
+ 
+
+ align:start position:0%
+else okay so it has to be that b
+survives stochastic Extinction and a
+
+ align:start position:0%
+survives stochastic Extinction and a
+ 
+
+ align:start position:0%
+survives stochastic Extinction and a
+doesn't survive uh the this initial
+
+ align:start position:0%
+doesn't survive uh the this initial
+ 
+
+ align:start position:0%
+doesn't survive uh the this initial
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+okay right and this thing all right so
+
+ align:start position:0%
+okay right and this thing all right so
+ 
+
+ align:start position:0%
+okay right and this thing all right so
+the pro so that means that the
+
+ align:start position:0%
+the pro so that means that the
+ 
+
+ align:start position:0%
+the pro so that means that the
+probability that b fixes is going to be
+
+ align:start position:0%
+probability that b fixes is going to be
+ 
+
+ align:start position:0%
+probability that b fixes is going to be
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay the probability that b survive
+
+ align:start position:0%
+okay the probability that b survive
+ 
+
+ align:start position:0%
+okay the probability that b survive
+stochastic Extinction is going to be
+
+ align:start position:0%
+stochastic Extinction is going to be
+ 
+
+ align:start position:0%
+stochastic Extinction is going to be
+1% right the probability that a survives
+
+ align:start position:0%
+1% right the probability that a survives
+ 
+
+ align:start position:0%
+1% right the probability that a survives
+is a half so the probability that it
+
+ align:start position:0%
+is a half so the probability that it
+ 
+
+ align:start position:0%
+is a half so the probability that it
+doesn't survive is also a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now the half just to remind
+
+ align:start position:0%
+okay now the half just to remind
+ 
+
+ align:start position:0%
+okay now the half just to remind
+ourselves comes from this thing X1 for a
+
+ align:start position:0%
+ourselves comes from this thing X1 for a
+ 
+
+ align:start position:0%
+ourselves comes from this thing X1 for a
+right there's this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over okay this
+
+ align:start position:0%
+over okay this
+ 
+
+ align:start position:0%
+over okay this
+thing is
+
+ align:start position:0%
+thing is
+ 
+
+ align:start position:0%
+thing is
+what right so right so this thing very
+
+ align:start position:0%
+what right so right so this thing very
+ 
+
+ align:start position:0%
+what right so right so this thing very
+quickly goes to zero right so this is 1
+
+ align:start position:0%
+quickly goes to zero right so this is 1
+ 
+
+ align:start position:0%
+quickly goes to zero right so this is 1
+half to the millionth power okay so
+
+ align:start position:0%
+half to the millionth power okay so
+ 
+
+ align:start position:0%
+half to the millionth power okay so
+that's zero so we just get one minus a
+
+ align:start position:0%
+that's zero so we just get one minus a
+ 
+
+ align:start position:0%
+that's zero so we just get one minus a
+half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes what are we assuming it's to me
+
+ align:start position:0%
+okay yes what are we assuming it's to me
+ 
+
+ align:start position:0%
+okay yes what are we assuming it's to me
+this we're assuming they're completely
+
+ align:start position:0%
+this we're assuming they're completely
+ 
+
+ align:start position:0%
+this we're assuming they're completely
+independent can multip that's right
+
+ align:start position:0%
+independent can multip that's right
+ 
+
+ align:start position:0%
+independent can multip that's right
+together so yeah that's right uh and I
+
+ align:start position:0%
+together so yeah that's right uh and I
+ 
+
+ align:start position:0%
+together so yeah that's right uh and I
+would say that for from the standpoint
+
+ align:start position:0%
+would say that for from the standpoint
+ 
+
+ align:start position:0%
+would say that for from the standpoint
+of a population of a million these are
+
+ align:start position:0%
+of a population of a million these are
+ 
+
+ align:start position:0%
+of a population of a million these are
+totally non-interacting processes you
+
+ align:start position:0%
+totally non-interacting processes you
+ 
+
+ align:start position:0%
+totally non-interacting processes you
+know in in you know uh for all intents
+
+ align:start position:0%
+know in in you know uh for all intents
+ 
+
+ align:start position:0%
+know in in you know uh for all intents
+and purposes you know if you if you were
+
+ align:start position:0%
+and purposes you know if you if you were
+ 
+
+ align:start position:0%
+and purposes you know if you if you were
+down to a population size of 10 then you
+
+ align:start position:0%
+down to a population size of 10 then you
+ 
+
+ align:start position:0%
+down to a population size of 10 then you
+might have to worry that that um that
+
+ align:start position:0%
+might have to worry that that um that
+ 
+
+ align:start position:0%
+might have to worry that that um that
+they're going to interact more but you
+
+ align:start position:0%
+they're going to interact more but you
+ 
+
+ align:start position:0%
+they're going to interact more but you
+know in the in this process of um of you
+
+ align:start position:0%
+know in the in this process of um of you
+ 
+
+ align:start position:0%
+know in the in this process of um of you
+know this Moran process you know you
+
+ align:start position:0%
+know this Moran process you know you
+ 
+
+ align:start position:0%
+know this Moran process you know you
+have a million individuals if sure this
+
+ align:start position:0%
+have a million individuals if sure this
+ 
+
+ align:start position:0%
+have a million individuals if sure this
+is twice as likely to be chosen to
+
+ align:start position:0%
+is twice as likely to be chosen to
+ 
+
+ align:start position:0%
+is twice as likely to be chosen to
+divide as a normal cell but you're
+
+ align:start position:0%
+divide as a normal cell but you're
+ 
+
+ align:start position:0%
+divide as a normal cell but you're
+talking about a million cells in that
+
+ align:start position:0%
+talking about a million cells in that
+ 
+
+ align:start position:0%
+talking about a million cells in that
+population right so the the the
+
+ align:start position:0%
+population right so the the the
+ 
+
+ align:start position:0%
+population right so the the the
+correction to the things that you're
+
+ align:start position:0%
+correction to the things that you're
+ 
+
+ align:start position:0%
+correction to the things that you're
+worrying about is of order is a part in
+
+ align:start position:0%
+worrying about is of order is a part in
+ 
+
+ align:start position:0%
+worrying about is of order is a part in
+10 to the six so the thing the thing
+
+ align:start position:0%
+10 to the six so the thing the thing
+ 
+
+ align:start position:0%
+10 to the six so the thing the thing
+yeah um but if ra and RB were closer
+
+ align:start position:0%
+yeah um but if ra and RB were closer
+ 
+
+ align:start position:0%
+yeah um but if ra and RB were closer
+actually that correction no it's not
+
+ align:start position:0%
+actually that correction no it's not
+ 
+
+ align:start position:0%
+actually that correction no it's not
+about how how close ra and RB are to
+
+ align:start position:0%
+about how how close ra and RB are to
+ 
+
+ align:start position:0%
+about how how close ra and RB are to
+each other um you even if they had the
+
+ align:start position:0%
+each other um you even if they had the
+ 
+
+ align:start position:0%
+each other um you even if they had the
+exact
+
+ align:start position:0%
+exact
+ 
+
+ align:start position:0%
+exact
+same relative Fitness even if they were
+
+ align:start position:0%
+same relative Fitness even if they were
+ 
+
+ align:start position:0%
+same relative Fitness even if they were
+both two or both 1.01 then they would
+
+ align:start position:0%
+both two or both 1.01 then they would
+ 
+
+ align:start position:0%
+both two or both 1.01 then they would
+still be non-interacting that's just
+
+ align:start position:0%
+still be non-interacting that's just
+ 
+
+ align:start position:0%
+still be non-interacting that's just
+because they're in this sea of
+
+ align:start position:0%
+because they're in this sea of
+ 
+
+ align:start position:0%
+because they're in this sea of
+individuals but the thing that I'm
+
+ align:start position:0%
+individuals but the thing that I'm
+ 
+
+ align:start position:0%
+individuals but the thing that I'm
+worried about is for example ra could
+
+ align:start position:0%
+worried about is for example ra could
+ 
+
+ align:start position:0%
+worried about is for example ra could
+take over quickly and then RB take right
+
+ align:start position:0%
+take over quickly and then RB take right
+ 
+
+ align:start position:0%
+take over quickly and then RB take right
+and that okay uh would not be right
+
+ align:start position:0%
+and that okay uh would not be right
+ 
+
+ align:start position:0%
+and that okay uh would not be right
+okay so um and that's not reasonable
+
+ align:start position:0%
+okay so um and that's not reasonable
+ 
+
+ align:start position:0%
+okay so um and that's not reasonable
+this takes over RB the effective RB
+
+ align:start position:0%
+this takes over RB the effective RB
+ 
+
+ align:start position:0%
+this takes over RB the effective RB
+right okay so there is one problem right
+
+ align:start position:0%
+right okay so there is one problem right
+ 
+
+ align:start position:0%
+right okay so there is one problem right
+okay so I should be careful if if the
+
+ align:start position:0%
+okay so I should be careful if if the
+ 
+
+ align:start position:0%
+okay so I should be careful if if the
+two if the two mutants have exactly the
+
+ align:start position:0%
+two if the two mutants have exactly the
+ 
+
+ align:start position:0%
+two if the two mutants have exactly the
+same Fitness then if they both survive
+
+ align:start position:0%
+same Fitness then if they both survive
+ 
+
+ align:start position:0%
+same Fitness then if they both survive
+stas extinction they're going to then
+
+ align:start position:0%
+stas extinction they're going to then
+ 
+
+ align:start position:0%
+stas extinction they're going to then
+they then you can describe everything as
+
+ align:start position:0%
+they then you can describe everything as
+ 
+
+ align:start position:0%
+they then you can describe everything as
+a differential and this is this is the
+
+ align:start position:0%
+a differential and this is this is the
+ 
+
+ align:start position:0%
+a differential and this is this is the
+distinction between between this initial
+
+ align:start position:0%
+distinction between between this initial
+ 
+
+ align:start position:0%
+distinction between between this initial
+phase of trying to become established as
+
+ align:start position:0%
+phase of trying to become established as
+ 
+
+ align:start position:0%
+phase of trying to become established as
+compared to the later Dynamics and that
+
+ align:start position:0%
+compared to the later Dynamics and that
+ 
+
+ align:start position:0%
+compared to the later Dynamics and that
+uh the established means that if it's a
+
+ align:start position:0%
+uh the established means that if it's a
+ 
+
+ align:start position:0%
+uh the established means that if it's a
+beneficial mutation it will spread and
+
+ align:start position:0%
+beneficial mutation it will spread and
+ 
+
+ align:start position:0%
+beneficial mutation it will spread and
+basically determinist ically right so in
+
+ align:start position:0%
+basically determinist ically right so in
+ 
+
+ align:start position:0%
+basically determinist ically right so in
+that situation if you had two mutants
+
+ align:start position:0%
+that situation if you had two mutants
+ 
+
+ align:start position:0%
+that situation if you had two mutants
+both of relative Fitness uh 1.01 then
+
+ align:start position:0%
+both of relative Fitness uh 1.01 then
+ 
+
+ align:start position:0%
+both of relative Fitness uh 1.01 then
+they both would try to survive stas
+
+ align:start position:0%
+they both would try to survive stas
+ 
+
+ align:start position:0%
+they both would try to survive stas
+extinction and let's say that they both
+
+ align:start position:0%
+extinction and let's say that they both
+ 
+
+ align:start position:0%
+extinction and let's say that they both
+did then they would both uh spread in
+
+ align:start position:0%
+did then they would both uh spread in
+ 
+
+ align:start position:0%
+did then they would both uh spread in
+the population exponentially of course
+
+ align:start position:0%
+the population exponentially of course
+ 
+
+ align:start position:0%
+the population exponentially of course
+um given that the initial Dynamics are
+
+ align:start position:0%
+um given that the initial Dynamics are
+ 
+
+ align:start position:0%
+um given that the initial Dynamics are
+stochastic then um it would still be the
+
+ align:start position:0%
+stochastic then um it would still be the
+ 
+
+ align:start position:0%
+stochastic then um it would still be the
+case that one of them would just happen
+
+ align:start position:0%
+case that one of them would just happen
+ 
+
+ align:start position:0%
+case that one of them would just happen
+to be above the other one and then but
+
+ align:start position:0%
+to be above the other one and then but
+ 
+
+ align:start position:0%
+to be above the other one and then but
+then they would then they would grow
+
+ align:start position:0%
+then they would then they would grow
+ 
+
+ align:start position:0%
+then they would then they would grow
+exponentially together um that's a more
+
+ align:start position:0%
+exponentially together um that's a more
+ 
+
+ align:start position:0%
+exponentially together um that's a more
+complicated situation than what we're
+
+ align:start position:0%
+complicated situation than what we're
+ 
+
+ align:start position:0%
+complicated situation than what we're
+going to um discuss and that would
+
+ align:start position:0%
+going to um discuss and that would
+ 
+
+ align:start position:0%
+going to um discuss and that would
+actually be very rare right because each
+
+ align:start position:0%
+actually be very rare right because each
+ 
+
+ align:start position:0%
+actually be very rare right because each
+one of these mutants would only have a
+
+ align:start position:0%
+one of these mutants would only have a
+ 
+
+ align:start position:0%
+one of these mutants would only have a
+1% chance of surviving so only one and
+
+ align:start position:0%
+1% chance of surviving so only one and
+ 
+
+ align:start position:0%
+1% chance of surviving so only one and
+10 the four kind of times would you end
+
+ align:start position:0%
+10 the four kind of times would you end
+ 
+
+ align:start position:0%
+10 the four kind of times would you end
+up with both of these mutants surviving
+
+ align:start position:0%
+up with both of these mutants surviving
+ 
+
+ align:start position:0%
+up with both of these mutants surviving
+stochastic Extinction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right any other questions about okay so
+
+ align:start position:0%
+right any other questions about okay so
+ 
+
+ align:start position:0%
+right any other questions about okay so
+I just want to be clear here so this is
+
+ align:start position:0%
+I just want to be clear here so this is
+ 
+
+ align:start position:0%
+I just want to be clear here so this is
+um you know this is when a is equal to
+
+ align:start position:0%
+um you know this is when a is equal to
+ 
+
+ align:start position:0%
+um you know this is when a is equal to
+you know the number of a individuals is
+
+ align:start position:0%
+you know the number of a individuals is
+ 
+
+ align:start position:0%
+you know the number of a individuals is
+one and number of B individuals equal to
+
+ align:start position:0%
+one and number of B individuals equal to
+ 
+
+ align:start position:0%
+one and number of B individuals equal to
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all there was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question what what if we started with a
+
+ align:start position:0%
+question what what if we started with a
+ 
+
+ align:start position:0%
+question what what if we started with a
+equal to 10 right so um let's say that
+
+ align:start position:0%
+equal to 10 right so um let's say that
+ 
+
+ align:start position:0%
+equal to 10 right so um let's say that
+yeah let's say actually let's say we
+
+ align:start position:0%
+yeah let's say actually let's say we
+ 
+
+ align:start position:0%
+yeah let's say actually let's say we
+start with 10 a and 10 B for
+
+ align:start position:0%
+start with 10 a and 10 B for
+ 
+
+ align:start position:0%
+start with 10 a and 10 B for
+example right so instead of starting
+
+ align:start position:0%
+example right so instead of starting
+ 
+
+ align:start position:0%
+example right so instead of starting
+with uh just one mutant a one mutant B
+
+ align:start position:0%
+with uh just one mutant a one mutant B
+ 
+
+ align:start position:0%
+with uh just one mutant a one mutant B
+now we have 10 of
+
+ align:start position:0%
+now we have 10 of
+ 
+
+ align:start position:0%
+now we have 10 of
+each right so we we're changing things
+
+ align:start position:0%
+each right so we we're changing things
+ 
+
+ align:start position:0%
+each right so we we're changing things
+symmetrically
+
+ align:start position:0%
+symmetrically
+ 
+
+ align:start position:0%
+symmetrically
+right what's going to be the probability
+
+ align:start position:0%
+right what's going to be the probability
+ 
+
+ align:start position:0%
+right what's going to be the probability
+that b
+
+ align:start position:0%
+that b
+ 
+
+ align:start position:0%
+that b
+fixes you know
+
+ align:start position:0%
+fixes you know
+ 
+
+ align:start position:0%
+fixes you know
+approximately all this is going to be a
+
+ align:start position:0%
+approximately all this is going to be a
+ 
+
+ align:start position:0%
+approximately all this is going to be a
+little funny somehow but okay
+
+ align:start position:0%
+little funny somehow but okay
+ 
+
+ align:start position:0%
+little funny somehow but okay
+well um just think about it for 15
+
+ align:start position:0%
+well um just think about it for 15
+ 
+
+ align:start position:0%
+well um just think about it for 15
+seconds what's going to be the
+
+ align:start position:0%
+seconds what's going to be the
+ 
+
+ align:start position:0%
+seconds what's going to be the
+probability that b fixes if um in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right I'm worried you guys are not
+
+ align:start position:0%
+all right I'm worried you guys are not
+ 
+
+ align:start position:0%
+all right I'm worried you guys are not
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+trying sure yeah yeah yeah okay so what
+
+ align:start position:0%
+trying sure yeah yeah yeah okay so what
+ 
+
+ align:start position:0%
+trying sure yeah yeah yeah okay so what
+I want to know is so so we just did the
+
+ align:start position:0%
+I want to know is so so we just did the
+ 
+
+ align:start position:0%
+I want to know is so so we just did the
+problem when we had a single mutant a
+
+ align:start position:0%
+problem when we had a single mutant a
+ 
+
+ align:start position:0%
+problem when we had a single mutant a
+and a single mutant B and we found the
+
+ align:start position:0%
+and a single mutant B and we found the
+ 
+
+ align:start position:0%
+and a single mutant B and we found the
+probability that b fixes was
+
+ align:start position:0%
+probability that b fixes was
+ 
+
+ align:start position:0%
+probability that b fixes was
+0.5 now I want to know is does anything
+
+ align:start position:0%
+0.5 now I want to know is does anything
+ 
+
+ align:start position:0%
+0.5 now I want to know is does anything
+change if instead of having a single a
+
+ align:start position:0%
+change if instead of having a single a
+ 
+
+ align:start position:0%
+change if instead of having a single a
+and single B now what we have is 10 a 10
+
+ align:start position:0%
+and single B now what we have is 10 a 10
+ 
+
+ align:start position:0%
+and single B now what we have is 10 a 10
+B and then the rest of them just being
+
+ align:start position:0%
+B and then the rest of them just being
+ 
+
+ align:start position:0%
+B and then the rest of them just being
+Rel of Fitness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all
+
+ align:start position:0%
+one all
+ 
+
+ align:start position:0%
+one all
+right so it's not fancy math but it
+
+ align:start position:0%
+right so it's not fancy math but it
+ 
+
+ align:start position:0%
+right so it's not fancy math but it
+still gets you a little confused
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just want to see where we are okay
+
+ align:start position:0%
+I just want to see where we are okay
+ 
+
+ align:start position:0%
+I just want to see where we are okay
+we'll use the same options here okay
+
+ align:start position:0%
+we'll use the same options here okay
+ 
+
+ align:start position:0%
+we'll use the same options here okay
+um you know whatever's
+
+ align:start position:0%
+um you know whatever's
+ 
+
+ align:start position:0%
+um you know whatever's
+closest and we can argue about what
+
+ align:start position:0%
+closest and we can argue about what
+ 
+
+ align:start position:0%
+closest and we can argue about what
+close means in a moment all right ready
+
+ align:start position:0%
+close means in a moment all right ready
+ 
+
+ align:start position:0%
+close means in a moment all right ready
+uh three two
+
+ align:start position:0%
+uh three two
+ 
+
+ align:start position:0%
+uh three two
+one okay I'd say yeah all right so it's
+
+ align:start position:0%
+one okay I'd say yeah all right so it's
+ 
+
+ align:start position:0%
+one okay I'd say yeah all right so it's
+kind of some A's and
+
+ align:start position:0%
+kind of some A's and
+ 
+
+ align:start position:0%
+kind of some A's and
+B's some e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um okay well okay well we'll we'll talk
+
+ align:start position:0%
+um okay well okay well we'll we'll talk
+ 
+
+ align:start position:0%
+um okay well okay well we'll we'll talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um all right I maybe I'll we'll jump
+
+ align:start position:0%
+um all right I maybe I'll we'll jump
+ 
+
+ align:start position:0%
+um all right I maybe I'll we'll jump
+ahead to the group discussion just
+
+ align:start position:0%
+ahead to the group discussion just
+ 
+
+ align:start position:0%
+ahead to the group discussion just
+because I don't want to spend too much
+
+ align:start position:0%
+because I don't want to spend too much
+ 
+
+ align:start position:0%
+because I don't want to spend too much
+time on this problem but these are these
+
+ align:start position:0%
+time on this problem but these are these
+ 
+
+ align:start position:0%
+time on this problem but these are these
+are the kinds of problems I think it's
+
+ align:start position:0%
+are the kinds of problems I think it's
+ 
+
+ align:start position:0%
+are the kinds of problems I think it's
+very important to to practice with
+
+ align:start position:0%
+very important to to practice with
+ 
+
+ align:start position:0%
+very important to to practice with
+because they just develop your intuition
+
+ align:start position:0%
+because they just develop your intuition
+ 
+
+ align:start position:0%
+because they just develop your intuition
+for the stochastic dynamics that occur
+
+ align:start position:0%
+for the stochastic dynamics that occur
+ 
+
+ align:start position:0%
+for the stochastic dynamics that occur
+in populations right um okay so let's
+
+ align:start position:0%
+in populations right um okay so let's
+ 
+
+ align:start position:0%
+in populations right um okay so let's
+let's you know it's G to be something
+
+ align:start position:0%
+let's you know it's G to be something
+ 
+
+ align:start position:0%
+let's you know it's G to be something
+like B you know that's not where I put
+
+ align:start position:0%
+like B you know that's not where I put
+ 
+
+ align:start position:0%
+like B you know that's not where I put
+why I put B in there because but okay
+
+ align:start position:0%
+why I put B in there because but okay
+ 
+
+ align:start position:0%
+why I put B in there because but okay
+but let's just see how it goes it's
+
+ align:start position:0%
+but let's just see how it goes it's
+ 
+
+ align:start position:0%
+but let's just see how it goes it's
+going to be all right and and the way to
+
+ align:start position:0%
+going to be all right and and the way to
+ 
+
+ align:start position:0%
+going to be all right and and the way to
+find the answer here is the same as what
+
+ align:start position:0%
+find the answer here is the same as what
+ 
+
+ align:start position:0%
+find the answer here is the same as what
+we did before except that now we have to
+
+ align:start position:0%
+we did before except that now we have to
+ 
+
+ align:start position:0%
+we did before except that now we have to
+think about these processes somewhat
+
+ align:start position:0%
+think about these processes somewhat
+ 
+
+ align:start position:0%
+think about these processes somewhat
+differently okay so first of all uh in
+
+ align:start position:0%
+differently okay so first of all uh in
+ 
+
+ align:start position:0%
+differently okay so first of all uh in
+order for B to fix it requires that b
+
+ align:start position:0%
+order for B to fix it requires that b
+ 
+
+ align:start position:0%
+order for B to fix it requires that b
+still B has to survive stochastic
+
+ align:start position:0%
+still B has to survive stochastic
+ 
+
+ align:start position:0%
+still B has to survive stochastic
+Extinction okay so we still have the the
+
+ align:start position:0%
+Extinction okay so we still have the the
+ 
+
+ align:start position:0%
+Extinction okay so we still have the the
+same 0.01
+
+ align:start position:0%
+same 0.01
+ 
+
+ align:start position:0%
+same 0.01
+here okay but now we have to think about
+
+ align:start position:0%
+here okay but now we have to think about
+ 
+
+ align:start position:0%
+here okay but now we have to think about
+the probability that a doesn't survive
+
+ align:start position:0%
+the probability that a doesn't survive
+ 
+
+ align:start position:0%
+the probability that a doesn't survive
+okay and that's going to change now
+
+ align:start position:0%
+okay and that's going to change now
+ 
+
+ align:start position:0%
+okay and that's going to change now
+right oh I I I should be
+
+ align:start position:0%
+right oh I I I should be
+ 
+
+ align:start position:0%
+right oh I I I should be
+okay yeah okay no this is not okay I
+
+ align:start position:0%
+okay yeah okay no this is not okay I
+ 
+
+ align:start position:0%
+okay yeah okay no this is not okay I
+forgot that we had 10 here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's and we could calculate what it is
+
+ align:start position:0%
+it's and we could calculate what it is
+ 
+
+ align:start position:0%
+it's and we could calculate what it is
+and actually maybe we should have okay
+
+ align:start position:0%
+and actually maybe we should have okay
+ 
+
+ align:start position:0%
+and actually maybe we should have okay
+let's just yeah no let's let's calculate
+
+ align:start position:0%
+let's just yeah no let's let's calculate
+ 
+
+ align:start position:0%
+let's just yeah no let's let's calculate
+that all right so this is X1 for
+
+ align:start position:0%
+that all right so this is X1 for
+ 
+
+ align:start position:0%
+that all right so this is X1 for
+b um we still have you know 1.01 to the
+
+ align:start position:0%
+b um we still have you know 1.01 to the
+ 
+
+ align:start position:0%
+b um we still have you know 1.01 to the
+million so this is we can still ignore
+
+ align:start position:0%
+million so this is we can still ignore
+ 
+
+ align:start position:0%
+million so this is we can still ignore
+this bottom part um right but what it's
+
+ align:start position:0%
+this bottom part um right but what it's
+ 
+
+ align:start position:0%
+this bottom part um right but what it's
+going to be is oh no but this is X10 of
+
+ align:start position:0%
+going to be is oh no but this is X10 of
+ 
+
+ align:start position:0%
+going to be is oh no but this is X10 of
+B right we have 10 individuals so this
+
+ align:start position:0%
+B right we have 10 individuals so this
+ 
+
+ align:start position:0%
+B right we have 10 individuals so this
+is 1 minus 1.01 to the 10th power
+
+ align:start position:0%
+is 1 minus 1.01 to the 10th power
+ 
+
+ align:start position:0%
+is 1 minus 1.01 to the 10th power
+yeah but we have interference right okay
+
+ align:start position:0%
+yeah but we have interference right okay
+ 
+
+ align:start position:0%
+yeah but we have interference right okay
+so this is this is this is as if this we
+
+ align:start position:0%
+so this is this is this is as if this we
+ 
+
+ align:start position:0%
+so this is this is this is as if this we
+right now what we're trying to
+
+ align:start position:0%
+right now what we're trying to
+ 
+
+ align:start position:0%
+right now what we're trying to
+understand is if only we had B you know
+
+ align:start position:0%
+understand is if only we had B you know
+ 
+
+ align:start position:0%
+understand is if only we had B you know
+this is the this is the
+
+ align:start position:0%
+this is the this is the
+ 
+
+ align:start position:0%
+this is the this is the
+probability that of we're trying to
+
+ align:start position:0%
+probability that of we're trying to
+ 
+
+ align:start position:0%
+probability that of we're trying to
+calculate this this part of it all right
+
+ align:start position:0%
+calculate this this part of it all right
+ 
+
+ align:start position:0%
+calculate this this part of it all right
+so if we ignore a what's probably B
+
+ align:start position:0%
+so if we ignore a what's probably B
+ 
+
+ align:start position:0%
+so if we ignore a what's probably B
+survive stochastic Extinction um right
+
+ align:start position:0%
+survive stochastic Extinction um right
+ 
+
+ align:start position:0%
+survive stochastic Extinction um right
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+uh oh this is fine okay so this is this
+
+ align:start position:0%
+uh oh this is fine okay so this is this
+ 
+
+ align:start position:0%
+uh oh this is fine okay so this is this
+is yeah so it's it's a modest it's a
+
+ align:start position:0%
+is yeah so it's it's a modest it's a
+ 
+
+ align:start position:0%
+is yeah so it's it's a modest it's a
+modest change right okay so this is
+
+ align:start position:0%
+modest change right okay so this is
+ 
+
+ align:start position:0%
+modest change right okay so this is
+because this is going to
+
+ align:start position:0%
+because this is going to
+ 
+
+ align:start position:0%
+because this is going to
+be one
+
+ align:start position:0%
+be one
+ 
+
+ align:start position:0%
+be one
+minus uh so this thing is
+
+ align:start position:0%
+minus uh so this thing is
+ 
+
+ align:start position:0%
+minus uh so this thing is
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+1.1
+
+ align:start position:0%
+1.1
+ 
+
+ align:start position:0%
+1.1
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because 1 + x to the
+
+ align:start position:0%
+because 1 + x to the
+ 
+
+ align:start position:0%
+because 1 + x to the
+N is around 1 + NX for NX much less than
+
+ align:start position:0%
+N is around 1 + NX for NX much less than
+ 
+
+ align:start position:0%
+N is around 1 + NX for NX much less than
+one right okay so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.19 okay so this
+
+ align:start position:0%
+1.19 okay so this
+ 
+
+ align:start position:0%
+1.19 okay so this
+is okay am I going correct okay okay
+
+ align:start position:0%
+is okay am I going correct okay okay
+ 
+
+ align:start position:0%
+is okay am I going correct okay okay
+okay so right right so we had to get rid
+
+ align:start position:0%
+okay so right right so we had to get rid
+ 
+
+ align:start position:0%
+okay so right right so we had to get rid
+of okay so this is around 0.1
+
+ align:start position:0%
+of okay so this is around 0.1
+ 
+
+ align:start position:0%
+of okay so this is around 0.1
+right okay so indeed my you I'd
+
+ align:start position:0%
+right okay so indeed my you I'd
+ 
+
+ align:start position:0%
+right okay so indeed my you I'd
+forgotten that there was 10
+
+ align:start position:0%
+forgotten that there was 10
+ 
+
+ align:start position:0%
+forgotten that there was 10
+okay so all right so so given that we
+
+ align:start position:0%
+okay so all right so so given that we
+ 
+
+ align:start position:0%
+okay so all right so so given that we
+have 10 of these B individuals starting
+
+ align:start position:0%
+have 10 of these B individuals starting
+ 
+
+ align:start position:0%
+have 10 of these B individuals starting
+right they may survive you know in the
+
+ align:start position:0%
+right they may survive you know in the
+ 
+
+ align:start position:0%
+right they may survive you know in the
+we're ignoring a right now just on their
+
+ align:start position:0%
+we're ignoring a right now just on their
+ 
+
+ align:start position:0%
+we're ignoring a right now just on their
+own Dynamics they they may survive or
+
+ align:start position:0%
+own Dynamics they they may survive or
+ 
+
+ align:start position:0%
+own Dynamics they they may survive or
+they may drift down to zero and go
+
+ align:start position:0%
+they may drift down to zero and go
+ 
+
+ align:start position:0%
+they may drift down to zero and go
+extinct right and indeed even starting
+
+ align:start position:0%
+extinct right and indeed even starting
+ 
+
+ align:start position:0%
+extinct right and indeed even starting
+with 10 individuals 10 B individuals you
+
+ align:start position:0%
+with 10 individuals 10 B individuals you
+ 
+
+ align:start position:0%
+with 10 individuals 10 B individuals you
+actually still expect them to go extinct
+
+ align:start position:0%
+actually still expect them to go extinct
+ 
+
+ align:start position:0%
+actually still expect them to go extinct
+okay this actually calculation is very
+
+ align:start position:0%
+okay this actually calculation is very
+ 
+
+ align:start position:0%
+okay this actually calculation is very
+relevant for what we're about to think
+
+ align:start position:0%
+relevant for what we're about to think
+ 
+
+ align:start position:0%
+relevant for what we're about to think
+about which is this question of what
+
+ align:start position:0%
+about which is this question of what
+ 
+
+ align:start position:0%
+about which is this question of what
+does it mean to be established in a
+
+ align:start position:0%
+does it mean to be established in a
+ 
+
+ align:start position:0%
+does it mean to be established in a
+population and already you can kind of
+
+ align:start position:0%
+population and already you can kind of
+ 
+
+ align:start position:0%
+population and already you can kind of
+see what it's going to mean right how
+
+ align:start position:0%
+see what it's going to mean right how
+ 
+
+ align:start position:0%
+see what it's going to mean right how
+big do you need to get in the population
+
+ align:start position:0%
+big do you need to get in the population
+ 
+
+ align:start position:0%
+big do you need to get in the population
+before you're likely to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survive one/ s right this is because you
+
+ align:start position:0%
+survive one/ s right this is because you
+ 
+
+ align:start position:0%
+survive one/ s right this is because you
+can basically see how this is going to
+
+ align:start position:0%
+can basically see how this is going to
+ 
+
+ align:start position:0%
+can basically see how this is going to
+work out in this calculation that the
+
+ align:start position:0%
+work out in this calculation that the
+ 
+
+ align:start position:0%
+work out in this calculation that the
+number to be the number you have to get
+
+ align:start position:0%
+number to be the number you have to get
+ 
+
+ align:start position:0%
+number to be the number you have to get
+to to be established is around 1 over
+
+ align:start position:0%
+to to be established is around 1 over
+ 
+
+ align:start position:0%
+to to be established is around 1 over
+s okay so in this case you have to get
+
+ align:start position:0%
+s okay so in this case you have to get
+ 
+
+ align:start position:0%
+s okay so in this case you have to get
+to around 100 individuals before you are
+
+ align:start position:0%
+to around 100 individuals before you are
+ 
+
+ align:start position:0%
+to around 100 individuals before you are
+going to be more likely than not to
+
+ align:start position:0%
+going to be more likely than not to
+ 
+
+ align:start position:0%
+going to be more likely than not to
+survive okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's see if we can figure out this
+
+ align:start position:0%
+okay let's see if we can figure out this
+ 
+
+ align:start position:0%
+okay let's see if we can figure out this
+problem all right so we had point one
+
+ align:start position:0%
+problem all right so we had point one
+ 
+
+ align:start position:0%
+problem all right so we had point one
+was the probability that b would survive
+
+ align:start position:0%
+was the probability that b would survive
+ 
+
+ align:start position:0%
+was the probability that b would survive
+stochastic Extinction okay but then in
+
+ align:start position:0%
+stochastic Extinction okay but then in
+ 
+
+ align:start position:0%
+stochastic Extinction okay but then in
+in order for B to fix it has to not only
+
+ align:start position:0%
+in order for B to fix it has to not only
+ 
+
+ align:start position:0%
+in order for B to fix it has to not only
+survive stochastic Extinction but also a
+
+ align:start position:0%
+survive stochastic Extinction but also a
+ 
+
+ align:start position:0%
+survive stochastic Extinction but also a
+has to not
+
+ align:start position:0%
+has to not
+ 
+
+ align:start position:0%
+has to not
+survive
+
+ align:start position:0%
+survive
+ 
+
+ align:start position:0%
+survive
+okay and uh we can figure out what that
+
+ align:start position:0%
+okay and uh we can figure out what that
+ 
+
+ align:start position:0%
+okay and uh we can figure out what that
+is going to be here right this this is
+
+ align:start position:0%
+is going to be here right this this is
+ 
+
+ align:start position:0%
+is going to be here right this this is
+that term right and then we uh we need
+
+ align:start position:0%
+that term right and then we uh we need
+ 
+
+ align:start position:0%
+that term right and then we uh we need
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+one all right so this is this is X of
+
+ align:start position:0%
+one all right so this is this is X of
+ 
+
+ align:start position:0%
+one all right so this is this is X of
+tan of a right and this is again going
+
+ align:start position:0%
+tan of a right and this is again going
+ 
+
+ align:start position:0%
+tan of a right and this is again going
+to be 1 minus 12 to the 10th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power yeah right so it's always good to
+
+ align:start position:0%
+power yeah right so it's always good to
+ 
+
+ align:start position:0%
+power yeah right so it's always good to
+memorize a few of these things two to
+
+ align:start position:0%
+memorize a few of these things two to
+ 
+
+ align:start position:0%
+memorize a few of these things two to
+the 10 is approximately a
+
+ align:start position:0%
+the 10 is approximately a
+ 
+
+ align:start position:0%
+the 10 is approximately a
+thousand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right but we want not this right so
+
+ align:start position:0%
+right but we want not this right so
+ 
+
+ align:start position:0%
+right but we want not this right so
+we're going to subtract this one away so
+
+ align:start position:0%
+we're going to subtract this one away so
+ 
+
+ align:start position:0%
+we're going to subtract this one away so
+we're going to get 10us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 do you guys see how that right so
+
+ align:start position:0%
+3 do you guys see how that right so
+ 
+
+ align:start position:0%
+3 do you guys see how that right so
+given that we start with 10 individuals
+
+ align:start position:0%
+given that we start with 10 individuals
+ 
+
+ align:start position:0%
+given that we start with 10 individuals
+of a with relative Fitness two then
+
+ align:start position:0%
+of a with relative Fitness two then
+ 
+
+ align:start position:0%
+of a with relative Fitness two then
+there's only a one in a thousand chance
+
+ align:start position:0%
+there's only a one in a thousand chance
+ 
+
+ align:start position:0%
+there's only a one in a thousand chance
+that that those a individuals are going
+
+ align:start position:0%
+that that those a individuals are going
+ 
+
+ align:start position:0%
+that that those a individuals are going
+to uh go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extinct all right so the probability
+
+ align:start position:0%
+extinct all right so the probability
+ 
+
+ align:start position:0%
+extinct all right so the probability
+that b is going to fix in this situation
+
+ align:start position:0%
+that b is going to fix in this situation
+ 
+
+ align:start position:0%
+that b is going to fix in this situation
+is rather close to 10us 4 okay so I
+
+ align:start position:0%
+is rather close to 10us 4 okay so I
+ 
+
+ align:start position:0%
+is rather close to 10us 4 okay so I
+don't you know so it's somewhere in
+
+ align:start position:0%
+don't you know so it's somewhere in
+ 
+
+ align:start position:0%
+don't you know so it's somewhere in
+between there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+are there any questions about how that
+
+ align:start position:0%
+are there any questions about how that
+ 
+
+ align:start position:0%
+are there any questions about how that
+came
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about I feel like there's a fair amount
+
+ align:start position:0%
+about I feel like there's a fair amount
+ 
+
+ align:start position:0%
+about I feel like there's a fair amount
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+unhappiness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so it could be the
+
+ align:start position:0%
+um so it could be the
+ 
+
+ align:start position:0%
+um so it could be the
+logic of this or it could be the
+
+ align:start position:0%
+logic of this or it could be the
+ 
+
+ align:start position:0%
+logic of this or it could be the
+calculation of one of the two terms or
+
+ align:start position:0%
+calculation of one of the two terms or
+ 
+
+ align:start position:0%
+calculation of one of the two terms or
+it could be something else
+
+ align:start position:0%
+it could be something else
+ 
+
+ align:start position:0%
+it could be something else
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+sorry you
+
+ align:start position:0%
+sorry you
+ 
+
+ align:start position:0%
+sorry you
+get the probility of B surving again you
+
+ align:start position:0%
+get the probility of B surving again you
+ 
+
+ align:start position:0%
+get the probility of B surving again you
+you want to know this term or that term
+
+ align:start position:0%
+you want to know this term or that term
+ 
+
+ align:start position:0%
+you want to know this term or that term
+first term okay the first term right so
+
+ align:start position:0%
+first term okay the first term right so
+ 
+
+ align:start position:0%
+first term okay the first term right so
+the first term is just asking uh in if
+
+ align:start position:0%
+the first term is just asking uh in if
+ 
+
+ align:start position:0%
+the first term is just asking uh in if
+if there were no a okay what would be
+
+ align:start position:0%
+if there were no a okay what would be
+ 
+
+ align:start position:0%
+if there were no a okay what would be
+the probability that b would survive
+
+ align:start position:0%
+the probability that b would survive
+ 
+
+ align:start position:0%
+the probability that b would survive
+stochastic Extinction that's the same as
+
+ align:start position:0%
+stochastic Extinction that's the same as
+ 
+
+ align:start position:0%
+stochastic Extinction that's the same as
+the probability that it would um that it
+
+ align:start position:0%
+the probability that it would um that it
+ 
+
+ align:start position:0%
+the probability that it would um that it
+would fix because it's a beneficial
+
+ align:start position:0%
+would fix because it's a beneficial
+ 
+
+ align:start position:0%
+would fix because it's a beneficial
+mutation and if if B is the only thing
+
+ align:start position:0%
+mutation and if if B is the only thing
+ 
+
+ align:start position:0%
+mutation and if if B is the only thing
+right then so we use this
+
+ align:start position:0%
+right then so we use this
+ 
+
+ align:start position:0%
+right then so we use this
+okay yeah so we use we use this equation
+
+ align:start position:0%
+okay yeah so we use we use this equation
+ 
+
+ align:start position:0%
+okay yeah so we use we use this equation
+except this thing just goes to one so
+
+ align:start position:0%
+except this thing just goes to one so
+ 
+
+ align:start position:0%
+except this thing just goes to one so
+we're just left with this but we have to
+
+ align:start position:0%
+we're just left with this but we have to
+ 
+
+ align:start position:0%
+we're just left with this but we have to
+this equation is assuming that there's
+
+ align:start position:0%
+this equation is assuming that there's
+ 
+
+ align:start position:0%
+this equation is assuming that there's
+just one of the mutant individuals
+
+ align:start position:0%
+just one of the mutant individuals
+ 
+
+ align:start position:0%
+just one of the mutant individuals
+otherwise if we you know if you say x
+
+ align:start position:0%
+otherwise if we you know if you say x
+ 
+
+ align:start position:0%
+otherwise if we you know if you say x
+sub I then it's R to the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right so that was the equation
+
+ align:start position:0%
+here all right so that was the equation
+ 
+
+ align:start position:0%
+here all right so that was the equation
+that was derived in in chapter six of of
+
+ align:start position:0%
+that was derived in in chapter six of of
+ 
+
+ align:start position:0%
+that was derived in in chapter six of of
+evolutionary
+
+ align:start position:0%
+evolutionary
+ 
+
+ align:start position:0%
+evolutionary
+Dynamics
+
+ align:start position:0%
+Dynamics
+ 
+
+ align:start position:0%
+Dynamics
+okay but I think that that's not the
+
+ align:start position:0%
+okay but I think that that's not the
+ 
+
+ align:start position:0%
+okay but I think that that's not the
+only thing that people are unhappy about
+
+ align:start position:0%
+only thing that people are unhappy about
+ 
+
+ align:start position:0%
+only thing that people are unhappy about
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please
+
+ align:start position:0%
+please
+ 
+
+ align:start position:0%
+please
+no yes question one why don't you need
+
+ align:start position:0%
+no yes question one why don't you need
+ 
+
+ align:start position:0%
+no yes question one why don't you need
+to take into account B doesn't survive
+
+ align:start position:0%
+to take into account B doesn't survive
+ 
+
+ align:start position:0%
+to take into account B doesn't survive
+that probability that doesn't survive
+
+ align:start position:0%
+that probability that doesn't survive
+ 
+
+ align:start position:0%
+that probability that doesn't survive
+for the question that's the right now
+
+ align:start position:0%
+for the question that's the right now
+ 
+
+ align:start position:0%
+for the question that's the right now
+guess for the near nearly
+
+ align:start position:0%
+guess for the near nearly
+ 
+
+ align:start position:0%
+guess for the near nearly
+neutral oh okay so this was the very
+
+ align:start position:0%
+neutral oh okay so this was the very
+ 
+
+ align:start position:0%
+neutral oh okay so this was the very
+first one that we did okay um all right
+
+ align:start position:0%
+first one that we did okay um all right
+ 
+
+ align:start position:0%
+first one that we did okay um all right
+so you want to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like why don't you need to take into
+
+ align:start position:0%
+like why don't you need to take into
+ 
+
+ align:start position:0%
+like why don't you need to take into
+account the that does survive all right
+
+ align:start position:0%
+account the that does survive all right
+ 
+
+ align:start position:0%
+account the that does survive all right
+so in in this problem it's just that
+
+ align:start position:0%
+so in in this problem it's just that
+ 
+
+ align:start position:0%
+so in in this problem it's just that
+they all behave as if they were just
+
+ align:start position:0%
+they all behave as if they were just
+ 
+
+ align:start position:0%
+they all behave as if they were just
+neutral so the probability of each of
+
+ align:start position:0%
+neutral so the probability of each of
+ 
+
+ align:start position:0%
+neutral so the probability of each of
+these 10 individuals fixing in the
+
+ align:start position:0%
+these 10 individuals fixing in the
+ 
+
+ align:start position:0%
+these 10 individuals fixing in the
+population is the same essentially right
+
+ align:start position:0%
+population is the same essentially right
+ 
+
+ align:start position:0%
+population is the same essentially right
+and so they each have a one and 10
+
+ align:start position:0%
+and so they each have a one and 10
+ 
+
+ align:start position:0%
+and so they each have a one and 10
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+surviving and and in this case I would
+
+ align:start position:0%
+surviving and and in this case I would
+ 
+
+ align:start position:0%
+surviving and and in this case I would
+say that if if things are nearly neutral
+
+ align:start position:0%
+say that if if things are nearly neutral
+ 
+
+ align:start position:0%
+say that if if things are nearly neutral
+you don't talk about this idea of
+
+ align:start position:0%
+you don't talk about this idea of
+ 
+
+ align:start position:0%
+you don't talk about this idea of
+surviving stochastic extinction because
+
+ align:start position:0%
+surviving stochastic extinction because
+ 
+
+ align:start position:0%
+surviving stochastic extinction because
+it's all going to be it's you know you
+
+ align:start position:0%
+it's all going to be it's you know you
+ 
+
+ align:start position:0%
+it's all going to be it's you know you
+can't get big enough to the point where
+
+ align:start position:0%
+can't get big enough to the point where
+ 
+
+ align:start position:0%
+can't get big enough to the point where
+you will are guarant you know where
+
+ align:start position:0%
+you will are guarant you know where
+ 
+
+ align:start position:0%
+you will are guarant you know where
+you're really guaranteed to survive
+
+ align:start position:0%
+you're really guaranteed to survive
+ 
+
+ align:start position:0%
+you're really guaranteed to survive
+extinction because even if you've gone
+
+ align:start position:0%
+extinction because even if you've gone
+ 
+
+ align:start position:0%
+extinction because even if you've gone
+to occupy 75% of the
+
+ align:start position:0%
+to occupy 75% of the
+ 
+
+ align:start position:0%
+to occupy 75% of the
+population right what's your probability
+
+ align:start position:0%
+population right what's your probability
+ 
+
+ align:start position:0%
+population right what's your probability
+of fixing at that
+
+ align:start position:0%
+of fixing at that
+ 
+
+ align:start position:0%
+of fixing at that
+stage if you're nearly neutral and you
+
+ align:start position:0%
+stage if you're nearly neutral and you
+ 
+
+ align:start position:0%
+stage if you're nearly neutral and you
+get up to
+
+ align:start position:0%
+get up to
+ 
+
+ align:start position:0%
+get up to
+75% you have a 75% chance of fixing
+
+ align:start position:0%
+75% you have a 75% chance of fixing
+ 
+
+ align:start position:0%
+75% you have a 75% chance of fixing
+right so so there's no uh in the casee
+
+ align:start position:0%
+right so so there's no uh in the casee
+ 
+
+ align:start position:0%
+right so so there's no uh in the casee
+of neutral mutations uh there's no
+
+ align:start position:0%
+of neutral mutations uh there's no
+ 
+
+ align:start position:0%
+of neutral mutations uh there's no
+analogous idea of what it means to be um
+
+ align:start position:0%
+analogous idea of what it means to be um
+ 
+
+ align:start position:0%
+analogous idea of what it means to be um
+to be established because you could
+
+ align:start position:0%
+to be established because you could
+ 
+
+ align:start position:0%
+to be established because you could
+always just go back and go extinct with
+
+ align:start position:0%
+always just go back and go extinct with
+ 
+
+ align:start position:0%
+always just go back and go extinct with
+with finite
+
+ align:start position:0%
+with finite
+ 
+
+ align:start position:0%
+with finite
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+right this
+
+ align:start position:0%
+right this
+ 
+
+ align:start position:0%
+right this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+question okay well you know it's looking
+
+ align:start position:0%
+question okay well you know it's looking
+ 
+
+ align:start position:0%
+question okay well you know it's looking
+more and more likely to show up on the
+
+ align:start position:0%
+more and more likely to show up on the
+ 
+
+ align:start position:0%
+more and more likely to show up on the
+midterm on in in two weeks all right so
+
+ align:start position:0%
+midterm on in in two weeks all right so
+ 
+
+ align:start position:0%
+midterm on in in two weeks all right so
+now is your opportunity to ask a
+
+ align:start position:0%
+now is your opportunity to ask a
+ 
+
+ align:start position:0%
+now is your opportunity to ask a
+question about it if
+
+ align:start position:0%
+question about it if
+ 
+
+ align:start position:0%
+question about it if
+um can you can you talk about and
+
+ align:start position:0%
+um can you can you talk about and
+ 
+
+ align:start position:0%
+um can you can you talk about and
+established how you got it what it yes
+
+ align:start position:0%
+established how you got it what it yes
+ 
+
+ align:start position:0%
+established how you got it what it yes
+okay this is a good question all right
+
+ align:start position:0%
+okay this is a good question all right
+ 
+
+ align:start position:0%
+okay this is a good question all right
+right so when we talk about a mutation
+
+ align:start position:0%
+right so when we talk about a mutation
+ 
+
+ align:start position:0%
+right so when we talk about a mutation
+becoming
+
+ align:start position:0%
+becoming
+ 
+
+ align:start position:0%
+becoming
+established that you know that's asking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh course we know that even a rather
+
+ align:start position:0%
+uh course we know that even a rather
+ 
+
+ align:start position:0%
+uh course we know that even a rather
+beneficial mutation say something that
+
+ align:start position:0%
+beneficial mutation say something that
+ 
+
+ align:start position:0%
+beneficial mutation say something that
+confers an advantage of a few percent
+
+ align:start position:0%
+confers an advantage of a few percent
+ 
+
+ align:start position:0%
+confers an advantage of a few percent
+will probably go extinct okay uh however
+
+ align:start position:0%
+will probably go extinct okay uh however
+ 
+
+ align:start position:0%
+will probably go extinct okay uh however
+if it gets up to be a large enough um
+
+ align:start position:0%
+if it gets up to be a large enough um
+ 
+
+ align:start position:0%
+if it gets up to be a large enough um
+fraction or number in the population
+
+ align:start position:0%
+fraction or number in the population
+ 
+
+ align:start position:0%
+fraction or number in the population
+then uh it should then the Dynamics are
+
+ align:start position:0%
+then uh it should then the Dynamics are
+ 
+
+ align:start position:0%
+then uh it should then the Dynamics are
+going to be well described by a
+
+ align:start position:0%
+going to be well described by a
+ 
+
+ align:start position:0%
+going to be well described by a
+differential equation where it won't go
+
+ align:start position:0%
+differential equation where it won't go
+ 
+
+ align:start position:0%
+differential equation where it won't go
+extinct so this is for um this is for um
+
+ align:start position:0%
+extinct so this is for um this is for um
+ 
+
+ align:start position:0%
+extinct so this is for um this is for um
+this is established mutation and this
+
+ align:start position:0%
+this is established mutation and this
+ 
+
+ align:start position:0%
+this is established mutation and this
+this again we we really talk about only
+
+ align:start position:0%
+this again we we really talk about only
+ 
+
+ align:start position:0%
+this again we we really talk about only
+for for beneficial mutations because
+
+ align:start position:0%
+for for beneficial mutations because
+ 
+
+ align:start position:0%
+for for beneficial mutations because
+other other mutations can't really get
+
+ align:start position:0%
+other other mutations can't really get
+ 
+
+ align:start position:0%
+other other mutations can't really get
+established they could still
+
+ align:start position:0%
+established they could still
+ 
+
+ align:start position:0%
+established they could still
+stochastically fix but it's stochastic
+
+ align:start position:0%
+stochastically fix but it's stochastic
+ 
+
+ align:start position:0%
+stochastically fix but it's stochastic
+up to the very
+
+ align:start position:0%
+up to the very
+ 
+
+ align:start position:0%
+up to the very
+end okay and right so the question is at
+
+ align:start position:0%
+end okay and right so the question is at
+ 
+
+ align:start position:0%
+end okay and right so the question is at
+what number
+
+ align:start position:0%
+what number
+ 
+
+ align:start position:0%
+what number
+in the population do you have to get
+
+ align:start position:0%
+in the population do you have to get
+ 
+
+ align:start position:0%
+in the population do you have to get
+before you are expected to take over the
+
+ align:start position:0%
+before you are expected to take over the
+ 
+
+ align:start position:0%
+before you are expected to take over the
+population okay assuming that other
+
+ align:start position:0%
+population okay assuming that other
+ 
+
+ align:start position:0%
+population okay assuming that other
+other New Mutants don't arise
+
+ align:start position:0%
+other New Mutants don't arise
+ 
+
+ align:start position:0%
+other New Mutants don't arise
+okay and let me
+
+ align:start position:0%
+okay and let me
+ 
+
+ align:start position:0%
+okay and let me
+um right so this we can ask that
+
+ align:start position:0%
+um right so this we can ask that
+ 
+
+ align:start position:0%
+um right so this we can ask that
+corresponds to asking okay what this is
+
+ align:start position:0%
+corresponds to asking okay what this is
+ 
+
+ align:start position:0%
+corresponds to asking okay what this is
+the probability of fixation when you
+
+ align:start position:0%
+the probability of fixation when you
+ 
+
+ align:start position:0%
+the probability of fixation when you
+have I individuals in the population so
+
+ align:start position:0%
+have I individuals in the population so
+ 
+
+ align:start position:0%
+have I individuals in the population so
+this is just I mean okay so and this is
+
+ align:start position:0%
+this is just I mean okay so and this is
+ 
+
+ align:start position:0%
+this is just I mean okay so and this is
+this is what we saw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+okay this is permutation with relative
+
+ align:start position:0%
+okay this is permutation with relative
+ 
+
+ align:start position:0%
+okay this is permutation with relative
+Fitness R you have I individuals in the
+
+ align:start position:0%
+Fitness R you have I individuals in the
+ 
+
+ align:start position:0%
+Fitness R you have I individuals in the
+population total population size
+
+ align:start position:0%
+population total population size
+ 
+
+ align:start position:0%
+population total population size
+n right and what we want to know and and
+
+ align:start position:0%
+n right and what we want to know and and
+ 
+
+ align:start position:0%
+n right and what we want to know and and
+this becoming established means that XI
+
+ align:start position:0%
+this becoming established means that XI
+ 
+
+ align:start position:0%
+this becoming established means that XI
+is approximately equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+right um now in in in these situations
+
+ align:start position:0%
+right um now in in in these situations
+ 
+
+ align:start position:0%
+right um now in in in these situations
+it's going to be R to the N is again
+
+ align:start position:0%
+it's going to be R to the N is again
+ 
+
+ align:start position:0%
+it's going to be R to the N is again
+very very large so this thing we can
+
+ align:start position:0%
+very very large so this thing we can
+ 
+
+ align:start position:0%
+very very large so this thing we can
+ignore so this is really the same thing
+
+ align:start position:0%
+ignore so this is really the same thing
+ 
+
+ align:start position:0%
+ignore so this is really the same thing
+is asking that 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus right and this never gets to be
+
+ align:start position:0%
+minus right and this never gets to be
+ 
+
+ align:start position:0%
+minus right and this never gets to be
+exactly equal to one but what then we're
+
+ align:start position:0%
+exactly equal to one but what then we're
+ 
+
+ align:start position:0%
+exactly equal to one but what then we're
+really asking is that this thing is
+
+ align:start position:0%
+really asking is that this thing is
+ 
+
+ align:start position:0%
+really asking is that this thing is
+close to one I.E we
+
+ align:start position:0%
+close to one I.E we
+ 
+
+ align:start position:0%
+close to one I.E we
+can this equivalent to saying that what
+
+ align:start position:0%
+can this equivalent to saying that what
+ 
+
+ align:start position:0%
+can this equivalent to saying that what
+do we want to say that 1 over R to the I
+
+ align:start position:0%
+do we want to say that 1 over R to the I
+ 
+
+ align:start position:0%
+do we want to say that 1 over R to the I
+is much less than
+
+ align:start position:0%
+is much less than
+ 
+
+ align:start position:0%
+is much less than
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh right well that means the r
+
+ align:start position:0%
+okay and uh right well that means the r
+ 
+
+ align:start position:0%
+okay and uh right well that means the r
+to the I has much greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right so this is this is really
+
+ align:start position:0%
+one right so this is this is really
+ 
+
+ align:start position:0%
+one right so this is this is really
+saying that what you want is I * s to be
+
+ align:start position:0%
+saying that what you want is I * s to be
+ 
+
+ align:start position:0%
+saying that what you want is I * s to be
+much greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh and this is then so so n
+
+ align:start position:0%
+one uh and this is then so so n
+ 
+
+ align:start position:0%
+one uh and this is then so so n
+established which is in this case this
+
+ align:start position:0%
+established which is in this case this
+ 
+
+ align:start position:0%
+established which is in this case this
+this it's the I such that this is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um right has to be much greater than one
+
+ align:start position:0%
+um right has to be much greater than one
+ 
+
+ align:start position:0%
+um right has to be much greater than one
+/
+
+ align:start position:0%
+/
+ 
+
+ align:start position:0%
+/
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+okay and indeed I think that when when I
+
+ align:start position:0%
+okay and indeed I think that when when I
+ 
+
+ align:start position:0%
+okay and indeed I think that when when I
+is equal to 1 /
+
+ align:start position:0%
+is equal to 1 /
+ 
+
+ align:start position:0%
+is equal to 1 /
+s then the probability of fixation is
+
+ align:start position:0%
+s then the probability of fixation is
+ 
+
+ align:start position:0%
+s then the probability of fixation is
+um or I think it's the probability of
+
+ align:start position:0%
+um or I think it's the probability of
+ 
+
+ align:start position:0%
+um or I think it's the probability of
+Extinction is one over e if you kind of
+
+ align:start position:0%
+Extinction is one over e if you kind of
+ 
+
+ align:start position:0%
+Extinction is one over e if you kind of
+do the do the math okay so that means
+
+ align:start position:0%
+do the do the math okay so that means
+ 
+
+ align:start position:0%
+do the do the math okay so that means
+that this is kind of the crossing over
+
+ align:start position:0%
+that this is kind of the crossing over
+ 
+
+ align:start position:0%
+that this is kind of the crossing over
+point where you're more likely than not
+
+ align:start position:0%
+point where you're more likely than not
+ 
+
+ align:start position:0%
+point where you're more likely than not
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+survive
+
+ align:start position:0%
+survive
+ 
+
+ align:start position:0%
+survive
+okay and just to be concrete for many of
+
+ align:start position:0%
+okay and just to be concrete for many of
+ 
+
+ align:start position:0%
+okay and just to be concrete for many of
+the mutations we're going to be we're
+
+ align:start position:0%
+the mutations we're going to be we're
+ 
+
+ align:start position:0%
+the mutations we're going to be we're
+talking about and that you read about in
+
+ align:start position:0%
+talking about and that you read about in
+ 
+
+ align:start position:0%
+talking about and that you read about in
+Roy's paper uh s was a few percent right
+
+ align:start position:0%
+Roy's paper uh s was a few percent right
+ 
+
+ align:start position:0%
+Roy's paper uh s was a few percent right
+so this is saying that the population is
+
+ align:start position:0%
+so this is saying that the population is
+ 
+
+ align:start position:0%
+so this is saying that the population is
+established when the number of these
+
+ align:start position:0%
+established when the number of these
+ 
+
+ align:start position:0%
+established when the number of these
+mutant gets up to above 30 or you know a
+
+ align:start position:0%
+mutant gets up to above 30 or you know a
+ 
+
+ align:start position:0%
+mutant gets up to above 30 or you know a
+few times 30 so maybe 100 individuals
+
+ align:start position:0%
+few times 30 so maybe 100 individuals
+ 
+
+ align:start position:0%
+few times 30 so maybe 100 individuals
+means that it's unlikely to go extinct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stochastically
+
+ align:start position:0%
+stochastically
+ 
+
+ align:start position:0%
+stochastically
+okay so it's really it's once you get to
+
+ align:start position:0%
+okay so it's really it's once you get to
+ 
+
+ align:start position:0%
+okay so it's really it's once you get to
+This n established then the population
+
+ align:start position:0%
+This n established then the population
+ 
+
+ align:start position:0%
+This n established then the population
+will grow exponentially in the
+
+ align:start position:0%
+will grow exponentially in the
+ 
+
+ align:start position:0%
+will grow exponentially in the
+population and it's going to spread
+
+ align:start position:0%
+population and it's going to spread
+ 
+
+ align:start position:0%
+population and it's going to spread
+exponentially with an advantage s
+
+ align:start position:0%
+exponentially with an advantage s
+ 
+
+ align:start position:0%
+exponentially with an advantage s
+relative to the rest of the
+
+ align:start position:0%
+relative to the rest of the
+ 
+
+ align:start position:0%
+relative to the rest of the
+population okay so this discussion is
+
+ align:start position:0%
+population okay so this discussion is
+ 
+
+ align:start position:0%
+population okay so this discussion is
+actually very useful for the next thing
+
+ align:start position:0%
+actually very useful for the next thing
+ 
+
+ align:start position:0%
+actually very useful for the next thing
+we want to talk about but yeah are there
+
+ align:start position:0%
+we want to talk about but yeah are there
+ 
+
+ align:start position:0%
+we want to talk about but yeah are there
+any questions about how we got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah right so the probability of going
+
+ align:start position:0%
+yeah right so the probability of going
+ 
+
+ align:start position:0%
+yeah right so the probability of going
+extinct is um this is the probability of
+
+ align:start position:0%
+extinct is um this is the probability of
+ 
+
+ align:start position:0%
+extinct is um this is the probability of
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+extinct okay so the probability of going
+
+ align:start position:0%
+extinct okay so the probability of going
+ 
+
+ align:start position:0%
+extinct okay so the probability of going
+extinct here if you have I
+
+ align:start position:0%
+extinct here if you have I
+ 
+
+ align:start position:0%
+extinct here if you have I
+individuals is is is one over this guy
+
+ align:start position:0%
+individuals is is is one over this guy
+ 
+
+ align:start position:0%
+individuals is is is one over this guy
+so it's one over 1 plus s to the
+
+ align:start position:0%
+so it's one over 1 plus s to the
+ 
+
+ align:start position:0%
+so it's one over 1 plus s to the
+I right and then
+
+ align:start position:0%
+I right and then
+ 
+
+ align:start position:0%
+I right and then
+if I * s is 1
+
+ align:start position:0%
+if I * s is 1
+ 
+
+ align:start position:0%
+if I * s is 1
+but s is
+
+ align:start position:0%
+but s is
+ 
+
+ align:start position:0%
+but s is
+small okay I mean this is you know this
+
+ align:start position:0%
+small okay I mean this is you know this
+ 
+
+ align:start position:0%
+small okay I mean this is you know this
+is one of those definitions of of e to
+
+ align:start position:0%
+is one of those definitions of of e to
+ 
+
+ align:start position:0%
+is one of those definitions of of e to
+the x that I don't know do you guys
+
+ align:start position:0%
+the x that I don't know do you guys
+ 
+
+ align:start position:0%
+the x that I don't know do you guys
+remember this is it it's like oh my
+
+ align:start position:0%
+remember this is it it's like oh my
+ 
+
+ align:start position:0%
+remember this is it it's like oh my
+goodness e to the
+
+ align:start position:0%
+goodness e to the
+ 
+
+ align:start position:0%
+goodness e to the
+x is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit no no X is should be up there
+
+ align:start position:0%
+limit no no X is should be up there
+ 
+
+ align:start position:0%
+limit no no X is should be up there
+okay boy yeah and this you guys are
+
+ align:start position:0%
+okay boy yeah and this you guys are
+ 
+
+ align:start position:0%
+okay boy yeah and this you guys are
+taxing me all right um this is X over n
+
+ align:start position:0%
+taxing me all right um this is X over n
+ 
+
+ align:start position:0%
+taxing me all right um this is X over n
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+n and this is limit as n goes to
+
+ align:start position:0%
+n and this is limit as n goes to
+ 
+
+ align:start position:0%
+n and this is limit as n goes to
+Infinity is this yes we agree
+
+ align:start position:0%
+Infinity is this yes we agree
+ 
+
+ align:start position:0%
+Infinity is this yes we agree
+okay this makes sense right um right so
+
+ align:start position:0%
+okay this makes sense right um right so
+ 
+
+ align:start position:0%
+okay this makes sense right um right so
+you I mean just if if right so this is
+
+ align:start position:0%
+you I mean just if if right so this is
+ 
+
+ align:start position:0%
+you I mean just if if right so this is
+this is just equivalent of saying that
+
+ align:start position:0%
+this is just equivalent of saying that
+ 
+
+ align:start position:0%
+this is just equivalent of saying that
+if I * s equal to 1 but s is small then
+
+ align:start position:0%
+if I * s equal to 1 but s is small then
+ 
+
+ align:start position:0%
+if I * s equal to 1 but s is small then
+this thing is around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+okay um if you're confused by I I don't
+
+ align:start position:0%
+okay um if you're confused by I I don't
+ 
+
+ align:start position:0%
+okay um if you're confused by I I don't
+want I don't want to get into this too
+
+ align:start position:0%
+want I don't want to get into this too
+ 
+
+ align:start position:0%
+want I don't want to get into this too
+much because it's not quite Central to
+
+ align:start position:0%
+much because it's not quite Central to
+ 
+
+ align:start position:0%
+much because it's not quite Central to
+what we're talking about but uh come up
+
+ align:start position:0%
+what we're talking about but uh come up
+ 
+
+ align:start position:0%
+what we're talking about but uh come up
+and talk to me after the class and we'll
+
+ align:start position:0%
+and talk to me after the class and we'll
+ 
+
+ align:start position:0%
+and talk to me after the class and we'll
+derive this together okay but
+
+ align:start position:0%
+derive this together okay but
+ 
+
+ align:start position:0%
+derive this together okay but
+um right so the idea is that when when
+
+ align:start position:0%
+um right so the idea is that when when
+ 
+
+ align:start position:0%
+um right so the idea is that when when
+you've reached a population size of one
+
+ align:start position:0%
+you've reached a population size of one
+ 
+
+ align:start position:0%
+you've reached a population size of one
+/ s then you have a one over e
+
+ align:start position:0%
+/ s then you have a one over e
+ 
+
+ align:start position:0%
+/ s then you have a one over e
+probability of um going
+
+ align:start position:0%
+probability of um going
+ 
+
+ align:start position:0%
+probability of um going
+extinct okay so e pops up at all sorts
+
+ align:start position:0%
+extinct okay so e pops up at all sorts
+ 
+
+ align:start position:0%
+extinct okay so e pops up at all sorts
+of weird locations this is why you hear
+
+ align:start position:0%
+of weird locations this is why you hear
+ 
+
+ align:start position:0%
+of weird locations this is why you hear
+about it okay
+
+ align:start position:0%
+about it okay
+ 
+
+ align:start position:0%
+about it okay
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um right so what I want to do now is I
+
+ align:start position:0%
+um right so what I want to do now is I
+ 
+
+ align:start position:0%
+um right so what I want to do now is I
+want to discuss this uh idea of uh
+
+ align:start position:0%
+want to discuss this uh idea of uh
+ 
+
+ align:start position:0%
+want to discuss this uh idea of uh
+clonal interference a little bit more in
+
+ align:start position:0%
+clonal interference a little bit more in
+ 
+
+ align:start position:0%
+clonal interference a little bit more in
+particular ask all right in what
+
+ align:start position:0%
+particular ask all right in what
+ 
+
+ align:start position:0%
+particular ask all right in what
+situation um will we have clonal
+
+ align:start position:0%
+situation um will we have clonal
+ 
+
+ align:start position:0%
+situation um will we have clonal
+interference or equivalently when can we
+
+ align:start position:0%
+interference or equivalently when can we
+ 
+
+ align:start position:0%
+interference or equivalently when can we
+ignore colonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference all right can somebody say
+
+ align:start position:0%
+interference all right can somebody say
+ 
+
+ align:start position:0%
+interference all right can somebody say
+in words that when we're going to be
+
+ align:start position:0%
+in words that when we're going to be
+ 
+
+ align:start position:0%
+in words that when we're going to be
+able to ignore the effect of colonal
+
+ align:start position:0%
+able to ignore the effect of colonal
+ 
+
+ align:start position:0%
+able to ignore the effect of colonal
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+yes size is large that there's very lied
+
+ align:start position:0%
+yes size is large that there's very lied
+ 
+
+ align:start position:0%
+yes size is large that there's very lied
+that those
+
+ align:start position:0%
+that those
+ 
+
+ align:start position:0%
+that those
+two okay I think we're goingon to have
+
+ align:start position:0%
+two okay I think we're goingon to have
+ 
+
+ align:start position:0%
+two okay I think we're goingon to have
+to be careful here all right so because
+
+ align:start position:0%
+to be careful here all right so because
+ 
+
+ align:start position:0%
+to be careful here all right so because
+you're saying oh well if the
+
+ align:start position:0%
+you're saying oh well if the
+ 
+
+ align:start position:0%
+you're saying oh well if the
+population is large enough then that
+
+ align:start position:0%
+population is large enough then that
+ 
+
+ align:start position:0%
+population is large enough then that
+you're saying oh the mutations won't
+
+ align:start position:0%
+you're saying oh the mutations won't
+ 
+
+ align:start position:0%
+you're saying oh the mutations won't
+interact right not in the beginning well
+
+ align:start position:0%
+interact right not in the beginning well
+ 
+
+ align:start position:0%
+interact right not in the beginning well
+they don't interact at the beginning I
+
+ align:start position:0%
+they don't interact at the beginning I
+ 
+
+ align:start position:0%
+they don't interact at the beginning I
+think that's that statement I'm very
+
+ align:start position:0%
+think that's that statement I'm very
+ 
+
+ align:start position:0%
+think that's that statement I'm very
+happy with but the problem is that if
+
+ align:start position:0%
+happy with but the problem is that if
+ 
+
+ align:start position:0%
+happy with but the problem is that if
+they both survive sastic extinction and
+
+ align:start position:0%
+they both survive sastic extinction and
+ 
+
+ align:start position:0%
+they both survive sastic extinction and
+they start spreading then they really do
+
+ align:start position:0%
+they start spreading then they really do
+ 
+
+ align:start position:0%
+they start spreading then they really do
+then they do start to interact in this
+
+ align:start position:0%
+then they do start to interact in this
+ 
+
+ align:start position:0%
+then they do start to interact in this
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+population right did you just say that
+
+ align:start position:0%
+population right did you just say that
+ 
+
+ align:start position:0%
+population right did you just say that
+once they survive sastic extinction they
+
+ align:start position:0%
+once they survive sastic extinction they
+ 
+
+ align:start position:0%
+once they survive sastic extinction they
+pretty much behave like they behave
+
+ align:start position:0%
+pretty much behave like they behave
+ 
+
+ align:start position:0%
+pretty much behave like they behave
+deterministically but the thing is that
+
+ align:start position:0%
+deterministically but the thing is that
+ 
+
+ align:start position:0%
+deterministically but the thing is that
+if you have two subpopulations that are
+
+ align:start position:0%
+if you have two subpopulations that are
+ 
+
+ align:start position:0%
+if you have two subpopulations that are
+exponentially growing and there are
+
+ align:start position:0%
+exponentially growing and there are
+ 
+
+ align:start position:0%
+exponentially growing and there are
+these very nice diagrams that I guess in
+
+ align:start position:0%
+these very nice diagrams that I guess in
+ 
+
+ align:start position:0%
+these very nice diagrams that I guess in
+Roy's paper they don't show which is if
+
+ align:start position:0%
+Roy's paper they don't show which is if
+ 
+
+ align:start position:0%
+Roy's paper they don't show which is if
+you if you look at the somehow the
+
+ align:start position:0%
+you if you look at the somehow the
+ 
+
+ align:start position:0%
+you if you look at the somehow the
+population okay um kind of changing as a
+
+ align:start position:0%
+population okay um kind of changing as a
+ 
+
+ align:start position:0%
+population okay um kind of changing as a
+function of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you can think about okay well
+
+ align:start position:0%
+right you can think about okay well
+ 
+
+ align:start position:0%
+right you can think about okay well
+there's some this is we's say constant
+
+ align:start position:0%
+there's some this is we's say constant
+ 
+
+ align:start position:0%
+there's some this is we's say constant
+population size right and it starts out
+
+ align:start position:0%
+population size right and it starts out
+ 
+
+ align:start position:0%
+population size right and it starts out
+all being a particular type okay we'll
+
+ align:start position:0%
+all being a particular type okay we'll
+ 
+
+ align:start position:0%
+all being a particular type okay we'll
+say um there's you know some population
+
+ align:start position:0%
+say um there's you know some population
+ 
+
+ align:start position:0%
+say um there's you know some population
+of a and now new mutation arises and
+
+ align:start position:0%
+of a and now new mutation arises and
+ 
+
+ align:start position:0%
+of a and now new mutation arises and
+survives to C Extinction it starts
+
+ align:start position:0%
+survives to C Extinction it starts
+ 
+
+ align:start position:0%
+survives to C Extinction it starts
+spreading in the
+
+ align:start position:0%
+spreading in the
+ 
+
+ align:start position:0%
+spreading in the
+population all right this may be mutant
+
+ align:start position:0%
+population all right this may be mutant
+ 
+
+ align:start position:0%
+population all right this may be mutant
+B okay but then if another mutant
+
+ align:start position:0%
+B okay but then if another mutant
+ 
+
+ align:start position:0%
+B okay but then if another mutant
+appears over here that's even more
+
+ align:start position:0%
+appears over here that's even more
+ 
+
+ align:start position:0%
+appears over here that's even more
+fit
+
+ align:start position:0%
+fit
+ 
+
+ align:start position:0%
+fit
+then it can
+
+ align:start position:0%
+then it can
+ 
+
+ align:start position:0%
+then it can
+actually spread faster and indeed it can
+
+ align:start position:0%
+actually spread faster and indeed it can
+ 
+
+ align:start position:0%
+actually spread faster and indeed it can
+cause the B lineage to get out
+
+ align:start position:0%
+cause the B lineage to get out
+ 
+
+ align:start position:0%
+cause the B lineage to get out
+competed right so we start out with
+
+ align:start position:0%
+competed right so we start out with
+ 
+
+ align:start position:0%
+competed right so we start out with
+population a mutation B is more fit than
+
+ align:start position:0%
+population a mutation B is more fit than
+ 
+
+ align:start position:0%
+population a mutation B is more fit than
+a you know mutant B is more fit than a
+
+ align:start position:0%
+a you know mutant B is more fit than a
+ 
+
+ align:start position:0%
+a you know mutant B is more fit than a
+it's spreading exponentially but
+
+ align:start position:0%
+it's spreading exponentially but
+ 
+
+ align:start position:0%
+it's spreading exponentially but
+sometime later mutation C appears right
+
+ align:start position:0%
+sometime later mutation C appears right
+ 
+
+ align:start position:0%
+sometime later mutation C appears right
+now this C lineage is more fit than b so
+
+ align:start position:0%
+now this C lineage is more fit than b so
+ 
+
+ align:start position:0%
+now this C lineage is more fit than b so
+it's able to spread exponentially and
+
+ align:start position:0%
+it's able to spread exponentially and
+ 
+
+ align:start position:0%
+it's able to spread exponentially and
+indeed it out competes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay so this is this is exactly what
+
+ align:start position:0%
+B okay so this is this is exactly what
+ 
+
+ align:start position:0%
+B okay so this is this is exactly what
+we mean by clonal interference these two
+
+ align:start position:0%
+we mean by clonal interference these two
+ 
+
+ align:start position:0%
+we mean by clonal interference these two
+lineages are interfering with each other
+
+ align:start position:0%
+lineages are interfering with each other
+ 
+
+ align:start position:0%
+lineages are interfering with each other
+okay so this thing is this is indeed
+
+ align:start position:0%
+okay so this thing is this is indeed
+ 
+
+ align:start position:0%
+okay so this thing is this is indeed
+colonal interference um and there have
+
+ align:start position:0%
+colonal interference um and there have
+ 
+
+ align:start position:0%
+colonal interference um and there have
+been these drawings out you know for
+
+ align:start position:0%
+been these drawings out you know for
+ 
+
+ align:start position:0%
+been these drawings out you know for
+maybe 20 years people have been thinking
+
+ align:start position:0%
+maybe 20 years people have been thinking
+ 
+
+ align:start position:0%
+maybe 20 years people have been thinking
+about this like lensky wrote some
+
+ align:start position:0%
+about this like lensky wrote some
+ 
+
+ align:start position:0%
+about this like lensky wrote some
+classic papers thinking about this uh
+
+ align:start position:0%
+classic papers thinking about this uh
+ 
+
+ align:start position:0%
+classic papers thinking about this uh
+recently Michael
+
+ align:start position:0%
+recently Michael
+ 
+
+ align:start position:0%
+recently Michael
+Desai at Harvard has done some really
+
+ align:start position:0%
+Desai at Harvard has done some really
+ 
+
+ align:start position:0%
+Desai at Harvard has done some really
+beautiful work where he takes these
+
+ align:start position:0%
+beautiful work where he takes these
+ 
+
+ align:start position:0%
+beautiful work where he takes these
+evolving yeast populations he does high
+
+ align:start position:0%
+evolving yeast populations he does high
+ 
+
+ align:start position:0%
+evolving yeast populations he does high
+resolution um now resolution in both
+
+ align:start position:0%
+resolution um now resolution in both
+ 
+
+ align:start position:0%
+resolution um now resolution in both
+senses temporal as well as deep kind of
+
+ align:start position:0%
+senses temporal as well as deep kind of
+ 
+
+ align:start position:0%
+senses temporal as well as deep kind of
+deep sequencing in the population where
+
+ align:start position:0%
+deep sequencing in the population where
+ 
+
+ align:start position:0%
+deep sequencing in the population where
+he can actually directly see uh see
+
+ align:start position:0%
+he can actually directly see uh see
+ 
+
+ align:start position:0%
+he can actually directly see uh see
+these these lineages spreading and then
+
+ align:start position:0%
+these these lineages spreading and then
+ 
+
+ align:start position:0%
+these these lineages spreading and then
+being out competed and he sees multiple
+
+ align:start position:0%
+being out competed and he sees multiple
+ 
+
+ align:start position:0%
+being out competed and he sees multiple
+mutations kind of spreading through the
+
+ align:start position:0%
+mutations kind of spreading through the
+ 
+
+ align:start position:0%
+mutations kind of spreading through the
+population together because they got
+
+ align:start position:0%
+population together because they got
+ 
+
+ align:start position:0%
+population together because they got
+they were attached on some genome it's
+
+ align:start position:0%
+they were attached on some genome it's
+ 
+
+ align:start position:0%
+they were attached on some genome it's
+really uh it's a very nice
+
+ align:start position:0%
+really uh it's a very nice
+ 
+
+ align:start position:0%
+really uh it's a very nice
+paper uh I almost had you guys read it
+
+ align:start position:0%
+paper uh I almost had you guys read it
+ 
+
+ align:start position:0%
+paper uh I almost had you guys read it
+so it's it's maybe nature in
+
+ align:start position:0%
+so it's it's maybe nature in
+ 
+
+ align:start position:0%
+so it's it's maybe nature in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+13 I don't know possibly 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right so this this is the idea of
+
+ align:start position:0%
+okay right so this this is the idea of
+ 
+
+ align:start position:0%
+okay right so this this is the idea of
+colonal interference okay so it's it's
+
+ align:start position:0%
+colonal interference okay so it's it's
+ 
+
+ align:start position:0%
+colonal interference okay so it's it's
+after the initial stochastic Dynamics
+
+ align:start position:0%
+after the initial stochastic Dynamics
+ 
+
+ align:start position:0%
+after the initial stochastic Dynamics
+have played out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah so that is a result of clonal
+
+ align:start position:0%
+yes yeah so that is a result of clonal
+ 
+
+ align:start position:0%
+yes yeah so that is a result of clonal
+interference right because it's saying
+
+ align:start position:0%
+interference right because it's saying
+ 
+
+ align:start position:0%
+interference right because it's saying
+that that you know that half arises
+
+ align:start position:0%
+that that you know that half arises
+ 
+
+ align:start position:0%
+that that you know that half arises
+because if you know B maybe if it did
+
+ align:start position:0%
+because if you know B maybe if it did
+ 
+
+ align:start position:0%
+because if you know B maybe if it did
+survive it may still get out competed by
+
+ align:start position:0%
+survive it may still get out competed by
+ 
+
+ align:start position:0%
+survive it may still get out competed by
+a so that's that's that's clonal
+
+ align:start position:0%
+a so that's that's that's clonal
+ 
+
+ align:start position:0%
+a so that's that's that's clonal
+interference you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the right so the idea is that they don't
+
+ align:start position:0%
+the right so the idea is that they don't
+ 
+
+ align:start position:0%
+the right so the idea is that they don't
+interact initially because when they're
+
+ align:start position:0%
+interact initially because when they're
+ 
+
+ align:start position:0%
+interact initially because when they're
+when the mutations are present at very
+
+ align:start position:0%
+when the mutations are present at very
+ 
+
+ align:start position:0%
+when the mutations are present at very
+low frequency then they're really
+
+ align:start position:0%
+low frequency then they're really
+ 
+
+ align:start position:0%
+low frequency then they're really
+interacting with the bulk the rest of
+
+ align:start position:0%
+interacting with the bulk the rest of
+ 
+
+ align:start position:0%
+interacting with the bulk the rest of
+the population but 10 to the six there
+
+ align:start position:0%
+the population but 10 to the six there
+ 
+
+ align:start position:0%
+the population but 10 to the six there
+okay however if they survive stochastic
+
+ align:start position:0%
+okay however if they survive stochastic
+ 
+
+ align:start position:0%
+okay however if they survive stochastic
+Extinction and they start spreading in
+
+ align:start position:0%
+Extinction and they start spreading in
+ 
+
+ align:start position:0%
+Extinction and they start spreading in
+the population then there's the
+
+ align:start position:0%
+the population then there's the
+ 
+
+ align:start position:0%
+the population then there's the
+possibility of colonal
+
+ align:start position:0%
+possibility of colonal
+ 
+
+ align:start position:0%
+possibility of colonal
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+would that change
+
+ align:start position:0%
+would that change
+ 
+
+ align:start position:0%
+would that change
+that no I think that's why it's a
+
+ align:start position:0%
+that no I think that's why it's a
+ 
+
+ align:start position:0%
+that no I think that's why it's a
+half right because this factor of half
+
+ align:start position:0%
+half right because this factor of half
+ 
+
+ align:start position:0%
+half right because this factor of half
+is really just saying that you know even
+
+ align:start position:0%
+is really just saying that you know even
+ 
+
+ align:start position:0%
+is really just saying that you know even
+if B survives stochastic Extinction it
+
+ align:start position:0%
+if B survives stochastic Extinction it
+ 
+
+ align:start position:0%
+if B survives stochastic Extinction it
+only has a 50-50 shot of actually being
+
+ align:start position:0%
+only has a 50-50 shot of actually being
+ 
+
+ align:start position:0%
+only has a 50-50 shot of actually being
+able to take over because there's a 50%
+
+ align:start position:0%
+able to take over because there's a 50%
+ 
+
+ align:start position:0%
+able to take over because there's a 50%
+chance it's going to be it's going to
+
+ align:start position:0%
+chance it's going to be it's going to
+ 
+
+ align:start position:0%
+chance it's going to be it's going to
+experience colonal interference with
+
+ align:start position:0%
+experience colonal interference with
+ 
+
+ align:start position:0%
+experience colonal interference with
+this a lineage that's going to
+
+ align:start position:0%
+this a lineage that's going to
+ 
+
+ align:start position:0%
+this a lineage that's going to
+outcompete
+
+ align:start position:0%
+outcompete
+ 
+
+ align:start position:0%
+outcompete
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right uh you maybe if you know if
+
+ align:start position:0%
+okay right uh you maybe if you know if
+ 
+
+ align:start position:0%
+okay right uh you maybe if you know if
+there if you're unhappy about that
+
+ align:start position:0%
+there if you're unhappy about that
+ 
+
+ align:start position:0%
+there if you're unhappy about that
+statement harass me afterwards
+
+ align:start position:0%
+statement harass me afterwards
+ 
+
+ align:start position:0%
+statement harass me afterwards
+okay okay so but all right so from this
+
+ align:start position:0%
+okay okay so but all right so from this
+ 
+
+ align:start position:0%
+okay okay so but all right so from this
+discussion though um how can we think
+
+ align:start position:0%
+discussion though um how can we think
+ 
+
+ align:start position:0%
+discussion though um how can we think
+about the importance of colonal
+
+ align:start position:0%
+about the importance of colonal
+ 
+
+ align:start position:0%
+about the importance of colonal
+interference in particular um there are
+
+ align:start position:0%
+interference in particular um there are
+ 
+
+ align:start position:0%
+interference in particular um there are
+going to be two time scales and uh the
+
+ align:start position:0%
+going to be two time scales and uh the
+ 
+
+ align:start position:0%
+going to be two time scales and uh the
+question of whether there's going to be
+
+ align:start position:0%
+question of whether there's going to be
+ 
+
+ align:start position:0%
+question of whether there's going to be
+significant colon interference is
+
+ align:start position:0%
+significant colon interference is
+ 
+
+ align:start position:0%
+significant colon interference is
+related to which of these time scales is
+
+ align:start position:0%
+related to which of these time scales is
+ 
+
+ align:start position:0%
+related to which of these time scales is
+larger right all right so what what
+
+ align:start position:0%
+larger right all right so what what
+ 
+
+ align:start position:0%
+larger right all right so what what
+might the time scales
+
+ align:start position:0%
+might the time scales
+ 
+
+ align:start position:0%
+might the time scales
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or at least one of the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales I guess one should probably be
+
+ align:start position:0%
+scales I guess one should probably be
+ 
+
+ align:start position:0%
+scales I guess one should probably be
+the time to be established right to be
+
+ align:start position:0%
+the time to be established right to be
+ 
+
+ align:start position:0%
+the time to be established right to be
+established to reach the size
+
+ align:start position:0%
+established to reach the size
+ 
+
+ align:start position:0%
+established to reach the size
+established okay yeah as it turn yeah so
+
+ align:start position:0%
+established okay yeah as it turn yeah so
+ 
+
+ align:start position:0%
+established okay yeah as it turn yeah so
+this actually ends up not being um no
+
+ align:start position:0%
+this actually ends up not being um no
+ 
+
+ align:start position:0%
+this actually ends up not being um no
+but you know but it's very um right so
+
+ align:start position:0%
+but you know but it's very um right so
+ 
+
+ align:start position:0%
+but you know but it's very um right so
+the actual time that it takes from when
+
+ align:start position:0%
+the actual time that it takes from when
+ 
+
+ align:start position:0%
+the actual time that it takes from when
+a mutation appears to when it becomes
+
+ align:start position:0%
+a mutation appears to when it becomes
+ 
+
+ align:start position:0%
+a mutation appears to when it becomes
+established is um I mean there is a time
+
+ align:start position:0%
+established is um I mean there is a time
+ 
+
+ align:start position:0%
+established is um I mean there is a time
+time there but it's um it ends up not
+
+ align:start position:0%
+time there but it's um it ends up not
+ 
+
+ align:start position:0%
+time there but it's um it ends up not
+being the relevant thing because that's
+
+ align:start position:0%
+being the relevant thing because that's
+ 
+
+ align:start position:0%
+being the relevant thing because that's
+the regime where they're not actually uh
+
+ align:start position:0%
+the regime where they're not actually uh
+ 
+
+ align:start position:0%
+the regime where they're not actually uh
+interacting with that the mutant
+
+ align:start position:0%
+interacting with that the mutant
+ 
+
+ align:start position:0%
+interacting with that the mutant
+lineages are not interacting anyways
+
+ align:start position:0%
+lineages are not interacting anyways
+ 
+
+ align:start position:0%
+lineages are not interacting anyways
+right so there's a sense that it doesn't
+
+ align:start position:0%
+right so there's a sense that it doesn't
+ 
+
+ align:start position:0%
+right so there's a sense that it doesn't
+quite matter how long that takes at
+
+ align:start position:0%
+quite matter how long that takes at
+ 
+
+ align:start position:0%
+quite matter how long that takes at
+least to first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order right okay so yeah so I think so
+
+ align:start position:0%
+order right okay so yeah so I think so
+ 
+
+ align:start position:0%
+order right okay so yeah so I think so
+one of them is going to be that the it's
+
+ align:start position:0%
+one of them is going to be that the it's
+ 
+
+ align:start position:0%
+one of them is going to be that the it's
+the time to go from
+
+ align:start position:0%
+the time to go from
+ 
+
+ align:start position:0%
+the time to go from
+established to
+
+ align:start position:0%
+established to
+ 
+
+ align:start position:0%
+established to
+fixation right so it's actually the next
+
+ align:start position:0%
+fixation right so it's actually the next
+ 
+
+ align:start position:0%
+fixation right so it's actually the next
+time scale there because and actually
+
+ align:start position:0%
+time scale there because and actually
+ 
+
+ align:start position:0%
+time scale there because and actually
+the time to get established is actually
+
+ align:start position:0%
+the time to get established is actually
+ 
+
+ align:start position:0%
+the time to get established is actually
+rather short because the lineages that
+
+ align:start position:0%
+rather short because the lineages that
+ 
+
+ align:start position:0%
+rather short because the lineages that
+you know so a mutation appears it most
+
+ align:start position:0%
+you know so a mutation appears it most
+ 
+
+ align:start position:0%
+you know so a mutation appears it most
+of the time goes extinct but the ones
+
+ align:start position:0%
+of the time goes extinct but the ones
+ 
+
+ align:start position:0%
+of the time goes extinct but the ones
+that don't go extinct actually get
+
+ align:start position:0%
+that don't go extinct actually get
+ 
+
+ align:start position:0%
+that don't go extinct actually get
+established rather quickly right you
+
+ align:start position:0%
+established rather quickly right you
+ 
+
+ align:start position:0%
+established rather quickly right you
+know because that's a biased sampling
+
+ align:start position:0%
+know because that's a biased sampling
+ 
+
+ align:start position:0%
+know because that's a biased sampling
+over the trajectories um right but but
+
+ align:start position:0%
+over the trajectories um right but but
+ 
+
+ align:start position:0%
+over the trajectories um right but but
+there is a rather significant time that
+
+ align:start position:0%
+there is a rather significant time that
+ 
+
+ align:start position:0%
+there is a rather significant time that
+it takes for the lineage to go from
+
+ align:start position:0%
+it takes for the lineage to go from
+ 
+
+ align:start position:0%
+it takes for the lineage to go from
+being established to actually fixing in
+
+ align:start position:0%
+being established to actually fixing in
+ 
+
+ align:start position:0%
+being established to actually fixing in
+the population so this is kind of how
+
+ align:start position:0%
+the population so this is kind of how
+ 
+
+ align:start position:0%
+the population so this is kind of how
+long it takes for a mutation to take
+
+ align:start position:0%
+long it takes for a mutation to take
+ 
+
+ align:start position:0%
+long it takes for a mutation to take
+over a population right so um we might
+
+ align:start position:0%
+over a population right so um we might
+ 
+
+ align:start position:0%
+over a population right so um we might
+call this the time to spread or
+
+ align:start position:0%
+call this the time to spread or
+ 
+
+ align:start position:0%
+call this the time to spread or
+so okay and it turns out that that time
+
+ align:start position:0%
+so okay and it turns out that that time
+ 
+
+ align:start position:0%
+so okay and it turns out that that time
+yeah what is it going to depend
+
+ align:start position:0%
+yeah what is it going to depend
+ 
+
+ align:start position:0%
+yeah what is it going to depend
+on it's going to depend on S right so as
+
+ align:start position:0%
+on it's going to depend on S right so as
+ 
+
+ align:start position:0%
+on it's going to depend on S right so as
+s goes up then this
+
+ align:start position:0%
+s goes up then this
+ 
+
+ align:start position:0%
+s goes up then this
+goes down okay all right Perfect all
+
+ align:start position:0%
+goes down okay all right Perfect all
+ 
+
+ align:start position:0%
+goes down okay all right Perfect all
+right let's just go put a one over s
+
+ align:start position:0%
+right let's just go put a one over s
+ 
+
+ align:start position:0%
+right let's just go put a one over s
+there right this and this be this is
+
+ align:start position:0%
+there right this and this be this is
+ 
+
+ align:start position:0%
+there right this and this be this is
+because it's going to grow exponentially
+
+ align:start position:0%
+because it's going to grow exponentially
+ 
+
+ align:start position:0%
+because it's going to grow exponentially
+in the population okay and then uh what
+
+ align:start position:0%
+in the population okay and then uh what
+ 
+
+ align:start position:0%
+in the population okay and then uh what
+how else is it going to depend on n n
+
+ align:start position:0%
+how else is it going to depend on n n
+ 
+
+ align:start position:0%
+how else is it going to depend on n n
+right and indeed uh this is going to be
+
+ align:start position:0%
+right and indeed uh this is going to be
+ 
+
+ align:start position:0%
+right and indeed uh this is going to be
+the log of n * s it's really n Over N
+
+ align:start position:0%
+the log of n * s it's really n Over N
+ 
+
+ align:start position:0%
+the log of n * s it's really n Over N
+established right because the idea is
+
+ align:start position:0%
+established right because the idea is
+ 
+
+ align:start position:0%
+established right because the idea is
+that you start out and established you
+
+ align:start position:0%
+that you start out and established you
+ 
+
+ align:start position:0%
+that you start out and established you
+grow exponentially with rate s until you
+
+ align:start position:0%
+grow exponentially with rate s until you
+ 
+
+ align:start position:0%
+grow exponentially with rate s until you
+kind of take over the population size
+
+ align:start position:0%
+kind of take over the population size
+ 
+
+ align:start position:0%
+kind of take over the population size
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay this this ass appears because it's
+
+ align:start position:0%
+okay this this ass appears because it's
+ 
+
+ align:start position:0%
+okay this this ass appears because it's
+one over n
+
+ align:start position:0%
+one over n
+ 
+
+ align:start position:0%
+one over n
+established because this in in the log
+
+ align:start position:0%
+established because this in in the log
+ 
+
+ align:start position:0%
+established because this in in the log
+is really like kind of the population
+
+ align:start position:0%
+is really like kind of the population
+ 
+
+ align:start position:0%
+is really like kind of the population
+size divided by n established okay okay
+
+ align:start position:0%
+size divided by n established okay okay
+ 
+
+ align:start position:0%
+size divided by n established okay okay
+so this is one time scale right do you
+
+ align:start position:0%
+so this is one time scale right do you
+ 
+
+ align:start position:0%
+so this is one time scale right do you
+guys understand why it should be like
+
+ align:start position:0%
+guys understand why it should be like
+ 
+
+ align:start position:0%
+guys understand why it should be like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right and what's the other time
+
+ align:start position:0%
+all right and what's the other time
+ 
+
+ align:start position:0%
+all right and what's the other time
+scale that's relevant here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah how fast mutation
+
+ align:start position:0%
+yeah how fast mutation
+ 
+
+ align:start position:0%
+yeah how fast mutation
+yes how long you have to wait from one
+
+ align:start position:0%
+yes how long you have to wait from one
+ 
+
+ align:start position:0%
+yes how long you have to wait from one
+mutation to the Next Mutation right okay
+
+ align:start position:0%
+mutation to the Next Mutation right okay
+ 
+
+ align:start position:0%
+mutation to the Next Mutation right okay
+so this is this is how long you have to
+
+ align:start position:0%
+so this is this is how long you have to
+ 
+
+ align:start position:0%
+so this is this is how long you have to
+wait for one mutation right so this is
+
+ align:start position:0%
+wait for one mutation right so this is
+ 
+
+ align:start position:0%
+wait for one mutation right so this is
+this is t t we call might call T
+
+ align:start position:0%
+this is t t we call might call T
+ 
+
+ align:start position:0%
+this is t t we call might call T
+mutation all right now it's a little bit
+
+ align:start position:0%
+mutation all right now it's a little bit
+ 
+
+ align:start position:0%
+mutation all right now it's a little bit
+subtle to think about what this is going
+
+ align:start position:0%
+subtle to think about what this is going
+ 
+
+ align:start position:0%
+subtle to think about what this is going
+to what what this should be right but it
+
+ align:start position:0%
+to what what this should be right but it
+ 
+
+ align:start position:0%
+to what what this should be right but it
+should say something about the time it
+
+ align:start position:0%
+should say something about the time it
+ 
+
+ align:start position:0%
+should say something about the time it
+takes for mutations to appear in the
+
+ align:start position:0%
+takes for mutations to appear in the
+ 
+
+ align:start position:0%
+takes for mutations to appear in the
+population right so we'll um let's go
+
+ align:start position:0%
+population right so we'll um let's go
+ 
+
+ align:start position:0%
+population right so we'll um let's go
+ahead and just guess what this might be
+
+ align:start position:0%
+ahead and just guess what this might be
+ 
+
+ align:start position:0%
+ahead and just guess what this might be
+for t- mutation should be equal to what
+
+ align:start position:0%
+for t- mutation should be equal to what
+ 
+
+ align:start position:0%
+for t- mutation should be equal to what
+all right so it could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+um yeah right so yeah so I I you know so
+
+ align:start position:0%
+um yeah right so yeah so I I you know so
+ 
+
+ align:start position:0%
+um yeah right so yeah so I I you know so
+I guess I'm trying to get you to think
+
+ align:start position:0%
+I guess I'm trying to get you to think
+ 
+
+ align:start position:0%
+I guess I'm trying to get you to think
+about what this should mean to be
+
+ align:start position:0%
+about what this should mean to be
+ 
+
+ align:start position:0%
+about what this should mean to be
+relevant for determining the time scales
+
+ align:start position:0%
+relevant for determining the time scales
+ 
+
+ align:start position:0%
+relevant for determining the time scales
+of whether clonal interference is
+
+ align:start position:0%
+of whether clonal interference is
+ 
+
+ align:start position:0%
+of whether clonal interference is
+important mu is
+
+ align:start position:0%
+important mu is
+ 
+
+ align:start position:0%
+important mu is
+the probability per generation of having
+
+ align:start position:0%
+the probability per generation of having
+ 
+
+ align:start position:0%
+the probability per generation of having
+a beneficial mutation of magnitude s
+
+ align:start position:0%
+a beneficial mutation of magnitude s
+ 
+
+ align:start position:0%
+a beneficial mutation of magnitude s
+okay mu is the um is is you know is kind
+
+ align:start position:0%
+okay mu is the um is is you know is kind
+ 
+
+ align:start position:0%
+okay mu is the um is is you know is kind
+of the mutation rate is what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know right but we'll just assume that
+
+ align:start position:0%
+know right but we'll just assume that
+ 
+
+ align:start position:0%
+know right but we'll just assume that
+that that there's only one kind of
+
+ align:start position:0%
+that that there's only one kind of
+ 
+
+ align:start position:0%
+that that there's only one kind of
+beneficial mutation and every beneficial
+
+ align:start position:0%
+beneficial mutation and every beneficial
+ 
+
+ align:start position:0%
+beneficial mutation and every beneficial
+m mutation has magnitude s for
+
+ align:start position:0%
+m mutation has magnitude s for
+ 
+
+ align:start position:0%
+m mutation has magnitude s for
+Simplicity right so it's mutation rate
+
+ align:start position:0%
+Simplicity right so it's mutation rate
+ 
+
+ align:start position:0%
+Simplicity right so it's mutation rate
+per you know it's a beneficial mutation
+
+ align:start position:0%
+per you know it's a beneficial mutation
+ 
+
+ align:start position:0%
+per you know it's a beneficial mutation
+rate per generation of of leading to
+
+ align:start position:0%
+rate per generation of of leading to
+ 
+
+ align:start position:0%
+rate per generation of of leading to
+mutation s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you can just also say if you're
+
+ align:start position:0%
+um and you can just also say if you're
+ 
+
+ align:start position:0%
+um and you can just also say if you're
+if you have no idea why what I'm talking
+
+ align:start position:0%
+if you have no idea why what I'm talking
+ 
+
+ align:start position:0%
+if you have no idea why what I'm talking
+about it's fine but I just you know it's
+
+ align:start position:0%
+about it's fine but I just you know it's
+ 
+
+ align:start position:0%
+about it's fine but I just you know it's
+worth spending a little bit bit of time
+
+ align:start position:0%
+worth spending a little bit bit of time
+ 
+
+ align:start position:0%
+worth spending a little bit bit of time
+thinking about what should be the
+
+ align:start position:0%
+thinking about what should be the
+ 
+
+ align:start position:0%
+thinking about what should be the
+relevant time scale to compare to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and it's okay if you find this
+
+ align:start position:0%
+right and it's okay if you find this
+ 
+
+ align:start position:0%
+right and it's okay if you find this
+confusing because this is this is subtle
+
+ align:start position:0%
+confusing because this is this is subtle
+ 
+
+ align:start position:0%
+confusing because this is this is subtle
+but if you think about it for 30 seconds
+
+ align:start position:0%
+but if you think about it for 30 seconds
+ 
+
+ align:start position:0%
+but if you think about it for 30 seconds
+then maybe you'll be you know fertile
+
+ align:start position:0%
+then maybe you'll be you know fertile
+ 
+
+ align:start position:0%
+then maybe you'll be you know fertile
+ground to to for the disc discussion to
+
+ align:start position:0%
+ground to to for the disc discussion to
+ 
+
+ align:start position:0%
+ground to to for the disc discussion to
+follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right let's go ahead and vote and
+
+ align:start position:0%
+um all right let's go ahead and vote and
+ 
+
+ align:start position:0%
+um all right let's go ahead and vote and
+see where we are ready three two
+
+ align:start position:0%
+see where we are ready three two
+ 
+
+ align:start position:0%
+see where we are ready three two
+one all right
+
+ align:start position:0%
+one all right
+ 
+
+ align:start position:0%
+one all right
+I I all right this is very nice okay
+
+ align:start position:0%
+I I all right this is very nice okay
+ 
+
+ align:start position:0%
+I I all right this is very nice okay
+almost everybody is saying C although um
+
+ align:start position:0%
+almost everybody is saying C although um
+ 
+
+ align:start position:0%
+almost everybody is saying C although um
+it really should be D okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so s time and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay that's an interesting statement
+
+ align:start position:0%
+one okay that's an interesting statement
+ 
+
+ align:start position:0%
+one okay that's an interesting statement
+um all right so uh S I mean I guess this
+
+ align:start position:0%
+um all right so uh S I mean I guess this
+ 
+
+ align:start position:0%
+um all right so uh S I mean I guess this
+is a relative
+
+ align:start position:0%
+is a relative
+ 
+
+ align:start position:0%
+is a relative
+Fitness but you right there you have S
+
+ align:start position:0%
+Fitness but you right there you have S
+ 
+
+ align:start position:0%
+Fitness but you right there you have S
+to time
+
+ align:start position:0%
+to time
+ 
+
+ align:start position:0%
+to time
+one of boy it's a good you know yeah so
+
+ align:start position:0%
+one of boy it's a good you know yeah so
+ 
+
+ align:start position:0%
+one of boy it's a good you know yeah so
+the problem is that this is this is all
+
+ align:start position:0%
+the problem is that this is this is all
+ 
+
+ align:start position:0%
+the problem is that this is this is all
+in unit it's a a generation time right
+
+ align:start position:0%
+in unit it's a a generation time right
+ 
+
+ align:start position:0%
+in unit it's a a generation time right
+so this is because this is really
+
+ align:start position:0%
+so this is because this is really
+ 
+
+ align:start position:0%
+so this is because this is really
+telling us about the number of
+
+ align:start position:0%
+telling us about the number of
+ 
+
+ align:start position:0%
+telling us about the number of
+generations
+
+ align:start position:0%
+generations
+ 
+
+ align:start position:0%
+generations
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so um what is going on that's an
+
+ align:start position:0%
+so um what is going on that's an
+ 
+
+ align:start position:0%
+so um what is going on that's an
+interesting um because one of mu should
+
+ align:start position:0%
+interesting um because one of mu should
+ 
+
+ align:start position:0%
+interesting um because one of mu should
+also be a time right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah I I'm not sure if it yeah I
+
+ align:start position:0%
+yeah yeah I I'm not sure if it yeah I
+ 
+
+ align:start position:0%
+yeah yeah I I'm not sure if it yeah I
+mean since this is all in Generations
+
+ align:start position:0%
+mean since this is all in Generations
+ 
+
+ align:start position:0%
+mean since this is all in Generations
+I'm not sure if you even have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah I think it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I I like that statement but then
+
+ align:start position:0%
+okay I I like that statement but then
+ 
+
+ align:start position:0%
+okay I I like that statement but then
+that's not cons you know yeah but then
+
+ align:start position:0%
+that's not cons you know yeah but then
+ 
+
+ align:start position:0%
+that's not cons you know yeah but then
+he you know I mean
+
+ align:start position:0%
+he you know I mean
+ 
+
+ align:start position:0%
+he you know I mean
+one yeah know but he but then he this
+
+ align:start position:0%
+one yeah know but he but then he this
+ 
+
+ align:start position:0%
+one yeah know but he but then he this
+should have units of I mean I guess the
+
+ align:start position:0%
+should have units of I mean I guess the
+ 
+
+ align:start position:0%
+should have units of I mean I guess the
+the I I I agree with your statement but
+
+ align:start position:0%
+the I I I agree with your statement but
+ 
+
+ align:start position:0%
+the I I I agree with your statement but
+I also you know sort of agree with his
+
+ align:start position:0%
+I also you know sort of agree with his
+ 
+
+ align:start position:0%
+I also you know sort of agree with his
+that one over asked you know that's the
+
+ align:start position:0%
+that one over asked you know that's the
+ 
+
+ align:start position:0%
+that one over asked you know that's the
+problem is phasically yeah but I think
+
+ align:start position:0%
+problem is phasically yeah but I think
+ 
+
+ align:start position:0%
+problem is phasically yeah but I think
+that it's really that it's all you know
+
+ align:start position:0%
+that it's really that it's all you know
+ 
+
+ align:start position:0%
+that it's really that it's all you know
+it's all because everything in units of
+
+ align:start position:0%
+it's all because everything in units of
+ 
+
+ align:start position:0%
+it's all because everything in units of
+generation so it's it's really that all
+
+ align:start position:0%
+generation so it's it's really that all
+ 
+
+ align:start position:0%
+generation so it's it's really that all
+it's all unitless except for me yeah
+
+ align:start position:0%
+it's all unitless except for me yeah
+ 
+
+ align:start position:0%
+it's all unitless except for me yeah
+what I don't understand is why the how
+
+ align:start position:0%
+what I don't understand is why the how
+ 
+
+ align:start position:0%
+what I don't understand is why the how
+beneficial the mutation is should play
+
+ align:start position:0%
+beneficial the mutation is should play
+ 
+
+ align:start position:0%
+beneficial the mutation is should play
+into how yeah yeah no I agree it's this
+
+ align:start position:0%
+into how yeah yeah no I agree it's this
+ 
+
+ align:start position:0%
+into how yeah yeah no I agree it's this
+is subtle okay right so let's imagine
+
+ align:start position:0%
+is subtle okay right so let's imagine
+ 
+
+ align:start position:0%
+is subtle okay right so let's imagine
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time okay now 1 over mu is telling us um
+
+ align:start position:0%
+time okay now 1 over mu is telling us um
+ 
+
+ align:start position:0%
+time okay now 1 over mu is telling us um
+how much how how how much time there is
+
+ align:start position:0%
+how much how how how much time there is
+ 
+
+ align:start position:0%
+how much how how how much time there is
+between the initial appearance of these
+
+ align:start position:0%
+between the initial appearance of these
+ 
+
+ align:start position:0%
+between the initial appearance of these
+beneficial
+
+ align:start position:0%
+beneficial
+ 
+
+ align:start position:0%
+beneficial
+mutants right all right so here we get a
+
+ align:start position:0%
+mutants right all right so here we get a
+ 
+
+ align:start position:0%
+mutants right all right so here we get a
+beneficial
+
+ align:start position:0%
+beneficial
+ 
+
+ align:start position:0%
+beneficial
+mutation all right but what do you what
+
+ align:start position:0%
+mutation all right but what do you what
+ 
+
+ align:start position:0%
+mutation all right but what do you what
+do you think is going to happen to that
+
+ align:start position:0%
+do you think is going to happen to that
+ 
+
+ align:start position:0%
+do you think is going to happen to that
+beneficial
+
+ align:start position:0%
+beneficial
+ 
+
+ align:start position:0%
+beneficial
+mutation ah yeah that guy's dead he
+
+ align:start position:0%
+mutation ah yeah that guy's dead he
+ 
+
+ align:start position:0%
+mutation ah yeah that guy's dead he
+comes up okay all right how long do we
+
+ align:start position:0%
+comes up okay all right how long do we
+ 
+
+ align:start position:0%
+comes up okay all right how long do we
+have to wait before the next beneficial
+
+ align:start position:0%
+have to wait before the next beneficial
+ 
+
+ align:start position:0%
+have to wait before the next beneficial
+mutation one over mu is it going to be
+
+ align:start position:0%
+mutation one over mu is it going to be
+ 
+
+ align:start position:0%
+mutation one over mu is it going to be
+exactly that is it going to be peaked
+
+ align:start position:0%
+exactly that is it going to be peaked
+ 
+
+ align:start position:0%
+exactly that is it going to be peaked
+around that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right the all right verbal answer
+
+ align:start position:0%
+all right the all right verbal answer
+ 
+
+ align:start position:0%
+all right the all right verbal answer
+what is going to be the probability
+
+ align:start position:0%
+what is going to be the probability
+ 
+
+ align:start position:0%
+what is going to be the probability
+distribution between successive
+
+ align:start position:0%
+distribution between successive
+ 
+
+ align:start position:0%
+distribution between successive
+appearances of this beneficial mutation
+
+ align:start position:0%
+appearances of this beneficial mutation
+ 
+
+ align:start position:0%
+appearances of this beneficial mutation
+ready three two one exponential
+
+ align:start position:0%
+ready three two one exponential
+ 
+
+ align:start position:0%
+ready three two one exponential
+exponentially distributed okay so there
+
+ align:start position:0%
+exponentially distributed okay so there
+ 
+
+ align:start position:0%
+exponentially distributed okay so there
+might be another one that's going to
+
+ align:start position:0%
+might be another one that's going to
+ 
+
+ align:start position:0%
+might be another one that's going to
+appear here what do you think is going
+
+ align:start position:0%
+appear here what do you think is going
+ 
+
+ align:start position:0%
+appear here what do you think is going
+to happen to that guy oh he's dead yeah
+
+ align:start position:0%
+to happen to that guy oh he's dead yeah
+ 
+
+ align:start position:0%
+to happen to that guy oh he's dead yeah
+okay um all right another one okay so
+
+ align:start position:0%
+okay um all right another one okay so
+ 
+
+ align:start position:0%
+okay um all right another one okay so
+these guys are appearing at right but if
+
+ align:start position:0%
+these guys are appearing at right but if
+ 
+
+ align:start position:0%
+these guys are appearing at right but if
+if the magnitude of s is is say 02 that
+
+ align:start position:0%
+if the magnitude of s is is say 02 that
+ 
+
+ align:start position:0%
+if the magnitude of s is is say 02 that
+means we have to wait for 50 of these
+
+ align:start position:0%
+means we have to wait for 50 of these
+ 
+
+ align:start position:0%
+means we have to wait for 50 of these
+things to appear before we expect that
+
+ align:start position:0%
+things to appear before we expect that
+ 
+
+ align:start position:0%
+things to appear before we expect that
+one of them is actually going to get
+
+ align:start position:0%
+one of them is actually going to get
+ 
+
+ align:start position:0%
+one of them is actually going to get
+established and established means it
+
+ align:start position:0%
+established and established means it
+ 
+
+ align:start position:0%
+established and established means it
+gets up to one /
+
+ align:start position:0%
+gets up to one /
+ 
+
+ align:start position:0%
+gets up to one /
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so this guy once he's
+
+ align:start position:0%
+right okay so this guy once he's
+ 
+
+ align:start position:0%
+right okay so this guy once he's
+established he's going to grow
+
+ align:start position:0%
+established he's going to grow
+ 
+
+ align:start position:0%
+established he's going to grow
+exponentially in the
+
+ align:start position:0%
+exponentially in the
+ 
+
+ align:start position:0%
+exponentially in the
+population okay but the idea is that the
+
+ align:start position:0%
+population okay but the idea is that the
+ 
+
+ align:start position:0%
+population okay but the idea is that the
+time scale
+
+ align:start position:0%
+time scale
+ 
+
+ align:start position:0%
+time scale
+here of 1/ mu is the time between
+
+ align:start position:0%
+here of 1/ mu is the time between
+ 
+
+ align:start position:0%
+here of 1/ mu is the time between
+successive appearances of this
+
+ align:start position:0%
+successive appearances of this
+ 
+
+ align:start position:0%
+successive appearances of this
+beneficial mutation whereas 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ms is the time scale between successive
+
+ align:start position:0%
+Ms is the time scale between successive
+ 
+
+ align:start position:0%
+Ms is the time scale between successive
+establishments of these beneficial
+
+ align:start position:0%
+establishments of these beneficial
+ 
+
+ align:start position:0%
+establishments of these beneficial
+mutations and it's only if they get
+
+ align:start position:0%
+mutations and it's only if they get
+ 
+
+ align:start position:0%
+mutations and it's only if they get
+established that they're relevant
+
+ align:start position:0%
+established that they're relevant
+ 
+
+ align:start position:0%
+established that they're relevant
+okay so that's why what the T mutation
+
+ align:start position:0%
+okay so that's why what the T mutation
+ 
+
+ align:start position:0%
+okay so that's why what the T mutation
+established is one over
+
+ align:start position:0%
+established is one over
+ 
+
+ align:start position:0%
+established is one over
+Ms okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now no clonal interference means that
+
+ align:start position:0%
+now no clonal interference means that
+ 
+
+ align:start position:0%
+now no clonal interference means that
+one of these is larger than the other
+
+ align:start position:0%
+one of these is larger than the other
+ 
+
+ align:start position:0%
+one of these is larger than the other
+one okay which all right so which so no
+
+ align:start position:0%
+one okay which all right so which so no
+ 
+
+ align:start position:0%
+one okay which all right so which so no
+clonal interference means is it a this
+
+ align:start position:0%
+clonal interference means is it a this
+ 
+
+ align:start position:0%
+clonal interference means is it a this
+guy is larger or B this guy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+larger okay this is larger question mark
+
+ align:start position:0%
+larger okay this is larger question mark
+ 
+
+ align:start position:0%
+larger okay this is larger question mark
+this one that one right think about this
+
+ align:start position:0%
+this one that one right think about this
+ 
+
+ align:start position:0%
+this one that one right think about this
+for 15 seconds just to make sure that
+
+ align:start position:0%
+for 15 seconds just to make sure that
+ 
+
+ align:start position:0%
+for 15 seconds just to make sure that
+we're right make sure we're asking if
+
+ align:start position:0%
+we're right make sure we're asking if
+ 
+
+ align:start position:0%
+we're right make sure we're asking if
+there's no clonal inference it means
+
+ align:start position:0%
+there's no clonal inference it means
+ 
+
+ align:start position:0%
+there's no clonal inference it means
+that one of these is much larger than
+
+ align:start position:0%
+that one of these is much larger than
+ 
+
+ align:start position:0%
+that one of these is much larger than
+the other one which one okay ready 3 2
+
+ align:start position:0%
+the other one which one okay ready 3 2
+ 
+
+ align:start position:0%
+the other one which one okay ready 3 2
+1 okay it means that this thing is much
+
+ align:start position:0%
+1 okay it means that this thing is much
+ 
+
+ align:start position:0%
+1 okay it means that this thing is much
+larger than this one
+
+ align:start position:0%
+larger than this one
+ 
+
+ align:start position:0%
+larger than this one
+right so this thing has to be much
+
+ align:start position:0%
+right so this thing has to be much
+ 
+
+ align:start position:0%
+right so this thing has to be much
+larger
+
+ align:start position:0%
+larger
+ 
+
+ align:start position:0%
+larger
+than t t established to
+
+ align:start position:0%
+than t t established to
+ 
+
+ align:start position:0%
+than t t established to
+fix okay right because if it's the case
+
+ align:start position:0%
+fix okay right because if it's the case
+ 
+
+ align:start position:0%
+fix okay right because if it's the case
+this time scale is very large compared
+
+ align:start position:0%
+this time scale is very large compared
+ 
+
+ align:start position:0%
+this time scale is very large compared
+to this time scale of spreading then the
+
+ align:start position:0%
+to this time scale of spreading then the
+ 
+
+ align:start position:0%
+to this time scale of spreading then the
+patients don't ever uh clonally
+
+ align:start position:0%
+patients don't ever uh clonally
+ 
+
+ align:start position:0%
+patients don't ever uh clonally
+interfere
+
+ align:start position:0%
+interfere
+ 
+
+ align:start position:0%
+interfere
+okay I think it's very important that
+
+ align:start position:0%
+okay I think it's very important that
+ 
+
+ align:start position:0%
+okay I think it's very important that
+you uh can reconstruct this whole
+
+ align:start position:0%
+you uh can reconstruct this whole
+ 
+
+ align:start position:0%
+you uh can reconstruct this whole
+argument because
+
+ align:start position:0%
+argument because
+ 
+
+ align:start position:0%
+argument because
+it has all the ingredients of the
+
+ align:start position:0%
+it has all the ingredients of the
+ 
+
+ align:start position:0%
+it has all the ingredients of the
+Dynamics in terms of
+
+ align:start position:0%
+Dynamics in terms of
+ 
+
+ align:start position:0%
+Dynamics in terms of
+stochastic uh and then uh deterministic
+
+ align:start position:0%
+stochastic uh and then uh deterministic
+ 
+
+ align:start position:0%
+stochastic uh and then uh deterministic
+and and you know so uh if if you if you
+
+ align:start position:0%
+and and you know so uh if if you if you
+ 
+
+ align:start position:0%
+and and you know so uh if if you if you
+find this stuff confusing please uh go
+
+ align:start position:0%
+find this stuff confusing please uh go
+ 
+
+ align:start position:0%
+find this stuff confusing please uh go
+through it with a friend or uh come to
+
+ align:start position:0%
+through it with a friend or uh come to
+ 
+
+ align:start position:0%
+through it with a friend or uh come to
+me after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class all right so what U what we want
+
+ align:start position:0%
+class all right so what U what we want
+ 
+
+ align:start position:0%
+class all right so what U what we want
+to do for the last 20 minutes is then uh
+
+ align:start position:0%
+to do for the last 20 minutes is then uh
+ 
+
+ align:start position:0%
+to do for the last 20 minutes is then uh
+is talk about Roy's paper Okay um and I
+
+ align:start position:0%
+is talk about Roy's paper Okay um and I
+ 
+
+ align:start position:0%
+is talk about Roy's paper Okay um and I
+I think that this this paper is is
+
+ align:start position:0%
+I think that this this paper is is
+ 
+
+ align:start position:0%
+I think that this this paper is is
+interesting and and um subtle it's a
+
+ align:start position:0%
+interesting and and um subtle it's a
+ 
+
+ align:start position:0%
+interesting and and um subtle it's a
+little bit hard to tell how much of it
+
+ align:start position:0%
+little bit hard to tell how much of it
+ 
+
+ align:start position:0%
+little bit hard to tell how much of it
+is uh is an experimental kind of
+
+ align:start position:0%
+is uh is an experimental kind of
+ 
+
+ align:start position:0%
+is uh is an experimental kind of
+straightup demonstration or how much of
+
+ align:start position:0%
+straightup demonstration or how much of
+ 
+
+ align:start position:0%
+straightup demonstration or how much of
+it is that it's just a way of getting
+
+ align:start position:0%
+it is that it's just a way of getting
+ 
+
+ align:start position:0%
+it is that it's just a way of getting
+you to think new thoughts I um it's
+
+ align:start position:0%
+you to think new thoughts I um it's
+ 
+
+ align:start position:0%
+you to think new thoughts I um it's
+certainly is a way to get you to think
+
+ align:start position:0%
+certainly is a way to get you to think
+ 
+
+ align:start position:0%
+certainly is a way to get you to think
+new thoughts at least it very much got I
+
+ align:start position:0%
+new thoughts at least it very much got I
+ 
+
+ align:start position:0%
+new thoughts at least it very much got I
+I felt that it had that effect on me and
+
+ align:start position:0%
+I felt that it had that effect on me and
+ 
+
+ align:start position:0%
+I felt that it had that effect on me and
+that um I you know after reading it I
+
+ align:start position:0%
+that um I you know after reading it I
+ 
+
+ align:start position:0%
+that um I you know after reading it I
+kind I just got you know very excited
+
+ align:start position:0%
+kind I just got you know very excited
+ 
+
+ align:start position:0%
+kind I just got you know very excited
+about all the Dynamics that we at play
+
+ align:start position:0%
+about all the Dynamics that we at play
+ 
+
+ align:start position:0%
+about all the Dynamics that we at play
+here and how I you know out of the
+
+ align:start position:0%
+here and how I you know out of the
+ 
+
+ align:start position:0%
+here and how I you know out of the
+complexity of this colonial interference
+
+ align:start position:0%
+complexity of this colonial interference
+ 
+
+ align:start position:0%
+complexity of this colonial interference
+process maybe in some cases there might
+
+ align:start position:0%
+process maybe in some cases there might
+ 
+
+ align:start position:0%
+process maybe in some cases there might
+be some uh even simpler phenomenological
+
+ align:start position:0%
+be some uh even simpler phenomenological
+ 
+
+ align:start position:0%
+be some uh even simpler phenomenological
+type description of what was going on uh
+
+ align:start position:0%
+type description of what was going on uh
+ 
+
+ align:start position:0%
+type description of what was going on uh
+but I think that what is very
+
+ align:start position:0%
+but I think that what is very
+ 
+
+ align:start position:0%
+but I think that what is very
+interesting about that paper is this
+
+ align:start position:0%
+interesting about that paper is this
+ 
+
+ align:start position:0%
+interesting about that paper is this
+idea that what they really wanted to
+
+ align:start position:0%
+idea that what they really wanted to
+ 
+
+ align:start position:0%
+idea that what they really wanted to
+measure was this probability
+
+ align:start position:0%
+measure was this probability
+ 
+
+ align:start position:0%
+measure was this probability
+distribution of beneficial mutations
+
+ align:start position:0%
+distribution of beneficial mutations
+ 
+
+ align:start position:0%
+distribution of beneficial mutations
+okay so what we mean by that is that
+
+ align:start position:0%
+okay so what we mean by that is that
+ 
+
+ align:start position:0%
+okay so what we mean by that is that
+different beneficial mutations will have
+
+ align:start position:0%
+different beneficial mutations will have
+ 
+
+ align:start position:0%
+different beneficial mutations will have
+different effects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and in particular you can imagine
+
+ align:start position:0%
+right and in particular you can imagine
+ 
+
+ align:start position:0%
+right and in particular you can imagine
+a thought experiment where you take any
+
+ align:start position:0%
+a thought experiment where you take any
+ 
+
+ align:start position:0%
+a thought experiment where you take any
+ecoli cell uh how um how big is thecoli
+
+ align:start position:0%
+ecoli cell uh how um how big is thecoli
+ 
+
+ align:start position:0%
+ecoli cell uh how um how big is thecoli
+genome roughly um this is an just like
+
+ align:start position:0%
+genome roughly um this is an just like
+ 
+
+ align:start position:0%
+genome roughly um this is an just like
+it's always good to have guide posts for
+
+ align:start position:0%
+it's always good to have guide posts for
+ 
+
+ align:start position:0%
+it's always good to have guide posts for
+how long ago things happened it's also
+
+ align:start position:0%
+how long ago things happened it's also
+ 
+
+ align:start position:0%
+how long ago things happened it's also
+good to have guide posts for things like
+
+ align:start position:0%
+good to have guide posts for things like
+ 
+
+ align:start position:0%
+good to have guide posts for things like
+a just good to have a few genome sizes
+
+ align:start position:0%
+a just good to have a few genome sizes
+ 
+
+ align:start position:0%
+a just good to have a few genome sizes
+kind of memorized right uh yeah does
+
+ align:start position:0%
+kind of memorized right uh yeah does
+ 
+
+ align:start position:0%
+kind of memorized right uh yeah does
+anybody know the coli
+
+ align:start position:0%
+anybody know the coli
+ 
+
+ align:start position:0%
+anybody know the coli
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+genome 2,000 base
+
+ align:start position:0%
+genome 2,000 base
+ 
+
+ align:start position:0%
+genome 2,000 base
+pairs okay no no I just want to make
+
+ align:start position:0%
+pairs okay no no I just want to make
+ 
+
+ align:start position:0%
+pairs okay no no I just want to make
+sure that we're uh yeah yeah okay so
+
+ align:start position:0%
+sure that we're uh yeah yeah okay so
+ 
+
+ align:start position:0%
+sure that we're uh yeah yeah okay so
+yeah it's a bit more than that but yeah
+
+ align:start position:0%
+yeah it's a bit more than that but yeah
+ 
+
+ align:start position:0%
+yeah it's a bit more than that but yeah
+so it's um it's a it's a few million
+
+ align:start position:0%
+so it's um it's a it's a few million
+ 
+
+ align:start position:0%
+so it's um it's a it's a few million
+base pairs right three or four depending
+
+ align:start position:0%
+base pairs right three or four depending
+ 
+
+ align:start position:0%
+base pairs right three or four depending
+on the strain okay but you can imagine a
+
+ align:start position:0%
+on the strain okay but you can imagine a
+ 
+
+ align:start position:0%
+on the strain okay but you can imagine a
+thought experiment where you go in and
+
+ align:start position:0%
+thought experiment where you go in and
+ 
+
+ align:start position:0%
+thought experiment where you go in and
+for at every base pair you make um you
+
+ align:start position:0%
+for at every base pair you make um you
+ 
+
+ align:start position:0%
+for at every base pair you make um you
+make the three possible point mutations
+
+ align:start position:0%
+make the three possible point mutations
+ 
+
+ align:start position:0%
+make the three possible point mutations
+okay so then you can imagine having 10
+
+ align:start position:0%
+okay so then you can imagine having 10
+ 
+
+ align:start position:0%
+okay so then you can imagine having 10
+million different strains that are each
+
+ align:start position:0%
+million different strains that are each
+ 
+
+ align:start position:0%
+million different strains that are each
+different at one site okay and then what
+
+ align:start position:0%
+different at one site okay and then what
+ 
+
+ align:start position:0%
+different at one site okay and then what
+we can do is we can plot
+
+ align:start position:0%
+we can do is we can plot
+ 
+
+ align:start position:0%
+we can do is we can plot
+the the rate of population growth in
+
+ align:start position:0%
+the the rate of population growth in
+ 
+
+ align:start position:0%
+the the rate of population growth in
+some environment right so this is
+
+ align:start position:0%
+some environment right so this is
+ 
+
+ align:start position:0%
+some environment right so this is
+gamma it's the 1/ N DN
+
+ align:start position:0%
+gamma it's the 1/ N DN
+ 
+
+ align:start position:0%
+gamma it's the 1/ N DN
+DT you know basically division rate
+
+ align:start position:0%
+DT you know basically division rate
+ 
+
+ align:start position:0%
+DT you know basically division rate
+normalized
+
+ align:start position:0%
+normalized
+ 
+
+ align:start position:0%
+normalized
+by um the Y type division right okay I'm
+
+ align:start position:0%
+by um the Y type division right okay I'm
+ 
+
+ align:start position:0%
+by um the Y type division right okay I'm
+sorry I'm that's supposed to be down
+
+ align:start position:0%
+sorry I'm that's supposed to be down
+ 
+
+ align:start position:0%
+sorry I'm that's supposed to be down
+there so this is this is gamma U over
+
+ align:start position:0%
+there so this is this is gamma U over
+ 
+
+ align:start position:0%
+there so this is this is gamma U over
+gamma of wild type and this could be you
+
+ align:start position:0%
+gamma of wild type and this could be you
+ 
+
+ align:start position:0%
+gamma of wild type and this could be you
+know eoli
+
+ align:start position:0%
+know eoli
+ 
+
+ align:start position:0%
+know eoli
+in lb or minimal Media or you know at
+
+ align:start position:0%
+in lb or minimal Media or you know at
+ 
+
+ align:start position:0%
+in lb or minimal Media or you know at
+30C pick some reasonable environment
+
+ align:start position:0%
+30C pick some reasonable environment
+ 
+
+ align:start position:0%
+30C pick some reasonable environment
+okay the question is if you draw the
+
+ align:start position:0%
+okay the question is if you draw the
+ 
+
+ align:start position:0%
+okay the question is if you draw the
+histogram of what this thing should look
+
+ align:start position:0%
+histogram of what this thing should look
+ 
+
+ align:start position:0%
+histogram of what this thing should look
+like you know what should it
+
+ align:start position:0%
+like you know what should it
+ 
+
+ align:start position:0%
+like you know what should it
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now what I'm going to ask you
+
+ align:start position:0%
+all right now what I'm going to ask you
+ 
+
+ align:start position:0%
+all right now what I'm going to ask you
+to do is in 30
+
+ align:start position:0%
+to do is in 30
+ 
+
+ align:start position:0%
+to do is in 30
+seconds draw something on your sheet of
+
+ align:start position:0%
+seconds draw something on your sheet of
+ 
+
+ align:start position:0%
+seconds draw something on your sheet of
+paper right so this is this is what I'm
+
+ align:start position:0%
+paper right so this is this is what I'm
+ 
+
+ align:start position:0%
+paper right so this is this is what I'm
+this I'm trying this is supposed to be a
+
+ align:start position:0%
+this I'm trying this is supposed to be a
+ 
+
+ align:start position:0%
+this I'm trying this is supposed to be a
+frequency or a
+
+ align:start position:0%
+frequency or a
+ 
+
+ align:start position:0%
+frequency or a
+histogram over those 10 million m point
+
+ align:start position:0%
+histogram over those 10 million m point
+ 
+
+ align:start position:0%
+histogram over those 10 million m point
+point mutations right so we haven't
+
+ align:start position:0%
+point mutations right so we haven't
+ 
+
+ align:start position:0%
+point mutations right so we haven't
+actually done this experiment but I
+
+ align:start position:0%
+actually done this experiment but I
+ 
+
+ align:start position:0%
+actually done this experiment but I
+think it's um people have been doing
+
+ align:start position:0%
+think it's um people have been doing
+ 
+
+ align:start position:0%
+think it's um people have been doing
+some they actually we have made all
+
+ align:start position:0%
+some they actually we have made all
+ 
+
+ align:start position:0%
+some they actually we have made all
+possible Gene Knockouts in in uh in eoli
+
+ align:start position:0%
+possible Gene Knockouts in in uh in eoli
+ 
+
+ align:start position:0%
+possible Gene Knockouts in in uh in eoli
+so removing each of each of the genes
+
+ align:start position:0%
+so removing each of each of the genes
+ 
+
+ align:start position:0%
+so removing each of each of the genes
+right U and we've we've done that in in
+
+ align:start position:0%
+right U and we've we've done that in in
+ 
+
+ align:start position:0%
+right U and we've we've done that in in
+eoli we've done it in yeast and indeed
+
+ align:start position:0%
+eoli we've done it in yeast and indeed
+ 
+
+ align:start position:0%
+eoli we've done it in yeast and indeed
+in yeast they're actually making and
+
+ align:start position:0%
+in yeast they're actually making and
+ 
+
+ align:start position:0%
+in yeast they're actually making and
+measuring the division rate for all
+
+ align:start position:0%
+measuring the division rate for all
+ 
+
+ align:start position:0%
+measuring the division rate for all
+pairwise
+
+ align:start position:0%
+pairwise
+ 
+
+ align:start position:0%
+pairwise
+Knockouts right so the their their some
+
+ align:start position:0%
+Knockouts right so the their their some
+ 
+
+ align:start position:0%
+Knockouts right so the their their some
+fraction of the way through they
+
+ align:start position:0%
+fraction of the way through they
+ 
+
+ align:start position:0%
+fraction of the way through they
+published their first 10 million
+
+ align:start position:0%
+published their first 10 million
+ 
+
+ align:start position:0%
+published their first 10 million
+measurements for the division rate of
+
+ align:start position:0%
+measurements for the division rate of
+ 
+
+ align:start position:0%
+measurements for the division rate of
+The pairwise Knockouts in East Charlie
+
+ align:start position:0%
+The pairwise Knockouts in East Charlie
+ 
+
+ align:start position:0%
+The pairwise Knockouts in East Charlie
+Boon at Toronto it's an amazing data set
+
+ align:start position:0%
+Boon at Toronto it's an amazing data set
+ 
+
+ align:start position:0%
+Boon at Toronto it's an amazing data set
+okay but right this is a sorry this is a
+
+ align:start position:0%
+okay but right this is a sorry this is a
+ 
+
+ align:start position:0%
+okay but right this is a sorry this is a
+simpler one right so this is just if we
+
+ align:start position:0%
+simpler one right so this is just if we
+ 
+
+ align:start position:0%
+simpler one right so this is just if we
+make a histogram of the growth rate of
+
+ align:start position:0%
+make a histogram of the growth rate of
+ 
+
+ align:start position:0%
+make a histogram of the growth rate of
+eoli all possible all 10 million
+
+ align:start position:0%
+eoli all possible all 10 million
+ 
+
+ align:start position:0%
+eoli all possible all 10 million
+possible point mutations in equal what
+
+ align:start position:0%
+possible point mutations in equal what
+ 
+
+ align:start position:0%
+possible point mutations in equal what
+do you think it's going to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like all right and I'm going to come by
+
+ align:start position:0%
+like all right and I'm going to come by
+ 
+
+ align:start position:0%
+like all right and I'm going to come by
+and if I don't see a distribution drawn
+
+ align:start position:0%
+and if I don't see a distribution drawn
+ 
+
+ align:start position:0%
+and if I don't see a distribution drawn
+on your sheet of paper then you can um
+
+ align:start position:0%
+on your sheet of paper then you can um
+ 
+
+ align:start position:0%
+on your sheet of paper then you can um
+you you'll get to draw it up here on the
+
+ align:start position:0%
+you you'll get to draw it up here on the
+ 
+
+ align:start position:0%
+you you'll get to draw it up here on the
+board for
+
+ align:start position:0%
+board for
+ 
+
+ align:start position:0%
+board for
+all of us okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um totally a distribution okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right yeah what I find
+
+ align:start position:0%
+right all right yeah what I find
+ 
+
+ align:start position:0%
+right all right yeah what I find
+interesting about this exercise is that
+
+ align:start position:0%
+interesting about this exercise is that
+ 
+
+ align:start position:0%
+interesting about this exercise is that
+you get uh all possible
+
+ align:start position:0%
+you get uh all possible
+ 
+
+ align:start position:0%
+you get uh all possible
+distributions which is um no but it's
+
+ align:start position:0%
+distributions which is um no but it's
+ 
+
+ align:start position:0%
+distributions which is um no but it's
+funny because it's it's like a super
+
+ align:start position:0%
+funny because it's it's like a super
+ 
+
+ align:start position:0%
+funny because it's it's like a super
+basic question right um and somehow we
+
+ align:start position:0%
+basic question right um and somehow we
+ 
+
+ align:start position:0%
+basic question right um and somehow we
+don't necessarily think about it or
+
+ align:start position:0%
+don't necessarily think about it or
+ 
+
+ align:start position:0%
+don't necessarily think about it or
+whatnot right um all right can somebody
+
+ align:start position:0%
+whatnot right um all right can somebody
+ 
+
+ align:start position:0%
+whatnot right um all right can somebody
+throw out kind of what they think maybe
+
+ align:start position:0%
+throw out kind of what they think maybe
+ 
+
+ align:start position:0%
+throw out kind of what they think maybe
+should be going on
+
+ align:start position:0%
+should be going on
+ 
+
+ align:start position:0%
+should be going on
+yeah large
+
+ align:start position:0%
+yeah large
+ 
+
+ align:start position:0%
+yeah large
+Z okay right so it could be just
+
+ align:start position:0%
+Z okay right so it could be just
+ 
+
+ align:start position:0%
+Z okay right so it could be just
+that all right so it could be that
+
+ align:start position:0%
+that all right so it could be that
+ 
+
+ align:start position:0%
+that all right so it could be that
+they're all
+
+ align:start position:0%
+they're all
+ 
+
+ align:start position:0%
+they're all
+here you know most
+
+ align:start position:0%
+here you know most
+ 
+
+ align:start position:0%
+here you know most
+will large
+
+ align:start position:0%
+will large
+ 
+
+ align:start position:0%
+will large
+Frac right so it could be that a large
+
+ align:start position:0%
+Frac right so it could be that a large
+ 
+
+ align:start position:0%
+Frac right so it could be that a large
+fraction of these point mutations and
+
+ align:start position:0%
+fraction of these point mutations and
+ 
+
+ align:start position:0%
+fraction of these point mutations and
+the cell is just dead right yeah so this
+
+ align:start position:0%
+the cell is just dead right yeah so this
+ 
+
+ align:start position:0%
+the cell is just dead right yeah so this
+is this is what you call a pessimistic
+
+ align:start position:0%
+is this is what you call a pessimistic
+ 
+
+ align:start position:0%
+is this is what you call a pessimistic
+view of nature or of life you know he
+
+ align:start position:0%
+view of nature or of life you know he
+ 
+
+ align:start position:0%
+view of nature or of life you know he
+has trouble crossing the street because
+
+ align:start position:0%
+has trouble crossing the street because
+ 
+
+ align:start position:0%
+has trouble crossing the street because
+he's never sure you yeah what do you
+
+ align:start position:0%
+he's never sure you yeah what do you
+ 
+
+ align:start position:0%
+he's never sure you yeah what do you
+think I would actually think that
+
+ align:start position:0%
+think I would actually think that
+ 
+
+ align:start position:0%
+think I would actually think that
+there's a much larger traction where all
+
+ align:start position:0%
+there's a much larger traction where all
+ 
+
+ align:start position:0%
+there's a much larger traction where all
+of where it's exactly the same you've
+
+ align:start position:0%
+of where it's exactly the same you've
+ 
+
+ align:start position:0%
+of where it's exactly the same you've
+got a lot of Prim mutations that are
+
+ align:start position:0%
+got a lot of Prim mutations that are
+ 
+
+ align:start position:0%
+got a lot of Prim mutations that are
+just substitutions of yeah okay so lots
+
+ align:start position:0%
+just substitutions of yeah okay so lots
+ 
+
+ align:start position:0%
+just substitutions of yeah okay so lots
+of them maybe okay so may all right so
+
+ align:start position:0%
+of them maybe okay so may all right so
+ 
+
+ align:start position:0%
+of them maybe okay so may all right so
+all right so these are the two polar
+
+ align:start position:0%
+all right so these are the two polar
+ 
+
+ align:start position:0%
+all right so these are the two polar
+views of the world right that nothing
+
+ align:start position:0%
+views of the world right that nothing
+ 
+
+ align:start position:0%
+views of the world right that nothing
+matters or you're all dead
+
+ align:start position:0%
+matters or you're all dead
+ 
+
+ align:start position:0%
+matters or you're all dead
+um I think you can reconcile them I
+
+ align:start position:0%
+um I think you can reconcile them I
+ 
+
+ align:start position:0%
+um I think you can reconcile them I
+think you can say okay well now now I
+
+ align:start position:0%
+think you can say okay well now now I
+ 
+
+ align:start position:0%
+think you can say okay well now now I
+think you're being too uh how how we
+
+ align:start position:0%
+think you're being too uh how how we
+ 
+
+ align:start position:0%
+think you're being too uh how how we
+reconcile them so we know that there's
+
+ align:start position:0%
+reconcile them so we know that there's
+ 
+
+ align:start position:0%
+reconcile them so we know that there's
+the thiras right sure and so there's
+
+ align:start position:0%
+the thiras right sure and so there's
+ 
+
+ align:start position:0%
+the thiras right sure and so there's
+probably like at least one third of them
+
+ align:start position:0%
+probably like at least one third of them
+ 
+
+ align:start position:0%
+probably like at least one third of them
+where it just doesn't matter at all
+
+ align:start position:0%
+where it just doesn't matter at all
+ 
+
+ align:start position:0%
+where it just doesn't matter at all
+the same get the same code yeah yeah um
+
+ align:start position:0%
+the same get the same code yeah yeah um
+ 
+
+ align:start position:0%
+the same get the same code yeah yeah um
+although there are cases actually where
+
+ align:start position:0%
+although there are cases actually where
+ 
+
+ align:start position:0%
+although there are cases actually where
+even silent mutations end up changing
+
+ align:start position:0%
+even silent mutations end up changing
+ 
+
+ align:start position:0%
+even silent mutations end up changing
+protein expression level but yeah no
+
+ align:start position:0%
+protein expression level but yeah no
+ 
+
+ align:start position:0%
+protein expression level but yeah no
+right it's it I don't know if this
+
+ align:start position:0%
+right it's it I don't know if this
+ 
+
+ align:start position:0%
+right it's it I don't know if this
+reconciles the two views of the world
+
+ align:start position:0%
+reconciles the two views of the world
+ 
+
+ align:start position:0%
+reconciles the two views of the world
+but um right you know and then I'd say
+
+ align:start position:0%
+but um right you know and then I'd say
+ 
+
+ align:start position:0%
+but um right you know and then I'd say
+um you know and then some right so some
+
+ align:start position:0%
+um you know and then some right so some
+ 
+
+ align:start position:0%
+um you know and then some right so some
+people have drawn
+
+ align:start position:0%
+people have drawn
+ 
+
+ align:start position:0%
+people have drawn
+um you know things that look like this
+
+ align:start position:0%
+um you know things that look like this
+ 
+
+ align:start position:0%
+um you know things that look like this
+some or some people have drawn things
+
+ align:start position:0%
+some or some people have drawn things
+ 
+
+ align:start position:0%
+some or some people have drawn things
+that look like this sometime yeah so I'd
+
+ align:start position:0%
+that look like this sometime yeah so I'd
+ 
+
+ align:start position:0%
+that look like this sometime yeah so I'd
+say we have and we have a uniform
+
+ align:start position:0%
+say we have and we have a uniform
+ 
+
+ align:start position:0%
+say we have and we have a uniform
+distribution um you know if you're going
+
+ align:start position:0%
+distribution um you know if you're going
+ 
+
+ align:start position:0%
+distribution um you know if you're going
+to if you're going to make a null model
+
+ align:start position:0%
+to if you're going to make a null model
+ 
+
+ align:start position:0%
+to if you're going to make a null model
+I mean you I don't know okay right so
+
+ align:start position:0%
+I mean you I don't know okay right so
+ 
+
+ align:start position:0%
+I mean you I don't know okay right so
+IID say we we have enough information to
+
+ align:start position:0%
+IID say we we have enough information to
+ 
+
+ align:start position:0%
+IID say we we have enough information to
+say that something about what this thing
+
+ align:start position:0%
+say that something about what this thing
+ 
+
+ align:start position:0%
+say that something about what this thing
+should look like okay um right so first
+
+ align:start position:0%
+should look like okay um right so first
+ 
+
+ align:start position:0%
+should look like okay um right so first
+of all um you know some fraction of
+
+ align:start position:0%
+of all um you know some fraction of
+ 
+
+ align:start position:0%
+of all um you know some fraction of
+genes are indeed essential so you know
+
+ align:start position:0%
+genes are indeed essential so you know
+ 
+
+ align:start position:0%
+genes are indeed essential so you know
+we know that if you remove you know 10
+
+ align:start position:0%
+we know that if you remove you know 10
+ 
+
+ align:start position:0%
+we know that if you remove you know 10
+20% of Gene you know for 10 or to 20% of
+
+ align:start position:0%
+20% of Gene you know for 10 or to 20% of
+ 
+
+ align:start position:0%
+20% of Gene you know for 10 or to 20% of
+the genes if you remove it the cell is
+
+ align:start position:0%
+the genes if you remove it the cell is
+ 
+
+ align:start position:0%
+the genes if you remove it the cell is
+dead okay that doesn't mean that 10 to
+
+ align:start position:0%
+dead okay that doesn't mean that 10 to
+ 
+
+ align:start position:0%
+dead okay that doesn't mean that 10 to
+20% of point mutations will lead to a
+
+ align:start position:0%
+20% of point mutations will lead to a
+ 
+
+ align:start position:0%
+20% of point mutations will lead to a
+lethal U lethal phenotype but it means
+
+ align:start position:0%
+lethal U lethal phenotype but it means
+ 
+
+ align:start position:0%
+lethal U lethal phenotype but it means
+that if you if you do um inactivate or
+
+ align:start position:0%
+that if you if you do um inactivate or
+ 
+
+ align:start position:0%
+that if you if you do um inactivate or
+knock out that uh Gene then it will be
+
+ align:start position:0%
+knock out that uh Gene then it will be
+ 
+
+ align:start position:0%
+knock out that uh Gene then it will be
+lethal okay so that means that there are
+
+ align:start position:0%
+lethal okay so that means that there are
+ 
+
+ align:start position:0%
+lethal okay so that means that there are
+indeed some set
+
+ align:start position:0%
+indeed some set
+ 
+
+ align:start position:0%
+indeed some set
+of U these point mutations that are
+
+ align:start position:0%
+of U these point mutations that are
+ 
+
+ align:start position:0%
+of U these point mutations that are
+going to be lethal but it's going to
+
+ align:start position:0%
+going to be lethal but it's going to
+ 
+
+ align:start position:0%
+going to be lethal but it's going to
+be small I you know I and I I don't know
+
+ align:start position:0%
+be small I you know I and I I don't know
+ 
+
+ align:start position:0%
+be small I you know I and I I don't know
+what the actual number would be but you
+
+ align:start position:0%
+what the actual number would be but you
+ 
+
+ align:start position:0%
+what the actual number would be but you
+know maybe 1 and 10 to
+
+ align:start position:0%
+know maybe 1 and 10 to
+ 
+
+ align:start position:0%
+know maybe 1 and 10 to
+the four
+
+ align:start position:0%
+the four
+ 
+
+ align:start position:0%
+the four
+something something small right because
+
+ align:start position:0%
+something something small right because
+ 
+
+ align:start position:0%
+something something small right because
+it might you know because it's probably
+
+ align:start position:0%
+it might you know because it's probably
+ 
+
+ align:start position:0%
+it might you know because it's probably
+only 10% of the locations on the gene
+
+ align:start position:0%
+only 10% of the locations on the gene
+ 
+
+ align:start position:0%
+only 10% of the locations on the gene
+would actually knock it out okay I'm
+
+ align:start position:0%
+would actually knock it out okay I'm
+ 
+
+ align:start position:0%
+would actually knock it out okay I'm
+making up that number uh the pro the
+
+ align:start position:0%
+making up that number uh the pro the
+ 
+
+ align:start position:0%
+making up that number uh the pro the
+protein guys would have a much better
+
+ align:start position:0%
+protein guys would have a much better
+ 
+
+ align:start position:0%
+protein guys would have a much better
+sense but it's going to be it's going to
+
+ align:start position:0%
+sense but it's going to be it's going to
+ 
+
+ align:start position:0%
+sense but it's going to be it's going to
+be a small number it might only be 1% of
+
+ align:start position:0%
+be a small number it might only be 1% of
+ 
+
+ align:start position:0%
+be a small number it might only be 1% of
+the mutations actually would actually
+
+ align:start position:0%
+the mutations actually would actually
+ 
+
+ align:start position:0%
+the mutations actually would actually
+would actually knock out function of the
+
+ align:start position:0%
+would actually knock out function of the
+ 
+
+ align:start position:0%
+would actually knock out function of the
+protein right and then um not all of the
+
+ align:start position:0%
+protein right and then um not all of the
+ 
+
+ align:start position:0%
+protein right and then um not all of the
+genome actually codes for proteins right
+
+ align:start position:0%
+genome actually codes for proteins right
+ 
+
+ align:start position:0%
+genome actually codes for proteins right
+so you start multiplying small numbers
+
+ align:start position:0%
+so you start multiplying small numbers
+ 
+
+ align:start position:0%
+so you start multiplying small numbers
+together and you get something that's
+
+ align:start position:0%
+together and you get something that's
+ 
+
+ align:start position:0%
+together and you get something that's
+rather small but there but there will be
+
+ align:start position:0%
+rather small but there but there will be
+ 
+
+ align:start position:0%
+rather small but there but there will be
+some number mutations there uh however
+
+ align:start position:0%
+some number mutations there uh however
+ 
+
+ align:start position:0%
+some number mutations there uh however
+the vast majority of mutations will have
+
+ align:start position:0%
+the vast majority of mutations will have
+ 
+
+ align:start position:0%
+the vast majority of mutations will have
+no measurable Fitness effect okay so
+
+ align:start position:0%
+no measurable Fitness effect okay so
+ 
+
+ align:start position:0%
+no measurable Fitness effect okay so
+indeed this thing kind of Peaks
+
+ align:start position:0%
+indeed this thing kind of Peaks
+ 
+
+ align:start position:0%
+indeed this thing kind of Peaks
+here um and and then rather sharply
+
+ align:start position:0%
+here um and and then rather sharply
+ 
+
+ align:start position:0%
+here um and and then rather sharply
+comes down this is on a linear scale or
+
+ align:start position:0%
+comes down this is on a linear scale or
+ 
+
+ align:start position:0%
+comes down this is on a linear scale or
+something like that right so the width
+
+ align:start position:0%
+something like that right so the width
+ 
+
+ align:start position:0%
+something like that right so the width
+might indeed be you know a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+percent um but actually you know
+
+ align:start position:0%
+percent um but actually you know
+ 
+
+ align:start position:0%
+percent um but actually you know
+probably even less maybe 1% or half you
+
+ align:start position:0%
+probably even less maybe 1% or half you
+ 
+
+ align:start position:0%
+probably even less maybe 1% or half you
+know something small
+
+ align:start position:0%
+know something small
+ 
+
+ align:start position:0%
+know something small
+yeah howed is yeah uh so it's on a
+
+ align:start position:0%
+yeah howed is yeah uh so it's on a
+ 
+
+ align:start position:0%
+yeah howed is yeah uh so it's on a
+linear scale it doesn't look skewed on a
+
+ align:start position:0%
+linear scale it doesn't look skewed on a
+ 
+
+ align:start position:0%
+linear scale it doesn't look skewed on a
+log scale I think it does I mean the
+
+ align:start position:0%
+log scale I think it does I mean the
+ 
+
+ align:start position:0%
+log scale I think it does I mean the
+sense if if you um if you plot log
+
+ align:start position:0%
+sense if if you um if you plot log
+ 
+
+ align:start position:0%
+sense if if you um if you plot log
+frequency on this axis then there's a
+
+ align:start position:0%
+frequency on this axis then there's a
+ 
+
+ align:start position:0%
+frequency on this axis then there's a
+longer tail on the left than on the
+
+ align:start position:0%
+longer tail on the left than on the
+ 
+
+ align:start position:0%
+longer tail on the left than on the
+right but I'd say on a linear scale it's
+
+ align:start position:0%
+right but I'd say on a linear scale it's
+ 
+
+ align:start position:0%
+right but I'd say on a linear scale it's
+it's just pretty sharp function there so
+
+ align:start position:0%
+it's just pretty sharp function there so
+ 
+
+ align:start position:0%
+it's just pretty sharp function there so
+people have measured that all right so
+
+ align:start position:0%
+people have measured that all right so
+ 
+
+ align:start position:0%
+people have measured that all right so
+people have measured certainly for all
+
+ align:start position:0%
+people have measured certainly for all
+ 
+
+ align:start position:0%
+people have measured certainly for all
+the gene Knockouts we've we have
+
+ align:start position:0%
+the gene Knockouts we've we have
+ 
+
+ align:start position:0%
+the gene Knockouts we've we have
+measured this and that's that's things
+
+ align:start position:0%
+measured this and that's that's things
+ 
+
+ align:start position:0%
+measured this and that's that's things
+even that distribution is is sharply
+
+ align:start position:0%
+even that distribution is is sharply
+ 
+
+ align:start position:0%
+even that distribution is is sharply
+right so the point mutation distribution
+
+ align:start position:0%
+right so the point mutation distribution
+ 
+
+ align:start position:0%
+right so the point mutation distribution
+is going to be even more even more Ely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak yeah yeah so so for most genes at
+
+ align:start position:0%
+Peak yeah yeah so so for most genes at
+ 
+
+ align:start position:0%
+Peak yeah yeah so so for most genes at
+least in many environments right and of
+
+ align:start position:0%
+least in many environments right and of
+ 
+
+ align:start position:0%
+least in many environments right and of
+course you it depends on what
+
+ align:start position:0%
+course you it depends on what
+ 
+
+ align:start position:0%
+course you it depends on what
+environment you measure then but for
+
+ align:start position:0%
+environment you measure then but for
+ 
+
+ align:start position:0%
+environment you measure then but for
+most genes you can you can knock them
+
+ align:start position:0%
+most genes you can you can knock them
+ 
+
+ align:start position:0%
+most genes you can you can knock them
+out certainly in rich media most gen you
+
+ align:start position:0%
+out certainly in rich media most gen you
+ 
+
+ align:start position:0%
+out certainly in rich media most gen you
+can knock out
+
+ align:start position:0%
+can knock out
+ 
+
+ align:start position:0%
+can knock out
+right okay right so this is
+
+ align:start position:0%
+right okay right so this is
+ 
+
+ align:start position:0%
+right okay right so this is
+um you know and then of course there you
+
+ align:start position:0%
+um you know and then of course there you
+ 
+
+ align:start position:0%
+um you know and then of course there you
+know yeah this as I said might be one
+
+ align:start position:0%
+know yeah this as I said might be one
+ 
+
+ align:start position:0%
+know yeah this as I said might be one
+10 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theus 3 4 okay um you know it's I I
+
+ align:start position:0%
+Theus 3 4 okay um you know it's I I
+ 
+
+ align:start position:0%
+Theus 3 4 okay um you know it's I I
+might be off by a couple orders of
+
+ align:start position:0%
+might be off by a couple orders of
+ 
+
+ align:start position:0%
+might be off by a couple orders of
+magnitude okay but the point is that
+
+ align:start position:0%
+magnitude okay but the point is that
+ 
+
+ align:start position:0%
+magnitude okay but the point is that
+this is um it's it's a small fraction
+
+ align:start position:0%
+this is um it's it's a small fraction
+ 
+
+ align:start position:0%
+this is um it's it's a small fraction
+over here most most are here and there
+
+ align:start position:0%
+over here most most are here and there
+ 
+
+ align:start position:0%
+over here most most are here and there
+will be some point mutations that come
+
+ align:start position:0%
+will be some point mutations that come
+ 
+
+ align:start position:0%
+will be some point mutations that come
+down here but you know on a linear scale
+
+ align:start position:0%
+down here but you know on a linear scale
+ 
+
+ align:start position:0%
+down here but you know on a linear scale
+they're going to be it's going to be
+
+ align:start position:0%
+they're going to be it's going to be
+ 
+
+ align:start position:0%
+they're going to be it's going to be
+very small
+
+ align:start position:0%
+very small
+ 
+
+ align:start position:0%
+very small
+okay um okay now from the standpoint of
+
+ align:start position:0%
+okay um okay now from the standpoint of
+ 
+
+ align:start position:0%
+okay um okay now from the standpoint of
+a population evolving to a new
+
+ align:start position:0%
+a population evolving to a new
+ 
+
+ align:start position:0%
+a population evolving to a new
+environment which mutation are we most
+
+ align:start position:0%
+environment which mutation are we most
+ 
+
+ align:start position:0%
+environment which mutation are we most
+interested
+
+ align:start position:0%
+interested
+ 
+
+ align:start position:0%
+interested
+in the beneficial mutations right so
+
+ align:start position:0%
+in the beneficial mutations right so
+ 
+
+ align:start position:0%
+in the beneficial mutations right so
+we're most interested in uh in these
+
+ align:start position:0%
+we're most interested in uh in these
+ 
+
+ align:start position:0%
+we're most interested in uh in these
+guys okay um and indeed this is the
+
+ align:start position:0%
+guys okay um and indeed this is the
+ 
+
+ align:start position:0%
+guys okay um and indeed this is the
+distribution that that um heggerness and
+
+ align:start position:0%
+distribution that that um heggerness and
+ 
+
+ align:start position:0%
+distribution that that um heggerness and
+koni set out to try and measure in that
+
+ align:start position:0%
+koni set out to try and measure in that
+ 
+
+ align:start position:0%
+koni set out to try and measure in that
+experiment um that we just read about
+
+ align:start position:0%
+experiment um that we just read about
+ 
+
+ align:start position:0%
+experiment um that we just read about
+last night okay so he wanted to know if
+
+ align:start position:0%
+last night okay so he wanted to know if
+ 
+
+ align:start position:0%
+last night okay so he wanted to know if
+you plot if you kind of zoom in here
+
+ align:start position:0%
+you plot if you kind of zoom in here
+ 
+
+ align:start position:0%
+you plot if you kind of zoom in here
+because remember this this is even
+
+ align:start position:0%
+because remember this this is even
+ 
+
+ align:start position:0%
+because remember this this is even
+narrower than I've actually drawn right
+
+ align:start position:0%
+narrower than I've actually drawn right
+ 
+
+ align:start position:0%
+narrower than I've actually drawn right
+um but this distribtion
+
+ align:start position:0%
+um but this distribtion
+ 
+
+ align:start position:0%
+um but this distribtion
+the probability of a beneficial mutation
+
+ align:start position:0%
+the probability of a beneficial mutation
+ 
+
+ align:start position:0%
+the probability of a beneficial mutation
+of magnitude s s here is zero s um it's
+
+ align:start position:0%
+of magnitude s s here is zero s um it's
+ 
+
+ align:start position:0%
+of magnitude s s here is zero s um it's
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+to you know it's going to do
+
+ align:start position:0%
+to you know it's going to do
+ 
+
+ align:start position:0%
+to you know it's going to do
+something right many mutations that are
+
+ align:start position:0%
+something right many mutations that are
+ 
+
+ align:start position:0%
+something right many mutations that are
+nearly neutral but it's going to fall
+
+ align:start position:0%
+nearly neutral but it's going to fall
+ 
+
+ align:start position:0%
+nearly neutral but it's going to fall
+off in some way and they wanted to try
+
+ align:start position:0%
+off in some way and they wanted to try
+ 
+
+ align:start position:0%
+off in some way and they wanted to try
+and measure this right you know how many
+
+ align:start position:0%
+and measure this right you know how many
+ 
+
+ align:start position:0%
+and measure this right you know how many
+mutations caner a 2% Advantage 4% you
+
+ align:start position:0%
+mutations caner a 2% Advantage 4% you
+ 
+
+ align:start position:0%
+mutations caner a 2% Advantage 4% you
+know for this particular equ strain in
+
+ align:start position:0%
+know for this particular equ strain in
+ 
+
+ align:start position:0%
+know for this particular equ strain in
+that particular
+
+ align:start position:0%
+that particular
+ 
+
+ align:start position:0%
+that particular
+environment okay but it turned out being
+
+ align:start position:0%
+environment okay but it turned out being
+ 
+
+ align:start position:0%
+environment okay but it turned out being
+difficult to measure
+
+ align:start position:0%
+difficult to measure
+ 
+
+ align:start position:0%
+difficult to measure
+right and and what was the reason that
+
+ align:start position:0%
+right and and what was the reason that
+ 
+
+ align:start position:0%
+right and and what was the reason that
+they gave for why it was difficult to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure somebody anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please yes okay but the equivalence
+
+ align:start position:0%
+please yes okay but the equivalence
+ 
+
+ align:start position:0%
+please yes okay but the equivalence
+principle doesn't say that they're all
+
+ align:start position:0%
+principle doesn't say that they're all
+ 
+
+ align:start position:0%
+principle doesn't say that they're all
+equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessarily they each have
+
+ align:start position:0%
+necessarily they each have
+ 
+
+ align:start position:0%
+necessarily they each have
+their yeah you keep parameters for each
+
+ align:start position:0%
+their yeah you keep parameters for each
+ 
+
+ align:start position:0%
+their yeah you keep parameters for each
+of them that they will give you the
+
+ align:start position:0%
+of them that they will give you the
+ 
+
+ align:start position:0%
+of them that they will give you the
+same okay that's right right so what
+
+ align:start position:0%
+same okay that's right right so what
+ 
+
+ align:start position:0%
+same okay that's right right so what
+they found was that different underlying
+
+ align:start position:0%
+they found was that different underlying
+ 
+
+ align:start position:0%
+they found was that different underlying
+distributions this prob distribution for
+
+ align:start position:0%
+distributions this prob distribution for
+ 
+
+ align:start position:0%
+distributions this prob distribution for
+beneficial limitations function of s
+
+ align:start position:0%
+beneficial limitations function of s
+ 
+
+ align:start position:0%
+beneficial limitations function of s
+different underlying distributions could
+
+ align:start position:0%
+different underlying distributions could
+ 
+
+ align:start position:0%
+different underlying distributions could
+give you the same final output in their
+
+ align:start position:0%
+give you the same final output in their
+ 
+
+ align:start position:0%
+give you the same final output in their
+measurements okay but why was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+John right so you can only measure what
+
+ align:start position:0%
+John right so you can only measure what
+ 
+
+ align:start position:0%
+John right so you can only measure what
+fixes or what become uh or becomes
+
+ align:start position:0%
+fixes or what become uh or becomes
+ 
+
+ align:start position:0%
+fixes or what become uh or becomes
+significant fractional population 10%
+
+ align:start position:0%
+significant fractional population 10%
+ 
+
+ align:start position:0%
+significant fractional population 10%
+you know only measure what fixes or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grows okay and what does that
+
+ align:start position:0%
+grows okay and what does that
+ 
+
+ align:start position:0%
+grows okay and what does that
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+well it means that you're not
+
+ align:start position:0%
+well it means that you're not
+ 
+
+ align:start position:0%
+well it means that you're not
+prob right it means that we're not
+
+ align:start position:0%
+prob right it means that we're not
+ 
+
+ align:start position:0%
+prob right it means that we're not
+probing that distribution and why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not yeah okay but yeah but why is it
+
+ align:start position:0%
+not yeah okay but yeah but why is it
+ 
+
+ align:start position:0%
+not yeah okay but yeah but why is it
+that we only see part of this
+
+ align:start position:0%
+that we only see part of this
+ 
+
+ align:start position:0%
+that we only see part of this
+distribution what what was there I mean
+
+ align:start position:0%
+distribution what what was there I mean
+ 
+
+ align:start position:0%
+distribution what what was there I mean
+don't see out we don't see the ones that
+
+ align:start position:0%
+don't see out we don't see the ones that
+ 
+
+ align:start position:0%
+don't see out we don't see the ones that
+die out and and and why is it that they
+
+ align:start position:0%
+die out and and and why is it that they
+ 
+
+ align:start position:0%
+die out and and and why is it that they
+die out or why is it that
+
+ align:start position:0%
+die out or why is it that
+ 
+
+ align:start position:0%
+die out or why is it that
+they okay right okay yeah so sto yeah um
+
+ align:start position:0%
+they okay right okay yeah so sto yeah um
+ 
+
+ align:start position:0%
+they okay right okay yeah so sto yeah um
+yes so the the effect of stochastic
+
+ align:start position:0%
+yes so the the effect of stochastic
+ 
+
+ align:start position:0%
+yes so the the effect of stochastic
+Extinction is very relevant here and I
+
+ align:start position:0%
+Extinction is very relevant here and I
+ 
+
+ align:start position:0%
+Extinction is very relevant here and I
+think that in this paper they a little
+
+ align:start position:0%
+think that in this paper they a little
+ 
+
+ align:start position:0%
+think that in this paper they a little
+bit underplay that aspect of it right
+
+ align:start position:0%
+bit underplay that aspect of it right
+ 
+
+ align:start position:0%
+bit underplay that aspect of it right
+because they're primarily arguing that
+
+ align:start position:0%
+because they're primarily arguing that
+ 
+
+ align:start position:0%
+because they're primarily arguing that
+it was another effect that Led Led to
+
+ align:start position:0%
+it was another effect that Led Led to
+ 
+
+ align:start position:0%
+it was another effect that Led Led to
+this equivalence
+
+ align:start position:0%
+this equivalence
+ 
+
+ align:start position:0%
+this equivalence
+principle right competition yeah clonal
+
+ align:start position:0%
+principle right competition yeah clonal
+ 
+
+ align:start position:0%
+principle right competition yeah clonal
+interference right I mean that's why we
+
+ align:start position:0%
+interference right I mean that's why we
+ 
+
+ align:start position:0%
+interference right I mean that's why we
+spent the last hour talking about clonal
+
+ align:start position:0%
+spent the last hour talking about clonal
+ 
+
+ align:start position:0%
+spent the last hour talking about clonal
+interference right so there their their
+
+ align:start position:0%
+interference right so there their their
+ 
+
+ align:start position:0%
+interference right so there their their
+argument that in this paper was that as
+
+ align:start position:0%
+argument that in this paper was that as
+ 
+
+ align:start position:0%
+argument that in this paper was that as
+a result of colonal interference
+
+ align:start position:0%
+a result of colonal interference
+ 
+
+ align:start position:0%
+a result of colonal interference
+competition between these different
+
+ align:start position:0%
+competition between these different
+ 
+
+ align:start position:0%
+competition between these different
+lineages then the distribution of
+
+ align:start position:0%
+lineages then the distribution of
+ 
+
+ align:start position:0%
+lineages then the distribution of
+Fitness effects that you measure that
+
+ align:start position:0%
+Fitness effects that you measure that
+ 
+
+ align:start position:0%
+Fitness effects that you measure that
+fix is not the distrib that was the
+
+ align:start position:0%
+fix is not the distrib that was the
+ 
+
+ align:start position:0%
+fix is not the distrib that was the
+underlying
+
+ align:start position:0%
+underlying
+ 
+
+ align:start position:0%
+underlying
+distribution okay because less fit
+
+ align:start position:0%
+distribution okay because less fit
+ 
+
+ align:start position:0%
+distribution okay because less fit
+mutations less fit beneficial mutations
+
+ align:start position:0%
+mutations less fit beneficial mutations
+ 
+
+ align:start position:0%
+mutations less fit beneficial mutations
+get out competed okay but there's a very
+
+ align:start position:0%
+get out competed okay but there's a very
+ 
+
+ align:start position:0%
+get out competed okay but there's a very
+important question which is let's
+
+ align:start position:0%
+important question which is let's
+ 
+
+ align:start position:0%
+important question which is let's
+imagine that we have let's have mu go to
+
+ align:start position:0%
+imagine that we have let's have mu go to
+ 
+
+ align:start position:0%
+imagine that we have let's have mu go to
+zero okay or we go to small populations
+
+ align:start position:0%
+zero okay or we go to small populations
+ 
+
+ align:start position:0%
+zero okay or we go to small populations
+let's let's uh let's uh let's say that
+
+ align:start position:0%
+let's let's uh let's uh let's say that
+ 
+
+ align:start position:0%
+let's let's uh let's uh let's say that
+uh after reading his paper I said okay
+
+ align:start position:0%
+uh after reading his paper I said okay
+ 
+
+ align:start position:0%
+uh after reading his paper I said okay
+well yeah because of Clone interference
+
+ align:start position:0%
+well yeah because of Clone interference
+ 
+
+ align:start position:0%
+well yeah because of Clone interference
+I can't measure this probability
+
+ align:start position:0%
+I can't measure this probability
+ 
+
+ align:start position:0%
+I can't measure this probability
+distribution in the setup that he used
+
+ align:start position:0%
+distribution in the setup that he used
+ 
+
+ align:start position:0%
+distribution in the setup that he used
+but maybe if I go to small population
+
+ align:start position:0%
+but maybe if I go to small population
+ 
+
+ align:start position:0%
+but maybe if I go to small population
+sizes or I reduce the mutation rate
+
+ align:start position:0%
+sizes or I reduce the mutation rate
+ 
+
+ align:start position:0%
+sizes or I reduce the mutation rate
+somehow magic okay then would this allow
+
+ align:start position:0%
+somehow magic okay then would this allow
+ 
+
+ align:start position:0%
+somehow magic okay then would this allow
+me to measure that distribution right so
+
+ align:start position:0%
+me to measure that distribution right so
+ 
+
+ align:start position:0%
+me to measure that distribution right so
+I'm going to ask you guys to vote so
+
+ align:start position:0%
+I'm going to ask you guys to vote so
+ 
+
+ align:start position:0%
+I'm going to ask you guys to vote so
+let's say I experimentally have mu go to
+
+ align:start position:0%
+let's say I experimentally have mu go to
+ 
+
+ align:start position:0%
+let's say I experimentally have mu go to
+zero does this mean that when I then go
+
+ align:start position:0%
+zero does this mean that when I then go
+ 
+
+ align:start position:0%
+zero does this mean that when I then go
+do my right cfp
+
+ align:start position:0%
+do my right cfp
+ 
+
+ align:start position:0%
+do my right cfp
+yfp right they're 50/50 and then you
+
+ align:start position:0%
+yfp right they're 50/50 and then you
+ 
+
+ align:start position:0%
+yfp right they're 50/50 and then you
+start doing this and we measure the
+
+ align:start position:0%
+start doing this and we measure the
+ 
+
+ align:start position:0%
+start doing this and we measure the
+slope to get S right
+
+ align:start position:0%
+slope to get S right
+ 
+
+ align:start position:0%
+slope to get S right
+just like in this experiment okay will I
+
+ align:start position:0%
+just like in this experiment okay will I
+ 
+
+ align:start position:0%
+just like in this experiment okay will I
+extract if I plot the distribution of
+
+ align:start position:0%
+extract if I plot the distribution of
+ 
+
+ align:start position:0%
+extract if I plot the distribution of
+resulting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s's okay no colonal interference anymore
+
+ align:start position:0%
+s's okay no colonal interference anymore
+ 
+
+ align:start position:0%
+s's okay no colonal interference anymore
+right because I've set mu equal to zero
+
+ align:start position:0%
+right because I've set mu equal to zero
+ 
+
+ align:start position:0%
+right because I've set mu equal to zero
+so this thing goes to Infinity right do
+
+ align:start position:0%
+so this thing goes to Infinity right do
+ 
+
+ align:start position:0%
+so this thing goes to Infinity right do
+I recover this uh the underlying
+
+ align:start position:0%
+I recover this uh the underlying
+ 
+
+ align:start position:0%
+I recover this uh the underlying
+distribution okay ready okay so PB
+
+ align:start position:0%
+distribution okay ready okay so PB
+ 
+
+ align:start position:0%
+distribution okay ready okay so PB
+measured
+
+ align:start position:0%
+measured
+ 
+
+ align:start position:0%
+measured
+is it as a function of s is it equal to
+
+ align:start position:0%
+is it as a function of s is it equal to
+ 
+
+ align:start position:0%
+is it as a function of s is it equal to
+the underlying the true one question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mark all right I'm going to give you 15
+
+ align:start position:0%
+mark all right I'm going to give you 15
+ 
+
+ align:start position:0%
+mark all right I'm going to give you 15
+seconds to think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right ready three two
+
+ align:start position:0%
+all right ready three two
+ 
+
+ align:start position:0%
+all right ready three two
+one all right so we have many uh you
+
+ align:start position:0%
+one all right so we have many uh you
+ 
+
+ align:start position:0%
+one all right so we have many uh you
+know i' say majority of NOS okay and can
+
+ align:start position:0%
+know i' say majority of NOS okay and can
+ 
+
+ align:start position:0%
+know i' say majority of NOS okay and can
+somebody say why
+
+ align:start position:0%
+somebody say why
+ 
+
+ align:start position:0%
+somebody say why
+not we can only see the established mut
+
+ align:start position:0%
+not we can only see the established mut
+ 
+
+ align:start position:0%
+not we can only see the established mut
+that's right because even if you don't
+
+ align:start position:0%
+that's right because even if you don't
+ 
+
+ align:start position:0%
+that's right because even if you don't
+have clonal interference you still only
+
+ align:start position:0%
+have clonal interference you still only
+ 
+
+ align:start position:0%
+have clonal interference you still only
+see the mutations that survive
+
+ align:start position:0%
+see the mutations that survive
+ 
+
+ align:start position:0%
+see the mutations that survive
+stochastic Extinction okay and I think
+
+ align:start position:0%
+stochastic Extinction okay and I think
+ 
+
+ align:start position:0%
+stochastic Extinction okay and I think
+this is a really important point that at
+
+ align:start position:0%
+this is a really important point that at
+ 
+
+ align:start position:0%
+this is a really important point that at
+least in a first reading of the p paper
+
+ align:start position:0%
+least in a first reading of the p paper
+ 
+
+ align:start position:0%
+least in a first reading of the p paper
+you might not realize yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+John that's right so in principle we
+
+ align:start position:0%
+John that's right so in principle we
+ 
+
+ align:start position:0%
+John that's right so in principle we
+know that it it it that this probably
+
+ align:start position:0%
+know that it it it that this probably
+ 
+
+ align:start position:0%
+know that it it it that this probably
+survival goes as s right um but I'm just
+
+ align:start position:0%
+survival goes as s right um but I'm just
+ 
+
+ align:start position:0%
+survival goes as s right um but I'm just
+but you end up losing a fair amount of
+
+ align:start position:0%
+but you end up losing a fair amount of
+ 
+
+ align:start position:0%
+but you end up losing a fair amount of
+information right so for example let's
+
+ align:start position:0%
+information right so for example let's
+ 
+
+ align:start position:0%
+information right so for example let's
+say that this thing is an
+
+ align:start position:0%
+say that this thing is an
+ 
+
+ align:start position:0%
+say that this thing is an
+exponential okay so this is p b of s
+
+ align:start position:0%
+exponential okay so this is p b of s
+ 
+
+ align:start position:0%
+exponential okay so this is p b of s
+let's just say I it's an exponential um
+
+ align:start position:0%
+let's just say I it's an exponential um
+ 
+
+ align:start position:0%
+let's just say I it's an exponential um
+and indeed from some ideas from extreme
+
+ align:start position:0%
+and indeed from some ideas from extreme
+ 
+
+ align:start position:0%
+and indeed from some ideas from extreme
+value Theory there are arguments that
+
+ align:start position:0%
+value Theory there are arguments that
+ 
+
+ align:start position:0%
+value Theory there are arguments that
+that maybe this should be an exponential
+
+ align:start position:0%
+that maybe this should be an exponential
+ 
+
+ align:start position:0%
+that maybe this should be an exponential
+okay and if you're curious about this
+
+ align:start position:0%
+okay and if you're curious about this
+ 
+
+ align:start position:0%
+okay and if you're curious about this
+come and ask me after class okay all
+
+ align:start position:0%
+come and ask me after class okay all
+ 
+
+ align:start position:0%
+come and ask me after class okay all
+right but let's just imagine that this
+
+ align:start position:0%
+right but let's just imagine that this
+ 
+
+ align:start position:0%
+right but let's just imagine that this
+thing is exponential U now the question
+
+ align:start position:0%
+thing is exponential U now the question
+ 
+
+ align:start position:0%
+thing is exponential U now the question
+is what would we actually
+
+ align:start position:0%
+is what would we actually
+ 
+
+ align:start position:0%
+is what would we actually
+measure in the limit of in this
+
+ align:start position:0%
+measure in the limit of in this
+ 
+
+ align:start position:0%
+measure in the limit of in this
+experiment in the absence of clonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference right would we measure a
+
+ align:start position:0%
+interference right would we measure a
+ 
+
+ align:start position:0%
+interference right would we measure a
+distribution that would be would the
+
+ align:start position:0%
+distribution that would be would the
+ 
+
+ align:start position:0%
+distribution that would be would the
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+be maximal at zero or at some other
+
+ align:start position:0%
+be maximal at zero or at some other
+ 
+
+ align:start position:0%
+be maximal at zero or at some other
+value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verbally zero or other value ready three
+
+ align:start position:0%
+verbally zero or other value ready three
+ 
+
+ align:start position:0%
+verbally zero or other value ready three
+2 one other value right and indeed the
+
+ align:start position:0%
+2 one other value right and indeed the
+ 
+
+ align:start position:0%
+2 one other value right and indeed the
+probability of surviving Extinction
+
+ align:start position:0%
+probability of surviving Extinction
+ 
+
+ align:start position:0%
+probability of surviving Extinction
+remember this X1 goes as s means that
+
+ align:start position:0%
+remember this X1 goes as s means that
+ 
+
+ align:start position:0%
+remember this X1 goes as s means that
+the distribution you actually measure
+
+ align:start position:0%
+the distribution you actually measure
+ 
+
+ align:start position:0%
+the distribution you actually measure
+will start at zero grow
+
+ align:start position:0%
+will start at zero grow
+ 
+
+ align:start position:0%
+will start at zero grow
+linearly okay and then uh and then fall
+
+ align:start position:0%
+linearly okay and then uh and then fall
+ 
+
+ align:start position:0%
+linearly okay and then uh and then fall
+off okay so this distribution is
+
+ align:start position:0%
+off okay so this distribution is
+ 
+
+ align:start position:0%
+off okay so this distribution is
+essentially like this distribution of
+
+ align:start position:0%
+essentially like this distribution of
+ 
+
+ align:start position:0%
+essentially like this distribution of
+the convolution of two
+
+ align:start position:0%
+the convolution of two
+ 
+
+ align:start position:0%
+the convolution of two
+exponentials
+
+ align:start position:0%
+exponentials
+ 
+
+ align:start position:0%
+exponentials
+okay where um this thing should this
+
+ align:start position:0%
+okay where um this thing should this
+ 
+
+ align:start position:0%
+okay where um this thing should this
+thing goes up linearly and then and then
+
+ align:start position:0%
+thing goes up linearly and then and then
+ 
+
+ align:start position:0%
+thing goes up linearly and then and then
+curves off okay so I think that a very
+
+ align:start position:0%
+curves off okay so I think that a very
+ 
+
+ align:start position:0%
+curves off okay so I think that a very
+important point to realize in all this
+
+ align:start position:0%
+important point to realize in all this
+ 
+
+ align:start position:0%
+important point to realize in all this
+is that this is p this is prob
+
+ align:start position:0%
+is that this is p this is prob
+ 
+
+ align:start position:0%
+is that this is p this is prob
+distribution that's
+
+ align:start position:0%
+distribution that's
+ 
+
+ align:start position:0%
+distribution that's
+measured as a function of s with no
+
+ align:start position:0%
+measured as a function of s with no
+ 
+
+ align:start position:0%
+measured as a function of s with no
+colonal interference
+
+ align:start position:0%
+colonal interference
+ 
+
+ align:start position:0%
+colonal interference
+right right so the statement is that
+
+ align:start position:0%
+right right so the statement is that
+ 
+
+ align:start position:0%
+right right so the statement is that
+even if you don't have any colonal
+
+ align:start position:0%
+even if you don't have any colonal
+ 
+
+ align:start position:0%
+even if you don't have any colonal
+interference already you're going to
+
+ align:start position:0%
+interference already you're going to
+ 
+
+ align:start position:0%
+interference already you're going to
+measure a peak
+
+ align:start position:0%
+measure a peak
+ 
+
+ align:start position:0%
+measure a peak
+distribution right even if the under
+
+ align:start position:0%
+distribution right even if the under
+ 
+
+ align:start position:0%
+distribution right even if the under
+line distribution is you know it's going
+
+ align:start position:0%
+line distribution is you know it's going
+ 
+
+ align:start position:0%
+line distribution is you know it's going
+to be the underling distribution will be
+
+ align:start position:0%
+to be the underling distribution will be
+ 
+
+ align:start position:0%
+to be the underling distribution will be
+peaked at zero right and then um but the
+
+ align:start position:0%
+peaked at zero right and then um but the
+ 
+
+ align:start position:0%
+peaked at zero right and then um but the
+but what you measure is always going to
+
+ align:start position:0%
+but what you measure is always going to
+ 
+
+ align:start position:0%
+but what you measure is always going to
+be peaked somewhere else and indeed if
+
+ align:start position:0%
+be peaked somewhere else and indeed if
+ 
+
+ align:start position:0%
+be peaked somewhere else and indeed if
+you go and you look in the in the paper
+
+ align:start position:0%
+you go and you look in the in the paper
+ 
+
+ align:start position:0%
+you go and you look in the in the paper
+at the measured Alpha as a function of s
+
+ align:start position:0%
+at the measured Alpha as a function of s
+ 
+
+ align:start position:0%
+at the measured Alpha as a function of s
+what you see is something that looks
+
+ align:start position:0%
+what you see is something that looks
+ 
+
+ align:start position:0%
+what you see is something that looks
+kind of like this so uh it's a little
+
+ align:start position:0%
+kind of like this so uh it's a little
+ 
+
+ align:start position:0%
+kind of like this so uh it's a little
+bit difficult to be absolutely certain
+
+ align:start position:0%
+bit difficult to be absolutely certain
+ 
+
+ align:start position:0%
+bit difficult to be absolutely certain
+what's going on is that in the absence
+
+ align:start position:0%
+what's going on is that in the absence
+ 
+
+ align:start position:0%
+what's going on is that in the absence
+of Clone interference you get this with
+
+ align:start position:0%
+of Clone interference you get this with
+ 
+
+ align:start position:0%
+of Clone interference you get this with
+clone interference let's say you have
+
+ align:start position:0%
+clone interference let's say you have
+ 
+
+ align:start position:0%
+clone interference let's say you have
+two mutations and you want to know okay
+
+ align:start position:0%
+two mutations and you want to know okay
+ 
+
+ align:start position:0%
+two mutations and you want to know okay
+what are you going to measure well you
+
+ align:start position:0%
+what are you going to measure well you
+ 
+
+ align:start position:0%
+what are you going to measure well you
+sample from this distribution twice and
+
+ align:start position:0%
+sample from this distribution twice and
+ 
+
+ align:start position:0%
+sample from this distribution twice and
+you take the larger of the two
+
+ align:start position:0%
+you take the larger of the two
+ 
+
+ align:start position:0%
+you take the larger of the two
+right because this distribution is
+
+ align:start position:0%
+right because this distribution is
+ 
+
+ align:start position:0%
+right because this distribution is
+already the prob distribution of
+
+ align:start position:0%
+already the prob distribution of
+ 
+
+ align:start position:0%
+already the prob distribution of
+mutations that get established right so
+
+ align:start position:0%
+mutations that get established right so
+ 
+
+ align:start position:0%
+mutations that get established right so
+then this is going to grow as
+
+ align:start position:0%
+then this is going to grow as
+ 
+
+ align:start position:0%
+then this is going to grow as
+um as a quadratic here if you have more
+
+ align:start position:0%
+um as a quadratic here if you have more
+ 
+
+ align:start position:0%
+um as a quadratic here if you have more
+clonal interference then this thing
+
+ align:start position:0%
+clonal interference then this thing
+ 
+
+ align:start position:0%
+clonal interference then this thing
+shifts to the right and gets tighter
+
+ align:start position:0%
+shifts to the right and gets tighter
+ 
+
+ align:start position:0%
+shifts to the right and gets tighter
+right so this is the this is kind of the
+
+ align:start position:0%
+right so this is the this is kind of the
+ 
+
+ align:start position:0%
+right so this is the this is kind of the
+process by which you end up with a
+
+ align:start position:0%
+process by which you end up with a
+ 
+
+ align:start position:0%
+process by which you end up with a
+peaked
+
+ align:start position:0%
+peaked
+ 
+
+ align:start position:0%
+peaked
+distribution okay so what we're going to
+
+ align:start position:0%
+distribution okay so what we're going to
+ 
+
+ align:start position:0%
+distribution okay so what we're going to
+do is uh we're going to start uh by the
+
+ align:start position:0%
+do is uh we're going to start uh by the
+ 
+
+ align:start position:0%
+do is uh we're going to start uh by the
+first the first 15 minutes on Tuesday
+
+ align:start position:0%
+first the first 15 minutes on Tuesday
+ 
+
+ align:start position:0%
+first the first 15 minutes on Tuesday
+we'll um we'll talk about this
+
+ align:start position:0%
+we'll um we'll talk about this
+ 
+
+ align:start position:0%
+we'll um we'll talk about this
+experiment uh a bit more uh and then uh
+
+ align:start position:0%
+experiment uh a bit more uh and then uh
+ 
+
+ align:start position:0%
+experiment uh a bit more uh and then uh
+and then we'll go on to think about uh
+
+ align:start position:0%
+and then we'll go on to think about uh
+ 
+
+ align:start position:0%
+and then we'll go on to think about uh
+about Fitness Landscapes and uh and the
+
+ align:start position:0%
+about Fitness Landscapes and uh and the
+ 
+
+ align:start position:0%
+about Fitness Landscapes and uh and the
+rate of evolution if you have any
+
+ align:start position:0%
+rate of evolution if you have any
+ 
+
+ align:start position:0%
+rate of evolution if you have any
+questions about anything that we said uh
+
+ align:start position:0%
+questions about anything that we said uh
+ 
+
+ align:start position:0%
+questions about anything that we said uh
+please come on up okay
\ No newline at end of file
diff --git a/6UMv4vb4y7c.txt b/6UMv4vb4y7c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..49067067c0a3415ac1e70a36799c1904251ee4cc
--- /dev/null
+++ b/6UMv4vb4y7c.txt
@@ -0,0 +1,1387 @@
+align:start position:0%
+ 
+we now introduce normal random variables
+
+ align:start position:0%
+we now introduce normal random variables
+ 
+
+ align:start position:0%
+we now introduce normal random variables
+which are also often called Gaussian
+
+ align:start position:0%
+which are also often called Gaussian
+ 
+
+ align:start position:0%
+which are also often called Gaussian
+random variables normal random variables
+
+ align:start position:0%
+random variables normal random variables
+ 
+
+ align:start position:0%
+random variables normal random variables
+are perhaps the most important ones in
+
+ align:start position:0%
+are perhaps the most important ones in
+ 
+
+ align:start position:0%
+are perhaps the most important ones in
+probability theory they play a key role
+
+ align:start position:0%
+probability theory they play a key role
+ 
+
+ align:start position:0%
+probability theory they play a key role
+in the theory of the subject as we will
+
+ align:start position:0%
+in the theory of the subject as we will
+ 
+
+ align:start position:0%
+in the theory of the subject as we will
+see later in this class in the context
+
+ align:start position:0%
+see later in this class in the context
+ 
+
+ align:start position:0%
+see later in this class in the context
+of the central limit theorem
+
+ align:start position:0%
+of the central limit theorem
+ 
+
+ align:start position:0%
+of the central limit theorem
+they are also prevalent in applications
+
+ align:start position:0%
+they are also prevalent in applications
+ 
+
+ align:start position:0%
+they are also prevalent in applications
+for two reasons they have some nice
+
+ align:start position:0%
+for two reasons they have some nice
+ 
+
+ align:start position:0%
+for two reasons they have some nice
+analytical properties and they are also
+
+ align:start position:0%
+analytical properties and they are also
+ 
+
+ align:start position:0%
+analytical properties and they are also
+the most common model of random noise in
+
+ align:start position:0%
+the most common model of random noise in
+ 
+
+ align:start position:0%
+the most common model of random noise in
+general they are a good model of noise
+
+ align:start position:0%
+general they are a good model of noise
+ 
+
+ align:start position:0%
+general they are a good model of noise
+or randomness whenever that noise is due
+
+ align:start position:0%
+or randomness whenever that noise is due
+ 
+
+ align:start position:0%
+or randomness whenever that noise is due
+to the addition of many small
+
+ align:start position:0%
+to the addition of many small
+ 
+
+ align:start position:0%
+to the addition of many small
+independent noise terms and this is a
+
+ align:start position:0%
+independent noise terms and this is a
+ 
+
+ align:start position:0%
+independent noise terms and this is a
+very common situation in the real world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we define normal random variables by
+
+ align:start position:0%
+we define normal random variables by
+ 
+
+ align:start position:0%
+we define normal random variables by
+specifying their PDFs and we start with
+
+ align:start position:0%
+specifying their PDFs and we start with
+ 
+
+ align:start position:0%
+specifying their PDFs and we start with
+the simplest case of the so called
+
+ align:start position:0%
+the simplest case of the so called
+ 
+
+ align:start position:0%
+the simplest case of the so called
+standard normal the standard normal is
+
+ align:start position:0%
+standard normal the standard normal is
+ 
+
+ align:start position:0%
+standard normal the standard normal is
+indicated with this shorthand notation
+
+ align:start position:0%
+indicated with this shorthand notation
+ 
+
+ align:start position:0%
+indicated with this shorthand notation
+and we will see shortly why this
+
+ align:start position:0%
+and we will see shortly why this
+ 
+
+ align:start position:0%
+and we will see shortly why this
+notation is being used it is defined in
+
+ align:start position:0%
+notation is being used it is defined in
+ 
+
+ align:start position:0%
+notation is being used it is defined in
+terms of a PDF this PDF is defined for
+
+ align:start position:0%
+terms of a PDF this PDF is defined for
+ 
+
+ align:start position:0%
+terms of a PDF this PDF is defined for
+all values of X X can be any real number
+
+ align:start position:0%
+all values of X X can be any real number
+ 
+
+ align:start position:0%
+all values of X X can be any real number
+so this random variable takes values can
+
+ align:start position:0%
+so this random variable takes values can
+ 
+
+ align:start position:0%
+so this random variable takes values can
+take values anywhere on the real line
+
+ align:start position:0%
+take values anywhere on the real line
+ 
+
+ align:start position:0%
+take values anywhere on the real line
+and the formula for the PDF is this one
+
+ align:start position:0%
+and the formula for the PDF is this one
+ 
+
+ align:start position:0%
+and the formula for the PDF is this one
+let us try to understand this formula so
+
+ align:start position:0%
+let us try to understand this formula so
+ 
+
+ align:start position:0%
+let us try to understand this formula so
+we have the exponential of negative x
+
+ align:start position:0%
+we have the exponential of negative x
+ 
+
+ align:start position:0%
+we have the exponential of negative x
+squared over 2 now if we are to plot the
+
+ align:start position:0%
+squared over 2 now if we are to plot the
+ 
+
+ align:start position:0%
+squared over 2 now if we are to plot the
+x squared over 2 function it has a shape
+
+ align:start position:0%
+x squared over 2 function it has a shape
+ 
+
+ align:start position:0%
+x squared over 2 function it has a shape
+of this form and it is centered at 0 but
+
+ align:start position:0%
+of this form and it is centered at 0 but
+ 
+
+ align:start position:0%
+of this form and it is centered at 0 but
+then we take the negative exponential of
+
+ align:start position:0%
+then we take the negative exponential of
+ 
+
+ align:start position:0%
+then we take the negative exponential of
+this function now when you take the
+
+ align:start position:0%
+this function now when you take the
+ 
+
+ align:start position:0%
+this function now when you take the
+negative exponential whenever this thing
+
+ align:start position:0%
+negative exponential whenever this thing
+ 
+
+ align:start position:0%
+negative exponential whenever this thing
+is big the negative exponential is going
+
+ align:start position:0%
+is big the negative exponential is going
+ 
+
+ align:start position:0%
+is big the negative exponential is going
+to be small so the negative exponential
+
+ align:start position:0%
+to be small so the negative exponential
+ 
+
+ align:start position:0%
+to be small so the negative exponential
+would be equal to 1 when X is equal to 0
+
+ align:start position:0%
+would be equal to 1 when X is equal to 0
+ 
+
+ align:start position:0%
+would be equal to 1 when X is equal to 0
+but then as x increases because x
+
+ align:start position:0%
+but then as x increases because x
+ 
+
+ align:start position:0%
+but then as x increases because x
+squared also increases the negative
+
+ align:start position:0%
+squared also increases the negative
+ 
+
+ align:start position:0%
+squared also increases the negative
+exponential will fall off
+
+ align:start position:0%
+exponential will fall off
+ 
+
+ align:start position:0%
+exponential will fall off
+and so we obtain a shape of this kind
+
+ align:start position:0%
+and so we obtain a shape of this kind
+ 
+
+ align:start position:0%
+and so we obtain a shape of this kind
+and symmetrically on the other side as
+
+ align:start position:0%
+and symmetrically on the other side as
+ 
+
+ align:start position:0%
+and symmetrically on the other side as
+well and finally there is this constant
+
+ align:start position:0%
+well and finally there is this constant
+ 
+
+ align:start position:0%
+well and finally there is this constant
+where does this constant is coming from
+
+ align:start position:0%
+where does this constant is coming from
+ 
+
+ align:start position:0%
+where does this constant is coming from
+well there's a nice and not completely
+
+ align:start position:0%
+well there's a nice and not completely
+ 
+
+ align:start position:0%
+well there's a nice and not completely
+straightforward calculus exercise that
+
+ align:start position:0%
+straightforward calculus exercise that
+ 
+
+ align:start position:0%
+straightforward calculus exercise that
+tells us that the integral from minus
+
+ align:start position:0%
+tells us that the integral from minus
+ 
+
+ align:start position:0%
+tells us that the integral from minus
+infinity to plus infinity of e to the
+
+ align:start position:0%
+infinity to plus infinity of e to the
+ 
+
+ align:start position:0%
+infinity to plus infinity of e to the
+negative x squared over 2 DX is equal to
+
+ align:start position:0%
+negative x squared over 2 DX is equal to
+ 
+
+ align:start position:0%
+negative x squared over 2 DX is equal to
+the square root of 2 pi now we need a
+
+ align:start position:0%
+the square root of 2 pi now we need a
+ 
+
+ align:start position:0%
+the square root of 2 pi now we need a
+PDF to integrate to 1 and so for this to
+
+ align:start position:0%
+PDF to integrate to 1 and so for this to
+ 
+
+ align:start position:0%
+PDF to integrate to 1 and so for this to
+happen this is the constant that we need
+
+ align:start position:0%
+happen this is the constant that we need
+ 
+
+ align:start position:0%
+happen this is the constant that we need
+to put in front of this expression so
+
+ align:start position:0%
+to put in front of this expression so
+ 
+
+ align:start position:0%
+to put in front of this expression so
+that the integral becomes 1 and that
+
+ align:start position:0%
+that the integral becomes 1 and that
+ 
+
+ align:start position:0%
+that the integral becomes 1 and that
+explains the presence of this particular
+
+ align:start position:0%
+explains the presence of this particular
+ 
+
+ align:start position:0%
+explains the presence of this particular
+constant what is the mean of this random
+
+ align:start position:0%
+constant what is the mean of this random
+ 
+
+ align:start position:0%
+constant what is the mean of this random
+variable well x squared is symmetric
+
+ align:start position:0%
+variable well x squared is symmetric
+ 
+
+ align:start position:0%
+variable well x squared is symmetric
+around 0 and for this reason the PDF
+
+ align:start position:0%
+around 0 and for this reason the PDF
+ 
+
+ align:start position:0%
+around 0 and for this reason the PDF
+itself is symmetric around 0 and
+
+ align:start position:0%
+itself is symmetric around 0 and
+ 
+
+ align:start position:0%
+itself is symmetric around 0 and
+therefore by symmetry the mean has to be
+
+ align:start position:0%
+therefore by symmetry the mean has to be
+ 
+
+ align:start position:0%
+therefore by symmetry the mean has to be
+equal to 0 and that explains this entry
+
+ align:start position:0%
+equal to 0 and that explains this entry
+ 
+
+ align:start position:0%
+equal to 0 and that explains this entry
+here how about the variance well to
+
+ align:start position:0%
+here how about the variance well to
+ 
+
+ align:start position:0%
+here how about the variance well to
+calculate the variance you need to solve
+
+ align:start position:0%
+calculate the variance you need to solve
+ 
+
+ align:start position:0%
+calculate the variance you need to solve
+a calculus problem again you need to
+
+ align:start position:0%
+a calculus problem again you need to
+ 
+
+ align:start position:0%
+a calculus problem again you need to
+integrate by parts and after you carry
+
+ align:start position:0%
+integrate by parts and after you carry
+ 
+
+ align:start position:0%
+integrate by parts and after you carry
+out the calculation then you find that
+
+ align:start position:0%
+out the calculation then you find that
+ 
+
+ align:start position:0%
+out the calculation then you find that
+the variance is equal to 1 and that
+
+ align:start position:0%
+the variance is equal to 1 and that
+ 
+
+ align:start position:0%
+the variance is equal to 1 and that
+explains this entry here in the notation
+
+ align:start position:0%
+explains this entry here in the notation
+ 
+
+ align:start position:0%
+explains this entry here in the notation
+that we have been using let us now
+
+ align:start position:0%
+that we have been using let us now
+ 
+
+ align:start position:0%
+that we have been using let us now
+define general normal random variables
+
+ align:start position:0%
+define general normal random variables
+ 
+
+ align:start position:0%
+define general normal random variables
+general normal random variables are once
+
+ align:start position:0%
+general normal random variables are once
+ 
+
+ align:start position:0%
+general normal random variables are once
+more specified in terms of the
+
+ align:start position:0%
+more specified in terms of the
+ 
+
+ align:start position:0%
+more specified in terms of the
+corresponding PDF but this PDF is a
+
+ align:start position:0%
+corresponding PDF but this PDF is a
+ 
+
+ align:start position:0%
+corresponding PDF but this PDF is a
+little more complicated and in the
+
+ align:start position:0%
+little more complicated and in the
+ 
+
+ align:start position:0%
+little more complicated and in the
+involves two parameters mu and Sigma
+
+ align:start position:0%
+involves two parameters mu and Sigma
+ 
+
+ align:start position:0%
+involves two parameters mu and Sigma
+squared where Sigma is a given positive
+
+ align:start position:0%
+squared where Sigma is a given positive
+ 
+
+ align:start position:0%
+squared where Sigma is a given positive
+parameter once more it will have a bell
+
+ align:start position:0%
+parameter once more it will have a bell
+ 
+
+ align:start position:0%
+parameter once more it will have a bell
+shape but this Bell is no longer
+
+ align:start position:0%
+shape but this Bell is no longer
+ 
+
+ align:start position:0%
+shape but this Bell is no longer
+symmetric around 0 and there is some
+
+ align:start position:0%
+symmetric around 0 and there is some
+ 
+
+ align:start position:0%
+symmetric around 0 and there is some
+control over the width of it let us
+
+ align:start position:0%
+control over the width of it let us
+ 
+
+ align:start position:0%
+control over the width of it let us
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+the form of this PDF by focusing first
+
+ align:start position:0%
+the form of this PDF by focusing first
+ 
+
+ align:start position:0%
+the form of this PDF by focusing first
+on the exponent exactly as we did for
+
+ align:start position:0%
+on the exponent exactly as we did for
+ 
+
+ align:start position:0%
+on the exponent exactly as we did for
+the standard normal case the exponent is
+
+ align:start position:0%
+the standard normal case the exponent is
+ 
+
+ align:start position:0%
+the standard normal case the exponent is
+a quadratic and that quadratic is
+
+ align:start position:0%
+a quadratic and that quadratic is
+ 
+
+ align:start position:0%
+a quadratic and that quadratic is
+centered at X equal to MU so it vanishes
+
+ align:start position:0%
+centered at X equal to MU so it vanishes
+ 
+
+ align:start position:0%
+centered at X equal to MU so it vanishes
+when X is equal to MU and becomes
+
+ align:start position:0%
+when X is equal to MU and becomes
+ 
+
+ align:start position:0%
+when X is equal to MU and becomes
+positive L square then we take the
+
+ align:start position:0%
+positive L square then we take the
+ 
+
+ align:start position:0%
+positive L square then we take the
+negative exponential of this quadratic
+
+ align:start position:0%
+negative exponential of this quadratic
+ 
+
+ align:start position:0%
+negative exponential of this quadratic
+and we obtain a function which is
+
+ align:start position:0%
+and we obtain a function which is
+ 
+
+ align:start position:0%
+and we obtain a function which is
+largest at X equal to MU and falls off
+
+ align:start position:0%
+largest at X equal to MU and falls off
+ 
+
+ align:start position:0%
+largest at X equal to MU and falls off
+as we go further away from MU what is
+
+ align:start position:0%
+as we go further away from MU what is
+ 
+
+ align:start position:0%
+as we go further away from MU what is
+the mean of this random variable since
+
+ align:start position:0%
+the mean of this random variable since
+ 
+
+ align:start position:0%
+the mean of this random variable since
+this term is symmetric around mu the PDF
+
+ align:start position:0%
+this term is symmetric around mu the PDF
+ 
+
+ align:start position:0%
+this term is symmetric around mu the PDF
+is also symmetric around mu and
+
+ align:start position:0%
+is also symmetric around mu and
+ 
+
+ align:start position:0%
+is also symmetric around mu and
+therefore the mean is also equal to MU
+
+ align:start position:0%
+therefore the mean is also equal to MU
+ 
+
+ align:start position:0%
+therefore the mean is also equal to MU
+how about the variance it turns out and
+
+ align:start position:0%
+how about the variance it turns out and
+ 
+
+ align:start position:0%
+how about the variance it turns out and
+this is a calculus exercise that we will
+
+ align:start position:0%
+this is a calculus exercise that we will
+ 
+
+ align:start position:0%
+this is a calculus exercise that we will
+omit that the variance of this PDF is
+
+ align:start position:0%
+omit that the variance of this PDF is
+ 
+
+ align:start position:0%
+omit that the variance of this PDF is
+equal to Sigma squared and this explains
+
+ align:start position:0%
+equal to Sigma squared and this explains
+ 
+
+ align:start position:0%
+equal to Sigma squared and this explains
+this notation here we're dealing with a
+
+ align:start position:0%
+this notation here we're dealing with a
+ 
+
+ align:start position:0%
+this notation here we're dealing with a
+normal that has a mean of mu and the
+
+ align:start position:0%
+normal that has a mean of mu and the
+ 
+
+ align:start position:0%
+normal that has a mean of mu and the
+variance of Sigma squared to get a
+
+ align:start position:0%
+variance of Sigma squared to get a
+ 
+
+ align:start position:0%
+variance of Sigma squared to get a
+little bit of understanding of the role
+
+ align:start position:0%
+little bit of understanding of the role
+ 
+
+ align:start position:0%
+little bit of understanding of the role
+of Sigma in the form of this PDF let us
+
+ align:start position:0%
+of Sigma in the form of this PDF let us
+ 
+
+ align:start position:0%
+of Sigma in the form of this PDF let us
+consider the case where Sigma is small
+
+ align:start position:0%
+consider the case where Sigma is small
+ 
+
+ align:start position:0%
+consider the case where Sigma is small
+and see how the picture is going to
+
+ align:start position:0%
+and see how the picture is going to
+ 
+
+ align:start position:0%
+and see how the picture is going to
+change when Sigma is small and we plot
+
+ align:start position:0%
+change when Sigma is small and we plot
+ 
+
+ align:start position:0%
+change when Sigma is small and we plot
+the quadratic Sigma being small means
+
+ align:start position:0%
+the quadratic Sigma being small means
+ 
+
+ align:start position:0%
+the quadratic Sigma being small means
+that this quadratic becomes larger so it
+
+ align:start position:0%
+that this quadratic becomes larger so it
+ 
+
+ align:start position:0%
+that this quadratic becomes larger so it
+rises faster so we get a narrower
+
+ align:start position:0%
+rises faster so we get a narrower
+ 
+
+ align:start position:0%
+rises faster so we get a narrower
+quadratic and in that case the negative
+
+ align:start position:0%
+quadratic and in that case the negative
+ 
+
+ align:start position:0%
+quadratic and in that case the negative
+exponential is going to fall off much
+
+ align:start position:0%
+exponential is going to fall off much
+ 
+
+ align:start position:0%
+exponential is going to fall off much
+faster so when Sigma is small the PDF
+
+ align:start position:0%
+faster so when Sigma is small the PDF
+ 
+
+ align:start position:0%
+faster so when Sigma is small the PDF
+that we get is a narrower PDF and that
+
+ align:start position:0%
+that we get is a narrower PDF and that
+ 
+
+ align:start position:0%
+that we get is a narrower PDF and that
+will reflects itself in to the property
+
+ align:start position:0%
+will reflects itself in to the property
+ 
+
+ align:start position:0%
+will reflects itself in to the property
+that the variance will also be smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an important property of normal random
+
+ align:start position:0%
+an important property of normal random
+ 
+
+ align:start position:0%
+an important property of normal random
+variables is that they behave very
+
+ align:start position:0%
+variables is that they behave very
+ 
+
+ align:start position:0%
+variables is that they behave very
+nicely when you form linear functions of
+
+ align:start position:0%
+nicely when you form linear functions of
+ 
+
+ align:start position:0%
+nicely when you form linear functions of
+them and this is one of the reasons why
+
+ align:start position:0%
+them and this is one of the reasons why
+ 
+
+ align:start position:0%
+them and this is one of the reasons why
+they're analytically tractable and
+
+ align:start position:0%
+they're analytically tractable and
+ 
+
+ align:start position:0%
+they're analytically tractable and
+analytically very convenient here is
+
+ align:start position:0%
+analytically very convenient here is
+ 
+
+ align:start position:0%
+analytically very convenient here is
+what I mean let us start with a normal
+
+ align:start position:0%
+what I mean let us start with a normal
+ 
+
+ align:start position:0%
+what I mean let us start with a normal
+random variable with a given mean and
+
+ align:start position:0%
+random variable with a given mean and
+ 
+
+ align:start position:0%
+random variable with a given mean and
+variance and let us form a linear
+
+ align:start position:0%
+variance and let us form a linear
+ 
+
+ align:start position:0%
+variance and let us form a linear
+function of that random variable what is
+
+ align:start position:0%
+function of that random variable what is
+ 
+
+ align:start position:0%
+function of that random variable what is
+the mean of Y well we know what it is
+
+ align:start position:0%
+the mean of Y well we know what it is
+ 
+
+ align:start position:0%
+the mean of Y well we know what it is
+linear we have a linear function of a
+
+ align:start position:0%
+linear we have a linear function of a
+ 
+
+ align:start position:0%
+linear we have a linear function of a
+random variable the mean is going to be
+
+ align:start position:0%
+random variable the mean is going to be
+ 
+
+ align:start position:0%
+random variable the mean is going to be
+a times the expected value of x which is
+
+ align:start position:0%
+a times the expected value of x which is
+ 
+
+ align:start position:0%
+a times the expected value of x which is
+mu plus B what is the variance of Y we
+
+ align:start position:0%
+mu plus B what is the variance of Y we
+ 
+
+ align:start position:0%
+mu plus B what is the variance of Y we
+know what is the variance of a linear
+
+ align:start position:0%
+know what is the variance of a linear
+ 
+
+ align:start position:0%
+know what is the variance of a linear
+function of a random variable it is a
+
+ align:start position:0%
+function of a random variable it is a
+ 
+
+ align:start position:0%
+function of a random variable it is a
+squared times the variance of X which in
+
+ align:start position:0%
+squared times the variance of X which in
+ 
+
+ align:start position:0%
+squared times the variance of X which in
+our case is Sigma squared so there is
+
+ align:start position:0%
+our case is Sigma squared so there is
+ 
+
+ align:start position:0%
+our case is Sigma squared so there is
+nothing new so far but there is an
+
+ align:start position:0%
+nothing new so far but there is an
+ 
+
+ align:start position:0%
+nothing new so far but there is an
+additional important fact the random
+
+ align:start position:0%
+additional important fact the random
+ 
+
+ align:start position:0%
+additional important fact the random
+variable Y of course has the mean and
+
+ align:start position:0%
+variable Y of course has the mean and
+ 
+
+ align:start position:0%
+variable Y of course has the mean and
+variance that we know it should have but
+
+ align:start position:0%
+variance that we know it should have but
+ 
+
+ align:start position:0%
+variance that we know it should have but
+there is an additional fact namely that
+
+ align:start position:0%
+there is an additional fact namely that
+ 
+
+ align:start position:0%
+there is an additional fact namely that
+Y is a normal random variable so
+
+ align:start position:0%
+Y is a normal random variable so
+ 
+
+ align:start position:0%
+Y is a normal random variable so
+normality is preserved when we form
+
+ align:start position:0%
+normality is preserved when we form
+ 
+
+ align:start position:0%
+normality is preserved when we form
+linear functions there is one special
+
+ align:start position:0%
+linear functions there is one special
+ 
+
+ align:start position:0%
+linear functions there is one special
+case that we need to pay some attention
+
+ align:start position:0%
+case that we need to pay some attention
+ 
+
+ align:start position:0%
+case that we need to pay some attention
+to suppose that a is equal to 0 in this
+
+ align:start position:0%
+to suppose that a is equal to 0 in this
+ 
+
+ align:start position:0%
+to suppose that a is equal to 0 in this
+case the random variable Y is just equal
+
+ align:start position:0%
+case the random variable Y is just equal
+ 
+
+ align:start position:0%
+case the random variable Y is just equal
+to B it's a constant random variable it
+
+ align:start position:0%
+to B it's a constant random variable it
+ 
+
+ align:start position:0%
+to B it's a constant random variable it
+does not have a PDF it is a degenerate
+
+ align:start position:0%
+does not have a PDF it is a degenerate
+ 
+
+ align:start position:0%
+does not have a PDF it is a degenerate
+discrete random variable so could this
+
+ align:start position:0%
+discrete random variable so could this
+ 
+
+ align:start position:0%
+discrete random variable so could this
+fact be correct that Y is also normal
+
+ align:start position:0%
+fact be correct that Y is also normal
+ 
+
+ align:start position:0%
+fact be correct that Y is also normal
+one will will adopt this as convention
+
+ align:start position:0%
+one will will adopt this as convention
+ 
+
+ align:start position:0%
+one will will adopt this as convention
+when we have a discrete random variable
+
+ align:start position:0%
+when we have a discrete random variable
+ 
+
+ align:start position:0%
+when we have a discrete random variable
+which is constant it takes a constant
+
+ align:start position:0%
+which is constant it takes a constant
+ 
+
+ align:start position:0%
+which is constant it takes a constant
+value we can think of this as a special
+
+ align:start position:0%
+value we can think of this as a special
+ 
+
+ align:start position:0%
+value we can think of this as a special
+degenerate case of the normal with mean
+
+ align:start position:0%
+degenerate case of the normal with mean
+ 
+
+ align:start position:0%
+degenerate case of the normal with mean
+equal to B and with variance equal to 0
+
+ align:start position:0%
+equal to B and with variance equal to 0
+ 
+
+ align:start position:0%
+equal to B and with variance equal to 0
+even though it is discrete not
+
+ align:start position:0%
+even though it is discrete not
+ 
+
+ align:start position:0%
+even though it is discrete not
+continuous we will still think of it as
+
+ align:start position:0%
+continuous we will still think of it as
+ 
+
+ align:start position:0%
+continuous we will still think of it as
+a degenerate type of a normal random
+
+ align:start position:0%
+a degenerate type of a normal random
+ 
+
+ align:start position:0%
+a degenerate type of a normal random
+variable and by adopting this convention
+
+ align:start position:0%
+variable and by adopting this convention
+ 
+
+ align:start position:0%
+variable and by adopting this convention
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we'll always be true that a linear
+
+ align:start position:0%
+we'll always be true that a linear
+ 
+
+ align:start position:0%
+we'll always be true that a linear
+function of a normal random variable is
+
+ align:start position:0%
+function of a normal random variable is
+ 
+
+ align:start position:0%
+function of a normal random variable is
+normal even if a is equal to zero now
+
+ align:start position:0%
+normal even if a is equal to zero now
+ 
+
+ align:start position:0%
+normal even if a is equal to zero now
+that we have the definition and some
+
+ align:start position:0%
+that we have the definition and some
+ 
+
+ align:start position:0%
+that we have the definition and some
+properties of normal random variables
+
+ align:start position:0%
+properties of normal random variables
+ 
+
+ align:start position:0%
+properties of normal random variables
+the next question is whether we can
+
+ align:start position:0%
+the next question is whether we can
+ 
+
+ align:start position:0%
+the next question is whether we can
+calculate probabilities associated with
+
+ align:start position:0%
+calculate probabilities associated with
+ 
+
+ align:start position:0%
+calculate probabilities associated with
+normal random variables this will be the
+
+ align:start position:0%
+normal random variables this will be the
+ 
+
+ align:start position:0%
+normal random variables this will be the
+subject of the next segment
\ No newline at end of file
diff --git a/6wbWEDAg3B0.txt b/6wbWEDAg3B0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..94b109f3c3149a13a60a661800e7e931af3d438c
--- /dev/null
+++ b/6wbWEDAg3B0.txt
@@ -0,0 +1,6186 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this the main topic of this lecture
+
+ align:start position:0%
+now this the main topic of this lecture
+ 
+
+ align:start position:0%
+now this the main topic of this lecture
+is so important and so beautiful that I
+
+ align:start position:0%
+is so important and so beautiful that I
+ 
+
+ align:start position:0%
+is so important and so beautiful that I
+don't want to spend any time reviewing
+
+ align:start position:0%
+don't want to spend any time reviewing
+ 
+
+ align:start position:0%
+don't want to spend any time reviewing
+what I did last time at the beginning
+
+ align:start position:0%
+what I did last time at the beginning
+ 
+
+ align:start position:0%
+what I did last time at the beginning
+when we talked about the rigid rotor I
+
+ align:start position:0%
+when we talked about the rigid rotor I
+ 
+
+ align:start position:0%
+when we talked about the rigid rotor I
+said that this is a not just a simple
+
+ align:start position:0%
+said that this is a not just a simple
+ 
+
+ align:start position:0%
+said that this is a not just a simple
+exactly solve problem but it tells you
+
+ align:start position:0%
+exactly solve problem but it tells you
+ 
+
+ align:start position:0%
+exactly solve problem but it tells you
+about the angular part of every central
+
+ align:start position:0%
+about the angular part of every central
+ 
+
+ align:start position:0%
+about the angular part of every central
+force problem and it's even more than
+
+ align:start position:0%
+force problem and it's even more than
+ 
+
+ align:start position:0%
+force problem and it's even more than
+that it enables you to do a certain kind
+
+ align:start position:0%
+that it enables you to do a certain kind
+ 
+
+ align:start position:0%
+that it enables you to do a certain kind
+of algebra with operators which enables
+
+ align:start position:0%
+of algebra with operators which enables
+ 
+
+ align:start position:0%
+of algebra with operators which enables
+you to minimize the effort of
+
+ align:start position:0%
+you to minimize the effort of
+ 
+
+ align:start position:0%
+you to minimize the effort of
+calculating matrix elements and
+
+ align:start position:0%
+calculating matrix elements and
+ 
+
+ align:start position:0%
+calculating matrix elements and
+predicting selection rules simply by the
+
+ align:start position:0%
+predicting selection rules simply by the
+ 
+
+ align:start position:0%
+predicting selection rules simply by the
+basis of commutation rules of the
+
+ align:start position:0%
+basis of commutation rules of the
+ 
+
+ align:start position:0%
+basis of commutation rules of the
+operators without ever looking at wave
+
+ align:start position:0%
+operators without ever looking at wave
+ 
+
+ align:start position:0%
+operators without ever looking at wave
+functions without ever looking at
+
+ align:start position:0%
+functions without ever looking at
+ 
+
+ align:start position:0%
+functions without ever looking at
+differential operators this is a really
+
+ align:start position:0%
+differential operators this is a really
+ 
+
+ align:start position:0%
+differential operators this is a really
+beautiful thing about angular momentum
+
+ align:start position:0%
+beautiful thing about angular momentum
+ 
+
+ align:start position:0%
+beautiful thing about angular momentum
+that if we define the angular momentum
+
+ align:start position:0%
+that if we define the angular momentum
+ 
+
+ align:start position:0%
+that if we define the angular momentum
+in this abstract way and I'll describe
+
+ align:start position:0%
+in this abstract way and I'll describe
+ 
+
+ align:start position:0%
+in this abstract way and I'll describe
+what I mean by this epsilon ijk if we
+
+ align:start position:0%
+what I mean by this epsilon ijk if we
+ 
+
+ align:start position:0%
+what I mean by this epsilon ijk if we
+say we have an operator which obeys this
+
+ align:start position:0%
+say we have an operator which obeys this
+ 
+
+ align:start position:0%
+say we have an operator which obeys this
+sort of this commutation rule we will
+
+ align:start position:0%
+sort of this commutation rule we will
+ 
+
+ align:start position:0%
+sort of this commutation rule we will
+call it an angular momentum and we go
+
+ align:start position:0%
+call it an angular momentum and we go
+ 
+
+ align:start position:0%
+call it an angular momentum and we go
+through some arguments and we discover
+
+ align:start position:0%
+through some arguments and we discover
+ 
+
+ align:start position:0%
+through some arguments and we discover
+the properties of all angular momentum
+
+ align:start position:0%
+the properties of all angular momentum
+ 
+
+ align:start position:0%
+the properties of all angular momentum
+in quotes now we define an angular
+
+ align:start position:0%
+in quotes now we define an angular
+ 
+
+ align:start position:0%
+in quotes now we define an angular
+momentum classically it's R cross P it's
+
+ align:start position:0%
+momentum classically it's R cross P it's
+ 
+
+ align:start position:0%
+momentum classically it's R cross P it's
+a vector and now there are things where
+
+ align:start position:0%
+a vector and now there are things where
+ 
+
+ align:start position:0%
+a vector and now there are things where
+operators where there is no R or P what
+
+ align:start position:0%
+operators where there is no R or P what
+ 
+
+ align:start position:0%
+operators where there is no R or P what
+we would like to describe them as
+
+ align:start position:0%
+we would like to describe them as
+ 
+
+ align:start position:0%
+we would like to describe them as
+angular momenta one of them is electron
+
+ align:start position:0%
+angular momenta one of them is electron
+ 
+
+ align:start position:0%
+angular momenta one of them is electron
+spin something that we sort of take for
+
+ align:start position:0%
+spin something that we sort of take for
+ 
+
+ align:start position:0%
+spin something that we sort of take for
+granted and nuclear spin all of magnetic
+
+ align:start position:0%
+granted and nuclear spin all of magnetic
+ 
+
+ align:start position:0%
+granted and nuclear spin all of magnetic
+NMR
+
+ align:start position:0%
+NMR
+ 
+
+ align:start position:0%
+NMR
+is based on these things we call angular
+
+ align:start position:0%
+is based on these things we call angular
+ 
+
+ align:start position:0%
+is based on these things we call angular
+momenta because they obey some rules and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm going to do is show the
+
+ align:start position:0%
+so what I'm going to do is show the
+ 
+
+ align:start position:0%
+so what I'm going to do is show the
+rules and show where all of this comes
+
+ align:start position:0%
+rules and show where all of this comes
+ 
+
+ align:start position:0%
+rules and show where all of this comes
+from and that this is an abstract and so
+
+ align:start position:0%
+from and that this is an abstract and so
+ 
+
+ align:start position:0%
+from and that this is an abstract and so
+kind of dry derivation but it has
+
+ align:start position:0%
+kind of dry derivation but it has
+ 
+
+ align:start position:0%
+kind of dry derivation but it has
+astonishing consequences and basically
+
+ align:start position:0%
+astonishing consequences and basically
+ 
+
+ align:start position:0%
+astonishing consequences and basically
+it means that if you've got angular
+
+ align:start position:0%
+it means that if you've got angular
+ 
+
+ align:start position:0%
+it means that if you've got angular
+momenta if you know these rules you're
+
+ align:start position:0%
+momenta if you know these rules you're
+ 
+
+ align:start position:0%
+momenta if you know these rules you're
+never going to evaluate another matrix
+
+ align:start position:0%
+never going to evaluate another matrix
+ 
+
+ align:start position:0%
+never going to evaluate another matrix
+of them in your life now it has another
+
+ align:start position:0%
+of them in your life now it has another
+ 
+
+ align:start position:0%
+of them in your life now it has another
+level of complexity sometimes you have
+
+ align:start position:0%
+level of complexity sometimes you have
+ 
+
+ align:start position:0%
+level of complexity sometimes you have
+operators that are made out of
+
+ align:start position:0%
+operators that are made out of
+ 
+
+ align:start position:0%
+operators that are made out of
+combinations of angular momenta and you
+
+ align:start position:0%
+combinations of angular momenta and you
+ 
+
+ align:start position:0%
+combinations of angular momenta and you
+can use these sorts of arguments to
+
+ align:start position:0%
+can use these sorts of arguments to
+ 
+
+ align:start position:0%
+can use these sorts of arguments to
+derive the matrix elements of them
+
+ align:start position:0%
+derive the matrix elements of them
+ 
+
+ align:start position:0%
+derive the matrix elements of them
+that's called the Vigna record theorem
+
+ align:start position:0%
+that's called the Vigna record theorem
+ 
+
+ align:start position:0%
+that's called the Vigna record theorem
+and it means that the angular part of
+
+ align:start position:0%
+and it means that the angular part of
+ 
+
+ align:start position:0%
+and it means that the angular part of
+every operator is in your hands without
+
+ align:start position:0%
+every operator is in your hands without
+ 
+
+ align:start position:0%
+every operator is in your hands without
+ever looking at a wave function or a
+
+ align:start position:0%
+ever looking at a wave function or a
+ 
+
+ align:start position:0%
+ever looking at a wave function or a
+differential operator now we're not
+
+ align:start position:0%
+differential operator now we're not
+ 
+
+ align:start position:0%
+differential operator now we're not
+going to go there but this is a very
+
+ align:start position:0%
+going to go there but this is a very
+ 
+
+ align:start position:0%
+going to go there but this is a very
+important area of quantum mechanics and
+
+ align:start position:0%
+important area of quantum mechanics and
+ 
+
+ align:start position:0%
+important area of quantum mechanics and
+you've heard of three J symbols and
+
+ align:start position:0%
+you've heard of three J symbols and
+ 
+
+ align:start position:0%
+you've heard of three J symbols and
+raqqa coefficients and maybe you haven't
+
+ align:start position:0%
+raqqa coefficients and maybe you haven't
+ 
+
+ align:start position:0%
+raqqa coefficients and maybe you haven't
+but there is just a rich literature of
+
+ align:start position:0%
+but there is just a rich literature of
+ 
+
+ align:start position:0%
+but there is just a rich literature of
+this sort of stuff ok so today I'm going
+
+ align:start position:0%
+this sort of stuff ok so today I'm going
+ 
+
+ align:start position:0%
+this sort of stuff ok so today I'm going
+to talk briefly about rotational spectra
+
+ align:start position:0%
+to talk briefly about rotational spectra
+ 
+
+ align:start position:0%
+to talk briefly about rotational spectra
+because I'm a spectroscopy and from
+
+ align:start position:0%
+because I'm a spectroscopy and from
+ 
+
+ align:start position:0%
+because I'm a spectroscopy and from
+rotational spectra we learn about
+
+ align:start position:0%
+rotational spectra we learn about
+ 
+
+ align:start position:0%
+rotational spectra we learn about
+molecular geometry now it's really
+
+ align:start position:0%
+molecular geometry now it's really
+ 
+
+ align:start position:0%
+molecular geometry now it's really
+strange
+
+ align:start position:0%
+strange
+ 
+
+ align:start position:0%
+strange
+because why don't we just look at a
+
+ align:start position:0%
+because why don't we just look at a
+ 
+
+ align:start position:0%
+because why don't we just look at a
+molecule and measure it well we can't
+
+ align:start position:0%
+molecule and measure it well we can't
+ 
+
+ align:start position:0%
+molecule and measure it well we can't
+because it's smaller than the wavelength
+
+ align:start position:0%
+because it's smaller than the wavelength
+ 
+
+ align:start position:0%
+because it's smaller than the wavelength
+of light that we use we would use to
+
+ align:start position:0%
+of light that we use we would use to
+ 
+
+ align:start position:0%
+of light that we use we would use to
+illuminate our ruler and so we get the
+
+ align:start position:0%
+illuminate our ruler and so we get the
+ 
+
+ align:start position:0%
+illuminate our ruler and so we get the
+structure of a molecule the geometric
+
+ align:start position:0%
+structure of a molecule the geometric
+ 
+
+ align:start position:0%
+structure of a molecule the geometric
+structure at least part of it from the
+
+ align:start position:0%
+structure at least part of it from the
+ 
+
+ align:start position:0%
+structure at least part of it from the
+rotational spectrum now I'm only going
+
+ align:start position:0%
+rotational spectrum now I'm only going
+ 
+
+ align:start position:0%
+rotational spectrum now I'm only going
+to talk about the rotational spectrum of
+
+ align:start position:0%
+to talk about the rotational spectrum of
+ 
+
+ align:start position:0%
+to talk about the rotational spectrum of
+a diatomic molecule you don't want me to
+
+ align:start position:0%
+a diatomic molecule you don't want me to
+ 
+
+ align:start position:0%
+a diatomic molecule you don't want me to
+go further because polyatomic molecules
+
+ align:start position:0%
+go further because polyatomic molecules
+ 
+
+ align:start position:0%
+go further because polyatomic molecules
+have extra complexity which you could
+
+ align:start position:0%
+have extra complexity which you could
+ 
+
+ align:start position:0%
+have extra complexity which you could
+understand but I don't want to go there
+
+ align:start position:0%
+understand but I don't want to go there
+ 
+
+ align:start position:0%
+understand but I don't want to go there
+because we got a lot of other stuff to
+
+ align:start position:0%
+because we got a lot of other stuff to
+ 
+
+ align:start position:0%
+because we got a lot of other stuff to
+do I also had promised to talk about
+
+ align:start position:0%
+do I also had promised to talk about
+ 
+
+ align:start position:0%
+do I also had promised to talk about
+visualization of wave functions and I'll
+
+ align:start position:0%
+visualization of wave functions and I'll
+ 
+
+ align:start position:0%
+visualization of wave functions and I'll
+leave that to your previous experience
+
+ align:start position:0%
+leave that to your previous experience
+ 
+
+ align:start position:0%
+leave that to your previous experience
+but I do want to comment we often take a
+
+ align:start position:0%
+but I do want to comment we often take a
+ 
+
+ align:start position:0%
+but I do want to comment we often take a
+sum of wave functions for positive and
+
+ align:start position:0%
+sum of wave functions for positive and
+ 
+
+ align:start position:0%
+sum of wave functions for positive and
+negative projection quantum numbers to
+
+ align:start position:0%
+negative projection quantum numbers to
+ 
+
+ align:start position:0%
+negative projection quantum numbers to
+make them real or pure imaginary when we
+
+ align:start position:0%
+make them real or pure imaginary when we
+ 
+
+ align:start position:0%
+make them real or pure imaginary when we
+do that there are still I can functions
+
+ align:start position:0%
+do that there are still I can functions
+ 
+
+ align:start position:0%
+do that there are still I can functions
+of the angular momentum squared but
+
+ align:start position:0%
+of the angular momentum squared but
+ 
+
+ align:start position:0%
+of the angular momentum squared but
+they're not eigenfunctions of a
+
+ align:start position:0%
+they're not eigenfunctions of a
+ 
+
+ align:start position:0%
+they're not eigenfunctions of a
+projection and you could in fact maybe
+
+ align:start position:0%
+projection and you could in fact maybe
+ 
+
+ align:start position:0%
+projection and you could in fact maybe
+you will on Thursday
+
+ align:start position:0%
+you will on Thursday
+ 
+
+ align:start position:0%
+you will on Thursday
+actually evaluate L Z times a
+
+ align:start position:0%
+actually evaluate L Z times a
+ 
+
+ align:start position:0%
+actually evaluate L Z times a
+symmetrized function so by symmetry
+
+ align:start position:0%
+symmetrized function so by symmetry
+ 
+
+ align:start position:0%
+symmetrized function so by symmetry
+seing them you'll get to see the nodal
+
+ align:start position:0%
+seing them you'll get to see the nodal
+ 
+
+ align:start position:0%
+seing them you'll get to see the nodal
+structure which is nice but you lose the
+
+ align:start position:0%
+structure which is nice but you lose the
+ 
+
+ align:start position:0%
+structure which is nice but you lose the
+fact that you have Augen functions of a
+
+ align:start position:0%
+fact that you have Augen functions of a
+ 
+
+ align:start position:0%
+fact that you have Augen functions of a
+projection angular momentum and that's
+
+ align:start position:0%
+projection angular momentum and that's
+ 
+
+ align:start position:0%
+projection angular momentum and that's
+that's kind of sad okay so spectra and
+
+ align:start position:0%
+that's kind of sad okay so spectra and
+ 
+
+ align:start position:0%
+that's kind of sad okay so spectra and
+so we have a a diatomic molecule ma MB
+
+ align:start position:0%
+so we have a a diatomic molecule ma MB
+ 
+
+ align:start position:0%
+so we have a a diatomic molecule ma MB
+we have a center of mass and and so
+
+ align:start position:0%
+we have a center of mass and and so
+ 
+
+ align:start position:0%
+we have a center of mass and and so
+we're going to be interested in the
+
+ align:start position:0%
+we're going to be interested in the
+ 
+
+ align:start position:0%
+we're going to be interested in the
+energy levels for rotation of the
+
+ align:start position:0%
+energy levels for rotation of the
+ 
+
+ align:start position:0%
+energy levels for rotation of the
+molecule around an axis which is
+
+ align:start position:0%
+molecule around an axis which is
+ 
+
+ align:start position:0%
+molecule around an axis which is
+perpendicular to the bond axis and when
+
+ align:start position:0%
+perpendicular to the bond axis and when
+ 
+
+ align:start position:0%
+perpendicular to the bond axis and when
+we do that we discovered that the energy
+
+ align:start position:0%
+we do that we discovered that the energy
+ 
+
+ align:start position:0%
+we do that we discovered that the energy
+levels are given by the rotational
+
+ align:start position:0%
+levels are given by the rotational
+ 
+
+ align:start position:0%
+levels are given by the rotational
+Hamiltonian and for rotation it's free
+
+ align:start position:0%
+Hamiltonian and for rotation it's free
+ 
+
+ align:start position:0%
+Hamiltonian and for rotation it's free
+rotation so there's no potential and the
+
+ align:start position:0%
+rotation so there's no potential and the
+ 
+
+ align:start position:0%
+rotation so there's no potential and the
+operator is l squared or Jase
+
+ align:start position:0%
+operator is l squared or Jase
+ 
+
+ align:start position:0%
+operator is l squared or Jase
+that's another thing you know you
+
+ align:start position:0%
+that's another thing you know you
+ 
+
+ align:start position:0%
+that's another thing you know you
+already have experienced my use of L and
+
+ align:start position:0%
+already have experienced my use of L and
+ 
+
+ align:start position:0%
+already have experienced my use of L and
+J and maybe some other things they're
+
+ align:start position:0%
+J and maybe some other things they're
+ 
+
+ align:start position:0%
+J and maybe some other things they're
+all angular momenta they're all the same
+
+ align:start position:0%
+all angular momenta they're all the same
+ 
+
+ align:start position:0%
+all angular momenta they're all the same
+sort of thing although L is usually
+
+ align:start position:0%
+sort of thing although L is usually
+ 
+
+ align:start position:0%
+sort of thing although L is usually
+referring to electronic coordinates and
+
+ align:start position:0%
+referring to electronic coordinates and
+ 
+
+ align:start position:0%
+referring to electronic coordinates and
+J is usually referring to nuclear
+
+ align:start position:0%
+J is usually referring to nuclear
+ 
+
+ align:start position:0%
+J is usually referring to nuclear
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+Big D no but you get a sense that we're
+
+ align:start position:0%
+Big D no but you get a sense that we're
+ 
+
+ align:start position:0%
+Big D no but you get a sense that we're
+talking about a very rich rich idea
+
+ align:start position:0%
+talking about a very rich rich idea
+ 
+
+ align:start position:0%
+talking about a very rich rich idea
+where it doesn't matter what you name
+
+ align:start position:0%
+where it doesn't matter what you name
+ 
+
+ align:start position:0%
+where it doesn't matter what you name
+the things we they follow the same rules
+
+ align:start position:0%
+the things we they follow the same rules
+ 
+
+ align:start position:0%
+the things we they follow the same rules
+okay so we have a single term in the
+
+ align:start position:0%
+okay so we have a single term in the
+ 
+
+ align:start position:0%
+okay so we have a single term in the
+Hamiltonian you are zero squared or this
+
+ align:start position:0%
+Hamiltonian you are zero squared or this
+ 
+
+ align:start position:0%
+Hamiltonian you are zero squared or this
+might be the equilibrium instead of the
+
+ align:start position:0%
+might be the equilibrium instead of the
+ 
+
+ align:start position:0%
+might be the equilibrium instead of the
+the just affixed in your nuclear
+
+ align:start position:0%
+the just affixed in your nuclear
+ 
+
+ align:start position:0%
+the just affixed in your nuclear
+distance but we're talking about a rigid
+
+ align:start position:0%
+distance but we're talking about a rigid
+ 
+
+ align:start position:0%
+distance but we're talking about a rigid
+rotor so our zero is the inter nuclear
+
+ align:start position:0%
+rotor so our zero is the inter nuclear
+ 
+
+ align:start position:0%
+rotor so our zero is the inter nuclear
+distance and now I want to be able to
+
+ align:start position:0%
+distance and now I want to be able to
+ 
+
+ align:start position:0%
+distance and now I want to be able to
+the right okay so I want to have this
+
+ align:start position:0%
+the right okay so I want to have this
+ 
+
+ align:start position:0%
+the right okay so I want to have this
+quantity I want to have this quantity in
+
+ align:start position:0%
+quantity I want to have this quantity in
+ 
+
+ align:start position:0%
+quantity I want to have this quantity in
+reciprocal centimeter units because
+
+ align:start position:0%
+reciprocal centimeter units because
+ 
+
+ align:start position:0%
+reciprocal centimeter units because
+that's what all spectroscopy is do or
+
+ align:start position:0%
+that's what all spectroscopy is do or
+ 
+
+ align:start position:0%
+that's what all spectroscopy is do or
+sometimes they use megahertz in that
+
+ align:start position:0%
+sometimes they use megahertz in that
+ 
+
+ align:start position:0%
+sometimes they use megahertz in that
+case the the speed of light is gone and
+
+ align:start position:0%
+case the the speed of light is gone and
+ 
+
+ align:start position:0%
+case the the speed of light is gone and
+when I when I evaluate the effect of
+
+ align:start position:0%
+when I when I evaluate the effect of
+ 
+
+ align:start position:0%
+when I when I evaluate the effect of
+this operator on a wave function we get
+
+ align:start position:0%
+this operator on a wave function we get
+ 
+
+ align:start position:0%
+this operator on a wave function we get
+an H bar squared which cancels that we
+
+ align:start position:0%
+an H bar squared which cancels that we
+ 
+
+ align:start position:0%
+an H bar squared which cancels that we
+would like to have an energy level
+
+ align:start position:0%
+would like to have an energy level
+ 
+
+ align:start position:0%
+would like to have an energy level
+expression e JM is equal to HC be L so
+
+ align:start position:0%
+expression e JM is equal to HC be L so
+ 
+
+ align:start position:0%
+expression e JM is equal to HC be L so
+the units of be just accommodate the
+
+ align:start position:0%
+the units of be just accommodate the
+ 
+
+ align:start position:0%
+the units of be just accommodate the
+fact that we want it in wave numbers
+
+ align:start position:0%
+fact that we want it in wave numbers
+ 
+
+ align:start position:0%
+fact that we want it in wave numbers
+but this is energy so we need the HC and
+
+ align:start position:0%
+but this is energy so we need the HC and
+ 
+
+ align:start position:0%
+but this is energy so we need the HC and
+when the operator operates we get an H
+
+ align:start position:0%
+when the operator operates we get an H
+ 
+
+ align:start position:0%
+when the operator operates we get an H
+bar squared and that that's cancelled by
+
+ align:start position:0%
+bar squared and that that's cancelled by
+ 
+
+ align:start position:0%
+bar squared and that that's cancelled by
+this factor here and so the handy dandy
+
+ align:start position:0%
+this factor here and so the handy dandy
+ 
+
+ align:start position:0%
+this factor here and so the handy dandy
+expression for the rotational constant
+
+ align:start position:0%
+expression for the rotational constant
+ 
+
+ align:start position:0%
+expression for the rotational constant
+is sixteen point eight five six seven
+
+ align:start position:0%
+is sixteen point eight five six seven
+ 
+
+ align:start position:0%
+is sixteen point eight five six seven
+three times the reduced mass in a.m.
+
+ align:start position:0%
+three times the reduced mass in a.m.
+ 
+
+ align:start position:0%
+three times the reduced mass in a.m.
+units times the internuclear distance in
+
+ align:start position:0%
+units times the internuclear distance in
+ 
+
+ align:start position:0%
+units times the internuclear distance in
+angstrom units squared reciprocal so if
+
+ align:start position:0%
+angstrom units squared reciprocal so if
+ 
+
+ align:start position:0%
+angstrom units squared reciprocal so if
+you want to know the energy I want to
+
+ align:start position:0%
+you want to know the energy I want to
+ 
+
+ align:start position:0%
+you want to know the energy I want to
+know the rotational constant in wave
+
+ align:start position:0%
+know the rotational constant in wave
+ 
+
+ align:start position:0%
+know the rotational constant in wave
+number units this is the conversion big
+
+ align:start position:0%
+number units this is the conversion big
+ 
+
+ align:start position:0%
+number units this is the conversion big
+deal okay so the energy levels are
+
+ align:start position:0%
+deal okay so the energy levels are
+ 
+
+ align:start position:0%
+deal okay so the energy levels are
+simply well I'm gonna stick with a lemon
+
+ align:start position:0%
+simply well I'm gonna stick with a lemon
+ 
+
+ align:start position:0%
+simply well I'm gonna stick with a lemon
+even though I'm the hardwired to call it
+
+ align:start position:0%
+even though I'm the hardwired to call it
+ 
+
+ align:start position:0%
+even though I'm the hardwired to call it
+J now if I go back and forth between J
+
+ align:start position:0%
+J now if I go back and forth between J
+ 
+
+ align:start position:0%
+J now if I go back and forth between J
+and L have to forgive me because you
+
+ align:start position:0%
+and L have to forgive me because you
+ 
+
+ align:start position:0%
+and L have to forgive me because you
+know I just can't yes all right so we
+
+ align:start position:0%
+know I just can't yes all right so we
+ 
+
+ align:start position:0%
+know I just can't yes all right so we
+have the energy levels HC B times L L
+
+ align:start position:0%
+have the energy levels HC B times L L
+ 
+
+ align:start position:0%
+have the energy levels HC B times L L
+plus one now L is an integer and for the
+
+ align:start position:0%
+plus one now L is an integer and for the
+ 
+
+ align:start position:0%
+plus one now L is an integer and for the
+simple diatomic so you're going to deal
+
+ align:start position:0%
+simple diatomic so you're going to deal
+ 
+
+ align:start position:0%
+simple diatomic so you're going to deal
+with it's an injury can start at zero
+
+ align:start position:0%
+with it's an injury can start at zero
+ 
+
+ align:start position:0%
+with it's an injury can start at zero
+and so the energy levels be ll plus 1 B
+
+ align:start position:0%
+and so the energy levels be ll plus 1 B
+ 
+
+ align:start position:0%
+and so the energy levels be ll plus 1 B
+L plus 1 is 2 I want to make this look
+
+ align:start position:0%
+L plus 1 is 2 I want to make this look
+ 
+
+ align:start position:0%
+L plus 1 is 2 I want to make this look
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is 1 times 2 this is 2 times 3 and
+
+ align:start position:0%
+this is 1 times 2 this is 2 times 3 and
+ 
+
+ align:start position:0%
+this is 1 times 2 this is 2 times 3 and
+the 3 times 4 is 12
+
+ align:start position:0%
+the 3 times 4 is 12
+ 
+
+ align:start position:0%
+the 3 times 4 is 12
+and the important thing is that this
+
+ align:start position:0%
+and the important thing is that this
+ 
+
+ align:start position:0%
+and the important thing is that this
+energy difference is 2p this energy
+
+ align:start position:0%
+energy difference is 2p this energy
+ 
+
+ align:start position:0%
+energy difference is 2p this energy
+differences for B this energy difference
+
+ align:start position:0%
+differences for B this energy difference
+ 
+
+ align:start position:0%
+differences for B this energy difference
+is 6p and so what happens in the
+
+ align:start position:0%
+is 6p and so what happens in the
+ 
+
+ align:start position:0%
+is 6p and so what happens in the
+spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's energy here is 0 we have a line
+
+ align:start position:0%
+here's energy here is 0 we have a line
+ 
+
+ align:start position:0%
+here's energy here is 0 we have a line
+here it to be a line here at 4 b 6 b 8 b
+
+ align:start position:0%
+here it to be a line here at 4 b 6 b 8 b
+ 
+
+ align:start position:0%
+here it to be a line here at 4 b 6 b 8 b
+so if you were able to look at the
+
+ align:start position:0%
+so if you were able to look at the
+ 
+
+ align:start position:0%
+so if you were able to look at the
+rotational spectrum the lines in the
+
+ align:start position:0%
+rotational spectrum the lines in the
+ 
+
+ align:start position:0%
+rotational spectrum the lines in the
+spectrum would be evenly spaced the
+
+ align:start position:0%
+spectrum would be evenly spaced the
+ 
+
+ align:start position:0%
+spectrum would be evenly spaced the
+levels are not that's very important
+
+ align:start position:0%
+levels are not that's very important
+ 
+
+ align:start position:0%
+levels are not that's very important
+especially when you start doing
+
+ align:start position:0%
+especially when you start doing
+ 
+
+ align:start position:0%
+especially when you start doing
+perturbation theory because you're going
+
+ align:start position:0%
+perturbation theory because you're going
+ 
+
+ align:start position:0%
+perturbation theory because you're going
+to have energy denominators which are
+
+ align:start position:0%
+to have energy denominators which are
+ 
+
+ align:start position:0%
+to have energy denominators which are
+multiples of a common factor but they're
+
+ align:start position:0%
+multiples of a common factor but they're
+ 
+
+ align:start position:0%
+multiples of a common factor but they're
+not equal to each other okay but we have
+
+ align:start position:0%
+not equal to each other okay but we have
+ 
+
+ align:start position:0%
+not equal to each other okay but we have
+a spectrum and it looks really really
+
+ align:start position:0%
+a spectrum and it looks really really
+ 
+
+ align:start position:0%
+a spectrum and it looks really really
+trivial and textbooks don't talk about
+
+ align:start position:0%
+trivial and textbooks don't talk about
+ 
+
+ align:start position:0%
+trivial and textbooks don't talk about
+this but if you have a relatively light
+
+ align:start position:0%
+this but if you have a relatively light
+ 
+
+ align:start position:0%
+this but if you have a relatively light
+diatomic molecule and you have a
+
+ align:start position:0%
+diatomic molecule and you have a
+ 
+
+ align:start position:0%
+diatomic molecule and you have a
+laboratory which is equipped with a
+
+ align:start position:0%
+laboratory which is equipped with a
+ 
+
+ align:start position:0%
+laboratory which is equipped with a
+microwave spectrometer which is able to
+
+ align:start position:0%
+microwave spectrometer which is able to
+ 
+
+ align:start position:0%
+microwave spectrometer which is able to
+generate data that got you tenure and
+
+ align:start position:0%
+generate data that got you tenure and
+ 
+
+ align:start position:0%
+generate data that got you tenure and
+whatever it's it's probably a
+
+ align:start position:0%
+whatever it's it's probably a
+ 
+
+ align:start position:0%
+whatever it's it's probably a
+spectrometer where the tuning range of
+
+ align:start position:0%
+spectrometer where the tuning range of
+ 
+
+ align:start position:0%
+spectrometer where the tuning range of
+the microwave oscillator is about 30%
+
+ align:start position:0%
+the microwave oscillator is about 30%
+ 
+
+ align:start position:0%
+the microwave oscillator is about 30%
+that's a lot if you think about NMR the
+
+ align:start position:0%
+that's a lot if you think about NMR the
+ 
+
+ align:start position:0%
+that's a lot if you think about NMR the
+the tuning range is 30% is huge so you
+
+ align:start position:0%
+the tuning range is 30% is huge so you
+ 
+
+ align:start position:0%
+the tuning range is 30% is huge so you
+see this and you say oh yeah i could
+
+ align:start position:0%
+see this and you say oh yeah i could
+ 
+
+ align:start position:0%
+see this and you say oh yeah i could
+assign that spectrum because an obvious
+
+ align:start position:0%
+assign that spectrum because an obvious
+ 
+
+ align:start position:0%
+assign that spectrum because an obvious
+pattern but what happens in the spectrum
+
+ align:start position:0%
+pattern but what happens in the spectrum
+ 
+
+ align:start position:0%
+pattern but what happens in the spectrum
+is you get one line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you say well what is you know I
+
+ align:start position:0%
+and so you say well what is you know I
+ 
+
+ align:start position:0%
+and so you say well what is you know I
+need to know the inter nuclear distance
+
+ align:start position:0%
+need to know the inter nuclear distance
+ 
+
+ align:start position:0%
+need to know the inter nuclear distance
+in this molecule to six or eight or ten
+
+ align:start position:0%
+in this molecule to six or eight or ten
+ 
+
+ align:start position:0%
+in this molecule to six or eight or ten
+digits but I get one line there's no
+
+ align:start position:0%
+digits but I get one line there's no
+ 
+
+ align:start position:0%
+digits but I get one line there's no
+pattern the textbooks are so full of
+
+ align:start position:0%
+pattern the textbooks are so full of
+ 
+
+ align:start position:0%
+pattern the textbooks are so full of
+formulas that you know they don't they
+
+ align:start position:0%
+formulas that you know they don't they
+ 
+
+ align:start position:0%
+formulas that you know they don't they
+don't indicate that in reality you've
+
+ align:start position:0%
+don't indicate that in reality you've
+ 
+
+ align:start position:0%
+don't indicate that in reality you've
+got a problem and in fact in reality
+
+ align:start position:0%
+got a problem and in fact in reality
+ 
+
+ align:start position:0%
+got a problem and in fact in reality
+you've got something that's also a gift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's two things that happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isotopes and vibration so we have this
+
+ align:start position:0%
+isotopes and vibration so we have this
+ 
+
+ align:start position:0%
+isotopes and vibration so we have this
+one line we are very very strong very
+
+ align:start position:0%
+one line we are very very strong very
+ 
+
+ align:start position:0%
+one line we are very very strong very
+narrow you can measure the daylights out
+
+ align:start position:0%
+narrow you can measure the daylights out
+ 
+
+ align:start position:0%
+narrow you can measure the daylights out
+of it if you wanted to and then down
+
+ align:start position:0%
+of it if you wanted to and then down
+ 
+
+ align:start position:0%
+of it if you wanted to and then down
+here there's going to be well actually
+
+ align:start position:0%
+here there's going to be well actually
+ 
+
+ align:start position:0%
+here there's going to be well actually
+sometimes like in chlorine and bromine
+
+ align:start position:0%
+sometimes like in chlorine and bromine
+ 
+
+ align:start position:0%
+sometimes like in chlorine and bromine
+the there's a heavy isotope and a less
+
+ align:start position:0%
+the there's a heavy isotope and a less
+ 
+
+ align:start position:0%
+the there's a heavy isotope and a less
+and a light isotope and they have
+
+ align:start position:0%
+and a light isotope and they have
+ 
+
+ align:start position:0%
+and a light isotope and they have
+similar abundances and so you get
+
+ align:start position:0%
+similar abundances and so you get
+ 
+
+ align:start position:0%
+similar abundances and so you get
+isotope splittings and that's that's
+
+ align:start position:0%
+isotope splittings and that's that's
+ 
+
+ align:start position:0%
+isotope splittings and that's that's
+expressed in the reduced mass M a M B or
+
+ align:start position:0%
+expressed in the reduced mass M a M B or
+ 
+
+ align:start position:0%
+expressed in the reduced mass M a M B or
+M a plus MB now the isotope splittings
+
+ align:start position:0%
+M a plus MB now the isotope splittings
+ 
+
+ align:start position:0%
+M a plus MB now the isotope splittings
+can be really really small but these
+
+ align:start position:0%
+can be really really small but these
+ 
+
+ align:start position:0%
+can be really really small but these
+lines are I have a width of a partner
+
+ align:start position:0%
+lines are I have a width of a partner
+ 
+
+ align:start position:0%
+lines are I have a width of a partner
+million maybe maybe even never and so
+
+ align:start position:0%
+million maybe maybe even never and so
+ 
+
+ align:start position:0%
+million maybe maybe even never and so
+you can see isotope stuff that doesn't
+
+ align:start position:0%
+you can see isotope stuff that doesn't
+ 
+
+ align:start position:0%
+you can see isotope stuff that doesn't
+tell you anything at all that you didn't
+
+ align:start position:0%
+tell you anything at all that you didn't
+ 
+
+ align:start position:0%
+tell you anything at all that you didn't
+know except maybe that you were confused
+
+ align:start position:0%
+know except maybe that you were confused
+ 
+
+ align:start position:0%
+know except maybe that you were confused
+about what molecule it was because if
+
+ align:start position:0%
+about what molecule it was because if
+ 
+
+ align:start position:0%
+about what molecule it was because if
+you have a particular atom it's always
+
+ align:start position:0%
+you have a particular atom it's always
+ 
+
+ align:start position:0%
+you have a particular atom it's always
+born with the other with the normal
+
+ align:start position:0%
+born with the other with the normal
+ 
+
+ align:start position:0%
+born with the other with the normal
+isotope ratios except here we have a
+
+ align:start position:0%
+isotope ratios except here we have a
+ 
+
+ align:start position:0%
+isotope ratios except here we have a
+little problem where in sulfur if you
+
+ align:start position:0%
+little problem where in sulfur if you
+ 
+
+ align:start position:0%
+little problem where in sulfur if you
+look in minerals the isotope ratios are
+
+ align:start position:0%
+look in minerals the isotope ratios are
+ 
+
+ align:start position:0%
+look in minerals the isotope ratios are
+not the naturally abundant of sulfur
+
+ align:start position:0%
+not the naturally abundant of sulfur
+ 
+
+ align:start position:0%
+not the naturally abundant of sulfur
+isotope and this has to do with
+
+ align:start position:0%
+isotope and this has to do with
+ 
+
+ align:start position:0%
+isotope and this has to do with
+something really important that happened
+
+ align:start position:0%
+something really important that happened
+ 
+
+ align:start position:0%
+something really important that happened
+two and a half billion years ago right
+
+ align:start position:0%
+two and a half billion years ago right
+ 
+
+ align:start position:0%
+two and a half billion years ago right
+well oxygen happened was and and so
+
+ align:start position:0%
+well oxygen happened was and and so
+ 
+
+ align:start position:0%
+well oxygen happened was and and so
+isotope ratios are of some geological
+
+ align:start position:0%
+isotope ratios are of some geological
+ 
+
+ align:start position:0%
+isotope ratios are of some geological
+chemical significance but here you know
+
+ align:start position:0%
+chemical significance but here you know
+ 
+
+ align:start position:0%
+chemical significance but here you know
+if you know what the molecule is there
+
+ align:start position:0%
+if you know what the molecule is there
+ 
+
+ align:start position:0%
+if you know what the molecule is there
+will be isotope lines and they can be
+
+ align:start position:0%
+will be isotope lines and they can be
+ 
+
+ align:start position:0%
+will be isotope lines and they can be
+pretty strong because depending on the
+
+ align:start position:0%
+pretty strong because depending on the
+ 
+
+ align:start position:0%
+pretty strong because depending on the
+relative abundance of the different
+
+ align:start position:0%
+relative abundance of the different
+ 
+
+ align:start position:0%
+relative abundance of the different
+isotopes or they can be extremely weak
+
+ align:start position:0%
+isotopes or they can be extremely weak
+ 
+
+ align:start position:0%
+isotopes or they can be extremely weak
+but so there's their stuff there's some
+
+ align:start position:0%
+but so there's their stuff there's some
+ 
+
+ align:start position:0%
+but so there's their stuff there's some
+grass to be mowed on the base line in
+
+ align:start position:0%
+grass to be mowed on the base line in
+ 
+
+ align:start position:0%
+grass to be mowed on the base line in
+addition and this is something that
+
+ align:start position:0%
+addition and this is something that
+ 
+
+ align:start position:0%
+addition and this is something that
+really surprises people so here is V
+
+ align:start position:0%
+really surprises people so here is V
+ 
+
+ align:start position:0%
+really surprises people so here is V
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+and way up high is V equals one
+
+ align:start position:0%
+and way up high is V equals one
+ 
+
+ align:start position:0%
+and way up high is V equals one
+typically the vibrational intervals are
+
+ align:start position:0%
+typically the vibrational intervals are
+ 
+
+ align:start position:0%
+typically the vibrational intervals are
+on the order of a thousand times bigger
+
+ align:start position:0%
+on the order of a thousand times bigger
+ 
+
+ align:start position:0%
+on the order of a thousand times bigger
+than the rotational intervals and
+
+ align:start position:0%
+than the rotational intervals and
+ 
+
+ align:start position:0%
+than the rotational intervals and
+typically the rotational constant
+
+ align:start position:0%
+typically the rotational constant
+ 
+
+ align:start position:0%
+typically the rotational constant
+decreases in steps of about a tenth of a
+
+ align:start position:0%
+decreases in steps of about a tenth of a
+ 
+
+ align:start position:0%
+decreases in steps of about a tenth of a
+percent for vibration now we do care
+
+ align:start position:0%
+percent for vibration now we do care
+ 
+
+ align:start position:0%
+percent for vibration now we do care
+about how much it decreases because that
+
+ align:start position:0%
+about how much it decreases because that
+ 
+
+ align:start position:0%
+about how much it decreases because that
+allows us to know a whole bunch of stuff
+
+ align:start position:0%
+allows us to know a whole bunch of stuff
+ 
+
+ align:start position:0%
+allows us to know a whole bunch of stuff
+about how rotation and vibration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interact and I'm not probably going to
+
+ align:start position:0%
+interact and I'm not probably going to
+ 
+
+ align:start position:0%
+interact and I'm not probably going to
+do that the lecture on the rotation
+
+ align:start position:0%
+do that the lecture on the rotation
+ 
+
+ align:start position:0%
+do that the lecture on the rotation
+vibration interaction unless I have to
+
+ align:start position:0%
+vibration interaction unless I have to
+ 
+
+ align:start position:0%
+vibration interaction unless I have to
+give a lecture on something that I can't
+
+ align:start position:0%
+give a lecture on something that I can't
+ 
+
+ align:start position:0%
+give a lecture on something that I can't
+do I'll slip in that one okay so what
+
+ align:start position:0%
+do I'll slip in that one okay so what
+ 
+
+ align:start position:0%
+do I'll slip in that one okay so what
+happens is there is a there are
+
+ align:start position:0%
+happens is there is a there are
+ 
+
+ align:start position:0%
+happens is there is a there are
+vibrational satellites so here is V
+
+ align:start position:0%
+vibrational satellites so here is V
+ 
+
+ align:start position:0%
+vibrational satellites so here is V
+equals zero it has rotational structure
+
+ align:start position:0%
+equals zero it has rotational structure
+ 
+
+ align:start position:0%
+equals zero it has rotational structure
+and here is V equals one it has
+
+ align:start position:0%
+and here is V equals one it has
+ 
+
+ align:start position:0%
+and here is V equals one it has
+rotational structure the V equals one
+
+ align:start position:0%
+rotational structure the V equals one
+ 
+
+ align:start position:0%
+rotational structure the V equals one
+stuff is typically a hundred to a
+
+ align:start position:0%
+stuff is typically a hundred to a
+ 
+
+ align:start position:0%
+stuff is typically a hundred to a
+thousand times weaker than the V equals
+
+ align:start position:0%
+thousand times weaker than the V equals
+ 
+
+ align:start position:0%
+thousand times weaker than the V equals
+0 stuff and that's basically telling you
+
+ align:start position:0%
+0 stuff and that's basically telling you
+ 
+
+ align:start position:0%
+0 stuff and that's basically telling you
+how does the molecules change its
+
+ align:start position:0%
+how does the molecules change its
+ 
+
+ align:start position:0%
+how does the molecules change its
+average one over R squared as it
+
+ align:start position:0%
+average one over R squared as it
+ 
+
+ align:start position:0%
+average one over R squared as it
+vibrates and that's a useful thing may
+
+ align:start position:0%
+vibrates and that's a useful thing may
+ 
+
+ align:start position:0%
+vibrates and that's a useful thing may
+even be useful on Thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in addition to hyperfine there's
+
+ align:start position:0%
+so in addition to hyperfine there's
+ 
+
+ align:start position:0%
+so in addition to hyperfine there's
+other small stuff having to do with
+
+ align:start position:0%
+other small stuff having to do with
+ 
+
+ align:start position:0%
+other small stuff having to do with
+vibrations and in some experiments that
+
+ align:start position:0%
+vibrations and in some experiments that
+ 
+
+ align:start position:0%
+vibrations and in some experiments that
+I do we use UV light to break a molecule
+
+ align:start position:0%
+I do we use UV light to break a molecule
+ 
+
+ align:start position:0%
+I do we use UV light to break a molecule
+and the fragments that we make are borne
+
+ align:start position:0%
+and the fragments that we make are borne
+ 
+
+ align:start position:0%
+and the fragments that we make are borne
+vibrationally excited and so by looking
+
+ align:start position:0%
+vibrationally excited and so by looking
+ 
+
+ align:start position:0%
+vibrationally excited and so by looking
+at the the stuff near the v equals zero
+
+ align:start position:0%
+at the the stuff near the v equals zero
+ 
+
+ align:start position:0%
+at the the stuff near the v equals zero
+frequency you see a whole bunch of stuff
+
+ align:start position:0%
+frequency you see a whole bunch of stuff
+ 
+
+ align:start position:0%
+frequency you see a whole bunch of stuff
+which tells you the populations of the
+
+ align:start position:0%
+which tells you the populations of the
+ 
+
+ align:start position:0%
+which tells you the populations of the
+different vibrational levels and that's
+
+ align:start position:0%
+different vibrational levels and that's
+ 
+
+ align:start position:0%
+different vibrational levels and that's
+strange because vibration is not part of
+
+ align:start position:0%
+strange because vibration is not part of
+ 
+
+ align:start position:0%
+strange because vibration is not part of
+the rotational spectrum vibration is big
+
+ align:start position:0%
+the rotational spectrum vibration is big
+ 
+
+ align:start position:0%
+the rotational spectrum vibration is big
+but we get vibrational information from
+
+ align:start position:0%
+but we get vibrational information from
+ 
+
+ align:start position:0%
+but we get vibrational information from
+the rotational spectrum and because the
+
+ align:start position:0%
+the rotational spectrum and because the
+ 
+
+ align:start position:0%
+the rotational spectrum and because the
+rotational spectrum is at such high
+
+ align:start position:0%
+rotational spectrum is at such high
+ 
+
+ align:start position:0%
+rotational spectrum is at such high
+resolution it's trivial to resolve and
+
+ align:start position:0%
+resolution it's trivial to resolve and
+ 
+
+ align:start position:0%
+resolution it's trivial to resolve and
+to detect these weak other features so
+
+ align:start position:0%
+to detect these weak other features so
+ 
+
+ align:start position:0%
+to detect these weak other features so
+this is you know as much as I'm going to
+
+ align:start position:0%
+this is you know as much as I'm going to
+ 
+
+ align:start position:0%
+this is you know as much as I'm going to
+talk about spectroscopy it's a little
+
+ align:start position:0%
+talk about spectroscopy it's a little
+ 
+
+ align:start position:0%
+talk about spectroscopy it's a little
+bit more than I had originally planned
+
+ align:start position:0%
+bit more than I had originally planned
+ 
+
+ align:start position:0%
+bit more than I had originally planned
+and now we're going to move to this
+
+ align:start position:0%
+and now we're going to move to this
+ 
+
+ align:start position:0%
+and now we're going to move to this
+topic which is dear to my heart and it's
+
+ align:start position:0%
+topic which is dear to my heart and it's
+ 
+
+ align:start position:0%
+topic which is dear to my heart and it's
+an example of an abstract algebra that
+
+ align:start position:0%
+an example of an abstract algebra that
+ 
+
+ align:start position:0%
+an example of an abstract algebra that
+you use in quantum mechanics and there
+
+ align:start position:0%
+you use in quantum mechanics and there
+ 
+
+ align:start position:0%
+you use in quantum mechanics and there
+are people who only do this kind of
+
+ align:start position:0%
+are people who only do this kind of
+ 
+
+ align:start position:0%
+are people who only do this kind of
+thing as opposed to solving shorter
+
+ align:start position:0%
+thing as opposed to solving shorter
+ 
+
+ align:start position:0%
+thing as opposed to solving shorter
+equation or even just doing perturbation
+
+ align:start position:0%
+equation or even just doing perturbation
+ 
+
+ align:start position:0%
+equation or even just doing perturbation
+theory on on matrices okay so rest of
+
+ align:start position:0%
+theory on on matrices okay so rest of
+ 
+
+ align:start position:0%
+theory on on matrices okay so rest of
+today's lecture is going to be an
+
+ align:start position:0%
+today's lecture is going to be an
+ 
+
+ align:start position:0%
+today's lecture is going to be an
+excursion through here as much as I can
+
+ align:start position:0%
+excursion through here as much as I can
+ 
+
+ align:start position:0%
+excursion through here as much as I can
+do it's all clear in the notes but I
+
+ align:start position:0%
+do it's all clear in the notes but I
+ 
+
+ align:start position:0%
+do it's all clear in the notes but I
+think it's a little bit strange oh I
+
+ align:start position:0%
+think it's a little bit strange oh I
+ 
+
+ align:start position:0%
+think it's a little bit strange oh I
+want to say one more thing how do we
+
+ align:start position:0%
+want to say one more thing how do we
+ 
+
+ align:start position:0%
+want to say one more thing how do we
+make assignments you all took 511 1 or
+
+ align:start position:0%
+make assignments you all took 511 1 or
+ 
+
+ align:start position:0%
+make assignments you all took 511 1 or
+511 2 or or 309 1 and there are things
+
+ align:start position:0%
+511 2 or or 309 1 and there are things
+ 
+
+ align:start position:0%
+511 2 or or 309 1 and there are things
+that you learn about how big atoms are
+
+ align:start position:0%
+that you learn about how big atoms are
+ 
+
+ align:start position:0%
+that you learn about how big atoms are
+and so you can sort of estimate what the
+
+ align:start position:0%
+and so you can sort of estimate what the
+ 
+
+ align:start position:0%
+and so you can sort of estimate what the
+inter nuclear distance is and maybe 10
+
+ align:start position:0%
+inter nuclear distance is and maybe 10
+ 
+
+ align:start position:0%
+inter nuclear distance is and maybe 10
+or 20 percent that's not of any chemical
+
+ align:start position:0%
+or 20 percent that's not of any chemical
+ 
+
+ align:start position:0%
+or 20 percent that's not of any chemical
+use but it's enough to assign the
+
+ align:start position:0%
+use but it's enough to assign the
+ 
+
+ align:start position:0%
+use but it's enough to assign the
+spectrum so what you do is you assign
+
+ align:start position:0%
+spectrum so what you do is you assign
+ 
+
+ align:start position:0%
+spectrum so what you do is you assign
+you say okay I guess the internuclear
+
+ align:start position:0%
+you say okay I guess the internuclear
+ 
+
+ align:start position:0%
+you say okay I guess the internuclear
+distance exists that determines what
+
+ align:start position:0%
+distance exists that determines what
+ 
+
+ align:start position:0%
+distance exists that determines what
+rotational transition you were observing
+
+ align:start position:0%
+rotational transition you were observing
+ 
+
+ align:start position:0%
+rotational transition you were observing
+and ask
+
+ align:start position:0%
+and ask
+ 
+
+ align:start position:0%
+and ask
+sequences on suppose you're observing L
+
+ align:start position:0%
+sequences on suppose you're observing L
+ 
+
+ align:start position:0%
+sequences on suppose you're observing L
+to L plus one
+
+ align:start position:0%
+to L plus one
+ 
+
+ align:start position:0%
+to L plus one
+well what about L plus 1 l plus 2 or L
+
+ align:start position:0%
+well what about L plus 1 l plus 2 or L
+ 
+
+ align:start position:0%
+well what about L plus 1 l plus 2 or L
+minus 1 to L so if you make an
+
+ align:start position:0%
+minus 1 to L so if you make an
+ 
+
+ align:start position:0%
+minus 1 to L so if you make an
+assignment you can predict where the
+
+ align:start position:0%
+assignment you can predict where the
+ 
+
+ align:start position:0%
+assignment you can predict where the
+other guys are and and that would
+
+ align:start position:0%
+other guys are and and that would
+ 
+
+ align:start position:0%
+other guys are and and that would
+require going to one of your friends who
+
+ align:start position:0%
+require going to one of your friends who
+ 
+
+ align:start position:0%
+require going to one of your friends who
+has a different spectrometer and getting
+
+ align:start position:0%
+has a different spectrometer and getting
+ 
+
+ align:start position:0%
+has a different spectrometer and getting
+him to record a spectrum for you and
+
+ align:start position:0%
+him to record a spectrum for you and
+ 
+
+ align:start position:0%
+him to record a spectrum for you and
+that's good good for human relations and
+
+ align:start position:0%
+that's good good for human relations and
+ 
+
+ align:start position:0%
+that's good good for human relations and
+that then enables you to make
+
+ align:start position:0%
+that then enables you to make
+ 
+
+ align:start position:0%
+that then enables you to make
+assignments and know the rotational
+
+ align:start position:0%
+assignments and know the rotational
+ 
+
+ align:start position:0%
+assignments and know the rotational
+constants to as many digits as you
+
+ align:start position:0%
+constants to as many digits as you
+ 
+
+ align:start position:0%
+constants to as many digits as you
+possibly could want include all the way
+
+ align:start position:0%
+possibly could want include all the way
+ 
+
+ align:start position:0%
+possibly could want include all the way
+up to ten you know it's just crazy you
+
+ align:start position:0%
+up to ten you know it's just crazy you
+ 
+
+ align:start position:0%
+up to ten you know it's just crazy you
+really don't care about inter nuclear
+
+ align:start position:0%
+really don't care about inter nuclear
+ 
+
+ align:start position:0%
+really don't care about inter nuclear
+distances beyond about a thousandth of
+
+ align:start position:0%
+distances beyond about a thousandth of
+ 
+
+ align:start position:0%
+distances beyond about a thousandth of
+an angstrom but you can have them okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first of all you know we can define
+
+ align:start position:0%
+so first of all you know we can define
+ 
+
+ align:start position:0%
+so first of all you know we can define
+an angular momentum R cross P and we can
+
+ align:start position:0%
+an angular momentum R cross P and we can
+ 
+
+ align:start position:0%
+an angular momentum R cross P and we can
+write that as a vector a matrix okay now
+
+ align:start position:0%
+write that as a vector a matrix okay now
+ 
+
+ align:start position:0%
+write that as a vector a matrix okay now
+I suspect you've all seen this these are
+
+ align:start position:0%
+I suspect you've all seen this these are
+ 
+
+ align:start position:0%
+I suspect you've all seen this these are
+unit vectors along the x y&z directions
+
+ align:start position:0%
+unit vectors along the x y&z directions
+ 
+
+ align:start position:0%
+unit vectors along the x y&z directions
+and this is a vague amay tricked so I
+
+ align:start position:0%
+and this is a vague amay tricked so I
+ 
+
+ align:start position:0%
+and this is a vague amay tricked so I
+mean a vector so there are three
+
+ align:start position:0%
+mean a vector so there are three
+ 
+
+ align:start position:0%
+mean a vector so there are three
+components and we get three components
+
+ align:start position:0%
+components and we get three components
+ 
+
+ align:start position:0%
+components and we get three components
+here now you do want to make sure you
+
+ align:start position:0%
+here now you do want to make sure you
+ 
+
+ align:start position:0%
+here now you do want to make sure you
+know this notation and know how to use
+
+ align:start position:0%
+know this notation and know how to use
+ 
+
+ align:start position:0%
+know this notation and know how to use
+it okay so here is the magic equation L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to IH bar sum over K epsilon
+
+ align:start position:0%
+is equal to IH bar sum over K epsilon
+ 
+
+ align:start position:0%
+is equal to IH bar sum over K epsilon
+ijk okay well what is epsilon ijk well
+
+ align:start position:0%
+ijk okay well what is epsilon ijk well
+ 
+
+ align:start position:0%
+ijk okay well what is epsilon ijk well
+it's got many names but it's a really
+
+ align:start position:0%
+it's got many names but it's a really
+ 
+
+ align:start position:0%
+it's got many names but it's a really
+neat tool which is very wonderful in
+
+ align:start position:0%
+neat tool which is very wonderful in
+ 
+
+ align:start position:0%
+neat tool which is very wonderful in
+enabling you to to derive new equations
+
+ align:start position:0%
+enabling you to to derive new equations
+ 
+
+ align:start position:0%
+enabling you to to derive new equations
+so if I J and K correspond to XYZ in
+
+ align:start position:0%
+so if I J and K correspond to XYZ in
+ 
+
+ align:start position:0%
+so if I J and K correspond to XYZ in
+cyclic order in other words X Y Z Y
+
+ align:start position:0%
+cyclic order in other words X Y Z Y
+ 
+
+ align:start position:0%
+cyclic order in other words X Y Z Y
+the X etc then this is plus one if it's
+
+ align:start position:0%
+the X etc then this is plus one if it's
+ 
+
+ align:start position:0%
+the X etc then this is plus one if it's
+an anti cyclic order it's minus one and
+
+ align:start position:0%
+an anti cyclic order it's minus one and
+ 
+
+ align:start position:0%
+an anti cyclic order it's minus one and
+if any index is repeated it's zero so it
+
+ align:start position:0%
+if any index is repeated it's zero so it
+ 
+
+ align:start position:0%
+if any index is repeated it's zero so it
+packs a real punch but it enables you to
+
+ align:start position:0%
+packs a real punch but it enables you to
+ 
+
+ align:start position:0%
+packs a real punch but it enables you to
+do fantastic things
+
+ align:start position:0%
+do fantastic things
+ 
+
+ align:start position:0%
+do fantastic things
+so if we have LX ly it's equal to IH bar
+
+ align:start position:0%
+so if we have LX ly it's equal to IH bar
+ 
+
+ align:start position:0%
+so if we have LX ly it's equal to IH bar
+plus 1 times LZ ok and the point of this
+
+ align:start position:0%
+plus 1 times LZ ok and the point of this
+ 
+
+ align:start position:0%
+plus 1 times LZ ok and the point of this
+lecture is with this you can derive all
+
+ align:start position:0%
+lecture is with this you can derive all
+ 
+
+ align:start position:0%
+lecture is with this you can derive all
+of the matrix elements of an angular
+
+ align:start position:0%
+of the matrix elements of an angular
+ 
+
+ align:start position:0%
+of the matrix elements of an angular
+momentum l squared LC L plus minus and
+
+ align:start position:0%
+momentum l squared LC L plus minus and
+ 
+
+ align:start position:0%
+momentum l squared LC L plus minus and
+anything else but these are the
+
+ align:start position:0%
+anything else but these are the
+ 
+
+ align:start position:0%
+anything else but these are the
+important ones and this is what we want
+
+ align:start position:0%
+important ones and this is what we want
+ 
+
+ align:start position:0%
+important ones and this is what we want
+to derive from our excursion in matrix
+
+ align:start position:0%
+to derive from our excursion in matrix
+ 
+
+ align:start position:0%
+to derive from our excursion in matrix
+element land ok so the first thing we do
+
+ align:start position:0%
+element land ok so the first thing we do
+ 
+
+ align:start position:0%
+element land ok so the first thing we do
+is we extract some fundamental equations
+
+ align:start position:0%
+is we extract some fundamental equations
+ 
+
+ align:start position:0%
+is we extract some fundamental equations
+from this commutator so the first
+
+ align:start position:0%
+from this commutator so the first
+ 
+
+ align:start position:0%
+from this commutator so the first
+equation is that l squared L Z is equal
+
+ align:start position:0%
+equation is that l squared L Z is equal
+ 
+
+ align:start position:0%
+equation is that l squared L Z is equal
+to L x squared LC plus L Y squared LC
+
+ align:start position:0%
+to L x squared LC plus L Y squared LC
+ 
+
+ align:start position:0%
+to L x squared LC plus L Y squared LC
+plus L Z squared LZ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we see and we know this one is zero
+
+ align:start position:0%
+well we see and we know this one is zero
+ 
+
+ align:start position:0%
+well we see and we know this one is zero
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+ok this one there you have to do a
+
+ align:start position:0%
+ok this one there you have to do a
+ 
+
+ align:start position:0%
+ok this one there you have to do a
+little practice but you can write this
+
+ align:start position:0%
+little practice but you can write this
+ 
+
+ align:start position:0%
+little practice but you can write this
+angular this out of this commutation
+
+ align:start position:0%
+angular this out of this commutation
+ 
+
+ align:start position:0%
+angular this out of this commutation
+rule as LX x LX gamma L Z + LX gamma l z
+
+ align:start position:0%
+rule as LX x LX gamma L Z + LX gamma l z
+ 
+
+ align:start position:0%
+rule as LX x LX gamma L Z + LX gamma l z
+LX so if you have a square you take take
+
+ align:start position:0%
+LX so if you have a square you take take
+ 
+
+ align:start position:0%
+LX so if you have a square you take take
+it out front side and the back side and
+
+ align:start position:0%
+it out front side and the back side and
+ 
+
+ align:start position:0%
+it out front side and the back side and
+now we know with this
+
+ align:start position:0%
+now we know with this
+ 
+
+ align:start position:0%
+now we know with this
+this is minus IH bar know why and this
+
+ align:start position:0%
+this is minus IH bar know why and this
+ 
+
+ align:start position:0%
+this is minus IH bar know why and this
+is minus H bar ly and we do this one and
+
+ align:start position:0%
+is minus H bar ly and we do this one and
+ 
+
+ align:start position:0%
+is minus H bar ly and we do this one and
+we discover we have the same thing
+
+ align:start position:0%
+we discover we have the same thing
+ 
+
+ align:start position:0%
+we discover we have the same thing
+except with the opposite sign and so
+
+ align:start position:0%
+except with the opposite sign and so
+ 
+
+ align:start position:0%
+except with the opposite sign and so
+what we end up getting is that this is
+
+ align:start position:0%
+what we end up getting is that this is
+ 
+
+ align:start position:0%
+what we end up getting is that this is
+zero now I skip some steps I said them
+
+ align:start position:0%
+zero now I skip some steps I said them
+ 
+
+ align:start position:0%
+zero now I skip some steps I said them
+but I want you to just go through that
+
+ align:start position:0%
+but I want you to just go through that
+ 
+
+ align:start position:0%
+but I want you to just go through that
+and see okay so you know you know what
+
+ align:start position:0%
+and see okay so you know you know what
+ 
+
+ align:start position:0%
+and see okay so you know you know what
+this is it's gonna be ly and it's going
+
+ align:start position:0%
+this is it's gonna be ly and it's going
+ 
+
+ align:start position:0%
+this is it's gonna be ly and it's going
+to be minus ly x IH bar and you get the
+
+ align:start position:0%
+to be minus ly x IH bar and you get the
+ 
+
+ align:start position:0%
+to be minus ly x IH bar and you get the
+same thing here but then you have a LX
+
+ align:start position:0%
+same thing here but then you have a LX
+ 
+
+ align:start position:0%
+same thing here but then you have a LX
+ly and you have an LX ly oh yeah right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you do this do the same trick
+
+ align:start position:0%
+and when you do this do the same trick
+ 
+
+ align:start position:0%
+and when you do this do the same trick
+with this you're gonna get an L Y and an
+
+ align:start position:0%
+with this you're gonna get an L Y and an
+ 
+
+ align:start position:0%
+with this you're gonna get an L Y and an
+L X again and they'll be the opposite
+
+ align:start position:0%
+L X again and they'll be the opposite
+ 
+
+ align:start position:0%
+L X again and they'll be the opposite
+side okay so this one is really
+
+ align:start position:0%
+side okay so this one is really
+ 
+
+ align:start position:0%
+side okay so this one is really
+important because what it says is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can you can take any projection
+
+ align:start position:0%
+you can you can take any projection
+ 
+
+ align:start position:0%
+you can you can take any projection
+quantum number and it will commute with
+
+ align:start position:0%
+quantum number and it will commute with
+ 
+
+ align:start position:0%
+quantum number and it will commute with
+the magnitude squared the same argument
+
+ align:start position:0%
+the magnitude squared the same argument
+ 
+
+ align:start position:0%
+the magnitude squared the same argument
+works for ly you know LZ and LX so we
+
+ align:start position:0%
+works for ly you know LZ and LX so we
+ 
+
+ align:start position:0%
+works for ly you know LZ and LX so we
+have one really powerful commutator
+
+ align:start position:0%
+have one really powerful commutator
+ 
+
+ align:start position:0%
+have one really powerful commutator
+which is that l squared Li equals zero
+
+ align:start position:0%
+which is that l squared Li equals zero
+ 
+
+ align:start position:0%
+which is that l squared Li equals zero
+for x y and z which means since we like
+
+ align:start position:0%
+for x y and z which means since we like
+ 
+
+ align:start position:0%
+for x y and z which means since we like
+l squared and LZ we couldn't like LX
+
+ align:start position:0%
+l squared and LZ we couldn't like LX
+ 
+
+ align:start position:0%
+l squared and LZ we couldn't like LX
+instead of LZ but we tend to favor these
+
+ align:start position:0%
+instead of LZ but we tend to favor these
+ 
+
+ align:start position:0%
+instead of LZ but we tend to favor these
+that l squared and I'll see our
+
+ align:start position:0%
+that l squared and I'll see our
+ 
+
+ align:start position:0%
+that l squared and I'll see our
+operators that can have a common set of
+
+ align:start position:0%
+operators that can have a common set of
+ 
+
+ align:start position:0%
+operators that can have a common set of
+eigenfunctions if we have two operators
+
+ align:start position:0%
+eigenfunctions if we have two operators
+ 
+
+ align:start position:0%
+eigenfunctions if we have two operators
+that commute the eigenfunctions of one
+
+ align:start position:0%
+that commute the eigenfunctions of one
+ 
+
+ align:start position:0%
+that commute the eigenfunctions of one
+can be the eigenfunction of the other
+
+ align:start position:0%
+can be the eigenfunction of the other
+ 
+
+ align:start position:0%
+can be the eigenfunction of the other
+very convenient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then there's another operator that
+
+ align:start position:0%
+okay then there's another operator that
+ 
+
+ align:start position:0%
+okay then there's another operator that
+we can derive and that is let's define
+
+ align:start position:0%
+we can derive and that is let's define
+ 
+
+ align:start position:0%
+we can derive and that is let's define
+this thing a step up or step down or or
+
+ align:start position:0%
+this thing a step up or step down or or
+ 
+
+ align:start position:0%
+this thing a step up or step down or or
+a raising or lowering operator we don't
+
+ align:start position:0%
+a raising or lowering operator we don't
+ 
+
+ align:start position:0%
+a raising or lowering operator we don't
+know that yet LX plus or minus ily so we
+
+ align:start position:0%
+know that yet LX plus or minus ily so we
+ 
+
+ align:start position:0%
+know that yet LX plus or minus ily so we
+we might want to know the commutation
+
+ align:start position:0%
+we might want to know the commutation
+ 
+
+ align:start position:0%
+we might want to know the commutation
+rule of LZ with L plus minus okay we
+
+ align:start position:0%
+rule of LZ with L plus minus okay we
+ 
+
+ align:start position:0%
+rule of LZ with L plus minus okay we
+know how to write this out because we
+
+ align:start position:0%
+know how to write this out because we
+ 
+
+ align:start position:0%
+know how to write this out because we
+have LZ with LX and we know that's going
+
+ align:start position:0%
+have LZ with LX and we know that's going
+ 
+
+ align:start position:0%
+have LZ with LX and we know that's going
+to be a minus IH bar ly and we have LZ
+
+ align:start position:0%
+to be a minus IH bar ly and we have LZ
+ 
+
+ align:start position:0%
+to be a minus IH bar ly and we have LZ
+with ily and that's going to be a minus
+
+ align:start position:0%
+with ily and that's going to be a minus
+ 
+
+ align:start position:0%
+with ily and that's going to be a minus
+LX anyway I'm going to just write down
+
+ align:start position:0%
+LX anyway I'm going to just write down
+ 
+
+ align:start position:0%
+LX anyway I'm going to just write down
+the final result that this is equal to
+
+ align:start position:0%
+the final result that this is equal to
+ 
+
+ align:start position:0%
+the final result that this is equal to
+plus or minus h-bar times L plus minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the algebra of this operator enables you
+
+ align:start position:0%
+the algebra of this operator enables you
+ 
+
+ align:start position:0%
+the algebra of this operator enables you
+to slice through any derivation at the
+
+ align:start position:0%
+to slice through any derivation at the
+ 
+
+ align:start position:0%
+to slice through any derivation at the
+speed as fast as you can right once
+
+ align:start position:0%
+speed as fast as you can right once
+ 
+
+ align:start position:0%
+speed as fast as you can right once
+you've loaded this into your head yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like ex-wife it's like I'm sorry they
+
+ align:start position:0%
+like ex-wife it's like I'm sorry they
+ 
+
+ align:start position:0%
+like ex-wife it's like I'm sorry they
+used to hate the epsilon D epsilon ijk
+
+ align:start position:0%
+used to hate the epsilon D epsilon ijk
+ 
+
+ align:start position:0%
+used to hate the epsilon D epsilon ijk
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's just let's just do this a
+
+ align:start position:0%
+okay let's just let's just do this a
+ 
+
+ align:start position:0%
+okay let's just let's just do this a
+little bit let's say we have LX and ly
+
+ align:start position:0%
+little bit let's say we have LX and ly
+ 
+
+ align:start position:0%
+little bit let's say we have LX and ly
+well we know that that's going to give
+
+ align:start position:0%
+well we know that that's going to give
+ 
+
+ align:start position:0%
+well we know that that's going to give
+LZ okay and X Y Z IJ K that's cyclic
+
+ align:start position:0%
+LZ okay and X Y Z IJ K that's cyclic
+ 
+
+ align:start position:0%
+LZ okay and X Y Z IJ K that's cyclic
+order that's okay we say that's that's
+
+ align:start position:0%
+order that's okay we say that's that's
+ 
+
+ align:start position:0%
+order that's okay we say that's that's
+Homebase and if we have Y X Z that would
+
+ align:start position:0%
+Homebase and if we have Y X Z that would
+ 
+
+ align:start position:0%
+Homebase and if we have Y X Z that would
+be anti cyclic and so that would be a
+
+ align:start position:0%
+be anti cyclic and so that would be a
+ 
+
+ align:start position:0%
+be anti cyclic and so that would be a
+minus sign you know that just by looking
+
+ align:start position:0%
+minus sign you know that just by looking
+ 
+
+ align:start position:0%
+minus sign you know that just by looking
+at this and say oh if we switch this the
+
+ align:start position:0%
+at this and say oh if we switch this the
+ 
+
+ align:start position:0%
+at this and say oh if we switch this the
+sign of the commutator has to switch
+
+ align:start position:0%
+sign of the commutator has to switch
+ 
+
+ align:start position:0%
+sign of the commutator has to switch
+okay there's a lot of stuff loaded in
+
+ align:start position:0%
+okay there's a lot of stuff loaded in
+ 
+
+ align:start position:0%
+okay there's a lot of stuff loaded in
+there and once you've sort of processed
+
+ align:start position:0%
+there and once you've sort of processed
+ 
+
+ align:start position:0%
+there and once you've sort of processed
+it you know it becomes automatic and you
+
+ align:start position:0%
+it you know it becomes automatic and you
+ 
+
+ align:start position:0%
+it you know it becomes automatic and you
+forget the beauty of it okay so are you
+
+ align:start position:0%
+forget the beauty of it okay so are you
+ 
+
+ align:start position:0%
+forget the beauty of it okay so are you
+satisfied everybody else all right so
+
+ align:start position:0%
+satisfied everybody else all right so
+ 
+
+ align:start position:0%
+satisfied everybody else all right so
+now let's do another one let's look at L
+
+ align:start position:0%
+now let's do another one let's look at L
+ 
+
+ align:start position:0%
+now let's do another one let's look at L
+squared L plus minus well this one is
+
+ align:start position:0%
+squared L plus minus well this one is
+ 
+
+ align:start position:0%
+squared L plus minus well this one is
+super easy because we already know that
+
+ align:start position:0%
+super easy because we already know that
+ 
+
+ align:start position:0%
+super easy because we already know that
+l squared commutes with LX ly and LZ so
+
+ align:start position:0%
+l squared commutes with LX ly and LZ so
+ 
+
+ align:start position:0%
+l squared commutes with LX ly and LZ so
+I just need to just write zero here
+
+ align:start position:0%
+I just need to just write zero here
+ 
+
+ align:start position:0%
+I just need to just write zero here
+because this is LX plus or minus L ily
+
+ align:start position:0%
+because this is LX plus or minus L ily
+ 
+
+ align:start position:0%
+because this is LX plus or minus L ily
+and we know L does l squared commutes
+
+ align:start position:0%
+and we know L does l squared commutes
+ 
+
+ align:start position:0%
+and we know L does l squared commutes
+with both of them okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now comes the abstract and
+
+ align:start position:0%
+all right now comes the abstract and
+ 
+
+ align:start position:0%
+all right now comes the abstract and
+weird stuff we're starting to use the
+
+ align:start position:0%
+weird stuff we're starting to use the
+ 
+
+ align:start position:0%
+weird stuff we're starting to use the
+commutator z-- to derive the matrix
+
+ align:start position:0%
+commutator z-- to derive the matrix
+ 
+
+ align:start position:0%
+commutator z-- to derive the matrix
+elements and selection rules okay so let
+
+ align:start position:0%
+elements and selection rules okay so let
+ 
+
+ align:start position:0%
+elements and selection rules okay so let
+us say that we have some function which
+
+ align:start position:0%
+us say that we have some function which
+ 
+
+ align:start position:0%
+us say that we have some function which
+is an eigen function of l squared and LZ
+
+ align:start position:0%
+is an eigen function of l squared and LZ
+ 
+
+ align:start position:0%
+is an eigen function of l squared and LZ
+and so we're entitled to say that l
+
+ align:start position:0%
+and so we're entitled to say that l
+ 
+
+ align:start position:0%
+and so we're entitled to say that l
+squared operating on this function gives
+
+ align:start position:0%
+squared operating on this function gives
+ 
+
+ align:start position:0%
+squared operating on this function gives
+an eigenvalue we call L lambda and we
+
+ align:start position:0%
+an eigenvalue we call L lambda and we
+ 
+
+ align:start position:0%
+an eigenvalue we call L lambda and we
+can also say the LZ operating on the
+
+ align:start position:0%
+can also say the LZ operating on the
+ 
+
+ align:start position:0%
+can also say the LZ operating on the
+function gives a different a different
+
+ align:start position:0%
+function gives a different a different
+ 
+
+ align:start position:0%
+function gives a different a different
+constant mu now this lambda mu have no
+
+ align:start position:0%
+constant mu now this lambda mu have no
+ 
+
+ align:start position:0%
+constant mu now this lambda mu have no
+significance they're just numbers
+
+ align:start position:0%
+significance they're just numbers
+ 
+
+ align:start position:0%
+significance they're just numbers
+there's not something that's going to
+
+ align:start position:0%
+there's not something that's going to
+ 
+
+ align:start position:0%
+there's not something that's going to
+pop up here that says oh yeah that's
+
+ align:start position:0%
+pop up here that says oh yeah that's
+ 
+
+ align:start position:0%
+pop up here that says oh yeah that's
+this means something okay so now we're
+
+ align:start position:0%
+this means something okay so now we're
+ 
+
+ align:start position:0%
+this means something okay so now we're
+going to use the fact that this function
+
+ align:start position:0%
+going to use the fact that this function
+ 
+
+ align:start position:0%
+going to use the fact that this function
+which we're allowed to have as a
+
+ align:start position:0%
+which we're allowed to have as a
+ 
+
+ align:start position:0%
+which we're allowed to have as a
+simultaneous eigen function of l squared
+
+ align:start position:0%
+simultaneous eigen function of l squared
+ 
+
+ align:start position:0%
+simultaneous eigen function of l squared
+LC with its own set of eigen values this
+
+ align:start position:0%
+LC with its own set of eigen values this
+ 
+
+ align:start position:0%
+LC with its own set of eigen values this
+function we're going to operate on it
+
+ align:start position:0%
+function we're going to operate on it
+ 
+
+ align:start position:0%
+function we're going to operate on it
+and derive some useful results that all
+
+ align:start position:0%
+and derive some useful results that all
+ 
+
+ align:start position:0%
+and derive some useful results that all
+are based on the commutation rules so
+
+ align:start position:0%
+are based on the commutation rules so
+ 
+
+ align:start position:0%
+are based on the commutation rules so
+let us take L square operating on L plus
+
+ align:start position:0%
+let us take L square operating on L plus
+ 
+
+ align:start position:0%
+let us take L square operating on L plus
+minus times F and we know that L plus
+
+ align:start position:0%
+minus times F and we know that L plus
+ 
+
+ align:start position:0%
+minus times F and we know that L plus
+minus commutes with l squared so we can
+
+ align:start position:0%
+minus commutes with l squared so we can
+ 
+
+ align:start position:0%
+minus commutes with l squared so we can
+write L plus minus l squared F but l
+
+ align:start position:0%
+write L plus minus l squared F but l
+ 
+
+ align:start position:0%
+write L plus minus l squared F but l
+squared operating on F gives lambda we
+
+ align:start position:0%
+squared operating on F gives lambda we
+ 
+
+ align:start position:0%
+squared operating on F gives lambda we
+have L plus minus lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh isn't that interesting we have lambda
+
+ align:start position:0%
+oh isn't that interesting we have lambda
+ 
+
+ align:start position:0%
+oh isn't that interesting we have lambda
+times L plus minus F L plus minus F so
+
+ align:start position:0%
+times L plus minus F L plus minus F so
+ 
+
+ align:start position:0%
+times L plus minus F L plus minus F so
+it's saying that this thing is an
+
+ align:start position:0%
+it's saying that this thing is an
+ 
+
+ align:start position:0%
+it's saying that this thing is an
+eigenfunction of l squared with
+
+ align:start position:0%
+eigenfunction of l squared with
+ 
+
+ align:start position:0%
+eigenfunction of l squared with
+eigenvalue lambda well we knew that so L
+
+ align:start position:0%
+eigenvalue lambda well we knew that so L
+ 
+
+ align:start position:0%
+eigenvalue lambda well we knew that so L
+plus minus operating on F does not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change lambda the eigenvalue l squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's use another one let's use
+
+ align:start position:0%
+okay now let's use another one let's use
+ 
+
+ align:start position:0%
+okay now let's use another one let's use
+LZ l plus - well I derived that it's
+
+ align:start position:0%
+LZ l plus - well I derived that it's
+ 
+
+ align:start position:0%
+LZ l plus - well I derived that it's
+plus or minus H bar times L plus - and
+
+ align:start position:0%
+plus or minus H bar times L plus - and
+ 
+
+ align:start position:0%
+plus or minus H bar times L plus - and
+if I didn't derive it I should have but
+
+ align:start position:0%
+if I didn't derive it I should have but
+ 
+
+ align:start position:0%
+if I didn't derive it I should have but
+I'm pretty sure I did and and so now
+
+ align:start position:0%
+I'm pretty sure I did and and so now
+ 
+
+ align:start position:0%
+I'm pretty sure I did and and so now
+what we can do is write LZ L plus minus
+
+ align:start position:0%
+what we can do is write LZ L plus minus
+ 
+
+ align:start position:0%
+what we can do is write LZ L plus minus
+minus L plus minus L Z is equal to h
+
+ align:start position:0%
+minus L plus minus L Z is equal to h
+ 
+
+ align:start position:0%
+minus L plus minus L Z is equal to h
+plus or minus H bar plus - and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's stick in a function on the right F
+
+ align:start position:0%
+let's stick in a function on the right F
+ 
+
+ align:start position:0%
+let's stick in a function on the right F
+F F okay so now we have these operators
+
+ align:start position:0%
+F F okay so now we have these operators
+ 
+
+ align:start position:0%
+F F okay so now we have these operators
+operating on the same function and okay
+
+ align:start position:0%
+operating on the same function and okay
+ 
+
+ align:start position:0%
+operating on the same function and okay
+well we don't yet know what L plus minus
+
+ align:start position:0%
+well we don't yet know what L plus minus
+ 
+
+ align:start position:0%
+well we don't yet know what L plus minus
+does have but we know what LZ does to it
+
+ align:start position:0%
+does have but we know what LZ does to it
+ 
+
+ align:start position:0%
+does have but we know what LZ does to it
+and so what we can write immediately is
+
+ align:start position:0%
+and so what we can write immediately is
+ 
+
+ align:start position:0%
+and so what we can write immediately is
+that LZ operating on L plus - yeah is
+
+ align:start position:0%
+that LZ operating on L plus - yeah is
+ 
+
+ align:start position:0%
+that LZ operating on L plus - yeah is
+equal to plus or minus h-bar L plus
+
+ align:start position:0%
+equal to plus or minus h-bar L plus
+ 
+
+ align:start position:0%
+equal to plus or minus h-bar L plus
+minus F plus mu L plus minus F nice
+
+ align:start position:0%
+minus F plus mu L plus minus F nice
+ 
+
+ align:start position:0%
+minus F plus mu L plus minus F nice
+interesting so we see that we can
+
+ align:start position:0%
+interesting so we see that we can
+ 
+
+ align:start position:0%
+interesting so we see that we can
+rearrange this and we could write plus
+
+ align:start position:0%
+rearrange this and we could write plus
+ 
+
+ align:start position:0%
+rearrange this and we could write plus
+minus h-bar L plus minus F is equal to
+
+ align:start position:0%
+minus h-bar L plus minus F is equal to
+ 
+
+ align:start position:0%
+minus h-bar L plus minus F is equal to
+mu L plus minus F plus LZ L plus minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a tomorrow okay so oh I'm sorry
+
+ align:start position:0%
+that's a tomorrow okay so oh I'm sorry
+ 
+
+ align:start position:0%
+that's a tomorrow okay so oh I'm sorry
+L plus minus half in there okay what's
+
+ align:start position:0%
+L plus minus half in there okay what's
+ 
+
+ align:start position:0%
+L plus minus half in there okay what's
+this telling us so we can simply combine
+
+ align:start position:0%
+this telling us so we can simply combine
+ 
+
+ align:start position:0%
+this telling us so we can simply combine
+these terms we have the L plus minus F
+
+ align:start position:0%
+these terms we have the L plus minus F
+ 
+
+ align:start position:0%
+these terms we have the L plus minus F
+here and so we have + and so we can
+
+ align:start position:0%
+here and so we have + and so we can
+ 
+
+ align:start position:0%
+here and so we have + and so we can
+write mu plus h-bar times L plus minus F
+
+ align:start position:0%
+write mu plus h-bar times L plus minus F
+ 
+
+ align:start position:0%
+write mu plus h-bar times L plus minus F
+that's the point okay so we have this
+
+ align:start position:0%
+that's the point okay so we have this
+ 
+
+ align:start position:0%
+that's the point okay so we have this
+operator operating I'm sorry the first
+
+ align:start position:0%
+operator operating I'm sorry the first
+ 
+
+ align:start position:0%
+operator operating I'm sorry the first
+line goes straight there yep so I took
+
+ align:start position:0%
+line goes straight there yep so I took
+ 
+
+ align:start position:0%
+line goes straight there yep so I took
+this thing over to here but the so let's
+
+ align:start position:0%
+this thing over to here but the so let's
+ 
+
+ align:start position:0%
+this thing over to here but the so let's
+just rewrite that again we have L Z L
+
+ align:start position:0%
+just rewrite that again we have L Z L
+ 
+
+ align:start position:0%
+just rewrite that again we have L Z L
+plus minus F is equal to this and so
+
+ align:start position:0%
+plus minus F is equal to this and so
+ 
+
+ align:start position:0%
+plus minus F is equal to this and so
+here we have mu the eigenvalue and it's
+
+ align:start position:0%
+here we have mu the eigenvalue and it's
+ 
+
+ align:start position:0%
+here we have mu the eigenvalue and it's
+been increased by h-bar and so what that
+
+ align:start position:0%
+been increased by h-bar and so what that
+ 
+
+ align:start position:0%
+been increased by h-bar and so what that
+tells us is that we have a manifold of
+
+ align:start position:0%
+tells us is that we have a manifold of
+ 
+
+ align:start position:0%
+tells us is that we have a manifold of
+levels u etc so we get us a manifold of
+
+ align:start position:0%
+levels u etc so we get us a manifold of
+ 
+
+ align:start position:0%
+levels u etc so we get us a manifold of
+levels that are equally spaced spaced by
+
+ align:start position:0%
+levels that are equally spaced spaced by
+ 
+
+ align:start position:0%
+levels that are equally spaced spaced by
+H bars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+- right yeah okay so we have this
+
+ align:start position:0%
+- right yeah okay so we have this
+ 
+
+ align:start position:0%
+- right yeah okay so we have this
+manifold of levels and so what we could
+
+ align:start position:0%
+manifold of levels and so what we could
+ 
+
+ align:start position:0%
+manifold of levels and so what we could
+say as well this isn't going to go
+
+ align:start position:0%
+say as well this isn't going to go
+ 
+
+ align:start position:0%
+say as well this isn't going to go
+forever this is going to have a highest
+
+ align:start position:0%
+forever this is going to have a highest
+ 
+
+ align:start position:0%
+forever this is going to have a highest
+this is a ladder of equally spaced
+
+ align:start position:0%
+this is a ladder of equally spaced
+ 
+
+ align:start position:0%
+this is a ladder of equally spaced
+levels and it'll have a highest and the
+
+ align:start position:0%
+levels and it'll have a highest and the
+ 
+
+ align:start position:0%
+levels and it'll have a highest and the
+lowest member and so we can we can say
+
+ align:start position:0%
+lowest member and so we can we can say
+ 
+
+ align:start position:0%
+lowest member and so we can we can say
+alright well suppose we have F max you
+
+ align:start position:0%
+alright well suppose we have F max you
+ 
+
+ align:start position:0%
+alright well suppose we have F max you
+and we have L plus operating on it
+
+ align:start position:0%
+and we have L plus operating on it
+ 
+
+ align:start position:0%
+and we have L plus operating on it
+that's going to give zero and we at the
+
+ align:start position:0%
+that's going to give zero and we at the
+ 
+
+ align:start position:0%
+that's going to give zero and we at the
+same time we could say we have L minus
+
+ align:start position:0%
+same time we could say we have L minus
+ 
+
+ align:start position:0%
+same time we could say we have L minus
+min you that's gonna give zero we're
+
+ align:start position:0%
+min you that's gonna give zero we're
+ 
+
+ align:start position:0%
+min you that's gonna give zero we're
+gonna use both of these okay now I'm
+
+ align:start position:0%
+gonna use both of these okay now I'm
+ 
+
+ align:start position:0%
+gonna use both of these okay now I'm
+just gonna leave that there oh I'm not
+
+ align:start position:0%
+just gonna leave that there oh I'm not
+ 
+
+ align:start position:0%
+just gonna leave that there oh I'm not
+I'm gonna say all right so since since
+
+ align:start position:0%
+I'm gonna say all right so since since
+ 
+
+ align:start position:0%
+I'm gonna say all right so since since
+we have this arrangement all right I am
+
+ align:start position:0%
+we have this arrangement all right I am
+ 
+
+ align:start position:0%
+we have this arrangement all right I am
+skipping something and I don't want to
+
+ align:start position:0%
+skipping something and I don't want to
+ 
+
+ align:start position:0%
+skipping something and I don't want to
+skip it so if we have L plus operating
+
+ align:start position:0%
+skip it so if we have L plus operating
+ 
+
+ align:start position:0%
+skip it so if we have L plus operating
+on the maximum value of a view we get
+
+ align:start position:0%
+on the maximum value of a view we get
+ 
+
+ align:start position:0%
+on the maximum value of a view we get
+zero and the next one down is down by an
+
+ align:start position:0%
+zero and the next one down is down by an
+ 
+
+ align:start position:0%
+zero and the next one down is down by an
+integer number of L and so we can say
+
+ align:start position:0%
+integer number of L and so we can say
+ 
+
+ align:start position:0%
+integer number of L and so we can say
+that L Z operating on F max mu is equal
+
+ align:start position:0%
+that L Z operating on F max mu is equal
+ 
+
+ align:start position:0%
+that L Z operating on F max mu is equal
+to H bar L some integer now this this L
+
+ align:start position:0%
+to H bar L some integer now this this L
+ 
+
+ align:start position:0%
+to H bar L some integer now this this L
+is chosen with some prejudice yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now I have to cheat I'm going to
+
+ align:start position:0%
+okay now I have to cheat I'm going to
+ 
+
+ align:start position:0%
+okay now I have to cheat I'm going to
+apply an argument which is not based on
+
+ align:start position:0%
+apply an argument which is not based on
+ 
+
+ align:start position:0%
+apply an argument which is not based on
+just abstract vectors we have an angular
+
+ align:start position:0%
+just abstract vectors we have an angular
+ 
+
+ align:start position:0%
+just abstract vectors we have an angular
+momentum it has a certain length we know
+
+ align:start position:0%
+momentum it has a certain length we know
+ 
+
+ align:start position:0%
+momentum it has a certain length we know
+the projection of that angular momentum
+
+ align:start position:0%
+the projection of that angular momentum
+ 
+
+ align:start position:0%
+the projection of that angular momentum
+on some axis cannot be longer than its
+
+ align:start position:0%
+on some axis cannot be longer than its
+ 
+
+ align:start position:0%
+on some axis cannot be longer than its
+length okay that's so I'm you know I'm
+
+ align:start position:0%
+length okay that's so I'm you know I'm
+ 
+
+ align:start position:0%
+length okay that's so I'm you know I'm
+uncomfortable making an argument because
+
+ align:start position:0%
+uncomfortable making an argument because
+ 
+
+ align:start position:0%
+uncomfortable making an argument because
+I should be able to to say it you know
+
+ align:start position:0%
+I should be able to to say it you know
+ 
+
+ align:start position:0%
+I should be able to to say it you know
+in a more abstract way but this is in
+
+ align:start position:0%
+in a more abstract way but this is in
+ 
+
+ align:start position:0%
+in a more abstract way but this is in
+fact and you know if we we know there
+
+ align:start position:0%
+fact and you know if we we know there
+ 
+
+ align:start position:0%
+fact and you know if we we know there
+cannot be an infinite number of
+
+ align:start position:0%
+cannot be an infinite number of
+ 
+
+ align:start position:0%
+cannot be an infinite number of
+projection quantum numbers values of the
+
+ align:start position:0%
+projection quantum numbers values of the
+ 
+
+ align:start position:0%
+projection quantum numbers values of the
+projection quantum number that are
+
+ align:start position:0%
+projection quantum number that are
+ 
+
+ align:start position:0%
+projection quantum number that are
+reached by applying L plus and L - they
+
+ align:start position:0%
+reached by applying L plus and L - they
+ 
+
+ align:start position:0%
+reached by applying L plus and L - they
+must be limited and and so we're going
+
+ align:start position:0%
+must be limited and and so we're going
+ 
+
+ align:start position:0%
+must be limited and and so we're going
+to call the maximum value of mu H bar L
+
+ align:start position:0%
+to call the maximum value of mu H bar L
+ 
+
+ align:start position:0%
+to call the maximum value of mu H bar L
+or L okay now I have to derive a new
+
+ align:start position:0%
+or L okay now I have to derive a new
+ 
+
+ align:start position:0%
+or L okay now I have to derive a new
+commutation rule based on the original
+
+ align:start position:0%
+commutation rule based on the original
+ 
+
+ align:start position:0%
+commutation rule based on the original
+one no it's not let's not erase this we
+
+ align:start position:0%
+one no it's not let's not erase this we
+ 
+
+ align:start position:0%
+one no it's not let's not erase this we
+might want to see it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's ask well what does this
+
+ align:start position:0%
+okay so let's ask well what does this
+ 
+
+ align:start position:0%
+okay so let's ask well what does this
+combination of operators do okay well
+
+ align:start position:0%
+combination of operators do okay well
+ 
+
+ align:start position:0%
+combination of operators do okay well
+this is surely equal to LX squared and
+
+ align:start position:0%
+this is surely equal to LX squared and
+ 
+
+ align:start position:0%
+this is surely equal to LX squared and
+we get a might we get a plus I and a
+
+ align:start position:0%
+we get a might we get a plus I and a
+ 
+
+ align:start position:0%
+we get a might we get a plus I and a
+minus I and so it's going to be plus ly
+
+ align:start position:0%
+minus I and so it's going to be plus ly
+ 
+
+ align:start position:0%
+minus I and so it's going to be plus ly
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+and then we get I times L by L X and we
+
+ align:start position:0%
+and then we get I times L by L X and we
+ 
+
+ align:start position:0%
+and then we get I times L by L X and we
+get a minus I times LX ly this is l
+
+ align:start position:0%
+get a minus I times LX ly this is l
+ 
+
+ align:start position:0%
+get a minus I times LX ly this is l
+squared minus LZ squared right we have
+
+ align:start position:0%
+squared minus LZ squared right we have
+ 
+
+ align:start position:0%
+squared minus LZ squared right we have
+the square of two components of l
+
+ align:start position:0%
+the square of two components of l
+ 
+
+ align:start position:0%
+the square of two components of l
+squared and so this is equal to the the
+
+ align:start position:0%
+squared and so this is equal to the the
+ 
+
+ align:start position:0%
+squared and so this is equal to the the
+difference and and so and now we we
+
+ align:start position:0%
+difference and and so and now we we
+ 
+
+ align:start position:0%
+difference and and so and now we we
+express this as I x ly LX right and what
+
+ align:start position:0%
+express this as I x ly LX right and what
+ 
+
+ align:start position:0%
+express this as I x ly LX right and what
+is this this is plus IH bar LZ l LX okay
+
+ align:start position:0%
+is this this is plus IH bar LZ l LX okay
+ 
+
+ align:start position:0%
+is this this is plus IH bar LZ l LX okay
+let's just this is yes X and that's LZ I
+
+ align:start position:0%
+let's just this is yes X and that's LZ I
+ 
+
+ align:start position:0%
+let's just this is yes X and that's LZ I
+didn't like what I wrote because I I
+
+ align:start position:0%
+didn't like what I wrote because I I
+ 
+
+ align:start position:0%
+didn't like what I wrote because I I
+want to have everything but the X but
+
+ align:start position:0%
+want to have everything but the X but
+ 
+
+ align:start position:0%
+want to have everything but the X but
+the Z and the l squared disappearing and
+
+ align:start position:0%
+the Z and the l squared disappearing and
+ 
+
+ align:start position:0%
+the Z and the l squared disappearing and
+so we get that we have l squared minus
+
+ align:start position:0%
+so we get that we have l squared minus
+ 
+
+ align:start position:0%
+so we get that we have l squared minus
+LZ squared and then we have plus IH bar
+
+ align:start position:0%
+LZ squared and then we have plus IH bar
+ 
+
+ align:start position:0%
+LZ squared and then we have plus IH bar
+LZ and I have a I lost the plus and
+
+ align:start position:0%
+LZ and I have a I lost the plus and
+ 
+
+ align:start position:0%
+LZ and I have a I lost the plus and
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+no I didn't okay that's it and so we can
+
+ align:start position:0%
+no I didn't okay that's it and so we can
+ 
+
+ align:start position:0%
+no I didn't okay that's it and so we can
+rearrange this and say L squared is
+
+ align:start position:0%
+rearrange this and say L squared is
+ 
+
+ align:start position:0%
+rearrange this and say L squared is
+equal to LZ squared minus or plus h bar
+
+ align:start position:0%
+equal to LZ squared minus or plus h bar
+ 
+
+ align:start position:0%
+equal to LZ squared minus or plus h bar
+LZ plus plus minus minus plus e okay so
+
+ align:start position:0%
+LZ plus plus minus minus plus e okay so
+ 
+
+ align:start position:0%
+LZ plus plus minus minus plus e okay so
+we can use this equation
+
+ align:start position:0%
+we can use this equation
+ 
+
+ align:start position:0%
+we can use this equation
+okay they're not and to derive some good
+
+ align:start position:0%
+okay they're not and to derive some good
+ 
+
+ align:start position:0%
+okay they're not and to derive some good
+stuff I better erase some stuff for
+
+ align:start position:0%
+stuff I better erase some stuff for
+ 
+
+ align:start position:0%
+stuff I better erase some stuff for
+accessing okay we're actually pretty
+
+ align:start position:0%
+accessing okay we're actually pretty
+ 
+
+ align:start position:0%
+accessing okay we're actually pretty
+close to the end so I might actually
+
+ align:start position:0%
+close to the end so I might actually
+ 
+
+ align:start position:0%
+close to the end so I might actually
+finish this okay so we're gonna use this
+
+ align:start position:0%
+finish this okay so we're gonna use this
+ 
+
+ align:start position:0%
+finish this okay so we're gonna use this
+equation to find we want lamda the value
+
+ align:start position:0%
+equation to find we want lamda the value
+ 
+
+ align:start position:0%
+equation to find we want lamda the value
+of lambda for the top of the manifold
+
+ align:start position:0%
+of lambda for the top of the manifold
+ 
+
+ align:start position:0%
+of lambda for the top of the manifold
+over here so we yl squared F max mu and
+
+ align:start position:0%
+over here so we yl squared F max mu and
+ 
+
+ align:start position:0%
+over here so we yl squared F max mu and
+we know we have an equation here which
+
+ align:start position:0%
+we know we have an equation here which
+ 
+
+ align:start position:0%
+we know we have an equation here which
+enables us to evaluate what what the
+
+ align:start position:0%
+enables us to evaluate what what the
+ 
+
+ align:start position:0%
+enables us to evaluate what what the
+consequences of that will be in it the
+
+ align:start position:0%
+consequences of that will be in it the
+ 
+
+ align:start position:0%
+consequences of that will be in it the
+LZ squared F max u minus or plus h bar
+
+ align:start position:0%
+LZ squared F max u minus or plus h bar
+ 
+
+ align:start position:0%
+LZ squared F max u minus or plus h bar
+LZ F max okay so if we take the bottom
+
+ align:start position:0%
+LZ F max okay so if we take the bottom
+ 
+
+ align:start position:0%
+LZ F max okay so if we take the bottom
+sign then L plus on F max is going to
+
+ align:start position:0%
+sign then L plus on F max is going to
+ 
+
+ align:start position:0%
+sign then L plus on F max is going to
+give zero so we're looking at the bottom
+
+ align:start position:0%
+give zero so we're looking at the bottom
+ 
+
+ align:start position:0%
+give zero so we're looking at the bottom
+sign and we have a zero here and so we
+
+ align:start position:0%
+sign and we have a zero here and so we
+ 
+
+ align:start position:0%
+sign and we have a zero here and so we
+have L squared F max U is equal to L Z
+
+ align:start position:0%
+have L squared F max U is equal to L Z
+ 
+
+ align:start position:0%
+have L squared F max U is equal to L Z
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+if max minus or plus h bar LZ max mu
+
+ align:start position:0%
+if max minus or plus h bar LZ max mu
+ 
+
+ align:start position:0%
+if max minus or plus h bar LZ max mu
+plus zero interesting okay so we know
+
+ align:start position:0%
+plus zero interesting okay so we know
+ 
+
+ align:start position:0%
+plus zero interesting okay so we know
+that LZ is going to give so we're going
+
+ align:start position:0%
+that LZ is going to give so we're going
+ 
+
+ align:start position:0%
+that LZ is going to give so we're going
+to get an H bar squared and mu max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're gonna get a minus H bar H bar mu
+
+ align:start position:0%
+we're gonna get a minus H bar H bar mu
+ 
+
+ align:start position:0%
+we're gonna get a minus H bar H bar mu
+max so what this is telling us is that l
+
+ align:start position:0%
+max so what this is telling us is that l
+ 
+
+ align:start position:0%
+max so what this is telling us is that l
+squared operate on FX
+
+ align:start position:0%
+squared operate on FX
+ 
+
+ align:start position:0%
+squared operate on FX
+mu is given by L because we we said that
+
+ align:start position:0%
+mu is given by L because we we said that
+ 
+
+ align:start position:0%
+mu is given by L because we we said that
+we're going to take the maximum value of
+
+ align:start position:0%
+we're going to take the maximum value of
+ 
+
+ align:start position:0%
+we're going to take the maximum value of
+mu to be H bar L so so I shouldn't have
+
+ align:start position:0%
+mu to be H bar L so so I shouldn't have
+ 
+
+ align:start position:0%
+mu to be H bar L so so I shouldn't have
+had an extra H bar here okay so we get
+
+ align:start position:0%
+had an extra H bar here okay so we get
+ 
+
+ align:start position:0%
+had an extra H bar here okay so we get
+this result so lambda so l squared
+
+ align:start position:0%
+this result so lambda so l squared
+ 
+
+ align:start position:0%
+this result so lambda so l squared
+operating this gives the U so it's
+
+ align:start position:0%
+operating this gives the U so it's
+ 
+
+ align:start position:0%
+operating this gives the U so it's
+telling us that l squared F max mu is
+
+ align:start position:0%
+telling us that l squared F max mu is
+ 
+
+ align:start position:0%
+telling us that l squared F max mu is
+equal to H bar squared ll plus 1 now
+
+ align:start position:0%
+equal to H bar squared ll plus 1 now
+ 
+
+ align:start position:0%
+equal to H bar squared ll plus 1 now
+that is why we chose that that constant
+
+ align:start position:0%
+that is why we chose that that constant
+ 
+
+ align:start position:0%
+that is why we chose that that constant
+to be L and we do a similar argument for
+
+ align:start position:0%
+to be L and we do a similar argument for
+ 
+
+ align:start position:0%
+to be L and we do a similar argument for
+the lowest rung of the ladder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for the lowest rung of the ladder we
+
+ align:start position:0%
+and for the lowest rung of the ladder we
+ 
+
+ align:start position:0%
+and for the lowest rung of the ladder we
+know there must be lowest rung and so we
+
+ align:start position:0%
+know there must be lowest rung and so we
+ 
+
+ align:start position:0%
+know there must be lowest rung and so we
+will simply say okay for the lowest rung
+
+ align:start position:0%
+will simply say okay for the lowest rung
+ 
+
+ align:start position:0%
+will simply say okay for the lowest rung
+of the ladder we're going to get that
+
+ align:start position:0%
+of the ladder we're going to get that
+ 
+
+ align:start position:0%
+of the ladder we're going to get that
+that mu is equal to H bar lambda bar mu
+
+ align:start position:0%
+that mu is equal to H bar lambda bar mu
+ 
+
+ align:start position:0%
+that mu is equal to H bar lambda bar mu
+min okay and we could do some stuff and
+
+ align:start position:0%
+min okay and we could do some stuff and
+ 
+
+ align:start position:0%
+min okay and we could do some stuff and
+we discover that lambda has to be equal
+
+ align:start position:0%
+we discover that lambda has to be equal
+ 
+
+ align:start position:0%
+we discover that lambda has to be equal
+to H bar squared ll plus 1 and using the
+
+ align:start position:0%
+to H bar squared ll plus 1 and using the
+ 
+
+ align:start position:0%
+to H bar squared ll plus 1 and using the
+other this other relationship and the
+
+ align:start position:0%
+other this other relationship and the
+ 
+
+ align:start position:0%
+other this other relationship and the
+top sign we get H bar squared L bar L
+
+ align:start position:0%
+top sign we get H bar squared L bar L
+ 
+
+ align:start position:0%
+top sign we get H bar squared L bar L
+bar minus 1 okay and there's two wages
+
+ align:start position:0%
+bar minus 1 okay and there's two wages
+ 
+
+ align:start position:0%
+bar minus 1 okay and there's two wages
+at two ways to solve this one is that L
+
+ align:start position:0%
+at two ways to solve this one is that L
+ 
+
+ align:start position:0%
+at two ways to solve this one is that L
+is equal to minus L bar and the other is
+
+ align:start position:0%
+is equal to minus L bar and the other is
+ 
+
+ align:start position:0%
+is equal to minus L bar and the other is
+that L bar is equal to L plus 1 well
+
+ align:start position:0%
+that L bar is equal to L plus 1 well
+ 
+
+ align:start position:0%
+that L bar is equal to L plus 1 well
+this is the lowest rung of the ladder
+
+ align:start position:0%
+this is the lowest rung of the ladder
+ 
+
+ align:start position:0%
+this is the lowest rung of the ladder
+and wait a minute let me just make sure
+
+ align:start position:0%
+and wait a minute let me just make sure
+ 
+
+ align:start position:0%
+and wait a minute let me just make sure
+I'm doing the logic correctly okay it's
+
+ align:start position:0%
+I'm doing the logic correctly okay it's
+ 
+
+ align:start position:0%
+I'm doing the logic correctly okay it's
+not this one okay here so this is the
+
+ align:start position:0%
+not this one okay here so this is the
+ 
+
+ align:start position:0%
+not this one okay here so this is the
+lowest rung of the ladder and L bar is
+
+ align:start position:0%
+lowest rung of the ladder and L bar is
+ 
+
+ align:start position:0%
+lowest rung of the ladder and L bar is
+supposedly larger than L can't be so
+
+ align:start position:0%
+supposedly larger than L can't be so
+ 
+
+ align:start position:0%
+supposedly larger than L can't be so
+this is impossible this is correct and
+
+ align:start position:0%
+this is impossible this is correct and
+ 
+
+ align:start position:0%
+this is impossible this is correct and
+what we end up getting is this
+
+ align:start position:0%
+what we end up getting is this
+ 
+
+ align:start position:0%
+what we end up getting is this
+relationship and so mu can be equal to
+
+ align:start position:0%
+relationship and so mu can be equal to
+ 
+
+ align:start position:0%
+relationship and so mu can be equal to
+and this is L L minus 1 minus L steps of
+
+ align:start position:0%
+and this is L L minus 1 minus L steps of
+ 
+
+ align:start position:0%
+and this is L L minus 1 minus L steps of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this seems very weird and not very
+
+ align:start position:0%
+this seems very weird and not very
+ 
+
+ align:start position:0%
+this seems very weird and not very
+interesting until you say well how do i
+
+ align:start position:0%
+interesting until you say well how do i
+ 
+
+ align:start position:0%
+interesting until you say well how do i
+satisfy this
+
+ align:start position:0%
+satisfy this
+ 
+
+ align:start position:0%
+satisfy this
+well if L is an integer it's obvious if
+
+ align:start position:0%
+well if L is an integer it's obvious if
+ 
+
+ align:start position:0%
+well if L is an integer it's obvious if
+L is a half integer it shouldn't be
+
+ align:start position:0%
+L is a half integer it shouldn't be
+ 
+
+ align:start position:0%
+L is a half integer it shouldn't be
+quite so obvious but it's true so we can
+
+ align:start position:0%
+quite so obvious but it's true so we can
+ 
+
+ align:start position:0%
+quite so obvious but it's true so we can
+have integer hell and half integer L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's weird
+
+ align:start position:0%
+that's weird
+ 
+
+ align:start position:0%
+that's weird
+we can show no connection between the
+
+ align:start position:0%
+we can show no connection between the
+ 
+
+ align:start position:0%
+we can show no connection between the
+integer ELLs and the have integer else
+
+ align:start position:0%
+integer ELLs and the have integer else
+ 
+
+ align:start position:0%
+integer ELLs and the have integer else
+they belong to completely different
+
+ align:start position:0%
+they belong to completely different
+ 
+
+ align:start position:0%
+they belong to completely different
+problems but this abstract argument says
+
+ align:start position:0%
+problems but this abstract argument says
+ 
+
+ align:start position:0%
+problems but this abstract argument says
+yeah we can have integer else and half
+
+ align:start position:0%
+yeah we can have integer else and half
+ 
+
+ align:start position:0%
+yeah we can have integer else and half
+integer else and if we have have
+
+ align:start position:0%
+integer else and if we have have
+ 
+
+ align:start position:0%
+integer else and if we have have
+electron we call it electron spin
+
+ align:start position:0%
+electron we call it electron spin
+ 
+
+ align:start position:0%
+electron we call it electron spin
+because we want it to be an angular
+
+ align:start position:0%
+because we want it to be an angular
+ 
+
+ align:start position:0%
+because we want it to be an angular
+momentum spin as sort of an angular
+
+ align:start position:0%
+momentum spin as sort of an angular
+ 
+
+ align:start position:0%
+momentum spin as sort of an angular
+momentum or nuclear spin and we discover
+
+ align:start position:0%
+momentum or nuclear spin and we discover
+ 
+
+ align:start position:0%
+momentum or nuclear spin and we discover
+that there are patterns of energy levels
+
+ align:start position:0%
+that there are patterns of energy levels
+ 
+
+ align:start position:0%
+that there are patterns of energy levels
+which enable us to count the number of
+
+ align:start position:0%
+which enable us to count the number of
+ 
+
+ align:start position:0%
+which enable us to count the number of
+projection components and if you have an
+
+ align:start position:0%
+projection components and if you have an
+ 
+
+ align:start position:0%
+projection components and if you have an
+integer al you get 2 L plus 1 components
+
+ align:start position:0%
+integer al you get 2 L plus 1 components
+ 
+
+ align:start position:0%
+integer al you get 2 L plus 1 components
+which is an odd number and if it's half
+
+ align:start position:0%
+which is an odd number and if it's half
+ 
+
+ align:start position:0%
+which is an odd number and if it's half
+integer you get 2 L plus 1 components
+
+ align:start position:0%
+integer you get 2 L plus 1 components
+ 
+
+ align:start position:0%
+integer you get 2 L plus 1 components
+which is an even number and so it turns
+
+ align:start position:0%
+which is an even number and so it turns
+ 
+
+ align:start position:0%
+which is an even number and so it turns
+out that our definition of an angular
+
+ align:start position:0%
+out that our definition of an angular
+ 
+
+ align:start position:0%
+out that our definition of an angular
+momentum is more general than we thought
+
+ align:start position:0%
+momentum is more general than we thought
+ 
+
+ align:start position:0%
+momentum is more general than we thought
+it allows there to be both integer and
+
+ align:start position:0%
+it allows there to be both integer and
+ 
+
+ align:start position:0%
+it allows there to be both integer and
+happen at your angular momenta and this
+
+ align:start position:0%
+happen at your angular momenta and this
+ 
+
+ align:start position:0%
+happen at your angular momenta and this
+means we can have angular momenta where
+
+ align:start position:0%
+means we can have angular momenta where
+ 
+
+ align:start position:0%
+means we can have angular momenta where
+we can't define it in terms of R cross P
+
+ align:start position:0%
+we can't define it in terms of R cross P
+ 
+
+ align:start position:0%
+we can't define it in terms of R cross P
+it's defined by the commutation rule
+
+ align:start position:0%
+it's defined by the commutation rule
+ 
+
+ align:start position:0%
+it's defined by the commutation rule
+it's more general it's more abstract
+
+ align:start position:0%
+it's more general it's more abstract
+ 
+
+ align:start position:0%
+it's more general it's more abstract
+it's beautiful
+
+ align:start position:0%
+it's beautiful
+ 
+
+ align:start position:0%
+it's beautiful
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+I don't have time to finish the job but
+
+ align:start position:0%
+I don't have time to finish the job but
+ 
+
+ align:start position:0%
+I don't have time to finish the job but
+in the notes you can see that we can
+
+ align:start position:0%
+in the notes you can see that we can
+ 
+
+ align:start position:0%
+in the notes you can see that we can
+derive the matrix elements for the
+
+ align:start position:0%
+derive the matrix elements for the
+ 
+
+ align:start position:0%
+derive the matrix elements for the
+raising and lowering operators too and
+
+ align:start position:0%
+raising and lowering operators too and
+ 
+
+ align:start position:0%
+raising and lowering operators too and
+the angular momentum matrix elements are
+
+ align:start position:0%
+the angular momentum matrix elements are
+ 
+
+ align:start position:0%
+the angular momentum matrix elements are
+that the L plus minus operating on a
+
+ align:start position:0%
+that the L plus minus operating on a
+ 
+
+ align:start position:0%
+that the L plus minus operating on a
+function gives this combination square
+
+ align:start position:0%
+function gives this combination square
+ 
+
+ align:start position:0%
+function gives this combination square
+root and it raises or lowers M so it's
+
+ align:start position:0%
+root and it raises or lowers M so it's
+ 
+
+ align:start position:0%
+root and it raises or lowers M so it's
+sort of like what we have for the A's
+
+ align:start position:0%
+sort of like what we have for the A's
+ 
+
+ align:start position:0%
+sort of like what we have for the A's
+and a daggers for the harmonic
+
+ align:start position:0%
+and a daggers for the harmonic
+ 
+
+ align:start position:0%
+and a daggers for the harmonic
+oscillator but it's not as good because
+
+ align:start position:0%
+oscillator but it's not as good because
+ 
+
+ align:start position:0%
+oscillator but it's not as good because
+you can't generate all the else you can
+
+ align:start position:0%
+you can't generate all the else you can
+ 
+
+ align:start position:0%
+you can't generate all the else you can
+generate the MC bells and that's great
+
+ align:start position:0%
+generate the MC bells and that's great
+ 
+
+ align:start position:0%
+generate the MC bells and that's great
+but you know there's there still
+
+ align:start position:0%
+but you know there's there still
+ 
+
+ align:start position:0%
+but you know there's there still
+something that remains to be done to
+
+ align:start position:0%
+something that remains to be done to
+ 
+
+ align:start position:0%
+something that remains to be done to
+generate the different else it's not a
+
+ align:start position:0%
+generate the different else it's not a
+ 
+
+ align:start position:0%
+generate the different else it's not a
+problem it's just there's not a simple
+
+ align:start position:0%
+problem it's just there's not a simple
+ 
+
+ align:start position:0%
+problem it's just there's not a simple
+way to do it at least not simple to me
+
+ align:start position:0%
+way to do it at least not simple to me
+ 
+
+ align:start position:0%
+way to do it at least not simple to me
+and so now anytime we're faced with a
+
+ align:start position:0%
+and so now anytime we're faced with a
+ 
+
+ align:start position:0%
+and so now anytime we're faced with a
+problem involving angular momenta we
+
+ align:start position:0%
+problem involving angular momenta we
+ 
+
+ align:start position:0%
+problem involving angular momenta we
+have a prayer of writing down the matrix
+
+ align:start position:0%
+have a prayer of writing down the matrix
+ 
+
+ align:start position:0%
+have a prayer of writing down the matrix
+elements without ever looking at the
+
+ align:start position:0%
+elements without ever looking at the
+ 
+
+ align:start position:0%
+elements without ever looking at the
+wave function without ever looking at a
+
+ align:start position:0%
+wave function without ever looking at a
+ 
+
+ align:start position:0%
+wave function without ever looking at a
+differential operator and we can also
+
+ align:start position:0%
+differential operator and we can also
+ 
+
+ align:start position:0%
+differential operator and we can also
+say well let's suppose we had you know
+
+ align:start position:0%
+say well let's suppose we had you know
+ 
+
+ align:start position:0%
+say well let's suppose we had you know
+some operator that involves L and s now
+
+ align:start position:0%
+some operator that involves L and s now
+ 
+
+ align:start position:0%
+some operator that involves L and s now
+that we know that we have this things
+
+ align:start position:0%
+that we know that we have this things
+ 
+
+ align:start position:0%
+that we know that we have this things
+and L plus s can be called J so now we
+
+ align:start position:0%
+and L plus s can be called J so now we
+ 
+
+ align:start position:0%
+and L plus s can be called J so now we
+have two different operators two
+
+ align:start position:0%
+have two different operators two
+ 
+
+ align:start position:0%
+have two different operators two
+different angular 1 we have s and we
+
+ align:start position:0%
+different angular 1 we have s and we
+ 
+
+ align:start position:0%
+different angular 1 we have s and we
+have the total of J well they're all
+
+ align:start position:0%
+have the total of J well they're all
+ 
+
+ align:start position:0%
+have the total of J well they're all
+angular momenta they're going to satisfy
+
+ align:start position:0%
+angular momenta they're going to satisfy
+ 
+
+ align:start position:0%
+angular momenta they're going to satisfy
+there's selection rules and matrix
+
+ align:start position:0%
+there's selection rules and matrix
+ 
+
+ align:start position:0%
+there's selection rules and matrix
+elements and we can calculate all of
+
+ align:start position:0%
+elements and we can calculate all of
+ 
+
+ align:start position:0%
+elements and we can calculate all of
+these matrix elements including things
+
+ align:start position:0%
+these matrix elements including things
+ 
+
+ align:start position:0%
+these matrix elements including things
+like l dot s and whatever and and so it
+
+ align:start position:0%
+like l dot s and whatever and and so it
+ 
+
+ align:start position:0%
+like l dot s and whatever and and so it
+just opens up a huge area where before
+
+ align:start position:0%
+just opens up a huge area where before
+ 
+
+ align:start position:0%
+just opens up a huge area where before
+you would say well I got a look at the
+
+ align:start position:0%
+you would say well I got a look at the
+ 
+
+ align:start position:0%
+you would say well I got a look at the
+wave function I got it a look at this
+
+ align:start position:0%
+wave function I got it a look at this
+ 
+
+ align:start position:0%
+wave function I got it a look at this
+integral no more but there's one thing
+
+ align:start position:0%
+integral no more but there's one thing
+ 
+
+ align:start position:0%
+integral no more but there's one thing
+and that is these arguments do not
+
+ align:start position:0%
+and that is these arguments do not
+ 
+
+ align:start position:0%
+and that is these arguments do not
+termen I mean when you take the square
+
+ align:start position:0%
+termen I mean when you take the square
+ 
+
+ align:start position:0%
+termen I mean when you take the square
+root of something you have a positive
+
+ align:start position:0%
+root of something you have a positive
+ 
+
+ align:start position:0%
+root of something you have a positive
+value in a negative value that
+
+ align:start position:0%
+value in a negative value that
+ 
+
+ align:start position:0%
+value in a negative value that
+corresponds to a phase ambiguity these
+
+ align:start position:0%
+corresponds to a phase ambiguity these
+ 
+
+ align:start position:0%
+corresponds to a phase ambiguity these
+arguments don't resolve that at some
+
+ align:start position:0%
+arguments don't resolve that at some
+ 
+
+ align:start position:0%
+arguments don't resolve that at some
+point you have to decide on the phase
+
+ align:start position:0%
+point you have to decide on the phase
+ 
+
+ align:start position:0%
+point you have to decide on the phase
+and be consistent and since you're never
+
+ align:start position:0%
+and be consistent and since you're never
+ 
+
+ align:start position:0%
+and be consistent and since you're never
+looking at wave functions that actually
+
+ align:start position:0%
+looking at wave functions that actually
+ 
+
+ align:start position:0%
+looking at wave functions that actually
+is a frequent source of error but that's
+
+ align:start position:0%
+is a frequent source of error but that's
+ 
+
+ align:start position:0%
+is a frequent source of error but that's
+the only defect in this this whole thing
+
+ align:start position:0%
+the only defect in this this whole thing
+ 
+
+ align:start position:0%
+the only defect in this this whole thing
+okay so that's it for the exam I will
+
+ align:start position:0%
+okay so that's it for the exam I will
+ 
+
+ align:start position:0%
+okay so that's it for the exam I will
+talk about something that will make you
+
+ align:start position:0%
+talk about something that will make you
+ 
+
+ align:start position:0%
+talk about something that will make you
+a little bit more comfortable about one
+
+ align:start position:0%
+a little bit more comfortable about one
+ 
+
+ align:start position:0%
+a little bit more comfortable about one
+of the exams some of these you have
+
+ align:start position:0%
+of the exams some of these you have
+ 
+
+ align:start position:0%
+of the exams some of these you have
+questions on Wednesday but it's not
+
+ align:start position:0%
+questions on Wednesday but it's not
+ 
+
+ align:start position:0%
+questions on Wednesday but it's not
+going to be tested
\ No newline at end of file
diff --git a/76dhtgZt38A.txt b/76dhtgZt38A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fe80c71528fc18444e3e0096293e7b62a4f52d24
--- /dev/null
+++ b/76dhtgZt38A.txt
@@ -0,0 +1,9552 @@
+align:start position:0%
+ 
+all right let's get started
+
+ align:start position:0%
+all right let's get started
+ 
+
+ align:start position:0%
+all right let's get started
+welcome back to double06 today we are
+
+ align:start position:0%
+welcome back to double06 today we are
+ 
+
+ align:start position:0%
+welcome back to double06 today we are
+doing some of the coolest data
+
+ align:start position:0%
+doing some of the coolest data
+ 
+
+ align:start position:0%
+doing some of the coolest data
+structures we will see in this class
+
+ align:start position:0%
+structures we will see in this class
+ 
+
+ align:start position:0%
+structures we will see in this class
+maybe some of the coolest data
+
+ align:start position:0%
+maybe some of the coolest data
+ 
+
+ align:start position:0%
+maybe some of the coolest data
+structures ever binary trees
+
+ align:start position:0%
+structures ever binary trees
+ 
+
+ align:start position:0%
+structures ever binary trees
+uh you've certainly seen trees in many
+
+ align:start position:0%
+uh you've certainly seen trees in many
+ 
+
+ align:start position:0%
+uh you've certainly seen trees in many
+forms
+
+ align:start position:0%
+forms
+ 
+
+ align:start position:0%
+forms
+uh in the past including in this class
+
+ align:start position:0%
+uh in the past including in this class
+ 
+
+ align:start position:0%
+uh in the past including in this class
+we've talked to use trees as a lower
+
+ align:start position:0%
+we've talked to use trees as a lower
+ 
+
+ align:start position:0%
+we've talked to use trees as a lower
+bound tool
+
+ align:start position:0%
+bound tool
+ 
+
+ align:start position:0%
+bound tool
+for uh in the decision tree model
+
+ align:start position:0%
+for uh in the decision tree model
+ 
+
+ align:start position:0%
+for uh in the decision tree model
+but this lecture and the next lecture
+
+ align:start position:0%
+but this lecture and the next lecture
+ 
+
+ align:start position:0%
+but this lecture and the next lecture
+we're going to build
+
+ align:start position:0%
+we're going to build
+ 
+
+ align:start position:0%
+we're going to build
+one data structure that is almost
+
+ align:start position:0%
+one data structure that is almost
+ 
+
+ align:start position:0%
+one data structure that is almost
+superior to all data
+
+ align:start position:0%
+superior to all data
+ 
+
+ align:start position:0%
+superior to all data
+structures we have seen and can do
+
+ align:start position:0%
+structures we have seen and can do
+ 
+
+ align:start position:0%
+structures we have seen and can do
+almost anything
+
+ align:start position:0%
+almost anything
+ 
+
+ align:start position:0%
+almost anything
+really fast first recall all the data
+
+ align:start position:0%
+really fast first recall all the data
+ 
+
+ align:start position:0%
+really fast first recall all the data
+structures we've seen so far arrays
+
+ align:start position:0%
+structures we've seen so far arrays
+ 
+
+ align:start position:0%
+structures we've seen so far arrays
+linked lists
+
+ align:start position:0%
+linked lists
+ 
+
+ align:start position:0%
+linked lists
+dynamic arrays sorted arrays hash tables
+
+ align:start position:0%
+dynamic arrays sorted arrays hash tables
+ 
+
+ align:start position:0%
+dynamic arrays sorted arrays hash tables
+and the two sets of operations we're
+
+ align:start position:0%
+and the two sets of operations we're
+ 
+
+ align:start position:0%
+and the two sets of operations we're
+interested in supporting
+
+ align:start position:0%
+interested in supporting
+ 
+
+ align:start position:0%
+interested in supporting
+the two interfaces one was sequences
+
+ align:start position:0%
+the two interfaces one was sequences
+ 
+
+ align:start position:0%
+the two interfaces one was sequences
+where we're maintaining items in a
+
+ align:start position:0%
+where we're maintaining items in a
+ 
+
+ align:start position:0%
+where we're maintaining items in a
+specified order we want to be able to
+
+ align:start position:0%
+specified order we want to be able to
+ 
+
+ align:start position:0%
+specified order we want to be able to
+insert
+
+ align:start position:0%
+insert
+ 
+
+ align:start position:0%
+insert
+an item right after another item or
+
+ align:start position:0%
+an item right after another item or
+ 
+
+ align:start position:0%
+an item right after another item or
+delete an item in the middle of the list
+
+ align:start position:0%
+delete an item in the middle of the list
+ 
+
+ align:start position:0%
+delete an item in the middle of the list
+and always be able to access the ith
+
+ align:start position:0%
+and always be able to access the ith
+ 
+
+ align:start position:0%
+and always be able to access the ith
+item we haven't seen
+
+ align:start position:0%
+item we haven't seen
+ 
+
+ align:start position:0%
+item we haven't seen
+any good data structures for that
+
+ align:start position:0%
+any good data structures for that
+ 
+
+ align:start position:0%
+any good data structures for that
+problem we we're really good at
+
+ align:start position:0%
+problem we we're really good at
+ 
+
+ align:start position:0%
+problem we we're really good at
+inserting and deleting
+
+ align:start position:0%
+inserting and deleting
+ 
+
+ align:start position:0%
+inserting and deleting
+at the beginning or the end of the
+
+ align:start position:0%
+at the beginning or the end of the
+ 
+
+ align:start position:0%
+at the beginning or the end of the
+sequence but we haven't seen anything
+
+ align:start position:0%
+sequence but we haven't seen anything
+ 
+
+ align:start position:0%
+sequence but we haven't seen anything
+that's efficient at ins
+
+ align:start position:0%
+that's efficient at ins
+ 
+
+ align:start position:0%
+that's efficient at ins
+inserting in the middle of the list or
+
+ align:start position:0%
+inserting in the middle of the list or
+ 
+
+ align:start position:0%
+inserting in the middle of the list or
+deleting in the middle of the list
+
+ align:start position:0%
+deleting in the middle of the list
+ 
+
+ align:start position:0%
+deleting in the middle of the list
+linked list
+
+ align:start position:0%
+linked list
+ 
+
+ align:start position:0%
+linked list
+you can't even get to the middle in less
+
+ align:start position:0%
+you can't even get to the middle in less
+ 
+
+ align:start position:0%
+you can't even get to the middle in less
+than linear time
+
+ align:start position:0%
+than linear time
+ 
+
+ align:start position:0%
+than linear time
+uh array you can get to the middle but
+
+ align:start position:0%
+uh array you can get to the middle but
+ 
+
+ align:start position:0%
+uh array you can get to the middle but
+if you make any changes you have to do
+
+ align:start position:0%
+if you make any changes you have to do
+ 
+
+ align:start position:0%
+if you make any changes you have to do
+this shift which is very expensive
+
+ align:start position:0%
+this shift which is very expensive
+ 
+
+ align:start position:0%
+this shift which is very expensive
+so today or sorry next lecture for the
+
+ align:start position:0%
+so today or sorry next lecture for the
+ 
+
+ align:start position:0%
+so today or sorry next lecture for the
+first time we will see
+
+ align:start position:0%
+first time we will see
+ 
+
+ align:start position:0%
+first time we will see
+all of those operations efficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll mention our goal where efficient
+
+ align:start position:0%
+i'll mention our goal where efficient
+ 
+
+ align:start position:0%
+i'll mention our goal where efficient
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+logarithmic so we're not quite as good
+
+ align:start position:0%
+logarithmic so we're not quite as good
+ 
+
+ align:start position:0%
+logarithmic so we're not quite as good
+as linked lists and dynamic arrays at
+
+ align:start position:0%
+as linked lists and dynamic arrays at
+ 
+
+ align:start position:0%
+as linked lists and dynamic arrays at
+inserting and
+
+ align:start position:0%
+inserting and
+ 
+
+ align:start position:0%
+inserting and
+deleting at the ends those there that we
+
+ align:start position:0%
+deleting at the ends those there that we
+ 
+
+ align:start position:0%
+deleting at the ends those there that we
+achieve constant or constant amortized
+
+ align:start position:0%
+achieve constant or constant amortized
+ 
+
+ align:start position:0%
+achieve constant or constant amortized
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+but up to this log factor we're going to
+
+ align:start position:0%
+but up to this log factor we're going to
+ 
+
+ align:start position:0%
+but up to this log factor we're going to
+get the best of all worlds where we can
+
+ align:start position:0%
+get the best of all worlds where we can
+ 
+
+ align:start position:0%
+get the best of all worlds where we can
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+all the things all the operations that
+
+ align:start position:0%
+all the things all the operations that
+ 
+
+ align:start position:0%
+all the things all the operations that
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+build or iterate through the entire
+
+ align:start position:0%
+build or iterate through the entire
+ 
+
+ align:start position:0%
+build or iterate through the entire
+structure that of course takes linear
+
+ align:start position:0%
+structure that of course takes linear
+ 
+
+ align:start position:0%
+structure that of course takes linear
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+but we can do all the others in
+
+ align:start position:0%
+but we can do all the others in
+ 
+
+ align:start position:0%
+but we can do all the others in
+logarithmic time for sets
+
+ align:start position:0%
+logarithmic time for sets
+ 
+
+ align:start position:0%
+logarithmic time for sets
+sets were maintained maintaining a bunch
+
+ align:start position:0%
+sets were maintained maintaining a bunch
+ 
+
+ align:start position:0%
+sets were maintained maintaining a bunch
+of items which have
+
+ align:start position:0%
+of items which have
+ 
+
+ align:start position:0%
+of items which have
+intrinsic keys and we want to
+
+ align:start position:0%
+intrinsic keys and we want to
+ 
+
+ align:start position:0%
+intrinsic keys and we want to
+search by key so hash tables are great
+
+ align:start position:0%
+search by key so hash tables are great
+ 
+
+ align:start position:0%
+search by key so hash tables are great
+if you're only doing exact searches if
+
+ align:start position:0%
+if you're only doing exact searches if
+ 
+
+ align:start position:0%
+if you're only doing exact searches if
+you want to find a key
+
+ align:start position:0%
+you want to find a key
+ 
+
+ align:start position:0%
+you want to find a key
+and get yes or no is it in there and if
+
+ align:start position:0%
+and get yes or no is it in there and if
+ 
+
+ align:start position:0%
+and get yes or no is it in there and if
+it's in there give me the item
+
+ align:start position:0%
+it's in there give me the item
+ 
+
+ align:start position:0%
+it's in there give me the item
+that's what python dictionaries do and
+
+ align:start position:0%
+that's what python dictionaries do and
+ 
+
+ align:start position:0%
+that's what python dictionaries do and
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+great at inserting and deleting but
+
+ align:start position:0%
+great at inserting and deleting but
+ 
+
+ align:start position:0%
+great at inserting and deleting but
+they're really bad
+
+ align:start position:0%
+they're really bad
+ 
+
+ align:start position:0%
+they're really bad
+at find previous and find next this is a
+
+ align:start position:0%
+at find previous and find next this is a
+ 
+
+ align:start position:0%
+at find previous and find next this is a
+the unsuccessful case if i search for a
+
+ align:start position:0%
+the unsuccessful case if i search for a
+ 
+
+ align:start position:0%
+the unsuccessful case if i search for a
+key and it's not in my structure
+
+ align:start position:0%
+key and it's not in my structure
+ 
+
+ align:start position:0%
+key and it's not in my structure
+i would like to know more than just the
+
+ align:start position:0%
+i would like to know more than just the
+ 
+
+ align:start position:0%
+i would like to know more than just the
+answer no i'd like to know what the
+
+ align:start position:0%
+answer no i'd like to know what the
+ 
+
+ align:start position:0%
+answer no i'd like to know what the
+previous and next items that are
+
+ align:start position:0%
+previous and next items that are
+ 
+
+ align:start position:0%
+previous and next items that are
+actually in the structure
+
+ align:start position:0%
+actually in the structure
+ 
+
+ align:start position:0%
+actually in the structure
+so what are my nearest matches when i
+
+ align:start position:0%
+so what are my nearest matches when i
+ 
+
+ align:start position:0%
+so what are my nearest matches when i
+search by key that's a natural query
+
+ align:start position:0%
+search by key that's a natural query
+ 
+
+ align:start position:0%
+search by key that's a natural query
+and the only data structure we have
+
+ align:start position:0%
+and the only data structure we have
+ 
+
+ align:start position:0%
+and the only data structure we have
+that's good at it is a sorted array
+
+ align:start position:0%
+that's good at it is a sorted array
+ 
+
+ align:start position:0%
+that's good at it is a sorted array
+because binary search gives this to us
+
+ align:start position:0%
+because binary search gives this to us
+ 
+
+ align:start position:0%
+because binary search gives this to us
+if we search for a key by binary search
+
+ align:start position:0%
+if we search for a key by binary search
+ 
+
+ align:start position:0%
+if we search for a key by binary search
+and we don't find it
+
+ align:start position:0%
+and we don't find it
+ 
+
+ align:start position:0%
+and we don't find it
+the position that we end up at is right
+
+ align:start position:0%
+the position that we end up at is right
+ 
+
+ align:start position:0%
+the position that we end up at is right
+between the previous and next one
+
+ align:start position:0%
+between the previous and next one
+ 
+
+ align:start position:0%
+between the previous and next one
+but of course sorted arrays are terrible
+
+ align:start position:0%
+but of course sorted arrays are terrible
+ 
+
+ align:start position:0%
+but of course sorted arrays are terrible
+for dynamic
+
+ align:start position:0%
+for dynamic
+ 
+
+ align:start position:0%
+for dynamic
+operations we don't know how to maintain
+
+ align:start position:0%
+operations we don't know how to maintain
+ 
+
+ align:start position:0%
+operations we don't know how to maintain
+we can't maintain a sorted array without
+
+ align:start position:0%
+we can't maintain a sorted array without
+ 
+
+ align:start position:0%
+we can't maintain a sorted array without
+any gaps
+
+ align:start position:0%
+any gaps
+ 
+
+ align:start position:0%
+any gaps
+when we're doing insertions and
+
+ align:start position:0%
+when we're doing insertions and
+ 
+
+ align:start position:0%
+when we're doing insertions and
+deletions in some sense today
+
+ align:start position:0%
+deletions in some sense today
+ 
+
+ align:start position:0%
+deletions in some sense today
+and next class binary trees let us
+
+ align:start position:0%
+and next class binary trees let us
+ 
+
+ align:start position:0%
+and next class binary trees let us
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+a sorted order or in general an order of
+
+ align:start position:0%
+a sorted order or in general an order of
+ 
+
+ align:start position:0%
+a sorted order or in general an order of
+items
+
+ align:start position:0%
+items
+ 
+
+ align:start position:0%
+items
+dynamically and still allow us to do
+
+ align:start position:0%
+dynamically and still allow us to do
+ 
+
+ align:start position:0%
+dynamically and still allow us to do
+very fast things like get out of i and
+
+ align:start position:0%
+very fast things like get out of i and
+ 
+
+ align:start position:0%
+very fast things like get out of i and
+find previous of the key
+
+ align:start position:0%
+find previous of the key
+ 
+
+ align:start position:0%
+find previous of the key
+so that's our goal we're not going to
+
+ align:start position:0%
+so that's our goal we're not going to
+ 
+
+ align:start position:0%
+so that's our goal we're not going to
+quite get to this goal today
+
+ align:start position:0%
+quite get to this goal today
+ 
+
+ align:start position:0%
+quite get to this goal today
+we're going to get an incomparable thing
+
+ align:start position:0%
+we're going to get an incomparable thing
+ 
+
+ align:start position:0%
+we're going to get an incomparable thing
+called the height of the tree and then
+
+ align:start position:0%
+called the height of the tree and then
+ 
+
+ align:start position:0%
+called the height of the tree and then
+on thursday we'll be able to finish and
+
+ align:start position:0%
+on thursday we'll be able to finish and
+ 
+
+ align:start position:0%
+on thursday we'll be able to finish and
+achieve this goal today is just
+
+ align:start position:0%
+achieve this goal today is just
+ 
+
+ align:start position:0%
+achieve this goal today is just
+in service to that goal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is a binary tree
+
+ align:start position:0%
+so what is a binary tree
+ 
+
+ align:start position:0%
+so what is a binary tree
+let me draw an example
+
+ align:start position:0%
+let me draw an example
+ 
+
+ align:start position:0%
+let me draw an example
+and then define it more precisely
+
+ align:start position:0%
+and then define it more precisely
+ 
+
+ align:start position:0%
+and then define it more precisely
+mathematicians will call this a rooted
+
+ align:start position:0%
+mathematicians will call this a rooted
+ 
+
+ align:start position:0%
+mathematicians will call this a rooted
+binary tree
+
+ align:start position:0%
+binary tree
+ 
+
+ align:start position:0%
+binary tree
+because in case you've seen that in o42
+
+ align:start position:0%
+because in case you've seen that in o42
+ 
+
+ align:start position:0%
+because in case you've seen that in o42
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is a picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is an example of a binary tree
+
+ align:start position:0%
+so this is an example of a binary tree
+ 
+
+ align:start position:0%
+so this is an example of a binary tree
+it has a bunch of nodes which we're
+
+ align:start position:0%
+it has a bunch of nodes which we're
+ 
+
+ align:start position:0%
+it has a bunch of nodes which we're
+drawing in circles it has
+
+ align:start position:0%
+drawing in circles it has
+ 
+
+ align:start position:0%
+drawing in circles it has
+items in the nodes which were i'm
+
+ align:start position:0%
+items in the nodes which were i'm
+ 
+
+ align:start position:0%
+items in the nodes which were i'm
+writing as letters here
+
+ align:start position:0%
+writing as letters here
+ 
+
+ align:start position:0%
+writing as letters here
+so this is item a item b item c and it
+
+ align:start position:0%
+so this is item a item b item c and it
+ 
+
+ align:start position:0%
+so this is item a item b item c and it
+has these
+
+ align:start position:0%
+has these
+ 
+
+ align:start position:0%
+has these
+links between them this is like linked
+
+ align:start position:0%
+links between them this is like linked
+ 
+
+ align:start position:0%
+links between them this is like linked
+lists
+
+ align:start position:0%
+lists
+ 
+
+ align:start position:0%
+lists
+but in general a node
+
+ align:start position:0%
+but in general a node
+ 
+
+ align:start position:0%
+but in general a node
+x is going to have a parent pointer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a left child
+
+ align:start position:0%
+a left child
+ 
+
+ align:start position:0%
+a left child
+left pointer and a right child
+
+ align:start position:0%
+left pointer and a right child
+ 
+
+ align:start position:0%
+left pointer and a right child
+right pointer and it also has
+
+ align:start position:0%
+right pointer and it also has
+ 
+
+ align:start position:0%
+right pointer and it also has
+an item inside of it so i'm going to
+
+ align:start position:0%
+an item inside of it so i'm going to
+ 
+
+ align:start position:0%
+an item inside of it so i'm going to
+talk about node.left
+
+ align:start position:0%
+talk about node.left
+ 
+
+ align:start position:0%
+talk about node.left
+is a pointer to the left
+
+ align:start position:0%
+is a pointer to the left
+ 
+
+ align:start position:0%
+is a pointer to the left
+the node down here node.right
+
+ align:start position:0%
+the node down here node.right
+ 
+
+ align:start position:0%
+the node down here node.right
+node.parent node.item
+
+ align:start position:0%
+node.parent node.item
+ 
+
+ align:start position:0%
+node.parent node.item
+gives me so if i
+
+ align:start position:0%
+gives me so if i
+ 
+
+ align:start position:0%
+gives me so if i
+look at the node a its item is
+
+ align:start position:0%
+look at the node a its item is
+ 
+
+ align:start position:0%
+look at the node a its item is
+a so let me draw for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some examples
+
+ align:start position:0%
+some examples
+ 
+
+ align:start position:0%
+some examples
+okay the parent of a is nothing so we
+
+ align:start position:0%
+okay the parent of a is nothing so we
+ 
+
+ align:start position:0%
+okay the parent of a is nothing so we
+call a
+
+ align:start position:0%
+call a
+ 
+
+ align:start position:0%
+call a
+the root node there's going to be a
+
+ align:start position:0%
+the root node there's going to be a
+ 
+
+ align:start position:0%
+the root node there's going to be a
+unique node that has no parent
+
+ align:start position:0%
+unique node that has no parent
+ 
+
+ align:start position:0%
+unique node that has no parent
+it's uh sad to have no parents but there
+
+ align:start position:0%
+it's uh sad to have no parents but there
+ 
+
+ align:start position:0%
+it's uh sad to have no parents but there
+you go
+
+ align:start position:0%
+you go
+ 
+
+ align:start position:0%
+you go
+then we have node b which whose parent
+
+ align:start position:0%
+then we have node b which whose parent
+ 
+
+ align:start position:0%
+then we have node b which whose parent
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+node c is parent its apparent is a node
+
+ align:start position:0%
+node c is parent its apparent is a node
+ 
+
+ align:start position:0%
+node c is parent its apparent is a node
+d its parent is b
+
+ align:start position:0%
+d its parent is b
+ 
+
+ align:start position:0%
+d its parent is b
+node e its parent is b and node f its
+
+ align:start position:0%
+node e its parent is b and node f its
+ 
+
+ align:start position:0%
+node e its parent is b and node f its
+parent is d
+
+ align:start position:0%
+parent is d
+ 
+
+ align:start position:0%
+parent is d
+alphabetical order here happens to be
+
+ align:start position:0%
+alphabetical order here happens to be
+ 
+
+ align:start position:0%
+alphabetical order here happens to be
+ordered by parent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we have left pointers i'll just do
+
+ align:start position:0%
+then we have left pointers i'll just do
+ 
+
+ align:start position:0%
+then we have left pointers i'll just do
+a few of them so left pointer of
+
+ align:start position:0%
+a few of them so left pointer of
+ 
+
+ align:start position:0%
+a few of them so left pointer of
+a is b right pointer of a
+
+ align:start position:0%
+a is b right pointer of a
+ 
+
+ align:start position:0%
+a is b right pointer of a
+sorry b the node uh these should all be
+
+ align:start position:0%
+sorry b the node uh these should all be
+ 
+
+ align:start position:0%
+sorry b the node uh these should all be
+notes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm circling for nodes and just writing
+
+ align:start position:0%
+i'm circling for nodes and just writing
+ 
+
+ align:start position:0%
+i'm circling for nodes and just writing
+the letter for the item
+
+ align:start position:0%
+the letter for the item
+ 
+
+ align:start position:0%
+the letter for the item
+make it clear that those are different
+
+ align:start position:0%
+make it clear that those are different
+ 
+
+ align:start position:0%
+make it clear that those are different
+things uh the right pointer for a
+
+ align:start position:0%
+things uh the right pointer for a
+ 
+
+ align:start position:0%
+things uh the right pointer for a
+is c left pointer for b is d
+
+ align:start position:0%
+is c left pointer for b is d
+ 
+
+ align:start position:0%
+is c left pointer for b is d
+right pointer for b is e and so on
+
+ align:start position:0%
+right pointer for b is e and so on
+ 
+
+ align:start position:0%
+right pointer for b is e and so on
+okay so in other words each of these
+
+ align:start position:0%
+okay so in other words each of these
+ 
+
+ align:start position:0%
+okay so in other words each of these
+lines is a bi-directional pointer
+
+ align:start position:0%
+lines is a bi-directional pointer
+ 
+
+ align:start position:0%
+lines is a bi-directional pointer
+uh in this direction it's the parent
+
+ align:start position:0%
+uh in this direction it's the parent
+ 
+
+ align:start position:0%
+uh in this direction it's the parent
+direction in this direction it's left in
+
+ align:start position:0%
+direction in this direction it's left in
+ 
+
+ align:start position:0%
+direction in this direction it's left in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+because it's bidirectional we don't draw
+
+ align:start position:0%
+because it's bidirectional we don't draw
+ 
+
+ align:start position:0%
+because it's bidirectional we don't draw
+the arrows we just draw
+
+ align:start position:0%
+the arrows we just draw
+ 
+
+ align:start position:0%
+the arrows we just draw
+undirected lines okay
+
+ align:start position:0%
+undirected lines okay
+ 
+
+ align:start position:0%
+undirected lines okay
+this is in general what a binary tree
+
+ align:start position:0%
+this is in general what a binary tree
+ 
+
+ align:start position:0%
+this is in general what a binary tree
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+a key invariant is that if you take a
+
+ align:start position:0%
+a key invariant is that if you take a
+ 
+
+ align:start position:0%
+a key invariant is that if you take a
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+and say go to its left pointer left
+
+ align:start position:0%
+and say go to its left pointer left
+ 
+
+ align:start position:0%
+and say go to its left pointer left
+child and then go to that node's parent
+
+ align:start position:0%
+child and then go to that node's parent
+ 
+
+ align:start position:0%
+child and then go to that node's parent
+this should be the same as node right so
+
+ align:start position:0%
+this should be the same as node right so
+ 
+
+ align:start position:0%
+this should be the same as node right so
+that's just saying these
+
+ align:start position:0%
+that's just saying these
+ 
+
+ align:start position:0%
+that's just saying these
+are in parent is always the inverse of a
+
+ align:start position:0%
+are in parent is always the inverse of a
+ 
+
+ align:start position:0%
+are in parent is always the inverse of a
+left or right operation
+
+ align:start position:0%
+left or right operation
+ 
+
+ align:start position:0%
+left or right operation
+this is also true for write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that's a binary tree now the
+
+ align:start position:0%
+okay and that's a binary tree now the
+ 
+
+ align:start position:0%
+okay and that's a binary tree now the
+intuition of what's going on here
+
+ align:start position:0%
+intuition of what's going on here
+ 
+
+ align:start position:0%
+intuition of what's going on here
+is you could you could say it's we're
+
+ align:start position:0%
+is you could you could say it's we're
+ 
+
+ align:start position:0%
+is you could you could say it's we're
+inspired by
+
+ align:start position:0%
+inspired by
+ 
+
+ align:start position:0%
+inspired by
+a linked list linked list had a very
+
+ align:start position:0%
+a linked list linked list had a very
+ 
+
+ align:start position:0%
+a linked list linked list had a very
+similar structure
+
+ align:start position:0%
+similar structure
+ 
+
+ align:start position:0%
+similar structure
+maybe an item or there's a node it had
+
+ align:start position:0%
+maybe an item or there's a node it had
+ 
+
+ align:start position:0%
+maybe an item or there's a node it had
+an item in it
+
+ align:start position:0%
+an item in it
+ 
+
+ align:start position:0%
+an item in it
+and it had a next pointer and it had a
+
+ align:start position:0%
+and it had a next pointer and it had a
+ 
+
+ align:start position:0%
+and it had a next pointer and it had a
+previous pointer
+
+ align:start position:0%
+previous pointer
+ 
+
+ align:start position:0%
+previous pointer
+so in some sense what we're if it's
+
+ align:start position:0%
+so in some sense what we're if it's
+ 
+
+ align:start position:0%
+so in some sense what we're if it's
+doubly linked we had a previous pointer
+
+ align:start position:0%
+doubly linked we had a previous pointer
+ 
+
+ align:start position:0%
+doubly linked we had a previous pointer
+it was singly linked we only had a next
+
+ align:start position:0%
+it was singly linked we only had a next
+ 
+
+ align:start position:0%
+it was singly linked we only had a next
+pointer
+
+ align:start position:0%
+pointer
+ 
+
+ align:start position:0%
+pointer
+and if you think about the limits of
+
+ align:start position:0%
+and if you think about the limits of
+ 
+
+ align:start position:0%
+and if you think about the limits of
+linked lists especially singly linked
+
+ align:start position:0%
+linked lists especially singly linked
+ 
+
+ align:start position:0%
+linked lists especially singly linked
+lists
+
+ align:start position:0%
+lists
+ 
+
+ align:start position:0%
+lists
+if you just have one pointer per node
+
+ align:start position:0%
+if you just have one pointer per node
+ 
+
+ align:start position:0%
+if you just have one pointer per node
+you can only build a list
+
+ align:start position:0%
+you can only build a list
+ 
+
+ align:start position:0%
+you can only build a list
+and so the result is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this this node is going to have
+
+ align:start position:0%
+you know this this node is going to have
+ 
+
+ align:start position:0%
+you know this this node is going to have
+depth linear depth means how many
+
+ align:start position:0%
+depth linear depth means how many
+ 
+
+ align:start position:0%
+depth linear depth means how many
+pointers do i have to follow to get here
+
+ align:start position:0%
+pointers do i have to follow to get here
+ 
+
+ align:start position:0%
+pointers do i have to follow to get here
+from the root of the structure which for
+
+ align:start position:0%
+from the root of the structure which for
+ 
+
+ align:start position:0%
+from the root of the structure which for
+linked lists was the head
+
+ align:start position:0%
+linked lists was the head
+ 
+
+ align:start position:0%
+linked lists was the head
+it was doubly linked okay i can have a
+
+ align:start position:0%
+it was doubly linked okay i can have a
+ 
+
+ align:start position:0%
+it was doubly linked okay i can have a
+head and a tail and i can put
+
+ align:start position:0%
+head and a tail and i can put
+ 
+
+ align:start position:0%
+head and a tail and i can put
+bi-directions
+
+ align:start position:0%
+bi-directions
+ 
+
+ align:start position:0%
+bi-directions
+on here but then still the middle item
+
+ align:start position:0%
+on here but then still the middle item
+ 
+
+ align:start position:0%
+on here but then still the middle item
+has depth linear so there's no way to
+
+ align:start position:0%
+has depth linear so there's no way to
+ 
+
+ align:start position:0%
+has depth linear so there's no way to
+get there
+
+ align:start position:0%
+get there
+ 
+
+ align:start position:0%
+get there
+in less than linear time with binary
+
+ align:start position:0%
+in less than linear time with binary
+ 
+
+ align:start position:0%
+in less than linear time with binary
+trees because we use
+
+ align:start position:0%
+trees because we use
+ 
+
+ align:start position:0%
+trees because we use
+two types of next pointers left and
+
+ align:start position:0%
+two types of next pointers left and
+ 
+
+ align:start position:0%
+two types of next pointers left and
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we can build a tree and we know trees in
+
+ align:start position:0%
+we can build a tree and we know trees in
+ 
+
+ align:start position:0%
+we can build a tree and we know trees in
+general have logarithmic
+
+ align:start position:0%
+general have logarithmic
+ 
+
+ align:start position:0%
+general have logarithmic
+can have logarithmic height
+
+ align:start position:0%
+can have logarithmic height
+ 
+
+ align:start position:0%
+can have logarithmic height
+and so it's possible in a tree to get to
+
+ align:start position:0%
+and so it's possible in a tree to get to
+ 
+
+ align:start position:0%
+and so it's possible in a tree to get to
+any node starting from the root in only
+
+ align:start position:0%
+any node starting from the root in only
+ 
+
+ align:start position:0%
+any node starting from the root in only
+log n traversals so that's the intuition
+
+ align:start position:0%
+log n traversals so that's the intuition
+ 
+
+ align:start position:0%
+log n traversals so that's the intuition
+of what's going on
+
+ align:start position:0%
+of what's going on
+ 
+
+ align:start position:0%
+of what's going on
+now today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to talk about the height of
+
+ align:start position:0%
+we're going to talk about the height of
+ 
+
+ align:start position:0%
+we're going to talk about the height of
+a tree
+
+ align:start position:0%
+a tree
+ 
+
+ align:start position:0%
+a tree
+so let me define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to need a couple definitions
+
+ align:start position:0%
+i'm going to need a couple definitions
+ 
+
+ align:start position:0%
+i'm going to need a couple definitions
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree and height
+
+ align:start position:0%
+subtree and height
+ 
+
+ align:start position:0%
+subtree and height
+of a node uh
+
+ align:start position:0%
+of a node uh
+ 
+
+ align:start position:0%
+of a node uh
+so a tree decomposes into sub trees
+
+ align:start position:0%
+so a tree decomposes into sub trees
+ 
+
+ align:start position:0%
+so a tree decomposes into sub trees
+so for example the subtree rooted at b
+
+ align:start position:0%
+so for example the subtree rooted at b
+ 
+
+ align:start position:0%
+so for example the subtree rooted at b
+or the subtree of b
+
+ align:start position:0%
+or the subtree of b
+ 
+
+ align:start position:0%
+or the subtree of b
+is this portion of the tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's that node and all of the
+
+ align:start position:0%
+so it's that node and all of the
+ 
+
+ align:start position:0%
+so it's that node and all of the
+descendants of this node so because we
+
+ align:start position:0%
+descendants of this node so because we
+ 
+
+ align:start position:0%
+descendants of this node so because we
+have parents and children
+
+ align:start position:0%
+have parents and children
+ 
+
+ align:start position:0%
+have parents and children
+we can generalize in the familial tree
+
+ align:start position:0%
+we can generalize in the familial tree
+ 
+
+ align:start position:0%
+we can generalize in the familial tree
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+we can talk about ancestors of a node so
+
+ align:start position:0%
+we can talk about ancestors of a node so
+ 
+
+ align:start position:0%
+we can talk about ancestors of a node so
+the ancestors of f
+
+ align:start position:0%
+the ancestors of f
+ 
+
+ align:start position:0%
+the ancestors of f
+are its parent its grandparents its
+
+ align:start position:0%
+are its parent its grandparents its
+ 
+
+ align:start position:0%
+are its parent its grandparents its
+great grandparents and so on
+
+ align:start position:0%
+great grandparents and so on
+ 
+
+ align:start position:0%
+great grandparents and so on
+together all of these are called
+
+ align:start position:0%
+together all of these are called
+ 
+
+ align:start position:0%
+together all of these are called
+ancestors
+
+ align:start position:0%
+ancestors
+ 
+
+ align:start position:0%
+ancestors
+it's a it doesn't quite correspond to
+
+ align:start position:0%
+it's a it doesn't quite correspond to
+ 
+
+ align:start position:0%
+it's a it doesn't quite correspond to
+familiar trees because familial trees
+
+ align:start position:0%
+familiar trees because familial trees
+ 
+
+ align:start position:0%
+familiar trees because familial trees
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+two parents here you only have a unique
+
+ align:start position:0%
+two parents here you only have a unique
+ 
+
+ align:start position:0%
+two parents here you only have a unique
+parent
+
+ align:start position:0%
+parent
+ 
+
+ align:start position:0%
+parent
+or the poor root has no parent
+
+ align:start position:0%
+or the poor root has no parent
+ 
+
+ align:start position:0%
+or the poor root has no parent
+we also talk about it's like mixed
+
+ align:start position:0%
+we also talk about it's like mixed
+ 
+
+ align:start position:0%
+we also talk about it's like mixed
+metaphors
+
+ align:start position:0%
+metaphors
+ 
+
+ align:start position:0%
+metaphors
+leaves of the tree
+
+ align:start position:0%
+leaves of the tree
+ 
+
+ align:start position:0%
+leaves of the tree
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people with no children parents will
+
+ align:start position:0%
+people with no children parents will
+ 
+
+ align:start position:0%
+people with no children parents will
+complain about this
+
+ align:start position:0%
+complain about this
+ 
+
+ align:start position:0%
+complain about this
+but many like many of us in this room we
+
+ align:start position:0%
+but many like many of us in this room we
+ 
+
+ align:start position:0%
+but many like many of us in this room we
+have no children yet so we were called
+
+ align:start position:0%
+have no children yet so we were called
+ 
+
+ align:start position:0%
+have no children yet so we were called
+leaves
+
+ align:start position:0%
+leaves
+ 
+
+ align:start position:0%
+leaves
+you can tell your parents hey i'm just a
+
+ align:start position:0%
+you can tell your parents hey i'm just a
+ 
+
+ align:start position:0%
+you can tell your parents hey i'm just a
+leaf you know blowing in the wind
+
+ align:start position:0%
+leaf you know blowing in the wind
+ 
+
+ align:start position:0%
+leaf you know blowing in the wind
+so uh you know like this it's so many
+
+ align:start position:0%
+so uh you know like this it's so many
+ 
+
+ align:start position:0%
+so uh you know like this it's so many
+mixed metaphors but we
+
+ align:start position:0%
+mixed metaphors but we
+ 
+
+ align:start position:0%
+mixed metaphors but we
+always draw trees downwards like the
+
+ align:start position:0%
+always draw trees downwards like the
+ 
+
+ align:start position:0%
+always draw trees downwards like the
+root structure of a tree
+
+ align:start position:0%
+root structure of a tree
+ 
+
+ align:start position:0%
+root structure of a tree
+yet we call the ends of the roots leaves
+
+ align:start position:0%
+yet we call the ends of the roots leaves
+ 
+
+ align:start position:0%
+yet we call the ends of the roots leaves
+which is upside down
+
+ align:start position:0%
+which is upside down
+ 
+
+ align:start position:0%
+which is upside down
+anyway that's trees for you lots of
+
+ align:start position:0%
+anyway that's trees for you lots of
+ 
+
+ align:start position:0%
+anyway that's trees for you lots of
+entertaining analogies okay but
+
+ align:start position:0%
+entertaining analogies okay but
+ 
+
+ align:start position:0%
+entertaining analogies okay but
+ancestors are useful descendants are
+
+ align:start position:0%
+ancestors are useful descendants are
+ 
+
+ align:start position:0%
+ancestors are useful descendants are
+also useful
+
+ align:start position:0%
+also useful
+ 
+
+ align:start position:0%
+also useful
+so the descendants of b are all of its
+
+ align:start position:0%
+so the descendants of b are all of its
+ 
+
+ align:start position:0%
+so the descendants of b are all of its
+children and all of its grandchildren
+
+ align:start position:0%
+children and all of its grandchildren
+ 
+
+ align:start position:0%
+children and all of its grandchildren
+and all the way down
+
+ align:start position:0%
+and all the way down
+ 
+
+ align:start position:0%
+and all the way down
+but just within the subtree so subtree
+
+ align:start position:0%
+but just within the subtree so subtree
+ 
+
+ align:start position:0%
+but just within the subtree so subtree
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+consists of x and its descendants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we think of x being the root
+
+ align:start position:0%
+and we think of x being the root
+ 
+
+ align:start position:0%
+and we think of x being the root
+of that subtree so we're kind of
+
+ align:start position:0%
+of that subtree so we're kind of
+ 
+
+ align:start position:0%
+of that subtree so we're kind of
+forgetting about everything outside of
+
+ align:start position:0%
+forgetting about everything outside of
+ 
+
+ align:start position:0%
+forgetting about everything outside of
+the sub tree
+
+ align:start position:0%
+the sub tree
+ 
+
+ align:start position:0%
+the sub tree
+when we talk about sub tree of x let's
+
+ align:start position:0%
+when we talk about sub tree of x let's
+ 
+
+ align:start position:0%
+when we talk about sub tree of x let's
+talk about the
+
+ align:start position:0%
+talk about the
+ 
+
+ align:start position:0%
+talk about the
+depth of a node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depth of the node is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess the number of its ancestors
+
+ align:start position:0%
+i guess the number of its ancestors
+ 
+
+ align:start position:0%
+i guess the number of its ancestors
+right um but way i usually think of it
+
+ align:start position:0%
+right um but way i usually think of it
+ 
+
+ align:start position:0%
+right um but way i usually think of it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the number of number of edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in the path from
+
+ align:start position:0%
+and in the path from
+ 
+
+ align:start position:0%
+and in the path from
+x up to the root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so every node has a unique path that
+
+ align:start position:0%
+so every node has a unique path that
+ 
+
+ align:start position:0%
+so every node has a unique path that
+goes upwards
+
+ align:start position:0%
+goes upwards
+ 
+
+ align:start position:0%
+goes upwards
+until it can't go up anymore so the
+
+ align:start position:0%
+until it can't go up anymore so the
+ 
+
+ align:start position:0%
+until it can't go up anymore so the
+depth of e
+
+ align:start position:0%
+depth of e
+ 
+
+ align:start position:0%
+depth of e
+is two because there are two edges uh
+
+ align:start position:0%
+is two because there are two edges uh
+ 
+
+ align:start position:0%
+is two because there are two edges uh
+one two in the path from the root a to e
+
+ align:start position:0%
+one two in the path from the root a to e
+ 
+
+ align:start position:0%
+one two in the path from the root a to e
+so maybe i'll write some depths uh depth
+
+ align:start position:0%
+so maybe i'll write some depths uh depth
+ 
+
+ align:start position:0%
+so maybe i'll write some depths uh depth
+of e is two
+
+ align:start position:0%
+of e is two
+ 
+
+ align:start position:0%
+of e is two
+depth of these guys is one depth of the
+
+ align:start position:0%
+depth of these guys is one depth of the
+ 
+
+ align:start position:0%
+depth of these guys is one depth of the
+root is zero
+
+ align:start position:0%
+root is zero
+ 
+
+ align:start position:0%
+root is zero
+two three so those are
+
+ align:start position:0%
+two three so those are
+ 
+
+ align:start position:0%
+two three so those are
+depth i'm going to
+
+ align:start position:0%
+depth i'm going to
+ 
+
+ align:start position:0%
+depth i'm going to
+clean this up a little bit
+
+ align:start position:0%
+clean this up a little bit
+ 
+
+ align:start position:0%
+clean this up a little bit
+so we can focus on the image all right
+
+ align:start position:0%
+so we can focus on the image all right
+ 
+
+ align:start position:0%
+so we can focus on the image all right
+height so depth is measuring
+
+ align:start position:0%
+height so depth is measuring
+ 
+
+ align:start position:0%
+height so depth is measuring
+downwards because we you know if you
+
+ align:start position:0%
+downwards because we you know if you
+ 
+
+ align:start position:0%
+downwards because we you know if you
+imagine depth within water
+
+ align:start position:0%
+imagine depth within water
+ 
+
+ align:start position:0%
+imagine depth within water
+this is uh the surface of the water and
+
+ align:start position:0%
+this is uh the surface of the water and
+ 
+
+ align:start position:0%
+this is uh the surface of the water and
+then we measure how deep you are from
+
+ align:start position:0%
+then we measure how deep you are from
+ 
+
+ align:start position:0%
+then we measure how deep you are from
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+height is in the reverse direction we're
+
+ align:start position:0%
+height is in the reverse direction we're
+ 
+
+ align:start position:0%
+height is in the reverse direction we're
+going to measure from the leaf level
+
+ align:start position:0%
+going to measure from the leaf level
+ 
+
+ align:start position:0%
+going to measure from the leaf level
+up because leaves are the bottom of the
+
+ align:start position:0%
+up because leaves are the bottom of the
+ 
+
+ align:start position:0%
+up because leaves are the bottom of the
+tree so height
+
+ align:start position:0%
+tree so height
+ 
+
+ align:start position:0%
+tree so height
+of a node is going to be
+
+ align:start position:0%
+of a node is going to be
+ 
+
+ align:start position:0%
+of a node is going to be
+the number of edges
+
+ align:start position:0%
+the number of edges
+ 
+
+ align:start position:0%
+the number of edges
+in the longest downward path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which is the same thing as the
+
+ align:start position:0%
+okay which is the same thing as the
+ 
+
+ align:start position:0%
+okay which is the same thing as the
+maximum depth of a node
+
+ align:start position:0%
+maximum depth of a node
+ 
+
+ align:start position:0%
+maximum depth of a node
+in x's subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do height in red
+
+ align:start position:0%
+let's do height in red
+ 
+
+ align:start position:0%
+let's do height in red
+so uh how long is the longest path from
+
+ align:start position:0%
+so uh how long is the longest path from
+ 
+
+ align:start position:0%
+so uh how long is the longest path from
+f to a leaf well f is a leaf so all
+
+ align:start position:0%
+f to a leaf well f is a leaf so all
+ 
+
+ align:start position:0%
+f to a leaf well f is a leaf so all
+leaves have
+
+ align:start position:0%
+leaves have
+ 
+
+ align:start position:0%
+leaves have
+depth zero sorry height zero
+
+ align:start position:0%
+depth zero sorry height zero
+ 
+
+ align:start position:0%
+depth zero sorry height zero
+get it backwards um
+
+ align:start position:0%
+get it backwards um
+ 
+
+ align:start position:0%
+get it backwards um
+d here it's so there are two
+
+ align:start position:0%
+d here it's so there are two
+ 
+
+ align:start position:0%
+d here it's so there are two
+ways to go down this doesn't go to a
+
+ align:start position:0%
+ways to go down this doesn't go to a
+ 
+
+ align:start position:0%
+ways to go down this doesn't go to a
+leaf uh this one goes to a leaf
+
+ align:start position:0%
+leaf uh this one goes to a leaf
+ 
+
+ align:start position:0%
+leaf uh this one goes to a leaf
+and its height is zero so this height is
+
+ align:start position:0%
+and its height is zero so this height is
+ 
+
+ align:start position:0%
+and its height is zero so this height is
+one there's one edge to a leaf here b
+
+ align:start position:0%
+one there's one edge to a leaf here b
+ 
+
+ align:start position:0%
+one there's one edge to a leaf here b
+has two leaves it can get to we take the
+
+ align:start position:0%
+has two leaves it can get to we take the
+ 
+
+ align:start position:0%
+has two leaves it can get to we take the
+longest one so that's length two
+
+ align:start position:0%
+longest one so that's length two
+ 
+
+ align:start position:0%
+longest one so that's length two
+a similarly has height three
+
+ align:start position:0%
+a similarly has height three
+ 
+
+ align:start position:0%
+a similarly has height three
+okay so height we measure upward depth
+
+ align:start position:0%
+okay so height we measure upward depth
+ 
+
+ align:start position:0%
+okay so height we measure upward depth
+we measure
+
+ align:start position:0%
+we measure
+ 
+
+ align:start position:0%
+we measure
+downward well one thing we care about uh
+
+ align:start position:0%
+downward well one thing we care about uh
+ 
+
+ align:start position:0%
+downward well one thing we care about uh
+is just the height
+
+ align:start position:0%
+is just the height
+ 
+
+ align:start position:0%
+is just the height
+of the overall tree uh which
+
+ align:start position:0%
+of the overall tree uh which
+ 
+
+ align:start position:0%
+of the overall tree uh which
+is the height of the root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to call that h because
+
+ align:start position:0%
+and i'm going to call that h because
+ 
+
+ align:start position:0%
+and i'm going to call that h because
+we're going to use it a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what we're going to achieve today is
+
+ align:start position:0%
+and what we're going to achieve today is
+ 
+
+ align:start position:0%
+and what we're going to achieve today is
+all of these running times instead of
+
+ align:start position:0%
+all of these running times instead of
+ 
+
+ align:start position:0%
+all of these running times instead of
+being log n
+
+ align:start position:0%
+being log n
+ 
+
+ align:start position:0%
+being log n
+they're going to be order h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so today our goal is to get all the
+
+ align:start position:0%
+so today our goal is to get all the
+ 
+
+ align:start position:0%
+so today our goal is to get all the
+operations we care about
+
+ align:start position:0%
+operations we care about
+ 
+
+ align:start position:0%
+operations we care about
+in order h type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then next lecture we're going to
+
+ align:start position:0%
+and then next lecture we're going to
+ 
+
+ align:start position:0%
+and then next lecture we're going to
+guarantee that h is always log n
+
+ align:start position:0%
+guarantee that h is always log n
+ 
+
+ align:start position:0%
+guarantee that h is always log n
+and then we'll get log n time so we need
+
+ align:start position:0%
+and then we'll get log n time so we need
+ 
+
+ align:start position:0%
+and then we'll get log n time so we need
+to do a bunch of work to achieve log n
+
+ align:start position:0%
+to do a bunch of work to achieve log n
+ 
+
+ align:start position:0%
+to do a bunch of work to achieve log n
+today we'll do the work that's all the
+
+ align:start position:0%
+today we'll do the work that's all the
+ 
+
+ align:start position:0%
+today we'll do the work that's all the
+tree manipulation
+
+ align:start position:0%
+tree manipulation
+ 
+
+ align:start position:0%
+tree manipulation
+and as long as your tree is nice and
+
+ align:start position:0%
+and as long as your tree is nice and
+ 
+
+ align:start position:0%
+and as long as your tree is nice and
+shallow it doesn't have high height
+
+ align:start position:0%
+shallow it doesn't have high height
+ 
+
+ align:start position:0%
+shallow it doesn't have high height
+if it has logarithmic height everything
+
+ align:start position:0%
+if it has logarithmic height everything
+ 
+
+ align:start position:0%
+if it has logarithmic height everything
+will be log n of course there are trees
+
+ align:start position:0%
+will be log n of course there are trees
+ 
+
+ align:start position:0%
+will be log n of course there are trees
+that are really bad
+
+ align:start position:0%
+that are really bad
+ 
+
+ align:start position:0%
+that are really bad
+right we can have a tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a tree like this which is basically a
+
+ align:start position:0%
+a tree like this which is basically a
+ 
+
+ align:start position:0%
+a tree like this which is basically a
+linked list
+
+ align:start position:0%
+linked list
+ 
+
+ align:start position:0%
+linked list
+where we only use right pointers and all
+
+ align:start position:0%
+where we only use right pointers and all
+ 
+
+ align:start position:0%
+where we only use right pointers and all
+the left pointers are none
+
+ align:start position:0%
+the left pointers are none
+ 
+
+ align:start position:0%
+the left pointers are none
+so there are height there are trees that
+
+ align:start position:0%
+so there are height there are trees that
+ 
+
+ align:start position:0%
+so there are height there are trees that
+are very high
+
+ align:start position:0%
+are very high
+ 
+
+ align:start position:0%
+are very high
+have high height um we want to avoid
+
+ align:start position:0%
+have high height um we want to avoid
+ 
+
+ align:start position:0%
+have high height um we want to avoid
+these but we won't worry about that till
+
+ align:start position:0%
+these but we won't worry about that till
+ 
+
+ align:start position:0%
+these but we won't worry about that till
+next lecture question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the height of node c height of
+
+ align:start position:0%
+what is the height of node c height of
+ 
+
+ align:start position:0%
+what is the height of node c height of
+node c is zero
+
+ align:start position:0%
+node c is zero
+ 
+
+ align:start position:0%
+node c is zero
+because the length of the longest path
+
+ align:start position:0%
+because the length of the longest path
+ 
+
+ align:start position:0%
+because the length of the longest path
+the number of edges in the longest
+
+ align:start position:0%
+the number of edges in the longest
+ 
+
+ align:start position:0%
+the number of edges in the longest
+downward path is zero yeah we're
+
+ align:start position:0%
+downward path is zero yeah we're
+ 
+
+ align:start position:0%
+downward path is zero yeah we're
+counting edges not vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah so the height of the tree is of
+
+ align:start position:0%
+uh yeah so the height of the tree is of
+ 
+
+ align:start position:0%
+uh yeah so the height of the tree is of
+course just the depth
+
+ align:start position:0%
+course just the depth
+ 
+
+ align:start position:0%
+course just the depth
+the maximum depth i think that's right
+
+ align:start position:0%
+the maximum depth i think that's right
+ 
+
+ align:start position:0%
+the maximum depth i think that's right
+so the height here is
+
+ align:start position:0%
+so the height here is
+ 
+
+ align:start position:0%
+so the height here is
+three and the maximum depth is this
+
+ align:start position:0%
+three and the maximum depth is this
+ 
+
+ align:start position:0%
+three and the maximum depth is this
+terribly drawn three
+
+ align:start position:0%
+terribly drawn three
+ 
+
+ align:start position:0%
+terribly drawn three
+so these happen to correspond in the
+
+ align:start position:0%
+so these happen to correspond in the
+ 
+
+ align:start position:0%
+so these happen to correspond in the
+maximum case
+
+ align:start position:0%
+maximum case
+ 
+
+ align:start position:0%
+maximum case
+but we use height to always mean maximum
+
+ align:start position:0%
+but we use height to always mean maximum
+ 
+
+ align:start position:0%
+but we use height to always mean maximum
+and so that's why
+
+ align:start position:0%
+and so that's why
+ 
+
+ align:start position:0%
+and so that's why
+we talk about the height of the tree
+
+ align:start position:0%
+we talk about the height of the tree
+ 
+
+ align:start position:0%
+we talk about the height of the tree
+depth of the tree is not defined
+
+ align:start position:0%
+depth of the tree is not defined
+ 
+
+ align:start position:0%
+depth of the tree is not defined
+just depths of notes okay
+
+ align:start position:0%
+just depths of notes okay
+ 
+
+ align:start position:0%
+just depths of notes okay
+um how do we use these trees to
+
+ align:start position:0%
+um how do we use these trees to
+ 
+
+ align:start position:0%
+um how do we use these trees to
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+either a sequence or a set uh
+
+ align:start position:0%
+either a sequence or a set uh
+ 
+
+ align:start position:0%
+either a sequence or a set uh
+i claim that there is a natural order
+
+ align:start position:0%
+i claim that there is a natural order
+ 
+
+ align:start position:0%
+i claim that there is a natural order
+in trees called the traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of nodes or items
+
+ align:start position:0%
+of nodes or items
+ 
+
+ align:start position:0%
+of nodes or items
+and the tree so i'm going to define a
+
+ align:start position:0%
+and the tree so i'm going to define a
+ 
+
+ align:start position:0%
+and the tree so i'm going to define a
+particular order
+
+ align:start position:0%
+particular order
+ 
+
+ align:start position:0%
+particular order
+uh say in this example
+
+ align:start position:0%
+uh say in this example
+ 
+
+ align:start position:0%
+uh say in this example
+let's do the example first the
+
+ align:start position:0%
+let's do the example first the
+ 
+
+ align:start position:0%
+let's do the example first the
+traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to be f
+
+ align:start position:0%
+is going to be f
+ 
+
+ align:start position:0%
+is going to be f
+d b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e a
+
+ align:start position:0%
+e a
+ 
+
+ align:start position:0%
+e a
+c i feel like i'm in music class this is
+
+ align:start position:0%
+c i feel like i'm in music class this is
+ 
+
+ align:start position:0%
+c i feel like i'm in music class this is
+my guitar or something but it's not i
+
+ align:start position:0%
+my guitar or something but it's not i
+ 
+
+ align:start position:0%
+my guitar or something but it's not i
+hope um
+
+ align:start position:0%
+hope um
+ 
+
+ align:start position:0%
+hope um
+if it is a coincidence so
+
+ align:start position:0%
+if it is a coincidence so
+ 
+
+ align:start position:0%
+if it is a coincidence so
+what is this order what i'd like to do
+
+ align:start position:0%
+what is this order what i'd like to do
+ 
+
+ align:start position:0%
+what is this order what i'd like to do
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+recursively define an order where the
+
+ align:start position:0%
+recursively define an order where the
+ 
+
+ align:start position:0%
+recursively define an order where the
+root of the tree is somewhere in the
+
+ align:start position:0%
+root of the tree is somewhere in the
+ 
+
+ align:start position:0%
+root of the tree is somewhere in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+and everything in the left subtree is
+
+ align:start position:0%
+and everything in the left subtree is
+ 
+
+ align:start position:0%
+and everything in the left subtree is
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+earlier in the order than the root and
+
+ align:start position:0%
+earlier in the order than the root and
+ 
+
+ align:start position:0%
+earlier in the order than the root and
+everything in the right subtree is later
+
+ align:start position:0%
+everything in the right subtree is later
+ 
+
+ align:start position:0%
+everything in the right subtree is later
+so you can see here c comes after a and
+
+ align:start position:0%
+so you can see here c comes after a and
+ 
+
+ align:start position:0%
+so you can see here c comes after a and
+then all the other nodes come before
+
+ align:start position:0%
+then all the other nodes come before
+ 
+
+ align:start position:0%
+then all the other nodes come before
+a and recursively if i look at a node b
+
+ align:start position:0%
+a and recursively if i look at a node b
+ 
+
+ align:start position:0%
+a and recursively if i look at a node b
+this node b which appears over here e is
+
+ align:start position:0%
+this node b which appears over here e is
+ 
+
+ align:start position:0%
+this node b which appears over here e is
+to the right of it
+
+ align:start position:0%
+to the right of it
+ 
+
+ align:start position:0%
+to the right of it
+but it's this is all to the left of a so
+
+ align:start position:0%
+but it's this is all to the left of a so
+ 
+
+ align:start position:0%
+but it's this is all to the left of a so
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+is between b and a would be on the left
+
+ align:start position:0%
+is between b and a would be on the left
+ 
+
+ align:start position:0%
+is between b and a would be on the left
+and then f and d are to the left of that
+
+ align:start position:0%
+and then f and d are to the left of that
+ 
+
+ align:start position:0%
+and then f and d are to the left of that
+and again f comes before d
+
+ align:start position:0%
+and again f comes before d
+ 
+
+ align:start position:0%
+and again f comes before d
+because f is in the left subtree of d
+
+ align:start position:0%
+because f is in the left subtree of d
+ 
+
+ align:start position:0%
+because f is in the left subtree of d
+okay so we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for every node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the nodes
+
+ align:start position:0%
+the nodes
+ 
+
+ align:start position:0%
+the nodes
+in x dot left are before x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the nodes in x dot right are come
+
+ align:start position:0%
+and the nodes in x dot right are come
+ 
+
+ align:start position:0%
+and the nodes in x dot right are come
+after x
+
+ align:start position:0%
+after x
+ 
+
+ align:start position:0%
+after x
+and this uniquely defines an order
+
+ align:start position:0%
+and this uniquely defines an order
+ 
+
+ align:start position:0%
+and this uniquely defines an order
+called a traversal order
+
+ align:start position:0%
+called a traversal order
+ 
+
+ align:start position:0%
+called a traversal order
+it's also called the in-order traversal
+
+ align:start position:0%
+it's also called the in-order traversal
+ 
+
+ align:start position:0%
+it's also called the in-order traversal
+order it's called in order because it's
+
+ align:start position:0%
+order it's called in order because it's
+ 
+
+ align:start position:0%
+order it's called in order because it's
+in the traversal order so it's very
+
+ align:start position:0%
+in the traversal order so it's very
+ 
+
+ align:start position:0%
+in the traversal order so it's very
+circular but
+
+ align:start position:0%
+circular but
+ 
+
+ align:start position:0%
+circular but
+you may have seen inorder traversal this
+
+ align:start position:0%
+you may have seen inorder traversal this
+ 
+
+ align:start position:0%
+you may have seen inorder traversal this
+is the same thing
+
+ align:start position:0%
+is the same thing
+ 
+
+ align:start position:0%
+is the same thing
+there's a very simple algorithm for
+
+ align:start position:0%
+there's a very simple algorithm for
+ 
+
+ align:start position:0%
+there's a very simple algorithm for
+computing this
+
+ align:start position:0%
+computing this
+ 
+
+ align:start position:0%
+computing this
+if i want to iterate
+
+ align:start position:0%
+if i want to iterate
+ 
+
+ align:start position:0%
+if i want to iterate
+uh let's call this yeah if i want to
+
+ align:start position:0%
+uh let's call this yeah if i want to
+ 
+
+ align:start position:0%
+uh let's call this yeah if i want to
+iterate
+
+ align:start position:0%
+iterate
+ 
+
+ align:start position:0%
+iterate
+all the nodes within a subtree x rooted
+
+ align:start position:0%
+all the nodes within a subtree x rooted
+ 
+
+ align:start position:0%
+all the nodes within a subtree x rooted
+by x
+
+ align:start position:0%
+by x
+ 
+
+ align:start position:0%
+by x
+i just iterate on all of the
+
+ align:start position:0%
+i just iterate on all of the
+ 
+
+ align:start position:0%
+i just iterate on all of the
+nodes in the left subtree then i output
+
+ align:start position:0%
+nodes in the left subtree then i output
+ 
+
+ align:start position:0%
+nodes in the left subtree then i output
+x itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then i iterate on all the nodes in the
+
+ align:start position:0%
+then i iterate on all the nodes in the
+ 
+
+ align:start position:0%
+then i iterate on all the nodes in the
+right subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you may have seen that algorithm
+
+ align:start position:0%
+okay you may have seen that algorithm
+ 
+
+ align:start position:0%
+okay you may have seen that algorithm
+before this is just another way to
+
+ align:start position:0%
+before this is just another way to
+ 
+
+ align:start position:0%
+before this is just another way to
+codify the same thing
+
+ align:start position:0%
+codify the same thing
+ 
+
+ align:start position:0%
+codify the same thing
+the result is all the nodes within a
+
+ align:start position:0%
+the result is all the nodes within a
+ 
+
+ align:start position:0%
+the result is all the nodes within a
+subtree appear continuously with no
+
+ align:start position:0%
+subtree appear continuously with no
+ 
+
+ align:start position:0%
+subtree appear continuously with no
+interruptions
+
+ align:start position:0%
+interruptions
+ 
+
+ align:start position:0%
+interruptions
+and then the parent parent's going to
+
+ align:start position:0%
+and then the parent parent's going to
+ 
+
+ align:start position:0%
+and then the parent parent's going to
+come before after depending on whether
+
+ align:start position:0%
+come before after depending on whether
+ 
+
+ align:start position:0%
+come before after depending on whether
+it's the left or right child
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so and now it's just a matter of
+
+ align:start position:0%
+okay so and now it's just a matter of
+ 
+
+ align:start position:0%
+okay so and now it's just a matter of
+connecting the dots because we're
+
+ align:start position:0%
+connecting the dots because we're
+ 
+
+ align:start position:0%
+connecting the dots because we're
+representing an order
+
+ align:start position:0%
+representing an order
+ 
+
+ align:start position:0%
+representing an order
+and for sequence that is going to be the
+
+ align:start position:0%
+and for sequence that is going to be the
+ 
+
+ align:start position:0%
+and for sequence that is going to be the
+sequence order if we want to store n
+
+ align:start position:0%
+sequence order if we want to store n
+ 
+
+ align:start position:0%
+sequence order if we want to store n
+items x0 through x1
+
+ align:start position:0%
+items x0 through x1
+ 
+
+ align:start position:0%
+items x0 through x1
+we're going to build some kind of tree
+
+ align:start position:0%
+we're going to build some kind of tree
+ 
+
+ align:start position:0%
+we're going to build some kind of tree
+we're going to put x0 here
+
+ align:start position:0%
+we're going to put x0 here
+ 
+
+ align:start position:0%
+we're going to put x0 here
+x1 here x2 here x3 here x4 here x5
+
+ align:start position:0%
+x1 here x2 here x3 here x4 here x5
+ 
+
+ align:start position:0%
+x1 here x2 here x3 here x4 here x5
+here you can see i'm very used to
+
+ align:start position:0%
+here you can see i'm very used to
+ 
+
+ align:start position:0%
+here you can see i'm very used to
+dealing with traversal orders it takes a
+
+ align:start position:0%
+dealing with traversal orders it takes a
+ 
+
+ align:start position:0%
+dealing with traversal orders it takes a
+little while
+
+ align:start position:0%
+little while
+ 
+
+ align:start position:0%
+little while
+uh you could also see it here we're
+
+ align:start position:0%
+uh you could also see it here we're
+ 
+
+ align:start position:0%
+uh you could also see it here we're
+going to put x1 on this node x2
+
+ align:start position:0%
+going to put x1 on this node x2
+ 
+
+ align:start position:0%
+going to put x1 on this node x2
+sorry x0 here x1 here x2 here and so on
+
+ align:start position:0%
+sorry x0 here x1 here x2 here and so on
+ 
+
+ align:start position:0%
+sorry x0 here x1 here x2 here and so on
+that's the same order that i gave
+
+ align:start position:0%
+that's the same order that i gave
+ 
+
+ align:start position:0%
+that's the same order that i gave
+okay that's for sequences for sets that
+
+ align:start position:0%
+okay that's for sequences for sets that
+ 
+
+ align:start position:0%
+okay that's for sequences for sets that
+order is just going to be the sorted
+
+ align:start position:0%
+order is just going to be the sorted
+ 
+
+ align:start position:0%
+order is just going to be the sorted
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+and we're going to be effectively
+
+ align:start position:0%
+and we're going to be effectively
+ 
+
+ align:start position:0%
+and we're going to be effectively
+representing the sorted order of keys
+
+ align:start position:0%
+representing the sorted order of keys
+ 
+
+ align:start position:0%
+representing the sorted order of keys
+say increasing but before we get to that
+
+ align:start position:0%
+say increasing but before we get to that
+ 
+
+ align:start position:0%
+say increasing but before we get to that
+let's talk about different operations we
+
+ align:start position:0%
+let's talk about different operations we
+ 
+
+ align:start position:0%
+let's talk about different operations we
+can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just playing around with traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we're going to use these to
+
+ align:start position:0%
+and then we're going to use these to
+ 
+
+ align:start position:0%
+and then we're going to use these to
+build the sequence and set operations
+
+ align:start position:0%
+build the sequence and set operations
+ 
+
+ align:start position:0%
+build the sequence and set operations
+that we care about
+
+ align:start position:0%
+that we care about
+ 
+
+ align:start position:0%
+that we care about
+so first operation i'll call
+
+ align:start position:0%
+so first operation i'll call
+ 
+
+ align:start position:0%
+so first operation i'll call
+subtree first seems appropriate that
+
+ align:start position:0%
+subtree first seems appropriate that
+ 
+
+ align:start position:0%
+subtree first seems appropriate that
+it's called first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the first one so given a node
+
+ align:start position:0%
+it's the first one so given a node
+ 
+
+ align:start position:0%
+it's the first one so given a node
+which i'll call node uh this defines
+
+ align:start position:0%
+which i'll call node uh this defines
+ 
+
+ align:start position:0%
+which i'll call node uh this defines
+a subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which usually we draw subtrees as
+
+ align:start position:0%
+which usually we draw subtrees as
+ 
+
+ align:start position:0%
+which usually we draw subtrees as
+triangles hanging off of the node
+
+ align:start position:0%
+triangles hanging off of the node
+ 
+
+ align:start position:0%
+triangles hanging off of the node
+so here i would write x
+
+ align:start position:0%
+so here i would write x
+ 
+
+ align:start position:0%
+so here i would write x
+and then there's some subtree of all the
+
+ align:start position:0%
+and then there's some subtree of all the
+ 
+
+ align:start position:0%
+and then there's some subtree of all the
+descendants of x
+
+ align:start position:0%
+descendants of x
+ 
+
+ align:start position:0%
+descendants of x
+so with subtree first i would like to
+
+ align:start position:0%
+so with subtree first i would like to
+ 
+
+ align:start position:0%
+so with subtree first i would like to
+say among
+
+ align:start position:0%
+say among
+ 
+
+ align:start position:0%
+say among
+all the nodes in this subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which comes first in traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just restricting to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that subtree so tree of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so where is it in this tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh note is actually part of many sub
+
+ align:start position:0%
+uh note is actually part of many sub
+ 
+
+ align:start position:0%
+uh note is actually part of many sub
+trees good question uh
+
+ align:start position:0%
+trees good question uh
+ 
+
+ align:start position:0%
+trees good question uh
+f f is in its own in the sub tree of f
+
+ align:start position:0%
+f f is in its own in the sub tree of f
+ 
+
+ align:start position:0%
+f f is in its own in the sub tree of f
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+f is also in the subtree of d f is in
+
+ align:start position:0%
+f is also in the subtree of d f is in
+ 
+
+ align:start position:0%
+f is also in the subtree of d f is in
+the sub tree of b like i drew
+
+ align:start position:0%
+the sub tree of b like i drew
+ 
+
+ align:start position:0%
+the sub tree of b like i drew
+f is in the subtree of a it's in the
+
+ align:start position:0%
+f is in the subtree of a it's in the
+ 
+
+ align:start position:0%
+f is in the subtree of a it's in the
+subtree of exactly its ancestors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in this operation when we define
+
+ align:start position:0%
+but in this operation when we define
+ 
+
+ align:start position:0%
+but in this operation when we define
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+our node only defines one sub-tree it is
+
+ align:start position:0%
+our node only defines one sub-tree it is
+ 
+
+ align:start position:0%
+our node only defines one sub-tree it is
+the root of only one sub-tree
+
+ align:start position:0%
+the root of only one sub-tree
+ 
+
+ align:start position:0%
+the root of only one sub-tree
+and that's the sub-tree we're talking
+
+ align:start position:0%
+and that's the sub-tree we're talking
+ 
+
+ align:start position:0%
+and that's the sub-tree we're talking
+about and then i want to know among all
+
+ align:start position:0%
+about and then i want to know among all
+ 
+
+ align:start position:0%
+about and then i want to know among all
+those nodes which includes node itself
+
+ align:start position:0%
+those nodes which includes node itself
+ 
+
+ align:start position:0%
+those nodes which includes node itself
+and other things uh which one comes
+
+ align:start position:0%
+and other things uh which one comes
+ 
+
+ align:start position:0%
+and other things uh which one comes
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+in this traversal order this is like
+
+ align:start position:0%
+in this traversal order this is like
+ 
+
+ align:start position:0%
+in this traversal order this is like
+practice with traversal orders
+
+ align:start position:0%
+practice with traversal orders
+ 
+
+ align:start position:0%
+practice with traversal orders
+so where should i look for this node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the leftmost leaf
+
+ align:start position:0%
+yeah the leftmost leaf
+ 
+
+ align:start position:0%
+yeah the leftmost leaf
+in the picture it's here but pictures
+
+ align:start position:0%
+in the picture it's here but pictures
+ 
+
+ align:start position:0%
+in the picture it's here but pictures
+can be deceiving
+
+ align:start position:0%
+can be deceiving
+ 
+
+ align:start position:0%
+can be deceiving
+we just want to go left
+
+ align:start position:0%
+we just want to go left
+ 
+
+ align:start position:0%
+we just want to go left
+as much as possible when i say go left i
+
+ align:start position:0%
+as much as possible when i say go left i
+ 
+
+ align:start position:0%
+as much as possible when i say go left i
+mean this iteration node equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node.left you just look at our
+
+ align:start position:0%
+node.left you just look at our
+ 
+
+ align:start position:0%
+node.left you just look at our
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+all the nodes on the left come before x
+
+ align:start position:0%
+all the nodes on the left come before x
+ 
+
+ align:start position:0%
+all the nodes on the left come before x
+and all the nodes in the right so
+
+ align:start position:0%
+and all the nodes in the right so
+ 
+
+ align:start position:0%
+and all the nodes in the right so
+it's got to be in the left subtree if
+
+ align:start position:0%
+it's got to be in the left subtree if
+ 
+
+ align:start position:0%
+it's got to be in the left subtree if
+there is one uh
+
+ align:start position:0%
+there is one uh
+ 
+
+ align:start position:0%
+there is one uh
+of course we can't do this forever so
+
+ align:start position:0%
+of course we can't do this forever so
+ 
+
+ align:start position:0%
+of course we can't do this forever so
+say until we would fall off the tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means uh node is none
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we stopped uh before that would
+
+ align:start position:0%
+okay but we stopped uh before that would
+ 
+
+ align:start position:0%
+okay but we stopped uh before that would
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+so this is like uh the directions like
+
+ align:start position:0%
+so this is like uh the directions like
+ 
+
+ align:start position:0%
+so this is like uh the directions like
+oh you keep driving until you see the
+
+ align:start position:0%
+oh you keep driving until you see the
+ 
+
+ align:start position:0%
+oh you keep driving until you see the
+store
+
+ align:start position:0%
+store
+ 
+
+ align:start position:0%
+store
+and it's the block right before that
+
+ align:start position:0%
+and it's the block right before that
+ 
+
+ align:start position:0%
+and it's the block right before that
+it's like well that's not very helpful
+
+ align:start position:0%
+it's like well that's not very helpful
+ 
+
+ align:start position:0%
+it's like well that's not very helpful
+so uh you keep iterating node equals no
+
+ align:start position:0%
+so uh you keep iterating node equals no
+ 
+
+ align:start position:0%
+so uh you keep iterating node equals no
+dot left until node becomes
+
+ align:start position:0%
+dot left until node becomes
+ 
+
+ align:start position:0%
+dot left until node becomes
+none and then you undo one step okay you
+
+ align:start position:0%
+none and then you undo one step okay you
+ 
+
+ align:start position:0%
+none and then you undo one step okay you
+all know how to program that it's not
+
+ align:start position:0%
+all know how to program that it's not
+ 
+
+ align:start position:0%
+all know how to program that it's not
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+um so that last non-none
+
+ align:start position:0%
+um so that last non-none
+ 
+
+ align:start position:0%
+um so that last non-none
+node which might actually be the root it
+
+ align:start position:0%
+node which might actually be the root it
+ 
+
+ align:start position:0%
+node which might actually be the root it
+might be node
+
+ align:start position:0%
+might be node
+ 
+
+ align:start position:0%
+might be node
+maybe it has no left children but in
+
+ align:start position:0%
+maybe it has no left children but in
+ 
+
+ align:start position:0%
+maybe it has no left children but in
+that case i claim node is the very first
+
+ align:start position:0%
+that case i claim node is the very first
+ 
+
+ align:start position:0%
+that case i claim node is the very first
+in its in its subtree traversal order
+
+ align:start position:0%
+in its in its subtree traversal order
+ 
+
+ align:start position:0%
+in its in its subtree traversal order
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if there are no nodes in the left that
+
+ align:start position:0%
+if there are no nodes in the left that
+ 
+
+ align:start position:0%
+if there are no nodes in the left that
+come before x then x is actually first
+
+ align:start position:0%
+come before x then x is actually first
+ 
+
+ align:start position:0%
+come before x then x is actually first
+okay and that so that's it uh return
+
+ align:start position:0%
+okay and that so that's it uh return
+ 
+
+ align:start position:0%
+okay and that so that's it uh return
+node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm modifying node in place here and
+
+ align:start position:0%
+so i'm modifying node in place here and
+ 
+
+ align:start position:0%
+so i'm modifying node in place here and
+the very last one before i hit none
+
+ align:start position:0%
+the very last one before i hit none
+ 
+
+ align:start position:0%
+the very last one before i hit none
+that's the minimum
+
+ align:start position:0%
+that's the minimum
+ 
+
+ align:start position:0%
+that's the minimum
+that's the first item in the traversal
+
+ align:start position:0%
+that's the first item in the traversal
+ 
+
+ align:start position:0%
+that's the first item in the traversal
+order similarly you can define subtree
+
+ align:start position:0%
+order similarly you can define subtree
+ 
+
+ align:start position:0%
+order similarly you can define subtree
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+okay let's do a more interesting one
+
+ align:start position:0%
+okay let's do a more interesting one
+ 
+
+ align:start position:0%
+okay let's do a more interesting one
+successor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node so in this case i want to know what
+
+ align:start position:0%
+node so in this case i want to know what
+ 
+
+ align:start position:0%
+node so in this case i want to know what
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after node in the
+
+ align:start position:0%
+after node in the
+ 
+
+ align:start position:0%
+after node in the
+overall tree's traversal order okay here
+
+ align:start position:0%
+overall tree's traversal order okay here
+ 
+
+ align:start position:0%
+overall tree's traversal order okay here
+i was restricting to
+
+ align:start position:0%
+i was restricting to
+ 
+
+ align:start position:0%
+i was restricting to
+uh a single sub tree now i'm thinking
+
+ align:start position:0%
+uh a single sub tree now i'm thinking
+ 
+
+ align:start position:0%
+uh a single sub tree now i'm thinking
+about the entire tree in the entire
+
+ align:start position:0%
+about the entire tree in the entire
+ 
+
+ align:start position:0%
+about the entire tree in the entire
+traversal order
+
+ align:start position:0%
+traversal order
+ 
+
+ align:start position:0%
+traversal order
+and given a node i want to know which
+
+ align:start position:0%
+and given a node i want to know which
+ 
+
+ align:start position:0%
+and given a node i want to know which
+one comes next
+
+ align:start position:0%
+one comes next
+ 
+
+ align:start position:0%
+one comes next
+call this the successor i feel like i
+
+ align:start position:0%
+call this the successor i feel like i
+ 
+
+ align:start position:0%
+call this the successor i feel like i
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+make some kind of royal family joke now
+
+ align:start position:0%
+make some kind of royal family joke now
+ 
+
+ align:start position:0%
+make some kind of royal family joke now
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i don't know how um so
+
+ align:start position:0%
+i don't know how um so
+ 
+
+ align:start position:0%
+i don't know how um so
+every node has a unique successor let's
+
+ align:start position:0%
+every node has a unique successor let's
+ 
+
+ align:start position:0%
+every node has a unique successor let's
+do let's do some examples
+
+ align:start position:0%
+do let's do some examples
+ 
+
+ align:start position:0%
+do let's do some examples
+so we can start with f the successor of
+
+ align:start position:0%
+so we can start with f the successor of
+ 
+
+ align:start position:0%
+so we can start with f the successor of
+f if we just index into this
+
+ align:start position:0%
+f if we just index into this
+ 
+
+ align:start position:0%
+f if we just index into this
+list the successor is d okay
+
+ align:start position:0%
+list the successor is d okay
+ 
+
+ align:start position:0%
+list the successor is d okay
+successor of d is b successor b is ease
+
+ align:start position:0%
+successor of d is b successor b is ease
+ 
+
+ align:start position:0%
+successor of d is b successor b is ease
+okay it's very easy to read successors
+
+ align:start position:0%
+okay it's very easy to read successors
+ 
+
+ align:start position:0%
+okay it's very easy to read successors
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+when i have the traversal order written
+
+ align:start position:0%
+when i have the traversal order written
+ 
+
+ align:start position:0%
+when i have the traversal order written
+down but let's think about how to do it
+
+ align:start position:0%
+down but let's think about how to do it
+ 
+
+ align:start position:0%
+down but let's think about how to do it
+in the tree
+
+ align:start position:0%
+in the tree
+ 
+
+ align:start position:0%
+in the tree
+okay uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see there are going to be two
+
+ align:start position:0%
+let's see there are going to be two
+ 
+
+ align:start position:0%
+let's see there are going to be two
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+if i look at the successor of a it has a
+
+ align:start position:0%
+if i look at the successor of a it has a
+ 
+
+ align:start position:0%
+if i look at the successor of a it has a
+right child
+
+ align:start position:0%
+right child
+ 
+
+ align:start position:0%
+right child
+and in this case the right child of a is
+
+ align:start position:0%
+and in this case the right child of a is
+ 
+
+ align:start position:0%
+and in this case the right child of a is
+the successor but that's not always the
+
+ align:start position:0%
+the successor but that's not always the
+ 
+
+ align:start position:0%
+the successor but that's not always the
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+i don't have a good example but if i had
+
+ align:start position:0%
+i don't have a good example but if i had
+ 
+
+ align:start position:0%
+i don't have a good example but if i had
+another node here let's call it
+
+ align:start position:0%
+another node here let's call it
+ 
+
+ align:start position:0%
+another node here let's call it
+g uh the successor of a
+
+ align:start position:0%
+g uh the successor of a
+ 
+
+ align:start position:0%
+g uh the successor of a
+is actually g right because
+
+ align:start position:0%
+is actually g right because
+ 
+
+ align:start position:0%
+is actually g right because
+all of these items come after a in the
+
+ align:start position:0%
+all of these items come after a in the
+ 
+
+ align:start position:0%
+all of these items come after a in the
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+but which one comes first the leftmost
+
+ align:start position:0%
+but which one comes first the leftmost
+ 
+
+ align:start position:0%
+but which one comes first the leftmost
+leaf
+
+ align:start position:0%
+leaf
+ 
+
+ align:start position:0%
+leaf
+okay that's the problem we just solved
+
+ align:start position:0%
+okay that's the problem we just solved
+ 
+
+ align:start position:0%
+okay that's the problem we just solved
+so if a has a right child
+
+ align:start position:0%
+so if a has a right child
+ 
+
+ align:start position:0%
+so if a has a right child
+what we want is the leftmost leaf the
+
+ align:start position:0%
+what we want is the leftmost leaf the
+ 
+
+ align:start position:0%
+what we want is the leftmost leaf the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+thing in that subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the right subtree right child sub tree
+
+ align:start position:0%
+the right subtree right child sub tree
+ 
+
+ align:start position:0%
+the right subtree right child sub tree
+so this is case one
+
+ align:start position:0%
+so this is case one
+ 
+
+ align:start position:0%
+so this is case one
+if uh node.right
+
+ align:start position:0%
+if uh node.right
+ 
+
+ align:start position:0%
+if uh node.right
+so if we have a right child then
+
+ align:start position:0%
+so if we have a right child then
+ 
+
+ align:start position:0%
+so if we have a right child then
+what we want is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the right child
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great we can reduce to this other
+
+ align:start position:0%
+great we can reduce to this other
+ 
+
+ align:start position:0%
+great we can reduce to this other
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+but what if the node doesn't have a
+
+ align:start position:0%
+but what if the node doesn't have a
+ 
+
+ align:start position:0%
+but what if the node doesn't have a
+right child
+
+ align:start position:0%
+right child
+ 
+
+ align:start position:0%
+right child
+so for example it could be a leaf say
+
+ align:start position:0%
+so for example it could be a leaf say
+ 
+
+ align:start position:0%
+so for example it could be a leaf say
+we're taking
+
+ align:start position:0%
+we're taking
+ 
+
+ align:start position:0%
+we're taking
+the successor of i mean it doesn't have
+
+ align:start position:0%
+the successor of i mean it doesn't have
+ 
+
+ align:start position:0%
+the successor of i mean it doesn't have
+to be a leaf could be f which has no
+
+ align:start position:0%
+to be a leaf could be f which has no
+ 
+
+ align:start position:0%
+to be a leaf could be f which has no
+children it could be d which has one
+
+ align:start position:0%
+children it could be d which has one
+ 
+
+ align:start position:0%
+children it could be d which has one
+child but no right child
+
+ align:start position:0%
+child but no right child
+ 
+
+ align:start position:0%
+child but no right child
+so what's the successor of f well it's d
+
+ align:start position:0%
+so what's the successor of f well it's d
+ 
+
+ align:start position:0%
+so what's the successor of f well it's d
+which in this case is the parent but
+
+ align:start position:0%
+which in this case is the parent but
+ 
+
+ align:start position:0%
+which in this case is the parent but
+it's not always for example if we do
+
+ align:start position:0%
+it's not always for example if we do
+ 
+
+ align:start position:0%
+it's not always for example if we do
+successor of e
+
+ align:start position:0%
+successor of e
+ 
+
+ align:start position:0%
+successor of e
+its parent is actually earlier in the
+
+ align:start position:0%
+its parent is actually earlier in the
+ 
+
+ align:start position:0%
+its parent is actually earlier in the
+order because e was a right child
+
+ align:start position:0%
+order because e was a right child
+ 
+
+ align:start position:0%
+order because e was a right child
+here f was a left child and so its
+
+ align:start position:0%
+here f was a left child and so its
+ 
+
+ align:start position:0%
+here f was a left child and so its
+parent
+
+ align:start position:0%
+parent
+ 
+
+ align:start position:0%
+parent
+was after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+successor of d happens to be b because
+
+ align:start position:0%
+successor of d happens to be b because
+ 
+
+ align:start position:0%
+successor of d happens to be b because
+uh it's per it was the left child of its
+
+ align:start position:0%
+uh it's per it was the left child of its
+ 
+
+ align:start position:0%
+uh it's per it was the left child of its
+parent
+
+ align:start position:0%
+parent
+ 
+
+ align:start position:0%
+parent
+okay so that seems like the easy case if
+
+ align:start position:0%
+okay so that seems like the easy case if
+ 
+
+ align:start position:0%
+okay so that seems like the easy case if
+we're the left child of our parent
+
+ align:start position:0%
+we're the left child of our parent
+ 
+
+ align:start position:0%
+we're the left child of our parent
+then our successor is our parent okay
+
+ align:start position:0%
+then our successor is our parent okay
+ 
+
+ align:start position:0%
+then our successor is our parent okay
+basing on this small example but we can
+
+ align:start position:0%
+basing on this small example but we can
+ 
+
+ align:start position:0%
+basing on this small example but we can
+argue it generally in a moment
+
+ align:start position:0%
+argue it generally in a moment
+ 
+
+ align:start position:0%
+argue it generally in a moment
+what's the successor of e uh well it's
+
+ align:start position:0%
+what's the successor of e uh well it's
+ 
+
+ align:start position:0%
+what's the successor of e uh well it's
+not b because that comes earlier in fact
+
+ align:start position:0%
+not b because that comes earlier in fact
+ 
+
+ align:start position:0%
+not b because that comes earlier in fact
+all the things in this in b sub tree
+
+ align:start position:0%
+all the things in this in b sub tree
+ 
+
+ align:start position:0%
+all the things in this in b sub tree
+come earlier or equal to
+
+ align:start position:0%
+come earlier or equal to
+ 
+
+ align:start position:0%
+come earlier or equal to
+e um so we have to keep going up
+
+ align:start position:0%
+e um so we have to keep going up
+ 
+
+ align:start position:0%
+e um so we have to keep going up
+and then it turns out the successor of e
+
+ align:start position:0%
+and then it turns out the successor of e
+ 
+
+ align:start position:0%
+and then it turns out the successor of e
+is a because this subtree
+
+ align:start position:0%
+is a because this subtree
+ 
+
+ align:start position:0%
+is a because this subtree
+was the left child of a because b was a
+
+ align:start position:0%
+was the left child of a because b was a
+ 
+
+ align:start position:0%
+was the left child of a because b was a
+left child with a
+
+ align:start position:0%
+left child with a
+ 
+
+ align:start position:0%
+left child with a
+so the general strategy is walk up the
+
+ align:start position:0%
+so the general strategy is walk up the
+ 
+
+ align:start position:0%
+so the general strategy is walk up the
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+until we are we we go
+
+ align:start position:0%
+until we are we we go
+ 
+
+ align:start position:0%
+until we are we we go
+up a traversal whose reverse direction
+
+ align:start position:0%
+up a traversal whose reverse direction
+ 
+
+ align:start position:0%
+up a traversal whose reverse direction
+would be left
+
+ align:start position:0%
+would be left
+ 
+
+ align:start position:0%
+would be left
+okay so um walk
+
+ align:start position:0%
+okay so um walk
+ 
+
+ align:start position:0%
+okay so um walk
+up the tree when i say walk up i mean
+
+ align:start position:0%
+up the tree when i say walk up i mean
+ 
+
+ align:start position:0%
+up the tree when i say walk up i mean
+node equals node.parent
+
+ align:start position:0%
+node equals node.parent
+ 
+
+ align:start position:0%
+node equals node.parent
+iteration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+until
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we go up a left
+
+ align:start position:0%
+we go up a left
+ 
+
+ align:start position:0%
+we go up a left
+branch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this would mean that node before we
+
+ align:start position:0%
+so this would mean that node before we
+ 
+
+ align:start position:0%
+so this would mean that node before we
+do the change
+
+ align:start position:0%
+do the change
+ 
+
+ align:start position:0%
+do the change
+node equals node.parent node.parent.left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can check that and then after
+
+ align:start position:0%
+okay so we can check that and then after
+ 
+
+ align:start position:0%
+okay so we can check that and then after
+we do that traversal that parent
+
+ align:start position:0%
+we do that traversal that parent
+ 
+
+ align:start position:0%
+we do that traversal that parent
+is exactly the node we're looking for
+
+ align:start position:0%
+is exactly the node we're looking for
+ 
+
+ align:start position:0%
+is exactly the node we're looking for
+okay why is this true in general let me
+
+ align:start position:0%
+okay why is this true in general let me
+ 
+
+ align:start position:0%
+okay why is this true in general let me
+draw a more generic picture
+
+ align:start position:0%
+draw a more generic picture
+ 
+
+ align:start position:0%
+draw a more generic picture
+so we're starting at some node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say its parent is to the right
+
+ align:start position:0%
+and let's say its parent is to the right
+ 
+
+ align:start position:0%
+and let's say its parent is to the right
+so it comes later in the order
+
+ align:start position:0%
+so it comes later in the order
+ 
+
+ align:start position:0%
+so it comes later in the order
+for a while sorry get this backwards
+
+ align:start position:0%
+for a while sorry get this backwards
+ 
+
+ align:start position:0%
+for a while sorry get this backwards
+we're doing successor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it goes to left for a while
+
+ align:start position:0%
+so it goes to left for a while
+ 
+
+ align:start position:0%
+so it goes to left for a while
+so these are all these nodes will come
+
+ align:start position:0%
+so these are all these nodes will come
+ 
+
+ align:start position:0%
+so these are all these nodes will come
+earlier in the order because by the
+
+ align:start position:0%
+earlier in the order because by the
+ 
+
+ align:start position:0%
+earlier in the order because by the
+definition everything in the right
+
+ align:start position:0%
+definition everything in the right
+ 
+
+ align:start position:0%
+definition everything in the right
+subtree comes after
+
+ align:start position:0%
+subtree comes after
+ 
+
+ align:start position:0%
+subtree comes after
+and at some point we have a parent
+
+ align:start position:0%
+and at some point we have a parent
+ 
+
+ align:start position:0%
+and at some point we have a parent
+that's to the right meaning this node
+
+ align:start position:0%
+that's to the right meaning this node
+ 
+
+ align:start position:0%
+that's to the right meaning this node
+was the left
+
+ align:start position:0%
+was the left
+ 
+
+ align:start position:0%
+was the left
+child of this parent and that node by
+
+ align:start position:0%
+child of this parent and that node by
+ 
+
+ align:start position:0%
+child of this parent and that node by
+definition will come
+
+ align:start position:0%
+definition will come
+ 
+
+ align:start position:0%
+definition will come
+after all of the nodes in here
+
+ align:start position:0%
+after all of the nodes in here
+ 
+
+ align:start position:0%
+after all of the nodes in here
+and could there be anything in between
+
+ align:start position:0%
+and could there be anything in between
+ 
+
+ align:start position:0%
+and could there be anything in between
+node and this
+
+ align:start position:0%
+node and this
+ 
+
+ align:start position:0%
+node and this
+uh this parent grandparent ancestor
+
+ align:start position:0%
+uh this parent grandparent ancestor
+ 
+
+ align:start position:0%
+uh this parent grandparent ancestor
+only if there was something in this
+
+ align:start position:0%
+only if there was something in this
+ 
+
+ align:start position:0%
+only if there was something in this
+subtree and we're in the case here
+
+ align:start position:0%
+subtree and we're in the case here
+ 
+
+ align:start position:0%
+subtree and we're in the case here
+where there is no right subtree of our
+
+ align:start position:0%
+where there is no right subtree of our
+ 
+
+ align:start position:0%
+where there is no right subtree of our
+original node
+
+ align:start position:0%
+original node
+ 
+
+ align:start position:0%
+original node
+so this this is where all the nodes in
+
+ align:start position:0%
+so this this is where all the nodes in
+ 
+
+ align:start position:0%
+so this this is where all the nodes in
+between node and here would be
+
+ align:start position:0%
+between node and here would be
+ 
+
+ align:start position:0%
+between node and here would be
+but there aren't any and therefore this
+
+ align:start position:0%
+but there aren't any and therefore this
+ 
+
+ align:start position:0%
+but there aren't any and therefore this
+is the successor
+
+ align:start position:0%
+is the successor
+ 
+
+ align:start position:0%
+is the successor
+so that's sort of the general argument
+
+ align:start position:0%
+so that's sort of the general argument
+ 
+
+ align:start position:0%
+so that's sort of the general argument
+why this
+
+ align:start position:0%
+why this
+ 
+
+ align:start position:0%
+why this
+works i see a question yeah
+
+ align:start position:0%
+works i see a question yeah
+ 
+
+ align:start position:0%
+works i see a question yeah
+placed into the traverse order so the
+
+ align:start position:0%
+placed into the traverse order so the
+ 
+
+ align:start position:0%
+placed into the traverse order so the
+traversal order is never explicitly
+
+ align:start position:0%
+traversal order is never explicitly
+ 
+
+ align:start position:0%
+traversal order is never explicitly
+computed
+
+ align:start position:0%
+computed
+ 
+
+ align:start position:0%
+computed
+what we're taught it's always implicit
+
+ align:start position:0%
+what we're taught it's always implicit
+ 
+
+ align:start position:0%
+what we're taught it's always implicit
+we can't afford to maintain
+
+ align:start position:0%
+we can't afford to maintain
+ 
+
+ align:start position:0%
+we can't afford to maintain
+this as say an array this is just
+
+ align:start position:0%
+this as say an array this is just
+ 
+
+ align:start position:0%
+this as say an array this is just
+in our heads maybe i will draw it with a
+
+ align:start position:0%
+in our heads maybe i will draw it with a
+ 
+
+ align:start position:0%
+in our heads maybe i will draw it with a
+cloud around it we're just thinking this
+
+ align:start position:0%
+cloud around it we're just thinking this
+ 
+
+ align:start position:0%
+cloud around it we're just thinking this
+okay it's not in the computer explicitly
+
+ align:start position:0%
+okay it's not in the computer explicitly
+ 
+
+ align:start position:0%
+okay it's not in the computer explicitly
+in the computer all we store is this
+
+ align:start position:0%
+in the computer all we store is this
+ 
+
+ align:start position:0%
+in the computer all we store is this
+and the reason is this is expensive we
+
+ align:start position:0%
+and the reason is this is expensive we
+ 
+
+ align:start position:0%
+and the reason is this is expensive we
+don't we can't maintain an array of
+
+ align:start position:0%
+don't we can't maintain an array of
+ 
+
+ align:start position:0%
+don't we can't maintain an array of
+things and be able to insert in the
+
+ align:start position:0%
+things and be able to insert in the
+ 
+
+ align:start position:0%
+things and be able to insert in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+whereas this is cheap i can afford to
+
+ align:start position:0%
+whereas this is cheap i can afford to
+ 
+
+ align:start position:0%
+whereas this is cheap i can afford to
+maintain this structure
+
+ align:start position:0%
+maintain this structure
+ 
+
+ align:start position:0%
+maintain this structure
+and do all these things and so the
+
+ align:start position:0%
+and do all these things and so the
+ 
+
+ align:start position:0%
+and do all these things and so the
+reason we're talking about these
+
+ align:start position:0%
+reason we're talking about these
+ 
+
+ align:start position:0%
+reason we're talking about these
+operations is they're letting us
+
+ align:start position:0%
+operations is they're letting us
+ 
+
+ align:start position:0%
+operations is they're letting us
+manipulate the order or in this case
+
+ align:start position:0%
+manipulate the order or in this case
+ 
+
+ align:start position:0%
+manipulate the order or in this case
+letting us
+
+ align:start position:0%
+letting us
+ 
+
+ align:start position:0%
+letting us
+iterate through the order so this was an
+
+ align:start position:0%
+iterate through the order so this was an
+ 
+
+ align:start position:0%
+iterate through the order so this was an
+algorithm for iterating through the
+
+ align:start position:0%
+algorithm for iterating through the
+ 
+
+ align:start position:0%
+algorithm for iterating through the
+entire order
+
+ align:start position:0%
+entire order
+ 
+
+ align:start position:0%
+entire order
+but that takes linear time this was
+
+ align:start position:0%
+but that takes linear time this was
+ 
+
+ align:start position:0%
+but that takes linear time this was
+getting started in the order find me the
+
+ align:start position:0%
+getting started in the order find me the
+ 
+
+ align:start position:0%
+getting started in the order find me the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+first thing the order and this was given
+
+ align:start position:0%
+first thing the order and this was given
+ 
+
+ align:start position:0%
+first thing the order and this was given
+one node find me the next one
+
+ align:start position:0%
+one node find me the next one
+ 
+
+ align:start position:0%
+one node find me the next one
+how long do these operations take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right at most the height of the entire
+
+ align:start position:0%
+right at most the height of the entire
+ 
+
+ align:start position:0%
+right at most the height of the entire
+tree in fact it's going to be
+
+ align:start position:0%
+tree in fact it's going to be
+ 
+
+ align:start position:0%
+tree in fact it's going to be
+the depth of that first node but in the
+
+ align:start position:0%
+the depth of that first node but in the
+ 
+
+ align:start position:0%
+the depth of that first node but in the
+worst case that's the height of the
+
+ align:start position:0%
+worst case that's the height of the
+ 
+
+ align:start position:0%
+worst case that's the height of the
+entire tree
+
+ align:start position:0%
+entire tree
+ 
+
+ align:start position:0%
+entire tree
+in general all of these operations are
+
+ align:start position:0%
+in general all of these operations are
+ 
+
+ align:start position:0%
+in general all of these operations are
+going to be order h
+
+ align:start position:0%
+going to be order h
+ 
+
+ align:start position:0%
+going to be order h
+we need to think about it in each case
+
+ align:start position:0%
+we need to think about it in each case
+ 
+
+ align:start position:0%
+we need to think about it in each case
+except for this one which is order n
+
+ align:start position:0%
+except for this one which is order n
+ 
+
+ align:start position:0%
+except for this one which is order n
+so iterating through the whole thing um
+
+ align:start position:0%
+so iterating through the whole thing um
+ 
+
+ align:start position:0%
+so iterating through the whole thing um
+this in this case we're just calling
+
+ align:start position:0%
+this in this case we're just calling
+ 
+
+ align:start position:0%
+this in this case we're just calling
+subtree first so
+
+ align:start position:0%
+subtree first so
+ 
+
+ align:start position:0%
+subtree first so
+that takes order h time here we're
+
+ align:start position:0%
+that takes order h time here we're
+ 
+
+ align:start position:0%
+that takes order h time here we're
+walking up the tree instead of down but
+
+ align:start position:0%
+walking up the tree instead of down but
+ 
+
+ align:start position:0%
+walking up the tree instead of down but
+that's going to cost
+
+ align:start position:0%
+that's going to cost
+ 
+
+ align:start position:0%
+that's going to cost
+exactly the height of the node we happen
+
+ align:start position:0%
+exactly the height of the node we happen
+ 
+
+ align:start position:0%
+exactly the height of the node we happen
+to stop early but worst case order h
+
+ align:start position:0%
+to stop early but worst case order h
+ 
+
+ align:start position:0%
+to stop early but worst case order h
+for all this all the operations we
+
+ align:start position:0%
+for all this all the operations we
+ 
+
+ align:start position:0%
+for all this all the operations we
+consider today we just want to get an
+
+ align:start position:0%
+consider today we just want to get an
+ 
+
+ align:start position:0%
+consider today we just want to get an
+order h bound
+
+ align:start position:0%
+order h bound
+ 
+
+ align:start position:0%
+order h bound
+and later we will bound h so the point
+
+ align:start position:0%
+and later we will bound h so the point
+ 
+
+ align:start position:0%
+and later we will bound h so the point
+is these are
+
+ align:start position:0%
+is these are
+ 
+
+ align:start position:0%
+is these are
+fast if h is small like log n these are
+
+ align:start position:0%
+fast if h is small like log n these are
+ 
+
+ align:start position:0%
+fast if h is small like log n these are
+almost instantaneous
+
+ align:start position:0%
+almost instantaneous
+ 
+
+ align:start position:0%
+almost instantaneous
+whereas if i had to update the explicit
+
+ align:start position:0%
+whereas if i had to update the explicit
+ 
+
+ align:start position:0%
+whereas if i had to update the explicit
+traversal order
+
+ align:start position:0%
+traversal order
+ 
+
+ align:start position:0%
+traversal order
+say as an array i would have to spend
+
+ align:start position:0%
+say as an array i would have to spend
+ 
+
+ align:start position:0%
+say as an array i would have to spend
+linear time every time i make a change
+
+ align:start position:0%
+linear time every time i make a change
+ 
+
+ align:start position:0%
+linear time every time i make a change
+and yes it would be fast to do successor
+
+ align:start position:0%
+and yes it would be fast to do successor
+ 
+
+ align:start position:0%
+and yes it would be fast to do successor
+if i had this stored explicitly
+
+ align:start position:0%
+if i had this stored explicitly
+ 
+
+ align:start position:0%
+if i had this stored explicitly
+but maintaining it would be impossible
+
+ align:start position:0%
+but maintaining it would be impossible
+ 
+
+ align:start position:0%
+but maintaining it would be impossible
+maintaining it efficiently would be
+
+ align:start position:0%
+maintaining it efficiently would be
+ 
+
+ align:start position:0%
+maintaining it efficiently would be
+impossible
+
+ align:start position:0%
+impossible
+ 
+
+ align:start position:0%
+impossible
+question questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool um so these were queries
+
+ align:start position:0%
+cool um so these were queries
+ 
+
+ align:start position:0%
+cool um so these were queries
+where i want to follow
+
+ align:start position:0%
+where i want to follow
+ 
+
+ align:start position:0%
+where i want to follow
+see what's what's next in the traversal
+
+ align:start position:0%
+see what's what's next in the traversal
+ 
+
+ align:start position:0%
+see what's what's next in the traversal
+sequence now let's talk about actually
+
+ align:start position:0%
+sequence now let's talk about actually
+ 
+
+ align:start position:0%
+sequence now let's talk about actually
+changing the traversal sequence so these
+
+ align:start position:0%
+changing the traversal sequence so these
+ 
+
+ align:start position:0%
+changing the traversal sequence so these
+are insert and delete operations
+
+ align:start position:0%
+are insert and delete operations
+ 
+
+ align:start position:0%
+are insert and delete operations
+these will correspond roughly to insert
+
+ align:start position:0%
+these will correspond roughly to insert
+ 
+
+ align:start position:0%
+these will correspond roughly to insert
+at or delete at
+
+ align:start position:0%
+at or delete at
+ 
+
+ align:start position:0%
+at or delete at
+but they're not quite we're not quite in
+
+ align:start position:0%
+but they're not quite we're not quite in
+ 
+
+ align:start position:0%
+but they're not quite we're not quite in
+sequence world yet
+
+ align:start position:0%
+sequence world yet
+ 
+
+ align:start position:0%
+sequence world yet
+instead we're going to focus on
+
+ align:start position:0%
+instead we're going to focus on
+ 
+
+ align:start position:0%
+instead we're going to focus on
+inserting or deleting in the middle
+
+ align:start position:0%
+inserting or deleting in the middle
+ 
+
+ align:start position:0%
+inserting or deleting in the middle
+of a subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to have two nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the traversal order
+
+ align:start position:0%
+in the traversal order
+ 
+
+ align:start position:0%
+in the traversal order
+so node already exists in the tree new
+
+ align:start position:0%
+so node already exists in the tree new
+ 
+
+ align:start position:0%
+so node already exists in the tree new
+is a new node that does not yet exist in
+
+ align:start position:0%
+is a new node that does not yet exist in
+ 
+
+ align:start position:0%
+is a new node that does not yet exist in
+the tree hence i call it new
+
+ align:start position:0%
+the tree hence i call it new
+ 
+
+ align:start position:0%
+the tree hence i call it new
+and what i'd like to do is insert new
+
+ align:start position:0%
+and what i'd like to do is insert new
+ 
+
+ align:start position:0%
+and what i'd like to do is insert new
+right after node and there's a symmetric
+
+ align:start position:0%
+right after node and there's a symmetric
+ 
+
+ align:start position:0%
+right after node and there's a symmetric
+operation which is insert before
+
+ align:start position:0%
+operation which is insert before
+ 
+
+ align:start position:0%
+operation which is insert before
+it will be implemented almost
+
+ align:start position:0%
+it will be implemented almost
+ 
+
+ align:start position:0%
+it will be implemented almost
+identically so we'll just focus on after
+
+ align:start position:0%
+identically so we'll just focus on after
+ 
+
+ align:start position:0%
+identically so we'll just focus on after
+so i want to insert this new node in the
+
+ align:start position:0%
+so i want to insert this new node in the
+ 
+
+ align:start position:0%
+so i want to insert this new node in the
+traversal order which again is in our
+
+ align:start position:0%
+traversal order which again is in our
+ 
+
+ align:start position:0%
+traversal order which again is in our
+heads this is all
+
+ align:start position:0%
+heads this is all
+ 
+
+ align:start position:0%
+heads this is all
+in in our thought bubble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what we want to achieve and we
+
+ align:start position:0%
+that's what we want to achieve and we
+ 
+
+ align:start position:0%
+that's what we want to achieve and we
+have to do it by manipulating
+
+ align:start position:0%
+have to do it by manipulating
+ 
+
+ align:start position:0%
+have to do it by manipulating
+this tree and however we change the tree
+
+ align:start position:0%
+this tree and however we change the tree
+ 
+
+ align:start position:0%
+this tree and however we change the tree
+it defines a new traversal order
+
+ align:start position:0%
+it defines a new traversal order
+ 
+
+ align:start position:0%
+it defines a new traversal order
+so maybe let's do an example first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually i probably want this universal
+
+ align:start position:0%
+actually i probably want this universal
+ 
+
+ align:start position:0%
+actually i probably want this universal
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+keep track of that so uh
+
+ align:start position:0%
+keep track of that so uh
+ 
+
+ align:start position:0%
+keep track of that so uh
+let's say the first thing we want to do
+
+ align:start position:0%
+let's say the first thing we want to do
+ 
+
+ align:start position:0%
+let's say the first thing we want to do
+uh is insert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g before e
+
+ align:start position:0%
+g before e
+ 
+
+ align:start position:0%
+g before e
+i want to illustrate both of the
+
+ align:start position:0%
+i want to illustrate both of the
+ 
+
+ align:start position:0%
+i want to illustrate both of the
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+insert h
+
+ align:start position:0%
+insert h
+ 
+
+ align:start position:0%
+insert h
+after e
+
+ align:start position:0%
+after e
+ 
+
+ align:start position:0%
+after e
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so insert g before e so conceptually
+
+ align:start position:0%
+so insert g before e so conceptually
+ 
+
+ align:start position:0%
+so insert g before e so conceptually
+what we want to do is insert g
+
+ align:start position:0%
+what we want to do is insert g
+ 
+
+ align:start position:0%
+what we want to do is insert g
+here and the way so we're given the node
+
+ align:start position:0%
+here and the way so we're given the node
+ 
+
+ align:start position:0%
+here and the way so we're given the node
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+and we're given a sort of empty node i
+
+ align:start position:0%
+and we're given a sort of empty node i
+ 
+
+ align:start position:0%
+and we're given a sort of empty node i
+mean a node that just contains g it
+
+ align:start position:0%
+mean a node that just contains g it
+ 
+
+ align:start position:0%
+mean a node that just contains g it
+doesn't have any pointers yet
+
+ align:start position:0%
+doesn't have any pointers yet
+ 
+
+ align:start position:0%
+doesn't have any pointers yet
+and we would like to put it before e
+
+ align:start position:0%
+and we would like to put it before e
+ 
+
+ align:start position:0%
+and we would like to put it before e
+where should i put it
+
+ align:start position:0%
+where should i put it
+ 
+
+ align:start position:0%
+where should i put it
+left child all right so that's
+
+ align:start position:0%
+left child all right so that's
+ 
+
+ align:start position:0%
+left child all right so that's
+this is an easy case if i'm trying to
+
+ align:start position:0%
+this is an easy case if i'm trying to
+ 
+
+ align:start position:0%
+this is an easy case if i'm trying to
+insert before and there's no left child
+
+ align:start position:0%
+insert before and there's no left child
+ 
+
+ align:start position:0%
+insert before and there's no left child
+stick it there if i'm trying to insert
+
+ align:start position:0%
+stick it there if i'm trying to insert
+ 
+
+ align:start position:0%
+stick it there if i'm trying to insert
+after and there's no right child
+
+ align:start position:0%
+after and there's no right child
+ 
+
+ align:start position:0%
+after and there's no right child
+stick it there easy so let me write down
+
+ align:start position:0%
+stick it there easy so let me write down
+ 
+
+ align:start position:0%
+stick it there easy so let me write down
+case one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we're inserting after so if
+
+ align:start position:0%
+so here we're inserting after so if
+ 
+
+ align:start position:0%
+so here we're inserting after so if
+there's no
+
+ align:start position:0%
+there's no
+ 
+
+ align:start position:0%
+there's no
+uh right child
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put new
+
+ align:start position:0%
+put new
+ 
+
+ align:start position:0%
+put new
+there okay i'm using informal language
+
+ align:start position:0%
+there okay i'm using informal language
+ 
+
+ align:start position:0%
+there okay i'm using informal language
+here putting
+
+ align:start position:0%
+here putting
+ 
+
+ align:start position:0%
+here putting
+this new node there
+
+ align:start position:0%
+this new node there
+ 
+
+ align:start position:0%
+this new node there
+b instead of writing for example
+
+ align:start position:0%
+b instead of writing for example
+ 
+
+ align:start position:0%
+b instead of writing for example
+node.write equals new
+
+ align:start position:0%
+node.write equals new
+ 
+
+ align:start position:0%
+node.write equals new
+because that's only one operation you
+
+ align:start position:0%
+because that's only one operation you
+ 
+
+ align:start position:0%
+because that's only one operation you
+need to do one thing you would do is set
+
+ align:start position:0%
+need to do one thing you would do is set
+ 
+
+ align:start position:0%
+need to do one thing you would do is set
+node.write equals to new but you also
+
+ align:start position:0%
+node.write equals to new but you also
+ 
+
+ align:start position:0%
+node.write equals to new but you also
+have to set new's parent to be
+
+ align:start position:0%
+have to set new's parent to be
+ 
+
+ align:start position:0%
+have to set new's parent to be
+node.write
+
+ align:start position:0%
+node.write
+ 
+
+ align:start position:0%
+node.write
+so instead of worrying about those two
+
+ align:start position:0%
+so instead of worrying about those two
+ 
+
+ align:start position:0%
+so instead of worrying about those two
+pointer changes because we always do
+
+ align:start position:0%
+pointer changes because we always do
+ 
+
+ align:start position:0%
+pointer changes because we always do
+bi-directional pointer changes i'm just
+
+ align:start position:0%
+bi-directional pointer changes i'm just
+ 
+
+ align:start position:0%
+bi-directional pointer changes i'm just
+going to use
+
+ align:start position:0%
+going to use
+ 
+
+ align:start position:0%
+going to use
+pseudocode and then in recitation you'll
+
+ align:start position:0%
+pseudocode and then in recitation you'll
+ 
+
+ align:start position:0%
+pseudocode and then in recitation you'll
+see actual python code that does all
+
+ align:start position:0%
+see actual python code that does all
+ 
+
+ align:start position:0%
+see actual python code that does all
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh so then there's the other case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that should be the second example
+
+ align:start position:0%
+so that should be the second example
+ 
+
+ align:start position:0%
+so that should be the second example
+insert h
+
+ align:start position:0%
+insert h
+ 
+
+ align:start position:0%
+insert h
+after a right
+
+ align:start position:0%
+after a right
+ 
+
+ align:start position:0%
+after a right
+insert h after a so we already have a
+
+ align:start position:0%
+insert h after a so we already have a
+ 
+
+ align:start position:0%
+insert h after a so we already have a
+node after a
+
+ align:start position:0%
+node after a
+ 
+
+ align:start position:0%
+node after a
+in the right child in this right subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so where do i want to put
+
+ align:start position:0%
+so where do i want to put
+ 
+
+ align:start position:0%
+so where do i want to put
+h relative to a
+
+ align:start position:0%
+h relative to a
+ 
+
+ align:start position:0%
+h relative to a
+well it should be to the right of a but
+
+ align:start position:0%
+well it should be to the right of a but
+ 
+
+ align:start position:0%
+well it should be to the right of a but
+it should be
+
+ align:start position:0%
+it should be
+ 
+
+ align:start position:0%
+it should be
+before c it should be to the left of c
+
+ align:start position:0%
+before c it should be to the left of c
+ 
+
+ align:start position:0%
+before c it should be to the left of c
+so that would mean we want to put it
+
+ align:start position:0%
+so that would mean we want to put it
+ 
+
+ align:start position:0%
+so that would mean we want to put it
+here okay in this case it was pretty
+
+ align:start position:0%
+here okay in this case it was pretty
+ 
+
+ align:start position:0%
+here okay in this case it was pretty
+easy because this tree was small
+
+ align:start position:0%
+easy because this tree was small
+ 
+
+ align:start position:0%
+easy because this tree was small
+where do i want to put it in general
+
+ align:start position:0%
+where do i want to put it in general
+ 
+
+ align:start position:0%
+where do i want to put it in general
+well wherever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree first tells me to put it right
+
+ align:start position:0%
+subtree first tells me to put it right
+ 
+
+ align:start position:0%
+subtree first tells me to put it right
+subtree first is going to give me
+
+ align:start position:0%
+subtree first is going to give me
+ 
+
+ align:start position:0%
+subtree first is going to give me
+the successor these are all kind of
+
+ align:start position:0%
+the successor these are all kind of
+ 
+
+ align:start position:0%
+the successor these are all kind of
+parallel um
+
+ align:start position:0%
+parallel um
+ 
+
+ align:start position:0%
+parallel um
+we're in the case now where our node has
+
+ align:start position:0%
+we're in the case now where our node has
+ 
+
+ align:start position:0%
+we're in the case now where our node has
+a right child
+
+ align:start position:0%
+a right child
+ 
+
+ align:start position:0%
+a right child
+and then successor tells us where the
+
+ align:start position:0%
+and then successor tells us where the
+ 
+
+ align:start position:0%
+and then successor tells us where the
+successor is it is the first
+
+ align:start position:0%
+successor is it is the first
+ 
+
+ align:start position:0%
+successor is it is the first
+node which is the leftmost descendant in
+
+ align:start position:0%
+node which is the leftmost descendant in
+ 
+
+ align:start position:0%
+node which is the leftmost descendant in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right subtree of the node okay a lot of
+
+ align:start position:0%
+right subtree of the node okay a lot of
+ 
+
+ align:start position:0%
+right subtree of the node okay a lot of
+pointers to follow in that sentence but
+
+ align:start position:0%
+pointers to follow in that sentence but
+ 
+
+ align:start position:0%
+pointers to follow in that sentence but
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+clear in the picture so this
+
+ align:start position:0%
+clear in the picture so this
+ 
+
+ align:start position:0%
+clear in the picture so this
+in this case we had node and there was
+
+ align:start position:0%
+in this case we had node and there was
+ 
+
+ align:start position:0%
+in this case we had node and there was
+no right child so we just added
+
+ align:start position:0%
+no right child so we just added
+ 
+
+ align:start position:0%
+no right child so we just added
+new to be its right child okay in the
+
+ align:start position:0%
+new to be its right child okay in the
+ 
+
+ align:start position:0%
+new to be its right child okay in the
+other case
+
+ align:start position:0%
+other case
+ 
+
+ align:start position:0%
+other case
+we had a right child so here is node
+
+ align:start position:0%
+we had a right child so here is node
+ 
+
+ align:start position:0%
+we had a right child so here is node
+there's uh there's this node here
+
+ align:start position:0%
+there's uh there's this node here
+ 
+
+ align:start position:0%
+there's uh there's this node here
+node.right
+
+ align:start position:0%
+node.right
+ 
+
+ align:start position:0%
+node.right
+which now we're supposing exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it defines a whole subtree there's
+
+ align:start position:0%
+and it defines a whole subtree there's
+ 
+
+ align:start position:0%
+and it defines a whole subtree there's
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+which is the first node in the traversal
+
+ align:start position:0%
+which is the first node in the traversal
+ 
+
+ align:start position:0%
+which is the first node in the traversal
+order of the subtree also known as the
+
+ align:start position:0%
+order of the subtree also known as the
+ 
+
+ align:start position:0%
+order of the subtree also known as the
+successor of node
+
+ align:start position:0%
+successor of node
+ 
+
+ align:start position:0%
+successor of node
+so i'll call this successor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of node in the current traversal order
+
+ align:start position:0%
+of node in the current traversal order
+ 
+
+ align:start position:0%
+of node in the current traversal order
+but of course we'd like to make
+
+ align:start position:0%
+but of course we'd like to make
+ 
+
+ align:start position:0%
+but of course we'd like to make
+new the new successor of the node so
+
+ align:start position:0%
+new the new successor of the node so
+ 
+
+ align:start position:0%
+new the new successor of the node so
+where does it go
+
+ align:start position:0%
+where does it go
+ 
+
+ align:start position:0%
+where does it go
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to add it as a left child
+
+ align:start position:0%
+we want to add it as a left child
+ 
+
+ align:start position:0%
+we want to add it as a left child
+to the old successor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so put uh
+
+ align:start position:0%
+okay so put uh
+ 
+
+ align:start position:0%
+okay so put uh
+node as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so take the successor and if you look at
+
+ align:start position:0%
+so take the successor and if you look at
+ 
+
+ align:start position:0%
+so take the successor and if you look at
+the code for successor we're in this
+
+ align:start position:0%
+the code for successor we're in this
+ 
+
+ align:start position:0%
+the code for successor we're in this
+case so we know it will just call
+
+ align:start position:0%
+case so we know it will just call
+ 
+
+ align:start position:0%
+case so we know it will just call
+subtree first of node.right and remember
+
+ align:start position:0%
+subtree first of node.right and remember
+ 
+
+ align:start position:0%
+subtree first of node.right and remember
+subtree first
+
+ align:start position:0%
+subtree first
+ 
+
+ align:start position:0%
+subtree first
+went left as much as it possibly could
+
+ align:start position:0%
+went left as much as it possibly could
+ 
+
+ align:start position:0%
+went left as much as it possibly could
+so what that means is this successor
+
+ align:start position:0%
+so what that means is this successor
+ 
+
+ align:start position:0%
+so what that means is this successor
+node is guaranteed to not
+
+ align:start position:0%
+node is guaranteed to not
+ 
+
+ align:start position:0%
+node is guaranteed to not
+have a left child right because it was
+
+ align:start position:0%
+have a left child right because it was
+ 
+
+ align:start position:0%
+have a left child right because it was
+defined by going right once and then
+
+ align:start position:0%
+defined by going right once and then
+ 
+
+ align:start position:0%
+defined by going right once and then
+going left as much as you could
+
+ align:start position:0%
+going left as much as you could
+ 
+
+ align:start position:0%
+going left as much as you could
+so there's no more left which means we
+
+ align:start position:0%
+so there's no more left which means we
+ 
+
+ align:start position:0%
+so there's no more left which means we
+can make one more left
+
+ align:start position:0%
+can make one more left
+ 
+
+ align:start position:0%
+can make one more left
+just add new there and we're done
+
+ align:start position:0%
+just add new there and we're done
+ 
+
+ align:start position:0%
+just add new there and we're done
+now if you look at the traversal order
+
+ align:start position:0%
+now if you look at the traversal order
+ 
+
+ align:start position:0%
+now if you look at the traversal order
+it will be node then new
+
+ align:start position:0%
+it will be node then new
+ 
+
+ align:start position:0%
+it will be node then new
+then the old successor and then the rest
+
+ align:start position:0%
+then the old successor and then the rest
+ 
+
+ align:start position:0%
+then the old successor and then the rest
+of that subtree
+
+ align:start position:0%
+of that subtree
+ 
+
+ align:start position:0%
+of that subtree
+okay it's kind of cool in all cases
+
+ align:start position:0%
+okay it's kind of cool in all cases
+ 
+
+ align:start position:0%
+okay it's kind of cool in all cases
+uh i mean this was constant time
+
+ align:start position:0%
+uh i mean this was constant time
+ 
+
+ align:start position:0%
+uh i mean this was constant time
+here we spent constant time after we
+
+ align:start position:0%
+here we spent constant time after we
+ 
+
+ align:start position:0%
+here we spent constant time after we
+called successor successor costs order h
+
+ align:start position:0%
+called successor successor costs order h
+ 
+
+ align:start position:0%
+called successor successor costs order h
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so this is order h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new new okay
+
+ align:start position:0%
+new new okay
+ 
+
+ align:start position:0%
+new new okay
+put new there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear okay that was insertion
+
+ align:start position:0%
+clear okay that was insertion
+ 
+
+ align:start position:0%
+clear okay that was insertion
+let's do deletion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get the spec right and the example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of these are going to have two cases
+
+ align:start position:0%
+all of these are going to have two cases
+ 
+
+ align:start position:0%
+all of these are going to have two cases
+uh so let me
+
+ align:start position:0%
+uh so let me
+ 
+
+ align:start position:0%
+uh so let me
+oh i didn't update so now h is after a
+
+ align:start position:0%
+oh i didn't update so now h is after a
+ 
+
+ align:start position:0%
+oh i didn't update so now h is after a
+so it should be like this
+
+ align:start position:0%
+so it should be like this
+ 
+
+ align:start position:0%
+so it should be like this
+you can check the new traverse order of
+
+ align:start position:0%
+you can check the new traverse order of
+ 
+
+ align:start position:0%
+you can check the new traverse order of
+this tree is exactly that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next i'm going to do a couple of
+
+ align:start position:0%
+next i'm going to do a couple of
+ 
+
+ align:start position:0%
+next i'm going to do a couple of
+deletions
+
+ align:start position:0%
+deletions
+ 
+
+ align:start position:0%
+deletions
+let's delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f first and then we're going to
+
+ align:start position:0%
+f first and then we're going to
+ 
+
+ align:start position:0%
+f first and then we're going to
+well this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+confusing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we're going to delete a so
+
+ align:start position:0%
+and then we're going to delete a so
+ 
+
+ align:start position:0%
+and then we're going to delete a so
+where's f we're supposing we're given a
+
+ align:start position:0%
+where's f we're supposing we're given a
+ 
+
+ align:start position:0%
+where's f we're supposing we're given a
+pointer to f this node
+
+ align:start position:0%
+pointer to f this node
+ 
+
+ align:start position:0%
+pointer to f this node
+well it's a leaf so if i want to delete
+
+ align:start position:0%
+well it's a leaf so if i want to delete
+ 
+
+ align:start position:0%
+well it's a leaf so if i want to delete
+it i just erase it
+
+ align:start position:0%
+it i just erase it
+ 
+
+ align:start position:0%
+it i just erase it
+easy leaves are easy to delete there's
+
+ align:start position:0%
+easy leaves are easy to delete there's
+ 
+
+ align:start position:0%
+easy leaves are easy to delete there's
+no work to do so what that means is i'm
+
+ align:start position:0%
+no work to do so what that means is i'm
+ 
+
+ align:start position:0%
+no work to do so what that means is i'm
+removing the pointer from d
+
+ align:start position:0%
+removing the pointer from d
+ 
+
+ align:start position:0%
+removing the pointer from d
+to f okay we just erase that guy
+
+ align:start position:0%
+to f okay we just erase that guy
+ 
+
+ align:start position:0%
+to f okay we just erase that guy
+uh okay now here's a trickier one
+
+ align:start position:0%
+uh okay now here's a trickier one
+ 
+
+ align:start position:0%
+uh okay now here's a trickier one
+suppose i want to delete the root of the
+
+ align:start position:0%
+suppose i want to delete the root of the
+ 
+
+ align:start position:0%
+suppose i want to delete the root of the
+tree this is kind of
+
+ align:start position:0%
+tree this is kind of
+ 
+
+ align:start position:0%
+tree this is kind of
+the hardest case but in general it would
+
+ align:start position:0%
+the hardest case but in general it would
+ 
+
+ align:start position:0%
+the hardest case but in general it would
+be somewhere in between leaf and root
+
+ align:start position:0%
+be somewhere in between leaf and root
+ 
+
+ align:start position:0%
+be somewhere in between leaf and root
+so if i want to delete a if i just
+
+ align:start position:0%
+so if i want to delete a if i just
+ 
+
+ align:start position:0%
+so if i want to delete a if i just
+erased it then suddenly there are these
+
+ align:start position:0%
+erased it then suddenly there are these
+ 
+
+ align:start position:0%
+erased it then suddenly there are these
+pointers to nowhere
+
+ align:start position:0%
+pointers to nowhere
+ 
+
+ align:start position:0%
+pointers to nowhere
+and i disconnect the tree into two parts
+
+ align:start position:0%
+and i disconnect the tree into two parts
+ 
+
+ align:start position:0%
+and i disconnect the tree into two parts
+i don't want to do that i need to keep
+
+ align:start position:0%
+i don't want to do that i need to keep
+ 
+
+ align:start position:0%
+i don't want to do that i need to keep
+my tree connected
+
+ align:start position:0%
+my tree connected
+ 
+
+ align:start position:0%
+my tree connected
+so i'm going to play this trick
+
+ align:start position:0%
+so i'm going to play this trick
+ 
+
+ align:start position:0%
+so i'm going to play this trick
+which is i forget if i use successor or
+
+ align:start position:0%
+which is i forget if i use successor or
+ 
+
+ align:start position:0%
+which is i forget if i use successor or
+predecessor
+
+ align:start position:0%
+predecessor
+ 
+
+ align:start position:0%
+predecessor
+predecessor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to uh look at a we already
+
+ align:start position:0%
+so i'm going to uh look at a we already
+ 
+
+ align:start position:0%
+so i'm going to uh look at a we already
+have defined successor and
+
+ align:start position:0%
+have defined successor and
+ 
+
+ align:start position:0%
+have defined successor and
+there by predecessor so i'm going to
+
+ align:start position:0%
+there by predecessor so i'm going to
+ 
+
+ align:start position:0%
+there by predecessor so i'm going to
+look at the predecessor of a
+
+ align:start position:0%
+look at the predecessor of a
+ 
+
+ align:start position:0%
+look at the predecessor of a
+which is e you can check that here the
+
+ align:start position:0%
+which is e you can check that here the
+ 
+
+ align:start position:0%
+which is e you can check that here the
+one before
+
+ align:start position:0%
+one before
+ 
+
+ align:start position:0%
+one before
+a is e this is in the left subtree
+
+ align:start position:0%
+a is e this is in the left subtree
+ 
+
+ align:start position:0%
+a is e this is in the left subtree
+uh find me the rightmost item keep going
+
+ align:start position:0%
+uh find me the rightmost item keep going
+ 
+
+ align:start position:0%
+uh find me the rightmost item keep going
+right until i can't that's e
+
+ align:start position:0%
+right until i can't that's e
+ 
+
+ align:start position:0%
+right until i can't that's e
+so now these guys are adjacent in the
+
+ align:start position:0%
+so now these guys are adjacent in the
+ 
+
+ align:start position:0%
+so now these guys are adjacent in the
+order and i'm about to remove a from the
+
+ align:start position:0%
+order and i'm about to remove a from the
+ 
+
+ align:start position:0%
+order and i'm about to remove a from the
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+so i can momentarily cheat and swap
+
+ align:start position:0%
+so i can momentarily cheat and swap
+ 
+
+ align:start position:0%
+so i can momentarily cheat and swap
+their labels
+
+ align:start position:0%
+their labels
+ 
+
+ align:start position:0%
+their labels
+i'm going to erase a and e here and put
+
+ align:start position:0%
+i'm going to erase a and e here and put
+ 
+
+ align:start position:0%
+i'm going to erase a and e here and put
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+after a why because it moves a
+
+ align:start position:0%
+after a why because it moves a
+ 
+
+ align:start position:0%
+after a why because it moves a
+down in the tree and if i get to the
+
+ align:start position:0%
+down in the tree and if i get to the
+ 
+
+ align:start position:0%
+down in the tree and if i get to the
+leaf i'm done
+
+ align:start position:0%
+leaf i'm done
+ 
+
+ align:start position:0%
+leaf i'm done
+so i'm not quite done because this is
+
+ align:start position:0%
+so i'm not quite done because this is
+ 
+
+ align:start position:0%
+so i'm not quite done because this is
+not a leaf so again i look at a's
+
+ align:start position:0%
+not a leaf so again i look at a's
+ 
+
+ align:start position:0%
+not a leaf so again i look at a's
+predecessor it's now
+
+ align:start position:0%
+predecessor it's now
+ 
+
+ align:start position:0%
+predecessor it's now
+g predecessor
+
+ align:start position:0%
+g predecessor
+ 
+
+ align:start position:0%
+g predecessor
+we hope is always in the uh
+
+ align:start position:0%
+we hope is always in the uh
+ 
+
+ align:start position:0%
+we hope is always in the uh
+farther down in the tree and then i swap
+
+ align:start position:0%
+farther down in the tree and then i swap
+ 
+
+ align:start position:0%
+farther down in the tree and then i swap
+a with g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay i have preserved the traversal
+
+ align:start position:0%
+okay i have preserved the traversal
+ 
+
+ align:start position:0%
+okay i have preserved the traversal
+order except where a
+
+ align:start position:0%
+order except where a
+ 
+
+ align:start position:0%
+order except where a
+falls just by moving a earlier in the
+
+ align:start position:0%
+falls just by moving a earlier in the
+ 
+
+ align:start position:0%
+falls just by moving a earlier in the
+order here
+
+ align:start position:0%
+order here
+ 
+
+ align:start position:0%
+order here
+and now a is a leaf and i can erase it
+
+ align:start position:0%
+and now a is a leaf and i can erase it
+ 
+
+ align:start position:0%
+and now a is a leaf and i can erase it
+okay so that's what we're going to
+
+ align:start position:0%
+okay so that's what we're going to
+ 
+
+ align:start position:0%
+okay so that's what we're going to
+follow now in actuality it's a little
+
+ align:start position:0%
+follow now in actuality it's a little
+ 
+
+ align:start position:0%
+follow now in actuality it's a little
+tricky sometimes we need to use
+
+ align:start position:0%
+tricky sometimes we need to use
+ 
+
+ align:start position:0%
+tricky sometimes we need to use
+predecessors sometimes we need to use
+
+ align:start position:0%
+predecessors sometimes we need to use
+ 
+
+ align:start position:0%
+predecessors sometimes we need to use
+successor okay so the cases are
+
+ align:start position:0%
+successor okay so the cases are
+ 
+
+ align:start position:0%
+successor okay so the cases are
+if the node is a leaf just
+
+ align:start position:0%
+if the node is a leaf just
+ 
+
+ align:start position:0%
+if the node is a leaf just
+detach it from the parent easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's sort of our base case in the
+
+ align:start position:0%
+that's sort of our base case in the
+ 
+
+ align:start position:0%
+that's sort of our base case in the
+recursion otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are two cases if
+
+ align:start position:0%
+there are two cases if
+ 
+
+ align:start position:0%
+there are two cases if
+so if we're not a leaf that means we
+
+ align:start position:0%
+so if we're not a leaf that means we
+ 
+
+ align:start position:0%
+so if we're not a leaf that means we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+a left child or a right child or both
+
+ align:start position:0%
+a left child or a right child or both
+ 
+
+ align:start position:0%
+a left child or a right child or both
+both is going to be the easy case
+
+ align:start position:0%
+both is going to be the easy case
+ 
+
+ align:start position:0%
+both is going to be the easy case
+but in general i have either there's a
+
+ align:start position:0%
+but in general i have either there's a
+ 
+
+ align:start position:0%
+but in general i have either there's a
+left child
+
+ align:start position:0%
+left child
+ 
+
+ align:start position:0%
+left child
+or there's a right child in either case
+
+ align:start position:0%
+or there's a right child in either case
+ 
+
+ align:start position:0%
+or there's a right child in either case
+i'm going to be happy so i don't need a
+
+ align:start position:0%
+i'm going to be happy so i don't need a
+ 
+
+ align:start position:0%
+i'm going to be happy so i don't need a
+both case
+
+ align:start position:0%
+both case
+ 
+
+ align:start position:0%
+both case
+uh okay so what do i do in if i have a
+
+ align:start position:0%
+uh okay so what do i do in if i have a
+ 
+
+ align:start position:0%
+uh okay so what do i do in if i have a
+left child
+
+ align:start position:0%
+left child
+ 
+
+ align:start position:0%
+left child
+that guarantees to me that if the node's
+
+ align:start position:0%
+that guarantees to me that if the node's
+ 
+
+ align:start position:0%
+that guarantees to me that if the node's
+predecessor
+
+ align:start position:0%
+predecessor
+ 
+
+ align:start position:0%
+predecessor
+is inside that left sub-tree which means
+
+ align:start position:0%
+is inside that left sub-tree which means
+ 
+
+ align:start position:0%
+is inside that left sub-tree which means
+it's lower in the tree
+
+ align:start position:0%
+it's lower in the tree
+ 
+
+ align:start position:0%
+it's lower in the tree
+if i didn't have a left child the
+
+ align:start position:0%
+if i didn't have a left child the
+ 
+
+ align:start position:0%
+if i didn't have a left child the
+predecessor would actually be higher in
+
+ align:start position:0%
+predecessor would actually be higher in
+ 
+
+ align:start position:0%
+predecessor would actually be higher in
+the tree and i don't want to go higher
+
+ align:start position:0%
+the tree and i don't want to go higher
+ 
+
+ align:start position:0%
+the tree and i don't want to go higher
+okay so if i have a left child i know
+
+ align:start position:0%
+okay so if i have a left child i know
+ 
+
+ align:start position:0%
+okay so if i have a left child i know
+the predecessor is lower
+
+ align:start position:0%
+the predecessor is lower
+ 
+
+ align:start position:0%
+the predecessor is lower
+and so i'm going to swap
+
+ align:start position:0%
+and so i'm going to swap
+ 
+
+ align:start position:0%
+and so i'm going to swap
+my item the contents of my node
+
+ align:start position:0%
+my item the contents of my node
+ 
+
+ align:start position:0%
+my item the contents of my node
+with my predecessor's item
+
+ align:start position:0%
+with my predecessor's item
+ 
+
+ align:start position:0%
+with my predecessor's item
+and then i'm going to recursively delete
+
+ align:start position:0%
+and then i'm going to recursively delete
+ 
+
+ align:start position:0%
+and then i'm going to recursively delete
+the predecessor okay that's the case
+
+ align:start position:0%
+the predecessor okay that's the case
+ 
+
+ align:start position:0%
+the predecessor okay that's the case
+that we looked at in this code
+
+ align:start position:0%
+that we looked at in this code
+ 
+
+ align:start position:0%
+that we looked at in this code
+in this example because we always had a
+
+ align:start position:0%
+in this example because we always had a
+ 
+
+ align:start position:0%
+in this example because we always had a
+left child if we have a right child but
+
+ align:start position:0%
+left child if we have a right child but
+ 
+
+ align:start position:0%
+left child if we have a right child but
+no left child we just do the reverse we
+
+ align:start position:0%
+no left child we just do the reverse we
+ 
+
+ align:start position:0%
+no left child we just do the reverse we
+swap with our successors
+
+ align:start position:0%
+swap with our successors
+ 
+
+ align:start position:0%
+swap with our successors
+item and then delete the successor in
+
+ align:start position:0%
+item and then delete the successor in
+ 
+
+ align:start position:0%
+item and then delete the successor in
+either case we're going down
+
+ align:start position:0%
+either case we're going down
+ 
+
+ align:start position:0%
+either case we're going down
+and so if we start at some node like the
+
+ align:start position:0%
+and so if we start at some node like the
+ 
+
+ align:start position:0%
+and so if we start at some node like the
+route every time we do this operation
+
+ align:start position:0%
+route every time we do this operation
+ 
+
+ align:start position:0%
+route every time we do this operation
+we're walking down and then we're
+
+ align:start position:0%
+we're walking down and then we're
+ 
+
+ align:start position:0%
+we're walking down and then we're
+walking down
+
+ align:start position:0%
+walking down
+ 
+
+ align:start position:0%
+walking down
+and in general we'll keep walking down
+
+ align:start position:0%
+and in general we'll keep walking down
+ 
+
+ align:start position:0%
+and in general we'll keep walking down
+resuming where we left off which means
+
+ align:start position:0%
+resuming where we left off which means
+ 
+
+ align:start position:0%
+resuming where we left off which means
+total amount of time we spend is
+
+ align:start position:0%
+total amount of time we spend is
+ 
+
+ align:start position:0%
+total amount of time we spend is
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+the height of the tree in the worst case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+right so e didn't used to have a right
+
+ align:start position:0%
+right so e didn't used to have a right
+ 
+
+ align:start position:0%
+right so e didn't used to have a right
+child so we're changing identities of
+
+ align:start position:0%
+child so we're changing identities of
+ 
+
+ align:start position:0%
+child so we're changing identities of
+nodes when we do this
+
+ align:start position:0%
+nodes when we do this
+ 
+
+ align:start position:0%
+nodes when we do this
+because we uh this that we didn't
+
+ align:start position:0%
+because we uh this that we didn't
+ 
+
+ align:start position:0%
+because we uh this that we didn't
+actually move this
+
+ align:start position:0%
+actually move this
+ 
+
+ align:start position:0%
+actually move this
+circle the circle stayed in place and
+
+ align:start position:0%
+circle the circle stayed in place and
+ 
+
+ align:start position:0%
+circle the circle stayed in place and
+what we changed was the item that was
+
+ align:start position:0%
+what we changed was the item that was
+ 
+
+ align:start position:0%
+what we changed was the item that was
+stored in that circle
+
+ align:start position:0%
+stored in that circle
+ 
+
+ align:start position:0%
+stored in that circle
+so whether you call this node e or a
+
+ align:start position:0%
+so whether you call this node e or a
+ 
+
+ align:start position:0%
+so whether you call this node e or a
+it doesn't really matter it is just the
+
+ align:start position:0%
+it doesn't really matter it is just the
+ 
+
+ align:start position:0%
+it doesn't really matter it is just the
+root note
+
+ align:start position:0%
+root note
+ 
+
+ align:start position:0%
+root note
+okay so we're gonna play a lot of these
+
+ align:start position:0%
+okay so we're gonna play a lot of these
+ 
+
+ align:start position:0%
+okay so we're gonna play a lot of these
+tricks of moving the items around so far
+
+ align:start position:0%
+tricks of moving the items around so far
+ 
+
+ align:start position:0%
+tricks of moving the items around so far
+we hadn't been doing that we've just
+
+ align:start position:0%
+we hadn't been doing that we've just
+ 
+
+ align:start position:0%
+we hadn't been doing that we've just
+been creating
+
+ align:start position:0%
+been creating
+ 
+
+ align:start position:0%
+been creating
+nodes and placing them somewhere but now
+
+ align:start position:0%
+nodes and placing them somewhere but now
+ 
+
+ align:start position:0%
+nodes and placing them somewhere but now
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+in this delete operation is the first
+
+ align:start position:0%
+in this delete operation is the first
+ 
+
+ align:start position:0%
+in this delete operation is the first
+time where we're changing what's stored
+
+ align:start position:0%
+time where we're changing what's stored
+ 
+
+ align:start position:0%
+time where we're changing what's stored
+in the nodes
+
+ align:start position:0%
+in the nodes
+ 
+
+ align:start position:0%
+in the nodes
+but we still can define the traversal
+
+ align:start position:0%
+but we still can define the traversal
+ 
+
+ align:start position:0%
+but we still can define the traversal
+order right the traverse order of this
+
+ align:start position:0%
+order right the traverse order of this
+ 
+
+ align:start position:0%
+order right the traverse order of this
+tree is dbgehc
+
+ align:start position:0%
+tree is dbgehc
+ 
+
+ align:start position:0%
+tree is dbgehc
+which should be what we get here if i
+
+ align:start position:0%
+which should be what we get here if i
+ 
+
+ align:start position:0%
+which should be what we get here if i
+delete f and
+
+ align:start position:0%
+delete f and
+ 
+
+ align:start position:0%
+delete f and
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sorry can f
+
+ align:start position:0%
+and sorry can f
+ 
+
+ align:start position:0%
+and sorry can f
+trees will not preserve connections
+
+ align:start position:0%
+trees will not preserve connections
+ 
+
+ align:start position:0%
+trees will not preserve connections
+that's just the name of the game we are
+
+ align:start position:0%
+that's just the name of the game we are
+ 
+
+ align:start position:0%
+that's just the name of the game we are
+we have to allow this otherwise we can't
+
+ align:start position:0%
+we have to allow this otherwise we can't
+ 
+
+ align:start position:0%
+we have to allow this otherwise we can't
+do anything that's the short
+
+ align:start position:0%
+do anything that's the short
+ 
+
+ align:start position:0%
+do anything that's the short
+version okay okay in the last few
+
+ align:start position:0%
+version okay okay in the last few
+ 
+
+ align:start position:0%
+version okay okay in the last few
+minutes let me talk about how we take
+
+ align:start position:0%
+minutes let me talk about how we take
+ 
+
+ align:start position:0%
+minutes let me talk about how we take
+these trees and implement a set
+
+ align:start position:0%
+these trees and implement a set
+ 
+
+ align:start position:0%
+these trees and implement a set
+or sequence okay i've already alluded to
+
+ align:start position:0%
+or sequence okay i've already alluded to
+ 
+
+ align:start position:0%
+or sequence okay i've already alluded to
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just make the traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to the the order that we're trying
+
+ align:start position:0%
+equal to the the order that we're trying
+ 
+
+ align:start position:0%
+equal to the the order that we're trying
+to represent
+
+ align:start position:0%
+to represent
+ 
+
+ align:start position:0%
+to represent
+the sequence order
+
+ align:start position:0%
+the sequence order
+ 
+
+ align:start position:0%
+the sequence order
+and if we're trying to source set items
+
+ align:start position:0%
+and if we're trying to source set items
+ 
+
+ align:start position:0%
+and if we're trying to source set items
+with keys we're going to make the
+
+ align:start position:0%
+with keys we're going to make the
+ 
+
+ align:start position:0%
+with keys we're going to make the
+traversal order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to ordered by increasing key
+
+ align:start position:0%
+equal to ordered by increasing key
+ 
+
+ align:start position:0%
+equal to ordered by increasing key
+increasing item
+
+ align:start position:0%
+increasing item
+ 
+
+ align:start position:0%
+increasing item
+key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some sense that's it but then we need to
+
+ align:start position:0%
+some sense that's it but then we need to
+ 
+
+ align:start position:0%
+some sense that's it but then we need to
+think about how do we implement
+
+ align:start position:0%
+think about how do we implement
+ 
+
+ align:start position:0%
+think about how do we implement
+all of these operations so maybe most
+
+ align:start position:0%
+all of these operations so maybe most
+ 
+
+ align:start position:0%
+all of these operations so maybe most
+enlightening is for starters is
+
+ align:start position:0%
+enlightening is for starters is
+ 
+
+ align:start position:0%
+enlightening is for starters is
+finding a key in a tree
+
+ align:start position:0%
+finding a key in a tree
+ 
+
+ align:start position:0%
+finding a key in a tree
+so this is going to correspond to binary
+
+ align:start position:0%
+so this is going to correspond to binary
+ 
+
+ align:start position:0%
+so this is going to correspond to binary
+search
+
+ align:start position:0%
+search
+ 
+
+ align:start position:0%
+search
+if i'm searching for a key let's say i'm
+
+ align:start position:0%
+if i'm searching for a key let's say i'm
+ 
+
+ align:start position:0%
+if i'm searching for a key let's say i'm
+searching for
+
+ align:start position:0%
+searching for
+ 
+
+ align:start position:0%
+searching for
+g's key and i know this
+
+ align:start position:0%
+g's key and i know this
+ 
+
+ align:start position:0%
+g's key and i know this
+may be hard in this example maybe i'll
+
+ align:start position:0%
+may be hard in this example maybe i'll
+ 
+
+ align:start position:0%
+may be hard in this example maybe i'll
+replace these all with numbers
+
+ align:start position:0%
+replace these all with numbers
+ 
+
+ align:start position:0%
+replace these all with numbers
+so i can think about key values
+
+ align:start position:0%
+so i can think about key values
+ 
+
+ align:start position:0%
+so i can think about key values
+okay so let's say 1 7
+
+ align:start position:0%
+okay so let's say 1 7
+ 
+
+ align:start position:0%
+okay so let's say 1 7
+12 17
+
+ align:start position:0%
+12 17
+ 
+
+ align:start position:0%
+12 17
+19 and 23.
+
+ align:start position:0%
+19 and 23.
+ 
+
+ align:start position:0%
+19 and 23.
+this is now in key order if you think of
+
+ align:start position:0%
+this is now in key order if you think of
+ 
+
+ align:start position:0%
+this is now in key order if you think of
+the traversal order
+
+ align:start position:0%
+the traversal order
+ 
+
+ align:start position:0%
+the traversal order
+the property is that all the keys in the
+
+ align:start position:0%
+the property is that all the keys in the
+ 
+
+ align:start position:0%
+the property is that all the keys in the
+left subtree of the root
+
+ align:start position:0%
+left subtree of the root
+ 
+
+ align:start position:0%
+left subtree of the root
+are less than the root and the root is
+
+ align:start position:0%
+are less than the root and the root is
+ 
+
+ align:start position:0%
+are less than the root and the root is
+less than all the keys in the right
+
+ align:start position:0%
+less than all the keys in the right
+ 
+
+ align:start position:0%
+less than all the keys in the right
+subtree and recursively all the way down
+
+ align:start position:0%
+subtree and recursively all the way down
+ 
+
+ align:start position:0%
+subtree and recursively all the way down
+this is something called the
+
+ align:start position:0%
+this is something called the
+ 
+
+ align:start position:0%
+this is something called the
+binary search tree property bst property
+
+ align:start position:0%
+binary search tree property bst property
+ 
+
+ align:start position:0%
+binary search tree property bst property
+these here we're calling them binary
+
+ align:start position:0%
+these here we're calling them binary
+ 
+
+ align:start position:0%
+these here we're calling them binary
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+sets or set binary trees but they're
+
+ align:start position:0%
+sets or set binary trees but they're
+ 
+
+ align:start position:0%
+sets or set binary trees but they're
+also known in the literature as binary
+
+ align:start position:0%
+also known in the literature as binary
+ 
+
+ align:start position:0%
+also known in the literature as binary
+search trees term you may have heard
+
+ align:start position:0%
+search trees term you may have heard
+ 
+
+ align:start position:0%
+search trees term you may have heard
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+so this is a special case of what we're
+
+ align:start position:0%
+so this is a special case of what we're
+ 
+
+ align:start position:0%
+so this is a special case of what we're
+doing where we're storing the keys in
+
+ align:start position:0%
+doing where we're storing the keys in
+ 
+
+ align:start position:0%
+doing where we're storing the keys in
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+and then if i want to search for a key
+
+ align:start position:0%
+and then if i want to search for a key
+ 
+
+ align:start position:0%
+and then if i want to search for a key
+like uh 13
+
+ align:start position:0%
+like uh 13
+ 
+
+ align:start position:0%
+like uh 13
+i compare that key with the root i see
+
+ align:start position:0%
+i compare that key with the root i see
+ 
+
+ align:start position:0%
+i compare that key with the root i see
+oh it's not
+
+ align:start position:0%
+oh it's not
+ 
+
+ align:start position:0%
+oh it's not
+equal and it's to the left because it's
+
+ align:start position:0%
+equal and it's to the left because it's
+ 
+
+ align:start position:0%
+equal and it's to the left because it's
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+17. so 13 is left of here 13 is right of
+
+ align:start position:0%
+17. so 13 is left of here 13 is right of
+ 
+
+ align:start position:0%
+17. so 13 is left of here 13 is right of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+13 is right of 12 and so i know that
+
+ align:start position:0%
+13 is right of 12 and so i know that
+ 
+
+ align:start position:0%
+13 is right of 12 and so i know that
+this is where 13 would belong
+
+ align:start position:0%
+this is where 13 would belong
+ 
+
+ align:start position:0%
+this is where 13 would belong
+but there's no right child there and so
+
+ align:start position:0%
+but there's no right child there and so
+ 
+
+ align:start position:0%
+but there's no right child there and so
+i know in find i just returned nothing
+
+ align:start position:0%
+i know in find i just returned nothing
+ 
+
+ align:start position:0%
+i know in find i just returned nothing
+if i was doing find previous i would
+
+ align:start position:0%
+if i was doing find previous i would
+ 
+
+ align:start position:0%
+if i was doing find previous i would
+return this note
+
+ align:start position:0%
+return this note
+ 
+
+ align:start position:0%
+return this note
+because i have tried to go to the right
+
+ align:start position:0%
+because i have tried to go to the right
+ 
+
+ align:start position:0%
+because i have tried to go to the right
+the last time before i fell off the tree
+
+ align:start position:0%
+the last time before i fell off the tree
+ 
+
+ align:start position:0%
+the last time before i fell off the tree
+i was trying to go to the right and
+
+ align:start position:0%
+i was trying to go to the right and
+ 
+
+ align:start position:0%
+i was trying to go to the right and
+therefore that last note i had was the
+
+ align:start position:0%
+therefore that last note i had was the
+ 
+
+ align:start position:0%
+therefore that last note i had was the
+previous item if i was trying to define
+
+ align:start position:0%
+previous item if i was trying to define
+ 
+
+ align:start position:0%
+previous item if i was trying to define
+next what would i do i would just take
+
+ align:start position:0%
+next what would i do i would just take
+ 
+
+ align:start position:0%
+next what would i do i would just take
+this node and compute its successor
+
+ align:start position:0%
+this node and compute its successor
+ 
+
+ align:start position:0%
+this node and compute its successor
+which we already know how to do and that
+
+ align:start position:0%
+which we already know how to do and that
+ 
+
+ align:start position:0%
+which we already know how to do and that
+happens to be the root
+
+ align:start position:0%
+happens to be the root
+ 
+
+ align:start position:0%
+happens to be the root
+okay so now i can do these inexact
+
+ align:start position:0%
+okay so now i can do these inexact
+ 
+
+ align:start position:0%
+okay so now i can do these inexact
+searches when i do find previous and
+
+ align:start position:0%
+searches when i do find previous and
+ 
+
+ align:start position:0%
+searches when i do find previous and
+find next
+
+ align:start position:0%
+find next
+ 
+
+ align:start position:0%
+find next
+when i fall off the tree i find either
+
+ align:start position:0%
+when i fall off the tree i find either
+ 
+
+ align:start position:0%
+when i fall off the tree i find either
+the previous or the next
+
+ align:start position:0%
+the previous or the next
+ 
+
+ align:start position:0%
+the previous or the next
+and then with predecessor or successor i
+
+ align:start position:0%
+and then with predecessor or successor i
+ 
+
+ align:start position:0%
+and then with predecessor or successor i
+can find the other one
+
+ align:start position:0%
+can find the other one
+ 
+
+ align:start position:0%
+can find the other one
+okay so that's how we can do find and
+
+ align:start position:0%
+okay so that's how we can do find and
+ 
+
+ align:start position:0%
+okay so that's how we can do find and
+find previous
+
+ align:start position:0%
+find previous
+ 
+
+ align:start position:0%
+find previous
+and find next to do
+
+ align:start position:0%
+and find next to do
+ 
+
+ align:start position:0%
+and find next to do
+uh sequences we need a little bit more
+
+ align:start position:0%
+uh sequences we need a little bit more
+ 
+
+ align:start position:0%
+uh sequences we need a little bit more
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+we'll do that next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/7Cvytz8rLLo.txt b/7Cvytz8rLLo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..05f43f2ae36f7996c9985e5ee360afe9a6a549f4
--- /dev/null
+++ b/7Cvytz8rLLo.txt
@@ -0,0 +1,3971 @@
+align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right I'd like to talk about this next
+
+ align:start position:0%
+right I'd like to talk about this next
+ 
+
+ align:start position:0%
+right I'd like to talk about this next
+project in
+
+ align:start position:0%
+project in
+ 
+
+ align:start position:0%
+project in
+um about four different
+
+ align:start position:0%
+um about four different
+ 
+
+ align:start position:0%
+um about four different
+ways and I'm going to break it down and
+
+ align:start position:0%
+ways and I'm going to break it down and
+ 
+
+ align:start position:0%
+ways and I'm going to break it down and
+you might take some notes if you
+
+ align:start position:0%
+you might take some notes if you
+ 
+
+ align:start position:0%
+you might take some notes if you
+would uh the first will be about the
+
+ align:start position:0%
+would uh the first will be about the
+ 
+
+ align:start position:0%
+would uh the first will be about the
+site the second is about the
+
+ align:start position:0%
+site the second is about the
+ 
+
+ align:start position:0%
+site the second is about the
+program uh the third is s of what we're
+
+ align:start position:0%
+program uh the third is s of what we're
+ 
+
+ align:start position:0%
+program uh the third is s of what we're
+doing in terms of the architecture the
+
+ align:start position:0%
+doing in terms of the architecture the
+ 
+
+ align:start position:0%
+doing in terms of the architecture the
+space the
+
+ align:start position:0%
+space the
+ 
+
+ align:start position:0%
+space the
+determinance and the fourth is this
+
+ align:start position:0%
+determinance and the fourth is this
+ 
+
+ align:start position:0%
+determinance and the fourth is this
+issue of nature if we call it that quote
+
+ align:start position:0%
+issue of nature if we call it that quote
+ 
+
+ align:start position:0%
+issue of nature if we call it that quote
+in the city so I'm going to start with
+
+ align:start position:0%
+in the city so I'm going to start with
+ 
+
+ align:start position:0%
+in the city so I'm going to start with
+the site Jen has uh for you and she'll
+
+ align:start position:0%
+the site Jen has uh for you and she'll
+ 
+
+ align:start position:0%
+the site Jen has uh for you and she'll
+be here a copy of of the section at 16th
+
+ align:start position:0%
+be here a copy of of the section at 16th
+ 
+
+ align:start position:0%
+be here a copy of of the section at 16th
+scale of the site this photo montage of
+
+ align:start position:0%
+scale of the site this photo montage of
+ 
+
+ align:start position:0%
+scale of the site this photo montage of
+the site a 16th scale plan and an NA
+
+ align:start position:0%
+the site a 16th scale plan and an NA
+ 
+
+ align:start position:0%
+the site a 16th scale plan and an NA
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+plan uh she should have when she arrives
+
+ align:start position:0%
+plan uh she should have when she arrives
+ 
+
+ align:start position:0%
+plan uh she should have when she arrives
+copies of everything of
+
+ align:start position:0%
+copies of everything of
+ 
+
+ align:start position:0%
+copies of everything of
+this the site is no U stranger to you
+
+ align:start position:0%
+this the site is no U stranger to you
+ 
+
+ align:start position:0%
+this the site is no U stranger to you
+you do know it uh some of you
+
+ align:start position:0%
+you do know it uh some of you
+ 
+
+ align:start position:0%
+you do know it uh some of you
+intimately uh sorry well here and
+
+ align:start position:0%
+intimately uh sorry well here and
+ 
+
+ align:start position:0%
+intimately uh sorry well here and
+certainly these two guys um and many of
+
+ align:start position:0%
+certainly these two guys um and many of
+ 
+
+ align:start position:0%
+certainly these two guys um and many of
+them as you know looking into
+
+ align:start position:0%
+them as you know looking into
+ 
+
+ align:start position:0%
+them as you know looking into
+it the site is roughly an area that is
+
+ align:start position:0%
+it the site is roughly an area that is
+ 
+
+ align:start position:0%
+it the site is roughly an area that is
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and is
+
+ align:start position:0%
+this and is
+ 
+
+ align:start position:0%
+this and is
+a interesting site I won't call it
+
+ align:start position:0%
+a interesting site I won't call it
+ 
+
+ align:start position:0%
+a interesting site I won't call it
+difficult but it's an interesting site
+
+ align:start position:0%
+difficult but it's an interesting site
+ 
+
+ align:start position:0%
+difficult but it's an interesting site
+and there are some ways of describing
+
+ align:start position:0%
+and there are some ways of describing
+ 
+
+ align:start position:0%
+and there are some ways of describing
+it for the purposes of this project we
+
+ align:start position:0%
+it for the purposes of this project we
+ 
+
+ align:start position:0%
+it for the purposes of this project we
+are considering it to be completely
+
+ align:start position:0%
+are considering it to be completely
+ 
+
+ align:start position:0%
+are considering it to be completely
+flat it's it's not entirely flat but
+
+ align:start position:0%
+flat it's it's not entirely flat but
+ 
+
+ align:start position:0%
+flat it's it's not entirely flat but
+it's close enough to being
+
+ align:start position:0%
+it's close enough to being
+ 
+
+ align:start position:0%
+it's close enough to being
+flat there is a driveway that goes down
+
+ align:start position:0%
+flat there is a driveway that goes down
+ 
+
+ align:start position:0%
+flat there is a driveway that goes down
+to a garage here that we're considering
+
+ align:start position:0%
+to a garage here that we're considering
+ 
+
+ align:start position:0%
+to a garage here that we're considering
+isn't there it shouldn't have been there
+
+ align:start position:0%
+isn't there it shouldn't have been there
+ 
+
+ align:start position:0%
+isn't there it shouldn't have been there
+in the first place actually it's
+
+ align:start position:0%
+in the first place actually it's
+ 
+
+ align:start position:0%
+in the first place actually it's
+illegal but we're considering it's not
+
+ align:start position:0%
+illegal but we're considering it's not
+ 
+
+ align:start position:0%
+illegal but we're considering it's not
+there there is a and you can see on here
+
+ align:start position:0%
+there there is a and you can see on here
+ 
+
+ align:start position:0%
+there there is a and you can see on here
+called a lane lands
+
+ align:start position:0%
+called a lane lands
+ 
+
+ align:start position:0%
+called a lane lands
+Court um which I probably would guess
+
+ align:start position:0%
+Court um which I probably would guess
+ 
+
+ align:start position:0%
+Court um which I probably would guess
+originally
+
+ align:start position:0%
+originally
+ 
+
+ align:start position:0%
+originally
+there was houses like this here and then
+
+ align:start position:0%
+there was houses like this here and then
+ 
+
+ align:start position:0%
+there was houses like this here and then
+houses like this
+
+ align:start position:0%
+houses like this
+ 
+
+ align:start position:0%
+houses like this
+here and the tunnel came along and
+
+ align:start position:0%
+here and the tunnel came along and
+ 
+
+ align:start position:0%
+here and the tunnel came along and
+blasted everything away because they
+
+ align:start position:0%
+blasted everything away because they
+ 
+
+ align:start position:0%
+blasted everything away because they
+probably had to dig underneath this to
+
+ align:start position:0%
+probably had to dig underneath this to
+ 
+
+ align:start position:0%
+probably had to dig underneath this to
+do this because this is where the I
+
+ align:start position:0%
+do this because this is where the I
+ 
+
+ align:start position:0%
+do this because this is where the I
+think the tunnel goes down so that's why
+
+ align:start position:0%
+think the tunnel goes down so that's why
+ 
+
+ align:start position:0%
+think the tunnel goes down so that's why
+it's like this but for the purpose of
+
+ align:start position:0%
+it's like this but for the purpose of
+ 
+
+ align:start position:0%
+it's like this but for the purpose of
+our project this is part of our of our
+
+ align:start position:0%
+our project this is part of our of our
+ 
+
+ align:start position:0%
+our project this is part of our of our
+site and this is also part of our site
+
+ align:start position:0%
+site and this is also part of our site
+ 
+
+ align:start position:0%
+site and this is also part of our site
+therefore we don't worry about cars
+
+ align:start position:0%
+therefore we don't worry about cars
+ 
+
+ align:start position:0%
+therefore we don't worry about cars
+going back through here they don't do it
+
+ align:start position:0%
+going back through here they don't do it
+ 
+
+ align:start position:0%
+going back through here they don't do it
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+now this is parking this is nothing and
+
+ align:start position:0%
+now this is parking this is nothing and
+ 
+
+ align:start position:0%
+now this is parking this is nothing and
+this is playground and we're just going
+
+ align:start position:0%
+this is playground and we're just going
+ 
+
+ align:start position:0%
+this is playground and we're just going
+to forget about the playground for the
+
+ align:start position:0%
+to forget about the playground for the
+ 
+
+ align:start position:0%
+to forget about the playground for the
+time being I know Felix that you may not
+
+ align:start position:0%
+time being I know Felix that you may not
+ 
+
+ align:start position:0%
+time being I know Felix that you may not
+like that but you can move it over to
+
+ align:start position:0%
+like that but you can move it over to
+ 
+
+ align:start position:0%
+like that but you can move it over to
+here which is a nice playground space or
+
+ align:start position:0%
+here which is a nice playground space or
+ 
+
+ align:start position:0%
+here which is a nice playground space or
+in incorporated into your so keep paring
+
+ align:start position:0%
+in incorporated into your so keep paring
+ 
+
+ align:start position:0%
+in incorporated into your so keep paring
+so that's the first point is that that
+
+ align:start position:0%
+so that's the first point is that that
+ 
+
+ align:start position:0%
+so that's the first point is that that
+is flat and the and the rways and the
+
+ align:start position:0%
+is flat and the and the rways and the
+ 
+
+ align:start position:0%
+is flat and the and the rways and the
+driveways you can keep I mean you uh you
+
+ align:start position:0%
+driveways you can keep I mean you uh you
+ 
+
+ align:start position:0%
+driveways you can keep I mean you uh you
+ignore there are are however some nice
+
+ align:start position:0%
+ignore there are are however some nice
+ 
+
+ align:start position:0%
+ignore there are are however some nice
+trees that you have to think
+
+ align:start position:0%
+trees that you have to think
+ 
+
+ align:start position:0%
+trees that you have to think
+about I think two but oh
+
+ align:start position:0%
+about I think two but oh
+ 
+
+ align:start position:0%
+about I think two but oh
+wait oh they don't look very nice on
+
+ align:start position:0%
+wait oh they don't look very nice on
+ 
+
+ align:start position:0%
+wait oh they don't look very nice on
+this oh no here they are yeah two
+
+ align:start position:0%
+this oh no here they are yeah two
+ 
+
+ align:start position:0%
+this oh no here they are yeah two
+there's one here didn't
+
+ align:start position:0%
+there's one here didn't
+ 
+
+ align:start position:0%
+there's one here didn't
+know oh this little building you don't
+
+ align:start position:0%
+know oh this little building you don't
+ 
+
+ align:start position:0%
+know oh this little building you don't
+worry about either it's not on here
+
+ align:start position:0%
+worry about either it's not on here
+ 
+
+ align:start position:0%
+worry about either it's not on here
+there's a little building here but
+
+ align:start position:0%
+there's a little building here but
+ 
+
+ align:start position:0%
+there's a little building here but
+forget
+
+ align:start position:0%
+forget
+ 
+
+ align:start position:0%
+forget
+that whenever in architecture you
+
+ align:start position:0%
+that whenever in architecture you
+ 
+
+ align:start position:0%
+that whenever in architecture you
+destroy a tree think about it very
+
+ align:start position:0%
+destroy a tree think about it very
+ 
+
+ align:start position:0%
+destroy a tree think about it very
+seriously you can now transplant trees
+
+ align:start position:0%
+seriously you can now transplant trees
+ 
+
+ align:start position:0%
+seriously you can now transplant trees
+but they're expensive um these are not
+
+ align:start position:0%
+but they're expensive um these are not
+ 
+
+ align:start position:0%
+but they're expensive um these are not
+mature trees by any means but they have
+
+ align:start position:0%
+mature trees by any means but they have
+ 
+
+ align:start position:0%
+mature trees by any means but they have
+had a life of 20 probably 25 years that
+
+ align:start position:0%
+had a life of 20 probably 25 years that
+ 
+
+ align:start position:0%
+had a life of 20 probably 25 years that
+doesn't mean you can't take
+
+ align:start position:0%
+doesn't mean you can't take
+ 
+
+ align:start position:0%
+doesn't mean you can't take
+them or relocate them but think about it
+
+ align:start position:0%
+them or relocate them but think about it
+ 
+
+ align:start position:0%
+them or relocate them but think about it
+before you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I have the following um criteria for
+
+ align:start position:0%
+do I have the following um criteria for
+ 
+
+ align:start position:0%
+do I have the following um criteria for
+you that this wall which has Windows on
+
+ align:start position:0%
+you that this wall which has Windows on
+ 
+
+ align:start position:0%
+you that this wall which has Windows on
+it you have to keep those windows
+
+ align:start position:0%
+it you have to keep those windows
+ 
+
+ align:start position:0%
+it you have to keep those windows
+and therefore somehow you got to get
+
+ align:start position:0%
+and therefore somehow you got to get
+ 
+
+ align:start position:0%
+and therefore somehow you got to get
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+into these
+
+ align:start position:0%
+into these
+ 
+
+ align:start position:0%
+into these
+guys however this one which has Windows
+
+ align:start position:0%
+guys however this one which has Windows
+ 
+
+ align:start position:0%
+guys however this one which has Windows
+on it you don't have to keep because in
+
+ align:start position:0%
+on it you don't have to keep because in
+ 
+
+ align:start position:0%
+on it you don't have to keep because in
+the Northend vocabulary it's on the
+
+ align:start position:0%
+the Northend vocabulary it's on the
+ 
+
+ align:start position:0%
+the Northend vocabulary it's on the
+corner but most of the time it does not
+
+ align:start position:0%
+corner but most of the time it does not
+ 
+
+ align:start position:0%
+corner but most of the time it does not
+have Windows because it's a bearing wall
+
+ align:start position:0%
+have Windows because it's a bearing wall
+ 
+
+ align:start position:0%
+have Windows because it's a bearing wall
+this one may not have been because of
+
+ align:start position:0%
+this one may not have been because of
+ 
+
+ align:start position:0%
+this one may not have been because of
+the Lan but we can assume that there's
+
+ align:start position:0%
+the Lan but we can assume that there's
+ 
+
+ align:start position:0%
+the Lan but we can assume that there's
+no windows here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you are welcome to build then up against
+
+ align:start position:0%
+you are welcome to build then up against
+ 
+
+ align:start position:0%
+you are welcome to build then up against
+this oops up against this but
+
+ align:start position:0%
+this oops up against this but
+ 
+
+ align:start position:0%
+this oops up against this but
+not not against this and of course
+
+ align:start position:0%
+not not against this and of course
+ 
+
+ align:start position:0%
+not not against this and of course
+you're welcome to build up against a
+
+ align:start position:0%
+you're welcome to build up against a
+ 
+
+ align:start position:0%
+you're welcome to build up against a
+ventilator building in anywhere you see
+
+ align:start position:0%
+ventilator building in anywhere you see
+ 
+
+ align:start position:0%
+ventilator building in anywhere you see
+fit as we've already done
+
+ align:start position:0%
+fit as we've already done
+ 
+
+ align:start position:0%
+fit as we've already done
+any well this class is a good poke
+
+ align:start position:0%
+any well this class is a good poke
+ 
+
+ align:start position:0%
+any well this class is a good poke
+through class you know there's been a
+
+ align:start position:0%
+through class you know there's been a
+ 
+
+ align:start position:0%
+through class you know there's been a
+lot of poking that's been going on here
+
+ align:start position:0%
+lot of poking that's been going on here
+ 
+
+ align:start position:0%
+lot of poking that's been going on here
+um everybody's three or four been poking
+
+ align:start position:0%
+um everybody's three or four been poking
+ 
+
+ align:start position:0%
+um everybody's three or four been poking
+um yes you can poke which I don't think
+
+ align:start position:0%
+um yes you can poke which I don't think
+ 
+
+ align:start position:0%
+um yes you can poke which I don't think
+you can poke in this territory just like
+
+ align:start position:0%
+you can poke in this territory just like
+ 
+
+ align:start position:0%
+you can poke in this territory just like
+to are we taking project into account
+
+ align:start position:0%
+to are we taking project into account
+ 
+
+ align:start position:0%
+to are we taking project into account
+assuming that all the ls are there well
+
+ align:start position:0%
+assuming that all the ls are there well
+ 
+
+ align:start position:0%
+assuming that all the ls are there well
+in theory uh yes this is your community
+
+ align:start position:0%
+in theory uh yes this is your community
+ 
+
+ align:start position:0%
+in theory uh yes this is your community
+you're all living here now and that
+
+ align:start position:0%
+you're all living here now and that
+ 
+
+ align:start position:0%
+you're all living here now and that
+relates to the
+
+ align:start position:0%
+relates to the
+ 
+
+ align:start position:0%
+relates to the
+program and you should be thinking about
+
+ align:start position:0%
+program and you should be thinking about
+ 
+
+ align:start position:0%
+program and you should be thinking about
+that um but you may have a discussion
+
+ align:start position:0%
+that um but you may have a discussion
+ 
+
+ align:start position:0%
+that um but you may have a discussion
+with her if you feel it's important um
+
+ align:start position:0%
+with her if you feel it's important um
+ 
+
+ align:start position:0%
+with her if you feel it's important um
+and there's one here that you need to
+
+ align:start position:0%
+and there's one here that you need to
+ 
+
+ align:start position:0%
+and there's one here that you need to
+have a discuss discussion with you just
+
+ align:start position:0%
+have a discuss discussion with you just
+ 
+
+ align:start position:0%
+have a discuss discussion with you just
+have like a little elevator right up to
+
+ align:start position:0%
+have like a little elevator right up to
+ 
+
+ align:start position:0%
+have like a little elevator right up to
+my house well in your in all these cases
+
+ align:start position:0%
+my house well in your in all these cases
+ 
+
+ align:start position:0%
+my house well in your in all these cases
+you're getting into your house in some
+
+ align:start position:0%
+you're getting into your house in some
+ 
+
+ align:start position:0%
+you're getting into your house in some
+way which we're not worrying about but
+
+ align:start position:0%
+way which we're not worrying about but
+ 
+
+ align:start position:0%
+way which we're not worrying about but
+it's not on the
+
+ align:start position:0%
+it's not on the
+ 
+
+ align:start position:0%
+it's not on the
+site uh except for
+
+ align:start position:0%
+site uh except for
+ 
+
+ align:start position:0%
+site uh except for
+her so she may have to mod modify it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so got it so far with
+
+ align:start position:0%
+so got it so far with
+ 
+
+ align:start position:0%
+so got it so far with
+me again uh just to put it in
+
+ align:start position:0%
+me again uh just to put it in
+ 
+
+ align:start position:0%
+me again uh just to put it in
+perspective this is at 16th this is at
+
+ align:start position:0%
+perspective this is at 16th this is at
+ 
+
+ align:start position:0%
+perspective this is at 16th this is at
+8th we're going to start working at 16th
+
+ align:start position:0%
+8th we're going to start working at 16th
+ 
+
+ align:start position:0%
+8th we're going to start working at 16th
+then we'll move to 8th and quarter and
+
+ align:start position:0%
+then we'll move to 8th and quarter and
+ 
+
+ align:start position:0%
+then we'll move to 8th and quarter and
+full size and
+
+ align:start position:0%
+full size and
+ 
+
+ align:start position:0%
+full size and
+so well we may I'm hoping that we're
+
+ align:start position:0%
+so well we may I'm hoping that we're
+ 
+
+ align:start position:0%
+so well we may I'm hoping that we're
+going to build a piece of this at four
+
+ align:start position:0%
+going to build a piece of this at four
+ 
+
+ align:start position:0%
+going to build a piece of this at four
+not the whole
+
+ align:start position:0%
+not the whole
+ 
+
+ align:start position:0%
+not the whole
+thing now there's another issue that I
+
+ align:start position:0%
+thing now there's another issue that I
+ 
+
+ align:start position:0%
+thing now there's another issue that I
+want to talk about which is what I call
+
+ align:start position:0%
+want to talk about which is what I call
+ 
+
+ align:start position:0%
+want to talk about which is what I call
+the ordinary and the
+
+ align:start position:0%
+the ordinary and the
+ 
+
+ align:start position:0%
+the ordinary and the
+extraordinary and that is that there's
+
+ align:start position:0%
+extraordinary and that is that there's
+ 
+
+ align:start position:0%
+extraordinary and that is that there's
+an ordinary environment coming down this
+
+ align:start position:0%
+an ordinary environment coming down this
+ 
+
+ align:start position:0%
+an ordinary environment coming down this
+street b b b b b b Bo and then there's
+
+ align:start position:0%
+street b b b b b b Bo and then there's
+ 
+
+ align:start position:0%
+street b b b b b b Bo and then there's
+some something that you might call
+
+ align:start position:0%
+some something that you might call
+ 
+
+ align:start position:0%
+some something that you might call
+extraordinary but not very nice the
+
+ align:start position:0%
+extraordinary but not very nice the
+ 
+
+ align:start position:0%
+extraordinary but not very nice the
+ventilator
+
+ align:start position:0%
+ventilator
+ 
+
+ align:start position:0%
+ventilator
+Tower and in the nature of this design
+
+ align:start position:0%
+Tower and in the nature of this design
+ 
+
+ align:start position:0%
+Tower and in the nature of this design
+I'd like to have you pay attention to
+
+ align:start position:0%
+I'd like to have you pay attention to
+ 
+
+ align:start position:0%
+I'd like to have you pay attention to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ordinary as it relates to the this if
+
+ align:start position:0%
+ordinary as it relates to the this if
+ 
+
+ align:start position:0%
+ordinary as it relates to the this if
+you so choose to work here which does
+
+ align:start position:0%
+you so choose to work here which does
+ 
+
+ align:start position:0%
+you so choose to work here which does
+not mean fake clonal whatever this is by
+
+ align:start position:0%
+not mean fake clonal whatever this is by
+ 
+
+ align:start position:0%
+not mean fake clonal whatever this is by
+any means but it means being compatible
+
+ align:start position:0%
+any means but it means being compatible
+ 
+
+ align:start position:0%
+any means but it means being compatible
+to it and then you might move into
+
+ align:start position:0%
+to it and then you might move into
+ 
+
+ align:start position:0%
+to it and then you might move into
+something that's more unusual
+
+ align:start position:0%
+something that's more unusual
+ 
+
+ align:start position:0%
+something that's more unusual
+extraordinary so we're going from the
+
+ align:start position:0%
+extraordinary so we're going from the
+ 
+
+ align:start position:0%
+extraordinary so we're going from the
+ordinary on this side to the
+
+ align:start position:0%
+ordinary on this side to the
+ 
+
+ align:start position:0%
+ordinary on this side to the
+extraordinary that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense the site has one more interesting
+
+ align:start position:0%
+sense the site has one more interesting
+ 
+
+ align:start position:0%
+sense the site has one more interesting
+and difficult issue what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+yes it does have that too and that's an
+
+ align:start position:0%
+yes it does have that too and that's an
+ 
+
+ align:start position:0%
+yes it does have that too and that's an
+interesting issue but there's another
+
+ align:start position:0%
+interesting issue but there's another
+ 
+
+ align:start position:0%
+interesting issue but there's another
+one is it on a grade sorry is it on a
+
+ align:start position:0%
+one is it on a grade sorry is it on a
+ 
+
+ align:start position:0%
+one is it on a grade sorry is it on a
+grade no it's flat we're making it flat
+
+ align:start position:0%
+grade no it's flat we're making it flat
+ 
+
+ align:start position:0%
+grade no it's flat we're making it flat
+space huh space well it's a bunch of
+
+ align:start position:0%
+space huh space well it's a bunch of
+ 
+
+ align:start position:0%
+space huh space well it's a bunch of
+dead spaces and that's our point of
+
+ align:start position:0%
+dead spaces and that's our point of
+ 
+
+ align:start position:0%
+dead spaces and that's our point of
+taking it to make life to it what else
+
+ align:start position:0%
+taking it to make life to it what else
+ 
+
+ align:start position:0%
+taking it to make life to it what else
+about the site
+
+ align:start position:0%
+about the site
+ 
+
+ align:start position:0%
+about the site
+Street this is forget about this forget
+
+ align:start position:0%
+Street this is forget about this forget
+ 
+
+ align:start position:0%
+Street this is forget about this forget
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this the height of it what about height
+
+ align:start position:0%
+this the height of it what about height
+ 
+
+ align:start position:0%
+this the height of it what about height
+well it it's sort of it's like the Cory
+
+ align:start position:0%
+well it it's sort of it's like the Cory
+ 
+
+ align:start position:0%
+well it it's sort of it's like the Cory
+because that's like the water part of it
+
+ align:start position:0%
+because that's like the water part of it
+ 
+
+ align:start position:0%
+because that's like the water part of it
+the lower part
+
+ align:start position:0%
+the lower part
+ 
+
+ align:start position:0%
+the lower part
+else yeah but and huh come on come on
+
+ align:start position:0%
+else yeah but and huh come on come on
+ 
+
+ align:start position:0%
+else yeah but and huh come on come on
+Southern the things BL the
+
+ align:start position:0%
+Southern the things BL the
+ 
+
+ align:start position:0%
+Southern the things BL the
+southern so you don't have a lot of
+
+ align:start position:0%
+southern so you don't have a lot of
+ 
+
+ align:start position:0%
+southern so you don't have a lot of
+light yeah it's not a nice sight I mean
+
+ align:start position:0%
+light yeah it's not a nice sight I mean
+ 
+
+ align:start position:0%
+light yeah it's not a nice sight I mean
+you got a it's uh the sun is in the
+
+ align:start position:0%
+you got a it's uh the sun is in the
+ 
+
+ align:start position:0%
+you got a it's uh the sun is in the
+let's do it the sun in the winter is is
+
+ align:start position:0%
+let's do it the sun in the winter is is
+ 
+
+ align:start position:0%
+let's do it the sun in the winter is is
+it's rising somewhere in
+
+ align:start position:0%
+it's rising somewhere in
+ 
+
+ align:start position:0%
+it's rising somewhere in
+here I think it might get a little light
+
+ align:start position:0%
+here I think it might get a little light
+ 
+
+ align:start position:0%
+here I think it might get a little light
+no not at rise but maybe at noon it's
+
+ align:start position:0%
+no not at rise but maybe at noon it's
+ 
+
+ align:start position:0%
+no not at rise but maybe at noon it's
+going to get some light and then it's
+
+ align:start position:0%
+going to get some light and then it's
+ 
+
+ align:start position:0%
+going to get some light and then it's
+coming around and setting probably about
+
+ align:start position:0%
+coming around and setting probably about
+ 
+
+ align:start position:0%
+coming around and setting probably about
+here and now you get a little light on
+
+ align:start position:0%
+here and now you get a little light on
+ 
+
+ align:start position:0%
+here and now you get a little light on
+here on the summer it's better it's
+
+ align:start position:0%
+here on the summer it's better it's
+ 
+
+ align:start position:0%
+here on the summer it's better it's
+rising over here and probably get some
+
+ align:start position:0%
+rising over here and probably get some
+ 
+
+ align:start position:0%
+rising over here and probably get some
+light and maybe get some light all day
+
+ align:start position:0%
+light and maybe get some light all day
+ 
+
+ align:start position:0%
+light and maybe get some light all day
+but clearly these guys being so tall are
+
+ align:start position:0%
+but clearly these guys being so tall are
+ 
+
+ align:start position:0%
+but clearly these guys being so tall are
+casting
+
+ align:start position:0%
+casting
+ 
+
+ align:start position:0%
+casting
+Shadows most sites that you get in
+
+ align:start position:0%
+Shadows most sites that you get in
+ 
+
+ align:start position:0%
+Shadows most sites that you get in
+architectural School are south facing
+
+ align:start position:0%
+architectural School are south facing
+ 
+
+ align:start position:0%
+architectural School are south facing
+with a beautiful view that's not the
+
+ align:start position:0%
+with a beautiful view that's not the
+ 
+
+ align:start position:0%
+with a beautiful view that's not the
+case here this is uh North facing with a
+
+ align:start position:0%
+case here this is uh North facing with a
+ 
+
+ align:start position:0%
+case here this is uh North facing with a
+great view because we're seeing Sarah's
+
+ align:start position:0%
+great view because we're seeing Sarah's
+ 
+
+ align:start position:0%
+great view because we're seeing Sarah's
+wonderful building across the
+
+ align:start position:0%
+wonderful building across the
+ 
+
+ align:start position:0%
+wonderful building across the
+street um but it's
+
+ align:start position:0%
+street um but it's
+ 
+
+ align:start position:0%
+street um but it's
+different so light is an extreme
+
+ align:start position:0%
+different so light is an extreme
+ 
+
+ align:start position:0%
+different so light is an extreme
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+issue how we bounce light around how we
+
+ align:start position:0%
+issue how we bounce light around how we
+ 
+
+ align:start position:0%
+issue how we bounce light around how we
+get sunlight down into it and that makes
+
+ align:start position:0%
+get sunlight down into it and that makes
+ 
+
+ align:start position:0%
+get sunlight down into it and that makes
+this site
+
+ align:start position:0%
+this site
+ 
+
+ align:start position:0%
+this site
+unique you have to think about
+
+ align:start position:0%
+unique you have to think about
+ 
+
+ align:start position:0%
+unique you have to think about
+that I want you to go back to the site
+
+ align:start position:0%
+that I want you to go back to the site
+ 
+
+ align:start position:0%
+that I want you to go back to the site
+and look at the site now from the eyes
+
+ align:start position:0%
+and look at the site now from the eyes
+ 
+
+ align:start position:0%
+and look at the site now from the eyes
+of this project which I'm going to give
+
+ align:start position:0%
+of this project which I'm going to give
+ 
+
+ align:start position:0%
+of this project which I'm going to give
+you uh and of course you're aware of it
+
+ align:start position:0%
+you uh and of course you're aware of it
+ 
+
+ align:start position:0%
+you uh and of course you're aware of it
+one of the things that did not come out
+
+ align:start position:0%
+one of the things that did not come out
+ 
+
+ align:start position:0%
+one of the things that did not come out
+in the last project which you might
+
+ align:start position:0%
+in the last project which you might
+ 
+
+ align:start position:0%
+in the last project which you might
+think about is views from this site that
+
+ align:start position:0%
+think about is views from this site that
+ 
+
+ align:start position:0%
+think about is views from this site that
+you might see custom house tower down
+
+ align:start position:0%
+you might see custom house tower down
+ 
+
+ align:start position:0%
+you might see custom house tower down
+the street Etc next question what are we
+
+ align:start position:0%
+the street Etc next question what are we
+ 
+
+ align:start position:0%
+the street Etc next question what are we
+going to do with
+
+ align:start position:0%
+going to do with
+ 
+
+ align:start position:0%
+going to do with
+it this is the most important part I
+
+ align:start position:0%
+it this is the most important part I
+ 
+
+ align:start position:0%
+it this is the most important part I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+think we are going to make and design a
+
+ align:start position:0%
+think we are going to make and design a
+ 
+
+ align:start position:0%
+think we are going to make and design a
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+here that will bring together you guys
+
+ align:start position:0%
+here that will bring together you guys
+ 
+
+ align:start position:0%
+here that will bring together you guys
+in your community in the sky North
+
+ align:start position:0%
+in your community in the sky North
+ 
+
+ align:start position:0%
+in your community in the sky North
+Enders who are living here tourists and
+
+ align:start position:0%
+Enders who are living here tourists and
+ 
+
+ align:start position:0%
+Enders who are living here tourists and
+anyone else you might think of into a
+
+ align:start position:0%
+anyone else you might think of into a
+ 
+
+ align:start position:0%
+anyone else you might think of into a
+meeting
+
+ align:start position:0%
+meeting
+ 
+
+ align:start position:0%
+meeting
+place which used to be called a
+
+ align:start position:0%
+place which used to be called a
+ 
+
+ align:start position:0%
+place which used to be called a
+community center which of course is the
+
+ align:start position:0%
+community center which of course is the
+ 
+
+ align:start position:0%
+community center which of course is the
+kiss of death to making anything
+
+ align:start position:0%
+kiss of death to making anything
+ 
+
+ align:start position:0%
+kiss of death to making anything
+Community if you ever label Community
+
+ align:start position:0%
+Community if you ever label Community
+ 
+
+ align:start position:0%
+Community if you ever label Community
+Center nobody will go there so we're not
+
+ align:start position:0%
+Center nobody will go there so we're not
+ 
+
+ align:start position:0%
+Center nobody will go there so we're not
+making in the typical sense a community
+
+ align:start position:0%
+making in the typical sense a community
+ 
+
+ align:start position:0%
+making in the typical sense a community
+center but we are making a place for
+
+ align:start position:0%
+center but we are making a place for
+ 
+
+ align:start position:0%
+center but we are making a place for
+people to come together in our age in in
+
+ align:start position:0%
+people to come together in our age in in
+ 
+
+ align:start position:0%
+people to come together in our age in in
+this age you guys could sit here all day
+
+ align:start position:0%
+this age you guys could sit here all day
+ 
+
+ align:start position:0%
+this age you guys could sit here all day
+long in your
+
+ align:start position:0%
+long in your
+ 
+
+ align:start position:0%
+long in your
+computer uh and do something but there
+
+ align:start position:0%
+computer uh and do something but there
+ 
+
+ align:start position:0%
+computer uh and do something but there
+may be a question about the quality of
+
+ align:start position:0%
+may be a question about the quality of
+ 
+
+ align:start position:0%
+may be a question about the quality of
+life that you have that may want you to
+
+ align:start position:0%
+life that you have that may want you to
+ 
+
+ align:start position:0%
+life that you have that may want you to
+get out for some reason for work or for
+
+ align:start position:0%
+get out for some reason for work or for
+ 
+
+ align:start position:0%
+get out for some reason for work or for
+whatever we are making that place of
+
+ align:start position:0%
+whatever we are making that place of
+ 
+
+ align:start position:0%
+whatever we are making that place of
+bringing together not only you
+
+ align:start position:0%
+bringing together not only you
+ 
+
+ align:start position:0%
+bringing together not only you
+guys but also North Enders because life
+
+ align:start position:0%
+guys but also North Enders because life
+ 
+
+ align:start position:0%
+guys but also North Enders because life
+is about meeting other people and
+
+ align:start position:0%
+is about meeting other people and
+ 
+
+ align:start position:0%
+is about meeting other people and
+architecture is about bringing people
+
+ align:start position:0%
+architecture is about bringing people
+ 
+
+ align:start position:0%
+architecture is about bringing people
+together so we're making a coming
+
+ align:start position:0%
+together so we're making a coming
+ 
+
+ align:start position:0%
+together so we're making a coming
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+space that's our program
+
+ align:start position:0%
+space that's our program
+ 
+
+ align:start position:0%
+space that's our program
+basically and that's up to you to
+
+ align:start position:0%
+basically and that's up to you to
+ 
+
+ align:start position:0%
+basically and that's up to you to
+decide to be a good architect is
+
+ align:start position:0%
+decide to be a good architect is
+ 
+
+ align:start position:0%
+decide to be a good architect is
+important to be a good
+
+ align:start position:0%
+important to be a good
+ 
+
+ align:start position:0%
+important to be a good
+designer but to be a good programmer to
+
+ align:start position:0%
+designer but to be a good programmer to
+ 
+
+ align:start position:0%
+designer but to be a good programmer to
+think about the spirit of what the
+
+ align:start position:0%
+think about the spirit of what the
+ 
+
+ align:start position:0%
+think about the spirit of what the
+architecture is going to be is a real
+
+ align:start position:0%
+architecture is going to be is a real
+ 
+
+ align:start position:0%
+architecture is going to be is a real
+genius and that's what I'm asking you
+
+ align:start position:0%
+genius and that's what I'm asking you
+ 
+
+ align:start position:0%
+genius and that's what I'm asking you
+guys to
+
+ align:start position:0%
+guys to
+ 
+
+ align:start position:0%
+guys to
+be I'm asking you to be very creative in
+
+ align:start position:0%
+be I'm asking you to be very creative in
+ 
+
+ align:start position:0%
+be I'm asking you to be very creative in
+thinking about what brings people
+
+ align:start position:0%
+thinking about what brings people
+ 
+
+ align:start position:0%
+thinking about what brings people
+together and then design the most
+
+ align:start position:0%
+together and then design the most
+ 
+
+ align:start position:0%
+together and then design the most
+beautiful place for
+
+ align:start position:0%
+beautiful place for
+ 
+
+ align:start position:0%
+beautiful place for
+it I believe very much in this way of
+
+ align:start position:0%
+it I believe very much in this way of
+ 
+
+ align:start position:0%
+it I believe very much in this way of
+working because otherwise I think you
+
+ align:start position:0%
+working because otherwise I think you
+ 
+
+ align:start position:0%
+working because otherwise I think you
+come out to be teats in the way that you
+
+ align:start position:0%
+come out to be teats in the way that you
+ 
+
+ align:start position:0%
+come out to be teats in the way that you
+are just hired architects and do what
+
+ align:start position:0%
+are just hired architects and do what
+ 
+
+ align:start position:0%
+are just hired architects and do what
+somebody tells you and I believe that
+
+ align:start position:0%
+somebody tells you and I believe that
+ 
+
+ align:start position:0%
+somebody tells you and I believe that
+the architecture profession can offer
+
+ align:start position:0%
+the architecture profession can offer
+ 
+
+ align:start position:0%
+the architecture profession can offer
+more than that you're not Engineers
+
+ align:start position:0%
+more than that you're not Engineers
+ 
+
+ align:start position:0%
+more than that you're not Engineers
+you're not designing just a bridge to
+
+ align:start position:0%
+you're not designing just a bridge to
+ 
+
+ align:start position:0%
+you're not designing just a bridge to
+stay up you're designing life or an echo
+
+ align:start position:0%
+stay up you're designing life or an echo
+ 
+
+ align:start position:0%
+stay up you're designing life or an echo
+of life so in this case what is it that
+
+ align:start position:0%
+of life so in this case what is it that
+ 
+
+ align:start position:0%
+of life so in this case what is it that
+the echo
+
+ align:start position:0%
+the echo
+ 
+
+ align:start position:0%
+the echo
+is the program which I'll hand out in a
+
+ align:start position:0%
+is the program which I'll hand out in a
+ 
+
+ align:start position:0%
+is the program which I'll hand out in a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is about 6,000 square feet of of
+
+ align:start position:0%
+um is about 6,000 square feet of of
+ 
+
+ align:start position:0%
+um is about 6,000 square feet of of
+stuff which is more than that's about uh
+
+ align:start position:0%
+stuff which is more than that's about uh
+ 
+
+ align:start position:0%
+stuff which is more than that's about uh
+well we all cheated but that's about six
+
+ align:start position:0%
+well we all cheated but that's about six
+ 
+
+ align:start position:0%
+well we all cheated but that's about six
+of these right five of
+
+ align:start position:0%
+of these right five of
+ 
+
+ align:start position:0%
+of these right five of
+these or it should
+
+ align:start position:0%
+these or it should
+ 
+
+ align:start position:0%
+these or it should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+um so somehow you're going to get 6,000
+
+ align:start position:0%
+um so somehow you're going to get 6,000
+ 
+
+ align:start position:0%
+um so somehow you're going to get 6,000
+roughly 6,000 it can be
+
+ align:start position:0%
+roughly 6,000 it can be
+ 
+
+ align:start position:0%
+roughly 6,000 it can be
+more there should be in that
+
+ align:start position:0%
+more there should be in that
+ 
+
+ align:start position:0%
+more there should be in that
+program no matter what you're doing some
+
+ align:start position:0%
+program no matter what you're doing some
+ 
+
+ align:start position:0%
+program no matter what you're doing some
+space in there where a good number of
+
+ align:start position:0%
+space in there where a good number of
+ 
+
+ align:start position:0%
+space in there where a good number of
+people can
+
+ align:start position:0%
+people can
+ 
+
+ align:start position:0%
+people can
+meet together a a meeting
+
+ align:start position:0%
+meet together a a meeting
+ 
+
+ align:start position:0%
+meet together a a meeting
+place I don't know what that is is that
+
+ align:start position:0%
+place I don't know what that is is that
+ 
+
+ align:start position:0%
+place I don't know what that is is that
+an exhibition hall for art is that a
+
+ align:start position:0%
+an exhibition hall for art is that a
+ 
+
+ align:start position:0%
+an exhibition hall for art is that a
+movie theater is that an ice skating
+
+ align:start position:0%
+movie theater is that an ice skating
+ 
+
+ align:start position:0%
+movie theater is that an ice skating
+rink I don't know what it is that's up
+
+ align:start position:0%
+rink I don't know what it is that's up
+ 
+
+ align:start position:0%
+rink I don't know what it is that's up
+to you to think
+
+ align:start position:0%
+to you to think
+ 
+
+ align:start position:0%
+to you to think
+about there should be some spaces in
+
+ align:start position:0%
+about there should be some spaces in
+ 
+
+ align:start position:0%
+about there should be some spaces in
+here that are mediumsized
+
+ align:start position:0%
+here that are mediumsized
+ 
+
+ align:start position:0%
+here that are mediumsized
+where people might come together to have
+
+ align:start position:0%
+where people might come together to have
+ 
+
+ align:start position:0%
+where people might come together to have
+meetings or
+
+ align:start position:0%
+meetings or
+ 
+
+ align:start position:0%
+meetings or
+daycare or elder
+
+ align:start position:0%
+daycare or elder
+ 
+
+ align:start position:0%
+daycare or elder
+care and there should be some small
+
+ align:start position:0%
+care and there should be some small
+ 
+
+ align:start position:0%
+care and there should be some small
+spaces in here here where you might work
+
+ align:start position:0%
+spaces in here here where you might work
+ 
+
+ align:start position:0%
+spaces in here here where you might work
+maybe you work all day on your computer
+
+ align:start position:0%
+maybe you work all day on your computer
+ 
+
+ align:start position:0%
+maybe you work all day on your computer
+and in virtual world but this is your
+
+ align:start position:0%
+and in virtual world but this is your
+ 
+
+ align:start position:0%
+and in virtual world but this is your
+true life is making
+
+ align:start position:0%
+true life is making
+ 
+
+ align:start position:0%
+true life is making
+furniture and we may be shifting in our
+
+ align:start position:0%
+furniture and we may be shifting in our
+ 
+
+ align:start position:0%
+furniture and we may be shifting in our
+ways of thinking about work and
+
+ align:start position:0%
+ways of thinking about work and
+ 
+
+ align:start position:0%
+ways of thinking about work and
+life uh as it's been before so maybe you
+
+ align:start position:0%
+life uh as it's been before so maybe you
+ 
+
+ align:start position:0%
+life uh as it's been before so maybe you
+make furniture there and you sell it on
+
+ align:start position:0%
+make furniture there and you sell it on
+ 
+
+ align:start position:0%
+make furniture there and you sell it on
+your computer in your house I don't know
+
+ align:start position:0%
+your computer in your house I don't know
+ 
+
+ align:start position:0%
+your computer in your house I don't know
+that's up to you so it might be
+
+ align:start position:0%
+that's up to you so it might be
+ 
+
+ align:start position:0%
+that's up to you so it might be
+workspaces there the point is there's
+
+ align:start position:0%
+workspaces there the point is there's
+ 
+
+ align:start position:0%
+workspaces there the point is there's
+some small there's some medium siiz and
+
+ align:start position:0%
+some small there's some medium siiz and
+ 
+
+ align:start position:0%
+some small there's some medium siiz and
+there's one big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one as I said before all good
+
+ align:start position:0%
+one as I said before all good
+ 
+
+ align:start position:0%
+one as I said before all good
+architecture has a vertical connection
+
+ align:start position:0%
+architecture has a vertical connection
+ 
+
+ align:start position:0%
+architecture has a vertical connection
+and a horizontal connection of space
+
+ align:start position:0%
+and a horizontal connection of space
+ 
+
+ align:start position:0%
+and a horizontal connection of space
+this building should have that a
+
+ align:start position:0%
+this building should have that a
+ 
+
+ align:start position:0%
+this building should have that a
+vertical and a horizontal so therefore
+
+ align:start position:0%
+vertical and a horizontal so therefore
+ 
+
+ align:start position:0%
+vertical and a horizontal so therefore
+space in some way should be flowing
+
+ align:start position:0%
+space in some way should be flowing
+ 
+
+ align:start position:0%
+space in some way should be flowing
+through the building vertically and
+
+ align:start position:0%
+through the building vertically and
+ 
+
+ align:start position:0%
+through the building vertically and
+horizontally some part of the building
+
+ align:start position:0%
+horizontally some part of the building
+ 
+
+ align:start position:0%
+horizontally some part of the building
+but not all should get up to be a
+
+ align:start position:0%
+but not all should get up to be a
+ 
+
+ align:start position:0%
+but not all should get up to be a
+companion to these ever buildings which
+
+ align:start position:0%
+companion to these ever buildings which
+ 
+
+ align:start position:0%
+companion to these ever buildings which
+is three stories or so
+
+ align:start position:0%
+is three stories or so
+ 
+
+ align:start position:0%
+is three stories or so
+but the whole thing doesn't have to do
+
+ align:start position:0%
+but the whole thing doesn't have to do
+ 
+
+ align:start position:0%
+but the whole thing doesn't have to do
+that now let me just put in parenthesis
+
+ align:start position:0%
+that now let me just put in parenthesis
+ 
+
+ align:start position:0%
+that now let me just put in parenthesis
+part of this project is to get you to
+
+ align:start position:0%
+part of this project is to get you to
+ 
+
+ align:start position:0%
+part of this project is to get you to
+think about three-dimensional
+
+ align:start position:0%
+think about three-dimensional
+ 
+
+ align:start position:0%
+think about three-dimensional
+programming and how you express that
+
+ align:start position:0%
+programming and how you express that
+ 
+
+ align:start position:0%
+programming and how you express that
+architecturally because for the most
+
+ align:start position:0%
+architecturally because for the most
+ 
+
+ align:start position:0%
+architecturally because for the most
+part you've been doing it on in your
+
+ align:start position:0%
+part you've been doing it on in your
+ 
+
+ align:start position:0%
+part you've been doing it on in your
+head you're able to keep track of one or
+
+ align:start position:0%
+head you're able to keep track of one or
+ 
+
+ align:start position:0%
+head you're able to keep track of one or
+two or three stories but now you can't
+
+ align:start position:0%
+two or three stories but now you can't
+ 
+
+ align:start position:0%
+two or three stories but now you can't
+you're going to have to think
+
+ align:start position:0%
+you're going to have to think
+ 
+
+ align:start position:0%
+you're going to have to think
+three-dimensionally and work
+
+ align:start position:0%
+three-dimensionally and work
+ 
+
+ align:start position:0%
+three-dimensionally and work
+three-dimensionally so the program is
+
+ align:start position:0%
+three-dimensionally so the program is
+ 
+
+ align:start position:0%
+three-dimensionally so the program is
+intended not to be horizontal suburb
+
+ align:start position:0%
+intended not to be horizontal suburb
+ 
+
+ align:start position:0%
+intended not to be horizontal suburb
+Community Center right it's not
+
+ align:start position:0%
+Community Center right it's not
+ 
+
+ align:start position:0%
+Community Center right it's not
+that about 2third of the side should be
+
+ align:start position:0%
+that about 2third of the side should be
+ 
+
+ align:start position:0%
+that about 2third of the side should be
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+open or left
+
+ align:start position:0%
+open or left
+ 
+
+ align:start position:0%
+open or left
+untouched so that which is in the last
+
+ align:start position:0%
+untouched so that which is in the last
+ 
+
+ align:start position:0%
+untouched so that which is in the last
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+this that wonderful experience that we
+
+ align:start position:0%
+this that wonderful experience that we
+ 
+
+ align:start position:0%
+this that wonderful experience that we
+had the very first day of going to the
+
+ align:start position:0%
+had the very first day of going to the
+ 
+
+ align:start position:0%
+had the very first day of going to the
+Quarry of nature call it nature water it
+
+ align:start position:0%
+Quarry of nature call it nature water it
+ 
+
+ align:start position:0%
+Quarry of nature call it nature water it
+wasn't nature but that's okay we in some
+
+ align:start position:0%
+wasn't nature but that's okay we in some
+ 
+
+ align:start position:0%
+wasn't nature but that's okay we in some
+form are bringing nature back into the
+
+ align:start position:0%
+form are bringing nature back into the
+ 
+
+ align:start position:0%
+form are bringing nature back into the
+city which is badly needed in this part
+
+ align:start position:0%
+city which is badly needed in this part
+ 
+
+ align:start position:0%
+city which is badly needed in this part
+of this city nothing is staying this
+
+ align:start position:0%
+of this city nothing is staying this
+ 
+
+ align:start position:0%
+of this city nothing is staying this
+here but I'm inviting you to think about
+
+ align:start position:0%
+here but I'm inviting you to think about
+ 
+
+ align:start position:0%
+here but I'm inviting you to think about
+what does it mean to bring nature back
+
+ align:start position:0%
+what does it mean to bring nature back
+ 
+
+ align:start position:0%
+what does it mean to bring nature back
+into the city for a place that's as
+
+ align:start position:0%
+into the city for a place that's as
+ 
+
+ align:start position:0%
+into the city for a place that's as
+dense as this that they have one tree
+
+ align:start position:0%
+dense as this that they have one tree
+ 
+
+ align:start position:0%
+dense as this that they have one tree
+here and one here and I guess some here
+
+ align:start position:0%
+here and one here and I guess some here
+ 
+
+ align:start position:0%
+here and one here and I guess some here
+no water anywhere in the except for the
+
+ align:start position:0%
+no water anywhere in the except for the
+ 
+
+ align:start position:0%
+no water anywhere in the except for the
+Fountain and and the PA R's
+
+ align:start position:0%
+Fountain and and the PA R's
+ 
+
+ align:start position:0%
+Fountain and and the PA R's
+wall to my knowledge no natural um stone
+
+ align:start position:0%
+wall to my knowledge no natural um stone
+ 
+
+ align:start position:0%
+wall to my knowledge no natural um stone
+or no natural so-call natural grass in
+
+ align:start position:0%
+or no natural so-call natural grass in
+ 
+
+ align:start position:0%
+or no natural so-call natural grass in
+anywhere in the nor fin for a community
+
+ align:start position:0%
+anywhere in the nor fin for a community
+ 
+
+ align:start position:0%
+anywhere in the nor fin for a community
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+private so what does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean you might bring water into this
+
+ align:start position:0%
+mean you might bring water into this
+ 
+
+ align:start position:0%
+mean you might bring water into this
+site because it used to be Water by the
+
+ align:start position:0%
+site because it used to be Water by the
+ 
+
+ align:start position:0%
+site because it used to be Water by the
+way this was a short
+
+ align:start position:0%
+way this was a short
+ 
+
+ align:start position:0%
+way this was a short
+one you might bring trees into this site
+
+ align:start position:0%
+one you might bring trees into this site
+ 
+
+ align:start position:0%
+one you might bring trees into this site
+but if you're bring
+
+ align:start position:0%
+but if you're bring
+ 
+
+ align:start position:0%
+but if you're bring
+trees do not do what Architects do which
+
+ align:start position:0%
+trees do not do what Architects do which
+ 
+
+ align:start position:0%
+trees do not do what Architects do which
+is what I call throwing darts at the
+
+ align:start position:0%
+is what I call throwing darts at the
+ 
+
+ align:start position:0%
+is what I call throwing darts at the
+drawing 10 minutes before it's do and
+
+ align:start position:0%
+drawing 10 minutes before it's do and
+ 
+
+ align:start position:0%
+drawing 10 minutes before it's do and
+placing
+
+ align:start position:0%
+placing
+ 
+
+ align:start position:0%
+placing
+trees and then you know they you put
+
+ align:start position:0%
+trees and then you know they you put
+ 
+
+ align:start position:0%
+trees and then you know they you put
+trees and then you put little benches on
+
+ align:start position:0%
+trees and then you put little benches on
+ 
+
+ align:start position:0%
+trees and then you put little benches on
+it and you call it open space you think
+
+ align:start position:0%
+it and you call it open space you think
+ 
+
+ align:start position:0%
+it and you call it open space you think
+people are going to H live happily ever
+
+ align:start position:0%
+people are going to H live happily ever
+ 
+
+ align:start position:0%
+people are going to H live happily ever
+after and they're not it's going to have
+
+ align:start position:0%
+after and they're not it's going to have
+ 
+
+ align:start position:0%
+after and they're not it's going to have
+to be more than that if you do trees or
+
+ align:start position:0%
+to be more than that if you do trees or
+ 
+
+ align:start position:0%
+to be more than that if you do trees or
+any kind of
+
+ align:start position:0%
+any kind of
+ 
+
+ align:start position:0%
+any kind of
+vegetation it could be a way of using uh
+
+ align:start position:0%
+vegetation it could be a way of using uh
+ 
+
+ align:start position:0%
+vegetation it could be a way of using uh
+materials Stone from the Quarry maybe
+
+ align:start position:0%
+materials Stone from the Quarry maybe
+ 
+
+ align:start position:0%
+materials Stone from the Quarry maybe
+you go back to the quy and get some
+
+ align:start position:0%
+you go back to the quy and get some
+ 
+
+ align:start position:0%
+you go back to the quy and get some
+Quarry materials and bring it here and
+
+ align:start position:0%
+Quarry materials and bring it here and
+ 
+
+ align:start position:0%
+Quarry materials and bring it here and
+civilize it in some way combine it with
+
+ align:start position:0%
+civilize it in some way combine it with
+ 
+
+ align:start position:0%
+civilize it in some way combine it with
+water and trees
+
+ align:start position:0%
+water and trees
+ 
+
+ align:start position:0%
+water and trees
+that's up to you decide what that is but
+
+ align:start position:0%
+that's up to you decide what that is but
+ 
+
+ align:start position:0%
+that's up to you decide what that is but
+when you're
+
+ align:start position:0%
+when you're
+ 
+
+ align:start position:0%
+when you're
+done with this and
+
+ align:start position:0%
+done with this and
+ 
+
+ align:start position:0%
+done with this and
+this people no longer are going down the
+
+ align:start position:0%
+this people no longer are going down the
+ 
+
+ align:start position:0%
+this people no longer are going down the
+red line to see Paul R's house they're
+
+ align:start position:0%
+red line to see Paul R's house they're
+ 
+
+ align:start position:0%
+red line to see Paul R's house they're
+going down a purple line to see your
+
+ align:start position:0%
+going down a purple line to see your
+ 
+
+ align:start position:0%
+going down a purple line to see your
+place because it's much better than
+
+ align:start position:0%
+place because it's much better than
+ 
+
+ align:start position:0%
+place because it's much better than
+anything that they ever seen so those
+
+ align:start position:0%
+anything that they ever seen so those
+ 
+
+ align:start position:0%
+anything that they ever seen so those
+people coming from Ohio where I came
+
+ align:start position:0%
+people coming from Ohio where I came
+ 
+
+ align:start position:0%
+people coming from Ohio where I came
+from could care less about Paul's Place
+
+ align:start position:0%
+from could care less about Paul's Place
+ 
+
+ align:start position:0%
+from could care less about Paul's Place
+but they really care about your place
+
+ align:start position:0%
+but they really care about your place
+ 
+
+ align:start position:0%
+but they really care about your place
+such as a little Park in New York where
+
+ align:start position:0%
+such as a little Park in New York where
+ 
+
+ align:start position:0%
+such as a little Park in New York where
+there's a waterfall at the back you know
+
+ align:start position:0%
+there's a waterfall at the back you know
+ 
+
+ align:start position:0%
+there's a waterfall at the back you know
+and never know the name of it you
+
+ align:start position:0%
+and never know the name of it you
+ 
+
+ align:start position:0%
+and never know the name of it you
+another one yep wonderful little Oasis
+
+ align:start position:0%
+another one yep wonderful little Oasis
+ 
+
+ align:start position:0%
+another one yep wonderful little Oasis
+in the middle of Chaos in my opinion um
+
+ align:start position:0%
+in the middle of Chaos in my opinion um
+ 
+
+ align:start position:0%
+in the middle of Chaos in my opinion um
+those are special places that's what
+
+ align:start position:0%
+those are special places that's what
+ 
+
+ align:start position:0%
+those are special places that's what
+you're making a very special
+
+ align:start position:0%
+you're making a very special
+ 
+
+ align:start position:0%
+you're making a very special
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+the turn or the complete James Joy cycle
+
+ align:start position:0%
+the turn or the complete James Joy cycle
+ 
+
+ align:start position:0%
+the turn or the complete James Joy cycle
+from the beginning of the quy back to
+
+ align:start position:0%
+from the beginning of the quy back to
+ 
+
+ align:start position:0%
+from the beginning of the quy back to
+something like the
+
+ align:start position:0%
+something like the
+ 
+
+ align:start position:0%
+something like the
+quy you with me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+um well I've already said that the
+
+ align:start position:0%
+um well I've already said that the
+ 
+
+ align:start position:0%
+um well I've already said that the
+ordinary and the extraordinary has to be
+
+ align:start position:0%
+ordinary and the extraordinary has to be
+ 
+
+ align:start position:0%
+ordinary and the extraordinary has to be
+combined somehow on the site so you're
+
+ align:start position:0%
+combined somehow on the site so you're
+ 
+
+ align:start position:0%
+combined somehow on the site so you're
+not parking a spaceship in here
+
+ align:start position:0%
+not parking a spaceship in here
+ 
+
+ align:start position:0%
+not parking a spaceship in here
+know that's not what you're doing it's
+
+ align:start position:0%
+know that's not what you're doing it's
+ 
+
+ align:start position:0%
+know that's not what you're doing it's
+not a landing field landing pad
+
+ align:start position:0%
+not a landing field landing pad
+ 
+
+ align:start position:0%
+not a landing field landing pad
+for sorry you thought I had forgotten
+
+ align:start position:0%
+for sorry you thought I had forgotten
+ 
+
+ align:start position:0%
+for sorry you thought I had forgotten
+but I will remember it for 20
+
+ align:start position:0%
+but I will remember it for 20
+ 
+
+ align:start position:0%
+but I will remember it for 20
+years um so you're not doing that but
+
+ align:start position:0%
+years um so you're not doing that but
+ 
+
+ align:start position:0%
+years um so you're not doing that but
+you're also not imitating what's there
+
+ align:start position:0%
+you're also not imitating what's there
+ 
+
+ align:start position:0%
+you're also not imitating what's there
+it's it's a bore don't do that no you
+
+ align:start position:0%
+it's it's a bore don't do that no you
+ 
+
+ align:start position:0%
+it's it's a bore don't do that no you
+guys none of you guys did that in
+
+ align:start position:0%
+guys none of you guys did that in
+ 
+
+ align:start position:0%
+guys none of you guys did that in
+this um how can you make a billboard in
+
+ align:start position:0%
+this um how can you make a billboard in
+ 
+
+ align:start position:0%
+this um how can you make a billboard in
+there like that which I'm not suggesting
+
+ align:start position:0%
+there like that which I'm not suggesting
+ 
+
+ align:start position:0%
+there like that which I'm not suggesting
+you did but also relate incredible
+
+ align:start position:0%
+you did but also relate incredible
+ 
+
+ align:start position:0%
+you did but also relate incredible
+problems beautiful idea I mean how to do
+
+ align:start position:0%
+problems beautiful idea I mean how to do
+ 
+
+ align:start position:0%
+problems beautiful idea I mean how to do
+that I don't
+
+ align:start position:0%
+that I don't
+ 
+
+ align:start position:0%
+that I don't
+know but that's what your that's your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+challenge finally in my opinion in any
+
+ align:start position:0%
+challenge finally in my opinion in any
+ 
+
+ align:start position:0%
+challenge finally in my opinion in any
+good building it's the public space of
+
+ align:start position:0%
+good building it's the public space of
+ 
+
+ align:start position:0%
+good building it's the public space of
+paths and places
+
+ align:start position:0%
+paths and places
+ 
+
+ align:start position:0%
+paths and places
+which I will talk about the space
+
+ align:start position:0%
+which I will talk about the space
+ 
+
+ align:start position:0%
+which I will talk about the space
+between the U
+
+ align:start position:0%
+between the U
+ 
+
+ align:start position:0%
+between the U
+assignment number
+
+ align:start position:0%
+assignment number
+ 
+
+ align:start position:0%
+assignment number
+six uh in the sequence of things first
+
+ align:start position:0%
+six uh in the sequence of things first
+ 
+
+ align:start position:0%
+six uh in the sequence of things first
+for this which is due next
+
+ align:start position:0%
+for this which is due next
+ 
+
+ align:start position:0%
+for this which is due next
+Tuesday uh I'm going to read it for this
+
+ align:start position:0%
+Tuesday uh I'm going to read it for this
+ 
+
+ align:start position:0%
+Tuesday uh I'm going to read it for this
+assignment you are asked to think about
+
+ align:start position:0%
+assignment you are asked to think about
+ 
+
+ align:start position:0%
+assignment you are asked to think about
+what this building wants to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be I'm asking you
+
+ align:start position:0%
+be I'm asking you
+ 
+
+ align:start position:0%
+be I'm asking you
+again what is the program that would
+
+ align:start position:0%
+again what is the program that would
+ 
+
+ align:start position:0%
+again what is the program that would
+satis ify your needs and bring people
+
+ align:start position:0%
+satis ify your needs and bring people
+ 
+
+ align:start position:0%
+satis ify your needs and bring people
+together in the
+
+ align:start position:0%
+together in the
+ 
+
+ align:start position:0%
+together in the
+community how can we get people to come
+
+ align:start position:0%
+community how can we get people to come
+ 
+
+ align:start position:0%
+community how can we get people to come
+together again I'm
+
+ align:start position:0%
+together again I'm
+ 
+
+ align:start position:0%
+together again I'm
+reiterating what kind of spaces for work
+
+ align:start position:0%
+reiterating what kind of spaces for work
+ 
+
+ align:start position:0%
+reiterating what kind of spaces for work
+would you want and
+
+ align:start position:0%
+would you want and
+ 
+
+ align:start position:0%
+would you want and
+need how can we design buildings in our
+
+ align:start position:0%
+need how can we design buildings in our
+ 
+
+ align:start position:0%
+need how can we design buildings in our
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+Society present Society being the
+
+ align:start position:0%
+Society present Society being the
+ 
+
+ align:start position:0%
+Society present Society being the
+Society of Technology of
+
+ align:start position:0%
+Society of Technology of
+ 
+
+ align:start position:0%
+Society of Technology of
+computers um that can bring people
+
+ align:start position:0%
+computers um that can bring people
+ 
+
+ align:start position:0%
+computers um that can bring people
+together and address the issue of
+
+ align:start position:0%
+together and address the issue of
+ 
+
+ align:start position:0%
+together and address the issue of
+community because we're still we still
+
+ align:start position:0%
+community because we're still we still
+ 
+
+ align:start position:0%
+community because we're still we still
+want to come together
+
+ align:start position:0%
+want to come together
+ 
+
+ align:start position:0%
+want to come together
+somehow yet the machine the technology
+
+ align:start position:0%
+somehow yet the machine the technology
+ 
+
+ align:start position:0%
+somehow yet the machine the technology
+age is pushing us away from each other
+
+ align:start position:0%
+age is pushing us away from each other
+ 
+
+ align:start position:0%
+age is pushing us away from each other
+to a certain
+
+ align:start position:0%
+to a certain
+ 
+
+ align:start position:0%
+to a certain
+extent what is the connection to
+
+ align:start position:0%
+extent what is the connection to
+ 
+
+ align:start position:0%
+extent what is the connection to
+nature which is also a basic need of
+
+ align:start position:0%
+nature which is also a basic need of
+ 
+
+ align:start position:0%
+nature which is also a basic need of
+us how can nature be introduced into the
+
+ align:start position:0%
+us how can nature be introduced into the
+ 
+
+ align:start position:0%
+us how can nature be introduced into the
+city these are all questions I'm asking
+
+ align:start position:0%
+city these are all questions I'm asking
+ 
+
+ align:start position:0%
+city these are all questions I'm asking
+you for the program
+
+ align:start position:0%
+you for the program
+ 
+
+ align:start position:0%
+you for the program
+I say it would be a good time to revisit
+
+ align:start position:0%
+I say it would be a good time to revisit
+ 
+
+ align:start position:0%
+I say it would be a good time to revisit
+the site and understand more of the
+
+ align:start position:0%
+the site and understand more of the
+ 
+
+ align:start position:0%
+the site and understand more of the
+community uh you might do this by being
+
+ align:start position:0%
+community uh you might do this by being
+ 
+
+ align:start position:0%
+community uh you might do this by being
+there at different times of the day by
+
+ align:start position:0%
+there at different times of the day by
+ 
+
+ align:start position:0%
+there at different times of the day by
+talking with people who live there or by
+
+ align:start position:0%
+talking with people who live there or by
+ 
+
+ align:start position:0%
+talking with people who live there or by
+understanding the history of the area
+
+ align:start position:0%
+understanding the history of the area
+ 
+
+ align:start position:0%
+understanding the history of the area
+which you do understand to a certain
+
+ align:start position:0%
+which you do understand to a certain
+ 
+
+ align:start position:0%
+which you do understand to a certain
+extent but more so so you might go down
+
+ align:start position:0%
+extent but more so so you might go down
+ 
+
+ align:start position:0%
+extent but more so so you might go down
+today go in the night go in the weekend
+
+ align:start position:0%
+today go in the night go in the weekend
+ 
+
+ align:start position:0%
+today go in the night go in the weekend
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+somebody from your observations ideas
+
+ align:start position:0%
+somebody from your observations ideas
+ 
+
+ align:start position:0%
+somebody from your observations ideas
+for the program and form should come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+it for next
+
+ align:start position:0%
+it for next
+ 
+
+ align:start position:0%
+it for next
+Tuesday we're going to have a pin up the
+
+ align:start position:0%
+Tuesday we're going to have a pin up the
+ 
+
+ align:start position:0%
+Tuesday we're going to have a pin up the
+following should be done two 20x 50
+
+ align:start position:0%
+following should be done two 20x 50
+ 
+
+ align:start position:0%
+following should be done two 20x 50
+boards to include your attitude quote
+
+ align:start position:0%
+boards to include your attitude quote
+ 
+
+ align:start position:0%
+boards to include your attitude quote
+attitude about the building program uses
+
+ align:start position:0%
+attitude about the building program uses
+ 
+
+ align:start position:0%
+attitude about the building program uses
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+sizes I'm looking for you to produce
+
+ align:start position:0%
+sizes I'm looking for you to produce
+ 
+
+ align:start position:0%
+sizes I'm looking for you to produce
+Montage boards again that express your
+
+ align:start position:0%
+Montage boards again that express your
+ 
+
+ align:start position:0%
+Montage boards again that express your
+idea about how we're going to come
+
+ align:start position:0%
+idea about how we're going to come
+ 
+
+ align:start position:0%
+idea about how we're going to come
+together on this site
+
+ align:start position:0%
+together on this site
+ 
+
+ align:start position:0%
+together on this site
+I'm also asking you to make areas of
+
+ align:start position:0%
+I'm also asking you to make areas of
+ 
+
+ align:start position:0%
+I'm also asking you to make areas of
+colored paper to show the sizes of the
+
+ align:start position:0%
+colored paper to show the sizes of the
+ 
+
+ align:start position:0%
+colored paper to show the sizes of the
+program at the scale of 16 which we're
+
+ align:start position:0%
+program at the scale of 16 which we're
+ 
+
+ align:start position:0%
+program at the scale of 16 which we're
+working at which is
+
+ align:start position:0%
+working at which is
+ 
+
+ align:start position:0%
+working at which is
+this um that talks about the size of the
+
+ align:start position:0%
+this um that talks about the size of the
+ 
+
+ align:start position:0%
+this um that talks about the size of the
+building remember this is a vertical
+
+ align:start position:0%
+building remember this is a vertical
+ 
+
+ align:start position:0%
+building remember this is a vertical
+building so that's on the boards that's
+
+ align:start position:0%
+building so that's on the boards that's
+ 
+
+ align:start position:0%
+building so that's on the boards that's
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+boards and I'm asking you sketches about
+
+ align:start position:0%
+boards and I'm asking you sketches about
+ 
+
+ align:start position:0%
+boards and I'm asking you sketches about
+how you might use the
+
+ align:start position:0%
+how you might use the
+ 
+
+ align:start position:0%
+how you might use the
+site include at 116 scale at least one
+
+ align:start position:0%
+site include at 116 scale at least one
+ 
+
+ align:start position:0%
+site include at 116 scale at least one
+General SK sketch plan but more I'm
+
+ align:start position:0%
+General SK sketch plan but more I'm
+ 
+
+ align:start position:0%
+General SK sketch plan but more I'm
+looking for more than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
\ No newline at end of file
diff --git a/7eQ4Xt5mAXQ.txt b/7eQ4Xt5mAXQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8dc65cda1372edef52d20f0f217eae40f528c911
--- /dev/null
+++ b/7eQ4Xt5mAXQ.txt
@@ -0,0 +1,8427 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how does a writer like Butler
+
+ align:start position:0%
+so how does a writer like Butler
+ 
+
+ align:start position:0%
+so how does a writer like Butler
+sort hit upon this subject I mean is
+
+ align:start position:0%
+sort hit upon this subject I mean is
+ 
+
+ align:start position:0%
+sort hit upon this subject I mean is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um I mean Butler was
+
+ align:start position:0%
+um I mean Butler was
+ 
+
+ align:start position:0%
+um I mean Butler was
+U he was a generation younger than
+
+ align:start position:0%
+U he was a generation younger than
+ 
+
+ align:start position:0%
+U he was a generation younger than
+Darwin but you know not that not that
+
+ align:start position:0%
+Darwin but you know not that not that
+ 
+
+ align:start position:0%
+Darwin but you know not that not that
+much younger he had met Darwin Darwin
+
+ align:start position:0%
+much younger he had met Darwin Darwin
+ 
+
+ align:start position:0%
+much younger he had met Darwin Darwin
+after the this book was published Darwin
+
+ align:start position:0%
+after the this book was published Darwin
+ 
+
+ align:start position:0%
+after the this book was published Darwin
+invited him to his house he was very
+
+ align:start position:0%
+invited him to his house he was very
+ 
+
+ align:start position:0%
+invited him to his house he was very
+interested uh he wanted to explore this
+
+ align:start position:0%
+interested uh he wanted to explore this
+ 
+
+ align:start position:0%
+interested uh he wanted to explore this
+what you know what's going on in this
+
+ align:start position:0%
+what you know what's going on in this
+ 
+
+ align:start position:0%
+what you know what's going on in this
+guy's mind because there were lots of
+
+ align:start position:0%
+guy's mind because there were lots of
+ 
+
+ align:start position:0%
+guy's mind because there were lots of
+things going on here that uh uh you know
+
+ align:start position:0%
+things going on here that uh uh you know
+ 
+
+ align:start position:0%
+things going on here that uh uh you know
+Darwin found rather fascinating so why
+
+ align:start position:0%
+Darwin found rather fascinating so why
+ 
+
+ align:start position:0%
+Darwin found rather fascinating so why
+would Darwin even care about a book like
+
+ align:start position:0%
+would Darwin even care about a book like
+ 
+
+ align:start position:0%
+would Darwin even care about a book like
+this what's in this book
+
+ align:start position:0%
+this what's in this book
+ 
+
+ align:start position:0%
+this what's in this book
+that might interest uh you know great
+
+ align:start position:0%
+that might interest uh you know great
+ 
+
+ align:start position:0%
+that might interest uh you know great
+scientists like Charles
+
+ align:start position:0%
+scientists like Charles
+ 
+
+ align:start position:0%
+scientists like Charles
+Darwin I'm not saying that Butler and
+
+ align:start position:0%
+Darwin I'm not saying that Butler and
+ 
+
+ align:start position:0%
+Darwin I'm not saying that Butler and
+Darwin got along but Dar invited him
+
+ align:start position:0%
+Darwin got along but Dar invited him
+ 
+
+ align:start position:0%
+Darwin got along but Dar invited him
+down to his house for a weekend to um
+
+ align:start position:0%
+down to his house for a weekend to um
+ 
+
+ align:start position:0%
+down to his house for a weekend to um
+talk with him so what's here yeah TR
+
+ align:start position:0%
+talk with him so what's here yeah TR
+ 
+
+ align:start position:0%
+talk with him so what's here yeah TR
+well kind of um in in a way the
+
+ align:start position:0%
+well kind of um in in a way the
+ 
+
+ align:start position:0%
+well kind of um in in a way the
+professor like the professor did for
+
+ align:start position:0%
+professor like the professor did for
+ 
+
+ align:start position:0%
+professor like the professor did for
+machines what Darwin did for living
+
+ align:start position:0%
+machines what Darwin did for living
+ 
+
+ align:start position:0%
+machines what Darwin did for living
+living things in terms of
+
+ align:start position:0%
+living things in terms of
+ 
+
+ align:start position:0%
+living things in terms of
+how like the like machines can like they
+
+ align:start position:0%
+how like the like machines can like they
+ 
+
+ align:start position:0%
+how like the like machines can like they
+all have their own varieties there's
+
+ align:start position:0%
+all have their own varieties there's
+ 
+
+ align:start position:0%
+all have their own varieties there's
+like variation and then there's also
+
+ align:start position:0%
+like variation and then there's also
+ 
+
+ align:start position:0%
+like variation and then there's also
+like gradual increments how they just
+
+ align:start position:0%
+like gradual increments how they just
+ 
+
+ align:start position:0%
+like gradual increments how they just
+get better and better and then obviously
+
+ align:start position:0%
+get better and better and then obviously
+ 
+
+ align:start position:0%
+get better and better and then obviously
+like if they don't get
+
+ align:start position:0%
+like if they don't get
+ 
+
+ align:start position:0%
+like if they don't get
+better like they just like get discarded
+
+ align:start position:0%
+better like they just like get discarded
+ 
+
+ align:start position:0%
+better like they just like get discarded
+and so it's kind of like Evolution for
+
+ align:start position:0%
+and so it's kind of like Evolution for
+ 
+
+ align:start position:0%
+and so it's kind of like Evolution for
+machines yeah so it's really I mean we
+
+ align:start position:0%
+machines yeah so it's really I mean we
+ 
+
+ align:start position:0%
+machines yeah so it's really I mean we
+certainly all admit don't we that
+
+ align:start position:0%
+certainly all admit don't we that
+ 
+
+ align:start position:0%
+certainly all admit don't we that
+machines are constantly being improved
+
+ align:start position:0%
+machines are constantly being improved
+ 
+
+ align:start position:0%
+machines are constantly being improved
+upon and the first versions are rarely
+
+ align:start position:0%
+upon and the first versions are rarely
+ 
+
+ align:start position:0%
+upon and the first versions are rarely
+you know the ones that are the
+
+ align:start position:0%
+you know the ones that are the
+ 
+
+ align:start position:0%
+you know the ones that are the
+Contemporary ones yeah I think like up
+
+ align:start position:0%
+Contemporary ones yeah I think like up
+ 
+
+ align:start position:0%
+Contemporary ones yeah I think like up
+until this point obviously we've been
+
+ align:start position:0%
+until this point obviously we've been
+ 
+
+ align:start position:0%
+until this point obviously we've been
+controlling that progression and the
+
+ align:start position:0%
+controlling that progression and the
+ 
+
+ align:start position:0%
+controlling that progression and the
+book to a point where they're like
+
+ align:start position:0%
+book to a point where they're like
+ 
+
+ align:start position:0%
+book to a point where they're like
+almost evolving
+
+ align:start position:0%
+almost evolving
+ 
+
+ align:start position:0%
+almost evolving
+naturally and I don't yeah yeah no this
+
+ align:start position:0%
+naturally and I don't yeah yeah no this
+ 
+
+ align:start position:0%
+naturally and I don't yeah yeah no this
+is this is we we're not going to Grant
+
+ align:start position:0%
+is this is we we're not going to Grant
+ 
+
+ align:start position:0%
+is this is we we're not going to Grant
+this crazy Professor his his points here
+
+ align:start position:0%
+this crazy Professor his his points here
+ 
+
+ align:start position:0%
+this crazy Professor his his points here
+but we want to to sort of use these to
+
+ align:start position:0%
+but we want to to sort of use these to
+ 
+
+ align:start position:0%
+but we want to to sort of use these to
+sort of think about some of these
+
+ align:start position:0%
+sort of think about some of these
+ 
+
+ align:start position:0%
+sort of think about some of these
+questions uh and you know we're going to
+
+ align:start position:0%
+questions uh and you know we're going to
+ 
+
+ align:start position:0%
+questions uh and you know we're going to
+read some further works but uh somehow
+
+ align:start position:0%
+read some further works but uh somehow
+ 
+
+ align:start position:0%
+read some further works but uh somehow
+how does uh how does this whole subject
+
+ align:start position:0%
+how does uh how does this whole subject
+ 
+
+ align:start position:0%
+how does uh how does this whole subject
+of machines come into this book why why
+
+ align:start position:0%
+of machines come into this book why why
+ 
+
+ align:start position:0%
+of machines come into this book why why
+why are the aians Care One Way or
+
+ align:start position:0%
+why are the aians Care One Way or
+ 
+
+ align:start position:0%
+why are the aians Care One Way or
+Another about
+
+ align:start position:0%
+Another about
+ 
+
+ align:start position:0%
+Another about
+machines and in fact you know as The
+
+ align:start position:0%
+machines and in fact you know as The
+ 
+
+ align:start position:0%
+machines and in fact you know as The
+Story Goes they all rose up against
+
+ align:start position:0%
+Story Goes they all rose up against
+ 
+
+ align:start position:0%
+Story Goes they all rose up against
+machines and destroyed the machines
+
+ align:start position:0%
+machines and destroyed the machines
+ 
+
+ align:start position:0%
+machines and destroyed the machines
+because they were cons conc ered that
+
+ align:start position:0%
+because they were cons conc ered that
+ 
+
+ align:start position:0%
+because they were cons conc ered that
+the machines were evolving into
+
+ align:start position:0%
+the machines were evolving into
+ 
+
+ align:start position:0%
+the machines were evolving into
+something that uh was going to
+
+ align:start position:0%
+something that uh was going to
+ 
+
+ align:start position:0%
+something that uh was going to
+be uh you know they were going to
+
+ align:start position:0%
+be uh you know they were going to
+ 
+
+ align:start position:0%
+be uh you know they were going to
+compete so
+
+ align:start position:0%
+compete so
+ 
+
+ align:start position:0%
+compete so
+uh this this sort of came in so the
+
+ align:start position:0%
+uh this this sort of came in so the
+ 
+
+ align:start position:0%
+uh this this sort of came in so the
+aians uh what's their take what how did
+
+ align:start position:0%
+aians uh what's their take what how did
+ 
+
+ align:start position:0%
+aians uh what's their take what how did
+this all become so urgent for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+I any sense why machines would bother
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ionians I'm not sure not sure okay I
+
+ align:start position:0%
+ionians I'm not sure not sure okay I
+ 
+
+ align:start position:0%
+ionians I'm not sure not sure okay I
+mean the Iranians are very concerned
+
+ align:start position:0%
+mean the Iranians are very concerned
+ 
+
+ align:start position:0%
+mean the Iranians are very concerned
+about you know
+
+ align:start position:0%
+about you know
+ 
+
+ align:start position:0%
+about you know
+being as fit as they possibly
+
+ align:start position:0%
+being as fit as they possibly
+ 
+
+ align:start position:0%
+being as fit as they possibly
+can how do machines influence in in this
+
+ align:start position:0%
+can how do machines influence in in this
+ 
+
+ align:start position:0%
+can how do machines influence in in this
+book how how do this book see machines
+
+ align:start position:0%
+book how how do this book see machines
+ 
+
+ align:start position:0%
+book how how do this book see machines
+as influencing
+
+ align:start position:0%
+as influencing
+ 
+
+ align:start position:0%
+as influencing
+Fitness there some kind
+
+ align:start position:0%
+Fitness there some kind
+ 
+
+ align:start position:0%
+Fitness there some kind
+of Yeah the more you have to rely on
+
+ align:start position:0%
+of Yeah the more you have to rely on
+ 
+
+ align:start position:0%
+of Yeah the more you have to rely on
+machines unless you have to rely on your
+
+ align:start position:0%
+machines unless you have to rely on your
+ 
+
+ align:start position:0%
+machines unless you have to rely on your
+own like abilities yeah yeah machines
+
+ align:start position:0%
+own like abilities yeah yeah machines
+ 
+
+ align:start position:0%
+own like abilities yeah yeah machines
+sort of uh as we were saying last class
+
+ align:start position:0%
+sort of uh as we were saying last class
+ 
+
+ align:start position:0%
+sort of uh as we were saying last class
+they kind of uh you know they make up
+
+ align:start position:0%
+they kind of uh you know they make up
+ 
+
+ align:start position:0%
+they kind of uh you know they make up
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+defects that individual aeronian might
+
+ align:start position:0%
+defects that individual aeronian might
+ 
+
+ align:start position:0%
+defects that individual aeronian might
+have so the and aonian philosophy is to
+
+ align:start position:0%
+have so the and aonian philosophy is to
+ 
+
+ align:start position:0%
+have so the and aonian philosophy is to
+uh you know make humans uh absolutely
+
+ align:start position:0%
+uh you know make humans uh absolutely
+ 
+
+ align:start position:0%
+uh you know make humans uh absolutely
+the strongest and best and you know
+
+ align:start position:0%
+the strongest and best and you know
+ 
+
+ align:start position:0%
+the strongest and best and you know
+they're they're sort of self- selecting
+
+ align:start position:0%
+they're they're sort of self- selecting
+ 
+
+ align:start position:0%
+they're they're sort of self- selecting
+for strength and intelligence and so on
+
+ align:start position:0%
+for strength and intelligence and so on
+ 
+
+ align:start position:0%
+for strength and intelligence and so on
+not necessarily for Brilliance because
+
+ align:start position:0%
+not necessarily for Brilliance because
+ 
+
+ align:start position:0%
+not necessarily for Brilliance because
+they're not you know they don't
+
+ align:start position:0%
+they're not you know they don't
+ 
+
+ align:start position:0%
+they're not you know they don't
+like uh individuals who get too far
+
+ align:start position:0%
+like uh individuals who get too far
+ 
+
+ align:start position:0%
+like uh individuals who get too far
+beyond the average the
+
+ align:start position:0%
+beyond the average the
+ 
+
+ align:start position:0%
+beyond the average the
+aonian model and ideal is to fit within
+
+ align:start position:0%
+aonian model and ideal is to fit within
+ 
+
+ align:start position:0%
+aonian model and ideal is to fit within
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+average to be in the middle of the herd
+
+ align:start position:0%
+average to be in the middle of the herd
+ 
+
+ align:start position:0%
+average to be in the middle of the herd
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+place not too far behind and not too far
+
+ align:start position:0%
+place not too far behind and not too far
+ 
+
+ align:start position:0%
+place not too far behind and not too far
+ahead but you know a nice
+
+ align:start position:0%
+ahead but you know a nice
+ 
+
+ align:start position:0%
+ahead but you know a nice
+healthy uh member of the aonian herd if
+
+ align:start position:0%
+healthy uh member of the aonian herd if
+ 
+
+ align:start position:0%
+healthy uh member of the aonian herd if
+you will so machines uh take the uh they
+
+ align:start position:0%
+you will so machines uh take the uh they
+ 
+
+ align:start position:0%
+you will so machines uh take the uh they
+compensate they compensate for certain
+
+ align:start position:0%
+compensate they compensate for certain
+ 
+
+ align:start position:0%
+compensate they compensate for certain
+types of things that uh you know uh
+
+ align:start position:0%
+types of things that uh you know uh
+ 
+
+ align:start position:0%
+types of things that uh you know uh
+individuals might not be able to manage
+
+ align:start position:0%
+individuals might not be able to manage
+ 
+
+ align:start position:0%
+individuals might not be able to manage
+and so in compensating what is that what
+
+ align:start position:0%
+and so in compensating what is that what
+ 
+
+ align:start position:0%
+and so in compensating what is that what
+does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean those individuals can have children
+
+ align:start position:0%
+mean those individuals can have children
+ 
+
+ align:start position:0%
+mean those individuals can have children
+and those children will inherit those
+
+ align:start position:0%
+and those children will inherit those
+ 
+
+ align:start position:0%
+and those children will inherit those
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+uh less well-developed or less
+
+ align:start position:0%
+uh less well-developed or less
+ 
+
+ align:start position:0%
+uh less well-developed or less
+competitive features so that's how this
+
+ align:start position:0%
+competitive features so that's how this
+ 
+
+ align:start position:0%
+competitive features so that's how this
+Society works so as I said last time
+
+ align:start position:0%
+Society works so as I said last time
+ 
+
+ align:start position:0%
+Society works so as I said last time
+it's it's uh it's the first kind of uh
+
+ align:start position:0%
+it's it's uh it's the first kind of uh
+ 
+
+ align:start position:0%
+it's it's uh it's the first kind of uh
+uh eugenical soci Society I
+
+ align:start position:0%
+uh eugenical soci Society I
+ 
+
+ align:start position:0%
+uh eugenical soci Society I
+mean the word isn't being used here and
+
+ align:start position:0%
+mean the word isn't being used here and
+ 
+
+ align:start position:0%
+mean the word isn't being used here and
+I don't think Butlers had the word in
+
+ align:start position:0%
+I don't think Butlers had the word in
+ 
+
+ align:start position:0%
+I don't think Butlers had the word in
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+vocabulary but you know it's it's it's
+
+ align:start position:0%
+vocabulary but you know it's it's it's
+ 
+
+ align:start position:0%
+vocabulary but you know it's it's it's
+there and it's being offered uh of
+
+ align:start position:0%
+there and it's being offered uh of
+ 
+
+ align:start position:0%
+there and it's being offered uh of
+course this this Society is being
+
+ align:start position:0%
+course this this Society is being
+ 
+
+ align:start position:0%
+course this this Society is being
+offered as a kind of a satire so it's
+
+ align:start position:0%
+offered as a kind of a satire so it's
+ 
+
+ align:start position:0%
+offered as a kind of a satire so it's
+it's not something he's recommending and
+
+ align:start position:0%
+it's not something he's recommending and
+ 
+
+ align:start position:0%
+it's not something he's recommending and
+you know he's
+
+ align:start position:0%
+you know he's
+ 
+
+ align:start position:0%
+you know he's
+obviously positioned this professor's
+
+ align:start position:0%
+obviously positioned this professor's
+ 
+
+ align:start position:0%
+obviously positioned this professor's
+Treatise the book of the machines
+
+ align:start position:0%
+Treatise the book of the machines
+ 
+
+ align:start position:0%
+Treatise the book of the machines
+how is that position in the book in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Aran you know it's it comes from a
+
+ align:start position:0%
+Aran you know it's it comes from a
+ 
+
+ align:start position:0%
+Aran you know it's it comes from a
+professor in the colleges of
+
+ align:start position:0%
+professor in the colleges of
+ 
+
+ align:start position:0%
+professor in the colleges of
+unreason I didn't have you read all the
+
+ align:start position:0%
+unreason I didn't have you read all the
+ 
+
+ align:start position:0%
+unreason I didn't have you read all the
+chapters but uh this is uh these are
+
+ align:start position:0%
+chapters but uh this is uh these are
+ 
+
+ align:start position:0%
+chapters but uh this is uh these are
+colleges that uh uh Butler used to
+
+ align:start position:0%
+colleges that uh uh Butler used to
+ 
+
+ align:start position:0%
+colleges that uh uh Butler used to
+satire as a satire against camridge
+
+ align:start position:0%
+satire as a satire against camridge
+ 
+
+ align:start position:0%
+satire as a satire against camridge
+because they they uh he he spent a lot
+
+ align:start position:0%
+because they they uh he he spent a lot
+ 
+
+ align:start position:0%
+because they they uh he he spent a lot
+of time learning Latin
+
+ align:start position:0%
+of time learning Latin
+ 
+
+ align:start position:0%
+of time learning Latin
+and uh he couldn't figure out what the
+
+ align:start position:0%
+and uh he couldn't figure out what the
+ 
+
+ align:start position:0%
+and uh he couldn't figure out what the
+Latin was for what the use was going to
+
+ align:start position:0%
+Latin was for what the use was going to
+ 
+
+ align:start position:0%
+Latin was for what the use was going to
+be so in the colleges of
+
+ align:start position:0%
+be so in the colleges of
+ 
+
+ align:start position:0%
+be so in the colleges of
+unreason which uh you know he was making
+
+ align:start position:0%
+unreason which uh you know he was making
+ 
+
+ align:start position:0%
+unreason which uh you know he was making
+fun
+
+ align:start position:0%
+fun
+ 
+
+ align:start position:0%
+fun
+of um the students are taught what they
+
+ align:start position:0%
+of um the students are taught what they
+ 
+
+ align:start position:0%
+of um the students are taught what they
+call a quote hypothetical language and
+
+ align:start position:0%
+call a quote hypothetical language and
+ 
+
+ align:start position:0%
+call a quote hypothetical language and
+the hypothetical language was you know
+
+ align:start position:0%
+the hypothetical language was you know
+ 
+
+ align:start position:0%
+the hypothetical language was you know
+it really didn't have any application
+
+ align:start position:0%
+it really didn't have any application
+ 
+
+ align:start position:0%
+it really didn't have any application
+you just sort of learned it in order to
+
+ align:start position:0%
+you just sort of learned it in order to
+ 
+
+ align:start position:0%
+you just sort of learned it in order to
+learn it uh but not for any particular
+
+ align:start position:0%
+learn it uh but not for any particular
+ 
+
+ align:start position:0%
+learn it uh but not for any particular
+application so he was sort of making fun
+
+ align:start position:0%
+application so he was sort of making fun
+ 
+
+ align:start position:0%
+application so he was sort of making fun
+of the rigorous Latin course that he had
+
+ align:start position:0%
+of the rigorous Latin course that he had
+ 
+
+ align:start position:0%
+of the rigorous Latin course that he had
+to spend and you know he spent a lot of
+
+ align:start position:0%
+to spend and you know he spent a lot of
+ 
+
+ align:start position:0%
+to spend and you know he spent a lot of
+his undergraduate years mastering
+
+ align:start position:0%
+his undergraduate years mastering
+ 
+
+ align:start position:0%
+his undergraduate years mastering
+Latin some other things too but uh a lot
+
+ align:start position:0%
+Latin some other things too but uh a lot
+ 
+
+ align:start position:0%
+Latin some other things too but uh a lot
+of the work that he he felt that a lot
+
+ align:start position:0%
+of the work that he he felt that a lot
+ 
+
+ align:start position:0%
+of the work that he he felt that a lot
+of the work that he had done as an
+
+ align:start position:0%
+of the work that he had done as an
+ 
+
+ align:start position:0%
+of the work that he had done as an
+undergraduate was not really
+
+ align:start position:0%
+undergraduate was not really
+ 
+
+ align:start position:0%
+undergraduate was not really
+particularly useful for
+
+ align:start position:0%
+particularly useful for
+ 
+
+ align:start position:0%
+particularly useful for
+anything and that it was more or less
+
+ align:start position:0%
+anything and that it was more or less
+ 
+
+ align:start position:0%
+anything and that it was more or less
+that he was who's being expected to go
+
+ align:start position:0%
+that he was who's being expected to go
+ 
+
+ align:start position:0%
+that he was who's being expected to go
+go through hoops so uh it was a satire
+
+ align:start position:0%
+go through hoops so uh it was a satire
+ 
+
+ align:start position:0%
+go through hoops so uh it was a satire
+and I think we all have the experience
+
+ align:start position:0%
+and I think we all have the experience
+ 
+
+ align:start position:0%
+and I think we all have the experience
+of sometimes being in classes where in
+
+ align:start position:0%
+of sometimes being in classes where in
+ 
+
+ align:start position:0%
+of sometimes being in classes where in
+University where we wonder what is this
+
+ align:start position:0%
+University where we wonder what is this
+ 
+
+ align:start position:0%
+University where we wonder what is this
+for anyway you know exactly how am I
+
+ align:start position:0%
+for anyway you know exactly how am I
+ 
+
+ align:start position:0%
+for anyway you know exactly how am I
+going to use this so I mean this is a
+
+ align:start position:0%
+going to use this so I mean this is a
+ 
+
+ align:start position:0%
+going to use this so I mean this is a
+this is a you you might say a universal
+
+ align:start position:0%
+this is a you you might say a universal
+ 
+
+ align:start position:0%
+this is a you you might say a universal
+undergraduate experience of encountering
+
+ align:start position:0%
+undergraduate experience of encountering
+ 
+
+ align:start position:0%
+undergraduate experience of encountering
+certain types of things that you really
+
+ align:start position:0%
+certain types of things that you really
+ 
+
+ align:start position:0%
+certain types of things that you really
+wonder you know what's the value of
+
+ align:start position:0%
+wonder you know what's the value of
+ 
+
+ align:start position:0%
+wonder you know what's the value of
+this so so he's uh as I said this is a
+
+ align:start position:0%
+this so so he's uh as I said this is a
+ 
+
+ align:start position:0%
+this so so he's uh as I said this is a
+this book is a satire it it's really in
+
+ align:start position:0%
+this book is a satire it it's really in
+ 
+
+ align:start position:0%
+this book is a satire it it's really in
+many ways like candid only you know it's
+
+ align:start position:0%
+many ways like candid only you know it's
+ 
+
+ align:start position:0%
+many ways like candid only you know it's
+it's another
+
+ align:start position:0%
+it's another
+ 
+
+ align:start position:0%
+it's another
+generation a couple of generations down
+
+ align:start position:0%
+generation a couple of generations down
+ 
+
+ align:start position:0%
+generation a couple of generations down
+the line so it's much more in tune with
+
+ align:start position:0%
+the line so it's much more in tune with
+ 
+
+ align:start position:0%
+the line so it's much more in tune with
+the 19th century post darwinian
+
+ align:start position:0%
+the 19th century post darwinian
+ 
+
+ align:start position:0%
+the 19th century post darwinian
+world so this Treatise that that uh
+
+ align:start position:0%
+world so this Treatise that that uh
+ 
+
+ align:start position:0%
+world so this Treatise that that uh
+Chris was just giving us an introduction
+
+ align:start position:0%
+Chris was just giving us an introduction
+ 
+
+ align:start position:0%
+Chris was just giving us an introduction
+to uh is really A Treatise written by a
+
+ align:start position:0%
+to uh is really A Treatise written by a
+ 
+
+ align:start position:0%
+to uh is really A Treatise written by a
+professor who is a member of uh this
+
+ align:start position:0%
+professor who is a member of uh this
+ 
+
+ align:start position:0%
+professor who is a member of uh this
+this college of En reason and you know
+
+ align:start position:0%
+this college of En reason and you know
+ 
+
+ align:start position:0%
+this college of En reason and you know
+he's sort of giving a
+
+ align:start position:0%
+he's sort of giving a
+ 
+
+ align:start position:0%
+he's sort of giving a
+history um and he's articulating a
+
+ align:start position:0%
+history um and he's articulating a
+ 
+
+ align:start position:0%
+history um and he's articulating a
+theory of why and and this is A Treatise
+
+ align:start position:0%
+theory of why and and this is A Treatise
+ 
+
+ align:start position:0%
+theory of why and and this is A Treatise
+uh that convinced the Iranians to go up
+
+ align:start position:0%
+uh that convinced the Iranians to go up
+ 
+
+ align:start position:0%
+uh that convinced the Iranians to go up
+against machines and to battle against
+
+ align:start position:0%
+against machines and to battle against
+ 
+
+ align:start position:0%
+against machines and to battle against
+them and so they became the sort of an
+
+ align:start position:0%
+them and so they became the sort of an
+ 
+
+ align:start position:0%
+them and so they became the sort of an
+anti-machine
+
+ align:start position:0%
+anti-machine
+ 
+
+ align:start position:0%
+anti-machine
+uh uh group and they fought with the
+
+ align:start position:0%
+uh uh group and they fought with the
+ 
+
+ align:start position:0%
+uh uh group and they fought with the
+supporters of the machines and the
+
+ align:start position:0%
+supporters of the machines and the
+ 
+
+ align:start position:0%
+supporters of the machines and the
+anti-machine group
+
+ align:start position:0%
+anti-machine group
+ 
+
+ align:start position:0%
+anti-machine group
+W and so U and this is A Treatise that
+
+ align:start position:0%
+W and so U and this is A Treatise that
+ 
+
+ align:start position:0%
+W and so U and this is A Treatise that
+they that convinced them to go to war
+
+ align:start position:0%
+they that convinced them to go to war
+ 
+
+ align:start position:0%
+they that convinced them to go to war
+against all people who would uh use
+
+ align:start position:0%
+against all people who would uh use
+ 
+
+ align:start position:0%
+against all people who would uh use
+machines and that's why Butler uh the
+
+ align:start position:0%
+machines and that's why Butler uh the
+ 
+
+ align:start position:0%
+machines and that's why Butler uh the
+that's why the uh Butler's uh narrator
+
+ align:start position:0%
+that's why the uh Butler's uh narrator
+ 
+
+ align:start position:0%
+that's why the uh Butler's uh narrator
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+book is jailed because because they find
+
+ align:start position:0%
+book is jailed because because they find
+ 
+
+ align:start position:0%
+book is jailed because because they find
+the watch that's that's what gets them
+
+ align:start position:0%
+the watch that's that's what gets them
+ 
+
+ align:start position:0%
+the watch that's that's what gets them
+into trouble with this these aonian okay
+
+ align:start position:0%
+into trouble with this these aonian okay
+ 
+
+ align:start position:0%
+into trouble with this these aonian okay
+so that's that's sort of the framework
+
+ align:start position:0%
+so that's that's sort of the framework
+ 
+
+ align:start position:0%
+so that's that's sort of the framework
+for this this
+
+ align:start position:0%
+for this this
+ 
+
+ align:start position:0%
+for this this
+piece okay so uh let me uh let me just
+
+ align:start position:0%
+piece okay so uh let me uh let me just
+ 
+
+ align:start position:0%
+piece okay so uh let me uh let me just
+say a little bit about the background
+
+ align:start position:0%
+say a little bit about the background
+ 
+
+ align:start position:0%
+say a little bit about the background
+because this book is in the middle of a
+
+ align:start position:0%
+because this book is in the middle of a
+ 
+
+ align:start position:0%
+because this book is in the middle of a
+you know there there's a very large
+
+ align:start position:0%
+you know there there's a very large
+ 
+
+ align:start position:0%
+you know there there's a very large
+context for some of the things that uh
+
+ align:start position:0%
+context for some of the things that uh
+ 
+
+ align:start position:0%
+context for some of the things that uh
+are being explored in the book and um I
+
+ align:start position:0%
+are being explored in the book and um I
+ 
+
+ align:start position:0%
+are being explored in the book and um I
+sent you out some slides and just say a
+
+ align:start position:0%
+sent you out some slides and just say a
+ 
+
+ align:start position:0%
+sent you out some slides and just say a
+few things about these but um uh you
+
+ align:start position:0%
+few things about these but um uh you
+ 
+
+ align:start position:0%
+few things about these but um uh you
+know the the existence of machines in
+
+ align:start position:0%
+know the the existence of machines in
+ 
+
+ align:start position:0%
+know the the existence of machines in
+Butler's day in in the 18 in the mid
+
+ align:start position:0%
+Butler's day in in the 18 in the mid
+ 
+
+ align:start position:0%
+Butler's day in in the 18 in the mid
+1800s machines had proliferated in many
+
+ align:start position:0%
+1800s machines had proliferated in many
+ 
+
+ align:start position:0%
+1800s machines had proliferated in many
+many different
+
+ align:start position:0%
+many different
+ 
+
+ align:start position:0%
+many different
+ways uh you know steam engines were
+
+ align:start position:0%
+ways uh you know steam engines were
+ 
+
+ align:start position:0%
+ways uh you know steam engines were
+quite common that's that's what he's
+
+ align:start position:0%
+quite common that's that's what he's
+ 
+
+ align:start position:0%
+quite common that's that's what he's
+referring to with uh when he talks about
+
+ align:start position:0%
+referring to with uh when he talks about
+ 
+
+ align:start position:0%
+referring to with uh when he talks about
+the vapor engine here uh and there had
+
+ align:start position:0%
+the vapor engine here uh and there had
+ 
+
+ align:start position:0%
+the vapor engine here uh and there had
+been an incredible amount of development
+
+ align:start position:0%
+been an incredible amount of development
+ 
+
+ align:start position:0%
+been an incredible amount of development
+of uh technology around Steam power I
+
+ align:start position:0%
+of uh technology around Steam power I
+ 
+
+ align:start position:0%
+of uh technology around Steam power I
+mean steam power was amazing addition to
+
+ align:start position:0%
+mean steam power was amazing addition to
+ 
+
+ align:start position:0%
+mean steam power was amazing addition to
+uh the possibilities for uh
+
+ align:start position:0%
+uh the possibilities for uh
+ 
+
+ align:start position:0%
+uh the possibilities for uh
+for using and dis for applying motive
+
+ align:start position:0%
+for using and dis for applying motive
+ 
+
+ align:start position:0%
+for using and dis for applying motive
+Force to various types of
+
+ align:start position:0%
+Force to various types of
+ 
+
+ align:start position:0%
+Force to various types of
+tasks and uh it was uh uh steam power
+
+ align:start position:0%
+tasks and uh it was uh uh steam power
+ 
+
+ align:start position:0%
+tasks and uh it was uh uh steam power
+was widely widely
+
+ align:start position:0%
+was widely widely
+ 
+
+ align:start position:0%
+was widely widely
+used um in in uh the Victorian
+
+ align:start position:0%
+used um in in uh the Victorian
+ 
+
+ align:start position:0%
+used um in in uh the Victorian
+era and it um it led to the development
+
+ align:start position:0%
+era and it um it led to the development
+ 
+
+ align:start position:0%
+era and it um it led to the development
+of all sorts of things including U the
+
+ align:start position:0%
+of all sorts of things including U the
+ 
+
+ align:start position:0%
+of all sorts of things including U the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+Railways and as most people know the
+
+ align:start position:0%
+Railways and as most people know the
+ 
+
+ align:start position:0%
+Railways and as most people know the
+railways really began to develop in a
+
+ align:start position:0%
+railways really began to develop in a
+ 
+
+ align:start position:0%
+railways really began to develop in a
+big way in the
+
+ align:start position:0%
+big way in the
+ 
+
+ align:start position:0%
+big way in the
+1800s uh both in England in the
+
+ align:start position:0%
+1800s uh both in England in the
+ 
+
+ align:start position:0%
+1800s uh both in England in the
+US but uh in England uh the railway
+
+ align:start position:0%
+US but uh in England uh the railway
+ 
+
+ align:start position:0%
+US but uh in England uh the railway
+system uh just exploded it just
+
+ align:start position:0%
+system uh just exploded it just
+ 
+
+ align:start position:0%
+system uh just exploded it just
+developed and so much so that people
+
+ align:start position:0%
+developed and so much so that people
+ 
+
+ align:start position:0%
+developed and so much so that people
+began to feel you know railways were uh
+
+ align:start position:0%
+began to feel you know railways were uh
+ 
+
+ align:start position:0%
+began to feel you know railways were uh
+uh rather becoming rather
+
+ align:start position:0%
+uh rather becoming rather
+ 
+
+ align:start position:0%
+uh rather becoming rather
+intrusive Butler himself the
+
+ align:start position:0%
+intrusive Butler himself the
+ 
+
+ align:start position:0%
+intrusive Butler himself the
+author was a a tremendous user of
+
+ align:start position:0%
+author was a a tremendous user of
+ 
+
+ align:start position:0%
+author was a a tremendous user of
+Railways he traveled all over England
+
+ align:start position:0%
+Railways he traveled all over England
+ 
+
+ align:start position:0%
+Railways he traveled all over England
+and all over uh Europe on
+
+ align:start position:0%
+and all over uh Europe on
+ 
+
+ align:start position:0%
+and all over uh Europe on
+Railways um before that you had to hire
+
+ align:start position:0%
+Railways um before that you had to hire
+ 
+
+ align:start position:0%
+Railways um before that you had to hire
+a trap with a horse or something like
+
+ align:start position:0%
+a trap with a horse or something like
+ 
+
+ align:start position:0%
+a trap with a horse or something like
+that and uh in the years that Butler
+
+ align:start position:0%
+that and uh in the years that Butler
+ 
+
+ align:start position:0%
+that and uh in the years that Butler
+lived in New Zealand land a new Railway
+
+ align:start position:0%
+lived in New Zealand land a new Railway
+ 
+
+ align:start position:0%
+lived in New Zealand land a new Railway
+was put
+
+ align:start position:0%
+was put
+ 
+
+ align:start position:0%
+was put
+in uh to bring uh goods from the harbor
+
+ align:start position:0%
+in uh to bring uh goods from the harbor
+ 
+
+ align:start position:0%
+in uh to bring uh goods from the harbor
+up to the city of Christ Church where
+
+ align:start position:0%
+up to the city of Christ Church where
+ 
+
+ align:start position:0%
+up to the city of Christ Church where
+Butler went to on the south island of
+
+ align:start position:0%
+Butler went to on the south island of
+ 
+
+ align:start position:0%
+Butler went to on the south island of
+New Zealand so and he knew uh he knew uh
+
+ align:start position:0%
+New Zealand so and he knew uh he knew uh
+ 
+
+ align:start position:0%
+New Zealand so and he knew uh he knew uh
+the gentleman who developed the railway
+
+ align:start position:0%
+the gentleman who developed the railway
+ 
+
+ align:start position:0%
+the gentleman who developed the railway
+system and was one of the first people
+
+ align:start position:0%
+system and was one of the first people
+ 
+
+ align:start position:0%
+system and was one of the first people
+to ride on one of the first rides of the
+
+ align:start position:0%
+to ride on one of the first rides of the
+ 
+
+ align:start position:0%
+to ride on one of the first rides of the
+Railway so there is this sense of the
+
+ align:start position:0%
+Railway so there is this sense of the
+ 
+
+ align:start position:0%
+Railway so there is this sense of the
+presence of machines
+
+ align:start position:0%
+presence of machines
+ 
+
+ align:start position:0%
+presence of machines
+becoming rather
+
+ align:start position:0%
+becoming rather
+ 
+
+ align:start position:0%
+becoming rather
+extensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh there were other things happening in
+
+ align:start position:0%
+uh there were other things happening in
+ 
+
+ align:start position:0%
+uh there were other things happening in
+the in the time and he refers to some of
+
+ align:start position:0%
+the in the time and he refers to some of
+ 
+
+ align:start position:0%
+the in the time and he refers to some of
+this so I'm just I'm just uh uh giving
+
+ align:start position:0%
+this so I'm just I'm just uh uh giving
+ 
+
+ align:start position:0%
+this so I'm just I'm just uh uh giving
+you some background on some of he he
+
+ align:start position:0%
+you some background on some of he he
+ 
+
+ align:start position:0%
+you some background on some of he he
+talks about the power of machines in in
+
+ align:start position:0%
+talks about the power of machines in in
+ 
+
+ align:start position:0%
+talks about the power of machines in in
+in in in the book of the
+
+ align:start position:0%
+in in in the book of the
+ 
+
+ align:start position:0%
+in in in the book of the
+machines in aan there's a there's a
+
+ align:start position:0%
+machines in aan there's a there's a
+ 
+
+ align:start position:0%
+machines in aan there's a there's a
+mention to the power machines for
+
+ align:start position:0%
+mention to the power machines for
+ 
+
+ align:start position:0%
+mention to the power machines for
+calculating and uh
+
+ align:start position:0%
+calculating and uh
+ 
+
+ align:start position:0%
+calculating and uh
+Charles babage anybody here ever hear of
+
+ align:start position:0%
+Charles babage anybody here ever hear of
+ 
+
+ align:start position:0%
+Charles babage anybody here ever hear of
+Charles
+
+ align:start position:0%
+Charles
+ 
+
+ align:start position:0%
+Charles
+babage he a great Victorian thinker
+
+ align:start position:0%
+babage he a great Victorian thinker
+ 
+
+ align:start position:0%
+babage he a great Victorian thinker
+somebody who uh Darwin knew Darwin knew
+
+ align:start position:0%
+somebody who uh Darwin knew Darwin knew
+ 
+
+ align:start position:0%
+somebody who uh Darwin knew Darwin knew
+Charles
+
+ align:start position:0%
+Charles
+ 
+
+ align:start position:0%
+Charles
+babage and uh babage was known as uh the
+
+ align:start position:0%
+babage and uh babage was known as uh the
+ 
+
+ align:start position:0%
+babage and uh babage was known as uh the
+I mean he was a genius he was a
+
+ align:start position:0%
+I mean he was a genius he was a
+ 
+
+ align:start position:0%
+I mean he was a genius he was a
+wonderful
+
+ align:start position:0%
+wonderful
+ 
+
+ align:start position:0%
+wonderful
+incredible uh fertile mind just uh
+
+ align:start position:0%
+incredible uh fertile mind just uh
+ 
+
+ align:start position:0%
+incredible uh fertile mind just uh
+thinking about difference engines
+
+ align:start position:0%
+thinking about difference engines
+ 
+
+ align:start position:0%
+thinking about difference engines
+calculating engines and how to use
+
+ align:start position:0%
+calculating engines and how to use
+ 
+
+ align:start position:0%
+calculating engines and how to use
+mechanical Power
+
+ align:start position:0%
+mechanical Power
+ 
+
+ align:start position:0%
+mechanical Power
+to do numerical
+
+ align:start position:0%
+to do numerical
+ 
+
+ align:start position:0%
+to do numerical
+calculations and the whole notion that
+
+ align:start position:0%
+calculations and the whole notion that
+ 
+
+ align:start position:0%
+calculations and the whole notion that
+uh something like this could be
+
+ align:start position:0%
+uh something like this could be
+ 
+
+ align:start position:0%
+uh something like this could be
+um if this
+
+ align:start position:0%
+um if this
+ 
+
+ align:start position:0%
+um if this
+will well that's not the one I
+
+ align:start position:0%
+will well that's not the one I
+ 
+
+ align:start position:0%
+will well that's not the one I
+wanted
+
+ align:start position:0%
+wanted
+ 
+
+ align:start position:0%
+wanted
+um okay well I I I sent you an inset
+
+ align:start position:0%
+um okay well I I I sent you an inset
+ 
+
+ align:start position:0%
+um okay well I I I sent you an inset
+this machine um this Difference Engine
+
+ align:start position:0%
+this machine um this Difference Engine
+ 
+
+ align:start position:0%
+this machine um this Difference Engine
+uh babage designed and and
+
+ align:start position:0%
+uh babage designed and and
+ 
+
+ align:start position:0%
+uh babage designed and and
+sort of described how it should be built
+
+ align:start position:0%
+sort of described how it should be built
+ 
+
+ align:start position:0%
+sort of described how it should be built
+but he did not have the resources to
+
+ align:start position:0%
+but he did not have the resources to
+ 
+
+ align:start position:0%
+but he did not have the resources to
+build it so it was always a big question
+
+ align:start position:0%
+build it so it was always a big question
+ 
+
+ align:start position:0%
+build it so it was always a big question
+well do babies's machines really work
+
+ align:start position:0%
+well do babies's machines really work
+ 
+
+ align:start position:0%
+well do babies's machines really work
+and uh I sent you a clip in this so if
+
+ align:start position:0%
+and uh I sent you a clip in this so if
+ 
+
+ align:start position:0%
+and uh I sent you a clip in this so if
+you go back to the slides of uh a uh
+
+ align:start position:0%
+you go back to the slides of uh a uh
+ 
+
+ align:start position:0%
+you go back to the slides of uh a uh
+Professor out University of California
+
+ align:start position:0%
+Professor out University of California
+ 
+
+ align:start position:0%
+Professor out University of California
+Berkeley who actually built babies's
+
+ align:start position:0%
+Berkeley who actually built babies's
+ 
+
+ align:start position:0%
+Berkeley who actually built babies's
+machine and he has a
+
+ align:start position:0%
+machine and he has a
+ 
+
+ align:start position:0%
+machine and he has a
+actual a grinder for it and he actually
+
+ align:start position:0%
+actual a grinder for it and he actually
+ 
+
+ align:start position:0%
+actual a grinder for it and he actually
+had a recent conference demoed it and uh
+
+ align:start position:0%
+had a recent conference demoed it and uh
+ 
+
+ align:start position:0%
+had a recent conference demoed it and uh
+his uh Difference Engine Works quite
+
+ align:start position:0%
+his uh Difference Engine Works quite
+ 
+
+ align:start position:0%
+his uh Difference Engine Works quite
+beautifully so he actually built it to
+
+ align:start position:0%
+beautifully so he actually built it to
+ 
+
+ align:start position:0%
+beautifully so he actually built it to
+scale he babby didn't have the resources
+
+ align:start position:0%
+scale he babby didn't have the resources
+ 
+
+ align:start position:0%
+scale he babby didn't have the resources
+and he was one of these P people who
+
+ align:start position:0%
+and he was one of these P people who
+ 
+
+ align:start position:0%
+and he was one of these P people who
+worked and worked and worked and was
+
+ align:start position:0%
+worked and worked and worked and was
+ 
+
+ align:start position:0%
+worked and worked and worked and was
+always always short of money and never
+
+ align:start position:0%
+always always short of money and never
+ 
+
+ align:start position:0%
+always always short of money and never
+had quite enough to carry out all his
+
+ align:start position:0%
+had quite enough to carry out all his
+ 
+
+ align:start position:0%
+had quite enough to carry out all his
+different uh schemes but what he did
+
+ align:start position:0%
+different uh schemes but what he did
+ 
+
+ align:start position:0%
+different uh schemes but what he did
+show is machines Mechanical
+
+ align:start position:0%
+show is machines Mechanical
+ 
+
+ align:start position:0%
+show is machines Mechanical
+Devices could be used to process things
+
+ align:start position:0%
+Devices could be used to process things
+ 
+
+ align:start position:0%
+Devices could be used to process things
+that we think of as
+
+ align:start position:0%
+that we think of as
+ 
+
+ align:start position:0%
+that we think of as
+thought and so again this this notion of
+
+ align:start position:0%
+thought and so again this this notion of
+ 
+
+ align:start position:0%
+thought and so again this this notion of
+uh the mechanical
+
+ align:start position:0%
+uh the mechanical
+ 
+
+ align:start position:0%
+uh the mechanical
+world and is
+
+ align:start position:0%
+world and is
+ 
+
+ align:start position:0%
+world and is
+capabilities among many many victorians
+
+ align:start position:0%
+capabilities among many many victorians
+ 
+
+ align:start position:0%
+capabilities among many many victorians
+19th century people had become uh uh a
+
+ align:start position:0%
+19th century people had become uh uh a
+ 
+
+ align:start position:0%
+19th century people had become uh uh a
+very uh powerful and and uh
+
+ align:start position:0%
+very uh powerful and and uh
+ 
+
+ align:start position:0%
+very uh powerful and and uh
+compelling
+
+ align:start position:0%
+compelling
+ 
+
+ align:start position:0%
+compelling
+idea and people like
+
+ align:start position:0%
+idea and people like
+ 
+
+ align:start position:0%
+idea and people like
+Darwin and the technical
+
+ align:start position:0%
+Darwin and the technical
+ 
+
+ align:start position:0%
+Darwin and the technical
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Elites were were quite familiar with
+
+ align:start position:0%
+Elites were were quite familiar with
+ 
+
+ align:start position:0%
+Elites were were quite familiar with
+with these
+
+ align:start position:0%
+with these
+ 
+
+ align:start position:0%
+with these
+possibilities and also these Notions of
+
+ align:start position:0%
+possibilities and also these Notions of
+ 
+
+ align:start position:0%
+possibilities and also these Notions of
+mechanical and the the the the the
+
+ align:start position:0%
+mechanical and the the the the the
+ 
+
+ align:start position:0%
+mechanical and the the the the the
+prevalence of the mechanical world and
+
+ align:start position:0%
+prevalence of the mechanical world and
+ 
+
+ align:start position:0%
+prevalence of the mechanical world and
+its its uh capabilities uh were not just
+
+ align:start position:0%
+its its uh capabilities uh were not just
+ 
+
+ align:start position:0%
+its its uh capabilities uh were not just
+Elites there were you know many many
+
+ align:start position:0%
+Elites there were you know many many
+ 
+
+ align:start position:0%
+Elites there were you know many many
+people in the middle class and in the
+
+ align:start position:0%
+people in the middle class and in the
+ 
+
+ align:start position:0%
+people in the middle class and in the
+working class
+
+ align:start position:0%
+working class
+ 
+
+ align:start position:0%
+working class
+were in the same environments and
+
+ align:start position:0%
+were in the same environments and
+ 
+
+ align:start position:0%
+were in the same environments and
+understood that these forms of progress
+
+ align:start position:0%
+understood that these forms of progress
+ 
+
+ align:start position:0%
+understood that these forms of progress
+were uh were uh Trend setting and and
+
+ align:start position:0%
+were uh were uh Trend setting and and
+ 
+
+ align:start position:0%
+were uh were uh Trend setting and and
+Incredibly important um and transforming
+
+ align:start position:0%
+Incredibly important um and transforming
+ 
+
+ align:start position:0%
+Incredibly important um and transforming
+the uh transforming the way people
+
+ align:start position:0%
+the uh transforming the way people
+ 
+
+ align:start position:0%
+the uh transforming the way people
+lived uh there were a number of people
+
+ align:start position:0%
+lived uh there were a number of people
+ 
+
+ align:start position:0%
+lived uh there were a number of people
+of bab's machines uh ad LEL uh Lord
+
+ align:start position:0%
+of bab's machines uh ad LEL uh Lord
+ 
+
+ align:start position:0%
+of bab's machines uh ad LEL uh Lord
+Byron's daughter the poet's daughter um
+
+ align:start position:0%
+Byron's daughter the poet's daughter um
+ 
+
+ align:start position:0%
+Byron's daughter the poet's daughter um
+she was one of the first programmers she
+
+ align:start position:0%
+she was one of the first programmers she
+ 
+
+ align:start position:0%
+she was one of the first programmers she
+was a mathematician and she wrote
+
+ align:start position:0%
+was a mathematician and she wrote
+ 
+
+ align:start position:0%
+was a mathematician and she wrote
+program for uh babbage's machines and
+
+ align:start position:0%
+program for uh babbage's machines and
+ 
+
+ align:start position:0%
+program for uh babbage's machines and
+she understood the whole notion of
+
+ align:start position:0%
+she understood the whole notion of
+ 
+
+ align:start position:0%
+she understood the whole notion of
+programming the idea that you would
+
+ align:start position:0%
+programming the idea that you would
+ 
+
+ align:start position:0%
+programming the idea that you would
+create instructions for machines then
+
+ align:start position:0%
+create instructions for machines then
+ 
+
+ align:start position:0%
+create instructions for machines then
+you could feed them into machines and
+
+ align:start position:0%
+you could feed them into machines and
+ 
+
+ align:start position:0%
+you could feed them into machines and
+machines could carry out your
+
+ align:start position:0%
+machines could carry out your
+ 
+
+ align:start position:0%
+machines could carry out your
+instructions so when we when we think of
+
+ align:start position:0%
+instructions so when we when we think of
+ 
+
+ align:start position:0%
+instructions so when we when we think of
+these uh these ravings of this professor
+
+ align:start position:0%
+these uh these ravings of this professor
+ 
+
+ align:start position:0%
+these uh these ravings of this professor
+here keep in mind that uh Butler's aware
+
+ align:start position:0%
+here keep in mind that uh Butler's aware
+ 
+
+ align:start position:0%
+here keep in mind that uh Butler's aware
+of all this world and you know he's not
+
+ align:start position:0%
+of all this world and you know he's not
+ 
+
+ align:start position:0%
+of all this world and you know he's not
+just kind of coming up out of nowhere
+
+ align:start position:0%
+just kind of coming up out of nowhere
+ 
+
+ align:start position:0%
+just kind of coming up out of nowhere
+with these these
+
+ align:start position:0%
+with these these
+ 
+
+ align:start position:0%
+with these these
+Notions uh but he's using them also in a
+
+ align:start position:0%
+Notions uh but he's using them also in a
+ 
+
+ align:start position:0%
+Notions uh but he's using them also in a
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+U you know it's it's a sort of satire
+
+ align:start position:0%
+U you know it's it's a sort of satire
+ 
+
+ align:start position:0%
+U you know it's it's a sort of satire
+he's not being totally serious but he's
+
+ align:start position:0%
+he's not being totally serious but he's
+ 
+
+ align:start position:0%
+he's not being totally serious but he's
+also you know trying to tweak your
+
+ align:start position:0%
+also you know trying to tweak your
+ 
+
+ align:start position:0%
+also you know trying to tweak your
+imagination into thinking about it and
+
+ align:start position:0%
+imagination into thinking about it and
+ 
+
+ align:start position:0%
+imagination into thinking about it and
+that's what the book for it's it's it's
+
+ align:start position:0%
+that's what the book for it's it's it's
+ 
+
+ align:start position:0%
+that's what the book for it's it's it's
+not to tell you that this is exactly
+
+ align:start position:0%
+not to tell you that this is exactly
+ 
+
+ align:start position:0%
+not to tell you that this is exactly
+what's going to happen it's just to make
+
+ align:start position:0%
+what's going to happen it's just to make
+ 
+
+ align:start position:0%
+what's going to happen it's just to make
+you think about it and think a little
+
+ align:start position:0%
+you think about it and think a little
+ 
+
+ align:start position:0%
+you think about it and think a little
+more deeply and get beyond your everyday
+
+ align:start position:0%
+more deeply and get beyond your everyday
+ 
+
+ align:start position:0%
+more deeply and get beyond your everyday
+assumptions and that's the spirit of the
+
+ align:start position:0%
+assumptions and that's the spirit of the
+ 
+
+ align:start position:0%
+assumptions and that's the spirit of the
+book so he says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um at the start of chapter one uh of the
+
+ align:start position:0%
+um at the start of chapter one uh of the
+ 
+
+ align:start position:0%
+um at the start of chapter one uh of the
+uh chapter the first chapter on the book
+
+ align:start position:0%
+uh chapter the first chapter on the book
+ 
+
+ align:start position:0%
+uh chapter the first chapter on the book
+of the machines it runs
+
+ align:start position:0%
+of the machines it runs
+ 
+
+ align:start position:0%
+of the machines it runs
+through three chapters he says uh there
+
+ align:start position:0%
+through three chapters he says uh there
+ 
+
+ align:start position:0%
+through three chapters he says uh there
+was a time when the Earth was was to all
+
+ align:start position:0%
+was a time when the Earth was was to all
+ 
+
+ align:start position:0%
+was a time when the Earth was was to all
+appearance utterly destitute both of
+
+ align:start position:0%
+appearance utterly destitute both of
+ 
+
+ align:start position:0%
+appearance utterly destitute both of
+animal and vegetable life and when
+
+ align:start position:0%
+animal and vegetable life and when
+ 
+
+ align:start position:0%
+animal and vegetable life and when
+according to the opinion of our best
+
+ align:start position:0%
+according to the opinion of our best
+ 
+
+ align:start position:0%
+according to the opinion of our best
+philosophers it was simply a hot round
+
+ align:start position:0%
+philosophers it was simply a hot round
+ 
+
+ align:start position:0%
+philosophers it was simply a hot round
+ball with a crust gradually
+
+ align:start position:0%
+ball with a crust gradually
+ 
+
+ align:start position:0%
+ball with a crust gradually
+cooling now if a human being had existed
+
+ align:start position:0%
+cooling now if a human being had existed
+ 
+
+ align:start position:0%
+cooling now if a human being had existed
+while the Earth was in this state and
+
+ align:start position:0%
+while the Earth was in this state and
+ 
+
+ align:start position:0%
+while the Earth was in this state and
+had been allowed to see it as though it
+
+ align:start position:0%
+had been allowed to see it as though it
+ 
+
+ align:start position:0%
+had been allowed to see it as though it
+were some other world with which he had
+
+ align:start position:0%
+were some other world with which he had
+ 
+
+ align:start position:0%
+were some other world with which he had
+no concern and if at the same time he
+
+ align:start position:0%
+no concern and if at the same time he
+ 
+
+ align:start position:0%
+no concern and if at the same time he
+were entirely ignorant of all physical
+
+ align:start position:0%
+were entirely ignorant of all physical
+ 
+
+ align:start position:0%
+were entirely ignorant of all physical
+science would he not have pronounced it
+
+ align:start position:0%
+science would he not have pronounced it
+ 
+
+ align:start position:0%
+science would he not have pronounced it
+in possible that creatures possessed of
+
+ align:start position:0%
+in possible that creatures possessed of
+ 
+
+ align:start position:0%
+in possible that creatures possessed of
+anything like
+
+ align:start position:0%
+anything like
+ 
+
+ align:start position:0%
+anything like
+Consciousness should be evolved from the
+
+ align:start position:0%
+Consciousness should be evolved from the
+ 
+
+ align:start position:0%
+Consciousness should be evolved from the
+seeming Cinder which he was
+
+ align:start position:0%
+seeming Cinder which he was
+ 
+
+ align:start position:0%
+seeming Cinder which he was
+beholding would he not have denied that
+
+ align:start position:0%
+beholding would he not have denied that
+ 
+
+ align:start position:0%
+beholding would he not have denied that
+it contained any potentiality of
+
+ align:start position:0%
+it contained any potentiality of
+ 
+
+ align:start position:0%
+it contained any potentiality of
+Consciousness yet in the course of time
+
+ align:start position:0%
+Consciousness yet in the course of time
+ 
+
+ align:start position:0%
+Consciousness yet in the course of time
+Consciousness
+
+ align:start position:0%
+Consciousness
+ 
+
+ align:start position:0%
+Consciousness
+came is it not possible then that there
+
+ align:start position:0%
+came is it not possible then that there
+ 
+
+ align:start position:0%
+came is it not possible then that there
+may be even yet new channels dug out for
+
+ align:start position:0%
+may be even yet new channels dug out for
+ 
+
+ align:start position:0%
+may be even yet new channels dug out for
+Consciousness though we can detect no
+
+ align:start position:0%
+Consciousness though we can detect no
+ 
+
+ align:start position:0%
+Consciousness though we can detect no
+signs of them at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+so what's he
+
+ align:start position:0%
+so what's he
+ 
+
+ align:start position:0%
+so what's he
+saying I mean how do we understand this
+
+ align:start position:0%
+saying I mean how do we understand this
+ 
+
+ align:start position:0%
+saying I mean how do we understand this
+what does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean Jake what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+think he says that Consciousness no one
+
+ align:start position:0%
+think he says that Consciousness no one
+ 
+
+ align:start position:0%
+think he says that Consciousness no one
+would imagine consciousness looking at
+
+ align:start position:0%
+would imagine consciousness looking at
+ 
+
+ align:start position:0%
+would imagine consciousness looking at
+the Earth before just as it was at the
+
+ align:start position:0%
+the Earth before just as it was at the
+ 
+
+ align:start position:0%
+the Earth before just as it was at the
+very earliest stage so well he's he's
+
+ align:start position:0%
+very earliest stage so well he's he's
+ 
+
+ align:start position:0%
+very earliest stage so well he's he's
+saying that if you look at the very
+
+ align:start position:0%
+saying that if you look at the very
+ 
+
+ align:start position:0%
+saying that if you look at the very
+stages not only is there no life at all
+
+ align:start position:0%
+stages not only is there no life at all
+ 
+
+ align:start position:0%
+stages not only is there no life at all
+MH but if you think you think of
+
+ align:start position:0%
+MH but if you think you think of
+ 
+
+ align:start position:0%
+MH but if you think you think of
+Consciousness as like a it's an advanced
+
+ align:start position:0%
+Consciousness as like a it's an advanced
+ 
+
+ align:start position:0%
+Consciousness as like a it's an advanced
+concept really and you look at the very
+
+ align:start position:0%
+concept really and you look at the very
+ 
+
+ align:start position:0%
+concept really and you look at the very
+basic Earth no life right you think well
+
+ align:start position:0%
+basic Earth no life right you think well
+ 
+
+ align:start position:0%
+basic Earth no life right you think well
+maybe some basic life
+
+ align:start position:0%
+maybe some basic life
+ 
+
+ align:start position:0%
+maybe some basic life
+bacteria viruses I mean the real basic
+
+ align:start position:0%
+bacteria viruses I mean the real basic
+ 
+
+ align:start position:0%
+bacteria viruses I mean the real basic
+stuff come out of that
+
+ align:start position:0%
+stuff come out of that
+ 
+
+ align:start position:0%
+stuff come out of that
+maybe but you think about complex things
+
+ align:start position:0%
+maybe but you think about complex things
+ 
+
+ align:start position:0%
+maybe but you think about complex things
+like self-awareness and cognizance and I
+
+ align:start position:0%
+like self-awareness and cognizance and I
+ 
+
+ align:start position:0%
+like self-awareness and cognizance and I
+mean you don't you really don't see that
+
+ align:start position:0%
+mean you don't you really don't see that
+ 
+
+ align:start position:0%
+mean you don't you really don't see that
+coming that's that's what his point is
+
+ align:start position:0%
+coming that's that's what his point is
+ 
+
+ align:start position:0%
+coming that's that's what his point is
+his point is that these complex things
+
+ align:start position:0%
+his point is that these complex things
+ 
+
+ align:start position:0%
+his point is that these complex things
+aren't justop s popping up all over the
+
+ align:start position:0%
+aren't justop s popping up all over the
+ 
+
+ align:start position:0%
+aren't justop s popping up all over the
+place that it just doesn't make sense to
+
+ align:start position:0%
+place that it just doesn't make sense to
+ 
+
+ align:start position:0%
+place that it just doesn't make sense to
+see that happen Okay and then I think he
+
+ align:start position:0%
+see that happen Okay and then I think he
+ 
+
+ align:start position:0%
+see that happen Okay and then I think he
+also leaves it open
+
+ align:start position:0%
+also leaves it open
+ 
+
+ align:start position:0%
+also leaves it open
+for kind of like the
+
+ align:start position:0%
+for kind of like the
+ 
+
+ align:start position:0%
+for kind of like the
+unfathomable you know Beyond like if our
+
+ align:start position:0%
+unfathomable you know Beyond like if our
+ 
+
+ align:start position:0%
+unfathomable you know Beyond like if our
+Consciousness came out of this nothing
+
+ align:start position:0%
+Consciousness came out of this nothing
+ 
+
+ align:start position:0%
+Consciousness came out of this nothing
+this you know ball of like
+
+ align:start position:0%
+this you know ball of like
+ 
+
+ align:start position:0%
+this you know ball of like
+magma then then in another you know
+
+ align:start position:0%
+magma then then in another you know
+ 
+
+ align:start position:0%
+magma then then in another you know
+however many Millennia what could
+
+ align:start position:0%
+however many Millennia what could
+ 
+
+ align:start position:0%
+however many Millennia what could
+Consciousness evolve to what's the next
+
+ align:start position:0%
+Consciousness evolve to what's the next
+ 
+
+ align:start position:0%
+Consciousness evolve to what's the next
+level of
+
+ align:start position:0%
+level of
+ 
+
+ align:start position:0%
+level of
+Consciousness yeah it's pretty
+
+ align:start position:0%
+Consciousness yeah it's pretty
+ 
+
+ align:start position:0%
+Consciousness yeah it's pretty
+impressive that uh you know I
+
+ align:start position:0%
+impressive that uh you know I
+ 
+
+ align:start position:0%
+impressive that uh you know I
+mean from a naturalistic point of view
+
+ align:start position:0%
+mean from a naturalistic point of view
+ 
+
+ align:start position:0%
+mean from a naturalistic point of view
+it's pretty impressive that uh
+
+ align:start position:0%
+it's pretty impressive that uh
+ 
+
+ align:start position:0%
+it's pretty impressive that uh
+self-awareness Consciousness and things
+
+ align:start position:0%
+self-awareness Consciousness and things
+ 
+
+ align:start position:0%
+self-awareness Consciousness and things
+of those sorts
+
+ align:start position:0%
+of those sorts
+ 
+
+ align:start position:0%
+of those sorts
+uh that level of activity emerged
+
+ align:start position:0%
+uh that level of activity emerged
+ 
+
+ align:start position:0%
+uh that level of activity emerged
+from a planet that was uh at least in
+
+ align:start position:0%
+from a planet that was uh at least in
+ 
+
+ align:start position:0%
+from a planet that was uh at least in
+the scientific framework of
+
+ align:start position:0%
+the scientific framework of
+ 
+
+ align:start position:0%
+the scientific framework of
+understanding pretty much a Barren
+
+ align:start position:0%
+understanding pretty much a Barren
+ 
+
+ align:start position:0%
+understanding pretty much a Barren
+planet with nothing on it so this notion
+
+ align:start position:0%
+planet with nothing on it so this notion
+ 
+
+ align:start position:0%
+planet with nothing on it so this notion
+of progress things I mean you know this
+
+ align:start position:0%
+of progress things I mean you know this
+ 
+
+ align:start position:0%
+of progress things I mean you know this
+this notion that change takes place
+
+ align:start position:0%
+this notion that change takes place
+ 
+
+ align:start position:0%
+this notion that change takes place
+somehow in this endlessly iterative
+
+ align:start position:0%
+somehow in this endlessly iterative
+ 
+
+ align:start position:0%
+somehow in this endlessly iterative
+process that's the key here
+
+ align:start position:0%
+process that's the key here
+ 
+
+ align:start position:0%
+process that's the key here
+and his his his application of it to
+
+ align:start position:0%
+and his his his application of it to
+ 
+
+ align:start position:0%
+and his his his application of it to
+machines can make us think back to what
+
+ align:start position:0%
+machines can make us think back to what
+ 
+
+ align:start position:0%
+machines can make us think back to what
+is it special about natural selection
+
+ align:start position:0%
+is it special about natural selection
+ 
+
+ align:start position:0%
+is it special about natural selection
+what is it about the selection
+
+ align:start position:0%
+what is it about the selection
+ 
+
+ align:start position:0%
+what is it about the selection
+process that delivers something not just
+
+ align:start position:0%
+process that delivers something not just
+ 
+
+ align:start position:0%
+process that delivers something not just
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same but it
+
+ align:start position:0%
+same but it
+ 
+
+ align:start position:0%
+same but it
+delivers incremental change David well I
+
+ align:start position:0%
+delivers incremental change David well I
+ 
+
+ align:start position:0%
+delivers incremental change David well I
+think it's interesting that like if if
+
+ align:start position:0%
+think it's interesting that like if if
+ 
+
+ align:start position:0%
+think it's interesting that like if if
+something doesn't work if a mutation
+
+ align:start position:0%
+something doesn't work if a mutation
+ 
+
+ align:start position:0%
+something doesn't work if a mutation
+doesn't work if a change doesn't work it
+
+ align:start position:0%
+doesn't work if a change doesn't work it
+ 
+
+ align:start position:0%
+doesn't work if a change doesn't work it
+just disappears you know it it isn't
+
+ align:start position:0%
+just disappears you know it it isn't
+ 
+
+ align:start position:0%
+just disappears you know it it isn't
+allowed to progress at all
+
+ align:start position:0%
+allowed to progress at all
+ 
+
+ align:start position:0%
+allowed to progress at all
+um so I mean it keeps that from
+
+ align:start position:0%
+um so I mean it keeps that from
+ 
+
+ align:start position:0%
+um so I mean it keeps that from
+stagnating and it and it always drives
+
+ align:start position:0%
+stagnating and it and it always drives
+ 
+
+ align:start position:0%
+stagnating and it and it always drives
+something forward whether it's more
+
+ align:start position:0%
+something forward whether it's more
+ 
+
+ align:start position:0%
+something forward whether it's more
+complex and more you know works
+
+ align:start position:0%
+complex and more you know works
+ 
+
+ align:start position:0%
+complex and more you know works
+better so yeah so when you say drive
+
+ align:start position:0%
+better so yeah so when you say drive
+ 
+
+ align:start position:0%
+better so yeah so when you say drive
+forward what you're really referring to
+
+ align:start position:0%
+forward what you're really referring to
+ 
+
+ align:start position:0%
+forward what you're really referring to
+is the fact that you know there is a
+
+ align:start position:0%
+is the fact that you know there is a
+ 
+
+ align:start position:0%
+is the fact that you know there is a
+what we might call a figure of Merit or
+
+ align:start position:0%
+what we might call a figure of Merit or
+ 
+
+ align:start position:0%
+what we might call a figure of Merit or
+there's some concept of you know
+
+ align:start position:0%
+there's some concept of you know
+ 
+
+ align:start position:0%
+there's some concept of you know
+something can have
+
+ align:start position:0%
+something can have
+ 
+
+ align:start position:0%
+something can have
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+adaptation than something else so there
+
+ align:start position:0%
+adaptation than something else so there
+ 
+
+ align:start position:0%
+adaptation than something else so there
+there there's an incremental advantage
+
+ align:start position:0%
+there there's an incremental advantage
+ 
+
+ align:start position:0%
+there there's an incremental advantage
+or incremental there's a differential
+
+ align:start position:0%
+or incremental there's a differential
+ 
+
+ align:start position:0%
+or incremental there's a differential
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+favors A or B over a so there's some
+
+ align:start position:0%
+favors A or B over a so there's some
+ 
+
+ align:start position:0%
+favors A or B over a so there's some
+differential and through this iterative
+
+ align:start position:0%
+differential and through this iterative
+ 
+
+ align:start position:0%
+differential and through this iterative
+process and then
+
+ align:start position:0%
+process and then
+ 
+
+ align:start position:0%
+process and then
+the lack
+
+ align:start position:0%
+the lack
+ 
+
+ align:start position:0%
+the lack
+of uh resources to support everything
+
+ align:start position:0%
+of uh resources to support everything
+ 
+
+ align:start position:0%
+of uh resources to support everything
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+know as as as malus and Endor both said
+
+ align:start position:0%
+know as as as malus and Endor both said
+ 
+
+ align:start position:0%
+know as as as malus and Endor both said
+you know if everything were supported
+
+ align:start position:0%
+you know if everything were supported
+ 
+
+ align:start position:0%
+you know if everything were supported
+one single species would totally occupy
+
+ align:start position:0%
+one single species would totally occupy
+ 
+
+ align:start position:0%
+one single species would totally occupy
+the earth so there's not enough but
+
+ align:start position:0%
+the earth so there's not enough but
+ 
+
+ align:start position:0%
+the earth so there's not enough but
+there's there's something happening here
+
+ align:start position:0%
+there's there's something happening here
+ 
+
+ align:start position:0%
+there's there's something happening here
+right at the heart of this iterative
+
+ align:start position:0%
+right at the heart of this iterative
+ 
+
+ align:start position:0%
+right at the heart of this iterative
+process there is some kind of variation
+
+ align:start position:0%
+process there is some kind of variation
+ 
+
+ align:start position:0%
+process there is some kind of variation
+process that takes
+
+ align:start position:0%
+process that takes
+ 
+
+ align:start position:0%
+process that takes
+place and there's a selecting
+
+ align:start position:0%
+place and there's a selecting
+ 
+
+ align:start position:0%
+place and there's a selecting
+force and with that really really
+
+ align:start position:0%
+force and with that really really
+ 
+
+ align:start position:0%
+force and with that really really
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+Dynamic over large periods of time you
+
+ align:start position:0%
+Dynamic over large periods of time you
+ 
+
+ align:start position:0%
+Dynamic over large periods of time you
+get dramatic
+
+ align:start position:0%
+get dramatic
+ 
+
+ align:start position:0%
+get dramatic
+changes but it's always uh not a known
+
+ align:start position:0%
+changes but it's always uh not a known
+ 
+
+ align:start position:0%
+changes but it's always uh not a known
+facet
+
+ align:start position:0%
+facet
+ 
+
+ align:start position:0%
+facet
+salum nature does not uh go through
+
+ align:start position:0%
+salum nature does not uh go through
+ 
+
+ align:start position:0%
+salum nature does not uh go through
+jumps or does not jump through its its
+
+ align:start position:0%
+jumps or does not jump through its its
+ 
+
+ align:start position:0%
+jumps or does not jump through its its
+development so so this is uh this this
+
+ align:start position:0%
+development so so this is uh this this
+ 
+
+ align:start position:0%
+development so so this is uh this this
+notion of Consciousness is a product of
+
+ align:start position:0%
+notion of Consciousness is a product of
+ 
+
+ align:start position:0%
+notion of Consciousness is a product of
+that I mean that's that's what he's he's
+
+ align:start position:0%
+that I mean that's that's what he's he's
+ 
+
+ align:start position:0%
+that I mean that's that's what he's he's
+pointing out this this notion of
+
+ align:start position:0%
+pointing out this this notion of
+ 
+
+ align:start position:0%
+pointing out this this notion of
+Consciousness is a product of that long
+
+ align:start position:0%
+Consciousness is a product of that long
+ 
+
+ align:start position:0%
+Consciousness is a product of that long
+iteration
+
+ align:start position:0%
+iteration
+ 
+
+ align:start position:0%
+iteration
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+then our our uh our philosopher here
+
+ align:start position:0%
+then our our uh our philosopher here
+ 
+
+ align:start position:0%
+then our our uh our philosopher here
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+um if this can happen with materials
+
+ align:start position:0%
+um if this can happen with materials
+ 
+
+ align:start position:0%
+um if this can happen with materials
+that we would basic basic Bally consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-living why why could it not happen
+
+ align:start position:0%
+non-living why why could it not happen
+ 
+
+ align:start position:0%
+non-living why why could it not happen
+with machines so what about this analogy
+
+ align:start position:0%
+with machines so what about this analogy
+ 
+
+ align:start position:0%
+with machines so what about this analogy
+with machines are we back into the the
+
+ align:start position:0%
+with machines are we back into the the
+ 
+
+ align:start position:0%
+with machines are we back into the the
+realm of U cleanthes with uh you know
+
+ align:start position:0%
+realm of U cleanthes with uh you know
+ 
+
+ align:start position:0%
+realm of U cleanthes with uh you know
+analogies that really don't
+
+ align:start position:0%
+analogies that really don't
+ 
+
+ align:start position:0%
+analogies that really don't
+work uh I mean
+
+ align:start position:0%
+work uh I mean
+ 
+
+ align:start position:0%
+work uh I mean
+is why does he apply this concept of
+
+ align:start position:0%
+is why does he apply this concept of
+ 
+
+ align:start position:0%
+is why does he apply this concept of
+machines what is it about
+
+ align:start position:0%
+machines what is it about
+ 
+
+ align:start position:0%
+machines what is it about
+machines uh as opposed to rocks or
+
+ align:start position:0%
+machines uh as opposed to rocks or
+ 
+
+ align:start position:0%
+machines uh as opposed to rocks or
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like in terms of national selection
+
+ align:start position:0%
+like in terms of national selection
+ 
+
+ align:start position:0%
+like in terms of national selection
+machines are very very good at what they
+
+ align:start position:0%
+machines are very very good at what they
+ 
+
+ align:start position:0%
+machines are very very good at what they
+do so they're all like they they can all
+
+ align:start position:0%
+do so they're all like they they can all
+ 
+
+ align:start position:0%
+do so they're all like they they can all
+they can almost evolve by by by through
+
+ align:start position:0%
+they can almost evolve by by by through
+ 
+
+ align:start position:0%
+they can almost evolve by by by through
+through us and then they be start
+
+ align:start position:0%
+through us and then they be start
+ 
+
+ align:start position:0%
+through us and then they be start
+becoming the best of what they do to the
+
+ align:start position:0%
+becoming the best of what they do to the
+ 
+
+ align:start position:0%
+becoming the best of what they do to the
+point where they're even better than
+
+ align:start position:0%
+point where they're even better than
+ 
+
+ align:start position:0%
+point where they're even better than
+humans so I guess if you take it from
+
+ align:start position:0%
+humans so I guess if you take it from
+ 
+
+ align:start position:0%
+humans so I guess if you take it from
+that stance you could say that they
+
+ align:start position:0%
+that stance you could say that they
+ 
+
+ align:start position:0%
+that stance you could say that they
+could continue evolving what they better
+
+ align:start position:0%
+could continue evolving what they better
+ 
+
+ align:start position:0%
+could continue evolving what they better
+than hum by
+
+ align:start position:0%
+than hum by
+ 
+
+ align:start position:0%
+than hum by
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+yeah machines uh don't stay the same
+
+ align:start position:0%
+yeah machines uh don't stay the same
+ 
+
+ align:start position:0%
+yeah machines uh don't stay the same
+because we interact with them is that
+
+ align:start position:0%
+because we interact with them is that
+ 
+
+ align:start position:0%
+because we interact with them is that
+correct I mean that's that's how we put
+
+ align:start position:0%
+correct I mean that's that's how we put
+ 
+
+ align:start position:0%
+correct I mean that's that's how we put
+it so we are in some sense a selecting
+
+ align:start position:0%
+it so we are in some sense a selecting
+ 
+
+ align:start position:0%
+it so we are in some sense a selecting
+Force now in what way is this different
+
+ align:start position:0%
+Force now in what way is this different
+ 
+
+ align:start position:0%
+Force now in what way is this different
+from natural
+
+ align:start position:0%
+from natural
+ 
+
+ align:start position:0%
+from natural
+selection the human selecting force on
+
+ align:start position:0%
+selection the human selecting force on
+ 
+
+ align:start position:0%
+selection the human selecting force on
+machines making machines better that
+
+ align:start position:0%
+machines making machines better that
+ 
+
+ align:start position:0%
+machines making machines better that
+primitive uh steam machine of watt as we
+
+ align:start position:0%
+primitive uh steam machine of watt as we
+ 
+
+ align:start position:0%
+primitive uh steam machine of watt as we
+all know
+
+ align:start position:0%
+all know
+ 
+
+ align:start position:0%
+all know
+developed into this these incredible
+
+ align:start position:0%
+developed into this these incredible
+ 
+
+ align:start position:0%
+developed into this these incredible
+Railway
+
+ align:start position:0%
+Railway
+ 
+
+ align:start position:0%
+Railway
+engines so
+
+ align:start position:0%
+engines so
+ 
+
+ align:start position:0%
+engines so
+what how is that similar and different
+
+ align:start position:0%
+what how is that similar and different
+ 
+
+ align:start position:0%
+what how is that similar and different
+from natural
+
+ align:start position:0%
+from natural
+ 
+
+ align:start position:0%
+from natural
+selection well in the case of machines
+
+ align:start position:0%
+selection well in the case of machines
+ 
+
+ align:start position:0%
+selection well in the case of machines
+the humans are constantly adapting the
+
+ align:start position:0%
+the humans are constantly adapting the
+ 
+
+ align:start position:0%
+the humans are constantly adapting the
+machines um and I think Darwin said
+
+ align:start position:0%
+machines um and I think Darwin said
+ 
+
+ align:start position:0%
+machines um and I think Darwin said
+something about like how natural
+
+ align:start position:0%
+something about like how natural
+ 
+
+ align:start position:0%
+something about like how natural
+selection never occurs for one animal
+
+ align:start position:0%
+selection never occurs for one animal
+ 
+
+ align:start position:0%
+selection never occurs for one animal
+like one animal doesn't evolve
+
+ align:start position:0%
+like one animal doesn't evolve
+ 
+
+ align:start position:0%
+like one animal doesn't evolve
+to benefit another animal like it always
+
+ align:start position:0%
+to benefit another animal like it always
+ 
+
+ align:start position:0%
+to benefit another animal like it always
+evolves to benefit itself it always
+
+ align:start position:0%
+evolves to benefit itself it always
+ 
+
+ align:start position:0%
+evolves to benefit itself it always
+selects for things for itself yes I know
+
+ align:start position:0%
+selects for things for itself yes I know
+ 
+
+ align:start position:0%
+selects for things for itself yes I know
+that was in the Instinct chapter but I
+
+ align:start position:0%
+that was in the Instinct chapter but I
+ 
+
+ align:start position:0%
+that was in the Instinct chapter but I
+think it you're you're you're you're
+
+ align:start position:0%
+think it you're you're you're you're
+ 
+
+ align:start position:0%
+think it you're you're you're you're
+absolutely correct the whole he says if
+
+ align:start position:0%
+absolutely correct the whole he says if
+ 
+
+ align:start position:0%
+absolutely correct the whole he says if
+you can tell you can show me something
+
+ align:start position:0%
+you can tell you can show me something
+ 
+
+ align:start position:0%
+you can tell you can show me something
+that doesn't my whole Theory would have
+
+ align:start position:0%
+that doesn't my whole Theory would have
+ 
+
+ align:start position:0%
+that doesn't my whole Theory would have
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+reconsidered so so the machines would
+
+ align:start position:0%
+reconsidered so so the machines would
+ 
+
+ align:start position:0%
+reconsidered so so the machines would
+have to reach some threshold where they
+
+ align:start position:0%
+have to reach some threshold where they
+ 
+
+ align:start position:0%
+have to reach some threshold where they
+could somehow Supply the change
+
+ align:start position:0%
+could somehow Supply the change
+ 
+
+ align:start position:0%
+could somehow Supply the change
+themselves okay okay other thoughts on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this well
+
+ align:start position:0%
+this well
+ 
+
+ align:start position:0%
+this well
+uh is there an instance In Darwin's work
+
+ align:start position:0%
+uh is there an instance In Darwin's work
+ 
+
+ align:start position:0%
+uh is there an instance In Darwin's work
+in in the origin where we do have
+
+ align:start position:0%
+in in the origin where we do have
+ 
+
+ align:start position:0%
+in in the origin where we do have
+organisms that are changing for other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organisms how about the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chapter domestication
+
+ align:start position:0%
+chapter domestication
+ 
+
+ align:start position:0%
+chapter domestication
+I mean those those organisms are
+
+ align:start position:0%
+I mean those those organisms are
+ 
+
+ align:start position:0%
+I mean those those organisms are
+changing for the benefit of other
+
+ align:start position:0%
+changing for the benefit of other
+ 
+
+ align:start position:0%
+changing for the benefit of other
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+I.E
+
+ align:start position:0%
+I.E
+ 
+
+ align:start position:0%
+I.E
+as yeah but we're select you know the
+
+ align:start position:0%
+as yeah but we're select you know the
+ 
+
+ align:start position:0%
+as yeah but we're select you know the
+the humans whether it's conscious
+
+ align:start position:0%
+the humans whether it's conscious
+ 
+
+ align:start position:0%
+the humans whether it's conscious
+selection or unconscious selection are
+
+ align:start position:0%
+selection or unconscious selection are
+ 
+
+ align:start position:0%
+selection or unconscious selection are
+selecting
+
+ align:start position:0%
+selecting
+ 
+
+ align:start position:0%
+selecting
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+individuals whether it's sheep or
+
+ align:start position:0%
+individuals whether it's sheep or
+ 
+
+ align:start position:0%
+individuals whether it's sheep or
+chickens or whatever they're breeding
+
+ align:start position:0%
+chickens or whatever they're breeding
+ 
+
+ align:start position:0%
+chickens or whatever they're breeding
+them into domestic species for their own
+
+ align:start position:0%
+them into domestic species for their own
+ 
+
+ align:start position:0%
+them into domestic species for their own
+purposes yes the difference between that
+
+ align:start position:0%
+purposes yes the difference between that
+ 
+
+ align:start position:0%
+purposes yes the difference between that
+and machines is that um machines aren't
+
+ align:start position:0%
+and machines is that um machines aren't
+ 
+
+ align:start position:0%
+and machines is that um machines aren't
+their own source of mutation okay the
+
+ align:start position:0%
+their own source of mutation okay the
+ 
+
+ align:start position:0%
+their own source of mutation okay the
+humans are what the selector and the
+
+ align:start position:0%
+humans are what the selector and the
+ 
+
+ align:start position:0%
+humans are what the selector and the
+source of mutation is in selection of
+
+ align:start position:0%
+source of mutation is in selection of
+ 
+
+ align:start position:0%
+source of mutation is in selection of
+animals they create Rand mutations than
+
+ align:start position:0%
+animals they create Rand mutations than
+ 
+
+ align:start position:0%
+animals they create Rand mutations than
+yeah yeah they're working with naturally
+
+ align:start position:0%
+yeah yeah they're working with naturally
+ 
+
+ align:start position:0%
+yeah yeah they're working with naturally
+yeah provid good point
+
+ align:start position:0%
+yeah provid good point
+ 
+
+ align:start position:0%
+yeah provid good point
+absolutely so maybe maybe we have
+
+ align:start position:0%
+absolutely so maybe maybe we have
+ 
+
+ align:start position:0%
+absolutely so maybe maybe we have
+to revise our theories somewhat does
+
+ align:start position:0%
+to revise our theories somewhat does
+ 
+
+ align:start position:0%
+to revise our theories somewhat does
+this and the question is does this is
+
+ align:start position:0%
+this and the question is does this is
+ 
+
+ align:start position:0%
+this and the question is does this is
+this enough to
+
+ align:start position:0%
+this enough to
+ 
+
+ align:start position:0%
+this enough to
+say uh these ideas don't work for
+
+ align:start position:0%
+say uh these ideas don't work for
+ 
+
+ align:start position:0%
+say uh these ideas don't work for
+machines Elisha you were going to
+
+ align:start position:0%
+machines Elisha you were going to
+ 
+
+ align:start position:0%
+machines Elisha you were going to
+say yeah
+
+ align:start position:0%
+say yeah
+ 
+
+ align:start position:0%
+say yeah
+okay about the difference between
+
+ align:start position:0%
+okay about the difference between
+ 
+
+ align:start position:0%
+okay about the difference between
+conscious and unconscious selection
+
+ align:start position:0%
+conscious and unconscious selection
+ 
+
+ align:start position:0%
+conscious and unconscious selection
+okay all right so yeah conscious and
+
+ align:start position:0%
+okay all right so yeah conscious and
+ 
+
+ align:start position:0%
+okay all right so yeah conscious and
+unconscious selection are in the
+
+ align:start position:0%
+unconscious selection are in the
+ 
+
+ align:start position:0%
+unconscious selection are in the
+background here and certainly um
+
+ align:start position:0%
+background here and certainly um
+ 
+
+ align:start position:0%
+background here and certainly um
+probably a lot of machine but but the
+
+ align:start position:0%
+probably a lot of machine but but the
+ 
+
+ align:start position:0%
+probably a lot of machine but but the
+fact is is humans are selecting
+
+ align:start position:0%
+fact is is humans are selecting
+ 
+
+ align:start position:0%
+fact is is humans are selecting
+machines
+
+ align:start position:0%
+machines
+ 
+
+ align:start position:0%
+machines
+and I I don't know maybe selecting is
+
+ align:start position:0%
+and I I don't know maybe selecting is
+ 
+
+ align:start position:0%
+and I I don't know maybe selecting is
+not all I mean selecting is not all are
+
+ align:start position:0%
+not all I mean selecting is not all are
+ 
+
+ align:start position:0%
+not all I mean selecting is not all are
+doing humans are building them too
+
+ align:start position:0%
+doing humans are building them too
+ 
+
+ align:start position:0%
+doing humans are building them too
+yeah the humans are coding the machine
+
+ align:start position:0%
+yeah the humans are coding the machine
+ 
+
+ align:start position:0%
+yeah the humans are coding the machine
+so so whereas you know DNA can vary on
+
+ align:start position:0%
+so so whereas you know DNA can vary on
+ 
+
+ align:start position:0%
+so so whereas you know DNA can vary on
+its own you know if if there's a
+
+ align:start position:0%
+its own you know if if there's a
+ 
+
+ align:start position:0%
+its own you know if if there's a
+variance in uh in like computer code
+
+ align:start position:0%
+variance in uh in like computer code
+ 
+
+ align:start position:0%
+variance in uh in like computer code
+then it's something that we've done and
+
+ align:start position:0%
+then it's something that we've done and
+ 
+
+ align:start position:0%
+then it's something that we've done and
+we can probably fix but we're not
+
+ align:start position:0%
+we can probably fix but we're not
+ 
+
+ align:start position:0%
+we can probably fix but we're not
+necessarily perfect in our programming
+
+ align:start position:0%
+necessarily perfect in our programming
+ 
+
+ align:start position:0%
+necessarily perfect in our programming
+ways what if we made an unconscious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mistake you remember the Terminator uh
+
+ align:start position:0%
+mistake you remember the Terminator uh
+ 
+
+ align:start position:0%
+mistake you remember the Terminator uh
+film where I say uh what is it oh you
+
+ align:start position:0%
+film where I say uh what is it oh you
+ 
+
+ align:start position:0%
+film where I say uh what is it oh you
+haven't seen it yeah so there's this
+
+ align:start position:0%
+haven't seen it yeah so there's this
+ 
+
+ align:start position:0%
+haven't seen it yeah so there's this
+moment where there there's this this
+
+ align:start position:0%
+moment where there there's this this
+ 
+
+ align:start position:0%
+moment where there there's this this
+this this this sort of network of
+
+ align:start position:0%
+this this this sort of network of
+ 
+
+ align:start position:0%
+this this this sort of network of
+computers sky sky Skynet
+
+ align:start position:0%
+computers sky sky Skynet
+ 
+
+ align:start position:0%
+computers sky sky Skynet
+has achieved Consciousness at 10
+
+ align:start position:0%
+has achieved Consciousness at 10
+ 
+
+ align:start position:0%
+has achieved Consciousness at 10
+something or they say and boom suddenly
+
+ align:start position:0%
+something or they say and boom suddenly
+ 
+
+ align:start position:0%
+something or they say and boom suddenly
+you know all this network computing is
+
+ align:start position:0%
+you know all this network computing is
+ 
+
+ align:start position:0%
+you know all this network computing is
+thinking for itself and you know it's
+
+ align:start position:0%
+thinking for itself and you know it's
+ 
+
+ align:start position:0%
+thinking for itself and you know it's
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+wow I mean that's that's science fiction
+
+ align:start position:0%
+wow I mean that's that's science fiction
+ 
+
+ align:start position:0%
+wow I mean that's that's science fiction
+but uh but it brings up uh one important
+
+ align:start position:0%
+but uh but it brings up uh one important
+ 
+
+ align:start position:0%
+but uh but it brings up uh one important
+thing and that is uh Butler's concept of
+
+ align:start position:0%
+thing and that is uh Butler's concept of
+ 
+
+ align:start position:0%
+thing and that is uh Butler's concept of
+machine and our more contemporary
+
+ align:start position:0%
+machine and our more contemporary
+ 
+
+ align:start position:0%
+machine and our more contemporary
+concept of machine how do they differ
+
+ align:start position:0%
+concept of machine how do they differ
+ 
+
+ align:start position:0%
+concept of machine how do they differ
+how are they similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think Butler's concept of
+
+ align:start position:0%
+I think Butler's concept of
+ 
+
+ align:start position:0%
+I think Butler's concept of
+machine I don't think it's like
+
+ align:start position:0%
+machine I don't think it's like
+ 
+
+ align:start position:0%
+machine I don't think it's like
+impossible like in the future like given
+
+ align:start position:0%
+impossible like in the future like given
+ 
+
+ align:start position:0%
+impossible like in the future like given
+the way we've advanced
+
+ align:start position:0%
+the way we've advanced
+ 
+
+ align:start position:0%
+the way we've advanced
+technology I mean I don't think it's
+
+ align:start position:0%
+technology I mean I don't think it's
+ 
+
+ align:start position:0%
+technology I mean I don't think it's
+impossible to one day imagine machines
+
+ align:start position:0%
+impossible to one day imagine machines
+ 
+
+ align:start position:0%
+impossible to one day imagine machines
+at that level at you know like Butler's
+
+ align:start position:0%
+at that level at you know like Butler's
+ 
+
+ align:start position:0%
+at that level at you know like Butler's
+level at the science fiction level yeah
+
+ align:start position:0%
+level at the science fiction level yeah
+ 
+
+ align:start position:0%
+level at the science fiction level yeah
+yeah I mean he certainly is is uh aware
+
+ align:start position:0%
+yeah I mean he certainly is is uh aware
+ 
+
+ align:start position:0%
+yeah I mean he certainly is is uh aware
+of uh you know machines being capable of
+
+ align:start position:0%
+of uh you know machines being capable of
+ 
+
+ align:start position:0%
+of uh you know machines being capable of
+calculating
+
+ align:start position:0%
+calculating
+ 
+
+ align:start position:0%
+calculating
+things and thinking as he says as as as
+
+ align:start position:0%
+things and thinking as he says as as as
+ 
+
+ align:start position:0%
+things and thinking as he says as as as
+the writer in the book says the man
+
+ align:start position:0%
+the writer in the book says the man
+ 
+
+ align:start position:0%
+the writer in the book says the man
+professor says you know when we need to
+
+ align:start position:0%
+professor says you know when we need to
+ 
+
+ align:start position:0%
+professor says you know when we need to
+do numbers we fly to our machines
+
+ align:start position:0%
+do numbers we fly to our machines
+ 
+
+ align:start position:0%
+do numbers we fly to our machines
+they're faster they don't need to rest
+
+ align:start position:0%
+they're faster they don't need to rest
+ 
+
+ align:start position:0%
+they're faster they don't need to rest
+and they're more accurate than we
+
+ align:start position:0%
+and they're more accurate than we
+ 
+
+ align:start position:0%
+and they're more accurate than we
+are uh of course we build them and we
+
+ align:start position:0%
+are uh of course we build them and we
+ 
+
+ align:start position:0%
+are uh of course we build them and we
+keep them going and so forth but
+
+ align:start position:0%
+keep them going and so forth but
+ 
+
+ align:start position:0%
+keep them going and so forth but
+nevertheless they function better at
+
+ align:start position:0%
+nevertheless they function better at
+ 
+
+ align:start position:0%
+nevertheless they function better at
+certain levels
+
+ align:start position:0%
+certain levels
+ 
+
+ align:start position:0%
+certain levels
+so uh he's aware of this but most of his
+
+ align:start position:0%
+so uh he's aware of this but most of his
+ 
+
+ align:start position:0%
+so uh he's aware of this but most of his
+mechanical examples here are 19th
+
+ align:start position:0%
+mechanical examples here are 19th
+ 
+
+ align:start position:0%
+mechanical examples here are 19th
+century
+
+ align:start position:0%
+century
+ 
+
+ align:start position:0%
+century
+mechanical the computational
+
+ align:start position:0%
+mechanical the computational
+ 
+
+ align:start position:0%
+mechanical the computational
+world that we see coming in just in its
+
+ align:start position:0%
+world that we see coming in just in its
+ 
+
+ align:start position:0%
+world that we see coming in just in its
+early nent stage with
+
+ align:start position:0%
+early nent stage with
+ 
+
+ align:start position:0%
+early nent stage with
+babage is going to
+
+ align:start position:0%
+babage is going to
+ 
+
+ align:start position:0%
+babage is going to
+explode later but that's going to be
+
+ align:start position:0%
+explode later but that's going to be
+ 
+
+ align:start position:0%
+explode later but that's going to be
+after Butler's time but the concept of a
+
+ align:start position:0%
+after Butler's time but the concept of a
+ 
+
+ align:start position:0%
+after Butler's time but the concept of a
+machine as a device
+
+ align:start position:0%
+machine as a device
+ 
+
+ align:start position:0%
+machine as a device
+for achieving a certain end will become
+
+ align:start position:0%
+for achieving a certain end will become
+ 
+
+ align:start position:0%
+for achieving a certain end will become
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+complicated the early versions of
+
+ align:start position:0%
+complicated the early versions of
+ 
+
+ align:start position:0%
+complicated the early versions of
+machine the steam machines and things of
+
+ align:start position:0%
+machine the steam machines and things of
+ 
+
+ align:start position:0%
+machine the steam machines and things of
+that sort are you know powerful very
+
+ align:start position:0%
+that sort are you know powerful very
+ 
+
+ align:start position:0%
+that sort are you know powerful very
+very effective at what they do and
+
+ align:start position:0%
+very effective at what they do and
+ 
+
+ align:start position:0%
+very effective at what they do and
+prevalent but in that
+
+ align:start position:0%
+prevalent but in that
+ 
+
+ align:start position:0%
+prevalent but in that
+very evolution of things machines are
+
+ align:start position:0%
+very evolution of things machines are
+ 
+
+ align:start position:0%
+very evolution of things machines are
+going to be become vastly more
+
+ align:start position:0%
+going to be become vastly more
+ 
+
+ align:start position:0%
+going to be become vastly more
+complicated vastly more
+
+ align:start position:0%
+complicated vastly more
+ 
+
+ align:start position:0%
+complicated vastly more
+capable this is more what we would
+
+ align:start position:0%
+capable this is more what we would
+ 
+
+ align:start position:0%
+capable this is more what we would
+associate with a lamaran model of the
+
+ align:start position:0%
+associate with a lamaran model of the
+ 
+
+ align:start position:0%
+associate with a lamaran model of the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+transmission of
+
+ align:start position:0%
+transmission of
+ 
+
+ align:start position:0%
+transmission of
+innovative features so this whole
+
+ align:start position:0%
+innovative features so this whole
+ 
+
+ align:start position:0%
+innovative features so this whole
+concept that uh uh inheritance actually
+
+ align:start position:0%
+concept that uh uh inheritance actually
+ 
+
+ align:start position:0%
+concept that uh uh inheritance actually
+works and
+
+ align:start position:0%
+works and
+ 
+
+ align:start position:0%
+works and
+transmits
+
+ align:start position:0%
+transmits
+ 
+
+ align:start position:0%
+transmits
+the uh the new
+
+ align:start position:0%
+the uh the new
+ 
+
+ align:start position:0%
+the uh the new
+level of adap adaptation of the parent
+
+ align:start position:0%
+level of adap adaptation of the parent
+ 
+
+ align:start position:0%
+level of adap adaptation of the parent
+that has been achieved by the parent
+
+ align:start position:0%
+that has been achieved by the parent
+ 
+
+ align:start position:0%
+that has been achieved by the parent
+that kind of model for uh that's a
+
+ align:start position:0%
+that kind of model for uh that's a
+ 
+
+ align:start position:0%
+that kind of model for uh that's a
+that's a model for very rapid change
+
+ align:start position:0%
+that's a model for very rapid change
+ 
+
+ align:start position:0%
+that's a model for very rapid change
+it's still
+
+ align:start position:0%
+it's still
+ 
+
+ align:start position:0%
+it's still
+systematic these these changes all seem
+
+ align:start position:0%
+systematic these these changes all seem
+ 
+
+ align:start position:0%
+systematic these these changes all seem
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh I mean they're made because they
+
+ align:start position:0%
+uh I mean they're made because they
+ 
+
+ align:start position:0%
+uh I mean they're made because they
+Advance functionality and adaptability
+
+ align:start position:0%
+Advance functionality and adaptability
+ 
+
+ align:start position:0%
+Advance functionality and adaptability
+if you will to the
+
+ align:start position:0%
+if you will to the
+ 
+
+ align:start position:0%
+if you will to the
+task so but there there's some kind of
+
+ align:start position:0%
+task so but there there's some kind of
+ 
+
+ align:start position:0%
+task so but there there's some kind of
+mechanism here and you know this this
+
+ align:start position:0%
+mechanism here and you know this this
+ 
+
+ align:start position:0%
+mechanism here and you know this this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um you know the the argument in in the
+
+ align:start position:0%
+um you know the the argument in in the
+ 
+
+ align:start position:0%
+um you know the the argument in in the
+book uh of machines here is yeah okay so
+
+ align:start position:0%
+book uh of machines here is yeah okay so
+ 
+
+ align:start position:0%
+book uh of machines here is yeah okay so
+machines evolve through the
+
+ align:start position:0%
+machines evolve through the
+ 
+
+ align:start position:0%
+machines evolve through the
+intermediary of
+
+ align:start position:0%
+intermediary of
+ 
+
+ align:start position:0%
+intermediary of
+humans but so
+
+ align:start position:0%
+humans but so
+ 
+
+ align:start position:0%
+humans but so
+what they still
+
+ align:start position:0%
+what they still
+ 
+
+ align:start position:0%
+what they still
+evolve and so yeah it's a different
+
+ align:start position:0%
+evolve and so yeah it's a different
+ 
+
+ align:start position:0%
+evolve and so yeah it's a different
+form but we would want to think of it at
+
+ align:start position:0%
+form but we would want to think of it at
+ 
+
+ align:start position:0%
+form but we would want to think of it at
+least in these terms because in many
+
+ align:start position:0%
+least in these terms because in many
+ 
+
+ align:start position:0%
+least in these terms because in many
+ways they're doing the same things as or
+
+ align:start position:0%
+ways they're doing the same things as or
+ 
+
+ align:start position:0%
+ways they're doing the same things as or
+they're they're performing functions and
+
+ align:start position:0%
+they're they're performing functions and
+ 
+
+ align:start position:0%
+they're they're performing functions and
+in many ways these these functions
+
+ align:start position:0%
+in many ways these these functions
+ 
+
+ align:start position:0%
+in many ways these these functions
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+advancing
+
+ align:start position:0%
+advancing
+ 
+
+ align:start position:0%
+advancing
+in function in in in
+
+ align:start position:0%
+in function in in in
+ 
+
+ align:start position:0%
+in function in in in
+ability so it's it's Happ it
+
+ align:start position:0%
+ability so it's it's Happ it
+ 
+
+ align:start position:0%
+ability so it's it's Happ it
+and this this notion and of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+self-replication uh you know do things
+
+ align:start position:0%
+self-replication uh you know do things
+ 
+
+ align:start position:0%
+self-replication uh you know do things
+have to be uh
+
+ align:start position:0%
+have to be uh
+ 
+
+ align:start position:0%
+have to be uh
+intentional
+
+ align:start position:0%
+intentional
+ 
+
+ align:start position:0%
+intentional
+uh is you know is it necessary for
+
+ align:start position:0%
+uh is you know is it necessary for
+ 
+
+ align:start position:0%
+uh is you know is it necessary for
+self-consciousness to uh be part of
+
+ align:start position:0%
+self-consciousness to uh be part of
+ 
+
+ align:start position:0%
+self-consciousness to uh be part of
+self-replication um and what is the Mad
+
+ align:start position:0%
+self-replication um and what is the Mad
+ 
+
+ align:start position:0%
+self-replication um and what is the Mad
+professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argue well he says one thing what is
+
+ align:start position:0%
+argue well he says one thing what is
+ 
+
+ align:start position:0%
+argue well he says one thing what is
+consciousness I mean do we have a
+
+ align:start position:0%
+consciousness I mean do we have a
+ 
+
+ align:start position:0%
+consciousness I mean do we have a
+definition of Consciousness I mean we
+
+ align:start position:0%
+definition of Consciousness I mean we
+ 
+
+ align:start position:0%
+definition of Consciousness I mean we
+all think we know what Consciousness is
+
+ align:start position:0%
+all think we know what Consciousness is
+ 
+
+ align:start position:0%
+all think we know what Consciousness is
+but uh you know how do we know I mean
+
+ align:start position:0%
+but uh you know how do we know I mean
+ 
+
+ align:start position:0%
+but uh you know how do we know I mean
+how do I know you all aren't zombies who
+
+ align:start position:0%
+how do I know you all aren't zombies who
+ 
+
+ align:start position:0%
+how do I know you all aren't zombies who
+come here to my class to how do you know
+
+ align:start position:0%
+come here to my class to how do you know
+ 
+
+ align:start position:0%
+come here to my class to how do you know
+I'm not just some kind of programmed you
+
+ align:start position:0%
+I'm not just some kind of programmed you
+ 
+
+ align:start position:0%
+I'm not just some kind of programmed you
+know something that MIT is testing out
+
+ align:start position:0%
+know something that MIT is testing out
+ 
+
+ align:start position:0%
+know something that MIT is testing out
+and they have this guy showing up every
+
+ align:start position:0%
+and they have this guy showing up every
+ 
+
+ align:start position:0%
+and they have this guy showing up every
+every morning and he's he's trying to
+
+ align:start position:0%
+every morning and he's he's trying to
+ 
+
+ align:start position:0%
+every morning and he's he's trying to
+teach this class and you know there's
+
+ align:start position:0%
+teach this class and you know there's
+ 
+
+ align:start position:0%
+teach this class and you know there's
+some person just behind
+
+ align:start position:0%
+some person just behind
+ 
+
+ align:start position:0%
+some person just behind
+the the wall who's manipulating me you
+
+ align:start position:0%
+the the wall who's manipulating me you
+ 
+
+ align:start position:0%
+the the wall who's manipulating me you
+know I mean do you know do you know
+
+ align:start position:0%
+know I mean do you know do you know
+ 
+
+ align:start position:0%
+know I mean do you know do you know
+what's in somebody else's head yeah I
+
+ align:start position:0%
+what's in somebody else's head yeah I
+ 
+
+ align:start position:0%
+what's in somebody else's head yeah I
+think our ideas of Consciousness is like
+
+ align:start position:0%
+think our ideas of Consciousness is like
+ 
+
+ align:start position:0%
+think our ideas of Consciousness is like
+from earlier in the year it's one of
+
+ align:start position:0%
+from earlier in the year it's one of
+ 
+
+ align:start position:0%
+from earlier in the year it's one of
+those things that we only really know
+
+ align:start position:0%
+those things that we only really know
+ 
+
+ align:start position:0%
+those things that we only really know
+through our daily experience with it but
+
+ align:start position:0%
+through our daily experience with it but
+ 
+
+ align:start position:0%
+through our daily experience with it but
+when we get outside of sort of our
+
+ align:start position:0%
+when we get outside of sort of our
+ 
+
+ align:start position:0%
+when we get outside of sort of our
+comfort zone things get fuzzy MH okay so
+
+ align:start position:0%
+comfort zone things get fuzzy MH okay so
+ 
+
+ align:start position:0%
+comfort zone things get fuzzy MH okay so
+we sort of know what we
+
+ align:start position:0%
+we sort of know what we
+ 
+
+ align:start position:0%
+we sort of know what we
+know and you know
+
+ align:start position:0%
+know and you know
+ 
+
+ align:start position:0%
+know and you know
+uh as day cart says I think therefore I
+
+ align:start position:0%
+uh as day cart says I think therefore I
+ 
+
+ align:start position:0%
+uh as day cart says I think therefore I
+am that's a pretty confident
+
+ align:start position:0%
+am that's a pretty confident
+ 
+
+ align:start position:0%
+am that's a pretty confident
+statement but do you think and therefore
+
+ align:start position:0%
+statement but do you think and therefore
+ 
+
+ align:start position:0%
+statement but do you think and therefore
+are you I mean we we we we we can't
+
+ align:start position:0%
+are you I mean we we we we we can't
+ 
+
+ align:start position:0%
+are you I mean we we we we we can't
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+verify you know the so and and even even
+
+ align:start position:0%
+verify you know the so and and even even
+ 
+
+ align:start position:0%
+verify you know the so and and even even
+then even if we can still what is what
+
+ align:start position:0%
+then even if we can still what is what
+ 
+
+ align:start position:0%
+then even if we can still what is what
+it what is the definition of
+
+ align:start position:0%
+it what is the definition of
+ 
+
+ align:start position:0%
+it what is the definition of
+self-consciousness
+
+ align:start position:0%
+self-consciousness
+ 
+
+ align:start position:0%
+self-consciousness
+you know we we we struggle with that
+
+ align:start position:0%
+you know we we we struggle with that
+ 
+
+ align:start position:0%
+you know we we we struggle with that
+especially when we try to I mean we
+
+ align:start position:0%
+especially when we try to I mean we
+ 
+
+ align:start position:0%
+especially when we try to I mean we
+don't struggle with it at the level of
+
+ align:start position:0%
+don't struggle with it at the level of
+ 
+
+ align:start position:0%
+don't struggle with it at the level of
+say the
+
+ align:start position:0%
+say the
+ 
+
+ align:start position:0%
+say the
+novel or I mean certainly some novels
+
+ align:start position:0%
+novel or I mean certainly some novels
+ 
+
+ align:start position:0%
+novel or I mean certainly some novels
+take up the questions of Consciousness
+
+ align:start position:0%
+take up the questions of Consciousness
+ 
+
+ align:start position:0%
+take up the questions of Consciousness
+PR was very into questions like this and
+
+ align:start position:0%
+PR was very into questions like this and
+ 
+
+ align:start position:0%
+PR was very into questions like this and
+but you
+
+ align:start position:0%
+but you
+ 
+
+ align:start position:0%
+but you
+know where where we really begin to
+
+ align:start position:0%
+know where where we really begin to
+ 
+
+ align:start position:0%
+know where where we really begin to
+struggle with self-consciousness when we
+
+ align:start position:0%
+struggle with self-consciousness when we
+ 
+
+ align:start position:0%
+struggle with self-consciousness when we
+begin to try to think of it in a
+
+ align:start position:0%
+begin to try to think of it in a
+ 
+
+ align:start position:0%
+begin to try to think of it in a
+scientific framework work of analyzing
+
+ align:start position:0%
+scientific framework work of analyzing
+ 
+
+ align:start position:0%
+scientific framework work of analyzing
+it and producing it I mean what would it
+
+ align:start position:0%
+it and producing it I mean what would it
+ 
+
+ align:start position:0%
+it and producing it I mean what would it
+mean to produce
+
+ align:start position:0%
+mean to produce
+ 
+
+ align:start position:0%
+mean to produce
+Consciousness well you got you have to
+
+ align:start position:0%
+Consciousness well you got you have to
+ 
+
+ align:start position:0%
+Consciousness well you got you have to
+come up with some definitions
+
+ align:start position:0%
+come up with some definitions
+ 
+
+ align:start position:0%
+come up with some definitions
+definitions aren't all that
+
+ align:start position:0%
+definitions aren't all that
+ 
+
+ align:start position:0%
+definitions aren't all that
+easy yeah David I think like part of us
+
+ align:start position:0%
+easy yeah David I think like part of us
+ 
+
+ align:start position:0%
+easy yeah David I think like part of us
+being unable to deal with you know with
+
+ align:start position:0%
+being unable to deal with you know with
+ 
+
+ align:start position:0%
+being unable to deal with you know with
+the concept of Consciousness with
+
+ align:start position:0%
+the concept of Consciousness with
+ 
+
+ align:start position:0%
+the concept of Consciousness with
+machines is if you look at you know as
+
+ align:start position:0%
+machines is if you look at you know as
+ 
+
+ align:start position:0%
+machines is if you look at you know as
+machines become more and
+
+ align:start position:0%
+machines become more and
+ 
+
+ align:start position:0%
+machines become more and
+more uh I guess used like in the home or
+
+ align:start position:0%
+more uh I guess used like in the home or
+ 
+
+ align:start position:0%
+more uh I guess used like in the home or
+whatever it
+
+ align:start position:0%
+whatever it
+ 
+
+ align:start position:0%
+whatever it
+okay a specific example like imagine you
+
+ align:start position:0%
+okay a specific example like imagine you
+ 
+
+ align:start position:0%
+okay a specific example like imagine you
+know the little robotic vacuums right um
+
+ align:start position:0%
+know the little robotic vacuums right um
+ 
+
+ align:start position:0%
+know the little robotic vacuums right um
+that kind of autonomously go around the
+
+ align:start position:0%
+that kind of autonomously go around the
+ 
+
+ align:start position:0%
+that kind of autonomously go around the
+house like like how many people do you
+
+ align:start position:0%
+house like like how many people do you
+ 
+
+ align:start position:0%
+house like like how many people do you
+know personify those vacuums like they
+
+ align:start position:0%
+know personify those vacuums like they
+ 
+
+ align:start position:0%
+know personify those vacuums like they
+consider like a pet like they you know
+
+ align:start position:0%
+consider like a pet like they you know
+ 
+
+ align:start position:0%
+consider like a pet like they you know
+it's it's easy for us to imagine that
+
+ align:start position:0%
+it's it's easy for us to imagine that
+ 
+
+ align:start position:0%
+it's it's easy for us to imagine that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+vacuum has a little goal in mind while
+
+ align:start position:0%
+vacuum has a little goal in mind while
+ 
+
+ align:start position:0%
+vacuum has a little goal in mind while
+it's vacuuming just because we're so
+
+ align:start position:0%
+it's vacuuming just because we're so
+ 
+
+ align:start position:0%
+it's vacuuming just because we're so
+used to a Consciousness that it's hard
+
+ align:start position:0%
+used to a Consciousness that it's hard
+ 
+
+ align:start position:0%
+used to a Consciousness that it's hard
+for us to see a
+
+ align:start position:0%
+for us to see a
+ 
+
+ align:start position:0%
+for us to see a
+machine acting like a us or performing a
+
+ align:start position:0%
+machine acting like a us or performing a
+ 
+
+ align:start position:0%
+machine acting like a us or performing a
+task like us and not expected to have
+
+ align:start position:0%
+task like us and not expected to have
+ 
+
+ align:start position:0%
+task like us and not expected to have
+any type of right internal this is this
+
+ align:start position:0%
+any type of right internal this is this
+ 
+
+ align:start position:0%
+any type of right internal this is this
+is a big absolute I mean Turing would
+
+ align:start position:0%
+is a big absolute I mean Turing would
+ 
+
+ align:start position:0%
+is a big absolute I mean Turing would
+come up with the Turing test we're going
+
+ align:start position:0%
+come up with the Turing test we're going
+ 
+
+ align:start position:0%
+come up with the Turing test we're going
+to read Turing a little later but you
+
+ align:start position:0%
+to read Turing a little later but you
+ 
+
+ align:start position:0%
+to read Turing a little later but you
+know Alan Turing thought about these
+
+ align:start position:0%
+know Alan Turing thought about these
+ 
+
+ align:start position:0%
+know Alan Turing thought about these
+problems he tried to understand them and
+
+ align:start position:0%
+problems he tried to understand them and
+ 
+
+ align:start position:0%
+problems he tried to understand them and
+tried to come up with ways of thinking
+
+ align:start position:0%
+tried to come up with ways of thinking
+ 
+
+ align:start position:0%
+tried to come up with ways of thinking
+about them not always successful but
+
+ align:start position:0%
+about them not always successful but
+ 
+
+ align:start position:0%
+about them not always successful but
+pretty pretty
+
+ align:start position:0%
+pretty pretty
+ 
+
+ align:start position:0%
+pretty pretty
+penetrating
+
+ align:start position:0%
+penetrating
+ 
+
+ align:start position:0%
+penetrating
+um but uh certainly
+
+ align:start position:0%
+um but uh certainly
+ 
+
+ align:start position:0%
+um but uh certainly
+a lot of the things you know do you
+
+ align:start position:0%
+a lot of the things you know do you
+ 
+
+ align:start position:0%
+a lot of the things you know do you
+think we're all our all we are
+
+ align:start position:0%
+think we're all our all we are
+ 
+
+ align:start position:0%
+think we're all our all we are
+constantly self-conscious of everything
+
+ align:start position:0%
+constantly self-conscious of everything
+ 
+
+ align:start position:0%
+constantly self-conscious of everything
+that we do I mean we do a tremendous
+
+ align:start position:0%
+that we do I mean we do a tremendous
+ 
+
+ align:start position:0%
+that we do I mean we do a tremendous
+amount of work
+
+ align:start position:0%
+amount of work
+ 
+
+ align:start position:0%
+amount of work
+labor which we don't think consciously
+
+ align:start position:0%
+labor which we don't think consciously
+ 
+
+ align:start position:0%
+labor which we don't think consciously
+about it as we do it I mean so this
+
+ align:start position:0%
+about it as we do it I mean so this
+ 
+
+ align:start position:0%
+about it as we do it I mean so this
+whole notion of Consciousness is you
+
+ align:start position:0%
+whole notion of Consciousness is you
+ 
+
+ align:start position:0%
+whole notion of Consciousness is you
+know it's it's not always present in
+
+ align:start position:0%
+know it's it's not always present in
+ 
+
+ align:start position:0%
+know it's it's not always present in
+behavior and so you know it it sort of
+
+ align:start position:0%
+behavior and so you know it it sort of
+ 
+
+ align:start position:0%
+behavior and so you know it it sort of
+Glides it's it's it's uh and
+
+ align:start position:0%
+Glides it's it's it's uh and
+ 
+
+ align:start position:0%
+Glides it's it's it's uh and
+and the Book of the machines argues
+
+ align:start position:0%
+and the Book of the machines argues
+ 
+
+ align:start position:0%
+and the Book of the machines argues
+something to the effect that how can we
+
+ align:start position:0%
+something to the effect that how can we
+ 
+
+ align:start position:0%
+something to the effect that how can we
+know a potato doesn't have I mean a
+
+ align:start position:0%
+know a potato doesn't have I mean a
+ 
+
+ align:start position:0%
+know a potato doesn't have I mean a
+potato in a in a Cellar grows roots and
+
+ align:start position:0%
+potato in a in a Cellar grows roots and
+ 
+
+ align:start position:0%
+potato in a in a Cellar grows roots and
+tries
+
+ align:start position:0%
+tries
+ 
+
+ align:start position:0%
+tries
+to we say try uh these roots go toward
+
+ align:start position:0%
+to we say try uh these roots go toward
+ 
+
+ align:start position:0%
+to we say try uh these roots go toward
+uh they phototropic or whatever they are
+
+ align:start position:0%
+uh they phototropic or whatever they are
+ 
+
+ align:start position:0%
+uh they phototropic or whatever they are
+and they look for opportunities to uh
+
+ align:start position:0%
+and they look for opportunities to uh
+ 
+
+ align:start position:0%
+and they look for opportunities to uh
+implant themselves into some source of
+
+ align:start position:0%
+implant themselves into some source of
+ 
+
+ align:start position:0%
+implant themselves into some source of
+sustenance and uh as the professor says
+
+ align:start position:0%
+sustenance and uh as the professor says
+ 
+
+ align:start position:0%
+sustenance and uh as the professor says
+in the book he says isn't this a sort of
+
+ align:start position:0%
+in the book he says isn't this a sort of
+ 
+
+ align:start position:0%
+in the book he says isn't this a sort of
+low form of
+
+ align:start position:0%
+low form of
+ 
+
+ align:start position:0%
+low form of
+Consciousness I mean at what level does
+
+ align:start position:0%
+Consciousness I mean at what level does
+ 
+
+ align:start position:0%
+Consciousness I mean at what level does
+Consciousness start in the animal
+
+ align:start position:0%
+Consciousness start in the animal
+ 
+
+ align:start position:0%
+Consciousness start in the animal
+world or insex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conscious what do you think
+
+ align:start position:0%
+conscious what do you think
+ 
+
+ align:start position:0%
+conscious what do you think
+Charles
+
+ align:start position:0%
+Charles
+ 
+
+ align:start position:0%
+Charles
+um I think coming up from the very
+
+ align:start position:0%
+um I think coming up from the very
+ 
+
+ align:start position:0%
+um I think coming up from the very
+bottom of nature where like there's
+
+ align:start position:0%
+bottom of nature where like there's
+ 
+
+ align:start position:0%
+bottom of nature where like there's
+always the question of the line between
+
+ align:start position:0%
+always the question of the line between
+ 
+
+ align:start position:0%
+always the question of the line between
+being conscious and not conscious and as
+
+ align:start position:0%
+being conscious and not conscious and as
+ 
+
+ align:start position:0%
+being conscious and not conscious and as
+we so very obviously like individual
+
+ align:start position:0%
+we so very obviously like individual
+ 
+
+ align:start position:0%
+we so very obviously like individual
+cells are not conscious because like
+
+ align:start position:0%
+cells are not conscious because like
+ 
+
+ align:start position:0%
+cells are not conscious because like
+it's just one cell and there's no
+
+ align:start position:0%
+it's just one cell and there's no
+ 
+
+ align:start position:0%
+it's just one cell and there's no
+different components that can allow for
+
+ align:start position:0%
+different components that can allow for
+ 
+
+ align:start position:0%
+different components that can allow for
+a cell to be like functioning but also
+
+ align:start position:0%
+a cell to be like functioning but also
+ 
+
+ align:start position:0%
+a cell to be like functioning but also
+other parts that can allow it to think
+
+ align:start position:0%
+other parts that can allow it to think
+ 
+
+ align:start position:0%
+other parts that can allow it to think
+but like obviously there's like I think
+
+ align:start position:0%
+but like obviously there's like I think
+ 
+
+ align:start position:0%
+but like obviously there's like I think
+Consciousness is just a man
+
+ align:start position:0%
+Consciousness is just a man
+ 
+
+ align:start position:0%
+Consciousness is just a man
+manifestation of natural
+
+ align:start position:0%
+manifestation of natural
+ 
+
+ align:start position:0%
+manifestation of natural
+response um that all organ organisms
+
+ align:start position:0%
+response um that all organ organisms
+ 
+
+ align:start position:0%
+response um that all organ organisms
+have to outside stimuli like if you
+
+ align:start position:0%
+have to outside stimuli like if you
+ 
+
+ align:start position:0%
+have to outside stimuli like if you
+stimulate a cell if you make like one
+
+ align:start position:0%
+stimulate a cell if you make like one
+ 
+
+ align:start position:0%
+stimulate a cell if you make like one
+region hot like things are going to like
+
+ align:start position:0%
+region hot like things are going to like
+ 
+
+ align:start position:0%
+region hot like things are going to like
+creatures small creatures are going to
+
+ align:start position:0%
+creatures small creatures are going to
+ 
+
+ align:start position:0%
+creatures small creatures are going to
+move away from it so you're saying
+
+ align:start position:0%
+move away from it so you're saying
+ 
+
+ align:start position:0%
+move away from it so you're saying
+protozone has a kind of a
+
+ align:start position:0%
+protozone has a kind of a
+ 
+
+ align:start position:0%
+protozone has a kind of a
+Consciousness it
+
+ align:start position:0%
+Consciousness it
+ 
+
+ align:start position:0%
+Consciousness it
+has has an
+
+ align:start position:0%
+has has an
+ 
+
+ align:start position:0%
+has has an
+instinct without actually being an
+
+ align:start position:0%
+instinct without actually being an
+ 
+
+ align:start position:0%
+instinct without actually being an
+instinct it has a tendency to want to
+
+ align:start position:0%
+instinct it has a tendency to want to
+ 
+
+ align:start position:0%
+instinct it has a tendency to want to
+survive and I think it Consciousness is
+
+ align:start position:0%
+survive and I think it Consciousness is
+ 
+
+ align:start position:0%
+survive and I think it Consciousness is
+just a manifestation of that and the
+
+ align:start position:0%
+just a manifestation of that and the
+ 
+
+ align:start position:0%
+just a manifestation of that and the
+line where like what we feel is
+
+ align:start position:0%
+line where like what we feel is
+ 
+
+ align:start position:0%
+line where like what we feel is
+consciousness is hard to
+
+ align:start position:0%
+consciousness is hard to
+ 
+
+ align:start position:0%
+consciousness is hard to
+nail well let me just read this quick
+
+ align:start position:0%
+nail well let me just read this quick
+ 
+
+ align:start position:0%
+nail well let me just read this quick
+but who can say that the vapor engine
+
+ align:start position:0%
+but who can say that the vapor engine
+ 
+
+ align:start position:0%
+but who can say that the vapor engine
+has not a kind of Consciousness where
+
+ align:start position:0%
+has not a kind of Consciousness where
+ 
+
+ align:start position:0%
+has not a kind of Consciousness where
+does Consciousness begin and where end
+
+ align:start position:0%
+does Consciousness begin and where end
+ 
+
+ align:start position:0%
+does Consciousness begin and where end
+who can draw the line who can draw any l
+
+ align:start position:0%
+who can draw the line who can draw any l
+ 
+
+ align:start position:0%
+who can draw the line who can draw any l
+line is not everything interwoven with
+
+ align:start position:0%
+line is not everything interwoven with
+ 
+
+ align:start position:0%
+line is not everything interwoven with
+everything well he's getting is not
+
+ align:start position:0%
+everything well he's getting is not
+ 
+
+ align:start position:0%
+everything well he's getting is not
+Machinery linked with animal life in an
+
+ align:start position:0%
+Machinery linked with animal life in an
+ 
+
+ align:start position:0%
+Machinery linked with animal life in an
+infinite variety of
+
+ align:start position:0%
+infinite variety of
+ 
+
+ align:start position:0%
+infinite variety of
+ways so David you had your hand on like
+
+ align:start position:0%
+ways so David you had your hand on like
+ 
+
+ align:start position:0%
+ways so David you had your hand on like
+there's a few lines there like instinct
+
+ align:start position:0%
+there's a few lines there like instinct
+ 
+
+ align:start position:0%
+there's a few lines there like instinct
+there's Consciousness and there's like
+
+ align:start position:0%
+there's Consciousness and there's like
+ 
+
+ align:start position:0%
+there's Consciousness and there's like
+self-awareness because I think we can
+
+ align:start position:0%
+self-awareness because I think we can
+ 
+
+ align:start position:0%
+self-awareness because I think we can
+okay I think we can agree that like most
+
+ align:start position:0%
+okay I think we can agree that like most
+ 
+
+ align:start position:0%
+okay I think we can agree that like most
+complex animals are conscious you know
+
+ align:start position:0%
+complex animals are conscious you know
+ 
+
+ align:start position:0%
+complex animals are conscious you know
+but you know like my cat is conscious
+
+ align:start position:0%
+but you know like my cat is conscious
+ 
+
+ align:start position:0%
+but you know like my cat is conscious
+but does my cat is my cat self-aware
+
+ align:start position:0%
+but does my cat is my cat self-aware
+ 
+
+ align:start position:0%
+but does my cat is my cat self-aware
+does it like consider its own existence
+
+ align:start position:0%
+does it like consider its own existence
+ 
+
+ align:start position:0%
+does it like consider its own existence
+you know I think that's a big line too
+
+ align:start position:0%
+you know I think that's a big line too
+ 
+
+ align:start position:0%
+you know I think that's a big line too
+so yeah people are studying the these
+
+ align:start position:0%
+so yeah people are studying the these
+ 
+
+ align:start position:0%
+so yeah people are studying the these
+questions even as we sit here um he says
+
+ align:start position:0%
+questions even as we sit here um he says
+ 
+
+ align:start position:0%
+questions even as we sit here um he says
+further on
+
+ align:start position:0%
+further on
+ 
+
+ align:start position:0%
+further on
+um uh you know he says uh whether those
+
+ align:start position:0%
+um uh you know he says uh whether those
+ 
+
+ align:start position:0%
+um uh you know he says uh whether those
+things which we deem most purely
+
+ align:start position:0%
+things which we deem most purely
+ 
+
+ align:start position:0%
+things which we deem most purely
+spiritual are anything but disturbances
+
+ align:start position:0%
+spiritual are anything but disturbances
+ 
+
+ align:start position:0%
+spiritual are anything but disturbances
+of equilibrium in an infinite series of
+
+ align:start position:0%
+of equilibrium in an infinite series of
+ 
+
+ align:start position:0%
+of equilibrium in an infinite series of
+levers so we're coming back to you
+
+ align:start position:0%
+levers so we're coming back to you
+ 
+
+ align:start position:0%
+levers so we're coming back to you
+remember py how beautifully he outlined
+
+ align:start position:0%
+remember py how beautifully he outlined
+ 
+
+ align:start position:0%
+remember py how beautifully he outlined
+the body as a as a mechanism in his
+
+ align:start position:0%
+the body as a as a mechanism in his
+ 
+
+ align:start position:0%
+the body as a as a mechanism in his
+effort to show that it had this
+
+ align:start position:0%
+effort to show that it had this
+ 
+
+ align:start position:0%
+effort to show that it had this
+wonderful design so so in some sense the
+
+ align:start position:0%
+wonderful design so so in some sense the
+ 
+
+ align:start position:0%
+wonderful design so so in some sense the
+design people now he's coming back to
+
+ align:start position:0%
+design people now he's coming back to
+ 
+
+ align:start position:0%
+design people now he's coming back to
+them because uh pale and showing and
+
+ align:start position:0%
+them because uh pale and showing and
+ 
+
+ align:start position:0%
+them because uh pale and showing and
+other people too I mean I showed you a
+
+ align:start position:0%
+other people too I mean I showed you a
+ 
+
+ align:start position:0%
+other people too I mean I showed you a
+lot of different but in showing the body
+
+ align:start position:0%
+lot of different but in showing the body
+ 
+
+ align:start position:0%
+lot of different but in showing the body
+as this
+
+ align:start position:0%
+as this
+ 
+
+ align:start position:0%
+as this
+mechanism and you know Gray's Anatomy
+
+ align:start position:0%
+mechanism and you know Gray's Anatomy
+ 
+
+ align:start position:0%
+mechanism and you know Gray's Anatomy
+showing all the parts of the body and
+
+ align:start position:0%
+showing all the parts of the body and
+ 
+
+ align:start position:0%
+showing all the parts of the body and
+beautifully dis seting it out and so
+
+ align:start position:0%
+beautifully dis seting it out and so
+ 
+
+ align:start position:0%
+beautifully dis seting it out and so
+forth we see you know body's really a
+
+ align:start position:0%
+forth we see you know body's really a
+ 
+
+ align:start position:0%
+forth we see you know body's really a
+incredible
+
+ align:start position:0%
+incredible
+ 
+
+ align:start position:0%
+incredible
+machine so now we're coming back to you
+
+ align:start position:0%
+machine so now we're coming back to you
+ 
+
+ align:start position:0%
+machine so now we're coming back to you
+know revisiting this from another point
+
+ align:start position:0%
+know revisiting this from another point
+ 
+
+ align:start position:0%
+know revisiting this from another point
+of view well this machine is indeed a
+
+ align:start position:0%
+of view well this machine is indeed a
+ 
+
+ align:start position:0%
+of view well this machine is indeed a
+machine and why should we think of it as
+
+ align:start position:0%
+machine and why should we think of it as
+ 
+
+ align:start position:0%
+machine and why should we think of it as
+a totally different machine from other
+
+ align:start position:0%
+a totally different machine from other
+ 
+
+ align:start position:0%
+a totally different machine from other
+machines yeah it has
+
+ align:start position:0%
+machines yeah it has
+ 
+
+ align:start position:0%
+machines yeah it has
+Consciousness an
+
+ align:start position:0%
+Consciousness an
+ 
+
+ align:start position:0%
+Consciousness an
+intentionality but as this thinker here
+
+ align:start position:0%
+intentionality but as this thinker here
+ 
+
+ align:start position:0%
+intentionality but as this thinker here
+is saying well what is consciousness and
+
+ align:start position:0%
+is saying well what is consciousness and
+ 
+
+ align:start position:0%
+is saying well what is consciousness and
+what is what is intention so he says
+
+ align:start position:0%
+what is what is intention so he says
+ 
+
+ align:start position:0%
+what is what is intention so he says
+here the disturbances
+
+ align:start position:0%
+here the disturbances
+ 
+
+ align:start position:0%
+here the disturbances
+uh those things which we deem most
+
+ align:start position:0%
+uh those things which we deem most
+ 
+
+ align:start position:0%
+uh those things which we deem most
+purely spiritual are anything but
+
+ align:start position:0%
+purely spiritual are anything but
+ 
+
+ align:start position:0%
+purely spiritual are anything but
+disturbances of equilibrium and an
+
+ align:start position:0%
+disturbances of equilibrium and an
+ 
+
+ align:start position:0%
+disturbances of equilibrium and an
+infinite series of levers beginning with
+
+ align:start position:0%
+infinite series of levers beginning with
+ 
+
+ align:start position:0%
+infinite series of levers beginning with
+those that are too small for microscopic
+
+ align:start position:0%
+those that are too small for microscopic
+ 
+
+ align:start position:0%
+those that are too small for microscopic
+detection and going up to the human arm
+
+ align:start position:0%
+detection and going up to the human arm
+ 
+
+ align:start position:0%
+detection and going up to the human arm
+and and the appliances which it makes
+
+ align:start position:0%
+and and the appliances which it makes
+ 
+
+ align:start position:0%
+and and the appliances which it makes
+use of whether there not be a molecular
+
+ align:start position:0%
+use of whether there not be a molecular
+ 
+
+ align:start position:0%
+use of whether there not be a molecular
+action of
+
+ align:start position:0%
+action of
+ 
+
+ align:start position:0%
+action of
+thought that was an outrageous statement
+
+ align:start position:0%
+thought that was an outrageous statement
+ 
+
+ align:start position:0%
+thought that was an outrageous statement
+in Butler's day is it outrageous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today no cognitive scientists in here I
+
+ align:start position:0%
+today no cognitive scientists in here I
+ 
+
+ align:start position:0%
+today no cognitive scientists in here I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+see brain and Cog go over and ask them
+
+ align:start position:0%
+see brain and Cog go over and ask them
+ 
+
+ align:start position:0%
+see brain and Cog go over and ask them
+is is thought process somehow mechanical
+
+ align:start position:0%
+is is thought process somehow mechanical
+ 
+
+ align:start position:0%
+is is thought process somehow mechanical
+are there mechanical
+
+ align:start position:0%
+are there mechanical
+ 
+
+ align:start position:0%
+are there mechanical
+electrical chemical aspects to it is it
+
+ align:start position:0%
+electrical chemical aspects to it is it
+ 
+
+ align:start position:0%
+electrical chemical aspects to it is it
+uh I'm sure nobody will give you
+
+ align:start position:0%
+uh I'm sure nobody will give you
+ 
+
+ align:start position:0%
+uh I'm sure nobody will give you
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh definitive answer but certainly it's
+
+ align:start position:0%
+uh definitive answer but certainly it's
+ 
+
+ align:start position:0%
+uh definitive answer but certainly it's
+it's it's the realm of of uh
+
+ align:start position:0%
+it's it's the realm of of uh
+ 
+
+ align:start position:0%
+it's it's the realm of of uh
+investigation today right here as we
+
+ align:start position:0%
+investigation today right here as we
+ 
+
+ align:start position:0%
+investigation today right here as we
+sit yeah CH well I mean the way the
+
+ align:start position:0%
+sit yeah CH well I mean the way the
+ 
+
+ align:start position:0%
+sit yeah CH well I mean the way the
+nerves work there are it is chemicals
+
+ align:start position:0%
+nerves work there are it is chemicals
+ 
+
+ align:start position:0%
+nerves work there are it is chemicals
+firing in and out of cell Cur electrical
+
+ align:start position:0%
+firing in and out of cell Cur electrical
+ 
+
+ align:start position:0%
+firing in and out of cell Cur electrical
+impulse but I don't know if there can be
+
+ align:start position:0%
+impulse but I don't know if there can be
+ 
+
+ align:start position:0%
+impulse but I don't know if there can be
+cuz I don't think again not not a
+
+ align:start position:0%
+cuz I don't think again not not a
+ 
+
+ align:start position:0%
+cuz I don't think again not not a
+Brandon Cod side but I don't think it's
+
+ align:start position:0%
+Brandon Cod side but I don't think it's
+ 
+
+ align:start position:0%
+Brandon Cod side but I don't think it's
+f understood how those electrical
+
+ align:start position:0%
+f understood how those electrical
+ 
+
+ align:start position:0%
+f understood how those electrical
+impulses translate into like thoughts
+
+ align:start position:0%
+impulses translate into like thoughts
+ 
+
+ align:start position:0%
+impulses translate into like thoughts
+and I mean not cognitive sence we're
+
+ align:start position:0%
+and I mean not cognitive sence we're
+ 
+
+ align:start position:0%
+and I mean not cognitive sence we're
+we're reading a novel but what's
+
+ align:start position:0%
+we're reading a novel but what's
+ 
+
+ align:start position:0%
+we're reading a novel but what's
+interesting is how this this uh this
+
+ align:start position:0%
+interesting is how this this uh this
+ 
+
+ align:start position:0%
+interesting is how this this uh this
+piece of speculation brings up
+
+ align:start position:0%
+piece of speculation brings up
+ 
+
+ align:start position:0%
+piece of speculation brings up
+questions that you know within the
+
+ align:start position:0%
+questions that you know within the
+ 
+
+ align:start position:0%
+questions that you know within the
+framework of evolutionary thinking I
+
+ align:start position:0%
+framework of evolutionary thinking I
+ 
+
+ align:start position:0%
+framework of evolutionary thinking I
+mean he he couldn't have come up with
+
+ align:start position:0%
+mean he he couldn't have come up with
+ 
+
+ align:start position:0%
+mean he he couldn't have come up with
+these questions
+
+ align:start position:0%
+these questions
+ 
+
+ align:start position:0%
+these questions
+without the evolutionary framework
+
+ align:start position:0%
+without the evolutionary framework
+ 
+
+ align:start position:0%
+without the evolutionary framework
+you understand that because he's
+
+ align:start position:0%
+you understand that because he's
+ 
+
+ align:start position:0%
+you understand that because he's
+thinking of it as this kind of
+
+ align:start position:0%
+thinking of it as this kind of
+ 
+
+ align:start position:0%
+thinking of it as this kind of
+incremental process that has delivered
+
+ align:start position:0%
+incremental process that has delivered
+ 
+
+ align:start position:0%
+incremental process that has delivered
+greater and greater functionality over
+
+ align:start position:0%
+greater and greater functionality over
+ 
+
+ align:start position:0%
+greater and greater functionality over
+time and he's saying why not for
+
+ align:start position:0%
+time and he's saying why not for
+ 
+
+ align:start position:0%
+time and he's saying why not for
+mechanical devices so he's jumping
+
+ align:start position:0%
+mechanical devices so he's jumping
+ 
+
+ align:start position:0%
+mechanical devices so he's jumping
+directly from organic to what we would
+
+ align:start position:0%
+directly from organic to what we would
+ 
+
+ align:start position:0%
+directly from organic to what we would
+call the inorganic
+
+ align:start position:0%
+call the inorganic
+ 
+
+ align:start position:0%
+call the inorganic
+world but he's saying look you know
+
+ align:start position:0%
+world but he's saying look you know
+ 
+
+ align:start position:0%
+world but he's saying look you know
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+parallels are not outr
+
+ align:start position:0%
+parallels are not outr
+ 
+
+ align:start position:0%
+parallels are not outr
+rageous and we can use one to think
+
+ align:start position:0%
+rageous and we can use one to think
+ 
+
+ align:start position:0%
+rageous and we can use one to think
+about the other so yeah we we can't come
+
+ align:start position:0%
+about the other so yeah we we can't come
+ 
+
+ align:start position:0%
+about the other so yeah we we can't come
+to a definitive answer here on you know
+
+ align:start position:0%
+to a definitive answer here on you know
+ 
+
+ align:start position:0%
+to a definitive answer here on you know
+the question but we know that the
+
+ align:start position:0%
+the question but we know that the
+ 
+
+ align:start position:0%
+the question but we know that the
+question is not an outrageous question
+
+ align:start position:0%
+question is not an outrageous question
+ 
+
+ align:start position:0%
+question is not an outrageous question
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+longer and the theories and arguments in
+
+ align:start position:0%
+longer and the theories and arguments in
+ 
+
+ align:start position:0%
+longer and the theories and arguments in
+this outrageous as they were in their
+
+ align:start position:0%
+this outrageous as they were in their
+ 
+
+ align:start position:0%
+this outrageous as they were in their
+time when he uh says man is a masate
+
+ align:start position:0%
+time when he uh says man is a masate
+ 
+
+ align:start position:0%
+time when he uh says man is a masate
+animal I mean yeah we are merging with
+
+ align:start position:0%
+animal I mean yeah we are merging with
+ 
+
+ align:start position:0%
+animal I mean yeah we are merging with
+machines we do all sorts of weird things
+
+ align:start position:0%
+machines we do all sorts of weird things
+ 
+
+ align:start position:0%
+machines we do all sorts of weird things
+with machines but certainly machines
+
+ align:start position:0%
+with machines but certainly machines
+ 
+
+ align:start position:0%
+with machines but certainly machines
+have U extended our
+
+ align:start position:0%
+have U extended our
+ 
+
+ align:start position:0%
+have U extended our
+functionality in dramatic
+
+ align:start position:0%
+functionality in dramatic
+ 
+
+ align:start position:0%
+functionality in dramatic
+ways and so there's a there's
+
+ align:start position:0%
+ways and so there's a there's
+ 
+
+ align:start position:0%
+ways and so there's a there's
+uh I mean this this uh limb here you
+
+ align:start position:0%
+uh I mean this this uh limb here you
+ 
+
+ align:start position:0%
+uh I mean this this uh limb here you
+know they're are people using artificial
+
+ align:start position:0%
+know they're are people using artificial
+ 
+
+ align:start position:0%
+know they're are people using artificial
+limbs that are highly
+
+ align:start position:0%
+limbs that are highly
+ 
+
+ align:start position:0%
+limbs that are highly
+functional and have merged with in you
+
+ align:start position:0%
+functional and have merged with in you
+ 
+
+ align:start position:0%
+functional and have merged with in you
+know I suppose you could do a thought
+
+ align:start position:0%
+know I suppose you could do a thought
+ 
+
+ align:start position:0%
+know I suppose you could do a thought
+experiment I'm going to have to break
+
+ align:start position:0%
+experiment I'm going to have to break
+ 
+
+ align:start position:0%
+experiment I'm going to have to break
+here soon because I I have to leave
+
+ align:start position:0%
+here soon because I I have to leave
+ 
+
+ align:start position:0%
+here soon because I I have to leave
+early today but uh a person could do a
+
+ align:start position:0%
+early today but uh a person could do a
+ 
+
+ align:start position:0%
+early today but uh a person could do a
+thought experiment and say well how many
+
+ align:start position:0%
+thought experiment and say well how many
+ 
+
+ align:start position:0%
+thought experiment and say well how many
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+artificial things do we have for the
+
+ align:start position:0%
+artificial things do we have for the
+ 
+
+ align:start position:0%
+artificial things do we have for the
+body today we have artificial hands we
+
+ align:start position:0%
+body today we have artificial hands we
+ 
+
+ align:start position:0%
+body today we have artificial hands we
+have artificial limbs we have AR we're
+
+ align:start position:0%
+have artificial limbs we have AR we're
+ 
+
+ align:start position:0%
+have artificial limbs we have AR we're
+working on artificial Hearts we're
+
+ align:start position:0%
+working on artificial Hearts we're
+ 
+
+ align:start position:0%
+working on artificial Hearts we're
+working on
+
+ align:start position:0%
+working on
+ 
+
+ align:start position:0%
+working on
+artificial I don't know all kinds of
+
+ align:start position:0%
+artificial I don't know all kinds of
+ 
+
+ align:start position:0%
+artificial I don't know all kinds of
+artificial things
+
+ align:start position:0%
+artificial things
+ 
+
+ align:start position:0%
+artificial things
+so if we did a thought experiment and we
+
+ align:start position:0%
+so if we did a thought experiment and we
+ 
+
+ align:start position:0%
+so if we did a thought experiment and we
+replaced a
+
+ align:start position:0%
+replaced a
+ 
+
+ align:start position:0%
+replaced a
+person every single part with something
+
+ align:start position:0%
+person every single part with something
+ 
+
+ align:start position:0%
+person every single part with something
+artificial if we could all make it if we
+
+ align:start position:0%
+artificial if we could all make it if we
+ 
+
+ align:start position:0%
+artificial if we could all make it if we
+can make it all work together we might
+
+ align:start position:0%
+can make it all work together we might
+ 
+
+ align:start position:0%
+can make it all work together we might
+eventually end up with entirely
+
+ align:start position:0%
+eventually end up with entirely
+ 
+
+ align:start position:0%
+eventually end up with entirely
+mechanical entity when do they actually
+
+ align:start position:0%
+mechanical entity when do they actually
+ 
+
+ align:start position:0%
+mechanical entity when do they actually
+die yeah that's a good
+
+ align:start position:0%
+die yeah that's a good
+ 
+
+ align:start position:0%
+die yeah that's a good
+question I mean dve would the like
+
+ align:start position:0%
+question I mean dve would the like
+ 
+
+ align:start position:0%
+question I mean dve would the like
+regrowth of organs be considered
+
+ align:start position:0%
+regrowth of organs be considered
+ 
+
+ align:start position:0%
+regrowth of organs be considered
+artificial as well well that's a that's
+
+ align:start position:0%
+artificial as well well that's a that's
+ 
+
+ align:start position:0%
+artificial as well well that's a that's
+a that's a good question um because we
+
+ align:start position:0%
+a that's a good question um because we
+ 
+
+ align:start position:0%
+a that's a good question um because we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+start we can start making our
+
+ align:start position:0%
+start we can start making our
+ 
+
+ align:start position:0%
+start we can start making our
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+organic
+
+ align:start position:0%
+organic
+ 
+
+ align:start position:0%
+organic
+objects so uh this is a huge area of
+
+ align:start position:0%
+objects so uh this is a huge area of
+ 
+
+ align:start position:0%
+objects so uh this is a huge area of
+research that people are engaged in and
+
+ align:start position:0%
+research that people are engaged in and
+ 
+
+ align:start position:0%
+research that people are engaged in and
+so to what degree is that a human
+
+ align:start position:0%
+so to what degree is that a human
+ 
+
+ align:start position:0%
+so to what degree is that a human
+fabrication I.E in some sense of
+
+ align:start position:0%
+fabrication I.E in some sense of
+ 
+
+ align:start position:0%
+fabrication I.E in some sense of
+mechanical
+
+ align:start position:0%
+mechanical
+ 
+
+ align:start position:0%
+mechanical
+device only the mechanics are a bi
+
+ align:start position:0%
+device only the mechanics are a bi
+ 
+
+ align:start position:0%
+device only the mechanics are a bi
+biological mechanics that we have become
+
+ align:start position:0%
+biological mechanics that we have become
+ 
+
+ align:start position:0%
+biological mechanics that we have become
+so good at that we're beginning to
+
+ align:start position:0%
+so good at that we're beginning to
+ 
+
+ align:start position:0%
+so good at that we're beginning to
+build the biology and it's you know it's
+
+ align:start position:0%
+build the biology and it's you know it's
+ 
+
+ align:start position:0%
+build the biology and it's you know it's
+not made up of
+
+ align:start position:0%
+not made up of
+ 
+
+ align:start position:0%
+not made up of
+uh all these inorganic things we're
+
+ align:start position:0%
+uh all these inorganic things we're
+ 
+
+ align:start position:0%
+uh all these inorganic things we're
+building it out of organic tools and
+
+ align:start position:0%
+building it out of organic tools and
+ 
+
+ align:start position:0%
+building it out of organic tools and
+organic
+
+ align:start position:0%
+organic
+ 
+
+ align:start position:0%
+organic
+materials so you know where are the
+
+ align:start position:0%
+materials so you know where are the
+ 
+
+ align:start position:0%
+materials so you know where are the
+lines so that's that's what this is is
+
+ align:start position:0%
+lines so that's that's what this is is
+ 
+
+ align:start position:0%
+lines so that's that's what this is is
+is is is dealing about is dealing with
+
+ align:start position:0%
+is is is dealing about is dealing with
+ 
+
+ align:start position:0%
+is is is dealing about is dealing with
+is you know these lines that we think
+
+ align:start position:0%
+is you know these lines that we think
+ 
+
+ align:start position:0%
+is you know these lines that we think
+are so clear from a distance when we get
+
+ align:start position:0%
+are so clear from a distance when we get
+ 
+
+ align:start position:0%
+are so clear from a distance when we get
+closer and closer up aren't so
+
+ align:start position:0%
+closer and closer up aren't so
+ 
+
+ align:start position:0%
+closer and closer up aren't so
+clear and it's uh it's it's it's worth
+
+ align:start position:0%
+clear and it's uh it's it's it's worth
+ 
+
+ align:start position:0%
+clear and it's uh it's it's it's worth
+thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+well it's a you know it's it's a fun
+
+ align:start position:0%
+well it's a you know it's it's a fun
+ 
+
+ align:start position:0%
+well it's a you know it's it's a fun
+chapter three chapters mainly because
+
+ align:start position:0%
+chapter three chapters mainly because
+ 
+
+ align:start position:0%
+chapter three chapters mainly because
+you know he talks about reproduction you
+
+ align:start position:0%
+you know he talks about reproduction you
+ 
+
+ align:start position:0%
+you know he talks about reproduction you
+know yes the machine to be reproduced
+
+ align:start position:0%
+know yes the machine to be reproduced
+ 
+
+ align:start position:0%
+know yes the machine to be reproduced
+outside of the body of the other machine
+
+ align:start position:0%
+outside of the body of the other machine
+ 
+
+ align:start position:0%
+outside of the body of the other machine
+but you know there are precedents for
+
+ align:start position:0%
+but you know there are precedents for
+ 
+
+ align:start position:0%
+but you know there are precedents for
+things like this in
+
+ align:start position:0%
+things like this in
+ 
+
+ align:start position:0%
+things like this in
+nature just because reproduction takes
+
+ align:start position:0%
+nature just because reproduction takes
+ 
+
+ align:start position:0%
+nature just because reproduction takes
+place on the factory
+
+ align:start position:0%
+place on the factory
+ 
+
+ align:start position:0%
+place on the factory
+line uh it's you know things are being
+
+ align:start position:0%
+line uh it's you know things are being
+ 
+
+ align:start position:0%
+line uh it's you know things are being
+produced and they're following certain
+
+ align:start position:0%
+produced and they're following certain
+ 
+
+ align:start position:0%
+produced and they're following certain
+models and so uh and these models are
+
+ align:start position:0%
+models and so uh and these models are
+ 
+
+ align:start position:0%
+models and so uh and these models are
+evolving into greater and greater
+
+ align:start position:0%
+evolving into greater and greater
+ 
+
+ align:start position:0%
+evolving into greater and greater
+functionality uh according to our our
+
+ align:start position:0%
+functionality uh according to our our
+ 
+
+ align:start position:0%
+functionality uh according to our our
+desires so this is where the design part
+
+ align:start position:0%
+desires so this is where the design part
+ 
+
+ align:start position:0%
+desires so this is where the design part
+of the human and the design part of the
+
+ align:start position:0%
+of the human and the design part of the
+ 
+
+ align:start position:0%
+of the human and the design part of the
+natural sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+merge
\ No newline at end of file
diff --git a/8DlysThtgbM.txt b/8DlysThtgbM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c72d3e0433a3e192355d87ae3f65ad7a0f9b7c81
--- /dev/null
+++ b/8DlysThtgbM.txt
@@ -0,0 +1,1211 @@
+align:start position:0%
+ 
+so just imagine that instead of this is
+
+ align:start position:0%
+so just imagine that instead of this is
+ 
+
+ align:start position:0%
+so just imagine that instead of this is
+for two choices two outcomes two stages
+
+ align:start position:0%
+for two choices two outcomes two stages
+ 
+
+ align:start position:0%
+for two choices two outcomes two stages
+just a match extension of three of each
+
+ align:start position:0%
+just a match extension of three of each
+ 
+
+ align:start position:0%
+just a match extension of three of each
+and you're now talking about a really
+
+ align:start position:0%
+and you're now talking about a really
+ 
+
+ align:start position:0%
+and you're now talking about a really
+really complicated and i have just to
+
+ align:start position:0%
+really complicated and i have just to
+ 
+
+ align:start position:0%
+really complicated and i have just to
+set up and i haven't deliberately i
+
+ align:start position:0%
+set up and i haven't deliberately i
+ 
+
+ align:start position:0%
+set up and i haven't deliberately i
+haven't tried to show you the way to
+
+ align:start position:0%
+haven't tried to show you the way to
+ 
+
+ align:start position:0%
+haven't tried to show you the way to
+calculate the revisions of the prior
+
+ align:start position:0%
+calculate the revisions of the prior
+ 
+
+ align:start position:0%
+calculate the revisions of the prior
+probabilities and learn about the future
+
+ align:start position:0%
+probabilities and learn about the future
+ 
+
+ align:start position:0%
+probabilities and learn about the future
+bottom line here is there's a good
+
+ align:start position:0%
+bottom line here is there's a good
+ 
+
+ align:start position:0%
+bottom line here is there's a good
+chance of a messy bush
+
+ align:start position:0%
+chance of a messy bush
+ 
+
+ align:start position:0%
+chance of a messy bush
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's uh
+
+ align:start position:0%
+it's uh
+ 
+
+ align:start position:0%
+it's uh
+something to warn you about
+
+ align:start position:0%
+something to warn you about
+ 
+
+ align:start position:0%
+something to warn you about
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's a reason however to show you
+
+ align:start position:0%
+there's a reason however to show you
+ 
+
+ align:start position:0%
+there's a reason however to show you
+this and the which is one of which is
+
+ align:start position:0%
+this and the which is one of which is
+ 
+
+ align:start position:0%
+this and the which is one of which is
+because other people use it as
+
+ align:start position:0%
+because other people use it as
+ 
+
+ align:start position:0%
+because other people use it as
+chevron's this uh decision analysis
+
+ align:start position:0%
+chevron's this uh decision analysis
+ 
+
+ align:start position:0%
+chevron's this uh decision analysis
+manual but it also allows you at least
+
+ align:start position:0%
+manual but it also allows you at least
+ 
+
+ align:start position:0%
+manual but it also allows you at least
+to have some insight insights into
+
+ align:start position:0%
+to have some insight insights into
+ 
+
+ align:start position:0%
+to have some insight insights into
+something important which is the value
+
+ align:start position:0%
+something important which is the value
+ 
+
+ align:start position:0%
+something important which is the value
+of information which will be the topic
+
+ align:start position:0%
+of information which will be the topic
+ 
+
+ align:start position:0%
+of information which will be the topic
+of la of next time
+
+ align:start position:0%
+of la of next time
+ 
+
+ align:start position:0%
+of la of next time
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's now step back a little bit from it
+
+ align:start position:0%
+let's now step back a little bit from it
+ 
+
+ align:start position:0%
+let's now step back a little bit from it
+but to realize that with the end
+
+ align:start position:0%
+but to realize that with the end
+ 
+
+ align:start position:0%
+but to realize that with the end
+as a result of the decision analysis we
+
+ align:start position:0%
+as a result of the decision analysis we
+ 
+
+ align:start position:0%
+as a result of the decision analysis we
+don't have a simple plan so and
+
+ align:start position:0%
+don't have a simple plan so and
+ 
+
+ align:start position:0%
+don't have a simple plan so and
+instead of saying all right
+
+ align:start position:0%
+instead of saying all right
+ 
+
+ align:start position:0%
+instead of saying all right
+we must our best approach is to listen
+
+ align:start position:0%
+we must our best approach is to listen
+ 
+
+ align:start position:0%
+we must our best approach is to listen
+to the weather forecast and then to take
+
+ align:start position:0%
+to the weather forecast and then to take
+ 
+
+ align:start position:0%
+to the weather forecast and then to take
+the raincoat
+
+ align:start position:0%
+the raincoat
+ 
+
+ align:start position:0%
+the raincoat
+no it's to listen to the weather
+
+ align:start position:0%
+no it's to listen to the weather
+ 
+
+ align:start position:0%
+no it's to listen to the weather
+forecast if one thing happens then maybe
+
+ align:start position:0%
+forecast if one thing happens then maybe
+ 
+
+ align:start position:0%
+forecast if one thing happens then maybe
+we take the raincoat if
+
+ align:start position:0%
+we take the raincoat if
+ 
+
+ align:start position:0%
+we take the raincoat if
+another thing happens then we don't take
+
+ align:start position:0%
+another thing happens then we don't take
+ 
+
+ align:start position:0%
+another thing happens then we don't take
+the raincoat so it is
+
+ align:start position:0%
+the raincoat so it is
+ 
+
+ align:start position:0%
+the raincoat so it is
+not okay
+
+ align:start position:0%
+not okay
+ 
+
+ align:start position:0%
+not okay
+step one phase one phase two phase three
+
+ align:start position:0%
+step one phase one phase two phase three
+ 
+
+ align:start position:0%
+step one phase one phase two phase three
+here is the right choice it is okay
+
+ align:start position:0%
+here is the right choice it is okay
+ 
+
+ align:start position:0%
+here is the right choice it is okay
+here is the right start
+
+ align:start position:0%
+here is the right start
+ 
+
+ align:start position:0%
+here is the right start
+and then we should
+
+ align:start position:0%
+and then we should
+ 
+
+ align:start position:0%
+and then we should
+do something else later on so for
+
+ align:start position:0%
+do something else later on so for
+ 
+
+ align:start position:0%
+do something else later on so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+you might say
+
+ align:start position:0%
+you might say
+ 
+
+ align:start position:0%
+you might say
+the first stage is to build your planet
+
+ align:start position:0%
+the first stage is to build your planet
+ 
+
+ align:start position:0%
+the first stage is to build your planet
+in the second phase if there's growth
+
+ align:start position:0%
+in the second phase if there's growth
+ 
+
+ align:start position:0%
+in the second phase if there's growth
+expand it
+
+ align:start position:0%
+expand it
+ 
+
+ align:start position:0%
+expand it
+if there's no particular growth
+
+ align:start position:0%
+if there's no particular growth
+ 
+
+ align:start position:0%
+if there's no particular growth
+don't do anything
+
+ align:start position:0%
+don't do anything
+ 
+
+ align:start position:0%
+don't do anything
+if it's failing
+
+ align:start position:0%
+if it's failing
+ 
+
+ align:start position:0%
+if it's failing
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+close it for example so you can you
+
+ align:start position:0%
+close it for example so you can you
+ 
+
+ align:start position:0%
+close it for example so you can you
+don't have one plan
+
+ align:start position:0%
+don't have one plan
+ 
+
+ align:start position:0%
+don't have one plan
+you have you have a strategy a dynamic
+
+ align:start position:0%
+you have you have a strategy a dynamic
+ 
+
+ align:start position:0%
+you have you have a strategy a dynamic
+plan that uh
+
+ align:start position:0%
+plan that uh
+ 
+
+ align:start position:0%
+plan that uh
+lasts through time
+
+ align:start position:0%
+lasts through time
+ 
+
+ align:start position:0%
+lasts through time
+now coming back to the decision analysis
+
+ align:start position:0%
+now coming back to the decision analysis
+ 
+
+ align:start position:0%
+now coming back to the decision analysis
+consequences
+
+ align:start position:0%
+consequences
+ 
+
+ align:start position:0%
+consequences
+is it going through this kind of process
+
+ align:start position:0%
+is it going through this kind of process
+ 
+
+ align:start position:0%
+is it going through this kind of process
+of showing the complexity of it is an
+
+ align:start position:0%
+of showing the complexity of it is an
+ 
+
+ align:start position:0%
+of showing the complexity of it is an
+education for the client
+
+ align:start position:0%
+education for the client
+ 
+
+ align:start position:0%
+education for the client
+for the person you're trying to do
+
+ align:start position:0%
+for the person you're trying to do
+ 
+
+ align:start position:0%
+for the person you're trying to do
+and it also shows a strategy a dynamic
+
+ align:start position:0%
+and it also shows a strategy a dynamic
+ 
+
+ align:start position:0%
+and it also shows a strategy a dynamic
+plan is better than having a step one
+
+ align:start position:0%
+plan is better than having a step one
+ 
+
+ align:start position:0%
+plan is better than having a step one
+step two step three a phased this is
+
+ align:start position:0%
+step two step three a phased this is
+ 
+
+ align:start position:0%
+step two step three a phased this is
+what we're going to do through time we
+
+ align:start position:0%
+what we're going to do through time we
+ 
+
+ align:start position:0%
+what we're going to do through time we
+just generally they don't work out that
+
+ align:start position:0%
+just generally they don't work out that
+ 
+
+ align:start position:0%
+just generally they don't work out that
+way anyway
+
+ align:start position:0%
+way anyway
+ 
+
+ align:start position:0%
+way anyway
+moreover often it's the second best
+
+ align:start position:0%
+moreover often it's the second best
+ 
+
+ align:start position:0%
+moreover often it's the second best
+strategy that is optimal for winning any
+
+ align:start position:0%
+strategy that is optimal for winning any
+ 
+
+ align:start position:0%
+strategy that is optimal for winning any
+one outcome for example it's best to buy
+
+ align:start position:0%
+one outcome for example it's best to buy
+ 
+
+ align:start position:0%
+one outcome for example it's best to buy
+insurance
+
+ align:start position:0%
+insurance
+ 
+
+ align:start position:0%
+insurance
+so thinking about
+
+ align:start position:0%
+so thinking about
+ 
+
+ align:start position:0%
+so thinking about
+um you can choose to have a car or not
+
+ align:start position:0%
+um you can choose to have a car or not
+ 
+
+ align:start position:0%
+um you can choose to have a car or not
+if you if it's within your means
+
+ align:start position:0%
+if you if it's within your means
+ 
+
+ align:start position:0%
+if you if it's within your means
+and then if you have an accident
+
+ align:start position:0%
+and then if you have an accident
+ 
+
+ align:start position:0%
+and then if you have an accident
+and you're
+
+ align:start position:0%
+and you're
+ 
+
+ align:start position:0%
+and you're
+really hurt and everything
+
+ align:start position:0%
+really hurt and everything
+ 
+
+ align:start position:0%
+really hurt and everything
+you could look back and say driving was
+
+ align:start position:0%
+you could look back and say driving was
+ 
+
+ align:start position:0%
+you could look back and say driving was
+not a good idea
+
+ align:start position:0%
+not a good idea
+ 
+
+ align:start position:0%
+not a good idea
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and it would have been better not to
+
+ align:start position:0%
+and it would have been better not to
+ 
+
+ align:start position:0%
+and it would have been better not to
+drive at all
+
+ align:start position:0%
+drive at all
+ 
+
+ align:start position:0%
+drive at all
+if you have no accident you might say
+
+ align:start position:0%
+if you have no accident you might say
+ 
+
+ align:start position:0%
+if you have no accident you might say
+gee i did i
+
+ align:start position:0%
+gee i did i
+ 
+
+ align:start position:0%
+gee i did i
+my best choice would have been to
+
+ align:start position:0%
+my best choice would have been to
+ 
+
+ align:start position:0%
+my best choice would have been to
+not have insurance
+
+ align:start position:0%
+not have insurance
+ 
+
+ align:start position:0%
+not have insurance
+insurance was a bad idea to have because
+
+ align:start position:0%
+insurance was a bad idea to have because
+ 
+
+ align:start position:0%
+insurance was a bad idea to have because
+i didn't use it
+
+ align:start position:0%
+i didn't use it
+ 
+
+ align:start position:0%
+i didn't use it
+so the optimal choice would might be to
+
+ align:start position:0%
+so the optimal choice would might be to
+ 
+
+ align:start position:0%
+so the optimal choice would might be to
+drive with insurance which is never the
+
+ align:start position:0%
+drive with insurance which is never the
+ 
+
+ align:start position:0%
+drive with insurance which is never the
+best which would not be the best choice
+
+ align:start position:0%
+best which would not be the best choice
+ 
+
+ align:start position:0%
+best which would not be the best choice
+your first core choice in terms of the
+
+ align:start position:0%
+your first core choice in terms of the
+ 
+
+ align:start position:0%
+your first core choice in terms of the
+outcomes if the outcomes
+
+ align:start position:0%
+outcomes if the outcomes
+ 
+
+ align:start position:0%
+outcomes if the outcomes
+um were that you didn't have any
+
+ align:start position:0%
+um were that you didn't have any
+ 
+
+ align:start position:0%
+um were that you didn't have any
+accident you spent all that money that
+
+ align:start position:0%
+accident you spent all that money that
+ 
+
+ align:start position:0%
+accident you spent all that money that
+you didn't need to
+
+ align:start position:0%
+you didn't need to
+ 
+
+ align:start position:0%
+you didn't need to
+that would have been the better choice
+
+ align:start position:0%
+that would have been the better choice
+ 
+
+ align:start position:0%
+that would have been the better choice
+if you did have a bad accident then
+
+ align:start position:0%
+if you did have a bad accident then
+ 
+
+ align:start position:0%
+if you did have a bad accident then
+maybe you shouldn't have been into doing
+
+ align:start position:0%
+maybe you shouldn't have been into doing
+ 
+
+ align:start position:0%
+maybe you shouldn't have been into doing
+that kind of activity anyway
+
+ align:start position:0%
+that kind of activity anyway
+ 
+
+ align:start position:0%
+that kind of activity anyway
+so it's the idea that
+
+ align:start position:0%
+so it's the idea that
+ 
+
+ align:start position:0%
+so it's the idea that
+the better choice like to drive
+
+ align:start position:0%
+the better choice like to drive
+ 
+
+ align:start position:0%
+the better choice like to drive
+insurance is never the best choice for
+
+ align:start position:0%
+insurance is never the best choice for
+ 
+
+ align:start position:0%
+insurance is never the best choice for
+all is not necessarily the best choice
+
+ align:start position:0%
+all is not necessarily the best choice
+ 
+
+ align:start position:0%
+all is not necessarily the best choice
+for all the possible outcomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me now step back and put this
+
+ align:start position:0%
+so let me now step back and put this
+ 
+
+ align:start position:0%
+so let me now step back and put this
+decision analysis versus flexibility
+
+ align:start position:0%
+decision analysis versus flexibility
+ 
+
+ align:start position:0%
+decision analysis versus flexibility
+analysis so this decision analysis
+
+ align:start position:0%
+analysis so this decision analysis
+ 
+
+ align:start position:0%
+analysis so this decision analysis
+assumes you can
+
+ align:start position:0%
+assumes you can
+ 
+
+ align:start position:0%
+assumes you can
+define the choices to take in any stages
+
+ align:start position:0%
+define the choices to take in any stages
+ 
+
+ align:start position:0%
+define the choices to take in any stages
+that's essential to building your
+
+ align:start position:0%
+that's essential to building your
+ 
+
+ align:start position:0%
+that's essential to building your
+decision trees to say
+
+ align:start position:0%
+decision trees to say
+ 
+
+ align:start position:0%
+decision trees to say
+at stage two here's what i can do at
+
+ align:start position:0%
+at stage two here's what i can do at
+ 
+
+ align:start position:0%
+at stage two here's what i can do at
+stage three here's what i can do
+
+ align:start position:0%
+stage three here's what i can do
+ 
+
+ align:start position:0%
+stage three here's what i can do
+contrarily decision and flexibility
+
+ align:start position:0%
+contrarily decision and flexibility
+ 
+
+ align:start position:0%
+contrarily decision and flexibility
+encourage you to explore what decision
+
+ align:start position:0%
+encourage you to explore what decision
+ 
+
+ align:start position:0%
+encourage you to explore what decision
+to take and when to take them
+
+ align:start position:0%
+to take and when to take them
+ 
+
+ align:start position:0%
+to take and when to take them
+it doesn't tell you what you have to do
+
+ align:start position:0%
+it doesn't tell you what you have to do
+ 
+
+ align:start position:0%
+it doesn't tell you what you have to do
+and it doesn't tell you when to do it so
+
+ align:start position:0%
+and it doesn't tell you when to do it so
+ 
+
+ align:start position:0%
+and it doesn't tell you when to do it so
+the simulation analysis allows you to
+
+ align:start position:0%
+the simulation analysis allows you to
+ 
+
+ align:start position:0%
+the simulation analysis allows you to
+look at those
+
+ align:start position:0%
+look at those
+ 
+
+ align:start position:0%
+look at those
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+secondly
+
+ align:start position:0%
+secondly
+ 
+
+ align:start position:0%
+secondly
+the decision analysis focuses on a few
+
+ align:start position:0%
+the decision analysis focuses on a few
+ 
+
+ align:start position:0%
+the decision analysis focuses on a few
+distinct choices we do this that or the
+
+ align:start position:0%
+distinct choices we do this that or the
+ 
+
+ align:start position:0%
+distinct choices we do this that or the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+whereas a flexibility analysis
+
+ align:start position:0%
+whereas a flexibility analysis
+ 
+
+ align:start position:0%
+whereas a flexibility analysis
+allows you via excel to be as granular
+
+ align:start position:0%
+allows you via excel to be as granular
+ 
+
+ align:start position:0%
+allows you via excel to be as granular
+as you as desired you can look through 2
+
+ align:start position:0%
+as you as desired you can look through 2
+ 
+
+ align:start position:0%
+as you as desired you can look through 2
+000 simulations and it's easy to do does
+
+ align:start position:0%
+000 simulations and it's easy to do does
+ 
+
+ align:start position:0%
+000 simulations and it's easy to do does
+it in seconds but
+
+ align:start position:0%
+it in seconds but
+ 
+
+ align:start position:0%
+it in seconds but
+this is not really possible on
+
+ align:start position:0%
+this is not really possible on
+ 
+
+ align:start position:0%
+this is not really possible on
+with decision analysis so
+
+ align:start position:0%
+with decision analysis so
+ 
+
+ align:start position:0%
+with decision analysis so
+having said that
+
+ align:start position:0%
+having said that
+ 
+
+ align:start position:0%
+having said that
+well it emphasizes the reasons why uh
+
+ align:start position:0%
+well it emphasizes the reasons why uh
+ 
+
+ align:start position:0%
+well it emphasizes the reasons why uh
+decision analysis which was popular um
+
+ align:start position:0%
+decision analysis which was popular um
+ 
+
+ align:start position:0%
+decision analysis which was popular um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+was a breakthrough frankly speaking uh
+
+ align:start position:0%
+was a breakthrough frankly speaking uh
+ 
+
+ align:start position:0%
+was a breakthrough frankly speaking uh
+into thinking uh a long time ago for me
+
+ align:start position:0%
+into thinking uh a long time ago for me
+ 
+
+ align:start position:0%
+into thinking uh a long time ago for me
+a long time ago for before you were born
+
+ align:start position:0%
+a long time ago for before you were born
+ 
+
+ align:start position:0%
+a long time ago for before you were born
+even perhaps possibly um it is really
+
+ align:start position:0%
+even perhaps possibly um it is really
+ 
+
+ align:start position:0%
+even perhaps possibly um it is really
+not so relevant uh today although it
+
+ align:start position:0%
+not so relevant uh today although it
+ 
+
+ align:start position:0%
+not so relevant uh today although it
+does exist and is used and has some
+
+ align:start position:0%
+does exist and is used and has some
+ 
+
+ align:start position:0%
+does exist and is used and has some
+insights which
+
+ align:start position:0%
+insights which
+ 
+
+ align:start position:0%
+insights which
+i'll be sharing with you in terms of
+
+ align:start position:0%
+i'll be sharing with you in terms of
+ 
+
+ align:start position:0%
+i'll be sharing with you in terms of
+value of information
\ No newline at end of file
diff --git a/8O2EPwUtWyY.txt b/8O2EPwUtWyY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dff99b4762d528d033e244d511ac19e82e780ce1
--- /dev/null
+++ b/8O2EPwUtWyY.txt
@@ -0,0 +1,3091 @@
+Hello, everyone.
+
+Welcome.
+
+I'm Krishna Rajagopal, MIT's
+Dean for Digital Learning.
+
+And I'm here to welcome
+everyone to this joyous occasion
+
+as OpenCourseWare turns 20.
+
+Today, we celebrate
+OCW's first 20 years,
+
+and look ahead to the potential
+and the plans for OCW,
+
+and the entire ecosystem of
+open educational resources
+
+that OCW sits within,
+in its next 20.
+
+The mission of OCW
+since its founding
+
+was to unlock knowledge
+and empower minds
+
+by publishing materials from
+virtually all MIT courses,
+
+and extend the reach of those
+materials via the OER movement
+
+which OCW played a
+key role in seeding.
+
+Charles Vest, who is
+the president of MIT who
+
+launched OCW 20 years
+ago, spoke at that time
+
+about how surprising and
+audacious the vision of OCW
+
+that came to him from a founding
+group of MIT faculty members
+
+was.
+
+Put all of our materials
+on the internet, openly?
+
+This came as a big surprise to
+President Vest 20 years ago.
+
+One way to see how right
+the faculty were back then,
+
+those founding faculty,
+is to say that today,
+
+sharing our pedagogy, our
+perspective, our insights,
+
+openly via OCW is simply
+unquestioned at MIT.
+
+It's seen as just a
+part of what we do.
+
+It comes from who we are.
+
+Of course we do this.
+
+And the fact that so much
+has changed in 20 years
+
+is a sign that the
+founders, the pioneers,
+
+were as right as
+in fact, they were.
+
+So, jumping ahead today,
+let's look at OCW today.
+
+2,500 courses on OCW.
+
+Material from 2,500 courses.
+
+From 1,700 MIT instructors.
+
+OCW is the largest .edu
+YouTube channel in the world,
+
+with 2.97 million subscribers.
+
+And over the history of
+that YouTube channel,
+
+more than 2 billion minutes
+of learning on that YouTube
+
+channel.
+
+And I'll remind you that OCW
+was founded long before YouTube.
+
+And the idea that OCW would
+include video in this way
+
+was something that came after
+the founding, it's more recent.
+
+And yet, here we are.
+
+What about the OCW website,
+which is where it all began?
+
+To date, 210 million
+visitors to the OCW website.
+
+And just time on
+the website itself,
+
+more than a billion
+minutes of learning.
+
+And really, untold
+billions, we don't
+
+know how many more
+billions, of minutes
+
+of learning that OCW has
+made possible, as people
+
+use the materials
+from the website.
+
+Download a problem
+set, learn by doing.
+
+As people share the
+materials from that website.
+
+As people teach
+their own students
+
+using the materials
+from that website.
+
+The learning that has resulted
+as a consequence of OCW
+
+is inestimable.
+
+And furthermore,
+the magic of OER
+
+is that these materials morph,
+and get reshaped, and shared,
+
+and ripple outwards
+in myriad ways,
+
+as educators and organizations
+within the OER world
+
+take them and make
+them their own.
+
+For all of this, we, and
+millions around the world,
+
+owe our thanks to so many.
+
+Let me first thank the founding
+generation, the faculty who
+
+were there at the
+beginning who had
+
+the-- created the
+vision of OCW, one of whom
+
+you'll be hearing
+from later today.
+
+I also want to thank 1,700
+MIT faculty and instructors
+
+who have contributed,
+and continue
+
+to contribute, their
+insights from their teaching,
+
+the artifacts of their teaching,
+the products of their labors,
+
+what they've created
+as they teach
+
+on campus in MIT's classrooms.
+
+Next, I want to thank
+thousands and thousands
+
+of generous supporters who
+have made this all possible,
+
+including two key foundations,
+the William and Flora Hewlett
+
+Foundation, and the Andrew
+W. Mellon Foundation,
+
+without whom none of
+this would have happened.
+
+I also want to thank key
+corporate supporters, of whom
+
+there are a number, including
+in particular Ab Initio
+
+and MathWorks, as well as
+major individual supporters,
+
+including people like
+MIT alum John Gruber,
+
+and thousands more.
+
+And some of the supporters, many
+of these supporters, in fact,
+
+are here with us today, all of
+whose generosity we gratefully
+
+acknowledge today as a
+part of this celebration.
+
+And last but far from least, I
+want to thank the devoted OCW
+
+team itself.
+
+17 devoted people who make
+the magic of OCW happen.
+
+Their work, their
+continuing efforts,
+
+realizes MIT's
+sustained and ongoing
+
+institutional commitment to OCW,
+for which we're also grateful.
+
+For the institutional
+commitment to OCW,
+
+this wonderful incarnation
+of MIT's mission and values.
+
+If you look at the
+mission of MIT,
+
+you see creating, sharing,
+and preserving knowledge.
+
+OCW does that in spades.
+
+And then you see a
+phrase in the mission
+
+that says that MIT is committed
+to working with others,
+
+to bring knowledge to bear on
+the world's great challenges.
+
+As we look to the future,
+now, to the evolving place
+
+of OCW in the OER landscape,
+OER is the embodiment, for OCW,
+
+of working with others
+to bring knowledge
+
+to bear on the great
+challenges of the world.
+
+We see a path, as we
+look ahead, to going
+
+from the magnificent access
+that OCW has already created--
+
+access to knowledge,
+access to learning,
+
+access to MIT's teaching.
+
+Going forward, we see
+a path from that access
+
+to greater equity.
+
+And the way to get
+from access to equity
+
+involves collaboration.
+
+Collaboration with educators and
+OER institutions, each of whom
+
+bring knowledge to people
+whom they know well,
+
+to people in widely varying
+contexts with widely
+
+varying starting points.
+
+This is a key part of our
+vision for the future.
+
+So we will return to
+the OCW of the future
+
+at the end of the hour, after
+hearing from a distinguished
+
+panel.
+
+But first, let's kick
+this birthday party
+
+off with a
+magnificent video that
+
+was produced by Joe McMaster
+and MIT Video Production.
+
+In creating OCW, MIT
+launched a quiet but profound
+
+educational revolution.
+
+It unleashed the global
+open-sharing movement,
+
+and helped pave the way for
+the worldwide phenomenon
+
+of open digital learning.
+
+What are two or three
+words to describe
+
+OpenCourseWare's impact?
+
+I would say knowledge and scale.
+
+Eye-opening.
+
+Enlightening.
+
+Choose your own adventure.
+
+A whole new world.
+
+Wow, 20 years of
+MIT's OpenCourseWare.
+
+It's just amazing
+to think about.
+
+We've had more than 200
+million people come to OCW
+
+and learn from the materials
+that MIT is sharing.
+
+My initial introduction
+to OpenCourseWare
+
+was actually at Bunker
+Hill Community College.
+
+My linear algebra
+professor would give us
+
+these weekly quizzes.
+
+We told her it was hard,
+and she said, actually,
+
+this is an MIT quiz.
+
+And I was kind of blown away
+that I did some part of it.
+
+And when I inquired how
+she got the quiz, she said,
+
+oh, there's this thing
+called MIT OpenCourseWare.
+
+It imparted me with
+this confidence of oh,
+
+I can do this.
+
+I can survive an MIT course.
+
+And that drove me to say,
+maybe I can thrive at MIT.
+
+OCW was the pioneer.
+
+It opened everybody's
+eyes to the possibility
+
+of connecting to learners who
+are in different countries,
+
+and different situations,
+different ages.
+
+We are making MIT OCW available
+in universities and community
+
+libraries which do not
+have internet connection.
+
+It has encouraged me to learn,
+to find out about things,
+
+to understand and to apply.
+
+There is so much that can be
+achieved by just giving people
+
+complete, wide open
+access to this knowledge
+
+that they can use
+whenever, wherever.
+
+As much as they need,
+as little as they need.
+
+It takes this very kind of
+privileged and elite education
+
+that we make accessible
+to our students,
+
+and opens it up to
+a broader public.
+
+The very existence of MIT's
+OpenCourseWare is inspiring.
+
+It's a shining example
+for institutions of higher
+
+education around the world.
+
+I think there's also
+great value in showing
+
+the range of disciplines
+that are taught at MIT,
+
+and showing the fact that the
+humanities and social sciences
+
+are as much a strength of what
+MIT has to offer as the STEM
+
+disciplines.
+
+This course that I created
+is now part of the record,
+
+and is now something that
+someone else can build on.
+
+Everything is there, even the
+syllabus, even the instructions
+
+of the teacher's,
+thesis, assignments.
+
+OCW is, perhaps, one of the
+best things that has happened
+
+to education Worldwide.
+
+It's like being so unselfish.
+
+You're giving everything
+of what you have,
+
+and sharing it with
+the other people,
+
+especially in developing
+countries like the Philippines.
+
+OpenCourseWare quite
+literally changed my life.
+
+It gave me the education
+I needed when there wasn't
+
+another place to find it.
+
+You're giving people
+the tools that
+
+will allow them to
+achieve their potential.
+
+We have real problems in the
+world that need to be solved,
+
+and we need problem solvers
+from every area of the planet
+
+to work on these.
+
+We've created this powerful
+foundation of free access
+
+to knowledge, and together
+we'll keep growing it.
+
+We're creating better ways
+for learners and teachers
+
+to find and to use
+that OCW content.
+
+And we'll keep sharing
+that vibrant reflection
+
+of the teaching and
+creativity from MIT.
+
+As we think about equity, we
+think about collaborators,
+
+so that we can bring
+more people, starting
+
+from different starting points,
+coming in different ways,
+
+to the point that they
+can learn from OCW.
+
+Together, we're
+forging new paths
+
+where everyone's contributing to
+the world's growing knowledge.
+
+And we're all using and sharing
+that knowledge every day
+
+to solve the world's
+great challenges.
+
+I want OCW to attract people.
+
+So it's not just a neutral,
+if you want it come get it,
+
+I want OCW to be calling on
+people to educate themselves,
+
+to empower themselves,
+to build and to have
+
+the necessary tools to do
+what they think is important.
+
+And I'm hoping that, over time,
+this snowball from 20 years ago
+
+becomes an avalanche of
+intellectual exchange
+
+amongst humanity.
+
+All right, well that was
+deeply inspiring for me
+
+to watch every time I see it.
+
+And I'm really glad that we
+could share that with you.
+
+Next, we're going to
+have a live conversation
+
+with several people
+from the MIT community
+
+who've made this possible,
+continue to make it possible,
+
+and are leading us
+together into the future.
+
+My name is Curt Newton as
+Director of OpenCourseWare.
+
+I joined the team shortly
+after it launched in 2004,
+
+and I've been director
+for the last few years.
+
+And I'm happy to introduce
+now my four co-panelists, Hal
+
+Abelson, professor
+of Computer Science
+
+and Engineering, part of
+the original faculty team
+
+who conceived of OpenCourseWare.
+
+He was a very busy
+guy around 2000, 2001,
+
+also helping launch things like
+the Creative Commons, which
+
+we are so glad to be partners
+in this enterprise with.
+
+Mussie Demisse,
+current MIT undergrad
+
+who we were introduced
+to in that video.
+
+As we heard, transferred to MIT
+after studying computer science
+
+at Bunker Hill
+Community College,
+
+and we've been really
+glad to work with him
+
+this year on our
+advisory committee.
+
+Anjali Sastry, senior lecturer
+at Sloan School of Management
+
+and founder of MIT Sloan's
+GlobalHealth Lab, where she's
+
+been building collaborations
+engaging students
+
+around the world to
+improve healthcare
+
+in places like sub-Saharan
+Africa and South Asia.
+
+And last but not least, Mike
+Short, Associate Professor
+
+of Nuclear Science
+and Engineering.
+
+He started as a student at MIT
+right when OCW was launched.
+
+Completed his master's in 2005,
+completed a doctorate in 2010,
+
+and is now a professor
+of nuclear science
+
+and engineering.
+
+Has produced a number
+of courses on OCW,
+
+including the build-your-own
+Geiger counter short course,
+
+lots of inspiration out there.
+
+So I'd like to ask
+each of our panelists
+
+to take, maybe, another
+minute to introduce yourself
+
+a little more fully,
+and in particular maybe
+
+if you can share a reflection
+on what OCW has meant to you.
+
+And I'd like to
+start off with Hal,
+
+and then we'll
+move on to Mussie.
+
+OK Curt, thanks a lot.
+
+And, Krishna, thank you for
+that wonderful introduction.
+
+Today is a wonderful
+20th anniversary,
+
+but actually it's a
+triple 20th anniversary.
+
+Because there are
+three initiatives that
+
+are interlinked, that all
+have to do with this notion
+
+of open sharing.
+
+OCW is, I think, the
+most revolutionary.
+
+But there's also
+Creative Commons,
+
+which says, how do we
+align this idea of sharing
+
+with the technicalities
+of US copyright law?
+
+And then there is DSpace
+in the MIT libraries, which
+
+is how do we take that same
+vision of sharing, not just MIT
+
+educational courses, but
+MIT research publications?
+
+These all sit
+together, they all join
+
+in supporting this idea of
+open sharing of knowledge
+
+and what is the right--
+
+what's the appropriate
+stance for a great world
+
+leading university
+to take, in terms
+
+of benefiting humanity through
+its intellectual productions?
+
+These all build
+on the internet
+
+as a vision of sharing.
+
+And it's worth noting,
+we talk about vision.
+
+There were other
+initiatives 20 years ago
+
+that had the same vision.
+
+Almost none of
+them survive today.
+
+And so the three things
+that we're talking about
+
+are all there, are
+all productive,
+
+and are all improving humanity.
+
+We often talk about MIT
+as a wonderful vision.
+
+The reality is that visions at
+this place are a dime a dozen.
+
+What's important is
+that you carry through,
+
+and you make something
+that's actually
+
+implemented and sustainable.
+
+And when I think about what MIT
+started 20 years ago, the fact
+
+that we're still here,
+and still producing,
+
+unlike so many
+other initiatives,
+
+is something that makes me
+enormously proud of MIT.
+
+Thank you, Hal.
+
+Thank you for helping
+us get that kicked off.
+
+Mussie.
+
+All right.
+
+Me and OCW, I kind of wish
+I knew OCW much earlier.
+
+I'm originally from
+Ethiopia, and there
+
+were times where, being in
+kind of a low-resource area,
+
+the issue is not that
+you don't want to learn.
+
+It's not that you don't want
+to build your capabilities.
+
+But you really don't see the
+pathways and the roads that
+
+will allow you to get there.
+
+So, for me, what
+OCW really means is,
+
+it's an opportunity for me
+to accomplish the things
+
+that I want.
+
+It's a pathway.
+
+And it's not just for me,
+but it's for my brothers
+
+and sisters all over the world.
+
+Thank you.
+
+Thank you.
+
+Anjali.
+
+Great comments.
+
+I was thinking about my
+own youth, now long ago.
+
+And I would read books
+and get an escape
+
+to the rest of the
+world, from the novels
+
+and non-fiction books I read.
+
+And now, there's OCW.
+
+You can walk through
+another door,
+
+and find out all
+kinds of information
+
+that's presented
+in ways that allow
+
+you to make your own path
+through at the pace that
+
+works for you as an
+instructor or as a learner.
+
+I benefit a ton from
+teaching with OCW in my mind,
+
+because it encourages
+me to reflect,
+
+to be conscious about
+what I'm teaching.
+
+I now write all my
+syllabi, for instance,
+
+with links to
+open-source content,
+
+so that others can benefit
+from it and I can share freely.
+
+I love that it
+mirrors our commitment
+
+to a physically open campus.
+
+I also have gone to
+other universities
+
+where you have to always
+unlock every door,
+
+and it's pretty cool
+that MIT's so open.
+
+Not amid COVID, but
+soon we will be again.
+
+And finally, when I launched
+my global health work,
+
+I went to Kenya and
+met all kinds of folks.
+
+I was just learning
+about the discipline.
+
+And somebody I
+met very early on,
+
+just randomly on
+the street, said,
+
+I use a mirror site in Rwanda.
+
+Thank you, thank you MIT for
+sharing all this material.
+
+We use it all the time.
+
+I didn't even know.
+
+I didn't even know there were
+people all over the world who
+
+were feeling part of MIT.
+
+So that's pretty cool.
+
+Thank you Anjali.
+
+And Mike.
+
+Sure.
+
+Well, I'd like to say that
+I'm not just a contributor,
+
+but I was also a client of OCW.
+
+I started at MIT in 2001 as a
+first year, and for me it's--
+
+I've watched OCW give back to
+the world, and even to MIT,
+
+in so many more dimensions
+than I could have imagined.
+
+As a first year, I was
+an example-based learner.
+
+And OpenCourseWare gave me the examples
+
+I needed to survive MIT, because
+without them, I'm not sure
+
+I would have been able to.
+
+I started off, grade-wise, kind
+of at the bottom of the pack,
+
+and once I found and
+used OCW, that changed.
+
+And now, as a
+faculty member, I've
+
+got the opportunity to
+travel all over the world,
+
+despite not moving an
+inch, in the past 20 years.
+
+I've been able to travel
+outwards, and look back
+
+inwards.
+
+And to echo something
+that was said before,
+
+the number of people around
+the world that use and are
+
+thankful for OCW is incredible.
+
+I had an IAE mission
+to the National University
+
+of Mongolia, and for
+many of their courses
+
+their syllabus is the
+OpenCourseWare syllabus.
+
+And to see ways that
+not just students learn,
+
+and they feel amazing when
+they conquer MIT problem
+
+sets of material, but how
+instructors reinterpret
+
+our material gives
+me inspiration
+
+to bring back, to make
+the courses at MIT better.
+
+Thank you.
+
+I'm so glad that we're all
+able to have this conversation
+
+together, and I'd like
+to invite everybody who's
+
+watching this
+session to please put
+
+your questions in the
+chats, and in the places
+
+where you can enter questions,
+and those will be fed back
+
+to us, and we'll definitely
+spend a few minutes
+
+at the end of the
+panel sharing thoughts
+
+on some of those questions.
+
+So I'd like to return
+and ask each of you a bit
+
+of a follow up
+question, if I could.
+
+Again, starting with Hal as
+part of our founding team, what
+
+was in the water in 2001?
+
+What do you think led to
+this flowering of openness
+
+at that time?
+
+What has it led to?
+
+So it's a little hard to
+remember what 2001 was like.
+
+This was sort of the first
+kind of explosion of enthusiasm
+
+around the internet.
+
+And Chuck Vest, president
+of MIT at that time,
+
+would go around talking, and
+alumni and other groups
+
+would say to him,
+there's this internet.
+
+What's MIT going to do about it?
+
+And there was this
+notion about, there's
+
+an enormous opportunity, but we
+didn't really know what it was.
+
+And then there was a whole study
+we took, first with McKinsey,
+
+and then with Booz Allen, trying
+to come up with something.
+
+And this revolutionary idea,
+that we should just open it up
+
+to the world, kind of emerged,
+was extremely counterintuitive,
+
+because where universities were,
+in those days by and large,
+
+was that their
+courses were going
+
+to be enormous gold mines.
+
+That they were going to
+sell to alumni and others,
+
+and we did a study
+at MIT and said,
+
+well, know, that's not
+really going to work for MIT.
+
+And then there was
+this enormous insight,
+
+I think Dick Yue had it
+when he was getting food out
+
+of the refrigerator
+at night, that
+
+said, why don't we
+just give it away?
+
+And the amazing thing is that
+the MIT administration took it
+
+seriously.
+
+And really put MIT's
+force behind it,
+
+and MIT's credibility behind it.
+
+And that's really
+how it happened.
+
+As I mentioned before, many of
+those other places, involving
+
+Stanford, and Princeton,
+and Columbia, and all that,
+
+don't exist anymore.
+
+The one exception is eCornell.
+
+And we had this very,
+very funny thing
+
+where MIT has been asked by some
+of those organizations to join.
+
+Remember that person who was
+running Fathom, which came out
+
+came out of Columbia,
+came by to MIT,
+
+trying to get MIT to join
+the commercial Fathom.
+
+And this was like
+the day before we
+
+were going to announce
+OpenCourseWare,
+
+and it was just
+kind of funny, it
+
+was kind of
+ confidential, it was
+
+kind of funny, kind of sitting
+there and saying, oh, yeah,
+
+well, you know,
+about tomorrow, we're
+
+about to take all of this stuff,
+and revolutionize and make it
+
+free.
+
+But it's a little hard to
+appreciate the real fervent
+
+around the internet, and
+I think we'll say later,
+
+when we talk about
+the future, we're
+
+in the reflection of
+that period today,
+
+and it's something we should
+be thinking about very, very
+
+hard as we think about
+the climate today,
+
+as compared to the
+climate 20 years ago.
+
+Yeah, thank you.
+
+Yeah.
+
+Let's come back
+to that, for sure.
+
+I'd like to ask Mussie,
+as a beneficiary of some
+
+of that openness, what
+would you like people
+
+to know about how open
+education is affecting
+
+students' lives today?
+
+What did you experience,
+and what do you
+
+see both at your community
+college colleagues,
+
+and here at MIT?
+
+So before-- OER is the
+solution to the problem
+
+of the cost of educational
+resources becoming
+
+a barrier to education.
+
+And that happens at
+different levels.
+
+There's the, I'm taking a
+course, I want to know more,
+
+I want to get a more in-depth
+knowledge, and I'm interested.
+
+That's one aspect that OCW
+really tackles directly.
+
+You can just go to the website,
+it's in an organized manner,
+
+which, in my
+personal experience,
+
+the internet usually isn't.
+
+It's just like, hey, here's
+bits and pieces of everything.
+
+The other aspect of it
+is, in order for classes
+
+to get accreditation and so on,
+professors in these community
+
+colleges are almost forced
+to have these textbooks
+
+that larger organizations can--
+
+the larger institutions,
+educational institutions, use.
+
+So what, by MIT producing
+open educational resources
+
+like this, basically
+what it's saying is,
+
+it's putting its big name,
+its big powerful name,
+
+behind open educational
+resources, which really gives
+
+freedom back to instructors
+in these community colleges
+
+to kind of say, hey,
+there's this textbook,
+
+but MIT has kind
+of validated this,
+
+and we can kind of approach it.
+
+So, for me and my friends and
+all, the basic point is this.
+
+We're trying to
+get an education.
+
+And OCW is just an easier way.
+
+It just removes certain
+cost-based barriers.
+
+Yeah.
+
+That cost foundation has
+become such a core issue
+
+in the open education
+resources movement.
+
+We hear that, Mussie, a lot.
+
+Anjali, in your experience
+trying to work globally,
+
+I'm curious how you see
+open knowledge sharing
+
+playing out and helping people
+build, achieve, solutions
+
+more rapidly, more
+effectively, and to what extent
+
+is the free-ness and
+the openness of it
+
+making that happen?
+
+So almost 15 years
+ago, when I started
+
+working in global
+health, I realized
+
+this is a domain in which we
+are, by definition, neophytes.
+
+MIT doesn't have a
+medical school or school
+
+of public health.
+
+So I already had to collaborate
+in order to just get the course
+
+going, I set up collaborations
+with Harvard Medical
+
+School, clinicians all over
+the world that I could find,
+
+who would serve as guides,
+as partners, help me source
+
+and develop projects.
+
+But the minute I
+started doing that, I
+
+realized I need to share.
+
+So I am relying on others to
+share with me, I need to share.
+
+So there was a really
+nice fit with OCW,
+
+It's interesting, because you
+think of online, I don't know,
+
+short videos being very kind
+of procedural or instructional,
+
+but OCW can handle a
+lot of complexity, too.
+
+And I've really been
+wrestling over these years
+
+with how best to present
+and frame that complexity.
+
+So I guess there's two
+themes in my answer.
+
+One is I think we all
+rely on many others
+
+to fuel our learning, and
+being conscious of that
+
+when you share what
+you've developed
+
+is, I think, just a really
+good way to keep you
+
+honest about the
+role of expertise
+
+from all over the place.
+
+And it also allows me to honor
+everybody's contributions,
+
+because I can record
+and share in OCW.
+
+And third, by kind of
+archiving and building
+
+on work year-to-year,
+it's really good for me
+
+as an instructor, for my
+students over the years,
+
+to be able to see, how
+has our thinking evolved?
+
+And I'll say to students, we're
+going to be archiving this.
+
+And we put student work up.
+
+So we disguise it, we
+get their permission,
+
+we remove any proprietary
+or confidential information,
+
+but because we
+share every year, we
+
+can generate an
+amazing dialogue,
+
+not only with potential
+students like Mussie,
+
+but also with alums and
+with potential partners.
+
+We get to show our work
+in a new way, which
+
+I think is really cool.
+
+Yeah.
+
+Yeah.
+
+I think this theme of opening
+up the sharing of knowledge,
+
+the access to knowledge,
+across all forms of expertise
+
+is so powerful.
+
+I'd like to ask Mike,
+maybe, to start off.
+
+Having been a student
+at MIT, and watched how
+
+this institute has evolved.
+
+What do you think about the way
+that students are contributing
+
+to this knowledge, and
+colleagues around the world
+
+are contributing to this
+knowledge, all together mixed
+
+up with what the MIT
+faculty are teaching?
+
+What does that indicate
+to us about the power
+
+of this movement?
+
+Sure, I'd be happy
+to answer that.
+
+So in terms of how does the
+mere presence of OpenCourseWare
+
+enable students, and colleagues,
+and other instructors
+
+from around the
+world to contribute,
+
+just the very fact
+that it exists
+
+in this purely open and
+free environment, like Hal
+
+so well said, is
+the deciding factor
+
+that just allows humanity
+to share its knowledge.
+
+This, to me, is the single
+best thing in education.
+
+It's the largest thing I know of
+just free knowledge access to the world.
+
+And so, in every interaction
+I have, from the emails
+
+I'm getting during the
+pandemic of people saying,
+
+I've watched all your
+lectures and they've
+
+kept me going and
+intellectually stimulated,
+
+to hearing how other faculty at
+the schools around the country
+
+and around the world have said,
+hey, I took your lectures,
+
+and we added these
+other new labs.
+
+Bring them back to MIT.
+
+This, the whole
+idea of open sharing
+
+is infectious in the
+best possible way.
+
+And once you get hooked,
+it's hard to stop,
+
+which also gets at
+one of the questions I
+
+saw on the chat, which is,
+how do you convince faculty
+
+to participate?
+
+I think by participating.
+
+It's the single
+biggest factor to me,
+
+as somebody who has both
+benefited from and contributed
+
+to OCW, it's altruism.
+
+It's the desire for your, 
+what you learned
+
+and what you can teach to
+impact humanity for the better.
+
+That's, to me, the whole
+reason I get up in the morning,
+
+and I think that's the case
+for most people in the world,
+
+they want to do good.
+
+They want to see
+themselves do good.
+
+And OpenCourseWare provides
+this enormous attractive force
+
+for everyone to see
+a part of themselves
+
+in this rapidly
+evolving and improving
+
+open educational space.
+
+Yeah.
+
+Yeah.
+
+Thanks.
+
+It's great to see that some
+of the questions coming in,
+
+I'd like to encourage
+people, again,
+
+to keep those questions coming.
+
+I think that question
+of, what would you
+
+say to folks who are a little
+unsure about participating
+
+in open sharing, they may
+have some hesitations.
+
+I'd like to open that up to
+the whole panel for a moment
+
+and invite other
+reflections on that.
+
+Mussie, Anjali--
+
+So, I would say that
+the act of sharing
+
+gets you to be
+reflective in a way
+
+that I think can serve your
+goals as an instructor,
+
+and a teacher.
+
+So that's one reason to share.
+
+And the other is, to Mike's
+point, it is pretty addictive.
+
+I keep coming up with new
+ideas of things to share.
+
+Like, little
+experiments I've tried.
+
+Let's put that up,
+let's share that.
+
+Or reflections I have.
+
+I love the educator
+version of courses
+
+that allows you,
+as the instructor,
+
+to have a kind of sidebar
+conversation with the audience,
+
+and talk through
+your experience,
+
+and your philosophy.
+
+I think that's a
+pretty cool feature.
+
+And OCW has not been
+afraid to do all kinds
+
+of different experiments.
+
+So I had students
+a few years ago
+
+who were from
+Spanish-speaking countries
+
+and Portuguese-speaking
+countries.
+
+We tried getting-- they recorded
+their experience in English,
+
+but also in their
+native languages.
+
+And that was pretty cool.
+
+We just gave that a shot.
+
+OCW was totally
+willing to do it.
+
+And we didn't actually have
+that capability hard-baked
+
+into the OCW
+platform at the time,
+
+but that didn't stop you guys
+from helping to figure it out.
+
+It's fun, figuring those
+things out together.
+
+Yeah.
+
+Mussie?
+
+Yeah.
+
+So I kind of want to
+answer this in two ways.
+
+The first is, to
+a certain extent,
+
+it's really about
+vulnerability, isn't it?
+
+You're putting all your
+content out as an institution.
+
+You're kind of saying,
+this is what I do.
+
+And you'll get feedback,
+whether you like it or not.
+
+But that vulnerability
+comes with a grain of,
+
+you can learn.
+
+You, as the
+institution, can learn
+
+how to do what you're
+supposed to be doing better.
+
+And the other part
+of it is, and I
+
+think for a lot of
+institutions, it's
+
+the fear of, well, the
+value that students
+
+pay for will be open for free.
+
+And for institutions,
+that fear that, I really
+
+want to pose the question
+of, is that your only value?
+
+Is the content your only value?
+
+And if it is, there's a
+world of content coming.
+
+Don't be Blockbuster when
+Netflix came up and not adapt.
+
+Find and create value,
+in education still,
+
+but find a way that's
+not just only content,
+
+and ride the wave,
+as opposed to--
+
+Yeah.
+
+Good.
+
+Great.
+
+So I think there are enormous
+opportunities for MIT,
+
+and as Mussie just
+mentioned, you know,
+
+what's really MIT's value?
+
+It's not a kid sitting
+down watching television.
+
+But I wanted to make
+a more general point,
+
+that when we openly share
+things, for anyone, not just
+
+MIT, we're enriching
+the fount that's
+
+the source of our creativity.
+
+When we started MIT, when
+we started OpenCourseWare,
+
+Chuck Vest wrote a
+nice little piece
+
+of about that where he said, he
+thought the image of students
+
+all over the world sitting and
+all looking at presentations
+
+by the top faculty in the
+world, that, for him, he said,
+
+was one of his
+recurring nightmares.
+
+That's not what
+OpenCourseWare is about.
+
+OpenCourseWare is enriching
+the basis by which we all
+
+do creativity, not just a couple
+of top classes, but everyone.
+
+I wanted to
+introduce a word that
+
+comes from Jonathan Zittrain
+at Harvard Law School called
+
+A Generative Platform.
+
+A generative platform
+is where there are many,
+
+many, many people openly
+collaborating and creating
+
+new things,
+including things that
+
+were not anticipated
+by the people who
+
+created the platform.
+
+So what I'm hoping,
+and OpenCourseWare
+
+is doing so well, is really
+being generative in that way.
+
+Because it's not that
+MIT and five other places
+
+can make a vision of
+education for all of humanity,
+
+it's that we can enable other
+people to build on our work.
+
+Yeah Yeah.
+
+I'd love to use that
+as a springboard
+
+into a reflection
+on what we'd like
+
+to see from the future of OCW.
+
+If you can project 20 years out,
+that's great, but I'll take 5.
+
+Where do you think we can go
+with this generative potential?
+
+Maybe start with Mussie?
+
+So, I've had the opportunity
+to be a user, and come to MIT
+
+and kind of see that
+increase in value.
+
+And, again, I would
+love if OCW drove that.
+
+So what I mean by
+that is collaboration.
+
+A huge part of my MIT
+experience has been the fact
+
+that I can work on
+problems with people.
+
+I can see how they think,
+they can see how I think,
+
+and we end up thinking better.
+
+So seeing OCW become a
+platform for everyone
+
+in the world to kind
+of come together.
+
+For people that
+don't necessarily
+
+know each other to go on a
+path of education together,
+
+I think, would be a huge help.
+
+Especially because
+me, as a user,
+
+it was somewhat
+difficult doing it alone.
+
+It's easy to kind of
+fall off the wagon.
+
+Another vision of OCW I
+have is that we, again,
+
+lead this movement of open
+educational resources.
+
+And that goes back to my
+very first point of we
+
+put our name behind it, and
+we pull other institutions
+
+with us.
+
+We bring them in and we
+sell them on the idea
+
+that if we open this
+up, there is real value
+
+to be created for the whole.
+
+I like it.
+
+Yeah, and you sort of answered
+a question we had from Mustaffa
+
+about getting students
+to meet around the world,
+
+is there some way to
+use OCW in that spirit?
+
+Yeah, we see great
+potential in that.
+
+It's an area that we've
+experimented with,
+
+off and on, over the years.
+
+Continue to be
+working on, and yeah.
+
+I hope to see more take shape.
+
+Let's see, Anjali,
+thoughts for the future?
+
+So I have many
+conflicting thoughts.
+
+I'll just share a couple.
+
+I love the idea of
+meetups of some kind.
+
+I think that a
+recommendation engine
+
+of some kind, or a linkage
+engine of some kind
+
+would be really interesting.
+
+And maybe not just a very
+predictable, like, now that
+
+you've taken Linear Algebra I
+take Linear Algebra II,
+
+but something that kind
+of pushes us a little bit.
+
+And we know that
+people are looking
+
+at using expert
+systems and other methods
+
+to pull out content
+from learners
+
+to figure out what they
+need to learn next.
+
+I do like that idea.
+
+I also think we've
+seen a huge growth
+
+in open educational materials,
+and teaching management,
+
+I mean really, some
+of it is not great.
+
+So I think we also need to
+think about the quality piece.
+
+Do we just assume, because
+it comes out of MIT,
+
+it's all great?
+
+What's our method for
+figuring out and validating
+
+excellent content?
+
+If you teach a course at
+MIT, you know it's good,
+
+but there may be ways in which--
+
+maybe by stitching together
+more meta information,
+
+we could round out
+the picture more.
+
+So if you take a class
+on, I don't know,
+
+financial models for
+something, maybe you also
+
+learn about poverty,
+or something.
+
+Something that kind of
+rounds it out a little,
+
+so that we're getting
+well-rounded views.
+
+I think we've sparked a
+revolution in open education.
+
+I saw that a lot with medical
+information, for instance.
+
+I think there's a lot
+more work to be done.
+
+So I'm really excited
+for the next chapter.
+
+Yeah.
+
+Me too.
+
+Thank you.
+
+Mike, any reflections
+on the future?
+
+Sure.
+
+I'd sum it up with three
+words, which would be renewal,
+
+enrichment, and humanization.
+
+I'll start with renewal, which
+I think is the easiest one.
+
+We've created this
+amazing engine
+
+for getting content out there,
+and we need to keep it current.
+
+And that's not just
+going to involve
+
+getting the next piece that's
+up there every five years,
+
+but convincing new faculty
+to have new interpretations
+
+of the courses, so that
+there'll be multiple teaching
+
+styles for each
+one, and students
+
+can look through some of
+the lectures and ideas,
+
+and find the one
+that suits them best.
+
+I'd say enrichment,
+because there
+
+are things that OpenCourseWare
+is doing now that I
+
+think we need to do more of.
+
+For example, podcasts with
+some of the instructors
+
+on their educational philosophy.
+
+On how they design
+courses, how they
+
+get hands-on elements
+into what could
+
+be dry and boring courses.
+
+That also feeds into
+humanization of knowledge.
+
+To build on something
+Mussie was saying,
+
+if there's no downside
+to contributing to OCW,
+
+and the upsides are
+enormous besides the ones
+
+that we've talked about here.
+
+To me, it's the humanization of
+not just knowledge in general,
+
+but of these supposedly lofty
+MIT faculty in particular.
+
+Those of us here know that
+we all make mistakes, and say
+
+stupid things, and the power
+structure here is pretty flat,
+
+but I've come to
+learn that's not
+
+how we're viewed
+from the outside
+
+unless you already know us.
+
+And I think it's important
+to be on YouTube, making
+
+occasional mistakes,
+which I certainly
+
+did in my 22.01 Intro to
+Nuclear Physics lectures.
+
+I had a couple of goofs on
+the length of the control rods
+
+from Chernobyl, which
+you might imagine
+
+is a pretty popular
+topic to watch
+
+because of the TV
+series going on now,
+
+and that's not a downside.
+
+There's an upside to be able
+to crowdsource corrections,
+
+and project your own
+humanity in the fact
+
+that, yeah, we're at MIT
+but we make mistakes too,
+
+you can watch us do
+it for all eternity.
+
+It doesn't scare me.
+
+To me, it's a bonus.
+
+Great.
+
+Yeah.
+
+Love that spirit.
+
+Hal, there's a question
+in the chat that
+
+maybe sort of pertains to
+one aspect of projecting
+
+the future, how you
+had raised the three
+
+things at the beginning.
+
+Somebody has asked about
+the future of open research
+
+and how, maybe, that
+connects and supports
+
+the mission of OCW.
+
+If you care to respond
+to that, or anything
+
+else about the future.
+
+Yeah, well, the future
+is hard to predict.
+
+You talked about 20
+years, or 5 years.
+
+I would actually be happy,
+now, with about 6 months.
+
+Because what's happening now
+is, this is like 20 years ago,
+
+where there is this enormous
+sense of possibility
+
+coming from the internet.
+
+And OpenCourseWare latched into
+that, and when we look back,
+
+we're all delighted
+with how that worked out
+
+and we say that what we did
+then was counterintuitive,
+
+but it was right
+and kind of obvious.
+
+But the world is changing.
+
+This is like 20 years
+ago, but vastly different.
+
+When we thought
+about OpenCourseWare,
+
+we thought about
+new opportunities,
+
+we thought about changes, we
+thought about what happened
+
+but what we didn't
+think about is
+
+enormous change in
+the very structure
+
+of tertiary education.
+
+And that's what we're
+talking about now.
+
+You know, especially
+accelerated by COVID,
+
+but coming before that.
+
+So I talked--
+
+I mentioned a little bit about
+how the founders of Columbia
+
+Fathom came to us and
+in 2000, 2001, and said,
+
+you know, why don't you join
+us, and we were going down
+
+this path of openness.
+
+I'll tell you another story.
+
+In 2012, the founders
+of Coursera came to us
+
+and said, Stanford is
+about to create Coursera,
+
+and would MIT like to partner
+in making this tremendous thing
+
+about online courses?
+
+And we sort of said,
+well, you know,
+
+they're thinking about a closed,
+proprietary architecture,
+
+and not a thing that
+people can contribute to.
+
+And at MIT, we sort
+of said, well, no.
+
+OK.
+
+Last week, Coursera had its
+IPO, it went up 45% at IPO,
+
+and it's valued now
+at about $60 billion.
+
+That's something to think about.
+
+Are we still thinking
+about openness?
+
+Are we still thinking
+about the importance
+
+of generative platforms to
+the extent that we were then?
+
+This is a real challenge.
+
+And it's really something
+that we need to think about.
+
+And it is not obvious.
+
+So while we're celebrating
+having made, certainly,
+
+the right choice 20 years ago,
+what does that mean for today?
+
+I think we all need to think
+about that very seriously.
+
+Thank you.
+
+Yeah, looking
+forward to continuing
+
+to work with you
+and everybody else
+
+around our community
+on that one.
+
+Yeah, so thank you all for
+a really great discussion.
+
+And I appreciate all the
+points that you've raised.
+
+Lots more to keep talking about.
+
+In the last few
+minutes, we're going
+
+to project forward into
+our future in a more
+
+kind of concrete way, and
+talk about the next generation
+
+OCW.
+
+And I'd like to welcome
+my colleague Krishna back
+
+into the call to start sharing
+some reflections and more
+
+information about the
+next generation of OCW.
+
+Thank you very much, Curt.
+
+And thank you Hal,
+Mussie, Anjali, and Mike
+
+for that great discussion.
+
+I, actually, I can't resist.
+
+I'll say to Hal the singular
+moment in 2001 that you
+
+described is real and
+critical, but I also
+
+think that in another way, what
+you and others did back then
+
+flowed from 100 years
+of history at MIT,
+
+and a sense of our
+values and principles.
+
+And if you go back to
+the very founding of MIT,
+
+President William Barton
+Rogers, who founded MIT,
+
+thought he had a great way to
+teach that was new at the time.
+
+This is in the 1870s.
+
+And he rode by train up
+and down the East Coast,
+
+spreading his way of
+teaching to places like Yale,
+
+and Princeton, and that place,
+other place in Cambridge,
+
+Massachusetts.
+
+So this goes back to
+the very beginning.
+
+Of course, the technological
+means of sharing
+
+was completely different
+in 2001 than in 1870.
+
+Curt, can you share your slide?
+
+I don't know if that has
+already happened or not.
+
+So as we look to
+the coming 20 years,
+
+as we celebrate
+OCW's 20th birthday
+
+and look ahead to
+its next 20 years,
+
+we are very excited
+to be developing
+
+a next generation
+platform and program
+
+that Curt and I are
+going to tell you
+
+a little bit about now.
+
+And I want to emphasize,
+platform and program.
+
+This is as much about
+program as platform,
+
+although it's about both.
+
+Many of the things that I'll
+say in the next few minutes
+
+actually come directly from
+what was said by the panelists.
+
+One of our central
+goals in thinking
+
+about the next generation
+OCW platform and program,
+
+is to make sure
+that we can offer
+
+the world a vibrant and
+up-to-date sharing of the MIT
+
+curriculum, as it evolves.
+
+This is something
+that Mike spoke about.
+
+Its content will
+evolve as we at MIT
+
+address grand
+challenges of today,
+
+like social justice,
+and sustainability,
+
+and the future of computing.
+
+The means by which
+we teach also evolve.
+
+It's our hope that going
+into the future, as now, OCW
+
+will be the place that MIT
+faculty can share openly
+
+the way that they
+teach, how they teach,
+
+as well as what they teach.
+
+And that requires a new
+platform in many, many senses.
+
+On the back end, it
+requires a platform
+
+that will allow us to
+update, and refresh, and keep
+
+vibrant hundreds and hundreds
+of courses every year,
+
+which is something that
+we're not able to do today,
+
+but we will be able
+to do very soon.
+
+I'll also, for riff a minute
+on Mussie, what Mussie said.
+
+What you come to MIT for,
+which goes beyond the content
+
+that we can share through
+OCW and many other means,
+
+is engagement.
+
+And what we want
+to do with OCW is
+
+to give learners and
+educators elsewhere,
+
+in their communities,
+the ability
+
+to create their own magic, just
+as MIT students and faculty
+
+create with the engagement
+that they experience on campus.
+
+Engagement in so many
+different senses.
+
+We hope that we empower that,
+but the educators elsewhere
+
+who use these
+materials to create
+
+the engagement
+for their students
+
+are the key, actually, to that.
+
+Returning to the
+platform side of it,
+
+the new platform which all of
+you, Curt, is very exciting--
+
+Curt is going to tell
+you in a few minutes
+
+how you can get a sneak
+peek, an early look,
+
+at our new platform, which
+will offer a seamless discovery
+
+and learning experiences,
+new modes of discovery,
+
+new modes of search, learning
+experiences on mobile devices.
+
+Early look at this starting
+today for all of you
+
+who are here.
+
+We anticipate launching this
+new platform later this calendar
+
+year, and we look forward
+to getting feedback from all
+
+of you, starting today in fact.
+
+Another aspect of
+the new platform
+
+will be integrations with the
+learning management systems
+
+that educational
+institutions use,
+
+so that open content
+from OCW can better
+
+flow into the
+educational ecosystems
+
+of other institutions.
+
+Again, platform and program.
+
+And I already spoke
+at the beginning
+
+about the importance of
+collaborations across the OER
+
+ecosystem if we want to
+build from access to equity.
+
+OCW has done a magnificent
+job now for of offering access
+
+to the curriculum from MIT,
+to the teaching from MIT,
+
+to the learning from MIT.
+
+I'll also mention that we
+already have a podcast,
+
+it was mentioned by Mike.
+
+Chalk Radio is a podcast where
+you can listen to MIT faculty
+
+as they tell you how
+to use these materials
+
+in your teaching, because they
+will describe how they use it
+
+in theirs.
+
+We have instructor insights,
+but to really realize
+
+a vision of equity, we
+need learning pathways
+
+that are different
+for different people,
+
+because different people come
+from different starting points.
+
+And that means we
+need the entire OER
+
+ecosystem, a web of
+institutions and entities
+
+across the ecosystem,
+collaborating
+
+and working together to
+realize this grand vision.
+
+That's a brief intro to this
+vision behind NextGen OCW.
+
+Curt now it's going to
+give you a sneak peek.
+
+Thanks Krishna.
+
+And I'd like to
+invite people to drop
+
+your thoughts in the
+chat of whatever you're
+
+using to watch this event.
+
+What would you wish for
+from the future of OCW?
+
+We'd love to hear from you.
+
+Now, it is my great
+pleasure to introduce to you
+
+the current working,
+very early draft
+
+version of the next
+generation OCW website.
+
+And as Krishna said, we're going
+to invite people to join us
+
+in this process of working
+with it, experimenting with it,
+
+and giving us your feedback.
+
+So this is the site, and
+links should be going out
+
+in the chats of your streams
+for how you can sign up to be
+
+a beta tester on this site.
+
+We are those 2,500
+courses to the site,
+
+and they're all up
+here in various forms.
+
+And we're keeping up with
+the latest hot topics
+
+out in the world.
+
+Let's take blockchain
+for instance.
+
+Our blockchain course, taught
+by Professor Gary Gensler
+
+is on here.
+
+And you can explore it not
+only on the current regular
+
+ocw.mit.edu website,
+but here on NextGen,
+
+and explore, for instance, the
+very popular video lectures.
+
+They are all here for you to
+watch and keep checking out.
+
+There's, again, all the courses
+from across the collection
+
+that you'll find here.
+
+Courses, for instance, World
+Water Day was last week,
+
+you want to learn about
+the intersection of water
+
+and climate change.
+
+We've got great courses on
+topics like this as well.
+
+What I'm showing you here is
+kind of the laptop, or computer
+
+version.
+
+We're really excited that the
+next generation platform will
+
+be able to work well on mobile,
+and so I just shrink down
+
+the size of the window here, you
+can see how the template adapts
+
+and you can continue
+to work effectively
+
+on your mobile phone,
+because we know,
+
+for many people around
+the world, their phone,
+
+their smartphone is the device.
+
+And so giving people a really
+good experience on the phone
+
+is an essential part of
+what we're setting up
+
+to do with Next Generation.
+
+So, again, you have
+an opportunity.
+
+We invite you to join
+us in testing out
+
+this next generation platform
+as it evolves through the summer
+
+and into the fall.
+
+And we're really excited
+about what the future brings.
+
+Many of the things
+that have been talked
+
+about in the panel, and
+people have been asking about,
+
+we are actively working on.
+
+Anjali mentioned better
+ways to discover content.
+
+We're exploring with bringing
+the latest techniques
+
+in machine learning, and so on,
+to make our search interface
+
+work better.
+
+Better ways for people to find
+and collaborate with each other
+
+when they are users of OCW.
+
+Language translations.
+
+Continuing to run the podcast,
+the Chalk Radio podcast.
+
+All of these things
+will be continuing.
+
+So do, please do reach out to us--
+
+If I can just jump in and just
+say to everyone, first of all,
+
+thank you in advance
+for all your feedback.
+
+But second of all, I
+hope you're starting
+
+to see how we can respond
+to some of the challenges
+
+from the questions
+from the audience.
+
+In fact, one of you asked,
+how do we motivate faculty
+
+to participate?
+
+I actually think, I think
+what we, inside of MIT,
+
+will have the opposite problem.
+
+As we launch this NextGen
+platform and program,
+
+we're going to have to
+handle a flood of faculty who
+
+want to participate.
+
+And not only the
+flood of faculty
+
+want to participate, but
+actually the students of MIT.
+
+Mussie is a tremendous
+example, but we
+
+are hearing from other
+students how they, too,
+
+want to participate
+in contributing
+
+to OCW, and in prompting
+faculty to contribute.
+
+So we look forward
+to taking advantage
+
+of this next platform, this
+NextGen platform and program,
+
+to handle a flood of
+interest, and this, I think,
+
+really does flow from
+what everyone-- what's
+
+not to like about
+sharing on OCW,
+
+given what you've heard
+from Anjali and Mike?
+
+And Hal? We have to be
+ready for a 1,000 faculty who
+
+want to do so, and we look
+forward to this challenge.
+
+Well put.
+
+Yeah.
+
+The future is very
+bright, thank you.
+
+Thank you, Krishna.
+
+So, we're so glad that
+you joined us today
+
+to celebrate this
+auspicious 20th anniversary,
+
+and look forward with
+us into the future.
+
+We really value your
+continued support,
+
+whether that's sharing
+OCW with your networks,
+
+using it in whatever
+learning capacity
+
+that you would like to.
+
+Please do join us,
+if you're willing,
+
+as a beta tester for the
+emergent next generation OCW
+
+site, and in any other
+ways that you can see.
+
+We love to hear from you.
+
+Please sign up at our
+monthly newsletter
+
+to stay on top of it.
+
+Follow us on all the
+social media channels.
+
+And we very much look forward
+to continuing to support you
+
+in your learning journeys.
+
+Yeah.
+
+Thank you so much.
\ No newline at end of file
diff --git a/8kM9quINTHI.txt b/8kM9quINTHI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ecb715fee934a643c6ab9f1d95735fde422465a6
--- /dev/null
+++ b/8kM9quINTHI.txt
@@ -0,0 +1,5739 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're now starting to get into
+
+ align:start position:0%
+okay so we're now starting to get into
+ 
+
+ align:start position:0%
+okay so we're now starting to get into
+really familiar territory which is the
+
+ align:start position:0%
+really familiar territory which is the
+ 
+
+ align:start position:0%
+really familiar territory which is the
+hydrogen atom and it's a short step from
+
+ align:start position:0%
+hydrogen atom and it's a short step from
+ 
+
+ align:start position:0%
+hydrogen atom and it's a short step from
+hydrogen atom to molecules and we're
+
+ align:start position:0%
+hydrogen atom to molecules and we're
+ 
+
+ align:start position:0%
+hydrogen atom to molecules and we're
+chemists we make molecules and so but
+
+ align:start position:0%
+chemists we make molecules and so but
+ 
+
+ align:start position:0%
+chemists we make molecules and so but
+one question would that would be a
+
+ align:start position:0%
+one question would that would be a
+ 
+
+ align:start position:0%
+one question would that would be a
+legitimate question to ask is what is
+
+ align:start position:0%
+legitimate question to ask is what is
+ 
+
+ align:start position:0%
+legitimate question to ask is what is
+the hydrogen atom have to do with
+
+ align:start position:0%
+the hydrogen atom have to do with
+ 
+
+ align:start position:0%
+the hydrogen atom have to do with
+molecules because it's an atom and it's
+
+ align:start position:0%
+molecules because it's an atom and it's
+ 
+
+ align:start position:0%
+molecules because it's an atom and it's
+a simplest atom and and what I hope to
+
+ align:start position:0%
+a simplest atom and and what I hope to
+ 
+
+ align:start position:0%
+a simplest atom and and what I hope to
+show is that what we learn from looking
+
+ align:start position:0%
+show is that what we learn from looking
+ 
+
+ align:start position:0%
+show is that what we learn from looking
+at the hydrogen atom has all sorts of
+
+ align:start position:0%
+at the hydrogen atom has all sorts of
+ 
+
+ align:start position:0%
+at the hydrogen atom has all sorts of
+good non textbook stuff that prepares
+
+ align:start position:0%
+good non textbook stuff that prepares
+ 
+
+ align:start position:0%
+good non textbook stuff that prepares
+you for understanding stuff in molecules
+
+ align:start position:0%
+you for understanding stuff in molecules
+ 
+
+ align:start position:0%
+you for understanding stuff in molecules
+and I am going to stress that because
+
+ align:start position:0%
+and I am going to stress that because
+ 
+
+ align:start position:0%
+and I am going to stress that because
+you're not going to see any macquarie
+
+ align:start position:0%
+you're not going to see any macquarie
+ 
+
+ align:start position:0%
+you're not going to see any macquarie
+and you've probably never seen it
+
+ align:start position:0%
+and you've probably never seen it
+ 
+
+ align:start position:0%
+and you've probably never seen it
+elsewhere except in freshman chemistry
+
+ align:start position:0%
+elsewhere except in freshman chemistry
+ 
+
+ align:start position:0%
+elsewhere except in freshman chemistry
+when they expect that you understand the
+
+ align:start position:0%
+when they expect that you understand the
+ 
+
+ align:start position:0%
+when they expect that you understand the
+periodic table based on some simple
+
+ align:start position:0%
+periodic table based on some simple
+ 
+
+ align:start position:0%
+periodic table based on some simple
+concepts and they come from the hydrogen
+
+ align:start position:0%
+concepts and they come from the hydrogen
+ 
+
+ align:start position:0%
+concepts and they come from the hydrogen
+atom and and so I've learned it attempt
+
+ align:start position:0%
+atom and and so I've learned it attempt
+ 
+
+ align:start position:0%
+atom and and so I've learned it attempt
+to make those connections my last
+
+ align:start position:0%
+to make those connections my last
+ 
+
+ align:start position:0%
+to make those connections my last
+lecture was I told you something we're
+
+ align:start position:0%
+lecture was I told you something we're
+ 
+
+ align:start position:0%
+lecture was I told you something we're
+not you're not going to be tested on but
+
+ align:start position:0%
+not you're not going to be tested on but
+ 
+
+ align:start position:0%
+not you're not going to be tested on but
+it's about spectroscopy that's how we
+
+ align:start position:0%
+it's about spectroscopy that's how we
+ 
+
+ align:start position:0%
+it's about spectroscopy that's how we
+learn almost everything we know about
+
+ align:start position:0%
+learn almost everything we know about
+ 
+
+ align:start position:0%
+learn almost everything we know about
+small molecules and a lot of stuff about
+
+ align:start position:0%
+small molecules and a lot of stuff about
+ 
+
+ align:start position:0%
+small molecules and a lot of stuff about
+big molecules - the crucial
+
+ align:start position:0%
+big molecules - the crucial
+ 
+
+ align:start position:0%
+big molecules - the crucial
+approximations in that were that the
+
+ align:start position:0%
+approximations in that were that the
+ 
+
+ align:start position:0%
+approximations in that were that the
+dipole approximation where the radiation
+
+ align:start position:0%
+dipole approximation where the radiation
+ 
+
+ align:start position:0%
+dipole approximation where the radiation
+field is such that the molecule fields a
+
+ align:start position:0%
+field is such that the molecule fields a
+ 
+
+ align:start position:0%
+field is such that the molecule fields a
+uniform but oscillating electromagnetic
+
+ align:start position:0%
+uniform but oscillating electromagnetic
+ 
+
+ align:start position:0%
+uniform but oscillating electromagnetic
+field in developing the theory that I
+
+ align:start position:0%
+field in developing the theory that I
+ 
+
+ align:start position:0%
+field in developing the theory that I
+presented we assumed that only one of
+
+ align:start position:0%
+presented we assumed that only one of
+ 
+
+ align:start position:0%
+presented we assumed that only one of
+the initial eigenstates is populated at
+
+ align:start position:0%
+the initial eigenstates is populated at
+ 
+
+ align:start position:0%
+the initial eigenstates is populated at
+T equals zero and only one final
+
+ align:start position:0%
+T equals zero and only one final
+ 
+
+ align:start position:0%
+T equals zero and only one final
+eigenstate gets tickled and so that it
+
+ align:start position:0%
+eigenstate gets tickled and so that it
+ 
+
+ align:start position:0%
+eigenstate gets tickled and so that it
+gets populated
+
+ align:start position:0%
+gets populated
+ 
+
+ align:start position:0%
+gets populated
+and so that even though there's an
+
+ align:start position:0%
+and so that even though there's an
+ 
+
+ align:start position:0%
+and so that even though there's an
+infinity of states the the theory's
+
+ align:start position:0%
+infinity of states the the theory's
+ 
+
+ align:start position:0%
+infinity of states the the theory's
+specifies we start with one definite one
+
+ align:start position:0%
+specifies we start with one definite one
+ 
+
+ align:start position:0%
+specifies we start with one definite one
+and only one final state gets selected
+
+ align:start position:0%
+and only one final state gets selected
+ 
+
+ align:start position:0%
+and only one final state gets selected
+because of resonance and this is what we
+
+ align:start position:0%
+because of resonance and this is what we
+ 
+
+ align:start position:0%
+because of resonance and this is what we
+do all the time we we have an infinite
+
+ align:start position:0%
+do all the time we we have an infinite
+ 
+
+ align:start position:0%
+do all the time we we have an infinite
+dimension problem and we we discover
+
+ align:start position:0%
+dimension problem and we we discover
+ 
+
+ align:start position:0%
+dimension problem and we we discover
+that we only really need to worry about
+
+ align:start position:0%
+that we only really need to worry about
+ 
+
+ align:start position:0%
+that we only really need to worry about
+a very small number of states and and
+
+ align:start position:0%
+a very small number of states and and
+ 
+
+ align:start position:0%
+a very small number of states and and
+then we deal with that there are a
+
+ align:start position:0%
+then we deal with that there are a
+ 
+
+ align:start position:0%
+then we deal with that there are a
+couple of other assumptions that were
+
+ align:start position:0%
+couple of other assumptions that were
+ 
+
+ align:start position:0%
+couple of other assumptions that were
+essential for this first step into a
+
+ align:start position:0%
+essential for this first step into a
+ 
+
+ align:start position:0%
+essential for this first step into a
+Hamiltonian and that is the field is
+
+ align:start position:0%
+Hamiltonian and that is the field is
+ 
+
+ align:start position:0%
+Hamiltonian and that is the field is
+weak and so you get linear response that
+
+ align:start position:0%
+weak and so you get linear response that
+ 
+
+ align:start position:0%
+weak and so you get linear response that
+means that the increase in the mixing
+
+ align:start position:0%
+means that the increase in the mixing
+ 
+
+ align:start position:0%
+means that the increase in the mixing
+coefficient for the final state is
+
+ align:start position:0%
+coefficient for the final state is
+ 
+
+ align:start position:0%
+coefficient for the final state is
+proportional to the coupling matrix
+
+ align:start position:0%
+proportional to the coupling matrix
+ 
+
+ align:start position:0%
+proportional to the coupling matrix
+element times time now mixing
+
+ align:start position:0%
+element times time now mixing
+ 
+
+ align:start position:0%
+element times time now mixing
+coefficients can't get larger than one
+
+ align:start position:0%
+coefficients can't get larger than one
+ 
+
+ align:start position:0%
+coefficients can't get larger than one
+and so clearly we can't use a simple
+
+ align:start position:0%
+and so clearly we can't use a simple
+ 
+
+ align:start position:0%
+and so clearly we can't use a simple
+theory without saying ok we don't care
+
+ align:start position:0%
+theory without saying ok we don't care
+ 
+
+ align:start position:0%
+theory without saying ok we don't care
+about the mixing coefficients we care
+
+ align:start position:0%
+about the mixing coefficients we care
+ 
+
+ align:start position:0%
+about the mixing coefficients we care
+about the rate of increase and so by
+
+ align:start position:0%
+about the rate of increase and so by
+ 
+
+ align:start position:0%
+about the rate of increase and so by
+going from amplitudes to rates we are
+
+ align:start position:0%
+going from amplitudes to rates we are
+ 
+
+ align:start position:0%
+going from amplitudes to rates we are
+able to have a theory that's generally
+
+ align:start position:0%
+able to have a theory that's generally
+ 
+
+ align:start position:0%
+able to have a theory that's generally
+applicable now what I did was to talk
+
+ align:start position:0%
+applicable now what I did was to talk
+ 
+
+ align:start position:0%
+applicable now what I did was to talk
+about a CW radiation field continuous
+
+ align:start position:0%
+about a CW radiation field continuous
+ 
+
+ align:start position:0%
+about a CW radiation field continuous
+many experiments use pulsed fields many
+
+ align:start position:0%
+many experiments use pulsed fields many
+ 
+
+ align:start position:0%
+many experiments use pulsed fields many
+experiments use an extremely strong
+
+ align:start position:0%
+experiments use an extremely strong
+ 
+
+ align:start position:0%
+experiments use an extremely strong
+pulsed field that I hope to revisit
+
+ align:start position:0%
+pulsed field that I hope to revisit
+ 
+
+ align:start position:0%
+pulsed field that I hope to revisit
+later in the course but the CW problem
+
+ align:start position:0%
+later in the course but the CW problem
+ 
+
+ align:start position:0%
+later in the course but the CW problem
+is the best way to begin ok so now let's
+
+ align:start position:0%
+is the best way to begin ok so now let's
+ 
+
+ align:start position:0%
+is the best way to begin ok so now let's
+talk about that regime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we did the rigid rotor and that led to
+
+ align:start position:0%
+we did the rigid rotor and that led to
+ 
+
+ align:start position:0%
+we did the rigid rotor and that led to
+some angular momenta well it's just a
+
+ align:start position:0%
+some angular momenta well it's just a
+ 
+
+ align:start position:0%
+some angular momenta well it's just a
+picture so we have this rigid rotor and
+
+ align:start position:0%
+picture so we have this rigid rotor and
+ 
+
+ align:start position:0%
+picture so we have this rigid rotor and
+it's rotating about the center mass and
+
+ align:start position:0%
+it's rotating about the center mass and
+ 
+
+ align:start position:0%
+it's rotating about the center mass and
+the Schrodinger equation tells us the
+
+ align:start position:0%
+the Schrodinger equation tells us the
+ 
+
+ align:start position:0%
+the Schrodinger equation tells us the
+probability amplitudes of the rotor axis
+
+ align:start position:0%
+probability amplitudes of the rotor axis
+ 
+
+ align:start position:0%
+probability amplitudes of the rotor axis
+relative to the laboratory frame and we
+
+ align:start position:0%
+relative to the laboratory frame and we
+ 
+
+ align:start position:0%
+relative to the laboratory frame and we
+got angular momenta which we can we can
+
+ align:start position:0%
+got angular momenta which we can we can
+ 
+
+ align:start position:0%
+got angular momenta which we can we can
+denote by little L Big L J and many
+
+ align:start position:0%
+denote by little L Big L J and many
+ 
+
+ align:start position:0%
+denote by little L Big L J and many
+other things and this is important
+
+ align:start position:0%
+other things and this is important
+ 
+
+ align:start position:0%
+other things and this is important
+because if it's an angular momentum you
+
+ align:start position:0%
+because if it's an angular momentum you
+ 
+
+ align:start position:0%
+because if it's an angular momentum you
+know it you know everything about it and
+
+ align:start position:0%
+know it you know everything about it and
+ 
+
+ align:start position:0%
+know it you know everything about it and
+you don't know yet that if you have two
+
+ align:start position:0%
+you don't know yet that if you have two
+ 
+
+ align:start position:0%
+you don't know yet that if you have two
+angular momenta you could know
+
+ align:start position:0%
+angular momenta you could know
+ 
+
+ align:start position:0%
+angular momenta you could know
+everything about the interactions
+
+ align:start position:0%
+everything about the interactions
+ 
+
+ align:start position:0%
+everything about the interactions
+between them that's called the Vigna
+
+ align:start position:0%
+between them that's called the Vigna
+ 
+
+ align:start position:0%
+between them that's called the Vigna
+record theorem that's not in this course
+
+ align:start position:0%
+record theorem that's not in this course
+ 
+
+ align:start position:0%
+record theorem that's not in this course
+but the important thing is if you got
+
+ align:start position:0%
+but the important thing is if you got
+ 
+
+ align:start position:0%
+but the important thing is if you got
+angular momenta you're on solid ground
+
+ align:start position:0%
+angular momenta you're on solid ground
+ 
+
+ align:start position:0%
+angular momenta you're on solid ground
+and you can do stuff that doesn't ever
+
+ align:start position:0%
+and you can do stuff that doesn't ever
+ 
+
+ align:start position:0%
+and you can do stuff that doesn't ever
+need to be repeated and so you know one
+
+ align:start position:0%
+need to be repeated and so you know one
+ 
+
+ align:start position:0%
+need to be repeated and so you know one
+of the things that we learned about the
+
+ align:start position:0%
+of the things that we learned about the
+ 
+
+ align:start position:0%
+of the things that we learned about the
+angular momenta was that we have now I'm
+
+ align:start position:0%
+angular momenta was that we have now I'm
+ 
+
+ align:start position:0%
+angular momenta was that we have now I'm
+going to switch even though it's it's
+
+ align:start position:0%
+going to switch even though it's it's
+ 
+
+ align:start position:0%
+going to switch even though it's it's
+going to be L as the angular momentum
+
+ align:start position:0%
+going to be L as the angular momentum
+ 
+
+ align:start position:0%
+going to be L as the angular momentum
+mostly in the hydrogen atom I'm going to
+
+ align:start position:0%
+mostly in the hydrogen atom I'm going to
+ 
+
+ align:start position:0%
+mostly in the hydrogen atom I'm going to
+straight switch to J which is my
+
+ align:start position:0%
+straight switch to J which is my
+ 
+
+ align:start position:0%
+straight switch to J which is my
+favorite notation so J squared operating
+
+ align:start position:0%
+favorite notation so J squared operating
+ 
+
+ align:start position:0%
+favorite notation so J squared operating
+on a state now I can denote it like this
+
+ align:start position:0%
+on a state now I can denote it like this
+ 
+
+ align:start position:0%
+on a state now I can denote it like this
+or I can let a denote it like this it's
+
+ align:start position:0%
+or I can let a denote it like this it's
+ 
+
+ align:start position:0%
+or I can let a denote it like this it's
+the same general idea these are not
+
+ align:start position:0%
+the same general idea these are not
+ 
+
+ align:start position:0%
+the same general idea these are not
+quite equivalent things but we'll and
+
+ align:start position:0%
+quite equivalent things but we'll and
+ 
+
+ align:start position:0%
+quite equivalent things but we'll and
+and you get H bar squared J plus 1 J m
+
+ align:start position:0%
+and you get H bar squared J plus 1 J m
+ 
+
+ align:start position:0%
+and you get H bar squared J plus 1 J m
+and we have JZ operating on J M you get
+
+ align:start position:0%
+and we have JZ operating on J M you get
+ 
+
+ align:start position:0%
+and we have JZ operating on J M you get
+H bar m JM and we can have J plus minus
+
+ align:start position:0%
+H bar m JM and we can have J plus minus
+ 
+
+ align:start position:0%
+H bar m JM and we can have J plus minus
+operating on J M and that's H bar and
+
+ align:start position:0%
+operating on J M and that's H bar and
+ 
+
+ align:start position:0%
+operating on J M and that's H bar and
+it's just more complicated looking thing
+
+ align:start position:0%
+it's just more complicated looking thing
+ 
+
+ align:start position:0%
+it's just more complicated looking thing
+j j plus 1 is M and plus or minus 1 so
+
+ align:start position:0%
+j j plus 1 is M and plus or minus 1 so
+ 
+
+ align:start position:0%
+j j plus 1 is M and plus or minus 1 so
+that's the only bit you have to remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you might say well is it plus or
+
+ align:start position:0%
+and you might say well is it plus or
+ 
+
+ align:start position:0%
+and you might say well is it plus or
+minus 1 or minus or plus 1 and so if you
+
+ align:start position:0%
+minus 1 or minus or plus 1 and so if you
+ 
+
+ align:start position:0%
+minus 1 or minus or plus 1 and so if you
+choose M is equal to J then you know
+
+ align:start position:0%
+choose M is equal to J then you know
+ 
+
+ align:start position:0%
+choose M is equal to J then you know
+that if if you you have m is equal to J
+
+ align:start position:0%
+that if if you you have m is equal to J
+ 
+
+ align:start position:0%
+that if if you you have m is equal to J
+this is going to be 0 if we're doing
+
+ align:start position:0%
+this is going to be 0 if we're doing
+ 
+
+ align:start position:0%
+this is going to be 0 if we're doing
+raising operator and so there's nothing
+
+ align:start position:0%
+raising operator and so there's nothing
+ 
+
+ align:start position:0%
+raising operator and so there's nothing
+to remember if you are willing to go to
+
+ align:start position:0%
+to remember if you are willing to go to
+ 
+
+ align:start position:0%
+to remember if you are willing to go to
+an extreme situation and decide whether
+
+ align:start position:0%
+an extreme situation and decide whether
+ 
+
+ align:start position:0%
+an extreme situation and decide whether
+it's plus minus or minus or plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now the rigid rotor is a universal
+
+ align:start position:0%
+okay now the rigid rotor is a universal
+ 
+
+ align:start position:0%
+okay now the rigid rotor is a universal
+problem which is solved it deals with
+
+ align:start position:0%
+problem which is solved it deals with
+ 
+
+ align:start position:0%
+problem which is solved it deals with
+all central force problems everything
+
+ align:start position:0%
+all central force problems everything
+ 
+
+ align:start position:0%
+all central force problems everything
+that's round in the original donor is a
+
+ align:start position:0%
+that's round in the original donor is a
+ 
+
+ align:start position:0%
+that's round in the original donor is a
+fantastic starting point so one electron
+
+ align:start position:0%
+fantastic starting point so one electron
+ 
+
+ align:start position:0%
+fantastic starting point so one electron
+atoms for sure many electron atoms maybe
+
+ align:start position:0%
+atoms for sure many electron atoms maybe
+ 
+
+ align:start position:0%
+atoms for sure many electron atoms maybe
+will see and but anything that's round
+
+ align:start position:0%
+will see and but anything that's round
+ 
+
+ align:start position:0%
+will see and but anything that's round
+the rigid rotor is a good zero point for
+
+ align:start position:0%
+the rigid rotor is a good zero point for
+ 
+
+ align:start position:0%
+the rigid rotor is a good zero point for
+dealing with the angular part of the
+
+ align:start position:0%
+dealing with the angular part of the
+ 
+
+ align:start position:0%
+dealing with the angular part of the
+problem so for the hydrogen atom we have
+
+ align:start position:0%
+problem so for the hydrogen atom we have
+ 
+
+ align:start position:0%
+problem so for the hydrogen atom we have
+a potential it looks like this and so
+
+ align:start position:0%
+a potential it looks like this and so
+ 
+
+ align:start position:0%
+a potential it looks like this and so
+the radial potential is new if for the
+
+ align:start position:0%
+the radial potential is new if for the
+ 
+
+ align:start position:0%
+the radial potential is new if for the
+for the rigid rotor the radial potential
+
+ align:start position:0%
+for the rigid rotor the radial potential
+ 
+
+ align:start position:0%
+for the rigid rotor the radial potential
+was it's it's just 0 for the R is equal
+
+ align:start position:0%
+was it's it's just 0 for the R is equal
+ 
+
+ align:start position:0%
+was it's it's just 0 for the R is equal
+to R 0 and not 0 then the potential is
+
+ align:start position:0%
+to R 0 and not 0 then the potential is
+ 
+
+ align:start position:0%
+to R 0 and not 0 then the potential is
+infinite now here we have potential
+
+ align:start position:0%
+infinite now here we have potential
+ 
+
+ align:start position:0%
+infinite now here we have potential
+which doesn't go to infinity here and it
+
+ align:start position:0%
+which doesn't go to infinity here and it
+ 
+
+ align:start position:0%
+which doesn't go to infinity here and it
+does something strange
+
+ align:start position:0%
+does something strange
+ 
+
+ align:start position:0%
+does something strange
+because you can't get to negative R in
+
+ align:start position:0%
+because you can't get to negative R in
+ 
+
+ align:start position:0%
+because you can't get to negative R in
+spherical polar coordinates so this is
+
+ align:start position:0%
+spherical polar coordinates so this is
+ 
+
+ align:start position:0%
+spherical polar coordinates so this is
+is it a boundary condition or is it just
+
+ align:start position:0%
+is it a boundary condition or is it just
+ 
+
+ align:start position:0%
+is it a boundary condition or is it just
+an accident of the way we use
+
+ align:start position:0%
+an accident of the way we use
+ 
+
+ align:start position:0%
+an accident of the way we use
+coordinates okay so we're going to talk
+
+ align:start position:0%
+coordinates okay so we're going to talk
+ 
+
+ align:start position:0%
+coordinates okay so we're going to talk
+we're going to apply what we know about
+
+ align:start position:0%
+we're going to apply what we know about
+ 
+
+ align:start position:0%
+we're going to apply what we know about
+angular momenta to the hydrogen atom so
+
+ align:start position:0%
+angular momenta to the hydrogen atom so
+ 
+
+ align:start position:0%
+angular momenta to the hydrogen atom so
+our potential the hydrogen atom is going
+
+ align:start position:0%
+our potential the hydrogen atom is going
+ 
+
+ align:start position:0%
+our potential the hydrogen atom is going
+to be expressed in terms of the distance
+
+ align:start position:0%
+to be expressed in terms of the distance
+ 
+
+ align:start position:0%
+to be expressed in terms of the distance
+of the electron from the nucleus and
+
+ align:start position:0%
+of the electron from the nucleus and
+ 
+
+ align:start position:0%
+of the electron from the nucleus and
+then the Theta Phi coordinates which you
+
+ align:start position:0%
+then the Theta Phi coordinates which you
+ 
+
+ align:start position:0%
+then the Theta Phi coordinates which you
+already know and the theta phi part is
+
+ align:start position:0%
+already know and the theta phi part is
+ 
+
+ align:start position:0%
+already know and the theta phi part is
+universal and the r part is unique is
+
+ align:start position:0%
+universal and the r part is unique is
+ 
+
+ align:start position:0%
+universal and the r part is unique is
+special to each problem that as
+
+ align:start position:0%
+special to each problem that as
+ 
+
+ align:start position:0%
+special to each problem that as
+spherical symmetry and there are
+
+ align:start position:0%
+spherical symmetry and there are
+ 
+
+ align:start position:0%
+spherical symmetry and there are
+different kinds of approximations you
+
+ align:start position:0%
+different kinds of approximations you
+ 
+
+ align:start position:0%
+different kinds of approximations you
+use to be able to deal with them the
+
+ align:start position:0%
+use to be able to deal with them the
+ 
+
+ align:start position:0%
+use to be able to deal with them the
+nice thing about it is it's
+
+ align:start position:0%
+nice thing about it is it's
+ 
+
+ align:start position:0%
+nice thing about it is it's
+one-dimensional and we're very good at
+
+ align:start position:0%
+one-dimensional and we're very good at
+ 
+
+ align:start position:0%
+one-dimensional and we're very good at
+thinking about one-dimensional problems
+
+ align:start position:0%
+thinking about one-dimensional problems
+ 
+
+ align:start position:0%
+thinking about one-dimensional problems
+and even if the problem isn't exactly
+
+ align:start position:0%
+and even if the problem isn't exactly
+ 
+
+ align:start position:0%
+and even if the problem isn't exactly
+one-dimensional it has some hidden stuff
+
+ align:start position:0%
+one-dimensional it has some hidden stuff
+ 
+
+ align:start position:0%
+one-dimensional it has some hidden stuff
+to it we can we can extend what we know
+
+ align:start position:0%
+to it we can we can extend what we know
+ 
+
+ align:start position:0%
+to it we can we can extend what we know
+from one-dimensional problems and get a
+
+ align:start position:0%
+from one-dimensional problems and get a
+ 
+
+ align:start position:0%
+from one-dimensional problems and get a
+great deal of insight and if you have a
+
+ align:start position:0%
+great deal of insight and if you have a
+ 
+
+ align:start position:0%
+great deal of insight and if you have a
+one-dimensional problem it's very easy
+
+ align:start position:0%
+one-dimensional problem it's very easy
+ 
+
+ align:start position:0%
+one-dimensional problem it's very easy
+to describe the potential in one
+
+ align:start position:0%
+to describe the potential in one
+ 
+
+ align:start position:0%
+to describe the potential in one
+dimension and the eigenfunctions in one
+
+ align:start position:0%
+dimension and the eigenfunctions in one
+ 
+
+ align:start position:0%
+dimension and the eigenfunctions in one
+dimension and so we can begin to really
+
+ align:start position:0%
+dimension and so we can begin to really
+ 
+
+ align:start position:0%
+dimension and so we can begin to really
+understand everything ok so we're going
+
+ align:start position:0%
+understand everything ok so we're going
+ 
+
+ align:start position:0%
+understand everything ok so we're going
+to have a wave function which is going
+
+ align:start position:0%
+to have a wave function which is going
+ 
+
+ align:start position:0%
+to have a wave function which is going
+to have quantum numbers and we're going
+
+ align:start position:0%
+to have quantum numbers and we're going
+ 
+
+ align:start position:0%
+to have quantum numbers and we're going
+to be able to write it as a product of
+
+ align:start position:0%
+to be able to write it as a product of
+ 
+
+ align:start position:0%
+to be able to write it as a product of
+two parts well this is the same thing we
+
+ align:start position:0%
+two parts well this is the same thing we
+ 
+
+ align:start position:0%
+two parts well this is the same thing we
+had before for the rigid rotor so we're
+
+ align:start position:0%
+had before for the rigid rotor so we're
+ 
+
+ align:start position:0%
+had before for the rigid rotor so we're
+going to be able to take this order
+
+ align:start position:0%
+going to be able to take this order
+ 
+
+ align:start position:0%
+going to be able to take this order
+equation and separate the wave function
+
+ align:start position:0%
+equation and separate the wave function
+ 
+
+ align:start position:0%
+equation and separate the wave function
+into two parts a radial part and an
+
+ align:start position:0%
+into two parts a radial part and an
+ 
+
+ align:start position:0%
+into two parts a radial part and an
+angular part
+
+ align:start position:0%
+angular part
+ 
+
+ align:start position:0%
+angular part
+and this is old and this is new because
+
+ align:start position:0%
+and this is old and this is new because
+ 
+
+ align:start position:0%
+and this is old and this is new because
+we've got this we can use all of that
+
+ align:start position:0%
+we've got this we can use all of that
+ 
+
+ align:start position:0%
+we've got this we can use all of that
+stuff without taking a breath except
+
+ align:start position:0%
+stuff without taking a breath except
+ 
+
+ align:start position:0%
+stuff without taking a breath except
+maybe getting the right number letter L
+
+ align:start position:0%
+maybe getting the right number letter L
+ 
+
+ align:start position:0%
+maybe getting the right number letter L
+J s whatever so that's that's so really
+
+ align:start position:0%
+J s whatever so that's that's so really
+ 
+
+ align:start position:0%
+J s whatever so that's that's so really
+the hydrogen atom it's just one thing
+
+ align:start position:0%
+the hydrogen atom it's just one thing
+ 
+
+ align:start position:0%
+the hydrogen atom it's just one thing
+with some curveballs thrown at you in in
+
+ align:start position:0%
+with some curveballs thrown at you in in
+ 
+
+ align:start position:0%
+with some curveballs thrown at you in in
+the latter stages okay one of the things
+
+ align:start position:0%
+the latter stages okay one of the things
+ 
+
+ align:start position:0%
+the latter stages okay one of the things
+you also want to be able to do because
+
+ align:start position:0%
+you also want to be able to do because
+ 
+
+ align:start position:0%
+you also want to be able to do because
+nodes are so important in determining
+
+ align:start position:0%
+nodes are so important in determining
+ 
+
+ align:start position:0%
+nodes are so important in determining
+both the names of the states and how
+
+ align:start position:0%
+both the names of the states and how
+ 
+
+ align:start position:0%
+both the names of the states and how
+they perform how they behave in various
+
+ align:start position:0%
+they perform how they behave in various
+ 
+
+ align:start position:0%
+they perform how they behave in various
+situations including external fields in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excitation by electromagnetic radiation
+
+ align:start position:0%
+excitation by electromagnetic radiation
+ 
+
+ align:start position:0%
+excitation by electromagnetic radiation
+you want to be able to understand the
+
+ align:start position:0%
+you want to be able to understand the
+ 
+
+ align:start position:0%
+you want to be able to understand the
+nodal surfaces and you already know this
+
+ align:start position:0%
+nodal surfaces and you already know this
+ 
+
+ align:start position:0%
+nodal surfaces and you already know this
+one so how many nodal surfaces are there
+
+ align:start position:0%
+one so how many nodal surfaces are there
+ 
+
+ align:start position:0%
+one so how many nodal surfaces are there
+if you have a particular value of L yes
+
+ align:start position:0%
+if you have a particular value of L yes
+ 
+
+ align:start position:0%
+if you have a particular value of L yes
+right and if you have a particular value
+
+ align:start position:0%
+right and if you have a particular value
+ 
+
+ align:start position:0%
+right and if you have a particular value
+of M how many nodes are there in the XY
+
+ align:start position:0%
+of M how many nodes are there in the XY
+ 
+
+ align:start position:0%
+of M how many nodes are there in the XY
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your hot probability density is oriented
+
+ align:start position:0%
+your hot probability density is oriented
+ 
+
+ align:start position:0%
+your hot probability density is oriented
+along Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now you're saying things that I
+
+ align:start position:0%
+okay now you're saying things that I
+ 
+
+ align:start position:0%
+okay now you're saying things that I
+have to stop and think about because
+
+ align:start position:0%
+have to stop and think about because
+ 
+
+ align:start position:0%
+have to stop and think about because
+you're not telling me what I expected to
+
+ align:start position:0%
+you're not telling me what I expected to
+ 
+
+ align:start position:0%
+you're not telling me what I expected to
+know so if M M is equal to zero L is
+
+ align:start position:0%
+know so if M M is equal to zero L is
+ 
+
+ align:start position:0%
+know so if M M is equal to zero L is
+perpendicular to the quantization axis
+
+ align:start position:0%
+perpendicular to the quantization axis
+ 
+
+ align:start position:0%
+perpendicular to the quantization axis
+and there are no nodes that that's true
+
+ align:start position:0%
+and there are no nodes that that's true
+ 
+
+ align:start position:0%
+and there are no nodes that that's true
+but that's the where the axis is is
+
+ align:start position:0%
+but that's the where the axis is is
+ 
+
+ align:start position:0%
+but that's the where the axis is is
+determined by theta and when you're when
+
+ align:start position:0%
+determined by theta and when you're when
+ 
+
+ align:start position:0%
+determined by theta and when you're when
+theta is equal to PI over two you're in
+
+ align:start position:0%
+theta is equal to PI over two you're in
+ 
+
+ align:start position:0%
+theta is equal to PI over two you're in
+the XY plane and depending and then the
+
+ align:start position:0%
+the XY plane and depending and then the
+ 
+
+ align:start position:0%
+the XY plane and depending and then the
+number of nodes in the XY plane is M or
+
+ align:start position:0%
+number of nodes in the XY plane is M or
+ 
+
+ align:start position:0%
+number of nodes in the XY plane is M or
+absolute value of M the Phi part of the
+
+ align:start position:0%
+absolute value of M the Phi part of the
+ 
+
+ align:start position:0%
+absolute value of M the Phi part of the
+rigid rotor is simple it's a
+
+ align:start position:0%
+rigid rotor is simple it's a
+ 
+
+ align:start position:0%
+rigid rotor is simple it's a
+differential equation that everybody can
+
+ align:start position:0%
+differential equation that everybody can
+ 
+
+ align:start position:0%
+differential equation that everybody can
+solve we already know that one and we
+
+ align:start position:0%
+solve we already know that one and we
+ 
+
+ align:start position:0%
+solve we already know that one and we
+know what the wave functions look like
+
+ align:start position:0%
+know what the wave functions look like
+ 
+
+ align:start position:0%
+know what the wave functions look like
+okay so we can write the equation and
+
+ align:start position:0%
+okay so we can write the equation and
+ 
+
+ align:start position:0%
+okay so we can write the equation and
+it's very quick to show separation of
+
+ align:start position:0%
+it's very quick to show separation of
+ 
+
+ align:start position:0%
+it's very quick to show separation of
+variables I'll do that in a minute and
+
+ align:start position:0%
+variables I'll do that in a minute and
+ 
+
+ align:start position:0%
+variables I'll do that in a minute and
+then we have the pictures of the
+
+ align:start position:0%
+then we have the pictures of the
+ 
+
+ align:start position:0%
+then we have the pictures of the
+separated parts yr NLM and essential in
+
+ align:start position:0%
+separated parts yr NLM and essential in
+ 
+
+ align:start position:0%
+separated parts yr NLM and essential in
+these pictures is the number of nodes
+
+ align:start position:0%
+these pictures is the number of nodes
+ 
+
+ align:start position:0%
+these pictures is the number of nodes
+and the spacing between nodes remember
+
+ align:start position:0%
+and the spacing between nodes remember
+ 
+
+ align:start position:0%
+and the spacing between nodes remember
+the semi-classical approximation we know
+
+ align:start position:0%
+the semi-classical approximation we know
+ 
+
+ align:start position:0%
+the semi-classical approximation we know
+that mr. Dubrow I really hit it out of
+
+ align:start position:0%
+that mr. Dubrow I really hit it out of
+ 
+
+ align:start position:0%
+that mr. Dubrow I really hit it out of
+the park by saying the the the wave
+
+ align:start position:0%
+the park by saying the the the wave
+ 
+
+ align:start position:0%
+the park by saying the the the wave
+length is H over P for
+
+ align:start position:0%
+length is H over P for
+ 
+
+ align:start position:0%
+length is H over P for
+one dimensional problem we know what to
+
+ align:start position:0%
+one dimensional problem we know what to
+ 
+
+ align:start position:0%
+one dimensional problem we know what to
+do with that and we're going to discover
+
+ align:start position:0%
+do with that and we're going to discover
+ 
+
+ align:start position:0%
+do with that and we're going to discover
+that for the radial problem we have a
+
+ align:start position:0%
+that for the radial problem we have a
+ 
+
+ align:start position:0%
+that for the radial problem we have a
+very simple way of determining what the
+
+ align:start position:0%
+very simple way of determining what the
+ 
+
+ align:start position:0%
+very simple way of determining what the
+classical momentum is and so we know
+
+ align:start position:0%
+classical momentum is and so we know
+ 
+
+ align:start position:0%
+classical momentum is and so we know
+everything about the nodes and the node
+
+ align:start position:0%
+everything about the nodes and the node
+ 
+
+ align:start position:0%
+everything about the nodes and the node
+spacing and the amplitudes between nodes
+
+ align:start position:0%
+spacing and the amplitudes between nodes
+ 
+
+ align:start position:0%
+spacing and the amplitudes between nodes
+and how to evaluate every integral of
+
+ align:start position:0%
+and how to evaluate every integral of
+ 
+
+ align:start position:0%
+and how to evaluate every integral of
+some power of R or Z and and so there's
+
+ align:start position:0%
+some power of R or Z and and so there's
+ 
+
+ align:start position:0%
+some power of R or Z and and so there's
+just an enormous amount gotten from the
+
+ align:start position:0%
+just an enormous amount gotten from the
+ 
+
+ align:start position:0%
+just an enormous amount gotten from the
+semi-classical picture once you are
+
+ align:start position:0%
+semi-classical picture once you are
+ 
+
+ align:start position:0%
+semi-classical picture once you are
+familiar with this okay and so we can we
+
+ align:start position:0%
+familiar with this okay and so we can we
+ 
+
+ align:start position:0%
+familiar with this okay and so we can we
+can say that we have the classical wave
+
+ align:start position:0%
+can say that we have the classical wave
+ 
+
+ align:start position:0%
+can say that we have the classical wave
+length or the semi-classical wave length
+
+ align:start position:0%
+length or the semi-classical wave length
+ 
+
+ align:start position:0%
+length or the semi-classical wave length
+it has an index R and so we have a
+
+ align:start position:0%
+it has an index R and so we have a
+ 
+
+ align:start position:0%
+it has an index R and so we have a
+momentum a linear momentum with a
+
+ align:start position:0%
+momentum a linear momentum with a
+ 
+
+ align:start position:0%
+momentum a linear momentum with a
+quantum number on it for L you see
+
+ align:start position:0%
+quantum number on it for L you see
+ 
+
+ align:start position:0%
+quantum number on it for L you see
+that's a little strange but that tells
+
+ align:start position:0%
+that's a little strange but that tells
+ 
+
+ align:start position:0%
+that's a little strange but that tells
+us what the potential is going to be and
+
+ align:start position:0%
+us what the potential is going to be and
+ 
+
+ align:start position:0%
+us what the potential is going to be and
+that tells us what to use in order to
+
+ align:start position:0%
+that tells us what to use in order to
+ 
+
+ align:start position:0%
+that tells us what to use in order to
+determine the wave length and this is
+
+ align:start position:0%
+determine the wave length and this is
+ 
+
+ align:start position:0%
+determine the wave length and this is
+really the core of how we can go way
+
+ align:start position:0%
+really the core of how we can go way
+ 
+
+ align:start position:0%
+really the core of how we can go way
+beyond textbooks we can do in our heads
+
+ align:start position:0%
+beyond textbooks we can do in our heads
+ 
+
+ align:start position:0%
+beyond textbooks we can do in our heads
+or on a simple piece of paper we can do
+
+ align:start position:0%
+or on a simple piece of paper we can do
+ 
+
+ align:start position:0%
+or on a simple piece of paper we can do
+this and we can draw we can draw
+
+ align:start position:0%
+this and we can draw we can draw
+ 
+
+ align:start position:0%
+this and we can draw we can draw
+pictures and we can evaluate matrix
+
+ align:start position:0%
+pictures and we can evaluate matrix
+ 
+
+ align:start position:0%
+pictures and we can evaluate matrix
+elements very without any complicated
+
+ align:start position:0%
+elements very without any complicated
+ 
+
+ align:start position:0%
+elements very without any complicated
+integral tables just you can you can
+
+ align:start position:0%
+integral tables just you can you can
+ 
+
+ align:start position:0%
+integral tables just you can you can
+make estimates that are incredibly
+
+ align:start position:0%
+make estimates that are incredibly
+ 
+
+ align:start position:0%
+make estimates that are incredibly
+important and from that you can get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation values and also non off
+
+ align:start position:0%
+expectation values and also non off
+ 
+
+ align:start position:0%
+expectation values and also non off
+diagonal matrix elements of integer
+
+ align:start position:0%
+diagonal matrix elements of integer
+ 
+
+ align:start position:0%
+diagonal matrix elements of integer
+powers of the coordinate and that it's
+
+ align:start position:0%
+powers of the coordinate and that it's
+ 
+
+ align:start position:0%
+powers of the coordinate and that it's
+an enormous amount of stuff that you can
+
+ align:start position:0%
+an enormous amount of stuff that you can
+ 
+
+ align:start position:0%
+an enormous amount of stuff that you can
+do now you can't do it yet but after -
+
+ align:start position:0%
+do now you can't do it yet but after -
+ 
+
+ align:start position:0%
+do now you can't do it yet but after -
+after Wednesday's lecture you will and
+
+ align:start position:0%
+after Wednesday's lecture you will and
+ 
+
+ align:start position:0%
+after Wednesday's lecture you will and
+so this will be Wednesday this and then
+
+ align:start position:0%
+so this will be Wednesday this and then
+ 
+
+ align:start position:0%
+so this will be Wednesday this and then
+we'll have evidence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron spin and I will get to that
+
+ align:start position:0%
+electron spin and I will get to that
+ 
+
+ align:start position:0%
+electron spin and I will get to that
+today okay so this is the menu and now
+
+ align:start position:0%
+today okay so this is the menu and now
+ 
+
+ align:start position:0%
+today okay so this is the menu and now
+let's let's start delivering some of
+
+ align:start position:0%
+let's let's start delivering some of
+ 
+
+ align:start position:0%
+let's let's start delivering some of
+this stuff I have to write some big
+
+ align:start position:0%
+this stuff I have to write some big
+ 
+
+ align:start position:0%
+this stuff I have to write some big
+equations so the Hamiltonian is kinetic
+
+ align:start position:0%
+equations so the Hamiltonian is kinetic
+ 
+
+ align:start position:0%
+equations so the Hamiltonian is kinetic
+energy plus potential energy and the
+
+ align:start position:0%
+energy plus potential energy and the
+ 
+
+ align:start position:0%
+energy plus potential energy and the
+kinetic energy was I'm sorry for the for
+
+ align:start position:0%
+kinetic energy was I'm sorry for the for
+ 
+
+ align:start position:0%
+kinetic energy was I'm sorry for the for
+the rigid rotor V was zero right and
+
+ align:start position:0%
+the rigid rotor V was zero right and
+ 
+
+ align:start position:0%
+the rigid rotor V was zero right and
+everything was in the kinetic energy
+
+ align:start position:0%
+everything was in the kinetic energy
+ 
+
+ align:start position:0%
+everything was in the kinetic energy
+well it's not quite true and so for
+
+ align:start position:0%
+well it's not quite true and so for
+ 
+
+ align:start position:0%
+well it's not quite true and so for
+hydrogen so we know this is P squared
+
+ align:start position:0%
+hydrogen so we know this is P squared
+ 
+
+ align:start position:0%
+hydrogen so we know this is P squared
+over 2m you and me'll for the hydrogen
+
+ align:start position:0%
+over 2m you and me'll for the hydrogen
+ 
+
+ align:start position:0%
+over 2m you and me'll for the hydrogen
+atom reduced mass and and and we know
+
+ align:start position:0%
+atom reduced mass and and and we know
+ 
+
+ align:start position:0%
+atom reduced mass and and and we know
+this is just Coulomb's law - e squared
+
+ align:start position:0%
+this is just Coulomb's law - e squared
+ 
+
+ align:start position:0%
+this is just Coulomb's law - e squared
+over 4 PI epsilon 0 H bar squared
+
+ align:start position:0%
+over 4 PI epsilon 0 H bar squared
+ 
+
+ align:start position:0%
+over 4 PI epsilon 0 H bar squared
+there's I'm sorry it was it was so this
+
+ align:start position:0%
+there's I'm sorry it was it was so this
+ 
+
+ align:start position:0%
+there's I'm sorry it was it was so this
+is the classical so these are the parts
+
+ align:start position:0%
+is the classical so these are the parts
+ 
+
+ align:start position:0%
+is the classical so these are the parts
+and but that since it's spherical we're
+
+ align:start position:0%
+and but that since it's spherical we're
+ 
+
+ align:start position:0%
+and but that since it's spherical we're
+not going to work in Cartesian
+
+ align:start position:0%
+not going to work in Cartesian
+ 
+
+ align:start position:0%
+not going to work in Cartesian
+coordinates and in fact that's a very
+
+ align:start position:0%
+coordinates and in fact that's a very
+ 
+
+ align:start position:0%
+coordinates and in fact that's a very
+strong statement if you have a spherical
+
+ align:start position:0%
+strong statement if you have a spherical
+ 
+
+ align:start position:0%
+strong statement if you have a spherical
+problem don't start in Cartesian
+
+ align:start position:0%
+problem don't start in Cartesian
+ 
+
+ align:start position:0%
+problem don't start in Cartesian
+coordinates because it's a horrible mess
+
+ align:start position:0%
+coordinates because it's a horrible mess
+ 
+
+ align:start position:0%
+coordinates because it's a horrible mess
+transforming to spherical polar
+
+ align:start position:0%
+transforming to spherical polar
+ 
+
+ align:start position:0%
+transforming to spherical polar
+coordinates just remember the spherical
+
+ align:start position:0%
+coordinates just remember the spherical
+ 
+
+ align:start position:0%
+coordinates just remember the spherical
+polar quit and okay so you know how
+
+ align:start position:0%
+polar quit and okay so you know how
+ 
+
+ align:start position:0%
+polar quit and okay so you know how
+spherical polar coordinates work I'm not
+
+ align:start position:0%
+spherical polar coordinates work I'm not
+ 
+
+ align:start position:0%
+spherical polar coordinates work I'm not
+going to draw it so the the kinetic
+
+ align:start position:0%
+going to draw it so the the kinetic
+ 
+
+ align:start position:0%
+going to draw it so the the kinetic
+energy term is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the laplacian and that's a
+
+ align:start position:0%
+and this is the laplacian and that's a
+ 
+
+ align:start position:0%
+and this is the laplacian and that's a
+terrible thing and del squared is it
+
+ align:start position:0%
+terrible thing and del squared is it
+ 
+
+ align:start position:0%
+terrible thing and del squared is it
+looks like it's going to be a real
+
+ align:start position:0%
+looks like it's going to be a real
+ 
+
+ align:start position:0%
+looks like it's going to be a real
+nightmare partial with respect to our
+
+ align:start position:0%
+nightmare partial with respect to our
+ 
+
+ align:start position:0%
+nightmare partial with respect to our
+our square parcel with respect to our
+
+ align:start position:0%
+our square parcel with respect to our
+ 
+
+ align:start position:0%
+our square parcel with respect to our
+then we have 1 over R squared sine
+
+ align:start position:0%
+then we have 1 over R squared sine
+ 
+
+ align:start position:0%
+then we have 1 over R squared sine
+squared theta partial with respect to
+
+ align:start position:0%
+squared theta partial with respect to
+ 
+
+ align:start position:0%
+squared theta partial with respect to
+theta sine theta partial with respect to
+
+ align:start position:0%
+theta sine theta partial with respect to
+ 
+
+ align:start position:0%
+theta sine theta partial with respect to
+theta and then a third term 1 over R
+
+ align:start position:0%
+theta and then a third term 1 over R
+ 
+
+ align:start position:0%
+theta and then a third term 1 over R
+squared sine squared I got the square
+
+ align:start position:0%
+squared sine squared I got the square
+ 
+
+ align:start position:0%
+squared sine squared I got the square
+here that's wrong and this is sine
+
+ align:start position:0%
+here that's wrong and this is sine
+ 
+
+ align:start position:0%
+here that's wrong and this is sine
+squared theta I heard a member of mumble
+
+ align:start position:0%
+squared theta I heard a member of mumble
+ 
+
+ align:start position:0%
+squared theta I heard a member of mumble
+over there yeah but I haven't I'm just
+
+ align:start position:0%
+over there yeah but I haven't I'm just
+ 
+
+ align:start position:0%
+over there yeah but I haven't I'm just
+doing del squared right oh yes it looks
+
+ align:start position:0%
+doing del squared right oh yes it looks
+ 
+
+ align:start position:0%
+doing del squared right oh yes it looks
+like a terrible thing all right and the
+
+ align:start position:0%
+like a terrible thing all right and the
+ 
+
+ align:start position:0%
+like a terrible thing all right and the
+last part is second derivative with
+
+ align:start position:0%
+last part is second derivative with
+ 
+
+ align:start position:0%
+last part is second derivative with
+respect to Phi ok this looks like a
+
+ align:start position:0%
+respect to Phi ok this looks like a
+ 
+
+ align:start position:0%
+respect to Phi ok this looks like a
+terrible thing to build to build on but
+
+ align:start position:0%
+terrible thing to build to build on but
+ 
+
+ align:start position:0%
+terrible thing to build to build on but
+with a little bit of trickery and that
+
+ align:start position:0%
+with a little bit of trickery and that
+ 
+
+ align:start position:0%
+with a little bit of trickery and that
+is suppose we multiply this equation by
+
+ align:start position:0%
+is suppose we multiply this equation by
+ 
+
+ align:start position:0%
+is suppose we multiply this equation by
+R squared then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have killed the r-squared terms here
+
+ align:start position:0%
+we have killed the r-squared terms here
+ 
+
+ align:start position:0%
+we have killed the r-squared terms here
+here and we're going to be able to
+
+ align:start position:0%
+here and we're going to be able to
+ 
+
+ align:start position:0%
+here and we're going to be able to
+separate it and so we are able to write
+
+ align:start position:0%
+separate it and so we are able to write
+ 
+
+ align:start position:0%
+separate it and so we are able to write
+an equation which as the separate ility
+
+ align:start position:0%
+an equation which as the separate ility
+ 
+
+ align:start position:0%
+an equation which as the separate ility
+built-in and so parcel with respect to
+
+ align:start position:0%
+built-in and so parcel with respect to
+ 
+
+ align:start position:0%
+built-in and so parcel with respect to
+our our squared partials with respect to
+
+ align:start position:0%
+our our squared partials with respect to
+ 
+
+ align:start position:0%
+our our squared partials with respect to
+r plus l squared plus 2 mu H R squared V
+
+ align:start position:0%
+r plus l squared plus 2 mu H R squared V
+ 
+
+ align:start position:0%
+r plus l squared plus 2 mu H R squared V
+of our that's a string equation so we
+
+ align:start position:0%
+of our that's a string equation so we
+ 
+
+ align:start position:0%
+of our that's a string equation so we
+have an R dependent term and another our
+
+ align:start position:0%
+have an R dependent term and another our
+ 
+
+ align:start position:0%
+have an R dependent term and another our
+dependent term and if they defy
+
+ align:start position:0%
+dependent term and if they defy
+ 
+
+ align:start position:0%
+dependent term and if they defy
+dependent term all in this one nice
+
+ align:start position:0%
+dependent term all in this one nice
+ 
+
+ align:start position:0%
+dependent term all in this one nice
+operator that we've understood so now
+
+ align:start position:0%
+operator that we've understood so now
+ 
+
+ align:start position:0%
+operator that we've understood so now
+there's one more trick in order for the
+
+ align:start position:0%
+there's one more trick in order for the
+ 
+
+ align:start position:0%
+there's one more trick in order for the
+shorter equation to be separated into a
+
+ align:start position:0%
+shorter equation to be separated into a
+ 
+
+ align:start position:0%
+shorter equation to be separated into a
+Theta Phi part and in our part is we
+
+ align:start position:0%
+Theta Phi part and in our part is we
+ 
+
+ align:start position:0%
+Theta Phi part and in our part is we
+need a commutator and so that commutator
+
+ align:start position:0%
+need a commutator and so that commutator
+ 
+
+ align:start position:0%
+need a commutator and so that commutator
+is this what is the commutator between l
+
+ align:start position:0%
+is this what is the commutator between l
+ 
+
+ align:start position:0%
+is this what is the commutator between l
+squared and any function of R yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely that's really important we
+
+ align:start position:0%
+absolutely that's really important we
+ 
+
+ align:start position:0%
+absolutely that's really important we
+often encounter operators that depend on
+
+ align:start position:0%
+often encounter operators that depend on
+ 
+
+ align:start position:0%
+often encounter operators that depend on
+different variables and when they do
+
+ align:start position:0%
+different variables and when they do
+ 
+
+ align:start position:0%
+different variables and when they do
+they can do with each other which is an
+
+ align:start position:0%
+they can do with each other which is an
+ 
+
+ align:start position:0%
+they can do with each other which is an
+incredibly convenient thing because that
+
+ align:start position:0%
+incredibly convenient thing because that
+ 
+
+ align:start position:0%
+incredibly convenient thing because that
+means we can set up the problem as a
+
+ align:start position:0%
+means we can set up the problem as a
+ 
+
+ align:start position:0%
+means we can set up the problem as a
+product of eigenfunctions of the
+
+ align:start position:0%
+product of eigenfunctions of the
+ 
+
+ align:start position:0%
+product of eigenfunctions of the
+different operators so this means that
+
+ align:start position:0%
+different operators so this means that
+ 
+
+ align:start position:0%
+different operators so this means that
+we can write a theta phi term which we
+
+ align:start position:0%
+we can write a theta phi term which we
+ 
+
+ align:start position:0%
+we can write a theta phi term which we
+completely know and in our term which we
+
+ align:start position:0%
+completely know and in our term which we
+ 
+
+ align:start position:0%
+completely know and in our term which we
+don't know and contains all of the
+
+ align:start position:0%
+don't know and contains all of the
+ 
+
+ align:start position:0%
+don't know and contains all of the
+interesting stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's forget about date and Phi let's
+
+ align:start position:0%
+so let's forget about date and Phi let's
+ 
+
+ align:start position:0%
+so let's forget about date and Phi let's
+just look at the the are part okay well
+
+ align:start position:0%
+just look at the the are part okay well
+ 
+
+ align:start position:0%
+just look at the the are part okay well
+the way we separated variables we had
+
+ align:start position:0%
+the way we separated variables we had
+ 
+
+ align:start position:0%
+the way we separated variables we had
+this written equation and we divided by
+
+ align:start position:0%
+this written equation and we divided by
+ 
+
+ align:start position:0%
+this written equation and we divided by
+the wave function which would be our of
+
+ align:start position:0%
+the wave function which would be our of
+ 
+
+ align:start position:0%
+the wave function which would be our of
+our y LM of Theta Phi and on one side of
+
+ align:start position:0%
+our y LM of Theta Phi and on one side of
+ 
+
+ align:start position:0%
+our y LM of Theta Phi and on one side of
+the equality we have only the the angle
+
+ align:start position:0%
+the equality we have only the the angle
+ 
+
+ align:start position:0%
+the equality we have only the the angle
+part and so when we do that when we
+
+ align:start position:0%
+part and so when we do that when we
+ 
+
+ align:start position:0%
+part and so when we do that when we
+divide by r we kill the are part on this
+
+ align:start position:0%
+divide by r we kill the are part on this
+ 
+
+ align:start position:0%
+divide by r we kill the are part on this
+side and on the other side it's the
+
+ align:start position:0%
+side and on the other side it's the
+ 
+
+ align:start position:0%
+side and on the other side it's the
+opposite and so we get a two pieces one
+
+ align:start position:0%
+opposite and so we get a two pieces one
+ 
+
+ align:start position:0%
+opposite and so we get a two pieces one
+or it's only dependent on theta and Phi
+
+ align:start position:0%
+or it's only dependent on theta and Phi
+ 
+
+ align:start position:0%
+or it's only dependent on theta and Phi
+and one is only dependent on our so they
+
+ align:start position:0%
+and one is only dependent on our so they
+ 
+
+ align:start position:0%
+and one is only dependent on our so they
+both have to be a constant so we get two
+
+ align:start position:0%
+both have to be a constant so we get two
+ 
+
+ align:start position:0%
+both have to be a constant so we get two
+separate differential equations and
+
+ align:start position:0%
+separate differential equations and
+ 
+
+ align:start position:0%
+separate differential equations and
+we've already dealt with one of them so
+
+ align:start position:0%
+we've already dealt with one of them so
+ 
+
+ align:start position:0%
+we've already dealt with one of them so
+well you end up getting is one over R
+
+ align:start position:0%
+well you end up getting is one over R
+ 
+
+ align:start position:0%
+well you end up getting is one over R
+times stuff is equal to times R Bar is
+
+ align:start position:0%
+times stuff is equal to times R Bar is
+ 
+
+ align:start position:0%
+times stuff is equal to times R Bar is
+equal to 1 over y LM L square y LM sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so this is the separation this is all
+
+ align:start position:0%
+ok so this is the separation this is all
+ 
+
+ align:start position:0%
+ok so this is the separation this is all
+our stuff this is all theta stuff and
+
+ align:start position:0%
+our stuff this is all theta stuff and
+ 
+
+ align:start position:0%
+our stuff this is all theta stuff and
+separation constant
+
+ align:start position:0%
+separation constant
+ 
+
+ align:start position:0%
+separation constant
+well this one is inviting a separation
+
+ align:start position:0%
+well this one is inviting a separation
+ 
+
+ align:start position:0%
+well this one is inviting a separation
+constant because l squared operating on
+
+ align:start position:0%
+constant because l squared operating on
+ 
+
+ align:start position:0%
+constant because l squared operating on
+ylm is H bar squared ll plus 1 that's
+
+ align:start position:0%
+ylm is H bar squared ll plus 1 that's
+ 
+
+ align:start position:0%
+ylm is H bar squared ll plus 1 that's
+the separation constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's look for the only time
+
+ align:start position:0%
+okay so now let's look for the only time
+ 
+
+ align:start position:0%
+okay so now let's look for the only time
+at the are part of the differential
+
+ align:start position:0%
+at the are part of the differential
+ 
+
+ align:start position:0%
+at the are part of the differential
+equation and so this is writing out all
+
+ align:start position:0%
+equation and so this is writing out all
+ 
+
+ align:start position:0%
+equation and so this is writing out all
+the pieces honestly we haven't one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the shorter equation for the
+
+ align:start position:0%
+so that's the shorter equation for the
+ 
+
+ align:start position:0%
+so that's the shorter equation for the
+radial part it looks a little bit
+
+ align:start position:0%
+radial part it looks a little bit
+ 
+
+ align:start position:0%
+radial part it looks a little bit
+annoying the important trick is that
+
+ align:start position:0%
+annoying the important trick is that
+ 
+
+ align:start position:0%
+annoying the important trick is that
+we've we've taken the separator
+
+ align:start position:0%
+we've we've taken the separator
+ 
+
+ align:start position:0%
+we've we've taken the separator
+separation constant and it has an hour
+
+ align:start position:0%
+separation constant and it has an hour
+ 
+
+ align:start position:0%
+separation constant and it has an hour
+dependence but when we divide through by
+
+ align:start position:0%
+dependence but when we divide through by
+ 
+
+ align:start position:0%
+dependence but when we divide through by
+2 mu H R squared and we say oh well
+
+ align:start position:0%
+2 mu H R squared and we say oh well
+ 
+
+ align:start position:0%
+2 mu H R squared and we say oh well
+let's call these two things together the
+
+ align:start position:0%
+let's call these two things together the
+ 
+
+ align:start position:0%
+let's call these two things together the
+L of R this is the effective potential
+
+ align:start position:0%
+L of R this is the effective potential
+ 
+
+ align:start position:0%
+L of R this is the effective potential
+and it depends on the value of L so this
+
+ align:start position:0%
+and it depends on the value of L so this
+ 
+
+ align:start position:0%
+and it depends on the value of L so this
+is just like an ordinary one-dimensional
+
+ align:start position:0%
+is just like an ordinary one-dimensional
+ 
+
+ align:start position:0%
+is just like an ordinary one-dimensional
+problem except now for every value of L
+
+ align:start position:0%
+problem except now for every value of L
+ 
+
+ align:start position:0%
+problem except now for every value of L
+we have a different potential and this
+
+ align:start position:0%
+we have a different potential and this
+ 
+
+ align:start position:0%
+we have a different potential and this
+potential is okay it when L is not equal
+
+ align:start position:0%
+potential is okay it when L is not equal
+ 
+
+ align:start position:0%
+potential is okay it when L is not equal
+to 0 this potential goes to infinity at
+
+ align:start position:0%
+to 0 this potential goes to infinity at
+ 
+
+ align:start position:0%
+to 0 this potential goes to infinity at
+R equals 0 which is bad except it's good
+
+ align:start position:0%
+R equals 0 which is bad except it's good
+ 
+
+ align:start position:0%
+R equals 0 which is bad except it's good
+because it keeps the particle ever from
+
+ align:start position:0%
+because it keeps the particle ever from
+ 
+
+ align:start position:0%
+because it keeps the particle ever from
+getting close to the nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what mr. Schrodinger I'm
+
+ align:start position:0%
+and that's what mr. Schrodinger I'm
+ 
+
+ align:start position:0%
+and that's what mr. Schrodinger I'm
+sorry what mr. Bora was thinking about
+
+ align:start position:0%
+sorry what mr. Bora was thinking about
+ 
+
+ align:start position:0%
+sorry what mr. Bora was thinking about
+that we have only circular orbits or we
+
+ align:start position:0%
+that we have only circular orbits or we
+ 
+
+ align:start position:0%
+that we have only circular orbits or we
+have only orbits that are you know are
+
+ align:start position:0%
+have only orbits that are you know are
+ 
+
+ align:start position:0%
+have only orbits that are you know are
+away from the eye from the place where
+
+ align:start position:0%
+away from the eye from the place where
+ 
+
+ align:start position:0%
+away from the eye from the place where
+the Coulomb interaction would be
+
+ align:start position:0%
+the Coulomb interaction would be
+ 
+
+ align:start position:0%
+the Coulomb interaction would be
+infinite and I mean there are several
+
+ align:start position:0%
+infinite and I mean there are several
+ 
+
+ align:start position:0%
+infinite and I mean there are several
+things is wrong with poor's picture one
+
+ align:start position:0%
+things is wrong with poor's picture one
+ 
+
+ align:start position:0%
+things is wrong with poor's picture one
+is that we have orbits and the other is
+
+ align:start position:0%
+is that we have orbits and the other is
+ 
+
+ align:start position:0%
+is that we have orbits and the other is
+that we don't include l equals zero but
+
+ align:start position:0%
+that we don't include l equals zero but
+ 
+
+ align:start position:0%
+that we don't include l equals zero but
+this is sort of telling you a lot of
+
+ align:start position:0%
+this is sort of telling you a lot of
+ 
+
+ align:start position:0%
+this is sort of telling you a lot of
+really important stuff because the value
+
+ align:start position:0%
+really important stuff because the value
+ 
+
+ align:start position:0%
+really important stuff because the value
+of L determines the importance of this
+
+ align:start position:0%
+of L determines the importance of this
+ 
+
+ align:start position:0%
+of L determines the importance of this
+thing that goes to infinity at R equals
+
+ align:start position:0%
+thing that goes to infinity at R equals
+ 
+
+ align:start position:0%
+thing that goes to infinity at R equals
+zero that has very significant
+
+ align:start position:0%
+zero that has very significant
+ 
+
+ align:start position:0%
+zero that has very significant
+consequences as far as which orbital
+
+ align:start position:0%
+consequences as far as which orbital
+ 
+
+ align:start position:0%
+consequences as far as which orbital
+angular momentum States we're dealing
+
+ align:start position:0%
+angular momentum States we're dealing
+ 
+
+ align:start position:0%
+angular momentum States we're dealing
+with okay so we're going to get the
+
+ align:start position:0%
+with okay so we're going to get the
+ 
+
+ align:start position:0%
+with okay so we're going to get the
+usual l ml a lot of numbers and we're
+
+ align:start position:0%
+usual l ml a lot of numbers and we're
+ 
+
+ align:start position:0%
+usual l ml a lot of numbers and we're
+going to get another one from the radial
+
+ align:start position:0%
+going to get another one from the radial
+ 
+
+ align:start position:0%
+going to get another one from the radial
+part and since this is a 1d equation
+
+ align:start position:0%
+part and since this is a 1d equation
+ 
+
+ align:start position:0%
+part and since this is a 1d equation
+there's only one quantum number and
+
+ align:start position:0%
+there's only one quantum number and
+ 
+
+ align:start position:0%
+there's only one quantum number and
+we're going to call it L and now there's
+
+ align:start position:0%
+we're going to call it L and now there's
+ 
+
+ align:start position:0%
+we're going to call it L and now there's
+this word principle and there's really
+
+ align:start position:0%
+this word principle and there's really
+ 
+
+ align:start position:0%
+this word principle and there's really
+two words principle with an le and
+
+ align:start position:0%
+two words principle with an le and
+ 
+
+ align:start position:0%
+two words principle with an le and
+principle with an al which one do you
+
+ align:start position:0%
+principle with an al which one do you
+ 
+
+ align:start position:0%
+principle with an al which one do you
+think is appropriate I'm sorry I can't
+
+ align:start position:0%
+think is appropriate I'm sorry I can't
+ 
+
+ align:start position:0%
+think is appropriate I'm sorry I can't
+hear hey al is there appropriate one
+
+ align:start position:0%
+hear hey al is there appropriate one
+ 
+
+ align:start position:0%
+hear hey al is there appropriate one
+principle has to do with something
+
+ align:start position:0%
+principle has to do with something
+ 
+
+ align:start position:0%
+principle has to do with something
+fundamental this is you know the
+
+ align:start position:0%
+fundamental this is you know the
+ 
+
+ align:start position:0%
+fundamental this is you know the
+principle has to do with something
+
+ align:start position:0%
+principle has to do with something
+ 
+
+ align:start position:0%
+principle has to do with something
+that's important okay and I can't tell
+
+ align:start position:0%
+that's important okay and I can't tell
+ 
+
+ align:start position:0%
+that's important okay and I can't tell
+you how many times people who should
+
+ align:start position:0%
+you how many times people who should
+ 
+
+ align:start position:0%
+you how many times people who should
+know better use the wrong principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you'll never do that now because
+
+ align:start position:0%
+okay you'll never do that now because
+ 
+
+ align:start position:0%
+okay you'll never do that now because
+you know it's like what's new C over
+
+ align:start position:0%
+you know it's like what's new C over
+ 
+
+ align:start position:0%
+you know it's like what's new C over
+lambda right okay so this is the right
+
+ align:start position:0%
+lambda right okay so this is the right
+ 
+
+ align:start position:0%
+lambda right okay so this is the right
+principle and now let us if we if we do
+
+ align:start position:0%
+principle and now let us if we if we do
+ 
+
+ align:start position:0%
+principle and now let us if we if we do
+something clever and we have the radial
+
+ align:start position:0%
+something clever and we have the radial
+ 
+
+ align:start position:0%
+something clever and we have the radial
+part and we say let us replace it by one
+
+ align:start position:0%
+part and we say let us replace it by one
+ 
+
+ align:start position:0%
+part and we say let us replace it by one
+of our times this new function Chi L bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well when we do that this equation
+
+ align:start position:0%
+well when we do that this equation
+ 
+
+ align:start position:0%
+well when we do that this equation
+becomes really simple so what we get
+
+ align:start position:0%
+becomes really simple so what we get
+ 
+
+ align:start position:0%
+becomes really simple so what we get
+when we make that substitution is H bar
+
+ align:start position:0%
+when we make that substitution is H bar
+ 
+
+ align:start position:0%
+when we make that substitution is H bar
+squared over 2 mu H second derivative
+
+ align:start position:0%
+squared over 2 mu H second derivative
+ 
+
+ align:start position:0%
+squared over 2 mu H second derivative
+with respect to R plus the L bar minus e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals 0 that looks like a differential
+
+ align:start position:0%
+equals 0 that looks like a differential
+ 
+
+ align:start position:0%
+equals 0 that looks like a differential
+equation we've seen before
+
+ align:start position:0%
+equation we've seen before
+ 
+
+ align:start position:0%
+equation we've seen before
+it's a simple one dimensional
+
+ align:start position:0%
+it's a simple one dimensional
+ 
+
+ align:start position:0%
+it's a simple one dimensional
+differential equation kinetic energy
+
+ align:start position:0%
+differential equation kinetic energy
+ 
+
+ align:start position:0%
+differential equation kinetic energy
+potential this is not there's some
+
+ align:start position:0%
+potential this is not there's some
+ 
+
+ align:start position:0%
+potential this is not there's some
+kinetic energy hidden in the potential
+
+ align:start position:0%
+kinetic energy hidden in the potential
+ 
+
+ align:start position:0%
+kinetic energy hidden in the potential
+energy but this is simple
+
+ align:start position:0%
+energy but this is simple
+ 
+
+ align:start position:0%
+energy but this is simple
+and we can deal with this a lot I'm not
+
+ align:start position:0%
+and we can deal with this a lot I'm not
+ 
+
+ align:start position:0%
+and we can deal with this a lot I'm not
+going to but if you're going to actually
+
+ align:start position:0%
+going to but if you're going to actually
+ 
+
+ align:start position:0%
+going to but if you're going to actually
+do stuff you're going to be wanting to
+
+ align:start position:0%
+do stuff you're going to be wanting to
+ 
+
+ align:start position:0%
+do stuff you're going to be wanting to
+look at this differential equation okay
+
+ align:start position:0%
+look at this differential equation okay
+ 
+
+ align:start position:0%
+look at this differential equation okay
+but I'm going to forego that pleasure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the problems with the radial
+
+ align:start position:0%
+one of the problems with the radial
+ 
+
+ align:start position:0%
+one of the problems with the radial
+equation is the fact that r is a special
+
+ align:start position:0%
+equation is the fact that r is a special
+ 
+
+ align:start position:0%
+equation is the fact that r is a special
+kind of coordinate it can't go negative
+
+ align:start position:0%
+kind of coordinate it can't go negative
+ 
+
+ align:start position:0%
+kind of coordinate it can't go negative
+and so treating the boundary condition
+
+ align:start position:0%
+and so treating the boundary condition
+ 
+
+ align:start position:0%
+and so treating the boundary condition
+for R is equal to 0 is a little subtle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it turns out
+
+ align:start position:0%
+and it turns out
+ 
+
+ align:start position:0%
+and it turns out
+that when L is equal to zero then R of 0
+
+ align:start position:0%
+that when L is equal to zero then R of 0
+ 
+
+ align:start position:0%
+that when L is equal to zero then R of 0
+is not 0 but for all other values of L R
+
+ align:start position:0%
+is not 0 but for all other values of L R
+ 
+
+ align:start position:0%
+is not 0 but for all other values of L R
+of 0 is 0 and all event of R depends on
+
+ align:start position:0%
+of 0 is 0 and all event of R depends on
+ 
+
+ align:start position:0%
+of 0 is 0 and all event of R depends on
+L being 0 because the electron feels the
+
+ align:start position:0%
+L being 0 because the electron feels the
+ 
+
+ align:start position:0%
+L being 0 because the electron feels the
+nucleus it doesn't experience an
+
+ align:start position:0%
+nucleus it doesn't experience an
+ 
+
+ align:start position:0%
+nucleus it doesn't experience an
+infinite singularity it it feels the
+
+ align:start position:0%
+infinite singularity it it feels the
+ 
+
+ align:start position:0%
+infinite singularity it it feels the
+nucleus and when L is not equal to 0
+
+ align:start position:0%
+nucleus and when L is not equal to 0
+ 
+
+ align:start position:0%
+nucleus and when L is not equal to 0
+then it's sensing the nucleus at a
+
+ align:start position:0%
+then it's sensing the nucleus at a
+ 
+
+ align:start position:0%
+then it's sensing the nucleus at a
+distance and that leads to some very
+
+ align:start position:0%
+distance and that leads to some very
+ 
+
+ align:start position:0%
+distance and that leads to some very
+small splittings called hyperfine and so
+
+ align:start position:0%
+small splittings called hyperfine and so
+ 
+
+ align:start position:0%
+small splittings called hyperfine and so
+there's there's different kinds of
+
+ align:start position:0%
+there's there's different kinds of
+ 
+
+ align:start position:0%
+there's there's different kinds of
+hyperfine structure but anyway this is a
+
+ align:start position:0%
+hyperfine structure but anyway this is a
+ 
+
+ align:start position:0%
+hyperfine structure but anyway this is a
+really subtle and important point ok ok
+
+ align:start position:0%
+really subtle and important point ok ok
+ 
+
+ align:start position:0%
+really subtle and important point ok ok
+yes No ok so and now pictures of
+
+ align:start position:0%
+yes No ok so and now pictures of
+ 
+
+ align:start position:0%
+yes No ok so and now pictures of
+orbitals so we the problem with pictures
+
+ align:start position:0%
+orbitals so we the problem with pictures
+ 
+
+ align:start position:0%
+orbitals so we the problem with pictures
+of orbitals is now we have a function of
+
+ align:start position:0%
+of orbitals is now we have a function of
+ 
+
+ align:start position:0%
+of orbitals is now we have a function of
+three variables and it's equal to some
+
+ align:start position:0%
+three variables and it's equal to some
+ 
+
+ align:start position:0%
+three variables and it's equal to some
+complex number so we need sort of two
+
+ align:start position:0%
+complex number so we need sort of two
+ 
+
+ align:start position:0%
+complex number so we need sort of two
+degrees of freedom to represent a
+
+ align:start position:0%
+degrees of freedom to represent a
+ 
+
+ align:start position:0%
+degrees of freedom to represent a
+complex number and we have three
+
+ align:start position:0%
+complex number and we have three
+ 
+
+ align:start position:0%
+complex number and we have three
+variables and so you know representing
+
+ align:start position:0%
+variables and so you know representing
+ 
+
+ align:start position:0%
+variables and so you know representing
+that on a two-dimensional sheet of paper
+
+ align:start position:0%
+that on a two-dimensional sheet of paper
+ 
+
+ align:start position:0%
+that on a two-dimensional sheet of paper
+is horrible but we have this wonderful
+
+ align:start position:0%
+is horrible but we have this wonderful
+ 
+
+ align:start position:0%
+is horrible but we have this wonderful
+factorization where we have our R and we
+
+ align:start position:0%
+factorization where we have our R and we
+ 
+
+ align:start position:0%
+factorization where we have our R and we
+could draw that easily we don't need any
+
+ align:start position:0%
+could draw that easily we don't need any
+ 
+
+ align:start position:0%
+could draw that easily we don't need any
+special skill and we have ylm of theta
+
+ align:start position:0%
+special skill and we have ylm of theta
+ 
+
+ align:start position:0%
+special skill and we have ylm of theta
+phi and we've got lots of practice with
+
+ align:start position:0%
+phi and we've got lots of practice with
+ 
+
+ align:start position:0%
+phi and we've got lots of practice with
+that although what we've practiced with
+
+ align:start position:0%
+that although what we've practiced with
+ 
+
+ align:start position:0%
+that although what we've practiced with
+may not be completely understood yet but
+
+ align:start position:0%
+may not be completely understood yet but
+ 
+
+ align:start position:0%
+may not be completely understood yet but
+so we have ways of representing these
+
+ align:start position:0%
+so we have ways of representing these
+ 
+
+ align:start position:0%
+so we have ways of representing these
+and and so we go through the the
+
+ align:start position:0%
+and and so we go through the the
+ 
+
+ align:start position:0%
+and and so we go through the the
+understanding of the hydrogen atom
+
+ align:start position:0%
+understanding of the hydrogen atom
+ 
+
+ align:start position:0%
+understanding of the hydrogen atom
+by looking at these two things
+
+ align:start position:0%
+by looking at these two things
+ 
+
+ align:start position:0%
+by looking at these two things
+separately okay now for the radial part
+
+ align:start position:0%
+separately okay now for the radial part
+ 
+
+ align:start position:0%
+separately okay now for the radial part
+the energy levels where this is the
+
+ align:start position:0%
+the energy levels where this is the
+ 
+
+ align:start position:0%
+the energy levels where this is the
+Redbird constant it's a combination of
+
+ align:start position:0%
+Redbird constant it's a combination of
+ 
+
+ align:start position:0%
+Redbird constant it's a combination of
+fundamental constants and for hydrogen
+
+ align:start position:0%
+fundamental constants and for hydrogen
+ 
+
+ align:start position:0%
+fundamental constants and for hydrogen
+the Redbird constant is equal to 109
+
+ align:start position:0%
+the Redbird constant is equal to 109
+ 
+
+ align:start position:0%
+the Redbird constant is equal to 109
+seven thirty seven point three one nine
+
+ align:start position:0%
+seven thirty seven point three one nine
+ 
+
+ align:start position:0%
+seven thirty seven point three one nine
+there's actually more digits wave
+
+ align:start position:0%
+there's actually more digits wave
+ 
+
+ align:start position:0%
+there's actually more digits wave
+numbers times nu eight over a mu
+
+ align:start position:0%
+numbers times nu eight over a mu
+ 
+
+ align:start position:0%
+numbers times nu eight over a mu
+infinite well this is actually the
+
+ align:start position:0%
+infinite well this is actually the
+ 
+
+ align:start position:0%
+infinite well this is actually the
+Redbird constant for an infinite mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now and so mu H is equal to the mass of
+
+ align:start position:0%
+now and so mu H is equal to the mass of
+ 
+
+ align:start position:0%
+now and so mu H is equal to the mass of
+the electron times the mass of the
+
+ align:start position:0%
+the electron times the mass of the
+ 
+
+ align:start position:0%
+the electron times the mass of the
+proton over the mass of the electron
+
+ align:start position:0%
+proton over the mass of the electron
+ 
+
+ align:start position:0%
+proton over the mass of the electron
+plus the mass of the proton now the mass
+
+ align:start position:0%
+plus the mass of the proton now the mass
+ 
+
+ align:start position:0%
+plus the mass of the proton now the mass
+of the proton is much bigger than the
+
+ align:start position:0%
+of the proton is much bigger than the
+ 
+
+ align:start position:0%
+of the proton is much bigger than the
+mass of the electron and so you can use
+
+ align:start position:0%
+mass of the electron and so you can use
+ 
+
+ align:start position:0%
+mass of the electron and so you can use
+this as a trick you can say well what is
+
+ align:start position:0%
+this as a trick you can say well what is
+ 
+
+ align:start position:0%
+this as a trick you can say well what is
+it well we know what this is it's easy
+
+ align:start position:0%
+it well we know what this is it's easy
+ 
+
+ align:start position:0%
+it well we know what this is it's easy
+to calculate but there are two limits
+
+ align:start position:0%
+to calculate but there are two limits
+ 
+
+ align:start position:0%
+to calculate but there are two limits
+what is the smallest possible reduced
+
+ align:start position:0%
+what is the smallest possible reduced
+ 
+
+ align:start position:0%
+what is the smallest possible reduced
+mass and that would be for if if the
+
+ align:start position:0%
+mass and that would be for if if the
+ 
+
+ align:start position:0%
+mass and that would be for if if the
+mass of the proton is infinite then we
+
+ align:start position:0%
+mass of the proton is infinite then we
+ 
+
+ align:start position:0%
+mass of the proton is infinite then we
+just get the mass of the electrons
+
+ align:start position:0%
+just get the mass of the electrons
+ 
+
+ align:start position:0%
+just get the mass of the electrons
+that's the biggest reduced mass and the
+
+ align:start position:0%
+that's the biggest reduced mass and the
+ 
+
+ align:start position:0%
+that's the biggest reduced mass and the
+smallest is if we have positronium where
+
+ align:start position:0%
+smallest is if we have positronium where
+ 
+
+ align:start position:0%
+smallest is if we have positronium where
+we have an electron bound to a to a
+
+ align:start position:0%
+we have an electron bound to a to a
+ 
+
+ align:start position:0%
+we have an electron bound to a to a
+proton and then when we do that we get
+
+ align:start position:0%
+proton and then when we do that we get
+ 
+
+ align:start position:0%
+proton and then when we do that we get
+1/2 I'm sorry it's not a proton it's to
+
+ align:start position:0%
+1/2 I'm sorry it's not a proton it's to
+ 
+
+ align:start position:0%
+1/2 I'm sorry it's not a proton it's to
+a positive positive positively charged
+
+ align:start position:0%
+a positive positive positively charged
+ 
+
+ align:start position:0%
+a positive positive positively charged
+particle which we call positive a
+
+ align:start position:0%
+particle which we call positive a
+ 
+
+ align:start position:0%
+particle which we call positive a
+positron and so it's electron pot and so
+
+ align:start position:0%
+positron and so it's electron pot and so
+ 
+
+ align:start position:0%
+positron and so it's electron pot and so
+each of the terms here is one is the
+
+ align:start position:0%
+each of the terms here is one is the
+ 
+
+ align:start position:0%
+each of the terms here is one is the
+mass of the electron and so the range is
+
+ align:start position:0%
+mass of the electron and so the range is
+ 
+
+ align:start position:0%
+mass of the electron and so the range is
+from 1/2 a me to Emmy the pending on
+
+ align:start position:0%
+from 1/2 a me to Emmy the pending on
+ 
+
+ align:start position:0%
+from 1/2 a me to Emmy the pending on
+what particles you're dealing with and
+
+ align:start position:0%
+what particles you're dealing with and
+ 
+
+ align:start position:0%
+what particles you're dealing with and
+so that's a useful thing and so the rid
+
+ align:start position:0%
+so that's a useful thing and so the rid
+ 
+
+ align:start position:0%
+so that's a useful thing and so the rid
+berg constant for hydrogen is smaller
+
+ align:start position:0%
+berg constant for hydrogen is smaller
+ 
+
+ align:start position:0%
+berg constant for hydrogen is smaller
+than the reduced mass of the infinite
+
+ align:start position:0%
+than the reduced mass of the infinite
+ 
+
+ align:start position:0%
+than the reduced mass of the infinite
+I'm sorry it's smaller than that for the
+
+ align:start position:0%
+I'm sorry it's smaller than that for the
+ 
+
+ align:start position:0%
+I'm sorry it's smaller than that for the
+infinite the mass nucleus and it is the
+
+ align:start position:0%
+infinite the mass nucleus and it is the
+ 
+
+ align:start position:0%
+infinite the mass nucleus and it is the
+value that made mr. four very happy 679
+
+ align:start position:0%
+value that made mr. four very happy 679
+ 
+
+ align:start position:0%
+value that made mr. four very happy 679
+so the important thing is this mass
+
+ align:start position:0%
+so the important thing is this mass
+ 
+
+ align:start position:0%
+so the important thing is this mass
+killed or reduced mass scale dripper
+
+ align:start position:0%
+killed or reduced mass scale dripper
+ 
+
+ align:start position:0%
+killed or reduced mass scale dripper
+constant explains to a part in 10 to the
+
+ align:start position:0%
+constant explains to a part in 10 to the
+ 
+
+ align:start position:0%
+constant explains to a part in 10 to the
+10th all of the energy levels of one
+
+ align:start position:0%
+10th all of the energy levels of one
+ 
+
+ align:start position:0%
+10th all of the energy levels of one
+electron systems hydrogen helium plus
+
+ align:start position:0%
+electron systems hydrogen helium plus
+ 
+
+ align:start position:0%
+electron systems hydrogen helium plus
+lithium 2-plus
+
+ align:start position:0%
+lithium 2-plus
+ 
+
+ align:start position:0%
+lithium 2-plus
+that's it and that's fantastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we have to talk to become
+
+ align:start position:0%
+okay now we have to talk to become
+ 
+
+ align:start position:0%
+okay now we have to talk to become
+really familiar with this rnl of our
+
+ align:start position:0%
+really familiar with this rnl of our
+ 
+
+ align:start position:0%
+really familiar with this rnl of our
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the questions is how many
+
+ align:start position:0%
+and one of the questions is how many
+ 
+
+ align:start position:0%
+and one of the questions is how many
+radial nodes and you know that for one s
+
+ align:start position:0%
+radial nodes and you know that for one s
+ 
+
+ align:start position:0%
+radial nodes and you know that for one s
+there aren't any nodes and you know for
+
+ align:start position:0%
+there aren't any nodes and you know for
+ 
+
+ align:start position:0%
+there aren't any nodes and you know for
+two P
+
+ align:start position:0%
+two P
+ 
+
+ align:start position:0%
+two P
+there aren't any radial nodes and so
+
+ align:start position:0%
+there aren't any radial nodes and so
+ 
+
+ align:start position:0%
+there aren't any radial nodes and so
+what we need is something that that goes
+
+ align:start position:0%
+what we need is something that that goes
+ 
+
+ align:start position:0%
+what we need is something that that goes
+like n minus L minus 1 the number of
+
+ align:start position:0%
+like n minus L minus 1 the number of
+ 
+
+ align:start position:0%
+like n minus L minus 1 the number of
+radial nodes which is all you need to
+
+ align:start position:0%
+radial nodes which is all you need to
+ 
+
+ align:start position:0%
+radial nodes which is all you need to
+know about the radio wave function is
+
+ align:start position:0%
+know about the radio wave function is
+ 
+
+ align:start position:0%
+know about the radio wave function is
+how many notes are are and how far they
+
+ align:start position:0%
+how many notes are are and how far they
+ 
+
+ align:start position:0%
+how many notes are are and how far they
+apart and what's the amplitude of each
+
+ align:start position:0%
+apart and what's the amplitude of each
+ 
+
+ align:start position:0%
+apart and what's the amplitude of each
+loop between nodes semi-classical theory
+
+ align:start position:0%
+loop between nodes semi-classical theory
+ 
+
+ align:start position:0%
+loop between nodes semi-classical theory
+gives you all of that and often when
+
+ align:start position:0%
+gives you all of that and often when
+ 
+
+ align:start position:0%
+gives you all of that and often when
+you're calculating an integral all you
+
+ align:start position:0%
+you're calculating an integral all you
+ 
+
+ align:start position:0%
+you're calculating an integral all you
+care about is the amplitude in the first
+
+ align:start position:0%
+care about is the amplitude in the first
+ 
+
+ align:start position:0%
+care about is the amplitude in the first
+loop and so instead of having to
+
+ align:start position:0%
+loop and so instead of having to
+ 
+
+ align:start position:0%
+loop and so instead of having to
+evaluate an integral you just uh you
+
+ align:start position:0%
+evaluate an integral you just uh you
+ 
+
+ align:start position:0%
+evaluate an integral you just uh you
+just figure out what is the the envelope
+
+ align:start position:0%
+just figure out what is the the envelope
+ 
+
+ align:start position:0%
+just figure out what is the the envelope
+function based on the classical momentum
+
+ align:start position:0%
+function based on the classical momentum
+ 
+
+ align:start position:0%
+function based on the classical momentum
+function okay now the thing that
+
+ align:start position:0%
+function okay now the thing that
+ 
+
+ align:start position:0%
+function okay now the thing that
+everybody's been waiting for spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember we know an angular momentum
+
+ align:start position:0%
+so remember we know an angular momentum
+ 
+
+ align:start position:0%
+so remember we know an angular momentum
+is our cross peak and we know that there
+
+ align:start position:0%
+is our cross peak and we know that there
+ 
+
+ align:start position:0%
+is our cross peak and we know that there
+isn't any internal structure or at least
+
+ align:start position:0%
+isn't any internal structure or at least
+ 
+
+ align:start position:0%
+isn't any internal structure or at least
+we don't know about internal structure
+
+ align:start position:0%
+we don't know about internal structure
+ 
+
+ align:start position:0%
+we don't know about internal structure
+of the electron or proton and so we
+
+ align:start position:0%
+of the electron or proton and so we
+ 
+
+ align:start position:0%
+of the electron or proton and so we
+can't somehow say well it's our cross P
+
+ align:start position:0%
+can't somehow say well it's our cross P
+ 
+
+ align:start position:0%
+can't somehow say well it's our cross P
+so we have the same on effect so we can
+
+ align:start position:0%
+so we have the same on effect so we can
+ 
+
+ align:start position:0%
+so we have the same on effect so we can
+look at the same on effect for an atom
+
+ align:start position:0%
+look at the same on effect for an atom
+ 
+
+ align:start position:0%
+look at the same on effect for an atom
+in a magnetic field and we have several
+
+ align:start position:0%
+in a magnetic field and we have several
+ 
+
+ align:start position:0%
+in a magnetic field and we have several
+things that we know so we have the
+
+ align:start position:0%
+things that we know so we have the
+ 
+
+ align:start position:0%
+things that we know so we have the
+magnetic moment of the electron is equal
+
+ align:start position:0%
+magnetic moment of the electron is equal
+ 
+
+ align:start position:0%
+magnetic moment of the electron is equal
+to minus the charge on the electron
+
+ align:start position:0%
+to minus the charge on the electron
+ 
+
+ align:start position:0%
+to minus the charge on the electron
+times 2m e times L well that's an
+
+ align:start position:0%
+times 2m e times L well that's an
+ 
+
+ align:start position:0%
+times 2m e times L well that's an
+angular momentum so if we had
+
+ align:start position:0%
+angular momentum so if we had
+ 
+
+ align:start position:0%
+angular momentum so if we had
+circulating charge
+
+ align:start position:0%
+circulating charge
+ 
+
+ align:start position:0%
+circulating charge
+well that circulating charge will
+
+ align:start position:0%
+well that circulating charge will
+ 
+
+ align:start position:0%
+well that circulating charge will
+produce a magnetic moment which has a
+
+ align:start position:0%
+produce a magnetic moment which has a
+ 
+
+ align:start position:0%
+produce a magnetic moment which has a
+magnitude which is related to the
+
+ align:start position:0%
+magnitude which is related to the
+ 
+
+ align:start position:0%
+magnitude which is related to the
+velocity and well what is L divided by
+
+ align:start position:0%
+velocity and well what is L divided by
+ 
+
+ align:start position:0%
+velocity and well what is L divided by
+mass it's a velocity and we have the
+
+ align:start position:0%
+mass it's a velocity and we have the
+ 
+
+ align:start position:0%
+mass it's a velocity and we have the
+charge here so this is a perfectly
+
+ align:start position:0%
+charge here so this is a perfectly
+ 
+
+ align:start position:0%
+charge here so this is a perfectly
+reasonable thing and so and that's good
+
+ align:start position:0%
+reasonable thing and so and that's good
+ 
+
+ align:start position:0%
+reasonable thing and so and that's good
+because we know that if we have
+
+ align:start position:0%
+because we know that if we have
+ 
+
+ align:start position:0%
+because we know that if we have
+electrons with some kind of internal
+
+ align:start position:0%
+electrons with some kind of internal
+ 
+
+ align:start position:0%
+electrons with some kind of internal
+structure we know what this is going to
+
+ align:start position:0%
+structure we know what this is going to
+ 
+
+ align:start position:0%
+structure we know what this is going to
+do so now a magnetic potential is equal
+
+ align:start position:0%
+do so now a magnetic potential is equal
+ 
+
+ align:start position:0%
+do so now a magnetic potential is equal
+to minus the magnetic moment times the
+
+ align:start position:0%
+to minus the magnetic moment times the
+ 
+
+ align:start position:0%
+to minus the magnetic moment times the
+external magnetic field and so what we
+
+ align:start position:0%
+external magnetic field and so what we
+ 
+
+ align:start position:0%
+external magnetic field and so what we
+have is e BC LZ
+
+ align:start position:0%
+have is e BC LZ
+ 
+
+ align:start position:0%
+have is e BC LZ
+over to me well this is another very
+
+ align:start position:0%
+over to me well this is another very
+ 
+
+ align:start position:0%
+over to me well this is another very
+good thing because not only do we know
+
+ align:start position:0%
+good thing because not only do we know
+ 
+
+ align:start position:0%
+good thing because not only do we know
+what this is we know that it has only
+
+ align:start position:0%
+what this is we know that it has only
+ 
+
+ align:start position:0%
+what this is we know that it has only
+diagonal elements and so we can do first
+
+ align:start position:0%
+diagonal elements and so we can do first
+ 
+
+ align:start position:0%
+diagonal elements and so we can do first
+order perturbation theory this is so
+
+ align:start position:0%
+order perturbation theory this is so
+ 
+
+ align:start position:0%
+order perturbation theory this is so
+easy this if this is the Hamiltonian we
+
+ align:start position:0%
+easy this if this is the Hamiltonian we
+ 
+
+ align:start position:0%
+easy this if this is the Hamiltonian we
+can just tack that on and it adds an
+
+ align:start position:0%
+can just tack that on and it adds an
+ 
+
+ align:start position:0%
+can just tack that on and it adds an
+extra splitting to our energy levels the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only tricky thing is we don't know that
+
+ align:start position:0%
+only tricky thing is we don't know that
+ 
+
+ align:start position:0%
+only tricky thing is we don't know that
+it's LZ we just know that it has a
+
+ align:start position:0%
+it's LZ we just know that it has a
+ 
+
+ align:start position:0%
+it's LZ we just know that it has a
+magnetic moment or could have a magnetic
+
+ align:start position:0%
+magnetic moment or could have a magnetic
+ 
+
+ align:start position:0%
+magnetic moment or could have a magnetic
+net magnetic moment okay and so this
+
+ align:start position:0%
+net magnetic moment okay and so this
+ 
+
+ align:start position:0%
+net magnetic moment okay and so this
+wonderful experiment suppose you start
+
+ align:start position:0%
+wonderful experiment suppose you start
+ 
+
+ align:start position:0%
+wonderful experiment suppose you start
+with a 1s state and you go to a 2p State
+
+ align:start position:0%
+with a 1s state and you go to a 2p State
+ 
+
+ align:start position:0%
+with a 1s state and you go to a 2p State
+now this is the this implies that we
+
+ align:start position:0%
+now this is the this implies that we
+ 
+
+ align:start position:0%
+now this is the this implies that we
+know something about the selection rules
+
+ align:start position:0%
+know something about the selection rules
+ 
+
+ align:start position:0%
+know something about the selection rules
+for electromagnetic transitions and so
+
+ align:start position:0%
+for electromagnetic transitions and so
+ 
+
+ align:start position:0%
+for electromagnetic transitions and so
+for an electric dipole transition we go
+
+ align:start position:0%
+for an electric dipole transition we go
+ 
+
+ align:start position:0%
+for an electric dipole transition we go
+from s 1 s 2 2 P now this is not how it
+
+ align:start position:0%
+from s 1 s 2 2 P now this is not how it
+ 
+
+ align:start position:0%
+from s 1 s 2 2 P now this is not how it
+was done initially because that was this
+
+ align:start position:0%
+was done initially because that was this
+ 
+
+ align:start position:0%
+was done initially because that was this
+the frequency of this transition is well
+
+ align:start position:0%
+the frequency of this transition is well
+ 
+
+ align:start position:0%
+the frequency of this transition is well
+into the vacuum ultraviolet and then in
+
+ align:start position:0%
+into the vacuum ultraviolet and then in
+ 
+
+ align:start position:0%
+into the vacuum ultraviolet and then in
+the days when quantum mechanics was
+
+ align:start position:0%
+the days when quantum mechanics was
+ 
+
+ align:start position:0%
+the days when quantum mechanics was
+being developed that was a hard
+
+ align:start position:0%
+being developed that was a hard
+ 
+
+ align:start position:0%
+being developed that was a hard
+experiment so one used an s to P
+
+ align:start position:0%
+experiment so one used an s to P
+ 
+
+ align:start position:0%
+experiment so one used an s to P
+transition on some other atom like
+
+ align:start position:0%
+transition on some other atom like
+ 
+
+ align:start position:0%
+transition on some other atom like
+mercury but let's pretend it was
+
+ align:start position:0%
+mercury but let's pretend it was
+ 
+
+ align:start position:0%
+mercury but let's pretend it was
+hydrogen so this is an angular momentum
+
+ align:start position:0%
+hydrogen so this is an angular momentum
+ 
+
+ align:start position:0%
+hydrogen so this is an angular momentum
+of 0 so we would expect it would be ml
+
+ align:start position:0%
+of 0 so we would expect it would be ml
+ 
+
+ align:start position:0%
+of 0 so we would expect it would be ml
+equals 0 and here we have it could split
+
+ align:start position:0%
+equals 0 and here we have it could split
+ 
+
+ align:start position:0%
+equals 0 and here we have it could split
+into three components and this is ml
+
+ align:start position:0%
+into three components and this is ml
+ 
+
+ align:start position:0%
+into three components and this is ml
+equals 1 0 and minus 1 because this
+
+ align:start position:0%
+equals 1 0 and minus 1 because this
+ 
+
+ align:start position:0%
+equals 1 0 and minus 1 because this
+minus minus sign there was a minus sign
+
+ align:start position:0%
+minus minus sign there was a minus sign
+ 
+
+ align:start position:0%
+minus minus sign there was a minus sign
+somewhere anyway that's what we expect
+
+ align:start position:0%
+somewhere anyway that's what we expect
+ 
+
+ align:start position:0%
+somewhere anyway that's what we expect
+and so being naive
+
+ align:start position:0%
+and so being naive
+ 
+
+ align:start position:0%
+and so being naive
+you might expect transitions like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the transitions where you do not
+
+ align:start position:0%
+well the transitions where you do not
+ 
+
+ align:start position:0%
+well the transitions where you do not
+change the projection quantum number are
+
+ align:start position:0%
+change the projection quantum number are
+ 
+
+ align:start position:0%
+change the projection quantum number are
+done with Z polarized radiation and so
+
+ align:start position:0%
+done with Z polarized radiation and so
+ 
+
+ align:start position:0%
+done with Z polarized radiation and so
+if it's Z polarize you get only Delta M
+
+ align:start position:0%
+if it's Z polarize you get only Delta M
+ 
+
+ align:start position:0%
+if it's Z polarize you get only Delta M
+L equals zero and if you're back some
+
+ align:start position:0%
+L equals zero and if you're back some
+ 
+
+ align:start position:0%
+L equals zero and if you're back some
+wine you have Delta ml equals plus minus
+
+ align:start position:0%
+wine you have Delta ml equals plus minus
+ 
+
+ align:start position:0%
+wine you have Delta ml equals plus minus
+one so depending on how the experiment
+
+ align:start position:0%
+one so depending on how the experiment
+ 
+
+ align:start position:0%
+one so depending on how the experiment
+was done you would expect to see one two
+
+ align:start position:0%
+was done you would expect to see one two
+ 
+
+ align:start position:0%
+was done you would expect to see one two
+or three is a mod components and they
+
+ align:start position:0%
+or three is a mod components and they
+ 
+
+ align:start position:0%
+or three is a mod components and they
+did the experiment and they saw more
+
+ align:start position:0%
+did the experiment and they saw more
+ 
+
+ align:start position:0%
+did the experiment and they saw more
+than three components they saw five
+
+ align:start position:0%
+than three components they saw five
+ 
+
+ align:start position:0%
+than three components they saw five
+components and that's puzzling for a
+
+ align:start position:0%
+components and that's puzzling for a
+ 
+
+ align:start position:0%
+components and that's puzzling for a
+number of reasons but they saw five
+
+ align:start position:0%
+number of reasons but they saw five
+ 
+
+ align:start position:0%
+number of reasons but they saw five
+components so they knew that there was
+
+ align:start position:0%
+components so they knew that there was
+ 
+
+ align:start position:0%
+components so they knew that there was
+something else going on and so you have
+
+ align:start position:0%
+something else going on and so you have
+ 
+
+ align:start position:0%
+something else going on and so you have
+to try to collect enough information to
+
+ align:start position:0%
+to try to collect enough information to
+ 
+
+ align:start position:0%
+to try to collect enough information to
+have a simple-minded picture that will
+
+ align:start position:0%
+have a simple-minded picture that will
+ 
+
+ align:start position:0%
+have a simple-minded picture that will
+will explain it all so one thing you
+
+ align:start position:0%
+will explain it all so one thing you
+ 
+
+ align:start position:0%
+will explain it all so one thing you
+might do is say okay suppose there is
+
+ align:start position:0%
+might do is say okay suppose there is
+ 
+
+ align:start position:0%
+might do is say okay suppose there is
+another quantum number another thing and
+
+ align:start position:0%
+another quantum number another thing and
+ 
+
+ align:start position:0%
+another quantum number another thing and
+we're going to call it spin and we don't
+
+ align:start position:0%
+we're going to call it spin and we don't
+ 
+
+ align:start position:0%
+we're going to call it spin and we don't
+know whether spin is integer or half
+
+ align:start position:0%
+know whether spin is integer or half
+ 
+
+ align:start position:0%
+know whether spin is integer or half
+integer we know from our exercise with
+
+ align:start position:0%
+integer we know from our exercise with
+ 
+
+ align:start position:0%
+integer we know from our exercise with
+commutation rules that both half integer
+
+ align:start position:0%
+commutation rules that both half integer
+ 
+
+ align:start position:0%
+commutation rules that both half integer
+and integer angular momenta are possible
+
+ align:start position:0%
+and integer angular momenta are possible
+ 
+
+ align:start position:0%
+and integer angular momenta are possible
+and so we can say we have a spin and it
+
+ align:start position:0%
+and so we can say we have a spin and it
+ 
+
+ align:start position:0%
+and so we can say we have a spin and it
+could be one half it could be one it
+
+ align:start position:0%
+could be one half it could be one it
+ 
+
+ align:start position:0%
+could be one half it could be one it
+could be anything and then we start
+
+ align:start position:0%
+could be anything and then we start
+ 
+
+ align:start position:0%
+could be anything and then we start
+looking at the details of what we
+
+ align:start position:0%
+looking at the details of what we
+ 
+
+ align:start position:0%
+looking at the details of what we
+observe and what we find is all we need
+
+ align:start position:0%
+observe and what we find is all we need
+ 
+
+ align:start position:0%
+observe and what we find is all we need
+to spin 1/2 to account for almost
+
+ align:start position:0%
+to spin 1/2 to account for almost
+ 
+
+ align:start position:0%
+to spin 1/2 to account for almost
+everything however if it were spend 1/2
+
+ align:start position:0%
+everything however if it were spend 1/2
+ 
+
+ align:start position:0%
+everything however if it were spend 1/2
+then you get to here and you get you'd
+
+ align:start position:0%
+then you get to here and you get you'd
+ 
+
+ align:start position:0%
+then you get to here and you get you'd
+get to here to here and to here and
+
+ align:start position:0%
+get to here to here and to here and
+ 
+
+ align:start position:0%
+get to here to here and to here and
+six that's bigger than five so you need
+
+ align:start position:0%
+six that's bigger than five so you need
+ 
+
+ align:start position:0%
+six that's bigger than five so you need
+to know something else
+
+ align:start position:0%
+to know something else
+ 
+
+ align:start position:0%
+to know something else
+and one thing is quite reasonable you
+
+ align:start position:0%
+and one thing is quite reasonable you
+ 
+
+ align:start position:0%
+and one thing is quite reasonable you
+can say well the spin thing is
+
+ align:start position:0%
+can say well the spin thing is
+ 
+
+ align:start position:0%
+can say well the spin thing is
+mysterious and electromagnetic radiation
+
+ align:start position:0%
+mysterious and electromagnetic radiation
+ 
+
+ align:start position:0%
+mysterious and electromagnetic radiation
+acts on the spatial coordinates and
+
+ align:start position:0%
+acts on the spatial coordinates and
+ 
+
+ align:start position:0%
+acts on the spatial coordinates and
+there aren't any spatial coordinates of
+
+ align:start position:0%
+there aren't any spatial coordinates of
+ 
+
+ align:start position:0%
+there aren't any spatial coordinates of
+the internal structure of the electron
+
+ align:start position:0%
+the internal structure of the electron
+ 
+
+ align:start position:0%
+the internal structure of the electron
+and so we have a selection rule Delta M
+
+ align:start position:0%
+and so we have a selection rule Delta M
+ 
+
+ align:start position:0%
+and so we have a selection rule Delta M
+s equals zero that still doesn't do it
+
+ align:start position:0%
+s equals zero that still doesn't do it
+ 
+
+ align:start position:0%
+s equals zero that still doesn't do it
+you still need something else and that
+
+ align:start position:0%
+you still need something else and that
+ 
+
+ align:start position:0%
+you still need something else and that
+is that the proportionality constant
+
+ align:start position:0%
+is that the proportionality constant
+ 
+
+ align:start position:0%
+is that the proportionality constant
+between the angular momentum and the
+
+ align:start position:0%
+between the angular momentum and the
+ 
+
+ align:start position:0%
+between the angular momentum and the
+energy which is called the G factor for
+
+ align:start position:0%
+energy which is called the G factor for
+ 
+
+ align:start position:0%
+energy which is called the G factor for
+for any orbital angular momentum the G
+
+ align:start position:0%
+for any orbital angular momentum the G
+ 
+
+ align:start position:0%
+for any orbital angular momentum the G
+factor is one or the proportionality
+
+ align:start position:0%
+factor is one or the proportionality
+ 
+
+ align:start position:0%
+factor is one or the proportionality
+constant is one so the G factor is L and
+
+ align:start position:0%
+constant is one so the G factor is L and
+ 
+
+ align:start position:0%
+constant is one so the G factor is L and
+the G factor for the electron turns out
+
+ align:start position:0%
+the G factor for the electron turns out
+ 
+
+ align:start position:0%
+the G factor for the electron turns out
+to be - not exactly - just a little more
+
+ align:start position:0%
+to be - not exactly - just a little more
+ 
+
+ align:start position:0%
+to be - not exactly - just a little more
+than two Nobel Prize for that and and so
+
+ align:start position:0%
+than two Nobel Prize for that and and so
+ 
+
+ align:start position:0%
+than two Nobel Prize for that and and so
+with those extra little things then
+
+ align:start position:0%
+with those extra little things then
+ 
+
+ align:start position:0%
+with those extra little things then
+every detail of the same on effect is
+
+ align:start position:0%
+every detail of the same on effect is
+ 
+
+ align:start position:0%
+every detail of the same on effect is
+understood and we say oh the electron
+
+ align:start position:0%
+understood and we say oh the electron
+ 
+
+ align:start position:0%
+understood and we say oh the electron
+has a spin of 1/2 and it like it acts
+
+ align:start position:0%
+has a spin of 1/2 and it like it acts
+ 
+
+ align:start position:0%
+has a spin of 1/2 and it like it acts
+like an angular matter it obeys the
+
+ align:start position:0%
+like an angular matter it obeys the
+ 
+
+ align:start position:0%
+like an angular matter it obeys the
+angular momentum commutation rules it
+
+ align:start position:0%
+angular momentum commutation rules it
+ 
+
+ align:start position:0%
+angular momentum commutation rules it
+also obeys the commutation rules I won't
+
+ align:start position:0%
+also obeys the commutation rules I won't
+ 
+
+ align:start position:0%
+also obeys the commutation rules I won't
+say that ok so I should stop there are
+
+ align:start position:0%
+say that ok so I should stop there are
+ 
+
+ align:start position:0%
+say that ok so I should stop there are
+other things that provide us information
+
+ align:start position:0%
+other things that provide us information
+ 
+
+ align:start position:0%
+other things that provide us information
+that there is something else and one I'm
+
+ align:start position:0%
+that there is something else and one I'm
+ 
+
+ align:start position:0%
+that there is something else and one I'm
+I'm called by some people the spin orbit
+
+ align:start position:0%
+I'm called by some people the spin orbit
+ 
+
+ align:start position:0%
+I'm called by some people the spin orbit
+kid because I've made a whole lot of
+
+ align:start position:0%
+kid because I've made a whole lot of
+ 
+
+ align:start position:0%
+kid because I've made a whole lot of
+mileage on using spin orbit splittings
+
+ align:start position:0%
+mileage on using spin orbit splittings
+ 
+
+ align:start position:0%
+mileage on using spin orbit splittings
+and the spin orbit Hamiltonian has the
+
+ align:start position:0%
+and the spin orbit Hamiltonian has the
+ 
+
+ align:start position:0%
+and the spin orbit Hamiltonian has the
+form l dot s and this gives rise to
+
+ align:start position:0%
+form l dot s and this gives rise to
+ 
+
+ align:start position:0%
+form l dot s and this gives rise to
+splittings of a doublet P state for
+
+ align:start position:0%
+splittings of a doublet P state for
+ 
+
+ align:start position:0%
+splittings of a doublet P state for
+example as what you would see in the
+
+ align:start position:0%
+example as what you would see in the
+ 
+
+ align:start position:0%
+example as what you would see in the
+excited state of hydrogen into two
+
+ align:start position:0%
+excited state of hydrogen into two
+ 
+
+ align:start position:0%
+excited state of hydrogen into two
+components at zero field
+
+ align:start position:0%
+components at zero field
+ 
+
+ align:start position:0%
+components at zero field
+and so there's all sorts of really
+
+ align:start position:0%
+and so there's all sorts of really
+ 
+
+ align:start position:0%
+and so there's all sorts of really
+wonderful stuff and I'm going to cheat
+
+ align:start position:0%
+wonderful stuff and I'm going to cheat
+ 
+
+ align:start position:0%
+wonderful stuff and I'm going to cheat
+you out of almost all of it because
+
+ align:start position:0%
+you out of almost all of it because
+ 
+
+ align:start position:0%
+you out of almost all of it because
+we're going to go over to the
+
+ align:start position:0%
+we're going to go over to the
+ 
+
+ align:start position:0%
+we're going to go over to the
+semi-classical picture next time and
+
+ align:start position:0%
+semi-classical picture next time and
+ 
+
+ align:start position:0%
+semi-classical picture next time and
+we'll understand everything about rid
+
+ align:start position:0%
+we'll understand everything about rid
+ 
+
+ align:start position:0%
+we'll understand everything about rid
+Berk States and about how do we how do
+
+ align:start position:0%
+Berk States and about how do we how do
+ 
+
+ align:start position:0%
+Berk States and about how do we how do
+we estimate everything having to do with
+
+ align:start position:0%
+we estimate everything having to do with
+ 
+
+ align:start position:0%
+we estimate everything having to do with
+the radial part of the wave function and
+
+ align:start position:0%
+the radial part of the wave function and
+ 
+
+ align:start position:0%
+the radial part of the wave function and
+there are some astonishing things okay
\ No newline at end of file
diff --git a/A6Ud6oUCRak.txt b/A6Ud6oUCRak.txt
new file mode 100644
index 0000000000000000000000000000000000000000..704f19700a1fb43b4712961ce0fa052061c5aa08
--- /dev/null
+++ b/A6Ud6oUCRak.txt
@@ -0,0 +1,2186 @@
+PATRICK WINSTON: Here we are,
+down to the final sprint.
+
+Three to go.
+
+And we're going to take some of
+the last three, maybe two
+
+of the last three, to talk a
+little bit about stuff having
+
+to do with probabilistic
+approaches--
+
+use of probability in artificial
+intelligence.
+
+Now, for many of you, this
+will be kind of a review,
+
+because I know many of you
+learned about probability over
+
+the [? sand ?] table and
+every year since then.
+
+But maybe we'll put another
+little twist into it,
+
+especially toward the end of
+the hour when we get into a
+
+discussion of that which has
+come to be called belief nets.
+
+But first, I was driving in this
+morning, and I was quite
+
+astonished to see, as I drove
+in, this thing here.
+
+And my first reaction was, oh
+my god, it's the world's
+
+greatest hack.
+
+And then I decided, well, maybe
+it's a piece of art.
+
+So I'd like to address the
+question of how I could come
+
+to grips with that issue.
+
+There's a distinct possibility
+that this thing is a
+
+consequence of a hat, possibly
+the result of
+
+some kind of art show.
+
+And in any event, some sort of
+statue appeared, and statues
+
+don't usually appear
+like that.
+
+So I got the possibility of
+thinking about how all these
+
+things might occur together
+or not occur together.
+
+So the natural thing is to
+build myself some sort of
+
+table to keep track of
+my observations.
+
+So I have three columns
+in my table.
+
+I've got the possibility of
+a statue appearing, a hack
+
+having occurred, and some
+sort of art show.
+
+And so I can make a table of all
+the combinations of those
+
+things that might appear.
+
+And I happen to have already
+guessed that there are going
+
+to be eight rows in my table.
+
+So it's going to
+look like this.
+
+And this is the set of
+combinations in this row where
+
+none of that occurs at all.
+
+And down here is the situation
+where all of
+
+those things occur.
+
+After all, it's possible that
+we can have an art show and
+
+have a hack be a legitimate
+participant in the art show.
+
+That's why we have
+that final row.
+
+So we have all manner of
+combinations in between.
+
+So those are those
+combinations.
+
+Then we have F, F, T, T, F, F,
+T, T, F, T, F, T, F, T, F, T.
+
+So it's plain that the number of
+rows in the table, or these
+
+binary possibilities, is 2 to
+the number of variables.
+
+And that could be
+a big number.
+
+In fact, I'd love to do a bigger
+example, but I don't
+
+have the patience to do it.
+
+But anyhow, what we might do is
+in order to figure out how
+
+likely any of these combinations
+are, is we might
+
+have observed the area outside
+the student center and rest of
+
+campus over a long period of
+time and keep track of what
+
+happens on 1,000 days.
+
+Or maybe 1,000 months
+or 1,000 years.
+
+I don't know.
+
+The trouble is, these events
+don't happen very often.
+
+So the period of time that I use
+for measurement needs to
+
+be fairly long.
+
+Probably a day is not
+short enough.
+
+But in any case, I can keep a
+tally of how often I see these
+
+various combinations.
+
+So this one might be, for
+example, 405, this one might
+
+be 45, this one might be
+225, this one might
+
+be 40, and so on.
+
+And so having done all those
+measurements, kept track of
+
+all that data, then I could
+say, well, the probability
+
+that at any given time period
+one of these things occurs
+
+will just be the frequency--
+
+the number of tallies
+divided by the
+
+total number of tallies.
+
+So that would be a number
+between 0 and 1.
+
+So that's the probability for
+each of these events.
+
+And it's readily calculated
+from my data.
+
+And once I do that, then I can
+say that I got myself a joint
+
+probability table, and I could
+perform all manner of miracles
+
+using that joint probability
+table.
+
+So let me perform a few
+of those miracles,
+
+while we're at it.
+
+There's the table.
+
+And now, what I want to do
+is I want to count up the
+
+probability in all the rows
+where the statue appears.
+
+So that's going to be
+the probability
+
+of the statue appearing.
+
+So I'll just check off those
+four boxes there.
+
+And it looks like the
+probability of the statue
+
+appearing is about 0.355
+in my model.
+
+I don't think it's quite that
+frequent, but this is a
+
+classroom exercise, right?
+
+So I can make up whatever
+numbers I want.
+
+Now, I could say, well, what's
+the probability of a statue
+
+occurring given that there's
+an art show?
+
+Well, I can limit my tallies to
+those in which art show is
+
+true, like so.
+
+And in that case,
+the probability
+
+has just zoomed up.
+
+So if I know there's an art
+show, there's a much higher
+
+probability that a statue
+will appear.
+
+And if I know there's a hack as
+well as an art show going
+
+on, it goes up higher
+still to 0.9.
+
+We can also do other
+kinds of things.
+
+For example, we can go back
+to the original table.
+
+And instead of counting up the
+probability we've got a
+
+statue, as we just did, we're
+going to calculate the
+
+probability that there
+is an art show.
+
+I guess that would be that one
+and that one, not that one,
+
+but that one.
+
+So the probability there's an
+art show is one chance in 10.
+
+Or we can do the same
+thing with a hack.
+
+In that case, we get that one
+off, that one on, that one
+
+off, that one on, that
+one off, that one
+
+on, that one off.
+
+So the probability of a hack
+on any given time period is
+
+about 50-50.
+
+So I've cooked up this little
+demo so it does the "ands" of
+
+all these things.
+
+It could do "ors," too, with
+a little more work.
+
+But these are just the "ands" of
+these various combinations.
+
+Then you can ask more
+complicated questions, like
+
+for example, you could say, what
+is the probability of a
+
+hack given that there's
+a statue?
+
+And that would be limiting the
+calculations to those rows in
+
+which the statue
+thing is true.
+
+And then what I get is 0.781.
+
+Now, what would happen to the
+probability that it's a hack
+
+if I know that there's
+an art show?
+
+Will that number
+go up or down?
+
+Well, let's try it.
+
+Ah, it went down.
+
+So that's sort of because the
+existence of the art show sort
+
+of explains why the statue
+might be there.
+
+Now, just for fun, I'm going
+to switch to another
+
+situation, very similar.
+
+And the situation here is that
+a neighbor's dog often barks.
+
+It might be because
+of a burglar.
+
+It might be because
+of a raccoon.
+
+Sometimes, there's a burglar
+and a raccoon.
+
+Sometimes, the damn
+dog just barks.
+
+So let's do some calculations
+there and calculate the
+
+probability that a raccoon
+is true, similar to
+
+what we did last time.
+
+Looks like on any
+given night--
+
+it's kind of a wooded are--
+there's a high probability of
+
+a raccoon showing up.
+
+And then we can ask, well, what
+is the probability of the
+
+dog barking given that
+a raccoon shows up?
+
+Well, in that case, we want to
+just limit the number of rows
+
+to those where a raccoon--
+
+or where the dog is barking.
+
+Looks like the probability of
+the dog barking, knowing
+
+nothing else, is about
+[? 3/7. ?]
+
+But now we want to know the
+probability of the raccoon--
+
+that's these guys here
+need to get checked.
+
+These are off.
+
+So that's the probability
+of a raccoon.
+
+Did I get that right?
+
+Oh, that's probability
+of a burglar.
+
+Sorry, that was too hard.
+
+So let me go back
+and calculate--
+
+I want to get the probability
+of a raccoon.
+
+That's true, false, true, false,
+true, false, true.
+
+So the probability of
+a raccoon, as I
+
+said before is 0.5.
+
+Now, what happens to that
+probability if I know the dog
+
+is barking?
+
+Well, all I need to do is limit
+my rows to those where
+
+the dog is barking,
+those bottom four.
+
+And I'll click that there, and
+you'll notice all these
+
+tallies up above the midpoint
+have gone to zero, because
+
+we're only considering
+those cases
+
+where the dog is barking.
+
+In that case, the probability
+that there's a raccoon--
+
+just the number of
+tallies over the
+
+total number of tallies--
+
+gee, I guess it's 225 plus
+50 divided by 370.
+
+That turns out to be 0.743.
+
+So about 75% of the time, the
+dog barking is accounted for--
+
+well, the probability of a
+raccoon under those conditions
+
+is pretty high.
+
+And now, once again, I'm going
+to ask, well, what is the
+
+probability of a raccoon, given
+that the dog is barking
+
+and there's a burglar?
+
+Any guess what will
+happen there?
+
+We did this once before
+with the statue.
+
+Probability first went up when
+we saw the statue and then
+
+went down when we saw
+another explanation.
+
+Here's this one here.
+
+Wow, look at that.
+
+It went back to its original
+condition, its a priori
+
+probability.
+
+So somehow, the existence of
+the burglar and the dog
+
+barking means that the
+probability of a raccoon is
+
+just what it was before
+we started this game.
+
+So those are kind of interesting
+questions, and
+
+there's a lot we can do when we
+have this table by way of
+
+those kinds of calculations.
+
+And in fact, the whole miracle
+of probabilistic inference is
+
+right in front of us.
+
+It's the table.
+
+So why don't we go home?
+
+Well, because there's a little
+problem with this table--
+
+with these two tables that
+I've shown you by way of
+
+illustration.
+
+And the problem is that there
+are a lot of rows.
+
+And I had a hard time making
+up those numbers.
+
+I didn't have the patience to
+wait and make observations.
+
+That would take too long.
+
+So I had to kind of
+make some guesses.
+
+And I could kind of manage
+it with eight rows--
+
+those up there.
+
+I could put in some tallies.
+
+It wasn't that big of a deal.
+
+So I got myself all those
+eight numbers
+
+up there like that.
+
+And similarly, for the art show
+calculations, produced
+
+eight numbers.
+
+But what if I added something
+else to the mix?
+
+What if I added the
+day of the week or
+
+what I had for breakfast?
+
+Each of those things would
+double the number of rows of
+
+their binary variables.
+
+So if I have to consider 10
+influences all working
+
+together, then I'd have
+2 to the 10th.
+
+I'd have 1,000 numbers
+to deal with.
+
+And that would be hard.
+
+But if I had a joint probability
+table, then I can
+
+do these kinds of miracles.
+
+But Dave, if I could have this
+little projector now, please.
+
+I just want to emphasize that
+although we're talking about
+
+probabilistic inference, and
+it's a very powerful tool,
+
+it's not the only tool
+we need in our bag.
+
+Trouble with most ideas in
+artificial intelligence is
+
+that their hardcore proponents
+think that they're the only
+
+thing to do.
+
+And probabilistic inference
+has a role to play in
+
+developing a theory of
+human intelligence.
+
+And it certainly has a practical
+value, but it's not
+
+the only thing.
+
+And to illustrate that point,
+I'd like to imagine for a few
+
+moments that MIT were founded in
+1861 BC instead of 1861 AD.
+
+And if that were so, then it
+might be the case that there
+
+would be a research program
+on what floats.
+
+And this, of course, would be
+a problem in experimental
+
+physics, and we could imagine
+that those people back there
+
+in that early MIT would, being
+experimentally minded, try
+
+some things.
+
+Oh, I didn't know that's
+what happened.
+
+It looks like chalk floats.
+
+Here's a rock.
+
+No, it didn't float.
+
+Here's some money.
+
+Doesn't float.
+
+Here's a pencil.
+
+No, it doesn't float.
+
+Here's a pen.
+
+Here's a piece of tin foil
+I got from Kendra.
+
+That floats.
+
+That's a metal.
+
+The other stuff's metal, too.
+
+Now I'm really getting
+confused.
+
+Here's a little wad of paper.
+
+Here's a cell ph--
+no, actually,
+
+I've tried that before.
+
+They don't float.
+
+And they also don't work
+afterward, either.
+
+I don't need to do any of that
+in the MIT of 1861 AD and
+
+beyond, because I know
+that Archimedes
+
+worked this all out.
+
+And all I have to do is measure
+the volume of the
+
+stuff, divide that by the
+weight, and if that ratio is
+
+big enough, then the
+thing will float.
+
+But back in the old days, I
+would have to try a lot of
+
+stuff and make a big table,
+taking into account such
+
+factors as how hard it is, how
+big it is, how heavy it is,
+
+whether it's alive or not.
+
+Most things that are
+alive float.
+
+Some don't.
+
+Fish don't, for instance.
+
+So it would be foolhardy
+to do that.
+
+That's sort of a probabilistic
+inference.
+
+On the other hand, there are
+lots of things where I don't
+
+know all the stuff I need to
+know in order to make the
+
+calculation.
+
+I know all the stuff I need to
+know in order to decide if
+
+something floats, but not all
+the stuff I need to know in
+
+order, for example, to decide
+if the child of a Republican
+
+is likely to be a Republican.
+
+There are a lot of subtle
+influences there, and it is
+
+the case that the children of
+Republicans and the children
+
+of Democrats are more likely to
+share the political party
+
+of their parents.
+
+But I don't have any direct
+way of calculating whether
+
+that will be true or not.
+
+All I can do in that case is
+what I've done over here, is
+
+do some measurements, get some
+frequencies, take some
+
+snapshots of the way the world
+is and incorporate that into a
+
+set of probabilities that can
+help me determine if any given
+
+parent is a Republican, given
+that I've observed the voting
+
+behavior their children.
+
+So probability has a place,
+but it's not the
+
+only tool we need.
+
+And that is an important
+preamble to all the stuff
+
+we're going to do today.
+
+Now, we're really through,
+because this joint probability
+
+table is all that there is to
+it, except for the fact we
+
+can't either record all those
+numbers, and it becomes
+
+quickly a pain to
+guess at them.
+
+There are two ways to think
+about all this.
+
+We can think about these
+probabilities as probabilities
+
+that come out of looking
+at some data.
+
+That's a frequentist view
+of the probabilities.
+
+Or we could say, well, we can't
+do those measurements.
+
+So I can just make them up.
+
+That's sort of the subjective
+view of where these
+
+probabilities come from.
+
+And in some cases, some people
+like to talk about natural
+
+propensities, like in
+quantum mechanics.
+
+But for our purposes, we either
+make them up, or we do
+
+some tallying.
+
+Trouble is, we can't deal
+with this kind of table.
+
+So as a consequence of not being
+able to deal with this
+
+kind of table, a gigantic
+industry has emerged for
+
+dealing with probabilities
+without the need to work up
+
+this full table.
+
+And that's where we're
+going to go for
+
+the rest of the hour.
+
+And here's the path we're
+going to take.
+
+We're going to talk about some
+basic overview of basic
+
+probability.
+
+Then we're going to move
+ourselves step by step toward
+
+the so-called belief networks,
+which make it possible to make
+
+this a practical tool.
+
+So let us begin.
+
+The first thing is basic
+probability.
+
+Let us say basic.
+
+And basic probability--
+
+all probability flows from
+a small number of axioms.
+
+We have the probability of some
+event a has got to be
+
+greater than 0 and
+less than 1.
+
+That's axiom number one.
+
+In a binary world, things have
+a probability of being true.
+
+Some have a probability
+of being false.
+
+But the true event doesn't have
+any possibility of being
+
+anything other than true, so
+the probability of true is
+
+equal to 1, and the probability
+of false--
+
+the false event, the
+false condition--
+
+has no possibility of being
+true, so that's 0.
+
+Then the third of the axioms
+of probability is that the
+
+probability of a plus the
+probability of b minus the
+
+probability of a and
+b is equal to the
+
+probability of a or b.
+
+Yeah, that makes sense, right?
+
+I guess it would make more sense
+if I didn't switch my
+
+notation in midstream--
+
+a and b.
+
+So those are the axioms that
+mathematicians love to start
+
+up that way, and they can derive
+everything there is to
+
+derive from that.
+
+But I never can deal with
+stuff that way.
+
+I have to draw a picture and
+think of this stuff in a more
+
+intuitionist type of way.
+
+So that's the formal approach
+to dealing with probability,
+
+and it's mirrored by intuitions
+that have to do
+
+with discussions of spaces,
+like so, in which we have
+
+circles, or areas, representing
+a and b.
+
+And to keep my notation
+consistent,
+
+I'll make those lowercase.
+
+So you can think of those as
+spaces of all possible worlds
+
+in which these things
+might occur.
+
+Or you can think of them
+as sample spaces.
+
+But in any event, you associate
+with the probability
+
+of a the size of this area here
+relative to the total
+
+area in the rectangle--
+
+the universe.
+
+So the probability of a is the
+size of this circle divided by
+
+the size of this rectangle
+in this picture.
+
+So now all these axioms
+make sense.
+
+The probability that a is
+certain is just when that
+
+fills up the whole thing, and
+there's no other place for a
+
+sample to be, that means
+it has to be a.
+
+So that probability goes
+all the way up to 1.
+
+On the other hand, if the size
+of a is just an infinitesimal
+
+dot, then the chances of landing
+in that world is 0.
+
+That's the bound on
+the other end.
+
+So this--
+
+axiom number one-- makes
+sense in terms of that
+
+picture over there.
+
+Likewise, axiom number two.
+
+What about axiom number three?
+
+Does that make sense in terms
+of all this stuff?
+
+And the answer is, sure, because
+we can just look at
+
+those areas with a little
+bit of colored chalk.
+
+And so the probability of a
+is just this area here.
+
+The probability of b
+is this area here.
+
+And if we want to know the
+probability that we're in
+
+either a or b, then we just have
+to add up those areas.
+
+But when we add up those areas,
+this intersection part
+
+is added in twice.
+
+So we've got to subtract that
+off in order to make this
+
+thing make a rational equation,
+so that makes sense.
+
+And axiom three makes
+sense, just as
+
+axioms one and two did.
+
+So that's all there is
+to basic probability.
+
+And now you could do all sorts
+of algebra on that, and it's
+
+elegant, because it's like
+circuit theory or
+
+electromagnetism, because
+from a very
+
+small number of axioms--
+
+in this case three--
+
+you can build an elegant
+mathematical system.
+
+And that's what probability
+subjects do.
+
+But we're not going to go there,
+because we're sort of
+
+focused on getting down to a
+point where we can deal with
+
+that joint probability
+table that we
+
+currently can't deal with.
+
+So we're not going to go into
+a whole lot of algebra with
+
+these things.
+
+Just what we need in order to
+go through that network.
+
+So the next thing we need to
+deal with is conditional
+
+probability.
+
+And whereas those are axioms,
+this is a definition.
+
+We say that the probability of
+a given b is equal to, by
+
+definition, the probability
+of a and b.
+
+I'm using that common notation
+to mean [INAUDIBLE]
+
+as is conventional
+in the field.
+
+And then we're going to divide
+that by the probability of B.
+
+You can take that as a
+definition, and then it's just
+
+a little bit of mysterious
+algebra.
+
+Or you could do like we did up
+there and take an intuitionist
+
+approach and ask what that
+stuff means in terms of a
+
+circle diagram and some
+sort of space.
+
+And let's see, what
+does that mean?
+
+It means that we're trying to
+restrict the probability of a
+
+to those circumstances where
+b is known to be so.
+
+And we're going to say that--
+
+we've got this part here,
+and then we've got the
+
+intersection of a with b.
+
+And so it does make sense as a
+definition, because it says
+
+that if you've got b, then the
+probability that you're going
+
+to get a is the size of
+that intersection--
+
+the pink and orange stuff--
+
+divided by the whole of b.
+
+So it's as if we restricted the
+universe of consideration
+
+to just that part of the
+original universe
+
+as covered by b.
+
+So that makes sense
+as a definition.
+
+And we can rewrite that, of
+course, as P of a and b is
+
+equal to the probability
+of a given b times the
+
+probability of b.
+
+That's all basic stuff.
+
+Now, we do want to do a little
+bit of algebra here, because I
+
+want to consider not just two
+cases, but what if we divide
+
+this space up into
+three parts?
+
+Then we'll say that the
+probability of a, b, and c is
+
+equal to what?
+
+Well, there are lots of ways
+to think about that.
+
+But one way to think about it is
+that we are restricting the
+
+universe to that part
+of the world where b
+
+and c are both true.
+
+So let's say that y is
+equal to b and c--
+
+the intersection of b and c,
+where a and b are both true.
+
+Then we can use this formula
+over here to say that
+
+probability of a, b, and c is
+equal to the probability of a
+
+and y, which is equal to the
+probability of a given y times
+
+the probability of y.
+
+And then we can expand that back
+out and say that P of a
+
+given b and c is equal
+to the probability--
+
+sorry, times the probability
+of y, but y is equal to the
+
+probability of b
+and c, like so.
+
+Ah, but wait--
+
+we can run this idea over that
+one, too, and we can say that
+
+this whole works is equal to the
+probability of a given b
+
+and c times the probability
+of b given c times the
+
+probability of c.
+
+And now, when we stand back and
+let that sing to us, we
+
+can see that some magic is
+beginning to happen here,
+
+because we've taken this
+probability of all things
+
+being so, and we've broken up
+into a product of three
+
+probabilities.
+
+The first two are conditional
+probabilities, so they're
+
+really all conditional
+probabilities.
+
+The last one's conditional
+on nothing.
+
+But look what happens as we
+go from left to right.
+
+a is dependent on two things.
+
+b is only dependent on one thing
+and nothing to the left.
+
+c is dependent on nothing
+and nothing to the left.
+
+So you can sense a
+generalization coming.
+
+So let's write it down.
+
+So let's go from here over
+to here and say that the
+
+probability of a whole
+bunch of things--
+
+x1 through x10--
+
+is equal to some product
+of probabilities.
+
+We'll let the index
+i run from n to 1.
+
+Probability of x to the last one
+in the series, conditioned
+
+on all the other ones--
+
+sorry, that's probability
+of i, i minus 1
+
+down to x1 like so.
+
+And for the first one in this
+product, i will be equal to n.
+
+For the second one, i will
+be equal to n minus 1.
+
+But you'll notice that as I
+go from n toward 1, these
+
+conditionals get smaller--
+
+the number of things on
+condition get smaller, and
+
+none of these things
+are on the left.
+
+They're only stuff that
+I have on the right.
+
+So what I mean to say is all of
+these things have an index
+
+that's smaller than
+this index.
+
+None of the ones that have a
+higher index are appearing in
+
+that conditional.
+
+So it's a way of taking a
+probability of the end of a
+
+whole bunch of things and
+writing it as a product of
+
+conditional probabilities.
+
+So we're making good progress.
+
+We've done one.
+
+We've done two.
+
+And now we've done three,
+because this
+
+is the chain rule.
+
+And we're about halfway through
+our diagram, halfway
+
+to the point where we can
+do something fun.
+
+But we still have a couple more
+concepts to deal with,
+
+and the next concept is the
+concept of conditional
+
+probability.
+
+So that's all this
+stuff up here--
+
+oops.
+
+All this stuff here is the
+definition of conditional
+
+probability.
+
+And now I want to go to the
+definition of independence.
+
+So that's another definitional
+deal.
+
+But it's another definitional
+deal that makes some sense
+
+with a diagram as well.
+
+So the definition
+goes like this.
+
+We say that P of a given b
+is equal to P of a if a
+
+independent of b.
+
+So that says that the
+probability of a doesn't
+
+depend on what's going
+on with b.
+
+It's the same either way.
+
+So it's independent.
+
+b doesn't matter.
+
+So what does that look like
+if we try to do an
+
+intuitionist diagram?
+
+Well, let's see.
+
+Here's a.
+
+Here's b.
+
+Now, the probability
+of a given b--
+
+well, let's see.
+
+That must be this part here
+divided by this part here.
+
+So the ratio of those areas is
+the probability of a given b.
+
+So that's the probability of
+this way divided by the
+
+probability of both ways.
+
+So what's the probability of
+a in terms of these areas?
+
+Well, probability of a in terms
+of these areas is the
+
+probability--
+
+let's see, have I
+got this right?
+
+I've got this upside down.
+
+The probability of a given b
+is the probability of the
+
+stuff in the intersection--
+
+so that's both ways--
+
+divided by the probability
+of the stuff in b, which
+
+is going this way.
+
+And let's see, the probability
+of a not conditioned on
+
+anything except being in this
+universe is all these hash
+
+marks, like so, divided
+by the universe.
+
+So when we say that something's
+independent, it
+
+means that those two ratios
+are the same.
+
+That's all it means in the
+intuitionist's point of view.
+
+So it says that this little
+area here divided by this
+
+whole area is the same as this
+whole area for a divided by
+
+the size of the universe.
+
+So that's what independence
+means.
+
+Now, that's quite
+a lot of work.
+
+But we're not done with
+independence, because we've
+
+got conditional independence
+to deal with.
+
+And that, too, can be viewed
+as a definition.
+
+And what we're going to say is
+that the probability of a
+
+given b and z is equal to the
+probability of a given z.
+
+What's that mean?
+
+That means that if you know
+that we're dealing with z,
+
+then the probability of
+a doesn't depend on b.
+
+b doesn't matter anymore
+once you're
+
+restricted to being in z.
+
+So you can look at
+that this way.
+
+Here's a, and here's
+b, and here is z.
+
+So what we're saying is that
+we're restricting the world to
+
+being in this part of the
+universe where z is.
+
+So the probability of a given b
+and z is this piece in here.
+
+a given b and z is
+that part there.
+
+And the probability of a given
+z is this part here
+
+divided by all of z.
+
+So we're saying that the ratio
+of this little piece here to
+
+this part, which I'll mark that
+way, ratio of this to
+
+this is the same as the
+ratio of that to that.
+
+So that's conditional
+independence.
+
+So you can infer from these
+things, with a little bit of
+
+algebra, that P of a and b given
+z is equal to P of a
+
+given z times P of b in z.
+
+Boy, that's been quite a
+journey, but we got all the
+
+way through one, two, three,
+four, and five.
+
+And now the next thing is belief
+nets, and I'm going to
+
+ask you to forget everything
+I've said for a minute or two.
+
+And we'll come back to it.
+
+I want to talk about the dog
+and the burglar and the
+
+raccoon again.
+
+And now, forgetting about
+probability, I can say, look,
+
+the dog barks if a
+raccoon shows up.
+
+The dog barks if a
+burglar shows up.
+
+A burglar doesn't show up
+because the dog is barking.
+
+A raccoon doesn't show up
+because the dog is barking.
+
+So the causality flows from the
+burglar and the raccoon to
+
+the barking.
+
+So we can make a diagram
+of that.
+
+And our diagram will
+look like this.
+
+Here is the burglar, and
+here is the raccoon.
+
+And these have causal relations
+to the dog barking.
+
+So that's an interesting idea,
+because now I can say that--
+
+well, I can't say anything yet,
+because I want to add a
+
+little more complexity to it.
+
+I'm going to add two
+more variables.
+
+You might call the police,
+depending on how vigorous the
+
+dog is barking, I guess.
+
+And the raccoon has a propensity
+to knocking over
+
+the trash can.
+
+So now, I've got
+five variables.
+
+How big a joint probability
+table am I going to need to
+
+keep my tallies straight?
+
+Well, it'll be 2 to the 5th.
+
+That's 32.
+
+But what I'm going to say is
+that this diagram is a
+
+statement, that every node in it
+depends on its parents and
+
+nothing else that's
+not a descendant.
+
+Now, I need to say that about
+50 times, because you've got
+
+to say it right.
+
+Every node there is independent
+of every
+
+non-descendant other
+then its parents.
+
+No, that's not quite right.
+
+Given its parents, every node
+is independent of all other
+
+non-descendants.
+
+Well, what does that mean?
+
+Here's the deal with
+calling the police.
+
+Here's its one and
+only parent.
+
+So given this parent, the
+probability that they were
+
+going to call the police doesn't
+depend on anything
+
+like B, R, or T. It's because
+all of the causality is
+
+flowing through this
+dog barking.
+
+I'm not going to call the
+police in a way that's
+
+dependent on anything else other
+than whether the dog is
+
+barking or not.
+
+Because this guy has this as
+a parent, and these are not
+
+descendants of calling the
+police, so this is independent
+
+of B, R, and T.
+
+So let's go walk through
+the others.
+
+Here's the dog.
+
+The dog's parents are burger
+
+appearing and raccoon appearing.
+
+So the probability that the dog
+appears is independent of
+
+that trash can over there,
+because that's not a
+
+descendant.
+
+It is dependent on
+these parents.
+
+How about the trash can?
+
+It depends only on
+the raccoon.
+
+It doesn't depend on any other
+non-descendant, so therefore,
+
+it doesn't depend on D,
+B, or P. How about B?
+
+It has no parents.
+
+So it depends on nothing else,
+because everything else is
+
+either a non-descendant, because
+B does not dependent
+
+on R and T, because they're
+not descendants.
+
+It's interesting that B might
+depend on D and P, because
+
+those are descendants.
+
+So it's important to understand
+that there's this
+
+business of independence given
+the parents of all other
+
+non-descendants.
+
+And you'll see why that funny,
+strange language is important
+
+in a minute.
+
+But now, let's see--
+
+I want to make a model of what's
+going to happen here.
+
+So let me see what kind of
+probabilities I'm going to
+
+have to figure out.
+
+This guy doesn't depend
+on anything upstream.
+
+So we could just say that
+all we need there is the
+
+probability that a burglar
+is going to appear.
+
+Let's say it's a fairly
+high-crime neighborhood--
+
+1 chance in 10--
+
+1 day in 10, a burglar
+appears.
+
+The raccoon doesn't depend on
+anything other than its own
+
+propensity, so its probability,
+
+we'll say, is 0.5.
+
+Raccoons love the place, so it
+shows up about 1 day in 2.
+
+So what about the dog barking?
+
+That depends on whether there's
+a burglar, and the
+
+other parent is whether
+there's a raccoon.
+
+So we need to keep track of the
+probability that the dog
+
+will bark for all four
+combinations.
+
+So this will be the burglar, and
+this will be the raccoon.
+
+This will be false, false,
+true, true--
+
+oops-- false, false,
+true, false,
+
+false, true, true, true.
+
+So let's say it's a wonderful
+dog, and it always barks if
+
+there's a burglar.
+
+So that would say that the
+probability here is 1.0, and
+
+the probability here is 1.0.
+
+And if there's neither a burglar
+nor a raccoon, the dog
+
+still likes to bark
+just for fun.
+
+So we'll say that's a
+chance of 1 in 10.
+
+And then in case there's a
+burglar, let's say this.
+
+There's no burglar, but
+there is a raccoon--
+
+he's tired of the raccoons, so
+he only barks half the time.
+
+Do these numbers, by the way,
+have to add up to 1?
+
+They clearly don't.
+
+These numbers don't
+add up to one.
+
+What adds up to 1 is this
+is the probability
+
+that the dog barks.
+
+And then the other phantom
+probability is out here.
+
+And these have to add up to 1.
+
+So that would be 0.9, that would
+be 0.0, that would be
+
+0.5, and this would be 0.0.
+
+So because those are just 1
+minus the numbers in these
+
+columns, I don't bother
+to write them down.
+
+Well, we still have a couple
+more things to do.
+
+The probability that we'll call
+the police depends only
+
+on the dog.
+
+So we'll have a column for the
+dog, and then we'll have a
+
+probability of calling
+the police.
+
+There's a probability for that
+being false and a probability
+
+for that being true.
+
+So if the dog doesn't bark,
+there's really hardly any
+
+chance we'll call the police.
+
+So make that 0, 0, 1.
+
+If the dog is barking, if he
+barks vigorously enough, maybe
+
+1 chance in 10.
+
+Here, we have the trash can--
+the final thing we have to
+
+think about.
+
+There's the trash can;
+rather, the raccoon.
+
+And here's the trash
+can probability.
+
+Depends on the raccoon being
+either present or not present.
+
+If the raccoon is not present,
+the probability the trash can
+
+is knocked over by, say,
+the wind is 1 in 1,000.
+
+If the raccoon is there, oh man,
+that guy always likes to
+
+go in there, so that's 0.8.
+
+So now I'm done specifying
+this model.
+
+And the question is, how many
+numbers did I have to specify?
+
+Well, let's see.
+
+I have to specify that one, that
+one, that one, that one,
+
+that one, that one-- that's
+6, 7, 8, 9, 10.
+
+So I had to specify
+10 numbers.
+
+If I just try to build myself
+a joint probability table
+
+straightaway, how many numbers
+would I have to supply?
+
+Well, it's 2 to the n.
+
+So it's 2 to the
+5th, that's 32.
+
+Considerable saving.
+
+By the way, how do you suppose
+I made that table?
+
+Not by doing all
+those numbers.
+
+By making this belief network
+and then using the belief
+
+network to calculate
+those numbers.
+
+And that's why this is a
+miracle, because with these
+
+numbers, I can calculate those
+numbers instead of making them
+
+up or making a whole lot of
+tally-type measurements.
+
+So I'd like to make sure
+that that's true.
+
+And I can use this stuff here
+to calculate the full joint
+
+probability table.
+
+So here's how this works.
+
+I have the probability
+of some combination--
+
+let's say the police, the dog,
+the burglar, the trash can,
+
+and the raccoon.
+
+All the combinations that are
+possible there will give me an
+
+entry in the table-- one row.
+
+But let's see--
+
+there's some miracle here.
+
+Oh, this chain rule.
+
+Let's use the chain rule.
+
+We can write that as a
+probability that we call the
+
+police given d, b, t, and r.
+
+And then the next one in my
+chain is probability of d
+
+given b, t, and r.
+
+Then the next one in the chain
+is the probability of
+
+b given t and r.
+
+And the next one in my chain
+is P of t given r.
+
+And the final one in
+my chain is p of r.
+
+Now, we have some conditional
+independence
+
+knowledge, too, don't we?
+
+We know that this probability
+here depends only on d because
+
+there are no descendants.
+
+So therefore, we don't have to
+think about that, and all the
+
+numbers we need here are
+produced by this table.
+
+How about this one here?
+
+Probability that the dog barks
+depends only on its parents, b
+
+and r, so it doesn't
+depend on t.
+
+So b, in turn, depends on--
+
+what does it depend on?
+
+It doesn't depend on anything.
+
+So we can scratch those.
+
+Probability of t given r, yeah,
+there's a probability
+
+there, but we can get
+that from the table.
+
+And finally, P or r.
+
+So that's why I went through
+all that probability junk,
+
+because if we arrange things in
+the expansion of this, from
+
+bottom to top, then we arrange
+things so that none of these
+
+guys depends on a descendant
+in this formula.
+
+And we have a limited number
+of things that it
+
+depends on above it.
+
+So that's the way we can
+calculate back the full joint
+
+probability table.
+
+And that brings us to the end
+of the discussion today.
+
+But the thing we're going to
+think about is, how much
+
+saving do we really
+get out of this?
+
+In this particular case, we
+only had to devise 10
+
+numbers out of 32.
+
+What if we had 10 properties
+or 100 properties?
+
+How much saving would
+we get then?
+
+That's what we'll take
+up next time,
+
+after the quiz on Wednesday.
\ No newline at end of file
diff --git a/Ayvwr28VKBk.txt b/Ayvwr28VKBk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..02262dba5c683c82889a9da2d89fadb56cee39bd
--- /dev/null
+++ b/Ayvwr28VKBk.txt
@@ -0,0 +1,14643 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's jump ahead here let me
+
+ align:start position:0%
+all right let's jump ahead here let me
+ 
+
+ align:start position:0%
+all right let's jump ahead here let me
+talk a little bit about manufacturing in
+
+ align:start position:0%
+talk a little bit about manufacturing in
+ 
+
+ align:start position:0%
+talk a little bit about manufacturing in
+general and the competitive challenged
+
+ align:start position:0%
+general and the competitive challenged
+ 
+
+ align:start position:0%
+general and the competitive challenged
+us manufacturers of the 1990s
+
+ align:start position:0%
+us manufacturers of the 1990s
+ 
+
+ align:start position:0%
+us manufacturers of the 1990s
+manufacturing moves 30% of US economic
+
+ align:start position:0%
+manufacturing moves 30% of US economic
+ 
+
+ align:start position:0%
+manufacturing moves 30% of US economic
+growth it had men fight ran two times
+
+ align:start position:0%
+growth it had men fight ran two times
+ 
+
+ align:start position:0%
+growth it had men fight ran two times
+the productivity level of the services
+
+ align:start position:0%
+the productivity level of the services
+ 
+
+ align:start position:0%
+the productivity level of the services
+so manufacture almost invariably has a
+
+ align:start position:0%
+so manufacture almost invariably has a
+ 
+
+ align:start position:0%
+so manufacture almost invariably has a
+much higher productivity level than a
+
+ align:start position:0%
+much higher productivity level than a
+ 
+
+ align:start position:0%
+much higher productivity level than a
+service us 80% services so if you really
+
+ align:start position:0%
+service us 80% services so if you really
+ 
+
+ align:start position:0%
+service us 80% services so if you really
+want a high productivity growth and a
+
+ align:start position:0%
+want a high productivity growth and a
+ 
+
+ align:start position:0%
+want a high productivity growth and a
+factory is a way of scaling who is an
+
+ align:start position:0%
+factory is a way of scaling who is an
+ 
+
+ align:start position:0%
+factory is a way of scaling who is an
+effect product quickly service sector
+
+ align:start position:0%
+effect product quickly service sector
+ 
+
+ align:start position:0%
+effect product quickly service sector
+scale much more slowly has little more
+
+ align:start position:0%
+scale much more slowly has little more
+ 
+
+ align:start position:0%
+scale much more slowly has little more
+face to face so you probably want a
+
+ align:start position:0%
+face to face so you probably want a
+ 
+
+ align:start position:0%
+face to face so you probably want a
+significant component of your economy in
+
+ align:start position:0%
+significant component of your economy in
+ 
+
+ align:start position:0%
+significant component of your economy in
+something that scales three and it
+
+ align:start position:0%
+something that scales three and it
+ 
+
+ align:start position:0%
+something that scales three and it
+introduces productivity effectively and
+
+ align:start position:0%
+introduces productivity effectively and
+ 
+
+ align:start position:0%
+introduces productivity effectively and
+that tends to be manufactured so
+
+ align:start position:0%
+that tends to be manufactured so
+ 
+
+ align:start position:0%
+that tends to be manufactured so
+manufacturing is also traditionally and
+
+ align:start position:0%
+manufacturing is also traditionally and
+ 
+
+ align:start position:0%
+manufacturing is also traditionally and
+I are paying jobs in 2001 there were 23
+
+ align:start position:0%
+I are paying jobs in 2001 there were 23
+ 
+
+ align:start position:0%
+I are paying jobs in 2001 there were 23
+percent higher than the services sector
+
+ align:start position:0%
+percent higher than the services sector
+ 
+
+ align:start position:0%
+percent higher than the services sector
+the ratio is not all that different
+
+ align:start position:0%
+the ratio is not all that different
+ 
+
+ align:start position:0%
+the ratio is not all that different
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+so it's manufacturing is an important
+
+ align:start position:0%
+so it's manufacturing is an important
+ 
+
+ align:start position:0%
+so it's manufacturing is an important
+part of you as it coming to be it's
+
+ align:start position:0%
+part of you as it coming to be it's
+ 
+
+ align:start position:0%
+part of you as it coming to be it's
+about 12% of GDP and it's it funds
+
+ align:start position:0%
+about 12% of GDP and it's it funds
+ 
+
+ align:start position:0%
+about 12% of GDP and it's it funds
+two-thirds industrial rd in funds
+
+ align:start position:0%
+two-thirds industrial rd in funds
+ 
+
+ align:start position:0%
+two-thirds industrial rd in funds
+three-quarters of industrial research
+
+ align:start position:0%
+three-quarters of industrial research
+ 
+
+ align:start position:0%
+three-quarters of industrial research
+development and about two-thirds of over
+
+ align:start position:0%
+development and about two-thirds of over
+ 
+
+ align:start position:0%
+development and about two-thirds of over
+you overall US army and manufacturing
+
+ align:start position:0%
+you overall US army and manufacturing
+ 
+
+ align:start position:0%
+you overall US army and manufacturing
+firms account for a greater percentage
+
+ align:start position:0%
+firms account for a greater percentage
+ 
+
+ align:start position:0%
+firms account for a greater percentage
+of real GDP than all these other kinds
+
+ align:start position:0%
+of real GDP than all these other kinds
+ 
+
+ align:start position:0%
+of real GDP than all these other kinds
+of cycles right so it remains a very
+
+ align:start position:0%
+of cycles right so it remains a very
+ 
+
+ align:start position:0%
+of cycles right so it remains a very
+significant player but it's also big
+
+ align:start position:0%
+significant player but it's also big
+ 
+
+ align:start position:0%
+significant player but it's also big
+enabler from the other sectors so
+
+ align:start position:0%
+enabler from the other sectors so
+ 
+
+ align:start position:0%
+enabler from the other sectors so
+manufacturing jobs and there's a lot of
+
+ align:start position:0%
+manufacturing jobs and there's a lot of
+ 
+
+ align:start position:0%
+manufacturing jobs and there's a lot of
+debate as to what the multiplier is a
+
+ align:start position:0%
+debate as to what the multiplier is a
+ 
+
+ align:start position:0%
+debate as to what the multiplier is a
+difference differs from sector to sector
+
+ align:start position:0%
+difference differs from sector to sector
+ 
+
+ align:start position:0%
+difference differs from sector to sector
+but it is the biggest job multiplying in
+
+ align:start position:0%
+but it is the biggest job multiplying in
+ 
+
+ align:start position:0%
+but it is the biggest job multiplying in
+our economy in other words a
+
+ align:start position:0%
+our economy in other words a
+ 
+
+ align:start position:0%
+our economy in other words a
+manufacturing job tends to create
+
+ align:start position:0%
+manufacturing job tends to create
+ 
+
+ align:start position:0%
+manufacturing job tends to create
+additional employment to be kind of
+
+ align:start position:0%
+additional employment to be kind of
+ 
+
+ align:start position:0%
+additional employment to be kind of
+value chains that is connected in a
+
+ align:start position:0%
+value chains that is connected in a
+ 
+
+ align:start position:0%
+value chains that is connected in a
+services sector and supplier sector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the US has been running frightening
+
+ align:start position:0%
+so the US has been running frightening
+ 
+
+ align:start position:0%
+so the US has been running frightening
+trade deficits in that effective goods
+
+ align:start position:0%
+trade deficits in that effective goods
+ 
+
+ align:start position:0%
+trade deficits in that effective goods
+for a significant period of time right
+
+ align:start position:0%
+for a significant period of time right
+ 
+
+ align:start position:0%
+for a significant period of time right
+and it began under President Nixon and
+
+ align:start position:0%
+and it began under President Nixon and
+ 
+
+ align:start position:0%
+and it began under President Nixon and
+has continued to grow since then the
+
+ align:start position:0%
+has continued to grow since then the
+ 
+
+ align:start position:0%
+has continued to grow since then the
+most problematic number is the trade
+
+ align:start position:0%
+most problematic number is the trade
+ 
+
+ align:start position:0%
+most problematic number is the trade
+deficit the US has in advanced
+
+ align:start position:0%
+deficit the US has in advanced
+ 
+
+ align:start position:0%
+deficit the US has in advanced
+manufacturing this no it's complete
+
+ align:start position:0%
+manufacturing this no it's complete
+ 
+
+ align:start position:0%
+manufacturing this no it's complete
+sight value goods the u.s. is running a
+
+ align:start position:0%
+sight value goods the u.s. is running a
+ 
+
+ align:start position:0%
+sight value goods the u.s. is running a
+hundred billion dollar trade deficit in
+
+ align:start position:0%
+hundred billion dollar trade deficit in
+ 
+
+ align:start position:0%
+hundred billion dollar trade deficit in
+those goods so the theory that weed seed
+
+ align:start position:0%
+those goods so the theory that weed seed
+ 
+
+ align:start position:0%
+those goods so the theory that weed seed
+low-end production but make it up by
+
+ align:start position:0%
+low-end production but make it up by
+ 
+
+ align:start position:0%
+low-end production but make it up by
+retaining I n production it's not
+
+ align:start position:0%
+retaining I n production it's not
+ 
+
+ align:start position:0%
+retaining I n production it's not
+working and manufacturing job loss you
+
+ align:start position:0%
+working and manufacturing job loss you
+ 
+
+ align:start position:0%
+working and manufacturing job loss you
+know has a pretty painful history 2.7
+
+ align:start position:0%
+know has a pretty painful history 2.7
+ 
+
+ align:start position:0%
+know has a pretty painful history 2.7
+million jobs were lost in that 2002-2003
+
+ align:start position:0%
+million jobs were lost in that 2002-2003
+ 
+
+ align:start position:0%
+million jobs were lost in that 2002-2003
+recession five point eight million jobs
+
+ align:start position:0%
+recession five point eight million jobs
+ 
+
+ align:start position:0%
+recession five point eight million jobs
+between 2000 2010 the majority of those
+
+ align:start position:0%
+between 2000 2010 the majority of those
+ 
+
+ align:start position:0%
+between 2000 2010 the majority of those
+focused on that 2008 recession in that
+
+ align:start position:0%
+focused on that 2008 recession in that
+ 
+
+ align:start position:0%
+focused on that 2008 recession in that
+2000 and 2010 timetable we shut down
+
+ align:start position:0%
+2000 and 2010 timetable we shut down
+ 
+
+ align:start position:0%
+2000 and 2010 timetable we shut down
+about 62,000 factories net the US has
+
+ align:start position:0%
+about 62,000 factories net the US has
+ 
+
+ align:start position:0%
+about 62,000 factories net the US has
+been moving its percentage of
+
+ align:start position:0%
+been moving its percentage of
+ 
+
+ align:start position:0%
+been moving its percentage of
+manufacturing employment ever downward
+
+ align:start position:0%
+manufacturing employment ever downward
+ 
+
+ align:start position:0%
+manufacturing employment ever downward
+so worried about 8 percent of US
+
+ align:start position:0%
+so worried about 8 percent of US
+ 
+
+ align:start position:0%
+so worried about 8 percent of US
+employment is the manufacturing sector
+
+ align:start position:0%
+employment is the manufacturing sector
+ 
+
+ align:start position:0%
+employment is the manufacturing sector
+other countries don't do that
+
+ align:start position:0%
+other countries don't do that
+ 
+
+ align:start position:0%
+other countries don't do that
+so Germany employs about 20 percent of
+
+ align:start position:0%
+so Germany employs about 20 percent of
+ 
+
+ align:start position:0%
+so Germany employs about 20 percent of
+its workforce in manufacturing Italy 19
+
+ align:start position:0%
+its workforce in manufacturing Italy 19
+ 
+
+ align:start position:0%
+its workforce in manufacturing Italy 19
+Japan 22 South Korea 31 in other words
+
+ align:start position:0%
+Japan 22 South Korea 31 in other words
+ 
+
+ align:start position:0%
+Japan 22 South Korea 31 in other words
+other country you know it's
+
+ align:start position:0%
+other country you know it's
+ 
+
+ align:start position:0%
+other country you know it's
+manufacturing as a source of higher
+
+ align:start position:0%
+manufacturing as a source of higher
+ 
+
+ align:start position:0%
+manufacturing as a source of higher
+wages and it's a job multiplier right
+
+ align:start position:0%
+wages and it's a job multiplier right
+ 
+
+ align:start position:0%
+wages and it's a job multiplier right
+you can kind of see some of the
+
+ align:start position:0%
+you can kind of see some of the
+ 
+
+ align:start position:0%
+you can kind of see some of the
+potential competitive advantages for
+
+ align:start position:0%
+potential competitive advantages for
+ 
+
+ align:start position:0%
+potential competitive advantages for
+retaining a substantial make sure the
+
+ align:start position:0%
+retaining a substantial make sure the
+ 
+
+ align:start position:0%
+retaining a substantial make sure the
+search so those are kind of background
+
+ align:start position:0%
+search so those are kind of background
+ 
+
+ align:start position:0%
+search so those are kind of background
+points let me do a couple of pieces now
+
+ align:start position:0%
+points let me do a couple of pieces now
+ 
+
+ align:start position:0%
+points let me do a couple of pieces now
+I'll do Glen long and Lynn sue Kim
+
+ align:start position:0%
+I'll do Glen long and Lynn sue Kim
+ 
+
+ align:start position:0%
+I'll do Glen long and Lynn sue Kim
+so when teaches at Thunderbird in
+
+ align:start position:0%
+so when teaches at Thunderbird in
+ 
+
+ align:start position:0%
+so when teaches at Thunderbird in
+Arizona
+
+ align:start position:0%
+Arizona
+ 
+
+ align:start position:0%
+Arizona
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+find school for International Business
+
+ align:start position:0%
+find school for International Business
+ 
+
+ align:start position:0%
+find school for International Business
+and he wrote a piece in 98 about what
+
+ align:start position:0%
+and he wrote a piece in 98 about what
+ 
+
+ align:start position:0%
+and he wrote a piece in 98 about what
+was happening in Japan so in that time
+
+ align:start position:0%
+was happening in Japan so in that time
+ 
+
+ align:start position:0%
+was happening in Japan so in that time
+so Japan is on a complete take off as a
+
+ align:start position:0%
+so Japan is on a complete take off as a
+ 
+
+ align:start position:0%
+so Japan is on a complete take off as a
+leading world economy until the 1990
+
+ align:start position:0%
+leading world economy until the 1990
+ 
+
+ align:start position:0%
+leading world economy until the 1990
+timeframe and then it misses the IT
+
+ align:start position:0%
+timeframe and then it misses the IT
+ 
+
+ align:start position:0%
+timeframe and then it misses the IT
+Innovation Lab as we discussed earlier
+
+ align:start position:0%
+Innovation Lab as we discussed earlier
+ 
+
+ align:start position:0%
+Innovation Lab as we discussed earlier
+and it starts to have to reorganize its
+
+ align:start position:0%
+and it starts to have to reorganize its
+ 
+
+ align:start position:0%
+and it starts to have to reorganize its
+and rethink its innovation system so
+
+ align:start position:0%
+and rethink its innovation system so
+ 
+
+ align:start position:0%
+and rethink its innovation system so
+Glenn argues that there were essentially
+
+ align:start position:0%
+Glenn argues that there were essentially
+ 
+
+ align:start position:0%
+Glenn argues that there were essentially
+three historical stages to contain
+
+ align:start position:0%
+three historical stages to contain
+ 
+
+ align:start position:0%
+three historical stages to contain
+japan's competitive pattern so first it
+
+ align:start position:0%
+japan's competitive pattern so first it
+ 
+
+ align:start position:0%
+japan's competitive pattern so first it
+was the pursuer after the plan here with
+
+ align:start position:0%
+was the pursuer after the plan here with
+ 
+
+ align:start position:0%
+was the pursuer after the plan here with
+us being the kind of innovation plan in
+
+ align:start position:0%
+us being the kind of innovation plan in
+ 
+
+ align:start position:0%
+us being the kind of innovation plan in
+there then it's a follower right at the
+
+ align:start position:0%
+there then it's a follower right at the
+ 
+
+ align:start position:0%
+there then it's a follower right at the
+frontier with us and then it becomes a
+
+ align:start position:0%
+frontier with us and then it becomes a
+ 
+
+ align:start position:0%
+frontier with us and then it becomes a
+world-class competitor and he argues
+
+ align:start position:0%
+world-class competitor and he argues
+ 
+
+ align:start position:0%
+world-class competitor and he argues
+that as Japan became a world-class
+
+ align:start position:0%
+that as Japan became a world-class
+ 
+
+ align:start position:0%
+that as Japan became a world-class
+competitor and had to rethink its more
+
+ align:start position:0%
+competitor and had to rethink its more
+ 
+
+ align:start position:0%
+competitor and had to rethink its more
+centralized organization with its
+
+ align:start position:0%
+centralized organization with its
+ 
+
+ align:start position:0%
+centralized organization with its
+innovations so the old thesis about
+
+ align:start position:0%
+innovations so the old thesis about
+ 
+
+ align:start position:0%
+innovations so the old thesis about
+Japan Glenn argues is that it was
+
+ align:start position:0%
+Japan Glenn argues is that it was
+ 
+
+ align:start position:0%
+Japan Glenn argues is that it was
+focused on national industrial
+
+ align:start position:0%
+focused on national industrial
+ 
+
+ align:start position:0%
+focused on national industrial
+performance and a corresponding
+
+ align:start position:0%
+performance and a corresponding
+ 
+
+ align:start position:0%
+performance and a corresponding
+competitive balance between nations
+
+ align:start position:0%
+competitive balance between nations
+ 
+
+ align:start position:0%
+competitive balance between nations
+based on national industrial components
+
+ align:start position:0%
+based on national industrial components
+ 
+
+ align:start position:0%
+based on national industrial components
+and it was set by you know political
+
+ align:start position:0%
+and it was set by you know political
+ 
+
+ align:start position:0%
+and it was set by you know political
+economies really operating at the
+
+ align:start position:0%
+economies really operating at the
+ 
+
+ align:start position:0%
+economies really operating at the
+national scale event at the governmental
+
+ align:start position:0%
+national scale event at the governmental
+ 
+
+ align:start position:0%
+national scale event at the governmental
+kind of Steel is strong governmental
+
+ align:start position:0%
+kind of Steel is strong governmental
+ 
+
+ align:start position:0%
+kind of Steel is strong governmental
+role but then a more pragmatic kind of
+
+ align:start position:0%
+role but then a more pragmatic kind of
+ 
+
+ align:start position:0%
+role but then a more pragmatic kind of
+approach matter of law so meaty which I
+
+ align:start position:0%
+approach matter of law so meaty which I
+ 
+
+ align:start position:0%
+approach matter of law so meaty which I
+mentioned earlier was the key organizing
+
+ align:start position:0%
+mentioned earlier was the key organizing
+ 
+
+ align:start position:0%
+mentioned earlier was the key organizing
+institution around getting collaboration
+
+ align:start position:0%
+institution around getting collaboration
+ 
+
+ align:start position:0%
+institution around getting collaboration
+from government industry and setting
+
+ align:start position:0%
+from government industry and setting
+ 
+
+ align:start position:0%
+from government industry and setting
+industry agendas in Japan in its older
+
+ align:start position:0%
+industry agendas in Japan in its older
+ 
+
+ align:start position:0%
+industry agendas in Japan in its older
+period you know it would set technology
+
+ align:start position:0%
+period you know it would set technology
+ 
+
+ align:start position:0%
+period you know it would set technology
+initiatives that were selected by
+
+ align:start position:0%
+initiatives that were selected by
+ 
+
+ align:start position:0%
+initiatives that were selected by
+high-level governmental leaders
+
+ align:start position:0%
+high-level governmental leaders
+ 
+
+ align:start position:0%
+high-level governmental leaders
+including it immediately and then in a
+
+ align:start position:0%
+including it immediately and then in a
+ 
+
+ align:start position:0%
+including it immediately and then in a
+more recent period it's had to move
+
+ align:start position:0%
+more recent period it's had to move
+ 
+
+ align:start position:0%
+more recent period it's had to move
+or is technology initiatives they're
+
+ align:start position:0%
+or is technology initiatives they're
+ 
+
+ align:start position:0%
+or is technology initiatives they're
+really selectively industry in other
+
+ align:start position:0%
+really selectively industry in other
+ 
+
+ align:start position:0%
+really selectively industry in other
+words it's reached it at the frontier
+
+ align:start position:0%
+words it's reached it at the frontier
+ 
+
+ align:start position:0%
+words it's reached it at the frontier
+the ability of government to pick the
+
+ align:start position:0%
+the ability of government to pick the
+ 
+
+ align:start position:0%
+the ability of government to pick the
+technology menu becomes more problematic
+
+ align:start position:0%
+technology menu becomes more problematic
+ 
+
+ align:start position:0%
+technology menu becomes more problematic
+you've got to get that down to industry
+
+ align:start position:0%
+you've got to get that down to industry
+ 
+
+ align:start position:0%
+you've got to get that down to industry
+decision-makers that are much closer to
+
+ align:start position:0%
+decision-makers that are much closer to
+ 
+
+ align:start position:0%
+decision-makers that are much closer to
+markets and much less of the innovation
+
+ align:start position:0%
+markets and much less of the innovation
+ 
+
+ align:start position:0%
+markets and much less of the innovation
+system itself and that has evolved in
+
+ align:start position:0%
+system itself and that has evolved in
+ 
+
+ align:start position:0%
+system itself and that has evolved in
+Japan that high officials just can't
+
+ align:start position:0%
+Japan that high officials just can't
+ 
+
+ align:start position:0%
+Japan that high officials just can't
+keep an eye on the rapidly evolving
+
+ align:start position:0%
+keep an eye on the rapidly evolving
+ 
+
+ align:start position:0%
+keep an eye on the rapidly evolving
+critics technologies so that's kind of
+
+ align:start position:0%
+critics technologies so that's kind of
+ 
+
+ align:start position:0%
+critics technologies so that's kind of
+technology initiatives then there was
+
+ align:start position:0%
+technology initiatives then there was
+ 
+
+ align:start position:0%
+technology initiatives then there was
+technology targeting in the old period
+
+ align:start position:0%
+technology targeting in the old period
+ 
+
+ align:start position:0%
+technology targeting in the old period
+there was direct government targeting of
+
+ align:start position:0%
+there was direct government targeting of
+ 
+
+ align:start position:0%
+there was direct government targeting of
+one or two specific technologies right
+
+ align:start position:0%
+one or two specific technologies right
+ 
+
+ align:start position:0%
+one or two specific technologies right
+that we're going to be pursued by the
+
+ align:start position:0%
+that we're going to be pursued by the
+ 
+
+ align:start position:0%
+that we're going to be pursued by the
+government and the funding was a you
+
+ align:start position:0%
+government and the funding was a you
+ 
+
+ align:start position:0%
+government and the funding was a you
+know at the late development stages
+
+ align:start position:0%
+know at the late development stages
+ 
+
+ align:start position:0%
+know at the late development stages
+right the government funding was focused
+
+ align:start position:0%
+right the government funding was focused
+ 
+
+ align:start position:0%
+right the government funding was focused
+really on advanced prototyping and
+
+ align:start position:0%
+really on advanced prototyping and
+ 
+
+ align:start position:0%
+really on advanced prototyping and
+engineering development that's what the
+
+ align:start position:0%
+engineering development that's what the
+ 
+
+ align:start position:0%
+engineering development that's what the
+government support was going in the
+
+ align:start position:0%
+government support was going in the
+ 
+
+ align:start position:0%
+government support was going in the
+newer period Japan shifted towards more
+
+ align:start position:0%
+newer period Japan shifted towards more
+ 
+
+ align:start position:0%
+newer period Japan shifted towards more
+fundamental research money and along
+
+ align:start position:0%
+fundamental research money and along
+ 
+
+ align:start position:0%
+fundamental research money and along
+with it supplied and put to put a
+
+ align:start position:0%
+with it supplied and put to put a
+ 
+
+ align:start position:0%
+with it supplied and put to put a
+broader range of technology alternatives
+
+ align:start position:0%
+broader range of technology alternatives
+ 
+
+ align:start position:0%
+broader range of technology alternatives
+onto the table as Glenn characterizes it
+
+ align:start position:0%
+onto the table as Glenn characterizes it
+ 
+
+ align:start position:0%
+onto the table as Glenn characterizes it
+moved to a kind of shotgun approach not
+
+ align:start position:0%
+moved to a kind of shotgun approach not
+ 
+
+ align:start position:0%
+moved to a kind of shotgun approach not
+a kind of more narrow rifle shot and
+
+ align:start position:0%
+a kind of more narrow rifle shot and
+ 
+
+ align:start position:0%
+a kind of more narrow rifle shot and
+then finally industry targeting in the
+
+ align:start position:0%
+then finally industry targeting in the
+ 
+
+ align:start position:0%
+then finally industry targeting in the
+older period meanie would actually pick
+
+ align:start position:0%
+older period meanie would actually pick
+ 
+
+ align:start position:0%
+older period meanie would actually pick
+winning companies it would decide who's
+
+ align:start position:0%
+winning companies it would decide who's
+ 
+
+ align:start position:0%
+winning companies it would decide who's
+going to win designating specific
+
+ align:start position:0%
+going to win designating specific
+ 
+
+ align:start position:0%
+going to win designating specific
+companies for funding and it would you
+
+ align:start position:0%
+companies for funding and it would you
+ 
+
+ align:start position:0%
+companies for funding and it would you
+know attempt to influence corporate
+
+ align:start position:0%
+know attempt to influence corporate
+ 
+
+ align:start position:0%
+know attempt to influence corporate
+mergers and consolidations to develop
+
+ align:start position:0%
+mergers and consolidations to develop
+ 
+
+ align:start position:0%
+mergers and consolidations to develop
+strong companies so it's intervening at
+
+ align:start position:0%
+strong companies so it's intervening at
+ 
+
+ align:start position:0%
+strong companies so it's intervening at
+the company stage pretty systematically
+
+ align:start position:0%
+the company stage pretty systematically
+ 
+
+ align:start position:0%
+the company stage pretty systematically
+at critical areas and in newer period
+
+ align:start position:0%
+at critical areas and in newer period
+ 
+
+ align:start position:0%
+at critical areas and in newer period
+media became much more collaborative and
+
+ align:start position:0%
+media became much more collaborative and
+ 
+
+ align:start position:0%
+media became much more collaborative and
+its funding a range of companies at a
+
+ align:start position:0%
+its funding a range of companies at a
+ 
+
+ align:start position:0%
+its funding a range of companies at a
+range of collaboration models not
+
+ align:start position:0%
+range of collaboration models not
+ 
+
+ align:start position:0%
+range of collaboration models not
+attempting to target particular
+
+ align:start position:0%
+attempting to target particular
+ 
+
+ align:start position:0%
+attempting to target particular
+surviving firms and winners so you know
+
+ align:start position:0%
+surviving firms and winners so you know
+ 
+
+ align:start position:0%
+surviving firms and winners so you know
+in the in the computing area for example
+
+ align:start position:0%
+in the in the computing area for example
+ 
+
+ align:start position:0%
+in the in the computing area for example
+meeting goes from funding three firms
+
+ align:start position:0%
+meeting goes from funding three firms
+ 
+
+ align:start position:0%
+meeting goes from funding three firms
+over a 30-year period to 25 firms
+
+ align:start position:0%
+over a 30-year period to 25 firms
+ 
+
+ align:start position:0%
+over a 30-year period to 25 firms
+you know at the end of that period so
+
+ align:start position:0%
+you know at the end of that period so
+ 
+
+ align:start position:0%
+you know at the end of that period so
+it's moving towards a system that is
+
+ align:start position:0%
+it's moving towards a system that is
+ 
+
+ align:start position:0%
+it's moving towards a system that is
+less centralized and more reflective of
+
+ align:start position:0%
+less centralized and more reflective of
+ 
+
+ align:start position:0%
+less centralized and more reflective of
+industry leadership and away from an
+
+ align:start position:0%
+industry leadership and away from an
+ 
+
+ align:start position:0%
+industry leadership and away from an
+integral from an interventionist
+
+ align:start position:0%
+integral from an interventionist
+ 
+
+ align:start position:0%
+integral from an interventionist
+government kind of goal so that's kind
+
+ align:start position:0%
+government kind of goal so that's kind
+ 
+
+ align:start position:0%
+government kind of goal so that's kind
+of interesting Japan gets to the to the
+
+ align:start position:0%
+of interesting Japan gets to the to the
+ 
+
+ align:start position:0%
+of interesting Japan gets to the to the
+innovation frontier to its significant
+
+ align:start position:0%
+innovation frontier to its significant
+ 
+
+ align:start position:0%
+innovation frontier to its significant
+governmental role though when it's at
+
+ align:start position:0%
+governmental role though when it's at
+ 
+
+ align:start position:0%
+governmental role though when it's at
+the frontier and it's truly a world
+
+ align:start position:0%
+the frontier and it's truly a world
+ 
+
+ align:start position:0%
+the frontier and it's truly a world
+hence competitor it's got a development
+
+ align:start position:0%
+hence competitor it's got a development
+ 
+
+ align:start position:0%
+hence competitor it's got a development
+much more decentralized approach that
+
+ align:start position:0%
+much more decentralized approach that
+ 
+
+ align:start position:0%
+much more decentralized approach that
+allows ideas to rise up from that system
+
+ align:start position:0%
+allows ideas to rise up from that system
+ 
+
+ align:start position:0%
+allows ideas to rise up from that system
+so that may be an important
+
+ align:start position:0%
+so that may be an important
+ 
+
+ align:start position:0%
+so that may be an important
+organizational model for us to consider
+
+ align:start position:0%
+organizational model for us to consider
+ 
+
+ align:start position:0%
+organizational model for us to consider
+that organizational model course is more
+
+ align:start position:0%
+that organizational model course is more
+ 
+
+ align:start position:0%
+that organizational model course is more
+like like us had a whole one now let me
+
+ align:start position:0%
+like like us had a whole one now let me
+ 
+
+ align:start position:0%
+like like us had a whole one now let me
+put Lin sue Kim into this mix too and
+
+ align:start position:0%
+put Lin sue Kim into this mix too and
+ 
+
+ align:start position:0%
+put Lin sue Kim into this mix too and
+his book human innovation is kind of a
+
+ align:start position:0%
+his book human innovation is kind of a
+ 
+
+ align:start position:0%
+his book human innovation is kind of a
+classic in looking at the amazing
+
+ align:start position:0%
+classic in looking at the amazing
+ 
+
+ align:start position:0%
+classic in looking at the amazing
+evolution of the Korean product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the thing to understand about the Korean
+
+ align:start position:0%
+the thing to understand about the Korean
+ 
+
+ align:start position:0%
+the thing to understand about the Korean
+economy is that the country was just
+
+ align:start position:0%
+economy is that the country was just
+ 
+
+ align:start position:0%
+economy is that the country was just
+totally destroyed
+
+ align:start position:0%
+totally destroyed
+ 
+
+ align:start position:0%
+totally destroyed
+and every inch of that nation was fought
+
+ align:start position:0%
+and every inch of that nation was fought
+ 
+
+ align:start position:0%
+and every inch of that nation was fought
+over over a multi-year period and
+
+ align:start position:0%
+over over a multi-year period and
+ 
+
+ align:start position:0%
+over over a multi-year period and
+because nothing was outstanding it's a
+
+ align:start position:0%
+because nothing was outstanding it's a
+ 
+
+ align:start position:0%
+because nothing was outstanding it's a
+complete tragedy and the population is
+
+ align:start position:0%
+complete tragedy and the population is
+ 
+
+ align:start position:0%
+complete tragedy and the population is
+completely disrupted it's forced to no
+
+ align:start position:0%
+completely disrupted it's forced to no
+ 
+
+ align:start position:0%
+completely disrupted it's forced to no
+move wall about the country families are
+
+ align:start position:0%
+move wall about the country families are
+ 
+
+ align:start position:0%
+move wall about the country families are
+disrupted communities and villages and
+
+ align:start position:0%
+disrupted communities and villages and
+ 
+
+ align:start position:0%
+disrupted communities and villages and
+we disrupted it's all thrown together
+
+ align:start position:0%
+we disrupted it's all thrown together
+ 
+
+ align:start position:0%
+we disrupted it's all thrown together
+and it's it's truly tragic and yet out
+
+ align:start position:0%
+and it's it's truly tragic and yet out
+ 
+
+ align:start position:0%
+and it's it's truly tragic and yet out
+of that tragedy is one of the most
+
+ align:start position:0%
+of that tragedy is one of the most
+ 
+
+ align:start position:0%
+of that tragedy is one of the most
+remarkable stories of you know
+
+ align:start position:0%
+remarkable stories of you know
+ 
+
+ align:start position:0%
+remarkable stories of you know
+industries scale-up and growth and
+
+ align:start position:0%
+industries scale-up and growth and
+ 
+
+ align:start position:0%
+industries scale-up and growth and
+growth of the country that it's an
+
+ align:start position:0%
+growth of the country that it's an
+ 
+
+ align:start position:0%
+growth of the country that it's an
+amazing story right and essentially in a
+
+ align:start position:0%
+amazing story right and essentially in a
+ 
+
+ align:start position:0%
+amazing story right and essentially in a
+thirty year period to construct an
+
+ align:start position:0%
+thirty year period to construct an
+ 
+
+ align:start position:0%
+thirty year period to construct an
+economy literally nothing that's right
+
+ align:start position:0%
+economy literally nothing that's right
+ 
+
+ align:start position:0%
+economy literally nothing that's right
+is pretty advanced so what's behind this
+
+ align:start position:0%
+is pretty advanced so what's behind this
+ 
+
+ align:start position:0%
+is pretty advanced so what's behind this
+so in the 1960s period
+
+ align:start position:0%
+so in the 1960s period
+ 
+
+ align:start position:0%
+so in the 1960s period
+Vincent Kim argues that you know Korean
+
+ align:start position:0%
+Vincent Kim argues that you know Korean
+ 
+
+ align:start position:0%
+Vincent Kim argues that you know Korean
+firms are on eight what he calls a
+
+ align:start position:0%
+firms are on eight what he calls a
+ 
+
+ align:start position:0%
+firms are on eight what he calls a
+leadership trajectory and the government
+
+ align:start position:0%
+leadership trajectory and the government
+ 
+
+ align:start position:0%
+leadership trajectory and the government
+is on a model of what he calls forced
+
+ align:start position:0%
+is on a model of what he calls forced
+ 
+
+ align:start position:0%
+is on a model of what he calls forced
+march industrialization so the
+
+ align:start position:0%
+march industrialization so the
+ 
+
+ align:start position:0%
+march industrialization so the
+government is supplying education
+
+ align:start position:0%
+government is supplying education
+ 
+
+ align:start position:0%
+government is supplying education
+through college on the demand side it's
+
+ align:start position:0%
+through college on the demand side it's
+ 
+
+ align:start position:0%
+through college on the demand side it's
+creating shape bowls which are somewhat
+
+ align:start position:0%
+creating shape bowls which are somewhat
+ 
+
+ align:start position:0%
+creating shape bowls which are somewhat
+akin to the Koretz of model we were
+
+ align:start position:0%
+akin to the Koretz of model we were
+ 
+
+ align:start position:0%
+akin to the Koretz of model we were
+threatening that of Japan other words
+
+ align:start position:0%
+threatening that of Japan other words
+ 
+
+ align:start position:0%
+threatening that of Japan other words
+these are major industry leaders and you
+
+ align:start position:0%
+these are major industry leaders and you
+ 
+
+ align:start position:0%
+these are major industry leaders and you
+know the difficulty in this mix in the
+
+ align:start position:0%
+know the difficulty in this mix in the
+ 
+
+ align:start position:0%
+know the difficulty in this mix in the
+government of the time was its
+
+ align:start position:0%
+government of the time was its
+ 
+
+ align:start position:0%
+government of the time was its
+corruption and this is Korean Korea
+
+ align:start position:0%
+corruption and this is Korean Korea
+ 
+
+ align:start position:0%
+corruption and this is Korean Korea
+still innate in the hands of a
+
+ align:start position:0%
+still innate in the hands of a
+ 
+
+ align:start position:0%
+still innate in the hands of a
+dictatorship with corruption problems
+
+ align:start position:0%
+dictatorship with corruption problems
+ 
+
+ align:start position:0%
+dictatorship with corruption problems
+and problem with corruption is creates
+
+ align:start position:0%
+and problem with corruption is creates
+ 
+
+ align:start position:0%
+and problem with corruption is creates
+two minutes uncertainty and your
+
+ align:start position:0%
+two minutes uncertainty and your
+ 
+
+ align:start position:0%
+two minutes uncertainty and your
+business and you know that was a you
+
+ align:start position:0%
+business and you know that was a you
+ 
+
+ align:start position:0%
+business and you know that was a you
+know kind of a difficult factor but
+
+ align:start position:0%
+know kind of a difficult factor but
+ 
+
+ align:start position:0%
+know kind of a difficult factor but
+nonetheless the government is planet key
+
+ align:start position:0%
+nonetheless the government is planet key
+ 
+
+ align:start position:0%
+nonetheless the government is planet key
+role and kind of pushing these major
+
+ align:start position:0%
+role and kind of pushing these major
+ 
+
+ align:start position:0%
+role and kind of pushing these major
+companies on a march to to strong
+
+ align:start position:0%
+companies on a march to to strong
+ 
+
+ align:start position:0%
+companies on a march to to strong
+Internet
+
+ align:start position:0%
+Internet
+ 
+
+ align:start position:0%
+Internet
+could you clarify what you mean by
+
+ align:start position:0%
+could you clarify what you mean by
+ 
+
+ align:start position:0%
+could you clarify what you mean by
+corruption creates tremendous business
+
+ align:start position:0%
+corruption creates tremendous business
+ 
+
+ align:start position:0%
+corruption creates tremendous business
+uncertainty you're not competing with
+
+ align:start position:0%
+uncertainty you're not competing with
+ 
+
+ align:start position:0%
+uncertainty you're not competing with
+other firms based upon your superior
+
+ align:start position:0%
+other firms based upon your superior
+ 
+
+ align:start position:0%
+other firms based upon your superior
+products and her superior ability to
+
+ align:start position:0%
+products and her superior ability to
+ 
+
+ align:start position:0%
+products and her superior ability to
+manufacture suddenly a wild card is
+
+ align:start position:0%
+manufacture suddenly a wild card is
+ 
+
+ align:start position:0%
+manufacture suddenly a wild card is
+thrown into the mix and you've got to
+
+ align:start position:0%
+thrown into the mix and you've got to
+ 
+
+ align:start position:0%
+thrown into the mix and you've got to
+you know cope with the government and
+
+ align:start position:0%
+you know cope with the government and
+ 
+
+ align:start position:0%
+you know cope with the government and
+buying off the government and buying
+
+ align:start position:0%
+buying off the government and buying
+ 
+
+ align:start position:0%
+buying off the government and buying
+government support if you want to stay
+
+ align:start position:0%
+government support if you want to stay
+ 
+
+ align:start position:0%
+government support if you want to stay
+ahead so it creates a whole new variable
+
+ align:start position:0%
+ahead so it creates a whole new variable
+ 
+
+ align:start position:0%
+ahead so it creates a whole new variable
+it's much less they can't be managed by
+
+ align:start position:0%
+it's much less they can't be managed by
+ 
+
+ align:start position:0%
+it's much less they can't be managed by
+your business processes and systems so
+
+ align:start position:0%
+your business processes and systems so
+ 
+
+ align:start position:0%
+your business processes and systems so
+that's why when we read the that world
+
+ align:start position:0%
+that's why when we read the that world
+ 
+
+ align:start position:0%
+that's why when we read the that world
+economic report that's why corruption
+
+ align:start position:0%
+economic report that's why corruption
+ 
+
+ align:start position:0%
+economic report that's why corruption
+was actually one of the factors that was
+
+ align:start position:0%
+was actually one of the factors that was
+ 
+
+ align:start position:0%
+was actually one of the factors that was
+considered in the strength of your
+
+ align:start position:0%
+considered in the strength of your
+ 
+
+ align:start position:0%
+considered in the strength of your
+economic is because it can be so
+
+ align:start position:0%
+economic is because it can be so
+ 
+
+ align:start position:0%
+economic is because it can be so
+disruptive but the ability to have a
+
+ align:start position:0%
+disruptive but the ability to have a
+ 
+
+ align:start position:0%
+disruptive but the ability to have a
+reasonable unfair competition system so
+
+ align:start position:0%
+reasonable unfair competition system so
+ 
+
+ align:start position:0%
+reasonable unfair competition system so
+the table's to go back to our discussion
+
+ align:start position:0%
+the table's to go back to our discussion
+ 
+
+ align:start position:0%
+the table's to go back to our discussion
+that J polls were key to building and
+
+ align:start position:0%
+that J polls were key to building and
+ 
+
+ align:start position:0%
+that J polls were key to building and
+capturing these large scale industries
+
+ align:start position:0%
+capturing these large scale industries
+ 
+
+ align:start position:0%
+capturing these large scale industries
+now Korea will increase these major
+
+ align:start position:0%
+now Korea will increase these major
+ 
+
+ align:start position:0%
+now Korea will increase these major
+companies that dominate industrial
+
+ align:start position:0%
+companies that dominate industrial
+ 
+
+ align:start position:0%
+companies that dominate industrial
+sectors they tend to flock entry by
+
+ align:start position:0%
+sectors they tend to flock entry by
+ 
+
+ align:start position:0%
+sectors they tend to flock entry by
+small and medium sized enterprises so
+
+ align:start position:0%
+small and medium sized enterprises so
+ 
+
+ align:start position:0%
+small and medium sized enterprises so
+Korea at the same time is not creating a
+
+ align:start position:0%
+Korea at the same time is not creating a
+ 
+
+ align:start position:0%
+Korea at the same time is not creating a
+system of strong small and mid-sized
+
+ align:start position:0%
+system of strong small and mid-sized
+ 
+
+ align:start position:0%
+system of strong small and mid-sized
+firms right it's really focused on
+
+ align:start position:0%
+firms right it's really focused on
+ 
+
+ align:start position:0%
+firms right it's really focused on
+creating these big tables that can
+
+ align:start position:0%
+creating these big tables that can
+ 
+
+ align:start position:0%
+creating these big tables that can
+really function in the international
+
+ align:start position:0%
+really function in the international
+ 
+
+ align:start position:0%
+really function in the international
+market places but that in turn can
+
+ align:start position:0%
+market places but that in turn can
+ 
+
+ align:start position:0%
+market places but that in turn can
+create inefficiencies as well their
+
+ align:start position:0%
+create inefficiencies as well their
+ 
+
+ align:start position:0%
+create inefficiencies as well their
+markets in education Korea hit on a
+
+ align:start position:0%
+markets in education Korea hit on a
+ 
+
+ align:start position:0%
+markets in education Korea hit on a
+model of widespread education and that
+
+ align:start position:0%
+model of widespread education and that
+ 
+
+ align:start position:0%
+model of widespread education and that
+is it's a dramatic story I mean the
+
+ align:start position:0%
+is it's a dramatic story I mean the
+ 
+
+ align:start position:0%
+is it's a dramatic story I mean the
+college completion right there is
+
+ align:start position:0%
+college completion right there is
+ 
+
+ align:start position:0%
+college completion right there is
+breathtaking and you know the focus is
+
+ align:start position:0%
+breathtaking and you know the focus is
+ 
+
+ align:start position:0%
+breathtaking and you know the focus is
+to get a very highly educated population
+
+ align:start position:0%
+to get a very highly educated population
+ 
+
+ align:start position:0%
+to get a very highly educated population
+which they have achieved right and then
+
+ align:start position:0%
+which they have achieved right and then
+ 
+
+ align:start position:0%
+which they have achieved right and then
+that highly educated population is able
+
+ align:start position:0%
+that highly educated population is able
+ 
+
+ align:start position:0%
+that highly educated population is able
+to staff ever more sophisticated
+
+ align:start position:0%
+to staff ever more sophisticated
+ 
+
+ align:start position:0%
+to staff ever more sophisticated
+industries right that's that's the model
+
+ align:start position:0%
+industries right that's that's the model
+ 
+
+ align:start position:0%
+industries right that's that's the model
+and it works the one thing they don't do
+
+ align:start position:0%
+and it works the one thing they don't do
+ 
+
+ align:start position:0%
+and it works the one thing they don't do
+is move their colleges into research
+
+ align:start position:0%
+is move their colleges into research
+ 
+
+ align:start position:0%
+is move their colleges into research
+universities
+
+ align:start position:0%
+universities
+ 
+
+ align:start position:0%
+universities
+which Kim argues is still a part of the
+
+ align:start position:0%
+which Kim argues is still a part of the
+ 
+
+ align:start position:0%
+which Kim argues is still a part of the
+model in Easton achieved there's a very
+
+ align:start position:0%
+model in Easton achieved there's a very
+ 
+
+ align:start position:0%
+model in Easton achieved there's a very
+strong export strategy in Korea and the
+
+ align:start position:0%
+strong export strategy in Korea and the
+ 
+
+ align:start position:0%
+strong export strategy in Korea and the
+Martino resource institutions do they
+
+ align:start position:0%
+Martino resource institutions do they
+ 
+
+ align:start position:0%
+Martino resource institutions do they
+just like to send their people to study
+
+ align:start position:0%
+just like to send their people to study
+ 
+
+ align:start position:0%
+just like to send their people to study
+at those institutions in yeah they have
+
+ align:start position:0%
+at those institutions in yeah they have
+ 
+
+ align:start position:0%
+at those institutions in yeah they have
+government only supported research
+
+ align:start position:0%
+government only supported research
+ 
+
+ align:start position:0%
+government only supported research
+institutions a little more on that in a
+
+ align:start position:0%
+institutions a little more on that in a
+ 
+
+ align:start position:0%
+institutions a little more on that in a
+second wisdom of the u.s. model is that
+
+ align:start position:0%
+second wisdom of the u.s. model is that
+ 
+
+ align:start position:0%
+second wisdom of the u.s. model is that
+you combine the education system with
+
+ align:start position:0%
+you combine the education system with
+ 
+
+ align:start position:0%
+you combine the education system with
+the resources and therefore you create a
+
+ align:start position:0%
+the resources and therefore you create a
+ 
+
+ align:start position:0%
+the resources and therefore you create a
+tremendous amount of learning by doing
+
+ align:start position:0%
+tremendous amount of learning by doing
+ 
+
+ align:start position:0%
+tremendous amount of learning by doing
+right seems to work pretty well if
+
+ align:start position:0%
+right seems to work pretty well if
+ 
+
+ align:start position:0%
+right seems to work pretty well if
+you're just supporting research in
+
+ align:start position:0%
+you're just supporting research in
+ 
+
+ align:start position:0%
+you're just supporting research in
+separate research entities you miss that
+
+ align:start position:0%
+separate research entities you miss that
+ 
+
+ align:start position:0%
+separate research entities you miss that
+the dynamics of that education
+
+ align:start position:0%
+the dynamics of that education
+ 
+
+ align:start position:0%
+the dynamics of that education
+connection time right doesn't work as
+
+ align:start position:0%
+connection time right doesn't work as
+ 
+
+ align:start position:0%
+connection time right doesn't work as
+smooth as I think it must be with
+
+ align:start position:0%
+smooth as I think it must be with
+ 
+
+ align:start position:0%
+smooth as I think it must be with
+resources might be more complex so they
+
+ align:start position:0%
+resources might be more complex so they
+ 
+
+ align:start position:0%
+resources might be more complex so they
+focus on making a really good college
+
+ align:start position:0%
+focus on making a really good college
+ 
+
+ align:start position:0%
+focus on making a really good college
+education that exporting their people to
+
+ align:start position:0%
+education that exporting their people to
+ 
+
+ align:start position:0%
+education that exporting their people to
+do research with in other countries they
+
+ align:start position:0%
+do research with in other countries they
+ 
+
+ align:start position:0%
+do research with in other countries they
+might just it just might be something to
+
+ align:start position:0%
+might just it just might be something to
+ 
+
+ align:start position:0%
+might just it just might be something to
+make it more efficient I think there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one thing that the Korean government did
+
+ align:start position:0%
+one thing that the Korean government did
+ 
+
+ align:start position:0%
+one thing that the Korean government did
+do was enforced its big companies in the
+
+ align:start position:0%
+do was enforced its big companies in the
+ 
+
+ align:start position:0%
+do was enforced its big companies in the
+international competition so they've got
+
+ align:start position:0%
+international competition so they've got
+ 
+
+ align:start position:0%
+international competition so they've got
+a you know freely mercantilist model of
+
+ align:start position:0%
+a you know freely mercantilist model of
+ 
+
+ align:start position:0%
+a you know freely mercantilist model of
+not allowing of protecting a domestic
+
+ align:start position:0%
+not allowing of protecting a domestic
+ 
+
+ align:start position:0%
+not allowing of protecting a domestic
+market for their companies but it's not
+
+ align:start position:0%
+market for their companies but it's not
+ 
+
+ align:start position:0%
+market for their companies but it's not
+that big a domestic market they've gotta
+
+ align:start position:0%
+that big a domestic market they've gotta
+ 
+
+ align:start position:0%
+that big a domestic market they've gotta
+force their companies out at the
+
+ align:start position:0%
+force their companies out at the
+ 
+
+ align:start position:0%
+force their companies out at the
+international competition and they do it
+
+ align:start position:0%
+international competition and they do it
+ 
+
+ align:start position:0%
+international competition and they do it
+right and that builds to mendes
+
+ align:start position:0%
+right and that builds to mendes
+ 
+
+ align:start position:0%
+right and that builds to mendes
+competitive strength in these firms and
+
+ align:start position:0%
+competitive strength in these firms and
+ 
+
+ align:start position:0%
+competitive strength in these firms and
+you know we look around and see the
+
+ align:start position:0%
+you know we look around and see the
+ 
+
+ align:start position:0%
+you know we look around and see the
+strong Korean firms it's pretty
+
+ align:start position:0%
+strong Korean firms it's pretty
+ 
+
+ align:start position:0%
+strong Korean firms it's pretty
+inaudible story in terms of tech trend
+
+ align:start position:0%
+inaudible story in terms of tech trend
+ 
+
+ align:start position:0%
+inaudible story in terms of tech trend
+transfer policy that policy was
+
+ align:start position:0%
+transfer policy that policy was
+ 
+
+ align:start position:0%
+transfer policy that policy was
+initially largely reverse engineering of
+
+ align:start position:0%
+initially largely reverse engineering of
+ 
+
+ align:start position:0%
+initially largely reverse engineering of
+technologies brought a broad but
+
+ align:start position:0%
+technologies brought a broad but
+ 
+
+ align:start position:0%
+technologies brought a broad but
+critical capabilities are being
+
+ align:start position:0%
+critical capabilities are being
+ 
+
+ align:start position:0%
+critical capabilities are being
+developed as part of this reverse
+
+ align:start position:0%
+developed as part of this reverse
+ 
+
+ align:start position:0%
+developed as part of this reverse
+engineering effort R&D policy it's
+
+ align:start position:0%
+engineering effort R&D policy it's
+ 
+
+ align:start position:0%
+engineering effort R&D policy it's
+focused as I mentioned before on these
+
+ align:start position:0%
+focused as I mentioned before on these
+ 
+
+ align:start position:0%
+focused as I mentioned before on these
+government research institutions the GRI
+
+ align:start position:0%
+government research institutions the GRI
+ 
+
+ align:start position:0%
+government research institutions the GRI
+is provide more of a rather than
+
+ align:start position:0%
+is provide more of a rather than
+ 
+
+ align:start position:0%
+is provide more of a rather than
+influencing industry R&D as much it's
+
+ align:start position:0%
+influencing industry R&D as much it's
+ 
+
+ align:start position:0%
+influencing industry R&D as much it's
+more of a
+
+ align:start position:0%
+more of a
+ 
+
+ align:start position:0%
+more of a
+talent base and support base as you were
+
+ align:start position:0%
+talent base and support base as you were
+ 
+
+ align:start position:0%
+talent base and support base as you were
+indeed suggesting martini for companies
+
+ align:start position:0%
+indeed suggesting martini for companies
+ 
+
+ align:start position:0%
+indeed suggesting martini for companies
+that Kim also has this very interesting
+
+ align:start position:0%
+that Kim also has this very interesting
+ 
+
+ align:start position:0%
+that Kim also has this very interesting
+discussion of Korean culture here and
+
+ align:start position:0%
+discussion of Korean culture here and
+ 
+
+ align:start position:0%
+discussion of Korean culture here and
+what's going woman that matches the
+
+ align:start position:0%
+what's going woman that matches the
+ 
+
+ align:start position:0%
+what's going woman that matches the
+evolution of this so he argues that in
+
+ align:start position:0%
+evolution of this so he argues that in
+ 
+
+ align:start position:0%
+evolution of this so he argues that in
+Korea this interesting blend of of an
+
+ align:start position:0%
+Korea this interesting blend of of an
+ 
+
+ align:start position:0%
+Korea this interesting blend of of an
+Asian Confucian culture of family and
+
+ align:start position:0%
+Asian Confucian culture of family and
+ 
+
+ align:start position:0%
+Asian Confucian culture of family and
+collective support and a collective
+
+ align:start position:0%
+collective support and a collective
+ 
+
+ align:start position:0%
+collective support and a collective
+orientation gets merged with a pretty
+
+ align:start position:0%
+orientation gets merged with a pretty
+ 
+
+ align:start position:0%
+orientation gets merged with a pretty
+high level of quite high level of
+
+ align:start position:0%
+high level of quite high level of
+ 
+
+ align:start position:0%
+high level of quite high level of
+Christianity and it's individualism for
+
+ align:start position:0%
+Christianity and it's individualism for
+ 
+
+ align:start position:0%
+Christianity and it's individualism for
+a very interesting combination effects
+
+ align:start position:0%
+a very interesting combination effects
+ 
+
+ align:start position:0%
+a very interesting combination effects
+strengths on both ends strengths them to
+
+ align:start position:0%
+strengths on both ends strengths them to
+ 
+
+ align:start position:0%
+strengths on both ends strengths them to
+call it pivot II side but also strengths
+
+ align:start position:0%
+call it pivot II side but also strengths
+ 
+
+ align:start position:0%
+call it pivot II side but also strengths
+on the individual inside some of you may
+
+ align:start position:0%
+on the individual inside some of you may
+ 
+
+ align:start position:0%
+on the individual inside some of you may
+have floods about that also the Korean
+
+ align:start position:0%
+have floods about that also the Korean
+ 
+
+ align:start position:0%
+have floods about that also the Korean
+War itself as we discussed love the
+
+ align:start position:0%
+War itself as we discussed love the
+ 
+
+ align:start position:0%
+War itself as we discussed love the
+country destroyed and you know ended
+
+ align:start position:0%
+country destroyed and you know ended
+ 
+
+ align:start position:0%
+country destroyed and you know ended
+village culture but amalgamated the
+
+ align:start position:0%
+village culture but amalgamated the
+ 
+
+ align:start position:0%
+village culture but amalgamated the
+population in a way that created a
+
+ align:start position:0%
+population in a way that created a
+ 
+
+ align:start position:0%
+population in a way that created a
+certain kind of flexibility as the old
+
+ align:start position:0%
+certain kind of flexibility as the old
+ 
+
+ align:start position:0%
+certain kind of flexibility as the old
+social and cultural barriers were swept
+
+ align:start position:0%
+social and cultural barriers were swept
+ 
+
+ align:start position:0%
+social and cultural barriers were swept
+away so that it wasn't all bad I guess
+
+ align:start position:0%
+away so that it wasn't all bad I guess
+ 
+
+ align:start position:0%
+away so that it wasn't all bad I guess
+what would be kim's conclusion and then
+
+ align:start position:0%
+what would be kim's conclusion and then
+ 
+
+ align:start position:0%
+what would be kim's conclusion and then
+because it's a country that has constant
+
+ align:start position:0%
+because it's a country that has constant
+ 
+
+ align:start position:0%
+because it's a country that has constant
+threat of war with North Korea the
+
+ align:start position:0%
+threat of war with North Korea the
+ 
+
+ align:start position:0%
+threat of war with North Korea the
+University Universal military service
+
+ align:start position:0%
+University Universal military service
+ 
+
+ align:start position:0%
+University Universal military service
+provides a huge training opportunity for
+
+ align:start position:0%
+provides a huge training opportunity for
+ 
+
+ align:start position:0%
+provides a huge training opportunity for
+a management class in effect and you
+
+ align:start position:0%
+a management class in effect and you
+ 
+
+ align:start position:0%
+a management class in effect and you
+know since military's to be affect it
+
+ align:start position:0%
+know since military's to be affect it
+ 
+
+ align:start position:0%
+know since military's to be affect it
+has to be pretty meritocratic right it
+
+ align:start position:0%
+has to be pretty meritocratic right it
+ 
+
+ align:start position:0%
+has to be pretty meritocratic right it
+introduces a whole meritocracy system
+
+ align:start position:0%
+introduces a whole meritocracy system
+ 
+
+ align:start position:0%
+introduces a whole meritocracy system
+into Korean society and culture you know
+
+ align:start position:0%
+into Korean society and culture you know
+ 
+
+ align:start position:0%
+into Korean society and culture you know
+replacing an older village more
+
+ align:start position:0%
+replacing an older village more
+ 
+
+ align:start position:0%
+replacing an older village more
+classroom culture so it tends to create
+
+ align:start position:0%
+classroom culture so it tends to create
+ 
+
+ align:start position:0%
+classroom culture so it tends to create
+a significant there's a series of forces
+
+ align:start position:0%
+a significant there's a series of forces
+ 
+
+ align:start position:0%
+a significant there's a series of forces
+here that tend to create a certain
+
+ align:start position:0%
+here that tend to create a certain
+ 
+
+ align:start position:0%
+here that tend to create a certain
+amount of social mobility and
+
+ align:start position:0%
+amount of social mobility and
+ 
+
+ align:start position:0%
+amount of social mobility and
+elimination of historic social classes
+
+ align:start position:0%
+elimination of historic social classes
+ 
+
+ align:start position:0%
+elimination of historic social classes
+which is part of the story that enables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Kent Margot is Korea to to thrive you
+
+ align:start position:0%
+Kent Margot is Korea to to thrive you
+ 
+
+ align:start position:0%
+Kent Margot is Korea to to thrive you
+know that military services in an artist
+
+ align:start position:0%
+know that military services in an artist
+ 
+
+ align:start position:0%
+know that military services in an artist
+feature right I mean our military back
+
+ align:start position:0%
+feature right I mean our military back
+ 
+
+ align:start position:0%
+feature right I mean our military back
+in the days which I can remember you
+
+ align:start position:0%
+in the days which I can remember you
+ 
+
+ align:start position:0%
+in the days which I can remember you
+can't when they draft the US military
+
+ align:start position:0%
+can't when they draft the US military
+ 
+
+ align:start position:0%
+can't when they draft the US military
+was actually a very important integrated
+
+ align:start position:0%
+was actually a very important integrated
+ 
+
+ align:start position:0%
+was actually a very important integrated
+force in the society right that was a
+
+ align:start position:0%
+force in the society right that was a
+ 
+
+ align:start position:0%
+force in the society right that was a
+very critical step in the u.s. to
+
+ align:start position:0%
+very critical step in the u.s. to
+ 
+
+ align:start position:0%
+very critical step in the u.s. to
+promote racial integration when you add
+
+ align:start position:0%
+promote racial integration when you add
+ 
+
+ align:start position:0%
+promote racial integration when you add
+integrated military units the height of
+
+ align:start position:0%
+integrated military units the height of
+ 
+
+ align:start position:0%
+integrated military units the height of
+threats of warfare in combat it really
+
+ align:start position:0%
+threats of warfare in combat it really
+ 
+
+ align:start position:0%
+threats of warfare in combat it really
+changed a lot of things in the society
+
+ align:start position:0%
+changed a lot of things in the society
+ 
+
+ align:start position:0%
+changed a lot of things in the society
+so it's there's just an interesting side
+
+ align:start position:0%
+so it's there's just an interesting side
+ 
+
+ align:start position:0%
+so it's there's just an interesting side
+note there about what that kind of
+
+ align:start position:0%
+note there about what that kind of
+ 
+
+ align:start position:0%
+note there about what that kind of
+social organization can mean in a social
+
+ align:start position:0%
+social organization can mean in a social
+ 
+
+ align:start position:0%
+social organization can mean in a social
+context but if Kim argues that it's
+
+ align:start position:0%
+context but if Kim argues that it's
+ 
+
+ align:start position:0%
+context but if Kim argues that it's
+important in Korea so Korea develops he
+
+ align:start position:0%
+important in Korea so Korea develops he
+ 
+
+ align:start position:0%
+important in Korea so Korea develops he
+argues a learning technology culture so
+
+ align:start position:0%
+argues a learning technology culture so
+ 
+
+ align:start position:0%
+argues a learning technology culture so
+that firms go from what he calls
+
+ align:start position:0%
+that firms go from what he calls
+ 
+
+ align:start position:0%
+that firms go from what he calls
+poaching and kind of reverse engineering
+
+ align:start position:0%
+poaching and kind of reverse engineering
+ 
+
+ align:start position:0%
+poaching and kind of reverse engineering
+and then to reverse engineering then to
+
+ align:start position:0%
+and then to reverse engineering then to
+ 
+
+ align:start position:0%
+and then to reverse engineering then to
+R&D and then to true innovation right so
+
+ align:start position:0%
+R&D and then to true innovation right so
+ 
+
+ align:start position:0%
+R&D and then to true innovation right so
+Chris let me right at the technology
+
+ align:start position:0%
+Chris let me right at the technology
+ 
+
+ align:start position:0%
+Chris let me right at the technology
+front in our whole series of areas and
+
+ align:start position:0%
+front in our whole series of areas and
+ 
+
+ align:start position:0%
+front in our whole series of areas and
+they moved through a series of steps to
+
+ align:start position:0%
+they moved through a series of steps to
+ 
+
+ align:start position:0%
+they moved through a series of steps to
+get there and Kim artists that these are
+
+ align:start position:0%
+get there and Kim artists that these are
+ 
+
+ align:start position:0%
+get there and Kim artists that these are
+these are steps and you know we tend to
+
+ align:start position:0%
+these are steps and you know we tend to
+ 
+
+ align:start position:0%
+these are steps and you know we tend to
+frown on poaching reverse engineering
+
+ align:start position:0%
+frown on poaching reverse engineering
+ 
+
+ align:start position:0%
+frown on poaching reverse engineering
+but let me remind remind us that you
+
+ align:start position:0%
+but let me remind remind us that you
+ 
+
+ align:start position:0%
+but let me remind remind us that you
+know the first textile industry in the
+
+ align:start position:0%
+know the first textile industry in the
+ 
+
+ align:start position:0%
+know the first textile industry in the
+US was set up and popped up in Rhode
+
+ align:start position:0%
+US was set up and popped up in Rhode
+ 
+
+ align:start position:0%
+US was set up and popped up in Rhode
+Island by an English immigrant named
+
+ align:start position:0%
+Island by an English immigrant named
+ 
+
+ align:start position:0%
+Island by an English immigrant named
+Samuel Slater and Samuel Slater is
+
+ align:start position:0%
+Samuel Slater and Samuel Slater is
+ 
+
+ align:start position:0%
+Samuel Slater and Samuel Slater is
+working in the British textile factories
+
+ align:start position:0%
+working in the British textile factories
+ 
+
+ align:start position:0%
+working in the British textile factories
+and the British textile factories
+
+ align:start position:0%
+and the British textile factories
+ 
+
+ align:start position:0%
+and the British textile factories
+realize they've got a monopoly on
+
+ align:start position:0%
+realize they've got a monopoly on
+ 
+
+ align:start position:0%
+realize they've got a monopoly on
+textile production efficiency worldwide
+
+ align:start position:0%
+textile production efficiency worldwide
+ 
+
+ align:start position:0%
+textile production efficiency worldwide
+and they don't want anybody else to have
+
+ align:start position:0%
+and they don't want anybody else to have
+ 
+
+ align:start position:0%
+and they don't want anybody else to have
+it so you're subjected to a body search
+
+ align:start position:0%
+it so you're subjected to a body search
+ 
+
+ align:start position:0%
+it so you're subjected to a body search
+to make sure you're not walking out with
+
+ align:start position:0%
+to make sure you're not walking out with
+ 
+
+ align:start position:0%
+to make sure you're not walking out with
+plans if you're an employee in these
+
+ align:start position:0%
+plans if you're an employee in these
+ 
+
+ align:start position:0%
+plans if you're an employee in these
+factories
+
+ align:start position:0%
+factories
+ 
+
+ align:start position:0%
+factories
+and Slater is you know served every kind
+
+ align:start position:0%
+and Slater is you know served every kind
+ 
+
+ align:start position:0%
+and Slater is you know served every kind
+of Lisa Finn agree what his British
+
+ align:start position:0%
+of Lisa Finn agree what his British
+ 
+
+ align:start position:0%
+of Lisa Finn agree what his British
+employers didn't realize is that he had
+
+ align:start position:0%
+employers didn't realize is that he had
+ 
+
+ align:start position:0%
+employers didn't realize is that he had
+a photographic memory right so he worked
+
+ align:start position:0%
+a photographic memory right so he worked
+ 
+
+ align:start position:0%
+a photographic memory right so he worked
+for this textile equipment because the
+
+ align:start position:0%
+for this textile equipment because the
+ 
+
+ align:start position:0%
+for this textile equipment because the
+United States since up the seams and
+
+ align:start position:0%
+United States since up the seams and
+ 
+
+ align:start position:0%
+United States since up the seams and
+brings you know textile industry so talk
+
+ align:start position:0%
+brings you know textile industry so talk
+ 
+
+ align:start position:0%
+brings you know textile industry so talk
+about poaching that straight poaching so
+
+ align:start position:0%
+about poaching that straight poaching so
+ 
+
+ align:start position:0%
+about poaching that straight poaching so
+the textile industry the United States
+
+ align:start position:0%
+the textile industry the United States
+ 
+
+ align:start position:0%
+the textile industry the United States
+is organized essentially do the same
+
+ align:start position:0%
+is organized essentially do the same
+ 
+
+ align:start position:0%
+is organized essentially do the same
+model and that arguably the same stage
+
+ align:start position:0%
+model and that arguably the same stage
+ 
+
+ align:start position:0%
+model and that arguably the same stage
+we went through when Lawrence and Lowell
+
+ align:start position:0%
+we went through when Lawrence and Lowell
+ 
+
+ align:start position:0%
+we went through when Lawrence and Lowell
+are established here in Massachusetts
+
+ align:start position:0%
+are established here in Massachusetts
+ 
+
+ align:start position:0%
+are established here in Massachusetts
+we're definitely into technological
+
+ align:start position:0%
+we're definitely into technological
+ 
+
+ align:start position:0%
+we're definitely into technological
+advances at the frontier of textile
+
+ align:start position:0%
+advances at the frontier of textile
+ 
+
+ align:start position:0%
+advances at the frontier of textile
+commercial so in a way we went to
+
+ align:start position:0%
+commercial so in a way we went to
+ 
+
+ align:start position:0%
+commercial so in a way we went to
+similar stages are in the investment so
+
+ align:start position:0%
+similar stages are in the investment so
+ 
+
+ align:start position:0%
+similar stages are in the investment so
+that is very heavy aren't the
+
+ align:start position:0%
+that is very heavy aren't the
+ 
+
+ align:start position:0%
+that is very heavy aren't the
+investments by the trick in the industry
+
+ align:start position:0%
+investments by the trick in the industry
+ 
+
+ align:start position:0%
+investments by the trick in the industry
+che polls but the issue Kim raises is
+
+ align:start position:0%
+che polls but the issue Kim raises is
+ 
+
+ align:start position:0%
+che polls but the issue Kim raises is
+that there's not enough SME small and
+
+ align:start position:0%
+that there's not enough SME small and
+ 
+
+ align:start position:0%
+that there's not enough SME small and
+mid-sized enterprises to provide
+
+ align:start position:0%
+mid-sized enterprises to provide
+ 
+
+ align:start position:0%
+mid-sized enterprises to provide
+out-of-the-box kind of ideas of thinking
+
+ align:start position:0%
+out-of-the-box kind of ideas of thinking
+ 
+
+ align:start position:0%
+out-of-the-box kind of ideas of thinking
+in the next and that that's a problem in
+
+ align:start position:0%
+in the next and that that's a problem in
+ 
+
+ align:start position:0%
+in the next and that that's a problem in
+the system the argues things needs to be
+
+ align:start position:0%
+the system the argues things needs to be
+ 
+
+ align:start position:0%
+the system the argues things needs to be
+changed
+
+ align:start position:0%
+changed
+ 
+
+ align:start position:0%
+changed
+the creole overall it's got a very high
+
+ align:start position:0%
+the creole overall it's got a very high
+ 
+
+ align:start position:0%
+the creole overall it's got a very high
+R&D to gene information higher than us
+
+ align:start position:0%
+R&D to gene information higher than us
+ 
+
+ align:start position:0%
+R&D to gene information higher than us
+so the problems are limited university
+
+ align:start position:0%
+so the problems are limited university
+ 
+
+ align:start position:0%
+so the problems are limited university
+are in need of the need for a larger SME
+
+ align:start position:0%
+are in need of the need for a larger SME
+ 
+
+ align:start position:0%
+are in need of the need for a larger SME
+entrepreneurial base he argues that a
+
+ align:start position:0%
+entrepreneurial base he argues that a
+ 
+
+ align:start position:0%
+entrepreneurial base he argues that a
+more liberalized economy away from the
+
+ align:start position:0%
+more liberalized economy away from the
+ 
+
+ align:start position:0%
+more liberalized economy away from the
+kind of elite tribal control is an
+
+ align:start position:0%
+kind of elite tribal control is an
+ 
+
+ align:start position:0%
+kind of elite tribal control is an
+important step but there's a lot of
+
+ align:start position:0%
+important step but there's a lot of
+ 
+
+ align:start position:0%
+important step but there's a lot of
+lessons from korea the role of a strong
+
+ align:start position:0%
+lessons from korea the role of a strong
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+
+ align:start position:0%
+lessons from korea the role of a strong
+governmental the leadership in creating
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+ align:start position:0%
+governmental the leadership in creating
+ 
+
+ align:start position:0%
+governmental the leadership in creating
+strong firms but in effect of forcing
+
+ align:start position:0%
+strong firms but in effect of forcing
+ 
+
+ align:start position:0%
+strong firms but in effect of forcing
+them into international competition it's
+
+ align:start position:0%
+them into international competition it's
+ 
+
+ align:start position:0%
+them into international competition it's
+darling and the government education
+
+ align:start position:0%
+darling and the government education
+ 
+
+ align:start position:0%
+darling and the government education
+programs that facilitate
+
+ align:start position:0%
+programs that facilitate
+ 
+
+ align:start position:0%
+programs that facilitate
+very very strong talent base country
+
+ align:start position:0%
+very very strong talent base country
+ 
+
+ align:start position:0%
+very very strong talent base country
+were clearly key and the university of
+
+ align:start position:0%
+were clearly key and the university of
+ 
+
+ align:start position:0%
+were clearly key and the university of
+euclid a government used crisis to kind
+
+ align:start position:0%
+euclid a government used crisis to kind
+ 
+
+ align:start position:0%
+euclid a government used crisis to kind
+of force its firms would in effect force
+
+ align:start position:0%
+of force its firms would in effect force
+ 
+
+ align:start position:0%
+of force its firms would in effect force
+its firms into a crisis kind of
+
+ align:start position:0%
+its firms into a crisis kind of
+ 
+
+ align:start position:0%
+its firms into a crisis kind of
+circumstance
+
+ align:start position:0%
+circumstance
+ 
+
+ align:start position:0%
+circumstance
+so they really learn how to compete and
+
+ align:start position:0%
+so they really learn how to compete and
+ 
+
+ align:start position:0%
+so they really learn how to compete and
+survive so those are all kind of
+
+ align:start position:0%
+survive so those are all kind of
+ 
+
+ align:start position:0%
+survive so those are all kind of
+interesting lessons from Korea so who
+
+ align:start position:0%
+interesting lessons from Korea so who
+ 
+
+ align:start position:0%
+interesting lessons from Korea so who
+has got Lin sue Kim and who's got
+
+ align:start position:0%
+has got Lin sue Kim and who's got
+ 
+
+ align:start position:0%
+has got Lin sue Kim and who's got
+platforms I have okay and you've got
+
+ align:start position:0%
+platforms I have okay and you've got
+ 
+
+ align:start position:0%
+platforms I have okay and you've got
+plentiful so why don't we start with you
+
+ align:start position:0%
+plentiful so why don't we start with you
+ 
+
+ align:start position:0%
+plentiful so why don't we start with you
+Matt so I think this job covering a lot
+
+ align:start position:0%
+Matt so I think this job covering a lot
+ 
+
+ align:start position:0%
+Matt so I think this job covering a lot
+of his main points I think you know
+
+ align:start position:0%
+of his main points I think you know
+ 
+
+ align:start position:0%
+of his main points I think you know
+really interesting is when Fogg he kind
+
+ align:start position:0%
+really interesting is when Fogg he kind
+ 
+
+ align:start position:0%
+really interesting is when Fogg he kind
+of turns this argument instead where
+
+ align:start position:0%
+of turns this argument instead where
+ 
+
+ align:start position:0%
+of turns this argument instead where
+most people would think about your
+
+ align:start position:0%
+most people would think about your
+ 
+
+ align:start position:0%
+most people would think about your
+political structures kind of determining
+
+ align:start position:0%
+political structures kind of determining
+ 
+
+ align:start position:0%
+political structures kind of determining
+how competitive in economy is letting go
+
+ align:start position:0%
+how competitive in economy is letting go
+ 
+
+ align:start position:0%
+how competitive in economy is letting go
+Ted the competitiveness of the economy
+
+ align:start position:0%
+Ted the competitiveness of the economy
+ 
+
+ align:start position:0%
+Ted the competitiveness of the economy
+international competitive
+
+ align:start position:0%
+international competitive
+ 
+
+ align:start position:0%
+international competitive
+competitiveness driving the imperative
+
+ align:start position:0%
+competitiveness driving the imperative
+ 
+
+ align:start position:0%
+competitiveness driving the imperative
+of the political structure and how
+
+ align:start position:0%
+of the political structure and how
+ 
+
+ align:start position:0%
+of the political structure and how
+involved is he comes as the country
+
+ align:start position:0%
+involved is he comes as the country
+ 
+
+ align:start position:0%
+involved is he comes as the country
+moves from pursuer after the pioneer to
+
+ align:start position:0%
+moves from pursuer after the pioneer to
+ 
+
+ align:start position:0%
+moves from pursuer after the pioneer to
+follower at the frontier and he gives
+
+ align:start position:0%
+follower at the frontier and he gives
+ 
+
+ align:start position:0%
+follower at the frontier and he gives
+the example of Japan one one theme that
+
+ align:start position:0%
+the example of Japan one one theme that
+ 
+
+ align:start position:0%
+the example of Japan one one theme that
+I saw throughout the question is how
+
+ align:start position:0%
+I saw throughout the question is how
+ 
+
+ align:start position:0%
+I saw throughout the question is how
+much of that process is a conscious
+
+ align:start position:0%
+much of that process is a conscious
+ 
+
+ align:start position:0%
+much of that process is a conscious
+decision or how much of it just kind of
+
+ align:start position:0%
+decision or how much of it just kind of
+ 
+
+ align:start position:0%
+decision or how much of it just kind of
+happens naturally is there a certain
+
+ align:start position:0%
+happens naturally is there a certain
+ 
+
+ align:start position:0%
+happens naturally is there a certain
+point when they win the government says
+
+ align:start position:0%
+point when they win the government says
+ 
+
+ align:start position:0%
+point when they win the government says
+hey we are you know approaching your
+
+ align:start position:0%
+hey we are you know approaching your
+ 
+
+ align:start position:0%
+hey we are you know approaching your
+frontier now we should be hands-off or
+
+ align:start position:0%
+frontier now we should be hands-off or
+ 
+
+ align:start position:0%
+frontier now we should be hands-off or
+how does that end up happening in
+
+ align:start position:0%
+how does that end up happening in
+ 
+
+ align:start position:0%
+how does that end up happening in
+practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think the approach is probably the
+
+ align:start position:0%
+I think the approach is probably the
+ 
+
+ align:start position:0%
+I think the approach is probably the
+most difficult part of the process just
+
+ align:start position:0%
+most difficult part of the process just
+ 
+
+ align:start position:0%
+most difficult part of the process just
+as you have to sort of set up and
+
+ align:start position:0%
+as you have to sort of set up and
+ 
+
+ align:start position:0%
+as you have to sort of set up and
+protect sort of the tables and systems
+
+ align:start position:0%
+protect sort of the tables and systems
+ 
+
+ align:start position:0%
+protect sort of the tables and systems
+have to be put in place that kind of
+
+ align:start position:0%
+have to be put in place that kind of
+ 
+
+ align:start position:0%
+have to be put in place that kind of
+borrow on eserve cultural values you
+
+ align:start position:0%
+borrow on eserve cultural values you
+ 
+
+ align:start position:0%
+borrow on eserve cultural values you
+mentioned the strong military service at
+
+ align:start position:0%
+mentioned the strong military service at
+ 
+
+ align:start position:0%
+mentioned the strong military service at
+this point and a lot of other things
+
+ align:start position:0%
+this point and a lot of other things
+ 
+
+ align:start position:0%
+this point and a lot of other things
+sort of have to come together and so I
+
+ align:start position:0%
+sort of have to come together and so I
+ 
+
+ align:start position:0%
+sort of have to come together and so I
+would peg the approaches or the hardest
+
+ align:start position:0%
+would peg the approaches or the hardest
+ 
+
+ align:start position:0%
+would peg the approaches or the hardest
+part but I think once you have your
+
+ align:start position:0%
+part but I think once you have your
+ 
+
+ align:start position:0%
+part but I think once you have your
+system set up and you're looking to sort
+
+ align:start position:0%
+system set up and you're looking to sort
+ 
+
+ align:start position:0%
+system set up and you're looking to sort
+of compete like internationally I think
+
+ align:start position:0%
+of compete like internationally I think
+ 
+
+ align:start position:0%
+of compete like internationally I think
+that's the point where you have to sort
+
+ align:start position:0%
+that's the point where you have to sort
+ 
+
+ align:start position:0%
+that's the point where you have to sort
+of kind of let go but I think you need
+
+ align:start position:0%
+of kind of let go but I think you need
+ 
+
+ align:start position:0%
+of kind of let go but I think you need
+to reach some sort of maturity and I
+
+ align:start position:0%
+to reach some sort of maturity and I
+ 
+
+ align:start position:0%
+to reach some sort of maturity and I
+think it's pretty easy to say like okay
+
+ align:start position:0%
+think it's pretty easy to say like okay
+ 
+
+ align:start position:0%
+think it's pretty easy to say like okay
+look we've copied everything we've you
+
+ align:start position:0%
+look we've copied everything we've you
+ 
+
+ align:start position:0%
+look we've copied everything we've you
+know been able to copy like what's next
+
+ align:start position:0%
+know been able to copy like what's next
+ 
+
+ align:start position:0%
+know been able to copy like what's next
+I would if you don't have anything
+
+ align:start position:0%
+I would if you don't have anything
+ 
+
+ align:start position:0%
+I would if you don't have anything
+that's like it might be tough to sort of
+
+ align:start position:0%
+that's like it might be tough to sort of
+ 
+
+ align:start position:0%
+that's like it might be tough to sort of
+kind of diversify and kind of like
+
+ align:start position:0%
+kind of diversify and kind of like
+ 
+
+ align:start position:0%
+kind of diversify and kind of like
+things go so is she just use conforms to
+
+ align:start position:0%
+things go so is she just use conforms to
+ 
+
+ align:start position:0%
+things go so is she just use conforms to
+terms and correct me if I've got this
+
+ align:start position:0%
+terms and correct me if I've got this
+ 
+
+ align:start position:0%
+terms and correct me if I've got this
+but when you move from pursuer of a
+
+ align:start position:0%
+but when you move from pursuer of a
+ 
+
+ align:start position:0%
+but when you move from pursuer of a
+pioneer to right at the technological
+
+ align:start position:0%
+pioneer to right at the technological
+ 
+
+ align:start position:0%
+pioneer to right at the technological
+frontier that's the moment where you
+
+ align:start position:0%
+frontier that's the moment where you
+ 
+
+ align:start position:0%
+frontier that's the moment where you
+ought to think about your organization a
+
+ align:start position:0%
+ought to think about your organization a
+ 
+
+ align:start position:0%
+ought to think about your organization a
+lot because to get to that world-class
+
+ align:start position:0%
+lot because to get to that world-class
+ 
+
+ align:start position:0%
+lot because to get to that world-class
+leadership like this may require you to
+
+ align:start position:0%
+leadership like this may require you to
+ 
+
+ align:start position:0%
+leadership like this may require you to
+decentralize and change your
+
+ align:start position:0%
+decentralize and change your
+ 
+
+ align:start position:0%
+decentralize and change your
+governmental role more collaborative
+
+ align:start position:0%
+governmental role more collaborative
+ 
+
+ align:start position:0%
+governmental role more collaborative
+model rely on larger number of players
+
+ align:start position:0%
+model rely on larger number of players
+ 
+
+ align:start position:0%
+model rely on larger number of players
+that be you agree Matt with that yeah I
+
+ align:start position:0%
+that be you agree Matt with that yeah I
+ 
+
+ align:start position:0%
+that be you agree Matt with that yeah I
+think well the way that you said it
+
+ align:start position:0%
+think well the way that you said it
+ 
+
+ align:start position:0%
+think well the way that you said it
+almost no implies that there's a very
+
+ align:start position:0%
+almost no implies that there's a very
+ 
+
+ align:start position:0%
+almost no implies that there's a very
+conscious decision about how how much
+
+ align:start position:0%
+conscious decision about how how much
+ 
+
+ align:start position:0%
+conscious decision about how how much
+the only thing he bought I think for
+
+ align:start position:0%
+the only thing he bought I think for
+ 
+
+ align:start position:0%
+the only thing he bought I think for
+Japan what happened was they realized
+
+ align:start position:0%
+Japan what happened was they realized
+ 
+
+ align:start position:0%
+Japan what happened was they realized
+the misty ID bush right that was lived
+
+ align:start position:0%
+the misty ID bush right that was lived
+ 
+
+ align:start position:0%
+the misty ID bush right that was lived
+by US companies and we'll read about
+
+ align:start position:0%
+by US companies and we'll read about
+ 
+
+ align:start position:0%
+by US companies and we'll read about
+DARPA and the IT revolution in the labor
+
+ align:start position:0%
+DARPA and the IT revolution in the labor
+ 
+
+ align:start position:0%
+DARPA and the IT revolution in the labor
+class but you'll see where that comes
+
+ align:start position:0%
+class but you'll see where that comes
+ 
+
+ align:start position:0%
+class but you'll see where that comes
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+by having an R&D system those refocused
+
+ align:start position:0%
+by having an R&D system those refocused
+ 
+
+ align:start position:0%
+by having an R&D system those refocused
+on applied work with industry
+
+ align:start position:0%
+on applied work with industry
+ 
+
+ align:start position:0%
+on applied work with industry
+as opposed to university search you get
+
+ align:start position:0%
+as opposed to university search you get
+ 
+
+ align:start position:0%
+as opposed to university search you get
+very good at the incremental advances
+
+ align:start position:0%
+very good at the incremental advances
+ 
+
+ align:start position:0%
+very good at the incremental advances
+but you made this fundamental
+
+ align:start position:0%
+but you made this fundamental
+ 
+
+ align:start position:0%
+but you made this fundamental
+breakthroughs and so I think Japan is
+
+ align:start position:0%
+breakthroughs and so I think Japan is
+ 
+
+ align:start position:0%
+breakthroughs and so I think Japan is
+waking up and 1998 to these realities
+
+ align:start position:0%
+waking up and 1998 to these realities
+ 
+
+ align:start position:0%
+waking up and 1998 to these realities
+and trying to think about its innovation
+
+ align:start position:0%
+and trying to think about its innovation
+ 
+
+ align:start position:0%
+and trying to think about its innovation
+organisation larger than you of
+
+ align:start position:0%
+organisation larger than you of
+ 
+
+ align:start position:0%
+organisation larger than you of
+innovation that would be my guess the
+
+ align:start position:0%
+innovation that would be my guess the
+ 
+
+ align:start position:0%
+innovation that would be my guess the
+other thing I had was uses Japan as an
+
+ align:start position:0%
+other thing I had was uses Japan as an
+ 
+
+ align:start position:0%
+other thing I had was uses Japan as an
+example I like looking at Korea and
+
+ align:start position:0%
+example I like looking at Korea and
+ 
+
+ align:start position:0%
+example I like looking at Korea and
+those seem to fit you know the motto but
+
+ align:start position:0%
+those seem to fit you know the motto but
+ 
+
+ align:start position:0%
+those seem to fit you know the motto but
+you know to what extent does does this
+
+ align:start position:0%
+you know to what extent does does this
+ 
+
+ align:start position:0%
+you know to what extent does does this
+model actually general and so rather top
+
+ align:start position:0%
+model actually general and so rather top
+ 
+
+ align:start position:0%
+model actually general and so rather top
+of my head if you think of like you know
+
+ align:start position:0%
+of my head if you think of like you know
+ 
+
+ align:start position:0%
+of my head if you think of like you know
+the u.s. space program with like the
+
+ align:start position:0%
+the u.s. space program with like the
+ 
+
+ align:start position:0%
+the u.s. space program with like the
+Manhattan Project but it's very much at
+
+ align:start position:0%
+Manhattan Project but it's very much at
+ 
+
+ align:start position:0%
+Manhattan Project but it's very much at
+the competitive frontier but strong
+
+ align:start position:0%
+the competitive frontier but strong
+ 
+
+ align:start position:0%
+the competitive frontier but strong
+government involvement and basically
+
+ align:start position:0%
+government involvement and basically
+ 
+
+ align:start position:0%
+government involvement and basically
+targeting technologies did lead to major
+
+ align:start position:0%
+targeting technologies did lead to major
+ 
+
+ align:start position:0%
+targeting technologies did lead to major
+advances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I do do we think that it that the model
+
+ align:start position:0%
+I do do we think that it that the model
+ 
+
+ align:start position:0%
+I do do we think that it that the model
+actually works all the time or is it
+
+ align:start position:0%
+actually works all the time or is it
+ 
+
+ align:start position:0%
+actually works all the time or is it
+necessary use the best thing to be doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+help out Matthew Jemaine I hear it's got
+
+ align:start position:0%
+help out Matthew Jemaine I hear it's got
+ 
+
+ align:start position:0%
+help out Matthew Jemaine I hear it's got
+a lifeline out there which won't drink
+
+ align:start position:0%
+a lifeline out there which won't drink
+ 
+
+ align:start position:0%
+a lifeline out there which won't drink
+since why me in the general discourse of
+
+ align:start position:0%
+since why me in the general discourse of
+ 
+
+ align:start position:0%
+since why me in the general discourse of
+innovation only pay attention take these
+
+ align:start position:0%
+innovation only pay attention take these
+ 
+
+ align:start position:0%
+innovation only pay attention take these
+Asian countries or largely pay attention
+
+ align:start position:0%
+Asian countries or largely pay attention
+ 
+
+ align:start position:0%
+Asian countries or largely pay attention
+to these Asian countries because you
+
+ align:start position:0%
+to these Asian countries because you
+ 
+
+ align:start position:0%
+to these Asian countries because you
+never hear about United States and
+
+ align:start position:0%
+never hear about United States and
+ 
+
+ align:start position:0%
+never hear about United States and
+innovations here being just supposed to
+
+ align:start position:0%
+innovations here being just supposed to
+ 
+
+ align:start position:0%
+innovations here being just supposed to
+say innovations in Central or South
+
+ align:start position:0%
+say innovations in Central or South
+ 
+
+ align:start position:0%
+say innovations in Central or South
+America or even Eastern Europe and
+
+ align:start position:0%
+America or even Eastern Europe and
+ 
+
+ align:start position:0%
+America or even Eastern Europe and
+perhaps you know technological advances
+
+ align:start position:0%
+perhaps you know technological advances
+ 
+
+ align:start position:0%
+perhaps you know technological advances
+are not as impressive this sort of
+
+ align:start position:0%
+are not as impressive this sort of
+ 
+
+ align:start position:0%
+are not as impressive this sort of
+breadth of their compact is not as
+
+ align:start position:0%
+breadth of their compact is not as
+ 
+
+ align:start position:0%
+breadth of their compact is not as
+extensive and at the same time I think
+
+ align:start position:0%
+extensive and at the same time I think
+ 
+
+ align:start position:0%
+extensive and at the same time I think
+there has to be innovation occurring in
+
+ align:start position:0%
+there has to be innovation occurring in
+ 
+
+ align:start position:0%
+there has to be innovation occurring in
+other parts of the world they're not
+
+ align:start position:0%
+other parts of the world they're not
+ 
+
+ align:start position:0%
+other parts of the world they're not
+South Korea Germany China and Japan so
+
+ align:start position:0%
+South Korea Germany China and Japan so
+ 
+
+ align:start position:0%
+South Korea Germany China and Japan so
+to what extent is that sort of premise
+
+ align:start position:0%
+to what extent is that sort of premise
+ 
+
+ align:start position:0%
+to what extent is that sort of premise
+Don that kind of American paranoia that
+
+ align:start position:0%
+Don that kind of American paranoia that
+ 
+
+ align:start position:0%
+Don that kind of American paranoia that
+was highlighted in the Hughes piece
+
+ align:start position:0%
+was highlighted in the Hughes piece
+ 
+
+ align:start position:0%
+was highlighted in the Hughes piece
+against East Asia yeah I think maybe
+
+ align:start position:0%
+against East Asia yeah I think maybe
+ 
+
+ align:start position:0%
+against East Asia yeah I think maybe
+good follow-up is like we don't have
+
+ align:start position:0%
+good follow-up is like we don't have
+ 
+
+ align:start position:0%
+good follow-up is like we don't have
+enough counter example for you just cuz
+
+ align:start position:0%
+enough counter example for you just cuz
+ 
+
+ align:start position:0%
+enough counter example for you just cuz
+the press in the highlight and the
+
+ align:start position:0%
+the press in the highlight and the
+ 
+
+ align:start position:0%
+the press in the highlight and the
+attention hasn't been put there and I
+
+ align:start position:0%
+attention hasn't been put there and I
+ 
+
+ align:start position:0%
+attention hasn't been put there and I
+would hope yeah in central South
+
+ align:start position:0%
+would hope yeah in central South
+ 
+
+ align:start position:0%
+would hope yeah in central South
+American and these Eastern European
+
+ align:start position:0%
+American and these Eastern European
+ 
+
+ align:start position:0%
+American and these Eastern European
+countries they're seeing sort of the
+
+ align:start position:0%
+countries they're seeing sort of the
+ 
+
+ align:start position:0%
+countries they're seeing sort of the
+pervasiveness of these different models
+
+ align:start position:0%
+pervasiveness of these different models
+ 
+
+ align:start position:0%
+pervasiveness of these different models
+and there's no way they're not thinking
+
+ align:start position:0%
+and there's no way they're not thinking
+ 
+
+ align:start position:0%
+and there's no way they're not thinking
+about these things are adapting their
+
+ align:start position:0%
+about these things are adapting their
+ 
+
+ align:start position:0%
+about these things are adapting their
+mouths
+
+ align:start position:0%
+mouths
+ 
+
+ align:start position:0%
+mouths
+these sort of things I mean I noticed
+
+ align:start position:0%
+these sort of things I mean I noticed
+ 
+
+ align:start position:0%
+these sort of things I mean I noticed
+him at the I was at the Charlie has
+
+ align:start position:0%
+him at the I was at the Charlie has
+ 
+
+ align:start position:0%
+him at the I was at the Charlie has
+meeting last week and some of the people
+
+ align:start position:0%
+meeting last week and some of the people
+ 
+
+ align:start position:0%
+meeting last week and some of the people
+who were coming in from Russia we're
+
+ align:start position:0%
+who were coming in from Russia we're
+ 
+
+ align:start position:0%
+who were coming in from Russia we're
+saying that they had found that some of
+
+ align:start position:0%
+saying that they had found that some of
+ 
+
+ align:start position:0%
+saying that they had found that some of
+the advances that were just being noted
+
+ align:start position:0%
+the advances that were just being noted
+ 
+
+ align:start position:0%
+the advances that were just being noted
+in North America had been made in Russia
+
+ align:start position:0%
+in North America had been made in Russia
+ 
+
+ align:start position:0%
+in North America had been made in Russia
+think a decade ago and they had just
+
+ align:start position:0%
+think a decade ago and they had just
+ 
+
+ align:start position:0%
+think a decade ago and they had just
+never transferred to the International
+
+ align:start position:0%
+never transferred to the International
+ 
+
+ align:start position:0%
+never transferred to the International
+constant community because they were
+
+ align:start position:0%
+constant community because they were
+ 
+
+ align:start position:0%
+constant community because they were
+Russian centric and I thought that that
+
+ align:start position:0%
+Russian centric and I thought that that
+ 
+
+ align:start position:0%
+Russian centric and I thought that that
+was a really fascinating component about
+
+ align:start position:0%
+was a really fascinating component about
+ 
+
+ align:start position:0%
+was a really fascinating component about
+knowledge transfer its knowledge sharing
+
+ align:start position:0%
+knowledge transfer its knowledge sharing
+ 
+
+ align:start position:0%
+knowledge transfer its knowledge sharing
+because if our focus is only on
+
+ align:start position:0%
+because if our focus is only on
+ 
+
+ align:start position:0%
+because if our focus is only on
+competing with East Asian countries and
+
+ align:start position:0%
+competing with East Asian countries and
+ 
+
+ align:start position:0%
+competing with East Asian countries and
+Germany to what extent to our team it's
+
+ align:start position:0%
+Germany to what extent to our team it's
+ 
+
+ align:start position:0%
+Germany to what extent to our team it's
+an opportunity and it's a pain of paying
+
+ align:start position:0%
+an opportunity and it's a pain of paying
+ 
+
+ align:start position:0%
+an opportunity and it's a pain of paying
+attention to other countries that who
+
+ align:start position:0%
+attention to other countries that who
+ 
+
+ align:start position:0%
+attention to other countries that who
+might have interesting innovation cycles
+
+ align:start position:0%
+might have interesting innovation cycles
+ 
+
+ align:start position:0%
+might have interesting innovation cycles
+are products that we can learn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well against to add on to that so I
+
+ align:start position:0%
+well against to add on to that so I
+ 
+
+ align:start position:0%
+well against to add on to that so I
+think the reason we look into age lot
+
+ align:start position:0%
+think the reason we look into age lot
+ 
+
+ align:start position:0%
+think the reason we look into age lot
+because ha
+
+ align:start position:0%
+because ha
+ 
+
+ align:start position:0%
+because ha
+they were like economies that weren't
+
+ align:start position:0%
+they were like economies that weren't
+ 
+
+ align:start position:0%
+they were like economies that weren't
+doing great and they pretty much like
+
+ align:start position:0%
+doing great and they pretty much like
+ 
+
+ align:start position:0%
+doing great and they pretty much like
+did a 360 turn like I wouldn't a be like
+
+ align:start position:0%
+did a 360 turn like I wouldn't a be like
+ 
+
+ align:start position:0%
+did a 360 turn like I wouldn't a be like
+in less than like 30 years and there's a
+
+ align:start position:0%
+in less than like 30 years and there's a
+ 
+
+ align:start position:0%
+in less than like 30 years and there's a
+lot of factors to it a lot of that was
+
+ align:start position:0%
+lot of factors to it a lot of that was
+ 
+
+ align:start position:0%
+lot of factors to it a lot of that was
+having very strong leaders going from
+
+ align:start position:0%
+having very strong leaders going from
+ 
+
+ align:start position:0%
+having very strong leaders going from
+periods of like not doing too well so
+
+ align:start position:0%
+periods of like not doing too well so
+ 
+
+ align:start position:0%
+periods of like not doing too well so
+they're more unified and then having a
+
+ align:start position:0%
+they're more unified and then having a
+ 
+
+ align:start position:0%
+they're more unified and then having a
+strong young population so most the
+
+ align:start position:0%
+strong young population so most the
+ 
+
+ align:start position:0%
+strong young population so most the
+countries that did really well next
+
+ align:start position:0%
+countries that did really well next
+ 
+
+ align:start position:0%
+countries that did really well next
+period like for the age pyramid like
+
+ align:start position:0%
+period like for the age pyramid like
+ 
+
+ align:start position:0%
+period like for the age pyramid like
+this it's a lot of young people very few
+
+ align:start position:0%
+this it's a lot of young people very few
+ 
+
+ align:start position:0%
+this it's a lot of young people very few
+old people and they were they were able
+
+ align:start position:0%
+old people and they were they were able
+ 
+
+ align:start position:0%
+old people and they were they were able
+to move very quickly and it's just
+
+ align:start position:0%
+to move very quickly and it's just
+ 
+
+ align:start position:0%
+to move very quickly and it's just
+because they have these strong leaders
+
+ align:start position:0%
+because they have these strong leaders
+ 
+
+ align:start position:0%
+because they have these strong leaders
+these other countries I think a lot of
+
+ align:start position:0%
+these other countries I think a lot of
+ 
+
+ align:start position:0%
+these other countries I think a lot of
+in Latin America they they don't have
+
+ align:start position:0%
+in Latin America they they don't have
+ 
+
+ align:start position:0%
+in Latin America they they don't have
+these kind of strong leaders or these
+
+ align:start position:0%
+these kind of strong leaders or these
+ 
+
+ align:start position:0%
+these kind of strong leaders or these
+periods that come up beforehand so there
+
+ align:start position:0%
+periods that come up beforehand so there
+ 
+
+ align:start position:0%
+periods that come up beforehand so there
+hasn't been rapid growth like
+
+ align:start position:0%
+hasn't been rapid growth like
+ 
+
+ align:start position:0%
+hasn't been rapid growth like
+innovations you know there has been a
+
+ align:start position:0%
+innovations you know there has been a
+ 
+
+ align:start position:0%
+innovations you know there has been a
+lot of innovations especially
+
+ align:start position:0%
+lot of innovations especially
+ 
+
+ align:start position:0%
+lot of innovations especially
+manufacturing Raziel parts of Mexico so
+
+ align:start position:0%
+manufacturing Raziel parts of Mexico so
+ 
+
+ align:start position:0%
+manufacturing Raziel parts of Mexico so
+I think it's just we haven't we paid too
+
+ align:start position:0%
+I think it's just we haven't we paid too
+ 
+
+ align:start position:0%
+I think it's just we haven't we paid too
+much attention to it but it doesn't seem
+
+ align:start position:0%
+much attention to it but it doesn't seem
+ 
+
+ align:start position:0%
+much attention to it but it doesn't seem
+like a threat but II thought I cut
+
+ align:start position:0%
+like a threat but II thought I cut
+ 
+
+ align:start position:0%
+like a threat but II thought I cut
+through some hoops so quickly that it
+
+ align:start position:0%
+through some hoops so quickly that it
+ 
+
+ align:start position:0%
+through some hoops so quickly that it
+does see you can see more than threat
+
+ align:start position:0%
+does see you can see more than threat
+ 
+
+ align:start position:0%
+does see you can see more than threat
+because if you look at Singapore like it
+
+ align:start position:0%
+because if you look at Singapore like it
+ 
+
+ align:start position:0%
+because if you look at Singapore like it
+was a country that was privileged not
+
+ align:start position:0%
+was a country that was privileged not
+ 
+
+ align:start position:0%
+was a country that was privileged not
+there they had a very strong leader was
+
+ align:start position:0%
+there they had a very strong leader was
+ 
+
+ align:start position:0%
+there they had a very strong leader was
+able to make quick decisions that are
+
+ align:start position:0%
+able to make quick decisions that are
+ 
+
+ align:start position:0%
+able to make quick decisions that are
+very strong and be very strong saying
+
+ align:start position:0%
+very strong and be very strong saying
+ 
+
+ align:start position:0%
+very strong and be very strong saying
+this is what I believe this is what I
+
+ align:start position:0%
+this is what I believe this is what I
+ 
+
+ align:start position:0%
+this is what I believe this is what I
+think we should do and then going after
+
+ align:start position:0%
+think we should do and then going after
+ 
+
+ align:start position:0%
+think we should do and then going after
+it and they were able to completely get
+
+ align:start position:0%
+it and they were able to completely get
+ 
+
+ align:start position:0%
+it and they were able to completely get
+just 180 their economy and I think we're
+
+ align:start position:0%
+just 180 their economy and I think we're
+ 
+
+ align:start position:0%
+just 180 their economy and I think we're
+also talking about like the role over
+
+ align:start position:0%
+also talking about like the role over
+ 
+
+ align:start position:0%
+also talking about like the role over
+government the US has like committees
+
+ align:start position:0%
+government the US has like committees
+ 
+
+ align:start position:0%
+government the US has like committees
+making decisions for innovation but
+
+ align:start position:0%
+making decisions for innovation but
+ 
+
+ align:start position:0%
+making decisions for innovation but
+actually Charlie Munger who everyone
+
+ align:start position:0%
+actually Charlie Munger who everyone
+ 
+
+ align:start position:0%
+actually Charlie Munger who everyone
+knows Warren Buffett right more or less
+
+ align:start position:0%
+knows Warren Buffett right more or less
+ 
+
+ align:start position:0%
+knows Warren Buffett right more or less
+Charlie Munger's his right-hand person
+
+ align:start position:0%
+Charlie Munger's his right-hand person
+ 
+
+ align:start position:0%
+Charlie Munger's his right-hand person
+and he says like in the past in general
+
+ align:start position:0%
+and he says like in the past in general
+ 
+
+ align:start position:0%
+and he says like in the past in general
+its countries do better when it was once
+
+ align:start position:0%
+its countries do better when it was once
+ 
+
+ align:start position:0%
+its countries do better when it was once
+very smart talented leader because they
+
+ align:start position:0%
+very smart talented leader because they
+ 
+
+ align:start position:0%
+very smart talented leader because they
+can make these hard decisions in the US
+
+ align:start position:0%
+can make these hard decisions in the US
+ 
+
+ align:start position:0%
+can make these hard decisions in the US
+we do have kind of like an executive but
+
+ align:start position:0%
+we do have kind of like an executive but
+ 
+
+ align:start position:0%
+we do have kind of like an executive but
+I think everybody in this table career
+
+ align:start position:0%
+I think everybody in this table career
+ 
+
+ align:start position:0%
+I think everybody in this table career
+that people don't really like say oh he
+
+ align:start position:0%
+that people don't really like say oh he
+ 
+
+ align:start position:0%
+that people don't really like say oh he
+said that we should do it so like the
+
+ align:start position:0%
+said that we should do it so like the
+ 
+
+ align:start position:0%
+said that we should do it so like the
+benefit is like these are very credible
+
+ align:start position:0%
+benefit is like these are very credible
+ 
+
+ align:start position:0%
+benefit is like these are very credible
+leaders that most of the time when they
+
+ align:start position:0%
+leaders that most of the time when they
+ 
+
+ align:start position:0%
+leaders that most of the time when they
+make it to that position for a bear from
+
+ align:start position:0%
+make it to that position for a bear from
+ 
+
+ align:start position:0%
+make it to that position for a bear from
+a downturn period are very talented and
+
+ align:start position:0%
+a downturn period are very talented and
+ 
+
+ align:start position:0%
+a downturn period are very talented and
+skilled and they that you make bets like
+
+ align:start position:0%
+skilled and they that you make bets like
+ 
+
+ align:start position:0%
+skilled and they that you make bets like
+they can make things are about the
+
+ align:start position:0%
+they can make things are about the
+ 
+
+ align:start position:0%
+they can make things are about the
+saying you know what this is an industry
+
+ align:start position:0%
+saying you know what this is an industry
+ 
+
+ align:start position:0%
+saying you know what this is an industry
+that's gonna grow very quickly let's put
+
+ align:start position:0%
+that's gonna grow very quickly let's put
+ 
+
+ align:start position:0%
+that's gonna grow very quickly let's put
+three people there's like three 30 40
+
+ align:start position:0%
+three people there's like three 30 40
+ 
+
+ align:start position:0%
+three people there's like three 30 40
+companies that could do well but I think
+
+ align:start position:0%
+companies that could do well but I think
+ 
+
+ align:start position:0%
+companies that could do well but I think
+these three are really gonna win
+
+ align:start position:0%
+these three are really gonna win
+ 
+
+ align:start position:0%
+these three are really gonna win
+we're gonna put all our eggs on this
+
+ align:start position:0%
+we're gonna put all our eggs on this
+ 
+
+ align:start position:0%
+we're gonna put all our eggs on this
+basket and we're gonna do well and
+
+ align:start position:0%
+basket and we're gonna do well and
+ 
+
+ align:start position:0%
+basket and we're gonna do well and
+that's something that's very I guess
+
+ align:start position:0%
+that's something that's very I guess
+ 
+
+ align:start position:0%
+that's something that's very I guess
+alcohol on American because we're very
+
+ align:start position:0%
+alcohol on American because we're very
+ 
+
+ align:start position:0%
+alcohol on American because we're very
+much like everybody can go about it we
+
+ align:start position:0%
+much like everybody can go about it we
+ 
+
+ align:start position:0%
+much like everybody can go about it we
+want to leave opportunity but these
+
+ align:start position:0%
+want to leave opportunity but these
+ 
+
+ align:start position:0%
+want to leave opportunity but these
+countries do have this capability and
+
+ align:start position:0%
+countries do have this capability and
+ 
+
+ align:start position:0%
+countries do have this capability and
+they have parties shows that they can
+
+ align:start position:0%
+they have parties shows that they can
+ 
+
+ align:start position:0%
+they have parties shows that they can
+grow so quickly versus other countries I
+
+ align:start position:0%
+grow so quickly versus other countries I
+ 
+
+ align:start position:0%
+grow so quickly versus other countries I
+think I think another thing too is like
+
+ align:start position:0%
+think I think another thing too is like
+ 
+
+ align:start position:0%
+think I think another thing too is like
+Latin America Russia we still see a lot
+
+ align:start position:0%
+Latin America Russia we still see a lot
+ 
+
+ align:start position:0%
+Latin America Russia we still see a lot
+of corruption these other countries to
+
+ align:start position:0%
+of corruption these other countries to
+ 
+
+ align:start position:0%
+of corruption these other countries to
+get rid of it like Singapore what Lee
+
+ align:start position:0%
+get rid of it like Singapore what Lee
+ 
+
+ align:start position:0%
+get rid of it like Singapore what Lee
+Kuan Yew did we'll say okay I'm gonna
+
+ align:start position:0%
+Kuan Yew did we'll say okay I'm gonna
+ 
+
+ align:start position:0%
+Kuan Yew did we'll say okay I'm gonna
+pay everyone about twice as much but if
+
+ align:start position:0%
+pay everyone about twice as much but if
+ 
+
+ align:start position:0%
+pay everyone about twice as much but if
+I find out that you're being corrupt you
+
+ align:start position:0%
+I find out that you're being corrupt you
+ 
+
+ align:start position:0%
+I find out that you're being corrupt you
+guys are pretty much done it was like a
+
+ align:start position:0%
+guys are pretty much done it was like a
+ 
+
+ align:start position:0%
+guys are pretty much done it was like a
+death penalty or it was like very severe
+
+ align:start position:0%
+death penalty or it was like very severe
+ 
+
+ align:start position:0%
+death penalty or it was like very severe
+sanctions but also severe sanctions upon
+
+ align:start position:0%
+sanctions but also severe sanctions upon
+ 
+
+ align:start position:0%
+sanctions but also severe sanctions upon
+them and their families so that's a
+
+ align:start position:0%
+them and their families so that's a
+ 
+
+ align:start position:0%
+them and their families so that's a
+completely different way of going about
+
+ align:start position:0%
+completely different way of going about
+ 
+
+ align:start position:0%
+completely different way of going about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so I think we did just all see other
+
+ align:start position:0%
+so I think we did just all see other
+ 
+
+ align:start position:0%
+so I think we did just all see other
+pensions a threat even though they have
+
+ align:start position:0%
+pensions a threat even though they have
+ 
+
+ align:start position:0%
+pensions a threat even though they have
+good capabilities but these funders
+
+ align:start position:0%
+good capabilities but these funders
+ 
+
+ align:start position:0%
+good capabilities but these funders
+didn't do amazing things
+
+ align:start position:0%
+didn't do amazing things
+ 
+
+ align:start position:0%
+didn't do amazing things
+30 20 years that can but you could also
+
+ align:start position:0%
+30 20 years that can but you could also
+ 
+
+ align:start position:0%
+30 20 years that can but you could also
+debate that was because there was very
+
+ align:start position:0%
+debate that was because there was very
+ 
+
+ align:start position:0%
+debate that was because there was very
+young populations because also Japan and
+
+ align:start position:0%
+young populations because also Japan and
+ 
+
+ align:start position:0%
+young populations because also Japan and
+South Korea had Steck nations right
+
+ align:start position:0%
+South Korea had Steck nations right
+ 
+
+ align:start position:0%
+South Korea had Steck nations right
+after so and finals like Martina it's a
+
+ align:start position:0%
+after so and finals like Martina it's a
+ 
+
+ align:start position:0%
+after so and finals like Martina it's a
+very it's a very political economy
+
+ align:start position:0%
+very it's a very political economy
+ 
+
+ align:start position:0%
+very it's a very political economy
+perspective right and I you know going
+
+ align:start position:0%
+perspective right and I you know going
+ 
+
+ align:start position:0%
+perspective right and I you know going
+back to some of the points that Matt was
+
+ align:start position:0%
+back to some of the points that Matt was
+ 
+
+ align:start position:0%
+back to some of the points that Matt was
+making earlier I think the central Glenn
+
+ align:start position:0%
+making earlier I think the central Glenn
+ 
+
+ align:start position:0%
+making earlier I think the central Glenn
+Forum argument is that that may get you
+
+ align:start position:0%
+Forum argument is that that may get you
+ 
+
+ align:start position:0%
+Forum argument is that that may get you
+a fair distance for a period of time as
+
+ align:start position:0%
+a fair distance for a period of time as
+ 
+
+ align:start position:0%
+a fair distance for a period of time as
+you're getting to the frontier but then
+
+ align:start position:0%
+you're getting to the frontier but then
+ 
+
+ align:start position:0%
+you're getting to the frontier but then
+when you get to the frontier you better
+
+ align:start position:0%
+when you get to the frontier you better
+ 
+
+ align:start position:0%
+when you get to the frontier you better
+figure out ain't more bottom-up more
+
+ align:start position:0%
+figure out ain't more bottom-up more
+ 
+
+ align:start position:0%
+figure out ain't more bottom-up more
+collaborative kind of model if you want
+
+ align:start position:0%
+collaborative kind of model if you want
+ 
+
+ align:start position:0%
+collaborative kind of model if you want
+to keep the ideas if you need that big
+
+ align:start position:0%
+to keep the ideas if you need that big
+ 
+
+ align:start position:0%
+to keep the ideas if you need that big
+mix of ideas that's going to enable you
+
+ align:start position:0%
+mix of ideas that's going to enable you
+ 
+
+ align:start position:0%
+mix of ideas that's going to enable you
+to go to a series of the next things
+
+ align:start position:0%
+to go to a series of the next things
+ 
+
+ align:start position:0%
+to go to a series of the next things
+that's that's phone's argument and that
+
+ align:start position:0%
+that's that's phone's argument and that
+ 
+
+ align:start position:0%
+that's that's phone's argument and that
+his point is that just hand really had
+
+ align:start position:0%
+his point is that just hand really had
+ 
+
+ align:start position:0%
+his point is that just hand really had
+to reorganize and since innovation
+
+ align:start position:0%
+to reorganize and since innovation
+ 
+
+ align:start position:0%
+to reorganize and since innovation
+system away from the political economy
+
+ align:start position:0%
+system away from the political economy
+ 
+
+ align:start position:0%
+system away from the political economy
+kind of approach to describing or to
+
+ align:start position:0%
+kind of approach to describing or to
+ 
+
+ align:start position:0%
+kind of approach to describing or to
+really a very different organization
+
+ align:start position:0%
+really a very different organization
+ 
+
+ align:start position:0%
+really a very different organization
+when it reached that you know innovation
+
+ align:start position:0%
+when it reached that you know innovation
+ 
+
+ align:start position:0%
+when it reached that you know innovation
+competition but it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mr. Anya this wants to your question you
+
+ align:start position:0%
+mr. Anya this wants to your question you
+ 
+
+ align:start position:0%
+mr. Anya this wants to your question you
+know I want to go back to what we talked
+
+ align:start position:0%
+know I want to go back to what we talked
+ 
+
+ align:start position:0%
+know I want to go back to what we talked
+about in the first class for a long time
+
+ align:start position:0%
+about in the first class for a long time
+ 
+
+ align:start position:0%
+about in the first class for a long time
+we thought that this innovation system
+
+ align:start position:0%
+we thought that this innovation system
+ 
+
+ align:start position:0%
+we thought that this innovation system
+stuff was the wing which the rich
+
+ align:start position:0%
+stuff was the wing which the rich
+ 
+
+ align:start position:0%
+stuff was the wing which the rich
+countries got Richmond right it was just
+
+ align:start position:0%
+countries got Richmond right it was just
+ 
+
+ align:start position:0%
+countries got Richmond right it was just
+a way to build further wealth you know
+
+ align:start position:0%
+a way to build further wealth you know
+ 
+
+ align:start position:0%
+a way to build further wealth you know
+relatively modest number of countries
+
+ align:start position:0%
+relatively modest number of countries
+ 
+
+ align:start position:0%
+relatively modest number of countries
+that figured out how to dominate and
+
+ align:start position:0%
+that figured out how to dominate and
+ 
+
+ align:start position:0%
+that figured out how to dominate and
+leave these these innovation systems but
+
+ align:start position:0%
+leave these these innovation systems but
+ 
+
+ align:start position:0%
+leave these these innovation systems but
+then other things start happening right
+
+ align:start position:0%
+then other things start happening right
+ 
+
+ align:start position:0%
+then other things start happening right
+Korea comes up from being totally
+
+ align:start position:0%
+Korea comes up from being totally
+ 
+
+ align:start position:0%
+Korea comes up from being totally
+destroyed right Taiwan somewhat you know
+
+ align:start position:0%
+destroyed right Taiwan somewhat you know
+ 
+
+ align:start position:0%
+destroyed right Taiwan somewhat you know
+economies like India which is obviously
+
+ align:start position:0%
+economies like India which is obviously
+ 
+
+ align:start position:0%
+economies like India which is obviously
+one of the forests of the world is able
+
+ align:start position:0%
+one of the forests of the world is able
+ 
+
+ align:start position:0%
+one of the forests of the world is able
+to start building a very significant
+
+ align:start position:0%
+to start building a very significant
+ 
+
+ align:start position:0%
+to start building a very significant
+middle class and you know China is the
+
+ align:start position:0%
+middle class and you know China is the
+ 
+
+ align:start position:0%
+middle class and you know China is the
+latest element in the story in other
+
+ align:start position:0%
+latest element in the story in other
+ 
+
+ align:start position:0%
+latest element in the story in other
+words an innovation based growth model
+
+ align:start position:0%
+words an innovation based growth model
+ 
+
+ align:start position:0%
+words an innovation based growth model
+can be pervasive and work in the
+
+ align:start position:0%
+can be pervasive and work in the
+ 
+
+ align:start position:0%
+can be pervasive and work in the
+development world now we've managed to
+
+ align:start position:0%
+development world now we've managed to
+ 
+
+ align:start position:0%
+development world now we've managed to
+translate that a pretty interesting
+
+ align:start position:0%
+translate that a pretty interesting
+ 
+
+ align:start position:0%
+translate that a pretty interesting
+scale you know get parts of Asia
+
+ align:start position:0%
+scale you know get parts of Asia
+ 
+
+ align:start position:0%
+scale you know get parts of Asia
+we haven't you're exactly like we
+
+ align:start position:0%
+we haven't you're exactly like we
+ 
+
+ align:start position:0%
+we haven't you're exactly like we
+haven't translated the possible
+
+ align:start position:0%
+haven't translated the possible
+ 
+
+ align:start position:0%
+haven't translated the possible
+exception of Brazil into a pervasive
+
+ align:start position:0%
+exception of Brazil into a pervasive
+ 
+
+ align:start position:0%
+exception of Brazil into a pervasive
+monogamous and so it's you know one of
+
+ align:start position:0%
+monogamous and so it's you know one of
+ 
+
+ align:start position:0%
+monogamous and so it's you know one of
+the options for doing a paper in this
+
+ align:start position:0%
+the options for doing a paper in this
+ 
+
+ align:start position:0%
+the options for doing a paper in this
+course is to look at national and other
+
+ align:start position:0%
+course is to look at national and other
+ 
+
+ align:start position:0%
+course is to look at national and other
+national innovation systems that dive
+
+ align:start position:0%
+national innovation systems that dive
+ 
+
+ align:start position:0%
+national innovation systems that dive
+into them and I really hope somebody
+
+ align:start position:0%
+into them and I really hope somebody
+ 
+
+ align:start position:0%
+into them and I really hope somebody
+will pursue this it's you know we don't
+
+ align:start position:0%
+will pursue this it's you know we don't
+ 
+
+ align:start position:0%
+will pursue this it's you know we don't
+particularly focus on this in this class
+
+ align:start position:0%
+particularly focus on this in this class
+ 
+
+ align:start position:0%
+particularly focus on this in this class
+so that we could but the Brazil stories
+
+ align:start position:0%
+so that we could but the Brazil stories
+ 
+
+ align:start position:0%
+so that we could but the Brazil stories
+absolutely fast and a remarkable story
+
+ align:start position:0%
+absolutely fast and a remarkable story
+ 
+
+ align:start position:0%
+absolutely fast and a remarkable story
+obviously they're in a fair amount of
+
+ align:start position:0%
+obviously they're in a fair amount of
+ 
+
+ align:start position:0%
+obviously they're in a fair amount of
+economic trouble from macro factors but
+
+ align:start position:0%
+economic trouble from macro factors but
+ 
+
+ align:start position:0%
+economic trouble from macro factors but
+nonetheless it's a very promising story
+
+ align:start position:0%
+nonetheless it's a very promising story
+ 
+
+ align:start position:0%
+nonetheless it's a very promising story
+yeah I think there are others and there
+
+ align:start position:0%
+yeah I think there are others and there
+ 
+
+ align:start position:0%
+yeah I think there are others and there
+are other parts of the culture so
+
+ align:start position:0%
+are other parts of the culture so
+ 
+
+ align:start position:0%
+are other parts of the culture so
+putting a much resume is longer talking
+
+ align:start position:0%
+putting a much resume is longer talking
+ 
+
+ align:start position:0%
+putting a much resume is longer talking
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+I remember that there's sort of major
+
+ align:start position:0%
+I remember that there's sort of major
+ 
+
+ align:start position:0%
+I remember that there's sort of major
+airplane companies or if I manufacture
+
+ align:start position:0%
+airplane companies or if I manufacture
+ 
+
+ align:start position:0%
+airplane companies or if I manufacture
+so you think like Boeing I throw up on
+
+ align:start position:0%
+so you think like Boeing I throw up on
+ 
+
+ align:start position:0%
+so you think like Boeing I throw up on
+when this morning ever air yeah exactly
+
+ align:start position:0%
+when this morning ever air yeah exactly
+ 
+
+ align:start position:0%
+when this morning ever air yeah exactly
+and there Jase
+
+ align:start position:0%
+and there Jase
+ 
+
+ align:start position:0%
+and there Jase
+and they're from Brazil and basic result
+
+ align:start position:0%
+and they're from Brazil and basic result
+ 
+
+ align:start position:0%
+and they're from Brazil and basic result
+and they basically are really important
+
+ align:start position:0%
+and they basically are really important
+ 
+
+ align:start position:0%
+and they basically are really important
+sort of now and will be important in the
+
+ align:start position:0%
+sort of now and will be important in the
+ 
+
+ align:start position:0%
+sort of now and will be important in the
+coming years because going in everyone's
+
+ align:start position:0%
+coming years because going in everyone's
+ 
+
+ align:start position:0%
+coming years because going in everyone's
+dominate he's like very large big
+
+ align:start position:0%
+dominate he's like very large big
+ 
+
+ align:start position:0%
+dominate he's like very large big
+airplanes looks like 787's like these
+
+ align:start position:0%
+airplanes looks like 787's like these
+ 
+
+ align:start position:0%
+airplanes looks like 787's like these
+very large aircraft this sort of all
+
+ align:start position:0%
+very large aircraft this sort of all
+ 
+
+ align:start position:0%
+very large aircraft this sort of all
+tend to get bigger in scale Embraer is
+
+ align:start position:0%
+tend to get bigger in scale Embraer is
+ 
+
+ align:start position:0%
+tend to get bigger in scale Embraer is
+important because they focus on sort of
+
+ align:start position:0%
+important because they focus on sort of
+ 
+
+ align:start position:0%
+important because they focus on sort of
+shorter flight distances with smaller
+
+ align:start position:0%
+shorter flight distances with smaller
+ 
+
+ align:start position:0%
+shorter flight distances with smaller
+aircraft and developing out of that
+
+ align:start position:0%
+aircraft and developing out of that
+ 
+
+ align:start position:0%
+aircraft and developing out of that
+market but I just looked and they were
+
+ align:start position:0%
+market but I just looked and they were
+ 
+
+ align:start position:0%
+market but I just looked and they were
+actually in the 90s sort of this
+
+ align:start position:0%
+actually in the 90s sort of this
+ 
+
+ align:start position:0%
+actually in the 90s sort of this
+public-private partnership so came while
+
+ align:start position:0%
+public-private partnership so came while
+ 
+
+ align:start position:0%
+public-private partnership so came while
+Brazil is looking at sort of shorter
+
+ align:start position:0%
+Brazil is looking at sort of shorter
+ 
+
+ align:start position:0%
+Brazil is looking at sort of shorter
+distance flights and doing that a lot
+
+ align:start position:0%
+distance flights and doing that a lot
+ 
+
+ align:start position:0%
+distance flights and doing that a lot
+better but it does come sort of this
+
+ align:start position:0%
+better but it does come sort of this
+ 
+
+ align:start position:0%
+better but it does come sort of this
+pursue after pioneer and I think they're
+
+ align:start position:0%
+pursue after pioneer and I think they're
+ 
+
+ align:start position:0%
+pursue after pioneer and I think they're
+now probably shifting to build more
+
+ align:start position:0%
+now probably shifting to build more
+ 
+
+ align:start position:0%
+now probably shifting to build more
+aircrafts there's instead of like
+
+ align:start position:0%
+aircrafts there's instead of like
+ 
+
+ align:start position:0%
+aircrafts there's instead of like
+copying smaller aircraft designs they're
+
+ align:start position:0%
+copying smaller aircraft designs they're
+ 
+
+ align:start position:0%
+copying smaller aircraft designs they're
+sort of having to now become the
+
+ align:start position:0%
+sort of having to now become the
+ 
+
+ align:start position:0%
+sort of having to now become the
+pioneers and like really start building
+
+ align:start position:0%
+pioneers and like really start building
+ 
+
+ align:start position:0%
+pioneers and like really start building
+new just like smaller scale aircraft and
+
+ align:start position:0%
+new just like smaller scale aircraft and
+ 
+
+ align:start position:0%
+new just like smaller scale aircraft and
+take that market and Brazil is
+
+ align:start position:0%
+take that market and Brazil is
+ 
+
+ align:start position:0%
+take that market and Brazil is
+interesting just cuz they were allowed
+
+ align:start position:0%
+interesting just cuz they were allowed
+ 
+
+ align:start position:0%
+interesting just cuz they were allowed
+to do that and I don't know what sort of
+
+ align:start position:0%
+to do that and I don't know what sort of
+ 
+
+ align:start position:0%
+to do that and I don't know what sort of
+factors played into them being allowed
+
+ align:start position:0%
+factors played into them being allowed
+ 
+
+ align:start position:0%
+factors played into them being allowed
+to initially start that public-private
+
+ align:start position:0%
+to initially start that public-private
+ 
+
+ align:start position:0%
+to initially start that public-private
+partnership and about the 90s when
+
+ align:start position:0%
+partnership and about the 90s when
+ 
+
+ align:start position:0%
+partnership and about the 90s when
+Embraer started but I think now they're
+
+ align:start position:0%
+Embraer started but I think now they're
+ 
+
+ align:start position:0%
+Embraer started but I think now they're
+probably gonna have to ship pretty
+
+ align:start position:0%
+probably gonna have to ship pretty
+ 
+
+ align:start position:0%
+probably gonna have to ship pretty
+drastically radically and looking to do
+
+ align:start position:0%
+drastically radically and looking to do
+ 
+
+ align:start position:0%
+drastically radically and looking to do
+that so that's a place I don't think
+
+ align:start position:0%
+that so that's a place I don't think
+ 
+
+ align:start position:0%
+that so that's a place I don't think
+we've touched yet is presumably I think
+
+ align:start position:0%
+we've touched yet is presumably I think
+ 
+
+ align:start position:0%
+we've touched yet is presumably I think
+there was a lot of pushback from their
+
+ align:start position:0%
+there was a lot of pushback from their
+ 
+
+ align:start position:0%
+there was a lot of pushback from their
+competitors for that Emperor was getting
+
+ align:start position:0%
+competitors for that Emperor was getting
+ 
+
+ align:start position:0%
+competitors for that Emperor was getting
+unfair treatment from their government
+
+ align:start position:0%
+unfair treatment from their government
+ 
+
+ align:start position:0%
+unfair treatment from their government
+in terms of like other trade agreements
+
+ align:start position:0%
+in terms of like other trade agreements
+ 
+
+ align:start position:0%
+in terms of like other trade agreements
+and donar specifically but it does call
+
+ align:start position:0%
+and donar specifically but it does call
+ 
+
+ align:start position:0%
+and donar specifically but it does call
+a Chris Chris I'm going to shift over to
+
+ align:start position:0%
+a Chris Chris I'm going to shift over to
+ 
+
+ align:start position:0%
+a Chris Chris I'm going to shift over to
+you and we're gonna do let sue Kim so I
+
+ align:start position:0%
+you and we're gonna do let sue Kim so I
+ 
+
+ align:start position:0%
+you and we're gonna do let sue Kim so I
+think they'll really give a good
+
+ align:start position:0%
+think they'll really give a good
+ 
+
+ align:start position:0%
+think they'll really give a good
+background on the article but you don't
+
+ align:start position:0%
+background on the article but you don't
+ 
+
+ align:start position:0%
+background on the article but you don't
+have to say that but to go into a bit
+
+ align:start position:0%
+have to say that but to go into a bit
+ 
+
+ align:start position:0%
+have to say that but to go into a bit
+more about the process of how Korea kind
+
+ align:start position:0%
+more about the process of how Korea kind
+ 
+
+ align:start position:0%
+more about the process of how Korea kind
+of came up to speed on the forefront of
+
+ align:start position:0%
+of came up to speed on the forefront of
+ 
+
+ align:start position:0%
+of came up to speed on the forefront of
+the innovation frontier at that time
+
+ align:start position:0%
+the innovation frontier at that time
+ 
+
+ align:start position:0%
+the innovation frontier at that time
+they really went through this process of
+
+ align:start position:0%
+they really went through this process of
+ 
+
+ align:start position:0%
+they really went through this process of
+imitating what was out there and then
+
+ align:start position:0%
+imitating what was out there and then
+ 
+
+ align:start position:0%
+imitating what was out there and then
+from that basis going on to innovate and
+
+ align:start position:0%
+from that basis going on to innovate and
+ 
+
+ align:start position:0%
+from that basis going on to innovate and
+do their own R&D
+
+ align:start position:0%
+do their own R&D
+ 
+
+ align:start position:0%
+do their own R&D
+in Korea
+
+ align:start position:0%
+in Korea
+ 
+
+ align:start position:0%
+in Korea
+more advances for those problems those
+
+ align:start position:0%
+more advances for those problems those
+ 
+
+ align:start position:0%
+more advances for those problems those
+products and this trend was really
+
+ align:start position:0%
+products and this trend was really
+ 
+
+ align:start position:0%
+products and this trend was really
+supported by those clothes intertwine
+
+ align:start position:0%
+supported by those clothes intertwine
+ 
+
+ align:start position:0%
+supported by those clothes intertwine
+partnerships and almost interdependence
+
+ align:start position:0%
+partnerships and almost interdependence
+ 
+
+ align:start position:0%
+partnerships and almost interdependence
+between the government and the tables
+
+ align:start position:0%
+between the government and the tables
+ 
+
+ align:start position:0%
+between the government and the tables
+and the table still exists like even to
+
+ align:start position:0%
+and the table still exists like even to
+ 
+
+ align:start position:0%
+and the table still exists like even to
+this day they're really like family
+
+ align:start position:0%
+this day they're really like family
+ 
+
+ align:start position:0%
+this day they're really like family
+centric dynastic corporations like the
+
+ align:start position:0%
+centric dynastic corporations like the
+ 
+
+ align:start position:0%
+centric dynastic corporations like the
+Lee family has controlled Samsung for
+
+ align:start position:0%
+Lee family has controlled Samsung for
+ 
+
+ align:start position:0%
+Lee family has controlled Samsung for
+however long they've been in business
+
+ align:start position:0%
+however long they've been in business
+ 
+
+ align:start position:0%
+however long they've been in business
+and that centralist kind of government
+
+ align:start position:0%
+and that centralist kind of government
+ 
+
+ align:start position:0%
+and that centralist kind of government
+support and structure has really allowed
+
+ align:start position:0%
+support and structure has really allowed
+ 
+
+ align:start position:0%
+support and structure has really allowed
+them to enter really high capital
+
+ align:start position:0%
+them to enter really high capital
+ 
+
+ align:start position:0%
+them to enter really high capital
+industries and really get to the front
+
+ align:start position:0%
+industries and really get to the front
+ 
+
+ align:start position:0%
+industries and really get to the front
+really quickly as we've been discussing
+
+ align:start position:0%
+really quickly as we've been discussing
+ 
+
+ align:start position:0%
+really quickly as we've been discussing
+has been a factor also in Japan so just
+
+ align:start position:0%
+has been a factor also in Japan so just
+ 
+
+ align:start position:0%
+has been a factor also in Japan so just
+focusing on this right now we discussed
+
+ align:start position:0%
+focusing on this right now we discussed
+ 
+
+ align:start position:0%
+focusing on this right now we discussed
+how you know the focus on the
+
+ align:start position:0%
+how you know the focus on the
+ 
+
+ align:start position:0%
+how you know the focus on the
+partnerships between the table and the
+
+ align:start position:0%
+partnerships between the table and the
+ 
+
+ align:start position:0%
+partnerships between the table and the
+government has kind of stymied the
+
+ align:start position:0%
+government has kind of stymied the
+ 
+
+ align:start position:0%
+government has kind of stymied the
+ability of SMEs and the smaller funds to
+
+ align:start position:0%
+ability of SMEs and the smaller funds to
+ 
+
+ align:start position:0%
+ability of SMEs and the smaller funds to
+enter the space so one question that
+
+ align:start position:0%
+enter the space so one question that
+ 
+
+ align:start position:0%
+enter the space so one question that
+someone had was like how can the come to
+
+ align:start position:0%
+someone had was like how can the come to
+ 
+
+ align:start position:0%
+someone had was like how can the come to
+the country catch up the economy and
+
+ align:start position:0%
+the country catch up the economy and
+ 
+
+ align:start position:0%
+the country catch up the economy and
+foster both aspects of you know the
+
+ align:start position:0%
+foster both aspects of you know the
+ 
+
+ align:start position:0%
+foster both aspects of you know the
+larger corporations as well as the
+
+ align:start position:0%
+larger corporations as well as the
+ 
+
+ align:start position:0%
+larger corporations as well as the
+smaller businesses like do they have to
+
+ align:start position:0%
+smaller businesses like do they have to
+ 
+
+ align:start position:0%
+smaller businesses like do they have to
+partition funds kind of have different
+
+ align:start position:0%
+partition funds kind of have different
+ 
+
+ align:start position:0%
+partition funds kind of have different
+initiatives or approaches for both kind
+
+ align:start position:0%
+initiatives or approaches for both kind
+ 
+
+ align:start position:0%
+initiatives or approaches for both kind
+of sectors or how do you guys think they
+
+ align:start position:0%
+of sectors or how do you guys think they
+ 
+
+ align:start position:0%
+of sectors or how do you guys think they
+should approach that kind of growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess it seems like the tables are
+
+ align:start position:0%
+I guess it seems like the tables are
+ 
+
+ align:start position:0%
+I guess it seems like the tables are
+kind of focused in specific industries
+
+ align:start position:0%
+kind of focused in specific industries
+ 
+
+ align:start position:0%
+kind of focused in specific industries
+right now like construction and
+
+ align:start position:0%
+right now like construction and
+ 
+
+ align:start position:0%
+right now like construction and
+electronics so it's probably going to be
+
+ align:start position:0%
+electronics so it's probably going to be
+ 
+
+ align:start position:0%
+electronics so it's probably going to be
+harder to get smaller firms to get a
+
+ align:start position:0%
+harder to get smaller firms to get a
+ 
+
+ align:start position:0%
+harder to get smaller firms to get a
+footing in those industries so my
+
+ align:start position:0%
+footing in those industries so my
+ 
+
+ align:start position:0%
+footing in those industries so my
+opinion to make more sense to kind of
+
+ align:start position:0%
+opinion to make more sense to kind of
+ 
+
+ align:start position:0%
+opinion to make more sense to kind of
+pick something new and focus attention
+
+ align:start position:0%
+pick something new and focus attention
+ 
+
+ align:start position:0%
+pick something new and focus attention
+on developing those industries so I
+
+ align:start position:0%
+on developing those industries so I
+ 
+
+ align:start position:0%
+on developing those industries so I
+don't make this me get like I start up
+
+ align:start position:0%
+don't make this me get like I start up
+ 
+
+ align:start position:0%
+don't make this me get like I start up
+they can compete with Hyundai but maybe
+
+ align:start position:0%
+they can compete with Hyundai but maybe
+ 
+
+ align:start position:0%
+they can compete with Hyundai but maybe
+there's something and energy or IT that
+
+ align:start position:0%
+there's something and energy or IT that
+ 
+
+ align:start position:0%
+there's something and energy or IT that
+they have to grow more or maybe even
+
+ align:start position:0%
+they have to grow more or maybe even
+ 
+
+ align:start position:0%
+they have to grow more or maybe even
+focus SM needs are more domestic affairs
+
+ align:start position:0%
+focus SM needs are more domestic affairs
+ 
+
+ align:start position:0%
+focus SM needs are more domestic affairs
+like I don't know if agriculture or some
+
+ align:start position:0%
+like I don't know if agriculture or some
+ 
+
+ align:start position:0%
+like I don't know if agriculture or some
+industries in Korea might be a good
+
+ align:start position:0%
+industries in Korea might be a good
+ 
+
+ align:start position:0%
+industries in Korea might be a good
+target for them I think you just need to
+
+ align:start position:0%
+target for them I think you just need to
+ 
+
+ align:start position:0%
+target for them I think you just need to
+offer governmental support and financial
+
+ align:start position:0%
+offer governmental support and financial
+ 
+
+ align:start position:0%
+offer governmental support and financial
+protections probably a little bit
+
+ align:start position:0%
+protections probably a little bit
+ 
+
+ align:start position:0%
+protections probably a little bit
+different than obviously the tables need
+
+ align:start position:0%
+different than obviously the tables need
+ 
+
+ align:start position:0%
+different than obviously the tables need
+or don't need but you just have to
+
+ align:start position:0%
+or don't need but you just have to
+ 
+
+ align:start position:0%
+or don't need but you just have to
+decide what's the scale that you're
+
+ align:start position:0%
+decide what's the scale that you're
+ 
+
+ align:start position:0%
+decide what's the scale that you're
+trying to look and build that if you're
+
+ align:start position:0%
+trying to look and build that if you're
+ 
+
+ align:start position:0%
+trying to look and build that if you're
+trying to build a circus smaller sectors
+
+ align:start position:0%
+trying to build a circus smaller sectors
+ 
+
+ align:start position:0%
+trying to build a circus smaller sectors
+and my diner develop like agriculture
+
+ align:start position:0%
+and my diner develop like agriculture
+ 
+
+ align:start position:0%
+and my diner develop like agriculture
+for example I just have to look a little
+
+ align:start position:0%
+for example I just have to look a little
+ 
+
+ align:start position:0%
+for example I just have to look a little
+bit smaller I'm like it's trying to
+
+ align:start position:0%
+bit smaller I'm like it's trying to
+ 
+
+ align:start position:0%
+bit smaller I'm like it's trying to
+cater to you know one or two or three
+
+ align:start position:0%
+cater to you know one or two or three
+ 
+
+ align:start position:0%
+cater to you know one or two or three
+Chabot companies offer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chris do you think that from your
+
+ align:start position:0%
+Chris do you think that from your
+ 
+
+ align:start position:0%
+Chris do you think that from your
+reading of Kennedy do you agree with him
+
+ align:start position:0%
+reading of Kennedy do you agree with him
+ 
+
+ align:start position:0%
+reading of Kennedy do you agree with him
+that Korea needs to foster an SME
+
+ align:start position:0%
+that Korea needs to foster an SME
+ 
+
+ align:start position:0%
+that Korea needs to foster an SME
+startup kind of community you mean in
+
+ align:start position:0%
+startup kind of community you mean in
+ 
+
+ align:start position:0%
+startup kind of community you mean in
+the context of present-day present-day
+
+ align:start position:0%
+the context of present-day present-day
+ 
+
+ align:start position:0%
+the context of present-day present-day
+with is that can be an enhancement to
+
+ align:start position:0%
+with is that can be an enhancement to
+ 
+
+ align:start position:0%
+with is that can be an enhancement to
+Korea's innovation capable or do they do
+
+ align:start position:0%
+Korea's innovation capable or do they do
+ 
+
+ align:start position:0%
+Korea's innovation capable or do they do
+they really need to do this what do you
+
+ align:start position:0%
+they really need to do this what do you
+ 
+
+ align:start position:0%
+they really need to do this what do you
+think personally I think their structure
+
+ align:start position:0%
+think personally I think their structure
+ 
+
+ align:start position:0%
+think personally I think their structure
+that really focuses on the bigger
+
+ align:start position:0%
+that really focuses on the bigger
+ 
+
+ align:start position:0%
+that really focuses on the bigger
+corporations and their impact and their
+
+ align:start position:0%
+corporations and their impact and their
+ 
+
+ align:start position:0%
+corporations and their impact and their
+ability to really compete globally has
+
+ align:start position:0%
+ability to really compete globally has
+ 
+
+ align:start position:0%
+ability to really compete globally has
+been working so I do think that the
+
+ align:start position:0%
+been working so I do think that the
+ 
+
+ align:start position:0%
+been working so I do think that the
+corporation kind of push has been
+
+ align:start position:0%
+corporation kind of push has been
+ 
+
+ align:start position:0%
+corporation kind of push has been
+successful whether SM ease should be
+
+ align:start position:0%
+successful whether SM ease should be
+ 
+
+ align:start position:0%
+successful whether SM ease should be
+sort of supported from the government I
+
+ align:start position:0%
+sort of supported from the government I
+ 
+
+ align:start position:0%
+sort of supported from the government I
+think it's worth kind of exploring I do
+
+ align:start position:0%
+think it's worth kind of exploring I do
+ 
+
+ align:start position:0%
+think it's worth kind of exploring I do
+think that kind of finding them Anish is
+
+ align:start position:0%
+think that kind of finding them Anish is
+ 
+
+ align:start position:0%
+think that kind of finding them Anish is
+really important because there's kind of
+
+ align:start position:0%
+really important because there's kind of
+ 
+
+ align:start position:0%
+really important because there's kind of
+no point or kind of redundant for them
+
+ align:start position:0%
+no point or kind of redundant for them
+ 
+
+ align:start position:0%
+no point or kind of redundant for them
+to try to enter industries that the
+
+ align:start position:0%
+to try to enter industries that the
+ 
+
+ align:start position:0%
+to try to enter industries that the
+corporations have a hold on to the first
+
+ align:start position:0%
+corporations have a hold on to the first
+ 
+
+ align:start position:0%
+corporations have a hold on to the first
+digital camera but because of the way
+
+ align:start position:0%
+digital camera but because of the way
+ 
+
+ align:start position:0%
+digital camera but because of the way
+their supply chain and their current
+
+ align:start position:0%
+their supply chain and their current
+ 
+
+ align:start position:0%
+their supply chain and their current
+business was they couldn't they didn't
+
+ align:start position:0%
+business was they couldn't they didn't
+ 
+
+ align:start position:0%
+business was they couldn't they didn't
+want to make a factory be the ruler of
+
+ align:start position:0%
+want to make a factory be the ruler of
+ 
+
+ align:start position:0%
+want to make a factory be the ruler of
+existing business so danger of having a
+
+ align:start position:0%
+existing business so danger of having a
+ 
+
+ align:start position:0%
+existing business so danger of having a
+too big of giant is in order to innovate
+
+ align:start position:0%
+too big of giant is in order to innovate
+ 
+
+ align:start position:0%
+too big of giant is in order to innovate
+it takes so much effort on them that
+
+ align:start position:0%
+it takes so much effort on them that
+ 
+
+ align:start position:0%
+it takes so much effort on them that
+they won't do it and if your economy is
+
+ align:start position:0%
+they won't do it and if your economy is
+ 
+
+ align:start position:0%
+they won't do it and if your economy is
+based off of that and based on those
+
+ align:start position:0%
+based off of that and based on those
+ 
+
+ align:start position:0%
+based off of that and based on those
+four giants especially with rapid techno
+
+ align:start position:0%
+four giants especially with rapid techno
+ 
+
+ align:start position:0%
+four giants especially with rapid techno
+techno much motivation you really don't
+
+ align:start position:0%
+techno much motivation you really don't
+ 
+
+ align:start position:0%
+techno much motivation you really don't
+want to be in that position so have you
+
+ align:start position:0%
+want to be in that position so have you
+ 
+
+ align:start position:0%
+want to be in that position so have you
+got any special medicine yeah I kind of
+
+ align:start position:0%
+got any special medicine yeah I kind of
+ 
+
+ align:start position:0%
+got any special medicine yeah I kind of
+want to hit on both of those so with the
+
+ align:start position:0%
+want to hit on both of those so with the
+ 
+
+ align:start position:0%
+want to hit on both of those so with the
+cable over just SME the structure in
+
+ align:start position:0%
+cable over just SME the structure in
+ 
+
+ align:start position:0%
+cable over just SME the structure in
+Korea I'm wondering are the are the
+
+ align:start position:0%
+Korea I'm wondering are the are the
+ 
+
+ align:start position:0%
+Korea I'm wondering are the are the
+major major legacy sort of corporations
+
+ align:start position:0%
+major major legacy sort of corporations
+ 
+
+ align:start position:0%
+major major legacy sort of corporations
+are they profitable enough and large
+
+ align:start position:0%
+are they profitable enough and large
+ 
+
+ align:start position:0%
+are they profitable enough and large
+enough to be self-sufficient they don't
+
+ align:start position:0%
+enough to be self-sufficient they don't
+ 
+
+ align:start position:0%
+enough to be self-sufficient they don't
+really need the input from the
+
+ align:start position:0%
+really need the input from the
+ 
+
+ align:start position:0%
+really need the input from the
+government as they did decades ago could
+
+ align:start position:0%
+government as they did decades ago could
+ 
+
+ align:start position:0%
+government as they did decades ago could
+the government focus more on SMEs and
+
+ align:start position:0%
+the government focus more on SMEs and
+ 
+
+ align:start position:0%
+the government focus more on SMEs and
+would that be a more strategic way to go
+
+ align:start position:0%
+would that be a more strategic way to go
+ 
+
+ align:start position:0%
+would that be a more strategic way to go
+about things or do they
+
+ align:start position:0%
+about things or do they
+ 
+
+ align:start position:0%
+about things or do they
+have a situation in Korea I don't I
+
+ align:start position:0%
+have a situation in Korea I don't I
+ 
+
+ align:start position:0%
+have a situation in Korea I don't I
+don't know I haven't only been there
+
+ align:start position:0%
+don't know I haven't only been there
+ 
+
+ align:start position:0%
+don't know I haven't only been there
+once it was only for about a week so I
+
+ align:start position:0%
+once it was only for about a week so I
+ 
+
+ align:start position:0%
+once it was only for about a week so I
+don't really know do they have the
+
+ align:start position:0%
+don't really know do they have the
+ 
+
+ align:start position:0%
+don't really know do they have the
+situation similar to what I think we
+
+ align:start position:0%
+situation similar to what I think we
+ 
+
+ align:start position:0%
+situation similar to what I think we
+faced in the United States where we yes
+
+ align:start position:0%
+faced in the United States where we yes
+ 
+
+ align:start position:0%
+faced in the United States where we yes
+we have legacy technologies and sectors
+
+ align:start position:0%
+we have legacy technologies and sectors
+ 
+
+ align:start position:0%
+we have legacy technologies and sectors
+that are probably self-sufficient at
+
+ align:start position:0%
+that are probably self-sufficient at
+ 
+
+ align:start position:0%
+that are probably self-sufficient at
+this point and highly profitable but we
+
+ align:start position:0%
+this point and highly profitable but we
+ 
+
+ align:start position:0%
+this point and highly profitable but we
+are so ingrained the government still
+
+ align:start position:0%
+are so ingrained the government still
+ 
+
+ align:start position:0%
+are so ingrained the government still
+gives subsidies to fossil fuel
+
+ align:start position:0%
+gives subsidies to fossil fuel
+ 
+
+ align:start position:0%
+gives subsidies to fossil fuel
+industries subsidize their R&D and that
+
+ align:start position:0%
+industries subsidize their R&D and that
+ 
+
+ align:start position:0%
+industries subsidize their R&D and that
+although they shouldn't necessarily need
+
+ align:start position:0%
+although they shouldn't necessarily need
+ 
+
+ align:start position:0%
+although they shouldn't necessarily need
+that it's it's like that and they they
+
+ align:start position:0%
+that it's it's like that and they they
+ 
+
+ align:start position:0%
+that it's it's like that and they they
+have power so they can continue to get
+
+ align:start position:0%
+have power so they can continue to get
+ 
+
+ align:start position:0%
+have power so they can continue to get
+those funds so what is the situation in
+
+ align:start position:0%
+those funds so what is the situation in
+ 
+
+ align:start position:0%
+those funds so what is the situation in
+Korea today are they ingrained and can't
+
+ align:start position:0%
+Korea today are they ingrained and can't
+ 
+
+ align:start position:0%
+Korea today are they ingrained and can't
+really separate at this point or what I
+
+ align:start position:0%
+really separate at this point or what I
+ 
+
+ align:start position:0%
+really separate at this point or what I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+definitely it's still very ingrained a
+
+ align:start position:0%
+definitely it's still very ingrained a
+ 
+
+ align:start position:0%
+definitely it's still very ingrained a
+lot of the Corporations have I don't
+
+ align:start position:0%
+lot of the Corporations have I don't
+ 
+
+ align:start position:0%
+lot of the Corporations have I don't
+know if it's soap I don't think it's
+
+ align:start position:0%
+know if it's soap I don't think it's
+ 
+
+ align:start position:0%
+know if it's soap I don't think it's
+corruption necessarily but close
+
+ align:start position:0%
+corruption necessarily but close
+ 
+
+ align:start position:0%
+corruption necessarily but close
+political ties to the government and
+
+ align:start position:0%
+political ties to the government and
+ 
+
+ align:start position:0%
+political ties to the government and
+power so it might be difficult I think
+
+ align:start position:0%
+power so it might be difficult I think
+ 
+
+ align:start position:0%
+power so it might be difficult I think
+to separate the two and going back to
+
+ align:start position:0%
+to separate the two and going back to
+ 
+
+ align:start position:0%
+to separate the two and going back to
+the point of whether SMEs could be like
+
+ align:start position:0%
+the point of whether SMEs could be like
+ 
+
+ align:start position:0%
+the point of whether SMEs could be like
+on the rise in the future I think it's
+
+ align:start position:0%
+on the rise in the future I think it's
+ 
+
+ align:start position:0%
+on the rise in the future I think it's
+also a cultural difference because in my
+
+ align:start position:0%
+also a cultural difference because in my
+ 
+
+ align:start position:0%
+also a cultural difference because in my
+Korean and Asian culture it's often like
+
+ align:start position:0%
+Korean and Asian culture it's often like
+ 
+
+ align:start position:0%
+Korean and Asian culture it's often like
+more traditional and that it's very
+
+ align:start position:0%
+more traditional and that it's very
+ 
+
+ align:start position:0%
+more traditional and that it's very
+prestigious obviously to go into these
+
+ align:start position:0%
+prestigious obviously to go into these
+ 
+
+ align:start position:0%
+prestigious obviously to go into these
+very developed and long-standing
+
+ align:start position:0%
+very developed and long-standing
+ 
+
+ align:start position:0%
+very developed and long-standing
+companies and there's not so much an
+
+ align:start position:0%
+companies and there's not so much an
+ 
+
+ align:start position:0%
+companies and there's not so much an
+innovation drive like there is here that
+
+ align:start position:0%
+innovation drive like there is here that
+ 
+
+ align:start position:0%
+innovation drive like there is here that
+like startup culture it's really
+
+ align:start position:0%
+like startup culture it's really
+ 
+
+ align:start position:0%
+like startup culture it's really
+attractive to a lot of the young
+
+ align:start position:0%
+attractive to a lot of the young
+ 
+
+ align:start position:0%
+attractive to a lot of the young
+Millennials I don't think that exists so
+
+ align:start position:0%
+Millennials I don't think that exists so
+ 
+
+ align:start position:0%
+Millennials I don't think that exists so
+much let's say in Korea so whether it be
+
+ align:start position:0%
+much let's say in Korea so whether it be
+ 
+
+ align:start position:0%
+much let's say in Korea so whether it be
+a job to like go to an SME or go to a
+
+ align:start position:0%
+a job to like go to an SME or go to a
+ 
+
+ align:start position:0%
+a job to like go to an SME or go to a
+big corporation I feel like that
+
+ align:start position:0%
+big corporation I feel like that
+ 
+
+ align:start position:0%
+big corporation I feel like that
+wouldn't even be a decision that would
+
+ align:start position:0%
+wouldn't even be a decision that would
+ 
+
+ align:start position:0%
+wouldn't even be a decision that would
+be like it'd be obvious to go to a big
+
+ align:start position:0%
+be like it'd be obvious to go to a big
+ 
+
+ align:start position:0%
+be like it'd be obvious to go to a big
+corporation so I don't know if kind of a
+
+ align:start position:0%
+corporation so I don't know if kind of a
+ 
+
+ align:start position:0%
+corporation so I don't know if kind of a
+cultural stigmas and the standards kind
+
+ align:start position:0%
+cultural stigmas and the standards kind
+ 
+
+ align:start position:0%
+cultural stigmas and the standards kind
+of a guided right so another attack
+
+ align:start position:0%
+of a guided right so another attack
+ 
+
+ align:start position:0%
+of a guided right so another attack
+another cultural point here we're
+
+ align:start position:0%
+another cultural point here we're
+ 
+
+ align:start position:0%
+another cultural point here we're
+dealing with about risk-taking really
+
+ align:start position:0%
+dealing with about risk-taking really
+ 
+
+ align:start position:0%
+dealing with about risk-taking really
+which is a pretty key element of us is
+
+ align:start position:0%
+which is a pretty key element of us is
+ 
+
+ align:start position:0%
+which is a pretty key element of us is
+pretty high tolerance resilient
+
+ align:start position:0%
+pretty high tolerance resilient
+ 
+
+ align:start position:0%
+pretty high tolerance resilient
+all right well good summaries to get
+
+ align:start position:0%
+all right well good summaries to get
+ 
+
+ align:start position:0%
+all right well good summaries to get
+through this I'm gonna push one to our
+
+ align:start position:0%
+through this I'm gonna push one to our
+ 
+
+ align:start position:0%
+through this I'm gonna push one to our
+next let me just do one short to see
+
+ align:start position:0%
+next let me just do one short to see
+ 
+
+ align:start position:0%
+next let me just do one short to see
+know what recessions look like in the US
+
+ align:start position:0%
+know what recessions look like in the US
+ 
+
+ align:start position:0%
+know what recessions look like in the US
+right and what's been going on and
+
+ align:start position:0%
+right and what's been going on and
+ 
+
+ align:start position:0%
+right and what's been going on and
+repeated sequences of recession here's
+
+ align:start position:0%
+repeated sequences of recession here's
+ 
+
+ align:start position:0%
+repeated sequences of recession here's
+the 1981 recession hit on fries right
+
+ align:start position:0%
+the 1981 recession hit on fries right
+ 
+
+ align:start position:0%
+the 1981 recession hit on fries right
+and jobs come back relatively quickly
+
+ align:start position:0%
+and jobs come back relatively quickly
+ 
+
+ align:start position:0%
+and jobs come back relatively quickly
+then 1919 start stretching it out
+
+ align:start position:0%
+then 1919 start stretching it out
+ 
+
+ align:start position:0%
+then 1919 start stretching it out
+further right then in 2001 you know the
+
+ align:start position:0%
+further right then in 2001 you know the
+ 
+
+ align:start position:0%
+further right then in 2001 you know the
+jobs recovery it's really slow markedly
+
+ align:start position:0%
+jobs recovery it's really slow markedly
+ 
+
+ align:start position:0%
+jobs recovery it's really slow markedly
+slow right and then 2008 9 recession you
+
+ align:start position:0%
+slow right and then 2008 9 recession you
+ 
+
+ align:start position:0%
+slow right and then 2008 9 recession you
+know even further out on the level of
+
+ align:start position:0%
+know even further out on the level of
+ 
+
+ align:start position:0%
+know even further out on the level of
+jaw reductions and now painful reality
+
+ align:start position:0%
+jaw reductions and now painful reality
+ 
+
+ align:start position:0%
+jaw reductions and now painful reality
+is that you still never recovered from
+
+ align:start position:0%
+is that you still never recovered from
+ 
+
+ align:start position:0%
+is that you still never recovered from
+the 2001 recession by the time in 2007 8
+
+ align:start position:0%
+the 2001 recession by the time in 2007 8
+ 
+
+ align:start position:0%
+the 2001 recession by the time in 2007 8
+9 decision is among us right so there
+
+ align:start position:0%
+9 decision is among us right so there
+ 
+
+ align:start position:0%
+9 decision is among us right so there
+may be an argument that something
+
+ align:start position:0%
+may be an argument that something
+ 
+
+ align:start position:0%
+may be an argument that something
+fundamental is going on structurally and
+
+ align:start position:0%
+fundamental is going on structurally and
+ 
+
+ align:start position:0%
+fundamental is going on structurally and
+again money right when you see a chart
+
+ align:start position:0%
+again money right when you see a chart
+ 
+
+ align:start position:0%
+again money right when you see a chart
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+right in each successive recession it's
+
+ align:start position:0%
+right in each successive recession it's
+ 
+
+ align:start position:0%
+right in each successive recession it's
+less of a business cycle it's more
+
+ align:start position:0%
+less of a business cycle it's more
+ 
+
+ align:start position:0%
+less of a business cycle it's more
+structural right and it looks like there
+
+ align:start position:0%
+structural right and it looks like there
+ 
+
+ align:start position:0%
+structural right and it looks like there
+are deep structural causes in these
+
+ align:start position:0%
+are deep structural causes in these
+ 
+
+ align:start position:0%
+are deep structural causes in these
+manufacturing employment Alliance when
+
+ align:start position:0%
+manufacturing employment Alliance when
+ 
+
+ align:start position:0%
+manufacturing employment Alliance when
+you starts with a chart like this we'll
+
+ align:start position:0%
+you starts with a chart like this we'll
+ 
+
+ align:start position:0%
+you starts with a chart like this we'll
+talk more about it next week
+
+ align:start position:0%
+talk more about it next week
+ 
+
+ align:start position:0%
+talk more about it next week
+but here's declining median income for
+
+ align:start position:0%
+but here's declining median income for
+ 
+
+ align:start position:0%
+but here's declining median income for
+us which we'll talk more about next week
+
+ align:start position:0%
+us which we'll talk more about next week
+ 
+
+ align:start position:0%
+us which we'll talk more about next week
+too so you know particularly pay
+
+ align:start position:0%
+too so you know particularly pay
+ 
+
+ align:start position:0%
+too so you know particularly pay
+attention to men who work tend to
+
+ align:start position:0%
+attention to men who work tend to
+ 
+
+ align:start position:0%
+attention to men who work tend to
+historically have played a larger role
+
+ align:start position:0%
+historically have played a larger role
+ 
+
+ align:start position:0%
+historically have played a larger role
+in manufacturing this really nice right
+
+ align:start position:0%
+in manufacturing this really nice right
+ 
+
+ align:start position:0%
+in manufacturing this really nice right
+so this is changing median real earnings
+
+ align:start position:0%
+so this is changing median real earnings
+ 
+
+ align:start position:0%
+so this is changing median real earnings
+for men with him from 1990 to 2015
+
+ align:start position:0%
+for men with him from 1990 to 2015
+ 
+
+ align:start position:0%
+for men with him from 1990 to 2015
+so you know the extended period 9215 no
+
+ align:start position:0%
+so you know the extended period 9215 no
+ 
+
+ align:start position:0%
+so you know the extended period 9215 no
+high school diploma then median income
+
+ align:start position:0%
+high school diploma then median income
+ 
+
+ align:start position:0%
+high school diploma then median income
+decline in that
+
+ align:start position:0%
+decline in that
+ 
+
+ align:start position:0%
+decline in that
+20 high school diploma Wars some college
+
+ align:start position:0%
+20 high school diploma Wars some college
+ 
+
+ align:start position:0%
+20 high school diploma Wars some college
+13 and then advanced degrees 21 point
+
+ align:start position:0%
+13 and then advanced degrees 21 point
+ 
+
+ align:start position:0%
+13 and then advanced degrees 21 point
+rise bachelor's degrees 16 point for us
+
+ align:start position:0%
+rise bachelor's degrees 16 point for us
+ 
+
+ align:start position:0%
+rise bachelor's degrees 16 point for us
+this is a society that's going like this
+
+ align:start position:0%
+this is a society that's going like this
+ 
+
+ align:start position:0%
+this is a society that's going like this
+right and that's what we're dealing with
+
+ align:start position:0%
+right and that's what we're dealing with
+ 
+
+ align:start position:0%
+right and that's what we're dealing with
+and arguably is related to this let me
+
+ align:start position:0%
+and arguably is related to this let me
+ 
+
+ align:start position:0%
+and arguably is related to this let me
+let me move to Suzanne burger you should
+
+ align:start position:0%
+let me move to Suzanne burger you should
+ 
+
+ align:start position:0%
+let me move to Suzanne burger you should
+get to know her she's around here has
+
+ align:start position:0%
+get to know her she's around here has
+ 
+
+ align:start position:0%
+get to know her she's around here has
+been a great teacher for me this is her
+
+ align:start position:0%
+been a great teacher for me this is her
+ 
+
+ align:start position:0%
+been a great teacher for me this is her
+2005 book called how we compete and four
+
+ align:start position:0%
+2005 book called how we compete and four
+ 
+
+ align:start position:0%
+2005 book called how we compete and four
+essential point is that there are
+
+ align:start position:0%
+essential point is that there are
+ 
+
+ align:start position:0%
+essential point is that there are
+different varieties of capitalism we've
+
+ align:start position:0%
+different varieties of capitalism we've
+ 
+
+ align:start position:0%
+different varieties of capitalism we've
+been talking a lot about that today and
+
+ align:start position:0%
+been talking a lot about that today and
+ 
+
+ align:start position:0%
+been talking a lot about that today and
+the different approaches emerged between
+
+ align:start position:0%
+the different approaches emerged between
+ 
+
+ align:start position:0%
+the different approaches emerged between
+the u.s. and Asian economies in advanced
+
+ align:start position:0%
+the u.s. and Asian economies in advanced
+ 
+
+ align:start position:0%
+the u.s. and Asian economies in advanced
+technology goods in this later part of
+
+ align:start position:0%
+technology goods in this later part of
+ 
+
+ align:start position:0%
+technology goods in this later part of
+the 1990s early early 2000s time true so
+
+ align:start position:0%
+the 1990s early early 2000s time true so
+ 
+
+ align:start position:0%
+the 1990s early early 2000s time true so
+what's going on here
+
+ align:start position:0%
+what's going on here
+ 
+
+ align:start position:0%
+what's going on here
+IT as a driver and codable spec's
+
+ align:start position:0%
+IT as a driver and codable spec's
+ 
+
+ align:start position:0%
+IT as a driver and codable spec's
+time to you know computer driven
+
+ align:start position:0%
+time to you know computer driven
+ 
+
+ align:start position:0%
+time to you know computer driven
+equipment is enabling a divorce between
+
+ align:start position:0%
+equipment is enabling a divorce between
+ 
+
+ align:start position:0%
+equipment is enabling a divorce between
+production and design right so in the
+
+ align:start position:0%
+production and design right so in the
+ 
+
+ align:start position:0%
+production and design right so in the
+old time period right in the prior time
+
+ align:start position:0%
+old time period right in the prior time
+ 
+
+ align:start position:0%
+old time period right in the prior time
+period suzanne argues that manufacturing
+
+ align:start position:0%
+period suzanne argues that manufacturing
+ 
+
+ align:start position:0%
+period suzanne argues that manufacturing
+company's production firms were a lot
+
+ align:start position:0%
+company's production firms were a lot
+ 
+
+ align:start position:0%
+company's production firms were a lot
+like model airplanes right and you all
+
+ align:start position:0%
+like model airplanes right and you all
+ 
+
+ align:start position:0%
+like model airplanes right and you all
+probably don't remember fear of plastic
+
+ align:start position:0%
+probably don't remember fear of plastic
+ 
+
+ align:start position:0%
+probably don't remember fear of plastic
+model airplanes I do
+
+ align:start position:0%
+model airplanes I do
+ 
+
+ align:start position:0%
+model airplanes I do
+but you get this you know batch of
+
+ align:start position:0%
+but you get this you know batch of
+ 
+
+ align:start position:0%
+but you get this you know batch of
+plastic parts and they never you'd have
+
+ align:start position:0%
+plastic parts and they never you'd have
+ 
+
+ align:start position:0%
+plastic parts and they never you'd have
+to work them and you get glue all over
+
+ align:start position:0%
+to work them and you get glue all over
+ 
+
+ align:start position:0%
+to work them and you get glue all over
+them and a glue it's spillover right and
+
+ align:start position:0%
+them and a glue it's spillover right and
+ 
+
+ align:start position:0%
+them and a glue it's spillover right and
+it would just be a mess and you try and
+
+ align:start position:0%
+it would just be a mess and you try and
+ 
+
+ align:start position:0%
+it would just be a mess and you try and
+clean up the hood with clean accident
+
+ align:start position:0%
+clean up the hood with clean accident
+ 
+
+ align:start position:0%
+clean up the hood with clean accident
+you know and that and we've never and
+
+ align:start position:0%
+you know and that and we've never and
+ 
+
+ align:start position:0%
+you know and that and we've never and
+you'd put rubber bands around it to try
+
+ align:start position:0%
+you'd put rubber bands around it to try
+ 
+
+ align:start position:0%
+you'd put rubber bands around it to try
+and get it lock in place a new
+
+ align:start position:0%
+and get it lock in place a new
+ 
+
+ align:start position:0%
+and get it lock in place a new
+breakdancing try to fix it was just
+
+ align:start position:0%
+breakdancing try to fix it was just
+ 
+
+ align:start position:0%
+breakdancing try to fix it was just
+that's what manufacturing used to be
+
+ align:start position:0%
+that's what manufacturing used to be
+ 
+
+ align:start position:0%
+that's what manufacturing used to be
+like she argues right and to manage that
+
+ align:start position:0%
+like she argues right and to manage that
+ 
+
+ align:start position:0%
+like she argues right and to manage that
+you needed a very integrated vertical
+
+ align:start position:0%
+you needed a very integrated vertical
+ 
+
+ align:start position:0%
+you needed a very integrated vertical
+system with all parts of that system
+
+ align:start position:0%
+system with all parts of that system
+ 
+
+ align:start position:0%
+system with all parts of that system
+tied and connected together to get
+
+ align:start position:0%
+tied and connected together to get
+ 
+
+ align:start position:0%
+tied and connected together to get
+around that difficulty of the corrosion
+
+ align:start position:0%
+around that difficulty of the corrosion
+ 
+
+ align:start position:0%
+around that difficulty of the corrosion
+process but with codable IT based specs
+
+ align:start position:0%
+process but with codable IT based specs
+ 
+
+ align:start position:0%
+process but with codable IT based specs
+and computer equipment he moved to an
+
+ align:start position:0%
+and computer equipment he moved to an
+ 
+
+ align:start position:0%
+and computer equipment he moved to an
+ear up like us right it's all computer
+
+ align:start position:0%
+ear up like us right it's all computer
+ 
+
+ align:start position:0%
+ear up like us right it's all computer
+driven you're gonna be producing Legos
+
+ align:start position:0%
+driven you're gonna be producing Legos
+ 
+
+ align:start position:0%
+driven you're gonna be producing Legos
+and they are always gonna snap perfectly
+
+ align:start position:0%
+and they are always gonna snap perfectly
+ 
+
+ align:start position:0%
+and they are always gonna snap perfectly
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+
+ align:start position:0%
+in place right that's how the production
+ 
+
+ align:start position:0%
+in place right that's how the production
+system changed she argued in these two
+
+ align:start position:0%
+system changed she argued in these two
+ 
+
+ align:start position:0%
+system changed she argued in these two
+from these two different eras and the
+
+ align:start position:0%
+from these two different eras and the
+ 
+
+ align:start position:0%
+from these two different eras and the
+classic example is the iPod you know
+
+ align:start position:0%
+classic example is the iPod you know
+ 
+
+ align:start position:0%
+classic example is the iPod you know
+Apple was able to pick a mix of mp3 best
+
+ align:start position:0%
+Apple was able to pick a mix of mp3 best
+ 
+
+ align:start position:0%
+Apple was able to pick a mix of mp3 best
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+
+ align:start position:0%
+technologies and they tied it to a new
+ 
+
+ align:start position:0%
+technologies and they tied it to a new
+software access system for music and
+
+ align:start position:0%
+software access system for music and
+ 
+
+ align:start position:0%
+software access system for music and
+database once you all know now I was
+
+ align:start position:0%
+database once you all know now I was
+ 
+
+ align:start position:0%
+database once you all know now I was
+video as well they're doing some you
+
+ align:start position:0%
+video as well they're doing some you
+ 
+
+ align:start position:0%
+video as well they're doing some you
+know a classic Apple movie right the
+
+ align:start position:0%
+know a classic Apple movie right the
+ 
+
+ align:start position:0%
+know a classic Apple movie right the
+problem mp3 players before Apple was
+
+ align:start position:0%
+problem mp3 players before Apple was
+ 
+
+ align:start position:0%
+problem mp3 players before Apple was
+that you had to commit a crime in order
+
+ align:start position:0%
+that you had to commit a crime in order
+ 
+
+ align:start position:0%
+that you had to commit a crime in order
+to use the mp3 player he was stealing
+
+ align:start position:0%
+to use the mp3 player he was stealing
+ 
+
+ align:start position:0%
+to use the mp3 player he was stealing
+someone's music right and you know this
+
+ align:start position:0%
+someone's music right and you know this
+ 
+
+ align:start position:0%
+someone's music right and you know this
+is a criminal act right what kind of
+
+ align:start position:0%
+is a criminal act right what kind of
+ 
+
+ align:start position:0%
+is a criminal act right what kind of
+product forces you to commit a criminal
+
+ align:start position:0%
+product forces you to commit a criminal
+ 
+
+ align:start position:0%
+product forces you to commit a criminal
+act and it's not a great product
+
+ align:start position:0%
+act and it's not a great product
+ 
+
+ align:start position:0%
+act and it's not a great product
+all right so Apple invents an entirely
+
+ align:start position:0%
+all right so Apple invents an entirely
+ 
+
+ align:start position:0%
+all right so Apple invents an entirely
+different way of organizing the music
+
+ align:start position:0%
+different way of organizing the music
+ 
+
+ align:start position:0%
+different way of organizing the music
+industry but it ties it to existing mp3
+
+ align:start position:0%
+industry but it ties it to existing mp3
+ 
+
+ align:start position:0%
+industry but it ties it to existing mp3
+player technology which it precedes to
+
+ align:start position:0%
+player technology which it precedes to
+ 
+
+ align:start position:0%
+player technology which it precedes to
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+
+ align:start position:0%
+perfect and how does it how is it able
+ 
+
+ align:start position:0%
+perfect and how does it how is it able
+to do this we do this remarkably short
+
+ align:start position:0%
+to do this we do this remarkably short
+ 
+
+ align:start position:0%
+to do this we do this remarkably short
+period - it's a matter of months right
+
+ align:start position:0%
+period - it's a matter of months right
+ 
+
+ align:start position:0%
+period - it's a matter of months right
+so it figures out what the optimal mp3
+
+ align:start position:0%
+so it figures out what the optimal mp3
+ 
+
+ align:start position:0%
+so it figures out what the optimal mp3
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+
+ align:start position:0%
+player of technologies are who is
+ 
+
+ align:start position:0%
+player of technologies are who is
+producing them right and go to them and
+
+ align:start position:0%
+producing them right and go to them and
+ 
+
+ align:start position:0%
+producing them right and go to them and
+enter into contracts with all over the
+
+ align:start position:0%
+enter into contracts with all over the
+ 
+
+ align:start position:0%
+enter into contracts with all over the
+world to clean China but elsewhere as
+
+ align:start position:0%
+world to clean China but elsewhere as
+ 
+
+ align:start position:0%
+world to clean China but elsewhere as
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+well and it knows that they're gonna
+ 
+
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+snap together like Legos in the end
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+
+ align:start position:0%
+snap together like Legos in the end
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+
+ align:start position:0%
+because they are using credible specs on
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+
+ align:start position:0%
+because they are using credible specs on
+computer driven equipment right so you
+
+ align:start position:0%
+computer driven equipment right so you
+ 
+
+ align:start position:0%
+computer driven equipment right so you
+can now distribute your production model
+
+ align:start position:0%
+can now distribute your production model
+ 
+
+ align:start position:0%
+can now distribute your production model
+so Apple doesn't have can do this in a
+
+ align:start position:0%
+so Apple doesn't have can do this in a
+ 
+
+ align:start position:0%
+so Apple doesn't have can do this in a
+matter of months it doesn't have to go
+
+ align:start position:0%
+matter of months it doesn't have to go
+ 
+
+ align:start position:0%
+matter of months it doesn't have to go
+by you know green space right you know
+
+ align:start position:0%
+by you know green space right you know
+ 
+
+ align:start position:0%
+by you know green space right you know
+outside Wilmington North Carolina or
+
+ align:start position:0%
+outside Wilmington North Carolina or
+ 
+
+ align:start position:0%
+outside Wilmington North Carolina or
+something and build a new factory and
+
+ align:start position:0%
+something and build a new factory and
+ 
+
+ align:start position:0%
+something and build a new factory and
+get all the permitting and spend years
+
+ align:start position:0%
+get all the permitting and spend years
+ 
+
+ align:start position:0%
+get all the permitting and spend years
+doing this and raise a billion dollars
+
+ align:start position:0%
+doing this and raise a billion dollars
+ 
+
+ align:start position:0%
+doing this and raise a billion dollars
+to do it right instead it quickly enters
+
+ align:start position:0%
+to do it right instead it quickly enters
+ 
+
+ align:start position:0%
+to do it right instead it quickly enters
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+
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+into a deal a series of deals with
+ 
+
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+existing producers but as knows that it
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+
+ align:start position:0%
+existing producers but as knows that it
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+
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+can bring the product back right because
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+
+ align:start position:0%
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+
+ align:start position:0%
+it's going to be Legos and they're gonna
+ 
+
+ align:start position:0%
+it's going to be Legos and they're gonna
+snap into place right please all right
+
+ align:start position:0%
+snap into place right please all right
+ 
+
+ align:start position:0%
+snap into place right please all right
+absolutely and you know I was in Japan
+
+ align:start position:0%
+absolutely and you know I was in Japan
+ 
+
+ align:start position:0%
+absolutely and you know I was in Japan
+in 2006 and in January it's been a
+
+ align:start position:0%
+in 2006 and in January it's been a
+ 
+
+ align:start position:0%
+in 2006 and in January it's been a
+wonderful day as it was snowing in Kyoto
+
+ align:start position:0%
+wonderful day as it was snowing in Kyoto
+ 
+
+ align:start position:0%
+wonderful day as it was snowing in Kyoto
+which was completely it was mostly back
+
+ align:start position:0%
+which was completely it was mostly back
+ 
+
+ align:start position:0%
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+in Tokyo and the headline in the leading
+
+ align:start position:0%
+in Tokyo and the headline in the leading
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+
+ align:start position:0%
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+
+ align:start position:0%
+english-language newspaper in Tokyo was
+ 
+
+ align:start position:0%
+english-language newspaper in Tokyo was
+Apple sells 14 million iPods in two
+
+ align:start position:0%
+Apple sells 14 million iPods in two
+ 
+
+ align:start position:0%
+Apple sells 14 million iPods in two
+weeks semicolon where is Sony
+
+ align:start position:0%
+weeks semicolon where is Sony
+ 
+
+ align:start position:0%
+weeks semicolon where is Sony
+exclamation point exclamation it was
+
+ align:start position:0%
+exclamation point exclamation it was
+ 
+
+ align:start position:0%
+exclamation point exclamation it was
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+
+ align:start position:0%
+just you know a reality that Apple
+ 
+
+ align:start position:0%
+just you know a reality that Apple
+available to kind of spring to this
+
+ align:start position:0%
+available to kind of spring to this
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+
+ align:start position:0%
+available to kind of spring to this
+whole new product plan
+
+ align:start position:0%
+whole new product plan
+ 
+
+ align:start position:0%
+whole new product plan
+remarkably short period of time by using
+
+ align:start position:0%
+remarkably short period of time by using
+ 
+
+ align:start position:0%
+remarkably short period of time by using
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+
+ align:start position:0%
+a digital dispersed distributed
+ 
+
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+
+ align:start position:0%
+production law and it's it's pretty
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+
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+
+ align:start position:0%
+irresistible because you get that level
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+irresistible because you get that level
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+of time and investments you have to
+ 
+
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+of time and investments you have to
+assemble ahead of time makes this really
+
+ align:start position:0%
+assemble ahead of time makes this really
+ 
+
+ align:start position:0%
+assemble ahead of time makes this really
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+ align:start position:0%
+quite convenient so lots of US firms
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+
+ align:start position:0%
+quite convenient so lots of US firms
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+
+ align:start position:0%
+move to this model and they're in
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+
+ align:start position:0%
+move to this model and they're in
+technologically enabled by these
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+technologically enabled by these
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+
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+ align:start position:0%
+technological advances to do so now
+ 
+
+ align:start position:0%
+technological advances to do so now
+Suzanne also goes on to argue pay other
+
+ align:start position:0%
+Suzanne also goes on to argue pay other
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+
+ align:start position:0%
+Suzanne also goes on to argue pay other
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+
+ align:start position:0%
+people and she's looking at group of
+ 
+
+ align:start position:0%
+people and she's looking at group of
+Asian countries and friends are not
+
+ align:start position:0%
+Asian countries and friends are not
+ 
+
+ align:start position:0%
+Asian countries and friends are not
+necessarily doing this right so in Korea
+
+ align:start position:0%
+necessarily doing this right so in Korea
+ 
+
+ align:start position:0%
+necessarily doing this right so in Korea
+samsung continues to control the key
+
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+samsung continues to control the key
+ 
+
+ align:start position:0%
+samsung continues to control the key
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+
+ align:start position:0%
+components it allows a certain amount of
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+
+ align:start position:0%
+components it allows a certain amount of
+assembly offshore in Japan there is a
+
+ align:start position:0%
+assembly offshore in Japan there is a
+ 
+
+ align:start position:0%
+assembly offshore in Japan there is a
+conscious effort to keep integrated in
+
+ align:start position:0%
+conscious effort to keep integrated in
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+
+ align:start position:0%
+conscious effort to keep integrated in
+an integrated innovation model and
+
+ align:start position:0%
+an integrated innovation model and
+ 
+
+ align:start position:0%
+an integrated innovation model and
+control all the critical stages so the
+
+ align:start position:0%
+control all the critical stages so the
+ 
+
+ align:start position:0%
+control all the critical stages so the
+risk in the Apple model is that your
+
+ align:start position:0%
+risk in the Apple model is that your
+ 
+
+ align:start position:0%
+risk in the Apple model is that your
+offshoring your production capability
+
+ align:start position:0%
+offshoring your production capability
+ 
+
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+offshoring your production capability
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+and a certain amount of the innovation
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+
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+and a certain amount of the innovation
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+
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+capability is going to follow right
+ 
+
+ align:start position:0%
+capability is going to follow right
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+
+ align:start position:0%
+that's the risk and to avoid that
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+
+ align:start position:0%
+that's the risk and to avoid that
+companies in Japan and Korea are moving
+
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+companies in Japan and Korea are moving
+ 
+
+ align:start position:0%
+companies in Japan and Korea are moving
+in a very different kind of
+
+ align:start position:0%
+in a very different kind of
+ 
+
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+organizational model both models she
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+
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+argue argues may well work right so
+ 
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+
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+these are a varieties of capitalism at
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+
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+these are a varieties of capitalism at
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+ align:start position:0%
+first time really historically several
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+
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+first time really historically several
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+ align:start position:0%
+irresistible to do so because you
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+
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+irresistible to do so because you
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+significantly reduce your risk and
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+upfront so that's why she would argue US
+
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+upfront so that's why she would argue US
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+
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+
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+firms tend to pursue this problem and
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+firms tend to pursue this problem and
+won't go to her next book next week and
+
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+won't go to her next book next week and
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+
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+won't go to her next book next week and
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+discover why the model may not
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+
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+ align:start position:0%
+necessarily be optimal till next week so
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+
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+necessarily be optimal till next week so
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+
+ align:start position:0%
+who's got who's got Suzanne
+ 
+
+ align:start position:0%
+who's got who's got Suzanne
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+
+ align:start position:0%
+let's go ahead so in how we can keep
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+
+ align:start position:0%
+let's go ahead so in how we can keep
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+
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+basically they look at a whole bunch of
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+
+ align:start position:0%
+basically they look at a whole bunch of
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+
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+different companies and many different
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+
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+industries and try to find what it is
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+ align:start position:0%
+that
+ 
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+that
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+he's competitive so they find that
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+
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+
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+there's no single paradigm and I wanted
+ 
+
+ align:start position:0%
+there's no single paradigm and I wanted
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+
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+the key lines there's that there's
+ 
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+the key lines there's that there's
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+
+ align:start position:0%
+there's no sunset industries just sunset
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+
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+there's no sunset industries just sunset
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+
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+strategies so we need to be competitive
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+
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+
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+
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+process he's looking for ways to
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+
+ align:start position:0%
+innovate and then you know I got out of
+ 
+
+ align:start position:0%
+innovate and then you know I got out of
+it were primarily two different balances
+
+ align:start position:0%
+it were primarily two different balances
+ 
+
+ align:start position:0%
+it were primarily two different balances
+one is this idea of intelligent
+
+ align:start position:0%
+one is this idea of intelligent
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+one is this idea of intelligent
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+
+ align:start position:0%
+offshoring where you know maybe option
+ 
+
+ align:start position:0%
+offshoring where you know maybe option
+outsourcing all you're all here
+
+ align:start position:0%
+outsourcing all you're all here
+ 
+
+ align:start position:0%
+outsourcing all you're all here
+manufacturing is not the best idea
+
+ align:start position:0%
+manufacturing is not the best idea
+ 
+
+ align:start position:0%
+manufacturing is not the best idea
+because there's there are other costs
+
+ align:start position:0%
+because there's there are other costs
+ 
+
+ align:start position:0%
+because there's there are other costs
+involved with that and can create
+
+ align:start position:0%
+involved with that and can create
+ 
+
+ align:start position:0%
+involved with that and can create
+innovation gaps within within your own
+
+ align:start position:0%
+innovation gaps within within your own
+ 
+
+ align:start position:0%
+innovation gaps within within your own
+country and then the other balance being
+
+ align:start position:0%
+country and then the other balance being
+ 
+
+ align:start position:0%
+country and then the other balance being
+with IP and how do you create a a
+
+ align:start position:0%
+with IP and how do you create a a
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+
+ align:start position:0%
+with IP and how do you create a a
+collaborative environment where that's
+
+ align:start position:0%
+collaborative environment where that's
+ 
+
+ align:start position:0%
+collaborative environment where that's
+conducive to growth and development but
+
+ align:start position:0%
+conducive to growth and development but
+ 
+
+ align:start position:0%
+conducive to growth and development but
+also kind of protecting your IP so that
+
+ align:start position:0%
+also kind of protecting your IP so that
+ 
+
+ align:start position:0%
+also kind of protecting your IP so that
+you don't create your own competitor and
+
+ align:start position:0%
+you don't create your own competitor and
+ 
+
+ align:start position:0%
+you don't create your own competitor and
+so I have some questions I think one of
+
+ align:start position:0%
+so I have some questions I think one of
+ 
+
+ align:start position:0%
+so I have some questions I think one of
+the first things is you know how do you
+
+ align:start position:0%
+the first things is you know how do you
+ 
+
+ align:start position:0%
+the first things is you know how do you
+companies in your sleep competitive
+
+ align:start position:0%
+companies in your sleep competitive
+ 
+
+ align:start position:0%
+companies in your sleep competitive
+sectors actually set themselves up so
+
+ align:start position:0%
+sectors actually set themselves up so
+ 
+
+ align:start position:0%
+sectors actually set themselves up so
+you constantly be innovating it's the
+
+ align:start position:0%
+you constantly be innovating it's the
+ 
+
+ align:start position:0%
+you constantly be innovating it's the
+tough thing to do yeah let me go to
+
+ align:start position:0%
+tough thing to do yeah let me go to
+ 
+
+ align:start position:0%
+tough thing to do yeah let me go to
+square the importance we push the number
+
+ align:start position:0%
+square the importance we push the number
+ 
+
+ align:start position:0%
+square the importance we push the number
+of companies that are 100 years old and
+
+ align:start position:0%
+of companies that are 100 years old and
+ 
+
+ align:start position:0%
+of companies that are 100 years old and
+they go through disruption that may
+
+ align:start position:0%
+they go through disruption that may
+ 
+
+ align:start position:0%
+they go through disruption that may
+change and they die and it's long
+
+ align:start position:0%
+change and they die and it's long
+ 
+
+ align:start position:0%
+change and they die and it's long
+lasting monitoring companies are rare
+
+ align:start position:0%
+lasting monitoring companies are rare
+ 
+
+ align:start position:0%
+lasting monitoring companies are rare
+and it's retaining this innovation
+
+ align:start position:0%
+and it's retaining this innovation
+ 
+
+ align:start position:0%
+and it's retaining this innovation
+capability that's so great so you're
+
+ align:start position:0%
+capability that's so great so you're
+ 
+
+ align:start position:0%
+capability that's so great so you're
+driving our really key questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because when you mention like innovative
+
+ align:start position:0%
+because when you mention like innovative
+ 
+
+ align:start position:0%
+because when you mention like innovative
+firms it burns a keep staying at the
+
+ align:start position:0%
+firms it burns a keep staying at the
+ 
+
+ align:start position:0%
+firms it burns a keep staying at the
+head I think my first thought is Apple
+
+ align:start position:0%
+head I think my first thought is Apple
+ 
+
+ align:start position:0%
+head I think my first thought is Apple
+and I think Apple so I like 30 years old
+
+ align:start position:0%
+and I think Apple so I like 30 years old
+ 
+
+ align:start position:0%
+and I think Apple so I like 30 years old
+now so it's like now give it and it
+
+ align:start position:0%
+now so it's like now give it and it
+ 
+
+ align:start position:0%
+now so it's like now give it and it
+hasn't even proven that it can would
+
+ align:start position:0%
+hasn't even proven that it can would
+ 
+
+ align:start position:0%
+hasn't even proven that it can would
+stay like the trend but so I'm trying to
+
+ align:start position:0%
+stay like the trend but so I'm trying to
+ 
+
+ align:start position:0%
+stay like the trend but so I'm trying to
+think of something that is actually like
+
+ align:start position:0%
+think of something that is actually like
+ 
+
+ align:start position:0%
+think of something that is actually like
+more than 50 years old as inconsistently
+
+ align:start position:0%
+more than 50 years old as inconsistently
+ 
+
+ align:start position:0%
+more than 50 years old as inconsistently
+I got talking things I think coke is
+
+ align:start position:0%
+I got talking things I think coke is
+ 
+
+ align:start position:0%
+I got talking things I think coke is
+probably my favorite example yeah I
+
+ align:start position:0%
+probably my favorite example yeah I
+ 
+
+ align:start position:0%
+probably my favorite example yeah I
+think IBM I know more about just as they
+
+ align:start position:0%
+think IBM I know more about just as they
+ 
+
+ align:start position:0%
+think IBM I know more about just as they
+develop sort of in the wave in the
+
+ align:start position:0%
+develop sort of in the wave in the
+ 
+
+ align:start position:0%
+develop sort of in the wave in the
+context of like the u.s. is looking for
+
+ align:start position:0%
+context of like the u.s. is looking for
+ 
+
+ align:start position:0%
+context of like the u.s. is looking for
+sort of answers in the semiconductor
+
+ align:start position:0%
+sort of answers in the semiconductor
+ 
+
+ align:start position:0%
+sort of answers in the semiconductor
+round but more importantly like they had
+
+ align:start position:0%
+round but more importantly like they had
+ 
+
+ align:start position:0%
+round but more importantly like they had
+to deal with the whole advent of
+
+ align:start position:0%
+to deal with the whole advent of
+ 
+
+ align:start position:0%
+to deal with the whole advent of
+personal computing and then they shifted
+
+ align:start position:0%
+personal computing and then they shifted
+ 
+
+ align:start position:0%
+personal computing and then they shifted
+now it's more like IT based services and
+
+ align:start position:0%
+now it's more like IT based services and
+ 
+
+ align:start position:0%
+now it's more like IT based services and
+so they just contract out and I solve
+
+ align:start position:0%
+so they just contract out and I solve
+ 
+
+ align:start position:0%
+so they just contract out and I solve
+your problems and I think it's like you
+
+ align:start position:0%
+your problems and I think it's like you
+ 
+
+ align:start position:0%
+your problems and I think it's like you
+have to be sensitive just sort of these
+
+ align:start position:0%
+have to be sensitive just sort of these
+ 
+
+ align:start position:0%
+have to be sensitive just sort of these
+big technological disruptions and then
+
+ align:start position:0%
+big technological disruptions and then
+ 
+
+ align:start position:0%
+big technological disruptions and then
+sort of ride the wave or like get out
+
+ align:start position:0%
+sort of ride the wave or like get out
+ 
+
+ align:start position:0%
+sort of ride the wave or like get out
+completely and sort of like being able
+
+ align:start position:0%
+completely and sort of like being able
+ 
+
+ align:start position:0%
+completely and sort of like being able
+to shut down kind of large sections of
+
+ align:start position:0%
+to shut down kind of large sections of
+ 
+
+ align:start position:0%
+to shut down kind of large sections of
+your like it was previously haven't ages
+
+ align:start position:0%
+your like it was previously haven't ages
+ 
+
+ align:start position:0%
+your like it was previously haven't ages
+maybe for coda to use disposable cameras
+
+ align:start position:0%
+maybe for coda to use disposable cameras
+ 
+
+ align:start position:0%
+maybe for coda to use disposable cameras
+but now we have digital cameras and so
+
+ align:start position:0%
+but now we have digital cameras and so
+ 
+
+ align:start position:0%
+but now we have digital cameras and so
+yeah it would be like okay we're gonna
+
+ align:start position:0%
+yeah it would be like okay we're gonna
+ 
+
+ align:start position:0%
+yeah it would be like okay we're gonna
+really radically change the course of
+
+ align:start position:0%
+really radically change the course of
+ 
+
+ align:start position:0%
+really radically change the course of
+our company in order to like sustain and
+
+ align:start position:0%
+our company in order to like sustain and
+ 
+
+ align:start position:0%
+our company in order to like sustain and
+stay alive and that's kind of our
+
+ align:start position:0%
+stay alive and that's kind of our
+ 
+
+ align:start position:0%
+stay alive and that's kind of our
+decision to have to be able to think and
+
+ align:start position:0%
+decision to have to be able to think and
+ 
+
+ align:start position:0%
+decision to have to be able to think and
+so I think the resistance to change
+
+ align:start position:0%
+so I think the resistance to change
+ 
+
+ align:start position:0%
+so I think the resistance to change
+piece
+
+ align:start position:0%
+piece
+ 
+
+ align:start position:0%
+piece
+it's probably the differentiates your
+
+ align:start position:0%
+it's probably the differentiates your
+ 
+
+ align:start position:0%
+it's probably the differentiates your
+cokes from survey maybe you're less all
+
+ align:start position:0%
+cokes from survey maybe you're less all
+ 
+
+ align:start position:0%
+cokes from survey maybe you're less all
+messing companies and next week you're
+
+ align:start position:0%
+messing companies and next week you're
+ 
+
+ align:start position:0%
+messing companies and next week you're
+gonna start to read our textbook which
+
+ align:start position:0%
+gonna start to read our textbook which
+ 
+
+ align:start position:0%
+gonna start to read our textbook which
+is about the difficulty of innovation in
+
+ align:start position:0%
+is about the difficulty of innovation in
+ 
+
+ align:start position:0%
+is about the difficulty of innovation in
+complex established legacy economics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in answering your question I mean the
+
+ align:start position:0%
+in answering your question I mean the
+ 
+
+ align:start position:0%
+in answering your question I mean the
+question - is just like if there's these
+
+ align:start position:0%
+question - is just like if there's these
+ 
+
+ align:start position:0%
+question - is just like if there's these
+new capabilities and you don't use them
+
+ align:start position:0%
+new capabilities and you don't use them
+ 
+
+ align:start position:0%
+new capabilities and you don't use them
+somebody will so it's kind of like a
+
+ align:start position:0%
+somebody will so it's kind of like a
+ 
+
+ align:start position:0%
+somebody will so it's kind of like a
+Pandora's box because like I might not
+
+ align:start position:0%
+Pandora's box because like I might not
+ 
+
+ align:start position:0%
+Pandora's box because like I might not
+want to change my whole supply chain and
+
+ align:start position:0%
+want to change my whole supply chain and
+ 
+
+ align:start position:0%
+want to change my whole supply chain and
+like I was called get rid of a jobs for
+
+ align:start position:0%
+like I was called get rid of a jobs for
+ 
+
+ align:start position:0%
+like I was called get rid of a jobs for
+my employees because of the all things
+
+ align:start position:0%
+my employees because of the all things
+ 
+
+ align:start position:0%
+my employees because of the all things
+that will happen after but my
+
+ align:start position:0%
+that will happen after but my
+ 
+
+ align:start position:0%
+that will happen after but my
+competitors probably gonna do it and if
+
+ align:start position:0%
+competitors probably gonna do it and if
+ 
+
+ align:start position:0%
+competitors probably gonna do it and if
+I don't do it then he's gonna have lower
+
+ align:start position:0%
+I don't do it then he's gonna have lower
+ 
+
+ align:start position:0%
+I don't do it then he's gonna have lower
+prop like he's gonna lower this cost and
+
+ align:start position:0%
+prop like he's gonna lower this cost and
+ 
+
+ align:start position:0%
+prop like he's gonna lower this cost and
+he'll the most likely big me to market
+
+ align:start position:0%
+he'll the most likely big me to market
+ 
+
+ align:start position:0%
+he'll the most likely big me to market
+and there's a quote from Carnac from
+
+ align:start position:0%
+and there's a quote from Carnac from
+ 
+
+ align:start position:0%
+and there's a quote from Carnac from
+Andrew Carnegie where he goes like you
+
+ align:start position:0%
+Andrew Carnegie where he goes like you
+ 
+
+ align:start position:0%
+Andrew Carnegie where he goes like you
+should always use the best tools even if
+
+ align:start position:0%
+should always use the best tools even if
+ 
+
+ align:start position:0%
+should always use the best tools even if
+it's very hard to cheat your old tools
+
+ align:start position:0%
+it's very hard to cheat your old tools
+ 
+
+ align:start position:0%
+it's very hard to cheat your old tools
+because like as a Titan of industry if
+
+ align:start position:0%
+because like as a Titan of industry if
+ 
+
+ align:start position:0%
+because like as a Titan of industry if
+you don't somebody else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other thing I'd like to say so if
+
+ align:start position:0%
+the other thing I'd like to say so if
+ 
+
+ align:start position:0%
+the other thing I'd like to say so if
+you've got I know it goes a little bit
+
+ align:start position:0%
+you've got I know it goes a little bit
+ 
+
+ align:start position:0%
+you've got I know it goes a little bit
+into into next week's everything to get
+
+ align:start position:0%
+into into next week's everything to get
+ 
+
+ align:start position:0%
+into into next week's everything to get
+but I to what extent do you think that
+
+ align:start position:0%
+but I to what extent do you think that
+ 
+
+ align:start position:0%
+but I to what extent do you think that
+the design of manufacturing can actually
+
+ align:start position:0%
+the design of manufacturing can actually
+ 
+
+ align:start position:0%
+the design of manufacturing can actually
+be be separated I know yeah I might see
+
+ align:start position:0%
+be be separated I know yeah I might see
+ 
+
+ align:start position:0%
+be be separated I know yeah I might see
+like in the kind of engineering
+
+ align:start position:0%
+like in the kind of engineering
+ 
+
+ align:start position:0%
+like in the kind of engineering
+department you know there's so big
+
+ align:start position:0%
+department you know there's so big
+ 
+
+ align:start position:0%
+department you know there's so big
+emphasis on taking the manufacturing
+
+ align:start position:0%
+emphasis on taking the manufacturing
+ 
+
+ align:start position:0%
+emphasis on taking the manufacturing
+classes in terms of just understanding
+
+ align:start position:0%
+classes in terms of just understanding
+ 
+
+ align:start position:0%
+classes in terms of just understanding
+like when you're designing what is it
+
+ align:start position:0%
+like when you're designing what is it
+ 
+
+ align:start position:0%
+like when you're designing what is it
+feasible it is what is possible at the
+
+ align:start position:0%
+feasible it is what is possible at the
+ 
+
+ align:start position:0%
+feasible it is what is possible at the
+manufactures it may be with 3d printing
+
+ align:start position:0%
+manufactures it may be with 3d printing
+ 
+
+ align:start position:0%
+manufactures it may be with 3d printing
+like it's a little bit more separate
+
+ align:start position:0%
+like it's a little bit more separate
+ 
+
+ align:start position:0%
+like it's a little bit more separate
+you've basically said anything can be
+
+ align:start position:0%
+you've basically said anything can be
+ 
+
+ align:start position:0%
+you've basically said anything can be
+made but uh but there's just a lot of
+
+ align:start position:0%
+made but uh but there's just a lot of
+ 
+
+ align:start position:0%
+made but uh but there's just a lot of
+know-how kind of embodied in and having
+
+ align:start position:0%
+know-how kind of embodied in and having
+ 
+
+ align:start position:0%
+know-how kind of embodied in and having
+the manufacturing there to it I know I
+
+ align:start position:0%
+the manufacturing there to it I know I
+ 
+
+ align:start position:0%
+the manufacturing there to it I know I
+don't fully think that it can be like or
+
+ align:start position:0%
+don't fully think that it can be like or
+ 
+
+ align:start position:0%
+don't fully think that it can be like or
+it's wise to fully separate them I want
+
+ align:start position:0%
+it's wise to fully separate them I want
+ 
+
+ align:start position:0%
+it's wise to fully separate them I want
+to see if people also have some thoughts
+
+ align:start position:0%
+to see if people also have some thoughts
+ 
+
+ align:start position:0%
+to see if people also have some thoughts
+day I I was gonna say that maybe the
+
+ align:start position:0%
+day I I was gonna say that maybe the
+ 
+
+ align:start position:0%
+day I I was gonna say that maybe the
+separation is just a figment of our
+
+ align:start position:0%
+separation is just a figment of our
+ 
+
+ align:start position:0%
+separation is just a figment of our
+imaginations because I know that when
+
+ align:start position:0%
+imaginations because I know that when
+ 
+
+ align:start position:0%
+imaginations because I know that when
+Suzanne Berger was on the panel and the
+
+ align:start position:0%
+Suzanne Berger was on the panel and the
+ 
+
+ align:start position:0%
+Suzanne Berger was on the panel and the
+boot camp course I think it was Suzanne
+
+ align:start position:0%
+boot camp course I think it was Suzanne
+ 
+
+ align:start position:0%
+boot camp course I think it was Suzanne
+who said that the people who the
+
+ align:start position:0%
+who said that the people who the
+ 
+
+ align:start position:0%
+who said that the people who the
+designers for Apple spend most of their
+
+ align:start position:0%
+designers for Apple spend most of their
+ 
+
+ align:start position:0%
+designers for Apple spend most of their
+time not who's been their time in the
+
+ align:start position:0%
+time not who's been their time in the
+ 
+
+ align:start position:0%
+time not who's been their time in the
+menu back to the offshore manufacturing
+
+ align:start position:0%
+menu back to the offshore manufacturing
+ 
+
+ align:start position:0%
+menu back to the offshore manufacturing
+ship
+
+ align:start position:0%
+ship
+ 
+
+ align:start position:0%
+ship
+so they're not really separate although
+
+ align:start position:0%
+so they're not really separate although
+ 
+
+ align:start position:0%
+so they're not really separate although
+their quote-unquote separate yeah I
+
+ align:start position:0%
+their quote-unquote separate yeah I
+ 
+
+ align:start position:0%
+their quote-unquote separate yeah I
+think also objective is kind of
+
+ align:start position:0%
+think also objective is kind of
+ 
+
+ align:start position:0%
+think also objective is kind of
+important in like if you're trying to
+
+ align:start position:0%
+important in like if you're trying to
+ 
+
+ align:start position:0%
+important in like if you're trying to
+separate like what are you trying to
+
+ align:start position:0%
+separate like what are you trying to
+ 
+
+ align:start position:0%
+separate like what are you trying to
+separate in order to do if you're trying
+
+ align:start position:0%
+separate in order to do if you're trying
+ 
+
+ align:start position:0%
+separate in order to do if you're trying
+to separate or cut costs yeah like
+
+ align:start position:0%
+to separate or cut costs yeah like
+ 
+
+ align:start position:0%
+to separate or cut costs yeah like
+you'll find a way because it'll be more
+
+ align:start position:0%
+you'll find a way because it'll be more
+ 
+
+ align:start position:0%
+you'll find a way because it'll be more
+advantageous for you to kind of send
+
+ align:start position:0%
+advantageous for you to kind of send
+ 
+
+ align:start position:0%
+advantageous for you to kind of send
+your manufacturing section over it here
+
+ align:start position:0%
+your manufacturing section over it here
+ 
+
+ align:start position:0%
+your manufacturing section over it here
+Apple but like even if you do that
+
+ align:start position:0%
+Apple but like even if you do that
+ 
+
+ align:start position:0%
+Apple but like even if you do that
+you're gonna have to send your designers
+
+ align:start position:0%
+you're gonna have to send your designers
+ 
+
+ align:start position:0%
+you're gonna have to send your designers
+in order to do the next day and really
+
+ align:start position:0%
+in order to do the next day and really
+ 
+
+ align:start position:0%
+in order to do the next day and really
+consider how am I going to manufacture
+
+ align:start position:0%
+consider how am I going to manufacture
+ 
+
+ align:start position:0%
+consider how am I going to manufacture
+this thing that I've designed and I
+
+ align:start position:0%
+this thing that I've designed and I
+ 
+
+ align:start position:0%
+this thing that I've designed and I
+could never do that like you can't
+
+ align:start position:0%
+could never do that like you can't
+ 
+
+ align:start position:0%
+could never do that like you can't
+separate them so the mechanical
+
+ align:start position:0%
+separate them so the mechanical
+ 
+
+ align:start position:0%
+separate them so the mechanical
+engineering department I think it's
+
+ align:start position:0%
+engineering department I think it's
+ 
+
+ align:start position:0%
+engineering department I think it's
+probably pretty smart by like training
+
+ align:start position:0%
+probably pretty smart by like training
+ 
+
+ align:start position:0%
+probably pretty smart by like training
+when trading all the mechanical
+
+ align:start position:0%
+when trading all the mechanical
+ 
+
+ align:start position:0%
+when trading all the mechanical
+engineers we're then going to go out
+
+ align:start position:0%
+engineers we're then going to go out
+ 
+
+ align:start position:0%
+engineers we're then going to go out
+design and manufacture steel you might
+
+ align:start position:0%
+design and manufacture steel you might
+ 
+
+ align:start position:0%
+design and manufacture steel you might
+specialize and one of the other like you
+
+ align:start position:0%
+specialize and one of the other like you
+ 
+
+ align:start position:0%
+specialize and one of the other like you
+need to have a strong basis and a
+
+ align:start position:0%
+need to have a strong basis and a
+ 
+
+ align:start position:0%
+need to have a strong basis and a
+foundation of both and understand that
+
+ align:start position:0%
+foundation of both and understand that
+ 
+
+ align:start position:0%
+foundation of both and understand that
+both are critical in order to like do
+
+ align:start position:0%
+both are critical in order to like do
+ 
+
+ align:start position:0%
+both are critical in order to like do
+anything that's probably long last year
+
+ align:start position:0%
+anything that's probably long last year
+ 
+
+ align:start position:0%
+anything that's probably long last year
+meaningful
+
+ align:start position:0%
+meaningful
+ 
+
+ align:start position:0%
+meaningful
+I guess quote innovative let me talk
+
+ align:start position:0%
+I guess quote innovative let me talk
+ 
+
+ align:start position:0%
+I guess quote innovative let me talk
+about the design what do we do mean the
+
+ align:start position:0%
+about the design what do we do mean the
+ 
+
+ align:start position:0%
+about the design what do we do mean the
+designer of an industrial system do we
+
+ align:start position:0%
+designer of an industrial system do we
+ 
+
+ align:start position:0%
+designer of an industrial system do we
+mean the designer of an industrial
+
+ align:start position:0%
+mean the designer of an industrial
+ 
+
+ align:start position:0%
+mean the designer of an industrial
+appliance do mean the designer of
+
+ align:start position:0%
+appliance do mean the designer of
+ 
+
+ align:start position:0%
+appliance do mean the designer of
+hardware do me the designer of software
+
+ align:start position:0%
+hardware do me the designer of software
+ 
+
+ align:start position:0%
+hardware do me the designer of software
+what components and design are we
+
+ align:start position:0%
+what components and design are we
+ 
+
+ align:start position:0%
+what components and design are we
+concerned about and in what ways is this
+
+ align:start position:0%
+concerned about and in what ways is this
+ 
+
+ align:start position:0%
+concerned about and in what ways is this
+sort of relevant and the conversation
+
+ align:start position:0%
+sort of relevant and the conversation
+ 
+
+ align:start position:0%
+sort of relevant and the conversation
+we're having right now about integration
+
+ align:start position:0%
+we're having right now about integration
+ 
+
+ align:start position:0%
+we're having right now about integration
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+oh I was viewing it when we see like
+
+ align:start position:0%
+oh I was viewing it when we see like
+ 
+
+ align:start position:0%
+oh I was viewing it when we see like
+we're comparing the design of
+
+ align:start position:0%
+we're comparing the design of
+ 
+
+ align:start position:0%
+we're comparing the design of
+manufacturing so I wouldn't think of it
+
+ align:start position:0%
+manufacturing so I wouldn't think of it
+ 
+
+ align:start position:0%
+manufacturing so I wouldn't think of it
+so much as like software and primarily
+
+ align:start position:0%
+so much as like software and primarily
+ 
+
+ align:start position:0%
+so much as like software and primarily
+Hardware where the design may be you
+
+ align:start position:0%
+Hardware where the design may be you
+ 
+
+ align:start position:0%
+Hardware where the design may be you
+know having a dream on or a you know way
+
+ align:start position:0%
+know having a dream on or a you know way
+ 
+
+ align:start position:0%
+know having a dream on or a you know way
+out of my my circuit board you know that
+
+ align:start position:0%
+out of my my circuit board you know that
+ 
+
+ align:start position:0%
+out of my my circuit board you know that
+I'm going to send to a manufacturer and
+
+ align:start position:0%
+I'm going to send to a manufacturer and
+ 
+
+ align:start position:0%
+I'm going to send to a manufacturer and
+the other side of the world who will you
+
+ align:start position:0%
+the other side of the world who will you
+ 
+
+ align:start position:0%
+the other side of the world who will you
+know actually make those components
+
+ align:start position:0%
+know actually make those components
+ 
+
+ align:start position:0%
+know actually make those components
+together that's what I guess a reason
+
+ align:start position:0%
+together that's what I guess a reason
+ 
+
+ align:start position:0%
+together that's what I guess a reason
+are concerned because it delight myself
+
+ align:start position:0%
+are concerned because it delight myself
+ 
+
+ align:start position:0%
+are concerned because it delight myself
+I think of myself as a design researcher
+
+ align:start position:0%
+I think of myself as a design researcher
+ 
+
+ align:start position:0%
+I think of myself as a design researcher
+right because I think about the ways in
+
+ align:start position:0%
+right because I think about the ways in
+ 
+
+ align:start position:0%
+right because I think about the ways in
+which you can take systems engineering
+
+ align:start position:0%
+which you can take systems engineering
+ 
+
+ align:start position:0%
+which you can take systems engineering
+approaches to social issues and there's
+
+ align:start position:0%
+approaches to social issues and there's
+ 
+
+ align:start position:0%
+approaches to social issues and there's
+a big debate right now in the design
+
+ align:start position:0%
+a big debate right now in the design
+ 
+
+ align:start position:0%
+a big debate right now in the design
+community about who gets to create it
+
+ align:start position:0%
+community about who gets to create it
+ 
+
+ align:start position:0%
+community about who gets to create it
+and there's even more of a debate about
+
+ align:start position:0%
+and there's even more of a debate about
+ 
+
+ align:start position:0%
+and there's even more of a debate about
+the sort of nuances and in exerting the
+
+ align:start position:0%
+the sort of nuances and in exerting the
+ 
+
+ align:start position:0%
+the sort of nuances and in exerting the
+power in creating something right like
+
+ align:start position:0%
+power in creating something right like
+ 
+
+ align:start position:0%
+power in creating something right like
+all of these partner choices are
+
+ align:start position:0%
+all of these partner choices are
+ 
+
+ align:start position:0%
+all of these partner choices are
+political choices and they have impacts
+
+ align:start position:0%
+political choices and they have impacts
+ 
+
+ align:start position:0%
+political choices and they have impacts
+on both the user and the society in
+
+ align:start position:0%
+on both the user and the society in
+ 
+
+ align:start position:0%
+on both the user and the society in
+which they're implemented so that's why
+
+ align:start position:0%
+which they're implemented so that's why
+ 
+
+ align:start position:0%
+which they're implemented so that's why
+I think it's important to really
+
+ align:start position:0%
+I think it's important to really
+ 
+
+ align:start position:0%
+I think it's important to really
+consider when both the author and we
+
+ align:start position:0%
+consider when both the author and we
+ 
+
+ align:start position:0%
+consider when both the author and we
+talk about design what kind of design
+
+ align:start position:0%
+talk about design what kind of design
+ 
+
+ align:start position:0%
+talk about design what kind of design
+were talking about and we view it not
+
+ align:start position:0%
+were talking about and we view it not
+ 
+
+ align:start position:0%
+were talking about and we view it not
+necessarily as a neutral and apolitical
+
+ align:start position:0%
+necessarily as a neutral and apolitical
+ 
+
+ align:start position:0%
+necessarily as a neutral and apolitical
+actually but very much as a reflection
+
+ align:start position:0%
+actually but very much as a reflection
+ 
+
+ align:start position:0%
+actually but very much as a reflection
+of what that's corporation values and
+
+ align:start position:0%
+of what that's corporation values and
+ 
+
+ align:start position:0%
+of what that's corporation values and
+what kind of the values they want to
+
+ align:start position:0%
+what kind of the values they want to
+ 
+
+ align:start position:0%
+what kind of the values they want to
+promote in a society so this you know
+
+ align:start position:0%
+promote in a society so this you know
+ 
+
+ align:start position:0%
+promote in a society so this you know
+when I look at this laptop I don't think
+
+ align:start position:0%
+when I look at this laptop I don't think
+ 
+
+ align:start position:0%
+when I look at this laptop I don't think
+oh this is you know beautiful this is an
+
+ align:start position:0%
+oh this is you know beautiful this is an
+ 
+
+ align:start position:0%
+oh this is you know beautiful this is an
+elegant this is functional I think this
+
+ align:start position:0%
+elegant this is functional I think this
+ 
+
+ align:start position:0%
+elegant this is functional I think this
+is how this company wants that
+
+ align:start position:0%
+is how this company wants that
+ 
+
+ align:start position:0%
+is how this company wants that
+look like and this is their long-lasting
+
+ align:start position:0%
+look like and this is their long-lasting
+ 
+
+ align:start position:0%
+look like and this is their long-lasting
+and material vision form of the world
+
+ align:start position:0%
+and material vision form of the world
+ 
+
+ align:start position:0%
+and material vision form of the world
+could look like for the long run
+
+ align:start position:0%
+could look like for the long run
+ 
+
+ align:start position:0%
+could look like for the long run
+eternally I think a lot of design
+
+ align:start position:0%
+eternally I think a lot of design
+ 
+
+ align:start position:0%
+eternally I think a lot of design
+thinking actually is pretty company's
+
+ align:start position:0%
+thinking actually is pretty company's
+ 
+
+ align:start position:0%
+thinking actually is pretty company's
+yeah that while we're looking at what
+
+ align:start position:0%
+yeah that while we're looking at what
+ 
+
+ align:start position:0%
+yeah that while we're looking at what
+they what we think their vision has been
+
+ align:start position:0%
+they what we think their vision has been
+ 
+
+ align:start position:0%
+they what we think their vision has been
+oh when we look at say math look and go
+
+ align:start position:0%
+oh when we look at say math look and go
+ 
+
+ align:start position:0%
+oh when we look at say math look and go
+out of them I looking to you and you
+
+ align:start position:0%
+out of them I looking to you and you
+ 
+
+ align:start position:0%
+out of them I looking to you and you
+know Apple wouldn't say and their design
+
+ align:start position:0%
+know Apple wouldn't say and their design
+ 
+
+ align:start position:0%
+know Apple wouldn't say and their design
+process they're going after users and
+
+ align:start position:0%
+process they're going after users and
+ 
+
+ align:start position:0%
+process they're going after users and
+seeing what what the users actually want
+
+ align:start position:0%
+seeing what what the users actually want
+ 
+
+ align:start position:0%
+seeing what what the users actually want
+awesome it's like a lot of looking both
+
+ align:start position:0%
+awesome it's like a lot of looking both
+ 
+
+ align:start position:0%
+awesome it's like a lot of looking both
+ways from up from a capitalist
+
+ align:start position:0%
+ways from up from a capitalist
+ 
+
+ align:start position:0%
+ways from up from a capitalist
+perspective look at it it's pretty much
+
+ align:start position:0%
+perspective look at it it's pretty much
+ 
+
+ align:start position:0%
+perspective look at it it's pretty much
+like okay one of the main fetching
+
+ align:start position:0%
+like okay one of the main fetching
+ 
+
+ align:start position:0%
+like okay one of the main fetching
+abilities how much does it cost me how
+
+ align:start position:0%
+abilities how much does it cost me how
+ 
+
+ align:start position:0%
+abilities how much does it cost me how
+long is going to take what can be the
+
+ align:start position:0%
+long is going to take what can be the
+ 
+
+ align:start position:0%
+long is going to take what can be the
+issues don't make it complicated some
+
+ align:start position:0%
+issues don't make it complicated some
+ 
+
+ align:start position:0%
+issues don't make it complicated some
+flights and why so funny because in the
+
+ align:start position:0%
+flights and why so funny because in the
+ 
+
+ align:start position:0%
+flights and why so funny because in the
+execution it's gonna be way more complex
+
+ align:start position:0%
+execution it's gonna be way more complex
+ 
+
+ align:start position:0%
+execution it's gonna be way more complex
+I'm not trying to deal with that and
+
+ align:start position:0%
+I'm not trying to deal with that and
+ 
+
+ align:start position:0%
+I'm not trying to deal with that and
+pretty much like okay I'll make it make
+
+ align:start position:0%
+pretty much like okay I'll make it make
+ 
+
+ align:start position:0%
+pretty much like okay I'll make it make
+sure it's slightly different in the my
+
+ align:start position:0%
+sure it's slightly different in the my
+ 
+
+ align:start position:0%
+sure it's slightly different in the my
+competitors make sure it follows the
+
+ align:start position:0%
+competitors make sure it follows the
+ 
+
+ align:start position:0%
+competitors make sure it follows the
+values of my company that's certain by
+
+ align:start position:0%
+values of my company that's certain by
+ 
+
+ align:start position:0%
+values of my company that's certain by
+the way and then when I market maybe you
+
+ align:start position:0%
+the way and then when I market maybe you
+ 
+
+ align:start position:0%
+the way and then when I market maybe you
+think it's something more than it
+
+ align:start position:0%
+think it's something more than it
+ 
+
+ align:start position:0%
+think it's something more than it
+actually is because they don't buy it
+
+ align:start position:0%
+actually is because they don't buy it
+ 
+
+ align:start position:0%
+actually is because they don't buy it
+because it's worth about I think maybe
+
+ align:start position:0%
+because it's worth about I think maybe
+ 
+
+ align:start position:0%
+because it's worth about I think maybe
+American Apparel and sort of what the
+
+ align:start position:0%
+American Apparel and sort of what the
+ 
+
+ align:start position:0%
+American Apparel and sort of what the
+internet like American Apparel a lot of
+
+ align:start position:0%
+internet like American Apparel a lot of
+ 
+
+ align:start position:0%
+internet like American Apparel a lot of
+brand jeans and some other companies
+
+ align:start position:0%
+brand jeans and some other companies
+ 
+
+ align:start position:0%
+brand jeans and some other companies
+they're like very heavy are their models
+
+ align:start position:0%
+they're like very heavy are their models
+ 
+
+ align:start position:0%
+they're like very heavy are their models
+are like particularly because they're
+
+ align:start position:0%
+are like particularly because they're
+ 
+
+ align:start position:0%
+are like particularly because they're
+based in the US and even though it might
+
+ align:start position:0%
+based in the US and even though it might
+ 
+
+ align:start position:0%
+based in the US and even though it might
+be less expensive to sort of like build
+
+ align:start position:0%
+be less expensive to sort of like build
+ 
+
+ align:start position:0%
+be less expensive to sort of like build
+and like manufacture your jeans or your
+
+ align:start position:0%
+and like manufacture your jeans or your
+ 
+
+ align:start position:0%
+and like manufacture your jeans or your
+t-shirts for example outside of Los
+
+ align:start position:0%
+t-shirts for example outside of Los
+ 
+
+ align:start position:0%
+t-shirts for example outside of Los
+Angeles
+
+ align:start position:0%
+Angeles
+ 
+
+ align:start position:0%
+Angeles
+you lose sort of other factors which is
+
+ align:start position:0%
+you lose sort of other factors which is
+ 
+
+ align:start position:0%
+you lose sort of other factors which is
+sort of like being able to say like
+
+ align:start position:0%
+sort of like being able to say like
+ 
+
+ align:start position:0%
+sort of like being able to say like
+maybe say well wha but also like you
+
+ align:start position:0%
+maybe say well wha but also like you
+ 
+
+ align:start position:0%
+maybe say well wha but also like you
+gain sort of production speed and like
+
+ align:start position:0%
+gain sort of production speed and like
+ 
+
+ align:start position:0%
+gain sort of production speed and like
+all these things of our team is talking
+
+ align:start position:0%
+all these things of our team is talking
+ 
+
+ align:start position:0%
+all these things of our team is talking
+about some kind of a couple you design
+
+ align:start position:0%
+about some kind of a couple you design
+ 
+
+ align:start position:0%
+about some kind of a couple you design
+in the manufacturing processes it like
+
+ align:start position:0%
+in the manufacturing processes it like
+ 
+
+ align:start position:0%
+in the manufacturing processes it like
+people in here but at the end of the day
+
+ align:start position:0%
+people in here but at the end of the day
+ 
+
+ align:start position:0%
+people in here but at the end of the day
+I think you do a cost-benefit analysis
+
+ align:start position:0%
+I think you do a cost-benefit analysis
+ 
+
+ align:start position:0%
+I think you do a cost-benefit analysis
+in Stalag Martine said and then just
+
+ align:start position:0%
+in Stalag Martine said and then just
+ 
+
+ align:start position:0%
+in Stalag Martine said and then just
+make sure that your company values is in
+
+ align:start position:0%
+make sure that your company values is in
+ 
+
+ align:start position:0%
+make sure that your company values is in
+line with sort of the product and like
+
+ align:start position:0%
+line with sort of the product and like
+ 
+
+ align:start position:0%
+line with sort of the product and like
+how do you want people to interface with
+
+ align:start position:0%
+how do you want people to interface with
+ 
+
+ align:start position:0%
+how do you want people to interface with
+the world through your problem going off
+
+ align:start position:0%
+the world through your problem going off
+ 
+
+ align:start position:0%
+the world through your problem going off
+that I'm curious how much of those
+
+ align:start position:0%
+that I'm curious how much of those
+ 
+
+ align:start position:0%
+that I'm curious how much of those
+advantages that you get from producing
+
+ align:start position:0%
+advantages that you get from producing
+ 
+
+ align:start position:0%
+advantages that you get from producing
+in the US can query like whatever
+
+ align:start position:0%
+in the US can query like whatever
+ 
+
+ align:start position:0%
+in the US can query like whatever
+they're kind of gimmick is how
+
+ align:start position:0%
+they're kind of gimmick is how
+ 
+
+ align:start position:0%
+they're kind of gimmick is how
+like along those last like American
+
+ align:start position:0%
+like along those last like American
+ 
+
+ align:start position:0%
+like along those last like American
+Apparel just closed all their stories
+
+ align:start position:0%
+Apparel just closed all their stories
+ 
+
+ align:start position:0%
+Apparel just closed all their stories
+like does that mean that that approach
+
+ align:start position:0%
+like does that mean that that approach
+ 
+
+ align:start position:0%
+like does that mean that that approach
+isn't sustainable and that they should
+
+ align:start position:0%
+isn't sustainable and that they should
+ 
+
+ align:start position:0%
+isn't sustainable and that they should
+have taken another look at outsourcing
+
+ align:start position:0%
+have taken another look at outsourcing
+ 
+
+ align:start position:0%
+have taken another look at outsourcing
+or is it just I mean there are other
+
+ align:start position:0%
+or is it just I mean there are other
+ 
+
+ align:start position:0%
+or is it just I mean there are other
+factors contributing to it but is that
+
+ align:start position:0%
+factors contributing to it but is that
+ 
+
+ align:start position:0%
+factors contributing to it but is that
+like do these companies have to pick
+
+ align:start position:0%
+like do these companies have to pick
+ 
+
+ align:start position:0%
+like do these companies have to pick
+like what society will watch as their
+
+ align:start position:0%
+like what society will watch as their
+ 
+
+ align:start position:0%
+like what society will watch as their
+special sauce and hope that it wants
+
+ align:start position:0%
+special sauce and hope that it wants
+ 
+
+ align:start position:0%
+special sauce and hope that it wants
+long enough or are they eventually going
+
+ align:start position:0%
+long enough or are they eventually going
+ 
+
+ align:start position:0%
+long enough or are they eventually going
+to need to think about these
+
+ align:start position:0%
+to need to think about these
+ 
+
+ align:start position:0%
+to need to think about these
+alternatives they definitely should
+
+ align:start position:0%
+alternatives they definitely should
+ 
+
+ align:start position:0%
+alternatives they definitely should
+consider the alternatives but I mean
+
+ align:start position:0%
+consider the alternatives but I mean
+ 
+
+ align:start position:0%
+consider the alternatives but I mean
+when at least for the American girl like
+
+ align:start position:0%
+when at least for the American girl like
+ 
+
+ align:start position:0%
+when at least for the American girl like
+you were saying yeah there's probably a
+
+ align:start position:0%
+you were saying yeah there's probably a
+ 
+
+ align:start position:0%
+you were saying yeah there's probably a
+ton of factors and I think just to
+
+ align:start position:0%
+ton of factors and I think just to
+ 
+
+ align:start position:0%
+ton of factors and I think just to
+answer that question we just need more
+
+ align:start position:0%
+answer that question we just need more
+ 
+
+ align:start position:0%
+answer that question we just need more
+data so we need to somehow control for
+
+ align:start position:0%
+data so we need to somehow control for
+ 
+
+ align:start position:0%
+data so we need to somehow control for
+the type of industry the time period the
+
+ align:start position:0%
+the type of industry the time period the
+ 
+
+ align:start position:0%
+the type of industry the time period the
+location etc etc and then you could
+
+ align:start position:0%
+location etc etc and then you could
+ 
+
+ align:start position:0%
+location etc etc and then you could
+compare just like based on the
+
+ align:start position:0%
+compare just like based on the
+ 
+
+ align:start position:0%
+compare just like based on the
+information that we have the question we
+
+ align:start position:0%
+information that we have the question we
+ 
+
+ align:start position:0%
+information that we have the question we
+just don't have those numbers to back up
+
+ align:start position:0%
+just don't have those numbers to back up
+ 
+
+ align:start position:0%
+just don't have those numbers to back up
+the other side or another example I
+
+ align:start position:0%
+the other side or another example I
+ 
+
+ align:start position:0%
+the other side or another example I
+think that this was written before Zahra
+
+ align:start position:0%
+think that this was written before Zahra
+ 
+
+ align:start position:0%
+think that this was written before Zahra
+came under fire for a bunch of basically
+
+ align:start position:0%
+came under fire for a bunch of basically
+ 
+
+ align:start position:0%
+came under fire for a bunch of basically
+human oh no I can't even afraid I can't
+
+ align:start position:0%
+human oh no I can't even afraid I can't
+ 
+
+ align:start position:0%
+human oh no I can't even afraid I can't
+articulate it well or Martine of you
+
+ align:start position:0%
+articulate it well or Martine of you
+ 
+
+ align:start position:0%
+articulate it well or Martine of you
+give mom and you it's it's an example
+
+ align:start position:0%
+give mom and you it's it's an example
+ 
+
+ align:start position:0%
+give mom and you it's it's an example
+that Suzanne Berger uses and the point
+
+ align:start position:0%
+that Suzanne Berger uses and the point
+ 
+
+ align:start position:0%
+that Suzanne Berger uses and the point
+about Zara is that by locating its
+
+ align:start position:0%
+about Zara is that by locating its
+ 
+
+ align:start position:0%
+about Zara is that by locating its
+production facilities very close to his
+
+ align:start position:0%
+production facilities very close to his
+ 
+
+ align:start position:0%
+production facilities very close to his
+markets is able to move from production
+
+ align:start position:0%
+markets is able to move from production
+ 
+
+ align:start position:0%
+markets is able to move from production
+to its sale system in a very very short
+
+ align:start position:0%
+to its sale system in a very very short
+ 
+
+ align:start position:0%
+to its sale system in a very very short
+period of time so by tracking fashion
+
+ align:start position:0%
+period of time so by tracking fashion
+ 
+
+ align:start position:0%
+period of time so by tracking fashion
+markets and what appears to be moving as
+
+ align:start position:0%
+markets and what appears to be moving as
+ 
+
+ align:start position:0%
+markets and what appears to be moving as
+selling is able to shift its production
+
+ align:start position:0%
+selling is able to shift its production
+ 
+
+ align:start position:0%
+selling is able to shift its production
+system quickly on to kind of new styles
+
+ align:start position:0%
+system quickly on to kind of new styles
+ 
+
+ align:start position:0%
+system quickly on to kind of new styles
+and emerge whereas if you're shipping
+
+ align:start position:0%
+and emerge whereas if you're shipping
+ 
+
+ align:start position:0%
+and emerge whereas if you're shipping
+that style across a 8,000 miles of ocean
+
+ align:start position:0%
+that style across a 8,000 miles of ocean
+ 
+
+ align:start position:0%
+that style across a 8,000 miles of ocean
+in a container ship that's moving
+
+ align:start position:0%
+in a container ship that's moving
+ 
+
+ align:start position:0%
+in a container ship that's moving
+that's right you're not in the game
+
+ align:start position:0%
+that's right you're not in the game
+ 
+
+ align:start position:0%
+that's right you're not in the game
+right so as our has figured out how to
+
+ align:start position:0%
+right so as our has figured out how to
+ 
+
+ align:start position:0%
+right so as our has figured out how to
+keep that relationship between
+
+ align:start position:0%
+keep that relationship between
+ 
+
+ align:start position:0%
+keep that relationship between
+production facility market and sales
+
+ align:start position:0%
+production facility market and sales
+ 
+
+ align:start position:0%
+production facility market and sales
+facility very tight and therefore be
+
+ align:start position:0%
+facility very tight and therefore be
+ 
+
+ align:start position:0%
+facility very tight and therefore be
+able to serve emerging markets and you
+
+ align:start position:0%
+able to serve emerging markets and you
+ 
+
+ align:start position:0%
+able to serve emerging markets and you
+know fashion is so much different in
+
+ align:start position:0%
+know fashion is so much different in
+ 
+
+ align:start position:0%
+know fashion is so much different in
+other areas but I think is still there
+
+ align:start position:0%
+other areas but I think is still there
+ 
+
+ align:start position:0%
+other areas but I think is still there
+but serve emerging markets very quickly
+
+ align:start position:0%
+but serve emerging markets very quickly
+ 
+
+ align:start position:0%
+but serve emerging markets very quickly
+so rising to you market opportunities
+
+ align:start position:0%
+so rising to you market opportunities
+ 
+
+ align:start position:0%
+so rising to you market opportunities
+integration roots of time how's that
+
+ align:start position:0%
+integration roots of time how's that
+ 
+
+ align:start position:0%
+integration roots of time how's that
+Martina said I was like pretty much what
+
+ align:start position:0%
+Martina said I was like pretty much what
+ 
+
+ align:start position:0%
+Martina said I was like pretty much what
+they do it's like big go into the
+
+ align:start position:0%
+they do it's like big go into the
+ 
+
+ align:start position:0%
+they do it's like big go into the
+Fashion Week like oh there's a really
+
+ align:start position:0%
+Fashion Week like oh there's a really
+ 
+
+ align:start position:0%
+Fashion Week like oh there's a really
+expensive thing we're gonna do is we're
+
+ align:start position:0%
+expensive thing we're gonna do is we're
+ 
+
+ align:start position:0%
+expensive thing we're gonna do is we're
+gonna find a very quick doing it they
+
+ align:start position:0%
+gonna find a very quick doing it they
+ 
+
+ align:start position:0%
+gonna find a very quick doing it they
+have it on the market like by two weeks
+
+ align:start position:0%
+have it on the market like by two weeks
+ 
+
+ align:start position:0%
+have it on the market like by two weeks
+pretty much of a like rapidly design and
+
+ align:start position:0%
+pretty much of a like rapidly design and
+ 
+
+ align:start position:0%
+pretty much of a like rapidly design and
+they go for a low price point and
+
+ align:start position:0%
+they go for a low price point and
+ 
+
+ align:start position:0%
+they go for a low price point and
+they'll put it into the market and then
+
+ align:start position:0%
+they'll put it into the market and then
+ 
+
+ align:start position:0%
+they'll put it into the market and then
+people will buy it but you're not really
+
+ align:start position:0%
+people will buy it but you're not really
+ 
+
+ align:start position:0%
+people will buy it but you're not really
+buying it because it's like you're not
+
+ align:start position:0%
+buying it because it's like you're not
+ 
+
+ align:start position:0%
+buying it because it's like you're not
+mine for value you're buying because
+
+ align:start position:0%
+mine for value you're buying because
+ 
+
+ align:start position:0%
+mine for value you're buying because
+this is trendy and I always spend that
+
+ align:start position:0%
+this is trendy and I always spend that
+ 
+
+ align:start position:0%
+this is trendy and I always spend that
+much and that's kind of their value
+
+ align:start position:0%
+much and that's kind of their value
+ 
+
+ align:start position:0%
+much and that's kind of their value
+problem right now because they're
+
+ align:start position:0%
+problem right now because they're
+ 
+
+ align:start position:0%
+problem right now because they're
+usually like slightly more than H&M but
+
+ align:start position:0%
+usually like slightly more than H&M but
+ 
+
+ align:start position:0%
+usually like slightly more than H&M but
+it just like that right model for like I
+
+ align:start position:0%
+it just like that right model for like I
+ 
+
+ align:start position:0%
+it just like that right model for like I
+want to buy a good amount now from like
+
+ align:start position:0%
+want to buy a good amount now from like
+ 
+
+ align:start position:0%
+want to buy a good amount now from like
+ten years ago said some people early
+
+ align:start position:0%
+ten years ago said some people early
+ 
+
+ align:start position:0%
+ten years ago said some people early
+because there's our there's H&M but like
+
+ align:start position:0%
+because there's our there's H&M but like
+ 
+
+ align:start position:0%
+because there's our there's H&M but like
+there's not too much of a difference and
+
+ align:start position:0%
+there's not too much of a difference and
+ 
+
+ align:start position:0%
+there's not too much of a difference and
+I'm pretty sure they have different
+
+ align:start position:0%
+I'm pretty sure they have different
+ 
+
+ align:start position:0%
+I'm pretty sure they have different
+products so much somebody might be like
+
+ align:start position:0%
+products so much somebody might be like
+ 
+
+ align:start position:0%
+products so much somebody might be like
+oh I really like this sweater from like
+
+ align:start position:0%
+oh I really like this sweater from like
+ 
+
+ align:start position:0%
+oh I really like this sweater from like
+bizarra so I'll definitely go that way I
+
+ align:start position:0%
+bizarra so I'll definitely go that way I
+ 
+
+ align:start position:0%
+bizarra so I'll definitely go that way I
+think it's a very I wouldn't debate that
+
+ align:start position:0%
+think it's a very I wouldn't debate that
+ 
+
+ align:start position:0%
+think it's a very I wouldn't debate that
+there's a very small percentage they'll
+
+ align:start position:0%
+there's a very small percentage they'll
+ 
+
+ align:start position:0%
+there's a very small percentage they'll
+be like oh I'm totally never gonna buy
+
+ align:start position:0%
+be like oh I'm totally never gonna buy
+ 
+
+ align:start position:0%
+be like oh I'm totally never gonna buy
+from the store again or I'm totally not
+
+ align:start position:0%
+from the store again or I'm totally not
+ 
+
+ align:start position:0%
+from the store again or I'm totally not
+gonna buy from the store again and then
+
+ align:start position:0%
+gonna buy from the store again and then
+ 
+
+ align:start position:0%
+gonna buy from the store again and then
+not go back to buy from it like two
+
+ align:start position:0%
+not go back to buy from it like two
+ 
+
+ align:start position:0%
+not go back to buy from it like two
+weeks later so I'm gonna bring us back
+
+ align:start position:0%
+weeks later so I'm gonna bring us back
+ 
+
+ align:start position:0%
+weeks later so I'm gonna bring us back
+the mats inside I'll go on offer to the
+
+ align:start position:0%
+the mats inside I'll go on offer to the
+ 
+
+ align:start position:0%
+the mats inside I'll go on offer to the
+fashion back this is more fundamental do
+
+ align:start position:0%
+fashion back this is more fundamental do
+ 
+
+ align:start position:0%
+fashion back this is more fundamental do
+you have some closing point you want to
+
+ align:start position:0%
+you have some closing point you want to
+ 
+
+ align:start position:0%
+you have some closing point you want to
+make on susan's but what I think is
+
+ align:start position:0%
+make on susan's but what I think is
+ 
+
+ align:start position:0%
+make on susan's but what I think is
+really key I think one key point that
+
+ align:start position:0%
+really key I think one key point that
+ 
+
+ align:start position:0%
+really key I think one key point that
+maybe get as much time to talk on is
+
+ align:start position:0%
+maybe get as much time to talk on is
+ 
+
+ align:start position:0%
+maybe get as much time to talk on is
+that maybe we have as Americans you know
+
+ align:start position:0%
+that maybe we have as Americans you know
+ 
+
+ align:start position:0%
+that maybe we have as Americans you know
+his idea of a birthright to being at the
+
+ align:start position:0%
+his idea of a birthright to being at the
+ 
+
+ align:start position:0%
+his idea of a birthright to being at the
+forefront of innovation and really
+
+ align:start position:0%
+forefront of innovation and really
+ 
+
+ align:start position:0%
+forefront of innovation and really
+pointing out that no one who's
+
+ align:start position:0%
+pointing out that no one who's
+ 
+
+ align:start position:0%
+pointing out that no one who's
+complacent and sitting
+
+ align:start position:0%
+complacent and sitting
+ 
+
+ align:start position:0%
+complacent and sitting
+or we'll stay in that position I think
+
+ align:start position:0%
+or we'll stay in that position I think
+ 
+
+ align:start position:0%
+or we'll stay in that position I think
+there's a good truck contrast to me may
+
+ align:start position:0%
+there's a good truck contrast to me may
+ 
+
+ align:start position:0%
+there's a good truck contrast to me may
+teach me her ideas on outsourcing
+
+ align:start position:0%
+teach me her ideas on outsourcing
+ 
+
+ align:start position:0%
+teach me her ideas on outsourcing
+where's it's versus burgers good good
+
+ align:start position:0%
+where's it's versus burgers good good
+ 
+
+ align:start position:0%
+where's it's versus burgers good good
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right that brings us to our closing
+
+ align:start position:0%
+all right that brings us to our closing
+ 
+
+ align:start position:0%
+all right that brings us to our closing
+reading this is what about might these
+
+ align:start position:0%
+reading this is what about might these
+ 
+
+ align:start position:0%
+reading this is what about might these
+great Provost Joel Moses who was deeply
+
+ align:start position:0%
+great Provost Joel Moses who was deeply
+ 
+
+ align:start position:0%
+great Provost Joel Moses who was deeply
+involved in the early and indeed later
+
+ align:start position:0%
+involved in the early and indeed later
+ 
+
+ align:start position:0%
+involved in the early and indeed later
+stages of the computing revolution so
+
+ align:start position:0%
+stages of the computing revolution so
+ 
+
+ align:start position:0%
+stages of the computing revolution so
+this is a young Joel at project Mac at
+
+ align:start position:0%
+this is a young Joel at project Mac at
+ 
+
+ align:start position:0%
+this is a young Joel at project Mac at
+MIT which just might ease implementation
+
+ align:start position:0%
+MIT which just might ease implementation
+ 
+
+ align:start position:0%
+MIT which just might ease implementation
+engine for a lot of the early computing
+
+ align:start position:0%
+engine for a lot of the early computing
+ 
+
+ align:start position:0%
+engine for a lot of the early computing
+advances so Jules steps back and likes
+
+ align:start position:0%
+advances so Jules steps back and likes
+ 
+
+ align:start position:0%
+advances so Jules steps back and likes
+this kind of fun piece which I wanted to
+
+ align:start position:0%
+this kind of fun piece which I wanted to
+ 
+
+ align:start position:0%
+this kind of fun piece which I wanted to
+throw in here at the end to pick up our
+
+ align:start position:0%
+throw in here at the end to pick up our
+ 
+
+ align:start position:0%
+throw in here at the end to pick up our
+determinism theme one more time
+
+ align:start position:0%
+determinism theme one more time
+ 
+
+ align:start position:0%
+determinism theme one more time
+we've been talking about different kinds
+
+ align:start position:0%
+we've been talking about different kinds
+ 
+
+ align:start position:0%
+we've been talking about different kinds
+of innovation systems and how different
+
+ align:start position:0%
+of innovation systems and how different
+ 
+
+ align:start position:0%
+of innovation systems and how different
+countries have varieties of capitalism
+
+ align:start position:0%
+countries have varieties of capitalism
+ 
+
+ align:start position:0%
+countries have varieties of capitalism
+and varieties of innovation systems and
+
+ align:start position:0%
+and varieties of innovation systems and
+ 
+
+ align:start position:0%
+and varieties of innovation systems and
+Joel takes us back a step and gives us
+
+ align:start position:0%
+Joel takes us back a step and gives us
+ 
+
+ align:start position:0%
+Joel takes us back a step and gives us
+more of a 10,000 foot kind of look which
+
+ align:start position:0%
+more of a 10,000 foot kind of look which
+ 
+
+ align:start position:0%
+more of a 10,000 foot kind of look which
+I was you know I was I've always been
+
+ align:start position:0%
+I was you know I was I've always been
+ 
+
+ align:start position:0%
+I was you know I was I've always been
+intrigued with he argues that there are
+
+ align:start position:0%
+intrigued with he argues that there are
+ 
+
+ align:start position:0%
+intrigued with he argues that there are
+three fundamentally different design
+
+ align:start position:0%
+three fundamentally different design
+ 
+
+ align:start position:0%
+three fundamentally different design
+methodologies so this is a design
+
+ align:start position:0%
+methodologies so this is a design
+ 
+
+ align:start position:0%
+methodologies so this is a design
+methodology and the societal sense
+
+ align:start position:0%
+methodology and the societal sense
+ 
+
+ align:start position:0%
+methodology and the societal sense
+rather than engineering design that map
+
+ align:start position:0%
+rather than engineering design that map
+ 
+
+ align:start position:0%
+rather than engineering design that map
+he was leading us to earlier and he
+
+ align:start position:0%
+he was leading us to earlier and he
+ 
+
+ align:start position:0%
+he was leading us to earlier and he
+argues that historically the US has used
+
+ align:start position:0%
+argues that historically the US has used
+ 
+
+ align:start position:0%
+argues that historically the US has used
+what he calls a tree and branch
+
+ align:start position:0%
+what he calls a tree and branch
+ 
+
+ align:start position:0%
+what he calls a tree and branch
+organization will attempt which creates
+
+ align:start position:0%
+organization will attempt which creates
+ 
+
+ align:start position:0%
+organization will attempt which creates
+very hierarchical firms and he argues
+
+ align:start position:0%
+very hierarchical firms and he argues
+ 
+
+ align:start position:0%
+very hierarchical firms and he argues
+that this very hierarchical system right
+
+ align:start position:0%
+that this very hierarchical system right
+ 
+
+ align:start position:0%
+that this very hierarchical system right
+and you can picture what the
+
+ align:start position:0%
+and you can picture what the
+ 
+
+ align:start position:0%
+and you can picture what the
+organization chart looks like it's like
+
+ align:start position:0%
+organization chart looks like it's like
+ 
+
+ align:start position:0%
+organization chart looks like it's like
+a tree right top management you know
+
+ align:start position:0%
+a tree right top management you know
+ 
+
+ align:start position:0%
+a tree right top management you know
+all the way down through many different
+
+ align:start position:0%
+all the way down through many different
+ 
+
+ align:start position:0%
+all the way down through many different
+hierarchies of levels that that fits a
+
+ align:start position:0%
+hierarchies of levels that that fits a
+ 
+
+ align:start position:0%
+hierarchies of levels that that fits a
+mass production economy this is the kind
+
+ align:start position:0%
+mass production economy this is the kind
+ 
+
+ align:start position:0%
+mass production economy this is the kind
+of economy that was compelled coming out
+
+ align:start position:0%
+of economy that was compelled coming out
+ 
+
+ align:start position:0%
+of economy that was compelled coming out
+of the Industrial Revolution and its
+
+ align:start position:0%
+of the Industrial Revolution and its
+ 
+
+ align:start position:0%
+of the Industrial Revolution and its
+organizing for manufacturing at a
+
+ align:start position:0%
+organizing for manufacturing at a
+ 
+
+ align:start position:0%
+organizing for manufacturing at a
+national scale for national markets
+
+ align:start position:0%
+national scale for national markets
+ 
+
+ align:start position:0%
+national scale for national markets
+where a lot of vertical integration is
+
+ align:start position:0%
+where a lot of vertical integration is
+ 
+
+ align:start position:0%
+where a lot of vertical integration is
+required so think about the big three us
+
+ align:start position:0%
+required so think about the big three us
+ 
+
+ align:start position:0%
+required so think about the big three us
+car companies now many makes an
+
+ align:start position:0%
+car companies now many makes an
+ 
+
+ align:start position:0%
+car companies now many makes an
+interesting additional point which is
+
+ align:start position:0%
+interesting additional point which is
+ 
+
+ align:start position:0%
+interesting additional point which is
+this by the way it's an Aristotelian a
+
+ align:start position:0%
+this by the way it's an Aristotelian a
+ 
+
+ align:start position:0%
+this by the way it's an Aristotelian a
+hierarchy of ordered knowledge right
+
+ align:start position:0%
+hierarchy of ordered knowledge right
+ 
+
+ align:start position:0%
+hierarchy of ordered knowledge right
+this is the way in which Western thought
+
+ align:start position:0%
+this is the way in which Western thought
+ 
+
+ align:start position:0%
+this is the way in which Western thought
+are organizes science right that's what
+
+ align:start position:0%
+are organizes science right that's what
+ 
+
+ align:start position:0%
+are organizes science right that's what
+Aristotle is doing he's creating these
+
+ align:start position:0%
+Aristotle is doing he's creating these
+ 
+
+ align:start position:0%
+Aristotle is doing he's creating these
+tree branch systems surprise it shows up
+
+ align:start position:0%
+tree branch systems surprise it shows up
+ 
+
+ align:start position:0%
+tree branch systems surprise it shows up
+in industrial organization in the West
+
+ align:start position:0%
+in industrial organization in the West
+ 
+
+ align:start position:0%
+in industrial organization in the West
+but he argues that the tree and branch
+
+ align:start position:0%
+but he argues that the tree and branch
+ 
+
+ align:start position:0%
+but he argues that the tree and branch
+hierarchy means tremendous in and
+
+ align:start position:0%
+hierarchy means tremendous in and
+ 
+
+ align:start position:0%
+hierarchy means tremendous in and
+flexibility and great difficulty and
+
+ align:start position:0%
+flexibility and great difficulty and
+ 
+
+ align:start position:0%
+flexibility and great difficulty and
+managing change because you've got to
+
+ align:start position:0%
+managing change because you've got to
+ 
+
+ align:start position:0%
+managing change because you've got to
+bring all those different systems all
+
+ align:start position:0%
+bring all those different systems all
+ 
+
+ align:start position:0%
+bring all those different systems all
+those different levels in line in order
+
+ align:start position:0%
+those different levels in line in order
+ 
+
+ align:start position:0%
+those different levels in line in order
+to pursue change so the second design
+
+ align:start position:0%
+to pursue change so the second design
+ 
+
+ align:start position:0%
+to pursue change so the second design
+methodology is around what he calls a
+
+ align:start position:0%
+methodology is around what he calls a
+ 
+
+ align:start position:0%
+methodology is around what he calls a
+layer system and he argues that Japan's
+
+ align:start position:0%
+layer system and he argues that Japan's
+ 
+
+ align:start position:0%
+layer system and he argues that Japan's
+incredible success of the 70s and 80s
+
+ align:start position:0%
+incredible success of the 70s and 80s
+ 
+
+ align:start position:0%
+incredible success of the 70s and 80s
+it's not just a different industrial
+
+ align:start position:0%
+it's not just a different industrial
+ 
+
+ align:start position:0%
+it's not just a different industrial
+right a quality production it's deeper
+
+ align:start position:0%
+right a quality production it's deeper
+ 
+
+ align:start position:0%
+right a quality production it's deeper
+than that there's a whole social
+
+ align:start position:0%
+than that there's a whole social
+ 
+
+ align:start position:0%
+than that there's a whole social
+organization so issues that's coming
+
+ align:start position:0%
+organization so issues that's coming
+ 
+
+ align:start position:0%
+organization so issues that's coming
+with it and it's tough it's tough on you
+
+ align:start position:0%
+with it and it's tough it's tough on you
+ 
+
+ align:start position:0%
+with it and it's tough it's tough on you
+you were driving towards some of these
+
+ align:start position:0%
+you were driving towards some of these
+ 
+
+ align:start position:0%
+you were driving towards some of these
+points I think so
+
+ align:start position:0%
+points I think so
+ 
+
+ align:start position:0%
+points I think so
+in Japan's system there are separate
+
+ align:start position:0%
+in Japan's system there are separate
+ 
+
+ align:start position:0%
+in Japan's system there are separate
+kind of layered levels and you tend to
+
+ align:start position:0%
+kind of layered levels and you tend to
+ 
+
+ align:start position:0%
+kind of layered levels and you tend to
+move through your career with your age
+
+ align:start position:0%
+move through your career with your age
+ 
+
+ align:start position:0%
+move through your career with your age
+cohort and as a group you move from
+
+ align:start position:0%
+cohort and as a group you move from
+ 
+
+ align:start position:0%
+cohort and as a group you move from
+level to level and there's obviously
+
+ align:start position:0%
+level to level and there's obviously
+ 
+
+ align:start position:0%
+level to level and there's obviously
+several levels here
+
+ align:start position:0%
+several levels here
+ 
+
+ align:start position:0%
+several levels here
+it's much less tree and branch
+
+ align:start position:0%
+it's much less tree and branch
+ 
+
+ align:start position:0%
+it's much less tree and branch
+hierarchical it is pretty flat within
+
+ align:start position:0%
+hierarchical it is pretty flat within
+ 
+
+ align:start position:0%
+hierarchical it is pretty flat within
+that age cohort right and you tend to
+
+ align:start position:0%
+that age cohort right and you tend to
+ 
+
+ align:start position:0%
+that age cohort right and you tend to
+know that you're going to move with your
+
+ align:start position:0%
+know that you're going to move with your
+ 
+
+ align:start position:0%
+know that you're going to move with your
+level in two successive positions so it
+
+ align:start position:0%
+level in two successive positions so it
+ 
+
+ align:start position:0%
+level in two successive positions so it
+forces a significant amount of consensus
+
+ align:start position:0%
+forces a significant amount of consensus
+ 
+
+ align:start position:0%
+forces a significant amount of consensus
+right so Joel's
+
+ align:start position:0%
+right so Joel's
+ 
+
+ align:start position:0%
+right so Joel's
+interesting comparison is you know this
+
+ align:start position:0%
+interesting comparison is you know this
+ 
+
+ align:start position:0%
+interesting comparison is you know this
+is Plato's Republic the philosopher king
+
+ align:start position:0%
+is Plato's Republic the philosopher king
+ 
+
+ align:start position:0%
+is Plato's Republic the philosopher king
+the Guardians the citizens those are
+
+ align:start position:0%
+the Guardians the citizens those are
+ 
+
+ align:start position:0%
+the Guardians the citizens those are
+kind of layers so not an Aristotelian
+
+ align:start position:0%
+kind of layers so not an Aristotelian
+ 
+
+ align:start position:0%
+kind of layers so not an Aristotelian
+but a they play tonic model and then he
+
+ align:start position:0%
+but a they play tonic model and then he
+ 
+
+ align:start position:0%
+but a they play tonic model and then he
+says there's a third right and this is
+
+ align:start position:0%
+says there's a third right and this is
+ 
+
+ align:start position:0%
+says there's a third right and this is
+the network model that the u.s. nurtured
+
+ align:start position:0%
+the network model that the u.s. nurtured
+ 
+
+ align:start position:0%
+the network model that the u.s. nurtured
+coming out of the IP refuge which is
+
+ align:start position:0%
+coming out of the IP refuge which is
+ 
+
+ align:start position:0%
+coming out of the IP refuge which is
+much flatter right much less
+
+ align:start position:0%
+much flatter right much less
+ 
+
+ align:start position:0%
+much flatter right much less
+hierarchical not even layer right it's
+
+ align:start position:0%
+hierarchical not even layer right it's
+ 
+
+ align:start position:0%
+hierarchical not even layer right it's
+pretty flat and it's driven by the kind
+
+ align:start position:0%
+pretty flat and it's driven by the kind
+ 
+
+ align:start position:0%
+pretty flat and it's driven by the kind
+of collaborative group innovation
+
+ align:start position:0%
+of collaborative group innovation
+ 
+
+ align:start position:0%
+of collaborative group innovation
+systems that are required for the
+
+ align:start position:0%
+systems that are required for the
+ 
+
+ align:start position:0%
+systems that are required for the
+development of the IT sector that a
+
+ align:start position:0%
+development of the IT sector that a
+ 
+
+ align:start position:0%
+development of the IT sector that a
+legit ranch hierarchy is just not going
+
+ align:start position:0%
+legit ranch hierarchy is just not going
+ 
+
+ align:start position:0%
+legit ranch hierarchy is just not going
+to work in that IT world which requires
+
+ align:start position:0%
+to work in that IT world which requires
+ 
+
+ align:start position:0%
+to work in that IT world which requires
+a tremendous amount of homos
+
+ align:start position:0%
+a tremendous amount of homos
+ 
+
+ align:start position:0%
+a tremendous amount of homos
+democratization workforce right so back
+
+ align:start position:0%
+democratization workforce right so back
+ 
+
+ align:start position:0%
+democratization workforce right so back
+Marteen to your to your Andy Grove
+
+ align:start position:0%
+Marteen to your to your Andy Grove
+ 
+
+ align:start position:0%
+Marteen to your to your Andy Grove
+analogy when the leaders of Intel when
+
+ align:start position:0%
+analogy when the leaders of Intel when
+ 
+
+ align:start position:0%
+analogy when the leaders of Intel when
+Bob Noyce and wove board more betting on
+
+ align:start position:0%
+Bob Noyce and wove board more betting on
+ 
+
+ align:start position:0%
+Bob Noyce and wove board more betting on
+Intel right there no offices right
+
+ align:start position:0%
+Intel right there no offices right
+ 
+
+ align:start position:0%
+Intel right there no offices right
+everybody's got a cubicle including
+
+ align:start position:0%
+everybody's got a cubicle including
+ 
+
+ align:start position:0%
+everybody's got a cubicle including
+noise and more rope right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Joel's complaint is that I mean the
+
+ align:start position:0%
+Joel's complaint is that I mean the
+ 
+
+ align:start position:0%
+Joel's complaint is that I mean the
+network model Joel argues is actually
+
+ align:start position:0%
+network model Joel argues is actually
+ 
+
+ align:start position:0%
+network model Joel argues is actually
+much faster and much more flexible and
+
+ align:start position:0%
+much faster and much more flexible and
+ 
+
+ align:start position:0%
+much faster and much more flexible and
+much more subject to change than fun the
+
+ align:start position:0%
+much more subject to change than fun the
+ 
+
+ align:start position:0%
+much more subject to change than fun the
+layered model that Japan presented and
+
+ align:start position:0%
+layered model that Japan presented and
+ 
+
+ align:start position:0%
+layered model that Japan presented and
+so you start thinking here geez no
+
+ align:start position:0%
+so you start thinking here geez no
+ 
+
+ align:start position:0%
+so you start thinking here geez no
+wonder the US auto ministry got rolled
+
+ align:start position:0%
+wonder the US auto ministry got rolled
+ 
+
+ align:start position:0%
+wonder the US auto ministry got rolled
+when it came up against Japan's layered
+
+ align:start position:0%
+when it came up against Japan's layered
+ 
+
+ align:start position:0%
+when it came up against Japan's layered
+model and then you start thinking oh no
+
+ align:start position:0%
+model and then you start thinking oh no
+ 
+
+ align:start position:0%
+model and then you start thinking oh no
+wonder Japan is the IT revolution if the
+
+ align:start position:0%
+wonder Japan is the IT revolution if the
+ 
+
+ align:start position:0%
+wonder Japan is the IT revolution if the
+organizational model required this
+
+ align:start position:0%
+organizational model required this
+ 
+
+ align:start position:0%
+organizational model required this
+network now what these are highly
+
+ align:start position:0%
+network now what these are highly
+ 
+
+ align:start position:0%
+network now what these are highly
+speculative we'll never beat these right
+
+ align:start position:0%
+speculative we'll never beat these right
+ 
+
+ align:start position:0%
+speculative we'll never beat these right
+they're really only for discussion
+
+ align:start position:0%
+they're really only for discussion
+ 
+
+ align:start position:0%
+they're really only for discussion
+purposes all of us kind of know that
+
+ align:start position:0%
+purposes all of us kind of know that
+ 
+
+ align:start position:0%
+purposes all of us kind of know that
+they're more complex stories be like wow
+
+ align:start position:0%
+they're more complex stories be like wow
+ 
+
+ align:start position:0%
+they're more complex stories be like wow
+but I think there is an idea right about
+
+ align:start position:0%
+but I think there is an idea right about
+ 
+
+ align:start position:0%
+but I think there is an idea right about
+the relationship between social
+
+ align:start position:0%
+the relationship between social
+ 
+
+ align:start position:0%
+the relationship between social
+organization and the kind of industrial
+
+ align:start position:0%
+organization and the kind of industrial
+ 
+
+ align:start position:0%
+organization and the kind of industrial
+developments that your society is going
+
+ align:start position:0%
+developments that your society is going
+ 
+
+ align:start position:0%
+developments that your society is going
+through and the kind of organizational
+
+ align:start position:0%
+through and the kind of organizational
+ 
+
+ align:start position:0%
+through and the kind of organizational
+models as those compel joel's great
+
+ align:start position:0%
+models as those compel joel's great
+ 
+
+ align:start position:0%
+models as those compel joel's great
+complaint is that engineering lacks the
+
+ align:start position:0%
+complaint is that engineering lacks the
+ 
+
+ align:start position:0%
+complaint is that engineering lacks the
+models to be able to grasp these
+
+ align:start position:0%
+models to be able to grasp these
+ 
+
+ align:start position:0%
+models to be able to grasp these
+different organizational structures
+
+ align:start position:0%
+different organizational structures
+ 
+
+ align:start position:0%
+different organizational structures
+though that you can't really fit that
+
+ align:start position:0%
+though that you can't really fit that
+ 
+
+ align:start position:0%
+though that you can't really fit that
+within a traditional kind of engineering
+
+ align:start position:0%
+within a traditional kind of engineering
+ 
+
+ align:start position:0%
+within a traditional kind of engineering
+analysis and that engineering therefore
+
+ align:start position:0%
+analysis and that engineering therefore
+ 
+
+ align:start position:0%
+analysis and that engineering therefore
+needs to rethink this that's part of the
+
+ align:start position:0%
+needs to rethink this that's part of the
+ 
+
+ align:start position:0%
+needs to rethink this that's part of the
+reason why he's a major leader might
+
+ align:start position:0%
+reason why he's a major leader might
+ 
+
+ align:start position:0%
+reason why he's a major leader might
+ease engineering systems division right
+
+ align:start position:0%
+ease engineering systems division right
+ 
+
+ align:start position:0%
+ease engineering systems division right
+which of course has now been closed but
+
+ align:start position:0%
+which of course has now been closed but
+ 
+
+ align:start position:0%
+which of course has now been closed but
+that's part of what Joel and some of his
+
+ align:start position:0%
+that's part of what Joel and some of his
+ 
+
+ align:start position:0%
+that's part of what Joel and some of his
+colleagues are trying to do when they
+
+ align:start position:0%
+colleagues are trying to do when they
+ 
+
+ align:start position:0%
+colleagues are trying to do when they
+set up ESD I mean that's you know I just
+
+ align:start position:0%
+set up ESD I mean that's you know I just
+ 
+
+ align:start position:0%
+set up ESD I mean that's you know I just
+want to kind of close out by saying that
+
+ align:start position:0%
+want to kind of close out by saying that
+ 
+
+ align:start position:0%
+want to kind of close out by saying that
+there's another thing that we'll need to
+
+ align:start position:0%
+there's another thing that we'll need to
+ 
+
+ align:start position:0%
+there's another thing that we'll need to
+consider as we move into next week's
+
+ align:start position:0%
+consider as we move into next week's
+ 
+
+ align:start position:0%
+consider as we move into next week's
+class that the whole nature of
+
+ align:start position:0%
+class that the whole nature of
+ 
+
+ align:start position:0%
+class that the whole nature of
+competition is changing and
+
+ align:start position:0%
+competition is changing and
+ 
+
+ align:start position:0%
+competition is changing and
+manufacturing that is no longer a world
+
+ align:start position:0%
+manufacturing that is no longer a world
+ 
+
+ align:start position:0%
+manufacturing that is no longer a world
+of manufacturing Goods is a world of
+
+ align:start position:0%
+of manufacturing Goods is a world of
+ 
+
+ align:start position:0%
+of manufacturing Goods is a world of
+manufactured goods that are fused but I
+
+ align:start position:0%
+manufactured goods that are fused but I
+ 
+
+ align:start position:0%
+manufactured goods that are fused but I
+t's technologies that in turn are
+
+ align:start position:0%
+t's technologies that in turn are
+ 
+
+ align:start position:0%
+t's technologies that in turn are
+service delivery models so that
+
+ align:start position:0%
+service delivery models so that
+ 
+
+ align:start position:0%
+service delivery models so that
+or fusion of services and manufacturing
+
+ align:start position:0%
+or fusion of services and manufacturing
+ 
+
+ align:start position:0%
+or fusion of services and manufacturing
+going one that makes some of the stories
+
+ align:start position:0%
+going one that makes some of the stories
+ 
+
+ align:start position:0%
+going one that makes some of the stories
+we've been talking about today it's more
+
+ align:start position:0%
+we've been talking about today it's more
+ 
+
+ align:start position:0%
+we've been talking about today it's more
+complicated in past decades the story
+
+ align:start position:0%
+complicated in past decades the story
+ 
+
+ align:start position:0%
+complicated in past decades the story
+was quality now there's a whole level of
+
+ align:start position:0%
+was quality now there's a whole level of
+ 
+
+ align:start position:0%
+was quality now there's a whole level of
+customization and speed and customer
+
+ align:start position:0%
+customization and speed and customer
+ 
+
+ align:start position:0%
+customization and speed and customer
+responsiveness that we have to think
+
+ align:start position:0%
+responsiveness that we have to think
+ 
+
+ align:start position:0%
+responsiveness that we have to think
+about as well and your ability to get on
+
+ align:start position:0%
+about as well and your ability to get on
+ 
+
+ align:start position:0%
+about as well and your ability to get on
+top of those as well as on quality
+
+ align:start position:0%
+top of those as well as on quality
+ 
+
+ align:start position:0%
+top of those as well as on quality
+becomes key it's not simply the best
+
+ align:start position:0%
+becomes key it's not simply the best
+ 
+
+ align:start position:0%
+becomes key it's not simply the best
+technology but it's the best technology
+
+ align:start position:0%
+technology but it's the best technology
+ 
+
+ align:start position:0%
+technology but it's the best technology
+plus the best business models and
+
+ align:start position:0%
+plus the best business models and
+ 
+
+ align:start position:0%
+plus the best business models and
+delivery models didn't have to be
+
+ align:start position:0%
+delivery models didn't have to be
+ 
+
+ align:start position:0%
+delivery models didn't have to be
+thought about you know there used to be
+
+ align:start position:0%
+thought about you know there used to be
+ 
+
+ align:start position:0%
+thought about you know there used to be
+trade in goods traded product now is
+
+ align:start position:0%
+trade in goods traded product now is
+ 
+
+ align:start position:0%
+trade in goods traded product now is
+traded all kinds of knowledge management
+
+ align:start position:0%
+traded all kinds of knowledge management
+ 
+
+ align:start position:0%
+traded all kinds of knowledge management
+and services they're tied to these
+
+ align:start position:0%
+and services they're tied to these
+ 
+
+ align:start position:0%
+and services they're tied to these
+products that becomes critical factors
+
+ align:start position:0%
+products that becomes critical factors
+ 
+
+ align:start position:0%
+products that becomes critical factors
+in your ability to in the past it was
+
+ align:start position:0%
+in your ability to in the past it was
+ 
+
+ align:start position:0%
+in your ability to in the past it was
+that workforce skills side now it's much
+
+ align:start position:0%
+that workforce skills side now it's much
+ 
+
+ align:start position:0%
+that workforce skills side now it's much
+more continuous learning in your course
+
+ align:start position:0%
+more continuous learning in your course
+ 
+
+ align:start position:0%
+more continuous learning in your course
+then it was low cost of capital now its
+
+ align:start position:0%
+then it was low cost of capital now its
+ 
+
+ align:start position:0%
+then it was low cost of capital now its
+efficiency in all the financial services
+
+ align:start position:0%
+efficiency in all the financial services
+ 
+
+ align:start position:0%
+efficiency in all the financial services
+stages that you've got to get through
+
+ align:start position:0%
+stages that you've got to get through
+ 
+
+ align:start position:0%
+stages that you've got to get through
+those right not just the initial capital
+
+ align:start position:0%
+those right not just the initial capital
+ 
+
+ align:start position:0%
+those right not just the initial capital
+goods so and there's a whole evolution
+
+ align:start position:0%
+goods so and there's a whole evolution
+ 
+
+ align:start position:0%
+goods so and there's a whole evolution
+of intangible capital as well so there's
+
+ align:start position:0%
+of intangible capital as well so there's
+ 
+
+ align:start position:0%
+of intangible capital as well so there's
+a whole new set of factors that's coming
+
+ align:start position:0%
+a whole new set of factors that's coming
+ 
+
+ align:start position:0%
+a whole new set of factors that's coming
+into the manufacturing world that we've
+
+ align:start position:0%
+into the manufacturing world that we've
+ 
+
+ align:start position:0%
+into the manufacturing world that we've
+only started to collapse from today's
+
+ align:start position:0%
+only started to collapse from today's
+ 
+
+ align:start position:0%
+only started to collapse from today's
+the special but let's go back to Joel
+
+ align:start position:0%
+the special but let's go back to Joel
+ 
+
+ align:start position:0%
+the special but let's go back to Joel
+and his three models Chris is all yours
+
+ align:start position:0%
+and his three models Chris is all yours
+ 
+
+ align:start position:0%
+and his three models Chris is all yours
+so that gets to summarize Joel is
+
+ align:start position:0%
+so that gets to summarize Joel is
+ 
+
+ align:start position:0%
+so that gets to summarize Joel is
+presenting these three models the
+
+ align:start position:0%
+presenting these three models the
+ 
+
+ align:start position:0%
+presenting these three models the
+hierarchical decomposition model where
+
+ align:start position:0%
+hierarchical decomposition model where
+ 
+
+ align:start position:0%
+hierarchical decomposition model where
+it's branched restructure the network
+
+ align:start position:0%
+it's branched restructure the network
+ 
+
+ align:start position:0%
+it's branched restructure the network
+design model and then the layered design
+
+ align:start position:0%
+design model and then the layered design
+ 
+
+ align:start position:0%
+design model and then the layered design
+model and then he basically goes on to
+
+ align:start position:0%
+model and then he basically goes on to
+ 
+
+ align:start position:0%
+model and then he basically goes on to
+outline a bunch of examples where you
+
+ align:start position:0%
+outline a bunch of examples where you
+ 
+
+ align:start position:0%
+outline a bunch of examples where you
+could present or sorry apply different
+
+ align:start position:0%
+could present or sorry apply different
+ 
+
+ align:start position:0%
+could present or sorry apply different
+methodologies into analyzing various
+
+ align:start position:0%
+methodologies into analyzing various
+ 
+
+ align:start position:0%
+methodologies into analyzing various
+systems so he goes through like
+
+ align:start position:0%
+systems so he goes through like
+ 
+
+ align:start position:0%
+systems so he goes through like
+philosophy example he goes through
+
+ align:start position:0%
+philosophy example he goes through
+ 
+
+ align:start position:0%
+philosophy example he goes through
+manufacturing even kind
+
+ align:start position:0%
+manufacturing even kind
+ 
+
+ align:start position:0%
+manufacturing even kind
+more science-based like the models the
+
+ align:start position:0%
+more science-based like the models the
+ 
+
+ align:start position:0%
+more science-based like the models the
+human mind and body and one of them I
+
+ align:start position:0%
+human mind and body and one of them I
+ 
+
+ align:start position:0%
+human mind and body and one of them I
+found particularly interesting was where
+
+ align:start position:0%
+found particularly interesting was where
+ 
+
+ align:start position:0%
+found particularly interesting was where
+he brought up culture and how the
+
+ align:start position:0%
+he brought up culture and how the
+ 
+
+ align:start position:0%
+he brought up culture and how the
+preconceptions of how engineering and
+
+ align:start position:0%
+preconceptions of how engineering and
+ 
+
+ align:start position:0%
+preconceptions of how engineering and
+manufacturing is viewed here versus
+
+ align:start position:0%
+manufacturing is viewed here versus
+ 
+
+ align:start position:0%
+manufacturing is viewed here versus
+let's say Germany or Japan has really
+
+ align:start position:0%
+let's say Germany or Japan has really
+ 
+
+ align:start position:0%
+let's say Germany or Japan has really
+impacted the way these countries have
+
+ align:start position:0%
+impacted the way these countries have
+ 
+
+ align:start position:0%
+impacted the way these countries have
+responded toward some ships
+
+ align:start position:0%
+responded toward some ships
+ 
+
+ align:start position:0%
+responded toward some ships
+manufacturing and how that industry
+
+ align:start position:0%
+manufacturing and how that industry
+ 
+
+ align:start position:0%
+manufacturing and how that industry
+develops and also have cooperation and
+
+ align:start position:0%
+develops and also have cooperation and
+ 
+
+ align:start position:0%
+develops and also have cooperation and
+japanese culture has really allowed the
+
+ align:start position:0%
+japanese culture has really allowed the
+ 
+
+ align:start position:0%
+japanese culture has really allowed the
+precipitous like rise of their industry
+
+ align:start position:0%
+precipitous like rise of their industry
+ 
+
+ align:start position:0%
+precipitous like rise of their industry
+manufacturing capabilities and how that
+
+ align:start position:0%
+manufacturing capabilities and how that
+ 
+
+ align:start position:0%
+manufacturing capabilities and how that
+shaped and kind of forced American firms
+
+ align:start position:0%
+shaped and kind of forced American firms
+ 
+
+ align:start position:0%
+shaped and kind of forced American firms
+to adopt a similar structure or
+
+ align:start position:0%
+to adopt a similar structure or
+ 
+
+ align:start position:0%
+to adopt a similar structure or
+methodology in order to compete so
+
+ align:start position:0%
+methodology in order to compete so
+ 
+
+ align:start position:0%
+methodology in order to compete so
+that's just one example of how
+
+ align:start position:0%
+that's just one example of how
+ 
+
+ align:start position:0%
+that's just one example of how
+interestingly enough a lot of the
+
+ align:start position:0%
+interestingly enough a lot of the
+ 
+
+ align:start position:0%
+interestingly enough a lot of the
+examples were not really engineering
+
+ align:start position:0%
+examples were not really engineering
+ 
+
+ align:start position:0%
+examples were not really engineering
+based even though he started from the
+
+ align:start position:0%
+based even though he started from the
+ 
+
+ align:start position:0%
+based even though he started from the
+hierarchical model which is seen very
+
+ align:start position:0%
+hierarchical model which is seen very
+ 
+
+ align:start position:0%
+hierarchical model which is seen very
+often in engineering and I thought that
+
+ align:start position:0%
+often in engineering and I thought that
+ 
+
+ align:start position:0%
+often in engineering and I thought that
+was really interesting
+
+ align:start position:0%
+was really interesting
+ 
+
+ align:start position:0%
+was really interesting
+you can definitely go into some of the
+
+ align:start position:0%
+you can definitely go into some of the
+ 
+
+ align:start position:0%
+you can definitely go into some of the
+examples more if anyone has a particular
+
+ align:start position:0%
+examples more if anyone has a particular
+ 
+
+ align:start position:0%
+examples more if anyone has a particular
+one to go into but to start off the
+
+ align:start position:0%
+one to go into but to start off the
+ 
+
+ align:start position:0%
+one to go into but to start off the
+discussion I thought this question was
+
+ align:start position:0%
+discussion I thought this question was
+ 
+
+ align:start position:0%
+discussion I thought this question was
+really interesting how does a country
+
+ align:start position:0%
+really interesting how does a country
+ 
+
+ align:start position:0%
+really interesting how does a country
+shift from a tree structure so the
+
+ align:start position:0%
+shift from a tree structure so the
+ 
+
+ align:start position:0%
+shift from a tree structure so the
+higher your hierarchy one to more
+
+ align:start position:0%
+higher your hierarchy one to more
+ 
+
+ align:start position:0%
+higher your hierarchy one to more
+layered or network structure once it's
+
+ align:start position:0%
+layered or network structure once it's
+ 
+
+ align:start position:0%
+layered or network structure once it's
+already been established so there's any
+
+ align:start position:0%
+already been established so there's any
+ 
+
+ align:start position:0%
+already been established so there's any
+thoughts don't be good
+
+ align:start position:0%
+thoughts don't be good
+ 
+
+ align:start position:0%
+thoughts don't be good
+throw them so a two class called like
+
+ align:start position:0%
+throw them so a two class called like
+ 
+
+ align:start position:0%
+throw them so a two class called like
+structural organizations and it talks
+
+ align:start position:0%
+structural organizations and it talks
+ 
+
+ align:start position:0%
+structural organizations and it talks
+about like so it's not like there's a
+
+ align:start position:0%
+about like so it's not like there's a
+ 
+
+ align:start position:0%
+about like so it's not like there's a
+right or wrong answer it's really
+
+ align:start position:0%
+right or wrong answer it's really
+ 
+
+ align:start position:0%
+right or wrong answer it's really
+recommend what you're trying to do
+
+ align:start position:0%
+recommend what you're trying to do
+ 
+
+ align:start position:0%
+recommend what you're trying to do
+so in general when it's more networked
+
+ align:start position:0%
+so in general when it's more networked
+ 
+
+ align:start position:0%
+so in general when it's more networked
+again it's one make better decisions but
+
+ align:start position:0%
+again it's one make better decisions but
+ 
+
+ align:start position:0%
+again it's one make better decisions but
+the drawback is I don't take a much
+
+ align:start position:0%
+the drawback is I don't take a much
+ 
+
+ align:start position:0%
+the drawback is I don't take a much
+longer time parallel you might not make
+
+ align:start position:0%
+longer time parallel you might not make
+ 
+
+ align:start position:0%
+longer time parallel you might not make
+great decisions but you make them very
+
+ align:start position:0%
+great decisions but you make them very
+ 
+
+ align:start position:0%
+great decisions but you make them very
+quickly and as long as people respect
+
+ align:start position:0%
+quickly and as long as people respect
+ 
+
+ align:start position:0%
+quickly and as long as people respect
+that the person who's making decision is
+
+ align:start position:0%
+that the person who's making decision is
+ 
+
+ align:start position:0%
+that the person who's making decision is
+ensured of you pretty much okay in terms
+
+ align:start position:0%
+ensured of you pretty much okay in terms
+ 
+
+ align:start position:0%
+ensured of you pretty much okay in terms
+of a comedy I think it really does
+
+ align:start position:0%
+of a comedy I think it really does
+ 
+
+ align:start position:0%
+of a comedy I think it really does
+depend it's like you know I think
+
+ align:start position:0%
+depend it's like you know I think
+ 
+
+ align:start position:0%
+depend it's like you know I think
+network structure works we're great for
+
+ align:start position:0%
+network structure works we're great for
+ 
+
+ align:start position:0%
+network structure works we're great for
+like a Facebook or like something with
+
+ align:start position:0%
+like a Facebook or like something with
+ 
+
+ align:start position:0%
+like a Facebook or like something with
+the internet base where you're really
+
+ align:start position:0%
+the internet base where you're really
+ 
+
+ align:start position:0%
+the internet base where you're really
+competing for ideas you're trying to
+
+ align:start position:0%
+competing for ideas you're trying to
+ 
+
+ align:start position:0%
+competing for ideas you're trying to
+come up with ideas things move quickly
+
+ align:start position:0%
+come up with ideas things move quickly
+ 
+
+ align:start position:0%
+come up with ideas things move quickly
+so you want to get irate quickly versus
+
+ align:start position:0%
+so you want to get irate quickly versus
+ 
+
+ align:start position:0%
+so you want to get irate quickly versus
+I think it was like manufacturing as
+
+ align:start position:0%
+I think it was like manufacturing as
+ 
+
+ align:start position:0%
+I think it was like manufacturing as
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chris did you agree with Joel's
+
+ align:start position:0%
+Chris did you agree with Joel's
+ 
+
+ align:start position:0%
+Chris did you agree with Joel's
+presentation here do these models make
+
+ align:start position:0%
+presentation here do these models make
+ 
+
+ align:start position:0%
+presentation here do these models make
+sense to you I thought it was
+
+ align:start position:0%
+sense to you I thought it was
+ 
+
+ align:start position:0%
+sense to you I thought it was
+interesting how he presented kind of
+
+ align:start position:0%
+interesting how he presented kind of
+ 
+
+ align:start position:0%
+interesting how he presented kind of
+three frameworks for looking at
+
+ align:start position:0%
+three frameworks for looking at
+ 
+
+ align:start position:0%
+three frameworks for looking at
+different firms and then went about kind
+
+ align:start position:0%
+different firms and then went about kind
+ 
+
+ align:start position:0%
+different firms and then went about kind
+of applying that model to different
+
+ align:start position:0%
+of applying that model to different
+ 
+
+ align:start position:0%
+of applying that model to different
+situations companies industries I
+
+ align:start position:0%
+situations companies industries I
+ 
+
+ align:start position:0%
+situations companies industries I
+thought that was interesting
+
+ align:start position:0%
+thought that was interesting
+ 
+
+ align:start position:0%
+thought that was interesting
+again just like some of you I had a
+
+ align:start position:0%
+again just like some of you I had a
+ 
+
+ align:start position:0%
+again just like some of you I had a
+little bit of trouble distinguishing
+
+ align:start position:0%
+little bit of trouble distinguishing
+ 
+
+ align:start position:0%
+little bit of trouble distinguishing
+between some of them as I was reading
+
+ align:start position:0%
+between some of them as I was reading
+ 
+
+ align:start position:0%
+between some of them as I was reading
+reading it so perhaps kind of going into
+
+ align:start position:0%
+reading it so perhaps kind of going into
+ 
+
+ align:start position:0%
+reading it so perhaps kind of going into
+more about defining the differences
+
+ align:start position:0%
+more about defining the differences
+ 
+
+ align:start position:0%
+more about defining the differences
+between the different models and also
+
+ align:start position:0%
+between the different models and also
+ 
+
+ align:start position:0%
+between the different models and also
+maybe even trying to generalize which
+
+ align:start position:0%
+maybe even trying to generalize which
+ 
+
+ align:start position:0%
+maybe even trying to generalize which
+model would be applicable to like what
+
+ align:start position:0%
+model would be applicable to like what
+ 
+
+ align:start position:0%
+model would be applicable to like what
+characteristics would be most amenable
+
+ align:start position:0%
+characteristics would be most amenable
+ 
+
+ align:start position:0%
+characteristics would be most amenable
+to these models that could be an
+
+ align:start position:0%
+to these models that could be an
+ 
+
+ align:start position:0%
+to these models that could be an
+interesting and additional step okay all
+
+ align:start position:0%
+interesting and additional step okay all
+ 
+
+ align:start position:0%
+interesting and additional step okay all
+right I think on that good note you will
+
+ align:start position:0%
+right I think on that good note you will
+ 
+
+ align:start position:0%
+right I think on that good note you will
+have a few minutes early
\ No newline at end of file
diff --git a/CKncVaiv_08.txt b/CKncVaiv_08.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eaeca85f81b62fad12b196f1e254086e442af509
--- /dev/null
+++ b/CKncVaiv_08.txt
@@ -0,0 +1,8739 @@
+align:start position:0%
+ 
+so what I'd like to do
+
+ align:start position:0%
+so what I'd like to do
+ 
+
+ align:start position:0%
+so what I'd like to do
+today is talk about an entirely
+
+ align:start position:0%
+today is talk about an entirely
+ 
+
+ align:start position:0%
+today is talk about an entirely
+different class of switching power
+
+ align:start position:0%
+different class of switching power
+ 
+
+ align:start position:0%
+different class of switching power
+converter than they've talked about
+
+ align:start position:0%
+converter than they've talked about
+ 
+
+ align:start position:0%
+converter than they've talked about
+before and um we are going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to we are going to um look at this for
+
+ align:start position:0%
+to we are going to um look at this for
+ 
+
+ align:start position:0%
+to we are going to um look at this for
+this class and next class uh we're going
+
+ align:start position:0%
+this class and next class uh we're going
+ 
+
+ align:start position:0%
+this class and next class uh we're going
+to talk about switched capacitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converters and that's uh principles of
+
+ align:start position:0%
+converters and that's uh principles of
+ 
+
+ align:start position:0%
+converters and that's uh principles of
+Power
+
+ align:start position:0%
+Power
+ 
+
+ align:start position:0%
+Power
+Electronics chapter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay most
+
+ align:start position:0%
+okay most
+ 
+
+ align:start position:0%
+okay most
+converters introduce magnetics in them
+
+ align:start position:0%
+converters introduce magnetics in them
+ 
+
+ align:start position:0%
+converters introduce magnetics in them
+right they have some magnetic component
+
+ align:start position:0%
+right they have some magnetic component
+ 
+
+ align:start position:0%
+right they have some magnetic component
+in why do you want why do you want say
+
+ align:start position:0%
+in why do you want why do you want say
+ 
+
+ align:start position:0%
+in why do you want why do you want say
+an inductor or an inductive energy
+
+ align:start position:0%
+an inductor or an inductive energy
+ 
+
+ align:start position:0%
+an inductor or an inductive energy
+storage El in your converter that's
+
+ align:start position:0%
+storage El in your converter that's
+ 
+
+ align:start position:0%
+storage El in your converter that's
+because if I put a voltage difference
+
+ align:start position:0%
+because if I put a voltage difference
+ 
+
+ align:start position:0%
+because if I put a voltage difference
+across it from say an input voltage or
+
+ align:start position:0%
+across it from say an input voltage or
+ 
+
+ align:start position:0%
+across it from say an input voltage or
+an output voltage or two voltages the
+
+ align:start position:0%
+an output voltage or two voltages the
+ 
+
+ align:start position:0%
+an output voltage or two voltages the
+inductor can instantaneously take that
+
+ align:start position:0%
+inductor can instantaneously take that
+ 
+
+ align:start position:0%
+inductor can instantaneously take that
+energy difference absorb the voltage
+
+ align:start position:0%
+energy difference absorb the voltage
+ 
+
+ align:start position:0%
+energy difference absorb the voltage
+difference absorb energy that then we
+
+ align:start position:0%
+difference absorb energy that then we
+ 
+
+ align:start position:0%
+difference absorb energy that then we
+can recover later right and that's sort
+
+ align:start position:0%
+can recover later right and that's sort
+ 
+
+ align:start position:0%
+can recover later right and that's sort
+of the principle we operate on and
+
+ align:start position:0%
+of the principle we operate on and
+ 
+
+ align:start position:0%
+of the principle we operate on and
+that's why almost all these converters
+
+ align:start position:0%
+that's why almost all these converters
+ 
+
+ align:start position:0%
+that's why almost all these converters
+use magnetics or something that acts
+
+ align:start position:0%
+use magnetics or something that acts
+ 
+
+ align:start position:0%
+use magnetics or something that acts
+like a magnetic component
+
+ align:start position:0%
+like a magnetic component
+ 
+
+ align:start position:0%
+like a magnetic component
+on the other hand sometimes you can get
+
+ align:start position:0%
+on the other hand sometimes you can get
+ 
+
+ align:start position:0%
+on the other hand sometimes you can get
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+without any magnetic components without
+
+ align:start position:0%
+without any magnetic components without
+ 
+
+ align:start position:0%
+without any magnetic components without
+any inductors in your circuit and why
+
+ align:start position:0%
+any inductors in your circuit and why
+ 
+
+ align:start position:0%
+any inductors in your circuit and why
+might you want to do that well because
+
+ align:start position:0%
+might you want to do that well because
+ 
+
+ align:start position:0%
+might you want to do that well because
+if you look at things that are on you
+
+ align:start position:0%
+if you look at things that are on you
+ 
+
+ align:start position:0%
+if you look at things that are on you
+know the scale of my thumb or something
+
+ align:start position:0%
+know the scale of my thumb or something
+ 
+
+ align:start position:0%
+know the scale of my thumb or something
+you know some some small element the
+
+ align:start position:0%
+you know some some small element the
+ 
+
+ align:start position:0%
+you know some some small element the
+energy density you can achieve with a
+
+ align:start position:0%
+energy density you can achieve with a
+ 
+
+ align:start position:0%
+energy density you can achieve with a
+capacitor is orders of magnitude higher
+
+ align:start position:0%
+capacitor is orders of magnitude higher
+ 
+
+ align:start position:0%
+capacitor is orders of magnitude higher
+than the energy density you can achieve
+
+ align:start position:0%
+than the energy density you can achieve
+ 
+
+ align:start position:0%
+than the energy density you can achieve
+with a a magnetic component at similar
+
+ align:start position:0%
+with a a magnetic component at similar
+ 
+
+ align:start position:0%
+with a a magnetic component at similar
+uh efficiencies and energy storage
+
+ align:start position:0%
+uh efficiencies and energy storage
+ 
+
+ align:start position:0%
+uh efficiencies and energy storage
+levels right so you know capacitors are
+
+ align:start position:0%
+levels right so you know capacitors are
+ 
+
+ align:start position:0%
+levels right so you know capacitors are
+just extremely highly energy dense so if
+
+ align:start position:0%
+just extremely highly energy dense so if
+ 
+
+ align:start position:0%
+just extremely highly energy dense so if
+I happen to have an application where I
+
+ align:start position:0%
+I happen to have an application where I
+ 
+
+ align:start position:0%
+I happen to have an application where I
+can get away with only capacitive energy
+
+ align:start position:0%
+can get away with only capacitive energy
+ 
+
+ align:start position:0%
+can get away with only capacitive energy
+storage you can build a much smaller
+
+ align:start position:0%
+storage you can build a much smaller
+ 
+
+ align:start position:0%
+storage you can build a much smaller
+more efficient converter okay but that
+
+ align:start position:0%
+more efficient converter okay but that
+ 
+
+ align:start position:0%
+more efficient converter okay but that
+application space is limited and we're
+
+ align:start position:0%
+application space is limited and we're
+ 
+
+ align:start position:0%
+application space is limited and we're
+going to get into why so switch
+
+ align:start position:0%
+going to get into why so switch
+ 
+
+ align:start position:0%
+going to get into why so switch
+capacitor converters are essentially you
+
+ align:start position:0%
+capacitor converters are essentially you
+ 
+
+ align:start position:0%
+capacitor converters are essentially you
+know to come back to their definition
+
+ align:start position:0%
+know to come back to their definition
+ 
+
+ align:start position:0%
+know to come back to their definition
+are essentially converters where I
+
+ align:start position:0%
+are essentially converters where I
+ 
+
+ align:start position:0%
+are essentially converters where I
+process all my energy using capacitors
+
+ align:start position:0%
+process all my energy using capacitors
+ 
+
+ align:start position:0%
+process all my energy using capacitors
+and so I have capacitors and switches to
+
+ align:start position:0%
+and so I have capacitors and switches to
+ 
+
+ align:start position:0%
+and so I have capacitors and switches to
+do the energy throughput I brought a
+
+ align:start position:0%
+do the energy throughput I brought a
+ 
+
+ align:start position:0%
+do the energy throughput I brought a
+couple of examples with these These are
+
+ align:start position:0%
+couple of examples with these These are
+ 
+
+ align:start position:0%
+couple of examples with these These are
+both uh kind of prototype designs this
+
+ align:start position:0%
+both uh kind of prototype designs this
+ 
+
+ align:start position:0%
+both uh kind of prototype designs this
+one is a very small power low power one
+
+ align:start position:0%
+one is a very small power low power one
+ 
+
+ align:start position:0%
+one is a very small power low power one
+you'll see much of it on the front and
+
+ align:start position:0%
+you'll see much of it on the front and
+ 
+
+ align:start position:0%
+you'll see much of it on the front and
+it has some energy storage capacitors on
+
+ align:start position:0%
+it has some energy storage capacitors on
+ 
+
+ align:start position:0%
+it has some energy storage capacitors on
+the back this is another overall circuit
+
+ align:start position:0%
+the back this is another overall circuit
+ 
+
+ align:start position:0%
+the back this is another overall circuit
+and this part over here is a switch
+
+ align:start position:0%
+and this part over here is a switch
+ 
+
+ align:start position:0%
+and this part over here is a switch
+capacitor converter of a certain type so
+
+ align:start position:0%
+capacitor converter of a certain type so
+ 
+
+ align:start position:0%
+capacitor converter of a certain type so
+just to kind of illustrate what we're
+
+ align:start position:0%
+just to kind of illustrate what we're
+ 
+
+ align:start position:0%
+just to kind of illustrate what we're
+talking about you can take a look at
+
+ align:start position:0%
+talking about you can take a look at
+ 
+
+ align:start position:0%
+talking about you can take a look at
+these okay and so let's in order to sort
+
+ align:start position:0%
+these okay and so let's in order to sort
+ 
+
+ align:start position:0%
+these okay and so let's in order to sort
+of illustrate their strengths and
+
+ align:start position:0%
+of illustrate their strengths and
+ 
+
+ align:start position:0%
+of illustrate their strengths and
+weaknesses let's look at the simplest
+
+ align:start position:0%
+weaknesses let's look at the simplest
+ 
+
+ align:start position:0%
+weaknesses let's look at the simplest
+switch capacitor converter I can think
+
+ align:start position:0%
+switch capacitor converter I can think
+ 
+
+ align:start position:0%
+switch capacitor converter I can think
+of and this is sometimes known as a two
+
+ align:start position:0%
+of and this is sometimes known as a two
+ 
+
+ align:start position:0%
+of and this is sometimes known as a two
+to1 step down converter although uh
+
+ align:start position:0%
+to1 step down converter although uh
+ 
+
+ align:start position:0%
+to1 step down converter although uh
+we'll come back to why people call it
+
+ align:start position:0%
+we'll come back to why people call it
+ 
+
+ align:start position:0%
+we'll come back to why people call it
+that but but what its tradeoffs are so
+
+ align:start position:0%
+that but but what its tradeoffs are so
+ 
+
+ align:start position:0%
+that but but what its tradeoffs are so
+here's the idea I had some input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage okay from which I'm going to
+
+ align:start position:0%
+voltage okay from which I'm going to
+ 
+
+ align:start position:0%
+voltage okay from which I'm going to
+draw a power and I'm going to have a
+
+ align:start position:0%
+draw a power and I'm going to have a
+ 
+
+ align:start position:0%
+draw a power and I'm going to have a
+capacitor here and this capacitor is my
+
+ align:start position:0%
+capacitor here and this capacitor is my
+ 
+
+ align:start position:0%
+capacitor here and this capacitor is my
+energy transfer transfer capacitor so
+
+ align:start position:0%
+energy transfer transfer capacitor so
+ 
+
+ align:start position:0%
+energy transfer transfer capacitor so
+here c i and VC okay so in this example
+
+ align:start position:0%
+here c i and VC okay so in this example
+ 
+
+ align:start position:0%
+here c i and VC okay so in this example
+I'm going to do this is this element is
+
+ align:start position:0%
+I'm going to do this is this element is
+ 
+
+ align:start position:0%
+I'm going to do this is this element is
+where I'm storing the
+
+ align:start position:0%
+where I'm storing the
+ 
+
+ align:start position:0%
+where I'm storing the
+energy in the intermediate form to do
+
+ align:start position:0%
+energy in the intermediate form to do
+ 
+
+ align:start position:0%
+energy in the intermediate form to do
+this energy procing okay so I'll have uh
+
+ align:start position:0%
+this energy procing okay so I'll have uh
+ 
+
+ align:start position:0%
+this energy procing okay so I'll have uh
+switches okay and then I will have
+
+ align:start position:0%
+switches okay and then I will have
+ 
+
+ align:start position:0%
+switches okay and then I will have
+delivered some output I'm going to call
+
+ align:start position:0%
+delivered some output I'm going to call
+ 
+
+ align:start position:0%
+delivered some output I'm going to call
+this c big this is like my filter
+
+ align:start position:0%
+this c big this is like my filter
+ 
+
+ align:start position:0%
+this c big this is like my filter
+capacitor okay and then you know here I
+
+ align:start position:0%
+capacitor okay and then you know here I
+ 
+
+ align:start position:0%
+capacitor okay and then you know here I
+have some output current this is the
+
+ align:start position:0%
+have some output current this is the
+ 
+
+ align:start position:0%
+have some output current this is the
+load
+
+ align:start position:0%
+load
+ 
+
+ align:start position:0%
+load
+current okay and this is V
+
+ align:start position:0%
+current okay and this is V
+ 
+
+ align:start position:0%
+current okay and this is V
+out okay so
+
+ align:start position:0%
+out okay so
+ 
+
+ align:start position:0%
+out okay so
+I'm going to have these two capacitor
+
+ align:start position:0%
+I'm going to have these two capacitor
+ 
+
+ align:start position:0%
+I'm going to have these two capacitor
+these two switches and these are phase
+
+ align:start position:0%
+these two switches and these are phase
+ 
+
+ align:start position:0%
+these two switches and these are phase
+one switches okay then I'm going to put
+
+ align:start position:0%
+one switches okay then I'm going to put
+ 
+
+ align:start position:0%
+one switches okay then I'm going to put
+two more switches in I'm going to call
+
+ align:start position:0%
+two more switches in I'm going to call
+ 
+
+ align:start position:0%
+two more switches in I'm going to call
+these phase two switches okay so here's
+
+ align:start position:0%
+these phase two switches okay so here's
+ 
+
+ align:start position:0%
+these phase two switches okay so here's
+one one and 2
+
+ align:start position:0%
+one one and 2
+ 
+
+ align:start position:0%
+one one and 2
+two okay and the idea here is that we're
+
+ align:start position:0%
+two okay and the idea here is that we're
+ 
+
+ align:start position:0%
+two okay and the idea here is that we're
+going to alternately take the
+
+ align:start position:0%
+going to alternately take the
+ 
+
+ align:start position:0%
+going to alternately take the
+switches that are labeled one and close
+
+ align:start position:0%
+switches that are labeled one and close
+ 
+
+ align:start position:0%
+switches that are labeled one and close
+them together and then at some other
+
+ align:start position:0%
+them together and then at some other
+ 
+
+ align:start position:0%
+them together and then at some other
+point in the we're going to open those
+
+ align:start position:0%
+point in the we're going to open those
+ 
+
+ align:start position:0%
+point in the we're going to open those
+switches and close the switches that are
+
+ align:start position:0%
+switches and close the switches that are
+ 
+
+ align:start position:0%
+switches and close the switches that are
+labeled two together okay what you're
+
+ align:start position:0%
+labeled two together okay what you're
+ 
+
+ align:start position:0%
+labeled two together okay what you're
+going to see one of the characteristics
+
+ align:start position:0%
+going to see one of the characteristics
+ 
+
+ align:start position:0%
+going to see one of the characteristics
+of switch capacitor converters they tend
+
+ align:start position:0%
+of switch capacitor converters they tend
+ 
+
+ align:start position:0%
+of switch capacitor converters they tend
+to have a lot of switches and in fact if
+
+ align:start position:0%
+to have a lot of switches and in fact if
+ 
+
+ align:start position:0%
+to have a lot of switches and in fact if
+you want High conversion ratios they
+
+ align:start position:0%
+you want High conversion ratios they
+ 
+
+ align:start position:0%
+you want High conversion ratios they
+have lots of switches and lots of
+
+ align:start position:0%
+have lots of switches and lots of
+ 
+
+ align:start position:0%
+have lots of switches and lots of
+capacitors we'll talk about that a
+
+ align:start position:0%
+capacitors we'll talk about that a
+ 
+
+ align:start position:0%
+capacitors we'll talk about that a
+little bit more so this is you know this
+
+ align:start position:0%
+little bit more so this is you know this
+ 
+
+ align:start position:0%
+little bit more so this is you know this
+beast in the Box here if you will I
+
+ align:start position:0%
+beast in the Box here if you will I
+ 
+
+ align:start position:0%
+beast in the Box here if you will I
+don't know you can include the output
+
+ align:start position:0%
+don't know you can include the output
+ 
+
+ align:start position:0%
+don't know you can include the output
+capacitor I suppose is a the simplest
+
+ align:start position:0%
+capacitor I suppose is a the simplest
+ 
+
+ align:start position:0%
+capacitor I suppose is a the simplest
+switch capacitor converter I can think
+
+ align:start position:0%
+switch capacitor converter I can think
+ 
+
+ align:start position:0%
+switch capacitor converter I can think
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+to analyze it let me just simplify it
+
+ align:start position:0%
+to analyze it let me just simplify it
+ 
+
+ align:start position:0%
+to analyze it let me just simplify it
+I'm going to think about this is a
+
+ align:start position:0%
+I'm going to think about this is a
+ 
+
+ align:start position:0%
+I'm going to think about this is a
+really big output capacitor so for the
+
+ align:start position:0%
+really big output capacitor so for the
+ 
+
+ align:start position:0%
+really big output capacitor so for the
+moment let me just replace him with a
+
+ align:start position:0%
+moment let me just replace him with a
+ 
+
+ align:start position:0%
+moment let me just replace him with a
+voltage source V out okay so for my
+
+ align:start position:0%
+voltage source V out okay so for my
+ 
+
+ align:start position:0%
+voltage source V out okay so for my
+analysis I'm going to uh simplify this
+
+ align:start position:0%
+analysis I'm going to uh simplify this
+ 
+
+ align:start position:0%
+analysis I'm going to uh simplify this
+just a little and I'll say we have um an
+
+ align:start position:0%
+just a little and I'll say we have um an
+ 
+
+ align:start position:0%
+just a little and I'll say we have um an
+input voltage
+
+ align:start position:0%
+input voltage
+ 
+
+ align:start position:0%
+input voltage
+VN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's my
+
+ align:start position:0%
+okay here's my
+ 
+
+ align:start position:0%
+okay here's my
+capacitor VC
+
+ align:start position:0%
+capacitor VC
+ 
+
+ align:start position:0%
+capacitor VC
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+c my two switches I'm just going to
+
+ align:start position:0%
+c my two switches I'm just going to
+ 
+
+ align:start position:0%
+c my two switches I'm just going to
+replace this with an output voltage V
+
+ align:start position:0%
+replace this with an output voltage V
+ 
+
+ align:start position:0%
+replace this with an output voltage V
+out okay and then I'm going to have this
+
+ align:start position:0%
+out okay and then I'm going to have this
+ 
+
+ align:start position:0%
+out okay and then I'm going to have this
+is switch one switch
+
+ align:start position:0%
+is switch one switch
+ 
+
+ align:start position:0%
+is switch one switch
+one switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two and switch
+
+ align:start position:0%
+two and switch
+ 
+
+ align:start position:0%
+two and switch
+two okay and this is the circuit we're
+
+ align:start position:0%
+two okay and this is the circuit we're
+ 
+
+ align:start position:0%
+two okay and this is the circuit we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+analyze Okay so State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right I basically have these two
+
+ align:start position:0%
+one right I basically have these two
+ 
+
+ align:start position:0%
+one right I basically have these two
+switches closed so in state one the
+
+ align:start position:0%
+switches closed so in state one the
+ 
+
+ align:start position:0%
+switches closed so in state one the
+converter looks like this
+
+ align:start position:0%
+converter looks like this
+ 
+
+ align:start position:0%
+converter looks like this
+BN right a first switch is going to be
+
+ align:start position:0%
+BN right a first switch is going to be
+ 
+
+ align:start position:0%
+BN right a first switch is going to be
+on I'll call that R switch right then
+
+ align:start position:0%
+on I'll call that R switch right then
+ 
+
+ align:start position:0%
+on I'll call that R switch right then
+I'm going to have my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor and then I'm going to have my
+
+ align:start position:0%
+capacitor and then I'm going to have my
+ 
+
+ align:start position:0%
+capacitor and then I'm going to have my
+second s
+
+ align:start position:0%
+second s
+ 
+
+ align:start position:0%
+second s
+s and then that's going to go to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output okay and in my second state state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two the input's now going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disconnected okay but I am going to
+
+ align:start position:0%
+disconnected okay but I am going to
+ 
+
+ align:start position:0%
+disconnected okay but I am going to
+connect my capacitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through a resistor to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay any questions about the two
+
+ align:start position:0%
+this okay any questions about the two
+ 
+
+ align:start position:0%
+this okay any questions about the two
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+configurations let's just for Simplicity
+
+ align:start position:0%
+configurations let's just for Simplicity
+ 
+
+ align:start position:0%
+configurations let's just for Simplicity
+assume I'm going to flop back and fourth
+
+ align:start position:0%
+assume I'm going to flop back and fourth
+ 
+
+ align:start position:0%
+assume I'm going to flop back and fourth
+at 50% duty cycle between these two
+
+ align:start position:0%
+at 50% duty cycle between these two
+ 
+
+ align:start position:0%
+at 50% duty cycle between these two
+states although we'll see in some cases
+
+ align:start position:0%
+states although we'll see in some cases
+ 
+
+ align:start position:0%
+states although we'll see in some cases
+the duty cycle matters and some cases it
+
+ align:start position:0%
+the duty cycle matters and some cases it
+ 
+
+ align:start position:0%
+the duty cycle matters and some cases it
+doesn't all right any
+
+ align:start position:0%
+doesn't all right any
+ 
+
+ align:start position:0%
+doesn't all right any
+questions yeah so in this case we can't
+
+ align:start position:0%
+questions yeah so in this case we can't
+ 
+
+ align:start position:0%
+questions yeah so in this case we can't
+deal with IDE switches we have to think
+
+ align:start position:0%
+deal with IDE switches we have to think
+ 
+
+ align:start position:0%
+deal with IDE switches we have to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh it it helps to think about the
+
+ align:start position:0%
+uh it it helps to think about the
+ 
+
+ align:start position:0%
+uh it it helps to think about the
+parasitic resistance um because we were
+
+ align:start position:0%
+parasitic resistance um because we were
+ 
+
+ align:start position:0%
+parasitic resistance um because we were
+going to worry about how much energy we
+
+ align:start position:0%
+going to worry about how much energy we
+ 
+
+ align:start position:0%
+going to worry about how much energy we
+dissipate in the switches but if I let
+
+ align:start position:0%
+dissipate in the switches but if I let
+ 
+
+ align:start position:0%
+dissipate in the switches but if I let
+the switch resistances go to zero the
+
+ align:start position:0%
+the switch resistances go to zero the
+ 
+
+ align:start position:0%
+the switch resistances go to zero the
+answer doesn't change
+
+ align:start position:0%
+answer doesn't change
+ 
+
+ align:start position:0%
+answer doesn't change
+actually um so yeah we'll come back to
+
+ align:start position:0%
+actually um so yeah we'll come back to
+ 
+
+ align:start position:0%
+actually um so yeah we'll come back to
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+point okay okay so let's think about
+
+ align:start position:0%
+point okay okay so let's think about
+ 
+
+ align:start position:0%
+point okay okay so let's think about
+this now in order to analyze this what
+
+ align:start position:0%
+this now in order to analyze this what
+ 
+
+ align:start position:0%
+this now in order to analyze this what
+I'd like to do is focus on uh here I
+
+ align:start position:0%
+I'd like to do is focus on uh here I
+ 
+
+ align:start position:0%
+I'd like to do is focus on uh here I
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VN here's
+
+ align:start position:0%
+VN here's
+ 
+
+ align:start position:0%
+VN here's
+VN let me talk about the current I in
+
+ align:start position:0%
+VN let me talk about the current I in
+ 
+
+ align:start position:0%
+VN let me talk about the current I in
+going into
+
+ align:start position:0%
+going into
+ 
+
+ align:start position:0%
+going into
+VN okay and here I have V
+
+ align:start position:0%
+VN okay and here I have V
+ 
+
+ align:start position:0%
+VN okay and here I have V
+out and here's I
+
+ align:start position:0%
+out and here's I
+ 
+
+ align:start position:0%
+out and here's I
+out and then I have VC
+
+ align:start position:0%
+out and then I have VC
+ 
+
+ align:start position:0%
+out and then I have VC
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+I I guess I should have drawn this on
+
+ align:start position:0%
+I I guess I should have drawn this on
+ 
+
+ align:start position:0%
+I I guess I should have drawn this on
+the main circuit right so this is uh
+
+ align:start position:0%
+the main circuit right so this is uh
+ 
+
+ align:start position:0%
+the main circuit right so this is uh
+VN I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in V
+
+ align:start position:0%
+in V
+ 
+
+ align:start position:0%
+in V
+out I
+
+ align:start position:0%
+out I
+ 
+
+ align:start position:0%
+out I
+out and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vciic okay and what I would like to
+
+ align:start position:0%
+vciic okay and what I would like to
+ 
+
+ align:start position:0%
+vciic okay and what I would like to
+do is um track
+
+ align:start position:0%
+do is um track
+ 
+
+ align:start position:0%
+do is um track
+the charge flowing through this
+
+ align:start position:0%
+the charge flowing through this
+ 
+
+ align:start position:0%
+the charge flowing through this
+converter okay which is going to let me
+
+ align:start position:0%
+converter okay which is going to let me
+ 
+
+ align:start position:0%
+converter okay which is going to let me
+sort of understand what its conversion
+
+ align:start position:0%
+sort of understand what its conversion
+ 
+
+ align:start position:0%
+sort of understand what its conversion
+ratio is and analyzing any switch
+
+ align:start position:0%
+ratio is and analyzing any switch
+ 
+
+ align:start position:0%
+ratio is and analyzing any switch
+capacitor converter more or less comes
+
+ align:start position:0%
+capacitor converter more or less comes
+ 
+
+ align:start position:0%
+capacitor converter more or less comes
+down to the process I'm following there
+
+ align:start position:0%
+down to the process I'm following there
+ 
+
+ align:start position:0%
+down to the process I'm following there
+are ways that you we can sort of
+
+ align:start position:0%
+are ways that you we can sort of
+ 
+
+ align:start position:0%
+are ways that you we can sort of
+organize it to do the general case okay
+
+ align:start position:0%
+organize it to do the general case okay
+ 
+
+ align:start position:0%
+organize it to do the general case okay
+but let's just think about this case and
+
+ align:start position:0%
+but let's just think about this case and
+ 
+
+ align:start position:0%
+but let's just think about this case and
+what I'm going to think about is um
+
+ align:start position:0%
+what I'm going to think about is um
+ 
+
+ align:start position:0%
+what I'm going to think about is um
+let's suppose that when I close the
+
+ align:start position:0%
+let's suppose that when I close the
+ 
+
+ align:start position:0%
+let's suppose that when I close the
+switches and I have some switch
+
+ align:start position:0%
+switches and I have some switch
+ 
+
+ align:start position:0%
+switches and I have some switch
+resistances the values don't matter but
+
+ align:start position:0%
+resistances the values don't matter but
+ 
+
+ align:start position:0%
+resistances the values don't matter but
+let's ask what does the final voltage of
+
+ align:start position:0%
+let's ask what does the final voltage of
+ 
+
+ align:start position:0%
+let's ask what does the final voltage of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+capacitor uh end up at right so at the
+
+ align:start position:0%
+capacitor uh end up at right so at the
+ 
+
+ align:start position:0%
+capacitor uh end up at right so at the
+end of State one what I'm going to
+
+ align:start position:0%
+end of State one what I'm going to
+ 
+
+ align:start position:0%
+end of State one what I'm going to
+assume for my first analysis and this is
+
+ align:start position:0%
+assume for my first analysis and this is
+ 
+
+ align:start position:0%
+assume for my first analysis and this is
+what's known as the slow switching limit
+
+ align:start position:0%
+what's known as the slow switching limit
+ 
+
+ align:start position:0%
+what's known as the slow switching limit
+is that you know I I close my switches
+
+ align:start position:0%
+is that you know I I close my switches
+ 
+
+ align:start position:0%
+is that you know I I close my switches
+and this capacitor charges to some final
+
+ align:start position:0%
+and this capacitor charges to some final
+ 
+
+ align:start position:0%
+and this capacitor charges to some final
+value and then stops
+
+ align:start position:0%
+value and then stops
+ 
+
+ align:start position:0%
+value and then stops
+charging okay so what would be the final
+
+ align:start position:0%
+charging okay so what would be the final
+ 
+
+ align:start position:0%
+charging okay so what would be the final
+value of the capacitor in this state one
+
+ align:start position:0%
+value of the capacitor in this state one
+ 
+
+ align:start position:0%
+value of the capacitor in this state one
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VC um at the in state one at the
+
+ align:start position:0%
+VC um at the in state one at the
+ 
+
+ align:start position:0%
+VC um at the in state one at the
+N what what voltage would VC charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to has to be VN minus V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out and in state
+
+ align:start position:0%
+out and in state
+ 
+
+ align:start position:0%
+out and in state
+two at the
+
+ align:start position:0%
+two at the
+ 
+
+ align:start position:0%
+two at the
+end correspond L VC has to go to V
+
+ align:start position:0%
+end correspond L VC has to go to V
+ 
+
+ align:start position:0%
+end correspond L VC has to go to V
+out okay so the idea is if I looked at
+
+ align:start position:0%
+out okay so the idea is if I looked at
+ 
+
+ align:start position:0%
+out okay so the idea is if I looked at
+what VC was going to
+
+ align:start position:0%
+what VC was going to
+ 
+
+ align:start position:0%
+what VC was going to
+do it's going to start off when I enter
+
+ align:start position:0%
+do it's going to start off when I enter
+ 
+
+ align:start position:0%
+do it's going to start off when I enter
+State one or if if they into state two
+
+ align:start position:0%
+State one or if if they into state two
+ 
+
+ align:start position:0%
+State one or if if they into state two
+I'm going to be at V out I'm going to
+
+ align:start position:0%
+I'm going to be at V out I'm going to
+ 
+
+ align:start position:0%
+I'm going to be at V out I'm going to
+flip my switches and then VC is going to
+
+ align:start position:0%
+flip my switches and then VC is going to
+ 
+
+ align:start position:0%
+flip my switches and then VC is going to
+charge to Vin minus V out and I'm going
+
+ align:start position:0%
+charge to Vin minus V out and I'm going
+ 
+
+ align:start position:0%
+charge to Vin minus V out and I'm going
+to switch my switches then VC is going
+
+ align:start position:0%
+to switch my switches then VC is going
+ 
+
+ align:start position:0%
+to switch my switches then VC is going
+to discharge in this case back to V out
+
+ align:start position:0%
+to discharge in this case back to V out
+ 
+
+ align:start position:0%
+to discharge in this case back to V out
+and it's going to repeat
+
+ align:start position:0%
+and it's going to repeat
+ 
+
+ align:start position:0%
+and it's going to repeat
+that make sense everybody so I'm sort of
+
+ align:start position:0%
+that make sense everybody so I'm sort of
+ 
+
+ align:start position:0%
+that make sense everybody so I'm sort of
+assuming and this is the slow switching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit that what my capacitor voltage is
+
+ align:start position:0%
+limit that what my capacitor voltage is
+ 
+
+ align:start position:0%
+limit that what my capacitor voltage is
+going to do versus time you know if this
+
+ align:start position:0%
+going to do versus time you know if this
+ 
+
+ align:start position:0%
+going to do versus time you know if this
+is sort of State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and this is sort of state two I'm
+
+ align:start position:0%
+one and this is sort of state two I'm
+ 
+
+ align:start position:0%
+one and this is sort of state two I'm
+going to have I'm going to basically my
+
+ align:start position:0%
+going to have I'm going to basically my
+ 
+
+ align:start position:0%
+going to have I'm going to basically my
+capacitor is going to charge from V
+
+ align:start position:0%
+capacitor is going to charge from V
+ 
+
+ align:start position:0%
+capacitor is going to charge from V
+out up to to V Inus V
+
+ align:start position:0%
+out up to to V Inus V
+ 
+
+ align:start position:0%
+out up to to V Inus V
+out and then it's going to charge from
+
+ align:start position:0%
+out and then it's going to charge from
+ 
+
+ align:start position:0%
+out and then it's going to charge from
+vnus V out down to V out and it's going
+
+ align:start position:0%
+vnus V out down to V out and it's going
+ 
+
+ align:start position:0%
+vnus V out down to V out and it's going
+to do something like this with some RC
+
+ align:start position:0%
+to do something like this with some RC
+ 
+
+ align:start position:0%
+to do something like this with some RC
+time charge constant and so I'm just
+
+ align:start position:0%
+time charge constant and so I'm just
+ 
+
+ align:start position:0%
+time charge constant and so I'm just
+assuming so this is going to at the end
+
+ align:start position:0%
+assuming so this is going to at the end
+ 
+
+ align:start position:0%
+assuming so this is going to at the end
+of State one it's going to V in minus V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out and it's and it's then in the next
+
+ align:start position:0%
+out and it's and it's then in the next
+ 
+
+ align:start position:0%
+out and it's and it's then in the next
+state in state two is going to charge to
+
+ align:start position:0%
+state in state two is going to charge to
+ 
+
+ align:start position:0%
+state in state two is going to charge to
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+out okay so my only assumption is I'm
+
+ align:start position:0%
+out okay so my only assumption is I'm
+ 
+
+ align:start position:0%
+out okay so my only assumption is I'm
+going to sort of each cycle I'm going to
+
+ align:start position:0%
+going to sort of each cycle I'm going to
+ 
+
+ align:start position:0%
+going to sort of each cycle I'm going to
+charge up I'm going to charge down and
+
+ align:start position:0%
+charge up I'm going to charge down and
+ 
+
+ align:start position:0%
+charge up I'm going to charge down and
+I'm going to sort of finish the charging
+
+ align:start position:0%
+I'm going to sort of finish the charging
+ 
+
+ align:start position:0%
+I'm going to sort of finish the charging
+I'm going to let this RC time constant
+
+ align:start position:0%
+I'm going to let this RC time constant
+ 
+
+ align:start position:0%
+I'm going to let this RC time constant
+sort of go to where he's fully
+
+ align:start position:0%
+sort of go to where he's fully
+ 
+
+ align:start position:0%
+sort of go to where he's fully
+charged okay so let's think about how
+
+ align:start position:0%
+charged okay so let's think about how
+ 
+
+ align:start position:0%
+charged okay so let's think about how
+much charge I transfer in each component
+
+ align:start position:0%
+much charge I transfer in each component
+ 
+
+ align:start position:0%
+much charge I transfer in each component
+okay in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right what do I have Delta
+
+ align:start position:0%
+one right what do I have Delta
+ 
+
+ align:start position:0%
+one right what do I have Delta
+QC in State One
+
+ align:start position:0%
+QC in State One
+ 
+
+ align:start position:0%
+QC in State One
+the amount of charge that gets put onto
+
+ align:start position:0%
+the amount of charge that gets put onto
+ 
+
+ align:start position:0%
+the amount of charge that gets put onto
+the capacitor in state one well what's
+
+ align:start position:0%
+the capacitor in state one well what's
+ 
+
+ align:start position:0%
+the capacitor in state one well what's
+that going to be that's going to be
+
+ align:start position:0%
+that going to be that's going to be
+ 
+
+ align:start position:0%
+that going to be that's going to be
+equal to Delta Q is C Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V right which is going to be c times the
+
+ align:start position:0%
+V right which is going to be c times the
+ 
+
+ align:start position:0%
+V right which is going to be c times the
+change in voltage across state one he's
+
+ align:start position:0%
+change in voltage across state one he's
+ 
+
+ align:start position:0%
+change in voltage across state one he's
+starting at V out and he's going up to
+
+ align:start position:0%
+starting at V out and he's going up to
+ 
+
+ align:start position:0%
+starting at V out and he's going up to
+VN minus V out so it's going to be vnus
+
+ align:start position:0%
+VN minus V out so it's going to be vnus
+ 
+
+ align:start position:0%
+VN minus V out so it's going to be vnus
+V out minus V out is going to be C *
+
+ align:start position:0%
+V out minus V out is going to be C *
+ 
+
+ align:start position:0%
+V out minus V out is going to be C *
+vnus 2v
+
+ align:start position:0%
+vnus 2v
+ 
+
+ align:start position:0%
+vnus 2v
+out okay so that that's how much charge
+
+ align:start position:0%
+out okay so that that's how much charge
+ 
+
+ align:start position:0%
+out okay so that that's how much charge
+gets put on
+
+ align:start position:0%
+gets put on
+ 
+
+ align:start position:0%
+gets put on
+to uh this capacitor during State one in
+
+ align:start position:0%
+to uh this capacitor during State one in
+ 
+
+ align:start position:0%
+to uh this capacitor during State one in
+periodic steady
+
+ align:start position:0%
+periodic steady
+ 
+
+ align:start position:0%
+periodic steady
+state any questions about that because
+
+ align:start position:0%
+state any questions about that because
+ 
+
+ align:start position:0%
+state any questions about that because
+the rest of the analysis proceeds just
+
+ align:start position:0%
+the rest of the analysis proceeds just
+ 
+
+ align:start position:0%
+the rest of the analysis proceeds just
+like this so want to make sure people
+
+ align:start position:0%
+like this so want to make sure people
+ 
+
+ align:start position:0%
+like this so want to make sure people
+get what I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculating in PSS I charge and
+
+ align:start position:0%
+calculating in PSS I charge and
+ 
+
+ align:start position:0%
+calculating in PSS I charge and
+discharge between two points and I'm
+
+ align:start position:0%
+discharge between two points and I'm
+ 
+
+ align:start position:0%
+discharge between two points and I'm
+just saying how much charge went under
+
+ align:start position:0%
+just saying how much charge went under
+ 
+
+ align:start position:0%
+just saying how much charge went under
+the capacitor and State one and that's
+
+ align:start position:0%
+the capacitor and State one and that's
+ 
+
+ align:start position:0%
+the capacitor and State one and that's
+it okay well how much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge went into the input in state
+
+ align:start position:0%
+charge went into the input in state
+ 
+
+ align:start position:0%
+charge went into the input in state
+one okay well the way I've defined it
+
+ align:start position:0%
+one okay well the way I've defined it
+ 
+
+ align:start position:0%
+one okay well the way I've defined it
+here the input and and I've defined it
+
+ align:start position:0%
+here the input and and I've defined it
+ 
+
+ align:start position:0%
+here the input and and I've defined it
+here because the general analyses tend
+
+ align:start position:0%
+here because the general analyses tend
+ 
+
+ align:start position:0%
+here because the general analyses tend
+to do it this way is exact the current
+
+ align:start position:0%
+to do it this way is exact the current
+ 
+
+ align:start position:0%
+to do it this way is exact the current
+going in the capacitor is exactly the
+
+ align:start position:0%
+going in the capacitor is exactly the
+ 
+
+ align:start position:0%
+going in the capacitor is exactly the
+opposite of the current going into the
+
+ align:start position:0%
+opposite of the current going into the
+ 
+
+ align:start position:0%
+opposite of the current going into the
+input in state one right so the current
+
+ align:start position:0%
+input in state one right so the current
+ 
+
+ align:start position:0%
+input in state one right so the current
+the charge into the input just has to be
+
+ align:start position:0%
+the charge into the input just has to be
+ 
+
+ align:start position:0%
+the charge into the input just has to be
+the opposite this this going to be minus
+
+ align:start position:0%
+the opposite this this going to be minus
+ 
+
+ align:start position:0%
+the opposite this this going to be minus
+c v in minus 2v
+
+ align:start position:0%
+c v in minus 2v
+ 
+
+ align:start position:0%
+c v in minus 2v
+out okay and likewise the charge that
+
+ align:start position:0%
+out okay and likewise the charge that
+ 
+
+ align:start position:0%
+out okay and likewise the charge that
+got transferred into the output during
+
+ align:start position:0%
+got transferred into the output during
+ 
+
+ align:start position:0%
+got transferred into the output during
+State one is exactly equal to the charge
+
+ align:start position:0%
+State one is exactly equal to the charge
+ 
+
+ align:start position:0%
+State one is exactly equal to the charge
+in the Capac they transferred onto the
+
+ align:start position:0%
+in the Capac they transferred onto the
+ 
+
+ align:start position:0%
+in the Capac they transferred onto the
+capacitor and I get Delta Q out in state
+
+ align:start position:0%
+capacitor and I get Delta Q out in state
+ 
+
+ align:start position:0%
+capacitor and I get Delta Q out in state
+one is equal to C VN minus 2v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out does that make sense everybody
+
+ align:start position:0%
+out does that make sense everybody
+ 
+
+ align:start position:0%
+out does that make sense everybody
+any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions let's think about state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay Delta QC how much
+
+ align:start position:0%
+two okay Delta QC how much
+ 
+
+ align:start position:0%
+two okay Delta QC how much
+charge goes on the capacitor in state 2
+
+ align:start position:0%
+charge goes on the capacitor in state 2
+ 
+
+ align:start position:0%
+charge goes on the capacitor in state 2
+is equal to C Delta V well in state 2 I
+
+ align:start position:0%
+is equal to C Delta V well in state 2 I
+ 
+
+ align:start position:0%
+is equal to C Delta V well in state 2 I
+started at V in minus V out and I ended
+
+ align:start position:0%
+started at V in minus V out and I ended
+ 
+
+ align:start position:0%
+started at V in minus V out and I ended
+V out so it's going to be V in minus V
+
+ align:start position:0%
+V out so it's going to be V in minus V
+ 
+
+ align:start position:0%
+V out so it's going to be V in minus V
+out minus V out
+
+ align:start position:0%
+out minus V out
+ 
+
+ align:start position:0%
+out minus V out
+is what I'm going to get right but
+
+ align:start position:0%
+is what I'm going to get right but
+ 
+
+ align:start position:0%
+is what I'm going to get right but
+um keep in mind
+
+ align:start position:0%
+um keep in mind
+ 
+
+ align:start position:0%
+um keep in mind
+that I could write this that this
+
+ align:start position:0%
+that I could write this that this
+ 
+
+ align:start position:0%
+that I could write this that this
+uh this is the charge is going to he's
+
+ align:start position:0%
+uh this is the charge is going to he's
+ 
+
+ align:start position:0%
+uh this is the charge is going to he's
+going to end up at V
+
+ align:start position:0%
+going to end up at V
+ 
+
+ align:start position:0%
+going to end up at V
+out minus VN minus V out so it's V out
+
+ align:start position:0%
+out minus VN minus V out so it's V out
+ 
+
+ align:start position:0%
+out minus VN minus V out so it's V out
+minus VN minus V out it's 2v out minus
+
+ align:start position:0%
+minus VN minus V out it's 2v out minus
+ 
+
+ align:start position:0%
+minus VN minus V out it's 2v out minus
+VN * C okay but I could write that as
+
+ align:start position:0%
+VN * C okay but I could write that as
+ 
+
+ align:start position:0%
+VN * C okay but I could write that as
+minus C * V in - 2v
+
+ align:start position:0%
+minus C * V in - 2v
+ 
+
+ align:start position:0%
+minus C * V in - 2v
+out okay and the reason I'm going to
+
+ align:start position:0%
+out okay and the reason I'm going to
+ 
+
+ align:start position:0%
+out okay and the reason I'm going to
+write first of all does everybody get
+
+ align:start position:0%
+write first of all does everybody get
+ 
+
+ align:start position:0%
+write first of all does everybody get
+what I just did all I did was I just
+
+ align:start position:0%
+what I just did all I did was I just
+ 
+
+ align:start position:0%
+what I just did all I did was I just
+expressed it as a with a minus sign out
+
+ align:start position:0%
+expressed it as a with a minus sign out
+ 
+
+ align:start position:0%
+expressed it as a with a minus sign out
+here I pulled the minus sign out here
+
+ align:start position:0%
+here I pulled the minus sign out here
+ 
+
+ align:start position:0%
+here I pulled the minus sign out here
+why did I pull the minus sign out here
+
+ align:start position:0%
+why did I pull the minus sign out here
+ 
+
+ align:start position:0%
+why did I pull the minus sign out here
+because I want to
+
+ align:start position:0%
+because I want to
+ 
+
+ align:start position:0%
+because I want to
+emphasize um that this is going to be a
+
+ align:start position:0%
+emphasize um that this is going to be a
+ 
+
+ align:start position:0%
+emphasize um that this is going to be a
+negative net charge or another way I
+
+ align:start position:0%
+negative net charge or another way I
+ 
+
+ align:start position:0%
+negative net charge or another way I
+ought to think about it is is look I'm
+
+ align:start position:0%
+ought to think about it is is look I'm
+ 
+
+ align:start position:0%
+ought to think about it is is look I'm
+running this converter back and forth
+
+ align:start position:0%
+running this converter back and forth
+ 
+
+ align:start position:0%
+running this converter back and forth
+between State 1 and state two in
+
+ align:start position:0%
+between State 1 and state two in
+ 
+
+ align:start position:0%
+between State 1 and state two in
+periodic steady state
+
+ align:start position:0%
+periodic steady state
+ 
+
+ align:start position:0%
+periodic steady state
+right what is the net charge that I'm
+
+ align:start position:0%
+right what is the net charge that I'm
+ 
+
+ align:start position:0%
+right what is the net charge that I'm
+going to transfer through the capacitor
+
+ align:start position:0%
+going to transfer through the capacitor
+ 
+
+ align:start position:0%
+going to transfer through the capacitor
+in periodic steady
+
+ align:start position:0%
+in periodic steady
+ 
+
+ align:start position:0%
+in periodic steady
+state zero right so that means that
+
+ align:start position:0%
+state zero right so that means that
+ 
+
+ align:start position:0%
+state zero right so that means that
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+qc1 the charge transferred onto the
+
+ align:start position:0%
+qc1 the charge transferred onto the
+ 
+
+ align:start position:0%
+qc1 the charge transferred onto the
+capacitor in state one plus Delta qc2
+
+ align:start position:0%
+capacitor in state one plus Delta qc2
+ 
+
+ align:start position:0%
+capacitor in state one plus Delta qc2
+the charge transfer onto the capacitor
+
+ align:start position:0%
+the charge transfer onto the capacitor
+ 
+
+ align:start position:0%
+the charge transfer onto the capacitor
+State 2 better add to zero and you can
+
+ align:start position:0%
+State 2 better add to zero and you can
+ 
+
+ align:start position:0%
+State 2 better add to zero and you can
+see that it does if I write it this way
+
+ align:start position:0%
+see that it does if I write it this way
+ 
+
+ align:start position:0%
+see that it does if I write it this way
+right it's C vnus 2v out plus minus C
+
+ align:start position:0%
+right it's C vnus 2v out plus minus C
+ 
+
+ align:start position:0%
+right it's C vnus 2v out plus minus C
+vnus 2v out so they add to zero so
+
+ align:start position:0%
+vnus 2v out so they add to zero so
+ 
+
+ align:start position:0%
+vnus 2v out so they add to zero so
+indeed if I made the assumption that
+
+ align:start position:0%
+indeed if I made the assumption that
+ 
+
+ align:start position:0%
+indeed if I made the assumption that
+it's charged to its initial and final
+
+ align:start position:0%
+it's charged to its initial and final
+ 
+
+ align:start position:0%
+it's charged to its initial and final
+States um this does satisfy the periodic
+
+ align:start position:0%
+States um this does satisfy the periodic
+ 
+
+ align:start position:0%
+States um this does satisfy the periodic
+St state requirements on the
+
+ align:start position:0%
+St state requirements on the
+ 
+
+ align:start position:0%
+St state requirements on the
+capacitor okay any questions about
+
+ align:start position:0%
+capacitor okay any questions about
+ 
+
+ align:start position:0%
+capacitor okay any questions about
+that so let's just say what
+
+ align:start position:0%
+that so let's just say what
+ 
+
+ align:start position:0%
+that so let's just say what
+happens what's Delta Q in in state 2
+
+ align:start position:0%
+happens what's Delta Q in in state 2
+ 
+
+ align:start position:0%
+happens what's Delta Q in in state 2
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+anybody tell me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is
+
+ align:start position:0%
+that this is
+ 
+
+ align:start position:0%
+that this is
+VN this is I in how much charge is
+
+ align:start position:0%
+VN this is I in how much charge is
+ 
+
+ align:start position:0%
+VN this is I in how much charge is
+transferred into the
+
+ align:start position:0%
+transferred into the
+ 
+
+ align:start position:0%
+transferred into the
+input in state
+
+ align:start position:0%
+input in state
+ 
+
+ align:start position:0%
+input in state
+two zero right no charge transfering the
+
+ align:start position:0%
+two zero right no charge transfering the
+ 
+
+ align:start position:0%
+two zero right no charge transfering the
+input okay how much charge is
+
+ align:start position:0%
+input okay how much charge is
+ 
+
+ align:start position:0%
+input okay how much charge is
+transferred to the
+
+ align:start position:0%
+transferred to the
+ 
+
+ align:start position:0%
+transferred to the
+output in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two well
+
+ align:start position:0%
+two well
+ 
+
+ align:start position:0%
+two well
+uh this is Let's Be careful about signs
+
+ align:start position:0%
+uh this is Let's Be careful about signs
+ 
+
+ align:start position:0%
+uh this is Let's Be careful about signs
+here here's V out here's I out right the
+
+ align:start position:0%
+here here's V out here's I out right the
+ 
+
+ align:start position:0%
+here here's V out here's I out right the
+negative of the capacitor current is
+
+ align:start position:0%
+negative of the capacitor current is
+ 
+
+ align:start position:0%
+negative of the capacitor current is
+going into the output so whatever charge
+
+ align:start position:0%
+going into the output so whatever charge
+ 
+
+ align:start position:0%
+going into the output so whatever charge
+went into the capacitor the negative of
+
+ align:start position:0%
+went into the capacitor the negative of
+ 
+
+ align:start position:0%
+went into the capacitor the negative of
+that charge went into the output right
+
+ align:start position:0%
+that charge went into the output right
+ 
+
+ align:start position:0%
+that charge went into the output right
+so Delta Q out2 must be positive
+
+ align:start position:0%
+so Delta Q out2 must be positive
+ 
+
+ align:start position:0%
+so Delta Q out2 must be positive
+c v in minus 2v out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody okay so uh what is the we know
+
+ align:start position:0%
+everybody okay so uh what is the we know
+ 
+
+ align:start position:0%
+everybody okay so uh what is the we know
+that the net total charge transferred on
+
+ align:start position:0%
+that the net total charge transferred on
+ 
+
+ align:start position:0%
+that the net total charge transferred on
+this energy storage capacitor in
+
+ align:start position:0%
+this energy storage capacitor in
+ 
+
+ align:start position:0%
+this energy storage capacitor in
+periodic steady state better be zero
+
+ align:start position:0%
+periodic steady state better be zero
+ 
+
+ align:start position:0%
+periodic steady state better be zero
+right but that's not true of the input
+
+ align:start position:0%
+right but that's not true of the input
+ 
+
+ align:start position:0%
+right but that's not true of the input
+of the output so why don't we just find
+
+ align:start position:0%
+of the output so why don't we just find
+ 
+
+ align:start position:0%
+of the output so why don't we just find
+out what that is um we could then
+
+ align:start position:0%
+out what that is um we could then
+ 
+
+ align:start position:0%
+out what that is um we could then
+write um Delta
+
+ align:start position:0%
+write um Delta
+ 
+
+ align:start position:0%
+write um Delta
+qn is equal to Q
+
+ align:start position:0%
+qn is equal to Q
+ 
+
+ align:start position:0%
+qn is equal to Q
+n in state 1 plus Delta Q in in state 2
+
+ align:start position:0%
+n in state 1 plus Delta Q in in state 2
+ 
+
+ align:start position:0%
+n in state 1 plus Delta Q in in state 2
+and if I just add those up that's going
+
+ align:start position:0%
+and if I just add those up that's going
+ 
+
+ align:start position:0%
+and if I just add those up that's going
+to be 2 c v in minus 2v
+
+ align:start position:0%
+to be 2 c v in minus 2v
+ 
+
+ align:start position:0%
+to be 2 c v in minus 2v
+out okay and Delta Q
+
+ align:start position:0%
+out okay and Delta Q
+ 
+
+ align:start position:0%
+out okay and Delta Q
+out is going to be equal to Delta Q out
+
+ align:start position:0%
+out is going to be equal to Delta Q out
+ 
+
+ align:start position:0%
+out is going to be equal to Delta Q out
+in state one and Delta Q
+
+ align:start position:0%
+in state one and Delta Q
+ 
+
+ align:start position:0%
+in state one and Delta Q
+out in state two and if I add those up
+
+ align:start position:0%
+out in state two and if I add those up
+ 
+
+ align:start position:0%
+out in state two and if I add those up
+it's going to be
+
+ align:start position:0%
+it's going to be
+ 
+
+ align:start position:0%
+it's going to be
+minus c v Inus 2v
+
+ align:start position:0%
+minus c v Inus 2v
+ 
+
+ align:start position:0%
+minus c v Inus 2v
+out okay
+
+ align:start position:0%
+out okay
+ 
+
+ align:start position:0%
+out okay
+now how much what's the current at the
+
+ align:start position:0%
+now how much what's the current at the
+ 
+
+ align:start position:0%
+now how much what's the current at the
+input on average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh yes thank
+
+ align:start position:0%
+yeah uh yes thank
+ 
+
+ align:start position:0%
+yeah uh yes thank
+you huh how did I do
+
+ align:start position:0%
+you huh how did I do
+ 
+
+ align:start position:0%
+you huh how did I do
+that well it's easier to do it this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way thank you Somebody's Watching okay
+
+ align:start position:0%
+way thank you Somebody's Watching okay
+ 
+
+ align:start position:0%
+way thank you Somebody's Watching okay
+so um we have our input and output net
+
+ align:start position:0%
+so um we have our input and output net
+ 
+
+ align:start position:0%
+so um we have our input and output net
+charge okay if I wanted to talk about
+
+ align:start position:0%
+charge okay if I wanted to talk about
+ 
+
+ align:start position:0%
+charge okay if I wanted to talk about
+the average current going to the input
+
+ align:start position:0%
+the average current going to the input
+ 
+
+ align:start position:0%
+the average current going to the input
+or the output averaged over a
+
+ align:start position:0%
+or the output averaged over a
+ 
+
+ align:start position:0%
+or the output averaged over a
+cycle really it's the charge divided by
+
+ align:start position:0%
+cycle really it's the charge divided by
+ 
+
+ align:start position:0%
+cycle really it's the charge divided by
+the period or equivalently the charge
+
+ align:start position:0%
+the period or equivalently the charge
+ 
+
+ align:start position:0%
+the period or equivalently the charge
+times the switching frequency right so
+
+ align:start position:0%
+times the switching frequency right so
+ 
+
+ align:start position:0%
+times the switching frequency right so
+the local average in or the average in
+
+ align:start position:0%
+the local average in or the average in
+ 
+
+ align:start position:0%
+the local average in or the average in
+periodic steady state I could infer from
+
+ align:start position:0%
+periodic steady state I could infer from
+ 
+
+ align:start position:0%
+periodic steady state I could infer from
+this is that uh I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in is equal to uh c times the switching
+
+ align:start position:0%
+in is equal to uh c times the switching
+ 
+
+ align:start position:0%
+in is equal to uh c times the switching
+frequency it's one over the period
+
+ align:start position:0%
+frequency it's one over the period
+ 
+
+ align:start position:0%
+frequency it's one over the period
+times uh V in minus 2v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out and I should put my minus sign here
+
+ align:start position:0%
+out and I should put my minus sign here
+ 
+
+ align:start position:0%
+out and I should put my minus sign here
+and that's this is the current going
+
+ align:start position:0%
+and that's this is the current going
+ 
+
+ align:start position:0%
+and that's this is the current going
+into the input right uh and likewise I
+
+ align:start position:0%
+into the input right uh and likewise I
+ 
+
+ align:start position:0%
+into the input right uh and likewise I
+out is equal to 2 c f switch time vnus
+
+ align:start position:0%
+out is equal to 2 c f switch time vnus
+ 
+
+ align:start position:0%
+out is equal to 2 c f switch time vnus
+2v
+
+ align:start position:0%
+2v
+ 
+
+ align:start position:0%
+2v
+out okay so if you look at this the
+
+ align:start position:0%
+out okay so if you look at this the
+ 
+
+ align:start position:0%
+out okay so if you look at this the
+magnitude of I
+
+ align:start position:0%
+magnitude of I
+ 
+
+ align:start position:0%
+magnitude of I
+out is equal to 2 * the magnitude of I
+
+ align:start position:0%
+out is equal to 2 * the magnitude of I
+ 
+
+ align:start position:0%
+out is equal to 2 * the magnitude of I
+in okay why because what happens is
+
+ align:start position:0%
+in okay why because what happens is
+ 
+
+ align:start position:0%
+in okay why because what happens is
+essentially and and what's the re deal
+
+ align:start position:0%
+essentially and and what's the re deal
+ 
+
+ align:start position:0%
+essentially and and what's the re deal
+with the minus sign the minus sign is
+
+ align:start position:0%
+with the minus sign the minus sign is
+ 
+
+ align:start position:0%
+with the minus sign the minus sign is
+because I chose to Define I in going
+
+ align:start position:0%
+because I chose to Define I in going
+ 
+
+ align:start position:0%
+because I chose to Define I in going
+this way had I defined it going this way
+
+ align:start position:0%
+this way had I defined it going this way
+ 
+
+ align:start position:0%
+this way had I defined it going this way
+I'd have I out is equal to twice I in
+
+ align:start position:0%
+I'd have I out is equal to twice I in
+ 
+
+ align:start position:0%
+I'd have I out is equal to twice I in
+right but let's just worry about the
+
+ align:start position:0%
+right but let's just worry about the
+ 
+
+ align:start position:0%
+right but let's just worry about the
+magnitudes here so what's going on in
+
+ align:start position:0%
+magnitudes here so what's going on in
+ 
+
+ align:start position:0%
+magnitudes here so what's going on in
+the first part of the cycle I dump a
+
+ align:start position:0%
+the first part of the cycle I dump a
+ 
+
+ align:start position:0%
+the first part of the cycle I dump a
+certain amount of charge from the input
+
+ align:start position:0%
+certain amount of charge from the input
+ 
+
+ align:start position:0%
+certain amount of charge from the input
+to the output through the capacitor I
+
+ align:start position:0%
+to the output through the capacitor I
+ 
+
+ align:start position:0%
+to the output through the capacitor I
+charge the capacitor up so that's some
+
+ align:start position:0%
+charge the capacitor up so that's some
+ 
+
+ align:start position:0%
+charge the capacitor up so that's some
+amount of charge in the second part of
+
+ align:start position:0%
+amount of charge in the second part of
+ 
+
+ align:start position:0%
+amount of charge in the second part of
+the cycle this capacitor then dumps that
+
+ align:start position:0%
+the cycle this capacitor then dumps that
+ 
+
+ align:start position:0%
+the cycle this capacitor then dumps that
+same amount of charge into the output
+
+ align:start position:0%
+same amount of charge into the output
+ 
+
+ align:start position:0%
+same amount of charge into the output
+again so the output gets twice the
+
+ align:start position:0%
+again so the output gets twice the
+ 
+
+ align:start position:0%
+again so the output gets twice the
+amount of charge the input over the
+
+ align:start position:0%
+amount of charge the input over the
+ 
+
+ align:start position:0%
+amount of charge the input over the
+cycle and then I go back to the next
+
+ align:start position:0%
+cycle and then I go back to the next
+ 
+
+ align:start position:0%
+cycle and then I go back to the next
+cycle and I
+
+ align:start position:0%
+cycle and I
+ 
+
+ align:start position:0%
+cycle and I
+repeat okay so whatever the current
+
+ align:start position:0%
+repeat okay so whatever the current
+ 
+
+ align:start position:0%
+repeat okay so whatever the current
+coming in from coming coming into the
+
+ align:start position:0%
+coming in from coming coming into the
+ 
+
+ align:start position:0%
+coming in from coming coming into the
+converter from the input is exactly half
+
+ align:start position:0%
+converter from the input is exactly half
+ 
+
+ align:start position:0%
+converter from the input is exactly half
+the current going to the output by
+
+ align:start position:0%
+the current going to the output by
+ 
+
+ align:start position:0%
+the current going to the output by
+periodic steady state and charge balance
+
+ align:start position:0%
+periodic steady state and charge balance
+ 
+
+ align:start position:0%
+periodic steady state and charge balance
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+capacitor okay any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should say that this is the defining
+
+ align:start position:0%
+I should say that this is the defining
+ 
+
+ align:start position:0%
+I should say that this is the defining
+feature of a switch capacitor converter
+
+ align:start position:0%
+feature of a switch capacitor converter
+ 
+
+ align:start position:0%
+feature of a switch capacitor converter
+okay you will always have some rational
+
+ align:start position:0%
+okay you will always have some rational
+ 
+
+ align:start position:0%
+okay you will always have some rational
+relationship rational meaning you know
+
+ align:start position:0%
+relationship rational meaning you know
+ 
+
+ align:start position:0%
+relationship rational meaning you know
+an actual fraction relating the current
+
+ align:start position:0%
+an actual fraction relating the current
+ 
+
+ align:start position:0%
+an actual fraction relating the current
+from the input to the current on the
+
+ align:start position:0%
+from the input to the current on the
+ 
+
+ align:start position:0%
+from the input to the current on the
+output why because this is a very simple
+
+ align:start position:0%
+output why because this is a very simple
+ 
+
+ align:start position:0%
+output why because this is a very simple
+converter we've got one capacitor that
+
+ align:start position:0%
+converter we've got one capacitor that
+ 
+
+ align:start position:0%
+converter we've got one capacitor that
+we're flipping around but generally
+
+ align:start position:0%
+we're flipping around but generally
+ 
+
+ align:start position:0%
+we're flipping around but generally
+you're going to be taking energy storing
+
+ align:start position:0%
+you're going to be taking energy storing
+ 
+
+ align:start position:0%
+you're going to be taking energy storing
+charge from the input doing something
+
+ align:start position:0%
+charge from the input doing something
+ 
+
+ align:start position:0%
+charge from the input doing something
+and throwing it to the output and those
+
+ align:start position:0%
+and throwing it to the output and those
+ 
+
+ align:start position:0%
+and throwing it to the output and those
+are always going to be related in some
+
+ align:start position:0%
+are always going to be related in some
+ 
+
+ align:start position:0%
+are always going to be related in some
+rational
+
+ align:start position:0%
+rational
+ 
+
+ align:start position:0%
+rational
+way okay um so that's what the core
+
+ align:start position:0%
+way okay um so that's what the core
+ 
+
+ align:start position:0%
+way okay um so that's what the core
+thing that a switch capacitor converter
+
+ align:start position:0%
+thing that a switch capacitor converter
+ 
+
+ align:start position:0%
+thing that a switch capacitor converter
+do is by charge balance it's going to
+
+ align:start position:0%
+do is by charge balance it's going to
+ 
+
+ align:start position:0%
+do is by charge balance it's going to
+give you some con current conversion
+
+ align:start position:0%
+give you some con current conversion
+ 
+
+ align:start position:0%
+give you some con current conversion
+ratio between the input and the output
+
+ align:start position:0%
+ratio between the input and the output
+ 
+
+ align:start position:0%
+ratio between the input and the output
+that's fixed by the topology and the
+
+ align:start position:0%
+that's fixed by the topology and the
+ 
+
+ align:start position:0%
+that's fixed by the topology and the
+switching sequence
+
+ align:start position:0%
+switching sequence
+ 
+
+ align:start position:0%
+switching sequence
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right um what else can we say
+
+ align:start position:0%
+um all right um what else can we say
+ 
+
+ align:start position:0%
+um all right um what else can we say
+about about this well look at this
+
+ align:start position:0%
+about about this well look at this
+ 
+
+ align:start position:0%
+about about this well look at this
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+here first of all any questions about
+
+ align:start position:0%
+here first of all any questions about
+ 
+
+ align:start position:0%
+here first of all any questions about
+what got me to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah is this assuming a 50% duty
+
+ align:start position:0%
+that yeah is this assuming a 50% duty
+ 
+
+ align:start position:0%
+that yeah is this assuming a 50% duty
+cycle oh that's a good question so long
+
+ align:start position:0%
+cycle oh that's a good question so long
+ 
+
+ align:start position:0%
+cycle oh that's a good question so long
+as the intervals are such that I fully
+
+ align:start position:0%
+as the intervals are such that I fully
+ 
+
+ align:start position:0%
+as the intervals are such that I fully
+charge and fully discharge in each sub
+
+ align:start position:0%
+charge and fully discharge in each sub
+ 
+
+ align:start position:0%
+charge and fully discharge in each sub
+interval in state one and state two the
+
+ align:start position:0%
+interval in state one and state two the
+ 
+
+ align:start position:0%
+interval in state one and state two the
+actual Duty ratio doesn't matter in this
+
+ align:start position:0%
+actual Duty ratio doesn't matter in this
+ 
+
+ align:start position:0%
+actual Duty ratio doesn't matter in this
+mode of operation
+
+ align:start position:0%
+mode of operation
+ 
+
+ align:start position:0%
+mode of operation
+so the only thing I've assumed is that
+
+ align:start position:0%
+so the only thing I've assumed is that
+ 
+
+ align:start position:0%
+so the only thing I've assumed is that
+I'm waiting long enough in state one for
+
+ align:start position:0%
+I'm waiting long enough in state one for
+ 
+
+ align:start position:0%
+I'm waiting long enough in state one for
+the cap passor to get to his final
+
+ align:start position:0%
+the cap passor to get to his final
+ 
+
+ align:start position:0%
+the cap passor to get to his final
+voltage and I'm waiting long enough in
+
+ align:start position:0%
+voltage and I'm waiting long enough in
+ 
+
+ align:start position:0%
+voltage and I'm waiting long enough in
+state two for the passor to get to its
+
+ align:start position:0%
+state two for the passor to get to its
+ 
+
+ align:start position:0%
+state two for the passor to get to its
+final voltage and as long as I've waited
+
+ align:start position:0%
+final voltage and as long as I've waited
+ 
+
+ align:start position:0%
+final voltage and as long as I've waited
+long enough in both States what their
+
+ align:start position:0%
+long enough in both States what their
+ 
+
+ align:start position:0%
+long enough in both States what their
+actual fraction of on times are doesn't
+
+ align:start position:0%
+actual fraction of on times are doesn't
+ 
+
+ align:start position:0%
+actual fraction of on times are doesn't
+matter we'll come back to that shortly
+
+ align:start position:0%
+matter we'll come back to that shortly
+ 
+
+ align:start position:0%
+matter we'll come back to that shortly
+yeah I a question this is called the
+
+ align:start position:0%
+yeah I a question this is called the
+ 
+
+ align:start position:0%
+yeah I a question this is called the
+slow
+
+ align:start position:0%
+slow
+ 
+
+ align:start position:0%
+slow
+switching yes and like that's why we
+
+ align:start position:0%
+switching yes and like that's why we
+ 
+
+ align:start position:0%
+switching yes and like that's why we
+didn't include the culations this
+
+ align:start position:0%
+didn't include the culations this
+ 
+
+ align:start position:0%
+didn't include the culations this
+effects
+
+ align:start position:0%
+effects
+ 
+
+ align:start position:0%
+effects
+or like those switches there are
+
+ align:start position:0%
+or like those switches there are
+ 
+
+ align:start position:0%
+or like those switches there are
+represented as resistors yeah so like
+
+ align:start position:0%
+represented as resistors yeah so like
+ 
+
+ align:start position:0%
+represented as resistors yeah so like
+the the Char doesn't see resistance well
+
+ align:start position:0%
+the the Char doesn't see resistance well
+ 
+
+ align:start position:0%
+the the Char doesn't see resistance well
+no it does we've we've included the
+
+ align:start position:0%
+no it does we've we've included the
+ 
+
+ align:start position:0%
+no it does we've we've included the
+resistance right all I've said is
+
+ align:start position:0%
+resistance right all I've said is
+ 
+
+ align:start position:0%
+resistance right all I've said is
+um the only thing you really need to
+
+ align:start position:0%
+um the only thing you really need to
+ 
+
+ align:start position:0%
+um the only thing you really need to
+know in this is where did the capacitor
+
+ align:start position:0%
+know in this is where did the capacitor
+ 
+
+ align:start position:0%
+know in this is where did the capacitor
+start in terms of its voltage and where
+
+ align:start position:0%
+start in terms of its voltage and where
+ 
+
+ align:start position:0%
+start in terms of its voltage and where
+did it end and if you know that then you
+
+ align:start position:0%
+did it end and if you know that then you
+ 
+
+ align:start position:0%
+did it end and if you know that then you
+know how much charge went into it so we
+
+ align:start position:0%
+know how much charge went into it so we
+ 
+
+ align:start position:0%
+know how much charge went into it so we
+have actually included the effect of the
+
+ align:start position:0%
+have actually included the effect of the
+ 
+
+ align:start position:0%
+have actually included the effect of the
+resistances it's those RC charging
+
+ align:start position:0%
+resistances it's those RC charging
+ 
+
+ align:start position:0%
+resistances it's those RC charging
+things if the r if the resistances get
+
+ align:start position:0%
+things if the r if the resistances get
+ 
+
+ align:start position:0%
+things if the r if the resistances get
+small I just make those RC chargings
+
+ align:start position:0%
+small I just make those RC chargings
+ 
+
+ align:start position:0%
+small I just make those RC chargings
+shorter okay I see thanks yeah but
+
+ align:start position:0%
+shorter okay I see thanks yeah but
+ 
+
+ align:start position:0%
+shorter okay I see thanks yeah but
+wouldn't wouldn't the on State and off
+
+ align:start position:0%
+wouldn't wouldn't the on State and off
+ 
+
+ align:start position:0%
+wouldn't wouldn't the on State and off
+State voltages
+
+ align:start position:0%
+State voltages
+ 
+
+ align:start position:0%
+State voltages
+change wouldn't there just wouldn't
+
+ align:start position:0%
+change wouldn't there just wouldn't
+ 
+
+ align:start position:0%
+change wouldn't there just wouldn't
+there be potential differences across
+
+ align:start position:0%
+there be potential differences across
+ 
+
+ align:start position:0%
+there be potential differences across
+the resistors well um if I've if I've
+
+ align:start position:0%
+the resistors well um if I've if I've
+ 
+
+ align:start position:0%
+the resistors well um if I've if I've
+assumed that the capacitor is fully
+
+ align:start position:0%
+assumed that the capacitor is fully
+ 
+
+ align:start position:0%
+assumed that the capacitor is fully
+charged the vol voltage across this
+
+ align:start position:0%
+charged the vol voltage across this
+ 
+
+ align:start position:0%
+charged the vol voltage across this
+resistor went to Zero by the end right
+
+ align:start position:0%
+resistor went to Zero by the end right
+ 
+
+ align:start position:0%
+resistor went to Zero by the end right
+so the only assumption I've made is you
+
+ align:start position:0%
+so the only assumption I've made is you
+ 
+
+ align:start position:0%
+so the only assumption I've made is you
+know this capacitor charges once the
+
+ align:start position:0%
+know this capacitor charges once the
+ 
+
+ align:start position:0%
+know this capacitor charges once the
+capacitor current goes to zero these
+
+ align:start position:0%
+capacitor current goes to zero these
+ 
+
+ align:start position:0%
+capacitor current goes to zero these
+voltage drops go to
+
+ align:start position:0%
+voltage drops go to
+ 
+
+ align:start position:0%
+voltage drops go to
+zero yeah we'll relax that assumption
+
+ align:start position:0%
+zero yeah we'll relax that assumption
+ 
+
+ align:start position:0%
+zero yeah we'll relax that assumption
+shortly okay so let me start from this
+
+ align:start position:0%
+shortly okay so let me start from this
+ 
+
+ align:start position:0%
+shortly okay so let me start from this
+relationship and let me see if I can
+
+ align:start position:0%
+relationship and let me see if I can
+ 
+
+ align:start position:0%
+relationship and let me see if I can
+give you what the voltage relationship
+
+ align:start position:0%
+give you what the voltage relationship
+ 
+
+ align:start position:0%
+give you what the voltage relationship
+is I've sort of told you here this is
+
+ align:start position:0%
+is I've sort of told you here this is
+ 
+
+ align:start position:0%
+is I've sort of told you here this is
+the current relationship of the
+
+ align:start position:0%
+the current relationship of the
+ 
+
+ align:start position:0%
+the current relationship of the
+converter right that's the fundamental
+
+ align:start position:0%
+converter right that's the fundamental
+ 
+
+ align:start position:0%
+converter right that's the fundamental
+thing that this converter does okay well
+
+ align:start position:0%
+thing that this converter does okay well
+ 
+
+ align:start position:0%
+thing that this converter does okay well
+how are the input and output voltage
+
+ align:start position:0%
+how are the input and output voltage
+ 
+
+ align:start position:0%
+how are the input and output voltage
+related well that's by this guy here
+
+ align:start position:0%
+related well that's by this guy here
+ 
+
+ align:start position:0%
+related well that's by this guy here
+okay and I can rearrange this so all I
+
+ align:start position:0%
+okay and I can rearrange this so all I
+ 
+
+ align:start position:0%
+okay and I can rearrange this so all I
+could do is maybe solve for V out and if
+
+ align:start position:0%
+could do is maybe solve for V out and if
+ 
+
+ align:start position:0%
+could do is maybe solve for V out and if
+I solve this equation for v out what I'm
+
+ align:start position:0%
+I solve this equation for v out what I'm
+ 
+
+ align:start position:0%
+I solve this equation for v out what I'm
+going to get is V
+
+ align:start position:0%
+going to get is V
+ 
+
+ align:start position:0%
+going to get is V
+out is equal to 12 of v
+
+ align:start position:0%
+out is equal to 12 of v
+ 
+
+ align:start position:0%
+out is equal to 12 of v
+in minus 1
+
+ align:start position:0%
+in minus 1
+ 
+
+ align:start position:0%
+in minus 1
+over4 uh F switch C
+
+ align:start position:0%
+over4 uh F switch C
+ 
+
+ align:start position:0%
+over4 uh F switch C
+time I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay this this is an equivalent
+
+ align:start position:0%
+out okay this this is an equivalent
+ 
+
+ align:start position:0%
+out okay this this is an equivalent
+statement as
+
+ align:start position:0%
+statement as
+ 
+
+ align:start position:0%
+statement as
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay so what does that mean in as a in a
+
+ align:start position:0%
+okay so what does that mean in as a in a
+ 
+
+ align:start position:0%
+okay so what does that mean in as a in a
+practical
+
+ align:start position:0%
+practical
+ 
+
+ align:start position:0%
+practical
+matter well let me create for you an
+
+ align:start position:0%
+matter well let me create for you an
+ 
+
+ align:start position:0%
+matter well let me create for you an
+equivalent circuit which does the same
+
+ align:start position:0%
+equivalent circuit which does the same
+ 
+
+ align:start position:0%
+equivalent circuit which does the same
+thing right so I told you you know this
+
+ align:start position:0%
+thing right so I told you you know this
+ 
+
+ align:start position:0%
+thing right so I told you you know this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+my converter
+
+ align:start position:0%
+my converter
+ 
+
+ align:start position:0%
+my converter
+right if I wanted a periodic steady
+
+ align:start position:0%
+right if I wanted a periodic steady
+ 
+
+ align:start position:0%
+right if I wanted a periodic steady
+state model for what this thing does I
+
+ align:start position:0%
+state model for what this thing does I
+ 
+
+ align:start position:0%
+state model for what this thing does I
+have some input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage right and then I have some load
+
+ align:start position:0%
+voltage right and then I have some load
+ 
+
+ align:start position:0%
+voltage right and then I have some load
+current connected to it that I'm going
+
+ align:start position:0%
+current connected to it that I'm going
+ 
+
+ align:start position:0%
+current connected to it that I'm going
+to call I out what is the relationship
+
+ align:start position:0%
+to call I out what is the relationship
+ 
+
+ align:start position:0%
+to call I out what is the relationship
+between what's in there it's defined by
+
+ align:start position:0%
+between what's in there it's defined by
+ 
+
+ align:start position:0%
+between what's in there it's defined by
+this well here's a circuit that gives
+
+ align:start position:0%
+this well here's a circuit that gives
+ 
+
+ align:start position:0%
+this well here's a circuit that gives
+you this same relationship right if I
+
+ align:start position:0%
+you this same relationship right if I
+ 
+
+ align:start position:0%
+you this same relationship right if I
+had an ideal 2:1 transform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mer if this is VN this voltage would be
+
+ align:start position:0%
+mer if this is VN this voltage would be
+ 
+
+ align:start position:0%
+mer if this is VN this voltage would be
+half the
+
+ align:start position:0%
+half the
+ 
+
+ align:start position:0%
+half the
+in right because that's what the
+
+ align:start position:0%
+in right because that's what the
+ 
+
+ align:start position:0%
+in right because that's what the
+Transformer does and then I would have
+
+ align:start position:0%
+Transformer does and then I would have
+ 
+
+ align:start position:0%
+Transformer does and then I would have
+an equivalent
+
+ align:start position:0%
+an equivalent
+ 
+
+ align:start position:0%
+an equivalent
+resistance that would give me a voltage
+
+ align:start position:0%
+resistance that would give me a voltage
+ 
+
+ align:start position:0%
+resistance that would give me a voltage
+drop that was I out time 1 over4 F
+
+ align:start position:0%
+drop that was I out time 1 over4 F
+ 
+
+ align:start position:0%
+drop that was I out time 1 over4 F
+switch so I'd have an equivalent
+
+ align:start position:0%
+switch so I'd have an equivalent
+ 
+
+ align:start position:0%
+switch so I'd have an equivalent
+resistance of 1 over 4 F switch C
+
+ align:start position:0%
+resistance of 1 over 4 F switch C
+ 
+
+ align:start position:0%
+resistance of 1 over 4 F switch C
+okay and I could put this whole thing in
+
+ align:start position:0%
+okay and I could put this whole thing in
+ 
+
+ align:start position:0%
+okay and I could put this whole thing in
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box and this is a
+
+ align:start position:0%
+box and this is a
+ 
+
+ align:start position:0%
+box and this is a
+DC equivalent model for how this thing
+
+ align:start position:0%
+DC equivalent model for how this thing
+ 
+
+ align:start position:0%
+DC equivalent model for how this thing
+behaves right in other words this is V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so this gives me the right
+
+ align:start position:0%
+out so this gives me the right
+ 
+
+ align:start position:0%
+out so this gives me the right
+relationships between V in and V out
+
+ align:start position:0%
+relationships between V in and V out
+ 
+
+ align:start position:0%
+relationships between V in and V out
+right V out is half VN
+
+ align:start position:0%
+right V out is half VN
+ 
+
+ align:start position:0%
+right V out is half VN
+minus um
+
+ align:start position:0%
+minus um
+ 
+
+ align:start position:0%
+minus um
+minus the uh voltage drop across this
+
+ align:start position:0%
+minus the uh voltage drop across this
+ 
+
+ align:start position:0%
+minus the uh voltage drop across this
+which is I out over 4 CF
+
+ align:start position:0%
+which is I out over 4 CF
+ 
+
+ align:start position:0%
+which is I out over 4 CF
+switch likewise if I have a current
+
+ align:start position:0%
+switch likewise if I have a current
+ 
+
+ align:start position:0%
+switch likewise if I have a current
+coming I out this way the current this
+
+ align:start position:0%
+coming I out this way the current this
+ 
+
+ align:start position:0%
+coming I out this way the current this
+way through the ideal Transformer is
+
+ align:start position:0%
+way through the ideal Transformer is
+ 
+
+ align:start position:0%
+way through the ideal Transformer is
+going to be exactly half of that right
+
+ align:start position:0%
+going to be exactly half of that right
+ 
+
+ align:start position:0%
+going to be exactly half of that right
+and that means the current this way is
+
+ align:start position:0%
+and that means the current this way is
+ 
+
+ align:start position:0%
+and that means the current this way is
+minus 12 I out all right so this model
+
+ align:start position:0%
+minus 12 I out all right so this model
+ 
+
+ align:start position:0%
+minus 12 I out all right so this model
+in yellow here precisely captures the
+
+ align:start position:0%
+in yellow here precisely captures the
+ 
+
+ align:start position:0%
+in yellow here precisely captures the
+the average circuit behavior of this
+
+ align:start position:0%
+the average circuit behavior of this
+ 
+
+ align:start position:0%
+the average circuit behavior of this
+system does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody now this is this
+
+ align:start position:0%
+everybody now this is this
+ 
+
+ align:start position:0%
+everybody now this is this
+converter any other switch capacitor
+
+ align:start position:0%
+converter any other switch capacitor
+ 
+
+ align:start position:0%
+converter any other switch capacitor
+converter I want to model you can model
+
+ align:start position:0%
+converter I want to model you can model
+ 
+
+ align:start position:0%
+converter I want to model you can model
+likewise as
+
+ align:start position:0%
+likewise as
+ 
+
+ align:start position:0%
+likewise as
+some ideal Transformer
+
+ align:start position:0%
+some ideal Transformer
+ 
+
+ align:start position:0%
+some ideal Transformer
+relationship this gives me my current
+
+ align:start position:0%
+relationship this gives me my current
+ 
+
+ align:start position:0%
+relationship this gives me my current
+conversion ratio right this the the
+
+ align:start position:0%
+conversion ratio right this the the
+ 
+
+ align:start position:0%
+conversion ratio right this the the
+input and the output current are related
+
+ align:start position:0%
+input and the output current are related
+ 
+
+ align:start position:0%
+input and the output current are related
+by the ideal Transformer and then a
+
+ align:start position:0%
+by the ideal Transformer and then a
+ 
+
+ align:start position:0%
+by the ideal Transformer and then a
+voltage drop that's related by some uh
+
+ align:start position:0%
+voltage drop that's related by some uh
+ 
+
+ align:start position:0%
+voltage drop that's related by some uh
+equivalent resistance that's related to
+
+ align:start position:0%
+equivalent resistance that's related to
+ 
+
+ align:start position:0%
+equivalent resistance that's related to
+the energy transfer capacitors and the
+
+ align:start position:0%
+the energy transfer capacitors and the
+ 
+
+ align:start position:0%
+the energy transfer capacitors and the
+switching frequency okay so the details
+
+ align:start position:0%
+switching frequency okay so the details
+ 
+
+ align:start position:0%
+switching frequency okay so the details
+will vary but this model really captures
+
+ align:start position:0%
+will vary but this model really captures
+ 
+
+ align:start position:0%
+will vary but this model really captures
+what's going on okay now if I asked if I
+
+ align:start position:0%
+what's going on okay now if I asked if I
+ 
+
+ align:start position:0%
+what's going on okay now if I asked if I
+said well what's a what's an out you
+
+ align:start position:0%
+said well what's a what's an out you
+ 
+
+ align:start position:0%
+said well what's a what's an out you
+know if I wanted to just look back from
+
+ align:start position:0%
+know if I wanted to just look back from
+ 
+
+ align:start position:0%
+know if I wanted to just look back from
+the output and get a Fant equivalent
+
+ align:start position:0%
+the output and get a Fant equivalent
+ 
+
+ align:start position:0%
+the output and get a Fant equivalent
+looking backwards all I would see is
+
+ align:start position:0%
+looking backwards all I would see is
+ 
+
+ align:start position:0%
+looking backwards all I would see is
+another way to think about this is 1 12
+
+ align:start position:0%
+another way to think about this is 1 12
+ 
+
+ align:start position:0%
+another way to think about this is 1 12
+VN right is a th in voltage and the F
+
+ align:start position:0%
+VN right is a th in voltage and the F
+ 
+
+ align:start position:0%
+VN right is a th in voltage and the F
+resistance would be
+
+ align:start position:0%
+resistance would be
+ 
+
+ align:start position:0%
+resistance would be
+req is equal to 1 over4 F switch
+
+ align:start position:0%
+req is equal to 1 over4 F switch
+ 
+
+ align:start position:0%
+req is equal to 1 over4 F switch
+C okay this is a Fant equivalent look
+
+ align:start position:0%
+C okay this is a Fant equivalent look
+ 
+
+ align:start position:0%
+C okay this is a Fant equivalent look
+model looking back into the switch
+
+ align:start position:0%
+model looking back into the switch
+ 
+
+ align:start position:0%
+model looking back into the switch
+capacitor converter from some at least
+
+ align:start position:0%
+capacitor converter from some at least
+ 
+
+ align:start position:0%
+capacitor converter from some at least
+the DC this is
+
+ align:start position:0%
+the DC this is
+ 
+
+ align:start position:0%
+the DC this is
+legitimate does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody now we could say what's the
+
+ align:start position:0%
+everybody now we could say what's the
+ 
+
+ align:start position:0%
+everybody now we could say what's the
+efficiency of the
+
+ align:start position:0%
+efficiency of the
+ 
+
+ align:start position:0%
+efficiency of the
+converter okay well the
+
+ align:start position:0%
+converter okay well the
+ 
+
+ align:start position:0%
+converter okay well the
+efficiency is equal
+
+ align:start position:0%
+efficiency is equal
+ 
+
+ align:start position:0%
+efficiency is equal
+to um V out I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out divided by VN or minus VN I in right
+
+ align:start position:0%
+out divided by VN or minus VN I in right
+ 
+
+ align:start position:0%
+out divided by VN or minus VN I in right
+and since I
+
+ align:start position:0%
+and since I
+ 
+
+ align:start position:0%
+and since I
+out is
+
+ align:start position:0%
+out is
+ 
+
+ align:start position:0%
+out is
+um I out is twice minus I in this would
+
+ align:start position:0%
+um I out is twice minus I in this would
+ 
+
+ align:start position:0%
+um I out is twice minus I in this would
+be equal to
+
+ align:start position:0%
+be equal to
+ 
+
+ align:start position:0%
+be equal to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+2 time V out over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VN
+
+ align:start position:0%
+VN
+ 
+
+ align:start position:0%
+VN
+right and we have an expression for V
+
+ align:start position:0%
+right and we have an expression for V
+ 
+
+ align:start position:0%
+right and we have an expression for V
+out right here I could write this as
+
+ align:start position:0%
+out right here I could write this as
+ 
+
+ align:start position:0%
+out right here I could write this as
+also equal to V out over 12
+
+ align:start position:0%
+also equal to V out over 12
+ 
+
+ align:start position:0%
+also equal to V out over 12
+VN so to the extent that V out is
+
+ align:start position:0%
+VN so to the extent that V out is
+ 
+
+ align:start position:0%
+VN so to the extent that V out is
+smaller than half in the efficiency is
+
+ align:start position:0%
+smaller than half in the efficiency is
+ 
+
+ align:start position:0%
+smaller than half in the efficiency is
+less than one right well we can see see
+
+ align:start position:0%
+less than one right well we can see see
+ 
+
+ align:start position:0%
+less than one right well we can see see
+that the output is smaller than half in
+
+ align:start position:0%
+that the output is smaller than half in
+ 
+
+ align:start position:0%
+that the output is smaller than half in
+by whatever drop is across this
+
+ align:start position:0%
+by whatever drop is across this
+ 
+
+ align:start position:0%
+by whatever drop is across this
+resistor right so this model is actually
+
+ align:start position:0%
+resistor right so this model is actually
+ 
+
+ align:start position:0%
+resistor right so this model is actually
+useful for calculating eff this this
+
+ align:start position:0%
+useful for calculating eff this this
+ 
+
+ align:start position:0%
+useful for calculating eff this this
+model is actually useful for calculating
+
+ align:start position:0%
+model is actually useful for calculating
+ 
+
+ align:start position:0%
+model is actually useful for calculating
+efficiency as well and I could rewrite
+
+ align:start position:0%
+efficiency as well and I could rewrite
+ 
+
+ align:start position:0%
+efficiency as well and I could rewrite
+that if I plug that in what I would get
+
+ align:start position:0%
+that if I plug that in what I would get
+ 
+
+ align:start position:0%
+that if I plug that in what I would get
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um I could rewrite this as what the
+
+ align:start position:0%
+um I could rewrite this as what the
+ 
+
+ align:start position:0%
+um I could rewrite this as what the
+efficiency simply is equal to 1 minus I
+
+ align:start position:0%
+efficiency simply is equal to 1 minus I
+ 
+
+ align:start position:0%
+efficiency simply is equal to 1 minus I
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+req over
+
+ align:start position:0%
+req over
+ 
+
+ align:start position:0%
+req over
+12n okay this is just illustrating if my
+
+ align:start position:0%
+12n okay this is just illustrating if my
+ 
+
+ align:start position:0%
+12n okay this is just illustrating if my
+if my load current goes to zero the
+
+ align:start position:0%
+if my load current goes to zero the
+ 
+
+ align:start position:0%
+if my load current goes to zero the
+efficiency then goes to
+
+ align:start position:0%
+efficiency then goes to
+ 
+
+ align:start position:0%
+efficiency then goes to
+one if my load current gets really big
+
+ align:start position:0%
+one if my load current gets really big
+ 
+
+ align:start position:0%
+one if my load current gets really big
+the output droops down right as my
+
+ align:start position:0%
+the output droops down right as my
+ 
+
+ align:start position:0%
+the output droops down right as my
+output gets really big I get a bigger
+
+ align:start position:0%
+output gets really big I get a bigger
+ 
+
+ align:start position:0%
+output gets really big I get a bigger
+and bigger drop across this equivalent
+
+ align:start position:0%
+and bigger drop across this equivalent
+ 
+
+ align:start position:0%
+and bigger drop across this equivalent
+resistor and my efficiency starts to
+
+ align:start position:0%
+resistor and my efficiency starts to
+ 
+
+ align:start position:0%
+resistor and my efficiency starts to
+decline
+
+ align:start position:0%
+decline
+ 
+
+ align:start position:0%
+decline
+does that make sense everybody now when
+
+ align:start position:0%
+does that make sense everybody now when
+ 
+
+ align:start position:0%
+does that make sense everybody now when
+I'm saying this what what losses am i
+
+ align:start position:0%
+I'm saying this what what losses am i
+ 
+
+ align:start position:0%
+I'm saying this what what losses am i
+counting when I'm calculating this
+
+ align:start position:0%
+counting when I'm calculating this
+ 
+
+ align:start position:0%
+counting when I'm calculating this
+efficiency the losses I'm counting are
+
+ align:start position:0%
+efficiency the losses I'm counting are
+ 
+
+ align:start position:0%
+efficiency the losses I'm counting are
+essentially the resistor loss the losses
+
+ align:start position:0%
+essentially the resistor loss the losses
+ 
+
+ align:start position:0%
+essentially the resistor loss the losses
+in the switch resistances and in the
+
+ align:start position:0%
+in the switch resistances and in the
+ 
+
+ align:start position:0%
+in the switch resistances and in the
+Capac like any parasitics in the
+
+ align:start position:0%
+Capac like any parasitics in the
+ 
+
+ align:start position:0%
+Capac like any parasitics in the
+capacitor it's what we would call um
+
+ align:start position:0%
+capacitor it's what we would call um
+ 
+
+ align:start position:0%
+capacitor it's what we would call um
+sort of capacitor charging
+
+ align:start position:0%
+sort of capacitor charging
+ 
+
+ align:start position:0%
+sort of capacitor charging
+loss right so the only loss I'm I'm not
+
+ align:start position:0%
+loss right so the only loss I'm I'm not
+ 
+
+ align:start position:0%
+loss right so the only loss I'm I'm not
+counting like you know if these switch
+
+ align:start position:0%
+counting like you know if these switch
+ 
+
+ align:start position:0%
+counting like you know if these switch
+have gate drives and the Gate Drive gate
+
+ align:start position:0%
+have gate drives and the Gate Drive gate
+ 
+
+ align:start position:0%
+have gate drives and the Gate Drive gate
+capacit inside charge and discharge or
+
+ align:start position:0%
+capacit inside charge and discharge or
+ 
+
+ align:start position:0%
+capacit inside charge and discharge or
+other losses like that they're internal
+
+ align:start position:0%
+other losses like that they're internal
+ 
+
+ align:start position:0%
+other losses like that they're internal
+to the switches but the loss associated
+
+ align:start position:0%
+to the switches but the loss associated
+ 
+
+ align:start position:0%
+to the switches but the loss associated
+with Char the switches delivering
+
+ align:start position:0%
+with Char the switches delivering
+ 
+
+ align:start position:0%
+with Char the switches delivering
+current through to charge the capacitor
+
+ align:start position:0%
+current through to charge the capacitor
+ 
+
+ align:start position:0%
+current through to charge the capacitor
+and discharge the capacitor now it
+
+ align:start position:0%
+and discharge the capacitor now it
+ 
+
+ align:start position:0%
+and discharge the capacitor now it
+doesn't matter you notice the switch
+
+ align:start position:0%
+doesn't matter you notice the switch
+ 
+
+ align:start position:0%
+doesn't matter you notice the switch
+resistance isn't even in here anywhere
+
+ align:start position:0%
+resistance isn't even in here anywhere
+ 
+
+ align:start position:0%
+resistance isn't even in here anywhere
+it doesn't really matter what the switch
+
+ align:start position:0%
+it doesn't really matter what the switch
+ 
+
+ align:start position:0%
+it doesn't really matter what the switch
+resistance is okay the only constraint I
+
+ align:start position:0%
+resistance is okay the only constraint I
+ 
+
+ align:start position:0%
+resistance is okay the only constraint I
+have is that I have to finish charging
+
+ align:start position:0%
+have is that I have to finish charging
+ 
+
+ align:start position:0%
+have is that I have to finish charging
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+discharging okay and that's just because
+
+ align:start position:0%
+discharging okay and that's just because
+ 
+
+ align:start position:0%
+discharging okay and that's just because
+of you can do this by basically charge
+
+ align:start position:0%
+of you can do this by basically charge
+ 
+
+ align:start position:0%
+of you can do this by basically charge
+methods to to find out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+efficiency could you could you say it
+
+ align:start position:0%
+efficiency could you could you say it
+ 
+
+ align:start position:0%
+efficiency could you could you say it
+again like where the power is being
+
+ align:start position:0%
+again like where the power is being
+ 
+
+ align:start position:0%
+again like where the power is being
+dissipated the power is being
+
+ align:start position:0%
+dissipated the power is being
+ 
+
+ align:start position:0%
+dissipated the power is being
+dissipated in if if if the
+
+ align:start position:0%
+dissipated in if if if the
+ 
+
+ align:start position:0%
+dissipated in if if if the
+only elements right I mean the power is
+
+ align:start position:0%
+only elements right I mean the power is
+ 
+
+ align:start position:0%
+only elements right I mean the power is
+being dissipated in any parasitic
+
+ align:start position:0%
+being dissipated in any parasitic
+ 
+
+ align:start position:0%
+being dissipated in any parasitic
+resistance in the charge and discharge
+
+ align:start position:0%
+resistance in the charge and discharge
+ 
+
+ align:start position:0%
+resistance in the charge and discharge
+path okay so if I turn the switch on it
+
+ align:start position:0%
+path okay so if I turn the switch on it
+ 
+
+ align:start position:0%
+path okay so if I turn the switch on it
+has some voltage drop across it or if
+
+ align:start position:0%
+has some voltage drop across it or if
+ 
+
+ align:start position:0%
+has some voltage drop across it or if
+the capacitor has some parasitic
+
+ align:start position:0%
+the capacitor has some parasitic
+ 
+
+ align:start position:0%
+the capacitor has some parasitic
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+it loses some energy in that what
+
+ align:start position:0%
+it loses some energy in that what
+ 
+
+ align:start position:0%
+it loses some energy in that what
+happens you you say well what happens if
+
+ align:start position:0%
+happens you you say well what happens if
+ 
+
+ align:start position:0%
+happens you you say well what happens if
+I make my switch resistance go to zero
+
+ align:start position:0%
+I make my switch resistance go to zero
+ 
+
+ align:start position:0%
+I make my switch resistance go to zero
+well all that happens is that the peak
+
+ align:start position:0%
+well all that happens is that the peak
+ 
+
+ align:start position:0%
+well all that happens is that the peak
+charging current gets
+
+ align:start position:0%
+charging current gets
+ 
+
+ align:start position:0%
+charging current gets
+higher and it goes for a shorter time
+
+ align:start position:0%
+higher and it goes for a shorter time
+ 
+
+ align:start position:0%
+higher and it goes for a shorter time
+and the total loss is the same thing
+
+ align:start position:0%
+and the total loss is the same thing
+ 
+
+ align:start position:0%
+and the total loss is the same thing
+okay so mathematically it works out the
+
+ align:start position:0%
+okay so mathematically it works out the
+ 
+
+ align:start position:0%
+okay so mathematically it works out the
+actual value of the resistance doesn't
+
+ align:start position:0%
+actual value of the resistance doesn't
+ 
+
+ align:start position:0%
+actual value of the resistance doesn't
+matter it doesn't even matter if the
+
+ align:start position:0%
+matter it doesn't even matter if the
+ 
+
+ align:start position:0%
+matter it doesn't even matter if the
+resistance is linear or nonlinear
+
+ align:start position:0%
+resistance is linear or nonlinear
+ 
+
+ align:start position:0%
+resistance is linear or nonlinear
+um but you get the same net loss so it's
+
+ align:start position:0%
+um but you get the same net loss so it's
+ 
+
+ align:start position:0%
+um but you get the same net loss so it's
+basically the CH the loss that I incur
+
+ align:start position:0%
+basically the CH the loss that I incur
+ 
+
+ align:start position:0%
+basically the CH the loss that I incur
+in putting the Capac charge on the
+
+ align:start position:0%
+in putting the Capac charge on the
+ 
+
+ align:start position:0%
+in putting the Capac charge on the
+capacitor and then taking the charge
+
+ align:start position:0%
+capacitor and then taking the charge
+ 
+
+ align:start position:0%
+capacitor and then taking the charge
+back off to the capacitor of the output
+
+ align:start position:0%
+back off to the capacitor of the output
+ 
+
+ align:start position:0%
+back off to the capacitor of the output
+that's the loss that's
+
+ align:start position:0%
+that's the loss that's
+ 
+
+ align:start position:0%
+that's the loss that's
+included yeah so if you use a smaller
+
+ align:start position:0%
+included yeah so if you use a smaller
+ 
+
+ align:start position:0%
+included yeah so if you use a smaller
+capacitor which takes less time to
+
+ align:start position:0%
+capacitor which takes less time to
+ 
+
+ align:start position:0%
+capacitor which takes less time to
+charge and charge can you see smaller
+
+ align:start position:0%
+charge and charge can you see smaller
+ 
+
+ align:start position:0%
+charge and charge can you see smaller
+losses
+
+ align:start position:0%
+losses
+ 
+
+ align:start position:0%
+losses
+ah so if I wanted to reduce my losses
+
+ align:start position:0%
+ah so if I wanted to reduce my losses
+ 
+
+ align:start position:0%
+ah so if I wanted to reduce my losses
+let's go back and look at my efficiency
+
+ align:start position:0%
+let's go back and look at my efficiency
+ 
+
+ align:start position:0%
+let's go back and look at my efficiency
+characteristic if I want smaller losses
+
+ align:start position:0%
+characteristic if I want smaller losses
+ 
+
+ align:start position:0%
+characteristic if I want smaller losses
+I should make req small right to make R
+
+ align:start position:0%
+I should make req small right to make R
+ 
+
+ align:start position:0%
+I should make req small right to make R
+equivalent small I should make either C
+
+ align:start position:0%
+equivalent small I should make either C
+ 
+
+ align:start position:0%
+equivalent small I should make either C
+big or switching frequency big and the
+
+ align:start position:0%
+big or switching frequency big and the
+ 
+
+ align:start position:0%
+big or switching frequency big and the
+notion is and we'll come we'll come back
+
+ align:start position:0%
+notion is and we'll come we'll come back
+ 
+
+ align:start position:0%
+notion is and we'll come we'll come back
+to this and we'll look at this next
+
+ align:start position:0%
+to this and we'll look at this next
+ 
+
+ align:start position:0%
+to this and we'll look at this next
+class it's sort of comes down to the
+
+ align:start position:0%
+class it's sort of comes down to the
+ 
+
+ align:start position:0%
+class it's sort of comes down to the
+amount I'm charging and discharging the
+
+ align:start position:0%
+amount I'm charging and discharging the
+ 
+
+ align:start position:0%
+amount I'm charging and discharging the
+capacitor when I when I charge the
+
+ align:start position:0%
+capacitor when I when I charge the
+ 
+
+ align:start position:0%
+capacitor when I when I charge the
+capacitor over a small tiny Delta
+
+ align:start position:0%
+capacitor over a small tiny Delta
+ 
+
+ align:start position:0%
+capacitor over a small tiny Delta
+voltage I don't lose much energy in
+
+ align:start position:0%
+voltage I don't lose much energy in
+ 
+
+ align:start position:0%
+voltage I don't lose much energy in
+doing it and so if I want lower loss
+
+ align:start position:0%
+doing it and so if I want lower loss
+ 
+
+ align:start position:0%
+doing it and so if I want lower loss
+it's a very great Insight on your part
+
+ align:start position:0%
+it's a very great Insight on your part
+ 
+
+ align:start position:0%
+it's a very great Insight on your part
+but if I want lower loss I want to make
+
+ align:start position:0%
+but if I want lower loss I want to make
+ 
+
+ align:start position:0%
+but if I want lower loss I want to make
+the capacitor bigger are not
+
+ align:start position:0%
+the capacitor bigger are not
+ 
+
+ align:start position:0%
+the capacitor bigger are not
+smaller for a given load
+
+ align:start position:0%
+smaller for a given load
+ 
+
+ align:start position:0%
+smaller for a given load
+current okay so this
+
+ align:start position:0%
+current okay so this
+ 
+
+ align:start position:0%
+current okay so this
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+um you know I in fact if I wanted if I
+
+ align:start position:0%
+um you know I in fact if I wanted if I
+ 
+
+ align:start position:0%
+um you know I in fact if I wanted if I
+put a resistive load on here the
+
+ align:start position:0%
+put a resistive load on here the
+ 
+
+ align:start position:0%
+put a resistive load on here the
+efficiency is exactly just the
+
+ align:start position:0%
+efficiency is exactly just the
+ 
+
+ align:start position:0%
+efficiency is exactly just the
+efficiency of a voltage
+
+ align:start position:0%
+efficiency of a voltage
+ 
+
+ align:start position:0%
+efficiency of a voltage
+divider right so it's it's um this is a
+
+ align:start position:0%
+divider right so it's it's um this is a
+ 
+
+ align:start position:0%
+divider right so it's it's um this is a
+very good model and the only thing that
+
+ align:start position:0%
+very good model and the only thing that
+ 
+
+ align:start position:0%
+very good model and the only thing that
+would Mo vary if I model any other
+
+ align:start position:0%
+would Mo vary if I model any other
+ 
+
+ align:start position:0%
+would Mo vary if I model any other
+switch capacitor converter would be this
+
+ align:start position:0%
+switch capacitor converter would be this
+ 
+
+ align:start position:0%
+switch capacitor converter would be this
+Transformer ratio which relates to that
+
+ align:start position:0%
+Transformer ratio which relates to that
+ 
+
+ align:start position:0%
+Transformer ratio which relates to that
+perfect current conversion ratio we
+
+ align:start position:0%
+perfect current conversion ratio we
+ 
+
+ align:start position:0%
+perfect current conversion ratio we
+calculated and what the exact value of
+
+ align:start position:0%
+calculated and what the exact value of
+ 
+
+ align:start position:0%
+calculated and what the exact value of
+this output resistance would look like
+
+ align:start position:0%
+this output resistance would look like
+ 
+
+ align:start position:0%
+this output resistance would look like
+okay which is again dictated by the
+
+ align:start position:0%
+okay which is again dictated by the
+ 
+
+ align:start position:0%
+okay which is again dictated by the
+losses okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so let's think about
+
+ align:start position:0%
+so let's think about
+ 
+
+ align:start position:0%
+so let's think about
+um what
+
+ align:start position:0%
+um what
+ 
+
+ align:start position:0%
+um what
+other uh case I might consider we said
+
+ align:start position:0%
+other uh case I might consider we said
+ 
+
+ align:start position:0%
+other uh case I might consider we said
+okay suppose I want to and by the way
+
+ align:start position:0%
+okay suppose I want to and by the way
+ 
+
+ align:start position:0%
+okay suppose I want to and by the way
+why do we like these converters because
+
+ align:start position:0%
+why do we like these converters because
+ 
+
+ align:start position:0%
+why do we like these converters because
+they can be hyper efficient if I go buy
+
+ align:start position:0%
+they can be hyper efficient if I go buy
+ 
+
+ align:start position:0%
+they can be hyper efficient if I go buy
+a a really big capacitor
+
+ align:start position:0%
+a a really big capacitor
+ 
+
+ align:start position:0%
+a a really big capacitor
+here or I switch really fast this
+
+ align:start position:0%
+here or I switch really fast this
+ 
+
+ align:start position:0%
+here or I switch really fast this
+equivalent resistance can be very small
+
+ align:start position:0%
+equivalent resistance can be very small
+ 
+
+ align:start position:0%
+equivalent resistance can be very small
+and I can get an almost perfect 2:1
+
+ align:start position:0%
+and I can get an almost perfect 2:1
+ 
+
+ align:start position:0%
+and I can get an almost perfect 2:1
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+conversion okay and in fact people would
+
+ align:start position:0%
+conversion okay and in fact people would
+ 
+
+ align:start position:0%
+conversion okay and in fact people would
+call this thing a two to two to one step
+
+ align:start position:0%
+call this thing a two to two to one step
+ 
+
+ align:start position:0%
+call this thing a two to two to one step
+down switch capacitor converter why
+
+ align:start position:0%
+down switch capacitor converter why
+ 
+
+ align:start position:0%
+down switch capacitor converter why
+because they're thinking of the voltage
+
+ align:start position:0%
+because they're thinking of the voltage
+ 
+
+ align:start position:0%
+because they're thinking of the voltage
+right the the ideally speaking if I make
+
+ align:start position:0%
+right the the ideally speaking if I make
+ 
+
+ align:start position:0%
+right the the ideally speaking if I make
+this resist really small I'm really just
+
+ align:start position:0%
+this resist really small I'm really just
+ 
+
+ align:start position:0%
+this resist really small I'm really just
+doing sort of like an ideal Transformer
+
+ align:start position:0%
+doing sort of like an ideal Transformer
+ 
+
+ align:start position:0%
+doing sort of like an ideal Transformer
+2:
+
+ align:start position:0%
+2:
+ 
+
+ align:start position:0%
+2:
+one okay and so people would call that a
+
+ align:start position:0%
+one okay and so people would call that a
+ 
+
+ align:start position:0%
+one okay and so people would call that a
+2:1 on the other hand it's only
+
+ align:start position:0%
+2:1 on the other hand it's only
+ 
+
+ align:start position:0%
+2:1 on the other hand it's only
+approximately two: one because this is
+
+ align:start position:0%
+approximately two: one because this is
+ 
+
+ align:start position:0%
+approximately two: one because this is
+not zero this is some finite value of
+
+ align:start position:0%
+not zero this is some finite value of
+ 
+
+ align:start position:0%
+not zero this is some finite value of
+resistance what it is is a one to2
+
+ align:start position:0%
+resistance what it is is a one to2
+ 
+
+ align:start position:0%
+resistance what it is is a one to2
+current converter switch capacitor
+
+ align:start position:0%
+current converter switch capacitor
+ 
+
+ align:start position:0%
+current converter switch capacitor
+converter and that relationship is
+
+ align:start position:0%
+converter and that relationship is
+ 
+
+ align:start position:0%
+converter and that relationship is
+precise right so you know what should
+
+ align:start position:0%
+precise right so you know what should
+ 
+
+ align:start position:0%
+precise right so you know what should
+people call this they should call this a
+
+ align:start position:0%
+people call this they should call this a
+ 
+
+ align:start position:0%
+people call this they should call this a
+one to two current conversion switch
+
+ align:start position:0%
+one to two current conversion switch
+ 
+
+ align:start position:0%
+one to two current conversion switch
+capacitor converter but that's not what
+
+ align:start position:0%
+capacitor converter but that's not what
+ 
+
+ align:start position:0%
+capacitor converter but that's not what
+they call it they call it a two to1
+
+ align:start position:0%
+they call it they call it a two to1
+ 
+
+ align:start position:0%
+they call it they call it a two to1
+voltage converter because everybody
+
+ align:start position:0%
+voltage converter because everybody
+ 
+
+ align:start position:0%
+voltage converter because everybody
+likes to think about voltages okay so
+
+ align:start position:0%
+likes to think about voltages okay so
+ 
+
+ align:start position:0%
+likes to think about voltages okay so
+it's just you're stuck with the you're
+
+ align:start position:0%
+it's just you're stuck with the you're
+ 
+
+ align:start position:0%
+it's just you're stuck with the you're
+stuck with what people call things but
+
+ align:start position:0%
+stuck with what people call things but
+ 
+
+ align:start position:0%
+stuck with what people call things but
+maybe it's not fair um so what do I get
+
+ align:start position:0%
+maybe it's not fair um so what do I get
+ 
+
+ align:start position:0%
+maybe it's not fair um so what do I get
+um if I wanted to
+
+ align:start position:0%
+um if I wanted to
+ 
+
+ align:start position:0%
+um if I wanted to
+um go up in performance suppose I want
+
+ align:start position:0%
+um go up in performance suppose I want
+ 
+
+ align:start position:0%
+um go up in performance suppose I want
+so so when would I I should say when
+
+ align:start position:0%
+so so when would I I should say when
+ 
+
+ align:start position:0%
+so so when would I I should say when
+would I want to use a switch capacitor
+
+ align:start position:0%
+would I want to use a switch capacitor
+ 
+
+ align:start position:0%
+would I want to use a switch capacitor
+converter I'd want use switch capacitor
+
+ align:start position:0%
+converter I'd want use switch capacitor
+ 
+
+ align:start position:0%
+converter I'd want use switch capacitor
+converter for so for example I have you
+
+ align:start position:0%
+converter for so for example I have you
+ 
+
+ align:start position:0%
+converter for so for example I have you
+know 5 volts and I need 2.5 volts right
+
+ align:start position:0%
+know 5 volts and I need 2.5 volts right
+ 
+
+ align:start position:0%
+know 5 volts and I need 2.5 volts right
+I want exactly half the
+
+ align:start position:0%
+I want exactly half the
+ 
+
+ align:start position:0%
+I want exactly half the
+voltage then to the extent that I can
+
+ align:start position:0%
+voltage then to the extent that I can
+ 
+
+ align:start position:0%
+voltage then to the extent that I can
+make this equivalent resistance small
+
+ align:start position:0%
+make this equivalent resistance small
+ 
+
+ align:start position:0%
+make this equivalent resistance small
+this is a great converter on the other
+
+ align:start position:0%
+this is a great converter on the other
+ 
+
+ align:start position:0%
+this is a great converter on the other
+hand I wouldn't want to use this
+
+ align:start position:0%
+hand I wouldn't want to use this
+ 
+
+ align:start position:0%
+hand I wouldn't want to use this
+converter when my input voltage was 5
+
+ align:start position:0%
+converter when my input voltage was 5
+ 
+
+ align:start position:0%
+converter when my input voltage was 5
+volts and my output voltage was 2
+
+ align:start position:0%
+volts and my output voltage was 2
+ 
+
+ align:start position:0%
+volts and my output voltage was 2
+volts right because then my efficiency
+
+ align:start position:0%
+volts right because then my efficiency
+ 
+
+ align:start position:0%
+volts right because then my efficiency
+would be two 2 over 2.5 which isn't that
+
+ align:start position:0%
+would be two 2 over 2.5 which isn't that
+ 
+
+ align:start position:0%
+would be two 2 over 2.5 which isn't that
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+right so uh switch capacitors or
+
+ align:start position:0%
+right so uh switch capacitors or
+ 
+
+ align:start position:0%
+right so uh switch capacitors or
+converters are very efficient when your
+
+ align:start position:0%
+converters are very efficient when your
+ 
+
+ align:start position:0%
+converters are very efficient when your
+voltage conversion ratio is very close
+
+ align:start position:0%
+voltage conversion ratio is very close
+ 
+
+ align:start position:0%
+voltage conversion ratio is very close
+to the inverse of your intrinsic current
+
+ align:start position:0%
+to the inverse of your intrinsic current
+ 
+
+ align:start position:0%
+to the inverse of your intrinsic current
+conversion ratio and then their
+
+ align:start position:0%
+conversion ratio and then their
+ 
+
+ align:start position:0%
+conversion ratio and then their
+efficiency droops down outside of that
+
+ align:start position:0%
+efficiency droops down outside of that
+ 
+
+ align:start position:0%
+efficiency droops down outside of that
+range sometimes actually people use this
+
+ align:start position:0%
+range sometimes actually people use this
+ 
+
+ align:start position:0%
+range sometimes actually people use this
+and Vary this equivalent resistor to
+
+ align:start position:0%
+and Vary this equivalent resistor to
+ 
+
+ align:start position:0%
+and Vary this equivalent resistor to
+give yourself a linear regulator kind of
+
+ align:start position:0%
+give yourself a linear regulator kind of
+ 
+
+ align:start position:0%
+give yourself a linear regulator kind of
+action too so but instead of linear
+
+ align:start position:0%
+action too so but instead of linear
+ 
+
+ align:start position:0%
+action too so but instead of linear
+regulating down from VN you linear
+
+ align:start position:0%
+regulating down from VN you linear
+ 
+
+ align:start position:0%
+regulating down from VN you linear
+regulate down from half VN so you get an
+
+ align:start position:0%
+regulate down from half VN so you get an
+ 
+
+ align:start position:0%
+regulate down from half VN so you get an
+advantage that way but if you want to
+
+ align:start position:0%
+advantage that way but if you want to
+ 
+
+ align:start position:0%
+advantage that way but if you want to
+talk about pure switch mode operation
+
+ align:start position:0%
+talk about pure switch mode operation
+ 
+
+ align:start position:0%
+talk about pure switch mode operation
+you're usually trying to make this very
+
+ align:start position:0%
+you're usually trying to make this very
+ 
+
+ align:start position:0%
+you're usually trying to make this very
+small how do I make that small I either
+
+ align:start position:0%
+small how do I make that small I either
+ 
+
+ align:start position:0%
+small how do I make that small I either
+get big capacitors or I switch fast okay
+
+ align:start position:0%
+get big capacitors or I switch fast okay
+ 
+
+ align:start position:0%
+get big capacitors or I switch fast okay
+now there's an exception to what I
+
+ align:start position:0%
+now there's an exception to what I
+ 
+
+ align:start position:0%
+now there's an exception to what I
+said uh or a limit to what I said this
+
+ align:start position:0%
+said uh or a limit to what I said this
+ 
+
+ align:start position:0%
+said uh or a limit to what I said this
+operation is all in what I'm calling the
+
+ align:start position:0%
+operation is all in what I'm calling the
+ 
+
+ align:start position:0%
+operation is all in what I'm calling the
+what I've been calling the slow
+
+ align:start position:0%
+what I've been calling the slow
+ 
+
+ align:start position:0%
+what I've been calling the slow
+switching limit right this limit right
+
+ align:start position:0%
+switching limit right this limit right
+ 
+
+ align:start position:0%
+switching limit right this limit right
+here where I'm fully charging and fully
+
+ align:start position:0%
+here where I'm fully charging and fully
+ 
+
+ align:start position:0%
+here where I'm fully charging and fully
+discharging if I suppose I want to get
+
+ align:start position:0%
+discharging if I suppose I want to get
+ 
+
+ align:start position:0%
+discharging if I suppose I want to get
+higher efficiency and I'm for I'm
+
+ align:start position:0%
+higher efficiency and I'm for I'm
+ 
+
+ align:start position:0%
+higher efficiency and I'm for I'm
+forgetting about gate losses and
+
+ align:start position:0%
+forgetting about gate losses and
+ 
+
+ align:start position:0%
+forgetting about gate losses and
+capacitor discharge losses and stuff
+
+ align:start position:0%
+capacitor discharge losses and stuff
+ 
+
+ align:start position:0%
+capacitor discharge losses and stuff
+inside the switches I'm just talking
+
+ align:start position:0%
+inside the switches I'm just talking
+ 
+
+ align:start position:0%
+inside the switches I'm just talking
+about the charge transfer losses I can
+
+ align:start position:0%
+about the charge transfer losses I can
+ 
+
+ align:start position:0%
+about the charge transfer losses I can
+switch faster and faster and faster that
+
+ align:start position:0%
+switch faster and faster and faster that
+ 
+
+ align:start position:0%
+switch faster and faster and faster that
+output resistance keeps drooping right
+
+ align:start position:0%
+output resistance keeps drooping right
+ 
+
+ align:start position:0%
+output resistance keeps drooping right
+keeps getting smaller and that's better
+
+ align:start position:0%
+keeps getting smaller and that's better
+ 
+
+ align:start position:0%
+keeps getting smaller and that's better
+but eventually I get to the point where
+
+ align:start position:0%
+but eventually I get to the point where
+ 
+
+ align:start position:0%
+but eventually I get to the point where
+if I increase my switching frequency
+
+ align:start position:0%
+if I increase my switching frequency
+ 
+
+ align:start position:0%
+if I increase my switching frequency
+suppose I just keep each time period
+
+ align:start position:0%
+suppose I just keep each time period
+ 
+
+ align:start position:0%
+suppose I just keep each time period
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+that this time period is going to get so
+
+ align:start position:0%
+that this time period is going to get so
+ 
+
+ align:start position:0%
+that this time period is going to get so
+short that my capacitor doesn't fully
+
+ align:start position:0%
+short that my capacitor doesn't fully
+ 
+
+ align:start position:0%
+short that my capacitor doesn't fully
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+up and he doesn't fully charge down
+
+ align:start position:0%
+up and he doesn't fully charge down
+ 
+
+ align:start position:0%
+up and he doesn't fully charge down
+right if I keep pushing my switching
+
+ align:start position:0%
+right if I keep pushing my switching
+ 
+
+ align:start position:0%
+right if I keep pushing my switching
+frequency up enough I'm going to violate
+
+ align:start position:0%
+frequency up enough I'm going to violate
+ 
+
+ align:start position:0%
+frequency up enough I'm going to violate
+the Assumption under which I did this
+
+ align:start position:0%
+the Assumption under which I did this
+ 
+
+ align:start position:0%
+the Assumption under which I did this
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+okay the extreme limit of that is the
+
+ align:start position:0%
+okay the extreme limit of that is the
+ 
+
+ align:start position:0%
+okay the extreme limit of that is the
+capacitor sitting close to some voltage
+
+ align:start position:0%
+capacitor sitting close to some voltage
+ 
+
+ align:start position:0%
+capacitor sitting close to some voltage
+and he only charges up and down a
+
+ align:start position:0%
+and he only charges up and down a
+ 
+
+ align:start position:0%
+and he only charges up and down a
+little right so in other words suppose I
+
+ align:start position:0%
+little right so in other words suppose I
+ 
+
+ align:start position:0%
+little right so in other words suppose I
+made my time scale really short and I
+
+ align:start position:0%
+made my time scale really short and I
+ 
+
+ align:start position:0%
+made my time scale really short and I
+will have you know here State one and
+
+ align:start position:0%
+will have you know here State one and
+ 
+
+ align:start position:0%
+will have you know here State one and
+here state
+
+ align:start position:0%
+here state
+ 
+
+ align:start position:0%
+here state
+two right and in state one he just does
+
+ align:start position:0%
+two right and in state one he just does
+ 
+
+ align:start position:0%
+two right and in state one he just does
+this he charges a tiny bit which is part
+
+ align:start position:0%
+this he charges a tiny bit which is part
+ 
+
+ align:start position:0%
+this he charges a tiny bit which is part
+of a much
+
+ align:start position:0%
+of a much
+ 
+
+ align:start position:0%
+of a much
+bigger RC
+
+ align:start position:0%
+bigger RC
+ 
+
+ align:start position:0%
+bigger RC
+charge and then in state two he
+
+ align:start position:0%
+charge and then in state two he
+ 
+
+ align:start position:0%
+charge and then in state two he
+discharges just a tiny
+
+ align:start position:0%
+discharges just a tiny
+ 
+
+ align:start position:0%
+discharges just a tiny
+bit which is part of a muchow longer RC
+
+ align:start position:0%
+bit which is part of a muchow longer RC
+ 
+
+ align:start position:0%
+bit which is part of a muchow longer RC
+time time charge right so I can almost
+
+ align:start position:0%
+time time charge right so I can almost
+ 
+
+ align:start position:0%
+time time charge right so I can almost
+think in the fast switching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit VC is almost
+
+ align:start position:0%
+limit VC is almost
+ 
+
+ align:start position:0%
+limit VC is almost
+constant right I don't have enough time
+
+ align:start position:0%
+constant right I don't have enough time
+ 
+
+ align:start position:0%
+constant right I don't have enough time
+to charge up or down substantially the
+
+ align:start position:0%
+to charge up or down substantially the
+ 
+
+ align:start position:0%
+to charge up or down substantially the
+Delta voltage I get is nowhere near the
+
+ align:start position:0%
+Delta voltage I get is nowhere near the
+ 
+
+ align:start position:0%
+Delta voltage I get is nowhere near the
+full
+
+ align:start position:0%
+full
+ 
+
+ align:start position:0%
+full
+swing okay and I can just start to think
+
+ align:start position:0%
+swing okay and I can just start to think
+ 
+
+ align:start position:0%
+swing okay and I can just start to think
+about the capacitor as being at constant
+
+ align:start position:0%
+about the capacitor as being at constant
+ 
+
+ align:start position:0%
+about the capacitor as being at constant
+voltage okay okay but it's a special
+
+ align:start position:0%
+voltage okay okay but it's a special
+ 
+
+ align:start position:0%
+voltage okay okay but it's a special
+constant voltage because nonetheless if
+
+ align:start position:0%
+constant voltage because nonetheless if
+ 
+
+ align:start position:0%
+constant voltage because nonetheless if
+I'm going to be in periodic steady state
+
+ align:start position:0%
+I'm going to be in periodic steady state
+ 
+
+ align:start position:0%
+I'm going to be in periodic steady state
+however much he charges in the first
+
+ align:start position:0%
+however much he charges in the first
+ 
+
+ align:start position:0%
+however much he charges in the first
+state must balance the Char amount of
+
+ align:start position:0%
+state must balance the Char amount of
+ 
+
+ align:start position:0%
+state must balance the Char amount of
+discharges in the second state right
+
+ align:start position:0%
+discharges in the second state right
+ 
+
+ align:start position:0%
+discharges in the second state right
+that I haven't gotten around that kind
+
+ align:start position:0%
+that I haven't gotten around that kind
+ 
+
+ align:start position:0%
+that I haven't gotten around that kind
+of rule uh but nonetheless we can think
+
+ align:start position:0%
+of rule uh but nonetheless we can think
+ 
+
+ align:start position:0%
+of rule uh but nonetheless we can think
+about this fast switching limit as the
+
+ align:start position:0%
+about this fast switching limit as the
+ 
+
+ align:start position:0%
+about this fast switching limit as the
+capacitor voltage almost becoming
+
+ align:start position:0%
+capacitor voltage almost becoming
+ 
+
+ align:start position:0%
+capacitor voltage almost becoming
+constant right so let's think about what
+
+ align:start position:0%
+constant right so let's think about what
+ 
+
+ align:start position:0%
+constant right so let's think about what
+would a converter do in the fast
+
+ align:start position:0%
+would a converter do in the fast
+ 
+
+ align:start position:0%
+would a converter do in the fast
+switching limit in the FSL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um in state so so let me just think
+
+ align:start position:0%
+um in state so so let me just think
+ 
+
+ align:start position:0%
+um in state so so let me just think
+about I'm going to no now mentally
+
+ align:start position:0%
+about I'm going to no now mentally
+ 
+
+ align:start position:0%
+about I'm going to no now mentally
+replace this capacitor with just a fixed
+
+ align:start position:0%
+replace this capacitor with just a fixed
+ 
+
+ align:start position:0%
+replace this capacitor with just a fixed
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+VC and in this other state he's also
+
+ align:start position:0%
+VC and in this other state he's also
+ 
+
+ align:start position:0%
+VC and in this other state he's also
+going to be a fixed voltage VC and the
+
+ align:start position:0%
+going to be a fixed voltage VC and the
+ 
+
+ align:start position:0%
+going to be a fixed voltage VC and the
+only thing I need is the net charge that
+
+ align:start position:0%
+only thing I need is the net charge that
+ 
+
+ align:start position:0%
+only thing I need is the net charge that
+goes into VC over a cycle to be zero
+
+ align:start position:0%
+goes into VC over a cycle to be zero
+ 
+
+ align:start position:0%
+goes into VC over a cycle to be zero
+right so how much charge do I transfer
+
+ align:start position:0%
+right so how much charge do I transfer
+ 
+
+ align:start position:0%
+right so how much charge do I transfer
+in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay and I'm going to do FSL with
+
+ align:start position:0%
+one okay and I'm going to do FSL with
+ 
+
+ align:start position:0%
+one okay and I'm going to do FSL with
+50% Duty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ratio in other words I'm going to assume
+
+ align:start position:0%
+ratio in other words I'm going to assume
+ 
+
+ align:start position:0%
+ratio in other words I'm going to assume
+that in state one I spend half a period
+
+ align:start position:0%
+that in state one I spend half a period
+ 
+
+ align:start position:0%
+that in state one I spend half a period
+and state two I'm going to spend half a
+
+ align:start position:0%
+and state two I'm going to spend half a
+ 
+
+ align:start position:0%
+and state two I'm going to spend half a
+period um because in the FSL the fast
+
+ align:start position:0%
+period um because in the FSL the fast
+ 
+
+ align:start position:0%
+period um because in the FSL the fast
+switching limit how much time I spend in
+
+ align:start position:0%
+switching limit how much time I spend in
+ 
+
+ align:start position:0%
+switching limit how much time I spend in
+the two and States matters but let's
+
+ align:start position:0%
+the two and States matters but let's
+ 
+
+ align:start position:0%
+the two and States matters but let's
+just assume I'm going to spend half in
+
+ align:start position:0%
+just assume I'm going to spend half in
+ 
+
+ align:start position:0%
+just assume I'm going to spend half in
+each state for purposes of this analysis
+
+ align:start position:0%
+each state for purposes of this analysis
+ 
+
+ align:start position:0%
+each state for purposes of this analysis
+so in state one what do I get for Delta
+
+ align:start position:0%
+so in state one what do I get for Delta
+ 
+
+ align:start position:0%
+so in state one what do I get for Delta
+qc1 okay well Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qc1 is going to be what I'm going to say
+
+ align:start position:0%
+qc1 is going to be what I'm going to say
+ 
+
+ align:start position:0%
+qc1 is going to be what I'm going to say
+all right if he's a constant voltage I'm
+
+ align:start position:0%
+all right if he's a constant voltage I'm
+ 
+
+ align:start position:0%
+all right if he's a constant voltage I'm
+going to get a current that's going to
+
+ align:start position:0%
+going to get a current that's going to
+ 
+
+ align:start position:0%
+going to get a current that's going to
+be V in minus v c minus V out divid 2
+
+ align:start position:0%
+be V in minus v c minus V out divid 2
+ 
+
+ align:start position:0%
+be V in minus v c minus V out divid 2
+our switch right that's the current
+
+ align:start position:0%
+our switch right that's the current
+ 
+
+ align:start position:0%
+our switch right that's the current
+current in state one so that's going to
+
+ align:start position:0%
+current in state one so that's going to
+ 
+
+ align:start position:0%
+current in state one so that's going to
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+VN minus VC minus V
+
+ align:start position:0%
+VN minus VC minus V
+ 
+
+ align:start position:0%
+VN minus VC minus V
+out divided by 2 R
+
+ align:start position:0%
+out divided by 2 R
+ 
+
+ align:start position:0%
+out divided by 2 R
+switch and that's going to happen for
+
+ align:start position:0%
+switch and that's going to happen for
+ 
+
+ align:start position:0%
+switch and that's going to happen for
+how long that's going to happen
+
+ align:start position:0%
+how long that's going to happen
+ 
+
+ align:start position:0%
+how long that's going to happen
+Fort or I could write that as 1 over 2f
+
+ align:start position:0%
+Fort or I could write that as 1 over 2f
+ 
+
+ align:start position:0%
+Fort or I could write that as 1 over 2f
+switch right this is times half a
+
+ align:start position:0%
+switch right this is times half a
+ 
+
+ align:start position:0%
+switch right this is times half a
+period okay what is Delta Q
+
+ align:start position:0%
+period okay what is Delta Q
+ 
+
+ align:start position:0%
+period okay what is Delta Q
+in1 look like that's just going to be
+
+ align:start position:0%
+in1 look like that's just going to be
+ 
+
+ align:start position:0%
+in1 look like that's just going to be
+minus Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qc1 and what's Delta qn 2 look like
+
+ align:start position:0%
+qc1 and what's Delta qn 2 look like
+ 
+
+ align:start position:0%
+qc1 and what's Delta qn 2 look like
+that's just going to be equal to uh
+
+ align:start position:0%
+that's just going to be equal to uh
+ 
+
+ align:start position:0%
+that's just going to be equal to uh
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+qc1 right other words all I'm saying is
+
+ align:start position:0%
+qc1 right other words all I'm saying is
+ 
+
+ align:start position:0%
+qc1 right other words all I'm saying is
+that here the input got the negative of
+
+ align:start position:0%
+that here the input got the negative of
+ 
+
+ align:start position:0%
+that here the input got the negative of
+the charge of the capacitor and the
+
+ align:start position:0%
+the charge of the capacitor and the
+ 
+
+ align:start position:0%
+the charge of the capacitor and the
+output got the charge that went through
+
+ align:start position:0%
+output got the charge that went through
+ 
+
+ align:start position:0%
+output got the charge that went through
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+capacitor make sense to everybody
+
+ align:start position:0%
+capacitor make sense to everybody
+ 
+
+ align:start position:0%
+capacitor make sense to everybody
+if I if I do this for state
+
+ align:start position:0%
+if I if I do this for state
+ 
+
+ align:start position:0%
+if I if I do this for state
+two okay state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two right what I'm going to get is Delta
+
+ align:start position:0%
+two right what I'm going to get is Delta
+ 
+
+ align:start position:0%
+two right what I'm going to get is Delta
+QC 2 is simply going to be what it's
+
+ align:start position:0%
+QC 2 is simply going to be what it's
+ 
+
+ align:start position:0%
+QC 2 is simply going to be what it's
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+um V out minus VC over 2R switch right
+
+ align:start position:0%
+um V out minus VC over 2R switch right
+ 
+
+ align:start position:0%
+um V out minus VC over 2R switch right
+or it's going to be be
+
+ align:start position:0%
+or it's going to be be
+ 
+
+ align:start position:0%
+or it's going to be be
+um V out minus VC over two our switch
+
+ align:start position:0%
+um V out minus VC over two our switch
+ 
+
+ align:start position:0%
+um V out minus VC over two our switch
+we're going to it's going to be
+
+ align:start position:0%
+we're going to it's going to be
+ 
+
+ align:start position:0%
+we're going to it's going to be
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+uh VC minus V out over 2 R switch times
+
+ align:start position:0%
+uh VC minus V out over 2 R switch times
+ 
+
+ align:start position:0%
+uh VC minus V out over 2 R switch times
+1 over 2f
+
+ align:start position:0%
+1 over 2f
+ 
+
+ align:start position:0%
+1 over 2f
+switch right Delta
+
+ align:start position:0%
+switch right Delta
+ 
+
+ align:start position:0%
+switch right Delta
+Q in two is going to be zero and Delta Q
+
+ align:start position:0%
+Q in two is going to be zero and Delta Q
+ 
+
+ align:start position:0%
+Q in two is going to be zero and Delta Q
+out2 is going to be equal to the
+
+ align:start position:0%
+out2 is going to be equal to the
+ 
+
+ align:start position:0%
+out2 is going to be equal to the
+negative of this which is going to be
+
+ align:start position:0%
+negative of this which is going to be
+ 
+
+ align:start position:0%
+negative of this which is going to be
+minus Delta QC 2 does that make sense
+
+ align:start position:0%
+minus Delta QC 2 does that make sense
+ 
+
+ align:start position:0%
+minus Delta QC 2 does that make sense
+everybody yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+em yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that's what happens when I Rush thank
+
+ align:start position:0%
+uh that's what happens when I Rush thank
+ 
+
+ align:start position:0%
+uh that's what happens when I Rush thank
+you all
+
+ align:start position:0%
+you all
+ 
+
+ align:start position:0%
+you all
+right um what constraint do I get off of
+
+ align:start position:0%
+right um what constraint do I get off of
+ 
+
+ align:start position:0%
+right um what constraint do I get off of
+this well what I need is Delta QC of 1
+
+ align:start position:0%
+this well what I need is Delta QC of 1
+ 
+
+ align:start position:0%
+this well what I need is Delta QC of 1
+plus Delta QC of 2 have to add up to
+
+ align:start position:0%
+plus Delta QC of 2 have to add up to
+ 
+
+ align:start position:0%
+plus Delta QC of 2 have to add up to
+zero right I mean that's a that's a
+
+ align:start position:0%
+zero right I mean that's a that's a
+ 
+
+ align:start position:0%
+zero right I mean that's a that's a
+constraint for periodic steady state
+
+ align:start position:0%
+constraint for periodic steady state
+ 
+
+ align:start position:0%
+constraint for periodic steady state
+right so what I get is for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PSS um what I get is Delta Delta QC of 1
+
+ align:start position:0%
+PSS um what I get is Delta Delta QC of 1
+ 
+
+ align:start position:0%
+PSS um what I get is Delta Delta QC of 1
+plus Delta QC for 2 is equal to zero
+
+ align:start position:0%
+plus Delta QC for 2 is equal to zero
+ 
+
+ align:start position:0%
+plus Delta QC for 2 is equal to zero
+which gives me um I can ignore the one
+
+ align:start position:0%
+which gives me um I can ignore the one
+ 
+
+ align:start position:0%
+which gives me um I can ignore the one
+over4 F switch R switch that gives me V
+
+ align:start position:0%
+over4 F switch R switch that gives me V
+ 
+
+ align:start position:0%
+over4 F switch R switch that gives me V
+in minus VC minus V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+um V out minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VC plus v out minus VC is equal to
+
+ align:start position:0%
+VC plus v out minus VC is equal to
+ 
+
+ align:start position:0%
+VC plus v out minus VC is equal to
+zero okay and what this gives me is that
+
+ align:start position:0%
+zero okay and what this gives me is that
+ 
+
+ align:start position:0%
+zero okay and what this gives me is that
+um VC is going to be half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VN so in periodic steady state I'm going
+
+ align:start position:0%
+VN so in periodic steady state I'm going
+ 
+
+ align:start position:0%
+VN so in periodic steady state I'm going
+to be charging and discharging the
+
+ align:start position:0%
+to be charging and discharging the
+ 
+
+ align:start position:0%
+to be charging and discharging the
+capacitor but he's going to sit in an
+
+ align:start position:0%
+capacitor but he's going to sit in an
+ 
+
+ align:start position:0%
+capacitor but he's going to sit in an
+average value of half
+
+ align:start position:0%
+average value of half
+ 
+
+ align:start position:0%
+average value of half
+VM okay I can then go and plug this
+
+ align:start position:0%
+VM okay I can then go and plug this
+ 
+
+ align:start position:0%
+VM okay I can then go and plug this
+value back in and I'm kind of running
+
+ align:start position:0%
+value back in and I'm kind of running
+ 
+
+ align:start position:0%
+value back in and I'm kind of running
+out of time here I can go plug this back
+
+ align:start position:0%
+out of time here I can go plug this back
+ 
+
+ align:start position:0%
+out of time here I can go plug this back
+in and find Q out one and Q in one right
+
+ align:start position:0%
+in and find Q out one and Q in one right
+ 
+
+ align:start position:0%
+in and find Q out one and Q in one right
+I can do the same game I do over here
+
+ align:start position:0%
+I can do the same game I do over here
+ 
+
+ align:start position:0%
+I can do the same game I do over here
+and um if you do that
+
+ align:start position:0%
+and um if you do that
+ 
+
+ align:start position:0%
+and um if you do that
+calculation it's it's pretty easy I can
+
+ align:start position:0%
+calculation it's it's pretty easy I can
+ 
+
+ align:start position:0%
+calculation it's it's pretty easy I can
+calculate I out as being the sum of q1 Q
+
+ align:start position:0%
+calculate I out as being the sum of q1 Q
+ 
+
+ align:start position:0%
+calculate I out as being the sum of q1 Q
+in and Q out and what I get is V
+
+ align:start position:0%
+in and Q out and what I get is V
+ 
+
+ align:start position:0%
+in and Q out and what I get is V
+out is equal to 12
+
+ align:start position:0%
+out is equal to 12
+ 
+
+ align:start position:0%
+out is equal to 12
+VN
+
+ align:start position:0%
+VN
+ 
+
+ align:start position:0%
+VN
+minus uh 2 R switch I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay so it's of the exact same
+
+ align:start position:0%
+out okay so it's of the exact same
+ 
+
+ align:start position:0%
+out okay so it's of the exact same
+format
+
+ align:start position:0%
+format
+ 
+
+ align:start position:0%
+format
+that I had up
+
+ align:start position:0%
+that I had up
+ 
+
+ align:start position:0%
+that I had up
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+here I get this in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SSL and in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FSL in the
+
+ align:start position:0%
+FSL in the
+ 
+
+ align:start position:0%
+FSL in the
+FSL maybe I should use a different
+
+ align:start position:0%
+FSL maybe I should use a different
+ 
+
+ align:start position:0%
+FSL maybe I should use a different
+color in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FSL
+
+ align:start position:0%
+FSL
+ 
+
+ align:start position:0%
+FSL
+req is simply equal to 2R switch
+
+ align:start position:0%
+req is simply equal to 2R switch
+ 
+
+ align:start position:0%
+req is simply equal to 2R switch
+okay well that actually kind of feels
+
+ align:start position:0%
+okay well that actually kind of feels
+ 
+
+ align:start position:0%
+okay well that actually kind of feels
+good in some sense because you think
+
+ align:start position:0%
+good in some sense because you think
+ 
+
+ align:start position:0%
+good in some sense because you think
+about it in either of these two states
+
+ align:start position:0%
+about it in either of these two states
+ 
+
+ align:start position:0%
+about it in either of these two states
+I'm always dumping
+
+ align:start position:0%
+I'm always dumping
+ 
+
+ align:start position:0%
+I'm always dumping
+current through two
+
+ align:start position:0%
+current through two
+ 
+
+ align:start position:0%
+current through two
+switches right so so you know half the
+
+ align:start position:0%
+switches right so so you know half the
+ 
+
+ align:start position:0%
+switches right so so you know half the
+time I'm doing in this configuration
+
+ align:start position:0%
+time I'm doing in this configuration
+ 
+
+ align:start position:0%
+time I'm doing in this configuration
+half the time in that configuration but
+
+ align:start position:0%
+half the time in that configuration but
+ 
+
+ align:start position:0%
+half the time in that configuration but
+if I think of the capacitor current as
+
+ align:start position:0%
+if I think of the capacitor current as
+ 
+
+ align:start position:0%
+if I think of the capacitor current as
+being sort of a plus and minus Square
+
+ align:start position:0%
+being sort of a plus and minus Square
+ 
+
+ align:start position:0%
+being sort of a plus and minus Square
+wave of
+
+ align:start position:0%
+wave of
+ 
+
+ align:start position:0%
+wave of
+current uh the input current is constant
+
+ align:start position:0%
+current uh the input current is constant
+ 
+
+ align:start position:0%
+current uh the input current is constant
+coming here and the output currents I'm
+
+ align:start position:0%
+coming here and the output currents I'm
+ 
+
+ align:start position:0%
+coming here and the output currents I'm
+sorry the input current's a a pulse
+
+ align:start position:0%
+sorry the input current's a a pulse
+ 
+
+ align:start position:0%
+sorry the input current's a a pulse
+Square the output current is kind of
+
+ align:start position:0%
+Square the output current is kind of
+ 
+
+ align:start position:0%
+Square the output current is kind of
+constant um but the point is I'm always
+
+ align:start position:0%
+constant um but the point is I'm always
+ 
+
+ align:start position:0%
+constant um but the point is I'm always
+putting my charging and discharging
+
+ align:start position:0%
+putting my charging and discharging
+ 
+
+ align:start position:0%
+putting my charging and discharging
+current through two switch resistances
+
+ align:start position:0%
+current through two switch resistances
+ 
+
+ align:start position:0%
+current through two switch resistances
+so it's not maybe surprising that I get
+
+ align:start position:0%
+so it's not maybe surprising that I get
+ 
+
+ align:start position:0%
+so it's not maybe surprising that I get
+down to this equivalent resistance being
+
+ align:start position:0%
+down to this equivalent resistance being
+ 
+
+ align:start position:0%
+down to this equivalent resistance being
+two switch
+
+ align:start position:0%
+two switch
+ 
+
+ align:start position:0%
+two switch
+resistances okay so what happens in the
+
+ align:start position:0%
+resistances okay so what happens in the
+ 
+
+ align:start position:0%
+resistances okay so what happens in the
+real world is if I have a switch
+
+ align:start position:0%
+real world is if I have a switch
+ 
+
+ align:start position:0%
+real world is if I have a switch
+capacitor converter and I say I'm going
+
+ align:start position:0%
+capacitor converter and I say I'm going
+ 
+
+ align:start position:0%
+capacitor converter and I say I'm going
+to have this model for Its Behavior
+
+ align:start position:0%
+to have this model for Its Behavior
+ 
+
+ align:start position:0%
+to have this model for Its Behavior
+okay all I'm going to
+
+ align:start position:0%
+okay all I'm going to
+ 
+
+ align:start position:0%
+okay all I'm going to
+get is if I plotted our equivalent on a
+
+ align:start position:0%
+get is if I plotted our equivalent on a
+ 
+
+ align:start position:0%
+get is if I plotted our equivalent on a
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+scale versus switching frequency on a
+
+ align:start position:0%
+scale versus switching frequency on a
+ 
+
+ align:start position:0%
+scale versus switching frequency on a
+log scale what I'm going to get is
+
+ align:start position:0%
+log scale what I'm going to get is
+ 
+
+ align:start position:0%
+log scale what I'm going to get is
+something that falls
+
+ align:start position:0%
+something that falls
+ 
+
+ align:start position:0%
+something that falls
+linearly this is 1 over4 CF
+
+ align:start position:0%
+linearly this is 1 over4 CF
+ 
+
+ align:start position:0%
+linearly this is 1 over4 CF
+switch okay and then he's going to have
+
+ align:start position:0%
+switch okay and then he's going to have
+ 
+
+ align:start position:0%
+switch okay and then he's going to have
+some minimum
+
+ align:start position:0%
+some minimum
+ 
+
+ align:start position:0%
+some minimum
+value which is to our switch
+
+ align:start position:0%
+value which is to our switch
+ 
+
+ align:start position:0%
+value which is to our switch
+right and the actual value you're going
+
+ align:start position:0%
+right and the actual value you're going
+ 
+
+ align:start position:0%
+right and the actual value you're going
+to get is going to you know sort of do
+
+ align:start position:0%
+to get is going to you know sort of do
+ 
+
+ align:start position:0%
+to get is going to you know sort of do
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this all right so you kind of there's
+
+ align:start position:0%
+this all right so you kind of there's
+ 
+
+ align:start position:0%
+this all right so you kind of there's
+kind of some limiting efficiency you can
+
+ align:start position:0%
+kind of some limiting efficiency you can
+ 
+
+ align:start position:0%
+kind of some limiting efficiency you can
+get to well if I'm charging through two
+
+ align:start position:0%
+get to well if I'm charging through two
+ 
+
+ align:start position:0%
+get to well if I'm charging through two
+switches all the time I got to eat the
+
+ align:start position:0%
+switches all the time I got to eat the
+ 
+
+ align:start position:0%
+switches all the time I got to eat the
+loss of the on-state loss of those
+
+ align:start position:0%
+loss of the on-state loss of those
+ 
+
+ align:start position:0%
+loss of the on-state loss of those
+switches right I mean I can't have 100%
+
+ align:start position:0%
+switches right I mean I can't have 100%
+ 
+
+ align:start position:0%
+switches right I mean I can't have 100%
+efficiency but you know if I'm using 10
+
+ align:start position:0%
+efficiency but you know if I'm using 10
+ 
+
+ align:start position:0%
+efficiency but you know if I'm using 10
+mli ohm switches maybe that's pretty
+
+ align:start position:0%
+mli ohm switches maybe that's pretty
+ 
+
+ align:start position:0%
+mli ohm switches maybe that's pretty
+damn low right so
+
+ align:start position:0%
+damn low right so
+ 
+
+ align:start position:0%
+damn low right so
+um essentially what I would tend to do
+
+ align:start position:0%
+um essentially what I would tend to do
+ 
+
+ align:start position:0%
+um essentially what I would tend to do
+is keep turning up the switching
+
+ align:start position:0%
+is keep turning up the switching
+ 
+
+ align:start position:0%
+is keep turning up the switching
+frequency until I get down to this
+
+ align:start position:0%
+frequency until I get down to this
+ 
+
+ align:start position:0%
+frequency until I get down to this
+regime where turning it up anymore
+
+ align:start position:0%
+regime where turning it up anymore
+ 
+
+ align:start position:0%
+regime where turning it up anymore
+doesn't reduce my output resistance
+
+ align:start position:0%
+doesn't reduce my output resistance
+ 
+
+ align:start position:0%
+doesn't reduce my output resistance
+because at that point there are other
+
+ align:start position:0%
+because at that point there are other
+ 
+
+ align:start position:0%
+because at that point there are other
+losses like Gate Drive losses and stuff
+
+ align:start position:0%
+losses like Gate Drive losses and stuff
+ 
+
+ align:start position:0%
+losses like Gate Drive losses and stuff
+which get worse with frequency so I
+
+ align:start position:0%
+which get worse with frequency so I
+ 
+
+ align:start position:0%
+which get worse with frequency so I
+ought to just go high enough that I can
+
+ align:start position:0%
+ought to just go high enough that I can
+ 
+
+ align:start position:0%
+ought to just go high enough that I can
+get to very high efficiencies and the
+
+ align:start position:0%
+get to very high efficiencies and the
+ 
+
+ align:start position:0%
+get to very high efficiencies and the
+result of this is if what I want is a
+
+ align:start position:0%
+result of this is if what I want is a
+ 
+
+ align:start position:0%
+result of this is if what I want is a
+fixed conversion ratio close to this I
+
+ align:start position:0%
+fixed conversion ratio close to this I
+ 
+
+ align:start position:0%
+fixed conversion ratio close to this I
+can get extraordinarily High
+
+ align:start position:0%
+can get extraordinarily High
+ 
+
+ align:start position:0%
+can get extraordinarily High
+efficiencies and power
+
+ align:start position:0%
+efficiencies and power
+ 
+
+ align:start position:0%
+efficiencies and power
+densities if I deviate the voltage
+
+ align:start position:0%
+densities if I deviate the voltage
+ 
+
+ align:start position:0%
+densities if I deviate the voltage
+conversion ratio away from that then the
+
+ align:start position:0%
+conversion ratio away from that then the
+ 
+
+ align:start position:0%
+conversion ratio away from that then the
+efficiencies start to droop but for what
+
+ align:start position:0%
+efficiencies start to droop but for what
+ 
+
+ align:start position:0%
+efficiencies start to droop but for what
+they're good at switch capacitor
+
+ align:start position:0%
+they're good at switch capacitor
+ 
+
+ align:start position:0%
+they're good at switch capacitor
+converters are very hard to beat and if
+
+ align:start position:0%
+converters are very hard to beat and if
+ 
+
+ align:start position:0%
+converters are very hard to beat and if
+I was to come back and analyze any other
+
+ align:start position:0%
+I was to come back and analyze any other
+ 
+
+ align:start position:0%
+I was to come back and analyze any other
+switch capacitor converter it's the same
+
+ align:start position:0%
+switch capacitor converter it's the same
+ 
+
+ align:start position:0%
+switch capacitor converter it's the same
+deal it's some charge transfer analysis
+
+ align:start position:0%
+deal it's some charge transfer analysis
+ 
+
+ align:start position:0%
+deal it's some charge transfer analysis
+through the different capacitors and I
+
+ align:start position:0%
+through the different capacitors and I
+ 
+
+ align:start position:0%
+through the different capacitors and I
+use charge balance and you can work that
+
+ align:start position:0%
+use charge balance and you can work that
+ 
+
+ align:start position:0%
+use charge balance and you can work that
+out to being a current conversion ratio
+
+ align:start position:0%
+out to being a current conversion ratio
+ 
+
+ align:start position:0%
+out to being a current conversion ratio
+and then some equivalent resistance with
+
+ align:start position:0%
+and then some equivalent resistance with
+ 
+
+ align:start position:0%
+and then some equivalent resistance with
+a slow switching limit and a fast
+
+ align:start position:0%
+a slow switching limit and a fast
+ 
+
+ align:start position:0%
+a slow switching limit and a fast
+switching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll take this up again next class but
+
+ align:start position:0%
+we'll take this up again next class but
+ 
+
+ align:start position:0%
+we'll take this up again next class but
+are there any final
+
+ align:start position:0%
+are there any final
+ 
+
+ align:start position:0%
+are there any final
+questions yeah now that you're switching
+
+ align:start position:0%
+questions yeah now that you're switching
+ 
+
+ align:start position:0%
+questions yeah now that you're switching
+quickly can the duty ratio change the
+
+ align:start position:0%
+quickly can the duty ratio change the
+ 
+
+ align:start position:0%
+quickly can the duty ratio change the
+conversion
+
+ align:start position:0%
+conversion
+ 
+
+ align:start position:0%
+conversion
+ratio uh well the yes but only through
+
+ align:start position:0%
+ratio uh well the yes but only through
+ 
+
+ align:start position:0%
+ratio uh well the yes but only through
+the action of essentially what this
+
+ align:start position:0%
+the action of essentially what this
+ 
+
+ align:start position:0%
+the action of essentially what this
+resistance is so you can make the you
+
+ align:start position:0%
+resistance is so you can make the you
+ 
+
+ align:start position:0%
+resistance is so you can make the you
+know there's a duty ratio for any given
+
+ align:start position:0%
+know there's a duty ratio for any given
+ 
+
+ align:start position:0%
+know there's a duty ratio for any given
+converter there's a duty ratio that will
+
+ align:start position:0%
+converter there's a duty ratio that will
+ 
+
+ align:start position:0%
+converter there's a duty ratio that will
+sort of give you the lowest output
+
+ align:start position:0%
+sort of give you the lowest output
+ 
+
+ align:start position:0%
+sort of give you the lowest output
+resistance even in slow switching limit
+
+ align:start position:0%
+resistance even in slow switching limit
+ 
+
+ align:start position:0%
+resistance even in slow switching limit
+you can change the conversion ratio but
+
+ align:start position:0%
+you can change the conversion ratio but
+ 
+
+ align:start position:0%
+you can change the conversion ratio but
+you're doing it through a resistive drop
+
+ align:start position:0%
+you're doing it through a resistive drop
+ 
+
+ align:start position:0%
+you're doing it through a resistive drop
+it's sort of like you have an ideal
+
+ align:start position:0%
+it's sort of like you have an ideal
+ 
+
+ align:start position:0%
+it's sort of like you have an ideal
+Transformer and then a linear regulator
+
+ align:start position:0%
+Transformer and then a linear regulator
+ 
+
+ align:start position:0%
+Transformer and then a linear regulator
+kind of thing so you can always use
+
+ align:start position:0%
+kind of thing so you can always use
+ 
+
+ align:start position:0%
+kind of thing so you can always use
+switching frequency or D and in fast
+
+ align:start position:0%
+switching frequency or D and in fast
+ 
+
+ align:start position:0%
+switching frequency or D and in fast
+switching limit Duty ratio to change the
+
+ align:start position:0%
+switching limit Duty ratio to change the
+ 
+
+ align:start position:0%
+switching limit Duty ratio to change the
+conversion ratio but not in a perfectly
+
+ align:start position:0%
+conversion ratio but not in a perfectly
+ 
+
+ align:start position:0%
+conversion ratio but not in a perfectly
+efficient
+
+ align:start position:0%
+efficient
+ 
+
+ align:start position:0%
+efficient
+sense the voltage conversion ratio all
+
+ align:start position:0%
+sense the voltage conversion ratio all
+ 
+
+ align:start position:0%
+sense the voltage conversion ratio all
+right great we'll pick this up next
+
+ align:start position:0%
+right great we'll pick this up next
+ 
+
+ align:start position:0%
+right great we'll pick this up next
+class
\ No newline at end of file
diff --git a/Cn5K8R8cEiI.txt b/Cn5K8R8cEiI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18cbbdc95e6978329fb903c24c923e829f7e959a
--- /dev/null
+++ b/Cn5K8R8cEiI.txt
@@ -0,0 +1,14059 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so today what we want
+
+ align:start position:0%
+ocw.mit.edu okay so today what we want
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so today what we want
+to do is uh we want to talk about uh
+
+ align:start position:0%
+to do is uh we want to talk about uh
+ 
+
+ align:start position:0%
+to do is uh we want to talk about uh
+kind of two related topics so the first
+
+ align:start position:0%
+kind of two related topics so the first
+ 
+
+ align:start position:0%
+kind of two related topics so the first
+is going to be this question of uh the
+
+ align:start position:0%
+is going to be this question of uh the
+ 
+
+ align:start position:0%
+is going to be this question of uh the
+evolution of variance and how to model
+
+ align:start position:0%
+evolution of variance and how to model
+ 
+
+ align:start position:0%
+evolution of variance and how to model
+host parasite and actions more broadly
+
+ align:start position:0%
+host parasite and actions more broadly
+ 
+
+ align:start position:0%
+host parasite and actions more broadly
+all right that's kind of modeled on
+
+ align:start position:0%
+all right that's kind of modeled on
+ 
+
+ align:start position:0%
+all right that's kind of modeled on
+chapter 11 of Martin's book we'll focus
+
+ align:start position:0%
+chapter 11 of Martin's book we'll focus
+ 
+
+ align:start position:0%
+chapter 11 of Martin's book we'll focus
+on the first half of it for the
+
+ align:start position:0%
+on the first half of it for the
+ 
+
+ align:start position:0%
+on the first half of it for the
+discussions today right this is in the
+
+ align:start position:0%
+discussions today right this is in the
+ 
+
+ align:start position:0%
+discussions today right this is in the
+context of when a given host can only
+
+ align:start position:0%
+context of when a given host can only
+ 
+
+ align:start position:0%
+context of when a given host can only
+have one uh one strain of the parasite
+
+ align:start position:0%
+have one uh one strain of the parasite
+ 
+
+ align:start position:0%
+have one uh one strain of the parasite
+or virus or whatnot uh inside um inside
+
+ align:start position:0%
+or virus or whatnot uh inside um inside
+ 
+
+ align:start position:0%
+or virus or whatnot uh inside um inside
+that body okay the the model presented
+
+ align:start position:0%
+that body okay the the model presented
+ 
+
+ align:start position:0%
+that body okay the the model presented
+in Martin's book is um is very similar
+
+ align:start position:0%
+in Martin's book is um is very similar
+ 
+
+ align:start position:0%
+in Martin's book is um is very similar
+to kind of classic models in
+
+ align:start position:0%
+to kind of classic models in
+ 
+
+ align:start position:0%
+to kind of classic models in
+epidemiology which are the so-called sir
+
+ align:start position:0%
+epidemiology which are the so-called sir
+ 
+
+ align:start position:0%
+epidemiology which are the so-called sir
+type models uh where you divide up the
+
+ align:start position:0%
+type models uh where you divide up the
+ 
+
+ align:start position:0%
+type models uh where you divide up the
+host population into whether the they
+
+ align:start position:0%
+host population into whether the they
+ 
+
+ align:start position:0%
+host population into whether the they
+are uh sensitive I.E non-infected
+
+ align:start position:0%
+are uh sensitive I.E non-infected
+ 
+
+ align:start position:0%
+are uh sensitive I.E non-infected
+infected or resistant okay and then
+
+ align:start position:0%
+infected or resistant okay and then
+ 
+
+ align:start position:0%
+infected or resistant okay and then
+we'll we'll kind of draw the parallels
+
+ align:start position:0%
+we'll we'll kind of draw the parallels
+ 
+
+ align:start position:0%
+we'll we'll kind of draw the parallels
+of how we get from the model that we
+
+ align:start position:0%
+of how we get from the model that we
+ 
+
+ align:start position:0%
+of how we get from the model that we
+talked about in Martin's book or that
+
+ align:start position:0%
+talked about in Martin's book or that
+ 
+
+ align:start position:0%
+talked about in Martin's book or that
+you read about in Martin's book to the
+
+ align:start position:0%
+you read about in Martin's book to the
+ 
+
+ align:start position:0%
+you read about in Martin's book to the
+classic sir models okay but in both of
+
+ align:start position:0%
+classic sir models okay but in both of
+ 
+
+ align:start position:0%
+classic sir models okay but in both of
+these cases the the fundamental
+
+ align:start position:0%
+these cases the the fundamental
+ 
+
+ align:start position:0%
+these cases the the fundamental
+parameter that drives these things is
+
+ align:start position:0%
+parameter that drives these things is
+ 
+
+ align:start position:0%
+parameter that drives these things is
+this R not parameter it tells us about
+
+ align:start position:0%
+this R not parameter it tells us about
+ 
+
+ align:start position:0%
+this R not parameter it tells us about
+uh the expected number of individuals
+
+ align:start position:0%
+uh the expected number of individuals
+ 
+
+ align:start position:0%
+uh the expected number of individuals
+that will be of new cases that will
+
+ align:start position:0%
+that will be of new cases that will
+ 
+
+ align:start position:0%
+that will be of new cases that will
+result when you introduce one infected
+
+ align:start position:0%
+result when you introduce one infected
+ 
+
+ align:start position:0%
+result when you introduce one infected
+member into the
+
+ align:start position:0%
+member into the
+ 
+
+ align:start position:0%
+member into the
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+talk uh only a little bit but uh I would
+
+ align:start position:0%
+talk uh only a little bit but uh I would
+ 
+
+ align:start position:0%
+talk uh only a little bit but uh I would
+say depending on time if if you're
+
+ align:start position:0%
+say depending on time if if you're
+ 
+
+ align:start position:0%
+say depending on time if if you're
+interested in in the super infection
+
+ align:start position:0%
+interested in in the super infection
+ 
+
+ align:start position:0%
+interested in in the super infection
+discussion more uh we can talk about it
+
+ align:start position:0%
+discussion more uh we can talk about it
+ 
+
+ align:start position:0%
+discussion more uh we can talk about it
+after class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe right okay so for the second half
+
+ align:start position:0%
+maybe right okay so for the second half
+ 
+
+ align:start position:0%
+maybe right okay so for the second half
+of the class what we're going to do
+
+ align:start position:0%
+of the class what we're going to do
+ 
+
+ align:start position:0%
+of the class what we're going to do
+though is we're going to talk about the
+
+ align:start position:0%
+though is we're going to talk about the
+ 
+
+ align:start position:0%
+though is we're going to talk about the
+possible evolutionary benefit benefits
+
+ align:start position:0%
+possible evolutionary benefit benefits
+ 
+
+ align:start position:0%
+possible evolutionary benefit benefits
+of sex right and in particular we'll
+
+ align:start position:0%
+of sex right and in particular we'll
+ 
+
+ align:start position:0%
+of sex right and in particular we'll
+we'll talk about this hypothesis which
+
+ align:start position:0%
+we'll talk about this hypothesis which
+ 
+
+ align:start position:0%
+we'll talk about this hypothesis which
+is one of the reigning hypothesis for
+
+ align:start position:0%
+is one of the reigning hypothesis for
+ 
+
+ align:start position:0%
+is one of the reigning hypothesis for
+why it might be that sax is as
+
+ align:start position:0%
+why it might be that sax is as
+ 
+
+ align:start position:0%
+why it might be that sax is as
+widespread as it is which is this uh the
+
+ align:start position:0%
+widespread as it is which is this uh the
+ 
+
+ align:start position:0%
+widespread as it is which is this uh the
+Red Queen hypothesis right from uh from
+
+ align:start position:0%
+Red Queen hypothesis right from uh from
+ 
+
+ align:start position:0%
+Red Queen hypothesis right from uh from
+L Carol's novel is kind of uh and and
+
+ align:start position:0%
+L Carol's novel is kind of uh and and
+ 
+
+ align:start position:0%
+L Carol's novel is kind of uh and and
+and we're going to discuss this paper
+
+ align:start position:0%
+and we're going to discuss this paper
+ 
+
+ align:start position:0%
+and we're going to discuss this paper
+that you guys read about uh running with
+
+ align:start position:0%
+that you guys read about uh running with
+ 
+
+ align:start position:0%
+that you guys read about uh running with
+the Red Queen which I think is kind of a
+
+ align:start position:0%
+the Red Queen which I think is kind of a
+ 
+
+ align:start position:0%
+the Red Queen which I think is kind of a
+nice has a nice discussion of this
+
+ align:start position:0%
+nice has a nice discussion of this
+ 
+
+ align:start position:0%
+nice has a nice discussion of this
+debate and then some nice experiments
+
+ align:start position:0%
+debate and then some nice experiments
+ 
+
+ align:start position:0%
+debate and then some nice experiments
+looking at experimental coevolution
+
+ align:start position:0%
+looking at experimental coevolution
+ 
+
+ align:start position:0%
+looking at experimental coevolution
+between uh seelan worm and it's
+
+ align:start position:0%
+between uh seelan worm and it's
+ 
+
+ align:start position:0%
+between uh seelan worm and it's
+infecting parasite which is a sera
+
+ align:start position:0%
+infecting parasite which is a sera
+ 
+
+ align:start position:0%
+infecting parasite which is a sera
+bacterium
+
+ align:start position:0%
+bacterium
+ 
+
+ align:start position:0%
+bacterium
+any any questions before we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going okay what I want to do is is start
+
+ align:start position:0%
+going okay what I want to do is is start
+ 
+
+ align:start position:0%
+going okay what I want to do is is start
+by discussing
+
+ align:start position:0%
+by discussing
+ 
+
+ align:start position:0%
+by discussing
+uh this model in Martin's uh in Martin's
+
+ align:start position:0%
+uh this model in Martin's uh in Martin's
+ 
+
+ align:start position:0%
+uh this model in Martin's uh in Martin's
+book but also a little bit there's a
+
+ align:start position:0%
+book but also a little bit there's a
+ 
+
+ align:start position:0%
+book but also a little bit there's a
+little bit of this pH philosophical
+
+ align:start position:0%
+little bit of this pH philosophical
+ 
+
+ align:start position:0%
+little bit of this pH philosophical
+question you know anytime that you have
+
+ align:start position:0%
+question you know anytime that you have
+ 
+
+ align:start position:0%
+question you know anytime that you have
+uh you have you have modeling you you
+
+ align:start position:0%
+uh you have you have modeling you you
+ 
+
+ align:start position:0%
+uh you have you have modeling you you
+always have to make decisions about uh
+
+ align:start position:0%
+always have to make decisions about uh
+ 
+
+ align:start position:0%
+always have to make decisions about uh
+which of the details you want to try to
+
+ align:start position:0%
+which of the details you want to try to
+ 
+
+ align:start position:0%
+which of the details you want to try to
+model and which of the details you do
+
+ align:start position:0%
+model and which of the details you do
+ 
+
+ align:start position:0%
+model and which of the details you do
+not want to model and uh depending upon
+
+ align:start position:0%
+not want to model and uh depending upon
+ 
+
+ align:start position:0%
+not want to model and uh depending upon
+the the situation it may be that some
+
+ align:start position:0%
+the the situation it may be that some
+ 
+
+ align:start position:0%
+the the situation it may be that some
+assumptions are more or less appropriate
+
+ align:start position:0%
+assumptions are more or less appropriate
+ 
+
+ align:start position:0%
+assumptions are more or less appropriate
+than others right now in the model that
+
+ align:start position:0%
+than others right now in the model that
+ 
+
+ align:start position:0%
+than others right now in the model that
+uh that Martin wrote down uh you can uh
+
+ align:start position:0%
+uh that Martin wrote down uh you can uh
+ 
+
+ align:start position:0%
+uh that Martin wrote down uh you can uh
+well okay well we'll try to figure out
+
+ align:start position:0%
+well okay well we'll try to figure out
+ 
+
+ align:start position:0%
+well okay well we'll try to figure out
+what the assumptions are here okay so we
+
+ align:start position:0%
+what the assumptions are here okay so we
+ 
+
+ align:start position:0%
+what the assumptions are here okay so we
+have uh we have these what you might
+
+ align:start position:0%
+have uh we have these what you might
+ 
+
+ align:start position:0%
+have uh we have these what you might
+think of as some sensitive individuals
+
+ align:start position:0%
+think of as some sensitive individuals
+ 
+
+ align:start position:0%
+think of as some sensitive individuals
+uh plus the infected
+
+ align:start position:0%
+uh plus the infected
+ 
+
+ align:start position:0%
+uh plus the infected
+individuals are going to interact and
+
+ align:start position:0%
+individuals are going to interact and
+ 
+
+ align:start position:0%
+individuals are going to interact and
+some rate beta so this is how the
+
+ align:start position:0%
+some rate beta so this is how the
+ 
+
+ align:start position:0%
+some rate beta so this is how the
+sensitive become infected and it results
+
+ align:start position:0%
+sensitive become infected and it results
+ 
+
+ align:start position:0%
+sensitive become infected and it results
+in now two infected
+
+ align:start position:0%
+in now two infected
+ 
+
+ align:start position:0%
+in now two infected
+individuals okay now of course each of
+
+ align:start position:0%
+individuals okay now of course each of
+ 
+
+ align:start position:0%
+individuals okay now of course each of
+these individuals will uh say have some
+
+ align:start position:0%
+these individuals will uh say have some
+ 
+
+ align:start position:0%
+these individuals will uh say have some
+lifespan or die at some rate right so
+
+ align:start position:0%
+lifespan or die at some rate right so
+ 
+
+ align:start position:0%
+lifespan or die at some rate right so
+this we're going to say this die the
+
+ align:start position:0%
+this we're going to say this die the
+ 
+
+ align:start position:0%
+this we're going to say this die the
+sensitive or uninfected in individuals
+
+ align:start position:0%
+sensitive or uninfected in individuals
+ 
+
+ align:start position:0%
+sensitive or uninfected in individuals
+diet rate U whereas infected individuals
+
+ align:start position:0%
+diet rate U whereas infected individuals
+ 
+
+ align:start position:0%
+diet rate U whereas infected individuals
+uh there's uh an increase in the death
+
+ align:start position:0%
+uh there's uh an increase in the death
+ 
+
+ align:start position:0%
+uh there's uh an increase in the death
+rate described by some virulence V okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now uh the model as written what's
+
+ align:start position:0%
+okay now uh the model as written what's
+ 
+
+ align:start position:0%
+okay now uh the model as written what's
+going to be the fate of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population yeah yeah everyone's gonna
+
+ align:start position:0%
+population yeah yeah everyone's gonna
+ 
+
+ align:start position:0%
+population yeah yeah everyone's gonna
+die right and and that's even true in
+
+ align:start position:0%
+die right and and that's even true in
+ 
+
+ align:start position:0%
+die right and and that's even true in
+the ABS it's not even that the
+
+ align:start position:0%
+the ABS it's not even that the
+ 
+
+ align:start position:0%
+the ABS it's not even that the
+population is dying as a result of the
+
+ align:start position:0%
+population is dying as a result of the
+ 
+
+ align:start position:0%
+population is dying as a result of the
+infection right because even in the
+
+ align:start position:0%
+infection right because even in the
+ 
+
+ align:start position:0%
+infection right because even in the
+absence of any infected
+
+ align:start position:0%
+absence of any infected
+ 
+
+ align:start position:0%
+absence of any infected
+individuals you know you just have
+
+ align:start position:0%
+individuals you know you just have
+ 
+
+ align:start position:0%
+individuals you know you just have
+people dying right so you need to have
+
+ align:start position:0%
+people dying right so you need to have
+ 
+
+ align:start position:0%
+people dying right so you need to have
+some way of keeping the population going
+
+ align:start position:0%
+some way of keeping the population going
+ 
+
+ align:start position:0%
+some way of keeping the population going
+so that you can study it perhaps and
+
+ align:start position:0%
+so that you can study it perhaps and
+ 
+
+ align:start position:0%
+so that you can study it perhaps and
+what what we're going to assume is that
+
+ align:start position:0%
+what what we're going to assume is that
+ 
+
+ align:start position:0%
+what what we're going to assume is that
+that sensitive individuals or uninfected
+
+ align:start position:0%
+that sensitive individuals or uninfected
+ 
+
+ align:start position:0%
+that sensitive individuals or uninfected
+individuals will enter the population
+
+ align:start position:0%
+individuals will enter the population
+ 
+
+ align:start position:0%
+individuals will enter the population
+just at some rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K right now and okay right so in terms
+
+ align:start position:0%
+K right now and okay right so in terms
+ 
+
+ align:start position:0%
+K right now and okay right so in terms
+of in terms of the philosophical
+
+ align:start position:0%
+of in terms of the philosophical
+ 
+
+ align:start position:0%
+of in terms of the philosophical
+question uh that in the beginning of of
+
+ align:start position:0%
+question uh that in the beginning of of
+ 
+
+ align:start position:0%
+question uh that in the beginning of of
+the chapter Martin uh talks a bit about
+
+ align:start position:0%
+the chapter Martin uh talks a bit about
+ 
+
+ align:start position:0%
+the chapter Martin uh talks a bit about
+this question of micro parasites versus
+
+ align:start position:0%
+this question of micro parasites versus
+ 
+
+ align:start position:0%
+this question of micro parasites versus
+macro
+
+ align:start position:0%
+macro
+ 
+
+ align:start position:0%
+macro
+parasites and can can somebody remind us
+
+ align:start position:0%
+parasites and can can somebody remind us
+ 
+
+ align:start position:0%
+parasites and can can somebody remind us
+what what's the distinction and what
+
+ align:start position:0%
+what what's the distinction and what
+ 
+
+ align:start position:0%
+what what's the distinction and what
+kind of uh what kind of parasite might
+
+ align:start position:0%
+kind of uh what kind of parasite might
+ 
+
+ align:start position:0%
+kind of uh what kind of parasite might
+this be intended to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes what I got from it is that micro
+
+ align:start position:0%
+yes what I got from it is that micro
+ 
+
+ align:start position:0%
+yes what I got from it is that micro
+micro parasites
+
+ align:start position:0%
+micro parasites
+ 
+
+ align:start position:0%
+micro parasites
+are on the order of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right and you know and I'd say
+
+ align:start position:0%
+right right and you know and I'd say
+ 
+
+ align:start position:0%
+right right and you know and I'd say
+that just given this distinction between
+
+ align:start position:0%
+that just given this distinction between
+ 
+
+ align:start position:0%
+that just given this distinction between
+the micro parasites that might be
+
+ align:start position:0%
+the micro parasites that might be
+ 
+
+ align:start position:0%
+the micro parasites that might be
+viruses and bacteria as compared to the
+
+ align:start position:0%
+viruses and bacteria as compared to the
+ 
+
+ align:start position:0%
+viruses and bacteria as compared to the
+macro parasites that are things like you
+
+ align:start position:0%
+macro parasites that are things like you
+ 
+
+ align:start position:0%
+macro parasites that are things like you
+know tapeworms and so forth
+
+ align:start position:0%
+know tapeworms and so forth
+ 
+
+ align:start position:0%
+know tapeworms and so forth
+it's not obvious from that that you
+
+ align:start position:0%
+it's not obvious from that that you
+ 
+
+ align:start position:0%
+it's not obvious from that that you
+would have two different kind of
+
+ align:start position:0%
+would have two different kind of
+ 
+
+ align:start position:0%
+would have two different kind of
+modeling Frameworks but what what is the
+
+ align:start position:0%
+modeling Frameworks but what what is the
+ 
+
+ align:start position:0%
+modeling Frameworks but what what is the
+argument that um that is made in in
+
+ align:start position:0%
+argument that um that is made in in
+ 
+
+ align:start position:0%
+argument that um that is made in in
+Martin's Martin's book or can you think
+
+ align:start position:0%
+Martin's Martin's book or can you think
+ 
+
+ align:start position:0%
+Martin's Martin's book or can you think
+up an argument for why it is that it
+
+ align:start position:0%
+up an argument for why it is that it
+ 
+
+ align:start position:0%
+up an argument for why it is that it
+might be this kind of model you would
+
+ align:start position:0%
+might be this kind of model you would
+ 
+
+ align:start position:0%
+might be this kind of model you would
+want to use for micro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parasites
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes large individual we don't have to
+
+ align:start position:0%
+yes large individual we don't have to
+ 
+
+ align:start position:0%
+yes large individual we don't have to
+keep track of the internal
+
+ align:start position:0%
+keep track of the internal
+ 
+
+ align:start position:0%
+keep track of the internal
+that's right I'd say that and some of
+
+ align:start position:0%
+that's right I'd say that and some of
+ 
+
+ align:start position:0%
+that's right I'd say that and some of
+it's maybe even a historical thing that
+
+ align:start position:0%
+it's maybe even a historical thing that
+ 
+
+ align:start position:0%
+it's maybe even a historical thing that
+we there might be right huge numbers of
+
+ align:start position:0%
+we there might be right huge numbers of
+ 
+
+ align:start position:0%
+we there might be right huge numbers of
+viruses you know a flu virus or so in in
+
+ align:start position:0%
+viruses you know a flu virus or so in in
+ 
+
+ align:start position:0%
+viruses you know a flu virus or so in in
+an infected individual and in some ways
+
+ align:start position:0%
+an infected individual and in some ways
+ 
+
+ align:start position:0%
+an infected individual and in some ways
+maybe the number of viruses that is in
+
+ align:start position:0%
+maybe the number of viruses that is in
+ 
+
+ align:start position:0%
+maybe the number of viruses that is in
+that host is not the most relevant thing
+
+ align:start position:0%
+that host is not the most relevant thing
+ 
+
+ align:start position:0%
+that host is not the most relevant thing
+uh and it certainly would be much more
+
+ align:start position:0%
+uh and it certainly would be much more
+ 
+
+ align:start position:0%
+uh and it certainly would be much more
+complicated to try to keep track of that
+
+ align:start position:0%
+complicated to try to keep track of that
+ 
+
+ align:start position:0%
+complicated to try to keep track of that
+right so if uh if you can get um kind of
+
+ align:start position:0%
+right so if uh if you can get um kind of
+ 
+
+ align:start position:0%
+right so if uh if you can get um kind of
+meaningful predictions by instead of
+
+ align:start position:0%
+meaningful predictions by instead of
+ 
+
+ align:start position:0%
+meaningful predictions by instead of
+keeping track rather than keeping track
+
+ align:start position:0%
+keeping track rather than keeping track
+ 
+
+ align:start position:0%
+keeping track rather than keeping track
+of the number of viruses say in each
+
+ align:start position:0%
+of the number of viruses say in each
+ 
+
+ align:start position:0%
+of the number of viruses say in each
+host instead you just put the hosts into
+
+ align:start position:0%
+host instead you just put the hosts into
+ 
+
+ align:start position:0%
+host instead you just put the hosts into
+different classes you know sensitive and
+
+ align:start position:0%
+different classes you know sensitive and
+ 
+
+ align:start position:0%
+different classes you know sensitive and
+infected for example later we'll talk
+
+ align:start position:0%
+infected for example later we'll talk
+ 
+
+ align:start position:0%
+infected for example later we'll talk
+about what happens if you have a
+
+ align:start position:0%
+about what happens if you have a
+ 
+
+ align:start position:0%
+about what happens if you have a
+resistant type of class right but but
+
+ align:start position:0%
+resistant type of class right but but
+ 
+
+ align:start position:0%
+resistant type of class right but but
+the idea there is that there's maybe
+
+ align:start position:0%
+the idea there is that there's maybe
+ 
+
+ align:start position:0%
+the idea there is that there's maybe
+even also some separation of time scales
+
+ align:start position:0%
+even also some separation of time scales
+ 
+
+ align:start position:0%
+even also some separation of time scales
+right because you get infected and kind
+
+ align:start position:0%
+right because you get infected and kind
+ 
+
+ align:start position:0%
+right because you get infected and kind
+of quickly you come to you're just sick
+
+ align:start position:0%
+of quickly you come to you're just sick
+ 
+
+ align:start position:0%
+of quickly you come to you're just sick
+and maybe
+
+ align:start position:0%
+and maybe
+ 
+
+ align:start position:0%
+and maybe
+infective and but at some rate you get
+
+ align:start position:0%
+infective and but at some rate you get
+ 
+
+ align:start position:0%
+infective and but at some rate you get
+you get better and it's not that uh it
+
+ align:start position:0%
+you get better and it's not that uh it
+ 
+
+ align:start position:0%
+you get better and it's not that uh it
+you'll necessarily gain very much by
+
+ align:start position:0%
+you'll necessarily gain very much by
+ 
+
+ align:start position:0%
+you'll necessarily gain very much by
+keeping track of the precise number of
+
+ align:start position:0%
+keeping track of the precise number of
+ 
+
+ align:start position:0%
+keeping track of the precise number of
+viruses in the h post okay of course
+
+ align:start position:0%
+viruses in the h post okay of course
+ 
+
+ align:start position:0%
+viruses in the h post okay of course
+this is ultimately an experimental
+
+ align:start position:0%
+this is ultimately an experimental
+ 
+
+ align:start position:0%
+this is ultimately an experimental
+observational question of whether this
+
+ align:start position:0%
+observational question of whether this
+ 
+
+ align:start position:0%
+observational question of whether this
+sort of model provides you the Insight
+
+ align:start position:0%
+sort of model provides you the Insight
+ 
+
+ align:start position:0%
+sort of model provides you the Insight
+that that you're going to need to make
+
+ align:start position:0%
+that that you're going to need to make
+ 
+
+ align:start position:0%
+that that you're going to need to make
+sense of these diseases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's right so the mechanism of
+
+ align:start position:0%
+right that's right so the mechanism of
+ 
+
+ align:start position:0%
+right that's right so the mechanism of
+transmission and this this depends very
+
+ align:start position:0%
+transmission and this this depends very
+ 
+
+ align:start position:0%
+transmission and this this depends very
+much on uh on the disease that you're
+
+ align:start position:0%
+much on uh on the disease that you're
+ 
+
+ align:start position:0%
+much on uh on the disease that you're
+studying right uh and the macro
+
+ align:start position:0%
+studying right uh and the macro
+ 
+
+ align:start position:0%
+studying right uh and the macro
+parasites in many cases they're they're
+
+ align:start position:0%
+parasites in many cases they're they're
+ 
+
+ align:start position:0%
+parasites in many cases they're they're
+transmitted not from direct interactions
+
+ align:start position:0%
+transmitted not from direct interactions
+ 
+
+ align:start position:0%
+transmitted not from direct interactions
+between the hosts but through
+
+ align:start position:0%
+between the hosts but through
+ 
+
+ align:start position:0%
+between the hosts but through
+uh you know through the environment or
+
+ align:start position:0%
+uh you know through the environment or
+ 
+
+ align:start position:0%
+uh you know through the environment or
+something else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um it's also perhaps just worth
+
+ align:start position:0%
+yeah um it's also perhaps just worth
+ 
+
+ align:start position:0%
+yeah um it's also perhaps just worth
+pointing out that uh that parasites are
+
+ align:start position:0%
+pointing out that uh that parasites are
+ 
+
+ align:start position:0%
+pointing out that uh that parasites are
+just a ubiquitous aspect of life right
+
+ align:start position:0%
+just a ubiquitous aspect of life right
+ 
+
+ align:start position:0%
+just a ubiquitous aspect of life right
+so you can kind of uh name an organism
+
+ align:start position:0%
+so you can kind of uh name an organism
+ 
+
+ align:start position:0%
+so you can kind of uh name an organism
+and you can pretty much uh be guaranteed
+
+ align:start position:0%
+and you can pretty much uh be guaranteed
+ 
+
+ align:start position:0%
+and you can pretty much uh be guaranteed
+that there's going to be some notion of
+
+ align:start position:0%
+that there's going to be some notion of
+ 
+
+ align:start position:0%
+that there's going to be some notion of
+a parasite on on that organism and there
+
+ align:start position:0%
+a parasite on on that organism and there
+ 
+
+ align:start position:0%
+a parasite on on that organism and there
+can be multiple uh multiple layers of
+
+ align:start position:0%
+can be multiple uh multiple layers of
+ 
+
+ align:start position:0%
+can be multiple uh multiple layers of
+this right so U you know we certainly
+
+ align:start position:0%
+this right so U you know we certainly
+ 
+
+ align:start position:0%
+this right so U you know we certainly
+have many parasites we we we're infected
+
+ align:start position:0%
+have many parasites we we we're infected
+ 
+
+ align:start position:0%
+have many parasites we we we're infected
+by many viruses and bacteria and and
+
+ align:start position:0%
+by many viruses and bacteria and and
+ 
+
+ align:start position:0%
+by many viruses and bacteria and and
+other things right but uh but bacteria
+
+ align:start position:0%
+other things right but uh but bacteria
+ 
+
+ align:start position:0%
+other things right but uh but bacteria
+even though you know we think of them as
+
+ align:start position:0%
+even though you know we think of them as
+ 
+
+ align:start position:0%
+even though you know we think of them as
+being very small but they're also prayed
+
+ align:start position:0%
+being very small but they're also prayed
+ 
+
+ align:start position:0%
+being very small but they're also prayed
+upon by by these Fage right which are uh
+
+ align:start position:0%
+upon by by these Fage right which are uh
+ 
+
+ align:start position:0%
+upon by by these Fage right which are uh
+which is it's a it's a parasite that
+
+ align:start position:0%
+which is it's a it's a parasite that
+ 
+
+ align:start position:0%
+which is it's a it's a parasite that
+targets specifically bacteria right so
+
+ align:start position:0%
+targets specifically bacteria right so
+ 
+
+ align:start position:0%
+targets specifically bacteria right so
+it's not just that it's an incidental
+
+ align:start position:0%
+it's not just that it's an incidental
+ 
+
+ align:start position:0%
+it's not just that it's an incidental
+thing that but these are really uh
+
+ align:start position:0%
+thing that but these are really uh
+ 
+
+ align:start position:0%
+thing that but these are really uh
+viruses that have evolved specifically
+
+ align:start position:0%
+viruses that have evolved specifically
+ 
+
+ align:start position:0%
+viruses that have evolved specifically
+to to divide in bacteria right um and in
+
+ align:start position:0%
+to to divide in bacteria right um and in
+ 
+
+ align:start position:0%
+to to divide in bacteria right um and in
+uh we didn't really talk about this very
+
+ align:start position:0%
+uh we didn't really talk about this very
+ 
+
+ align:start position:0%
+uh we didn't really talk about this very
+much but one of the classic models for
+
+ align:start position:0%
+much but one of the classic models for
+ 
+
+ align:start position:0%
+much but one of the classic models for
+uh cooperation and cheating uh is based
+
+ align:start position:0%
+uh cooperation and cheating uh is based
+ 
+
+ align:start position:0%
+uh cooperation and cheating uh is based
+on what you could think about as some
+
+ align:start position:0%
+on what you could think about as some
+ 
+
+ align:start position:0%
+on what you could think about as some
+sort of uh parasitic subpopulation
+
+ align:start position:0%
+sort of uh parasitic subpopulation
+ 
+
+ align:start position:0%
+sort of uh parasitic subpopulation
+within phage right so this is a classic
+
+ align:start position:0%
+within phage right so this is a classic
+ 
+
+ align:start position:0%
+within phage right so this is a classic
+paper by lyncha where he showed that if
+
+ align:start position:0%
+paper by lyncha where he showed that if
+ 
+
+ align:start position:0%
+paper by lyncha where he showed that if
+you evolve phage in bacteria in a
+
+ align:start position:0%
+you evolve phage in bacteria in a
+ 
+
+ align:start position:0%
+you evolve phage in bacteria in a
+condition where many Fage infect a given
+
+ align:start position:0%
+condition where many Fage infect a given
+ 
+
+ align:start position:0%
+condition where many Fage infect a given
+bacteria then uh you can evolve what you
+
+ align:start position:0%
+bacteria then uh you can evolve what you
+ 
+
+ align:start position:0%
+bacteria then uh you can evolve what you
+could think of as cheater uh cheater
+
+ align:start position:0%
+could think of as cheater uh cheater
+ 
+
+ align:start position:0%
+could think of as cheater uh cheater
+strategies or cheater Fage because these
+
+ align:start position:0%
+strategies or cheater Fage because these
+ 
+
+ align:start position:0%
+strategies or cheater Fage because these
+are Fage that don't um they maybe can't
+
+ align:start position:0%
+are Fage that don't um they maybe can't
+ 
+
+ align:start position:0%
+are Fage that don't um they maybe can't
+reproduce on their own but have shorter
+
+ align:start position:0%
+reproduce on their own but have shorter
+ 
+
+ align:start position:0%
+reproduce on their own but have shorter
+genomes and can kind of out produ you
+
+ align:start position:0%
+genomes and can kind of out produ you
+ 
+
+ align:start position:0%
+genomes and can kind of out produ you
+know can out replicate the normal phage
+
+ align:start position:0%
+know can out replicate the normal phage
+ 
+
+ align:start position:0%
+know can out replicate the normal phage
+so if these both of these end up in a
+
+ align:start position:0%
+so if these both of these end up in a
+ 
+
+ align:start position:0%
+so if these both of these end up in a
+single bacterial cell then these cheater
+
+ align:start position:0%
+single bacterial cell then these cheater
+ 
+
+ align:start position:0%
+single bacterial cell then these cheater
+Fage can spread by by taking advantage
+
+ align:start position:0%
+Fage can spread by by taking advantage
+ 
+
+ align:start position:0%
+Fage can spread by by taking advantage
+of the say the replication Machinery
+
+ align:start position:0%
+of the say the replication Machinery
+ 
+
+ align:start position:0%
+of the say the replication Machinery
+from the rest of the Fage so this is in
+
+ align:start position:0%
+from the rest of the Fage so this is in
+ 
+
+ align:start position:0%
+from the rest of the Fage so this is in
+some ways you might call that a some
+
+ align:start position:0%
+some ways you might call that a some
+ 
+
+ align:start position:0%
+some ways you might call that a some
+sort of DNA parasite or or so right so
+
+ align:start position:0%
+sort of DNA parasite or or so right so
+ 
+
+ align:start position:0%
+sort of DNA parasite or or so right so
+there's really parasites at many many
+
+ align:start position:0%
+there's really parasites at many many
+ 
+
+ align:start position:0%
+there's really parasites at many many
+different levels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you know uh I I would say that yeah
+
+ align:start position:0%
+yeah you know uh I I would say that yeah
+ 
+
+ align:start position:0%
+yeah you know uh I I would say that yeah
+the K is in some ways not a very
+
+ align:start position:0%
+the K is in some ways not a very
+ 
+
+ align:start position:0%
+the K is in some ways not a very
+satisfying feature of this model because
+
+ align:start position:0%
+satisfying feature of this model because
+ 
+
+ align:start position:0%
+satisfying feature of this model because
+it makes it feel that the model is very
+
+ align:start position:0%
+it makes it feel that the model is very
+ 
+
+ align:start position:0%
+it makes it feel that the model is very
+special right but I mean in an actual
+
+ align:start position:0%
+special right but I mean in an actual
+ 
+
+ align:start position:0%
+special right but I mean in an actual
+population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people uh yeah yes so I guess that that
+
+ align:start position:0%
+people uh yeah yes so I guess that that
+ 
+
+ align:start position:0%
+people uh yeah yes so I guess that that
+was the example I was going to give it's
+
+ align:start position:0%
+was the example I was going to give it's
+ 
+
+ align:start position:0%
+was the example I was going to give it's
+not clear that um that this is of course
+
+ align:start position:0%
+not clear that um that this is of course
+ 
+
+ align:start position:0%
+not clear that um that this is of course
+it requires Ires somebody to give birth
+
+ align:start position:0%
+it requires Ires somebody to give birth
+ 
+
+ align:start position:0%
+it requires Ires somebody to give birth
+to kids right so you know so in that
+
+ align:start position:0%
+to kids right so you know so in that
+ 
+
+ align:start position:0%
+to kids right so you know so in that
+sense modeling this is a constant number
+
+ align:start position:0%
+sense modeling this is a constant number
+ 
+
+ align:start position:0%
+sense modeling this is a constant number
+per unit time which is what we're doing
+
+ align:start position:0%
+per unit time which is what we're doing
+ 
+
+ align:start position:0%
+per unit time which is what we're doing
+this rate K right is is a little bit
+
+ align:start position:0%
+this rate K right is is a little bit
+ 
+
+ align:start position:0%
+this rate K right is is a little bit
+funny because then what you'd really
+
+ align:start position:0%
+funny because then what you'd really
+ 
+
+ align:start position:0%
+funny because then what you'd really
+want to do is say oh maybe that it's
+
+ align:start position:0%
+want to do is say oh maybe that it's
+ 
+
+ align:start position:0%
+want to do is say oh maybe that it's
+it's these guys that give birth at some
+
+ align:start position:0%
+it's these guys that give birth at some
+ 
+
+ align:start position:0%
+it's these guys that give birth at some
+rate or so if you really wanted it to be
+
+ align:start position:0%
+rate or so if you really wanted it to be
+ 
+
+ align:start position:0%
+rate or so if you really wanted it to be
+accurate so I'd say that this is u in
+
+ align:start position:0%
+accurate so I'd say that this is u in
+ 
+
+ align:start position:0%
+accurate so I'd say that this is u in
+some ways just a mathematical
+
+ align:start position:0%
+some ways just a mathematical
+ 
+
+ align:start position:0%
+some ways just a mathematical
+simplification so that we can uh get at
+
+ align:start position:0%
+simplification so that we can uh get at
+ 
+
+ align:start position:0%
+simplification so that we can uh get at
+the heart of the Dynamics and what we'll
+
+ align:start position:0%
+the heart of the Dynamics and what we'll
+ 
+
+ align:start position:0%
+the heart of the Dynamics and what we'll
+see is that in these sir models uh you
+
+ align:start position:0%
+see is that in these sir models uh you
+ 
+
+ align:start position:0%
+see is that in these sir models uh you
+don't invoke anything like uh like this
+
+ align:start position:0%
+don't invoke anything like uh like this
+ 
+
+ align:start position:0%
+don't invoke anything like uh like this
+but rather what you do is you assume
+
+ align:start position:0%
+but rather what you do is you assume
+ 
+
+ align:start position:0%
+but rather what you do is you assume
+that at some rate in infected
+
+ align:start position:0%
+that at some rate in infected
+ 
+
+ align:start position:0%
+that at some rate in infected
+individuals uh can um well they don't
+
+ align:start position:0%
+individuals uh can um well they don't
+ 
+
+ align:start position:0%
+individuals uh can um well they don't
+just die but they they become resistant
+
+ align:start position:0%
+just die but they they become resistant
+ 
+
+ align:start position:0%
+just die but they they become resistant
+and then maybe later they become
+
+ align:start position:0%
+and then maybe later they become
+ 
+
+ align:start position:0%
+and then maybe later they become
+sensitive again right so so you just
+
+ align:start position:0%
+sensitive again right so so you just
+ 
+
+ align:start position:0%
+sensitive again right so so you just
+need you need some way of making sure
+
+ align:start position:0%
+need you need some way of making sure
+ 
+
+ align:start position:0%
+need you need some way of making sure
+that it's not the case that everybody
+
+ align:start position:0%
+that it's not the case that everybody
+ 
+
+ align:start position:0%
+that it's not the case that everybody
+just always dies
+
+ align:start position:0%
+just always dies
+ 
+
+ align:start position:0%
+just always dies
+right so in some ways this is more
+
+ align:start position:0%
+right so in some ways this is more
+ 
+
+ align:start position:0%
+right so in some ways this is more
+mathematical convenience and uh the
+
+ align:start position:0%
+mathematical convenience and uh the
+ 
+
+ align:start position:0%
+mathematical convenience and uh the
+basic conclusions end up being very
+
+ align:start position:0%
+basic conclusions end up being very
+ 
+
+ align:start position:0%
+basic conclusions end up being very
+robust to these sorts of things
+
+ align:start position:0%
+robust to these sorts of things
+ 
+
+ align:start position:0%
+robust to these sorts of things
+okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so it's uh you know in in these
+
+ align:start position:0%
+right so it's uh you know in in these
+ 
+
+ align:start position:0%
+right so it's uh you know in in these
+models it's always good to be clear
+
+ align:start position:0%
+models it's always good to be clear
+ 
+
+ align:start position:0%
+models it's always good to be clear
+about uh how we kind of go from this
+
+ align:start position:0%
+about uh how we kind of go from this
+ 
+
+ align:start position:0%
+about uh how we kind of go from this
+framework to something that is is more
+
+ align:start position:0%
+framework to something that is is more
+ 
+
+ align:start position:0%
+framework to something that is is more
+of a differential equation uh and what
+
+ align:start position:0%
+of a differential equation uh and what
+ 
+
+ align:start position:0%
+of a differential equation uh and what
+we're what we can do is we can think
+
+ align:start position:0%
+we're what we can do is we can think
+ 
+
+ align:start position:0%
+we're what we can do is we can think
+about the uh these uninfected
+
+ align:start position:0%
+about the uh these uninfected
+ 
+
+ align:start position:0%
+about the uh these uninfected
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+uninfected I.E the S's and as compared
+
+ align:start position:0%
+uninfected I.E the S's and as compared
+ 
+
+ align:start position:0%
+uninfected I.E the S's and as compared
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infected and we're going to have these
+
+ align:start position:0%
+infected and we're going to have these
+ 
+
+ align:start position:0%
+infected and we're going to have these
+guys be
+
+ align:start position:0%
+guys be
+ 
+
+ align:start position:0%
+guys be
+X right so first of all all the way that
+
+ align:start position:0%
+X right so first of all all the way that
+ 
+
+ align:start position:0%
+X right so first of all all the way that
+the and this is okay this is s and I
+
+ align:start position:0%
+the and this is okay this is s and I
+ 
+
+ align:start position:0%
+the and this is okay this is s and I
+right so the way that that the that X
+
+ align:start position:0%
+right so the way that that the that X
+ 
+
+ align:start position:0%
+right so the way that that the that X
+will be changing is that you we're
+
+ align:start position:0%
+will be changing is that you we're
+ 
+
+ align:start position:0%
+will be changing is that you we're
+assuming that that there's always some
+
+ align:start position:0%
+assuming that that there's always some
+ 
+
+ align:start position:0%
+assuming that that there's always some
+influx of individuals which could be
+
+ align:start position:0%
+influx of individuals which could be
+ 
+
+ align:start position:0%
+influx of individuals which could be
+birth or migration or something else
+
+ align:start position:0%
+birth or migration or something else
+ 
+
+ align:start position:0%
+birth or migration or something else
+right that are just always entering okay
+
+ align:start position:0%
+right that are just always entering okay
+ 
+
+ align:start position:0%
+right that are just always entering okay
+but then there's going to be two ways
+
+ align:start position:0%
+but then there's going to be two ways
+ 
+
+ align:start position:0%
+but then there's going to be two ways
+that uh that X is going to decrease
+
+ align:start position:0%
+that uh that X is going to decrease
+ 
+
+ align:start position:0%
+that uh that X is going to decrease
+right one is that there's just a death
+
+ align:start position:0%
+right one is that there's just a death
+ 
+
+ align:start position:0%
+right one is that there's just a death
+rate that is resulting uh in the absence
+
+ align:start position:0%
+rate that is resulting uh in the absence
+ 
+
+ align:start position:0%
+rate that is resulting uh in the absence
+of infection okay but then also there's
+
+ align:start position:0%
+of infection okay but then also there's
+ 
+
+ align:start position:0%
+of infection okay but then also there's
+going to be some of infection which is
+
+ align:start position:0%
+going to be some of infection which is
+ 
+
+ align:start position:0%
+going to be some of infection which is
+going to be proportional to Beta right
+
+ align:start position:0%
+going to be proportional to Beta right
+ 
+
+ align:start position:0%
+going to be proportional to Beta right
+so this is the simplest way that you can
+
+ align:start position:0%
+so this is the simplest way that you can
+ 
+
+ align:start position:0%
+so this is the simplest way that you can
+imagine uh uh capturing this this
+
+ align:start position:0%
+imagine uh uh capturing this this
+ 
+
+ align:start position:0%
+imagine uh uh capturing this this
+element that that the infected
+
+ align:start position:0%
+element that that the infected
+ 
+
+ align:start position:0%
+element that that the infected
+individuals uh can uh can transmit the
+
+ align:start position:0%
+individuals uh can uh can transmit the
+ 
+
+ align:start position:0%
+individuals uh can uh can transmit the
+infection to the sensitive individuals
+
+ align:start position:0%
+infection to the sensitive individuals
+ 
+
+ align:start position:0%
+infection to the sensitive individuals
+okay so it's proportional to someh we're
+
+ align:start position:0%
+okay so it's proportional to someh we're
+ 
+
+ align:start position:0%
+okay so it's proportional to someh we're
+we're modeling them as it's just a well-
+
+ align:start position:0%
+we're modeling them as it's just a well-
+ 
+
+ align:start position:0%
+we're modeling them as it's just a well-
+mixed population just like in chemical
+
+ align:start position:0%
+mixed population just like in chemical
+ 
+
+ align:start position:0%
+mixed population just like in chemical
+reactions and uh somehow the the rate of
+
+ align:start position:0%
+reactions and uh somehow the the rate of
+ 
+
+ align:start position:0%
+reactions and uh somehow the the rate of
+infection is proportional to the kind of
+
+ align:start position:0%
+infection is proportional to the kind of
+ 
+
+ align:start position:0%
+infection is proportional to the kind of
+frequency that they they hit each other
+
+ align:start position:0%
+frequency that they they hit each other
+ 
+
+ align:start position:0%
+frequency that they they hit each other
+right certainly the simplest simplest
+
+ align:start position:0%
+right certainly the simplest simplest
+ 
+
+ align:start position:0%
+right certainly the simplest simplest
+kind of model you can imagine okay all
+
+ align:start position:0%
+kind of model you can imagine okay all
+ 
+
+ align:start position:0%
+kind of model you can imagine okay all
+right whereas the infected individuals
+
+ align:start position:0%
+right whereas the infected individuals
+ 
+
+ align:start position:0%
+right whereas the infected individuals
+well what we're going to have is we're
+
+ align:start position:0%
+well what we're going to have is we're
+ 
+
+ align:start position:0%
+well what we're going to have is we're
+going to have an increased rate of death
+
+ align:start position:0%
+going to have an increased rate of death
+ 
+
+ align:start position:0%
+going to have an increased rate of death
+right uh so the simp all right this is a
+
+ align:start position:0%
+right uh so the simp all right this is a
+ 
+
+ align:start position:0%
+right uh so the simp all right this is a
+simplified way to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay right so this is really that
+
+ align:start position:0%
+it okay right so this is really that
+ 
+
+ align:start position:0%
+it okay right so this is really that
+there's a minus kind of a u plus v * y
+
+ align:start position:0%
+there's a minus kind of a u plus v * y
+ 
+
+ align:start position:0%
+there's a minus kind of a u plus v * y
+so this is just the death rate okay but
+
+ align:start position:0%
+so this is just the death rate okay but
+ 
+
+ align:start position:0%
+so this is just the death rate okay but
+then uh any individual that leaves the
+
+ align:start position:0%
+then uh any individual that leaves the
+ 
+
+ align:start position:0%
+then uh any individual that leaves the
+sensitive class this Min minus beta XY
+
+ align:start position:0%
+sensitive class this Min minus beta XY
+ 
+
+ align:start position:0%
+sensitive class this Min minus beta XY
+enters the uh infected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class right right so this this makes a
+
+ align:start position:0%
+class right right so this this makes a
+ 
+
+ align:start position:0%
+class right right so this this makes a
+lot of sense I think and now the
+
+ align:start position:0%
+lot of sense I think and now the
+ 
+
+ align:start position:0%
+lot of sense I think and now the
+question is um can we can we kind of
+
+ align:start position:0%
+question is um can we can we kind of
+ 
+
+ align:start position:0%
+question is um can we can we kind of
+make make sense of what's going on now
+
+ align:start position:0%
+make make sense of what's going on now
+ 
+
+ align:start position:0%
+make make sense of what's going on now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the right so you you saw in your reading
+
+ align:start position:0%
+the right so you you saw in your reading
+ 
+
+ align:start position:0%
+the right so you you saw in your reading
+what this R not parameter was right you
+
+ align:start position:0%
+what this R not parameter was right you
+ 
+
+ align:start position:0%
+what this R not parameter was right you
+should always remember that it's defined
+
+ align:start position:0%
+should always remember that it's defined
+ 
+
+ align:start position:0%
+should always remember that it's defined
+as this thing of if you kind of have one
+
+ align:start position:0%
+as this thing of if you kind of have one
+ 
+
+ align:start position:0%
+as this thing of if you kind of have one
+if you introduce one infected individual
+
+ align:start position:0%
+if you introduce one infected individual
+ 
+
+ align:start position:0%
+if you introduce one infected individual
+into a population of sensitive
+
+ align:start position:0%
+into a population of sensitive
+ 
+
+ align:start position:0%
+into a population of sensitive
+individuals what is the mean number of
+
+ align:start position:0%
+individuals what is the mean number of
+ 
+
+ align:start position:0%
+individuals what is the mean number of
+new infections that you get right and it
+
+ align:start position:0%
+new infections that you get right and it
+ 
+
+ align:start position:0%
+new infections that you get right and it
+makes sense that that the key thing is
+
+ align:start position:0%
+makes sense that that the key thing is
+ 
+
+ align:start position:0%
+makes sense that that the key thing is
+whether that that are not is kind of
+
+ align:start position:0%
+whether that that are not is kind of
+ 
+
+ align:start position:0%
+whether that that are not is kind of
+greater or less than one because if it's
+
+ align:start position:0%
+greater or less than one because if it's
+ 
+
+ align:start position:0%
+greater or less than one because if it's
+greater than one that leads to this
+
+ align:start position:0%
+greater than one that leads to this
+ 
+
+ align:start position:0%
+greater than one that leads to this
+exponential kind of explosion of the
+
+ align:start position:0%
+exponential kind of explosion of the
+ 
+
+ align:start position:0%
+exponential kind of explosion of the
+infected individuals doesn't mean that
+
+ align:start position:0%
+infected individuals doesn't mean that
+ 
+
+ align:start position:0%
+infected individuals doesn't mean that
+everyone's going to die necessarily
+
+ align:start position:0%
+everyone's going to die necessarily
+ 
+
+ align:start position:0%
+everyone's going to die necessarily
+because uh well we'll get into that but
+
+ align:start position:0%
+because uh well we'll get into that but
+ 
+
+ align:start position:0%
+because uh well we'll get into that but
+okay but if R not is less than one then
+
+ align:start position:0%
+okay but if R not is less than one then
+ 
+
+ align:start position:0%
+okay but if R not is less than one then
+then you expect that uh that infection
+
+ align:start position:0%
+then you expect that uh that infection
+ 
+
+ align:start position:0%
+then you expect that uh that infection
+to kind of die out right so why is it
+
+ align:start position:0%
+to kind of die out right so why is it
+ 
+
+ align:start position:0%
+to kind of die out right so why is it
+that that when you int if if R not is
+
+ align:start position:0%
+that that when you int if if R not is
+ 
+
+ align:start position:0%
+that that when you int if if R not is
+greater than one and you introduce one
+
+ align:start position:0%
+greater than one and you introduce one
+ 
+
+ align:start position:0%
+greater than one and you introduce one
+infected individual doesn't necessarily
+
+ align:start position:0%
+infected individual doesn't necessarily
+ 
+
+ align:start position:0%
+infected individual doesn't necessarily
+lead to you know kind of you know wipe
+
+ align:start position:0%
+lead to you know kind of you know wipe
+ 
+
+ align:start position:0%
+lead to you know kind of you know wipe
+out of the entire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population or maybe it does
+
+ align:start position:0%
+population or maybe it does
+ 
+
+ align:start position:0%
+population or maybe it does
+I this model is a little funny because
+
+ align:start position:0%
+I this model is a little funny because
+ 
+
+ align:start position:0%
+I this model is a little funny because
+you always have individuals entering
+
+ align:start position:0%
+you always have individuals entering
+ 
+
+ align:start position:0%
+you always have individuals entering
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but right okay so if it's very virent
+
+ align:start position:0%
+but right okay so if it's very virent
+ 
+
+ align:start position:0%
+but right okay so if it's very virent
+then the infected individuals may die
+
+ align:start position:0%
+then the infected individuals may die
+ 
+
+ align:start position:0%
+then the infected individuals may die
+quickly and this gets into this question
+
+ align:start position:0%
+quickly and this gets into this question
+ 
+
+ align:start position:0%
+quickly and this gets into this question
+of there may be some trade-offs in terms
+
+ align:start position:0%
+of there may be some trade-offs in terms
+ 
+
+ align:start position:0%
+of there may be some trade-offs in terms
+of veilance and we'll talk more about
+
+ align:start position:0%
+of veilance and we'll talk more about
+ 
+
+ align:start position:0%
+of veilance and we'll talk more about
+then the EV evolution of veilance but I
+
+ align:start position:0%
+then the EV evolution of veilance but I
+ 
+
+ align:start position:0%
+then the EV evolution of veilance but I
+guess the question is uh in in in
+
+ align:start position:0%
+guess the question is uh in in in
+ 
+
+ align:start position:0%
+guess the question is uh in in in
+there's a wide variety of classes of
+
+ align:start position:0%
+there's a wide variety of classes of
+ 
+
+ align:start position:0%
+there's a wide variety of classes of
+models not just where the ones where you
+
+ align:start position:0%
+models not just where the ones where you
+ 
+
+ align:start position:0%
+models not just where the ones where you
+have K entering but the the question
+
+ align:start position:0%
+have K entering but the the question
+ 
+
+ align:start position:0%
+have K entering but the the question
+somehow is um just because R not as
+
+ align:start position:0%
+somehow is um just because R not as
+ 
+
+ align:start position:0%
+somehow is um just because R not as
+greater than one that doesn't mean that
+
+ align:start position:0%
+greater than one that doesn't mean that
+ 
+
+ align:start position:0%
+greater than one that doesn't mean that
+the entire population will necessarily
+
+ align:start position:0%
+the entire population will necessarily
+ 
+
+ align:start position:0%
+the entire population will necessarily
+become infected right so because we have
+
+ align:start position:0%
+become infected right so because we have
+ 
+
+ align:start position:0%
+become infected right so because we have
+this idea of an exponential growth of
+
+ align:start position:0%
+this idea of an exponential growth of
+ 
+
+ align:start position:0%
+this idea of an exponential growth of
+the infected population if R kns greater
+
+ align:start position:0%
+the infected population if R kns greater
+ 
+
+ align:start position:0%
+the infected population if R kns greater
+than one
+
+ align:start position:0%
+than one
+ 
+
+ align:start position:0%
+than one
+right so why is it that it's not
+
+ align:start position:0%
+right so why is it that it's not
+ 
+
+ align:start position:0%
+right so why is it that it's not
+necessarily going to happen that the
+
+ align:start position:0%
+necessarily going to happen that the
+ 
+
+ align:start position:0%
+necessarily going to happen that the
+entire population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this question is a little bit ill
+
+ align:start position:0%
+is this question is a little bit ill
+ 
+
+ align:start position:0%
+is this question is a little bit ill
+posed in this
+
+ align:start position:0%
+posed in this
+ 
+
+ align:start position:0%
+posed in this
+model it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because some that's right okay I think
+
+ align:start position:0%
+because some that's right okay I think
+ 
+
+ align:start position:0%
+because some that's right okay I think
+this is the basic intuition that as the
+
+ align:start position:0%
+this is the basic intuition that as the
+ 
+
+ align:start position:0%
+this is the basic intuition that as the
+infected as more and more uh members of
+
+ align:start position:0%
+infected as more and more uh members of
+ 
+
+ align:start position:0%
+infected as more and more uh members of
+the population become infected then that
+
+ align:start position:0%
+the population become infected then that
+ 
+
+ align:start position:0%
+the population become infected then that
+could in principle reduce the um the
+
+ align:start position:0%
+could in principle reduce the um the
+ 
+
+ align:start position:0%
+could in principle reduce the um the
+possibilities for uh for new individuals
+
+ align:start position:0%
+possibilities for uh for new individuals
+ 
+
+ align:start position:0%
+possibilities for uh for new individuals
+to be Su you know kind of
+
+ align:start position:0%
+to be Su you know kind of
+ 
+
+ align:start position:0%
+to be Su you know kind of
+susceptible
+
+ align:start position:0%
+susceptible
+ 
+
+ align:start position:0%
+susceptible
+okay right and I'm using susceptible and
+
+ align:start position:0%
+okay right and I'm using susceptible and
+ 
+
+ align:start position:0%
+okay right and I'm using susceptible and
+sensitive at the same you know
+
+ align:start position:0%
+sensitive at the same you know
+ 
+
+ align:start position:0%
+sensitive at the same you know
+interchangeably um right and and So So
+
+ align:start position:0%
+interchangeably um right and and So So
+ 
+
+ align:start position:0%
+interchangeably um right and and So So
+eventually this exponential rate of uh
+
+ align:start position:0%
+eventually this exponential rate of uh
+ 
+
+ align:start position:0%
+eventually this exponential rate of uh
+kind of growth of the population can be
+
+ align:start position:0%
+kind of growth of the population can be
+ 
+
+ align:start position:0%
+kind of growth of the population can be
+kind of limited in some way right we
+
+ align:start position:0%
+kind of limited in some way right we
+ 
+
+ align:start position:0%
+kind of limited in some way right we
+we'll maybe look at this a little bit
+
+ align:start position:0%
+we'll maybe look at this a little bit
+ 
+
+ align:start position:0%
+we'll maybe look at this a little bit
+more in this s model because it's more
+
+ align:start position:0%
+more in this s model because it's more
+ 
+
+ align:start position:0%
+more in this s model because it's more
+clear um the B the basic reproductive
+
+ align:start position:0%
+clear um the B the basic reproductive
+ 
+
+ align:start position:0%
+clear um the B the basic reproductive
+or not is a
+
+ align:start position:0%
+or not is a
+ 
+
+ align:start position:0%
+or not is a
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+uh no it's it's it's it's it's a number
+
+ align:start position:0%
+uh no it's it's it's it's it's a number
+ 
+
+ align:start position:0%
+uh no it's it's it's it's it's a number
+right it's this expected number of new
+
+ align:start position:0%
+right it's this expected number of new
+ 
+
+ align:start position:0%
+right it's this expected number of new
+infections you get when you introduce
+
+ align:start position:0%
+infections you get when you introduce
+ 
+
+ align:start position:0%
+infections you get when you introduce
+one infected individual into the
+
+ align:start position:0%
+one infected individual into the
+ 
+
+ align:start position:0%
+one infected individual into the
+population all right and we like period
+
+ align:start position:0%
+population all right and we like period
+ 
+
+ align:start position:0%
+population all right and we like period
+so there's no not like per unit time or
+
+ align:start position:0%
+so there's no not like per unit time or
+ 
+
+ align:start position:0%
+so there's no not like per unit time or
+it's a number okay period so you expect
+
+ align:start position:0%
+it's a number okay period so you expect
+ 
+
+ align:start position:0%
+it's a number okay period so you expect
+that if you if you have r equal to one
+
+ align:start position:0%
+that if you if you have r equal to one
+ 
+
+ align:start position:0%
+that if you if you have r equal to one
+you expect that you introduce an
+
+ align:start position:0%
+you expect that you introduce an
+ 
+
+ align:start position:0%
+you expect that you introduce an
+infected individual into a population of
+
+ align:start position:0%
+infected individual into a population of
+ 
+
+ align:start position:0%
+infected individual into a population of
+sensive individuals you will get one
+
+ align:start position:0%
+sensive individuals you will get one
+ 
+
+ align:start position:0%
+sensive individuals you will get one
+other infected that's right so that's
+
+ align:start position:0%
+other infected that's right so that's
+ 
+
+ align:start position:0%
+other infected that's right so that's
+kind of the neutrally stable situation
+
+ align:start position:0%
+kind of the neutrally stable situation
+ 
+
+ align:start position:0%
+kind of the neutrally stable situation
+if R's one then you you add one
+
+ align:start position:0%
+if R's one then you you add one
+ 
+
+ align:start position:0%
+if R's one then you you add one
+infectant individual and you expect to
+
+ align:start position:0%
+infectant individual and you expect to
+ 
+
+ align:start position:0%
+infectant individual and you expect to
+get one other one so you have a random
+
+ align:start position:0%
+get one other one so you have a random
+ 
+
+ align:start position:0%
+get one other one so you have a random
+walk and it'll either it'll well in
+
+ align:start position:0%
+walk and it'll either it'll well in
+ 
+
+ align:start position:0%
+walk and it'll either it'll well in
+general it'll it'll randomly go extinct
+
+ align:start position:0%
+general it'll it'll randomly go extinct
+ 
+
+ align:start position:0%
+general it'll it'll randomly go extinct
+eventually yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes right so it depends upon a number
+
+ align:start position:0%
+yes right so it depends upon a number
+ 
+
+ align:start position:0%
+yes right so it depends upon a number
+yeah so let that's what we're going to
+
+ align:start position:0%
+yeah so let that's what we're going to
+ 
+
+ align:start position:0%
+yeah so let that's what we're going to
+do right now is is uh see if we can
+
+ align:start position:0%
+do right now is is uh see if we can
+ 
+
+ align:start position:0%
+do right now is is uh see if we can
+reconstruct what this R is equal to in
+
+ align:start position:0%
+reconstruct what this R is equal to in
+ 
+
+ align:start position:0%
+reconstruct what this R is equal to in
+in this model another question what's
+
+ align:start position:0%
+in this model another question what's
+ 
+
+ align:start position:0%
+in this model another question what's
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distrib deterministic yes exactly right
+
+ align:start position:0%
+distrib deterministic yes exactly right
+ 
+
+ align:start position:0%
+distrib deterministic yes exactly right
+so this is this is very interesting uh
+
+ align:start position:0%
+so this is this is very interesting uh
+ 
+
+ align:start position:0%
+so this is this is very interesting uh
+right so the question is what is going
+
+ align:start position:0%
+right so the question is what is going
+ 
+
+ align:start position:0%
+right so the question is what is going
+to be the distribution of the number of
+
+ align:start position:0%
+to be the distribution of the number of
+ 
+
+ align:start position:0%
+to be the distribution of the number of
+infected individuals right and in this
+
+ align:start position:0%
+infected individuals right and in this
+ 
+
+ align:start position:0%
+infected individuals right and in this
+model we're assuming that every infected
+
+ align:start position:0%
+model we're assuming that every infected
+ 
+
+ align:start position:0%
+model we're assuming that every infected
+individual is the same right so we
+
+ align:start position:0%
+individual is the same right so we
+ 
+
+ align:start position:0%
+individual is the same right so we
+should be able to all right I wish that
+
+ align:start position:0%
+should be able to all right I wish that
+ 
+
+ align:start position:0%
+should be able to all right I wish that
+we just on the wall somewhere had our
+
+ align:start position:0%
+we just on the wall somewhere had our
+ 
+
+ align:start position:0%
+we just on the wall somewhere had our
+five different standard probability
+
+ align:start position:0%
+five different standard probability
+ 
+
+ align:start position:0%
+five different standard probability
+distributions right so that we could
+
+ align:start position:0%
+distributions right so that we could
+ 
+
+ align:start position:0%
+distributions right so that we could
+always go back to them right but what uh
+
+ align:start position:0%
+always go back to them right but what uh
+ 
+
+ align:start position:0%
+always go back to them right but what uh
+right so the question is in this model
+
+ align:start position:0%
+right so the question is in this model
+ 
+
+ align:start position:0%
+right so the question is in this model
+if you have if you introduce one
+
+ align:start position:0%
+if you have if you introduce one
+ 
+
+ align:start position:0%
+if you have if you introduce one
+infected individual in the population
+
+ align:start position:0%
+infected individual in the population
+ 
+
+ align:start position:0%
+infected individual in the population
+how many new infected individuals you
+
+ align:start position:0%
+how many new infected individuals you
+ 
+
+ align:start position:0%
+how many new infected individuals you
+get are not tells you about the mean
+
+ align:start position:0%
+get are not tells you about the mean
+ 
+
+ align:start position:0%
+get are not tells you about the mean
+right but will you always get the mean
+
+ align:start position:0%
+right but will you always get the mean
+ 
+
+ align:start position:0%
+right but will you always get the mean
+no right uh all right so let's let's all
+
+ align:start position:0%
+no right uh all right so let's let's all
+ 
+
+ align:start position:0%
+no right uh all right so let's let's all
+think about this for 10 seconds and we
+
+ align:start position:0%
+think about this for 10 seconds and we
+ 
+
+ align:start position:0%
+think about this for 10 seconds and we
+will verbally kind of yell out what we
+
+ align:start position:0%
+will verbally kind of yell out what we
+ 
+
+ align:start position:0%
+will verbally kind of yell out what we
+think the distribution will be of the
+
+ align:start position:0%
+think the distribution will be of the
+ 
+
+ align:start position:0%
+think the distribution will be of the
+number of new infections from a single
+
+ align:start position:0%
+number of new infections from a single
+ 
+
+ align:start position:0%
+number of new infections from a single
+infected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+individual okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we're verbally ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five all right everybody thinks it's Pon
+
+ align:start position:0%
+five all right everybody thinks it's Pon
+ 
+
+ align:start position:0%
+five all right everybody thinks it's Pon
+why why would it be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pon
+
+ align:start position:0%
+Pon
+ 
+
+ align:start position:0%
+Pon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+ini right okay okay so the idea is we
+
+ align:start position:0%
+ini right okay okay so the idea is we
+ 
+
+ align:start position:0%
+ini right okay okay so the idea is we
+have okay now we imagine we're infected
+
+ align:start position:0%
+have okay now we imagine we're infected
+ 
+
+ align:start position:0%
+have okay now we imagine we're infected
+individual and there's some rate that we
+
+ align:start position:0%
+individual and there's some rate that we
+ 
+
+ align:start position:0%
+individual and there's some rate that we
+are infecting others right okay now if I
+
+ align:start position:0%
+are infecting others right okay now if I
+ 
+
+ align:start position:0%
+are infecting others right okay now if I
+ask you the question oh H how many
+
+ align:start position:0%
+ask you the question oh H how many
+ 
+
+ align:start position:0%
+ask you the question oh H how many
+individuals will I infect in the
+
+ align:start position:0%
+individuals will I infect in the
+ 
+
+ align:start position:0%
+individuals will I infect in the
+next 10 days or we could do 21 days if
+
+ align:start position:0%
+next 10 days or we could do 21 days if
+ 
+
+ align:start position:0%
+next 10 days or we could do 21 days if
+you guys like that okay so uh right so
+
+ align:start position:0%
+you guys like that okay so uh right so
+ 
+
+ align:start position:0%
+you guys like that okay so uh right so
+if I ask okay how many do I infect in
+
+ align:start position:0%
+if I ask okay how many do I infect in
+ 
+
+ align:start position:0%
+if I ask okay how many do I infect in
+the next 10 days right now I'm assuming
+
+ align:start position:0%
+the next 10 days right now I'm assuming
+ 
+
+ align:start position:0%
+the next 10 days right now I'm assuming
+that I Stay Alive okay but let's say
+
+ align:start position:0%
+that I Stay Alive okay but let's say
+ 
+
+ align:start position:0%
+that I Stay Alive okay but let's say
+assuming I Stay Alive how many do I
+
+ align:start position:0%
+assuming I Stay Alive how many do I
+ 
+
+ align:start position:0%
+assuming I Stay Alive how many do I
+infect over the next 10 days that's
+
+ align:start position:0%
+infect over the next 10 days that's
+ 
+
+ align:start position:0%
+infect over the next 10 days that's
+going to be distributed
+
+ align:start position:0%
+going to be distributed
+ 
+
+ align:start position:0%
+going to be distributed
+as that is Plus on right but the
+
+ align:start position:0%
+as that is Plus on right but the
+ 
+
+ align:start position:0%
+as that is Plus on right but the
+question that you're asking is a
+
+ align:start position:0%
+question that you're asking is a
+ 
+
+ align:start position:0%
+question that you're asking is a
+different one you're asking what is
+
+ align:start position:0%
+different one you're asking what is
+ 
+
+ align:start position:0%
+different one you're asking what is
+going to be the total what is going to
+
+ align:start position:0%
+going to be the total what is going to
+ 
+
+ align:start position:0%
+going to be the total what is going to
+be the distribution of the total number
+
+ align:start position:0%
+be the distribution of the total number
+ 
+
+ align:start position:0%
+be the distribution of the total number
+of new infections that I cause right and
+
+ align:start position:0%
+of new infections that I cause right and
+ 
+
+ align:start position:0%
+of new infections that I cause right and
+this is precisely the
+
+ align:start position:0%
+this is precisely the
+ 
+
+ align:start position:0%
+this is precisely the
+same situation that we've analyzed lots
+
+ align:start position:0%
+same situation that we've analyzed lots
+ 
+
+ align:start position:0%
+same situation that we've analyzed lots
+and lots of times right what does it
+
+ align:start position:0%
+and lots of times right what does it
+ 
+
+ align:start position:0%
+and lots of times right what does it
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like H geomet okay okay yes it's going
+
+ align:start position:0%
+like H geomet okay okay yes it's going
+ 
+
+ align:start position:0%
+like H geomet okay okay yes it's going
+to be a geometric distribution but why
+
+ align:start position:0%
+to be a geometric distribution but why
+ 
+
+ align:start position:0%
+to be a geometric distribution but why
+it well because like you can have an
+
+ align:start position:0%
+it well because like you can have an
+ 
+
+ align:start position:0%
+it well because like you can have an
+infection another infection like
+
+ align:start position:0%
+infection another infection like
+ 
+
+ align:start position:0%
+infection another infection like
+multiple that's right so what what we
+
+ align:start position:0%
+multiple that's right so what what we
+ 
+
+ align:start position:0%
+multiple that's right so what what we
+have is because we have we have an
+
+ align:start position:0%
+have is because we have we have an
+ 
+
+ align:start position:0%
+have is because we have we have an
+infected individual there's two things
+
+ align:start position:0%
+infected individual there's two things
+ 
+
+ align:start position:0%
+infected individual there's two things
+that can happen right where we have they
+
+ align:start position:0%
+that can happen right where we have they
+ 
+
+ align:start position:0%
+that can happen right where we have they
+he's going to die at some rate and he
+
+ align:start position:0%
+he's going to die at some rate and he
+ 
+
+ align:start position:0%
+he's going to die at some rate and he
+will also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um have another there's this other rate
+
+ align:start position:0%
+um have another there's this other rate
+ 
+
+ align:start position:0%
+um have another there's this other rate
+which is going to go as beta time X or
+
+ align:start position:0%
+which is going to go as beta time X or
+ 
+
+ align:start position:0%
+which is going to go as beta time X or
+so right telling us about the rate of
+
+ align:start position:0%
+so right telling us about the rate of
+ 
+
+ align:start position:0%
+so right telling us about the rate of
+new infections and we want to know how
+
+ align:start position:0%
+new infections and we want to know how
+ 
+
+ align:start position:0%
+new infections and we want to know how
+many times we go around this Loop before
+
+ align:start position:0%
+many times we go around this Loop before
+ 
+
+ align:start position:0%
+many times we go around this Loop before
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+degrade or die or something you know
+
+ align:start position:0%
+degrade or die or something you know
+ 
+
+ align:start position:0%
+degrade or die or something you know
+disappear from the population does this
+
+ align:start position:0%
+disappear from the population does this
+ 
+
+ align:start position:0%
+disappear from the population does this
+look at all familiar all right were you
+
+ align:start position:0%
+look at all familiar all right were you
+ 
+
+ align:start position:0%
+look at all familiar all right were you
+guys the same same students that were
+
+ align:start position:0%
+guys the same same students that were
+ 
+
+ align:start position:0%
+guys the same same students that were
+here for the first half of the class
+
+ align:start position:0%
+here for the first half of the class
+ 
+
+ align:start position:0%
+here for the first half of the class
+yeah and so like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the it's like
+
+ align:start position:0%
+the it's like
+ 
+
+ align:start position:0%
+the it's like
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's yeah evaluated when the all right
+
+ align:start position:0%
+it's yeah evaluated when the all right
+ 
+
+ align:start position:0%
+it's yeah evaluated when the all right
+so R KN is the mean size of protein
+
+ align:start position:0%
+so R KN is the mean size of protein
+ 
+
+ align:start position:0%
+so R KN is the mean size of protein
+bursts in the context of this other
+
+ align:start position:0%
+bursts in the context of this other
+ 
+
+ align:start position:0%
+bursts in the context of this other
+model which was what was the
+
+ align:start position:0%
+model which was what was the
+ 
+
+ align:start position:0%
+model which was what was the
+situation and this one's really good one
+
+ align:start position:0%
+situation and this one's really good one
+ 
+
+ align:start position:0%
+situation and this one's really good one
+for you guys to know it's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful yeah so yeah what we saw this
+
+ align:start position:0%
+useful yeah so yeah what we saw this
+ 
+
+ align:start position:0%
+useful yeah so yeah what we saw this
+exact model in the context of gene
+
+ align:start position:0%
+exact model in the context of gene
+ 
+
+ align:start position:0%
+exact model in the context of gene
+expression and what was the what was the
+
+ align:start position:0%
+expression and what was the what was the
+ 
+
+ align:start position:0%
+expression and what was the what was the
+situation that
+
+ align:start position:0%
+situation that
+ 
+
+ align:start position:0%
+situation that
+we production of from yeah production of
+
+ align:start position:0%
+we production of from yeah production of
+ 
+
+ align:start position:0%
+we production of from yeah production of
+proteins from a single mRNA right
+
+ align:start position:0%
+proteins from a single mRNA right
+ 
+
+ align:start position:0%
+proteins from a single mRNA right
+because remember we had this thing where
+
+ align:start position:0%
+because remember we had this thing where
+ 
+
+ align:start position:0%
+because remember we had this thing where
+we had the M we and we said oh well the
+
+ align:start position:0%
+we had the M we and we said oh well the
+ 
+
+ align:start position:0%
+we had the M we and we said oh well the
+Mna is going to be degraded at some rate
+
+ align:start position:0%
+Mna is going to be degraded at some rate
+ 
+
+ align:start position:0%
+Mna is going to be degraded at some rate
+but there's also it's going to be trans
+
+ align:start position:0%
+but there's also it's going to be trans
+ 
+
+ align:start position:0%
+but there's also it's going to be trans
+it's going to be translated at some rate
+
+ align:start position:0%
+it's going to be translated at some rate
+ 
+
+ align:start position:0%
+it's going to be translated at some rate
+so the distribution number of times that
+
+ align:start position:0%
+so the distribution number of times that
+ 
+
+ align:start position:0%
+so the distribution number of times that
+it's translated before it degrades is
+
+ align:start position:0%
+it's translated before it degrades is
+ 
+
+ align:start position:0%
+it's translated before it degrades is
+going to be geometric because we go
+
+ align:start position:0%
+going to be geometric because we go
+ 
+
+ align:start position:0%
+going to be geometric because we go
+around this Loop some number of times
+
+ align:start position:0%
+around this Loop some number of times
+ 
+
+ align:start position:0%
+around this Loop some number of times
+right so this is the same same
+
+ align:start position:0%
+right so this is the same same
+ 
+
+ align:start position:0%
+right so this is the same same
+thing okay and the uh
+
+ align:start position:0%
+thing okay and the uh
+ 
+
+ align:start position:0%
+thing okay and the uh
+the right the paper that I um that I put
+
+ align:start position:0%
+the right the paper that I um that I put
+ 
+
+ align:start position:0%
+the right the paper that I um that I put
+a supplementary reading by Jam Lloyd
+
+ align:start position:0%
+a supplementary reading by Jam Lloyd
+ 
+
+ align:start position:0%
+a supplementary reading by Jam Lloyd
+Smith I always get his name and Jamie
+
+ align:start position:0%
+Smith I always get his name and Jamie
+ 
+
+ align:start position:0%
+Smith I always get his name and Jamie
+Lloyd right right something mixed up but
+
+ align:start position:0%
+Lloyd right right something mixed up but
+ 
+
+ align:start position:0%
+Lloyd right right something mixed up but
+yeah Jamie Smith um so he he was uh
+
+ align:start position:0%
+yeah Jamie Smith um so he he was uh
+ 
+
+ align:start position:0%
+yeah Jamie Smith um so he he was uh
+studying the the Dynamics of um of
+
+ align:start position:0%
+studying the the Dynamics of um of
+ 
+
+ align:start position:0%
+studying the the Dynamics of um of
+infections when you have this thing
+
+ align:start position:0%
+infections when you have this thing
+ 
+
+ align:start position:0%
+infections when you have this thing
+where there's there's intrinsic
+
+ align:start position:0%
+where there's there's intrinsic
+ 
+
+ align:start position:0%
+where there's there's intrinsic
+variation in say the infectivity of an
+
+ align:start position:0%
+variation in say the infectivity of an
+ 
+
+ align:start position:0%
+variation in say the infectivity of an
+individual right because here you get
+
+ align:start position:0%
+individual right because here you get
+ 
+
+ align:start position:0%
+individual right because here you get
+this geometric distribution even though
+
+ align:start position:0%
+this geometric distribution even though
+ 
+
+ align:start position:0%
+this geometric distribution even though
+all the individuals are principal
+
+ align:start position:0%
+all the individuals are principal
+ 
+
+ align:start position:0%
+all the individuals are principal
+identical right now the question is if
+
+ align:start position:0%
+identical right now the question is if
+ 
+
+ align:start position:0%
+identical right now the question is if
+you there's some distributions of say
+
+ align:start position:0%
+you there's some distributions of say
+ 
+
+ align:start position:0%
+you there's some distributions of say
+infectivities then you'll get an even uh
+
+ align:start position:0%
+infectivities then you'll get an even uh
+ 
+
+ align:start position:0%
+infectivities then you'll get an even uh
+kind of broader distribution of
+
+ align:start position:0%
+kind of broader distribution of
+ 
+
+ align:start position:0%
+kind of broader distribution of
+resulting number of new infections right
+
+ align:start position:0%
+resulting number of new infections right
+ 
+
+ align:start position:0%
+resulting number of new infections right
+uh right so there's this classic thing
+
+ align:start position:0%
+uh right so there's this classic thing
+ 
+
+ align:start position:0%
+uh right so there's this classic thing
+of Typhoid Mary who was she was a nurse
+
+ align:start position:0%
+of Typhoid Mary who was she was a nurse
+ 
+
+ align:start position:0%
+of Typhoid Mary who was she was a nurse
+that okay now I'm I don't remember the
+
+ align:start position:0%
+that okay now I'm I don't remember the
+ 
+
+ align:start position:0%
+that okay now I'm I don't remember the
+story um yeah she was a cook a cook cook
+
+ align:start position:0%
+story um yeah she was a cook a cook cook
+ 
+
+ align:start position:0%
+story um yeah she was a cook a cook cook
+she cooked for a lot of people okay so
+
+ align:start position:0%
+she cooked for a lot of people okay so
+ 
+
+ align:start position:0%
+she cooked for a lot of people okay so
+right so she was somehow resistant
+
+ align:start position:0%
+right so she was somehow resistant
+ 
+
+ align:start position:0%
+right so she was somehow resistant
+typhoid but then uh but then she was
+
+ align:start position:0%
+typhoid but then uh but then she was
+ 
+
+ align:start position:0%
+typhoid but then uh but then she was
+cooking for other people and so then
+
+ align:start position:0%
+cooking for other people and so then
+ 
+
+ align:start position:0%
+cooking for other people and so then
+caused a bunch of infections is that
+
+ align:start position:0%
+caused a bunch of infections is that
+ 
+
+ align:start position:0%
+caused a bunch of infections is that
+okay U yes so this would be an example
+
+ align:start position:0%
+okay U yes so this would be an example
+ 
+
+ align:start position:0%
+okay U yes so this would be an example
+of a very infective individual right
+
+ align:start position:0%
+of a very infective individual right
+ 
+
+ align:start position:0%
+of a very infective individual right
+that's beyond the beyond the assumptions
+
+ align:start position:0%
+that's beyond the beyond the assumptions
+ 
+
+ align:start position:0%
+that's beyond the beyond the assumptions
+in this model right and as you can
+
+ align:start position:0%
+in this model right and as you can
+ 
+
+ align:start position:0%
+in this model right and as you can
+imagine if you have variations in this
+
+ align:start position:0%
+imagine if you have variations in this
+ 
+
+ align:start position:0%
+imagine if you have variations in this
+infectivity then what it does is it for
+
+ align:start position:0%
+infectivity then what it does is it for
+ 
+
+ align:start position:0%
+infectivity then what it does is it for
+a given R not so if you fix R not then
+
+ align:start position:0%
+a given R not so if you fix R not then
+ 
+
+ align:start position:0%
+a given R not so if you fix R not then
+you have a broader distributions of
+
+ align:start position:0%
+you have a broader distributions of
+ 
+
+ align:start position:0%
+you have a broader distributions of
+infectivities what it means is that a
+
+ align:start position:0%
+infectivities what it means is that a
+ 
+
+ align:start position:0%
+infectivities what it means is that a
+larger fraction of the infections will
+
+ align:start position:0%
+larger fraction of the infections will
+ 
+
+ align:start position:0%
+larger fraction of the infections will
+go extinct but those that get going will
+
+ align:start position:0%
+go extinct but those that get going will
+ 
+
+ align:start position:0%
+go extinct but those that get going will
+kind of be
+
+ align:start position:0%
+kind of be
+ 
+
+ align:start position:0%
+kind of be
+explosive okay if you're curious about
+
+ align:start position:0%
+explosive okay if you're curious about
+ 
+
+ align:start position:0%
+explosive okay if you're curious about
+these sorts of ideas you should you
+
+ align:start position:0%
+these sorts of ideas you should you
+ 
+
+ align:start position:0%
+these sorts of ideas you should you
+should look at the uh this optional
+
+ align:start position:0%
+should look at the uh this optional
+ 
+
+ align:start position:0%
+should look at the uh this optional
+reading paper that I I put out
+
+ align:start position:0%
+reading paper that I I put out
+ 
+
+ align:start position:0%
+reading paper that I I put out
+there okay all right so I just want to
+
+ align:start position:0%
+there okay all right so I just want to
+ 
+
+ align:start position:0%
+there okay all right so I just want to
+be clear this is geometric geometric
+
+ align:start position:0%
+be clear this is geometric geometric
+ 
+
+ align:start position:0%
+be clear this is geometric geometric
+number of new
+
+ align:start position:0%
+number of new
+ 
+
+ align:start position:0%
+number of new
+infections
+
+ align:start position:0%
+infections
+ 
+
+ align:start position:0%
+infections
+distribution uh of new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes all right so this this is the right
+
+ align:start position:0%
+yes all right so this this is the right
+ 
+
+ align:start position:0%
+yes all right so this this is the right
+so we're talking about the number of
+
+ align:start position:0%
+so we're talking about the number of
+ 
+
+ align:start position:0%
+so we're talking about the number of
+infections that result when you just add
+
+ align:start position:0%
+infections that result when you just add
+ 
+
+ align:start position:0%
+infections that result when you just add
+one infected individual to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population well well U we are not yet
+
+ align:start position:0%
+population well well U we are not yet
+ 
+
+ align:start position:0%
+population well well U we are not yet
+thinking about them although in in this
+
+ align:start position:0%
+thinking about them although in in this
+ 
+
+ align:start position:0%
+thinking about them although in in this
+case those are all those are also
+
+ align:start position:0%
+case those are all those are also
+ 
+
+ align:start position:0%
+case those are all those are also
+geometrically distributed but what you
+
+ align:start position:0%
+geometrically distributed but what you
+ 
+
+ align:start position:0%
+geometrically distributed but what you
+expect is that the mean of those things
+
+ align:start position:0%
+expect is that the mean of those things
+ 
+
+ align:start position:0%
+expect is that the mean of those things
+will change because the number of uh uh
+
+ align:start position:0%
+will change because the number of uh uh
+ 
+
+ align:start position:0%
+will change because the number of uh uh
+susceptible or whatnot individuals
+
+ align:start position:0%
+susceptible or whatnot individuals
+ 
+
+ align:start position:0%
+susceptible or whatnot individuals
+that's going to change right but uh so
+
+ align:start position:0%
+that's going to change right but uh so
+ 
+
+ align:start position:0%
+that's going to change right but uh so
+so the the mean the mean number is going
+
+ align:start position:0%
+so the the mean the mean number is going
+ 
+
+ align:start position:0%
+so the the mean the mean number is going
+to change but the distributions will
+
+ align:start position:0%
+to change but the distributions will
+ 
+
+ align:start position:0%
+to change but the distributions will
+still be geometric but in total that
+
+ align:start position:0%
+still be geometric but in total that
+ 
+
+ align:start position:0%
+still be geometric but in total that
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+geom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number no so just because each of these
+
+ align:start position:0%
+number no so just because each of these
+ 
+
+ align:start position:0%
+number no so just because each of these
+substeps is geometric does not mean that
+
+ align:start position:0%
+substeps is geometric does not mean that
+ 
+
+ align:start position:0%
+substeps is geometric does not mean that
+um that you end up with a geometric
+
+ align:start position:0%
+um that you end up with a geometric
+ 
+
+ align:start position:0%
+um that you end up with a geometric
+distribution indeed if you add up many
+
+ align:start position:0%
+distribution indeed if you add up many
+ 
+
+ align:start position:0%
+distribution indeed if you add up many
+let's say that I put in 20 infected
+
+ align:start position:0%
+let's say that I put in 20 infected
+ 
+
+ align:start position:0%
+let's say that I put in 20 infected
+individuals into the population and I
+
+ align:start position:0%
+individuals into the population and I
+ 
+
+ align:start position:0%
+individuals into the population and I
+ask what's going to be the distribution
+
+ align:start position:0%
+ask what's going to be the distribution
+ 
+
+ align:start position:0%
+ask what's going to be the distribution
+of the number of infections caused
+
+ align:start position:0%
+of the number of infections caused
+ 
+
+ align:start position:0%
+of the number of infections caused
+immediately from those 20 that's going
+
+ align:start position:0%
+immediately from those 20 that's going
+ 
+
+ align:start position:0%
+immediately from those 20 that's going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+what gamma and and for 20 or it's going
+
+ align:start position:0%
+what gamma and and for 20 or it's going
+ 
+
+ align:start position:0%
+what gamma and and for 20 or it's going
+to be basically gaan or okay well if I
+
+ align:start position:0%
+to be basically gaan or okay well if I
+ 
+
+ align:start position:0%
+to be basically gaan or okay well if I
+said 100 then you know definitely gaan
+
+ align:start position:0%
+said 100 then you know definitely gaan
+ 
+
+ align:start position:0%
+said 100 then you know definitely gaan
+yeah yeah it's a gamma distribution that
+
+ align:start position:0%
+yeah yeah it's a gamma distribution that
+ 
+
+ align:start position:0%
+yeah yeah it's a gamma distribution that
+looks very much like a gaussian in that
+
+ align:start position:0%
+looks very much like a gaussian in that
+ 
+
+ align:start position:0%
+looks very much like a gaussian in that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+okay all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay we so we've been talking
+
+ align:start position:0%
+right okay we so we've been talking
+ 
+
+ align:start position:0%
+right okay we so we've been talking
+about the definition of this rot but of
+
+ align:start position:0%
+about the definition of this rot but of
+ 
+
+ align:start position:0%
+about the definition of this rot but of
+course we should figure out what it uh
+
+ align:start position:0%
+course we should figure out what it uh
+ 
+
+ align:start position:0%
+course we should figure out what it uh
+what it is right we want to know R KN is
+
+ align:start position:0%
+what it is right we want to know R KN is
+ 
+
+ align:start position:0%
+what it is right we want to know R KN is
+equal to and what I'm going to tell you
+
+ align:start position:0%
+equal to and what I'm going to tell you
+ 
+
+ align:start position:0%
+equal to and what I'm going to tell you
+is that it
+
+ align:start position:0%
+is that it
+ 
+
+ align:start position:0%
+is that it
+is uh there's a one over U plus b okay
+
+ align:start position:0%
+is uh there's a one over U plus b okay
+ 
+
+ align:start position:0%
+is uh there's a one over U plus b okay
+but then there are some other terms and
+
+ align:start position:0%
+but then there are some other terms and
+ 
+
+ align:start position:0%
+but then there are some other terms and
+I have un fortunately lost my notes
+
+ align:start position:0%
+I have un fortunately lost my notes
+ 
+
+ align:start position:0%
+I have un fortunately lost my notes
+right so uh you guys are going to have
+
+ align:start position:0%
+right so uh you guys are going to have
+ 
+
+ align:start position:0%
+right so uh you guys are going to have
+to help me figure this out all right um
+
+ align:start position:0%
+to help me figure this out all right um
+ 
+
+ align:start position:0%
+to help me figure this out all right um
+and what you're going to do is you're
+
+ align:start position:0%
+and what you're going to do is you're
+ 
+
+ align:start position:0%
+and what you're going to do is you're
+going to take advantage of your cards
+
+ align:start position:0%
+going to take advantage of your cards
+ 
+
+ align:start position:0%
+going to take advantage of your cards
+and again put things in the numerators
+
+ align:start position:0%
+and again put things in the numerators
+ 
+
+ align:start position:0%
+and again put things in the numerators
+and put things in the denominators
+
+ align:start position:0%
+and put things in the denominators
+ 
+
+ align:start position:0%
+and put things in the denominators
+corresponding to how I'm supposed to
+
+ align:start position:0%
+corresponding to how I'm supposed to
+ 
+
+ align:start position:0%
+corresponding to how I'm supposed to
+fill out this equation all
+
+ align:start position:0%
+fill out this equation all
+ 
+
+ align:start position:0%
+fill out this equation all
+right you can start thinking about it
+
+ align:start position:0%
+right you can start thinking about it
+ 
+
+ align:start position:0%
+right you can start thinking about it
+while I give you the options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what uh although I guess you
+
+ align:start position:0%
+okay so what uh although I guess you
+ 
+
+ align:start position:0%
+okay so what uh although I guess you
+could recapitulate this by just putting
+
+ align:start position:0%
+could recapitulate this by just putting
+ 
+
+ align:start position:0%
+could recapitulate this by just putting
+B and C although maybe you need it more
+
+ align:start position:0%
+B and C although maybe you need it more
+ 
+
+ align:start position:0%
+B and C although maybe you need it more
+than once I all right do what you will
+
+ align:start position:0%
+than once I all right do what you will
+ 
+
+ align:start position:0%
+than once I all right do what you will
+do you understand the do you understand
+
+ align:start position:0%
+do you understand the do you understand
+ 
+
+ align:start position:0%
+do you understand the do you understand
+the question right I'm going to have to
+
+ align:start position:0%
+the question right I'm going to have to
+ 
+
+ align:start position:0%
+the question right I'm going to have to
+there going to be something else I'm
+
+ align:start position:0%
+there going to be something else I'm
+ 
+
+ align:start position:0%
+there going to be something else I'm
+going to put right here and I want to
+
+ align:start position:0%
+going to put right here and I want to
+ 
+
+ align:start position:0%
+going to put right here and I want to
+know there going to be some things in
+
+ align:start position:0%
+know there going to be some things in
+ 
+
+ align:start position:0%
+know there going to be some things in
+the numerator or some things in the
+
+ align:start position:0%
+the numerator or some things in the
+ 
+
+ align:start position:0%
+the numerator or some things in the
+denominator okay I'm going to give you
+
+ align:start position:0%
+denominator okay I'm going to give you
+ 
+
+ align:start position:0%
+denominator okay I'm going to give you
+uh I'm going to give you 30 seconds to
+
+ align:start position:0%
+uh I'm going to give you 30 seconds to
+ 
+
+ align:start position:0%
+uh I'm going to give you 30 seconds to
+think about it because this is uh it's
+
+ align:start position:0%
+think about it because this is uh it's
+ 
+
+ align:start position:0%
+think about it because this is uh it's
+important to be able to reason your way
+
+ align:start position:0%
+important to be able to reason your way
+ 
+
+ align:start position:0%
+important to be able to reason your way
+through this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right do you need more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time I'll give you another 15 seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's go ahead and vote all
+
+ align:start position:0%
+all right let's go ahead and vote all
+ 
+
+ align:start position:0%
+all right let's go ahead and vote all
+right ready three two
+
+ align:start position:0%
+right ready three two
+ 
+
+ align:start position:0%
+right ready three two
+one all right I think I like it we're
+
+ align:start position:0%
+one all right I think I like it we're
+ 
+
+ align:start position:0%
+one all right I think I like it we're
+really looking quite nice all right so
+
+ align:start position:0%
+really looking quite nice all right so
+ 
+
+ align:start position:0%
+really looking quite nice all right so
+there's a claim that it's going to be a
+
+ align:start position:0%
+there's a claim that it's going to be a
+ 
+
+ align:start position:0%
+there's a claim that it's going to be a
+d over B I.E that it's going to be we
+
+ align:start position:0%
+d over B I.E that it's going to be we
+ 
+
+ align:start position:0%
+d over B I.E that it's going to be we
+should be writing a beta K over
+
+ align:start position:0%
+should be writing a beta K over
+ 
+
+ align:start position:0%
+should be writing a beta K over
+you all right can somebody can somebody
+
+ align:start position:0%
+you all right can somebody can somebody
+ 
+
+ align:start position:0%
+you all right can somebody can somebody
+explain how they got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there yes please um well it's it's going
+
+ align:start position:0%
+there yes please um well it's it's going
+ 
+
+ align:start position:0%
+there yes please um well it's it's going
+to be uh
+
+ align:start position:0%
+to be uh
+ 
+
+ align:start position:0%
+to be uh
+these these two okay yeah this this
+
+ align:start position:0%
+these these two okay yeah this this
+ 
+
+ align:start position:0%
+these these two okay yeah this this
+helped right okay good right so perfect
+
+ align:start position:0%
+helped right okay good right so perfect
+ 
+
+ align:start position:0%
+helped right okay good right so perfect
+so exactly so what this this thing is
+
+ align:start position:0%
+so exactly so what this this thing is
+ 
+
+ align:start position:0%
+so exactly so what this this thing is
+what what is this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here right uh and which means that this
+
+ align:start position:0%
+here right uh and which means that this
+ 
+
+ align:start position:0%
+here right uh and which means that this
+whole the one over it is it's the it's
+
+ align:start position:0%
+whole the one over it is it's the it's
+ 
+
+ align:start position:0%
+whole the one over it is it's the it's
+the expected lifetime of an infected
+
+ align:start position:0%
+the expected lifetime of an infected
+ 
+
+ align:start position:0%
+the expected lifetime of an infected
+individual right so we the definition of
+
+ align:start position:0%
+individual right so we the definition of
+ 
+
+ align:start position:0%
+individual right so we the definition of
+AR not is you put an infected individual
+
+ align:start position:0%
+AR not is you put an infected individual
+ 
+
+ align:start position:0%
+AR not is you put an infected individual
+into a population right of of
+
+ align:start position:0%
+into a population right of of
+ 
+
+ align:start position:0%
+into a population right of of
+susceptibles right now we want okay well
+
+ align:start position:0%
+susceptibles right now we want okay well
+ 
+
+ align:start position:0%
+susceptibles right now we want okay well
+there's a lifetime expected lifetime of
+
+ align:start position:0%
+there's a lifetime expected lifetime of
+ 
+
+ align:start position:0%
+there's a lifetime expected lifetime of
+this infected individual which is given
+
+ align:start position:0%
+this infected individual which is given
+ 
+
+ align:start position:0%
+this infected individual which is given
+by this okay and then we have to think
+
+ align:start position:0%
+by this okay and then we have to think
+ 
+
+ align:start position:0%
+by this okay and then we have to think
+about okay well what's the rate that
+
+ align:start position:0%
+about okay well what's the rate that
+ 
+
+ align:start position:0%
+about okay well what's the rate that
+we're going to be infecting individuals
+
+ align:start position:0%
+we're going to be infecting individuals
+ 
+
+ align:start position:0%
+we're going to be infecting individuals
+and that's going to be beta time
+
+ align:start position:0%
+and that's going to be beta time
+ 
+
+ align:start position:0%
+and that's going to be beta time
+x right but what we want to know is that
+
+ align:start position:0%
+x right but what we want to know is that
+ 
+
+ align:start position:0%
+x right but what we want to know is that
+is X before there we add any infection
+
+ align:start position:0%
+is X before there we add any infection
+ 
+
+ align:start position:0%
+is X before there we add any infection
+right and without any infection then we
+
+ align:start position:0%
+right and without any infection then we
+ 
+
+ align:start position:0%
+right and without any infection then we
+just have a rate of entry and then a
+
+ align:start position:0%
+just have a rate of entry and then a
+ 
+
+ align:start position:0%
+just have a rate of entry and then a
+death rate so it's just K Over
+
+ align:start position:0%
+death rate so it's just K Over
+ 
+
+ align:start position:0%
+death rate so it's just K Over
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+okay right now the key thing in all of
+
+ align:start position:0%
+okay right now the key thing in all of
+ 
+
+ align:start position:0%
+okay right now the key thing in all of
+these epidem ological models is whether
+
+ align:start position:0%
+these epidem ological models is whether
+ 
+
+ align:start position:0%
+these epidem ological models is whether
+this R KN is greater or less than one
+
+ align:start position:0%
+this R KN is greater or less than one
+ 
+
+ align:start position:0%
+this R KN is greater or less than one
+and that's going to tell us whether the
+
+ align:start position:0%
+and that's going to tell us whether the
+ 
+
+ align:start position:0%
+and that's going to tell us whether the
+disease becomes uh endemic or not right
+
+ align:start position:0%
+disease becomes uh endemic or not right
+ 
+
+ align:start position:0%
+disease becomes uh endemic or not right
+whether at steady state we have uh you
+
+ align:start position:0%
+whether at steady state we have uh you
+ 
+
+ align:start position:0%
+whether at steady state we have uh you
+know we have a population of infected
+
+ align:start position:0%
+know we have a population of infected
+ 
+
+ align:start position:0%
+know we have a population of infected
+individuals okay so are not greater than
+
+ align:start position:0%
+individuals okay so are not greater than
+ 
+
+ align:start position:0%
+individuals okay so are not greater than
+one means it's an endemic
+
+ align:start position:0%
+one means it's an endemic
+ 
+
+ align:start position:0%
+one means it's an endemic
+population okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now from uh in this model we
+
+ align:start position:0%
+all right now from uh in this model we
+ 
+
+ align:start position:0%
+all right now from uh in this model we
+can then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ask um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's all right so do you like a Donuts
+
+ align:start position:0%
+that's all right so do you like a Donuts
+ 
+
+ align:start position:0%
+that's all right so do you like a Donuts
+B cupcakes or C carrots um yeah that's
+
+ align:start position:0%
+B cupcakes or C carrots um yeah that's
+ 
+
+ align:start position:0%
+B cupcakes or C carrots um yeah that's
+quite nice does anybody have any notion
+
+ align:start position:0%
+quite nice does anybody have any notion
+ 
+
+ align:start position:0%
+quite nice does anybody have any notion
+of of why somebody might have all right
+
+ align:start position:0%
+of of why somebody might have all right
+ 
+
+ align:start position:0%
+of of why somebody might have all right
+so Sam likes cupcakes okay that's good
+
+ align:start position:0%
+so Sam likes cupcakes okay that's good
+ 
+
+ align:start position:0%
+so Sam likes cupcakes okay that's good
+to know I I I yeah they're so pretty
+
+ align:start position:0%
+to know I I I yeah they're so pretty
+ 
+
+ align:start position:0%
+to know I I I yeah they're so pretty
+that I actually feel bad erasing it uh
+
+ align:start position:0%
+that I actually feel bad erasing it uh
+ 
+
+ align:start position:0%
+that I actually feel bad erasing it uh
+okay well we'll go ahead we'll we'll
+
+ align:start position:0%
+okay well we'll go ahead we'll we'll
+ 
+
+ align:start position:0%
+okay well we'll go ahead we'll we'll
+we'll leave it up there for a little bit
+
+ align:start position:0%
+we'll leave it up there for a little bit
+ 
+
+ align:start position:0%
+we'll leave it up there for a little bit
+longer so that um you know everybody can
+
+ align:start position:0%
+longer so that um you know everybody can
+ 
+
+ align:start position:0%
+longer so that um you know everybody can
+just smile because they know that the
+
+ align:start position:0%
+just smile because they know that the
+ 
+
+ align:start position:0%
+just smile because they know that the
+the drawing is back there
+
+ align:start position:0%
+the drawing is back there
+ 
+
+ align:start position:0%
+the drawing is back there
+um all right uh okay
+
+ align:start position:0%
+um all right uh okay
+ 
+
+ align:start position:0%
+um all right uh okay
+so in this model uh the fact that that R
+
+ align:start position:0%
+so in this model uh the fact that that R
+ 
+
+ align:start position:0%
+so in this model uh the fact that that R
+nod is this parameter that tells us
+
+ align:start position:0%
+nod is this parameter that tells us
+ 
+
+ align:start position:0%
+nod is this parameter that tells us
+about whether there's going to be an
+
+ align:start position:0%
+about whether there's going to be an
+ 
+
+ align:start position:0%
+about whether there's going to be an
+epidemic and then indeed whether later
+
+ align:start position:0%
+epidemic and then indeed whether later
+ 
+
+ align:start position:0%
+epidemic and then indeed whether later
+it's go the disease will be endemic
+
+ align:start position:0%
+it's go the disease will be endemic
+ 
+
+ align:start position:0%
+it's go the disease will be endemic
+right does that does that already tell
+
+ align:start position:0%
+right does that does that already tell
+ 
+
+ align:start position:0%
+right does that does that already tell
+us that R not is what's maximized by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+selection no right what was the key
+
+ align:start position:0%
+selection no right what was the key
+ 
+
+ align:start position:0%
+selection no right what was the key
+thing that uh that Martin does in the
+
+ align:start position:0%
+thing that uh that Martin does in the
+ 
+
+ align:start position:0%
+thing that uh that Martin does in the
+chapter in order to try to understand
+
+ align:start position:0%
+chapter in order to try to understand
+ 
+
+ align:start position:0%
+chapter in order to try to understand
+something about what strain is selected
+
+ align:start position:0%
+something about what strain is selected
+ 
+
+ align:start position:0%
+something about what strain is selected
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes right okay
+
+ align:start position:0%
+yes right okay
+ 
+
+ align:start position:0%
+yes right okay
+so yes although the the part of the
+
+ align:start position:0%
+so yes although the the part of the
+ 
+
+ align:start position:0%
+so yes although the the part of the
+chapter you're thinking about is I think
+
+ align:start position:0%
+chapter you're thinking about is I think
+ 
+
+ align:start position:0%
+chapter you're thinking about is I think
+this the second half is talking about
+
+ align:start position:0%
+this the second half is talking about
+ 
+
+ align:start position:0%
+this the second half is talking about
+super infection where there's all these
+
+ align:start position:0%
+super infection where there's all these
+ 
+
+ align:start position:0%
+super infection where there's all these
+different types and their craziness and
+
+ align:start position:0%
+different types and their craziness and
+ 
+
+ align:start position:0%
+different types and their craziness and
+so forth but um the initial insight
+
+ align:start position:0%
+so forth but um the initial insight
+ 
+
+ align:start position:0%
+so forth but um the initial insight
+about what is going to be selected for
+
+ align:start position:0%
+about what is going to be selected for
+ 
+
+ align:start position:0%
+about what is going to be selected for
+comes from a simpler model than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah so you don't have to think
+
+ align:start position:0%
+that yeah so you don't have to think
+ 
+
+ align:start position:0%
+that yeah so you don't have to think
+about all those many parasites and those
+
+ align:start position:0%
+about all those many parasites and those
+ 
+
+ align:start position:0%
+about all those many parasites and those
+triangles and all the craziness instead
+
+ align:start position:0%
+triangles and all the craziness instead
+ 
+
+ align:start position:0%
+triangles and all the craziness instead
+there was a simple simpler model that
+
+ align:start position:0%
+there was a simple simpler model that
+ 
+
+ align:start position:0%
+there was a simple simpler model that
+yeah you have multiple
+
+ align:start position:0%
+yeah you have multiple
+ 
+
+ align:start position:0%
+yeah you have multiple
+parasites only
+
+ align:start position:0%
+parasites only
+ 
+
+ align:start position:0%
+parasites only
+one that's right and so what what what
+
+ align:start position:0%
+one that's right and so what what what
+ 
+
+ align:start position:0%
+one that's right and so what what what
+he does is he just writes down kind of
+
+ align:start position:0%
+he does is he just writes down kind of
+ 
+
+ align:start position:0%
+he does is he just writes down kind of
+this model where he now allows kind of
+
+ align:start position:0%
+this model where he now allows kind of
+ 
+
+ align:start position:0%
+this model where he now allows kind of
+two different parasites with and to to
+
+ align:start position:0%
+two different parasites with and to to
+ 
+
+ align:start position:0%
+two different parasites with and to to
+take uh to to be spreading the
+
+ align:start position:0%
+take uh to to be spreading the
+ 
+
+ align:start position:0%
+take uh to to be spreading the
+population and and at the beginning well
+
+ align:start position:0%
+population and and at the beginning well
+ 
+
+ align:start position:0%
+population and and at the beginning well
+we'll write we'll write it down and we
+
+ align:start position:0%
+we'll write we'll write it down and we
+ 
+
+ align:start position:0%
+we'll write we'll write it down and we
+want to be clear about what there's a
+
+ align:start position:0%
+want to be clear about what there's a
+ 
+
+ align:start position:0%
+want to be clear about what there's a
+very important assumption that he makes
+
+ align:start position:0%
+very important assumption that he makes
+ 
+
+ align:start position:0%
+very important assumption that he makes
+okay what what he's going to find is
+
+ align:start position:0%
+okay what what he's going to find is
+ 
+
+ align:start position:0%
+okay what what he's going to find is
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+selection maximizes R not the ba the the
+
+ align:start position:0%
+selection maximizes R not the ba the the
+ 
+
+ align:start position:0%
+selection maximizes R not the ba the the
+basic reproductive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ratio right R not and it's going to be
+
+ align:start position:0%
+ratio right R not and it's going to be
+ 
+
+ align:start position:0%
+ratio right R not and it's going to be
+in this model that I'm writing down now
+
+ align:start position:0%
+in this model that I'm writing down now
+ 
+
+ align:start position:0%
+in this model that I'm writing down now
+so there's this x dot and things look
+
+ align:start position:0%
+so there's this x dot and things look
+ 
+
+ align:start position:0%
+so there's this x dot and things look
+very similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now the question is what is
+
+ align:start position:0%
+all right now the question is what is
+ 
+
+ align:start position:0%
+all right now the question is what is
+the key assumption that we're making in
+
+ align:start position:0%
+the key assumption that we're making in
+ 
+
+ align:start position:0%
+the key assumption that we're making in
+writing down these equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thought that's right a host cannot be
+
+ align:start position:0%
+thought that's right a host cannot be
+ 
+
+ align:start position:0%
+thought that's right a host cannot be
+infected by more than one type of strain
+
+ align:start position:0%
+infected by more than one type of strain
+ 
+
+ align:start position:0%
+infected by more than one type of strain
+right so that's very very important okay
+
+ align:start position:0%
+right so that's very very important okay
+ 
+
+ align:start position:0%
+right so that's very very important okay
+so there's no super infection as they
+
+ align:start position:0%
+so there's no super infection as they
+ 
+
+ align:start position:0%
+so there's no super infection as they
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and and depending on the disease
+
+ align:start position:0%
+okay and and depending on the disease
+ 
+
+ align:start position:0%
+okay and and depending on the disease
+this could either be a better or worse
+
+ align:start position:0%
+this could either be a better or worse
+ 
+
+ align:start position:0%
+this could either be a better or worse
+assumption right uh but then what what
+
+ align:start position:0%
+assumption right uh but then what what
+ 
+
+ align:start position:0%
+assumption right uh but then what what
+is it that is defining that these two
+
+ align:start position:0%
+is it that is defining that these two
+ 
+
+ align:start position:0%
+is it that is defining that these two
+strains then in what ways are they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different their virulence is different
+
+ align:start position:0%
+different their virulence is different
+ 
+
+ align:start position:0%
+different their virulence is different
+right and the virulence here is and and
+
+ align:start position:0%
+right and the virulence here is and and
+ 
+
+ align:start position:0%
+right and the virulence here is and and
+what what is veilance again how it is
+
+ align:start position:0%
+what what is veilance again how it is
+ 
+
+ align:start position:0%
+what what is veilance again how it is
+but it's K that's right it's the
+
+ align:start position:0%
+but it's K that's right it's the
+ 
+
+ align:start position:0%
+but it's K that's right it's the
+additional mortality that is caused by
+
+ align:start position:0%
+additional mortality that is caused by
+ 
+
+ align:start position:0%
+additional mortality that is caused by
+the being infected by that by that
+
+ align:start position:0%
+the being infected by that by that
+ 
+
+ align:start position:0%
+the being infected by that by that
+strain is that the only way that they're
+
+ align:start position:0%
+strain is that the only way that they're
+ 
+
+ align:start position:0%
+strain is that the only way that they're
+different no what else is
+
+ align:start position:0%
+different no what else is
+ 
+
+ align:start position:0%
+different no what else is
+different the infectivity right so the
+
+ align:start position:0%
+different the infectivity right so the
+ 
+
+ align:start position:0%
+different the infectivity right so the
+betas are also different okay and right
+
+ align:start position:0%
+betas are also different okay and right
+ 
+
+ align:start position:0%
+betas are also different okay and right
+so it's important to not that in this
+
+ align:start position:0%
+so it's important to not that in this
+ 
+
+ align:start position:0%
+so it's important to not that in this
+model it's a very simple model but we're
+
+ align:start position:0%
+model it's a very simple model but we're
+ 
+
+ align:start position:0%
+model it's a very simple model but we're
+allowing the the strains to be different
+
+ align:start position:0%
+allowing the the strains to be different
+ 
+
+ align:start position:0%
+allowing the the strains to be different
+in these two ways okay and I think that
+
+ align:start position:0%
+in these two ways okay and I think that
+ 
+
+ align:start position:0%
+in these two ways okay and I think that
+it's it's very intuitive to just say oh
+
+ align:start position:0%
+it's it's very intuitive to just say oh
+ 
+
+ align:start position:0%
+it's it's very intuitive to just say oh
+well the beta should s you want to have
+
+ align:start position:0%
+well the beta should s you want to have
+ 
+
+ align:start position:0%
+well the beta should s you want to have
+a larger beta all of the things equal
+
+ align:start position:0%
+a larger beta all of the things equal
+ 
+
+ align:start position:0%
+a larger beta all of the things equal
+right because you would like to spread
+
+ align:start position:0%
+right because you would like to spread
+ 
+
+ align:start position:0%
+right because you would like to spread
+okay but uh it's I'd say maybe it's not
+
+ align:start position:0%
+okay but uh it's I'd say maybe it's not
+ 
+
+ align:start position:0%
+okay but uh it's I'd say maybe it's not
+as obvious what happens in terms of
+
+ align:start position:0%
+as obvious what happens in terms of
+ 
+
+ align:start position:0%
+as obvious what happens in terms of
+variance and then of course if you if
+
+ align:start position:0%
+variance and then of course if you if
+ 
+
+ align:start position:0%
+variance and then of course if you if
+you think about these two parameters in
+
+ align:start position:0%
+you think about these two parameters in
+ 
+
+ align:start position:0%
+you think about these two parameters in
+any biological context may be coupled in
+
+ align:start position:0%
+any biological context may be coupled in
+ 
+
+ align:start position:0%
+any biological context may be coupled in
+which case uh in which case things are
+
+ align:start position:0%
+which case uh in which case things are
+ 
+
+ align:start position:0%
+which case uh in which case things are
+more subtle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah I think that this very this
+
+ align:start position:0%
+okay yeah I think that this very this
+ 
+
+ align:start position:0%
+okay yeah I think that this very this
+depends on the disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that that would be the that's
+
+ align:start position:0%
+right so that that would be the that's
+ 
+
+ align:start position:0%
+right so that that would be the that's
+kind of somehow the argument that um you
+
+ align:start position:0%
+kind of somehow the argument that um you
+ 
+
+ align:start position:0%
+kind of somehow the argument that um you
+know and I'd say that there there's
+
+ align:start position:0%
+know and I'd say that there there's
+ 
+
+ align:start position:0%
+know and I'd say that there there's
+there this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can depending on whether you're thinking
+
+ align:start position:0%
+can depending on whether you're thinking
+ 
+
+ align:start position:0%
+can depending on whether you're thinking
+about the host at the level of an
+
+ align:start position:0%
+about the host at the level of an
+ 
+
+ align:start position:0%
+about the host at the level of an
+organism or a cell then then this would
+
+ align:start position:0%
+organism or a cell then then this would
+ 
+
+ align:start position:0%
+organism or a cell then then this would
+correspond to very different worlds um
+
+ align:start position:0%
+correspond to very different worlds um
+ 
+
+ align:start position:0%
+correspond to very different worlds um
+there so certainly in the context of uh
+
+ align:start position:0%
+there so certainly in the context of uh
+ 
+
+ align:start position:0%
+there so certainly in the context of uh
+viral infections in individual cells
+
+ align:start position:0%
+viral infections in individual cells
+ 
+
+ align:start position:0%
+viral infections in individual cells
+there are various mechanisms where if
+
+ align:start position:0%
+there are various mechanisms where if
+ 
+
+ align:start position:0%
+there are various mechanisms where if
+one strain kind of gets in then other
+
+ align:start position:0%
+one strain kind of gets in then other
+ 
+
+ align:start position:0%
+one strain kind of gets in then other
+strains have trouble getting in right uh
+
+ align:start position:0%
+strains have trouble getting in right uh
+ 
+
+ align:start position:0%
+strains have trouble getting in right uh
+and or if they do get in they can't do
+
+ align:start position:0%
+and or if they do get in they can't do
+ 
+
+ align:start position:0%
+and or if they do get in they can't do
+anything right so then so yeah so I
+
+ align:start position:0%
+anything right so then so yeah so I
+ 
+
+ align:start position:0%
+anything right so then so yeah so I
+think it really this really depends on
+
+ align:start position:0%
+think it really this really depends on
+ 
+
+ align:start position:0%
+think it really this really depends on
+the biology of the situation whether
+
+ align:start position:0%
+the biology of the situation whether
+ 
+
+ align:start position:0%
+the biology of the situation whether
+this is a reasonable assumption or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so I'm not going to go
+
+ align:start position:0%
+okay all right so I'm not going to go
+ 
+
+ align:start position:0%
+okay all right so I'm not going to go
+through all of the math because it ends
+
+ align:start position:0%
+through all of the math because it ends
+ 
+
+ align:start position:0%
+through all of the math because it ends
+up being a little uh a little bit
+
+ align:start position:0%
+up being a little uh a little bit
+ 
+
+ align:start position:0%
+up being a little uh a little bit
+involved but there's an in I think it's
+
+ align:start position:0%
+involved but there's an in I think it's
+ 
+
+ align:start position:0%
+involved but there's an in I think it's
+the condition for the mutual
+
+ align:start position:0%
+the condition for the mutual
+ 
+
+ align:start position:0%
+the condition for the mutual
+invasibility of the two strains is um is
+
+ align:start position:0%
+invasibility of the two strains is um is
+ 
+
+ align:start position:0%
+invasibility of the two strains is um is
+a little bit subtle so I do want to I do
+
+ align:start position:0%
+a little bit subtle so I do want to I do
+ 
+
+ align:start position:0%
+a little bit subtle so I do want to I do
+want to talk about that a little bit
+
+ align:start position:0%
+want to talk about that a little bit
+ 
+
+ align:start position:0%
+want to talk about that a little bit
+okay right so in general in this
+
+ align:start position:0%
+okay right so in general in this
+ 
+
+ align:start position:0%
+okay right so in general in this
+model there is some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xar and Y
+
+ align:start position:0%
+xar and Y
+ 
+
+ align:start position:0%
+xar and Y
+star and indeed there will generally be
+
+ align:start position:0%
+star and indeed there will generally be
+ 
+
+ align:start position:0%
+star and indeed there will generally be
+damped oscillations to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium okay this is in the model
+
+ align:start position:0%
+equilibrium okay this is in the model
+ 
+
+ align:start position:0%
+equilibrium okay this is in the model
+where there's just a single strain
+
+ align:start position:0%
+where there's just a single strain
+ 
+
+ align:start position:0%
+where there's just a single strain
+that's described by su beta and some V
+
+ align:start position:0%
+that's described by su beta and some V
+ 
+
+ align:start position:0%
+that's described by su beta and some V
+okay of course you can also think about
+
+ align:start position:0%
+okay of course you can also think about
+ 
+
+ align:start position:0%
+okay of course you can also think about
+the equilibria E1 and E2 that would
+
+ align:start position:0%
+the equilibria E1 and E2 that would
+ 
+
+ align:start position:0%
+the equilibria E1 and E2 that would
+result uh when you have so so E1 is kind
+
+ align:start position:0%
+result uh when you have so so E1 is kind
+ 
+
+ align:start position:0%
+result uh when you have so so E1 is kind
+of what would happen it's the
+
+ align:start position:0%
+of what would happen it's the
+ 
+
+ align:start position:0%
+of what would happen it's the
+equilibrium when you have X star
+
+ align:start position:0%
+equilibrium when you have X star
+ 
+
+ align:start position:0%
+equilibrium when you have X star
+evaluated at you know for for the
+
+ align:start position:0%
+evaluated at you know for for the
+ 
+
+ align:start position:0%
+evaluated at you know for for the
+particular parameters of strain one I.E
+
+ align:start position:0%
+particular parameters of strain one I.E
+ 
+
+ align:start position:0%
+particular parameters of strain one I.E
+evaluated for beta 1 and for V1 xar and
+
+ align:start position:0%
+evaluated for beta 1 and for V1 xar and
+ 
+
+ align:start position:0%
+evaluated for beta 1 and for V1 xar and
+that's also y Star right whereas you
+
+ align:start position:0%
+that's also y Star right whereas you
+ 
+
+ align:start position:0%
+that's also y Star right whereas you
+would have a different equilibrium E2 uh
+
+ align:start position:0%
+would have a different equilibrium E2 uh
+ 
+
+ align:start position:0%
+would have a different equilibrium E2 uh
+you so this is X star and a y
+
+ align:start position:0%
+you so this is X star and a y
+ 
+
+ align:start position:0%
+you so this is X star and a y
+star evaluated at beta 2 and V2 do do
+
+ align:start position:0%
+star evaluated at beta 2 and V2 do do
+ 
+
+ align:start position:0%
+star evaluated at beta 2 and V2 do do
+you understand what what I'm saying so
+
+ align:start position:0%
+you understand what what I'm saying so
+ 
+
+ align:start position:0%
+you understand what what I'm saying so
+these are the equili you would have if
+
+ align:start position:0%
+these are the equili you would have if
+ 
+
+ align:start position:0%
+these are the equili you would have if
+this was the only strain that was
+
+ align:start position:0%
+this was the only strain that was
+ 
+
+ align:start position:0%
+this was the only strain that was
+present in the population or if or if
+
+ align:start position:0%
+present in the population or if or if
+ 
+
+ align:start position:0%
+present in the population or if or if
+this was the only strain in the pop
+
+ align:start position:0%
+this was the only strain in the pop
+ 
+
+ align:start position:0%
+this was the only strain in the pop
+okay now it's not obvious that those are
+
+ align:start position:0%
+okay now it's not obvious that those are
+ 
+
+ align:start position:0%
+okay now it's not obvious that those are
+the equilibria that result when you have
+
+ align:start position:0%
+the equilibria that result when you have
+ 
+
+ align:start position:0%
+the equilibria that result when you have
+both strains present in the population
+
+ align:start position:0%
+both strains present in the population
+ 
+
+ align:start position:0%
+both strains present in the population
+and but that's what we kind of want to
+
+ align:start position:0%
+and but that's what we kind of want to
+ 
+
+ align:start position:0%
+and but that's what we kind of want to
+try to figure out
+
+ align:start position:0%
+try to figure out
+ 
+
+ align:start position:0%
+try to figure out
+right but certainly if you only added
+
+ align:start position:0%
+right but certainly if you only added
+ 
+
+ align:start position:0%
+right but certainly if you only added
+strain one and you didn't add strain two
+
+ align:start position:0%
+strain one and you didn't add strain two
+ 
+
+ align:start position:0%
+strain one and you didn't add strain two
+you would come to the equilibrium E1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right so the question is how can we
+
+ align:start position:0%
+okay right so the question is how can we
+ 
+
+ align:start position:0%
+okay right so the question is how can we
+determine that if we start out at
+
+ align:start position:0%
+determine that if we start out at
+ 
+
+ align:start position:0%
+determine that if we start out at
+equilibrium E1 how is it we can
+
+ align:start position:0%
+equilibrium E1 how is it we can
+ 
+
+ align:start position:0%
+equilibrium E1 how is it we can
+determine what happens if we now add uh
+
+ align:start position:0%
+determine what happens if we now add uh
+ 
+
+ align:start position:0%
+determine what happens if we now add uh
+an infected individual uh but infected
+
+ align:start position:0%
+an infected individual uh but infected
+ 
+
+ align:start position:0%
+an infected individual uh but infected
+by strain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two right so what we want to know is all
+
+ align:start position:0%
+two right so what we want to know is all
+ 
+
+ align:start position:0%
+two right so what we want to know is all
+right strain two can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invade right and and really what we're
+
+ align:start position:0%
+invade right and and really what we're
+ 
+
+ align:start position:0%
+invade right and and really what we're
+we're thinking about is a situation
+
+ align:start position:0%
+we're thinking about is a situation
+ 
+
+ align:start position:0%
+we're thinking about is a situation
+these These are the equilibria if it's
+
+ align:start position:0%
+these These are the equilibria if it's
+ 
+
+ align:start position:0%
+these These are the equilibria if it's
+the case that R1 is greater than one and
+
+ align:start position:0%
+the case that R1 is greater than one and
+ 
+
+ align:start position:0%
+the case that R1 is greater than one and
+R2 is greater than one right because in
+
+ align:start position:0%
+R2 is greater than one right because in
+ 
+
+ align:start position:0%
+R2 is greater than one right because in
+some ways it's clear what happens if the
+
+ align:start position:0%
+some ways it's clear what happens if the
+ 
+
+ align:start position:0%
+some ways it's clear what happens if the
+if if both of the R1 and R2 is are less
+
+ align:start position:0%
+if if both of the R1 and R2 is are less
+ 
+
+ align:start position:0%
+if if both of the R1 and R2 is are less
+than one then what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens they both die out right if one
+
+ align:start position:0%
+happens they both die out right if one
+ 
+
+ align:start position:0%
+happens they both die out right if one
+of them is greater than one one's less
+
+ align:start position:0%
+of them is greater than one one's less
+ 
+
+ align:start position:0%
+of them is greater than one one's less
+than one then you know right it's you
+
+ align:start position:0%
+than one then you know right it's you
+ 
+
+ align:start position:0%
+than one then you know right it's you
+know the strain that's below one goes
+
+ align:start position:0%
+know the strain that's below one goes
+ 
+
+ align:start position:0%
+know the strain that's below one goes
+out you know so the only interesting or
+
+ align:start position:0%
+out you know so the only interesting or
+ 
+
+ align:start position:0%
+out you know so the only interesting or
+the only the only non-obvious question
+
+ align:start position:0%
+the only the only non-obvious question
+ 
+
+ align:start position:0%
+the only the only non-obvious question
+somehow is what happens if they're both
+
+ align:start position:0%
+somehow is what happens if they're both
+ 
+
+ align:start position:0%
+somehow is what happens if they're both
+larger uh larger than one right what
+
+ align:start position:0%
+larger uh larger than one right what
+ 
+
+ align:start position:0%
+larger uh larger than one right what
+that means is that for example if you if
+
+ align:start position:0%
+that means is that for example if you if
+ 
+
+ align:start position:0%
+that means is that for example if you if
+you had a population of susceptible
+
+ align:start position:0%
+you had a population of susceptible
+ 
+
+ align:start position:0%
+you had a population of susceptible
+individuals and you added one strain one
+
+ align:start position:0%
+individuals and you added one strain one
+ 
+
+ align:start position:0%
+individuals and you added one strain one
+one stra you know one infected strain
+
+ align:start position:0%
+one stra you know one infected strain
+ 
+
+ align:start position:0%
+one stra you know one infected strain
+one one infected by strain two right
+
+ align:start position:0%
+one one infected by strain two right
+ 
+
+ align:start position:0%
+one one infected by strain two right
+then in the deterministic kind of
+
+ align:start position:0%
+then in the deterministic kind of
+ 
+
+ align:start position:0%
+then in the deterministic kind of
+differential equation limit they would
+
+ align:start position:0%
+differential equation limit they would
+ 
+
+ align:start position:0%
+differential equation limit they would
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+spread right so they're both
+
+ align:start position:0%
+spread right so they're both
+ 
+
+ align:start position:0%
+spread right so they're both
+exponentially growing right does that
+
+ align:start position:0%
+exponentially growing right does that
+ 
+
+ align:start position:0%
+exponentially growing right does that
+already tell us that they're going
+
+ align:start position:0%
+already tell us that they're going
+ 
+
+ align:start position:0%
+already tell us that they're going
+you're going to have coexistence of the
+
+ align:start position:0%
+you're going to have coexistence of the
+ 
+
+ align:start position:0%
+you're going to have coexistence of the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+strains no right it means that you know
+
+ align:start position:0%
+strains no right it means that you know
+ 
+
+ align:start position:0%
+strains no right it means that you know
+they're both exponentially spreading who
+
+ align:start position:0%
+they're both exponentially spreading who
+ 
+
+ align:start position:0%
+they're both exponentially spreading who
+knows what's going to happen later right
+
+ align:start position:0%
+knows what's going to happen later right
+ 
+
+ align:start position:0%
+knows what's going to happen later right
+and indeed uh what you can show is that
+
+ align:start position:0%
+and indeed uh what you can show is that
+ 
+
+ align:start position:0%
+and indeed uh what you can show is that
+only one of the two strains is going to
+
+ align:start position:0%
+only one of the two strains is going to
+ 
+
+ align:start position:0%
+only one of the two strains is going to
+win and it's the strain with the higher
+
+ align:start position:0%
+win and it's the strain with the higher
+ 
+
+ align:start position:0%
+win and it's the strain with the higher
+reproductive ratio the higher r notd or
+
+ align:start position:0%
+reproductive ratio the higher r notd or
+ 
+
+ align:start position:0%
+reproductive ratio the higher r notd or
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+case okay all right so how is it that we
+
+ align:start position:0%
+case okay all right so how is it that we
+ 
+
+ align:start position:0%
+case okay all right so how is it that we
+can determine if strain two can invade
+
+ align:start position:0%
+can determine if strain two can invade
+ 
+
+ align:start position:0%
+can determine if strain two can invade
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+one it's if and only if something does
+
+ align:start position:0%
+one it's if and only if something does
+ 
+
+ align:start position:0%
+one it's if and only if something does
+anybody remember what this condition
+
+ align:start position:0%
+anybody remember what this condition
+ 
+
+ align:start position:0%
+anybody remember what this condition
+ended up being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right Y2 dot at E1 has to be
+
+ align:start position:0%
+all right Y2 dot at E1 has to be
+ 
+
+ align:start position:0%
+all right Y2 dot at E1 has to be
+positive right okay yes and and this
+
+ align:start position:0%
+positive right okay yes and and this
+ 
+
+ align:start position:0%
+positive right okay yes and and this
+ends up being equivalent I think to what
+
+ align:start position:0%
+ends up being equivalent I think to what
+ 
+
+ align:start position:0%
+ends up being equivalent I think to what
+he writes and okay so let's write what
+
+ align:start position:0%
+he writes and okay so let's write what
+ 
+
+ align:start position:0%
+he writes and okay so let's write what
+let's I'll write tell you what so the
+
+ align:start position:0%
+let's I'll write tell you what so the
+ 
+
+ align:start position:0%
+let's I'll write tell you what so the
+way he wrote it is that it's it's it's
+
+ align:start position:0%
+way he wrote it is that it's it's it's
+ 
+
+ align:start position:0%
+way he wrote it is that it's it's it's
+Y2 dot with respect to
+
+ align:start position:0%
+Y2 dot with respect to
+ 
+
+ align:start position:0%
+Y2 dot with respect to
+Y2 um but I think that this is really
+
+ align:start position:0%
+Y2 um but I think that this is really
+ 
+
+ align:start position:0%
+Y2 um but I think that this is really
+equivalent to what you said though um
+
+ align:start position:0%
+equivalent to what you said though um
+ 
+
+ align:start position:0%
+equivalent to what you said though um
+but it's a little bit
+
+ align:start position:0%
+but it's a little bit
+ 
+
+ align:start position:0%
+but it's a little bit
+um right because you said okay it's Y2
+
+ align:start position:0%
+um right because you said okay it's Y2
+ 
+
+ align:start position:0%
+um right because you said okay it's Y2
+dot has to be something right but then
+
+ align:start position:0%
+dot has to be something right but then
+ 
+
+ align:start position:0%
+dot has to be something right but then
+Y2 dot evaluated what and you would say
+
+ align:start position:0%
+Y2 dot evaluated what and you would say
+ 
+
+ align:start position:0%
+Y2 dot evaluated what and you would say
+oh evaluated at E1 but then at E1 yeah
+
+ align:start position:0%
+oh evaluated at E1 but then at E1 yeah
+ 
+
+ align:start position:0%
+oh evaluated at E1 but then at E1 yeah
+so what is Y2 dot evaluated at
+
+ align:start position:0%
+so what is Y2 dot evaluated at
+ 
+
+ align:start position:0%
+so what is Y2 dot evaluated at
+E1 zero right because at E1 there's zero
+
+ align:start position:0%
+E1 zero right because at E1 there's zero
+ 
+
+ align:start position:0%
+E1 zero right because at E1 there's zero
+Y2 so then of course Y2 do is zero right
+
+ align:start position:0%
+Y2 so then of course Y2 do is zero right
+ 
+
+ align:start position:0%
+Y2 so then of course Y2 do is zero right
+so it's almost what you want but not
+
+ align:start position:0%
+so it's almost what you want but not
+ 
+
+ align:start position:0%
+so it's almost what you want but not
+quite right and so this condition which
+
+ align:start position:0%
+quite right and so this condition which
+ 
+
+ align:start position:0%
+quite right and so this condition which
+looks very weird it's really saying that
+
+ align:start position:0%
+looks very weird it's really saying that
+ 
+
+ align:start position:0%
+looks very weird it's really saying that
+right if we are at we're at E1 at E1 so
+
+ align:start position:0%
+right if we are at we're at E1 at E1 so
+ 
+
+ align:start position:0%
+right if we are at we're at E1 at E1 so
+there's no um infected uh type two
+
+ align:start position:0%
+there's no um infected uh type two
+ 
+
+ align:start position:0%
+there's no um infected uh type two
+infections right what we want to do is
+
+ align:start position:0%
+infections right what we want to do is
+ 
+
+ align:start position:0%
+infections right what we want to do is
+kind of add a little bit of Y2 and then
+
+ align:start position:0%
+kind of add a little bit of Y2 and then
+ 
+
+ align:start position:0%
+kind of add a little bit of Y2 and then
+we want to ask what is Y2 dot right this
+
+ align:start position:0%
+we want to ask what is Y2 dot right this
+ 
+
+ align:start position:0%
+we want to ask what is Y2 dot right this
+derivative evaluated E1 somehow allows
+
+ align:start position:0%
+derivative evaluated E1 somehow allows
+ 
+
+ align:start position:0%
+derivative evaluated E1 somehow allows
+you to do
+
+ align:start position:0%
+you to do
+ 
+
+ align:start position:0%
+you to do
+that right and do we want this to be
+
+ align:start position:0%
+that right and do we want this to be
+ 
+
+ align:start position:0%
+that right and do we want this to be
+greater than zero or less than zero
+
+ align:start position:0%
+greater than zero or less than zero
+ 
+
+ align:start position:0%
+greater than zero or less than zero
+right we're going to do ver uh verbal
+
+ align:start position:0%
+right we're going to do ver uh verbal
+ 
+
+ align:start position:0%
+right we're going to do ver uh verbal
+answer ready three two one greater right
+
+ align:start position:0%
+answer ready three two one greater right
+ 
+
+ align:start position:0%
+answer ready three two one greater right
+because if it's saying you add a Y2 you
+
+ align:start position:0%
+because if it's saying you add a Y2 you
+ 
+
+ align:start position:0%
+because if it's saying you add a Y2 you
+want Y2 to start growing
+
+ align:start position:0%
+want Y2 to start growing
+ 
+
+ align:start position:0%
+want Y2 to start growing
+okay uh so you want this thing to be
+
+ align:start position:0%
+okay uh so you want this thing to be
+ 
+
+ align:start position:0%
+okay uh so you want this thing to be
+greater than zero and um this looks
+
+ align:start position:0%
+greater than zero and um this looks
+ 
+
+ align:start position:0%
+greater than zero and um this looks
+really crazy but it's actually pretty
+
+ align:start position:0%
+really crazy but it's actually pretty
+ 
+
+ align:start position:0%
+really crazy but it's actually pretty
+easy to do because you take the
+
+ align:start position:0%
+easy to do because you take the
+ 
+
+ align:start position:0%
+easy to do because you take the
+derivative of this thing with respect to
+
+ align:start position:0%
+derivative of this thing with respect to
+ 
+
+ align:start position:0%
+derivative of this thing with respect to
+Y2 and you just get the thing in
+
+ align:start position:0%
+Y2 and you just get the thing in
+ 
+
+ align:start position:0%
+Y2 and you just get the thing in
+parentheses right but you evaluate it at
+
+ align:start position:0%
+parentheses right but you evaluate it at
+ 
+
+ align:start position:0%
+parentheses right but you evaluate it at
+E1 so it's it's beta 2 and this is X
+
+ align:start position:0%
+E1 so it's it's beta 2 and this is X
+ 
+
+ align:start position:0%
+E1 so it's it's beta 2 and this is X
+star at um at
+
+ align:start position:0%
+star at um at
+ 
+
+ align:start position:0%
+star at um at
+E1 right minus uus V2 and this thing has
+
+ align:start position:0%
+E1 right minus uus V2 and this thing has
+ 
+
+ align:start position:0%
+E1 right minus uus V2 and this thing has
+to be greater than zero
+
+ align:start position:0%
+to be greater than zero
+ 
+
+ align:start position:0%
+to be greater than zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but this
+
+ align:start position:0%
+but this
+ 
+
+ align:start position:0%
+but this
+is X at E1 that's U plus V1 divid beta 1
+
+ align:start position:0%
+is X at E1 that's U plus V1 divid beta 1
+ 
+
+ align:start position:0%
+is X at E1 that's U plus V1 divid beta 1
+okay so what we have is a beta 2 then U
+
+ align:start position:0%
+okay so what we have is a beta 2 then U
+ 
+
+ align:start position:0%
+okay so what we have is a beta 2 then U
++
+
+ align:start position:0%
++
+ 
+
+ align:start position:0%
++
+V1 divid beta
+
+ align:start position:0%
+V1 divid beta
+ 
+
+ align:start position:0%
+V1 divid beta
+1 and this thing has to be greater than
+
+ align:start position:0%
+1 and this thing has to be greater than
+ 
+
+ align:start position:0%
+1 and this thing has to be greater than
+and we'll move this over to the other
+
+ align:start position:0%
+and we'll move this over to the other
+ 
+
+ align:start position:0%
+and we'll move this over to the other
+side U +
+
+ align:start position:0%
+side U +
+ 
+
+ align:start position:0%
+side U +
+V2 okay so this is not so horrible right
+
+ align:start position:0%
+V2 okay so this is not so horrible right
+ 
+
+ align:start position:0%
+V2 okay so this is not so horrible right
+there's a u plus V1 beta 1 right I just
+
+ align:start position:0%
+there's a u plus V1 beta 1 right I just
+ 
+
+ align:start position:0%
+there's a u plus V1 beta 1 right I just
+want to make sure I write U plus
+
+ align:start position:0%
+want to make sure I write U plus
+ 
+
+ align:start position:0%
+want to make sure I write U plus
+V1 okay we have to put these in the
+
+ align:start position:0%
+V1 okay we have to put these in the
+ 
+
+ align:start position:0%
+V1 okay we have to put these in the
+denominators now somehow
+
+ align:start position:0%
+denominators now somehow
+ 
+
+ align:start position:0%
+denominators now somehow
+um okay so we'll put divide by both of
+
+ align:start position:0%
+um okay so we'll put divide by both of
+ 
+
+ align:start position:0%
+um okay so we'll put divide by both of
+these things so we have a 1 divid a u +
+
+ align:start position:0%
+these things so we have a 1 divid a u +
+ 
+
+ align:start position:0%
+these things so we have a 1 divid a u +
+V2 1id U +
+
+ align:start position:0%
+V2 1id U +
+ 
+
+ align:start position:0%
+V2 1id U +
+V1 right so we put these things in the
+
+ align:start position:0%
+V1 right so we put these things in the
+ 
+
+ align:start position:0%
+V1 right so we put these things in the
+denominator right and then now the beta
+
+ align:start position:0%
+denominator right and then now the beta
+ 
+
+ align:start position:0%
+denominator right and then now the beta
+one's going to come up here so we have a
+
+ align:start position:0%
+one's going to come up here so we have a
+ 
+
+ align:start position:0%
+one's going to come up here so we have a
+a beta 1 and a beta 2 and there still is
+
+ align:start position:0%
+a beta 1 and a beta 2 and there still is
+ 
+
+ align:start position:0%
+a beta 1 and a beta 2 and there still is
+a greater than sign did I did I screw
+
+ align:start position:0%
+a greater than sign did I did I screw
+ 
+
+ align:start position:0%
+a greater than sign did I did I screw
+anything up
+
+ align:start position:0%
+anything up
+ 
+
+ align:start position:0%
+anything up
+yet maybe no all
+
+ align:start position:0%
+yet maybe no all
+ 
+
+ align:start position:0%
+yet maybe no all
+right okay now we can do something
+
+ align:start position:0%
+right okay now we can do something
+ 
+
+ align:start position:0%
+right okay now we can do something
+wonderful which is we can just multiply
+
+ align:start position:0%
+wonderful which is we can just multiply
+ 
+
+ align:start position:0%
+wonderful which is we can just multiply
+by Kid by U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so what does this say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R2 R2 is greater than R1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and what were we trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculate how did we get started on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+math right we wanted to ask strain two
+
+ align:start position:0%
+math right we wanted to ask strain two
+ 
+
+ align:start position:0%
+math right we wanted to ask strain two
+can invade the equilibrium one if and
+
+ align:start position:0%
+can invade the equilibrium one if and
+ 
+
+ align:start position:0%
+can invade the equilibrium one if and
+only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if oh no no oh sorry R2 is greater than
+
+ align:start position:0%
+if oh no no oh sorry R2 is greater than
+ 
+
+ align:start position:0%
+if oh no no oh sorry R2 is greater than
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now that's interesting right so that's
+
+ align:start position:0%
+now that's interesting right so that's
+ 
+
+ align:start position:0%
+now that's interesting right so that's
+saying that if you start out with the
+
+ align:start position:0%
+saying that if you start out with the
+ 
+
+ align:start position:0%
+saying that if you start out with the
+endemic strain one and you add the uh
+
+ align:start position:0%
+endemic strain one and you add the uh
+ 
+
+ align:start position:0%
+endemic strain one and you add the uh
+strain two in there it's going to be
+
+ align:start position:0%
+strain two in there it's going to be
+ 
+
+ align:start position:0%
+strain two in there it's going to be
+able to invade if its R2 is greater than
+
+ align:start position:0%
+able to invade if its R2 is greater than
+ 
+
+ align:start position:0%
+able to invade if its R2 is greater than
+R1 that's not obvious right because R2
+
+ align:start position:0%
+R1 that's not obvious right because R2
+ 
+
+ align:start position:0%
+R1 that's not obvious right because R2
+and R1 that was tell that was telling us
+
+ align:start position:0%
+and R1 that was tell that was telling us
+ 
+
+ align:start position:0%
+and R1 that was tell that was telling us
+some a different situation right that
+
+ align:start position:0%
+some a different situation right that
+ 
+
+ align:start position:0%
+some a different situation right that
+was telling us about what happens when
+
+ align:start position:0%
+was telling us about what happens when
+ 
+
+ align:start position:0%
+was telling us about what happens when
+you add those infected uh individuals
+
+ align:start position:0%
+you add those infected uh individuals
+ 
+
+ align:start position:0%
+you add those infected uh individuals
+into a population of susceptibles okay
+
+ align:start position:0%
+into a population of susceptibles okay
+ 
+
+ align:start position:0%
+into a population of susceptibles okay
+but this also ends up telling us about
+
+ align:start position:0%
+but this also ends up telling us about
+ 
+
+ align:start position:0%
+but this also ends up telling us about
+the um about what happens when the
+
+ align:start position:0%
+the um about what happens when the
+ 
+
+ align:start position:0%
+the um about what happens when the
+strains are competing against each other
+
+ align:start position:0%
+strains are competing against each other
+ 
+
+ align:start position:0%
+strains are competing against each other
+right I think so this is I think it's
+
+ align:start position:0%
+right I think so this is I think it's
+ 
+
+ align:start position:0%
+right I think so this is I think it's
+not it's so simple that it feels trivial
+
+ align:start position:0%
+not it's so simple that it feels trivial
+ 
+
+ align:start position:0%
+not it's so simple that it feels trivial
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+I I I'm sure that if you understood it
+
+ align:start position:0%
+I I I'm sure that if you understood it
+ 
+
+ align:start position:0%
+I I I'm sure that if you understood it
+well enough it would be trivial but
+
+ align:start position:0%
+well enough it would be trivial but
+ 
+
+ align:start position:0%
+well enough it would be trivial but
+you'd have to think about it more than I
+
+ align:start position:0%
+you'd have to think about it more than I
+ 
+
+ align:start position:0%
+you'd have to think about it more than I
+have okay so I think this is surprising
+
+ align:start position:0%
+have okay so I think this is surprising
+ 
+
+ align:start position:0%
+have okay so I think this is surprising
+now you can also ask the same question
+
+ align:start position:0%
+now you can also ask the same question
+ 
+
+ align:start position:0%
+now you can also ask the same question
+which is that um
+
+ align:start position:0%
+which is that um
+ 
+
+ align:start position:0%
+which is that um
+is strain two can um about whether
+
+ align:start position:0%
+is strain two can um about whether
+ 
+
+ align:start position:0%
+is strain two can um about whether
+strain one can evade strain two right
+
+ align:start position:0%
+strain one can evade strain two right
+ 
+
+ align:start position:0%
+strain one can evade strain two right
+and that is kind of the same thing you
+
+ align:start position:0%
+and that is kind of the same thing you
+ 
+
+ align:start position:0%
+and that is kind of the same thing you
+know so it all comes down to the
+
+ align:start position:0%
+know so it all comes down to the
+ 
+
+ align:start position:0%
+know so it all comes down to the
+orderings of R2 and
+
+ align:start position:0%
+orderings of R2 and
+ 
+
+ align:start position:0%
+orderings of R2 and
+R1 okay and uh what you what you find is
+
+ align:start position:0%
+R1 okay and uh what you what you find is
+ 
+
+ align:start position:0%
+R1 okay and uh what you what you find is
+that uh is that strain two in this if
+
+ align:start position:0%
+that uh is that strain two in this if
+ 
+
+ align:start position:0%
+that uh is that strain two in this if
+this condition is satisfied strain two
+
+ align:start position:0%
+this condition is satisfied strain two
+ 
+
+ align:start position:0%
+this condition is satisfied strain two
+will drive strain one uh out of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population right so if they're the same
+
+ align:start position:0%
+population right so if they're the same
+ 
+
+ align:start position:0%
+population right so if they're the same
+then you can get
+
+ align:start position:0%
+then you can get
+ 
+
+ align:start position:0%
+then you can get
+coexistence um but it's it's as uh as
+
+ align:start position:0%
+coexistence um but it's it's as uh as
+ 
+
+ align:start position:0%
+coexistence um but it's it's as uh as
+Martin says it's non-generic in the
+
+ align:start position:0%
+Martin says it's non-generic in the
+ 
+
+ align:start position:0%
+Martin says it's non-generic in the
+sense that it's kind of a coincidence or
+
+ align:start position:0%
+sense that it's kind of a coincidence or
+ 
+
+ align:start position:0%
+sense that it's kind of a coincidence or
+you know it's of measure zero the
+
+ align:start position:0%
+you know it's of measure zero the
+ 
+
+ align:start position:0%
+you know it's of measure zero the
+situations in which the two will um have
+
+ align:start position:0%
+situations in which the two will um have
+ 
+
+ align:start position:0%
+situations in which the two will um have
+the same you know R
+
+ align:start position:0%
+the same you know R
+ 
+
+ align:start position:0%
+the same you know R
+parameters right but um but of course
+
+ align:start position:0%
+parameters right but um but of course
+ 
+
+ align:start position:0%
+parameters right but um but of course
+you can imagine just like we talked
+
+ align:start position:0%
+you can imagine just like we talked
+ 
+
+ align:start position:0%
+you can imagine just like we talked
+about this neutral Evolution business
+
+ align:start position:0%
+about this neutral Evolution business
+ 
+
+ align:start position:0%
+about this neutral Evolution business
+things are nearly neutral and so forth
+
+ align:start position:0%
+things are nearly neutral and so forth
+ 
+
+ align:start position:0%
+things are nearly neutral and so forth
+you can kind of invoke similar ideas
+
+ align:start position:0%
+you can kind of invoke similar ideas
+ 
+
+ align:start position:0%
+you can kind of invoke similar ideas
+because you can imagine that as these
+
+ align:start position:0%
+because you can imagine that as these
+ 
+
+ align:start position:0%
+because you can imagine that as these
+two become closer and closer to each
+
+ align:start position:0%
+two become closer and closer to each
+ 
+
+ align:start position:0%
+two become closer and closer to each
+other it's going to take longer and
+
+ align:start position:0%
+other it's going to take longer and
+ 
+
+ align:start position:0%
+other it's going to take longer and
+longer for the um for the sort of more
+
+ align:start position:0%
+longer for the um for the sort of more
+ 
+
+ align:start position:0%
+longer for the um for the sort of more
+fit strain to out compete the less fit
+
+ align:start position:0%
+fit strain to out compete the less fit
+ 
+
+ align:start position:0%
+fit strain to out compete the less fit
+strain
+
+ align:start position:0%
+strain
+ 
+
+ align:start position:0%
+strain
+okay right now um even though this is
+
+ align:start position:0%
+okay right now um even though this is
+ 
+
+ align:start position:0%
+okay right now um even though this is
+such a
+
+ align:start position:0%
+such a
+ 
+
+ align:start position:0%
+such a
+simple condition and the r parameters
+
+ align:start position:0%
+simple condition and the r parameters
+ 
+
+ align:start position:0%
+simple condition and the r parameters
+have such a simple kind of uh physical
+
+ align:start position:0%
+have such a simple kind of uh physical
+ 
+
+ align:start position:0%
+have such a simple kind of uh physical
+uh kind of origin or mathematical origin
+
+ align:start position:0%
+uh kind of origin or mathematical origin
+ 
+
+ align:start position:0%
+uh kind of origin or mathematical origin
+um the actual expression for the RS is
+
+ align:start position:0%
+um the actual expression for the RS is
+ 
+
+ align:start position:0%
+um the actual expression for the RS is
+is kind of complicated right so again
+
+ align:start position:0%
+is kind of complicated right so again
+ 
+
+ align:start position:0%
+is kind of complicated right so again
+it's it's a combination of all of these
+
+ align:start position:0%
+it's it's a combination of all of these
+ 
+
+ align:start position:0%
+it's it's a combination of all of these
+different parameters where it's the
+
+ align:start position:0%
+different parameters where it's the
+ 
+
+ align:start position:0%
+different parameters where it's the
+beta1 V1 or beta 2
+
+ align:start position:0%
+beta1 V1 or beta 2
+ 
+
+ align:start position:0%
+beta1 V1 or beta 2
+V2
+
+ align:start position:0%
+V2
+ 
+
+ align:start position:0%
+V2
+okay right so from from this you can
+
+ align:start position:0%
+okay right so from from this you can
+ 
+
+ align:start position:0%
+okay right so from from this you can
+start to think about
+
+ align:start position:0%
+start to think about
+ 
+
+ align:start position:0%
+start to think about
+um what will be okay
+
+ align:start position:0%
+um what will be okay
+ 
+
+ align:start position:0%
+um what will be okay
+which all
+
+ align:start position:0%
+which all
+ 
+
+ align:start position:0%
+which all
+right which board do you think is less
+
+ align:start position:0%
+right which board do you think is less
+ 
+
+ align:start position:0%
+right which board do you think is less
+uh least useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no all right well I don't like this one
+
+ align:start position:0%
+no all right well I don't like this one
+ 
+
+ align:start position:0%
+no all right well I don't like this one
+anymore uh but in particular we want to
+
+ align:start position:0%
+anymore uh but in particular we want to
+ 
+
+ align:start position:0%
+anymore uh but in particular we want to
+say something about the evolution of
+
+ align:start position:0%
+say something about the evolution of
+ 
+
+ align:start position:0%
+say something about the evolution of
+variance okay in this model and and what
+
+ align:start position:0%
+variance okay in this model and and what
+ 
+
+ align:start position:0%
+variance okay in this model and and what
+the expectation is okay so what we're
+
+ align:start position:0%
+the expectation is okay so what we're
+ 
+
+ align:start position:0%
+the expectation is okay so what we're
+going to do is I'm going to give you
+
+ align:start position:0%
+going to do is I'm going to give you
+ 
+
+ align:start position:0%
+going to do is I'm going to give you
+some different situations in terms of
+
+ align:start position:0%
+some different situations in terms of
+ 
+
+ align:start position:0%
+some different situations in terms of
+how the uh infectivity uh depends upon
+
+ align:start position:0%
+how the uh infectivity uh depends upon
+ 
+
+ align:start position:0%
+how the uh infectivity uh depends upon
+the virulence and then you get guys will
+
+ align:start position:0%
+the virulence and then you get guys will
+ 
+
+ align:start position:0%
+the virulence and then you get guys will
+get to tell me what um how the virence
+
+ align:start position:0%
+get to tell me what um how the virence
+ 
+
+ align:start position:0%
+get to tell me what um how the virence
+will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evolve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right this is a varul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right so first situation is if
+
+ align:start position:0%
+right all right so first situation is if
+ 
+
+ align:start position:0%
+right all right so first situation is if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+beta as a function of the veilance so
+
+ align:start position:0%
+beta as a function of the veilance so
+ 
+
+ align:start position:0%
+beta as a function of the veilance so
+the the infectivity as a function of
+
+ align:start position:0%
+the the infectivity as a function of
+ 
+
+ align:start position:0%
+the the infectivity as a function of
+veilance is some uh we'll say some beta
+
+ align:start position:0%
+veilance is some uh we'll say some beta
+ 
+
+ align:start position:0%
+veilance is some uh we'll say some beta
+knot right so it doesn't so first the
+
+ align:start position:0%
+knot right so it doesn't so first the
+ 
+
+ align:start position:0%
+knot right so it doesn't so first the
+question is if the infectivity does not
+
+ align:start position:0%
+question is if the infectivity does not
+ 
+
+ align:start position:0%
+question is if the infectivity does not
+depend upon the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+virulence right where will the where
+
+ align:start position:0%
+virulence right where will the where
+ 
+
+ align:start position:0%
+virulence right where will the where
+will variance go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to you have
+
+ align:start position:0%
+to you have
+ 
+
+ align:start position:0%
+to you have
+equation various places that'll help you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right do you need more time no all
+
+ align:start position:0%
+all right do you need more time no all
+ 
+
+ align:start position:0%
+all right do you need more time no all
+right ready three two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay we got many A's that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great right so if it's the case that it
+
+ align:start position:0%
+great right so if it's the case that it
+ 
+
+ align:start position:0%
+great right so if it's the case that it
+doesn't matter how you know that the the
+
+ align:start position:0%
+doesn't matter how you know that the the
+ 
+
+ align:start position:0%
+doesn't matter how you know that the the
+parasite regardless of how rapidly it's
+
+ align:start position:0%
+parasite regardless of how rapidly it's
+ 
+
+ align:start position:0%
+parasite regardless of how rapidly it's
+killing the individual if it has the
+
+ align:start position:0%
+killing the individual if it has the
+ 
+
+ align:start position:0%
+killing the individual if it has the
+same rate of getting to other
+
+ align:start position:0%
+same rate of getting to other
+ 
+
+ align:start position:0%
+same rate of getting to other
+individuals that case we want to make
+
+ align:start position:0%
+individuals that case we want to make
+ 
+
+ align:start position:0%
+individuals that case we want to make
+the rot get as uh as large as possible
+
+ align:start position:0%
+the rot get as uh as large as possible
+ 
+
+ align:start position:0%
+the rot get as uh as large as possible
+so then we make V go as small as
+
+ align:start position:0%
+so then we make V go as small as
+ 
+
+ align:start position:0%
+so then we make V go as small as
+possible right that's the mathematical
+
+ align:start position:0%
+possible right that's the mathematical
+ 
+
+ align:start position:0%
+possible right that's the mathematical
+thing you can look at and why does this
+
+ align:start position:0%
+thing you can look at and why does this
+ 
+
+ align:start position:0%
+thing you can look at and why does this
+make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense yeah right so from the standpoint
+
+ align:start position:0%
+sense yeah right so from the standpoint
+ 
+
+ align:start position:0%
+sense yeah right so from the standpoint
+of of the uh of the parasite if uh in
+
+ align:start position:0%
+of of the uh of the parasite if uh in
+ 
+
+ align:start position:0%
+of of the uh of the parasite if uh in
+this situation where the infectivity
+
+ align:start position:0%
+this situation where the infectivity
+ 
+
+ align:start position:0%
+this situation where the infectivity
+doesn't depend on the virulence well in
+
+ align:start position:0%
+doesn't depend on the virulence well in
+ 
+
+ align:start position:0%
+doesn't depend on the virulence well in
+that case uh you don't want to kill your
+
+ align:start position:0%
+that case uh you don't want to kill your
+ 
+
+ align:start position:0%
+that case uh you don't want to kill your
+host because uh the longer that the host
+
+ align:start position:0%
+host because uh the longer that the host
+ 
+
+ align:start position:0%
+host because uh the longer that the host
+lives the more other individuals you can
+
+ align:start position:0%
+lives the more other individuals you can
+ 
+
+ align:start position:0%
+lives the more other individuals you can
+infect
+
+ align:start position:0%
+infect
+ 
+
+ align:start position:0%
+infect
+right and this is the basic kind of
+
+ align:start position:0%
+right and this is the basic kind of
+ 
+
+ align:start position:0%
+right and this is the basic kind of
+statement underlying the the statement
+
+ align:start position:0%
+statement underlying the the statement
+ 
+
+ align:start position:0%
+statement underlying the the statement
+that you often hear that a well-adapted
+
+ align:start position:0%
+that you often hear that a well-adapted
+ 
+
+ align:start position:0%
+that you often hear that a well-adapted
+parasite does not harm its
+
+ align:start position:0%
+parasite does not harm its
+ 
+
+ align:start position:0%
+parasite does not harm its
+host and I think that this is one of
+
+ align:start position:0%
+host and I think that this is one of
+ 
+
+ align:start position:0%
+host and I think that this is one of
+those things
+
+ align:start position:0%
+those things
+ 
+
+ align:start position:0%
+those things
+that you can write down a simple model
+
+ align:start position:0%
+that you can write down a simple model
+ 
+
+ align:start position:0%
+that you can write down a simple model
+and convince yourself should be true uh
+
+ align:start position:0%
+and convince yourself should be true uh
+ 
+
+ align:start position:0%
+and convince yourself should be true uh
+you can maybe find a few case studies
+
+ align:start position:0%
+you can maybe find a few case studies
+ 
+
+ align:start position:0%
+you can maybe find a few case studies
+where it seems to be true uh but then uh
+
+ align:start position:0%
+where it seems to be true uh but then uh
+ 
+
+ align:start position:0%
+where it seems to be true uh but then uh
+you always have to be careful about what
+
+ align:start position:0%
+you always have to be careful about what
+ 
+
+ align:start position:0%
+you always have to be careful about what
+you know how strongly you should believe
+
+ align:start position:0%
+you know how strongly you should believe
+ 
+
+ align:start position:0%
+you know how strongly you should believe
+such a statement based on those kinds of
+
+ align:start position:0%
+such a statement based on those kinds of
+ 
+
+ align:start position:0%
+such a statement based on those kinds of
+evidence right because it's a very
+
+ align:start position:0%
+evidence right because it's a very
+ 
+
+ align:start position:0%
+evidence right because it's a very
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+model it's a making assumption that is
+
+ align:start position:0%
+model it's a making assumption that is
+ 
+
+ align:start position:0%
+model it's a making assumption that is
+very likely not true and actually many
+
+ align:start position:0%
+very likely not true and actually many
+ 
+
+ align:start position:0%
+very likely not true and actually many
+assumptions that are very very likely
+
+ align:start position:0%
+assumptions that are very very likely
+ 
+
+ align:start position:0%
+assumptions that are very very likely
+not true and there are counter examples
+
+ align:start position:0%
+not true and there are counter examples
+ 
+
+ align:start position:0%
+not true and there are counter examples
+right so Martin talks about malaria
+
+ align:start position:0%
+right so Martin talks about malaria
+ 
+
+ align:start position:0%
+right so Martin talks about malaria
+which which is which humans have had for
+
+ align:start position:0%
+which which is which humans have had for
+ 
+
+ align:start position:0%
+which which is which humans have had for
+uh millions of years and uh and still
+
+ align:start position:0%
+uh millions of years and uh and still
+ 
+
+ align:start position:0%
+uh millions of years and uh and still
+caus us a lot of problems
+
+ align:start position:0%
+caus us a lot of problems
+ 
+
+ align:start position:0%
+caus us a lot of problems
+right and so you might imagine that well
+
+ align:start position:0%
+right and so you might imagine that well
+ 
+
+ align:start position:0%
+right and so you might imagine that well
+what would happen if um if the
+
+ align:start position:0%
+what would happen if um if the
+ 
+
+ align:start position:0%
+what would happen if um if the
+infectivity is a function of the
+
+ align:start position:0%
+infectivity is a function of the
+ 
+
+ align:start position:0%
+infectivity is a function of the
+veilance maybe it's just proportional to
+
+ align:start position:0%
+veilance maybe it's just proportional to
+ 
+
+ align:start position:0%
+veilance maybe it's just proportional to
+the variance right and this kind of
+
+ align:start position:0%
+the variance right and this kind of
+ 
+
+ align:start position:0%
+the variance right and this kind of
+would make me make sense because you
+
+ align:start position:0%
+would make me make sense because you
+ 
+
+ align:start position:0%
+would make me make sense because you
+could say oh well let's imagine that the
+
+ align:start position:0%
+could say oh well let's imagine that the
+ 
+
+ align:start position:0%
+could say oh well let's imagine that the
+number of viruses in the host right that
+
+ align:start position:0%
+number of viruses in the host right that
+ 
+
+ align:start position:0%
+number of viruses in the host right that
+somehow the the additional ver the
+
+ align:start position:0%
+somehow the the additional ver the
+ 
+
+ align:start position:0%
+somehow the the additional ver the
+veillance is just proportional to that
+
+ align:start position:0%
+veillance is just proportional to that
+ 
+
+ align:start position:0%
+veillance is just proportional to that
+number and also the infectivity is
+
+ align:start position:0%
+number and also the infectivity is
+ 
+
+ align:start position:0%
+number and also the infectivity is
+proportional to that number right in
+
+ align:start position:0%
+proportional to that number right in
+ 
+
+ align:start position:0%
+proportional to that number right in
+that case infectivity will just scale
+
+ align:start position:0%
+that case infectivity will just scale
+ 
+
+ align:start position:0%
+that case infectivity will just scale
+linearly with v right does that it's
+
+ align:start position:0%
+linearly with v right does that it's
+ 
+
+ align:start position:0%
+linearly with v right does that it's
+kind of another reasonable world
+
+ align:start position:0%
+kind of another reasonable world
+ 
+
+ align:start position:0%
+kind of another reasonable world
+right okay so in this situation where
+
+ align:start position:0%
+right okay so in this situation where
+ 
+
+ align:start position:0%
+right okay so in this situation where
+does uh where does the variance of all
+
+ align:start position:0%
+does uh where does the variance of all
+ 
+
+ align:start position:0%
+does uh where does the variance of all
+to all right we'll um think about this
+
+ align:start position:0%
+to all right we'll um think about this
+ 
+
+ align:start position:0%
+to all right we'll um think about this
+for 10 seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right ready three two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay all right so now we actually
+
+ align:start position:0%
+one okay all right so now we actually
+ 
+
+ align:start position:0%
+one okay all right so now we actually
+have votes that are pretty distributed
+
+ align:start position:0%
+have votes that are pretty distributed
+ 
+
+ align:start position:0%
+have votes that are pretty distributed
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+um okay I I I'm just going to write down
+
+ align:start position:0%
+um okay I I I'm just going to write down
+ 
+
+ align:start position:0%
+um okay I I I'm just going to write down
+the expression just cuz I think we can
+
+ align:start position:0%
+the expression just cuz I think we can
+ 
+
+ align:start position:0%
+the expression just cuz I think we can
+do it quickly right so now the r KN is
+
+ align:start position:0%
+do it quickly right so now the r KN is
+ 
+
+ align:start position:0%
+do it quickly right so now the r KN is
+going to be given by we're going to be
+
+ align:start position:0%
+going to be given by we're going to be
+ 
+
+ align:start position:0%
+going to be given by we're going to be
+thinking about a one there's a u plus v
+
+ align:start position:0%
+thinking about a one there's a u plus v
+ 
+
+ align:start position:0%
+thinking about a one there's a u plus v
+down here but beta now there's a we're
+
+ align:start position:0%
+down here but beta now there's a we're
+ 
+
+ align:start position:0%
+down here but beta now there's a we're
+going to put beta here this is a a * V
+
+ align:start position:0%
+going to put beta here this is a a * V
+ 
+
+ align:start position:0%
+going to put beta here this is a a * V
+and then a k over
+
+ align:start position:0%
+and then a k over
+ 
+
+ align:start position:0%
+and then a k over
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+right so if we plot this as a function
+
+ align:start position:0%
+right so if we plot this as a function
+ 
+
+ align:start position:0%
+right so if we plot this as a function
+of v what does it look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like monotonically increases this is a
+
+ align:start position:0%
+like monotonically increases this is a
+ 
+
+ align:start position:0%
+like monotonically increases this is a
+michis metan type form right
+
+ align:start position:0%
+michis metan type form right
+ 
+
+ align:start position:0%
+michis metan type form right
+where uh the r nod is a function of V
+
+ align:start position:0%
+where uh the r nod is a function of V
+ 
+
+ align:start position:0%
+where uh the r nod is a function of V
+starts out linear and then
+
+ align:start position:0%
+starts out linear and then
+ 
+
+ align:start position:0%
+starts out linear and then
+saturates right and we're trying
+
+ align:start position:0%
+saturates right and we're trying
+ 
+
+ align:start position:0%
+saturates right and we're trying
+to oops this is not V this is
+
+ align:start position:0%
+to oops this is not V this is
+ 
+
+ align:start position:0%
+to oops this is not V this is
+R okay right if we want to maximize R
+
+ align:start position:0%
+R okay right if we want to maximize R
+ 
+
+ align:start position:0%
+R okay right if we want to maximize R
+then V goes
+
+ align:start position:0%
+then V goes
+ 
+
+ align:start position:0%
+then V goes
+to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay there was one other model
+
+ align:start position:0%
+right okay there was one other model
+ 
+
+ align:start position:0%
+right okay there was one other model
+that that Martin talked about which was
+
+ align:start position:0%
+that that Martin talked about which was
+ 
+
+ align:start position:0%
+that that Martin talked about which was
+the situation if the infectivity itself
+
+ align:start position:0%
+the situation if the infectivity itself
+ 
+
+ align:start position:0%
+the situation if the infectivity itself
+had a kind of M Menan type form right
+
+ align:start position:0%
+had a kind of M Menan type form right
+ 
+
+ align:start position:0%
+had a kind of M Menan type form right
+and this was again this was okay we
+
+ align:start position:0%
+and this was again this was okay we
+ 
+
+ align:start position:0%
+and this was again this was okay we
+still have an A there so it's some AV
+
+ align:start position:0%
+still have an A there so it's some AV
+ 
+
+ align:start position:0%
+still have an A there so it's some AV
+v c plus v right so this would be the
+
+ align:start position:0%
+v c plus v right so this would be the
+ 
+
+ align:start position:0%
+v c plus v right so this would be the
+situation where initially the
+
+ align:start position:0%
+situation where initially the
+ 
+
+ align:start position:0%
+situation where initially the
+infectivity increases with virence but
+
+ align:start position:0%
+infectivity increases with virence but
+ 
+
+ align:start position:0%
+infectivity increases with virence but
+um Beyond some uh some virence you no
+
+ align:start position:0%
+um Beyond some uh some virence you no
+ 
+
+ align:start position:0%
+um Beyond some uh some virence you no
+longer get an increased infectivity so
+
+ align:start position:0%
+longer get an increased infectivity so
+ 
+
+ align:start position:0%
+longer get an increased infectivity so
+for example if it's the case that every
+
+ align:start position:0%
+for example if it's the case that every
+ 
+
+ align:start position:0%
+for example if it's the case that every
+time you sneeze on somebody you're going
+
+ align:start position:0%
+time you sneeze on somebody you're going
+ 
+
+ align:start position:0%
+time you sneeze on somebody you're going
+to infect them then it doesn't matter if
+
+ align:start position:0%
+to infect them then it doesn't matter if
+ 
+
+ align:start position:0%
+to infect them then it doesn't matter if
+you double the number of viruses that
+
+ align:start position:0%
+you double the number of viruses that
+ 
+
+ align:start position:0%
+you double the number of viruses that
+you have you're still you still
+
+ align:start position:0%
+you have you're still you still
+ 
+
+ align:start position:0%
+you have you're still you still
+saturated the infe effectivity
+
+ align:start position:0%
+saturated the infe effectivity
+ 
+
+ align:start position:0%
+saturated the infe effectivity
+okay right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now all right I I'll just tell you that
+
+ align:start position:0%
+now all right I I'll just tell you that
+ 
+
+ align:start position:0%
+now all right I I'll just tell you that
+in this case there ends up being uh some
+
+ align:start position:0%
+in this case there ends up being uh some
+ 
+
+ align:start position:0%
+in this case there ends up being uh some
+intermediate uh infectivity that you
+
+ align:start position:0%
+intermediate uh infectivity that you
+ 
+
+ align:start position:0%
+intermediate uh infectivity that you
+evolv to which comes here and indeed
+
+ align:start position:0%
+evolv to which comes here and indeed
+ 
+
+ align:start position:0%
+evolv to which comes here and indeed
+this kind of makes sense as
+
+ align:start position:0%
+this kind of makes sense as
+ 
+
+ align:start position:0%
+this kind of makes sense as
+as um C goes to
+
+ align:start position:0%
+as um C goes to
+ 
+
+ align:start position:0%
+as um C goes to
+Infinity then you end up wait what do I
+
+ align:start position:0%
+Infinity then you end up wait what do I
+ 
+
+ align:start position:0%
+Infinity then you end up wait what do I
+want right oh yeah so if C is very large
+
+ align:start position:0%
+want right oh yeah so if C is very large
+ 
+
+ align:start position:0%
+want right oh yeah so if C is very large
+then it just kind of looks like this all
+
+ align:start position:0%
+then it just kind of looks like this all
+ 
+
+ align:start position:0%
+then it just kind of looks like this all
+right it's divided by something large
+
+ align:start position:0%
+right it's divided by something large
+ 
+
+ align:start position:0%
+right it's divided by something large
+but in terms of the scaling with v it's
+
+ align:start position:0%
+but in terms of the scaling with v it's
+ 
+
+ align:start position:0%
+but in terms of the scaling with v it's
+just linear in V right and that means
+
+ align:start position:0%
+just linear in V right and that means
+ 
+
+ align:start position:0%
+just linear in V right and that means
+that the evolved virulence goes uh very
+
+ align:start position:0%
+that the evolved virulence goes uh very
+ 
+
+ align:start position:0%
+that the evolved virulence goes uh very
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+okay does that make
+
+ align:start position:0%
+okay does that make
+ 
+
+ align:start position:0%
+okay does that make
+sense no okay I'm so I guess all what I
+
+ align:start position:0%
+sense no okay I'm so I guess all what I
+ 
+
+ align:start position:0%
+sense no okay I'm so I guess all what I
+was saying is that if if C you know if
+
+ align:start position:0%
+was saying is that if if C you know if
+ 
+
+ align:start position:0%
+was saying is that if if C you know if
+you're in the region where C is somehow
+
+ align:start position:0%
+you're in the region where C is somehow
+ 
+
+ align:start position:0%
+you're in the region where C is somehow
+very large okay then um then you end up
+
+ align:start position:0%
+very large okay then um then you end up
+ 
+
+ align:start position:0%
+very large okay then um then you end up
+with the infectivity just being kind of
+
+ align:start position:0%
+with the infectivity just being kind of
+ 
+
+ align:start position:0%
+with the infectivity just being kind of
+proportional to the
+
+ align:start position:0%
+proportional to the
+ 
+
+ align:start position:0%
+proportional to the
+variance right because the the the
+
+ align:start position:0%
+variance right because the the the
+ 
+
+ align:start position:0%
+variance right because the the the
+virulence the V here in the denominator
+
+ align:start position:0%
+virulence the V here in the denominator
+ 
+
+ align:start position:0%
+virulence the V here in the denominator
+doesn't really contribute very much
+
+ align:start position:0%
+doesn't really contribute very much
+ 
+
+ align:start position:0%
+doesn't really contribute very much
+right and if you if you're in this that
+
+ align:start position:0%
+right and if you if you're in this that
+ 
+
+ align:start position:0%
+right and if you if you're in this that
+means that it's going to be the same
+
+ align:start position:0%
+means that it's going to be the same
+ 
+
+ align:start position:0%
+means that it's going to be the same
+kind of functional form as this except
+
+ align:start position:0%
+kind of functional form as this except
+ 
+
+ align:start position:0%
+kind of functional form as this except
+if it's a divided by C but it's still
+
+ align:start position:0%
+if it's a divided by C but it's still
+ 
+
+ align:start position:0%
+if it's a divided by C but it's still
+proportional to the variance and that
+
+ align:start position:0%
+proportional to the variance and that
+ 
+
+ align:start position:0%
+proportional to the variance and that
+that leads to a larger and larger
+
+ align:start position:0%
+that leads to a larger and larger
+ 
+
+ align:start position:0%
+that leads to a larger and larger
+evolved
+
+ align:start position:0%
+evolved
+ 
+
+ align:start position:0%
+evolved
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+okay yep yes is it possible like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than just yeah right right um so I think
+
+ align:start position:0%
+than just yeah right right um so I think
+ 
+
+ align:start position:0%
+than just yeah right right um so I think
+from real data I think people do uh
+
+ align:start position:0%
+from real data I think people do uh
+ 
+
+ align:start position:0%
+from real data I think people do uh
+people do argue about it but I think
+
+ align:start position:0%
+people do argue about it but I think
+ 
+
+ align:start position:0%
+people do argue about it but I think
+that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it seems to be you know I guess if
+
+ align:start position:0%
+um it seems to be you know I guess if
+ 
+
+ align:start position:0%
+um it seems to be you know I guess if
+you had to there is some sense that uh
+
+ align:start position:0%
+you had to there is some sense that uh
+ 
+
+ align:start position:0%
+you had to there is some sense that uh
+that it it does Plateau but it does but
+
+ align:start position:0%
+that it it does Plateau but it does but
+ 
+
+ align:start position:0%
+that it it does Plateau but it does but
+it's it is a function of it's an
+
+ align:start position:0%
+it's it is a function of it's an
+ 
+
+ align:start position:0%
+it's it is a function of it's an
+increasing fun of V but not sublinear
+
+ align:start position:0%
+increasing fun of V but not sublinear
+ 
+
+ align:start position:0%
+increasing fun of V but not sublinear
+right the question is how strong of a
+
+ align:start position:0%
+right the question is how strong of a
+ 
+
+ align:start position:0%
+right the question is how strong of a
+statement you can make there because
+
+ align:start position:0%
+statement you can make there because
+ 
+
+ align:start position:0%
+statement you can make there because
+also in many cases there is super
+
+ align:start position:0%
+also in many cases there is super
+ 
+
+ align:start position:0%
+also in many cases there is super
+infection and super infection tends to
+
+ align:start position:0%
+infection and super infection tends to
+ 
+
+ align:start position:0%
+infection and super infection tends to
+lead to even higher uh virulence than
+
+ align:start position:0%
+lead to even higher uh virulence than
+ 
+
+ align:start position:0%
+lead to even higher uh virulence than
+what you would expect from this um
+
+ align:start position:0%
+what you would expect from this um
+ 
+
+ align:start position:0%
+what you would expect from this um
+because you're competing against uh
+
+ align:start position:0%
+because you're competing against uh
+ 
+
+ align:start position:0%
+because you're competing against uh
+viruses in the same host right so you
+
+ align:start position:0%
+viruses in the same host right so you
+ 
+
+ align:start position:0%
+viruses in the same host right so you
+you kind of have to out comp out compete
+
+ align:start position:0%
+you kind of have to out comp out compete
+ 
+
+ align:start position:0%
+you kind of have to out comp out compete
+the other parasite in the host as well
+
+ align:start position:0%
+the other parasite in the host as well
+ 
+
+ align:start position:0%
+the other parasite in the host as well
+as kind of go on and you don't pay the
+
+ align:start position:0%
+as kind of go on and you don't pay the
+ 
+
+ align:start position:0%
+as kind of go on and you don't pay the
+full cost associated with keeping the
+
+ align:start position:0%
+full cost associated with keeping the
+ 
+
+ align:start position:0%
+full cost associated with keeping the
+host alive right so when you have super
+
+ align:start position:0%
+host alive right so when you have super
+ 
+
+ align:start position:0%
+host alive right so when you have super
+infection there's this notion that it it
+
+ align:start position:0%
+infection there's this notion that it it
+ 
+
+ align:start position:0%
+infection there's this notion that it it
+may the the better strategy from the
+
+ align:start position:0%
+may the the better strategy from the
+ 
+
+ align:start position:0%
+may the the better strategy from the
+standpoint of the parasite can be to
+
+ align:start position:0%
+standpoint of the parasite can be to
+ 
+
+ align:start position:0%
+standpoint of the parasite can be to
+just evolve very high virulence right so
+
+ align:start position:0%
+just evolve very high virulence right so
+ 
+
+ align:start position:0%
+just evolve very high virulence right so
+you're going to kill the host but you
+
+ align:start position:0%
+you're going to kill the host but you
+ 
+
+ align:start position:0%
+you're going to kill the host but you
+can get out quickly right so then then
+
+ align:start position:0%
+can get out quickly right so then then
+ 
+
+ align:start position:0%
+can get out quickly right so then then
+you can imagine that the the less
+
+ align:start position:0%
+you can imagine that the the less
+ 
+
+ align:start position:0%
+you can imagine that the the less
+virulent strain was kind of stranded in
+
+ align:start position:0%
+virulent strain was kind of stranded in
+ 
+
+ align:start position:0%
+virulent strain was kind of stranded in
+that host that died right uh so from
+
+ align:start position:0%
+that host that died right uh so from
+ 
+
+ align:start position:0%
+that host that died right uh so from
+that standpoint you can think about Evol
+
+ align:start position:0%
+that standpoint you can think about Evol
+ 
+
+ align:start position:0%
+that standpoint you can think about Evol
+you know in some cases for a parasite
+
+ align:start position:0%
+you know in some cases for a parasite
+ 
+
+ align:start position:0%
+you know in some cases for a parasite
+evolving low virulence is somehow like
+
+ align:start position:0%
+evolving low virulence is somehow like
+ 
+
+ align:start position:0%
+evolving low virulence is somehow like
+some Cooperative Behavior because uh
+
+ align:start position:0%
+some Cooperative Behavior because uh
+ 
+
+ align:start position:0%
+some Cooperative Behavior because uh
+you're you're keeping this host alive so
+
+ align:start position:0%
+you're you're keeping this host alive so
+ 
+
+ align:start position:0%
+you're you're keeping this host alive so
+that you can uh you're using the
+
+ align:start position:0%
+that you can uh you're using the
+ 
+
+ align:start position:0%
+that you can uh you're using the
+resources in a wise way so that you can
+
+ align:start position:0%
+resources in a wise way so that you can
+ 
+
+ align:start position:0%
+resources in a wise way so that you can
+uh you can infect other individuals but
+
+ align:start position:0%
+uh you can infect other individuals but
+ 
+
+ align:start position:0%
+uh you can infect other individuals but
+then uh that that kind of strategy is
+
+ align:start position:0%
+then uh that that kind of strategy is
+ 
+
+ align:start position:0%
+then uh that that kind of strategy is
+susceptible to these cheating strategies
+
+ align:start position:0%
+susceptible to these cheating strategies
+ 
+
+ align:start position:0%
+susceptible to these cheating strategies
+that just have high veilance and kill
+
+ align:start position:0%
+that just have high veilance and kill
+ 
+
+ align:start position:0%
+that just have high veilance and kill
+the host and then get get onto a new
+
+ align:start position:0%
+the host and then get get onto a new
+ 
+
+ align:start position:0%
+the host and then get get onto a new
+host right yeah so I think there are
+
+ align:start position:0%
+host right yeah so I think there are
+ 
+
+ align:start position:0%
+host right yeah so I think there are
+enough of these sorts of issues that
+
+ align:start position:0%
+enough of these sorts of issues that
+ 
+
+ align:start position:0%
+enough of these sorts of issues that
+it's hard to take any of this too
+
+ align:start position:0%
+it's hard to take any of this too
+ 
+
+ align:start position:0%
+it's hard to take any of this too
+seriously I would say that perhaps where
+
+ align:start position:0%
+seriously I would say that perhaps where
+ 
+
+ align:start position:0%
+seriously I would say that perhaps where
+this field has had the the biggest
+
+ align:start position:0%
+this field has had the the biggest
+ 
+
+ align:start position:0%
+this field has had the the biggest
+impact is in the context of of
+
+ align:start position:0%
+impact is in the context of of
+ 
+
+ align:start position:0%
+impact is in the context of of
+vaccinations all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because uh you can really measure our
+
+ align:start position:0%
+because uh you can really measure our
+ 
+
+ align:start position:0%
+because uh you can really measure our
+knot for many different uh many
+
+ align:start position:0%
+knot for many different uh many
+ 
+
+ align:start position:0%
+knot for many different uh many
+different diseases and I think that
+
+ align:start position:0%
+different diseases and I think that
+ 
+
+ align:start position:0%
+different diseases and I think that
+that's somehow easier to measure than
+
+ align:start position:0%
+that's somehow easier to measure than
+ 
+
+ align:start position:0%
+that's somehow easier to measure than
+many other things because you can uh try
+
+ align:start position:0%
+many other things because you can uh try
+ 
+
+ align:start position:0%
+many other things because you can uh try
+to do uh tracing of um of infections
+
+ align:start position:0%
+to do uh tracing of um of infections
+ 
+
+ align:start position:0%
+to do uh tracing of um of infections
+right so if you think about somebody
+
+ align:start position:0%
+right so if you think about somebody
+ 
+
+ align:start position:0%
+right so if you think about somebody
+that gets infected and moves to a new
+
+ align:start position:0%
+that gets infected and moves to a new
+ 
+
+ align:start position:0%
+that gets infected and moves to a new
+city or you know lands in a new city you
+
+ align:start position:0%
+city or you know lands in a new city you
+ 
+
+ align:start position:0%
+city or you know lands in a new city you
+can try to figure out who they who they
+
+ align:start position:0%
+can try to figure out who they who they
+ 
+
+ align:start position:0%
+can try to figure out who they who they
+infected right so then you can go and
+
+ align:start position:0%
+infected right so then you can go and
+ 
+
+ align:start position:0%
+infected right so then you can go and
+measure these R not parameters right and
+
+ align:start position:0%
+measure these R not parameters right and
+ 
+
+ align:start position:0%
+measure these R not parameters right and
+uh and of course the diseases that we we
+
+ align:start position:0%
+uh and of course the diseases that we we
+ 
+
+ align:start position:0%
+uh and of course the diseases that we we
+worry about tend to have AR knots larger
+
+ align:start position:0%
+worry about tend to have AR knots larger
+ 
+
+ align:start position:0%
+worry about tend to have AR knots larger
+than one right um and how large they are
+
+ align:start position:0%
+than one right um and how large they are
+ 
+
+ align:start position:0%
+than one right um and how large they are
+tells you about how difficult um kind of
+
+ align:start position:0%
+tells you about how difficult um kind of
+ 
+
+ align:start position:0%
+tells you about how difficult um kind of
+vaccination will be in order to um in
+
+ align:start position:0%
+vaccination will be in order to um in
+ 
+
+ align:start position:0%
+vaccination will be in order to um in
+order to be successful and and to remove
+
+ align:start position:0%
+order to be successful and and to remove
+ 
+
+ align:start position:0%
+order to be successful and and to remove
+um the disease from the population right
+
+ align:start position:0%
+um the disease from the population right
+ 
+
+ align:start position:0%
+um the disease from the population right
+so uh if you're if you're curious after
+
+ align:start position:0%
+so uh if you're if you're curious after
+ 
+
+ align:start position:0%
+so uh if you're if you're curious after
+class you can come up and there's a nice
+
+ align:start position:0%
+class you can come up and there's a nice
+ 
+
+ align:start position:0%
+class you can come up and there's a nice
+table uh that I have here for small poox
+
+ align:start position:0%
+table uh that I have here for small poox
+ 
+
+ align:start position:0%
+table uh that I have here for small poox
+measles whipping cough German Measles
+
+ align:start position:0%
+measles whipping cough German Measles
+ 
+
+ align:start position:0%
+measles whipping cough German Measles
+chickenpox diptheria scarlet fever mumps
+
+ align:start position:0%
+chickenpox diptheria scarlet fever mumps
+ 
+
+ align:start position:0%
+chickenpox diptheria scarlet fever mumps
+and poliomyelitis
+
+ align:start position:0%
+and poliomyelitis
+ 
+
+ align:start position:0%
+and poliomyelitis
+uh estimates of uh of R knots right and
+
+ align:start position:0%
+uh estimates of uh of R knots right and
+ 
+
+ align:start position:0%
+uh estimates of uh of R knots right and
+they they kind of range U they're kind
+
+ align:start position:0%
+they they kind of range U they're kind
+ 
+
+ align:start position:0%
+they they kind of range U they're kind
+of five to five to 15 to give you a
+
+ align:start position:0%
+of five to five to 15 to give you a
+ 
+
+ align:start position:0%
+of five to five to 15 to give you a
+sense right uh and so which diseases U
+
+ align:start position:0%
+sense right uh and so which diseases U
+ 
+
+ align:start position:0%
+sense right uh and so which diseases U
+right so if you want to remove the
+
+ align:start position:0%
+right so if you want to remove the
+ 
+
+ align:start position:0%
+right so if you want to remove the
+disease from the population what is it
+
+ align:start position:0%
+disease from the population what is it
+ 
+
+ align:start position:0%
+disease from the population what is it
+that changes in terms of
+
+ align:start position:0%
+that changes in terms of
+ 
+
+ align:start position:0%
+that changes in terms of
+vaccination uh in order to REM remove
+
+ align:start position:0%
+vaccination uh in order to REM remove
+ 
+
+ align:start position:0%
+vaccination uh in order to REM remove
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disease yes are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not that's right so you you um by
+
+ align:start position:0%
+not that's right so you you um by
+ 
+
+ align:start position:0%
+not that's right so you you um by
+vaccinating you're kind of removing
+
+ align:start position:0%
+vaccinating you're kind of removing
+ 
+
+ align:start position:0%
+vaccinating you're kind of removing
+susceptible individuals from the
+
+ align:start position:0%
+susceptible individuals from the
+ 
+
+ align:start position:0%
+susceptible individuals from the
+population and making them resistant
+
+ align:start position:0%
+population and making them resistant
+ 
+
+ align:start position:0%
+population and making them resistant
+somehow right and uh and the r not
+
+ align:start position:0%
+somehow right and uh and the r not
+ 
+
+ align:start position:0%
+somehow right and uh and the r not
+parameter tells you about what fraction
+
+ align:start position:0%
+parameter tells you about what fraction
+ 
+
+ align:start position:0%
+parameter tells you about what fraction
+of the population you have to vaccinate
+
+ align:start position:0%
+of the population you have to vaccinate
+ 
+
+ align:start position:0%
+of the population you have to vaccinate
+in order to remove the uh the parasite
+
+ align:start position:0%
+in order to remove the uh the parasite
+ 
+
+ align:start position:0%
+in order to remove the uh the parasite
+from the population right so there're
+
+ align:start position:0%
+from the population right so there're
+ 
+
+ align:start position:0%
+from the population right so there're
+basically you have to vaccinate a
+
+ align:start position:0%
+basically you have to vaccinate a
+ 
+
+ align:start position:0%
+basically you have to vaccinate a
+fraction of percentage or
+
+ align:start position:0%
+fraction of percentage or
+ 
+
+ align:start position:0%
+fraction of percentage or
+P that's greater than 1 minus one/ r KN
+
+ align:start position:0%
+P that's greater than 1 minus one/ r KN
+ 
+
+ align:start position:0%
+P that's greater than 1 minus one/ r KN
+okay so as R KN kind of gets very large
+
+ align:start position:0%
+okay so as R KN kind of gets very large
+ 
+
+ align:start position:0%
+okay so as R KN kind of gets very large
+it means that you have to vaccinate
+
+ align:start position:0%
+it means that you have to vaccinate
+ 
+
+ align:start position:0%
+it means that you have to vaccinate
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+everybody okay so if if you have R knot
+
+ align:start position:0%
+everybody okay so if if you have R knot
+ 
+
+ align:start position:0%
+everybody okay so if if you have R knot
+of say five which is typical of many of
+
+ align:start position:0%
+of say five which is typical of many of
+ 
+
+ align:start position:0%
+of say five which is typical of many of
+these diseases it's saying you kind of
+
+ align:start position:0%
+these diseases it's saying you kind of
+ 
+
+ align:start position:0%
+these diseases it's saying you kind of
+have to vaccinate uh kind of 80% of the
+
+ align:start position:0%
+have to vaccinate uh kind of 80% of the
+ 
+
+ align:start position:0%
+have to vaccinate uh kind of 80% of the
+population right you can never get to
+
+ align:start position:0%
+population right you can never get to
+ 
+
+ align:start position:0%
+population right you can never get to
+100% right and that that's why it's very
+
+ align:start position:0%
+100% right and that that's why it's very
+ 
+
+ align:start position:0%
+100% right and that that's why it's very
+difficult to get rid of these get rid of
+
+ align:start position:0%
+difficult to get rid of these get rid of
+ 
+
+ align:start position:0%
+difficult to get rid of these get rid of
+these diseases with large R
+
+ align:start position:0%
+these diseases with large R
+ 
+
+ align:start position:0%
+these diseases with large R
+knots and incidentally they note that
+
+ align:start position:0%
+knots and incidentally they note that
+ 
+
+ align:start position:0%
+knots and incidentally they note that
+small pox
+
+ align:start position:0%
+small pox
+ 
+
+ align:start position:0%
+small pox
+has an R knot of kind of three to
+
+ align:start position:0%
+has an R knot of kind of three to
+ 
+
+ align:start position:0%
+has an R knot of kind of three to
+five in and this is of this always
+
+ align:start position:0%
+five in and this is of this always
+ 
+
+ align:start position:0%
+five in and this is of this always
+depends on the environment but in the
+
+ align:start position:0%
+depends on the environment but in the
+ 
+
+ align:start position:0%
+depends on the environment but in the
+case where they measured uh small pox
+
+ align:start position:0%
+case where they measured uh small pox
+ 
+
+ align:start position:0%
+case where they measured uh small pox
+are not it's kind of three to five and
+
+ align:start position:0%
+are not it's kind of three to five and
+ 
+
+ align:start position:0%
+are not it's kind of three to five and
+and this is sort of small as compared to
+
+ align:start position:0%
+and this is sort of small as compared to
+ 
+
+ align:start position:0%
+and this is sort of small as compared to
+many of these diseases and this is
+
+ align:start position:0%
+many of these diseases and this is
+ 
+
+ align:start position:0%
+many of these diseases and this is
+telling us that that small pox is
+
+ align:start position:0%
+telling us that that small pox is
+ 
+
+ align:start position:0%
+telling us that that small pox is
+easier to get rid of via vaccinations
+
+ align:start position:0%
+easier to get rid of via vaccinations
+ 
+
+ align:start position:0%
+easier to get rid of via vaccinations
+than many of these other diseases and
+
+ align:start position:0%
+than many of these other diseases and
+ 
+
+ align:start position:0%
+than many of these other diseases and
+indeed we've um you know the the
+
+ align:start position:0%
+indeed we've um you know the the
+ 
+
+ align:start position:0%
+indeed we've um you know the the
+vaccination uh procedures have been more
+
+ align:start position:0%
+vaccination uh procedures have been more
+ 
+
+ align:start position:0%
+vaccination uh procedures have been more
+successful in small pox than it than the
+
+ align:start position:0%
+successful in small pox than it than the
+ 
+
+ align:start position:0%
+successful in small pox than it than the
+others right you
+
+ align:start position:0%
+others right you
+ 
+
+ align:start position:0%
+others right you
+know I I don't um but if you know maybe
+
+ align:start position:0%
+know I I don't um but if you know maybe
+ 
+
+ align:start position:0%
+know I I don't um but if you know maybe
+maybe in the next 20 minutes somebody
+
+ align:start position:0%
+maybe in the next 20 minutes somebody
+ 
+
+ align:start position:0%
+maybe in the next 20 minutes somebody
+can Google uh this and U at least I we
+
+ align:start position:0%
+can Google uh this and U at least I we
+ 
+
+ align:start position:0%
+can Google uh this and U at least I we
+can we can estimate this right right now
+
+ align:start position:0%
+can we can estimate this right right now
+ 
+
+ align:start position:0%
+can we can estimate this right right now
+though you know I mean we had we've had
+
+ align:start position:0%
+though you know I mean we had we've had
+ 
+
+ align:start position:0%
+though you know I mean we had we've had
+what you know five Ebola patients come
+
+ align:start position:0%
+what you know five Ebola patients come
+ 
+
+ align:start position:0%
+what you know five Ebola patients come
+to the United States and we've gotten
+
+ align:start position:0%
+to the United States and we've gotten
+ 
+
+ align:start position:0%
+to the United States and we've gotten
+two or three infections so I I'll say
+
+ align:start position:0%
+two or three infections so I I'll say
+ 
+
+ align:start position:0%
+two or three infections so I I'll say
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+fifths this it obviously depends on the
+
+ align:start position:0%
+fifths this it obviously depends on the
+ 
+
+ align:start position:0%
+fifths this it obviously depends on the
+environment right yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess in York City measure you how many
+
+ align:start position:0%
+guess in York City measure you how many
+ 
+
+ align:start position:0%
+guess in York City measure you how many
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+right yeah no but but AR no the thing is
+
+ align:start position:0%
+right yeah no but but AR no the thing is
+ 
+
+ align:start position:0%
+right yeah no but but AR no the thing is
+you don't have to do you don't have to
+
+ align:start position:0%
+you don't have to do you don't have to
+ 
+
+ align:start position:0%
+you don't have to do you don't have to
+do anything that's so immoral because
+
+ align:start position:0%
+do anything that's so immoral because
+ 
+
+ align:start position:0%
+do anything that's so immoral because
+what you're interested in is the are not
+
+ align:start position:0%
+what you're interested in is the are not
+ 
+
+ align:start position:0%
+what you're interested in is the are not
+for an individual in an actual
+
+ align:start position:0%
+for an individual in an actual
+ 
+
+ align:start position:0%
+for an individual in an actual
+environment that they're actually going
+
+ align:start position:0%
+environment that they're actually going
+ 
+
+ align:start position:0%
+environment that they're actually going
+to be in right so this is a situation
+
+ align:start position:0%
+to be in right so this is a situation
+ 
+
+ align:start position:0%
+to be in right so this is a situation
+where you know the doctor comes back
+
+ align:start position:0%
+where you know the doctor comes back
+ 
+
+ align:start position:0%
+where you know the doctor comes back
+from Africa after working with Doctors
+
+ align:start position:0%
+from Africa after working with Doctors
+ 
+
+ align:start position:0%
+from Africa after working with Doctors
+Without Borders right he knows you know
+
+ align:start position:0%
+Without Borders right he knows you know
+ 
+
+ align:start position:0%
+Without Borders right he knows you know
+in this day you know he knows that he
+
+ align:start position:0%
+in this day you know he knows that he
+ 
+
+ align:start position:0%
+in this day you know he knows that he
+has to watch out for a fever and and
+
+ align:start position:0%
+has to watch out for a fever and and
+ 
+
+ align:start position:0%
+has to watch out for a fever and and
+then if he gets a fever he calls in and
+
+ align:start position:0%
+then if he gets a fever he calls in and
+ 
+
+ align:start position:0%
+then if he gets a fever he calls in and
+he's brought to the hospital right and
+
+ align:start position:0%
+he's brought to the hospital right and
+ 
+
+ align:start position:0%
+he's brought to the hospital right and
+that's the world that we're interested
+
+ align:start position:0%
+that's the world that we're interested
+ 
+
+ align:start position:0%
+that's the world that we're interested
+in of what the AR not is right it's not
+
+ align:start position:0%
+in of what the AR not is right it's not
+ 
+
+ align:start position:0%
+in of what the AR not is right it's not
+the world in which you know there's Fe
+
+ align:start position:0%
+the world in which you know there's Fe
+ 
+
+ align:start position:0%
+the world in which you know there's Fe
+fevers everywhere and nobody know you
+
+ align:start position:0%
+fevers everywhere and nobody know you
+ 
+
+ align:start position:0%
+fevers everywhere and nobody know you
+know and you know right so it's um so
+
+ align:start position:0%
+know and you know right so it's um so
+ 
+
+ align:start position:0%
+know and you know right so it's um so
+the the r not for in the United States
+
+ align:start position:0%
+the the r not for in the United States
+ 
+
+ align:start position:0%
+the the r not for in the United States
+is going to be much lower than the r not
+
+ align:start position:0%
+is going to be much lower than the r not
+ 
+
+ align:start position:0%
+is going to be much lower than the r not
+in you know somewhere else right yeah is
+
+ align:start position:0%
+in you know somewhere else right yeah is
+ 
+
+ align:start position:0%
+in you know somewhere else right yeah is
+there a of disase that you don't Transit
+
+ align:start position:0%
+there a of disase that you don't Transit
+ 
+
+ align:start position:0%
+there a of disase that you don't Transit
+between people you get
+
+ align:start position:0%
+between people you get
+ 
+
+ align:start position:0%
+between people you get
+yeah right so I I think
+
+ align:start position:0%
+yeah right so I I think
+ 
+
+ align:start position:0%
+yeah right so I I think
+that you could try to generate a similar
+
+ align:start position:0%
+that you could try to generate a similar
+ 
+
+ align:start position:0%
+that you could try to generate a similar
+kind of R not for those disease all it's
+
+ align:start position:0%
+kind of R not for those disease all it's
+ 
+
+ align:start position:0%
+kind of R not for those disease all it's
+going to be very muddled right in the
+
+ align:start position:0%
+going to be very muddled right in the
+ 
+
+ align:start position:0%
+going to be very muddled right in the
+case of where you have all the vectors
+
+ align:start position:0%
+case of where you have all the vectors
+ 
+
+ align:start position:0%
+case of where you have all the vectors
+and so forth because it's not even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear yeah I yeah I'm hesitant I'm
+
+ align:start position:0%
+clear yeah I yeah I'm hesitant I'm
+ 
+
+ align:start position:0%
+clear yeah I yeah I'm hesitant I'm
+hesitant to to say too much because I
+
+ align:start position:0%
+hesitant to to say too much because I
+ 
+
+ align:start position:0%
+hesitant to to say too much because I
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+anything it's 1.5 2.5 for Ebola here or
+
+ align:start position:0%
+anything it's 1.5 2.5 for Ebola here or
+ 
+
+ align:start position:0%
+anything it's 1.5 2.5 for Ebola here or
+in um
+
+ align:start position:0%
+in um
+ 
+
+ align:start position:0%
+in um
+it says the 2014 West
+
+ align:start position:0%
+it says the 2014 West
+ 
+
+ align:start position:0%
+it says the 2014 West
+Africa ah okay so this is this is in
+
+ align:start position:0%
+Africa ah okay so this is this is in
+ 
+
+ align:start position:0%
+Africa ah okay so this is this is in
+West Africa then okay right yeah and and
+
+ align:start position:0%
+West Africa then okay right yeah and and
+ 
+
+ align:start position:0%
+West Africa then okay right yeah and and
+the idea is that it has obviously spread
+
+ align:start position:0%
+the idea is that it has obviously spread
+ 
+
+ align:start position:0%
+the idea is that it has obviously spread
+exponentially which means it has it had
+
+ align:start position:0%
+exponentially which means it has it had
+ 
+
+ align:start position:0%
+exponentially which means it has it had
+to have been larger than one right but
+
+ align:start position:0%
+to have been larger than one right but
+ 
+
+ align:start position:0%
+to have been larger than one right but
+and I think it's important to remember
+
+ align:start position:0%
+and I think it's important to remember
+ 
+
+ align:start position:0%
+and I think it's important to remember
+that you know just because you have a
+
+ align:start position:0%
+that you know just because you have a
+ 
+
+ align:start position:0%
+that you know just because you have a
+chart with a bunch of rots this is not
+
+ align:start position:0%
+chart with a bunch of rots this is not
+ 
+
+ align:start position:0%
+chart with a bunch of rots this is not
+set in stone right public policy hygiene
+
+ align:start position:0%
+set in stone right public policy hygiene
+ 
+
+ align:start position:0%
+set in stone right public policy hygiene
+and everything changes this right and
+
+ align:start position:0%
+and everything changes this right and
+ 
+
+ align:start position:0%
+and everything changes this right and
+we'd like to drive it down yeah was
+
+ align:start position:0%
+we'd like to drive it down yeah was
+ 
+
+ align:start position:0%
+we'd like to drive it down yeah was
+there a question in the back I was just
+
+ align:start position:0%
+there a question in the back I was just
+ 
+
+ align:start position:0%
+there a question in the back I was just
+going to say
+
+ align:start position:0%
+going to say
+ 
+
+ align:start position:0%
+going to say
+same thing about two okay all right um
+
+ align:start position:0%
+same thing about two okay all right um
+ 
+
+ align:start position:0%
+same thing about two okay all right um
+right so that means that uh that we can
+
+ align:start position:0%
+right so that means that uh that we can
+ 
+
+ align:start position:0%
+right so that means that uh that we can
+actually in principle vaccinate against
+
+ align:start position:0%
+actually in principle vaccinate against
+ 
+
+ align:start position:0%
+actually in principle vaccinate against
+Ebola we only have to get you know over
+
+ align:start position:0%
+Ebola we only have to get you know over
+ 
+
+ align:start position:0%
+Ebola we only have to get you know over
+50% of the population vaccinated in West
+
+ align:start position:0%
+50% of the population vaccinated in West
+ 
+
+ align:start position:0%
+50% of the population vaccinated in West
+Africa and then we can maybe uh make it
+
+ align:start position:0%
+Africa and then we can maybe uh make it
+ 
+
+ align:start position:0%
+Africa and then we can maybe uh make it
+so it cannot spread and become an
+
+ align:start position:0%
+so it cannot spread and become an
+ 
+
+ align:start position:0%
+so it cannot spread and become an
+epidemic right of course we need to have
+
+ align:start position:0%
+epidemic right of course we need to have
+ 
+
+ align:start position:0%
+epidemic right of course we need to have
+a vaccine first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right so I I think that I'm
+
+ align:start position:0%
+right all right so I I think that I'm
+ 
+
+ align:start position:0%
+right all right so I I think that I'm
+going to skip the discussion of Sir
+
+ align:start position:0%
+going to skip the discussion of Sir
+ 
+
+ align:start position:0%
+going to skip the discussion of Sir
+models because you are going to uh play
+
+ align:start position:0%
+models because you are going to uh play
+ 
+
+ align:start position:0%
+models because you are going to uh play
+with some of them in the context of your
+
+ align:start position:0%
+with some of them in the context of your
+ 
+
+ align:start position:0%
+with some of them in the context of your
+problem set um and if you just Google
+
+ align:start position:0%
+problem set um and if you just Google
+ 
+
+ align:start position:0%
+problem set um and if you just Google
+sir you can find it very similar uh kind
+
+ align:start position:0%
+sir you can find it very similar uh kind
+ 
+
+ align:start position:0%
+sir you can find it very similar uh kind
+of intuition that you get from this
+
+ align:start position:0%
+of intuition that you get from this
+ 
+
+ align:start position:0%
+of intuition that you get from this
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+okay um I do uh because I do want to
+
+ align:start position:0%
+okay um I do uh because I do want to
+ 
+
+ align:start position:0%
+okay um I do uh because I do want to
+spend the last 15 minutes at least uh
+
+ align:start position:0%
+spend the last 15 minutes at least uh
+ 
+
+ align:start position:0%
+spend the last 15 minutes at least uh
+talking about the evolution of sex
+
+ align:start position:0%
+talking about the evolution of sex
+ 
+
+ align:start position:0%
+talking about the evolution of sex
+because it is an interesting topic and
+
+ align:start position:0%
+because it is an interesting topic and
+ 
+
+ align:start position:0%
+because it is an interesting topic and
+and and I think the paper is kind of a
+
+ align:start position:0%
+and and I think the paper is kind of a
+ 
+
+ align:start position:0%
+and and I think the paper is kind of a
+nice disc uh discussion of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right so can somebody say why
+
+ align:start position:0%
+right all right so can somebody say why
+ 
+
+ align:start position:0%
+right all right so can somebody say why
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that this is a you know kind of a puzzle
+
+ align:start position:0%
+that this is a you know kind of a puzzle
+ 
+
+ align:start position:0%
+that this is a you know kind of a puzzle
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah almost all situations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imag that's right um all right so
+
+ align:start position:0%
+imag that's right um all right so
+ 
+
+ align:start position:0%
+imag that's right um all right so
+so right so sex is costly and in
+
+ align:start position:0%
+so right so sex is costly and in
+ 
+
+ align:start position:0%
+so right so sex is costly and in
+particular if you have this obligate
+
+ align:start position:0%
+particular if you have this obligate
+ 
+
+ align:start position:0%
+particular if you have this obligate
+biparental sex right then there's in
+
+ align:start position:0%
+biparental sex right then there's in
+ 
+
+ align:start position:0%
+biparental sex right then there's in
+particular there's the so-called uh
+
+ align:start position:0%
+particular there's the so-called uh
+ 
+
+ align:start position:0%
+particular there's the so-called uh
+two-fold cost uh two-fold cost of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+males because you can imagine comparing
+
+ align:start position:0%
+males because you can imagine comparing
+ 
+
+ align:start position:0%
+males because you can imagine comparing
+uh kind of these two populations right
+
+ align:start position:0%
+uh kind of these two populations right
+ 
+
+ align:start position:0%
+uh kind of these two populations right
+one of which has both males and females
+
+ align:start position:0%
+one of which has both males and females
+ 
+
+ align:start position:0%
+one of which has both males and females
+and one of them is just maybe either
+
+ align:start position:0%
+and one of them is just maybe either
+ 
+
+ align:start position:0%
+and one of them is just maybe either
+reproducing uh asexually or
+
+ align:start position:0%
+reproducing uh asexually or
+ 
+
+ align:start position:0%
+reproducing uh asexually or
+parthenogenic or hermitically or whatnot
+
+ align:start position:0%
+parthenogenic or hermitically or whatnot
+ 
+
+ align:start position:0%
+parthenogenic or hermitically or whatnot
+yeah okay um and you know so you know
+
+ align:start position:0%
+yeah okay um and you know so you know
+ 
+
+ align:start position:0%
+yeah okay um and you know so you know
+you just imagine well if you have a male
+
+ align:start position:0%
+you just imagine well if you have a male
+ 
+
+ align:start position:0%
+you just imagine well if you have a male
+and a female then on average if they
+
+ align:start position:0%
+and a female then on average if they
+ 
+
+ align:start position:0%
+and a female then on average if they
+have two kids you end up with another
+
+ align:start position:0%
+have two kids you end up with another
+ 
+
+ align:start position:0%
+have two kids you end up with another
+male and a female right and you know of
+
+ align:start position:0%
+male and a female right and you know of
+ 
+
+ align:start position:0%
+male and a female right and you know of
+course this can be many different males
+
+ align:start position:0%
+course this can be many different males
+ 
+
+ align:start position:0%
+course this can be many different males
+and females so you don't have to have
+
+ align:start position:0%
+and females so you don't have to have
+ 
+
+ align:start position:0%
+and females so you don't have to have
+any sibling anything right okay but if
+
+ align:start position:0%
+any sibling anything right okay but if
+ 
+
+ align:start position:0%
+any sibling anything right okay but if
+everybody is having two gener if if
+
+ align:start position:0%
+everybody is having two gener if if
+ 
+
+ align:start position:0%
+everybody is having two gener if if
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+generation each uh each female is giving
+
+ align:start position:0%
+generation each uh each female is giving
+ 
+
+ align:start position:0%
+generation each uh each female is giving
+birth to two um two progyny then you end
+
+ align:start position:0%
+birth to two um two progyny then you end
+ 
+
+ align:start position:0%
+birth to two um two progyny then you end
+up with a constant population size right
+
+ align:start position:0%
+up with a constant population size right
+ 
+
+ align:start position:0%
+up with a constant population size right
+whereas if you started out in a
+
+ align:start position:0%
+whereas if you started out in a
+ 
+
+ align:start position:0%
+whereas if you started out in a
+population with just two females and
+
+ align:start position:0%
+population with just two females and
+ 
+
+ align:start position:0%
+population with just two females and
+they were reproducing uh hermitically
+
+ align:start position:0%
+they were reproducing uh hermitically
+ 
+
+ align:start position:0%
+they were reproducing uh hermitically
+then you end up
+
+ align:start position:0%
+then you end up
+ 
+
+ align:start position:0%
+then you end up
+with you know whatever more okay eight
+
+ align:start position:0%
+with you know whatever more okay eight
+ 
+
+ align:start position:0%
+with you know whatever more okay eight
+okay so you can see that you get a
+
+ align:start position:0%
+okay so you can see that you get a
+ 
+
+ align:start position:0%
+okay so you can see that you get a
+factor of two in the rate of exponential
+
+ align:start position:0%
+factor of two in the rate of exponential
+ 
+
+ align:start position:0%
+factor of two in the rate of exponential
+growth of the population yeah I mean it
+
+ align:start position:0%
+growth of the population yeah I mean it
+ 
+
+ align:start position:0%
+growth of the population yeah I mean it
+seems to the
+
+ align:start position:0%
+seems to the
+ 
+
+ align:start position:0%
+seems to the
+question why
+
+ align:start position:0%
+question why
+ 
+
+ align:start position:0%
+question why
+Mal yeah yes yeah okay right so I think
+
+ align:start position:0%
+Mal yeah yes yeah okay right so I think
+ 
+
+ align:start position:0%
+Mal yeah yes yeah okay right so I think
+that uh right so this is the most
+
+ align:start position:0%
+that uh right so this is the most
+ 
+
+ align:start position:0%
+that uh right so this is the most
+extreme cost of sex right but then also
+
+ align:start position:0%
+extreme cost of sex right but then also
+ 
+
+ align:start position:0%
+extreme cost of sex right but then also
+you can you can think about even just
+
+ align:start position:0%
+you can you can think about even just
+ 
+
+ align:start position:0%
+you can you can think about even just
+hor Al Gene transfer among bacteria that
+
+ align:start position:0%
+hor Al Gene transfer among bacteria that
+ 
+
+ align:start position:0%
+hor Al Gene transfer among bacteria that
+it's a costly behavior in some way or
+
+ align:start position:0%
+it's a costly behavior in some way or
+ 
+
+ align:start position:0%
+it's a costly behavior in some way or
+another it's not as costly as this right
+
+ align:start position:0%
+another it's not as costly as this right
+ 
+
+ align:start position:0%
+another it's not as costly as this right
+but if you're going to think about U
+
+ align:start position:0%
+but if you're going to think about U
+ 
+
+ align:start position:0%
+but if you're going to think about U
+bacteria that uh that in their competent
+
+ align:start position:0%
+bacteria that uh that in their competent
+ 
+
+ align:start position:0%
+bacteria that uh that in their competent
+State when bodus kind of pulls in DNA
+
+ align:start position:0%
+State when bodus kind of pulls in DNA
+ 
+
+ align:start position:0%
+State when bodus kind of pulls in DNA
+you know it stops dividing and then it
+
+ align:start position:0%
+you know it stops dividing and then it
+ 
+
+ align:start position:0%
+you know it stops dividing and then it
+enters a state where it kind of reels
+
+ align:start position:0%
+enters a state where it kind of reels
+ 
+
+ align:start position:0%
+enters a state where it kind of reels
+things in and it can pick up um you know
+
+ align:start position:0%
+things in and it can pick up um you know
+ 
+
+ align:start position:0%
+things in and it can pick up um you know
+DNA that may be harmful in some cases
+
+ align:start position:0%
+DNA that may be harmful in some cases
+ 
+
+ align:start position:0%
+DNA that may be harmful in some cases
+right so there there are various costs
+
+ align:start position:0%
+right so there there are various costs
+ 
+
+ align:start position:0%
+right so there there are various costs
+that are uh for um for the you know if
+
+ align:start position:0%
+that are uh for um for the you know if
+ 
+
+ align:start position:0%
+that are uh for um for the you know if
+you want to call horizontal Gene
+
+ align:start position:0%
+you want to call horizontal Gene
+ 
+
+ align:start position:0%
+you want to call horizontal Gene
+transfer sex right but in in um um right
+
+ align:start position:0%
+transfer sex right but in in um um right
+ 
+
+ align:start position:0%
+transfer sex right but in in um um right
+so the key thing of sexual reproduction
+
+ align:start position:0%
+so the key thing of sexual reproduction
+ 
+
+ align:start position:0%
+so the key thing of sexual reproduction
+is it's it's somehow is um is the
+
+ align:start position:0%
+is it's it's somehow is um is the
+ 
+
+ align:start position:0%
+is it's it's somehow is um is the
+sharing of the of the DNA and I'd say
+
+ align:start position:0%
+sharing of the of the DNA and I'd say
+ 
+
+ align:start position:0%
+sharing of the of the DNA and I'd say
+that this can either be uh relatively
+
+ align:start position:0%
+that this can either be uh relatively
+ 
+
+ align:start position:0%
+that this can either be uh relatively
+low cost or relatively high cost but
+
+ align:start position:0%
+low cost or relatively high cost but
+ 
+
+ align:start position:0%
+low cost or relatively high cost but
+this is the most extreme version of it
+
+ align:start position:0%
+this is the most extreme version of it
+ 
+
+ align:start position:0%
+this is the most extreme version of it
+and I'd say um as you know as a species
+
+ align:start position:0%
+and I'd say um as you know as a species
+ 
+
+ align:start position:0%
+and I'd say um as you know as a species
+that reproduces sexually obl with
+
+ align:start position:0%
+that reproduces sexually obl with
+ 
+
+ align:start position:0%
+that reproduces sexually obl with
+obligate biparental sex then I'd say
+
+ align:start position:0%
+obligate biparental sex then I'd say
+ 
+
+ align:start position:0%
+obligate biparental sex then I'd say
+that and you know not only humans but Mo
+
+ align:start position:0%
+that and you know not only humans but Mo
+ 
+
+ align:start position:0%
+that and you know not only humans but Mo
+almost all uh you know animals uh have
+
+ align:start position:0%
+almost all uh you know animals uh have
+ 
+
+ align:start position:0%
+almost all uh you know animals uh have
+uh this form of reproduction it's it's I
+
+ align:start position:0%
+uh this form of reproduction it's it's I
+ 
+
+ align:start position:0%
+uh this form of reproduction it's it's I
+would say it's sort of surprising given
+
+ align:start position:0%
+would say it's sort of surprising given
+ 
+
+ align:start position:0%
+would say it's sort of surprising given
+that this is a huge
+
+ align:start position:0%
+that this is a huge
+ 
+
+ align:start position:0%
+that this is a huge
+cost right yeah so it's but it's not
+
+ align:start position:0%
+cost right yeah so it's but it's not
+ 
+
+ align:start position:0%
+cost right yeah so it's but it's not
+that all species that engage in any sort
+
+ align:start position:0%
+that all species that engage in any sort
+ 
+
+ align:start position:0%
+that all species that engage in any sort
+of uh Gene transfer H bear this large
+
+ align:start position:0%
+of uh Gene transfer H bear this large
+ 
+
+ align:start position:0%
+of uh Gene transfer H bear this large
+cost but they they bear more modest
+
+ align:start position:0%
+cost but they they bear more modest
+ 
+
+ align:start position:0%
+cost but they they bear more modest
+costs although yeah of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likees this by just like having multiple
+
+ align:start position:0%
+likees this by just like having multiple
+ 
+
+ align:start position:0%
+likees this by just like having multiple
+children per
+
+ align:start position:0%
+children per
+ 
+
+ align:start position:0%
+children per
+sex you're you're just saying that they
+
+ align:start position:0%
+sex you're you're just saying that they
+ 
+
+ align:start position:0%
+sex you're you're just saying that they
+can just have more kids um yeah yeah
+
+ align:start position:0%
+can just have more kids um yeah yeah
+ 
+
+ align:start position:0%
+can just have more kids um yeah yeah
+although I mean the basic statement is
+
+ align:start position:0%
+although I mean the basic statement is
+ 
+
+ align:start position:0%
+although I mean the basic statement is
+still true though let's say that the
+
+ align:start position:0%
+still true though let's say that the
+ 
+
+ align:start position:0%
+still true though let's say that the
+these females all have three three kids
+
+ align:start position:0%
+these females all have three three kids
+ 
+
+ align:start position:0%
+these females all have three three kids
+they get to grow exponentially but then
+
+ align:start position:0%
+they get to grow exponentially but then
+ 
+
+ align:start position:0%
+they get to grow exponentially but then
+these guys grow faster and ultimately
+
+ align:start position:0%
+these guys grow faster and ultimately
+ 
+
+ align:start position:0%
+these guys grow faster and ultimately
+there there's going to be competition
+
+ align:start position:0%
+there there's going to be competition
+ 
+
+ align:start position:0%
+there there's going to be competition
+for resources and these ones will still
+
+ align:start position:0%
+for resources and these ones will still
+ 
+
+ align:start position:0%
+for resources and these ones will still
+win yeah right so the question is if you
+
+ align:start position:0%
+win yeah right so the question is if you
+ 
+
+ align:start position:0%
+win yeah right so the question is if you
+you can imagine you have a population
+
+ align:start position:0%
+you can imagine you have a population
+ 
+
+ align:start position:0%
+you can imagine you have a population
+that's reproducing sexually if there one
+
+ align:start position:0%
+that's reproducing sexually if there one
+ 
+
+ align:start position:0%
+that's reproducing sexually if there one
+female has a mutation that leads her to
+
+ align:start position:0%
+female has a mutation that leads her to
+ 
+
+ align:start position:0%
+female has a mutation that leads her to
+start reproducing parthenogenic that
+
+ align:start position:0%
+start reproducing parthenogenic that
+ 
+
+ align:start position:0%
+start reproducing parthenogenic that
+mutation you'd expect should spread
+
+ align:start position:0%
+mutation you'd expect should spread
+ 
+
+ align:start position:0%
+mutation you'd expect should spread
+throughout the population very rapidly
+
+ align:start position:0%
+throughout the population very rapidly
+ 
+
+ align:start position:0%
+throughout the population very rapidly
+right and indeed there there there are
+
+ align:start position:0%
+right and indeed there there there are
+ 
+
+ align:start position:0%
+right and indeed there there there are
+these cases of for example sharks held
+
+ align:start position:0%
+these cases of for example sharks held
+ 
+
+ align:start position:0%
+these cases of for example sharks held
+in captivity where a female held in
+
+ align:start position:0%
+in captivity where a female held in
+ 
+
+ align:start position:0%
+in captivity where a female held in
+captivity for for years EV gives birth
+
+ align:start position:0%
+captivity for for years EV gives birth
+ 
+
+ align:start position:0%
+captivity for for years EV gives birth
+to to you know to daughters right so
+
+ align:start position:0%
+to to you know to daughters right so
+ 
+
+ align:start position:0%
+to to you know to daughters right so
+this this and um as far as you know it's
+
+ align:start position:0%
+this this and um as far as you know it's
+ 
+
+ align:start position:0%
+this this and um as far as you know it's
+so so this sort of Virgin birth is is
+
+ align:start position:0%
+so so this sort of Virgin birth is is
+ 
+
+ align:start position:0%
+so so this sort of Virgin birth is is
+possible I'm not aware okay well I'm not
+
+ align:start position:0%
+possible I'm not aware okay well I'm not
+ 
+
+ align:start position:0%
+possible I'm not aware okay well I'm not
+going to talk okay okay but um but yeah
+
+ align:start position:0%
+going to talk okay okay but um but yeah
+ 
+
+ align:start position:0%
+going to talk okay okay but um but yeah
+so but it in some animals it is at least
+
+ align:start position:0%
+so but it in some animals it is at least
+ 
+
+ align:start position:0%
+so but it in some animals it is at least
+possible I'll say okay all right okay so
+
+ align:start position:0%
+possible I'll say okay all right okay so
+ 
+
+ align:start position:0%
+possible I'll say okay all right okay so
+then you you have to ask well okay well
+
+ align:start position:0%
+then you you have to ask well okay well
+ 
+
+ align:start position:0%
+then you you have to ask well okay well
+what's um what kind of selected
+
+ align:start position:0%
+what's um what kind of selected
+ 
+
+ align:start position:0%
+what's um what kind of selected
+Advantage could sexual reproduction have
+
+ align:start position:0%
+Advantage could sexual reproduction have
+ 
+
+ align:start position:0%
+Advantage could sexual reproduction have
+that could possibly compensate for this
+
+ align:start position:0%
+that could possibly compensate for this
+ 
+
+ align:start position:0%
+that could possibly compensate for this
+so-called twofold cost of sex or
+
+ align:start position:0%
+so-called twofold cost of sex or
+ 
+
+ align:start position:0%
+so-called twofold cost of sex or
+two-fold cost of
+
+ align:start position:0%
+two-fold cost of
+ 
+
+ align:start position:0%
+two-fold cost of
+males
+
+ align:start position:0%
+males
+ 
+
+ align:start position:0%
+males
+okay and what what is the
+
+ align:start position:0%
+okay and what what is the
+ 
+
+ align:start position:0%
+okay and what what is the
+uh what is the argument that's made in
+
+ align:start position:0%
+uh what is the argument that's made in
+ 
+
+ align:start position:0%
+uh what is the argument that's made in
+this uh this
+
+ align:start position:0%
+this uh this
+ 
+
+ align:start position:0%
+this uh this
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paper anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes that's right right so this this
+
+ align:start position:0%
+yes that's right right so this this
+ 
+
+ align:start position:0%
+yes that's right right so this this
+recombination is favoring uh genetic
+
+ align:start position:0%
+recombination is favoring uh genetic
+ 
+
+ align:start position:0%
+recombination is favoring uh genetic
+diversity right so there are a number of
+
+ align:start position:0%
+diversity right so there are a number of
+ 
+
+ align:start position:0%
+diversity right so there are a number of
+different mechanisms um I say that the
+
+ align:start position:0%
+different mechanisms um I say that the
+ 
+
+ align:start position:0%
+different mechanisms um I say that the
+at the heart of it okay so this idea of
+
+ align:start position:0%
+at the heart of it okay so this idea of
+ 
+
+ align:start position:0%
+at the heart of it okay so this idea of
+the red the Red Queen hypothesis is um
+
+ align:start position:0%
+the red the Red Queen hypothesis is um
+ 
+
+ align:start position:0%
+the red the Red Queen hypothesis is um
+all right so let me see if I can find
+
+ align:start position:0%
+all right so let me see if I can find
+ 
+
+ align:start position:0%
+all right so let me see if I can find
+the actual quote for you guys U maybe
+
+ align:start position:0%
+the actual quote for you guys U maybe
+ 
+
+ align:start position:0%
+the actual quote for you guys U maybe
+not um so it's from a Lewis car novel
+
+ align:start position:0%
+not um so it's from a Lewis car novel
+ 
+
+ align:start position:0%
+not um so it's from a Lewis car novel
+Through the Looking Glass the quote was
+
+ align:start position:0%
+Through the Looking Glass the quote was
+ 
+
+ align:start position:0%
+Through the Looking Glass the quote was
+something you have to run is oh shoot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right never mind okay I can't
+
+ align:start position:0%
+um all right never mind okay I can't
+ 
+
+ align:start position:0%
+um all right never mind okay I can't
+remember what the quote was um but
+
+ align:start position:0%
+remember what the quote was um but
+ 
+
+ align:start position:0%
+remember what the quote was um but
+um the idea the idea is that sexual
+
+ align:start position:0%
+um the idea the idea is that sexual
+ 
+
+ align:start position:0%
+um the idea the idea is that sexual
+reproduction may allow a population to
+
+ align:start position:0%
+reproduction may allow a population to
+ 
+
+ align:start position:0%
+reproduction may allow a population to
+adapt against say changing environments
+
+ align:start position:0%
+adapt against say changing environments
+ 
+
+ align:start position:0%
+adapt against say changing environments
+more rapidly okay and and this has a
+
+ align:start position:0%
+more rapidly okay and and this has a
+ 
+
+ align:start position:0%
+more rapidly okay and and this has a
+couple of reasons because you generate
+
+ align:start position:0%
+couple of reasons because you generate
+ 
+
+ align:start position:0%
+couple of reasons because you generate
+genetic diversity um you you don't have
+
+ align:start position:0%
+genetic diversity um you you don't have
+ 
+
+ align:start position:0%
+genetic diversity um you you don't have
+the same clone interference kinds of
+
+ align:start position:0%
+the same clone interference kinds of
+ 
+
+ align:start position:0%
+the same clone interference kinds of
+effects that we talked about earlier all
+
+ align:start position:0%
+effects that we talked about earlier all
+ 
+
+ align:start position:0%
+effects that we talked about earlier all
+right so if you have asexual lineages
+
+ align:start position:0%
+right so if you have asexual lineages
+ 
+
+ align:start position:0%
+right so if you have asexual lineages
+then if you have two beneficial
+
+ align:start position:0%
+then if you have two beneficial
+ 
+
+ align:start position:0%
+then if you have two beneficial
+mutations they cannot both fix right so
+
+ align:start position:0%
+mutations they cannot both fix right so
+ 
+
+ align:start position:0%
+mutations they cannot both fix right so
+the more fit version is going to fix and
+
+ align:start position:0%
+the more fit version is going to fix and
+ 
+
+ align:start position:0%
+the more fit version is going to fix and
+then you have to wait for the next one
+
+ align:start position:0%
+then you have to wait for the next one
+ 
+
+ align:start position:0%
+then you have to wait for the next one
+right whereas in sexually reproducing
+
+ align:start position:0%
+right whereas in sexually reproducing
+ 
+
+ align:start position:0%
+right whereas in sexually reproducing
+populations the um those genes can
+
+ align:start position:0%
+populations the um those genes can
+ 
+
+ align:start position:0%
+populations the um those genes can
+spread throughout the population sort of
+
+ align:start position:0%
+spread throughout the population sort of
+ 
+
+ align:start position:0%
+spread throughout the population sort of
+as genes rather than being tied to a
+
+ align:start position:0%
+as genes rather than being tied to a
+ 
+
+ align:start position:0%
+as genes rather than being tied to a
+particular individual okay so that means
+
+ align:start position:0%
+particular individual okay so that means
+ 
+
+ align:start position:0%
+particular individual okay so that means
+that if you find yourself in a new
+
+ align:start position:0%
+that if you find yourself in a new
+ 
+
+ align:start position:0%
+that if you find yourself in a new
+environment it may be the case that
+
+ align:start position:0%
+environment it may be the case that
+ 
+
+ align:start position:0%
+environment it may be the case that
+sexual reproduction can allow for the
+
+ align:start position:0%
+sexual reproduction can allow for the
+ 
+
+ align:start position:0%
+sexual reproduction can allow for the
+population to adapt more rapidly but
+
+ align:start position:0%
+population to adapt more rapidly but
+ 
+
+ align:start position:0%
+population to adapt more rapidly but
+what's you know on one hand you might
+
+ align:start position:0%
+what's you know on one hand you might
+ 
+
+ align:start position:0%
+what's you know on one hand you might
+say well the environment's always
+
+ align:start position:0%
+say well the environment's always
+ 
+
+ align:start position:0%
+say well the environment's always
+changing so that can always favor the
+
+ align:start position:0%
+changing so that can always favor the
+ 
+
+ align:start position:0%
+changing so that can always favor the
+sexually reproducing populations but
+
+ align:start position:0%
+sexually reproducing populations but
+ 
+
+ align:start position:0%
+sexually reproducing populations but
+then there's a feeling out there that
+
+ align:start position:0%
+then there's a feeling out there that
+ 
+
+ align:start position:0%
+then there's a feeling out there that
+maybe that's not enough in the sense
+
+ align:start position:0%
+maybe that's not enough in the sense
+ 
+
+ align:start position:0%
+maybe that's not enough in the sense
+that the environment is not changing
+
+ align:start position:0%
+that the environment is not changing
+ 
+
+ align:start position:0%
+that the environment is not changing
+rapidly enough and dramatically enough
+
+ align:start position:0%
+rapidly enough and dramatically enough
+ 
+
+ align:start position:0%
+rapidly enough and dramatically enough
+to force uh the population to um
+
+ align:start position:0%
+to force uh the population to um
+ 
+
+ align:start position:0%
+to force uh the population to um
+reproduce sexually as compared to
+
+ align:start position:0%
+reproduce sexually as compared to
+ 
+
+ align:start position:0%
+reproduce sexually as compared to
+asexually right um and so the the the
+
+ align:start position:0%
+asexually right um and so the the the
+ 
+
+ align:start position:0%
+asexually right um and so the the the
+proposal from the Red Queen hypothesis
+
+ align:start position:0%
+proposal from the Red Queen hypothesis
+ 
+
+ align:start position:0%
+proposal from the Red Queen hypothesis
+is that the the the constantly changing
+
+ align:start position:0%
+is that the the the constantly changing
+ 
+
+ align:start position:0%
+is that the the the constantly changing
+environment is a result of co-evolution
+
+ align:start position:0%
+environment is a result of co-evolution
+ 
+
+ align:start position:0%
+environment is a result of co-evolution
+between host
+
+ align:start position:0%
+between host
+ 
+
+ align:start position:0%
+between host
+and they're parasites right because
+
+ align:start position:0%
+and they're parasites right because
+ 
+
+ align:start position:0%
+and they're parasites right because
+parasites are always trying to Target uh
+
+ align:start position:0%
+parasites are always trying to Target uh
+ 
+
+ align:start position:0%
+parasites are always trying to Target uh
+kind of common host genotypes because
+
+ align:start position:0%
+kind of common host genotypes because
+ 
+
+ align:start position:0%
+kind of common host genotypes because
+that they can spread on those right so
+
+ align:start position:0%
+that they can spread on those right so
+ 
+
+ align:start position:0%
+that they can spread on those right so
+they're always the parasites are
+
+ align:start position:0%
+they're always the parasites are
+ 
+
+ align:start position:0%
+they're always the parasites are
+evolving but then the host is sort of
+
+ align:start position:0%
+evolving but then the host is sort of
+ 
+
+ align:start position:0%
+evolving but then the host is sort of
+being host population or genotypes are
+
+ align:start position:0%
+being host population or genotypes are
+ 
+
+ align:start position:0%
+being host population or genotypes are
+kind of being chased Away by those
+
+ align:start position:0%
+kind of being chased Away by those
+ 
+
+ align:start position:0%
+kind of being chased Away by those
+parasites that are targeting them right
+
+ align:start position:0%
+parasites that are targeting them right
+ 
+
+ align:start position:0%
+parasites that are targeting them right
+so the the notion is that parasites as a
+
+ align:start position:0%
+so the the notion is that parasites as a
+ 
+
+ align:start position:0%
+so the the notion is that parasites as a
+result of this coevolution can be the
+
+ align:start position:0%
+result of this coevolution can be the
+ 
+
+ align:start position:0%
+result of this coevolution can be the
+source for the constantly changing
+
+ align:start position:0%
+source for the constantly changing
+ 
+
+ align:start position:0%
+source for the constantly changing
+environment that may be driving U the
+
+ align:start position:0%
+environment that may be driving U the
+ 
+
+ align:start position:0%
+environment that may be driving U the
+evolution of sex yeah
+
+ align:start position:0%
+evolution of sex yeah
+ 
+
+ align:start position:0%
+evolution of sex yeah
+question I would isia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right yes right so so the question is
+
+ align:start position:0%
+right yes right so so the question is
+ 
+
+ align:start position:0%
+right yes right so so the question is
+why you know
+
+ align:start position:0%
+why you know
+ 
+
+ align:start position:0%
+why you know
+if yeah right um okay so I can give you
+
+ align:start position:0%
+if yeah right um okay so I can give you
+ 
+
+ align:start position:0%
+if yeah right um okay so I can give you
+my best guess on this all right first of
+
+ align:start position:0%
+my best guess on this all right first of
+ 
+
+ align:start position:0%
+my best guess on this all right first of
+all I saying not everybody agrees that
+
+ align:start position:0%
+all I saying not everybody agrees that
+ 
+
+ align:start position:0%
+all I saying not everybody agrees that
+that the Red Queen kind of hypothesis is
+
+ align:start position:0%
+that the Red Queen kind of hypothesis is
+ 
+
+ align:start position:0%
+that the Red Queen kind of hypothesis is
+the sort of true explanation if a true
+
+ align:start position:0%
+the sort of true explanation if a true
+ 
+
+ align:start position:0%
+the sort of true explanation if a true
+explanation even exists right um but
+
+ align:start position:0%
+explanation even exists right um but
+ 
+
+ align:start position:0%
+explanation even exists right um but
+within this framework uh you you you
+
+ align:start position:0%
+within this framework uh you you you
+ 
+
+ align:start position:0%
+within this framework uh you you you
+definitely want to try to explain why it
+
+ align:start position:0%
+definitely want to try to explain why it
+ 
+
+ align:start position:0%
+definitely want to try to explain why it
+is that uh kind of large life forms seem
+
+ align:start position:0%
+is that uh kind of large life forms seem
+ 
+
+ align:start position:0%
+is that uh kind of large life forms seem
+to have a lot of obligate sexual
+
+ align:start position:0%
+to have a lot of obligate sexual
+ 
+
+ align:start position:0%
+to have a lot of obligate sexual
+reproduction right because this is a
+
+ align:start position:0%
+reproduction right because this is a
+ 
+
+ align:start position:0%
+reproduction right because this is a
+very strong pattern that you see right
+
+ align:start position:0%
+very strong pattern that you see right
+ 
+
+ align:start position:0%
+very strong pattern that you see right
+uh and I guess what I would say is that
+
+ align:start position:0%
+uh and I guess what I would say is that
+ 
+
+ align:start position:0%
+uh and I guess what I would say is that
+there's certainly a correlation between
+
+ align:start position:0%
+there's certainly a correlation between
+ 
+
+ align:start position:0%
+there's certainly a correlation between
+size uh physical size and um and
+
+ align:start position:0%
+size uh physical size and um and
+ 
+
+ align:start position:0%
+size uh physical size and um and
+generation time right and that
+
+ align:start position:0%
+generation time right and that
+ 
+
+ align:start position:0%
+generation time right and that
+generation time tells you about
+
+ align:start position:0%
+generation time tells you about
+ 
+
+ align:start position:0%
+generation time tells you about
+something about the typical time scales
+
+ align:start position:0%
+something about the typical time scales
+ 
+
+ align:start position:0%
+something about the typical time scales
+over which you can evolve right so my
+
+ align:start position:0%
+over which you can evolve right so my
+ 
+
+ align:start position:0%
+over which you can evolve right so my
+sense of this is it just maybe that uh
+
+ align:start position:0%
+sense of this is it just maybe that uh
+ 
+
+ align:start position:0%
+sense of this is it just maybe that uh
+that animals you know in general you
+
+ align:start position:0%
+that animals you know in general you
+ 
+
+ align:start position:0%
+that animals you know in general you
+know large animals they by their nature
+
+ align:start position:0%
+know large animals they by their nature
+ 
+
+ align:start position:0%
+know large animals they by their nature
+will evolve rather slowly as compared to
+
+ align:start position:0%
+will evolve rather slowly as compared to
+ 
+
+ align:start position:0%
+will evolve rather slowly as compared to
+their their parasites and so that means
+
+ align:start position:0%
+their their parasites and so that means
+ 
+
+ align:start position:0%
+their their parasites and so that means
+that they are kind of the populations
+
+ align:start position:0%
+that they are kind of the populations
+ 
+
+ align:start position:0%
+that they are kind of the populations
+that are most in need of evolving um of
+
+ align:start position:0%
+that are most in need of evolving um of
+ 
+
+ align:start position:0%
+that are most in need of evolving um of
+of speeding up their
+
+ align:start position:0%
+of speeding up their
+ 
+
+ align:start position:0%
+of speeding up their
+evolution um and it's hard to know how
+
+ align:start position:0%
+evolution um and it's hard to know how
+ 
+
+ align:start position:0%
+evolution um and it's hard to know how
+convincing that argument should be but
+
+ align:start position:0%
+convincing that argument should be but
+ 
+
+ align:start position:0%
+convincing that argument should be but
+yeah yes what's the what's the
+
+ align:start position:0%
+yeah yes what's the what's the
+ 
+
+ align:start position:0%
+yeah yes what's the what's the
+difference in in
+
+ align:start position:0%
+difference in in
+ 
+
+ align:start position:0%
+difference in in
+reproductive time between
+
+ align:start position:0%
+reproductive time between
+ 
+
+ align:start position:0%
+reproductive time between
+bacteria yeah right uh okay so yeah so
+
+ align:start position:0%
+bacteria yeah right uh okay so yeah so
+ 
+
+ align:start position:0%
+bacteria yeah right uh okay so yeah so
+bacteria can well as we were discuss as
+
+ align:start position:0%
+bacteria can well as we were discuss as
+ 
+
+ align:start position:0%
+bacteria can well as we were discuss as
+we've discussed uh division times are
+
+ align:start position:0%
+we've discussed uh division times are
+ 
+
+ align:start position:0%
+we've discussed uh division times are
+kind of order hour and Fage uh I think
+
+ align:start position:0%
+kind of order hour and Fage uh I think
+ 
+
+ align:start position:0%
+kind of order hour and Fage uh I think
+yeah so when you get a Fage
+
+ align:start position:0%
+yeah so when you get a Fage
+ 
+
+ align:start position:0%
+yeah so when you get a Fage
+infection uh so what happens is the Fage
+
+ align:start position:0%
+infection uh so what happens is the Fage
+ 
+
+ align:start position:0%
+infection uh so what happens is the Fage
+you can infect as a single Fage and then
+
+ align:start position:0%
+you can infect as a single Fage and then
+ 
+
+ align:start position:0%
+you can infect as a single Fage and then
+uh they will generate uh burst they
+
+ align:start position:0%
+uh they will generate uh burst they
+ 
+
+ align:start position:0%
+uh they will generate uh burst they
+they'll kind of divide within the
+
+ align:start position:0%
+they'll kind of divide within the
+ 
+
+ align:start position:0%
+they'll kind of divide within the
+bacterial bacterial cell and then burst
+
+ align:start position:0%
+bacterial bacterial cell and then burst
+ 
+
+ align:start position:0%
+bacterial bacterial cell and then burst
+out as a population of um you know 100
+
+ align:start position:0%
+out as a population of um you know 100
+ 
+
+ align:start position:0%
+out as a population of um you know 100
+200 kind of tle F and I think that that
+
+ align:start position:0%
+200 kind of tle F and I think that that
+ 
+
+ align:start position:0%
+200 kind of tle F and I think that that
+that might take you know four five hours
+
+ align:start position:0%
+that might take you know four five hours
+ 
+
+ align:start position:0%
+that might take you know four five hours
+is kind of my sense right so it's I'd
+
+ align:start position:0%
+is kind of my sense right so it's I'd
+ 
+
+ align:start position:0%
+is kind of my sense right so it's I'd
+say that um and then and then they go
+
+ align:start position:0%
+say that um and then and then they go
+ 
+
+ align:start position:0%
+say that um and then and then they go
+off and they find they find new bacteria
+
+ align:start position:0%
+off and they find they find new bacteria
+ 
+
+ align:start position:0%
+off and they find they find new bacteria
+so in that sense they they may have yeah
+
+ align:start position:0%
+so in that sense they they may have yeah
+ 
+
+ align:start position:0%
+so in that sense they they may have yeah
+so it's it's a little bit faster than
+
+ align:start position:0%
+so it's it's a little bit faster than
+ 
+
+ align:start position:0%
+so it's it's a little bit faster than
+the bacteria I'd say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay right so what um Can somebody
+
+ align:start position:0%
+yeah okay right so what um Can somebody
+ 
+
+ align:start position:0%
+yeah okay right so what um Can somebody
+say what the core experiment was that
+
+ align:start position:0%
+say what the core experiment was that
+ 
+
+ align:start position:0%
+say what the core experiment was that
+they did in in this experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right so there there going to be
+
+ align:start position:0%
+that's right so there there going to be
+ 
+
+ align:start position:0%
+that's right so there there going to be
+um so this worm seagon it's sort of a
+
+ align:start position:0%
+um so this worm seagon it's sort of a
+ 
+
+ align:start position:0%
+um so this worm seagon it's sort of a
+millimeter in size right and they're
+
+ align:start position:0%
+millimeter in size right and they're
+ 
+
+ align:start position:0%
+millimeter in size right and they're
+going to be three different conditions
+
+ align:start position:0%
+going to be three different conditions
+ 
+
+ align:start position:0%
+going to be three different conditions
+one is there there's kind of the um the
+
+ align:start position:0%
+one is there there's kind of the um the
+ 
+
+ align:start position:0%
+one is there there's kind of the um the
+while type that can uh can outcross can
+
+ align:start position:0%
+while type that can uh can outcross can
+ 
+
+ align:start position:0%
+while type that can uh can outcross can
+can have males mate some that are then
+
+ align:start position:0%
+can have males mate some that are then
+ 
+
+ align:start position:0%
+can have males mate some that are then
+there's the
+
+ align:start position:0%
+there's the
+ 
+
+ align:start position:0%
+there's the
+obligate outcrossing which means there's
+
+ align:start position:0%
+obligate outcrossing which means there's
+ 
+
+ align:start position:0%
+obligate outcrossing which means there's
+they they're going to be it's they have
+
+ align:start position:0%
+they they're going to be it's they have
+ 
+
+ align:start position:0%
+they they're going to be it's they have
+to mate with males and then there's the
+
+ align:start position:0%
+to mate with males and then there's the
+ 
+
+ align:start position:0%
+to mate with males and then there's the
+uh the obligate um what do they call it
+
+ align:start position:0%
+uh the obligate um what do they call it
+ 
+
+ align:start position:0%
+uh the obligate um what do they call it
+not not obligate selfing obligate
+
+ align:start position:0%
+not not obligate selfing obligate
+ 
+
+ align:start position:0%
+not not obligate selfing obligate
+selfing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then what do they do with those
+
+ align:start position:0%
+okay and then what do they do with those
+ 
+
+ align:start position:0%
+okay and then what do they do with those
+worms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right so then there's a bacterial
+
+ align:start position:0%
+that's right so then there's a bacterial
+ 
+
+ align:start position:0%
+that's right so then there's a bacterial
+pathogen Sera morassin that um and
+
+ align:start position:0%
+pathogen Sera morassin that um and
+ 
+
+ align:start position:0%
+pathogen Sera morassin that um and
+they're going to have these three
+
+ align:start position:0%
+they're going to have these three
+ 
+
+ align:start position:0%
+they're going to have these three
+different conditions right where they're
+
+ align:start position:0%
+different conditions right where they're
+ 
+
+ align:start position:0%
+different conditions right where they're
+going to uh for the for the SM the
+
+ align:start position:0%
+going to uh for the for the SM the
+ 
+
+ align:start position:0%
+going to uh for the for the SM the
+bacteria they're either going to have uh
+
+ align:start position:0%
+bacteria they're either going to have uh
+ 
+
+ align:start position:0%
+bacteria they're either going to have uh
+they're going to allow for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+co-evolution uh where they take the
+
+ align:start position:0%
+co-evolution uh where they take the
+ 
+
+ align:start position:0%
+co-evolution uh where they take the
+bacteria from each of the infections and
+
+ align:start position:0%
+bacteria from each of the infections and
+ 
+
+ align:start position:0%
+bacteria from each of the infections and
+prop
+
+ align:start position:0%
+prop
+ 
+
+ align:start position:0%
+prop
+or they're going to do kind of the the
+
+ align:start position:0%
+or they're going to do kind of the the
+ 
+
+ align:start position:0%
+or they're going to do kind of the the
+no Evolution where you just compete
+
+ align:start position:0%
+no Evolution where you just compete
+ 
+
+ align:start position:0%
+no Evolution where you just compete
+against the the ancestor right and
+
+ align:start position:0%
+against the the ancestor right and
+ 
+
+ align:start position:0%
+against the the ancestor right and
+there's also control okay so there's
+
+ align:start position:0%
+there's also control okay so there's
+ 
+
+ align:start position:0%
+there's also control okay so there's
+coevolution there's kind of this no
+
+ align:start position:0%
+coevolution there's kind of this no
+ 
+
+ align:start position:0%
+coevolution there's kind of this no
+evolution of the of the bacteria and
+
+ align:start position:0%
+evolution of the of the bacteria and
+ 
+
+ align:start position:0%
+evolution of the of the bacteria and
+then there's also control where there's
+
+ align:start position:0%
+then there's also control where there's
+ 
+
+ align:start position:0%
+then there's also control where there's
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacteria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and what was the most striking
+
+ align:start position:0%
+right and what was the most striking
+ 
+
+ align:start position:0%
+right and what was the most striking
+thing that they saw in this experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess that's right right so if you
+
+ align:start position:0%
+guess that's right right so if you
+ 
+
+ align:start position:0%
+guess that's right right so if you
+allowed the bacteria to to be evolving
+
+ align:start position:0%
+allowed the bacteria to to be evolving
+ 
+
+ align:start position:0%
+allowed the bacteria to to be evolving
+against this obligately selfing
+
+ align:start position:0%
+against this obligately selfing
+ 
+
+ align:start position:0%
+against this obligately selfing
+population this this
+
+ align:start position:0%
+population this this
+ 
+
+ align:start position:0%
+population this this
+killed uh this killed the worms
+
+ align:start position:0%
+killed uh this killed the worms
+ 
+
+ align:start position:0%
+killed uh this killed the worms
+right and what was the other thing that
+
+ align:start position:0%
+right and what was the other thing that
+ 
+
+ align:start position:0%
+right and what was the other thing that
+was maybe very striking about their
+
+ align:start position:0%
+was maybe very striking about their
+ 
+
+ align:start position:0%
+was maybe very striking about their
+experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so this was this was kind of
+
+ align:start position:0%
+yeah yeah so this was this was kind of
+ 
+
+ align:start position:0%
+yeah yeah so this was this was kind of
+amazing right so they saw as a function
+
+ align:start position:0%
+amazing right so they saw as a function
+ 
+
+ align:start position:0%
+amazing right so they saw as a function
+of time if you look at outc
+
+ align:start position:0%
+of time if you look at outc
+ 
+
+ align:start position:0%
+of time if you look at outc
+Crossing so kind of the rate of mating
+
+ align:start position:0%
+Crossing so kind of the rate of mating
+ 
+
+ align:start position:0%
+Crossing so kind of the rate of mating
+with the males this started out at kind
+
+ align:start position:0%
+with the males this started out at kind
+ 
+
+ align:start position:0%
+with the males this started out at kind
+of like 0
+
+ align:start position:0%
+of like 0
+ 
+
+ align:start position:0%
+of like 0
+2 U and then in the presence of the
+
+ align:start position:0%
+2 U and then in the presence of the
+ 
+
+ align:start position:0%
+2 U and then in the presence of the
+co-evolution it kind of went up and it
+
+ align:start position:0%
+co-evolution it kind of went up and it
+ 
+
+ align:start position:0%
+co-evolution it kind of went up and it
+goes up to 80 you know maybe 80%
+
+ align:start position:0%
+goes up to 80 you know maybe 80%
+ 
+
+ align:start position:0%
+goes up to 80 you know maybe 80%
+okay and for Co Evolution it stayed up
+
+ align:start position:0%
+okay and for Co Evolution it stayed up
+ 
+
+ align:start position:0%
+okay and for Co Evolution it stayed up
+high whereas if the wild
+
+ align:start position:0%
+high whereas if the wild
+ 
+
+ align:start position:0%
+high whereas if the wild
+type uh if the wild type worms if they
+
+ align:start position:0%
+type uh if the wild type worms if they
+ 
+
+ align:start position:0%
+type uh if the wild type worms if they
+continued to be just challenged by The
+
+ align:start position:0%
+continued to be just challenged by The
+ 
+
+ align:start position:0%
+continued to be just challenged by The
+ancestral
+
+ align:start position:0%
+ancestral
+ 
+
+ align:start position:0%
+ancestral
+bacteria it initially came up but then
+
+ align:start position:0%
+bacteria it initially came up but then
+ 
+
+ align:start position:0%
+bacteria it initially came up but then
+it came back down so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+co-evolution and this is um this is the
+
+ align:start position:0%
+co-evolution and this is um this is the
+ 
+
+ align:start position:0%
+co-evolution and this is um this is the
+ancestral uh the ancestral uh
+
+ align:start position:0%
+ancestral uh the ancestral uh
+ 
+
+ align:start position:0%
+ancestral uh the ancestral uh
+SM right so that there was a sense that
+
+ align:start position:0%
+SM right so that there was a sense that
+ 
+
+ align:start position:0%
+SM right so that there was a sense that
+that wild type population and initially
+
+ align:start position:0%
+that wild type population and initially
+ 
+
+ align:start position:0%
+that wild type population and initially
+out it evolved to outcross more but then
+
+ align:start position:0%
+out it evolved to outcross more but then
+ 
+
+ align:start position:0%
+out it evolved to outcross more but then
+once it had solved this problem of how
+
+ align:start position:0%
+once it had solved this problem of how
+ 
+
+ align:start position:0%
+once it had solved this problem of how
+to handle the ancestral sertia the
+
+ align:start position:0%
+to handle the ancestral sertia the
+ 
+
+ align:start position:0%
+to handle the ancestral sertia the
+outcrossing rate went back down right um
+
+ align:start position:0%
+outcrossing rate went back down right um
+ 
+
+ align:start position:0%
+outcrossing rate went back down right um
+so we we are um pretty much out of time
+
+ align:start position:0%
+so we we are um pretty much out of time
+ 
+
+ align:start position:0%
+so we we are um pretty much out of time
+but I do want to I don't know if you
+
+ align:start position:0%
+but I do want to I don't know if you
+ 
+
+ align:start position:0%
+but I do want to I don't know if you
+guys noticed the last sentence of the
+
+ align:start position:0%
+guys noticed the last sentence of the
+ 
+
+ align:start position:0%
+guys noticed the last sentence of the
+paper it is amazing that they got this
+
+ align:start position:0%
+paper it is amazing that they got this
+ 
+
+ align:start position:0%
+paper it is amazing that they got this
+through um through the publication
+
+ align:start position:0%
+through um through the publication
+ 
+
+ align:start position:0%
+through um through the publication
+process right
+
+ align:start position:0%
+process right
+ 
+
+ align:start position:0%
+process right
+um all right so you know so they say
+
+ align:start position:0%
+um all right so you know so they say
+ 
+
+ align:start position:0%
+um all right so you know so they say
+taken together the results demonstrate
+
+ align:start position:0%
+taken together the results demonstrate
+ 
+
+ align:start position:0%
+taken together the results demonstrate
+that sex can facilitate adaptation to
+
+ align:start position:0%
+that sex can facilitate adaptation to
+ 
+
+ align:start position:0%
+that sex can facilitate adaptation to
+novel envir ments but the long-term
+
+ align:start position:0%
+novel envir ments but the long-term
+ 
+
+ align:start position:0%
+novel envir ments but the long-term
+maintenance of sex requires that the
+
+ align:start position:0%
+maintenance of sex requires that the
+ 
+
+ align:start position:0%
+maintenance of sex requires that the
+novelty does not wear
+
+ align:start position:0%
+novelty does not wear
+ 
+
+ align:start position:0%
+novelty does not wear
+off I you know it's one it's one of
+
+ align:start position:0%
+off I you know it's one it's one of
+ 
+
+ align:start position:0%
+off I you know it's one it's one of
+those things that you read and you you
+
+ align:start position:0%
+those things that you read and you you
+ 
+
+ align:start position:0%
+those things that you read and you you
+you you you think okay so I will leave I
+
+ align:start position:0%
+you you you think okay so I will leave I
+ 
+
+ align:start position:0%
+you you you think okay so I will leave I
+will leave that sentence with you and
+
+ align:start position:0%
+will leave that sentence with you and
+ 
+
+ align:start position:0%
+will leave that sentence with you and
+then um we'll uh we'll uh meet on
+
+ align:start position:0%
+then um we'll uh we'll uh meet on
+ 
+
+ align:start position:0%
+then um we'll uh we'll uh meet on
+Tuesday okay
\ No newline at end of file
diff --git a/E7oR_JBgUzA.txt b/E7oR_JBgUzA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..860ab0fdea89d99aed0a8fb84bfd35ff688e0253
--- /dev/null
+++ b/E7oR_JBgUzA.txt
@@ -0,0 +1,3587 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I'd like us to do two things the first
+
+ align:start position:0%
+I'd like us to do two things the first
+ 
+
+ align:start position:0%
+I'd like us to do two things the first
+thing we're going to do is we're going
+
+ align:start position:0%
+thing we're going to do is we're going
+ 
+
+ align:start position:0%
+thing we're going to do is we're going
+to graph the curve r equal 1 plus cosine
+
+ align:start position:0%
+to graph the curve r equal 1 plus cosine
+ 
+
+ align:start position:0%
+to graph the curve r equal 1 plus cosine
+Theta over 2 for Theta between 0 and 4
+
+ align:start position:0%
+Theta over 2 for Theta between 0 and 4
+ 
+
+ align:start position:0%
+Theta over 2 for Theta between 0 and 4
+pi and we're going to graph it in the XY
+
+ align:start position:0%
+pi and we're going to graph it in the XY
+ 
+
+ align:start position:0%
+pi and we're going to graph it in the XY
+plane and then after we've done that
+
+ align:start position:0%
+plane and then after we've done that
+ 
+
+ align:start position:0%
+plane and then after we've done that
+we're going to take a look at some some
+
+ align:start position:0%
+we're going to take a look at some some
+ 
+
+ align:start position:0%
+we're going to take a look at some some
+components of that curve and we're going
+
+ align:start position:0%
+components of that curve and we're going
+ 
+
+ align:start position:0%
+components of that curve and we're going
+to calculate the area of some some
+
+ align:start position:0%
+to calculate the area of some some
+ 
+
+ align:start position:0%
+to calculate the area of some some
+components that close up so what I'd
+
+ align:start position:0%
+components that close up so what I'd
+ 
+
+ align:start position:0%
+components that close up so what I'd
+like you to do first is get a good
+
+ align:start position:0%
+like you to do first is get a good
+ 
+
+ align:start position:0%
+like you to do first is get a good
+picture of this curve uh in the XY plane
+
+ align:start position:0%
+picture of this curve uh in the XY plane
+ 
+
+ align:start position:0%
+picture of this curve uh in the XY plane
+I'll give you a little while to do that
+
+ align:start position:0%
+I'll give you a little while to do that
+ 
+
+ align:start position:0%
+I'll give you a little while to do that
+so why don't you pause the video get a
+
+ align:start position:0%
+so why don't you pause the video get a
+ 
+
+ align:start position:0%
+so why don't you pause the video get a
+good picture of that curve then come
+
+ align:start position:0%
+good picture of that curve then come
+ 
+
+ align:start position:0%
+good picture of that curve then come
+back when you're ready and I'll show you
+
+ align:start position:0%
+back when you're ready and I'll show you
+ 
+
+ align:start position:0%
+back when you're ready and I'll show you
+how I graph it and then we'll get into
+
+ align:start position:0%
+how I graph it and then we'll get into
+ 
+
+ align:start position:0%
+how I graph it and then we'll get into
+these area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems okay welcome back so the goal
+
+ align:start position:0%
+problems okay welcome back so the goal
+ 
+
+ align:start position:0%
+problems okay welcome back so the goal
+again was to graph a certain curve
+
+ align:start position:0%
+again was to graph a certain curve
+ 
+
+ align:start position:0%
+again was to graph a certain curve
+described by R and Theta but in the XY
+
+ align:start position:0%
+described by R and Theta but in the XY
+ 
+
+ align:start position:0%
+described by R and Theta but in the XY
+plane and for Theta between zero and pi
+
+ align:start position:0%
+plane and for Theta between zero and pi
+ 
+
+ align:start position:0%
+plane and for Theta between zero and pi
+over4 and when I do these problems we uh
+
+ align:start position:0%
+over4 and when I do these problems we uh
+ 
+
+ align:start position:0%
+over4 and when I do these problems we uh
+we want to we want to make sure that we
+
+ align:start position:0%
+we want to we want to make sure that we
+ 
+
+ align:start position:0%
+we want to we want to make sure that we
+understand how R depends on Theta that's
+
+ align:start position:0%
+understand how R depends on Theta that's
+ 
+
+ align:start position:0%
+understand how R depends on Theta that's
+sort of the main goal to graph this
+
+ align:start position:0%
+sort of the main goal to graph this
+ 
+
+ align:start position:0%
+sort of the main goal to graph this
+curve so what I do actually is I look at
+
+ align:start position:0%
+curve so what I do actually is I look at
+ 
+
+ align:start position:0%
+curve so what I do actually is I look at
+this not in the XY plane which was what
+
+ align:start position:0%
+this not in the XY plane which was what
+ 
+
+ align:start position:0%
+this not in the XY plane which was what
+I said to do in the problem but I first
+
+ align:start position:0%
+I said to do in the problem but I first
+ 
+
+ align:start position:0%
+I said to do in the problem but I first
+look at it and what we see as the r
+
+ align:start position:0%
+look at it and what we see as the r
+ 
+
+ align:start position:0%
+look at it and what we see as the r
+Theta plane and what we mean by that is
+
+ align:start position:0%
+Theta plane and what we mean by that is
+ 
+
+ align:start position:0%
+Theta plane and what we mean by that is
+we're going to graph this just like we
+
+ align:start position:0%
+we're going to graph this just like we
+ 
+
+ align:start position:0%
+we're going to graph this just like we
+would if these this variable was X and
+
+ align:start position:0%
+would if these this variable was X and
+ 
+
+ align:start position:0%
+would if these this variable was X and
+this variable was y so we move out of
+
+ align:start position:0%
+this variable was y so we move out of
+ 
+
+ align:start position:0%
+this variable was y so we move out of
+move out of the what we know about how R
+
+ align:start position:0%
+move out of the what we know about how R
+ 
+
+ align:start position:0%
+move out of the what we know about how R
+relates to X and Y and how Theta relates
+
+ align:start position:0%
+relates to X and Y and how Theta relates
+ 
+
+ align:start position:0%
+relates to X and Y and how Theta relates
+to X and Y and we just look at how R
+
+ align:start position:0%
+to X and Y and we just look at how R
+ 
+
+ align:start position:0%
+to X and Y and we just look at how R
+relates to Theta so let me draw that
+
+ align:start position:0%
+relates to Theta so let me draw that
+ 
+
+ align:start position:0%
+relates to Theta so let me draw that
+first and we'll see if we can sort of
+
+ align:start position:0%
+first and we'll see if we can sort of
+ 
+
+ align:start position:0%
+first and we'll see if we can sort of
+understand what I mean by that and then
+
+ align:start position:0%
+understand what I mean by that and then
+ 
+
+ align:start position:0%
+understand what I mean by that and then
+we'll put that picture use those use
+
+ align:start position:0%
+we'll put that picture use those use
+ 
+
+ align:start position:0%
+we'll put that picture use those use
+that curve to put that into the XY plane
+
+ align:start position:0%
+that curve to put that into the XY plane
+ 
+
+ align:start position:0%
+that curve to put that into the XY plane
+okay so the first thing we
+
+ align:start position:0%
+okay so the first thing we
+ 
+
+ align:start position:0%
+okay so the first thing we
+do is I'm going to let this be the Theta
+
+ align:start position:0%
+do is I'm going to let this be the Theta
+ 
+
+ align:start position:0%
+do is I'm going to let this be the Theta
+axis and this be the r AIS and let's
+
+ align:start position:0%
+axis and this be the r AIS and let's
+ 
+
+ align:start position:0%
+axis and this be the r AIS and let's
+look at I want to write down over here
+
+ align:start position:0%
+look at I want to write down over here
+ 
+
+ align:start position:0%
+look at I want to write down over here
+what the uh what the equation is so I
+
+ align:start position:0%
+what the uh what the equation is so I
+ 
+
+ align:start position:0%
+what the uh what the equation is so I
+don't have to keep turning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around so again this is not I don't want
+
+ align:start position:0%
+around so again this is not I don't want
+ 
+
+ align:start position:0%
+around so again this is not I don't want
+to think about this as the XY plane
+
+ align:start position:0%
+to think about this as the XY plane
+ 
+
+ align:start position:0%
+to think about this as the XY plane
+because in the XY plane Theta has
+
+ align:start position:0%
+because in the XY plane Theta has
+ 
+
+ align:start position:0%
+because in the XY plane Theta has
+certain values at each point that are
+
+ align:start position:0%
+certain values at each point that are
+ 
+
+ align:start position:0%
+certain values at each point that are
+that are fixed based on the angle but
+
+ align:start position:0%
+that are fixed based on the angle but
+ 
+
+ align:start position:0%
+that are fixed based on the angle but
+now I'm letting Theta vary in this
+
+ align:start position:0%
+now I'm letting Theta vary in this
+ 
+
+ align:start position:0%
+now I'm letting Theta vary in this
+direction and R is varying in this
+
+ align:start position:0%
+direction and R is varying in this
+ 
+
+ align:start position:0%
+direction and R is varying in this
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and my Theta I said was between 0 and pi
+
+ align:start position:0%
+and my Theta I said was between 0 and pi
+ 
+
+ align:start position:0%
+and my Theta I said was between 0 and pi
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+4 sorry not pi over 4 4 Pi zero and four
+
+ align:start position:0%
+4 sorry not pi over 4 4 Pi zero and four
+ 
+
+ align:start position:0%
+4 sorry not pi over 4 4 Pi zero and four
+Pi Pi four would be a very small
+
+ align:start position:0%
+Pi Pi four would be a very small
+ 
+
+ align:start position:0%
+Pi Pi four would be a very small
+component of this that I'm interested in
+
+ align:start position:0%
+component of this that I'm interested in
+ 
+
+ align:start position:0%
+component of this that I'm interested in
+and let's think about what what happens
+
+ align:start position:0%
+and let's think about what what happens
+ 
+
+ align:start position:0%
+and let's think about what what happens
+what kind of Transformations have been
+
+ align:start position:0%
+what kind of Transformations have been
+ 
+
+ align:start position:0%
+what kind of Transformations have been
+done to the normal cosine function so if
+
+ align:start position:0%
+done to the normal cosine function so if
+ 
+
+ align:start position:0%
+done to the normal cosine function so if
+I took the normal cosine function and I
+
+ align:start position:0%
+I took the normal cosine function and I
+ 
+
+ align:start position:0%
+I took the normal cosine function and I
+and I take it instead of cosine Theta I
+
+ align:start position:0%
+and I take it instead of cosine Theta I
+ 
+
+ align:start position:0%
+and I take it instead of cosine Theta I
+look at cosine Theta over 2 what that's
+
+ align:start position:0%
+look at cosine Theta over 2 what that's
+ 
+
+ align:start position:0%
+look at cosine Theta over 2 what that's
+doing is that's stretching it
+
+ align:start position:0%
+doing is that's stretching it
+ 
+
+ align:start position:0%
+doing is that's stretching it
+horizontally out so think about the
+
+ align:start position:0%
+horizontally out so think about the
+ 
+
+ align:start position:0%
+horizontally out so think about the
+period of the cosine function usually is
+
+ align:start position:0%
+period of the cosine function usually is
+ 
+
+ align:start position:0%
+period of the cosine function usually is
+2 pi but notice what happens when I put
+
+ align:start position:0%
+2 pi but notice what happens when I put
+ 
+
+ align:start position:0%
+2 pi but notice what happens when I put
+in 2 pi for Theta I'm getting cosine of
+
+ align:start position:0%
+in 2 pi for Theta I'm getting cosine of
+ 
+
+ align:start position:0%
+in 2 pi for Theta I'm getting cosine of
+pi if I want to get cosine of 2 pi I
+
+ align:start position:0%
+pi if I want to get cosine of 2 pi I
+ 
+
+ align:start position:0%
+pi if I want to get cosine of 2 pi I
+have to let Theta go to 4 Pi which is
+
+ align:start position:0%
+have to let Theta go to 4 Pi which is
+ 
+
+ align:start position:0%
+have to let Theta go to 4 Pi which is
+why I'm letting Theta be between Zer and
+
+ align:start position:0%
+why I'm letting Theta be between Zer and
+ 
+
+ align:start position:0%
+why I'm letting Theta be between Zer and
+four Pi so dividing dividing the input
+
+ align:start position:0%
+four Pi so dividing dividing the input
+ 
+
+ align:start position:0%
+four Pi so dividing dividing the input
+value by two doubles your period so the
+
+ align:start position:0%
+value by two doubles your period so the
+ 
+
+ align:start position:0%
+value by two doubles your period so the
+period is now 4 Pi so to get all the way
+
+ align:start position:0%
+period is now 4 Pi so to get all the way
+ 
+
+ align:start position:0%
+period is now 4 Pi so to get all the way
+through I'm going to have to go up to 4
+
+ align:start position:0%
+through I'm going to have to go up to 4
+ 
+
+ align:start position:0%
+through I'm going to have to go up to 4
+pi so let me just make a 2 pi here
+
+ align:start position:0%
+pi so let me just make a 2 pi here
+ 
+
+ align:start position:0%
+pi so let me just make a 2 pi here
+there's about a 4 Pi here so here's
+
+ align:start position:0%
+there's about a 4 Pi here so here's
+ 
+
+ align:start position:0%
+there's about a 4 Pi here so here's
+around 3 pi and here's around
+
+ align:start position:0%
+around 3 pi and here's around
+ 
+
+ align:start position:0%
+around 3 pi and here's around
+Pi so that now instead of instead of the
+
+ align:start position:0%
+Pi so that now instead of instead of the
+ 
+
+ align:start position:0%
+Pi so that now instead of instead of the
+usual cosine function it's going to take
+
+ align:start position:0%
+usual cosine function it's going to take
+ 
+
+ align:start position:0%
+usual cosine function it's going to take
+twice as long to get all the way through
+
+ align:start position:0%
+twice as long to get all the way through
+ 
+
+ align:start position:0%
+twice as long to get all the way through
+that's one thing we know what else have
+
+ align:start position:0%
+that's one thing we know what else have
+ 
+
+ align:start position:0%
+that's one thing we know what else have
+we done to the usual cosine function we
+
+ align:start position:0%
+we done to the usual cosine function we
+ 
+
+ align:start position:0%
+we done to the usual cosine function we
+moved it up by one and so instead of
+
+ align:start position:0%
+moved it up by one and so instead of
+ 
+
+ align:start position:0%
+moved it up by one and so instead of
+starting out when when your input is
+
+ align:start position:0%
+starting out when when your input is
+ 
+
+ align:start position:0%
+starting out when when your input is
+zero starting out at height one when
+
+ align:start position:0%
+zero starting out at height one when
+ 
+
+ align:start position:0%
+zero starting out at height one when
+your input is zero you start out at at
+
+ align:start position:0%
+your input is zero you start out at at
+ 
+
+ align:start position:0%
+your input is zero you start out at at
+height 1+ one you start out at height
+
+ align:start position:0%
+height 1+ one you start out at height
+ 
+
+ align:start position:0%
+height 1+ one you start out at height
+two so in fact this function let
+
+ align:start position:0%
+two so in fact this function let
+ 
+
+ align:start position:0%
+two so in fact this function let
+me let me point out it's going to start
+
+ align:start position:0%
+me let me point out it's going to start
+ 
+
+ align:start position:0%
+me let me point out it's going to start
+at two which means it also is going to
+
+ align:start position:0%
+at two which means it also is going to
+ 
+
+ align:start position:0%
+at two which means it also is going to
+end over here because it's periodic it's
+
+ align:start position:0%
+end over here because it's periodic it's
+ 
+
+ align:start position:0%
+end over here because it's periodic it's
+going to end at two and let's think
+
+ align:start position:0%
+going to end at two and let's think
+ 
+
+ align:start position:0%
+going to end at two and let's think
+about what else we know we know that the
+
+ align:start position:0%
+about what else we know we know that the
+ 
+
+ align:start position:0%
+about what else we know we know that the
+usual cosine function goes down to
+
+ align:start position:0%
+usual cosine function goes down to
+ 
+
+ align:start position:0%
+usual cosine function goes down to
+negative 1 but I've added one to it so
+
+ align:start position:0%
+negative 1 but I've added one to it so
+ 
+
+ align:start position:0%
+negative 1 but I've added one to it so
+now it only goes down to
+
+ align:start position:0%
+now it only goes down to
+ 
+
+ align:start position:0%
+now it only goes down to
+zero okay hopefully that makes sense
+
+ align:start position:0%
+zero okay hopefully that makes sense
+ 
+
+ align:start position:0%
+zero okay hopefully that makes sense
+maybe I should even uh even
+
+ align:start position:0%
+maybe I should even uh even
+ 
+
+ align:start position:0%
+maybe I should even uh even
+on H I don't want to draw the actual
+
+ align:start position:0%
+on H I don't want to draw the actual
+ 
+
+ align:start position:0%
+on H I don't want to draw the actual
+cosine function again right on here but
+
+ align:start position:0%
+cosine function again right on here but
+ 
+
+ align:start position:0%
+cosine function again right on here but
+let me draw the regular cosine function
+
+ align:start position:0%
+let me draw the regular cosine function
+ 
+
+ align:start position:0%
+let me draw the regular cosine function
+here so we have it the regular cosine
+
+ align:start position:0%
+here so we have it the regular cosine
+ 
+
+ align:start position:0%
+here so we have it the regular cosine
+function because I keep talking about it
+
+ align:start position:0%
+function because I keep talking about it
+ 
+
+ align:start position:0%
+function because I keep talking about it
+does does something like this it goes at
+
+ align:start position:0%
+does does something like this it goes at
+ 
+
+ align:start position:0%
+does does something like this it goes at
+one here and it's at one again here and
+
+ align:start position:0%
+one here and it's at one again here and
+ 
+
+ align:start position:0%
+one here and it's at one again here and
+so it's at minus one at
+
+ align:start position:0%
+so it's at minus one at
+ 
+
+ align:start position:0%
+so it's at minus one at
+pi and so very roughly it looks
+
+ align:start position:0%
+pi and so very roughly it looks
+ 
+
+ align:start position:0%
+pi and so very roughly it looks
+something like this right so I keep
+
+ align:start position:0%
+something like this right so I keep
+ 
+
+ align:start position:0%
+something like this right so I keep
+referencing the cosine function so this
+
+ align:start position:0%
+referencing the cosine function so this
+ 
+
+ align:start position:0%
+referencing the cosine function so this
+is the part part I'm referencing so we
+
+ align:start position:0%
+is the part part I'm referencing so we
+ 
+
+ align:start position:0%
+is the part part I'm referencing so we
+have to stretch it by two and then shift
+
+ align:start position:0%
+have to stretch it by two and then shift
+ 
+
+ align:start position:0%
+have to stretch it by two and then shift
+it up by one and so we see what was it
+
+ align:start position:0%
+it up by one and so we see what was it
+ 
+
+ align:start position:0%
+it up by one and so we see what was it
+Pi at
+
+ align:start position:0%
+Pi at
+ 
+
+ align:start position:0%
+Pi at
+pi1 I'm now going to be at 2 pi
+
+ align:start position:0%
+pi1 I'm now going to be at 2 pi
+ 
+
+ align:start position:0%
+pi1 I'm now going to be at 2 pi
+0 and then where do these points go this
+
+ align:start position:0%
+0 and then where do these points go this
+ 
+
+ align:start position:0%
+0 and then where do these points go this
+was pi over 2 the x value is going to be
+
+ align:start position:0%
+was pi over 2 the x value is going to be
+ 
+
+ align:start position:0%
+was pi over 2 the x value is going to be
+doubled I'm going to be at pi and the Y
+
+ align:start position:0%
+doubled I'm going to be at pi and the Y
+ 
+
+ align:start position:0%
+doubled I'm going to be at pi and the Y
+value is going to go up by one so I'm at
+
+ align:start position:0%
+value is going to go up by one so I'm at
+ 
+
+ align:start position:0%
+value is going to go up by one so I'm at
+Pi one and 3 Pi 1 and so the Curve will
+
+ align:start position:0%
+Pi one and 3 Pi 1 and so the Curve will
+ 
+
+ align:start position:0%
+Pi one and 3 Pi 1 and so the Curve will
+look something like this
+
+ align:start position:0%
+look something like this
+ 
+
+ align:start position:0%
+look something like this
+I'm not an expert here but hopefully
+
+ align:start position:0%
+I'm not an expert here but hopefully
+ 
+
+ align:start position:0%
+I'm not an expert here but hopefully
+that looks something like the cosine
+
+ align:start position:0%
+that looks something like the cosine
+ 
+
+ align:start position:0%
+that looks something like the cosine
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+but with a stretch and a and a shift so
+
+ align:start position:0%
+but with a stretch and a and a shift so
+ 
+
+ align:start position:0%
+but with a stretch and a and a shift so
+that is the curve r equal 1 + cosine
+
+ align:start position:0%
+that is the curve r equal 1 + cosine
+ 
+
+ align:start position:0%
+that is the curve r equal 1 + cosine
+Theta / 2 in what we consider the the r
+
+ align:start position:0%
+Theta / 2 in what we consider the the r
+ 
+
+ align:start position:0%
+Theta / 2 in what we consider the the r
+Theta plane so Theta is varying in this
+
+ align:start position:0%
+Theta plane so Theta is varying in this
+ 
+
+ align:start position:0%
+Theta plane so Theta is varying in this
+direction and R is varying in this
+
+ align:start position:0%
+direction and R is varying in this
+ 
+
+ align:start position:0%
+direction and R is varying in this
+direction but how do I transfer that to
+
+ align:start position:0%
+direction but how do I transfer that to
+ 
+
+ align:start position:0%
+direction but how do I transfer that to
+the XY plane that's the real point point
+
+ align:start position:0%
+the XY plane that's the real point point
+ 
+
+ align:start position:0%
+the XY plane that's the real point point
+that I I want to make about this problem
+
+ align:start position:0%
+that I I want to make about this problem
+ 
+
+ align:start position:0%
+that I I want to make about this problem
+so let's look at what's happening in the
+
+ align:start position:0%
+so let's look at what's happening in the
+ 
+
+ align:start position:0%
+so let's look at what's happening in the
+XY plane so this will be X and this will
+
+ align:start position:0%
+XY plane so this will be X and this will
+ 
+
+ align:start position:0%
+XY plane so this will be X and this will
+be y let's pick some points and try and
+
+ align:start position:0%
+be y let's pick some points and try and
+ 
+
+ align:start position:0%
+be y let's pick some points and try and
+figure out what's happening so where is
+
+ align:start position:0%
+figure out what's happening so where is
+ 
+
+ align:start position:0%
+figure out what's happening so where is
+this point this is the point 0 comma 2
+
+ align:start position:0%
+this point this is the point 0 comma 2
+ 
+
+ align:start position:0%
+this point this is the point 0 comma 2
+when Theta is zero R equals 2 where is
+
+ align:start position:0%
+when Theta is zero R equals 2 where is
+ 
+
+ align:start position:0%
+when Theta is zero R equals 2 where is
+Theta equal to zero in this picture it's
+
+ align:start position:0%
+Theta equal to zero in this picture it's
+ 
+
+ align:start position:0%
+Theta equal to zero in this picture it's
+in the X direction right that's theta
+
+ align:start position:0%
+in the X direction right that's theta
+ 
+
+ align:start position:0%
+in the X direction right that's theta
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+z and also 2 pi and 4 Pi any any uh
+
+ align:start position:0%
+z and also 2 pi and 4 Pi any any uh
+ 
+
+ align:start position:0%
+z and also 2 pi and 4 Pi any any uh
+multiple of 2 pi is Theta is pointing in
+
+ align:start position:0%
+multiple of 2 pi is Theta is pointing in
+ 
+
+ align:start position:0%
+multiple of 2 pi is Theta is pointing in
+this direction and R equals 2 there so
+
+ align:start position:0%
+this direction and R equals 2 there so
+ 
+
+ align:start position:0%
+this direction and R equals 2 there so
+in a strange twist this is the point two
+
+ align:start position:0%
+in a strange twist this is the point two
+ 
+
+ align:start position:0%
+in a strange twist this is the point two
+on the XY plane but that's not gonna
+
+ align:start position:0%
+on the XY plane but that's not gonna
+ 
+
+ align:start position:0%
+on the XY plane but that's not gonna
+that's just a coincidence okay don't
+
+ align:start position:0%
+that's just a coincidence okay don't
+ 
+
+ align:start position:0%
+that's just a coincidence okay don't
+think oh I'm just going to flip the
+
+ align:start position:0%
+think oh I'm just going to flip the
+ 
+
+ align:start position:0%
+think oh I'm just going to flip the
+values everywhere that's not going to
+
+ align:start position:0%
+values everywhere that's not going to
+ 
+
+ align:start position:0%
+values everywhere that's not going to
+happen okay actually and also before I
+
+ align:start position:0%
+happen okay actually and also before I
+ 
+
+ align:start position:0%
+happen okay actually and also before I
+make a mistake I'm going to make this a
+
+ align:start position:0%
+make a mistake I'm going to make this a
+ 
+
+ align:start position:0%
+make a mistake I'm going to make this a
+little bit bigger I want it to be
+
+ align:start position:0%
+little bit bigger I want it to be
+ 
+
+ align:start position:0%
+little bit bigger I want it to be
+bigger so I don't want this to be two I
+
+ align:start position:0%
+bigger so I don't want this to be two I
+ 
+
+ align:start position:0%
+bigger so I don't want this to be two I
+want this to be one I'm going to make
+
+ align:start position:0%
+want this to be one I'm going to make
+ 
+
+ align:start position:0%
+want this to be one I'm going to make
+this two
+
+ align:start position:0%
+this two
+ 
+
+ align:start position:0%
+this two
+Z I want to have a little bigger
+
+ align:start position:0%
+Z I want to have a little bigger
+ 
+
+ align:start position:0%
+Z I want to have a little bigger
+picture okay so it's going to be
+
+ align:start position:0%
+picture okay so it's going to be
+ 
+
+ align:start position:0%
+picture okay so it's going to be
+two at theta equals 0 and r equal 2 is
+
+ align:start position:0%
+two at theta equals 0 and r equal 2 is
+ 
+
+ align:start position:0%
+two at theta equals 0 and r equal 2 is
+it ever going to hit this point again
+
+ align:start position:0%
+it ever going to hit this point again
+ 
+
+ align:start position:0%
+it ever going to hit this point again
+well it is and it's going to hit that
+
+ align:start position:0%
+well it is and it's going to hit that
+ 
+
+ align:start position:0%
+well it is and it's going to hit that
+point again because it's periodic and
+
+ align:start position:0%
+point again because it's periodic and
+ 
+
+ align:start position:0%
+point again because it's periodic and
+I've gone out to four Pi if I rotate all
+
+ align:start position:0%
+I've gone out to four Pi if I rotate all
+ 
+
+ align:start position:0%
+I've gone out to four Pi if I rotate all
+the way around I'm at 2 pi for Theta if
+
+ align:start position:0%
+the way around I'm at 2 pi for Theta if
+ 
+
+ align:start position:0%
+the way around I'm at 2 pi for Theta if
+I rotate all the way around again I'm at
+
+ align:start position:0%
+I rotate all the way around again I'm at
+ 
+
+ align:start position:0%
+I rotate all the way around again I'm at
+4 Pi for Theta and my radius there is
+
+ align:start position:0%
+4 Pi for Theta and my radius there is
+ 
+
+ align:start position:0%
+4 Pi for Theta and my radius there is
+two also so this two 0 happens again
+
+ align:start position:0%
+two also so this two 0 happens again
+ 
+
+ align:start position:0%
+two also so this two 0 happens again
+when I have this point so it's going to
+
+ align:start position:0%
+when I have this point so it's going to
+ 
+
+ align:start position:0%
+when I have this point so it's going to
+close up okay and then what else happens
+
+ align:start position:0%
+close up okay and then what else happens
+ 
+
+ align:start position:0%
+close up okay and then what else happens
+well as Theta is rotating let's take
+
+ align:start position:0%
+well as Theta is rotating let's take
+ 
+
+ align:start position:0%
+well as Theta is rotating let's take
+Theta between zero and Pi Theta rotates
+
+ align:start position:0%
+Theta between zero and Pi Theta rotates
+ 
+
+ align:start position:0%
+Theta between zero and Pi Theta rotates
+from 0 to Pi going like this notice
+
+ align:start position:0%
+from 0 to Pi going like this notice
+ 
+
+ align:start position:0%
+from 0 to Pi going like this notice
+what's happening to the R value the R
+
+ align:start position:0%
+what's happening to the R value the R
+ 
+
+ align:start position:0%
+what's happening to the R value the R
+value is going from two down to one now
+
+ align:start position:0%
+value is going from two down to one now
+ 
+
+ align:start position:0%
+value is going from two down to one now
+I'm not going to be totally
+
+ align:start position:0%
+I'm not going to be totally
+ 
+
+ align:start position:0%
+I'm not going to be totally
+exact but here's minus one okay in the
+
+ align:start position:0%
+exact but here's minus one okay in the
+ 
+
+ align:start position:0%
+exact but here's minus one okay in the
+XY plane I'm not going to be totally but
+
+ align:start position:0%
+XY plane I'm not going to be totally but
+ 
+
+ align:start position:0%
+XY plane I'm not going to be totally but
+this curve is going to look something
+
+ align:start position:0%
+this curve is going to look something
+ 
+
+ align:start position:0%
+this curve is going to look something
+like see there's two it's going to look
+
+ align:start position:0%
+like see there's two it's going to look
+ 
+
+ align:start position:0%
+like see there's two it's going to look
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like oops I overshot we'll make that
+
+ align:start position:0%
+like oops I overshot we'll make that
+ 
+
+ align:start position:0%
+like oops I overshot we'll make that
+negative one something like this okay
+
+ align:start position:0%
+negative one something like this okay
+ 
+
+ align:start position:0%
+negative one something like this okay
+and what's the point the point is that I
+
+ align:start position:0%
+and what's the point the point is that I
+ 
+
+ align:start position:0%
+and what's the point the point is that I
+start at Radius 2 and by the time I get
+
+ align:start position:0%
+start at Radius 2 and by the time I get
+ 
+
+ align:start position:0%
+start at Radius 2 and by the time I get
+to theta equals Pi I've gone down until
+
+ align:start position:0%
+to theta equals Pi I've gone down until
+ 
+
+ align:start position:0%
+to theta equals Pi I've gone down until
+my radius is one this has radius one and
+
+ align:start position:0%
+my radius is one this has radius one and
+ 
+
+ align:start position:0%
+my radius is one this has radius one and
+angle
+
+ align:start position:0%
+angle
+ 
+
+ align:start position:0%
+angle
+Pi so that represents this part of the
+
+ align:start position:0%
+Pi so that represents this part of the
+ 
+
+ align:start position:0%
+Pi so that represents this part of the
+curve that's this part of the
+
+ align:start position:0%
+curve that's this part of the
+ 
+
+ align:start position:0%
+curve that's this part of the
+curve now what's what's nice about this
+
+ align:start position:0%
+curve now what's what's nice about this
+ 
+
+ align:start position:0%
+curve now what's what's nice about this
+drawing is that we know this part of the
+
+ align:start position:0%
+drawing is that we know this part of the
+ 
+
+ align:start position:0%
+drawing is that we know this part of the
+curve and this part of the curve should
+
+ align:start position:0%
+curve and this part of the curve should
+ 
+
+ align:start position:0%
+curve and this part of the curve should
+look exactly the same so once I've drawn
+
+ align:start position:0%
+look exactly the same so once I've drawn
+ 
+
+ align:start position:0%
+look exactly the same so once I've drawn
+half of this I'm going to know I'm going
+
+ align:start position:0%
+half of this I'm going to know I'm going
+ 
+
+ align:start position:0%
+half of this I'm going to know I'm going
+to know everything once I've gone from
+
+ align:start position:0%
+to know everything once I've gone from
+ 
+
+ align:start position:0%
+to know everything once I've gone from
+Zer to 2 pi I can just reflect it
+
+ align:start position:0%
+Zer to 2 pi I can just reflect it
+ 
+
+ align:start position:0%
+Zer to 2 pi I can just reflect it
+basically we'll see what I mean by
+
+ align:start position:0%
+basically we'll see what I mean by
+ 
+
+ align:start position:0%
+basically we'll see what I mean by
+reflect in this case but the same radi
+
+ align:start position:0%
+reflect in this case but the same radi
+ 
+
+ align:start position:0%
+reflect in this case but the same radi
+are happening again in some sort of
+
+ align:start position:0%
+are happening again in some sort of
+ 
+
+ align:start position:0%
+are happening again in some sort of
+symmetric f fashion Okay so we've got 0
+
+ align:start position:0%
+symmetric f fashion Okay so we've got 0
+ 
+
+ align:start position:0%
+symmetric f fashion Okay so we've got 0
+to Pi now what happens between pi and 2
+
+ align:start position:0%
+to Pi now what happens between pi and 2
+ 
+
+ align:start position:0%
+to Pi now what happens between pi and 2
+pi notice pi to 2 pi in the Theta
+
+ align:start position:0%
+pi notice pi to 2 pi in the Theta
+ 
+
+ align:start position:0%
+pi notice pi to 2 pi in the Theta
+Direction on the XY plane is I start in
+
+ align:start position:0%
+Direction on the XY plane is I start in
+ 
+
+ align:start position:0%
+Direction on the XY plane is I start in
+this direction I don't know if you can
+
+ align:start position:0%
+this direction I don't know if you can
+ 
+
+ align:start position:0%
+this direction I don't know if you can
+see that I'm starting let me come over
+
+ align:start position:0%
+see that I'm starting let me come over
+ 
+
+ align:start position:0%
+see that I'm starting let me come over
+this side I start in in this direction
+
+ align:start position:0%
+this side I start in in this direction
+ 
+
+ align:start position:0%
+this side I start in in this direction
+for pi and I'm going to rotate down this
+
+ align:start position:0%
+for pi and I'm going to rotate down this
+ 
+
+ align:start position:0%
+for pi and I'm going to rotate down this
+is 3 pi over 2 and this is 2 pi those
+
+ align:start position:0%
+is 3 pi over 2 and this is 2 pi those
+ 
+
+ align:start position:0%
+is 3 pi over 2 and this is 2 pi those
+are my angles so what are my radi well I
+
+ align:start position:0%
+are my angles so what are my radi well I
+ 
+
+ align:start position:0%
+are my angles so what are my radi well I
+start at I start at radius one and I'm
+
+ align:start position:0%
+start at I start at radius one and I'm
+ 
+
+ align:start position:0%
+start at I start at radius one and I'm
+going to radius Z
+
+ align:start position:0%
+going to radius Z
+ 
+
+ align:start position:0%
+going to radius Z
+and so what happens is I'm coming
+
+ align:start position:0%
+and so what happens is I'm coming
+ 
+
+ align:start position:0%
+and so what happens is I'm coming
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+this1 and I'm coming
+
+ align:start position:0%
+this1 and I'm coming
+ 
+
+ align:start position:0%
+this1 and I'm coming
+around and then by the time I get it's
+
+ align:start position:0%
+around and then by the time I get it's
+ 
+
+ align:start position:0%
+around and then by the time I get it's
+going to be something like this by the
+
+ align:start position:0%
+going to be something like this by the
+ 
+
+ align:start position:0%
+going to be something like this by the
+time I get to 2 pi my radius is zero now
+
+ align:start position:0%
+time I get to 2 pi my radius is zero now
+ 
+
+ align:start position:0%
+time I get to 2 pi my radius is zero now
+just to make sure this curve makes sense
+
+ align:start position:0%
+just to make sure this curve makes sense
+ 
+
+ align:start position:0%
+just to make sure this curve makes sense
+to you you could pick a place an angle
+
+ align:start position:0%
+to you you could pick a place an angle
+ 
+
+ align:start position:0%
+to you you could pick a place an angle
+maybe like right here I don't know if
+
+ align:start position:0%
+maybe like right here I don't know if
+ 
+
+ align:start position:0%
+maybe like right here I don't know if
+that's easy to see but maybe that angle
+
+ align:start position:0%
+that's easy to see but maybe that angle
+ 
+
+ align:start position:0%
+that's easy to see but maybe that angle
+right there that angle is between 3 pi
+
+ align:start position:0%
+right there that angle is between 3 pi
+ 
+
+ align:start position:0%
+right there that angle is between 3 pi
+over 2 and 2 pi is there positive radius
+
+ align:start position:0%
+over 2 and 2 pi is there positive radius
+ 
+
+ align:start position:0%
+over 2 and 2 pi is there positive radius
+there yeah there is positive radius
+
+ align:start position:0%
+there yeah there is positive radius
+ 
+
+ align:start position:0%
+there yeah there is positive radius
+there so in fact this curve does come
+
+ align:start position:0%
+there so in fact this curve does come
+ 
+
+ align:start position:0%
+there so in fact this curve does come
+into this fourth quadrant here and then
+
+ align:start position:0%
+into this fourth quadrant here and then
+ 
+
+ align:start position:0%
+into this fourth quadrant here and then
+curve back
+
+ align:start position:0%
+curve back
+ 
+
+ align:start position:0%
+curve back
+in okay it does curve back in all right
+
+ align:start position:0%
+in okay it does curve back in all right
+ 
+
+ align:start position:0%
+in okay it does curve back in all right
+so then what happens between two pi and
+
+ align:start position:0%
+so then what happens between two pi and
+ 
+
+ align:start position:0%
+so then what happens between two pi and
+3 Pi okay hopefully this this picture is
+
+ align:start position:0%
+3 Pi okay hopefully this this picture is
+ 
+
+ align:start position:0%
+3 Pi okay hopefully this this picture is
+clear so far I'm going to come back to
+
+ align:start position:0%
+clear so far I'm going to come back to
+ 
+
+ align:start position:0%
+clear so far I'm going to come back to
+the other side okay what happens between
+
+ align:start position:0%
+the other side okay what happens between
+ 
+
+ align:start position:0%
+the other side okay what happens between
+2 pi and 3 Pi 2 pi were here and 3 Pi
+
+ align:start position:0%
+2 pi and 3 Pi 2 pi were here and 3 Pi
+ 
+
+ align:start position:0%
+2 pi and 3 Pi 2 pi were here and 3 Pi
+we're back over here again and notice
+
+ align:start position:0%
+we're back over here again and notice
+ 
+
+ align:start position:0%
+we're back over here again and notice
+that the radius is going to be doing the
+
+ align:start position:0%
+that the radius is going to be doing the
+ 
+
+ align:start position:0%
+that the radius is going to be doing the
+same kind of growth that it did between
+
+ align:start position:0%
+same kind of growth that it did between
+ 
+
+ align:start position:0%
+same kind of growth that it did between
+2 pi and 3 pi as it did Decay from from
+
+ align:start position:0%
+2 pi and 3 pi as it did Decay from from
+ 
+
+ align:start position:0%
+2 pi and 3 pi as it did Decay from from
+PI to 2 pi okay because the radi now
+
+ align:start position:0%
+PI to 2 pi okay because the radi now
+ 
+
+ align:start position:0%
+PI to 2 pi okay because the radi now
+there's a symmetry with how the radi
+
+ align:start position:0%
+there's a symmetry with how the radi
+ 
+
+ align:start position:0%
+there's a symmetry with how the radi
+behave so from 2 pi to 3 Pi I start off
+
+ align:start position:0%
+behave so from 2 pi to 3 Pi I start off
+ 
+
+ align:start position:0%
+behave so from 2 pi to 3 Pi I start off
+with a with radius zero and I have a
+
+ align:start position:0%
+with a with radius zero and I have a
+ 
+
+ align:start position:0%
+with a with radius zero and I have a
+small radius and then once I get to uh 3
+
+ align:start position:0%
+small radius and then once I get to uh 3
+ 
+
+ align:start position:0%
+small radius and then once I get to uh 3
+pi over here I'm G to have radius one
+
+ align:start position:0%
+pi over here I'm G to have radius one
+ 
+
+ align:start position:0%
+pi over here I'm G to have radius one
+again I'm going to be at radius one
+
+ align:start position:0%
+again I'm going to be at radius one
+ 
+
+ align:start position:0%
+again I'm going to be at radius one
+which is going to correspond to this
+
+ align:start position:0%
+which is going to correspond to this
+ 
+
+ align:start position:0%
+which is going to correspond to this
+point so I'm G to have exactly the same
+
+ align:start position:0%
+point so I'm G to have exactly the same
+ 
+
+ align:start position:0%
+point so I'm G to have exactly the same
+picture which is dangerous because I
+
+ align:start position:0%
+picture which is dangerous because I
+ 
+
+ align:start position:0%
+picture which is dangerous because I
+probably would do it wrong but I'll try
+
+ align:start position:0%
+probably would do it wrong but I'll try
+ 
+
+ align:start position:0%
+probably would do it wrong but I'll try
+and draw it this way and then talk about
+
+ align:start position:0%
+and draw it this way and then talk about
+ 
+
+ align:start position:0%
+and draw it this way and then talk about
+it hopefully that looks about the
+
+ align:start position:0%
+it hopefully that looks about the
+ 
+
+ align:start position:0%
+it hopefully that looks about the
+same so this this curve coming through
+
+ align:start position:0%
+same so this this curve coming through
+ 
+
+ align:start position:0%
+same so this this curve coming through
+here was from PI to 2 pi this curve
+
+ align:start position:0%
+here was from PI to 2 pi this curve
+ 
+
+ align:start position:0%
+here was from PI to 2 pi this curve
+coming through here was from 2 pi to 3
+
+ align:start position:0%
+coming through here was from 2 pi to 3
+ 
+
+ align:start position:0%
+coming through here was from 2 pi to 3
+pi and then to finish it off 3 pi to 4
+
+ align:start position:0%
+pi and then to finish it off 3 pi to 4
+ 
+
+ align:start position:0%
+pi and then to finish it off 3 pi to 4
+Pi is going to look like this curve here
+
+ align:start position:0%
+Pi is going to look like this curve here
+ 
+
+ align:start position:0%
+Pi is going to look like this curve here
+so I come through o this is where it
+
+ align:start position:0%
+so I come through o this is where it
+ 
+
+ align:start position:0%
+so I come through o this is where it
+starts to get really dangerous but let's
+
+ align:start position:0%
+starts to get really dangerous but let's
+ 
+
+ align:start position:0%
+starts to get really dangerous but let's
+say that's pretty close
+
+ align:start position:0%
+say that's pretty close
+ 
+
+ align:start position:0%
+say that's pretty close
+so there's my 3 pi to 4 Pi it's again
+
+ align:start position:0%
+so there's my 3 pi to 4 Pi it's again
+ 
+
+ align:start position:0%
+so there's my 3 pi to 4 Pi it's again
+the same growth the way it was decaying
+
+ align:start position:0%
+the same growth the way it was decaying
+ 
+
+ align:start position:0%
+the same growth the way it was decaying
+between zero and Pi so this is your
+
+ align:start position:0%
+between zero and Pi so this is your
+ 
+
+ align:start position:0%
+between zero and Pi so this is your
+picture in the r in the XY plane of the
+
+ align:start position:0%
+picture in the r in the XY plane of the
+ 
+
+ align:start position:0%
+picture in the r in the XY plane of the
+curve Ral 1 + cosine Theta over 2 now we
+
+ align:start position:0%
+curve Ral 1 + cosine Theta over 2 now we
+ 
+
+ align:start position:0%
+curve Ral 1 + cosine Theta over 2 now we
+haven't calculated any area problems yet
+
+ align:start position:0%
+haven't calculated any area problems yet
+ 
+
+ align:start position:0%
+haven't calculated any area problems yet
+so what I'd like us to do is I'm going
+
+ align:start position:0%
+so what I'd like us to do is I'm going
+ 
+
+ align:start position:0%
+so what I'd like us to do is I'm going
+to shade two regions and I want us to
+
+ align:start position:0%
+to shade two regions and I want us to
+ 
+
+ align:start position:0%
+to shade two regions and I want us to
+just write down the form the integral
+
+ align:start position:0%
+just write down the form the integral
+ 
+
+ align:start position:0%
+just write down the form the integral
+form to find the area for each of these
+
+ align:start position:0%
+form to find the area for each of these
+ 
+
+ align:start position:0%
+form to find the area for each of these
+regions so the first region of
+
+ align:start position:0%
+regions so the first region of
+ 
+
+ align:start position:0%
+regions so the first region of
+interest is the pink region I'm going to
+
+ align:start position:0%
+interest is the pink region I'm going to
+ 
+
+ align:start position:0%
+interest is the pink region I'm going to
+ask us to find the area of the pink
+
+ align:start position:0%
+ask us to find the area of the pink
+ 
+
+ align:start position:0%
+ask us to find the area of the pink
+region and then I'm going to ask us to
+
+ align:start position:0%
+region and then I'm going to ask us to
+ 
+
+ align:start position:0%
+region and then I'm going to ask us to
+find the area of everything else the
+
+ align:start position:0%
+find the area of everything else the
+ 
+
+ align:start position:0%
+find the area of everything else the
+blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region so let's think about how to do
+
+ align:start position:0%
+region so let's think about how to do
+ 
+
+ align:start position:0%
+region so let's think about how to do
+that and I think I'm going to have to
+
+ align:start position:0%
+that and I think I'm going to have to
+ 
+
+ align:start position:0%
+that and I think I'm going to have to
+come over to the other side to write
+
+ align:start position:0%
+come over to the other side to write
+ 
+
+ align:start position:0%
+come over to the other side to write
+down the integrals but I'll be coming
+
+ align:start position:0%
+down the integrals but I'll be coming
+ 
+
+ align:start position:0%
+down the integrals but I'll be coming
+back and forth so just to remind you
+
+ align:start position:0%
+back and forth so just to remind you
+ 
+
+ align:start position:0%
+back and forth so just to remind you
+what you saw in lecture was that da is
+
+ align:start position:0%
+what you saw in lecture was that da is
+ 
+
+ align:start position:0%
+what you saw in lecture was that da is
+equal to r2/ 2 D
+
+ align:start position:0%
+equal to r2/ 2 D
+ 
+
+ align:start position:0%
+equal to r2/ 2 D
+Theta that's what da is and so this is
+
+ align:start position:0%
+Theta that's what da is and so this is
+ 
+
+ align:start position:0%
+Theta that's what da is and so this is
+going to be an integral in Theta and we
+
+ align:start position:0%
+going to be an integral in Theta and we
+ 
+
+ align:start position:0%
+going to be an integral in Theta and we
+know what R is as a function of theta
+
+ align:start position:0%
+know what R is as a function of theta
+ 
+
+ align:start position:0%
+know what R is as a function of theta
+and so if I want to find actually I
+
+ align:start position:0%
+and so if I want to find actually I
+ 
+
+ align:start position:0%
+and so if I want to find actually I
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+even use my colors appropriately I
+
+ align:start position:0%
+even use my colors appropriately I
+ 
+
+ align:start position:0%
+even use my colors appropriately I
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+say area the pink area is going to be
+
+ align:start position:0%
+say area the pink area is going to be
+ 
+
+ align:start position:0%
+say area the pink area is going to be
+equal to an integral and I'm going to
+
+ align:start position:0%
+equal to an integral and I'm going to
+ 
+
+ align:start position:0%
+equal to an integral and I'm going to
+and I'm going to write the uh r s I know
+
+ align:start position:0%
+and I'm going to write the uh r s I know
+ 
+
+ align:start position:0%
+and I'm going to write the uh r s I know
+what R squ is it's 1 + cosine Theta over
+
+ align:start position:0%
+what R squ is it's 1 + cosine Theta over
+ 
+
+ align:start position:0%
+what R squ is it's 1 + cosine Theta over
+2 squared and then an over two D Theta
+
+ align:start position:0%
+2 squared and then an over two D Theta
+ 
+
+ align:start position:0%
+2 squared and then an over two D Theta
+and then what is important about this
+
+ align:start position:0%
+and then what is important about this
+ 
+
+ align:start position:0%
+and then what is important about this
+it's our bounds right our bounds are
+
+ align:start position:0%
+it's our bounds right our bounds are
+ 
+
+ align:start position:0%
+it's our bounds right our bounds are
+what's important and so let's go back
+
+ align:start position:0%
+what's important and so let's go back
+ 
+
+ align:start position:0%
+what's important and so let's go back
+and let's look at our picture what are
+
+ align:start position:0%
+and let's look at our picture what are
+ 
+
+ align:start position:0%
+and let's look at our picture what are
+the bounds on Theta for the pink region
+
+ align:start position:0%
+the bounds on Theta for the pink region
+ 
+
+ align:start position:0%
+the bounds on Theta for the pink region
+okay so where does that pink region
+
+ align:start position:0%
+okay so where does that pink region
+ 
+
+ align:start position:0%
+okay so where does that pink region
+start and stop and maybe we even need to
+
+ align:start position:0%
+start and stop and maybe we even need to
+ 
+
+ align:start position:0%
+start and stop and maybe we even need to
+look at this top graph also so if we
+
+ align:start position:0%
+look at this top graph also so if we
+ 
+
+ align:start position:0%
+look at this top graph also so if we
+think about it we we went from zero to
+
+ align:start position:0%
+think about it we we went from zero to
+ 
+
+ align:start position:0%
+think about it we we went from zero to
+Pi to get this outer curve so how do we
+
+ align:start position:0%
+Pi to get this outer curve so how do we
+ 
+
+ align:start position:0%
+Pi to get this outer curve so how do we
+get the inner curve the inner curve
+
+ align:start position:0%
+get the inner curve the inner curve
+ 
+
+ align:start position:0%
+get the inner curve the inner curve
+started at theta equals Pi went to here
+
+ align:start position:0%
+started at theta equals Pi went to here
+ 
+
+ align:start position:0%
+started at theta equals Pi went to here
+went to here that was theta equals 3 Pi
+
+ align:start position:0%
+went to here that was theta equals 3 Pi
+ 
+
+ align:start position:0%
+went to here that was theta equals 3 Pi
+so it went all the way from PI to 3 Pi
+
+ align:start position:0%
+so it went all the way from PI to 3 Pi
+ 
+
+ align:start position:0%
+so it went all the way from PI to 3 Pi
+now if you're paying if you're paying
+
+ align:start position:0%
+now if you're paying if you're paying
+ 
+
+ align:start position:0%
+now if you're paying if you're paying
+good attention you can say well
+
+ align:start position:0%
+good attention you can say well
+ 
+
+ align:start position:0%
+good attention you can say well
+Christine we know that this region is
+
+ align:start position:0%
+Christine we know that this region is
+ 
+
+ align:start position:0%
+Christine we know that this region is
+totally symmetric trick so why don't I
+
+ align:start position:0%
+totally symmetric trick so why don't I
+ 
+
+ align:start position:0%
+totally symmetric trick so why don't I
+just take the area from PI to 2 pi and
+
+ align:start position:0%
+just take the area from PI to 2 pi and
+ 
+
+ align:start position:0%
+just take the area from PI to 2 pi and
+multiply by two and you can you can do
+
+ align:start position:0%
+multiply by two and you can you can do
+ 
+
+ align:start position:0%
+multiply by two and you can you can do
+it either way so you can either take the
+
+ align:start position:0%
+it either way so you can either take the
+ 
+
+ align:start position:0%
+it either way so you can either take the
+integral from all the way from PI to 3
+
+ align:start position:0%
+integral from all the way from PI to 3
+ 
+
+ align:start position:0%
+integral from all the way from PI to 3
+Pi which corresponds to starting at this
+
+ align:start position:0%
+Pi which corresponds to starting at this
+ 
+
+ align:start position:0%
+Pi which corresponds to starting at this
+angle going all the way around and
+
+ align:start position:0%
+angle going all the way around and
+ 
+
+ align:start position:0%
+angle going all the way around and
+coming back to there which takes you all
+
+ align:start position:0%
+coming back to there which takes you all
+ 
+
+ align:start position:0%
+coming back to there which takes you all
+the way around this curve or you can go
+
+ align:start position:0%
+the way around this curve or you can go
+ 
+
+ align:start position:0%
+the way around this curve or you can go
+from PI to two pi and multiply that by
+
+ align:start position:0%
+from PI to two pi and multiply that by
+ 
+
+ align:start position:0%
+from PI to two pi and multiply that by
+two so let me come back and let me write
+
+ align:start position:0%
+two so let me come back and let me write
+ 
+
+ align:start position:0%
+two so let me come back and let me write
+that down it's either pi to 3
+
+ align:start position:0%
+that down it's either pi to 3
+ 
+
+ align:start position:0%
+that down it's either pi to 3
+Pi of this or you just write it as
+
+ align:start position:0%
+Pi of this or you just write it as
+ 
+
+ align:start position:0%
+Pi of this or you just write it as
+integral from PI to 2 pi and If I
+
+ align:start position:0%
+integral from PI to 2 pi and If I
+ 
+
+ align:start position:0%
+integral from PI to 2 pi and If I
+multiply this by two the two drops out
+
+ align:start position:0%
+multiply this by two the two drops out
+ 
+
+ align:start position:0%
+multiply this by two the two drops out
+the two in the denominator drops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out I'm not going to solve this problem
+
+ align:start position:0%
+out I'm not going to solve this problem
+ 
+
+ align:start position:0%
+out I'm not going to solve this problem
+for you but I do want to point out the
+
+ align:start position:0%
+for you but I do want to point out the
+ 
+
+ align:start position:0%
+for you but I do want to point out the
+kinds of terms you would have you would
+
+ align:start position:0%
+kinds of terms you would have you would
+ 
+
+ align:start position:0%
+kinds of terms you would have you would
+have a constant term when you square
+
+ align:start position:0%
+have a constant term when you square
+ 
+
+ align:start position:0%
+have a constant term when you square
+this you would have a term that was two
+
+ align:start position:0%
+this you would have a term that was two
+ 
+
+ align:start position:0%
+this you would have a term that was two
+cosine Theta over two which is easy to
+
+ align:start position:0%
+cosine Theta over two which is easy to
+ 
+
+ align:start position:0%
+cosine Theta over two which is easy to
+integrate by a u substitution and then
+
+ align:start position:0%
+integrate by a u substitution and then
+ 
+
+ align:start position:0%
+integrate by a u substitution and then
+you would have a cosine squared Theta
+
+ align:start position:0%
+you would have a cosine squared Theta
+ 
+
+ align:start position:0%
+you would have a cosine squared Theta
+over 2 which you want to use the double
+
+ align:start position:0%
+over 2 which you want to use the double
+ 
+
+ align:start position:0%
+over 2 which you want to use the double
+angle formula or the half angle formula
+
+ align:start position:0%
+angle formula or the half angle formula
+ 
+
+ align:start position:0%
+angle formula or the half angle formula
+that you've seen used to manipulate
+
+ align:start position:0%
+that you've seen used to manipulate
+ 
+
+ align:start position:0%
+that you've seen used to manipulate
+these integrals that involve just a
+
+ align:start position:0%
+these integrals that involve just a
+ 
+
+ align:start position:0%
+these integrals that involve just a
+cosine squared or a s squared so that
+
+ align:start position:0%
+cosine squared or a s squared so that
+ 
+
+ align:start position:0%
+cosine squared or a s squared so that
+would be your strategy okay now let's
+
+ align:start position:0%
+would be your strategy okay now let's
+ 
+
+ align:start position:0%
+would be your strategy okay now let's
+look at the Blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Area okay so to find the blue area again
+
+ align:start position:0%
+Area okay so to find the blue area again
+ 
+
+ align:start position:0%
+Area okay so to find the blue area again
+I know all that matters is really the
+
+ align:start position:0%
+I know all that matters is really the
+ 
+
+ align:start position:0%
+I know all that matters is really the
+bounds we're going to see we have to do
+
+ align:start position:0%
+bounds we're going to see we have to do
+ 
+
+ align:start position:0%
+bounds we're going to see we have to do
+a little extra work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is our first setup and now
+
+ align:start position:0%
+but this is our first setup and now
+ 
+
+ align:start position:0%
+but this is our first setup and now
+let's go look at the bounds okay so we
+
+ align:start position:0%
+let's go look at the bounds okay so we
+ 
+
+ align:start position:0%
+let's go look at the bounds okay so we
+go back to the
+
+ align:start position:0%
+go back to the
+ 
+
+ align:start position:0%
+go back to the
+curve all right what is the Blue Area
+
+ align:start position:0%
+curve all right what is the Blue Area
+ 
+
+ align:start position:0%
+curve all right what is the Blue Area
+well the blue
+
+ align:start position:0%
+well the blue
+ 
+
+ align:start position:0%
+well the blue
+area that's a little harder so let's see
+
+ align:start position:0%
+area that's a little harder so let's see
+ 
+
+ align:start position:0%
+area that's a little harder so let's see
+what happens if I were to if I were to
+
+ align:start position:0%
+what happens if I were to if I were to
+ 
+
+ align:start position:0%
+what happens if I were to if I were to
+take Theta from zero to Pi what would
+
+ align:start position:0%
+take Theta from zero to Pi what would
+ 
+
+ align:start position:0%
+take Theta from zero to Pi what would
+happen I would not only pick up the blue
+
+ align:start position:0%
+happen I would not only pick up the blue
+ 
+
+ align:start position:0%
+happen I would not only pick up the blue
+area but I'd pick up this pink stuff
+
+ align:start position:0%
+area but I'd pick up this pink stuff
+ 
+
+ align:start position:0%
+area but I'd pick up this pink stuff
+inside but I don't want the pink stuff I
+
+ align:start position:0%
+inside but I don't want the pink stuff I
+ 
+
+ align:start position:0%
+inside but I don't want the pink stuff I
+just want the blue stuff so what am I
+
+ align:start position:0%
+just want the blue stuff so what am I
+ 
+
+ align:start position:0%
+just want the blue stuff so what am I
+going to have to do to find the Blue
+
+ align:start position:0%
+going to have to do to find the Blue
+ 
+
+ align:start position:0%
+going to have to do to find the Blue
+Area just say from0 up to Pi I'm going
+
+ align:start position:0%
+Area just say from0 up to Pi I'm going
+ 
+
+ align:start position:0%
+Area just say from0 up to Pi I'm going
+to have to find the area from 0 to Pi
+
+ align:start position:0%
+to have to find the area from 0 to Pi
+ 
+
+ align:start position:0%
+to have to find the area from 0 to Pi
+and then I'm going to have to subtract
+
+ align:start position:0%
+and then I'm going to have to subtract
+ 
+
+ align:start position:0%
+and then I'm going to have to subtract
+off the area of this component okay but
+
+ align:start position:0%
+off the area of this component okay but
+ 
+
+ align:start position:0%
+off the area of this component okay but
+we know actually how to find the area of
+
+ align:start position:0%
+we know actually how to find the area of
+ 
+
+ align:start position:0%
+we know actually how to find the area of
+this component okay so hopefully this
+
+ align:start position:0%
+this component okay so hopefully this
+ 
+
+ align:start position:0%
+this component okay so hopefully this
+makes sense because let's think about
+
+ align:start position:0%
+makes sense because let's think about
+ 
+
+ align:start position:0%
+makes sense because let's think about
+when I'm finding area I'm going from the
+
+ align:start position:0%
+when I'm finding area I'm going from the
+ 
+
+ align:start position:0%
+when I'm finding area I'm going from the
+origin and I'm coming out and I have the
+
+ align:start position:0%
+origin and I'm coming out and I have the
+ 
+
+ align:start position:0%
+origin and I'm coming out and I have the
+radius out there so when I integrate
+
+ align:start position:0%
+radius out there so when I integrate
+ 
+
+ align:start position:0%
+radius out there so when I integrate
+this da from 0 to Pi for Theta I'm
+
+ align:start position:0%
+this da from 0 to Pi for Theta I'm
+ 
+
+ align:start position:0%
+this da from 0 to Pi for Theta I'm
+picking up pieces that come out little
+
+ align:start position:0%
+picking up pieces that come out little
+ 
+
+ align:start position:0%
+picking up pieces that come out little
+sectors that come out like this between
+
+ align:start position:0%
+sectors that come out like this between
+ 
+
+ align:start position:0%
+sectors that come out like this between
+pi 2 and Pi so I'm getting more area
+
+ align:start position:0%
+pi 2 and Pi so I'm getting more area
+ 
+
+ align:start position:0%
+pi 2 and Pi so I'm getting more area
+than I want if I just let Theta go
+
+ align:start position:0%
+than I want if I just let Theta go
+ 
+
+ align:start position:0%
+than I want if I just let Theta go
+between zero and Pi so I have to
+
+ align:start position:0%
+between zero and Pi so I have to
+ 
+
+ align:start position:0%
+between zero and Pi so I have to
+calculate all of it and then I have to
+
+ align:start position:0%
+calculate all of it and then I have to
+ 
+
+ align:start position:0%
+calculate all of it and then I have to
+take away the extra stuff okay so the
+
+ align:start position:0%
+take away the extra stuff okay so the
+ 
+
+ align:start position:0%
+take away the extra stuff okay so the
+blue area is actually the bigger area
+
+ align:start position:0%
+blue area is actually the bigger area
+ 
+
+ align:start position:0%
+blue area is actually the bigger area
+subtracting the smaller area and so how
+
+ align:start position:0%
+subtracting the smaller area and so how
+ 
+
+ align:start position:0%
+subtracting the smaller area and so how
+I'm going to write this if we come back
+
+ align:start position:0%
+I'm going to write this if we come back
+ 
+
+ align:start position:0%
+I'm going to write this if we come back
+over I'm just going to take two times
+
+ align:start position:0%
+over I'm just going to take two times
+ 
+
+ align:start position:0%
+over I'm just going to take two times
+this whole thing so I'm going to take
+
+ align:start position:0%
+this whole thing so I'm going to take
+ 
+
+ align:start position:0%
+this whole thing so I'm going to take
+two times this and I know I have to
+
+ align:start position:0%
+two times this and I know I have to
+ 
+
+ align:start position:0%
+two times this and I know I have to
+integrate it from 0 to
+
+ align:start position:0%
+integrate it from 0 to
+ 
+
+ align:start position:0%
+integrate it from 0 to
+Pi and I'm taking two times cuz it's
+
+ align:start position:0%
+Pi and I'm taking two times cuz it's
+ 
+
+ align:start position:0%
+Pi and I'm taking two times cuz it's
+symmetric remember and then I'm going to
+
+ align:start position:0%
+symmetric remember and then I'm going to
+ 
+
+ align:start position:0%
+symmetric remember and then I'm going to
+subtract off this one that's two times
+
+ align:start position:0%
+subtract off this one that's two times
+ 
+
+ align:start position:0%
+subtract off this one that's two times
+the thing from PI to 2 pi now you might
+
+ align:start position:0%
+the thing from PI to 2 pi now you might
+ 
+
+ align:start position:0%
+the thing from PI to 2 pi now you might
+say well Christine the pink stuff I'm
+
+ align:start position:0%
+say well Christine the pink stuff I'm
+ 
+
+ align:start position:0%
+say well Christine the pink stuff I'm
+interested in between zero and Pi is
+
+ align:start position:0%
+interested in between zero and Pi is
+ 
+
+ align:start position:0%
+interested in between zero and Pi is
+actually Theta between not pi and two Pi
+
+ align:start position:0%
+actually Theta between not pi and two Pi
+ 
+
+ align:start position:0%
+actually Theta between not pi and two Pi
+but 2 pi and 3 Pi but again there's all
+
+ align:start position:0%
+but 2 pi and 3 Pi but again there's all
+ 
+
+ align:start position:0%
+but 2 pi and 3 Pi but again there's all
+this symmetry in the problem so it
+
+ align:start position:0%
+this symmetry in the problem so it
+ 
+
+ align:start position:0%
+this symmetry in the problem so it
+doesn't really matter but if you're a
+
+ align:start position:0%
+doesn't really matter but if you're a
+ 
+
+ align:start position:0%
+doesn't really matter but if you're a
+stickler I guess I'll even write it this
+
+ align:start position:0%
+stickler I guess I'll even write it this
+ 
+
+ align:start position:0%
+stickler I guess I'll even write it this
+way just to make sure so I'll write it
+
+ align:start position:0%
+way just to make sure so I'll write it
+ 
+
+ align:start position:0%
+way just to make sure so I'll write it
+as 2 pi to 3 Pi so that everyone's very
+
+ align:start position:0%
+as 2 pi to 3 Pi so that everyone's very
+ 
+
+ align:start position:0%
+as 2 pi to 3 Pi so that everyone's very
+happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again what did I what do we
+
+ align:start position:0%
+okay so again what did I what do we
+ 
+
+ align:start position:0%
+okay so again what did I what do we
+do these twos divide out so from 0 to Pi
+
+ align:start position:0%
+do these twos divide out so from 0 to Pi
+ 
+
+ align:start position:0%
+do these twos divide out so from 0 to Pi
+of R 2 D Theta that's going to give me
+
+ align:start position:0%
+of R 2 D Theta that's going to give me
+ 
+
+ align:start position:0%
+of R 2 D Theta that's going to give me
+the area of the blue plus the
+
+ align:start position:0%
+the area of the blue plus the
+ 
+
+ align:start position:0%
+the area of the blue plus the
+pink and then 2 pi to 3 Pi of 1 plus
+
+ align:start position:0%
+pink and then 2 pi to 3 Pi of 1 plus
+ 
+
+ align:start position:0%
+pink and then 2 pi to 3 Pi of 1 plus
+cosine Theta over 2^ 2 D Theta is going
+
+ align:start position:0%
+cosine Theta over 2^ 2 D Theta is going
+ 
+
+ align:start position:0%
+cosine Theta over 2^ 2 D Theta is going
+to give me the area of the pink so the
+
+ align:start position:0%
+to give me the area of the pink so the
+ 
+
+ align:start position:0%
+to give me the area of the pink so the
+the blue plus the pink is over here and
+
+ align:start position:0%
+the blue plus the pink is over here and
+ 
+
+ align:start position:0%
+the blue plus the pink is over here and
+then the pink is over here so when I
+
+ align:start position:0%
+then the pink is over here so when I
+ 
+
+ align:start position:0%
+then the pink is over here so when I
+subtract that off I just get the
+
+ align:start position:0%
+subtract that off I just get the
+ 
+
+ align:start position:0%
+subtract that off I just get the
+blue okay let me again just uh go back
+
+ align:start position:0%
+blue okay let me again just uh go back
+ 
+
+ align:start position:0%
+blue okay let me again just uh go back
+one more time and point out what we did
+
+ align:start position:0%
+one more time and point out what we did
+ 
+
+ align:start position:0%
+one more time and point out what we did
+at the very beginning to remind us what
+
+ align:start position:0%
+at the very beginning to remind us what
+ 
+
+ align:start position:0%
+at the very beginning to remind us what
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+happening um and then I will finish so
+
+ align:start position:0%
+happening um and then I will finish so
+ 
+
+ align:start position:0%
+happening um and then I will finish so
+let's come back over here so the idea
+
+ align:start position:0%
+let's come back over here so the idea
+ 
+
+ align:start position:0%
+let's come back over here so the idea
+was to graph this curve that was in R as
+
+ align:start position:0%
+was to graph this curve that was in R as
+ 
+
+ align:start position:0%
+was to graph this curve that was in R as
+a function of theta and I was supposed
+
+ align:start position:0%
+a function of theta and I was supposed
+ 
+
+ align:start position:0%
+a function of theta and I was supposed
+to understand what that looked like in
+
+ align:start position:0%
+to understand what that looked like in
+ 
+
+ align:start position:0%
+to understand what that looked like in
+the XY
+
+ align:start position:0%
+the XY
+ 
+
+ align:start position:0%
+the XY
+plane and so my trick was to take the
+
+ align:start position:0%
+plane and so my trick was to take the
+ 
+
+ align:start position:0%
+plane and so my trick was to take the
+the relationship between R and Theta and
+
+ align:start position:0%
+the relationship between R and Theta and
+ 
+
+ align:start position:0%
+the relationship between R and Theta and
+graph that explicitly in in an R Theta
+
+ align:start position:0%
+graph that explicitly in in an R Theta
+ 
+
+ align:start position:0%
+graph that explicitly in in an R Theta
+plane so I let Theta vary in the
+
+ align:start position:0%
+plane so I let Theta vary in the
+ 
+
+ align:start position:0%
+plane so I let Theta vary in the
+horizontal Direction and R vary in the
+
+ align:start position:0%
+horizontal Direction and R vary in the
+ 
+
+ align:start position:0%
+horizontal Direction and R vary in the
+vertical Direction and I can do that
+
+ align:start position:0%
+vertical Direction and I can do that
+ 
+
+ align:start position:0%
+vertical Direction and I can do that
+very easily and then translate that into
+
+ align:start position:0%
+very easily and then translate that into
+ 
+
+ align:start position:0%
+very easily and then translate that into
+the XY plane so my curve again went the
+
+ align:start position:0%
+the XY plane so my curve again went the
+ 
+
+ align:start position:0%
+the XY plane so my curve again went the
+big part the little part here little
+
+ align:start position:0%
+big part the little part here little
+ 
+
+ align:start position:0%
+big part the little part here little
+part here big part here that was the
+
+ align:start position:0%
+part here big part here that was the
+ 
+
+ align:start position:0%
+part here big part here that was the
+order so if you need uh if you need
+
+ align:start position:0%
+order so if you need uh if you need
+ 
+
+ align:start position:0%
+order so if you need uh if you need
+arrows on it this was the order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then once I had that the problem was
+
+ align:start position:0%
+and then once I had that the problem was
+ 
+
+ align:start position:0%
+and then once I had that the problem was
+about areas and there was a lot of
+
+ align:start position:0%
+about areas and there was a lot of
+ 
+
+ align:start position:0%
+about areas and there was a lot of
+symmetry in this problem um but the main
+
+ align:start position:0%
+symmetry in this problem um but the main
+ 
+
+ align:start position:0%
+symmetry in this problem um but the main
+point I wanted to show was just knowing
+
+ align:start position:0%
+point I wanted to show was just knowing
+ 
+
+ align:start position:0%
+point I wanted to show was just knowing
+where uh where your Theta starts and
+
+ align:start position:0%
+where uh where your Theta starts and
+ 
+
+ align:start position:0%
+where uh where your Theta starts and
+stops is not enough to determine an area
+
+ align:start position:0%
+stops is not enough to determine an area
+ 
+
+ align:start position:0%
+stops is not enough to determine an area
+of a region if that region is excluding
+
+ align:start position:0%
+of a region if that region is excluding
+ 
+
+ align:start position:0%
+of a region if that region is excluding
+some part that's that would be
+
+ align:start position:0%
+some part that's that would be
+ 
+
+ align:start position:0%
+some part that's that would be
+potentially counted twice so that was
+
+ align:start position:0%
+potentially counted twice so that was
+ 
+
+ align:start position:0%
+potentially counted twice so that was
+the reason I wanted you to calculate not
+
+ align:start position:0%
+the reason I wanted you to calculate not
+ 
+
+ align:start position:0%
+the reason I wanted you to calculate not
+just the pink area but also see that the
+
+ align:start position:0%
+just the pink area but also see that the
+ 
+
+ align:start position:0%
+just the pink area but also see that the
+blue is not from Theta Theta from 0 to
+
+ align:start position:0%
+blue is not from Theta Theta from 0 to
+ 
+
+ align:start position:0%
+blue is not from Theta Theta from 0 to
+Pi but you have to subtract off this
+
+ align:start position:0%
+Pi but you have to subtract off this
+ 
+
+ align:start position:0%
+Pi but you have to subtract off this
+extra stuff that you
+
+ align:start position:0%
+extra stuff that you
+ 
+
+ align:start position:0%
+extra stuff that you
+counted and I guess that is where I will
+
+ align:start position:0%
+counted and I guess that is where I will
+ 
+
+ align:start position:0%
+counted and I guess that is where I will
+stop
\ No newline at end of file
diff --git a/EQjwWn-WrdI.txt b/EQjwWn-WrdI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da6825d33a0482c754e17e496e72e39390e97204
--- /dev/null
+++ b/EQjwWn-WrdI.txt
@@ -0,0 +1,15168 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit open courseware at ocw.mit.edu
+
+ align:start position:0%
+visit mit open courseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit mit open courseware at ocw.mit.edu
+okay so welcome back this is the second
+
+ align:start position:0%
+okay so welcome back this is the second
+ 
+
+ align:start position:0%
+okay so welcome back this is the second
+half of our
+
+ align:start position:0%
+half of our
+ 
+
+ align:start position:0%
+half of our
+two lectures on distributed algorithms
+
+ align:start position:0%
+two lectures on distributed algorithms
+ 
+
+ align:start position:0%
+two lectures on distributed algorithms
+this week
+
+ align:start position:0%
+this week
+ 
+
+ align:start position:0%
+this week
+to turn that on all right so
+
+ align:start position:0%
+to turn that on all right so
+ 
+
+ align:start position:0%
+to turn that on all right so
+i'll start with a quick review this week
+
+ align:start position:0%
+i'll start with a quick review this week
+ 
+
+ align:start position:0%
+i'll start with a quick review this week
+we're just looking at synchronous and
+
+ align:start position:0%
+we're just looking at synchronous and
+ 
+
+ align:start position:0%
+we're just looking at synchronous and
+asynchronous distributed algorithms not
+
+ align:start position:0%
+asynchronous distributed algorithms not
+ 
+
+ align:start position:0%
+asynchronous distributed algorithms not
+worrying about
+
+ align:start position:0%
+worrying about
+ 
+
+ align:start position:0%
+worrying about
+interesting stuff like failures last
+
+ align:start position:0%
+interesting stuff like failures last
+ 
+
+ align:start position:0%
+interesting stuff like failures last
+time we
+
+ align:start position:0%
+time we
+ 
+
+ align:start position:0%
+time we
+looked at leader election maximal
+
+ align:start position:0%
+looked at leader election maximal
+ 
+
+ align:start position:0%
+looked at leader election maximal
+independence set
+
+ align:start position:0%
+independence set
+ 
+
+ align:start position:0%
+independence set
+breadth first spanning trees and we
+
+ align:start position:0%
+breadth first spanning trees and we
+ 
+
+ align:start position:0%
+breadth first spanning trees and we
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+looking at shortest paths trees we'll
+
+ align:start position:0%
+looking at shortest paths trees we'll
+ 
+
+ align:start position:0%
+looking at shortest paths trees we'll
+finish that today and then we'll move on
+
+ align:start position:0%
+finish that today and then we'll move on
+ 
+
+ align:start position:0%
+finish that today and then we'll move on
+to the main topic for today which is
+
+ align:start position:0%
+to the main topic for today which is
+ 
+
+ align:start position:0%
+to the main topic for today which is
+asynchronous distributed algorithms
+
+ align:start position:0%
+asynchronous distributed algorithms
+ 
+
+ align:start position:0%
+asynchronous distributed algorithms
+where things start getting much more
+
+ align:start position:0%
+where things start getting much more
+ 
+
+ align:start position:0%
+where things start getting much more
+complicated because not everything is
+
+ align:start position:0%
+complicated because not everything is
+ 
+
+ align:start position:0%
+complicated because not everything is
+going on
+
+ align:start position:0%
+going on
+ 
+
+ align:start position:0%
+going on
+in synchronous rounds and we'll revisit
+
+ align:start position:0%
+in synchronous rounds and we'll revisit
+ 
+
+ align:start position:0%
+in synchronous rounds and we'll revisit
+the same two problems breadth first and
+
+ align:start position:0%
+the same two problems breadth first and
+ 
+
+ align:start position:0%
+the same two problems breadth first and
+shortest paths uh spanning trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a quick review uh all of our
+
+ align:start position:0%
+okay so a quick review uh all of our
+ 
+
+ align:start position:0%
+okay so a quick review uh all of our
+um algorithms are
+
+ align:start position:0%
+um algorithms are
+ 
+
+ align:start position:0%
+um algorithms are
+using a model that's based on an
+
+ align:start position:0%
+using a model that's based on an
+ 
+
+ align:start position:0%
+using a model that's based on an
+undirected graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we using this notation gamma for the
+
+ align:start position:0%
+we using this notation gamma for the
+ 
+
+ align:start position:0%
+we using this notation gamma for the
+neighbors of a vertex
+
+ align:start position:0%
+neighbors of a vertex
+ 
+
+ align:start position:0%
+neighbors of a vertex
+talk about the degree of a vertex we
+
+ align:start position:0%
+talk about the degree of a vertex we
+ 
+
+ align:start position:0%
+talk about the degree of a vertex we
+have a process
+
+ align:start position:0%
+have a process
+ 
+
+ align:start position:0%
+have a process
+then associated with every vertex in the
+
+ align:start position:0%
+then associated with every vertex in the
+ 
+
+ align:start position:0%
+then associated with every vertex in the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+and we associate communication channels
+
+ align:start position:0%
+and we associate communication channels
+ 
+
+ align:start position:0%
+and we associate communication channels
+in both directions
+
+ align:start position:0%
+in both directions
+ 
+
+ align:start position:0%
+in both directions
+on every edge okay
+
+ align:start position:0%
+on every edge okay
+ 
+
+ align:start position:0%
+on every edge okay
+so last time we looked at synchronous
+
+ align:start position:0%
+so last time we looked at synchronous
+ 
+
+ align:start position:0%
+so last time we looked at synchronous
+distributed algorithms in the
+
+ align:start position:0%
+distributed algorithms in the
+ 
+
+ align:start position:0%
+distributed algorithms in the
+synchronous model
+
+ align:start position:0%
+synchronous model
+ 
+
+ align:start position:0%
+synchronous model
+we have the processes of the graph
+
+ align:start position:0%
+we have the processes of the graph
+ 
+
+ align:start position:0%
+we have the processes of the graph
+vertices they communicate using messages
+
+ align:start position:0%
+vertices they communicate using messages
+ 
+
+ align:start position:0%
+vertices they communicate using messages
+the processes have local ports that they
+
+ align:start position:0%
+the processes have local ports that they
+ 
+
+ align:start position:0%
+the processes have local ports that they
+know by some kind of local name
+
+ align:start position:0%
+know by some kind of local name
+ 
+
+ align:start position:0%
+know by some kind of local name
+and the ports connect to their
+
+ align:start position:0%
+and the ports connect to their
+ 
+
+ align:start position:0%
+and the ports connect to their
+communication channel
+
+ align:start position:0%
+communication channel
+ 
+
+ align:start position:0%
+communication channel
+the algorithm executes in synchronous
+
+ align:start position:0%
+the algorithm executes in synchronous
+ 
+
+ align:start position:0%
+the algorithm executes in synchronous
+rounds where in every round
+
+ align:start position:0%
+rounds where in every round
+ 
+
+ align:start position:0%
+rounds where in every round
+every process is going to decide what to
+
+ align:start position:0%
+every process is going to decide what to
+ 
+
+ align:start position:0%
+every process is going to decide what to
+send on all of its ports
+
+ align:start position:0%
+send on all of its ports
+ 
+
+ align:start position:0%
+send on all of its ports
+and the messages then get put into the
+
+ align:start position:0%
+and the messages then get put into the
+ 
+
+ align:start position:0%
+and the messages then get put into the
+channel delivered to the processes at
+
+ align:start position:0%
+channel delivered to the processes at
+ 
+
+ align:start position:0%
+channel delivered to the processes at
+the other end
+
+ align:start position:0%
+the other end
+ 
+
+ align:start position:0%
+the other end
+and everybody looks at all the messages
+
+ align:start position:0%
+and everybody looks at all the messages
+ 
+
+ align:start position:0%
+and everybody looks at all the messages
+they get at that round all at once
+
+ align:start position:0%
+they get at that round all at once
+ 
+
+ align:start position:0%
+they get at that round all at once
+and they determine a new state to
+
+ align:start position:0%
+and they determine a new state to
+ 
+
+ align:start position:0%
+and they determine a new state to
+compute a new state
+
+ align:start position:0%
+compute a new state
+ 
+
+ align:start position:0%
+compute a new state
+based on all of those arriving messages
+
+ align:start position:0%
+based on all of those arriving messages
+ 
+
+ align:start position:0%
+based on all of those arriving messages
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+so we started with leader election i
+
+ align:start position:0%
+so we started with leader election i
+ 
+
+ align:start position:0%
+so we started with leader election i
+won't repeat the problem definition but
+
+ align:start position:0%
+won't repeat the problem definition but
+ 
+
+ align:start position:0%
+won't repeat the problem definition but
+here's the results that we got last time
+
+ align:start position:0%
+here's the results that we got last time
+ 
+
+ align:start position:0%
+here's the results that we got last time
+uh we looked at a special case of a
+
+ align:start position:0%
+uh we looked at a special case of a
+ 
+
+ align:start position:0%
+uh we looked at a special case of a
+graph that's just a
+
+ align:start position:0%
+graph that's just a
+ 
+
+ align:start position:0%
+graph that's just a
+simple clique and if the processes
+
+ align:start position:0%
+simple clique and if the processes
+ 
+
+ align:start position:0%
+simple clique and if the processes
+don't have any uh distinguishing
+
+ align:start position:0%
+don't have any uh distinguishing
+ 
+
+ align:start position:0%
+don't have any uh distinguishing
+information like unique identifiers
+
+ align:start position:0%
+information like unique identifiers
+ 
+
+ align:start position:0%
+information like unique identifiers
+and they're deterministic then there's
+
+ align:start position:0%
+and they're deterministic then there's
+ 
+
+ align:start position:0%
+and they're deterministic then there's
+no way to break the symmetry and you can
+
+ align:start position:0%
+no way to break the symmetry and you can
+ 
+
+ align:start position:0%
+no way to break the symmetry and you can
+prove an impossibility result
+
+ align:start position:0%
+prove an impossibility result
+ 
+
+ align:start position:0%
+prove an impossibility result
+that says that you can't in a
+
+ align:start position:0%
+that says that you can't in a
+ 
+
+ align:start position:0%
+that says that you can't in a
+deterministic indistinguishable case you
+
+ align:start position:0%
+deterministic indistinguishable case you
+ 
+
+ align:start position:0%
+deterministic indistinguishable case you
+can't guarantee to elect a leader
+
+ align:start position:0%
+can't guarantee to elect a leader
+ 
+
+ align:start position:0%
+can't guarantee to elect a leader
+in this kind of a graph just as an aside
+
+ align:start position:0%
+in this kind of a graph just as an aside
+ 
+
+ align:start position:0%
+in this kind of a graph just as an aside
+i should say that distributed computing
+
+ align:start position:0%
+i should say that distributed computing
+ 
+
+ align:start position:0%
+i should say that distributed computing
+theory is
+
+ align:start position:0%
+theory is
+ 
+
+ align:start position:0%
+theory is
+just filled with impossibility results
+
+ align:start position:0%
+just filled with impossibility results
+ 
+
+ align:start position:0%
+just filled with impossibility results
+and they're all based on this limitation
+
+ align:start position:0%
+and they're all based on this limitation
+ 
+
+ align:start position:0%
+and they're all based on this limitation
+of distributed computing where
+
+ align:start position:0%
+of distributed computing where
+ 
+
+ align:start position:0%
+of distributed computing where
+each node only knows what's happening to
+
+ align:start position:0%
+each node only knows what's happening to
+ 
+
+ align:start position:0%
+each node only knows what's happening to
+itself and
+
+ align:start position:0%
+itself and
+ 
+
+ align:start position:0%
+itself and
+in its neighborhood nobody knows what's
+
+ align:start position:0%
+in its neighborhood nobody knows what's
+ 
+
+ align:start position:0%
+in its neighborhood nobody knows what's
+happening in the entire
+
+ align:start position:0%
+happening in the entire
+ 
+
+ align:start position:0%
+happening in the entire
+uh system so that's a very strong
+
+ align:start position:0%
+uh system so that's a very strong
+ 
+
+ align:start position:0%
+uh system so that's a very strong
+limitation
+
+ align:start position:0%
+limitation
+ 
+
+ align:start position:0%
+limitation
+and as you might expect that would make
+
+ align:start position:0%
+and as you might expect that would make
+ 
+
+ align:start position:0%
+and as you might expect that would make
+a lot of things impossible or difficult
+
+ align:start position:0%
+a lot of things impossible or difficult
+ 
+
+ align:start position:0%
+a lot of things impossible or difficult
+okay then we went on and got two
+
+ align:start position:0%
+okay then we went on and got two
+ 
+
+ align:start position:0%
+okay then we went on and got two
+positive results a theorem that
+
+ align:start position:0%
+positive results a theorem that
+ 
+
+ align:start position:0%
+positive results a theorem that
+um well an algorithm that is
+
+ align:start position:0%
+um well an algorithm that is
+ 
+
+ align:start position:0%
+um well an algorithm that is
+deterministic but the processes have
+
+ align:start position:0%
+deterministic but the processes have
+ 
+
+ align:start position:0%
+deterministic but the processes have
+unique identifiers
+
+ align:start position:0%
+unique identifiers
+ 
+
+ align:start position:0%
+unique identifiers
+and then you can elect a leader quickly
+
+ align:start position:0%
+and then you can elect a leader quickly
+ 
+
+ align:start position:0%
+and then you can elect a leader quickly
+or if you don't have unique identifiers
+
+ align:start position:0%
+or if you don't have unique identifiers
+ 
+
+ align:start position:0%
+or if you don't have unique identifiers
+but you have a
+
+ align:start position:0%
+but you have a
+ 
+
+ align:start position:0%
+but you have a
+probability so you can make random
+
+ align:start position:0%
+probability so you can make random
+ 
+
+ align:start position:0%
+probability so you can make random
+choices you can essentially
+
+ align:start position:0%
+choices you can essentially
+ 
+
+ align:start position:0%
+choices you can essentially
+choose an identifier and then it works
+
+ align:start position:0%
+choose an identifier and then it works
+ 
+
+ align:start position:0%
+choose an identifier and then it works
+almost as well
+
+ align:start position:0%
+almost as well
+ 
+
+ align:start position:0%
+almost as well
+with those identifiers okay then we
+
+ align:start position:0%
+with those identifiers okay then we
+ 
+
+ align:start position:0%
+with those identifiers okay then we
+looked at maximal independent set
+
+ align:start position:0%
+looked at maximal independent set
+ 
+
+ align:start position:0%
+looked at maximal independent set
+um remember what it means no two
+
+ align:start position:0%
+um remember what it means no two
+ 
+
+ align:start position:0%
+um remember what it means no two
+neighbors should both be in the set but
+
+ align:start position:0%
+neighbors should both be in the set but
+ 
+
+ align:start position:0%
+neighbors should both be in the set but
+you don't want to be able to
+
+ align:start position:0%
+you don't want to be able to
+ 
+
+ align:start position:0%
+you don't want to be able to
+add any more nodes while keeping these
+
+ align:start position:0%
+add any more nodes while keeping these
+ 
+
+ align:start position:0%
+add any more nodes while keeping these
+nodes independent in other words every
+
+ align:start position:0%
+nodes independent in other words every
+ 
+
+ align:start position:0%
+nodes independent in other words every
+node is either in the set or has a
+
+ align:start position:0%
+node is either in the set or has a
+ 
+
+ align:start position:0%
+node is either in the set or has a
+neighbor in the set
+
+ align:start position:0%
+neighbor in the set
+ 
+
+ align:start position:0%
+neighbor in the set
+okay and we gave this algorithm i'm just
+
+ align:start position:0%
+okay and we gave this algorithm i'm just
+ 
+
+ align:start position:0%
+okay and we gave this algorithm i'm just
+including it here for as a reminder
+
+ align:start position:0%
+including it here for as a reminder
+ 
+
+ align:start position:0%
+including it here for as a reminder
+luby's algorithm which basically
+
+ align:start position:0%
+luby's algorithm which basically
+ 
+
+ align:start position:0%
+luby's algorithm which basically
+goes through a number of phases in each
+
+ align:start position:0%
+goes through a number of phases in each
+ 
+
+ align:start position:0%
+goes through a number of phases in each
+phase some processes
+
+ align:start position:0%
+phase some processes
+ 
+
+ align:start position:0%
+phase some processes
+decide to join the mis and their
+
+ align:start position:0%
+decide to join the mis and their
+ 
+
+ align:start position:0%
+decide to join the mis and their
+neighbors
+
+ align:start position:0%
+neighbors
+ 
+
+ align:start position:0%
+neighbors
+decide not to join and you just repeat
+
+ align:start position:0%
+decide not to join and you just repeat
+ 
+
+ align:start position:0%
+decide not to join and you just repeat
+this you do this
+
+ align:start position:0%
+this you do this
+ 
+
+ align:start position:0%
+this you do this
+based on choosing random ideas again
+
+ align:start position:0%
+based on choosing random ideas again
+ 
+
+ align:start position:0%
+based on choosing random ideas again
+okay and we proved that the theorem
+
+ align:start position:0%
+okay and we proved that the theorem
+ 
+
+ align:start position:0%
+okay and we proved that the theorem
+correctly computes an mis and
+
+ align:start position:0%
+correctly computes an mis and
+ 
+
+ align:start position:0%
+correctly computes an mis and
+with a good probability all the nodes
+
+ align:start position:0%
+with a good probability all the nodes
+ 
+
+ align:start position:0%
+with a good probability all the nodes
+decide within only
+
+ align:start position:0%
+decide within only
+ 
+
+ align:start position:0%
+decide within only
+logarithm logarithmic phases n here is
+
+ align:start position:0%
+logarithm logarithmic phases n here is
+ 
+
+ align:start position:0%
+logarithm logarithmic phases n here is
+the number of nodes
+
+ align:start position:0%
+the number of nodes
+ 
+
+ align:start position:0%
+the number of nodes
+okay all right then we went on to
+
+ align:start position:0%
+okay all right then we went on to
+ 
+
+ align:start position:0%
+okay all right then we went on to
+breadth first spanning trees
+
+ align:start position:0%
+breadth first spanning trees
+ 
+
+ align:start position:0%
+breadth first spanning trees
+here we have now a graph that already
+
+ align:start position:0%
+here we have now a graph that already
+ 
+
+ align:start position:0%
+here we have now a graph that already
+has a leader it has a distinguished
+
+ align:start position:0%
+has a leader it has a distinguished
+ 
+
+ align:start position:0%
+has a leader it has a distinguished
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+and the process that's sitting there
+
+ align:start position:0%
+and the process that's sitting there
+ 
+
+ align:start position:0%
+and the process that's sitting there
+knows that it's the leader
+
+ align:start position:0%
+knows that it's the leader
+ 
+
+ align:start position:0%
+knows that it's the leader
+uh the processes now are going to
+
+ align:start position:0%
+uh the processes now are going to
+ 
+
+ align:start position:0%
+uh the processes now are going to
+produce a breadth-first spanning tree
+
+ align:start position:0%
+produce a breadth-first spanning tree
+ 
+
+ align:start position:0%
+produce a breadth-first spanning tree
+rooted
+
+ align:start position:0%
+rooted
+ 
+
+ align:start position:0%
+rooted
+at that vertex now for the rest of the
+
+ align:start position:0%
+at that vertex now for the rest of the
+ 
+
+ align:start position:0%
+at that vertex now for the rest of the
+time we'll assume unique identifiers but
+
+ align:start position:0%
+time we'll assume unique identifiers but
+ 
+
+ align:start position:0%
+time we'll assume unique identifiers but
+the processes don't know anything about
+
+ align:start position:0%
+the processes don't know anything about
+ 
+
+ align:start position:0%
+the processes don't know anything about
+the graph except the
+
+ align:start position:0%
+the graph except the
+ 
+
+ align:start position:0%
+the graph except the
+their own id and their neighbor's ids
+
+ align:start position:0%
+their own id and their neighbor's ids
+ 
+
+ align:start position:0%
+their own id and their neighbor's ids
+and we want the processes to eventually
+
+ align:start position:0%
+and we want the processes to eventually
+ 
+
+ align:start position:0%
+and we want the processes to eventually
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+the id of their parent and here's
+
+ align:start position:0%
+the id of their parent and here's
+ 
+
+ align:start position:0%
+the id of their parent and here's
+uh just to repeat uh the simple
+
+ align:start position:0%
+uh just to repeat uh the simple
+ 
+
+ align:start position:0%
+uh just to repeat uh the simple
+algorithm that we used
+
+ align:start position:0%
+algorithm that we used
+ 
+
+ align:start position:0%
+algorithm that we used
+so basically it's uh processes just mark
+
+ align:start position:0%
+so basically it's uh processes just mark
+ 
+
+ align:start position:0%
+so basically it's uh processes just mark
+themselves as they get included in the
+
+ align:start position:0%
+themselves as they get included in the
+ 
+
+ align:start position:0%
+themselves as they get included in the
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+starts out with just the root being
+
+ align:start position:0%
+starts out with just the root being
+ 
+
+ align:start position:0%
+starts out with just the root being
+marked he sends a special search message
+
+ align:start position:0%
+marked he sends a special search message
+ 
+
+ align:start position:0%
+marked he sends a special search message
+out to his neighbors and as soon as they
+
+ align:start position:0%
+out to his neighbors and as soon as they
+ 
+
+ align:start position:0%
+out to his neighbors and as soon as they
+get it they get marked
+
+ align:start position:0%
+get it they get marked
+ 
+
+ align:start position:0%
+get it they get marked
+and pass it on so everybody gets marked
+
+ align:start position:0%
+and pass it on so everybody gets marked
+ 
+
+ align:start position:0%
+and pass it on so everybody gets marked
+in a number of rounds that corresponds
+
+ align:start position:0%
+in a number of rounds that corresponds
+ 
+
+ align:start position:0%
+in a number of rounds that corresponds
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+their depth in the their distance from
+
+ align:start position:0%
+their depth in the their distance from
+ 
+
+ align:start position:0%
+their depth in the their distance from
+the uh the root of the tree depth in the
+
+ align:start position:0%
+the uh the root of the tree depth in the
+ 
+
+ align:start position:0%
+the uh the root of the tree depth in the
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+okay we talked about correctness in
+
+ align:start position:0%
+okay we talked about correctness in
+ 
+
+ align:start position:0%
+okay we talked about correctness in
+terms of invariance so what this
+
+ align:start position:0%
+terms of invariance so what this
+ 
+
+ align:start position:0%
+terms of invariance so what this
+algorithm guarantees is
+
+ align:start position:0%
+algorithm guarantees is
+ 
+
+ align:start position:0%
+algorithm guarantees is
+at the end of any number r of rounds
+
+ align:start position:0%
+at the end of any number r of rounds
+ 
+
+ align:start position:0%
+at the end of any number r of rounds
+exactly the processes at distance up to
+
+ align:start position:0%
+exactly the processes at distance up to
+ 
+
+ align:start position:0%
+exactly the processes at distance up to
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+are marked and the processes
+
+ align:start position:0%
+are marked and the processes
+ 
+
+ align:start position:0%
+are marked and the processes
+that are marked have their parents
+
+ align:start position:0%
+that are marked have their parents
+ 
+
+ align:start position:0%
+that are marked have their parents
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+and if your parents defined it's correct
+
+ align:start position:0%
+and if your parents defined it's correct
+ 
+
+ align:start position:0%
+and if your parents defined it's correct
+it's the uid of a process
+
+ align:start position:0%
+it's the uid of a process
+ 
+
+ align:start position:0%
+it's the uid of a process
+that has distance d minus one from
+
+ align:start position:0%
+that has distance d minus one from
+ 
+
+ align:start position:0%
+that has distance d minus one from
+the root if you're at distance d your
+
+ align:start position:0%
+the root if you're at distance d your
+ 
+
+ align:start position:0%
+the root if you're at distance d your
+parent should be somebody who's
+
+ align:start position:0%
+parent should be somebody who's
+ 
+
+ align:start position:0%
+parent should be somebody who's
+correct has the correct distance d minus
+
+ align:start position:0%
+correct has the correct distance d minus
+ 
+
+ align:start position:0%
+correct has the correct distance d minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay we analyze the complexity time
+
+ align:start position:0%
+okay we analyze the complexity time
+ 
+
+ align:start position:0%
+okay we analyze the complexity time
+is counting the number of rounds and
+
+ align:start position:0%
+is counting the number of rounds and
+ 
+
+ align:start position:0%
+is counting the number of rounds and
+that's going to be at worst the diameter
+
+ align:start position:0%
+that's going to be at worst the diameter
+ 
+
+ align:start position:0%
+that's going to be at worst the diameter
+of the network it's really
+
+ align:start position:0%
+of the network it's really
+ 
+
+ align:start position:0%
+of the network it's really
+the distance from a particular vertex v0
+
+ align:start position:0%
+the distance from a particular vertex v0
+ 
+
+ align:start position:0%
+the distance from a particular vertex v0
+the message complexity uh there's only
+
+ align:start position:0%
+the message complexity uh there's only
+ 
+
+ align:start position:0%
+the message complexity uh there's only
+one message sent in each direction on
+
+ align:start position:0%
+one message sent in each direction on
+ 
+
+ align:start position:0%
+one message sent in each direction on
+each edge so that's going to be only
+
+ align:start position:0%
+each edge so that's going to be only
+ 
+
+ align:start position:0%
+each edge so that's going to be only
+order of the number of edges and we
+
+ align:start position:0%
+order of the number of edges and we
+ 
+
+ align:start position:0%
+order of the number of edges and we
+talked about how you can get
+
+ align:start position:0%
+talked about how you can get
+ 
+
+ align:start position:0%
+talked about how you can get
+child pointers this just gives you
+
+ align:start position:0%
+child pointers this just gives you
+ 
+
+ align:start position:0%
+child pointers this just gives you
+parents but if you want to also find out
+
+ align:start position:0%
+parents but if you want to also find out
+ 
+
+ align:start position:0%
+parents but if you want to also find out
+your children then every
+
+ align:start position:0%
+your children then every
+ 
+
+ align:start position:0%
+your children then every
+search message should get a response
+
+ align:start position:0%
+search message should get a response
+ 
+
+ align:start position:0%
+search message should get a response
+either saying you're my parent or you're
+
+ align:start position:0%
+either saying you're my parent or you're
+ 
+
+ align:start position:0%
+either saying you're my parent or you're
+not my parent
+
+ align:start position:0%
+not my parent
+ 
+
+ align:start position:0%
+not my parent
+and we can do uh termination using
+
+ align:start position:0%
+and we can do uh termination using
+ 
+
+ align:start position:0%
+and we can do uh termination using
+converge cast and
+
+ align:start position:0%
+converge cast and
+ 
+
+ align:start position:0%
+converge cast and
+there's some applications we talked
+
+ align:start position:0%
+there's some applications we talked
+ 
+
+ align:start position:0%
+there's some applications we talked
+about as well
+
+ align:start position:0%
+about as well
+ 
+
+ align:start position:0%
+about as well
+okay all right and then at the end of
+
+ align:start position:0%
+okay all right and then at the end of
+ 
+
+ align:start position:0%
+okay all right and then at the end of
+the hour we
+
+ align:start position:0%
+the hour we
+ 
+
+ align:start position:0%
+the hour we
+started talking about a generalization
+
+ align:start position:0%
+started talking about a generalization
+ 
+
+ align:start position:0%
+started talking about a generalization
+of breadth first spanning trees which
+
+ align:start position:0%
+of breadth first spanning trees which
+ 
+
+ align:start position:0%
+of breadth first spanning trees which
+adds weights
+
+ align:start position:0%
+adds weights
+ 
+
+ align:start position:0%
+adds weights
+so you have shortest paths trees okay so
+
+ align:start position:0%
+so you have shortest paths trees okay so
+ 
+
+ align:start position:0%
+so you have shortest paths trees okay so
+now you have weights on the edges
+
+ align:start position:0%
+now you have weights on the edges
+ 
+
+ align:start position:0%
+now you have weights on the edges
+processes still have unique identifiers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they don't know anything about the graph
+
+ align:start position:0%
+they don't know anything about the graph
+ 
+
+ align:start position:0%
+they don't know anything about the graph
+except their immediate neighborhood
+
+ align:start position:0%
+except their immediate neighborhood
+ 
+
+ align:start position:0%
+except their immediate neighborhood
+information and they have to produce a
+
+ align:start position:0%
+information and they have to produce a
+ 
+
+ align:start position:0%
+information and they have to produce a
+shortest path spanning tree
+
+ align:start position:0%
+shortest path spanning tree
+ 
+
+ align:start position:0%
+shortest path spanning tree
+rooted at a vertex v zero
+
+ align:start position:0%
+rooted at a vertex v zero
+ 
+
+ align:start position:0%
+rooted at a vertex v zero
+okay so you know what a spanning tree is
+
+ align:start position:0%
+okay so you know what a spanning tree is
+ 
+
+ align:start position:0%
+okay so you know what a spanning tree is
+and shortest paths are in terms of the
+
+ align:start position:0%
+and shortest paths are in terms of the
+ 
+
+ align:start position:0%
+and shortest paths are in terms of the
+total weight of the path
+
+ align:start position:0%
+total weight of the path
+ 
+
+ align:start position:0%
+total weight of the path
+so now we want each node each process to
+
+ align:start position:0%
+so now we want each node each process to
+ 
+
+ align:start position:0%
+so now we want each node each process to
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+its parent in the shortest path and also
+
+ align:start position:0%
+its parent in the shortest path and also
+ 
+
+ align:start position:0%
+its parent in the shortest path and also
+the distance from
+
+ align:start position:0%
+the distance from
+ 
+
+ align:start position:0%
+the distance from
+the original vertex v0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so at the end of the hour we looked
+
+ align:start position:0%
+okay so at the end of the hour we looked
+ 
+
+ align:start position:0%
+okay so at the end of the hour we looked
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+a version of bellman ford which you've
+
+ align:start position:0%
+a version of bellman ford which you've
+ 
+
+ align:start position:0%
+a version of bellman ford which you've
+already seen
+
+ align:start position:0%
+already seen
+ 
+
+ align:start position:0%
+already seen
+for sequential algorithm as a sequential
+
+ align:start position:0%
+for sequential algorithm as a sequential
+ 
+
+ align:start position:0%
+for sequential algorithm as a sequential
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+but as a distributed algorithm everybody
+
+ align:start position:0%
+but as a distributed algorithm everybody
+ 
+
+ align:start position:0%
+but as a distributed algorithm everybody
+keeps track of their best guess
+
+ align:start position:0%
+keeps track of their best guess
+ 
+
+ align:start position:0%
+keeps track of their best guess
+their best current guess of the distance
+
+ align:start position:0%
+their best current guess of the distance
+ 
+
+ align:start position:0%
+their best current guess of the distance
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+the initial vertex and they keep track
+
+ align:start position:0%
+the initial vertex and they keep track
+ 
+
+ align:start position:0%
+the initial vertex and they keep track
+of their
+
+ align:start position:0%
+of their
+ 
+
+ align:start position:0%
+of their
+parent on some path that gave it
+
+ align:start position:0%
+parent on some path that gave it
+ 
+
+ align:start position:0%
+parent on some path that gave it
+this distance estimate and they keep
+
+ align:start position:0%
+this distance estimate and they keep
+ 
+
+ align:start position:0%
+this distance estimate and they keep
+their unique identifier
+
+ align:start position:0%
+their unique identifier
+ 
+
+ align:start position:0%
+their unique identifier
+okay so the complete algorithm now is
+
+ align:start position:0%
+okay so the complete algorithm now is
+ 
+
+ align:start position:0%
+okay so the complete algorithm now is
+everybody's going to keep sending their
+
+ align:start position:0%
+everybody's going to keep sending their
+ 
+
+ align:start position:0%
+everybody's going to keep sending their
+distance around i mean we could optimize
+
+ align:start position:0%
+distance around i mean we could optimize
+ 
+
+ align:start position:0%
+distance around i mean we could optimize
+that but
+
+ align:start position:0%
+that but
+ 
+
+ align:start position:0%
+that but
+this is simple so at every round
+
+ align:start position:0%
+this is simple so at every round
+ 
+
+ align:start position:0%
+this is simple so at every round
+everybody sends
+
+ align:start position:0%
+everybody sends
+ 
+
+ align:start position:0%
+everybody sends
+their current distance estimate to all
+
+ align:start position:0%
+their current distance estimate to all
+ 
+
+ align:start position:0%
+their current distance estimate to all
+their neighbors they all they collect
+
+ align:start position:0%
+their neighbors they all they collect
+ 
+
+ align:start position:0%
+their neighbors they all they collect
+the distance estimates from all their
+
+ align:start position:0%
+the distance estimates from all their
+ 
+
+ align:start position:0%
+the distance estimates from all their
+neighbors
+
+ align:start position:0%
+neighbors
+ 
+
+ align:start position:0%
+neighbors
+and then they do a relaxation step if
+
+ align:start position:0%
+and then they do a relaxation step if
+ 
+
+ align:start position:0%
+and then they do a relaxation step if
+they get anything that's better than
+
+ align:start position:0%
+they get anything that's better than
+ 
+
+ align:start position:0%
+they get anything that's better than
+what they had before
+
+ align:start position:0%
+what they had before
+ 
+
+ align:start position:0%
+what they had before
+they look at the best new estimate they
+
+ align:start position:0%
+they look at the best new estimate they
+ 
+
+ align:start position:0%
+they look at the best new estimate they
+could get so they take the minimum of
+
+ align:start position:0%
+could get so they take the minimum of
+ 
+
+ align:start position:0%
+could get so they take the minimum of
+their old estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stop shaking good and the minimum
+
+ align:start position:0%
+stop shaking good and the minimum
+ 
+
+ align:start position:0%
+stop shaking good and the minimum
+of uh all of the uh estimates they would
+
+ align:start position:0%
+of uh all of the uh estimates they would
+ 
+
+ align:start position:0%
+of uh all of the uh estimates they would
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+by looking at the incoming information
+
+ align:start position:0%
+by looking at the incoming information
+ 
+
+ align:start position:0%
+by looking at the incoming information
+plus adding the weight
+
+ align:start position:0%
+plus adding the weight
+ 
+
+ align:start position:0%
+plus adding the weight
+of the edge between the sender
+
+ align:start position:0%
+of the edge between the sender
+ 
+
+ align:start position:0%
+of the edge between the sender
+and and the note itself okay so this way
+
+ align:start position:0%
+and and the note itself okay so this way
+ 
+
+ align:start position:0%
+and and the note itself okay so this way
+you get a better
+
+ align:start position:0%
+you get a better
+ 
+
+ align:start position:0%
+you get a better
+you may get a better estimate and if you
+
+ align:start position:0%
+you may get a better estimate and if you
+ 
+
+ align:start position:0%
+you may get a better estimate and if you
+do you you would reset your parent
+
+ align:start position:0%
+do you you would reset your parent
+ 
+
+ align:start position:0%
+do you you would reset your parent
+to be the sender of this
+
+ align:start position:0%
+to be the sender of this
+ 
+
+ align:start position:0%
+to be the sender of this
+improved information and again you can
+
+ align:start position:0%
+improved information and again you can
+ 
+
+ align:start position:0%
+improved information and again you can
+pick
+
+ align:start position:0%
+pick
+ 
+
+ align:start position:0%
+pick
+if there's a tie you can pick um
+
+ align:start position:0%
+if there's a tie you can pick um
+ 
+
+ align:start position:0%
+if there's a tie you can pick um
+any of the the nodes that sends the the
+
+ align:start position:0%
+any of the the nodes that sends the the
+ 
+
+ align:start position:0%
+any of the the nodes that sends the the
+information leading to the the best
+
+ align:start position:0%
+information leading to the the best
+ 
+
+ align:start position:0%
+information leading to the the best
+new guess you can set your parent to any
+
+ align:start position:0%
+new guess you can set your parent to any
+ 
+
+ align:start position:0%
+new guess you can set your parent to any
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+okay and then this just repeats
+
+ align:start position:0%
+okay and then this just repeats
+ 
+
+ align:start position:0%
+okay and then this just repeats
+okay so at the very end of the hour we
+
+ align:start position:0%
+okay so at the very end of the hour we
+ 
+
+ align:start position:0%
+okay so at the very end of the hour we
+we showed a
+
+ align:start position:0%
+we showed a
+ 
+
+ align:start position:0%
+we showed a
+an animation which i'm not going to
+
+ align:start position:0%
+an animation which i'm not going to
+ 
+
+ align:start position:0%
+an animation which i'm not going to
+repeat now which basically shows how you
+
+ align:start position:0%
+repeat now which basically shows how you
+ 
+
+ align:start position:0%
+repeat now which basically shows how you
+can get lots of
+
+ align:start position:0%
+can get lots of
+ 
+
+ align:start position:0%
+can get lots of
+corrections there you can have
+
+ align:start position:0%
+corrections there you can have
+ 
+
+ align:start position:0%
+corrections there you can have
+many pads that are set up that look good
+
+ align:start position:0%
+many pads that are set up that look good
+ 
+
+ align:start position:0%
+many pads that are set up that look good
+after just one round but then they get
+
+ align:start position:0%
+after just one round but then they get
+ 
+
+ align:start position:0%
+after just one round but then they get
+corrected
+
+ align:start position:0%
+corrected
+ 
+
+ align:start position:0%
+corrected
+as the rounds go on so you get much
+
+ align:start position:0%
+as the rounds go on so you get much
+ 
+
+ align:start position:0%
+as the rounds go on so you get much
+lower weight paths by having a
+
+ align:start position:0%
+lower weight paths by having a
+ 
+
+ align:start position:0%
+lower weight paths by having a
+roundabout
+
+ align:start position:0%
+roundabout
+ 
+
+ align:start position:0%
+roundabout
+multi-hop path to a node you can get a
+
+ align:start position:0%
+multi-hop path to a node you can get a
+ 
+
+ align:start position:0%
+multi-hop path to a node you can get a
+better total cost
+
+ align:start position:0%
+better total cost
+ 
+
+ align:start position:0%
+better total cost
+okay so here's where we got to last time
+
+ align:start position:0%
+okay so here's where we got to last time
+ 
+
+ align:start position:0%
+okay so here's where we got to last time
+so now why does this work well what we
+
+ align:start position:0%
+so now why does this work well what we
+ 
+
+ align:start position:0%
+so now why does this work well what we
+need is eventually
+
+ align:start position:0%
+need is eventually
+ 
+
+ align:start position:0%
+need is eventually
+every process should get the correct
+
+ align:start position:0%
+every process should get the correct
+ 
+
+ align:start position:0%
+every process should get the correct
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+and the parent should be its predecessor
+
+ align:start position:0%
+and the parent should be its predecessor
+ 
+
+ align:start position:0%
+and the parent should be its predecessor
+on some shortest path
+
+ align:start position:0%
+on some shortest path
+ 
+
+ align:start position:0%
+on some shortest path
+in order to prove that okay so you
+
+ align:start position:0%
+in order to prove that okay so you
+ 
+
+ align:start position:0%
+in order to prove that okay so you
+always look for an invariant
+
+ align:start position:0%
+always look for an invariant
+ 
+
+ align:start position:0%
+always look for an invariant
+something that's true at intermediate
+
+ align:start position:0%
+something that's true at intermediate
+ 
+
+ align:start position:0%
+something that's true at intermediate
+steps of the algorithm that you can show
+
+ align:start position:0%
+steps of the algorithm that you can show
+ 
+
+ align:start position:0%
+steps of the algorithm that you can show
+by induction will hold and that will
+
+ align:start position:0%
+by induction will hold and that will
+ 
+
+ align:start position:0%
+by induction will hold and that will
+imply the result that you want at the
+
+ align:start position:0%
+imply the result that you want at the
+ 
+
+ align:start position:0%
+imply the result that you want at the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+so here um what's the key invariant at
+
+ align:start position:0%
+so here um what's the key invariant at
+ 
+
+ align:start position:0%
+so here um what's the key invariant at
+the end
+
+ align:start position:0%
+the end
+ 
+
+ align:start position:0%
+the end
+of some number r of rounds
+
+ align:start position:0%
+of some number r of rounds
+ 
+
+ align:start position:0%
+of some number r of rounds
+what do processes have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay after r rounds have passed in this
+
+ align:start position:0%
+okay after r rounds have passed in this
+ 
+
+ align:start position:0%
+okay after r rounds have passed in this
+kind of algorithm
+
+ align:start position:0%
+kind of algorithm
+ 
+
+ align:start position:0%
+kind of algorithm
+what what do the estimates look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well after one round everybody's got
+
+ align:start position:0%
+well after one round everybody's got
+ 
+
+ align:start position:0%
+well after one round everybody's got
+their best
+
+ align:start position:0%
+their best
+ 
+
+ align:start position:0%
+their best
+estimate uh that could happen on a
+
+ align:start position:0%
+estimate uh that could happen on a
+ 
+
+ align:start position:0%
+estimate uh that could happen on a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+that could result from a single hot path
+
+ align:start position:0%
+that could result from a single hot path
+ 
+
+ align:start position:0%
+that could result from a single hot path
+from v zero
+
+ align:start position:0%
+from v zero
+ 
+
+ align:start position:0%
+from v zero
+after two rounds you also get the best
+
+ align:start position:0%
+after two rounds you also get the best
+ 
+
+ align:start position:0%
+after two rounds you also get the best
+guesses from two hot pads
+
+ align:start position:0%
+guesses from two hot pads
+ 
+
+ align:start position:0%
+guesses from two hot pads
+and after r rounds in general um you
+
+ align:start position:0%
+and after r rounds in general um you
+ 
+
+ align:start position:0%
+and after r rounds in general um you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+your distance and parent corresponding
+
+ align:start position:0%
+your distance and parent corresponding
+ 
+
+ align:start position:0%
+your distance and parent corresponding
+to a shortest path
+
+ align:start position:0%
+to a shortest path
+ 
+
+ align:start position:0%
+to a shortest path
+chosen from among those that have it
+
+ align:start position:0%
+chosen from among those that have it
+ 
+
+ align:start position:0%
+chosen from among those that have it
+most are hops
+
+ align:start position:0%
+most are hops
+ 
+
+ align:start position:0%
+most are hops
+yes that makes sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no yeah okay all right and
+
+ align:start position:0%
+no yeah okay all right and
+ 
+
+ align:start position:0%
+no yeah okay all right and
+if there is no path of our hops or fewer
+
+ align:start position:0%
+if there is no path of our hops or fewer
+ 
+
+ align:start position:0%
+if there is no path of our hops or fewer
+to get to a node they're still going to
+
+ align:start position:0%
+to get to a node they're still going to
+ 
+
+ align:start position:0%
+to get to a node they're still going to
+have their distance estimate be
+
+ align:start position:0%
+have their distance estimate be
+ 
+
+ align:start position:0%
+have their distance estimate be
+infinity after r rounds
+
+ align:start position:0%
+infinity after r rounds
+ 
+
+ align:start position:0%
+infinity after r rounds
+so this is not a complete proof but it's
+
+ align:start position:0%
+so this is not a complete proof but it's
+ 
+
+ align:start position:0%
+so this is not a complete proof but it's
+the key invariant that makes this work
+
+ align:start position:0%
+the key invariant that makes this work
+ 
+
+ align:start position:0%
+the key invariant that makes this work
+so you can see that after
+
+ align:start position:0%
+so you can see that after
+ 
+
+ align:start position:0%
+so you can see that after
+enough rounds corresponding to the
+
+ align:start position:0%
+enough rounds corresponding to the
+ 
+
+ align:start position:0%
+enough rounds corresponding to the
+number of nodes for example
+
+ align:start position:0%
+number of nodes for example
+ 
+
+ align:start position:0%
+number of nodes for example
+everybody will have the correct shortest
+
+ align:start position:0%
+everybody will have the correct shortest
+ 
+
+ align:start position:0%
+everybody will have the correct shortest
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+of any length okay
+
+ align:start position:0%
+of any length okay
+ 
+
+ align:start position:0%
+of any length okay
+so the number of rounds until every
+
+ align:start position:0%
+so the number of rounds until every
+ 
+
+ align:start position:0%
+so the number of rounds until every
+estimate stabilized all the estimates
+
+ align:start position:0%
+estimate stabilized all the estimates
+ 
+
+ align:start position:0%
+estimate stabilized all the estimates
+stabilize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to be n minus 1 right
+
+ align:start position:0%
+it's going to be n minus 1 right
+ 
+
+ align:start position:0%
+it's going to be n minus 1 right
+because the longest simple path
+
+ align:start position:0%
+because the longest simple path
+ 
+
+ align:start position:0%
+because the longest simple path
+to any node is going to be n minus 1 if
+
+ align:start position:0%
+to any node is going to be n minus 1 if
+ 
+
+ align:start position:0%
+to any node is going to be n minus 1 if
+it goes through all the nodes
+
+ align:start position:0%
+it goes through all the nodes
+ 
+
+ align:start position:0%
+it goes through all the nodes
+of the network before reaching it makes
+
+ align:start position:0%
+of the network before reaching it makes
+ 
+
+ align:start position:0%
+of the network before reaching it makes
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+so if you want to make sure you have the
+
+ align:start position:0%
+so if you want to make sure you have the
+ 
+
+ align:start position:0%
+so if you want to make sure you have the
+best estimate you have to wait n
+
+ align:start position:0%
+best estimate you have to wait n
+ 
+
+ align:start position:0%
+best estimate you have to wait n
+minus 1 rounds to make sure the
+
+ align:start position:0%
+minus 1 rounds to make sure the
+ 
+
+ align:start position:0%
+minus 1 rounds to make sure the
+information has reached you
+
+ align:start position:0%
+information has reached you
+ 
+
+ align:start position:0%
+information has reached you
+the message complexity well that since
+
+ align:start position:0%
+the message complexity well that since
+ 
+
+ align:start position:0%
+the message complexity well that since
+there's all these repeated estimates
+
+ align:start position:0%
+there's all these repeated estimates
+ 
+
+ align:start position:0%
+there's all these repeated estimates
+it's no longer just
+
+ align:start position:0%
+it's no longer just
+ 
+
+ align:start position:0%
+it's no longer just
+proportional to the number of edges but
+
+ align:start position:0%
+proportional to the number of edges but
+ 
+
+ align:start position:0%
+proportional to the number of edges but
+you have to take into account that there
+
+ align:start position:0%
+you have to take into account that there
+ 
+
+ align:start position:0%
+you have to take into account that there
+can be many new estimates sent
+
+ align:start position:0%
+can be many new estimates sent
+ 
+
+ align:start position:0%
+can be many new estimates sent
+on on each edge in fact the way i've
+
+ align:start position:0%
+on on each edge in fact the way i've
+ 
+
+ align:start position:0%
+on on each edge in fact the way i've
+written this
+
+ align:start position:0%
+written this
+ 
+
+ align:start position:0%
+written this
+you just keep sending your distance at
+
+ align:start position:0%
+you just keep sending your distance at
+ 
+
+ align:start position:0%
+you just keep sending your distance at
+every round so it's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number of edges times the number of
+
+ align:start position:0%
+the number of edges times the number of
+ 
+
+ align:start position:0%
+the number of edges times the number of
+rounds so
+
+ align:start position:0%
+rounds so
+ 
+
+ align:start position:0%
+rounds so
+you know you can do somewhat better than
+
+ align:start position:0%
+you know you can do somewhat better than
+ 
+
+ align:start position:0%
+you know you can do somewhat better than
+this but it's worse than
+
+ align:start position:0%
+this but it's worse than
+ 
+
+ align:start position:0%
+this but it's worse than
+than just the simple bfs case
+
+ align:start position:0%
+than just the simple bfs case
+ 
+
+ align:start position:0%
+than just the simple bfs case
+okay so this is more expensive because
+
+ align:start position:0%
+okay so this is more expensive because
+ 
+
+ align:start position:0%
+okay so this is more expensive because
+bfs just had
+
+ align:start position:0%
+bfs just had
+ 
+
+ align:start position:0%
+bfs just had
+diameter rounds and this now has n
+
+ align:start position:0%
+diameter rounds and this now has n
+ 
+
+ align:start position:0%
+diameter rounds and this now has n
+or n minus one rounds and bfs just had
+
+ align:start position:0%
+or n minus one rounds and bfs just had
+ 
+
+ align:start position:0%
+or n minus one rounds and bfs just had
+one message
+
+ align:start position:0%
+one message
+ 
+
+ align:start position:0%
+one message
+ever sent on each edge and now we have
+
+ align:start position:0%
+ever sent on each edge and now we have
+ 
+
+ align:start position:0%
+ever sent on each edge and now we have
+to send many
+
+ align:start position:0%
+to send many
+ 
+
+ align:start position:0%
+to send many
+comments questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so is it clear that the time
+
+ align:start position:0%
+okay okay so is it clear that the time
+ 
+
+ align:start position:0%
+okay okay so is it clear that the time
+bound really does depend on
+
+ align:start position:0%
+bound really does depend on
+ 
+
+ align:start position:0%
+bound really does depend on
+n and not on the diameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for breadth-first search it was
+
+ align:start position:0%
+okay for breadth-first search it was
+ 
+
+ align:start position:0%
+okay for breadth-first search it was
+enough just to
+
+ align:start position:0%
+enough just to
+ 
+
+ align:start position:0%
+enough just to
+um have enough rounds to correspond to
+
+ align:start position:0%
+um have enough rounds to correspond to
+ 
+
+ align:start position:0%
+um have enough rounds to correspond to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance and hops to each node but now
+
+ align:start position:0%
+distance and hops to each node but now
+ 
+
+ align:start position:0%
+distance and hops to each node but now
+you need enough rounds to take care of
+
+ align:start position:0%
+you need enough rounds to take care of
+ 
+
+ align:start position:0%
+you need enough rounds to take care of
+these indirect pads that might go
+
+ align:start position:0%
+these indirect pads that might go
+ 
+
+ align:start position:0%
+these indirect pads that might go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+many nodes but still end up with a
+
+ align:start position:0%
+many nodes but still end up with a
+ 
+
+ align:start position:0%
+many nodes but still end up with a
+shorter
+
+ align:start position:0%
+shorter
+ 
+
+ align:start position:0%
+shorter
+with a smaller total weight okay so is
+
+ align:start position:0%
+with a smaller total weight okay so is
+ 
+
+ align:start position:0%
+with a smaller total weight okay so is
+it clear to everybody why the bound
+
+ align:start position:0%
+it clear to everybody why the bound
+ 
+
+ align:start position:0%
+it clear to everybody why the bound
+depends on
+
+ align:start position:0%
+depends on
+ 
+
+ align:start position:0%
+depends on
+n actually the animation that i had last
+
+ align:start position:0%
+n actually the animation that i had last
+ 
+
+ align:start position:0%
+n actually the animation that i had last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+showed uh how there were lots of
+
+ align:start position:0%
+showed uh how there were lots of
+ 
+
+ align:start position:0%
+showed uh how there were lots of
+corrections and and
+
+ align:start position:0%
+corrections and and
+ 
+
+ align:start position:0%
+corrections and and
+you had enough you had rounds that
+
+ align:start position:0%
+you had enough you had rounds that
+ 
+
+ align:start position:0%
+you had enough you had rounds that
+depended on the total number of nodes
+
+ align:start position:0%
+depended on the total number of nodes
+ 
+
+ align:start position:0%
+depended on the total number of nodes
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um but like could you like keep
+
+ align:start position:0%
+yeah um but like could you like keep
+ 
+
+ align:start position:0%
+yeah um but like could you like keep
+track of like
+
+ align:start position:0%
+track of like
+ 
+
+ align:start position:0%
+track of like
+uh each round if if the values if any of
+
+ align:start position:0%
+uh each round if if the values if any of
+ 
+
+ align:start position:0%
+uh each round if if the values if any of
+the guys didn't
+
+ align:start position:0%
+the guys didn't
+ 
+
+ align:start position:0%
+the guys didn't
+relax so like if you if everything stops
+
+ align:start position:0%
+relax so like if you if everything stops
+ 
+
+ align:start position:0%
+relax so like if you if everything stops
+changing after less than n rounds
+
+ align:start position:0%
+changing after less than n rounds
+ 
+
+ align:start position:0%
+changing after less than n rounds
+you might not have to okay so you're
+
+ align:start position:0%
+you might not have to okay so you're
+ 
+
+ align:start position:0%
+you might not have to okay so you're
+asking about termination
+
+ align:start position:0%
+asking about termination
+ 
+
+ align:start position:0%
+asking about termination
+ah okay well so that's probably the next
+
+ align:start position:0%
+ah okay well so that's probably the next
+ 
+
+ align:start position:0%
+ah okay well so that's probably the next
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+first let's deal with the child pointers
+
+ align:start position:0%
+first let's deal with the child pointers
+ 
+
+ align:start position:0%
+first let's deal with the child pointers
+and we'll come back to termination okay
+
+ align:start position:0%
+and we'll come back to termination okay
+ 
+
+ align:start position:0%
+and we'll come back to termination okay
+so first this just gives you your
+
+ align:start position:0%
+so first this just gives you your
+ 
+
+ align:start position:0%
+so first this just gives you your
+parents if you want your children you
+
+ align:start position:0%
+parents if you want your children you
+ 
+
+ align:start position:0%
+parents if you want your children you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+do the same thing that we did last time
+
+ align:start position:0%
+do the same thing that we did last time
+ 
+
+ align:start position:0%
+do the same thing that we did last time
+when a process gets a message
+
+ align:start position:0%
+when a process gets a message
+ 
+
+ align:start position:0%
+when a process gets a message
+and the message doesn't make the sender
+
+ align:start position:0%
+and the message doesn't make the sender
+ 
+
+ align:start position:0%
+and the message doesn't make the sender
+its parent
+
+ align:start position:0%
+its parent
+ 
+
+ align:start position:0%
+its parent
+this is not giving it an improved
+
+ align:start position:0%
+this is not giving it an improved
+ 
+
+ align:start position:0%
+this is not giving it an improved
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+then the node can just respond
+
+ align:start position:0%
+then the node can just respond
+ 
+
+ align:start position:0%
+then the node can just respond
+non-parent
+
+ align:start position:0%
+non-parent
+ 
+
+ align:start position:0%
+non-parent
+but if a process receives a message that
+
+ align:start position:0%
+but if a process receives a message that
+ 
+
+ align:start position:0%
+but if a process receives a message that
+does improve the distance it says
+
+ align:start position:0%
+does improve the distance it says
+ 
+
+ align:start position:0%
+does improve the distance it says
+ah okay you are my parent but
+
+ align:start position:0%
+ah okay you are my parent but
+ 
+
+ align:start position:0%
+ah okay you are my parent but
+it might have also told another node it
+
+ align:start position:0%
+it might have also told another node it
+ 
+
+ align:start position:0%
+it might have also told another node it
+might have another parent another node
+
+ align:start position:0%
+might have another parent another node
+ 
+
+ align:start position:0%
+might have another parent another node
+that previously it thought was
+
+ align:start position:0%
+that previously it thought was
+ 
+
+ align:start position:0%
+that previously it thought was
+his parent so it has to do more work in
+
+ align:start position:0%
+his parent so it has to do more work in
+ 
+
+ align:start position:0%
+his parent so it has to do more work in
+this case to correct the erroneous
+
+ align:start position:0%
+this case to correct the erroneous
+ 
+
+ align:start position:0%
+this case to correct the erroneous
+parent information
+
+ align:start position:0%
+parent information
+ 
+
+ align:start position:0%
+parent information
+so it has to send its previous
+
+ align:start position:0%
+so it has to send its previous
+ 
+
+ align:start position:0%
+so it has to send its previous
+parent a non-parent message to correct
+
+ align:start position:0%
+parent a non-parent message to correct
+ 
+
+ align:start position:0%
+parent a non-parent message to correct
+the previous parent message
+
+ align:start position:0%
+the previous parent message
+ 
+
+ align:start position:0%
+the previous parent message
+okay so things are getting a little bit
+
+ align:start position:0%
+okay so things are getting a little bit
+ 
+
+ align:start position:0%
+okay so things are getting a little bit
+trickier here
+
+ align:start position:0%
+trickier here
+ 
+
+ align:start position:0%
+trickier here
+on the other end if somebody is keeping
+
+ align:start position:0%
+on the other end if somebody is keeping
+ 
+
+ align:start position:0%
+on the other end if somebody is keeping
+track of its children it has to
+
+ align:start position:0%
+track of its children it has to
+ 
+
+ align:start position:0%
+track of its children it has to
+make adjustments to is because things
+
+ align:start position:0%
+make adjustments to is because things
+ 
+
+ align:start position:0%
+make adjustments to is because things
+can change during the algorithm
+
+ align:start position:0%
+can change during the algorithm
+ 
+
+ align:start position:0%
+can change during the algorithm
+okay so let's say a process keeps track
+
+ align:start position:0%
+okay so let's say a process keeps track
+ 
+
+ align:start position:0%
+okay so let's say a process keeps track
+of its children in some set
+
+ align:start position:0%
+of its children in some set
+ 
+
+ align:start position:0%
+of its children in some set
+it has a set children okay if it gets a
+
+ align:start position:0%
+it has a set children okay if it gets a
+ 
+
+ align:start position:0%
+it has a set children okay if it gets a
+non-parent message from a child
+
+ align:start position:0%
+non-parent message from a child
+ 
+
+ align:start position:0%
+non-parent message from a child
+even if that child that child might be
+
+ align:start position:0%
+even if that child that child might be
+ 
+
+ align:start position:0%
+even if that child that child might be
+or from a neighbor
+
+ align:start position:0%
+or from a neighbor
+ 
+
+ align:start position:0%
+or from a neighbor
+that neighbor might be and it set
+
+ align:start position:0%
+that neighbor might be and it set
+ 
+
+ align:start position:0%
+that neighbor might be and it set
+children and this could be a correction
+
+ align:start position:0%
+children and this could be a correction
+ 
+
+ align:start position:0%
+children and this could be a correction
+then the process has to take that
+
+ align:start position:0%
+then the process has to take that
+ 
+
+ align:start position:0%
+then the process has to take that
+neighbor out of the set of children
+
+ align:start position:0%
+neighbor out of the set of children
+ 
+
+ align:start position:0%
+neighbor out of the set of children
+okay and suppose the process
+
+ align:start position:0%
+okay and suppose the process
+ 
+
+ align:start position:0%
+okay and suppose the process
+improves its own distance well now it's
+
+ align:start position:0%
+improves its own distance well now it's
+ 
+
+ align:start position:0%
+improves its own distance well now it's
+kind of starting over
+
+ align:start position:0%
+kind of starting over
+ 
+
+ align:start position:0%
+kind of starting over
+it's going to send that distance to its
+
+ align:start position:0%
+it's going to send that distance to its
+ 
+
+ align:start position:0%
+it's going to send that distance to its
+all of its neighbors again
+
+ align:start position:0%
+all of its neighbors again
+ 
+
+ align:start position:0%
+all of its neighbors again
+and collect new information about
+
+ align:start position:0%
+and collect new information about
+ 
+
+ align:start position:0%
+and collect new information about
+whether they're children or not so
+
+ align:start position:0%
+whether they're children or not so
+ 
+
+ align:start position:0%
+whether they're children or not so
+the simple thing to do here is just
+
+ align:start position:0%
+the simple thing to do here is just
+ 
+
+ align:start position:0%
+the simple thing to do here is just
+empty
+
+ align:start position:0%
+empty
+ 
+
+ align:start position:0%
+empty
+zero out your children set and start
+
+ align:start position:0%
+zero out your children set and start
+ 
+
+ align:start position:0%
+zero out your children set and start
+over now you send
+
+ align:start position:0%
+over now you send
+ 
+
+ align:start position:0%
+over now you send
+your your new messages to your neighbors
+
+ align:start position:0%
+your your new messages to your neighbors
+ 
+
+ align:start position:0%
+your your new messages to your neighbors
+and wait for them to respond again
+
+ align:start position:0%
+and wait for them to respond again
+ 
+
+ align:start position:0%
+and wait for them to respond again
+so there's tricky bookkeeping to do to
+
+ align:start position:0%
+so there's tricky bookkeeping to do to
+ 
+
+ align:start position:0%
+so there's tricky bookkeeping to do to
+handle corrections
+
+ align:start position:0%
+handle corrections
+ 
+
+ align:start position:0%
+handle corrections
+as the structure of this tree changes so
+
+ align:start position:0%
+as the structure of this tree changes so
+ 
+
+ align:start position:0%
+as the structure of this tree changes so
+getting child pointers is a little more
+
+ align:start position:0%
+getting child pointers is a little more
+ 
+
+ align:start position:0%
+getting child pointers is a little more
+complicated than before
+
+ align:start position:0%
+complicated than before
+ 
+
+ align:start position:0%
+complicated than before
+make sense okay all right so now back to
+
+ align:start position:0%
+make sense okay all right so now back to
+ 
+
+ align:start position:0%
+make sense okay all right so now back to
+your question
+
+ align:start position:0%
+your question
+ 
+
+ align:start position:0%
+your question
+uh termination um
+
+ align:start position:0%
+uh termination um
+ 
+
+ align:start position:0%
+uh termination um
+so how do all the processes know when
+
+ align:start position:0%
+so how do all the processes know when
+ 
+
+ align:start position:0%
+so how do all the processes know when
+the tree
+
+ align:start position:0%
+the tree
+ 
+
+ align:start position:0%
+the tree
+is complete in fact we have a worse
+
+ align:start position:0%
+is complete in fact we have a worse
+ 
+
+ align:start position:0%
+is complete in fact we have a worse
+problem we this problem we hit for
+
+ align:start position:0%
+problem we this problem we hit for
+ 
+
+ align:start position:0%
+problem we this problem we hit for
+a breath first search but we have an
+
+ align:start position:0%
+a breath first search but we have an
+ 
+
+ align:start position:0%
+a breath first search but we have an
+even worse problem now what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+before we had each individual node once
+
+ align:start position:0%
+before we had each individual node once
+ 
+
+ align:start position:0%
+before we had each individual node once
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+figured out who its parent was it could
+
+ align:start position:0%
+figured out who its parent was it could
+ 
+
+ align:start position:0%
+figured out who its parent was it could
+just output that
+
+ align:start position:0%
+just output that
+ 
+
+ align:start position:0%
+just output that
+and now you can figure out your parent
+
+ align:start position:0%
+and now you can figure out your parent
+ 
+
+ align:start position:0%
+and now you can figure out your parent
+but it's just a guess
+
+ align:start position:0%
+but it's just a guess
+ 
+
+ align:start position:0%
+but it's just a guess
+and you don't know when you can output
+
+ align:start position:0%
+and you don't know when you can output
+ 
+
+ align:start position:0%
+and you don't know when you can output
+this so how does a process
+
+ align:start position:0%
+this so how does a process
+ 
+
+ align:start position:0%
+this so how does a process
+even an individual process even figure
+
+ align:start position:0%
+even an individual process even figure
+ 
+
+ align:start position:0%
+even an individual process even figure
+out its own parent and distance
+
+ align:start position:0%
+out its own parent and distance
+ 
+
+ align:start position:0%
+out its own parent and distance
+so there's two aspects here
+
+ align:start position:0%
+so there's two aspects here
+ 
+
+ align:start position:0%
+so there's two aspects here
+determination one is how do you know the
+
+ align:start position:0%
+determination one is how do you know the
+ 
+
+ align:start position:0%
+determination one is how do you know the
+whole thing is finished
+
+ align:start position:0%
+whole thing is finished
+ 
+
+ align:start position:0%
+whole thing is finished
+but the other one is even how do you
+
+ align:start position:0%
+but the other one is even how do you
+ 
+
+ align:start position:0%
+but the other one is even how do you
+know when you're done with your own
+
+ align:start position:0%
+know when you're done with your own
+ 
+
+ align:start position:0%
+know when you're done with your own
+parent and distance
+
+ align:start position:0%
+parent and distance
+ 
+
+ align:start position:0%
+parent and distance
+okay well you know if you knew something
+
+ align:start position:0%
+okay well you know if you knew something
+ 
+
+ align:start position:0%
+okay well you know if you knew something
+about the graph like an upper bound on
+
+ align:start position:0%
+about the graph like an upper bound on
+ 
+
+ align:start position:0%
+about the graph like an upper bound on
+the total number of nodes then you could
+
+ align:start position:0%
+the total number of nodes then you could
+ 
+
+ align:start position:0%
+the total number of nodes then you could
+just wait until that number of rounds
+
+ align:start position:0%
+just wait until that number of rounds
+ 
+
+ align:start position:0%
+just wait until that number of rounds
+and be done but what if you
+
+ align:start position:0%
+and be done but what if you
+ 
+
+ align:start position:0%
+and be done but what if you
+don't have that information about the
+
+ align:start position:0%
+don't have that information about the
+ 
+
+ align:start position:0%
+don't have that information about the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+what might you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we yeah down the information when we
+
+ align:start position:0%
+we yeah down the information when we
+ 
+
+ align:start position:0%
+we yeah down the information when we
+reach
+
+ align:start position:0%
+reach
+ 
+
+ align:start position:0%
+reach
+the size of the graph oh maybe i think
+
+ align:start position:0%
+the size of the graph oh maybe i think
+ 
+
+ align:start position:0%
+the size of the graph oh maybe i think
+okay what is the strategy we use for
+
+ align:start position:0%
+okay what is the strategy we use for
+ 
+
+ align:start position:0%
+okay what is the strategy we use for
+termination for bfs
+
+ align:start position:0%
+termination for bfs
+ 
+
+ align:start position:0%
+termination for bfs
+let's start with that one it's a little
+
+ align:start position:0%
+let's start with that one it's a little
+ 
+
+ align:start position:0%
+let's start with that one it's a little
+easier
+
+ align:start position:0%
+easier
+ 
+
+ align:start position:0%
+easier
+you did the subtree thing we call
+
+ align:start position:0%
+you did the subtree thing we call
+ 
+
+ align:start position:0%
+you did the subtree thing we call
+converge cast the information
+
+ align:start position:0%
+converge cast the information
+ 
+
+ align:start position:0%
+converge cast the information
+when you had a leaf he knew he was a
+
+ align:start position:0%
+when you had a leaf he knew he was a
+ 
+
+ align:start position:0%
+when you had a leaf he knew he was a
+leaf and he could send his done
+
+ align:start position:0%
+leaf and he could send his done
+ 
+
+ align:start position:0%
+leaf and he could send his done
+information up to his parent and that
+
+ align:start position:0%
+information up to his parent and that
+ 
+
+ align:start position:0%
+information up to his parent and that
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+converged cast up to the top of the tree
+
+ align:start position:0%
+converged cast up to the top of the tree
+ 
+
+ align:start position:0%
+converged cast up to the top of the tree
+okay so can we converge cast in this
+
+ align:start position:0%
+okay so can we converge cast in this
+ 
+
+ align:start position:0%
+okay so can we converge cast in this
+setting
+
+ align:start position:0%
+setting
+ 
+
+ align:start position:0%
+setting
+turns out we can but since things are
+
+ align:start position:0%
+turns out we can but since things are
+ 
+
+ align:start position:0%
+turns out we can but since things are
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+um you're going to be sending done
+
+ align:start position:0%
+um you're going to be sending done
+ 
+
+ align:start position:0%
+um you're going to be sending done
+messages and then something might change
+
+ align:start position:0%
+messages and then something might change
+ 
+
+ align:start position:0%
+messages and then something might change
+you might be participating in the
+
+ align:start position:0%
+you might be participating in the
+ 
+
+ align:start position:0%
+you might be participating in the
+converged cast many times
+
+ align:start position:0%
+converged cast many times
+ 
+
+ align:start position:0%
+converged cast many times
+okay so since the tree structure is
+
+ align:start position:0%
+okay so since the tree structure is
+ 
+
+ align:start position:0%
+okay so since the tree structure is
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+the main idea is anybody can send a done
+
+ align:start position:0%
+the main idea is anybody can send a done
+ 
+
+ align:start position:0%
+the main idea is anybody can send a done
+message
+
+ align:start position:0%
+message
+ 
+
+ align:start position:0%
+message
+to its current the parent that he
+
+ align:start position:0%
+to its current the parent that he
+ 
+
+ align:start position:0%
+to its current the parent that he
+the note he believes is his parent
+
+ align:start position:0%
+the note he believes is his parent
+ 
+
+ align:start position:0%
+the note he believes is his parent
+provided
+
+ align:start position:0%
+provided
+ 
+
+ align:start position:0%
+provided
+his received responses to all of its uh
+
+ align:start position:0%
+his received responses to all of its uh
+ 
+
+ align:start position:0%
+his received responses to all of its uh
+distance messages so it thinks it's no
+
+ align:start position:0%
+distance messages so it thinks it's no
+ 
+
+ align:start position:0%
+distance messages so it thinks it's no
+it knows who all its children are okay
+
+ align:start position:0%
+it knows who all its children are okay
+ 
+
+ align:start position:0%
+it knows who all its children are okay
+so it has a current estimate of all the
+
+ align:start position:0%
+so it has a current estimate of all the
+ 
+
+ align:start position:0%
+so it has a current estimate of all the
+children
+
+ align:start position:0%
+children
+ 
+
+ align:start position:0%
+children
+and okay so if it knows all its children
+
+ align:start position:0%
+and okay so if it knows all its children
+ 
+
+ align:start position:0%
+and okay so if it knows all its children
+and they have all sent him done messages
+
+ align:start position:0%
+and they have all sent him done messages
+ 
+
+ align:start position:0%
+and they have all sent him done messages
+so for all your current children your
+
+ align:start position:0%
+so for all your current children your
+ 
+
+ align:start position:0%
+so for all your current children your
+current belief or who your children are
+
+ align:start position:0%
+current belief or who your children are
+ 
+
+ align:start position:0%
+current belief or who your children are
+if they've all send you
+
+ align:start position:0%
+if they've all send you
+ 
+
+ align:start position:0%
+if they've all send you
+sent you done messages then you can send
+
+ align:start position:0%
+sent you done messages then you can send
+ 
+
+ align:start position:0%
+sent you done messages then you can send
+a done message up the tree
+
+ align:start position:0%
+a done message up the tree
+ 
+
+ align:start position:0%
+a done message up the tree
+okay but this can get a little more
+
+ align:start position:0%
+okay but this can get a little more
+ 
+
+ align:start position:0%
+okay but this can get a little more
+complicated than it sounds because
+
+ align:start position:0%
+complicated than it sounds because
+ 
+
+ align:start position:0%
+complicated than it sounds because
+you can change who your children are
+
+ align:start position:0%
+you can change who your children are
+ 
+
+ align:start position:0%
+you can change who your children are
+so this what this means is that the same
+
+ align:start position:0%
+so this what this means is that the same
+ 
+
+ align:start position:0%
+so this what this means is that the same
+process can be involved several times in
+
+ align:start position:0%
+process can be involved several times in
+ 
+
+ align:start position:0%
+process can be involved several times in
+the converge cast
+
+ align:start position:0%
+the converge cast
+ 
+
+ align:start position:0%
+the converge cast
+based on improving the estimates
+
+ align:start position:0%
+based on improving the estimates
+ 
+
+ align:start position:0%
+based on improving the estimates
+so here's an example um
+
+ align:start position:0%
+so here's an example um
+ 
+
+ align:start position:0%
+so here's an example um
+so of the kind of thing that can happen
+
+ align:start position:0%
+so of the kind of thing that can happen
+ 
+
+ align:start position:0%
+so of the kind of thing that can happen
+so let's say you start out
+
+ align:start position:0%
+so let's say you start out
+ 
+
+ align:start position:0%
+so let's say you start out
+you have these huge weights and then you
+
+ align:start position:0%
+you have these huge weights and then you
+ 
+
+ align:start position:0%
+you have these huge weights and then you
+have a long path with small weights so
+
+ align:start position:0%
+have a long path with small weights so
+ 
+
+ align:start position:0%
+have a long path with small weights so
+i zero starts out and sends
+
+ align:start position:0%
+i zero starts out and sends
+ 
+
+ align:start position:0%
+i zero starts out and sends
+its distance information on its three
+
+ align:start position:0%
+its distance information on its three
+ 
+
+ align:start position:0%
+its distance information on its three
+nodes three to its three neighbors
+
+ align:start position:0%
+nodes three to its three neighbors
+ 
+
+ align:start position:0%
+nodes three to its three neighbors
+and this guy at the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now has a distance estimate of 100 and
+
+ align:start position:0%
+now has a distance estimate of 100 and
+ 
+
+ align:start position:0%
+now has a distance estimate of 100 and
+it's going to decide it's a leaf
+
+ align:start position:0%
+it's going to decide it's a leaf
+ 
+
+ align:start position:0%
+it's going to decide it's a leaf
+why because when it sends
+
+ align:start position:0%
+why because when it sends
+ 
+
+ align:start position:0%
+why because when it sends
+messages to its children to its
+
+ align:start position:0%
+messages to its children to its
+ 
+
+ align:start position:0%
+messages to its children to its
+neighbors
+
+ align:start position:0%
+neighbors
+ 
+
+ align:start position:0%
+neighbors
+they're not able to improve their
+
+ align:start position:0%
+they're not able to improve their
+ 
+
+ align:start position:0%
+they're not able to improve their
+estimates based on the new information
+
+ align:start position:0%
+estimates based on the new information
+ 
+
+ align:start position:0%
+estimates based on the new information
+that he's sending
+
+ align:start position:0%
+that he's sending
+ 
+
+ align:start position:0%
+that he's sending
+so this guy decides that he's a leaf
+
+ align:start position:0%
+so this guy decides that he's a leaf
+ 
+
+ align:start position:0%
+so this guy decides that he's a leaf
+right away
+
+ align:start position:0%
+right away
+ 
+
+ align:start position:0%
+right away
+and he sends that information back to
+
+ align:start position:0%
+and he sends that information back to
+ 
+
+ align:start position:0%
+and he sends that information back to
+node i zero on the other hand this guy
+
+ align:start position:0%
+node i zero on the other hand this guy
+ 
+
+ align:start position:0%
+node i zero on the other hand this guy
+has the same estimate of a hundred
+
+ align:start position:0%
+has the same estimate of a hundred
+ 
+
+ align:start position:0%
+has the same estimate of a hundred
+and he's n he sends out his messages to
+
+ align:start position:0%
+and he's n he sends out his messages to
+ 
+
+ align:start position:0%
+and he's n he sends out his messages to
+try to find out if he's a leaf
+
+ align:start position:0%
+try to find out if he's a leaf
+ 
+
+ align:start position:0%
+try to find out if he's a leaf
+but he finds out when he sends a message
+
+ align:start position:0%
+but he finds out when he sends a message
+ 
+
+ align:start position:0%
+but he finds out when he sends a message
+this way that he's actually able to
+
+ align:start position:0%
+this way that he's actually able to
+ 
+
+ align:start position:0%
+this way that he's actually able to
+improve that neighbor's estimate because
+
+ align:start position:0%
+improve that neighbor's estimate because
+ 
+
+ align:start position:0%
+improve that neighbor's estimate because
+that was infinity up to
+
+ align:start position:0%
+that was infinity up to
+ 
+
+ align:start position:0%
+that was infinity up to
+till then so he doesn't think he's a
+
+ align:start position:0%
+till then so he doesn't think he's a
+ 
+
+ align:start position:0%
+till then so he doesn't think he's a
+leaf
+
+ align:start position:0%
+leaf
+ 
+
+ align:start position:0%
+leaf
+okay so we have this one guy who thinks
+
+ align:start position:0%
+okay so we have this one guy who thinks
+ 
+
+ align:start position:0%
+okay so we have this one guy who thinks
+he's a leaf and responds so this i zero
+
+ align:start position:0%
+he's a leaf and responds so this i zero
+ 
+
+ align:start position:0%
+he's a leaf and responds so this i zero
+is sitting there
+
+ align:start position:0%
+is sitting there
+ 
+
+ align:start position:0%
+is sitting there
+he has to wait to hear from his other
+
+ align:start position:0%
+he has to wait to hear from his other
+ 
+
+ align:start position:0%
+he has to wait to hear from his other
+children
+
+ align:start position:0%
+children
+ 
+
+ align:start position:0%
+children
+okay so far all right so in in the
+
+ align:start position:0%
+okay so far all right so in in the
+ 
+
+ align:start position:0%
+okay so far all right so in in the
+meantime the messages are going to
+
+ align:start position:0%
+meantime the messages are going to
+ 
+
+ align:start position:0%
+meantime the messages are going to
+eventually creep around
+
+ align:start position:0%
+eventually creep around
+ 
+
+ align:start position:0%
+eventually creep around
+and this node is going to get
+
+ align:start position:0%
+and this node is going to get
+ 
+
+ align:start position:0%
+and this node is going to get
+a smaller estimate based on the length
+
+ align:start position:0%
+a smaller estimate based on the length
+ 
+
+ align:start position:0%
+a smaller estimate based on the length
+of that long mini hop
+
+ align:start position:0%
+of that long mini hop
+ 
+
+ align:start position:0%
+of that long mini hop
+uh path okay so then he's going to
+
+ align:start position:0%
+uh path okay so then he's going to
+ 
+
+ align:start position:0%
+uh path okay so then he's going to
+decide he is not a child of
+
+ align:start position:0%
+decide he is not a child of
+ 
+
+ align:start position:0%
+decide he is not a child of
+i zero so he's going to tell i zero i am
+
+ align:start position:0%
+i zero so he's going to tell i zero i am
+ 
+
+ align:start position:0%
+i zero so he's going to tell i zero i am
+i'm really not your child which means
+
+ align:start position:0%
+i'm really not your child which means
+ 
+
+ align:start position:0%
+i'm really not your child which means
+that i zero stops waiting for it
+
+ align:start position:0%
+that i zero stops waiting for it
+ 
+
+ align:start position:0%
+that i zero stops waiting for it
+but also this guy decides he's not a
+
+ align:start position:0%
+but also this guy decides he's not a
+ 
+
+ align:start position:0%
+but also this guy decides he's not a
+child as well
+
+ align:start position:0%
+child as well
+ 
+
+ align:start position:0%
+child as well
+he becomes a child at the node right up
+
+ align:start position:0%
+he becomes a child at the node right up
+ 
+
+ align:start position:0%
+he becomes a child at the node right up
+right above him
+
+ align:start position:0%
+right above him
+ 
+
+ align:start position:0%
+right above him
+so i zero now will realize he only has
+
+ align:start position:0%
+so i zero now will realize he only has
+ 
+
+ align:start position:0%
+so i zero now will realize he only has
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+one child but this guy
+
+ align:start position:0%
+one child but this guy
+ 
+
+ align:start position:0%
+one child but this guy
+believes he's a leaf again after trying
+
+ align:start position:0%
+believes he's a leaf again after trying
+ 
+
+ align:start position:0%
+believes he's a leaf again after trying
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+to find children and now the done
+
+ align:start position:0%
+to find children and now the done
+ 
+
+ align:start position:0%
+to find children and now the done
+information propagates all the way up
+
+ align:start position:0%
+information propagates all the way up
+ 
+
+ align:start position:0%
+information propagates all the way up
+the tree which is now just this one long
+
+ align:start position:0%
+the tree which is now just this one long
+ 
+
+ align:start position:0%
+the tree which is now just this one long
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+okay so they start trying to converge
+
+ align:start position:0%
+okay so they start trying to converge
+ 
+
+ align:start position:0%
+okay so they start trying to converge
+cast
+
+ align:start position:0%
+cast
+ 
+
+ align:start position:0%
+cast
+but then oops they were wrong they have
+
+ align:start position:0%
+but then oops they were wrong they have
+ 
+
+ align:start position:0%
+but then oops they were wrong they have
+to make a correction
+
+ align:start position:0%
+to make a correction
+ 
+
+ align:start position:0%
+to make a correction
+and that they are forming a new tree
+
+ align:start position:0%
+and that they are forming a new tree
+ 
+
+ align:start position:0%
+and that they are forming a new tree
+eventually the tree is going to
+
+ align:start position:0%
+eventually the tree is going to
+ 
+
+ align:start position:0%
+eventually the tree is going to
+stabilize
+
+ align:start position:0%
+stabilize
+ 
+
+ align:start position:0%
+stabilize
+and eventually the done information will
+
+ align:start position:0%
+and eventually the done information will
+ 
+
+ align:start position:0%
+and eventually the done information will
+get all the way up to the top
+
+ align:start position:0%
+get all the way up to the top
+ 
+
+ align:start position:0%
+get all the way up to the top
+but there can be lots of false starts in
+
+ align:start position:0%
+but there can be lots of false starts in
+ 
+
+ align:start position:0%
+but there can be lots of false starts in
+the meantime
+
+ align:start position:0%
+the meantime
+ 
+
+ align:start position:0%
+the meantime
+okay it's sort of confusing but that's
+
+ align:start position:0%
+okay it's sort of confusing but that's
+ 
+
+ align:start position:0%
+okay it's sort of confusing but that's
+the kind of thing that happens yeah
+
+ align:start position:0%
+the kind of thing that happens yeah
+ 
+
+ align:start position:0%
+the kind of thing that happens yeah
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so the root note isn't going to
+
+ align:start position:0%
+yeah so the root note isn't going to
+ 
+
+ align:start position:0%
+yeah so the root note isn't going to
+terminate until it hears from everybody
+
+ align:start position:0%
+terminate until it hears from everybody
+ 
+
+ align:start position:0%
+terminate until it hears from everybody
+you kind of have to close out the whole
+
+ align:start position:0%
+you kind of have to close out the whole
+ 
+
+ align:start position:0%
+you kind of have to close out the whole
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+so it's always pending waiting for
+
+ align:start position:0%
+so it's always pending waiting for
+ 
+
+ align:start position:0%
+so it's always pending waiting for
+somebody if it hasn't heard from someone
+
+ align:start position:0%
+somebody if it hasn't heard from someone
+ 
+
+ align:start position:0%
+somebody if it hasn't heard from someone
+if things switch they'll join in on
+
+ align:start position:0%
+if things switch they'll join in on
+ 
+
+ align:start position:0%
+if things switch they'll join in on
+another part of the tree
+
+ align:start position:0%
+another part of the tree
+ 
+
+ align:start position:0%
+another part of the tree
+i think the best thing to do here is
+
+ align:start position:0%
+i think the best thing to do here is
+ 
+
+ align:start position:0%
+i think the best thing to do here is
+sort of construct some little examples
+
+ align:start position:0%
+sort of construct some little examples
+ 
+
+ align:start position:0%
+sort of construct some little examples
+by hand
+
+ align:start position:0%
+by hand
+ 
+
+ align:start position:0%
+by hand
+i mean we're not going to get into how
+
+ align:start position:0%
+i mean we're not going to get into how
+ 
+
+ align:start position:0%
+i mean we're not going to get into how
+you do formal proofs of things like this
+
+ align:start position:0%
+you do formal proofs of things like this
+ 
+
+ align:start position:0%
+you do formal proofs of things like this
+we don't even have right now a simulator
+
+ align:start position:0%
+we don't even have right now a simulator
+ 
+
+ align:start position:0%
+we don't even have right now a simulator
+you can use to play with these
+
+ align:start position:0%
+you can use to play with these
+ 
+
+ align:start position:0%
+you can use to play with these
+algorithms although if anybody's
+
+ align:start position:0%
+algorithms although if anybody's
+ 
+
+ align:start position:0%
+algorithms although if anybody's
+interested there
+
+ align:start position:0%
+interested there
+ 
+
+ align:start position:0%
+interested there
+some students in my class last term
+
+ align:start position:0%
+some students in my class last term
+ 
+
+ align:start position:0%
+some students in my class last term
+actually wrote a simulator it might be a
+
+ align:start position:0%
+actually wrote a simulator it might be a
+ 
+
+ align:start position:0%
+actually wrote a simulator it might be a
+belt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+all right so that's uh what you get for
+
+ align:start position:0%
+all right so that's uh what you get for
+ 
+
+ align:start position:0%
+all right so that's uh what you get for
+a synchronous
+
+ align:start position:0%
+a synchronous
+ 
+
+ align:start position:0%
+a synchronous
+some example synchronous distributed
+
+ align:start position:0%
+some example synchronous distributed
+ 
+
+ align:start position:0%
+some example synchronous distributed
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+so now let's look at something more
+
+ align:start position:0%
+so now let's look at something more
+ 
+
+ align:start position:0%
+so now let's look at something more
+complicated when you get into
+
+ align:start position:0%
+complicated when you get into
+ 
+
+ align:start position:0%
+complicated when you get into
+asynchronous algorithms
+
+ align:start position:0%
+asynchronous algorithms
+ 
+
+ align:start position:0%
+asynchronous algorithms
+okay so so far complications that you've
+
+ align:start position:0%
+okay so so far complications that you've
+ 
+
+ align:start position:0%
+okay so so far complications that you've
+seen over the rest of this course
+
+ align:start position:0%
+seen over the rest of this course
+ 
+
+ align:start position:0%
+seen over the rest of this course
+um you have now processes that are
+
+ align:start position:0%
+um you have now processes that are
+ 
+
+ align:start position:0%
+um you have now processes that are
+acting concurrently
+
+ align:start position:0%
+acting concurrently
+ 
+
+ align:start position:0%
+acting concurrently
+and we had a little bit of
+
+ align:start position:0%
+and we had a little bit of
+ 
+
+ align:start position:0%
+and we had a little bit of
+non-determinism nothing important
+
+ align:start position:0%
+non-determinism nothing important
+ 
+
+ align:start position:0%
+non-determinism nothing important
+but now things are about to get much
+
+ align:start position:0%
+but now things are about to get much
+ 
+
+ align:start position:0%
+but now things are about to get much
+worse um
+
+ align:start position:0%
+worse um
+ 
+
+ align:start position:0%
+worse um
+we don't have rounds anymore uh so now
+
+ align:start position:0%
+we don't have rounds anymore uh so now
+ 
+
+ align:start position:0%
+we don't have rounds anymore uh so now
+we're going to have processes taking
+
+ align:start position:0%
+we're going to have processes taking
+ 
+
+ align:start position:0%
+we're going to have processes taking
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+messages getting delivered at absolutely
+
+ align:start position:0%
+messages getting delivered at absolutely
+ 
+
+ align:start position:0%
+messages getting delivered at absolutely
+arbitrary times arbitrary orders
+
+ align:start position:0%
+arbitrary times arbitrary orders
+ 
+
+ align:start position:0%
+arbitrary times arbitrary orders
+okay the processes can get completely
+
+ align:start position:0%
+okay the processes can get completely
+ 
+
+ align:start position:0%
+okay the processes can get completely
+out of sync
+
+ align:start position:0%
+out of sync
+ 
+
+ align:start position:0%
+out of sync
+um and so you have lots lots more
+
+ align:start position:0%
+um and so you have lots lots more
+ 
+
+ align:start position:0%
+um and so you have lots lots more
+non-determinism
+
+ align:start position:0%
+non-determinism
+ 
+
+ align:start position:0%
+non-determinism
+in the algorithm the non-determinism has
+
+ align:start position:0%
+in the algorithm the non-determinism has
+ 
+
+ align:start position:0%
+in the algorithm the non-determinism has
+to do with who's doing what in what
+
+ align:start position:0%
+to do with who's doing what in what
+ 
+
+ align:start position:0%
+to do with who's doing what in what
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+okay so understanding
+
+ align:start position:0%
+okay so understanding
+ 
+
+ align:start position:0%
+okay so understanding
+that type of algorithm is really
+
+ align:start position:0%
+that type of algorithm is really
+ 
+
+ align:start position:0%
+that type of algorithm is really
+different from understanding the
+
+ align:start position:0%
+different from understanding the
+ 
+
+ align:start position:0%
+different from understanding the
+algorithms that you've seen all term and
+
+ align:start position:0%
+algorithms that you've seen all term and
+ 
+
+ align:start position:0%
+algorithms that you've seen all term and
+even synchronous
+
+ align:start position:0%
+even synchronous
+ 
+
+ align:start position:0%
+even synchronous
+uh distributed algorithms because there
+
+ align:start position:0%
+uh distributed algorithms because there
+ 
+
+ align:start position:0%
+uh distributed algorithms because there
+isn't just one way the algorithm is
+
+ align:start position:0%
+isn't just one way the algorithm is
+ 
+
+ align:start position:0%
+isn't just one way the algorithm is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+execute the execution can proceed in
+
+ align:start position:0%
+execute the execution can proceed in
+ 
+
+ align:start position:0%
+execute the execution can proceed in
+many different ways
+
+ align:start position:0%
+many different ways
+ 
+
+ align:start position:0%
+many different ways
+uh just depending on the order of the
+
+ align:start position:0%
+uh just depending on the order of the
+ 
+
+ align:start position:0%
+uh just depending on the order of the
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+okay so you can't ever hope to
+
+ align:start position:0%
+okay so you can't ever hope to
+ 
+
+ align:start position:0%
+okay so you can't ever hope to
+understand exactly how this kind of
+
+ align:start position:0%
+understand exactly how this kind of
+ 
+
+ align:start position:0%
+understand exactly how this kind of
+algorithm is
+
+ align:start position:0%
+algorithm is
+ 
+
+ align:start position:0%
+algorithm is
+executing so what can you do well you
+
+ align:start position:0%
+executing so what can you do well you
+ 
+
+ align:start position:0%
+executing so what can you do well you
+can play with it but
+
+ align:start position:0%
+can play with it but
+ 
+
+ align:start position:0%
+can play with it but
+in the end what you have to understand
+
+ align:start position:0%
+in the end what you have to understand
+ 
+
+ align:start position:0%
+in the end what you have to understand
+is some abstract properties some
+
+ align:start position:0%
+is some abstract properties some
+ 
+
+ align:start position:0%
+is some abstract properties some
+properties of the executions rather than
+
+ align:start position:0%
+properties of the executions rather than
+ 
+
+ align:start position:0%
+properties of the executions rather than
+exactly what happens at every step and
+
+ align:start position:0%
+exactly what happens at every step and
+ 
+
+ align:start position:0%
+exactly what happens at every step and
+that's a a jump it's a new way of
+
+ align:start position:0%
+that's a a jump it's a new way of
+ 
+
+ align:start position:0%
+that's a a jump it's a new way of
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+okay so we can look at asynchronous
+
+ align:start position:0%
+okay so we can look at asynchronous
+ 
+
+ align:start position:0%
+okay so we can look at asynchronous
+stuff if you want from my book
+
+ align:start position:0%
+stuff if you want from my book
+ 
+
+ align:start position:0%
+stuff if you want from my book
+uh now okay we still have processes at
+
+ align:start position:0%
+uh now okay we still have processes at
+ 
+
+ align:start position:0%
+uh now okay we still have processes at
+the nodes of a graph
+
+ align:start position:0%
+the nodes of a graph
+ 
+
+ align:start position:0%
+the nodes of a graph
+and now we have communication channels
+
+ align:start position:0%
+and now we have communication channels
+ 
+
+ align:start position:0%
+and now we have communication channels
+associated with the edges
+
+ align:start position:0%
+associated with the edges
+ 
+
+ align:start position:0%
+associated with the edges
+so now the processes are going to be
+
+ align:start position:0%
+so now the processes are going to be
+ 
+
+ align:start position:0%
+so now the processes are going to be
+some kind of automata
+
+ align:start position:0%
+some kind of automata
+ 
+
+ align:start position:0%
+some kind of automata
+but the channels will also be some kind
+
+ align:start position:0%
+but the channels will also be some kind
+ 
+
+ align:start position:0%
+but the channels will also be some kind
+of automata we'll have all these
+
+ align:start position:0%
+of automata we'll have all these
+ 
+
+ align:start position:0%
+of automata we'll have all these
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+and we'll be modeling all of them
+
+ align:start position:0%
+and we'll be modeling all of them
+ 
+
+ align:start position:0%
+and we'll be modeling all of them
+processes still have their ports they
+
+ align:start position:0%
+processes still have their ports they
+ 
+
+ align:start position:0%
+processes still have their ports they
+need not in general have uh
+
+ align:start position:0%
+need not in general have uh
+ 
+
+ align:start position:0%
+need not in general have uh
+identifiers okay so what's a channel
+
+ align:start position:0%
+identifiers okay so what's a channel
+ 
+
+ align:start position:0%
+identifiers okay so what's a channel
+okay so a channel is a kind of an
+
+ align:start position:0%
+okay so a channel is a kind of an
+ 
+
+ align:start position:0%
+okay so a channel is a kind of an
+automaton infinite state automaton that
+
+ align:start position:0%
+automaton infinite state automaton that
+ 
+
+ align:start position:0%
+automaton infinite state automaton that
+has some inputs
+
+ align:start position:0%
+has some inputs
+ 
+
+ align:start position:0%
+has some inputs
+and some outputs so here this is just a
+
+ align:start position:0%
+and some outputs so here this is just a
+ 
+
+ align:start position:0%
+and some outputs so here this is just a
+little picture of a channel from one
+
+ align:start position:0%
+little picture of a channel from one
+ 
+
+ align:start position:0%
+little picture of a channel from one
+node to
+
+ align:start position:0%
+node to
+ 
+
+ align:start position:0%
+node to
+from node u to node v
+
+ align:start position:0%
+from node u to node v
+ 
+
+ align:start position:0%
+from node u to node v
+so channel uv is just this cloud thing
+
+ align:start position:0%
+so channel uv is just this cloud thing
+ 
+
+ align:start position:0%
+so channel uv is just this cloud thing
+that delivers messages
+
+ align:start position:0%
+that delivers messages
+ 
+
+ align:start position:0%
+that delivers messages
+it has inputs the inputs are messages
+
+ align:start position:0%
+it has inputs the inputs are messages
+ 
+
+ align:start position:0%
+it has inputs the inputs are messages
+get sent on the channel
+
+ align:start position:0%
+get sent on the channel
+ 
+
+ align:start position:0%
+get sent on the channel
+so you can have one process at one end
+
+ align:start position:0%
+so you can have one process at one end
+ 
+
+ align:start position:0%
+so you can have one process at one end
+sending a message m
+
+ align:start position:0%
+sending a message m
+ 
+
+ align:start position:0%
+sending a message m
+and the outputs at the other end are the
+
+ align:start position:0%
+and the outputs at the other end are the
+ 
+
+ align:start position:0%
+and the outputs at the other end are the
+deliveries let's say receive
+
+ align:start position:0%
+deliveries let's say receive
+ 
+
+ align:start position:0%
+deliveries let's say receive
+message m uh at the other end
+
+ align:start position:0%
+message m uh at the other end
+ 
+
+ align:start position:0%
+message m uh at the other end
+node v okay
+
+ align:start position:0%
+node v okay
+ 
+
+ align:start position:0%
+node v okay
+um okay to model this the best thing is
+
+ align:start position:0%
+um okay to model this the best thing is
+ 
+
+ align:start position:0%
+um okay to model this the best thing is
+actually to
+
+ align:start position:0%
+actually to
+ 
+
+ align:start position:0%
+actually to
+instead of just describing what it does
+
+ align:start position:0%
+instead of just describing what it does
+ 
+
+ align:start position:0%
+instead of just describing what it does
+to give an explicit model of its state
+
+ align:start position:0%
+to give an explicit model of its state
+ 
+
+ align:start position:0%
+to give an explicit model of its state
+and what happens when the inputs and
+
+ align:start position:0%
+and what happens when the inputs and
+ 
+
+ align:start position:0%
+and what happens when the inputs and
+outputs occur
+
+ align:start position:0%
+outputs occur
+ 
+
+ align:start position:0%
+outputs occur
+so if you want these messages to be
+
+ align:start position:0%
+so if you want these messages to be
+ 
+
+ align:start position:0%
+so if you want these messages to be
+delivered say in fifo order
+
+ align:start position:0%
+delivered say in fifo order
+ 
+
+ align:start position:0%
+delivered say in fifo order
+fine so you can make the state of the
+
+ align:start position:0%
+fine so you can make the state of the
+ 
+
+ align:start position:0%
+fine so you can make the state of the
+channel be an actual cue
+
+ align:start position:0%
+channel be an actual cue
+ 
+
+ align:start position:0%
+channel be an actual cue
+mq would just be a fifo queue of
+
+ align:start position:0%
+mq would just be a fifo queue of
+ 
+
+ align:start position:0%
+mq would just be a fifo queue of
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+it starts out empty then when messages
+
+ align:start position:0%
+it starts out empty then when messages
+ 
+
+ align:start position:0%
+it starts out empty then when messages
+get sent they get added to the end and
+
+ align:start position:0%
+get sent they get added to the end and
+ 
+
+ align:start position:0%
+get sent they get added to the end and
+get delivered they get removed from the
+
+ align:start position:0%
+get delivered they get removed from the
+ 
+
+ align:start position:0%
+get delivered they get removed from the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+so all that we need to describe this is
+
+ align:start position:0%
+so all that we need to describe this is
+ 
+
+ align:start position:0%
+so all that we need to describe this is
+a sort of a pseudocode
+
+ align:start position:0%
+a sort of a pseudocode
+ 
+
+ align:start position:0%
+a sort of a pseudocode
+all we need to describe uh to write in
+
+ align:start position:0%
+all we need to describe uh to write in
+ 
+
+ align:start position:0%
+all we need to describe uh to write in
+order to describe what this
+
+ align:start position:0%
+order to describe what this
+ 
+
+ align:start position:0%
+order to describe what this
+channel does is what happens when a send
+
+ align:start position:0%
+channel does is what happens when a send
+ 
+
+ align:start position:0%
+channel does is what happens when a send
+occurs
+
+ align:start position:0%
+occurs
+ 
+
+ align:start position:0%
+occurs
+and when can this channel do uh deliver
+
+ align:start position:0%
+and when can this channel do uh deliver
+ 
+
+ align:start position:0%
+and when can this channel do uh deliver
+a message and what happens when it does
+
+ align:start position:0%
+a message and what happens when it does
+ 
+
+ align:start position:0%
+a message and what happens when it does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so ascend which can just come in at any
+
+ align:start position:0%
+so ascend which can just come in at any
+ 
+
+ align:start position:0%
+so ascend which can just come in at any
+time and the effect is just to add this
+
+ align:start position:0%
+time and the effect is just to add this
+ 
+
+ align:start position:0%
+time and the effect is just to add this
+message
+
+ align:start position:0%
+message
+ 
+
+ align:start position:0%
+message
+to the end of the queue the receive
+
+ align:start position:0%
+to the end of the queue the receive
+ 
+
+ align:start position:0%
+to the end of the queue the receive
+stop moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the receive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that cannot be construction we'd hear
+
+ align:start position:0%
+that cannot be construction we'd hear
+ 
+
+ align:start position:0%
+that cannot be construction we'd hear
+noise
+
+ align:start position:0%
+noise
+ 
+
+ align:start position:0%
+noise
+it's gremlins we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a receive can occur only when this
+
+ align:start position:0%
+a receive can occur only when this
+ 
+
+ align:start position:0%
+a receive can occur only when this
+message is at the head of the queue
+
+ align:start position:0%
+message is at the head of the queue
+ 
+
+ align:start position:0%
+message is at the head of the queue
+and when it occurs it gets removed from
+
+ align:start position:0%
+and when it occurs it gets removed from
+ 
+
+ align:start position:0%
+and when it occurs it gets removed from
+the queue
+
+ align:start position:0%
+the queue
+ 
+
+ align:start position:0%
+the queue
+so does this make sense as a description
+
+ align:start position:0%
+so does this make sense as a description
+ 
+
+ align:start position:0%
+so does this make sense as a description
+of what a channel does
+
+ align:start position:0%
+of what a channel does
+ 
+
+ align:start position:0%
+of what a channel does
+messages come in get added to it and
+
+ align:start position:0%
+messages come in get added to it and
+ 
+
+ align:start position:0%
+messages come in get added to it and
+then messages can get delivered
+
+ align:start position:0%
+then messages can get delivered
+ 
+
+ align:start position:0%
+then messages can get delivered
+in certain situations and they get
+
+ align:start position:0%
+in certain situations and they get
+ 
+
+ align:start position:0%
+in certain situations and they get
+removed
+
+ align:start position:0%
+removed
+ 
+
+ align:start position:0%
+removed
+okay so that's a description of a
+
+ align:start position:0%
+okay so that's a description of a
+ 
+
+ align:start position:0%
+okay so that's a description of a
+channel in it to be used in asynchronous
+
+ align:start position:0%
+channel in it to be used in asynchronous
+ 
+
+ align:start position:0%
+channel in it to be used in asynchronous
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+okay a process the rest of the the
+
+ align:start position:0%
+okay a process the rest of the the
+ 
+
+ align:start position:0%
+okay a process the rest of the the
+system consists of processes
+
+ align:start position:0%
+system consists of processes
+ 
+
+ align:start position:0%
+system consists of processes
+associated with graph vertices so let's
+
+ align:start position:0%
+associated with graph vertices so let's
+ 
+
+ align:start position:0%
+associated with graph vertices so let's
+say p
+
+ align:start position:0%
+say p
+ 
+
+ align:start position:0%
+say p
+u is a process that's associated with
+
+ align:start position:0%
+u is a process that's associated with
+ 
+
+ align:start position:0%
+u is a process that's associated with
+vertex u
+
+ align:start position:0%
+vertex u
+ 
+
+ align:start position:0%
+vertex u
+but i'm writing that just sort of as a
+
+ align:start position:0%
+but i'm writing that just sort of as a
+ 
+
+ align:start position:0%
+but i'm writing that just sort of as a
+shorthand because u is the
+
+ align:start position:0%
+shorthand because u is the
+ 
+
+ align:start position:0%
+shorthand because u is the
+vertex in the graph and the process
+
+ align:start position:0%
+vertex in the graph and the process
+ 
+
+ align:start position:0%
+vertex in the graph and the process
+doesn't actually know
+
+ align:start position:0%
+doesn't actually know
+ 
+
+ align:start position:0%
+doesn't actually know
+the name of the vertex it just has like
+
+ align:start position:0%
+the name of the vertex it just has like
+ 
+
+ align:start position:0%
+the name of the vertex it just has like
+its own unique id
+
+ align:start position:0%
+its own unique id
+ 
+
+ align:start position:0%
+its own unique id
+or something but i'm going to be a
+
+ align:start position:0%
+or something but i'm going to be a
+ 
+
+ align:start position:0%
+or something but i'm going to be a
+little sloppy about that now
+
+ align:start position:0%
+little sloppy about that now
+ 
+
+ align:start position:0%
+little sloppy about that now
+okay so the process at vertex u
+
+ align:start position:0%
+okay so the process at vertex u
+ 
+
+ align:start position:0%
+okay so the process at vertex u
+can perform send outputs to put messages
+
+ align:start position:0%
+can perform send outputs to put messages
+ 
+
+ align:start position:0%
+can perform send outputs to put messages
+on the channel
+
+ align:start position:0%
+on the channel
+ 
+
+ align:start position:0%
+on the channel
+and it will get receive inputs for
+
+ align:start position:0%
+and it will get receive inputs for
+ 
+
+ align:start position:0%
+and it will get receive inputs for
+messages to come in on the channels
+
+ align:start position:0%
+messages to come in on the channels
+ 
+
+ align:start position:0%
+messages to come in on the channels
+but the processes might also have some
+
+ align:start position:0%
+but the processes might also have some
+ 
+
+ align:start position:0%
+but the processes might also have some
+external interface where somebody is
+
+ align:start position:0%
+external interface where somebody is
+ 
+
+ align:start position:0%
+external interface where somebody is
+submitting some inputs to the process
+
+ align:start position:0%
+submitting some inputs to the process
+ 
+
+ align:start position:0%
+submitting some inputs to the process
+and the process has to produce some
+
+ align:start position:0%
+and the process has to produce some
+ 
+
+ align:start position:0%
+and the process has to produce some
+output at the end
+
+ align:start position:0%
+output at the end
+ 
+
+ align:start position:0%
+output at the end
+so there can be other inputs and outputs
+
+ align:start position:0%
+so there can be other inputs and outputs
+ 
+
+ align:start position:0%
+so there can be other inputs and outputs
+okay uh and we'll model it with state
+
+ align:start position:0%
+okay uh and we'll model it with state
+ 
+
+ align:start position:0%
+okay uh and we'll model it with state
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+okay process is supposed to keep taking
+
+ align:start position:0%
+okay process is supposed to keep taking
+ 
+
+ align:start position:0%
+okay process is supposed to keep taking
+steps the channel is supposed to keep
+
+ align:start position:0%
+steps the channel is supposed to keep
+ 
+
+ align:start position:0%
+steps the channel is supposed to keep
+delivering messages that's a
+
+ align:start position:0%
+delivering messages that's a
+ 
+
+ align:start position:0%
+delivering messages that's a
+it's a property called liveness you want
+
+ align:start position:0%
+it's a property called liveness you want
+ 
+
+ align:start position:0%
+it's a property called liveness you want
+to make sure that your components in
+
+ align:start position:0%
+to make sure that your components in
+ 
+
+ align:start position:0%
+to make sure that your components in
+your system all keep
+
+ align:start position:0%
+your system all keep
+ 
+
+ align:start position:0%
+your system all keep
+doing things they don't just do some
+
+ align:start position:0%
+doing things they don't just do some
+ 
+
+ align:start position:0%
+doing things they don't just do some
+steps and then stop
+
+ align:start position:0%
+steps and then stop
+ 
+
+ align:start position:0%
+steps and then stop
+okay so here's a simple example a
+
+ align:start position:0%
+okay so here's a simple example a
+ 
+
+ align:start position:0%
+okay so here's a simple example a
+process that
+
+ align:start position:0%
+process that
+ 
+
+ align:start position:0%
+process that
+that's remembering the maximum number
+
+ align:start position:0%
+that's remembering the maximum number
+ 
+
+ align:start position:0%
+that's remembering the maximum number
+it's ever seen
+
+ align:start position:0%
+it's ever seen
+ 
+
+ align:start position:0%
+it's ever seen
+so there's a max process automaton it
+
+ align:start position:0%
+so there's a max process automaton it
+ 
+
+ align:start position:0%
+so there's a max process automaton it
+receives
+
+ align:start position:0%
+receives
+ 
+
+ align:start position:0%
+receives
+some messages m some value
+
+ align:start position:0%
+some messages m some value
+ 
+
+ align:start position:0%
+some messages m some value
+and it will send it out it keeps track
+
+ align:start position:0%
+and it will send it out it keeps track
+ 
+
+ align:start position:0%
+and it will send it out it keeps track
+of the max that's a
+
+ align:start position:0%
+of the max that's a
+ 
+
+ align:start position:0%
+of the max that's a
+max state variable it starts out with
+
+ align:start position:0%
+max state variable it starts out with
+ 
+
+ align:start position:0%
+max state variable it starts out with
+its own initial value so x for u
+
+ align:start position:0%
+its own initial value so x for u
+ 
+
+ align:start position:0%
+its own initial value so x for u
+x sub u is its initial value
+
+ align:start position:0%
+x sub u is its initial value
+ 
+
+ align:start position:0%
+x sub u is its initial value
+and then it has for every neighbor
+
+ align:start position:0%
+and then it has for every neighbor
+ 
+
+ align:start position:0%
+and then it has for every neighbor
+it has a a little um hue
+
+ align:start position:0%
+it has a a little um hue
+ 
+
+ align:start position:0%
+it has a a little um hue
+here it's just a boolean uh asking
+
+ align:start position:0%
+here it's just a boolean uh asking
+ 
+
+ align:start position:0%
+here it's just a boolean uh asking
+whether it's supposed to send
+
+ align:start position:0%
+whether it's supposed to send
+ 
+
+ align:start position:0%
+whether it's supposed to send
+to that neighbor okay
+
+ align:start position:0%
+to that neighbor okay
+ 
+
+ align:start position:0%
+to that neighbor okay
+um so this is the pseudo code for uh the
+
+ align:start position:0%
+um so this is the pseudo code for uh the
+ 
+
+ align:start position:0%
+um so this is the pseudo code for uh the
+max process
+
+ align:start position:0%
+max process
+ 
+
+ align:start position:0%
+max process
+what does it do when it receives a
+
+ align:start position:0%
+what does it do when it receives a
+ 
+
+ align:start position:0%
+what does it do when it receives a
+message well it sees if that
+
+ align:start position:0%
+message well it sees if that
+ 
+
+ align:start position:0%
+message well it sees if that
+value is bigger than what it had before
+
+ align:start position:0%
+value is bigger than what it had before
+ 
+
+ align:start position:0%
+value is bigger than what it had before
+and if so it resets the max
+
+ align:start position:0%
+and if so it resets the max
+ 
+
+ align:start position:0%
+and if so it resets the max
+and it also makes a note that it's
+
+ align:start position:0%
+and it also makes a note that it's
+ 
+
+ align:start position:0%
+and it also makes a note that it's
+supposed to send this out to all its
+
+ align:start position:0%
+supposed to send this out to all its
+ 
+
+ align:start position:0%
+supposed to send this out to all its
+neighbors whenever it gets new
+
+ align:start position:0%
+neighbors whenever it gets new
+ 
+
+ align:start position:0%
+neighbors whenever it gets new
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+it will want to propagate it to its
+
+ align:start position:0%
+it will want to propagate it to its
+ 
+
+ align:start position:0%
+it will want to propagate it to its
+neighbors
+
+ align:start position:0%
+neighbors
+ 
+
+ align:start position:0%
+neighbors
+so you see how this is written you just
+
+ align:start position:0%
+so you see how this is written you just
+ 
+
+ align:start position:0%
+so you see how this is written you just
+say you know reset the max and
+
+ align:start position:0%
+say you know reset the max and
+ 
+
+ align:start position:0%
+say you know reset the max and
+then get ready to send to all your
+
+ align:start position:0%
+then get ready to send to all your
+ 
+
+ align:start position:0%
+then get ready to send to all your
+neighbors
+
+ align:start position:0%
+neighbors
+ 
+
+ align:start position:0%
+neighbors
+and the last part is just sort of
+
+ align:start position:0%
+and the last part is just sort of
+ 
+
+ align:start position:0%
+and the last part is just sort of
+trivial code it says if you
+
+ align:start position:0%
+trivial code it says if you
+ 
+
+ align:start position:0%
+trivial code it says if you
+are ready to send then you can send and
+
+ align:start position:0%
+are ready to send then you can send and
+ 
+
+ align:start position:0%
+are ready to send then you can send and
+then you you know you're done and you
+
+ align:start position:0%
+then you you know you're done and you
+ 
+
+ align:start position:0%
+then you you know you're done and you
+can set the send flags to false
+
+ align:start position:0%
+can set the send flags to false
+ 
+
+ align:start position:0%
+can set the send flags to false
+yeah um for every
+
+ align:start position:0%
+yeah um for every
+ 
+
+ align:start position:0%
+yeah um for every
+neighbor oh i wrote neighbor v before
+
+ align:start position:0%
+neighbor oh i wrote neighbor v before
+ 
+
+ align:start position:0%
+neighbor oh i wrote neighbor v before
+and then i
+
+ align:start position:0%
+and then i
+ 
+
+ align:start position:0%
+and then i
+yeah i wrote neighbor oh i know why i
+
+ align:start position:0%
+yeah i wrote neighbor oh i know why i
+ 
+
+ align:start position:0%
+yeah i wrote neighbor oh i know why i
+wrote w
+
+ align:start position:0%
+wrote w
+ 
+
+ align:start position:0%
+wrote w
+so here i'm talking about if you receive
+
+ align:start position:0%
+so here i'm talking about if you receive
+ 
+
+ align:start position:0%
+so here i'm talking about if you receive
+a message from a particular neighbor v
+
+ align:start position:0%
+a message from a particular neighbor v
+ 
+
+ align:start position:0%
+a message from a particular neighbor v
+then you have to send it to all your
+
+ align:start position:0%
+then you have to send it to all your
+ 
+
+ align:start position:0%
+then you have to send it to all your
+neighbors so before i
+
+ align:start position:0%
+neighbors so before i
+ 
+
+ align:start position:0%
+neighbors so before i
+i used v to denote a generic neighbor
+
+ align:start position:0%
+i used v to denote a generic neighbor
+ 
+
+ align:start position:0%
+i used v to denote a generic neighbor
+but now i can't do that anymore
+
+ align:start position:0%
+but now i can't do that anymore
+ 
+
+ align:start position:0%
+but now i can't do that anymore
+because v is the center of the message
+
+ align:start position:0%
+because v is the center of the message
+ 
+
+ align:start position:0%
+because v is the center of the message
+just technical
+
+ align:start position:0%
+just technical
+ 
+
+ align:start position:0%
+just technical
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we we have these process
+
+ align:start position:0%
+okay so we we have these process
+ 
+
+ align:start position:0%
+okay so we we have these process
+automata we have these channel
+
+ align:start position:0%
+automata we have these channel
+ 
+
+ align:start position:0%
+automata we have these channel
+automata now we want to build the system
+
+ align:start position:0%
+automata now we want to build the system
+ 
+
+ align:start position:0%
+automata now we want to build the system
+we paste them together
+
+ align:start position:0%
+we paste them together
+ 
+
+ align:start position:0%
+we paste them together
+okay so how we paste them is just we
+
+ align:start position:0%
+okay so how we paste them is just we
+ 
+
+ align:start position:0%
+okay so how we paste them is just we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+outputs from processes that can match up
+
+ align:start position:0%
+outputs from processes that can match up
+ 
+
+ align:start position:0%
+outputs from processes that can match up
+with inputs to channels
+
+ align:start position:0%
+with inputs to channels
+ 
+
+ align:start position:0%
+with inputs to channels
+and vice versa if a process has a send
+
+ align:start position:0%
+and vice versa if a process has a send
+ 
+
+ align:start position:0%
+and vice versa if a process has a send
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+let's say send from u to v that will
+
+ align:start position:0%
+let's say send from u to v that will
+ 
+
+ align:start position:0%
+let's say send from u to v that will
+match up with
+
+ align:start position:0%
+match up with
+ 
+
+ align:start position:0%
+match up with
+the channel that has send uv as an input
+
+ align:start position:0%
+the channel that has send uv as an input
+ 
+
+ align:start position:0%
+the channel that has send uv as an input
+and the receive from the channel matches
+
+ align:start position:0%
+and the receive from the channel matches
+ 
+
+ align:start position:0%
+and the receive from the channel matches
+up with the process that has that
+
+ align:start position:0%
+up with the process that has that
+ 
+
+ align:start position:0%
+up with the process that has that
+received as an input
+
+ align:start position:0%
+received as an input
+ 
+
+ align:start position:0%
+received as an input
+okay so all i'm doing is matching up
+
+ align:start position:0%
+okay so all i'm doing is matching up
+ 
+
+ align:start position:0%
+okay so all i'm doing is matching up
+these um
+
+ align:start position:0%
+these um
+ 
+
+ align:start position:0%
+these um
+components i'm hooking together these
+
+ align:start position:0%
+components i'm hooking together these
+ 
+
+ align:start position:0%
+components i'm hooking together these
+components by matching up their action
+
+ align:start position:0%
+components by matching up their action
+ 
+
+ align:start position:0%
+components by matching up their action
+names
+
+ align:start position:0%
+names
+ 
+
+ align:start position:0%
+names
+does that make sense so i'm
+
+ align:start position:0%
+does that make sense so i'm
+ 
+
+ align:start position:0%
+does that make sense so i'm
+saying how i build a system out of all
+
+ align:start position:0%
+saying how i build a system out of all
+ 
+
+ align:start position:0%
+saying how i build a system out of all
+these components and i just have a
+
+ align:start position:0%
+these components and i just have a
+ 
+
+ align:start position:0%
+these components and i just have a
+syntactic way of saying
+
+ align:start position:0%
+syntactic way of saying
+ 
+
+ align:start position:0%
+syntactic way of saying
+what actions match up in different
+
+ align:start position:0%
+what actions match up in different
+ 
+
+ align:start position:0%
+what actions match up in different
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+questions this is all new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so when when this system takes a
+
+ align:start position:0%
+okay so when when this system takes a
+ 
+
+ align:start position:0%
+okay so when when this system takes a
+step well
+
+ align:start position:0%
+step well
+ 
+
+ align:start position:0%
+step well
+if there's um if somebody's performing
+
+ align:start position:0%
+if there's um if somebody's performing
+ 
+
+ align:start position:0%
+if there's um if somebody's performing
+an action
+
+ align:start position:0%
+an action
+ 
+
+ align:start position:0%
+an action
+and someone else has that same action
+
+ align:start position:0%
+and someone else has that same action
+ 
+
+ align:start position:0%
+and someone else has that same action
+let's say a process is doing ascend the
+
+ align:start position:0%
+let's say a process is doing ascend the
+ 
+
+ align:start position:0%
+let's say a process is doing ascend the
+channel has ascend
+
+ align:start position:0%
+channel has ascend
+ 
+
+ align:start position:0%
+channel has ascend
+they both take their transitions at the
+
+ align:start position:0%
+they both take their transitions at the
+ 
+
+ align:start position:0%
+they both take their transitions at the
+same time the process sends a message
+
+ align:start position:0%
+same time the process sends a message
+ 
+
+ align:start position:0%
+same time the process sends a message
+it gets put into the channel at the end
+
+ align:start position:0%
+it gets put into the channel at the end
+ 
+
+ align:start position:0%
+it gets put into the channel at the end
+of its queue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+makes sense okay
+
+ align:start position:0%
+makes sense okay
+ 
+
+ align:start position:0%
+makes sense okay
+so how does this thing execute well
+
+ align:start position:0%
+so how does this thing execute well
+ 
+
+ align:start position:0%
+so how does this thing execute well
+there's no synchronous rounds
+
+ align:start position:0%
+there's no synchronous rounds
+ 
+
+ align:start position:0%
+there's no synchronous rounds
+so the the system just operates by the
+
+ align:start position:0%
+so the the system just operates by the
+ 
+
+ align:start position:0%
+so the the system just operates by the
+processes and the channels just perform
+
+ align:start position:0%
+processes and the channels just perform
+ 
+
+ align:start position:0%
+processes and the channels just perform
+their steps in any order
+
+ align:start position:0%
+their steps in any order
+ 
+
+ align:start position:0%
+their steps in any order
+one at a time but it can be in any order
+
+ align:start position:0%
+one at a time but it can be in any order
+ 
+
+ align:start position:0%
+one at a time but it can be in any order
+so it's a sequence model you just have a
+
+ align:start position:0%
+so it's a sequence model you just have a
+ 
+
+ align:start position:0%
+so it's a sequence model you just have a
+sequence of individual steps
+
+ align:start position:0%
+sequence of individual steps
+ 
+
+ align:start position:0%
+sequence of individual steps
+um there's no concurrency here in the
+
+ align:start position:0%
+um there's no concurrency here in the
+ 
+
+ align:start position:0%
+um there's no concurrency here in the
+the synchronous model we had
+
+ align:start position:0%
+the synchronous model we had
+ 
+
+ align:start position:0%
+the synchronous model we had
+everybody taking their steps in one big
+
+ align:start position:0%
+everybody taking their steps in one big
+ 
+
+ align:start position:0%
+everybody taking their steps in one big
+block and here it's just
+
+ align:start position:0%
+block and here it's just
+ 
+
+ align:start position:0%
+block and here it's just
+uh they take steps one at a time but it
+
+ align:start position:0%
+uh they take steps one at a time but it
+ 
+
+ align:start position:0%
+uh they take steps one at a time but it
+could be in any order
+
+ align:start position:0%
+could be in any order
+ 
+
+ align:start position:0%
+could be in any order
+okay and we have to make sure that
+
+ align:start position:0%
+okay and we have to make sure that
+ 
+
+ align:start position:0%
+okay and we have to make sure that
+everybody keeps taking steps that
+
+ align:start position:0%
+everybody keeps taking steps that
+ 
+
+ align:start position:0%
+everybody keeps taking steps that
+every channel continues to deliver
+
+ align:start position:0%
+every channel continues to deliver
+ 
+
+ align:start position:0%
+every channel continues to deliver
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+and every process always performs
+
+ align:start position:0%
+and every process always performs
+ 
+
+ align:start position:0%
+and every process always performs
+some step that's enabled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for the max processes well we can
+
+ align:start position:0%
+so for the max processes well we can
+ 
+
+ align:start position:0%
+so for the max processes well we can
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a bunch of processes each one now
+
+ align:start position:0%
+have a bunch of processes each one now
+ 
+
+ align:start position:0%
+have a bunch of processes each one now
+starting with its initial value
+
+ align:start position:0%
+starting with its initial value
+ 
+
+ align:start position:0%
+starting with its initial value
+and what happens when we plug them
+
+ align:start position:0%
+and what happens when we plug them
+ 
+
+ align:start position:0%
+and what happens when we plug them
+together with all their channels between
+
+ align:start position:0%
+together with all their channels between
+ 
+
+ align:start position:0%
+together with all their channels between
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+in you know for what corresponding to
+
+ align:start position:0%
+in you know for what corresponding to
+ 
+
+ align:start position:0%
+in you know for what corresponding to
+whatever graph they're in they just have
+
+ align:start position:0%
+whatever graph they're in they just have
+ 
+
+ align:start position:0%
+whatever graph they're in they just have
+channels on the edges
+
+ align:start position:0%
+channels on the edges
+ 
+
+ align:start position:0%
+channels on the edges
+so what's the behavior of this if
+
+ align:start position:0%
+so what's the behavior of this if
+ 
+
+ align:start position:0%
+so what's the behavior of this if
+everybo
+
+ align:start position:0%
+everybo
+ 
+
+ align:start position:0%
+everybo
+all the processes are like the ones i
+
+ align:start position:0%
+all the processes are like the ones i
+ 
+
+ align:start position:0%
+all the processes are like the ones i
+just showed you
+
+ align:start position:0%
+just showed you
+ 
+
+ align:start position:0%
+just showed you
+they wait till they hear some new max
+
+ align:start position:0%
+they wait till they hear some new max
+ 
+
+ align:start position:0%
+they wait till they hear some new max
+and then they send it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay um all all across the seats
+
+ align:start position:0%
+yeah okay um all all across the seats
+ 
+
+ align:start position:0%
+yeah okay um all all across the seats
+eventually have a global impact
+
+ align:start position:0%
+eventually have a global impact
+ 
+
+ align:start position:0%
+eventually have a global impact
+yep they'll all eventually get the
+
+ align:start position:0%
+yep they'll all eventually get the
+ 
+
+ align:start position:0%
+yep they'll all eventually get the
+global max they'll keep propagating
+
+ align:start position:0%
+global max they'll keep propagating
+ 
+
+ align:start position:0%
+global max they'll keep propagating
+until everybody receives it so here's a
+
+ align:start position:0%
+until everybody receives it so here's a
+ 
+
+ align:start position:0%
+until everybody receives it so here's a
+animation if everybody starts with the
+
+ align:start position:0%
+animation if everybody starts with the
+ 
+
+ align:start position:0%
+animation if everybody starts with the
+values that are written in these circles
+
+ align:start position:0%
+values that are written in these circles
+ 
+
+ align:start position:0%
+values that are written in these circles
+um okay so now remember before they were
+
+ align:start position:0%
+um okay so now remember before they were
+ 
+
+ align:start position:0%
+um okay so now remember before they were
+all sending it once now
+
+ align:start position:0%
+all sending it once now
+ 
+
+ align:start position:0%
+all sending it once now
+no more let's say the first thing that
+
+ align:start position:0%
+no more let's say the first thing that
+ 
+
+ align:start position:0%
+no more let's say the first thing that
+happens is the process that started with
+
+ align:start position:0%
+happens is the process that started with
+ 
+
+ align:start position:0%
+happens is the process that started with
+five sends its message out
+
+ align:start position:0%
+five sends its message out
+ 
+
+ align:start position:0%
+five sends its message out
+on one of its channels okay so the five
+
+ align:start position:0%
+on one of its channels okay so the five
+ 
+
+ align:start position:0%
+on one of its channels okay so the five
+goes out
+
+ align:start position:0%
+goes out
+ 
+
+ align:start position:0%
+goes out
+the next thing that might happen is the
+
+ align:start position:0%
+the next thing that might happen is the
+ 
+
+ align:start position:0%
+the next thing that might happen is the
+other process with the seven might send
+
+ align:start position:0%
+other process with the seven might send
+ 
+
+ align:start position:0%
+other process with the seven might send
+the seven out on one of its channels
+
+ align:start position:0%
+the seven out on one of its channels
+ 
+
+ align:start position:0%
+the seven out on one of its channels
+and these are three more steps somebody
+
+ align:start position:0%
+and these are three more steps somebody
+ 
+
+ align:start position:0%
+and these are three more steps somebody
+sends a ten somebody sends a seven
+
+ align:start position:0%
+sends a ten somebody sends a seven
+ 
+
+ align:start position:0%
+sends a ten somebody sends a seven
+uh somebody um received a message and
+
+ align:start position:0%
+uh somebody um received a message and
+ 
+
+ align:start position:0%
+uh somebody um received a message and
+updated
+
+ align:start position:0%
+updated
+ 
+
+ align:start position:0%
+updated
+its value as a result and we continue
+
+ align:start position:0%
+its value as a result and we continue
+ 
+
+ align:start position:0%
+its value as a result and we continue
+i'm
+
+ align:start position:0%
+i'm
+ 
+
+ align:start position:0%
+i'm
+depicting several steps at once because
+
+ align:start position:0%
+depicting several steps at once because
+ 
+
+ align:start position:0%
+depicting several steps at once because
+it's boring to really do them one at a
+
+ align:start position:0%
+it's boring to really do them one at a
+ 
+
+ align:start position:0%
+it's boring to really do them one at a
+time but
+
+ align:start position:0%
+time but
+ 
+
+ align:start position:0%
+time but
+the model really says they take steps in
+
+ align:start position:0%
+the model really says they take steps in
+ 
+
+ align:start position:0%
+the model really says they take steps in
+some order
+
+ align:start position:0%
+some order
+ 
+
+ align:start position:0%
+some order
+so everybody's propagating the largest
+
+ align:start position:0%
+so everybody's propagating the largest
+ 
+
+ align:start position:0%
+so everybody's propagating the largest
+thing you've seen
+
+ align:start position:0%
+thing you've seen
+ 
+
+ align:start position:0%
+thing you've seen
+and eventually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you wind up with everybody having the
+
+ align:start position:0%
+you wind up with everybody having the
+ 
+
+ align:start position:0%
+you wind up with everybody having the
+maximum value the 10.
+
+ align:start position:0%
+maximum value the 10.
+ 
+
+ align:start position:0%
+maximum value the 10.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that's how an asynchronous
+
+ align:start position:0%
+all right so that's how an asynchronous
+ 
+
+ align:start position:0%
+all right so that's how an asynchronous
+system operates
+
+ align:start position:0%
+system operates
+ 
+
+ align:start position:0%
+system operates
+um we can analyze the message complexity
+
+ align:start position:0%
+um we can analyze the message complexity
+ 
+
+ align:start position:0%
+um we can analyze the message complexity
+of this uh the total number of messages
+
+ align:start position:0%
+of this uh the total number of messages
+ 
+
+ align:start position:0%
+of this uh the total number of messages
+sent during the entire execution at
+
+ align:start position:0%
+sent during the entire execution at
+ 
+
+ align:start position:0%
+sent during the entire execution at
+worst
+
+ align:start position:0%
+worst
+ 
+
+ align:start position:0%
+worst
+on every edge you can send the
+
+ align:start position:0%
+on every edge you can send the
+ 
+
+ align:start position:0%
+on every edge you can send the
+successively improved estimates so
+
+ align:start position:0%
+successively improved estimates so
+ 
+
+ align:start position:0%
+successively improved estimates so
+that's again
+
+ align:start position:0%
+that's again
+ 
+
+ align:start position:0%
+that's again
+order n times the number of edges
+
+ align:start position:0%
+order n times the number of edges
+ 
+
+ align:start position:0%
+order n times the number of edges
+time complexity is an issue okay so
+
+ align:start position:0%
+time complexity is an issue okay so
+ 
+
+ align:start position:0%
+time complexity is an issue okay so
+when we had synchronous algorithms we
+
+ align:start position:0%
+when we had synchronous algorithms we
+ 
+
+ align:start position:0%
+when we had synchronous algorithms we
+just counted the number of rounds and
+
+ align:start position:0%
+just counted the number of rounds and
+ 
+
+ align:start position:0%
+just counted the number of rounds and
+that was easy
+
+ align:start position:0%
+that was easy
+ 
+
+ align:start position:0%
+that was easy
+but what do we measure now how do we
+
+ align:start position:0%
+but what do we measure now how do we
+ 
+
+ align:start position:0%
+but what do we measure now how do we
+count the time
+
+ align:start position:0%
+count the time
+ 
+
+ align:start position:0%
+count the time
+when you know you have all these
+
+ align:start position:0%
+when you know you have all these
+ 
+
+ align:start position:0%
+when you know you have all these
+processes and channels taking steps
+
+ align:start position:0%
+processes and channels taking steps
+ 
+
+ align:start position:0%
+processes and channels taking steps
+whenever they want
+
+ align:start position:0%
+whenever they want
+ 
+
+ align:start position:0%
+whenever they want
+yeah so this really isn't obvious
+
+ align:start position:0%
+yeah so this really isn't obvious
+ 
+
+ align:start position:0%
+yeah so this really isn't obvious
+there's a solution that's commonly used
+
+ align:start position:0%
+there's a solution that's commonly used
+ 
+
+ align:start position:0%
+there's a solution that's commonly used
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+okay we're going to use real time
+
+ align:start position:0%
+okay we're going to use real time
+ 
+
+ align:start position:0%
+okay we're going to use real time
+and we're going to make some assumptions
+
+ align:start position:0%
+and we're going to make some assumptions
+ 
+
+ align:start position:0%
+and we're going to make some assumptions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um certain basic steps taking at most
+
+ align:start position:0%
+um certain basic steps taking at most
+ 
+
+ align:start position:0%
+um certain basic steps taking at most
+a certain amount of time like
+
+ align:start position:0%
+a certain amount of time like
+ 
+
+ align:start position:0%
+a certain amount of time like
+let's say that local computation time
+
+ align:start position:0%
+let's say that local computation time
+ 
+
+ align:start position:0%
+let's say that local computation time
+for a process to perform
+
+ align:start position:0%
+for a process to perform
+ 
+
+ align:start position:0%
+for a process to perform
+its next step is little l you just give
+
+ align:start position:0%
+its next step is little l you just give
+ 
+
+ align:start position:0%
+its next step is little l you just give
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a local time bound and then you have d
+
+ align:start position:0%
+a local time bound and then you have d
+ 
+
+ align:start position:0%
+a local time bound and then you have d
+for a channel to deliver
+
+ align:start position:0%
+for a channel to deliver
+ 
+
+ align:start position:0%
+for a channel to deliver
+one message the first message that's
+
+ align:start position:0%
+one message the first message that's
+ 
+
+ align:start position:0%
+one message the first message that's
+currently in the channel
+
+ align:start position:0%
+currently in the channel
+ 
+
+ align:start position:0%
+currently in the channel
+if you have assumptions like that you
+
+ align:start position:0%
+if you have assumptions like that you
+ 
+
+ align:start position:0%
+if you have assumptions like that you
+could use those to infer
+
+ align:start position:0%
+could use those to infer
+ 
+
+ align:start position:0%
+could use those to infer
+a real-time upper bound for solving the
+
+ align:start position:0%
+a real-time upper bound for solving the
+ 
+
+ align:start position:0%
+a real-time upper bound for solving the
+whole problem i mean if you know
+
+ align:start position:0%
+whole problem i mean if you know
+ 
+
+ align:start position:0%
+whole problem i mean if you know
+it takes no longer than d to deliver one
+
+ align:start position:0%
+it takes no longer than d to deliver one
+ 
+
+ align:start position:0%
+it takes no longer than d to deliver one
+message
+
+ align:start position:0%
+message
+ 
+
+ align:start position:0%
+message
+then you can bound how long it takes to
+
+ align:start position:0%
+then you can bound how long it takes to
+ 
+
+ align:start position:0%
+then you can bound how long it takes to
+deliver to empty out a cue
+
+ align:start position:0%
+deliver to empty out a cue
+ 
+
+ align:start position:0%
+deliver to empty out a cue
+a channel and how long it takes for
+
+ align:start position:0%
+a channel and how long it takes for
+ 
+
+ align:start position:0%
+a channel and how long it takes for
+messages to propagate through the
+
+ align:start position:0%
+messages to propagate through the
+ 
+
+ align:start position:0%
+messages to propagate through the
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+okay so this is
+
+ align:start position:0%
+okay so this is
+ 
+
+ align:start position:0%
+okay so this is
+it's tricky but this is uh about the
+
+ align:start position:0%
+it's tricky but this is uh about the
+ 
+
+ align:start position:0%
+it's tricky but this is uh about the
+only thing you can do in a setting where
+
+ align:start position:0%
+only thing you can do in a setting where
+ 
+
+ align:start position:0%
+only thing you can do in a setting where
+you don't actually have rounds to
+
+ align:start position:0%
+you don't actually have rounds to
+ 
+
+ align:start position:0%
+you don't actually have rounds to
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+okay so then for the max system how long
+
+ align:start position:0%
+okay so then for the max system how long
+ 
+
+ align:start position:0%
+okay so then for the max system how long
+does it take well let's just ignore the
+
+ align:start position:0%
+does it take well let's just ignore the
+ 
+
+ align:start position:0%
+does it take well let's just ignore the
+local processing time
+
+ align:start position:0%
+local processing time
+ 
+
+ align:start position:0%
+local processing time
+usually that's assumed to be very small
+
+ align:start position:0%
+usually that's assumed to be very small
+ 
+
+ align:start position:0%
+usually that's assumed to be very small
+so let's say it's zero
+
+ align:start position:0%
+so let's say it's zero
+ 
+
+ align:start position:0%
+so let's say it's zero
+we can get a very simple pessimistic
+
+ align:start position:0%
+we can get a very simple pessimistic
+ 
+
+ align:start position:0%
+we can get a very simple pessimistic
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+upper bound that says the real time
+
+ align:start position:0%
+upper bound that says the real time
+ 
+
+ align:start position:0%
+upper bound that says the real time
+for finishing the whole thing is the
+
+ align:start position:0%
+for finishing the whole thing is the
+ 
+
+ align:start position:0%
+for finishing the whole thing is the
+order of the diameter of the network
+
+ align:start position:0%
+order of the diameter of the network
+ 
+
+ align:start position:0%
+order of the diameter of the network
+times the number of nodes times
+
+ align:start position:0%
+times the number of nodes times
+ 
+
+ align:start position:0%
+times the number of nodes times
+little d is the amount of time for a
+
+ align:start position:0%
+little d is the amount of time for a
+ 
+
+ align:start position:0%
+little d is the amount of time for a
+message queue to deliver its first
+
+ align:start position:0%
+message queue to deliver its first
+ 
+
+ align:start position:0%
+message queue to deliver its first
+message
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so as a naive way of analyzing this
+
+ align:start position:0%
+okay so as a naive way of analyzing this
+ 
+
+ align:start position:0%
+okay so as a naive way of analyzing this
+you just consider how long it takes for
+
+ align:start position:0%
+you just consider how long it takes for
+ 
+
+ align:start position:0%
+you just consider how long it takes for
+the max to reach some particular vertex
+
+ align:start position:0%
+the max to reach some particular vertex
+ 
+
+ align:start position:0%
+the max to reach some particular vertex
+u along the shortest path well it has to
+
+ align:start position:0%
+u along the shortest path well it has to
+ 
+
+ align:start position:0%
+u along the shortest path well it has to
+go through all the
+
+ align:start position:0%
+go through all the
+ 
+
+ align:start position:0%
+go through all the
+hops on the path so
+
+ align:start position:0%
+hops on the path so
+ 
+
+ align:start position:0%
+hops on the path so
+that would be the diameter and
+
+ align:start position:0%
+that would be the diameter and
+ 
+
+ align:start position:0%
+that would be the diameter and
+how long does it have to wait in each
+
+ align:start position:0%
+how long does it have to wait in each
+ 
+
+ align:start position:0%
+how long does it have to wait in each
+channel before it gets to
+
+ align:start position:0%
+channel before it gets to
+ 
+
+ align:start position:0%
+channel before it gets to
+move another hop well it might be at the
+
+ align:start position:0%
+move another hop well it might be at the
+ 
+
+ align:start position:0%
+move another hop well it might be at the
+end of a q
+
+ align:start position:0%
+end of a q
+ 
+
+ align:start position:0%
+end of a q
+how big could the q be well at worst end
+
+ align:start position:0%
+how big could the q be well at worst end
+ 
+
+ align:start position:0%
+how big could the q be well at worst end
+for the improved estimates
+
+ align:start position:0%
+for the improved estimates
+ 
+
+ align:start position:0%
+for the improved estimates
+so let's say it's n times the delivery
+
+ align:start position:0%
+so let's say it's n times the delivery
+ 
+
+ align:start position:0%
+so let's say it's n times the delivery
+time on the channel
+
+ align:start position:0%
+time on the channel
+ 
+
+ align:start position:0%
+time on the channel
+just to traverse one channel what i'm
+
+ align:start position:0%
+just to traverse one channel what i'm
+ 
+
+ align:start position:0%
+just to traverse one channel what i'm
+doing is modeling
+
+ align:start position:0%
+doing is modeling
+ 
+
+ align:start position:0%
+doing is modeling
+possible congestion on the queue to see
+
+ align:start position:0%
+possible congestion on the queue to see
+ 
+
+ align:start position:0%
+possible congestion on the queue to see
+how long it takes for
+
+ align:start position:0%
+how long it takes for
+ 
+
+ align:start position:0%
+how long it takes for
+for a message to traverse one channel
+
+ align:start position:0%
+for a message to traverse one channel
+ 
+
+ align:start position:0%
+for a message to traverse one channel
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+are we just assuming that processes
+
+ align:start position:0%
+are we just assuming that processes
+ 
+
+ align:start position:0%
+are we just assuming that processes
+process things and messages are
+
+ align:start position:0%
+process things and messages are
+ 
+
+ align:start position:0%
+process things and messages are
+delivered as soon as they can possibly
+
+ align:start position:0%
+delivered as soon as they can possibly
+ 
+
+ align:start position:0%
+delivered as soon as they can possibly
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+um good yeah so and we we normally have
+
+ align:start position:0%
+um good yeah so and we we normally have
+ 
+
+ align:start position:0%
+um good yeah so and we we normally have
+i'm sort of skipping over some things in
+
+ align:start position:0%
+i'm sort of skipping over some things in
+ 
+
+ align:start position:0%
+i'm sort of skipping over some things in
+the model but you have
+
+ align:start position:0%
+the model but you have
+ 
+
+ align:start position:0%
+the model but you have
+a um a liveness assumption that says
+
+ align:start position:0%
+a um a liveness assumption that says
+ 
+
+ align:start position:0%
+a um a liveness assumption that says
+that a process keeps taking steps
+
+ align:start position:0%
+that a process keeps taking steps
+ 
+
+ align:start position:0%
+that a process keeps taking steps
+as long as it has anything to do and so
+
+ align:start position:0%
+as long as it has anything to do and so
+ 
+
+ align:start position:0%
+as long as it has anything to do and so
+we would be putting time bounds
+
+ align:start position:0%
+we would be putting time bounds
+ 
+
+ align:start position:0%
+we would be putting time bounds
+on how long it takes between those steps
+
+ align:start position:0%
+on how long it takes between those steps
+ 
+
+ align:start position:0%
+on how long it takes between those steps
+that'd be the local processing
+
+ align:start position:0%
+that'd be the local processing
+ 
+
+ align:start position:0%
+that'd be the local processing
+time here i'm saying that zero so we can
+
+ align:start position:0%
+time here i'm saying that zero so we can
+ 
+
+ align:start position:0%
+time here i'm saying that zero so we can
+do that wouldn't you be able to like
+
+ align:start position:0%
+do that wouldn't you be able to like
+ 
+
+ align:start position:0%
+do that wouldn't you be able to like
+get some amount of information about
+
+ align:start position:0%
+get some amount of information about
+ 
+
+ align:start position:0%
+get some amount of information about
+what were things happening
+
+ align:start position:0%
+what were things happening
+ 
+
+ align:start position:0%
+what were things happening
+ah okay so here's this is a very subtle
+
+ align:start position:0%
+ah okay so here's this is a very subtle
+ 
+
+ align:start position:0%
+ah okay so here's this is a very subtle
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+so what you think is that if i'm making
+
+ align:start position:0%
+so what you think is that if i'm making
+ 
+
+ align:start position:0%
+so what you think is that if i'm making
+all these timing assumptions the
+
+ align:start position:0%
+all these timing assumptions the
+ 
+
+ align:start position:0%
+all these timing assumptions the
+processes should be able to figure that
+
+ align:start position:0%
+processes should be able to figure that
+ 
+
+ align:start position:0%
+processes should be able to figure that
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+but actually you can't figure anything
+
+ align:start position:0%
+but actually you can't figure anything
+ 
+
+ align:start position:0%
+but actually you can't figure anything
+out just based on
+
+ align:start position:0%
+out just based on
+ 
+
+ align:start position:0%
+out just based on
+these assumptions about these upper
+
+ align:start position:0%
+these assumptions about these upper
+ 
+
+ align:start position:0%
+these assumptions about these upper
+bounds
+
+ align:start position:0%
+bounds
+ 
+
+ align:start position:0%
+bounds
+putting upper bounds on the time between
+
+ align:start position:0%
+putting upper bounds on the time between
+ 
+
+ align:start position:0%
+putting upper bounds on the time between
+steps does not in any way restrict the
+
+ align:start position:0%
+steps does not in any way restrict the
+ 
+
+ align:start position:0%
+steps does not in any way restrict the
+orderings
+
+ align:start position:0%
+orderings
+ 
+
+ align:start position:0%
+orderings
+you still have all the same possible
+
+ align:start position:0%
+you still have all the same possible
+ 
+
+ align:start position:0%
+you still have all the same possible
+orderings of steps
+
+ align:start position:0%
+orderings of steps
+ 
+
+ align:start position:0%
+orderings of steps
+so nobody can see anything different
+
+ align:start position:0%
+so nobody can see anything different
+ 
+
+ align:start position:0%
+so nobody can see anything different
+these times are not visible in any sense
+
+ align:start position:0%
+these times are not visible in any sense
+ 
+
+ align:start position:0%
+these times are not visible in any sense
+they're not marked anywhere for the
+
+ align:start position:0%
+they're not marked anywhere for the
+ 
+
+ align:start position:0%
+they're not marked anywhere for the
+processes to read
+
+ align:start position:0%
+processes to read
+ 
+
+ align:start position:0%
+processes to read
+they're just something that we're using
+
+ align:start position:0%
+they're just something that we're using
+ 
+
+ align:start position:0%
+they're just something that we're using
+to evaluate the cost the time
+
+ align:start position:0%
+to evaluate the cost the time
+ 
+
+ align:start position:0%
+to evaluate the cost the time
+cost of the execution
+
+ align:start position:0%
+cost of the execution
+ 
+
+ align:start position:0%
+cost of the execution
+and you're not um you're not restricting
+
+ align:start position:0%
+and you're not um you're not restricting
+ 
+
+ align:start position:0%
+and you're not um you're not restricting
+the execution by putting just
+
+ align:start position:0%
+the execution by putting just
+ 
+
+ align:start position:0%
+the execution by putting just
+upper bounds on the time if you were
+
+ align:start position:0%
+upper bounds on the time if you were
+ 
+
+ align:start position:0%
+upper bounds on the time if you were
+restricting the execution like you had
+
+ align:start position:0%
+restricting the execution like you had
+ 
+
+ align:start position:0%
+restricting the execution like you had
+upper bounds and lower bounds on the
+
+ align:start position:0%
+upper bounds and lower bounds on the
+ 
+
+ align:start position:0%
+upper bounds and lower bounds on the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+then the processes might know a lot more
+
+ align:start position:0%
+then the processes might know a lot more
+ 
+
+ align:start position:0%
+then the processes might know a lot more
+they might in fact be acting more like a
+
+ align:start position:0%
+they might in fact be acting more like a
+ 
+
+ align:start position:0%
+they might in fact be acting more like a
+synchronous
+
+ align:start position:0%
+synchronous
+ 
+
+ align:start position:0%
+synchronous
+system okay so these are times that are
+
+ align:start position:0%
+system okay so these are times that are
+ 
+
+ align:start position:0%
+system okay so these are times that are
+just used for analyzing complexity
+
+ align:start position:0%
+just used for analyzing complexity
+ 
+
+ align:start position:0%
+just used for analyzing complexity
+they're not anything known to the
+
+ align:start position:0%
+they're not anything known to the
+ 
+
+ align:start position:0%
+they're not anything known to the
+processes in the system
+
+ align:start position:0%
+processes in the system
+ 
+
+ align:start position:0%
+processes in the system
+okay all right so now let's revisit the
+
+ align:start position:0%
+okay all right so now let's revisit the
+ 
+
+ align:start position:0%
+okay all right so now let's revisit the
+breadth first spanning tree problem
+
+ align:start position:0%
+breadth first spanning tree problem
+ 
+
+ align:start position:0%
+breadth first spanning tree problem
+we want to now compute a breadth first
+
+ align:start position:0%
+we want to now compute a breadth first
+ 
+
+ align:start position:0%
+we want to now compute a breadth first
+spanning tree in an asynchronous network
+
+ align:start position:0%
+spanning tree in an asynchronous network
+ 
+
+ align:start position:0%
+spanning tree in an asynchronous network
+connected graph distinguished root
+
+ align:start position:0%
+connected graph distinguished root
+ 
+
+ align:start position:0%
+connected graph distinguished root
+vertex processes have no knowledge of
+
+ align:start position:0%
+vertex processes have no knowledge of
+ 
+
+ align:start position:0%
+vertex processes have no knowledge of
+the graph
+
+ align:start position:0%
+the graph
+ 
+
+ align:start position:0%
+the graph
+they have uids all this is the same as
+
+ align:start position:0%
+they have uids all this is the same as
+ 
+
+ align:start position:0%
+they have uids all this is the same as
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+in the synchronous case everybody's
+
+ align:start position:0%
+in the synchronous case everybody's
+ 
+
+ align:start position:0%
+in the synchronous case everybody's
+supposed to output
+
+ align:start position:0%
+supposed to output
+ 
+
+ align:start position:0%
+supposed to output
+its parent information when it's done
+
+ align:start position:0%
+its parent information when it's done
+ 
+
+ align:start position:0%
+its parent information when it's done
+okay so here's
+
+ align:start position:0%
+okay so here's
+ 
+
+ align:start position:0%
+okay so here's
+here's an idea suppose we just take that
+
+ align:start position:0%
+here's an idea suppose we just take that
+ 
+
+ align:start position:0%
+here's an idea suppose we just take that
+nice simple
+
+ align:start position:0%
+nice simple
+ 
+
+ align:start position:0%
+nice simple
+synchronous algorithm that i reviewed at
+
+ align:start position:0%
+synchronous algorithm that i reviewed at
+ 
+
+ align:start position:0%
+synchronous algorithm that i reviewed at
+the beginning of the hour
+
+ align:start position:0%
+the beginning of the hour
+ 
+
+ align:start position:0%
+the beginning of the hour
+where everybody just sends a search
+
+ align:start position:0%
+where everybody just sends a search
+ 
+
+ align:start position:0%
+where everybody just sends a search
+message as soon as they get it and they
+
+ align:start position:0%
+message as soon as they get it and they
+ 
+
+ align:start position:0%
+message as soon as they get it and they
+just adopt the first parent they see
+
+ align:start position:0%
+just adopt the first parent they see
+ 
+
+ align:start position:0%
+just adopt the first parent they see
+okay what happens if i run that
+
+ align:start position:0%
+okay what happens if i run that
+ 
+
+ align:start position:0%
+okay what happens if i run that
+asynchronously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i just send it and i get a search
+
+ align:start position:0%
+i just send it and i get a search
+ 
+
+ align:start position:0%
+i just send it and i get a search
+message then i send it out to my parents
+
+ align:start position:0%
+message then i send it out to my parents
+ 
+
+ align:start position:0%
+message then i send it out to my parents
+whenever and everybody's doing this
+
+ align:start position:0%
+whenever and everybody's doing this
+ 
+
+ align:start position:0%
+whenever and everybody's doing this
+whatever they get whenever they get
+
+ align:start position:0%
+whatever they get whenever they get
+ 
+
+ align:start position:0%
+whatever they get whenever they get
+their first search message they decide
+
+ align:start position:0%
+their first search message they decide
+ 
+
+ align:start position:0%
+their first search message they decide
+the sender is its parent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keeps yeah not moving not obeying the
+
+ align:start position:0%
+keeps yeah not moving not obeying the
+ 
+
+ align:start position:0%
+keeps yeah not moving not obeying the
+fanning property of the vfs
+
+ align:start position:0%
+fanning property of the vfs
+ 
+
+ align:start position:0%
+fanning property of the vfs
+yeah it could be that because we don't
+
+ align:start position:0%
+yeah it could be that because we don't
+ 
+
+ align:start position:0%
+yeah it could be that because we don't
+have any restriction on how
+
+ align:start position:0%
+have any restriction on how
+ 
+
+ align:start position:0%
+have any restriction on how
+fast the messages might be sent and
+
+ align:start position:0%
+fast the messages might be sent and
+ 
+
+ align:start position:0%
+fast the messages might be sent and
+the order of steps it could be that some
+
+ align:start position:0%
+the order of steps it could be that some
+ 
+
+ align:start position:0%
+the order of steps it could be that some
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+get sent very quickly on some long path
+
+ align:start position:0%
+get sent very quickly on some long path
+ 
+
+ align:start position:0%
+get sent very quickly on some long path
+so someone
+
+ align:start position:0%
+so someone
+ 
+
+ align:start position:0%
+so someone
+sitting at the far end of the network
+
+ align:start position:0%
+sitting at the far end of the network
+ 
+
+ align:start position:0%
+sitting at the far end of the network
+might get a message first on a long path
+
+ align:start position:0%
+might get a message first on a long path
+ 
+
+ align:start position:0%
+might get a message first on a long path
+and later on a short path
+
+ align:start position:0%
+and later on a short path
+ 
+
+ align:start position:0%
+and later on a short path
+and the first one it gets if it decides
+
+ align:start position:0%
+and the first one it gets if it decides
+ 
+
+ align:start position:0%
+and the first one it gets if it decides
+that's its parent
+
+ align:start position:0%
+that's its parent
+ 
+
+ align:start position:0%
+that's its parent
+then it's stuck this is not an algorithm
+
+ align:start position:0%
+then it's stuck this is not an algorithm
+ 
+
+ align:start position:0%
+then it's stuck this is not an algorithm
+that makes corrections
+
+ align:start position:0%
+that makes corrections
+ 
+
+ align:start position:0%
+that makes corrections
+okay so all right
+
+ align:start position:0%
+okay so all right
+ 
+
+ align:start position:0%
+okay so all right
+well we before we had a little bit of
+
+ align:start position:0%
+well we before we had a little bit of
+ 
+
+ align:start position:0%
+well we before we had a little bit of
+non-determinism when we had this
+
+ align:start position:0%
+non-determinism when we had this
+ 
+
+ align:start position:0%
+non-determinism when we had this
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+in the synchronous case because we could
+
+ align:start position:0%
+in the synchronous case because we could
+ 
+
+ align:start position:0%
+in the synchronous case because we could
+have two
+
+ align:start position:0%
+have two
+ 
+
+ align:start position:0%
+have two
+messages arriving at once and you have
+
+ align:start position:0%
+messages arriving at once and you have
+ 
+
+ align:start position:0%
+messages arriving at once and you have
+to pick one to be your parent
+
+ align:start position:0%
+to pick one to be your parent
+ 
+
+ align:start position:0%
+to pick one to be your parent
+now that doesn't happen because you only
+
+ align:start position:0%
+now that doesn't happen because you only
+ 
+
+ align:start position:0%
+now that doesn't happen because you only
+get one message at a time
+
+ align:start position:0%
+get one message at a time
+ 
+
+ align:start position:0%
+get one message at a time
+but you have a lot more non-determinism
+
+ align:start position:0%
+but you have a lot more non-determinism
+ 
+
+ align:start position:0%
+but you have a lot more non-determinism
+now okay now you have
+
+ align:start position:0%
+now okay now you have
+ 
+
+ align:start position:0%
+now okay now you have
+all this non-determinism from the order
+
+ align:start position:0%
+all this non-determinism from the order
+ 
+
+ align:start position:0%
+all this non-determinism from the order
+in which the messages get
+
+ align:start position:0%
+in which the messages get
+ 
+
+ align:start position:0%
+in which the messages get
+sent and processes take their steps so
+
+ align:start position:0%
+sent and processes take their steps so
+ 
+
+ align:start position:0%
+sent and processes take their steps so
+there's plenty of non-determinism and
+
+ align:start position:0%
+there's plenty of non-determinism and
+ 
+
+ align:start position:0%
+there's plenty of non-determinism and
+remember the way we treat
+
+ align:start position:0%
+remember the way we treat
+ 
+
+ align:start position:0%
+remember the way we treat
+non-determinism
+
+ align:start position:0%
+non-determinism
+ 
+
+ align:start position:0%
+non-determinism
+for distributed algorithms is it's
+
+ align:start position:0%
+for distributed algorithms is it's
+ 
+
+ align:start position:0%
+for distributed algorithms is it's
+supposed to work regardless of how those
+
+ align:start position:0%
+supposed to work regardless of how those
+ 
+
+ align:start position:0%
+supposed to work regardless of how those
+non-deterministic choices get made
+
+ align:start position:0%
+non-deterministic choices get made
+ 
+
+ align:start position:0%
+non-deterministic choices get made
+okay so how would we describe i'll just
+
+ align:start position:0%
+okay so how would we describe i'll just
+ 
+
+ align:start position:0%
+okay so how would we describe i'll just
+write some pseudo code here for
+
+ align:start position:0%
+write some pseudo code here for
+ 
+
+ align:start position:0%
+write some pseudo code here for
+a process that's just mimicking the
+
+ align:start position:0%
+a process that's just mimicking the
+ 
+
+ align:start position:0%
+a process that's just mimicking the
+trivial algorithm
+
+ align:start position:0%
+trivial algorithm
+ 
+
+ align:start position:0%
+trivial algorithm
+it can receive a search message that's
+
+ align:start position:0%
+it can receive a search message that's
+ 
+
+ align:start position:0%
+it can receive a search message that's
+the inputs and it can
+
+ align:start position:0%
+the inputs and it can
+ 
+
+ align:start position:0%
+the inputs and it can
+send a search message as its output
+
+ align:start position:0%
+send a search message as its output
+ 
+
+ align:start position:0%
+send a search message as its output
+it can also output parent when it's
+
+ align:start position:0%
+it can also output parent when it's
+ 
+
+ align:start position:0%
+it can also output parent when it's
+ready to do that
+
+ align:start position:0%
+ready to do that
+ 
+
+ align:start position:0%
+ready to do that
+okay so what does it have to keep track
+
+ align:start position:0%
+okay so what does it have to keep track
+ 
+
+ align:start position:0%
+okay so what does it have to keep track
+of well keeps track of its
+
+ align:start position:0%
+of well keeps track of its
+ 
+
+ align:start position:0%
+of well keeps track of its
+its parent keeps track of whether it's
+
+ align:start position:0%
+its parent keeps track of whether it's
+ 
+
+ align:start position:0%
+its parent keeps track of whether it's
+reported its parent
+
+ align:start position:0%
+reported its parent
+ 
+
+ align:start position:0%
+reported its parent
+and it has some send buffers with
+
+ align:start position:0%
+and it has some send buffers with
+ 
+
+ align:start position:0%
+and it has some send buffers with
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+it's ready to send to its neighbors
+
+ align:start position:0%
+it's ready to send to its neighbors
+ 
+
+ align:start position:0%
+it's ready to send to its neighbors
+could be search messages or nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this bottom symbol is just a placeholder
+
+ align:start position:0%
+this bottom symbol is just a placeholder
+ 
+
+ align:start position:0%
+this bottom symbol is just a placeholder
+symbol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what happens when
+
+ align:start position:0%
+okay so what happens when
+ 
+
+ align:start position:0%
+okay so what happens when
+the process receives a search message
+
+ align:start position:0%
+the process receives a search message
+ 
+
+ align:start position:0%
+the process receives a search message
+just following the simple algorithm
+
+ align:start position:0%
+just following the simple algorithm
+ 
+
+ align:start position:0%
+just following the simple algorithm
+well if it doesn't have a parent yet
+
+ align:start position:0%
+well if it doesn't have a parent yet
+ 
+
+ align:start position:0%
+well if it doesn't have a parent yet
+then it sets its parent to be the sender
+
+ align:start position:0%
+then it sets its parent to be the sender
+ 
+
+ align:start position:0%
+then it sets its parent to be the sender
+of that search message
+
+ align:start position:0%
+of that search message
+ 
+
+ align:start position:0%
+of that search message
+and it gets ready to send the search
+
+ align:start position:0%
+and it gets ready to send the search
+ 
+
+ align:start position:0%
+and it gets ready to send the search
+message to all of its neighbors
+
+ align:start position:0%
+message to all of its neighbors
+ 
+
+ align:start position:0%
+message to all of its neighbors
+so that's really the heart of the
+
+ align:start position:0%
+so that's really the heart of the
+ 
+
+ align:start position:0%
+so that's really the heart of the
+algorithm that you saw
+
+ align:start position:0%
+algorithm that you saw
+ 
+
+ align:start position:0%
+algorithm that you saw
+for the simple algorithm for the the
+
+ align:start position:0%
+for the simple algorithm for the the
+ 
+
+ align:start position:0%
+for the simple algorithm for the the
+synchronous case so that's the same code
+
+ align:start position:0%
+synchronous case so that's the same code
+ 
+
+ align:start position:0%
+synchronous case so that's the same code
+the rest of the code is it just sends
+
+ align:start position:0%
+the rest of the code is it just sends
+ 
+
+ align:start position:0%
+the rest of the code is it just sends
+the search messages out when it's got
+
+ align:start position:0%
+the search messages out when it's got
+ 
+
+ align:start position:0%
+the search messages out when it's got
+them in
+
+ align:start position:0%
+them in
+ 
+
+ align:start position:0%
+them in
+the send buffers and it can announce its
+
+ align:start position:0%
+the send buffers and it can announce its
+ 
+
+ align:start position:0%
+the send buffers and it can announce its
+parent once the parent is set
+
+ align:start position:0%
+parent once the parent is set
+ 
+
+ align:start position:0%
+parent once the parent is set
+and uh then it doesn't this flag just
+
+ align:start position:0%
+and uh then it doesn't this flag just
+ 
+
+ align:start position:0%
+and uh then it doesn't this flag just
+means it doesn't keep announcing it over
+
+ align:start position:0%
+means it doesn't keep announcing it over
+ 
+
+ align:start position:0%
+means it doesn't keep announcing it over
+and over again
+
+ align:start position:0%
+and over again
+ 
+
+ align:start position:0%
+and over again
+okay so it makes sense that this
+
+ align:start position:0%
+okay so it makes sense that this
+ 
+
+ align:start position:0%
+okay so it makes sense that this
+describes that simple algorithm
+
+ align:start position:0%
+describes that simple algorithm
+ 
+
+ align:start position:0%
+describes that simple algorithm
+it's pretty concise just what does it do
+
+ align:start position:0%
+it's pretty concise just what does it do
+ 
+
+ align:start position:0%
+it's pretty concise just what does it do
+in all these different steps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now if you run this
+
+ align:start position:0%
+okay okay so now if you run this
+ 
+
+ align:start position:0%
+okay okay so now if you run this
+asynchronously
+
+ align:start position:0%
+asynchronously
+ 
+
+ align:start position:0%
+asynchronously
+as you already noted it isn't going to
+
+ align:start position:0%
+as you already noted it isn't going to
+ 
+
+ align:start position:0%
+as you already noted it isn't going to
+necessarily work right
+
+ align:start position:0%
+necessarily work right
+ 
+
+ align:start position:0%
+necessarily work right
+so you can have this guy sending search
+
+ align:start position:0%
+so you can have this guy sending search
+ 
+
+ align:start position:0%
+so you can have this guy sending search
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+but some are going to arrive faster than
+
+ align:start position:0%
+but some are going to arrive faster than
+ 
+
+ align:start position:0%
+but some are going to arrive faster than
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+and you see you can have the search
+
+ align:start position:0%
+and you see you can have the search
+ 
+
+ align:start position:0%
+and you see you can have the search
+messages creeping around
+
+ align:start position:0%
+messages creeping around
+ 
+
+ align:start position:0%
+messages creeping around
+in an indirect path which causes a
+
+ align:start position:0%
+in an indirect path which causes a
+ 
+
+ align:start position:0%
+in an indirect path which causes a
+spanning tree like this one to be
+
+ align:start position:0%
+spanning tree like this one to be
+ 
+
+ align:start position:0%
+spanning tree like this one to be
+created
+
+ align:start position:0%
+created
+ 
+
+ align:start position:0%
+created
+which is definitely not a breadth for a
+
+ align:start position:0%
+which is definitely not a breadth for a
+ 
+
+ align:start position:0%
+which is definitely not a breadth for a
+spanning tree the bread first tree is
+
+ align:start position:0%
+spanning tree the bread first tree is
+ 
+
+ align:start position:0%
+spanning tree the bread first tree is
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+a breath first tree okay so you have
+
+ align:start position:0%
+a breath first tree okay so you have
+ 
+
+ align:start position:0%
+a breath first tree okay so you have
+these roundabout pads
+
+ align:start position:0%
+these roundabout pads
+ 
+
+ align:start position:0%
+these roundabout pads
+okay so this doesn't work so what do we
+
+ align:start position:0%
+okay so this doesn't work so what do we
+ 
+
+ align:start position:0%
+okay so this doesn't work so what do we
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to try to synchronize them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+that is related to a homework question
+
+ align:start position:0%
+that is related to a homework question
+ 
+
+ align:start position:0%
+that is related to a homework question
+this week very good
+
+ align:start position:0%
+this week very good
+ 
+
+ align:start position:0%
+this week very good
+we're going to do something different
+
+ align:start position:0%
+we're going to do something different
+ 
+
+ align:start position:0%
+we're going to do something different
+other suggestions
+
+ align:start position:0%
+other suggestions
+ 
+
+ align:start position:0%
+other suggestions
+yeah we could like keep a variable
+
+ align:start position:0%
+yeah we could like keep a variable
+ 
+
+ align:start position:0%
+yeah we could like keep a variable
+in each process that so like you can do
+
+ align:start position:0%
+in each process that so like you can do
+ 
+
+ align:start position:0%
+in each process that so like you can do
+something like down and forward
+
+ align:start position:0%
+something like down and forward
+ 
+
+ align:start position:0%
+something like down and forward
+yeah so you can do what we did for
+
+ align:start position:0%
+yeah so you can do what we did for
+ 
+
+ align:start position:0%
+yeah so you can do what we did for
+bellman ford but now the setting is
+
+ align:start position:0%
+bellman ford but now the setting is
+ 
+
+ align:start position:0%
+bellman ford but now the setting is
+completely different we did it for
+
+ align:start position:0%
+completely different we did it for
+ 
+
+ align:start position:0%
+completely different we did it for
+bellman ford
+
+ align:start position:0%
+bellman ford
+ 
+
+ align:start position:0%
+bellman ford
+when it was synchronous and we had
+
+ align:start position:0%
+when it was synchronous and we had
+ 
+
+ align:start position:0%
+when it was synchronous and we had
+weights now it's asynchronous and there
+
+ align:start position:0%
+weights now it's asynchronous and there
+ 
+
+ align:start position:0%
+weights now it's asynchronous and there
+are no weights
+
+ align:start position:0%
+are no weights
+ 
+
+ align:start position:0%
+are no weights
+okay so oh there's some remarks on
+
+ align:start position:0%
+okay so oh there's some remarks on
+ 
+
+ align:start position:0%
+okay so oh there's some remarks on
+a couple of slides here so this is just
+
+ align:start position:0%
+a couple of slides here so this is just
+ 
+
+ align:start position:0%
+a couple of slides here so this is just
+belaboring the point that the paths that
+
+ align:start position:0%
+belaboring the point that the paths that
+ 
+
+ align:start position:0%
+belaboring the point that the paths that
+you get by this algorithm can be longer
+
+ align:start position:0%
+you get by this algorithm can be longer
+ 
+
+ align:start position:0%
+you get by this algorithm can be longer
+than the shortest paths
+
+ align:start position:0%
+than the shortest paths
+ 
+
+ align:start position:0%
+than the shortest paths
+and yeah you can analyze the
+
+ align:start position:0%
+and yeah you can analyze the
+ 
+
+ align:start position:0%
+and yeah you can analyze the
+message and time complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the complexity here is order of
+
+ align:start position:0%
+okay so the complexity here is order of
+ 
+
+ align:start position:0%
+okay so the complexity here is order of
+the diameter
+
+ align:start position:0%
+the diameter
+ 
+
+ align:start position:0%
+the diameter
+times the message delay on one uh
+
+ align:start position:0%
+times the message delay on one uh
+ 
+
+ align:start position:0%
+times the message delay on one uh
+link and um
+
+ align:start position:0%
+link and um
+ 
+
+ align:start position:0%
+link and um
+why is it diameter even though the path
+
+ align:start position:0%
+why is it diameter even though the path
+ 
+
+ align:start position:0%
+why is it diameter even though the path
+some paths may be very long
+
+ align:start position:0%
+some paths may be very long
+ 
+
+ align:start position:0%
+some paths may be very long
+this is a real-time upper bound that
+
+ align:start position:0%
+this is a real-time upper bound that
+ 
+
+ align:start position:0%
+this is a real-time upper bound that
+is that depends on the the actual
+
+ align:start position:0%
+is that depends on the the actual
+ 
+
+ align:start position:0%
+is that depends on the the actual
+diameter of the graph
+
+ align:start position:0%
+diameter of the graph
+ 
+
+ align:start position:0%
+diameter of the graph
+not on the total number of nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why would the an upper bound on the
+
+ align:start position:0%
+why would the an upper bound on the
+ 
+
+ align:start position:0%
+why would the an upper bound on the
+running time for this simple algorithm
+
+ align:start position:0%
+running time for this simple algorithm
+ 
+
+ align:start position:0%
+running time for this simple algorithm
+depend
+
+ align:start position:0%
+depend
+ 
+
+ align:start position:0%
+depend
+on the diameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because you only have a longer
+
+ align:start position:0%
+yeah because you only have a longer
+ 
+
+ align:start position:0%
+yeah because you only have a longer
+packet that's faster than that
+
+ align:start position:0%
+packet that's faster than that
+ 
+
+ align:start position:0%
+packet that's faster than that
+exactly the way we're modeling it it's a
+
+ align:start position:0%
+exactly the way we're modeling it it's a
+ 
+
+ align:start position:0%
+exactly the way we're modeling it it's a
+little strange maybe but we're saying
+
+ align:start position:0%
+little strange maybe but we're saying
+ 
+
+ align:start position:0%
+little strange maybe but we're saying
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+something can travel on a long path only
+
+ align:start position:0%
+something can travel on a long path only
+ 
+
+ align:start position:0%
+something can travel on a long path only
+if it's going very fast
+
+ align:start position:0%
+if it's going very fast
+ 
+
+ align:start position:0%
+if it's going very fast
+but the actual uh shortest paths still
+
+ align:start position:0%
+but the actual uh shortest paths still
+ 
+
+ align:start position:0%
+but the actual uh shortest paths still
+move along at worst at the you know
+
+ align:start position:0%
+move along at worst at the you know
+ 
+
+ align:start position:0%
+move along at worst at the you know
+d time per hop so at worst
+
+ align:start position:0%
+d time per hop so at worst
+ 
+
+ align:start position:0%
+d time per hop so at worst
+the shortest path information would get
+
+ align:start position:0%
+the shortest path information would get
+ 
+
+ align:start position:0%
+the shortest path information would get
+there within time d
+
+ align:start position:0%
+there within time d
+ 
+
+ align:start position:0%
+there within time d
+so something's going to get there within
+
+ align:start position:0%
+so something's going to get there within
+ 
+
+ align:start position:0%
+so something's going to get there within
+time d even though something else might
+
+ align:start position:0%
+time d even though something else might
+ 
+
+ align:start position:0%
+time d even though something else might
+get there faster
+
+ align:start position:0%
+get there faster
+ 
+
+ align:start position:0%
+get there faster
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+so yeah so we can set up the child
+
+ align:start position:0%
+so yeah so we can set up the child
+ 
+
+ align:start position:0%
+so yeah so we can set up the child
+pointers and
+
+ align:start position:0%
+pointers and
+ 
+
+ align:start position:0%
+pointers and
+um we can do termination using converge
+
+ align:start position:0%
+um we can do termination using converge
+ 
+
+ align:start position:0%
+um we can do termination using converge
+cast
+
+ align:start position:0%
+cast
+ 
+
+ align:start position:0%
+cast
+it's just one tree there's nothing
+
+ align:start position:0%
+it's just one tree there's nothing
+ 
+
+ align:start position:0%
+it's just one tree there's nothing
+changing here
+
+ align:start position:0%
+changing here
+ 
+
+ align:start position:0%
+changing here
+okay and application same as before okay
+
+ align:start position:0%
+okay and application same as before okay
+ 
+
+ align:start position:0%
+okay and application same as before okay
+but that didn't work so we're going to
+
+ align:start position:0%
+but that didn't work so we're going to
+ 
+
+ align:start position:0%
+but that didn't work so we're going to
+back to the point we were talking about
+
+ align:start position:0%
+back to the point we were talking about
+ 
+
+ align:start position:0%
+back to the point we were talking about
+a minute ago we're going to use a
+
+ align:start position:0%
+a minute ago we're going to use a
+ 
+
+ align:start position:0%
+a minute ago we're going to use a
+relaxation algorithm like bellman ford
+
+ align:start position:0%
+relaxation algorithm like bellman ford
+ 
+
+ align:start position:0%
+relaxation algorithm like bellman ford
+so in the synchronous case we corrected
+
+ align:start position:0%
+so in the synchronous case we corrected
+ 
+
+ align:start position:0%
+so in the synchronous case we corrected
+for pads that had many hops but low
+
+ align:start position:0%
+for pads that had many hops but low
+ 
+
+ align:start position:0%
+for pads that had many hops but low
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+but now we're going to correct for the
+
+ align:start position:0%
+but now we're going to correct for the
+ 
+
+ align:start position:0%
+but now we're going to correct for the
+asynchrony errors
+
+ align:start position:0%
+asynchrony errors
+ 
+
+ align:start position:0%
+asynchrony errors
+all the errors that you get because of
+
+ align:start position:0%
+all the errors that you get because of
+ 
+
+ align:start position:0%
+all the errors that you get because of
+things traveling fast on long paths
+
+ align:start position:0%
+things traveling fast on long paths
+ 
+
+ align:start position:0%
+things traveling fast on long paths
+we're going to correct for those using
+
+ align:start position:0%
+we're going to correct for those using
+ 
+
+ align:start position:0%
+we're going to correct for those using
+the same strategy
+
+ align:start position:0%
+the same strategy
+ 
+
+ align:start position:0%
+the same strategy
+okay so everybody is going to keep track
+
+ align:start position:0%
+okay so everybody is going to keep track
+ 
+
+ align:start position:0%
+okay so everybody is going to keep track
+of the hop distance
+
+ align:start position:0%
+of the hop distance
+ 
+
+ align:start position:0%
+of the hop distance
+no weights now just the hop distance and
+
+ align:start position:0%
+no weights now just the hop distance and
+ 
+
+ align:start position:0%
+no weights now just the hop distance and
+they will change the parent when they
+
+ align:start position:0%
+they will change the parent when they
+ 
+
+ align:start position:0%
+they will change the parent when they
+learn of a shorter path
+
+ align:start position:0%
+learn of a shorter path
+ 
+
+ align:start position:0%
+learn of a shorter path
+okay and then they will propagate the
+
+ align:start position:0%
+okay and then they will propagate the
+ 
+
+ align:start position:0%
+okay and then they will propagate the
+improved distance so it's exactly like
+
+ align:start position:0%
+improved distance so it's exactly like
+ 
+
+ align:start position:0%
+improved distance so it's exactly like
+bellman ford
+
+ align:start position:0%
+bellman ford
+ 
+
+ align:start position:0%
+bellman ford
+and eventually this will stabilize to an
+
+ align:start position:0%
+and eventually this will stabilize to an
+ 
+
+ align:start position:0%
+and eventually this will stabilize to an
+actual breadth first spanning tree
+
+ align:start position:0%
+actual breadth first spanning tree
+ 
+
+ align:start position:0%
+actual breadth first spanning tree
+okay so here's a description of this new
+
+ align:start position:0%
+okay so here's a description of this new
+ 
+
+ align:start position:0%
+okay so here's a description of this new
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+everybody keeps track of their parent
+
+ align:start position:0%
+everybody keeps track of their parent
+ 
+
+ align:start position:0%
+everybody keeps track of their parent
+and now they keep track of their hop
+
+ align:start position:0%
+and now they keep track of their hop
+ 
+
+ align:start position:0%
+and now they keep track of their hop
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+and they have their channels okay so
+
+ align:start position:0%
+and they have their channels okay so
+ 
+
+ align:start position:0%
+and they have their channels okay so
+here's the key when you get
+
+ align:start position:0%
+here's the key when you get
+ 
+
+ align:start position:0%
+here's the key when you get
+new information you receive some new
+
+ align:start position:0%
+new information you receive some new
+ 
+
+ align:start position:0%
+new information you receive some new
+information this m
+
+ align:start position:0%
+information this m
+ 
+
+ align:start position:0%
+information this m
+is a number of hops that your neighbor
+
+ align:start position:0%
+is a number of hops that your neighbor
+ 
+
+ align:start position:0%
+is a number of hops that your neighbor
+is telling you
+
+ align:start position:0%
+is telling you
+ 
+
+ align:start position:0%
+is telling you
+well if m plus one which would be your
+
+ align:start position:0%
+well if m plus one which would be your
+ 
+
+ align:start position:0%
+well if m plus one which would be your
+new estimate for a number of hops if
+
+ align:start position:0%
+new estimate for a number of hops if
+ 
+
+ align:start position:0%
+new estimate for a number of hops if
+that's better
+
+ align:start position:0%
+that's better
+ 
+
+ align:start position:0%
+that's better
+than what you already have then you just
+
+ align:start position:0%
+than what you already have then you just
+ 
+
+ align:start position:0%
+than what you already have then you just
+replace your estimate by this
+
+ align:start position:0%
+replace your estimate by this
+ 
+
+ align:start position:0%
+replace your estimate by this
+new number of hops and you
+
+ align:start position:0%
+new number of hops and you
+ 
+
+ align:start position:0%
+new number of hops and you
+set your you know to a new parent you
+
+ align:start position:0%
+set your you know to a new parent you
+ 
+
+ align:start position:0%
+set your you know to a new parent you
+set your parent pointer to the
+
+ align:start position:0%
+set your parent pointer to the
+ 
+
+ align:start position:0%
+set your parent pointer to the
+the sender and you propagate this
+
+ align:start position:0%
+the sender and you propagate this
+ 
+
+ align:start position:0%
+the sender and you propagate this
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+so it's exactly the same as what we had
+
+ align:start position:0%
+so it's exactly the same as what we had
+ 
+
+ align:start position:0%
+so it's exactly the same as what we had
+before but now we're correcting
+
+ align:start position:0%
+before but now we're correcting
+ 
+
+ align:start position:0%
+before but now we're correcting
+for the asynchrony
+
+ align:start position:0%
+for the asynchrony
+ 
+
+ align:start position:0%
+for the asynchrony
+we get shorter hop paths later make
+
+ align:start position:0%
+we get shorter hop paths later make
+ 
+
+ align:start position:0%
+we get shorter hop paths later make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so and the rest of this is just you
+
+ align:start position:0%
+okay so and the rest of this is just you
+ 
+
+ align:start position:0%
+okay so and the rest of this is just you
+send the message okay and notice we
+
+ align:start position:0%
+send the message okay and notice we
+ 
+
+ align:start position:0%
+send the message okay and notice we
+don't have any terminating actions why
+
+ align:start position:0%
+don't have any terminating actions why
+ 
+
+ align:start position:0%
+don't have any terminating actions why
+because we have the same problem that we
+
+ align:start position:0%
+because we have the same problem that we
+ 
+
+ align:start position:0%
+because we have the same problem that we
+had before
+
+ align:start position:0%
+had before
+ 
+
+ align:start position:0%
+had before
+with having processes no know when
+
+ align:start position:0%
+with having processes no know when
+ 
+
+ align:start position:0%
+with having processes no know when
+they're done
+
+ align:start position:0%
+they're done
+ 
+
+ align:start position:0%
+they're done
+if you keep get getting corrections how
+
+ align:start position:0%
+if you keep get getting corrections how
+ 
+
+ align:start position:0%
+if you keep get getting corrections how
+do you know when you're finished
+
+ align:start position:0%
+do you know when you're finished
+ 
+
+ align:start position:0%
+do you know when you're finished
+and how do you know this is going to
+
+ align:start position:0%
+and how do you know this is going to
+ 
+
+ align:start position:0%
+and how do you know this is going to
+work in the synchronous case
+
+ align:start position:0%
+work in the synchronous case
+ 
+
+ align:start position:0%
+work in the synchronous case
+we could get an exact characterization
+
+ align:start position:0%
+we could get an exact characterization
+ 
+
+ align:start position:0%
+we could get an exact characterization
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+what exactly the situation is after any
+
+ align:start position:0%
+what exactly the situation is after any
+ 
+
+ align:start position:0%
+what exactly the situation is after any
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+of rounds and we can't do that now
+
+ align:start position:0%
+of rounds and we can't do that now
+ 
+
+ align:start position:0%
+of rounds and we can't do that now
+because things can happen in so many
+
+ align:start position:0%
+because things can happen in so many
+ 
+
+ align:start position:0%
+because things can happen in so many
+orders so we we have to instead
+
+ align:start position:0%
+orders so we we have to instead
+ 
+
+ align:start position:0%
+orders so we we have to instead
+state some higher level abstract
+
+ align:start position:0%
+state some higher level abstract
+ 
+
+ align:start position:0%
+state some higher level abstract
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+either in variants or you'll see some
+
+ align:start position:0%
+either in variants or you'll see some
+ 
+
+ align:start position:0%
+either in variants or you'll see some
+other kinds of
+
+ align:start position:0%
+other kinds of
+ 
+
+ align:start position:0%
+other kinds of
+properties as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we could say for instance as an
+
+ align:start position:0%
+we could say for instance as an
+ 
+
+ align:start position:0%
+we could say for instance as an
+invariant that all the distance
+
+ align:start position:0%
+invariant that all the distance
+ 
+
+ align:start position:0%
+invariant that all the distance
+information you get
+
+ align:start position:0%
+information you get
+ 
+
+ align:start position:0%
+information you get
+is correct okay
+
+ align:start position:0%
+is correct okay
+ 
+
+ align:start position:0%
+is correct okay
+if you ever have your distance set to
+
+ align:start position:0%
+if you ever have your distance set to
+ 
+
+ align:start position:0%
+if you ever have your distance set to
+something it's the actual distance on
+
+ align:start position:0%
+something it's the actual distance on
+ 
+
+ align:start position:0%
+something it's the actual distance on
+some path and your parent is
+
+ align:start position:0%
+some path and your parent is
+ 
+
+ align:start position:0%
+some path and your parent is
+correct um correctly set to be your
+
+ align:start position:0%
+correct um correctly set to be your
+ 
+
+ align:start position:0%
+correct um correctly set to be your
+predecessor on such a path
+
+ align:start position:0%
+predecessor on such a path
+ 
+
+ align:start position:0%
+predecessor on such a path
+okay so this is just saying whatever you
+
+ align:start position:0%
+okay so this is just saying whatever you
+ 
+
+ align:start position:0%
+okay so this is just saying whatever you
+get is correct information this doesn't
+
+ align:start position:0%
+get is correct information this doesn't
+ 
+
+ align:start position:0%
+get is correct information this doesn't
+say that eventually you're going to
+
+ align:start position:0%
+say that eventually you're going to
+ 
+
+ align:start position:0%
+say that eventually you're going to
+finish though it just says what you get
+
+ align:start position:0%
+finish though it just says what you get
+ 
+
+ align:start position:0%
+finish though it just says what you get
+is correct okay so if
+
+ align:start position:0%
+is correct okay so if
+ 
+
+ align:start position:0%
+is correct okay so if
+if you want to show that eventually you
+
+ align:start position:0%
+if you want to show that eventually you
+ 
+
+ align:start position:0%
+if you want to show that eventually you
+get the right answer you have to do
+
+ align:start position:0%
+get the right answer you have to do
+ 
+
+ align:start position:0%
+get the right answer you have to do
+something with the timing you have to
+
+ align:start position:0%
+something with the timing you have to
+ 
+
+ align:start position:0%
+something with the timing you have to
+say something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a certain time that depends on on
+
+ align:start position:0%
+by a certain time that depends on on
+ 
+
+ align:start position:0%
+by a certain time that depends on on
+the distance well if there's an at most
+
+ align:start position:0%
+the distance well if there's an at most
+ 
+
+ align:start position:0%
+the distance well if there's an at most
+r hop path to a node then it will learn
+
+ align:start position:0%
+r hop path to a node then it will learn
+ 
+
+ align:start position:0%
+r hop path to a node then it will learn
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+by a certain time but that depends on
+
+ align:start position:0%
+by a certain time but that depends on
+ 
+
+ align:start position:0%
+by a certain time but that depends on
+the length of the path
+
+ align:start position:0%
+the length of the path
+ 
+
+ align:start position:0%
+the length of the path
+and um the message delivery time and the
+
+ align:start position:0%
+and um the message delivery time and the
+ 
+
+ align:start position:0%
+and um the message delivery time and the
+number of nodes because there can be
+
+ align:start position:0%
+number of nodes because there can be
+ 
+
+ align:start position:0%
+number of nodes because there can be
+congestion
+
+ align:start position:0%
+congestion
+ 
+
+ align:start position:0%
+congestion
+okay so you have to not only say things
+
+ align:start position:0%
+okay so you have to not only say things
+ 
+
+ align:start position:0%
+okay so you have to not only say things
+are correct but you have to say
+
+ align:start position:0%
+are correct but you have to say
+ 
+
+ align:start position:0%
+are correct but you have to say
+eventually
+
+ align:start position:0%
+eventually
+ 
+
+ align:start position:0%
+eventually
+you get the right result and here it
+
+ align:start position:0%
+you get the right result and here it
+ 
+
+ align:start position:0%
+you get the right result and here it
+will say by a certain time you get the
+
+ align:start position:0%
+will say by a certain time you get the
+ 
+
+ align:start position:0%
+will say by a certain time you get the
+right result
+
+ align:start position:0%
+right result
+ 
+
+ align:start position:0%
+right result
+makes sense so this is how you would
+
+ align:start position:0%
+makes sense so this is how you would
+ 
+
+ align:start position:0%
+makes sense so this is how you would
+understand an algorithm like this one
+
+ align:start position:0%
+understand an algorithm like this one
+ 
+
+ align:start position:0%
+understand an algorithm like this one
+okay message complexity
+
+ align:start position:0%
+okay message complexity
+ 
+
+ align:start position:0%
+okay message complexity
+since there's all these corrections
+
+ align:start position:0%
+since there's all these corrections
+ 
+
+ align:start position:0%
+since there's all these corrections
+you're back in number of edges times
+
+ align:start position:0%
+you're back in number of edges times
+ 
+
+ align:start position:0%
+you're back in number of edges times
+possibly the number of nodes
+
+ align:start position:0%
+possibly the number of nodes
+ 
+
+ align:start position:0%
+possibly the number of nodes
+and the time complexity till all the
+
+ align:start position:0%
+and the time complexity till all the
+ 
+
+ align:start position:0%
+and the time complexity till all the
+the distances and parent values
+
+ align:start position:0%
+the distances and parent values
+ 
+
+ align:start position:0%
+the distances and parent values
+stabilize
+
+ align:start position:0%
+stabilize
+ 
+
+ align:start position:0%
+stabilize
+could be this is pessimistic again the
+
+ align:start position:0%
+could be this is pessimistic again the
+ 
+
+ align:start position:0%
+could be this is pessimistic again the
+diameter times the number of nodes times
+
+ align:start position:0%
+diameter times the number of nodes times
+ 
+
+ align:start position:0%
+diameter times the number of nodes times
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+because uh there can be congestion in
+
+ align:start position:0%
+because uh there can be congestion in
+ 
+
+ align:start position:0%
+because uh there can be congestion in
+each of the links
+
+ align:start position:0%
+each of the links
+ 
+
+ align:start position:0%
+each of the links
+because of the corrections okay
+
+ align:start position:0%
+because of the corrections okay
+ 
+
+ align:start position:0%
+because of the corrections okay
+so how do you know when this is done how
+
+ align:start position:0%
+so how do you know when this is done how
+ 
+
+ align:start position:0%
+so how do you know when this is done how
+can a process know when it can finish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+before we we had said well if you knew n
+
+ align:start position:0%
+before we we had said well if you knew n
+ 
+
+ align:start position:0%
+before we we had said well if you knew n
+if you knew the number of nodes you
+
+ align:start position:0%
+if you knew the number of nodes you
+ 
+
+ align:start position:0%
+if you knew the number of nodes you
+could weight that number of rounds
+
+ align:start position:0%
+could weight that number of rounds
+ 
+
+ align:start position:0%
+could weight that number of rounds
+that doesn't even help you here even if
+
+ align:start position:0%
+that doesn't even help you here even if
+ 
+
+ align:start position:0%
+that doesn't even help you here even if
+you know then
+
+ align:start position:0%
+you know then
+ 
+
+ align:start position:0%
+you know then
+have a good upper bound on the number of
+
+ align:start position:0%
+have a good upper bound on the number of
+ 
+
+ align:start position:0%
+have a good upper bound on the number of
+nodes in the network
+
+ align:start position:0%
+nodes in the network
+ 
+
+ align:start position:0%
+nodes in the network
+there's no rounds to count
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can't tell even knowing the
+
+ align:start position:0%
+so you can't tell even knowing the
+ 
+
+ align:start position:0%
+so you can't tell even knowing the
+number of nodes you can't tell so how
+
+ align:start position:0%
+number of nodes you can't tell so how
+ 
+
+ align:start position:0%
+number of nodes you can't tell so how
+might you detect termination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well but even if you know that
+
+ align:start position:0%
+yeah well but even if you know that
+ 
+
+ align:start position:0%
+yeah well but even if you know that
+you can't count time see this is the
+
+ align:start position:0%
+you can't count time see this is the
+ 
+
+ align:start position:0%
+you can't count time see this is the
+thing about asynchronous algorithms you
+
+ align:start position:0%
+thing about asynchronous algorithms you
+ 
+
+ align:start position:0%
+thing about asynchronous algorithms you
+don't have
+
+ align:start position:0%
+don't have
+ 
+
+ align:start position:0%
+don't have
+although we're using time to measure how
+
+ align:start position:0%
+although we're using time to measure how
+ 
+
+ align:start position:0%
+although we're using time to measure how
+long its
+
+ align:start position:0%
+long its
+ 
+
+ align:start position:0%
+long its
+termination takes we the processes in
+
+ align:start position:0%
+termination takes we the processes in
+ 
+
+ align:start position:0%
+termination takes we the processes in
+there don't have that
+
+ align:start position:0%
+there don't have that
+ 
+
+ align:start position:0%
+there don't have that
+they're just these asynchronous guys who
+
+ align:start position:0%
+they're just these asynchronous guys who
+ 
+
+ align:start position:0%
+they're just these asynchronous guys who
+just take their steps they're ignorant
+
+ align:start position:0%
+just take their steps they're ignorant
+ 
+
+ align:start position:0%
+just take their steps they're ignorant
+of any
+
+ align:start position:0%
+of any
+ 
+
+ align:start position:0%
+of any
+anything to do with time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other ideas yeah can you use the same
+
+ align:start position:0%
+other ideas yeah can you use the same
+ 
+
+ align:start position:0%
+other ideas yeah can you use the same
+convergence
+
+ align:start position:0%
+convergence
+ 
+
+ align:start position:0%
+convergence
+same thing we're just going to use
+
+ align:start position:0%
+same thing we're just going to use
+ 
+
+ align:start position:0%
+same thing we're just going to use
+converge cast again same idea
+
+ align:start position:0%
+converge cast again same idea
+ 
+
+ align:start position:0%
+converge cast again same idea
+you just compute and you recompute your
+
+ align:start position:0%
+you just compute and you recompute your
+ 
+
+ align:start position:0%
+you just compute and you recompute your
+child pointers
+
+ align:start position:0%
+child pointers
+ 
+
+ align:start position:0%
+child pointers
+you send a done to your current parent
+
+ align:start position:0%
+you send a done to your current parent
+ 
+
+ align:start position:0%
+you send a done to your current parent
+after you've gotten responses to all
+
+ align:start position:0%
+after you've gotten responses to all
+ 
+
+ align:start position:0%
+after you've gotten responses to all
+your messages so you think you know your
+
+ align:start position:0%
+your messages so you think you know your
+ 
+
+ align:start position:0%
+your messages so you think you know your
+children and they've all told you
+
+ align:start position:0%
+children and they've all told you
+ 
+
+ align:start position:0%
+children and they've all told you
+they're done
+
+ align:start position:0%
+they're done
+ 
+
+ align:start position:0%
+they're done
+and but then you might have to make
+
+ align:start position:0%
+and but then you might have to make
+ 
+
+ align:start position:0%
+and but then you might have to make
+corrections so as in
+
+ align:start position:0%
+corrections so as in
+ 
+
+ align:start position:0%
+corrections so as in
+what we saw before you can be involved
+
+ align:start position:0%
+what we saw before you can be involved
+ 
+
+ align:start position:0%
+what we saw before you can be involved
+in this converge cast several times till
+
+ align:start position:0%
+in this converge cast several times till
+ 
+
+ align:start position:0%
+in this converge cast several times till
+it finally
+
+ align:start position:0%
+it finally
+ 
+
+ align:start position:0%
+it finally
+reaches all the way to the root okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once you have these you can use them the
+
+ align:start position:0%
+once you have these you can use them the
+ 
+
+ align:start position:0%
+once you have these you can use them the
+same way as before you
+
+ align:start position:0%
+same way as before you
+ 
+
+ align:start position:0%
+same way as before you
+now have costs that are better than this
+
+ align:start position:0%
+now have costs that are better than this
+ 
+
+ align:start position:0%
+now have costs that are better than this
+simple tree that didn't have shortest
+
+ align:start position:0%
+simple tree that didn't have shortest
+ 
+
+ align:start position:0%
+simple tree that didn't have shortest
+paths because it now takes you less time
+
+ align:start position:0%
+paths because it now takes you less time
+ 
+
+ align:start position:0%
+paths because it now takes you less time
+to use the tree for computing functions
+
+ align:start position:0%
+to use the tree for computing functions
+ 
+
+ align:start position:0%
+to use the tree for computing functions
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+disseminating information because the
+
+ align:start position:0%
+disseminating information because the
+ 
+
+ align:start position:0%
+disseminating information because the
+tree is is shallower
+
+ align:start position:0%
+tree is is shallower
+ 
+
+ align:start position:0%
+tree is is shallower
+okay so finally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens when we want to find
+
+ align:start position:0%
+what happens when we want to find
+ 
+
+ align:start position:0%
+what happens when we want to find
+shortest path trees
+
+ align:start position:0%
+shortest path trees
+ 
+
+ align:start position:0%
+shortest path trees
+in an asynchronous setting
+
+ align:start position:0%
+in an asynchronous setting
+ 
+
+ align:start position:0%
+in an asynchronous setting
+so now we're going to add to the
+
+ align:start position:0%
+so now we're going to add to the
+ 
+
+ align:start position:0%
+so now we're going to add to the
+complications that we just saw of all
+
+ align:start position:0%
+complications that we just saw of all
+ 
+
+ align:start position:0%
+complications that we just saw of all
+the asynchrony
+
+ align:start position:0%
+the asynchrony
+ 
+
+ align:start position:0%
+the asynchrony
+the uh complications of having weights
+
+ align:start position:0%
+the uh complications of having weights
+ 
+
+ align:start position:0%
+the uh complications of having weights
+on the edges
+
+ align:start position:0%
+on the edges
+ 
+
+ align:start position:0%
+on the edges
+right so the problem is get a shortest
+
+ align:start position:0%
+right so the problem is get a shortest
+ 
+
+ align:start position:0%
+right so the problem is get a shortest
+path spanning tree
+
+ align:start position:0%
+path spanning tree
+ 
+
+ align:start position:0%
+path spanning tree
+now in an asynchronous network
+
+ align:start position:0%
+now in an asynchronous network
+ 
+
+ align:start position:0%
+now in an asynchronous network
+weighted graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes don't know about the graph
+
+ align:start position:0%
+processes don't know about the graph
+ 
+
+ align:start position:0%
+processes don't know about the graph
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+they have uids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and everybody's supposed to output its
+
+ align:start position:0%
+and everybody's supposed to output its
+ 
+
+ align:start position:0%
+and everybody's supposed to output its
+distance and parent in the tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+we're going to use another relaxation
+
+ align:start position:0%
+we're going to use another relaxation
+ 
+
+ align:start position:0%
+we're going to use another relaxation
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+okay so now think about what the
+
+ align:start position:0%
+okay so now think about what the
+ 
+
+ align:start position:0%
+okay so now think about what the
+relaxation is going to be doing for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have two kinds of corrections to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could have long paths that have
+
+ align:start position:0%
+you could have long paths that have
+ 
+
+ align:start position:0%
+you could have long paths that have
+small weight
+
+ align:start position:0%
+small weight
+ 
+
+ align:start position:0%
+small weight
+that showed up for bellman ford in the
+
+ align:start position:0%
+that showed up for bellman ford in the
+ 
+
+ align:start position:0%
+that showed up for bellman ford in the
+synchronous setting
+
+ align:start position:0%
+synchronous setting
+ 
+
+ align:start position:0%
+synchronous setting
+so we have to correct for those but you
+
+ align:start position:0%
+so we have to correct for those but you
+ 
+
+ align:start position:0%
+so we have to correct for those but you
+could also have because of asynchrony
+
+ align:start position:0%
+could also have because of asynchrony
+ 
+
+ align:start position:0%
+could also have because of asynchrony
+you could have information traveling
+
+ align:start position:0%
+you could have information traveling
+ 
+
+ align:start position:0%
+you could have information traveling
+fast on uh
+
+ align:start position:0%
+fast on uh
+ 
+
+ align:start position:0%
+fast on uh
+many hops and you have to correct for
+
+ align:start position:0%
+many hops and you have to correct for
+ 
+
+ align:start position:0%
+many hops and you have to correct for
+that as well so there's like two kinds
+
+ align:start position:0%
+that as well so there's like two kinds
+ 
+
+ align:start position:0%
+that as well so there's like two kinds
+of things you're going to be correcting
+
+ align:start position:0%
+of things you're going to be correcting
+ 
+
+ align:start position:0%
+of things you're going to be correcting
+for in one algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is going to and this is
+
+ align:start position:0%
+okay so this is going to and this is
+ 
+
+ align:start position:0%
+okay so this is going to and this is
+pretty surprising it's going to lead to
+
+ align:start position:0%
+pretty surprising it's going to lead to
+ 
+
+ align:start position:0%
+pretty surprising it's going to lead to
+ridiculously high
+
+ align:start position:0%
+ridiculously high
+ 
+
+ align:start position:0%
+ridiculously high
+complexity message and time complexity
+
+ align:start position:0%
+complexity message and time complexity
+ 
+
+ align:start position:0%
+complexity message and time complexity
+if you really have unbridled asynchrony
+
+ align:start position:0%
+if you really have unbridled asynchrony
+ 
+
+ align:start position:0%
+if you really have unbridled asynchrony
+and weights
+
+ align:start position:0%
+and weights
+ 
+
+ align:start position:0%
+and weights
+this is going to give you a very costly
+
+ align:start position:0%
+this is going to give you a very costly
+ 
+
+ align:start position:0%
+this is going to give you a very costly
+algorithm you're going to
+
+ align:start position:0%
+algorithm you're going to
+ 
+
+ align:start position:0%
+algorithm you're going to
+see some exponential is going to creep
+
+ align:start position:0%
+see some exponential is going to creep
+ 
+
+ align:start position:0%
+see some exponential is going to creep
+in there
+
+ align:start position:0%
+in there
+ 
+
+ align:start position:0%
+in there
+okay so here's the the algorithm for the
+
+ align:start position:0%
+okay so here's the the algorithm for the
+ 
+
+ align:start position:0%
+okay so here's the the algorithm for the
+asynchronous bellman ford
+
+ align:start position:0%
+asynchronous bellman ford
+ 
+
+ align:start position:0%
+asynchronous bellman ford
+algorithm everyone keeps track of their
+
+ align:start position:0%
+algorithm everyone keeps track of their
+ 
+
+ align:start position:0%
+algorithm everyone keeps track of their
+parent
+
+ align:start position:0%
+parent
+ 
+
+ align:start position:0%
+parent
+their conjecture distance and
+
+ align:start position:0%
+their conjecture distance and
+ 
+
+ align:start position:0%
+their conjecture distance and
+they have now messages that they're
+
+ align:start position:0%
+they have now messages that they're
+ 
+
+ align:start position:0%
+they have now messages that they're
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+to send to the neighbors let's say you
+
+ align:start position:0%
+to send to the neighbors let's say you
+ 
+
+ align:start position:0%
+to send to the neighbors let's say you
+have a queue because there could be
+
+ align:start position:0%
+have a queue because there could be
+ 
+
+ align:start position:0%
+have a queue because there could be
+successive
+
+ align:start position:0%
+successive
+ 
+
+ align:start position:0%
+successive
+estimates so we'll have a queue there
+
+ align:start position:0%
+estimates so we'll have a queue there
+ 
+
+ align:start position:0%
+estimates so we'll have a queue there
+um key step the relaxation step is what
+
+ align:start position:0%
+um key step the relaxation step is what
+ 
+
+ align:start position:0%
+um key step the relaxation step is what
+happens when you receive
+
+ align:start position:0%
+happens when you receive
+ 
+
+ align:start position:0%
+happens when you receive
+a new um estimate of the best distance
+
+ align:start position:0%
+a new um estimate of the best distance
+ 
+
+ align:start position:0%
+a new um estimate of the best distance
+this is weighted distance now from a
+
+ align:start position:0%
+this is weighted distance now from a
+ 
+
+ align:start position:0%
+this is weighted distance now from a
+neighbor
+
+ align:start position:0%
+neighbor
+ 
+
+ align:start position:0%
+neighbor
+well you look at that distance plus the
+
+ align:start position:0%
+well you look at that distance plus the
+ 
+
+ align:start position:0%
+well you look at that distance plus the
+weight of the edge in between
+
+ align:start position:0%
+weight of the edge in between
+ 
+
+ align:start position:0%
+weight of the edge in between
+and you see if that's better than your
+
+ align:start position:0%
+and you see if that's better than your
+ 
+
+ align:start position:0%
+and you see if that's better than your
+current distance
+
+ align:start position:0%
+current distance
+ 
+
+ align:start position:0%
+current distance
+just like synchronous bellman ford and
+
+ align:start position:0%
+just like synchronous bellman ford and
+ 
+
+ align:start position:0%
+just like synchronous bellman ford and
+if it is
+
+ align:start position:0%
+if it is
+ 
+
+ align:start position:0%
+if it is
+then you improve your distance
+
+ align:start position:0%
+then you improve your distance
+ 
+
+ align:start position:0%
+then you improve your distance
+reset your parent and send this the
+
+ align:start position:0%
+reset your parent and send this the
+ 
+
+ align:start position:0%
+reset your parent and send this the
+distance out to your neighbors
+
+ align:start position:0%
+distance out to your neighbors
+ 
+
+ align:start position:0%
+distance out to your neighbors
+so it's exactly like the synchronous
+
+ align:start position:0%
+so it's exactly like the synchronous
+ 
+
+ align:start position:0%
+so it's exactly like the synchronous
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+but we're going to be running this
+
+ align:start position:0%
+but we're going to be running this
+ 
+
+ align:start position:0%
+but we're going to be running this
+asynchronously
+
+ align:start position:0%
+asynchronously
+ 
+
+ align:start position:0%
+asynchronously
+and since you're going to be correcting
+
+ align:start position:0%
+and since you're going to be correcting
+ 
+
+ align:start position:0%
+and since you're going to be correcting
+um every time you see a new estimate
+
+ align:start position:0%
+um every time you see a new estimate
+ 
+
+ align:start position:0%
+um every time you see a new estimate
+this is actually going to handle both
+
+ align:start position:0%
+this is actually going to handle both
+ 
+
+ align:start position:0%
+this is actually going to handle both
+kinds of corrections
+
+ align:start position:0%
+kinds of corrections
+ 
+
+ align:start position:0%
+kinds of corrections
+whether it comes because of you know
+
+ align:start position:0%
+whether it comes because of you know
+ 
+
+ align:start position:0%
+whether it comes because of you know
+a mini hop path with a smaller weight or
+
+ align:start position:0%
+a mini hop path with a smaller weight or
+ 
+
+ align:start position:0%
+a mini hop path with a smaller weight or
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+it just comes because of the asynchrony
+
+ align:start position:0%
+it just comes because of the asynchrony
+ 
+
+ align:start position:0%
+it just comes because of the asynchrony
+whenever you get a better estimate
+
+ align:start position:0%
+whenever you get a better estimate
+ 
+
+ align:start position:0%
+whenever you get a better estimate
+you're going to make the correction
+
+ align:start position:0%
+you're going to make the correction
+ 
+
+ align:start position:0%
+you're going to make the correction
+okay is it clear this is all you really
+
+ align:start position:0%
+okay is it clear this is all you really
+ 
+
+ align:start position:0%
+okay is it clear this is all you really
+need to do in the algorithm just what's
+
+ align:start position:0%
+need to do in the algorithm just what's
+ 
+
+ align:start position:0%
+need to do in the algorithm just what's
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+this code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the receive and then the
+
+ align:start position:0%
+okay so that's the receive and then the
+ 
+
+ align:start position:0%
+okay so that's the receive and then the
+rest of the algorithm is just you send
+
+ align:start position:0%
+rest of the algorithm is just you send
+ 
+
+ align:start position:0%
+rest of the algorithm is just you send
+it out
+
+ align:start position:0%
+it out
+ 
+
+ align:start position:0%
+it out
+when it's when you're ready to send
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then we have the same uh issue
+
+ align:start position:0%
+okay and then we have the same uh issue
+ 
+
+ align:start position:0%
+okay and then we have the same uh issue
+about termination
+
+ align:start position:0%
+about termination
+ 
+
+ align:start position:0%
+about termination
+there's no uh no termination
+
+ align:start position:0%
+there's no uh no termination
+ 
+
+ align:start position:0%
+there's no uh no termination
+terminating actions we'll come back to
+
+ align:start position:0%
+terminating actions we'll come back to
+ 
+
+ align:start position:0%
+terminating actions we'll come back to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so you know it's really hard to come up
+
+ align:start position:0%
+so you know it's really hard to come up
+ 
+
+ align:start position:0%
+so you know it's really hard to come up
+with invariance and timing properties
+
+ align:start position:0%
+with invariance and timing properties
+ 
+
+ align:start position:0%
+with invariance and timing properties
+now for this
+
+ align:start position:0%
+now for this
+ 
+
+ align:start position:0%
+now for this
+setting you can certainly have an
+
+ align:start position:0%
+setting you can certainly have an
+ 
+
+ align:start position:0%
+setting you can certainly have an
+invariant like the one that we just had
+
+ align:start position:0%
+invariant like the one that we just had
+ 
+
+ align:start position:0%
+invariant like the one that we just had
+for asynchronous breadth first search
+
+ align:start position:0%
+for asynchronous breadth first search
+ 
+
+ align:start position:0%
+for asynchronous breadth first search
+you can say that at any point whatever
+
+ align:start position:0%
+you can say that at any point whatever
+ 
+
+ align:start position:0%
+you can say that at any point whatever
+distance you have
+
+ align:start position:0%
+distance you have
+ 
+
+ align:start position:0%
+distance you have
+is an actual distance it's achievable
+
+ align:start position:0%
+is an actual distance it's achievable
+ 
+
+ align:start position:0%
+is an actual distance it's achievable
+along some path
+
+ align:start position:0%
+along some path
+ 
+
+ align:start position:0%
+along some path
+and the parent is correct
+
+ align:start position:0%
+and the parent is correct
+ 
+
+ align:start position:0%
+and the parent is correct
+we'd also like to have something that
+
+ align:start position:0%
+we'd also like to have something that
+ 
+
+ align:start position:0%
+we'd also like to have something that
+says eventually you get the right
+
+ align:start position:0%
+says eventually you get the right
+ 
+
+ align:start position:0%
+says eventually you get the right
+distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you want to state a timing property
+
+ align:start position:0%
+so you want to state a timing property
+ 
+
+ align:start position:0%
+so you want to state a timing property
+that says fine if you have an at most
+
+ align:start position:0%
+that says fine if you have an at most
+ 
+
+ align:start position:0%
+that says fine if you have an at most
+r hop path by a certain time you'd like
+
+ align:start position:0%
+r hop path by a certain time you'd like
+ 
+
+ align:start position:0%
+r hop path by a certain time you'd like
+to know that your distance
+
+ align:start position:0%
+to know that your distance
+ 
+
+ align:start position:0%
+to know that your distance
+is at least as good as what you could
+
+ align:start position:0%
+is at least as good as what you could
+ 
+
+ align:start position:0%
+is at least as good as what you could
+get on that path
+
+ align:start position:0%
+get on that path
+ 
+
+ align:start position:0%
+get on that path
+the quest the problem is what are you
+
+ align:start position:0%
+the quest the problem is what are you
+ 
+
+ align:start position:0%
+the quest the problem is what are you
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+have here for the amount of time how
+
+ align:start position:0%
+have here for the amount of time how
+ 
+
+ align:start position:0%
+have here for the amount of time how
+long would it possibly
+
+ align:start position:0%
+long would it possibly
+ 
+
+ align:start position:0%
+long would it possibly
+take in order to get
+
+ align:start position:0%
+take in order to get
+ 
+
+ align:start position:0%
+take in order to get
+the best estimate that you could for
+
+ align:start position:0%
+the best estimate that you could for
+ 
+
+ align:start position:0%
+the best estimate that you could for
+a path of at most our hops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a guess
+
+ align:start position:0%
+okay a guess
+ 
+
+ align:start position:0%
+okay a guess
+i was able to calculate something
+
+ align:start position:0%
+i was able to calculate something
+ 
+
+ align:start position:0%
+i was able to calculate something
+reasonable for the breadth first search
+
+ align:start position:0%
+reasonable for the breadth first search
+ 
+
+ align:start position:0%
+reasonable for the breadth first search
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+but now this is going to be much much
+
+ align:start position:0%
+but now this is going to be much much
+ 
+
+ align:start position:0%
+but now this is going to be much much
+worse
+
+ align:start position:0%
+worse
+ 
+
+ align:start position:0%
+worse
+it's not obvious at all it's actually
+
+ align:start position:0%
+it's not obvious at all it's actually
+ 
+
+ align:start position:0%
+it's not obvious at all it's actually
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+depend on how many messages could pile
+
+ align:start position:0%
+depend on how many messages could pile
+ 
+
+ align:start position:0%
+depend on how many messages could pile
+up in a channel
+
+ align:start position:0%
+up in a channel
+ 
+
+ align:start position:0%
+up in a channel
+and that can be an awful lot an
+
+ align:start position:0%
+and that can be an awful lot an
+ 
+
+ align:start position:0%
+and that can be an awful lot an
+exponential number
+
+ align:start position:0%
+exponential number
+ 
+
+ align:start position:0%
+exponential number
+exponential and the number of nodes in
+
+ align:start position:0%
+exponential and the number of nodes in
+ 
+
+ align:start position:0%
+exponential and the number of nodes in
+the network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to produce an execution for
+
+ align:start position:0%
+i'm going to produce an execution for
+ 
+
+ align:start position:0%
+i'm going to produce an execution for
+you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can generate a huge number of messages
+
+ align:start position:0%
+can generate a huge number of messages
+ 
+
+ align:start position:0%
+can generate a huge number of messages
+which then will take a long
+
+ align:start position:0%
+which then will take a long
+ 
+
+ align:start position:0%
+which then will take a long
+time to deliver and delay the
+
+ align:start position:0%
+time to deliver and delay the
+ 
+
+ align:start position:0%
+time to deliver and delay the
+termination of the algorithm
+
+ align:start position:0%
+termination of the algorithm
+ 
+
+ align:start position:0%
+termination of the algorithm
+first let's look at an upper bound what
+
+ align:start position:0%
+first let's look at an upper bound what
+ 
+
+ align:start position:0%
+first let's look at an upper bound what
+can we say for an upper bound
+
+ align:start position:0%
+can we say for an upper bound
+ 
+
+ align:start position:0%
+can we say for an upper bound
+well there's many different paths from
+
+ align:start position:0%
+well there's many different paths from
+ 
+
+ align:start position:0%
+well there's many different paths from
+v0
+
+ align:start position:0%
+v0
+ 
+
+ align:start position:0%
+v0
+to any other particular node so
+
+ align:start position:0%
+to any other particular node so
+ 
+
+ align:start position:0%
+to any other particular node so
+we might have to traverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all the simple paths in the graph
+
+ align:start position:0%
+all the simple paths in the graph
+ 
+
+ align:start position:0%
+all the simple paths in the graph
+perhaps
+
+ align:start position:0%
+perhaps
+ 
+
+ align:start position:0%
+perhaps
+and how many are there well
+
+ align:start position:0%
+and how many are there well
+ 
+
+ align:start position:0%
+and how many are there well
+as an upper bound you could say order n
+
+ align:start position:0%
+as an upper bound you could say order n
+ 
+
+ align:start position:0%
+as an upper bound you could say order n
+factorial for the number of different
+
+ align:start position:0%
+factorial for the number of different
+ 
+
+ align:start position:0%
+factorial for the number of different
+paths that you can
+
+ align:start position:0%
+paths that you can
+ 
+
+ align:start position:0%
+paths that you can
+traverse to get from v0 to some
+
+ align:start position:0%
+traverse to get from v0 to some
+ 
+
+ align:start position:0%
+traverse to get from v0 to some
+particular other node
+
+ align:start position:0%
+particular other node
+ 
+
+ align:start position:0%
+particular other node
+so that's exponential in n certainly
+
+ align:start position:0%
+so that's exponential in n certainly
+ 
+
+ align:start position:0%
+so that's exponential in n certainly
+it's order n to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this says that the number of
+
+ align:start position:0%
+okay so this says that the number of
+ 
+
+ align:start position:0%
+okay so this says that the number of
+messages that you might send on any
+
+ align:start position:0%
+messages that you might send on any
+ 
+
+ align:start position:0%
+messages that you might send on any
+channel could correspond to
+
+ align:start position:0%
+channel could correspond to
+ 
+
+ align:start position:0%
+channel could correspond to
+doing that many corrections so this can
+
+ align:start position:0%
+doing that many corrections so this can
+ 
+
+ align:start position:0%
+doing that many corrections so this can
+blow up your message complexity
+
+ align:start position:0%
+blow up your message complexity
+ 
+
+ align:start position:0%
+blow up your message complexity
+into n to the n times the number of
+
+ align:start position:0%
+into n to the n times the number of
+ 
+
+ align:start position:0%
+into n to the n times the number of
+edges and your time complexity
+
+ align:start position:0%
+edges and your time complexity
+ 
+
+ align:start position:0%
+edges and your time complexity
+in uh to n to the n times
+
+ align:start position:0%
+in uh to n to the n times
+ 
+
+ align:start position:0%
+in uh to n to the n times
+um n times d because on every edge
+
+ align:start position:0%
+um n times d because on every edge
+ 
+
+ align:start position:0%
+um n times d because on every edge
+you might have to wait for that many
+
+ align:start position:0%
+you might have to wait for that many
+ 
+
+ align:start position:0%
+you might have to wait for that many
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+corrected messages sitting in front of
+
+ align:start position:0%
+corrected messages sitting in front of
+ 
+
+ align:start position:0%
+corrected messages sitting in front of
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+okay so you know that seems pretty awful
+
+ align:start position:0%
+okay so you know that seems pretty awful
+ 
+
+ align:start position:0%
+okay so you know that seems pretty awful
+does it actually happen can you actually
+
+ align:start position:0%
+does it actually happen can you actually
+ 
+
+ align:start position:0%
+does it actually happen can you actually
+construct an execution of this algorithm
+
+ align:start position:0%
+construct an execution of this algorithm
+ 
+
+ align:start position:0%
+construct an execution of this algorithm
+where you get exponential bounds like
+
+ align:start position:0%
+where you get exponential bounds like
+ 
+
+ align:start position:0%
+where you get exponential bounds like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and we'll see that yes uh you can any
+
+ align:start position:0%
+and we'll see that yes uh you can any
+ 
+
+ align:start position:0%
+and we'll see that yes uh you can any
+questions so far
+
+ align:start position:0%
+questions so far
+ 
+
+ align:start position:0%
+questions so far
+okay so here's a bad example
+
+ align:start position:0%
+okay so here's a bad example
+ 
+
+ align:start position:0%
+okay so here's a bad example
+so this is a network consists of a
+
+ align:start position:0%
+so this is a network consists of a
+ 
+
+ align:start position:0%
+so this is a network consists of a
+sequence of
+
+ align:start position:0%
+sequence of
+ 
+
+ align:start position:0%
+sequence of
+let's say k k plus 1 no k plus 2 i guess
+
+ align:start position:0%
+let's say k k plus 1 no k plus 2 i guess
+ 
+
+ align:start position:0%
+let's say k k plus 1 no k plus 2 i guess
+nodes in a line
+
+ align:start position:0%
+nodes in a line
+ 
+
+ align:start position:0%
+nodes in a line
+and i'm going to throw in
+
+ align:start position:0%
+and i'm going to throw in
+ 
+
+ align:start position:0%
+and i'm going to throw in
+some little detour nodes in between each
+
+ align:start position:0%
+some little detour nodes in between each
+ 
+
+ align:start position:0%
+some little detour nodes in between each
+consecutive pair of nodes
+
+ align:start position:0%
+consecutive pair of nodes
+ 
+
+ align:start position:0%
+consecutive pair of nodes
+in this graph and now let me play with
+
+ align:start position:0%
+in this graph and now let me play with
+ 
+
+ align:start position:0%
+in this graph and now let me play with
+the weights
+
+ align:start position:0%
+the weights
+ 
+
+ align:start position:0%
+the weights
+let's say on this path this direct path
+
+ align:start position:0%
+let's say on this path this direct path
+ 
+
+ align:start position:0%
+let's say on this path this direct path
+from v 0 to v k plus 1 all the weights
+
+ align:start position:0%
+from v 0 to v k plus 1 all the weights
+ 
+
+ align:start position:0%
+from v 0 to v k plus 1 all the weights
+are zero
+
+ align:start position:0%
+are zero
+ 
+
+ align:start position:0%
+are zero
+so that's going to be the the shortest
+
+ align:start position:0%
+so that's going to be the the shortest
+ 
+
+ align:start position:0%
+so that's going to be the the shortest
+path the best weight path
+
+ align:start position:0%
+path the best weight path
+ 
+
+ align:start position:0%
+path the best weight path
+from v zero to v k plus one
+
+ align:start position:0%
+from v zero to v k plus one
+ 
+
+ align:start position:0%
+from v zero to v k plus one
+but now i'm going to have some detours
+
+ align:start position:0%
+but now i'm going to have some detours
+ 
+
+ align:start position:0%
+but now i'm going to have some detours
+and on on the detours i have two edges
+
+ align:start position:0%
+and on on the detours i have two edges
+ 
+
+ align:start position:0%
+and on on the detours i have two edges
+one of weight zero and the other one of
+
+ align:start position:0%
+one of weight zero and the other one of
+ 
+
+ align:start position:0%
+one of weight zero and the other one of
+weight that's the power of two
+
+ align:start position:0%
+weight that's the power of two
+ 
+
+ align:start position:0%
+weight that's the power of two
+i'm going to start with high powers of 2
+
+ align:start position:0%
+i'm going to start with high powers of 2
+ 
+
+ align:start position:0%
+i'm going to start with high powers of 2
+2 to the k minus 1 then go down
+
+ align:start position:0%
+2 to the k minus 1 then go down
+ 
+
+ align:start position:0%
+2 to the k minus 1 then go down
+2 to the k minus 2 down to 2 to the 1 2
+
+ align:start position:0%
+2 to the k minus 2 down to 2 to the 1 2
+ 
+
+ align:start position:0%
+2 to the k minus 2 down to 2 to the 1 2
+to the 0.
+
+ align:start position:0%
+to the 0.
+ 
+
+ align:start position:0%
+to the 0.
+okay so you see what this graph is is
+
+ align:start position:0%
+okay so you see what this graph is is
+ 
+
+ align:start position:0%
+okay so you see what this graph is is
+doing it has a very fast path in the
+
+ align:start position:0%
+doing it has a very fast path in the
+ 
+
+ align:start position:0%
+doing it has a very fast path in the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+if you'd like to hear about as soon as
+
+ align:start position:0%
+if you'd like to hear about as soon as
+ 
+
+ align:start position:0%
+if you'd like to hear about as soon as
+you can but
+
+ align:start position:0%
+you can but
+ 
+
+ align:start position:0%
+you can but
+actually there's detours which could
+
+ align:start position:0%
+actually there's detours which could
+ 
+
+ align:start position:0%
+actually there's detours which could
+give you much worse paths
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see how this might execute to
+
+ align:start position:0%
+so let's see how this might execute to
+ 
+
+ align:start position:0%
+so let's see how this might execute to
+make a lot of messages pile up in a
+
+ align:start position:0%
+make a lot of messages pile up in a
+ 
+
+ align:start position:0%
+make a lot of messages pile up in a
+channel
+
+ align:start position:0%
+channel
+ 
+
+ align:start position:0%
+channel
+okay so my claim is that there's an
+
+ align:start position:0%
+okay so my claim is that there's an
+ 
+
+ align:start position:0%
+okay so my claim is that there's an
+execution of that network
+
+ align:start position:0%
+execution of that network
+ 
+
+ align:start position:0%
+execution of that network
+in which the last node vk
+
+ align:start position:0%
+in which the last node vk
+ 
+
+ align:start position:0%
+in which the last node vk
+sends two to the k
+
+ align:start position:0%
+sends two to the k
+ 
+
+ align:start position:0%
+sends two to the k
+messages to the next node v k plus one
+
+ align:start position:0%
+messages to the next node v k plus one
+ 
+
+ align:start position:0%
+messages to the next node v k plus one
+so he's really going to send an
+
+ align:start position:0%
+so he's really going to send an
+ 
+
+ align:start position:0%
+so he's really going to send an
+exponential number of messages
+
+ align:start position:0%
+exponential number of messages
+ 
+
+ align:start position:0%
+exponential number of messages
+corresponding to his
+
+ align:start position:0%
+corresponding to his
+ 
+
+ align:start position:0%
+corresponding to his
+corrections he's going to keep making
+
+ align:start position:0%
+corrections he's going to keep making
+ 
+
+ align:start position:0%
+corrections he's going to keep making
+corrections for better and better
+
+ align:start position:0%
+corrections for better and better
+ 
+
+ align:start position:0%
+corrections for better and better
+estimates
+
+ align:start position:0%
+estimates
+ 
+
+ align:start position:0%
+estimates
+okay and if all this happens relatively
+
+ align:start position:0%
+okay and if all this happens relatively
+ 
+
+ align:start position:0%
+okay and if all this happens relatively
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+that just means you have a channel with
+
+ align:start position:0%
+that just means you have a channel with
+ 
+
+ align:start position:0%
+that just means you have a channel with
+an exponential number of messages in it
+
+ align:start position:0%
+an exponential number of messages in it
+ 
+
+ align:start position:0%
+an exponential number of messages in it
+emptying that will take exponential time
+
+ align:start position:0%
+emptying that will take exponential time
+ 
+
+ align:start position:0%
+emptying that will take exponential time
+okay okay so
+
+ align:start position:0%
+okay okay so
+ 
+
+ align:start position:0%
+okay okay so
+you have an idea how this might happen
+
+ align:start position:0%
+you have an idea how this might happen
+ 
+
+ align:start position:0%
+you have an idea how this might happen
+how could this node
+
+ align:start position:0%
+how could this node
+ 
+
+ align:start position:0%
+how could this node
+be k get so many successively improved
+
+ align:start position:0%
+be k get so many successively improved
+ 
+
+ align:start position:0%
+be k get so many successively improved
+estimates one after the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what's the biggest estimate it
+
+ align:start position:0%
+well what's the biggest estimate it
+ 
+
+ align:start position:0%
+well what's the biggest estimate it
+might get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could get two to the k minus one well
+
+ align:start position:0%
+could get two to the k minus one well
+ 
+
+ align:start position:0%
+could get two to the k minus one well
+let's see could do that
+
+ align:start position:0%
+let's see could do that
+ 
+
+ align:start position:0%
+let's see could do that
+and it could do that plus 2 plus 2 to
+
+ align:start position:0%
+and it could do that plus 2 plus 2 to
+ 
+
+ align:start position:0%
+and it could do that plus 2 plus 2 to
+the k minus 2 plus
+
+ align:start position:0%
+the k minus 2 plus
+ 
+
+ align:start position:0%
+the k minus 2 plus
+all the way down to plus 2 to the zero
+
+ align:start position:0%
+all the way down to plus 2 to the zero
+ 
+
+ align:start position:0%
+all the way down to plus 2 to the zero
+so you could be following this really
+
+ align:start position:0%
+so you could be following this really
+ 
+
+ align:start position:0%
+so you could be following this really
+inefficient path just all the detours
+
+ align:start position:0%
+inefficient path just all the detours
+ 
+
+ align:start position:0%
+inefficient path just all the detours
+before the messages actually arrive on
+
+ align:start position:0%
+before the messages actually arrive on
+ 
+
+ align:start position:0%
+before the messages actually arrive on
+the edges on the spine yeah so
+
+ align:start position:0%
+the edges on the spine yeah so
+ 
+
+ align:start position:0%
+the edges on the spine yeah so
+you follow all oh oh you said two to the
+
+ align:start position:0%
+you follow all oh oh you said two to the
+ 
+
+ align:start position:0%
+you follow all oh oh you said two to the
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+minus one parentheses yeah that's
+
+ align:start position:0%
+minus one parentheses yeah that's
+ 
+
+ align:start position:0%
+minus one parentheses yeah that's
+exactly right
+
+ align:start position:0%
+exactly right
+ 
+
+ align:start position:0%
+exactly right
+that's all right we can't
+
+ align:start position:0%
+that's all right we can't
+ 
+
+ align:start position:0%
+that's all right we can't
+parenthesize our speech so all right
+
+ align:start position:0%
+parenthesize our speech so all right
+ 
+
+ align:start position:0%
+parenthesize our speech so all right
+so the possible estimates that bk can
+
+ align:start position:0%
+so the possible estimates that bk can
+ 
+
+ align:start position:0%
+so the possible estimates that bk can
+take on
+
+ align:start position:0%
+take on
+ 
+
+ align:start position:0%
+take on
+are actually 2 to the k
+
+ align:start position:0%
+are actually 2 to the k
+ 
+
+ align:start position:0%
+are actually 2 to the k
+as you said 2 to the k minus 1
+
+ align:start position:0%
+as you said 2 to the k minus 1
+ 
+
+ align:start position:0%
+as you said 2 to the k minus 1
+which you would get by taking all the
+
+ align:start position:0%
+which you would get by taking all the
+ 
+
+ align:start position:0%
+which you would get by taking all the
+detours adding up the powers of 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it could also have an estimate which
+
+ align:start position:0%
+but it could also have an estimate which
+ 
+
+ align:start position:0%
+but it could also have an estimate which
+is 2 to the k minus 2
+
+ align:start position:0%
+is 2 to the k minus 2
+ 
+
+ align:start position:0%
+is 2 to the k minus 2
+or 2 to the k minus 3. all of those are
+
+ align:start position:0%
+or 2 to the k minus 3. all of those are
+ 
+
+ align:start position:0%
+or 2 to the k minus 3. all of those are
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+moreover you can have a single execution
+
+ align:start position:0%
+moreover you can have a single execution
+ 
+
+ align:start position:0%
+moreover you can have a single execution
+of this asynchronous algorithm
+
+ align:start position:0%
+of this asynchronous algorithm
+ 
+
+ align:start position:0%
+of this asynchronous algorithm
+in which node bk actually acquires
+
+ align:start position:0%
+in which node bk actually acquires
+ 
+
+ align:start position:0%
+in which node bk actually acquires
+all those estimates in sequence one at a
+
+ align:start position:0%
+all those estimates in sequence one at a
+ 
+
+ align:start position:0%
+all those estimates in sequence one at a
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so how much that work first the messages
+
+ align:start position:0%
+so how much that work first the messages
+ 
+
+ align:start position:0%
+so how much that work first the messages
+travel all the detours
+
+ align:start position:0%
+travel all the detours
+ 
+
+ align:start position:0%
+travel all the detours
+fine v k gets two to the k minus one
+
+ align:start position:0%
+fine v k gets two to the k minus one
+ 
+
+ align:start position:0%
+fine v k gets two to the k minus one
+then there's a message traveling
+
+ align:start position:0%
+then there's a message traveling
+ 
+
+ align:start position:0%
+then there's a message traveling
+well this guy sends a message on the
+
+ align:start position:0%
+well this guy sends a message on the
+ 
+
+ align:start position:0%
+well this guy sends a message on the
+lower link
+
+ align:start position:0%
+lower link
+ 
+
+ align:start position:0%
+lower link
+so this guy has only heard about the
+
+ align:start position:0%
+so this guy has only heard about the
+ 
+
+ align:start position:0%
+so this guy has only heard about the
+messages on the detours up to that point
+
+ align:start position:0%
+messages on the detours up to that point
+ 
+
+ align:start position:0%
+messages on the detours up to that point
+but he sends that on this lower link
+
+ align:start position:0%
+but he sends that on this lower link
+ 
+
+ align:start position:0%
+but he sends that on this lower link
+which means you've kind of bypassed this
+
+ align:start position:0%
+which means you've kind of bypassed this
+ 
+
+ align:start position:0%
+which means you've kind of bypassed this
+weight of one
+
+ align:start position:0%
+weight of one
+ 
+
+ align:start position:0%
+weight of one
+so vk gets a little bit of an
+
+ align:start position:0%
+so vk gets a little bit of an
+ 
+
+ align:start position:0%
+so vk gets a little bit of an
+improvement
+
+ align:start position:0%
+improvement
+ 
+
+ align:start position:0%
+improvement
+which gives it 2 to the k minus 2 as its
+
+ align:start position:0%
+which gives it 2 to the k minus 2 as its
+ 
+
+ align:start position:0%
+which gives it 2 to the k minus 2 as its
+estimate
+
+ align:start position:0%
+estimate
+ 
+
+ align:start position:0%
+estimate
+okay so what happens next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we step one back and the node from
+
+ align:start position:0%
+well we step one back and the node from
+ 
+
+ align:start position:0%
+well we step one back and the node from
+node k minus two can send a message
+
+ align:start position:0%
+node k minus two can send a message
+ 
+
+ align:start position:0%
+node k minus two can send a message
+on the lower link
+
+ align:start position:0%
+on the lower link
+ 
+
+ align:start position:0%
+on the lower link
+which has weight zero uh to be k minus
+
+ align:start position:0%
+which has weight zero uh to be k minus
+ 
+
+ align:start position:0%
+which has weight zero uh to be k minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+but that corrected estimate might then
+
+ align:start position:0%
+but that corrected estimate might then
+ 
+
+ align:start position:0%
+but that corrected estimate might then
+traverse
+
+ align:start position:0%
+traverse
+ 
+
+ align:start position:0%
+traverse
+the detour to get to
+
+ align:start position:0%
+the detour to get to
+ 
+
+ align:start position:0%
+the detour to get to
+node vk so if you get the correction
+
+ align:start position:0%
+node vk so if you get the correction
+ 
+
+ align:start position:0%
+node vk so if you get the correction
+for node bk minus 1 but then you follow
+
+ align:start position:0%
+for node bk minus 1 but then you follow
+ 
+
+ align:start position:0%
+for node bk minus 1 but then you follow
+the detour
+
+ align:start position:0%
+the detour
+ 
+
+ align:start position:0%
+the detour
+you haven't improved that much you've
+
+ align:start position:0%
+you haven't improved that much you've
+ 
+
+ align:start position:0%
+you haven't improved that much you've
+just improved by
+
+ align:start position:0%
+just improved by
+ 
+
+ align:start position:0%
+just improved by
+1. so this way you get 2 to the k minus
+
+ align:start position:0%
+1. so this way you get 2 to the k minus
+ 
+
+ align:start position:0%
+1. so this way you get 2 to the k minus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+as the new estimate but then again on
+
+ align:start position:0%
+as the new estimate but then again on
+ 
+
+ align:start position:0%
+as the new estimate but then again on
+the lower link
+
+ align:start position:0%
+the lower link
+ 
+
+ align:start position:0%
+the lower link
+the message eventually arrives which
+
+ align:start position:0%
+the message eventually arrives which
+ 
+
+ align:start position:0%
+the message eventually arrives which
+gives you
+
+ align:start position:0%
+gives you
+ 
+
+ align:start position:0%
+gives you
+2 to the k minus 4. so you see the
+
+ align:start position:0%
+2 to the k minus 4. so you see the
+ 
+
+ align:start position:0%
+2 to the k minus 4. so you see the
+pattern sort of
+
+ align:start position:0%
+pattern sort of
+ 
+
+ align:start position:0%
+pattern sort of
+you're going to be counting down in
+
+ align:start position:0%
+you're going to be counting down in
+ 
+
+ align:start position:0%
+you're going to be counting down in
+binary by
+
+ align:start position:0%
+binary by
+ 
+
+ align:start position:0%
+binary by
+successively having nodes further to the
+
+ align:start position:0%
+successively having nodes further to the
+ 
+
+ align:start position:0%
+successively having nodes further to the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+deliver their messages but then they do
+
+ align:start position:0%
+deliver their messages but then they do
+ 
+
+ align:start position:0%
+deliver their messages but then they do
+the worst possible thing of getting the
+
+ align:start position:0%
+the worst possible thing of getting the
+ 
+
+ align:start position:0%
+the worst possible thing of getting the
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+to vk he has to deal with all those
+
+ align:start position:0%
+to vk he has to deal with all those
+ 
+
+ align:start position:0%
+to vk he has to deal with all those
+other estimates in between
+
+ align:start position:0%
+other estimates in between
+ 
+
+ align:start position:0%
+other estimates in between
+so if this happens quickly what you get
+
+ align:start position:0%
+so if this happens quickly what you get
+ 
+
+ align:start position:0%
+so if this happens quickly what you get
+is a pile up of
+
+ align:start position:0%
+is a pile up of
+ 
+
+ align:start position:0%
+is a pile up of
+an exponential number of search messages
+
+ align:start position:0%
+an exponential number of search messages
+ 
+
+ align:start position:0%
+an exponential number of search messages
+in one channel
+
+ align:start position:0%
+in one channel
+ 
+
+ align:start position:0%
+in one channel
+and then that information has to go on
+
+ align:start position:0%
+and then that information has to go on
+ 
+
+ align:start position:0%
+and then that information has to go on
+to the next node or the rest of the
+
+ align:start position:0%
+to the next node or the rest of the
+ 
+
+ align:start position:0%
+to the next node or the rest of the
+network whatever it's going to take an
+
+ align:start position:0%
+network whatever it's going to take an
+ 
+
+ align:start position:0%
+network whatever it's going to take an
+exponential amount of time in the worst
+
+ align:start position:0%
+exponential amount of time in the worst
+ 
+
+ align:start position:0%
+exponential amount of time in the worst
+case to empty that
+
+ align:start position:0%
+case to empty that
+ 
+
+ align:start position:0%
+case to empty that
+all out okay
+
+ align:start position:0%
+all out okay
+ 
+
+ align:start position:0%
+all out okay
+so this is pretty bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but the algorithm is correct
+
+ align:start position:0%
+okay but the algorithm is correct
+ 
+
+ align:start position:0%
+okay but the algorithm is correct
+and so how do you learn when
+
+ align:start position:0%
+and so how do you learn when
+ 
+
+ align:start position:0%
+and so how do you learn when
+everything is finished and how does a
+
+ align:start position:0%
+everything is finished and how does a
+ 
+
+ align:start position:0%
+everything is finished and how does a
+process know when it it can
+
+ align:start position:0%
+process know when it it can
+ 
+
+ align:start position:0%
+process know when it it can
+output its own correct distance
+
+ align:start position:0%
+output its own correct distance
+ 
+
+ align:start position:0%
+output its own correct distance
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+how can we figure out when this is all
+
+ align:start position:0%
+how can we figure out when this is all
+ 
+
+ align:start position:0%
+how can we figure out when this is all
+stabilized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same thing as before so okay
+
+ align:start position:0%
+same thing as before so okay
+ 
+
+ align:start position:0%
+same thing as before so okay
+we can just do a converge cast i mean
+
+ align:start position:0%
+we can just do a converge cast i mean
+ 
+
+ align:start position:0%
+we can just do a converge cast i mean
+this is more corrections but it's still
+
+ align:start position:0%
+this is more corrections but it's still
+ 
+
+ align:start position:0%
+this is more corrections but it's still
+the same kind of corrections so we can
+
+ align:start position:0%
+the same kind of corrections so we can
+ 
+
+ align:start position:0%
+the same kind of corrections so we can
+converge casts and eventually
+
+ align:start position:0%
+converge casts and eventually
+ 
+
+ align:start position:0%
+converge casts and eventually
+this is going to converge cast all the
+
+ align:start position:0%
+this is going to converge cast all the
+ 
+
+ align:start position:0%
+this is going to converge cast all the
+way up to the root
+
+ align:start position:0%
+way up to the root
+ 
+
+ align:start position:0%
+way up to the root
+and then the root knows it's done and
+
+ align:start position:0%
+and then the root knows it's done and
+ 
+
+ align:start position:0%
+and then the root knows it's done and
+can tell everyone else
+
+ align:start position:0%
+can tell everyone else
+ 
+
+ align:start position:0%
+can tell everyone else
+okay okay so a moral here
+
+ align:start position:0%
+okay okay so a moral here
+ 
+
+ align:start position:0%
+okay okay so a moral here
+and you've had a quick dose of a lot of
+
+ align:start position:0%
+and you've had a quick dose of a lot of
+ 
+
+ align:start position:0%
+and you've had a quick dose of a lot of
+asynchrony
+
+ align:start position:0%
+asynchrony
+ 
+
+ align:start position:0%
+asynchrony
+so yeah if you don't do anything about
+
+ align:start position:0%
+so yeah if you don't do anything about
+ 
+
+ align:start position:0%
+so yeah if you don't do anything about
+it if you just use unrestrained
+
+ align:start position:0%
+it if you just use unrestrained
+ 
+
+ align:start position:0%
+it if you just use unrestrained
+asynchrony in the worst case
+
+ align:start position:0%
+asynchrony in the worst case
+ 
+
+ align:start position:0%
+asynchrony in the worst case
+uh you're going to have some pretty bad
+
+ align:start position:0%
+uh you're going to have some pretty bad
+ 
+
+ align:start position:0%
+uh you're going to have some pretty bad
+performance so
+
+ align:start position:0%
+performance so
+ 
+
+ align:start position:0%
+performance so
+the question is what do you do about
+
+ align:start position:0%
+the question is what do you do about
+ 
+
+ align:start position:0%
+the question is what do you do about
+that and there are various techniques
+
+ align:start position:0%
+that and there are various techniques
+ 
+
+ align:start position:0%
+that and there are various techniques
+and if you want to take my course next
+
+ align:start position:0%
+and if you want to take my course next
+ 
+
+ align:start position:0%
+and if you want to take my course next
+fall so we'll
+
+ align:start position:0%
+fall so we'll
+ 
+
+ align:start position:0%
+fall so we'll
+cover some of those okay if i'll say a
+
+ align:start position:0%
+cover some of those okay if i'll say a
+ 
+
+ align:start position:0%
+cover some of those okay if i'll say a
+little bit about the course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a basic it's a tqe level uh
+
+ align:start position:0%
+so it's a basic it's a tqe level uh
+ 
+
+ align:start position:0%
+so it's a basic it's a tqe level uh
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+uh grad course we do synchronous
+
+ align:start position:0%
+uh grad course we do synchronous
+ 
+
+ align:start position:0%
+uh grad course we do synchronous
+asynchronous and some
+
+ align:start position:0%
+asynchronous and some
+ 
+
+ align:start position:0%
+asynchronous and some
+other stuff where the nodes really know
+
+ align:start position:0%
+other stuff where the nodes really know
+ 
+
+ align:start position:0%
+other stuff where the nodes really know
+about something about time
+
+ align:start position:0%
+about something about time
+ 
+
+ align:start position:0%
+about something about time
+um here's some of the synchronous
+
+ align:start position:0%
+um here's some of the synchronous
+ 
+
+ align:start position:0%
+um here's some of the synchronous
+problems some
+
+ align:start position:0%
+problems some
+ 
+
+ align:start position:0%
+problems some
+like the ones you've already seen but
+
+ align:start position:0%
+like the ones you've already seen but
+ 
+
+ align:start position:0%
+like the ones you've already seen but
+building many other kinds of structures
+
+ align:start position:0%
+building many other kinds of structures
+ 
+
+ align:start position:0%
+building many other kinds of structures
+in graphs and then we get into fall
+
+ align:start position:0%
+in graphs and then we get into fall
+ 
+
+ align:start position:0%
+in graphs and then we get into fall
+tolerance
+
+ align:start position:0%
+tolerance
+ 
+
+ align:start position:0%
+tolerance
+so there's a lot of questions about what
+
+ align:start position:0%
+so there's a lot of questions about what
+ 
+
+ align:start position:0%
+so there's a lot of questions about what
+happens when some of the
+
+ align:start position:0%
+happens when some of the
+ 
+
+ align:start position:0%
+happens when some of the
+components can fail or they're even
+
+ align:start position:0%
+components can fail or they're even
+ 
+
+ align:start position:0%
+components can fail or they're even
+malicious
+
+ align:start position:0%
+malicious
+ 
+
+ align:start position:0%
+malicious
+and you know you have to deal with the
+
+ align:start position:0%
+and you know you have to deal with the
+ 
+
+ align:start position:0%
+and you know you have to deal with the
+effects of of malicious
+
+ align:start position:0%
+effects of of malicious
+ 
+
+ align:start position:0%
+effects of of malicious
+processes in your system and then
+
+ align:start position:0%
+processes in your system and then
+ 
+
+ align:start position:0%
+processes in your system and then
+for asynchronous algorithms um we'll do
+
+ align:start position:0%
+for asynchronous algorithms um we'll do
+ 
+
+ align:start position:0%
+for asynchronous algorithms um we'll do
+not only
+
+ align:start position:0%
+not only
+ 
+
+ align:start position:0%
+not only
+individual problems like the ones you've
+
+ align:start position:0%
+individual problems like the ones you've
+ 
+
+ align:start position:0%
+individual problems like the ones you've
+just seen but there's some general
+
+ align:start position:0%
+just seen but there's some general
+ 
+
+ align:start position:0%
+just seen but there's some general
+techniques like synchronizers
+
+ align:start position:0%
+techniques like synchronizers
+ 
+
+ align:start position:0%
+techniques like synchronizers
+um notion of logical time that's um
+
+ align:start position:0%
+um notion of logical time that's um
+ 
+
+ align:start position:0%
+um notion of logical time that's um
+leslie lamport's first and biggest
+
+ align:start position:0%
+leslie lamport's first and biggest
+ 
+
+ align:start position:0%
+leslie lamport's first and biggest
+contribution he won the touring award
+
+ align:start position:0%
+contribution he won the touring award
+ 
+
+ align:start position:0%
+contribution he won the touring award
+last year other techniques like taking
+
+ align:start position:0%
+last year other techniques like taking
+ 
+
+ align:start position:0%
+last year other techniques like taking
+global snapshots of the of the entire
+
+ align:start position:0%
+global snapshots of the of the entire
+ 
+
+ align:start position:0%
+global snapshots of the of the entire
+system while it's running
+
+ align:start position:0%
+system while it's running
+ 
+
+ align:start position:0%
+system while it's running
+in addition to talking about networks as
+
+ align:start position:0%
+in addition to talking about networks as
+ 
+
+ align:start position:0%
+in addition to talking about networks as
+we've been doing this week
+
+ align:start position:0%
+we've been doing this week
+ 
+
+ align:start position:0%
+we've been doing this week
+we'll talk about shared memory
+
+ align:start position:0%
+we'll talk about shared memory
+ 
+
+ align:start position:0%
+we'll talk about shared memory
+multiprocessors
+
+ align:start position:0%
+multiprocessors
+ 
+
+ align:start position:0%
+multiprocessors
+accessing shared memory and
+
+ align:start position:0%
+accessing shared memory and
+ 
+
+ align:start position:0%
+accessing shared memory and
+solving problems that are of use in
+
+ align:start position:0%
+solving problems that are of use in
+ 
+
+ align:start position:0%
+solving problems that are of use in
+multiprocessors like mutual exclusion
+
+ align:start position:0%
+multiprocessors like mutual exclusion
+ 
+
+ align:start position:0%
+multiprocessors like mutual exclusion
+and again fault tolerance fault
+
+ align:start position:0%
+and again fault tolerance fault
+ 
+
+ align:start position:0%
+and again fault tolerance fault
+tolerance then
+
+ align:start position:0%
+tolerance then
+ 
+
+ align:start position:0%
+tolerance then
+gets us into a study of data objects
+
+ align:start position:0%
+gets us into a study of data objects
+ 
+
+ align:start position:0%
+gets us into a study of data objects
+with consistency conditions which is the
+
+ align:start position:0%
+with consistency conditions which is the
+ 
+
+ align:start position:0%
+with consistency conditions which is the
+sort of stuff that's
+
+ align:start position:0%
+sort of stuff that's
+ 
+
+ align:start position:0%
+sort of stuff that's
+useful in cloud computing if you want to
+
+ align:start position:0%
+useful in cloud computing if you want to
+ 
+
+ align:start position:0%
+useful in cloud computing if you want to
+have coherent access to data that's
+
+ align:start position:0%
+have coherent access to data that's
+ 
+
+ align:start position:0%
+have coherent access to data that's
+stored at many locations you need to
+
+ align:start position:0%
+stored at many locations you need to
+ 
+
+ align:start position:0%
+stored at many locations you need to
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+um interesting distributed algorithms
+
+ align:start position:0%
+um interesting distributed algorithms
+ 
+
+ align:start position:0%
+um interesting distributed algorithms
+self-stabilization if you plunge your
+
+ align:start position:0%
+self-stabilization if you plunge your
+ 
+
+ align:start position:0%
+self-stabilization if you plunge your
+system into some arbitrary state and
+
+ align:start position:0%
+system into some arbitrary state and
+ 
+
+ align:start position:0%
+system into some arbitrary state and
+you'd like it to converge to a good
+
+ align:start position:0%
+you'd like it to converge to a good
+ 
+
+ align:start position:0%
+you'd like it to converge to a good
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+that's the topic of self-stabilization
+
+ align:start position:0%
+that's the topic of self-stabilization
+ 
+
+ align:start position:0%
+that's the topic of self-stabilization
+and depending on time there's things
+
+ align:start position:0%
+and depending on time there's things
+ 
+
+ align:start position:0%
+and depending on time there's things
+that use use time in the algorithms
+
+ align:start position:0%
+that use use time in the algorithms
+ 
+
+ align:start position:0%
+that use use time in the algorithms
+and the newer work that we're working on
+
+ align:start position:0%
+and the newer work that we're working on
+ 
+
+ align:start position:0%
+and the newer work that we're working on
+in research is very dynamic you have
+
+ align:start position:0%
+in research is very dynamic you have
+ 
+
+ align:start position:0%
+in research is very dynamic you have
+distributed algorithms where the network
+
+ align:start position:0%
+distributed algorithms where the network
+ 
+
+ align:start position:0%
+distributed algorithms where the network
+itself is changing during the execution
+
+ align:start position:0%
+itself is changing during the execution
+ 
+
+ align:start position:0%
+itself is changing during the execution
+that comes up in wireless networks and
+
+ align:start position:0%
+that comes up in wireless networks and
+ 
+
+ align:start position:0%
+that comes up in wireless networks and
+lately we're actually looking at insect
+
+ align:start position:0%
+lately we're actually looking at insect
+ 
+
+ align:start position:0%
+lately we're actually looking at insect
+colony algorithms
+
+ align:start position:0%
+colony algorithms
+ 
+
+ align:start position:0%
+colony algorithms
+where what distributed algorithms do
+
+ align:start position:0%
+where what distributed algorithms do
+ 
+
+ align:start position:0%
+where what distributed algorithms do
+ants use to
+
+ align:start position:0%
+ants use to
+ 
+
+ align:start position:0%
+ants use to
+decide on how to select a new nest when
+
+ align:start position:0%
+decide on how to select a new nest when
+ 
+
+ align:start position:0%
+decide on how to select a new nest when
+the researchers smash their old nest in
+
+ align:start position:0%
+the researchers smash their old nest in
+ 
+
+ align:start position:0%
+the researchers smash their old nest in
+the laboratory
+
+ align:start position:0%
+the laboratory
+ 
+
+ align:start position:0%
+the laboratory
+so that kind of question okay
+
+ align:start position:0%
+so that kind of question okay
+ 
+
+ align:start position:0%
+so that kind of question okay
+so so that's it for the distributed
+
+ align:start position:0%
+so so that's it for the distributed
+ 
+
+ align:start position:0%
+so so that's it for the distributed
+algorithms week
+
+ align:start position:0%
+algorithms week
+ 
+
+ align:start position:0%
+algorithms week
+and we'll see you next next week is um
+
+ align:start position:0%
+and we'll see you next next week is um
+ 
+
+ align:start position:0%
+and we'll see you next next week is um
+security okay yep
+
+ align:start position:0%
+security okay yep
+ 
+
+ align:start position:0%
+security okay yep
+whoa
\ No newline at end of file
diff --git a/Ehteu_SG3tI.txt b/Ehteu_SG3tI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c5874475e92786f617d5741a7871f78722a88e2a
--- /dev/null
+++ b/Ehteu_SG3tI.txt
@@ -0,0 +1,1789 @@
+align:start position:0%
+ 
+hi welcome to recitation today's problem
+
+ align:start position:0%
+hi welcome to recitation today's problem
+ 
+
+ align:start position:0%
+hi welcome to recitation today's problem
+is about change of bases it says the
+
+ align:start position:0%
+is about change of bases it says the
+ 
+
+ align:start position:0%
+is about change of bases it says the
+vector space of polinomial in X of
+
+ align:start position:0%
+vector space of polinomial in X of
+ 
+
+ align:start position:0%
+vector space of polinomial in X of
+degree up to two has a basis 1 x and x
+
+ align:start position:0%
+degree up to two has a basis 1 x and x
+ 
+
+ align:start position:0%
+degree up to two has a basis 1 x and x
+squ that's the obvious basis that you
+
+ align:start position:0%
+squ that's the obvious basis that you
+ 
+
+ align:start position:0%
+squ that's the obvious basis that you
+would write for that space Vector space
+
+ align:start position:0%
+would write for that space Vector space
+ 
+
+ align:start position:0%
+would write for that space Vector space
+but today we're going to consider
+
+ align:start position:0%
+but today we're going to consider
+ 
+
+ align:start position:0%
+but today we're going to consider
+another basis W1 W2 and W3 and we don't
+
+ align:start position:0%
+another basis W1 W2 and W3 and we don't
+ 
+
+ align:start position:0%
+another basis W1 W2 and W3 and we don't
+know what W1 W2 and W3 are explicitly
+
+ align:start position:0%
+know what W1 W2 and W3 are explicitly
+ 
+
+ align:start position:0%
+know what W1 W2 and W3 are explicitly
+what we know is that their values at X =
+
+ align:start position:0%
+what we know is that their values at X =
+ 
+
+ align:start position:0%
+what we know is that their values at X =
+Min -1 0 and 1 are given by this this
+
+ align:start position:0%
+Min -1 0 and 1 are given by this this
+ 
+
+ align:start position:0%
+Min -1 0 and 1 are given by this this
+table here so there are 1 0 0 0 1 0 and
+
+ align:start position:0%
+table here so there are 1 0 0 0 1 0 and
+ 
+
+ align:start position:0%
+table here so there are 1 0 0 0 1 0 and
+0 0 1 we're asked to do the following
+
+ align:start position:0%
+0 0 1 we're asked to do the following
+ 
+
+ align:start position:0%
+0 0 1 we're asked to do the following
+we're asked to express this polinomial
+
+ align:start position:0%
+we're asked to express this polinomial
+ 
+
+ align:start position:0%
+we're asked to express this polinomial
+so y of X is - x + 5 in this Bas is W1
+
+ align:start position:0%
+so y of X is - x + 5 in this Bas is W1
+ 
+
+ align:start position:0%
+so y of X is - x + 5 in this Bas is W1
+W2 W3 we're asked to find the change of
+
+ align:start position:0%
+W2 W3 we're asked to find the change of
+ 
+
+ align:start position:0%
+W2 W3 we're asked to find the change of
+basis matrices between these two bases 1
+
+ align:start position:0%
+basis matrices between these two bases 1
+ 
+
+ align:start position:0%
+basis matrices between these two bases 1
+x x² and W1 W2 W3 and finally we're
+
+ align:start position:0%
+x x² and W1 W2 W3 and finally we're
+ 
+
+ align:start position:0%
+x x² and W1 W2 W3 and finally we're
+asked to find the Matrix of taking
+
+ align:start position:0%
+asked to find the Matrix of taking
+ 
+
+ align:start position:0%
+asked to find the Matrix of taking
+derivatives which is a linear map on
+
+ align:start position:0%
+derivatives which is a linear map on
+ 
+
+ align:start position:0%
+derivatives which is a linear map on
+this space in both of these bases and
+
+ align:start position:0%
+this space in both of these bases and
+ 
+
+ align:start position:0%
+this space in both of these bases and
+let me give you an extra level of of of
+
+ align:start position:0%
+let me give you an extra level of of of
+ 
+
+ align:start position:0%
+let me give you an extra level of of of
+um challenge which is to try to do as
+
+ align:start position:0%
+um challenge which is to try to do as
+ 
+
+ align:start position:0%
+um challenge which is to try to do as
+much of this as possible without
+
+ align:start position:0%
+much of this as possible without
+ 
+
+ align:start position:0%
+much of this as possible without
+explicitly finding W1 W2 and W3 uh I'll
+
+ align:start position:0%
+explicitly finding W1 W2 and W3 uh I'll
+ 
+
+ align:start position:0%
+explicitly finding W1 W2 and W3 uh I'll
+let you think about the problem and then
+
+ align:start position:0%
+let you think about the problem and then
+ 
+
+ align:start position:0%
+let you think about the problem and then
+you can come back and compare Your
+
+ align:start position:0%
+you can come back and compare Your
+ 
+
+ align:start position:0%
+you can come back and compare Your
+solution with mine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi welcome back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to start with a problem a we need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find we need to find coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beta And GMA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that y of X is expressed through with
+
+ align:start position:0%
+so that y of X is expressed through with
+ 
+
+ align:start position:0%
+so that y of X is expressed through with
+this coefficients in this new basis W1
+
+ align:start position:0%
+this coefficients in this new basis W1
+ 
+
+ align:start position:0%
+this coefficients in this new basis W1
+W2 and W3 now one way to do that would
+
+ align:start position:0%
+W2 and W3 now one way to do that would
+ 
+
+ align:start position:0%
+W2 and W3 now one way to do that would
+be to look at this look at this table of
+
+ align:start position:0%
+be to look at this look at this table of
+ 
+
+ align:start position:0%
+be to look at this look at this table of
+values explicitly find W1 W2 and W3 so a
+
+ align:start position:0%
+values explicitly find W1 W2 and W3 so a
+ 
+
+ align:start position:0%
+values explicitly find W1 W2 and W3 so a
+quadratic polinomial is um all the
+
+ align:start position:0%
+quadratic polinomial is um all the
+ 
+
+ align:start position:0%
+quadratic polinomial is um all the
+information we need about it is in three
+
+ align:start position:0%
+information we need about it is in three
+ 
+
+ align:start position:0%
+information we need about it is in three
+Val is in values at three points so say
+
+ align:start position:0%
+Val is in values at three points so say
+ 
+
+ align:start position:0%
+Val is in values at three points so say
+W1 is A1 Plus B * X plus C * um x^2 find
+
+ align:start position:0%
+W1 is A1 Plus B * X plus C * um x^2 find
+ 
+
+ align:start position:0%
+W1 is A1 Plus B * X plus C * um x^2 find
+a b and c find W1 W2 W3 explicitly and
+
+ align:start position:0%
+a b and c find W1 W2 W3 explicitly and
+ 
+
+ align:start position:0%
+a b and c find W1 W2 W3 explicitly and
+then go back to this system and try to
+
+ align:start position:0%
+then go back to this system and try to
+ 
+
+ align:start position:0%
+then go back to this system and try to
+find it and try to find alpha beta and
+
+ align:start position:0%
+find it and try to find alpha beta and
+ 
+
+ align:start position:0%
+find it and try to find alpha beta and
+gamma however there's a trick let's try
+
+ align:start position:0%
+gamma however there's a trick let's try
+ 
+
+ align:start position:0%
+gamma however there's a trick let's try
+to do let's try to see if we can do it
+
+ align:start position:0%
+to do let's try to see if we can do it
+ 
+
+ align:start position:0%
+to do let's try to see if we can do it
+without finding W1 W2 and W3 explicitly
+
+ align:start position:0%
+without finding W1 W2 and W3 explicitly
+ 
+
+ align:start position:0%
+without finding W1 W2 and W3 explicitly
+so let me try to see what are the values
+
+ align:start position:0%
+so let me try to see what are the values
+ 
+
+ align:start position:0%
+so let me try to see what are the values
+of Y at these points so Y is - x + 5 so
+
+ align:start position:0%
+of Y at these points so Y is - x + 5 so
+ 
+
+ align:start position:0%
+of Y at these points so Y is - x + 5 so
+the values are six
+
+ align:start position:0%
+the values are six
+ 
+
+ align:start position:0%
+the values are six
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+5 and
+
+ align:start position:0%
+5 and
+ 
+
+ align:start position:0%
+5 and
+four and let me instead of considering
+
+ align:start position:0%
+four and let me instead of considering
+ 
+
+ align:start position:0%
+four and let me instead of considering
+this this equation let me evaluate it at
+
+ align:start position:0%
+this this equation let me evaluate it at
+ 
+
+ align:start position:0%
+this this equation let me evaluate it at
+X is minus one x
+
+ align:start position:0%
+X is minus one x
+ 
+
+ align:start position:0%
+X is minus one x
+is0 and x is
+
+ align:start position:0%
+is0 and x is
+ 
+
+ align:start position:0%
+is0 and x is
+one what I get through this
+
+ align:start position:0%
+one what I get through this
+ 
+
+ align:start position:0%
+one what I get through this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that w at at minus one um actually let
+
+ align:start position:0%
+that w at at minus one um actually let
+ 
+
+ align:start position:0%
+that w at at minus one um actually let
+me write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I get that W minus1 which is a number
+
+ align:start position:0%
+I get that W minus1 which is a number
+ 
+
+ align:start position:0%
+I get that W minus1 which is a number
+equals Alpha *
+
+ align:start position:0%
+equals Alpha *
+ 
+
+ align:start position:0%
+equals Alpha *
+W1 at Min -1 which is a number plus beta
+
+ align:start position:0%
+W1 at Min -1 which is a number plus beta
+ 
+
+ align:start position:0%
+W1 at Min -1 which is a number plus beta
+* W2 at minus1 plus GMA *
+
+ align:start position:0%
+* W2 at minus1 plus GMA *
+ 
+
+ align:start position:0%
+* W2 at minus1 plus GMA *
+W3 at minus
+
+ align:start position:0%
+W3 at minus
+ 
+
+ align:start position:0%
+W3 at minus
+one and similarly at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and similarly at one and now let me
+
+ align:start position:0%
+zero and similarly at one and now let me
+ 
+
+ align:start position:0%
+zero and similarly at one and now let me
+think of this as a linear system that
+
+ align:start position:0%
+think of this as a linear system that
+ 
+
+ align:start position:0%
+think of this as a linear system that
+has unknowns alpha beta and gamma
+
+ align:start position:0%
+has unknowns alpha beta and gamma
+ 
+
+ align:start position:0%
+has unknowns alpha beta and gamma
+coefficient these values here at
+
+ align:start position:0%
+coefficient these values here at
+ 
+
+ align:start position:0%
+coefficient these values here at
+minus10 and 1 and the right hand side
+
+ align:start position:0%
+minus10 and 1 and the right hand side
+ 
+
+ align:start position:0%
+minus10 and 1 and the right hand side
+well what's written here on the left
+
+ align:start position:0%
+well what's written here on the left
+ 
+
+ align:start position:0%
+well what's written here on the left
+hand side Y at minus one Y at zero and Y
+
+ align:start position:0%
+hand side Y at minus one Y at zero and Y
+ 
+
+ align:start position:0%
+hand side Y at minus one Y at zero and Y
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+one if you write
+
+ align:start position:0%
+one if you write
+ 
+
+ align:start position:0%
+one if you write
+this in a matrix and read off
+
+ align:start position:0%
+this in a matrix and read off
+ 
+
+ align:start position:0%
+this in a matrix and read off
+coefficients from there you get the
+
+ align:start position:0%
+coefficients from there you get the
+ 
+
+ align:start position:0%
+coefficients from there you get the
+following system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the Matrix of the system read
+
+ align:start position:0%
+so this is the Matrix of the system read
+ 
+
+ align:start position:0%
+so this is the Matrix of the system read
+of from
+
+ align:start position:0%
+of from
+ 
+
+ align:start position:0%
+of from
+here these are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unknowns and these are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values of the right hand side and I hope
+
+ align:start position:0%
+values of the right hand side and I hope
+ 
+
+ align:start position:0%
+values of the right hand side and I hope
+you'll agree that this is a very easy
+
+ align:start position:0%
+you'll agree that this is a very easy
+ 
+
+ align:start position:0%
+you'll agree that this is a very easy
+system to solve we just get Alpha is 6
+
+ align:start position:0%
+system to solve we just get Alpha is 6
+ 
+
+ align:start position:0%
+system to solve we just get Alpha is 6
+beta is 5 and GMA is four so the
+
+ align:start position:0%
+beta is 5 and GMA is four so the
+ 
+
+ align:start position:0%
+beta is 5 and GMA is four so the
+solution to the first part is y equal
+
+ align:start position:0%
+solution to the first part is y equal
+ 
+
+ align:start position:0%
+solution to the first part is y equal
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+W1 + 5
+
+ align:start position:0%
+W1 + 5
+ 
+
+ align:start position:0%
+W1 + 5
+W2 + 4
+
+ align:start position:0%
+W2 + 4
+ 
+
+ align:start position:0%
+W2 + 4
+W3 and let's notice another thing no
+
+ align:start position:0%
+W3 and let's notice another thing no
+ 
+
+ align:start position:0%
+W3 and let's notice another thing no
+matter what we what values we put here
+
+ align:start position:0%
+matter what we what values we put here
+ 
+
+ align:start position:0%
+matter what we what values we put here
+this Matrix is always going to stay the
+
+ align:start position:0%
+this Matrix is always going to stay the
+ 
+
+ align:start position:0%
+this Matrix is always going to stay the
+same it's only the right hand side
+
+ align:start position:0%
+same it's only the right hand side
+ 
+
+ align:start position:0%
+same it's only the right hand side
+that's going to change so if we're given
+
+ align:start position:0%
+that's going to change so if we're given
+ 
+
+ align:start position:0%
+that's going to change so if we're given
+any other polinomial now to express in a
+
+ align:start position:0%
+any other polinomial now to express in a
+ 
+
+ align:start position:0%
+any other polinomial now to express in a
+basis W1 W2 and W3 we don't have to do
+
+ align:start position:0%
+basis W1 W2 and W3 we don't have to do
+ 
+
+ align:start position:0%
+basis W1 W2 and W3 we don't have to do
+any thinking we don't have to do any
+
+ align:start position:0%
+any thinking we don't have to do any
+ 
+
+ align:start position:0%
+any thinking we don't have to do any
+computations what we do is go back to
+
+ align:start position:0%
+computations what we do is go back to
+ 
+
+ align:start position:0%
+computations what we do is go back to
+our table at the beginning and just read
+
+ align:start position:0%
+our table at the beginning and just read
+ 
+
+ align:start position:0%
+our table at the beginning and just read
+off let's go back to the table and just
+
+ align:start position:0%
+off let's go back to the table and just
+ 
+
+ align:start position:0%
+off let's go back to the table and just
+read off this values so in this case Y
+
+ align:start position:0%
+read off this values so in this case Y
+ 
+
+ align:start position:0%
+read off this values so in this case Y
+is 6 * W1 5 * W2 and 3 *
+
+ align:start position:0%
+is 6 * W1 5 * W2 and 3 *
+ 
+
+ align:start position:0%
+is 6 * W1 5 * W2 and 3 *
+W3 and that's already a hint to solving
+
+ align:start position:0%
+W3 and that's already a hint to solving
+ 
+
+ align:start position:0%
+W3 and that's already a hint to solving
+the B part which is find the change of
+
+ align:start position:0%
+the B part which is find the change of
+ 
+
+ align:start position:0%
+the B part which is find the change of
+basis matrices between 1 x x^2 and W1 W2
+
+ align:start position:0%
+basis matrices between 1 x x^2 and W1 W2
+ 
+
+ align:start position:0%
+basis matrices between 1 x x^2 and W1 W2
+W3 change of basis matrices means
+
+ align:start position:0%
+W3 change of basis matrices means
+ 
+
+ align:start position:0%
+W3 change of basis matrices means
+expressing one basis in terms of another
+
+ align:start position:0%
+expressing one basis in terms of another
+ 
+
+ align:start position:0%
+expressing one basis in terms of another
+so as a part part of the problem we will
+
+ align:start position:0%
+so as a part part of the problem we will
+ 
+
+ align:start position:0%
+so as a part part of the problem we will
+have to express 1 x and x2 in terms of
+
+ align:start position:0%
+have to express 1 x and x2 in terms of
+ 
+
+ align:start position:0%
+have to express 1 x and x2 in terms of
+W1 W2 and W3 so let's just find their
+
+ align:start position:0%
+W1 W2 and W3 so let's just find their
+ 
+
+ align:start position:0%
+W1 W2 and W3 so let's just find their
+values at these three points one is a
+
+ align:start position:0%
+values at these three points one is a
+ 
+
+ align:start position:0%
+values at these three points one is a
+constant it just takes value one
+
+ align:start position:0%
+constant it just takes value one
+ 
+
+ align:start position:0%
+constant it just takes value one
+everywhere X takes value minus one at
+
+ align:start position:0%
+everywhere X takes value minus one at
+ 
+
+ align:start position:0%
+everywhere X takes value minus one at
+minus one 0 at 0 and one at 1 and X squ
+
+ align:start position:0%
+minus one 0 at 0 and one at 1 and X squ
+ 
+
+ align:start position:0%
+minus one 0 at 0 and one at 1 and X squ
+takes values 1 0 and 1 at minus one 0
+
+ align:start position:0%
+takes values 1 0 and 1 at minus one 0
+ 
+
+ align:start position:0%
+takes values 1 0 and 1 at minus one 0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one and from this we can already
+
+ align:start position:0%
+one and from this we can already
+ 
+
+ align:start position:0%
+one and from this we can already
+conclude let's go the B here we can
+
+ align:start position:0%
+conclude let's go the B here we can
+ 
+
+ align:start position:0%
+conclude let's go the B here we can
+conclude that 1 equal W1 + W2 +
+
+ align:start position:0%
+conclude that 1 equal W1 + W2 +
+ 
+
+ align:start position:0%
+conclude that 1 equal W1 + W2 +
+W3 that x equals um - W1 + W3 and that
+
+ align:start position:0%
+W3 that x equals um - W1 + W3 and that
+ 
+
+ align:start position:0%
+W3 that x equals um - W1 + W3 and that
+x^2 =
+
+ align:start position:0%
+x^2 =
+ 
+
+ align:start position:0%
+x^2 =
+W1 +
+
+ align:start position:0%
+W1 +
+ 
+
+ align:start position:0%
+W1 +
+W3 and from this we can immediately
+
+ align:start position:0%
+W3 and from this we can immediately
+ 
+
+ align:start position:0%
+W3 and from this we can immediately
+write one change of basis Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+namely since we know how to express One
+
+ align:start position:0%
+namely since we know how to express One
+ 
+
+ align:start position:0%
+namely since we know how to express One
+X and X squ in terms of W1
+
+ align:start position:0%
+X and X squ in terms of W1
+ 
+
+ align:start position:0%
+X and X squ in terms of W1
+W2 and W3 we can just copy this
+
+ align:start position:0%
+W2 and W3 we can just copy this
+ 
+
+ align:start position:0%
+W2 and W3 we can just copy this
+information over to this Matrix getting
+
+ align:start position:0%
+information over to this Matrix getting
+ 
+
+ align:start position:0%
+information over to this Matrix getting
+1 1 1 - 1 0 1 and 1 0 one so which
+
+ align:start position:0%
+1 1 1 - 1 0 1 and 1 0 one so which
+ 
+
+ align:start position:0%
+1 1 1 - 1 0 1 and 1 0 one so which
+Matrix is this this is a matrix so so we
+
+ align:start position:0%
+Matrix is this this is a matrix so so we
+ 
+
+ align:start position:0%
+Matrix is this this is a matrix so so we
+have 1 x and x squar um expressed in
+
+ align:start position:0%
+have 1 x and x squar um expressed in
+ 
+
+ align:start position:0%
+have 1 x and x squar um expressed in
+terms of W1 W2 and W3 so if we feed this
+
+ align:start position:0%
+terms of W1 W2 and W3 so if we feed this
+ 
+
+ align:start position:0%
+terms of W1 W2 and W3 so if we feed this
+Matrix something expressed in the bases
+
+ align:start position:0%
+Matrix something expressed in the bases
+ 
+
+ align:start position:0%
+Matrix something expressed in the bases
+1 x and x squ say a b and c what it's
+
+ align:start position:0%
+1 x and x squ say a b and c what it's
+ 
+
+ align:start position:0%
+1 x and x squ say a b and c what it's
+going to throw out is the same
+
+ align:start position:0%
+going to throw out is the same
+ 
+
+ align:start position:0%
+going to throw out is the same
+polinomial expressed in this basis here
+
+ align:start position:0%
+polinomial expressed in this basis here
+ 
+
+ align:start position:0%
+polinomial expressed in this basis here
+W1 W2 and W3 so I'm going to just write
+
+ align:start position:0%
+W1 W2 and W3 so I'm going to just write
+ 
+
+ align:start position:0%
+W1 W2 and W3 so I'm going to just write
+that this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a a matrix of this basis change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how do we get the other one well
+
+ align:start position:0%
+okay how do we get the other one well
+ 
+
+ align:start position:0%
+okay how do we get the other one well
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+easy we know it's just the
+
+ align:start position:0%
+easy we know it's just the
+ 
+
+ align:start position:0%
+easy we know it's just the
+inverse of a so this is going to
+
+ align:start position:0%
+inverse of a so this is going to
+ 
+
+ align:start position:0%
+inverse of a so this is going to
+be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix that takes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something written in this basis and
+
+ align:start position:0%
+something written in this basis and
+ 
+
+ align:start position:0%
+something written in this basis and
+transfers it to this basis I'm not going
+
+ align:start position:0%
+transfers it to this basis I'm not going
+ 
+
+ align:start position:0%
+transfers it to this basis I'm not going
+to calculate the inverse of a matrix in
+
+ align:start position:0%
+to calculate the inverse of a matrix in
+ 
+
+ align:start position:0%
+to calculate the inverse of a matrix in
+front of you instead I'm going to
+
+ align:start position:0%
+front of you instead I'm going to
+ 
+
+ align:start position:0%
+front of you instead I'm going to
+consult my
+
+ align:start position:0%
+consult my
+ 
+
+ align:start position:0%
+consult my
+Oracle sorry about
+
+ align:start position:0%
+Oracle sorry about
+ 
+
+ align:start position:0%
+Oracle sorry about
+that and my Oracle says that the inverse
+
+ align:start position:0%
+that and my Oracle says that the inverse
+ 
+
+ align:start position:0%
+that and my Oracle says that the inverse
+should be 0 1
+
+ align:start position:0%
+should be 0 1
+ 
+
+ align:start position:0%
+should be 0 1
+0 um Min - 12 0 1 12
+
+ align:start position:0%
+0 um Min - 12 0 1 12
+ 
+
+ align:start position:0%
+0 um Min - 12 0 1 12
+and 12 minus one
+
+ align:start position:0%
+and 12 minus one
+ 
+
+ align:start position:0%
+and 12 minus one
+12 and that solves the B
+
+ align:start position:0%
+12 and that solves the B
+ 
+
+ align:start position:0%
+12 and that solves the B
+part let's go on to the C part the C
+
+ align:start position:0%
+part let's go on to the C part the C
+ 
+
+ align:start position:0%
+part let's go on to the C part the C
+part required us to find the Matrix of
+
+ align:start position:0%
+part required us to find the Matrix of
+ 
+
+ align:start position:0%
+part required us to find the Matrix of
+taking derivatives which is a linear map
+
+ align:start position:0%
+taking derivatives which is a linear map
+ 
+
+ align:start position:0%
+taking derivatives which is a linear map
+on the spa on the space of polinomial in
+
+ align:start position:0%
+on the spa on the space of polinomial in
+ 
+
+ align:start position:0%
+on the spa on the space of polinomial in
+both of these
+
+ align:start position:0%
+both of these
+ 
+
+ align:start position:0%
+both of these
+bases so let's first do the One X X squ
+
+ align:start position:0%
+bases so let's first do the One X X squ
+ 
+
+ align:start position:0%
+bases so let's first do the One X X squ
+basis because that one's
+
+ align:start position:0%
+basis because that one's
+ 
+
+ align:start position:0%
+basis because that one's
+easier I'm going to call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX so I'm going to work in basis 1 x X2
+
+ align:start position:0%
+DX so I'm going to work in basis 1 x X2
+ 
+
+ align:start position:0%
+DX so I'm going to work in basis 1 x X2
+and what I want to what I want to
+
+ align:start position:0%
+and what I want to what I want to
+ 
+
+ align:start position:0%
+and what I want to what I want to
+express is the transformation of taking
+
+ align:start position:0%
+express is the transformation of taking
+ 
+
+ align:start position:0%
+express is the transformation of taking
+derivatives so here I'm going to write
+
+ align:start position:0%
+derivatives so here I'm going to write
+ 
+
+ align:start position:0%
+derivatives so here I'm going to write
+the vector to which taking derivatives
+
+ align:start position:0%
+the vector to which taking derivatives
+ 
+
+ align:start position:0%
+the vector to which taking derivatives
+Maps the polinomial one which is
+
+ align:start position:0%
+Maps the polinomial one which is
+ 
+
+ align:start position:0%
+Maps the polinomial one which is
+zero and that's this expressed in the
+
+ align:start position:0%
+zero and that's this expressed in the
+ 
+
+ align:start position:0%
+zero and that's this expressed in the
+basis 1 x
+
+ align:start position:0%
+basis 1 x
+ 
+
+ align:start position:0%
+basis 1 x
+x^2 in the second column I'm going to
+
+ align:start position:0%
+x^2 in the second column I'm going to
+ 
+
+ align:start position:0%
+x^2 in the second column I'm going to
+write X Prime the the vector to which DX
+
+ align:start position:0%
+write X Prime the the vector to which DX
+ 
+
+ align:start position:0%
+write X Prime the the vector to which DX
+send the vector X and that's equal to
+
+ align:start position:0%
+send the vector X and that's equal to
+ 
+
+ align:start position:0%
+send the vector X and that's equal to
+one which expressed in this basis is one
+
+ align:start position:0%
+one which expressed in this basis is one
+ 
+
+ align:start position:0%
+one which expressed in this basis is one
+0 0 and here I'm going to write x 2 x^2
+
+ align:start position:0%
+0 0 and here I'm going to write x 2 x^2
+ 
+
+ align:start position:0%
+0 0 and here I'm going to write x 2 x^2
+Prime which is 2x which expressed in
+
+ align:start position:0%
+Prime which is 2x which expressed in
+ 
+
+ align:start position:0%
+Prime which is 2x which expressed in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+basis is just
+
+ align:start position:0%
+basis is just
+ 
+
+ align:start position:0%
+basis is just
+this okay that one was easy for the
+
+ align:start position:0%
+this okay that one was easy for the
+ 
+
+ align:start position:0%
+this okay that one was easy for the
+other one well we could calculate W1 W2
+
+ align:start position:0%
+other one well we could calculate W1 W2
+ 
+
+ align:start position:0%
+other one well we could calculate W1 W2
+W3 explicitly take their derivatives go
+
+ align:start position:0%
+W3 explicitly take their derivatives go
+ 
+
+ align:start position:0%
+W3 explicitly take their derivatives go
+back to the table and try to find and
+
+ align:start position:0%
+back to the table and try to find and
+ 
+
+ align:start position:0%
+back to the table and try to find and
+repeat the procedure that we did already
+
+ align:start position:0%
+repeat the procedure that we did already
+ 
+
+ align:start position:0%
+repeat the procedure that we did already
+so expressing these derivatives in terms
+
+ align:start position:0%
+so expressing these derivatives in terms
+ 
+
+ align:start position:0%
+so expressing these derivatives in terms
+of W1 W2 W3 and that's a lot of work but
+
+ align:start position:0%
+of W1 W2 W3 and that's a lot of work but
+ 
+
+ align:start position:0%
+of W1 W2 W3 and that's a lot of work but
+we pretty much already did most of this
+
+ align:start position:0%
+we pretty much already did most of this
+ 
+
+ align:start position:0%
+we pretty much already did most of this
+work so we know how to take derivatives
+
+ align:start position:0%
+work so we know how to take derivatives
+ 
+
+ align:start position:0%
+work so we know how to take derivatives
+in this basis and we know how to go
+
+ align:start position:0%
+in this basis and we know how to go
+ 
+
+ align:start position:0%
+in this basis and we know how to go
+between these two bases so if we want to
+
+ align:start position:0%
+between these two bases so if we want to
+ 
+
+ align:start position:0%
+between these two bases so if we want to
+take a derivative of something written
+
+ align:start position:0%
+take a derivative of something written
+ 
+
+ align:start position:0%
+take a derivative of something written
+in the basis W1 W2 W3 well let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first write this something in basis 1 x
+
+ align:start position:0%
+first write this something in basis 1 x
+ 
+
+ align:start position:0%
+first write this something in basis 1 x
+x^2 then let's take a derivative of
+
+ align:start position:0%
+x^2 then let's take a derivative of
+ 
+
+ align:start position:0%
+x^2 then let's take a derivative of
+it and then let's write it back in the
+
+ align:start position:0%
+it and then let's write it back in the
+ 
+
+ align:start position:0%
+it and then let's write it back in the
+original basis that we want so it's
+
+ align:start position:0%
+original basis that we want so it's
+ 
+
+ align:start position:0%
+original basis that we want so it's
+multiplication of three
+
+ align:start position:0%
+multiplication of three
+ 
+
+ align:start position:0%
+multiplication of three
+matrices we have all three matrix
+
+ align:start position:0%
+matrices we have all three matrix
+ 
+
+ align:start position:0%
+matrices we have all three matrix
+multiplication is easy and my Oracle
+
+ align:start position:0%
+multiplication is easy and my Oracle
+ 
+
+ align:start position:0%
+multiplication is easy and my Oracle
+again says that this should be - 3 over
+
+ align:start position:0%
+again says that this should be - 3 over
+ 
+
+ align:start position:0%
+again says that this should be - 3 over
+2 2 - 1 /
+
+ align:start position:0%
+2 2 - 1 /
+ 
+
+ align:start position:0%
+2 2 - 1 /
+2 - 1 / 2 0 1 / 2 and 1 / 2 -
+
+ align:start position:0%
+2 - 1 / 2 0 1 / 2 and 1 / 2 -
+ 
+
+ align:start position:0%
+2 - 1 / 2 0 1 / 2 and 1 / 2 -
+2 3
+
+ align:start position:0%
+2 3
+ 
+
+ align:start position:0%
+2 3
+over2 and that solves the problem
+
+ align:start position:0%
+over2 and that solves the problem
+ 
+
+ align:start position:0%
+over2 and that solves the problem
+now one thing that I would want to
+
+ align:start position:0%
+now one thing that I would want to
+ 
+
+ align:start position:0%
+now one thing that I would want to
+discuss in the end is how did we do with
+
+ align:start position:0%
+discuss in the end is how did we do with
+ 
+
+ align:start position:0%
+discuss in the end is how did we do with
+respect to my challenge which was let's
+
+ align:start position:0%
+respect to my challenge which was let's
+ 
+
+ align:start position:0%
+respect to my challenge which was let's
+try to do as much of it as possible
+
+ align:start position:0%
+try to do as much of it as possible
+ 
+
+ align:start position:0%
+try to do as much of it as possible
+without finding W1 W2 and W3 explicitly
+
+ align:start position:0%
+without finding W1 W2 and W3 explicitly
+ 
+
+ align:start position:0%
+without finding W1 W2 and W3 explicitly
+and it seems like we did really well
+
+ align:start position:0%
+and it seems like we did really well
+ 
+
+ align:start position:0%
+and it seems like we did really well
+there's nowhere on the board written W1
+
+ align:start position:0%
+there's nowhere on the board written W1
+ 
+
+ align:start position:0%
+there's nowhere on the board written W1
+equals W2 equals and W3 equals but is it
+
+ align:start position:0%
+equals W2 equals and W3 equals but is it
+ 
+
+ align:start position:0%
+equals W2 equals and W3 equals but is it
+really so it's not we calculated the
+
+ align:start position:0%
+really so it's not we calculated the
+ 
+
+ align:start position:0%
+really so it's not we calculated the
+Matrix of a inverse here and what this
+
+ align:start position:0%
+Matrix of a inverse here and what this
+ 
+
+ align:start position:0%
+Matrix of a inverse here and what this
+really means is that W1 W2 and W3
+
+ align:start position:0%
+really means is that W1 W2 and W3
+ 
+
+ align:start position:0%
+really means is that W1 W2 and W3
+written in the basis 1 x and x^2 are as
+
+ align:start position:0%
+written in the basis 1 x and x^2 are as
+ 
+
+ align:start position:0%
+written in the basis 1 x and x^2 are as
+follows W1 is - 12 x +2 x^2 W2 is 1 -
+
+ align:start position:0%
+follows W1 is - 12 x +2 x^2 W2 is 1 -
+ 
+
+ align:start position:0%
+follows W1 is - 12 x +2 x^2 W2 is 1 -
+x^2 and W3 is 12 x +2 x^2 so you can
+
+ align:start position:0%
+x^2 and W3 is 12 x +2 x^2 so you can
+ 
+
+ align:start position:0%
+x^2 and W3 is 12 x +2 x^2 so you can
+check your work with with the help of
+
+ align:start position:0%
+check your work with with the help of
+ 
+
+ align:start position:0%
+check your work with with the help of
+this Matrix in case you did find W1 W2
+
+ align:start position:0%
+this Matrix in case you did find W1 W2
+ 
+
+ align:start position:0%
+this Matrix in case you did find W1 W2
+and W3 explicitly and that's all I
+
+ align:start position:0%
+and W3 explicitly and that's all I
+ 
+
+ align:start position:0%
+and W3 explicitly and that's all I
+wanted to say today
\ No newline at end of file
diff --git a/EsiGSf2bt9k.txt b/EsiGSf2bt9k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0e7673b2d82ec0635fca59d0c02407e96d3d8f8
--- /dev/null
+++ b/EsiGSf2bt9k.txt
@@ -0,0 +1,4137 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at MIT.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to this
+
+lecture on non-linear finite
+element analysis of solids and
+
+structures.
+
+In this lecture, I'd like to
+continue with our discussion
+
+of structural elements, and
+in particular, I'd like to
+
+concentrate our attention first
+on the formulation of
+
+beam elements.
+
+After that, I'd like to talk
+more about the formulation of
+
+shell elements, and then
+show you applications.
+
+When we talk about beam
+elements, we might think about
+
+the usual Hermitian beam
+elements, in which the
+
+transverse placements cubically
+interpolated, and
+
+the longitudinal displacements
+are linearly interpolated.
+
+This is an element that is
+usually used in linear
+
+analysis, and very
+widely used--
+
+you might have used it quite
+a bit yourself--
+
+and it is also very effective
+in the analysis of linear
+
+response of structures.
+
+However, in my discussion now,
+I will talk about the
+
+isoparametric beam element,
+and how we formulate the
+
+isoparametric beam element, in
+other words, and how we apply
+
+it in the analysis
+of structures.
+
+So when I talk about the beam
+element, I really mean this
+
+isoparametric beam element that
+we are formulating in
+
+this lecture.
+
+The isoparametric beam
+formulation can be very
+
+effective for the analysis of
+curve themes, for the analysis
+
+of geometrically nonlinear
+problems, and for the analysis
+
+of stiffened shell structures,
+where we couple the
+
+isoparametric beam with the
+isoparametrically formulated
+
+shell elements.
+
+The formulation is quite
+analogous to the formulation
+
+of the isoparametric degenerate
+shell elements that
+
+we discussed in the previous
+lecture, and so we can go a
+
+bit fast over the formulation
+of the beam element here.
+
+I'm showing a typical
+beam element,
+
+rectangular cross section.
+
+Here we show three nodes.
+
+Actually, the beam element can
+be used with two nodes, three
+
+nodes, or four nodes, as we will
+discuss further later on.
+
+We notice that the depth off
+the element is ak, the
+
+thickness of the
+element is bk.
+
+And notice that at these nodes,
+we measure certain
+
+nodal point variables.
+
+and here I'm showing the nodal
+point variables that we do
+
+measure at the nodes.
+
+Three displacements, incremental
+displacements, and
+
+three incremental rotations.
+
+Notice that the description of
+the beam element follows much
+
+the same as the geometric
+description of the beam
+
+element follows, much the same
+way as we are dealing with the
+
+shell element.
+
+We introduce director vectors.
+
+Now we have two director
+vectors.
+
+In the shell, of course,
+we had only one
+
+director vector per node.
+
+Now we have two.
+
+Here we show tvsk, the director
+vector at time t into
+
+the S-direction, corresponding
+to node k.
+
+Notice here tvtk.
+
+The director vector at time t
+corresponding to node k into
+
+the t direction.
+
+this t means direction t that
+t opting out means time t
+
+Notice that corresponding to
+this direction t here, we have
+
+the t isoparametric
+coordinate.
+
+And of course, this t
+isoparametric coordinate also
+
+runs into the thickness ak.
+
+Notice that corresponding to
+bk, we have the s-direction
+
+coordinate, and that s-direction
+coordinate,
+
+s-isoparametric coordinate, runs
+into the direction of the
+
+director vector, tvsk.
+
+So these are the variables used
+to describe the geometry
+
+and the displacement of
+the beam element.
+
+We start with the general
+equation for the
+
+geometry at time t.
+
+Here we have txi.
+
+The coordinates of a material
+particle within the
+
+element at time t--
+
+and remember, these are the
+coordinates measured in the
+
+stationary coordinate system.
+
+And these coordinates are
+obtained as shown on the
+
+right-hand side.
+
+Let's have a close look
+at what we see on
+
+the right-hand side.
+
+We have the hk interpolation
+function.
+
+This is the interpolation
+function corresponding to the
+
+r-direction running through
+the nodes of the element,
+
+along the mid-surface
+of the element.
+
+And it's a one-dimensional
+interpolation function, the
+
+same one that we used to see
+for the truss element.
+
+These are the nodal point
+coordinates at time t.
+
+We are summing over all the
+nodal points, k from 1 to n,
+
+and n can be equal to 2, 3, or
+4, as I mentioned earlier.
+
+Then we add to this term a term
+that comes in because of
+
+the sickness of the beam into
+the t-direction, ak, thickness
+
+off the beam into the
+t-direction--
+
+here is a t-coordinate.
+
+The isoparametric coordinates
+going from minus 1 to plus 1.
+
+Here we have hk, same
+interpolation function as
+
+there, and here we have the
+direction, cosines of the
+
+director vector in the
+t-direction at time t.
+
+A similar term, similar to this
+one, is added for the
+
+f-direction.
+
+s, the isoparametric coordinate,
+running from minus
+
+1 to plus 1, bk being the
+thickness into the s-direction
+
+at node k, hk, same
+interpolation function that we
+
+have seen up here already, and
+these are the direction
+
+cosines of the director vector
+in the s-direction,
+
+corresponding to node
+k at time t.
+
+This equation is very similar
+to the equation that we used
+
+in the shell element
+formation.
+
+Of course, in the shell element
+formulation, we
+
+interpolated here in a
+two-dimensional domain over
+
+the shell mid-surface.
+
+Now we only run along the
+neutral axis of the beam.
+
+And we had only one term in the
+shell corresponding to the
+
+director vector.
+
+There was only one direction,
+namely, the one normal to the
+
+mid-surface of the shell.
+
+Here we have two directions
+to deal with.
+
+Since the displacements can
+directly be obtained from the
+
+geometry interpolation at time
+t minus the geometry
+
+interpolation at time 0,
+of course this geometry
+
+interpolation is obtained by
+simply substituting in the
+
+equation that we just looked
+at for time t, the time 0.
+
+Since we obtain tui, as shown
+here, this is the result.
+
+We simply apply our geometry
+interpolation at time t, and
+
+at time 0, subtract.
+
+This is what you get on
+the right-hand side.
+
+Nodal point displacement from
+time 0 to time t, measured in
+
+the stationary global Cartesian
+coordinate system.
+
+Here change in the director
+vector cosines, or I should
+
+say, more precisely maybe, the
+change in the cosine of the
+
+angle director vector time 0,
+director vector time t.
+
+Of course, remember here we
+have direction cosines
+
+corresponding to time t.
+
+Here we have direction cosines
+corresponding to time 0.
+
+We subtract, and that
+goes in here.
+
+Here, same kind of term,
+but for direction s.
+
+Also the incremental
+displacements are obtained
+
+from this relationship here, and
+if you apply the geometry
+
+interpolation at time t plus
+delta t and at time t, you
+
+directly obtain this
+right-hand side.
+
+These are the increment in the
+direction cosine from time t
+
+to time t plus delta t of the
+director vector in the
+
+t-direction.
+
+Similar here for the
+s-direction.
+
+Of course, we are used very well
+to deal with increment
+
+and nodal point displacement,
+but we cannot very well deal
+
+with these quantities
+here, vti and vsi.
+
+We want to deal with nodal
+point rotation.
+
+And so what we do is, we express
+this quantity and that
+
+quantity in terms of nodal
+point rotations, and that
+
+those expressions are
+given down here.
+
+These are the two expressions.
+
+You can simply multiply out, and
+you would immediately see
+
+that they indeed hold.
+
+With these geometry and
+displacement interpolations
+
+established, we can now
+directly calculate or
+
+establish the strain
+displacement matrices
+
+corresponding to the Cartesian
+strain components, and then a
+
+simple transformation, standard
+transformation gives
+
+us the strain displacement
+matrices corresponding to the
+
+eta zeta psi directions.
+
+Of course, these are the
+directions with the components
+
+of strains and stresses that we
+need to deal with for the
+
+beam formulation.
+
+Notice that zeta here is a
+physical coordinate running
+
+into the direction, so to say,
+of the a thickness of the
+
+beam, and zeta corresponds to
+the t-isoparametric coordinate
+
+that we just talked about.
+
+Psi here corresponds to the
+s-isoparametric coordinate,
+
+and runs into the b width,
+so to say, of the beam.
+
+Eta here corresponds to the
+r-isoparametric coordinate.
+
+Of course, these zeta, eta, and
+psi are actual physical
+
+coordinates that we
+are dealing with.
+
+We have to, of course, calculate
+the tau psi eta, the
+
+tau eta eta, and the tau vita
+psi stress components and
+
+corresponding strain components
+for the beam
+
+formulation.
+
+And the stress-strain law,
+corresponding to these
+
+components, is given here.
+
+Notice tau eta eta is obtained
+by taking the Young's modulus
+
+and multiplying the Young's
+modulus by epsilon
+
+eta eta, and so on.
+
+Notice here we have one share
+component and another share
+
+component corresponding to this
+column and corresponding
+
+to that column, and here we
+have k factor, the share
+
+correction factor, that we
+already used from the shell
+
+analysis formulation that
+we discussed earlier.
+
+Notice that via the same
+approach, we can also directly
+
+obtain a beam element for
+
+elastoplastic and creep analysis.
+
+In this particular case, of
+course, the only stress
+
+component that would be non-zero
+again would be tau
+
+eta eta, tau eta zeta,
+and tau eta psi.
+
+The approach here is very
+similar to what we have
+
+discussed earlier regarding the
+shell element formation.
+
+There is one important point
+in the beam element
+
+formulation.
+
+Namely that with the kinematic
+assumptions used so far for
+
+the beam element, we do not
+allow cross-sectional
+
+out-of-plane displacement.
+
+We do not allow warping.
+
+Our interpolation does not
+contain the effect of warping.
+
+In torsion or loading, however,
+we know that warping
+
+is very important, and for that
+reason, we need to amend
+
+our displacement assumptions
+by two or more displacement
+
+patterns, so to say.
+
+We allow these displacements to
+take place in the element.
+
+u eta is equal to alpha
+times psi beta.
+
+This is the exact warping
+displacement for infinitely
+
+narrow sections.
+
+And this term here, with beta
+a constant, is the exact
+
+warping displacement for
+a square cross section.
+
+Now the actual section might
+not be infinitely narrow,
+
+might not be square, but we can
+easily test, and I will
+
+show you just now an example
+of that in fact, a
+
+superposition of these functions
+and the evaluation
+
+of alpha and beta by static
+condensation actually yields
+
+good results, even for
+cross-sections that are not
+
+infinitely narrow, and that
+are not exactly square.
+
+Let's look at an example,
+linear elasticity.
+
+If we take a section and simply
+put it into torsion
+
+with b/a equal to 1, the
+analytical value given by
+
+Timoshenko for this k constant
+here in that formula is 0.141.
+
+And we obtain with
+this formulation
+
+exactly that same value.
+
+We need to get it, because we
+have embedded the proper
+
+interpolation for u eta into
+our formulation, and then u
+
+static condensation, of course,
+to condense out these
+
+two constants, alpha and beta,
+that I just talked about.
+
+For b/a, a very large, very
+narrow section, we also get
+
+the exact result in our finite
+element solution, the exact
+
+analytical result.
+
+In between, we have a small
+arrow, an arrow that, however,
+
+we believe is quite
+acceptable.
+
+Let's look at one example that
+I'd like to show you the
+
+results of.
+
+You might be interested
+in this example.
+
+Here we have a narrow ring.
+
+Here you have a plan view of
+that ring with the dimensions
+
+given, and Young's modulus and
+Poisson's ratio given for that
+
+ring, subject to these
+bending moments.
+
+Of course, the twisting
+capability or capacity of the
+
+beam is of utmost importance
+now, has to be properly
+
+modelled under this
+loading condition.
+
+The model that we use
+to analyze the
+
+problem is shown here.
+
+And you can see, at one side of
+the ring, we have fixed it,
+
+and at the other side,
+we prescribed a
+
+rotation, see eta x.
+
+We use here four node
+elements as shown.
+
+This analysis was actually
+inspired by us looking around
+
+in our office and seeing a
+magnetic tape lying there.
+
+And if you look around, you
+might have yourself a magnetic
+
+tape there.
+
+And you pick up this little ring
+from the magnetic tape.
+
+And here I'd like to just
+demonstrate to you briefly
+
+what we are doing.
+
+You see here, we have this ring,
+much alike of what I've
+
+shown you on the view graph.
+
+I'm fixing it on the one side,
+and on my right hand now,
+
+these two fingers, I'm going
+to put a rotation onto that
+
+ring, and I'm going to turn
+my fingers 180 degrees.
+
+So please watch closely.
+
+This is what I'm doing.
+
+I'm just turning my fingers
+180 degrees.
+
+And by turning my fingers 180
+degrees, if you watch very
+
+closely, you can see that the
+top of the ring does not touch
+
+the bottom of the ring.
+
+There is actually a little gap
+in between, of course, because
+
+of the elasticity in the ring.
+
+So this is what I've tried to
+do now on the computer.
+
+And what I'm particularly
+interested to see is the
+
+amount of moment required in my
+right hand, so to say, to
+
+be transmitted to the ring
+in order to twist it.
+
+Well, here we have the results
+for the computer solution.
+
+Notice here, we have a force
+deflection, curve, rotation
+
+here, up to 180 degrees.
+
+Moment plotted here
+in pounds, inch.
+
+And you can see that there's
+fairly linear behavior first,
+
+but then a highly non-linear
+behavior as the rotation
+
+becomes very large.
+
+Here we use the TL formulation
+for the beam element.
+
+And once again, we rotated it
+180 degrees, as I have shown
+
+you with my little
+experiment here.
+
+If you look at the beam, you see
+a top view like that, and
+
+the side view looks this way.
+
+I've pointed out that
+top and bottom do
+
+not touch each other.
+
+There's a little air
+gap in between.
+
+I'd like to show you now another
+solution regarding the
+
+torsion in an analysis.
+
+And let me walk over to the
+slides here, where I actually
+
+have two slides regarding
+that solution.
+
+The interesting part of this
+problem is that we now, in
+
+this particular analysis, are
+using the same displacement
+
+interpolation functions for
+which I've shown you already--
+
+two analyses in which the
+material remained elastic.
+
+The same interpolation functions
+are now also used to
+
+analyze an elastoplastic
+problem.
+
+And the problem is described
+here, where we have now a
+
+square section subjected
+to a torque.
+
+The material data that Greenberg
+used are given here.
+
+And in our analysis, we used
+this material data, where the
+
+yield stress and the
+strain-hardening modulus are
+
+matched to this stress-strain
+law here.
+
+Now notice what is going to
+happen is, we are increasing
+
+this torque incrementally, and
+we want to bring, of course,
+
+this section into the
+elastoplastic regime to see
+
+how the section will
+take the torque.
+
+On this slide now, we have
+plotted the torque vertically
+
+and the rotation horizontally,
+both quantities with some
+
+constants attached,
+as you can see.
+
+And the Greenberg result and
+the Adina result are indeed
+
+very close.
+
+Please look at the reference
+that is given in the study
+
+guide if you're interested in
+seeing and reading more about
+
+this problem.
+
+Let me now walk back to the view
+graph and continue with
+
+the discussion of the material
+relating to isoparametric
+
+beams and shell elements.
+
+The next topic that I like to
+talk to you about is the
+
+actual use of these elements.
+
+Of course, the shell element
+that I'm here talking about,
+
+or that I will share some more
+experiences with you upon, is
+
+the shell element that I have
+been already discussing in the
+
+earlier lecture.
+
+So please refer back to that
+lecture with respect to this
+
+discussion.
+
+One interesting point is that
+these elements can all be
+
+programmed for use with
+different numbers of nodes.
+
+For the beam, we can have two,
+three, or four nodes, as
+
+already mentioned earlier, and
+for the shell, we could have
+
+4, 8, 9, up to 16 nodes,
+as I mentioned also
+
+in the earlier lecture.
+
+The elements with these nodal
+point configurations can be
+
+employed for analysis of
+moderately thick structures.
+
+Remember, shear deformations
+are
+
+approximately taken into account.
+
+However, if the sink of the
+analysis of thin structures,
+
+then we have to be very careful,
+and only certain
+
+elements of the ones that
+I just referred
+
+to should be employed.
+
+For shells, we can only
+recommend to use a 16-node
+
+element with 4-by-4 Gauss
+integration over the
+
+mid-surface.
+
+This element is depicted here.
+
+1, 2, 3, 4, 4 times gives
+us 16 nodes, and 4-by-4
+
+integration indicated
+by the blue crosses.
+
+For beams, we'd best use the
+2-node beam element with
+
+1-point integration along the
+r-direction, or the 3-node
+
+beam element with 2-point
+integration along the
+
+r-direction, all or with Gauss
+integration, or the 4-node
+
+beam element with 3-point Gauss
+integration along the
+
+r-direction.
+
+We have to ask, of course,
+now, why is that so?
+
+Well, the reason is that the
+other elements become overly
+
+and artificially stiff when we
+use them to model thin and
+
+curved structures.
+
+Two phenomena occur--
+
+shear locking and membrane
+locking.
+
+Most interesting phenomena.
+
+And I'd like to share with you
+now some information regarding
+
+these phenomena.
+
+The 2-, 3-, and 4-node beam
+elements with 1-, 2-, and
+
+3-point Gauss integration along
+the beam axes do not
+
+display these phenomena,
+these shear- and
+
+membrane-locking phenomena.
+
+But please notice, I'm using
+1-, 2-, and 3-point Gauss
+
+integration corresponding
+to the 2-, 3-,
+
+and 4-node beam element.
+
+The 16-node element with 4-by-4
+integration, Gauss
+
+integration, is also relatively
+immune to shear and
+
+membrane locking.
+
+However, we have to
+be careful here.
+
+The element should not be
+distorted for best predictive
+
+capability.
+
+Let us study what this shear
+locking phenomenon is.
+
+And to do so, let us look at a
+2-noded beam, a very simple
+
+beam, in just 2-dimensional
+action.
+
+So we have one node here and
+one node here, and the
+
+defomations of the beam are
+described by w1 and theta 1 at
+
+this node, and w2 and theta
+2 at this node.
+
+Notice the deformations of the
+beam, of course, are given by
+
+w, the transverse displacement,
+and beta, the
+
+section rotation.
+
+The transverse displacement and
+section rotation, w and
+
+beta, are interpolated linearly,
+as shown here, via
+
+the nodal point displacements
+and rotations.
+
+Notice the linear interpolation,
+of course, is
+
+given here via this expression
+and that expression, and
+
+similarly here via this
+expression and that
+
+expression.
+
+Now there's one important point,
+namely that w and beta
+
+are independent quantities.
+
+If you are familiar, as
+you probably are, with
+
+Euler-Bernoulli beam theory,
+you recognize that in
+
+Euler-Bernoulli beam theory,
+they are not independent
+
+quantities.
+
+In fact, beta is dw dr, or dw
+dx, x being the physical
+
+coordinate.
+
+Here in our formation,
+isoparametric degenerate
+
+element, we have that beta and
+w, these two quantities, once
+
+again, are independent and
+linearly interpolated in this
+
+particular beam element.
+
+Of course, these two quantities
+are tied together
+
+by the physics, and that is
+by the shear deformation.
+
+So let's look at that next.
+
+Here we have that gamma shear
+strain is equal to a del w del
+
+x minus beta.
+
+And this is shown here
+on the picture.
+
+Notice this is a neutral axis of
+the beam, which originally
+
+of course was horizontal.
+
+Here we have a vertical line
+shown in green, and the
+
+section rotation is shown
+at the angle beta here.
+
+These are the material particles
+shown in red that
+
+were originally, of course, at
+right angles to the neutral
+
+axes, and that were originally
+lying vertically up.
+
+In other words, this line here,
+this red line was a
+
+vertical line originally, and
+was originally at right angles
+
+to the neutral axis.
+
+That right angle is not
+preserved because gamma is
+
+there, and gamma is, in
+general, a non-zero.
+
+This is here of course dw dx.
+
+So this picture here
+shows what we are
+
+calculating up here.
+
+And you can see that gamma
+ties together w and beta,
+
+which are, however, by
+themselves, interpolated
+
+independently.
+
+Consider now the simple case of
+a cantilever subjected to a
+
+tip-bending moment.
+
+And we use one 2-node beam
+element to model the
+
+cantilever.
+
+Clearly at this end, the section
+rotation is 0, and w1,
+
+the transverse displacement
+is also 0.
+
+So these are the bounded
+conditions at this end of the
+
+cantilever.
+
+And if we use these bounded
+conditions and put them into
+
+our general equation, we get
+directly that beta is given as
+
+shown here, and gamma is
+given as shown here.
+
+Now look at this equation
+carefully.
+
+We have a constant term and
+a linear varying term.
+
+The exact solution to this
+problem, analytical solution
+
+to this problem, if we use
+elementary beam theory, we
+
+would immediately recognize that
+the shear strain must be
+
+0 for this element, or for
+this beam situation.
+
+The shear strain should be 0.
+
+Now, if we look at this
+carefully, we can see that
+
+gamma can only be 0 if w2
+is 0, and theta 2 is 0.
+
+But if theta 2 and w2 are 0,
+rotation and transverse
+
+displacement right here at this
+end, then the beam would
+
+have not deflected.
+
+Of course, that is not
+borne out in physics.
+
+We know that if we take a beam
+and put a bending moment on
+
+it, then we get a deflection
+here and a
+
+rotation at this end.
+
+So you can see already from this
+equation here that there
+
+will be some difficulty.
+
+There will be some difficulty
+because gamma should be 0
+
+physically, and this equation
+tells us that gamma can't
+
+really be exactly 0.
+
+Well, that is once more
+summarized in
+
+this sentence here--
+
+clearly, gamma cannot be 0 at
+all the points along the beam
+
+unless theta 2 and
+w2 are both 0.
+
+But then also beta would be 0,
+and there would be no bending
+
+of the beam.
+
+Let's look now at this point.
+
+Since for the beam, the bending
+strain energy is
+
+proportional to h cubed,
+elementary beam theory again,
+
+the shear strain energy
+is proportional to h--
+
+elementary beam theory--
+
+we see immediately that any
+arrow in the shear strains due
+
+to the finite element
+interpolation functions
+
+becomes increasingly
+more detrimental
+
+is h becomes small.
+
+Why is that the case?
+
+If h becomes small, then
+this number becomes
+
+very rapidly small.
+
+This number here become small,
+but this one goes much faster
+
+to us, very small, so to say.
+
+And if there's an error in the
+shear strain energy, that
+
+error, because of this
+proportionality sign, is going
+
+to be magnified relative to any
+error that we would see
+
+here, and it's going to be
+detrimental in our solution.
+
+Let's look at an example.
+
+For the cantilever example, this
+very simple example that
+
+we just studied already a bit,
+the shear strain energy should
+
+be 0, and as h decreases, the
+relative error in the shear
+
+strain increases rapidly, and
+in effect introduces an
+
+artificial stiffness which
+we identify as
+
+locking of the model.
+
+This is the terminology that
+is quite widely used now.
+
+We say that the model locks.
+
+Let's look at some results.
+
+In this table, we show the
+results for h/L with L equal
+
+to 100 for these three values.
+
+The analytical value for the
+rotation at the end where the
+
+bending moment is applied
+is given here.
+
+Bernoulli beam theory.
+
+The finite element solution,
+using, of course, exact
+
+integration--
+
+I always assume I should
+maybe point that very
+
+strongly still out.
+
+We assume that we use exact
+integration of the K matrix.
+
+Meaning in this particular
+case, we're using 2-point
+
+Gauss integration along the
+length of the beam.
+
+With that scheme then, we obtain
+with a h/L being 0.5.
+
+Well, an error, but something
+still reasonable.
+
+After all, we're only
+using one element.
+
+Of course, we are pretty far
+off, but still something
+
+reasonable.
+
+But now notice, as you decrease
+h, h/L, of course,
+
+becomes much smaller.
+
+Theta analytical goes up.
+
+The beam basically
+bends, is very
+
+flexible as it gets thinner.
+
+And the finite element solution
+also becomes more
+
+flexible, gives us a more
+flexible beam, but is much too
+
+stiff when compared to the
+analytical solution.
+
+Notice for orders of magnitudes
+difference.
+
+If you plot it, this is
+basically 0 compared to that
+
+value, and that means
+the beam locks.
+
+It doesn't really at all
+bend anymore as h
+
+becomes very thin.
+
+This behavior is, of course,
+also observed when you take
+
+more than 1 element
+to model the beam.
+
+Here we show more elements than
+just one, and notice that
+
+each of these elements
+should still carry a
+
+constant bending moment.
+
+If it cannot do so, it develops,
+in other words,
+
+these furious shear strains.
+
+We are going to have a very
+stiff model, even when we use
+
+that many elements.
+
+Let's look at this particular
+example close off.
+
+And here we have an example
+beam, in other words,
+
+cantilever beam, subjected
+to the bending moment.
+
+l equals 10 meter.
+
+Square cross section,
+height 0.1 meter.
+
+We use the 2-noded beam
+elements to model this
+
+cantilever, and we plot the tip
+deflection as a function
+
+of the number of elements.
+
+A most interesting graph.
+
+Look, here is the beam
+theory solution.
+
+And here we plot the number
+of elements--
+
+here we talk about 400 elements,
+because there's
+
+times 10 to the 2 down here.
+
+400 elements at this point.
+
+600 elements, 800 elements,
+200 elements.
+
+At this point we have
+100 elements.
+
+The height of an element
+is equal to the
+
+length of the element.
+
+And at this point, we still
+don't even get a good
+
+approximation to the beam
+theory solution.
+
+We need basically something like
+400 to 500, 600 elements
+
+to get close to the beam
+theory solution.
+
+However, if we take a very large
+number of elements, we
+
+actually do converge, but we
+need a lot of elements, as you
+
+can see here.
+
+Of course, it is quite
+impractical to use this kind
+
+of 2-noded beam element to model
+thin structures, then
+
+beams. Once again, I must point
+out that we use 2-point
+
+Gauss integration into the
+r-direction, and therefore,
+
+we're dealing with the exact K
+matrix corresponding to the
+
+interpolation that we have
+embedded into the element.
+
+In fact, if we look in this
+regime down here, we find that
+
+as shown on this view graph,
+the solution really becomes
+
+beta very slowly as the number
+of elements is increased.
+
+Notice that the solution really
+doesn't increase in
+
+accuracy much at all as we go
+from 10, 20, to 30 elements.
+
+A remedy for the 2-node beam
+element is to only use 1-point
+
+integration along
+the beam axis.
+
+This then corresponds to
+assuming a constant transverse
+
+shear strain.
+
+However, by using 1-point
+integration, we still
+
+integrate the bending
+strain exactly.
+
+Because remember, beta is
+linear, del beta del x is
+
+constant, and 1-point
+integration will pick up that
+
+term exactly.
+
+If we look at the results, now
+once again, of this problem,
+
+cantilever problem, the
+cantilever beam is subjected
+
+to an end moment,
+tip end moment.
+
+We find now which h/l, as shown
+here, theta analytical,
+
+shown here, and our finite
+elements solution with just
+
+one element, using one element,
+of course now with
+
+1-point integration in
+r-direction, gives us
+
+excellent results.
+
+In fact, the exact results,
+as you can see here.
+
+The 3- and 4-note beam elements,
+evaluated using 2-
+
+and 3-point integration,
+are similarly affected.
+
+In fact, they give us also the
+exact results for this problem
+
+that we've considered.
+
+We should note now that these
+theme elements, based on what
+
+one might reduced integration,
+are actually reliable
+
+elements, because they do not
+possess any spurious zero
+
+energy modes.
+
+They have, in other words, only
+six zero energy modes
+
+corresponding to the actual
+physical rigid body mode that
+
+the elements should contain,
+should be able to represent,
+
+in its three-dimensional
+space.
+
+So they only have those six zero
+eigenvalues in this 3D
+
+analysis that they should have,
+and no spurious zero
+
+energy modes.
+
+The formulation can actually
+be interpreted as a mixed
+
+interpolation of displacements
+and transferred shear strains.
+
+And this is really the key for
+developing all the low-order
+
+effective shell elements.
+
+I will get back to that in
+just a little while.
+
+So far, we have talked
+about shear locking.
+
+I mentioned earlier also that
+there is a phenomenon of
+
+membrane-locking.
+
+Membrane-locking means that in
+addition to not exhibiting
+
+erroneous shear strains, the
+beam model must also not
+
+contain erroneous mid-surface
+membrane strains, particularly
+
+when we analyze curved
+structures.
+
+The beam elements that I just
+mentioned, 2-noded beam with
+
+1-point r-integration, 3-noded
+beam with 2-point
+
+r-integration, 4-noded beam with
+3-point r-integration, do
+
+also not membrane-lock.
+
+Let's consider here, once again,
+a simple example--
+
+a simple curve beam subjected
+to a bending moment,
+
+tip-bending moment, fixed
+at the other end.
+
+Here is an angle alpha that
+the beam spans out.
+
+The exactly integrated 3-noded
+beam element, when curved,
+
+does contain erroneous shear
+strains and erroneous
+
+mid-surface membrane strains.
+
+In other words, shear locks
+and membrane locks.
+
+And that is shown in
+this table here, at
+
+least to some extent.
+
+What I can't show is how much
+there is shear-locking and how
+
+much there is membrane-locking.
+
+You would see that both effects
+are very significant.
+
+If you were to run, for example,
+this beam element
+
+with a computer program, using,
+for this beam element,
+
+3-point integration into the r
+direction and printing out the
+
+stresses, print out all the
+stress components and look at
+
+the shear component and the
+membrane components, in other
+
+words, the normal stress
+components,
+
+along the neutral axes.
+
+If you do so, you would see that
+they are very significant
+
+shear stresses and very
+significant membrane stresses,
+
+which of course should be
+0 for this problem.
+
+And these are, of course,
+causing the locking effect.
+
+Here we have the results in
+terms of just rotations, h/R
+
+now, with R equal to 100, given
+here, analytical value
+
+given here, finite element
+solutions, 3-node element with
+
+3-point integration, you can
+see we have a locking
+
+phenomenon right here.
+
+Once again, how much there is
+membrane, and how much shear
+
+locking you would see by
+actually running as a problem
+
+and looking at the
+shear stress and
+
+the membrane stress.
+
+And the finite element
+solution with 2-point
+
+integration gives excellent
+results.
+
+So this is, of course, the
+element that we would be using
+
+in engineering practice.
+
+Similarly, we can study
+the use of the
+
+4-node cubic beam element.
+
+And here we find that for h/R,
+these values, analytical value
+
+once more listed here, we find
+that the 4-node element with
+
+4-point integration gives also
+very good results, and the
+
+3-point integration gives
+also excellent results.
+
+So we note that the cubic beam
+element performs well, even
+
+when using full integration.
+
+It is not susceptible to
+membrane and shear locking.
+
+But notice, we have our
+third-point node exactly at
+
+the third point of
+the elements.
+
+Once we start shifting these
+nodes, then we would also not
+
+get as good results
+as shown here.
+
+We would not get these good
+results once you shift the
+
+node at the third point away
+from their physical third
+
+point locations.
+
+Now, considering the analysis
+of shells, the phenomenon of
+
+shear and membrane locking
+are also present, but the
+
+difficulty lies in that this
+simple reduced integration
+
+approach that we're using for
+the beam elements cannot be
+
+directly applied, because the
+resulting elements contain
+
+spurious zero energy modes.
+
+For example, if you integrate
+the 4-node shell element just
+
+with 1-point integration,
+contains 6 spurious zero
+
+energy modes.
+
+In other words, it has
+altogether 12 zero eigenvalues
+
+where it should only have 6.
+
+The 6 of them are
+spurious modes.
+
+And such spurious energy modes
+can lead to very large errors
+
+in the solution that, unless
+we have a comparison with
+
+accurate results, are not known,
+and therefore, it can
+
+be very dangerous to
+use such elements.
+
+We want to have elements that
+are reliable in general
+
+applications, and these elements
+should only contain
+
+the actual physical rigid
+body modes, no
+
+spurious zero energy modes.
+
+And of course, should also
+have high predictive
+
+capability, not have any shear
+or membrane locking.
+
+For this reason, we can only
+recommend the 16-node shell
+
+element with 4-by-4
+Gauss integration.
+
+The cubic beam element result
+that I just showed you
+
+regarding the analysis of the
+curve beam already indicated
+
+that the cubic element
+does quite well.
+
+In fact, that is also
+borne out by the
+
+16-node shell element.
+
+Using 4-by-4 Gauss integration
+on the shell mid-surface, we
+
+have an element that is
+relatively immune to membrane
+
+and shear locking, but I
+mentioned already that the
+
+element should not
+be distorted.
+
+And if it's not distorted,
+it performs best.
+
+I'd just like to share now
+with you some thoughts
+
+regarding development that
+we have recently pursued.
+
+Namely, recently we have
+developed elements based on
+
+the mixed interpolation of
+tensorial components.
+
+This sounds very complicated.
+
+Actually, if you look closely at
+what we're doing, it is not
+
+that complicated.
+
+The elements, however, do not
+lock in shear or membrane
+
+action, and also do not contain
+any spurious zero
+
+energy mode.
+
+And of course, that is the key
+of success of an element.
+
+We will use later on in the
+example solutions a 4-node
+
+element that is based on this
+mixed interpolation of
+
+tensorial components.
+
+We call that element the MITC4,
+Mixed Interpolation
+
+Tensorial Component with 4 nodes
+element, and I want to
+
+discuss this element just
+briefly with you now.
+
+We also have developed
+an element that
+
+we call MITC8 element.
+
+It's an 8-node element based
+on mixed interpolation of
+
+tensorial components.
+
+A most interesting
+development.
+
+If you're interested in that
+development, please refer to
+
+the paper that is given, or that
+is being referred to, in
+
+the study guide.
+
+I'd like to discuss with you
+now the MITC4 element, and
+
+then show you example
+solutions.
+
+However, we have, in order to be
+able to do that, to change
+
+now the reel, so let us just do
+so, and then continue with
+
+this discussion.
+
+So let us look then at the MITC4
+element briefly, the
+
+element that I mentioned before
+we had the break.
+
+The element is described
+using four nodes.
+
+We have the same isoparametric
+coordinate system that we are
+
+usually having.
+
+Notice here director vector,
+same description as for the
+
+shell element that we discussed
+
+in the earlier lecture.
+
+Each node has 5 degrees of
+freedom, 2 rotational degrees
+
+of freedom, and 3
+
+translational degrees of freedom.
+
+Once again, the way we have
+been discussing it in the
+
+earlier lecture.
+
+We use the element for analysis
+of plates and for the
+
+analysis of moderately thick
+shells, and also thin shells.
+
+And that is the important
+point.
+
+This element is directly
+applicable in a very effective
+
+manner to thin shell analysis.
+
+The key step in the formulation
+of the element is
+
+to interpolate the geometry
+and the displacement as
+
+earlier described,
+as we discussed
+
+in the earlier lecture.
+
+But to interpret the transverse
+shear strain tensor
+
+components separately, and
+these interpolations are
+
+selected judiciously, to tie,
+then, the intensities of these
+
+components to the values
+evaluated using the
+
+displacement interpolations.
+
+Let's look at what I'm saying
+here now pictorially.
+
+The strain tensor interpolation
+that we are
+
+using is shown here in blue
+on the black element.
+
+These are the rt transfer
+shear strain tensor
+
+components.
+
+This is one interpolation
+function, and this is the
+
+other interpolation function.
+
+Notice that if we look at the
+r- and s-axes, the rt strain
+
+tensor component is constant
+in r, but varies
+
+linearly with s.
+
+Here, too, constant in 4,
+varying linearly with s.
+
+Now it's these intensities, one
+here and one there, that
+
+we tie to the nodal point
+displacements and rotations.
+
+Here for this intensity, we
+use these nodal point
+
+descriptions, and for this
+intensity, we use these nodal
+
+point descriptions, or nodal
+point degrees of freedom.
+
+So if you recognize that these
+are, it seems, unknown
+
+quantities that enter into the
+formulation since we're using
+
+these two interpolations--
+
+this one is an unknown quantity
+that enters into the
+
+formulation, that one is an
+unknown quantity that enters
+
+into the formulation--
+
+if you recognize that, then you
+have to ask yourself, what
+
+do we do with these unknown
+quantities?
+
+Well, we eliminate these
+unknown quantities by
+
+expressing them in terms of
+the nodal point degrees of
+
+freedom, these two nodes here
+and these two nodes.
+
+And thus we eliminate these
+tensor component intensities.
+
+And in the K matrix and the F
+vector, we end up having then
+
+only the nodal point
+
+displacement degrees of freedom.
+
+And that's the key part.
+
+For the ft transfer shear strain
+tensor components, we
+
+use these two interpolations.
+
+Now we notice that we have a
+linear description in r and
+
+constant in s for both of
+these two components.
+
+We proceed, of course, to
+eliminate this intensity and
+
+that intensity in terms
+of the nodal
+
+point degrees of freedom.
+
+Same way as we are
+proceeding here.
+
+This element, the MITC4 element,
+has only 6 zero
+
+eigenvalues, no spurious
+zero energy modes.
+
+It passes a patch test. And
+this is a very important
+
+point-- that the element process
+the patch test. What
+
+do we mean by the patch test?
+
+Well, the idea in the patch
+test is that any arbitrary
+
+patch of elements should be
+able to represent constant
+
+stress conditions.
+
+Let's see how we perform that
+patch test. Here we take an
+
+arbitrary patch of elements.
+
+Some of the elements in that
+patch of elements would be
+
+geometrically distorted.
+
+And we subject this patch to
+the minimum displacement
+
+rotation boundary conditions
+to eliminate the physical
+
+rigid body molds, and then
+constant boundary tractions
+
+corresponding to the
+constant stress
+
+condition that is tested.
+
+These two items we apply to
+the patch of elements, and
+
+then we calculate
+all nodal point
+
+displacement and element stresses.
+
+The patch test is passed if
+the calculated element
+
+internal stresses
+and nodal point
+
+displacements are correct.
+
+In other words, let's
+go through this
+
+thought once again.
+
+What we're doing,
+really, is we're
+
+looking at this structure.
+
+In essence, we are taking out
+of this big mesh of elements
+
+in the structure a certain
+set of elements.
+
+We call that set of elements
+a patch of elements.
+
+We apply to this patch of
+elements the minimum boundary
+
+conditions to eliminate the
+rigid body molds and traction
+
+along the boundary that should
+result in constant stress
+
+conditions within
+the elements.
+
+If in fact, our solution for
+that patch of elements gives
+
+us constant stress conditions
+and nodal point displacement
+
+that correspond to these
+constant stress conditions,
+
+then the patch test is passed.
+
+and this means that we would
+have an element that
+
+ultimately, as the mesh is made
+finer and finer with that
+
+element, the solution
+will converge
+
+to the correct solution.
+
+That's the patch test, and
+the most important test,
+
+particularly for shell elements,
+when we have these
+
+complications of various kinds
+of interpolations in the
+
+element formulation,
+and so on.
+
+Well, here, schematically, I
+show such patch of elements.
+
+x1-axis, x2-axes, flat
+patch of elements.
+
+Notice the elements
+not distorted,
+
+not rectangular elements.
+
+We take certain material
+properties,
+
+assign a certain thickness.
+
+We make it a thin patch
+of elements.
+
+The plate that we're looking at
+here is, in essence, thin.
+
+Notice thickness 0.01, width
+10 in both directions.
+
+And so if the elements would
+lock do to shear or membrane
+
+locking, the way we discussed
+earlier, we would certainly
+
+see it by subjecting this patch
+of elements to bending
+
+moment boundary conditions.
+
+The membrane test would
+correspond to these stress
+
+conditions.
+
+The bending twisting test would
+correspond to these
+
+stress conditions.
+
+These are the externally applied
+forces, tractions that
+
+the patch of element is
+subjected for bending twisting
+
+tests, here for membrane
+tests.
+
+And once again, we adjust the
+rigid body modes from the
+
+patch of elements by setting
+the appropriate number of
+
+degrees of freedom, nodal point
+degrees of freedom,
+
+equal to zero, and then subject
+that patch of elements
+
+to the tractions corresponding
+to these stress conditions,
+
+the six ones that I'm
+showing here.
+
+And we measure the internal
+stresses, and find whether
+
+these internal stresses indeed
+correspond to the constant
+
+stress situation.
+
+Also, since only those nodal
+point degrees of freedom have
+
+been removed on the boundary
+that take out the rigid body
+
+modes, we should also see that
+the other nodal point degrees
+
+of freedom, of course, have
+taken on the exact analytical
+
+value corresponding to
+the constant stress
+
+condition that is tested.
+
+This one, that one, that one,
+or the other three here.
+
+That's the patch test.
+
+Well, let us now to look at some
+examples regarding the
+
+elements that we have discussed
+in the previous
+
+lecture and this lecture.
+
+And the first example that I
+like to look at with you is
+
+the analysis of a spherical
+shell with a hole.
+
+There's a hole here, and you
+see the sphere here.
+
+Here's the backside
+of the sphere,
+
+shown by a dashed line.
+
+And this sphere is subjected to
+concentrated forces, shown
+
+by these arrows.
+
+Radius given here, thickness
+given here, and the material
+
+property of the sphere
+given right there.
+
+The first step is to select
+director vectors.
+
+We talked in the previous
+lecture very heavily about the
+
+fact that we use director
+vectors, and we have to define
+
+these director vectors.
+
+The initial director vectors,
+or the director vectors for
+
+the initial configuration.
+
+And we in fact, in this
+particular case, can quite
+
+easily generate the director
+vectors for each node.
+
+The director vector for each
+node, in this particular case,
+
+is chosen to be parallel
+to the radial vector.
+
+So if we look, this is the skin
+of the shell from the
+
+midpoint out via the radial
+vector, we would see the
+
+director vector right here
+in two dimensions, of
+
+course, x and y.
+
+So we generate these
+director vectors.
+
+In ADINA, that can be
+done automatically.
+
+And then we would select the
+boundary, displacement
+
+boundary conditions.
+
+If we look at what happens, for
+example, in the zx phase,
+
+using symmetry conditions, of
+course we would only look at a
+
+particular part of the shell.
+
+The part of the shell, in fact,
+maybe I should show you
+
+that one first, that we want
+to look at is shown here.
+
+Notice here we have the part of
+the shell that we analyze
+
+because of symmetry
+conditions.
+
+We have here a symmetry
+boundary and
+
+there a symmetry boundary.
+
+Notice that we have x, y, and z,
+the coordinate system used
+
+here, and that this part of the
+shell really lies in the
+
+part of the coordinate system
+that we're looking at.
+
+In other words, zy, y here,
+z up there, xz, x
+
+here, z comes out there.
+
+So here we have y equal to 0 on
+this face, and on this face
+
+here, we have x equal to 0.
+
+And what I'd like to now talk
+briefly about is about the
+
+selection of the boundary
+conditions
+
+along these two faces.
+
+Well, these boundary conditions,
+if we look at the
+
+zx face, in other words, this
+face here, we see on this view
+
+graph here the x face--
+here is the shell.
+
+Here we would have our director
+vector at time 0, and
+
+at time t, that director vector
+would have moved as
+
+indicated by the red here.
+
+Notice that with this movement,
+the only rotation
+
+that we can have is the
+theta y rotation.
+
+And that is now shown on
+the next view graph.
+
+Notice theta y here is free,
+a free rotation.
+
+Theta x must be 0.
+
+Theta z must be 0.
+
+And of course uy must be 0,
+because these are material
+
+particles, and in particular
+that one there is a material
+
+particle on the zx phase.
+
+So uy is 0.
+
+uz and ux are have free.
+
+The free degrees of freedom,
+once again, uz,
+
+ux, and theta y.
+
+Well, to impose, then, the
+boundary condition, we would
+
+proceed as shown for this
+material particle along all
+
+the nodes on this face, and
+similarly, of course, on the
+
+other face--
+
+the face on the zy.
+
+To prevent the rigid body
+translations, we would also
+
+have to take 1 degree of freedom
+out, namely one z
+
+degree of freedom out, one
+displacement degree of freedom
+
+corresponding to the
+z-direction out.
+
+And that then would basically
+give us all the boundary
+
+conditions that we have to
+apply for this problem.
+
+So let's look at this view graph
+here to show the mesh
+
+that we are Using.
+
+And we show here that at this
+node, we set uz equal to 0 to
+
+prevent the rigid body motion
+into this direction.
+
+The linear elastic analysis
+results for this problem are
+
+given here.
+
+Notice displacement at
+the point of load
+
+application is 0.0936.
+
+The analytical value
+is shown here.
+
+Pictorially, the original mesh
+is shown in black, and the
+
+deformed mesh is shown in red.
+
+The important point of this
+problem, and I'd like to go
+
+back to it once more, is really
+that when we look at
+
+this mesh, that we define the
+director vectors at each of
+
+these nodes--
+
+and that can be done
+automatically, they can be
+
+generated--
+
+that at each all of these
+internal nodes, we use 5
+
+degrees of freedom, we have two
+locally aligned alpha and
+
+beta degrees of freedom, the one
+that I talked about in the
+
+earlier lecture, at each of
+these internal nodes.
+
+I like to distinguish the
+internal nodes here from the
+
+boundary nodes.
+
+On the boundary nodes, we of
+course have also only 5
+
+natural degrees of freedom, but
+we assign now 6 degrees of
+
+freedom there.
+
+Meaning that the alpha and beta
+degrees of freedom are
+
+rotated into the three Cartesian
+coordinate axes so
+
+as to have three rotations at
+each of these nodes on the
+
+symmetry faces.
+
+And then we can very easily
+impose the symmetry boundary
+
+condition that I just
+talked about.
+
+That's the important point
+of this problem, really--
+
+how we model the boundary
+conditions, and what degrees
+
+of freedom are assigned
+to each of the nodes.
+
+Well as a second example, I'd
+like to consider with you the
+
+analysis of an open box,
+a 5-sided open box.
+
+Here we show the box upside
+down, or open site down.
+
+The open side, in other
+words, is down here.
+
+And the box lies on a rigid,
+frictionless surface.
+
+On top here, we have pressure
+applied to the face.
+
+The box is modelled using
+shell elements.
+
+The point of this problem is to
+discuss with you how we are
+
+modelling this box using the
+concept of director vectors, 5
+
+degrees of freedom, 6 degrees of
+freedom, that we discussed
+
+in the earlier lecture.
+
+So what we need to do here is
+choose initial director
+
+vectors, choose 5 or 6 degrees
+of freedom for each node, and
+
+choose the appropriate
+boundary conditions.
+
+The way we proceed there
+is as follows.
+
+We recognize that we could deal
+with director vectors at
+
+every one of the nodes, but if
+we do so, at a corner, you
+
+would have no unique
+director vectors.
+
+You could, of course, assign
+there a mean normal.
+
+In other words, if you look
+closely here, my hands show
+
+the corner, and the pointer
+shows the mean
+
+normal at that corner.
+
+And that mean normal, mean in
+quotes, would be the direction
+
+of the director vector.
+
+Let me show it from
+up like that.
+
+Here you have the right angle
+between my hands, and you have
+
+the pointer giving you
+the director vector.
+
+That would be one possibility.
+
+However, if you use ADINA, then,
+in this particular case,
+
+it is more effective to not
+input director vectors.
+
+Because if you don't do so
+with ADINA, then for each
+
+node, ADINA will generate
+automatically a mid-surface
+
+normal vector.
+
+In other words, if no director
+vector has input for a node,
+
+then ADINA generates for each
+element connected to the node
+
+a nodal point mid-surface this
+normal vector at that node
+
+from the element geometry.
+
+Now, what does this mean?
+
+It means that if you use this
+option, there will then be as
+
+many different nodal point
+mid-surface normal vectors at
+
+the node as there are elements
+connected to the node.
+
+Now we will have to look at
+this statement much more
+
+closely for this particular
+example.
+
+In this particular case, using
+the option of automatic
+
+generation of element nodal
+point mid-surface normal
+
+vectors, we find that at a node
+away from an edge, we
+
+will end up with just one
+mid-surface normal vector.
+
+Because see, this is a flat
+surface, and the program will
+
+calculate for this element and
+that element and that element
+
+and this element, corresponding
+to that node,
+
+the same normal vector.
+
+And that is the normal
+vector that the
+
+program will then use.
+
+However, if we look at an edge,
+along an edge, and pick
+
+a node there, then at this node,
+there will be 1 normal
+
+vector calculated for this
+element and that element at
+
+that node, shown by this red
+arrow, and one normal vector
+
+at this node calculated for this
+element and that element,
+
+shown by this red arrow.
+
+Of course here, you would have
+three normal vectors.
+
+One on that phase, that
+phase, and this phase.
+
+Well, with these normal vectors,
+then, given, you
+
+recognize that there will be no
+stiffness corresponding to
+
+the rotation about this vector,
+because these elements
+
+don't carry stiffness in this
+rotational degree of freedom.
+
+We have to be careful with that,
+and we have got to make
+
+sure that we solve the problem
+with this rotation, the
+
+rotation corresponding to this
+vector here or about this
+
+vector, being deleted
+in the model.
+
+Whereas at this node here, we
+assign 6 degrees of freedom to
+
+the model, because the rotation
+corresponding around
+
+this vector will have stiffness,
+around this vector
+
+will have stiffness, and if you
+think of a rotation in the
+
+direction of that vector but
+at this node, about this
+
+direction, you will have
+also stiffness.
+
+So we need 6 degrees of freedom
+being assigned at a
+
+node that corresponds to
+an edge or corner.
+
+We have 5 degrees of freedom
+to be assigned
+
+to all other nodes.
+
+This is once more
+summarized here.
+
+5 degrees of freedom at all
+the nodes inside a face.
+
+6 degrees of freedom along
+an edge, and of
+
+course also at a corner.
+
+Let us look now overall at the
+boundary conditions that we
+
+have to assign to the box
+in order to be able
+
+to solve the problem.
+
+Here we show now the
+box open side up.
+
+So this is really the side on
+which the box is placed, but
+
+we just switch the box around
+so that we can more easily
+
+look at what happens on
+this boundary here.
+
+Well, we have nodes that we
+might call internal nodes
+
+along here, nodes that
+are not corner nodes.
+
+And these nodes would have the
+following boundary condition.
+
+First of all, all the rotational
+degrees of freedom
+
+shown by this arrow,
+this double arrow,
+
+must have been deleted.
+
+This I just discussed.
+
+It is due to the fact that
+there is no stiffness
+
+corresponding to this rotation
+at that node, because all the
+
+elements coming into that node
+don't have stiffness
+
+corresponding to this rotational
+degree of freedom.
+
+This degree of freedom
+is free.
+
+That one is free.
+
+This rotation is free.
+
+That rotation is free.
+
+This translation is
+also deleted.
+
+That is due to the fact that the
+box can't move vertically.
+
+It's placed on the
+rigid surface.
+
+If we look at a node that is a
+corner node-- and let's pick a
+
+more typical one.
+
+Here we have one.
+
+Then at this node, we only take
+out, as you can see, the
+
+z displacement degree
+of freedom.
+
+Because, once again,
+the box lies on
+
+the rigid flat surface.
+
+But notice that these
+rotations, all three
+
+rotations, are left free.
+
+They all carry stiffness the
+way I already discussed it.
+
+Also these translations
+are free.
+
+Typical corner node, another
+typical corner node, the same
+
+action as this corner node.
+
+Now here we see something
+in addition.
+
+We see that this degree of
+freedom is taken out, the same
+
+way as over there.
+
+But we also see that
+this degree of
+
+freedom is taken out.
+
+This one is taken out in order
+to prevent a rigid body
+
+rotation about my
+pointer here.
+
+That's why we take
+this one out.
+
+And we take this one out and
+that one out to also prevent
+
+the rigid body rotation that I
+just mentioned, and to prevent
+
+the rigid body translation.
+
+See, this translation has to be
+taken out as well, and that
+
+translation has to be taken out,
+and this rotation has to
+
+be taken out.
+
+I repeat, this translation,
+that translation, and that
+
+rotation, all of those
+have to be taken out.
+
+And that is achieved by knocking
+out this degree of
+
+freedom, that one,
+and that one.
+
+So these are the boundary
+conditions that we apply to
+
+the nodes on the edges
+that are lying
+
+on the rigid surface.
+
+If we perform now a linear
+elastic static analysis of the
+
+box with a uniform pressure
+applied to the top off the
+
+box, using our 4-node MITC4
+element, here is a typical
+
+element shown, this is
+[? the measure ?]
+
+that we use, we find that the
+deformations are magnified,
+
+quite highly magnified,
+looking like that.
+
+Very reasonable deformation.
+
+We could not compare here
+with any other solution.
+
+But it's still a very
+interesting demonstrative
+
+example, because of the way we
+are dealing with the director
+
+vectors, which actually
+we don't define.
+
+We let the program generate
+
+mid-surface nodal point vectors.
+
+And because we could discuss the
+use of the shell element
+
+degrees of freedom, freedom is
+the imposition of boundary
+
+conditions, and other aspects.
+
+This, then, brings me to the
+end of what I wanted to
+
+discuss this you related to the
+view graph, and I'd like
+
+to now share some further
+experiences with you that I
+
+documented on the slides.
+
+So let me walk over here and let
+us discuss the information
+
+that is even on the slides.
+
+The first slide here relates
+to the analysis of a simply
+
+supported plate under
+uniform pressure.
+
+This plate is modelled
+as shown here.
+
+We only model 1/4 of the plate
+because of symmetry
+
+conditions.
+
+And as you can see here, n is
+equal to 2 for 4 elements.
+
+We analyze this plate and
+we calculate the center
+
+displacement, which means the
+displacement at that point,
+
+and compare that center
+displacement to
+
+the analytical solution.
+
+Notice that in this particular
+case, l/H is equal to 1000, so
+
+it's a very thin plate.
+
+And certainly we would get very
+bad results if we had a
+
+shear locking phenomenon in the
+element that we're using.
+
+As I pointed out earlier, the
+MITC4 element does not have
+
+any shear locking.
+
+And as you can see now here, as
+we increase N, as shown in
+
+this axes, we get excellent
+convergence behavior to the
+
+analytical solution.
+
+Now the next slide shows
+the analysis of a
+
+very similar plate.
+
+Again, a square plate, l/H
+still being 1,000.
+
+Simply supported plate.
+
+But now the plate is subjected
+to a concentrated load.
+
+And in this particular case,
+we see the solution results
+
+obtained with the MITC4 element
+as a function of N--
+
+same number N that I referred
+to in the earlier slide.
+
+We see that we get also very
+good convergence behavior in
+
+this particular case.
+
+Not quite as good as for the
+uniformly distributed pressure
+
+case, but still very
+good as well here.
+
+The next slide shows the plate
+now clamped at its edges.
+
+Not any more simply supported.
+
+l/H still 1,000, so still
+a very thin plate.
+
+And here we once again
+calculate the center
+
+displacement as a function
+of N, the
+
+number of elements used.
+
+Remember, N equal 1
+means 4 elements.
+
+Remember N equals 4
+means 16 elements.
+
+Once again, we see excellent
+convergence behavior to the
+
+exact analytical solution.
+
+And finally, this was a case
+for uniform pressure.
+
+Now we look at the case for a
+concentrated load applied at
+
+the center.
+
+And here we see this convergence
+behavior.
+
+Of course, this is quite a
+complicated, difficult problem
+
+to analyze, because of the
+concentrated load and the
+
+clamp boundary conditions.
+
+Here in this analysis, we used
+nice square elements.
+
+A very important consideration
+in a practical analysis is to
+
+identify how well an
+element performs
+
+when it becomes distorted.
+
+And the next slides now relates
+to that question.
+
+Here we now model 1/4 of the
+plate using mesh 1, shown
+
+here, and using mesh
+2, shown here.
+
+Notice the elements that we're
+now using in these analyses is
+
+still the MITC4 element.
+
+Each of these elements is an
+MITC4 element, but it's a
+
+distorted element.
+
+And our objective is really to
+identify what displacement
+
+predictions we obtain at the
+center, at point c of the
+
+plate, when the plate is subject
+to uniform pressure,
+
+and the plate is also
+simply supported.
+
+And what displacement
+predictions do we obtain for
+
+these two measures at
+these two points?
+
+How much do they deteriorate
+when compared to the usage of
+
+nice square elements?
+
+Well, the displacement
+predictions are given here.
+
+Finite element over Kirchhoff
+theory results.
+
+Mesh 1, 0.93, mesh 2, 1.01.
+
+Notice mesh 2 has
+just 1% error.
+
+Mesh 1 has 7% error.
+
+But with mesh 1, we have a very
+coarse mesh, and highly
+
+distorted elements.
+
+It's of course also of interest
+to see what moment
+
+predictions one obtains, and
+here we compare the finite
+
+element moment versus the
+Kirchhoff moment at point c.
+
+And you can see 15% error for
+mesh 1, 2% error for mesh 2.
+
+Actually also very good
+results for moment
+
+prediction, as well.
+
+I should also emphasize, please,
+that l/H is equal to
+
+1,000, so we are still talking
+about this very thin plate.
+
+The next slide now shows how
+the element behaves in the
+
+analysis of a skew plate.
+
+It's also now a distorted
+element mesh, or rather, the
+
+elements used in the meshing
+of this plate are distorted
+
+elements, but they're a little
+bit more regular distorted.
+
+In fact, they are parallelogram
+elements.
+
+Notice, please, that this is a
+top view, so we are seeing a
+
+plan view of the plate.
+
+And--
+
+SPEAKER: Pick up lecture
+20, tape B, slide
+
+20-7, time code 20:33:18.
+
+Take one.
+
+PROFESSOR: The next analysis
+that I like to consider now is
+
+the analysis of the
+skew plate.
+
+Here we show a top view of the
+skew plate with an angle of
+
+skew of 30 degrees.
+
+So it's a highly skewed plate.
+
+And this is the kind of
+mesh we want to use.
+
+Here we show the 4-by-4 mesh
+of MITC4 elements.
+
+Notice the elements are
+distorted, but sort of
+
+regularly distorted, because
+they are having a
+
+parallelogram shape.
+
+The boundary conditions on the
+plate are simply supported
+
+boundary conditions, which I
+should point out are modelled
+
+using the isoparametric
+degenerate plate elements,
+
+shell elements, that
+we talked about.
+
+These boundary conditions are
+modelled by simply setting
+
+only the transverse displacement
+at the nodes, on
+
+the boundary equal to 0.
+
+In other words, the
+displacements corresponding to
+
+the z-axis, pointing out of the
+slide, are set equal to 0,
+
+but the rotations on the
+boundary nodes are left free.
+
+This is a very interesting
+point, most interesting point.
+
+And if you like to read up on
+it, please refer to the
+
+reference that is given
+in the study guide
+
+related to this slide.
+
+Well, we use these kinds of
+meshes to analyze the plate.
+
+Notice the material data
+are given here.
+
+The thickness of the plate
+is given here.
+
+B is equal to 1, so we have a
+thickness with ratio of 1/100.
+
+It's a fairly thin plate.
+
+And we are considering uniform
+pressure applied to the plate.
+
+The next slide now shows
+analysis results.
+
+4-by-4 mesh, 8-by-8, 16-by-16,
+32-by-32 meshes were used.
+
+We compare our finite element
+solution at the point C, the
+
+midpoint of the plate,
+versus the Morley
+
+solution at that point.
+
+And you can see that we really
+have obtained very nice
+
+conversions to the
+Morley solution.
+
+Notice here, we're looking
+at the principal moments,
+
+actually the maximum and the
+minimum moments, at that
+
+midpoint of the plate again,
+point C, and we're comparing
+
+finite element solutions
+with Morley solutions.
+
+And here once again, quite
+good convergence for the
+
+moment, as well.
+
+Now in this analysis, we use the
+kind of mesh, this 4-by-4
+
+mesh, that we had on
+the previous slide.
+
+And one can ask, of course, is
+that a good mesh to use?
+
+Well, we deliberately wanted
+to use this mesh in this
+
+analysis to test the capability
+of the element.
+
+Of course, one could use
+a different mesh.
+
+And on the next slide now, I'm
+showing the results obtained
+
+by using just four elements,
+a 2-by-2 mesh, to
+
+model 1/4 of the plate.
+
+And you can see, with this
+2-by-2 mesh, we get already
+
+excellent predictions of the
+displacement at the point C.
+
+This is where point
+C is, once again.
+
+Excellent prediction of the
+displacement at point C when
+
+compared with Morley solution.
+
+The moment is quite poorly
+predicted, still.
+
+The two moments that
+I defined earlier.
+
+If we go to a finer mesh, 4-by-4
+mesh, the moments, of
+
+course, are much better, and
+so is the displacement
+
+prediction.
+
+But the displacement prediction
+was already goods,
+
+so there is not that much
+of an improvement.
+
+But in general, one can say,
+this here, certainly for
+
+displacement predictions, is a
+much better mesh to use than
+
+the earlier meshes that
+we used for the
+
+earlier table results.
+
+Now I'd like to look at another
+problem, the analysis
+
+of a cantilever subjected to
+an end-bending moment, and
+
+undergoing very large
+displacement.
+
+Here are the data given
+corresponding to the
+
+cantilever, an elastic
+structure that
+
+we're looking at.
+
+And we will be measuring v, phi,
+and u, and u, v, and phi
+
+would take on large values.
+
+In fact, we will actually
+normalize u and v to the
+
+length of the cantilever.
+
+The next slide now shows
+the results obtained.
+
+v/l, u/l, and phi over
+2 pi as a function
+
+of the moment applied.
+
+We're using here moment
+parameter, but of course, the
+
+moment increases along this
+axis, and here we are plotting
+
+u/l, v/l, and phi over 2 pi.
+
+Notice that even for very large
+displacement, v/l being
+
+0.7, with 1 cubic element, cubic
+in the direction of the
+
+cantilever, excellent results.
+
+This is, in other words, the use
+of the cubic element, in
+
+general the 16-node
+shell element, for
+
+these types of analyses.
+
+And it shows that the 16-node
+shell element is
+
+really quite effective.
+
+The next slide now shows
+how we would
+
+apply the MITC4 element.
+
+Here we use just two elements
+to model the cantilever,
+
+bending moment applied
+here, clamped
+
+boundary conditions here.
+
+And you can see that here we
+are plotting u/l, w/l, phi
+
+over 2 pi, as before, moment
+parameter along here.
+
+And you can see that we're
+getting really excellent
+
+results just with 2 elements for
+w/l 0.6, or certainly up
+
+0.5, very close to the
+analytical solution.
+
+The analytical solution is
+given by the solid line.
+
+The next slide now shows the
+result obtained using three
+
+MITC4 elements to model
+the same cantilever.
+
+Notice these are now the nodes
+that we also have used when
+
+using the cubic element
+in our first result.
+
+And note this excellent
+comparison with the analytical
+
+solution for u/l, w/l,
+and phi over 2 pi.
+
+Very large displacement under
+very large displacement
+
+conditions.
+
+The next slide now shows the
+analysis of an I-section
+
+clamped at this end
+and subjected to a
+
+torque at this end.
+
+This is actually quite a
+complicated problem if you
+
+think deeper about the problem
+and recognize that you have
+
+torsional conditions, restrained
+warping here,
+
+[UNINTELLIGIBLE]
+
+torsion here, then of course you
+have bending in the beam,
+
+et cetera, et cetera.
+
+It's not a very easy
+problem if you look
+
+deeply into the problem.
+
+And we wanted to obtain some
+relatively good prediction for
+
+this structural response when
+the structure goes into the
+
+elastoplastic regime.
+
+Here we have the material data
+used in the analysis.
+
+You can see perfectly plastic
+conditions by using tangent
+
+material modulus equal to 0.
+
+The slide here now shows one
+model that we use, namely the
+
+use of altogether 9
+isoparametric cubic elements.
+
+These are rectangular
+elements.
+
+Notice this is 1 isoparametric
+element.
+
+This is the mid-surface or the
+neutral axis of that one
+
+isoparametric cubic rectangular
+section element.
+
+We are modeling the whole
+I-beam by assembling the
+
+I-beam using 9 such elements.
+
+Of course we discussed earlier
+that these elements contain
+
+the proper warping conditions.
+
+We have supplemented our
+isoparametric interpolation by
+
+warping functions, and those
+now of course will be
+
+activated in picking up the
+torsional response, or
+
+modelling the torsional
+response.
+
+This is a free end, that's
+the fixed end.
+
+This was one model that we used,
+and in addition, we used
+
+another model, which
+is shown here--
+
+a model of shell elements,
+9-node shell
+
+elements, 9 such elements.
+
+Of course, a better response
+would have been obtained by
+
+using the 16-node element, but
+that of course would have been
+
+a more expensive analysis.
+
+So in this particular case, we
+wanted to test this model
+
+versus the isoparametric beam
+model that I just showed you.
+
+Notice one interesting point,
+how we are modelling this
+
+connection here.
+
+You see a blown-up
+figure of it.
+
+At this point node c, we have
+just 5 degrees of freedom.
+
+No rotational stiffness about
+this vector here.
+
+So that is not a degree
+of freedom.
+
+Here we have 6 degrees of
+freedom, 3 translational
+
+degrees of freedom and 3
+rotational degrees of freedom.
+
+Here we have 5 degrees
+of freedom.
+
+No degree of freedom, no
+stiffness corresponding to the
+
+rotation about this
+vector here.
+
+That's one of the important
+points that we discussed
+
+earlier already.
+
+Well, to proceed with the
+analysis, we actually use the
+
+longitudinal element dimensions
+shown here.
+
+Notice that we use a shorter
+element at the fixed end than
+
+here at the free end, because we
+anticipate heavy plasticity
+
+here that we wanted to model
+quite accurately.
+
+Once again, the torque is
+applied here, and theta x is
+
+measured here.
+
+And on the next slide now, we
+show the variation of the
+
+torque as a function of
+the theta x [? rate ?]
+
+rotation.
+
+Notice here you have the isobeam
+model solution, and
+
+here you have the shell
+model solution.
+
+We compare our results with
+a sand heap solution and a
+
+Merchant's upper
+bound solution.
+
+These are simplified analytical
+
+solutions to this problem.
+
+Our results here are somewhat
+close, but not very close.
+
+Of course, one could make a
+much deeper study of this
+
+problem, a very interesting
+problem.
+
+But the way we now already have
+concluded our study and
+
+the way I show you the results,
+see, I think it's
+
+already quite valuable, because
+we have learned a bit
+
+regarding the modeling of
+this type of problem.
+
+Well, the next slide now shows
+a final problem for which I
+
+wanted to show you some
+solution results.
+
+Here we have a cylindrical
+shell supported on rigid
+
+diaphragms at the end,
+and the shell is
+
+subjected to uniform pressure.
+
+We measure here wB, the
+displacement at that
+
+particular point B. The data
+corresponding to the shell are
+
+given here.
+
+Notice that we model the shell
+as an elastic, perfectly
+
+plastic material, and notice
+that in the shell, we modeled
+
+only this part of the shell,
+this quarter part of the
+
+shell, using a 9-by-9
+uniform mesh of the
+
+4-node MITC4 element.
+
+The results are now given
+on the slide shown here.
+
+Pressure applied plotted along
+this axis, wB plotted along
+
+this axis, and this is a
+non-linear solution response
+
+we have obtained using the MITC4
+element, and we compare
+
+our solution with the solution
+given by Krakeland.
+
+I might point out that in this
+analysis, we used our
+
+automatic load-stepping scheme
+that we discussed when we
+
+talked about the solution of the
+non-linear finite element
+
+equations in an earlier
+lecture.
+
+Very good comparison
+up to this point
+
+with Krakeland's solution.
+
+We did not go much further
+than that solution given,
+
+because we could not
+compare with any
+
+other solution anyway.
+
+Well, this brings me now to the
+end of what I wanted to
+
+discuss with you regarding
+shell elements.
+
+Of course, please remember
+there is a lot more
+
+information that we could have
+discussed and that we could
+
+have studied together, but we
+only have two lectures, and
+
+this is the information that I
+wanted to share with you in
+
+these two lectures.
+
+I hope you enjoyed it.
+
+Please also refer to the papers
+that are given as
+
+references for these two
+lectures, particularly for the
+
+slides, where you will find much
+more information, many
+
+more details regarding this
+material that we discussed.
+
+Thank you very much for
+your attention.
\ No newline at end of file
diff --git a/Fj1OICPboCU.txt b/Fj1OICPboCU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77e2f709b93fa97b67d485fed8c6980cf4887eca
--- /dev/null
+++ b/Fj1OICPboCU.txt
@@ -0,0 +1,4723 @@
+align:start position:0%
+ 
+alexa
+
+ align:start position:0%
+alexa
+ 
+
+ align:start position:0%
+alexa
+turn off the lights
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+alexa turn on the lights
+
+ align:start position:0%
+alexa turn on the lights
+ 
+
+ align:start position:0%
+alexa turn on the lights
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+today on chalk radio robots and humans
+
+ align:start position:0%
+today on chalk radio robots and humans
+ 
+
+ align:start position:0%
+today on chalk radio robots and humans
+become collaborative partners
+
+ align:start position:0%
+become collaborative partners
+ 
+
+ align:start position:0%
+become collaborative partners
+it's not about let's build machines that
+
+ align:start position:0%
+it's not about let's build machines that
+ 
+
+ align:start position:0%
+it's not about let's build machines that
+look like people and act like people
+
+ align:start position:0%
+look like people and act like people
+ 
+
+ align:start position:0%
+look like people and act like people
+it's let's build machines that dovetail
+
+ align:start position:0%
+it's let's build machines that dovetail
+ 
+
+ align:start position:0%
+it's let's build machines that dovetail
+with us in a way that we can bring forth
+
+ align:start position:0%
+with us in a way that we can bring forth
+ 
+
+ align:start position:0%
+with us in a way that we can bring forth
+all of ourselves to help us achieve the
+
+ align:start position:0%
+all of ourselves to help us achieve the
+ 
+
+ align:start position:0%
+all of ourselves to help us achieve the
+goals that are really important to us
+
+ align:start position:0%
+goals that are really important to us
+ 
+
+ align:start position:0%
+goals that are really important to us
+i'm your host sarah hansen
+
+ align:start position:0%
+i'm your host sarah hansen
+ 
+
+ align:start position:0%
+i'm your host sarah hansen
+this week we're talking with a
+
+ align:start position:0%
+this week we're talking with a
+ 
+
+ align:start position:0%
+this week we're talking with a
+researcher and educator who's working to
+
+ align:start position:0%
+researcher and educator who's working to
+ 
+
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+researcher and educator who's working to
+bridge the gap between human well-being
+
+ align:start position:0%
+bridge the gap between human well-being
+ 
+
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+bridge the gap between human well-being
+and artificial intelligence
+
+ align:start position:0%
+and artificial intelligence
+ 
+
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+and artificial intelligence
+from kindergarten to college classrooms
+
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+from kindergarten to college classrooms
+ 
+
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+from kindergarten to college classrooms
+she's preparing the next generation of
+
+ align:start position:0%
+she's preparing the next generation of
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+
+ align:start position:0%
+she's preparing the next generation of
+informed technology users and empathetic
+
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+informed technology users and empathetic
+ 
+
+ align:start position:0%
+informed technology users and empathetic
+designers
+
+ align:start position:0%
+designers
+ 
+
+ align:start position:0%
+designers
+i'm cynthia brazil i'm a professor at
+
+ align:start position:0%
+i'm cynthia brazil i'm a professor at
+ 
+
+ align:start position:0%
+i'm cynthia brazil i'm a professor at
+mit at the media lab
+
+ align:start position:0%
+mit at the media lab
+ 
+
+ align:start position:0%
+mit at the media lab
+i'm also director of a new mit wide
+
+ align:start position:0%
+i'm also director of a new mit wide
+ 
+
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+i'm also director of a new mit wide
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+initiative
+called responsible ai for social
+
+ align:start position:0%
+called responsible ai for social
+ 
+
+ align:start position:0%
+called responsible ai for social
+empowerment and education we call it
+
+ align:start position:0%
+empowerment and education we call it
+ 
+
+ align:start position:0%
+empowerment and education we call it
+raise for short
+
+ align:start position:0%
+raise for short
+ 
+
+ align:start position:0%
+raise for short
+and i very recently am the dean for
+
+ align:start position:0%
+and i very recently am the dean for
+ 
+
+ align:start position:0%
+and i very recently am the dean for
+digital learning
+
+ align:start position:0%
+digital learning
+ 
+
+ align:start position:0%
+digital learning
+cynthia's fascination with artificial
+
+ align:start position:0%
+cynthia's fascination with artificial
+ 
+
+ align:start position:0%
+cynthia's fascination with artificial
+intelligence began a long time ago in a
+
+ align:start position:0%
+intelligence began a long time ago in a
+ 
+
+ align:start position:0%
+intelligence began a long time ago in a
+galaxy far far away
+
+ align:start position:0%
+galaxy far far away
+ 
+
+ align:start position:0%
+galaxy far far away
+when i was 10 i saw star wars and
+
+ align:start position:0%
+when i was 10 i saw star wars and
+ 
+
+ align:start position:0%
+when i was 10 i saw star wars and
+that forever shaped my
+
+ align:start position:0%
+that forever shaped my
+ 
+
+ align:start position:0%
+that forever shaped my
+i guess vision of what a robot could be
+
+ align:start position:0%
+i guess vision of what a robot could be
+ 
+
+ align:start position:0%
+i guess vision of what a robot could be
+for us i mean it wasn't just a mindless
+
+ align:start position:0%
+for us i mean it wasn't just a mindless
+ 
+
+ align:start position:0%
+for us i mean it wasn't just a mindless
+automaton it was an entity that had you
+
+ align:start position:0%
+automaton it was an entity that had you
+ 
+
+ align:start position:0%
+automaton it was an entity that had you
+know in the movie like they were
+
+ align:start position:0%
+know in the movie like they were
+ 
+
+ align:start position:0%
+know in the movie like they were
+full-fledged characters right they had
+
+ align:start position:0%
+full-fledged characters right they had
+ 
+
+ align:start position:0%
+full-fledged characters right they had
+friendships they were mission driven to
+
+ align:start position:0%
+friendships they were mission driven to
+ 
+
+ align:start position:0%
+friendships they were mission driven to
+save the universe i mean all of that and
+
+ align:start position:0%
+save the universe i mean all of that and
+ 
+
+ align:start position:0%
+save the universe i mean all of that and
+of course they had relationships not
+
+ align:start position:0%
+of course they had relationships not
+ 
+
+ align:start position:0%
+of course they had relationships not
+just with you know the robots but with
+
+ align:start position:0%
+just with you know the robots but with
+ 
+
+ align:start position:0%
+just with you know the robots but with
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+cynthia followed that vision of complex
+
+ align:start position:0%
+cynthia followed that vision of complex
+ 
+
+ align:start position:0%
+cynthia followed that vision of complex
+human-machine relationships all the way
+
+ align:start position:0%
+human-machine relationships all the way
+ 
+
+ align:start position:0%
+human-machine relationships all the way
+to a phd program at mit
+
+ align:start position:0%
+to a phd program at mit
+ 
+
+ align:start position:0%
+to a phd program at mit
+there she designed kismet the world's
+
+ align:start position:0%
+there she designed kismet the world's
+ 
+
+ align:start position:0%
+there she designed kismet the world's
+first social robot
+
+ align:start position:0%
+first social robot
+ 
+
+ align:start position:0%
+first social robot
+that kind of started this whole question
+
+ align:start position:0%
+that kind of started this whole question
+ 
+
+ align:start position:0%
+that kind of started this whole question
+of socially and emotionally intelligent
+
+ align:start position:0%
+of socially and emotionally intelligent
+ 
+
+ align:start position:0%
+of socially and emotionally intelligent
+interaction with machines because we
+
+ align:start position:0%
+interaction with machines because we
+ 
+
+ align:start position:0%
+interaction with machines because we
+are profoundly socially and emotional
+
+ align:start position:0%
+are profoundly socially and emotional
+ 
+
+ align:start position:0%
+are profoundly socially and emotional
+creatures if we want design technologies
+
+ align:start position:0%
+creatures if we want design technologies
+ 
+
+ align:start position:0%
+creatures if we want design technologies
+that can interact with us and treat us
+
+ align:start position:0%
+that can interact with us and treat us
+ 
+
+ align:start position:0%
+that can interact with us and treat us
+again as people we need to understand
+
+ align:start position:0%
+again as people we need to understand
+ 
+
+ align:start position:0%
+again as people we need to understand
+that dimension
+
+ align:start position:0%
+that dimension
+ 
+
+ align:start position:0%
+that dimension
+you know a lot of the early work was
+
+ align:start position:0%
+you know a lot of the early work was
+ 
+
+ align:start position:0%
+you know a lot of the early work was
+pushing on i would say the algorithmic
+
+ align:start position:0%
+pushing on i would say the algorithmic
+ 
+
+ align:start position:0%
+pushing on i would say the algorithmic
+side of that we looked at a lot of
+
+ align:start position:0%
+side of that we looked at a lot of
+ 
+
+ align:start position:0%
+side of that we looked at a lot of
+models of emotion and people and animals
+
+ align:start position:0%
+models of emotion and people and animals
+ 
+
+ align:start position:0%
+models of emotion and people and animals
+and like what is the function of it and
+
+ align:start position:0%
+and like what is the function of it and
+ 
+
+ align:start position:0%
+and like what is the function of it and
+how might you implement aspects of that
+
+ align:start position:0%
+how might you implement aspects of that
+ 
+
+ align:start position:0%
+how might you implement aspects of that
+for intelligent communication and
+
+ align:start position:0%
+for intelligent communication and
+ 
+
+ align:start position:0%
+for intelligent communication and
+interaction with machines
+
+ align:start position:0%
+interaction with machines
+ 
+
+ align:start position:0%
+interaction with machines
+and then we started thinking about okay
+
+ align:start position:0%
+and then we started thinking about okay
+ 
+
+ align:start position:0%
+and then we started thinking about okay
+so what's this really good for so it's
+
+ align:start position:0%
+so what's this really good for so it's
+ 
+
+ align:start position:0%
+so what's this really good for so it's
+fascinating you know from a scientific
+
+ align:start position:0%
+fascinating you know from a scientific
+ 
+
+ align:start position:0%
+fascinating you know from a scientific
+perspective it's fascinating from a
+
+ align:start position:0%
+perspective it's fascinating from a
+ 
+
+ align:start position:0%
+perspective it's fascinating from a
+technical perspective
+
+ align:start position:0%
+technical perspective
+ 
+
+ align:start position:0%
+technical perspective
+but what does this mean about how
+
+ align:start position:0%
+but what does this mean about how
+ 
+
+ align:start position:0%
+but what does this mean about how
+we will interact with
+
+ align:start position:0%
+we will interact with
+ 
+
+ align:start position:0%
+we will interact with
+robots with intelligent machines in our
+
+ align:start position:0%
+robots with intelligent machines in our
+ 
+
+ align:start position:0%
+robots with intelligent machines in our
+lives in our future and so then we
+
+ align:start position:0%
+lives in our future and so then we
+ 
+
+ align:start position:0%
+lives in our future and so then we
+started thinking about so what are what
+
+ align:start position:0%
+started thinking about so what are what
+ 
+
+ align:start position:0%
+started thinking about so what are what
+are these big societal challenges that
+
+ align:start position:0%
+are these big societal challenges that
+ 
+
+ align:start position:0%
+are these big societal challenges that
+we face where
+
+ align:start position:0%
+we face where
+ 
+
+ align:start position:0%
+we face where
+potentially an ai cut more from this
+
+ align:start position:0%
+potentially an ai cut more from this
+ 
+
+ align:start position:0%
+potentially an ai cut more from this
+kind of cloth or this philosophy might
+
+ align:start position:0%
+kind of cloth or this philosophy might
+ 
+
+ align:start position:0%
+kind of cloth or this philosophy might
+really make a difference
+
+ align:start position:0%
+really make a difference
+ 
+
+ align:start position:0%
+really make a difference
+after kismet cynthia began working on a
+
+ align:start position:0%
+after kismet cynthia began working on a
+ 
+
+ align:start position:0%
+after kismet cynthia began working on a
+new social robot named gebo
+
+ align:start position:0%
+new social robot named gebo
+ 
+
+ align:start position:0%
+new social robot named gebo
+gebo is actually these concentric
+
+ align:start position:0%
+gebo is actually these concentric
+ 
+
+ align:start position:0%
+gebo is actually these concentric
+rotating circles that are kind of off
+
+ align:start position:0%
+rotating circles that are kind of off
+ 
+
+ align:start position:0%
+rotating circles that are kind of off
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+and with that he can kind of
+
+ align:start position:0%
+and with that he can kind of
+ 
+
+ align:start position:0%
+and with that he can kind of
+create what's called an animational line
+
+ align:start position:0%
+create what's called an animational line
+ 
+
+ align:start position:0%
+create what's called an animational line
+of action so he can change his posture
+
+ align:start position:0%
+of action so he can change his posture
+ 
+
+ align:start position:0%
+of action so he can change his posture
+right so he can look like he's upright
+
+ align:start position:0%
+right so he can look like he's upright
+ 
+
+ align:start position:0%
+right so he can look like he's upright
+or he can like stoop over or lean to the
+
+ align:start position:0%
+or he can like stoop over or lean to the
+ 
+
+ align:start position:0%
+or he can like stoop over or lean to the
+side and [ __ ] his head like he can go
+
+ align:start position:0%
+side and [ __ ] his head like he can go
+ 
+
+ align:start position:0%
+side and [ __ ] his head like he can go
+through all of these kind of expressive
+
+ align:start position:0%
+through all of these kind of expressive
+ 
+
+ align:start position:0%
+through all of these kind of expressive
+postures that are
+
+ align:start position:0%
+postures that are
+ 
+
+ align:start position:0%
+postures that are
+really foundational to an animator when
+
+ align:start position:0%
+really foundational to an animator when
+ 
+
+ align:start position:0%
+really foundational to an animator when
+they want to express something through
+
+ align:start position:0%
+they want to express something through
+ 
+
+ align:start position:0%
+they want to express something through
+characters
+
+ align:start position:0%
+characters
+ 
+
+ align:start position:0%
+characters
+technologies tend to move in rectilinear
+
+ align:start position:0%
+technologies tend to move in rectilinear
+ 
+
+ align:start position:0%
+technologies tend to move in rectilinear
+trajectories
+
+ align:start position:0%
+trajectories
+ 
+
+ align:start position:0%
+trajectories
+living things move in arcs
+
+ align:start position:0%
+living things move in arcs
+ 
+
+ align:start position:0%
+living things move in arcs
+and so all of gebo's motions was based
+
+ align:start position:0%
+and so all of gebo's motions was based
+ 
+
+ align:start position:0%
+and so all of gebo's motions was based
+on arcs right so he naturally moved in a
+
+ align:start position:0%
+on arcs right so he naturally moved in a
+ 
+
+ align:start position:0%
+on arcs right so he naturally moved in a
+way that she seemed much more lifelike
+
+ align:start position:0%
+way that she seemed much more lifelike
+ 
+
+ align:start position:0%
+way that she seemed much more lifelike
+and expressive because he fundamentally
+
+ align:start position:0%
+and expressive because he fundamentally
+ 
+
+ align:start position:0%
+and expressive because he fundamentally
+was designed to move in arcs you have to
+
+ align:start position:0%
+was designed to move in arcs you have to
+ 
+
+ align:start position:0%
+was designed to move in arcs you have to
+see gebo move you have to actually watch
+
+ align:start position:0%
+see gebo move you have to actually watch
+ 
+
+ align:start position:0%
+see gebo move you have to actually watch
+him dance because like he's like it's
+
+ align:start position:0%
+him dance because like he's like it's
+ 
+
+ align:start position:0%
+him dance because like he's like it's
+incredible to watch this robot dance
+
+ align:start position:0%
+incredible to watch this robot dance
+ 
+
+ align:start position:0%
+incredible to watch this robot dance
+gebo didn't just look and move
+
+ align:start position:0%
+gebo didn't just look and move
+ 
+
+ align:start position:0%
+gebo didn't just look and move
+differently from other robots he
+
+ align:start position:0%
+differently from other robots he
+ 
+
+ align:start position:0%
+differently from other robots he
+functioned differently too
+
+ align:start position:0%
+functioned differently too
+ 
+
+ align:start position:0%
+functioned differently too
+i often use the language of there's like
+
+ align:start position:0%
+i often use the language of there's like
+ 
+
+ align:start position:0%
+i often use the language of there's like
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+digital assistant like this is what like
+
+ align:start position:0%
+digital assistant like this is what like
+ 
+
+ align:start position:0%
+digital assistant like this is what like
+google and like they're all called
+
+ align:start position:0%
+google and like they're all called
+ 
+
+ align:start position:0%
+google and like they're all called
+digital assistants and they're kind of
+
+ align:start position:0%
+digital assistants and they're kind of
+ 
+
+ align:start position:0%
+digital assistants and they're kind of
+modeled after the executive assistant
+
+ align:start position:0%
+modeled after the executive assistant
+ 
+
+ align:start position:0%
+modeled after the executive assistant
+we talk about jib as being a helpful
+
+ align:start position:0%
+we talk about jib as being a helpful
+ 
+
+ align:start position:0%
+we talk about jib as being a helpful
+companion
+
+ align:start position:0%
+companion
+ 
+
+ align:start position:0%
+companion
+so that speaks more to the social
+
+ align:start position:0%
+so that speaks more to the social
+ 
+
+ align:start position:0%
+so that speaks more to the social
+emotional the relational aspects of it
+
+ align:start position:0%
+emotional the relational aspects of it
+ 
+
+ align:start position:0%
+emotional the relational aspects of it
+but jibo is also helpful right he can
+
+ align:start position:0%
+but jibo is also helpful right he can
+ 
+
+ align:start position:0%
+but jibo is also helpful right he can
+actually do things
+
+ align:start position:0%
+actually do things
+ 
+
+ align:start position:0%
+actually do things
+but it's the way he does things are much
+
+ align:start position:0%
+but it's the way he does things are much
+ 
+
+ align:start position:0%
+but it's the way he does things are much
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+humanistic i would say human centered in
+
+ align:start position:0%
+humanistic i would say human centered in
+ 
+
+ align:start position:0%
+humanistic i would say human centered in
+its design less transactional you know
+
+ align:start position:0%
+its design less transactional you know
+ 
+
+ align:start position:0%
+its design less transactional you know
+the way he expresses himself through
+
+ align:start position:0%
+the way he expresses himself through
+ 
+
+ align:start position:0%
+the way he expresses himself through
+movement and also just the language he
+
+ align:start position:0%
+movement and also just the language he
+ 
+
+ align:start position:0%
+movement and also just the language he
+uses
+
+ align:start position:0%
+uses
+ 
+
+ align:start position:0%
+uses
+it's much more
+
+ align:start position:0%
+it's much more
+ 
+
+ align:start position:0%
+it's much more
+warm i would say like there's cool tech
+
+ align:start position:0%
+warm i would say like there's cool tech
+ 
+
+ align:start position:0%
+warm i would say like there's cool tech
+jima was warm tech
+
+ align:start position:0%
+jima was warm tech
+ 
+
+ align:start position:0%
+jima was warm tech
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+one exciting new application for jibo
+
+ align:start position:0%
+one exciting new application for jibo
+ 
+
+ align:start position:0%
+one exciting new application for jibo
+that's currently being explored
+
+ align:start position:0%
+that's currently being explored
+ 
+
+ align:start position:0%
+that's currently being explored
+is how he might help provide mental
+
+ align:start position:0%
+is how he might help provide mental
+ 
+
+ align:start position:0%
+is how he might help provide mental
+health care
+
+ align:start position:0%
+health care
+ 
+
+ align:start position:0%
+health care
+one of the studies we did we we
+
+ align:start position:0%
+one of the studies we did we we
+ 
+
+ align:start position:0%
+one of the studies we did we we
+literally designed a emotional wellness
+
+ align:start position:0%
+literally designed a emotional wellness
+ 
+
+ align:start position:0%
+literally designed a emotional wellness
+coach skill
+
+ align:start position:0%
+coach skill
+ 
+
+ align:start position:0%
+coach skill
+for gebo and we deployed jivo in mit
+
+ align:start position:0%
+for gebo and we deployed jivo in mit
+ 
+
+ align:start position:0%
+for gebo and we deployed jivo in mit
+student dorms because as you probably
+
+ align:start position:0%
+student dorms because as you probably
+ 
+
+ align:start position:0%
+student dorms because as you probably
+know mental health is like a huge issue
+
+ align:start position:0%
+know mental health is like a huge issue
+ 
+
+ align:start position:0%
+know mental health is like a huge issue
+i mean even before the pandemic
+
+ align:start position:0%
+i mean even before the pandemic
+ 
+
+ align:start position:0%
+i mean even before the pandemic
+mental health emotional wellness of
+
+ align:start position:0%
+mental health emotional wellness of
+ 
+
+ align:start position:0%
+mental health emotional wellness of
+students at a lot of top colleges was
+
+ align:start position:0%
+students at a lot of top colleges was
+ 
+
+ align:start position:0%
+students at a lot of top colleges was
+like really concerning
+
+ align:start position:0%
+like really concerning
+ 
+
+ align:start position:0%
+like really concerning
+so we decided to explore whether gebo as
+
+ align:start position:0%
+so we decided to explore whether gebo as
+ 
+
+ align:start position:0%
+so we decided to explore whether gebo as
+an emotional wellness coach could
+
+ align:start position:0%
+an emotional wellness coach could
+ 
+
+ align:start position:0%
+an emotional wellness coach could
+actually help
+
+ align:start position:0%
+actually help
+ 
+
+ align:start position:0%
+actually help
+mitigate the stress and anxiety that
+
+ align:start position:0%
+mitigate the stress and anxiety that
+ 
+
+ align:start position:0%
+mitigate the stress and anxiety that
+students experience when they're at a
+
+ align:start position:0%
+students experience when they're at a
+ 
+
+ align:start position:0%
+students experience when they're at a
+you know an elite university like mit
+
+ align:start position:0%
+you know an elite university like mit
+ 
+
+ align:start position:0%
+you know an elite university like mit
+so we developed some best in breed
+
+ align:start position:0%
+so we developed some best in breed
+ 
+
+ align:start position:0%
+so we developed some best in breed
+therapeutic interactions that typically
+
+ align:start position:0%
+therapeutic interactions that typically
+ 
+
+ align:start position:0%
+therapeutic interactions that typically
+a human would do like a coach would do
+
+ align:start position:0%
+a human would do like a coach would do
+ 
+
+ align:start position:0%
+a human would do like a coach would do
+with their client or whatever right so
+
+ align:start position:0%
+with their client or whatever right so
+ 
+
+ align:start position:0%
+with their client or whatever right so
+typically it's human human
+
+ align:start position:0%
+typically it's human human
+ 
+
+ align:start position:0%
+typically it's human human
+we took these proven methods and we just
+
+ align:start position:0%
+we took these proven methods and we just
+ 
+
+ align:start position:0%
+we took these proven methods and we just
+now gebo was just doing it with the
+
+ align:start position:0%
+now gebo was just doing it with the
+ 
+
+ align:start position:0%
+now gebo was just doing it with the
+person and you know we published that
+
+ align:start position:0%
+person and you know we published that
+ 
+
+ align:start position:0%
+person and you know we published that
+work and basically the punchline is we
+
+ align:start position:0%
+work and basically the punchline is we
+ 
+
+ align:start position:0%
+work and basically the punchline is we
+were able to show that yeah jebos seemed
+
+ align:start position:0%
+were able to show that yeah jebos seemed
+ 
+
+ align:start position:0%
+were able to show that yeah jebos seemed
+to make a positive difference so in
+
+ align:start position:0%
+to make a positive difference so in
+ 
+
+ align:start position:0%
+to make a positive difference so in
+terms of the future of health right
+
+ align:start position:0%
+terms of the future of health right
+ 
+
+ align:start position:0%
+terms of the future of health right
+people could go into hospitals
+
+ align:start position:0%
+people could go into hospitals
+ 
+
+ align:start position:0%
+people could go into hospitals
+potentially and get you know world
+
+ align:start position:0%
+potentially and get you know world
+ 
+
+ align:start position:0%
+potentially and get you know world
+quality care but what happens when they
+
+ align:start position:0%
+quality care but what happens when they
+ 
+
+ align:start position:0%
+quality care but what happens when they
+go home
+
+ align:start position:0%
+go home
+ 
+
+ align:start position:0%
+go home
+so again something like ajibo or social
+
+ align:start position:0%
+so again something like ajibo or social
+ 
+
+ align:start position:0%
+so again something like ajibo or social
+robot or whatever the idea that they can
+
+ align:start position:0%
+robot or whatever the idea that they can
+ 
+
+ align:start position:0%
+robot or whatever the idea that they can
+extend the quality of care and support
+
+ align:start position:0%
+extend the quality of care and support
+ 
+
+ align:start position:0%
+extend the quality of care and support
+from the doctors and nurses in the
+
+ align:start position:0%
+from the doctors and nurses in the
+ 
+
+ align:start position:0%
+from the doctors and nurses in the
+hospital to the home where patients are
+
+ align:start position:0%
+hospital to the home where patients are
+ 
+
+ align:start position:0%
+hospital to the home where patients are
+living every day
+
+ align:start position:0%
+living every day
+ 
+
+ align:start position:0%
+living every day
+that's a huge unmet need
+
+ align:start position:0%
+that's a huge unmet need
+ 
+
+ align:start position:0%
+that's a huge unmet need
+and that's a role where potentially i
+
+ align:start position:0%
+and that's a role where potentially i
+ 
+
+ align:start position:0%
+and that's a role where potentially i
+think an intelligent
+
+ align:start position:0%
+think an intelligent
+ 
+
+ align:start position:0%
+think an intelligent
+kind of again collaborative allied agent
+
+ align:start position:0%
+kind of again collaborative allied agent
+ 
+
+ align:start position:0%
+kind of again collaborative allied agent
+with this different kind of interaction
+
+ align:start position:0%
+with this different kind of interaction
+ 
+
+ align:start position:0%
+with this different kind of interaction
+paradigm could make a big difference
+
+ align:start position:0%
+paradigm could make a big difference
+ 
+
+ align:start position:0%
+paradigm could make a big difference
+one of the fascinating design decisions
+
+ align:start position:0%
+one of the fascinating design decisions
+ 
+
+ align:start position:0%
+one of the fascinating design decisions
+behind jibo was choosing just how human
+
+ align:start position:0%
+behind jibo was choosing just how human
+ 
+
+ align:start position:0%
+behind jibo was choosing just how human
+to make him
+
+ align:start position:0%
+to make him
+ 
+
+ align:start position:0%
+to make him
+when we
+
+ align:start position:0%
+when we
+ 
+
+ align:start position:0%
+when we
+developed g-bow we
+
+ align:start position:0%
+developed g-bow we
+ 
+
+ align:start position:0%
+developed g-bow we
+were very intentional in saying there's
+
+ align:start position:0%
+were very intentional in saying there's
+ 
+
+ align:start position:0%
+were very intentional in saying there's
+the character of gebo
+
+ align:start position:0%
+the character of gebo
+ 
+
+ align:start position:0%
+the character of gebo
+when you talk about
+
+ align:start position:0%
+when you talk about
+ 
+
+ align:start position:0%
+when you talk about
+the perception of how
+
+ align:start position:0%
+the perception of how
+ 
+
+ align:start position:0%
+the perception of how
+children or adults perceive these agents
+
+ align:start position:0%
+children or adults perceive these agents
+ 
+
+ align:start position:0%
+children or adults perceive these agents
+jibo was what you know as the character
+
+ align:start position:0%
+jibo was what you know as the character
+ 
+
+ align:start position:0%
+jibo was what you know as the character
+was very aware that jibo was a robot and
+
+ align:start position:0%
+was very aware that jibo was a robot and
+ 
+
+ align:start position:0%
+was very aware that jibo was a robot and
+you know if you tried to ask jibo things
+
+ align:start position:0%
+you know if you tried to ask jibo things
+ 
+
+ align:start position:0%
+you know if you tried to ask jibo things
+that really a robot would have no
+
+ align:start position:0%
+that really a robot would have no
+ 
+
+ align:start position:0%
+that really a robot would have no
+business answering like things around
+
+ align:start position:0%
+business answering like things around
+ 
+
+ align:start position:0%
+business answering like things around
+religion or whatnot like jeeba would say
+
+ align:start position:0%
+religion or whatnot like jeeba would say
+ 
+
+ align:start position:0%
+religion or whatnot like jeeba would say
+this like hey i'm just a robot you know
+
+ align:start position:0%
+this like hey i'm just a robot you know
+ 
+
+ align:start position:0%
+this like hey i'm just a robot you know
+it's probably something that'd be good
+
+ align:start position:0%
+it's probably something that'd be good
+ 
+
+ align:start position:0%
+it's probably something that'd be good
+to talk about another person with but
+
+ align:start position:0%
+to talk about another person with but
+ 
+
+ align:start position:0%
+to talk about another person with but
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+i'm just a robot so jiba was very
+
+ align:start position:0%
+i'm just a robot so jiba was very
+ 
+
+ align:start position:0%
+i'm just a robot so jiba was very
+upfront and like transparent about his
+
+ align:start position:0%
+upfront and like transparent about his
+ 
+
+ align:start position:0%
+upfront and like transparent about his
+robotness
+
+ align:start position:0%
+robotness
+ 
+
+ align:start position:0%
+robotness
+collaborative allied agents like gebo
+
+ align:start position:0%
+collaborative allied agents like gebo
+ 
+
+ align:start position:0%
+collaborative allied agents like gebo
+have huge potential to improve the lives
+
+ align:start position:0%
+have huge potential to improve the lives
+ 
+
+ align:start position:0%
+have huge potential to improve the lives
+of humans
+
+ align:start position:0%
+of humans
+ 
+
+ align:start position:0%
+of humans
+but as cynthia pointed out they can't
+
+ align:start position:0%
+but as cynthia pointed out they can't
+ 
+
+ align:start position:0%
+but as cynthia pointed out they can't
+replace the power of real human social
+
+ align:start position:0%
+replace the power of real human social
+ 
+
+ align:start position:0%
+replace the power of real human social
+networks
+
+ align:start position:0%
+networks
+ 
+
+ align:start position:0%
+networks
+this gets into the ethics and the
+
+ align:start position:0%
+this gets into the ethics and the
+ 
+
+ align:start position:0%
+this gets into the ethics and the
+responsible design of these things i
+
+ align:start position:0%
+responsible design of these things i
+ 
+
+ align:start position:0%
+responsible design of these things i
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+first and foremost
+
+ align:start position:0%
+first and foremost
+ 
+
+ align:start position:0%
+first and foremost
+people need people we need
+
+ align:start position:0%
+people need people we need
+ 
+
+ align:start position:0%
+people need people we need
+our human social networks are in person
+
+ align:start position:0%
+our human social networks are in person
+ 
+
+ align:start position:0%
+our human social networks are in person
+caring human social networks to come
+
+ align:start position:0%
+caring human social networks to come
+ 
+
+ align:start position:0%
+caring human social networks to come
+around us when we're in trouble
+
+ align:start position:0%
+around us when we're in trouble
+ 
+
+ align:start position:0%
+around us when we're in trouble
+social media companies that will try to
+
+ align:start position:0%
+social media companies that will try to
+ 
+
+ align:start position:0%
+social media companies that will try to
+tell you like your network of 5000
+
+ align:start position:0%
+tell you like your network of 5000
+ 
+
+ align:start position:0%
+tell you like your network of 5000
+people you don't know is just as
+
+ align:start position:0%
+people you don't know is just as
+ 
+
+ align:start position:0%
+people you don't know is just as
+important as your actual like real
+
+ align:start position:0%
+important as your actual like real
+ 
+
+ align:start position:0%
+important as your actual like real
+in-person relationships
+
+ align:start position:0%
+in-person relationships
+ 
+
+ align:start position:0%
+in-person relationships
+real in-person relationships are
+
+ align:start position:0%
+real in-person relationships are
+ 
+
+ align:start position:0%
+real in-person relationships are
+absolutely essential they're essential
+
+ align:start position:0%
+absolutely essential they're essential
+ 
+
+ align:start position:0%
+absolutely essential they're essential
+for our well-being
+
+ align:start position:0%
+for our well-being
+ 
+
+ align:start position:0%
+for our well-being
+they're essential for children's
+
+ align:start position:0%
+they're essential for children's
+ 
+
+ align:start position:0%
+they're essential for children's
+development i mean they're just critical
+
+ align:start position:0%
+development i mean they're just critical
+ 
+
+ align:start position:0%
+development i mean they're just critical
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+it signals i think we're living in this
+
+ align:start position:0%
+it signals i think we're living in this
+ 
+
+ align:start position:0%
+it signals i think we're living in this
+time when
+
+ align:start position:0%
+time when
+ 
+
+ align:start position:0%
+time when
+people's time and attention has become
+
+ align:start position:0%
+people's time and attention has become
+ 
+
+ align:start position:0%
+people's time and attention has become
+like this incredibly precious resource
+
+ align:start position:0%
+like this incredibly precious resource
+ 
+
+ align:start position:0%
+like this incredibly precious resource
+where the fact that someone will stop
+
+ align:start position:0%
+where the fact that someone will stop
+ 
+
+ align:start position:0%
+where the fact that someone will stop
+and take that time out for you
+
+ align:start position:0%
+and take that time out for you
+ 
+
+ align:start position:0%
+and take that time out for you
+signals something of like you're you're
+
+ align:start position:0%
+signals something of like you're you're
+ 
+
+ align:start position:0%
+signals something of like you're you're
+valued you are really valued and you're
+
+ align:start position:0%
+valued you are really valued and you're
+ 
+
+ align:start position:0%
+valued you are really valued and you're
+you're meaningful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a parent the importance of real
+
+ align:start position:0%
+as a parent the importance of real
+ 
+
+ align:start position:0%
+as a parent the importance of real
+social networks for children really
+
+ align:start position:0%
+social networks for children really
+ 
+
+ align:start position:0%
+social networks for children really
+feels true to me
+
+ align:start position:0%
+feels true to me
+ 
+
+ align:start position:0%
+feels true to me
+but i also know that my child is growing
+
+ align:start position:0%
+but i also know that my child is growing
+ 
+
+ align:start position:0%
+but i also know that my child is growing
+up in a world where digital interactions
+
+ align:start position:0%
+up in a world where digital interactions
+ 
+
+ align:start position:0%
+up in a world where digital interactions
+are becoming more and more common and
+
+ align:start position:0%
+are becoming more and more common and
+ 
+
+ align:start position:0%
+are becoming more and more common and
+potentially fraught with ethical
+
+ align:start position:0%
+potentially fraught with ethical
+ 
+
+ align:start position:0%
+potentially fraught with ethical
+implications
+
+ align:start position:0%
+implications
+ 
+
+ align:start position:0%
+implications
+so i shared with cynthia a recording of
+
+ align:start position:0%
+so i shared with cynthia a recording of
+ 
+
+ align:start position:0%
+so i shared with cynthia a recording of
+my child talking with our home executive
+
+ align:start position:0%
+my child talking with our home executive
+ 
+
+ align:start position:0%
+my child talking with our home executive
+assistant
+
+ align:start position:0%
+assistant
+ 
+
+ align:start position:0%
+assistant
+alexa what's your favorite
+
+ align:start position:0%
+alexa what's your favorite
+ 
+
+ align:start position:0%
+alexa what's your favorite
+color i like ultra violet
+
+ align:start position:0%
+color i like ultra violet
+ 
+
+ align:start position:0%
+color i like ultra violet
+it glows with everything
+
+ align:start position:0%
+it glows with everything
+ 
+
+ align:start position:0%
+it glows with everything
+and here's another fun fact about me
+
+ align:start position:0%
+and here's another fun fact about me
+ 
+
+ align:start position:0%
+and here's another fun fact about me
+if you'd like i can learn your voice to
+
+ align:start position:0%
+if you'd like i can learn your voice to
+ 
+
+ align:start position:0%
+if you'd like i can learn your voice to
+do all sorts of neat things like
+
+ align:start position:0%
+do all sorts of neat things like
+ 
+
+ align:start position:0%
+do all sorts of neat things like
+greeting you by name
+
+ align:start position:0%
+greeting you by name
+ 
+
+ align:start position:0%
+greeting you by name
+you'll need your own profile i can
+
+ align:start position:0%
+you'll need your own profile i can
+ 
+
+ align:start position:0%
+you'll need your own profile i can
+create one for you now
+
+ align:start position:0%
+create one for you now
+ 
+
+ align:start position:0%
+create one for you now
+what's your name
+
+ align:start position:0%
+what's your name
+ 
+
+ align:start position:0%
+what's your name
+alexa off
+
+ align:start position:0%
+alexa off
+ 
+
+ align:start position:0%
+alexa off
+i'll create a new profile
+
+ align:start position:0%
+i'll create a new profile
+ 
+
+ align:start position:0%
+i'll create a new profile
+and send information about alexa terms
+
+ align:start position:0%
+and send information about alexa terms
+ 
+
+ align:start position:0%
+and send information about alexa terms
+and our privacy notice to your app
+
+ align:start position:0%
+and our privacy notice to your app
+ 
+
+ align:start position:0%
+and our privacy notice to your app
+should i go ahead and create a profile
+
+ align:start position:0%
+should i go ahead and create a profile
+ 
+
+ align:start position:0%
+should i go ahead and create a profile
+with the name off alexa off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+as illustrated by that that clip
+
+ align:start position:0%
+as illustrated by that that clip
+ 
+
+ align:start position:0%
+as illustrated by that that clip
+kids are growing up
+
+ align:start position:0%
+kids are growing up
+ 
+
+ align:start position:0%
+kids are growing up
+in a time when they will have always
+
+ align:start position:0%
+in a time when they will have always
+ 
+
+ align:start position:0%
+in a time when they will have always
+been able to talk and interact with
+
+ align:start position:0%
+been able to talk and interact with
+ 
+
+ align:start position:0%
+been able to talk and interact with
+intelligent machines and not just you
+
+ align:start position:0%
+intelligent machines and not just you
+ 
+
+ align:start position:0%
+intelligent machines and not just you
+know in this verbal way that we heard in
+
+ align:start position:0%
+know in this verbal way that we heard in
+ 
+
+ align:start position:0%
+know in this verbal way that we heard in
+the clip but
+
+ align:start position:0%
+the clip but
+ 
+
+ align:start position:0%
+the clip but
+hidden ways right so
+
+ align:start position:0%
+hidden ways right so
+ 
+
+ align:start position:0%
+hidden ways right so
+when you're on social media and it's
+
+ align:start position:0%
+when you're on social media and it's
+ 
+
+ align:start position:0%
+when you're on social media and it's
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+learn your kind of what your preferences
+
+ align:start position:0%
+learn your kind of what your preferences
+ 
+
+ align:start position:0%
+learn your kind of what your preferences
+are and giving you recommendations that
+
+ align:start position:0%
+are and giving you recommendations that
+ 
+
+ align:start position:0%
+are and giving you recommendations that
+are not trying to
+
+ align:start position:0%
+are not trying to
+ 
+
+ align:start position:0%
+are not trying to
+broaden your perspective but if anything
+
+ align:start position:0%
+broaden your perspective but if anything
+ 
+
+ align:start position:0%
+broaden your perspective but if anything
+narrow and narrow and narrow narrow
+
+ align:start position:0%
+narrow and narrow and narrow narrow
+ 
+
+ align:start position:0%
+narrow and narrow and narrow narrow
+or you know of course what we're
+
+ align:start position:0%
+or you know of course what we're
+ 
+
+ align:start position:0%
+or you know of course what we're
+learning is what gets your attention
+
+ align:start position:0%
+learning is what gets your attention
+ 
+
+ align:start position:0%
+learning is what gets your attention
+what tends to get shared
+
+ align:start position:0%
+what tends to get shared
+ 
+
+ align:start position:0%
+what tends to get shared
+things that really upset you
+
+ align:start position:0%
+things that really upset you
+ 
+
+ align:start position:0%
+things that really upset you
+you know those are the things that
+
+ align:start position:0%
+you know those are the things that
+ 
+
+ align:start position:0%
+you know those are the things that
+really you know so that's what it tends
+
+ align:start position:0%
+really you know so that's what it tends
+ 
+
+ align:start position:0%
+really you know so that's what it tends
+to feed you
+
+ align:start position:0%
+to feed you
+ 
+
+ align:start position:0%
+to feed you
+surprisingly quickly right you know so
+
+ align:start position:0%
+surprisingly quickly right you know so
+ 
+
+ align:start position:0%
+surprisingly quickly right you know so
+it's important for people of all ages
+
+ align:start position:0%
+it's important for people of all ages
+ 
+
+ align:start position:0%
+it's important for people of all ages
+but i think it's important for kids
+
+ align:start position:0%
+but i think it's important for kids
+ 
+
+ align:start position:0%
+but i think it's important for kids
+because like
+
+ align:start position:0%
+because like
+ 
+
+ align:start position:0%
+because like
+the average age of when kids get their
+
+ align:start position:0%
+the average age of when kids get their
+ 
+
+ align:start position:0%
+the average age of when kids get their
+first smartphone right it's like 10
+
+ align:start position:0%
+first smartphone right it's like 10
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+
+ align:start position:0%
+first smartphone right it's like 10
+years old right
+
+ align:start position:0%
+years old right
+ 
+
+ align:start position:0%
+years old right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+social interaction
+
+ align:start position:0%
+social interaction
+ 
+
+ align:start position:0%
+social interaction
+through technology becomes
+
+ align:start position:0%
+through technology becomes
+ 
+
+ align:start position:0%
+through technology becomes
+such a
+
+ align:start position:0%
+such a
+ 
+
+ align:start position:0%
+such a
+key way
+
+ align:start position:0%
+key way
+ 
+
+ align:start position:0%
+key way
+they interact with each other so the
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+ align:start position:0%
+they interact with each other so the
+ 
+
+ align:start position:0%
+they interact with each other so the
+digital mediated communication is it
+
+ align:start position:0%
+digital mediated communication is it
+ 
+
+ align:start position:0%
+digital mediated communication is it
+just becomes such an important way for
+
+ align:start position:0%
+just becomes such an important way for
+ 
+
+ align:start position:0%
+just becomes such an important way for
+them to
+
+ align:start position:0%
+them to
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+
+ align:start position:0%
+them to
+connect and express themselves
+
+ align:start position:0%
+connect and express themselves
+ 
+
+ align:start position:0%
+connect and express themselves
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+just understanding
+
+ align:start position:0%
+just understanding
+ 
+
+ align:start position:0%
+just understanding
+what's under the hood
+
+ align:start position:0%
+what's under the hood
+ 
+
+ align:start position:0%
+what's under the hood
+how it could be
+
+ align:start position:0%
+how it could be
+ 
+
+ align:start position:0%
+how it could be
+biasing you know shaping
+
+ align:start position:0%
+biasing you know shaping
+ 
+
+ align:start position:0%
+biasing you know shaping
+their attitudes
+
+ align:start position:0%
+their attitudes
+ 
+
+ align:start position:0%
+their attitudes
+potentially shaping behaviors this is
+
+ align:start position:0%
+potentially shaping behaviors this is
+ 
+
+ align:start position:0%
+potentially shaping behaviors this is
+what's really critical and you know and
+
+ align:start position:0%
+what's really critical and you know and
+ 
+
+ align:start position:0%
+what's really critical and you know and
+why who's doing it and why
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+may 13 2022
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+may 13 2022
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+demystifying it as well so
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+ align:start position:0%
+yeah
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+
+ align:start position:0%
+yeah
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+
+ align:start position:0%
+so where can teachers go to sign up and
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+so where can teachers go to sign up and
+is there a fee associated so it's it's
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+ align:start position:0%
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+ align:start position:0%
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+also offer free teacher training you can
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+for a online training session we are
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+ align:start position:0%
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+we are in almost all 50 states now
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+
+ align:start position:0%
+access to ai education
+and they're also informing how we teach
+
+ align:start position:0%
+and they're also informing how we teach
+ 
+
+ align:start position:0%
+and they're also informing how we teach
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+it is an open question still about what
+
+ align:start position:0%
+it is an open question still about what
+ 
+
+ align:start position:0%
+it is an open question still about what
+are the most effective ways of
+
+ align:start position:0%
+are the most effective ways of
+ 
+
+ align:start position:0%
+are the most effective ways of
+educating students at variety of ages
+
+ align:start position:0%
+educating students at variety of ages
+ 
+
+ align:start position:0%
+educating students at variety of ages
+and backgrounds about what artificial
+
+ align:start position:0%
+and backgrounds about what artificial
+ 
+
+ align:start position:0%
+and backgrounds about what artificial
+intelligence is
+
+ align:start position:0%
+intelligence is
+ 
+
+ align:start position:0%
+intelligence is
+and how it works we still have much we
+
+ align:start position:0%
+and how it works we still have much we
+ 
+
+ align:start position:0%
+and how it works we still have much we
+need to understand in terms of what
+
+ align:start position:0%
+need to understand in terms of what
+ 
+
+ align:start position:0%
+need to understand in terms of what
+grades what preparation what concepts
+
+ align:start position:0%
+grades what preparation what concepts
+ 
+
+ align:start position:0%
+grades what preparation what concepts
+how can we demystify
+
+ align:start position:0%
+how can we demystify
+ 
+
+ align:start position:0%
+how can we demystify
+ai and these computational methods in a
+
+ align:start position:0%
+ai and these computational methods in a
+ 
+
+ align:start position:0%
+ai and these computational methods in a
+way that's great and age-appropriate how
+
+ align:start position:0%
+way that's great and age-appropriate how
+ 
+
+ align:start position:0%
+way that's great and age-appropriate how
+we can prepare teachers there's a whole
+
+ align:start position:0%
+we can prepare teachers there's a whole
+ 
+
+ align:start position:0%
+we can prepare teachers there's a whole
+bunch of research questions there what
+
+ align:start position:0%
+bunch of research questions there what
+ 
+
+ align:start position:0%
+bunch of research questions there what
+are the right approaches
+
+ align:start position:0%
+are the right approaches
+ 
+
+ align:start position:0%
+are the right approaches
+methods of professional development for
+
+ align:start position:0%
+methods of professional development for
+ 
+
+ align:start position:0%
+methods of professional development for
+teachers who i mean i can tell you they
+
+ align:start position:0%
+teachers who i mean i can tell you they
+ 
+
+ align:start position:0%
+teachers who i mean i can tell you they
+didn't major in ai
+
+ align:start position:0%
+didn't major in ai
+ 
+
+ align:start position:0%
+didn't major in ai
+in college right so this is new to them
+
+ align:start position:0%
+in college right so this is new to them
+ 
+
+ align:start position:0%
+in college right so this is new to them
+too so how do we do that effectively
+
+ align:start position:0%
+too so how do we do that effectively
+ 
+
+ align:start position:0%
+too so how do we do that effectively
+what are the longer impacts of this in
+
+ align:start position:0%
+what are the longer impacts of this in
+ 
+
+ align:start position:0%
+what are the longer impacts of this in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+attitudes and dispositions that students
+
+ align:start position:0%
+attitudes and dispositions that students
+ 
+
+ align:start position:0%
+attitudes and dispositions that students
+may form about these technologies and
+
+ align:start position:0%
+may form about these technologies and
+ 
+
+ align:start position:0%
+may form about these technologies and
+about kind of themselves and their
+
+ align:start position:0%
+about kind of themselves and their
+ 
+
+ align:start position:0%
+about kind of themselves and their
+relationship to these technologies
+
+ align:start position:0%
+relationship to these technologies
+ 
+
+ align:start position:0%
+relationship to these technologies
+and then as we do this you know how do
+
+ align:start position:0%
+and then as we do this you know how do
+ 
+
+ align:start position:0%
+and then as we do this you know how do
+we again holistically develop the whole
+
+ align:start position:0%
+we again holistically develop the whole
+ 
+
+ align:start position:0%
+we again holistically develop the whole
+person as well so teamwork collaboration
+
+ align:start position:0%
+person as well so teamwork collaboration
+ 
+
+ align:start position:0%
+person as well so teamwork collaboration
+communication critical thinking creative
+
+ align:start position:0%
+communication critical thinking creative
+ 
+
+ align:start position:0%
+communication critical thinking creative
+you know they all are they can all be
+
+ align:start position:0%
+you know they all are they can all be
+ 
+
+ align:start position:0%
+you know they all are they can all be
+kind of woven into this tapestry of how
+
+ align:start position:0%
+kind of woven into this tapestry of how
+ 
+
+ align:start position:0%
+kind of woven into this tapestry of how
+we try to address ai literacy
+
+ align:start position:0%
+we try to address ai literacy
+ 
+
+ align:start position:0%
+we try to address ai literacy
+through positioning students as the
+
+ align:start position:0%
+through positioning students as the
+ 
+
+ align:start position:0%
+through positioning students as the
+designers and creators and makers of the
+
+ align:start position:0%
+designers and creators and makers of the
+ 
+
+ align:start position:0%
+designers and creators and makers of the
+solutions with these technologies
+
+ align:start position:0%
+solutions with these technologies
+ 
+
+ align:start position:0%
+solutions with these technologies
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+design these activities and then we
+
+ align:start position:0%
+design these activities and then we
+ 
+
+ align:start position:0%
+design these activities and then we
+evaluate them right so we will reach out
+
+ align:start position:0%
+evaluate them right so we will reach out
+ 
+
+ align:start position:0%
+evaluate them right so we will reach out
+and recruit
+
+ align:start position:0%
+and recruit
+ 
+
+ align:start position:0%
+and recruit
+students and teachers and we will engage
+
+ align:start position:0%
+students and teachers and we will engage
+ 
+
+ align:start position:0%
+students and teachers and we will engage
+them we often engage in co-design with
+
+ align:start position:0%
+them we often engage in co-design with
+ 
+
+ align:start position:0%
+them we often engage in co-design with
+them so even as we're developing these
+
+ align:start position:0%
+them so even as we're developing these
+ 
+
+ align:start position:0%
+them so even as we're developing these
+materials we will work with teachers and
+
+ align:start position:0%
+materials we will work with teachers and
+ 
+
+ align:start position:0%
+materials we will work with teachers and
+students as we develop them to make sure
+
+ align:start position:0%
+students as we develop them to make sure
+ 
+
+ align:start position:0%
+students as we develop them to make sure
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+they're you know effective in responding
+
+ align:start position:0%
+they're you know effective in responding
+ 
+
+ align:start position:0%
+they're you know effective in responding
+and engaging
+
+ align:start position:0%
+and engaging
+ 
+
+ align:start position:0%
+and engaging
+and then we go do rigorous
+
+ align:start position:0%
+and then we go do rigorous
+ 
+
+ align:start position:0%
+and then we go do rigorous
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+what are they understanding or not
+
+ align:start position:0%
+what are they understanding or not
+ 
+
+ align:start position:0%
+what are they understanding or not
+understanding what is their pathway to
+
+ align:start position:0%
+understanding what is their pathway to
+ 
+
+ align:start position:0%
+understanding what is their pathway to
+understanding and what is the
+
+ align:start position:0%
+understanding and what is the
+ 
+
+ align:start position:0%
+understanding and what is the
+implication of that for how we think
+
+ align:start position:0%
+implication of that for how we think
+ 
+
+ align:start position:0%
+implication of that for how we think
+about staging these concepts and ideas
+
+ align:start position:0%
+about staging these concepts and ideas
+ 
+
+ align:start position:0%
+about staging these concepts and ideas
+are we seeing evidence that they are
+
+ align:start position:0%
+are we seeing evidence that they are
+ 
+
+ align:start position:0%
+are we seeing evidence that they are
+developing dispositions about ai that
+
+ align:start position:0%
+developing dispositions about ai that
+ 
+
+ align:start position:0%
+developing dispositions about ai that
+are empowering for them or do they find
+
+ align:start position:0%
+are empowering for them or do they find
+ 
+
+ align:start position:0%
+are empowering for them or do they find
+it as being intimidating or not for them
+
+ align:start position:0%
+it as being intimidating or not for them
+ 
+
+ align:start position:0%
+it as being intimidating or not for them
+right so there's a lot of questions that
+
+ align:start position:0%
+right so there's a lot of questions that
+ 
+
+ align:start position:0%
+right so there's a lot of questions that
+we're trying to assess
+
+ align:start position:0%
+we're trying to assess
+ 
+
+ align:start position:0%
+we're trying to assess
+and then when we have something we think
+
+ align:start position:0%
+and then when we have something we think
+ 
+
+ align:start position:0%
+and then when we have something we think
+is solid you know then we
+
+ align:start position:0%
+is solid you know then we
+ 
+
+ align:start position:0%
+is solid you know then we
+we make it available for free it's all
+
+ align:start position:0%
+we make it available for free it's all
+ 
+
+ align:start position:0%
+we make it available for free it's all
+creative commons we're like our goal is
+
+ align:start position:0%
+creative commons we're like our goal is
+ 
+
+ align:start position:0%
+creative commons we're like our goal is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+to help empower teachers
+
+ align:start position:0%
+to help empower teachers
+ 
+
+ align:start position:0%
+to help empower teachers
+non-profits you know like get these
+
+ align:start position:0%
+non-profits you know like get these
+ 
+
+ align:start position:0%
+non-profits you know like get these
+materials out there and share them
+
+ align:start position:0%
+materials out there and share them
+ 
+
+ align:start position:0%
+materials out there and share them
+freely
+
+ align:start position:0%
+freely
+ 
+
+ align:start position:0%
+freely
+but again no matter how good robots or
+
+ align:start position:0%
+but again no matter how good robots or
+ 
+
+ align:start position:0%
+but again no matter how good robots or
+ai get
+
+ align:start position:0%
+ai get
+ 
+
+ align:start position:0%
+ai get
+they're no replacement for the real
+
+ align:start position:0%
+they're no replacement for the real
+ 
+
+ align:start position:0%
+they're no replacement for the real
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+i think a lot of ai has assumed when
+
+ align:start position:0%
+i think a lot of ai has assumed when
+ 
+
+ align:start position:0%
+i think a lot of ai has assumed when
+you're trying to build these social and
+
+ align:start position:0%
+you're trying to build these social and
+ 
+
+ align:start position:0%
+you're trying to build these social and
+emotional qualities into technology it's
+
+ align:start position:0%
+emotional qualities into technology it's
+ 
+
+ align:start position:0%
+emotional qualities into technology it's
+about the robot
+
+ align:start position:0%
+about the robot
+ 
+
+ align:start position:0%
+about the robot
+and i'm like no it's about the people
+
+ align:start position:0%
+and i'm like no it's about the people
+ 
+
+ align:start position:0%
+and i'm like no it's about the people
+because this is what people need to
+
+ align:start position:0%
+because this is what people need to
+ 
+
+ align:start position:0%
+because this is what people need to
+engage the more deeply we can engage
+
+ align:start position:0%
+engage the more deeply we can engage
+ 
+
+ align:start position:0%
+engage the more deeply we can engage
+of our holistic self not just our
+
+ align:start position:0%
+of our holistic self not just our
+ 
+
+ align:start position:0%
+of our holistic self not just our
+cognitive selves but our social selves
+
+ align:start position:0%
+cognitive selves but our social selves
+ 
+
+ align:start position:0%
+cognitive selves but our social selves
+our emotional selves our physical self
+
+ align:start position:0%
+our emotional selves our physical self
+ 
+
+ align:start position:0%
+our emotional selves our physical self
+so more deeply we can engage not
+
+ align:start position:0%
+so more deeply we can engage not
+ 
+
+ align:start position:0%
+so more deeply we can engage not
+surprisingly the more successful we are
+
+ align:start position:0%
+surprisingly the more successful we are
+ 
+
+ align:start position:0%
+surprisingly the more successful we are
+the better our outcome so it's to say
+
+ align:start position:0%
+the better our outcome so it's to say
+ 
+
+ align:start position:0%
+the better our outcome so it's to say
+it's not about let's build machines that
+
+ align:start position:0%
+it's not about let's build machines that
+ 
+
+ align:start position:0%
+it's not about let's build machines that
+look like people and act like people
+
+ align:start position:0%
+look like people and act like people
+ 
+
+ align:start position:0%
+look like people and act like people
+it's let's build machines that dovetail
+
+ align:start position:0%
+it's let's build machines that dovetail
+ 
+
+ align:start position:0%
+it's let's build machines that dovetail
+with us in a way that we can bring forth
+
+ align:start position:0%
+with us in a way that we can bring forth
+ 
+
+ align:start position:0%
+with us in a way that we can bring forth
+all of ourselves to help us achieve the
+
+ align:start position:0%
+all of ourselves to help us achieve the
+ 
+
+ align:start position:0%
+all of ourselves to help us achieve the
+goals that are really important to us
+
+ align:start position:0%
+goals that are really important to us
+ 
+
+ align:start position:0%
+goals that are really important to us
+this is why i like when we talk about
+
+ align:start position:0%
+this is why i like when we talk about
+ 
+
+ align:start position:0%
+this is why i like when we talk about
+ai as pedagogical agents right i'm like
+
+ align:start position:0%
+ai as pedagogical agents right i'm like
+ 
+
+ align:start position:0%
+ai as pedagogical agents right i'm like
+we will never get rid of human teachers
+
+ align:start position:0%
+we will never get rid of human teachers
+ 
+
+ align:start position:0%
+we will never get rid of human teachers
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+they are essential for children to know
+
+ align:start position:0%
+they are essential for children to know
+ 
+
+ align:start position:0%
+they are essential for children to know
+that in this community of human beings
+
+ align:start position:0%
+that in this community of human beings
+ 
+
+ align:start position:0%
+that in this community of human beings
+adults
+
+ align:start position:0%
+adults
+ 
+
+ align:start position:0%
+adults
+invest their time
+
+ align:start position:0%
+invest their time
+ 
+
+ align:start position:0%
+invest their time
+in children's learning and development
+
+ align:start position:0%
+in children's learning and development
+ 
+
+ align:start position:0%
+in children's learning and development
+like you matter i'm taking time and
+
+ align:start position:0%
+like you matter i'm taking time and
+ 
+
+ align:start position:0%
+like you matter i'm taking time and
+energy to do this because it's that
+
+ align:start position:0%
+energy to do this because it's that
+ 
+
+ align:start position:0%
+energy to do this because it's that
+important and you are that important
+
+ align:start position:0%
+important and you are that important
+ 
+
+ align:start position:0%
+important and you are that important
+yeah you just can't underestimate that
+
+ align:start position:0%
+yeah you just can't underestimate that
+ 
+
+ align:start position:0%
+yeah you just can't underestimate that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to take part in the day of ai on may
+
+ align:start position:0%
+to take part in the day of ai on may
+ 
+
+ align:start position:0%
+to take part in the day of ai on may
+13th go to
+
+ align:start position:0%
+13th go to
+ 
+
+ align:start position:0%
+13th go to
+dayofai.org
+
+ align:start position:0%
+dayofai.org
+ 
+
+ align:start position:0%
+dayofai.org
+you can access free teacher training and
+
+ align:start position:0%
+you can access free teacher training and
+ 
+
+ align:start position:0%
+you can access free teacher training and
+other creative commons educational
+
+ align:start position:0%
+other creative commons educational
+ 
+
+ align:start position:0%
+other creative commons educational
+materials at raise.mit.edu
+
+ align:start position:0%
+materials at raise.mit.edu
+ 
+
+ align:start position:0%
+materials at raise.mit.edu
+or you can access them through our
+
+ align:start position:0%
+or you can access them through our
+ 
+
+ align:start position:0%
+or you can access them through our
+website at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can also find cynthia's free and
+
+ align:start position:0%
+you can also find cynthia's free and
+ 
+
+ align:start position:0%
+you can also find cynthia's free and
+open teaching materials from our mit
+
+ align:start position:0%
+open teaching materials from our mit
+ 
+
+ align:start position:0%
+open teaching materials from our mit
+courses on our website
+
+ align:start position:0%
+courses on our website
+ 
+
+ align:start position:0%
+courses on our website
+thank you so much for listening
+
+ align:start position:0%
+thank you so much for listening
+ 
+
+ align:start position:0%
+thank you so much for listening
+until next time signing off from a
+
+ align:start position:0%
+until next time signing off from a
+ 
+
+ align:start position:0%
+until next time signing off from a
+galaxy not too far away i'm sarah hansen
+
+ align:start position:0%
+galaxy not too far away i'm sarah hansen
+ 
+
+ align:start position:0%
+galaxy not too far away i'm sarah hansen
+from mit opencourseware
+
+ align:start position:0%
+from mit opencourseware
+ 
+
+ align:start position:0%
+from mit opencourseware
+chalk radio's producers include myself
+
+ align:start position:0%
+chalk radio's producers include myself
+ 
+
+ align:start position:0%
+chalk radio's producers include myself
+red pachy and dave lashansky
+
+ align:start position:0%
+red pachy and dave lashansky
+ 
+
+ align:start position:0%
+red pachy and dave lashansky
+scriptwriting assistance from aubry
+
+ align:start position:0%
+scriptwriting assistance from aubry
+ 
+
+ align:start position:0%
+scriptwriting assistance from aubry
+callaway
+
+ align:start position:0%
+callaway
+ 
+
+ align:start position:0%
+callaway
+show notes for this episode were written
+
+ align:start position:0%
+show notes for this episode were written
+ 
+
+ align:start position:0%
+show notes for this episode were written
+by peter chipman
+
+ align:start position:0%
+by peter chipman
+ 
+
+ align:start position:0%
+by peter chipman
+the rey's online publication was shared
+
+ align:start position:0%
+the rey's online publication was shared
+ 
+
+ align:start position:0%
+the rey's online publication was shared
+on mit open courseware by sharon lin
+
+ align:start position:0%
+on mit open courseware by sharon lin
+ 
+
+ align:start position:0%
+on mit open courseware by sharon lin
+we're funded by mit open learning and
+
+ align:start position:0%
+we're funded by mit open learning and
+ 
+
+ align:start position:0%
+we're funded by mit open learning and
+supporters like you
\ No newline at end of file
diff --git a/GCFd0VVnWTw.txt b/GCFd0VVnWTw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b569aeb36d37cf1f4ccf5a4588af8ea9d2ea97cc
--- /dev/null
+++ b/GCFd0VVnWTw.txt
@@ -0,0 +1,3550 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, let's get started
+again on finite-state
+
+Markov chains.
+
+Sorry I was away last week.
+
+It was a long-term commitment
+that I had to honor.
+
+But I think I will
+be around for all
+
+the rest of the lectures.
+
+So I want to start out by
+reviewing just a little bit.
+
+I'm spending a lot more time on
+finite-state Markov chains
+
+than we usually do in this
+course, partly because I've
+
+rewritten this section, partly
+because I think the material
+
+is very important.
+
+It's sort of bread-and-butter
+stuff, of
+
+discrete stochastic processes.
+
+You use it all the time.
+
+It's a foundation for almost
+everything else.
+
+And after thinking about it
+for a long time, it really
+
+isn't all that complicated.
+
+I used to think that all these
+details of finding eigenvalues
+
+and eigenvectors and so on
+was extremely tedious.
+
+And it turns out that
+there's a very nice
+
+pleasant theory there.
+
+You can find all of these things
+after you know what
+
+you're doing by very simple
+computer packages.
+
+But they don't help if you don't
+know what's going on.
+
+So here, we're trying to figure
+out what's going on.
+
+So let's start out by reviewing
+what we know about
+
+ergodic unit chains and
+proceed from there.
+
+An ergodic finite-state Markov
+chain has transition
+
+probabilities which, if you look
+at the transition matrix
+
+raised to the nth power, what
+that gives you is the
+
+transition probabilities of
+an n-step Markov chain.
+
+In other words, you start at
+time 0, and at time n, you
+
+look at what state you're in.
+
+P sub ij to the nth power is
+then the probability that
+
+you're in state j at time
+n, given that you're in
+
+state i at time 0.
+
+So this has all the information
+that you want
+
+about what happens to Markov
+chain as time gets large.
+
+One of the things we're most
+concerned with is, do you go
+
+to steady state?
+
+And if you do go to steady
+state, how fast do you go to
+
+steady state?
+
+And of course, this matrix
+tells you the whole story
+
+there, because if you go to
+steady state, and the Markov
+
+chain forgets where it started,
+then P sub ij to the
+
+n goes to some constant, pi sub
+j, which is independent of
+
+the starting state, i,
+and independent of m,
+
+asymptotically, as n gets big.
+
+So this pi is a strictly
+positive probability vector.
+
+I shouldn't say so it is.
+
+That's something that
+was shown last time.
+
+If you multiply both sides of
+this equation by P sub jk in
+
+sum over k, then what
+do you get?
+
+You get P sub ik to
+the n plus 1.
+
+That goes to a limit also.
+
+If the limit in n
+goes to infin--
+
+then the limit as n plus 1 goes
+to infinity is clearly
+
+the same thing.
+
+So this quantity here is
+the sum over j, of pi
+
+sub j, P sub jk.
+
+And this quantity is equal to
+pi sub k, just by definition
+
+of this quantity.
+
+So P sub k is equal
+to sum of pi j.
+
+Pjk, what does that say?
+
+That's the definition of
+a steady state vector.
+
+That's the definition of, if
+your probabilities of being in
+
+state k satisfy this equation,
+then one step later, you still
+
+have the same probability
+of being in state k.
+
+Two steps later, you still have
+the same probability of
+
+being in state k.
+
+So this is called the steady
+state equation.
+
+And a solution to that is called
+a steady state vector.
+
+And that satisfies this.
+
+In matrix terms, if you rate
+this out, what does it say?
+
+It says the limit as n
+approaches infinity of p to
+
+the n is equal to the column
+vector, e of all 1s.
+
+The transpose here means
+it's a column vector.
+
+So you have a column vector
+times a row vector.
+
+Now, you know if you have a
+row vector times a column
+
+vector, that just gives
+you a number.
+
+If you have a column
+vector times a row
+
+vector, what happens?
+
+Well, for each element
+of the column, you
+
+get this whole row.
+
+And for the next element of the
+column, you get the whole
+
+row down beneath it multiplied
+by the element of the column,
+
+and so forth, day on.
+
+So a column vector times
+a row vector is, in
+
+fact, a whole matrix.
+
+It's a j by j matrix.
+
+And since e is all 1s, what
+that matrix is is a matrix
+
+where every row is a steady
+state vector pi.
+
+So we're saying not only does
+this pi that we're talking
+
+about satisfy this steady
+state equation, but more
+
+important, it's this limiting
+vector here.
+
+And as n goes to infinity,
+you in fact do
+
+forget where you were.
+
+And the entire matrix of where
+you are at time n, given where
+
+you were at time 0, goes to
+just this fixed vector pi.
+
+So this is a column vector, and
+pi is a row vector then.
+
+The same result almost holds
+for ergodic unit chains.
+
+What's an ergodic unit chain?
+
+An ergodic unit chain is an
+ergodic set of states plus a
+
+whole bunch of transient
+states.
+
+Doesn't matter whether the
+transient states are one class
+
+of transient states or whether
+it's multiple classes of
+
+transient states.
+
+It's just transient states.
+
+And there's one recurrent
+class.
+
+And we're assuming here
+that it's recurrent.
+
+So you can almost see
+intuitively that if you start
+
+out in any one of these
+transient states, you bum
+
+around through the transient
+states for a while.
+
+And eventually, you flop off
+into the recurrent class.
+
+And once you're in
+the recurrent
+
+class, there's no return.
+
+So you stay there forever.
+
+Now, that's something that
+has to be proven.
+
+And it's proven in the notes.
+
+It was probably proven
+last time.
+
+But anyway, what happens then
+is that the sole difference
+
+between ergodic unit chains and
+just having a completely
+
+ergodic Markov chain is that the
+steady state factor is now
+
+positive for all ergodic states
+and it's 0 for all
+
+transient states.
+
+And aside from that, you still
+get the same behavior still.
+
+As n gets large, you go to the
+steady state vector, which is
+
+the steady state vector
+of the ergodic chain.
+
+If you're doing this stuff by
+hand, how do you do it?
+
+Well, you start out just
+with the ergodic class.
+
+I mean, you might as well
+ignore everything else,
+
+because you know that eventually
+you're in that
+
+ergodic class.
+
+And you find the steady state
+vector in that ergodic class,
+
+and that's the steady
+state vector you're
+
+going to wind up with.
+
+This is one advantage of
+understanding what you're
+
+doing, because if you don't
+understand what you're doing
+
+and you're just using computer
+programs, then you never have
+
+any idea what's ergodic,
+what's not
+
+ergodic or anything else.
+
+You just plug it, you grind
+away, you get some answer and
+
+say, ah, I'll publish a paper.
+
+And you put down exactly what
+the computer says, but you
+
+have no interpretation
+of it at all.
+
+So the other way of looking at
+this is, when you have a bunch
+
+of transient states, and you
+also have an ergodic class,
+
+you can represent a matrix if
+the recurrent states are at
+
+the end of the chain and the
+transient states are at the
+
+beginning of the chain.
+
+This matrix here is the matrix
+of transition probabilities
+
+within the recurrent class.
+
+These are the probabilities for
+going from the transient
+
+states to the recurrent class.
+
+And once you get over
+here, the only place
+
+to go is down here.
+
+And the transient class is
+just a t by t class.
+
+And the recurrent class
+is just a j minus t
+
+by j minus t matrix.
+
+So the idea is that each
+transient state eventually has
+
+a transition to a recurrent
+state, and the class of
+
+recurrent states leads to
+study state as before.
+
+So that really, all that
+analysis of ergodic unit
+
+chains, if you look at it
+intuitively, it's all obvious.
+
+Now, as in much of mathematics,
+knowing that
+
+something is obvious does not
+relieve you of the need to
+
+prove it, because sometimes you
+find that something that
+
+looks obvious is true
+most of the time but
+
+not all of the time.
+
+And that's the purpose of
+doing these things.
+
+There's another way to express
+this eigenvalue, eigenvector
+
+equation we have here.
+
+And that is that the transition
+matrix minus lambda
+
+times the identity matrix times
+the column vector v is
+
+equal to 0.
+
+That's the same as the equation
+p times v is equal to
+
+v. That's the same as
+a right eigenvector.
+
+Well, this is the equation
+for an eigenvalue 1.
+
+This is an equation for an
+arbitrary eigenvalue lambda.
+
+But p times v equals lambda
+times v is the same as p minus
+
+lambda i times v equals 0.
+
+Why do we even bother to say
+something so obvious?
+
+Well, because when you look at
+linear algebra, how many of
+
+you have never studied any
+linear algebra at all or have
+
+only studied completely
+mathematical linear algebra,
+
+where you never deal with
+n-tuples as vectors or
+
+matrices or any things
+like this?
+
+Is there anyone?
+
+If you don't have this
+background, pick up--
+
+what's his name?
+
+AUDIENCE: Strang.
+
+PROFESSOR: Strang.
+
+Strang's book.
+
+It's a remarkably simple-minded
+book which says
+
+everything as clearly
+as it can be stated.
+
+And it tells you everything
+you have to know.
+
+And it does it in a very
+straightforward way.
+
+So I highly recommend it to get
+any of the background that
+
+you might need.
+
+Most of you, I'm sure, are very
+
+familiar with these things.
+
+So I'm just reminding
+you of then.
+
+Now, a square matrix is singular
+if there's a vector
+
+v, such that a times
+v is equal to 0.
+
+That's just a definition
+as a singularity.
+
+Now, lambda is an eigenvalue of
+a matrix p if and only if p
+
+minus lambda times
+i is singular.
+
+In other words, if there's
+some v for which p minus
+
+lambda i times v is equal to
+0, that's what this says.
+
+You put p minus lambda i in
+for a, and it says it's
+
+singular if there's some v
+for which this matrix--
+
+this matrix is singular if
+there's some v such that p
+
+minus lambda i times
+v is equal to 0.
+
+So let a1 to am be
+the columns of a.
+
+Then a is going to be
+singular if a1 to am
+
+are linearly dependent.
+
+In other words, if there's some
+set of coefficients you
+
+can attach to a1 times v1 plus
+a2 times v2, plus up to am
+
+times vm such that that sum is
+equal to 0, that means that a1
+
+to am are linearly dependent.
+
+It also means that the matrix a
+times that v is equal to 0.
+
+So those two things say
+the same thing again.
+
+So the square matrix, a, is
+singular if and only if the
+
+rows of a are linearly
+independent.
+
+We set columns here.
+
+Here, we're doing the
+same thing for rows.
+
+It still holds true.
+
+And one new thing, if and only
+if the determinant of a is
+
+equal to 0.
+
+One of the nice things about
+determinants is that
+
+determinants are 0 if the matrix
+is singular, if and
+
+only if the matrix
+is singular.
+
+So the summary of all of this
+for a matrix which is a
+
+transition matrix--
+
+namely, a stochastic matrix--
+
+is lambda, is an eigenvalue of
+p, if and only if p minus
+
+lambda i is singular, if and
+only if the determinant of p
+
+minus lambda i is equal to 0,
+if and only if p times some
+
+vector v equals lambda v, and
+if and only if u times p
+
+equals lambda u for some u.
+
+Yes?
+
+AUDIENCE: The second to last
+statement is actually linearly
+
+independent, you said?
+
+The second to last.
+
+Square matrix a.
+
+No, above that.
+
+PROFESSOR: Oh, above that.
+
+A square matrix a is singular
+if and only if the rows of a
+
+are linearly dependent, yes.
+
+AUDIENCE: Dependent.
+
+PROFESSOR: Dependent, yes.
+
+In other words, if there's
+some vector v such that a
+
+times v is equal to 0, that
+means that those columns are
+
+linearly dependent.
+
+So we need all of those
+relationships.
+
+It says for every stochastic
+matrix--
+
+oh, now this is something new.
+
+For every stochastic matrix,
+P times e is equal to e.
+
+Obviously, because if you sum
+up the sum of Pij over j is
+
+equal to 1.
+
+P sub ij is the probability,
+given that you start in state
+
+i, that in the next step,
+you'll be in state j.
+
+You have to be somewhere
+in the next step.
+
+So if you sum these quantities
+up, you have to get 1, which
+
+says you have to
+be some place.
+
+So that's all this is saying.
+
+That's true for every
+finite-state Markov chain in
+
+the world, no matter how ugly
+it is, how many sets of
+
+recurrent states it has, how
+much periodicity it has.
+
+A complete generality, P
+times e is equal to e.
+
+So lambda is always an
+eigenvalue of a stochastic
+
+matrix, and e is always
+a right eigenvector.
+
+Well, from what we've just said,
+that means there has to
+
+be a left eigenvector also.
+
+So there has to be some
+pi such that pi times
+
+P is equal to pi.
+
+So suddenly, we find there's
+also a left eigenvector.
+
+What we haven't shown yet is
+that that pi that satisfies
+
+this equation is a probability
+vector.
+
+Namely, we haven't shown that
+all the components of pi are
+
+greater than or equal to 0.
+
+We still have to do that.
+
+And in fact, that's not
+completely trivial.
+
+If we can find such a vector
+that is a probability vector,
+
+the compound in sum to 1 and
+they're not negative, then
+
+this is the equation for
+a steady state vector.
+
+So what we don't know yet
+is whether a steady
+
+state vector exists.
+
+We do know that a left
+eigenvector exists.
+
+We're going to show later
+that there is a steady
+
+state vector pi.
+
+In other words, a non-negative
+vector which sums to 1 for all
+
+finite-state Markov chains.
+
+In other words, no matter how
+messy it is, just like e, the
+
+column vector of all 1s is
+always a right eigenvector of
+
+eigenvalue 1.
+
+There is always a non-negative
+vector pi whose components sum
+
+to 1, which is a left
+eigenvector with eigenvalue 1.
+
+So these two relationships
+hold everywhere.
+
+Incidentally, the notes
+at one point claim
+
+to have shown this.
+
+And the notes really
+don't show it.
+
+I'm going to show
+it to you today.
+
+I'm sorry for that.
+
+It's something I've known for so
+long that I find it hard to
+
+say is this true or not.
+
+Of course it's true.
+
+But it does have to be shown,
+and I will show it
+
+to you later on.
+
+Chapter three of the notes is
+largely rewritten this year.
+
+And it has a few more typos
+in it than most
+
+of the other chapters.
+
+And a few of the typos
+are fairly important.
+
+I'll try to point some
+of them out as we go.
+
+But I'm sure I haven't
+caught them all yet.
+
+Now, what is the determinant
+of an M by M matrix?
+
+It's this very simple-looking
+but rather messy formula,
+
+which says the determinant of
+a square matrix A is the sum
+
+over all partitions--
+
+and then there's a plus
+minus here, which
+
+I'll talk about later--
+
+of the product from i equals
+1 to M. M is the number of
+
+states of A sub i.
+
+This is the component
+of the ij position.
+
+And we're taking A sub i.
+
+And then the partition that
+we're dealing with, mu sub i.
+
+So what we're doing is taking
+a matrix with all sorts of
+
+terms in it--
+
+A11 up to A1j on to Aj1
+up to A sub jj.
+
+And these partitions we're
+talking about are ways of
+
+selecting one element from each
+row and one element from
+
+each column.
+
+Namely, that first sum there is
+talking about one element
+
+from each row.
+
+And then when we're talking
+about a permutation here,
+
+we're doing something like, for
+this row, we're looking
+
+at, say, this element.
+
+For this row, we might be
+looking at this element.
+
+For this row, we might be
+looking at this element, and
+
+so forth down, until finally,
+we're looking at some
+
+element down here.
+
+Now, we've picked out every
+column and every row in doing
+
+this, but we only have one
+element in each row and one
+
+element in each column.
+
+If you've studied linear algebra
+and you're at all
+
+interested in computation, the
+first thing that everybody
+
+tells you is that this is a
+god-awful way to ever compute
+
+a determinant, because the
+number of permutations grows
+
+very, very fast with the
+size of the matrix.
+
+And therefore you don't
+want to use this
+
+formula very often.
+
+It's a very useful formula
+conceptually, though, because
+
+if we look at the determinant
+of p minus lambda i, if we
+
+want to ask the question, how
+many eigenvalues does this
+
+transition matrix have?
+
+well, the number of eigenvalues
+it has is the
+
+number of values of lambda such
+that the determinant of p
+
+minus lambda i is 0.
+
+Now, how many such
+values are there?
+
+Well, you look the matrix for
+that, and you get A11 minus
+
+lambda A12 and A22 minus lambda
+Ajj minus lambda.
+
+And none of the other elements
+have lambda in it.
+
+So when you're looking at this
+formula for finding the
+
+determinant, one of the
+partitions is this partition,
+
+which is a polynomial of
+degree j in lambda.
+
+All of the others are
+polynomials of degree less
+
+than j in lambda.
+
+And therefore this whole
+bloody mess here is a
+
+polynomial of degree
+j and lambda.
+
+So the equation, determinant of
+p minus lambda i, which is
+
+a polynomial of degree j
+in lambda, equals 0.
+
+How many roots does it have?
+
+Well, the fundamental theorem
+of algebra says that a
+
+polynomial of degree j,
+of complex numbers--
+
+and real is a special
+case of complex--
+
+that it has exactly j roots.
+
+So there are exactly,
+in this case, M--
+
+excuse me, I've been
+calling it j
+
+sometimes and M sometimes.
+
+This equation here has exactly
+M roots to it.
+
+And since it has exactly M
+roots, that's the number of
+
+eigenvalues there are.
+
+There's one flaw in
+that argument.
+
+And that is, some of the roots
+might be repeated.
+
+Say you have M roots
+altogether.
+
+Some of them appear more than
+one time, so you'll have roots
+
+of multiplicity, something
+or other.
+
+And when you add up the
+multiplicities of each of the
+
+distinct eigenvalues, you
+get capital M, which is
+
+the number of states.
+
+So the number of different
+eigenvalues is less than or
+
+equal to M. And the number of
+distinct eigenvalues times the
+
+multiplicity of each eigenvalue
+is equal to M.
+
+That's a simple, straightforward
+fact.
+
+And it's worth remembering.
+
+So there are M roots
+to the equation.
+
+Determinant p minus
+lambda i equals 0.
+
+And therefore there are
+M eigenvalues of p.
+
+And therefore you might think
+that there are M eigenvectors.
+
+That, unfortunately, is
+not true necessarily.
+
+That's one of the really--
+
+it's probably the only really
+ugly thing in linear algebra.
+
+I mean, linear algebra is
+a beautiful theory.
+
+I mean, it's like Poisson's
+stochastic processes.
+
+Everything that can
+be true is true.
+
+And if something isn't true,
+there's a simple
+
+counter-example of why
+it can't be true.
+
+This thing is just
+a bloody mess.
+
+But unfortunately, if you have
+M states in a finite-state
+
+Markov chain, you might not have
+M different eigenvectors.
+
+And that's unfortunate, but we
+will forget about that for as
+
+long as we can, and we'll
+finally come back to it
+
+towards the end.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: What?
+
+AUDIENCE: Why would we care
+about all the eigenvectors if
+
+we are only concerned with the
+ones that [INAUDIBLE]?
+
+PROFESSOR: Well, because we're
+interested in the other ones
+
+because that tells us how fast
+p to the M converges to what
+
+it should be.
+
+I mean, all those other
+eigenvalues, as we'll see, are
+
+the error terms in p to the
+M as it approaches this
+
+asymptotic value.
+
+And therefore we want to know
+what those eigenvalues are.
+
+At least we want to
+know what the
+
+second-biggest eigenvalue is.
+
+Now, let's look at just
+a case of two states.
+
+Most of the things that can
+happen will happen with two
+
+states, except for this ugly
+thing that I told you about
+
+that can't happen
+with two states.
+
+And therefore two states is a
+good thing to look at, because
+
+with two states, you can
+calculate everything very
+
+easily and you don't have to
+use any linear algebra.
+
+So if we look at a Markov chain
+with two states, P sub
+
+ij is this set of transition
+probabilities.
+
+The left eigenvector equation
+is pi 1 times P11 times pi 2
+
+times P21 is equal
+to lambda pi 1.
+
+And so this is writing out
+what we said before.
+
+The vector pi times the matrix
+P is equal to lambda
+
+times the vector pi.
+
+That covers both of
+these equations.
+
+Since M is only 2,
+we only have to
+
+write things out twice.
+
+Same thing for the right
+eigenvector equation.
+
+That's this.
+
+The determinant of P minus
+lambda i, if we use this
+
+formula that we talked about
+here, you put A11 minus
+
+lambda, A22 minus lambda.
+
+Well, then you're done.
+
+So all you need is P11 minus
+lambda times P22 minus lambda.
+
+That's this permutation there.
+
+And then you have an odd
+permutation, A12 times A21.
+
+How do you know which
+permutations are even and
+
+which permutations are odd?
+
+It's how many flips
+you have to do.
+
+But to see that that's
+consistent, you really have to
+
+look at Strang or some book on
+linear algebra, because it's
+
+not relevant here.
+
+But anyway, that determinant
+is equal to
+
+this quantity here.
+
+That's a polynomial of
+degree 2 in lambda.
+
+If you solve it, you find
+out that one solution is
+
+lambda 1 equals 1.
+
+The other solution is lambda
+2 is 1 minus P12 minus P21.
+
+Now, there are a bunch of
+cases to look at here.
+
+If the off-diagonal transition
+probabilities are both 0, what
+
+does that mean?
+
+It means if you start in state
+0, you stay there.
+
+If you start in state 1,
+you stay there forever.
+
+If you start in state 2,
+you stay there forever.
+
+That's a very boring Markov
+chain, but it's not very nice
+
+for the theory.
+
+So we're going to leave that
+case out for the time being.
+
+But anyway, if you have that
+case, then the chain has two
+
+recurrent classes.
+
+Lambda equals 1, has
+multiplicity 2.
+
+You have two eigenvalues of
+algebraic multiplicity 2.
+
+I mean, it's just one number,
+but it appears twice in this
+
+determinant equation.
+
+And it also appears twice in
+the sense that you have two
+
+recurrent classes.
+
+And you will find that there are
+two linearly independent
+
+left eigenvectors, two linearly
+independent right
+
+eigenvectors.
+
+And how do you find those?
+
+You use your common sense and
+you say, well, if you start in
+
+state 1, you're always there.
+
+If you start in state 2,
+you're always there.
+
+Why do I even look at
+these two states?
+
+This is a crazy thing where
+wherever I start, I stay there
+
+and I only look at state
+1 or state 2.
+
+It's scarcely even
+a Markov chain.
+
+If P12 and P21 are both 1, what
+it means is you can never
+
+go from state 1 to state 1.
+
+You always go from state
+1 to state 2.
+
+And you always go from
+state 2 to state 1.
+
+It means you have a two-state
+periodic chain.
+
+And that's the other
+crazy case.
+
+The other case is not
+very interesting.
+
+There's nothing stochastic
+about it at all.
+
+So the chain is periodic.
+
+And if you look at this equation
+here, the second
+
+eigenvalue is equal
+to minus 1.
+
+I might as well tell you that,
+in general, if you have a
+
+periodic Markov chain, just one
+recurrent class and it's
+
+periodic, a period d, then the
+eigenvalues turn out to be the
+
+uniformly spaced eigenvalues
+around the unit circle.
+
+One is one of the eigenvalues.
+
+We've already seen that.
+
+And the other d minus 1
+eigenvalues are those
+
+uniformly spaced around
+the unit circle.
+
+So they add up to 360 degrees
+when you get all done with it.
+
+So that's an easy case.
+
+Proving that is tedious.
+
+It's done in the notes.
+
+It's not even done
+in the notes.
+
+It's done in one of
+the exercises.
+
+And you can do it
+if you choose.
+
+So let's look at these
+eigenvector equations and the
+
+eigenvalue equations.
+
+Incidentally, if you don't know
+what the eigenvalues are,
+
+is this a linear set
+of equations?
+
+No, it's a nonlinear
+set of equations.
+
+This is a nonlinear set
+of equations in pi
+
+1, pi 2, and lambda.
+
+How do you solve non-linear
+equations like that?
+
+Well, if you have much sense,
+you first find out what lambda
+
+is and then you solve
+linear equations.
+
+And you can always do that.
+
+We've said that these solutions
+for lambda, there
+
+can only be M of them.
+
+And you can find
+them by solving
+
+this polynomial equation.
+
+Then you can solve the linear
+equation by finding the
+
+eigenvectors.
+
+There are packages to do all
+of these things, so there's
+
+nothing you should waste
+time on doing here.
+
+It's just knowing what the
+results are that's important.
+
+From now on, I'm going to assume
+that P12 or P21 are
+
+greater than 0.
+
+In other words, I'm going to
+assume that we don't have the
+
+periodic case and we don't have
+the case where you have
+
+two classes of states.
+
+In other words, I'm going to
+assume that our Markov chain
+
+is actually ergodic.
+
+That's the assumption that
+I'm making here.
+
+If you then solve these
+equations using lambda 1
+
+equals 1, you'll find
+out that pi 1 is the
+
+component sum to 1.
+
+First component is
+P21 over the sum.
+
+Second component is
+P12 over the sum.
+
+Not very interesting.
+
+Why is the steady state
+probability weighted towards
+
+the largest of these transition
+probabilities?
+
+If P21 is bigger than P12, how
+do you know intuitively that
+
+you're going to be in state 1
+more than you're in state 2?
+
+Is this intuitively
+obvious to-- yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Because you make more
+transistors from 2 to 1.
+
+Well, actually you don't make
+more transitions from 2 to 1.
+
+You make exactly the same number
+of transitions, but
+
+since the probability is higher,
+it means you have to
+
+be in state 1 more
+of the time.
+
+Good.
+
+So these are the two.
+
+And this is the left eigenvector
+for the second
+
+eigenvalue--
+
+namely, the smaller
+eigenvalue.
+
+Now, if you look at these
+equations, you'll notice that
+
+the vector pi, the left i-th
+eigenvector, multiplied by the
+
+right j-th eigenvector, is
+always equal to delta ij.
+
+In other words, the left
+eigenvectors are orthogonal to
+
+the right eigenvectors.
+
+I mean, you can see this just
+by multiplying it out.
+
+You multiply pi 1 times nu
+1, and what do you get?
+
+You get this plus this,
+which is 1.
+
+Delta 11 means there's something
+which is 1 when i is
+
+equal j and 0 when i
+is unequal to j.
+
+You take this and you
+multiply it by this,
+
+and what do you get?
+
+You get P21 times P12
+over the square.
+
+Minus P12 times P21, it's 0.
+
+Same thing here.
+
+1 minus 1, that vector times
+this vector, is 0 again.
+
+So the cross-terms are 0.
+
+The diagonal terms are 1.
+
+That's the way it is.
+
+So let's move on with this.
+
+These right eigenvector
+equations, you can write them
+
+in matrix form.
+
+I'm doing this slowly.
+
+I hope I'm not boring those who
+have done a lot of linear
+
+algebra too much.
+
+But they won't go on forever,
+and it gets us to where we
+
+want to go.
+
+So if you take these two
+equations and you write them
+
+in matrix form, what you get
+is P times u, where u is a
+
+matrix whose columns are
+the vector nu 1 and
+
+the vector nu 2.
+
+And capital lambda is the
+diagonal matrix of the
+
+eigenvalues.
+
+If you multiply P times the
+first column of u, and then
+
+you look at the first column of
+this matrix, what you get--
+
+yes, that's exactly the
+right way to do it.
+
+And if you're not doing that,
+you're probably not
+
+understanding it.
+
+But if you just think of
+ordinary matrix vector
+
+multiplication, this
+all works out.
+
+Because of this orthogonality
+relationship, we see that the
+
+matrix whose rows are the left
+eigenvectors times the matrix
+
+whose columns are the
+right eigenvectors,
+
+that's equal to i.
+
+Namely, it's equal to
+the identity matrix.
+
+That's what this orthogonality
+relationship means.
+
+This means that this matrix is
+the inverse of this matrix.
+
+This proves that u
+is invertible.
+
+And in fact, we've done this
+just for m equals 2.
+
+But in fact, this proof is
+general and holds for
+
+arbitrary Markov chains if the
+eigenvectors span the space.
+
+And we'll see that later.
+
+We're doing this for m equals
+2 now, so we how to proceed
+
+when we have an arbitrary
+Markov chain.
+
+u is invertible.
+
+u to the minus 1 has pi
+1 and pi 2 as rows.
+
+And thus P is going
+to be equal to--
+
+I guess we should--
+
+oh, we set it up here.
+
+P times u is equal to
+u times lambda.
+
+We've shown here that u is
+invertible, therefore we can
+
+multiply this equation
+by u to the minus 1.
+
+And we get the transition matrix
+P is equal to u times
+
+the diagonal matrix lambda
+times the matrix u
+
+to the minus 1.
+
+What happens if we try
+to find P squared?
+
+Well, it's u times lambda
+times u to the minus 1.
+
+One of the nice things about
+matrices is you can multiply
+
+them, if you don't
+worry about the
+
+details, almost like numbers.
+
+Times u times lambda times
+u to the minus 1.
+
+Except you don't have
+commutativity.
+
+That's the only thing
+that you don't have.
+
+But anyway, you have u times
+lambda times u to the minus 1
+
+times u times lambda times
+u to t he minus 1.
+
+This and this turn out to be
+the identity matrix, so you
+
+have u times lambda times
+lambda, which is lambda
+
+squared, times u
+to the minus 1.
+
+You still have this diagonal
+matrix here, but the
+
+eigenvalues have all
+been doubled.
+
+If you keep doing that
+repeatedly, you find out that
+
+P to the n-- namely, this
+long-term transition matrix,
+
+which is the thing we're
+interested in--
+
+is the matrix u times this
+diagonal matrix, lambda to the
+
+n, times u to the minus 1.
+
+Equation 329 in the text has a
+typo, and it should be this.
+
+It's given as u to the minus 1
+times lambda to the n times u,
+
+which is not at all right.
+
+That's probably the worst typo,
+because if you try to
+
+say something from that, you'll
+get very confused.
+
+You can solve one in general if
+all the M eigenvalues are
+
+distinct as easily as
+for M equals 2.
+
+This is still valid
+so long as the
+
+eigenvectors span the space.
+
+So now the thing we want to
+do is relatively simple.
+
+This lambda to the n is
+a diagonal matrix.
+
+I can represent it as the sum
+of M different matrices.
+
+And each of those matrices
+has only one
+
+diagonal element, non-0.
+
+In other words, for the case
+here, what we're doing is
+
+taking lambda 1, 0 to the n,
+0 lambda 2 to the n, and
+
+representing this as lambda 1 to
+the n, 0, 0, 0, plus 0, 0,
+
+0 lambda 2 to the n.
+
+So we have those trivial
+matrices with u on the left
+
+side and u to the minus
+1 on the right side.
+
+And we think of how to multiply
+the matrix u, which
+
+is a matrix whose columns are
+the eigenvectors, times this
+
+matrix with only one non-0
+element, times the matrix
+
+here, whose elements are
+the left eigenvectors.
+
+And how do you do that?
+
+Well, if you do this for a
+while, and you think of what
+
+this one element here times
+a matrix whose rows are
+
+eigenvectors does, this non-0
+term in here picks out the
+
+appropriate row here.
+
+And this non-0 element
+picks out the
+
+appropriate column here.
+
+So what that gives you is p to
+the n is equal to the sum over
+
+the number of states in the
+Markov chain times lambda sub
+
+i-- the i-th value to
+the nth power--
+
+times nu to the i times
+pi to the i.
+
+pi to the i is the i-th
+eigenvector of p.
+
+nu to the i is the i-th right
+eigenvector of p.
+
+They have nothing
+to do with n.
+
+The only thing that n affects
+is this eigenvalue here.
+
+And what this is saying is that
+p to the n is just the
+
+sum of eigenvalues which are,
+if lambda is bigger than 1,
+
+this is exploding.
+
+If lambda 1 is less than
+1, it's going to 0.
+
+And if lambda 1 is equal to
+1, it's staying constant.
+
+If lambda 1 is complex but has
+magnitude 1, then it's just
+
+gradually rotating around and
+not doing much of interest at
+
+all, but it's going away.
+
+So that's what this
+equation means.
+
+It says that we've converted the
+problem of finding the nth
+
+power of p just to this problem
+of finding the nth
+
+power of these eigenvalues.
+
+So we've made some
+real progress.
+
+AUDIENCE: Professor, what
+is nu i right here?
+
+PROFESSOR: What?
+
+AUDIENCE: What is nu i?
+
+PROFESSOR: nu sub i is the i-th
+of the right eigenvectors
+
+of the matrix p.
+
+AUDIENCE: And pi i?
+
+PROFESSOR: And pi i is the
+i-th left eigenvector.
+
+And what we've shown is that
+these are orthogonal to each
+
+other, orthonormal.
+
+AUDIENCE: Can you please say
+again what happens when lambda
+
+is complex?
+
+PROFESSOR: What?
+
+AUDIENCE: When lambda is
+complex, what exactly happens?
+
+PROFESSOR: Oh, if lambda i is
+complex and the magnitude is
+
+less than 1, it just
+dies away.
+
+if the magnitude is bigger than
+1, it explodes, which
+
+will be very strange.
+
+And we'll see that
+can't happen.
+
+And if the magnitude is 1, as
+you take powers of a complex
+
+number of magnitude 1, I mean,
+it start out here, it goes
+
+here, then here.
+
+I mean, it just rotates around
+in some crazy way.
+
+But it maintains its magnitude
+as being equal
+
+to 1 all the time.
+
+So this is just repeating
+what we had before.
+
+These are the eigenvectors.
+
+If you calculate this very
+quickly using this and this,
+
+and if you recognize that the
+right eigenvector, nu 2, is
+
+the first part of it is pi sub
+2, the second part of it minus
+
+pi sub 1, where pi is just this
+first eigenvector here.
+
+So if you do this
+multiplication, you find that
+
+nu to the 1--
+
+oh, I thought I had all
+of these things out.
+
+This should be nu.
+
+The first right eigenvector
+times the first left
+
+eigenvector.
+
+Oh, but this is all right,
+because I'm saying the first
+
+left eigenvector is a steady
+state vector, which is the
+
+thing we're interested in.
+
+That's pi 1, pi 2, pi 1,
+pi 2, where pi 1 is
+
+this and pi 2 is this.
+
+nu 2 times pi 2 is just this.
+
+So when we calculate p sub n,
+we get pi 1 plus pi 2 times
+
+this eigenvalue to
+the nth power.
+
+Pi 1 minus pi 1, lambda
+2 to the nth power.
+
+pi 2 and pi 2 is what we get
+for the main eigenvalue.
+
+This is what we get for
+the little eigenvalue.
+
+This little eigenvalue here is
+1 minus P12 minus P21, which
+
+has magnitude less than 1,
+unless we either have the
+
+situation where P12 is equal to
+P21 is equal to 0, or both
+
+of them are 1.
+
+So these are the terms
+that go to 0.
+
+This solution is exact.
+
+There were no approximations
+in here.
+
+Before, when we analyzed what
+happened to P to the n, we saw
+
+that we converged, but
+we didn't really
+
+see how fast we converged.
+
+Now we know how fast
+we converge.
+
+The rate of convergence is
+the value of this second
+
+eigenvalue here.
+
+And that's a pretty
+general result.
+
+You converged like the
+second-largest eigenvalue.
+
+And we'll see how
+that works out.
+
+Now, let's go on to the case
+where you have an arbitrary
+
+number of states.
+
+We've almost solved that
+already, because as we were
+
+looking at the case with two
+states, we were doing most of
+
+the things in general.
+
+If you have an n state Markov
+chain, a determinant of P
+
+minus lambda is a polynomial
+of degree M in lambda.
+
+That was what we said
+a while ago.
+
+It has M roots, eigenvalues.
+
+And here, we're going to assume
+that those roots are
+
+all distinct.
+
+So we don't have to worry
+about what happens with
+
+repeated roots.
+
+Each eigenvalue lambda sub i--
+there are M of them now--
+
+has a right eigenvector,
+nu sub i, and a left
+
+eigenvector, pi sub i.
+
+And we have seen that--
+
+well, we haven't seen it yet.
+
+We're going to show
+it in a second.
+
+pi super i times nu super
+j is equal to j for each
+
+ij unequal to i.
+
+If you scale either this or
+that, when you saw this
+
+eigenvector equation, you have
+a pi on both sides or a nu on
+
+both sides, and you have a scale
+factor which can't be
+
+determined from the eigenvector
+equation.
+
+So you have to choose that
+scaling factor somehow.
+
+If we choose the scaling factor
+appropriately, we get
+
+pi, the i-th left eigenvector,
+times the i-th right
+
+eigenvector.
+
+This is just a number now.
+
+It's that times that.
+
+We can scale things, so
+that's equal to 1.
+
+Then as before, let u be the
+matrix with columns nu 1 to nu
+
+M, and let v have the rows, pi
+1 to pi M. Because of this
+
+orthogonality relationship we've
+set up, v times u is
+
+equal to i.
+
+So again, the left eigenvector
+rows forms a matrix which is
+
+the inverse of the right
+eigenvector columns.
+
+So that says v is equal
+to u to the minus 1.
+
+Thus the eigenvector is nu, the
+first right eigenvector up
+
+to the nth right eigenvector,
+these are linearly
+
+independent.
+
+And they span M space.
+
+That's a very peculiar
+thing we've done.
+
+We've said we have all these
+M right eigenvectors.
+
+We don't know anything about
+them, but what we do know is
+
+we also have M left
+eigenvectors.
+
+And the left eigenvectors, as
+we're going to show in just a
+
+second, are orthogonal to
+the right eigenvectors.
+
+And therefore, when we look at
+these two matrices, we can
+
+multiply them and get
+the identity matrix.
+
+And that means that the right
+eigenvectors have to be--
+
+when we look at the matrix of
+the right eigenvectors, is
+
+non-singular.
+
+Very, very peculiar argument.
+
+I mean, we find out that those
+right eigenvectors span the
+
+space, not by looking at the
+right eigenvectors, but by
+
+looking at how they relate
+to the left eigenvectors.
+
+But anyway, that's perfectly
+all right.
+
+And so long as we can show
+that we can satisfy this
+
+orthogonality condition, then in
+fact all this works out. v
+
+is equal to u to the minus 1.
+
+These eigenvectors are linearly
+independent and they
+
+span M space.
+
+Same here.
+
+And putting these equations
+together, P times u equals u
+
+times lambda.
+
+This is exactly what
+we did before.
+
+Post-multiplying by u to the
+minus 1, we get P equals u
+
+times lambda times
+u to the minus 1.
+
+P to the n is then u times
+lambda to the n times u
+
+to the minus 1.
+
+All this stuff about convergence
+is all revolving
+
+down to simply the question
+of what happens to these
+
+eigenvalues.
+
+I mean, there's a mess first,
+finding out what all these
+
+right eigenvectors are and
+what all these left
+
+eigenvectors are.
+
+But once you do that, P to the
+n is just looking at this
+
+quantity, breaking up
+lambda to the n
+
+the way we did before.
+
+P to the n is just
+this sum here.
+
+Now, each row of P sums to 1, so
+e is a right eigenvector of
+
+eigenvalue 1.
+
+So we have a theorem that says
+the left eigenvector pi of
+
+eigenvalue 1 is a steady state
+vector if it's normalized to
+
+pi times e equals 1.
+
+So we almost did that before,
+but now we want to be a little
+
+more careful about it.
+
+Oh, excuse me.
+
+The theorem is that the left
+eigenvector pi is a steady
+
+state vector if it's normalized
+in this way.
+
+In other words, we know that
+there is a left eigenvector
+
+pi, which has eigenvalue 1,
+because there's a right
+
+eigenvector.
+
+If there's a right eigenvector,
+there has to be a
+
+left eigenvector.
+
+What we don't know is
+that pi actually has
+
+non-negative terms.
+
+So that's the thing
+we want to show.
+
+The proof is, there must be
+a left eigenvector pi for
+
+eigenvalue 1.
+
+We already know that.
+
+For every j, Pi sub j is equal
+to the sum over k times pi sub
+
+k times p sub kj.
+
+We don't know whether these
+are complex or real.
+
+We don't know whether they're
+positive or negative, if
+
+they're real.
+
+But we do know that since they
+satisfy this eigenvector
+
+equation, they satisfy
+this equation.
+
+If I take the magnitudes
+of all of these
+
+things, what do I get?
+
+The magnitude on this side
+is pi sub j magnitude.
+
+This is less than or equal to
+the sum of the magnitudes of
+
+these terms.
+
+If you take two complex numbers
+and you add them up,
+
+you get something which, in
+magnitude, is less than or
+
+equal to the sum of
+the magnitudes.
+
+It might sound strange,
+but if you look
+
+in the complex plane--
+
+imaginary, real--
+
+and you look at one complex
+number, and you add it to
+
+another complex number, this
+distance here is less than or
+
+equal to this magnitude
+plus this magnitude.
+
+That's all that equation
+is saying.
+
+And this is equal to this
+distance plus this distance if
+
+and only if each of these
+components of the eigenvector
+
+that we're talking about, if and
+only if those components
+
+are all heading off in
+the same direction
+
+in the complex plane.
+
+Now what do we do?
+
+Well, you look at this for a
+while and you say, OK, what
+
+happens if I sum this
+inequality over j?
+
+Well, if I sum this
+over j, I get one.
+
+And therefore when I sum both
+sides over j, the sum over j
+
+of the magnitudes of these
+eigenvector components is less
+
+than or equal to the sum over
+k of the magnitude.
+
+This is the same as this.
+
+This j is just a dummy
+index of summation.
+
+This is a dummy index
+of summation.
+
+Obviously, this is less
+than or equal to this.
+
+But what's interesting here is
+that this is equal to this.
+
+And the only way this can be
+equal to this is if every one
+
+of these things are satisfied
+with equality.
+
+If any one of these are
+satisfied with inequality,
+
+then when you add them all up,
+this will be satisfied with
+
+inequality also, which
+is impossible.
+
+So all of these are satisfied
+with equality, which says that
+
+the magnitude of pi sub j, the
+vector whose elements are the
+
+magnitudes of this thing we
+started with, in fact form a
+
+steady state vector if we
+normalize them to 1.
+
+It says these magnitudes
+satisfy the
+
+steady state equation.
+
+These magnitudes are real
+and they're positive.
+
+So when we normalize them to
+sum to 1, we have a steady
+
+state vector.
+
+And therefore the left
+eigenvector pi of eigenvalue 1
+
+is a steady state vector if it's
+normalized to pi times e
+
+equals 1, which is the way we
+want to normalize them.
+
+So there always is a steady
+state vector for every
+
+finite-state Markov chain.
+
+So this is a non-negative vector
+satisfying a steady
+
+state vector equation.
+
+And normalizing it, we have
+a steady state vector.
+
+So we've demonstrated the
+existence of a left
+
+eigenvector which is a
+steady state vector.
+
+Another theorem is that every
+eigenvalue satisfies lambda,
+
+magnitude of the eigenvalue is
+less than or equal to 1.
+
+This, again, is sort of obvious,
+because if you have
+
+an eigenvalue which is bigger
+than 1 and you start taking
+
+powers of it, it starts marching
+off to infinity.
+
+Now, you might say, maybe
+something else
+
+is balancing that.
+
+But since you only have a finite
+number of these things,
+
+that sounds pretty weird.
+
+And in fact, it is.
+
+So the proof of this is, we want
+to assume that pi super l
+
+is the l-th of these
+eigenvectors of P. Its
+
+eigenvalue is lambda sub l.
+
+It also is a left eigenvector of
+P to the n with eigenvalue
+
+lambda to the n.
+
+That's what we've
+shown before.
+
+I mean, you can multiply this
+matrix P, and all you're doing
+
+is just taking powers
+of the eigenvalue.
+
+So if we start out with lambda
+to the n, let's forget about
+
+the l's, because we're just
+looking at a fixed l now.
+
+Lambda to the nth power times
+the j-th component of pi is
+
+equal to the sum over i of the
+i-th component of pi times Pij
+
+to the n, for all j.
+
+Now I take the magnitude of
+everything is before.
+
+The magnitude of this is, again,
+less than or equal to
+
+the magnitude of this.
+
+I want to let beta be the
+largest of these quantities.
+
+And when I put that maximizing
+j in here, lambda to the l
+
+times beta is less than or equal
+to the sum over i of--
+
+I can upper-bound
+these by beta.
+
+So I wind up with lambda to the
+l times beta is less than
+
+or equal to the sum over i of
+beta times Pij to the n.
+
+I don't know what these powers
+are, but they're certainly
+
+less than or equal to 1.
+
+So lambda sub l is less
+than or equal to n.
+
+That's what this said.
+
+When you take this magnitude of
+the l-th eigenvalue, it's
+
+less than or equal
+to this number n.
+
+Now, if this number were larger
+than 1, if it was 1
+
+plus 10 to the minus sixth,
+and you multiplied it by a
+
+large enough number n, that
+this would grow to be
+
+arbitrarily large.
+
+It can't grow to be arbitrarily
+large, therefore
+
+the magnitude of lambda
+sub l has to be less
+
+than or equal to 1.
+
+Tedious proof, but
+unfortunately, the notes just
+
+assume this.
+
+Maybe I had some good, simple
+reason for it before.
+
+I don't have any now, so I have
+to go through a proof.
+
+Anyway, these two theorems, if
+you look at them, are valid
+
+for all finite-state
+Markov chains.
+
+There was no place that we
+used the fact that we had
+
+anything with distinct
+eigenvalues or anything.
+
+But now when we had distinct
+eigenvalues, we have the nth
+
+power of P is the sum here again
+over right eigenvectors
+
+times left eigenvectors.
+
+When you take a right
+eigenvector, which is a column
+
+vector, times a left
+eigenvector, which is a row
+
+vector, you get an
+M by M matrix.
+
+I don't know what that matrix
+is, but it's a matrix.
+
+It's a fixed matrix
+independent of n.
+
+And the only thing that's
+varying with n is these
+
+eigenvalues.
+
+These quantities are less
+than or equal to 1.
+
+So if the chain is an ergodic
+unit chain, we've already seen
+
+that one eigenvalue is 1, and
+the rest of the eigenvalues
+
+are strictly less than
+1 in magnitude.
+
+We saw that by showing that for
+an ergodic unit chain, P
+
+to the n converged.
+
+So the rate at which P to the
+n approaches e times pi is
+
+going to be determined
+by the second-largest
+
+eigenvalue in here.
+
+And that second-largest
+eigenvalue is going to be less
+
+than 1, strictly less than 1.
+
+We don't know what it is.
+
+Before, we knew this convergence
+here for an
+
+ergodic unit chain
+is exponential.
+
+Now we know that it's
+exponential and we know
+
+exactly how fast it goes,
+because the speed of
+
+convergence is just the
+second-largest eigenvalue.
+
+If you want to know how fast P
+to the n approaches e times
+
+the steady state vector pi,
+all you have to do is find
+
+that second-largest eigenvalue,
+and that tells you
+
+how fast the convergence is,
+except for calculating these
+
+things, which are just fixed.
+
+If P is a periodic unit chain
+with period d, then if you
+
+read the notes--
+
+you should read the notes--
+
+there are d eigenvalues
+equally spaced
+
+around the unit circle.
+
+P to the n doesn't converge.
+
+The only thing you can say here
+is, what happens if you
+
+look at P to the d-th power?
+
+And you can imagine what happens
+if you look at P to
+
+the d-th power without
+doing any analysis.
+
+I mean, we know that what
+happens in a periodic chain is
+
+that you rotate from one set
+of states to another set of
+
+states to another set of states
+to another set of
+
+states, and then back
+to the set of
+
+states you started with.
+
+And you keep rotating around.
+
+Now, there are d sets of states
+going around here.
+
+What happens if I
+take P to the d?
+
+P to the d is looking at
+the d-step transitions.
+
+So it's looking at, if you start
+here, after d steps,
+
+you're back here again,
+after d steps,
+
+you're back here again.
+
+So the matrix, P to the d, is
+in fact the matrix of d
+
+ergodic subclasses.
+
+And for each one of them,
+whatever subclass you start
+
+in, you stay in that
+subclass forever.
+
+So the analysis of a periodic
+unit chain, really the classy
+
+way to do it is to look
+at P to the d and see
+
+what happens there.
+
+And you see that you get
+convergence within each
+
+subclass, but you just keep
+rotating among subclasses.
+
+So there's nothing very
+fancy going on there.
+
+You just rotate from one
+subclass to another.
+
+And that's the way it is.
+
+And P to the n doesn't
+converge.
+
+But P to the d times
+n does converge.
+
+Now, let's look at the next-most
+complicated state.
+
+Suppose we have M states and
+we have M independent
+
+eigenvectors.
+
+OK, remember I told you that
+there was a very ugly thing in
+
+linear algebra that said, when
+you had an eigenvalue of
+
+multiplicity k, you might not
+have k linearly independent
+
+eigenvectors.
+
+You might have a smaller
+number of them.
+
+We'll look at an example
+of that later.
+
+But here, I'm saying, let's
+forget about that case,
+
+because it's ugly.
+
+Let's assume that whatever
+multiplicity each of these
+
+eigenvalues has, if you have
+an eigenvalue with
+
+multiplicity k, then you have
+k linearly independent right
+
+eigenvectors and k linearly
+independent left eigenvectors
+
+to correspond to that.
+
+And then when you add up all of
+the eigenvectors, you have
+
+M linearly independent
+eigenvectors.
+
+And what happens when you have M
+linearly independent vectors
+
+in a space of dimension M?
+
+If you have M linearly
+independent vectors in a space
+
+of dimension N, you expand the
+whole space, which says that
+
+the vector of these eigenvectors
+is in fact
+
+non-singular, which says, again,
+we can do all of the
+
+stuff we did before.
+
+There's a little bit of a trick
+in showing that the left
+
+eigenvectors and the right
+eigenvectors can be made
+
+orthogonal.
+
+But aside from that,
+P to the n is again
+
+equal to the same form.
+
+And what this form says is, if
+all of the eigenvalues except
+
+one are less than 1, then you're
+again going to approach
+
+steady state.
+
+What does that mean?
+
+Suppose I have more than one
+ergodic chain, more than one
+
+ergodic class, or suppose I
+have a periodic class or
+
+something else.
+
+Is it possible to have one
+eigenvalue equal to 1 and all
+
+the other eigenvalues
+be smaller?
+
+If there's one eigenvalue that's
+equal to 1, according
+
+to this formula here, eventually
+P to the n
+
+converges to that one
+value equal to 1.
+
+And right eigenvector
+can be taken as e.
+
+Left eigenvector can be taken
+as a steady state vector pi.
+
+And we have the case
+of convergence.
+
+Can you have convergence to all
+the rows being the same if
+
+you have multiple
+ergodic classes?
+
+No.
+
+If you have multiple ergodic
+classes and you start out in
+
+one class, you stay there.
+
+You can't get out of it.
+
+If you have a periodic class
+and you start out in that
+
+periodic class, you can't
+have convergence there.
+
+So in this situation here, where
+all the eigenvalues are
+
+distinct, you can only have
+one eigenvalue equal to 1.
+
+Here, when we're going to this
+more general case, we might
+
+have more than one eigenvalue
+equal to 1.
+
+But if in fact we only have one
+eigenvalue equal to 1, and
+
+all the others are strictly
+smaller in magnitude, then in
+
+fact you're just talking about
+this case of an ergodic unit
+
+chain again.
+
+It's the only place
+you can be.
+
+So let's look at an
+example of this.
+
+Suppose you have a Markov
+chain which has l
+
+ergodic sets of states.
+
+You have one set of states.
+
+So we have one set of states
+over here, which will all go
+
+back and forth to each other.
+
+Then another set of
+states over here.
+
+Let's let l equal
+2 in this case.
+
+So what happens in
+this situation?
+
+We'll have to work quickly
+before it gets up.
+
+Anybody with any sense, faced
+with a Markov chain like this,
+
+would say if we start here,
+we're going to stay here, if
+
+we start here, we're
+going to stay here.
+
+Let's just analyze this first.
+
+And then after we're done
+analyzing this,
+
+we'll analyze this.
+
+And then we'll put the
+whole thing together.
+
+And what we will find is
+a transition matrix
+
+which looks like this.
+
+And if you're here,
+you stay here.
+
+If you're here, you stay here.
+
+We can find the eigenvalues
+and eigenvectors of this.
+
+We can find the eigenvalues
+and eigenvectors of this.
+
+If you look at this crazy
+formula for finding
+
+determinants, what you're stuck
+with is permutations
+
+within here times permutations
+within here.
+
+So the eigenvalues that you wind
+up with are products of
+
+the two eigenvalues.
+
+Or any eigenvalue here is an
+eigenvalue of the whole thing.
+
+Any eigenvalue here is an
+eigenvalue of the whole thing.
+
+And we just look at the sum of
+the number of eigenvalues here
+
+and the number there.
+
+So we have a very boring
+case here.
+
+Each ergodic set has an
+eigenvalue equal to 1, has a
+
+right eigenvector equal to 1.
+
+When the steps of that state
+and 0 elsewhere.
+
+There's also a steady state
+vector on that set of states.
+
+We've already seen that.
+
+So P to the n converges to a
+block diagonal matrix, where
+
+for each ergodic set, the rows
+within that set are the same.
+
+So P to the n then
+is pi 1, pi 1.
+
+And then here, we have
+pi 2, pi 2, pi 2.
+
+So that's all that
+can happen here.
+
+This is limit.
+
+So one message of this is that,
+after you understand
+
+ergodic unit chains, you
+understand almost everything.
+
+You still have to worry about
+periodic unit chains.
+
+But you just take a power of
+them, and then you have
+
+ergodic sets of states.
+
+one final thing.
+
+Good, I have five minutes
+to talk about this.
+
+I don't want any more time to
+talk about it, because I'll
+
+get terribly confused if I do.
+
+And it's a topic which, if you
+want to read more about it,
+
+read about it in Strang.
+
+He obviously doesn't like
+the topic either.
+
+Nobody likes the topic.
+
+Strang at least was driven to
+say something clear about it.
+
+Most people don't even
+bother to say
+
+something clear about it.
+
+There's a theorem, due to, I
+guess, Jordan, because it's
+
+called a Jordan form.
+
+And what Jordan said is, in
+the nice cases we talked
+
+about, you have this
+decomposition of the
+
+transition matrix in P into a
+matrix here whose columns are
+
+the right eigenvectors times
+a matrix here, which is a
+
+diagonal matrix with the
+eigenvalues along it.
+
+And this, finally, is a matrix
+which is the inverse of this,
+
+and, which properly normalized,
+is the left
+
+eigenvectors of P. And you can
+replace this form by what's
+
+called a Jordan form, where P
+is equal to some matrix u
+
+times the Jordan form matrix
+j times the inverse of u.
+
+Now, u is no longer the
+right eigenvectors.
+
+It can't be the right
+eigenvectors, because when we
+
+needed Jordan form, we don't
+have enough right eigenvectors
+
+to span the space.
+
+So it has to be something
+else.
+
+And like everyone else,
+we say, I don't care
+
+what that matrix is.
+
+Jordan proved that there is such
+a matrix, and that's all
+
+we want to know.
+
+The important thing is that this
+matrix j in here is as
+
+close as you can get it.
+
+It's a matrix, which along the
+main diagonal, has all the
+
+eigenvalues with their
+appropriate multiplicity.
+
+Namely, lambda 1 is
+an eigenvalue with
+
+multiplicity 2.
+
+Lambda 2 is an eigenvalue
+of multiplicity 3.
+
+And in this situation, you have
+two eigenvectors here, so
+
+nothing appears up there.
+
+With this multiplicity 3
+eigenvalue, there are only two
+
+linearly independent
+eigenvectors.
+
+And therefore Jordan says, why
+don't we stick a 1 in here and
+
+then solve everything else?
+
+And his theorem says, if you
+do that, it in fact works.
+
+So every time--
+
+well, the eigenvalue is on the
+main diagonal, the ones on the
+
+next diagonal up, the only place
+would be anything non-0
+
+is on the main diagonal in this
+form, and on the next
+
+diagonal up, where you
+occasionally have a 1.
+
+And the 1 is to replace
+the need for deficient
+
+eigenvectors.
+
+So every time you have a
+deficient eigenvector, you
+
+have some 1 appearing there.
+
+And then there's a way
+to solve for u.
+
+And I don't have any idea what
+it is, and I don't care.
+
+But if you get interested in it,
+I think that's wonderful.
+
+But please don't tell
+me about it.
+
+Nice example of this is
+this matrix here.
+
+What happens if you try to
+take the determinant of P
+
+minus lambda i?
+
+Well, you have 1/2 minus lambda,
+1/2 minus lambda, 1
+
+minus lambda.
+
+What are all the permutations
+here that you can take?
+
+There's the permutation of
+the main diagonal itself.
+
+If I try to include that
+element, there's nothing I can
+
+do but have some element
+down here.
+
+And all these elements are 0.
+
+So those elements don't
+contribute to a
+
+determinant at all.
+
+So I have one eigenvalue
+which is equal to 1.
+
+I have two values at
+multiplicity 2, eigenvalue
+
+which is 1/2.
+
+If you try to find the
+eigenvector here, you find
+
+there is only one.
+
+So in fact, this corresponds
+to a Jordan form,
+
+where you have 1/2.
+
+1, and a 0, and a 1 here,
+and 0 everywhere else.
+
+And now if I want to find P to
+the n, I have u times this j
+
+times u to the minus
+1 times u.
+
+All the u's in the middle
+cancel out, so I wind up
+
+eventually with u times j
+to the nth power times u
+
+to the minus 1.
+
+What is j to the nth power?
+
+What happens if I multiply this
+matrix by itself n times?
+
+Well, it turns out that what
+happens is that this main
+
+diagonal here, you wind
+up with a 1/4 and
+
+then 1/8 and so forth.
+
+This term here, it goes
+down exponential.
+
+Well, if you multiply this by
+itself, eventually, you can
+
+see what's going on here more
+easily if you draw the Markov
+
+chain for it.
+
+You have state 1, state
+2, and state 3.
+
+State 1, there's a transition
+1/2 and a transition 1/2.
+
+State 2, there's a transition
+1/2 and a transition 1/2, And
+
+state 3, you just stay there.
+
+So the amount of time that it
+takes you to get to steady
+
+state is the amount of
+time it takes you--
+
+you start in state 1.
+
+You've got to make this
+transition eventually, and
+
+then you've got to make this
+transition eventually.
+
+And the amount of time that it
+takes you to do that is the
+
+sum of the amount of time it
+takes you to go there, plus
+
+the amount of time that
+it takes to go there.
+
+So you have two random
+variables.
+
+One is the time to go here.
+
+The other is the time
+to go here.
+
+Both of those are geometrically
+decreasing
+
+random variables.
+
+When we convolve those things
+with each other, what we get
+
+is an extra term n.
+
+So we get an n times
+1/2 to the n.
+
+So the thing which is different
+in the Jordan form
+
+is, instead of having an
+eigenvalue to the nth power,
+
+you have an eigenvalue times--
+
+if there's only a single one
+there, there's an n there.
+
+If there are two 1s both
+together, you get an n times n
+
+minus 1, and so forth.
+
+So worst case, you've got a
+polynomial to the nth power
+
+times an eigenvalue.
+
+For all practical purposes, this
+is still the eigenvalue
+
+going down exponentially.
+
+So for all practical purposes,
+what you wind up with is the
+
+second-largest eigenvalue still
+determines how fast you
+
+get convergence.
+
+Sorry, I took eight minutes
+talking about the Jordan form.
+
+I wanted to take five minutes
+talking about it.
+
+You can read more about
+it in the notes.
\ No newline at end of file
diff --git a/GOmLwHaa8Ik.txt b/GOmLwHaa8Ik.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d0a928719017a443b5547d41b749ca90122627b
--- /dev/null
+++ b/GOmLwHaa8Ik.txt
@@ -0,0 +1,1051 @@
+align:start position:0%
+ 
+by now we have defined the notion of
+
+ align:start position:0%
+by now we have defined the notion of
+ 
+
+ align:start position:0%
+by now we have defined the notion of
+independence of events and also the
+
+ align:start position:0%
+independence of events and also the
+ 
+
+ align:start position:0%
+independence of events and also the
+notion of independence of random
+
+ align:start position:0%
+notion of independence of random
+ 
+
+ align:start position:0%
+notion of independence of random
+variables the two definitions look
+
+ align:start position:0%
+variables the two definitions look
+ 
+
+ align:start position:0%
+variables the two definitions look
+fairly similar but the details are not
+
+ align:start position:0%
+fairly similar but the details are not
+ 
+
+ align:start position:0%
+fairly similar but the details are not
+exactly the same because the two
+
+ align:start position:0%
+exactly the same because the two
+ 
+
+ align:start position:0%
+exactly the same because the two
+definitions refer to different
+
+ align:start position:0%
+definitions refer to different
+ 
+
+ align:start position:0%
+definitions refer to different
+situations for two events we know what
+
+ align:start position:0%
+situations for two events we know what
+ 
+
+ align:start position:0%
+situations for two events we know what
+it means for them to be independence the
+
+ align:start position:0%
+it means for them to be independence the
+ 
+
+ align:start position:0%
+it means for them to be independence the
+probability of their intersection is the
+
+ align:start position:0%
+probability of their intersection is the
+ 
+
+ align:start position:0%
+probability of their intersection is the
+product of their individual
+
+ align:start position:0%
+product of their individual
+ 
+
+ align:start position:0%
+product of their individual
+probabilities now to make a relation
+
+ align:start position:0%
+probabilities now to make a relation
+ 
+
+ align:start position:0%
+probabilities now to make a relation
+with random variables we introduced the
+
+ align:start position:0%
+with random variables we introduced the
+ 
+
+ align:start position:0%
+with random variables we introduced the
+so called indicator random variables so
+
+ align:start position:0%
+so called indicator random variables so
+ 
+
+ align:start position:0%
+so called indicator random variables so
+for example the random variable X is
+
+ align:start position:0%
+for example the random variable X is
+ 
+
+ align:start position:0%
+for example the random variable X is
+defined to be equal to 1 if event a
+
+ align:start position:0%
+defined to be equal to 1 if event a
+ 
+
+ align:start position:0%
+defined to be equal to 1 if event a
+occurs and to be equal to 0 if event
+
+ align:start position:0%
+occurs and to be equal to 0 if event
+ 
+
+ align:start position:0%
+occurs and to be equal to 0 if event
+does not occur and there is a similar
+
+ align:start position:0%
+does not occur and there is a similar
+ 
+
+ align:start position:0%
+does not occur and there is a similar
+definition for random variable Y in
+
+ align:start position:0%
+definition for random variable Y in
+ 
+
+ align:start position:0%
+definition for random variable Y in
+particular the probability that random
+
+ align:start position:0%
+particular the probability that random
+ 
+
+ align:start position:0%
+particular the probability that random
+variable X takes the value of 1 this is
+
+ align:start position:0%
+variable X takes the value of 1 this is
+ 
+
+ align:start position:0%
+variable X takes the value of 1 this is
+the probability that event a occurs it
+
+ align:start position:0%
+the probability that event a occurs it
+ 
+
+ align:start position:0%
+the probability that event a occurs it
+turns out that the independence of the
+
+ align:start position:0%
+turns out that the independence of the
+ 
+
+ align:start position:0%
+turns out that the independence of the
+two events a and B is equivalent to the
+
+ align:start position:0%
+two events a and B is equivalent to the
+ 
+
+ align:start position:0%
+two events a and B is equivalent to the
+independence of the two indicator random
+
+ align:start position:0%
+independence of the two indicator random
+ 
+
+ align:start position:0%
+independence of the two indicator random
+variables and there is a similar
+
+ align:start position:0%
+variables and there is a similar
+ 
+
+ align:start position:0%
+variables and there is a similar
+statement which is true more generally
+
+ align:start position:0%
+statement which is true more generally
+ 
+
+ align:start position:0%
+statement which is true more generally
+that is and events are independent if
+
+ align:start position:0%
+that is and events are independent if
+ 
+
+ align:start position:0%
+that is and events are independent if
+and only if be associated an indicator
+
+ align:start position:0%
+and only if be associated an indicator
+ 
+
+ align:start position:0%
+and only if be associated an indicator
+random variables are independent this is
+
+ align:start position:0%
+random variables are independent this is
+ 
+
+ align:start position:0%
+random variables are independent this is
+a useful statement because it allows us
+
+ align:start position:0%
+a useful statement because it allows us
+ 
+
+ align:start position:0%
+a useful statement because it allows us
+to sometimes instead of manipulating
+
+ align:start position:0%
+to sometimes instead of manipulating
+ 
+
+ align:start position:0%
+to sometimes instead of manipulating
+events to manipulate random variables
+
+ align:start position:0%
+events to manipulate random variables
+ 
+
+ align:start position:0%
+events to manipulate random variables
+and vice versa and depending on the
+
+ align:start position:0%
+and vice versa and depending on the
+ 
+
+ align:start position:0%
+and vice versa and depending on the
+context one may be easier than the other
+
+ align:start position:0%
+context one may be easier than the other
+ 
+
+ align:start position:0%
+context one may be easier than the other
+now the intuitive content is that event
+
+ align:start position:0%
+now the intuitive content is that event
+ 
+
+ align:start position:0%
+now the intuitive content is that event
+a and B are independent if the
+
+ align:start position:0%
+a and B are independent if the
+ 
+
+ align:start position:0%
+a and B are independent if the
+occurrence of event a does not change
+
+ align:start position:0%
+occurrence of event a does not change
+ 
+
+ align:start position:0%
+occurrence of event a does not change
+your beliefs about B and in terms of
+
+ align:start position:0%
+your beliefs about B and in terms of
+ 
+
+ align:start position:0%
+your beliefs about B and in terms of
+random variables one random variable
+
+ align:start position:0%
+random variables one random variable
+ 
+
+ align:start position:0%
+random variables one random variable
+taking a certain value which indicates
+
+ align:start position:0%
+taking a certain value which indicates
+ 
+
+ align:start position:0%
+taking a certain value which indicates
+whether event a has occurred or not does
+
+ align:start position:0%
+whether event a has occurred or not does
+ 
+
+ align:start position:0%
+whether event a has occurred or not does
+not give you any information about the
+
+ align:start position:0%
+not give you any information about the
+ 
+
+ align:start position:0%
+not give you any information about the
+other random variable which would tell
+
+ align:start position:0%
+other random variable which would tell
+ 
+
+ align:start position:0%
+other random variable which would tell
+you whether event B has occurred or not
+
+ align:start position:0%
+you whether event B has occurred or not
+ 
+
+ align:start position:0%
+you whether event B has occurred or not
+it is instructive now to go through the
+
+ align:start position:0%
+it is instructive now to go through the
+ 
+
+ align:start position:0%
+it is instructive now to go through the
+derivation of this
+
+ align:start position:0%
+derivation of this
+ 
+
+ align:start position:0%
+derivation of this
+at least for the case of two events
+
+ align:start position:0%
+at least for the case of two events
+ 
+
+ align:start position:0%
+at least for the case of two events
+because it gives us perhaps some
+
+ align:start position:0%
+because it gives us perhaps some
+ 
+
+ align:start position:0%
+because it gives us perhaps some
+additional understanding about the
+
+ align:start position:0%
+additional understanding about the
+ 
+
+ align:start position:0%
+additional understanding about the
+precise content of the definitions we
+
+ align:start position:0%
+precise content of the definitions we
+ 
+
+ align:start position:0%
+precise content of the definitions we
+have introduced so let us suppose that
+
+ align:start position:0%
+have introduced so let us suppose that
+ 
+
+ align:start position:0%
+have introduced so let us suppose that
+random variables x and y are independent
+
+ align:start position:0%
+random variables x and y are independent
+ 
+
+ align:start position:0%
+random variables x and y are independent
+what does that mean independence means
+
+ align:start position:0%
+what does that mean independence means
+ 
+
+ align:start position:0%
+what does that mean independence means
+that the joint pmf of the two random
+
+ align:start position:0%
+that the joint pmf of the two random
+ 
+
+ align:start position:0%
+that the joint pmf of the two random
+variables x and y factors as a product
+
+ align:start position:0%
+variables x and y factors as a product
+ 
+
+ align:start position:0%
+variables x and y factors as a product
+of the corresponding marginal pmfs and
+
+ align:start position:0%
+of the corresponding marginal pmfs and
+ 
+
+ align:start position:0%
+of the corresponding marginal pmfs and
+this factorization must be true no
+
+ align:start position:0%
+this factorization must be true no
+ 
+
+ align:start position:0%
+this factorization must be true no
+matter what arguments we use inside the
+
+ align:start position:0%
+matter what arguments we use inside the
+ 
+
+ align:start position:0%
+matter what arguments we use inside the
+joint pmf and the combination of x and y
+
+ align:start position:0%
+joint pmf and the combination of x and y
+ 
+
+ align:start position:0%
+joint pmf and the combination of x and y
+in this instance have a total of four
+
+ align:start position:0%
+in this instance have a total of four
+ 
+
+ align:start position:0%
+in this instance have a total of four
+possible values these are the
+
+ align:start position:0%
+possible values these are the
+ 
+
+ align:start position:0%
+possible values these are the
+combinations of zeros and ones that we
+
+ align:start position:0%
+combinations of zeros and ones that we
+ 
+
+ align:start position:0%
+combinations of zeros and ones that we
+can form and for this reason we have a
+
+ align:start position:0%
+can form and for this reason we have a
+ 
+
+ align:start position:0%
+can form and for this reason we have a
+total of four equations these four
+
+ align:start position:0%
+total of four equations these four
+ 
+
+ align:start position:0%
+total of four equations these four
+equality's are what is required for x
+
+ align:start position:0%
+equality's are what is required for x
+ 
+
+ align:start position:0%
+equality's are what is required for x
+and y to be independent so suppose that
+
+ align:start position:0%
+and y to be independent so suppose that
+ 
+
+ align:start position:0%
+and y to be independent so suppose that
+this is true the trend that the random
+
+ align:start position:0%
+this is true the trend that the random
+ 
+
+ align:start position:0%
+this is true the trend that the random
+variables are independent let us take
+
+ align:start position:0%
+variables are independent let us take
+ 
+
+ align:start position:0%
+variables are independent let us take
+this first relation and write it in
+
+ align:start position:0%
+this first relation and write it in
+ 
+
+ align:start position:0%
+this first relation and write it in
+probability notation the random variable
+
+ align:start position:0%
+probability notation the random variable
+ 
+
+ align:start position:0%
+probability notation the random variable
+X taking the value of 1 that's the same
+
+ align:start position:0%
+X taking the value of 1 that's the same
+ 
+
+ align:start position:0%
+X taking the value of 1 that's the same
+as event a occurring and random variable
+
+ align:start position:0%
+as event a occurring and random variable
+ 
+
+ align:start position:0%
+as event a occurring and random variable
+Y taking the value of 1 that's the same
+
+ align:start position:0%
+Y taking the value of 1 that's the same
+ 
+
+ align:start position:0%
+Y taking the value of 1 that's the same
+as event B occurring so the joint PMF
+
+ align:start position:0%
+as event B occurring so the joint PMF
+ 
+
+ align:start position:0%
+as event B occurring so the joint PMF
+evaluated at 1 1 is the probability that
+
+ align:start position:0%
+evaluated at 1 1 is the probability that
+ 
+
+ align:start position:0%
+evaluated at 1 1 is the probability that
+events a and B both occur on the other
+
+ align:start position:0%
+events a and B both occur on the other
+ 
+
+ align:start position:0%
+events a and B both occur on the other
+side of the equation we have the
+
+ align:start position:0%
+side of the equation we have the
+ 
+
+ align:start position:0%
+side of the equation we have the
+probability that X is equal to 1 which
+
+ align:start position:0%
+probability that X is equal to 1 which
+ 
+
+ align:start position:0%
+probability that X is equal to 1 which
+is a probability that a occurs and
+
+ align:start position:0%
+is a probability that a occurs and
+ 
+
+ align:start position:0%
+is a probability that a occurs and
+similarly the probability that B occurs
+
+ align:start position:0%
+similarly the probability that B occurs
+ 
+
+ align:start position:0%
+similarly the probability that B occurs
+but if this is true then by definition a
+
+ align:start position:0%
+but if this is true then by definition a
+ 
+
+ align:start position:0%
+but if this is true then by definition a
+and B are independent events so we have
+
+ align:start position:0%
+and B are independent events so we have
+ 
+
+ align:start position:0%
+and B are independent events so we have
+verified one direction of the statement
+
+ align:start position:0%
+verified one direction of the statement
+ 
+
+ align:start position:0%
+verified one direction of the statement
+if the random variables are independent
+
+ align:start position:0%
+if the random variables are independent
+ 
+
+ align:start position:0%
+if the random variables are independent
+then events a and B are independent now
+
+ align:start position:0%
+then events a and B are independent now
+ 
+
+ align:start position:0%
+then events a and B are independent now
+we would like to verify the reverse
+
+ align:start position:0%
+we would like to verify the reverse
+ 
+
+ align:start position:0%
+we would like to verify the reverse
+statement so suppose that events a and B
+
+ align:start position:0%
+statement so suppose that events a and B
+ 
+
+ align:start position:0%
+statement so suppose that events a and B
+are independent in that case this
+
+ align:start position:0%
+are independent in that case this
+ 
+
+ align:start position:0%
+are independent in that case this
+relation is true and as we just argued
+
+ align:start position:0%
+relation is true and as we just argued
+ 
+
+ align:start position:0%
+relation is true and as we just argued
+this relation is the
+
+ align:start position:0%
+this relation is the
+ 
+
+ align:start position:0%
+this relation is the
+as this relation but just written in
+
+ align:start position:0%
+as this relation but just written in
+ 
+
+ align:start position:0%
+as this relation but just written in
+different notation so we have song that
+
+ align:start position:0%
+different notation so we have song that
+ 
+
+ align:start position:0%
+different notation so we have song that
+if a and B are independent this relation
+
+ align:start position:0%
+if a and B are independent this relation
+ 
+
+ align:start position:0%
+if a and B are independent this relation
+will be true but how about the remaining
+
+ align:start position:0%
+will be true but how about the remaining
+ 
+
+ align:start position:0%
+will be true but how about the remaining
+three relations we have more work to do
+
+ align:start position:0%
+three relations we have more work to do
+ 
+
+ align:start position:0%
+three relations we have more work to do
+here's how we can proceed if a and B are
+
+ align:start position:0%
+here's how we can proceed if a and B are
+ 
+
+ align:start position:0%
+here's how we can proceed if a and B are
+independent we have shown some time ago
+
+ align:start position:0%
+independent we have shown some time ago
+ 
+
+ align:start position:0%
+independent we have shown some time ago
+that events a and B complement will also
+
+ align:start position:0%
+that events a and B complement will also
+ 
+
+ align:start position:0%
+that events a and B complement will also
+be independent intuitively a doesn't
+
+ align:start position:0%
+be independent intuitively a doesn't
+ 
+
+ align:start position:0%
+be independent intuitively a doesn't
+tell you anything about B occurring or
+
+ align:start position:0%
+tell you anything about B occurring or
+ 
+
+ align:start position:0%
+tell you anything about B occurring or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+so a does not tell you anything about
+
+ align:start position:0%
+so a does not tell you anything about
+ 
+
+ align:start position:0%
+so a does not tell you anything about
+whether B complement will occur or not
+
+ align:start position:0%
+whether B complement will occur or not
+ 
+
+ align:start position:0%
+whether B complement will occur or not
+now these two events being independent
+
+ align:start position:0%
+now these two events being independent
+ 
+
+ align:start position:0%
+now these two events being independent
+by the definition of Independence we
+
+ align:start position:0%
+by the definition of Independence we
+ 
+
+ align:start position:0%
+by the definition of Independence we
+have that the probability of a
+
+ align:start position:0%
+have that the probability of a
+ 
+
+ align:start position:0%
+have that the probability of a
+intersection with B complement is the
+
+ align:start position:0%
+intersection with B complement is the
+ 
+
+ align:start position:0%
+intersection with B complement is the
+product of the probabilities of a and of
+
+ align:start position:0%
+product of the probabilities of a and of
+ 
+
+ align:start position:0%
+product of the probabilities of a and of
+B complement and then we realize that
+
+ align:start position:0%
+B complement and then we realize that
+ 
+
+ align:start position:0%
+B complement and then we realize that
+this equality is written in PMF notation
+
+ align:start position:0%
+this equality is written in PMF notation
+ 
+
+ align:start position:0%
+this equality is written in PMF notation
+corresponds exactly to this equation
+
+ align:start position:0%
+corresponds exactly to this equation
+ 
+
+ align:start position:0%
+corresponds exactly to this equation
+here a event a corresponds to X taking
+
+ align:start position:0%
+here a event a corresponds to X taking
+ 
+
+ align:start position:0%
+here a event a corresponds to X taking
+the value of one event B complement
+
+ align:start position:0%
+the value of one event B complement
+ 
+
+ align:start position:0%
+the value of one event B complement
+corresponds to the event that Y takes
+
+ align:start position:0%
+corresponds to the event that Y takes
+ 
+
+ align:start position:0%
+corresponds to the event that Y takes
+the value of zero by similar arguments B
+
+ align:start position:0%
+the value of zero by similar arguments B
+ 
+
+ align:start position:0%
+the value of zero by similar arguments B
+and a complement will be independent and
+
+ align:start position:0%
+and a complement will be independent and
+ 
+
+ align:start position:0%
+and a complement will be independent and
+we translate that into probability
+
+ align:start position:0%
+we translate that into probability
+ 
+
+ align:start position:0%
+we translate that into probability
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we translate this equality into
+
+ align:start position:0%
+and then we translate this equality into
+ 
+
+ align:start position:0%
+and then we translate this equality into
+PMF notation and we get this relation
+
+ align:start position:0%
+PMF notation and we get this relation
+ 
+
+ align:start position:0%
+PMF notation and we get this relation
+finally using the same property that we
+
+ align:start position:0%
+finally using the same property that we
+ 
+
+ align:start position:0%
+finally using the same property that we
+use to do the first step here we have
+
+ align:start position:0%
+use to do the first step here we have
+ 
+
+ align:start position:0%
+use to do the first step here we have
+that a compliment and B complement are
+
+ align:start position:0%
+that a compliment and B complement are
+ 
+
+ align:start position:0%
+that a compliment and B complement are
+also independent and by following the
+
+ align:start position:0%
+also independent and by following the
+ 
+
+ align:start position:0%
+also independent and by following the
+same line of reasoning this applies the
+
+ align:start position:0%
+same line of reasoning this applies the
+ 
+
+ align:start position:0%
+same line of reasoning this applies the
+fourth relation as well so we have
+
+ align:start position:0%
+fourth relation as well so we have
+ 
+
+ align:start position:0%
+fourth relation as well so we have
+verified that if events a and B are
+
+ align:start position:0%
+verified that if events a and B are
+ 
+
+ align:start position:0%
+verified that if events a and B are
+independent then we can argue that all
+
+ align:start position:0%
+independent then we can argue that all
+ 
+
+ align:start position:0%
+independent then we can argue that all
+of these four equations will be true and
+
+ align:start position:0%
+of these four equations will be true and
+ 
+
+ align:start position:0%
+of these four equations will be true and
+therefore random variables x and y will
+
+ align:start position:0%
+therefore random variables x and y will
+ 
+
+ align:start position:0%
+therefore random variables x and y will
+also be independent
\ No newline at end of file
diff --git a/Hz1S82W8F04.txt b/Hz1S82W8F04.txt
new file mode 100644
index 0000000000000000000000000000000000000000..33d88785ecdafb50d108802b30997a8656770f29
--- /dev/null
+++ b/Hz1S82W8F04.txt
@@ -0,0 +1,4806 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+So for the course, we have
+four days of lectures.
+
+Today we'll try to convince
+you that it was actually a
+
+good idea to come here, why
+randomized evaluation is such
+
+a useful tool and why it's
+superior to many other kinds
+
+of impact evaluation.
+
+Once we've convinced you that
+it's a good idea to come here,
+
+then we'll start going through
+the nuts and bolts of actually
+
+how to run randomized
+evaluations.
+
+Tomorrow we'll go over some
+of the general design
+
+possibilities.
+
+The following day we'll go
+into some more of the
+
+technical aspects like sample
+size and measurement.
+
+The last day we'll kind of
+discuss the fact that even in
+
+randomized evaluations, things
+can go wrong, and how
+
+you deal with that.
+
+And throughout the entire course
+as you're learning
+
+this, you'll be incorporating
+what you learn by designing in
+
+step with the lectures your own
+randomized evaluation in
+
+the groups that you've
+been preassigned.
+
+So if you check out your name
+tags, you'll see that you have
+
+a group number.
+
+Find other people with the
+same color and number and
+
+those will be your
+group members.
+
+We tried to put you together
+in ways that made sense.
+
+So we tried to have people who
+were interested in agriculture
+
+work with other people
+within agriculture.
+
+And over the course of the four
+days, you'll be designing
+
+your own randomized
+evaluation.
+
+And on the last day, on
+Saturday, you will be
+
+presenting your evaluation
+to the entire group.
+
+So that is pretty much
+what to expect over
+
+the next five days.
+
+Have I forgotten anything?
+
+Then let me reintroduce
+Rachel who will start
+
+five minutes early.
+
+RACHEL GLENNERSTER: The group
+the Mark was talking about is
+
+a really integral part
+of the course.
+
+So unfortunately that is not
+something that you'll be able
+
+to get online.
+
+But hopefully it's a chance for
+you to go through, each
+
+time we present an idea in the
+lecture, you then need to go
+
+and apply it in the case that
+you're developing in your
+
+evaluation you're developing
+in your group.
+
+And that's what all the teaching
+assistants are here,
+
+to help you go through the
+case studies, but also to
+
+develop your own evaluations.
+
+So I'm going to start with the
+general question of what is an
+
+impact evaluation and when
+should we do one.
+
+One of the objectives of this
+lecture is just to make sure
+
+that we're all on the same page
+when we start using terms
+
+like process evaluation
+and impact evaluation.
+
+Because I realize the more I
+spend time with people who are
+
+kind of professional evaluators,
+I realize that
+
+economists and professional
+evaluators use the same terms
+
+but to mean different things,
+which is incredibly confusing.
+
+So I'm sure a lot of this will
+be familiar to you, but on the
+
+other hand, we need to make sure
+that every one is at the
+
+same level in using the terms in
+the same way before we kind
+
+of head into the
+nuts and bolts.
+
+But I also have incorporated in
+this discussion about when
+
+you should do an impact
+evaluation, which is something
+
+that comes up an awful lot
+when I go and talk to
+
+organizations who are trying
+to think through their
+
+evaluation strategy.
+
+They've heard that they ought
+to be doing more impact
+
+evaluations.
+
+There's lots of focus on this.
+
+But they're expensive.
+
+So how do they decide which of
+their programs to evaluate and
+
+at what stage to evaluate it.
+
+They're getting pressure
+from donors to do this.
+
+But they're not quite sure
+when it's appropriate.
+
+So we'll try and cover
+those ideas.
+
+So we'll start with why is it
+that we here at J-PAL are
+
+focused on impact evaluation.
+
+Because there's lots of other
+things in evaluating our
+
+programs that are important.
+
+But we just do impact
+evaluation.
+
+We also only do randomized
+impact evaluation.
+
+And that's not to say that's
+the only thing
+
+that's worth doing.
+
+We certainly don't think that.
+
+That's what we do.
+
+There's a reason we
+do it, because
+
+we think it's important.
+
+But it's certainly not the only
+thing that you should be
+
+doing in your organizations.
+
+So step back and look at the
+objectives of evaluation and a
+
+model of change, which is very
+important in terms of how to
+
+think about your evaluation,
+how to design it, different
+
+types of evaluation, how
+evaluation feeds into cost
+
+benefit analysis, and then
+into why to do an impact
+
+evaluation, and putting
+it all together into
+
+an evaluation strategy.
+
+And then coming back
+to how do we learn.
+
+How do we make an organization
+that learns from its
+
+evaluation strategy rather
+than just doing this as
+
+something a funder wants
+me to do or I have to
+
+do to tick a box.
+
+How do I develop an organization
+that learns from
+
+its evaluations and makes it
+a better organization?
+
+So this is the motivation
+for what we do.
+
+And I think this point is sort
+of the main point here.
+
+If you step back and you think
+about how much evidence we
+
+have in development, to make the
+decisions that we need to
+
+make, it's really quite
+appalling how little
+
+information we have.
+
+If you think about some of the
+biggest challenges in the
+
+world in development about how
+to prevent the spread of
+
+HIV/AIDS in Sub-Saharan Africa,
+how to improve the
+
+productivity of small farmers
+across the world, it's really
+
+amazing how little really
+rigorous evidence we have to
+
+make those decisions.
+
+And we may know that this
+project may work or that
+
+project may work, but we very
+rarely know what is the most
+
+cost-effective place to put
+a dollar that I have.
+
+If I'm choosing in HIV
+prevention, if I've got to
+
+choose between a lot of
+different seemingly great
+
+projects, what is the project
+that's going to give me the
+
+most bang for my buck?
+
+And we really don't have that
+kind of consistent rigorous
+
+impact evaluation data in order
+to make those decisions.
+
+And that was really the reason
+why J-PAL was started, because
+
+of the feeling that we could
+do so much better if we had
+
+that kind of data.
+
+And it's also too often the
+case that decisions about
+
+development are based on emotion
+rather than data.
+
+You can see this in proposals
+that people write and the
+
+discussions that people have,
+very compelling, personal
+
+stories, which are important,
+but aren't really what we
+
+should be making all
+our decisions on.
+
+That may be very motivating
+to get people involved.
+
+But when you're talking about
+trade-offs, you've got to have
+
+a lot more rigorous evidence.
+
+If we had that kind of evidence,
+we could be a lot
+
+more effective with the
+money that we have.
+
+I also think it's true,
+sometimes people say oh, well
+
+you're just talking about
+passing a dollar and spending
+
+it in a slightly more marginally
+effective way.
+
+But what we really need
+is more money going
+
+into poverty really.
+
+But arguably, potentially one of
+the most important ways to
+
+get more money to go into
+poverty relief is to convince
+
+people that the money that's
+going in is actually used
+
+effectively.
+
+So I don't see these
+as either/or.
+
+Using the money effectively
+and raising more money, I
+
+think, both can come from
+having more evidence.
+
+So it's also important, I think,
+in a way, to move from
+
+what I think is a very damaging
+and nonconstructive
+
+debate between the aid
+optimists and the aid
+
+pessimists.
+
+It's a very kind of polarized
+debate with Jeff Sachs on one
+
+side and Bill Easterly
+on the other.
+
+This is a quote from Jeff Sachs:
+"I've identified the
+
+specific investments
+that are needed"--
+
+from the previous sentence,
+you know that
+
+this is to end poverty--
+
+"found ways to plan and
+implement them and show that
+
+they can be affordable."
+
+Now if you think we
+know everything
+
+about development already--
+
+we know what's needed, we know
+how to implement it-- then,
+
+kind of, this is the wrong
+course for you.
+
+But I think most of us would
+agree that that's slightly
+
+overstating how much information
+we have about how
+
+to end poverty.
+
+There's a lot more questions out
+there than that suggests.
+
+His argument is, but we have
+to get people motivated.
+
+So we have got to say that
+we know everything.
+
+I don't think we have to be
+quite that optimistic.
+
+On the other hand, I think this
+is way too pessimistic.
+
+After $2.3 trillion over five
+decades, why the desperate
+
+needs of the world's poor still
+so tragically unmet?
+
+Isn't it finally time to end the
+impunity of foreign aid?
+
+So Bill Easterly is kind of
+saying, oh, it has not worked.
+
+So let's throw it all away.
+
+We've got to find a middle
+ground here.
+
+It's just about time that
+we have a development.
+
+And they're talking about aid.
+
+And I would argue it's
+much more about
+
+development than aid.
+
+Aid is only a small fraction of
+the money that's spent on
+
+reducing poverty in developing
+countries.
+
+Development pessimism
+is just as bad.
+
+We've got to think more
+strategically about not just
+
+that all aid is bad or
+development funding is wasted,
+
+but how do we focus the money
+on the right things.
+
+So that's kind of
+the motivation
+
+for what we're doing.
+
+But if you think on a very
+grand scale, but thinking
+
+about the objective of
+evaluation in general, you can
+
+think of it as three things.
+
+Accountability, did we do what
+we say we were going to do?
+
+And again, this is true of aid
+agencies, NGOs, government.
+
+And did we have a positive
+impact on people's lives?
+
+So those are two different
+aspects of accountability that
+
+evaluation needs to speak to.
+
+Evaluation isn't only about
+accountability though.
+
+I think it's very importantly
+about lesson learning so we do
+
+better in the future.
+
+And that's about does a
+particular program work or
+
+not, and what's the most
+effective route to achieve a
+
+certain outcome?
+
+Are there similarities?
+
+Are there lessons that you can
+learn across projects?
+
+Are there similarities about
+what we're finding in the
+
+evaluation of this project
+and that project?
+
+For example, are there are
+ways that you're learning
+
+about how to change people's
+behavior in health, and
+
+agriculture, and education?
+
+Are there similarities, sort of
+underlying principles, that
+
+we're learning about that we can
+use in different contexts?
+
+And ultimately, to reduce
+poverty through more effective
+
+programs is the ultimate
+objective of evaluation.
+
+So using that as a framework,
+what makes a good evaluation?
+
+Well, the key thing is
+it's got to answer
+
+an important question.
+
+But it's no good if it answers
+an important question but it
+
+answers it badly.
+
+It's got to answer it
+in an unbiased way.
+
+What do I mean by that?
+
+I mean that it's got to
+find the truthful
+
+answer to the question.
+
+And really to do that, you
+need to have a model or a
+
+theory of change about how the
+project is working so that you
+
+can test the different
+steps in the model.
+
+And that's the best way to
+then learn the most.
+
+If we simply say, we test
+whether the project worked or
+
+didn't work, we learned
+something, but we learn an
+
+awful lot more if you have a
+specific model of how the
+
+project is going to work and you
+test the different steps
+
+along the way.
+
+Sometimes people say--
+
+this is something that drives
+me mad in the evaluation
+
+literature--
+
+you hear people saying,
+well, randomized
+
+evaluations are a black box.
+
+They can tell you whether
+something works or not, but
+
+they can't tell you why.
+
+I hope in the next few days,
+we're going show to you how
+
+you design an evaluation that
+tells you not just whether it
+
+works or not at the end, but
+why and how, and the steps
+
+along the way, and design it
+cleverly so that you learn as
+
+much as you possibly can from
+the evaluation about the
+
+fundamental question.
+
+And that's about getting
+the questions
+
+right at the beginning.
+
+And it's about doing your model
+correctly and thinking
+
+of indicators along the way that
+are going to allow you to
+
+get to all those steps and
+really understand the theory
+
+of change that's happening.
+
+The model is going to start with
+what is it we're trying
+
+to do, who are the targets,
+and what are their needs.
+
+So in an evaluation in
+development, this would often
+
+be called a needs assessment.
+
+And what are their needs?
+
+But then what's the program
+seeking to change?
+
+And looking at precise and
+individual bits of the
+
+program, what's the precise
+program or part of the program
+
+that's being evaluation,
+so asking
+
+very specific questions.
+
+So let's look at an example.
+
+And all of this we're going
+to come back to
+
+and do in more detail.
+
+How do you do a logframe?
+
+Again, maybe some of you
+have done that before.
+
+Maybe you haven't.
+
+But hopefully you'll learn more
+about how we think about
+
+doing a logframe.
+
+So here's an example of an
+evaluation that looked, a very
+
+simple one, does giving
+textbooks to children in Kenya
+
+improve test scores was
+the evaluation.
+
+But what was the need?
+
+What was the problem that the
+program was trying to test?
+
+Well poor children in Busia
+District in Kenya had low
+
+learning levels.
+
+They also had low incomes.
+
+They had few books.
+
+That meant that they couldn't
+take the books home, and that,
+
+the theory was, made
+it hard to learn.
+
+So it was hard to learn because
+they didn't have a
+
+book in front of them in class,
+but also because there
+
+were so few, they couldn't take
+them home and read up
+
+more and do exercises at home.
+
+So what was the input?
+
+The input was that a local NGO
+bought additional textbooks.
+
+In order to get to your
+long-term goal, you not only
+
+need the books, you
+need to make sure
+
+that they're delivered.
+
+Because, again, making this
+chain along the way will help
+
+you understand if it doesn't
+work, where did it go wrong,
+
+if the books were bought but
+they never got there, or they
+
+were stuck in the cupboard.
+
+How many times have we been to
+schools and oh, yes, we have
+
+lots of books.
+
+And we don't want them to get
+messy when the children are
+
+using them.
+
+So they're all nicely in
+their sealed package.
+
+Well you need to be able to
+distinguish if something
+
+doesn't work, is it because it's
+stuck in the cupboard?
+
+Or was it because even when the
+books are out there they
+
+didn't get used or
+they didn't help?
+
+So the books are delivered
+and used.
+
+The children use the books and
+they're able to study better.
+
+And finally, the impact, which
+is what we're about here, is
+
+yes, you got all of
+those steps done.
+
+But did it actually change
+their lives?
+
+Did it actually achieve the
+impact you are hoping to get
+
+is high test scores?
+
+The long-term goal would be not
+just high test scores but
+
+higher income.
+
+And that long-term goal may be
+very difficult to test in the
+
+evaluation.
+
+And you may use some other
+work that may have linked
+
+these in previous studies in the
+same country to make the
+
+assumption that if we got higher
+test scores, it will
+
+have a positive impact.
+
+So again, that's a decision
+when you make in your
+
+evaluation how far along this
+chain you go, if it's a
+
+process evaluation you
+may stop here.
+
+If it's an impact evaluation
+you have to stop here.
+
+But you may not have enough
+money to take it all the way
+
+through to the finest, finest
+level that you would like to.
+
+Oh, I didn't do my little red
+triangles at right point.
+
+OK.
+
+So I've already, in a
+sense, introduced
+
+some of these concepts.
+
+But again, let's review them so
+we know we're talking about
+
+the same thing.
+
+There are many different
+kinds of evaluation.
+
+And needs assessment is where
+you go in and look at a
+
+population, see what
+are the issues.
+
+How many of them
+have bed nets?
+
+What are test scores
+at the moment?
+
+How many books are there?
+
+What's class size?
+
+What are the problems in
+your target population?
+
+In our process evaluation, does
+someone want to tell me
+
+what they would see as
+a process evaluation?
+
+We talked a little
+bit about it.
+
+Someone?
+
+Yeah.
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE] the
+
+chain that you just presented
+to see how you get from the
+
+input to the output from the
+output to the outcome of this
+
+RACHEL GLENNERSTER: Right.
+
+AUDIENCE: Are we successful in
+doing that in transforming our
+
+input into output?
+
+RACHEL GLENNERSTER: Right.
+
+So process evaluation looks at
+did we buy the textbooks?
+
+Were they delivered?
+
+Were they used?
+
+So moving inputs, outputs,
+outcomes, but stopping short
+
+before we get to the impact.
+
+And that's a very useful thing
+to do, and should be done
+
+basically everywhere you do a
+program, or at least some of
+
+those steps need to be measured
+almost every time you
+
+do a program.
+
+But it kind of stops short
+before you get
+
+to the impact stage.
+
+Have we actually changed
+people's lives?
+
+We wanted to build a school.
+
+Did we build a school?
+
+We wanted to build a bridge.
+
+Did we build a bridge?
+
+We wanted to deliver things?
+
+Did we deliver things?
+
+But it's stopping before you
+get the point of knowing
+
+whether this has actually
+changed people's lives.
+
+So an impact evaluation then
+goes to the next stage and
+
+says, given that we have done
+what we said we're going to
+
+do, has that actually
+changed things?
+
+And this is where there
+was a big gap in
+
+terms of what we know.
+
+There's a lot of
+lesson learning
+
+you can do from process.
+
+But in terms of knowing what
+kind of project is going to be
+
+successful in reducing poverty,
+you really need to go
+
+this next step.
+
+Now we used to just talk
+about those three.
+
+But increasingly, as I say as
+I have more contact outside
+
+economics and the more research
+side of evaluation to
+
+work a lot with DFID and other
+organizations, other
+
+foundations, and other agencies,
+I realize a lot of
+
+what people outside the academic
+community call
+
+evaluation I would
+call review.
+
+It's very weird.
+
+Because they would often call
+what I call something else.
+
+But what I mean by review is,
+it's sort of an assessment.
+
+It's sending a knowledgeable
+person in and reviewing the
+
+program and giving their
+comments on it, which can be
+
+extremely helpful if you have
+a good person going and
+
+talking to the people involved,
+and saying, well, in
+
+my experience, it could have
+been done differently.
+
+But it doesn't quite actually
+do any of these things.
+
+It's not just focused in
+did I build the school.
+
+But it's asking questions
+about was there enough
+
+participation.
+
+How well organized
+was the NGO?
+
+And a lot of this is
+very subjective.
+
+So I'm not saying that
+this is bad.
+
+It's just kind of different.
+
+And if you have someone
+very good doing it,
+
+it can be very useful.
+
+My concern with it, is that it's
+very subjective to the
+
+person who's going.
+
+Yeah.
+
+Logan?
+
+AUDIENCE: I think that you see
+so many reviews simply because
+
+the way-- you just
+mentioned DFID.
+
+USAID, I think, is
+the same way.
+
+It's all retroactive.
+
+The way that contracts are
+awarded and things like that,
+
+usually it's because it's a
+requirement to evaluate a
+
+certain number of programs.
+
+And it's not until after the
+program is actually done that
+
+they decide they're going
+to evaluate it.
+
+And it's obviously cheaper to
+send one person over and do
+
+the simple review.
+
+I think it would
+be interesting.
+
+We'll probably get to this when
+we talk about how you can
+
+apply some of the randomized
+control test methodology to
+
+something that you're
+doing retroactively.
+
+RACHEL GLENNERSTER: So just to
+repeat, the argument is we do
+
+a lot of reviews because a
+lot of evaluation is done
+
+retroactively.
+
+What you can do at that
+point is very limited.
+
+Yes.
+
+So this is a big distinction
+between the kinds of
+
+evaluations, is one that's set
+up beforehand and one that is
+
+after the event.
+
+We've got this program.
+
+We want to know whether
+it works.
+
+Basically it's really
+hard to do that.
+
+You've already kind of shot
+yourself in the foot if you
+
+haven't set it up beforehand.
+
+If we think about what I was
+saying about it's crucial to
+
+have a theory of change, a model
+about what we're trying
+
+to achieve and how we're going
+to try and achieve it, and
+
+measuring each of those steps,
+if you're coming in
+
+afterwards, then you're kind
+of adhoc-ly making up what
+
+your theory of change is.
+
+And you haven't set up systems
+to measure those steps along
+
+the way, it's going to
+be very hard to do.
+
+And that's exactly why you end
+up with a lot of reviews.
+
+You're in this mess.
+
+And so you just send someone
+knowledgeable and hope they
+
+can figure it out.
+
+To answer your specific question
+though, you can't do
+
+a randomized evaluation
+after the event.
+
+Because the whole point is
+you're moving people into
+
+treatment and control based
+on a flip of the coin.
+
+And then after the event, people
+have been allocated to
+
+the treatment or not
+the treatment.
+
+And it's very difficult to know
+afterwards were these
+
+people similar beforehand.
+
+It's impossible to
+distinguish.
+
+They may look different now.
+
+But you don't know whether
+they look different now
+
+because they were different in
+the beginning or because
+
+they're different because
+of the program.
+
+Yeah?
+
+AUDIENCE: I was really
+interested to read the first
+
+case study because it seemed
+that you were applying
+
+randomized control
+methodology.
+
+But it seemed to be actually
+done retroactively.
+
+RACHEL GLENNERSTER: No.
+
+It wasn't.
+
+It might look that way.
+
+But it was set up so the first
+case study uses a lot of
+
+different methodologies,
+compares different
+
+methodologies.
+
+But they couldn't use all those
+methodologies if they
+
+hadn't designed it as a
+randomized study at the
+
+beginning actually.
+
+If you've set up a randomized
+evaluation, you can always do
+
+a non-randomized evaluation
+of it.
+
+But if you haven't done it as
+a randomized to start with,
+
+you can't make it randomized.
+
+Prospective evaluation, setting
+up the evaluation from
+
+the beginning, is very important
+I would say in any
+
+methodology you use.
+
+But it's impossible to do it.
+
+There are a couple of examples
+where people have done a
+
+randomized evaluation afterwards
+or an evaluation
+
+afterwards.
+
+And that is because the
+randomization happened
+
+beforehand.
+
+But it wasn't done because
+it was an evaluation.
+
+So if you look at the case on
+the women's empowerment in
+
+India, you will do later in the
+week, that was not set up
+
+as an evaluation.
+
+It was set up as a randomized
+program.
+
+And the rationale was they
+wanted to be fair.
+
+So where there's limited
+resources, sometimes
+
+governments are the people who
+randomized in order to be fair
+
+to the different participants.
+
+Some people, in this
+case, will have to
+
+get a women's leader.
+
+In Colombia Project, that you'll
+find on our website,
+
+the Colombian government wanted
+to provide vouchers to
+
+go to private school.
+
+But they couldn't afford
+it for every one.
+
+So they randomized who
+would get them.
+
+So that's the one case where
+you can do a randomized
+
+evaluation after the event,
+when somebody else is
+
+randomized beforehand, but they
+weren't actually thinking
+
+of it as an evaluation.
+
+But even then, it would've
+been nice to have data
+
+beforehand.
+
+So the last thing on this list
+is cost-benefit analysis,
+
+which is something that you can
+do with the input from all
+
+of these other things.
+
+As they say, the piece of
+information that we have so
+
+little of is what's the effect
+of a dollar here versus a
+
+dollar here.
+
+And you can only do that if
+that's one of your ultimate
+
+objectives when you're doing
+these other impact evaluations
+
+or these other evaluation
+methodologies.
+
+Because you need to be
+collecting data about costs.
+
+And the benefits will come from
+your impact evaluation.
+
+But you need to get your costs
+from your process evaluation.
+
+And you can put the
+two together.
+
+And you can do a cost
+effectiveness.
+
+Then if somebody else has done
+that in their other study, you
+
+can do a cost effectiveness
+comparison across studies.
+
+Or even you can evaluate a range
+of different options on
+
+your impact evaluation.
+
+And that will give
+you comparative
+
+cost-effectiveness across.
+
+So going into a bit more detail
+in some of these, needs
+
+assessment.
+
+We'll look at who's the
+target population.
+
+Is it all children or are we
+particularly focused on
+
+helping the lowest-achieving
+in the group?
+
+What's the nature of the
+problem being solved?
+
+Many of these communities will
+have lots of problems.
+
+So what are we particularly
+trying to focus on here?
+
+Is a test schools?
+
+Is it attendance at school?
+
+How will textbooks solve
+the problem?
+
+I was talking about textbooks.
+
+Maybe it's because they
+can take them home.
+
+Well, if that's part of your
+model, your theory of change,
+
+you need to be actually
+measuring that, not just did
+
+they arrive.
+
+How does the service fit
+into the environment?
+
+How many times have we sat
+in an office and designed
+
+something that we thought made
+complete sense, and gone out
+
+to the field and thought,
+what was I thinking?
+
+This isn't going to work.
+
+How does it feel for
+the teachers?
+
+Do they understand
+the new books?
+
+Do they know how to
+teach from them?
+
+How do the books fit
+into the curricula?
+
+What are you trying to
+get out of this?
+
+As they say, you want a clear
+sense of the target
+
+population.
+
+So then you want to see are
+the students responding?
+
+If you're particularly worried
+about low-performing kids, are
+
+they responding to
+the textbooks?
+
+Students who are falling behind,
+a sense of the needs
+
+the program will fill, what
+are the teachers lacking?
+
+How are we going to deliver
+the textbooks?
+
+How many textbooks are
+we going to deliver?
+
+And what are the potential
+barriers for people learning
+
+from the textbooks?
+
+Then a clear articulation of
+the program benefits, and a
+
+sense of alternatives.
+
+And as I say, if you want to
+look at cost-effectiveness of
+
+alternative approaches, it's
+very important to think
+
+through not just this program in
+isolation, but what are the
+
+alternatives that we
+could be doing?
+
+And how does that
+fit with them?
+
+Is this one is the most
+expensive things we're going
+
+to try, one of the cheapest
+things we want to try, and
+
+everything in between?
+
+So you may be thinking in this
+context, is this a replicable
+
+program that I'm going to
+be able to do elsewhere?
+
+Is this the gold-plated version
+that I'll do if I get
+
+lots of funding?
+
+Or is this something that
+I can replicate in
+
+lots of other places?
+
+Process evaluation, I've really
+sort of talked quite a
+
+bit about these.
+
+So I'm going through
+them faster.
+
+And when you do an impact
+evaluation, because the impact
+
+evaluation is the last thing on
+that chain, you need to do
+
+all the other bits on
+the chain as well.
+
+You can't do an impact
+evaluation without a process
+
+evaluation or you won't
+understand what the hell your
+
+answer is meaning at the end.
+
+So as we say, a process
+evaluation is asking are the
+
+services being delivered?
+
+Is the money being spent?
+
+Are the textbooks reaching
+the classroom?
+
+Are they being used?
+
+And it's also, as I say,
+important to be asking
+
+yourself, what are
+the alternatives.
+
+Could you do this
+in a better way?
+
+Just like a company is always
+thinking are there ways to
+
+reduce costs.
+
+You should be thinking
+are their ways to
+
+do this more cheaply.
+
+Are the services reaching
+the right populations?
+
+Which students are
+taking them home?
+
+Is it the ones that I'm
+targeting or only the most
+
+motivated ones?
+
+And also, are the clients
+satisfied?
+
+What's their response
+to the program?
+
+So an impact evaluation, am
+i missing a top bit here?
+
+No.
+
+OK.
+
+Here we go.
+
+We're out of order.
+
+So an impact evaluation
+is, as they say,
+
+taking it from there.
+
+So assuming once you've got all
+the processes working, and
+
+it's all happening, but
+if it happens, does
+
+it produce an impact?
+
+Take our theory of
+change seriously.
+
+And say what we might expect
+to change if that theory of
+
+change is happening.
+
+So we've got this theory of
+change that says, this is how
+
+we expect things to change.
+
+These are the processes by which
+we expect, like the kids
+
+taking the books home.
+
+So we want to design some
+intermediate indicators and
+
+final outcomes that will
+trace out that model.
+
+So our primary focus is going to
+be, did the textbooks cause
+
+children to learn more.
+
+But we might also be
+interested in some
+
+distributional issues.
+
+Not just on average, we might
+also be interested in was it
+
+the high achieving kids
+that learned more?
+
+Was it the low-achieving kids?
+
+Because very often in
+development, we're just as
+
+interested in the distributional
+implications of
+
+a project as the average.
+
+So who is it who learned?
+
+How does impact differ
+from process?
+
+In the process, we describe
+what happened.
+
+And you can do that from
+reading documents,
+
+interviewing people in
+administrative records.
+
+In an impact question, we need
+to compare what happened to
+
+the people who got the program
+with what would have happened.
+
+This is the fundamental question
+that Dan is going to
+
+hammer on about in his lecture
+about why do we use randomized
+
+evaluations.
+
+We talk about this is
+the counterfactual.
+
+What would have happened if the
+program hadn't happened?
+
+That's the fundamental
+question that we're
+
+trying to get at.
+
+Obviously it's impossible to
+know exactly what would have
+
+happened if the program
+hadn't happened.
+
+But that's what we're
+trying to get at.
+
+Just one second.
+
+Yeah?
+
+AUDIENCE: So one thing that
+would seem to fit in somewhere
+
+with the impact thing but
+doesn't quite meet the
+
+criteria that you've just
+described that we've use
+
+sometimes is this
+pre-post test.
+
+And that isn't necessarily
+going to say
+
+what would have happened.
+
+But it will say, well,
+what were the
+
+conditions when you started?
+
+And we extrapolate from that
+looking at where we are when
+
+we ended, what can we say
+about the impact of the
+
+intervention?
+
+RACHEL GLENNERSTER: Right.
+
+So that is one way that people
+often try and do an impact
+
+evaluation and measure are
+they having an impact.
+
+And I guess it can give you some
+sense of whether you're
+
+having an impact or
+flag problems.
+
+It's to say, well, what were
+conditions at the beginning?
+
+What are they like now?
+
+Then you have this assumption,
+which is that all the
+
+difference between then and
+now is due to the program.
+
+And often that's not a very
+appropriate assumption.
+
+Often things happen.
+
+If we take our example of
+schools, the kids will know
+
+more at the end of
+the year then
+
+they knew at the beginning.
+
+Well would they have known more
+even if we hadn't given
+
+them more textbooks.
+
+Probably.
+
+So that's kind of
+the fundamental
+
+assumption you're making.
+
+And it's a difficult
+one to make.
+
+It's also the case that we
+talked to people who were
+
+doing a project in Gujarat.
+
+And they were tearing their hair
+out and saying, well, we
+
+seem to be doing terribly.
+
+Our program is doing terribly.
+
+People now are worse off
+than when we started.
+
+This was, well Mark will know
+the years of the riots and
+
+earthquake in Gujarat.
+
+They'd basically taken data
+when they started.
+
+In the meantime, there had been
+a massive earthquake and
+
+massive ethnic riots against
+Muslims in Gujarat.
+
+Of course people
+were worse off.
+
+And that's not because of you.
+
+So if can go either
+way actually.
+
+You can assume that your program
+is doing much better
+
+because other things are coming
+
+along and helping people.
+
+And you're attributing all the
+change to your program.
+
+Or it could be the case in
+this extreme example.
+
+There's a massive earthquake
+and massive religious and
+
+ethnic riots and you
+attribute all the
+
+negative to your program.
+
+So it's a way that sometimes
+people use of
+
+trying to get an impact.
+
+It's not a very accurate way of
+getting your impact, which
+
+is why a randomized evaluation
+would help.
+
+So, as you say, it doesn't
+quite fit this criteria.
+
+Because it doesn't
+quite answer.
+
+It says what happened
+over the period.
+
+It doesn't say what would
+have happened.
+
+It is not a comparison of what
+would have happened with what
+
+actually had.
+
+And that's how you want
+to get at your impact.
+
+So there are various
+ways to get at it.
+
+But some of them are more
+effective than others.
+
+So let's go back to our
+objectives and see if we get a
+
+match these different kinds of
+evaluations to our different
+
+objectives for evaluation and
+find out which evaluation will
+
+answer which question.
+
+So accountability: the first
+question for accountability is
+
+just did we do what we said
+we were going to do.
+
+Now that you can use a process
+evaluation to do that.
+
+Because did I do what I said
+I was going to do.
+
+I promised to deliver books.
+
+Did I actually deliver books?
+
+Process evaluation is fine
+for that kind of level of
+
+accountability.
+
+If my accountability is not just
+did I do what I said, but
+
+did what I do help?
+
+Ultimately I'm there
+to help people.
+
+Am I actually helping people?
+
+That's a deeper level
+of accountability.
+
+And that, you can only answer
+with an impact evaluation.
+
+Did I actually make the change
+that I wanted to happen?
+
+If we look at lesson learning,
+the first kind of lesson
+
+learning is, does a particular
+program work or not work.
+
+So an impact evaluation can tell
+you whether a particular
+
+program worked.
+
+If you look at different
+impact evaluations of
+
+different programs, you can
+start saying which ones
+
+worked, whether they work in
+different situations, or
+
+whether a particular kind of
+program works in different
+
+situations or not.
+
+Now what is the most effective
+route for achieving a certain
+
+outcome is kind of an even
+deeper level of learning.
+
+What kind of thing is the best
+thing to do in this situation?
+
+And there you want to have
+a cost-benefit analysis
+
+comparing several programs based
+on a number of different
+
+impact evaluations.
+
+And then we said an even
+deeper level is, can I
+
+understand how we
+change behavior?
+
+Understand deep parameters of
+what makes a successful
+
+program, of how do we change
+behavior from health to
+
+agriculture?
+
+What are some similarities and
+understanding of how people
+
+tick, and how we can use that
+to design better programs?
+
+And again, that's linking our
+results back to theories.
+
+You have got to have a deeper
+theory understanding it, and
+
+then test that with different
+impact evaluations.
+
+And you can get some kind of
+general lessons from looking
+
+across impact evaluations.
+
+And then if we want to have our
+reduced poverty through
+
+more effective programs, which
+is our ultimate objective of
+
+doing evaluations, we've got to
+say, did we learn from our
+
+impact evaluations?
+
+Because if we don't learn from
+them and change our programs
+
+as a result, then we're not
+going to achieve that.
+
+And I guess to say that solid,
+reliable impact evaluations
+
+are a building block.
+
+You're not going to get
+everything out of one impact
+
+evaluation.
+
+But if you build up enough, you
+can generate the general
+
+lessons that you need
+to do that.
+
+I've said quite a lot
+of this already.
+
+But needs assessments give you
+the metric for defining the
+
+cost-benefit ratio.
+
+So when we're looking at
+cost-benefit analysis, we're
+
+looking at what's the most
+cost-effective way of
+
+achieving x?
+
+Well, you need a needs
+assessment to
+
+say what's the x?
+
+What's the thing that I should
+be really trying to solve?
+
+Process evaluation gives you the
+costs for your inputs to
+
+do a cost-benefit analysis.
+
+And an impact evaluation
+tells you the benefit.
+
+So all of these different inputs
+and needed to be able
+
+to do an effective cost-benefit
+analysis.
+
+AUDIENCE: Rachel?
+
+RACHEL GLENNERSTER: Yeah?
+
+AUDIENCE: The needs assessment
+seems to be more of a program
+
+design sort of a
+[UNINTELLIGIBLE], whereas the
+
+remaining three are more like
+the program has already been
+
+designed and we are being
+cautious, we have thought that
+
+this is the right program
+to go with.
+
+Please design a process
+evaluation for this or a
+
+program evaluation for this.
+
+How has that needs assessment
+different from the one that
+
+feeds into program design?
+
+RACHEL GLENNERSTER: Well, in a
+sense, there's two different
+
+concepts here.
+
+You're right.
+
+There's a needs assessment
+for a particular project.
+
+We're working with an NGO in
+India called [UNINTELLIGIBLE]
+
+working in rural Rajasthan.
+
+And they said, we want to
+do more on health in our
+
+communities.
+
+We've done a lot of education
+and community building.
+
+But we want to do a lot
+more in health.
+
+But before we start, we want
+to know what are the health
+
+problems in this community?
+
+It doesn't make sense
+to design the
+
+project until you know.
+
+So we went in and did., what
+are the health problems?
+
+What's the level of services?
+
+Who are they getting
+their health from?
+
+We did a very comprehensive
+analysis of the issues.
+
+And that was a needs assessment
+for that particular
+
+NGO in that particular area.
+
+But you can kind of think of
+that in a wider context of
+
+saying, what are the key
+problems in health in India or
+
+in developing countries?
+
+What are the top priority
+things that we should be
+
+focusing on?
+
+Because again--
+
+and I'm going to get on to
+strategy in a minute-- if
+
+you're thinking as an
+organization, you can't do an
+
+impact evaluation
+for everything.
+
+You can't look at comparative
+cost-effectiveness for
+
+outcomes in the world.
+
+Or at least you've got
+to start somewhere.
+
+You've got to start on, what
+do I most want to know?
+
+What's the main thing I want
+to change to see what's the
+
+cost of changing that thing?
+
+So is it test scores
+in schools?
+
+Or is it attendance?
+
+Am I most concerned about
+improving attendance?
+
+If you look at the Millennium
+Development Goals, in the
+
+sense, that's the world's
+prioritizing.
+
+They're saying, these are the
+things that I most want to
+
+change in the world.
+
+And there they made the
+decision, rightly or wrongly,
+
+on education, that they wanted
+to get kids in school.
+
+And there isn't anything about
+actually learning.
+
+And whether your needs is
+getting kids in school or
+
+learning, you would design
+very different projects.
+
+But you would also design
+different impact evaluations,
+
+because those are two very
+different questions.
+
+So the needs assessment
+is telling you
+
+what are the problems?
+
+What am I prioritizing for my
+programs, but also for my
+
+impact evaluations?
+
+Yeah?
+
+AUDIENCE: Do you need to make
+a decision early on whether
+
+you're interested in actually
+doing a cost-effectiveness
+
+analysis as opposed
+to a cost-benefit.
+
+RACHEL GLENNERSTER:
+[INTERPOSING VOICE]
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE].
+
+efficiency measure, where as
+cost [UNINTELLIGIBLE}--
+
+RACHEL GLENNERSTER: So I'm kind
+of using those too easily
+
+interchangeably.
+
+I don't think it's so
+important here.
+
+How would you define the
+difference between them?
+
+AUDIENCE: As I understand it,
+but [UNINTELLIGIBLE PHRASE]
+
+they getting a better answer.
+
+But cost-effectiveness is
+a productivity measure.
+
+And it would mean that you
+would have to, in an
+
+evaluation say, OK, I'm going to
+look at I put one buck into
+
+this program and I get
+how many more days of
+
+schooling out of it.
+
+Right?
+
+RACHEL GLENNERSTER: Right.
+
+AUDIENCE: Whereas cost-benefit
+requires that it all be in
+
+dollars or some other
+[UNINTELLIGIBLE].
+
+RACHEL GLENNERSTER: So you've
+got to change your benefit
+
+into dollars.
+
+So I'll give you an example
+of the difference.
+
+AUDIENCE: Like
+[INAUDIBLE PHRASE].
+
+RACHEL GLENNERSTER: Let's make
+sure everybody's following
+
+this discussion.
+
+A cost-effectiveness question
+would be to say, I want to
+
+increase the number
+of kids in school.
+
+How much would it cost to get
+an additional year of
+
+schooling from all of these
+different programs?
+
+And I'm just assuming that
+getting kids in school is a
+
+good thing to do.
+
+Right?
+
+I want to do it.
+
+So I'm asking what's the cost
+per additional year of
+
+schooling from conditional cash
+transfer, from making it
+
+cheaper to go to school by
+giving free school uniforms,
+
+or providing school meals.
+
+There are many different things
+I could that will
+
+encourage children to
+come to school.
+
+But I know I want children
+to come to school.
+
+I'm not questioning that goal.
+
+So I just want to
+know the cost of
+
+getting a child in school.
+
+Cost-benefit kind of
+squishes is it all.
+
+And it really asks the question,
+is it worth getting
+
+kids in school?
+
+Because then you can say, if I
+get kids in school, they will
+
+earn more and that will
+generate income.
+
+So if I put a dollar in, am
+I going to get more than a
+
+dollar out at the end?
+
+I'm not going to flick all
+the way back to it.
+
+But if you remember that chart
+that went through the process
+
+and impact, and then the final
+thing of high test scores was
+
+higher income, ultimately am I
+getting more money out of it
+
+than I'm putting in?
+
+I think that's sort of a
+philosophical decision for the
+
+organization to make.
+
+It's very convincing to be able
+to say, for every dollar
+
+we put in, I think for the
+deworming case that you've got
+
+and you do later in the
+week, they do both,
+
+cost-effectiveness
+and cost-benefit.
+
+And the cost-effectiveness
+says, this is the most
+
+cost-effective way to get
+children in school.
+
+But they also then go further
+and say, assuming that these
+
+studies that look at children in
+school in Kenya earn higher
+
+incomes are correct, then given
+how much it costs to get
+
+an additional year of schooling,
+and given an
+
+assumption about how much extra
+kids will in the future
+
+because they went to school,
+then for every dollar we put
+
+in, I think it's you
+get $30 back.
+
+So you kind of have to make an
+awful lot more assumptions.
+
+You have to go to that
+final thing and put
+
+everything on income.
+
+Now if I was doing the women's
+empowerment study, then I'm
+
+not sure that I would want
+to reduce women's
+
+empowerment to dollars.
+
+I might just care about it.
+
+I might care that women are more
+empowered whether or not
+
+it actually leads to
+higher incomes.
+
+So it kind of depends on the
+argument that you're making.
+
+If you want to try and make a
+this is really worth it, this
+
+is a great program, not just
+because it's more effective
+
+than another program, but that
+it generates more income then
+
+I'm putting in.
+
+That's a great motivation.
+
+But I wouldn't say you always
+have to reduce it to dollars.
+
+Because you have to make an
+awful lot of assumptions.
+
+And we don't necessarily
+always want to reduce
+
+everything to dollars.
+
+So here it is.
+
+We've just been talking
+about it.
+
+So this is a cost-effectiveness.
+
+So this is the cost per
+additional year
+
+of schooling induced.
+
+We're not linking it back to
+dollars we're measuring.
+
+We're just assuming that
+we want kids in school.
+
+Millennium Development Goals
+have it as a goal.
+
+we just think it's a good
+thing, whether or not it
+
+generates income.
+
+What we did is take all the
+randomized impact evaluations
+
+that had as an outcome getting
+more children in school and
+
+calculated the cost per
+additional year of schooling
+
+the resulted.
+
+So you see a very wide range
+of different things.
+
+Now conditional cash transfers
+turn out to be by far the most
+
+expensive way of getting an
+additional year of schooling.
+
+Now that's partly because mainly
+they're done in Latin
+
+America where enrollment rates
+are already very high.
+
+So it's often more expensive to
+get the last kid in school
+
+than the 50th percentile
+kid in school.
+
+And then the other thing, of
+course, in general, things
+
+cost more in Mexico than in
+Kenya, especially when you're
+
+talking about people.
+
+Teacher's wages or
+wages outside of
+
+school are more expensive.
+
+But the thing that was amazing
+was that providing children
+
+with deworming tablets
+was just unbelievably
+
+cost-effective.
+
+So $3.50 for an additional year
+of schooling induced.
+
+And putting it this way I think
+really brought out that
+
+difference.
+
+The other thing I should say
+in comparing this is, there
+
+were other benefits
+to these programs.
+
+So Progresa actually gave
+people cash as well.
+
+So it wasn't just about getting
+kids in school.
+
+So of course it was
+expensive, right?
+
+And we haven't calculated
+in those costs.
+
+In cost-benefit, if we reduced
+everything to dollars, it
+
+would look very different
+because you've got a value of
+
+all these other benefits.
+
+But again, deworming
+had other benefits.
+
+It had health benefits as well
+as education benefits.
+
+So we're just looking at one
+measure of outcomes here.
+
+AUDIENCE: Excuse me.
+
+RACHEL GLENNERSTER: Yeah?
+
+AUDIENCE: Are these being
+adjusted for Purchasing Power
+
+Parity, PPP?
+
+RACHEL GLENNERSTER: So
+this is not PPP.
+
+This is absolute.
+
+So again, we've sort
+of debated it
+
+backwards and forwards.
+
+So if you're a country, you
+care more about PPP.
+
+But if you're a donor and you're
+wondering whether to
+
+send a dollar or a pound to
+Mexico or Kenya, you don't
+
+care about PPP.
+
+You care about where your dollar
+is going to get most
+
+kids in school.
+
+So there's different ways
+of thinking about it.
+
+It sort of depends on the
+question you're asking and
+
+who's the person.
+
+For a donor, I think this
+is the relevant way.
+
+If you're a donor who only cares
+about getting kids in
+
+school, this is what
+you care about.
+
+We also can redo this taking
+out the transfers.
+
+There's this other benefit,
+the families,
+
+of getting the money.
+
+So this is the cost
+to a donor.
+
+So that's one way of
+presenting it.
+
+But you can present it
+in other ways too.
+
+AUDIENCE: Can you also sometimes
+do a cost-benefit of
+
+the evaluation itself?
+
+RACHEL GLENNERSTER: That's kind
+of hard to do because the
+
+benefits may come
+ten years later.
+
+The way to think about that is
+to think about who's going to
+
+use it, and only do it if you
+think it's going to actually
+
+have some benefits in terms of
+being used and not just maybe
+
+within the organization.
+
+But if it's expensive,
+is it going to be
+
+useful for other people?
+
+Is it answering a general
+question that lots of people
+
+will find useful?
+
+So often evaluations are
+expensive in the context of a
+
+particular program.
+
+But they're answering a question
+the lots of other
+
+people will benefit from.
+
+So the Progresa evaluation has
+spurred not just the expansion
+
+of Progresa in Mexico, but it
+has spurred it in many other
+
+countries as well because it
+did prove very effective.
+
+Although it's slightly less
+cost-effective in these terms.
+
+But it led to an awful
+lot of learning in
+
+many, many other countries.
+
+So, I think, in that sense, it
+was an extremely effective
+
+program evaluation.
+
+AUDIENCE: Excuse me, I just have
+a question on that very
+
+last item there.
+
+RACHEL GLENNERSTER: OK, so this
+one is even cheaper and
+
+it's a relatively new result.
+
+But it only works in certain
+circumstances.
+
+When people don't know the
+benefits of staying on in
+
+school, ie., how much higher
+wages they're going to get if
+
+they have a primary education,
+then telling them that
+
+information is very cheap.
+
+And both in the Dominican
+Republic and Madagascar--
+
+so two completely different
+contexts, different rates of
+
+staying on in school, different
+continents, very
+
+different schooling systems--
+
+in both cases it was extremely
+effective at increasing the
+
+number of kids staying
+on in school.
+
+But that only works if people
+are underestimating the
+
+returns of staying
+on in school.
+
+If they're overestimating them,
+then it would reduce
+
+staying on in school or if they
+know already, then it's
+
+not going to be effective.
+
+So this is something that I
+think is a very interesting
+
+thing ti do, and again,
+is worth doing.
+
+But you need to first go in and
+test whether people know
+
+what the benefits of staying
+on in school are.
+
+Basically they just told them
+what's the wage if you
+
+complete primary education
+versus what's the wage if you
+
+don't complete primary
+education.
+
+It's very cheap.
+
+So if it changes anything, it's
+incredibly effective.
+
+AUDIENCE: Is the issue of
+marginal returns a problem?
+
+Do you have to say that every
+program is only relevant to
+
+places where it's
+at same level of
+
+enrollment or admission?
+
+RACHEL GLENNERSTER: Well this is
+a sort of wider question of
+
+external validity.
+
+When we do a randomized
+evaluation, we look at what's
+
+the impact of a project
+in that situation.
+
+Now at least you know whether
+it worked in that situation,
+
+which is better than not really
+knowing whether it
+
+worked in that situation.
+
+Then you've got to make a
+decision about whether you
+
+think that is useful to
+another situation.
+
+A great way of doing that is
+to test it in a couple of
+
+different places.
+
+So again, this was tested in two
+very different situations.
+
+The deworming had very
+similar effects.
+
+In rural primary schools in
+Kenya, it works through
+
+reducing anemia.
+
+Reducing anemia in preschool
+urban India had almost
+
+identical effects.
+
+Getting rid of worms in a
+non-randomized evaluation to
+
+be true, but kind of a really
+nicely designed one in the
+
+south of the United
+States had almost
+
+exactly the same effect.
+
+So they got rid of hookworm
+in the 1900s.
+
+And again, it would increase
+school attendance, increase
+
+test scores, and actually
+increase wages just from
+
+getting rid of hookworm.
+
+And they reckoned a quite
+substantial percentage.
+
+This paper by Hoyt Bleakley at
+Chicago found that quite a
+
+substantial difference in the
+income of the North and the
+
+South of United States in 1900
+was simply due to hookworm.
+
+So this is being tested.
+
+So ideally you test something
+in very different
+
+environments.
+
+But you also think about whether
+it makes sense that it
+
+replicates.
+
+So if I take the findings of the
+women's empowerment study
+
+in India where it works through
+local governance
+
+bodies that are quite active in
+India and have quite a lot
+
+of power, and tried to replicate
+in Bangladesh where
+
+there is no equivalent system,
+I would worry about it.
+
+Whereas worms cause anemia
+around the world.
+
+And anemia causes
+you to be tired.
+
+And being tired is likely to
+affect you going to school.
+
+That's something that seems
+like it would replicate.
+
+So you have to think through
+these things and
+
+ideally test them.
+
+If I'm doing microfinance,
+would I assume it has
+
+identical effects in Africa, or
+Asia, and Latin American?
+
+No.
+
+Because it's very dependent
+on what are the learning
+
+opportunities in those
+environments.
+
+And they're likely to
+be very different.
+
+So I'd want to test it in those
+different environments.
+
+We're falling a bit behind.
+
+So I promised to do when to
+do an impact evaluation.
+
+So there are important
+questions you need to
+
+know the answer to.
+
+So that might be because there's
+a program that you do
+
+in lots of places, and you have
+no idea whether it works.
+
+That would be a reason
+to do one.
+
+You're very uncertain about
+which strategy to
+
+use to solve a problem.
+
+Or there are key questions that
+underline a lot of your
+
+programs, for example, adding
+beneficiary control, having
+
+some participatory element
+to your program.
+
+It might be something that you
+do in lots of different
+
+programs when you don't know
+what's the best way to do it
+
+or whether it's being
+effective.
+
+An opportunity to do it is when
+you're rolling out a big
+
+new program.
+
+And you're going to invest an
+awful lot of money in this
+
+program, you want to know
+whether it works.
+
+This is a tricky one.
+
+You're developing a new
+program and you
+
+want to scale it up.
+
+At what point in that process
+should you do the impact
+
+evaluation?
+
+Well you don't want to do it
+once you've scaled it up for
+
+everywhere.
+
+Because then you find out it
+doesn't work, and you've just
+
+spend millions of dollars
+scaling it up.
+
+Well that's not a good idea.
+
+On the other hand, you don't
+want to do it when it's your
+
+very first designs.
+
+Because often it changes an
+awful lot in the first couple
+
+of years as your tweaking it,
+and developing it, and
+
+understanding how to make
+it work on the ground.
+
+So you want to wait until you've
+got the basic kinks
+
+ironed out.
+
+But you want to do it before
+you scale it up too far.
+
+We've done a lot of work
+with this NGO in
+
+India called Pratham.
+
+And we started doing
+some work for them.
+
+And by the time we finished
+doing an evaluation, their
+
+program had completely
+changed.
+
+So we kind of did another one.
+
+So we probably did that one
+a little bit too early.
+
+But on the other hand, now
+they're scaling up massively.
+
+And it would be silly to wait
+until they'd done the whole of
+
+India before we evaluated it.
+
+AUDIENCE: You said it may be
+more appropriate to do a
+
+process evaluation initially to
+get a program to the point
+
+where it can be fully
+implemented and all the kinks
+
+are worked out.
+
+RACHEL GLENNERSTER:
+Yeah, exactly.
+
+If we're going back to our
+textbook example again, you
+
+don't want to be doing it until
+you've got your delivery
+
+system for the textbooks worked
+out, and you've made
+
+sure you've got the
+right textbook.
+
+It's a bit of a waste of money
+until you've got those things.
+
+And exactly, a process
+evaluation can tell you
+
+whether you've got those
+things working.
+
+The other thing that makes it a
+good time or a good program
+
+to do an impact evaluation of
+is one that's representative
+
+and not gold-plated.
+
+Because if Millennium
+Development Villages, $1
+
+million per village.
+
+If we find that that has an
+impact on people's lives,
+
+that's great.
+
+But what do we do with that?
+
+We can't give $1 million to
+every village in Africa.
+
+So it's not quite,
+what's the point?
+
+But it's less useful than
+testing something that you
+
+could replicate across the whole
+of Africa, that you have
+
+enough money to replicate
+in a big scale.
+
+So that's interesting because
+you can use it more.
+
+Because if you throw everything
+at a community,
+
+yes, you can probably
+change things.
+
+But what are you learning
+from it?
+
+So it takes time, and
+expertise, and
+
+money to do it right.
+
+So it's very important to think
+about when you're going
+
+to do it and designing the right
+evaluation to answer the
+
+right question that you're
+going to learn from.
+
+AUDIENCE: If a program hasn't
+been successful, have you
+
+found that the NGO's have
+abandoned that program?
+
+RACHEL GLENNERSTER:
+Yes, mainly.
+
+We worked with an NGO in
+Kenya that didn't work.
+
+They just moved on to
+something else.
+
+Pratham, we actually did two
+things, both of which worked,
+
+but one which was more
+cost-effective than the other.
+
+And they dumped the computer
+assisted learning even though
+
+it was like phenomenally
+successful.
+
+But the other one was
+even cheaper.
+
+So they really scaled that up.
+
+And they haven't really done
+computer assisted learning
+
+even though it had a very big
+effect on math test scores.
+
+And compared to anybody else
+doing education, it was very
+
+cost-effective But compared to
+their other approach, which
+
+was even more cost-effective,
+they were like, OK.
+
+We'll do the one that's
+most cost-effective.
+
+Now there are some organizations
+that
+
+kind of do one thing.
+
+And it's much harder for them
+to stop doing that one thing
+
+if you find it doesn't work.
+
+They tend to think, well,
+how can I adapt it?
+
+But these organizations that do
+many things are often very
+
+happy to, OK, that
+didn't work.
+
+We'll go this direction.
+
+So we want to develop an
+evaluation strategy to help us
+
+prioritize what evaluations
+to do when.
+
+So the first thing to do is step
+back and ask, what are
+
+the key questions for
+your organization?
+
+What are the things that I
+really, really need to know?
+
+What are the things that would
+make me be more successful,
+
+that I'm spending lots of money
+on but I don't know the
+
+answer, or some of these more
+fundamental questions, as they
+
+say, about how do I get
+beneficiary control across my
+
+different programs.
+
+The other key thing is you're
+not going to be able to answer
+
+all of them by your own
+impact evaluations.
+
+And as they say, it's expensive
+to do them.
+
+So the first thing to do is to
+go out and see if somebody
+
+else has done a really good
+impact evaluation that's
+
+relevant to you to answer
+your questions already.
+
+Or half answer or more gives you
+the hypotheses to look at.
+
+How many can I answer just
+from improved process?
+
+Because if my problems are about
+logistics, and getting
+
+things to people, and getting
+cooperation from people, then
+
+I can get that from process
+evaluation.
+
+So from that you can select your
+top priority questions
+
+for an impact evaluation
+and establish a plan
+
+for answering them.
+
+So then you've go to look for
+opportunities where you can
+
+develop an impact evaluation
+that will enable you to answer
+
+those questions.
+
+So am I rolling out a new
+program in a new area?
+
+And I can do an impact
+evaluation there.
+
+Or you might even want to
+say, I want to set up an
+
+experimental site.
+
+I don't really know whether to
+go this way or that way.
+
+So I'm just going to
+take a place and
+
+try different things.
+
+And it's not going to be really
+part of my general
+
+rollout But I'm going to focus
+in on the questions.
+
+Should I be charging
+for this or not?
+
+How much should I charge?
+
+Or how should I present
+this to people?
+
+And you can take a site and
+kind of try a bunch of
+
+different things against each
+other, figure out your design,
+
+really hone it down, and
+then roll that out.
+
+So those are two kinds of
+different options of thinking
+
+about how to do it.
+
+And then, when you've got those
+key questions of your
+
+impact, you can combine that
+with process evaluations to
+
+get your global impact.
+
+What do I mean by that?
+
+Let's go back to our
+textbook example.
+
+If you're giving out textbooks
+across many states or
+
+throughout the country,
+you've evaluated it
+
+carefully in one region.
+
+And you find that the impact
+on test scores
+
+is whatever it is.
+
+And then you know very
+carefully, and maybe you've
+
+tested it in two different
+locations in the country and
+
+you've got very similar
+results.
+
+So then you can say, well I know
+that every time I give a
+
+textbook, I get this impact
+on test schools.
+
+Then from the process
+evaluation, you know how many
+
+textbooks are getting in
+the hands of kids.
+
+Then you can combine the two,
+multiply up your impact
+
+numbers by the number of
+textbooks you give out.
+
+Malaria control with bed nets,
+if I hand out this many bed
+
+nets, then I'm saving
+this many lives.
+
+I've done that through a careful
+impact evaluation.
+
+And then all I need to do is
+just count the number of bed
+
+nets that are getting
+to people and I
+
+know my overall impact.
+
+So that's a way that you
+can combine the two.
+
+You don't have to do an impact
+evaluation for every single
+
+bed net you hand out.
+
+Because you've really got the
+underlying evaluation impact
+
+model, and you can
+extrapolate.
+
+AUDIENCE: Rachel?
+
+RACHEL GLENNERSTER: Yeah?
+
+AUDIENCE: Do you think in the
+beginning when you got a
+
+program that you're interested
+in, do you think that's the
+
+moment to think about the size
+of the impact that you're
+
+looking at that people expect?
+
+And also, as part of that,
+what's going to be the
+
+audience, the ultimate audience
+that you're trying to
+
+get to if you're successful
+with a scale-up.
+
+And those two things, I think,
+frequently come together.
+
+Because it's the scaling up
+process where people are going
+
+to start to look at those
+cost-effectiveness measures
+
+and cost-benefit.
+
+RACHEL GLENNERSTER: I mean, I
+would argue that you've always
+
+got to be thinking about your
+ultimate plans for scaling it
+
+up when you're designing
+the project.
+
+Because you design a project
+very differently if you're
+
+just trying to treat a small
+area than if you're thinking
+
+about, if I get this right,
+I want to do it on
+
+a much wider area.
+
+If you've always got that in
+mind, you're thinking a lot
+
+about is this scalable?
+
+Am I using a resource that is
+either money or expertise that
+
+is in very short supply, in
+which case there's no point in
+
+designing it this way because
+I won't able to scale it
+
+beyond this small study area.
+
+So if that's your ultimate
+objective, you need to be
+
+putting that into the impact
+evaluation from the moment.
+
+Because there's no point in
+doing the impact evaluation,
+
+very resource-intensive
+project, and
+
+say, well, that works.
+
+But I can't do that
+everywhere.
+
+Well then what have
+you learned?
+
+You want to be testing the thing
+that ultimately you're
+
+going to be able to
+bring everywhere.
+
+So in a lot of our cases, we're
+encouraging our partners
+
+to scale it back.
+
+Because you won't be able to
+do this on a big scale.
+
+So scale it back to what you
+would actually be doing if
+
+you're trying to do the
+whole of India or the
+
+whole of this state.
+
+Because that's what's
+useful to learn.
+
+And you want to be able
+to sell to someone
+
+to finance the scale-up.
+
+So I think having those ideas in
+your mind at the beginning
+
+is very important, and as they
+say, making it into a
+
+strategy, not a project by
+project evaluation, but
+
+thinking about where do I want
+to go as an organization.
+
+What's the evidence I need to
+get there, and then designing
+
+the impact evaluations to
+get you that evidence.
+
+And people often ask me about
+how do you make sure that
+
+people use the evidence from
+impact evaluations.
+
+And I think the main
+answer to that is
+
+ask the right question.
+
+Because it's not about
+browbeating people to make
+
+them read studies afterwards.
+
+If you find the answer to an
+interesting question, it'll
+
+take off like wildfire.
+
+It will be used.
+
+But if you answer a stupid
+question, then nobody is going
+
+to want to read your results.
+
+So we're learning from an impact
+evaluation, so learning
+
+from in a single study did the
+program work in this context?
+
+Should we expand it to
+a similar population?
+
+Learning from an accumulation
+of studies, which is what we
+
+want to get to eventually, is
+did the same program work in a
+
+range of different contexts,
+India, Kenya, south of the
+
+United States?
+
+And that's incredibly valuable
+because then your learning is
+
+much wider and you can take
+it to many more places.
+
+Did some variation in the same
+program work differently, ie.,
+
+take one program and try
+different variants of it and
+
+test it out so that we know
+how to design it.
+
+Did this same mechanism
+seem to be present
+
+in different areas?
+
+So there's a lot of studies
+looking at the impact of user
+
+fees in education and health.
+
+You seem to get some very
+similar results.
+
+And again, that's even
+more useful.
+
+Because then you're not just
+talking about moving deworming
+
+to another country.
+
+You're talking about
+user fees.
+
+What have we learned about
+user fees across a lot of
+
+different sectors?
+
+There's some common
+understandings and learnings
+
+to take to even a sector
+that we may not
+
+have studied before.
+
+And then, as they say, putting
+these learnings in the place,
+
+in filling in an overall
+strategy of what were my gaps
+
+in knowledge?
+
+And am I slowly filling
+them in?
+
+So, I think that's it.
+
+So I'm sorry the last bit
+was a little bit rushed.
+
+The idea was to kind of
+motivate why we're
+
+doing all of this.
+
+Today you're going to
+be in your groups.
+
+The task for your groups today,
+as well as doing the
+
+case, is to decide on a question
+for an evaluation
+
+that you're going to design
+over the next five days.
+
+So hopefully that's made you
+think about what's an
+
+interesting question.
+
+What should we be testing?
+
+Because I think often an
+underlooked element of
+
+designing an evaluation is
+what's the question that we
+
+want to be answering with
+this evaluation?
+
+Is it a useful question?
+
+How am I going to use it?
+
+What's it going to tell me for
+making my program, my whole
+
+organization more effective
+in the future?
+
+So any questions?
+
+AUDIENCE: What would you say
+are some of the main
+
+limitations of randomization?
+
+So I assume one of them is
+extrapolate the populations
+
+that are different?
+
+Are there other main ones
+that you can think of?
+
+RACHEL GLENNERSTER: So it's
+important to distinguish when
+
+we talk about limitations.
+
+One is just general, what's
+the limitation to say,
+
+extrapolating beyond?
+
+But the other thing is to think
+of it in the context of
+
+what's the limitation versus
+other mechanisms?
+
+Because, for example, the
+extrapolating to other
+
+populations is not really a
+limitation of randomized
+
+evaluations compared to
+any other impact.
+
+Any impact evaluation is done
+on a particular population.
+
+And so there's always a question
+as to whether it
+
+generalizes to another
+population.
+
+And the way to deal with that is
+to design it in a way that
+
+you learn as much as you
+possibly can about the
+
+mechanisms, about the routes
+through which it worked.
+
+And then you can ask yourself
+when you bring it to another
+
+population, do those routes
+seem like they might be
+
+applicable, or is there
+an obvious gap?
+
+This worked through the
+local organization.
+
+But if that organization isn't
+there, is there another
+
+organization that it could work
+through there or not?
+
+If you think that deworming
+works through the mechanism of
+
+anemia, well it works between
+the mechanism of there being
+
+worms and of anemia, you
+can go out and test.
+
+Are there worms in the area?
+
+Is the population anemic because
+there may be worms and
+
+they're not anemic.
+
+So that's a way to design the
+evaluation to limit that
+
+limitation or reduce the problem
+of that limitation.
+
+But it's not like the very
+active flipping a coin and
+
+randomizing causes the
+problem of not being
+
+able to extend it.
+
+It's true of any impact
+evaluation.
+
+I think one limitation which
+you will find in your
+
+frustration as you want to try
+and answer every single
+
+question that you have, and you
+get into the mechanics of
+
+sample size and how much
+sample size do I need--
+
+and again, that's not
+necessarily just of a
+
+randomized evaluation, but any
+quantitative evaluation--
+
+you can test a limited
+number of hypotheses.
+
+And every hypothesis you want
+to test needs more sample.
+
+And so the number of questions
+you can answer very rigorously
+
+is limited.
+
+And I think that's the
+limitation that we often find
+
+very binding.
+
+Again, any rigorous quantitative
+evaluation will
+
+have that limitation.
+
+We'll talk a lot tomorrow
+about sometimes
+
+you just can't randomize.
+
+Freedom of the press is not
+something that you can
+
+randomize except by country.
+
+And then we'd need every
+country in the world.
+
+It's just not going to happen.
+
+So we'll look at a lot of new
+techniques or different
+
+techniques that you can use to
+bring randomization to areas
+
+where you think it would be
+impossible to bring it to.
+
+Compared to other quantitative
+evaluations, you sometimes
+
+have political constraints about
+where you can randomize.
+
+But as I say, quantitative
+versus qualitative, the
+
+qualitative isn't so limited
+by sample size constraints.
+
+And you're not so limited
+to answer very specific
+
+hypotheses.
+
+The flip side is you don't
+answer any specific
+
+hypotheses.
+
+And it's the same
+rigorous way.
+
+But it's much more open.
+
+So very often what we do is we
+combine a qualitative and
+
+quantitative, and spend a lot
+of time doing qualitative
+
+before to hone our hypotheses,
+and then use a randomized
+
+impact evaluation to test
+those specific.
+
+But if you sit in your office
+and design your hypotheses
+
+without any going out into the
+field, you will almost
+
+certainly waste your money
+because you won't have asked
+
+the right question.
+
+You won't have designed it.
+
+So you need some element of
+qualitative to make sure some
+
+needs assessment, some work on
+the ground to make sure that
+
+you are asking, you're designing
+your hypotheses
+
+correctly because you've
+only got a few shots.
+
+Yeah?
+
+AUDIENCE: I was wondering,
+do you know of some good
+
+evaluation or randomized
+impact evaluation on
+
+conservation programs?
+
+RACHEL GLENNERSTER: On
+conservation programs?
+
+I can't think of any, I'm
+afraid, but eminently doable.
+
+But we can talk about that if
+you can persuade your group to
+
+think about designing one.
+
+Anyone else think of a
+conservation program?
+
+Yes?
+
+AUDIENCE: I don't
+have an example.
+
+I wish I did.
+
+And you've mentioned this.
+
+I just need to really underline
+it for myself.
+
+A lot of the programs that
+my organization does are
+
+comprehensive in nature.
+
+So they have lots of different
+elements meant to in the end,
+
+collectively,
+[UNINTELLIGIBLE PHRASE].
+
+What I'm understanding here is
+that you could do an impact
+
+evaluation of all of
+those collectively.
+
+But really it would be more
+useful to pull them out and
+
+look at the different
+interventions
+
+side by side or something.
+
+Because that way you'll
+get a more targeted--
+
+RACHEL GLENNERSTER: It's true.
+
+The question was, if you have a
+big package of programs that
+
+does lots of things, you can do
+an evaluation of the whole
+
+package and see whether
+it works as a package.
+
+But in terms of learning about
+how you should design future
+
+programs, you would probably
+learn more by trying to tease
+
+out, take one away, or
+try them separately.
+
+Because there might be elements
+of the package that
+
+are very expensive but are not
+generating as much benefit as
+
+they are cost.
+
+And you would get more effect by
+doing a smaller package in
+
+more places.
+
+You don't know unless you
+take the package apart.
+
+Now then if you test each one
+individually, that's a very
+
+expensive process.
+
+Because it needs a lot of
+sample size to test each
+
+individually.
+
+There's also a very interesting
+hypothesis that's
+
+true in lots of different
+areas.
+
+People often feel, where there
+are lots of barriers, so we
+
+have to attack all of them.
+
+It only makes sense.
+
+You won't get any movement
+unless you do.
+
+There are lots of things
+stopping kids going to school.
+
+There's stopping, say, girls
+going to school.
+
+They're needed a home.
+
+There are attitudes.
+
+There is their own health.
+
+There's maybe they
+are sick a lot.
+
+So we have to address all
+of those if we're
+
+going to have an impact.
+
+We don't know, the answer is.
+
+And indeed, in that example
+where we're working with Save
+
+the Children in Bangladesh,
+they had this
+
+comprehensive approach.
+
+Where there are all
+these problems.
+
+So let's tackle them all.
+
+We convinced them to divide it
+up a bit, and test different
+
+things, and see some of their
+own worked, or whether you
+
+needed to do all of them
+together before you changed
+
+anything, which is a perfectly
+possible hypotheses and one
+
+that a lot of people have, but
+hasn't really been tested.
+
+The idea that you've got to get
+over a critical threshold.
+
+And you've got to
+build up to it.
+
+And only once you're over there
+do you see any movement.
+
+Well actually on girls going
+to school, it's quite
+
+interesting.
+
+Most of the evaluations that
+have looked at, just
+
+generally, improving attendance
+at school, have had
+
+their biggest impact on girls.
+
+I should say most of those were
+not done in the toughest
+
+environments for girls
+going to school.
+
+They're not in Afghanistan
+or somewhere where it's
+
+particularly difficult.
+
+But it is interesting.
+
+Just general things and
+approaches in Africa and India
+
+have had their biggest impacts
+on girls, which suggests that
+
+you've got a hit every
+possible thing
+
+is maybe not right.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+and the political constraints
+[INAUDIBLE PHRASE].
+
+RACHEL GLENNERSTER: Right.
+
+So we'll talk actually tomorrow
+quite a lot about the
+
+politics of introducing an
+evaluation or at least the
+
+different ways that you can
+introduce randomization to
+
+make it more politically
+acceptable.
+
+That's slightly different from
+whether the senior political
+
+figures want to know whether
+the program works or are
+
+willing to fund an evaluation.
+
+I've actually been amazingly
+surprised.
+
+Obviously we find that
+some places.
+
+There are certain partners
+or people we've
+
+started talking with.
+
+And you can see the moment the
+penny drops that they're not
+
+going to have any control.
+
+Because you're going to do
+a treatment comparison.
+
+You're going to stand back.
+
+At the end of the day the
+results going to be that.
+
+There's no fiddling with it,
+which is one of the beauties
+
+of the design.
+
+But it will be what it will be,
+which is kind of why it's
+
+convincing.
+
+But there are certain groups who
+kind of figure that out.
+
+And they run for the exit
+because there's going to be an
+
+MIT stamp of approval evaluation
+potentially saying
+
+their program doesn't work.
+
+That's life.
+
+Some people don't
+want to know.
+
+The best thing I can say in
+that situation is test
+
+alternatives.
+
+It's much less threatening
+to test alternatives.
+
+Because there's always some
+alternative of this versus
+
+that, that people don't know.
+
+And then you're not raising
+the does it work.
+
+You're saying well, does this
+work better than that?
+
+And that is much less
+threatening.
+
+It doesn't tell you
+quite as much.
+
+But it's much less
+threatening.
+
+There's a report called When
+Will We Ever Learn, looking at
+
+the politics of why don't we
+have more impact evaluations,
+
+which was very pessimistic.
+
+But if you look at somewhere
+like the World Bank that just
+
+put a purse of money for
+doing randomized impact
+
+evaluations out there.
+
+And anybody in the
+bank could apply.
+
+And people were like why?
+
+There's no incentives
+for them to do it.
+
+Program office's, they've
+already got a
+
+lot on their plate.
+
+Why would they add doing this?
+
+It's going to find out that
+they're opening themselves to
+
+all these risks because maybe
+their program doesn't work.
+
+Massively oversubscribed, first
+year, six times more
+
+applicants then there
+was money.
+
+It just came out of the woodwork
+as soon as there was
+
+some money to do it.
+
+So I'm not saying every
+organization is like that.
+
+Obviously not everybody in
+their bank did that.
+
+But it was, to me, actually
+quite surprising how many
+
+people were willing
+to come forward.
+
+Now we have the luxury of
+working with the willing,
+
+which if you're working within
+an organization, you don't
+
+necessarily have that luxury.
+
+You will see as you get into the
+details of these things,
+
+that you need absolutely full
+cooperation and complete
+
+dedication on the part of the
+practitioners who were doing
+
+these evaluations alongside
+the evaluators.
+
+You can't do this with
+a partner who
+
+doesn't want to be evaluated.
+
+It just doesn't work.
+
+They are so able to throw monkey
+wrenches in there if
+
+they don't want to find
+out the answer.
+
+Then it's just not worth
+doing it because it's a
+
+partnership like that.
+
+It's not someone coming along
+afterwards and interviewing.
+
+It is the practitioners and the
+evaluators working hand in
+
+hand throughout the
+whole process.
+
+And therefore if the
+practitioners don't want to be
+
+evaluated, there's not a hope
+in hell of getting a result.
+
+We should wrap up.
+
+A lot of these things we're
+going to talk about.
+
+But I'll take one more.
+
+Yeah?
+
+AUDIENCE: How important, or
+how relevant is it, or how
+
+much skepticism can there be
+about a case where the
+
+evaluators and the practitioners
+work for the
+
+same people or are funded
+by the same people?
+
+RACHEL GLENNERSTER: Yeah, we've
+even got practitioners
+
+as co-authors on our studies.
+
+This is another place where I
+kind of part company from the
+
+classic evaluation guidelines,
+which say that it's very
+
+important to be independent.
+
+I'd argue if your methodology is
+independent, what you want
+
+is not independence.
+
+You want objectivity.
+
+And the methodology of a
+randomized evaluation can
+
+provide you the objectivity.
+
+And therefore you don't have to
+worry about independence.
+
+Now there's one caveat
+to that.
+
+The beauty of the design is
+you set it up, as I say.
+
+Well you don't stand
+back in the sense.
+
+You've got to manage all your
+threats and things.
+
+But you can't fiddle very
+much with it at the end.
+
+The one exception
+to that is that
+
+you can look at subgroups.
+
+So there was an evaluation in
+UK of a welfare program.
+
+And it was a randomized
+evaluation.
+
+And there was some
+complaining.
+
+Because at the end, they went
+through and looked at every
+
+ethnic minority.
+
+and then you know I can't
+remember whether it did work
+
+in general.
+
+But it didn't work for one
+minority, or it didn't work.
+
+But anyway, you can find one
+subgroup for whom the result
+
+was flipped.
+
+And that was the thing on the
+front page of the newspapers,
+
+rather than the overall
+effect.
+
+So there's a way to deal with
+that, which is increasingly
+
+being stressed by people who are
+kind of looking over the
+
+shoulder and making sure that
+what is done in randomized
+
+evaluations is done properly,
+which is to say that you need
+
+to set out in advance--
+
+we'll talk about this a bit
+later on-- but you need to set
+
+out in advance what you're
+going to do.
+
+So if you want to look at a
+subgroup like does it affect
+
+the lowest performing kids in
+the school differently from
+
+the highest performing kids--
+
+do I care most about the
+lowest performing kid--
+
+if you want to do that, you need
+to say you're going to do
+
+that before you actually
+look at the numbers.
+
+Because even with a randomized
+evaluation, you can data mine
+
+to some extent.
+
+Well if I look at least ten
+kids, does it work for them?
+
+If I look at least ten kids,
+does it work for them?
+
+Statistically you will be able
+to find some subset of your
+
+sample for whom it does work.
+
+So you can't just keep trying
+100 different subgroups.
+
+Because eventually it will
+work for one of them.
+
+So on the whole, you
+need to look at the
+
+main average effect.
+
+What's the average effect
+for the whole sample?
+
+If you are particularly
+interested in a special group
+
+within the whole sample, you
+need to say that before you
+
+start looking at the data.
+
+So that's the only way in which
+you get to fiddle with
+
+the results.
+
+And otherwise it provides an
+enormous amount of objectivity
+
+in the methodology.
+
+And therefore, you don't have
+to worry so much about a
+
+Chinese wall between the
+evaluators and the
+
+practitioners, which, I think,
+is incredibly important.
+
+Because we couldn't do the work
+that we do if we had that
+
+Chinese wall.
+
+It just wouldn't make sense,
+doing your theory of change,
+
+finding out how it's working,
+designing it so it asks the
+
+right questions.
+
+None of that would be possible
+if you had wall between you.
+
+So it just wouldn't be anything
+like as useful.
+
+So getting your objectivity from
+the methodology allows
+
+you to be very integrated
+with the evaluation, and
+
+practitioners to be
+very integrated.
\ No newline at end of file
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+MIT OpenCourseWare is a publication of MIT
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+they have been taught at MIT.
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\ No newline at end of file
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@@ -0,0 +1,1570 @@
+All right, let's get moving.
+Good morning.
+
+Let me take a quick poll.
+So, how many of you have
+
+completed Lab 4.
+Completed Lab 4?
+
+Wow, that's great.
+So, how many people have begun
+
+Lab 4?
+OK, well that's good.
+
+I won't ask the last question.
+OK so, well I hope you're
+
+having fun with this lab.
+Lab 4 was designed to be almost
+
+like a mini-project.
+And, it sort of ties together a
+
+lot of the content of the entire
+course.
+
+And, it's not unlike the kind
+of systems that people design in
+
+industry, in systems that go
+into a variety of devices like,
+
+say, for example,
+digital CD players and stuff
+
+like that.
+A lot of mixed signal stuff
+
+goes in.
+OK, so today,
+
+I'm going to continue with our
+discussion of energy and CMOS.
+
+CMOS will be a new topic that I
+will introduce.
+
+So, the last lecture,
+we spent a fair bit of time
+
+talking about energy,
+and how to compute the energy
+
+of our inverter.
+So, let me start from where I
+
+left off, and I've given you a
+couple of extra pages of notes
+
+today just to sort of tie it to
+the previous lecture.
+
+Right now, I'm going to start
+off on page three.
+
+So, what we saw last time was
+an inverter of this sort,
+
+Vs, VIN, and we said,
+let's study the situation where
+
+this inverter was driving a load
+capacitor, C.
+
+Where did this load capacitor
+come from?
+
+Well, this inverter could be
+driving one, or two,
+
+or three, or four other larger
+gates, OK?
+
+So, this C is lumped value of
+the gate capacitances of all of
+
+those inverters.
+This may also include some
+
+component due to wiring
+capacitance and stuff like that.
+
+So, for an inverter like this,
+we showed in the last lecture
+
+that the formula for the average
+power was,
+
+so this was a static power
+independent of frequency,
+
+and this was called dynamic
+power, and it had some bearing,
+
+it's related to the frequency
+at which you clocked your
+
+circuit.
+So, this was related to standby
+
+power, and this to dynamic.
+So, what I also said is that I
+
+gave you a bunch of numbers so
+you could compute the power
+
+consumption of a chip that
+included 10^8 gates,
+
+100 million gates,
+and at a frequency of 1 GHz,
+
+and a bunch of other numbers.
+C was given to be 0.1
+
+femtofarads.
+Femto is 10^-15.
+
+So, F was 10^9.
+VS was 5V, and for these
+
+numbers, if you plonk them down
+in something like this,
+
+for 10^8 gates on a chip,
+the average power would be 10^8
+
+times these two.
+So, this would be five squared,
+
+which is 25,
+divided by twice.
+
+RL was given to be 10
+kilo-ohms, so,
+
+twice, 10^4.
+And here we had CVS^2.
+
+So, C was 10^-16,
+0.1 femtofarads.
+
+Vs^2 was 25,
+and F was 10^9.
+
+So, if you commence through the
+numbers here,
+
+what you end up getting is
+something that looks like this,
+
+10^8 times this guy here.
+This is 1.25mW plus this guy
+
+ends up being 2.5 microwatts.
+So, this should come as a bit
+
+of a shocker.
+If I take 1.25mW,
+
+and multiply that out by 10^8,
+this says that each gate
+
+suffers a standby power loss of
+1.25mW.
+
+So times 10^8,
+I get 125kW,
+
+and this guy yields 250W.
+OK, the 250W is manageable.
+
+It's still high,
+and just so you don't think
+
+that this is unreasonable,
+when the Pentium 4 first came
+
+out, it was consuming 170W of
+power.
+
+OK, you should see the heat
+sinks on there.
+
+There's actually a huge heat
+sink with a fan built into the
+
+top of the heat sink.
+OK, today it's down to more
+
+reasonable numbers like 100W and
+so on, but when it came out it
+
+was in this range.
+So it's high but not
+
+unreasonable.
+But this, of course,
+
+is totally wacko.
+OK, imagine carrying a laptop
+
+around, and the sucker is
+blowing 125kW.
+
+That'll be fun.
+So, clearly there's something
+
+wrong here.
+What this is saying is that
+
+this gate here consumes 125kW,
+there are 10^8 of these on a
+
+single chip.
+OK, so we clearly have to do
+
+something about this,
+otherwise the semiconductor
+
+industry would fail.
+So, anybody have any ideas?
+
+What do you think you might do
+here?
+
+What do you think you might do
+to this inverter to make this
+
+look better, to bring it down?
+What can I do?
+
+Anybody?
+Any ideas?
+
+What do you think?
+Well, the problem is that if I
+
+look at this 125kW,
+well, there's a VS term here
+
+and an RL term here.
+So, I can increase RL.
+
+OK, I can make RL four times or
+eight times as large.
+
+That'll bring the power down
+somewhat.
+
+Can anybody think of any
+problem with increasing RL?
+
+If I make RL really,
+really large,
+
+will I run into other problems?
+Yes?
+
+Exactly, the slowdown of the
+inverter.
+
+Remember, the rise time of the
+inverter depends on how quickly
+
+I can charge this capacitor
+through RL.
+
+So, if I make my RL really
+large, I will consume less
+
+standby power from hundreds of
+kilowatts to merely tens of
+
+kilowatts.
+But my gates will run as slow
+
+as molasses.
+So, clearly that's not a
+
+tradeoff I would like to make.
+So, I can reduce my voltage to
+
+maybe a volt.
+But that just reduces it by a
+
+factor of 25,
+VS squared.
+
+So clearly, this is not going
+to work.
+
+I have to somehow do something
+else, and that will be the topic
+
+of today's lecture.
+Also, I will dwell for a moment
+
+on this term.
+So, if you look at the spec
+
+sheet for the IBM's ASIC
+processor that we handed out,
+
+if you recall,
+we talked about power
+
+dissipation of 0.006 microwatts
+per MHz per gate.
+
+OK, now you see where this is
+coming from.
+
+Per MHz, that's because it's a
+multiple of f,
+
+the power.
+Second is that it's per gate,
+
+so this is the power per gate.
+So, as I have more gates,
+
+I just have that much more
+power dissipation.
+
+It also says power supply
+voltage in the range of 0.7 to
+
+1.3 right next to the power
+expression.
+
+So, you can see why they tell
+you all of that,
+
+because both voltage,
+and the frequency,
+
+and the number of gates come
+into the power of equation.
+
+OK, this really simple
+expression here,
+
+it's amazing how close this is
+to what people use for the
+
+dynamic power in chips.
+OK, so as the next step,
+
+what I'd like to do is,
+this guy, what do we do about
+
+that?
+OK, so we've taught you to
+
+build gates in a particular
+matter, but it's a non-starter.
+
+So, how do we get rid of static
+power?
+
+How do we get rid of static
+power?
+
+OK, to do so,
+let's build up a little bit of
+
+intuition.
+OK, so the intuition goes as
+
+follows.
+So let's say I take my
+
+inverter.
+Let me draw the circuit both on
+
+the on state and in the off
+state.
+
+So, when VIN is high,
+when VIN is high,
+
+I get the MOSFET turning on and
+has a resistance,
+
+RON, and Vo is the output
+voltage.
+
+Similarly, when VIN is low,
+so when VIN was high,
+
+Vo was low because RON is much
+less than RL.
+
+So, this voltage was low,
+while here, when VIN is low,
+
+the MOSFET is off,
+and so I have an open circuit
+
+out here.
+And because of that open
+
+circuit, the voltage here was
+going to be high because VS
+
+would simply appear there.
+So let's tailor this and see if
+
+we can build up some intuition
+as to what to do.
+
+So, when VIN is low,
+I don't have any static power
+
+being dissipated because I don't
+have a connection from VS to
+
+ground.
+OK, the current,
+
+i, is zero.
+And, VS simply appears at the
+
+output.
+The reason this is so is have a
+
+switch here.
+So when this is low,
+
+the switch opens up and cuts
+the path from power to ground.
+
+This is a nice situation.
+Here, when VIN was high,
+
+there was no switch that turns
+off.
+
+Rather, I get a connection from
+VS to ground.
+
+OK, so think about this
+situation here.
+
+The insight here is,
+just imagine if I could do the
+
+following.
+Imagine if I could somehow
+
+magically elevate RL to be a
+very, very, very large number,
+
+if I could make this so high as
+to make the power really low
+
+only in the situation when the
+input was high,
+
+OK?
+So, imagine if I could do
+
+something like this.
+Imagine I could open circuit
+
+this guy, RON,
+so when VIN was high,
+
+if I could, instead of having
+an RL here, what if somehow I
+
+could make this RL become
+infinity?
+
+OK, so in this case,
+output VO would be low.
+
+OK, I get many benefits by
+doing this.
+
+One benefit is that,
+look, I have opened this switch
+
+here so I don't have any standby
+current.
+
+OK, the standby current is
+zero.
+
+The second benefit is that my
+output gets dragged down to
+
+ground, OK?
+Out here, my output was VS
+
+multiplied by RON divided by the
+sum of these two.
+
+Out here, I have a direct
+connection to ground,
+
+and nothing to the power
+supply, VS, and so therefore I
+
+have a nice, solid low.
+So the question is that,
+
+can I get this situation?
+OK, that is a key insight.
+
+So, imagine that somehow,
+when this was high,
+
+I could get this to open up,
+much like when this was low,
+
+I got this to open up.
+OK, so think about it.
+
+So, the intuition is that what
+I need instead of a resistor
+
+here, what if I have something
+like the MOSFET that I have
+
+here?
+So, I have a MOSFET here that
+
+turned off when VIN was low.
+OK, what if I did the
+
+complementary thing?
+What if I put in some kind of
+
+MOSFET here that would turn off
+when VIN was high?
+
+OK, so, much like the MOSFET
+turned off when VIN was low down
+
+here, imagine if I could find a
+device that could turn off when
+
+VIN was high?
+OK, this would be on,
+
+but this would be off.
+So the behavior of this device
+
+would have to be complementary
+to this device.
+
+So, we need some sort of a
+switch to introduce this new,
+
+little MOSFET device with
+slightly different properties,
+
+let me quickly review for you
+the properties of the MOSFET
+
+that we know about,
+so our N channel MOSFET,
+
+also called the NFET,
+this is what we've been seeing
+
+all this while,
+is drawn like this.
+
+I have a gate;
+I have a drain;
+
+I have a source.
+And this guy is on when VGS is
+
+greater than or equal to VT,
+OK, and off when VGS is less
+
+than VT.
+You saw this before,
+
+OK, nothing new here.
+So, what I need is a device
+
+that behaves in a complementary
+manner.
+
+OK, so the device is a P
+channel MOSFET.
+
+By the way, I must point out,
+till about 1983-84 until the
+
+early '80s, that's exactly
+pretty much how chips were
+
+designed, OK,
+using an NFET for the switch
+
+looking down here,
+and a variety of different
+
+kinds of devices to be used as
+resistors.
+
+OK, that's when technology
+began moving towards this new
+
+kind of technology I'm going to
+talk about, and that
+
+dramatically reducing the power
+consumed.
+
+And, the P channel MOSFET was
+created, and this guy's called
+
+the PFET.
+It's a complementary device
+
+that looks as follows.
+OK, the difference here is
+
+that, to show this is
+complementary,
+
+I'll put a little circle here.
+It has a gate.
+
+Just to make things a little
+clearer, flip the drain and
+
+source terminals,
+and this guy is on at a
+
+distinguished threshold voltage
+of this with the NFET device,
+
+let me put an N here to say
+that this is the VT for the N
+
+channel device.
+And for this guy,
+
+this guy came on when VGS was
+greater than some voltage.
+
+So, VTN could be,
+for example,
+
+one volt.
+So, VGS was more than one.
+
+This turned on.
+In this case,
+
+I wanted this to turn on when
+VGS is some value which is lower
+
+than, or much lower than,
+the source voltage.
+
+OK, so this guy turns on when
+the gate voltage is higher.
+
+This guy should turn on when
+the gate voltage is
+
+significantly lower than the
+source voltage,
+
+just the complementary
+behavior.
+
+OK, so when VGS is less than or
+equal to VTP.
+
+And in this case,
+the threshold voltage for the
+
+PMOS device, say,
+just as an example,
+
+maybe -1V.
+So this means that if the
+
+source is at,
+say, 5V, OK,
+
+then this device would turn on
+if the gate, for example,
+
+using that example was less
+than 4V.
+
+So, this is five.
+If the gate fell below 4V,
+
+this guy would turn on.
+In this situation,
+
+remember, if this was at zero,
+the gate would have to be
+
+greater than 1V to turn on.
+In this situation,
+
+the gate has to be less than 4V
+if the source was at five to
+
+turn on.
+And, it's off.
+
+OK, so this is a complementary
+device that I postulate that
+
+behaves in a complementary
+manner.
+
+So, the gate voltage rises,
+this guy turns on,
+
+and in this situation,
+when the gate voltage drops
+
+below the source voltage,
+this guy turns on.
+
+OK, so when there's a rising
+guy that turns on in this
+
+particular situation when it
+falls, the gate turns on and
+
+shows some resistance.
+In this case,
+
+the resistance would be RON.
+And to show that it's N
+
+channel, let me say N.
+And in this case,
+
+the resistance,
+when it turns on,
+
+would be RONp to represent P
+channel.
+
+OK, so now consider the
+following circuit for the
+
+inverter.
+So, instead of my resistor,
+
+I put a complementary device,
+OK, and that's it.
+
+So all I've done here is
+replace my resistor with a
+
+MOSFET that behaves
+complementary to the N channel
+
+MOSFET.
+So this is my gate,
+
+my drain.
+This is my source,
+
+my gate, my source,
+and my drain.
+
+OK, and this guy is called a
+pull up, and this guy is called
+
+a pull down.
+OK, and the reason is that this
+
+guy pulls the output to ground
+when it's turned on,
+
+while this guy,
+when switched on,
+
+will pull this node up to VS.
+So, I pull it down or pull it
+
+up based on when the VIN is high
+or low.
+
+So, let's look at the two
+situations.
+
+So, let's say,
+as an example,
+
+my VS is 5V,
+and let's say VIN in one
+
+situation being 5V,
+and another situation being
+
+equal to 0V.
+Let's draw the equivalent
+
+circuit in both these cases.
+So, when VIN is high,
+
+I have my usual circuit.
+When VIN is high,
+
+this MOSFET,
+as before, when VIN is 5V,
+
+the N channel MOSFET below is
+turned on, and so I have an RON
+
+resistance here.
+But remember,
+
+VIN is 5, and VS is 5V,
+then the voltage across the
+
+source and the gate of this P
+channel FET is now equal,
+
+five and five.
+OK, so this one would turn off.
+
+And that's the circuit that I
+get.
+
+The output is suitably low.
+In this situation,
+
+if VIN is zero,
+what happens in this situation?
+
+Here's my output.
+If VIN is 0V,
+
+the lower device turns off.
+This is zero.
+
+This is zero.
+This guy turns off,
+
+and that's the situation for
+the N channel MOSFET.
+
+How about this guy here?
+What happens here?
+
+This is at 5.
+So let me just,
+
+this is at 5V.
+OK, and VIN is at 0V.
+
+OK, so therefore,
+the GS of this is -5V.
+
+If this is zero and this is
+five, G, source,
+
+and drain, GS is -5V,
+and -5V is significantly less
+
+than the threshold -1V in our
+example.
+
+So, this one will switch on.
+And if this one switches on,
+
+what I end up getting is RONp
+out there.
+
+So, when this one kicks in,
+it pulls the output high and VO
+
+goes high.
+So, all I've done is replaced
+
+my resistor with a complementary
+device, which switches off when
+
+the input is high,
+and switches on when the input
+
+is low.
+And the beauty of this is that
+
+at no point, assuming all the
+devices are ideal here,
+
+at no point do I have a short
+circuit between the output,
+
+do I have a current path from
+the output to the ground from
+
+the supply to ground,
+OK, I have this turned off or
+
+this turned off.
+So, this type of logic
+
+involving a PMOS transistor
+here, and the N channel
+
+transistor here is called CMOS
+logic for, OK,
+
+it's called complementary MOS
+logic.
+
+That's what CMOS comes from.
+OK, so I'm sure you've read in
+
+a number of places that most
+digital chips today use CMOS
+
+technology.
+It comes from complementary
+
+MOS, and complementary comes
+from the use of complementary
+
+transistors: N channel,
+P channel, turns on when high,
+
+turns off when high,
+turns off when low,
+
+turns on when low.
+OK, that's exactly
+
+complementary to each other.
+OK, so what you've seen here
+
+has been the workhorse of the
+digital industry for the past
+
+two decades, 20 years,
+CMOS logic.
+
+OK, and even the most advanced
+chip from Intel has an inverter
+
+that looks exactly like that.
+OK, if you count all the
+
+inverters in the universe today,
+I would say a significant
+
+fraction of those look exactly
+like that, no difference,
+
+just so simple.
+So, the key with something like
+
+that is there is no path from
+the power supply to the ground,
+
+and so by that model,
+I did not consume any standby
+
+power.
+OK, my standby power in that
+
+idealized model is zero.
+So, let's compute P.
+
+So, what is P dynamic?
+Let's use the method that we
+
+adopted in the last lecture,
+and draw the equivalent
+
+circuit, and compute the power.
+OK, so I'm going to model the
+
+following situation,
+and assume that I drive a
+
+capacitive load,
+C.
+
+OK, and as an input,
+as I did the last time,
+
+I'm going to assume I have some
+input voltage,
+
+VIN, that looks like this.
+The cycle time,
+
+T, and the frequency is 1/t,
+and let me assume that this is
+
+T1, and this is T2.
+OK, and I'm assuming that T1
+
+and T2 are both much larger than
+the respective time constants.
+
+OK, the time constants when,
+for discharging here,
+
+is C RONn, and here the
+relevant resistance is RONp.
+
+The charging time constant is
+RONp times C.
+
+OK, so T1 and T2 are assumed to
+be much greater than these two.
+
+So when you look at this,
+there's one other benefit
+
+besides the power benefit,
+OK, of using CMOS logic
+
+compared to using NMOS.
+OK, it not only cuts out my
+
+standby power,
+but there is another
+
+significant advantage which is
+almost equal to the power
+
+advantage of this kind of CMOS
+technology.
+
+Anybody have any ideas?
+What's the advantage?
+
+What does intuition tell you?
+Is CMOS going to be faster or
+
+slower than NMOS?
+Why?
+
+That's right.
+The key here is that the NMOS
+
+design I showed you earlier was
+relatively slow because it took
+
+me a while to charge up the load
+capacitor from RL.
+
+In this situation,
+RL will become really,
+
+really small;
+it's RONp.
+
+It's roughly the same magnitude
+as RONm.
+
+OK, if so both of these on
+resistances are more or less
+
+equal and small,
+then the rise time will be of
+
+the same order of magnitude as
+the fall time,
+
+which makes this much faster
+than the NMOS.
+
+In NMOS, my time constant was
+RLC, and RL was pretty large.
+
+In this case it's RONp C,
+and RONp can be made to be very
+
+small because when it's switched
+off, the resistance here is
+
+infinity.
+So, in this situation,
+
+if I assume T1 and T2 are much
+larger than the respective time
+
+constants, I can go ahead and
+draw my equivalent circuit.
+
+So, here's VS.
+So, for charging up,
+
+let's say this one is going to
+a one, or to a high.
+
+So, I have VS going through a
+resistor, RONp,
+
+to a capacitor,
+and this thing is a switch.
+
+So I have RONp,
+an ideal switch,
+
+going to a capacitor,
+C, this is my V out node,
+
+OK, so it's VS going through a
+resistance, RONp,
+
+an ideal switch,
+to a capacitor,
+
+C.
+That's a charging circuit.
+
+For discharging,
+I have C, discharging through
+
+an ideal switch with RONn.
+So, this situation,
+
+I have an ideal switch,
+RONn.
+
+OK, so that's the equivalent
+circuit for something like this.
+
+So, in this circuit,
+during T1, this guy's off,
+
+and this guy's on,
+on during T1,
+
+and off otherwise.
+This guy is on during T2,
+
+and off otherwise.
+OK, so just imagine,
+
+this guy switches on,
+this guy switches off,
+
+this guy switches on,
+this guy switches off,
+
+OK?
+And remember,
+
+this is exactly the circuit I
+had analyzed last time in the
+
+last lecture,
+and the result given by v
+
+double asterisk.
+And that result was simply
+
+average power being CVS^2f.
+That's the exact circuit we
+
+used to compute the dynamic
+power, CVS^2f.
+
+OK, so we're done.
+And how did this come about?
+
+This came about because the
+intuition here is that I'm
+
+charging up the capacitor fully,
+and then I'm discharging the
+
+capacitor through this other
+side, OK, and I'm consuming
+
+power, dissipating power,
+in these two resistances during
+
+charge up and during the
+discharge.
+
+Half the power gets consumed
+during charge up,
+
+and half during the discharge.
+So, I'd like to go back to
+
+doing a few numbers here,
+and taking a look at how,
+
+even with this expression,
+life can get pretty thorny as
+
+we go ahead into the next
+decade.
+
+OK, so for our previous
+example, we assumed that 10^8
+
+gates, F=1 GHz,
+C=0.1 femtofarads,
+
+VS was 5V, and I don't need RL
+anymore.
+
+OK, why is it that I don't have
+any resistance component here?
+
+I don't have it here because
+the power consumed by this
+
+circuit is independent of those
+resistances, provided T1 and T2
+
+are long enough,
+are much longer than the two
+
+time constants,
+RONp C, and RONn C.
+
+OK, so I don't have RL in my
+equation anymore.
+
+I don't have any standby power.
+So, based on this calculation,
+
+the calculation I did up there
+showed that I had 2.5 microwatts
+
+per gate, and for 10^8 gates I
+had 250W for a chip with 10^8
+
+gates.
+So, I'd like to dwell on this,
+
+if you can move over to page
+eight in your notes,
+
+here.
+Let me dwell on this for some
+
+time, and pontificate on a few
+things.
+
+First of all,
+this number,
+
+as I said before,
+is high, but not a disaster.
+
+OK, so you can't use this in
+laptops, but it's quite OK for a
+
+desktop or a server,
+and so on.
+
+If you just go and put your ear
+to a pedestal computer,
+
+you'll always hear it making a
+sound, and that sound is because
+
+of a big fan that's inside it.
+And, if you have a big enough
+
+fan, 250W is not such a big
+deal.
+
+But, this is certainly a real
+problem for mobile devices.
+
+For a laptop,
+this is unthinkable.
+
+OK, so we have to deal with
+this.
+
+The second issue is the
+following, that it's 250W for
+
+1GHz.
+Now, the fastest Pentium 4s
+
+that money can by today are,
+what, how many GHz?
+
+What's the fastest Pentium 4
+you can buy today?
+
+What's that?
+Does anybody have a 4GHz
+
+Pentium 4 here?
+Oh, darn, you beat me.
+
+Anybody have a 3?
+3GHz?
+
+A couple.
+So, I have a couple of 3GHz
+
+machines, and our lab has a
+whole ton of them.
+
+So, if Intel comes out with
+4GHz machines today,
+
+they've been going up by about
+1GHz roughly every year for the
+
+past couple of years.
+And, within three or four
+
+years, you're going to see
+chips, microprocessors that are
+
+in the 5-10GHz range,
+OK, assuming that all other
+
+things stay equal,
+which of course they're not,
+
+but just to give you some
+insight here,
+
+if I clock these guys and build
+circuits that are ten times
+
+faster, I very soon go up to
+2.5kW, again as I said,
+
+all things being equal which
+they're not.
+
+But just to give you a sense,
+as I increase my frequency,
+
+so does the power consumed by
+the chip, OK?
+
+So, I really have to do
+something here.
+
+So, if I stare at this
+equation, CVS^2f,
+
+I want to increase f because
+people will buy computers if I
+
+have higher frequencies.
+And, Intel has managed to use
+
+its marketing campaigns to
+pretty much convince consumers
+
+that high frequencies are a good
+thing.
+
+OK, and whether they really
+mean anything or not,
+
+that's a different issue.
+So, we've got this huge power
+
+for assuming 5V,
+OK, so it turns out that
+
+microprocessors,
+as they come out,
+
+newer and newer versions run at
+lower and lower voltages.
+
+OK, they invent technologies
+that use lower and lower
+
+voltages, and go from VS 5V to,
+today, VS on the order of 1.5
+
+to 1V, somewhere in that range.
+So the moment you do that,
+
+you get a 25x reduction in
+power.
+
+OK, so in going from 2.5kW,
+you would now come down to
+
+something on the order of 100W,
+which is, again,
+
+much more reasonable,
+again, all other things being
+
+equal.
+It turns out that the
+
+capacitance of devices also
+changes as you go to smaller and
+
+smaller devices.
+And, 100W is also pretty high,
+
+and still not good enough for
+mobile computers.
+
+So, there are many,
+many other tricks that people
+
+use to get even lower powers.
+One trick is to play games with
+
+the clock.
+OK, what you do is,
+
+let's say for example in some
+computation you are not going to
+
+be using your floating point
+unit.
+
+Or let's say I'm going to be
+using your integer adder unit.
+
+OK, so what you can do is you
+can turn off the clock to those
+
+devices so that those devices do
+not even switch when they're not
+
+working.
+OK, if I turn off the clock to
+
+a device, the device isn't even
+going to switch,
+
+it's just going to sit there in
+limbo without consuming any
+
+power.
+It's equivalent to turning off
+
+both transistors.
+If you turn off both the PMOS
+
+and NMOS somehow,
+OK, it's not consuming any
+
+power.
+And by doing that,
+
+you can further cut down the
+power.
+
+So, if you can idle some of
+your function units,
+
+it's called idling a function
+unit, idle a function unit for,
+
+let's say, half the time.
+OK, you would cut down power by
+
+another factor of two.
+We can idle,
+
+then, 75% of the time,
+come down to 25W.
+
+So, those are the classes of
+tricks that people play.
+
+I'm going to stop here and
+allow the underground guide
+
+folks to do the survey.
+But, suffice it to say that the
+
+power discussion that I've gone
+through with you is a very high
+
+level discussion as to the real
+thing.
+
+In real life,
+what actually happens is that
+
+there is a fair amount of
+standby power even for CMOS
+
+logic.
+It turns out that although I
+
+don't have a path from VS to
+ground for my two transistors,
+
+it turns out that there are
+many leakage currents.
+
+OK, currents leak through all
+kinds of places through the
+
+drain of the inverter,
+and so on and so forth.
+
+And so, there is some standby
+power.
+
+So, let me show you a quick
+demo while, I guess,
+
+the review handouts are going
+around.
+
+And this shows the temperature
+of my CMOS inverter,
+
+and as I increase the
+frequency, you can just watch
+
+the temperature go up,
+and hopefully we'll blow this
+
+transistor.
+So, I'm increasing the
+
+frequency as you can see on the
+side here, and higher frequency
+
+implies more power consumption,
+more temperature,
+
+OK, and hopefully you will see
+some smoke coming out of,
+
+OK, I think I blew the
+inverter.
+
+So, the output is gone.
+So, it's at 110 degrees there,
+
+and that blew it.
+Sometimes we see smoke come
+
+out, but I guess today is not
+one of our lucky days.
+
+OK, so let me stop here and
+have the underground guide folks
+
+go through the reviews.
\ No newline at end of file
diff --git a/JZ19Eot3lPc.txt b/JZ19Eot3lPc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77317d15edc477304122ae3618a825d6e71a7aac
--- /dev/null
+++ b/JZ19Eot3lPc.txt
@@ -0,0 +1,14235 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay I'd like to in this
+
+ align:start position:0%
+ocw.mit.edu okay I'd like to in this
+ 
+
+ align:start position:0%
+ocw.mit.edu okay I'd like to in this
+evening lecture what I'd like to do is
+
+ align:start position:0%
+evening lecture what I'd like to do is
+ 
+
+ align:start position:0%
+evening lecture what I'd like to do is
+continue a bit to expand on and
+
+ align:start position:0%
+continue a bit to expand on and
+ 
+
+ align:start position:0%
+continue a bit to expand on and
+complicate and maybe also deepen
+
+ align:start position:0%
+complicate and maybe also deepen
+ 
+
+ align:start position:0%
+complicate and maybe also deepen
+this idea I've been suggesting to you
+
+ align:start position:0%
+this idea I've been suggesting to you
+ 
+
+ align:start position:0%
+this idea I've been suggesting to you
+that I'm labeling the fedot principle
+
+ align:start position:0%
+that I'm labeling the fedot principle
+ 
+
+ align:start position:0%
+that I'm labeling the fedot principle
+really a shorthand way of describing the
+
+ align:start position:0%
+really a shorthand way of describing the
+ 
+
+ align:start position:0%
+really a shorthand way of describing the
+immensely complex and from an
+
+ align:start position:0%
+immensely complex and from an
+ 
+
+ align:start position:0%
+immensely complex and from an
+intellectual standpoint to historical
+
+ align:start position:0%
+intellectual standpoint to historical
+ 
+
+ align:start position:0%
+intellectual standpoint to historical
+standpoint immensely exciting and
+
+ align:start position:0%
+standpoint immensely exciting and
+ 
+
+ align:start position:0%
+standpoint immensely exciting and
+astonishing process whereby film went in
+
+ align:start position:0%
+astonishing process whereby film went in
+ 
+
+ align:start position:0%
+astonishing process whereby film went in
+an in an incredibly short time from
+
+ align:start position:0%
+an in an incredibly short time from
+ 
+
+ align:start position:0%
+an in an incredibly short time from
+being a mere novelty to being an
+
+ align:start position:0%
+being a mere novelty to being an
+ 
+
+ align:start position:0%
+being a mere novelty to being an
+embedded social formation in the United
+
+ align:start position:0%
+embedded social formation in the United
+ 
+
+ align:start position:0%
+embedded social formation in the United
+States and and in other industrialized
+
+ align:start position:0%
+States and and in other industrialized
+ 
+
+ align:start position:0%
+States and and in other industrialized
+societies and and not just only a so
+
+ align:start position:0%
+societies and and not just only a so
+ 
+
+ align:start position:0%
+societies and and not just only a so
+embedded social formation becoming by
+
+ align:start position:0%
+embedded social formation becoming by
+ 
+
+ align:start position:0%
+embedded social formation becoming by
+the end of the 1920s one of the central
+
+ align:start position:0%
+the end of the 1920s one of the central
+ 
+
+ align:start position:0%
+the end of the 1920s one of the central
+media for the expression of art an an
+
+ align:start position:0%
+media for the expression of art an an
+ 
+
+ align:start position:0%
+media for the expression of art an an
+artistic medium so that it went from
+
+ align:start position:0%
+artistic medium so that it went from
+ 
+
+ align:start position:0%
+artistic medium so that it went from
+being a mere novelty from Fred artne in
+
+ align:start position:0%
+being a mere novelty from Fred artne in
+ 
+
+ align:start position:0%
+being a mere novelty from Fred artne in
+20 years or so 25 years to being a
+
+ align:start position:0%
+20 years or so 25 years to being a
+ 
+
+ align:start position:0%
+20 years or so 25 years to being a
+medium of astonishingly rich and complex
+
+ align:start position:0%
+medium of astonishingly rich and complex
+ 
+
+ align:start position:0%
+medium of astonishingly rich and complex
+narrative art that progress uh is part
+
+ align:start position:0%
+narrative art that progress uh is part
+ 
+
+ align:start position:0%
+narrative art that progress uh is part
+of what I mean by the um Fred art
+
+ align:start position:0%
+of what I mean by the um Fred art
+ 
+
+ align:start position:0%
+of what I mean by the um Fred art
+principle and and it might be helpful if
+
+ align:start position:0%
+principle and and it might be helpful if
+ 
+
+ align:start position:0%
+principle and and it might be helpful if
+I if I concretize that a little bit more
+
+ align:start position:0%
+I if I concretize that a little bit more
+ 
+
+ align:start position:0%
+I if I concretize that a little bit more
+by mentioning a bit more about what I
+
+ align:start position:0%
+by mentioning a bit more about what I
+ 
+
+ align:start position:0%
+by mentioning a bit more about what I
+mean about the what I was implying or
+
+ align:start position:0%
+mean about the what I was implying or
+ 
+
+ align:start position:0%
+mean about the what I was implying or
+referring to when I spoke about that
+
+ align:start position:0%
+referring to when I spoke about that
+ 
+
+ align:start position:0%
+referring to when I spoke about that
+moment of imitation remember I said that
+
+ align:start position:0%
+moment of imitation remember I said that
+ 
+
+ align:start position:0%
+moment of imitation remember I said that
+there were essentially that the that the
+
+ align:start position:0%
+there were essentially that the that the
+ 
+
+ align:start position:0%
+there were essentially that the that the
+that silent film and incidentally I take
+
+ align:start position:0%
+that silent film and incidentally I take
+ 
+
+ align:start position:0%
+that silent film and incidentally I take
+it as a model for the way in which most
+
+ align:start position:0%
+it as a model for the way in which most
+ 
+
+ align:start position:0%
+it as a model for the way in which most
+New Media systems uh develop in culture
+
+ align:start position:0%
+New Media systems uh develop in culture
+ 
+
+ align:start position:0%
+New Media systems uh develop in culture
+you can apply this same basic schema to
+
+ align:start position:0%
+you can apply this same basic schema to
+ 
+
+ align:start position:0%
+you can apply this same basic schema to
+other forms of of popular entertainment
+
+ align:start position:0%
+other forms of of popular entertainment
+ 
+
+ align:start position:0%
+other forms of of popular entertainment
+including
+
+ align:start position:0%
+including
+ 
+
+ align:start position:0%
+including
+shocking as it may seem Shakespeare's
+
+ align:start position:0%
+shocking as it may seem Shakespeare's
+ 
+
+ align:start position:0%
+shocking as it may seem Shakespeare's
+public theater and I'll come back to the
+
+ align:start position:0%
+public theater and I'll come back to the
+ 
+
+ align:start position:0%
+public theater and I'll come back to the
+implications of that analogy the idea
+
+ align:start position:0%
+implications of that analogy the idea
+ 
+
+ align:start position:0%
+implications of that analogy the idea
+that Shakespeare was the movie of his
+
+ align:start position:0%
+that Shakespeare was the movie of his
+ 
+
+ align:start position:0%
+that Shakespeare was the movie of his
+time that Shakespeare's theater was the
+
+ align:start position:0%
+time that Shakespeare's theater was the
+ 
+
+ align:start position:0%
+time that Shakespeare's theater was the
+Hollywood studio system of of of the of
+
+ align:start position:0%
+Hollywood studio system of of of the of
+ 
+
+ align:start position:0%
+Hollywood studio system of of of the of
+the Elizabethan era is a very
+
+ align:start position:0%
+the Elizabethan era is a very
+ 
+
+ align:start position:0%
+the Elizabethan era is a very
+complicated one it's a very inspiring
+
+ align:start position:0%
+complicated one it's a very inspiring
+ 
+
+ align:start position:0%
+complicated one it's a very inspiring
+one and it's it's complicated because it
+
+ align:start position:0%
+one and it's it's complicated because it
+ 
+
+ align:start position:0%
+one and it's it's complicated because it
+makes us reassess our inherited Notions
+
+ align:start position:0%
+makes us reassess our inherited Notions
+ 
+
+ align:start position:0%
+makes us reassess our inherited Notions
+about what art is and where art comes
+
+ align:start position:0%
+about what art is and where art comes
+ 
+
+ align:start position:0%
+about what art is and where art comes
+from one of the subtexts in this course
+
+ align:start position:0%
+from one of the subtexts in this course
+ 
+
+ align:start position:0%
+from one of the subtexts in this course
+is precisely that the has to do with
+
+ align:start position:0%
+is precisely that the has to do with
+ 
+
+ align:start position:0%
+is precisely that the has to do with
+what I call the enabling conditions of
+
+ align:start position:0%
+what I call the enabling conditions of
+ 
+
+ align:start position:0%
+what I call the enabling conditions of
+Art and I'll come back to that again as
+
+ align:start position:0%
+Art and I'll come back to that again as
+ 
+
+ align:start position:0%
+Art and I'll come back to that again as
+a theme again and again in in the course
+
+ align:start position:0%
+a theme again and again in in the course
+ 
+
+ align:start position:0%
+a theme again and again in in the course
+so part of what I mean by the Fred art
+
+ align:start position:0%
+so part of what I mean by the Fred art
+ 
+
+ align:start position:0%
+so part of what I mean by the Fred art
+principle is this is this uh roing
+
+ align:start position:0%
+principle is this is this uh roing
+ 
+
+ align:start position:0%
+principle is this is this uh roing
+complex uh U um uh partly unpredictable
+
+ align:start position:0%
+complex uh U um uh partly unpredictable
+ 
+
+ align:start position:0%
+complex uh U um uh partly unpredictable
+process whereby uh a PO an enlarging
+
+ align:start position:0%
+process whereby uh a PO an enlarging
+ 
+
+ align:start position:0%
+process whereby uh a PO an enlarging
+population incredibly hungry for the
+
+ align:start position:0%
+population incredibly hungry for the
+ 
+
+ align:start position:0%
+population incredibly hungry for the
+Novelties being produced by this new
+
+ align:start position:0%
+Novelties being produced by this new
+ 
+
+ align:start position:0%
+Novelties being produced by this new
+technology create uh a kind of symbiotic
+
+ align:start position:0%
+technology create uh a kind of symbiotic
+ 
+
+ align:start position:0%
+technology create uh a kind of symbiotic
+relationship between the audience and
+
+ align:start position:0%
+relationship between the audience and
+ 
+
+ align:start position:0%
+relationship between the audience and
+the emerging medium so that as the
+
+ align:start position:0%
+the emerging medium so that as the
+ 
+
+ align:start position:0%
+the emerging medium so that as the
+medium be the medium grows more
+
+ align:start position:0%
+medium be the medium grows more
+ 
+
+ align:start position:0%
+medium be the medium grows more
+complicated in part because the audience
+
+ align:start position:0%
+complicated in part because the audience
+ 
+
+ align:start position:0%
+complicated in part because the audience
+okay after five or 10 or 15 visits to
+
+ align:start position:0%
+okay after five or 10 or 15 visits to
+ 
+
+ align:start position:0%
+okay after five or 10 or 15 visits to
+the to the Nickelodeon or uh or to the
+
+ align:start position:0%
+the to the Nickelodeon or uh or to the
+ 
+
+ align:start position:0%
+the to the Nickelodeon or uh or to the
+the after the movies moved out of after
+
+ align:start position:0%
+the after the movies moved out of after
+ 
+
+ align:start position:0%
+the after the movies moved out of after
+the movies moved out of the penny
+
+ align:start position:0%
+the movies moved out of the penny
+ 
+
+ align:start position:0%
+the movies moved out of the penny
+arcades and began to take their own
+
+ align:start position:0%
+arcades and began to take their own
+ 
+
+ align:start position:0%
+arcades and began to take their own
+space as some of you know and as as is
+
+ align:start position:0%
+space as some of you know and as as is
+ 
+
+ align:start position:0%
+space as some of you know and as as is
+recounted in our reading for this for
+
+ align:start position:0%
+recounted in our reading for this for
+ 
+
+ align:start position:0%
+recounted in our reading for this for
+these early weeks the movies first moved
+
+ align:start position:0%
+these early weeks the movies first moved
+ 
+
+ align:start position:0%
+these early weeks the movies first moved
+out into what were called Nickelodeon
+
+ align:start position:0%
+out into what were called Nickelodeon
+ 
+
+ align:start position:0%
+out into what were called Nickelodeon
+right they were they were uh storefronts
+
+ align:start position:0%
+right they were they were uh storefronts
+ 
+
+ align:start position:0%
+right they were they were uh storefronts
+in the for the most part in which
+
+ align:start position:0%
+in the for the most part in which
+ 
+
+ align:start position:0%
+in the for the most part in which
+mission was a nickel that's why they
+
+ align:start position:0%
+mission was a nickel that's why they
+ 
+
+ align:start position:0%
+mission was a nickel that's why they
+were called Nickelodeons uh and uh you
+
+ align:start position:0%
+were called Nickelodeons uh and uh you
+ 
+
+ align:start position:0%
+were called Nickelodeons uh and uh you
+sat in many of these on benches without
+
+ align:start position:0%
+sat in many of these on benches without
+ 
+
+ align:start position:0%
+sat in many of these on benches without
+backs next to strangers you didn't have
+
+ align:start position:0%
+backs next to strangers you didn't have
+ 
+
+ align:start position:0%
+backs next to strangers you didn't have
+private seats and you would sit in there
+
+ align:start position:0%
+private seats and you would sit in there
+ 
+
+ align:start position:0%
+private seats and you would sit in there
+and see a series of short films so but
+
+ align:start position:0%
+and see a series of short films so but
+ 
+
+ align:start position:0%
+and see a series of short films so but
+the fact that the Nickelodeons emerged
+
+ align:start position:0%
+the fact that the Nickelodeons emerged
+ 
+
+ align:start position:0%
+the fact that the Nickelodeons emerged
+so quickly is a mark of how popular an a
+
+ align:start position:0%
+so quickly is a mark of how popular an a
+ 
+
+ align:start position:0%
+so quickly is a mark of how popular an a
+film became even even in the even in its
+
+ align:start position:0%
+film became even even in the even in its
+ 
+
+ align:start position:0%
+film became even even in the even in its
+relatively primitive early form uh and
+
+ align:start position:0%
+relatively primitive early form uh and
+ 
+
+ align:start position:0%
+relatively primitive early form uh and
+and then of course within a few years of
+
+ align:start position:0%
+and then of course within a few years of
+ 
+
+ align:start position:0%
+and then of course within a few years of
+the Nickelodeon's appearing what else
+
+ align:start position:0%
+the Nickelodeon's appearing what else
+ 
+
+ align:start position:0%
+the Nickelodeon's appearing what else
+began to happen theaters made specially
+
+ align:start position:0%
+began to happen theaters made specially
+ 
+
+ align:start position:0%
+began to happen theaters made specially
+for the showing of motion pictures that
+
+ align:start position:0%
+for the showing of motion pictures that
+ 
+
+ align:start position:0%
+for the showing of motion pictures that
+were longer than the early shorts
+
+ align:start position:0%
+were longer than the early shorts
+ 
+
+ align:start position:0%
+were longer than the early shorts
+because film began to expand its length
+
+ align:start position:0%
+because film began to expand its length
+ 
+
+ align:start position:0%
+because film began to expand its length
+all through the period from 1910 through
+
+ align:start position:0%
+all through the period from 1910 through
+ 
+
+ align:start position:0%
+all through the period from 1910 through
+1920 right what what's the great moment
+
+ align:start position:0%
+1920 right what what's the great moment
+ 
+
+ align:start position:0%
+1920 right what what's the great moment
+when the feature film is born in the
+
+ align:start position:0%
+when the feature film is born in the
+ 
+
+ align:start position:0%
+when the feature film is born in the
+United States 1915 who's the director DW
+
+ align:start position:0%
+United States 1915 who's the director DW
+ 
+
+ align:start position:0%
+United States 1915 who's the director DW
+Griffith who's the what's the film Birth
+
+ align:start position:0%
+Griffith who's the what's the film Birth
+ 
+
+ align:start position:0%
+Griffith who's the what's the film Birth
+of a Nation Birth of a Nation a very
+
+ align:start position:0%
+of a Nation Birth of a Nation a very
+ 
+
+ align:start position:0%
+of a Nation Birth of a Nation a very
+complicated uh example because its
+
+ align:start position:0%
+complicated uh example because its
+ 
+
+ align:start position:0%
+complicated uh example because its
+content is disturbing in some ways it's
+
+ align:start position:0%
+content is disturbing in some ways it's
+ 
+
+ align:start position:0%
+content is disturbing in some ways it's
+a very reactionary and in some respects
+
+ align:start position:0%
+a very reactionary and in some respects
+ 
+
+ align:start position:0%
+a very reactionary and in some respects
+racist film it it it it it absorbs and
+
+ align:start position:0%
+racist film it it it it it absorbs and
+ 
+
+ align:start position:0%
+racist film it it it it it absorbs and
+Carries forward what we might think of
+
+ align:start position:0%
+Carries forward what we might think of
+ 
+
+ align:start position:0%
+Carries forward what we might think of
+as the the racial prejudices that were
+
+ align:start position:0%
+as the the racial prejudices that were
+ 
+
+ align:start position:0%
+as the the racial prejudices that were
+uh very widespread in American Society
+
+ align:start position:0%
+uh very widespread in American Society
+ 
+
+ align:start position:0%
+uh very widespread in American Society
+at the turn of the century and
+
+ align:start position:0%
+at the turn of the century and
+ 
+
+ align:start position:0%
+at the turn of the century and
+especially in the south from which
+
+ align:start position:0%
+especially in the south from which
+ 
+
+ align:start position:0%
+especially in the south from which
+Griffith himself was was a southerner
+
+ align:start position:0%
+Griffith himself was was a southerner
+ 
+
+ align:start position:0%
+Griffith himself was was a southerner
+and was born in the South and what his
+
+ align:start position:0%
+and was born in the South and what his
+ 
+
+ align:start position:0%
+and was born in the South and what his
+film was deeply influenced by a
+
+ align:start position:0%
+film was deeply influenced by a
+ 
+
+ align:start position:0%
+film was deeply influenced by a
+bestselling novel called the clansmen
+
+ align:start position:0%
+bestselling novel called the clansmen
+ 
+
+ align:start position:0%
+bestselling novel called the clansmen
+which was a celebration of the luux Clan
+
+ align:start position:0%
+which was a celebration of the luux Clan
+ 
+
+ align:start position:0%
+which was a celebration of the luux Clan
+uh and the uh Birth of a Nation so so
+
+ align:start position:0%
+uh and the uh Birth of a Nation so so
+ 
+
+ align:start position:0%
+uh and the uh Birth of a Nation so so
+the content of Birth of a Nation is very
+
+ align:start position:0%
+the content of Birth of a Nation is very
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+
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+the content of Birth of a Nation is very
+unsettling and disturbing and even when
+
+ align:start position:0%
+unsettling and disturbing and even when
+ 
+
+ align:start position:0%
+unsettling and disturbing and even when
+it was first uh um released to the
+
+ align:start position:0%
+it was first uh um released to the
+ 
+
+ align:start position:0%
+it was first uh um released to the
+public to great a claim because it it it
+
+ align:start position:0%
+public to great a claim because it it it
+ 
+
+ align:start position:0%
+public to great a claim because it it it
+it it expanded the possibilities of
+
+ align:start position:0%
+it it expanded the possibilities of
+ 
+
+ align:start position:0%
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+movies in all kinds of ways from a
+
+ align:start position:0%
+movies in all kinds of ways from a
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+
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+movies in all kinds of ways from a
+technical standpoint it is an
+
+ align:start position:0%
+technical standpoint it is an
+ 
+
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+technical standpoint it is an
+astonishingly important film and from a
+
+ align:start position:0%
+astonishingly important film and from a
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+
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+astonishingly important film and from a
+Content standpoint it's a very
+
+ align:start position:0%
+Content standpoint it's a very
+ 
+
+ align:start position:0%
+Content standpoint it's a very
+disturbing film It's a Wonderful
+
+ align:start position:0%
+disturbing film It's a Wonderful
+ 
+
+ align:start position:0%
+disturbing film It's a Wonderful
+reminder of the fact that this progress
+
+ align:start position:0%
+reminder of the fact that this progress
+ 
+
+ align:start position:0%
+reminder of the fact that this progress
+I'm describing to you is not an
+
+ align:start position:0%
+I'm describing to you is not an
+ 
+
+ align:start position:0%
+I'm describing to you is not an
+unalloyed triumphal story story uh even
+
+ align:start position:0%
+unalloyed triumphal story story uh even
+ 
+
+ align:start position:0%
+unalloyed triumphal story story uh even
+as the movies became more technically
+
+ align:start position:0%
+as the movies became more technically
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+
+ align:start position:0%
+as the movies became more technically
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+
+ align:start position:0%
+complicated and and uh more demanding
+ 
+
+ align:start position:0%
+complicated and and uh more demanding
+and longer and more interested in
+
+ align:start position:0%
+and longer and more interested in
+ 
+
+ align:start position:0%
+and longer and more interested in
+character they also nonetheless carried
+
+ align:start position:0%
+character they also nonetheless carried
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+
+ align:start position:0%
+character they also nonetheless carried
+the lies and prejudices and and um um um
+
+ align:start position:0%
+the lies and prejudices and and um um um
+ 
+
+ align:start position:0%
+the lies and prejudices and and um um um
+hierarchic assumptions that were
+
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+hierarchic assumptions that were
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+
+ align:start position:0%
+hierarchic assumptions that were
+embedded in the society from which they
+
+ align:start position:0%
+embedded in the society from which they
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+
+ align:start position:0%
+embedded in the society from which they
+arose how could it be otherwise every
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+arose how could it be otherwise every
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+arose how could it be otherwise every
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+important to make this point as a way of
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+important to make this point as a way of
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+
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+important to make this point as a way of
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+
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+reminding us that the story we're
+ 
+
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+reminding us that the story we're
+telling is not uh in some simple sense
+
+ align:start position:0%
+telling is not uh in some simple sense
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+
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+telling is not uh in some simple sense
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+
+ align:start position:0%
+just a kind of a kind of progress myth
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+
+ align:start position:0%
+just a kind of a kind of progress myth
+in which we're celebrating development
+
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+in which we're celebrating development
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+in which we're celebrating development
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+
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+and and and genius we we're we're we're
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+
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+complicated than that the process
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+
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+complicated than that the process
+whereby these cultural myths uh and
+
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+whereby these cultural myths uh and
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+
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+whereby these cultural myths uh and
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+
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+these stories that are drawn from
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+
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+these stories that are drawn from
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+
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+broadly more generally uh uh are are
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+
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+broadly more generally uh uh are are
+transformed into this new medium and
+
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+transformed into this new medium and
+ 
+
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+transformed into this new medium and
+they have a tremendous technical
+
+ align:start position:0%
+they have a tremendous technical
+ 
+
+ align:start position:0%
+they have a tremendous technical
+interest but very often they also have a
+
+ align:start position:0%
+interest but very often they also have a
+ 
+
+ align:start position:0%
+interest but very often they also have a
+kind of cultural or sociological
+
+ align:start position:0%
+kind of cultural or sociological
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+
+ align:start position:0%
+kind of cultural or sociological
+interest of a negative kind in the sense
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+ align:start position:0%
+interest of a negative kind in the sense
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+
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+interest of a negative kind in the sense
+that what they reveal are the prejudices
+
+ align:start position:0%
+that what they reveal are the prejudices
+ 
+
+ align:start position:0%
+that what they reveal are the prejudices
+the lies the limitations uh of the
+
+ align:start position:0%
+the lies the limitations uh of the
+ 
+
+ align:start position:0%
+the lies the limitations uh of the
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+
+ align:start position:0%
+society that's given the the mythologies
+ 
+
+ align:start position:0%
+society that's given the the mythologies
+that sustain the society again this is a
+
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+that sustain the society again this is a
+ 
+
+ align:start position:0%
+that sustain the society again this is a
+matter to which we'll return one of the
+
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+matter to which we'll return one of the
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+
+ align:start position:0%
+matter to which we'll return one of the
+deep cultural functions of American
+
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+deep cultural functions of American
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+
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+deep cultural functions of American
+movies especially was to promulgate a
+
+ align:start position:0%
+movies especially was to promulgate a
+ 
+
+ align:start position:0%
+movies especially was to promulgate a
+kind of Mythology of America and we'll
+
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+kind of Mythology of America and we'll
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+
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+kind of Mythology of America and we'll
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+talk more about this when we when we
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+
+ align:start position:0%
+talk more about this when we when we
+when we reach certain genre forms in the
+
+ align:start position:0%
+when we reach certain genre forms in the
+ 
+
+ align:start position:0%
+when we reach certain genre forms in the
+second segment of the course
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+second segment of the course
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+
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+second segment of the course
+I said something earlier this morning
+
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+I said something earlier this morning
+ 
+
+ align:start position:0%
+I said something earlier this morning
+that I want to make uh
+
+ align:start position:0%
+that I want to make uh
+ 
+
+ align:start position:0%
+that I want to make uh
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+
+ align:start position:0%
+explicit uh because I think it's an
+ 
+
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+explicit uh because I think it's an
+important another way of qualifying this
+
+ align:start position:0%
+important another way of qualifying this
+ 
+
+ align:start position:0%
+important another way of qualifying this
+triumphal story it's hard because I'm
+
+ align:start position:0%
+triumphal story it's hard because I'm
+ 
+
+ align:start position:0%
+triumphal story it's hard because I'm
+enthusiastic about what I'm looking at
+
+ align:start position:0%
+enthusiastic about what I'm looking at
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+
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+enthusiastic about what I'm looking at
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+and there is some material That's so
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+and there is some material That's so
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+exciting here to watch in a way what
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+birth of the movies we're watching the
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+
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+birth of the movies we're watching the
+the the discovery of the language of
+
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+the the discovery of the language of
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+
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+the the discovery of the language of
+Cinema in these early films and that's
+
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+Cinema in these early films and that's
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+
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+Cinema in these early films and that's
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+
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+why even though from an artistic
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+
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+why even though from an artistic
+standpoint some of these shorts are not
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+standpoint some of these shorts are not
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+
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+standpoint some of these shorts are not
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+
+ align:start position:0%
+very rich I hope they're interesting
+ 
+
+ align:start position:0%
+very rich I hope they're interesting
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+
+ align:start position:0%
+enough that I've made them interesting
+ 
+
+ align:start position:0%
+enough that I've made them interesting
+to you from a historical standpoint if
+
+ align:start position:0%
+to you from a historical standpoint if
+ 
+
+ align:start position:0%
+to you from a historical standpoint if
+you look at them closely you can see you
+
+ align:start position:0%
+you look at them closely you can see you
+ 
+
+ align:start position:0%
+you look at them closely you can see you
+can see the movies being born you can
+
+ align:start position:0%
+can see the movies being born you can
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+
+ align:start position:0%
+can see the movies being born you can
+see a language a Syntax for speaking in
+
+ align:start position:0%
+see a language a Syntax for speaking in
+ 
+
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+see a language a Syntax for speaking in
+pictures for for this new new visual
+
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+pictures for for this new new visual
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+pictures for for this new new visual
+language being this new visual medium
+
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+language being this new visual medium
+ 
+
+ align:start position:0%
+language being this new visual medium
+being developed uh and and I I'll if I
+
+ align:start position:0%
+being developed uh and and I I'll if I
+ 
+
+ align:start position:0%
+being developed uh and and I I'll if I
+have time this evening I'll give you a
+
+ align:start position:0%
+have time this evening I'll give you a
+ 
+
+ align:start position:0%
+have time this evening I'll give you a
+few more concrete examples of that but
+
+ align:start position:0%
+few more concrete examples of that but
+ 
+
+ align:start position:0%
+few more concrete examples of that but
+another way in which one can qualify
+
+ align:start position:0%
+another way in which one can qualify
+ 
+
+ align:start position:0%
+another way in which one can qualify
+this apparently triumphal story it's not
+
+ align:start position:0%
+this apparently triumphal story it's not
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+
+ align:start position:0%
+this apparently triumphal story it's not
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+
+ align:start position:0%
+a triumphal story even though it is a
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+
+ align:start position:0%
+a triumphal story even though it is a
+story of refinement development and
+
+ align:start position:0%
+story of refinement development and
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+
+ align:start position:0%
+story of refinement development and
+evolution of a of a kind that involves
+
+ align:start position:0%
+evolution of a of a kind that involves
+ 
+
+ align:start position:0%
+evolution of a of a kind that involves
+increasing complexity and Technical
+
+ align:start position:0%
+increasing complexity and Technical
+ 
+
+ align:start position:0%
+increasing complexity and Technical
+Perfection technical uh uh Mastery uh
+
+ align:start position:0%
+Perfection technical uh uh Mastery uh
+ 
+
+ align:start position:0%
+Perfection technical uh uh Mastery uh
+it's not merely that or not or not or
+
+ align:start position:0%
+it's not merely that or not or not or
+ 
+
+ align:start position:0%
+it's not merely that or not or not or
+not even primarily that it's very
+
+ align:start position:0%
+not even primarily that it's very
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+
+ align:start position:0%
+not even primarily that it's very
+important to recognize among other
+
+ align:start position:0%
+important to recognize among other
+ 
+
+ align:start position:0%
+important to recognize among other
+things as I implied this afternoon that
+
+ align:start position:0%
+things as I implied this afternoon that
+ 
+
+ align:start position:0%
+things as I implied this afternoon that
+uh not all the possibilities that are
+
+ align:start position:0%
+uh not all the possibilities that are
+ 
+
+ align:start position:0%
+uh not all the possibilities that are
+inherent in the in the in the nent
+
+ align:start position:0%
+inherent in the in the in the nent
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+
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+inherent in the in the in the nent
+medium AR necessarily exploited in a
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+medium AR necessarily exploited in a
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+
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+medium AR necessarily exploited in a
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+
+ align:start position:0%
+particular cultural moment or
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+
+ align:start position:0%
+particular cultural moment or
+or maybe ever exploited depending on how
+
+ align:start position:0%
+or maybe ever exploited depending on how
+ 
+
+ align:start position:0%
+or maybe ever exploited depending on how
+things develop that is to say uh I
+
+ align:start position:0%
+things develop that is to say uh I
+ 
+
+ align:start position:0%
+things develop that is to say uh I
+mentioned this this afternoon uh how for
+
+ align:start position:0%
+mentioned this this afternoon uh how for
+ 
+
+ align:start position:0%
+mentioned this this afternoon uh how for
+instance when Edison first conceived the
+
+ align:start position:0%
+instance when Edison first conceived the
+ 
+
+ align:start position:0%
+instance when Edison first conceived the
+apparatus before it was actually
+
+ align:start position:0%
+apparatus before it was actually
+ 
+
+ align:start position:0%
+apparatus before it was actually
+invented of the mo of the motion picture
+
+ align:start position:0%
+invented of the mo of the motion picture
+ 
+
+ align:start position:0%
+invented of the mo of the motion picture
+projector and the motion picture camera
+
+ align:start position:0%
+projector and the motion picture camera
+ 
+
+ align:start position:0%
+projector and the motion picture camera
+his first idea was that he would create
+
+ align:start position:0%
+his first idea was that he would create
+ 
+
+ align:start position:0%
+his first idea was that he would create
+an an item that would be a consumer what
+
+ align:start position:0%
+an an item that would be a consumer what
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+
+ align:start position:0%
+an an item that would be a consumer what
+we would today call a consumer item that
+
+ align:start position:0%
+we would today call a consumer item that
+ 
+
+ align:start position:0%
+we would today call a consumer item that
+would be sold to individual families and
+
+ align:start position:0%
+would be sold to individual families and
+ 
+
+ align:start position:0%
+would be sold to individual families and
+the film would become you know the an
+
+ align:start position:0%
+the film would become you know the an
+ 
+
+ align:start position:0%
+the film would become you know the an
+equivalent of a kind of a photo album
+
+ align:start position:0%
+equivalent of a kind of a photo album
+ 
+
+ align:start position:0%
+equivalent of a kind of a photo album
+although it would it would have Motion
+
+ align:start position:0%
+although it would it would have Motion
+ 
+
+ align:start position:0%
+although it would it would have Motion
+in it and and and as I suggested this
+
+ align:start position:0%
+in it and and and as I suggested this
+ 
+
+ align:start position:0%
+in it and and and as I suggested this
+this morning this afternoon there's no
+
+ align:start position:0%
+this morning this afternoon there's no
+ 
+
+ align:start position:0%
+this morning this afternoon there's no
+reason why given the nature of the
+
+ align:start position:0%
+reason why given the nature of the
+ 
+
+ align:start position:0%
+reason why given the nature of the
+technology itself that that vision of
+
+ align:start position:0%
+technology itself that that vision of
+ 
+
+ align:start position:0%
+technology itself that that vision of
+how film might develop was impossible in
+
+ align:start position:0%
+how film might develop was impossible in
+ 
+
+ align:start position:0%
+how film might develop was impossible in
+fact it wasn't impossible it was just
+
+ align:start position:0%
+fact it wasn't impossible it was just
+ 
+
+ align:start position:0%
+fact it wasn't impossible it was just
+incredibly ahead of its time it took it
+
+ align:start position:0%
+incredibly ahead of its time it took it
+ 
+
+ align:start position:0%
+incredibly ahead of its time it took it
+took half a century before something
+
+ align:start position:0%
+took half a century before something
+ 
+
+ align:start position:0%
+took half a century before something
+like that actually became available in
+
+ align:start position:0%
+like that actually became available in
+ 
+
+ align:start position:0%
+like that actually became available in
+society but there was no reason in terms
+
+ align:start position:0%
+society but there was no reason in terms
+ 
+
+ align:start position:0%
+society but there was no reason in terms
+of the the possibilities of the
+
+ align:start position:0%
+of the the possibilities of the
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+
+ align:start position:0%
+of the the possibilities of the
+technology that that that that needed to
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+ align:start position:0%
+technology that that that that needed to
+ 
+
+ align:start position:0%
+technology that that that that needed to
+happen what I'm calling your attention
+
+ align:start position:0%
+happen what I'm calling your attention
+ 
+
+ align:start position:0%
+happen what I'm calling your attention
+to is what is a very widespread myth
+
+ align:start position:0%
+to is what is a very widespread myth
+ 
+
+ align:start position:0%
+to is what is a very widespread myth
+it's especially pernicious and
+
+ align:start position:0%
+it's especially pernicious and
+ 
+
+ align:start position:0%
+it's especially pernicious and
+widespread at MIT and it's very for
+
+ align:start position:0%
+widespread at MIT and it's very for
+ 
+
+ align:start position:0%
+widespread at MIT and it's very for
+reasons that are obvious and
+
+ align:start position:0%
+reasons that are obvious and
+ 
+
+ align:start position:0%
+reasons that are obvious and
+understandable we at MIT love to believe
+
+ align:start position:0%
+understandable we at MIT love to believe
+ 
+
+ align:start position:0%
+understandable we at MIT love to believe
+that technology will solve all problems
+
+ align:start position:0%
+that technology will solve all problems
+ 
+
+ align:start position:0%
+that technology will solve all problems
+the truth of the matter is technology
+
+ align:start position:0%
+the truth of the matter is technology
+ 
+
+ align:start position:0%
+the truth of the matter is technology
+doesn't solve problems uh it it it
+
+ align:start position:0%
+doesn't solve problems uh it it it
+ 
+
+ align:start position:0%
+doesn't solve problems uh it it it
+solves some problems but it creates an
+
+ align:start position:0%
+solves some problems but it creates an
+ 
+
+ align:start position:0%
+solves some problems but it creates an
+equal number of new problems at a
+
+ align:start position:0%
+equal number of new problems at a
+ 
+
+ align:start position:0%
+equal number of new problems at a
+minimum the the fact of the matter is
+
+ align:start position:0%
+minimum the the fact of the matter is
+ 
+
+ align:start position:0%
+minimum the the fact of the matter is
+that when that that that uh it is not
+
+ align:start position:0%
+that when that that that uh it is not
+ 
+
+ align:start position:0%
+that when that that that uh it is not
+merely the case that that uh technology
+
+ align:start position:0%
+merely the case that that uh technology
+ 
+
+ align:start position:0%
+merely the case that that uh technology
+by itself is never a solution to any
+
+ align:start position:0%
+by itself is never a solution to any
+ 
+
+ align:start position:0%
+by itself is never a solution to any
+social or political problem even though
+
+ align:start position:0%
+social or political problem even though
+ 
+
+ align:start position:0%
+social or political problem even though
+it may have a may be a potential
+
+ align:start position:0%
+it may have a may be a potential
+ 
+
+ align:start position:0%
+it may have a may be a potential
+instrument for certain kinds of social
+
+ align:start position:0%
+instrument for certain kinds of social
+ 
+
+ align:start position:0%
+instrument for certain kinds of social
+or or or or or or or political outcomes
+
+ align:start position:0%
+or or or or or or or political outcomes
+ 
+
+ align:start position:0%
+or or or or or or or political outcomes
+but only a potential one the technology
+
+ align:start position:0%
+but only a potential one the technology
+ 
+
+ align:start position:0%
+but only a potential one the technology
+will always all new technologies will
+
+ align:start position:0%
+will always all new technologies will
+ 
+
+ align:start position:0%
+will always all new technologies will
+contain latencies possibilities that are
+
+ align:start position:0%
+contain latencies possibilities that are
+ 
+
+ align:start position:0%
+contain latencies possibilities that are
+not exploited uh roads not taken by the
+
+ align:start position:0%
+not exploited uh roads not taken by the
+ 
+
+ align:start position:0%
+not exploited uh roads not taken by the
+technology and we we have some very
+
+ align:start position:0%
+technology and we we have some very
+ 
+
+ align:start position:0%
+technology and we we have some very
+interesting alternative possibilities
+
+ align:start position:0%
+interesting alternative possibilities
+ 
+
+ align:start position:0%
+interesting alternative possibilities
+I'll give you one really scary one think
+
+ align:start position:0%
+I'll give you one really scary one think
+ 
+
+ align:start position:0%
+I'll give you one really scary one think
+about the way a movie is actually
+
+ align:start position:0%
+about the way a movie is actually
+ 
+
+ align:start position:0%
+about the way a movie is actually
+developed in the United States that
+
+ align:start position:0%
+developed in the United States that
+ 
+
+ align:start position:0%
+developed in the United States that
+basic that basic pattern with certain
+
+ align:start position:0%
+basic that basic pattern with certain
+ 
+
+ align:start position:0%
+basic that basic pattern with certain
+significant variations held pretty much
+
+ align:start position:0%
+significant variations held pretty much
+ 
+
+ align:start position:0%
+significant variations held pretty much
+in in other societies as well even in an
+
+ align:start position:0%
+in in other societies as well even in an
+ 
+
+ align:start position:0%
+in in other societies as well even in an
+odd way in societies where the
+
+ align:start position:0%
+odd way in societies where the
+ 
+
+ align:start position:0%
+odd way in societies where the
+production process was controlled more
+
+ align:start position:0%
+production process was controlled more
+ 
+
+ align:start position:0%
+production process was controlled more
+by government than it was by private
+
+ align:start position:0%
+by government than it was by private
+ 
+
+ align:start position:0%
+by government than it was by private
+Enterprise there was still a system in
+
+ align:start position:0%
+Enterprise there was still a system in
+ 
+
+ align:start position:0%
+Enterprise there was still a system in
+which audiences who were amateurs would
+
+ align:start position:0%
+which audiences who were amateurs would
+ 
+
+ align:start position:0%
+which audiences who were amateurs would
+go to a theater collect in the theater
+
+ align:start position:0%
+go to a theater collect in the theater
+ 
+
+ align:start position:0%
+go to a theater collect in the theater
+to watch a product that was made by
+
+ align:start position:0%
+to watch a product that was made by
+ 
+
+ align:start position:0%
+to watch a product that was made by
+profession by a professional Elite and
+
+ align:start position:0%
+profession by a professional Elite and
+ 
+
+ align:start position:0%
+profession by a professional Elite and
+again there's nothing in the technology
+
+ align:start position:0%
+again there's nothing in the technology
+ 
+
+ align:start position:0%
+again there's nothing in the technology
+that requires that right well what
+
+ align:start position:0%
+that requires that right well what
+ 
+
+ align:start position:0%
+that requires that right well what
+explains what explains it are the
+
+ align:start position:0%
+explains what explains it are the
+ 
+
+ align:start position:0%
+explains what explains it are the
+economic demographic social
+
+ align:start position:0%
+economic demographic social
+ 
+
+ align:start position:0%
+economic demographic social
+circumstances of the society at the
+
+ align:start position:0%
+circumstances of the society at the
+ 
+
+ align:start position:0%
+circumstances of the society at the
+moment when that technology became
+
+ align:start position:0%
+moment when that technology became
+ 
+
+ align:start position:0%
+moment when that technology became
+partly viable so the choices that are
+
+ align:start position:0%
+partly viable so the choices that are
+ 
+
+ align:start position:0%
+partly viable so the choices that are
+made are for how a technology will be
+
+ align:start position:0%
+made are for how a technology will be
+ 
+
+ align:start position:0%
+made are for how a technology will be
+used are always narrowing ones you all
+
+ align:start position:0%
+used are always narrowing ones you all
+ 
+
+ align:start position:0%
+used are always narrowing ones you all
+have have experience with this with w w
+
+ align:start position:0%
+have have experience with this with w w
+ 
+
+ align:start position:0%
+have have experience with this with w w
+w with with this process think of it
+
+ align:start position:0%
+w with with this process think of it
+ 
+
+ align:start position:0%
+w with with this process think of it
+think of for example the way cell phones
+
+ align:start position:0%
+think of for example the way cell phones
+ 
+
+ align:start position:0%
+think of for example the way cell phones
+have changed and the way uh and the or
+
+ align:start position:0%
+have changed and the way uh and the or
+ 
+
+ align:start position:0%
+have changed and the way uh and the or
+in fact in your it's an interesting
+
+ align:start position:0%
+in fact in your it's an interesting
+ 
+
+ align:start position:0%
+in fact in your it's an interesting
+thing because in your all of you have
+
+ align:start position:0%
+thing because in your all of you have
+ 
+
+ align:start position:0%
+thing because in your all of you have
+been alive in the period when cell
+
+ align:start position:0%
+been alive in the period when cell
+ 
+
+ align:start position:0%
+been alive in the period when cell
+phones essentially came into society and
+
+ align:start position:0%
+phones essentially came into society and
+ 
+
+ align:start position:0%
+phones essentially came into society and
+were elaborated but is there anyone here
+
+ align:start position:0%
+were elaborated but is there anyone here
+ 
+
+ align:start position:0%
+were elaborated but is there anyone here
+who can remember a time cannot remember
+
+ align:start position:0%
+who can remember a time cannot remember
+ 
+
+ align:start position:0%
+who can remember a time cannot remember
+a time before cell phones see all of you
+
+ align:start position:0%
+a time before cell phones see all of you
+ 
+
+ align:start position:0%
+a time before cell phones see all of you
+remember that right well you can think
+
+ align:start position:0%
+remember that right well you can think
+ 
+
+ align:start position:0%
+remember that right well you can think
+of what happened to the you can think of
+
+ align:start position:0%
+of what happened to the you can think of
+ 
+
+ align:start position:0%
+of what happened to the you can think of
+the elaboration and and the the
+
+ align:start position:0%
+the elaboration and and the the
+ 
+
+ align:start position:0%
+the elaboration and and the the
+development of cell phones as a as a as
+
+ align:start position:0%
+development of cell phones as a as a as
+ 
+
+ align:start position:0%
+development of cell phones as a as a as
+a kind of in some sense perverse model
+
+ align:start position:0%
+a kind of in some sense perverse model
+ 
+
+ align:start position:0%
+a kind of in some sense perverse model
+for what I'm talking about I say
+
+ align:start position:0%
+for what I'm talking about I say
+ 
+
+ align:start position:0%
+for what I'm talking about I say
+perverse because you can see how
+
+ align:start position:0%
+perverse because you can see how
+ 
+
+ align:start position:0%
+perverse because you can see how
+counterproductive in many ways some of
+
+ align:start position:0%
+counterproductive in many ways some of
+ 
+
+ align:start position:0%
+counterproductive in many ways some of
+the technological add-ons that are being
+
+ align:start position:0%
+the technological add-ons that are being
+ 
+
+ align:start position:0%
+the technological add-ons that are being
+created for cell phones are it's as if
+
+ align:start position:0%
+created for cell phones are it's as if
+ 
+
+ align:start position:0%
+created for cell phones are it's as if
+the industry in so far as it's a single
+
+ align:start position:0%
+the industry in so far as it's a single
+ 
+
+ align:start position:0%
+the industry in so far as it's a single
+industry can't exactly figure out what
+
+ align:start position:0%
+industry can't exactly figure out what
+ 
+
+ align:start position:0%
+industry can't exactly figure out what
+to do because the audience for the what
+
+ align:start position:0%
+to do because the audience for the what
+ 
+
+ align:start position:0%
+to do because the audience for the what
+the what we call the cell phone is such
+
+ align:start position:0%
+the what we call the cell phone is such
+ 
+
+ align:start position:0%
+the what we call the cell phone is such
+a diverse one and you know uh illiterate
+
+ align:start position:0%
+a diverse one and you know uh illiterate
+ 
+
+ align:start position:0%
+a diverse one and you know uh illiterate
+teenagers love to text message right so
+
+ align:start position:0%
+teenagers love to text message right so
+ 
+
+ align:start position:0%
+teenagers love to text message right so
+so you know even though it's not in in
+
+ align:start position:0%
+so you know even though it's not in in
+ 
+
+ align:start position:0%
+so you know even though it's not in in
+the English language anymore you can see
+
+ align:start position:0%
+the English language anymore you can see
+ 
+
+ align:start position:0%
+the English language anymore you can see
+and you can see the cell phone companies
+
+ align:start position:0%
+and you can see the cell phone companies
+ 
+
+ align:start position:0%
+and you can see the cell phone companies
+trying to teach the population how to
+
+ align:start position:0%
+trying to teach the population how to
+ 
+
+ align:start position:0%
+trying to teach the population how to
+how to speak in text message right in
+
+ align:start position:0%
+how to speak in text message right in
+ 
+
+ align:start position:0%
+how to speak in text message right in
+text M mesga or whatever you would say
+
+ align:start position:0%
+text M mesga or whatever you would say
+ 
+
+ align:start position:0%
+text M mesga or whatever you would say
+right have you ever seen the uh the
+
+ align:start position:0%
+right have you ever seen the uh the
+ 
+
+ align:start position:0%
+right have you ever seen the uh the
+stupid ad in which you see the old
+
+ align:start position:0%
+stupid ad in which you see the old
+ 
+
+ align:start position:0%
+stupid ad in which you see the old
+grandmother trying to say uh uh what did
+
+ align:start position:0%
+grandmother trying to say uh uh what did
+ 
+
+ align:start position:0%
+grandmother trying to say uh uh what did
+she say what she says mind your own
+
+ align:start position:0%
+she say what she says mind your own
+ 
+
+ align:start position:0%
+she say what she says mind your own
+business in texe what would she my yob B
+
+ align:start position:0%
+business in texe what would she my yob B
+ 
+
+ align:start position:0%
+business in texe what would she my yob B
+she says to her daughter as if
+
+ align:start position:0%
+she says to her daughter as if
+ 
+
+ align:start position:0%
+she says to her daughter as if
+grandmothers are going to begin to start
+
+ align:start position:0%
+grandmothers are going to begin to start
+ 
+
+ align:start position:0%
+grandmothers are going to begin to start
+texting uh I mean and the and of course
+
+ align:start position:0%
+texting uh I mean and the and of course
+ 
+
+ align:start position:0%
+texting uh I mean and the and of course
+if you think about it if you think about
+
+ align:start position:0%
+if you think about it if you think about
+ 
+
+ align:start position:0%
+if you think about it if you think about
+it from a technological standpoint it's
+
+ align:start position:0%
+it from a technological standpoint it's
+ 
+
+ align:start position:0%
+it from a technological standpoint it's
+actually a very inefficient use of the
+
+ align:start position:0%
+actually a very inefficient use of the
+ 
+
+ align:start position:0%
+actually a very inefficient use of the
+medium isn't it think how hard it is to
+
+ align:start position:0%
+medium isn't it think how hard it is to
+ 
+
+ align:start position:0%
+medium isn't it think how hard it is to
+type to type uh uh messages of any kind
+
+ align:start position:0%
+type to type uh uh messages of any kind
+ 
+
+ align:start position:0%
+type to type uh uh messages of any kind
+on cell phones what what what inadequate
+
+ align:start position:0%
+on cell phones what what what inadequate
+ 
+
+ align:start position:0%
+on cell phones what what what inadequate
+what inadequate uh uh environments they
+
+ align:start position:0%
+what inadequate uh uh environments they
+ 
+
+ align:start position:0%
+what inadequate uh uh environments they
+are for that and what one could say is
+
+ align:start position:0%
+are for that and what one could say is
+ 
+
+ align:start position:0%
+are for that and what one could say is
+that certain kinds of decisions are
+
+ align:start position:0%
+that certain kinds of decisions are
+ 
+
+ align:start position:0%
+that certain kinds of decisions are
+being made uh that don't really have to
+
+ align:start position:0%
+being made uh that don't really have to
+ 
+
+ align:start position:0%
+being made uh that don't really have to
+do with with uh uh the the uses to which
+
+ align:start position:0%
+do with with uh uh the the uses to which
+ 
+
+ align:start position:0%
+do with with uh uh the the uses to which
+you might put this tiny little device
+
+ align:start position:0%
+you might put this tiny little device
+ 
+
+ align:start position:0%
+you might put this tiny little device
+but have to do with the fact that there
+
+ align:start position:0%
+but have to do with the fact that there
+ 
+
+ align:start position:0%
+but have to do with the fact that there
+are so many latent possibilities in the
+
+ align:start position:0%
+are so many latent possibilities in the
+ 
+
+ align:start position:0%
+are so many latent possibilities in the
+digital technology that people are play
+
+ align:start position:0%
+digital technology that people are play
+ 
+
+ align:start position:0%
+digital technology that people are play
+playing that that that we're trying that
+
+ align:start position:0%
+playing that that that we're trying that
+ 
+
+ align:start position:0%
+playing that that that we're trying that
+that manufacturers are trying out a
+
+ align:start position:0%
+that manufacturers are trying out a
+ 
+
+ align:start position:0%
+that manufacturers are trying out a
+whole range of things some of which will
+
+ align:start position:0%
+whole range of things some of which will
+ 
+
+ align:start position:0%
+whole range of things some of which will
+definitely Fall by the wayside will be
+
+ align:start position:0%
+definitely Fall by the wayside will be
+ 
+
+ align:start position:0%
+definitely Fall by the wayside will be
+will disappear uh and in fact some I
+
+ align:start position:0%
+will disappear uh and in fact some I
+ 
+
+ align:start position:0%
+will disappear uh and in fact some I
+guess many of you may not know this but
+
+ align:start position:0%
+guess many of you may not know this but
+ 
+
+ align:start position:0%
+guess many of you may not know this but
+uh in the 1930s uh the American AT&T
+
+ align:start position:0%
+uh in the 1930s uh the American AT&T
+ 
+
+ align:start position:0%
+uh in the 1930s uh the American AT&T
+which then was the main Telephone
+
+ align:start position:0%
+which then was the main Telephone
+ 
+
+ align:start position:0%
+which then was the main Telephone
+Company in the society um uh decided
+
+ align:start position:0%
+Company in the society um uh decided
+ 
+
+ align:start position:0%
+Company in the society um uh decided
+that of course what what was needed more
+
+ align:start position:0%
+that of course what what was needed more
+ 
+
+ align:start position:0%
+that of course what what was needed more
+than anything else was a picture phone
+
+ align:start position:0%
+than anything else was a picture phone
+ 
+
+ align:start position:0%
+than anything else was a picture phone
+and they invested millions and millions
+
+ align:start position:0%
+and they invested millions and millions
+ 
+
+ align:start position:0%
+and they invested millions and millions
+of dollars in something called a picture
+
+ align:start position:0%
+of dollars in something called a picture
+ 
+
+ align:start position:0%
+of dollars in something called a picture
+phone and they tried to Market it there
+
+ align:start position:0%
+phone and they tried to Market it there
+ 
+
+ align:start position:0%
+phone and they tried to Market it there
+were elaborate marketing campaigns it
+
+ align:start position:0%
+were elaborate marketing campaigns it
+ 
+
+ align:start position:0%
+were elaborate marketing campaigns it
+didn't occur to them that you know when
+
+ align:start position:0%
+didn't occur to them that you know when
+ 
+
+ align:start position:0%
+didn't occur to them that you know when
+people are on the telephone they often
+
+ align:start position:0%
+people are on the telephone they often
+ 
+
+ align:start position:0%
+people are on the telephone they often
+don't want to be seen right and but it
+
+ align:start position:0%
+don't want to be seen right and but it
+ 
+
+ align:start position:0%
+don't want to be seen right and but it
+was because it was technologically
+
+ align:start position:0%
+was because it was technologically
+ 
+
+ align:start position:0%
+was because it was technologically
+possible to create a telephone that
+
+ align:start position:0%
+possible to create a telephone that
+ 
+
+ align:start position:0%
+possible to create a telephone that
+showed a person's
+
+ align:start position:0%
+showed a person's
+ 
+
+ align:start position:0%
+showed a person's
+features when they remember this was a
+
+ align:start position:0%
+features when they remember this was a
+ 
+
+ align:start position:0%
+features when they remember this was a
+time when all phones were Tethered to a
+
+ align:start position:0%
+time when all phones were Tethered to a
+ 
+
+ align:start position:0%
+time when all phones were Tethered to a
+line so you couldn't walk around and
+
+ align:start position:0%
+line so you couldn't walk around and
+ 
+
+ align:start position:0%
+line so you couldn't walk around and
+take pictures outside the the camera in
+
+ align:start position:0%
+take pictures outside the the camera in
+ 
+
+ align:start position:0%
+take pictures outside the the camera in
+the cell phone is a more interesting
+
+ align:start position:0%
+the cell phone is a more interesting
+ 
+
+ align:start position:0%
+the cell phone is a more interesting
+device because the cell phone itself is
+
+ align:start position:0%
+device because the cell phone itself is
+ 
+
+ align:start position:0%
+device because the cell phone itself is
+portable and it allows you to do certain
+
+ align:start position:0%
+portable and it allows you to do certain
+ 
+
+ align:start position:0%
+portable and it allows you to do certain
+kinds of certain kinds of things what
+
+ align:start position:0%
+kinds of certain kinds of things what
+ 
+
+ align:start position:0%
+kinds of certain kinds of things what
+and in fact the uses to which the cell
+
+ align:start position:0%
+and in fact the uses to which the cell
+ 
+
+ align:start position:0%
+and in fact the uses to which the cell
+phone camera is being put certainly are
+
+ align:start position:0%
+phone camera is being put certainly are
+ 
+
+ align:start position:0%
+phone camera is being put certainly are
+much more complicated now than they were
+
+ align:start position:0%
+much more complicated now than they were
+ 
+
+ align:start position:0%
+much more complicated now than they were
+when the people who who decided to put
+
+ align:start position:0%
+when the people who who decided to put
+ 
+
+ align:start position:0%
+when the people who who decided to put
+cameras in cell phones could have
+
+ align:start position:0%
+cameras in cell phones could have
+ 
+
+ align:start position:0%
+cameras in cell phones could have
+imagined right it's an example of how
+
+ align:start position:0%
+imagined right it's an example of how
+ 
+
+ align:start position:0%
+imagined right it's an example of how
+the audience begins to take the new
+
+ align:start position:0%
+the audience begins to take the new
+ 
+
+ align:start position:0%
+the audience begins to take the new
+technology and find new uses for uh uh
+
+ align:start position:0%
+technology and find new uses for uh uh
+ 
+
+ align:start position:0%
+technology and find new uses for uh uh
+uh possibilities that are embedded in
+
+ align:start position:0%
+uh possibilities that are embedded in
+ 
+
+ align:start position:0%
+uh possibilities that are embedded in
+the in the technology but to come back
+
+ align:start position:0%
+the in the technology but to come back
+ 
+
+ align:start position:0%
+the in the technology but to come back
+to the primary point the primary point
+
+ align:start position:0%
+to the primary point the primary point
+ 
+
+ align:start position:0%
+to the primary point the primary point
+is that is that every technology will
+
+ align:start position:0%
+is that is that every technology will
+ 
+
+ align:start position:0%
+is that is that every technology will
+have latent possibilities that are that
+
+ align:start position:0%
+have latent possibilities that are that
+ 
+
+ align:start position:0%
+have latent possibilities that are that
+are not exploited and the reasons that
+
+ align:start position:0%
+are not exploited and the reasons that
+ 
+
+ align:start position:0%
+are not exploited and the reasons that
+they're not exploited do not necessarily
+
+ align:start position:0%
+they're not exploited do not necessarily
+ 
+
+ align:start position:0%
+they're not exploited do not necessarily
+have to do with with uh uh intellectual
+
+ align:start position:0%
+have to do with with uh uh intellectual
+ 
+
+ align:start position:0%
+have to do with with uh uh intellectual
+or artistic questions or or or the best
+
+ align:start position:0%
+or artistic questions or or or the best
+ 
+
+ align:start position:0%
+or artistic questions or or or the best
+way to deploy this technology for the
+
+ align:start position:0%
+way to deploy this technology for the
+ 
+
+ align:start position:0%
+way to deploy this technology for the
+social good the reasons have to do with
+
+ align:start position:0%
+social good the reasons have to do with
+ 
+
+ align:start position:0%
+social good the reasons have to do with
+Market possibilities the American Market
+
+ align:start position:0%
+Market possibilities the American Market
+ 
+
+ align:start position:0%
+Market possibilities the American Market
+is so diverse that one of the things
+
+ align:start position:0%
+is so diverse that one of the things
+ 
+
+ align:start position:0%
+is so diverse that one of the things
+that encourages is an immense amount of
+
+ align:start position:0%
+that encourages is an immense amount of
+ 
+
+ align:start position:0%
+that encourages is an immense amount of
+duplication overlap and unnecessary
+
+ align:start position:0%
+duplication overlap and unnecessary
+ 
+
+ align:start position:0%
+duplication overlap and unnecessary
+competition in which different
+
+ align:start position:0%
+competition in which different
+ 
+
+ align:start position:0%
+competition in which different
+Technologies which perform the same
+
+ align:start position:0%
+Technologies which perform the same
+ 
+
+ align:start position:0%
+Technologies which perform the same
+function are at war with each other all
+
+ align:start position:0%
+function are at war with each other all
+ 
+
+ align:start position:0%
+function are at war with each other all
+the time we now have a new one having to
+
+ align:start position:0%
+the time we now have a new one having to
+ 
+
+ align:start position:0%
+the time we now have a new one having to
+do with the with the High defition
+
+ align:start position:0%
+do with the with the High defition
+ 
+
+ align:start position:0%
+do with the with the High defition
+movies and television right there are
+
+ align:start position:0%
+movies and television right there are
+ 
+
+ align:start position:0%
+movies and television right there are
+competing systems right that now the
+
+ align:start position:0%
+competing systems right that now the
+ 
+
+ align:start position:0%
+competing systems right that now the
+reason there are competing systems
+
+ align:start position:0%
+reason there are competing systems
+ 
+
+ align:start position:0%
+reason there are competing systems
+doesn't have to do with what's best for
+
+ align:start position:0%
+doesn't have to do with what's best for
+ 
+
+ align:start position:0%
+doesn't have to do with what's best for
+the consumer uh it has to do it has to
+
+ align:start position:0%
+the consumer uh it has to do it has to
+ 
+
+ align:start position:0%
+the consumer uh it has to do it has to
+do with the fact of of market and so so
+
+ align:start position:0%
+do with the fact of of market and so so
+ 
+
+ align:start position:0%
+do with the fact of of market and so so
+one of the things I'm suggesting to you
+
+ align:start position:0%
+one of the things I'm suggesting to you
+ 
+
+ align:start position:0%
+one of the things I'm suggesting to you
+what what the primary thing I'm
+
+ align:start position:0%
+what what the primary thing I'm
+ 
+
+ align:start position:0%
+what what the primary thing I'm
+suggesting to is that the evolution of
+
+ align:start position:0%
+suggesting to is that the evolution of
+ 
+
+ align:start position:0%
+suggesting to is that the evolution of
+the movies that I want you to be aware
+
+ align:start position:0%
+the movies that I want you to be aware
+ 
+
+ align:start position:0%
+the movies that I want you to be aware
+of this process of increasing complexity
+
+ align:start position:0%
+of this process of increasing complexity
+ 
+
+ align:start position:0%
+of this process of increasing complexity
+and and uh uh uh compression in which in
+
+ align:start position:0%
+and and uh uh uh compression in which in
+ 
+
+ align:start position:0%
+and and uh uh uh compression in which in
+in which the movies become a more and
+
+ align:start position:0%
+in which the movies become a more and
+ 
+
+ align:start position:0%
+in which the movies become a more and
+more independent form of expression in
+
+ align:start position:0%
+more independent form of expression in
+ 
+
+ align:start position:0%
+more independent form of expression in
+which the movies begin to discover the
+
+ align:start position:0%
+which the movies begin to discover the
+ 
+
+ align:start position:0%
+which the movies begin to discover the
+unique characteristics of the motion
+
+ align:start position:0%
+unique characteristics of the motion
+ 
+
+ align:start position:0%
+unique characteristics of the motion
+picture camera and of the environment of
+
+ align:start position:0%
+picture camera and of the environment of
+ 
+
+ align:start position:0%
+picture camera and of the environment of
+the movie theater that that the movie
+
+ align:start position:0%
+the movie theater that that the movie
+ 
+
+ align:start position:0%
+the movie theater that that the movie
+that the movies begin to explore those
+
+ align:start position:0%
+that the movies begin to explore those
+ 
+
+ align:start position:0%
+that the movies begin to explore those
+qualities in this new medium that are
+
+ align:start position:0%
+qualities in this new medium that are
+ 
+
+ align:start position:0%
+qualities in this new medium that are
+unique and special that process is
+
+ align:start position:0%
+unique and special that process is
+ 
+
+ align:start position:0%
+unique and special that process is
+important and I want you to be aware of
+
+ align:start position:0%
+important and I want you to be aware of
+ 
+
+ align:start position:0%
+important and I want you to be aware of
+it but I don't want you to embrace that
+
+ align:start position:0%
+it but I don't want you to embrace that
+ 
+
+ align:start position:0%
+it but I don't want you to embrace that
+principle too uncritically because I
+
+ align:start position:0%
+principle too uncritically because I
+ 
+
+ align:start position:0%
+principle too uncritically because I
+want you to recognize that what that
+
+ align:start position:0%
+want you to recognize that what that
+ 
+
+ align:start position:0%
+want you to recognize that what that
+that the technology itself does not
+
+ align:start position:0%
+that the technology itself does not
+ 
+
+ align:start position:0%
+that the technology itself does not
+explain this process the process is
+
+ align:start position:0%
+explain this process the process is
+ 
+
+ align:start position:0%
+explain this process the process is
+explained by cultural factors and social
+
+ align:start position:0%
+explained by cultural factors and social
+ 
+
+ align:start position:0%
+explained by cultural factors and social
+factors and even individual uh sometimes
+
+ align:start position:0%
+factors and even individual uh sometimes
+ 
+
+ align:start position:0%
+factors and even individual uh sometimes
+individual psychological factors right
+
+ align:start position:0%
+individual psychological factors right
+ 
+
+ align:start position:0%
+individual psychological factors right
+uh what we're talking about here is the
+
+ align:start position:0%
+uh what we're talking about here is the
+ 
+
+ align:start position:0%
+uh what we're talking about here is the
+myth of technological determinism the
+
+ align:start position:0%
+myth of technological determinism the
+ 
+
+ align:start position:0%
+myth of technological determinism the
+myth that technology drives culture the
+
+ align:start position:0%
+myth that technology drives culture the
+ 
+
+ align:start position:0%
+myth that technology drives culture the
+myth that the new invention obliterates
+
+ align:start position:0%
+myth that the new invention obliterates
+ 
+
+ align:start position:0%
+myth that the new invention obliterates
+old inventions the truth is much more
+
+ align:start position:0%
+old inventions the truth is much more
+ 
+
+ align:start position:0%
+old inventions the truth is much more
+complicated than that in fact even when
+
+ align:start position:0%
+complicated than that in fact even when
+ 
+
+ align:start position:0%
+complicated than that in fact even when
+new technologies come into a society and
+
+ align:start position:0%
+new technologies come into a society and
+ 
+
+ align:start position:0%
+new technologies come into a society and
+are successfully embedded in the social
+
+ align:start position:0%
+are successfully embedded in the social
+ 
+
+ align:start position:0%
+are successfully embedded in the social
+practices of a society very different
+
+ align:start position:0%
+practices of a society very different
+ 
+
+ align:start position:0%
+practices of a society very different
+from the new technology becoming
+
+ align:start position:0%
+from the new technology becoming
+ 
+
+ align:start position:0%
+from the new technology becoming
+available right and you can all think in
+
+ align:start position:0%
+available right and you can all think in
+ 
+
+ align:start position:0%
+available right and you can all think in
+your own lifetimes of certain
+
+ align:start position:0%
+your own lifetimes of certain
+ 
+
+ align:start position:0%
+your own lifetimes of certain
+technologies that are no longer around
+
+ align:start position:0%
+technologies that are no longer around
+ 
+
+ align:start position:0%
+technologies that are no longer around
+uh uh eight do you any of you remember
+
+ align:start position:0%
+uh uh eight do you any of you remember
+ 
+
+ align:start position:0%
+uh uh eight do you any of you remember
+uh eight track tapes that used they used
+
+ align:start position:0%
+uh eight track tapes that used they used
+ 
+
+ align:start position:0%
+uh eight track tapes that used they used
+to have in cars some of you are nodding
+
+ align:start position:0%
+to have in cars some of you are nodding
+ 
+
+ align:start position:0%
+to have in cars some of you are nodding
+right you can't find them anymore but in
+
+ align:start position:0%
+right you can't find them anymore but in
+ 
+
+ align:start position:0%
+right you can't find them anymore but in
+fact think think about what's happened
+
+ align:start position:0%
+fact think think about what's happened
+ 
+
+ align:start position:0%
+fact think think about what's happened
+just to computers I mean some of you
+
+ align:start position:0%
+just to computers I mean some of you
+ 
+
+ align:start position:0%
+just to computers I mean some of you
+must have old floppies that you can't
+
+ align:start position:0%
+must have old floppies that you can't
+ 
+
+ align:start position:0%
+must have old floppies that you can't
+use in your computers anymore I still I
+
+ align:start position:0%
+use in your computers anymore I still I
+ 
+
+ align:start position:0%
+use in your computers anymore I still I
+I still have an old computer that didn't
+
+ align:start position:0%
+I still have an old computer that didn't
+ 
+
+ align:start position:0%
+I still have an old computer that didn't
+have floppies that had a 256 uh uh uh uh
+
+ align:start position:0%
+have floppies that had a 256 uh uh uh uh
+ 
+
+ align:start position:0%
+have floppies that had a 256 uh uh uh uh
+kilobyte hard drive and that was the
+
+ align:start position:0%
+kilobyte hard drive and that was the
+ 
+
+ align:start position:0%
+kilobyte hard drive and that was the
+machine it was the first IBM machine uh
+
+ align:start position:0%
+machine it was the first IBM machine uh
+ 
+
+ align:start position:0%
+machine it was the first IBM machine uh
+so everything and you and then and what
+
+ align:start position:0%
+so everything and you and then and what
+ 
+
+ align:start position:0%
+so everything and you and then and what
+they they gave it to you with these
+
+ align:start position:0%
+they they gave it to you with these
+ 
+
+ align:start position:0%
+they they gave it to you with these
+giant big real floppies that's why they
+
+ align:start position:0%
+giant big real floppies that's why they
+ 
+
+ align:start position:0%
+giant big real floppies that's why they
+were called floppies they were very you
+
+ align:start position:0%
+were called floppies they were very you
+ 
+
+ align:start position:0%
+were called floppies they were very you
+could bend them you could and and that's
+
+ align:start position:0%
+could bend them you could and and that's
+ 
+
+ align:start position:0%
+could bend them you could and and that's
+become obsolete very quickly as well so
+
+ align:start position:0%
+become obsolete very quickly as well so
+ 
+
+ align:start position:0%
+become obsolete very quickly as well so
+so there's there's there's there's a
+
+ align:start position:0%
+so there's there's there's there's a
+ 
+
+ align:start position:0%
+so there's there's there's there's a
+principle of obsolescence that's built
+
+ align:start position:0%
+principle of obsolescence that's built
+ 
+
+ align:start position:0%
+principle of obsolescence that's built
+that's that that's built into the
+
+ align:start position:0%
+that's that that's built into the
+ 
+
+ align:start position:0%
+that's that that's built into the
+process uh as well but the primary point
+
+ align:start position:0%
+process uh as well but the primary point
+ 
+
+ align:start position:0%
+process uh as well but the primary point
+is the myth of technological determinism
+
+ align:start position:0%
+is the myth of technological determinism
+ 
+
+ align:start position:0%
+is the myth of technological determinism
+reminds us that it is not technological
+
+ align:start position:0%
+reminds us that it is not technological
+ 
+
+ align:start position:0%
+reminds us that it is not technological
+uh uh discoveries themselves that that
+
+ align:start position:0%
+uh uh discoveries themselves that that
+ 
+
+ align:start position:0%
+uh uh discoveries themselves that that
+explain uh why a particular technology
+
+ align:start position:0%
+explain uh why a particular technology
+ 
+
+ align:start position:0%
+explain uh why a particular technology
+becomes an embedded social form that has
+
+ align:start position:0%
+becomes an embedded social form that has
+ 
+
+ align:start position:0%
+becomes an embedded social form that has
+to do with the with the culture and the
+
+ align:start position:0%
+to do with the with the culture and the
+ 
+
+ align:start position:0%
+to do with the with the culture and the
+historical circumstances of the society
+
+ align:start position:0%
+historical circumstances of the society
+ 
+
+ align:start position:0%
+historical circumstances of the society
+in which the technology is
+
+ align:start position:0%
+in which the technology is
+ 
+
+ align:start position:0%
+in which the technology is
+embedded one of the most remarkable
+
+ align:start position:0%
+embedded one of the most remarkable
+ 
+
+ align:start position:0%
+embedded one of the most remarkable
+things about this evolutionary process
+
+ align:start position:0%
+things about this evolutionary process
+ 
+
+ align:start position:0%
+things about this evolutionary process
+I've been describing as I said earlier
+
+ align:start position:0%
+I've been describing as I said earlier
+ 
+
+ align:start position:0%
+I've been describing as I said earlier
+is how swift it is how fast it is how we
+
+ align:start position:0%
+is how swift it is how fast it is how we
+ 
+
+ align:start position:0%
+is how swift it is how fast it is how we
+go from being a mere novelty to becoming
+
+ align:start position:0%
+go from being a mere novelty to becoming
+ 
+
+ align:start position:0%
+go from being a mere novelty to becoming
+a a significant social form by 1910 or
+
+ align:start position:0%
+a a significant social form by 1910 or
+ 
+
+ align:start position:0%
+a a significant social form by 1910 or
+so and to becoming a a virtually
+
+ align:start position:0%
+so and to becoming a a virtually
+ 
+
+ align:start position:0%
+so and to becoming a a virtually
+Universal aesthetic and entertainment
+
+ align:start position:0%
+Universal aesthetic and entertainment
+ 
+
+ align:start position:0%
+Universal aesthetic and entertainment
+experience for the majority of the
+
+ align:start position:0%
+experience for the majority of the
+ 
+
+ align:start position:0%
+experience for the majority of the
+population in the country by 1920 so in
+
+ align:start position:0%
+population in the country by 1920 so in
+ 
+
+ align:start position:0%
+population in the country by 1920 so in
+something like 20 or 25 years the movies
+
+ align:start position:0%
+something like 20 or 25 years the movies
+ 
+
+ align:start position:0%
+something like 20 or 25 years the movies
+go from being an absolutely unknown or
+
+ align:start position:0%
+go from being an absolutely unknown or
+ 
+
+ align:start position:0%
+go from being an absolutely unknown or
+trivial novelty sharing space with
+
+ align:start position:0%
+trivial novelty sharing space with
+ 
+
+ align:start position:0%
+trivial novelty sharing space with
+fortune tellers and strip and and strip
+
+ align:start position:0%
+fortune tellers and strip and and strip
+ 
+
+ align:start position:0%
+fortune tellers and strip and and strip
+shows in the penny arcades to becoming
+
+ align:start position:0%
+shows in the penny arcades to becoming
+ 
+
+ align:start position:0%
+shows in the penny arcades to becoming
+not just an embedded social form but one
+
+ align:start position:0%
+not just an embedded social form but one
+ 
+
+ align:start position:0%
+not just an embedded social form but one
+of the dominant economic engines of the
+
+ align:start position:0%
+of the dominant economic engines of the
+ 
+
+ align:start position:0%
+of the dominant economic engines of the
+society employing tens of thousands of
+
+ align:start position:0%
+society employing tens of thousands of
+ 
+
+ align:start position:0%
+society employing tens of thousands of
+people in various uh direct and
+
+ align:start position:0%
+people in various uh direct and
+ 
+
+ align:start position:0%
+people in various uh direct and
+ancillary positions and mobilizing
+
+ align:start position:0%
+ancillary positions and mobilizing
+ 
+
+ align:start position:0%
+ancillary positions and mobilizing
+virtually the entire population of the
+
+ align:start position:0%
+virtually the entire population of the
+ 
+
+ align:start position:0%
+virtually the entire population of the
+country in an an in a regular routine
+
+ align:start position:0%
+country in an an in a regular routine
+ 
+
+ align:start position:0%
+country in an an in a regular routine
+and habitual experience uh um uh to
+
+ align:start position:0%
+and habitual experience uh um uh to
+ 
+
+ align:start position:0%
+and habitual experience uh um uh to
+which they return again and again and
+
+ align:start position:0%
+which they return again and again and
+ 
+
+ align:start position:0%
+which they return again and again and
+because the audience is returning again
+
+ align:start position:0%
+because the audience is returning again
+ 
+
+ align:start position:0%
+because the audience is returning again
+and again I remember I said there's a
+
+ align:start position:0%
+and again I remember I said there's a
+ 
+
+ align:start position:0%
+and again I remember I said there's a
+kind of symbiotic relation between the
+
+ align:start position:0%
+kind of symbiotic relation between the
+ 
+
+ align:start position:0%
+kind of symbiotic relation between the
+audience and the because the audience is
+
+ align:start position:0%
+audience and the because the audience is
+ 
+
+ align:start position:0%
+audience and the because the audience is
+returning again and again what happens
+
+ align:start position:0%
+returning again and again what happens
+ 
+
+ align:start position:0%
+returning again and again what happens
+that's also an aspect of the resources
+
+ align:start position:0%
+that's also an aspect of the resources
+ 
+
+ align:start position:0%
+that's also an aspect of the resources
+that are available to the medium what
+
+ align:start position:0%
+that are available to the medium what
+ 
+
+ align:start position:0%
+that are available to the medium what
+begins then to develop our form our are
+
+ align:start position:0%
+begins then to develop our form our are
+ 
+
+ align:start position:0%
+begins then to develop our form our are
+forms of Storytelling that rely on the
+
+ align:start position:0%
+forms of Storytelling that rely on the
+ 
+
+ align:start position:0%
+forms of Storytelling that rely on the
+audiences prior memory of other shows
+
+ align:start position:0%
+audiences prior memory of other shows
+ 
+
+ align:start position:0%
+audiences prior memory of other shows
+right so that one thing that emerges
+
+ align:start position:0%
+right so that one thing that emerges
+ 
+
+ align:start position:0%
+right so that one thing that emerges
+very quickly is what we might call a
+
+ align:start position:0%
+very quickly is what we might call a
+ 
+
+ align:start position:0%
+very quickly is what we might call a
+star system in which particular actors
+
+ align:start position:0%
+star system in which particular actors
+ 
+
+ align:start position:0%
+star system in which particular actors
+are become identified with particular
+
+ align:start position:0%
+are become identified with particular
+ 
+
+ align:start position:0%
+are become identified with particular
+kinds of roles and audiences want to I
+
+ align:start position:0%
+kinds of roles and audiences want to I
+ 
+
+ align:start position:0%
+kinds of roles and audiences want to I
+come back to see those Stars again and
+
+ align:start position:0%
+come back to see those Stars again and
+ 
+
+ align:start position:0%
+come back to see those Stars again and
+again what also begins to happen is the
+
+ align:start position:0%
+again what also begins to happen is the
+ 
+
+ align:start position:0%
+again what also begins to happen is the
+establishment of a very rigorous kind of
+
+ align:start position:0%
+establishment of a very rigorous kind of
+ 
+
+ align:start position:0%
+establishment of a very rigorous kind of
+genre system what's a
+
+ align:start position:0%
+genre system what's a
+ 
+
+ align:start position:0%
+genre system what's a
+genre a category of story The Western is
+
+ align:start position:0%
+genre a category of story The Western is
+ 
+
+ align:start position:0%
+genre a category of story The Western is
+a genre the detective story is a genre
+
+ align:start position:0%
+a genre the detective story is a genre
+ 
+
+ align:start position:0%
+a genre the detective story is a genre
+the elegy is a poetic genre right that
+
+ align:start position:0%
+the elegy is a poetic genre right that
+ 
+
+ align:start position:0%
+the elegy is a poetic genre right that
+so so genres so and and the movies the
+
+ align:start position:0%
+so so genres so and and the movies the
+ 
+
+ align:start position:0%
+so so genres so and and the movies the
+typical the fundamental movie genres
+
+ align:start position:0%
+typical the fundamental movie genres
+ 
+
+ align:start position:0%
+typical the fundamental movie genres
+begin to emerge relatively early There's
+
+ align:start position:0%
+begin to emerge relatively early There's
+ 
+
+ align:start position:0%
+begin to emerge relatively early There's
+a western adventure story there's a
+
+ align:start position:0%
+a western adventure story there's a
+ 
+
+ align:start position:0%
+a western adventure story there's a
+historical spectacle uh there are
+
+ align:start position:0%
+historical spectacle uh there are
+ 
+
+ align:start position:0%
+historical spectacle uh there are
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+
+ align:start position:0%
+certain for of urban crime narrative
+ 
+
+ align:start position:0%
+certain for of urban crime narrative
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+
+ align:start position:0%
+that that became our detective and crime
+ 
+
+ align:start position:0%
+that that became our detective and crime
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+
+ align:start position:0%
+films at a later at a later stage and
+ 
+
+ align:start position:0%
+films at a later at a later stage and
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+
+ align:start position:0%
+there are certain and there emerge
+ 
+
+ align:start position:0%
+there are certain and there emerge
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+
+ align:start position:0%
+especially certain forms of satire and
+ 
+
+ align:start position:0%
+especially certain forms of satire and
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+
+ align:start position:0%
+comedy so so a genre system begins to
+ 
+
+ align:start position:0%
+comedy so so a genre system begins to
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+
+ align:start position:0%
+emerge as well and there there are
+ 
+
+ align:start position:0%
+emerge as well and there there are
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+
+ align:start position:0%
+reasons of course why this kind of thing
+ 
+
+ align:start position:0%
+reasons of course why this kind of thing
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+
+ align:start position:0%
+is useful to a mass production system to
+ 
+
+ align:start position:0%
+is useful to a mass production system to
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+
+ align:start position:0%
+a system an assembly line system because
+ 
+
+ align:start position:0%
+a system an assembly line system because
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+
+ align:start position:0%
+look if you make seven westerns uh if
+ 
+
+ align:start position:0%
+look if you make seven westerns uh if
+the same uh movie studio makes seven
+
+ align:start position:0%
+the same uh movie studio makes seven
+ 
+
+ align:start position:0%
+the same uh movie studio makes seven
+westerns they can use the same horses
+
+ align:start position:0%
+westerns they can use the same horses
+ 
+
+ align:start position:0%
+westerns they can use the same horses
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+
+ align:start position:0%
+again and again they can use the same
+ 
+
+ align:start position:0%
+again and again they can use the same
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+
+ align:start position:0%
+set they can use the same hats they
+ 
+
+ align:start position:0%
+set they can use the same hats they
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+
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+might even be and this in fact happened
+ 
+
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+might even be and this in fact happened
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+
+ align:start position:0%
+they might even be be able to use the
+ 
+
+ align:start position:0%
+they might even be be able to use the
+same clip of film that shows a cattle
+
+ align:start position:0%
+same clip of film that shows a cattle
+ 
+
+ align:start position:0%
+same clip of film that shows a cattle
+Stampede in seven different movies
+
+ align:start position:0%
+Stampede in seven different movies
+ 
+
+ align:start position:0%
+Stampede in seven different movies
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+
+ align:start position:0%
+because nobody would actually see it so
+ 
+
+ align:start position:0%
+because nobody would actually see it so
+economies of scale become possible uh as
+
+ align:start position:0%
+economies of scale become possible uh as
+ 
+
+ align:start position:0%
+economies of scale become possible uh as
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+
+ align:start position:0%
+the system begins to regularize itself
+ 
+
+ align:start position:0%
+the system begins to regularize itself
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+
+ align:start position:0%
+once it stabilizes after that period of
+ 
+
+ align:start position:0%
+once it stabilizes after that period of
+imitation and patent Warfare right so
+
+ align:start position:0%
+imitation and patent Warfare right so
+ 
+
+ align:start position:0%
+imitation and patent Warfare right so
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+
+ align:start position:0%
+one of the things and there's and
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+
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+
+ align:start position:0%
+there's nothing Noble or artistic or or
+ 
+
+ align:start position:0%
+there's nothing Noble or artistic or or
+or conscious
+
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+or conscious
+ 
+
+ align:start position:0%
+or conscious
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+
+ align:start position:0%
+uh about this development that's part of
+ 
+
+ align:start position:0%
+uh about this development that's part of
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+
+ align:start position:0%
+what makes it so remarkable and it puts
+ 
+
+ align:start position:0%
+what makes it so remarkable and it puts
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+
+ align:start position:0%
+us in touch with a paradox that's at the
+ 
+
+ align:start position:0%
+us in touch with a paradox that's at the
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+
+ align:start position:0%
+very heart of what I hope to make you
+ 
+
+ align:start position:0%
+very heart of what I hope to make you
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+
+ align:start position:0%
+aware of in this course it's a paradox
+ 
+
+ align:start position:0%
+aware of in this course it's a paradox
+that I guess it animates my transition
+
+ align:start position:0%
+that I guess it animates my transition
+ 
+
+ align:start position:0%
+that I guess it animates my transition
+many years ago now from a traditional
+
+ align:start position:0%
+many years ago now from a traditional
+ 
+
+ align:start position:0%
+many years ago now from a traditional
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+
+ align:start position:0%
+literary scholar into someone interested
+ 
+
+ align:start position:0%
+literary scholar into someone interested
+in film and media and it's this Paradox
+
+ align:start position:0%
+in film and media and it's this Paradox
+ 
+
+ align:start position:0%
+in film and media and it's this Paradox
+that based on what I've been telling you
+
+ align:start position:0%
+that based on what I've been telling you
+ 
+
+ align:start position:0%
+that based on what I've been telling you
+about this Evolution this evolution of
+
+ align:start position:0%
+about this Evolution this evolution of
+ 
+
+ align:start position:0%
+about this Evolution this evolution of
+the medium of of the film medium it's
+
+ align:start position:0%
+the medium of of the film medium it's
+ 
+
+ align:start position:0%
+the medium of of the film medium it's
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+
+ align:start position:0%
+the Paradox that capitalist
+ 
+
+ align:start position:0%
+the Paradox that capitalist
+greed the crassest of alliances between
+
+ align:start position:0%
+greed the crassest of alliances between
+ 
+
+ align:start position:0%
+greed the crassest of alliances between
+Commerce and modern
+
+ align:start position:0%
+Commerce and modern
+ 
+
+ align:start position:0%
+Commerce and modern
+technology might be the enabling
+
+ align:start position:0%
+technology might be the enabling
+ 
+
+ align:start position:0%
+technology might be the enabling
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+
+ align:start position:0%
+conditions of a complex narrative art
+ 
+
+ align:start position:0%
+conditions of a complex narrative art
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+
+ align:start position:0%
+right where does art come from it's
+ 
+
+ align:start position:0%
+right where does art come from it's
+about the it's not just about art though
+
+ align:start position:0%
+about the it's not just about art though
+ 
+
+ align:start position:0%
+about the it's not just about art though
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+
+ align:start position:0%
+even about sort of social even if even
+ 
+
+ align:start position:0%
+even about sort of social even if even
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+
+ align:start position:0%
+if we forget the question of Art and
+ 
+
+ align:start position:0%
+if we forget the question of Art and
+just talk about sort of the the social
+
+ align:start position:0%
+just talk about sort of the the social
+ 
+
+ align:start position:0%
+just talk about sort of the the social
+and cultural importance of movieo in
+
+ align:start position:0%
+and cultural importance of movieo in
+ 
+
+ align:start position:0%
+and cultural importance of movieo in
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+
+ align:start position:0%
+modern societies leave out the question
+ 
+
+ align:start position:0%
+modern societies leave out the question
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+
+ align:start position:0%
+of whether it's an aesthetically
+ 
+
+ align:start position:0%
+of whether it's an aesthetically
+valuable experience it's so Central to
+
+ align:start position:0%
+valuable experience it's so Central to
+ 
+
+ align:start position:0%
+valuable experience it's so Central to
+Human Experience remain so Central to
+
+ align:start position:0%
+Human Experience remain so Central to
+ 
+
+ align:start position:0%
+Human Experience remain so Central to
+Human Experience that there's a
+
+ align:start position:0%
+Human Experience that there's a
+ 
+
+ align:start position:0%
+Human Experience that there's a
+tremendous par that there's a tremendous
+
+ align:start position:0%
+tremendous par that there's a tremendous
+ 
+
+ align:start position:0%
+tremendous par that there's a tremendous
+Paradox in this that the that the crest
+
+ align:start position:0%
+Paradox in this that the that the crest
+ 
+
+ align:start position:0%
+Paradox in this that the that the crest
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+
+ align:start position:0%
+of alliances between Commerce and
+ 
+
+ align:start position:0%
+of alliances between Commerce and
+Technology right nothing Noble or
+
+ align:start position:0%
+Technology right nothing Noble or
+ 
+
+ align:start position:0%
+Technology right nothing Noble or
+admirable about it nobody's sitting down
+
+ align:start position:0%
+admirable about it nobody's sitting down
+ 
+
+ align:start position:0%
+admirable about it nobody's sitting down
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+
+ align:start position:0%
+thinking I want to make a new great
+ 
+
+ align:start position:0%
+thinking I want to make a new great
+medium for art nonetheless become these
+
+ align:start position:0%
+medium for art nonetheless become these
+ 
+
+ align:start position:0%
+medium for art nonetheless become these
+this Alliance becomes the enabling
+
+ align:start position:0%
+this Alliance becomes the enabling
+ 
+
+ align:start position:0%
+this Alliance becomes the enabling
+conditions for a complex form of social
+
+ align:start position:0%
+conditions for a complex form of social
+ 
+
+ align:start position:0%
+conditions for a complex form of social
+experience and of narrative art well
+
+ align:start position:0%
+experience and of narrative art well
+ 
+
+ align:start position:0%
+experience and of narrative art well
+that Paradox is at the heart of a lot of
+
+ align:start position:0%
+that Paradox is at the heart of a lot of
+ 
+
+ align:start position:0%
+that Paradox is at the heart of a lot of
+what we will be looking at in this
+
+ align:start position:0%
+what we will be looking at in this
+ 
+
+ align:start position:0%
+what we will be looking at in this
+course so I hope you'll keep it in mind
+
+ align:start position:0%
+course so I hope you'll keep it in mind
+ 
+
+ align:start position:0%
+course so I hope you'll keep it in mind
+as we go on I'd like to say a couple of
+
+ align:start position:0%
+as we go on I'd like to say a couple of
+ 
+
+ align:start position:0%
+as we go on I'd like to say a couple of
+words not too many a couple of words
+
+ align:start position:0%
+words not too many a couple of words
+ 
+
+ align:start position:0%
+words not too many a couple of words
+about the um The Great Train Robbery the
+
+ align:start position:0%
+about the um The Great Train Robbery the
+ 
+
+ align:start position:0%
+about the um The Great Train Robbery the
+very first uh film that you've seen uh
+
+ align:start position:0%
+very first uh film that you've seen uh
+ 
+
+ align:start position:0%
+very first uh film that you've seen uh
+this The Great Train Robbery is
+
+ align:start position:0%
+this The Great Train Robbery is
+ 
+
+ align:start position:0%
+this The Great Train Robbery is
+discussed in some helpful detail in
+
+ align:start position:0%
+discussed in some helpful detail in
+ 
+
+ align:start position:0%
+discussed in some helpful detail in
+David Cook's history of narrative film
+
+ align:start position:0%
+David Cook's history of narrative film
+ 
+
+ align:start position:0%
+David Cook's history of narrative film
+and I urge you to look closely at his
+
+ align:start position:0%
+and I urge you to look closely at his
+ 
+
+ align:start position:0%
+and I urge you to look closely at his
+account of it but I want to remind you
+
+ align:start position:0%
+account of it but I want to remind you
+ 
+
+ align:start position:0%
+account of it but I want to remind you
+of about a couple of highlights one is
+
+ align:start position:0%
+of about a couple of highlights one is
+ 
+
+ align:start position:0%
+of about a couple of highlights one is
+that that although The Great Train
+
+ align:start position:0%
+that that although The Great Train
+ 
+
+ align:start position:0%
+that that although The Great Train
+Robbery seems very primitive to us it's
+
+ align:start position:0%
+Robbery seems very primitive to us it's
+ 
+
+ align:start position:0%
+Robbery seems very primitive to us it's
+important to realize that even The Great
+
+ align:start position:0%
+important to realize that even The Great
+ 
+
+ align:start position:0%
+important to realize that even The Great
+Train Robbery is already a refined text
+
+ align:start position:0%
+Train Robbery is already a refined text
+ 
+
+ align:start position:0%
+Train Robbery is already a refined text
+a almost most most of the most
+
+ align:start position:0%
+a almost most most of the most
+ 
+
+ align:start position:0%
+a almost most most of the most
+fundamental principles of what we might
+
+ align:start position:0%
+fundamental principles of what we might
+ 
+
+ align:start position:0%
+fundamental principles of what we might
+call the syntax or grammar of the movies
+
+ align:start position:0%
+call the syntax or grammar of the movies
+ 
+
+ align:start position:0%
+call the syntax or grammar of the movies
+is already embedded in The Great Train
+
+ align:start position:0%
+is already embedded in The Great Train
+ 
+
+ align:start position:0%
+is already embedded in The Great Train
+Robbery and what that means is that the
+
+ align:start position:0%
+Robbery and what that means is that the
+ 
+
+ align:start position:0%
+Robbery and what that means is that the
+period the five or six year period
+
+ align:start position:0%
+period the five or six year period
+ 
+
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+period the five or six year period
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+
+ align:start position:0%
+before that when there is all this
+ 
+
+ align:start position:0%
+before that when there is all this
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+
+ align:start position:0%
+practice in with non-narrative forms uh
+ 
+
+ align:start position:0%
+practice in with non-narrative forms uh
+lies behind The Great Train Robbery and
+
+ align:start position:0%
+lies behind The Great Train Robbery and
+ 
+
+ align:start position:0%
+lies behind The Great Train Robbery and
+some and what also lies behind The Great
+
+ align:start position:0%
+some and what also lies behind The Great
+ 
+
+ align:start position:0%
+some and what also lies behind The Great
+Train Robbery is this experience of
+
+ align:start position:0%
+Train Robbery is this experience of
+ 
+
+ align:start position:0%
+Train Robbery is this experience of
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+
+ align:start position:0%
+audiences going in to the to first to
+ 
+
+ align:start position:0%
+audiences going in to the to first to
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+
+ align:start position:0%
+the penny arcades then to the
+ 
+
+ align:start position:0%
+the penny arcades then to the
+Nickelodeons begin to open up in the in
+
+ align:start position:0%
+Nickelodeons begin to open up in the in
+ 
+
+ align:start position:0%
+Nickelodeons begin to open up in the in
+in the by the turn of the 20th century
+
+ align:start position:0%
+in the by the turn of the 20th century
+ 
+
+ align:start position:0%
+in the by the turn of the 20th century
+uh and becoming impatient with repeated
+
+ align:start position:0%
+uh and becoming impatient with repeated
+ 
+
+ align:start position:0%
+uh and becoming impatient with repeated
+scenes that simply show uh jokes uh
+
+ align:start position:0%
+scenes that simply show uh jokes uh
+ 
+
+ align:start position:0%
+scenes that simply show uh jokes uh
+hoses going off in people's faces or
+
+ align:start position:0%
+hoses going off in people's faces or
+ 
+
+ align:start position:0%
+hoses going off in people's faces or
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+
+ align:start position:0%
+trains coming into a state after a while
+ 
+
+ align:start position:0%
+trains coming into a state after a while
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+
+ align:start position:0%
+the novelty wears off the audience wants
+ 
+
+ align:start position:0%
+the novelty wears off the audience wants
+but of course the people who are making
+
+ align:start position:0%
+but of course the people who are making
+ 
+
+ align:start position:0%
+but of course the people who are making
+films are also interested in what
+
+ align:start position:0%
+films are also interested in what
+ 
+
+ align:start position:0%
+films are also interested in what
+they're doing you can feel especially if
+
+ align:start position:0%
+they're doing you can feel especially if
+ 
+
+ align:start position:0%
+they're doing you can feel especially if
+you look at DW Griffith's shorts and
+
+ align:start position:0%
+you look at DW Griffith's shorts and
+ 
+
+ align:start position:0%
+you look at DW Griffith's shorts and
+you've looked at two you will have
+
+ align:start position:0%
+you've looked at two you will have
+ 
+
+ align:start position:0%
+you've looked at two you will have
+looked at two of them in this course uh
+
+ align:start position:0%
+looked at two of them in this course uh
+ 
+
+ align:start position:0%
+looked at two of them in this course uh
+the uh a beast at Bay from last time and
+
+ align:start position:0%
+the uh a beast at Bay from last time and
+ 
+
+ align:start position:0%
+the uh a beast at Bay from last time and
+the Londale operator which you'll see
+
+ align:start position:0%
+the Londale operator which you'll see
+ 
+
+ align:start position:0%
+the Londale operator which you'll see
+tonight before we turn to the Kon films
+
+ align:start position:0%
+tonight before we turn to the Kon films
+ 
+
+ align:start position:0%
+tonight before we turn to the Kon films
+uh and you'll see in these are just a
+
+ align:start position:0%
+uh and you'll see in these are just a
+ 
+
+ align:start position:0%
+uh and you'll see in these are just a
+sampling of his of his early work but if
+
+ align:start position:0%
+sampling of his of his early work but if
+ 
+
+ align:start position:0%
+sampling of his of his early work but if
+you look closely at those where you can
+
+ align:start position:0%
+you look closely at those where you can
+ 
+
+ align:start position:0%
+you look closely at those where you can
+feel Griffith's own excitement at
+
+ align:start position:0%
+feel Griffith's own excitement at
+ 
+
+ align:start position:0%
+feel Griffith's own excitement at
+discovering the possibilities of the
+
+ align:start position:0%
+discovering the possibilities of the
+ 
+
+ align:start position:0%
+discovering the possibilities of the
+cinema learn in many cases these F you
+
+ align:start position:0%
+cinema learn in many cases these F you
+ 
+
+ align:start position:0%
+cinema learn in many cases these F you
+Griffith is doing what doing some things
+
+ align:start position:0%
+Griffith is doing what doing some things
+ 
+
+ align:start position:0%
+Griffith is doing what doing some things
+with the camera doing some things with
+
+ align:start position:0%
+with the camera doing some things with
+ 
+
+ align:start position:0%
+with the camera doing some things with
+narrative shape with the shaping of
+
+ align:start position:0%
+narrative shape with the shaping of
+ 
+
+ align:start position:0%
+narrative shape with the shaping of
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+
+ align:start position:0%
+narrative in in cinema that had never
+ 
+
+ align:start position:0%
+narrative in in cinema that had never
+been done before and you can feel his
+
+ align:start position:0%
+been done before and you can feel his
+ 
+
+ align:start position:0%
+been done before and you can feel his
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+
+ align:start position:0%
+own excitement at the possibility of
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+
+ align:start position:0%
+own excitement at the possibility of
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+
+ align:start position:0%
+this of this astonishing of this
+ 
+
+ align:start position:0%
+this of this astonishing of this
+astonishing technology well The Great
+
+ align:start position:0%
+astonishing technology well The Great
+ 
+
+ align:start position:0%
+astonishing technology well The Great
+Train Robbery the most important
+
+ align:start position:0%
+Train Robbery the most important
+ 
+
+ align:start position:0%
+Train Robbery the most important
+discovery that The Great Train Robbery
+
+ align:start position:0%
+discovery that The Great Train Robbery
+ 
+
+ align:start position:0%
+discovery that The Great Train Robbery
+shows us and again it seems so obvious
+
+ align:start position:0%
+shows us and again it seems so obvious
+ 
+
+ align:start position:0%
+shows us and again it seems so obvious
+and so embedded that we wouldn't even
+
+ align:start position:0%
+and so embedded that we wouldn't even
+ 
+
+ align:start position:0%
+and so embedded that we wouldn't even
+think about it today we've absorbed
+
+ align:start position:0%
+think about it today we've absorbed
+ 
+
+ align:start position:0%
+think about it today we've absorbed
+these principles so deeply into our DNA
+
+ align:start position:0%
+these principles so deeply into our DNA
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+
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+
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+when you see a particular gag of his a
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+could not have happened in the theater
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+it could not have been told to you
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+verbally the joke is visual the joke
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+involves motion the the joke in the joke
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+ align:start position:0%
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+
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+involves uh a recognition of the powers
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+
+ align:start position:0%
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+of the C of the powers of of of
+
+ align:start position:0%
+of the C of the powers of of of
+ 
+
+ align:start position:0%
+of the C of the powers of of of
+cinematic representation to tell stories
+
+ align:start position:0%
+cinematic representation to tell stories
+ 
+
+ align:start position:0%
+cinematic representation to tell stories
+uh and you'll see many examples of this
+
+ align:start position:0%
+uh and you'll see many examples of this
+ 
+
+ align:start position:0%
+uh and you'll see many examples of this
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+
+ align:start position:0%
+in the in the in the uh Katon materials
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+
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+tonight so the so the one of the very
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+
+ align:start position:0%
+first first discoveries that's made is
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+
+ align:start position:0%
+first first discoveries that's made is
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+
+ align:start position:0%
+the discovery that the shot is the basic
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
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+the recognition that you have to cut
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+
+ align:start position:0%
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+
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+
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+
+ align:start position:0%
+between shots rather rather than and Mo
+ 
+
+ align:start position:0%
+between shots rather rather than and Mo
+and mostly what you do is you let scenes
+
+ align:start position:0%
+and mostly what you do is you let scenes
+ 
+
+ align:start position:0%
+and mostly what you do is you let scenes
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+play out even though you might abruptly
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+
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+
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+completed one of that's another
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+
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+scene if a person starts to walk toward
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+
+ align:start position:0%
+scene if a person starts to walk toward
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+the door the first earliest films they
+ 
+
+ align:start position:0%
+the door the first earliest films they
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+
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+would show the person walking all the
+ 
+
+ align:start position:0%
+would show the person walking all the
+way to the end walking out of the door
+
+ align:start position:0%
+way to the end walking out of the door
+ 
+
+ align:start position:0%
+way to the end walking out of the door
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+
+ align:start position:0%
+then filmmakers discovered way there's a
+ 
+
+ align:start position:0%
+then filmmakers discovered way there's a
+way of creating a kind of quickness here
+
+ align:start position:0%
+way of creating a kind of quickness here
+ 
+
+ align:start position:0%
+way of creating a kind of quickness here
+because if I show thorburn walking
+
+ align:start position:0%
+because if I show thorburn walking
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+
+ align:start position:0%
+because if I show thorburn walking
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+
+ align:start position:0%
+toward the door starting and I cut and
+ 
+
+ align:start position:0%
+toward the door starting and I cut and
+he knocks his glasses off uh and then I
+
+ align:start position:0%
+he knocks his glasses off uh and then I
+ 
+
+ align:start position:0%
+he knocks his glasses off uh and then I
+and then I cut and I wait till he gets
+
+ align:start position:0%
+and then I cut and I wait till he gets
+ 
+
+ align:start position:0%
+and then I cut and I wait till he gets
+to the door and we see him leaving the
+
+ align:start position:0%
+to the door and we see him leaving the
+ 
+
+ align:start position:0%
+to the door and we see him leaving the
+door I don't have to watch him take
+
+ align:start position:0%
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+
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+door I don't have to watch him take
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+
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+those 17 steps that right so what what
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+those 17 steps that right so what what
+what's been discovered is a basic
+
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+what's been discovered is a basic
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+
+ align:start position:0%
+what's been discovered is a basic
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+
+ align:start position:0%
+principle of cinematic syntax right and
+ 
+
+ align:start position:0%
+principle of cinematic syntax right and
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+
+ align:start position:0%
+but what but but it seems so obvious to
+ 
+
+ align:start position:0%
+but what but but it seems so obvious to
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+
+ align:start position:0%
+us but of course it's really a great
+ 
+
+ align:start position:0%
+us but of course it's really a great
+discovery it's a uh in words the the
+
+ align:start position:0%
+discovery it's a uh in words the the
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+properties of the medium have to be
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+understood before you can really begin
+ 
+
+ align:start position:0%
+understood before you can really begin
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+
+ align:start position:0%
+to exploit it and that's why uh I've
+ 
+
+ align:start position:0%
+to exploit it and that's why uh I've
+asked you to look at some of these short
+
+ align:start position:0%
+asked you to look at some of these short
+ 
+
+ align:start position:0%
+asked you to look at some of these short
+films none of the short films I've shown
+
+ align:start position:0%
+films none of the short films I've shown
+ 
+
+ align:start position:0%
+films none of the short films I've shown
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+
+ align:start position:0%
+you are completely without uh some uh uh
+ 
+
+ align:start position:0%
+you are completely without uh some uh uh
+technical interest and uh even though of
+
+ align:start position:0%
+technical interest and uh even though of
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+course they're the only films I'm
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
+showing you that I wouldn't sort of make
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+
+ align:start position:0%
+arguments uh to defend them as works of
+ 
+
+ align:start position:0%
+arguments uh to defend them as works of
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+
+ align:start position:0%
+art but I certainly would make Arguments
+ 
+
+ align:start position:0%
+art but I certainly would make Arguments
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+
+ align:start position:0%
+for them as technically fascinating
+ 
+
+ align:start position:0%
+for them as technically fascinating
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+you'll look at them in in that light so
+ 
+
+ align:start position:0%
+you'll look at them in in that light so
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+
+ align:start position:0%
+the shot as a basic unit of Action
+ 
+
+ align:start position:0%
+the shot as a basic unit of Action
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+
+ align:start position:0%
+cutting between scenes
+ 
+
+ align:start position:0%
+cutting between scenes
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+
+ align:start position:0%
+a couple of other things in the in the
+ 
+
+ align:start position:0%
+a couple of other things in the in the
+that I think are important in The Great
+
+ align:start position:0%
+that I think are important in The Great
+ 
+
+ align:start position:0%
+that I think are important in The Great
+Train Rob one is that you can see in The
+
+ align:start position:0%
+Train Rob one is that you can see in The
+ 
+
+ align:start position:0%
+Train Rob one is that you can see in The
+Great Train Robbery they're beginning to
+
+ align:start position:0%
+Great Train Robbery they're beginning to
+ 
+
+ align:start position:0%
+Great Train Robbery they're beginning to
+discover the value of camera placement
+
+ align:start position:0%
+discover the value of camera placement
+ 
+
+ align:start position:0%
+discover the value of camera placement
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+
+ align:start position:0%
+what happens when you place the camera
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+in a particular position that if the
+ 
+
+ align:start position:0%
+in a particular position that if the
+camera uh especially if action is coming
+
+ align:start position:0%
+camera uh especially if action is coming
+ 
+
+ align:start position:0%
+camera uh especially if action is coming
+toward the camera if you that you might
+
+ align:start position:0%
+toward the camera if you that you might
+ 
+
+ align:start position:0%
+toward the camera if you that you might
+not want to place the camera directly in
+
+ align:start position:0%
+not want to place the camera directly in
+ 
+
+ align:start position:0%
+not want to place the camera directly in
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+you that something happens if you place
+ 
+
+ align:start position:0%
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+it slightly awart it so it can see it at
+
+ align:start position:0%
+it slightly awart it so it can see it at
+ 
+
+ align:start position:0%
+it slightly awart it so it can see it at
+a slight angle it creates a greater
+
+ align:start position:0%
+a slight angle it creates a greater
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+
+ align:start position:0%
+a slight angle it creates a greater
+illusion of depth in the image for
+
+ align:start position:0%
+illusion of depth in the image for
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+
+ align:start position:0%
+illusion of depth in the image for
+example and it does other kinds of it
+
+ align:start position:0%
+example and it does other kinds of it
+ 
+
+ align:start position:0%
+example and it does other kinds of it
+lets the action get closer to you before
+
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+lets the action get closer to you before
+ 
+
+ align:start position:0%
+lets the action get closer to you before
+before the uh scene has to be cut uh so
+
+ align:start position:0%
+before the uh scene has to be cut uh so
+ 
+
+ align:start position:0%
+before the uh scene has to be cut uh so
+camera placement is something that you
+
+ align:start position:0%
+camera placement is something that you
+ 
+
+ align:start position:0%
+camera placement is something that you
+can see is is beginning to be learned
+
+ align:start position:0%
+can see is is beginning to be learned
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+
+ align:start position:0%
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+
+ align:start position:0%
+beginning to be mastered in the great in
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+
+ align:start position:0%
+beginning to be mastered in the great in
+The Great Train Robbery and F camera or
+
+ align:start position:0%
+The Great Train Robbery and F camera or
+ 
+
+ align:start position:0%
+The Great Train Robbery and F camera or
+or camera position so there are other
+
+ align:start position:0%
+or camera position so there are other
+ 
+
+ align:start position:0%
+or camera position so there are other
+thing and finally one might mention one
+
+ align:start position:0%
+thing and finally one might mention one
+ 
+
+ align:start position:0%
+thing and finally one might mention one
+other thing that again establishes a
+
+ align:start position:0%
+other thing that again establishes a
+ 
+
+ align:start position:0%
+other thing that again establishes a
+principle that begins that that that
+
+ align:start position:0%
+principle that begins that that that
+ 
+
+ align:start position:0%
+principle that begins that that that
+then is continued continues in use for
+
+ align:start position:0%
+then is continued continues in use for
+ 
+
+ align:start position:0%
+then is continued continues in use for
+50 or 75 years and that's the principle
+
+ align:start position:0%
+50 or 75 years and that's the principle
+ 
+
+ align:start position:0%
+50 or 75 years and that's the principle
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+
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+of the process shot you can see in the
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+
+ align:start position:0%
+of the process shot you can see in the
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+ align:start position:0%
+Great Train Robbery that he that some
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+
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+
+ align:start position:0%
+effects have been created by tricks that
+ 
+
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+
+ align:start position:0%
+there's a that there's back projection
+ 
+
+ align:start position:0%
+there's a that there's back projection
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+
+ align:start position:0%
+going used in that it's it looks crude
+ 
+
+ align:start position:0%
+going used in that it's it looks crude
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+
+ align:start position:0%
+to us we can see through it but the
+ 
+
+ align:start position:0%
+to us we can see through it but the
+early audiences would would not have
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+recognized that we we we're so used to
+ 
+
+ align:start position:0%
+recognized that we we we're so used to
+location filming that we can pick out uh
+
+ align:start position:0%
+location filming that we can pick out uh
+ 
+
+ align:start position:0%
+location filming that we can pick out uh
+we today can see through the process
+
+ align:start position:0%
+we today can see through the process
+ 
+
+ align:start position:0%
+we today can see through the process
+shots of earlier films this in fact
+
+ align:start position:0%
+shots of earlier films this in fact
+ 
+
+ align:start position:0%
+shots of earlier films this in fact
+damages some of Hitchcock's films very
+
+ align:start position:0%
+damages some of Hitchcock's films very
+ 
+
+ align:start position:0%
+damages some of Hitchcock's films very
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+
+ align:start position:0%
+badly today because Hitchcock used a lot
+ 
+
+ align:start position:0%
+badly today because Hitchcock used a lot
+of processed shot effects in his films
+
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+of processed shot effects in his films
+ 
+
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+of processed shot effects in his films
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+when he made them the audiences were
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+
+ align:start position:0%
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+used to there was a Convention of film
+ 
+
+ align:start position:0%
+used to there was a Convention of film
+going today everything because cameras
+
+ align:start position:0%
+going today everything because cameras
+ 
+
+ align:start position:0%
+going today everything because cameras
+are so much more more mobile and light
+
+ align:start position:0%
+are so much more more mobile and light
+ 
+
+ align:start position:0%
+are so much more more mobile and light
+and so so much has been uh learned about
+
+ align:start position:0%
+and so so much has been uh learned about
+ 
+
+ align:start position:0%
+and so so much has been uh learned about
+how to even about filming in in low
+
+ align:start position:0%
+how to even about filming in in low
+ 
+
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+how to even about filming in in low
+light and so forth that they
+
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+light and so forth that they
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+
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+
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+that there's much less use of process
+ 
+
+ align:start position:0%
+that there's much less use of process
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+
+ align:start position:0%
+shots so well a new kind of process shot
+ 
+
+ align:start position:0%
+shots so well a new kind of process shot
+I suppose is emerging with digital
+
+ align:start position:0%
+I suppose is emerging with digital
+ 
+
+ align:start position:0%
+I suppose is emerging with digital
+animation and one could say it's sort of
+
+ align:start position:0%
+animation and one could say it's sort of
+ 
+
+ align:start position:0%
+animation and one could say it's sort of
+a return to the idea of manipulating the
+
+ align:start position:0%
+a return to the idea of manipulating the
+ 
+
+ align:start position:0%
+a return to the idea of manipulating the
+image in illegitimate ways um but the
+
+ align:start position:0%
+image in illegitimate ways um but the
+ 
+
+ align:start position:0%
+image in illegitimate ways um but the
+but but we can see even in The Great
+
+ align:start position:0%
+but but we can see even in The Great
+ 
+
+ align:start position:0%
+but but we can see even in The Great
+Train Robbery we we we can even see the
+
+ align:start position:0%
+Train Robbery we we we can even see the
+ 
+
+ align:start position:0%
+Train Robbery we we we can even see the
+beginnings of the use of process shots
+
+ align:start position:0%
+beginnings of the use of process shots
+ 
+
+ align:start position:0%
+beginnings of the use of process shots
+of recognizing that you can create
+
+ align:start position:0%
+of recognizing that you can create
+ 
+
+ align:start position:0%
+of recognizing that you can create
+effects in the movies that are unique
+
+ align:start position:0%
+effects in the movies that are unique
+ 
+
+ align:start position:0%
+effects in the movies that are unique
+and special that no other medium would
+
+ align:start position:0%
+and special that no other medium would
+ 
+
+ align:start position:0%
+and special that no other medium would
+allow you to do and what's embedded
+
+ align:start position:0%
+allow you to do and what's embedded
+ 
+
+ align:start position:0%
+allow you to do and what's embedded
+there is science fiction what's embedded
+
+ align:start position:0%
+there is science fiction what's embedded
+ 
+
+ align:start position:0%
+there is science fiction what's embedded
+there are all the kinds of imaginative
+
+ align:start position:0%
+there are all the kinds of imaginative
+ 
+
+ align:start position:0%
+there are all the kinds of imaginative
+not just science fiction all the kinds
+
+ align:start position:0%
+not just science fiction all the kinds
+ 
+
+ align:start position:0%
+not just science fiction all the kinds
+of imaginative movies that have been
+
+ align:start position:0%
+of imaginative movies that have been
+ 
+
+ align:start position:0%
+of imaginative movies that have been
+made that maybe take you inside people's
+
+ align:start position:0%
+made that maybe take you inside people's
+ 
+
+ align:start position:0%
+made that maybe take you inside people's
+nightmares or dreams where what the film
+
+ align:start position:0%
+nightmares or dreams where what the film
+ 
+
+ align:start position:0%
+nightmares or dreams where what the film
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+
+ align:start position:0%
+is showing you now what in other words
+ 
+
+ align:start position:0%
+is showing you now what in other words
+what what is embedded in that process
+
+ align:start position:0%
+what what is embedded in that process
+ 
+
+ align:start position:0%
+what what is embedded in that process
+shot even more fully embedded in in
+
+ align:start position:0%
+shot even more fully embedded in in
+ 
+
+ align:start position:0%
+shot even more fully embedded in in
+meles's the French directors films like
+
+ align:start position:0%
+meles's the French directors films like
+ 
+
+ align:start position:0%
+meles's the French directors films like
+trip to the moon where he explicitly
+
+ align:start position:0%
+trip to the moon where he explicitly
+ 
+
+ align:start position:0%
+trip to the moon where he explicitly
+goes into a realm of
+
+ align:start position:0%
+goes into a realm of
+ 
+
+ align:start position:0%
+goes into a realm of
+fantasy is not only that the film is the
+
+ align:start position:0%
+fantasy is not only that the film is the
+ 
+
+ align:start position:0%
+fantasy is not only that the film is the
+most profoundly realistic medium that
+
+ align:start position:0%
+most profoundly realistic medium that
+ 
+
+ align:start position:0%
+most profoundly realistic medium that
+was ever invented it may also be the
+
+ align:start position:0%
+was ever invented it may also be the
+ 
+
+ align:start position:0%
+was ever invented it may also be the
+most the the the the most expressive
+
+ align:start position:0%
+most the the the the most expressive
+ 
+
+ align:start position:0%
+most the the the the most expressive
+medium for the for the rendering of
+
+ align:start position:0%
+medium for the for the rendering of
+ 
+
+ align:start position:0%
+medium for the for the rendering of
+non-realistic states of dream of
+
+ align:start position:0%
+non-realistic states of dream of
+ 
+
+ align:start position:0%
+non-realistic states of dream of
+nightmare of fantasy uh exactly be
+
+ align:start position:0%
+nightmare of fantasy uh exactly be
+ 
+
+ align:start position:0%
+nightmare of fantasy uh exactly be
+because of the freedom that that uh the
+
+ align:start position:0%
+because of the freedom that that uh the
+ 
+
+ align:start position:0%
+because of the freedom that that uh the
+film medium allows and it even these
+
+ align:start position:0%
+film medium allows and it even these
+ 
+
+ align:start position:0%
+film medium allows and it even these
+implications are at least embedded in
+
+ align:start position:0%
+implications are at least embedded in
+ 
+
+ align:start position:0%
+implications are at least embedded in
+the use of the process shots in uh
+
+ align:start position:0%
+the use of the process shots in uh
+ 
+
+ align:start position:0%
+the use of the process shots in uh
+Porters The Great Train Robbery the the
+
+ align:start position:0%
+Porters The Great Train Robbery the the
+ 
+
+ align:start position:0%
+Porters The Great Train Robbery the the
+the other short that you're going to see
+
+ align:start position:0%
+the other short that you're going to see
+ 
+
+ align:start position:0%
+the other short that you're going to see
+tonight that is not by Keaton is called
+
+ align:start position:0%
+tonight that is not by Keaton is called
+ 
+
+ align:start position:0%
+tonight that is not by Keaton is called
+the lone Dale operator it's it's it was
+
+ align:start position:0%
+the lone Dale operator it's it's it was
+ 
+
+ align:start position:0%
+the lone Dale operator it's it's it was
+made in
+
+ align:start position:0%
+made in
+ 
+
+ align:start position:0%
+made in
+1911 um and uh it in a way it's the most
+
+ align:start position:0%
+1911 um and uh it in a way it's the most
+ 
+
+ align:start position:0%
+1911 um and uh it in a way it's the most
+it's the most advanced film of its time
+
+ align:start position:0%
+it's the most advanced film of its time
+ 
+
+ align:start position:0%
+it's the most advanced film of its time
+and that that's one re and I what I hope
+
+ align:start position:0%
+and that that's one re and I what I hope
+ 
+
+ align:start position:0%
+and that that's one re and I what I hope
+when you look at it you you'll watch
+
+ align:start position:0%
+when you look at it you you'll watch
+ 
+
+ align:start position:0%
+when you look at it you you'll watch
+especially for how much more complex it
+
+ align:start position:0%
+especially for how much more complex it
+ 
+
+ align:start position:0%
+especially for how much more complex it
+is than let's say The Great Train
+
+ align:start position:0%
+is than let's say The Great Train
+ 
+
+ align:start position:0%
+is than let's say The Great Train
+Robbery and it'll be a kind of small
+
+ align:start position:0%
+Robbery and it'll be a kind of small
+ 
+
+ align:start position:0%
+Robbery and it'll be a kind of small
+measure of this treed out principle I've
+
+ align:start position:0%
+measure of this treed out principle I've
+ 
+
+ align:start position:0%
+measure of this treed out principle I've
+been talking about let me mention a
+
+ align:start position:0%
+been talking about let me mention a
+ 
+
+ align:start position:0%
+been talking about let me mention a
+couple of things about uh the Londale
+
+ align:start position:0%
+couple of things about uh the Londale
+ 
+
+ align:start position:0%
+couple of things about uh the Londale
+operator between 1907 and 1911 most
+
+ align:start position:0%
+operator between 1907 and 1911 most
+ 
+
+ align:start position:0%
+operator between 1907 and 1911 most
+films consisted of no more than 24
+
+ align:start position:0%
+films consisted of no more than 24
+ 
+
+ align:start position:0%
+films consisted of no more than 24
+separate shots right between 1908 and
+
+ align:start position:0%
+separate shots right between 1908 and
+ 
+
+ align:start position:0%
+separate shots right between 1908 and
+1913 led by DW Griffith and his company
+
+ align:start position:0%
+1913 led by DW Griffith and his company
+ 
+
+ align:start position:0%
+1913 led by DW Griffith and his company
+the Biograph company many more shots
+
+ align:start position:0%
+the Biograph company many more shots
+ 
+
+ align:start position:0%
+the Biograph company many more shots
+were introduced into in into a single
+
+ align:start position:0%
+were introduced into in into a single
+ 
+
+ align:start position:0%
+were introduced into in into a single
+reel of film and in the lone Dale
+
+ align:start position:0%
+reel of film and in the lone Dale
+ 
+
+ align:start position:0%
+reel of film and in the lone Dale
+operator there are 98 shots six
+
+ align:start position:0%
+operator there are 98 shots six
+ 
+
+ align:start position:0%
+operator there are 98 shots six
+intertitles one main title and two
+
+ align:start position:0%
+intertitles one main title and two
+ 
+
+ align:start position:0%
+intertitles one main title and two
+written inserts all within a 17-minute
+
+ align:start position:0%
+written inserts all within a 17-minute
+ 
+
+ align:start position:0%
+written inserts all within a 17-minute
+length but think of the just the ad the
+
+ align:start position:0%
+length but think of the just the ad the
+ 
+
+ align:start position:0%
+length but think of the just the ad the
+the access of complexity that has
+
+ align:start position:0%
+the access of complexity that has
+ 
+
+ align:start position:0%
+the access of complexity that has
+occurred just in less than 10 years
+
+ align:start position:0%
+occurred just in less than 10 years
+ 
+
+ align:start position:0%
+occurred just in less than 10 years
+right uh
+
+ align:start position:0%
+right uh
+ 
+
+ align:start position:0%
+right uh
+um it's such a complicated film that one
+
+ align:start position:0%
+um it's such a complicated film that one
+ 
+
+ align:start position:0%
+um it's such a complicated film that one
+of the things we realize even looking at
+
+ align:start position:0%
+of the things we realize even looking at
+ 
+
+ align:start position:0%
+of the things we realize even looking at
+it if we look closely is that it
+
+ align:start position:0%
+it if we look closely is that it
+ 
+
+ align:start position:0%
+it if we look closely is that it
+actually required uh a kind of
+
+ align:start position:0%
+actually required uh a kind of
+ 
+
+ align:start position:0%
+actually required uh a kind of
+attentiveness that earlier films did not
+
+ align:start position:0%
+attentiveness that earlier films did not
+ 
+
+ align:start position:0%
+attentiveness that earlier films did not
+as filmmakers began to make these things
+
+ align:start position:0%
+as filmmakers began to make these things
+ 
+
+ align:start position:0%
+as filmmakers began to make these things
+and began to make them longer and began
+
+ align:start position:0%
+and began to make them longer and began
+ 
+
+ align:start position:0%
+and began to make them longer and began
+to make them more complicated they
+
+ align:start position:0%
+to make them more complicated they
+ 
+
+ align:start position:0%
+to make them more complicated they
+realized that they couldn't just bring
+
+ align:start position:0%
+realized that they couldn't just bring
+ 
+
+ align:start position:0%
+realized that they couldn't just bring
+the camera out and start shooting they
+
+ align:start position:0%
+the camera out and start shooting they
+ 
+
+ align:start position:0%
+the camera out and start shooting they
+began to develop the the the formal
+
+ align:start position:0%
+began to develop the the the formal
+ 
+
+ align:start position:0%
+began to develop the the the formal
+rationalizing strategies that led to the
+
+ align:start position:0%
+rationalizing strategies that led to the
+ 
+
+ align:start position:0%
+rationalizing strategies that led to the
+making of movies as we understand them
+
+ align:start position:0%
+making of movies as we understand them
+ 
+
+ align:start position:0%
+making of movies as we understand them
+there was a 4-day shooting schedule
+
+ align:start position:0%
+there was a 4-day shooting schedule
+ 
+
+ align:start position:0%
+there was a 4-day shooting schedule
+created for the Londale operator it was
+
+ align:start position:0%
+created for the Londale operator it was
+ 
+
+ align:start position:0%
+created for the Londale operator it was
+one of the first films to to to have uh
+
+ align:start position:0%
+one of the first films to to to have uh
+ 
+
+ align:start position:0%
+one of the first films to to to have uh
+this format and of course it's the
+
+ align:start position:0%
+this format and of course it's the
+ 
+
+ align:start position:0%
+this format and of course it's the
+format that is followed today with
+
+ align:start position:0%
+format that is followed today with
+ 
+
+ align:start position:0%
+format that is followed today with
+virtually every film uh in in in
+
+ align:start position:0%
+virtually every film uh in in in
+ 
+
+ align:start position:0%
+virtually every film uh in in in
+different in different uh aspects um uh
+
+ align:start position:0%
+different in different uh aspects um uh
+ 
+
+ align:start position:0%
+different in different uh aspects um uh
+and this also required a pre-planned
+
+ align:start position:0%
+and this also required a pre-planned
+ 
+
+ align:start position:0%
+and this also required a pre-planned
+shooting script A they had to they had
+
+ align:start position:0%
+shooting script A they had to they had
+ 
+
+ align:start position:0%
+shooting script A they had to they had
+to plan what they would pre plan all of
+
+ align:start position:0%
+to plan what they would pre plan all of
+ 
+
+ align:start position:0%
+to plan what they would pre plan all of
+their shooting all of their shots all of
+
+ align:start position:0%
+their shooting all of their shots all of
+ 
+
+ align:start position:0%
+their shooting all of their shots all of
+their camera angles they needed a
+
+ align:start position:0%
+their camera angles they needed a
+ 
+
+ align:start position:0%
+their camera angles they needed a
+shooting script a written script films
+
+ align:start position:0%
+shooting script a written script films
+ 
+
+ align:start position:0%
+shooting script a written script films
+didn't have written scripts at first but
+
+ align:start position:0%
+didn't have written scripts at first but
+ 
+
+ align:start position:0%
+didn't have written scripts at first but
+Londale did uh and it also required in
+
+ align:start position:0%
+Londale did uh and it also required in
+ 
+
+ align:start position:0%
+Londale did uh and it also required in
+order for them to make their schedule
+
+ align:start position:0%
+order for them to make their schedule
+ 
+
+ align:start position:0%
+order for them to make their schedule
+outof order shooting that is to say they
+
+ align:start position:0%
+outof order shooting that is to say they
+ 
+
+ align:start position:0%
+outof order shooting that is to say they
+had to shoot certain things not in the
+
+ align:start position:0%
+had to shoot certain things not in the
+ 
+
+ align:start position:0%
+had to shoot certain things not in the
+sequential order of the film and that's
+
+ align:start position:0%
+sequential order of the film and that's
+ 
+
+ align:start position:0%
+sequential order of the film and that's
+one of the most basic principles of film
+
+ align:start position:0%
+one of the most basic principles of film
+ 
+
+ align:start position:0%
+one of the most basic principles of film
+making because once you set up the
+
+ align:start position:0%
+making because once you set up the
+ 
+
+ align:start position:0%
+making because once you set up the
+camera for a for a a shot of a
+
+ align:start position:0%
+camera for a for a a shot of a
+ 
+
+ align:start position:0%
+camera for a for a a shot of a
+particular environment if that
+
+ align:start position:0%
+particular environment if that
+ 
+
+ align:start position:0%
+particular environment if that
+environment shows up later in the film
+
+ align:start position:0%
+environment shows up later in the film
+ 
+
+ align:start position:0%
+environment shows up later in the film
+it's unbelievably more expensive than
+
+ align:start position:0%
+it's unbelievably more expensive than
+ 
+
+ align:start position:0%
+it's unbelievably more expensive than
+timec consuming to reconstitute that
+
+ align:start position:0%
+timec consuming to reconstitute that
+ 
+
+ align:start position:0%
+timec consuming to reconstitute that
+whole set so the the B almost all films
+
+ align:start position:0%
+whole set so the the B almost all films
+ 
+
+ align:start position:0%
+whole set so the the B almost all films
+to this very day are still shot out of
+
+ align:start position:0%
+to this very day are still shot out of
+ 
+
+ align:start position:0%
+to this very day are still shot out of
+sequence in order to maximize the the uh
+
+ align:start position:0%
+sequence in order to maximize the the uh
+ 
+
+ align:start position:0%
+sequence in order to maximize the the uh
+uh the the the the the time you have in
+
+ align:start position:0%
+uh the the the the the time you have in
+ 
+
+ align:start position:0%
+uh the the the the the time you have in
+in order to work at your most efficient
+
+ align:start position:0%
+in order to work at your most efficient
+ 
+
+ align:start position:0%
+in order to work at your most efficient
+and was it's not an efficient way to
+
+ align:start position:0%
+and was it's not an efficient way to
+ 
+
+ align:start position:0%
+and was it's not an efficient way to
+make a movie to shoot it sequentially to
+
+ align:start position:0%
+make a movie to shoot it sequentially to
+ 
+
+ align:start position:0%
+make a movie to shoot it sequentially to
+follow the to follow the script in its
+
+ align:start position:0%
+follow the to follow the script in its
+ 
+
+ align:start position:0%
+follow the to follow the script in its
+chronological sequence uh and the lone
+
+ align:start position:0%
+chronological sequence uh and the lone
+ 
+
+ align:start position:0%
+chronological sequence uh and the lone
+Dale operator is one of the is maybe the
+
+ align:start position:0%
+Dale operator is one of the is maybe the
+ 
+
+ align:start position:0%
+Dale operator is one of the is maybe the
+first film to to have all of these
+
+ align:start position:0%
+first film to to have all of these
+ 
+
+ align:start position:0%
+first film to to have all of these
+features that we would associate with
+
+ align:start position:0%
+features that we would associate with
+ 
+
+ align:start position:0%
+features that we would associate with
+with uh W with a mo with a modern or a
+
+ align:start position:0%
+with uh W with a mo with a modern or a
+ 
+
+ align:start position:0%
+with uh W with a mo with a modern or a
+contemporary film uh you might notice in
+
+ align:start position:0%
+contemporary film uh you might notice in
+ 
+
+ align:start position:0%
+contemporary film uh you might notice in
+the it's a it's an immensely complex
+
+ align:start position:0%
+the it's a it's an immensely complex
+ 
+
+ align:start position:0%
+the it's a it's an immensely complex
+film even in terms of its content and I
+
+ align:start position:0%
+film even in terms of its content and I
+ 
+
+ align:start position:0%
+film even in terms of its content and I
+might leave that I I won't talk about
+
+ align:start position:0%
+might leave that I I won't talk about
+ 
+
+ align:start position:0%
+might leave that I I won't talk about
+that much now except to say this watch
+
+ align:start position:0%
+that much now except to say this watch
+ 
+
+ align:start position:0%
+that much now except to say this watch
+the way in which the film tries to deal
+
+ align:start position:0%
+the way in which the film tries to deal
+ 
+
+ align:start position:0%
+the way in which the film tries to deal
+with what we might call uh hierarchies
+
+ align:start position:0%
+with what we might call uh hierarchies
+ 
+
+ align:start position:0%
+with what we might call uh hierarchies
+of gender I mean the film is partly
+
+ align:start position:0%
+of gender I mean the film is partly
+ 
+
+ align:start position:0%
+of gender I mean the film is partly
+about how a woman takes on a man's job
+
+ align:start position:0%
+about how a woman takes on a man's job
+ 
+
+ align:start position:0%
+about how a woman takes on a man's job
+mean her I guess it's her father isn't
+
+ align:start position:0%
+mean her I guess it's her father isn't
+ 
+
+ align:start position:0%
+mean her I guess it's her father isn't
+it her father is ill and she has to take
+
+ align:start position:0%
+it her father is ill and she has to take
+ 
+
+ align:start position:0%
+it her father is ill and she has to take
+over running the the train station and
+
+ align:start position:0%
+over running the the train station and
+ 
+
+ align:start position:0%
+over running the the train station and
+she run runs in and and so there's a
+
+ align:start position:0%
+she run runs in and and so there's a
+ 
+
+ align:start position:0%
+she run runs in and and so there's a
+certain sense in which one of the things
+
+ align:start position:0%
+certain sense in which one of the things
+ 
+
+ align:start position:0%
+certain sense in which one of the things
+that's dramatized socially is is a woman
+
+ align:start position:0%
+that's dramatized socially is is a woman
+ 
+
+ align:start position:0%
+that's dramatized socially is is a woman
+sort of moving into a kind of masculine
+
+ align:start position:0%
+sort of moving into a kind of masculine
+ 
+
+ align:start position:0%
+sort of moving into a kind of masculine
+realm taking on a role that's more
+
+ align:start position:0%
+realm taking on a role that's more
+ 
+
+ align:start position:0%
+realm taking on a role that's more
+aggressive than is appropriate for for
+
+ align:start position:0%
+aggressive than is appropriate for for
+ 
+
+ align:start position:0%
+aggressive than is appropriate for for
+the for the gender ideologies that are
+
+ align:start position:0%
+the for the gender ideologies that are
+ 
+
+ align:start position:0%
+the for the gender ideologies that are
+dominant at the end of the 19th century
+
+ align:start position:0%
+dominant at the end of the 19th century
+ 
+
+ align:start position:0%
+dominant at the end of the 19th century
+in the United States but the film is
+
+ align:start position:0%
+in the United States but the film is
+ 
+
+ align:start position:0%
+in the United States but the film is
+pretty clever about this like many such
+
+ align:start position:0%
+pretty clever about this like many such
+ 
+
+ align:start position:0%
+pretty clever about this like many such
+popular texts because although it does
+
+ align:start position:0%
+popular texts because although it does
+ 
+
+ align:start position:0%
+popular texts because although it does
+Grant this woman a certain kind of
+
+ align:start position:0%
+Grant this woman a certain kind of
+ 
+
+ align:start position:0%
+Grant this woman a certain kind of
+masculine Authority and competence it
+
+ align:start position:0%
+masculine Authority and competence it
+ 
+
+ align:start position:0%
+masculine Authority and competence it
+also has other things in the film that
+
+ align:start position:0%
+also has other things in the film that
+ 
+
+ align:start position:0%
+also has other things in the film that
+balance that that remind us that she is
+
+ align:start position:0%
+balance that that remind us that she is
+ 
+
+ align:start position:0%
+balance that that remind us that she is
+still nonetheless uh a weak vessel that
+
+ align:start position:0%
+still nonetheless uh a weak vessel that
+ 
+
+ align:start position:0%
+still nonetheless uh a weak vessel that
+she is still a damsel in distress like
+
+ align:start position:0%
+she is still a damsel in distress like
+ 
+
+ align:start position:0%
+she is still a damsel in distress like
+the typical Victorian construction of
+
+ align:start position:0%
+the typical Victorian construction of
+ 
+
+ align:start position:0%
+the typical Victorian construction of
+women uh in words what you can see is
+
+ align:start position:0%
+women uh in words what you can see is
+ 
+
+ align:start position:0%
+women uh in words what you can see is
+that the movie exhibits an anxiety about
+
+ align:start position:0%
+that the movie exhibits an anxiety about
+ 
+
+ align:start position:0%
+that the movie exhibits an anxiety about
+gender roles that's also an anxiety
+
+ align:start position:0%
+gender roles that's also an anxiety
+ 
+
+ align:start position:0%
+gender roles that's also an anxiety
+that's resident in the society itself uh
+
+ align:start position:0%
+that's resident in the society itself uh
+ 
+
+ align:start position:0%
+that's resident in the society itself uh
+and I I won't talk more about this now
+
+ align:start position:0%
+and I I won't talk more about this now
+ 
+
+ align:start position:0%
+and I I won't talk more about this now
+it's something we will develop this
+
+ align:start position:0%
+it's something we will develop this
+ 
+
+ align:start position:0%
+it's something we will develop this
+aspect of the movies the movies as a
+
+ align:start position:0%
+aspect of the movies the movies as a
+ 
+
+ align:start position:0%
+aspect of the movies the movies as a
+reflection of social anxieties and
+
+ align:start position:0%
+reflection of social anxieties and
+ 
+
+ align:start position:0%
+reflection of social anxieties and
+social and social problems as the as the
+
+ align:start position:0%
+social and social problems as the as the
+ 
+
+ align:start position:0%
+social and social problems as the as the
+course goes on but I do want to call
+
+ align:start position:0%
+course goes on but I do want to call
+ 
+
+ align:start position:0%
+course goes on but I do want to call
+your attention to certain technical
+
+ align:start position:0%
+your attention to certain technical
+ 
+
+ align:start position:0%
+your attention to certain technical
+things that you can watch for to at
+
+ align:start position:0%
+things that you can watch for to at
+ 
+
+ align:start position:0%
+things that you can watch for to at
+least one technical item in the film it
+
+ align:start position:0%
+least one technical item in the film it
+ 
+
+ align:start position:0%
+least one technical item in the film it
+it contains what might be called rhyming
+
+ align:start position:0%
+it contains what might be called rhyming
+ 
+
+ align:start position:0%
+it contains what might be called rhyming
+scenes in which at one point in the film
+
+ align:start position:0%
+scenes in which at one point in the film
+ 
+
+ align:start position:0%
+scenes in which at one point in the film
+you'll see a sequence of scenes in a
+
+ align:start position:0%
+you'll see a sequence of scenes in a
+ 
+
+ align:start position:0%
+you'll see a sequence of scenes in a
+particular shot and then later in the
+
+ align:start position:0%
+particular shot and then later in the
+ 
+
+ align:start position:0%
+particular shot and then later in the
+film almost exactly the same shot will
+
+ align:start position:0%
+film almost exactly the same shot will
+ 
+
+ align:start position:0%
+film almost exactly the same shot will
+reappear and the effect of this of
+
+ align:start position:0%
+reappear and the effect of this of
+ 
+
+ align:start position:0%
+reappear and the effect of this of
+course is to create a sense of coherence
+
+ align:start position:0%
+course is to create a sense of coherence
+ 
+
+ align:start position:0%
+course is to create a sense of coherence
+and a sense of familiarity in the
+
+ align:start position:0%
+and a sense of familiarity in the
+ 
+
+ align:start position:0%
+and a sense of familiarity in the
+audience it's actually a very subtle and
+
+ align:start position:0%
+audience it's actually a very subtle and
+ 
+
+ align:start position:0%
+audience it's actually a very subtle and
+careful strategy that Griffith himself
+
+ align:start position:0%
+careful strategy that Griffith himself
+ 
+
+ align:start position:0%
+careful strategy that Griffith himself
+devised uh it creates a kind of
+
+ align:start position:0%
+devised uh it creates a kind of
+ 
+
+ align:start position:0%
+devised uh it creates a kind of
+continuity and Clarity to the whole film
+
+ align:start position:0%
+continuity and Clarity to the whole film
+ 
+
+ align:start position:0%
+continuity and Clarity to the whole film
+watch for example how the doorway to the
+
+ align:start position:0%
+watch for example how the doorway to the
+ 
+
+ align:start position:0%
+watch for example how the doorway to the
+Londale station is photographed when you
+
+ align:start position:0%
+Londale station is photographed when you
+ 
+
+ align:start position:0%
+Londale station is photographed when you
+first see it how this image anchors the
+
+ align:start position:0%
+first see it how this image anchors the
+ 
+
+ align:start position:0%
+first see it how this image anchors the
+film's spatial relationships and how the
+
+ align:start position:0%
+film's spatial relationships and how the
+ 
+
+ align:start position:0%
+film's spatial relationships and how the
+film has a certain trajectory of
+
+ align:start position:0%
+film has a certain trajectory of
+ 
+
+ align:start position:0%
+film has a certain trajectory of
+movement that is repeated as the film
+
+ align:start position:0%
+movement that is repeated as the film
+ 
+
+ align:start position:0%
+movement that is repeated as the film
+goes on so that for example early in the
+
+ align:start position:0%
+goes on so that for example early in the
+ 
+
+ align:start position:0%
+goes on so that for example early in the
+film we see the heroin go from the
+
+ align:start position:0%
+film we see the heroin go from the
+ 
+
+ align:start position:0%
+film we see the heroin go from the
+exterior to the interior of the ticket
+
+ align:start position:0%
+exterior to the interior of the ticket
+ 
+
+ align:start position:0%
+exterior to the interior of the ticket
+office and then to the inner Office of
+
+ align:start position:0%
+office and then to the inner Office of
+ 
+
+ align:start position:0%
+office and then to the inner Office of
+the telegraph operator and we see her do
+
+ align:start position:0%
+the telegraph operator and we see her do
+ 
+
+ align:start position:0%
+the telegraph operator and we see her do
+this right and then this sets up a kind
+
+ align:start position:0%
+this right and then this sets up a kind
+ 
+
+ align:start position:0%
+this right and then this sets up a kind
+of basic location and basic action for
+
+ align:start position:0%
+of basic location and basic action for
+ 
+
+ align:start position:0%
+of basic location and basic action for
+the entire film it's as if what happens
+
+ align:start position:0%
+the entire film it's as if what happens
+ 
+
+ align:start position:0%
+the entire film it's as if what happens
+in that moment sets up creates a
+
+ align:start position:0%
+in that moment sets up creates a
+ 
+
+ align:start position:0%
+in that moment sets up creates a
+familiarity with the for the audience
+
+ align:start position:0%
+familiarity with the for the audience
+ 
+
+ align:start position:0%
+familiarity with the for the audience
+with the sort of geography of the movie
+
+ align:start position:0%
+with the sort of geography of the movie
+ 
+
+ align:start position:0%
+with the sort of geography of the movie
+because a lot of the action then will
+
+ align:start position:0%
+because a lot of the action then will
+ 
+
+ align:start position:0%
+because a lot of the action then will
+depend on our understanding of that
+
+ align:start position:0%
+depend on our understanding of that
+ 
+
+ align:start position:0%
+depend on our understanding of that
+geography and then there are at least
+
+ align:start position:0%
+geography and then there are at least
+ 
+
+ align:start position:0%
+geography and then there are at least
+four different times that Griffith
+
+ align:start position:0%
+four different times that Griffith
+ 
+
+ align:start position:0%
+four different times that Griffith
+repeats that basic three shot trajectory
+
+ align:start position:0%
+repeats that basic three shot trajectory
+ 
+
+ align:start position:0%
+repeats that basic three shot trajectory
+from the um exterior to the interior of
+
+ align:start position:0%
+from the um exterior to the interior of
+ 
+
+ align:start position:0%
+from the um exterior to the interior of
+the ticket office and then from the
+
+ align:start position:0%
+the ticket office and then from the
+ 
+
+ align:start position:0%
+the ticket office and then from the
+inner to the inner Office of the
+
+ align:start position:0%
+inner to the inner Office of the
+ 
+
+ align:start position:0%
+inner to the inner Office of the
+telegraph operator it happens four times
+
+ align:start position:0%
+telegraph operator it happens four times
+ 
+
+ align:start position:0%
+telegraph operator it happens four times
+in the film so it so the film has a kind
+
+ align:start position:0%
+in the film so it so the film has a kind
+ 
+
+ align:start position:0%
+in the film so it so the film has a kind
+of visual coherence by the time you come
+
+ align:start position:0%
+of visual coherence by the time you come
+ 
+
+ align:start position:0%
+of visual coherence by the time you come
+to it the third or fourth time it's as
+
+ align:start position:0%
+to it the third or fourth time it's as
+ 
+
+ align:start position:0%
+to it the third or fourth time it's as
+if you intimate with the physical
+
+ align:start position:0%
+if you intimate with the physical
+ 
+
+ align:start position:0%
+if you intimate with the physical
+geography of the movie This is actually
+
+ align:start position:0%
+geography of the movie This is actually
+ 
+
+ align:start position:0%
+geography of the movie This is actually
+a structural feature that it's easy to
+
+ align:start position:0%
+a structural feature that it's easy to
+ 
+
+ align:start position:0%
+a structural feature that it's easy to
+miss it but it's it it's actually very
+
+ align:start position:0%
+miss it but it's it it's actually very
+ 
+
+ align:start position:0%
+miss it but it's it it's actually very
+Artful and we can see it's a it's a mark
+
+ align:start position:0%
+Artful and we can see it's a it's a mark
+ 
+
+ align:start position:0%
+Artful and we can see it's a it's a mark
+of how far film has come even by 1911
+
+ align:start position:0%
+of how far film has come even by 1911
+ 
+
+ align:start position:0%
+of how far film has come even by 1911
+this level of attentiveness uh is is
+
+ align:start position:0%
+this level of attentiveness uh is is
+ 
+
+ align:start position:0%
+this level of attentiveness uh is is
+available to us in the film there's much
+
+ align:start position:0%
+available to us in the film there's much
+ 
+
+ align:start position:0%
+available to us in the film there's much
+more that could be said about the lone
+
+ align:start position:0%
+more that could be said about the lone
+ 
+
+ align:start position:0%
+more that could be said about the lone
+Dale operator but I will leave it to
+
+ align:start position:0%
+Dale operator but I will leave it to
+ 
+
+ align:start position:0%
+Dale operator but I will leave it to
+your intelligence and your attentiveness
+
+ align:start position:0%
+your intelligence and your attentiveness
+ 
+
+ align:start position:0%
+your intelligence and your attentiveness
+to try to pick out more thing and again
+
+ align:start position:0%
+to try to pick out more thing and again
+ 
+
+ align:start position:0%
+to try to pick out more thing and again
+we're only talking about a 17 minute a
+
+ align:start position:0%
+we're only talking about a 17 minute a
+ 
+
+ align:start position:0%
+we're only talking about a 17 minute a
+17-minute film well
+
+ align:start position:0%
+17-minute film well
+ 
+
+ align:start position:0%
+17-minute film well
+uh Buster Keaton's career could be said
+
+ align:start position:0%
+uh Buster Keaton's career could be said
+ 
+
+ align:start position:0%
+uh Buster Keaton's career could be said
+in some degree to enact in small the
+
+ align:start position:0%
+in some degree to enact in small the
+ 
+
+ align:start position:0%
+in some degree to enact in small the
+larger processes I've been describing he
+
+ align:start position:0%
+larger processes I've been describing he
+ 
+
+ align:start position:0%
+larger processes I've been describing he
+comes into film late and in fact if we
+
+ align:start position:0%
+comes into film late and in fact if we
+ 
+
+ align:start position:0%
+comes into film late and in fact if we
+were working perfectly chronologically
+
+ align:start position:0%
+were working perfectly chronologically
+ 
+
+ align:start position:0%
+were working perfectly chronologically
+in terms of when chaplain became a
+
+ align:start position:0%
+in terms of when chaplain became a
+ 
+
+ align:start position:0%
+in terms of when chaplain became a
+director he would precede Katon but I've
+
+ align:start position:0%
+director he would precede Katon but I've
+ 
+
+ align:start position:0%
+director he would precede Katon but I've
+organized the film according to the
+
+ align:start position:0%
+organized the film according to the
+ 
+
+ align:start position:0%
+organized the film according to the
+feature the dates of the feature films
+
+ align:start position:0%
+feature the dates of the feature films
+ 
+
+ align:start position:0%
+feature the dates of the feature films
+and the general is an ear much a decade
+
+ align:start position:0%
+and the general is an ear much a decade
+ 
+
+ align:start position:0%
+and the general is an ear much a decade
+earlier than modern times which is the
+
+ align:start position:0%
+earlier than modern times which is the
+ 
+
+ align:start position:0%
+earlier than modern times which is the
+last quote silent film it's not really a
+
+ align:start position:0%
+last quote silent film it's not really a
+ 
+
+ align:start position:0%
+last quote silent film it's not really a
+silent film but it's the last silent
+
+ align:start position:0%
+silent film but it's the last silent
+ 
+
+ align:start position:0%
+silent film but it's the last silent
+film in a deep sense that was ever made
+
+ align:start position:0%
+film in a deep sense that was ever made
+ 
+
+ align:start position:0%
+film in a deep sense that was ever made
+it was made in the sound era in 1936 and
+
+ align:start position:0%
+it was made in the sound era in 1936 and
+ 
+
+ align:start position:0%
+it was made in the sound era in 1936 and
+when we next week we'll talk more about
+
+ align:start position:0%
+when we next week we'll talk more about
+ 
+
+ align:start position:0%
+when we next week we'll talk more about
+the implications of that and why that
+
+ align:start position:0%
+the implications of that and why that
+ 
+
+ align:start position:0%
+the implications of that and why that
+was a very daring thing for chaplain to
+
+ align:start position:0%
+was a very daring thing for chaplain to
+ 
+
+ align:start position:0%
+was a very daring thing for chaplain to
+to do something like almost a decade
+
+ align:start position:0%
+to do something like almost a decade
+ 
+
+ align:start position:0%
+to do something like almost a decade
+after the Advent of sound he made a
+
+ align:start position:0%
+after the Advent of sound he made a
+ 
+
+ align:start position:0%
+after the Advent of sound he made a
+movie that essentially had no dialogue
+
+ align:start position:0%
+movie that essentially had no dialogue
+ 
+
+ align:start position:0%
+movie that essentially had no dialogue
+in it and that recalled the silent film
+
+ align:start position:0%
+in it and that recalled the silent film
+ 
+
+ align:start position:0%
+in it and that recalled the silent film
+and everyone predicted that the film
+
+ align:start position:0%
+and everyone predicted that the film
+ 
+
+ align:start position:0%
+and everyone predicted that the film
+would be a flop that chaplain was M but
+
+ align:start position:0%
+would be a flop that chaplain was M but
+ 
+
+ align:start position:0%
+would be a flop that chaplain was M but
+of course they underestimated the
+
+ align:start position:0%
+of course they underestimated the
+ 
+
+ align:start position:0%
+of course they underestimated the
+affection and uh deep intimate Regard in
+
+ align:start position:0%
+affection and uh deep intimate Regard in
+ 
+
+ align:start position:0%
+affection and uh deep intimate Regard in
+which the in which the population of the
+
+ align:start position:0%
+which the in which the population of the
+ 
+
+ align:start position:0%
+which the in which the population of the
+world held the Charlie Chaplain
+
+ align:start position:0%
+world held the Charlie Chaplain
+ 
+
+ align:start position:0%
+world held the Charlie Chaplain
+character who by now was an icon more
+
+ align:start position:0%
+character who by now was an icon more
+ 
+
+ align:start position:0%
+character who by now was an icon more
+widely known in the world than any than
+
+ align:start position:0%
+widely known in the world than any than
+ 
+
+ align:start position:0%
+widely known in the world than any than
+any person in previous history I think
+
+ align:start position:0%
+any person in previous history I think
+ 
+
+ align:start position:0%
+any person in previous history I think
+even greater than more than Alexander
+
+ align:start position:0%
+even greater than more than Alexander
+ 
+
+ align:start position:0%
+even greater than more than Alexander
+the Great or any prior figure Charlie
+
+ align:start position:0%
+the Great or any prior figure Charlie
+ 
+
+ align:start position:0%
+the Great or any prior figure Charlie
+Chaplain was the first Global movie star
+
+ align:start position:0%
+Chaplain was the first Global movie star
+ 
+
+ align:start position:0%
+Chaplain was the first Global movie star
+was known virtually all over the world
+
+ align:start position:0%
+was known virtually all over the world
+ 
+
+ align:start position:0%
+was known virtually all over the world
+by the time he came to make modern times
+
+ align:start position:0%
+by the time he came to make modern times
+ 
+
+ align:start position:0%
+by the time he came to make modern times
+uh um um so Keaton came a little later
+
+ align:start position:0%
+uh um um so Keaton came a little later
+ 
+
+ align:start position:0%
+uh um um so Keaton came a little later
+comes into movie making uh after uh a
+
+ align:start position:0%
+comes into movie making uh after uh a
+ 
+
+ align:start position:0%
+comes into movie making uh after uh a
+little a few years after uh uh chaplain
+
+ align:start position:0%
+little a few years after uh uh chaplain
+ 
+
+ align:start position:0%
+little a few years after uh uh chaplain
+but his but his career has a similar
+
+ align:start position:0%
+but his but his career has a similar
+ 
+
+ align:start position:0%
+but his but his career has a similar
+trajectory he began his career in
+
+ align:start position:0%
+trajectory he began his career in
+ 
+
+ align:start position:0%
+trajectory he began his career in
+legitimate theater in Vaudeville and in
+
+ align:start position:0%
+legitimate theater in Vaudeville and in
+ 
+
+ align:start position:0%
+legitimate theater in Vaudeville and in
+and in and in on the performance circuit
+
+ align:start position:0%
+and in and in on the performance circuit
+ 
+
+ align:start position:0%
+and in and in on the performance circuit
+uh and and uh was an acrobat from a very
+
+ align:start position:0%
+uh and and uh was an acrobat from a very
+ 
+
+ align:start position:0%
+uh and and uh was an acrobat from a very
+young age from the age of two or three
+
+ align:start position:0%
+young age from the age of two or three
+ 
+
+ align:start position:0%
+young age from the age of two or three
+was in his parents stage act he was
+
+ align:start position:0%
+was in his parents stage act he was
+ 
+
+ align:start position:0%
+was in his parents stage act he was
+actually uh uh uh and in fact he learned
+
+ align:start position:0%
+actually uh uh uh and in fact he learned
+ 
+
+ align:start position:0%
+actually uh uh uh and in fact he learned
+a lot of his acrobatic Feats on his
+
+ align:start position:0%
+a lot of his acrobatic Feats on his
+ 
+
+ align:start position:0%
+a lot of his acrobatic Feats on his
+parents stage act one very famous uh
+
+ align:start position:0%
+parents stage act one very famous uh
+ 
+
+ align:start position:0%
+parents stage act one very famous uh
+passage in his his father used to take
+
+ align:start position:0%
+passage in his his father used to take
+ 
+
+ align:start position:0%
+passage in his his father used to take
+him he was just a young kid three or
+
+ align:start position:0%
+him he was just a young kid three or
+ 
+
+ align:start position:0%
+him he was just a young kid three or
+four years old five years old would take
+
+ align:start position:0%
+four years old five years old would take
+ 
+
+ align:start position:0%
+four years old five years old would take
+him by the legs and swing him back and
+
+ align:start position:0%
+him by the legs and swing him back and
+ 
+
+ align:start position:0%
+him by the legs and swing him back and
+forth like this he had very long hair
+
+ align:start position:0%
+forth like this he had very long hair
+ 
+
+ align:start position:0%
+forth like this he had very long hair
+and he would sweep the floor with his
+
+ align:start position:0%
+and he would sweep the floor with his
+ 
+
+ align:start position:0%
+and he would sweep the floor with his
+hair and then swing him two or three
+
+ align:start position:0%
+hair and then swing him two or three
+ 
+
+ align:start position:0%
+hair and then swing him two or three
+times this would happen live he would
+
+ align:start position:0%
+times this would happen live he would
+ 
+
+ align:start position:0%
+times this would happen live he would
+swing him like this and let him go and
+
+ align:start position:0%
+swing him like this and let him go and
+ 
+
+ align:start position:0%
+swing him like this and let him go and
+the kid 5 years old would fly against
+
+ align:start position:0%
+the kid 5 years old would fly against
+ 
+
+ align:start position:0%
+the kid 5 years old would fly against
+the wall and fall down it would look
+
+ align:start position:0%
+the wall and fall down it would look
+ 
+
+ align:start position:0%
+the wall and fall down it would look
+terrible and Keaton later in his life
+
+ align:start position:0%
+terrible and Keaton later in his life
+ 
+
+ align:start position:0%
+terrible and Keaton later in his life
+Katon talked about this there were
+
+ align:start position:0%
+Katon talked about this there were
+ 
+
+ align:start position:0%
+Katon talked about this there were
+actually some cities in which the the uh
+
+ align:start position:0%
+actually some cities in which the the uh
+ 
+
+ align:start position:0%
+actually some cities in which the the uh
+uh societies for the for for the
+
+ align:start position:0%
+uh societies for the for for the
+ 
+
+ align:start position:0%
+uh societies for the for for the
+Prevention of Cruelty to Children came
+
+ align:start position:0%
+Prevention of Cruelty to Children came
+ 
+
+ align:start position:0%
+Prevention of Cruelty to Children came
+in and shut down the shut down the ACT
+
+ align:start position:0%
+in and shut down the shut down the ACT
+ 
+
+ align:start position:0%
+in and shut down the shut down the ACT
+wouldn't allow the ACT to go on not
+
+ align:start position:0%
+wouldn't allow the ACT to go on not
+ 
+
+ align:start position:0%
+wouldn't allow the ACT to go on not
+stupid because his father was a drunkard
+
+ align:start position:0%
+stupid because his father was a drunkard
+ 
+
+ align:start position:0%
+stupid because his father was a drunkard
+and sometimes performed drunk and Keaton
+
+ align:start position:0%
+and sometimes performed drunk and Keaton
+ 
+
+ align:start position:0%
+and sometimes performed drunk and Keaton
+was sometimes injured he was also
+
+ align:start position:0%
+was sometimes injured he was also
+ 
+
+ align:start position:0%
+was sometimes injured he was also
+injured when he made his own movies for
+
+ align:start position:0%
+injured when he made his own movies for
+ 
+
+ align:start position:0%
+injured when he made his own movies for
+because he was such daring acrobat uh
+
+ align:start position:0%
+because he was such daring acrobat uh
+ 
+
+ align:start position:0%
+because he was such daring acrobat uh
+and uh Keaton recounts that when he
+
+ align:start position:0%
+and uh Keaton recounts that when he
+ 
+
+ align:start position:0%
+and uh Keaton recounts that when he
+first began to perform in this he would
+
+ align:start position:0%
+first began to perform in this he would
+ 
+
+ align:start position:0%
+first began to perform in this he would
+make faces you know faces that indicated
+
+ align:start position:0%
+make faces you know faces that indicated
+ 
+
+ align:start position:0%
+make faces you know faces that indicated
+pain or happiness or relief when his
+
+ align:start position:0%
+pain or happiness or relief when his
+ 
+
+ align:start position:0%
+pain or happiness or relief when his
+father was manipulating him this way but
+
+ align:start position:0%
+father was manipulating him this way but
+ 
+
+ align:start position:0%
+father was manipulating him this way but
+he found that the audience responded
+
+ align:start position:0%
+he found that the audience responded
+ 
+
+ align:start position:0%
+he found that the audience responded
+Much More comically Much More
+
+ align:start position:0%
+Much More comically Much More
+ 
+
+ align:start position:0%
+Much More comically Much More
+immediately if he just kept his face
+
+ align:start position:0%
+immediately if he just kept his face
+ 
+
+ align:start position:0%
+immediately if he just kept his face
+expressionless and that's where there
+
+ align:start position:0%
+expressionless and that's where there
+ 
+
+ align:start position:0%
+expressionless and that's where there
+developed the probably mistaken uh uh
+
+ align:start position:0%
+developed the probably mistaken uh uh
+ 
+
+ align:start position:0%
+developed the probably mistaken uh uh
+label for Katon of the great Stone face
+
+ align:start position:0%
+label for Katon of the great Stone face
+ 
+
+ align:start position:0%
+label for Katon of the great Stone face
+and in his films very often you'll see
+
+ align:start position:0%
+and in his films very often you'll see
+ 
+
+ align:start position:0%
+and in his films very often you'll see
+this young man facing Monumental
+
+ align:start position:0%
+this young man facing Monumental
+ 
+
+ align:start position:0%
+this young man facing Monumental
+catastrophe his face will look out at
+
+ align:start position:0%
+catastrophe his face will look out at
+ 
+
+ align:start position:0%
+catastrophe his face will look out at
+things without Ever Changing expression
+
+ align:start position:0%
+things without Ever Changing expression
+ 
+
+ align:start position:0%
+things without Ever Changing expression
+and there is something kind of kind of
+
+ align:start position:0%
+and there is something kind of kind of
+ 
+
+ align:start position:0%
+and there is something kind of kind of
+comical about that you'll see some
+
+ align:start position:0%
+comical about that you'll see some
+ 
+
+ align:start position:0%
+comical about that you'll see some
+examples of this in the in the general
+
+ align:start position:0%
+examples of this in the in the general
+ 
+
+ align:start position:0%
+examples of this in the in the general
+well you'll you'll see in the two short
+
+ align:start position:0%
+well you'll you'll see in the two short
+ 
+
+ align:start position:0%
+well you'll you'll see in the two short
+films that Keaton began to make that he
+
+ align:start position:0%
+films that Keaton began to make that he
+ 
+
+ align:start position:0%
+films that Keaton began to make that he
+enters film at already a relatively
+
+ align:start position:0%
+enters film at already a relatively
+ 
+
+ align:start position:0%
+enters film at already a relatively
+sophisticated time and and the shorts
+
+ align:start position:0%
+sophisticated time and and the shorts
+ 
+
+ align:start position:0%
+sophisticated time and and the shorts
+I'm asking you to look at are very
+
+ align:start position:0%
+I'm asking you to look at are very
+ 
+
+ align:start position:0%
+I'm asking you to look at are very
+interesting uh uh remarkable films in in
+
+ align:start position:0%
+interesting uh uh remarkable films in in
+ 
+
+ align:start position:0%
+interesting uh uh remarkable films in in
+their own way and one of the things they
+
+ align:start position:0%
+their own way and one of the things they
+ 
+
+ align:start position:0%
+their own way and one of the things they
+teach us and one of the reasons I want
+
+ align:start position:0%
+teach us and one of the reasons I want
+ 
+
+ align:start position:0%
+teach us and one of the reasons I want
+you to look closely at at at at uh
+
+ align:start position:0%
+you to look closely at at at at uh
+ 
+
+ align:start position:0%
+you to look closely at at at at uh
+Keaton is they is they show us yet again
+
+ align:start position:0%
+Keaton is they is they show us yet again
+ 
+
+ align:start position:0%
+Keaton is they is they show us yet again
+another aspect of what I mean when I
+
+ align:start position:0%
+another aspect of what I mean when I
+ 
+
+ align:start position:0%
+another aspect of what I mean when I
+talk about the Fred art principle this
+
+ align:start position:0%
+talk about the Fred art principle this
+ 
+
+ align:start position:0%
+talk about the Fred art principle this
+development of evolution and and and and
+
+ align:start position:0%
+development of evolution and and and and
+ 
+
+ align:start position:0%
+development of evolution and and and and
+and increasing and increasing complexity
+
+ align:start position:0%
+and increasing and increasing complexity
+ 
+
+ align:start position:0%
+and increasing and increasing complexity
+because if you look at cops or if you
+
+ align:start position:0%
+because if you look at cops or if you
+ 
+
+ align:start position:0%
+because if you look at cops or if you
+look at one week what you will see Katon
+
+ align:start position:0%
+look at one week what you will see Katon
+ 
+
+ align:start position:0%
+look at one week what you will see Katon
+doing in those films is learning how to
+
+ align:start position:0%
+doing in those films is learning how to
+ 
+
+ align:start position:0%
+doing in those films is learning how to
+link jokes together in some sort of a
+
+ align:start position:0%
+link jokes together in some sort of a
+ 
+
+ align:start position:0%
+link jokes together in some sort of a
+coherent way
+
+ align:start position:0%
+coherent way
+ 
+
+ align:start position:0%
+coherent way
+but the films and and there are
+
+ align:start position:0%
+but the films and and there are
+ 
+
+ align:start position:0%
+but the films and and there are
+wonderful coherent sequences in these
+
+ align:start position:0%
+wonderful coherent sequences in these
+ 
+
+ align:start position:0%
+wonderful coherent sequences in these
+films but still one doesn't feel that
+
+ align:start position:0%
+films but still one doesn't feel that
+ 
+
+ align:start position:0%
+films but still one doesn't feel that
+there's a real character in them that
+
+ align:start position:0%
+there's a real character in them that
+ 
+
+ align:start position:0%
+there's a real character in them that
+there's a sustained coherent uh
+
+ align:start position:0%
+there's a sustained coherent uh
+ 
+
+ align:start position:0%
+there's a sustained coherent uh
+fictional Universe being dramatized
+
+ align:start position:0%
+fictional Universe being dramatized
+ 
+
+ align:start position:0%
+fictional Universe being dramatized
+maybe in cops one does feel this there's
+
+ align:start position:0%
+maybe in cops one does feel this there's
+ 
+
+ align:start position:0%
+maybe in cops one does feel this there's
+much more sort of textural coherence in
+
+ align:start position:0%
+much more sort of textural coherence in
+ 
+
+ align:start position:0%
+much more sort of textural coherence in
+cops but what we can see Katon doing is
+
+ align:start position:0%
+cops but what we can see Katon doing is
+ 
+
+ align:start position:0%
+cops but what we can see Katon doing is
+beginning to move from the idea of a
+
+ align:start position:0%
+beginning to move from the idea of a
+ 
+
+ align:start position:0%
+beginning to move from the idea of a
+single joke to a sequence of jokes and
+
+ align:start position:0%
+single joke to a sequence of jokes and
+ 
+
+ align:start position:0%
+single joke to a sequence of jokes and
+then by the time we get to the general
+
+ align:start position:0%
+then by the time we get to the general
+ 
+
+ align:start position:0%
+then by the time we get to the general
+moving from a sequence of from a single
+
+ align:start position:0%
+moving from a sequence of from a single
+ 
+
+ align:start position:0%
+moving from a sequence of from a single
+joke to a sequence of jokes to a
+
+ align:start position:0%
+joke to a sequence of jokes to a
+ 
+
+ align:start position:0%
+joke to a sequence of jokes to a
+sustained narrative which incorporates
+
+ align:start position:0%
+sustained narrative which incorporates
+ 
+
+ align:start position:0%
+sustained narrative which incorporates
+within it various kinds of comical jokes
+
+ align:start position:0%
+within it various kinds of comical jokes
+ 
+
+ align:start position:0%
+within it various kinds of comical jokes
+and also sequence jokes because Keaton's
+
+ align:start position:0%
+and also sequence jokes because Keaton's
+ 
+
+ align:start position:0%
+and also sequence jokes because Keaton's
+best jokes are not single jokes at all
+
+ align:start position:0%
+best jokes are not single jokes at all
+ 
+
+ align:start position:0%
+best jokes are not single jokes at all
+not on liners but the the joke will be
+
+ align:start position:0%
+not on liners but the the joke will be
+ 
+
+ align:start position:0%
+not on liners but the the joke will be
+told again and again or what or really
+
+ align:start position:0%
+told again and again or what or really
+ 
+
+ align:start position:0%
+told again and again or what or really
+what will happen is he will do something
+
+ align:start position:0%
+what will happen is he will do something
+ 
+
+ align:start position:0%
+what will happen is he will do something
+he'll think how could and then he The
+
+ align:start position:0%
+he'll think how could and then he The
+ 
+
+ align:start position:0%
+he'll think how could and then he The
+Next Step will Top what he's done before
+
+ align:start position:0%
+Next Step will Top what he's done before
+ 
+
+ align:start position:0%
+Next Step will Top what he's done before
+and the next step will Top you think
+
+ align:start position:0%
+and the next step will Top you think
+ 
+
+ align:start position:0%
+and the next step will Top you think
+that he got to a point where it would be
+
+ align:start position:0%
+that he got to a point where it would be
+ 
+
+ align:start position:0%
+that he got to a point where it would be
+impossible to add another comic
+
+ align:start position:0%
+impossible to add another comic
+ 
+
+ align:start position:0%
+impossible to add another comic
+complication to what he's done when he
+
+ align:start position:0%
+complication to what he's done when he
+ 
+
+ align:start position:0%
+complication to what he's done when he
+of course does it uh and this becomes
+
+ align:start position:0%
+of course does it uh and this becomes
+ 
+
+ align:start position:0%
+of course does it uh and this becomes
+one of the deep principles of chaplain
+
+ align:start position:0%
+one of the deep principles of chaplain
+ 
+
+ align:start position:0%
+one of the deep principles of chaplain
+of of Keaton's comedy there are numerous
+
+ align:start position:0%
+of of Keaton's comedy there are numerous
+ 
+
+ align:start position:0%
+of of Keaton's comedy there are numerous
+examples of it in both the two shorts
+
+ align:start position:0%
+examples of it in both the two shorts
+ 
+
+ align:start position:0%
+examples of it in both the two shorts
+and in this in the longer film that I
+
+ align:start position:0%
+and in this in the longer film that I
+ 
+
+ align:start position:0%
+and in this in the longer film that I
+that uh the the general but let me
+
+ align:start position:0%
+that uh the the general but let me
+ 
+
+ align:start position:0%
+that uh the the general but let me
+mention an example from the general very
+
+ align:start position:0%
+mention an example from the general very
+ 
+
+ align:start position:0%
+mention an example from the general very
+early in the general there's a sequence
+
+ align:start position:0%
+early in the general there's a sequence
+ 
+
+ align:start position:0%
+early in the general there's a sequence
+it's probably the quintessential Katon
+
+ align:start position:0%
+it's probably the quintessential Katon
+ 
+
+ align:start position:0%
+it's probably the quintessential Katon
+sequence and I won't go into such detail
+
+ align:start position:0%
+sequence and I won't go into such detail
+ 
+
+ align:start position:0%
+sequence and I won't go into such detail
+as to spoil the film for you uh but let
+
+ align:start position:0%
+as to spoil the film for you uh but let
+ 
+
+ align:start position:0%
+as to spoil the film for you uh but let
+me just say it involves a Canon and it
+
+ align:start position:0%
+me just say it involves a Canon and it
+ 
+
+ align:start position:0%
+me just say it involves a Canon and it
+involves Katon uh who's chasing after
+
+ align:start position:0%
+involves Katon uh who's chasing after
+ 
+
+ align:start position:0%
+involves Katon uh who's chasing after
+Katon plays a uh the engineer of a of of
+
+ align:start position:0%
+Katon plays a uh the engineer of a of of
+ 
+
+ align:start position:0%
+Katon plays a uh the engineer of a of of
+a locomotive a locomotive engineer the
+
+ align:start position:0%
+a locomotive a locomotive engineer the
+ 
+
+ align:start position:0%
+a locomotive a locomotive engineer the
+general of the title is not a a a
+
+ align:start position:0%
+general of the title is not a a a
+ 
+
+ align:start position:0%
+general of the title is not a a a
+military General it's a locomotive the
+
+ align:start position:0%
+military General it's a locomotive the
+ 
+
+ align:start position:0%
+military General it's a locomotive the
+locomotive is called the general and
+
+ align:start position:0%
+locomotive is called the general and
+ 
+
+ align:start position:0%
+locomotive is called the general and
+this and the film recounts a
+
+ align:start position:0%
+this and the film recounts a
+ 
+
+ align:start position:0%
+this and the film recounts a
+historically true story of a of a time
+
+ align:start position:0%
+historically true story of a of a time
+ 
+
+ align:start position:0%
+historically true story of a of a time
+when the Union Army um he me uh that uh
+
+ align:start position:0%
+when the Union Army um he me uh that uh
+ 
+
+ align:start position:0%
+when the Union Army um he me uh that uh
+the Confederate Army uh the Union Army
+
+ align:start position:0%
+the Confederate Army uh the Union Army
+ 
+
+ align:start position:0%
+the Confederate Army uh the Union Army
+came into Confederate territory and
+
+ align:start position:0%
+came into Confederate territory and
+ 
+
+ align:start position:0%
+came into Confederate territory and
+stole a locomotive belonging to the
+
+ align:start position:0%
+stole a locomotive belonging to the
+ 
+
+ align:start position:0%
+stole a locomotive belonging to the
+Confederacy and this and and he was and
+
+ align:start position:0%
+Confederacy and this and and he was and
+ 
+
+ align:start position:0%
+Confederacy and this and and he was and
+Keaton in a comic vein retells retells
+
+ align:start position:0%
+Keaton in a comic vein retells retells
+ 
+
+ align:start position:0%
+Keaton in a comic vein retells retells
+this this story when you watch this
+
+ align:start position:0%
+this this story when you watch this
+ 
+
+ align:start position:0%
+this this story when you watch this
+Canon sequence you'll see exactly what I
+
+ align:start position:0%
+Canon sequence you'll see exactly what I
+ 
+
+ align:start position:0%
+Canon sequence you'll see exactly what I
+mean you'll and this sequence is at the
+
+ align:start position:0%
+mean you'll and this sequence is at the
+ 
+
+ align:start position:0%
+mean you'll and this sequence is at the
+heart of James AG's essay on the silent
+
+ align:start position:0%
+heart of James AG's essay on the silent
+ 
+
+ align:start position:0%
+heart of James AG's essay on the silent
+film comedy and when you read that essay
+
+ align:start position:0%
+film comedy and when you read that essay
+ 
+
+ align:start position:0%
+film comedy and when you read that essay
+you'll see even more clearly what I mean
+
+ align:start position:0%
+you'll see even more clearly what I mean
+ 
+
+ align:start position:0%
+you'll see even more clearly what I mean
+by a trajectory joke or a sequence joke
+
+ align:start position:0%
+by a trajectory joke or a sequence joke
+ 
+
+ align:start position:0%
+by a trajectory joke or a sequence joke
+which builds and builds and builds and
+
+ align:start position:0%
+which builds and builds and builds and
+ 
+
+ align:start position:0%
+which builds and builds and builds and
+keeps topping itself well this Canon
+
+ align:start position:0%
+keeps topping itself well this Canon
+ 
+
+ align:start position:0%
+keeps topping itself well this Canon
+sequence is a perfect example of that
+
+ align:start position:0%
+sequence is a perfect example of that
+ 
+
+ align:start position:0%
+sequence is a perfect example of that
+and it's a perfect example of it not
+
+ align:start position:0%
+and it's a perfect example of it not
+ 
+
+ align:start position:0%
+and it's a perfect example of it not
+only because we see the joke getting
+
+ align:start position:0%
+only because we see the joke getting
+ 
+
+ align:start position:0%
+only because we see the joke getting
+more complicated as it goes on but as
+
+ align:start position:0%
+more complicated as it goes on but as
+ 
+
+ align:start position:0%
+more complicated as it goes on but as
+the joke becomes more complicated
+
+ align:start position:0%
+the joke becomes more complicated
+ 
+
+ align:start position:0%
+the joke becomes more complicated
+something else happens
+
+ align:start position:0%
+something else happens
+ 
+
+ align:start position:0%
+something else happens
+the joke becomes more than a joke it
+
+ align:start position:0%
+the joke becomes more than a joke it
+ 
+
+ align:start position:0%
+the joke becomes more than a joke it
+becomes a kind of comment on experience
+
+ align:start position:0%
+becomes a kind of comment on experience
+ 
+
+ align:start position:0%
+becomes a kind of comment on experience
+it becomes a kind of comment on on on on
+
+ align:start position:0%
+it becomes a kind of comment on on on on
+ 
+
+ align:start position:0%
+it becomes a kind of comment on on on on
+on what life is like that is to say we
+
+ align:start position:0%
+on what life is like that is to say we
+ 
+
+ align:start position:0%
+on what life is like that is to say we
+move from something that simply makes us
+
+ align:start position:0%
+move from something that simply makes us
+ 
+
+ align:start position:0%
+move from something that simply makes us
+smile to something that makes us think
+
+ align:start position:0%
+smile to something that makes us think
+ 
+
+ align:start position:0%
+smile to something that makes us think
+about the world that comments on the
+
+ align:start position:0%
+about the world that comments on the
+ 
+
+ align:start position:0%
+about the world that comments on the
+world that imagines the world in a
+
+ align:start position:0%
+world that imagines the world in a
+ 
+
+ align:start position:0%
+world that imagines the world in a
+coherent way I'll try to be more
+
+ align:start position:0%
+coherent way I'll try to be more
+ 
+
+ align:start position:0%
+coherent way I'll try to be more
+explicit about this in a in a in in a
+
+ align:start position:0%
+explicit about this in a in a in in a
+ 
+
+ align:start position:0%
+explicit about this in a in a in in a
+moment so in Keaton's career we see him
+
+ align:start position:0%
+moment so in Keaton's career we see him
+ 
+
+ align:start position:0%
+moment so in Keaton's career we see him
+doing astonishing things as an acrobat
+
+ align:start position:0%
+doing astonishing things as an acrobat
+ 
+
+ align:start position:0%
+doing astonishing things as an acrobat
+and we would admire him just for
+
+ align:start position:0%
+and we would admire him just for
+ 
+
+ align:start position:0%
+and we would admire him just for
+acrobatic performances in these films
+
+ align:start position:0%
+acrobatic performances in these films
+ 
+
+ align:start position:0%
+acrobatic performances in these films
+watching this film in the in the general
+
+ align:start position:0%
+watching this film in the in the general
+ 
+
+ align:start position:0%
+watching this film in the in the general
+for example the way in which when he's
+
+ align:start position:0%
+for example the way in which when he's
+ 
+
+ align:start position:0%
+for example the way in which when he's
+piloting his locomotive chasing the
+
+ align:start position:0%
+piloting his locomotive chasing the
+ 
+
+ align:start position:0%
+piloting his locomotive chasing the
+people who have stolen his original
+
+ align:start position:0%
+people who have stolen his original
+ 
+
+ align:start position:0%
+people who have stolen his original
+locomotive how he's the only one on the
+
+ align:start position:0%
+locomotive how he's the only one on the
+ 
+
+ align:start position:0%
+locomotive how he's the only one on the
+train and he crawls all over the train
+
+ align:start position:0%
+train and he crawls all over the train
+ 
+
+ align:start position:0%
+train and he crawls all over the train
+he almost every while the train is
+
+ align:start position:0%
+he almost every while the train is
+ 
+
+ align:start position:0%
+he almost every while the train is
+running he'll crawl up to the front of
+
+ align:start position:0%
+running he'll crawl up to the front of
+ 
+
+ align:start position:0%
+running he'll crawl up to the front of
+it he'll run to the back of it to put
+
+ align:start position:0%
+it he'll run to the back of it to put
+ 
+
+ align:start position:0%
+it he'll run to the back of it to put
+more fuel in you what you can what you
+
+ align:start position:0%
+more fuel in you what you can what you
+ 
+
+ align:start position:0%
+more fuel in you what you can what you
+can see is and and also you can see this
+
+ align:start position:0%
+can see is and and also you can see this
+ 
+
+ align:start position:0%
+can see is and and also you can see this
+stuff happening in really happening it's
+
+ align:start position:0%
+stuff happening in really happening it's
+ 
+
+ align:start position:0%
+stuff happening in really happening it's
+not faked in any way because there's a
+
+ align:start position:0%
+not faked in any way because there's a
+ 
+
+ align:start position:0%
+not faked in any way because there's a
+there is a a camera following the train
+
+ align:start position:0%
+there is a a camera following the train
+ 
+
+ align:start position:0%
+there is a a camera following the train
+as it's moving you can see it's really
+
+ align:start position:0%
+as it's moving you can see it's really
+ 
+
+ align:start position:0%
+as it's moving you can see it's really
+moving because you can you can see it
+
+ align:start position:0%
+moving because you can you can see it
+ 
+
+ align:start position:0%
+moving because you can you can see it
+you can see it moving on the track and
+
+ align:start position:0%
+you can see it moving on the track and
+ 
+
+ align:start position:0%
+you can see it moving on the track and
+you can see the World Behind it and you
+
+ align:start position:0%
+you can see the World Behind it and you
+ 
+
+ align:start position:0%
+you can see the World Behind it and you
+can you can tell that Katon is not
+
+ align:start position:0%
+can you can tell that Katon is not
+ 
+
+ align:start position:0%
+can you can tell that Katon is not
+faking these effects well this Canon
+
+ align:start position:0%
+faking these effects well this Canon
+ 
+
+ align:start position:0%
+faking these effects well this Canon
+sequence is a is a is a sublimely rich
+
+ align:start position:0%
+sequence is a is a is a sublimely rich
+ 
+
+ align:start position:0%
+sequence is a is a is a sublimely rich
+example of this complex process I've
+
+ align:start position:0%
+example of this complex process I've
+ 
+
+ align:start position:0%
+example of this complex process I've
+been describing and it it has to do in
+
+ align:start position:0%
+been describing and it it has to do in
+ 
+
+ align:start position:0%
+been describing and it it has to do in
+part with what I call the multiplicity
+
+ align:start position:0%
+part with what I call the multiplicity
+ 
+
+ align:start position:0%
+part with what I call the multiplicity
+principle which I will Define in a
+
+ align:start position:0%
+principle which I will Define in a
+ 
+
+ align:start position:0%
+principle which I will Define in a
+moment so we see Katon as an actor as an
+
+ align:start position:0%
+moment so we see Katon as an actor as an
+ 
+
+ align:start position:0%
+moment so we see Katon as an actor as an
+acrobat as an acrobat actor as an
+
+ align:start position:0%
+acrobat as an acrobat actor as an
+ 
+
+ align:start position:0%
+acrobat as an acrobat actor as an
+incredibly in as a man much more than CH
+
+ align:start position:0%
+incredibly in as a man much more than CH
+ 
+
+ align:start position:0%
+incredibly in as a man much more than CH
+chaplain interested in the technology of
+
+ align:start position:0%
+chaplain interested in the technology of
+ 
+
+ align:start position:0%
+chaplain interested in the technology of
+Motion Pictures and of Cinema and you'll
+
+ align:start position:0%
+Motion Pictures and of Cinema and you'll
+ 
+
+ align:start position:0%
+Motion Pictures and of Cinema and you'll
+see a couple of examples in the films
+
+ align:start position:0%
+see a couple of examples in the films
+ 
+
+ align:start position:0%
+see a couple of examples in the films
+you're going to look at tonight in which
+
+ align:start position:0%
+you're going to look at tonight in which
+ 
+
+ align:start position:0%
+you're going to look at tonight in which
+we see Katon exploring uh in a somewhat
+
+ align:start position:0%
+we see Katon exploring uh in a somewhat
+ 
+
+ align:start position:0%
+we see Katon exploring uh in a somewhat
+systematic way the nature of the
+
+ align:start position:0%
+systematic way the nature of the
+ 
+
+ align:start position:0%
+systematic way the nature of the
+illusion of the Motion Pictures there's
+
+ align:start position:0%
+illusion of the Motion Pictures there's
+ 
+
+ align:start position:0%
+illusion of the Motion Pictures there's
+one remarkable moment comical moment in
+
+ align:start position:0%
+one remarkable moment comical moment in
+ 
+
+ align:start position:0%
+one remarkable moment comical moment in
+one week in which uh the heroin gets
+
+ align:start position:0%
+one week in which uh the heroin gets
+ 
+
+ align:start position:0%
+one week in which uh the heroin gets
+into a bathtub and it looks like you and
+
+ align:start position:0%
+into a bathtub and it looks like you and
+ 
+
+ align:start position:0%
+into a bathtub and it looks like you and
+she's sitting in the bathtub she's
+
+ align:start position:0%
+she's sitting in the bathtub she's
+ 
+
+ align:start position:0%
+she's sitting in the bathtub she's
+starting to get up and it looks like
+
+ align:start position:0%
+starting to get up and it looks like
+ 
+
+ align:start position:0%
+starting to get up and it looks like
+you're actually about to see some
+
+ align:start position:0%
+you're actually about to see some
+ 
+
+ align:start position:0%
+you're actually about to see some
+unmentioned able parts of her body and
+
+ align:start position:0%
+unmentioned able parts of her body and
+ 
+
+ align:start position:0%
+unmentioned able parts of her body and
+just as that's about to happen a hand
+
+ align:start position:0%
+just as that's about to happen a hand
+ 
+
+ align:start position:0%
+just as that's about to happen a hand
+comes in front of the camera and blocks
+
+ align:start position:0%
+comes in front of the camera and blocks
+ 
+
+ align:start position:0%
+comes in front of the camera and blocks
+you and it's actually a very disturbing
+
+ align:start position:0%
+you and it's actually a very disturbing
+ 
+
+ align:start position:0%
+you and it's actually a very disturbing
+moment in a way because it interrupts
+
+ align:start position:0%
+moment in a way because it interrupts
+ 
+
+ align:start position:0%
+moment in a way because it interrupts
+The Narrative flow it's it's a it's an
+
+ align:start position:0%
+The Narrative flow it's it's a it's an
+ 
+
+ align:start position:0%
+The Narrative flow it's it's a it's an
+intervention from the outside whose hand
+
+ align:start position:0%
+intervention from the outside whose hand
+ 
+
+ align:start position:0%
+intervention from the outside whose hand
+it is it's not a character in the film
+
+ align:start position:0%
+it is it's not a character in the film
+ 
+
+ align:start position:0%
+it is it's not a character in the film
+it's the director or so right it's very
+
+ align:start position:0%
+it's the director or so right it's very
+ 
+
+ align:start position:0%
+it's the director or so right it's very
+bold moment because what it does is it
+
+ align:start position:0%
+bold moment because what it does is it
+ 
+
+ align:start position:0%
+bold moment because what it does is it
+reminds you of the film as an artifact
+
+ align:start position:0%
+reminds you of the film as an artifact
+ 
+
+ align:start position:0%
+reminds you of the film as an artifact
+it reminds you that the film is uh an
+
+ align:start position:0%
+it reminds you that the film is uh an
+ 
+
+ align:start position:0%
+it reminds you that the film is uh an
+artifact in other words it's a moment of
+
+ align:start position:0%
+artifact in other words it's a moment of
+ 
+
+ align:start position:0%
+artifact in other words it's a moment of
+self-reflexiveness or self-consciousness
+
+ align:start position:0%
+self-reflexiveness or self-consciousness
+ 
+
+ align:start position:0%
+self-reflexiveness or self-consciousness
+that you would never see in a chaplain
+
+ align:start position:0%
+that you would never see in a chaplain
+ 
+
+ align:start position:0%
+that you would never see in a chaplain
+film but shows
+
+ align:start position:0%
+film but shows
+ 
+
+ align:start position:0%
+film but shows
+Keaton's astonishing interest in the
+
+ align:start position:0%
+Keaton's astonishing interest in the
+ 
+
+ align:start position:0%
+Keaton's astonishing interest in the
+technology of motion pictures uh I had
+
+ align:start position:0%
+technology of motion pictures uh I had
+ 
+
+ align:start position:0%
+technology of motion pictures uh I had
+many examples that Greg and I had ready
+
+ align:start position:0%
+many examples that Greg and I had ready
+ 
+
+ align:start position:0%
+many examples that Greg and I had ready
+but I don't have time to show them to
+
+ align:start position:0%
+but I don't have time to show them to
+ 
+
+ align:start position:0%
+but I don't have time to show them to
+you maybe you can put up while I'm
+
+ align:start position:0%
+you maybe you can put up while I'm
+ 
+
+ align:start position:0%
+you maybe you can put up while I'm
+talking the the playhouse one of his
+
+ align:start position:0%
+talking the the playhouse one of his
+ 
+
+ align:start position:0%
+talking the the playhouse one of his
+most famous examples of this is a film
+
+ align:start position:0%
+most famous examples of this is a film
+ 
+
+ align:start position:0%
+most famous examples of this is a film
+called the playhouse in which he ends up
+
+ align:start position:0%
+called the playhouse in which he ends up
+ 
+
+ align:start position:0%
+called the playhouse in which he ends up
+playing every role in the movie and the
+
+ align:start position:0%
+playing every role in the movie and the
+ 
+
+ align:start position:0%
+playing every role in the movie and the
+way he did this was incred was
+
+ align:start position:0%
+way he did this was incred was
+ 
+
+ align:start position:0%
+way he did this was incred was
+incredibly interesting he would shoot
+
+ align:start position:0%
+incredibly interesting he would shoot
+ 
+
+ align:start position:0%
+incredibly interesting he would shoot
+the film uh and then he he would shoot
+
+ align:start position:0%
+the film uh and then he he would shoot
+ 
+
+ align:start position:0%
+the film uh and then he he would shoot
+the film but he would but he put a he
+
+ align:start position:0%
+the film but he would but he put a he
+ 
+
+ align:start position:0%
+the film but he would but he put a he
+put masking tape over the lens of the
+
+ align:start position:0%
+put masking tape over the lens of the
+ 
+
+ align:start position:0%
+put masking tape over the lens of the
+camera and only one little tiny part of
+
+ align:start position:0%
+camera and only one little tiny part of
+ 
+
+ align:start position:0%
+camera and only one little tiny part of
+the of the lens of the camera was was
+
+ align:start position:0%
+the of the lens of the camera was was
+ 
+
+ align:start position:0%
+the of the lens of the camera was was
+would expose the film and he would he
+
+ align:start position:0%
+would expose the film and he would he
+ 
+
+ align:start position:0%
+would expose the film and he would he
+would shoot that then he would rewind
+
+ align:start position:0%
+would shoot that then he would rewind
+ 
+
+ align:start position:0%
+would shoot that then he would rewind
+the film and then if he were over in
+
+ align:start position:0%
+the film and then if he were over in
+ 
+
+ align:start position:0%
+the film and then if he were over in
+this corner for that shot then he'd move
+
+ align:start position:0%
+this corner for that shot then he'd move
+ 
+
+ align:start position:0%
+this corner for that shot then he'd move
+over and sit in the other corner he put
+
+ align:start position:0%
+over and sit in the other corner he put
+ 
+
+ align:start position:0%
+over and sit in the other corner he put
+a new kind of tape on the camera film it
+
+ align:start position:0%
+a new kind of tape on the camera film it
+ 
+
+ align:start position:0%
+a new kind of tape on the camera film it
+again and the film you're going to see
+
+ align:start position:0%
+again and the film you're going to see
+ 
+
+ align:start position:0%
+again and the film you're going to see
+will show this and you can see they're
+
+ align:start position:0%
+will show this and you can see they're
+ 
+
+ align:start position:0%
+will show this and you can see they're
+all Buster right it's a it's an it's a
+
+ align:start position:0%
+all Buster right it's a it's an it's a
+ 
+
+ align:start position:0%
+all Buster right it's a it's an it's a
+it's again what it shows is he's a
+
+ align:start position:0%
+it's again what it shows is he's a
+ 
+
+ align:start position:0%
+it's again what it shows is he's a
+technician he's interested in the
+
+ align:start position:0%
+technician he's interested in the
+ 
+
+ align:start position:0%
+technician he's interested in the
+technology of motion P of of of the of
+
+ align:start position:0%
+technology of motion P of of of the of
+ 
+
+ align:start position:0%
+technology of motion P of of of the of
+the uh motion picture camera and what
+
+ align:start position:0%
+the uh motion picture camera and what
+ 
+
+ align:start position:0%
+the uh motion picture camera and what
+kinds of manipulations are possible
+
+ align:start position:0%
+kinds of manipulations are possible
+ 
+
+ align:start position:0%
+kinds of manipulations are possible
+because he's the conductor right he's
+
+ align:start position:0%
+because he's the conductor right he's
+ 
+
+ align:start position:0%
+because he's the conductor right he's
+you'll as it turns out he's going to
+
+ align:start position:0%
+you'll as it turns out he's going to
+ 
+
+ align:start position:0%
+you'll as it turns out he's going to
+also end up being the the only person in
+
+ align:start position:0%
+also end up being the the only person in
+ 
+
+ align:start position:0%
+also end up being the the only person in
+the audience well um and then finally
+
+ align:start position:0%
+the audience well um and then finally
+ 
+
+ align:start position:0%
+the audience well um and then finally
+what what I've already implied is that
+
+ align:start position:0%
+what what I've already implied is that
+ 
+
+ align:start position:0%
+what what I've already implied is that
+Keaton's jokes and his technical
+
+ align:start position:0%
+Keaton's jokes and his technical
+ 
+
+ align:start position:0%
+Keaton's jokes and his technical
+interests also end up making him a
+
+ align:start position:0%
+interests also end up making him a
+ 
+
+ align:start position:0%
+interests also end up making him a
+metaphysician a philosopher an artist
+
+ align:start position:0%
+metaphysician a philosopher an artist
+ 
+
+ align:start position:0%
+metaphysician a philosopher an artist
+now Keaton himself could never
+
+ align:start position:0%
+now Keaton himself could never
+ 
+
+ align:start position:0%
+now Keaton himself could never
+articulate his own Ambitions in this way
+
+ align:start position:0%
+articulate his own Ambitions in this way
+ 
+
+ align:start position:0%
+articulate his own Ambitions in this way
+if you said Mr Keaton your vision of the
+
+ align:start position:0%
+if you said Mr Keaton your vision of the
+ 
+
+ align:start position:0%
+if you said Mr Keaton your vision of the
+Absurd universe is more complex and Rich
+
+ align:start position:0%
+Absurd universe is more complex and Rich
+ 
+
+ align:start position:0%
+Absurd universe is more complex and Rich
+than Jean Paul Sarge as in fact it is
+
+ align:start position:0%
+than Jean Paul Sarge as in fact it is
+ 
+
+ align:start position:0%
+than Jean Paul Sarge as in fact it is
+incidentally he would laugh he wouldn't
+
+ align:start position:0%
+incidentally he would laugh he wouldn't
+ 
+
+ align:start position:0%
+incidentally he would laugh he wouldn't
+even understand what you were talking
+
+ align:start position:0%
+even understand what you were talking
+ 
+
+ align:start position:0%
+even understand what you were talking
+about not only because he'd never read
+
+ align:start position:0%
+about not only because he'd never read
+ 
+
+ align:start position:0%
+about not only because he'd never read
+sart since he died before he would well
+
+ align:start position:0%
+sart since he died before he would well
+ 
+
+ align:start position:0%
+sart since he died before he would well
+s he was alive when s was alive actually
+
+ align:start position:0%
+s he was alive when s was alive actually
+ 
+
+ align:start position:0%
+s he was alive when s was alive actually
+but but he undoubtedly he did not re but
+
+ align:start position:0%
+but but he undoubtedly he did not re but
+ 
+
+ align:start position:0%
+but but he undoubtedly he did not re but
+the universe that he projects uh has has
+
+ align:start position:0%
+the universe that he projects uh has has
+ 
+
+ align:start position:0%
+the universe that he projects uh has has
+a kind of content or a meaning that's a
+
+ align:start position:0%
+a kind of content or a meaning that's a
+ 
+
+ align:start position:0%
+a kind of content or a meaning that's a
+function of how intelligent he is about
+
+ align:start position:0%
+function of how intelligent he is about
+ 
+
+ align:start position:0%
+function of how intelligent he is about
+exploiting his medium and telling his
+
+ align:start position:0%
+exploiting his medium and telling his
+ 
+
+ align:start position:0%
+exploiting his medium and telling his
+stories as if his jokes Express a vision
+
+ align:start position:0%
+stories as if his jokes Express a vision
+ 
+
+ align:start position:0%
+stories as if his jokes Express a vision
+of Life a sense of experience now this
+
+ align:start position:0%
+of Life a sense of experience now this
+ 
+
+ align:start position:0%
+of Life a sense of experience now this
+so you um and of course this is what
+
+ align:start position:0%
+so you um and of course this is what
+ 
+
+ align:start position:0%
+so you um and of course this is what
+you're looking at is sort of minor
+
+ align:start position:0%
+you're looking at is sort of minor
+ 
+
+ align:start position:0%
+you're looking at is sort of minor
+Keaton here but it but it shows his it
+
+ align:start position:0%
+Keaton here but it but it shows his it
+ 
+
+ align:start position:0%
+Keaton here but it but it shows his it
+shows his technical his technical
+
+ align:start position:0%
+shows his technical his technical
+ 
+
+ align:start position:0%
+shows his technical his technical
+interests well so what I mean so let me
+
+ align:start position:0%
+interests well so what I mean so let me
+ 
+
+ align:start position:0%
+interests well so what I mean so let me
+explain what I mean basically by the
+
+ align:start position:0%
+explain what I mean basically by the
+ 
+
+ align:start position:0%
+explain what I mean basically by the
+multiplicity principle this process of
+
+ align:start position:0%
+multiplicity principle this process of
+ 
+
+ align:start position:0%
+multiplicity principle this process of
+accretion and complexity I've described
+
+ align:start position:0%
+accretion and complexity I've described
+ 
+
+ align:start position:0%
+accretion and complexity I've described
+at a certain point you get to a
+
+ align:start position:0%
+at a certain point you get to a
+ 
+
+ align:start position:0%
+at a certain point you get to a
+situation you get to a point okay look
+
+ align:start position:0%
+situation you get to a point okay look
+ 
+
+ align:start position:0%
+situation you get to a point okay look
+I'm let's shut it off great because I
+
+ align:start position:0%
+I'm let's shut it off great because I
+ 
+
+ align:start position:0%
+I'm let's shut it off great because I
+can see it's just people are paying too
+
+ align:start position:0%
+can see it's just people are paying too
+ 
+
+ align:start position:0%
+can see it's just people are paying too
+much attention to this great artist and
+
+ align:start position:0%
+much attention to this great artist and
+ 
+
+ align:start position:0%
+much attention to this great artist and
+not to me and I want to end it U at a
+
+ align:start position:0%
+not to me and I want to end it U at a
+ 
+
+ align:start position:0%
+not to me and I want to end it U at a
+certain point you get to point where
+
+ align:start position:0%
+certain point you get to point where
+ 
+
+ align:start position:0%
+certain point you get to point where
+what what began as a gag or as a mere
+
+ align:start position:0%
+what what began as a gag or as a mere
+ 
+
+ align:start position:0%
+what what began as a gag or as a mere
+entertainment takes on a density or a
+
+ align:start position:0%
+entertainment takes on a density or a
+ 
+
+ align:start position:0%
+entertainment takes on a density or a
+texture that makes you think wait a
+
+ align:start position:0%
+texture that makes you think wait a
+ 
+
+ align:start position:0%
+texture that makes you think wait a
+second the vision of experience that's
+
+ align:start position:0%
+second the vision of experience that's
+ 
+
+ align:start position:0%
+second the vision of experience that's
+projected in this text is intrinsically
+
+ align:start position:0%
+projected in this text is intrinsically
+ 
+
+ align:start position:0%
+projected in this text is intrinsically
+interesting that is to say there's an
+
+ align:start position:0%
+interesting that is to say there's an
+ 
+
+ align:start position:0%
+interesting that is to say there's an
+understanding of life that's embedded in
+
+ align:start position:0%
+understanding of life that's embedded in
+ 
+
+ align:start position:0%
+understanding of life that's embedded in
+the story when you reach the point where
+
+ align:start position:0%
+the story when you reach the point where
+ 
+
+ align:start position:0%
+the story when you reach the point where
+the text itself embodies some sort of
+
+ align:start position:0%
+the text itself embodies some sort of
+ 
+
+ align:start position:0%
+the text itself embodies some sort of
+understanding of life and it's coherent
+
+ align:start position:0%
+understanding of life and it's coherent
+ 
+
+ align:start position:0%
+understanding of life and it's coherent
+an understanding of life that's
+
+ align:start position:0%
+an understanding of life that's
+ 
+
+ align:start position:0%
+an understanding of life that's
+coherently presented powerfully
+
+ align:start position:0%
+coherently presented powerfully
+ 
+
+ align:start position:0%
+coherently presented powerfully
+presented what you're what you're
+
+ align:start position:0%
+presented what you're what you're
+ 
+
+ align:start position:0%
+presented what you're what you're
+looking at is what I call Art there you
+
+ align:start position:0%
+looking at is what I call Art there you
+ 
+
+ align:start position:0%
+looking at is what I call Art there you
+might just call it more intelligent
+
+ align:start position:0%
+might just call it more intelligent
+ 
+
+ align:start position:0%
+might just call it more intelligent
+entertainment but this is a way of
+
+ align:start position:0%
+entertainment but this is a way of
+ 
+
+ align:start position:0%
+entertainment but this is a way of
+distinguishing between entertainment and
+
+ align:start position:0%
+distinguishing between entertainment and
+ 
+
+ align:start position:0%
+distinguishing between entertainment and
+art in other words there's a certain
+
+ align:start position:0%
+art in other words there's a certain
+ 
+
+ align:start position:0%
+art in other words there's a certain
+point at which entertainment becomes so
+
+ align:start position:0%
+point at which entertainment becomes so
+ 
+
+ align:start position:0%
+point at which entertainment becomes so
+complicated that it's more than mere
+
+ align:start position:0%
+complicated that it's more than mere
+ 
+
+ align:start position:0%
+complicated that it's more than mere
+entertainment when does that occur well
+
+ align:start position:0%
+entertainment when does that occur well
+ 
+
+ align:start position:0%
+entertainment when does that occur well
+one way to tell when it occurs is to
+
+ align:start position:0%
+one way to tell when it occurs is to
+ 
+
+ align:start position:0%
+one way to tell when it occurs is to
+watch for what I call the multiplicity
+
+ align:start position:0%
+watch for what I call the multiplicity
+ 
+
+ align:start position:0%
+watch for what I call the multiplicity
+principle when events in the film play
+
+ align:start position:0%
+principle when events in the film play
+ 
+
+ align:start position:0%
+principle when events in the film play
+more than one function do more than one
+
+ align:start position:0%
+more than one function do more than one
+ 
+
+ align:start position:0%
+more than one function do more than one
+job when they forward the story but also
+
+ align:start position:0%
+job when they forward the story but also
+ 
+
+ align:start position:0%
+job when they forward the story but also
+declare for character when they express
+
+ align:start position:0%
+declare for character when they express
+ 
+
+ align:start position:0%
+declare for character when they express
+when they make you laugh but also
+
+ align:start position:0%
+when they make you laugh but also
+ 
+
+ align:start position:0%
+when they make you laugh but also
+Express a vision of life and at the same
+
+ align:start position:0%
+Express a vision of life and at the same
+ 
+
+ align:start position:0%
+Express a vision of life and at the same
+time ex uh are consistent with the
+
+ align:start position:0%
+time ex uh are consistent with the
+ 
+
+ align:start position:0%
+time ex uh are consistent with the
+character psychological nature that
+
+ align:start position:0%
+character psychological nature that
+ 
+
+ align:start position:0%
+character psychological nature that
+multiplicity that density that texture
+
+ align:start position:0%
+multiplicity that density that texture
+ 
+
+ align:start position:0%
+multiplicity that density that texture
+is what we associate with works of art
+
+ align:start position:0%
+is what we associate with works of art
+ 
+
+ align:start position:0%
+is what we associate with works of art
+right uh a a bad example would be you're
+
+ align:start position:0%
+right uh a a bad example would be you're
+ 
+
+ align:start position:0%
+right uh a a bad example would be you're
+all familiar I hope with the kind of bad
+
+ align:start position:0%
+all familiar I hope with the kind of bad
+ 
+
+ align:start position:0%
+all familiar I hope with the kind of bad
+soap opera line in which a character
+
+ align:start position:0%
+soap opera line in which a character
+ 
+
+ align:start position:0%
+soap opera line in which a character
+comes in and says something like this oh
+
+ align:start position:0%
+comes in and says something like this oh
+ 
+
+ align:start position:0%
+comes in and says something like this oh
+hello John my long lost brother who just
+
+ align:start position:0%
+hello John my long lost brother who just
+ 
+
+ align:start position:0%
+hello John my long lost brother who just
+got out of the insane asylum after 15
+
+ align:start position:0%
+got out of the insane asylum after 15
+ 
+
+ align:start position:0%
+got out of the insane asylum after 15
+years of unfair misery right what's
+
+ align:start position:0%
+years of unfair misery right what's
+ 
+
+ align:start position:0%
+years of unfair misery right what's
+wrong with that line why is that a
+
+ align:start position:0%
+wrong with that line why is that a
+ 
+
+ align:start position:0%
+wrong with that line why is that a
+stupid line although we hear them all
+
+ align:start position:0%
+stupid line although we hear them all
+ 
+
+ align:start position:0%
+stupid line although we hear them all
+the time what what's wrong with it exed
+
+ align:start position:0%
+the time what what's wrong with it exed
+ 
+
+ align:start position:0%
+the time what what's wrong with it exed
+an awkward Exposition it's it's very
+
+ align:start position:0%
+an awkward Exposition it's it's very
+ 
+
+ align:start position:0%
+an awkward Exposition it's it's very
+awkward Exposition but why is it so
+
+ align:start position:0%
+awkward Exposition but why is it so
+ 
+
+ align:start position:0%
+awkward Exposition but why is it so
+awkward what makes it so awkward it's
+
+ align:start position:0%
+awkward what makes it so awkward it's
+ 
+
+ align:start position:0%
+awkward what makes it so awkward it's
+it's its intention is clear it wants to
+
+ align:start position:0%
+it's its intention is clear it wants to
+ 
+
+ align:start position:0%
+it's its intention is clear it wants to
+present information to the audience but
+
+ align:start position:0%
+present information to the audience but
+ 
+
+ align:start position:0%
+present information to the audience but
+in order to do that what what is it
+
+ align:start position:0%
+in order to do that what what is it
+ 
+
+ align:start position:0%
+in order to do that what what is it
+violated um it ceases to be something
+
+ align:start position:0%
+violated um it ceases to be something
+ 
+
+ align:start position:0%
+violated um it ceases to be something
+that follows the nature of the character
+
+ align:start position:0%
+that follows the nature of the character
+ 
+
+ align:start position:0%
+that follows the nature of the character
+it ceases to be something that is that
+
+ align:start position:0%
+it ceases to be something that is that
+ 
+
+ align:start position:0%
+it ceases to be something that is that
+honors the character's nature exactly
+
+ align:start position:0%
+honors the character's nature exactly
+ 
+
+ align:start position:0%
+honors the character's nature exactly
+right that's a very good answer what's
+
+ align:start position:0%
+right that's a very good answer what's
+ 
+
+ align:start position:0%
+right that's a very good answer what's
+your name Michael Michael thank Michael
+
+ align:start position:0%
+your name Michael Michael thank Michael
+ 
+
+ align:start position:0%
+your name Michael Michael thank Michael
+that's very good and what what happened
+
+ align:start position:0%
+that's very good and what what happened
+ 
+
+ align:start position:0%
+that's very good and what what happened
+okay I want to give information to the
+
+ align:start position:0%
+okay I want to give information to the
+ 
+
+ align:start position:0%
+okay I want to give information to the
+audience in order to do that I'll
+
+ align:start position:0%
+audience in order to do that I'll
+ 
+
+ align:start position:0%
+audience in order to do that I'll
+compromise the character's basic nature
+
+ align:start position:0%
+compromise the character's basic nature
+ 
+
+ align:start position:0%
+compromise the character's basic nature
+because no brother to no sister talking
+
+ align:start position:0%
+because no brother to no sister talking
+ 
+
+ align:start position:0%
+because no brother to no sister talking
+to a brother would recount the brother's
+
+ align:start position:0%
+to a brother would recount the brother's
+ 
+
+ align:start position:0%
+to a brother would recount the brother's
+history to the brother right that just
+
+ align:start position:0%
+history to the brother right that just
+ 
+
+ align:start position:0%
+history to the brother right that just
+wouldn't happen right so in order to
+
+ align:start position:0%
+wouldn't happen right so in order to
+ 
+
+ align:start position:0%
+wouldn't happen right so in order to
+accomplish one task the text has
+
+ align:start position:0%
+accomplish one task the text has
+ 
+
+ align:start position:0%
+accomplish one task the text has
+compromised itself on another test but
+
+ align:start position:0%
+compromised itself on another test but
+ 
+
+ align:start position:0%
+compromised itself on another test but
+imagine a story in which this
+
+ align:start position:0%
+imagine a story in which this
+ 
+
+ align:start position:0%
+imagine a story in which this
+information emerges in D in dramatic
+
+ align:start position:0%
+information emerges in D in dramatic
+ 
+
+ align:start position:0%
+information emerges in D in dramatic
+ways two characters are talking and Mary
+
+ align:start position:0%
+ways two characters are talking and Mary
+ 
+
+ align:start position:0%
+ways two characters are talking and Mary
+says to Joan oh Joan my brother's coming
+
+ align:start position:0%
+says to Joan oh Joan my brother's coming
+ 
+
+ align:start position:0%
+says to Joan oh Joan my brother's coming
+back from the Asylum and she says really
+
+ align:start position:0%
+back from the Asylum and she says really
+ 
+
+ align:start position:0%
+back from the Asylum and she says really
+I didn't even know he was in in the
+
+ align:start position:0%
+I didn't even know he was in in the
+ 
+
+ align:start position:0%
+I didn't even know he was in in the
+Asylum and Mary pulls back and says I
+
+ align:start position:0%
+Asylum and Mary pulls back and says I
+ 
+
+ align:start position:0%
+Asylum and Mary pulls back and says I
+don't know if I should tell you okay so
+
+ align:start position:0%
+don't know if I should tell you okay so
+ 
+
+ align:start position:0%
+don't know if I should tell you okay so
+we have a we have a dramatic scene in
+
+ align:start position:0%
+we have a we have a dramatic scene in
+ 
+
+ align:start position:0%
+we have a we have a dramatic scene in
+which what in which the information that
+
+ align:start position:0%
+which what in which the information that
+ 
+
+ align:start position:0%
+which what in which the information that
+the audience is supposed to have is
+
+ align:start position:0%
+the audience is supposed to have is
+ 
+
+ align:start position:0%
+the audience is supposed to have is
+presented in a way that maybe tells us
+
+ align:start position:0%
+presented in a way that maybe tells us
+ 
+
+ align:start position:0%
+presented in a way that maybe tells us
+something about Mary's nature and maybe
+
+ align:start position:0%
+something about Mary's nature and maybe
+ 
+
+ align:start position:0%
+something about Mary's nature and maybe
+tells us something about Joan's nature
+
+ align:start position:0%
+tells us something about Joan's nature
+ 
+
+ align:start position:0%
+tells us something about Joan's nature
+that is multiplicity right more that's
+
+ align:start position:0%
+that is multiplicity right more that's
+ 
+
+ align:start position:0%
+that is multiplicity right more that's
+what I mean by the multiplicity
+
+ align:start position:0%
+what I mean by the multiplicity
+ 
+
+ align:start position:0%
+what I mean by the multiplicity
+principle you will see many many
+
+ align:start position:0%
+principle you will see many many
+ 
+
+ align:start position:0%
+principle you will see many many
+instances of what of what I'm calling
+
+ align:start position:0%
+instances of what of what I'm calling
+ 
+
+ align:start position:0%
+instances of what of what I'm calling
+the multiplicity principle in Keaton's
+
+ align:start position:0%
+the multiplicity principle in Keaton's
+ 
+
+ align:start position:0%
+the multiplicity principle in Keaton's
+work and you will especially see it in
+
+ align:start position:0%
+work and you will especially see it in
+ 
+
+ align:start position:0%
+work and you will especially see it in
+these astonishing repeat
+
+ align:start position:0%
+these astonishing repeat
+ 
+
+ align:start position:0%
+these astonishing repeat
+um uh uh sequences in which we
+
+ align:start position:0%
+um uh uh sequences in which we
+ 
+
+ align:start position:0%
+um uh uh sequences in which we
+see in which we see the and I'm talking
+
+ align:start position:0%
+see in which we see the and I'm talking
+ 
+
+ align:start position:0%
+see in which we see the and I'm talking
+now in a way about the General in which
+
+ align:start position:0%
+now in a way about the General in which
+ 
+
+ align:start position:0%
+now in a way about the General in which
+we see the Keaton hero who sort of uh is
+
+ align:start position:0%
+we see the Keaton hero who sort of uh is
+ 
+
+ align:start position:0%
+we see the Keaton hero who sort of uh is
+steadfast but also a muddler he keeps he
+
+ align:start position:0%
+steadfast but also a muddler he keeps he
+ 
+
+ align:start position:0%
+steadfast but also a muddler he keeps he
+keeps doing the same things they're not
+
+ align:start position:0%
+keeps doing the same things they're not
+ 
+
+ align:start position:0%
+keeps doing the same things they're not
+really likely to help him and then he
+
+ align:start position:0%
+really likely to help him and then he
+ 
+
+ align:start position:0%
+really likely to help him and then he
+gets help from the outside and was what
+
+ align:start position:0%
+gets help from the outside and was what
+ 
+
+ align:start position:0%
+gets help from the outside and was what
+the what Keaton's jokes repeatedly
+
+ align:start position:0%
+the what Keaton's jokes repeatedly
+ 
+
+ align:start position:0%
+the what Keaton's jokes repeatedly
+depend upon the idea of of uh accident
+
+ align:start position:0%
+depend upon the idea of of uh accident
+ 
+
+ align:start position:0%
+depend upon the idea of of uh accident
+in a certain way and I I'll come back to
+
+ align:start position:0%
+in a certain way and I I'll come back to
+ 
+
+ align:start position:0%
+in a certain way and I I'll come back to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+finally in a second so so think about
+
+ align:start position:0%
+finally in a second so so think about
+ 
+
+ align:start position:0%
+finally in a second so so think about
+the multiplicity principle the
+
+ align:start position:0%
+the multiplicity principle the
+ 
+
+ align:start position:0%
+the multiplicity principle the
+difference between entertainment and art
+
+ align:start position:0%
+difference between entertainment and art
+ 
+
+ align:start position:0%
+difference between entertainment and art
+again this is a principle I'll come back
+
+ align:start position:0%
+again this is a principle I'll come back
+ 
+
+ align:start position:0%
+again this is a principle I'll come back
+to and try to illustrate with greater uh
+
+ align:start position:0%
+to and try to illustrate with greater uh
+ 
+
+ align:start position:0%
+to and try to illustrate with greater uh
+uh concreteness and greater leisure in
+
+ align:start position:0%
+uh concreteness and greater leisure in
+ 
+
+ align:start position:0%
+uh concreteness and greater leisure in
+later lectures but I want you to be
+
+ align:start position:0%
+later lectures but I want you to be
+ 
+
+ align:start position:0%
+later lectures but I want you to be
+aware of these of these issues so the
+
+ align:start position:0%
+aware of these of these issues so the
+ 
+
+ align:start position:0%
+aware of these of these issues so the
+general made in 1927 can be seen as a
+
+ align:start position:0%
+general made in 1927 can be seen as a
+ 
+
+ align:start position:0%
+general made in 1927 can be seen as a
+kind of culminating text I'm sorry I'm
+
+ align:start position:0%
+kind of culminating text I'm sorry I'm
+ 
+
+ align:start position:0%
+kind of culminating text I'm sorry I'm
+running over again I won't do it after
+
+ align:start position:0%
+running over again I won't do it after
+ 
+
+ align:start position:0%
+running over again I won't do it after
+today but what I've what I've tried to
+
+ align:start position:0%
+today but what I've what I've tried to
+ 
+
+ align:start position:0%
+today but what I've what I've tried to
+do you please forgive me about this but
+
+ align:start position:0%
+do you please forgive me about this but
+ 
+
+ align:start position:0%
+do you please forgive me about this but
+I I'm very respectful of the fact that
+
+ align:start position:0%
+I I'm very respectful of the fact that
+ 
+
+ align:start position:0%
+I I'm very respectful of the fact that
+you guys guys have schedules so I
+
+ align:start position:0%
+you guys guys have schedules so I
+ 
+
+ align:start position:0%
+you guys guys have schedules so I
+normally would not will not run over but
+
+ align:start position:0%
+normally would not will not run over but
+ 
+
+ align:start position:0%
+normally would not will not run over but
+I'm I I've condensed into into only two
+
+ align:start position:0%
+I'm I I've condensed into into only two
+ 
+
+ align:start position:0%
+I'm I I've condensed into into only two
+lectures what I normally do in four
+
+ align:start position:0%
+lectures what I normally do in four
+ 
+
+ align:start position:0%
+lectures what I normally do in four
+that's why I'm a little oppressed and
+
+ align:start position:0%
+that's why I'm a little oppressed and
+ 
+
+ align:start position:0%
+that's why I'm a little oppressed and
+not quite saying as much as I had hoped
+
+ align:start position:0%
+not quite saying as much as I had hoped
+ 
+
+ align:start position:0%
+not quite saying as much as I had hoped
+to say here um so the general can be
+
+ align:start position:0%
+to say here um so the general can be
+ 
+
+ align:start position:0%
+to say here um so the general can be
+understood as a kind of culminating text
+
+ align:start position:0%
+understood as a kind of culminating text
+ 
+
+ align:start position:0%
+understood as a kind of culminating text
+in at least two ways it's a culmination
+
+ align:start position:0%
+in at least two ways it's a culmination
+ 
+
+ align:start position:0%
+in at least two ways it's a culmination
+of Keaton's career that is to say the
+
+ align:start position:0%
+of Keaton's career that is to say the
+ 
+
+ align:start position:0%
+of Keaton's career that is to say the
+jokes and gags that are enacted in in uh
+
+ align:start position:0%
+jokes and gags that are enacted in in uh
+ 
+
+ align:start position:0%
+jokes and gags that are enacted in in uh
+in the film recall many earlier Katon
+
+ align:start position:0%
+in the film recall many earlier Katon
+ 
+
+ align:start position:0%
+in the film recall many earlier Katon
+films and the basic character of the
+
+ align:start position:0%
+films and the basic character of the
+ 
+
+ align:start position:0%
+films and the basic character of the
+general is the basic character of the
+
+ align:start position:0%
+general is the basic character of the
+ 
+
+ align:start position:0%
+general is the basic character of the
+Katon hero a steadfast unremarkable
+
+ align:start position:0%
+Katon hero a steadfast unremarkable
+ 
+
+ align:start position:0%
+Katon hero a steadfast unremarkable
+young man who perseveres in the face of
+
+ align:start position:0%
+young man who perseveres in the face of
+ 
+
+ align:start position:0%
+young man who perseveres in the face of
+catastrophic difficulties with mostly
+
+ align:start position:0%
+catastrophic difficulties with mostly
+ 
+
+ align:start position:0%
+catastrophic difficulties with mostly
+comic expectations very small
+
+ align:start position:0%
+comic expectations very small
+ 
+
+ align:start position:0%
+comic expectations very small
+expectations of success who often
+
+ align:start position:0%
+expectations of success who often
+ 
+
+ align:start position:0%
+expectations of success who often
+muddles through almost despite himself
+
+ align:start position:0%
+muddles through almost despite himself
+ 
+
+ align:start position:0%
+muddles through almost despite himself
+right now but it isn't merely but I say
+
+ align:start position:0%
+right now but it isn't merely but I say
+ 
+
+ align:start position:0%
+right now but it isn't merely but I say
+almost despite himself and this is where
+
+ align:start position:0%
+almost despite himself and this is where
+ 
+
+ align:start position:0%
+almost despite himself and this is where
+the complexity of Keaton's vision of
+
+ align:start position:0%
+the complexity of Keaton's vision of
+ 
+
+ align:start position:0%
+the complexity of Keaton's vision of
+Life comes in why I'm saying that Keaton
+
+ align:start position:0%
+Life comes in why I'm saying that Keaton
+ 
+
+ align:start position:0%
+Life comes in why I'm saying that Keaton
+moves from being merely a jokester or
+
+ align:start position:0%
+moves from being merely a jokester or
+ 
+
+ align:start position:0%
+moves from being merely a jokester or
+being merely a great Entertainer to
+
+ align:start position:0%
+being merely a great Entertainer to
+ 
+
+ align:start position:0%
+being merely a great Entertainer to
+being an artist his jokes embody an idea
+
+ align:start position:0%
+being an artist his jokes embody an idea
+ 
+
+ align:start position:0%
+being an artist his jokes embody an idea
+of what experience is like and it's a
+
+ align:start position:0%
+of what experience is like and it's a
+ 
+
+ align:start position:0%
+of what experience is like and it's a
+very powerful Morant mature idea of
+
+ align:start position:0%
+very powerful Morant mature idea of
+ 
+
+ align:start position:0%
+very powerful Morant mature idea of
+experience because what happens again
+
+ align:start position:0%
+experience because what happens again
+ 
+
+ align:start position:0%
+experience because what happens again
+and again in the small jokes the sequenc
+
+ align:start position:0%
+and again in the small jokes the sequenc
+ 
+
+ align:start position:0%
+and again in the small jokes the sequenc
+jokes in Keaton's work especially in the
+
+ align:start position:0%
+jokes in Keaton's work especially in the
+ 
+
+ align:start position:0%
+jokes in Keaton's work especially in the
+general and in the larger film what
+
+ align:start position:0%
+general and in the larger film what
+ 
+
+ align:start position:0%
+general and in the larger film what
+happens again and again is a is a a an
+
+ align:start position:0%
+happens again and again is a is a a an
+ 
+
+ align:start position:0%
+happens again and again is a is a a an
+adventure in which a steadfast
+
+ align:start position:0%
+adventure in which a steadfast
+ 
+
+ align:start position:0%
+adventure in which a steadfast
+Relentless young hero does everything he
+
+ align:start position:0%
+Relentless young hero does everything he
+ 
+
+ align:start position:0%
+Relentless young hero does everything he
+can to to uh accomplish his goal and
+
+ align:start position:0%
+can to to uh accomplish his goal and
+ 
+
+ align:start position:0%
+can to to uh accomplish his goal and
+it's obvious that he's up against forces
+
+ align:start position:0%
+it's obvious that he's up against forces
+ 
+
+ align:start position:0%
+it's obvious that he's up against forces
+far beyond himself that he could never
+
+ align:start position:0%
+far beyond himself that he could never
+ 
+
+ align:start position:0%
+far beyond himself that he could never
+that there's a unbelievable Mis mismatch
+
+ align:start position:0%
+that there's a unbelievable Mis mismatch
+ 
+
+ align:start position:0%
+that there's a unbelievable Mis mismatch
+between this minuscule tiny figure and
+
+ align:start position:0%
+between this minuscule tiny figure and
+ 
+
+ align:start position:0%
+between this minuscule tiny figure and
+the and his powers and the forces he's
+
+ align:start position:0%
+the and his powers and the forces he's
+ 
+
+ align:start position:0%
+the and his powers and the forces he's
+he's fighting against there's one Katon
+
+ align:start position:0%
+he's fighting against there's one Katon
+ 
+
+ align:start position:0%
+he's fighting against there's one Katon
+film called The Navigator in which the
+
+ align:start position:0%
+film called The Navigator in which the
+ 
+
+ align:start position:0%
+film called The Navigator in which the
+Katon character even more than with the
+
+ align:start position:0%
+Katon character even more than with the
+ 
+
+ align:start position:0%
+Katon character even more than with the
+locomotive in the general has to
+
+ align:start position:0%
+locomotive in the general has to
+ 
+
+ align:start position:0%
+locomotive in the general has to
+navigate an ocean liner and he's alone
+
+ align:start position:0%
+navigate an ocean liner and he's alone
+ 
+
+ align:start position:0%
+navigate an ocean liner and he's alone
+on the ocean liner and you see him
+
+ align:start position:0%
+on the ocean liner and you see him
+ 
+
+ align:start position:0%
+on the ocean liner and you see him
+running up and down into the engine room
+
+ align:start position:0%
+running up and down into the engine room
+ 
+
+ align:start position:0%
+running up and down into the engine room
+back up to the up to the bridge that
+
+ align:start position:0%
+back up to the up to the bridge that
+ 
+
+ align:start position:0%
+back up to the up to the bridge that
+running all over the ocean liner in a in
+
+ align:start position:0%
+running all over the ocean liner in a in
+ 
+
+ align:start position:0%
+running all over the ocean liner in a in
+in in great difficulties there's a
+
+ align:start position:0%
+in in great difficulties there's a
+ 
+
+ align:start position:0%
+in in great difficulties there's a
+Wonder Beau film late film made in 1928
+
+ align:start position:0%
+Wonder Beau film late film made in 1928
+ 
+
+ align:start position:0%
+Wonder Beau film late film made in 1928
+just his last silent film called
+
+ align:start position:0%
+just his last silent film called
+ 
+
+ align:start position:0%
+just his last silent film called
+Steamboat Bill Jr in which he dramatizes
+
+ align:start position:0%
+Steamboat Bill Jr in which he dramatizes
+ 
+
+ align:start position:0%
+Steamboat Bill Jr in which he dramatizes
+an astonishing song an astonishing an
+
+ align:start position:0%
+an astonishing song an astonishing an
+ 
+
+ align:start position:0%
+an astonishing song an astonishing an
+astonishing um uh hurricane uh a long
+
+ align:start position:0%
+astonishing um uh hurricane uh a long
+ 
+
+ align:start position:0%
+astonishing um uh hurricane uh a long
+extended sequence in which we see him
+
+ align:start position:0%
+extended sequence in which we see him
+ 
+
+ align:start position:0%
+extended sequence in which we see him
+trying to escape the hurricane uh trying
+
+ align:start position:0%
+trying to escape the hurricane uh trying
+ 
+
+ align:start position:0%
+trying to escape the hurricane uh trying
+to contend against this natural force
+
+ align:start position:0%
+to contend against this natural force
+ 
+
+ align:start position:0%
+to contend against this natural force
+that's so gigantic so the the so so the
+
+ align:start position:0%
+that's so gigantic so the the so so the
+ 
+
+ align:start position:0%
+that's so gigantic so the the so so the
+the general is a culmination in the
+
+ align:start position:0%
+the general is a culmination in the
+ 
+
+ align:start position:0%
+the general is a culmination in the
+sense that it gives us another version
+
+ align:start position:0%
+sense that it gives us another version
+ 
+
+ align:start position:0%
+sense that it gives us another version
+and the richest the richest version so
+
+ align:start position:0%
+and the richest the richest version so
+ 
+
+ align:start position:0%
+and the richest the richest version so
+far of the of The Adventures of this
+
+ align:start position:0%
+far of the of The Adventures of this
+ 
+
+ align:start position:0%
+far of the of The Adventures of this
+kind of Katon hero but what makes it a
+
+ align:start position:0%
+kind of Katon hero but what makes it a
+ 
+
+ align:start position:0%
+kind of Katon hero but what makes it a
+what makes it sort of metaphysical or
+
+ align:start position:0%
+what makes it sort of metaphysical or
+ 
+
+ align:start position:0%
+what makes it sort of metaphysical or
+philosophically interesting is that what
+
+ align:start position:0%
+philosophically interesting is that what
+ 
+
+ align:start position:0%
+philosophically interesting is that what
+what this joke repeatedly does and what
+
+ align:start position:0%
+what this joke repeatedly does and what
+ 
+
+ align:start position:0%
+what this joke repeatedly does and what
+the structure of the whole film
+
+ align:start position:0%
+the structure of the whole film
+ 
+
+ align:start position:0%
+the structure of the whole film
+repeatedly says is something like this
+
+ align:start position:0%
+repeatedly says is something like this
+ 
+
+ align:start position:0%
+repeatedly says is something like this
+we get through we make it through life
+
+ align:start position:0%
+we get through we make it through life
+ 
+
+ align:start position:0%
+we get through we make it through life
+not Mo mostly it's a it's a great comic
+
+ align:start position:0%
+not Mo mostly it's a it's a great comic
+ 
+
+ align:start position:0%
+not Mo mostly it's a it's a great comic
+more comic video we get through life
+
+ align:start position:0%
+more comic video we get through life
+ 
+
+ align:start position:0%
+more comic video we get through life
+mostly not because of anything we've
+
+ align:start position:0%
+mostly not because of anything we've
+ 
+
+ align:start position:0%
+mostly not because of anything we've
+done but because of accident we live in
+
+ align:start position:0%
+done but because of accident we live in
+ 
+
+ align:start position:0%
+done but because of accident we live in
+a contingent Universe right the idea of
+
+ align:start position:0%
+a contingent Universe right the idea of
+ 
+
+ align:start position:0%
+a contingent Universe right the idea of
+contingency is at the heart part of what
+
+ align:start position:0%
+contingency is at the heart part of what
+ 
+
+ align:start position:0%
+contingency is at the heart part of what
+of of of Keaton's jokes we could we
+
+ align:start position:0%
+of of of Keaton's jokes we could we
+ 
+
+ align:start position:0%
+of of of Keaton's jokes we could we
+could call them jokes about contingency
+
+ align:start position:0%
+could call them jokes about contingency
+ 
+
+ align:start position:0%
+could call them jokes about contingency
+the word contingent is interesting
+
+ align:start position:0%
+the word contingent is interesting
+ 
+
+ align:start position:0%
+the word contingent is interesting
+remember it means both Li it means
+
+ align:start position:0%
+remember it means both Li it means
+ 
+
+ align:start position:0%
+remember it means both Li it means
+liable but not certain but not certain
+
+ align:start position:0%
+liable but not certain but not certain
+ 
+
+ align:start position:0%
+liable but not certain but not certain
+to occur it means possible right so so
+
+ align:start position:0%
+to occur it means possible right so so
+ 
+
+ align:start position:0%
+to occur it means possible right so so
+uh for it's means dependent upon subject
+
+ align:start position:0%
+uh for it's means dependent upon subject
+ 
+
+ align:start position:0%
+uh for it's means dependent upon subject
+to conditioned by right in law you can
+
+ align:start position:0%
+to conditioned by right in law you can
+ 
+
+ align:start position:0%
+to conditioned by right in law you can
+say something uh you can say that
+
+ align:start position:0%
+say something uh you can say that
+ 
+
+ align:start position:0%
+say something uh you can say that
+something that is contingent is
+
+ align:start position:0%
+something that is contingent is
+ 
+
+ align:start position:0%
+something that is contingent is
+dependent for its effect on something
+
+ align:start position:0%
+dependent for its effect on something
+ 
+
+ align:start position:0%
+dependent for its effect on something
+that may or may not occur as in a
+
+ align:start position:0%
+that may or may not occur as in a
+ 
+
+ align:start position:0%
+that may or may not occur as in a
+contingent estate or Legacy right in
+
+ align:start position:0%
+contingent estate or Legacy right in
+ 
+
+ align:start position:0%
+contingent estate or Legacy right in
+Logic the same thing dependent upon some
+
+ align:start position:0%
+Logic the same thing dependent upon some
+ 
+
+ align:start position:0%
+Logic the same thing dependent upon some
+condition or upon the truth of something
+
+ align:start position:0%
+condition or upon the truth of something
+ 
+
+ align:start position:0%
+condition or upon the truth of something
+else not true a priori not necessary so
+
+ align:start position:0%
+else not true a priori not necessary so
+ 
+
+ align:start position:0%
+else not true a priori not necessary so
+what Keaton's jokes constantly do is
+
+ align:start position:0%
+what Keaton's jokes constantly do is
+ 
+
+ align:start position:0%
+what Keaton's jokes constantly do is
+they show us two things they show us a
+
+ align:start position:0%
+they show us two things they show us a
+ 
+
+ align:start position:0%
+they show us two things they show us a
+world in which human agency matters
+
+ align:start position:0%
+world in which human agency matters
+ 
+
+ align:start position:0%
+world in which human agency matters
+because if this schmendrick didn't keep
+
+ align:start position:0%
+because if this schmendrick didn't keep
+ 
+
+ align:start position:0%
+because if this schmendrick didn't keep
+that's a Jewish word for
+
+ align:start position:0%
+that's a Jewish word for
+ 
+
+ align:start position:0%
+that's a Jewish word for
+schlamazel it's a clown if this
+
+ align:start position:0%
+schlamazel it's a clown if this
+ 
+
+ align:start position:0%
+schlamazel it's a clown if this
+schmendrick did not if this schmendrick
+
+ align:start position:0%
+schmendrick did not if this schmendrick
+ 
+
+ align:start position:0%
+schmendrick did not if this schmendrick
+did not um keep on so Stead fastly he
+
+ align:start position:0%
+did not um keep on so Stead fastly he
+ 
+
+ align:start position:0%
+did not um keep on so Stead fastly he
+wouldn't survive but his keeping on so
+
+ align:start position:0%
+wouldn't survive but his keeping on so
+ 
+
+ align:start position:0%
+wouldn't survive but his keeping on so
+steadfastly still wouldn't make him
+
+ align:start position:0%
+steadfastly still wouldn't make him
+ 
+
+ align:start position:0%
+steadfastly still wouldn't make him
+survive if there weren't the
+
+ align:start position:0%
+survive if there weren't the
+ 
+
+ align:start position:0%
+survive if there weren't the
+intervention of mere accidents stuff he
+
+ align:start position:0%
+intervention of mere accidents stuff he
+ 
+
+ align:start position:0%
+intervention of mere accidents stuff he
+has no control over there's one
+
+ align:start position:0%
+has no control over there's one
+ 
+
+ align:start position:0%
+has no control over there's one
+magnificent moment in the in in one week
+
+ align:start position:0%
+magnificent moment in the in in one week
+ 
+
+ align:start position:0%
+magnificent moment in the in in one week
+for example where I think it's one week
+
+ align:start position:0%
+for example where I think it's one week
+ 
+
+ align:start position:0%
+for example where I think it's one week
+where he's standing in a certain place
+
+ align:start position:0%
+where he's standing in a certain place
+ 
+
+ align:start position:0%
+where he's standing in a certain place
+and the house and the house behind him
+
+ align:start position:0%
+and the house and the house behind him
+ 
+
+ align:start position:0%
+and the house and the house behind him
+falls down and he happens just by
+
+ align:start position:0%
+falls down and he happens just by
+ 
+
+ align:start position:0%
+falls down and he happens just by
+accident to be standing so that by the
+
+ align:start position:0%
+accident to be standing so that by the
+ 
+
+ align:start position:0%
+accident to be standing so that by the
+open window the house Falls so he
+
+ align:start position:0%
+open window the house Falls so he
+ 
+
+ align:start position:0%
+open window the house Falls so he
+doesn't get hurt he used this joke more
+
+ align:start position:0%
+doesn't get hurt he used this joke more
+ 
+
+ align:start position:0%
+doesn't get hurt he used this joke more
+than once in other films because such a
+
+ align:start position:0%
+than once in other films because such a
+ 
+
+ align:start position:0%
+than once in other films because such a
+great one but it's a perfect example of
+
+ align:start position:0%
+great one but it's a perfect example of
+ 
+
+ align:start position:0%
+great one but it's a perfect example of
+what I mean
+
+ align:start position:0%
+what I mean
+ 
+
+ align:start position:0%
+what I mean
+a partial example of what I mean because
+
+ align:start position:0%
+a partial example of what I mean because
+ 
+
+ align:start position:0%
+a partial example of what I mean because
+he's not responsible for the fact that
+
+ align:start position:0%
+he's not responsible for the fact that
+ 
+
+ align:start position:0%
+he's not responsible for the fact that
+he escaped on the other hand because he
+
+ align:start position:0%
+he escaped on the other hand because he
+ 
+
+ align:start position:0%
+he escaped on the other hand because he
+was trying to get away from difficulties
+
+ align:start position:0%
+was trying to get away from difficulties
+ 
+
+ align:start position:0%
+was trying to get away from difficulties
+maybe he was in that particular position
+
+ align:start position:0%
+maybe he was in that particular position
+ 
+
+ align:start position:0%
+maybe he was in that particular position
+because of Acts of his own so so what it
+
+ align:start position:0%
+because of Acts of his own so so what it
+ 
+
+ align:start position:0%
+because of Acts of his own so so what it
+says what what so what this joking
+
+ align:start position:0%
+says what what so what this joking
+ 
+
+ align:start position:0%
+says what what so what this joking
+Vision says about the world is something
+
+ align:start position:0%
+Vision says about the world is something
+ 
+
+ align:start position:0%
+Vision says about the world is something
+that's true we all love the idea that
+
+ align:start position:0%
+that's true we all love the idea that
+ 
+
+ align:start position:0%
+that's true we all love the idea that
+we've gotten to where we are by our own
+
+ align:start position:0%
+we've gotten to where we are by our own
+ 
+
+ align:start position:0%
+we've gotten to where we are by our own
+acts by our own conscious control the
+
+ align:start position:0%
+acts by our own conscious control the
+ 
+
+ align:start position:0%
+acts by our own conscious control the
+truth of the matter is that life that
+
+ align:start position:0%
+truth of the matter is that life that
+ 
+
+ align:start position:0%
+truth of the matter is that life that
+life is much more contingent than that
+
+ align:start position:0%
+life is much more contingent than that
+ 
+
+ align:start position:0%
+life is much more contingent than that
+it's partly accident it's partly luck
+
+ align:start position:0%
+it's partly accident it's partly luck
+ 
+
+ align:start position:0%
+it's partly accident it's partly luck
+and something deeper than that
+
+ align:start position:0%
+and something deeper than that
+ 
+
+ align:start position:0%
+and something deeper than that
+Keaton's vision of the universe is one
+
+ align:start position:0%
+Keaton's vision of the universe is one
+ 
+
+ align:start position:0%
+Keaton's vision of the universe is one
+which suggests that while the universe
+
+ align:start position:0%
+which suggests that while the universe
+ 
+
+ align:start position:0%
+which suggests that while the universe
+may screw you up sometimes it won't
+
+ align:start position:0%
+may screw you up sometimes it won't
+ 
+
+ align:start position:0%
+may screw you up sometimes it won't
+always do that that is to say it's not
+
+ align:start position:0%
+always do that that is to say it's not
+ 
+
+ align:start position:0%
+always do that that is to say it's not
+the universe in Keaton's world is not
+
+ align:start position:0%
+the universe in Keaton's world is not
+ 
+
+ align:start position:0%
+the universe in Keaton's world is not
+angry at us it's indifferent to us it
+
+ align:start position:0%
+angry at us it's indifferent to us it
+ 
+
+ align:start position:0%
+angry at us it's indifferent to us it
+doesn't give a damn about us it's not
+
+ align:start position:0%
+doesn't give a damn about us it's not
+ 
+
+ align:start position:0%
+doesn't give a damn about us it's not
+aware of us it's too big for us right
+
+ align:start position:0%
+aware of us it's too big for us right
+ 
+
+ align:start position:0%
+aware of us it's too big for us right
+you can't come away from Keaton's films
+
+ align:start position:0%
+you can't come away from Keaton's films
+ 
+
+ align:start position:0%
+you can't come away from Keaton's films
+without a simultaneous sense of the
+
+ align:start position:0%
+without a simultaneous sense of the
+ 
+
+ align:start position:0%
+without a simultaneous sense of the
+importance of Human Action of human
+
+ align:start position:0%
+importance of Human Action of human
+ 
+
+ align:start position:0%
+importance of Human Action of human
+agency but also of the inadequacy of
+
+ align:start position:0%
+agency but also of the inadequacy of
+ 
+
+ align:start position:0%
+agency but also of the inadequacy of
+human agency of how contingent every
+
+ align:start position:0%
+human agency of how contingent every
+ 
+
+ align:start position:0%
+human agency of how contingent every
+experience every Adventure every
+
+ align:start position:0%
+experience every Adventure every
+ 
+
+ align:start position:0%
+experience every Adventure every
+personality is and that and that meaning
+
+ align:start position:0%
+personality is and that and that meaning
+ 
+
+ align:start position:0%
+personality is and that and that meaning
+that idea of the world is a profound one
+
+ align:start position:0%
+that idea of the world is a profound one
+ 
+
+ align:start position:0%
+that idea of the world is a profound one
+I think it tells so that so that even
+
+ align:start position:0%
+I think it tells so that so that even
+ 
+
+ align:start position:0%
+I think it tells so that so that even
+though Keaton is telling a joke embedded
+
+ align:start position:0%
+though Keaton is telling a joke embedded
+ 
+
+ align:start position:0%
+though Keaton is telling a joke embedded
+in the joke is a kind of interpretation
+
+ align:start position:0%
+in the joke is a kind of interpretation
+ 
+
+ align:start position:0%
+in the joke is a kind of interpretation
+of life and embedded in the film is a
+
+ align:start position:0%
+of life and embedded in the film is a
+ 
+
+ align:start position:0%
+of life and embedded in the film is a
+kind of interpretation of Life uh when
+
+ align:start position:0%
+kind of interpretation of Life uh when
+ 
+
+ align:start position:0%
+kind of interpretation of Life uh when
+you're looking at the general I think
+
+ align:start position:0%
+you're looking at the general I think
+ 
+
+ align:start position:0%
+you're looking at the general I think
+you will see multiple examples of this
+
+ align:start position:0%
+you will see multiple examples of this
+ 
+
+ align:start position:0%
+you will see multiple examples of this
+kind of thing let me say one last thing
+
+ align:start position:0%
+kind of thing let me say one last thing
+ 
+
+ align:start position:0%
+kind of thing let me say one last thing
+I haven't mentioned anything about the
+
+ align:start position:0%
+I haven't mentioned anything about the
+ 
+
+ align:start position:0%
+I haven't mentioned anything about the
+structure of the film I'm a little out
+
+ align:start position:0%
+structure of the film I'm a little out
+ 
+
+ align:start position:0%
+structure of the film I'm a little out
+of of order watch how the film is
+
+ align:start position:0%
+of of order watch how the film is
+ 
+
+ align:start position:0%
+of of order watch how the film is
+structured it it's a it's a much more
+
+ align:start position:0%
+structured it it's a it's a much more
+ 
+
+ align:start position:0%
+structured it it's a it's a much more
+complex variation on what I said about
+
+ align:start position:0%
+complex variation on what I said about
+ 
+
+ align:start position:0%
+complex variation on what I said about
+Londale operator the film begins with
+
+ align:start position:0%
+Londale operator the film begins with
+ 
+
+ align:start position:0%
+Londale operator the film begins with
+him going up the track and then the
+
+ align:start position:0%
+him going up the track and then the
+ 
+
+ align:start position:0%
+him going up the track and then the
+second half of the film has him going
+
+ align:start position:0%
+second half of the film has him going
+ 
+
+ align:start position:0%
+second half of the film has him going
+back down the track you may not be aware
+
+ align:start position:0%
+back down the track you may not be aware
+ 
+
+ align:start position:0%
+back down the track you may not be aware
+of it but actually the film in a certain
+
+ align:start position:0%
+of it but actually the film in a certain
+ 
+
+ align:start position:0%
+of it but actually the film in a certain
+sense has its tail in its mouth when it
+
+ align:start position:0%
+sense has its tail in its mouth when it
+ 
+
+ align:start position:0%
+sense has its tail in its mouth when it
+goes up the track he has a series of
+
+ align:start position:0%
+goes up the track he has a series of
+ 
+
+ align:start position:0%
+goes up the track he has a series of
+Adventures when he comes back down he
+
+ align:start position:0%
+Adventures when he comes back down he
+ 
+
+ align:start position:0%
+Adventures when he comes back down he
+has a series of Adventures that in a
+
+ align:start position:0%
+has a series of Adventures that in a
+ 
+
+ align:start position:0%
+has a series of Adventures that in a
+certain sense replicate what's happened
+
+ align:start position:0%
+certain sense replicate what's happened
+ 
+
+ align:start position:0%
+certain sense replicate what's happened
+before the film mirrors itself in a way
+
+ align:start position:0%
+before the film mirrors itself in a way
+ 
+
+ align:start position:0%
+before the film mirrors itself in a way
+repeats itself what
+
+ align:start position:0%
+repeats itself what
+ 
+
+ align:start position:0%
+repeats itself what
+it's an incredibly elegant structure
+
+ align:start position:0%
+it's an incredibly elegant structure
+ 
+
+ align:start position:0%
+it's an incredibly elegant structure
+it's incred and and the Elegance of the
+
+ align:start position:0%
+it's incred and and the Elegance of the
+ 
+
+ align:start position:0%
+it's incred and and the Elegance of the
+structure reminds us also of the in its
+
+ align:start position:0%
+structure reminds us also of the in its
+ 
+
+ align:start position:0%
+structure reminds us also of the in its
+own way also reminds us of this
+
+ align:start position:0%
+own way also reminds us of this
+ 
+
+ align:start position:0%
+own way also reminds us of this
+principle of contingency that's at the
+
+ align:start position:0%
+principle of contingency that's at the
+ 
+
+ align:start position:0%
+principle of contingency that's at the
+heart of Keaton's vision of the world
+
+ align:start position:0%
+heart of Keaton's vision of the world
+ 
+
+ align:start position:0%
+heart of Keaton's vision of the world
+let me conclude by reminding you again
+
+ align:start position:0%
+let me conclude by reminding you again
+ 
+
+ align:start position:0%
+let me conclude by reminding you again
+of what I said earlier when I call
+
+ align:start position:0%
+of what I said earlier when I call
+ 
+
+ align:start position:0%
+of what I said earlier when I call
+Keaton a philosopher and a metaphysician
+
+ align:start position:0%
+Keaton a philosopher and a metaphysician
+ 
+
+ align:start position:0%
+Keaton a philosopher and a metaphysician
+and a wise person about the world I do
+
+ align:start position:0%
+and a wise person about the world I do
+ 
+
+ align:start position:0%
+and a wise person about the world I do
+not at all mean to suggest that if you
+
+ align:start position:0%
+not at all mean to suggest that if you
+ 
+
+ align:start position:0%
+not at all mean to suggest that if you
+asked Katon to explain how he thought
+
+ align:start position:0%
+asked Katon to explain how he thought
+ 
+
+ align:start position:0%
+asked Katon to explain how he thought
+about the world he could do this that's
+
+ align:start position:0%
+about the world he could do this that's
+ 
+
+ align:start position:0%
+about the world he could do this that's
+that's the job of professors and
+
+ align:start position:0%
+that's the job of professors and
+ 
+
+ align:start position:0%
+that's the job of professors and
+literary and film critics right what I'm
+
+ align:start position:0%
+literary and film critics right what I'm
+ 
+
+ align:start position:0%
+literary and film critics right what I'm
+saying to you is that Keaton like many
+
+ align:start position:0%
+saying to you is that Keaton like many
+ 
+
+ align:start position:0%
+saying to you is that Keaton like many
+great artists had an intuitive
+
+ align:start position:0%
+great artists had an intuitive
+ 
+
+ align:start position:0%
+great artists had an intuitive
+understanding of the world which he
+
+ align:start position:0%
+understanding of the world which he
+ 
+
+ align:start position:0%
+understanding of the world which he
+expressed with greater and greater
+
+ align:start position:0%
+expressed with greater and greater
+ 
+
+ align:start position:0%
+expressed with greater and greater
+complexity in the medium of the cinema
+
+ align:start position:0%
+complexity in the medium of the cinema
+ 
+
+ align:start position:0%
+complexity in the medium of the cinema
+and in the general we have what is
+
+ align:start position:0%
+and in the general we have what is
+ 
+
+ align:start position:0%
+and in the general we have what is
+ultimately a culminating instance of
+
+ align:start position:0%
+ultimately a culminating instance of
+ 
+
+ align:start position:0%
+ultimately a culminating instance of
+that one last point about the film as a
+
+ align:start position:0%
+that one last point about the film as a
+ 
+
+ align:start position:0%
+that one last point about the film as a
+culminating example it's not just a
+
+ align:start position:0%
+culminating example it's not just a
+ 
+
+ align:start position:0%
+culminating example it's not just a
+culmination of Keaton's career it's a
+
+ align:start position:0%
+culmination of Keaton's career it's a
+ 
+
+ align:start position:0%
+culmination of Keaton's career it's a
+culmination of silent film in in it in
+
+ align:start position:0%
+culmination of silent film in in it in
+ 
+
+ align:start position:0%
+culmination of silent film in in it in
+as a whole Katon would have expected his
+
+ align:start position:0%
+as a whole Katon would have expected his
+ 
+
+ align:start position:0%
+as a whole Katon would have expected his
+audience to recognize the degree to
+
+ align:start position:0%
+audience to recognize the degree to
+ 
+
+ align:start position:0%
+audience to recognize the degree to
+which this film was a parody or a
+
+ align:start position:0%
+which this film was a parody or a
+ 
+
+ align:start position:0%
+which this film was a parody or a
+mockery of famous historical films made
+
+ align:start position:0%
+mockery of famous historical films made
+ 
+
+ align:start position:0%
+mockery of famous historical films made
+by DW Griffith it puts down the
+
+ align:start position:0%
+by DW Griffith it puts down the
+ 
+
+ align:start position:0%
+by DW Griffith it puts down the
+pretentiousness and the Marshal Valor
+
+ align:start position:0%
+pretentiousness and the Marshal Valor
+ 
+
+ align:start position:0%
+pretentiousness and the Marshal Valor
+that's celebrated in so many of the
+
+ align:start position:0%
+that's celebrated in so many of the
+ 
+
+ align:start position:0%
+that's celebrated in so many of the
+historical spectacles that Griffith and
+
+ align:start position:0%
+historical spectacles that Griffith and
+ 
+
+ align:start position:0%
+historical spectacles that Griffith and
+other serious directors were making at
+
+ align:start position:0%
+other serious directors were making at
+ 
+
+ align:start position:0%
+other serious directors were making at
+the time uh and it and it also goes back
+
+ align:start position:0%
+the time uh and it and it also goes back
+ 
+
+ align:start position:0%
+the time uh and it and it also goes back
+in a certain way to the very roots of
+
+ align:start position:0%
+in a certain way to the very roots of
+ 
+
+ align:start position:0%
+in a certain way to the very roots of
+film what was the very first narrative
+
+ align:start position:0%
+film what was the very first narrative
+ 
+
+ align:start position:0%
+film what was the very first narrative
+film or one of the very first the the
+
+ align:start position:0%
+film or one of the very first the the
+ 
+
+ align:start position:0%
+film or one of the very first the the
+also a film about a train robbery right
+
+ align:start position:0%
+also a film about a train robbery right
+ 
+
+ align:start position:0%
+also a film about a train robbery right
+called The Great Train Robbery well this
+
+ align:start position:0%
+called The Great Train Robbery well this
+ 
+
+ align:start position:0%
+called The Great Train Robbery well this
+is about a train robbery too and who is
+
+ align:start position:0%
+is about a train robbery too and who is
+ 
+
+ align:start position:0%
+is about a train robbery too and who is
+the central character in this film
+
+ align:start position:0%
+the central character in this film
+ 
+
+ align:start position:0%
+the central character in this film
+really a a train is the central object
+
+ align:start position:0%
+really a a train is the central object
+ 
+
+ align:start position:0%
+really a a train is the central object
+the central more more interesting in
+
+ align:start position:0%
+the central more more interesting in
+ 
+
+ align:start position:0%
+the central more more interesting in
+some ways than the character himself
+
+ align:start position:0%
+some ways than the character himself
+ 
+
+ align:start position:0%
+some ways than the character himself
+there and there are many other ways in
+
+ align:start position:0%
+there and there are many other ways in
+ 
+
+ align:start position:0%
+there and there are many other ways in
+which the particular features of the
+
+ align:start position:0%
+which the particular features of the
+ 
+
+ align:start position:0%
+which the particular features of the
+general allude to and in some sense
+
+ align:start position:0%
+general allude to and in some sense
+ 
+
+ align:start position:0%
+general allude to and in some sense
+summarize the history of silent film and
+
+ align:start position:0%
+summarize the history of silent film and
+ 
+
+ align:start position:0%
+summarize the history of silent film and
+all of the original audience coming to
+
+ align:start position:0%
+all of the original audience coming to
+ 
+
+ align:start position:0%
+all of the original audience coming to
+see the general would have been of
+
+ align:start position:0%
+see the general would have been of
+ 
+
+ align:start position:0%
+see the general would have been of
+course alert to these connections would
+
+ align:start position:0%
+course alert to these connections would
+ 
+
+ align:start position:0%
+course alert to these connections would
+have been literate in these connections
+
+ align:start position:0%
+have been literate in these connections
+ 
+
+ align:start position:0%
+have been literate in these connections
+wouldn't needed footnotes or professors
+
+ align:start position:0%
+wouldn't needed footnotes or professors
+ 
+
+ align:start position:0%
+wouldn't needed footnotes or professors
+to tell them about it because they would
+
+ align:start position:0%
+to tell them about it because they would
+ 
+
+ align:start position:0%
+to tell them about it because they would
+have lived through the history they
+
+ align:start position:0%
+have lived through the history they
+ 
+
+ align:start position:0%
+have lived through the history they
+would have lived through the history of
+
+ align:start position:0%
+would have lived through the history of
+ 
+
+ align:start position:0%
+would have lived through the history of
+the previous 20 years they would have
+
+ align:start position:0%
+the previous 20 years they would have
+ 
+
+ align:start position:0%
+the previous 20 years they would have
+seen other Katon films they would have
+
+ align:start position:0%
+seen other Katon films they would have
+ 
+
+ align:start position:0%
+seen other Katon films they would have
+seen DW Griffith they would have the
+
+ align:start position:0%
+seen DW Griffith they would have the
+ 
+
+ align:start position:0%
+seen DW Griffith they would have the
+history of the of the uh medium of
+
+ align:start position:0%
+history of the of the uh medium of
+ 
+
+ align:start position:0%
+history of the of the uh medium of
+movies in their heads when they sat down
+
+ align:start position:0%
+movies in their heads when they sat down
+ 
+
+ align:start position:0%
+movies in their heads when they sat down
+to watch the general so that's another
+
+ align:start position:0%
+to watch the general so that's another
+ 
+
+ align:start position:0%
+to watch the general so that's another
+way in which the general is a profoundly
+
+ align:start position:0%
+way in which the general is a profoundly
+ 
+
+ align:start position:0%
+way in which the general is a profoundly
+culminating text I'm sorry I ran over I
+
+ align:start position:0%
+culminating text I'm sorry I ran over I
+ 
+
+ align:start position:0%
+culminating text I'm sorry I ran over I
+will not do it hereafter
\ No newline at end of file
diff --git a/K1dbnQDAG8Q.txt b/K1dbnQDAG8Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..866ac31cfa602288ad629ad344bf83071ad1e728
--- /dev/null
+++ b/K1dbnQDAG8Q.txt
@@ -0,0 +1,233 @@
+Serial point-to-point links
+are the modern replacement
+
+for the parallel
+communications bus
+
+with all its electrical
+and timing issues.
+
+0..08 Each link is
+unidirectional and has only
+
+a single driver and the receiver
+recovers the clock signal from
+
+the data stream, so there are
+no complications from sharing
+
+the channel, clock skew,
+and electrical problems.
+
+The very controlled electrical
+environment enables very high
+
+signaling rates, well up into
+the gigahertz range using
+
+today’s technologies.
+
+If more throughput
+is needed, you
+
+can use multiple serial
+links in parallel.
+
+Extra logic is needed to
+reassemble the original data
+
+from multiple packets sent in
+parallel over multiple links,
+
+but the cost of the
+required logic gates
+
+is very modest in
+current technologies.
+
+Note that the expansion
+strategy of modern systems
+
+still uses the notion
+of an add-in card that
+
+plugs into the motherboard.
+
+But instead of connecting
+to a parallel bus,
+
+the add-in card
+connects to one or more
+
+point-to-point
+communication links.
+
+Here’s the system-level
+communications diagram
+
+for a recent system based on
+an Intel Core i7 CPU chip.
+
+The CPU is connected
+directly to the memories
+
+for the highest-possible
+memory bandwidth,
+
+but talks to all
+the other components
+
+over the QuickPath
+Interconnect (QPI),
+
+which has 20
+differential signaling
+
+paths in each direction.
+
+QPI supports up to 6.4
+billion 20-bit transfers
+
+in each direction every second.
+
+All the other
+communication channels
+
+(USB, PCIe, networks,
+Serial ATA, Audio, etc.)
+
+are also serial links,
+providing various communication
+
+bandwidths depending
+on the application.
+
+Reading about the QPI
+channel used by the CPU
+
+reminded me a lot
+of the one ring
+
+that could be used
+to control all
+
+of Middle Earth in the Tolkien
+trilogy Lord of the Rings.
+
+Why mess around with a lot
+of specialized communication
+
+channels when you have a single
+solution that’s powerful enough
+
+to solve all your
+communication needs?
+
+PCI Express (PCIe) is often
+used as the communication
+
+link between components
+on the system motherboard.
+
+A single PCIe version 2 “lane”
+transmits data at 5 Gb/sec
+
+using low-voltage differential
+signaling (LVDS) over wires
+
+designed to have a 100-Ohm
+characteristic impedance.
+
+The PCIe lane is
+under the control
+
+of the same sort of network
+stack as described earlier.
+
+The physical layer transmits
+packet data through the wire.
+
+Each packet starts with
+a training sequence
+
+to synchronize the receiver’s
+clock-recovery circuitry,
+
+followed by a unique
+start sequence,
+
+then the packet’s data payload,
+and ends with a unique end
+
+sequence.
+
+The physical layer payload is
+organized as a sequence number,
+
+a transaction-layer payload
+and a cyclical redundancy check
+
+sequence that’s used
+to validate the data.
+
+Using the sequence number,
+the data link layer
+
+can tell when a packet
+has been dropped
+
+and request the transmitter
+restart transmission
+
+at the missing packet.
+
+It also deals with
+flow control issues.
+
+Finally, the transaction
+layer reassembles the message
+
+from the transaction layer
+payloads from all the lanes
+
+and uses the header to identify
+the intended recipient at the
+
+receive end.
+
+Altogether, a significant amount
+of logic is needed to send
+
+and receive messages
+on multiple PCIe lanes,
+
+but the cost is quite acceptable
+when using today’s integrated
+
+circuit technologies.
+
+Using 8 lanes, the maximum
+transfer rate is 4 GB/sec,
+
+capable of satisfying the needs
+of high-performance peripherals
+
+such as graphics cards.
+
+So knowledge from
+the networking world
+
+has reshaped how components
+communicate on the motherboard,
+
+driving the transition
+from parallel buses
+
+to a handful of serial
+point-to-point links.
+
+As a result today’s systems
+are faster, more reliable,
+
+more energy-efficient and
+smaller than ever before.
\ No newline at end of file
diff --git a/KKj4FAMF1Bk.txt b/KKj4FAMF1Bk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb33fc71ff6cc1ce7481ae6112bf023ff4c21331
--- /dev/null
+++ b/KKj4FAMF1Bk.txt
@@ -0,0 +1,251 @@
+align:start position:0%
+ 
+really good really good yeah yeah very
+
+ align:start position:0%
+really good really good yeah yeah very
+ 
+
+ align:start position:0%
+really good really good yeah yeah very
+very excited um I have like three most
+
+ align:start position:0%
+very excited um I have like three most
+ 
+
+ align:start position:0%
+very excited um I have like three most
+useful things so I don't know what what
+
+ align:start position:0%
+useful things so I don't know what what
+ 
+
+ align:start position:0%
+useful things so I don't know what what
+that counts is but I think you have like
+
+ align:start position:0%
+that counts is but I think you have like
+ 
+
+ align:start position:0%
+that counts is but I think you have like
+firstly you have preparation like I
+
+ align:start position:0%
+firstly you have preparation like I
+ 
+
+ align:start position:0%
+firstly you have preparation like I
+learned a lot about the preparation
+
+ align:start position:0%
+learned a lot about the preparation
+ 
+
+ align:start position:0%
+learned a lot about the preparation
+process in a video which I previously
+
+ align:start position:0%
+process in a video which I previously
+ 
+
+ align:start position:0%
+process in a video which I previously
+did actually consider I used to think of
+
+ align:start position:0%
+did actually consider I used to think of
+ 
+
+ align:start position:0%
+did actually consider I used to think of
+people with their shaky cameras I didn't
+
+ align:start position:0%
+people with their shaky cameras I didn't
+ 
+
+ align:start position:0%
+people with their shaky cameras I didn't
+actually have an idea of what they're
+
+ align:start position:0%
+actually have an idea of what they're
+ 
+
+ align:start position:0%
+actually have an idea of what they're
+doing but most of the time they probably
+
+ align:start position:0%
+doing but most of the time they probably
+ 
+
+ align:start position:0%
+doing but most of the time they probably
+had a storyboard and it's not like by
+
+ align:start position:0%
+had a storyboard and it's not like by
+ 
+
+ align:start position:0%
+had a storyboard and it's not like by
+accident and then eventually becomes the
+
+ align:start position:0%
+accident and then eventually becomes the
+ 
+
+ align:start position:0%
+accident and then eventually becomes the
+idea of iteration so you have to keep
+
+ align:start position:0%
+idea of iteration so you have to keep
+ 
+
+ align:start position:0%
+idea of iteration so you have to keep
+keep trying different scenes many many
+
+ align:start position:0%
+keep trying different scenes many many
+ 
+
+ align:start position:0%
+keep trying different scenes many many
+takes and never never came to my mind
+
+ align:start position:0%
+takes and never never came to my mind
+ 
+
+ align:start position:0%
+takes and never never came to my mind
+and lastly like you have to have the
+
+ align:start position:0%
+and lastly like you have to have the
+ 
+
+ align:start position:0%
+and lastly like you have to have the
+passion for this if because you would do
+
+ align:start position:0%
+passion for this if because you would do
+ 
+
+ align:start position:0%
+passion for this if because you would do
+a lot of takes you'll be pretty sleepy
+
+ align:start position:0%
+a lot of takes you'll be pretty sleepy
+ 
+
+ align:start position:0%
+a lot of takes you'll be pretty sleepy
+after a while but you pretty you you
+
+ align:start position:0%
+after a while but you pretty you you
+ 
+
+ align:start position:0%
+after a while but you pretty you you
+love what you're done and I'm kind of
+
+ align:start position:0%
+love what you're done and I'm kind of
+ 
+
+ align:start position:0%
+love what you're done and I'm kind of
+excited to show what I have yeah yeah I
+
+ align:start position:0%
+excited to show what I have yeah yeah I
+ 
+
+ align:start position:0%
+excited to show what I have yeah yeah I
+guess the hardest part is there's so
+
+ align:start position:0%
+guess the hardest part is there's so
+ 
+
+ align:start position:0%
+guess the hardest part is there's so
+much content and there's a lot of
+
+ align:start position:0%
+much content and there's a lot of
+ 
+
+ align:start position:0%
+much content and there's a lot of
+technical stuff that I wish I knew like
+
+ align:start position:0%
+technical stuff that I wish I knew like
+ 
+
+ align:start position:0%
+technical stuff that I wish I knew like
+I wish I knew more about the the
+
+ align:start position:0%
+I wish I knew more about the the
+ 
+
+ align:start position:0%
+I wish I knew more about the the
+creative suite and like the software so
+
+ align:start position:0%
+creative suite and like the software so
+ 
+
+ align:start position:0%
+creative suite and like the software so
+i guess i was a limited in that
+
+ align:start position:0%
+i guess i was a limited in that
+ 
+
+ align:start position:0%
+i guess i was a limited in that
+department but other than that I think
+
+ align:start position:0%
+department but other than that I think
+ 
+
+ align:start position:0%
+department but other than that I think
+the preparation part gives me that
+
+ align:start position:0%
+the preparation part gives me that
+ 
+
+ align:start position:0%
+the preparation part gives me that
+background helps me to do a lot of
+
+ align:start position:0%
+background helps me to do a lot of
+ 
+
+ align:start position:0%
+background helps me to do a lot of
+different things yeah yeah thank you
\ No newline at end of file
diff --git a/KlAjiDivJoQ.txt b/KlAjiDivJoQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..56a99aca1563e83fdf724da423bea88ad4d400cf
--- /dev/null
+++ b/KlAjiDivJoQ.txt
@@ -0,0 +1,10747 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today we are going to prove
+
+ align:start position:0%
+today we are going to prove
+ 
+
+ align:start position:0%
+today we are going to prove
+uh the theorem that I mentioned last
+
+ align:start position:0%
+uh the theorem that I mentioned last
+ 
+
+ align:start position:0%
+uh the theorem that I mentioned last
+time the Han banak theorem which is
+
+ align:start position:0%
+time the Han banak theorem which is
+ 
+
+ align:start position:0%
+time the Han banak theorem which is
+um a theorem about
+
+ align:start position:0%
+um a theorem about
+ 
+
+ align:start position:0%
+um a theorem about
+being able to extend uh bounded linear
+
+ align:start position:0%
+being able to extend uh bounded linear
+ 
+
+ align:start position:0%
+being able to extend uh bounded linear
+functionals on some Subspace of a norm
+
+ align:start position:0%
+functionals on some Subspace of a norm
+ 
+
+ align:start position:0%
+functionals on some Subspace of a norm
+space to all of the norm space and this
+
+ align:start position:0%
+space to all of the norm space and this
+ 
+
+ align:start position:0%
+space to all of the norm space and this
+will therefore you know answer the
+
+ align:start position:0%
+will therefore you know answer the
+ 
+
+ align:start position:0%
+will therefore you know answer the
+question that we posed at the beginning
+
+ align:start position:0%
+question that we posed at the beginning
+ 
+
+ align:start position:0%
+question that we posed at the beginning
+of this topic
+
+ align:start position:0%
+of this topic
+ 
+
+ align:start position:0%
+of this topic
+whether or not uh
+
+ align:start position:0%
+whether or not uh
+ 
+
+ align:start position:0%
+whether or not uh
+the Dual which is the space of all
+
+ align:start position:0%
+the Dual which is the space of all
+ 
+
+ align:start position:0%
+the Dual which is the space of all
+bounded linear functionals on a norm
+
+ align:start position:0%
+bounded linear functionals on a norm
+ 
+
+ align:start position:0%
+bounded linear functionals on a norm
+space is non-trivial for for every Norm
+
+ align:start position:0%
+space is non-trivial for for every Norm
+ 
+
+ align:start position:0%
+space is non-trivial for for every Norm
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+now one of the tools we're going to need
+
+ align:start position:0%
+now one of the tools we're going to need
+ 
+
+ align:start position:0%
+now one of the tools we're going to need
+is this uh
+
+ align:start position:0%
+is this uh
+ 
+
+ align:start position:0%
+is this uh
+Axiom or Lemma from set theory which is
+
+ align:start position:0%
+Axiom or Lemma from set theory which is
+ 
+
+ align:start position:0%
+Axiom or Lemma from set theory which is
+due to Zorn which is as following so
+
+ align:start position:0%
+due to Zorn which is as following so
+ 
+
+ align:start position:0%
+due to Zorn which is as following so
+um I'm gonna have to recall from the
+
+ align:start position:0%
+um I'm gonna have to recall from the
+ 
+
+ align:start position:0%
+um I'm gonna have to recall from the
+last lecture what some of these words
+
+ align:start position:0%
+last lecture what some of these words
+ 
+
+ align:start position:0%
+last lecture what some of these words
+mean but so Zorn's limma states that if
+
+ align:start position:0%
+mean but so Zorn's limma states that if
+ 
+
+ align:start position:0%
+mean but so Zorn's limma states that if
+every chain in a non-empty partially
+
+ align:start position:0%
+every chain in a non-empty partially
+ 
+
+ align:start position:0%
+every chain in a non-empty partially
+ordered set e has an upper bound then e
+
+ align:start position:0%
+ordered set e has an upper bound then e
+ 
+
+ align:start position:0%
+ordered set e has an upper bound then e
+has a maximal element so a partially
+
+ align:start position:0%
+has a maximal element so a partially
+ 
+
+ align:start position:0%
+has a maximal element so a partially
+ordered set e that means to set e with a
+
+ align:start position:0%
+ordered set e that means to set e with a
+ 
+
+ align:start position:0%
+ordered set e that means to set e with a
+relation that's basically like a less
+
+ align:start position:0%
+relation that's basically like a less
+ 
+
+ align:start position:0%
+relation that's basically like a less
+than or equal to okay that satisfies
+
+ align:start position:0%
+than or equal to okay that satisfies
+ 
+
+ align:start position:0%
+than or equal to okay that satisfies
+three properties so that it's like a
+
+ align:start position:0%
+three properties so that it's like a
+ 
+
+ align:start position:0%
+three properties so that it's like a
+extended less than or equal to
+
+ align:start position:0%
+extended less than or equal to
+ 
+
+ align:start position:0%
+extended less than or equal to
+and a chain is a subset of e so that any
+
+ align:start position:0%
+and a chain is a subset of e so that any
+ 
+
+ align:start position:0%
+and a chain is a subset of e so that any
+two elements in that subset can be
+
+ align:start position:0%
+two elements in that subset can be
+ 
+
+ align:start position:0%
+two elements in that subset can be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+can be compared okay one is either
+
+ align:start position:0%
+can be compared okay one is either
+ 
+
+ align:start position:0%
+can be compared okay one is either
+bigger than or equal to the other
+
+ align:start position:0%
+bigger than or equal to the other
+ 
+
+ align:start position:0%
+bigger than or equal to the other
+or one is always bigger than or equal to
+
+ align:start position:0%
+or one is always bigger than or equal to
+ 
+
+ align:start position:0%
+or one is always bigger than or equal to
+the other okay
+
+ align:start position:0%
+the other okay
+ 
+
+ align:start position:0%
+the other okay
+and so this theorem says that if every
+
+ align:start position:0%
+and so this theorem says that if every
+ 
+
+ align:start position:0%
+and so this theorem says that if every
+chain of a partially ordered set has an
+
+ align:start position:0%
+chain of a partially ordered set has an
+ 
+
+ align:start position:0%
+chain of a partially ordered set has an
+upper bound that has a pretty uh
+
+ align:start position:0%
+upper bound that has a pretty uh
+ 
+
+ align:start position:0%
+upper bound that has a pretty uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+clear meaning then e has a maximal
+
+ align:start position:0%
+clear meaning then e has a maximal
+ 
+
+ align:start position:0%
+clear meaning then e has a maximal
+element so a maximal element of e that
+
+ align:start position:0%
+element so a maximal element of e that
+ 
+
+ align:start position:0%
+element so a maximal element of e that
+means an element that is not less than
+
+ align:start position:0%
+means an element that is not less than
+ 
+
+ align:start position:0%
+means an element that is not less than
+or equal to something
+
+ align:start position:0%
+or equal to something
+ 
+
+ align:start position:0%
+or equal to something
+other than itself
+
+ align:start position:0%
+other than itself
+ 
+
+ align:start position:0%
+other than itself
+okay so anything bigger than or equal to
+
+ align:start position:0%
+okay so anything bigger than or equal to
+ 
+
+ align:start position:0%
+okay so anything bigger than or equal to
+this maximal element has to be that
+
+ align:start position:0%
+this maximal element has to be that
+ 
+
+ align:start position:0%
+this maximal element has to be that
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+okay a maximal element is not
+
+ align:start position:0%
+okay a maximal element is not
+ 
+
+ align:start position:0%
+okay a maximal element is not
+necessarily an upper bound okay a
+
+ align:start position:0%
+necessarily an upper bound okay a
+ 
+
+ align:start position:0%
+necessarily an upper bound okay a
+maximal element just means it cannot be
+
+ align:start position:0%
+maximal element just means it cannot be
+ 
+
+ align:start position:0%
+maximal element just means it cannot be
+uh you know nothing can get it get over
+
+ align:start position:0%
+uh you know nothing can get it get over
+ 
+
+ align:start position:0%
+uh you know nothing can get it get over
+its head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and so as a warm-up we're
+
+ align:start position:0%
+all right and so as a warm-up we're
+ 
+
+ align:start position:0%
+all right and so as a warm-up we're
+going to use Zorn's Lemma to prove a
+
+ align:start position:0%
+going to use Zorn's Lemma to prove a
+ 
+
+ align:start position:0%
+going to use Zorn's Lemma to prove a
+fact about
+
+ align:start position:0%
+fact about
+ 
+
+ align:start position:0%
+fact about
+Vector spaces
+
+ align:start position:0%
+Vector spaces
+ 
+
+ align:start position:0%
+Vector spaces
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a Hammel basis and I think I went over
+
+ align:start position:0%
+a Hammel basis and I think I went over
+ 
+
+ align:start position:0%
+a Hammel basis and I think I went over
+this at the end of class last time of a
+
+ align:start position:0%
+this at the end of class last time of a
+ 
+
+ align:start position:0%
+this at the end of class last time of a
+vector space V
+
+ align:start position:0%
+vector space V
+ 
+
+ align:start position:0%
+vector space V
+this is a linear independent set
+
+ align:start position:0%
+this is a linear independent set
+ 
+
+ align:start position:0%
+this is a linear independent set
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+such that every element of V is a finite
+
+ align:start position:0%
+such that every element of V is a finite
+ 
+
+ align:start position:0%
+such that every element of V is a finite
+linear combination of the elements from
+
+ align:start position:0%
+linear combination of the elements from
+ 
+
+ align:start position:0%
+linear combination of the elements from
+H so for example this set consisting of
+
+ align:start position:0%
+H so for example this set consisting of
+ 
+
+ align:start position:0%
+H so for example this set consisting of
+uh you know the vector 1 0 and the other
+
+ align:start position:0%
+uh you know the vector 1 0 and the other
+ 
+
+ align:start position:0%
+uh you know the vector 1 0 and the other
+and the vector 0 1 this is a Hamel basis
+
+ align:start position:0%
+and the vector 0 1 this is a Hamel basis
+ 
+
+ align:start position:0%
+and the vector 0 1 this is a Hamel basis
+for R2 every element in R2 can be
+
+ align:start position:0%
+for R2 every element in R2 can be
+ 
+
+ align:start position:0%
+for R2 every element in R2 can be
+written as a finite linear combination
+
+ align:start position:0%
+written as a finite linear combination
+ 
+
+ align:start position:0%
+written as a finite linear combination
+of these guys okay but you know
+
+ align:start position:0%
+of these guys okay but you know
+ 
+
+ align:start position:0%
+of these guys okay but you know
+and this is something uh
+
+ align:start position:0%
+and this is something uh
+ 
+
+ align:start position:0%
+and this is something uh
+you know the fact that finite
+
+ align:start position:0%
+you know the fact that finite
+ 
+
+ align:start position:0%
+you know the fact that finite
+dimensional spaces have bases is you
+
+ align:start position:0%
+dimensional spaces have bases is you
+ 
+
+ align:start position:0%
+dimensional spaces have bases is you
+know something you discuss in linear
+
+ align:start position:0%
+know something you discuss in linear
+ 
+
+ align:start position:0%
+know something you discuss in linear
+algebra but now we're in functional
+
+ align:start position:0%
+algebra but now we're in functional
+ 
+
+ align:start position:0%
+algebra but now we're in functional
+analysis which is linear algebra in
+
+ align:start position:0%
+analysis which is linear algebra in
+ 
+
+ align:start position:0%
+analysis which is linear algebra in
+infinite Dimensions
+
+ align:start position:0%
+infinite Dimensions
+ 
+
+ align:start position:0%
+infinite Dimensions
+um it's not so clear that every
+
+ align:start position:0%
+um it's not so clear that every
+ 
+
+ align:start position:0%
+um it's not so clear that every
+Vector space has a Hammel basis
+
+ align:start position:0%
+Vector space has a Hammel basis
+ 
+
+ align:start position:0%
+Vector space has a Hammel basis
+and so what we're going to do is we're
+
+ align:start position:0%
+and so what we're going to do is we're
+ 
+
+ align:start position:0%
+and so what we're going to do is we're
+going to apply Zorn's Lemma to prove
+
+ align:start position:0%
+going to apply Zorn's Lemma to prove
+ 
+
+ align:start position:0%
+going to apply Zorn's Lemma to prove
+that every Vector space does have a heml
+
+ align:start position:0%
+that every Vector space does have a heml
+ 
+
+ align:start position:0%
+that every Vector space does have a heml
+basis so this is the following theorem
+
+ align:start position:0%
+basis so this is the following theorem
+ 
+
+ align:start position:0%
+basis so this is the following theorem
+and this argument will kind of
+
+ align:start position:0%
+and this argument will kind of
+ 
+
+ align:start position:0%
+and this argument will kind of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+be a warm-up for how we'll apply Zorn to
+
+ align:start position:0%
+be a warm-up for how we'll apply Zorn to
+ 
+
+ align:start position:0%
+be a warm-up for how we'll apply Zorn to
+to prove the Han banak theorem so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if B is a vector space
+
+ align:start position:0%
+if B is a vector space
+ 
+
+ align:start position:0%
+if B is a vector space
+then V has
+
+ align:start position:0%
+then V has
+ 
+
+ align:start position:0%
+then V has
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hammel basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the proof
+
+ align:start position:0%
+for the proof
+ 
+
+ align:start position:0%
+for the proof
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I am going to apply Zorn so I need to
+
+ align:start position:0%
+I am going to apply Zorn so I need to
+ 
+
+ align:start position:0%
+I am going to apply Zorn so I need to
+have some ordered set and my ordered set
+
+ align:start position:0%
+have some ordered set and my ordered set
+ 
+
+ align:start position:0%
+have some ordered set and my ordered set
+is going to be
+
+ align:start position:0%
+is going to be
+ 
+
+ align:start position:0%
+is going to be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let e be the set of all uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linearly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsets of V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to Define an order on E
+
+ align:start position:0%
+and we're going to Define an order on E
+ 
+
+ align:start position:0%
+and we're going to Define an order on E
+so e is the set of all subsets of V that
+
+ align:start position:0%
+so e is the set of all subsets of V that
+ 
+
+ align:start position:0%
+so e is the set of all subsets of V that
+are linearly independent
+
+ align:start position:0%
+are linearly independent
+ 
+
+ align:start position:0%
+are linearly independent
+and we Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial order on E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inclusion so these are just the elements
+
+ align:start position:0%
+inclusion so these are just the elements
+ 
+
+ align:start position:0%
+inclusion so these are just the elements
+of e are subsets of V so we'll say one
+
+ align:start position:0%
+of e are subsets of V so we'll say one
+ 
+
+ align:start position:0%
+of e are subsets of V so we'll say one
+subset is less than or equal to another
+
+ align:start position:0%
+subset is less than or equal to another
+ 
+
+ align:start position:0%
+subset is less than or equal to another
+subset if one is included in the other
+
+ align:start position:0%
+subset if one is included in the other
+ 
+
+ align:start position:0%
+subset if one is included in the other
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e and e Prime and E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we'll say e is less than or equal
+
+ align:start position:0%
+then we'll say e is less than or equal
+ 
+
+ align:start position:0%
+then we'll say e is less than or equal
+to e Prime if and only if this subset of
+
+ align:start position:0%
+to e Prime if and only if this subset of
+ 
+
+ align:start position:0%
+to e Prime if and only if this subset of
+e this subset of v e is a subset of e
+
+ align:start position:0%
+e this subset of v e is a subset of e
+ 
+
+ align:start position:0%
+e this subset of v e is a subset of e
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+okay and again so I think I said this in
+
+ align:start position:0%
+okay and again so I think I said this in
+ 
+
+ align:start position:0%
+okay and again so I think I said this in
+a previous lecture I'm kind of used to
+
+ align:start position:0%
+a previous lecture I'm kind of used to
+ 
+
+ align:start position:0%
+a previous lecture I'm kind of used to
+using this notation for
+
+ align:start position:0%
+using this notation for
+ 
+
+ align:start position:0%
+using this notation for
+a subset not necessarily a strict subset
+
+ align:start position:0%
+a subset not necessarily a strict subset
+ 
+
+ align:start position:0%
+a subset not necessarily a strict subset
+just from teaching 18100a last semester
+
+ align:start position:0%
+just from teaching 18100a last semester
+ 
+
+ align:start position:0%
+just from teaching 18100a last semester
+so this does not mean a strict subset so
+
+ align:start position:0%
+so this does not mean a strict subset so
+ 
+
+ align:start position:0%
+so this does not mean a strict subset so
+maybe you know you know put that in
+
+ align:start position:0%
+maybe you know you know put that in
+ 
+
+ align:start position:0%
+maybe you know you know put that in
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is my partially ordered set
+
+ align:start position:0%
+okay so this is my partially ordered set
+ 
+
+ align:start position:0%
+okay so this is my partially ordered set
+which I hope to apply the Zorn Zorn's
+
+ align:start position:0%
+which I hope to apply the Zorn Zorn's
+ 
+
+ align:start position:0%
+which I hope to apply the Zorn Zorn's
+Lemma on and then what I will show is
+
+ align:start position:0%
+Lemma on and then what I will show is
+ 
+
+ align:start position:0%
+Lemma on and then what I will show is
+that the maximal element of this set
+
+ align:start position:0%
+that the maximal element of this set
+ 
+
+ align:start position:0%
+that the maximal element of this set
+once I show it exists in fact has to be
+
+ align:start position:0%
+once I show it exists in fact has to be
+ 
+
+ align:start position:0%
+once I show it exists in fact has to be
+a hammer basis for V
+
+ align:start position:0%
+a hammer basis for V
+ 
+
+ align:start position:0%
+a hammer basis for V
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now we'll apply Zorn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+towards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find Zorn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a chain in e
+
+ align:start position:0%
+be a chain in e
+ 
+
+ align:start position:0%
+be a chain in e
+okay that means any two elements of C
+
+ align:start position:0%
+okay that means any two elements of C
+ 
+
+ align:start position:0%
+okay that means any two elements of C
+can be compared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to find little C to be equal to
+
+ align:start position:0%
+to find little C to be equal to
+ 
+
+ align:start position:0%
+to find little C to be equal to
+Union overall
+
+ align:start position:0%
+Union overall
+ 
+
+ align:start position:0%
+Union overall
+e and capital c e
+
+ align:start position:0%
+e and capital c e
+ 
+
+ align:start position:0%
+e and capital c e
+all right so each of these Little E's
+
+ align:start position:0%
+all right so each of these Little E's
+ 
+
+ align:start position:0%
+all right so each of these Little E's
+this is a subset of V consisting of
+
+ align:start position:0%
+this is a subset of V consisting of
+ 
+
+ align:start position:0%
+this is a subset of V consisting of
+linearly independent elements and now
+
+ align:start position:0%
+linearly independent elements and now
+ 
+
+ align:start position:0%
+linearly independent elements and now
+what I'm taking little C to B is the
+
+ align:start position:0%
+what I'm taking little C to B is the
+ 
+
+ align:start position:0%
+what I'm taking little C to B is the
+union of all these subsets of linearly
+
+ align:start position:0%
+union of all these subsets of linearly
+ 
+
+ align:start position:0%
+union of all these subsets of linearly
+independent elements
+
+ align:start position:0%
+independent elements
+ 
+
+ align:start position:0%
+independent elements
+okay and I claim that this is a a
+
+ align:start position:0%
+okay and I claim that this is a a
+ 
+
+ align:start position:0%
+okay and I claim that this is a a
+linearly independent subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which you know since
+
+ align:start position:0%
+which you know since
+ 
+
+ align:start position:0%
+which you know since
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+subset or of V contains every element of
+
+ align:start position:0%
+subset or of V contains every element of
+ 
+
+ align:start position:0%
+subset or of V contains every element of
+c means C is bigger than or equal to all
+
+ align:start position:0%
+c means C is bigger than or equal to all
+ 
+
+ align:start position:0%
+c means C is bigger than or equal to all
+of E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C is
+
+ align:start position:0%
+C is
+ 
+
+ align:start position:0%
+C is
+an upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for C okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we just need to show that little c is
+
+ align:start position:0%
+so we just need to show that little c is
+ 
+
+ align:start position:0%
+so we just need to show that little c is
+now linearly independent subset and
+
+ align:start position:0%
+now linearly independent subset and
+ 
+
+ align:start position:0%
+now linearly independent subset and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+um all of these e's in this Capital C
+
+ align:start position:0%
+um all of these e's in this Capital C
+ 
+
+ align:start position:0%
+um all of these e's in this Capital C
+are bounded above by C and therefore C
+
+ align:start position:0%
+are bounded above by C and therefore C
+ 
+
+ align:start position:0%
+are bounded above by C and therefore C
+is an upper Bound for Capital C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+to show it's a linearly independent
+
+ align:start position:0%
+to show it's a linearly independent
+ 
+
+ align:start position:0%
+to show it's a linearly independent
+subset we're going to use the fact that
+
+ align:start position:0%
+subset we're going to use the fact that
+ 
+
+ align:start position:0%
+subset we're going to use the fact that
+Capital C is a chain that you can always
+
+ align:start position:0%
+Capital C is a chain that you can always
+ 
+
+ align:start position:0%
+Capital C is a chain that you can always
+compare two things all right so let's
+
+ align:start position:0%
+compare two things all right so let's
+ 
+
+ align:start position:0%
+compare two things all right so let's
+show that little C is a linearly
+
+ align:start position:0%
+show that little C is a linearly
+ 
+
+ align:start position:0%
+show that little C is a linearly
+independent subset that's uh something
+
+ align:start position:0%
+independent subset that's uh something
+ 
+
+ align:start position:0%
+independent subset that's uh something
+very specific so let B1 up to V in
+
+ align:start position:0%
+very specific so let B1 up to V in
+ 
+
+ align:start position:0%
+very specific so let B1 up to V in
+be in
+
+ align:start position:0%
+be in
+ 
+
+ align:start position:0%
+be in
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+little C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists E1 E2
+
+ align:start position:0%
+then there exists E1 E2
+ 
+
+ align:start position:0%
+then there exists E1 E2
+be in in capital c
+
+ align:start position:0%
+be in in capital c
+ 
+
+ align:start position:0%
+be in in capital c
+so little C is the union of all the E's
+
+ align:start position:0%
+so little C is the union of all the E's
+ 
+
+ align:start position:0%
+so little C is the union of all the E's
+so these have to come from somewhere
+
+ align:start position:0%
+so these have to come from somewhere
+ 
+
+ align:start position:0%
+so these have to come from somewhere
+such that uh for all J
+
+ align:start position:0%
+such that uh for all J
+ 
+
+ align:start position:0%
+such that uh for all J
+B J is in EJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um it's not difficult to show by
+
+ align:start position:0%
+um it's not difficult to show by
+ 
+
+ align:start position:0%
+um it's not difficult to show by
+induction that since I can compare any
+
+ align:start position:0%
+induction that since I can compare any
+ 
+
+ align:start position:0%
+induction that since I can compare any
+two elements in C I can compare
+
+ align:start position:0%
+two elements in C I can compare
+ 
+
+ align:start position:0%
+two elements in C I can compare
+uh any n elements
+
+ align:start position:0%
+uh any n elements
+ 
+
+ align:start position:0%
+uh any n elements
+of C meaning I can actually order any
+
+ align:start position:0%
+of C meaning I can actually order any
+ 
+
+ align:start position:0%
+of C meaning I can actually order any
+finitely many elements in C right so
+
+ align:start position:0%
+finitely many elements in C right so
+ 
+
+ align:start position:0%
+finitely many elements in C right so
+again linear so to say this is a
+
+ align:start position:0%
+again linear so to say this is a
+ 
+
+ align:start position:0%
+again linear so to say this is a
+chain means I can always order two
+
+ align:start position:0%
+chain means I can always order two
+ 
+
+ align:start position:0%
+chain means I can always order two
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+but by induction it's not difficult to
+
+ align:start position:0%
+but by induction it's not difficult to
+ 
+
+ align:start position:0%
+but by induction it's not difficult to
+show I can always order n elements of C
+
+ align:start position:0%
+show I can always order n elements of C
+ 
+
+ align:start position:0%
+show I can always order n elements of C
+so I'm just going to skip to that and
+
+ align:start position:0%
+so I'm just going to skip to that and
+ 
+
+ align:start position:0%
+so I'm just going to skip to that and
+I'll leave it to you
+
+ align:start position:0%
+I'll leave it to you
+ 
+
+ align:start position:0%
+I'll leave it to you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+meaning that I can always find a biggest
+
+ align:start position:0%
+meaning that I can always find a biggest
+ 
+
+ align:start position:0%
+meaning that I can always find a biggest
+element out of any finite collection of
+
+ align:start position:0%
+element out of any finite collection of
+ 
+
+ align:start position:0%
+element out of any finite collection of
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+since C is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+there exists capital j
+
+ align:start position:0%
+there exists capital j
+ 
+
+ align:start position:0%
+there exists capital j
+such that for all J equals one up to n
+
+ align:start position:0%
+such that for all J equals one up to n
+ 
+
+ align:start position:0%
+such that for all J equals one up to n
+e j
+
+ align:start position:0%
+e j
+ 
+
+ align:start position:0%
+e j
+is less than or equal to E capital j
+
+ align:start position:0%
+is less than or equal to E capital j
+ 
+
+ align:start position:0%
+is less than or equal to E capital j
+which again remember this means that e j
+
+ align:start position:0%
+which again remember this means that e j
+ 
+
+ align:start position:0%
+which again remember this means that e j
+is a subset of E capital J just by how
+
+ align:start position:0%
+is a subset of E capital J just by how
+ 
+
+ align:start position:0%
+is a subset of E capital J just by how
+we've defined this partial order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+since all of these ejs for J from 1 to n
+
+ align:start position:0%
+since all of these ejs for J from 1 to n
+ 
+
+ align:start position:0%
+since all of these ejs for J from 1 to n
+are contained in this e sub capital j
+
+ align:start position:0%
+are contained in this e sub capital j
+ 
+
+ align:start position:0%
+are contained in this e sub capital j
+that means that V1 up to VN are n e
+
+ align:start position:0%
+that means that V1 up to VN are n e
+ 
+
+ align:start position:0%
+that means that V1 up to VN are n e
+capital j
+
+ align:start position:0%
+capital j
+ 
+
+ align:start position:0%
+capital j
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I had this uh finitely many from C I
+
+ align:start position:0%
+so I had this uh finitely many from C I
+ 
+
+ align:start position:0%
+so I had this uh finitely many from C I
+can always compare any two of them and
+
+ align:start position:0%
+can always compare any two of them and
+ 
+
+ align:start position:0%
+can always compare any two of them and
+therefore I pick the biggest linearly
+
+ align:start position:0%
+therefore I pick the biggest linearly
+ 
+
+ align:start position:0%
+therefore I pick the biggest linearly
+independent subset out of this finitely
+
+ align:start position:0%
+independent subset out of this finitely
+ 
+
+ align:start position:0%
+independent subset out of this finitely
+mini and all of these vectors have to
+
+ align:start position:0%
+mini and all of these vectors have to
+ 
+
+ align:start position:0%
+mini and all of these vectors have to
+then come from that linearly independent
+
+ align:start position:0%
+then come from that linearly independent
+ 
+
+ align:start position:0%
+then come from that linearly independent
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+since this is a linearly independent
+
+ align:start position:0%
+since this is a linearly independent
+ 
+
+ align:start position:0%
+since this is a linearly independent
+subset that means these are linearly
+
+ align:start position:0%
+subset that means these are linearly
+ 
+
+ align:start position:0%
+subset that means these are linearly
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or linearly
+
+ align:start position:0%
+or linearly
+ 
+
+ align:start position:0%
+or linearly
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since e j
+
+ align:start position:0%
+since e j
+ 
+
+ align:start position:0%
+since e j
+is a linearly independent subset okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we've shown every finite
+
+ align:start position:0%
+and so we've shown every finite
+ 
+
+ align:start position:0%
+and so we've shown every finite
+collection of vectors and C is linearly
+
+ align:start position:0%
+collection of vectors and C is linearly
+ 
+
+ align:start position:0%
+collection of vectors and C is linearly
+independent so we've concluded that
+
+ align:start position:0%
+independent so we've concluded that
+ 
+
+ align:start position:0%
+independent so we've concluded that
+little C is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collection of linearly independent
+
+ align:start position:0%
+collection of linearly independent
+ 
+
+ align:start position:0%
+collection of linearly independent
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so we've now shown that the
+
+ align:start position:0%
+Okay so we've now shown that the
+ 
+
+ align:start position:0%
+Okay so we've now shown that the
+hypotheses of Zorn are verified that
+
+ align:start position:0%
+hypotheses of Zorn are verified that
+ 
+
+ align:start position:0%
+hypotheses of Zorn are verified that
+every chain has an upper bound
+
+ align:start position:0%
+every chain has an upper bound
+ 
+
+ align:start position:0%
+every chain has an upper bound
+and therefore this set e has a maximal
+
+ align:start position:0%
+and therefore this set e has a maximal
+ 
+
+ align:start position:0%
+and therefore this set e has a maximal
+element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+element which I'll call H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I claim that H now
+
+ align:start position:0%
+so I claim that H now
+ 
+
+ align:start position:0%
+so I claim that H now
+spans uh the vector space V meaning
+
+ align:start position:0%
+spans uh the vector space V meaning
+ 
+
+ align:start position:0%
+spans uh the vector space V meaning
+every element of V is can be written as
+
+ align:start position:0%
+every element of V is can be written as
+ 
+
+ align:start position:0%
+every element of V is can be written as
+a finite linear combination of of
+
+ align:start position:0%
+a finite linear combination of of
+ 
+
+ align:start position:0%
+a finite linear combination of of
+elements of H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim
+
+ align:start position:0%
+claim
+ 
+
+ align:start position:0%
+claim
+and H
+
+ align:start position:0%
+and H
+ 
+
+ align:start position:0%
+and H
+spans V so when I say h spans V that's
+
+ align:start position:0%
+spans V so when I say h spans V that's
+ 
+
+ align:start position:0%
+spans V so when I say h spans V that's
+just a short way of saying that every
+
+ align:start position:0%
+just a short way of saying that every
+ 
+
+ align:start position:0%
+just a short way of saying that every
+element of V can be written as a finite
+
+ align:start position:0%
+element of V can be written as a finite
+ 
+
+ align:start position:0%
+element of V can be written as a finite
+linear combination of elements of H
+
+ align:start position:0%
+linear combination of elements of H
+ 
+
+ align:start position:0%
+linear combination of elements of H
+so suppose not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists an element V in capital V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cannot be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+written as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+linear combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of elements
+
+ align:start position:0%
+of elements
+ 
+
+ align:start position:0%
+of elements
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+now it's you know something from linear
+
+ align:start position:0%
+now it's you know something from linear
+ 
+
+ align:start position:0%
+now it's you know something from linear
+algebra I'm sure they went over this
+
+ align:start position:0%
+algebra I'm sure they went over this
+ 
+
+ align:start position:0%
+algebra I'm sure they went over this
+before but if I have a linearly
+
+ align:start position:0%
+before but if I have a linearly
+ 
+
+ align:start position:0%
+before but if I have a linearly
+independent subset and an element that
+
+ align:start position:0%
+independent subset and an element that
+ 
+
+ align:start position:0%
+independent subset and an element that
+can't be written as a finite linear
+
+ align:start position:0%
+can't be written as a finite linear
+ 
+
+ align:start position:0%
+can't be written as a finite linear
+combination of elements from that subset
+
+ align:start position:0%
+combination of elements from that subset
+ 
+
+ align:start position:0%
+combination of elements from that subset
+than just by adding that element I now
+
+ align:start position:0%
+than just by adding that element I now
+ 
+
+ align:start position:0%
+than just by adding that element I now
+obtain a new linearly independent subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore I conclude that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set H Union B
+
+ align:start position:0%
+set H Union B
+ 
+
+ align:start position:0%
+set H Union B
+is linearly independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linearly independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+of V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H will be less than meaning it is less
+
+ align:start position:0%
+H will be less than meaning it is less
+ 
+
+ align:start position:0%
+H will be less than meaning it is less
+than or equal to but not equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies h
+
+ align:start position:0%
+which implies h
+ 
+
+ align:start position:0%
+which implies h
+is not maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a contradiction right remember
+
+ align:start position:0%
+which is a contradiction right remember
+ 
+
+ align:start position:0%
+which is a contradiction right remember
+H was supposed to be the maximal element
+
+ align:start position:0%
+H was supposed to be the maximal element
+ 
+
+ align:start position:0%
+H was supposed to be the maximal element
+of e nothing sits above H and if we
+
+ align:start position:0%
+of e nothing sits above H and if we
+ 
+
+ align:start position:0%
+of e nothing sits above H and if we
+assume that H does not span V then we
+
+ align:start position:0%
+assume that H does not span V then we
+ 
+
+ align:start position:0%
+assume that H does not span V then we
+can tack on to H something making a
+
+ align:start position:0%
+can tack on to H something making a
+ 
+
+ align:start position:0%
+can tack on to H something making a
+bigger linearly independent subset of v
+
+ align:start position:0%
+bigger linearly independent subset of v
+ 
+
+ align:start position:0%
+bigger linearly independent subset of v
+and that uh
+
+ align:start position:0%
+and that uh
+ 
+
+ align:start position:0%
+and that uh
+results in a contradiction so thus that
+
+ align:start position:0%
+results in a contradiction so thus that
+ 
+
+ align:start position:0%
+results in a contradiction so thus that
+must contradict our initial assumption
+
+ align:start position:0%
+must contradict our initial assumption
+ 
+
+ align:start position:0%
+must contradict our initial assumption
+initial assumption
+
+ align:start position:0%
+initial assumption
+ 
+
+ align:start position:0%
+initial assumption
+that H did not span V so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore by definition it's a
+
+ align:start position:0%
+and therefore by definition it's a
+ 
+
+ align:start position:0%
+and therefore by definition it's a
+handle basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Okay so we've seen this kind of exercise
+
+ align:start position:0%
+Okay so we've seen this kind of exercise
+ 
+
+ align:start position:0%
+Okay so we've seen this kind of exercise
+first exercise of using this very uh
+
+ align:start position:0%
+first exercise of using this very uh
+ 
+
+ align:start position:0%
+first exercise of using this very uh
+powerful weapon Zorn
+
+ align:start position:0%
+powerful weapon Zorn
+ 
+
+ align:start position:0%
+powerful weapon Zorn
+Zorn's Lemma to to prove this fact that
+
+ align:start position:0%
+Zorn's Lemma to to prove this fact that
+ 
+
+ align:start position:0%
+Zorn's Lemma to to prove this fact that
+every Vector space has a Hammel basis
+
+ align:start position:0%
+every Vector space has a Hammel basis
+ 
+
+ align:start position:0%
+every Vector space has a Hammel basis
+and now we're going to use it to prove
+
+ align:start position:0%
+and now we're going to use it to prove
+ 
+
+ align:start position:0%
+and now we're going to use it to prove
+the harmonic theorem so let me State uh
+
+ align:start position:0%
+the harmonic theorem so let me State uh
+ 
+
+ align:start position:0%
+the harmonic theorem so let me State uh
+the Han banak theorem for you
+
+ align:start position:0%
+the Han banak theorem for you
+ 
+
+ align:start position:0%
+the Han banak theorem for you
+and then we're going to discuss the
+
+ align:start position:0%
+and then we're going to discuss the
+ 
+
+ align:start position:0%
+and then we're going to discuss the
+strategy actually what I'm going to do
+
+ align:start position:0%
+strategy actually what I'm going to do
+ 
+
+ align:start position:0%
+strategy actually what I'm going to do
+is I'm going to State the hanbanek
+
+ align:start position:0%
+is I'm going to State the hanbanek
+ 
+
+ align:start position:0%
+is I'm going to State the hanbanek
+theorem I'm going to State a limma and
+
+ align:start position:0%
+theorem I'm going to State a limma and
+ 
+
+ align:start position:0%
+theorem I'm going to State a limma and
+then I'm going to give you how uh
+
+ align:start position:0%
+then I'm going to give you how uh
+ 
+
+ align:start position:0%
+then I'm going to give you how uh
+what the the plan is to proving for
+
+ align:start position:0%
+what the the plan is to proving for
+ 
+
+ align:start position:0%
+what the the plan is to proving for
+proving the harmonic theorem
+
+ align:start position:0%
+proving the harmonic theorem
+ 
+
+ align:start position:0%
+proving the harmonic theorem
+so the harmonic theorem is
+
+ align:start position:0%
+so the harmonic theorem is
+ 
+
+ align:start position:0%
+so the harmonic theorem is
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Subspace of V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and U going from m
+
+ align:start position:0%
+and U going from m
+ 
+
+ align:start position:0%
+and U going from m
+to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is linear
+
+ align:start position:0%
+is linear
+ 
+
+ align:start position:0%
+is linear
+such that so it's a bounded linear
+
+ align:start position:0%
+such that so it's a bounded linear
+ 
+
+ align:start position:0%
+such that so it's a bounded linear
+functional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well T and M
+
+ align:start position:0%
+well T and M
+ 
+
+ align:start position:0%
+well T and M
+U of T
+
+ align:start position:0%
+U of T
+ 
+
+ align:start position:0%
+U of T
+so this is now a complex number it's
+
+ align:start position:0%
+so this is now a complex number it's
+ 
+
+ align:start position:0%
+so this is now a complex number it's
+absolute value is less than or equal to
+
+ align:start position:0%
+absolute value is less than or equal to
+ 
+
+ align:start position:0%
+absolute value is less than or equal to
+constant times
+
+ align:start position:0%
+constant times
+ 
+
+ align:start position:0%
+constant times
+Norm of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+then there exists
+ 
+
+ align:start position:0%
+then there exists
+a continuous extension of you to the
+
+ align:start position:0%
+a continuous extension of you to the
+ 
+
+ align:start position:0%
+a continuous extension of you to the
+entire space and a continuous extension
+
+ align:start position:0%
+entire space and a continuous extension
+ 
+
+ align:start position:0%
+entire space and a continuous extension
+that has the same constant here so
+
+ align:start position:0%
+that has the same constant here so
+ 
+
+ align:start position:0%
+that has the same constant here so
+remember this is think of this as being
+
+ align:start position:0%
+remember this is think of this as being
+ 
+
+ align:start position:0%
+remember this is think of this as being
+the norm of little U and so we can
+
+ align:start position:0%
+the norm of little U and so we can
+ 
+
+ align:start position:0%
+the norm of little U and so we can
+extend it to a bounded linear functional
+
+ align:start position:0%
+extend it to a bounded linear functional
+ 
+
+ align:start position:0%
+extend it to a bounded linear functional
+with the same Norm essentially and there
+
+ align:start position:0%
+with the same Norm essentially and there
+ 
+
+ align:start position:0%
+with the same Norm essentially and there
+exists a capital u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded linear functional from V to C so
+
+ align:start position:0%
+bounded linear functional from V to C so
+ 
+
+ align:start position:0%
+bounded linear functional from V to C so
+it's an element of the Dual space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that now for all
+
+ align:start position:0%
+such that now for all
+ 
+
+ align:start position:0%
+such that now for all
+T and V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U of T is less than or equal to the same
+
+ align:start position:0%
+U of T is less than or equal to the same
+ 
+
+ align:start position:0%
+U of T is less than or equal to the same
+constant T and I should have said before
+
+ align:start position:0%
+constant T and I should have said before
+ 
+
+ align:start position:0%
+constant T and I should have said before
+such that capital u when I restrict to M
+
+ align:start position:0%
+such that capital u when I restrict to M
+ 
+
+ align:start position:0%
+such that capital u when I restrict to M
+gives me little U
+
+ align:start position:0%
+gives me little U
+ 
+
+ align:start position:0%
+gives me little U
+and for all T and V Capital U of T is
+
+ align:start position:0%
+and for all T and V Capital U of T is
+ 
+
+ align:start position:0%
+and for all T and V Capital U of T is
+less than or equal to a constant times
+
+ align:start position:0%
+less than or equal to a constant times
+ 
+
+ align:start position:0%
+less than or equal to a constant times
+the norm of t
+
+ align:start position:0%
+the norm of t
+ 
+
+ align:start position:0%
+the norm of t
+all right so this is a
+
+ align:start position:0%
+all right so this is a
+ 
+
+ align:start position:0%
+all right so this is a
+I should have put this here at the start
+
+ align:start position:0%
+I should have put this here at the start
+ 
+
+ align:start position:0%
+I should have put this here at the start
+of the theorem but this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on bionic theorem
+
+ align:start position:0%
+on bionic theorem
+ 
+
+ align:start position:0%
+on bionic theorem
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you know this is a very very useful
+
+ align:start position:0%
+and you know this is a very very useful
+ 
+
+ align:start position:0%
+and you know this is a very very useful
+theorem to have
+
+ align:start position:0%
+theorem to have
+ 
+
+ align:start position:0%
+theorem to have
+in fact in the exercises you can use
+
+ align:start position:0%
+in fact in the exercises you can use
+ 
+
+ align:start position:0%
+in fact in the exercises you can use
+this theorem to prove that the Dual of
+
+ align:start position:0%
+this theorem to prove that the Dual of
+ 
+
+ align:start position:0%
+this theorem to prove that the Dual of
+little L Infinity is not little L1
+
+ align:start position:0%
+little L Infinity is not little L1
+ 
+
+ align:start position:0%
+little L Infinity is not little L1
+okay so remember we from the second
+
+ align:start position:0%
+okay so remember we from the second
+ 
+
+ align:start position:0%
+okay so remember we from the second
+assignment and from what I've said in
+
+ align:start position:0%
+assignment and from what I've said in
+ 
+
+ align:start position:0%
+assignment and from what I've said in
+lectures you know the Duel of little LP
+
+ align:start position:0%
+lectures you know the Duel of little LP
+ 
+
+ align:start position:0%
+lectures you know the Duel of little LP
+is little lq where one over P plus one
+
+ align:start position:0%
+is little lq where one over P plus one
+ 
+
+ align:start position:0%
+is little lq where one over P plus one
+over Q equals one as long as p is bigger
+
+ align:start position:0%
+over Q equals one as long as p is bigger
+ 
+
+ align:start position:0%
+over Q equals one as long as p is bigger
+than or equal to one and less than
+
+ align:start position:0%
+than or equal to one and less than
+ 
+
+ align:start position:0%
+than or equal to one and less than
+infinity and it doesn't work for p
+
+ align:start position:0%
+infinity and it doesn't work for p
+ 
+
+ align:start position:0%
+infinity and it doesn't work for p
+equals infinity so using the harmonic
+
+ align:start position:0%
+equals infinity so using the harmonic
+ 
+
+ align:start position:0%
+equals infinity so using the harmonic
+theorem you can show that why it doesn't
+
+ align:start position:0%
+theorem you can show that why it doesn't
+ 
+
+ align:start position:0%
+theorem you can show that why it doesn't
+work for for little L infinity and
+
+ align:start position:0%
+work for for little L infinity and
+ 
+
+ align:start position:0%
+work for for little L infinity and
+that'll be in the assignment
+
+ align:start position:0%
+that'll be in the assignment
+ 
+
+ align:start position:0%
+that'll be in the assignment
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+now just for I'm gonna so I don't have
+
+ align:start position:0%
+now just for I'm gonna so I don't have
+ 
+
+ align:start position:0%
+now just for I'm gonna so I don't have
+to keep writing all of this over and
+
+ align:start position:0%
+to keep writing all of this over and
+ 
+
+ align:start position:0%
+to keep writing all of this over and
+over again
+
+ align:start position:0%
+over again
+ 
+
+ align:start position:0%
+over again
+I'm going to refer to this as
+
+ align:start position:0%
+I'm going to refer to this as
+ 
+
+ align:start position:0%
+I'm going to refer to this as
+U is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extension
+
+ align:start position:0%
+extension
+ 
+
+ align:start position:0%
+extension
+of little U okay although that's not
+
+ align:start position:0%
+of little U okay although that's not
+ 
+
+ align:start position:0%
+of little U okay although that's not
+quite precise because we are extending
+
+ align:start position:0%
+quite precise because we are extending
+ 
+
+ align:start position:0%
+quite precise because we are extending
+little U
+
+ align:start position:0%
+little U
+ 
+
+ align:start position:0%
+little U
+to a continuous
+
+ align:start position:0%
+to a continuous
+ 
+
+ align:start position:0%
+to a continuous
+so a bounded linear operator on V but
+
+ align:start position:0%
+so a bounded linear operator on V but
+ 
+
+ align:start position:0%
+so a bounded linear operator on V but
+we're also
+
+ align:start position:0%
+we're also
+ 
+
+ align:start position:0%
+we're also
+extending it so that the
+
+ align:start position:0%
+extending it so that the
+ 
+
+ align:start position:0%
+extending it so that the
+capital u satisfies the same bound as
+
+ align:start position:0%
+capital u satisfies the same bound as
+ 
+
+ align:start position:0%
+capital u satisfies the same bound as
+little U
+
+ align:start position:0%
+little U
+ 
+
+ align:start position:0%
+little U
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this is a little imprecise
+
+ align:start position:0%
+all right so this is a little imprecise
+ 
+
+ align:start position:0%
+all right so this is a little imprecise
+but I think you should you know get my
+
+ align:start position:0%
+but I think you should you know get my
+ 
+
+ align:start position:0%
+but I think you should you know get my
+meaning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+this assumption let me denote by star
+
+ align:start position:0%
+this assumption let me denote by star
+ 
+
+ align:start position:0%
+this assumption let me denote by star
+namely that we have a Subspace and we
+
+ align:start position:0%
+namely that we have a Subspace and we
+ 
+
+ align:start position:0%
+namely that we have a Subspace and we
+have a bounded linear functional on this
+
+ align:start position:0%
+have a bounded linear functional on this
+ 
+
+ align:start position:0%
+have a bounded linear functional on this
+Subspace that satisfies this bound so
+
+ align:start position:0%
+Subspace that satisfies this bound so
+ 
+
+ align:start position:0%
+Subspace that satisfies this bound so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I'm not going to prove the harmonic
+
+ align:start position:0%
+I'm not going to prove the harmonic
+ 
+
+ align:start position:0%
+I'm not going to prove the harmonic
+theorem just yet I'm going to prove a
+
+ align:start position:0%
+theorem just yet I'm going to prove a
+ 
+
+ align:start position:0%
+theorem just yet I'm going to prove a
+Lemma or I'm going to State a Lima and
+
+ align:start position:0%
+Lemma or I'm going to State a Lima and
+ 
+
+ align:start position:0%
+Lemma or I'm going to State a Lima and
+then tell you how we're going to prove
+
+ align:start position:0%
+then tell you how we're going to prove
+ 
+
+ align:start position:0%
+then tell you how we're going to prove
+use it to prove the harmonic theorem so
+
+ align:start position:0%
+use it to prove the harmonic theorem so
+ 
+
+ align:start position:0%
+use it to prove the harmonic theorem so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually you know what we'll say that uh
+
+ align:start position:0%
+actually you know what we'll say that uh
+ 
+
+ align:start position:0%
+actually you know what we'll say that uh
+slightly different I'm not going to use
+
+ align:start position:0%
+slightly different I'm not going to use
+ 
+
+ align:start position:0%
+slightly different I'm not going to use
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if V is a normed
+
+ align:start position:0%
+so if V is a normed
+ 
+
+ align:start position:0%
+so if V is a normed
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a subset of V is a Subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+from M to C is
+
+ align:start position:0%
+from M to C is
+ 
+
+ align:start position:0%
+from M to C is
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+little U of T
+
+ align:start position:0%
+little U of T
+ 
+
+ align:start position:0%
+little U of T
+is less than or equal to
+
+ align:start position:0%
+is less than or equal to
+ 
+
+ align:start position:0%
+is less than or equal to
+constant times the norm of T So for all
+
+ align:start position:0%
+constant times the norm of T So for all
+ 
+
+ align:start position:0%
+constant times the norm of T So for all
+T and M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you know what let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think the difference between capital u
+
+ align:start position:0%
+I think the difference between capital u
+ 
+
+ align:start position:0%
+I think the difference between capital u
+and little U is clear enough
+
+ align:start position:0%
+and little U is clear enough
+ 
+
+ align:start position:0%
+and little U is clear enough
+then I can extend it at least
+
+ align:start position:0%
+then I can extend it at least
+ 
+
+ align:start position:0%
+then I can extend it at least
+in One Direction so in other words
+
+ align:start position:0%
+in One Direction so in other words
+ 
+
+ align:start position:0%
+in One Direction so in other words
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m is
+
+ align:start position:0%
+m is
+ 
+
+ align:start position:0%
+m is
+and one last assumption and I take
+
+ align:start position:0%
+and one last assumption and I take
+ 
+
+ align:start position:0%
+and one last assumption and I take
+something that's not in the linear
+
+ align:start position:0%
+something that's not in the linear
+ 
+
+ align:start position:0%
+something that's not in the linear
+Subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I can extend it to uh the Subspace
+
+ align:start position:0%
+then I can extend it to uh the Subspace
+ 
+
+ align:start position:0%
+then I can extend it to uh the Subspace
+of V consisting of M and also the
+
+ align:start position:0%
+of V consisting of M and also the
+ 
+
+ align:start position:0%
+of V consisting of M and also the
+Direction X so then
+
+ align:start position:0%
+Direction X so then
+ 
+
+ align:start position:0%
+Direction X so then
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists U Prime
+
+ align:start position:0%
+there exists U Prime
+ 
+
+ align:start position:0%
+there exists U Prime
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and the dull so I shouldn't use U Prime
+
+ align:start position:0%
+and the dull so I shouldn't use U Prime
+ 
+
+ align:start position:0%
+and the dull so I shouldn't use U Prime
+let's say V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well let's use U Prime
+
+ align:start position:0%
+okay well let's use U Prime
+ 
+
+ align:start position:0%
+okay well let's use U Prime
+U Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+M Prime to C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+linear and here M Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is defined to be the subset or the
+
+ align:start position:0%
+is defined to be the subset or the
+ 
+
+ align:start position:0%
+is defined to be the subset or the
+Subspace M plus so this should be this
+
+ align:start position:0%
+Subspace M plus so this should be this
+ 
+
+ align:start position:0%
+Subspace M plus so this should be this
+does not mean
+
+ align:start position:0%
+does not mean
+ 
+
+ align:start position:0%
+does not mean
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know quotient space we were using
+
+ align:start position:0%
+you know quotient space we were using
+ 
+
+ align:start position:0%
+you know quotient space we were using
+pluses for for quotient spaces but this
+
+ align:start position:0%
+pluses for for quotient spaces but this
+ 
+
+ align:start position:0%
+pluses for for quotient spaces but this
+is the Subspace of V consisting of M
+
+ align:start position:0%
+is the Subspace of V consisting of M
+ 
+
+ align:start position:0%
+is the Subspace of V consisting of M
+plus elements of the form
+
+ align:start position:0%
+plus elements of the form
+ 
+
+ align:start position:0%
+plus elements of the form
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+constant times x so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements of the form t plus
+
+ align:start position:0%
+elements of the form t plus
+ 
+
+ align:start position:0%
+elements of the form t plus
+a x where
+
+ align:start position:0%
+a x where
+ 
+
+ align:start position:0%
+a x where
+T is in m
+
+ align:start position:0%
+T is in m
+ 
+
+ align:start position:0%
+T is in m
+a is in C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U Prime when we're stick restricted to M
+
+ align:start position:0%
+U Prime when we're stick restricted to M
+ 
+
+ align:start position:0%
+U Prime when we're stick restricted to M
+gives me U
+
+ align:start position:0%
+gives me U
+ 
+
+ align:start position:0%
+gives me U
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for all T Prime and M Prime
+
+ align:start position:0%
+for all T Prime and M Prime
+ 
+
+ align:start position:0%
+for all T Prime and M Prime
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+U Prime of T Prime absolute value is
+
+ align:start position:0%
+U Prime of T Prime absolute value is
+ 
+
+ align:start position:0%
+U Prime of T Prime absolute value is
+less than or equal to the same constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the norm of T Prime Okay so
+
+ align:start position:0%
+times the norm of T Prime Okay so
+ 
+
+ align:start position:0%
+times the norm of T Prime Okay so
+maybe I made a mess of that uh speaking
+
+ align:start position:0%
+maybe I made a mess of that uh speaking
+ 
+
+ align:start position:0%
+maybe I made a mess of that uh speaking
+while I was riding the limo but anyways
+
+ align:start position:0%
+while I was riding the limo but anyways
+ 
+
+ align:start position:0%
+while I was riding the limo but anyways
+so let's say you have a bounded linear
+
+ align:start position:0%
+so let's say you have a bounded linear
+ 
+
+ align:start position:0%
+so let's say you have a bounded linear
+functional on a Subspace of V and you
+
+ align:start position:0%
+functional on a Subspace of V and you
+ 
+
+ align:start position:0%
+functional on a Subspace of V and you
+take an element that's not an m
+
+ align:start position:0%
+take an element that's not an m
+ 
+
+ align:start position:0%
+take an element that's not an m
+so the way I'll draw the picture is
+
+ align:start position:0%
+so the way I'll draw the picture is
+ 
+
+ align:start position:0%
+so the way I'll draw the picture is
+there's m
+
+ align:start position:0%
+there's m
+ 
+
+ align:start position:0%
+there's m
+and here's something
+
+ align:start position:0%
+and here's something
+ 
+
+ align:start position:0%
+and here's something
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+X then
+
+ align:start position:0%
+X then
+ 
+
+ align:start position:0%
+X then
+I can extend this
+
+ align:start position:0%
+I can extend this
+ 
+
+ align:start position:0%
+I can extend this
+bounded linear functional which lives on
+
+ align:start position:0%
+bounded linear functional which lives on
+ 
+
+ align:start position:0%
+bounded linear functional which lives on
+M to now
+
+ align:start position:0%
+M to now
+ 
+
+ align:start position:0%
+M to now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the Subspace consisting of all elements
+
+ align:start position:0%
+the Subspace consisting of all elements
+ 
+
+ align:start position:0%
+the Subspace consisting of all elements
+of M plus elements uh plus scalar
+
+ align:start position:0%
+of M plus elements uh plus scalar
+ 
+
+ align:start position:0%
+of M plus elements uh plus scalar
+multiple multiples of x
+
+ align:start position:0%
+multiple multiples of x
+ 
+
+ align:start position:0%
+multiple multiples of x
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and I can do this in a continuous way
+
+ align:start position:0%
+and I can do this in a continuous way
+ 
+
+ align:start position:0%
+and I can do this in a continuous way
+meaning I get a bounded linear
+
+ align:start position:0%
+meaning I get a bounded linear
+ 
+
+ align:start position:0%
+meaning I get a bounded linear
+functional on M Prime which satisfies
+
+ align:start position:0%
+functional on M Prime which satisfies
+ 
+
+ align:start position:0%
+functional on M Prime which satisfies
+the same bound as you did okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so what's the strategy for
+
+ align:start position:0%
+all right so what's the strategy for
+ 
+
+ align:start position:0%
+all right so what's the strategy for
+using this to prove uh the hunbonic
+
+ align:start position:0%
+using this to prove uh the hunbonic
+ 
+
+ align:start position:0%
+using this to prove uh the hunbonic
+theorem so
+
+ align:start position:0%
+theorem so
+ 
+
+ align:start position:0%
+theorem so
+just so that we're clear on
+
+ align:start position:0%
+just so that we're clear on
+ 
+
+ align:start position:0%
+just so that we're clear on
+why we would be interested in such a
+
+ align:start position:0%
+why we would be interested in such a
+ 
+
+ align:start position:0%
+why we would be interested in such a
+such a thing
+
+ align:start position:0%
+such a thing
+ 
+
+ align:start position:0%
+such a thing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we apply Zorn's Lima to all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous extensions of little use so
+
+ align:start position:0%
+continuous extensions of little use so
+ 
+
+ align:start position:0%
+continuous extensions of little use so
+now I'm talking about how we prove Han
+
+ align:start position:0%
+now I'm talking about how we prove Han
+ 
+
+ align:start position:0%
+now I'm talking about how we prove Han
+Bonnet theorem okay
+
+ align:start position:0%
+Bonnet theorem okay
+ 
+
+ align:start position:0%
+Bonnet theorem okay
+so we Define as our linearly or as our
+
+ align:start position:0%
+so we Define as our linearly or as our
+ 
+
+ align:start position:0%
+so we Define as our linearly or as our
+partially ordered set would be the set
+
+ align:start position:0%
+partially ordered set would be the set
+ 
+
+ align:start position:0%
+partially ordered set would be the set
+of all continuous extensions of U and
+
+ align:start position:0%
+of all continuous extensions of U and
+ 
+
+ align:start position:0%
+of all continuous extensions of U and
+then we would put a partial order on
+
+ align:start position:0%
+then we would put a partial order on
+ 
+
+ align:start position:0%
+then we would put a partial order on
+that where
+
+ align:start position:0%
+that where
+ 
+
+ align:start position:0%
+that where
+one extension is bigger than or equal to
+
+ align:start position:0%
+one extension is bigger than or equal to
+ 
+
+ align:start position:0%
+one extension is bigger than or equal to
+another extension if that extension
+
+ align:start position:0%
+another extension if that extension
+ 
+
+ align:start position:0%
+another extension if that extension
+extends the smaller extension okay
+
+ align:start position:0%
+extends the smaller extension okay
+ 
+
+ align:start position:0%
+extends the smaller extension okay
+and using kind of the argument we did
+
+ align:start position:0%
+and using kind of the argument we did
+ 
+
+ align:start position:0%
+and using kind of the argument we did
+for uh proving the vector space has a
+
+ align:start position:0%
+for uh proving the vector space has a
+ 
+
+ align:start position:0%
+for uh proving the vector space has a
+Hamel basis we can then show that Zorn's
+
+ align:start position:0%
+Hamel basis we can then show that Zorn's
+ 
+
+ align:start position:0%
+Hamel basis we can then show that Zorn's
+Lemma applies okay and then we'll have a
+
+ align:start position:0%
+Lemma applies okay and then we'll have a
+ 
+
+ align:start position:0%
+Lemma applies okay and then we'll have a
+maximal element of this set of
+
+ align:start position:0%
+maximal element of this set of
+ 
+
+ align:start position:0%
+maximal element of this set of
+continuous extensions
+
+ align:start position:0%
+continuous extensions
+ 
+
+ align:start position:0%
+continuous extensions
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+of you now what we would like to
+
+ align:start position:0%
+of you now what we would like to
+ 
+
+ align:start position:0%
+of you now what we would like to
+conclude is that this maximal element
+
+ align:start position:0%
+conclude is that this maximal element
+ 
+
+ align:start position:0%
+conclude is that this maximal element
+this maximal continuous extension is
+
+ align:start position:0%
+this maximal continuous extension is
+ 
+
+ align:start position:0%
+this maximal continuous extension is
+defined on all of V
+
+ align:start position:0%
+defined on all of V
+ 
+
+ align:start position:0%
+defined on all of V
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so how would we prove uh that well we
+
+ align:start position:0%
+so how would we prove uh that well we
+ 
+
+ align:start position:0%
+so how would we prove uh that well we
+would do it just kind of like we did for
+
+ align:start position:0%
+would do it just kind of like we did for
+ 
+
+ align:start position:0%
+would do it just kind of like we did for
+the Hammel basis case we would suppose
+
+ align:start position:0%
+the Hammel basis case we would suppose
+ 
+
+ align:start position:0%
+the Hammel basis case we would suppose
+not and then we would show that if it
+
+ align:start position:0%
+not and then we would show that if it
+ 
+
+ align:start position:0%
+not and then we would show that if it
+was not defined on the entire Norm space
+
+ align:start position:0%
+was not defined on the entire Norm space
+ 
+
+ align:start position:0%
+was not defined on the entire Norm space
+then we can extend that maximal element
+
+ align:start position:0%
+then we can extend that maximal element
+ 
+
+ align:start position:0%
+then we can extend that maximal element
+again using this Lemma
+
+ align:start position:0%
+again using this Lemma
+ 
+
+ align:start position:0%
+again using this Lemma
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and therefore contradicting the fact
+
+ align:start position:0%
+and therefore contradicting the fact
+ 
+
+ align:start position:0%
+and therefore contradicting the fact
+that that extension was a maximal
+
+ align:start position:0%
+that that extension was a maximal
+ 
+
+ align:start position:0%
+that that extension was a maximal
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in short we apply Zorn's Lemma to all
+
+ align:start position:0%
+so in short we apply Zorn's Lemma to all
+ 
+
+ align:start position:0%
+so in short we apply Zorn's Lemma to all
+continuous extensions of view uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to get a maximal element
+
+ align:start position:0%
+to get a maximal element
+ 
+
+ align:start position:0%
+to get a maximal element
+capital u
+
+ align:start position:0%
+capital u
+ 
+
+ align:start position:0%
+capital u
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+we use the Lima
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to show you
+
+ align:start position:0%
+to show you
+ 
+
+ align:start position:0%
+to show you
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this extension is defined on
+
+ align:start position:0%
+this extension is defined on
+ 
+
+ align:start position:0%
+this extension is defined on
+all of capital B so these extensions
+
+ align:start position:0%
+all of capital B so these extensions
+ 
+
+ align:start position:0%
+all of capital B so these extensions
+will come with two pieces of information
+
+ align:start position:0%
+will come with two pieces of information
+ 
+
+ align:start position:0%
+will come with two pieces of information
+uh one is the Subspace which you know is
+
+ align:start position:0%
+uh one is the Subspace which you know is
+ 
+
+ align:start position:0%
+uh one is the Subspace which you know is
+bigger than M and then also the
+
+ align:start position:0%
+bigger than M and then also the
+ 
+
+ align:start position:0%
+bigger than M and then also the
+functional itself and so we'll use the
+
+ align:start position:0%
+functional itself and so we'll use the
+ 
+
+ align:start position:0%
+functional itself and so we'll use the
+limit to show that the Subspace that
+
+ align:start position:0%
+limit to show that the Subspace that
+ 
+
+ align:start position:0%
+limit to show that the Subspace that
+this capital u is defined on is all of V
+
+ align:start position:0%
+this capital u is defined on is all of V
+ 
+
+ align:start position:0%
+this capital u is defined on is all of V
+okay by showing that if it's not then we
+
+ align:start position:0%
+okay by showing that if it's not then we
+ 
+
+ align:start position:0%
+okay by showing that if it's not then we
+can extend it to a slightly bigger
+
+ align:start position:0%
+can extend it to a slightly bigger
+ 
+
+ align:start position:0%
+can extend it to a slightly bigger
+Subspace using the Lemma which would
+
+ align:start position:0%
+Subspace using the Lemma which would
+ 
+
+ align:start position:0%
+Subspace using the Lemma which would
+contradict the fact that this is a
+
+ align:start position:0%
+contradict the fact that this is a
+ 
+
+ align:start position:0%
+contradict the fact that this is a
+maximal element okay so that's that's
+
+ align:start position:0%
+maximal element okay so that's that's
+ 
+
+ align:start position:0%
+maximal element okay so that's that's
+the that's the plan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know since we have this limb already
+
+ align:start position:0%
+you know since we have this limb already
+ 
+
+ align:start position:0%
+you know since we have this limb already
+here and since I've said it so many
+
+ align:start position:0%
+here and since I've said it so many
+ 
+
+ align:start position:0%
+here and since I've said it so many
+times let's go ahead and just prove the
+
+ align:start position:0%
+times let's go ahead and just prove the
+ 
+
+ align:start position:0%
+times let's go ahead and just prove the
+hanbanek theorem assuming this Lima
+
+ align:start position:0%
+hanbanek theorem assuming this Lima
+ 
+
+ align:start position:0%
+hanbanek theorem assuming this Lima
+holds okay
+
+ align:start position:0%
+holds okay
+ 
+
+ align:start position:0%
+holds okay
+uh we don't need the proof of this Lima
+
+ align:start position:0%
+uh we don't need the proof of this Lima
+ 
+
+ align:start position:0%
+uh we don't need the proof of this Lima
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+actually prove the harmonic theorem we
+
+ align:start position:0%
+actually prove the harmonic theorem we
+ 
+
+ align:start position:0%
+actually prove the harmonic theorem we
+just need this statement so that's what
+
+ align:start position:0%
+just need this statement so that's what
+ 
+
+ align:start position:0%
+just need this statement so that's what
+we're going to do first and then we'll
+
+ align:start position:0%
+we're going to do first and then we'll
+ 
+
+ align:start position:0%
+we're going to do first and then we'll
+prove go back and prove this Lemma okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the proof of the Han banek
+
+ align:start position:0%
+so this is the proof of the Han banek
+ 
+
+ align:start position:0%
+so this is the proof of the Han banek
+theorem we'll go back and prove the limb
+
+ align:start position:0%
+theorem we'll go back and prove the limb
+ 
+
+ align:start position:0%
+theorem we'll go back and prove the limb
+in a second
+
+ align:start position:0%
+in a second
+ 
+
+ align:start position:0%
+in a second
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let e like I said this will be the set
+
+ align:start position:0%
+let e like I said this will be the set
+ 
+
+ align:start position:0%
+let e like I said this will be the set
+of all continuous extensions of little U
+
+ align:start position:0%
+of all continuous extensions of little U
+ 
+
+ align:start position:0%
+of all continuous extensions of little U
+so V comma uh
+
+ align:start position:0%
+so V comma uh
+ 
+
+ align:start position:0%
+so V comma uh
+say n
+
+ align:start position:0%
+say n
+ 
+
+ align:start position:0%
+say n
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a Subspace of V
+
+ align:start position:0%
+a Subspace of V
+ 
+
+ align:start position:0%
+a Subspace of V
+m is contained in N not strictly but
+
+ align:start position:0%
+m is contained in N not strictly but
+ 
+
+ align:start position:0%
+m is contained in N not strictly but
+it's a subset of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and V is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous extension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of U
+
+ align:start position:0%
+of U
+ 
+
+ align:start position:0%
+of U
+to capital N okay meaning it satisfies
+
+ align:start position:0%
+to capital N okay meaning it satisfies
+ 
+
+ align:start position:0%
+to capital N okay meaning it satisfies
+you know it's a bounded linear
+
+ align:start position:0%
+you know it's a bounded linear
+ 
+
+ align:start position:0%
+you know it's a bounded linear
+functional and Cat on capital N
+
+ align:start position:0%
+functional and Cat on capital N
+ 
+
+ align:start position:0%
+functional and Cat on capital N
+when you restrict it to capital M it
+
+ align:start position:0%
+when you restrict it to capital M it
+ 
+
+ align:start position:0%
+when you restrict it to capital M it
+equals U and it satisfies the same bound
+
+ align:start position:0%
+equals U and it satisfies the same bound
+ 
+
+ align:start position:0%
+equals U and it satisfies the same bound
+that little U does on the uh
+
+ align:start position:0%
+that little U does on the uh
+ 
+
+ align:start position:0%
+that little U does on the uh
+sub Vigor Subspace in okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and note this is non
+
+ align:start position:0%
+and note this is non
+ 
+
+ align:start position:0%
+and note this is non
+empty because well U and M are in this
+
+ align:start position:0%
+empty because well U and M are in this
+ 
+
+ align:start position:0%
+empty because well U and M are in this
+okay I'm not saying M has to be a strict
+
+ align:start position:0%
+okay I'm not saying M has to be a strict
+ 
+
+ align:start position:0%
+okay I'm not saying M has to be a strict
+Subspace of capital n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we'll Define a partial order on E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the following definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will say V1 N1
+
+ align:start position:0%
+we will say V1 N1
+ 
+
+ align:start position:0%
+we will say V1 N1
+is less than or equal to V2
+
+ align:start position:0%
+is less than or equal to V2
+ 
+
+ align:start position:0%
+is less than or equal to V2
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+N1 is contained in N2
+
+ align:start position:0%
+N1 is contained in N2
+ 
+
+ align:start position:0%
+N1 is contained in N2
+and V2
+
+ align:start position:0%
+and V2
+ 
+
+ align:start position:0%
+and V2
+uh when restricted to N1 gives me V1
+
+ align:start position:0%
+uh when restricted to N1 gives me V1
+ 
+
+ align:start position:0%
+uh when restricted to N1 gives me V1
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+V2 is if you'd like a continuous
+
+ align:start position:0%
+V2 is if you'd like a continuous
+ 
+
+ align:start position:0%
+V2 is if you'd like a continuous
+extension of V1
+
+ align:start position:0%
+extension of V1
+ 
+
+ align:start position:0%
+extension of V1
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+remember all of these functionals are
+
+ align:start position:0%
+remember all of these functionals are
+ 
+
+ align:start position:0%
+remember all of these functionals are
+set assumed to be satisfying the same
+
+ align:start position:0%
+set assumed to be satisfying the same
+ 
+
+ align:start position:0%
+set assumed to be satisfying the same
+bound as you did okay so with the same
+
+ align:start position:0%
+bound as you did okay so with the same
+ 
+
+ align:start position:0%
+bound as you did okay so with the same
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's not difficult to check just like
+
+ align:start position:0%
+so it's not difficult to check just like
+ 
+
+ align:start position:0%
+so it's not difficult to check just like
+you know I didn't check it for for uh
+
+ align:start position:0%
+you know I didn't check it for for uh
+ 
+
+ align:start position:0%
+you know I didn't check it for for uh
+inclusion but it's not hard to to check
+
+ align:start position:0%
+inclusion but it's not hard to to check
+ 
+
+ align:start position:0%
+inclusion but it's not hard to to check
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is in fact
+
+ align:start position:0%
+that this is in fact
+ 
+
+ align:start position:0%
+that this is in fact
+is a partial order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we want to apply Zorn's Lemma to
+
+ align:start position:0%
+so now we want to apply Zorn's Lemma to
+ 
+
+ align:start position:0%
+so now we want to apply Zorn's Lemma to
+get a maximal element of e which we want
+
+ align:start position:0%
+get a maximal element of e which we want
+ 
+
+ align:start position:0%
+get a maximal element of e which we want
+to show is in fact uh
+
+ align:start position:0%
+to show is in fact uh
+ 
+
+ align:start position:0%
+to show is in fact uh
+uh this uh that we say exists
+
+ align:start position:0%
+uh this uh that we say exists
+ 
+
+ align:start position:0%
+uh this uh that we say exists
+so we have to show every chain in E has
+
+ align:start position:0%
+so we have to show every chain in E has
+ 
+
+ align:start position:0%
+so we have to show every chain in E has
+an upper bound so let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which I'll
+
+ align:start position:0%
+which I'll
+ 
+
+ align:start position:0%
+which I'll
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to note as
+
+ align:start position:0%
+to note as
+ 
+
+ align:start position:0%
+to note as
+b i
+
+ align:start position:0%
+b i
+ 
+
+ align:start position:0%
+b i
+n i for I in some index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain and E so this is a set of a set of
+
+ align:start position:0%
+chain and E so this is a set of a set of
+ 
+
+ align:start position:0%
+chain and E so this is a set of a set of
+extensions and we can always compare any
+
+ align:start position:0%
+extensions and we can always compare any
+ 
+
+ align:start position:0%
+extensions and we can always compare any
+two extensions in there
+
+ align:start position:0%
+two extensions in there
+ 
+
+ align:start position:0%
+two extensions in there
+so let me just repeat or write down
+
+ align:start position:0%
+so let me just repeat or write down
+ 
+
+ align:start position:0%
+so let me just repeat or write down
+again what this means to be a chain this
+
+ align:start position:0%
+again what this means to be a chain this
+ 
+
+ align:start position:0%
+again what this means to be a chain this
+means then for all
+
+ align:start position:0%
+means then for all
+ 
+
+ align:start position:0%
+means then for all
+I won
+
+ align:start position:0%
+I won
+ 
+
+ align:start position:0%
+I won
+I2
+
+ align:start position:0%
+I2
+ 
+
+ align:start position:0%
+I2
+in this index that I'm using just to
+
+ align:start position:0%
+in this index that I'm using just to
+ 
+
+ align:start position:0%
+in this index that I'm using just to
+index these elements of the chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bi1
+
+ align:start position:0%
+bi1
+ 
+
+ align:start position:0%
+bi1
+in i1 is less than or equal to
+
+ align:start position:0%
+in i1 is less than or equal to
+ 
+
+ align:start position:0%
+in i1 is less than or equal to
+bi2
+
+ align:start position:0%
+bi2
+ 
+
+ align:start position:0%
+bi2
+in I2
+
+ align:start position:0%
+in I2
+ 
+
+ align:start position:0%
+in I2
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vice versa I can't remember if a c goes
+
+ align:start position:0%
+vice versa I can't remember if a c goes
+ 
+
+ align:start position:0%
+vice versa I can't remember if a c goes
+there or an S so I'm going to put an S
+
+ align:start position:0%
+there or an S so I'm going to put an S
+ 
+
+ align:start position:0%
+there or an S so I'm going to put an S
+okay so one is either bigger than
+
+ align:start position:0%
+okay so one is either bigger than
+ 
+
+ align:start position:0%
+okay so one is either bigger than
+whenever I have two elements or I can
+
+ align:start position:0%
+whenever I have two elements or I can
+ 
+
+ align:start position:0%
+whenever I have two elements or I can
+always compare them
+
+ align:start position:0%
+always compare them
+ 
+
+ align:start position:0%
+always compare them
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let N be
+
+ align:start position:0%
+let N be
+ 
+
+ align:start position:0%
+let N be
+uh the union of all these subspaces
+
+ align:start position:0%
+uh the union of all these subspaces
+ 
+
+ align:start position:0%
+uh the union of all these subspaces
+coming from this collection
+
+ align:start position:0%
+coming from this collection
+ 
+
+ align:start position:0%
+coming from this collection
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's again it's it's not difficult to
+
+ align:start position:0%
+it's again it's it's not difficult to
+ 
+
+ align:start position:0%
+it's again it's it's not difficult to
+show that end is in fact a Subspace so I
+
+ align:start position:0%
+show that end is in fact a Subspace so I
+ 
+
+ align:start position:0%
+show that end is in fact a Subspace so I
+claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in is a Subspace and again we're going
+
+ align:start position:0%
+in is a Subspace and again we're going
+ 
+
+ align:start position:0%
+in is a Subspace and again we're going
+to use the fact that c is a chain to be
+
+ align:start position:0%
+to use the fact that c is a chain to be
+ 
+
+ align:start position:0%
+to use the fact that c is a chain to be
+able to verify this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let V1
+
+ align:start position:0%
+let V1
+ 
+
+ align:start position:0%
+let V1
+V2 B and N
+
+ align:start position:0%
+V2 B and N
+ 
+
+ align:start position:0%
+V2 B and N
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh let's take two scalars A1
+
+ align:start position:0%
+uh let's take two scalars A1
+ 
+
+ align:start position:0%
+uh let's take two scalars A1
+A2 and C
+
+ align:start position:0%
+A2 and C
+ 
+
+ align:start position:0%
+A2 and C
+I want to show that A1 times V1 plus A2
+
+ align:start position:0%
+I want to show that A1 times V1 plus A2
+ 
+
+ align:start position:0%
+I want to show that A1 times V1 plus A2
+times V2 remains an n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists i1
+
+ align:start position:0%
+then there exists i1
+ 
+
+ align:start position:0%
+then there exists i1
+i22 indices such that V1 is in uh
+
+ align:start position:0%
+i22 indices such that V1 is in uh
+ 
+
+ align:start position:0%
+i22 indices such that V1 is in uh
+in i1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and V2 is in in
+
+ align:start position:0%
+and V2 is in in
+ 
+
+ align:start position:0%
+and V2 is in in
+all right too
+
+ align:start position:0%
+all right too
+ 
+
+ align:start position:0%
+all right too
+now I can always compare
+
+ align:start position:0%
+now I can always compare
+ 
+
+ align:start position:0%
+now I can always compare
+any two uh subspaces
+
+ align:start position:0%
+any two uh subspaces
+ 
+
+ align:start position:0%
+any two uh subspaces
+that are appearing in this
+
+ align:start position:0%
+that are appearing in this
+ 
+
+ align:start position:0%
+that are appearing in this
+you know set of ordered pairs forming
+
+ align:start position:0%
+you know set of ordered pairs forming
+ 
+
+ align:start position:0%
+you know set of ordered pairs forming
+this chain so one of these subspaces is
+
+ align:start position:0%
+this chain so one of these subspaces is
+ 
+
+ align:start position:0%
+this chain so one of these subspaces is
+bigger than the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then uh just by you know flipping
+
+ align:start position:0%
+then uh just by you know flipping
+ 
+
+ align:start position:0%
+then uh just by you know flipping
+one and two if I need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since C is a chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in i1 is contained in ni2
+
+ align:start position:0%
+uh in i1 is contained in ni2
+ 
+
+ align:start position:0%
+uh in i1 is contained in ni2
+without loss of generality so it's you
+
+ align:start position:0%
+without loss of generality so it's you
+ 
+
+ align:start position:0%
+without loss of generality so it's you
+know it will either be in i1 will be
+
+ align:start position:0%
+know it will either be in i1 will be
+ 
+
+ align:start position:0%
+know it will either be in i1 will be
+contained in ni2 or the other way around
+
+ align:start position:0%
+contained in ni2 or the other way around
+ 
+
+ align:start position:0%
+contained in ni2 or the other way around
+and if it's the other way around just
+
+ align:start position:0%
+and if it's the other way around just
+ 
+
+ align:start position:0%
+and if it's the other way around just
+flip the numbers one and two uh so I'm
+
+ align:start position:0%
+flip the numbers one and two uh so I'm
+ 
+
+ align:start position:0%
+flip the numbers one and two uh so I'm
+going to assume ni1 is contained in ni2
+
+ align:start position:0%
+going to assume ni1 is contained in ni2
+ 
+
+ align:start position:0%
+going to assume ni1 is contained in ni2
+then that mean that means both of these
+
+ align:start position:0%
+then that mean that means both of these
+ 
+
+ align:start position:0%
+then that mean that means both of these
+elements are contained in ni2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and V2 are both in the bigger one and
+
+ align:start position:0%
+and V2 are both in the bigger one and
+ 
+
+ align:start position:0%
+and V2 are both in the bigger one and
+since this is a Subspace this means that
+
+ align:start position:0%
+since this is a Subspace this means that
+ 
+
+ align:start position:0%
+since this is a Subspace this means that
+A1 V1 plus A2 V2 is in in I2
+
+ align:start position:0%
+A1 V1 plus A2 V2 is in in I2
+ 
+
+ align:start position:0%
+A1 V1 plus A2 V2 is in in I2
+which remember is a subset of
+
+ align:start position:0%
+which remember is a subset of
+ 
+
+ align:start position:0%
+which remember is a subset of
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore N is a Subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I now have a Subspace which contains
+
+ align:start position:0%
+so I now have a Subspace which contains
+ 
+
+ align:start position:0%
+so I now have a Subspace which contains
+all of these subspaces coming from the
+
+ align:start position:0%
+all of these subspaces coming from the
+ 
+
+ align:start position:0%
+all of these subspaces coming from the
+chain now I need to Define a linear
+
+ align:start position:0%
+chain now I need to Define a linear
+ 
+
+ align:start position:0%
+chain now I need to Define a linear
+functional on this Subspace in that
+
+ align:start position:0%
+functional on this Subspace in that
+ 
+
+ align:start position:0%
+functional on this Subspace in that
+extends all the VIS in a continuous way
+
+ align:start position:0%
+extends all the VIS in a continuous way
+ 
+
+ align:start position:0%
+extends all the VIS in a continuous way
+and therefore and this would give me an
+
+ align:start position:0%
+and therefore and this would give me an
+ 
+
+ align:start position:0%
+and therefore and this would give me an
+upper Bound for this chain but it's not
+
+ align:start position:0%
+upper Bound for this chain but it's not
+ 
+
+ align:start position:0%
+upper Bound for this chain but it's not
+difficult to to
+
+ align:start position:0%
+difficult to to
+ 
+
+ align:start position:0%
+difficult to to
+guess what that linear functional will
+
+ align:start position:0%
+guess what that linear functional will
+ 
+
+ align:start position:0%
+guess what that linear functional will
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we Define
+
+ align:start position:0%
+we Define
+ 
+
+ align:start position:0%
+we Define
+V or not I don't think I use V
+
+ align:start position:0%
+V or not I don't think I use V
+ 
+
+ align:start position:0%
+V or not I don't think I use V
+yeah I do well let's not do that
+
+ align:start position:0%
+yeah I do well let's not do that
+ 
+
+ align:start position:0%
+yeah I do well let's not do that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I mean I shouldn't have used V1
+
+ align:start position:0%
+okay so I mean I shouldn't have used V1
+ 
+
+ align:start position:0%
+okay so I mean I shouldn't have used V1
+and V2 when talking about this Subspace
+
+ align:start position:0%
+and V2 when talking about this Subspace
+ 
+
+ align:start position:0%
+and V2 when talking about this Subspace
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+business that was poor choice of of
+
+ align:start position:0%
+business that was poor choice of of
+ 
+
+ align:start position:0%
+business that was poor choice of of
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know so let's let's make that X1 X2
+
+ align:start position:0%
+you know so let's let's make that X1 X2
+ 
+
+ align:start position:0%
+you know so let's let's make that X1 X2
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the chain blah blah blah
+
+ align:start position:0%
+the chain blah blah blah
+ 
+
+ align:start position:0%
+the chain blah blah blah
+X1 X2 and therefore
+
+ align:start position:0%
+X1 X2 and therefore
+ 
+
+ align:start position:0%
+X1 X2 and therefore
+X1
+
+ align:start position:0%
+X1
+ 
+
+ align:start position:0%
+X1
+X2 is ending okay
+
+ align:start position:0%
+X2 is ending okay
+ 
+
+ align:start position:0%
+X2 is ending okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so I just don't want to mix up the
+
+ align:start position:0%
+so I just don't want to mix up the
+ 
+
+ align:start position:0%
+so I just don't want to mix up the
+elements of the vector space with these
+
+ align:start position:0%
+elements of the vector space with these
+ 
+
+ align:start position:0%
+elements of the vector space with these
+functionals which I'm labeling by V
+
+ align:start position:0%
+functionals which I'm labeling by V
+ 
+
+ align:start position:0%
+functionals which I'm labeling by V
+okay so now we Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a function V from n to C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if T is an element of this Union it
+
+ align:start position:0%
+so if T is an element of this Union it
+ 
+
+ align:start position:0%
+so if T is an element of this Union it
+has to be an element of one of these N
+
+ align:start position:0%
+has to be an element of one of these N
+ 
+
+ align:start position:0%
+has to be an element of one of these N
+Sub I's
+
+ align:start position:0%
+Sub I's
+ 
+
+ align:start position:0%
+Sub I's
+then I Define V of T to be simply
+
+ align:start position:0%
+then I Define V of T to be simply
+ 
+
+ align:start position:0%
+then I Define V of T to be simply
+V of t v sub I which is defined on this
+
+ align:start position:0%
+V of t v sub I which is defined on this
+ 
+
+ align:start position:0%
+V of t v sub I which is defined on this
+linear Subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so I take V of T to be the value of
+
+ align:start position:0%
+and so I take V of T to be the value of
+ 
+
+ align:start position:0%
+and so I take V of T to be the value of
+B sub I evaluated at T so now one
+
+ align:start position:0%
+B sub I evaluated at T so now one
+ 
+
+ align:start position:0%
+B sub I evaluated at T so now one
+question is is this well defined right
+
+ align:start position:0%
+question is is this well defined right
+ 
+
+ align:start position:0%
+question is is this well defined right
+because an element T in N Sub I
+
+ align:start position:0%
+because an element T in N Sub I
+ 
+
+ align:start position:0%
+because an element T in N Sub I
+could also have been an element of a
+
+ align:start position:0%
+could also have been an element of a
+ 
+
+ align:start position:0%
+could also have been an element of a
+different N Sub I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is this well defined so we have to
+
+ align:start position:0%
+so is this well defined so we have to
+ 
+
+ align:start position:0%
+so is this well defined so we have to
+check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it's in two of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does this imply question mark
+
+ align:start position:0%
+does this imply question mark
+ 
+
+ align:start position:0%
+does this imply question mark
+vi1 of T equals v i 2 of t
+
+ align:start position:0%
+vi1 of T equals v i 2 of t
+ 
+
+ align:start position:0%
+vi1 of T equals v i 2 of t
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and again we're going to use the fact
+
+ align:start position:0%
+and again we're going to use the fact
+ 
+
+ align:start position:0%
+and again we're going to use the fact
+that this is a chain to verify this
+
+ align:start position:0%
+that this is a chain to verify this
+ 
+
+ align:start position:0%
+that this is a chain to verify this
+so suppose
+
+ align:start position:0%
+so suppose
+ 
+
+ align:start position:0%
+so suppose
+T is In N Sub i1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersect N Sub I2
+
+ align:start position:0%
+intersect N Sub I2
+ 
+
+ align:start position:0%
+intersect N Sub I2
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you know again for any two elements of
+
+ align:start position:0%
+you know again for any two elements of
+ 
+
+ align:start position:0%
+you know again for any two elements of
+this chain we can compare them so let's
+
+ align:start position:0%
+this chain we can compare them so let's
+ 
+
+ align:start position:0%
+this chain we can compare them so let's
+assume I2 corresponds to the bigger
+
+ align:start position:0%
+assume I2 corresponds to the bigger
+ 
+
+ align:start position:0%
+assume I2 corresponds to the bigger
+index so
+
+ align:start position:0%
+index so
+ 
+
+ align:start position:0%
+index so
+vi1 in i1 is less than or equal to
+
+ align:start position:0%
+vi1 in i1 is less than or equal to
+ 
+
+ align:start position:0%
+vi1 in i1 is less than or equal to
+the I2
+
+ align:start position:0%
+the I2
+ 
+
+ align:start position:0%
+the I2
+and I2
+
+ align:start position:0%
+and I2
+ 
+
+ align:start position:0%
+and I2
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this order not only is defined in terms
+
+ align:start position:0%
+this order not only is defined in terms
+ 
+
+ align:start position:0%
+this order not only is defined in terms
+of the subspaces remember but in terms
+
+ align:start position:0%
+of the subspaces remember but in terms
+ 
+
+ align:start position:0%
+of the subspaces remember but in terms
+of the functionals defined on these
+
+ align:start position:0%
+of the functionals defined on these
+ 
+
+ align:start position:0%
+of the functionals defined on these
+subspaces and it's defined by the fact
+
+ align:start position:0%
+subspaces and it's defined by the fact
+ 
+
+ align:start position:0%
+subspaces and it's defined by the fact
+that this functional is an extension of
+
+ align:start position:0%
+that this functional is an extension of
+ 
+
+ align:start position:0%
+that this functional is an extension of
+this functional and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since vi2 is the bigger one it extends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller one
+
+ align:start position:0%
+smaller one
+ 
+
+ align:start position:0%
+smaller one
+this implies V I2 of T equals v i 1 of t
+
+ align:start position:0%
+this implies V I2 of T equals v i 1 of t
+ 
+
+ align:start position:0%
+this implies V I2 of T equals v i 1 of t
+and therefore uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well defined
+
+ align:start position:0%
+well defined
+ 
+
+ align:start position:0%
+well defined
+and not only that it's it's uh you know
+
+ align:start position:0%
+and not only that it's it's uh you know
+ 
+
+ align:start position:0%
+and not only that it's it's uh you know
+you can also so I wrote this out
+
+ align:start position:0%
+you can also so I wrote this out
+ 
+
+ align:start position:0%
+you can also so I wrote this out
+carefully
+
+ align:start position:0%
+carefully
+ 
+
+ align:start position:0%
+carefully
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+showing it's well defined but by a
+
+ align:start position:0%
+showing it's well defined but by a
+ 
+
+ align:start position:0%
+showing it's well defined but by a
+similar arguments you can then show that
+
+ align:start position:0%
+similar arguments you can then show that
+ 
+
+ align:start position:0%
+similar arguments you can then show that
+V is in fact linear and
+
+ align:start position:0%
+V is in fact linear and
+ 
+
+ align:start position:0%
+V is in fact linear and
+see do I do that or do I stop there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's well defined on N it's also an
+
+ align:start position:0%
+it's well defined on N it's also an
+ 
+
+ align:start position:0%
+it's well defined on N it's also an
+extension of every single functional
+
+ align:start position:0%
+extension of every single functional
+ 
+
+ align:start position:0%
+extension of every single functional
+defined on each N Sub I so the last
+
+ align:start position:0%
+defined on each N Sub I so the last
+ 
+
+ align:start position:0%
+defined on each N Sub I so the last
+thing to check is that it's linear and
+
+ align:start position:0%
+thing to check is that it's linear and
+ 
+
+ align:start position:0%
+thing to check is that it's linear and
+it's a continuous extension of all these
+
+ align:start position:0%
+it's a continuous extension of all these
+ 
+
+ align:start position:0%
+it's a continuous extension of all these
+VI's meaning it satisfies the same bound
+
+ align:start position:0%
+VI's meaning it satisfies the same bound
+ 
+
+ align:start position:0%
+VI's meaning it satisfies the same bound
+but all of the VI's satisfy that bound V
+
+ align:start position:0%
+but all of the VI's satisfy that bound V
+ 
+
+ align:start position:0%
+but all of the VI's satisfy that bound V
+is defined in terms of the V I's
+
+ align:start position:0%
+is defined in terms of the V I's
+ 
+
+ align:start position:0%
+is defined in terms of the V I's
+so I mean we can just read off from here
+
+ align:start position:0%
+so I mean we can just read off from here
+ 
+
+ align:start position:0%
+so I mean we can just read off from here
+that V will satisfy that same bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I will leave it to you that you can
+
+ align:start position:0%
+so I will leave it to you that you can
+ 
+
+ align:start position:0%
+so I will leave it to you that you can
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+V is an element of
+
+ align:start position:0%
+V is an element of
+ 
+
+ align:start position:0%
+V is an element of
+the Dual space of this Subspace in so
+
+ align:start position:0%
+the Dual space of this Subspace in so
+ 
+
+ align:start position:0%
+the Dual space of this Subspace in so
+it's a bounded linear functional on n
+
+ align:start position:0%
+it's a bounded linear functional on n
+ 
+
+ align:start position:0%
+it's a bounded linear functional on n
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a continuous
+
+ align:start position:0%
+a continuous
+ 
+
+ align:start position:0%
+a continuous
+extension
+
+ align:start position:0%
+extension
+ 
+
+ align:start position:0%
+extension
+of all
+
+ align:start position:0%
+of all
+ 
+
+ align:start position:0%
+of all
+VIs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ual okay
+
+ align:start position:0%
+ual okay
+ 
+
+ align:start position:0%
+ual okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all eye and little for little I and
+
+ align:start position:0%
+for all eye and little for little I and
+ 
+
+ align:start position:0%
+for all eye and little for little I and
+capital I we conclude b i
+
+ align:start position:0%
+capital I we conclude b i
+ 
+
+ align:start position:0%
+capital I we conclude b i
+n i is less than or equal to V in
+
+ align:start position:0%
+n i is less than or equal to V in
+ 
+
+ align:start position:0%
+n i is less than or equal to V in
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+v n is an upper bound of C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right so we've verified the
+
+ align:start position:0%
+all right so we've verified the
+ 
+
+ align:start position:0%
+all right so we've verified the
+hypotheses of Zorn's Lima which I've
+
+ align:start position:0%
+hypotheses of Zorn's Lima which I've
+ 
+
+ align:start position:0%
+hypotheses of Zorn's Lima which I've
+already which I just erased so that
+
+ align:start position:0%
+already which I just erased so that
+ 
+
+ align:start position:0%
+already which I just erased so that
+means the set e has a maximal element
+
+ align:start position:0%
+means the set e has a maximal element
+ 
+
+ align:start position:0%
+means the set e has a maximal element
+so by Zorn's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by Zorn
+
+ align:start position:0%
+by Zorn
+ 
+
+ align:start position:0%
+by Zorn
+uh the set e
+
+ align:start position:0%
+uh the set e
+ 
+
+ align:start position:0%
+uh the set e
+has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a maximal
+
+ align:start position:0%
+a maximal
+ 
+
+ align:start position:0%
+a maximal
+element capital u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I claim in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals V and therefore capital u does
+
+ align:start position:0%
+equals V and therefore capital u does
+ 
+
+ align:start position:0%
+equals V and therefore capital u does
+the job because remember U Capital uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since capital u capital N is an
+
+ align:start position:0%
+so since capital u capital N is an
+ 
+
+ align:start position:0%
+so since capital u capital N is an
+element of e that means capital u is a
+
+ align:start position:0%
+element of e that means capital u is a
+ 
+
+ align:start position:0%
+element of e that means capital u is a
+continuous extension of little U all
+
+ align:start position:0%
+continuous extension of little U all
+ 
+
+ align:start position:0%
+continuous extension of little U all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and now we just want to conclude that
+
+ align:start position:0%
+and now we just want to conclude that
+ 
+
+ align:start position:0%
+and now we just want to conclude that
+for this maximal element the Subspace on
+
+ align:start position:0%
+for this maximal element the Subspace on
+ 
+
+ align:start position:0%
+for this maximal element the Subspace on
+which it's defined is the entire space V
+
+ align:start position:0%
+which it's defined is the entire space V
+ 
+
+ align:start position:0%
+which it's defined is the entire space V
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let X
+
+ align:start position:0%
+let X
+ 
+
+ align:start position:0%
+let X
+be an element not an n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+the Lemma
+
+ align:start position:0%
+the Lemma
+ 
+
+ align:start position:0%
+the Lemma
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+extension
+
+ align:start position:0%
+extension
+ 
+
+ align:start position:0%
+extension
+of U capital u
+
+ align:start position:0%
+of U capital u
+ 
+
+ align:start position:0%
+of U capital u
+to the Subspace
+
+ align:start position:0%
+to the Subspace
+ 
+
+ align:start position:0%
+to the Subspace
+in Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the span of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a continuous extension of
+
+ align:start position:0%
+and this is a continuous extension of
+ 
+
+ align:start position:0%
+and this is a continuous extension of
+capital u which is a continuous
+
+ align:start position:0%
+capital u which is a continuous
+ 
+
+ align:start position:0%
+capital u which is a continuous
+extension of little U and therefore it's
+
+ align:start position:0%
+extension of little U and therefore it's
+ 
+
+ align:start position:0%
+extension of little U and therefore it's
+a continuous extension of little U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous extension let's call this
+
+ align:start position:0%
+continuous extension let's call this
+ 
+
+ align:start position:0%
+continuous extension let's call this
+something let's call it V Little V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh if the Subspace that capital u is
+
+ align:start position:0%
+so uh if the Subspace that capital u is
+ 
+
+ align:start position:0%
+so uh if the Subspace that capital u is
+defined on is not all of V then by the
+
+ align:start position:0%
+defined on is not all of V then by the
+ 
+
+ align:start position:0%
+defined on is not all of V then by the
+Lima we can extend capital u
+
+ align:start position:0%
+Lima we can extend capital u
+ 
+
+ align:start position:0%
+Lima we can extend capital u
+continuously to n plus uh the span of x
+
+ align:start position:0%
+continuously to n plus uh the span of x
+ 
+
+ align:start position:0%
+continuously to n plus uh the span of x
+and therefore this element will be a
+
+ align:start position:0%
+and therefore this element will be a
+ 
+
+ align:start position:0%
+and therefore this element will be a
+continuous extension of little U
+
+ align:start position:0%
+continuous extension of little U
+ 
+
+ align:start position:0%
+continuous extension of little U
+and therefore it's an element of E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+u n is smaller than
+
+ align:start position:0%
+u n is smaller than
+ 
+
+ align:start position:0%
+u n is smaller than
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+n Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this span of x
+
+ align:start position:0%
+this span of x
+ 
+
+ align:start position:0%
+this span of x
+right this is a bigger Subspace than
+
+ align:start position:0%
+right this is a bigger Subspace than
+ 
+
+ align:start position:0%
+right this is a bigger Subspace than
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+because X is not an n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies
+
+ align:start position:0%
+which implies
+ 
+
+ align:start position:0%
+which implies
+u n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not a maximal element and that's a
+
+ align:start position:0%
+not a maximal element and that's a
+ 
+
+ align:start position:0%
+not a maximal element and that's a
+contradiction and what do we contradict
+
+ align:start position:0%
+contradiction and what do we contradict
+ 
+
+ align:start position:0%
+contradiction and what do we contradict
+uh are what was the assumption that led
+
+ align:start position:0%
+uh are what was the assumption that led
+ 
+
+ align:start position:0%
+uh are what was the assumption that led
+us astray is the fact that uh we assume
+
+ align:start position:0%
+us astray is the fact that uh we assume
+ 
+
+ align:start position:0%
+us astray is the fact that uh we assume
+that this maximal element is not defined
+
+ align:start position:0%
+that this maximal element is not defined
+ 
+
+ align:start position:0%
+that this maximal element is not defined
+on uh all of the entire Norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+is defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the entire Norm space and it's a
+
+ align:start position:0%
+on the entire Norm space and it's a
+ 
+
+ align:start position:0%
+on the entire Norm space and it's a
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of little you
+
+ align:start position:0%
+of little you
+ 
+
+ align:start position:0%
+of little you
+and that's the proof of hanbana
+
+ align:start position:0%
+and that's the proof of hanbana
+ 
+
+ align:start position:0%
+and that's the proof of hanbana
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I hope that the proof uh was you know
+
+ align:start position:0%
+so I hope that the proof uh was you know
+ 
+
+ align:start position:0%
+so I hope that the proof uh was you know
+clear
+
+ align:start position:0%
+clear
+ 
+
+ align:start position:0%
+clear
+if you followed the Hammel basis
+
+ align:start position:0%
+if you followed the Hammel basis
+ 
+
+ align:start position:0%
+if you followed the Hammel basis
+argument this should be
+
+ align:start position:0%
+argument this should be
+ 
+
+ align:start position:0%
+argument this should be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable to expect too it's just you
+
+ align:start position:0%
+reasonable to expect too it's just you
+ 
+
+ align:start position:0%
+reasonable to expect too it's just you
+know this argument is almost the same as
+
+ align:start position:0%
+know this argument is almost the same as
+ 
+
+ align:start position:0%
+know this argument is almost the same as
+the Hamilton basis argument except now
+
+ align:start position:0%
+the Hamilton basis argument except now
+ 
+
+ align:start position:0%
+the Hamilton basis argument except now
+you know instead of the handle basis
+
+ align:start position:0%
+you know instead of the handle basis
+ 
+
+ align:start position:0%
+you know instead of the handle basis
+where the elements of our partially
+
+ align:start position:0%
+where the elements of our partially
+ 
+
+ align:start position:0%
+where the elements of our partially
+ordered set are just subsets we also
+
+ align:start position:0%
+ordered set are just subsets we also
+ 
+
+ align:start position:0%
+ordered set are just subsets we also
+have two pieces of data for our
+
+ align:start position:0%
+have two pieces of data for our
+ 
+
+ align:start position:0%
+have two pieces of data for our
+partially ordered set here one being the
+
+ align:start position:0%
+partially ordered set here one being the
+ 
+
+ align:start position:0%
+partially ordered set here one being the
+Subspace and the second being the
+
+ align:start position:0%
+Subspace and the second being the
+ 
+
+ align:start position:0%
+Subspace and the second being the
+functional that's defined on that
+
+ align:start position:0%
+functional that's defined on that
+ 
+
+ align:start position:0%
+functional that's defined on that
+Subspace that extends the original uh
+
+ align:start position:0%
+Subspace that extends the original uh
+ 
+
+ align:start position:0%
+Subspace that extends the original uh
+continuous linear functional that we
+
+ align:start position:0%
+continuous linear functional that we
+ 
+
+ align:start position:0%
+continuous linear functional that we
+wanted to to extend okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so let's
+
+ align:start position:0%
+um so let's
+ 
+
+ align:start position:0%
+um so let's
+let's prove dilemma and that'll conclude
+
+ align:start position:0%
+let's prove dilemma and that'll conclude
+ 
+
+ align:start position:0%
+let's prove dilemma and that'll conclude
+the proof of the harmonic theorem
+
+ align:start position:0%
+the proof of the harmonic theorem
+ 
+
+ align:start position:0%
+the proof of the harmonic theorem
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof of dilemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that limb up there if V is the norm
+
+ align:start position:0%
+so that limb up there if V is the norm
+ 
+
+ align:start position:0%
+so that limb up there if V is the norm
+space and and uh
+
+ align:start position:0%
+space and and uh
+ 
+
+ align:start position:0%
+space and and uh
+you take something that's not in uh
+
+ align:start position:0%
+you take something that's not in uh
+ 
+
+ align:start position:0%
+you take something that's not in uh
+the Subspace and you can extend you
+
+ align:start position:0%
+the Subspace and you can extend you
+ 
+
+ align:start position:0%
+the Subspace and you can extend you
+continuously to this bigger
+
+ align:start position:0%
+continuously to this bigger
+ 
+
+ align:start position:0%
+continuously to this bigger
+Subspace all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first off
+
+ align:start position:0%
+so first off
+ 
+
+ align:start position:0%
+so first off
+you know even though I keep saying that
+
+ align:start position:0%
+you know even though I keep saying that
+ 
+
+ align:start position:0%
+you know even though I keep saying that
+this is a Subspace I mean this is kind
+
+ align:start position:0%
+this is a Subspace I mean this is kind
+ 
+
+ align:start position:0%
+this is a Subspace I mean this is kind
+of something that needs to be I mean
+
+ align:start position:0%
+of something that needs to be I mean
+ 
+
+ align:start position:0%
+of something that needs to be I mean
+it's not difficult to check but still
+
+ align:start position:0%
+it's not difficult to check but still
+ 
+
+ align:start position:0%
+it's not difficult to check but still
+check but also so one thing we need is
+
+ align:start position:0%
+check but also so one thing we need is
+ 
+
+ align:start position:0%
+check but also so one thing we need is
+that every element in uh you know a
+
+ align:start position:0%
+that every element in uh you know a
+ 
+
+ align:start position:0%
+that every element in uh you know a
+Subspace plus
+
+ align:start position:0%
+Subspace plus
+ 
+
+ align:start position:0%
+Subspace plus
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this constant times x can be written
+
+ align:start position:0%
+this constant times x can be written
+ 
+
+ align:start position:0%
+this constant times x can be written
+uniquely so we first note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+equals t
+
+ align:start position:0%
+equals t
+ 
+
+ align:start position:0%
+equals t
+so T Prime is in M Prime which remember
+
+ align:start position:0%
+so T Prime is in M Prime which remember
+ 
+
+ align:start position:0%
+so T Prime is in M Prime which remember
+is M plus
+
+ align:start position:0%
+is M plus
+ 
+
+ align:start position:0%
+is M plus
+constant times x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists unique T and M
+
+ align:start position:0%
+there exists unique T and M
+ 
+
+ align:start position:0%
+there exists unique T and M
+and a and complex numbers
+
+ align:start position:0%
+and a and complex numbers
+ 
+
+ align:start position:0%
+and a and complex numbers
+such that t Prime equals t plus a times
+
+ align:start position:0%
+such that t Prime equals t plus a times
+ 
+
+ align:start position:0%
+such that t Prime equals t plus a times
+x okay
+
+ align:start position:0%
+x okay
+ 
+
+ align:start position:0%
+x okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+all right so why is that
+
+ align:start position:0%
+all right so why is that
+ 
+
+ align:start position:0%
+all right so why is that
+so why can an element of this space not
+
+ align:start position:0%
+so why can an element of this space not
+ 
+
+ align:start position:0%
+so why can an element of this space not
+have two different representations not
+
+ align:start position:0%
+have two different representations not
+ 
+
+ align:start position:0%
+have two different representations not
+be written as you know two different
+
+ align:start position:0%
+be written as you know two different
+ 
+
+ align:start position:0%
+be written as you know two different
+elements of M plus two different scalars
+
+ align:start position:0%
+elements of M plus two different scalars
+ 
+
+ align:start position:0%
+elements of M plus two different scalars
+times x well
+
+ align:start position:0%
+times x well
+ 
+
+ align:start position:0%
+times x well
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+t plus a x equals T tilde plus a tilde X
+
+ align:start position:0%
+t plus a x equals T tilde plus a tilde X
+ 
+
+ align:start position:0%
+t plus a x equals T tilde plus a tilde X
+then this implies that a minus a tilde
+
+ align:start position:0%
+then this implies that a minus a tilde
+ 
+
+ align:start position:0%
+then this implies that a minus a tilde
+times x is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T tilde minus t which is in M okay m is
+
+ align:start position:0%
+T tilde minus t which is in M okay m is
+ 
+
+ align:start position:0%
+T tilde minus t which is in M okay m is
+the Subspace so the difference of two
+
+ align:start position:0%
+the Subspace so the difference of two
+ 
+
+ align:start position:0%
+the Subspace so the difference of two
+elements of uh m is in m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a does not equal a tilde then that
+
+ align:start position:0%
+if a does not equal a tilde then that
+ 
+
+ align:start position:0%
+if a does not equal a tilde then that
+means X is equal to a constant multiple
+
+ align:start position:0%
+means X is equal to a constant multiple
+ 
+
+ align:start position:0%
+means X is equal to a constant multiple
+of something in m and therefore X is an
+
+ align:start position:0%
+of something in m and therefore X is an
+ 
+
+ align:start position:0%
+of something in m and therefore X is an
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+so we conclude that a must equal a tilde
+
+ align:start position:0%
+so we conclude that a must equal a tilde
+ 
+
+ align:start position:0%
+so we conclude that a must equal a tilde
+which implies from assuming they're
+
+ align:start position:0%
+which implies from assuming they're
+ 
+
+ align:start position:0%
+which implies from assuming they're
+equal that t equals T tilde
+
+ align:start position:0%
+equal that t equals T tilde
+ 
+
+ align:start position:0%
+equal that t equals T tilde
+all right so every element in this
+
+ align:start position:0%
+all right so every element in this
+ 
+
+ align:start position:0%
+all right so every element in this
+larger Subspace can be written uniquely
+
+ align:start position:0%
+larger Subspace can be written uniquely
+ 
+
+ align:start position:0%
+larger Subspace can be written uniquely
+as an element of M plus a scalar
+
+ align:start position:0%
+as an element of M plus a scalar
+ 
+
+ align:start position:0%
+as an element of M plus a scalar
+multiple of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now why do we need this fact we need
+
+ align:start position:0%
+now why do we need this fact we need
+ 
+
+ align:start position:0%
+now why do we need this fact we need
+this fact to be able to
+
+ align:start position:0%
+this fact to be able to
+ 
+
+ align:start position:0%
+this fact to be able to
+say that this linear functional that
+
+ align:start position:0%
+say that this linear functional that
+ 
+
+ align:start position:0%
+say that this linear functional that
+we're gonna
+
+ align:start position:0%
+we're gonna
+ 
+
+ align:start position:0%
+we're gonna
+Define that we hope to say extends you
+
+ align:start position:0%
+Define that we hope to say extends you
+ 
+
+ align:start position:0%
+Define that we hope to say extends you
+continuously
+
+ align:start position:0%
+continuously
+ 
+
+ align:start position:0%
+continuously
+um you know it is in fact well defined
+
+ align:start position:0%
+um you know it is in fact well defined
+ 
+
+ align:start position:0%
+um you know it is in fact well defined
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upon choosing
+
+ align:start position:0%
+upon choosing
+ 
+
+ align:start position:0%
+upon choosing
+a number Lambda
+
+ align:start position:0%
+a number Lambda
+ 
+
+ align:start position:0%
+a number Lambda
+in the complex numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U Prime of
+
+ align:start position:0%
+U Prime of
+ 
+
+ align:start position:0%
+U Prime of
+t plus
+
+ align:start position:0%
+t plus
+ 
+
+ align:start position:0%
+t plus
+ax
+
+ align:start position:0%
+ax
+ 
+
+ align:start position:0%
+ax
+given by U of T Plus
+
+ align:start position:0%
+given by U of T Plus
+ 
+
+ align:start position:0%
+given by U of T Plus
+a Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+well defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we've shown every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on M Prime
+
+ align:start position:0%
+on M Prime
+ 
+
+ align:start position:0%
+on M Prime
+because we've shown every element of
+
+ align:start position:0%
+because we've shown every element of
+ 
+
+ align:start position:0%
+because we've shown every element of
+imprime can be written uniquely in this
+
+ align:start position:0%
+imprime can be written uniquely in this
+ 
+
+ align:start position:0%
+imprime can be written uniquely in this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+is well defined on M Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and U Prime going from M Prime to C
+
+ align:start position:0%
+and U Prime going from M Prime to C
+ 
+
+ align:start position:0%
+and U Prime going from M Prime to C
+is linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if the
+
+ align:start position:0%
+if the
+ 
+
+ align:start position:0%
+if the
+original uh functional U little U is if
+
+ align:start position:0%
+original uh functional U little U is if
+ 
+
+ align:start position:0%
+original uh functional U little U is if
+that constant C is equal to zero then
+
+ align:start position:0%
+that constant C is equal to zero then
+ 
+
+ align:start position:0%
+that constant C is equal to zero then
+little U is just identically zero and we
+
+ align:start position:0%
+little U is just identically zero and we
+ 
+
+ align:start position:0%
+little U is just identically zero and we
+know how to extend the zero functional
+
+ align:start position:0%
+know how to extend the zero functional
+ 
+
+ align:start position:0%
+know how to extend the zero functional
+so let's suppose Capital C uh is
+
+ align:start position:0%
+so let's suppose Capital C uh is
+ 
+
+ align:start position:0%
+so let's suppose Capital C uh is
+non-zero
+
+ align:start position:0%
+non-zero
+ 
+
+ align:start position:0%
+non-zero
+and if I divide little U by Capital C I
+
+ align:start position:0%
+and if I divide little U by Capital C I
+ 
+
+ align:start position:0%
+and if I divide little U by Capital C I
+can then extend that functional uh
+
+ align:start position:0%
+can then extend that functional uh
+ 
+
+ align:start position:0%
+can then extend that functional uh
+with the case Capital C equals one and
+
+ align:start position:0%
+with the case Capital C equals one and
+ 
+
+ align:start position:0%
+with the case Capital C equals one and
+obtain an extension satisfying uh the
+
+ align:start position:0%
+obtain an extension satisfying uh the
+ 
+
+ align:start position:0%
+obtain an extension satisfying uh the
+bound I want
+
+ align:start position:0%
+bound I want
+ 
+
+ align:start position:0%
+bound I want
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh so what I'm saying
+
+ align:start position:0%
+uh so what I'm saying
+ 
+
+ align:start position:0%
+uh so what I'm saying
+kind of poorly is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll leave you a second to think about
+
+ align:start position:0%
+I'll leave you a second to think about
+ 
+
+ align:start position:0%
+I'll leave you a second to think about
+it it's not
+
+ align:start position:0%
+it it's not
+ 
+
+ align:start position:0%
+it it's not
+difficult to understand why without loss
+
+ align:start position:0%
+difficult to understand why without loss
+ 
+
+ align:start position:0%
+difficult to understand why without loss
+of generality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can assume
+
+ align:start position:0%
+we can assume
+ 
+
+ align:start position:0%
+we can assume
+C equals one okay
+
+ align:start position:0%
+C equals one okay
+ 
+
+ align:start position:0%
+C equals one okay
+you know if C is not equal to one so if
+
+ align:start position:0%
+you know if C is not equal to one so if
+ 
+
+ align:start position:0%
+you know if C is not equal to one so if
+we do this equals one case then for the
+
+ align:start position:0%
+we do this equals one case then for the
+ 
+
+ align:start position:0%
+we do this equals one case then for the
+KC not equal to one we extend U over
+
+ align:start position:0%
+KC not equal to one we extend U over
+ 
+
+ align:start position:0%
+KC not equal to one we extend U over
+capital c
+
+ align:start position:0%
+capital c
+ 
+
+ align:start position:0%
+capital c
+using the C equals one case and then the
+
+ align:start position:0%
+using the C equals one case and then the
+ 
+
+ align:start position:0%
+using the C equals one case and then the
+result follows so we'll just do the case
+
+ align:start position:0%
+result follows so we'll just do the case
+ 
+
+ align:start position:0%
+result follows so we'll just do the case
+C equals capital or Capital C equals one
+
+ align:start position:0%
+C equals capital or Capital C equals one
+ 
+
+ align:start position:0%
+C equals capital or Capital C equals one
+uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now our one free parameter is Lambda
+
+ align:start position:0%
+now our one free parameter is Lambda
+ 
+
+ align:start position:0%
+now our one free parameter is Lambda
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we want to be able to choose Lambda
+
+ align:start position:0%
+and we want to be able to choose Lambda
+ 
+
+ align:start position:0%
+and we want to be able to choose Lambda
+so that so this is already an extension
+
+ align:start position:0%
+so that so this is already an extension
+ 
+
+ align:start position:0%
+so that so this is already an extension
+of little U right if I take a equals 0
+
+ align:start position:0%
+of little U right if I take a equals 0
+ 
+
+ align:start position:0%
+of little U right if I take a equals 0
+so I'm just taking elements in M this is
+
+ align:start position:0%
+so I'm just taking elements in M this is
+ 
+
+ align:start position:0%
+so I'm just taking elements in M this is
+U Prime of what of T is equal to U of T
+
+ align:start position:0%
+U Prime of what of T is equal to U of T
+ 
+
+ align:start position:0%
+U Prime of what of T is equal to U of T
+so it's already an extension of little U
+
+ align:start position:0%
+so it's already an extension of little U
+ 
+
+ align:start position:0%
+so it's already an extension of little U
+to this bigger Subspace and now what we
+
+ align:start position:0%
+to this bigger Subspace and now what we
+ 
+
+ align:start position:0%
+to this bigger Subspace and now what we
+want to be able to choose Lambda so that
+
+ align:start position:0%
+want to be able to choose Lambda so that
+ 
+
+ align:start position:0%
+want to be able to choose Lambda so that
+it extends it in a continuous way with
+
+ align:start position:0%
+it extends it in a continuous way with
+ 
+
+ align:start position:0%
+it extends it in a continuous way with
+the same constant being one and that
+
+ align:start position:0%
+the same constant being one and that
+ 
+
+ align:start position:0%
+the same constant being one and that
+inequality up there okay so I keep
+
+ align:start position:0%
+inequality up there okay so I keep
+ 
+
+ align:start position:0%
+inequality up there okay so I keep
+pointing up there I don't think the
+
+ align:start position:0%
+pointing up there I don't think the
+ 
+
+ align:start position:0%
+pointing up there I don't think the
+camera's like
+
+ align:start position:0%
+camera's like
+ 
+
+ align:start position:0%
+camera's like
+looking up there so you'll have to
+
+ align:start position:0%
+looking up there so you'll have to
+ 
+
+ align:start position:0%
+looking up there so you'll have to
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+interpret my meaning correctly so we
+
+ align:start position:0%
+interpret my meaning correctly so we
+ 
+
+ align:start position:0%
+interpret my meaning correctly so we
+want to choose Lambda
+
+ align:start position:0%
+want to choose Lambda
+ 
+
+ align:start position:0%
+want to choose Lambda
+complex number
+
+ align:start position:0%
+complex number
+ 
+
+ align:start position:0%
+complex number
+such that the following holds
+
+ align:start position:0%
+such that the following holds
+ 
+
+ align:start position:0%
+such that the following holds
+for all T and M A and C
+
+ align:start position:0%
+for all T and M A and C
+ 
+
+ align:start position:0%
+for all T and M A and C
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+U Prime of
+
+ align:start position:0%
+U Prime of
+ 
+
+ align:start position:0%
+U Prime of
+t plus ax which is just U of T plus a
+
+ align:start position:0%
+t plus ax which is just U of T plus a
+ 
+
+ align:start position:0%
+t plus ax which is just U of T plus a
+Lambda and absolute value is less than
+
+ align:start position:0%
+Lambda and absolute value is less than
+ 
+
+ align:start position:0%
+Lambda and absolute value is less than
+or equal to
+
+ align:start position:0%
+or equal to
+ 
+
+ align:start position:0%
+or equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Norm of t plus a Lambda if we're able to
+
+ align:start position:0%
+Norm of t plus a Lambda if we're able to
+ 
+
+ align:start position:0%
+Norm of t plus a Lambda if we're able to
+do that then U Prime is then our
+
+ align:start position:0%
+do that then U Prime is then our
+ 
+
+ align:start position:0%
+do that then U Prime is then our
+continuous extension that we're looking
+
+ align:start position:0%
+continuous extension that we're looking
+ 
+
+ align:start position:0%
+continuous extension that we're looking
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is our
+
+ align:start position:0%
+is our
+ 
+
+ align:start position:0%
+is our
+continuous extension
+
+ align:start position:0%
+continuous extension
+ 
+
+ align:start position:0%
+continuous extension
+so all that we need to do now
+
+ align:start position:0%
+so all that we need to do now
+ 
+
+ align:start position:0%
+so all that we need to do now
+is find
+
+ align:start position:0%
+is find
+ 
+
+ align:start position:0%
+is find
+a Lambda
+
+ align:start position:0%
+a Lambda
+ 
+
+ align:start position:0%
+a Lambda
+so that this holds
+
+ align:start position:0%
+so that this holds
+ 
+
+ align:start position:0%
+so that this holds
+okay and once we've done that we've
+
+ align:start position:0%
+okay and once we've done that we've
+ 
+
+ align:start position:0%
+okay and once we've done that we've
+finished the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that thing I boxed in a minute ago
+
+ align:start position:0%
+now that thing I boxed in a minute ago
+ 
+
+ align:start position:0%
+now that thing I boxed in a minute ago
+uh we're gonna reduce it to kind of a
+
+ align:start position:0%
+uh we're gonna reduce it to kind of a
+ 
+
+ align:start position:0%
+uh we're gonna reduce it to kind of a
+simplest form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what's in the box holds regardless what
+
+ align:start position:0%
+what's in the box holds regardless what
+ 
+
+ align:start position:0%
+what's in the box holds regardless what
+Lambda is when a is equal to zero okay
+
+ align:start position:0%
+Lambda is when a is equal to zero okay
+ 
+
+ align:start position:0%
+Lambda is when a is equal to zero okay
+and now what I'm going to do is
+
+ align:start position:0%
+and now what I'm going to do is
+ 
+
+ align:start position:0%
+and now what I'm going to do is
+basically remove the fact that a can
+
+ align:start position:0%
+basically remove the fact that a can
+ 
+
+ align:start position:0%
+basically remove the fact that a can
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the estimate U
+
+ align:start position:0%
+the estimate U
+ 
+
+ align:start position:0%
+the estimate U
+t plus a Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less than or equal to t plus a Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when a equals zero
+
+ align:start position:0%
+when a equals zero
+ 
+
+ align:start position:0%
+when a equals zero
+regardless of how we've chosen Lambda so
+
+ align:start position:0%
+regardless of how we've chosen Lambda so
+ 
+
+ align:start position:0%
+regardless of how we've chosen Lambda so
+we just need to be able to choose Lambda
+
+ align:start position:0%
+we just need to be able to choose Lambda
+ 
+
+ align:start position:0%
+we just need to be able to choose Lambda
+so that this holds for a non-zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+trying to choose Lambda so that this
+
+ align:start position:0%
+trying to choose Lambda so that this
+ 
+
+ align:start position:0%
+trying to choose Lambda so that this
+holds for all uh a non-zero okay now let
+
+ align:start position:0%
+holds for all uh a non-zero okay now let
+ 
+
+ align:start position:0%
+holds for all uh a non-zero okay now let
+me take this inequality here
+
+ align:start position:0%
+me take this inequality here
+ 
+
+ align:start position:0%
+me take this inequality here
+and divide it by uh the absolute value
+
+ align:start position:0%
+and divide it by uh the absolute value
+ 
+
+ align:start position:0%
+and divide it by uh the absolute value
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+that inequality
+
+ align:start position:0%
+that inequality
+ 
+
+ align:start position:0%
+that inequality
+or a not equal to so so for all a not
+
+ align:start position:0%
+or a not equal to so so for all a not
+ 
+
+ align:start position:0%
+or a not equal to so so for all a not
+equal to zero this is equivalent to uh
+
+ align:start position:0%
+equal to zero this is equivalent to uh
+ 
+
+ align:start position:0%
+equal to zero this is equivalent to uh
+if I divide by
+
+ align:start position:0%
+if I divide by
+ 
+
+ align:start position:0%
+if I divide by
+the norm of a and bring this inside the
+
+ align:start position:0%
+the norm of a and bring this inside the
+ 
+
+ align:start position:0%
+the norm of a and bring this inside the
+module inside the norm
+
+ align:start position:0%
+module inside the norm
+ 
+
+ align:start position:0%
+module inside the norm
+U of
+
+ align:start position:0%
+U of
+ 
+
+ align:start position:0%
+U of
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+minus a
+
+ align:start position:0%
+minus a
+ 
+
+ align:start position:0%
+minus a
+minus Lambda
+
+ align:start position:0%
+minus Lambda
+ 
+
+ align:start position:0%
+minus Lambda
+is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I should say this is the absolute
+
+ align:start position:0%
+or I should say this is the absolute
+ 
+
+ align:start position:0%
+or I should say this is the absolute
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+and that's the absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less than or equal to uh
+
+ align:start position:0%
+less than or equal to uh
+ 
+
+ align:start position:0%
+less than or equal to uh
+T over minus a minus Lambda
+
+ align:start position:0%
+T over minus a minus Lambda
+ 
+
+ align:start position:0%
+T over minus a minus Lambda
+for all t
+
+ align:start position:0%
+for all t
+ 
+
+ align:start position:0%
+for all t
+in M now
+
+ align:start position:0%
+in M now
+ 
+
+ align:start position:0%
+in M now
+if T is an m t over minus a is also an m
+
+ align:start position:0%
+if T is an m t over minus a is also an m
+ 
+
+ align:start position:0%
+if T is an m t over minus a is also an m
+so this bound here
+
+ align:start position:0%
+so this bound here
+ 
+
+ align:start position:0%
+so this bound here
+is equivalent to showing that we can
+
+ align:start position:0%
+is equivalent to showing that we can
+ 
+
+ align:start position:0%
+is equivalent to showing that we can
+choose Lambda so that U of
+
+ align:start position:0%
+choose Lambda so that U of
+ 
+
+ align:start position:0%
+choose Lambda so that U of
+T minus Lambda is less than or equal to
+
+ align:start position:0%
+T minus Lambda is less than or equal to
+ 
+
+ align:start position:0%
+T minus Lambda is less than or equal to
+the norm of T minus Lambda
+
+ align:start position:0%
+the norm of T minus Lambda
+ 
+
+ align:start position:0%
+the norm of T minus Lambda
+for all T in M okay so since T is the
+
+ align:start position:0%
+for all T in M okay so since T is the
+ 
+
+ align:start position:0%
+for all T in M okay so since T is the
+Subspace proving this bound or choosing
+
+ align:start position:0%
+Subspace proving this bound or choosing
+ 
+
+ align:start position:0%
+Subspace proving this bound or choosing
+Lambda so that this bound holds is
+
+ align:start position:0%
+Lambda so that this bound holds is
+ 
+
+ align:start position:0%
+Lambda so that this bound holds is
+equivalent to choosing Lambda so that
+
+ align:start position:0%
+equivalent to choosing Lambda so that
+ 
+
+ align:start position:0%
+equivalent to choosing Lambda so that
+this bound holds Okay so
+
+ align:start position:0%
+this bound holds Okay so
+ 
+
+ align:start position:0%
+this bound holds Okay so
+in sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or in summary
+
+ align:start position:0%
+or in summary
+ 
+
+ align:start position:0%
+or in summary
+say In Sum it's
+
+ align:start position:0%
+say In Sum it's
+ 
+
+ align:start position:0%
+say In Sum it's
+I'm thinking in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in summary the thing that we wanted
+
+ align:start position:0%
+so in summary the thing that we wanted
+ 
+
+ align:start position:0%
+so in summary the thing that we wanted
+to show originally that we can choose
+
+ align:start position:0%
+to show originally that we can choose
+ 
+
+ align:start position:0%
+to show originally that we can choose
+Lambda so that for all T and M a complex
+
+ align:start position:0%
+Lambda so that for all T and M a complex
+ 
+
+ align:start position:0%
+Lambda so that for all T and M a complex
+number that inequality holds is
+
+ align:start position:0%
+number that inequality holds is
+ 
+
+ align:start position:0%
+number that inequality holds is
+equivalent to showing that we can choose
+
+ align:start position:0%
+equivalent to showing that we can choose
+ 
+
+ align:start position:0%
+equivalent to showing that we can choose
+Lambda so that this inequality holds
+
+ align:start position:0%
+Lambda so that this inequality holds
+ 
+
+ align:start position:0%
+Lambda so that this inequality holds
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's the point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now what we're going to do is we're
+
+ align:start position:0%
+and now what we're going to do is we're
+ 
+
+ align:start position:0%
+and now what we're going to do is we're
+going to choose the real and imaginary
+
+ align:start position:0%
+going to choose the real and imaginary
+ 
+
+ align:start position:0%
+going to choose the real and imaginary
+parts of Lambda okay and we'll choose
+
+ align:start position:0%
+parts of Lambda okay and we'll choose
+ 
+
+ align:start position:0%
+parts of Lambda okay and we'll choose
+the real part of Lambda first
+
+ align:start position:0%
+the real part of Lambda first
+ 
+
+ align:start position:0%
+the real part of Lambda first
+so we first prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weird I gotta get a different one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we first proved that there exists an
+
+ align:start position:0%
+we first proved that there exists an
+ 
+
+ align:start position:0%
+we first proved that there exists an
+alpha and r
+
+ align:start position:0%
+alpha and r
+ 
+
+ align:start position:0%
+alpha and r
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+uh W of t
+
+ align:start position:0%
+uh W of t
+ 
+
+ align:start position:0%
+uh W of t
+minus Alpha
+
+ align:start position:0%
+minus Alpha
+ 
+
+ align:start position:0%
+minus Alpha
+an absolute value is less than or equal
+
+ align:start position:0%
+an absolute value is less than or equal
+ 
+
+ align:start position:0%
+an absolute value is less than or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+T minus Alpha
+
+ align:start position:0%
+T minus Alpha
+ 
+
+ align:start position:0%
+T minus Alpha
+for all T and M
+
+ align:start position:0%
+for all T and M
+ 
+
+ align:start position:0%
+for all T and M
+and what is w of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to the real part
+
+ align:start position:0%
+this is equal to the real part
+ 
+
+ align:start position:0%
+this is equal to the real part
+of U of T
+
+ align:start position:0%
+of U of T
+ 
+
+ align:start position:0%
+of U of T
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which let me
+
+ align:start position:0%
+which let me
+ 
+
+ align:start position:0%
+which let me
+mind you this is just equal to U of T
+
+ align:start position:0%
+mind you this is just equal to U of T
+ 
+
+ align:start position:0%
+mind you this is just equal to U of T
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+u t complex conjugate over 2.
+
+ align:start position:0%
+u t complex conjugate over 2.
+ 
+
+ align:start position:0%
+u t complex conjugate over 2.
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+the real part of any complex number is
+
+ align:start position:0%
+the real part of any complex number is
+ 
+
+ align:start position:0%
+the real part of any complex number is
+always less than or equal to uh the
+
+ align:start position:0%
+always less than or equal to uh the
+ 
+
+ align:start position:0%
+always less than or equal to uh the
+absolute value of that complex number so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we haven't chosen what Alpha is yet I'll
+
+ align:start position:0%
+we haven't chosen what Alpha is yet I'll
+ 
+
+ align:start position:0%
+we haven't chosen what Alpha is yet I'll
+show you how to choose Alpha in just a
+
+ align:start position:0%
+show you how to choose Alpha in just a
+ 
+
+ align:start position:0%
+show you how to choose Alpha in just a
+minute note that for all T and M
+
+ align:start position:0%
+minute note that for all T and M
+ 
+
+ align:start position:0%
+minute note that for all T and M
+W of t
+
+ align:start position:0%
+W of t
+ 
+
+ align:start position:0%
+W of t
+an absolute value which remember is
+
+ align:start position:0%
+an absolute value which remember is
+ 
+
+ align:start position:0%
+an absolute value which remember is
+defined to be the real part of U of T
+
+ align:start position:0%
+defined to be the real part of U of T
+ 
+
+ align:start position:0%
+defined to be the real part of U of T
+this is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolute value of U of T because
+
+ align:start position:0%
+absolute value of U of T because
+ 
+
+ align:start position:0%
+absolute value of U of T because
+I should say the modulus of U of T the
+
+ align:start position:0%
+I should say the modulus of U of T the
+ 
+
+ align:start position:0%
+I should say the modulus of U of T the
+modulus of a complex number is the
+
+ align:start position:0%
+modulus of a complex number is the
+ 
+
+ align:start position:0%
+modulus of a complex number is the
+square root of the sum of the real part
+
+ align:start position:0%
+square root of the sum of the real part
+ 
+
+ align:start position:0%
+square root of the sum of the real part
+squared and the imaginary part squared
+
+ align:start position:0%
+squared and the imaginary part squared
+ 
+
+ align:start position:0%
+squared and the imaginary part squared
+so that's always less than or equal
+
+ align:start position:0%
+so that's always less than or equal
+ 
+
+ align:start position:0%
+so that's always less than or equal
+to that and by assumption this is less
+
+ align:start position:0%
+to that and by assumption this is less
+ 
+
+ align:start position:0%
+to that and by assumption this is less
+than or equal to
+
+ align:start position:0%
+than or equal to
+ 
+
+ align:start position:0%
+than or equal to
+the norm of t
+
+ align:start position:0%
+the norm of t
+ 
+
+ align:start position:0%
+the norm of t
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we're going to use the part that
+
+ align:start position:0%
+now we're going to use the part that
+ 
+
+ align:start position:0%
+now we're going to use the part that
+we're going to use the fact that W is
+
+ align:start position:0%
+we're going to use the fact that W is
+ 
+
+ align:start position:0%
+we're going to use the fact that W is
+real valued
+
+ align:start position:0%
+real valued
+ 
+
+ align:start position:0%
+real valued
+then W of T1 minus w
+
+ align:start position:0%
+then W of T1 minus w
+ 
+
+ align:start position:0%
+then W of T1 minus w
+of T2 so let me say for all T1 T2 and M
+
+ align:start position:0%
+of T2 so let me say for all T1 T2 and M
+ 
+
+ align:start position:0%
+of T2 so let me say for all T1 T2 and M
+if I look at w of T1 minus W of T2 this
+
+ align:start position:0%
+if I look at w of T1 minus W of T2 this
+ 
+
+ align:start position:0%
+if I look at w of T1 minus W of T2 this
+is equal to and Since U is linear and
+
+ align:start position:0%
+is equal to and Since U is linear and
+ 
+
+ align:start position:0%
+is equal to and Since U is linear and
+taking the real part is linear it's
+
+ align:start position:0%
+taking the real part is linear it's
+ 
+
+ align:start position:0%
+taking the real part is linear it's
+this is equal to W of T1
+
+ align:start position:0%
+this is equal to W of T1
+ 
+
+ align:start position:0%
+this is equal to W of T1
+minus W of T2 this is less than or equal
+
+ align:start position:0%
+minus W of T2 this is less than or equal
+ 
+
+ align:start position:0%
+minus W of T2 this is less than or equal
+to its absolute value this is where I'm
+
+ align:start position:0%
+to its absolute value this is where I'm
+ 
+
+ align:start position:0%
+to its absolute value this is where I'm
+using the fact that it's real valued
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and as we've just shown that this is
+
+ align:start position:0%
+and as we've just shown that this is
+ 
+
+ align:start position:0%
+and as we've just shown that this is
+always less than or equal to the
+
+ align:start position:0%
+always less than or equal to the
+ 
+
+ align:start position:0%
+always less than or equal to the
+absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have that
+
+ align:start position:0%
+we have that
+ 
+
+ align:start position:0%
+we have that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now I'm going to do one more thing
+
+ align:start position:0%
+and now I'm going to do one more thing
+ 
+
+ align:start position:0%
+and now I'm going to do one more thing
+and add and subtract X so this is you
+
+ align:start position:0%
+and add and subtract X so this is you
+ 
+
+ align:start position:0%
+and add and subtract X so this is you
+know in the end we want
+
+ align:start position:0%
+know in the end we want
+ 
+
+ align:start position:0%
+know in the end we want
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+whoa whoa whoa whoa
+
+ align:start position:0%
+whoa whoa whoa whoa
+ 
+
+ align:start position:0%
+whoa whoa whoa whoa
+this should have been X
+
+ align:start position:0%
+this should have been X
+ 
+
+ align:start position:0%
+this should have been X
+this should have been X sorry sorry I
+
+ align:start position:0%
+this should have been X sorry sorry I
+ 
+
+ align:start position:0%
+this should have been X sorry sorry I
+hope uh you fast forward forwarded to
+
+ align:start position:0%
+hope uh you fast forward forwarded to
+ 
+
+ align:start position:0%
+hope uh you fast forward forwarded to
+this point and saw that this should have
+
+ align:start position:0%
+this point and saw that this should have
+ 
+
+ align:start position:0%
+this point and saw that this should have
+been x and x okay
+
+ align:start position:0%
+been x and x okay
+ 
+
+ align:start position:0%
+been x and x okay
+so you know in the end we want to
+
+ align:start position:0%
+so you know in the end we want to
+ 
+
+ align:start position:0%
+so you know in the end we want to
+somehow connect
+
+ align:start position:0%
+somehow connect
+ 
+
+ align:start position:0%
+somehow connect
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this to and I did it again here x
+
+ align:start position:0%
+this to and I did it again here x
+ 
+
+ align:start position:0%
+this to and I did it again here x
+to the norm of T minus X so what I'm
+
+ align:start position:0%
+to the norm of T minus X so what I'm
+ 
+
+ align:start position:0%
+to the norm of T minus X so what I'm
+going to do is add and subtract X and
+
+ align:start position:0%
+going to do is add and subtract X and
+ 
+
+ align:start position:0%
+going to do is add and subtract X and
+use the triangle inequality and this is
+
+ align:start position:0%
+use the triangle inequality and this is
+ 
+
+ align:start position:0%
+use the triangle inequality and this is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+T1 minus X Plus
+
+ align:start position:0%
+T1 minus X Plus
+ 
+
+ align:start position:0%
+T1 minus X Plus
+T2 minus X
+
+ align:start position:0%
+T2 minus X
+ 
+
+ align:start position:0%
+T2 minus X
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore W of T1 minus the norm of
+
+ align:start position:0%
+and therefore W of T1 minus the norm of
+ 
+
+ align:start position:0%
+and therefore W of T1 minus the norm of
+T1 minus X
+
+ align:start position:0%
+T1 minus X
+ 
+
+ align:start position:0%
+T1 minus X
+is less than or equal to W of T2 plus
+
+ align:start position:0%
+is less than or equal to W of T2 plus
+ 
+
+ align:start position:0%
+is less than or equal to W of T2 plus
+Norm of
+
+ align:start position:0%
+Norm of
+ 
+
+ align:start position:0%
+Norm of
+T minus T2 minus X
+
+ align:start position:0%
+T minus T2 minus X
+ 
+
+ align:start position:0%
+T minus T2 minus X
+for all T1 and T2 and M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this holds for all T1 and T2 so I
+
+ align:start position:0%
+so this holds for all T1 and T2 so I
+ 
+
+ align:start position:0%
+so this holds for all T1 and T2 so I
+could fix uh T2 and take the soup over
+
+ align:start position:0%
+could fix uh T2 and take the soup over
+ 
+
+ align:start position:0%
+could fix uh T2 and take the soup over
+all t1s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies that
+
+ align:start position:0%
+which implies that
+ 
+
+ align:start position:0%
+which implies that
+soup of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's not make that a T1 I could just
+
+ align:start position:0%
+so let's not make that a T1 I could just
+ 
+
+ align:start position:0%
+so let's not make that a T1 I could just
+say t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is always less than or equal to W of T2
+
+ align:start position:0%
+is always less than or equal to W of T2
+ 
+
+ align:start position:0%
+is always less than or equal to W of T2
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+T2 minus X and this holds for all
+
+ align:start position:0%
+T2 minus X and this holds for all
+ 
+
+ align:start position:0%
+T2 minus X and this holds for all
+T2 and M
+
+ align:start position:0%
+T2 and M
+ 
+
+ align:start position:0%
+T2 and M
+so the fact that this holds for all T1
+
+ align:start position:0%
+so the fact that this holds for all T1
+ 
+
+ align:start position:0%
+so the fact that this holds for all T1
+tells you this thing is an upper bound
+
+ align:start position:0%
+tells you this thing is an upper bound
+ 
+
+ align:start position:0%
+tells you this thing is an upper bound
+of this for all T and M and therefore
+
+ align:start position:0%
+of this for all T and M and therefore
+ 
+
+ align:start position:0%
+of this for all T and M and therefore
+it's supremum is less than or equal to
+
+ align:start position:0%
+it's supremum is less than or equal to
+ 
+
+ align:start position:0%
+it's supremum is less than or equal to
+this thing for all T2 and M and
+
+ align:start position:0%
+this thing for all T2 and M and
+ 
+
+ align:start position:0%
+this thing for all T2 and M and
+therefore this quantity on the left is a
+
+ align:start position:0%
+therefore this quantity on the left is a
+ 
+
+ align:start position:0%
+therefore this quantity on the left is a
+lower Bound for this thing on the right
+
+ align:start position:0%
+lower Bound for this thing on the right
+ 
+
+ align:start position:0%
+lower Bound for this thing on the right
+for all T 2 and M
+
+ align:start position:0%
+for all T 2 and M
+ 
+
+ align:start position:0%
+for all T 2 and M
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+we conclude that the soup of T and M of
+
+ align:start position:0%
+we conclude that the soup of T and M of
+ 
+
+ align:start position:0%
+we conclude that the soup of T and M of
+w of T minus Norm of T minus X
+
+ align:start position:0%
+w of T minus Norm of T minus X
+ 
+
+ align:start position:0%
+w of T minus Norm of T minus X
+is all is less than or equal to
+
+ align:start position:0%
+is all is less than or equal to
+ 
+
+ align:start position:0%
+is all is less than or equal to
+the emph over all D and M
+
+ align:start position:0%
+the emph over all D and M
+ 
+
+ align:start position:0%
+the emph over all D and M
+uh W of t
+
+ align:start position:0%
+uh W of t
+ 
+
+ align:start position:0%
+uh W of t
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+T minus X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do I choose Alpha so I have these
+
+ align:start position:0%
+how do I choose Alpha so I have these
+ 
+
+ align:start position:0%
+how do I choose Alpha so I have these
+two numbers here which are related in
+
+ align:start position:0%
+two numbers here which are related in
+ 
+
+ align:start position:0%
+two numbers here which are related in
+this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I choose Alpha
+
+ align:start position:0%
+I choose Alpha
+ 
+
+ align:start position:0%
+I choose Alpha
+between these two numbers between this
+
+ align:start position:0%
+between these two numbers between this
+ 
+
+ align:start position:0%
+between these two numbers between this
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+and this number so there's a less than
+
+ align:start position:0%
+and this number so there's a less than
+ 
+
+ align:start position:0%
+and this number so there's a less than
+or equal to sign so I can pick some
+
+ align:start position:0%
+or equal to sign so I can pick some
+ 
+
+ align:start position:0%
+or equal to sign so I can pick some
+number uh in between them maybe these
+
+ align:start position:0%
+number uh in between them maybe these
+ 
+
+ align:start position:0%
+number uh in between them maybe these
+two things are equal and therefore Alpha
+
+ align:start position:0%
+two things are equal and therefore Alpha
+ 
+
+ align:start position:0%
+two things are equal and therefore Alpha
+is equal to the to both of them or I
+
+ align:start position:0%
+is equal to the to both of them or I
+ 
+
+ align:start position:0%
+is equal to the to both of them or I
+could just choose Alpha to be this one
+
+ align:start position:0%
+could just choose Alpha to be this one
+ 
+
+ align:start position:0%
+could just choose Alpha to be this one
+it doesn't matter so uh
+
+ align:start position:0%
+it doesn't matter so uh
+ 
+
+ align:start position:0%
+it doesn't matter so uh
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and the proof is uh just about
+
+ align:start position:0%
+all right and the proof is uh just about
+ 
+
+ align:start position:0%
+all right and the proof is uh just about
+completed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now I show that now I'm going to show
+
+ align:start position:0%
+now I show that now I'm going to show
+ 
+
+ align:start position:0%
+now I show that now I'm going to show
+that this Alpha works
+
+ align:start position:0%
+that this Alpha works
+ 
+
+ align:start position:0%
+that this Alpha works
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're all T in capital M
+
+ align:start position:0%
+we're all T in capital M
+ 
+
+ align:start position:0%
+we're all T in capital M
+I have W of t
+
+ align:start position:0%
+I have W of t
+ 
+
+ align:start position:0%
+I have W of t
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+Norm of T minus X is less than or equal
+
+ align:start position:0%
+Norm of T minus X is less than or equal
+ 
+
+ align:start position:0%
+Norm of T minus X is less than or equal
+to Alpha
+
+ align:start position:0%
+to Alpha
+ 
+
+ align:start position:0%
+to Alpha
+is less than or equal to
+
+ align:start position:0%
+is less than or equal to
+ 
+
+ align:start position:0%
+is less than or equal to
+W of t uh
+
+ align:start position:0%
+W of t uh
+ 
+
+ align:start position:0%
+W of t uh
+plus Norm of T minus X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's less than or equal to Alpha minus W
+
+ align:start position:0%
+it's less than or equal to Alpha minus W
+ 
+
+ align:start position:0%
+it's less than or equal to Alpha minus W
+of t
+
+ align:start position:0%
+of t
+ 
+
+ align:start position:0%
+of t
+is less than or equal to Norm of T minus
+
+ align:start position:0%
+is less than or equal to Norm of T minus
+ 
+
+ align:start position:0%
+is less than or equal to Norm of T minus
+X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the same as Alpha minus W of t
+
+ align:start position:0%
+which is the same as Alpha minus W of t
+ 
+
+ align:start position:0%
+which is the same as Alpha minus W of t
+um I should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we showed how to do it for
+
+ align:start position:0%
+all right so we showed how to do it for
+ 
+
+ align:start position:0%
+all right so we showed how to do it for
+we're able to choose an alpha so that
+
+ align:start position:0%
+we're able to choose an alpha so that
+ 
+
+ align:start position:0%
+we're able to choose an alpha so that
+essentially this inequality holds for
+
+ align:start position:0%
+essentially this inequality holds for
+ 
+
+ align:start position:0%
+essentially this inequality holds for
+the real part we can do that also for
+
+ align:start position:0%
+the real part we can do that also for
+ 
+
+ align:start position:0%
+the real part we can do that also for
+the imaginary part
\ No newline at end of file
diff --git a/LvI6V3VbL9Q.txt b/LvI6V3VbL9Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..79acace452fda87fe147034bff4faa6733e9442c
--- /dev/null
+++ b/LvI6V3VbL9Q.txt
@@ -0,0 +1,17491 @@
+align:start position:0%
+ 
+so last week i talked about
+
+ align:start position:0%
+so last week i talked about
+ 
+
+ align:start position:0%
+so last week i talked about
+uh what did i talk about i talked about
+
+ align:start position:0%
+uh what did i talk about i talked about
+ 
+
+ align:start position:0%
+uh what did i talk about i talked about
+uh an introduction to molecular biology
+
+ align:start position:0%
+uh an introduction to molecular biology
+ 
+
+ align:start position:0%
+uh an introduction to molecular biology
+for about 10 or 12 slides and then since
+
+ align:start position:0%
+for about 10 or 12 slides and then since
+ 
+
+ align:start position:0%
+for about 10 or 12 slides and then since
+we're going pretty quickly i covered
+
+ align:start position:0%
+we're going pretty quickly i covered
+ 
+
+ align:start position:0%
+we're going pretty quickly i covered
+a lot of this material on gene
+
+ align:start position:0%
+a lot of this material on gene
+ 
+
+ align:start position:0%
+a lot of this material on gene
+measurement techniques
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh so we've already had one question
+
+ align:start position:0%
+and uh so we've already had one question
+ 
+
+ align:start position:0%
+and uh so we've already had one question
+or one request to talk about something
+
+ align:start position:0%
+or one request to talk about something
+ 
+
+ align:start position:0%
+or one request to talk about something
+i've actually flipped pretty quickly
+
+ align:start position:0%
+i've actually flipped pretty quickly
+ 
+
+ align:start position:0%
+i've actually flipped pretty quickly
+through this concept of sage and how
+
+ align:start position:0%
+through this concept of sage and how
+ 
+
+ align:start position:0%
+through this concept of sage and how
+does sage use two metro microwaves and
+
+ align:start position:0%
+does sage use two metro microwaves and
+ 
+
+ align:start position:0%
+does sage use two metro microwaves and
+actually it's uh measure rna and it's
+
+ align:start position:0%
+actually it's uh measure rna and it's
+ 
+
+ align:start position:0%
+actually it's uh measure rna and it's
+quite important that we actually talk
+
+ align:start position:0%
+quite important that we actually talk
+ 
+
+ align:start position:0%
+quite important that we actually talk
+about sage i think but i'm going to
+
+ align:start position:0%
+about sage i think but i'm going to
+ 
+
+ align:start position:0%
+about sage i think but i'm going to
+start the discussion with sage talking
+
+ align:start position:0%
+start the discussion with sage talking
+ 
+
+ align:start position:0%
+start the discussion with sage talking
+about microarrays again for a second
+
+ align:start position:0%
+about microarrays again for a second
+ 
+
+ align:start position:0%
+about microarrays again for a second
+okay so i already talked about
+
+ align:start position:0%
+okay so i already talked about
+ 
+
+ align:start position:0%
+okay so i already talked about
+microarrays how these are man-made grids
+
+ align:start position:0%
+microarrays how these are man-made grids
+ 
+
+ align:start position:0%
+microarrays how these are man-made grids
+of dna each spot in the grid is looking
+
+ align:start position:0%
+of dna each spot in the grid is looking
+ 
+
+ align:start position:0%
+of dna each spot in the grid is looking
+for one particular
+
+ align:start position:0%
+for one particular
+ 
+
+ align:start position:0%
+for one particular
+rna
+
+ align:start position:0%
+rna
+ 
+
+ align:start position:0%
+rna
+and in fact more than one spot might be
+
+ align:start position:0%
+and in fact more than one spot might be
+ 
+
+ align:start position:0%
+and in fact more than one spot might be
+actually hybridizing to one rna it
+
+ align:start position:0%
+actually hybridizing to one rna it
+ 
+
+ align:start position:0%
+actually hybridizing to one rna it
+doesn't have to be one to one it could
+
+ align:start position:0%
+doesn't have to be one to one it could
+ 
+
+ align:start position:0%
+doesn't have to be one to one it could
+be many to one
+
+ align:start position:0%
+be many to one
+ 
+
+ align:start position:0%
+be many to one
+and i just want to talk about the
+
+ align:start position:0%
+and i just want to talk about the
+ 
+
+ align:start position:0%
+and i just want to talk about the
+differences of the two technologies for
+
+ align:start position:0%
+differences of the two technologies for
+ 
+
+ align:start position:0%
+differences of the two technologies for
+microarrays and then talk about how that
+
+ align:start position:0%
+microarrays and then talk about how that
+ 
+
+ align:start position:0%
+microarrays and then talk about how that
+actually leads itself to the sage
+
+ align:start position:0%
+actually leads itself to the sage
+ 
+
+ align:start position:0%
+actually leads itself to the sage
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+so for the past uh coming up on 10 years
+
+ align:start position:0%
+so for the past uh coming up on 10 years
+ 
+
+ align:start position:0%
+so for the past uh coming up on 10 years
+now there have been two technologies to
+
+ align:start position:0%
+now there have been two technologies to
+ 
+
+ align:start position:0%
+now there have been two technologies to
+make microarrays okay there's an
+
+ align:start position:0%
+make microarrays okay there's an
+ 
+
+ align:start position:0%
+make microarrays okay there's an
+oligonucleotide approach in the cdna
+
+ align:start position:0%
+oligonucleotide approach in the cdna
+ 
+
+ align:start position:0%
+oligonucleotide approach in the cdna
+approach the analogy i like to use is
+
+ align:start position:0%
+approach the analogy i like to use is
+ 
+
+ align:start position:0%
+approach the analogy i like to use is
+this okay if you think of a microwave as
+
+ align:start position:0%
+this okay if you think of a microwave as
+ 
+
+ align:start position:0%
+this okay if you think of a microwave as
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+manhattan with all the skyscrapers okay
+
+ align:start position:0%
+manhattan with all the skyscrapers okay
+ 
+
+ align:start position:0%
+manhattan with all the skyscrapers okay
+if you had to rebuild manhattan there's
+
+ align:start position:0%
+if you had to rebuild manhattan there's
+ 
+
+ align:start position:0%
+if you had to rebuild manhattan there's
+two ways you could do it
+
+ align:start position:0%
+two ways you could do it
+ 
+
+ align:start position:0%
+two ways you could do it
+you could take one skyscraper at a time
+
+ align:start position:0%
+you could take one skyscraper at a time
+ 
+
+ align:start position:0%
+you could take one skyscraper at a time
+and put them into place
+
+ align:start position:0%
+and put them into place
+ 
+
+ align:start position:0%
+and put them into place
+or you could just build all the first
+
+ align:start position:0%
+or you could just build all the first
+ 
+
+ align:start position:0%
+or you could just build all the first
+floors all the second floors all the
+
+ align:start position:0%
+floors all the second floors all the
+ 
+
+ align:start position:0%
+floors all the second floors all the
+third floors all the fourth floors and
+
+ align:start position:0%
+third floors all the fourth floors and
+ 
+
+ align:start position:0%
+third floors all the fourth floors and
+that's essentially the differences
+
+ align:start position:0%
+that's essentially the differences
+ 
+
+ align:start position:0%
+that's essentially the differences
+between these two technologies okay so
+
+ align:start position:0%
+between these two technologies okay so
+ 
+
+ align:start position:0%
+between these two technologies okay so
+the oligonucleotide arrays primarily
+
+ align:start position:0%
+the oligonucleotide arrays primarily
+ 
+
+ align:start position:0%
+the oligonucleotide arrays primarily
+made by femetrix they're made each of
+
+ align:start position:0%
+made by femetrix they're made each of
+ 
+
+ align:start position:0%
+made by femetrix they're made each of
+the skyscrapers the equivalent that each
+
+ align:start position:0%
+the skyscrapers the equivalent that each
+ 
+
+ align:start position:0%
+the skyscrapers the equivalent that each
+of the strands of dna are only 25
+
+ align:start position:0%
+of the strands of dna are only 25
+ 
+
+ align:start position:0%
+of the strands of dna are only 25
+nucleotides long but they're built one
+
+ align:start position:0%
+nucleotides long but they're built one
+ 
+
+ align:start position:0%
+nucleotides long but they're built one
+base pair at a time
+
+ align:start position:0%
+base pair at a time
+ 
+
+ align:start position:0%
+base pair at a time
+because they're only 25 nucleotides long
+
+ align:start position:0%
+because they're only 25 nucleotides long
+ 
+
+ align:start position:0%
+because they're only 25 nucleotides long
+and genes are much longer than that
+
+ align:start position:0%
+and genes are much longer than that
+ 
+
+ align:start position:0%
+and genes are much longer than that
+that's why they have multiple probes
+
+ align:start position:0%
+that's why they have multiple probes
+ 
+
+ align:start position:0%
+that's why they have multiple probes
+going against a particular gene
+
+ align:start position:0%
+going against a particular gene
+ 
+
+ align:start position:0%
+going against a particular gene
+the cdna on the other hand are
+
+ align:start position:0%
+the cdna on the other hand are
+ 
+
+ align:start position:0%
+the cdna on the other hand are
+essentially strands of dna that will
+
+ align:start position:0%
+essentially strands of dna that will
+ 
+
+ align:start position:0%
+essentially strands of dna that will
+hybridize the rna but the strands of dna
+
+ align:start position:0%
+hybridize the rna but the strands of dna
+ 
+
+ align:start position:0%
+hybridize the rna but the strands of dna
+that are just put into place using
+
+ align:start position:0%
+that are just put into place using
+ 
+
+ align:start position:0%
+that are just put into place using
+primarily using something like a robotic
+
+ align:start position:0%
+primarily using something like a robotic
+ 
+
+ align:start position:0%
+primarily using something like a robotic
+spotter so it might pick up four at a
+
+ align:start position:0%
+spotter so it might pick up four at a
+ 
+
+ align:start position:0%
+spotter so it might pick up four at a
+time or 16 at a time or just one at a
+
+ align:start position:0%
+time or 16 at a time or just one at a
+ 
+
+ align:start position:0%
+time or 16 at a time or just one at a
+time but that's how these two are made
+
+ align:start position:0%
+time but that's how these two are made
+ 
+
+ align:start position:0%
+time but that's how these two are made
+from beyond the technology difference
+
+ align:start position:0%
+from beyond the technology difference
+ 
+
+ align:start position:0%
+from beyond the technology difference
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+there's a major difference in what
+
+ align:start position:0%
+there's a major difference in what
+ 
+
+ align:start position:0%
+there's a major difference in what
+exactly these microwaves are measuring
+
+ align:start position:0%
+exactly these microwaves are measuring
+ 
+
+ align:start position:0%
+exactly these microwaves are measuring
+okay the cdna arrays are measuring
+
+ align:start position:0%
+okay the cdna arrays are measuring
+ 
+
+ align:start position:0%
+okay the cdna arrays are measuring
+relative expression amounts so you have
+
+ align:start position:0%
+relative expression amounts so you have
+ 
+
+ align:start position:0%
+relative expression amounts so you have
+to put two samples on there
+
+ align:start position:0%
+to put two samples on there
+ 
+
+ align:start position:0%
+to put two samples on there
+okay one of which the rna might be
+
+ align:start position:0%
+okay one of which the rna might be
+ 
+
+ align:start position:0%
+okay one of which the rna might be
+colored red another which the rna might
+
+ align:start position:0%
+colored red another which the rna might
+ 
+
+ align:start position:0%
+colored red another which the rna might
+be colored green
+
+ align:start position:0%
+be colored green
+ 
+
+ align:start position:0%
+be colored green
+and you'll look at the you know what
+
+ align:start position:0%
+and you'll look at the you know what
+ 
+
+ align:start position:0%
+and you'll look at the you know what
+people will do is after they've
+
+ align:start position:0%
+people will do is after they've
+ 
+
+ align:start position:0%
+people will do is after they've
+hybridized it they've taken the tiff
+
+ align:start position:0%
+hybridized it they've taken the tiff
+ 
+
+ align:start position:0%
+hybridized it they've taken the tiff
+image of this to look at the relative
+
+ align:start position:0%
+image of this to look at the relative
+ 
+
+ align:start position:0%
+image of this to look at the relative
+ratio of how much red is there compared
+
+ align:start position:0%
+ratio of how much red is there compared
+ 
+
+ align:start position:0%
+ratio of how much red is there compared
+to how much green so in that you always
+
+ align:start position:0%
+to how much green so in that you always
+ 
+
+ align:start position:0%
+to how much green so in that you always
+have a relative expression level
+
+ align:start position:0%
+have a relative expression level
+ 
+
+ align:start position:0%
+have a relative expression level
+in theory the oligonucleotide approach
+
+ align:start position:0%
+in theory the oligonucleotide approach
+ 
+
+ align:start position:0%
+in theory the oligonucleotide approach
+is different now this is relative
+
+ align:start position:0%
+is different now this is relative
+ 
+
+ align:start position:0%
+is different now this is relative
+because each of the strands of cd dna
+
+ align:start position:0%
+because each of the strands of cd dna
+ 
+
+ align:start position:0%
+because each of the strands of cd dna
+has its own properties okay each of the
+
+ align:start position:0%
+has its own properties okay each of the
+ 
+
+ align:start position:0%
+has its own properties okay each of the
+strands might have a different set of
+
+ align:start position:0%
+strands might have a different set of
+ 
+
+ align:start position:0%
+strands might have a different set of
+g's and a's and t's and c's different
+
+ align:start position:0%
+g's and a's and t's and c's different
+ 
+
+ align:start position:0%
+g's and a's and t's and c's different
+melting temperatures and that's why you
+
+ align:start position:0%
+melting temperatures and that's why you
+ 
+
+ align:start position:0%
+melting temperatures and that's why you
+can't really use that as an absolute
+
+ align:start position:0%
+can't really use that as an absolute
+ 
+
+ align:start position:0%
+can't really use that as an absolute
+measurement an intensity might be lower
+
+ align:start position:0%
+measurement an intensity might be lower
+ 
+
+ align:start position:0%
+measurement an intensity might be lower
+on one of these arrays not because
+
+ align:start position:0%
+on one of these arrays not because
+ 
+
+ align:start position:0%
+on one of these arrays not because
+there's less of a gene present just only
+
+ align:start position:0%
+there's less of a gene present just only
+ 
+
+ align:start position:0%
+there's less of a gene present just only
+because the actual cdna had a little bit
+
+ align:start position:0%
+because the actual cdna had a little bit
+ 
+
+ align:start position:0%
+because the actual cdna had a little bit
+different biochemical properties and
+
+ align:start position:0%
+different biochemical properties and
+ 
+
+ align:start position:0%
+different biochemical properties and
+wasn't hybridizing efficiently
+
+ align:start position:0%
+wasn't hybridizing efficiently
+ 
+
+ align:start position:0%
+wasn't hybridizing efficiently
+the oligonucleotide arrays on the other
+
+ align:start position:0%
+the oligonucleotide arrays on the other
+ 
+
+ align:start position:0%
+the oligonucleotide arrays on the other
+hand are in theory designed so that each
+
+ align:start position:0%
+hand are in theory designed so that each
+ 
+
+ align:start position:0%
+hand are in theory designed so that each
+of the probes
+
+ align:start position:0%
+of the probes
+ 
+
+ align:start position:0%
+of the probes
+has similar characteristics in terms of
+
+ align:start position:0%
+has similar characteristics in terms of
+ 
+
+ align:start position:0%
+has similar characteristics in terms of
+melting temperature and some of these
+
+ align:start position:0%
+melting temperature and some of these
+ 
+
+ align:start position:0%
+melting temperature and some of these
+other characteristics so in theory you
+
+ align:start position:0%
+other characteristics so in theory you
+ 
+
+ align:start position:0%
+other characteristics so in theory you
+can compare one spot to another spot and
+
+ align:start position:0%
+can compare one spot to another spot and
+ 
+
+ align:start position:0%
+can compare one spot to another spot and
+because of that these are made
+
+ align:start position:0%
+because of that these are made
+ 
+
+ align:start position:0%
+because of that these are made
+these are hybridized using a single
+
+ align:start position:0%
+these are hybridized using a single
+ 
+
+ align:start position:0%
+these are hybridized using a single
+sample so you put one sample on one
+
+ align:start position:0%
+sample so you put one sample on one
+ 
+
+ align:start position:0%
+sample so you put one sample on one
+array here if you want to do a relative
+
+ align:start position:0%
+array here if you want to do a relative
+ 
+
+ align:start position:0%
+array here if you want to do a relative
+difference you use two arrays
+
+ align:start position:0%
+difference you use two arrays
+ 
+
+ align:start position:0%
+difference you use two arrays
+now again in theory this is an absolute
+
+ align:start position:0%
+now again in theory this is an absolute
+ 
+
+ align:start position:0%
+now again in theory this is an absolute
+expression amount if people want to get
+
+ align:start position:0%
+expression amount if people want to get
+ 
+
+ align:start position:0%
+expression amount if people want to get
+to the most absolute measure like how
+
+ align:start position:0%
+to the most absolute measure like how
+ 
+
+ align:start position:0%
+to the most absolute measure like how
+many strands of rna is present okay or
+
+ align:start position:0%
+many strands of rna is present okay or
+ 
+
+ align:start position:0%
+many strands of rna is present okay or
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+then there's another technology called
+
+ align:start position:0%
+then there's another technology called
+ 
+
+ align:start position:0%
+then there's another technology called
+sage and that's well that's how i just
+
+ align:start position:0%
+sage and that's well that's how i just
+ 
+
+ align:start position:0%
+sage and that's well that's how i just
+want to introduce that discussion here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sage stands for serial analysis of
+
+ align:start position:0%
+so sage stands for serial analysis of
+ 
+
+ align:start position:0%
+so sage stands for serial analysis of
+gene expression i think the paper the
+
+ align:start position:0%
+gene expression i think the paper the
+ 
+
+ align:start position:0%
+gene expression i think the paper the
+original paper on this was in science it
+
+ align:start position:0%
+original paper on this was in science it
+ 
+
+ align:start position:0%
+original paper on this was in science it
+was like a one or two page paper back in
+
+ align:start position:0%
+was like a one or two page paper back in
+ 
+
+ align:start position:0%
+was like a one or two page paper back in
+1995 by uh it was victor velkalescu
+
+ align:start position:0%
+1995 by uh it was victor velkalescu
+ 
+
+ align:start position:0%
+1995 by uh it was victor velkalescu
+at hopkins and so this actually was
+
+ align:start position:0%
+at hopkins and so this actually was
+ 
+
+ align:start position:0%
+at hopkins and so this actually was
+developed around the same time as
+
+ align:start position:0%
+developed around the same time as
+ 
+
+ align:start position:0%
+developed around the same time as
+microwaves but actually gained a lot of
+
+ align:start position:0%
+microwaves but actually gained a lot of
+ 
+
+ align:start position:0%
+microwaves but actually gained a lot of
+popularity before microwaves became so
+
+ align:start position:0%
+popularity before microwaves became so
+ 
+
+ align:start position:0%
+popularity before microwaves became so
+commonly available essentially the way
+
+ align:start position:0%
+commonly available essentially the way
+ 
+
+ align:start position:0%
+commonly available essentially the way
+sage works is that it gives you an
+
+ align:start position:0%
+sage works is that it gives you an
+ 
+
+ align:start position:0%
+sage works is that it gives you an
+absolute expression level for a
+
+ align:start position:0%
+absolute expression level for a
+ 
+
+ align:start position:0%
+absolute expression level for a
+particular gene but it measures gene
+
+ align:start position:0%
+particular gene but it measures gene
+ 
+
+ align:start position:0%
+particular gene but it measures gene
+expression by sequencing and automated
+
+ align:start position:0%
+expression by sequencing and automated
+ 
+
+ align:start position:0%
+expression by sequencing and automated
+sequences were just coming around at the
+
+ align:start position:0%
+sequences were just coming around at the
+ 
+
+ align:start position:0%
+sequences were just coming around at the
+time and people realized that you can
+
+ align:start position:0%
+time and people realized that you can
+ 
+
+ align:start position:0%
+time and people realized that you can
+use this technique to use them to
+
+ align:start position:0%
+use this technique to use them to
+ 
+
+ align:start position:0%
+use this technique to use them to
+measure rna expression levels
+
+ align:start position:0%
+measure rna expression levels
+ 
+
+ align:start position:0%
+measure rna expression levels
+so the way this works is this is that in
+
+ align:start position:0%
+so the way this works is this is that in
+ 
+
+ align:start position:0%
+so the way this works is this is that in
+theory every rna or let's say every
+
+ align:start position:0%
+theory every rna or let's say every
+ 
+
+ align:start position:0%
+theory every rna or let's say every
+sequence every gene
+
+ align:start position:0%
+sequence every gene
+ 
+
+ align:start position:0%
+sequence every gene
+has what they call a is a sage tag here
+
+ align:start position:0%
+has what they call a is a sage tag here
+ 
+
+ align:start position:0%
+has what they call a is a sage tag here
+okay and all sage tag is is let's say 10
+
+ align:start position:0%
+okay and all sage tag is is let's say 10
+ 
+
+ align:start position:0%
+okay and all sage tag is is let's say 10
+nucleotides
+
+ align:start position:0%
+nucleotides
+ 
+
+ align:start position:0%
+nucleotides
+that hopefully uniquely identify that
+
+ align:start position:0%
+that hopefully uniquely identify that
+ 
+
+ align:start position:0%
+that hopefully uniquely identify that
+gene
+
+ align:start position:0%
+gene
+ 
+
+ align:start position:0%
+gene
+but the catch is it has to be after a
+
+ align:start position:0%
+but the catch is it has to be after a
+ 
+
+ align:start position:0%
+but the catch is it has to be after a
+catg and we'll see why in a moment okay
+
+ align:start position:0%
+catg and we'll see why in a moment okay
+ 
+
+ align:start position:0%
+catg and we'll see why in a moment okay
+so look at a gene you look for catg and
+
+ align:start position:0%
+so look at a gene you look for catg and
+ 
+
+ align:start position:0%
+so look at a gene you look for catg and
+the most downstream 10 nucleotides are
+
+ align:start position:0%
+the most downstream 10 nucleotides are
+ 
+
+ align:start position:0%
+the most downstream 10 nucleotides are
+going to be the tag for that gene
+
+ align:start position:0%
+going to be the tag for that gene
+ 
+
+ align:start position:0%
+going to be the tag for that gene
+hopefully that's enough to make it
+
+ align:start position:0%
+hopefully that's enough to make it
+ 
+
+ align:start position:0%
+hopefully that's enough to make it
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+but that's not always going to be the
+
+ align:start position:0%
+but that's not always going to be the
+ 
+
+ align:start position:0%
+but that's not always going to be the
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+so the way this works is this if you
+
+ align:start position:0%
+so the way this works is this if you
+ 
+
+ align:start position:0%
+so the way this works is this if you
+start with the strands of rna that
+
+ align:start position:0%
+start with the strands of rna that
+ 
+
+ align:start position:0%
+start with the strands of rna that
+you're going to measure
+
+ align:start position:0%
+you're going to measure
+ 
+
+ align:start position:0%
+you're going to measure
+the first thing you want to do is to
+
+ align:start position:0%
+the first thing you want to do is to
+ 
+
+ align:start position:0%
+the first thing you want to do is to
+make a strand of dna okay rna is very
+
+ align:start position:0%
+make a strand of dna okay rna is very
+ 
+
+ align:start position:0%
+make a strand of dna okay rna is very
+fragile you want to convert it to dna as
+
+ align:start position:0%
+fragile you want to convert it to dna as
+ 
+
+ align:start position:0%
+fragile you want to convert it to dna as
+quickly as you can otherwise it's going
+
+ align:start position:0%
+quickly as you can otherwise it's going
+ 
+
+ align:start position:0%
+quickly as you can otherwise it's going
+to start to degrade
+
+ align:start position:0%
+to start to degrade
+ 
+
+ align:start position:0%
+to start to degrade
+so the techniques for taking a strand of
+
+ align:start position:0%
+so the techniques for taking a strand of
+ 
+
+ align:start position:0%
+so the techniques for taking a strand of
+rna and making a strand of dna are
+
+ align:start position:0%
+rna and making a strand of dna are
+ 
+
+ align:start position:0%
+rna and making a strand of dna are
+commonly available it's a reverse
+
+ align:start position:0%
+commonly available it's a reverse
+ 
+
+ align:start position:0%
+commonly available it's a reverse
+transcriptase you can buy this off the
+
+ align:start position:0%
+transcriptase you can buy this off the
+ 
+
+ align:start position:0%
+transcriptase you can buy this off the
+shelf or you can buy from the store
+
+ align:start position:0%
+shelf or you can buy from the store
+ 
+
+ align:start position:0%
+shelf or you can buy from the store
+essentially it's going to start by going
+
+ align:start position:0%
+essentially it's going to start by going
+ 
+
+ align:start position:0%
+essentially it's going to start by going
+at one end you might give it a primer to
+
+ align:start position:0%
+at one end you might give it a primer to
+ 
+
+ align:start position:0%
+at one end you might give it a primer to
+get started and then it's just going to
+
+ align:start position:0%
+get started and then it's just going to
+ 
+
+ align:start position:0%
+get started and then it's just going to
+go all the way until it falls off the
+
+ align:start position:0%
+go all the way until it falls off the
+ 
+
+ align:start position:0%
+go all the way until it falls off the
+end so now you've made a cdna copy of
+
+ align:start position:0%
+end so now you've made a cdna copy of
+ 
+
+ align:start position:0%
+end so now you've made a cdna copy of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and what you do now is you can do that
+
+ align:start position:0%
+and what you do now is you can do that
+ 
+
+ align:start position:0%
+and what you do now is you can do that
+for the other strand as well so you have
+
+ align:start position:0%
+for the other strand as well so you have
+ 
+
+ align:start position:0%
+for the other strand as well so you have
+now you've gotten rid of the rna and you
+
+ align:start position:0%
+now you've gotten rid of the rna and you
+ 
+
+ align:start position:0%
+now you've gotten rid of the rna and you
+have two you have a double strand of dna
+
+ align:start position:0%
+have two you have a double strand of dna
+ 
+
+ align:start position:0%
+have two you have a double strand of dna
+representing the rna that you had in
+
+ align:start position:0%
+representing the rna that you had in
+ 
+
+ align:start position:0%
+representing the rna that you had in
+your original sample
+
+ align:start position:0%
+your original sample
+ 
+
+ align:start position:0%
+your original sample
+now it gets a little tricky
+
+ align:start position:0%
+now it gets a little tricky
+ 
+
+ align:start position:0%
+now it gets a little tricky
+because now we're essentially going to
+
+ align:start position:0%
+because now we're essentially going to
+ 
+
+ align:start position:0%
+because now we're essentially going to
+use a lot of molecular tools that
+
+ align:start position:0%
+use a lot of molecular tools that
+ 
+
+ align:start position:0%
+use a lot of molecular tools that
+bacteria have to actually do this kind
+
+ align:start position:0%
+bacteria have to actually do this kind
+ 
+
+ align:start position:0%
+bacteria have to actually do this kind
+of fancy cutting and pasting so that we
+
+ align:start position:0%
+of fancy cutting and pasting so that we
+ 
+
+ align:start position:0%
+of fancy cutting and pasting so that we
+can sequence this and figure out what
+
+ align:start position:0%
+can sequence this and figure out what
+ 
+
+ align:start position:0%
+can sequence this and figure out what
+the genes are what the gene expression
+
+ align:start position:0%
+the genes are what the gene expression
+ 
+
+ align:start position:0%
+the genes are what the gene expression
+level is there's a particular
+
+ align:start position:0%
+level is there's a particular
+ 
+
+ align:start position:0%
+level is there's a particular
+restriction enzyme so a restriction
+
+ align:start position:0%
+restriction enzyme so a restriction
+ 
+
+ align:start position:0%
+restriction enzyme so a restriction
+enzyme is actually a component it's a
+
+ align:start position:0%
+enzyme is actually a component it's a
+ 
+
+ align:start position:0%
+enzyme is actually a component it's a
+it's a protein certainly but it's an
+
+ align:start position:0%
+it's a protein certainly but it's an
+ 
+
+ align:start position:0%
+it's a protein certainly but it's an
+enzyme that's present in bacteria that
+
+ align:start position:0%
+enzyme that's present in bacteria that
+ 
+
+ align:start position:0%
+enzyme that's present in bacteria that
+goes around cutting dna at particular
+
+ align:start position:0%
+goes around cutting dna at particular
+ 
+
+ align:start position:0%
+goes around cutting dna at particular
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+there's a lot of restriction enzymes out
+
+ align:start position:0%
+there's a lot of restriction enzymes out
+ 
+
+ align:start position:0%
+there's a lot of restriction enzymes out
+there if you get the current catalog or
+
+ align:start position:0%
+there if you get the current catalog or
+ 
+
+ align:start position:0%
+there if you get the current catalog or
+the current poster they might be on the
+
+ align:start position:0%
+the current poster they might be on the
+ 
+
+ align:start position:0%
+the current poster they might be on the
+order of let's say about 300 of these
+
+ align:start position:0%
+order of let's say about 300 of these
+ 
+
+ align:start position:0%
+order of let's say about 300 of these
+restriction enzymes there are there are
+
+ align:start position:0%
+restriction enzymes there are there are
+ 
+
+ align:start position:0%
+restriction enzymes there are there are
+many ways to define them but one way
+
+ align:start position:0%
+many ways to define them but one way
+ 
+
+ align:start position:0%
+many ways to define them but one way
+people define restriction enzymes is
+
+ align:start position:0%
+people define restriction enzymes is
+ 
+
+ align:start position:0%
+people define restriction enzymes is
+based on the sequence it cuts
+
+ align:start position:0%
+based on the sequence it cuts
+ 
+
+ align:start position:0%
+based on the sequence it cuts
+and so there's some that cut dna giving
+
+ align:start position:0%
+and so there's some that cut dna giving
+ 
+
+ align:start position:0%
+and so there's some that cut dna giving
+absolutely flat ends and there's some
+
+ align:start position:0%
+absolutely flat ends and there's some
+ 
+
+ align:start position:0%
+absolutely flat ends and there's some
+that actually cut leaving sticky ends
+
+ align:start position:0%
+that actually cut leaving sticky ends
+ 
+
+ align:start position:0%
+that actually cut leaving sticky ends
+and so here this particular restriction
+
+ align:start position:0%
+and so here this particular restriction
+ 
+
+ align:start position:0%
+and so here this particular restriction
+enzyme called nla
+
+ align:start position:0%
+enzyme called nla
+ 
+
+ align:start position:0%
+enzyme called nla
+nla3
+
+ align:start position:0%
+nla3
+ 
+
+ align:start position:0%
+nla3
+takes any strand of double-stranded dna
+
+ align:start position:0%
+takes any strand of double-stranded dna
+ 
+
+ align:start position:0%
+takes any strand of double-stranded dna
+and cuts it at the catg but it leaves
+
+ align:start position:0%
+and cuts it at the catg but it leaves
+ 
+
+ align:start position:0%
+and cuts it at the catg but it leaves
+the catg as an overhang it doesn't cut
+
+ align:start position:0%
+the catg as an overhang it doesn't cut
+ 
+
+ align:start position:0%
+the catg as an overhang it doesn't cut
+it flat okay
+
+ align:start position:0%
+it flat okay
+ 
+
+ align:start position:0%
+it flat okay
+so these guys saw this and they said
+
+ align:start position:0%
+so these guys saw this and they said
+ 
+
+ align:start position:0%
+so these guys saw this and they said
+well we could do some interesting things
+
+ align:start position:0%
+well we could do some interesting things
+ 
+
+ align:start position:0%
+well we could do some interesting things
+a little bit of cutting and basically
+
+ align:start position:0%
+a little bit of cutting and basically
+ 
+
+ align:start position:0%
+a little bit of cutting and basically
+actually take advantage of this
+
+ align:start position:0%
+actually take advantage of this
+ 
+
+ align:start position:0%
+actually take advantage of this
+so to be clear here's this here's the
+
+ align:start position:0%
+so to be clear here's this here's the
+ 
+
+ align:start position:0%
+so to be clear here's this here's the
+sequence here's the citg and the unique
+
+ align:start position:0%
+sequence here's the citg and the unique
+ 
+
+ align:start position:0%
+sequence here's the citg and the unique
+tag and basically we're gonna even
+
+ align:start position:0%
+tag and basically we're gonna even
+ 
+
+ align:start position:0%
+tag and basically we're gonna even
+though the strand might be longer than
+
+ align:start position:0%
+though the strand might be longer than
+ 
+
+ align:start position:0%
+though the strand might be longer than
+this it's gonna get cut like this
+
+ align:start position:0%
+this it's gonna get cut like this
+ 
+
+ align:start position:0%
+this it's gonna get cut like this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now to use more fancy parts to this
+
+ align:start position:0%
+now to use more fancy parts to this
+ 
+
+ align:start position:0%
+now to use more fancy parts to this
+remember how i told you most messenger
+
+ align:start position:0%
+remember how i told you most messenger
+ 
+
+ align:start position:0%
+remember how i told you most messenger
+rna has a strand of a at the end right
+
+ align:start position:0%
+rna has a strand of a at the end right
+ 
+
+ align:start position:0%
+rna has a strand of a at the end right
+because as it's being copied off the dna
+
+ align:start position:0%
+because as it's being copied off the dna
+ 
+
+ align:start position:0%
+because as it's being copied off the dna
+it starts to stutter in some ways and
+
+ align:start position:0%
+it starts to stutter in some ways and
+ 
+
+ align:start position:0%
+it starts to stutter in some ways and
+just leaves a poly a
+
+ align:start position:0%
+just leaves a poly a
+ 
+
+ align:start position:0%
+just leaves a poly a
+and that you can cut you can bind to it
+
+ align:start position:0%
+and that you can cut you can bind to it
+ 
+
+ align:start position:0%
+and that you can cut you can bind to it
+or you can actually find it by using a
+
+ align:start position:0%
+or you can actually find it by using a
+ 
+
+ align:start position:0%
+or you can actually find it by using a
+poly t
+
+ align:start position:0%
+poly t
+ 
+
+ align:start position:0%
+poly t
+what they're using their technique what
+
+ align:start position:0%
+what they're using their technique what
+ 
+
+ align:start position:0%
+what they're using their technique what
+you can do is instead of just starting
+
+ align:start position:0%
+you can do is instead of just starting
+ 
+
+ align:start position:0%
+you can do is instead of just starting
+with p start it with something that's
+
+ align:start position:0%
+with p start it with something that's
+ 
+
+ align:start position:0%
+with p start it with something that's
+with peas and something sticky on the
+
+ align:start position:0%
+with peas and something sticky on the
+ 
+
+ align:start position:0%
+with peas and something sticky on the
+end okay in other words it's labeled in
+
+ align:start position:0%
+end okay in other words it's labeled in
+ 
+
+ align:start position:0%
+end okay in other words it's labeled in
+such a way that we can then fish these
+
+ align:start position:0%
+such a way that we can then fish these
+ 
+
+ align:start position:0%
+such a way that we can then fish these
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+after we apply a magnet to it for
+
+ align:start position:0%
+after we apply a magnet to it for
+ 
+
+ align:start position:0%
+after we apply a magnet to it for
+example or up uh or
+
+ align:start position:0%
+example or up uh or
+ 
+
+ align:start position:0%
+example or up uh or
+some people use uh streptavidin and
+
+ align:start position:0%
+some people use uh streptavidin and
+ 
+
+ align:start position:0%
+some people use uh streptavidin and
+biotinylation as a common way to
+
+ align:start position:0%
+biotinylation as a common way to
+ 
+
+ align:start position:0%
+biotinylation as a common way to
+actually pull fish these things out when
+
+ align:start position:0%
+actually pull fish these things out when
+ 
+
+ align:start position:0%
+actually pull fish these things out when
+you run through a column for example or
+
+ align:start position:0%
+you run through a column for example or
+ 
+
+ align:start position:0%
+you run through a column for example or
+spin it with particular beads however
+
+ align:start position:0%
+spin it with particular beads however
+ 
+
+ align:start position:0%
+spin it with particular beads however
+you do it so now we have a whole bunch
+
+ align:start position:0%
+you do it so now we have a whole bunch
+ 
+
+ align:start position:0%
+you do it so now we have a whole bunch
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the double stranded dnase except we have
+
+ align:start position:0%
+the double stranded dnase except we have
+ 
+
+ align:start position:0%
+the double stranded dnase except we have
+this little overhang here we've got all
+
+ align:start position:0%
+this little overhang here we've got all
+ 
+
+ align:start position:0%
+this little overhang here we've got all
+the a's and t's on that end we've fished
+
+ align:start position:0%
+the a's and t's on that end we've fished
+ 
+
+ align:start position:0%
+the a's and t's on that end we've fished
+them out of this big cellular pool
+
+ align:start position:0%
+them out of this big cellular pool
+ 
+
+ align:start position:0%
+them out of this big cellular pool
+cellular mess
+
+ align:start position:0%
+cellular mess
+ 
+
+ align:start position:0%
+cellular mess
+now what we're going to do okay it
+
+ align:start position:0%
+now what we're going to do okay it
+ 
+
+ align:start position:0%
+now what we're going to do okay it
+starts to get a little tricky but now so
+
+ align:start position:0%
+starts to get a little tricky but now so
+ 
+
+ align:start position:0%
+starts to get a little tricky but now so
+we have this tag here keep your eye on
+
+ align:start position:0%
+we have this tag here keep your eye on
+ 
+
+ align:start position:0%
+we have this tag here keep your eye on
+the red that's all i can say here in
+
+ align:start position:0%
+the red that's all i can say here in
+ 
+
+ align:start position:0%
+the red that's all i can say here in
+this technique okay because what you're
+
+ align:start position:0%
+this technique okay because what you're
+ 
+
+ align:start position:0%
+this technique okay because what you're
+going to do is in the end you're going
+
+ align:start position:0%
+going to do is in the end you're going
+ 
+
+ align:start position:0%
+going to do is in the end you're going
+to see
+
+ align:start position:0%
+to see
+ 
+
+ align:start position:0%
+to see
+how we're going to be able to use a
+
+ align:start position:0%
+how we're going to be able to use a
+ 
+
+ align:start position:0%
+how we're going to be able to use a
+sequencer to tell these rnas how much of
+
+ align:start position:0%
+sequencer to tell these rnas how much of
+ 
+
+ align:start position:0%
+sequencer to tell these rnas how much of
+each rna is present so we've got one rna
+
+ align:start position:0%
+each rna is present so we've got one rna
+ 
+
+ align:start position:0%
+each rna is present so we've got one rna
+going this way and we actually got this
+
+ align:start position:0%
+going this way and we actually got this
+ 
+
+ align:start position:0%
+going this way and we actually got this
+light blue for another rna going this
+
+ align:start position:0%
+light blue for another rna going this
+ 
+
+ align:start position:0%
+light blue for another rna going this
+way and you can see how they're going to
+
+ align:start position:0%
+way and you can see how they're going to
+ 
+
+ align:start position:0%
+way and you can see how they're going to
+end up being next to each other
+
+ align:start position:0%
+end up being next to each other
+ 
+
+ align:start position:0%
+end up being next to each other
+so what we have to do then is add an
+
+ align:start position:0%
+so what we have to do then is add an
+ 
+
+ align:start position:0%
+so what we have to do then is add an
+adapter that has another sticky end here
+
+ align:start position:0%
+adapter that has another sticky end here
+ 
+
+ align:start position:0%
+adapter that has another sticky end here
+and add it to this side here
+
+ align:start position:0%
+and add it to this side here
+ 
+
+ align:start position:0%
+and add it to this side here
+and we're going to use another
+
+ align:start position:0%
+and we're going to use another
+ 
+
+ align:start position:0%
+and we're going to use another
+restriction enzyme
+
+ align:start position:0%
+restriction enzyme
+ 
+
+ align:start position:0%
+restriction enzyme
+that's going to cut
+
+ align:start position:0%
+that's going to cut
+ 
+
+ align:start position:0%
+that's going to cut
+at the catg but it's going to cut after
+
+ align:start position:0%
+at the catg but it's going to cut after
+ 
+
+ align:start position:0%
+at the catg but it's going to cut after
+the tag there's one particular
+
+ align:start position:0%
+the tag there's one particular
+ 
+
+ align:start position:0%
+the tag there's one particular
+restriction enzyme called bsm f1
+
+ align:start position:0%
+restriction enzyme called bsm f1
+ 
+
+ align:start position:0%
+restriction enzyme called bsm f1
+that looks it for catg but doesn't cut
+
+ align:start position:0%
+that looks it for catg but doesn't cut
+ 
+
+ align:start position:0%
+that looks it for catg but doesn't cut
+at the ctg it cuts 14 base pairs
+
+ align:start position:0%
+at the ctg it cuts 14 base pairs
+ 
+
+ align:start position:0%
+at the ctg it cuts 14 base pairs
+downstream from there that's why our
+
+ align:start position:0%
+downstream from there that's why our
+ 
+
+ align:start position:0%
+downstream from there that's why our
+tags have to be 10 nucleotides long
+
+ align:start position:0%
+tags have to be 10 nucleotides long
+ 
+
+ align:start position:0%
+tags have to be 10 nucleotides long
+okay a lot of fancy biochemistry here to
+
+ align:start position:0%
+okay a lot of fancy biochemistry here to
+ 
+
+ align:start position:0%
+okay a lot of fancy biochemistry here to
+get this to work right
+
+ align:start position:0%
+get this to work right
+ 
+
+ align:start position:0%
+get this to work right
+so you got a tag here and you got a tag
+
+ align:start position:0%
+so you got a tag here and you got a tag
+ 
+
+ align:start position:0%
+so you got a tag here and you got a tag
+here and you got a little adapter here
+
+ align:start position:0%
+here and you got a little adapter here
+ 
+
+ align:start position:0%
+here and you got a little adapter here
+that we've added on on this side
+
+ align:start position:0%
+that we've added on on this side
+ 
+
+ align:start position:0%
+that we've added on on this side
+and then finally what we're gonna do
+
+ align:start position:0%
+and then finally what we're gonna do
+ 
+
+ align:start position:0%
+and then finally what we're gonna do
+we've cut
+
+ align:start position:0%
+we've cut
+ 
+
+ align:start position:0%
+we've cut
+we've cut it here and we've cut it here
+
+ align:start position:0%
+we've cut it here and we've cut it here
+ 
+
+ align:start position:0%
+we've cut it here and we've cut it here
+what we can do is add something called a
+
+ align:start position:0%
+what we can do is add something called a
+ 
+
+ align:start position:0%
+what we can do is add something called a
+ligase that basically takes all blunt
+
+ align:start position:0%
+ligase that basically takes all blunt
+ 
+
+ align:start position:0%
+ligase that basically takes all blunt
+ends and just tries to make
+
+ align:start position:0%
+ends and just tries to make
+ 
+
+ align:start position:0%
+ends and just tries to make
+pairs together tries to bring any small
+
+ align:start position:0%
+pairs together tries to bring any small
+ 
+
+ align:start position:0%
+pairs together tries to bring any small
+strands of dna with blunt ends and tries
+
+ align:start position:0%
+strands of dna with blunt ends and tries
+ 
+
+ align:start position:0%
+strands of dna with blunt ends and tries
+to attach them together so we have a
+
+ align:start position:0%
+to attach them together so we have a
+ 
+
+ align:start position:0%
+to attach them together so we have a
+blunt end that was here and a blend end
+
+ align:start position:0%
+blunt end that was here and a blend end
+ 
+
+ align:start position:0%
+blunt end that was here and a blend end
+that was here here's the first tag and
+
+ align:start position:0%
+that was here here's the first tag and
+ 
+
+ align:start position:0%
+that was here here's the first tag and
+here's the second tag
+
+ align:start position:0%
+here's the second tag
+ 
+
+ align:start position:0%
+here's the second tag
+and we're going to have a whole bunch of
+
+ align:start position:0%
+and we're going to have a whole bunch of
+ 
+
+ align:start position:0%
+and we're going to have a whole bunch of
+these and what we can do is just run it
+
+ align:start position:0%
+these and what we can do is just run it
+ 
+
+ align:start position:0%
+these and what we can do is just run it
+through a sequencer basically okay we're
+
+ align:start position:0%
+through a sequencer basically okay we're
+ 
+
+ align:start position:0%
+through a sequencer basically okay we're
+going to do some more fancy footwork to
+
+ align:start position:0%
+going to do some more fancy footwork to
+ 
+
+ align:start position:0%
+going to do some more fancy footwork to
+get these to be as compact as possible
+
+ align:start position:0%
+get these to be as compact as possible
+ 
+
+ align:start position:0%
+get these to be as compact as possible
+and in the end we'll have one stretch of
+
+ align:start position:0%
+and in the end we'll have one stretch of
+ 
+
+ align:start position:0%
+and in the end we'll have one stretch of
+dna
+
+ align:start position:0%
+dna
+ 
+
+ align:start position:0%
+dna
+with just one tag after another with
+
+ align:start position:0%
+with just one tag after another with
+ 
+
+ align:start position:0%
+with just one tag after another with
+some capg's in the middle as spacers so
+
+ align:start position:0%
+some capg's in the middle as spacers so
+ 
+
+ align:start position:0%
+some capg's in the middle as spacers so
+we can make sure we're getting we're
+
+ align:start position:0%
+we can make sure we're getting we're
+ 
+
+ align:start position:0%
+we can make sure we're getting we're
+staying synchronized
+
+ align:start position:0%
+staying synchronized
+ 
+
+ align:start position:0%
+staying synchronized
+now what you do is you run this through
+
+ align:start position:0%
+now what you do is you run this through
+ 
+
+ align:start position:0%
+now what you do is you run this through
+an automated sequencer and then you can
+
+ align:start position:0%
+an automated sequencer and then you can
+ 
+
+ align:start position:0%
+an automated sequencer and then you can
+just get you can read off the sequence
+
+ align:start position:0%
+just get you can read off the sequence
+ 
+
+ align:start position:0%
+just get you can read off the sequence
+just like this
+
+ align:start position:0%
+just like this
+ 
+
+ align:start position:0%
+just like this
+one then the other than the one the
+
+ align:start position:0%
+one then the other than the one the
+ 
+
+ align:start position:0%
+one then the other than the one the
+other and then search databases
+
+ align:start position:0%
+other and then search databases
+ 
+
+ align:start position:0%
+other and then search databases
+to see what gene do we think this is
+
+ align:start position:0%
+to see what gene do we think this is
+ 
+
+ align:start position:0%
+to see what gene do we think this is
+now the reason why this is an absolute
+
+ align:start position:0%
+now the reason why this is an absolute
+ 
+
+ align:start position:0%
+now the reason why this is an absolute
+gene expression measurement for sure is
+
+ align:start position:0%
+gene expression measurement for sure is
+ 
+
+ align:start position:0%
+gene expression measurement for sure is
+that if this gene is overrepresented two
+
+ align:start position:0%
+that if this gene is overrepresented two
+ 
+
+ align:start position:0%
+that if this gene is overrepresented two
+times more than this one you're sure
+
+ align:start position:0%
+times more than this one you're sure
+ 
+
+ align:start position:0%
+times more than this one you're sure
+you're going to see two times more tags
+
+ align:start position:0%
+you're going to see two times more tags
+ 
+
+ align:start position:0%
+you're going to see two times more tags
+than this one in theory
+
+ align:start position:0%
+than this one in theory
+ 
+
+ align:start position:0%
+than this one in theory
+okay there are efficiencies to each one
+
+ align:start position:0%
+okay there are efficiencies to each one
+ 
+
+ align:start position:0%
+okay there are efficiencies to each one
+of these steps that we talked about and
+
+ align:start position:0%
+of these steps that we talked about and
+ 
+
+ align:start position:0%
+of these steps that we talked about and
+this is not as simple as a microarray
+
+ align:start position:0%
+this is not as simple as a microarray
+ 
+
+ align:start position:0%
+this is not as simple as a microarray
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+literally you can take the sample if
+
+ align:start position:0%
+literally you can take the sample if
+ 
+
+ align:start position:0%
+literally you can take the sample if
+you're a physician at brigham's house or
+
+ align:start position:0%
+you're a physician at brigham's house or
+ 
+
+ align:start position:0%
+you're a physician at brigham's house or
+any of these hospitals essentially take
+
+ align:start position:0%
+any of these hospitals essentially take
+ 
+
+ align:start position:0%
+any of these hospitals essentially take
+it to a core and get a microarray done
+
+ align:start position:0%
+it to a core and get a microarray done
+ 
+
+ align:start position:0%
+it to a core and get a microarray done
+sage is a lot more involved
+
+ align:start position:0%
+sage is a lot more involved
+ 
+
+ align:start position:0%
+sage is a lot more involved
+but in theory this is a great way to
+
+ align:start position:0%
+but in theory this is a great way to
+ 
+
+ align:start position:0%
+but in theory this is a great way to
+pick up low expression
+
+ align:start position:0%
+pick up low expression
+ 
+
+ align:start position:0%
+pick up low expression
+genes with very low expression levels
+
+ align:start position:0%
+genes with very low expression levels
+ 
+
+ align:start position:0%
+genes with very low expression levels
+okay so that's why it was worth at least
+
+ align:start position:0%
+okay so that's why it was worth at least
+ 
+
+ align:start position:0%
+okay so that's why it was worth at least
+talking about sage because if you're
+
+ align:start position:0%
+talking about sage because if you're
+ 
+
+ align:start position:0%
+talking about sage because if you're
+looking at absolute expression levels
+
+ align:start position:0%
+looking at absolute expression levels
+ 
+
+ align:start position:0%
+looking at absolute expression levels
+this is where it's going
+
+ align:start position:0%
+this is where it's going
+ 
+
+ align:start position:0%
+this is where it's going
+for now this is a back burner kind of
+
+ align:start position:0%
+for now this is a back burner kind of
+ 
+
+ align:start position:0%
+for now this is a back burner kind of
+technology people still use it they're
+
+ align:start position:0%
+technology people still use it they're
+ 
+
+ align:start position:0%
+technology people still use it they're
+people who are religiously devoted to it
+
+ align:start position:0%
+people who are religiously devoted to it
+ 
+
+ align:start position:0%
+people who are religiously devoted to it
+but most people you end up using
+
+ align:start position:0%
+but most people you end up using
+ 
+
+ align:start position:0%
+but most people you end up using
+microrace today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tag is just happens to be a sequence
+
+ align:start position:0%
+the tag is just happens to be a sequence
+ 
+
+ align:start position:0%
+the tag is just happens to be a sequence
+so what we're calling a tag here is
+
+ align:start position:0%
+so what we're calling a tag here is
+ 
+
+ align:start position:0%
+so what we're calling a tag here is
+nothing we put there okay okay it's
+
+ align:start position:0%
+nothing we put there okay okay it's
+ 
+
+ align:start position:0%
+nothing we put there okay okay it's
+something that is next to a catg that's
+
+ align:start position:0%
+something that is next to a catg that's
+ 
+
+ align:start position:0%
+something that is next to a catg that's
+on this end of the gene
+
+ align:start position:0%
+on this end of the gene
+ 
+
+ align:start position:0%
+on this end of the gene
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if there's nothing there like that then
+
+ align:start position:0%
+if there's nothing there like that then
+ 
+
+ align:start position:0%
+if there's nothing there like that then
+we're not gonna find it okay so that's
+
+ align:start position:0%
+we're not gonna find it okay so that's
+ 
+
+ align:start position:0%
+we're not gonna find it okay so that's
+another catch okay if the first one is
+
+ align:start position:0%
+another catch okay if the first one is
+ 
+
+ align:start position:0%
+another catch okay if the first one is
+all the way up here we might not even
+
+ align:start position:0%
+all the way up here we might not even
+ 
+
+ align:start position:0%
+all the way up here we might not even
+get it so they're saying the average
+
+ align:start position:0%
+get it so they're saying the average
+ 
+
+ align:start position:0%
+get it so they're saying the average
+if you do the math there's at least one
+
+ align:start position:0%
+if you do the math there's at least one
+ 
+
+ align:start position:0%
+if you do the math there's at least one
+of these within 256 base pairs right
+
+ align:start position:0%
+of these within 256 base pairs right
+ 
+
+ align:start position:0%
+of these within 256 base pairs right
+because it's like four to the fourth
+
+ align:start position:0%
+because it's like four to the fourth
+ 
+
+ align:start position:0%
+because it's like four to the fourth
+so there should be one there but there
+
+ align:start position:0%
+so there should be one there but there
+ 
+
+ align:start position:0%
+so there should be one there but there
+might be degeneracies where it might not
+
+ align:start position:0%
+might be degeneracies where it might not
+ 
+
+ align:start position:0%
+might be degeneracies where it might not
+be there
+
+ align:start position:0%
+be there
+ 
+
+ align:start position:0%
+be there
+so that's the whole technique it's 10
+
+ align:start position:0%
+so that's the whole technique it's 10
+ 
+
+ align:start position:0%
+so that's the whole technique it's 10
+it's ctg only because of the
+
+ align:start position:0%
+it's ctg only because of the
+ 
+
+ align:start position:0%
+it's ctg only because of the
+peculiarities of the enzymes being used
+
+ align:start position:0%
+peculiarities of the enzymes being used
+ 
+
+ align:start position:0%
+peculiarities of the enzymes being used
+to actually cut these things apart and
+
+ align:start position:0%
+to actually cut these things apart and
+ 
+
+ align:start position:0%
+to actually cut these things apart and
+then just look at the tags
+
+ align:start position:0%
+then just look at the tags
+ 
+
+ align:start position:0%
+then just look at the tags
+any questions about that
+
+ align:start position:0%
+any questions about that
+ 
+
+ align:start position:0%
+any questions about that
+so that's basically that was the last
+
+ align:start position:0%
+so that's basically that was the last
+ 
+
+ align:start position:0%
+so that's basically that was the last
+thing i want to talk about in this
+
+ align:start position:0%
+thing i want to talk about in this
+ 
+
+ align:start position:0%
+thing i want to talk about in this
+section of uh gene measurement
+
+ align:start position:0%
+section of uh gene measurement
+ 
+
+ align:start position:0%
+section of uh gene measurement
+technologies or gene measurement
+
+ align:start position:0%
+technologies or gene measurement
+ 
+
+ align:start position:0%
+technologies or gene measurement
+techniques
+
+ align:start position:0%
+techniques
+ 
+
+ align:start position:0%
+techniques
+so now zach was suggesting that i talk
+
+ align:start position:0%
+so now zach was suggesting that i talk
+ 
+
+ align:start position:0%
+so now zach was suggesting that i talk
+about uh
+
+ align:start position:0%
+about uh
+ 
+
+ align:start position:0%
+about uh
+some of the stuff that we've been doing
+
+ align:start position:0%
+some of the stuff that we've been doing
+ 
+
+ align:start position:0%
+some of the stuff that we've been doing
+with diabetes only because this is
+
+ align:start position:0%
+with diabetes only because this is
+ 
+
+ align:start position:0%
+with diabetes only because this is
+supposed to be genomic medicine
+
+ align:start position:0%
+supposed to be genomic medicine
+ 
+
+ align:start position:0%
+supposed to be genomic medicine
+we can give you a real world example of
+
+ align:start position:0%
+we can give you a real world example of
+ 
+
+ align:start position:0%
+we can give you a real world example of
+how we've used microarrays to help us
+
+ align:start position:0%
+how we've used microarrays to help us
+ 
+
+ align:start position:0%
+how we've used microarrays to help us
+with diabetes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm a pediatric endocrinologist i
+
+ align:start position:0%
+so i'm a pediatric endocrinologist i
+ 
+
+ align:start position:0%
+so i'm a pediatric endocrinologist i
+spent most of my time over at the joslin
+
+ align:start position:0%
+spent most of my time over at the joslin
+ 
+
+ align:start position:0%
+spent most of my time over at the joslin
+diabetes center studying type 2 diabetes
+
+ align:start position:0%
+diabetes center studying type 2 diabetes
+ 
+
+ align:start position:0%
+diabetes center studying type 2 diabetes
+currently affects about 15 million
+
+ align:start position:0%
+currently affects about 15 million
+ 
+
+ align:start position:0%
+currently affects about 15 million
+people in the united states and in fact
+
+ align:start position:0%
+people in the united states and in fact
+ 
+
+ align:start position:0%
+people in the united states and in fact
+the cdc just estimated a couple months
+
+ align:start position:0%
+the cdc just estimated a couple months
+ 
+
+ align:start position:0%
+the cdc just estimated a couple months
+ago that a child born in the year 2000
+
+ align:start position:0%
+ago that a child born in the year 2000
+ 
+
+ align:start position:0%
+ago that a child born in the year 2000
+now has a 1-3 risk of getting type 2
+
+ align:start position:0%
+now has a 1-3 risk of getting type 2
+ 
+
+ align:start position:0%
+now has a 1-3 risk of getting type 2
+diabetes okay so it's 33 likelihood now
+
+ align:start position:0%
+diabetes okay so it's 33 likelihood now
+ 
+
+ align:start position:0%
+diabetes okay so it's 33 likelihood now
+of a child born just two years ago to
+
+ align:start position:0%
+of a child born just two years ago to
+ 
+
+ align:start position:0%
+of a child born just two years ago to
+get type 2 diabetes why because of the
+
+ align:start position:0%
+get type 2 diabetes why because of the
+ 
+
+ align:start position:0%
+get type 2 diabetes why because of the
+obesity problem okay so we all know kids
+
+ align:start position:0%
+obesity problem okay so we all know kids
+ 
+
+ align:start position:0%
+obesity problem okay so we all know kids
+the kids have less exercise today in
+
+ align:start position:0%
+the kids have less exercise today in
+ 
+
+ align:start position:0%
+the kids have less exercise today in
+school because they have to pass these
+
+ align:start position:0%
+school because they have to pass these
+ 
+
+ align:start position:0%
+school because they have to pass these
+tests and now schools have to give more
+
+ align:start position:0%
+tests and now schools have to give more
+ 
+
+ align:start position:0%
+tests and now schools have to give more
+courses so that they pass the m cases
+
+ align:start position:0%
+courses so that they pass the m cases
+ 
+
+ align:start position:0%
+courses so that they pass the m cases
+and things like that there's more tv
+
+ align:start position:0%
+and things like that there's more tv
+ 
+
+ align:start position:0%
+and things like that there's more tv
+there's more channels there's internet
+
+ align:start position:0%
+there's more channels there's internet
+ 
+
+ align:start position:0%
+there's more channels there's internet
+there's all these things that cause kids
+
+ align:start position:0%
+there's all these things that cause kids
+ 
+
+ align:start position:0%
+there's all these things that cause kids
+to basically sit in one place they don't
+
+ align:start position:0%
+to basically sit in one place they don't
+ 
+
+ align:start position:0%
+to basically sit in one place they don't
+get much exercise i think there was
+
+ align:start position:0%
+get much exercise i think there was
+ 
+
+ align:start position:0%
+get much exercise i think there was
+something on cnn last week about how
+
+ align:start position:0%
+something on cnn last week about how
+ 
+
+ align:start position:0%
+something on cnn last week about how
+even toddlers one or two years or just
+
+ align:start position:0%
+even toddlers one or two years or just
+ 
+
+ align:start position:0%
+even toddlers one or two years or just
+not getting as much exercise as they
+
+ align:start position:0%
+not getting as much exercise as they
+ 
+
+ align:start position:0%
+not getting as much exercise as they
+used to okay so this isn't even school
+
+ align:start position:0%
+used to okay so this isn't even school
+ 
+
+ align:start position:0%
+used to okay so this isn't even school
+age this is starting at basically age
+
+ align:start position:0%
+age this is starting at basically age
+ 
+
+ align:start position:0%
+age this is starting at basically age
+one or two
+
+ align:start position:0%
+one or two
+ 
+
+ align:start position:0%
+one or two
+so question we had here was this okay we
+
+ align:start position:0%
+so question we had here was this okay we
+ 
+
+ align:start position:0%
+so question we had here was this okay we
+know how to define i mean the diagnosis
+
+ align:start position:0%
+know how to define i mean the diagnosis
+ 
+
+ align:start position:0%
+know how to define i mean the diagnosis
+of diabetes is actually sort of
+
+ align:start position:0%
+of diabetes is actually sort of
+ 
+
+ align:start position:0%
+of diabetes is actually sort of
+arbitrary okay in fact the definition of
+
+ align:start position:0%
+arbitrary okay in fact the definition of
+ 
+
+ align:start position:0%
+arbitrary okay in fact the definition of
+diabetes keeps changing it turns out but
+
+ align:start position:0%
+diabetes keeps changing it turns out but
+ 
+
+ align:start position:0%
+diabetes keeps changing it turns out but
+for example at one point the definition
+
+ align:start position:0%
+for example at one point the definition
+ 
+
+ align:start position:0%
+for example at one point the definition
+of diabetes was having a fasting blood
+
+ align:start position:0%
+of diabetes was having a fasting blood
+ 
+
+ align:start position:0%
+of diabetes was having a fasting blood
+sugar so morning blood sugar greater
+
+ align:start position:0%
+sugar so morning blood sugar greater
+ 
+
+ align:start position:0%
+sugar so morning blood sugar greater
+than 127 i think it was milligrams per
+
+ align:start position:0%
+than 127 i think it was milligrams per
+ 
+
+ align:start position:0%
+than 127 i think it was milligrams per
+deciliter qualified you for having
+
+ align:start position:0%
+deciliter qualified you for having
+ 
+
+ align:start position:0%
+deciliter qualified you for having
+diabetes
+
+ align:start position:0%
+diabetes
+ 
+
+ align:start position:0%
+diabetes
+but what we know is that it's not just
+
+ align:start position:0%
+but what we know is that it's not just
+ 
+
+ align:start position:0%
+but what we know is that it's not just
+an on and off type of thing like you all
+
+ align:start position:0%
+an on and off type of thing like you all
+ 
+
+ align:start position:0%
+an on and off type of thing like you all
+of a sudden you don't have diabetes and
+
+ align:start position:0%
+of a sudden you don't have diabetes and
+ 
+
+ align:start position:0%
+of a sudden you don't have diabetes and
+now all of a sudden you do
+
+ align:start position:0%
+now all of a sudden you do
+ 
+
+ align:start position:0%
+now all of a sudden you do
+because diabetes is a very heritable
+
+ align:start position:0%
+because diabetes is a very heritable
+ 
+
+ align:start position:0%
+because diabetes is a very heritable
+trait okay
+
+ align:start position:0%
+trait okay
+ 
+
+ align:start position:0%
+trait okay
+it's controversial but some people say
+
+ align:start position:0%
+it's controversial but some people say
+ 
+
+ align:start position:0%
+it's controversial but some people say
+for example it's a very genetic trait
+
+ align:start position:0%
+for example it's a very genetic trait
+ 
+
+ align:start position:0%
+for example it's a very genetic trait
+let's put it that way
+
+ align:start position:0%
+let's put it that way
+ 
+
+ align:start position:0%
+let's put it that way
+there are some studies that show that in
+
+ align:start position:0%
+there are some studies that show that in
+ 
+
+ align:start position:0%
+there are some studies that show that in
+twin twin studies okay if you have one
+
+ align:start position:0%
+twin twin studies okay if you have one
+ 
+
+ align:start position:0%
+twin twin studies okay if you have one
+twin that has type 2 diabetes you have a
+
+ align:start position:0%
+twin that has type 2 diabetes you have a
+ 
+
+ align:start position:0%
+twin that has type 2 diabetes you have a
+98 likelihood that the other twins gonna
+
+ align:start position:0%
+98 likelihood that the other twins gonna
+ 
+
+ align:start position:0%
+98 likelihood that the other twins gonna
+get it if they don't already have it
+
+ align:start position:0%
+get it if they don't already have it
+ 
+
+ align:start position:0%
+get it if they don't already have it
+okay so it makes you think that it's
+
+ align:start position:0%
+okay so it makes you think that it's
+ 
+
+ align:start position:0%
+okay so it makes you think that it's
+incredibly genetic but the problem is
+
+ align:start position:0%
+incredibly genetic but the problem is
+ 
+
+ align:start position:0%
+incredibly genetic but the problem is
+the incidence is so high this is a
+
+ align:start position:0%
+the incidence is so high this is a
+ 
+
+ align:start position:0%
+the incidence is so high this is a
+common disease it's not very easy at all
+
+ align:start position:0%
+common disease it's not very easy at all
+ 
+
+ align:start position:0%
+common disease it's not very easy at all
+to find a particular mutation that
+
+ align:start position:0%
+to find a particular mutation that
+ 
+
+ align:start position:0%
+to find a particular mutation that
+causes this we haven't been that lucky
+
+ align:start position:0%
+causes this we haven't been that lucky
+ 
+
+ align:start position:0%
+causes this we haven't been that lucky
+so far
+
+ align:start position:0%
+so far
+ 
+
+ align:start position:0%
+so far
+we have found the field has found a
+
+ align:start position:0%
+we have found the field has found a
+ 
+
+ align:start position:0%
+we have found the field has found a
+number of mutations that do lead to
+
+ align:start position:0%
+number of mutations that do lead to
+ 
+
+ align:start position:0%
+number of mutations that do lead to
+diabetes but they might explain
+
+ align:start position:0%
+diabetes but they might explain
+ 
+
+ align:start position:0%
+diabetes but they might explain
+the sum total of maybe 0.01 of the
+
+ align:start position:0%
+the sum total of maybe 0.01 of the
+ 
+
+ align:start position:0%
+the sum total of maybe 0.01 of the
+people who have diabetes those are very
+
+ align:start position:0%
+people who have diabetes those are very
+ 
+
+ align:start position:0%
+people who have diabetes those are very
+rare forms the common form which seems
+
+ align:start position:0%
+rare forms the common form which seems
+ 
+
+ align:start position:0%
+rare forms the common form which seems
+like it's incredibly genetic is still a
+
+ align:start position:0%
+like it's incredibly genetic is still a
+ 
+
+ align:start position:0%
+like it's incredibly genetic is still a
+big mystery
+
+ align:start position:0%
+big mystery
+ 
+
+ align:start position:0%
+big mystery
+the point of what we were going to use
+
+ align:start position:0%
+the point of what we were going to use
+ 
+
+ align:start position:0%
+the point of what we were going to use
+genomic medicine for here was trying to
+
+ align:start position:0%
+genomic medicine for here was trying to
+ 
+
+ align:start position:0%
+genomic medicine for here was trying to
+define the patterns of how people might
+
+ align:start position:0%
+define the patterns of how people might
+ 
+
+ align:start position:0%
+define the patterns of how people might
+go from non-diabetes to diabetes there's
+
+ align:start position:0%
+go from non-diabetes to diabetes there's
+ 
+
+ align:start position:0%
+go from non-diabetes to diabetes there's
+a middle group in there okay in fact the
+
+ align:start position:0%
+a middle group in there okay in fact the
+ 
+
+ align:start position:0%
+a middle group in there okay in fact the
+ada the diabetes association now calls
+
+ align:start position:0%
+ada the diabetes association now calls
+ 
+
+ align:start position:0%
+ada the diabetes association now calls
+us pre-diabetes people who don't have a
+
+ align:start position:0%
+us pre-diabetes people who don't have a
+ 
+
+ align:start position:0%
+us pre-diabetes people who don't have a
+normal handling of sugar
+
+ align:start position:0%
+normal handling of sugar
+ 
+
+ align:start position:0%
+normal handling of sugar
+but don't strictly meet the criteria for
+
+ align:start position:0%
+but don't strictly meet the criteria for
+ 
+
+ align:start position:0%
+but don't strictly meet the criteria for
+diabetes today
+
+ align:start position:0%
+diabetes today
+ 
+
+ align:start position:0%
+diabetes today
+so question we had here
+
+ align:start position:0%
+so question we had here
+ 
+
+ align:start position:0%
+so question we had here
+using microarrays can we define patterns
+
+ align:start position:0%
+using microarrays can we define patterns
+ 
+
+ align:start position:0%
+using microarrays can we define patterns
+of gene expression in human subjects
+
+ align:start position:0%
+of gene expression in human subjects
+ 
+
+ align:start position:0%
+of gene expression in human subjects
+with diabetes specifically in their
+
+ align:start position:0%
+with diabetes specifically in their
+ 
+
+ align:start position:0%
+with diabetes specifically in their
+muscle samples
+
+ align:start position:0%
+muscle samples
+ 
+
+ align:start position:0%
+muscle samples
+to identify those that are at higher
+
+ align:start position:0%
+to identify those that are at higher
+ 
+
+ align:start position:0%
+to identify those that are at higher
+not just
+
+ align:start position:0%
+not just
+ 
+
+ align:start position:0%
+not just
+define what genes are different between
+
+ align:start position:0%
+define what genes are different between
+ 
+
+ align:start position:0%
+define what genes are different between
+diabetes and non-diabetes but also what
+
+ align:start position:0%
+diabetes and non-diabetes but also what
+ 
+
+ align:start position:0%
+diabetes and non-diabetes but also what
+genes were also different already
+
+ align:start position:0%
+genes were also different already
+ 
+
+ align:start position:0%
+genes were also different already
+different in those that were at high
+
+ align:start position:0%
+different in those that were at high
+ 
+
+ align:start position:0%
+different in those that were at high
+risk of getting diabetes specifically
+
+ align:start position:0%
+risk of getting diabetes specifically
+ 
+
+ align:start position:0%
+risk of getting diabetes specifically
+these are offspring of type 2 diabetics
+
+ align:start position:0%
+these are offspring of type 2 diabetics
+ 
+
+ align:start position:0%
+these are offspring of type 2 diabetics
+so this particular study that we did was
+
+ align:start position:0%
+so this particular study that we did was
+ 
+
+ align:start position:0%
+so this particular study that we did was
+in mexican-american subjects we have
+
+ align:start position:0%
+in mexican-american subjects we have
+ 
+
+ align:start position:0%
+in mexican-american subjects we have
+diabetes and family history of diabetes
+
+ align:start position:0%
+diabetes and family history of diabetes
+ 
+
+ align:start position:0%
+diabetes and family history of diabetes
+so we basically have three groups family
+
+ align:start position:0%
+so we basically have three groups family
+ 
+
+ align:start position:0%
+so we basically have three groups family
+history negative
+
+ align:start position:0%
+history negative
+ 
+
+ align:start position:0%
+history negative
+diabetes that's what obviously these are
+
+ align:start position:0%
+diabetes that's what obviously these are
+ 
+
+ align:start position:0%
+diabetes that's what obviously these are
+control and then we have family history
+
+ align:start position:0%
+control and then we have family history
+ 
+
+ align:start position:0%
+control and then we have family history
+positive okay so we've got three groups
+
+ align:start position:0%
+positive okay so we've got three groups
+ 
+
+ align:start position:0%
+positive okay so we've got three groups
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and you can look at the
+
+ align:start position:0%
+and you can look at the
+ 
+
+ align:start position:0%
+and you can look at the
+the subjects uh that we use for this
+
+ align:start position:0%
+the subjects uh that we use for this
+ 
+
+ align:start position:0%
+the subjects uh that we use for this
+particular study we had one that we used
+
+ align:start position:0%
+particular study we had one that we used
+ 
+
+ align:start position:0%
+particular study we had one that we used
+that we used for the arrays and we had
+
+ align:start position:0%
+that we used for the arrays and we had
+ 
+
+ align:start position:0%
+that we used for the arrays and we had
+another that we actually did validation
+
+ align:start position:0%
+another that we actually did validation
+ 
+
+ align:start position:0%
+another that we actually did validation
+were on some of the hypotheses that we
+
+ align:start position:0%
+were on some of the hypotheses that we
+ 
+
+ align:start position:0%
+were on some of the hypotheses that we
+came up with
+
+ align:start position:0%
+came up with
+ 
+
+ align:start position:0%
+came up with
+and so most of these characteristics are
+
+ align:start position:0%
+and so most of these characteristics are
+ 
+
+ align:start position:0%
+and so most of these characteristics are
+not different but they are different in
+
+ align:start position:0%
+not different but they are different in
+ 
+
+ align:start position:0%
+not different but they are different in
+a number of important ways so fasting
+
+ align:start position:0%
+a number of important ways so fasting
+ 
+
+ align:start position:0%
+a number of important ways so fasting
+glucose
+
+ align:start position:0%
+glucose
+ 
+
+ align:start position:0%
+glucose
+is 99 92 but 200 in the diabetics
+
+ align:start position:0%
+is 99 92 but 200 in the diabetics
+ 
+
+ align:start position:0%
+is 99 92 but 200 in the diabetics
+obviously because they have diabetes
+
+ align:start position:0%
+obviously because they have diabetes
+ 
+
+ align:start position:0%
+obviously because they have diabetes
+the two hour glucose was higher in the
+
+ align:start position:0%
+the two hour glucose was higher in the
+ 
+
+ align:start position:0%
+the two hour glucose was higher in the
+diet in the diabetics but the hemoglobin
+
+ align:start position:0%
+diet in the diabetics but the hemoglobin
+ 
+
+ align:start position:0%
+diet in the diabetics but the hemoglobin
+a1c was already high in the family
+
+ align:start position:0%
+a1c was already high in the family
+ 
+
+ align:start position:0%
+a1c was already high in the family
+history positives what is the hemoglobin
+
+ align:start position:0%
+history positives what is the hemoglobin
+ 
+
+ align:start position:0%
+history positives what is the hemoglobin
+a1c
+
+ align:start position:0%
+a1c
+ 
+
+ align:start position:0%
+a1c
+well that's one of our measurements for
+
+ align:start position:0%
+well that's one of our measurements for
+ 
+
+ align:start position:0%
+well that's one of our measurements for
+how high the blood sugar levels are over
+
+ align:start position:0%
+how high the blood sugar levels are over
+ 
+
+ align:start position:0%
+how high the blood sugar levels are over
+a span of 120 days okay so in fact most
+
+ align:start position:0%
+a span of 120 days okay so in fact most
+ 
+
+ align:start position:0%
+a span of 120 days okay so in fact most
+uh physicians now who take care of
+
+ align:start position:0%
+uh physicians now who take care of
+ 
+
+ align:start position:0%
+uh physicians now who take care of
+patients with diabetes we measure this
+
+ align:start position:0%
+patients with diabetes we measure this
+ 
+
+ align:start position:0%
+patients with diabetes we measure this
+hemoglobin a1c
+
+ align:start position:0%
+hemoglobin a1c
+ 
+
+ align:start position:0%
+hemoglobin a1c
+at least four times a year so that we
+
+ align:start position:0%
+at least four times a year so that we
+ 
+
+ align:start position:0%
+at least four times a year so that we
+can get a gauge as to what the blood
+
+ align:start position:0%
+can get a gauge as to what the blood
+ 
+
+ align:start position:0%
+can get a gauge as to what the blood
+sugars are like over the past 120 days
+
+ align:start position:0%
+sugars are like over the past 120 days
+ 
+
+ align:start position:0%
+sugars are like over the past 120 days
+because that's the lifespan of an
+
+ align:start position:0%
+because that's the lifespan of an
+ 
+
+ align:start position:0%
+because that's the lifespan of an
+erythrocyte for a red cell and as the
+
+ align:start position:0%
+erythrocyte for a red cell and as the
+ 
+
+ align:start position:0%
+erythrocyte for a red cell and as the
+glucose levels are higher in the blood
+
+ align:start position:0%
+glucose levels are higher in the blood
+ 
+
+ align:start position:0%
+glucose levels are higher in the blood
+that actually glycosylates the
+
+ align:start position:0%
+that actually glycosylates the
+ 
+
+ align:start position:0%
+that actually glycosylates the
+hemoglobin in the red cell so it's a
+
+ align:start position:0%
+hemoglobin in the red cell so it's a
+ 
+
+ align:start position:0%
+hemoglobin in the red cell so it's a
+byproduct of this
+
+ align:start position:0%
+byproduct of this
+ 
+
+ align:start position:0%
+byproduct of this
+but it's already high in the family
+
+ align:start position:0%
+but it's already high in the family
+ 
+
+ align:start position:0%
+but it's already high in the family
+history positive they're not exactly
+
+ align:start position:0%
+history positive they're not exactly
+ 
+
+ align:start position:0%
+history positive they're not exactly
+like the family history negatives here
+
+ align:start position:0%
+like the family history negatives here
+ 
+
+ align:start position:0%
+like the family history negatives here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+fasting insulin already high okay so the
+
+ align:start position:0%
+fasting insulin already high okay so the
+ 
+
+ align:start position:0%
+fasting insulin already high okay so the
+problem with type 2 diabetes just to
+
+ align:start position:0%
+problem with type 2 diabetes just to
+ 
+
+ align:start position:0%
+problem with type 2 diabetes just to
+make sure everyone's on the same page
+
+ align:start position:0%
+make sure everyone's on the same page
+ 
+
+ align:start position:0%
+make sure everyone's on the same page
+here it's not a problem with making the
+
+ align:start position:0%
+here it's not a problem with making the
+ 
+
+ align:start position:0%
+here it's not a problem with making the
+insulin from the pancreas the problem is
+
+ align:start position:0%
+insulin from the pancreas the problem is
+ 
+
+ align:start position:0%
+insulin from the pancreas the problem is
+that insulin is there it just doesn't
+
+ align:start position:0%
+that insulin is there it just doesn't
+ 
+
+ align:start position:0%
+that insulin is there it just doesn't
+act like it's supposed to in the target
+
+ align:start position:0%
+act like it's supposed to in the target
+ 
+
+ align:start position:0%
+act like it's supposed to in the target
+tissues
+
+ align:start position:0%
+tissues
+ 
+
+ align:start position:0%
+tissues
+okay now to use my analogy from last
+
+ align:start position:0%
+okay now to use my analogy from last
+ 
+
+ align:start position:0%
+okay now to use my analogy from last
+week i just had this great food from the
+
+ align:start position:0%
+week i just had this great food from the
+ 
+
+ align:start position:0%
+week i just had this great food from the
+chinese truck again okay
+
+ align:start position:0%
+chinese truck again okay
+ 
+
+ align:start position:0%
+chinese truck again okay
+my glucose levels are going up my
+
+ align:start position:0%
+my glucose levels are going up my
+ 
+
+ align:start position:0%
+my glucose levels are going up my
+insulin levels are going up and so
+
+ align:start position:0%
+insulin levels are going up and so
+ 
+
+ align:start position:0%
+insulin levels are going up and so
+insulin is now telling number of my
+
+ align:start position:0%
+insulin is now telling number of my
+ 
+
+ align:start position:0%
+insulin is now telling number of my
+tissues to do a number of things it's
+
+ align:start position:0%
+tissues to do a number of things it's
+ 
+
+ align:start position:0%
+tissues to do a number of things it's
+telling my liver to stop making sugar
+
+ align:start position:0%
+telling my liver to stop making sugar
+ 
+
+ align:start position:0%
+telling my liver to stop making sugar
+okay i just ate a whole huge meal i
+
+ align:start position:0%
+okay i just ate a whole huge meal i
+ 
+
+ align:start position:0%
+okay i just ate a whole huge meal i
+don't need the liver to start making
+
+ align:start position:0%
+don't need the liver to start making
+ 
+
+ align:start position:0%
+don't need the liver to start making
+more sugar because i just ate a whole
+
+ align:start position:0%
+more sugar because i just ate a whole
+ 
+
+ align:start position:0%
+more sugar because i just ate a whole
+bunch but more importantly it's telling
+
+ align:start position:0%
+bunch but more importantly it's telling
+ 
+
+ align:start position:0%
+bunch but more importantly it's telling
+that my muscle and my fat cells to start
+
+ align:start position:0%
+that my muscle and my fat cells to start
+ 
+
+ align:start position:0%
+that my muscle and my fat cells to start
+taking in the sugar
+
+ align:start position:0%
+taking in the sugar
+ 
+
+ align:start position:0%
+taking in the sugar
+okay and what happens with type 2
+
+ align:start position:0%
+okay and what happens with type 2
+ 
+
+ align:start position:0%
+okay and what happens with type 2
+diabetes is that that signal from the
+
+ align:start position:0%
+diabetes is that that signal from the
+ 
+
+ align:start position:0%
+diabetes is that that signal from the
+insulin to what the tissues are supposed
+
+ align:start position:0%
+insulin to what the tissues are supposed
+ 
+
+ align:start position:0%
+insulin to what the tissues are supposed
+to do is muted for some some reason we
+
+ align:start position:0%
+to do is muted for some some reason we
+ 
+
+ align:start position:0%
+to do is muted for some some reason we
+just don't know exactly why
+
+ align:start position:0%
+just don't know exactly why
+ 
+
+ align:start position:0%
+just don't know exactly why
+but that's the problem insulin is there
+
+ align:start position:0%
+but that's the problem insulin is there
+ 
+
+ align:start position:0%
+but that's the problem insulin is there
+in fact now these guys have a higher
+
+ align:start position:0%
+in fact now these guys have a higher
+ 
+
+ align:start position:0%
+in fact now these guys have a higher
+insulin level because already their
+
+ align:start position:0%
+insulin level because already their
+ 
+
+ align:start position:0%
+insulin level because already their
+bodies are realizing
+
+ align:start position:0%
+bodies are realizing
+ 
+
+ align:start position:0%
+bodies are realizing
+the same amount of insulin isn't doing
+
+ align:start position:0%
+the same amount of insulin isn't doing
+ 
+
+ align:start position:0%
+the same amount of insulin isn't doing
+what it's supposed to okay so pancreas
+
+ align:start position:0%
+what it's supposed to okay so pancreas
+ 
+
+ align:start position:0%
+what it's supposed to okay so pancreas
+sees that the sugar levels are not going
+
+ align:start position:0%
+sees that the sugar levels are not going
+ 
+
+ align:start position:0%
+sees that the sugar levels are not going
+down after the meals for example and
+
+ align:start position:0%
+down after the meals for example and
+ 
+
+ align:start position:0%
+down after the meals for example and
+it's saying oh i need to ramp up the
+
+ align:start position:0%
+it's saying oh i need to ramp up the
+ 
+
+ align:start position:0%
+it's saying oh i need to ramp up the
+amount of insulin i'm making
+
+ align:start position:0%
+amount of insulin i'm making
+ 
+
+ align:start position:0%
+amount of insulin i'm making
+but the primary problem is felt to be in
+
+ align:start position:0%
+but the primary problem is felt to be in
+ 
+
+ align:start position:0%
+but the primary problem is felt to be in
+the target tissues insulin resistance
+
+ align:start position:0%
+the target tissues insulin resistance
+ 
+
+ align:start position:0%
+the target tissues insulin resistance
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the group's already different and
+
+ align:start position:0%
+so the group's already different and
+ 
+
+ align:start position:0%
+so the group's already different and
+that's going to actually make this com
+
+ align:start position:0%
+that's going to actually make this com
+ 
+
+ align:start position:0%
+that's going to actually make this com
+analysis sort of complicated
+
+ align:start position:0%
+analysis sort of complicated
+ 
+
+ align:start position:0%
+analysis sort of complicated
+so we have five diabetics there
+
+ align:start position:0%
+so we have five diabetics there
+ 
+
+ align:start position:0%
+so we have five diabetics there
+four without diabetes with the family
+
+ align:start position:0%
+four without diabetes with the family
+ 
+
+ align:start position:0%
+four without diabetes with the family
+history of diabetes and six controls
+
+ align:start position:0%
+history of diabetes and six controls
+ 
+
+ align:start position:0%
+history of diabetes and six controls
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and when you do this you can compare
+
+ align:start position:0%
+and when you do this you can compare
+ 
+
+ align:start position:0%
+and when you do this you can compare
+each group to each other group so we can
+
+ align:start position:0%
+each group to each other group so we can
+ 
+
+ align:start position:0%
+each group to each other group so we can
+we took muscle samples from these
+
+ align:start position:0%
+we took muscle samples from these
+ 
+
+ align:start position:0%
+we took muscle samples from these
+individuals uh if they were on medicines
+
+ align:start position:0%
+individuals uh if they were on medicines
+ 
+
+ align:start position:0%
+individuals uh if they were on medicines
+for the diabetics they were actually
+
+ align:start position:0%
+for the diabetics they were actually
+ 
+
+ align:start position:0%
+for the diabetics they were actually
+taken off for a number of days they had
+
+ align:start position:0%
+taken off for a number of days they had
+ 
+
+ align:start position:0%
+taken off for a number of days they had
+no strenuous exercise beforehand
+
+ align:start position:0%
+no strenuous exercise beforehand
+ 
+
+ align:start position:0%
+no strenuous exercise beforehand
+and it's all informed consent and you
+
+ align:start position:0%
+and it's all informed consent and you
+ 
+
+ align:start position:0%
+and it's all informed consent and you
+get the
+
+ align:start position:0%
+get the
+ 
+
+ align:start position:0%
+get the
+muscle samples you extract out the rna
+
+ align:start position:0%
+muscle samples you extract out the rna
+ 
+
+ align:start position:0%
+muscle samples you extract out the rna
+we put them on these microarrays the
+
+ align:start position:0%
+we put them on these microarrays the
+ 
+
+ align:start position:0%
+we put them on these microarrays the
+microwaves at this when we did these
+
+ align:start position:0%
+microwaves at this when we did these
+ 
+
+ align:start position:0%
+microwaves at this when we did these
+experiments measured about 7000 genes
+
+ align:start position:0%
+experiments measured about 7000 genes
+ 
+
+ align:start position:0%
+experiments measured about 7000 genes
+today when you do this for the same
+
+ align:start position:0%
+today when you do this for the same
+ 
+
+ align:start position:0%
+today when you do this for the same
+price you get 44 000 genes okay
+
+ align:start position:0%
+price you get 44 000 genes okay
+ 
+
+ align:start position:0%
+price you get 44 000 genes okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we can use a number of different
+
+ align:start position:0%
+we can use a number of different
+ 
+
+ align:start position:0%
+we can use a number of different
+analytic techniques that you're going to
+
+ align:start position:0%
+analytic techniques that you're going to
+ 
+
+ align:start position:0%
+analytic techniques that you're going to
+be learning about over the next over the
+
+ align:start position:0%
+be learning about over the next over the
+ 
+
+ align:start position:0%
+be learning about over the next over the
+rest of the semester exactly how we make
+
+ align:start position:0%
+rest of the semester exactly how we make
+ 
+
+ align:start position:0%
+rest of the semester exactly how we make
+the distinction of which genes might be
+
+ align:start position:0%
+the distinction of which genes might be
+ 
+
+ align:start position:0%
+the distinction of which genes might be
+different what genes are not changing
+
+ align:start position:0%
+different what genes are not changing
+ 
+
+ align:start position:0%
+different what genes are not changing
+but if you compare family history
+
+ align:start position:0%
+but if you compare family history
+ 
+
+ align:start position:0%
+but if you compare family history
+negative to diabetes we found 187 genes
+
+ align:start position:0%
+negative to diabetes we found 187 genes
+ 
+
+ align:start position:0%
+negative to diabetes we found 187 genes
+that are different even if even if you
+
+ align:start position:0%
+that are different even if even if you
+ 
+
+ align:start position:0%
+that are different even if even if you
+compare family history positive to
+
+ align:start position:0%
+compare family history positive to
+ 
+
+ align:start position:0%
+compare family history positive to
+diabetes is 166 genes that are different
+
+ align:start position:0%
+diabetes is 166 genes that are different
+ 
+
+ align:start position:0%
+diabetes is 166 genes that are different
+so fewer and there's some overlap so 55
+
+ align:start position:0%
+so fewer and there's some overlap so 55
+ 
+
+ align:start position:0%
+so fewer and there's some overlap so 55
+genes between there are 55 genes that
+
+ align:start position:0%
+genes between there are 55 genes that
+ 
+
+ align:start position:0%
+genes between there are 55 genes that
+were in this list added this list
+
+ align:start position:0%
+were in this list added this list
+ 
+
+ align:start position:0%
+were in this list added this list
+and most of them coded for all sorts of
+
+ align:start position:0%
+and most of them coded for all sorts of
+ 
+
+ align:start position:0%
+and most of them coded for all sorts of
+interesting proteins okay for example
+
+ align:start position:0%
+interesting proteins okay for example
+ 
+
+ align:start position:0%
+interesting proteins okay for example
+mitochondrial proteins that are involved
+
+ align:start position:0%
+mitochondrial proteins that are involved
+ 
+
+ align:start position:0%
+mitochondrial proteins that are involved
+in actually energy metabolism or uh atp
+
+ align:start position:0%
+in actually energy metabolism or uh atp
+ 
+
+ align:start position:0%
+in actually energy metabolism or uh atp
+synthesis oxidative phosphorylation
+
+ align:start position:0%
+synthesis oxidative phosphorylation
+ 
+
+ align:start position:0%
+synthesis oxidative phosphorylation
+which we'll talk about in a moment
+
+ align:start position:0%
+which we'll talk about in a moment
+ 
+
+ align:start position:0%
+which we'll talk about in a moment
+and so this is one common way of how we
+
+ align:start position:0%
+and so this is one common way of how we
+ 
+
+ align:start position:0%
+and so this is one common way of how we
+actually like to look at these genes
+
+ align:start position:0%
+actually like to look at these genes
+ 
+
+ align:start position:0%
+actually like to look at these genes
+okay it's called a heat map or even a
+
+ align:start position:0%
+okay it's called a heat map or even a
+ 
+
+ align:start position:0%
+okay it's called a heat map or even a
+dendrogram depending on
+
+ align:start position:0%
+dendrogram depending on
+ 
+
+ align:start position:0%
+dendrogram depending on
+the different programs that you use but
+
+ align:start position:0%
+the different programs that you use but
+ 
+
+ align:start position:0%
+the different programs that you use but
+the green indicates so each of the rows
+
+ align:start position:0%
+the green indicates so each of the rows
+ 
+
+ align:start position:0%
+the green indicates so each of the rows
+indicates a gene each of the columns
+
+ align:start position:0%
+indicates a gene each of the columns
+ 
+
+ align:start position:0%
+indicates a gene each of the columns
+typically represents a sample and the
+
+ align:start position:0%
+typically represents a sample and the
+ 
+
+ align:start position:0%
+typically represents a sample and the
+green indicates a gene that's higher
+
+ align:start position:0%
+green indicates a gene that's higher
+ 
+
+ align:start position:0%
+green indicates a gene that's higher
+than the mean
+
+ align:start position:0%
+than the mean
+ 
+
+ align:start position:0%
+than the mean
+and the red indicates a gene that's
+
+ align:start position:0%
+and the red indicates a gene that's
+ 
+
+ align:start position:0%
+and the red indicates a gene that's
+lower than the mean
+
+ align:start position:0%
+lower than the mean
+ 
+
+ align:start position:0%
+lower than the mean
+and what we're showing here are
+
+ align:start position:0%
+and what we're showing here are
+ 
+
+ align:start position:0%
+and what we're showing here are
+a subset of those 55 genes that actually
+
+ align:start position:0%
+a subset of those 55 genes that actually
+ 
+
+ align:start position:0%
+a subset of those 55 genes that actually
+have something to do with energy
+
+ align:start position:0%
+have something to do with energy
+ 
+
+ align:start position:0%
+have something to do with energy
+metabolism
+
+ align:start position:0%
+metabolism
+ 
+
+ align:start position:0%
+metabolism
+and primarily most of the genes that
+
+ align:start position:0%
+and primarily most of the genes that
+ 
+
+ align:start position:0%
+and primarily most of the genes that
+have something to do with energy
+
+ align:start position:0%
+have something to do with energy
+ 
+
+ align:start position:0%
+have something to do with energy
+metabolism are higher in the family
+
+ align:start position:0%
+metabolism are higher in the family
+ 
+
+ align:start position:0%
+metabolism are higher in the family
+history negative they're lower in the
+
+ align:start position:0%
+history negative they're lower in the
+ 
+
+ align:start position:0%
+history negative they're lower in the
+diabetics and they're already low in the
+
+ align:start position:0%
+diabetics and they're already low in the
+ 
+
+ align:start position:0%
+diabetics and they're already low in the
+family history positive so the ones that
+
+ align:start position:0%
+family history positive so the ones that
+ 
+
+ align:start position:0%
+family history positive so the ones that
+are at risk for getting diabetes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we've got a piece of this puzzle
+
+ align:start position:0%
+so now we've got a piece of this puzzle
+ 
+
+ align:start position:0%
+so now we've got a piece of this puzzle
+we see that transcription of some of
+
+ align:start position:0%
+we see that transcription of some of
+ 
+
+ align:start position:0%
+we see that transcription of some of
+these mitochondrial genes metabolic
+
+ align:start position:0%
+these mitochondrial genes metabolic
+ 
+
+ align:start position:0%
+these mitochondrial genes metabolic
+related genes are is down
+
+ align:start position:0%
+related genes are is down
+ 
+
+ align:start position:0%
+related genes are is down
+that might be causing decreased
+
+ align:start position:0%
+that might be causing decreased
+ 
+
+ align:start position:0%
+that might be causing decreased
+oxidative phosphorylation so what
+
+ align:start position:0%
+oxidative phosphorylation so what
+ 
+
+ align:start position:0%
+oxidative phosphorylation so what
+happens is fat might fat is building up
+
+ align:start position:0%
+happens is fat might fat is building up
+ 
+
+ align:start position:0%
+happens is fat might fat is building up
+in the muscle and the fat cells and if
+
+ align:start position:0%
+in the muscle and the fat cells and if
+ 
+
+ align:start position:0%
+in the muscle and the fat cells and if
+you have less of these genes and
+
+ align:start position:0%
+you have less of these genes and
+ 
+
+ align:start position:0%
+you have less of these genes and
+presumably less of the proteins that
+
+ align:start position:0%
+presumably less of the proteins that
+ 
+
+ align:start position:0%
+presumably less of the proteins that
+we're using them as a proxy for we're
+
+ align:start position:0%
+we're using them as a proxy for we're
+ 
+
+ align:start position:0%
+we're using them as a proxy for we're
+getting decreased lipid oxidation
+
+ align:start position:0%
+getting decreased lipid oxidation
+ 
+
+ align:start position:0%
+getting decreased lipid oxidation
+as fat or lipid builds up in muscle it
+
+ align:start position:0%
+as fat or lipid builds up in muscle it
+ 
+
+ align:start position:0%
+as fat or lipid builds up in muscle it
+actually can cause the insulin to not
+
+ align:start position:0%
+actually can cause the insulin to not
+ 
+
+ align:start position:0%
+actually can cause the insulin to not
+work as well so maybe that's how we're
+
+ align:start position:0%
+work as well so maybe that's how we're
+ 
+
+ align:start position:0%
+work as well so maybe that's how we're
+getting to insulin resistance because of
+
+ align:start position:0%
+getting to insulin resistance because of
+ 
+
+ align:start position:0%
+getting to insulin resistance because of
+the increase in the lipid in the muscle
+
+ align:start position:0%
+the increase in the lipid in the muscle
+ 
+
+ align:start position:0%
+the increase in the lipid in the muscle
+well there's a huge half of this that's
+
+ align:start position:0%
+well there's a huge half of this that's
+ 
+
+ align:start position:0%
+well there's a huge half of this that's
+still unknown today okay and that's
+
+ align:start position:0%
+still unknown today okay and that's
+ 
+
+ align:start position:0%
+still unknown today okay and that's
+that's the part i want to focus on for a
+
+ align:start position:0%
+that's the part i want to focus on for a
+ 
+
+ align:start position:0%
+that's the part i want to focus on for a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+okay people show this slide all the time
+
+ align:start position:0%
+okay people show this slide all the time
+ 
+
+ align:start position:0%
+okay people show this slide all the time
+in all sorts of different contexts right
+
+ align:start position:0%
+in all sorts of different contexts right
+ 
+
+ align:start position:0%
+in all sorts of different contexts right
+huge formula here huge formula here the
+
+ align:start position:0%
+huge formula here huge formula here the
+ 
+
+ align:start position:0%
+huge formula here huge formula here the
+miracle occurs in the middle right
+
+ align:start position:0%
+miracle occurs in the middle right
+ 
+
+ align:start position:0%
+miracle occurs in the middle right
+and still the biggest problem with this
+
+ align:start position:0%
+and still the biggest problem with this
+ 
+
+ align:start position:0%
+and still the biggest problem with this
+type of study
+
+ align:start position:0%
+type of study
+ 
+
+ align:start position:0%
+type of study
+is that this miracle still has to occur
+
+ align:start position:0%
+is that this miracle still has to occur
+ 
+
+ align:start position:0%
+is that this miracle still has to occur
+to figure out why
+
+ align:start position:0%
+to figure out why
+ 
+
+ align:start position:0%
+to figure out why
+do we have this list of genes okay what
+
+ align:start position:0%
+do we have this list of genes okay what
+ 
+
+ align:start position:0%
+do we have this list of genes okay what
+is it about this list of genes that's
+
+ align:start position:0%
+is it about this list of genes that's
+ 
+
+ align:start position:0%
+is it about this list of genes that's
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+right how are we getting to this set of
+
+ align:start position:0%
+right how are we getting to this set of
+ 
+
+ align:start position:0%
+right how are we getting to this set of
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+what's the biology behind it
+
+ align:start position:0%
+what's the biology behind it
+ 
+
+ align:start position:0%
+what's the biology behind it
+so although many of my colleagues will
+
+ align:start position:0%
+so although many of my colleagues will
+ 
+
+ align:start position:0%
+so although many of my colleagues will
+argue with me about this you cannot
+
+ align:start position:0%
+argue with me about this you cannot
+ 
+
+ align:start position:0%
+argue with me about this you cannot
+ignore the biology here okay
+
+ align:start position:0%
+ignore the biology here okay
+ 
+
+ align:start position:0%
+ignore the biology here okay
+it's getting harder and harder to just
+
+ align:start position:0%
+it's getting harder and harder to just
+ 
+
+ align:start position:0%
+it's getting harder and harder to just
+say here's my list of genes go run with
+
+ align:start position:0%
+say here's my list of genes go run with
+ 
+
+ align:start position:0%
+say here's my list of genes go run with
+this okay you need to know what is it
+
+ align:start position:0%
+this okay you need to know what is it
+ 
+
+ align:start position:0%
+this okay you need to know what is it
+about this list what's causing this list
+
+ align:start position:0%
+about this list what's causing this list
+ 
+
+ align:start position:0%
+about this list what's causing this list
+of genes to be so special and
+
+ align:start position:0%
+of genes to be so special and
+ 
+
+ align:start position:0%
+of genes to be so special and
+unfortunate right now to informaticist
+
+ align:start position:0%
+unfortunate right now to informaticist
+ 
+
+ align:start position:0%
+unfortunate right now to informaticist
+it looks like a miracle occurs that
+
+ align:start position:0%
+it looks like a miracle occurs that
+ 
+
+ align:start position:0%
+it looks like a miracle occurs that
+someone has the insight to look at one
+
+ align:start position:0%
+someone has the insight to look at one
+ 
+
+ align:start position:0%
+someone has the insight to look at one
+particular factor and you actually get a
+
+ align:start position:0%
+particular factor and you actually get a
+ 
+
+ align:start position:0%
+particular factor and you actually get a
+causal chain of events and then you can
+
+ align:start position:0%
+causal chain of events and then you can
+ 
+
+ align:start position:0%
+causal chain of events and then you can
+get your list of genes here what we
+
+ align:start position:0%
+get your list of genes here what we
+ 
+
+ align:start position:0%
+get your list of genes here what we
+realized
+
+ align:start position:0%
+realized
+ 
+
+ align:start position:0%
+realized
+is that most of these genes are
+
+ align:start position:0%
+is that most of these genes are
+ 
+
+ align:start position:0%
+is that most of these genes are
+downstream of a transcription factor
+
+ align:start position:0%
+downstream of a transcription factor
+ 
+
+ align:start position:0%
+downstream of a transcription factor
+called nrf1 and another one called pgc1
+
+ align:start position:0%
+called nrf1 and another one called pgc1
+ 
+
+ align:start position:0%
+called nrf1 and another one called pgc1
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+it would be great if we had some
+
+ align:start position:0%
+it would be great if we had some
+ 
+
+ align:start position:0%
+it would be great if we had some
+database of these things of course we
+
+ align:start position:0%
+database of these things of course we
+ 
+
+ align:start position:0%
+database of these things of course we
+don't it'd be great if nrf1 was even on
+
+ align:start position:0%
+don't it'd be great if nrf1 was even on
+ 
+
+ align:start position:0%
+don't it'd be great if nrf1 was even on
+the chip it's not
+
+ align:start position:0%
+the chip it's not
+ 
+
+ align:start position:0%
+the chip it's not
+it's on today's chip but it wasn't on
+
+ align:start position:0%
+it's on today's chip but it wasn't on
+ 
+
+ align:start position:0%
+it's on today's chip but it wasn't on
+these chips from three generations ago
+
+ align:start position:0%
+these chips from three generations ago
+ 
+
+ align:start position:0%
+these chips from three generations ago
+so no amount of informatics and network
+
+ align:start position:0%
+so no amount of informatics and network
+ 
+
+ align:start position:0%
+so no amount of informatics and network
+building and bayes networks or any of
+
+ align:start position:0%
+building and bayes networks or any of
+ 
+
+ align:start position:0%
+building and bayes networks or any of
+that would have got us to this
+
+ align:start position:0%
+that would have got us to this
+ 
+
+ align:start position:0%
+that would have got us to this
+particular hypothesis because the gene
+
+ align:start position:0%
+particular hypothesis because the gene
+ 
+
+ align:start position:0%
+particular hypothesis because the gene
+wasn't even being measured at the time
+
+ align:start position:0%
+wasn't even being measured at the time
+ 
+
+ align:start position:0%
+wasn't even being measured at the time
+but all of these genes that i'm showing
+
+ align:start position:0%
+but all of these genes that i'm showing
+ 
+
+ align:start position:0%
+but all of these genes that i'm showing
+here again the subset of the previous
+
+ align:start position:0%
+here again the subset of the previous
+ 
+
+ align:start position:0%
+here again the subset of the previous
+subset are all downstream of nrf1 so
+
+ align:start position:0%
+subset are all downstream of nrf1 so
+ 
+
+ align:start position:0%
+subset are all downstream of nrf1 so
+that led us to actually think about the
+
+ align:start position:0%
+that led us to actually think about the
+ 
+
+ align:start position:0%
+that led us to actually think about the
+hypothesis maybe nrf1 is down and that's
+
+ align:start position:0%
+hypothesis maybe nrf1 is down and that's
+ 
+
+ align:start position:0%
+hypothesis maybe nrf1 is down and that's
+why all these other genes are down
+
+ align:start position:0%
+why all these other genes are down
+ 
+
+ align:start position:0%
+why all these other genes are down
+because it's much easier to come up with
+
+ align:start position:0%
+because it's much easier to come up with
+ 
+
+ align:start position:0%
+because it's much easier to come up with
+a causal explanation requiring just one
+
+ align:start position:0%
+a causal explanation requiring just one
+ 
+
+ align:start position:0%
+a causal explanation requiring just one
+thing to be wrong then 50 things to be
+
+ align:start position:0%
+thing to be wrong then 50 things to be
+ 
+
+ align:start position:0%
+thing to be wrong then 50 things to be
+wrong right that's occam's razor right
+
+ align:start position:0%
+wrong right that's occam's razor right
+ 
+
+ align:start position:0%
+wrong right that's occam's razor right
+simpler explanations so when you look at
+
+ align:start position:0%
+simpler explanations so when you look at
+ 
+
+ align:start position:0%
+simpler explanations so when you look at
+nrf levels again this is measuring a
+
+ align:start position:0%
+nrf levels again this is measuring a
+ 
+
+ align:start position:0%
+nrf levels again this is measuring a
+different population using a different
+
+ align:start position:0%
+different population using a different
+ 
+
+ align:start position:0%
+different population using a different
+technology rtpcr
+
+ align:start position:0%
+technology rtpcr
+ 
+
+ align:start position:0%
+technology rtpcr
+yeah the family has three negatives here
+
+ align:start position:0%
+yeah the family has three negatives here
+ 
+
+ align:start position:0%
+yeah the family has three negatives here
+positives here diabetics again and the
+
+ align:start position:0%
+positives here diabetics again and the
+ 
+
+ align:start position:0%
+positives here diabetics again and the
+gene actually has a significantly
+
+ align:start position:0%
+gene actually has a significantly
+ 
+
+ align:start position:0%
+gene actually has a significantly
+statistically significant drop in the
+
+ align:start position:0%
+statistically significant drop in the
+ 
+
+ align:start position:0%
+statistically significant drop in the
+diabetics
+
+ align:start position:0%
+diabetics
+ 
+
+ align:start position:0%
+diabetics
+but what's puzzling is that it's not
+
+ align:start position:0%
+but what's puzzling is that it's not
+ 
+
+ align:start position:0%
+but what's puzzling is that it's not
+dropping in the middle group but we saw
+
+ align:start position:0%
+dropping in the middle group but we saw
+ 
+
+ align:start position:0%
+dropping in the middle group but we saw
+those genes were down in the middle
+
+ align:start position:0%
+those genes were down in the middle
+ 
+
+ align:start position:0%
+those genes were down in the middle
+group so this isn't the perfect
+
+ align:start position:0%
+group so this isn't the perfect
+ 
+
+ align:start position:0%
+group so this isn't the perfect
+explanation at all
+
+ align:start position:0%
+explanation at all
+ 
+
+ align:start position:0%
+explanation at all
+another piece of biological knowledge
+
+ align:start position:0%
+another piece of biological knowledge
+ 
+
+ align:start position:0%
+another piece of biological knowledge
+led us to realize that nrf is actually
+
+ align:start position:0%
+led us to realize that nrf is actually
+ 
+
+ align:start position:0%
+led us to realize that nrf is actually
+itself is downstream or actually is
+
+ align:start position:0%
+itself is downstream or actually is
+ 
+
+ align:start position:0%
+itself is downstream or actually is
+co-activated by pgc1 alpha so when you
+
+ align:start position:0%
+co-activated by pgc1 alpha so when you
+ 
+
+ align:start position:0%
+co-activated by pgc1 alpha so when you
+actually measure that that you also get
+
+ align:start position:0%
+actually measure that that you also get
+ 
+
+ align:start position:0%
+actually measure that that you also get
+the clue that pgc1 alpha is down in both
+
+ align:start position:0%
+the clue that pgc1 alpha is down in both
+ 
+
+ align:start position:0%
+the clue that pgc1 alpha is down in both
+of these two groups as well as another
+
+ align:start position:0%
+of these two groups as well as another
+ 
+
+ align:start position:0%
+of these two groups as well as another
+form pgc1 beta which is down in these
+
+ align:start position:0%
+form pgc1 beta which is down in these
+ 
+
+ align:start position:0%
+form pgc1 beta which is down in these
+two groups
+
+ align:start position:0%
+two groups
+ 
+
+ align:start position:0%
+two groups
+the biggest problem though
+
+ align:start position:0%
+the biggest problem though
+ 
+
+ align:start position:0%
+the biggest problem though
+okay so now the hypothesis is that drops
+
+ align:start position:0%
+okay so now the hypothesis is that drops
+ 
+
+ align:start position:0%
+okay so now the hypothesis is that drops
+in pgc1 alpha and nrf are actually
+
+ align:start position:0%
+in pgc1 alpha and nrf are actually
+ 
+
+ align:start position:0%
+in pgc1 alpha and nrf are actually
+what's causing the difference between
+
+ align:start position:0%
+what's causing the difference between
+ 
+
+ align:start position:0%
+what's causing the difference between
+diabetics and non-diabetics and it's
+
+ align:start position:0%
+diabetics and non-diabetics and it's
+ 
+
+ align:start position:0%
+diabetics and non-diabetics and it's
+already showing a difference in the
+
+ align:start position:0%
+already showing a difference in the
+ 
+
+ align:start position:0%
+already showing a difference in the
+pre-diabetics
+
+ align:start position:0%
+pre-diabetics
+ 
+
+ align:start position:0%
+pre-diabetics
+the biggest problem though okay with
+
+ align:start position:0%
+the biggest problem though okay with
+ 
+
+ align:start position:0%
+the biggest problem though okay with
+this study is that what's the cause and
+
+ align:start position:0%
+this study is that what's the cause and
+ 
+
+ align:start position:0%
+this study is that what's the cause and
+what's the effect here okay
+
+ align:start position:0%
+what's the effect here okay
+ 
+
+ align:start position:0%
+what's the effect here okay
+already showing you that the glucose
+
+ align:start position:0%
+already showing you that the glucose
+ 
+
+ align:start position:0%
+already showing you that the glucose
+levels and insulin levels already high
+
+ align:start position:0%
+levels and insulin levels already high
+ 
+
+ align:start position:0%
+levels and insulin levels already high
+in that middle group
+
+ align:start position:0%
+in that middle group
+ 
+
+ align:start position:0%
+in that middle group
+how do i know this isn't just an effect
+
+ align:start position:0%
+how do i know this isn't just an effect
+ 
+
+ align:start position:0%
+how do i know this isn't just an effect
+of having high sugar levels
+
+ align:start position:0%
+of having high sugar levels
+ 
+
+ align:start position:0%
+of having high sugar levels
+how do i know this is causing the high
+
+ align:start position:0%
+how do i know this is causing the high
+ 
+
+ align:start position:0%
+how do i know this is causing the high
+sugar levels
+
+ align:start position:0%
+sugar levels
+ 
+
+ align:start position:0%
+sugar levels
+and that's the problem with this type of
+
+ align:start position:0%
+and that's the problem with this type of
+ 
+
+ align:start position:0%
+and that's the problem with this type of
+approach okay we can easily get samples
+
+ align:start position:0%
+approach okay we can easily get samples
+ 
+
+ align:start position:0%
+approach okay we can easily get samples
+now okay
+
+ align:start position:0%
+now okay
+ 
+
+ align:start position:0%
+now okay
+samples aren't the hard part
+
+ align:start position:0%
+samples aren't the hard part
+ 
+
+ align:start position:0%
+samples aren't the hard part
+the arrays are not the hard part
+
+ align:start position:0%
+the arrays are not the hard part
+ 
+
+ align:start position:0%
+the arrays are not the hard part
+the analysis is not the hard part
+
+ align:start position:0%
+the analysis is not the hard part
+ 
+
+ align:start position:0%
+the analysis is not the hard part
+informatics is not the hardware there's
+
+ align:start position:0%
+informatics is not the hardware there's
+ 
+
+ align:start position:0%
+informatics is not the hardware there's
+plenty of people around now plenty of
+
+ align:start position:0%
+plenty of people around now plenty of
+ 
+
+ align:start position:0%
+plenty of people around now plenty of
+software you can download
+
+ align:start position:0%
+software you can download
+ 
+
+ align:start position:0%
+software you can download
+the hard parts the interpretation in the
+
+ align:start position:0%
+the hard parts the interpretation in the
+ 
+
+ align:start position:0%
+the hard parts the interpretation in the
+end okay
+
+ align:start position:0%
+end okay
+ 
+
+ align:start position:0%
+end okay
+even though we have all these genome
+
+ align:start position:0%
+even though we have all these genome
+ 
+
+ align:start position:0%
+even though we have all these genome
+scale tools
+
+ align:start position:0%
+scale tools
+ 
+
+ align:start position:0%
+scale tools
+we still have nothing that makes the
+
+ align:start position:0%
+we still have nothing that makes the
+ 
+
+ align:start position:0%
+we still have nothing that makes the
+interpretation that much faster but that
+
+ align:start position:0%
+interpretation that much faster but that
+ 
+
+ align:start position:0%
+interpretation that much faster but that
+much easier
+
+ align:start position:0%
+much easier
+ 
+
+ align:start position:0%
+much easier
+so now it's still routine if i go to the
+
+ align:start position:0%
+so now it's still routine if i go to the
+ 
+
+ align:start position:0%
+so now it's still routine if i go to the
+johnson diabetes center look at their
+
+ align:start position:0%
+johnson diabetes center look at their
+ 
+
+ align:start position:0%
+johnson diabetes center look at their
+core facility i mean i'm just there a
+
+ align:start position:0%
+core facility i mean i'm just there a
+ 
+
+ align:start position:0%
+core facility i mean i'm just there a
+couple days ago they've literally built
+
+ align:start position:0%
+couple days ago they've literally built
+ 
+
+ align:start position:0%
+couple days ago they've literally built
+a pyramid of all the arrays they've done
+
+ align:start position:0%
+a pyramid of all the arrays they've done
+ 
+
+ align:start position:0%
+a pyramid of all the arrays they've done
+so far okay on the order of about
+
+ align:start position:0%
+so far okay on the order of about
+ 
+
+ align:start position:0%
+so far okay on the order of about
+fifteen hundred almost two thousand
+
+ align:start position:0%
+fifteen hundred almost two thousand
+ 
+
+ align:start position:0%
+fifteen hundred almost two thousand
+microarrays already done at the thousand
+
+ align:start position:0%
+microarrays already done at the thousand
+ 
+
+ align:start position:0%
+microarrays already done at the thousand
+diabetes center
+
+ align:start position:0%
+diabetes center
+ 
+
+ align:start position:0%
+diabetes center
+there's maybe been about two papers
+
+ align:start position:0%
+there's maybe been about two papers
+ 
+
+ align:start position:0%
+there's maybe been about two papers
+published so far
+
+ align:start position:0%
+published so far
+ 
+
+ align:start position:0%
+published so far
+with all of this array data okay you
+
+ align:start position:0%
+with all of this array data okay you
+ 
+
+ align:start position:0%
+with all of this array data okay you
+know this one which had about 30 samples
+
+ align:start position:0%
+know this one which had about 30 samples
+ 
+
+ align:start position:0%
+know this one which had about 30 samples
+another one that had about 10 samples
+
+ align:start position:0%
+another one that had about 10 samples
+ 
+
+ align:start position:0%
+another one that had about 10 samples
+and still there are thousands of arrays
+
+ align:start position:0%
+and still there are thousands of arrays
+ 
+
+ align:start position:0%
+and still there are thousands of arrays
+that have already been collected the
+
+ align:start position:0%
+that have already been collected the
+ 
+
+ align:start position:0%
+that have already been collected the
+data is already sitting there
+
+ align:start position:0%
+data is already sitting there
+ 
+
+ align:start position:0%
+data is already sitting there
+analysis has already been done but
+
+ align:start position:0%
+analysis has already been done but
+ 
+
+ align:start position:0%
+analysis has already been done but
+people cannot make the leap to the next
+
+ align:start position:0%
+people cannot make the leap to the next
+ 
+
+ align:start position:0%
+people cannot make the leap to the next
+step why is it this list of genes why is
+
+ align:start position:0%
+step why is it this list of genes why is
+ 
+
+ align:start position:0%
+step why is it this list of genes why is
+what's so interesting about that list of
+
+ align:start position:0%
+what's so interesting about that list of
+ 
+
+ align:start position:0%
+what's so interesting about that list of
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+i think that's going to be the hard part
+
+ align:start position:0%
+i think that's going to be the hard part
+ 
+
+ align:start position:0%
+i think that's going to be the hard part
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+in the next few years okay this is not
+
+ align:start position:0%
+in the next few years okay this is not
+ 
+
+ align:start position:0%
+in the next few years okay this is not
+that novel to take samples and put them
+
+ align:start position:0%
+that novel to take samples and put them
+ 
+
+ align:start position:0%
+that novel to take samples and put them
+on a race it's not that's not what the
+
+ align:start position:0%
+on a race it's not that's not what the
+ 
+
+ align:start position:0%
+on a race it's not that's not what the
+medicine part of it is going to be about
+
+ align:start position:0%
+medicine part of it is going to be about
+ 
+
+ align:start position:0%
+medicine part of it is going to be about
+it's going to be trying to get down to
+
+ align:start position:0%
+it's going to be trying to get down to
+ 
+
+ align:start position:0%
+it's going to be trying to get down to
+simpler explanations for what we're
+
+ align:start position:0%
+simpler explanations for what we're
+ 
+
+ align:start position:0%
+simpler explanations for what we're
+seeing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a final hypothesis here
+
+ align:start position:0%
+so this is a final hypothesis here
+ 
+
+ align:start position:0%
+so this is a final hypothesis here
+perhaps that pgc1 is down and that along
+
+ align:start position:0%
+perhaps that pgc1 is down and that along
+ 
+
+ align:start position:0%
+perhaps that pgc1 is down and that along
+with nrf is actually causing this list
+
+ align:start position:0%
+with nrf is actually causing this list
+ 
+
+ align:start position:0%
+with nrf is actually causing this list
+of genes to be different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about that so far any
+
+ align:start position:0%
+any questions about that so far any
+ 
+
+ align:start position:0%
+any questions about that so far any
+thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would you um
+
+ align:start position:0%
+would you um
+ 
+
+ align:start position:0%
+would you um
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a great question okay so this question
+
+ align:start position:0%
+a great question okay so this question
+ 
+
+ align:start position:0%
+a great question okay so this question
+is have we looked at the amp kinase
+
+ align:start position:0%
+is have we looked at the amp kinase
+ 
+
+ align:start position:0%
+is have we looked at the amp kinase
+pathway okay so we know for example when
+
+ align:start position:0%
+pathway okay so we know for example when
+ 
+
+ align:start position:0%
+pathway okay so we know for example when
+people exercise
+
+ align:start position:0%
+people exercise
+ 
+
+ align:start position:0%
+people exercise
+their sensitivity to insulin improves
+
+ align:start position:0%
+their sensitivity to insulin improves
+ 
+
+ align:start position:0%
+their sensitivity to insulin improves
+okay even if they have diabetes you can
+
+ align:start position:0%
+okay even if they have diabetes you can
+ 
+
+ align:start position:0%
+okay even if they have diabetes you can
+people who exercise the same molecule of
+
+ align:start position:0%
+people who exercise the same molecule of
+ 
+
+ align:start position:0%
+people who exercise the same molecule of
+insulin has more of an effect
+
+ align:start position:0%
+insulin has more of an effect
+ 
+
+ align:start position:0%
+insulin has more of an effect
+and that's media through a different
+
+ align:start position:0%
+and that's media through a different
+ 
+
+ align:start position:0%
+and that's media through a different
+pathway okay through the amp kinase
+
+ align:start position:0%
+pathway okay through the amp kinase
+ 
+
+ align:start position:0%
+pathway okay through the amp kinase
+pathway
+
+ align:start position:0%
+pathway
+ 
+
+ align:start position:0%
+pathway
+did we look at ap kinase levels here no
+
+ align:start position:0%
+did we look at ap kinase levels here no
+ 
+
+ align:start position:0%
+did we look at ap kinase levels here no
+did we look at the expression levels
+
+ align:start position:0%
+did we look at the expression levels
+ 
+
+ align:start position:0%
+did we look at the expression levels
+they might have been on the chip but
+
+ align:start position:0%
+they might have been on the chip but
+ 
+
+ align:start position:0%
+they might have been on the chip but
+they weren't different did we look at
+
+ align:start position:0%
+they weren't different did we look at
+ 
+
+ align:start position:0%
+they weren't different did we look at
+activity levels of protein levels no
+
+ align:start position:0%
+activity levels of protein levels no
+ 
+
+ align:start position:0%
+activity levels of protein levels no
+but you can bet in that towering pile of
+
+ align:start position:0%
+but you can bet in that towering pile of
+ 
+
+ align:start position:0%
+but you can bet in that towering pile of
+a thousand arrays laurie goodyear and
+
+ align:start position:0%
+a thousand arrays laurie goodyear and
+ 
+
+ align:start position:0%
+a thousand arrays laurie goodyear and
+others have done these arrays already
+
+ align:start position:0%
+others have done these arrays already
+ 
+
+ align:start position:0%
+others have done these arrays already
+but they're still stuck the same way
+
+ align:start position:0%
+but they're still stuck the same way
+ 
+
+ align:start position:0%
+but they're still stuck the same way
+okay i mean so how what what is it about
+
+ align:start position:0%
+okay i mean so how what what is it about
+ 
+
+ align:start position:0%
+okay i mean so how what what is it about
+these lists of genes
+
+ align:start position:0%
+these lists of genes
+ 
+
+ align:start position:0%
+these lists of genes
+that's going to get us to a hypothesis
+
+ align:start position:0%
+that's going to get us to a hypothesis
+ 
+
+ align:start position:0%
+that's going to get us to a hypothesis
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+it's very unwieldy it's very hard to
+
+ align:start position:0%
+it's very unwieldy it's very hard to
+ 
+
+ align:start position:0%
+it's very unwieldy it's very hard to
+deal with these lists of hundreds of
+
+ align:start position:0%
+deal with these lists of hundreds of
+ 
+
+ align:start position:0%
+deal with these lists of hundreds of
+genes okay
+
+ align:start position:0%
+genes okay
+ 
+
+ align:start position:0%
+genes okay
+it's not very validating anymore it's
+
+ align:start position:0%
+it's not very validating anymore it's
+ 
+
+ align:start position:0%
+it's not very validating anymore it's
+not very fun to work with these genes
+
+ align:start position:0%
+not very fun to work with these genes
+ 
+
+ align:start position:0%
+not very fun to work with these genes
+the hard part is to get down to the
+
+ align:start position:0%
+the hard part is to get down to the
+ 
+
+ align:start position:0%
+the hard part is to get down to the
+causal mechanism for those genes and
+
+ align:start position:0%
+causal mechanism for those genes and
+ 
+
+ align:start position:0%
+causal mechanism for those genes and
+that's where we have the least
+
+ align:start position:0%
+that's where we have the least
+ 
+
+ align:start position:0%
+that's where we have the least
+information right now what what's
+
+ align:start position:0%
+information right now what what's
+ 
+
+ align:start position:0%
+information right now what what's
+upstream of what for example
+
+ align:start position:0%
+upstream of what for example
+ 
+
+ align:start position:0%
+upstream of what for example
+you go back to the chicken and egg
+
+ align:start position:0%
+you go back to the chicken and egg
+ 
+
+ align:start position:0%
+you go back to the chicken and egg
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was just wondering now you're saying
+
+ align:start position:0%
+i was just wondering now you're saying
+ 
+
+ align:start position:0%
+i was just wondering now you're saying
+that you have a decrease in the ox loss
+
+ align:start position:0%
+that you have a decrease in the ox loss
+ 
+
+ align:start position:0%
+that you have a decrease in the ox loss
+lipid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're not uh primarily you're not
+
+ align:start position:0%
+you're not uh primarily you're not
+ 
+
+ align:start position:0%
+you're not uh primarily you're not
+generating atp as efficiently as you
+
+ align:start position:0%
+generating atp as efficiently as you
+ 
+
+ align:start position:0%
+generating atp as efficiently as you
+could okay or
+
+ align:start position:0%
+could okay or
+ 
+
+ align:start position:0%
+could okay or
+in a muscle yeah well if you're if
+
+ align:start position:0%
+in a muscle yeah well if you're if
+ 
+
+ align:start position:0%
+in a muscle yeah well if you're if
+you're if you're generating atp
+
+ align:start position:0%
+you're if you're generating atp
+ 
+
+ align:start position:0%
+you're if you're generating atp
+inefficiently
+
+ align:start position:0%
+inefficiently
+ 
+
+ align:start position:0%
+inefficiently
+that's the equivalent of like having off
+
+ align:start position:0%
+that's the equivalent of like having off
+ 
+
+ align:start position:0%
+that's the equivalent of like having off
+spots decoupling or something right
+
+ align:start position:0%
+spots decoupling or something right
+ 
+
+ align:start position:0%
+spots decoupling or something right
+exactly this is you're actually not
+
+ align:start position:0%
+exactly this is you're actually not
+ 
+
+ align:start position:0%
+exactly this is you're actually not
+generating the atp and instead yeah the
+
+ align:start position:0%
+generating the atp and instead yeah the
+ 
+
+ align:start position:0%
+generating the atp and instead yeah the
+pipe is straight exactly the pipe is not
+
+ align:start position:0%
+pipe is straight exactly the pipe is not
+ 
+
+ align:start position:0%
+pipe is straight exactly the pipe is not
+being full exactly the pipe is not being
+
+ align:start position:0%
+being full exactly the pipe is not being
+ 
+
+ align:start position:0%
+being full exactly the pipe is not being
+filled as efficiently as it can be right
+
+ align:start position:0%
+filled as efficiently as it can be right
+ 
+
+ align:start position:0%
+filled as efficiently as it can be right
+so absolutely if you use that and you go
+
+ align:start position:0%
+so absolutely if you use that and you go
+ 
+
+ align:start position:0%
+so absolutely if you use that and you go
+back and use your sort of backwards
+
+ align:start position:0%
+back and use your sort of backwards
+ 
+
+ align:start position:0%
+back and use your sort of backwards
+reasoning okay
+
+ align:start position:0%
+reasoning okay
+ 
+
+ align:start position:0%
+reasoning okay
+wouldn't that basically suggest that
+
+ align:start position:0%
+wouldn't that basically suggest that
+ 
+
+ align:start position:0%
+wouldn't that basically suggest that
+the initial perturbation is in
+
+ align:start position:0%
+the initial perturbation is in
+ 
+
+ align:start position:0%
+the initial perturbation is in
+nrf and uh
+
+ align:start position:0%
+nrf and uh
+ 
+
+ align:start position:0%
+nrf and uh
+dpar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's other ways we can there's
+
+ align:start position:0%
+so there's other ways we can there's
+ 
+
+ align:start position:0%
+so there's other ways we can there's
+other pieces of information that we can
+
+ align:start position:0%
+other pieces of information that we can
+ 
+
+ align:start position:0%
+other pieces of information that we can
+bring to this to try to figure out the
+
+ align:start position:0%
+bring to this to try to figure out the
+ 
+
+ align:start position:0%
+bring to this to try to figure out the
+ordering of them right so there are
+
+ align:start position:0%
+ordering of them right so there are
+ 
+
+ align:start position:0%
+ordering of them right so there are
+sequence polymorphisms that are known in
+
+ align:start position:0%
+sequence polymorphisms that are known in
+ 
+
+ align:start position:0%
+sequence polymorphisms that are known in
+these genes okay like uh specifically in
+
+ align:start position:0%
+these genes okay like uh specifically in
+ 
+
+ align:start position:0%
+these genes okay like uh specifically in
+pgc1 that go along to having diabetes
+
+ align:start position:0%
+pgc1 that go along to having diabetes
+ 
+
+ align:start position:0%
+pgc1 that go along to having diabetes
+okay so we think well if people if
+
+ align:start position:0%
+okay so we think well if people if
+ 
+
+ align:start position:0%
+okay so we think well if people if
+there's people have an abnormal sequence
+
+ align:start position:0%
+there's people have an abnormal sequence
+ 
+
+ align:start position:0%
+there's people have an abnormal sequence
+and they get diabetes maybe that's
+
+ align:start position:0%
+and they get diabetes maybe that's
+ 
+
+ align:start position:0%
+and they get diabetes maybe that's
+what's causing it
+
+ align:start position:0%
+what's causing it
+ 
+
+ align:start position:0%
+what's causing it
+okay right that's what puts this
+
+ align:start position:0%
+okay right that's what puts this
+ 
+
+ align:start position:0%
+okay right that's what puts this
+upstream of the actual having the high
+
+ align:start position:0%
+upstream of the actual having the high
+ 
+
+ align:start position:0%
+upstream of the actual having the high
+sugar levels
+
+ align:start position:0%
+sugar levels
+ 
+
+ align:start position:0%
+sugar levels
+but in this sample without without that
+
+ align:start position:0%
+but in this sample without without that
+ 
+
+ align:start position:0%
+but in this sample without without that
+a priori knowledge you can't tell that
+
+ align:start position:0%
+a priori knowledge you can't tell that
+ 
+
+ align:start position:0%
+a priori knowledge you can't tell that
+that's the issue but doesn't it suggest
+
+ align:start position:0%
+that's the issue but doesn't it suggest
+ 
+
+ align:start position:0%
+that's the issue but doesn't it suggest
+that now or is that a giant leap in
+
+ align:start position:0%
+that now or is that a giant leap in
+ 
+
+ align:start position:0%
+that now or is that a giant leap in
+other words in other words
+
+ align:start position:0%
+other words in other words
+ 
+
+ align:start position:0%
+other words in other words
+if the glucose level was high if the
+
+ align:start position:0%
+if the glucose level was high if the
+ 
+
+ align:start position:0%
+if the glucose level was high if the
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+perturbation for the elevated blood was
+
+ align:start position:0%
+perturbation for the elevated blood was
+ 
+
+ align:start position:0%
+perturbation for the elevated blood was
+though okay yep if it were that
+
+ align:start position:0%
+though okay yep if it were that
+ 
+
+ align:start position:0%
+though okay yep if it were that
+and that doesn't
+
+ align:start position:0%
+and that doesn't
+ 
+
+ align:start position:0%
+and that doesn't
+explain why you have
+
+ align:start position:0%
+explain why you have
+ 
+
+ align:start position:0%
+explain why you have
+uh up regulation of uh
+
+ align:start position:0%
+uh up regulation of uh
+ 
+
+ align:start position:0%
+uh up regulation of uh
+down regulation nrf and uh
+
+ align:start position:0%
+down regulation nrf and uh
+ 
+
+ align:start position:0%
+down regulation nrf and uh
+whatever it is is it up or down
+
+ align:start position:0%
+whatever it is is it up or down
+ 
+
+ align:start position:0%
+whatever it is is it up or down
+the nrf is down all i'm saying is with
+
+ align:start position:0%
+the nrf is down all i'm saying is with
+ 
+
+ align:start position:0%
+the nrf is down all i'm saying is with
+just this experiment i could put this
+
+ align:start position:0%
+just this experiment i could put this
+ 
+
+ align:start position:0%
+just this experiment i could put this
+square up here
+
+ align:start position:0%
+square up here
+ 
+
+ align:start position:0%
+square up here
+and say that is leading to this leading
+
+ align:start position:0%
+and say that is leading to this leading
+ 
+
+ align:start position:0%
+and say that is leading to this leading
+to this leading to this list of this
+
+ align:start position:0%
+to this leading to this list of this
+ 
+
+ align:start position:0%
+to this leading to this list of this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+i can't make that leap that this is
+
+ align:start position:0%
+i can't make that leap that this is
+ 
+
+ align:start position:0%
+i can't make that leap that this is
+causal
+
+ align:start position:0%
+causal
+ 
+
+ align:start position:0%
+causal
+it's more suggestive that the square is
+
+ align:start position:0%
+it's more suggestive that the square is
+ 
+
+ align:start position:0%
+it's more suggestive that the square is
+down there where am i not thinking about
+
+ align:start position:0%
+down there where am i not thinking about
+ 
+
+ align:start position:0%
+down there where am i not thinking about
+with the sequence by morphisms and
+
+ align:start position:0%
+with the sequence by morphisms and
+ 
+
+ align:start position:0%
+with the sequence by morphisms and
+things it makes me think that it's down
+
+ align:start position:0%
+things it makes me think that it's down
+ 
+
+ align:start position:0%
+things it makes me think that it's down
+here but just the experiment by itself
+
+ align:start position:0%
+here but just the experiment by itself
+ 
+
+ align:start position:0%
+here but just the experiment by itself
+without the a priori knowledge okay
+
+ align:start position:0%
+without the a priori knowledge okay
+ 
+
+ align:start position:0%
+without the a priori knowledge okay
+without knowing what the literature
+
+ align:start position:0%
+without knowing what the literature
+ 
+
+ align:start position:0%
+without knowing what the literature
+tells you
+
+ align:start position:0%
+tells you
+ 
+
+ align:start position:0%
+tells you
+how would you know that because these
+
+ align:start position:0%
+how would you know that because these
+ 
+
+ align:start position:0%
+how would you know that because these
+patients already have some degree of
+
+ align:start position:0%
+patients already have some degree of
+ 
+
+ align:start position:0%
+patients already have some degree of
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+that's the issue here right you need to
+
+ align:start position:0%
+that's the issue here right you need to
+ 
+
+ align:start position:0%
+that's the issue here right you need to
+know what the the biology cannot ignore
+
+ align:start position:0%
+know what the the biology cannot ignore
+ 
+
+ align:start position:0%
+know what the the biology cannot ignore
+the biology
+
+ align:start position:0%
+the biology
+ 
+
+ align:start position:0%
+the biology
+there's no question
+
+ align:start position:0%
+there's no question
+ 
+
+ align:start position:0%
+there's no question
+what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+exactly right so right and so you picked
+
+ align:start position:0%
+exactly right so right and so you picked
+ 
+
+ align:start position:0%
+exactly right so right and so you picked
+up on that as well i mean so um
+
+ align:start position:0%
+up on that as well i mean so um
+ 
+
+ align:start position:0%
+up on that as well i mean so um
+yeah body mass index is different too
+
+ align:start position:0%
+yeah body mass index is different too
+ 
+
+ align:start position:0%
+yeah body mass index is different too
+because it's hard to find
+
+ align:start position:0%
+because it's hard to find
+ 
+
+ align:start position:0%
+because it's hard to find
+i mean that's life in america now
+
+ align:start position:0%
+i mean that's life in america now
+ 
+
+ align:start position:0%
+i mean that's life in america now
+everyone is obese okay
+
+ align:start position:0%
+everyone is obese okay
+ 
+
+ align:start position:0%
+everyone is obese okay
+and so even teenagers that are obese
+
+ align:start position:0%
+and so even teenagers that are obese
+ 
+
+ align:start position:0%
+and so even teenagers that are obese
+have some would would might be in this
+
+ align:start position:0%
+have some would would might be in this
+ 
+
+ align:start position:0%
+have some would would might be in this
+middle group now they will have some
+
+ align:start position:0%
+middle group now they will have some
+ 
+
+ align:start position:0%
+middle group now they will have some
+impaired glucose tolerance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the control group was uh i mean their
+
+ align:start position:0%
+the control group was uh i mean their
+ 
+
+ align:start position:0%
+the control group was uh i mean their
+body mass index is still 30 okay that
+
+ align:start position:0%
+body mass index is still 30 okay that
+ 
+
+ align:start position:0%
+body mass index is still 30 okay that
+qualifies as obese today
+
+ align:start position:0%
+qualifies as obese today
+ 
+
+ align:start position:0%
+qualifies as obese today
+and the family history was actually
+
+ align:start position:0%
+and the family history was actually
+ 
+
+ align:start position:0%
+and the family history was actually
+slightly less but they're all obese
+
+ align:start position:0%
+slightly less but they're all obese
+ 
+
+ align:start position:0%
+slightly less but they're all obese
+basically right especially the controls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+yeah absolutely
+
+ align:start position:0%
+yeah absolutely
+ 
+
+ align:start position:0%
+yeah absolutely
+uh this one here
+
+ align:start position:0%
+uh this one here
+ 
+
+ align:start position:0%
+uh this one here
+yep exactly
+
+ align:start position:0%
+yep exactly
+ 
+
+ align:start position:0%
+yep exactly
+this is a one gene versus the other and
+
+ align:start position:0%
+this is a one gene versus the other and
+ 
+
+ align:start position:0%
+this is a one gene versus the other and
+you can see the body mass index here
+
+ align:start position:0%
+you can see the body mass index here
+ 
+
+ align:start position:0%
+you can see the body mass index here
+exactly and you got one all the way over
+
+ align:start position:0%
+exactly and you got one all the way over
+ 
+
+ align:start position:0%
+exactly and you got one all the way over
+here exactly that's destroying the mean
+
+ align:start position:0%
+here exactly that's destroying the mean
+ 
+
+ align:start position:0%
+here exactly that's destroying the mean
+so these are not otherwise equal groups
+
+ align:start position:0%
+so these are not otherwise equal groups
+ 
+
+ align:start position:0%
+so these are not otherwise equal groups
+that's the problem
+
+ align:start position:0%
+that's the problem
+ 
+
+ align:start position:0%
+that's the problem
+now you have to so
+
+ align:start position:0%
+now you have to so
+ 
+
+ align:start position:0%
+now you have to so
+why am i even showing all this if i'm if
+
+ align:start position:0%
+why am i even showing all this if i'm if
+ 
+
+ align:start position:0%
+why am i even showing all this if i'm if
+i have all these problems with this
+
+ align:start position:0%
+i have all these problems with this
+ 
+
+ align:start position:0%
+i have all these problems with this
+analysis and this data the whole point
+
+ align:start position:0%
+analysis and this data the whole point
+ 
+
+ align:start position:0%
+analysis and this data the whole point
+of this kind of course is not just to
+
+ align:start position:0%
+of this kind of course is not just to
+ 
+
+ align:start position:0%
+of this kind of course is not just to
+teach you how to
+
+ align:start position:0%
+teach you how to
+ 
+
+ align:start position:0%
+teach you how to
+look at how to do these types of
+
+ align:start position:0%
+look at how to do these types of
+ 
+
+ align:start position:0%
+look at how to do these types of
+experiments to me it would be great if
+
+ align:start position:0%
+experiments to me it would be great if
+ 
+
+ align:start position:0%
+experiments to me it would be great if
+you knew how to interpret these things
+
+ align:start position:0%
+you knew how to interpret these things
+ 
+
+ align:start position:0%
+you knew how to interpret these things
+that come out in the new england journal
+
+ align:start position:0%
+that come out in the new england journal
+ 
+
+ align:start position:0%
+that come out in the new england journal
+every day okay
+
+ align:start position:0%
+every day okay
+ 
+
+ align:start position:0%
+every day okay
+because every every month now we see a
+
+ align:start position:0%
+because every every month now we see a
+ 
+
+ align:start position:0%
+because every every month now we see a
+microwave paper say the new england
+
+ align:start position:0%
+microwave paper say the new england
+ 
+
+ align:start position:0%
+microwave paper say the new england
+journal or jama or other equivalent
+
+ align:start position:0%
+journal or jama or other equivalent
+ 
+
+ align:start position:0%
+journal or jama or other equivalent
+publications
+
+ align:start position:0%
+publications
+ 
+
+ align:start position:0%
+publications
+and i think we have to teach people to
+
+ align:start position:0%
+and i think we have to teach people to
+ 
+
+ align:start position:0%
+and i think we have to teach people to
+how to read these things with a critical
+
+ align:start position:0%
+how to read these things with a critical
+ 
+
+ align:start position:0%
+how to read these things with a critical
+eye
+
+ align:start position:0%
+eye
+ 
+
+ align:start position:0%
+eye
+okay because it looks so fancy to come
+
+ align:start position:0%
+okay because it looks so fancy to come
+ 
+
+ align:start position:0%
+okay because it looks so fancy to come
+out with 44 000 genes and these are the
+
+ align:start position:0%
+out with 44 000 genes and these are the
+ 
+
+ align:start position:0%
+out with 44 000 genes and these are the
+ones actually diagnostic but there's
+
+ align:start position:0%
+ones actually diagnostic but there's
+ 
+
+ align:start position:0%
+ones actually diagnostic but there's
+actually problems with experimental
+
+ align:start position:0%
+actually problems with experimental
+ 
+
+ align:start position:0%
+actually problems with experimental
+design if the experiment was not
+
+ align:start position:0%
+design if the experiment was not
+ 
+
+ align:start position:0%
+design if the experiment was not
+designed in exactly the way that the
+
+ align:start position:0%
+designed in exactly the way that the
+ 
+
+ align:start position:0%
+designed in exactly the way that the
+answer the question that was being asked
+
+ align:start position:0%
+answer the question that was being asked
+ 
+
+ align:start position:0%
+answer the question that was being asked
+no amount of fancy arrays is going to be
+
+ align:start position:0%
+no amount of fancy arrays is going to be
+ 
+
+ align:start position:0%
+no amount of fancy arrays is going to be
+able to help you can't salvage that okay
+
+ align:start position:0%
+able to help you can't salvage that okay
+ 
+
+ align:start position:0%
+able to help you can't salvage that okay
+that's what i'm trying to get across is
+
+ align:start position:0%
+that's what i'm trying to get across is
+ 
+
+ align:start position:0%
+that's what i'm trying to get across is
+to be how to be critical here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think the same thing okay when you see a
+
+ align:start position:0%
+think the same thing okay when you see a
+ 
+
+ align:start position:0%
+think the same thing okay when you see a
+bunch of genes that distinguishes a-l-l
+
+ align:start position:0%
+bunch of genes that distinguishes a-l-l
+ 
+
+ align:start position:0%
+bunch of genes that distinguishes a-l-l
+from aml
+
+ align:start position:0%
+from aml
+ 
+
+ align:start position:0%
+from aml
+okay just think about all the other
+
+ align:start position:0%
+okay just think about all the other
+ 
+
+ align:start position:0%
+okay just think about all the other
+things in their context that could be
+
+ align:start position:0%
+things in their context that could be
+ 
+
+ align:start position:0%
+things in their context that could be
+making a difference here okay
+
+ align:start position:0%
+making a difference here okay
+ 
+
+ align:start position:0%
+making a difference here okay
+when were the samples acquired where
+
+ align:start position:0%
+when were the samples acquired where
+ 
+
+ align:start position:0%
+when were the samples acquired where
+were they acquired you know our patients
+
+ align:start position:0%
+were they acquired you know our patients
+ 
+
+ align:start position:0%
+were they acquired you know our patients
+with aml preferentially sent to one
+
+ align:start position:0%
+with aml preferentially sent to one
+ 
+
+ align:start position:0%
+with aml preferentially sent to one
+center and the ones with all sent to
+
+ align:start position:0%
+center and the ones with all sent to
+ 
+
+ align:start position:0%
+center and the ones with all sent to
+another center
+
+ align:start position:0%
+another center
+ 
+
+ align:start position:0%
+another center
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+my favorite example i'd love to give is
+
+ align:start position:0%
+my favorite example i'd love to give is
+ 
+
+ align:start position:0%
+my favorite example i'd love to give is
+this okay let's say you're looking at a
+
+ align:start position:0%
+this okay let's say you're looking at a
+ 
+
+ align:start position:0%
+this okay let's say you're looking at a
+solid tumor and you're trying to
+
+ align:start position:0%
+solid tumor and you're trying to
+ 
+
+ align:start position:0%
+solid tumor and you're trying to
+distinguish the genes that are different
+
+ align:start position:0%
+distinguish the genes that are different
+ 
+
+ align:start position:0%
+distinguish the genes that are different
+between the metastatic form of this
+
+ align:start position:0%
+between the metastatic form of this
+ 
+
+ align:start position:0%
+between the metastatic form of this
+cancer and the non-metastatic form
+
+ align:start position:0%
+cancer and the non-metastatic form
+ 
+
+ align:start position:0%
+cancer and the non-metastatic form
+okay have you spent any time in the
+
+ align:start position:0%
+okay have you spent any time in the
+ 
+
+ align:start position:0%
+okay have you spent any time in the
+wards you know how surgeons work okay if
+
+ align:start position:0%
+wards you know how surgeons work okay if
+ 
+
+ align:start position:0%
+wards you know how surgeons work okay if
+you have a patient if a surgeon is
+
+ align:start position:0%
+you have a patient if a surgeon is
+ 
+
+ align:start position:0%
+you have a patient if a surgeon is
+looking at their caseload for the next
+
+ align:start position:0%
+looking at their caseload for the next
+ 
+
+ align:start position:0%
+looking at their caseload for the next
+day and they have a patient with
+
+ align:start position:0%
+day and they have a patient with
+ 
+
+ align:start position:0%
+day and they have a patient with
+metastatic and patient non-metastatic
+
+ align:start position:0%
+metastatic and patient non-metastatic
+ 
+
+ align:start position:0%
+metastatic and patient non-metastatic
+they're basically metastatic it's
+
+ align:start position:0%
+they're basically metastatic it's
+ 
+
+ align:start position:0%
+they're basically metastatic it's
+already metastasized the surgery is
+
+ align:start position:0%
+already metastasized the surgery is
+ 
+
+ align:start position:0%
+already metastasized the surgery is
+going to be a hell of a lot longer let's
+
+ align:start position:0%
+going to be a hell of a lot longer let's
+ 
+
+ align:start position:0%
+going to be a hell of a lot longer let's
+say okay because i have to go check this
+
+ align:start position:0%
+say okay because i have to go check this
+ 
+
+ align:start position:0%
+say okay because i have to go check this
+check that clean this out clean that out
+
+ align:start position:0%
+check that clean this out clean that out
+ 
+
+ align:start position:0%
+check that clean this out clean that out
+the surgeon might say i'm going to put
+
+ align:start position:0%
+the surgeon might say i'm going to put
+ 
+
+ align:start position:0%
+the surgeon might say i'm going to put
+that patient as the first case of the
+
+ align:start position:0%
+that patient as the first case of the
+ 
+
+ align:start position:0%
+that patient as the first case of the
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+okay and the simpler case i'm going to
+
+ align:start position:0%
+okay and the simpler case i'm going to
+ 
+
+ align:start position:0%
+okay and the simpler case i'm going to
+put on as a follow-on or an add-on case
+
+ align:start position:0%
+put on as a follow-on or an add-on case
+ 
+
+ align:start position:0%
+put on as a follow-on or an add-on case
+keep them waiting in the waiting room or
+
+ align:start position:0%
+keep them waiting in the waiting room or
+ 
+
+ align:start position:0%
+keep them waiting in the waiting room or
+in the recovery room ready to go and
+
+ align:start position:0%
+in the recovery room ready to go and
+ 
+
+ align:start position:0%
+in the recovery room ready to go and
+then we're going to do them after this
+
+ align:start position:0%
+then we're going to do them after this
+ 
+
+ align:start position:0%
+then we're going to do them after this
+first case is done
+
+ align:start position:0%
+first case is done
+ 
+
+ align:start position:0%
+first case is done
+so now imagine a study where you look at
+
+ align:start position:0%
+so now imagine a study where you look at
+ 
+
+ align:start position:0%
+so now imagine a study where you look at
+the difference between metastatic and
+
+ align:start position:0%
+the difference between metastatic and
+ 
+
+ align:start position:0%
+the difference between metastatic and
+non-metastatic forms of this particular
+
+ align:start position:0%
+non-metastatic forms of this particular
+ 
+
+ align:start position:0%
+non-metastatic forms of this particular
+cancer
+
+ align:start position:0%
+cancer
+ 
+
+ align:start position:0%
+cancer
+they got these samples from these
+
+ align:start position:0%
+they got these samples from these
+ 
+
+ align:start position:0%
+they got these samples from these
+surgeons who preferentially put the hard
+
+ align:start position:0%
+surgeons who preferentially put the hard
+ 
+
+ align:start position:0%
+surgeons who preferentially put the hard
+cases in the morning and the easy cases
+
+ align:start position:0%
+cases in the morning and the easy cases
+ 
+
+ align:start position:0%
+cases in the morning and the easy cases
+in the afternoon
+
+ align:start position:0%
+in the afternoon
+ 
+
+ align:start position:0%
+in the afternoon
+okay i'm an endocrinologist i know that
+
+ align:start position:0%
+okay i'm an endocrinologist i know that
+ 
+
+ align:start position:0%
+okay i'm an endocrinologist i know that
+they're hormones that are different
+
+ align:start position:0%
+they're hormones that are different
+ 
+
+ align:start position:0%
+they're hormones that are different
+between morning and evening right with
+
+ align:start position:0%
+between morning and evening right with
+ 
+
+ align:start position:0%
+between morning and evening right with
+insulin growth hormone cortisol
+
+ align:start position:0%
+insulin growth hormone cortisol
+ 
+
+ align:start position:0%
+insulin growth hormone cortisol
+who knows how many genes are downstream
+
+ align:start position:0%
+who knows how many genes are downstream
+ 
+
+ align:start position:0%
+who knows how many genes are downstream
+of those hormones
+
+ align:start position:0%
+of those hormones
+ 
+
+ align:start position:0%
+of those hormones
+and how do you know that the signal that
+
+ align:start position:0%
+and how do you know that the signal that
+ 
+
+ align:start position:0%
+and how do you know that the signal that
+you're seeing isn't because of that bias
+
+ align:start position:0%
+you're seeing isn't because of that bias
+ 
+
+ align:start position:0%
+you're seeing isn't because of that bias
+or the confounding there
+
+ align:start position:0%
+or the confounding there
+ 
+
+ align:start position:0%
+or the confounding there
+now this is not revolutionary stuff
+
+ align:start position:0%
+now this is not revolutionary stuff
+ 
+
+ align:start position:0%
+now this is not revolutionary stuff
+right if we looked at clinical tests or
+
+ align:start position:0%
+right if we looked at clinical tests or
+ 
+
+ align:start position:0%
+right if we looked at clinical tests or
+clinical trials in the past we need to
+
+ align:start position:0%
+clinical trials in the past we need to
+ 
+
+ align:start position:0%
+clinical trials in the past we need to
+look for these things but all of a
+
+ align:start position:0%
+look for these things but all of a
+ 
+
+ align:start position:0%
+look for these things but all of a
+sudden now that we have these fancy red
+
+ align:start position:0%
+sudden now that we have these fancy red
+ 
+
+ align:start position:0%
+sudden now that we have these fancy red
+grenograms and we have these microwaves
+
+ align:start position:0%
+grenograms and we have these microwaves
+ 
+
+ align:start position:0%
+grenograms and we have these microwaves
+people have forgotten about all of this
+
+ align:start position:0%
+people have forgotten about all of this
+ 
+
+ align:start position:0%
+people have forgotten about all of this
+traditional these traditional
+
+ align:start position:0%
+traditional these traditional
+ 
+
+ align:start position:0%
+traditional these traditional
+confounders
+
+ align:start position:0%
+confounders
+ 
+
+ align:start position:0%
+confounders
+okay we're measuring across the entire
+
+ align:start position:0%
+okay we're measuring across the entire
+ 
+
+ align:start position:0%
+okay we're measuring across the entire
+measurable genome the signal that you
+
+ align:start position:0%
+measurable genome the signal that you
+ 
+
+ align:start position:0%
+measurable genome the signal that you
+get just from endocrinology from
+
+ align:start position:0%
+get just from endocrinology from
+ 
+
+ align:start position:0%
+get just from endocrinology from
+circadian cycles might be stronger than
+
+ align:start position:0%
+circadian cycles might be stronger than
+ 
+
+ align:start position:0%
+circadian cycles might be stronger than
+the signal that you actually think
+
+ align:start position:0%
+the signal that you actually think
+ 
+
+ align:start position:0%
+the signal that you actually think
+you're measuring
+
+ align:start position:0%
+you're measuring
+ 
+
+ align:start position:0%
+you're measuring
+now you go back and look at the last
+
+ align:start position:0%
+now you go back and look at the last
+ 
+
+ align:start position:0%
+now you go back and look at the last
+three microarray papers that are in the
+
+ align:start position:0%
+three microarray papers that are in the
+ 
+
+ align:start position:0%
+three microarray papers that are in the
+new england journal medicine and just
+
+ align:start position:0%
+new england journal medicine and just
+ 
+
+ align:start position:0%
+new england journal medicine and just
+look to see if you can figure out what
+
+ align:start position:0%
+look to see if you can figure out what
+ 
+
+ align:start position:0%
+look to see if you can figure out what
+time of day these samples were acquired
+
+ align:start position:0%
+time of day these samples were acquired
+ 
+
+ align:start position:0%
+time of day these samples were acquired
+no way
+
+ align:start position:0%
+no way
+ 
+
+ align:start position:0%
+no way
+i know sensitive is something like that
+
+ align:start position:0%
+i know sensitive is something like that
+ 
+
+ align:start position:0%
+i know sensitive is something like that
+and well two part questions one you know
+
+ align:start position:0%
+and well two part questions one you know
+ 
+
+ align:start position:0%
+and well two part questions one you know
+it's a matter of like between 8 a.m and
+
+ align:start position:0%
+it's a matter of like between 8 a.m and
+ 
+
+ align:start position:0%
+it's a matter of like between 8 a.m and
+8 30 and that sort of thing and
+
+ align:start position:0%
+8 30 and that sort of thing and
+ 
+
+ align:start position:0%
+8 30 and that sort of thing and
+it's not even known
+
+ align:start position:0%
+it's not even known
+ 
+
+ align:start position:0%
+it's not even known
+right so it might not be known but then
+
+ align:start position:0%
+right so it might not be known but then
+ 
+
+ align:start position:0%
+right so it might not be known but then
+what i would say is we should randomize
+
+ align:start position:0%
+what i would say is we should randomize
+ 
+
+ align:start position:0%
+what i would say is we should randomize
+across that variable
+
+ align:start position:0%
+across that variable
+ 
+
+ align:start position:0%
+across that variable
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you could turn the lights on there
+
+ align:start position:0%
+you could turn the lights on there
+ 
+
+ align:start position:0%
+you could turn the lights on there
+we should randomize across that variable
+
+ align:start position:0%
+we should randomize across that variable
+ 
+
+ align:start position:0%
+we should randomize across that variable
+okay so for example someone should be
+
+ align:start position:0%
+okay so for example someone should be
+ 
+
+ align:start position:0%
+okay so for example someone should be
+looking at the clock and say well these
+
+ align:start position:0%
+looking at the clock and say well these
+ 
+
+ align:start position:0%
+looking at the clock and say well these
+are all acquired there's some that are
+
+ align:start position:0%
+are all acquired there's some that are
+ 
+
+ align:start position:0%
+are all acquired there's some that are
+here some that are here some that are
+
+ align:start position:0%
+here some that are here some that are
+ 
+
+ align:start position:0%
+here some that are here some that are
+here and just convince yourself that
+
+ align:start position:0%
+here and just convince yourself that
+ 
+
+ align:start position:0%
+here and just convince yourself that
+it's not just a gross bias
+
+ align:start position:0%
+it's not just a gross bias
+ 
+
+ align:start position:0%
+it's not just a gross bias
+i'm just making a fake you know a fake
+
+ align:start position:0%
+i'm just making a fake you know a fake
+ 
+
+ align:start position:0%
+i'm just making a fake you know a fake
+story here that's believable
+
+ align:start position:0%
+story here that's believable
+ 
+
+ align:start position:0%
+story here that's believable
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in the morning of the afternoon sure you
+
+ align:start position:0%
+in the morning of the afternoon sure you
+ 
+
+ align:start position:0%
+in the morning of the afternoon sure you
+can try to compensate from support some
+
+ align:start position:0%
+can try to compensate from support some
+ 
+
+ align:start position:0%
+can try to compensate from support some
+other way
+
+ align:start position:0%
+other way
+ 
+
+ align:start position:0%
+other way
+but it's going to be relative to their
+
+ align:start position:0%
+but it's going to be relative to their
+ 
+
+ align:start position:0%
+but it's going to be relative to their
+hormone levels too probably
+
+ align:start position:0%
+hormone levels too probably
+ 
+
+ align:start position:0%
+hormone levels too probably
+i guess the example that you gave in
+
+ align:start position:0%
+i guess the example that you gave in
+ 
+
+ align:start position:0%
+i guess the example that you gave in
+that is it's just sort of going out
+
+ align:start position:0%
+that is it's just sort of going out
+ 
+
+ align:start position:0%
+that is it's just sort of going out
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+uh but
+
+ align:start position:0%
+uh but
+ 
+
+ align:start position:0%
+uh but
+you know i i guess
+
+ align:start position:0%
+you know i i guess
+ 
+
+ align:start position:0%
+you know i i guess
+it's different than like in a laboratory
+
+ align:start position:0%
+it's different than like in a laboratory
+ 
+
+ align:start position:0%
+it's different than like in a laboratory
+setting
+
+ align:start position:0%
+setting
+ 
+
+ align:start position:0%
+setting
+exactly cells in a dish and you you know
+
+ align:start position:0%
+exactly cells in a dish and you you know
+ 
+
+ align:start position:0%
+exactly cells in a dish and you you know
+if they die it's like yeah
+
+ align:start position:0%
+if they die it's like yeah
+ 
+
+ align:start position:0%
+if they die it's like yeah
+exactly you know
+
+ align:start position:0%
+exactly you know
+ 
+
+ align:start position:0%
+exactly you know
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+exactly we've taken this technology that
+
+ align:start position:0%
+exactly we've taken this technology that
+ 
+
+ align:start position:0%
+exactly we've taken this technology that
+we've used in micro of using cells in
+
+ align:start position:0%
+we've used in micro of using cells in
+ 
+
+ align:start position:0%
+we've used in micro of using cells in
+cell culture from cell lines and rapidly
+
+ align:start position:0%
+cell culture from cell lines and rapidly
+ 
+
+ align:start position:0%
+cell culture from cell lines and rapidly
+moved it to patients right
+
+ align:start position:0%
+moved it to patients right
+ 
+
+ align:start position:0%
+moved it to patients right
+that exist in a context okay even the
+
+ align:start position:0%
+that exist in a context okay even the
+ 
+
+ align:start position:0%
+that exist in a context okay even the
+middle ground of just using them in lab
+
+ align:start position:0%
+middle ground of just using them in lab
+ 
+
+ align:start position:0%
+middle ground of just using them in lab
+mice okay look at the same mice same
+
+ align:start position:0%
+mice okay look at the same mice same
+ 
+
+ align:start position:0%
+mice okay look at the same mice same
+condition same everything there's genes
+
+ align:start position:0%
+condition same everything there's genes
+ 
+
+ align:start position:0%
+condition same everything there's genes
+that are different right
+
+ align:start position:0%
+that are different right
+ 
+
+ align:start position:0%
+that are different right
+one of the mice was an alpha male in
+
+ align:start position:0%
+one of the mice was an alpha male in
+ 
+
+ align:start position:0%
+one of the mice was an alpha male in
+that little cage and one wasn't you know
+
+ align:start position:0%
+that little cage and one wasn't you know
+ 
+
+ align:start position:0%
+that little cage and one wasn't you know
+there's differences between things that
+
+ align:start position:0%
+there's differences between things that
+ 
+
+ align:start position:0%
+there's differences between things that
+we think are otherwise the same but now
+
+ align:start position:0%
+we think are otherwise the same but now
+ 
+
+ align:start position:0%
+we think are otherwise the same but now
+we've taken to this extreme because
+
+ align:start position:0%
+we've taken to this extreme because
+ 
+
+ align:start position:0%
+we've taken to this extreme because
+there's a course you're in a course
+
+ align:start position:0%
+there's a course you're in a course
+ 
+
+ align:start position:0%
+there's a course you're in a course
+called genomic medicine and that's what
+
+ align:start position:0%
+called genomic medicine and that's what
+ 
+
+ align:start position:0%
+called genomic medicine and that's what
+we're doing today
+
+ align:start position:0%
+we're doing today
+ 
+
+ align:start position:0%
+we're doing today
+these are the problems that we have with
+
+ align:start position:0%
+these are the problems that we have with
+ 
+
+ align:start position:0%
+these are the problems that we have with
+that type of approach
+
+ align:start position:0%
+that type of approach
+ 
+
+ align:start position:0%
+that type of approach
+okay i i kid you not go back to the last
+
+ align:start position:0%
+okay i i kid you not go back to the last
+ 
+
+ align:start position:0%
+okay i i kid you not go back to the last
+few microwave papers in england journal
+
+ align:start position:0%
+few microwave papers in england journal
+ 
+
+ align:start position:0%
+few microwave papers in england journal
+you will not see what time of day
+
+ align:start position:0%
+you will not see what time of day
+ 
+
+ align:start position:0%
+you will not see what time of day
+if you go to supplemental material
+
+ align:start position:0%
+if you go to supplemental material
+ 
+
+ align:start position:0%
+if you go to supplemental material
+nobody might not i think people don't
+
+ align:start position:0%
+nobody might not i think people don't
+ 
+
+ align:start position:0%
+nobody might not i think people don't
+even write that stuff down
+
+ align:start position:0%
+even write that stuff down
+ 
+
+ align:start position:0%
+even write that stuff down
+and it's a problem i've only seen one
+
+ align:start position:0%
+and it's a problem i've only seen one
+ 
+
+ align:start position:0%
+and it's a problem i've only seen one
+paper so far address this issue so what
+
+ align:start position:0%
+paper so far address this issue so what
+ 
+
+ align:start position:0%
+paper so far address this issue so what
+would your suggestion be i mean
+
+ align:start position:0%
+would your suggestion be i mean
+ 
+
+ align:start position:0%
+would your suggestion be i mean
+obviously to us
+
+ align:start position:0%
+obviously to us
+ 
+
+ align:start position:0%
+obviously to us
+control for that it's a control for it
+
+ align:start position:0%
+control for that it's a control for it
+ 
+
+ align:start position:0%
+control for that it's a control for it
+but in that injury why there's labs that
+
+ align:start position:0%
+but in that injury why there's labs that
+ 
+
+ align:start position:0%
+but in that injury why there's labs that
+you know really maybe aren't speaking
+
+ align:start position:0%
+you know really maybe aren't speaking
+ 
+
+ align:start position:0%
+you know really maybe aren't speaking
+about this yep
+
+ align:start position:0%
+about this yep
+ 
+
+ align:start position:0%
+about this yep
+you can do whatever
+
+ align:start position:0%
+you can do whatever
+ 
+
+ align:start position:0%
+you can do whatever
+is saying
+
+ align:start position:0%
+is saying
+ 
+
+ align:start position:0%
+is saying
+no but you can try to model that okay so
+
+ align:start position:0%
+no but you can try to model that okay so
+ 
+
+ align:start position:0%
+no but you can try to model that okay so
+so take some other tissue that's related
+
+ align:start position:0%
+so take some other tissue that's related
+ 
+
+ align:start position:0%
+so take some other tissue that's related
+and see just across a sampling of time
+
+ align:start position:0%
+and see just across a sampling of time
+ 
+
+ align:start position:0%
+and see just across a sampling of time
+points what genes are different and
+
+ align:start position:0%
+points what genes are different and
+ 
+
+ align:start position:0%
+points what genes are different and
+maybe you can then subtract out that
+
+ align:start position:0%
+maybe you can then subtract out that
+ 
+
+ align:start position:0%
+maybe you can then subtract out that
+effect but more importantly what i would
+
+ align:start position:0%
+effect but more importantly what i would
+ 
+
+ align:start position:0%
+effect but more importantly what i would
+say is if you're going to make a list of
+
+ align:start position:0%
+say is if you're going to make a list of
+ 
+
+ align:start position:0%
+say is if you're going to make a list of
+genes that you think are diagnostic
+
+ align:start position:0%
+genes that you think are diagnostic
+ 
+
+ align:start position:0%
+genes that you think are diagnostic
+we're going to have to be as physicians
+
+ align:start position:0%
+we're going to have to be as physicians
+ 
+
+ align:start position:0%
+we're going to have to be as physicians
+we're going to have to look at that with
+
+ align:start position:0%
+we're going to have to look at that with
+ 
+
+ align:start position:0%
+we're going to have to look at that with
+a very skeptical eye okay because you
+
+ align:start position:0%
+a very skeptical eye okay because you
+ 
+
+ align:start position:0%
+a very skeptical eye okay because you
+cannot control for everything here
+
+ align:start position:0%
+cannot control for everything here
+ 
+
+ align:start position:0%
+cannot control for everything here
+right but we're measuring across so many
+
+ align:start position:0%
+right but we're measuring across so many
+ 
+
+ align:start position:0%
+right but we're measuring across so many
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+and have so few samples
+
+ align:start position:0%
+and have so few samples
+ 
+
+ align:start position:0%
+and have so few samples
+okay that no matter what we're going to
+
+ align:start position:0%
+okay that no matter what we're going to
+ 
+
+ align:start position:0%
+okay that no matter what we're going to
+be over fitting the data here that's
+
+ align:start position:0%
+be over fitting the data here that's
+ 
+
+ align:start position:0%
+be over fitting the data here that's
+what i'm worried about okay we're going
+
+ align:start position:0%
+what i'm worried about okay we're going
+ 
+
+ align:start position:0%
+what i'm worried about okay we're going
+to be over fitting what we have
+
+ align:start position:0%
+to be over fitting what we have
+ 
+
+ align:start position:0%
+to be over fitting what we have
+no amount of control samples is going to
+
+ align:start position:0%
+no amount of control samples is going to
+ 
+
+ align:start position:0%
+no amount of control samples is going to
+help us
+
+ align:start position:0%
+help us
+ 
+
+ align:start position:0%
+help us
+fix that problem i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are we doing for time okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk uh
+
+ align:start position:0%
+let's talk uh
+ 
+
+ align:start position:0%
+let's talk uh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+let's go let's go a little bit more into
+
+ align:start position:0%
+let's go let's go a little bit more into
+ 
+
+ align:start position:0%
+let's go let's go a little bit more into
+the diabetes so what i was planning to
+
+ align:start position:0%
+the diabetes so what i was planning to
+ 
+
+ align:start position:0%
+the diabetes so what i was planning to
+do is talk about uh one more diabetes
+
+ align:start position:0%
+do is talk about uh one more diabetes
+ 
+
+ align:start position:0%
+do is talk about uh one more diabetes
+project that we've been doing
+
+ align:start position:0%
+project that we've been doing
+ 
+
+ align:start position:0%
+project that we've been doing
+then i'm going to talk about some web
+
+ align:start position:0%
+then i'm going to talk about some web
+ 
+
+ align:start position:0%
+then i'm going to talk about some web
+based resources for doing some
+
+ align:start position:0%
+based resources for doing some
+ 
+
+ align:start position:0%
+based resources for doing some
+interesting hypothesis generation and
+
+ align:start position:0%
+interesting hypothesis generation and
+ 
+
+ align:start position:0%
+interesting hypothesis generation and
+we'll just end it at that point
+
+ align:start position:0%
+we'll just end it at that point
+ 
+
+ align:start position:0%
+we'll just end it at that point
+so our all you are so not all of you are
+
+ align:start position:0%
+so our all you are so not all of you are
+ 
+
+ align:start position:0%
+so our all you are so not all of you are
+actually in the uh are physicians or
+
+ align:start position:0%
+actually in the uh are physicians or
+ 
+
+ align:start position:0%
+actually in the uh are physicians or
+medical students but nonetheless i'll
+
+ align:start position:0%
+medical students but nonetheless i'll
+ 
+
+ align:start position:0%
+medical students but nonetheless i'll
+present this case of a patient that i
+
+ align:start position:0%
+present this case of a patient that i
+ 
+
+ align:start position:0%
+present this case of a patient that i
+saw okay
+
+ align:start position:0%
+saw okay
+ 
+
+ align:start position:0%
+saw okay
+it's a female presented with acanthosis
+
+ align:start position:0%
+it's a female presented with acanthosis
+ 
+
+ align:start position:0%
+it's a female presented with acanthosis
+nigricans random glucose of 162. so
+
+ align:start position:0%
+nigricans random glucose of 162. so
+ 
+
+ align:start position:0%
+nigricans random glucose of 162. so
+acanthosis niagara fans do you know what
+
+ align:start position:0%
+acanthosis niagara fans do you know what
+ 
+
+ align:start position:0%
+acanthosis niagara fans do you know what
+that is there's a dark patch that you
+
+ align:start position:0%
+that is there's a dark patch that you
+ 
+
+ align:start position:0%
+that is there's a dark patch that you
+can get in the back of your neck and
+
+ align:start position:0%
+can get in the back of your neck and
+ 
+
+ align:start position:0%
+can get in the back of your neck and
+your elbows and your underarms and what
+
+ align:start position:0%
+your elbows and your underarms and what
+ 
+
+ align:start position:0%
+your elbows and your underarms and what
+that means is that your insulin is too
+
+ align:start position:0%
+that means is that your insulin is too
+ 
+
+ align:start position:0%
+that means is that your insulin is too
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+okay because insulin is telling the
+
+ align:start position:0%
+okay because insulin is telling the
+ 
+
+ align:start position:0%
+okay because insulin is telling the
+melanocytes for for some through some
+
+ align:start position:0%
+melanocytes for for some through some
+ 
+
+ align:start position:0%
+melanocytes for for some through some
+unknown mechanism so
+
+ align:start position:0%
+unknown mechanism so
+ 
+
+ align:start position:0%
+unknown mechanism so
+melanocytes become darker
+
+ align:start position:0%
+melanocytes become darker
+ 
+
+ align:start position:0%
+melanocytes become darker
+so you you look just look at people on
+
+ align:start position:0%
+so you you look just look at people on
+ 
+
+ align:start position:0%
+so you you look just look at people on
+the street now and look to see if they
+
+ align:start position:0%
+the street now and look to see if they
+ 
+
+ align:start position:0%
+the street now and look to see if they
+have a dark patch here it's not dirt you
+
+ align:start position:0%
+have a dark patch here it's not dirt you
+ 
+
+ align:start position:0%
+have a dark patch here it's not dirt you
+can't scrub it off but that's a sign of
+
+ align:start position:0%
+can't scrub it off but that's a sign of
+ 
+
+ align:start position:0%
+can't scrub it off but that's a sign of
+acanthosis negative cancer someone's
+
+ align:start position:0%
+acanthosis negative cancer someone's
+ 
+
+ align:start position:0%
+acanthosis negative cancer someone's
+having a problem with insulin and it's
+
+ align:start position:0%
+having a problem with insulin and it's
+ 
+
+ align:start position:0%
+having a problem with insulin and it's
+too high
+
+ align:start position:0%
+too high
+ 
+
+ align:start position:0%
+too high
+did more studies the ldl is sky high i
+
+ align:start position:0%
+did more studies the ldl is sky high i
+ 
+
+ align:start position:0%
+did more studies the ldl is sky high i
+mean ldl is high total cholesterol sky
+
+ align:start position:0%
+mean ldl is high total cholesterol sky
+ 
+
+ align:start position:0%
+mean ldl is high total cholesterol sky
+high triglycerides are very high hdl is
+
+ align:start position:0%
+high triglycerides are very high hdl is
+ 
+
+ align:start position:0%
+high triglycerides are very high hdl is
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+so it's a metabolic syndrome or color
+
+ align:start position:0%
+so it's a metabolic syndrome or color
+ 
+
+ align:start position:0%
+so it's a metabolic syndrome or color
+it's called syndrome x
+
+ align:start position:0%
+it's called syndrome x
+ 
+
+ align:start position:0%
+it's called syndrome x
+fasting glucose 133 that meets criteria
+
+ align:start position:0%
+fasting glucose 133 that meets criteria
+ 
+
+ align:start position:0%
+fasting glucose 133 that meets criteria
+for diabetes insulin is 27 which means
+
+ align:start position:0%
+for diabetes insulin is 27 which means
+ 
+
+ align:start position:0%
+for diabetes insulin is 27 which means
+this is high but this is very high
+
+ align:start position:0%
+this is high but this is very high
+ 
+
+ align:start position:0%
+this is high but this is very high
+bringing that glucose trying to
+
+ align:start position:0%
+bringing that glucose trying to
+ 
+
+ align:start position:0%
+bringing that glucose trying to
+compensate for that hemoglobin a1c is
+
+ align:start position:0%
+compensate for that hemoglobin a1c is
+ 
+
+ align:start position:0%
+compensate for that hemoglobin a1c is
+7.3 the normal range is 4 to 6.
+
+ align:start position:0%
+7.3 the normal range is 4 to 6.
+ 
+
+ align:start position:0%
+7.3 the normal range is 4 to 6.
+and again to drive the whole point home
+
+ align:start position:0%
+and again to drive the whole point home
+ 
+
+ align:start position:0%
+and again to drive the whole point home
+there's a 12 year old girl with adult
+
+ align:start position:0%
+there's a 12 year old girl with adult
+ 
+
+ align:start position:0%
+there's a 12 year old girl with adult
+onset diabetes okay so this is her body
+
+ align:start position:0%
+onset diabetes okay so this is her body
+ 
+
+ align:start position:0%
+onset diabetes okay so this is her body
+mass index
+
+ align:start position:0%
+mass index
+ 
+
+ align:start position:0%
+mass index
+this is a 97th percentile curve and this
+
+ align:start position:0%
+this is a 97th percentile curve and this
+ 
+
+ align:start position:0%
+this is a 97th percentile curve and this
+is where she is well over the curve here
+
+ align:start position:0%
+is where she is well over the curve here
+ 
+
+ align:start position:0%
+is where she is well over the curve here
+and now she has type 2 diabetes she
+
+ align:start position:0%
+and now she has type 2 diabetes she
+ 
+
+ align:start position:0%
+and now she has type 2 diabetes she
+meets criteria for type 2 diabetes she
+
+ align:start position:0%
+meets criteria for type 2 diabetes she
+ 
+
+ align:start position:0%
+meets criteria for type 2 diabetes she
+was not even entering seventh grade when
+
+ align:start position:0%
+was not even entering seventh grade when
+ 
+
+ align:start position:0%
+was not even entering seventh grade when
+i started doing summer vacation last
+
+ align:start position:0%
+i started doing summer vacation last
+ 
+
+ align:start position:0%
+i started doing summer vacation last
+year one in three kids is going to be
+
+ align:start position:0%
+year one in three kids is going to be
+ 
+
+ align:start position:0%
+year one in three kids is going to be
+like this okay that's the problem so one
+
+ align:start position:0%
+like this okay that's the problem so one
+ 
+
+ align:start position:0%
+like this okay that's the problem so one
+way to study this problem is to study
+
+ align:start position:0%
+way to study this problem is to study
+ 
+
+ align:start position:0%
+way to study this problem is to study
+obesity and one way to think about and
+
+ align:start position:0%
+obesity and one way to think about and
+ 
+
+ align:start position:0%
+obesity and one way to think about and
+obesity related to diabetes so one way
+
+ align:start position:0%
+obesity related to diabetes so one way
+ 
+
+ align:start position:0%
+obesity related to diabetes so one way
+to study obesity is to think about the
+
+ align:start position:0%
+to study obesity is to think about the
+ 
+
+ align:start position:0%
+to study obesity is to think about the
+specifically what i'm interested in
+
+ align:start position:0%
+specifically what i'm interested in
+ 
+
+ align:start position:0%
+specifically what i'm interested in
+studying is how adipogenesis
+
+ align:start position:0%
+studying is how adipogenesis
+ 
+
+ align:start position:0%
+studying is how adipogenesis
+or the process of making fat cells might
+
+ align:start position:0%
+or the process of making fat cells might
+ 
+
+ align:start position:0%
+or the process of making fat cells might
+be related to how insulin works
+
+ align:start position:0%
+be related to how insulin works
+ 
+
+ align:start position:0%
+be related to how insulin works
+and the best established way to study
+
+ align:start position:0%
+and the best established way to study
+ 
+
+ align:start position:0%
+and the best established way to study
+that is to look at the insulin receptor
+
+ align:start position:0%
+that is to look at the insulin receptor
+ 
+
+ align:start position:0%
+that is to look at the insulin receptor
+okay so now we're zooming into one of
+
+ align:start position:0%
+okay so now we're zooming into one of
+ 
+
+ align:start position:0%
+okay so now we're zooming into one of
+these target tissues remember liver
+
+ align:start position:0%
+these target tissues remember liver
+ 
+
+ align:start position:0%
+these target tissues remember liver
+muscle and fat and the insulin receptor
+
+ align:start position:0%
+muscle and fat and the insulin receptor
+ 
+
+ align:start position:0%
+muscle and fat and the insulin receptor
+is a protein that sticks in the membrane
+
+ align:start position:0%
+is a protein that sticks in the membrane
+ 
+
+ align:start position:0%
+is a protein that sticks in the membrane
+of the cell okay like any other protein
+
+ align:start position:0%
+of the cell okay like any other protein
+ 
+
+ align:start position:0%
+of the cell okay like any other protein
+it's got a gene coding for it in the dna
+
+ align:start position:0%
+it's got a gene coding for it in the dna
+ 
+
+ align:start position:0%
+it's got a gene coding for it in the dna
+gets transcribed gets translated the
+
+ align:start position:0%
+gets transcribed gets translated the
+ 
+
+ align:start position:0%
+gets transcribed gets translated the
+protein goes out to the surface
+
+ align:start position:0%
+protein goes out to the surface
+ 
+
+ align:start position:0%
+protein goes out to the surface
+there are known mutations in the insulin
+
+ align:start position:0%
+there are known mutations in the insulin
+ 
+
+ align:start position:0%
+there are known mutations in the insulin
+receptor that can cause you to have
+
+ align:start position:0%
+receptor that can cause you to have
+ 
+
+ align:start position:0%
+receptor that can cause you to have
+problems with glucose handling and
+
+ align:start position:0%
+problems with glucose handling and
+ 
+
+ align:start position:0%
+problems with glucose handling and
+diabetes in fact there's a syndrome
+
+ align:start position:0%
+diabetes in fact there's a syndrome
+ 
+
+ align:start position:0%
+diabetes in fact there's a syndrome
+called leprechaunism
+
+ align:start position:0%
+called leprechaunism
+ 
+
+ align:start position:0%
+called leprechaunism
+where these kids look like leprechauns
+
+ align:start position:0%
+where these kids look like leprechauns
+ 
+
+ align:start position:0%
+where these kids look like leprechauns
+actually they die pretty quickly after
+
+ align:start position:0%
+actually they die pretty quickly after
+ 
+
+ align:start position:0%
+actually they die pretty quickly after
+birth but they have mutations in the
+
+ align:start position:0%
+birth but they have mutations in the
+ 
+
+ align:start position:0%
+birth but they have mutations in the
+insulin receptor
+
+ align:start position:0%
+insulin receptor
+ 
+
+ align:start position:0%
+insulin receptor
+it turns out you can actually be born
+
+ align:start position:0%
+it turns out you can actually be born
+ 
+
+ align:start position:0%
+it turns out you can actually be born
+without an insulin receptor there's been
+
+ align:start position:0%
+without an insulin receptor there's been
+ 
+
+ align:start position:0%
+without an insulin receptor there's been
+a null person there's been a one patient
+
+ align:start position:0%
+a null person there's been a one patient
+ 
+
+ align:start position:0%
+a null person there's been a one patient
+i think that was found to have no
+
+ align:start position:0%
+i think that was found to have no
+ 
+
+ align:start position:0%
+i think that was found to have no
+insulin receptors and obviously the
+
+ align:start position:0%
+insulin receptors and obviously the
+ 
+
+ align:start position:0%
+insulin receptors and obviously the
+insulin level was sky high in this baby
+
+ align:start position:0%
+insulin level was sky high in this baby
+ 
+
+ align:start position:0%
+insulin level was sky high in this baby
+at birth because it's not acting
+
+ align:start position:0%
+at birth because it's not acting
+ 
+
+ align:start position:0%
+at birth because it's not acting
+anywhere
+
+ align:start position:0%
+anywhere
+ 
+
+ align:start position:0%
+anywhere
+but what happens is what's supposed to
+
+ align:start position:0%
+but what happens is what's supposed to
+ 
+
+ align:start position:0%
+but what happens is what's supposed to
+happen is insulin binds to the insulin
+
+ align:start position:0%
+happen is insulin binds to the insulin
+ 
+
+ align:start position:0%
+happen is insulin binds to the insulin
+receptor and then these phosphate groups
+
+ align:start position:0%
+receptor and then these phosphate groups
+ 
+
+ align:start position:0%
+receptor and then these phosphate groups
+are added to itself
+
+ align:start position:0%
+are added to itself
+ 
+
+ align:start position:0%
+are added to itself
+and that changes the shape of this
+
+ align:start position:0%
+and that changes the shape of this
+ 
+
+ align:start position:0%
+and that changes the shape of this
+molecule in such a way
+
+ align:start position:0%
+molecule in such a way
+ 
+
+ align:start position:0%
+molecule in such a way
+that it can actually start to interact
+
+ align:start position:0%
+that it can actually start to interact
+ 
+
+ align:start position:0%
+that it can actually start to interact
+with other molecules and in fact the
+
+ align:start position:0%
+with other molecules and in fact the
+ 
+
+ align:start position:0%
+with other molecules and in fact the
+insulin receptor also adds phosphate
+
+ align:start position:0%
+insulin receptor also adds phosphate
+ 
+
+ align:start position:0%
+insulin receptor also adds phosphate
+groups to other things okay in fact
+
+ align:start position:0%
+groups to other things okay in fact
+ 
+
+ align:start position:0%
+groups to other things okay in fact
+these are insulin insulin receptor
+
+ align:start position:0%
+these are insulin insulin receptor
+ 
+
+ align:start position:0%
+these are insulin insulin receptor
+substrate one insulin receptor substrate
+
+ align:start position:0%
+substrate one insulin receptor substrate
+ 
+
+ align:start position:0%
+substrate one insulin receptor substrate
+two three and four and there's some
+
+ align:start position:0%
+two three and four and there's some
+ 
+
+ align:start position:0%
+two three and four and there's some
+others here
+
+ align:start position:0%
+others here
+ 
+
+ align:start position:0%
+others here
+so in collaboration with ron khan
+
+ align:start position:0%
+so in collaboration with ron khan
+ 
+
+ align:start position:0%
+so in collaboration with ron khan
+president of the dawson diabetes center
+
+ align:start position:0%
+president of the dawson diabetes center
+ 
+
+ align:start position:0%
+president of the dawson diabetes center
+he's created some mice where they've
+
+ align:start position:0%
+he's created some mice where they've
+ 
+
+ align:start position:0%
+he's created some mice where they've
+basically knocked out irs one two three
+
+ align:start position:0%
+basically knocked out irs one two three
+ 
+
+ align:start position:0%
+basically knocked out irs one two three
+and four in separate mice so these are
+
+ align:start position:0%
+and four in separate mice so these are
+ 
+
+ align:start position:0%
+and four in separate mice so these are
+otherwise normal mice missing this one
+
+ align:start position:0%
+otherwise normal mice missing this one
+ 
+
+ align:start position:0%
+otherwise normal mice missing this one
+particular gene
+
+ align:start position:0%
+particular gene
+ 
+
+ align:start position:0%
+particular gene
+if you take fat cells from these mice
+
+ align:start position:0%
+if you take fat cells from these mice
+ 
+
+ align:start position:0%
+if you take fat cells from these mice
+and trus in fact if you take pre-fat
+
+ align:start position:0%
+and trus in fact if you take pre-fat
+ 
+
+ align:start position:0%
+and trus in fact if you take pre-fat
+cells or pre-adipocytes
+
+ align:start position:0%
+cells or pre-adipocytes
+ 
+
+ align:start position:0%
+cells or pre-adipocytes
+you can make them go into fat cells
+
+ align:start position:0%
+you can make them go into fat cells
+ 
+
+ align:start position:0%
+you can make them go into fat cells
+using a standard cocktail of hormones
+
+ align:start position:0%
+using a standard cocktail of hormones
+ 
+
+ align:start position:0%
+using a standard cocktail of hormones
+okay this has been done for the past two
+
+ align:start position:0%
+okay this has been done for the past two
+ 
+
+ align:start position:0%
+okay this has been done for the past two
+decades you take three pre-fat cells and
+
+ align:start position:0%
+decades you take three pre-fat cells and
+ 
+
+ align:start position:0%
+decades you take three pre-fat cells and
+make them into fat cells with a
+
+ align:start position:0%
+make them into fat cells with a
+ 
+
+ align:start position:0%
+make them into fat cells with a
+particular cocktail and what happens is
+
+ align:start position:0%
+particular cocktail and what happens is
+ 
+
+ align:start position:0%
+particular cocktail and what happens is
+if you take normal pre-fat cells and
+
+ align:start position:0%
+if you take normal pre-fat cells and
+ 
+
+ align:start position:0%
+if you take normal pre-fat cells and
+make them into fat cells and stain for
+
+ align:start position:0%
+make them into fat cells and stain for
+ 
+
+ align:start position:0%
+make them into fat cells and stain for
+the fat or the lipid you get a big red
+
+ align:start position:0%
+the fat or the lipid you get a big red
+ 
+
+ align:start position:0%
+the fat or the lipid you get a big red
+circle here this is a dish of the cells
+
+ align:start position:0%
+circle here this is a dish of the cells
+ 
+
+ align:start position:0%
+circle here this is a dish of the cells
+if you knock out irs1 and try to do this
+
+ align:start position:0%
+if you knock out irs1 and try to do this
+ 
+
+ align:start position:0%
+if you knock out irs1 and try to do this
+you cannot get the fat cells to form so
+
+ align:start position:0%
+you cannot get the fat cells to form so
+ 
+
+ align:start position:0%
+you cannot get the fat cells to form so
+again pre-fat cells the same cocktail
+
+ align:start position:0%
+again pre-fat cells the same cocktail
+ 
+
+ align:start position:0%
+again pre-fat cells the same cocktail
+you don't get fat cells in the end
+
+ align:start position:0%
+you don't get fat cells in the end
+ 
+
+ align:start position:0%
+you don't get fat cells in the end
+there's no stain there's barely a stain
+
+ align:start position:0%
+there's no stain there's barely a stain
+ 
+
+ align:start position:0%
+there's no stain there's barely a stain
+for any red here and it turns out if you
+
+ align:start position:0%
+for any red here and it turns out if you
+ 
+
+ align:start position:0%
+for any red here and it turns out if you
+knock out iris three two and four in the
+
+ align:start position:0%
+knock out iris three two and four in the
+ 
+
+ align:start position:0%
+knock out iris three two and four in the
+middle here you get a gradation of the
+
+ align:start position:0%
+middle here you get a gradation of the
+ 
+
+ align:start position:0%
+middle here you get a gradation of the
+phenotype interestingly
+
+ align:start position:0%
+phenotype interestingly
+ 
+
+ align:start position:0%
+phenotype interestingly
+so it's not all or none these are if you
+
+ align:start position:0%
+so it's not all or none these are if you
+ 
+
+ align:start position:0%
+so it's not all or none these are if you
+knock out the other irs molecules you
+
+ align:start position:0%
+knock out the other irs molecules you
+ 
+
+ align:start position:0%
+knock out the other irs molecules you
+get a gradation of the phenotype
+
+ align:start position:0%
+get a gradation of the phenotype
+ 
+
+ align:start position:0%
+get a gradation of the phenotype
+curiously
+
+ align:start position:0%
+curiously
+ 
+
+ align:start position:0%
+curiously
+so what we did is in collaboration with
+
+ align:start position:0%
+so what we did is in collaboration with
+ 
+
+ align:start position:0%
+so what we did is in collaboration with
+ron khan we actually made a list of
+
+ align:start position:0%
+ron khan we actually made a list of
+ 
+
+ align:start position:0%
+ron khan we actually made a list of
+genes that behaved in this pattern okay
+
+ align:start position:0%
+genes that behaved in this pattern okay
+ 
+
+ align:start position:0%
+genes that behaved in this pattern okay
+now we don't have numbers here right but
+
+ align:start position:0%
+now we don't have numbers here right but
+ 
+
+ align:start position:0%
+now we don't have numbers here right but
+we're just trying to find genes that go
+
+ align:start position:0%
+we're just trying to find genes that go
+ 
+
+ align:start position:0%
+we're just trying to find genes that go
+along with that pattern so let me show
+
+ align:start position:0%
+along with that pattern so let me show
+ 
+
+ align:start position:0%
+along with that pattern so let me show
+you an example one of these things
+
+ align:start position:0%
+you an example one of these things
+ 
+
+ align:start position:0%
+you an example one of these things
+here's a gene here's wild type one
+
+ align:start position:0%
+here's a gene here's wild type one
+ 
+
+ align:start position:0%
+here's a gene here's wild type one
+here's wild type here's irs one knockout
+
+ align:start position:0%
+here's wild type here's irs one knockout
+ 
+
+ align:start position:0%
+here's wild type here's irs one knockout
+so no fat cells
+
+ align:start position:0%
+so no fat cells
+ 
+
+ align:start position:0%
+so no fat cells
+easy to make fat cells and we're taking
+
+ align:start position:0%
+easy to make fat cells and we're taking
+ 
+
+ align:start position:0%
+easy to make fat cells and we're taking
+the genes
+
+ align:start position:0%
+the genes
+ 
+
+ align:start position:0%
+the genes
+we're taking rna before we try to make
+
+ align:start position:0%
+we're taking rna before we try to make
+ 
+
+ align:start position:0%
+we're taking rna before we try to make
+them into fat cells okay the hypothesis
+
+ align:start position:0%
+them into fat cells okay the hypothesis
+ 
+
+ align:start position:0%
+them into fat cells okay the hypothesis
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+what genes are different
+
+ align:start position:0%
+what genes are different
+ 
+
+ align:start position:0%
+what genes are different
+before we try to make them into fat
+
+ align:start position:0%
+before we try to make them into fat
+ 
+
+ align:start position:0%
+before we try to make them into fat
+cells that might be impacting the
+
+ align:start position:0%
+cells that might be impacting the
+ 
+
+ align:start position:0%
+cells that might be impacting the
+process of making fat cells
+
+ align:start position:0%
+process of making fat cells
+ 
+
+ align:start position:0%
+process of making fat cells
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i'm going to take a second here i'm
+
+ align:start position:0%
+now i'm going to take a second here i'm
+ 
+
+ align:start position:0%
+now i'm going to take a second here i'm
+going to you're probably asking wait
+
+ align:start position:0%
+going to you're probably asking wait
+ 
+
+ align:start position:0%
+going to you're probably asking wait
+we're just talking about humans we're
+
+ align:start position:0%
+we're just talking about humans we're
+ 
+
+ align:start position:0%
+we're just talking about humans we're
+just talking about this kid that was
+
+ align:start position:0%
+just talking about this kid that was
+ 
+
+ align:start position:0%
+just talking about this kid that was
+obese and now we're talking about mice
+
+ align:start position:0%
+obese and now we're talking about mice
+ 
+
+ align:start position:0%
+obese and now we're talking about mice
+here okay i'm going to bring this back
+
+ align:start position:0%
+here okay i'm going to bring this back
+ 
+
+ align:start position:0%
+here okay i'm going to bring this back
+to the humans in a minute okay
+
+ align:start position:0%
+to the humans in a minute okay
+ 
+
+ align:start position:0%
+to the humans in a minute okay
+because i'm going to intersect this with
+
+ align:start position:0%
+because i'm going to intersect this with
+ 
+
+ align:start position:0%
+because i'm going to intersect this with
+other data sets and show you where i'm
+
+ align:start position:0%
+other data sets and show you where i'm
+ 
+
+ align:start position:0%
+other data sets and show you where i'm
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+but suffice it to say we have about 80
+
+ align:start position:0%
+but suffice it to say we have about 80
+ 
+
+ align:start position:0%
+but suffice it to say we have about 80
+genes that follow this kind of pattern
+
+ align:start position:0%
+genes that follow this kind of pattern
+ 
+
+ align:start position:0%
+genes that follow this kind of pattern
+they're high
+
+ align:start position:0%
+they're high
+ 
+
+ align:start position:0%
+they're high
+in the normals they're low in the irs1
+
+ align:start position:0%
+in the normals they're low in the irs1
+ 
+
+ align:start position:0%
+in the normals they're low in the irs1
+knockouts before adipogenesis and
+
+ align:start position:0%
+knockouts before adipogenesis and
+ 
+
+ align:start position:0%
+knockouts before adipogenesis and
+they're in this kind of monotonic
+
+ align:start position:0%
+they're in this kind of monotonic
+ 
+
+ align:start position:0%
+they're in this kind of monotonic
+pattern here or vice versa going down or
+
+ align:start position:0%
+pattern here or vice versa going down or
+ 
+
+ align:start position:0%
+pattern here or vice versa going down or
+up came up with listed about 88 genes
+
+ align:start position:0%
+up came up with listed about 88 genes
+ 
+
+ align:start position:0%
+up came up with listed about 88 genes
+that fit this kind of pattern
+
+ align:start position:0%
+that fit this kind of pattern
+ 
+
+ align:start position:0%
+that fit this kind of pattern
+now put those 88 genes
+
+ align:start position:0%
+now put those 88 genes
+ 
+
+ align:start position:0%
+now put those 88 genes
+on hold for a second
+
+ align:start position:0%
+on hold for a second
+ 
+
+ align:start position:0%
+on hold for a second
+let's talk about second disease
+
+ align:start position:0%
+let's talk about second disease
+ 
+
+ align:start position:0%
+let's talk about second disease
+i have been involved studying this
+
+ align:start position:0%
+i have been involved studying this
+ 
+
+ align:start position:0%
+i have been involved studying this
+particular syndrome called progeria
+
+ align:start position:0%
+particular syndrome called progeria
+ 
+
+ align:start position:0%
+particular syndrome called progeria
+progeria's advanced aging syndrome in
+
+ align:start position:0%
+progeria's advanced aging syndrome in
+ 
+
+ align:start position:0%
+progeria's advanced aging syndrome in
+children in fact it makes it very rare
+
+ align:start position:0%
+children in fact it makes it very rare
+ 
+
+ align:start position:0%
+children in fact it makes it very rare
+it's about one in eight million births
+
+ align:start position:0%
+it's about one in eight million births
+ 
+
+ align:start position:0%
+it's about one in eight million births
+and makes children look like they're
+
+ align:start position:0%
+and makes children look like they're
+ 
+
+ align:start position:0%
+and makes children look like they're
+getting older okay we've all heard of
+
+ align:start position:0%
+getting older okay we've all heard of
+ 
+
+ align:start position:0%
+getting older okay we've all heard of
+these kids and these this kind of story
+
+ align:start position:0%
+these kids and these this kind of story
+ 
+
+ align:start position:0%
+these kids and these this kind of story
+and specifically they lose their hair
+
+ align:start position:0%
+and specifically they lose their hair
+ 
+
+ align:start position:0%
+and specifically they lose their hair
+they have alopecia they're certainly
+
+ align:start position:0%
+they have alopecia they're certainly
+ 
+
+ align:start position:0%
+they have alopecia they're certainly
+short they're shorter than age-matched
+
+ align:start position:0%
+short they're shorter than age-matched
+ 
+
+ align:start position:0%
+short they're shorter than age-matched
+kids they have these skin changes that
+
+ align:start position:0%
+kids they have these skin changes that
+ 
+
+ align:start position:0%
+kids they have these skin changes that
+make them look old they don't go through
+
+ align:start position:0%
+make them look old they don't go through
+ 
+
+ align:start position:0%
+make them look old they don't go through
+puberty they have poor weight gain
+
+ align:start position:0%
+puberty they have poor weight gain
+ 
+
+ align:start position:0%
+puberty they have poor weight gain
+and usually they die at age 15 because
+
+ align:start position:0%
+and usually they die at age 15 because
+ 
+
+ align:start position:0%
+and usually they die at age 15 because
+of cardiovascular problems
+
+ align:start position:0%
+of cardiovascular problems
+ 
+
+ align:start position:0%
+of cardiovascular problems
+atherosclerosis gets strokes they get
+
+ align:start position:0%
+atherosclerosis gets strokes they get
+ 
+
+ align:start position:0%
+atherosclerosis gets strokes they get
+heart attacks now even though they look
+
+ align:start position:0%
+heart attacks now even though they look
+ 
+
+ align:start position:0%
+heart attacks now even though they look
+older
+
+ align:start position:0%
+older
+ 
+
+ align:start position:0%
+older
+they don't get everything associated
+
+ align:start position:0%
+they don't get everything associated
+ 
+
+ align:start position:0%
+they don't get everything associated
+with being old they don't get
+
+ align:start position:0%
+with being old they don't get
+ 
+
+ align:start position:0%
+with being old they don't get
+alzheimer's they don't get cancer
+
+ align:start position:0%
+alzheimer's they don't get cancer
+ 
+
+ align:start position:0%
+alzheimer's they don't get cancer
+it's only the atherosclerosis and these
+
+ align:start position:0%
+it's only the atherosclerosis and these
+ 
+
+ align:start position:0%
+it's only the atherosclerosis and these
+other changes here that they get
+
+ align:start position:0%
+other changes here that they get
+ 
+
+ align:start position:0%
+other changes here that they get
+now as you might know the gene for this
+
+ align:start position:0%
+now as you might know the gene for this
+ 
+
+ align:start position:0%
+now as you might know the gene for this
+was just recently discovered okay
+
+ align:start position:0%
+was just recently discovered okay
+ 
+
+ align:start position:0%
+was just recently discovered okay
+very amazing that they found this gene
+
+ align:start position:0%
+very amazing that they found this gene
+ 
+
+ align:start position:0%
+very amazing that they found this gene
+okay i got involved with this particular
+
+ align:start position:0%
+okay i got involved with this particular
+ 
+
+ align:start position:0%
+okay i got involved with this particular
+syndrome only because of my friend
+
+ align:start position:0%
+syndrome only because of my friend
+ 
+
+ align:start position:0%
+syndrome only because of my friend
+leslie gordon who was a medical school
+
+ align:start position:0%
+leslie gordon who was a medical school
+ 
+
+ align:start position:0%
+leslie gordon who was a medical school
+classmate of mine and who has a son with
+
+ align:start position:0%
+classmate of mine and who has a son with
+ 
+
+ align:start position:0%
+classmate of mine and who has a son with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and she's got an mvp she instead of just
+
+ align:start position:0%
+and she's got an mvp she instead of just
+ 
+
+ align:start position:0%
+and she's got an mvp she instead of just
+studying this disease herself she built
+
+ align:start position:0%
+studying this disease herself she built
+ 
+
+ align:start position:0%
+studying this disease herself she built
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+foundation called the progeria research
+
+ align:start position:0%
+foundation called the progeria research
+ 
+
+ align:start position:0%
+foundation called the progeria research
+foundation got francis collins
+
+ align:start position:0%
+foundation got francis collins
+ 
+
+ align:start position:0%
+foundation got francis collins
+interested you know the guy who's
+
+ align:start position:0%
+interested you know the guy who's
+ 
+
+ align:start position:0%
+interested you know the guy who's
+basically doing the genome project the
+
+ align:start position:0%
+basically doing the genome project the
+ 
+
+ align:start position:0%
+basically doing the genome project the
+head of nhgri and within 18 months of
+
+ align:start position:0%
+head of nhgri and within 18 months of
+ 
+
+ align:start position:0%
+head of nhgri and within 18 months of
+forming this foundation they found the
+
+ align:start position:0%
+forming this foundation they found the
+ 
+
+ align:start position:0%
+forming this foundation they found the
+gene for this
+
+ align:start position:0%
+gene for this
+ 
+
+ align:start position:0%
+gene for this
+incredibly difficult problem okay there
+
+ align:start position:0%
+incredibly difficult problem okay there
+ 
+
+ align:start position:0%
+incredibly difficult problem okay there
+are people who on the first date would
+
+ align:start position:0%
+are people who on the first date would
+ 
+
+ align:start position:0%
+are people who on the first date would
+not believe this is still a genetic
+
+ align:start position:0%
+not believe this is still a genetic
+ 
+
+ align:start position:0%
+not believe this is still a genetic
+syndrome
+
+ align:start position:0%
+syndrome
+ 
+
+ align:start position:0%
+syndrome
+one in eight million births is way less
+
+ align:start position:0%
+one in eight million births is way less
+ 
+
+ align:start position:0%
+one in eight million births is way less
+than the mutation frequency
+
+ align:start position:0%
+than the mutation frequency
+ 
+
+ align:start position:0%
+than the mutation frequency
+okay i mean we have a whole bunch of
+
+ align:start position:0%
+okay i mean we have a whole bunch of
+ 
+
+ align:start position:0%
+okay i mean we have a whole bunch of
+diseases that at one forty thousand one
+
+ align:start position:0%
+diseases that at one forty thousand one
+ 
+
+ align:start position:0%
+diseases that at one forty thousand one
+in a hundred thousand
+
+ align:start position:0%
+in a hundred thousand
+ 
+
+ align:start position:0%
+in a hundred thousand
+one eight million seems like it's so
+
+ align:start position:0%
+one eight million seems like it's so
+ 
+
+ align:start position:0%
+one eight million seems like it's so
+rare how where how could a mutation be
+
+ align:start position:0%
+rare how where how could a mutation be
+ 
+
+ align:start position:0%
+rare how where how could a mutation be
+that rare so it was very questionable
+
+ align:start position:0%
+that rare so it was very questionable
+ 
+
+ align:start position:0%
+that rare so it was very questionable
+and second they had a very hard time
+
+ align:start position:0%
+and second they had a very hard time
+ 
+
+ align:start position:0%
+and second they had a very hard time
+finding any families where two of these
+
+ align:start position:0%
+finding any families where two of these
+ 
+
+ align:start position:0%
+finding any families where two of these
+kids were in the same family
+
+ align:start position:0%
+kids were in the same family
+ 
+
+ align:start position:0%
+kids were in the same family
+so it was dumb luck that they were able
+
+ align:start position:0%
+so it was dumb luck that they were able
+ 
+
+ align:start position:0%
+so it was dumb luck that they were able
+to find this gene because in one of the
+
+ align:start position:0%
+to find this gene because in one of the
+ 
+
+ align:start position:0%
+to find this gene because in one of the
+individuals okay at any point there's
+
+ align:start position:0%
+individuals okay at any point there's
+ 
+
+ align:start position:0%
+individuals okay at any point there's
+only about 50 of these kids on the
+
+ align:start position:0%
+only about 50 of these kids on the
+ 
+
+ align:start position:0%
+only about 50 of these kids on the
+planet really okay and one of these kids
+
+ align:start position:0%
+planet really okay and one of these kids
+ 
+
+ align:start position:0%
+planet really okay and one of these kids
+in one of the samples someone with a
+
+ align:start position:0%
+in one of the samples someone with a
+ 
+
+ align:start position:0%
+in one of the samples someone with a
+sharp eye saw a piece of chromosome 1
+
+ align:start position:0%
+sharp eye saw a piece of chromosome 1
+ 
+
+ align:start position:0%
+sharp eye saw a piece of chromosome 1
+was actually inverted the bands those
+
+ align:start position:0%
+was actually inverted the bands those
+ 
+
+ align:start position:0%
+was actually inverted the bands those
+banding patterns was actually different
+
+ align:start position:0%
+banding patterns was actually different
+ 
+
+ align:start position:0%
+banding patterns was actually different
+in that one individual
+
+ align:start position:0%
+in that one individual
+ 
+
+ align:start position:0%
+in that one individual
+and that got francis collins to think
+
+ align:start position:0%
+and that got francis collins to think
+ 
+
+ align:start position:0%
+and that got francis collins to think
+maybe it's something on that particular
+
+ align:start position:0%
+maybe it's something on that particular
+ 
+
+ align:start position:0%
+maybe it's something on that particular
+arm of chromosome 1 and they sequence
+
+ align:start position:0%
+arm of chromosome 1 and they sequence
+ 
+
+ align:start position:0%
+arm of chromosome 1 and they sequence
+all the genes there and they found the
+
+ align:start position:0%
+all the genes there and they found the
+ 
+
+ align:start position:0%
+all the genes there and they found the
+particular mutation machine called lamin
+
+ align:start position:0%
+particular mutation machine called lamin
+ 
+
+ align:start position:0%
+particular mutation machine called lamin
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and it's not just laminate that causes
+
+ align:start position:0%
+and it's not just laminate that causes
+ 
+
+ align:start position:0%
+and it's not just laminate that causes
+it vitamin a has actually been involved
+
+ align:start position:0%
+it vitamin a has actually been involved
+ 
+
+ align:start position:0%
+it vitamin a has actually been involved
+in a lot of other diseases which we'll
+
+ align:start position:0%
+in a lot of other diseases which we'll
+ 
+
+ align:start position:0%
+in a lot of other diseases which we'll
+talk about in a second it's just this
+
+ align:start position:0%
+talk about in a second it's just this
+ 
+
+ align:start position:0%
+talk about in a second it's just this
+one mutation in this one gene that
+
+ align:start position:0%
+one mutation in this one gene that
+ 
+
+ align:start position:0%
+one mutation in this one gene that
+causes it
+
+ align:start position:0%
+causes it
+ 
+
+ align:start position:0%
+causes it
+now amazingly enough in the same issue
+
+ align:start position:0%
+now amazingly enough in the same issue
+ 
+
+ align:start position:0%
+now amazingly enough in the same issue
+of nature
+
+ align:start position:0%
+of nature
+ 
+
+ align:start position:0%
+of nature
+less than a year ago
+
+ align:start position:0%
+less than a year ago
+ 
+
+ align:start position:0%
+less than a year ago
+the mouse model for this was published
+
+ align:start position:0%
+the mouse model for this was published
+ 
+
+ align:start position:0%
+the mouse model for this was published
+how is that okay because this group at
+
+ align:start position:0%
+how is that okay because this group at
+ 
+
+ align:start position:0%
+how is that okay because this group at
+national cancer institute
+
+ align:start position:0%
+national cancer institute
+ 
+
+ align:start position:0%
+national cancer institute
+realized i mean lemon a is known to be
+
+ align:start position:0%
+realized i mean lemon a is known to be
+ 
+
+ align:start position:0%
+realized i mean lemon a is known to be
+involved in certain forms of muscular
+
+ align:start position:0%
+involved in certain forms of muscular
+ 
+
+ align:start position:0%
+involved in certain forms of muscular
+dystrophy they said well
+
+ align:start position:0%
+dystrophy they said well
+ 
+
+ align:start position:0%
+dystrophy they said well
+they wanted to create a mouse model of a
+
+ align:start position:0%
+they wanted to create a mouse model of a
+ 
+
+ align:start position:0%
+they wanted to create a mouse model of a
+particular form of muscular dystrophy
+
+ align:start position:0%
+particular form of muscular dystrophy
+ 
+
+ align:start position:0%
+particular form of muscular dystrophy
+they accidentally created a mouse model
+
+ align:start position:0%
+they accidentally created a mouse model
+ 
+
+ align:start position:0%
+they accidentally created a mouse model
+for progeria
+
+ align:start position:0%
+for progeria
+ 
+
+ align:start position:0%
+for progeria
+so the same issue you got the gene that
+
+ align:start position:0%
+so the same issue you got the gene that
+ 
+
+ align:start position:0%
+so the same issue you got the gene that
+causes it you got diagnostic tests and
+
+ align:start position:0%
+causes it you got diagnostic tests and
+ 
+
+ align:start position:0%
+causes it you got diagnostic tests and
+you got a mouse model to study it okay
+
+ align:start position:0%
+you got a mouse model to study it okay
+ 
+
+ align:start position:0%
+you got a mouse model to study it okay
+and just in a tour de force issue there
+
+ align:start position:0%
+and just in a tour de force issue there
+ 
+
+ align:start position:0%
+and just in a tour de force issue there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+imagine how long it takes for these
+
+ align:start position:0%
+imagine how long it takes for these
+ 
+
+ align:start position:0%
+imagine how long it takes for these
+things to happen for a disease
+
+ align:start position:0%
+things to happen for a disease
+ 
+
+ align:start position:0%
+things to happen for a disease
+start to finish 18 months here okay for
+
+ align:start position:0%
+start to finish 18 months here okay for
+ 
+
+ align:start position:0%
+start to finish 18 months here okay for
+something that affects maybe 50 people
+
+ align:start position:0%
+something that affects maybe 50 people
+ 
+
+ align:start position:0%
+something that affects maybe 50 people
+okay so if you put your mind to it you
+
+ align:start position:0%
+okay so if you put your mind to it you
+ 
+
+ align:start position:0%
+okay so if you put your mind to it you
+can solve these diseases it's amazing
+
+ align:start position:0%
+can solve these diseases it's amazing
+ 
+
+ align:start position:0%
+can solve these diseases it's amazing
+what the tools and the people can do
+
+ align:start position:0%
+what the tools and the people can do
+ 
+
+ align:start position:0%
+what the tools and the people can do
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+so in collaboration with the progeria
+
+ align:start position:0%
+so in collaboration with the progeria
+ 
+
+ align:start position:0%
+so in collaboration with the progeria
+foundation what we've done is this it
+
+ align:start position:0%
+foundation what we've done is this it
+ 
+
+ align:start position:0%
+foundation what we've done is this it
+turns out over the past 20 years when
+
+ align:start position:0%
+turns out over the past 20 years when
+ 
+
+ align:start position:0%
+turns out over the past 20 years when
+people thought they had kids with
+
+ align:start position:0%
+people thought they had kids with
+ 
+
+ align:start position:0%
+people thought they had kids with
+progeria that they were trying to treat
+
+ align:start position:0%
+progeria that they were trying to treat
+ 
+
+ align:start position:0%
+progeria that they were trying to treat
+kids with progeria they had no idea what
+
+ align:start position:0%
+kids with progeria they had no idea what
+ 
+
+ align:start position:0%
+kids with progeria they had no idea what
+to do so one thing they did is they took
+
+ align:start position:0%
+to do so one thing they did is they took
+ 
+
+ align:start position:0%
+to do so one thing they did is they took
+fibroblasts and they saved them in
+
+ align:start position:0%
+fibroblasts and they saved them in
+ 
+
+ align:start position:0%
+fibroblasts and they saved them in
+national repositories
+
+ align:start position:0%
+national repositories
+ 
+
+ align:start position:0%
+national repositories
+so there's a cor there's a cell
+
+ align:start position:0%
+so there's a cor there's a cell
+ 
+
+ align:start position:0%
+so there's a cor there's a cell
+repository called the corial cell
+
+ align:start position:0%
+repository called the corial cell
+ 
+
+ align:start position:0%
+repository called the corial cell
+repository where you can order
+
+ align:start position:0%
+repository where you can order
+ 
+
+ align:start position:0%
+repository where you can order
+fibroblast cell lines from patients with
+
+ align:start position:0%
+fibroblast cell lines from patients with
+ 
+
+ align:start position:0%
+fibroblast cell lines from patients with
+exceedingly rare disorders including
+
+ align:start position:0%
+exceedingly rare disorders including
+ 
+
+ align:start position:0%
+exceedingly rare disorders including
+progeria
+
+ align:start position:0%
+progeria
+ 
+
+ align:start position:0%
+progeria
+so we've gotten three cell lines from
+
+ align:start position:0%
+so we've gotten three cell lines from
+ 
+
+ align:start position:0%
+so we've gotten three cell lines from
+patients that were stored in the coriol
+
+ align:start position:0%
+patients that were stored in the coriol
+ 
+
+ align:start position:0%
+patients that were stored in the coriol
+collection over the past 10 years
+
+ align:start position:0%
+collection over the past 10 years
+ 
+
+ align:start position:0%
+collection over the past 10 years
+and we ordered them three times to make
+
+ align:start position:0%
+and we ordered them three times to make
+ 
+
+ align:start position:0%
+and we ordered them three times to make
+sure that we're controlling at least for
+
+ align:start position:0%
+sure that we're controlling at least for
+ 
+
+ align:start position:0%
+sure that we're controlling at least for
+passage number and things like that and
+
+ align:start position:0%
+passage number and things like that and
+ 
+
+ align:start position:0%
+passage number and things like that and
+we compare them to age match normal
+
+ align:start position:0%
+we compare them to age match normal
+ 
+
+ align:start position:0%
+we compare them to age match normal
+fibroblasts from the same coriol
+
+ align:start position:0%
+fibroblasts from the same coriol
+ 
+
+ align:start position:0%
+fibroblasts from the same coriol
+repository look at what genes are
+
+ align:start position:0%
+repository look at what genes are
+ 
+
+ align:start position:0%
+repository look at what genes are
+different between progeria and
+
+ align:start position:0%
+different between progeria and
+ 
+
+ align:start position:0%
+different between progeria and
+non-progeria
+
+ align:start position:0%
+non-progeria
+ 
+
+ align:start position:0%
+non-progeria
+and these are more up-to-date arrays
+
+ align:start position:0%
+and these are more up-to-date arrays
+ 
+
+ align:start position:0%
+and these are more up-to-date arrays
+there's a u-133 race on two the whole
+
+ align:start position:0%
+there's a u-133 race on two the whole
+ 
+
+ align:start position:0%
+there's a u-133 race on two the whole
+genome with two chips it gave us about
+
+ align:start position:0%
+genome with two chips it gave us about
+ 
+
+ align:start position:0%
+genome with two chips it gave us about
+33 000 genes and used a particular
+
+ align:start position:0%
+33 000 genes and used a particular
+ 
+
+ align:start position:0%
+33 000 genes and used a particular
+analytic technique and we got about a
+
+ align:start position:0%
+analytic technique and we got about a
+ 
+
+ align:start position:0%
+analytic technique and we got about a
+list of about 366 genes that were
+
+ align:start position:0%
+list of about 366 genes that were
+ 
+
+ align:start position:0%
+list of about 366 genes that were
+different between fibroblasts in
+
+ align:start position:0%
+different between fibroblasts in
+ 
+
+ align:start position:0%
+different between fibroblasts in
+progeria and fibroblasts from age match
+
+ align:start position:0%
+progeria and fibroblasts from age match
+ 
+
+ align:start position:0%
+progeria and fibroblasts from age match
+controls
+
+ align:start position:0%
+controls
+ 
+
+ align:start position:0%
+controls
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if you look at where these genes
+
+ align:start position:0%
+and so if you look at where these genes
+ 
+
+ align:start position:0%
+and so if you look at where these genes
+are what categories they're involved
+
+ align:start position:0%
+are what categories they're involved
+ 
+
+ align:start position:0%
+are what categories they're involved
+with you see interesting things like
+
+ align:start position:0%
+with you see interesting things like
+ 
+
+ align:start position:0%
+with you see interesting things like
+development signal transduction cell
+
+ align:start position:0%
+development signal transduction cell
+ 
+
+ align:start position:0%
+development signal transduction cell
+adhesion the only thing i want to point
+
+ align:start position:0%
+adhesion the only thing i want to point
+ 
+
+ align:start position:0%
+adhesion the only thing i want to point
+out is this okay these tables are made
+
+ align:start position:0%
+out is this okay these tables are made
+ 
+
+ align:start position:0%
+out is this okay these tables are made
+using a catalog called gene ontology
+
+ align:start position:0%
+using a catalog called gene ontology
+ 
+
+ align:start position:0%
+using a catalog called gene ontology
+you're going to learn about that in more
+
+ align:start position:0%
+you're going to learn about that in more
+ 
+
+ align:start position:0%
+you're going to learn about that in more
+in the future
+
+ align:start position:0%
+in the future
+ 
+
+ align:start position:0%
+in the future
+and every week or every other week the
+
+ align:start position:0%
+and every week or every other week the
+ 
+
+ align:start position:0%
+and every week or every other week the
+list of known properties of genes and
+
+ align:start position:0%
+list of known properties of genes and
+ 
+
+ align:start position:0%
+list of known properties of genes and
+proteins gets updated
+
+ align:start position:0%
+proteins gets updated
+ 
+
+ align:start position:0%
+proteins gets updated
+but still the majority of genes
+
+ align:start position:0%
+but still the majority of genes
+ 
+
+ align:start position:0%
+but still the majority of genes
+unclassified 161 okay no matter how
+
+ align:start position:0%
+unclassified 161 okay no matter how
+ 
+
+ align:start position:0%
+unclassified 161 okay no matter how
+interesting or how comprehensive we
+
+ align:start position:0%
+interesting or how comprehensive we
+ 
+
+ align:start position:0%
+interesting or how comprehensive we
+think gene ontology is the vast majority
+
+ align:start position:0%
+think gene ontology is the vast majority
+ 
+
+ align:start position:0%
+think gene ontology is the vast majority
+of genes are just have no i we have no
+
+ align:start position:0%
+of genes are just have no i we have no
+ 
+
+ align:start position:0%
+of genes are just have no i we have no
+idea where they are what they do what
+
+ align:start position:0%
+idea where they are what they do what
+ 
+
+ align:start position:0%
+idea where they are what they do what
+roles they play
+
+ align:start position:0%
+roles they play
+ 
+
+ align:start position:0%
+roles they play
+these are where the proteins that
+
+ align:start position:0%
+these are where the proteins that
+ 
+
+ align:start position:0%
+these are where the proteins that
+they're coding for actually are take
+
+ align:start position:0%
+they're coding for actually are take
+ 
+
+ align:start position:0%
+they're coding for actually are take
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+nucleus membrane unclassified 131 again
+
+ align:start position:0%
+nucleus membrane unclassified 131 again
+ 
+
+ align:start position:0%
+nucleus membrane unclassified 131 again
+no idea where these proteins even are in
+
+ align:start position:0%
+no idea where these proteins even are in
+ 
+
+ align:start position:0%
+no idea where these proteins even are in
+the cell that's life today okay we have
+
+ align:start position:0%
+the cell that's life today okay we have
+ 
+
+ align:start position:0%
+the cell that's life today okay we have
+a great taxonomy here of all of these
+
+ align:start position:0%
+a great taxonomy here of all of these
+ 
+
+ align:start position:0%
+a great taxonomy here of all of these
+terms and structure vocabulary but we
+
+ align:start position:0%
+terms and structure vocabulary but we
+ 
+
+ align:start position:0%
+terms and structure vocabulary but we
+have no there's very little data for
+
+ align:start position:0%
+have no there's very little data for
+ 
+
+ align:start position:0%
+have no there's very little data for
+most genes in this still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a bunch of genes that were
+
+ align:start position:0%
+and there's a bunch of genes that were
+ 
+
+ align:start position:0%
+and there's a bunch of genes that were
+upregulated that seem to already be
+
+ align:start position:0%
+upregulated that seem to already be
+ 
+
+ align:start position:0%
+upregulated that seem to already be
+known to play a role in atherosclerosis
+
+ align:start position:0%
+known to play a role in atherosclerosis
+ 
+
+ align:start position:0%
+known to play a role in atherosclerosis
+okay so this paper again talk about
+
+ align:start position:0%
+okay so this paper again talk about
+ 
+
+ align:start position:0%
+okay so this paper again talk about
+genome medicine this paper is going to
+
+ align:start position:0%
+genome medicine this paper is going to
+ 
+
+ align:start position:0%
+genome medicine this paper is going to
+end with this list
+
+ align:start position:0%
+end with this list
+ 
+
+ align:start position:0%
+end with this list
+only because a number of these are
+
+ align:start position:0%
+only because a number of these are
+ 
+
+ align:start position:0%
+only because a number of these are
+targets and pharmaceutical companies
+
+ align:start position:0%
+targets and pharmaceutical companies
+ 
+
+ align:start position:0%
+targets and pharmaceutical companies
+actually have drugs against a number of
+
+ align:start position:0%
+actually have drugs against a number of
+ 
+
+ align:start position:0%
+actually have drugs against a number of
+these already
+
+ align:start position:0%
+these already
+ 
+
+ align:start position:0%
+these already
+for kids with progeria it's basically a
+
+ align:start position:0%
+for kids with progeria it's basically a
+ 
+
+ align:start position:0%
+for kids with progeria it's basically a
+death sentence today we have no
+
+ align:start position:0%
+death sentence today we have no
+ 
+
+ align:start position:0%
+death sentence today we have no
+medicines we have not we treat them with
+
+ align:start position:0%
+medicines we have not we treat them with
+ 
+
+ align:start position:0%
+medicines we have not we treat them with
+nothing today there's maybe some people
+
+ align:start position:0%
+nothing today there's maybe some people
+ 
+
+ align:start position:0%
+nothing today there's maybe some people
+treat one or two kids with growth
+
+ align:start position:0%
+treat one or two kids with growth
+ 
+
+ align:start position:0%
+treat one or two kids with growth
+hormone to see if growth hormone does
+
+ align:start position:0%
+hormone to see if growth hormone does
+ 
+
+ align:start position:0%
+hormone to see if growth hormone does
+something but that's basically like a
+
+ align:start position:0%
+something but that's basically like a
+ 
+
+ align:start position:0%
+something but that's basically like a
+voodoo medicine kind of thing we have no
+
+ align:start position:0%
+voodoo medicine kind of thing we have no
+ 
+
+ align:start position:0%
+voodoo medicine kind of thing we have no
+proof of that doing anything
+
+ align:start position:0%
+proof of that doing anything
+ 
+
+ align:start position:0%
+proof of that doing anything
+now we can at least get to some
+
+ align:start position:0%
+now we can at least get to some
+ 
+
+ align:start position:0%
+now we can at least get to some
+information to possibly even think about
+
+ align:start position:0%
+information to possibly even think about
+ 
+
+ align:start position:0%
+information to possibly even think about
+clinical trials here
+
+ align:start position:0%
+clinical trials here
+ 
+
+ align:start position:0%
+clinical trials here
+but let's be let's be frank here these
+
+ align:start position:0%
+but let's be let's be frank here these
+ 
+
+ align:start position:0%
+but let's be let's be frank here these
+were fibroblasts that were frozen for
+
+ align:start position:0%
+were fibroblasts that were frozen for
+ 
+
+ align:start position:0%
+were fibroblasts that were frozen for
+years in the cell repository and we're
+
+ align:start position:0%
+years in the cell repository and we're
+ 
+
+ align:start position:0%
+years in the cell repository and we're
+now we're making a claim as to what
+
+ align:start position:0%
+now we're making a claim as to what
+ 
+
+ align:start position:0%
+now we're making a claim as to what
+their blood vessels look like not just
+
+ align:start position:0%
+their blood vessels look like not just
+ 
+
+ align:start position:0%
+their blood vessels look like not just
+their blood vessels but the intima of
+
+ align:start position:0%
+their blood vessels but the intima of
+ 
+
+ align:start position:0%
+their blood vessels but the intima of
+their blood vessels right this is not
+
+ align:start position:0%
+their blood vessels right this is not
+ 
+
+ align:start position:0%
+their blood vessels right this is not
+the same cell but fiberglass might have
+
+ align:start position:0%
+the same cell but fiberglass might have
+ 
+
+ align:start position:0%
+the same cell but fiberglass might have
+been taken from their cheek
+
+ align:start position:0%
+been taken from their cheek
+ 
+
+ align:start position:0%
+been taken from their cheek
+right but we're just making a claim here
+
+ align:start position:0%
+right but we're just making a claim here
+ 
+
+ align:start position:0%
+right but we're just making a claim here
+because we don't have access to the real
+
+ align:start position:0%
+because we don't have access to the real
+ 
+
+ align:start position:0%
+because we don't have access to the real
+tissue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of the reasons why i'm mentioning
+
+ align:start position:0%
+so one of the reasons why i'm mentioning
+ 
+
+ align:start position:0%
+so one of the reasons why i'm mentioning
+progeria here is remember that picture
+
+ align:start position:0%
+progeria here is remember that picture
+ 
+
+ align:start position:0%
+progeria here is remember that picture
+you just saw one of the ways that these
+
+ align:start position:0%
+you just saw one of the ways that these
+ 
+
+ align:start position:0%
+you just saw one of the ways that these
+kids get diagnosed is because by the
+
+ align:start position:0%
+kids get diagnosed is because by the
+ 
+
+ align:start position:0%
+kids get diagnosed is because by the
+time they get to age two they start to
+
+ align:start position:0%
+time they get to age two they start to
+ 
+
+ align:start position:0%
+time they get to age two they start to
+lose their hair but even more
+
+ align:start position:0%
+lose their hair but even more
+ 
+
+ align:start position:0%
+lose their hair but even more
+interestingly is they lose all their fat
+
+ align:start position:0%
+interestingly is they lose all their fat
+ 
+
+ align:start position:0%
+interestingly is they lose all their fat
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+okay it turns out in progeria you lose
+
+ align:start position:0%
+okay it turns out in progeria you lose
+ 
+
+ align:start position:0%
+okay it turns out in progeria you lose
+all your subcutaneous fat
+
+ align:start position:0%
+all your subcutaneous fat
+ 
+
+ align:start position:0%
+all your subcutaneous fat
+and by death and autopsy it's very tough
+
+ align:start position:0%
+and by death and autopsy it's very tough
+ 
+
+ align:start position:0%
+and by death and autopsy it's very tough
+to find any fat in the body
+
+ align:start position:0%
+to find any fat in the body
+ 
+
+ align:start position:0%
+to find any fat in the body
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+makes you think something is up with the
+
+ align:start position:0%
+makes you think something is up with the
+ 
+
+ align:start position:0%
+makes you think something is up with the
+actual process of making fat cells in
+
+ align:start position:0%
+actual process of making fat cells in
+ 
+
+ align:start position:0%
+actual process of making fat cells in
+these kids
+
+ align:start position:0%
+these kids
+ 
+
+ align:start position:0%
+these kids
+in one study these kids have been known
+
+ align:start position:0%
+in one study these kids have been known
+ 
+
+ align:start position:0%
+in one study these kids have been known
+to have some insulin resistance but it's
+
+ align:start position:0%
+to have some insulin resistance but it's
+ 
+
+ align:start position:0%
+to have some insulin resistance but it's
+just one study almost 10 years ago
+
+ align:start position:0%
+just one study almost 10 years ago
+ 
+
+ align:start position:0%
+just one study almost 10 years ago
+and the mouse model the last paragraph
+
+ align:start position:0%
+and the mouse model the last paragraph
+ 
+
+ align:start position:0%
+and the mouse model the last paragraph
+of that nature paper says that they saw
+
+ align:start position:0%
+of that nature paper says that they saw
+ 
+
+ align:start position:0%
+of that nature paper says that they saw
+some process where muscle was
+
+ align:start position:0%
+some process where muscle was
+ 
+
+ align:start position:0%
+some process where muscle was
+redifferentiating the fat basically
+
+ align:start position:0%
+redifferentiating the fat basically
+ 
+
+ align:start position:0%
+redifferentiating the fat basically
+there's some developmental problem going
+
+ align:start position:0%
+there's some developmental problem going
+ 
+
+ align:start position:0%
+there's some developmental problem going
+on but it's not very clear
+
+ align:start position:0%
+on but it's not very clear
+ 
+
+ align:start position:0%
+on but it's not very clear
+other mutations in lamin a cause
+
+ align:start position:0%
+other mutations in lamin a cause
+ 
+
+ align:start position:0%
+other mutations in lamin a cause
+lipodystrophy which is a syndrome where
+
+ align:start position:0%
+lipodystrophy which is a syndrome where
+ 
+
+ align:start position:0%
+lipodystrophy which is a syndrome where
+you lose all your fat cells
+
+ align:start position:0%
+you lose all your fat cells
+ 
+
+ align:start position:0%
+you lose all your fat cells
+so it makes us think that there is
+
+ align:start position:0%
+so it makes us think that there is
+ 
+
+ align:start position:0%
+so it makes us think that there is
+legitimately something wrong with fat
+
+ align:start position:0%
+legitimately something wrong with fat
+ 
+
+ align:start position:0%
+legitimately something wrong with fat
+cell development in kids with progeria
+
+ align:start position:0%
+cell development in kids with progeria
+ 
+
+ align:start position:0%
+cell development in kids with progeria
+so now i told you
+
+ align:start position:0%
+so now i told you
+ 
+
+ align:start position:0%
+so now i told you
+about where are we here hold on
+
+ align:start position:0%
+about where are we here hold on
+ 
+
+ align:start position:0%
+about where are we here hold on
+sorry about 80 or 90 genes that were in
+
+ align:start position:0%
+sorry about 80 or 90 genes that were in
+ 
+
+ align:start position:0%
+sorry about 80 or 90 genes that were in
+the mouse models going along with fat
+
+ align:start position:0%
+the mouse models going along with fat
+ 
+
+ align:start position:0%
+the mouse models going along with fat
+so about 360 genes that are different
+
+ align:start position:0%
+so about 360 genes that are different
+ 
+
+ align:start position:0%
+so about 360 genes that are different
+between progeria kids and age max
+
+ align:start position:0%
+between progeria kids and age max
+ 
+
+ align:start position:0%
+between progeria kids and age max
+controls and they have some problem with
+
+ align:start position:0%
+controls and they have some problem with
+ 
+
+ align:start position:0%
+controls and they have some problem with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+i have a third data set here which was
+
+ align:start position:0%
+i have a third data set here which was
+ 
+
+ align:start position:0%
+i have a third data set here which was
+published by gary robkins group over at
+
+ align:start position:0%
+published by gary robkins group over at
+ 
+
+ align:start position:0%
+published by gary robkins group over at
+mass general hospital this came out
+
+ align:start position:0%
+mass general hospital this came out
+ 
+
+ align:start position:0%
+mass general hospital this came out
+about last year and now this is in a
+
+ align:start position:0%
+about last year and now this is in a
+ 
+
+ align:start position:0%
+about last year and now this is in a
+totally different species this is in the
+
+ align:start position:0%
+totally different species this is in the
+ 
+
+ align:start position:0%
+totally different species this is in the
+worm to give you an idea of what we can
+
+ align:start position:0%
+worm to give you an idea of what we can
+ 
+
+ align:start position:0%
+worm to give you an idea of what we can
+do today what this group did is there
+
+ align:start position:0%
+do today what this group did is there
+ 
+
+ align:start position:0%
+do today what this group did is there
+they knocked out every single gene in
+
+ align:start position:0%
+they knocked out every single gene in
+ 
+
+ align:start position:0%
+they knocked out every single gene in
+the worm genome okay so worm has about
+
+ align:start position:0%
+the worm genome okay so worm has about
+ 
+
+ align:start position:0%
+the worm genome okay so worm has about
+16 17 000 genes
+
+ align:start position:0%
+16 17 000 genes
+ 
+
+ align:start position:0%
+16 17 000 genes
+and they basically serially knocked out
+
+ align:start position:0%
+and they basically serially knocked out
+ 
+
+ align:start position:0%
+and they basically serially knocked out
+each and every one of these genes to
+
+ align:start position:0%
+each and every one of these genes to
+ 
+
+ align:start position:0%
+each and every one of these genes to
+look at what happens to the one
+
+ align:start position:0%
+look at what happens to the one
+ 
+
+ align:start position:0%
+look at what happens to the one
+now worm it's actually pretty easy to do
+
+ align:start position:0%
+now worm it's actually pretty easy to do
+ 
+
+ align:start position:0%
+now worm it's actually pretty easy to do
+you can actually get bacteria to make a
+
+ align:start position:0%
+you can actually get bacteria to make a
+ 
+
+ align:start position:0%
+you can actually get bacteria to make a
+particular sequence called an rnai that
+
+ align:start position:0%
+particular sequence called an rnai that
+ 
+
+ align:start position:0%
+particular sequence called an rnai that
+interferes with the worms ability to
+
+ align:start position:0%
+interferes with the worms ability to
+ 
+
+ align:start position:0%
+interferes with the worms ability to
+make that gene so you don't even have to
+
+ align:start position:0%
+make that gene so you don't even have to
+ 
+
+ align:start position:0%
+make that gene so you don't even have to
+change the dna you could just
+
+ align:start position:0%
+change the dna you could just
+ 
+
+ align:start position:0%
+change the dna you could just
+effectively shut down the amount of that
+
+ align:start position:0%
+effectively shut down the amount of that
+ 
+
+ align:start position:0%
+effectively shut down the amount of that
+gene that's being made in the worm
+
+ align:start position:0%
+gene that's being made in the worm
+ 
+
+ align:start position:0%
+gene that's being made in the worm
+and basically it's very easy you don't
+
+ align:start position:0%
+and basically it's very easy you don't
+ 
+
+ align:start position:0%
+and basically it's very easy you don't
+even have to inject these worms you set
+
+ align:start position:0%
+even have to inject these worms you set
+ 
+
+ align:start position:0%
+even have to inject these worms you set
+up essentially set of 16 700 buckets of
+
+ align:start position:0%
+up essentially set of 16 700 buckets of
+ 
+
+ align:start position:0%
+up essentially set of 16 700 buckets of
+bacteria and just put the worms in it
+
+ align:start position:0%
+bacteria and just put the worms in it
+ 
+
+ align:start position:0%
+bacteria and just put the worms in it
+and they eat the bacteria and basically
+
+ align:start position:0%
+and they eat the bacteria and basically
+ 
+
+ align:start position:0%
+and they eat the bacteria and basically
+they knock out the gene
+
+ align:start position:0%
+they knock out the gene
+ 
+
+ align:start position:0%
+they knock out the gene
+themselves that's literally how it works
+
+ align:start position:0%
+themselves that's literally how it works
+ 
+
+ align:start position:0%
+themselves that's literally how it works
+all you have to do is get the worm to
+
+ align:start position:0%
+all you have to do is get the worm to
+ 
+
+ align:start position:0%
+all you have to do is get the worm to
+eat the bacteria that makes the rnai
+
+ align:start position:0%
+eat the bacteria that makes the rnai
+ 
+
+ align:start position:0%
+eat the bacteria that makes the rnai
+it's very easy it knocks out the g in
+
+ align:start position:0%
+it's very easy it knocks out the g in
+ 
+
+ align:start position:0%
+it's very easy it knocks out the g in
+that worm
+
+ align:start position:0%
+that worm
+ 
+
+ align:start position:0%
+that worm
+so what these guys did is they had
+
+ align:start position:0%
+so what these guys did is they had
+ 
+
+ align:start position:0%
+so what these guys did is they had
+back-to-back nature papers on this
+
+ align:start position:0%
+back-to-back nature papers on this
+ 
+
+ align:start position:0%
+back-to-back nature papers on this
+process the first one was on a whole
+
+ align:start position:0%
+process the first one was on a whole
+ 
+
+ align:start position:0%
+process the first one was on a whole
+bunch of different phenotypes but the
+
+ align:start position:0%
+bunch of different phenotypes but the
+ 
+
+ align:start position:0%
+bunch of different phenotypes but the
+second paper was looking at fat
+
+ align:start position:0%
+second paper was looking at fat
+ 
+
+ align:start position:0%
+second paper was looking at fat
+amazingly enough and here there's a
+
+ align:start position:0%
+amazingly enough and here there's a
+ 
+
+ align:start position:0%
+amazingly enough and here there's a
+picture of a worm and they're using the
+
+ align:start position:0%
+picture of a worm and they're using the
+ 
+
+ align:start position:0%
+picture of a worm and they're using the
+same stain for lipid that i showed you
+
+ align:start position:0%
+same stain for lipid that i showed you
+ 
+
+ align:start position:0%
+same stain for lipid that i showed you
+two or three slides ago okay what we
+
+ align:start position:0%
+two or three slides ago okay what we
+ 
+
+ align:start position:0%
+two or three slides ago okay what we
+were using in the mouse and basically
+
+ align:start position:0%
+were using in the mouse and basically
+ 
+
+ align:start position:0%
+were using in the mouse and basically
+they're saying for example if you knock
+
+ align:start position:0%
+they're saying for example if you knock
+ 
+
+ align:start position:0%
+they're saying for example if you knock
+out daf2 you get an increase in the fat
+
+ align:start position:0%
+out daf2 you get an increase in the fat
+ 
+
+ align:start position:0%
+out daf2 you get an increase in the fat
+if you're not gonna have to end that
+
+ align:start position:0%
+if you're not gonna have to end that
+ 
+
+ align:start position:0%
+if you're not gonna have to end that
+succeed you get a subsequent decrease
+
+ align:start position:0%
+succeed you get a subsequent decrease
+ 
+
+ align:start position:0%
+succeed you get a subsequent decrease
+the afternoon that three slightly more
+
+ align:start position:0%
+the afternoon that three slightly more
+ 
+
+ align:start position:0%
+the afternoon that three slightly more
+and they can quantitate the amount of
+
+ align:start position:0%
+and they can quantitate the amount of
+ 
+
+ align:start position:0%
+and they can quantitate the amount of
+fat that have that results after you've
+
+ align:start position:0%
+fat that have that results after you've
+ 
+
+ align:start position:0%
+fat that have that results after you've
+knocked out any of these genes and
+
+ align:start position:0%
+knocked out any of these genes and
+ 
+
+ align:start position:0%
+knocked out any of these genes and
+essentially they've made a list it's
+
+ align:start position:0%
+essentially they've made a list it's
+ 
+
+ align:start position:0%
+essentially they've made a list it's
+available on the internet amazingly
+
+ align:start position:0%
+available on the internet amazingly
+ 
+
+ align:start position:0%
+available on the internet amazingly
+you're not get any of these 112 genes it
+
+ align:start position:0%
+you're not get any of these 112 genes it
+ 
+
+ align:start position:0%
+you're not get any of these 112 genes it
+increases the amount of fat in the worm
+
+ align:start position:0%
+increases the amount of fat in the worm
+ 
+
+ align:start position:0%
+increases the amount of fat in the worm
+you're not getting any of these 305
+
+ align:start position:0%
+you're not getting any of these 305
+ 
+
+ align:start position:0%
+you're not getting any of these 305
+genes a decrease in the amount of fat in
+
+ align:start position:0%
+genes a decrease in the amount of fat in
+ 
+
+ align:start position:0%
+genes a decrease in the amount of fat in
+the worm
+
+ align:start position:0%
+the worm
+ 
+
+ align:start position:0%
+the worm
+so now we have three big data sets
+
+ align:start position:0%
+so now we have three big data sets
+ 
+
+ align:start position:0%
+so now we have three big data sets
+one in the mouse one in the human
+
+ align:start position:0%
+one in the mouse one in the human
+ 
+
+ align:start position:0%
+one in the mouse one in the human
+one in the worm
+
+ align:start position:0%
+one in the worm
+ 
+
+ align:start position:0%
+one in the worm
+two microarrays one rnai
+
+ align:start position:0%
+two microarrays one rnai
+ 
+
+ align:start position:0%
+two microarrays one rnai
+okay spanning all these but they all
+
+ align:start position:0%
+okay spanning all these but they all
+ 
+
+ align:start position:0%
+okay spanning all these but they all
+have something to do with each other
+
+ align:start position:0%
+have something to do with each other
+ 
+
+ align:start position:0%
+have something to do with each other
+because they're all thinking about fat
+
+ align:start position:0%
+because they're all thinking about fat
+ 
+
+ align:start position:0%
+because they're all thinking about fat
+and fat storage
+
+ align:start position:0%
+and fat storage
+ 
+
+ align:start position:0%
+and fat storage
+okay that storage in the worm is very
+
+ align:start position:0%
+okay that storage in the worm is very
+ 
+
+ align:start position:0%
+okay that storage in the worm is very
+different than the human but still a
+
+ align:start position:0%
+different than the human but still a
+ 
+
+ align:start position:0%
+different than the human but still a
+number of the genes are actually
+
+ align:start position:0%
+number of the genes are actually
+ 
+
+ align:start position:0%
+number of the genes are actually
+intersecting and really what we're
+
+ align:start position:0%
+intersecting and really what we're
+ 
+
+ align:start position:0%
+intersecting and really what we're
+talking about is intersecting these
+
+ align:start position:0%
+talking about is intersecting these
+ 
+
+ align:start position:0%
+talking about is intersecting these
+three data sets
+
+ align:start position:0%
+three data sets
+ 
+
+ align:start position:0%
+three data sets
+we've got the worm we've got the mouse
+
+ align:start position:0%
+we've got the worm we've got the mouse
+ 
+
+ align:start position:0%
+we've got the worm we've got the mouse
+we've got the progeria and we're looking
+
+ align:start position:0%
+we've got the progeria and we're looking
+ 
+
+ align:start position:0%
+we've got the progeria and we're looking
+at the intersection of all these three
+
+ align:start position:0%
+at the intersection of all these three
+ 
+
+ align:start position:0%
+at the intersection of all these three
+so this is what i've been working on
+
+ align:start position:0%
+so this is what i've been working on
+ 
+
+ align:start position:0%
+so this is what i've been working on
+over the past six months actually and
+
+ align:start position:0%
+over the past six months actually and
+ 
+
+ align:start position:0%
+over the past six months actually and
+this is what we're calling integrative
+
+ align:start position:0%
+this is what we're calling integrative
+ 
+
+ align:start position:0%
+this is what we're calling integrative
+biology or integrative genomics
+
+ align:start position:0%
+biology or integrative genomics
+ 
+
+ align:start position:0%
+biology or integrative genomics
+okay because these large data sets are
+
+ align:start position:0%
+okay because these large data sets are
+ 
+
+ align:start position:0%
+okay because these large data sets are
+not only they don't just exist in a
+
+ align:start position:0%
+not only they don't just exist in a
+ 
+
+ align:start position:0%
+not only they don't just exist in a
+large majority they are actually
+
+ align:start position:0%
+large majority they are actually
+ 
+
+ align:start position:0%
+large majority they are actually
+publicly available you could go to the
+
+ align:start position:0%
+publicly available you could go to the
+ 
+
+ align:start position:0%
+publicly available you could go to the
+national center for biotechnology
+
+ align:start position:0%
+national center for biotechnology
+ 
+
+ align:start position:0%
+national center for biotechnology
+information than ncbi geo
+
+ align:start position:0%
+information than ncbi geo
+ 
+
+ align:start position:0%
+information than ncbi geo
+and pull down any number of these kinds
+
+ align:start position:0%
+and pull down any number of these kinds
+ 
+
+ align:start position:0%
+and pull down any number of these kinds
+of data sets
+
+ align:start position:0%
+of data sets
+ 
+
+ align:start position:0%
+of data sets
+okay you could do it today as for your
+
+ align:start position:0%
+okay you could do it today as for your
+ 
+
+ align:start position:0%
+okay you could do it today as for your
+final project you can go download any of
+
+ align:start position:0%
+final project you can go download any of
+ 
+
+ align:start position:0%
+final project you can go download any of
+600 experiments with the micros already
+
+ align:start position:0%
+600 experiments with the micros already
+ 
+
+ align:start position:0%
+600 experiments with the micros already
+been collected
+
+ align:start position:0%
+been collected
+ 
+
+ align:start position:0%
+been collected
+the only hard part now is to have the
+
+ align:start position:0%
+the only hard part now is to have the
+ 
+
+ align:start position:0%
+the only hard part now is to have the
+interesting question
+
+ align:start position:0%
+interesting question
+ 
+
+ align:start position:0%
+interesting question
+okay you can't just pair something with
+
+ align:start position:0%
+okay you can't just pair something with
+ 
+
+ align:start position:0%
+okay you can't just pair something with
+something else you want to have to
+
+ align:start position:0%
+something else you want to have to
+ 
+
+ align:start position:0%
+something else you want to have to
+actually think about an interesting
+
+ align:start position:0%
+actually think about an interesting
+ 
+
+ align:start position:0%
+actually think about an interesting
+question because the resources in all
+
+ align:start position:0%
+question because the resources in all
+ 
+
+ align:start position:0%
+question because the resources in all
+likelihood are already there to actually
+
+ align:start position:0%
+likelihood are already there to actually
+ 
+
+ align:start position:0%
+likelihood are already there to actually
+try to answer your question whether
+
+ align:start position:0%
+try to answer your question whether
+ 
+
+ align:start position:0%
+try to answer your question whether
+you're interested in circadian rhythms
+
+ align:start position:0%
+you're interested in circadian rhythms
+ 
+
+ align:start position:0%
+you're interested in circadian rhythms
+or fat development or anything
+
+ align:start position:0%
+or fat development or anything
+ 
+
+ align:start position:0%
+or fat development or anything
+that's the hard part now is knowing
+
+ align:start position:0%
+that's the hard part now is knowing
+ 
+
+ align:start position:0%
+that's the hard part now is knowing
+enough biology to actually ask an
+
+ align:start position:0%
+enough biology to actually ask an
+ 
+
+ align:start position:0%
+enough biology to actually ask an
+interesting question in this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such as if you look at the genes in
+
+ align:start position:0%
+such as if you look at the genes in
+ 
+
+ align:start position:0%
+such as if you look at the genes in
+intersection just to give you an idea
+
+ align:start position:0%
+intersection just to give you an idea
+ 
+
+ align:start position:0%
+intersection just to give you an idea
+these winch genes wind is actually a
+
+ align:start position:0%
+these winch genes wind is actually a
+ 
+
+ align:start position:0%
+these winch genes wind is actually a
+hormone that's made
+
+ align:start position:0%
+hormone that's made
+ 
+
+ align:start position:0%
+hormone that's made
+wink genes are actually well known to be
+
+ align:start position:0%
+wink genes are actually well known to be
+ 
+
+ align:start position:0%
+wink genes are actually well known to be
+involved with adipogenesis and they are
+
+ align:start position:0%
+involved with adipogenesis and they are
+ 
+
+ align:start position:0%
+involved with adipogenesis and they are
+actually living in the intersection of
+
+ align:start position:0%
+actually living in the intersection of
+ 
+
+ align:start position:0%
+actually living in the intersection of
+these lists so the worm egl2 which is
+
+ align:start position:0%
+these lists so the worm egl2 which is
+ 
+
+ align:start position:0%
+these lists so the worm egl2 which is
+called wind 7b increases uh the amount
+
+ align:start position:0%
+called wind 7b increases uh the amount
+ 
+
+ align:start position:0%
+called wind 7b increases uh the amount
+of fat if it's knocked out the mouse
+
+ align:start position:0%
+of fat if it's knocked out the mouse
+ 
+
+ align:start position:0%
+of fat if it's knocked out the mouse
+wins 6 and 10a increase with
+
+ align:start position:0%
+wins 6 and 10a increase with
+ 
+
+ align:start position:0%
+wins 6 and 10a increase with
+dysadipogenesis depending on the irs
+
+ align:start position:0%
+dysadipogenesis depending on the irs
+ 
+
+ align:start position:0%
+dysadipogenesis depending on the irs
+knockouts and when 5a and wind 7b are
+
+ align:start position:0%
+knockouts and when 5a and wind 7b are
+ 
+
+ align:start position:0%
+knockouts and when 5a and wind 7b are
+down in progeria so that's an example of
+
+ align:start position:0%
+down in progeria so that's an example of
+ 
+
+ align:start position:0%
+down in progeria so that's an example of
+a gene that lives in the intersection of
+
+ align:start position:0%
+a gene that lives in the intersection of
+ 
+
+ align:start position:0%
+a gene that lives in the intersection of
+these three data sets i'm just amazed
+
+ align:start position:0%
+these three data sets i'm just amazed
+ 
+
+ align:start position:0%
+these three data sets i'm just amazed
+that we got any of these things to
+
+ align:start position:0%
+that we got any of these things to
+ 
+
+ align:start position:0%
+that we got any of these things to
+intersect because they're so different
+
+ align:start position:0%
+intersect because they're so different
+ 
+
+ align:start position:0%
+intersect because they're so different
+three different species we're not even
+
+ align:start position:0%
+three different species we're not even
+ 
+
+ align:start position:0%
+three different species we're not even
+looking at the fat cells here right but
+
+ align:start position:0%
+looking at the fat cells here right but
+ 
+
+ align:start position:0%
+looking at the fat cells here right but
+the progeria kids we're looking at a
+
+ align:start position:0%
+the progeria kids we're looking at a
+ 
+
+ align:start position:0%
+the progeria kids we're looking at a
+fibroblast which is a proxy for the
+
+ align:start position:0%
+fibroblast which is a proxy for the
+ 
+
+ align:start position:0%
+fibroblast which is a proxy for the
+pre-adipocyte which is a proxy for the
+
+ align:start position:0%
+pre-adipocyte which is a proxy for the
+ 
+
+ align:start position:0%
+pre-adipocyte which is a proxy for the
+adipocyte okay but still you can get
+
+ align:start position:0%
+adipocyte okay but still you can get
+ 
+
+ align:start position:0%
+adipocyte okay but still you can get
+some signal this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is this picture is just the same
+
+ align:start position:0%
+this is this picture is just the same
+ 
+
+ align:start position:0%
+this is this picture is just the same
+even my own daughter knows the
+
+ align:start position:0%
+even my own daughter knows the
+ 
+
+ align:start position:0%
+even my own daughter knows the
+difference between a human a mouse and a
+
+ align:start position:0%
+difference between a human a mouse and a
+ 
+
+ align:start position:0%
+difference between a human a mouse and a
+worm
+
+ align:start position:0%
+worm
+ 
+
+ align:start position:0%
+worm
+okay so there's caveats to all of this
+
+ align:start position:0%
+okay so there's caveats to all of this
+ 
+
+ align:start position:0%
+okay so there's caveats to all of this
+so we're doing a lot of this validation
+
+ align:start position:0%
+so we're doing a lot of this validation
+ 
+
+ align:start position:0%
+so we're doing a lot of this validation
+ourselves now in the bioinformatics
+
+ align:start position:0%
+ourselves now in the bioinformatics
+ 
+
+ align:start position:0%
+ourselves now in the bioinformatics
+group over at children's but this is the
+
+ align:start position:0%
+group over at children's but this is the
+ 
+
+ align:start position:0%
+group over at children's but this is the
+point here is integrated biology to me
+
+ align:start position:0%
+point here is integrated biology to me
+ 
+
+ align:start position:0%
+point here is integrated biology to me
+this is where i think a lot of fun is
+
+ align:start position:0%
+this is where i think a lot of fun is
+ 
+
+ align:start position:0%
+this is where i think a lot of fun is
+going to happen for me in the next few
+
+ align:start position:0%
+going to happen for me in the next few
+ 
+
+ align:start position:0%
+going to happen for me in the next few
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+okay we have a lot of these data sets
+
+ align:start position:0%
+okay we have a lot of these data sets
+ 
+
+ align:start position:0%
+okay we have a lot of these data sets
+and now i'm trying to come up with
+
+ align:start position:0%
+and now i'm trying to come up with
+ 
+
+ align:start position:0%
+and now i'm trying to come up with
+interesting questions so i can put these
+
+ align:start position:0%
+interesting questions so i can put these
+ 
+
+ align:start position:0%
+interesting questions so i can put these
+together to try to get a massive handle
+
+ align:start position:0%
+together to try to get a massive handle
+ 
+
+ align:start position:0%
+together to try to get a massive handle
+on these on these processes other people
+
+ align:start position:0%
+on these on these processes other people
+ 
+
+ align:start position:0%
+on these on these processes other people
+are just using one of these data might
+
+ align:start position:0%
+are just using one of these data might
+ 
+
+ align:start position:0%
+are just using one of these data might
+not be able to get a grasp on we've got
+
+ align:start position:0%
+not be able to get a grasp on we've got
+ 
+
+ align:start position:0%
+not be able to get a grasp on we've got
+gene expression we've got proteomic data
+
+ align:start position:0%
+gene expression we've got proteomic data
+ 
+
+ align:start position:0%
+gene expression we've got proteomic data
+we've talked about that we've got genome
+
+ align:start position:0%
+we've talked about that we've got genome
+ 
+
+ align:start position:0%
+we've talked about that we've got genome
+scans so we have uh joel hirschhorn's
+
+ align:start position:0%
+scans so we have uh joel hirschhorn's
+ 
+
+ align:start position:0%
+scans so we have uh joel hirschhorn's
+going to be talking about how you
+
+ align:start position:0%
+going to be talking about how you
+ 
+
+ align:start position:0%
+going to be talking about how you
+actually try to find genes that are
+
+ align:start position:0%
+actually try to find genes that are
+ 
+
+ align:start position:0%
+actually try to find genes that are
+associated with particular phenotype
+
+ align:start position:0%
+associated with particular phenotype
+ 
+
+ align:start position:0%
+associated with particular phenotype
+using snips
+
+ align:start position:0%
+using snips
+ 
+
+ align:start position:0%
+using snips
+they have the clinical measurements okay
+
+ align:start position:0%
+they have the clinical measurements okay
+ 
+
+ align:start position:0%
+they have the clinical measurements okay
+we have all of these data points that
+
+ align:start position:0%
+we have all of these data points that
+ 
+
+ align:start position:0%
+we have all of these data points that
+are collected all of these hospitals
+
+ align:start position:0%
+are collected all of these hospitals
+ 
+
+ align:start position:0%
+are collected all of these hospitals
+we have uh i'll talk about i'll talk
+
+ align:start position:0%
+we have uh i'll talk about i'll talk
+ 
+
+ align:start position:0%
+we have uh i'll talk about i'll talk
+about each of these separately
+
+ align:start position:0%
+about each of these separately
+ 
+
+ align:start position:0%
+about each of these separately
+enumetogenesis is a new technique where
+
+ align:start position:0%
+enumetogenesis is a new technique where
+ 
+
+ align:start position:0%
+enumetogenesis is a new technique where
+it's actually not so new but you could
+
+ align:start position:0%
+it's actually not so new but you could
+ 
+
+ align:start position:0%
+it's actually not so new but you could
+take mice
+
+ align:start position:0%
+take mice
+ 
+
+ align:start position:0%
+take mice
+and give them this particular chemical
+
+ align:start position:0%
+and give them this particular chemical
+ 
+
+ align:start position:0%
+and give them this particular chemical
+ethyl nitrosyl urea and causes mutations
+
+ align:start position:0%
+ethyl nitrosyl urea and causes mutations
+ 
+
+ align:start position:0%
+ethyl nitrosyl urea and causes mutations
+in their gametes so then all of their
+
+ align:start position:0%
+in their gametes so then all of their
+ 
+
+ align:start position:0%
+in their gametes so then all of their
+offspring basically are mutants
+
+ align:start position:0%
+offspring basically are mutants
+ 
+
+ align:start position:0%
+offspring basically are mutants
+and you do this for a couple generations
+
+ align:start position:0%
+and you do this for a couple generations
+ 
+
+ align:start position:0%
+and you do this for a couple generations
+and you find the interesting phenotype
+
+ align:start position:0%
+and you find the interesting phenotype
+ 
+
+ align:start position:0%
+and you find the interesting phenotype
+that you're that wow all of a sudden
+
+ align:start position:0%
+that you're that wow all of a sudden
+ 
+
+ align:start position:0%
+that you're that wow all of a sudden
+this one has diabetes you go back and
+
+ align:start position:0%
+this one has diabetes you go back and
+ 
+
+ align:start position:0%
+this one has diabetes you go back and
+see what do we mutate
+
+ align:start position:0%
+see what do we mutate
+ 
+
+ align:start position:0%
+see what do we mutate
+okay you're basically mutagenizing as
+
+ align:start position:0%
+okay you're basically mutagenizing as
+ 
+
+ align:start position:0%
+okay you're basically mutagenizing as
+much as you can you characterize the
+
+ align:start position:0%
+much as you can you characterize the
+ 
+
+ align:start position:0%
+much as you can you characterize the
+output and then go back to see what
+
+ align:start position:0%
+output and then go back to see what
+ 
+
+ align:start position:0%
+output and then go back to see what
+exactly where do we put the mutation in
+
+ align:start position:0%
+exactly where do we put the mutation in
+ 
+
+ align:start position:0%
+exactly where do we put the mutation in
+that's enu meteogenesis grade rnai we
+
+ align:start position:0%
+that's enu meteogenesis grade rnai we
+ 
+
+ align:start position:0%
+that's enu meteogenesis grade rnai we
+start to talk about with the worm where
+
+ align:start position:0%
+start to talk about with the worm where
+ 
+
+ align:start position:0%
+start to talk about with the worm where
+you basically can just knock out any
+
+ align:start position:0%
+you basically can just knock out any
+ 
+
+ align:start position:0%
+you basically can just knock out any
+particular gene very quickly people are
+
+ align:start position:0%
+particular gene very quickly people are
+ 
+
+ align:start position:0%
+particular gene very quickly people are
+starting to do this with humans and
+
+ align:start position:0%
+starting to do this with humans and
+ 
+
+ align:start position:0%
+starting to do this with humans and
+specifically with mouse models but it's
+
+ align:start position:0%
+specifically with mouse models but it's
+ 
+
+ align:start position:0%
+specifically with mouse models but it's
+already a number of pharmaceutical
+
+ align:start position:0%
+already a number of pharmaceutical
+ 
+
+ align:start position:0%
+already a number of pharmaceutical
+companies within a five mile radius if
+
+ align:start position:0%
+companies within a five mile radius if
+ 
+
+ align:start position:0%
+companies within a five mile radius if
+you're trying to come up with drugs like
+
+ align:start position:0%
+you're trying to come up with drugs like
+ 
+
+ align:start position:0%
+you're trying to come up with drugs like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and of course most importantly the prior
+
+ align:start position:0%
+and of course most importantly the prior
+ 
+
+ align:start position:0%
+and of course most importantly the prior
+biological knowledge this is what's
+
+ align:start position:0%
+biological knowledge this is what's
+ 
+
+ align:start position:0%
+biological knowledge this is what's
+going to drive the interesting questions
+
+ align:start position:0%
+going to drive the interesting questions
+ 
+
+ align:start position:0%
+going to drive the interesting questions
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about that so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to talk about something
+
+ align:start position:0%
+i'm going to talk about something
+ 
+
+ align:start position:0%
+i'm going to talk about something
+just to bring this home so we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can talk about at least you can see
+
+ align:start position:0%
+we can talk about at least you can see
+ 
+
+ align:start position:0%
+we can talk about at least you can see
+how easy it is to actually do this
+
+ align:start position:0%
+how easy it is to actually do this
+ 
+
+ align:start position:0%
+how easy it is to actually do this
+okay let me skip a couple slides here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah we can actually talk about
+
+ align:start position:0%
+okay so yeah we can actually talk about
+ 
+
+ align:start position:0%
+okay so yeah we can actually talk about
+some of this
+
+ align:start position:0%
+some of this
+ 
+
+ align:start position:0%
+some of this
+so let's say you're interested in doing
+
+ align:start position:0%
+so let's say you're interested in doing
+ 
+
+ align:start position:0%
+so let's say you're interested in doing
+some of this for a final project okay
+
+ align:start position:0%
+some of this for a final project okay
+ 
+
+ align:start position:0%
+some of this for a final project okay
+that you want to actually put some of
+
+ align:start position:0%
+that you want to actually put some of
+ 
+
+ align:start position:0%
+that you want to actually put some of
+these data sets together
+
+ align:start position:0%
+these data sets together
+ 
+
+ align:start position:0%
+these data sets together
+there are quite a number of sources
+
+ align:start position:0%
+there are quite a number of sources
+ 
+
+ align:start position:0%
+there are quite a number of sources
+where you can get web
+
+ align:start position:0%
+where you can get web
+ 
+
+ align:start position:0%
+where you can get web
+get microarray data and other genome
+
+ align:start position:0%
+get microarray data and other genome
+ 
+
+ align:start position:0%
+get microarray data and other genome
+size data today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you see some things in the
+
+ align:start position:0%
+and if you see some things in the
+ 
+
+ align:start position:0%
+and if you see some things in the
+description that you're actually
+
+ align:start position:0%
+description that you're actually
+ 
+
+ align:start position:0%
+description that you're actually
+biologically interested in you might be
+
+ align:start position:0%
+biologically interested in you might be
+ 
+
+ align:start position:0%
+biologically interested in you might be
+able to run with that for a final
+
+ align:start position:0%
+able to run with that for a final
+ 
+
+ align:start position:0%
+able to run with that for a final
+project i just want to point out a few
+
+ align:start position:0%
+project i just want to point out a few
+ 
+
+ align:start position:0%
+project i just want to point out a few
+of these data sources
+
+ align:start position:0%
+of these data sources
+ 
+
+ align:start position:0%
+of these data sources
+and then talk about one way how you can
+
+ align:start position:0%
+and then talk about one way how you can
+ 
+
+ align:start position:0%
+and then talk about one way how you can
+put this together using a web even just
+
+ align:start position:0%
+put this together using a web even just
+ 
+
+ align:start position:0%
+put this together using a web even just
+using a web browser
+
+ align:start position:0%
+using a web browser
+ 
+
+ align:start position:0%
+using a web browser
+so the cardiogenomics program is a
+
+ align:start position:0%
+so the cardiogenomics program is a
+ 
+
+ align:start position:0%
+so the cardiogenomics program is a
+source where i think there's over 150
+
+ align:start position:0%
+source where i think there's over 150
+ 
+
+ align:start position:0%
+source where i think there's over 150
+microarrays now
+
+ align:start position:0%
+microarrays now
+ 
+
+ align:start position:0%
+microarrays now
+this is over the headquarters of this is
+
+ align:start position:0%
+this is over the headquarters of this is
+ 
+
+ align:start position:0%
+this is over the headquarters of this is
+over at the bethesda deaconess across
+
+ align:start position:0%
+over at the bethesda deaconess across
+ 
+
+ align:start position:0%
+over at the bethesda deaconess across
+the street they have mass models of
+
+ align:start position:0%
+the street they have mass models of
+ 
+
+ align:start position:0%
+the street they have mass models of
+cardiac development so basically they
+
+ align:start position:0%
+cardiac development so basically they
+ 
+
+ align:start position:0%
+cardiac development so basically they
+have embryos and they have sections of
+
+ align:start position:0%
+have embryos and they have sections of
+ 
+
+ align:start position:0%
+have embryos and they have sections of
+their heart and basically all the genes
+
+ align:start position:0%
+their heart and basically all the genes
+ 
+
+ align:start position:0%
+their heart and basically all the genes
+are turned on and off at different parts
+
+ align:start position:0%
+are turned on and off at different parts
+ 
+
+ align:start position:0%
+are turned on and off at different parts
+during development
+
+ align:start position:0%
+during development
+ 
+
+ align:start position:0%
+during development
+there's all sorts of different
+
+ align:start position:0%
+there's all sorts of different
+ 
+
+ align:start position:0%
+there's all sorts of different
+components of cardiac growth so for
+
+ align:start position:0%
+components of cardiac growth so for
+ 
+
+ align:start position:0%
+components of cardiac growth so for
+example people know that if you one
+
+ align:start position:0%
+example people know that if you one
+ 
+
+ align:start position:0%
+example people know that if you one
+pathway or another pathway is involved
+
+ align:start position:0%
+pathway or another pathway is involved
+ 
+
+ align:start position:0%
+pathway or another pathway is involved
+in heart failure they have mouse models
+
+ align:start position:0%
+in heart failure they have mouse models
+ 
+
+ align:start position:0%
+in heart failure they have mouse models
+where those components are already
+
+ align:start position:0%
+where those components are already
+ 
+
+ align:start position:0%
+where those components are already
+knocked out
+
+ align:start position:0%
+knocked out
+ 
+
+ align:start position:0%
+knocked out
+they have a bunch of measures made in
+
+ align:start position:0%
+they have a bunch of measures made in
+ 
+
+ align:start position:0%
+they have a bunch of measures made in
+time series so they take a normal mice
+
+ align:start position:0%
+time series so they take a normal mice
+ 
+
+ align:start position:0%
+time series so they take a normal mice
+and they put them in this tank to swim
+
+ align:start position:0%
+and they put them in this tank to swim
+ 
+
+ align:start position:0%
+and they put them in this tank to swim
+and make them practice swimming certain
+
+ align:start position:0%
+and make them practice swimming certain
+ 
+
+ align:start position:0%
+and make them practice swimming certain
+number of hours for weeks then look at
+
+ align:start position:0%
+number of hours for weeks then look at
+ 
+
+ align:start position:0%
+number of hours for weeks then look at
+their hearts and this is what swimming
+
+ align:start position:0%
+their hearts and this is what swimming
+ 
+
+ align:start position:0%
+their hearts and this is what swimming
+does your heart for example they have
+
+ align:start position:0%
+does your heart for example they have
+ 
+
+ align:start position:0%
+does your heart for example they have
+those lists of genes available today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these slides are going to be online so
+
+ align:start position:0%
+these slides are going to be online so
+ 
+
+ align:start position:0%
+these slides are going to be online so
+you don't have to copy down every single
+
+ align:start position:0%
+you don't have to copy down every single
+ 
+
+ align:start position:0%
+you don't have to copy down every single
+uh url but if you just even write down
+
+ align:start position:0%
+uh url but if you just even write down
+ 
+
+ align:start position:0%
+uh url but if you just even write down
+the heading then you know which one to
+
+ align:start position:0%
+the heading then you know which one to
+ 
+
+ align:start position:0%
+the heading then you know which one to
+look for
+
+ align:start position:0%
+look for
+ 
+
+ align:start position:0%
+look for
+the whitehead institute obviously mother
+
+ align:start position:0%
+the whitehead institute obviously mother
+ 
+
+ align:start position:0%
+the whitehead institute obviously mother
+lode of diesel race okay at least 12
+
+ align:start position:0%
+lode of diesel race okay at least 12
+ 
+
+ align:start position:0%
+lode of diesel race okay at least 12
+maybe probably 14 publications now
+
+ align:start position:0%
+maybe probably 14 publications now
+ 
+
+ align:start position:0%
+maybe probably 14 publications now
+many different types of cancer that's
+
+ align:start position:0%
+many different types of cancer that's
+ 
+
+ align:start position:0%
+many different types of cancer that's
+their primary focus there a lot of
+
+ align:start position:0%
+their primary focus there a lot of
+ 
+
+ align:start position:0%
+their primary focus there a lot of
+clinical measurements with some i mean a
+
+ align:start position:0%
+clinical measurements with some i mean a
+ 
+
+ align:start position:0%
+clinical measurements with some i mean a
+lot of these are clinical samples but
+
+ align:start position:0%
+lot of these are clinical samples but
+ 
+
+ align:start position:0%
+lot of these are clinical samples but
+they might have one or two columns of
+
+ align:start position:0%
+they might have one or two columns of
+ 
+
+ align:start position:0%
+they might have one or two columns of
+clinical measurements like once it's a
+
+ align:start position:0%
+clinical measurements like once it's a
+ 
+
+ align:start position:0%
+clinical measurements like once it's a
+smoker was this a non-smoker
+
+ align:start position:0%
+smoker was this a non-smoker
+ 
+
+ align:start position:0%
+smoker was this a non-smoker
+that kind of thing how long does this
+
+ align:start position:0%
+that kind of thing how long does this
+ 
+
+ align:start position:0%
+that kind of thing how long does this
+patient relapse and not relapse but you
+
+ align:start position:0%
+patient relapse and not relapse but you
+ 
+
+ align:start position:0%
+patient relapse and not relapse but you
+got leukemias you got solid tumors here
+
+ align:start position:0%
+got leukemias you got solid tumors here
+ 
+
+ align:start position:0%
+got leukemias you got solid tumors here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+brain cancers things like that are in
+
+ align:start position:0%
+brain cancers things like that are in
+ 
+
+ align:start position:0%
+brain cancers things like that are in
+this data set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dc children's or children's national
+
+ align:start position:0%
+dc children's or children's national
+ 
+
+ align:start position:0%
+dc children's or children's national
+medical center
+
+ align:start position:0%
+medical center
+ 
+
+ align:start position:0%
+medical center
+500 arrays for many interesting human
+
+ align:start position:0%
+500 arrays for many interesting human
+ 
+
+ align:start position:0%
+500 arrays for many interesting human
+diseases muscular dystrophy
+
+ align:start position:0%
+diseases muscular dystrophy
+ 
+
+ align:start position:0%
+diseases muscular dystrophy
+dermatomyositis so it's rare types of
+
+ align:start position:0%
+dermatomyositis so it's rare types of
+ 
+
+ align:start position:0%
+dermatomyositis so it's rare types of
+rheumatological things heart failure as
+
+ align:start position:0%
+rheumatological things heart failure as
+ 
+
+ align:start position:0%
+rheumatological things heart failure as
+well as mouse rat and dog models of
+
+ align:start position:0%
+well as mouse rat and dog models of
+ 
+
+ align:start position:0%
+well as mouse rat and dog models of
+spinal cord injury if you want to see
+
+ align:start position:0%
+spinal cord injury if you want to see
+ 
+
+ align:start position:0%
+spinal cord injury if you want to see
+what are the similarities and
+
+ align:start position:0%
+what are the similarities and
+ 
+
+ align:start position:0%
+what are the similarities and
+differences there pulmonary disease
+
+ align:start position:0%
+differences there pulmonary disease
+ 
+
+ align:start position:0%
+differences there pulmonary disease
+including asthma and heart failure i
+
+ align:start position:0%
+including asthma and heart failure i
+ 
+
+ align:start position:0%
+including asthma and heart failure i
+mentioned heart failure twice there
+
+ align:start position:0%
+mentioned heart failure twice there
+ 
+
+ align:start position:0%
+mentioned heart failure twice there
+so that's dc children's and johns
+
+ align:start position:0%
+so that's dc children's and johns
+ 
+
+ align:start position:0%
+so that's dc children's and johns
+hopkins the human gene expression index
+
+ align:start position:0%
+hopkins the human gene expression index
+ 
+
+ align:start position:0%
+hopkins the human gene expression index
+i think it's the best is brigham and
+
+ align:start position:0%
+i think it's the best is brigham and
+ 
+
+ align:start position:0%
+i think it's the best is brigham and
+women's 121 microarrays just from normal
+
+ align:start position:0%
+women's 121 microarrays just from normal
+ 
+
+ align:start position:0%
+women's 121 microarrays just from normal
+tissues 19 normal human tissues it's
+
+ align:start position:0%
+tissues 19 normal human tissues it's
+ 
+
+ align:start position:0%
+tissues 19 normal human tissues it's
+also an interesting list to think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stanford's microwave is probably the
+
+ align:start position:0%
+stanford's microwave is probably the
+ 
+
+ align:start position:0%
+stanford's microwave is probably the
+largest besides the
+
+ align:start position:0%
+largest besides the
+ 
+
+ align:start position:0%
+largest besides the
+geo which we'll talk about a second
+
+ align:start position:0%
+geo which we'll talk about a second
+ 
+
+ align:start position:0%
+geo which we'll talk about a second
+stanford has probably close to 4 000
+
+ align:start position:0%
+stanford has probably close to 4 000
+ 
+
+ align:start position:0%
+stanford has probably close to 4 000
+arrays now measure across 11 species
+
+ align:start position:0%
+arrays now measure across 11 species
+ 
+
+ align:start position:0%
+arrays now measure across 11 species
+covering more than 80 publications
+
+ align:start position:0%
+covering more than 80 publications
+ 
+
+ align:start position:0%
+covering more than 80 publications
+okay many different fields most of which
+
+ align:start position:0%
+okay many different fields most of which
+ 
+
+ align:start position:0%
+okay many different fields most of which
+are yeast by the whole bunch of human
+
+ align:start position:0%
+are yeast by the whole bunch of human
+ 
+
+ align:start position:0%
+are yeast by the whole bunch of human
+ones as well
+
+ align:start position:0%
+ones as well
+ 
+
+ align:start position:0%
+ones as well
+the national ncbi gl
+
+ align:start position:0%
+the national ncbi gl
+ 
+
+ align:start position:0%
+the national ncbi gl
+it's basically right next to pubmed now
+
+ align:start position:0%
+it's basically right next to pubmed now
+ 
+
+ align:start position:0%
+it's basically right next to pubmed now
+it's the same website
+
+ align:start position:0%
+it's the same website
+ 
+
+ align:start position:0%
+it's the same website
+over 8 000 arrays from over 100
+
+ align:start position:0%
+over 8 000 arrays from over 100
+ 
+
+ align:start position:0%
+over 8 000 arrays from over 100
+different types of microarrays okay
+
+ align:start position:0%
+different types of microarrays okay
+ 
+
+ align:start position:0%
+different types of microarrays okay
+never mind how many experiments their
+
+ align:start position:0%
+never mind how many experiments their
+ 
+
+ align:start position:0%
+never mind how many experiments their
+database can handle over 100 different
+
+ align:start position:0%
+database can handle over 100 different
+ 
+
+ align:start position:0%
+database can handle over 100 different
+companies 100 different
+
+ align:start position:0%
+companies 100 different
+ 
+
+ align:start position:0%
+companies 100 different
+actual microwave products they can
+
+ align:start position:0%
+actual microwave products they can
+ 
+
+ align:start position:0%
+actual microwave products they can
+integrate across all of these
+
+ align:start position:0%
+integrate across all of these
+ 
+
+ align:start position:0%
+integrate across all of these
+t-rex is from
+
+ align:start position:0%
+t-rex is from
+ 
+
+ align:start position:0%
+t-rex is from
+tiger which is the institute for genome
+
+ align:start position:0%
+tiger which is the institute for genome
+ 
+
+ align:start position:0%
+tiger which is the institute for genome
+research over in gaithersburg and
+
+ align:start position:0%
+research over in gaithersburg and
+ 
+
+ align:start position:0%
+research over in gaithersburg and
+maryland outside of nih
+
+ align:start position:0%
+maryland outside of nih
+ 
+
+ align:start position:0%
+maryland outside of nih
+500 600 arrays for mouse and mouse and
+
+ align:start position:0%
+500 600 arrays for mouse and mouse and
+ 
+
+ align:start position:0%
+500 600 arrays for mouse and mouse and
+wrap models of sleep infection
+
+ align:start position:0%
+wrap models of sleep infection
+ 
+
+ align:start position:0%
+wrap models of sleep infection
+hypertension pulmonary disease
+
+ align:start position:0%
+hypertension pulmonary disease
+ 
+
+ align:start position:0%
+hypertension pulmonary disease
+it's all like for example if you're
+
+ align:start position:0%
+it's all like for example if you're
+ 
+
+ align:start position:0%
+it's all like for example if you're
+interested in asthma and you want to see
+
+ align:start position:0%
+interested in asthma and you want to see
+ 
+
+ align:start position:0%
+interested in asthma and you want to see
+differences between human asthma and the
+
+ align:start position:0%
+differences between human asthma and the
+ 
+
+ align:start position:0%
+differences between human asthma and the
+mouse model the data is there today
+
+ align:start position:0%
+mouse model the data is there today
+ 
+
+ align:start position:0%
+mouse model the data is there today
+i will guarantee you no one else has
+
+ align:start position:0%
+i will guarantee you no one else has
+ 
+
+ align:start position:0%
+i will guarantee you no one else has
+done that intersection okay if you find
+
+ align:start position:0%
+done that intersection okay if you find
+ 
+
+ align:start position:0%
+done that intersection okay if you find
+some interesting genes
+
+ align:start position:0%
+some interesting genes
+ 
+
+ align:start position:0%
+some interesting genes
+that you think might code for proteins
+
+ align:start position:0%
+that you think might code for proteins
+ 
+
+ align:start position:0%
+that you think might code for proteins
+that might be in the blood and you can
+
+ align:start position:0%
+that might be in the blood and you can
+ 
+
+ align:start position:0%
+that might be in the blood and you can
+use that as a measurement you can get
+
+ align:start position:0%
+use that as a measurement you can get
+ 
+
+ align:start position:0%
+use that as a measurement you can get
+some interesting part one of any
+
+ align:start position:0%
+some interesting part one of any
+ 
+
+ align:start position:0%
+some interesting part one of any
+collaborator in the longwood area to
+
+ align:start position:0%
+collaborator in the longwood area to
+ 
+
+ align:start position:0%
+collaborator in the longwood area to
+actually measure this in the blood
+
+ align:start position:0%
+actually measure this in the blood
+ 
+
+ align:start position:0%
+actually measure this in the blood
+that's it you have a finding right there
+
+ align:start position:0%
+that's it you have a finding right there
+ 
+
+ align:start position:0%
+that's it you have a finding right there
+okay because the data is there hardly
+
+ align:start position:0%
+okay because the data is there hardly
+ 
+
+ align:start position:0%
+okay because the data is there hardly
+anyone knows how to intersect these
+
+ align:start position:0%
+anyone knows how to intersect these
+ 
+
+ align:start position:0%
+anyone knows how to intersect these
+things at all
+
+ align:start position:0%
+things at all
+ 
+
+ align:start position:0%
+things at all
+and so what i'm going to talk about here
+
+ align:start position:0%
+and so what i'm going to talk about here
+ 
+
+ align:start position:0%
+and so what i'm going to talk about here
+for the last few minutes is this concept
+
+ align:start position:0%
+for the last few minutes is this concept
+ 
+
+ align:start position:0%
+for the last few minutes is this concept
+of discovery portal okay so what do i
+
+ align:start position:0%
+of discovery portal okay so what do i
+ 
+
+ align:start position:0%
+of discovery portal okay so what do i
+mean by that let me skip this part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we start with in vivo right experiments
+
+ align:start position:0%
+we start with in vivo right experiments
+ 
+
+ align:start position:0%
+we start with in vivo right experiments
+done in humans and mice then we had in
+
+ align:start position:0%
+done in humans and mice then we had in
+ 
+
+ align:start position:0%
+done in humans and mice then we had in
+vitro and cell culture now we have in
+
+ align:start position:0%
+vitro and cell culture now we have in
+ 
+
+ align:start position:0%
+vitro and cell culture now we have in
+http okay so here's an idea okay here's
+
+ align:start position:0%
+http okay so here's an idea okay here's
+ 
+
+ align:start position:0%
+http okay so here's an idea okay here's
+how you can go from uh actual thought to
+
+ align:start position:0%
+how you can go from uh actual thought to
+ 
+
+ align:start position:0%
+how you can go from uh actual thought to
+a pretty well established hypothesis
+
+ align:start position:0%
+a pretty well established hypothesis
+ 
+
+ align:start position:0%
+a pretty well established hypothesis
+without even leaving your web browser
+
+ align:start position:0%
+without even leaving your web browser
+ 
+
+ align:start position:0%
+without even leaving your web browser
+because all of these tools are available
+
+ align:start position:0%
+because all of these tools are available
+ 
+
+ align:start position:0%
+because all of these tools are available
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+over the next maybe 15 slides i'm going
+
+ align:start position:0%
+over the next maybe 15 slides i'm going
+ 
+
+ align:start position:0%
+over the next maybe 15 slides i'm going
+to flip through them pretty quickly i'm
+
+ align:start position:0%
+to flip through them pretty quickly i'm
+ 
+
+ align:start position:0%
+to flip through them pretty quickly i'm
+going to cover a number of different
+
+ align:start position:0%
+going to cover a number of different
+ 
+
+ align:start position:0%
+going to cover a number of different
+databases where you could get all sorts
+
+ align:start position:0%
+databases where you could get all sorts
+ 
+
+ align:start position:0%
+databases where you could get all sorts
+of inspirational ideas from so let's
+
+ align:start position:0%
+of inspirational ideas from so let's
+ 
+
+ align:start position:0%
+of inspirational ideas from so let's
+start with an interest move to a rat
+
+ align:start position:0%
+start with an interest move to a rat
+ 
+
+ align:start position:0%
+start with an interest move to a rat
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+we're going to cover qtls while we're
+
+ align:start position:0%
+we're going to cover qtls while we're
+ 
+
+ align:start position:0%
+we're going to cover qtls while we're
+there and physiological findings go to a
+
+ align:start position:0%
+there and physiological findings go to a
+ 
+
+ align:start position:0%
+there and physiological findings go to a
+rat genome map go to multiple species
+
+ align:start position:0%
+rat genome map go to multiple species
+ 
+
+ align:start position:0%
+rat genome map go to multiple species
+expression data and then end with the
+
+ align:start position:0%
+expression data and then end with the
+ 
+
+ align:start position:0%
+expression data and then end with the
+hypothesis here okay this is live you
+
+ align:start position:0%
+hypothesis here okay this is live you
+ 
+
+ align:start position:0%
+hypothesis here okay this is live you
+could do this yourself today
+
+ align:start position:0%
+could do this yourself today
+ 
+
+ align:start position:0%
+could do this yourself today
+we're going to start a website called
+
+ align:start position:0%
+we're going to start a website called
+ 
+
+ align:start position:0%
+we're going to start a website called
+fizzgen okay some of us in the room know
+
+ align:start position:0%
+fizzgen okay some of us in the room know
+ 
+
+ align:start position:0%
+fizzgen okay some of us in the room know
+about this this is uh at the uh this is
+
+ align:start position:0%
+about this this is uh at the uh this is
+ 
+
+ align:start position:0%
+about this this is uh at the uh this is
+a medical medical college of wisconsin
+
+ align:start position:0%
+a medical medical college of wisconsin
+ 
+
+ align:start position:0%
+a medical medical college of wisconsin
+what these guys do is they have a huge
+
+ align:start position:0%
+what these guys do is they have a huge
+ 
+
+ align:start position:0%
+what these guys do is they have a huge
+pipeline of things they do to mice and
+
+ align:start position:0%
+pipeline of things they do to mice and
+ 
+
+ align:start position:0%
+pipeline of things they do to mice and
+rats to measure things uh measure all
+
+ align:start position:0%
+rats to measure things uh measure all
+ 
+
+ align:start position:0%
+rats to measure things uh measure all
+sorts of different quantities how much
+
+ align:start position:0%
+sorts of different quantities how much
+ 
+
+ align:start position:0%
+sorts of different quantities how much
+does this rat pee versus that rat how
+
+ align:start position:0%
+does this rat pee versus that rat how
+ 
+
+ align:start position:0%
+does this rat pee versus that rat how
+much does this mouse breathe compared to
+
+ align:start position:0%
+much does this mouse breathe compared to
+ 
+
+ align:start position:0%
+much does this mouse breathe compared to
+this mouse etcetera etcetera and they
+
+ align:start position:0%
+this mouse etcetera etcetera and they
+ 
+
+ align:start position:0%
+this mouse etcetera etcetera and they
+have tables of all this data publicly
+
+ align:start position:0%
+have tables of all this data publicly
+ 
+
+ align:start position:0%
+have tables of all this data publicly
+available
+
+ align:start position:0%
+available
+ 
+
+ align:start position:0%
+available
+so if you go to fizzgen if you click on
+
+ align:start position:0%
+so if you go to fizzgen if you click on
+ 
+
+ align:start position:0%
+so if you go to fizzgen if you click on
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+if you click on animal model so genotype
+
+ align:start position:0%
+if you click on animal model so genotype
+ 
+
+ align:start position:0%
+if you click on animal model so genotype
+information for all strains
+
+ align:start position:0%
+information for all strains
+ 
+
+ align:start position:0%
+information for all strains
+if i scroll down a little
+
+ align:start position:0%
+if i scroll down a little
+ 
+
+ align:start position:0%
+if i scroll down a little
+i see a whole bunch of the rats
+
+ align:start position:0%
+i see a whole bunch of the rats
+ 
+
+ align:start position:0%
+i see a whole bunch of the rats
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i might remember because i went to
+
+ align:start position:0%
+now i might remember because i went to
+ 
+
+ align:start position:0%
+now i might remember because i went to
+the diabetes association conference last
+
+ align:start position:0%
+the diabetes association conference last
+ 
+
+ align:start position:0%
+the diabetes association conference last
+year i remember hearing that the brown
+
+ align:start position:0%
+year i remember hearing that the brown
+ 
+
+ align:start position:0%
+year i remember hearing that the brown
+norway has some problem with diabetes
+
+ align:start position:0%
+norway has some problem with diabetes
+ 
+
+ align:start position:0%
+norway has some problem with diabetes
+okay i might not have even gone to the
+
+ align:start position:0%
+okay i might not have even gone to the
+ 
+
+ align:start position:0%
+okay i might not have even gone to the
+seminars on the brown or but everyone
+
+ align:start position:0%
+seminars on the brown or but everyone
+ 
+
+ align:start position:0%
+seminars on the brown or but everyone
+kept talking about brown noir brown
+
+ align:start position:0%
+kept talking about brown noir brown
+ 
+
+ align:start position:0%
+kept talking about brown noir brown
+norway i remember brown orange has a
+
+ align:start position:0%
+norway i remember brown orange has a
+ 
+
+ align:start position:0%
+norway i remember brown orange has a
+problem with the seed let's go click on
+
+ align:start position:0%
+problem with the seed let's go click on
+ 
+
+ align:start position:0%
+problem with the seed let's go click on
+the brown norway strain report
+
+ align:start position:0%
+the brown norway strain report
+ 
+
+ align:start position:0%
+the brown norway strain report
+scroll down this is the bn or brown
+
+ align:start position:0%
+scroll down this is the bn or brown
+ 
+
+ align:start position:0%
+scroll down this is the bn or brown
+norway and i can see yes it does it has
+
+ align:start position:0%
+norway and i can see yes it does it has
+ 
+
+ align:start position:0%
+norway and i can see yes it does it has
+diabetes on here diabetes qtl so what is
+
+ align:start position:0%
+diabetes on here diabetes qtl so what is
+ 
+
+ align:start position:0%
+diabetes on here diabetes qtl so what is
+a qtl
+
+ align:start position:0%
+a qtl
+ 
+
+ align:start position:0%
+a qtl
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+got the rat and it's got its own genome
+
+ align:start position:0%
+got the rat and it's got its own genome
+ 
+
+ align:start position:0%
+got the rat and it's got its own genome
+like any other creature
+
+ align:start position:0%
+like any other creature
+ 
+
+ align:start position:0%
+like any other creature
+and what the qtl is is a quantitative
+
+ align:start position:0%
+and what the qtl is is a quantitative
+ 
+
+ align:start position:0%
+and what the qtl is is a quantitative
+trait loci so a particular portion
+
+ align:start position:0%
+trait loci so a particular portion
+ 
+
+ align:start position:0%
+trait loci so a particular portion
+of a particular chromosome
+
+ align:start position:0%
+of a particular chromosome
+ 
+
+ align:start position:0%
+of a particular chromosome
+appears to be statistically
+
+ align:start position:0%
+appears to be statistically
+ 
+
+ align:start position:0%
+appears to be statistically
+significantly associated with a
+
+ align:start position:0%
+significantly associated with a
+ 
+
+ align:start position:0%
+significantly associated with a
+particular phenotypic measurement
+
+ align:start position:0%
+particular phenotypic measurement
+ 
+
+ align:start position:0%
+particular phenotypic measurement
+that's a quantitative trait loci so in
+
+ align:start position:0%
+that's a quantitative trait loci so in
+ 
+
+ align:start position:0%
+that's a quantitative trait loci so in
+other words this particular region which
+
+ align:start position:0%
+other words this particular region which
+ 
+
+ align:start position:0%
+other words this particular region which
+we're going to look at in a second on
+
+ align:start position:0%
+we're going to look at in a second on
+ 
+
+ align:start position:0%
+we're going to look at in a second on
+chromosome 2 is statistically associated
+
+ align:start position:0%
+chromosome 2 is statistically associated
+ 
+
+ align:start position:0%
+chromosome 2 is statistically associated
+with the insulin level
+
+ align:start position:0%
+with the insulin level
+ 
+
+ align:start position:0%
+with the insulin level
+the fasting insulin level of a rat
+
+ align:start position:0%
+the fasting insulin level of a rat
+ 
+
+ align:start position:0%
+the fasting insulin level of a rat
+okay so notice if you have one version
+
+ align:start position:0%
+okay so notice if you have one version
+ 
+
+ align:start position:0%
+okay so notice if you have one version
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+you might have a low fasting insulin if
+
+ align:start position:0%
+you might have a low fasting insulin if
+ 
+
+ align:start position:0%
+you might have a low fasting insulin if
+you have another version you have a high
+
+ align:start position:0%
+you have another version you have a high
+ 
+
+ align:start position:0%
+you have another version you have a high
+fashion level but something in this
+
+ align:start position:0%
+fashion level but something in this
+ 
+
+ align:start position:0%
+fashion level but something in this
+region of a chromosome
+
+ align:start position:0%
+region of a chromosome
+ 
+
+ align:start position:0%
+region of a chromosome
+is associated okay we're not at the gene
+
+ align:start position:0%
+is associated okay we're not at the gene
+ 
+
+ align:start position:0%
+is associated okay we're not at the gene
+level yet but we're just in a region of
+
+ align:start position:0%
+level yet but we're just in a region of
+ 
+
+ align:start position:0%
+level yet but we're just in a region of
+a chromosome there's a starting point an
+
+ align:start position:0%
+a chromosome there's a starting point an
+ 
+
+ align:start position:0%
+a chromosome there's a starting point an
+ending point of this chromosome and some
+
+ align:start position:0%
+ending point of this chromosome and some
+ 
+
+ align:start position:0%
+ending point of this chromosome and some
+piece in the middle is associated
+
+ align:start position:0%
+piece in the middle is associated
+ 
+
+ align:start position:0%
+piece in the middle is associated
+there's all sorts of other measurements
+
+ align:start position:0%
+there's all sorts of other measurements
+ 
+
+ align:start position:0%
+there's all sorts of other measurements
+here you got x-ray hypersensitivity what
+
+ align:start position:0%
+here you got x-ray hypersensitivity what
+ 
+
+ align:start position:0%
+here you got x-ray hypersensitivity what
+does that mean well something on this
+
+ align:start position:0%
+does that mean well something on this
+ 
+
+ align:start position:0%
+does that mean well something on this
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+of chromosome one
+
+ align:start position:0%
+of chromosome one
+ 
+
+ align:start position:0%
+of chromosome one
+means you get more sensitive to x-rays
+
+ align:start position:0%
+means you get more sensitive to x-rays
+ 
+
+ align:start position:0%
+means you get more sensitive to x-rays
+okay you think about how esoteric these
+
+ align:start position:0%
+okay you think about how esoteric these
+ 
+
+ align:start position:0%
+okay you think about how esoteric these
+measurements are okay if you're
+
+ align:start position:0%
+measurements are okay if you're
+ 
+
+ align:start position:0%
+measurements are okay if you're
+interested in radiation effects there's
+
+ align:start position:0%
+interested in radiation effects there's
+ 
+
+ align:start position:0%
+interested in radiation effects there's
+your measure right there arthritis
+
+ align:start position:0%
+your measure right there arthritis
+ 
+
+ align:start position:0%
+your measure right there arthritis
+severity blood pressure body weight
+
+ align:start position:0%
+severity blood pressure body weight
+ 
+
+ align:start position:0%
+severity blood pressure body weight
+blood pressure blood pressure
+
+ align:start position:0%
+blood pressure blood pressure
+ 
+
+ align:start position:0%
+blood pressure blood pressure
+they're all sitting there waiting to be
+
+ align:start position:0%
+they're all sitting there waiting to be
+ 
+
+ align:start position:0%
+they're all sitting there waiting to be
+tapped into okay no one has enough time
+
+ align:start position:0%
+tapped into okay no one has enough time
+ 
+
+ align:start position:0%
+tapped into okay no one has enough time
+to look at every single one of these but
+
+ align:start position:0%
+to look at every single one of these but
+ 
+
+ align:start position:0%
+to look at every single one of these but
+we're mandated by nih to just put them
+
+ align:start position:0%
+we're mandated by nih to just put them
+ 
+
+ align:start position:0%
+we're mandated by nih to just put them
+out on the internet for people like you
+
+ align:start position:0%
+out on the internet for people like you
+ 
+
+ align:start position:0%
+out on the internet for people like you
+to study okay if you're interested in
+
+ align:start position:0%
+to study okay if you're interested in
+ 
+
+ align:start position:0%
+to study okay if you're interested in
+blood pressure there's three qtls right
+
+ align:start position:0%
+blood pressure there's three qtls right
+ 
+
+ align:start position:0%
+blood pressure there's three qtls right
+there that people by chance but people
+
+ align:start position:0%
+there that people by chance but people
+ 
+
+ align:start position:0%
+there that people by chance but people
+probably never even looked at
+
+ align:start position:0%
+probably never even looked at
+ 
+
+ align:start position:0%
+probably never even looked at
+let's click on this particular qtl to
+
+ align:start position:0%
+let's click on this particular qtl to
+ 
+
+ align:start position:0%
+let's click on this particular qtl to
+see what it looks like
+
+ align:start position:0%
+see what it looks like
+ 
+
+ align:start position:0%
+see what it looks like
+here's the name of the qtl nidd gk2
+
+ align:start position:0%
+here's the name of the qtl nidd gk2
+ 
+
+ align:start position:0%
+here's the name of the qtl nidd gk2
+it's in the brown norway
+
+ align:start position:0%
+it's in the brown norway
+ 
+
+ align:start position:0%
+it's in the brown norway
+and here's the marker for this
+
+ align:start position:0%
+and here's the marker for this
+ 
+
+ align:start position:0%
+and here's the marker for this
+particular peak so a marker
+
+ align:start position:0%
+particular peak so a marker
+ 
+
+ align:start position:0%
+particular peak so a marker
+means this is a unique sequence in the
+
+ align:start position:0%
+means this is a unique sequence in the
+ 
+
+ align:start position:0%
+means this is a unique sequence in the
+chromosome that it's going to tell me
+
+ align:start position:0%
+chromosome that it's going to tell me
+ 
+
+ align:start position:0%
+chromosome that it's going to tell me
+whether i have the one version of this
+
+ align:start position:0%
+whether i have the one version of this
+ 
+
+ align:start position:0%
+whether i have the one version of this
+or the other
+
+ align:start position:0%
+or the other
+ 
+
+ align:start position:0%
+or the other
+let me click on that marker
+
+ align:start position:0%
+let me click on that marker
+ 
+
+ align:start position:0%
+let me click on that marker
+d2 lux 23 and here is the pcr test i
+
+ align:start position:0%
+d2 lux 23 and here is the pcr test i
+ 
+
+ align:start position:0%
+d2 lux 23 and here is the pcr test i
+would need to do
+
+ align:start position:0%
+would need to do
+ 
+
+ align:start position:0%
+would need to do
+in the rat to tell me do i have the one
+
+ align:start position:0%
+in the rat to tell me do i have the one
+ 
+
+ align:start position:0%
+in the rat to tell me do i have the one
+letter or the other letter okay or in
+
+ align:start position:0%
+letter or the other letter okay or in
+ 
+
+ align:start position:0%
+letter or the other letter okay or in
+other words do i have the one do i have
+
+ align:start position:0%
+other words do i have the one do i have
+ 
+
+ align:start position:0%
+other words do i have the one do i have
+the high insulin version or the low
+
+ align:start position:0%
+the high insulin version or the low
+ 
+
+ align:start position:0%
+the high insulin version or the low
+insulin version of this particular peak
+
+ align:start position:0%
+insulin version of this particular peak
+ 
+
+ align:start position:0%
+insulin version of this particular peak
+so it even gives you the test you could
+
+ align:start position:0%
+so it even gives you the test you could
+ 
+
+ align:start position:0%
+so it even gives you the test you could
+just go order those oligonucleotides
+
+ align:start position:0%
+just go order those oligonucleotides
+ 
+
+ align:start position:0%
+just go order those oligonucleotides
+find a rat that's walking down longwood
+
+ align:start position:0%
+find a rat that's walking down longwood
+ 
+
+ align:start position:0%
+find a rat that's walking down longwood
+avenue at night and just test to see if
+
+ align:start position:0%
+avenue at night and just test to see if
+ 
+
+ align:start position:0%
+avenue at night and just test to see if
+there's a high insulin on low insulin
+
+ align:start position:0%
+there's a high insulin on low insulin
+ 
+
+ align:start position:0%
+there's a high insulin on low insulin
+you can do it today
+
+ align:start position:0%
+you can do it today
+ 
+
+ align:start position:0%
+you can do it today
+now out of dumb luck it just so happens
+
+ align:start position:0%
+now out of dumb luck it just so happens
+ 
+
+ align:start position:0%
+now out of dumb luck it just so happens
+that they've already done the work and
+
+ align:start position:0%
+that they've already done the work and
+ 
+
+ align:start position:0%
+that they've already done the work and
+they've told us in this region of the
+
+ align:start position:0%
+they've told us in this region of the
+ 
+
+ align:start position:0%
+they've told us in this region of the
+chromosome
+
+ align:start position:0%
+chromosome
+ 
+
+ align:start position:0%
+chromosome
+we know there's a gene there
+
+ align:start position:0%
+we know there's a gene there
+ 
+
+ align:start position:0%
+we know there's a gene there
+okay it doesn't have to be but there is
+
+ align:start position:0%
+okay it doesn't have to be but there is
+ 
+
+ align:start position:0%
+okay it doesn't have to be but there is
+a gene there s 100 a4
+
+ align:start position:0%
+a gene there s 100 a4
+ 
+
+ align:start position:0%
+a gene there s 100 a4
+okay that's a that's a gene that exists
+
+ align:start position:0%
+okay that's a that's a gene that exists
+ 
+
+ align:start position:0%
+okay that's a that's a gene that exists
+in this peak of significance
+
+ align:start position:0%
+in this peak of significance
+ 
+
+ align:start position:0%
+in this peak of significance
+now what we're going to do is go take
+
+ align:start position:0%
+now what we're going to do is go take
+ 
+
+ align:start position:0%
+now what we're going to do is go take
+that piece of information that name of
+
+ align:start position:0%
+that piece of information that name of
+ 
+
+ align:start position:0%
+that piece of information that name of
+that gene let's look more at that qtl
+
+ align:start position:0%
+that gene let's look more at that qtl
+ 
+
+ align:start position:0%
+that gene let's look more at that qtl
+region that region on the chromosome
+
+ align:start position:0%
+region that region on the chromosome
+ 
+
+ align:start position:0%
+region that region on the chromosome
+we're going to go to national center
+
+ align:start position:0%
+we're going to go to national center
+ 
+
+ align:start position:0%
+we're going to go to national center
+biotechnology information click on
+
+ align:start position:0%
+biotechnology information click on
+ 
+
+ align:start position:0%
+biotechnology information click on
+genomic biology
+
+ align:start position:0%
+genomic biology
+ 
+
+ align:start position:0%
+genomic biology
+i'm going to click on the rat
+
+ align:start position:0%
+i'm going to click on the rat
+ 
+
+ align:start position:0%
+i'm going to click on the rat
+and i'm going to just type in s100 a4
+
+ align:start position:0%
+and i'm going to just type in s100 a4
+ 
+
+ align:start position:0%
+and i'm going to just type in s100 a4
+the name of that gene that i told us was
+
+ align:start position:0%
+the name of that gene that i told us was
+ 
+
+ align:start position:0%
+the name of that gene that i told us was
+in that region
+
+ align:start position:0%
+in that region
+ 
+
+ align:start position:0%
+in that region
+where is it in the right chromosome here
+
+ align:start position:0%
+where is it in the right chromosome here
+ 
+
+ align:start position:0%
+where is it in the right chromosome here
+it is on chromosome 2.
+
+ align:start position:0%
+it is on chromosome 2.
+ 
+
+ align:start position:0%
+it is on chromosome 2.
+it's telling us s100a4 if i click on
+
+ align:start position:0%
+it's telling us s100a4 if i click on
+ 
+
+ align:start position:0%
+it's telling us s100a4 if i click on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if i zoom out a little
+
+ align:start position:0%
+if i zoom out a little
+ 
+
+ align:start position:0%
+if i zoom out a little
+here's s1 here a4 and here are all the
+
+ align:start position:0%
+here's s1 here a4 and here are all the
+ 
+
+ align:start position:0%
+here's s1 here a4 and here are all the
+neighboring genes
+
+ align:start position:0%
+neighboring genes
+ 
+
+ align:start position:0%
+neighboring genes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's interesting there's a bunch of
+
+ align:start position:0%
+that's interesting there's a bunch of
+ 
+
+ align:start position:0%
+that's interesting there's a bunch of
+other interesting genes first s1 or a4
+
+ align:start position:0%
+other interesting genes first s1 or a4
+ 
+
+ align:start position:0%
+other interesting genes first s1 or a4
+there's an a3 a6 a8 a9 this gene is one
+
+ align:start position:0%
+there's an a3 a6 a8 a9 this gene is one
+ 
+
+ align:start position:0%
+there's an a3 a6 a8 a9 this gene is one
+in many of a gene family okay so how new
+
+ align:start position:0%
+in many of a gene family okay so how new
+ 
+
+ align:start position:0%
+in many of a gene family okay so how new
+genes are often form it's through
+
+ align:start position:0%
+genes are often form it's through
+ 
+
+ align:start position:0%
+genes are often form it's through
+duplication events like this but to me
+
+ align:start position:0%
+duplication events like this but to me
+ 
+
+ align:start position:0%
+duplication events like this but to me
+more interestingly i see things like
+
+ align:start position:0%
+more interestingly i see things like
+ 
+
+ align:start position:0%
+more interestingly i see things like
+naturetic peptide receptor naturetic
+
+ align:start position:0%
+naturetic peptide receptor naturetic
+ 
+
+ align:start position:0%
+naturetic peptide receptor naturetic
+peptide is made in a number of different
+
+ align:start position:0%
+peptide is made in a number of different
+ 
+
+ align:start position:0%
+peptide is made in a number of different
+sources clean the heart has to do with
+
+ align:start position:0%
+sources clean the heart has to do with
+ 
+
+ align:start position:0%
+sources clean the heart has to do with
+blood pressure and blood volume
+
+ align:start position:0%
+blood pressure and blood volume
+ 
+
+ align:start position:0%
+blood pressure and blood volume
+regulation that's an interesting hormone
+
+ align:start position:0%
+regulation that's an interesting hormone
+ 
+
+ align:start position:0%
+regulation that's an interesting hormone
+i see some others interleukin-6 there
+
+ align:start position:0%
+i see some others interleukin-6 there
+ 
+
+ align:start position:0%
+i see some others interleukin-6 there
+might be some interesting things there
+
+ align:start position:0%
+might be some interesting things there
+ 
+
+ align:start position:0%
+might be some interesting things there
+but let's just keep running with this
+
+ align:start position:0%
+but let's just keep running with this
+ 
+
+ align:start position:0%
+but let's just keep running with this
+s100 a4 here
+
+ align:start position:0%
+s100 a4 here
+ 
+
+ align:start position:0%
+s100 a4 here
+now what i'm going to do is i'm going to
+
+ align:start position:0%
+now what i'm going to do is i'm going to
+ 
+
+ align:start position:0%
+now what i'm going to do is i'm going to
+look at where is this gene expressed
+
+ align:start position:0%
+look at where is this gene expressed
+ 
+
+ align:start position:0%
+look at where is this gene expressed
+okay i got it in a statistical peak
+
+ align:start position:0%
+okay i got it in a statistical peak
+ 
+
+ align:start position:0%
+okay i got it in a statistical peak
+i've seen what its neighbors are in the
+
+ align:start position:0%
+i've seen what its neighbors are in the
+ 
+
+ align:start position:0%
+i've seen what its neighbors are in the
+genome now i want to know why is it that
+
+ align:start position:0%
+genome now i want to know why is it that
+ 
+
+ align:start position:0%
+genome now i want to know why is it that
+this particular gene is associated with
+
+ align:start position:0%
+this particular gene is associated with
+ 
+
+ align:start position:0%
+this particular gene is associated with
+diabetes or insulin level
+
+ align:start position:0%
+diabetes or insulin level
+ 
+
+ align:start position:0%
+diabetes or insulin level
+well let's see where is that gene
+
+ align:start position:0%
+well let's see where is that gene
+ 
+
+ align:start position:0%
+well let's see where is that gene
+expressed in a whole bunch of different
+
+ align:start position:0%
+expressed in a whole bunch of different
+ 
+
+ align:start position:0%
+expressed in a whole bunch of different
+samples this is one particular search
+
+ align:start position:0%
+samples this is one particular search
+ 
+
+ align:start position:0%
+samples this is one particular search
+engine where you can just type in the
+
+ align:start position:0%
+engine where you can just type in the
+ 
+
+ align:start position:0%
+engine where you can just type in the
+name of the gene and see where is this
+
+ align:start position:0%
+name of the gene and see where is this
+ 
+
+ align:start position:0%
+name of the gene and see where is this
+gene expressed and about 1200 different
+
+ align:start position:0%
+gene expressed and about 1200 different
+ 
+
+ align:start position:0%
+gene expressed and about 1200 different
+samples
+
+ align:start position:0%
+samples
+ 
+
+ align:start position:0%
+samples
+this is specific cardiovascular
+
+ align:start position:0%
+this is specific cardiovascular
+ 
+
+ align:start position:0%
+this is specific cardiovascular
+i type in s184 it says which do you mean
+
+ align:start position:0%
+i type in s184 it says which do you mean
+ 
+
+ align:start position:0%
+i type in s184 it says which do you mean
+the human the mouse and the rat well we
+
+ align:start position:0%
+the human the mouse and the rat well we
+ 
+
+ align:start position:0%
+the human the mouse and the rat well we
+started with the wrap but let's see
+
+ align:start position:0%
+started with the wrap but let's see
+ 
+
+ align:start position:0%
+started with the wrap but let's see
+where the human ones are expressed click
+
+ align:start position:0%
+where the human ones are expressed click
+ 
+
+ align:start position:0%
+where the human ones are expressed click
+on that
+
+ align:start position:0%
+on that
+ 
+
+ align:start position:0%
+on that
+is measured in 10 microarrays by johns
+
+ align:start position:0%
+is measured in 10 microarrays by johns
+ 
+
+ align:start position:0%
+is measured in 10 microarrays by johns
+hopkins that's not that many let's go
+
+ align:start position:0%
+hopkins that's not that many let's go
+ 
+
+ align:start position:0%
+hopkins that's not that many let's go
+back let's look at the mouse one mouse
+
+ align:start position:0%
+back let's look at the mouse one mouse
+ 
+
+ align:start position:0%
+back let's look at the mouse one mouse
+is measured 142 by this group 100 by
+
+ align:start position:0%
+is measured 142 by this group 100 by
+ 
+
+ align:start position:0%
+is measured 142 by this group 100 by
+this group 84 by this group let's look
+
+ align:start position:0%
+this group 84 by this group let's look
+ 
+
+ align:start position:0%
+this group 84 by this group let's look
+at the 84 first
+
+ align:start position:0%
+at the 84 first
+ 
+
+ align:start position:0%
+at the 84 first
+and we can see the top samples okay this
+
+ align:start position:0%
+and we can see the top samples okay this
+ 
+
+ align:start position:0%
+and we can see the top samples okay this
+is the expression level this is the
+
+ align:start position:0%
+is the expression level this is the
+ 
+
+ align:start position:0%
+is the expression level this is the
+percentile of that gene on that chip on
+
+ align:start position:0%
+percentile of that gene on that chip on
+ 
+
+ align:start position:0%
+percentile of that gene on that chip on
+each chip
+
+ align:start position:0%
+each chip
+ 
+
+ align:start position:0%
+each chip
+muscle muscle muscle muscle muscle
+
+ align:start position:0%
+muscle muscle muscle muscle muscle
+ 
+
+ align:start position:0%
+muscle muscle muscle muscle muscle
+muscle muscle muscle
+
+ align:start position:0%
+muscle muscle muscle
+ 
+
+ align:start position:0%
+muscle muscle muscle
+at least for johns hopkins this gene is
+
+ align:start position:0%
+at least for johns hopkins this gene is
+ 
+
+ align:start position:0%
+at least for johns hopkins this gene is
+most highly expressed in their muscle
+
+ align:start position:0%
+most highly expressed in their muscle
+ 
+
+ align:start position:0%
+most highly expressed in their muscle
+samples specifically regenerating muscle
+
+ align:start position:0%
+samples specifically regenerating muscle
+ 
+
+ align:start position:0%
+samples specifically regenerating muscle
+we can look to see exactly what sample
+
+ align:start position:0%
+we can look to see exactly what sample
+ 
+
+ align:start position:0%
+we can look to see exactly what sample
+there is but let's go on let's hit the
+
+ align:start position:0%
+there is but let's go on let's hit the
+ 
+
+ align:start position:0%
+there is but let's go on let's hit the
+back button
+
+ align:start position:0%
+back button
+ 
+
+ align:start position:0%
+back button
+and let's look at cardiogenomics this is
+
+ align:start position:0%
+and let's look at cardiogenomics this is
+ 
+
+ align:start position:0%
+and let's look at cardiogenomics this is
+these guys at the beth israel
+
+ align:start position:0%
+these guys at the beth israel
+ 
+
+ align:start position:0%
+these guys at the beth israel
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+it's highly expressed in banded smooth
+
+ align:start position:0%
+it's highly expressed in banded smooth
+ 
+
+ align:start position:0%
+it's highly expressed in banded smooth
+muscle now it says band here
+
+ align:start position:0%
+muscle now it says band here
+ 
+
+ align:start position:0%
+muscle now it says band here
+that's banned 48 hours banned 48 hours
+
+ align:start position:0%
+that's banned 48 hours banned 48 hours
+ 
+
+ align:start position:0%
+that's banned 48 hours banned 48 hours
+24 hours what exactly did they do what
+
+ align:start position:0%
+24 hours what exactly did they do what
+ 
+
+ align:start position:0%
+24 hours what exactly did they do what
+exactly are these samples you click on
+
+ align:start position:0%
+exactly are these samples you click on
+ 
+
+ align:start position:0%
+exactly are these samples you click on
+overview it takes you to their website
+
+ align:start position:0%
+overview it takes you to their website
+ 
+
+ align:start position:0%
+overview it takes you to their website
+that tells you what was the experiment
+
+ align:start position:0%
+that tells you what was the experiment
+ 
+
+ align:start position:0%
+that tells you what was the experiment
+they did they actually did an experiment
+
+ align:start position:0%
+they did they actually did an experiment
+ 
+
+ align:start position:0%
+they did they actually did an experiment
+where they took these mice
+
+ align:start position:0%
+where they took these mice
+ 
+
+ align:start position:0%
+where they took these mice
+they opened them up
+
+ align:start position:0%
+they opened them up
+ 
+
+ align:start position:0%
+they opened them up
+and they put a little rubber band on
+
+ align:start position:0%
+and they put a little rubber band on
+ 
+
+ align:start position:0%
+and they put a little rubber band on
+their aortics
+
+ align:start position:0%
+their aortics
+ 
+
+ align:start position:0%
+their aortics
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and half of them the other have to just
+
+ align:start position:0%
+and half of them the other have to just
+ 
+
+ align:start position:0%
+and half of them the other have to just
+sew them up again they didn't do
+
+ align:start position:0%
+sew them up again they didn't do
+ 
+
+ align:start position:0%
+sew them up again they didn't do
+anything and so they made a list of
+
+ align:start position:0%
+anything and so they made a list of
+ 
+
+ align:start position:0%
+anything and so they made a list of
+genes that go up in the heart
+
+ align:start position:0%
+genes that go up in the heart
+ 
+
+ align:start position:0%
+genes that go up in the heart
+as a response to this pressure overload
+
+ align:start position:0%
+as a response to this pressure overload
+ 
+
+ align:start position:0%
+as a response to this pressure overload
+the genes are sitting there and i can
+
+ align:start position:0%
+the genes are sitting there and i can
+ 
+
+ align:start position:0%
+the genes are sitting there and i can
+guarantee you again not a single paper
+
+ align:start position:0%
+guarantee you again not a single paper
+ 
+
+ align:start position:0%
+guarantee you again not a single paper
+has been published on this list
+
+ align:start position:0%
+has been published on this list
+ 
+
+ align:start position:0%
+has been published on this list
+because we're so busy creating more data
+
+ align:start position:0%
+because we're so busy creating more data
+ 
+
+ align:start position:0%
+because we're so busy creating more data
+we have not had time to publish anything
+
+ align:start position:0%
+we have not had time to publish anything
+ 
+
+ align:start position:0%
+we have not had time to publish anything
+on this data
+
+ align:start position:0%
+on this data
+ 
+
+ align:start position:0%
+on this data
+so they were studying trying to study
+
+ align:start position:0%
+so they were studying trying to study
+ 
+
+ align:start position:0%
+so they were studying trying to study
+pressure overload induced cardiac
+
+ align:start position:0%
+pressure overload induced cardiac
+ 
+
+ align:start position:0%
+pressure overload induced cardiac
+hypertrophy so now here's the hypothesis
+
+ align:start position:0%
+hypertrophy so now here's the hypothesis
+ 
+
+ align:start position:0%
+hypertrophy so now here's the hypothesis
+i started
+
+ align:start position:0%
+i started
+ 
+
+ align:start position:0%
+i started
+with the brown orange rat and the brown
+
+ align:start position:0%
+with the brown orange rat and the brown
+ 
+
+ align:start position:0%
+with the brown orange rat and the brown
+already rat has signs of diabetes
+
+ align:start position:0%
+already rat has signs of diabetes
+ 
+
+ align:start position:0%
+already rat has signs of diabetes
+because of this gene s1 or a4 that's
+
+ align:start position:0%
+because of this gene s1 or a4 that's
+ 
+
+ align:start position:0%
+because of this gene s1 or a4 that's
+because s100 a4 was under that
+
+ align:start position:0%
+because s100 a4 was under that
+ 
+
+ align:start position:0%
+because s100 a4 was under that
+significance peak but i think it's
+
+ align:start position:0%
+significance peak but i think it's
+ 
+
+ align:start position:0%
+significance peak but i think it's
+because s1 or a4 is expressed in muscle
+
+ align:start position:0%
+because s1 or a4 is expressed in muscle
+ 
+
+ align:start position:0%
+because s1 or a4 is expressed in muscle
+under a variety of different conditions
+
+ align:start position:0%
+under a variety of different conditions
+ 
+
+ align:start position:0%
+under a variety of different conditions
+and i know muscle is an insulin target
+
+ align:start position:0%
+and i know muscle is an insulin target
+ 
+
+ align:start position:0%
+and i know muscle is an insulin target
+tissue
+
+ align:start position:0%
+tissue
+ 
+
+ align:start position:0%
+tissue
+so now i can get some clue as to what
+
+ align:start position:0%
+so now i can get some clue as to what
+ 
+
+ align:start position:0%
+so now i can get some clue as to what
+experiment i can do next maybe i should
+
+ align:start position:0%
+experiment i can do next maybe i should
+ 
+
+ align:start position:0%
+experiment i can do next maybe i should
+go look at muscle cells for s1 or a4
+
+ align:start position:0%
+go look at muscle cells for s1 or a4
+ 
+
+ align:start position:0%
+go look at muscle cells for s1 or a4
+if you actually do pubmed searches you
+
+ align:start position:0%
+if you actually do pubmed searches you
+ 
+
+ align:start position:0%
+if you actually do pubmed searches you
+can see s194 is associated at least it's
+
+ align:start position:0%
+can see s194 is associated at least it's
+ 
+
+ align:start position:0%
+can see s194 is associated at least it's
+being studied in diabetes today
+
+ align:start position:0%
+being studied in diabetes today
+ 
+
+ align:start position:0%
+being studied in diabetes today
+now i just picked the first peak i saw
+
+ align:start position:0%
+now i just picked the first peak i saw
+ 
+
+ align:start position:0%
+now i just picked the first peak i saw
+on that website okay you can go back and
+
+ align:start position:0%
+on that website okay you can go back and
+ 
+
+ align:start position:0%
+on that website okay you can go back and
+find any number of new genes there and
+
+ align:start position:0%
+find any number of new genes there and
+ 
+
+ align:start position:0%
+find any number of new genes there and
+come up with hypotheses and we didn't
+
+ align:start position:0%
+come up with hypotheses and we didn't
+ 
+
+ align:start position:0%
+come up with hypotheses and we didn't
+even leave the web browser
+
+ align:start position:0%
+even leave the web browser
+ 
+
+ align:start position:0%
+even leave the web browser
+okay you didn't even have to download a
+
+ align:start position:0%
+okay you didn't even have to download a
+ 
+
+ align:start position:0%
+okay you didn't even have to download a
+file to do any of this so you could do
+
+ align:start position:0%
+file to do any of this so you could do
+ 
+
+ align:start position:0%
+file to do any of this so you could do
+this today yourself just surfing from
+
+ align:start position:0%
+this today yourself just surfing from
+ 
+
+ align:start position:0%
+this today yourself just surfing from
+one of these sites to another from
+
+ align:start position:0%
+one of these sites to another from
+ 
+
+ align:start position:0%
+one of these sites to another from
+something you might have heard down the
+
+ align:start position:0%
+something you might have heard down the
+ 
+
+ align:start position:0%
+something you might have heard down the
+hall it's my actual hypothesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have about 10 minutes i'm just going
+
+ align:start position:0%
+we have about 10 minutes i'm just going
+ 
+
+ align:start position:0%
+we have about 10 minutes i'm just going
+to call it quits now to see if you have
+
+ align:start position:0%
+to call it quits now to see if you have
+ 
+
+ align:start position:0%
+to call it quits now to see if you have
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what at what point
+
+ align:start position:0%
+so what at what point
+ 
+
+ align:start position:0%
+so what at what point
+these various websites after data what
+
+ align:start position:0%
+these various websites after data what
+ 
+
+ align:start position:0%
+these various websites after data what
+point does that data get put on the
+
+ align:start position:0%
+point does that data get put on the
+ 
+
+ align:start position:0%
+point does that data get put on the
+website or after publication
+
+ align:start position:0%
+website or after publication
+ 
+
+ align:start position:0%
+website or after publication
+good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great question so ncbi geo you can
+
+ align:start position:0%
+great question so ncbi geo you can
+ 
+
+ align:start position:0%
+great question so ncbi geo you can
+submit data to them and then they'll
+
+ align:start position:0%
+submit data to them and then they'll
+ 
+
+ align:start position:0%
+submit data to them and then they'll
+keep it hidden until you say it's been
+
+ align:start position:0%
+keep it hidden until you say it's been
+ 
+
+ align:start position:0%
+keep it hidden until you say it's been
+published and then they can turn it on
+
+ align:start position:0%
+published and then they can turn it on
+ 
+
+ align:start position:0%
+published and then they can turn it on
+these other personal websites like the
+
+ align:start position:0%
+these other personal websites like the
+ 
+
+ align:start position:0%
+these other personal websites like the
+whitehead one stanford they typically
+
+ align:start position:0%
+whitehead one stanford they typically
+ 
+
+ align:start position:0%
+whitehead one stanford they typically
+appear after publication
+
+ align:start position:0%
+appear after publication
+ 
+
+ align:start position:0%
+appear after publication
+for these other websites in this pga
+
+ align:start position:0%
+for these other websites in this pga
+ 
+
+ align:start position:0%
+for these other websites in this pga
+these the the cardiovascular data keep
+
+ align:start position:0%
+these the the cardiovascular data keep
+ 
+
+ align:start position:0%
+these the the cardiovascular data keep
+showing you that data appears within 60
+
+ align:start position:0%
+showing you that data appears within 60
+ 
+
+ align:start position:0%
+showing you that data appears within 60
+days of its creation regardless of
+
+ align:start position:0%
+days of its creation regardless of
+ 
+
+ align:start position:0%
+days of its creation regardless of
+publication
+
+ align:start position:0%
+publication
+ 
+
+ align:start position:0%
+publication
+nih is more and more mandating that to
+
+ align:start position:0%
+nih is more and more mandating that to
+ 
+
+ align:start position:0%
+nih is more and more mandating that to
+be the model now okay
+
+ align:start position:0%
+be the model now okay
+ 
+
+ align:start position:0%
+be the model now okay
+because if they're paying for all this
+
+ align:start position:0%
+because if they're paying for all this
+ 
+
+ align:start position:0%
+because if they're paying for all this
+genomic work
+
+ align:start position:0%
+genomic work
+ 
+
+ align:start position:0%
+genomic work
+they don't want just one lab to to
+
+ align:start position:0%
+they don't want just one lab to to
+ 
+
+ align:start position:0%
+they don't want just one lab to to
+really be able to run with it because
+
+ align:start position:0%
+really be able to run with it because
+ 
+
+ align:start position:0%
+really be able to run with it because
+there's too much data for any one lab to
+
+ align:start position:0%
+there's too much data for any one lab to
+ 
+
+ align:start position:0%
+there's too much data for any one lab to
+deal with so they as for some of their
+
+ align:start position:0%
+deal with so they as for some of their
+ 
+
+ align:start position:0%
+deal with so they as for some of their
+grants they actually insist that this
+
+ align:start position:0%
+grants they actually insist that this
+ 
+
+ align:start position:0%
+grants they actually insist that this
+data be made available well before
+
+ align:start position:0%
+data be made available well before
+ 
+
+ align:start position:0%
+data be made available well before
+publication
+
+ align:start position:0%
+publication
+ 
+
+ align:start position:0%
+publication
+so right now cardiovascular and lung
+
+ align:start position:0%
+so right now cardiovascular and lung
+ 
+
+ align:start position:0%
+so right now cardiovascular and lung
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+and some a little bit of sleep as well
+
+ align:start position:0%
+and some a little bit of sleep as well
+ 
+
+ align:start position:0%
+and some a little bit of sleep as well
+you can get a lot of data
+
+ align:start position:0%
+you can get a lot of data
+ 
+
+ align:start position:0%
+you can get a lot of data
+1500 arrays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep these pga these programs and genomic
+
+ align:start position:0%
+yep these pga these programs and genomic
+ 
+
+ align:start position:0%
+yep these pga these programs and genomic
+applications pga was funded by the heart
+
+ align:start position:0%
+applications pga was funded by the heart
+ 
+
+ align:start position:0%
+applications pga was funded by the heart
+lung and blood institute that in
+
+ align:start position:0%
+lung and blood institute that in
+ 
+
+ align:start position:0%
+lung and blood institute that in
+particular has a lot of data that's
+
+ align:start position:0%
+particular has a lot of data that's
+ 
+
+ align:start position:0%
+particular has a lot of data that's
+already available hasn't been published
+
+ align:start position:0%
+already available hasn't been published
+ 
+
+ align:start position:0%
+already available hasn't been published
+on
\ No newline at end of file
diff --git a/MeFCYYCATw0.txt b/MeFCYYCATw0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5aa936717432c5beaf17f25e9cb9c9d313488822
--- /dev/null
+++ b/MeFCYYCATw0.txt
@@ -0,0 +1,14055 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay as you'll see with
+
+ align:start position:0%
+ocw.mit.edu okay as you'll see with
+ 
+
+ align:start position:0%
+ocw.mit.edu okay as you'll see with
+today's uh lecture I made a small change
+
+ align:start position:0%
+today's uh lecture I made a small change
+ 
+
+ align:start position:0%
+today's uh lecture I made a small change
+in the uh lecture sequence I basically
+
+ align:start position:0%
+in the uh lecture sequence I basically
+ 
+
+ align:start position:0%
+in the uh lecture sequence I basically
+combined the last part of of Tuesday's
+
+ align:start position:0%
+combined the last part of of Tuesday's
+ 
+
+ align:start position:0%
+combined the last part of of Tuesday's
+lecture with what I was going to talk
+
+ align:start position:0%
+lecture with what I was going to talk
+ 
+
+ align:start position:0%
+lecture with what I was going to talk
+about next week because they really go
+
+ align:start position:0%
+about next week because they really go
+ 
+
+ align:start position:0%
+about next week because they really go
+together better anyway which is multiv
+
+ align:start position:0%
+together better anyway which is multiv
+ 
+
+ align:start position:0%
+together better anyway which is multiv
+at SPC together with a couple of the
+
+ align:start position:0%
+at SPC together with a couple of the
+ 
+
+ align:start position:0%
+at SPC together with a couple of the
+advanced control charting and so next
+
+ align:start position:0%
+advanced control charting and so next
+ 
+
+ align:start position:0%
+advanced control charting and so next
+week we'll do the uh yield modeling uh
+
+ align:start position:0%
+week we'll do the uh yield modeling uh
+ 
+
+ align:start position:0%
+week we'll do the uh yield modeling uh
+lecture rather than uh rather than try
+
+ align:start position:0%
+lecture rather than uh rather than try
+ 
+
+ align:start position:0%
+lecture rather than uh rather than try
+to squish that in today so what I want
+
+ align:start position:0%
+to squish that in today so what I want
+ 
+
+ align:start position:0%
+to squish that in today so what I want
+to do today is first have a very brief
+
+ align:start position:0%
+to do today is first have a very brief
+ 
+
+ align:start position:0%
+to do today is first have a very brief
+warmup just get us back into the swing
+
+ align:start position:0%
+warmup just get us back into the swing
+ 
+
+ align:start position:0%
+warmup just get us back into the swing
+of things with conventional control
+
+ align:start position:0%
+of things with conventional control
+ 
+
+ align:start position:0%
+of things with conventional control
+charts and then talk a little bit about
+
+ align:start position:0%
+charts and then talk a little bit about
+ 
+
+ align:start position:0%
+charts and then talk a little bit about
+these alternative control charts with a
+
+ align:start position:0%
+these alternative control charts with a
+ 
+
+ align:start position:0%
+these alternative control charts with a
+little bit of increased sensitivity for
+
+ align:start position:0%
+little bit of increased sensitivity for
+ 
+
+ align:start position:0%
+little bit of increased sensitivity for
+Rapid detection of of of shifts uh as
+
+ align:start position:0%
+Rapid detection of of of shifts uh as
+ 
+
+ align:start position:0%
+Rapid detection of of of shifts uh as
+well as as drifts but primarily uh
+
+ align:start position:0%
+well as as drifts but primarily uh
+ 
+
+ align:start position:0%
+well as as drifts but primarily uh
+targeted at shifts and these are the
+
+ align:start position:0%
+targeted at shifts and these are the
+ 
+
+ align:start position:0%
+targeted at shifts and these are the
+moving average exponentially weighted
+
+ align:start position:0%
+moving average exponentially weighted
+ 
+
+ align:start position:0%
+moving average exponentially weighted
+moving average in the cumulative sum
+
+ align:start position:0%
+moving average in the cumulative sum
+ 
+
+ align:start position:0%
+moving average in the cumulative sum
+chart and then we'll move into uh
+
+ align:start position:0%
+chart and then we'll move into uh
+ 
+
+ align:start position:0%
+chart and then we'll move into uh
+multivariate
+
+ align:start position:0%
+multivariate
+ 
+
+ align:start position:0%
+multivariate
+SPC uh which is a little bit of a
+
+ align:start position:0%
+SPC uh which is a little bit of a
+ 
+
+ align:start position:0%
+SPC uh which is a little bit of a
+tutorial on multivariate uh statistics
+
+ align:start position:0%
+tutorial on multivariate uh statistics
+ 
+
+ align:start position:0%
+tutorial on multivariate uh statistics
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+so that's the plan so to get us warmed
+
+ align:start position:0%
+so that's the plan so to get us warmed
+ 
+
+ align:start position:0%
+so that's the plan so to get us warmed
+up we'll do a rapid design of a control
+
+ align:start position:0%
+up we'll do a rapid design of a control
+ 
+
+ align:start position:0%
+up we'll do a rapid design of a control
+chart how to do this uh relatively
+
+ align:start position:0%
+chart how to do this uh relatively
+ 
+
+ align:start position:0%
+chart how to do this uh relatively
+quickly I will tell you what that we
+
+ align:start position:0%
+quickly I will tell you what that we
+ 
+
+ align:start position:0%
+quickly I will tell you what that we
+have a model based on lots of historical
+
+ align:start position:0%
+have a model based on lots of historical
+ 
+
+ align:start position:0%
+have a model based on lots of historical
+data of this process that when it is in
+
+ align:start position:0%
+data of this process that when it is in
+ 
+
+ align:start position:0%
+data of this process that when it is in
+control it's operating as a normally
+
+ align:start position:0%
+control it's operating as a normally
+ 
+
+ align:start position:0%
+control it's operating as a normally
+distributed process with a mean of one
+
+ align:start position:0%
+distributed process with a mean of one
+ 
+
+ align:start position:0%
+distributed process with a mean of one
+and a variance of one we're going to be
+
+ align:start position:0%
+and a variance of one we're going to be
+ 
+
+ align:start position:0%
+and a variance of one we're going to be
+taking samples every nine parts then the
+
+ align:start position:0%
+taking samples every nine parts then the
+ 
+
+ align:start position:0%
+taking samples every nine parts then the
+next nine and so on
+
+ align:start position:0%
+next nine and so on
+ 
+
+ align:start position:0%
+next nine and so on
+so what should the here's the easy one
+
+ align:start position:0%
+so what should the here's the easy one
+ 
+
+ align:start position:0%
+so what should the here's the easy one
+to make wake you up in the morning what
+
+ align:start position:0%
+to make wake you up in the morning what
+ 
+
+ align:start position:0%
+to make wake you up in the morning what
+should the center line
+
+ align:start position:0%
+should the center line
+ 
+
+ align:start position:0%
+should the center line
+be five okay everybody how about the
+
+ align:start position:0%
+be five okay everybody how about the
+ 
+
+ align:start position:0%
+be five okay everybody how about the
+plusus 3 Sigma we're quite quite happy
+
+ align:start position:0%
+plusus 3 Sigma we're quite quite happy
+ 
+
+ align:start position:0%
+plusus 3 Sigma we're quite quite happy
+with the uh 1 and 370
+
+ align:start position:0%
+with the uh 1 and 370
+ 
+
+ align:start position:0%
+with the uh 1 and 370
+ARL uh with normal typical plusus 3
+
+ align:start position:0%
+ARL uh with normal typical plusus 3
+ 
+
+ align:start position:0%
+ARL uh with normal typical plusus 3
+Sigma control limits where should the
+
+ align:start position:0%
+Sigma control limits where should the
+ 
+
+ align:start position:0%
+Sigma control limits where should the
+plusus 3 Sigma control limits be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I hear a six and four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why I'm
+
+ align:start position:0%
+why I'm
+ 
+
+ align:start position:0%
+why I'm
+sorry okay which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh mu plus Sigma plusus three
+
+ align:start position:0%
+is uh mu plus Sigma plusus three
+ 
+
+ align:start position:0%
+is uh mu plus Sigma plusus three
+sigma three sigma over square root of
+
+ align:start position:0%
+sigma three sigma over square root of
+ 
+
+ align:start position:0%
+sigma three sigma over square root of
+sample size n so the three sigma and the
+
+ align:start position:0%
+sample size n so the three sigma and the
+ 
+
+ align:start position:0%
+sample size n so the three sigma and the
+three which comes from the root n and
+
+ align:start position:0%
+three which comes from the root n and
+ 
+
+ align:start position:0%
+three which comes from the root n and
+make it a nice uh plusus one and there's
+
+ align:start position:0%
+make it a nice uh plusus one and there's
+ 
+
+ align:start position:0%
+make it a nice uh plusus one and there's
+some data okay so i' I've plotted 99 we
+
+ align:start position:0%
+some data okay so i' I've plotted 99 we
+ 
+
+ align:start position:0%
+some data okay so i' I've plotted 99 we
+we ran the process 99 runs they have 11
+
+ align:start position:0%
+we ran the process 99 runs they have 11
+ 
+
+ align:start position:0%
+we ran the process 99 runs they have 11
+samples here's the question is the
+
+ align:start position:0%
+samples here's the question is the
+ 
+
+ align:start position:0%
+samples here's the question is the
+process in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+control we have a
+
+ align:start position:0%
+control we have a
+ 
+
+ align:start position:0%
+control we have a
+yes we have another yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I contend you don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know it's a little bit tricky
+
+ align:start position:0%
+know it's a little bit tricky
+ 
+
+ align:start position:0%
+know it's a little bit tricky
+here liit and
+
+ align:start position:0%
+here liit and
+ 
+
+ align:start position:0%
+here liit and
+see yeah I guess uh that's actually not
+
+ align:start position:0%
+see yeah I guess uh that's actually not
+ 
+
+ align:start position:0%
+see yeah I guess uh that's actually not
+what I have in mind you could go in and
+
+ align:start position:0%
+what I have in mind you could go in and
+ 
+
+ align:start position:0%
+what I have in mind you could go in and
+start uh down the path of looking and
+
+ align:start position:0%
+start uh down the path of looking and
+ 
+
+ align:start position:0%
+start uh down the path of looking and
+saying okay what's the probability of
+
+ align:start position:0%
+saying okay what's the probability of
+ 
+
+ align:start position:0%
+saying okay what's the probability of
+having for example three Rising points
+
+ align:start position:0%
+having for example three Rising points
+ 
+
+ align:start position:0%
+having for example three Rising points
+in a row and all the other Western but
+
+ align:start position:0%
+in a row and all the other Western but
+ 
+
+ align:start position:0%
+in a row and all the other Western but
+but uh I'll I'll
+
+ align:start position:0%
+but uh I'll I'll
+ 
+
+ align:start position:0%
+but uh I'll I'll
+say none of that's
+
+ align:start position:0%
+say none of that's
+ 
+
+ align:start position:0%
+say none of that's
+happening so I I will say that the
+
+ align:start position:0%
+happening so I I will say that the
+ 
+
+ align:start position:0%
+happening so I I will say that the
+mean there's nothing too strange
+
+ align:start position:0%
+mean there's nothing too strange
+ 
+
+ align:start position:0%
+mean there's nothing too strange
+happening with the mean that you can
+
+ align:start position:0%
+happening with the mean that you can
+ 
+
+ align:start position:0%
+happening with the mean that you can
+tell with this chart is the process in
+
+ align:start position:0%
+tell with this chart is the process in
+ 
+
+ align:start position:0%
+tell with this chart is the process in
+control like a
+
+ align:start position:0%
+control like a
+ 
+
+ align:start position:0%
+control like a
+Vari yeah Vari is getting compar to
+
+ align:start position:0%
+Vari yeah Vari is getting compar to
+ 
+
+ align:start position:0%
+Vari yeah Vari is getting compar to
+earlier points oh so you're saying the
+
+ align:start position:0%
+earlier points oh so you're saying the
+ 
+
+ align:start position:0%
+earlier points oh so you're saying the
+variance is getting
+
+ align:start position:0%
+variance is getting
+ 
+
+ align:start position:0%
+variance is getting
+larger maybe it's hard to tell with this
+
+ align:start position:0%
+larger maybe it's hard to tell with this
+ 
+
+ align:start position:0%
+larger maybe it's hard to tell with this
+this is a mean chart all it's telling
+
+ align:start position:0%
+this is a mean chart all it's telling
+ 
+
+ align:start position:0%
+this is a mean chart all it's telling
+you is a tracking of the mean we said
+
+ align:start position:0%
+you is a tracking of the mean we said
+ 
+
+ align:start position:0%
+you is a tracking of the mean we said
+that the process model is that we have
+
+ align:start position:0%
+that the process model is that we have
+ 
+
+ align:start position:0%
+that the process model is that we have
+this mean and this variance and so I
+
+ align:start position:0%
+this mean and this variance and so I
+ 
+
+ align:start position:0%
+this mean and this variance and so I
+guess the main point here is you don't
+
+ align:start position:0%
+guess the main point here is you don't
+ 
+
+ align:start position:0%
+guess the main point here is you don't
+really know if you're just tracking the
+
+ align:start position:0%
+really know if you're just tracking the
+ 
+
+ align:start position:0%
+really know if you're just tracking the
+mean what's happening also with the
+
+ align:start position:0%
+mean what's happening also with the
+ 
+
+ align:start position:0%
+mean what's happening also with the
+variance within your
+
+ align:start position:0%
+variance within your
+ 
+
+ align:start position:0%
+variance within your
+sample in fact uh on the next page this
+
+ align:start position:0%
+sample in fact uh on the next page this
+ 
+
+ align:start position:0%
+sample in fact uh on the next page this
+is the raw data all 99 points where we
+
+ align:start position:0%
+is the raw data all 99 points where we
+ 
+
+ align:start position:0%
+is the raw data all 99 points where we
+grouped 9 by 9 by9 to get the
+
+ align:start position:0%
+grouped 9 by 9 by9 to get the
+ 
+
+ align:start position:0%
+grouped 9 by 9 by9 to get the
+sample and if you saw this you might be
+
+ align:start position:0%
+sample and if you saw this you might be
+ 
+
+ align:start position:0%
+sample and if you saw this you might be
+a little less comfortable huh
+
+ align:start position:0%
+a little less comfortable huh
+ 
+
+ align:start position:0%
+a little less comfortable huh
+now you could always go back and look at
+
+ align:start position:0%
+now you could always go back and look at
+ 
+
+ align:start position:0%
+now you could always go back and look at
+Raw data and raw data is always really
+
+ align:start position:0%
+Raw data and raw data is always really
+ 
+
+ align:start position:0%
+Raw data and raw data is always really
+good to do but what you would also want
+
+ align:start position:0%
+good to do but what you would also want
+ 
+
+ align:start position:0%
+good to do but what you would also want
+to do is a typical s chart or a range
+
+ align:start position:0%
+to do is a typical s chart or a range
+ 
+
+ align:start position:0%
+to do is a typical s chart or a range
+chart something like that and in this
+
+ align:start position:0%
+chart something like that and in this
+ 
+
+ align:start position:0%
+chart something like that and in this
+case if you design the S chart with
+
+ align:start position:0%
+case if you design the S chart with
+ 
+
+ align:start position:0%
+case if you design the S chart with
+those AR
+
+ align:start position:0%
+those AR
+ 
+
+ align:start position:0%
+those AR
+priori um pieces of data sample size is
+
+ align:start position:0%
+priori um pieces of data sample size is
+ 
+
+ align:start position:0%
+priori um pieces of data sample size is
+nine and the uh process variance is
+
+ align:start position:0%
+nine and the uh process variance is
+ 
+
+ align:start position:0%
+nine and the uh process variance is
+one with the C4 correction factor and so
+
+ align:start position:0%
+one with the C4 correction factor and so
+ 
+
+ align:start position:0%
+one with the C4 correction factor and so
+on all of that just out of the the
+
+ align:start position:0%
+on all of that just out of the the
+ 
+
+ align:start position:0%
+on all of that just out of the the
+formula uh you get these control
+
+ align:start position:0%
+formula uh you get these control
+ 
+
+ align:start position:0%
+formula uh you get these control
+limits and uh sure enough at about uh
+
+ align:start position:0%
+limits and uh sure enough at about uh
+ 
+
+ align:start position:0%
+limits and uh sure enough at about uh
+sample 10 we're above the control limit
+
+ align:start position:0%
+sample 10 we're above the control limit
+ 
+
+ align:start position:0%
+sample 10 we're above the control limit
+sample 11 is even more above the control
+
+ align:start position:0%
+sample 11 is even more above the control
+ 
+
+ align:start position:0%
+sample 11 is even more above the control
+limit and that's indicative of
+
+ align:start position:0%
+limit and that's indicative of
+ 
+
+ align:start position:0%
+limit and that's indicative of
+essentially The increased variance of
+
+ align:start position:0%
+essentially The increased variance of
+ 
+
+ align:start position:0%
+essentially The increased variance of
+those two groups and I will tell you I
+
+ align:start position:0%
+those two groups and I will tell you I
+ 
+
+ align:start position:0%
+those two groups and I will tell you I
+generated this data with jump and sure
+
+ align:start position:0%
+generated this data with jump and sure
+ 
+
+ align:start position:0%
+generated this data with jump and sure
+enough right at the uh whatever it was
+
+ align:start position:0%
+enough right at the uh whatever it was
+ 
+
+ align:start position:0%
+enough right at the uh whatever it was
+the 77th uh point I resampled with a
+
+ align:start position:0%
+the 77th uh point I resampled with a
+ 
+
+ align:start position:0%
+the 77th uh point I resampled with a
+from a normal distribution with
+
+ align:start position:0%
+from a normal distribution with
+ 
+
+ align:start position:0%
+from a normal distribution with
+something like a variance of 1.9 or two
+
+ align:start position:0%
+something like a variance of 1.9 or two
+ 
+
+ align:start position:0%
+something like a variance of 1.9 or two
+or something like that so the main point
+
+ align:start position:0%
+or something like that so the main point
+ 
+
+ align:start position:0%
+or something like that so the main point
+here was you need to monitor both
+
+ align:start position:0%
+here was you need to monitor both
+ 
+
+ align:start position:0%
+here was you need to monitor both
+aspects uh both the mean and the
+
+ align:start position:0%
+aspects uh both the mean and the
+ 
+
+ align:start position:0%
+aspects uh both the mean and the
+variance to know whether your process
+
+ align:start position:0%
+variance to know whether your process
+ 
+
+ align:start position:0%
+variance to know whether your process
+model is is is still operative are we uh
+
+ align:start position:0%
+model is is is still operative are we uh
+ 
+
+ align:start position:0%
+model is is is still operative are we uh
+we're saying that for a normal
+
+ align:start position:0%
+we're saying that for a normal
+ 
+
+ align:start position:0%
+we're saying that for a normal
+distribution the mean and variance are
+
+ align:start position:0%
+distribution the mean and variance are
+ 
+
+ align:start position:0%
+distribution the mean and variance are
+really telling you
+
+ align:start position:0%
+really telling you
+ 
+
+ align:start position:0%
+really telling you
+everything now the other subo in here is
+
+ align:start position:0%
+everything now the other subo in here is
+ 
+
+ align:start position:0%
+everything now the other subo in here is
+that if you were actually looking at
+
+ align:start position:0%
+that if you were actually looking at
+ 
+
+ align:start position:0%
+that if you were actually looking at
+this run data there is a lot of noise
+
+ align:start position:0%
+this run data there is a lot of noise
+ 
+
+ align:start position:0%
+this run data there is a lot of noise
+there's inherent process noise and part
+
+ align:start position:0%
+there's inherent process noise and part
+ 
+
+ align:start position:0%
+there's inherent process noise and part
+of the goal here is you're you're trying
+
+ align:start position:0%
+of the goal here is you're you're trying
+ 
+
+ align:start position:0%
+of the goal here is you're you're trying
+to detect a mean in the face of that
+
+ align:start position:0%
+to detect a mean in the face of that
+ 
+
+ align:start position:0%
+to detect a mean in the face of that
+noise and so one way of thinking about
+
+ align:start position:0%
+noise and so one way of thinking about
+ 
+
+ align:start position:0%
+noise and so one way of thinking about
+sampling and calculating xar is that
+
+ align:start position:0%
+sampling and calculating xar is that
+ 
+
+ align:start position:0%
+sampling and calculating xar is that
+indeed you are
+
+ align:start position:0%
+indeed you are
+ 
+
+ align:start position:0%
+indeed you are
+filtering okay so you want to filter to
+
+ align:start position:0%
+filtering okay so you want to filter to
+ 
+
+ align:start position:0%
+filtering okay so you want to filter to
+suppress the additional variance effect
+
+ align:start position:0%
+suppress the additional variance effect
+ 
+
+ align:start position:0%
+suppress the additional variance effect
+when you're looking for the mean Trace
+
+ align:start position:0%
+when you're looking for the mean Trace
+ 
+
+ align:start position:0%
+when you're looking for the mean Trace
+but again you got to also monitor for
+
+ align:start position:0%
+but again you got to also monitor for
+ 
+
+ align:start position:0%
+but again you got to also monitor for
+for the variants but this noise makes it
+
+ align:start position:0%
+for the variants but this noise makes it
+ 
+
+ align:start position:0%
+for the variants but this noise makes it
+a little bit tricky in terms of uh being
+
+ align:start position:0%
+a little bit tricky in terms of uh being
+ 
+
+ align:start position:0%
+a little bit tricky in terms of uh being
+able to detect the mean so you want to
+
+ align:start position:0%
+able to detect the mean so you want to
+ 
+
+ align:start position:0%
+able to detect the mean so you want to
+filter and one of the ideas of these
+
+ align:start position:0%
+filter and one of the ideas of these
+ 
+
+ align:start position:0%
+filter and one of the ideas of these
+alternative control charts is explicitly
+
+ align:start position:0%
+alternative control charts is explicitly
+ 
+
+ align:start position:0%
+alternative control charts is explicitly
+think about the filtering action that
+
+ align:start position:0%
+think about the filtering action that
+ 
+
+ align:start position:0%
+think about the filtering action that
+you're doing a little bit almost from a
+
+ align:start position:0%
+you're doing a little bit almost from a
+ 
+
+ align:start position:0%
+you're doing a little bit almost from a
+more signal processing kind of uh point
+
+ align:start position:0%
+more signal processing kind of uh point
+ 
+
+ align:start position:0%
+more signal processing kind of uh point
+of view but not necessarily have to uh
+
+ align:start position:0%
+of view but not necessarily have to uh
+ 
+
+ align:start position:0%
+of view but not necessarily have to uh
+wait for an additional say nine runs
+
+ align:start position:0%
+wait for an additional say nine runs
+ 
+
+ align:start position:0%
+wait for an additional say nine runs
+before you call that a sample aggregate
+
+ align:start position:0%
+before you call that a sample aggregate
+ 
+
+ align:start position:0%
+before you call that a sample aggregate
+it and then plot it and then wait for
+
+ align:start position:0%
+it and then plot it and then wait for
+ 
+
+ align:start position:0%
+it and then plot it and then wait for
+another nine runs one alternative
+
+ align:start position:0%
+another nine runs one alternative
+ 
+
+ align:start position:0%
+another nine runs one alternative
+approach here is to take a running
+
+ align:start position:0%
+approach here is to take a running
+ 
+
+ align:start position:0%
+approach here is to take a running
+average so I take a window say of nine
+
+ align:start position:0%
+average so I take a window say of nine
+ 
+
+ align:start position:0%
+average so I take a window say of nine
+points and measurements calculate my
+
+ align:start position:0%
+points and measurements calculate my
+ 
+
+ align:start position:0%
+points and measurements calculate my
+statistics and then for each new run
+
+ align:start position:0%
+statistics and then for each new run
+ 
+
+ align:start position:0%
+statistics and then for each new run
+move my window over and recalculate my
+
+ align:start position:0%
+move my window over and recalculate my
+ 
+
+ align:start position:0%
+move my window over and recalculate my
+statistics so that I'm in some sense up
+
+ align:start position:0%
+statistics so that I'm in some sense up
+ 
+
+ align:start position:0%
+statistics so that I'm in some sense up
+dating what uh my best guess of the
+
+ align:start position:0%
+dating what uh my best guess of the
+ 
+
+ align:start position:0%
+dating what uh my best guess of the
+current state of the process is after
+
+ align:start position:0%
+current state of the process is after
+ 
+
+ align:start position:0%
+current state of the process is after
+every after every run and the advantages
+
+ align:start position:0%
+every after every run and the advantages
+ 
+
+ align:start position:0%
+every after every run and the advantages
+of this are that you can get more
+
+ align:start position:0%
+of this are that you can get more
+ 
+
+ align:start position:0%
+of this are that you can get more
+averages per unit of
+
+ align:start position:0%
+averages per unit of
+ 
+
+ align:start position:0%
+averages per unit of
+data okay um you can go ahead and run uh
+
+ align:start position:0%
+data okay um you can go ahead and run uh
+ 
+
+ align:start position:0%
+data okay um you can go ahead and run uh
+use the Run data
+
+ align:start position:0%
+use the Run data
+ 
+
+ align:start position:0%
+use the Run data
+Alone um if you wanted to you could
+
+ align:start position:0%
+Alone um if you wanted to you could
+ 
+
+ align:start position:0%
+Alone um if you wanted to you could
+actually plot for
+
+ align:start position:0%
+actually plot for
+ 
+
+ align:start position:0%
+actually plot for
+example uh the individual measurements
+
+ align:start position:0%
+example uh the individual measurements
+ 
+
+ align:start position:0%
+example uh the individual measurements
+and even do a hybrid sort of thing where
+
+ align:start position:0%
+and even do a hybrid sort of thing where
+ 
+
+ align:start position:0%
+and even do a hybrid sort of thing where
+you you did a running average just for
+
+ align:start position:0%
+you you did a running average just for
+ 
+
+ align:start position:0%
+you you did a running average just for
+the standard
+
+ align:start position:0%
+the standard
+ 
+
+ align:start position:0%
+the standard
+deviation but the real advantage of
+
+ align:start position:0%
+deviation but the real advantage of
+ 
+
+ align:start position:0%
+deviation but the real advantage of
+these is they essentially improve your
+
+ align:start position:0%
+these is they essentially improve your
+ 
+
+ align:start position:0%
+these is they essentially improve your
+ability to detect they improve the
+
+ align:start position:0%
+ability to detect they improve the
+ 
+
+ align:start position:0%
+ability to detect they improve the
+filtering action potentially because you
+
+ align:start position:0%
+filtering action potentially because you
+ 
+
+ align:start position:0%
+filtering action potentially because you
+can play with that window size to uh
+
+ align:start position:0%
+can play with that window size to uh
+ 
+
+ align:start position:0%
+can play with that window size to uh
+filter more but also be able to react
+
+ align:start position:0%
+filter more but also be able to react
+ 
+
+ align:start position:0%
+filter more but also be able to react
+potentially faster so I'm going to
+
+ align:start position:0%
+potentially faster so I'm going to
+ 
+
+ align:start position:0%
+potentially faster so I'm going to
+describe a couple of these alternative
+
+ align:start position:0%
+describe a couple of these alternative
+ 
+
+ align:start position:0%
+describe a couple of these alternative
+uh charts and I'm going to focus really
+
+ align:start position:0%
+uh charts and I'm going to focus really
+ 
+
+ align:start position:0%
+uh charts and I'm going to focus really
+on the running average average detection
+
+ align:start position:0%
+on the running average average detection
+ 
+
+ align:start position:0%
+on the running average average detection
+of the mean but the same idea also
+
+ align:start position:0%
+of the mean but the same idea also
+ 
+
+ align:start position:0%
+of the mean but the same idea also
+applies to filtering of the variant
+
+ align:start position:0%
+applies to filtering of the variant
+ 
+
+ align:start position:0%
+applies to filtering of the variant
+across multiple runs so there's
+
+ align:start position:0%
+across multiple runs so there's
+ 
+
+ align:start position:0%
+across multiple runs so there's
+also running s charts or running moving
+
+ align:start position:0%
+also running s charts or running moving
+ 
+
+ align:start position:0%
+also running s charts or running moving
+uh range charts and those sorts of
+
+ align:start position:0%
+uh range charts and those sorts of
+ 
+
+ align:start position:0%
+uh range charts and those sorts of
+things uh so don't forget the lesson we
+
+ align:start position:0%
+things uh so don't forget the lesson we
+ 
+
+ align:start position:0%
+things uh so don't forget the lesson we
+just learned a minute ago you got to
+
+ align:start position:0%
+just learned a minute ago you got to
+ 
+
+ align:start position:0%
+just learned a minute ago you got to
+monitor both mean and variance but for
+
+ align:start position:0%
+monitor both mean and variance but for
+ 
+
+ align:start position:0%
+monitor both mean and variance but for
+the for the next 10 15 slides I'm only
+
+ align:start position:0%
+the for the next 10 15 slides I'm only
+ 
+
+ align:start position:0%
+the for the next 10 15 slides I'm only
+going to talk talk about running
+
+ align:start position:0%
+going to talk talk about running
+ 
+
+ align:start position:0%
+going to talk talk about running
+averages on the on the
+
+ align:start position:0%
+averages on the on the
+ 
+
+ align:start position:0%
+averages on the on the
+average so one uh idea of the running
+
+ align:start position:0%
+average so one uh idea of the running
+ 
+
+ align:start position:0%
+average so one uh idea of the running
+average is a simple running average or
+
+ align:start position:0%
+average is a simple running average or
+ 
+
+ align:start position:0%
+average is a simple running average or
+or moving average where we'd simply take
+
+ align:start position:0%
+or moving average where we'd simply take
+ 
+
+ align:start position:0%
+or moving average where we'd simply take
+some uh n values of the past and
+
+ align:start position:0%
+some uh n values of the past and
+ 
+
+ align:start position:0%
+some uh n values of the past and
+calculate say a simple average and
+
+ align:start position:0%
+calculate say a simple average and
+ 
+
+ align:start position:0%
+calculate say a simple average and
+similarly we could do that for the
+
+ align:start position:0%
+similarly we could do that for the
+ 
+
+ align:start position:0%
+similarly we could do that for the
+variance so in that case this simplest
+
+ align:start position:0%
+variance so in that case this simplest
+ 
+
+ align:start position:0%
+variance so in that case this simplest
+picture this simple moving average is
+
+ align:start position:0%
+picture this simple moving average is
+ 
+
+ align:start position:0%
+picture this simple moving average is
+just a an equally weighted window you
+
+ align:start position:0%
+just a an equally weighted window you
+ 
+
+ align:start position:0%
+just a an equally weighted window you
+you pick your window size maybe it's
+
+ align:start position:0%
+you pick your window size maybe it's
+ 
+
+ align:start position:0%
+you pick your window size maybe it's
+a window size of nine and you calculate
+
+ align:start position:0%
+a window size of nine and you calculate
+ 
+
+ align:start position:0%
+a window size of nine and you calculate
+a new moving average statistic which
+
+ align:start position:0%
+a new moving average statistic which
+ 
+
+ align:start position:0%
+a new moving average statistic which
+I've labeled M subi here and so that's
+
+ align:start position:0%
+I've labeled M subi here and so that's
+ 
+
+ align:start position:0%
+I've labeled M subi here and so that's
+pretty trivial formula now how do you
+
+ align:start position:0%
+pretty trivial formula now how do you
+ 
+
+ align:start position:0%
+pretty trivial formula now how do you
+set the control limits on a moving
+
+ align:start position:0%
+set the control limits on a moving
+ 
+
+ align:start position:0%
+set the control limits on a moving
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+chart well you want plusus 3 Sigma say
+
+ align:start position:0%
+chart well you want plusus 3 Sigma say
+ 
+
+ align:start position:0%
+chart well you want plusus 3 Sigma say
+control limits based on the variance
+
+ align:start position:0%
+control limits based on the variance
+ 
+
+ align:start position:0%
+control limits based on the variance
+that you expect in your statistic right
+
+ align:start position:0%
+that you expect in your statistic right
+ 
+
+ align:start position:0%
+that you expect in your statistic right
+so previously would have sample
+
+ align:start position:0%
+so previously would have sample
+ 
+
+ align:start position:0%
+so previously would have sample
+size of of nine and we'd say well what
+
+ align:start position:0%
+size of of nine and we'd say well what
+ 
+
+ align:start position:0%
+size of of nine and we'd say well what
+the what's the variance it's one over
+
+ align:start position:0%
+the what's the variance it's one over
+ 
+
+ align:start position:0%
+the what's the variance it's one over
+it's Sigma over root n is the standard
+
+ align:start position:0%
+it's Sigma over root n is the standard
+ 
+
+ align:start position:0%
+it's Sigma over root n is the standard
+deviation associated with that move with
+
+ align:start position:0%
+deviation associated with that move with
+ 
+
+ align:start position:0%
+deviation associated with that move with
+with our normal sample size and that
+
+ align:start position:0%
+with our normal sample size and that
+ 
+
+ align:start position:0%
+with our normal sample size and that
+same formula ends up working here
+
+ align:start position:0%
+same formula ends up working here
+ 
+
+ align:start position:0%
+same formula ends up working here
+because we've got equal weighting right
+
+ align:start position:0%
+because we've got equal weighting right
+ 
+
+ align:start position:0%
+because we've got equal weighting right
+so if we simply
+
+ align:start position:0%
+so if we simply
+ 
+
+ align:start position:0%
+so if we simply
+apply uh again assuming uh not assuming
+
+ align:start position:0%
+apply uh again assuming uh not assuming
+ 
+
+ align:start position:0%
+apply uh again assuming uh not assuming
+each of the points are truly in process
+
+ align:start position:0%
+each of the points are truly in process
+ 
+
+ align:start position:0%
+each of the points are truly in process
+control and I do not have correlation in
+
+ align:start position:0%
+control and I do not have correlation in
+ 
+
+ align:start position:0%
+control and I do not have correlation in
+time between them uh it's it's very easy
+
+ align:start position:0%
+time between them uh it's it's very easy
+ 
+
+ align:start position:0%
+time between them uh it's it's very easy
+to see what the variance is now you'll
+
+ align:start position:0%
+to see what the variance is now you'll
+ 
+
+ align:start position:0%
+to see what the variance is now you'll
+notice something a little strange right
+
+ align:start position:0%
+notice something a little strange right
+ 
+
+ align:start position:0%
+notice something a little strange right
+here at the
+
+ align:start position:0%
+here at the
+ 
+
+ align:start position:0%
+here at the
+beginning this is kind of an artifact of
+
+ align:start position:0%
+beginning this is kind of an artifact of
+ 
+
+ align:start position:0%
+beginning this is kind of an artifact of
+the startup of the of the chart let's
+
+ align:start position:0%
+the startup of the of the chart let's
+ 
+
+ align:start position:0%
+the startup of the of the chart let's
+say I have just started the use of the
+
+ align:start position:0%
+say I have just started the use of the
+ 
+
+ align:start position:0%
+say I have just started the use of the
+control chart and I've only got five
+
+ align:start position:0%
+control chart and I've only got five
+ 
+
+ align:start position:0%
+control chart and I've only got five
+samples so far but I've got a moving
+
+ align:start position:0%
+samples so far but I've got a moving
+ 
+
+ align:start position:0%
+samples so far but I've got a moving
+average window of
+
+ align:start position:0%
+average window of
+ 
+
+ align:start position:0%
+average window of
+nine well I don't have nine data points
+
+ align:start position:0%
+nine well I don't have nine data points
+ 
+
+ align:start position:0%
+nine well I don't have nine data points
+yet I have to my moving average really
+
+ align:start position:0%
+yet I have to my moving average really
+ 
+
+ align:start position:0%
+yet I have to my moving average really
+with a window size only of five so far
+
+ align:start position:0%
+with a window size only of five so far
+ 
+
+ align:start position:0%
+with a window size only of five so far
+and because I'm taking the variance
+
+ align:start position:0%
+and because I'm taking the variance
+ 
+
+ align:start position:0%
+and because I'm taking the variance
+divided by five instead of divided by
+
+ align:start position:0%
+divided by five instead of divided by
+ 
+
+ align:start position:0%
+divided by five instead of divided by
+9 the variance of my average of a
+
+ align:start position:0%
+9 the variance of my average of a
+ 
+
+ align:start position:0%
+9 the variance of my average of a
+fivepoint sample is larger and you can
+
+ align:start position:0%
+fivepoint sample is larger and you can
+ 
+
+ align:start position:0%
+fivepoint sample is larger and you can
+see essentially each sample until I get
+
+ align:start position:0%
+see essentially each sample until I get
+ 
+
+ align:start position:0%
+see essentially each sample until I get
+to my full window size of nine has
+
+ align:start position:0%
+to my full window size of nine has
+ 
+
+ align:start position:0%
+to my full window size of nine has
+slightly larger control chart limits
+
+ align:start position:0%
+slightly larger control chart limits
+ 
+
+ align:start position:0%
+slightly larger control chart limits
+okay so that's what's going on
+
+ align:start position:0%
+okay so that's what's going on
+ 
+
+ align:start position:0%
+okay so that's what's going on
+there okay and you can also sort of see
+
+ align:start position:0%
+there okay and you can also sort of see
+ 
+
+ align:start position:0%
+there okay and you can also sort of see
+here now the filtering action at work
+
+ align:start position:0%
+here now the filtering action at work
+ 
+
+ align:start position:0%
+here now the filtering action at work
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+that uh each of these each of these
+
+ align:start position:0%
+that uh each of these each of these
+ 
+
+ align:start position:0%
+that uh each of these each of these
+samples don't vary dramatically from the
+
+ align:start position:0%
+samples don't vary dramatically from the
+ 
+
+ align:start position:0%
+samples don't vary dramatically from the
+from the previous one they are no longer
+
+ align:start position:0%
+from the previous one they are no longer
+ 
+
+ align:start position:0%
+from the previous one they are no longer
+uncorrelated from one sample to the next
+
+ align:start position:0%
+uncorrelated from one sample to the next
+ 
+
+ align:start position:0%
+uncorrelated from one sample to the next
+in fact with this equal waiting you know
+
+ align:start position:0%
+in fact with this equal waiting you know
+ 
+
+ align:start position:0%
+in fact with this equal waiting you know
+every new time Point
+
+ align:start position:0%
+every new time Point
+ 
+
+ align:start position:0%
+every new time Point
+shares
+
+ align:start position:0%
+shares
+ 
+
+ align:start position:0%
+shares
+88% of the data with the pr previous
+
+ align:start position:0%
+88% of the data with the pr previous
+ 
+
+ align:start position:0%
+88% of the data with the pr previous
+uh data point so there's a huge amount
+
+ align:start position:0%
+uh data point so there's a huge amount
+ 
+
+ align:start position:0%
+uh data point so there's a huge amount
+of correlation from one point in time
+
+ align:start position:0%
+of correlation from one point in time
+ 
+
+ align:start position:0%
+of correlation from one point in time
+and the next so you should
+
+ align:start position:0%
+and the next so you should
+ 
+
+ align:start position:0%
+and the next so you should
+not try to use things like the weo rules
+
+ align:start position:0%
+not try to use things like the weo rules
+ 
+
+ align:start position:0%
+not try to use things like the weo rules
+associated with three data points in a
+
+ align:start position:0%
+associated with three data points in a
+ 
+
+ align:start position:0%
+associated with three data points in a
+row or four or five data points in a row
+
+ align:start position:0%
+row or four or five data points in a row
+ 
+
+ align:start position:0%
+row or four or five data points in a row
+Rising those things are right out
+
+ align:start position:0%
+Rising those things are right out
+ 
+
+ align:start position:0%
+Rising those things are right out
+because this is a running control chart
+
+ align:start position:0%
+because this is a running control chart
+ 
+
+ align:start position:0%
+because this is a running control chart
+or moving average control chart and
+
+ align:start position:0%
+or moving average control chart and
+ 
+
+ align:start position:0%
+or moving average control chart and
+you've now got correlation its benefit
+
+ align:start position:0%
+you've now got correlation its benefit
+ 
+
+ align:start position:0%
+you've now got correlation its benefit
+though is that it is doing that
+
+ align:start position:0%
+though is that it is doing that
+ 
+
+ align:start position:0%
+though is that it is doing that
+filtering and you
+
+ align:start position:0%
+filtering and you
+ 
+
+ align:start position:0%
+filtering and you
+can take whatever current point that you
+
+ align:start position:0%
+can take whatever current point that you
+ 
+
+ align:start position:0%
+can take whatever current point that you
+get as a sort of your best guess of what
+
+ align:start position:0%
+get as a sort of your best guess of what
+ 
+
+ align:start position:0%
+get as a sort of your best guess of what
+the current state of the uh overall mean
+
+ align:start position:0%
+the current state of the uh overall mean
+ 
+
+ align:start position:0%
+the current state of the uh overall mean
+is and so you would trigger on alarms uh
+
+ align:start position:0%
+is and so you would trigger on alarms uh
+ 
+
+ align:start position:0%
+is and so you would trigger on alarms uh
+above or below the control
+
+ align:start position:0%
+above or below the control
+ 
+
+ align:start position:0%
+above or below the control
+limits
+
+ align:start position:0%
+limits
+ 
+
+ align:start position:0%
+limits
+okay so simple moving average this is
+
+ align:start position:0%
+okay so simple moving average this is
+ 
+
+ align:start position:0%
+okay so simple moving average this is
+relatively simple any questions on this
+
+ align:start position:0%
+relatively simple any questions on this
+ 
+
+ align:start position:0%
+relatively simple any questions on this
+before we do a
+
+ align:start position:0%
+before we do a
+ 
+
+ align:start position:0%
+before we do a
+unequally weighted moving
+
+ align:start position:0%
+unequally weighted moving
+ 
+
+ align:start position:0%
+unequally weighted moving
+average pretty
+
+ align:start position:0%
+average pretty
+ 
+
+ align:start position:0%
+average pretty
+clear I have a question Professor yes
+
+ align:start position:0%
+clear I have a question Professor yes
+ 
+
+ align:start position:0%
+clear I have a question Professor yes
+good these these questions have been
+
+ align:start position:0%
+good these these questions have been
+ 
+
+ align:start position:0%
+good these these questions have been
+wonderful by the way like the last
+
+ align:start position:0%
+wonderful by the way like the last
+ 
+
+ align:start position:0%
+wonderful by the way like the last
+couple of classes uh I think the
+
+ align:start position:0%
+couple of classes uh I think the
+ 
+
+ align:start position:0%
+couple of classes uh I think the
+questions have really uh been right on
+
+ align:start position:0%
+questions have really uh been right on
+ 
+
+ align:start position:0%
+questions have really uh been right on
+Target and it's been a lot of fun so we
+
+ align:start position:0%
+Target and it's been a lot of fun so we
+ 
+
+ align:start position:0%
+Target and it's been a lot of fun so we
+have high expectations for your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay so that's a lot of
+
+ align:start position:0%
+question okay so that's a lot of
+ 
+
+ align:start position:0%
+question okay so that's a lot of
+pressure but my question is that for the
+
+ align:start position:0%
+pressure but my question is that for the
+ 
+
+ align:start position:0%
+pressure but my question is that for the
+window size of nine so do do the two uh
+
+ align:start position:0%
+window size of nine so do do the two uh
+ 
+
+ align:start position:0%
+window size of nine so do do the two uh
+Windows next to each other they overlap
+
+ align:start position:0%
+Windows next to each other they overlap
+ 
+
+ align:start position:0%
+Windows next to each other they overlap
+by uh eight data points
+
+ align:start position:0%
+by uh eight data points
+ 
+
+ align:start position:0%
+by uh eight data points
+right okay that's it that's exactly
+
+ align:start position:0%
+right okay that's it that's exactly
+ 
+
+ align:start position:0%
+right okay that's it that's exactly
+right so okay thank
+
+ align:start position:0%
+right so okay thank
+ 
+
+ align:start position:0%
+right so okay thank
+you now one problem with that overlap of
+
+ align:start position:0%
+you now one problem with that overlap of
+ 
+
+ align:start position:0%
+you now one problem with that overlap of
+eight data points is by the time you get
+
+ align:start position:0%
+eight data points is by the time you get
+ 
+
+ align:start position:0%
+eight data points is by the time you get
+to uh you know eight points in the past
+
+ align:start position:0%
+to uh you know eight points in the past
+ 
+
+ align:start position:0%
+to uh you know eight points in the past
+it may be you
+
+ align:start position:0%
+it may be you
+ 
+
+ align:start position:0%
+it may be you
+know that's a long time ago depending on
+
+ align:start position:0%
+know that's a long time ago depending on
+ 
+
+ align:start position:0%
+know that's a long time ago depending on
+on you know how rapidly you're sampling
+
+ align:start position:0%
+on you know how rapidly you're sampling
+ 
+
+ align:start position:0%
+on you know how rapidly you're sampling
+or whatever and compared to the data
+
+ align:start position:0%
+or whatever and compared to the data
+ 
+
+ align:start position:0%
+or whatever and compared to the data
+point that you just took you might think
+
+ align:start position:0%
+point that you just took you might think
+ 
+
+ align:start position:0%
+point that you just took you might think
+that the data point you just took
+
+ align:start position:0%
+that the data point you just took
+ 
+
+ align:start position:0%
+that the data point you just took
+represents the current state of the
+
+ align:start position:0%
+represents the current state of the
+ 
+
+ align:start position:0%
+represents the current state of the
+process a lot better than the 789 time
+
+ align:start position:0%
+process a lot better than the 789 time
+ 
+
+ align:start position:0%
+process a lot better than the 789 time
+points ago and so there is a more
+
+ align:start position:0%
+points ago and so there is a more
+ 
+
+ align:start position:0%
+points ago and so there is a more
+General approach here where you can pick
+
+ align:start position:0%
+General approach here where you can pick
+ 
+
+ align:start position:0%
+General approach here where you can pick
+some waiting for how much you want to
+
+ align:start position:0%
+some waiting for how much you want to
+ 
+
+ align:start position:0%
+some waiting for how much you want to
+fold in data from different points in
+
+ align:start position:0%
+fold in data from different points in
+ 
+
+ align:start position:0%
+fold in data from different points in
+time okay and a classic way way to do
+
+ align:start position:0%
+time okay and a classic way way to do
+ 
+
+ align:start position:0%
+time okay and a classic way way to do
+the waiting is to use an exponentially
+
+ align:start position:0%
+the waiting is to use an exponentially
+ 
+
+ align:start position:0%
+the waiting is to use an exponentially
+weighted moving average where you might
+
+ align:start position:0%
+weighted moving average where you might
+ 
+
+ align:start position:0%
+weighted moving average where you might
+Define The Waiting function these a
+
+ align:start position:0%
+Define The Waiting function these a
+ 
+
+ align:start position:0%
+Define The Waiting function these a
+subis here I guess I've switched
+
+ align:start position:0%
+subis here I guess I've switched
+ 
+
+ align:start position:0%
+subis here I guess I've switched
+notation to a w here um when I'm at the
+
+ align:start position:0%
+notation to a w here um when I'm at the
+ 
+
+ align:start position:0%
+notation to a w here um when I'm at the
+current sample point or the current time
+
+ align:start position:0%
+current sample point or the current time
+ 
+
+ align:start position:0%
+current sample point or the current time
+Point T I might wait points backwards in
+
+ align:start position:0%
+Point T I might wait points backwards in
+ 
+
+ align:start position:0%
+Point T I might wait points backwards in
+time by index I I going from 1 to 9 to a
+
+ align:start position:0%
+time by index I I going from 1 to 9 to a
+ 
+
+ align:start position:0%
+time by index I I going from 1 to 9 to a
+th whatever uh by a function looking
+
+ align:start position:0%
+th whatever uh by a function looking
+ 
+
+ align:start position:0%
+th whatever uh by a function looking
+something like this with some
+
+ align:start position:0%
+something like this with some
+ 
+
+ align:start position:0%
+something like this with some
+r factor this where where R is sort of
+
+ align:start position:0%
+r factor this where where R is sort of
+ 
+
+ align:start position:0%
+r factor this where where R is sort of
+the waiting the waiting Factor so what
+
+ align:start position:0%
+the waiting the waiting Factor so what
+ 
+
+ align:start position:0%
+the waiting the waiting Factor so what
+happens here as I might think of r as
+
+ align:start position:0%
+happens here as I might think of r as
+ 
+
+ align:start position:0%
+happens here as I might think of r as
+being how much I believe my current data
+
+ align:start position:0%
+being how much I believe my current data
+ 
+
+ align:start position:0%
+being how much I believe my current data
+point and it might be I believe my
+
+ align:start position:0%
+point and it might be I believe my
+ 
+
+ align:start position:0%
+point and it might be I believe my
+current data point by
+
+ align:start position:0%
+current data point by
+ 
+
+ align:start position:0%
+current data point by
+90% And then the next data point one
+
+ align:start position:0%
+90% And then the next data point one
+ 
+
+ align:start position:0%
+90% And then the next data point one
+minus r is only 10% so I'm only mixing
+
+ align:start position:0%
+minus r is only 10% so I'm only mixing
+ 
+
+ align:start position:0%
+minus r is only 10% so I'm only mixing
+in 10% of that and then the next data
+
+ align:start position:0%
+in 10% of that and then the next data
+ 
+
+ align:start position:0%
+in 10% of that and then the next data
+point beyond that that it's maybe 0.1
+
+ align:start position:0%
+point beyond that that it's maybe 0.1
+ 
+
+ align:start position:0%
+point beyond that that it's maybe 0.1
+time 0.1 it's only 0.01 so I'm only
+
+ align:start position:0%
+time 0.1 it's only 0.01 so I'm only
+ 
+
+ align:start position:0%
+time 0.1 it's only 0.01 so I'm only
+mixing in 1% of the the previous data
+
+ align:start position:0%
+mixing in 1% of the the previous data
+ 
+
+ align:start position:0%
+mixing in 1% of the the previous data
+point so very rapidly I have this drop
+
+ align:start position:0%
+point so very rapidly I have this drop
+ 
+
+ align:start position:0%
+point so very rapidly I have this drop
+off as a function of uh data points in
+
+ align:start position:0%
+off as a function of uh data points in
+ 
+
+ align:start position:0%
+off as a function of uh data points in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+past this is my I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+index so that so that I much more
+
+ align:start position:0%
+index so that so that I much more
+ 
+
+ align:start position:0%
+index so that so that I much more
+heavily wait recent history and then
+
+ align:start position:0%
+heavily wait recent history and then
+ 
+
+ align:start position:0%
+heavily wait recent history and then
+exponentially Decay uh in into the
+
+ align:start position:0%
+exponentially Decay uh in into the
+ 
+
+ align:start position:0%
+exponentially Decay uh in into the
+past okay but I still have this degree
+
+ align:start position:0%
+past okay but I still have this degree
+ 
+
+ align:start position:0%
+past okay but I still have this degree
+of Freedom how much do I want to I can I
+
+ align:start position:0%
+of Freedom how much do I want to I can I
+ 
+
+ align:start position:0%
+of Freedom how much do I want to I can I
+can pick r i can sort of pick the
+
+ align:start position:0%
+can pick r i can sort of pick the
+ 
+
+ align:start position:0%
+can pick r i can sort of pick the
+relative weighting of of more recent
+
+ align:start position:0%
+relative weighting of of more recent
+ 
+
+ align:start position:0%
+relative weighting of of more recent
+data compared to compared to old
+
+ align:start position:0%
+data compared to compared to old
+ 
+
+ align:start position:0%
+data compared to compared to old
+data now one way of looking at this is
+
+ align:start position:0%
+data now one way of looking at this is
+ 
+
+ align:start position:0%
+data now one way of looking at this is
+actually I have access to all past
+
+ align:start position:0%
+actually I have access to all past
+ 
+
+ align:start position:0%
+actually I have access to all past
+data and I would apply this out to you
+
+ align:start position:0%
+data and I would apply this out to you
+ 
+
+ align:start position:0%
+data and I would apply this out to you
+know 20 data points or 50 or 100 with
+
+ align:start position:0%
+know 20 data points or 50 or 100 with
+ 
+
+ align:start position:0%
+know 20 data points or 50 or 100 with
+the appropriate waiting
+
+ align:start position:0%
+the appropriate waiting
+ 
+
+ align:start position:0%
+the appropriate waiting
+function right and I guess with computer
+
+ align:start position:0%
+function right and I guess with computer
+ 
+
+ align:start position:0%
+function right and I guess with computer
+systems these days it would be no
+
+ align:start position:0%
+systems these days it would be no
+ 
+
+ align:start position:0%
+systems these days it would be no
+problem to actually apply it in that in
+
+ align:start position:0%
+problem to actually apply it in that in
+ 
+
+ align:start position:0%
+problem to actually apply it in that in
+that fashion there's a beautiful thing
+
+ align:start position:0%
+that fashion there's a beautiful thing
+ 
+
+ align:start position:0%
+that fashion there's a beautiful thing
+about the exponentially weighted moving
+
+ align:start position:0%
+about the exponentially weighted moving
+ 
+
+ align:start position:0%
+about the exponentially weighted moving
+average which is I actually don't have
+
+ align:start position:0%
+average which is I actually don't have
+ 
+
+ align:start position:0%
+average which is I actually don't have
+to keep track of all of the raw
+
+ align:start position:0%
+to keep track of all of the raw
+ 
+
+ align:start position:0%
+to keep track of all of the raw
+data there's another way of thinking
+
+ align:start position:0%
+data there's another way of thinking
+ 
+
+ align:start position:0%
+data there's another way of thinking
+about what the ewma this exponential
+
+ align:start position:0%
+about what the ewma this exponential
+ 
+
+ align:start position:0%
+about what the ewma this exponential
+weighted moving average is doing and
+
+ align:start position:0%
+weighted moving average is doing and
+ 
+
+ align:start position:0%
+weighted moving average is doing and
+that's that I have my previous best
+
+ align:start position:0%
+that's that I have my previous best
+ 
+
+ align:start position:0%
+that's that I have my previous best
+estimate of the state of my variable my
+
+ align:start position:0%
+estimate of the state of my variable my
+ 
+
+ align:start position:0%
+estimate of the state of my variable my
+previous best estimate of the mean and
+
+ align:start position:0%
+previous best estimate of the mean and
+ 
+
+ align:start position:0%
+previous best estimate of the mean and
+now I have one new data point and I use
+
+ align:start position:0%
+now I have one new data point and I use
+ 
+
+ align:start position:0%
+now I have one new data point and I use
+that one new data point to update my
+
+ align:start position:0%
+that one new data point to update my
+ 
+
+ align:start position:0%
+that one new data point to update my
+best estimate my best estimate had
+
+ align:start position:0%
+best estimate my best estimate had
+ 
+
+ align:start position:0%
+best estimate my best estimate had
+embedded in it all of the past history
+
+ align:start position:0%
+embedded in it all of the past history
+ 
+
+ align:start position:0%
+embedded in it all of the past history
+so now with the additional new weight I
+
+ align:start position:0%
+so now with the additional new weight I
+ 
+
+ align:start position:0%
+so now with the additional new weight I
+can just do a simple update of my best
+
+ align:start position:0%
+can just do a simple update of my best
+ 
+
+ align:start position:0%
+can just do a simple update of my best
+state estimate and there is essentially
+
+ align:start position:0%
+state estimate and there is essentially
+ 
+
+ align:start position:0%
+state estimate and there is essentially
+a recursive formula that makes this
+
+ align:start position:0%
+a recursive formula that makes this
+ 
+
+ align:start position:0%
+a recursive formula that makes this
+explicit and it's exactly the same thing
+
+ align:start position:0%
+explicit and it's exactly the same thing
+ 
+
+ align:start position:0%
+explicit and it's exactly the same thing
+if you now apply it iteratively out to
+
+ align:start position:0%
+if you now apply it iteratively out to
+ 
+
+ align:start position:0%
+if you now apply it iteratively out to
+all history as actually performing that
+
+ align:start position:0%
+all history as actually performing that
+ 
+
+ align:start position:0%
+all history as actually performing that
+comp computation of applying the weights
+
+ align:start position:0%
+comp computation of applying the weights
+ 
+
+ align:start position:0%
+comp computation of applying the weights
+on all all past data so that is to say
+
+ align:start position:0%
+on all all past data so that is to say
+ 
+
+ align:start position:0%
+on all all past data so that is to say
+let's say a subi is my best estimate of
+
+ align:start position:0%
+let's say a subi is my best estimate of
+ 
+
+ align:start position:0%
+let's say a subi is my best estimate of
+of whatever my statistic is my mean
+
+ align:start position:0%
+of whatever my statistic is my mean
+ 
+
+ align:start position:0%
+of whatever my statistic is my mean
+again I might wait my current data point
+
+ align:start position:0%
+again I might wait my current data point
+ 
+
+ align:start position:0%
+again I might wait my current data point
+my most recent data point say 90% which
+
+ align:start position:0%
+my most recent data point say 90% which
+ 
+
+ align:start position:0%
+my most recent data point say 90% which
+would be you know really rapid update I
+
+ align:start position:0%
+would be you know really rapid update I
+ 
+
+ align:start position:0%
+would be you know really rapid update I
+really believe my most recent data and
+
+ align:start position:0%
+really believe my most recent data and
+ 
+
+ align:start position:0%
+really believe my most recent data and
+then my one minus r applies to my
+
+ align:start position:0%
+then my one minus r applies to my
+ 
+
+ align:start position:0%
+then my one minus r applies to my
+previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops to to my previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimate right so I'm believing only 10%
+
+ align:start position:0%
+estimate right so I'm believing only 10%
+ 
+
+ align:start position:0%
+estimate right so I'm believing only 10%
+my previous estimate and 90% my new
+
+ align:start position:0%
+my previous estimate and 90% my new
+ 
+
+ align:start position:0%
+my previous estimate and 90% my new
+estimate
+
+ align:start position:0%
+estimate
+ 
+
+ align:start position:0%
+estimate
+okay so it makes it a little bit easier
+
+ align:start position:0%
+okay so it makes it a little bit easier
+ 
+
+ align:start position:0%
+okay so it makes it a little bit easier
+in terms of uh the computation but I
+
+ align:start position:0%
+in terms of uh the computation but I
+ 
+
+ align:start position:0%
+in terms of uh the computation but I
+think it's also conceptually nice in
+
+ align:start position:0%
+think it's also conceptually nice in
+ 
+
+ align:start position:0%
+think it's also conceptually nice in
+terms of what the action here
+
+ align:start position:0%
+terms of what the action here
+ 
+
+ align:start position:0%
+terms of what the action here
+is now one can go through and do a
+
+ align:start position:0%
+is now one can go through and do a
+ 
+
+ align:start position:0%
+is now one can go through and do a
+little bit of the uh the the mathematics
+
+ align:start position:0%
+little bit of the uh the the mathematics
+ 
+
+ align:start position:0%
+little bit of the uh the the mathematics
+it's actually a little easier to do it
+
+ align:start position:0%
+it's actually a little easier to do it
+ 
+
+ align:start position:0%
+it's actually a little easier to do it
+on the full summation version but you
+
+ align:start position:0%
+on the full summation version but you
+ 
+
+ align:start position:0%
+on the full summation version but you
+just do basic uh expectation math on the
+
+ align:start position:0%
+just do basic uh expectation math on the
+ 
+
+ align:start position:0%
+just do basic uh expectation math on the
+variance of an
+
+ align:start position:0%
+variance of an
+ 
+
+ align:start position:0%
+variance of an
+ewma again drawing from a normal normal
+
+ align:start position:0%
+ewma again drawing from a normal normal
+ 
+
+ align:start position:0%
+ewma again drawing from a normal normal
+distribution that is in control and one
+
+ align:start position:0%
+distribution that is in control and one
+ 
+
+ align:start position:0%
+distribution that is in control and one
+can estimate the standard deviation of
+
+ align:start position:0%
+can estimate the standard deviation of
+ 
+
+ align:start position:0%
+can estimate the standard deviation of
+this a
+
+ align:start position:0%
+this a
+ 
+
+ align:start position:0%
+this a
+statistic and it's kind of a little bit
+
+ align:start position:0%
+statistic and it's kind of a little bit
+ 
+
+ align:start position:0%
+statistic and it's kind of a little bit
+messy it's got the underlying process
+
+ align:start position:0%
+messy it's got the underlying process
+ 
+
+ align:start position:0%
+messy it's got the underlying process
+variation in it the fact that you are
+
+ align:start position:0%
+variation in it the fact that you are
+ 
+
+ align:start position:0%
+variation in it the fact that you are
+still um you you can still be doing
+
+ align:start position:0%
+still um you you can still be doing
+ 
+
+ align:start position:0%
+still um you you can still be doing
+sampling for each x sub I that might be
+
+ align:start position:0%
+sampling for each x sub I that might be
+ 
+
+ align:start position:0%
+sampling for each x sub I that might be
+a sample of end data points very often
+
+ align:start position:0%
+a sample of end data points very often
+ 
+
+ align:start position:0%
+a sample of end data points very often
+you might simply be doing it one data
+
+ align:start position:0%
+you might simply be doing it one data
+ 
+
+ align:start position:0%
+you might simply be doing it one data
+point so n very often is just one and
+
+ align:start position:0%
+point so n very often is just one and
+ 
+
+ align:start position:0%
+point so n very often is just one and
+then this formula with r in it including
+
+ align:start position:0%
+then this formula with r in it including
+ 
+
+ align:start position:0%
+then this formula with r in it including
+this one - one - R to the 2T where T is
+
+ align:start position:0%
+this one - one - R to the 2T where T is
+ 
+
+ align:start position:0%
+this one - one - R to the 2T where T is
+how far along you are so it's kind of
+
+ align:start position:0%
+how far along you are so it's kind of
+ 
+
+ align:start position:0%
+how far along you are so it's kind of
+nasty but one thing that's nice is once
+
+ align:start position:0%
+nasty but one thing that's nice is once
+ 
+
+ align:start position:0%
+nasty but one thing that's nice is once
+you started up your control chart and
+
+ align:start position:0%
+you started up your control chart and
+ 
+
+ align:start position:0%
+you started up your control chart and
+you're away from that little artifact
+
+ align:start position:0%
+you're away from that little artifact
+ 
+
+ align:start position:0%
+you're away from that little artifact
+that we saw with the moving average
+
+ align:start position:0%
+that we saw with the moving average
+ 
+
+ align:start position:0%
+that we saw with the moving average
+where the variance limits sort of change
+
+ align:start position:0%
+where the variance limits sort of change
+ 
+
+ align:start position:0%
+where the variance limits sort of change
+once you get far enough away from that
+
+ align:start position:0%
+once you get far enough away from that
+ 
+
+ align:start position:0%
+once you get far enough away from that
+that startup your T is is large and that
+
+ align:start position:0%
+that startup your T is is large and that
+ 
+
+ align:start position:0%
+that startup your T is is large and that
+this whole term just drops
+
+ align:start position:0%
+this whole term just drops
+ 
+
+ align:start position:0%
+this whole term just drops
+out drops out more fast when or more
+
+ align:start position:0%
+out drops out more fast when or more
+ 
+
+ align:start position:0%
+out drops out more fast when or more
+rapidly you know for for uh large values
+
+ align:start position:0%
+rapidly you know for for uh large values
+ 
+
+ align:start position:0%
+rapidly you know for for uh large values
+of R because I'm really waiting more
+
+ align:start position:0%
+of R because I'm really waiting more
+ 
+
+ align:start position:0%
+of R because I'm really waiting more
+towards recent history but even for
+
+ align:start position:0%
+towards recent history but even for
+ 
+
+ align:start position:0%
+towards recent history but even for
+small or modest values of R after you
+
+ align:start position:0%
+small or modest values of R after you
+ 
+
+ align:start position:0%
+small or modest values of R after you
+get out you know 10 20 data points it
+
+ align:start position:0%
+get out you know 10 20 data points it
+ 
+
+ align:start position:0%
+get out you know 10 20 data points it
+typically drops away so now you've got
+
+ align:start position:0%
+typically drops away so now you've got
+ 
+
+ align:start position:0%
+typically drops away so now you've got
+an estimate for large t for the variance
+
+ align:start position:0%
+an estimate for large t for the variance
+ 
+
+ align:start position:0%
+an estimate for large t for the variance
+Sigma a of your statistic and you can
+
+ align:start position:0%
+Sigma a of your statistic and you can
+ 
+
+ align:start position:0%
+Sigma a of your statistic and you can
+simply plot plus minus 3 Sigma or
+
+ align:start position:0%
+simply plot plus minus 3 Sigma or
+ 
+
+ align:start position:0%
+simply plot plus minus 3 Sigma or
+whatever control limits you want
+
+ align:start position:0%
+whatever control limits you want
+ 
+
+ align:start position:0%
+whatever control limits you want
+depending on your false alarm rate
+
+ align:start position:0%
+depending on your false alarm rate
+ 
+
+ align:start position:0%
+depending on your false alarm rate
+Alpha so this is pretty
+
+ align:start position:0%
+Alpha so this is pretty
+ 
+
+ align:start position:0%
+Alpha so this is pretty
+cool uh one quick observation here is
+
+ align:start position:0%
+cool uh one quick observation here is
+ 
+
+ align:start position:0%
+cool uh one quick observation here is
+again we still have a lot of degrees of
+
+ align:start position:0%
+again we still have a lot of degrees of
+ 
+
+ align:start position:0%
+again we still have a lot of degrees of
+flexibility around the choice of R and
+
+ align:start position:0%
+flexibility around the choice of R and
+ 
+
+ align:start position:0%
+flexibility around the choice of R and
+if we look at this formula
+
+ align:start position:0%
+if we look at this formula
+ 
+
+ align:start position:0%
+if we look at this formula
+here and the effect of R i' sort of
+
+ align:start position:0%
+here and the effect of R i' sort of
+ 
+
+ align:start position:0%
+here and the effect of R i' sort of
+plotted uh this this out in this next
+
+ align:start position:0%
+plotted uh this this out in this next
+ 
+
+ align:start position:0%
+plotted uh this this out in this next
+chart this effect of r on the sigma
+
+ align:start position:0%
+chart this effect of r on the sigma
+ 
+
+ align:start position:0%
+chart this effect of r on the sigma
+multiplier oops sorry is this this
+
+ align:start position:0%
+multiplier oops sorry is this this
+ 
+
+ align:start position:0%
+multiplier oops sorry is this this
+Factor right here so in other words as R
+
+ align:start position:0%
+Factor right here so in other words as R
+ 
+
+ align:start position:0%
+Factor right here so in other words as R
+changes how do my control limits move
+
+ align:start position:0%
+changes how do my control limits move
+ 
+
+ align:start position:0%
+changes how do my control limits move
+what is this multiplier of my Sigma over
+
+ align:start position:0%
+what is this multiplier of my Sigma over
+ 
+
+ align:start position:0%
+what is this multiplier of my Sigma over
+root n from from my normal
+
+ align:start position:0%
+root n from from my normal
+ 
+
+ align:start position:0%
+root n from from my normal
+sampling and you can sort of look at it
+
+ align:start position:0%
+sampling and you can sort of look at it
+ 
+
+ align:start position:0%
+sampling and you can sort of look at it
+here and as R gets larger well that gets
+
+ align:start position:0%
+here and as R gets larger well that gets
+ 
+
+ align:start position:0%
+here and as R gets larger well that gets
+larger this gets a as R approaches one
+
+ align:start position:0%
+larger this gets a as R approaches one
+ 
+
+ align:start position:0%
+larger this gets a as R approaches one
+typically you don't ever go above one
+
+ align:start position:0%
+typically you don't ever go above one
+ 
+
+ align:start position:0%
+typically you don't ever go above one
+you can't believe your most recent data
+
+ align:start position:0%
+you can't believe your most recent data
+ 
+
+ align:start position:0%
+you can't believe your most recent data
+point more than 100 percent it's sort of
+
+ align:start position:0%
+point more than 100 percent it's sort of
+ 
+
+ align:start position:0%
+point more than 100 percent it's sort of
+a a ratio U or fraction of the percent
+
+ align:start position:0%
+a a ratio U or fraction of the percent
+ 
+
+ align:start position:0%
+a a ratio U or fraction of the percent
+you can see that as R gets uh
+
+ align:start position:0%
+you can see that as R gets uh
+ 
+
+ align:start position:0%
+you can see that as R gets uh
+larger this uh multiplier starts to
+
+ align:start position:0%
+larger this uh multiplier starts to
+ 
+
+ align:start position:0%
+larger this uh multiplier starts to
+approach uh approach some limit and
+
+ align:start position:0%
+approach uh approach some limit and
+ 
+
+ align:start position:0%
+approach uh approach some limit and
+finally when R is equal to one this
+
+ align:start position:0%
+finally when R is equal to one this
+ 
+
+ align:start position:0%
+finally when R is equal to one this
+multiplier is simply one right in the
+
+ align:start position:0%
+multiplier is simply one right in the
+ 
+
+ align:start position:0%
+multiplier is simply one right in the
+limit when R is equal to one what are we
+
+ align:start position:0%
+limit when R is equal to one what are we
+ 
+
+ align:start position:0%
+limit when R is equal to one what are we
+doing we're doing a 100% up update based
+
+ align:start position:0%
+doing we're doing a 100% up update based
+ 
+
+ align:start position:0%
+doing we're doing a 100% up update based
+on my most recent data point in other
+
+ align:start position:0%
+on my most recent data point in other
+ 
+
+ align:start position:0%
+on my most recent data point in other
+words I'm only looking at my most recent
+
+ align:start position:0%
+words I'm only looking at my most recent
+ 
+
+ align:start position:0%
+words I'm only looking at my most recent
+data point my variance is simply the
+
+ align:start position:0%
+data point my variance is simply the
+ 
+
+ align:start position:0%
+data point my variance is simply the
+process variance coming from sampling
+
+ align:start position:0%
+process variance coming from sampling
+ 
+
+ align:start position:0%
+process variance coming from sampling
+this all reduces to simple Sigma a being
+
+ align:start position:0%
+this all reduces to simple Sigma a being
+ 
+
+ align:start position:0%
+this all reduces to simple Sigma a being
+my sampling variance whatever size
+
+ align:start position:0%
+my sampling variance whatever size
+ 
+
+ align:start position:0%
+my sampling variance whatever size
+sample I was doing within each
+
+ align:start position:0%
+sample I was doing within each
+ 
+
+ align:start position:0%
+sample I was doing within each
+formulation so so in that case I I have
+
+ align:start position:0%
+formulation so so in that case I I have
+ 
+
+ align:start position:0%
+formulation so so in that case I I have
+no uh no factor or no multiplier on that
+
+ align:start position:0%
+no uh no factor or no multiplier on that
+ 
+
+ align:start position:0%
+no uh no factor or no multiplier on that
+Sigma a but for other values of r
+
+ align:start position:0%
+Sigma a but for other values of r
+ 
+
+ align:start position:0%
+Sigma a but for other values of r
+what's happening for smaller values of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R what do we
+
+ align:start position:0%
+R what do we
+ 
+
+ align:start position:0%
+R what do we
+see the sigma a is smaller than the
+
+ align:start position:0%
+see the sigma a is smaller than the
+ 
+
+ align:start position:0%
+see the sigma a is smaller than the
+sigma X over root n we're getting
+
+ align:start position:0%
+sigma X over root n we're getting
+ 
+
+ align:start position:0%
+sigma X over root n we're getting
+reduction in the variance because of
+
+ align:start position:0%
+reduction in the variance because of
+ 
+
+ align:start position:0%
+reduction in the variance because of
+filtering the variance of our estimate
+
+ align:start position:0%
+filtering the variance of our estimate
+ 
+
+ align:start position:0%
+filtering the variance of our estimate
+right so that was the whole idea is I
+
+ align:start position:0%
+right so that was the whole idea is I
+ 
+
+ align:start position:0%
+right so that was the whole idea is I
+can tighten my control limits
+
+ align:start position:0%
+can tighten my control limits
+ 
+
+ align:start position:0%
+can tighten my control limits
+essentially by by the filtering action
+
+ align:start position:0%
+essentially by by the filtering action
+ 
+
+ align:start position:0%
+essentially by by the filtering action
+okay so as I get smaller and smaller RS
+
+ align:start position:0%
+okay so as I get smaller and smaller RS
+ 
+
+ align:start position:0%
+okay so as I get smaller and smaller RS
+I we I do more and more aggressive
+
+ align:start position:0%
+I we I do more and more aggressive
+ 
+
+ align:start position:0%
+I we I do more and more aggressive
+filtering with lots of past data I get
+
+ align:start position:0%
+filtering with lots of past data I get
+ 
+
+ align:start position:0%
+filtering with lots of past data I get
+Tighter and Tighter limits but of course
+
+ align:start position:0%
+Tighter and Tighter limits but of course
+ 
+
+ align:start position:0%
+Tighter and Tighter limits but of course
+I'm also
+
+ align:start position:0%
+I'm also
+ 
+
+ align:start position:0%
+I'm also
+suppressing recent data a little bit a
+
+ align:start position:0%
+suppressing recent data a little bit a
+ 
+
+ align:start position:0%
+suppressing recent data a little bit a
+little bit more heavily so there is this
+
+ align:start position:0%
+little bit more heavily so there is this
+ 
+
+ align:start position:0%
+little bit more heavily so there is this
+so there is this tradeoff let's look at
+
+ align:start position:0%
+so there is this tradeoff let's look at
+ 
+
+ align:start position:0%
+so there is this tradeoff let's look at
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+examples oh well I guess I made these
+
+ align:start position:0%
+examples oh well I guess I made these
+ 
+
+ align:start position:0%
+examples oh well I guess I made these
+points already here again um the
+
+ align:start position:0%
+points already here again um the
+ 
+
+ align:start position:0%
+points already here again um the
+variance of this estimate for the mean
+
+ align:start position:0%
+variance of this estimate for the mean
+ 
+
+ align:start position:0%
+variance of this estimate for the mean
+for the your best guess of the of the
+
+ align:start position:0%
+for the your best guess of the of the
+ 
+
+ align:start position:0%
+for the your best guess of the of the
+mean is smaller uh than than you would
+
+ align:start position:0%
+mean is smaller uh than than you would
+ 
+
+ align:start position:0%
+mean is smaller uh than than you would
+have had with an xar chart because the
+
+ align:start position:0%
+have had with an xar chart because the
+ 
+
+ align:start position:0%
+have had with an xar chart because the
+xar chart remember for a sample size of
+
+ align:start position:0%
+xar chart remember for a sample size of
+ 
+
+ align:start position:0%
+xar chart remember for a sample size of
+n is simply is simply that so we do get
+
+ align:start position:0%
+n is simply is simply that so we do get
+ 
+
+ align:start position:0%
+n is simply is simply that so we do get
+this suppression and it is very nice
+
+ align:start position:0%
+this suppression and it is very nice
+ 
+
+ align:start position:0%
+this suppression and it is very nice
+that it also in the limit works out for
+
+ align:start position:0%
+that it also in the limit works out for
+ 
+
+ align:start position:0%
+that it also in the limit works out for
+both the sample size of one case these
+
+ align:start position:0%
+both the sample size of one case these
+ 
+
+ align:start position:0%
+both the sample size of one case these
+formulas still hold and also the full
+
+ align:start position:0%
+formulas still hold and also the full
+ 
+
+ align:start position:0%
+formulas still hold and also the full
+update case or the R equals 1 where we
+
+ align:start position:0%
+update case or the R equals 1 where we
+ 
+
+ align:start position:0%
+update case or the R equals 1 where we
+have completely unfiltered data you're
+
+ align:start position:0%
+have completely unfiltered data you're
+ 
+
+ align:start position:0%
+have completely unfiltered data you're
+just plotting your your pure run data uh
+
+ align:start position:0%
+just plotting your your pure run data uh
+ 
+
+ align:start position:0%
+just plotting your your pure run data uh
+on your chart so if what happens if I
+
+ align:start position:0%
+on your chart so if what happens if I
+ 
+
+ align:start position:0%
+on your chart so if what happens if I
+use much smaller RS like
+
+ align:start position:0%
+use much smaller RS like
+ 
+
+ align:start position:0%
+use much smaller RS like
+0.1 right I got much tighter control
+
+ align:start position:0%
+0.1 right I got much tighter control
+ 
+
+ align:start position:0%
+0.1 right I got much tighter control
+limits but I've got long delays
+
+ align:start position:0%
+limits but I've got long delays
+ 
+
+ align:start position:0%
+limits but I've got long delays
+potentially then in in detecting I've
+
+ align:start position:0%
+potentially then in in detecting I've
+ 
+
+ align:start position:0%
+potentially then in in detecting I've
+got a lot of noise supression but again
+
+ align:start position:0%
+got a lot of noise supression but again
+ 
+
+ align:start position:0%
+got a lot of noise supression but again
+I get back to Long delays in detecting
+
+ align:start position:0%
+I get back to Long delays in detecting
+ 
+
+ align:start position:0%
+I get back to Long delays in detecting
+or responding to a true shift in the
+
+ align:start position:0%
+or responding to a true shift in the
+ 
+
+ align:start position:0%
+or responding to a true shift in the
+mean so I want to look at a few examples
+
+ align:start position:0%
+mean so I want to look at a few examples
+ 
+
+ align:start position:0%
+mean so I want to look at a few examples
+here uh to give you a feel of the
+
+ align:start position:0%
+here uh to give you a feel of the
+ 
+
+ align:start position:0%
+here uh to give you a feel of the
+tradeoff between different RS for for
+
+ align:start position:0%
+tradeoff between different RS for for
+ 
+
+ align:start position:0%
+tradeoff between different RS for for
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+data and compare it as well to a typical
+
+ align:start position:0%
+data and compare it as well to a typical
+ 
+
+ align:start position:0%
+data and compare it as well to a typical
+xar
+
+ align:start position:0%
+xar
+ 
+
+ align:start position:0%
+xar
+chart okay so here's a uh set of data
+
+ align:start position:0%
+chart okay so here's a uh set of data
+ 
+
+ align:start position:0%
+chart okay so here's a uh set of data
+and we're seeing a comparison here
+
+ align:start position:0%
+and we're seeing a comparison here
+ 
+
+ align:start position:0%
+and we're seeing a comparison here
+between the xbar
+
+ align:start position:0%
+between the xbar
+ 
+
+ align:start position:0%
+between the xbar
+chart um so you can see let's see here
+
+ align:start position:0%
+chart um so you can see let's see here
+ 
+
+ align:start position:0%
+chart um so you can see let's see here
+are the up
+
+ align:start position:0%
+are the up
+ 
+
+ align:start position:0%
+are the up
+xbar uh upper and lower control limits
+
+ align:start position:0%
+xbar uh upper and lower control limits
+ 
+
+ align:start position:0%
+xbar uh upper and lower control limits
+and sure enough after 15
+
+ align:start position:0%
+and sure enough after 15
+ 
+
+ align:start position:0%
+and sure enough after 15
+runs where at uh I don't know about run
+
+ align:start position:0%
+runs where at uh I don't know about run
+ 
+
+ align:start position:0%
+runs where at uh I don't know about run
+90 we we make this shift in the process
+
+ align:start position:0%
+90 we we make this shift in the process
+ 
+
+ align:start position:0%
+90 we we make this shift in the process
+so we shift the whole process by a uh a
+
+ align:start position:0%
+so we shift the whole process by a uh a
+ 
+
+ align:start position:0%
+so we shift the whole process by a uh a
+half a standard deviation of the
+
+ align:start position:0%
+half a standard deviation of the
+ 
+
+ align:start position:0%
+half a standard deviation of the
+underlying process and sure enough by
+
+ align:start position:0%
+underlying process and sure enough by
+ 
+
+ align:start position:0%
+underlying process and sure enough by
+about I don't know run 140 we finally
+
+ align:start position:0%
+about I don't know run 140 we finally
+ 
+
+ align:start position:0%
+about I don't know run 140 we finally
+got a data point in the tail of the mean
+
+ align:start position:0%
+got a data point in the tail of the mean
+ 
+
+ align:start position:0%
+got a data point in the tail of the mean
+distribution the regular xar that fell
+
+ align:start position:0%
+distribution the regular xar that fell
+ 
+
+ align:start position:0%
+distribution the regular xar that fell
+out and we could actually calculate the
+
+ align:start position:0%
+out and we could actually calculate the
+ 
+
+ align:start position:0%
+out and we could actually calculate the
+average run length to detect a mean
+
+ align:start position:0%
+average run length to detect a mean
+ 
+
+ align:start position:0%
+average run length to detect a mean
+shift of 0.5 using some of the
+
+ align:start position:0%
+shift of 0.5 using some of the
+ 
+
+ align:start position:0%
+shift of 0.5 using some of the
+techniques we talked about last
+
+ align:start position:0%
+techniques we talked about last
+ 
+
+ align:start position:0%
+techniques we talked about last
+time and we might not be happy with that
+
+ align:start position:0%
+time and we might not be happy with that
+ 
+
+ align:start position:0%
+time and we might not be happy with that
+very long ARL and the question is would
+
+ align:start position:0%
+very long ARL and the question is would
+ 
+
+ align:start position:0%
+very long ARL and the question is would
+an ewma chart help us with this and this
+
+ align:start position:0%
+an ewma chart help us with this and this
+ 
+
+ align:start position:0%
+an ewma chart help us with this and this
+is an example where we're using about a
+
+ align:start position:0%
+is an example where we're using about a
+ 
+
+ align:start position:0%
+is an example where we're using about a
+30% update based on each new new data
+
+ align:start position:0%
+30% update based on each new new data
+ 
+
+ align:start position:0%
+30% update based on each new new data
+point and plotted in purple with the
+
+ align:start position:0%
+point and plotted in purple with the
+ 
+
+ align:start position:0%
+point and plotted in purple with the
+blue and the yellow uh are the upper and
+
+ align:start position:0%
+blue and the yellow uh are the upper and
+ 
+
+ align:start position:0%
+blue and the yellow uh are the upper and
+lower control limits for the
+
+ align:start position:0%
+lower control limits for the
+ 
+
+ align:start position:0%
+lower control limits for the
+ewma and what you see is the effect
+
+ align:start position:0%
+ewma and what you see is the effect
+ 
+
+ align:start position:0%
+ewma and what you see is the effect
+of averaging now I always
+
+ align:start position:0%
+of averaging now I always
+ 
+
+ align:start position:0%
+of averaging now I always
+find it easiest for me to conceptualize
+
+ align:start position:0%
+find it easiest for me to conceptualize
+ 
+
+ align:start position:0%
+find it easiest for me to conceptualize
+the action of an ewma chart as just kind
+
+ align:start position:0%
+the action of an ewma chart as just kind
+ 
+
+ align:start position:0%
+the action of an ewma chart as just kind
+of like a moving average the equally
+
+ align:start position:0%
+of like a moving average the equally
+ 
+
+ align:start position:0%
+of like a moving average the equally
+weighted moving average but weighted a
+
+ align:start position:0%
+weighted moving average but weighted a
+ 
+
+ align:start position:0%
+weighted moving average but weighted a
+little bit more towards recent history
+
+ align:start position:0%
+little bit more towards recent history
+ 
+
+ align:start position:0%
+little bit more towards recent history
+but the whole idea is I get that
+
+ align:start position:0%
+but the whole idea is I get that
+ 
+
+ align:start position:0%
+but the whole idea is I get that
+aggregation from a any kind of a moving
+
+ align:start position:0%
+aggregation from a any kind of a moving
+ 
+
+ align:start position:0%
+aggregation from a any kind of a moving
+average so that right after this shift
+
+ align:start position:0%
+average so that right after this shift
+ 
+
+ align:start position:0%
+average so that right after this shift
+right here now when I take into account
+
+ align:start position:0%
+right here now when I take into account
+ 
+
+ align:start position:0%
+right here now when I take into account
+with an R of3 you know I'm taking into
+
+ align:start position:0%
+with an R of3 you know I'm taking into
+ 
+
+ align:start position:0%
+with an R of3 you know I'm taking into
+account you know three four five data
+
+ align:start position:0%
+account you know three four five data
+ 
+
+ align:start position:0%
+account you know three four five data
+points I've got kind of an effective
+
+ align:start position:0%
+points I've got kind of an effective
+ 
+
+ align:start position:0%
+points I've got kind of an effective
+window weighted about 30% towards my
+
+ align:start position:0%
+window weighted about 30% towards my
+ 
+
+ align:start position:0%
+window weighted about 30% towards my
+most recent but including some past
+
+ align:start position:0%
+most recent but including some past
+ 
+
+ align:start position:0%
+most recent but including some past
+history that all of the plus Delta new
+
+ align:start position:0%
+history that all of the plus Delta new
+ 
+
+ align:start position:0%
+history that all of the plus Delta new
+data points all average and then my my
+
+ align:start position:0%
+data points all average and then my my
+ 
+
+ align:start position:0%
+data points all average and then my my
+normal process variation you know just
+
+ align:start position:0%
+normal process variation you know just
+ 
+
+ align:start position:0%
+normal process variation you know just
+cancels out each other and so it's
+
+ align:start position:0%
+cancels out each other and so it's
+ 
+
+ align:start position:0%
+cancels out each other and so it's
+very intuitive I think that this ewma is
+
+ align:start position:0%
+very intuitive I think that this ewma is
+ 
+
+ align:start position:0%
+very intuitive I think that this ewma is
+going to aggregate or respond to or
+
+ align:start position:0%
+going to aggregate or respond to or
+ 
+
+ align:start position:0%
+going to aggregate or respond to or
+sense the Delta shift in the mean more
+
+ align:start position:0%
+sense the Delta shift in the mean more
+ 
+
+ align:start position:0%
+sense the Delta shift in the mean more
+than an individual
+
+ align:start position:0%
+than an individual
+ 
+
+ align:start position:0%
+than an individual
+um uh xar chart would have been doing so
+
+ align:start position:0%
+um uh xar chart would have been doing so
+ 
+
+ align:start position:0%
+um uh xar chart would have been doing so
+that it responds in this case I don't
+
+ align:start position:0%
+that it responds in this case I don't
+ 
+
+ align:start position:0%
+that it responds in this case I don't
+know after about I don't know 15 or 20
+
+ align:start position:0%
+know after about I don't know 15 or 20
+ 
+
+ align:start position:0%
+know after about I don't know 15 or 20
+data points you you can start to see
+
+ align:start position:0%
+data points you you can start to see
+ 
+
+ align:start position:0%
+data points you you can start to see
+excursions beyond the the control
+
+ align:start position:0%
+excursions beyond the the control
+ 
+
+ align:start position:0%
+excursions beyond the the control
+limits question um at the beginning of
+
+ align:start position:0%
+limits question um at the beginning of
+ 
+
+ align:start position:0%
+limits question um at the beginning of
+the shark why are the control limits now
+
+ align:start position:0%
+the shark why are the control limits now
+ 
+
+ align:start position:0%
+the shark why are the control limits now
+spreading out and last time they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+were I think we had another sh
+
+ align:start position:0%
+were I think we had another sh
+ 
+
+ align:start position:0%
+were I think we had another sh
+wait why are the control limits I think
+
+ align:start position:0%
+wait why are the control limits I think
+ 
+
+ align:start position:0%
+wait why are the control limits I think
+you can go back to this formula and see
+
+ align:start position:0%
+you can go back to this formula and see
+ 
+
+ align:start position:0%
+you can go back to this formula and see
+if that
+
+ align:start position:0%
+if that
+ 
+
+ align:start position:0%
+if that
+works I think essentially what you've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got I bet if you look at the effect of
+
+ align:start position:0%
+got I bet if you look at the effect of
+ 
+
+ align:start position:0%
+got I bet if you look at the effect of
+the T
+
+ align:start position:0%
+the T
+ 
+
+ align:start position:0%
+the T
+action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh formulaically or analytically I think
+
+ align:start position:0%
+uh formulaically or analytically I think
+ 
+
+ align:start position:0%
+uh formulaically or analytically I think
+that as T starts out being very small
+
+ align:start position:0%
+that as T starts out being very small
+ 
+
+ align:start position:0%
+that as T starts out being very small
+so if T is very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small see so if T is zero this is
+
+ align:start position:0%
+small see so if T is zero this is
+ 
+
+ align:start position:0%
+small see so if T is zero this is
+essentially one if
+
+ align:start position:0%
+essentially one if
+ 
+
+ align:start position:0%
+essentially one if
+T is large well let's say t was one and
+
+ align:start position:0%
+T is large well let's say t was one and
+ 
+
+ align:start position:0%
+T is large well let's say t was one and
+R was3 i' got 7 so I've got a smaller
+
+ align:start position:0%
+R was3 i' got 7 so I've got a smaller
+ 
+
+ align:start position:0%
+R was3 i' got 7 so I've got a smaller
+I've got a reduction so I think for
+
+ align:start position:0%
+I've got a reduction so I think for
+ 
+
+ align:start position:0%
+I've got a reduction so I think for
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+T I've only got a limited amount of data
+
+ align:start position:0%
+T I've only got a limited amount of data
+ 
+
+ align:start position:0%
+T I've only got a limited amount of data
+and so I I'm not I don't have the long
+
+ align:start position:0%
+and so I I'm not I don't have the long
+ 
+
+ align:start position:0%
+and so I I'm not I don't have the long
+tail in the ewma so I think I'm I've
+
+ align:start position:0%
+tail in the ewma so I think I'm I've
+ 
+
+ align:start position:0%
+tail in the ewma so I think I'm I've
+only got a small amount of data with a
+
+ align:start position:0%
+only got a small amount of data with a
+ 
+
+ align:start position:0%
+only got a small amount of data with a
+larger weight and my control limits I
+
+ align:start position:0%
+larger weight and my control limits I
+ 
+
+ align:start position:0%
+larger weight and my control limits I
+think are smaller but then as T gets
+
+ align:start position:0%
+think are smaller but then as T gets
+ 
+
+ align:start position:0%
+think are smaller but then as T gets
+larger I've got a little bit
+
+ align:start position:0%
+larger I've got a little bit
+ 
+
+ align:start position:0%
+larger I've got a little bit
+more more data until T so I think if I
+
+ align:start position:0%
+more more data until T so I think if I
+ 
+
+ align:start position:0%
+more more data until T so I think if I
+were to plot this one - one minus r to
+
+ align:start position:0%
+were to plot this one - one minus r to
+ 
+
+ align:start position:0%
+were to plot this one - one minus r to
+the 2T kind of has a funky
+
+ align:start position:0%
+the 2T kind of has a funky
+ 
+
+ align:start position:0%
+the 2T kind of has a funky
+shape that that that that dies
+
+ align:start position:0%
+shape that that that that dies
+ 
+
+ align:start position:0%
+shape that that that that dies
+out but I wouldn't worry too much about
+
+ align:start position:0%
+out but I wouldn't worry too much about
+ 
+
+ align:start position:0%
+out but I wouldn't worry too much about
+the startup times I mean there're sort
+
+ align:start position:0%
+the startup times I mean there're sort
+ 
+
+ align:start position:0%
+the startup times I mean there're sort
+of artifacts when you start up a control
+
+ align:start position:0%
+of artifacts when you start up a control
+ 
+
+ align:start position:0%
+of artifacts when you start up a control
+chart but once you just start a control
+
+ align:start position:0%
+chart but once you just start a control
+ 
+
+ align:start position:0%
+chart but once you just start a control
+chart anyway you're you're still feeling
+
+ align:start position:0%
+chart anyway you're you're still feeling
+ 
+
+ align:start position:0%
+chart anyway you're you're still feeling
+out the process so I wouldn't I wouldn't
+
+ align:start position:0%
+out the process so I wouldn't I wouldn't
+ 
+
+ align:start position:0%
+out the process so I wouldn't I wouldn't
+worry too much about about the the
+
+ align:start position:0%
+worry too much about about the the
+ 
+
+ align:start position:0%
+worry too much about about the the
+startup times on these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah how do you decide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between yeah so so the question so if
+
+ align:start position:0%
+between yeah so so the question so if
+ 
+
+ align:start position:0%
+between yeah so so the question so if
+you didn't hear that uh in Singapore was
+
+ align:start position:0%
+you didn't hear that uh in Singapore was
+ 
+
+ align:start position:0%
+you didn't hear that uh in Singapore was
+when would you use an ewma or what are
+
+ align:start position:0%
+when would you use an ewma or what are
+ 
+
+ align:start position:0%
+when would you use an ewma or what are
+the factors in using an ew from an xar
+
+ align:start position:0%
+the factors in using an ew from an xar
+ 
+
+ align:start position:0%
+the factors in using an ew from an xar
+chart
+
+ align:start position:0%
+chart
+ 
+
+ align:start position:0%
+chart
+and um I think if you've got a lot of a
+
+ align:start position:0%
+and um I think if you've got a lot of a
+ 
+
+ align:start position:0%
+and um I think if you've got a lot of a
+lot of noise and you're
+
+ align:start position:0%
+lot of noise and you're
+ 
+
+ align:start position:0%
+lot of noise and you're
+really worried about detecting rapidly a
+
+ align:start position:0%
+really worried about detecting rapidly a
+ 
+
+ align:start position:0%
+really worried about detecting rapidly a
+shift in the process an ewma or and
+
+ align:start position:0%
+shift in the process an ewma or and
+ 
+
+ align:start position:0%
+shift in the process an ewma or and
+we'll see the in a minute has
+
+ align:start position:0%
+we'll see the in a minute has
+ 
+
+ align:start position:0%
+we'll see the in a minute has
+improved sensitivity to Rapid detection
+
+ align:start position:0%
+improved sensitivity to Rapid detection
+ 
+
+ align:start position:0%
+improved sensitivity to Rapid detection
+of the shift but it comes at one really
+
+ align:start position:0%
+of the shift but it comes at one really
+ 
+
+ align:start position:0%
+of the shift but it comes at one really
+important cost which is a loss in
+
+ align:start position:0%
+important cost which is a loss in
+ 
+
+ align:start position:0%
+important cost which is a loss in
+transparency in what's going on
+
+ align:start position:0%
+transparency in what's going on
+ 
+
+ align:start position:0%
+transparency in what's going on
+um the xar I think conceptually is a lot
+
+ align:start position:0%
+um the xar I think conceptually is a lot
+ 
+
+ align:start position:0%
+um the xar I think conceptually is a lot
+easier to understand have everybody on
+
+ align:start position:0%
+easier to understand have everybody on
+ 
+
+ align:start position:0%
+easier to understand have everybody on
+the line understand what it is the data
+
+ align:start position:0%
+the line understand what it is the data
+ 
+
+ align:start position:0%
+the line understand what it is the data
+if you also explode out and show the
+
+ align:start position:0%
+if you also explode out and show the
+ 
+
+ align:start position:0%
+if you also explode out and show the
+full data the xar and the and the the S
+
+ align:start position:0%
+full data the xar and the and the the S
+ 
+
+ align:start position:0%
+full data the xar and the and the the S
+gives you a good feel directly to the
+
+ align:start position:0%
+gives you a good feel directly to the
+ 
+
+ align:start position:0%
+gives you a good feel directly to the
+statistics of the process here you look
+
+ align:start position:0%
+statistics of the process here you look
+ 
+
+ align:start position:0%
+statistics of the process here you look
+at this and you lose touch I think a
+
+ align:start position:0%
+at this and you lose touch I think a
+ 
+
+ align:start position:0%
+at this and you lose touch I think a
+little bit with with the statistics of
+
+ align:start position:0%
+little bit with with the statistics of
+ 
+
+ align:start position:0%
+little bit with with the statistics of
+of uh uh and the Rel relationship to
+
+ align:start position:0%
+of uh uh and the Rel relationship to
+ 
+
+ align:start position:0%
+of uh uh and the Rel relationship to
+your raw data it's a little harder to
+
+ align:start position:0%
+your raw data it's a little harder to
+ 
+
+ align:start position:0%
+your raw data it's a little harder to
+get your mind around but if you're I um
+
+ align:start position:0%
+get your mind around but if you're I um
+ 
+
+ align:start position:0%
+get your mind around but if you're I um
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+find well I don't know 101 15 years ago
+
+ align:start position:0%
+find well I don't know 101 15 years ago
+ 
+
+ align:start position:0%
+find well I don't know 101 15 years ago
+I fell in love with the ewma uh chart
+
+ align:start position:0%
+I fell in love with the ewma uh chart
+ 
+
+ align:start position:0%
+I fell in love with the ewma uh chart
+and and approach not only for charting
+
+ align:start position:0%
+and and approach not only for charting
+ 
+
+ align:start position:0%
+and and approach not only for charting
+but also for doing Simple runby Run
+
+ align:start position:0%
+but also for doing Simple runby Run
+ 
+
+ align:start position:0%
+but also for doing Simple runby Run
+control and so I kind of like it but I
+
+ align:start position:0%
+control and so I kind of like it but I
+ 
+
+ align:start position:0%
+control and so I kind of like it but I
+can empathize with uh it being a little
+
+ align:start position:0%
+can empathize with uh it being a little
+ 
+
+ align:start position:0%
+can empathize with uh it being a little
+bit harder to explain and maintain on on
+
+ align:start position:0%
+bit harder to explain and maintain on on
+ 
+
+ align:start position:0%
+bit harder to explain and maintain on on
+the line
+
+ align:start position:0%
+the line
+ 
+
+ align:start position:0%
+the line
+um it's also got a little bit more
+
+ align:start position:0%
+um it's also got a little bit more
+ 
+
+ align:start position:0%
+um it's also got a little bit more
+calculation so you know if back in the
+
+ align:start position:0%
+calculation so you know if back in the
+ 
+
+ align:start position:0%
+calculation so you know if back in the
+days
+
+ align:start position:0%
+days
+ 
+
+ align:start position:0%
+days
+of and it's still true in some of the
+
+ align:start position:0%
+of and it's still true in some of the
+ 
+
+ align:start position:0%
+of and it's still true in some of the
+manufacturing lines I know when we went
+
+ align:start position:0%
+manufacturing lines I know when we went
+ 
+
+ align:start position:0%
+manufacturing lines I know when we went
+on the tour and some of the plants uh
+
+ align:start position:0%
+on the tour and some of the plants uh
+ 
+
+ align:start position:0%
+on the tour and some of the plants uh
+very very you know up-to-date plants in
+
+ align:start position:0%
+very very you know up-to-date plants in
+ 
+
+ align:start position:0%
+very very you know up-to-date plants in
+in in uh Singapore and other places
+
+ align:start position:0%
+in in uh Singapore and other places
+ 
+
+ align:start position:0%
+in in uh Singapore and other places
+around the world people are still often
+
+ align:start position:0%
+around the world people are still often
+ 
+
+ align:start position:0%
+around the world people are still often
+taking measurements by hand and doing
+
+ align:start position:0%
+taking measurements by hand and doing
+ 
+
+ align:start position:0%
+taking measurements by hand and doing
+the hand calculation and writing it on a
+
+ align:start position:0%
+the hand calculation and writing it on a
+ 
+
+ align:start position:0%
+the hand calculation and writing it on a
+chart this has an extra step you got to
+
+ align:start position:0%
+chart this has an extra step you got to
+ 
+
+ align:start position:0%
+chart this has an extra step you got to
+do an extra average you know the so
+
+ align:start position:0%
+do an extra average you know the so
+ 
+
+ align:start position:0%
+do an extra average you know the so
+so in modern day when almost all the uh
+
+ align:start position:0%
+so in modern day when almost all the uh
+ 
+
+ align:start position:0%
+so in modern day when almost all the uh
+calculations are are are automated the
+
+ align:start position:0%
+calculations are are are automated the
+ 
+
+ align:start position:0%
+calculations are are are automated the
+data collection is automated I think
+
+ align:start position:0%
+data collection is automated I think
+ 
+
+ align:start position:0%
+data collection is automated I think
+there's even more reason to go with an
+
+ align:start position:0%
+there's even more reason to go with an
+ 
+
+ align:start position:0%
+there's even more reason to go with an
+ewma so the thing I like about the best
+
+ align:start position:0%
+ewma so the thing I like about the best
+ 
+
+ align:start position:0%
+ewma so the thing I like about the best
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+ewma is I think of it as giving me my
+
+ align:start position:0%
+ewma is I think of it as giving me my
+ 
+
+ align:start position:0%
+ewma is I think of it as giving me my
+best current estimate based not only on
+
+ align:start position:0%
+best current estimate based not only on
+ 
+
+ align:start position:0%
+best current estimate based not only on
+on just my last data point but a little
+
+ align:start position:0%
+on just my last data point but a little
+ 
+
+ align:start position:0%
+on just my last data point but a little
+bit of filtering including past history
+
+ align:start position:0%
+bit of filtering including past history
+ 
+
+ align:start position:0%
+bit of filtering including past history
+is giving my my best educated state of
+
+ align:start position:0%
+is giving my my best educated state of
+ 
+
+ align:start position:0%
+is giving my my best educated state of
+the current
+
+ align:start position:0%
+the current
+ 
+
+ align:start position:0%
+the current
+process and why I liked that for then
+
+ align:start position:0%
+process and why I liked that for then
+ 
+
+ align:start position:0%
+process and why I liked that for then
+runby run control is based on my current
+
+ align:start position:0%
+runby run control is based on my current
+ 
+
+ align:start position:0%
+runby run control is based on my current
+model my updated on a recursive basis
+
+ align:start position:0%
+model my updated on a recursive basis
+ 
+
+ align:start position:0%
+model my updated on a recursive basis
+updated model of the current state of
+
+ align:start position:0%
+updated model of the current state of
+ 
+
+ align:start position:0%
+updated model of the current state of
+the process I can make a decision so
+
+ align:start position:0%
+the process I can make a decision so
+ 
+
+ align:start position:0%
+the process I can make a decision so
+here the decision in SPC is is the
+
+ align:start position:0%
+here the decision in SPC is is the
+ 
+
+ align:start position:0%
+here the decision in SPC is is the
+process in control or not but if you
+
+ align:start position:0%
+process in control or not but if you
+ 
+
+ align:start position:0%
+process in control or not but if you
+think of this being not just the ewma
+
+ align:start position:0%
+think of this being not just the ewma
+ 
+
+ align:start position:0%
+think of this being not just the ewma
+not giving you more information it's not
+
+ align:start position:0%
+not giving you more information it's not
+ 
+
+ align:start position:0%
+not giving you more information it's not
+just giving you am I in control or not
+
+ align:start position:0%
+just giving you am I in control or not
+ 
+
+ align:start position:0%
+just giving you am I in control or not
+given the random spread but if you
+
+ align:start position:0%
+given the random spread but if you
+ 
+
+ align:start position:0%
+given the random spread but if you
+interpret this little purple dat data
+
+ align:start position:0%
+interpret this little purple dat data
+ 
+
+ align:start position:0%
+interpret this little purple dat data
+point here
+
+ align:start position:0%
+point here
+ 
+
+ align:start position:0%
+point here
+as my best estimate of where the mean in
+
+ align:start position:0%
+as my best estimate of where the mean in
+ 
+
+ align:start position:0%
+as my best estimate of where the mean in
+the recent past has been if there is a
+
+ align:start position:0%
+the recent past has been if there is a
+ 
+
+ align:start position:0%
+the recent past has been if there is a
+little bit of drift or or movement maybe
+
+ align:start position:0%
+little bit of drift or or movement maybe
+ 
+
+ align:start position:0%
+little bit of drift or or movement maybe
+I do active control and not pure SPC
+
+ align:start position:0%
+I do active control and not pure SPC
+ 
+
+ align:start position:0%
+I do active control and not pure SPC
+control I'm not making any longer just
+
+ align:start position:0%
+control I'm not making any longer just
+ 
+
+ align:start position:0%
+control I'm not making any longer just
+the decision nothing has changed I'm
+
+ align:start position:0%
+the decision nothing has changed I'm
+ 
+
+ align:start position:0%
+the decision nothing has changed I'm
+saying there are small changes and maybe
+
+ align:start position:0%
+saying there are small changes and maybe
+ 
+
+ align:start position:0%
+saying there are small changes and maybe
+I want to go and make a small
+
+ align:start position:0%
+I want to go and make a small
+ 
+
+ align:start position:0%
+I want to go and make a small
+modification or an adjustment on the
+
+ align:start position:0%
+modification or an adjustment on the
+ 
+
+ align:start position:0%
+modification or an adjustment on the
+equipment now if you are in true
+
+ align:start position:0%
+equipment now if you are in true
+ 
+
+ align:start position:0%
+equipment now if you are in true
+statistical process control that would
+
+ align:start position:0%
+statistical process control that would
+ 
+
+ align:start position:0%
+statistical process control that would
+be the wrong thing to do you'd be over
+
+ align:start position:0%
+be the wrong thing to do you'd be over
+ 
+
+ align:start position:0%
+be the wrong thing to do you'd be over
+adjusting and we'll talk about that
+
+ align:start position:0%
+adjusting and we'll talk about that
+ 
+
+ align:start position:0%
+adjusting and we'll talk about that
+later but that's another thing I like
+
+ align:start position:0%
+later but that's another thing I like
+ 
+
+ align:start position:0%
+later but that's another thing I like
+about the ewma is very often there is a
+
+ align:start position:0%
+about the ewma is very often there is a
+ 
+
+ align:start position:0%
+about the ewma is very often there is a
+little bit of time correlation in the
+
+ align:start position:0%
+little bit of time correlation in the
+ 
+
+ align:start position:0%
+little bit of time correlation in the
+process and the ewma is tracking those
+
+ align:start position:0%
+process and the ewma is tracking those
+ 
+
+ align:start position:0%
+process and the ewma is tracking those
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+changes uh and filtering out some of the
+
+ align:start position:0%
+changes uh and filtering out some of the
+ 
+
+ align:start position:0%
+changes uh and filtering out some of the
+noise it's a good question uh I'll take
+
+ align:start position:0%
+noise it's a good question uh I'll take
+ 
+
+ align:start position:0%
+noise it's a good question uh I'll take
+a question there was somebody had a
+
+ align:start position:0%
+a question there was somebody had a
+ 
+
+ align:start position:0%
+a question there was somebody had a
+question in
+
+ align:start position:0%
+question in
+ 
+
+ align:start position:0%
+question in
+Singapore uh yes so uh I wonder smaller
+
+ align:start position:0%
+Singapore uh yes so uh I wonder smaller
+ 
+
+ align:start position:0%
+Singapore uh yes so uh I wonder smaller
+R will lead to the narrow control limit
+
+ align:start position:0%
+R will lead to the narrow control limit
+ 
+
+ align:start position:0%
+R will lead to the narrow control limit
+right that's right so the narrow control
+
+ align:start position:0%
+right that's right so the narrow control
+ 
+
+ align:start position:0%
+right that's right so the narrow control
+limit you will have a uh smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+uh so a smaller beta would be less
+
+ align:start position:0%
+uh so a smaller beta would be less
+ 
+
+ align:start position:0%
+uh so a smaller beta would be less
+chance smaller beta yes yeah t to error
+
+ align:start position:0%
+chance smaller beta yes yeah t to error
+ 
+
+ align:start position:0%
+chance smaller beta yes yeah t to error
+right but its power is uh then larger so
+
+ align:start position:0%
+right but its power is uh then larger so
+ 
+
+ align:start position:0%
+right but its power is uh then larger so
+the chance of detecting a true outof
+
+ align:start position:0%
+the chance of detecting a true outof
+ 
+
+ align:start position:0%
+the chance of detecting a true outof
+control Point
+
+ align:start position:0%
+control Point
+ 
+
+ align:start position:0%
+control Point
+increases but yeah so but there's a a
+
+ align:start position:0%
+increases but yeah so but there's a a
+ 
+
+ align:start position:0%
+increases but yeah so but there's a a
+very important additional factor which
+
+ align:start position:0%
+very important additional factor which
+ 
+
+ align:start position:0%
+very important additional factor which
+is there's additional time lag so I'm
+
+ align:start position:0%
+is there's additional time lag so I'm
+ 
+
+ align:start position:0%
+is there's additional time lag so I'm
+going to show a couple of examples
+
+ align:start position:0%
+going to show a couple of examples
+ 
+
+ align:start position:0%
+going to show a couple of examples
+because you can see uh in other examples
+
+ align:start position:0%
+because you can see uh in other examples
+ 
+
+ align:start position:0%
+because you can see uh in other examples
+the effect of the filtering and the time
+
+ align:start position:0%
+the effect of the filtering and the time
+ 
+
+ align:start position:0%
+the effect of the filtering and the time
+response that it takes to detect can go
+
+ align:start position:0%
+response that it takes to detect can go
+ 
+
+ align:start position:0%
+response that it takes to detect can go
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so another question here I was just
+
+ align:start position:0%
+okay so another question here I was just
+ 
+
+ align:start position:0%
+okay so another question here I was just
+curious what sample size were you using
+
+ align:start position:0%
+curious what sample size were you using
+ 
+
+ align:start position:0%
+curious what sample size were you using
+for the xar I don't know I I'm not sure
+
+ align:start position:0%
+for the xar I don't know I I'm not sure
+ 
+
+ align:start position:0%
+for the xar I don't know I I'm not sure
+what was used in the in the in the uh as
+
+ align:start position:0%
+what was used in the in the in the uh as
+ 
+
+ align:start position:0%
+what was used in the in the in the uh as
+a sample size I think you're just seeing
+
+ align:start position:0%
+a sample size I think you're just seeing
+ 
+
+ align:start position:0%
+a sample size I think you're just seeing
+the plot of the sample so the sample
+
+ align:start position:0%
+the plot of the sample so the sample
+ 
+
+ align:start position:0%
+the plot of the sample so the sample
+size is actually the same in both
+
+ align:start position:0%
+size is actually the same in both
+ 
+
+ align:start position:0%
+size is actually the same in both
+cases um but
+
+ align:start position:0%
+cases um but
+ 
+
+ align:start position:0%
+cases um but
+uh but I I don't know what was what was
+
+ align:start position:0%
+uh but I I don't know what was what was
+ 
+
+ align:start position:0%
+uh but I I don't know what was what was
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+used in some sense it doesn't actually
+
+ align:start position:0%
+used in some sense it doesn't actually
+ 
+
+ align:start position:0%
+used in some sense it doesn't actually
+matter too much the ewma is looking is
+
+ align:start position:0%
+matter too much the ewma is looking is
+ 
+
+ align:start position:0%
+matter too much the ewma is looking is
+an ewma over sample so I might still be
+
+ align:start position:0%
+an ewma over sample so I might still be
+ 
+
+ align:start position:0%
+an ewma over sample so I might still be
+forming I might have a thousand Parts an
+
+ align:start position:0%
+forming I might have a thousand Parts an
+ 
+
+ align:start position:0%
+forming I might have a thousand Parts an
+hour and every 15 minutes I might do a
+
+ align:start position:0%
+hour and every 15 minutes I might do a
+ 
+
+ align:start position:0%
+hour and every 15 minutes I might do a
+sample size of
+
+ align:start position:0%
+sample size of
+ 
+
+ align:start position:0%
+sample size of
+10 so I'm only getting sample size 10
+
+ align:start position:0%
+10 so I'm only getting sample size 10
+ 
+
+ align:start position:0%
+10 so I'm only getting sample size 10
+lots more and what's being plotted here
+
+ align:start position:0%
+lots more and what's being plotted here
+ 
+
+ align:start position:0%
+lots more and what's being plotted here
+in some sense is the
+
+ align:start position:0%
+in some sense is the
+ 
+
+ align:start position:0%
+in some sense is the
+sample so I have an xar where I might
+
+ align:start position:0%
+sample so I have an xar where I might
+ 
+
+ align:start position:0%
+sample so I have an xar where I might
+plot those samples here what I'm doing
+
+ align:start position:0%
+plot those samples here what I'm doing
+ 
+
+ align:start position:0%
+plot those samples here what I'm doing
+the ewma has enough it has the
+
+ align:start position:0%
+the ewma has enough it has the
+ 
+
+ align:start position:0%
+the ewma has enough it has the
+flexibility to extend to n equals 1
+
+ align:start position:0%
+flexibility to extend to n equals 1
+ 
+
+ align:start position:0%
+flexibility to extend to n equals 1
+sampling if that's what I'm doing but
+
+ align:start position:0%
+sampling if that's what I'm doing but
+ 
+
+ align:start position:0%
+sampling if that's what I'm doing but
+but in some sense it could also be used
+
+ align:start position:0%
+but in some sense it could also be used
+ 
+
+ align:start position:0%
+but in some sense it could also be used
+where instead of each of those nals 10
+
+ align:start position:0%
+where instead of each of those nals 10
+ 
+
+ align:start position:0%
+where instead of each of those nals 10
+samples was the only data I looked at
+
+ align:start position:0%
+samples was the only data I looked at
+ 
+
+ align:start position:0%
+samples was the only data I looked at
+each one of those is my T point in T and
+
+ align:start position:0%
+each one of those is my T point in T and
+ 
+
+ align:start position:0%
+each one of those is my T point in T and
+my previous sample of size 10 is T minus
+
+ align:start position:0%
+my previous sample of size 10 is T minus
+ 
+
+ align:start position:0%
+my previous sample of size 10 is T minus
+one my previous one but so so in some
+
+ align:start position:0%
+one my previous one but so so in some
+ 
+
+ align:start position:0%
+one my previous one but so so in some
+sense it's doing
+
+ align:start position:0%
+sense it's doing
+ 
+
+ align:start position:0%
+sense it's doing
+the whole sample by sample
+
+ align:start position:0%
+the whole sample by sample
+ 
+
+ align:start position:0%
+the whole sample by sample
+comparison so my point here was both the
+
+ align:start position:0%
+comparison so my point here was both the
+ 
+
+ align:start position:0%
+comparison so my point here was both the
+ewma and and the xar are using in this
+
+ align:start position:0%
+ewma and and the xar are using in this
+ 
+
+ align:start position:0%
+ewma and and the xar are using in this
+derivation the same sample size I'm not
+
+ align:start position:0%
+derivation the same sample size I'm not
+ 
+
+ align:start position:0%
+derivation the same sample size I'm not
+differentiating in that all I'm doing in
+
+ align:start position:0%
+differentiating in that all I'm doing in
+ 
+
+ align:start position:0%
+differentiating in that all I'm doing in
+this case really with the ewma is using
+
+ align:start position:0%
+this case really with the ewma is using
+ 
+
+ align:start position:0%
+this case really with the ewma is using
+multiple samples back in time and the
+
+ align:start position:0%
+multiple samples back in time and the
+ 
+
+ align:start position:0%
+multiple samples back in time and the
+xar only uses
+
+ align:start position:0%
+xar only uses
+ 
+
+ align:start position:0%
+xar only uses
+one so so so in fact
+
+ align:start position:0%
+one so so so in fact
+ 
+
+ align:start position:0%
+one so so so in fact
+if I go to R equals 1 the two converge
+
+ align:start position:0%
+if I go to R equals 1 the two converge
+ 
+
+ align:start position:0%
+if I go to R equals 1 the two converge
+they are the same the R equals 1 ewma is
+
+ align:start position:0%
+they are the same the R equals 1 ewma is
+ 
+
+ align:start position:0%
+they are the same the R equals 1 ewma is
+exactly the same as the xar but the
+
+ align:start position:0%
+exactly the same as the xar but the
+ 
+
+ align:start position:0%
+exactly the same as the xar but the
+larger my sample size is the less of a
+
+ align:start position:0%
+larger my sample size is the less of a
+ 
+
+ align:start position:0%
+larger my sample size is the less of a
+spread I get between my two they would
+
+ align:start position:0%
+spread I get between my two they would
+ 
+
+ align:start position:0%
+spread I get between my two they would
+all they would they would they would
+
+ align:start position:0%
+all they would they would they would
+ 
+
+ align:start position:0%
+all they would they would they would
+both go together though because I'd have
+
+ align:start position:0%
+both go together though because I'd have
+ 
+
+ align:start position:0%
+both go together though because I'd have
+the factor so back here on slide 12 if I
+
+ align:start position:0%
+the factor so back here on slide 12 if I
+ 
+
+ align:start position:0%
+the factor so back here on slide 12 if I
+change my sample size both Sigma a and
+
+ align:start position:0%
+change my sample size both Sigma a and
+ 
+
+ align:start position:0%
+change my sample size both Sigma a and
+my upper control limits and lower
+
+ align:start position:0%
+my upper control limits and lower
+ 
+
+ align:start position:0%
+my upper control limits and lower
+control limits the xar shrink exactly
+
+ align:start position:0%
+control limits the xar shrink exactly
+ 
+
+ align:start position:0%
+control limits the xar shrink exactly
+the same so I would scale both of them
+
+ align:start position:0%
+the same so I would scale both of them
+ 
+
+ align:start position:0%
+the same so I would scale both of them
+if I
+
+ align:start position:0%
+if I
+ 
+
+ align:start position:0%
+if I
+increased okay so what I was talking
+
+ align:start position:0%
+increased okay so what I was talking
+ 
+
+ align:start position:0%
+increased okay so what I was talking
+about here is with different values of
+
+ align:start position:0%
+about here is with different values of
+ 
+
+ align:start position:0%
+about here is with different values of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+R so um this was an r equal 0.3 here's a
+
+ align:start position:0%
+R so um this was an r equal 0.3 here's a
+ 
+
+ align:start position:0%
+R so um this was an r equal 0.3 here's a
+smaller R R equals 0.1 so what's
+
+ align:start position:0%
+smaller R R equals 0.1 so what's
+ 
+
+ align:start position:0%
+smaller R R equals 0.1 so what's
+happening here I'm only accepting my
+
+ align:start position:0%
+happening here I'm only accepting my
+ 
+
+ align:start position:0%
+happening here I'm only accepting my
+most recent data 10% and mixing past
+
+ align:start position:0%
+most recent data 10% and mixing past
+ 
+
+ align:start position:0%
+most recent data 10% and mixing past
+history in 90% that's more averaging of
+
+ align:start position:0%
+history in 90% that's more averaging of
+ 
+
+ align:start position:0%
+history in 90% that's more averaging of
+the past I'm using more past history and
+
+ align:start position:0%
+the past I'm using more past history and
+ 
+
+ align:start position:0%
+the past I'm using more past history and
+so in this case what you see is kind of
+
+ align:start position:0%
+so in this case what you see is kind of
+ 
+
+ align:start position:0%
+so in this case what you see is kind of
+a more slowly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drifting a more heavily excuse me a more
+
+ align:start position:0%
+drifting a more heavily excuse me a more
+ 
+
+ align:start position:0%
+drifting a more heavily excuse me a more
+heavily filtered version and here with
+
+ align:start position:0%
+heavily filtered version and here with
+ 
+
+ align:start position:0%
+heavily filtered version and here with
+the mean shift occurring about here you
+
+ align:start position:0%
+the mean shift occurring about here you
+ 
+
+ align:start position:0%
+the mean shift occurring about here you
+can start to see in this case a big mean
+
+ align:start position:0%
+can start to see in this case a big mean
+ 
+
+ align:start position:0%
+can start to see in this case a big mean
+shift of 0.5 with a I guess a sample
+
+ align:start position:0%
+shift of 0.5 with a I guess a sample
+ 
+
+ align:start position:0%
+shift of 0.5 with a I guess a sample
+size of of of five
+
+ align:start position:0%
+size of of of five
+ 
+
+ align:start position:0%
+size of of of five
+you do need to know the sample size in
+
+ align:start position:0%
+you do need to know the sample size in
+ 
+
+ align:start position:0%
+you do need to know the sample size in
+order to know the effect of the mean
+
+ align:start position:0%
+order to know the effect of the mean
+ 
+
+ align:start position:0%
+order to know the effect of the mean
+shift um and the ability to detect with
+
+ align:start position:0%
+shift um and the ability to detect with
+ 
+
+ align:start position:0%
+shift um and the ability to detect with
+either either
+
+ align:start position:0%
+either either
+ 
+
+ align:start position:0%
+either either
+chart so somewhere in here I guess
+
+ align:start position:0%
+chart so somewhere in here I guess
+ 
+
+ align:start position:0%
+chart so somewhere in here I guess
+around there I got I got lucky and I'm
+
+ align:start position:0%
+around there I got I got lucky and I'm
+ 
+
+ align:start position:0%
+around there I got I got lucky and I'm
+starting the sample
+
+ align:start position:0%
+starting the sample
+ 
+
+ align:start position:0%
+starting the sample
+now with the
+
+ align:start position:0%
+now with the
+ 
+
+ align:start position:0%
+now with the
+xar picking up that detection but with
+
+ align:start position:0%
+xar picking up that detection but with
+ 
+
+ align:start position:0%
+xar picking up that detection but with
+the ewma in some sense I've still got
+
+ align:start position:0%
+the ewma in some sense I've still got
+ 
+
+ align:start position:0%
+the ewma in some sense I've still got
+90% it takes you know nine or 10 days
+
+ align:start position:0%
+90% it takes you know nine or 10 days
+ 
+
+ align:start position:0%
+90% it takes you know nine or 10 days
+data points for the more recent data to
+
+ align:start position:0%
+data points for the more recent data to
+ 
+
+ align:start position:0%
+data points for the more recent data to
+outweigh the past data and so I've
+
+ align:start position:0%
+outweigh the past data and so I've
+ 
+
+ align:start position:0%
+outweigh the past data and so I've
+actually got in this case a time lag in
+
+ align:start position:0%
+actually got in this case a time lag in
+ 
+
+ align:start position:0%
+actually got in this case a time lag in
+in detecting the mean shift with the
+
+ align:start position:0%
+in detecting the mean shift with the
+ 
+
+ align:start position:0%
+in detecting the mean shift with the
+ewma compared to
+
+ align:start position:0%
+ewma compared to
+ 
+
+ align:start position:0%
+ewma compared to
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+xar so a question here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first different
+
+ align:start position:0%
+first different
+ 
+
+ align:start position:0%
+first different
+sces on the xar will effectively let us
+
+ align:start position:0%
+sces on the xar will effectively let us
+ 
+
+ align:start position:0%
+sces on the xar will effectively let us
+save the sample sizes by effectively
+
+ align:start position:0%
+save the sample sizes by effectively
+ 
+
+ align:start position:0%
+save the sample sizes by effectively
+moving for five time SC the other moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh so the question was how do you
+
+ align:start position:0%
+one uh so the question was how do you
+ 
+
+ align:start position:0%
+one uh so the question was how do you
+compare the time scales on these so
+
+ align:start position:0%
+compare the time scales on these so
+ 
+
+ align:start position:0%
+compare the time scales on these so
+here's what I think is going on uh and
+
+ align:start position:0%
+here's what I think is going on uh and
+ 
+
+ align:start position:0%
+here's what I think is going on uh and
+this is sort of what I was talking about
+
+ align:start position:0%
+this is sort of what I was talking about
+ 
+
+ align:start position:0%
+this is sort of what I was talking about
+a second ago but it's it's probably
+
+ align:start position:0%
+a second ago but it's it's probably
+ 
+
+ align:start position:0%
+a second ago but it's it's probably
+still a little confusing I believe that
+
+ align:start position:0%
+still a little confusing I believe that
+ 
+
+ align:start position:0%
+still a little confusing I believe that
+this n equals 5 sample size means that
+
+ align:start position:0%
+this n equals 5 sample size means that
+ 
+
+ align:start position:0%
+this n equals 5 sample size means that
+inside of this data point if I were to
+
+ align:start position:0%
+inside of this data point if I were to
+ 
+
+ align:start position:0%
+inside of this data point if I were to
+explode that it actually has five five
+
+ align:start position:0%
+explode that it actually has five five
+ 
+
+ align:start position:0%
+explode that it actually has five five
+data points inside of it and I'm only
+
+ align:start position:0%
+data points inside of it and I'm only
+ 
+
+ align:start position:0%
+data points inside of it and I'm only
+plotting the average of those five on
+
+ align:start position:0%
+plotting the average of those five on
+ 
+
+ align:start position:0%
+plotting the average of those five on
+here this data point also has those same
+
+ align:start position:0%
+here this data point also has those same
+ 
+
+ align:start position:0%
+here this data point also has those same
+five data points but then it also
+
+ align:start position:0%
+five data points but then it also
+ 
+
+ align:start position:0%
+five data points but then it also
+grabbed the data that was lurking in the
+
+ align:start position:0%
+grabbed the data that was lurking in the
+ 
+
+ align:start position:0%
+grabbed the data that was lurking in the
+previous one and it has its five data
+
+ align:start position:0%
+previous one and it has its five data
+ 
+
+ align:start position:0%
+previous one and it has its five data
+points and it's five so it's
+
+ align:start position:0%
+points and it's five so it's
+ 
+
+ align:start position:0%
+points and it's five so it's
+whoops yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to I think it was trying to uh exit me
+
+ align:start position:0%
+to I think it was trying to uh exit me
+ 
+
+ align:start position:0%
+to I think it was trying to uh exit me
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+here so while it's doing that the the
+
+ align:start position:0%
+here so while it's doing that the the
+ 
+
+ align:start position:0%
+here so while it's doing that the the
+point here was that that uh the N equals
+
+ align:start position:0%
+point here was that that uh the N equals
+ 
+
+ align:start position:0%
+point here was that that uh the N equals
+5 is not is not looking back five data
+
+ align:start position:0%
+5 is not is not looking back five data
+ 
+
+ align:start position:0%
+5 is not is not looking back five data
+points in the xar it's buried in each of
+
+ align:start position:0%
+points in the xar it's buried in each of
+ 
+
+ align:start position:0%
+points in the xar it's buried in each of
+the individual points so that both both
+
+ align:start position:0%
+the individual points so that both both
+ 
+
+ align:start position:0%
+the individual points so that both both
+ewma
+
+ align:start position:0%
+ewma
+ 
+
+ align:start position:0%
+ewma
+and both ewma and uh uh
+
+ align:start position:0%
+and both ewma and uh uh
+ 
+
+ align:start position:0%
+and both ewma and uh uh
+xbar are are are not affected by this n
+
+ align:start position:0%
+xbar are are are not affected by this n
+ 
+
+ align:start position:0%
+xbar are are are not affected by this n
+equals 5 sampling differently but then
+
+ align:start position:0%
+equals 5 sampling differently but then
+ 
+
+ align:start position:0%
+equals 5 sampling differently but then
+the time scale is correct in terms of
+
+ align:start position:0%
+the time scale is correct in terms of
+ 
+
+ align:start position:0%
+the time scale is correct in terms of
+xar only looks at my most recent sample
+
+ align:start position:0%
+xar only looks at my most recent sample
+ 
+
+ align:start position:0%
+xar only looks at my most recent sample
+the ewma does look back in history and
+
+ align:start position:0%
+the ewma does look back in history and
+ 
+
+ align:start position:0%
+the ewma does look back in history and
+that's why you've got this additional
+
+ align:start position:0%
+that's why you've got this additional
+ 
+
+ align:start position:0%
+that's why you've got this additional
+time lag was that getting at your
+
+ align:start position:0%
+time lag was that getting at your
+ 
+
+ align:start position:0%
+time lag was that getting at your
+question or your observation or is your
+
+ align:start position:0%
+question or your observation or is your
+ 
+
+ align:start position:0%
+question or your observation or is your
+question a little
+
+ align:start position:0%
+question a little
+ 
+
+ align:start position:0%
+question a little
+different okay okay and there was a
+
+ align:start position:0%
+different okay okay and there was a
+ 
+
+ align:start position:0%
+different okay okay and there was a
+question in
+
+ align:start position:0%
+question in
+ 
+
+ align:start position:0%
+question in
+Singapore yes so uh my question is sort
+
+ align:start position:0%
+Singapore yes so uh my question is sort
+ 
+
+ align:start position:0%
+Singapore yes so uh my question is sort
+of built on what Steven was asking so
+
+ align:start position:0%
+of built on what Steven was asking so
+ 
+
+ align:start position:0%
+of built on what Steven was asking so
+for a smaller R uh you have a higher
+
+ align:start position:0%
+for a smaller R uh you have a higher
+ 
+
+ align:start position:0%
+for a smaller R uh you have a higher
+probability of detecting the mean shift
+
+ align:start position:0%
+probability of detecting the mean shift
+ 
+
+ align:start position:0%
+probability of detecting the mean shift
+but at the same time for a smaller R the
+
+ align:start position:0%
+but at the same time for a smaller R the
+ 
+
+ align:start position:0%
+but at the same time for a smaller R the
+time it takes for you to detect the mean
+
+ align:start position:0%
+time it takes for you to detect the mean
+ 
+
+ align:start position:0%
+time it takes for you to detect the mean
+shift is longer how does these two
+
+ align:start position:0%
+shift is longer how does these two
+ 
+
+ align:start position:0%
+shift is longer how does these two
+coexist
+
+ align:start position:0%
+coexist
+ 
+
+ align:start position:0%
+coexist
+while you know it's you have higher
+
+ align:start position:0%
+while you know it's you have higher
+ 
+
+ align:start position:0%
+while you know it's you have higher
+chance of detecting it but it takes
+
+ align:start position:0%
+chance of detecting it but it takes
+ 
+
+ align:start position:0%
+chance of detecting it but it takes
+longer as well yes uh they're a
+
+ align:start position:0%
+longer as well yes uh they're a
+ 
+
+ align:start position:0%
+longer as well yes uh they're a
+trade-off and so so what you are
+
+ align:start position:0%
+trade-off and so so what you are
+ 
+
+ align:start position:0%
+trade-off and so so what you are
+basically given is a degree of Freedom
+
+ align:start position:0%
+basically given is a degree of Freedom
+ 
+
+ align:start position:0%
+basically given is a degree of Freedom
+that you get to play with or experiment
+
+ align:start position:0%
+that you get to play with or experiment
+ 
+
+ align:start position:0%
+that you get to play with or experiment
+with or adapt to your process so what
+
+ align:start position:0%
+with or adapt to your process so what
+ 
+
+ align:start position:0%
+with or adapt to your process so what
+are the factors in adapting to your
+
+ align:start position:0%
+are the factors in adapting to your
+ 
+
+ align:start position:0%
+are the factors in adapting to your
+process if your process is really noisy
+
+ align:start position:0%
+process if your process is really noisy
+ 
+
+ align:start position:0%
+process if your process is really noisy
+and you think it's going to be hard to
+
+ align:start position:0%
+and you think it's going to be hard to
+ 
+
+ align:start position:0%
+and you think it's going to be hard to
+detect a mean shift in the face of that
+
+ align:start position:0%
+detect a mean shift in the face of that
+ 
+
+ align:start position:0%
+detect a mean shift in the face of that
+noise then you do more averaging you'd
+
+ align:start position:0%
+noise then you do more averaging you'd
+ 
+
+ align:start position:0%
+noise then you do more averaging you'd
+have a smaller R if you're trying to
+
+ align:start position:0%
+have a smaller R if you're trying to
+ 
+
+ align:start position:0%
+have a smaller R if you're trying to
+detect maybe with a higher risk of a
+
+ align:start position:0%
+detect maybe with a higher risk of a
+ 
+
+ align:start position:0%
+detect maybe with a higher risk of a
+false alarm but you're trying to detect
+
+ align:start position:0%
+false alarm but you're trying to detect
+ 
+
+ align:start position:0%
+false alarm but you're trying to detect
+more quickly then I'd have a larger R so
+
+ align:start position:0%
+more quickly then I'd have a larger R so
+ 
+
+ align:start position:0%
+more quickly then I'd have a larger R so
+it it responds faster but doesn't filter
+
+ align:start position:0%
+it it responds faster but doesn't filter
+ 
+
+ align:start position:0%
+it it responds faster but doesn't filter
+as much so you can see here with the R
+
+ align:start position:0%
+as much so you can see here with the R
+ 
+
+ align:start position:0%
+as much so you can see here with the R
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+0.1 versus the R equals 0.3 this is the
+
+ align:start position:0%
+0.1 versus the R equals 0.3 this is the
+ 
+
+ align:start position:0%
+0.1 versus the R equals 0.3 this is the
+same data I believe is this the same
+
+ align:start position:0%
+same data I believe is this the same
+ 
+
+ align:start position:0%
+same data I believe is this the same
+data I I guess not it's just another
+
+ align:start position:0%
+data I I guess not it's just another
+ 
+
+ align:start position:0%
+data I I guess not it's just another
+example here's an r equal 0.3 uh kind of
+
+ align:start position:0%
+example here's an r equal 0.3 uh kind of
+ 
+
+ align:start position:0%
+example here's an r equal 0.3 uh kind of
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+where um you know for this data this
+
+ align:start position:0%
+where um you know for this data this
+ 
+
+ align:start position:0%
+where um you know for this data this
+looks like about the right tradeoff I'm
+
+ align:start position:0%
+looks like about the right tradeoff I'm
+ 
+
+ align:start position:0%
+looks like about the right tradeoff I'm
+getting reasonable filtering the black
+
+ align:start position:0%
+getting reasonable filtering the black
+ 
+
+ align:start position:0%
+getting reasonable filtering the black
+dots are my
+
+ align:start position:0%
+dots are my
+ 
+
+ align:start position:0%
+dots are my
+ewma and for a a mean shift here I've
+
+ align:start position:0%
+ewma and for a a mean shift here I've
+ 
+
+ align:start position:0%
+ewma and for a a mean shift here I've
+got very
+
+ align:start position:0%
+got very
+ 
+
+ align:start position:0%
+got very
+rapid I've got sort of Rapid
+
+ align:start position:0%
+rapid I've got sort of Rapid
+ 
+
+ align:start position:0%
+rapid I've got sort of Rapid
+detection much more rapid than in fact
+
+ align:start position:0%
+detection much more rapid than in fact
+ 
+
+ align:start position:0%
+detection much more rapid than in fact
+the uh xar which doesn't really trigger
+
+ align:start position:0%
+the uh xar which doesn't really trigger
+ 
+
+ align:start position:0%
+the uh xar which doesn't really trigger
+finally until way you know another 20 25
+
+ align:start position:0%
+finally until way you know another 20 25
+ 
+
+ align:start position:0%
+finally until way you know another 20 25
+runs
+
+ align:start position:0%
+runs
+ 
+
+ align:start position:0%
+runs
+later um so i' I I I think what you'd
+
+ align:start position:0%
+later um so i' I I I think what you'd
+ 
+
+ align:start position:0%
+later um so i' I I I think what you'd
+have to do is again make the tradeoffs
+
+ align:start position:0%
+have to do is again make the tradeoffs
+ 
+
+ align:start position:0%
+have to do is again make the tradeoffs
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+responsivity the size of the shift that
+
+ align:start position:0%
+responsivity the size of the shift that
+ 
+
+ align:start position:0%
+responsivity the size of the shift that
+you're trying to detect and how much
+
+ align:start position:0%
+you're trying to detect and how much
+ 
+
+ align:start position:0%
+you're trying to detect and how much
+costs you to uh have different delays in
+
+ align:start position:0%
+costs you to uh have different delays in
+ 
+
+ align:start position:0%
+costs you to uh have different delays in
+detecting the shift so we got two
+
+ align:start position:0%
+detecting the shift so we got two
+ 
+
+ align:start position:0%
+detecting the shift so we got two
+questions here one one here first is
+
+ align:start position:0%
+questions here one one here first is
+ 
+
+ align:start position:0%
+questions here one one here first is
+that ESS because it's almost like taking
+
+ align:start position:0%
+that ESS because it's almost like taking
+ 
+
+ align:start position:0%
+that ESS because it's almost like taking
+lar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+samples you're taking five samples per
+
+ align:start position:0%
+samples you're taking five samples per
+ 
+
+ align:start position:0%
+samples you're taking five samples per
+five measurements per sample plus five
+
+ align:start position:0%
+five measurements per sample plus five
+ 
+
+ align:start position:0%
+five measurements per sample plus five
+previously at a slightly lower weight
+
+ align:start position:0%
+previously at a slightly lower weight
+ 
+
+ align:start position:0%
+previously at a slightly lower weight
+plus five at a lower weight plus five at
+
+ align:start position:0%
+plus five at a lower weight plus five at
+ 
+
+ align:start position:0%
+plus five at a lower weight plus five at
+a low weight so you're just taking more
+
+ align:start position:0%
+a low weight so you're just taking more
+ 
+
+ align:start position:0%
+a low weight so you're just taking more
+samples per more measurements per data
+
+ align:start position:0%
+samples per more measurements per data
+ 
+
+ align:start position:0%
+samples per more measurements per data
+point right yes so that that's a fair
+
+ align:start position:0%
+point right yes so that that's a fair
+ 
+
+ align:start position:0%
+point right yes so that that's a fair
+way of looking at it I that's a good way
+
+ align:start position:0%
+way of looking at it I that's a good way
+ 
+
+ align:start position:0%
+way of looking at it I that's a good way
+of looking at it so just so everybody
+
+ align:start position:0%
+of looking at it so just so everybody
+ 
+
+ align:start position:0%
+of looking at it so just so everybody
+could hear with the xar I'd take my n
+
+ align:start position:0%
+could hear with the xar I'd take my n
+ 
+
+ align:start position:0%
+could hear with the xar I'd take my n
+equals whatever sample but with the
+
+ align:start position:0%
+equals whatever sample but with the
+ 
+
+ align:start position:0%
+equals whatever sample but with the
+ewma I've still got that from my most
+
+ align:start position:0%
+ewma I've still got that from my most
+ 
+
+ align:start position:0%
+ewma I've still got that from my most
+recent update but I'm doing additional
+
+ align:start position:0%
+recent update but I'm doing additional
+ 
+
+ align:start position:0%
+recent update but I'm doing additional
+filtering or averaging of past history
+
+ align:start position:0%
+filtering or averaging of past history
+ 
+
+ align:start position:0%
+filtering or averaging of past history
+in and the net effect of that is I've
+
+ align:start position:0%
+in and the net effect of that is I've
+ 
+
+ align:start position:0%
+in and the net effect of that is I've
+got a net aggregate more number of
+
+ align:start position:0%
+got a net aggregate more number of
+ 
+
+ align:start position:0%
+got a net aggregate more number of
+samples if you will unequally weighted
+
+ align:start position:0%
+samples if you will unequally weighted
+ 
+
+ align:start position:0%
+samples if you will unequally weighted
+but a more and therefore that makes
+
+ align:start position:0%
+but a more and therefore that makes
+ 
+
+ align:start position:0%
+but a more and therefore that makes
+perfect sense that your control limits
+
+ align:start position:0%
+perfect sense that your control limits
+ 
+
+ align:start position:0%
+perfect sense that your control limits
+come down that's exactly a good that's a
+
+ align:start position:0%
+come down that's exactly a good that's a
+ 
+
+ align:start position:0%
+come down that's exactly a good that's a
+very good way of looking at it so in the
+
+ align:start position:0%
+very good way of looking at it so in the
+ 
+
+ align:start position:0%
+very good way of looking at it so in the
+previous example does EW also trigger
+
+ align:start position:0%
+previous example does EW also trigger
+ 
+
+ align:start position:0%
+previous example does EW also trigger
+before X oh yes good point good point
+
+ align:start position:0%
+before X oh yes good point good point
+ 
+
+ align:start position:0%
+before X oh yes good point good point
+yes is there ever a case when X
+
+ align:start position:0%
+yes is there ever a case when X
+ 
+
+ align:start position:0%
+yes is there ever a case when X
+trigger good question is there are there
+
+ align:start position:0%
+trigger good question is there are there
+ 
+
+ align:start position:0%
+trigger good question is there are there
+ever situations where xbar might trigger
+
+ align:start position:0%
+ever situations where xbar might trigger
+ 
+
+ align:start position:0%
+ever situations where xbar might trigger
+still before an ewma for an xar
+
+ align:start position:0%
+still before an ewma for an xar
+ 
+
+ align:start position:0%
+still before an ewma for an xar
+chart um I don't quite know the
+
+ align:start position:0%
+chart um I don't quite know the
+ 
+
+ align:start position:0%
+chart um I don't quite know the
+tradeoffs and where what where where you
+
+ align:start position:0%
+tradeoffs and where what where where you
+ 
+
+ align:start position:0%
+tradeoffs and where what where where you
+get in the limits of the tradeoff I
+
+ align:start position:0%
+get in the limits of the tradeoff I
+ 
+
+ align:start position:0%
+get in the limits of the tradeoff I
+suspect you know you've always got ch
+
+ align:start position:0%
+suspect you know you've always got ch
+ 
+
+ align:start position:0%
+suspect you know you've always got ch
+at work and I suspect that with a large
+
+ align:start position:0%
+at work and I suspect that with a large
+ 
+
+ align:start position:0%
+at work and I suspect that with a large
+enough so I the following scenario
+
+ align:start position:0%
+enough so I the following scenario
+ 
+
+ align:start position:0%
+enough so I the following scenario
+probably comes closest let's say you had
+
+ align:start position:0%
+probably comes closest let's say you had
+ 
+
+ align:start position:0%
+probably comes closest let's say you had
+a very large mean shift but a very small
+
+ align:start position:0%
+a very large mean shift but a very small
+ 
+
+ align:start position:0%
+a very large mean shift but a very small
+R okay with an xar I react entirely to a
+
+ align:start position:0%
+R okay with an xar I react entirely to a
+ 
+
+ align:start position:0%
+R okay with an xar I react entirely to a
+sample drawn from the very large mean
+
+ align:start position:0%
+sample drawn from the very large mean
+ 
+
+ align:start position:0%
+sample drawn from the very large mean
+shift let's say it was a two Sigma or a
+
+ align:start position:0%
+shift let's say it was a two Sigma or a
+ 
+
+ align:start position:0%
+shift let's say it was a two Sigma or a
+three sigma mean shift but I have a very
+
+ align:start position:0%
+three sigma mean shift but I have a very
+ 
+
+ align:start position:0%
+three sigma mean shift but I have a very
+small R maybe I'm only calling that
+
+ align:start position:0%
+small R maybe I'm only calling that
+ 
+
+ align:start position:0%
+small R maybe I'm only calling that
+05 that 5% mix in of that most recent
+
+ align:start position:0%
+05 that 5% mix in of that most recent
+ 
+
+ align:start position:0%
+05 that 5% mix in of that most recent
+data point is probably swamped out by my
+
+ align:start position:0%
+data point is probably swamped out by my
+ 
+
+ align:start position:0%
+data point is probably swamped out by my
+past data still and so in that case I
+
+ align:start position:0%
+past data still and so in that case I
+ 
+
+ align:start position:0%
+past data still and so in that case I
+think my ewma would likely not detect
+
+ align:start position:0%
+think my ewma would likely not detect
+ 
+
+ align:start position:0%
+think my ewma would likely not detect
+the mean
+
+ align:start position:0%
+the mean
+ 
+
+ align:start position:0%
+the mean
+shift so I think of the ewma is
+
+ align:start position:0%
+shift so I think of the ewma is
+ 
+
+ align:start position:0%
+shift so I think of the ewma is
+especially good for improving
+
+ align:start position:0%
+especially good for improving
+ 
+
+ align:start position:0%
+especially good for improving
+responsivity and detection ability for
+
+ align:start position:0%
+responsivity and detection ability for
+ 
+
+ align:start position:0%
+responsivity and detection ability for
+small effects because it's aggregating
+
+ align:start position:0%
+small effects because it's aggregating
+ 
+
+ align:start position:0%
+small effects because it's aggregating
+just like the qon that we'll see in a
+
+ align:start position:0%
+just like the qon that we'll see in a
+ 
+
+ align:start position:0%
+just like the qon that we'll see in a
+second but I think if there are really
+
+ align:start position:0%
+second but I think if there are really
+ 
+
+ align:start position:0%
+second but I think if there are really
+big bigger effects you lose by the f in
+
+ align:start position:0%
+big bigger effects you lose by the f in
+ 
+
+ align:start position:0%
+big bigger effects you lose by the f in
+in the time time
+
+ align:start position:0%
+in the time time
+ 
+
+ align:start position:0%
+in the time time
+response was that an example you're
+
+ align:start position:0%
+response was that an example you're
+ 
+
+ align:start position:0%
+response was that an example you're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+suggest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think oh good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah so so other rules here
+
+ align:start position:0%
+yeah yeah yeah so so other rules here
+ 
+
+ align:start position:0%
+yeah yeah yeah so so other rules here
+would help yeah
+
+ align:start position:0%
+would help yeah
+ 
+
+ align:start position:0%
+would help yeah
+absolutely okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess this is sort of saying a little
+
+ align:start position:0%
+I guess this is sort of saying a little
+ 
+
+ align:start position:0%
+I guess this is sort of saying a little
+bit the same thing this I think is
+
+ align:start position:0%
+bit the same thing this I think is
+ 
+
+ align:start position:0%
+bit the same thing this I think is
+really good for small mean shifts um
+
+ align:start position:0%
+really good for small mean shifts um
+ 
+
+ align:start position:0%
+really good for small mean shifts um
+that are persistent it's not a onetime
+
+ align:start position:0%
+that are persistent it's not a onetime
+ 
+
+ align:start position:0%
+that are persistent it's not a onetime
+shot but I've got a a Delta Mu mean
+
+ align:start position:0%
+shot but I've got a a Delta Mu mean
+ 
+
+ align:start position:0%
+shot but I've got a a Delta Mu mean
+shift and this allows us to aggregate
+
+ align:start position:0%
+shift and this allows us to aggregate
+ 
+
+ align:start position:0%
+shift and this allows us to aggregate
+but there are additional ideas we can
+
+ align:start position:0%
+but there are additional ideas we can
+ 
+
+ align:start position:0%
+but there are additional ideas we can
+use Yeah question first electric
+
+ align:start position:0%
+use Yeah question first electric
+ 
+
+ align:start position:0%
+use Yeah question first electric
+don't no you would not want to Al so uh
+
+ align:start position:0%
+don't no you would not want to Al so uh
+ 
+
+ align:start position:0%
+don't no you would not want to Al so uh
+I think Hayden's Point here was on the
+
+ align:start position:0%
+I think Hayden's Point here was on the
+ 
+
+ align:start position:0%
+I think Hayden's Point here was on the
+purple data points you might apply which
+
+ align:start position:0%
+purple data points you might apply which
+ 
+
+ align:start position:0%
+purple data points you might apply which
+was just a an xar you might apply the
+
+ align:start position:0%
+was just a an xar you might apply the
+ 
+
+ align:start position:0%
+was just a an xar you might apply the
+weo rules but you should not there might
+
+ align:start position:0%
+weo rules but you should not there might
+ 
+
+ align:start position:0%
+weo rules but you should not there might
+be variants you could derive of some of
+
+ align:start position:0%
+be variants you could derive of some of
+ 
+
+ align:start position:0%
+be variants you could derive of some of
+the other weo
+
+ align:start position:0%
+the other weo
+ 
+
+ align:start position:0%
+the other weo
+rules but I don't know how you would how
+
+ align:start position:0%
+rules but I don't know how you would how
+ 
+
+ align:start position:0%
+rules but I don't know how you would how
+you would do that it's not intuitive I
+
+ align:start position:0%
+you would do that it's not intuitive I
+ 
+
+ align:start position:0%
+you would do that it's not intuitive I
+think for the ewma you pretty much are
+
+ align:start position:0%
+think for the ewma you pretty much are
+ 
+
+ align:start position:0%
+think for the ewma you pretty much are
+just trying to track the the mean and
+
+ align:start position:0%
+just trying to track the the mean and
+ 
+
+ align:start position:0%
+just trying to track the the mean and
+not additional Trends or
+
+ align:start position:0%
+not additional Trends or
+ 
+
+ align:start position:0%
+not additional Trends or
+so so I wouldn't I would not use any of
+
+ align:start position:0%
+so so I wouldn't I would not use any of
+ 
+
+ align:start position:0%
+so so I wouldn't I would not use any of
+the additional weo rules with an ewma
+
+ align:start position:0%
+the additional weo rules with an ewma
+ 
+
+ align:start position:0%
+the additional weo rules with an ewma
+chart so there's another chart that is
+
+ align:start position:0%
+chart so there's another chart that is
+ 
+
+ align:start position:0%
+chart so there's another chart that is
+very often used that's called a q sum
+
+ align:start position:0%
+very often used that's called a q sum
+ 
+
+ align:start position:0%
+very often used that's called a q sum
+and I just want to give you a quick feel
+
+ align:start position:0%
+and I just want to give you a quick feel
+ 
+
+ align:start position:0%
+and I just want to give you a quick feel
+for that and then move to some
+
+ align:start position:0%
+for that and then move to some
+ 
+
+ align:start position:0%
+for that and then move to some
+multivariate issues um which is
+
+ align:start position:0%
+multivariate issues um which is
+ 
+
+ align:start position:0%
+multivariate issues um which is
+also targeted at this idea that when I
+
+ align:start position:0%
+also targeted at this idea that when I
+ 
+
+ align:start position:0%
+also targeted at this idea that when I
+have a small mean shift what I'd like to
+
+ align:start position:0%
+have a small mean shift what I'd like to
+ 
+
+ align:start position:0%
+have a small mean shift what I'd like to
+do is use the fact that it is a
+
+ align:start position:0%
+do is use the fact that it is a
+ 
+
+ align:start position:0%
+do is use the fact that it is a
+persistent mean shift that I'm then
+
+ align:start position:0%
+persistent mean shift that I'm then
+ 
+
+ align:start position:0%
+persistent mean shift that I'm then
+sampling around within the process noise
+
+ align:start position:0%
+sampling around within the process noise
+ 
+
+ align:start position:0%
+sampling around within the process noise
+and if there were a simple way to
+
+ align:start position:0%
+and if there were a simple way to
+ 
+
+ align:start position:0%
+and if there were a simple way to
+aggregate the mean shift over many data
+
+ align:start position:0%
+aggregate the mean shift over many data
+ 
+
+ align:start position:0%
+aggregate the mean shift over many data
+points in the past I build up a signal
+
+ align:start position:0%
+points in the past I build up a signal
+ 
+
+ align:start position:0%
+points in the past I build up a signal
+that's larger and might improve my
+
+ align:start position:0%
+that's larger and might improve my
+ 
+
+ align:start position:0%
+that's larger and might improve my
+ability to uh detect that effect and
+
+ align:start position:0%
+ability to uh detect that effect and
+ 
+
+ align:start position:0%
+ability to uh detect that effect and
+reduce the average run length for for
+
+ align:start position:0%
+reduce the average run length for for
+ 
+
+ align:start position:0%
+reduce the average run length for for
+detecting that effect and this Q sum or
+
+ align:start position:0%
+detecting that effect and this Q sum or
+ 
+
+ align:start position:0%
+detecting that effect and this Q sum or
+cumulative sum is another way of
+
+ align:start position:0%
+cumulative sum is another way of
+ 
+
+ align:start position:0%
+cumulative sum is another way of
+thinking of it as a filter and in this
+
+ align:start position:0%
+thinking of it as a filter and in this
+ 
+
+ align:start position:0%
+thinking of it as a filter and in this
+case just a discrete time integrator
+
+ align:start position:0%
+case just a discrete time integrator
+ 
+
+ align:start position:0%
+case just a discrete time integrator
+which is looking at the sum of
+
+ align:start position:0%
+which is looking at the sum of
+ 
+
+ align:start position:0%
+which is looking at the sum of
+deviations of each of my sample point
+
+ align:start position:0%
+deviations of each of my sample point
+ 
+
+ align:start position:0%
+deviations of each of my sample point
+from the assumed grand mean so I'm not
+
+ align:start position:0%
+from the assumed grand mean so I'm not
+ 
+
+ align:start position:0%
+from the assumed grand mean so I'm not
+just filtering and plotting the average
+
+ align:start position:0%
+just filtering and plotting the average
+ 
+
+ align:start position:0%
+just filtering and plotting the average
+but I'm saying asking the question am I
+
+ align:start position:0%
+but I'm saying asking the question am I
+ 
+
+ align:start position:0%
+but I'm saying asking the question am I
+still in control at my assumed xbar bar
+
+ align:start position:0%
+still in control at my assumed xbar bar
+ 
+
+ align:start position:0%
+still in control at my assumed xbar bar
+my my mu not and if I'm not then this
+
+ align:start position:0%
+my my mu not and if I'm not then this
+ 
+
+ align:start position:0%
+my my mu not and if I'm not then this
+statistic this sum of being to one side
+
+ align:start position:0%
+statistic this sum of being to one side
+ 
+
+ align:start position:0%
+statistic this sum of being to one side
+of it the C subj here will grow if I've
+
+ align:start position:0%
+of it the C subj here will grow if I've
+ 
+
+ align:start position:0%
+of it the C subj here will grow if I've
+got a plus mean shift or it'll become
+
+ align:start position:0%
+got a plus mean shift or it'll become
+ 
+
+ align:start position:0%
+got a plus mean shift or it'll become
+more and more negative and grow if I've
+
+ align:start position:0%
+more and more negative and grow if I've
+ 
+
+ align:start position:0%
+more and more negative and grow if I've
+got a negative uh mean shift so that
+
+ align:start position:0%
+got a negative uh mean shift so that
+ 
+
+ align:start position:0%
+got a negative uh mean shift so that
+I'll convert a mean shift to an
+
+ align:start position:0%
+I'll convert a mean shift to an
+ 
+
+ align:start position:0%
+I'll convert a mean shift to an
+integration of a mean shift the mean
+
+ align:start position:0%
+integration of a mean shift the mean
+ 
+
+ align:start position:0%
+integration of a mean shift the mean
+shift is a step the integration of a
+
+ align:start position:0%
+shift is a step the integration of a
+ 
+
+ align:start position:0%
+shift is a step the integration of a
+step response is
+
+ align:start position:0%
+step response is
+ 
+
+ align:start position:0%
+step response is
+a ramp right so what we would hope to do
+
+ align:start position:0%
+a ramp right so what we would hope to do
+ 
+
+ align:start position:0%
+a ramp right so what we would hope to do
+with a Q sum chart is in improve our
+
+ align:start position:0%
+with a Q sum chart is in improve our
+ 
+
+ align:start position:0%
+with a Q sum chart is in improve our
+mean shift sensitivity and basically
+
+ align:start position:0%
+mean shift sensitivity and basically
+ 
+
+ align:start position:0%
+mean shift sensitivity and basically
+have charts that look like this when
+
+ align:start position:0%
+have charts that look like this when
+ 
+
+ align:start position:0%
+have charts that look like this when
+when I'm in
+
+ align:start position:0%
+when I'm in
+ 
+
+ align:start position:0%
+when I'm in
+control I might wander around the
+
+ align:start position:0%
+control I might wander around the
+ 
+
+ align:start position:0%
+control I might wander around the
+mean you know sometimes I'll be above
+
+ align:start position:0%
+mean you know sometimes I'll be above
+ 
+
+ align:start position:0%
+mean you know sometimes I'll be above
+sometimes below so this C subj this
+
+ align:start position:0%
+sometimes below so this C subj this
+ 
+
+ align:start position:0%
+sometimes below so this C subj this
+cumulative statistic does wander around
+
+ align:start position:0%
+cumulative statistic does wander around
+ 
+
+ align:start position:0%
+cumulative statistic does wander around
+a bit but if I do have a mean shift on
+
+ align:start position:0%
+a bit but if I do have a mean shift on
+ 
+
+ align:start position:0%
+a bit but if I do have a mean shift on
+average I keep adding to that that c
+
+ align:start position:0%
+average I keep adding to that that c
+ 
+
+ align:start position:0%
+average I keep adding to that that c
+subj sometimes I might go down a little
+
+ align:start position:0%
+subj sometimes I might go down a little
+ 
+
+ align:start position:0%
+subj sometimes I might go down a little
+bit because I'm still have something a
+
+ align:start position:0%
+bit because I'm still have something a
+ 
+
+ align:start position:0%
+bit because I'm still have something a
+little bit below the mean and so what
+
+ align:start position:0%
+little bit below the mean and so what
+ 
+
+ align:start position:0%
+little bit below the mean and so what
+you create is this this ramp you create
+
+ align:start position:0%
+you create is this this ramp you create
+ 
+
+ align:start position:0%
+you create is this this ramp you create
+a a slope caused by that that mean
+
+ align:start position:0%
+a a slope caused by that that mean
+ 
+
+ align:start position:0%
+a a slope caused by that that mean
+shift now one can also now apply some
+
+ align:start position:0%
+shift now one can also now apply some
+ 
+
+ align:start position:0%
+shift now one can also now apply some
+statistics and
+
+ align:start position:0%
+statistics and
+ 
+
+ align:start position:0%
+statistics and
+design uh control limits for that c subj
+
+ align:start position:0%
+design uh control limits for that c subj
+ 
+
+ align:start position:0%
+design uh control limits for that c subj
+statistic or use a couple of other uh uh
+
+ align:start position:0%
+statistic or use a couple of other uh uh
+ 
+
+ align:start position:0%
+statistic or use a couple of other uh uh
+approaches and one approach is this
+
+ align:start position:0%
+approaches and one approach is this
+ 
+
+ align:start position:0%
+approaches and one approach is this
+so-called
+
+ align:start position:0%
+so-called
+ 
+
+ align:start position:0%
+so-called
+vask that says
+
+ align:start position:0%
+vask that says
+ 
+
+ align:start position:0%
+vask that says
+say it what I would like to do is if if
+
+ align:start position:0%
+say it what I would like to do is if if
+ 
+
+ align:start position:0%
+say it what I would like to do is if if
+in fact I've got a mean shift this
+
+ align:start position:0%
+in fact I've got a mean shift this
+ 
+
+ align:start position:0%
+in fact I've got a mean shift this
+slope let me let me erase a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops there's so there's sort of two
+
+ align:start position:0%
+whoops there's so there's sort of two
+ 
+
+ align:start position:0%
+whoops there's so there's sort of two
+different approaches and I I I just want
+
+ align:start position:0%
+different approaches and I I I just want
+ 
+
+ align:start position:0%
+different approaches and I I I just want
+to briefly mention both of those for
+
+ align:start position:0%
+to briefly mention both of those for
+ 
+
+ align:start position:0%
+to briefly mention both of those for
+detecting things on these on these
+
+ align:start position:0%
+detecting things on these on these
+ 
+
+ align:start position:0%
+detecting things on these on these
+charts one is draw control limit for the
+
+ align:start position:0%
+charts one is draw control limit for the
+ 
+
+ align:start position:0%
+charts one is draw control limit for the
+aggregate of the C
+
+ align:start position:0%
+aggregate of the C
+ 
+
+ align:start position:0%
+aggregate of the C
+subj okay the other is to look and say
+
+ align:start position:0%
+subj okay the other is to look and say
+ 
+
+ align:start position:0%
+subj okay the other is to look and say
+once I've got a mean shift I start
+
+ align:start position:0%
+once I've got a mean shift I start
+ 
+
+ align:start position:0%
+once I've got a mean shift I start
+building data points with on average
+
+ align:start position:0%
+building data points with on average
+ 
+
+ align:start position:0%
+building data points with on average
+some slope that is different than a
+
+ align:start position:0%
+some slope that is different than a
+ 
+
+ align:start position:0%
+some slope that is different than a
+slope that I would
+
+ align:start position:0%
+slope that I would
+ 
+
+ align:start position:0%
+slope that I would
+expect by random chance alone just form
+
+ align:start position:0%
+expect by random chance alone just form
+ 
+
+ align:start position:0%
+expect by random chance alone just form
+form forming the sum statistic from a
+
+ align:start position:0%
+form forming the sum statistic from a
+ 
+
+ align:start position:0%
+form forming the sum statistic from a
+normally sampled uh process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tabular Q sum this idea of actually
+
+ align:start position:0%
+the tabular Q sum this idea of actually
+ 
+
+ align:start position:0%
+the tabular Q sum this idea of actually
+looking at the statistics of of let me
+
+ align:start position:0%
+looking at the statistics of of let me
+ 
+
+ align:start position:0%
+looking at the statistics of of let me
+skip this for a second uh this
+
+ align:start position:0%
+skip this for a second uh this
+ 
+
+ align:start position:0%
+skip this for a second uh this
+normalized statistic Z and S and looking
+
+ align:start position:0%
+normalized statistic Z and S and looking
+ 
+
+ align:start position:0%
+normalized statistic Z and S and looking
+and deciding on what control limits are
+
+ align:start position:0%
+and deciding on what control limits are
+ 
+
+ align:start position:0%
+and deciding on what control limits are
+and so on I'm actually going to skip
+
+ align:start position:0%
+and so on I'm actually going to skip
+ 
+
+ align:start position:0%
+and so on I'm actually going to skip
+that there's about five slides in here
+
+ align:start position:0%
+that there's about five slides in here
+ 
+
+ align:start position:0%
+that there's about five slides in here
+but it's described very nicely and I
+
+ align:start position:0%
+but it's described very nicely and I
+ 
+
+ align:start position:0%
+but it's described very nicely and I
+think chapter 8.1 in mon gum rate and I
+
+ align:start position:0%
+think chapter 8.1 in mon gum rate and I
+ 
+
+ align:start position:0%
+think chapter 8.1 in mon gum rate and I
+think that's pretty natur natural it's
+
+ align:start position:0%
+think that's pretty natur natural it's
+ 
+
+ align:start position:0%
+think that's pretty natur natural it's
+just sort of a statistic you know a
+
+ align:start position:0%
+just sort of a statistic you know a
+ 
+
+ align:start position:0%
+just sort of a statistic you know a
+little bit nag um you know confusing um
+
+ align:start position:0%
+little bit nag um you know confusing um
+ 
+
+ align:start position:0%
+little bit nag um you know confusing um
+uh derivation of the statistics that I
+
+ align:start position:0%
+uh derivation of the statistics that I
+ 
+
+ align:start position:0%
+uh derivation of the statistics that I
+just trust the statisticians to have
+
+ align:start position:0%
+just trust the statisticians to have
+ 
+
+ align:start position:0%
+just trust the statisticians to have
+done right um but there's also another
+
+ align:start position:0%
+done right um but there's also another
+ 
+
+ align:start position:0%
+done right um but there's also another
+picture here which is based on the slope
+
+ align:start position:0%
+picture here which is based on the slope
+ 
+
+ align:start position:0%
+picture here which is based on the slope
+idea and you can similarly derive some
+
+ align:start position:0%
+idea and you can similarly derive some
+ 
+
+ align:start position:0%
+idea and you can similarly derive some
+formulas based on uh Alpha and beta
+
+ align:start position:0%
+formulas based on uh Alpha and beta
+ 
+
+ align:start position:0%
+formulas based on uh Alpha and beta
+risks what size the Delta shift in the
+
+ align:start position:0%
+risks what size the Delta shift in the
+ 
+
+ align:start position:0%
+risks what size the Delta shift in the
+mean you would hope to uh detect and
+
+ align:start position:0%
+mean you would hope to uh detect and
+ 
+
+ align:start position:0%
+mean you would hope to uh detect and
+what kind of a slope you would expect to
+
+ align:start position:0%
+what kind of a slope you would expect to
+ 
+
+ align:start position:0%
+what kind of a slope you would expect to
+see uh in those cases and so you've got
+
+ align:start position:0%
+see uh in those cases and so you've got
+ 
+
+ align:start position:0%
+see uh in those cases and so you've got
+these two parameters that go towards the
+
+ align:start position:0%
+these two parameters that go towards the
+ 
+
+ align:start position:0%
+these two parameters that go towards the
+formulation of this V mask that you
+
+ align:start position:0%
+formulation of this V mask that you
+ 
+
+ align:start position:0%
+formulation of this V mask that you
+overlay on your data
+
+ align:start position:0%
+overlay on your data
+ 
+
+ align:start position:0%
+overlay on your data
+points based on an expected slope and
+
+ align:start position:0%
+points based on an expected slope and
+ 
+
+ align:start position:0%
+points based on an expected slope and
+you need a certain number of data points
+
+ align:start position:0%
+you need a certain number of data points
+ 
+
+ align:start position:0%
+you need a certain number of data points
+in order to be able to build up your
+
+ align:start position:0%
+in order to be able to build up your
+ 
+
+ align:start position:0%
+in order to be able to build up your
+estimate of the slope that's the Dead
+
+ align:start position:0%
+estimate of the slope that's the Dead
+ 
+
+ align:start position:0%
+estimate of the slope that's the Dead
+Zone and what you do for each data point
+
+ align:start position:0%
+Zone and what you do for each data point
+ 
+
+ align:start position:0%
+Zone and what you do for each data point
+here is overlay sort of the V mask and
+
+ align:start position:0%
+here is overlay sort of the V mask and
+ 
+
+ align:start position:0%
+here is overlay sort of the V mask and
+say look back in time and see did any of
+
+ align:start position:0%
+say look back in time and see did any of
+ 
+
+ align:start position:0%
+say look back in time and see did any of
+these points intersect with the The
+
+ align:start position:0%
+these points intersect with the The
+ 
+
+ align:start position:0%
+these points intersect with the The
+Mask have a higher slope than you would
+
+ align:start position:0%
+Mask have a higher slope than you would
+ 
+
+ align:start position:0%
+Mask have a higher slope than you would
+have expected and then you update that
+
+ align:start position:0%
+have expected and then you update that
+ 
+
+ align:start position:0%
+have expected and then you update that
+on a running basis so in this case here
+
+ align:start position:0%
+on a running basis so in this case here
+ 
+
+ align:start position:0%
+on a running basis so in this case here
+at time Point 18 or 19 whatever that is
+
+ align:start position:0%
+at time Point 18 or 19 whatever that is
+ 
+
+ align:start position:0%
+at time Point 18 or 19 whatever that is
+everything looks fine I go up everything
+
+ align:start position:0%
+everything looks fine I go up everything
+ 
+
+ align:start position:0%
+everything looks fine I go up everything
+is still looking fine still here I'm
+
+ align:start position:0%
+is still looking fine still here I'm
+ 
+
+ align:start position:0%
+is still looking fine still here I'm
+starting to get some evidence maybe that
+
+ align:start position:0%
+starting to get some evidence maybe that
+ 
+
+ align:start position:0%
+starting to get some evidence maybe that
+that things have changed but
+
+ align:start position:0%
+that things have changed but
+ 
+
+ align:start position:0%
+that things have changed but
+statistically speaking that's still
+
+ align:start position:0%
+statistically speaking that's still
+ 
+
+ align:start position:0%
+statistically speaking that's still
+within the range that I would expect
+
+ align:start position:0%
+within the range that I would expect
+ 
+
+ align:start position:0%
+within the range that I would expect
+with some Alpha
+
+ align:start position:0%
+with some Alpha
+ 
+
+ align:start position:0%
+with some Alpha
+error but then finally I get to a a a
+
+ align:start position:0%
+error but then finally I get to a a a
+ 
+
+ align:start position:0%
+error but then finally I get to a a a
+new data point here at time 23 where in
+
+ align:start position:0%
+new data point here at time 23 where in
+ 
+
+ align:start position:0%
+new data point here at time 23 where in
+aggregate I've got some indication that
+
+ align:start position:0%
+aggregate I've got some indication that
+ 
+
+ align:start position:0%
+aggregate I've got some indication that
+the slope is is too large so this is
+
+ align:start position:0%
+the slope is is too large so this is
+ 
+
+ align:start position:0%
+the slope is is too large so this is
+kind of a intuitive graphical approach
+
+ align:start position:0%
+kind of a intuitive graphical approach
+ 
+
+ align:start position:0%
+kind of a intuitive graphical approach
+that's talking about the slope
+
+ align:start position:0%
+that's talking about the slope
+ 
+
+ align:start position:0%
+that's talking about the slope
+associated with uh
+
+ align:start position:0%
+associated with uh
+ 
+
+ align:start position:0%
+associated with uh
+um a mean shift in the qm statistic yes
+
+ align:start position:0%
+um a mean shift in the qm statistic yes
+ 
+
+ align:start position:0%
+um a mean shift in the qm statistic yes
+would you also um perform a lar
+
+ align:start position:0%
+would you also um perform a lar
+ 
+
+ align:start position:0%
+would you also um perform a lar
+regression for the
+
+ align:start position:0%
+regression for the
+ 
+
+ align:start position:0%
+regression for the
+last so the question is can you perform
+
+ align:start position:0%
+last so the question is can you perform
+ 
+
+ align:start position:0%
+last so the question is can you perform
+a linear regression and and uh calculate
+
+ align:start position:0%
+a linear regression and and uh calculate
+ 
+
+ align:start position:0%
+a linear regression and and uh calculate
+the slope of that and I think that's
+
+ align:start position:0%
+the slope of that and I think that's
+ 
+
+ align:start position:0%
+the slope of that and I think that's
+identical to what this is doing
+
+ align:start position:0%
+identical to what this is doing
+ 
+
+ align:start position:0%
+identical to what this is doing
+graphically so in fact if you were
+
+ align:start position:0%
+graphically so in fact if you were
+ 
+
+ align:start position:0%
+graphically so in fact if you were
+numerically or you know implementing an
+
+ align:start position:0%
+numerically or you know implementing an
+ 
+
+ align:start position:0%
+numerically or you know implementing an
+automatic version of this that that
+
+ align:start position:0%
+automatic version of this that that
+ 
+
+ align:start position:0%
+automatic version of this that that
+would probably be how you would how you
+
+ align:start position:0%
+would probably be how you would how you
+ 
+
+ align:start position:0%
+would probably be how you would how you
+would implement
+
+ align:start position:0%
+would implement
+ 
+
+ align:start position:0%
+would implement
+it that might even give you some more
+
+ align:start position:0%
+it that might even give you some more
+ 
+
+ align:start position:0%
+it that might even give you some more
+flexibility in terms of looking at the
+
+ align:start position:0%
+flexibility in terms of looking at the
+ 
+
+ align:start position:0%
+flexibility in terms of looking at the
+goodness of that fit um but I think it's
+
+ align:start position:0%
+goodness of that fit um but I think it's
+ 
+
+ align:start position:0%
+goodness of that fit um but I think it's
+essentially identical to
+
+ align:start position:0%
+essentially identical to
+ 
+
+ align:start position:0%
+essentially identical to
+this okay so just to summarize these
+
+ align:start position:0%
+this okay so just to summarize these
+ 
+
+ align:start position:0%
+this okay so just to summarize these
+alternative charts there's a few simple
+
+ align:start position:0%
+alternative charts there's a few simple
+ 
+
+ align:start position:0%
+alternative charts there's a few simple
+messages uh noisy data if you're trying
+
+ align:start position:0%
+messages uh noisy data if you're trying
+ 
+
+ align:start position:0%
+messages uh noisy data if you're trying
+to detect a mean in the noisy data you
+
+ align:start position:0%
+to detect a mean in the noisy data you
+ 
+
+ align:start position:0%
+to detect a mean in the noisy data you
+might want to use some filtering we have
+
+ align:start position:0%
+might want to use some filtering we have
+ 
+
+ align:start position:0%
+might want to use some filtering we have
+the sample size that does some filtering
+
+ align:start position:0%
+the sample size that does some filtering
+ 
+
+ align:start position:0%
+the sample size that does some filtering
+but I might want to use more data in the
+
+ align:start position:0%
+but I might want to use more data in the
+ 
+
+ align:start position:0%
+but I might want to use more data in the
+past and uh sort of this linear discrete
+
+ align:start position:0%
+past and uh sort of this linear discrete
+ 
+
+ align:start position:0%
+past and uh sort of this linear discrete
+filtering either with the Q sum as a
+
+ align:start position:0%
+filtering either with the Q sum as a
+ 
+
+ align:start position:0%
+filtering either with the Q sum as a
+running integrator or an
+
+ align:start position:0%
+running integrator or an
+ 
+
+ align:start position:0%
+running integrator or an
+ewma um uh which is an iterative uh
+
+ align:start position:0%
+ewma um uh which is an iterative uh
+ 
+
+ align:start position:0%
+ewma um uh which is an iterative uh
+discrete filter uh can be applied and I
+
+ align:start position:0%
+discrete filter uh can be applied and I
+ 
+
+ align:start position:0%
+discrete filter uh can be applied and I
+think conceptually uh they're fairly
+
+ align:start position:0%
+think conceptually uh they're fairly
+ 
+
+ align:start position:0%
+think conceptually uh they're fairly
+nice in terms of that noise suppression
+
+ align:start position:0%
+nice in terms of that noise suppression
+ 
+
+ align:start position:0%
+nice in terms of that noise suppression
+for detecting detecting of the mean got
+
+ align:start position:0%
+for detecting detecting of the mean got
+ 
+
+ align:start position:0%
+for detecting detecting of the mean got
+to remember that your choice of factors
+
+ align:start position:0%
+to remember that your choice of factors
+ 
+
+ align:start position:0%
+to remember that your choice of factors
+like R in the ewma depends on your
+
+ align:start position:0%
+like R in the ewma depends on your
+ 
+
+ align:start position:0%
+like R in the ewma depends on your
+process the mix of noise and how fast
+
+ align:start position:0%
+process the mix of noise and how fast
+ 
+
+ align:start position:0%
+process the mix of noise and how fast
+you want to respond to be able to detect
+
+ align:start position:0%
+you want to respond to be able to detect
+ 
+
+ align:start position:0%
+you want to respond to be able to detect
+a mean shift and then going back to what
+
+ align:start position:0%
+a mean shift and then going back to what
+ 
+
+ align:start position:0%
+a mean shift and then going back to what
+we started with our little example at
+
+ align:start position:0%
+we started with our little example at
+ 
+
+ align:start position:0%
+we started with our little example at
+the very
+
+ align:start position:0%
+the very
+ 
+
+ align:start position:0%
+the very
+beginning noisy data needs some
+
+ align:start position:0%
+beginning noisy data needs some
+ 
+
+ align:start position:0%
+beginning noisy data needs some
+filtering we've talked about it with
+
+ align:start position:0%
+filtering we've talked about it with
+ 
+
+ align:start position:0%
+filtering we've talked about it with
+respect to the mean but if I'm filtering
+
+ align:start position:0%
+respect to the mean but if I'm filtering
+ 
+
+ align:start position:0%
+respect to the mean but if I'm filtering
+that data you also still want to look
+
+ align:start position:0%
+that data you also still want to look
+ 
+
+ align:start position:0%
+that data you also still want to look
+back and monitor the variance as well so
+
+ align:start position:0%
+back and monitor the variance as well so
+ 
+
+ align:start position:0%
+back and monitor the variance as well so
+you can apply these charts also to
+
+ align:start position:0%
+you can apply these charts also to
+ 
+
+ align:start position:0%
+you can apply these charts also to
+moving uh sbar charts uh and so
+
+ align:start position:0%
+moving uh sbar charts uh and so
+ 
+
+ align:start position:0%
+moving uh sbar charts uh and so
+on so what I want to do next is move a
+
+ align:start position:0%
+on so what I want to do next is move a
+ 
+
+ align:start position:0%
+on so what I want to do next is move a
+little bit to multivariate process
+
+ align:start position:0%
+little bit to multivariate process
+ 
+
+ align:start position:0%
+little bit to multivariate process
+control control charting when I've got
+
+ align:start position:0%
+control control charting when I've got
+ 
+
+ align:start position:0%
+control control charting when I've got
+more than one parameter that I I may be
+
+ align:start position:0%
+more than one parameter that I I may be
+ 
+
+ align:start position:0%
+more than one parameter that I I may be
+monitoring on the unit process or on the
+
+ align:start position:0%
+monitoring on the unit process or on the
+ 
+
+ align:start position:0%
+monitoring on the unit process or on the
+product and what's really interesting
+
+ align:start position:0%
+product and what's really interesting
+ 
+
+ align:start position:0%
+product and what's really interesting
+here is there are essentially two
+
+ align:start position:0%
+here is there are essentially two
+ 
+
+ align:start position:0%
+here is there are essentially two
+classic
+
+ align:start position:0%
+classic
+ 
+
+ align:start position:0%
+classic
+mistakes that are made again and again
+
+ align:start position:0%
+mistakes that are made again and again
+ 
+
+ align:start position:0%
+mistakes that are made again and again
+and I want to give you a feel for those
+
+ align:start position:0%
+and I want to give you a feel for those
+ 
+
+ align:start position:0%
+and I want to give you a feel for those
+two mistakes and strategies for avoiding
+
+ align:start position:0%
+two mistakes and strategies for avoiding
+ 
+
+ align:start position:0%
+two mistakes and strategies for avoiding
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay one classic problem is you've got
+
+ align:start position:0%
+okay one classic problem is you've got
+ 
+
+ align:start position:0%
+okay one classic problem is you've got
+more than one parameter you're
+
+ align:start position:0%
+more than one parameter you're
+ 
+
+ align:start position:0%
+more than one parameter you're
+monitoring you implement more than one
+
+ align:start position:0%
+monitoring you implement more than one
+ 
+
+ align:start position:0%
+monitoring you implement more than one
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+chart right seems natural but the
+
+ align:start position:0%
+chart right seems natural but the
+ 
+
+ align:start position:0%
+chart right seems natural but the
+problem is you can get many many many
+
+ align:start position:0%
+problem is you can get many many many
+ 
+
+ align:start position:0%
+problem is you can get many many many
+more false
+
+ align:start position:0%
+more false
+ 
+
+ align:start position:0%
+more false
+alarms than you might have expected or
+
+ align:start position:0%
+alarms than you might have expected or
+ 
+
+ align:start position:0%
+alarms than you might have expected or
+or or or believed you were going to to
+
+ align:start position:0%
+or or or believed you were going to to
+ 
+
+ align:start position:0%
+or or or believed you were going to to
+get because you're just monitoring more
+
+ align:start position:0%
+get because you're just monitoring more
+ 
+
+ align:start position:0%
+get because you're just monitoring more
+parameters and so I want to talk a
+
+ align:start position:0%
+parameters and so I want to talk a
+ 
+
+ align:start position:0%
+parameters and so I want to talk a
+little bit about that that's even if
+
+ align:start position:0%
+little bit about that that's even if
+ 
+
+ align:start position:0%
+little bit about that that's even if
+there's no correlation between your
+
+ align:start position:0%
+there's no correlation between your
+ 
+
+ align:start position:0%
+there's no correlation between your
+parameters okay or especially if there's
+
+ align:start position:0%
+parameters okay or especially if there's
+ 
+
+ align:start position:0%
+parameters okay or especially if there's
+no correlation between your parameters
+
+ align:start position:0%
+no correlation between your parameters
+ 
+
+ align:start position:0%
+no correlation between your parameters
+you can get just by the fact that you're
+
+ align:start position:0%
+you can get just by the fact that you're
+ 
+
+ align:start position:0%
+you can get just by the fact that you're
+you're monitoring more than one thing
+
+ align:start position:0%
+you're monitoring more than one thing
+ 
+
+ align:start position:0%
+you're monitoring more than one thing
+you got to think about false alarm rate
+
+ align:start position:0%
+you got to think about false alarm rate
+ 
+
+ align:start position:0%
+you got to think about false alarm rate
+a little bit differently and then the
+
+ align:start position:0%
+a little bit differently and then the
+ 
+
+ align:start position:0%
+a little bit differently and then the
+second classic problem is well there is
+
+ align:start position:0%
+second classic problem is well there is
+ 
+
+ align:start position:0%
+second classic problem is well there is
+correlation among the
+
+ align:start position:0%
+correlation among the
+ 
+
+ align:start position:0%
+correlation among the
+parameters the multiple parameters how
+
+ align:start position:0%
+parameters the multiple parameters how
+ 
+
+ align:start position:0%
+parameters the multiple parameters how
+do you deal with that and in fact in
+
+ align:start position:0%
+do you deal with that and in fact in
+ 
+
+ align:start position:0%
+do you deal with that and in fact in
+this case you often run into the
+
+ align:start position:0%
+this case you often run into the
+ 
+
+ align:start position:0%
+this case you often run into the
+opposite
+
+ align:start position:0%
+opposite
+ 
+
+ align:start position:0%
+opposite
+risk instead of too many false alarms
+
+ align:start position:0%
+risk instead of too many false alarms
+ 
+
+ align:start position:0%
+risk instead of too many false alarms
+you may have have points of data or
+
+ align:start position:0%
+you may have have points of data or
+ 
+
+ align:start position:0%
+you may have have points of data or
+product that is truly out of out of
+
+ align:start position:0%
+product that is truly out of out of
+ 
+
+ align:start position:0%
+product that is truly out of out of
+normal operation that you may not detect
+
+ align:start position:0%
+normal operation that you may not detect
+ 
+
+ align:start position:0%
+normal operation that you may not detect
+it's a highly unusual point that may in
+
+ align:start position:0%
+it's a highly unusual point that may in
+ 
+
+ align:start position:0%
+it's a highly unusual point that may in
+indicate something has changed in your
+
+ align:start position:0%
+indicate something has changed in your
+ 
+
+ align:start position:0%
+indicate something has changed in your
+process but if you're just monitoring
+
+ align:start position:0%
+process but if you're just monitoring
+ 
+
+ align:start position:0%
+process but if you're just monitoring
+with univariate control charts you'll
+
+ align:start position:0%
+with univariate control charts you'll
+ 
+
+ align:start position:0%
+with univariate control charts you'll
+never see it okay and so I want to talk
+
+ align:start position:0%
+never see it okay and so I want to talk
+ 
+
+ align:start position:0%
+never see it okay and so I want to talk
+about that as a common mistake number
+
+ align:start position:0%
+about that as a common mistake number
+ 
+
+ align:start position:0%
+about that as a common mistake number
+two let me talk about multiple charts as
+
+ align:start position:0%
+two let me talk about multiple charts as
+ 
+
+ align:start position:0%
+two let me talk about multiple charts as
+common mistake number one first
+
+ align:start position:0%
+common mistake number one first
+ 
+
+ align:start position:0%
+common mistake number one first
+if I truly have independent parameters
+
+ align:start position:0%
+if I truly have independent parameters
+ 
+
+ align:start position:0%
+if I truly have independent parameters
+being modeled monitored at my process
+
+ align:start position:0%
+being modeled monitored at my process
+ 
+
+ align:start position:0%
+being modeled monitored at my process
+step and I set each one of them up to
+
+ align:start position:0%
+step and I set each one of them up to
+ 
+
+ align:start position:0%
+step and I set each one of them up to
+have some acceptable Alpha rate false
+
+ align:start position:0%
+have some acceptable Alpha rate false
+ 
+
+ align:start position:0%
+have some acceptable Alpha rate false
+alarm rate one out of every 370 process
+
+ align:start position:0%
+alarm rate one out of every 370 process
+ 
+
+ align:start position:0%
+alarm rate one out of every 370 process
+steps sort of going with a plusus 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigma right three sigma control limits
+
+ align:start position:0%
+Sigma right three sigma control limits
+ 
+
+ align:start position:0%
+Sigma right three sigma control limits
+Alpha is about
+
+ align:start position:0%
+Alpha is about
+ 
+
+ align:start position:0%
+Alpha is about
+027 sometimes talked about 03 as an
+
+ align:start position:0%
+027 sometimes talked about 03 as an
+ 
+
+ align:start position:0%
+027 sometimes talked about 03 as an
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+but now I've got P of those separate
+
+ align:start position:0%
+but now I've got P of those separate
+ 
+
+ align:start position:0%
+but now I've got P of those separate
+charts what is the aggregate false alarm
+
+ align:start position:0%
+charts what is the aggregate false alarm
+ 
+
+ align:start position:0%
+charts what is the aggregate false alarm
+probability well to be careful about it
+
+ align:start position:0%
+probability well to be careful about it
+ 
+
+ align:start position:0%
+probability well to be careful about it
+if they are in fact independent that
+
+ align:start position:0%
+if they are in fact independent that
+ 
+
+ align:start position:0%
+if they are in fact independent that
+Alpha Prime my aggregate false alarm is
+
+ align:start position:0%
+Alpha Prime my aggregate false alarm is
+ 
+
+ align:start position:0%
+Alpha Prime my aggregate false alarm is
+1 minus 1 minus Alpha to the P right
+
+ align:start position:0%
+1 minus 1 minus Alpha to the P right
+ 
+
+ align:start position:0%
+1 minus 1 minus Alpha to the P right
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+probability um that I don't get a false
+
+ align:start position:0%
+probability um that I don't get a false
+ 
+
+ align:start position:0%
+probability um that I don't get a false
+alarm for each of for all of the other P
+
+ align:start position:0%
+alarm for each of for all of the other P
+ 
+
+ align:start position:0%
+alarm for each of for all of the other P
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+charts all at the same time and then
+
+ align:start position:0%
+charts all at the same time and then
+ 
+
+ align:start position:0%
+charts all at the same time and then
+oneus that is the chance that I did get
+
+ align:start position:0%
+oneus that is the chance that I did get
+ 
+
+ align:start position:0%
+oneus that is the chance that I did get
+one of them now for very small Alpha you
+
+ align:start position:0%
+one of them now for very small Alpha you
+ 
+
+ align:start position:0%
+one of them now for very small Alpha you
+do that expansion one minus X for small
+
+ align:start position:0%
+do that expansion one minus X for small
+ 
+
+ align:start position:0%
+do that expansion one minus X for small
+x to the p is simply 1 minus PX so you
+
+ align:start position:0%
+x to the p is simply 1 minus PX so you
+ 
+
+ align:start position:0%
+x to the p is simply 1 minus PX so you
+do that and you get sort of the nice
+
+ align:start position:0%
+do that and you get sort of the nice
+ 
+
+ align:start position:0%
+do that and you get sort of the nice
+intuitive result that if I've got 10
+
+ align:start position:0%
+intuitive result that if I've got 10
+ 
+
+ align:start position:0%
+intuitive result that if I've got 10
+independent control charts I've got
+
+ align:start position:0%
+independent control charts I've got
+ 
+
+ align:start position:0%
+independent control charts I've got
+about 10 times the rate of false alarm
+
+ align:start position:0%
+about 10 times the rate of false alarm
+ 
+
+ align:start position:0%
+about 10 times the rate of false alarm
+that I would have from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would you
+
+ align:start position:0%
+what would you
+ 
+
+ align:start position:0%
+what would you
+do let me let me say it this way um
+
+ align:start position:0%
+do let me let me say it this way um
+ 
+
+ align:start position:0%
+do let me let me say it this way um
+you've decided based on your cost
+
+ align:start position:0%
+you've decided based on your cost
+ 
+
+ align:start position:0%
+you've decided based on your cost
+analysis or whatever that you're willing
+
+ align:start position:0%
+analysis or whatever that you're willing
+ 
+
+ align:start position:0%
+analysis or whatever that you're willing
+about once every
+
+ align:start position:0%
+about once every
+ 
+
+ align:start position:0%
+about once every
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+runs
+
+ align:start position:0%
+runs
+ 
+
+ align:start position:0%
+runs
+to have a false alarm somewhere on this
+
+ align:start position:0%
+to have a false alarm somewhere on this
+ 
+
+ align:start position:0%
+to have a false alarm somewhere on this
+process that you want to at least look
+
+ align:start position:0%
+process that you want to at least look
+ 
+
+ align:start position:0%
+process that you want to at least look
+at maybe you look at it real quickly it
+
+ align:start position:0%
+at maybe you look at it real quickly it
+ 
+
+ align:start position:0%
+at maybe you look at it real quickly it
+doesn't take a long time but but that's
+
+ align:start position:0%
+doesn't take a long time but but that's
+ 
+
+ align:start position:0%
+doesn't take a long time but but that's
+about how often you want the operator to
+
+ align:start position:0%
+about how often you want the operator to
+ 
+
+ align:start position:0%
+about how often you want the operator to
+stop and take a look on average even
+
+ align:start position:0%
+stop and take a look on average even
+ 
+
+ align:start position:0%
+stop and take a look on average even
+when the process is in control so that's
+
+ align:start position:0%
+when the process is in control so that's
+ 
+
+ align:start position:0%
+when the process is in control so that's
+your false alarm rate that you're
+
+ align:start position:0%
+your false alarm rate that you're
+ 
+
+ align:start position:0%
+your false alarm rate that you're
+willing to accept but you're monitoring
+
+ align:start position:0%
+willing to accept but you're monitoring
+ 
+
+ align:start position:0%
+willing to accept but you're monitoring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters there are some approaches you
+
+ align:start position:0%
+parameters there are some approaches you
+ 
+
+ align:start position:0%
+parameters there are some approaches you
+would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use um you have to increase your control
+
+ align:start position:0%
+use um you have to increase your control
+ 
+
+ align:start position:0%
+use um you have to increase your control
+limits right perfect you would increase
+
+ align:start position:0%
+limits right perfect you would increase
+ 
+
+ align:start position:0%
+limits right perfect you would increase
+your control limits if I expand my
+
+ align:start position:0%
+your control limits if I expand my
+ 
+
+ align:start position:0%
+your control limits if I expand my
+control limits out a little bit I have
+
+ align:start position:0%
+control limits out a little bit I have
+ 
+
+ align:start position:0%
+control limits out a little bit I have
+smaller false alarm rate on each on each
+
+ align:start position:0%
+smaller false alarm rate on each on each
+ 
+
+ align:start position:0%
+smaller false alarm rate on each on each
+uh on each chart well I can basically
+
+ align:start position:0%
+uh on each chart well I can basically
+ 
+
+ align:start position:0%
+uh on each chart well I can basically
+decide what
+
+ align:start position:0%
+decide what
+ 
+
+ align:start position:0%
+decide what
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+um my
+
+ align:start position:0%
+um my
+ 
+
+ align:start position:0%
+um my
+aggregate false alarm rate would
+
+ align:start position:0%
+aggregate false alarm rate would
+ 
+
+ align:start position:0%
+aggregate false alarm rate would
+be 1 out of 370 and to set my false
+
+ align:start position:0%
+be 1 out of 370 and to set my false
+ 
+
+ align:start position:0%
+be 1 out of 370 and to set my false
+alarm rate on each individual chart just
+
+ align:start position:0%
+alarm rate on each individual chart just
+ 
+
+ align:start position:0%
+alarm rate on each individual chart just
+divide by how many charts I have now I
+
+ align:start position:0%
+divide by how many charts I have now I
+ 
+
+ align:start position:0%
+divide by how many charts I have now I
+might have a one in 300
+
+ align:start position:0%
+might have a one in 300
+ 
+
+ align:start position:0%
+might have a one in 300
+3,700 false alarm rate on each chart and
+
+ align:start position:0%
+3,700 false alarm rate on each chart and
+ 
+
+ align:start position:0%
+3,700 false alarm rate on each chart and
+I use that new Alpha to set my control
+
+ align:start position:0%
+I use that new Alpha to set my control
+ 
+
+ align:start position:0%
+I use that new Alpha to set my control
+limits they might end up being in that
+
+ align:start position:0%
+limits they might end up being in that
+ 
+
+ align:start position:0%
+limits they might end up being in that
+case plusus 3.4 Sigma control
+
+ align:start position:0%
+case plusus 3.4 Sigma control
+ 
+
+ align:start position:0%
+case plusus 3.4 Sigma control
+limits okay so the individual uh false
+
+ align:start position:0%
+limits okay so the individual uh false
+ 
+
+ align:start position:0%
+limits okay so the individual uh false
+alarm rate
+
+ align:start position:0%
+alarm rate
+ 
+
+ align:start position:0%
+alarm rate
+is is lower on each one because really
+
+ align:start position:0%
+is is lower on each one because really
+ 
+
+ align:start position:0%
+is is lower on each one because really
+the question you were asking the key
+
+ align:start position:0%
+the question you were asking the key
+ 
+
+ align:start position:0%
+the question you were asking the key
+question was not you know that
+
+ align:start position:0%
+question was not you know that
+ 
+
+ align:start position:0%
+question was not you know that
+individual parameter one you know but
+
+ align:start position:0%
+individual parameter one you know but
+ 
+
+ align:start position:0%
+individual parameter one you know but
+rather the question is my process in
+
+ align:start position:0%
+rather the question is my process in
+ 
+
+ align:start position:0%
+rather the question is my process in
+control in aggregate do I have an event
+
+ align:start position:0%
+control in aggregate do I have an event
+ 
+
+ align:start position:0%
+control in aggregate do I have an event
+that looks
+
+ align:start position:0%
+that looks
+ 
+
+ align:start position:0%
+that looks
+unlikely so unlikely that I
+
+ align:start position:0%
+unlikely so unlikely that I
+ 
+
+ align:start position:0%
+unlikely so unlikely that I
+have oneus Alpha
+
+ align:start position:0%
+have oneus Alpha
+ 
+
+ align:start position:0%
+have oneus Alpha
+confidence oneus Alpha Prime confidence
+
+ align:start position:0%
+confidence oneus Alpha Prime confidence
+ 
+
+ align:start position:0%
+confidence oneus Alpha Prime confidence
+evence that in fact something unusual is
+
+ align:start position:0%
+evence that in fact something unusual is
+ 
+
+ align:start position:0%
+evence that in fact something unusual is
+going on in the process okay so that's
+
+ align:start position:0%
+going on in the process okay so that's
+ 
+
+ align:start position:0%
+going on in the process okay so that's
+the that's the strategy I want to also
+
+ align:start position:0%
+the that's the strategy I want to also
+ 
+
+ align:start position:0%
+the that's the strategy I want to also
+point out and this is kind of a a neat
+
+ align:start position:0%
+point out and this is kind of a a neat
+ 
+
+ align:start position:0%
+point out and this is kind of a a neat
+little article that I found uh uh last
+
+ align:start position:0%
+little article that I found uh uh last
+ 
+
+ align:start position:0%
+little article that I found uh uh last
+year that this is a more generic problem
+
+ align:start position:0%
+year that this is a more generic problem
+ 
+
+ align:start position:0%
+year that this is a more generic problem
+a more generic common mistake than just
+
+ align:start position:0%
+a more generic common mistake than just
+ 
+
+ align:start position:0%
+a more generic common mistake than just
+control charting it applies all the time
+
+ align:start position:0%
+control charting it applies all the time
+ 
+
+ align:start position:0%
+control charting it applies all the time
+when people are doing significance tests
+
+ align:start position:0%
+when people are doing significance tests
+ 
+
+ align:start position:0%
+when people are doing significance tests
+or hypothesis tests but doing more than
+
+ align:start position:0%
+or hypothesis tests but doing more than
+ 
+
+ align:start position:0%
+or hypothesis tests but doing more than
+one of them at a time
+
+ align:start position:0%
+one of them at a time
+ 
+
+ align:start position:0%
+one of them at a time
+time right control chart is just a
+
+ align:start position:0%
+time right control chart is just a
+ 
+
+ align:start position:0%
+time right control chart is just a
+running hypothesis test now if I'm
+
+ align:start position:0%
+running hypothesis test now if I'm
+ 
+
+ align:start position:0%
+running hypothesis test now if I'm
+checking 10 hypotheses 10 control charts
+
+ align:start position:0%
+checking 10 hypotheses 10 control charts
+ 
+
+ align:start position:0%
+checking 10 hypotheses 10 control charts
+and 10
+
+ align:start position:0%
+and 10
+ 
+
+ align:start position:0%
+and 10
+parameters um my aggregate you know
+
+ align:start position:0%
+parameters um my aggregate you know
+ 
+
+ align:start position:0%
+parameters um my aggregate you know
+false alarm rate is is higher and
+
+ align:start position:0%
+false alarm rate is is higher and
+ 
+
+ align:start position:0%
+false alarm rate is is higher and
+there's this neat little article pulled
+
+ align:start position:0%
+there's this neat little article pulled
+ 
+
+ align:start position:0%
+there's this neat little article pulled
+from that I found in the economist uh
+
+ align:start position:0%
+from that I found in the economist uh
+ 
+
+ align:start position:0%
+from that I found in the economist uh
+last February that's called medical
+
+ align:start position:0%
+last February that's called medical
+ 
+
+ align:start position:0%
+last February that's called medical
+statistics signs of the times the
+
+ align:start position:0%
+statistics signs of the times the
+ 
+
+ align:start position:0%
+statistics signs of the times the
+subtitle here you may not be able to
+
+ align:start position:0%
+subtitle here you may not be able to
+ 
+
+ align:start position:0%
+subtitle here you may not be able to
+read it is why so much medical research
+
+ align:start position:0%
+read it is why so much medical research
+ 
+
+ align:start position:0%
+read it is why so much medical research
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+rot and uh the first I'll read you the
+
+ align:start position:0%
+rot and uh the first I'll read you the
+ 
+
+ align:start position:0%
+rot and uh the first I'll read you the
+first couple of sentences here people
+
+ align:start position:0%
+first couple of sentences here people
+ 
+
+ align:start position:0%
+first couple of sentences here people
+born under the astrological sign of Leo
+
+ align:start position:0%
+born under the astrological sign of Leo
+ 
+
+ align:start position:0%
+born under the astrological sign of Leo
+are 15% more likely to be admitted to
+
+ align:start position:0%
+are 15% more likely to be admitted to
+ 
+
+ align:start position:0%
+are 15% more likely to be admitted to
+hospital with gastric bleeding than
+
+ align:start position:0%
+hospital with gastric bleeding than
+ 
+
+ align:start position:0%
+hospital with gastric bleeding than
+those born with the other 11 signs
+
+ align:start position:0%
+those born with the other 11 signs
+ 
+
+ align:start position:0%
+those born with the other 11 signs
+sagittarians are 38% more likely than
+
+ align:start position:0%
+sagittarians are 38% more likely than
+ 
+
+ align:start position:0%
+sagittarians are 38% more likely than
+others to land up there because of a
+
+ align:start position:0%
+others to land up there because of a
+ 
+
+ align:start position:0%
+others to land up there because of a
+broken
+
+ align:start position:0%
+broken
+ 
+
+ align:start position:0%
+broken
+arm those are the conclusions that many
+
+ align:start position:0%
+arm those are the conclusions that many
+ 
+
+ align:start position:0%
+arm those are the conclusions that many
+medical researchers would be forced to
+
+ align:start position:0%
+medical researchers would be forced to
+ 
+
+ align:start position:0%
+medical researchers would be forced to
+make from a set of data presented to the
+
+ align:start position:0%
+make from a set of data presented to the
+ 
+
+ align:start position:0%
+make from a set of data presented to the
+American Association for the advancement
+
+ align:start position:0%
+American Association for the advancement
+ 
+
+ align:start position:0%
+American Association for the advancement
+of science um at least they would be
+
+ align:start position:0%
+of science um at least they would be
+ 
+
+ align:start position:0%
+of science um at least they would be
+forced to draw them if they applied the
+
+ align:start position:0%
+forced to draw them if they applied the
+ 
+
+ align:start position:0%
+forced to draw them if they applied the
+lack statistical methods of their own
+
+ align:start position:0%
+lack statistical methods of their own
+ 
+
+ align:start position:0%
+lack statistical methods of their own
+work to the records of Hospital
+
+ align:start position:0%
+work to the records of Hospital
+ 
+
+ align:start position:0%
+work to the records of Hospital
+admissions in Ontario
+
+ align:start position:0%
+admissions in Ontario
+ 
+
+ align:start position:0%
+admissions in Ontario
+Canada and the basic confusion drawn
+
+ align:start position:0%
+Canada and the basic confusion drawn
+ 
+
+ align:start position:0%
+Canada and the basic confusion drawn
+here in the in the red arises because
+
+ align:start position:0%
+here in the in the red arises because
+ 
+
+ align:start position:0%
+here in the in the red arises because
+each result is tested separately to see
+
+ align:start position:0%
+each result is tested separately to see
+ 
+
+ align:start position:0%
+each result is tested separately to see
+how likely in statistical terms it was
+
+ align:start position:0%
+how likely in statistical terms it was
+ 
+
+ align:start position:0%
+how likely in statistical terms it was
+to have happened by Chance the
+
+ align:start position:0%
+to have happened by Chance the
+ 
+
+ align:start position:0%
+to have happened by Chance the
+likelihood is below a certain threshold
+
+ align:start position:0%
+likelihood is below a certain threshold
+ 
+
+ align:start position:0%
+likelihood is below a certain threshold
+typically n uh 5% so we got a 95%
+
+ align:start position:0%
+typically n uh 5% so we got a 95%
+ 
+
+ align:start position:0%
+typically n uh 5% so we got a 95%
+confidence
+
+ align:start position:0%
+confidence
+ 
+
+ align:start position:0%
+confidence
+which says one in 20 times by chance
+
+ align:start position:0%
+which says one in 20 times by chance
+ 
+
+ align:start position:0%
+which says one in 20 times by chance
+alone I might see a signal that big by
+
+ align:start position:0%
+alone I might see a signal that big by
+ 
+
+ align:start position:0%
+alone I might see a signal that big by
+chance alone and now I check 12 maybe
+
+ align:start position:0%
+chance alone and now I check 12 maybe
+ 
+
+ align:start position:0%
+chance alone and now I check 12 maybe
+astrological sign is your 12 things I'm
+
+ align:start position:0%
+astrological sign is your 12 things I'm
+ 
+
+ align:start position:0%
+astrological sign is your 12 things I'm
+checking for as factors and I've got a
+
+ align:start position:0%
+checking for as factors and I've got a
+ 
+
+ align:start position:0%
+checking for as factors and I've got a
+one in 20 one in 20 chance and I check
+
+ align:start position:0%
+one in 20 one in 20 chance and I check
+ 
+
+ align:start position:0%
+one in 20 one in 20 chance and I check
+12 of them probably I'm going to pop up
+
+ align:start position:0%
+12 of them probably I'm going to pop up
+ 
+
+ align:start position:0%
+12 of them probably I'm going to pop up
+and say ah that one's
+
+ align:start position:0%
+and say ah that one's
+ 
+
+ align:start position:0%
+and say ah that one's
+significant right and so that's exactly
+
+ align:start position:0%
+significant right and so that's exactly
+ 
+
+ align:start position:0%
+significant right and so that's exactly
+the same common mistake that you can see
+
+ align:start position:0%
+the same common mistake that you can see
+ 
+
+ align:start position:0%
+the same common mistake that you can see
+with multiple control charts and so the
+
+ align:start position:0%
+with multiple control charts and so the
+ 
+
+ align:start position:0%
+with multiple control charts and so the
+point here would simply be you should if
+
+ align:start position:0%
+point here would simply be you should if
+ 
+
+ align:start position:0%
+point here would simply be you should if
+you're checking multiple factors you got
+
+ align:start position:0%
+you're checking multiple factors you got
+ 
+
+ align:start position:0%
+you're checking multiple factors you got
+to have a a stronger indication than any
+
+ align:start position:0%
+to have a a stronger indication than any
+ 
+
+ align:start position:0%
+to have a a stronger indication than any
+one factor otherwise you're just fishing
+
+ align:start position:0%
+one factor otherwise you're just fishing
+ 
+
+ align:start position:0%
+one factor otherwise you're just fishing
+and by chance alone you're going to find
+
+ align:start position:0%
+and by chance alone you're going to find
+ 
+
+ align:start position:0%
+and by chance alone you're going to find
+stuff okay so it's kind of a neat
+
+ align:start position:0%
+stuff okay so it's kind of a neat
+ 
+
+ align:start position:0%
+stuff okay so it's kind of a neat
+example and so here was the point I made
+
+ align:start position:0%
+example and so here was the point I made
+ 
+
+ align:start position:0%
+example and so here was the point I made
+about how you fix it you just fix your
+
+ align:start position:0%
+about how you fix it you just fix your
+ 
+
+ align:start position:0%
+about how you fix it you just fix your
+aggregate Alpha Prime you have your
+
+ align:start position:0%
+aggregate Alpha Prime you have your
+ 
+
+ align:start position:0%
+aggregate Alpha Prime you have your
+individual Alpha and then you pick your
+
+ align:start position:0%
+individual Alpha and then you pick your
+ 
+
+ align:start position:0%
+individual Alpha and then you pick your
+upper and lower control limits based on
+
+ align:start position:0%
+upper and lower control limits based on
+ 
+
+ align:start position:0%
+upper and lower control limits based on
+that Al
+
+ align:start position:0%
+that Al
+ 
+
+ align:start position:0%
+that Al
+Alpha there's a second common problem
+
+ align:start position:0%
+Alpha there's a second common problem
+ 
+
+ align:start position:0%
+Alpha there's a second common problem
+and and as I said it's the obverse of
+
+ align:start position:0%
+and and as I said it's the obverse of
+ 
+
+ align:start position:0%
+and and as I said it's the obverse of
+this which is you very often assume that
+
+ align:start position:0%
+this which is you very often assume that
+ 
+
+ align:start position:0%
+this which is you very often assume that
+if I'm monitoring 10 process control
+
+ align:start position:0%
+if I'm monitoring 10 process control
+ 
+
+ align:start position:0%
+if I'm monitoring 10 process control
+parameters I assume they're all
+
+ align:start position:0%
+parameters I assume they're all
+ 
+
+ align:start position:0%
+parameters I assume they're all
+independent but very often they are not
+
+ align:start position:0%
+independent but very often they are not
+ 
+
+ align:start position:0%
+independent but very often they are not
+there is correlation among those
+
+ align:start position:0%
+there is correlation among those
+ 
+
+ align:start position:0%
+there is correlation among those
+parameters and I want to give you a
+
+ align:start position:0%
+parameters and I want to give you a
+ 
+
+ align:start position:0%
+parameters and I want to give you a
+little bit of a feel for what that looks
+
+ align:start position:0%
+little bit of a feel for what that looks
+ 
+
+ align:start position:0%
+little bit of a feel for what that looks
+like and what the risk is and what
+
+ align:start position:0%
+like and what the risk is and what
+ 
+
+ align:start position:0%
+like and what the risk is and what
+approaches are for control charting in
+
+ align:start position:0%
+approaches are for control charting in
+ 
+
+ align:start position:0%
+approaches are for control charting in
+particular of this so here's an example
+
+ align:start position:0%
+particular of this so here's an example
+ 
+
+ align:start position:0%
+particular of this so here's an example
+drawn from some data that came from an
+
+ align:start position:0%
+drawn from some data that came from an
+ 
+
+ align:start position:0%
+drawn from some data that came from an
+lfm thesis a few years ago a body and
+
+ align:start position:0%
+lfm thesis a few years ago a body and
+ 
+
+ align:start position:0%
+lfm thesis a few years ago a body and
+white assembly so in body and white this
+
+ align:start position:0%
+white assembly so in body and white this
+ 
+
+ align:start position:0%
+white assembly so in body and white this
+is when they are basically uh putting
+
+ align:start position:0%
+is when they are basically uh putting
+ 
+
+ align:start position:0%
+is when they are basically uh putting
+together all of the different panels uh
+
+ align:start position:0%
+together all of the different panels uh
+ 
+
+ align:start position:0%
+together all of the different panels uh
+on the car and measuring uh many many
+
+ align:start position:0%
+on the car and measuring uh many many
+ 
+
+ align:start position:0%
+on the car and measuring uh many many
+points with all kinds of laser uh uh
+
+ align:start position:0%
+points with all kinds of laser uh uh
+ 
+
+ align:start position:0%
+points with all kinds of laser uh uh
+automated apparatus to be able to look
+
+ align:start position:0%
+automated apparatus to be able to look
+ 
+
+ align:start position:0%
+automated apparatus to be able to look
+at dimensional control of these panels
+
+ align:start position:0%
+at dimensional control of these panels
+ 
+
+ align:start position:0%
+at dimensional control of these panels
+in the assembly
+
+ align:start position:0%
+in the assembly
+ 
+
+ align:start position:0%
+in the assembly
+uh of some of these panels other
+
+ align:start position:0%
+uh of some of these panels other
+ 
+
+ align:start position:0%
+uh of some of these panels other
+correlated data comes up all over the
+
+ align:start position:0%
+correlated data comes up all over the
+ 
+
+ align:start position:0%
+correlated data comes up all over the
+place uh injection molding I think uh oh
+
+ align:start position:0%
+place uh injection molding I think uh oh
+ 
+
+ align:start position:0%
+place uh injection molding I think uh oh
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+missing I can't remember his name he he
+
+ align:start position:0%
+missing I can't remember his name he he
+ 
+
+ align:start position:0%
+missing I can't remember his name he he
+asked a question last time about
+
+ align:start position:0%
+asked a question last time about
+ 
+
+ align:start position:0%
+asked a question last time about
+critical dimensions on a semiconductor
+
+ align:start position:0%
+critical dimensions on a semiconductor
+ 
+
+ align:start position:0%
+critical dimensions on a semiconductor
+wafer yes they are often correlated um
+
+ align:start position:0%
+wafer yes they are often correlated um
+ 
+
+ align:start position:0%
+wafer yes they are often correlated um
+but here's the body and white example
+
+ align:start position:0%
+but here's the body and white example
+ 
+
+ align:start position:0%
+but here's the body and white example
+and what I'm sort of showing are these
+
+ align:start position:0%
+and what I'm sort of showing are these
+ 
+
+ align:start position:0%
+and what I'm sort of showing are these
+little coordinate measuring machine uh
+
+ align:start position:0%
+little coordinate measuring machine uh
+ 
+
+ align:start position:0%
+little coordinate measuring machine uh
+CMM kinds of U measurements of a few of
+
+ align:start position:0%
+CMM kinds of U measurements of a few of
+ 
+
+ align:start position:0%
+CMM kinds of U measurements of a few of
+these uh different different data points
+
+ align:start position:0%
+these uh different different data points
+ 
+
+ align:start position:0%
+these uh different different data points
+points and the point is if I think of
+
+ align:start position:0%
+points and the point is if I think of
+ 
+
+ align:start position:0%
+points and the point is if I think of
+this as a metal panel in some way and
+
+ align:start position:0%
+this as a metal panel in some way and
+ 
+
+ align:start position:0%
+this as a metal panel in some way and
+I'm measuring the position say of these
+
+ align:start position:0%
+I'm measuring the position say of these
+ 
+
+ align:start position:0%
+I'm measuring the position say of these
+four corner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points right you would expect there to
+
+ align:start position:0%
+points right you would expect there to
+ 
+
+ align:start position:0%
+points right you would expect there to
+be correlation among them and certain
+
+ align:start position:0%
+be correlation among them and certain
+ 
+
+ align:start position:0%
+be correlation among them and certain
+kinds of distortion might change
+
+ align:start position:0%
+kinds of distortion might change
+ 
+
+ align:start position:0%
+kinds of distortion might change
+relationships between them and in fact
+
+ align:start position:0%
+relationships between them and in fact
+ 
+
+ align:start position:0%
+relationships between them and in fact
+you might even come up with other
+
+ align:start position:0%
+you might even come up with other
+ 
+
+ align:start position:0%
+you might even come up with other
+statistics like a y1 and a Y3 and a y4
+
+ align:start position:0%
+statistics like a y1 and a Y3 and a y4
+ 
+
+ align:start position:0%
+statistics like a y1 and a Y3 and a y4
+that try to DET detect or look at
+
+ align:start position:0%
+that try to DET detect or look at
+ 
+
+ align:start position:0%
+that try to DET detect or look at
+tracking of a couple of these parameters
+
+ align:start position:0%
+tracking of a couple of these parameters
+ 
+
+ align:start position:0%
+tracking of a couple of these parameters
+and deviations but the point is I
+
+ align:start position:0%
+and deviations but the point is I
+ 
+
+ align:start position:0%
+and deviations but the point is I
+wouldn't necessarily want to monitor
+
+ align:start position:0%
+wouldn't necessarily want to monitor
+ 
+
+ align:start position:0%
+wouldn't necessarily want to monitor
+those four corner locations as
+
+ align:start position:0%
+those four corner locations as
+ 
+
+ align:start position:0%
+those four corner locations as
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters here's another example this
+
+ align:start position:0%
+parameters here's another example this
+ 
+
+ align:start position:0%
+parameters here's another example this
+comes from an ultrasonic uh welding set
+
+ align:start position:0%
+comes from an ultrasonic uh welding set
+ 
+
+ align:start position:0%
+comes from an ultrasonic uh welding set
+of data and you may not be able to see
+
+ align:start position:0%
+of data and you may not be able to see
+ 
+
+ align:start position:0%
+of data and you may not be able to see
+this this is a wonderful correlation
+
+ align:start position:0%
+this this is a wonderful correlation
+ 
+
+ align:start position:0%
+this this is a wonderful correlation
+plot of three four five six seven eight
+
+ align:start position:0%
+plot of three four five six seven eight
+ 
+
+ align:start position:0%
+plot of three four five six seven eight
+10 different parameters against each
+
+ align:start position:0%
+10 different parameters against each
+ 
+
+ align:start position:0%
+10 different parameters against each
+other uh there's different things like
+
+ align:start position:0%
+other uh there's different things like
+ 
+
+ align:start position:0%
+other uh there's different things like
+P2 weld energy P2 Peak power these are
+
+ align:start position:0%
+P2 weld energy P2 Peak power these are
+ 
+
+ align:start position:0%
+P2 weld energy P2 Peak power these are
+simply Scatter Plots of data drawn from
+
+ align:start position:0%
+simply Scatter Plots of data drawn from
+ 
+
+ align:start position:0%
+simply Scatter Plots of data drawn from
+that process you can see some of these
+
+ align:start position:0%
+that process you can see some of these
+ 
+
+ align:start position:0%
+that process you can see some of these
+parameters if I track down that's total
+
+ align:start position:0%
+parameters if I track down that's total
+ 
+
+ align:start position:0%
+parameters if I track down that's total
+weld energy versus P2 weld
+
+ align:start position:0%
+weld energy versus P2 weld
+ 
+
+ align:start position:0%
+weld energy versus P2 weld
+energy just I don't even know what those
+
+ align:start position:0%
+energy just I don't even know what those
+ 
+
+ align:start position:0%
+energy just I don't even know what those
+things mean but they sure sound like
+
+ align:start position:0%
+things mean but they sure sound like
+ 
+
+ align:start position:0%
+things mean but they sure sound like
+they're going to be correlated don't
+
+ align:start position:0%
+they're going to be correlated don't
+ 
+
+ align:start position:0%
+they're going to be correlated don't
+they and sure enough there's extremely
+
+ align:start position:0%
+they and sure enough there's extremely
+ 
+
+ align:start position:0%
+they and sure enough there's extremely
+strong correlation in that data there's
+
+ align:start position:0%
+strong correlation in that data there's
+ 
+
+ align:start position:0%
+strong correlation in that data there's
+other cases where there's
+
+ align:start position:0%
+other cases where there's
+ 
+
+ align:start position:0%
+other cases where there's
+also fairly strong correlation so again
+
+ align:start position:0%
+also fairly strong correlation so again
+ 
+
+ align:start position:0%
+also fairly strong correlation so again
+these these kinds of correlated data
+
+ align:start position:0%
+these these kinds of correlated data
+ 
+
+ align:start position:0%
+these these kinds of correlated data
+where knowing something about one of the
+
+ align:start position:0%
+where knowing something about one of the
+ 
+
+ align:start position:0%
+where knowing something about one of the
+measurements tells you about the
+
+ align:start position:0%
+measurements tells you about the
+ 
+
+ align:start position:0%
+measurements tells you about the
+likelihood of the other
+
+ align:start position:0%
+likelihood of the other
+ 
+
+ align:start position:0%
+likelihood of the other
+measurement uh uh occur all the
+
+ align:start position:0%
+measurement uh uh occur all the
+ 
+
+ align:start position:0%
+measurement uh uh occur all the
+time so what if you have truly random
+
+ align:start position:0%
+time so what if you have truly random
+ 
+
+ align:start position:0%
+time so what if you have truly random
+independent variables what would a
+
+ align:start position:0%
+independent variables what would a
+ 
+
+ align:start position:0%
+independent variables what would a
+scatter plot look like and how do we go
+
+ align:start position:0%
+scatter plot look like and how do we go
+ 
+
+ align:start position:0%
+scatter plot look like and how do we go
+about setting the control limits that's
+
+ align:start position:0%
+about setting the control limits that's
+ 
+
+ align:start position:0%
+about setting the control limits that's
+pretty natural right so here's an
+
+ align:start position:0%
+pretty natural right so here's an
+ 
+
+ align:start position:0%
+pretty natural right so here's an
+example where we had X1 and X2 the
+
+ align:start position:0%
+example where we had X1 and X2 the
+ 
+
+ align:start position:0%
+example where we had X1 and X2 the
+scatter plot you know it kind of
+
+ align:start position:0%
+scatter plot you know it kind of
+ 
+
+ align:start position:0%
+scatter plot you know it kind of
+basically looks like a cloud of data and
+
+ align:start position:0%
+basically looks like a cloud of data and
+ 
+
+ align:start position:0%
+basically looks like a cloud of data and
+if I added more data you start to
+
+ align:start position:0%
+if I added more data you start to
+ 
+
+ align:start position:0%
+if I added more data you start to
+depending on the scaling if I were
+
+ align:start position:0%
+depending on the scaling if I were
+ 
+
+ align:start position:0%
+depending on the scaling if I were
+simply to draw uh say a a joint 95%
+
+ align:start position:0%
+simply to draw uh say a a joint 95%
+ 
+
+ align:start position:0%
+simply to draw uh say a a joint 95%
+confidence interval it's just kind of a
+
+ align:start position:0%
+confidence interval it's just kind of a
+ 
+
+ align:start position:0%
+confidence interval it's just kind of a
+cloud of data but there's
+
+ align:start position:0%
+cloud of data but there's
+ 
+
+ align:start position:0%
+cloud of data but there's
+no cross information between X1 and x2
+
+ align:start position:0%
+no cross information between X1 and x2
+ 
+
+ align:start position:0%
+no cross information between X1 and x2
+in other words if I told you that X1 was
+
+ align:start position:0%
+in other words if I told you that X1 was
+ 
+
+ align:start position:0%
+in other words if I told you that X1 was
+right here the value of X1 was this
+
+ align:start position:0%
+right here the value of X1 was this
+ 
+
+ align:start position:0%
+right here the value of X1 was this
+value that really doesn't tell me very
+
+ align:start position:0%
+value that really doesn't tell me very
+ 
+
+ align:start position:0%
+value that really doesn't tell me very
+much about what value of X2 could be it
+
+ align:start position:0%
+much about what value of X2 could be it
+ 
+
+ align:start position:0%
+much about what value of X2 could be it
+it still
+
+ align:start position:0%
+it still
+ 
+
+ align:start position:0%
+it still
+Falls anywhere within its distribution
+
+ align:start position:0%
+Falls anywhere within its distribution
+ 
+
+ align:start position:0%
+Falls anywhere within its distribution
+these are two independent random
+
+ align:start position:0%
+these are two independent random
+ 
+
+ align:start position:0%
+these are two independent random
+variables and you can decide what the
+
+ align:start position:0%
+variables and you can decide what the
+ 
+
+ align:start position:0%
+variables and you can decide what the
+proper limits are now you know enough
+
+ align:start position:0%
+proper limits are now you know enough
+ 
+
+ align:start position:0%
+proper limits are now you know enough
+about picking X1 and X2 and I would do
+
+ align:start position:0%
+about picking X1 and X2 and I would do
+ 
+
+ align:start position:0%
+about picking X1 and X2 and I would do
+the alpha Prime idea to pick independent
+
+ align:start position:0%
+the alpha Prime idea to pick independent
+ 
+
+ align:start position:0%
+the alpha Prime idea to pick independent
+limits on those two
+
+ align:start position:0%
+limits on those two
+ 
+
+ align:start position:0%
+limits on those two
+cases this is an example scatter plot
+
+ align:start position:0%
+cases this is an example scatter plot
+ 
+
+ align:start position:0%
+cases this is an example scatter plot
+for correlated random variables in in
+
+ align:start position:0%
+for correlated random variables in in
+ 
+
+ align:start position:0%
+for correlated random variables in in
+this case you know it starts to look
+
+ align:start position:0%
+this case you know it starts to look
+ 
+
+ align:start position:0%
+this case you know it starts to look
+like an oval or a football kind of kind
+
+ align:start position:0%
+like an oval or a football kind of kind
+ 
+
+ align:start position:0%
+like an oval or a football kind of kind
+of shape where there is statistical
+
+ align:start position:0%
+of shape where there is statistical
+ 
+
+ align:start position:0%
+of shape where there is statistical
+correlation between these two parameters
+
+ align:start position:0%
+correlation between these two parameters
+ 
+
+ align:start position:0%
+correlation between these two parameters
+by which I mean if I tell you that X1 is
+
+ align:start position:0%
+by which I mean if I tell you that X1 is
+ 
+
+ align:start position:0%
+by which I mean if I tell you that X1 is
+in this range that tells you something
+
+ align:start position:0%
+in this range that tells you something
+ 
+
+ align:start position:0%
+in this range that tells you something
+about where the value of X2 is likely to
+
+ align:start position:0%
+about where the value of X2 is likely to
+ 
+
+ align:start position:0%
+about where the value of X2 is likely to
+fall it might not fall within its full
+
+ align:start position:0%
+fall it might not fall within its full
+ 
+
+ align:start position:0%
+fall it might not fall within its full
+natural range there is cross information
+
+ align:start position:0%
+natural range there is cross information
+ 
+
+ align:start position:0%
+natural range there is cross information
+or cross correlation between the two now
+
+ align:start position:0%
+or cross correlation between the two now
+ 
+
+ align:start position:0%
+or cross correlation between the two now
+if I were to plot X1 and X2
+
+ align:start position:0%
+if I were to plot X1 and X2
+ 
+
+ align:start position:0%
+if I were to plot X1 and X2
+separately it looks an awful lot like
+
+ align:start position:0%
+separately it looks an awful lot like
+ 
+
+ align:start position:0%
+separately it looks an awful lot like
+the uncorrelated case so if I had
+
+ align:start position:0%
+the uncorrelated case so if I had
+ 
+
+ align:start position:0%
+the uncorrelated case so if I had
+independent control charts for the two
+
+ align:start position:0%
+independent control charts for the two
+ 
+
+ align:start position:0%
+independent control charts for the two
+the two variables essentially what I'm
+
+ align:start position:0%
+the two variables essentially what I'm
+ 
+
+ align:start position:0%
+the two variables essentially what I'm
+doing is just
+
+ align:start position:0%
+doing is just
+ 
+
+ align:start position:0%
+doing is just
+projecting all of these data points I
+
+ align:start position:0%
+projecting all of these data points I
+ 
+
+ align:start position:0%
+projecting all of these data points I
+project all of these data points to get
+
+ align:start position:0%
+project all of these data points to get
+ 
+
+ align:start position:0%
+project all of these data points to get
+my range for X2 and I project all of
+
+ align:start position:0%
+my range for X2 and I project all of
+ 
+
+ align:start position:0%
+my range for X2 and I project all of
+these data points and in fact if I plot
+
+ align:start position:0%
+these data points and in fact if I plot
+ 
+
+ align:start position:0%
+these data points and in fact if I plot
+both of those X1 and X2
+
+ align:start position:0%
+both of those X1 and X2
+ 
+
+ align:start position:0%
+both of those X1 and X2
+I would likely get yikes want to do that
+
+ align:start position:0%
+I would likely get yikes want to do that
+ 
+
+ align:start position:0%
+I would likely get yikes want to do that
+I would likely get two
+
+ align:start position:0%
+I would likely get two
+ 
+
+ align:start position:0%
+I would likely get two
+separate normally distributed variables
+
+ align:start position:0%
+separate normally distributed variables
+ 
+
+ align:start position:0%
+separate normally distributed variables
+and I might be inclined to Simply plot
+
+ align:start position:0%
+and I might be inclined to Simply plot
+ 
+
+ align:start position:0%
+and I might be inclined to Simply plot
+them both
+
+ align:start position:0%
+them both
+ 
+
+ align:start position:0%
+them both
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+xbar uh and S kinds of control
+
+ align:start position:0%
+xbar uh and S kinds of control
+ 
+
+ align:start position:0%
+xbar uh and S kinds of control
+charts the risk
+
+ align:start position:0%
+charts the risk
+ 
+
+ align:start position:0%
+charts the risk
+here though when you do that is you
+
+ align:start position:0%
+here though when you do that is you
+ 
+
+ align:start position:0%
+here though when you do that is you
+might miss outliers
+
+ align:start position:0%
+might miss outliers
+ 
+
+ align:start position:0%
+might miss outliers
+data points that do not fall in the nor
+
+ align:start position:0%
+data points that do not fall in the nor
+ 
+
+ align:start position:0%
+data points that do not fall in the nor
+in the normal or the natural variation
+
+ align:start position:0%
+in the normal or the natural variation
+ 
+
+ align:start position:0%
+in the normal or the natural variation
+of the process this being the natural
+
+ align:start position:0%
+of the process this being the natural
+ 
+
+ align:start position:0%
+of the process this being the natural
+variation of the process that I will not
+
+ align:start position:0%
+variation of the process that I will not
+ 
+
+ align:start position:0%
+variation of the process that I will not
+detect right this data point still looks
+
+ align:start position:0%
+detect right this data point still looks
+ 
+
+ align:start position:0%
+detect right this data point still looks
+like it's within that distribution in
+
+ align:start position:0%
+like it's within that distribution in
+ 
+
+ align:start position:0%
+like it's within that distribution in
+fact it's very close to the mean of
+
+ align:start position:0%
+fact it's very close to the mean of
+ 
+
+ align:start position:0%
+fact it's very close to the mean of
+X2 and it's still within this
+
+ align:start position:0%
+X2 and it's still within this
+ 
+
+ align:start position:0%
+X2 and it's still within this
+distribution but within the natural
+
+ align:start position:0%
+distribution but within the natural
+ 
+
+ align:start position:0%
+distribution but within the natural
+variation of the process within that
+
+ align:start position:0%
+variation of the process within that
+ 
+
+ align:start position:0%
+variation of the process within that
+oval its
+
+ align:start position:0%
+oval its
+ 
+
+ align:start position:0%
+oval its
+distance in some sense from the from the
+
+ align:start position:0%
+distance in some sense from the from the
+ 
+
+ align:start position:0%
+distance in some sense from the from the
+central moments of that of that
+
+ align:start position:0%
+central moments of that of that
+ 
+
+ align:start position:0%
+central moments of that of that
+distribution it's pretty distant it's
+
+ align:start position:0%
+distribution it's pretty distant it's
+ 
+
+ align:start position:0%
+distribution it's pretty distant it's
+not indicative of the normal operation
+
+ align:start position:0%
+not indicative of the normal operation
+ 
+
+ align:start position:0%
+not indicative of the normal operation
+it's a highly unlikely by chance alone
+
+ align:start position:0%
+it's a highly unlikely by chance alone
+ 
+
+ align:start position:0%
+it's a highly unlikely by chance alone
+data point and I would never see it on
+
+ align:start position:0%
+data point and I would never see it on
+ 
+
+ align:start position:0%
+data point and I would never see it on
+the control
+
+ align:start position:0%
+the control
+ 
+
+ align:start position:0%
+the control
+chart so there are multivariate
+
+ align:start position:0%
+chart so there are multivariate
+ 
+
+ align:start position:0%
+chart so there are multivariate
+charts
+
+ align:start position:0%
+charts
+ 
+
+ align:start position:0%
+charts
+that let us get at and chart on the
+
+ align:start position:0%
+that let us get at and chart on the
+ 
+
+ align:start position:0%
+that let us get at and chart on the
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+chart multiple
+
+ align:start position:0%
+chart multiple
+ 
+
+ align:start position:0%
+chart multiple
+factors that are correlated together and
+
+ align:start position:0%
+factors that are correlated together and
+ 
+
+ align:start position:0%
+factors that are correlated together and
+detect those kinds of kinds of uh
+
+ align:start position:0%
+detect those kinds of kinds of uh
+ 
+
+ align:start position:0%
+detect those kinds of kinds of uh
+problems what I want to give you is a
+
+ align:start position:0%
+problems what I want to give you is a
+ 
+
+ align:start position:0%
+problems what I want to give you is a
+notion first of a
+
+ align:start position:0%
+notion first of a
+ 
+
+ align:start position:0%
+notion first of a
+statistic that Aggregates in some sense
+
+ align:start position:0%
+statistic that Aggregates in some sense
+ 
+
+ align:start position:0%
+statistic that Aggregates in some sense
+uh numerically Aggregates exactly what I
+
+ align:start position:0%
+uh numerically Aggregates exactly what I
+ 
+
+ align:start position:0%
+uh numerically Aggregates exactly what I
+was talking about qualitatively here
+
+ align:start position:0%
+was talking about qualitatively here
+ 
+
+ align:start position:0%
+was talking about qualitatively here
+that tells you this notion of what is
+
+ align:start position:0%
+that tells you this notion of what is
+ 
+
+ align:start position:0%
+that tells you this notion of what is
+the distance from the
+
+ align:start position:0%
+the distance from the
+ 
+
+ align:start position:0%
+the distance from the
+correlated variation cloud of each of my
+
+ align:start position:0%
+correlated variation cloud of each of my
+ 
+
+ align:start position:0%
+correlated variation cloud of each of my
+measurement points and if I have a
+
+ align:start position:0%
+measurement points and if I have a
+ 
+
+ align:start position:0%
+measurement points and if I have a
+statistic and I know it's
+
+ align:start position:0%
+statistic and I know it's
+ 
+
+ align:start position:0%
+statistic and I know it's
+PDF then I can set control limits on
+
+ align:start position:0%
+PDF then I can set control limits on
+ 
+
+ align:start position:0%
+PDF then I can set control limits on
+that statistic and that statistic is the
+
+ align:start position:0%
+that statistic and that statistic is the
+ 
+
+ align:start position:0%
+that statistic and that statistic is the
+hoteling t^2 is is one very important
+
+ align:start position:0%
+hoteling t^2 is is one very important
+ 
+
+ align:start position:0%
+hoteling t^2 is is one very important
+one we can also monitor uh
+
+ align:start position:0%
+one we can also monitor uh
+ 
+
+ align:start position:0%
+one we can also monitor uh
+um have ewma and Q some extensions of
+
+ align:start position:0%
+um have ewma and Q some extensions of
+ 
+
+ align:start position:0%
+um have ewma and Q some extensions of
+these which I'm not really going to talk
+
+ align:start position:0%
+these which I'm not really going to talk
+ 
+
+ align:start position:0%
+these which I'm not really going to talk
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+about so what we have to do here is have
+
+ align:start position:0%
+about so what we have to do here is have
+ 
+
+ align:start position:0%
+about so what we have to do here is have
+a slight extension to our notion of a
+
+ align:start position:0%
+a slight extension to our notion of a
+ 
+
+ align:start position:0%
+a slight extension to our notion of a
+probability density function to have
+
+ align:start position:0%
+probability density function to have
+ 
+
+ align:start position:0%
+probability density function to have
+joint probability density functions that
+
+ align:start position:0%
+joint probability density functions that
+ 
+
+ align:start position:0%
+joint probability density functions that
+tell me if I've got say two variables or
+
+ align:start position:0%
+tell me if I've got say two variables or
+ 
+
+ align:start position:0%
+tell me if I've got say two variables or
+three or four or whatever what is the
+
+ align:start position:0%
+three or four or whatever what is the
+ 
+
+ align:start position:0%
+three or four or whatever what is the
+probability density associated with
+
+ align:start position:0%
+probability density associated with
+ 
+
+ align:start position:0%
+probability density associated with
+those and what we want is a single scale
+
+ align:start position:0%
+those and what we want is a single scale
+ 
+
+ align:start position:0%
+those and what we want is a single scale
+control chart that Aggregates
+
+ align:start position:0%
+control chart that Aggregates
+ 
+
+ align:start position:0%
+control chart that Aggregates
+these now I've got uh a little bit of
+
+ align:start position:0%
+these now I've got uh a little bit of
+ 
+
+ align:start position:0%
+these now I've got uh a little bit of
+mathematical notation in here that uh
+
+ align:start position:0%
+mathematical notation in here that uh
+ 
+
+ align:start position:0%
+mathematical notation in here that uh
+I'm not going to go through the careful
+
+ align:start position:0%
+I'm not going to go through the careful
+ 
+
+ align:start position:0%
+I'm not going to go through the careful
+full explanation derivation of what I
+
+ align:start position:0%
+full explanation derivation of what I
+ 
+
+ align:start position:0%
+full explanation derivation of what I
+want to Simply show you is how a
+
+ align:start position:0%
+want to Simply show you is how a
+ 
+
+ align:start position:0%
+want to Simply show you is how a
+multivariate expression of the same
+
+ align:start position:0%
+multivariate expression of the same
+ 
+
+ align:start position:0%
+multivariate expression of the same
+variables we've been using all along
+
+ align:start position:0%
+variables we've been using all along
+ 
+
+ align:start position:0%
+variables we've been using all along
+gives you a nice qualitative feel for
+
+ align:start position:0%
+gives you a nice qualitative feel for
+ 
+
+ align:start position:0%
+gives you a nice qualitative feel for
+what this statistic looks like so if we
+
+ align:start position:0%
+what this statistic looks like so if we
+ 
+
+ align:start position:0%
+what this statistic looks like so if we
+have a vector of measurements let's say
+
+ align:start position:0%
+have a vector of measurements let's say
+ 
+
+ align:start position:0%
+have a vector of measurements let's say
+I have P parameters I'm measuring 10
+
+ align:start position:0%
+I have P parameters I'm measuring 10
+ 
+
+ align:start position:0%
+I have P parameters I'm measuring 10
+different parameters body and white or
+
+ align:start position:0%
+different parameters body and white or
+ 
+
+ align:start position:0%
+different parameters body and white or
+or or whatever it is for for for that
+
+ align:start position:0%
+or or whatever it is for for for that
+ 
+
+ align:start position:0%
+or or whatever it is for for for that
+particular process and put those in an X
+
+ align:start position:0%
+particular process and put those in an X
+ 
+
+ align:start position:0%
+particular process and put those in an X
+underscore an X X vector and then I can
+
+ align:start position:0%
+underscore an X X vector and then I can
+ 
+
+ align:start position:0%
+underscore an X X vector and then I can
+define a vector of means so I have a set
+
+ align:start position:0%
+define a vector of means so I have a set
+ 
+
+ align:start position:0%
+define a vector of means so I have a set
+of means for all 10 parameters and I can
+
+ align:start position:0%
+of means for all 10 parameters and I can
+ 
+
+ align:start position:0%
+of means for all 10 parameters and I can
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+calculate if I have lots and lots of
+
+ align:start position:0%
+calculate if I have lots and lots of
+ 
+
+ align:start position:0%
+calculate if I have lots and lots of
+historical data there is an a true
+
+ align:start position:0%
+historical data there is an a true
+ 
+
+ align:start position:0%
+historical data there is an a true
+underlying covariance Matrix that talks
+
+ align:start position:0%
+underlying covariance Matrix that talks
+ 
+
+ align:start position:0%
+underlying covariance Matrix that talks
+about or characterizes how these data go
+
+ align:start position:0%
+about or characterizes how these data go
+ 
+
+ align:start position:0%
+about or characterizes how these data go
+together with each other now I can
+
+ align:start position:0%
+together with each other now I can
+ 
+
+ align:start position:0%
+together with each other now I can
+estimate that covariance Matrix based on
+
+ align:start position:0%
+estimate that covariance Matrix based on
+ 
+
+ align:start position:0%
+estimate that covariance Matrix based on
+Sample data so I similarly have a true
+
+ align:start position:0%
+Sample data so I similarly have a true
+ 
+
+ align:start position:0%
+Sample data so I similarly have a true
+mean and a true covariance that I might
+
+ align:start position:0%
+mean and a true covariance that I might
+ 
+
+ align:start position:0%
+mean and a true covariance that I might
+estimate with an
+
+ align:start position:0%
+estimate with an
+ 
+
+ align:start position:0%
+estimate with an
+xbar and an S here I'm using a capital S
+
+ align:start position:0%
+xbar and an S here I'm using a capital S
+ 
+
+ align:start position:0%
+xbar and an S here I'm using a capital S
+to be a sample covariance Matrix and
+
+ align:start position:0%
+to be a sample covariance Matrix and
+ 
+
+ align:start position:0%
+to be a sample covariance Matrix and
+there are formulas in the in the book
+
+ align:start position:0%
+there are formulas in the in the book
+ 
+
+ align:start position:0%
+there are formulas in the in the book
+using a very you know simple uh linear
+
+ align:start position:0%
+using a very you know simple uh linear
+ 
+
+ align:start position:0%
+using a very you know simple uh linear
+Matrix uh linear algebra for for how you
+
+ align:start position:0%
+Matrix uh linear algebra for for how you
+ 
+
+ align:start position:0%
+Matrix uh linear algebra for for how you
+would do that given a a particular set
+
+ align:start position:0%
+would do that given a a particular set
+ 
+
+ align:start position:0%
+would do that given a a particular set
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+data they look a lot like sort of the
+
+ align:start position:0%
+data they look a lot like sort of the
+ 
+
+ align:start position:0%
+data they look a lot like sort of the
+univariate
+
+ align:start position:0%
+univariate
+ 
+
+ align:start position:0%
+univariate
+example but I did want to point out that
+
+ align:start position:0%
+example but I did want to point out that
+ 
+
+ align:start position:0%
+example but I did want to point out that
+there's both embedded in this the notion
+
+ align:start position:0%
+there's both embedded in this the notion
+ 
+
+ align:start position:0%
+there's both embedded in this the notion
+of variance how variable two varies
+
+ align:start position:0%
+of variance how variable two varies
+ 
+
+ align:start position:0%
+of variance how variable two varies
+together with variable two that's sort
+
+ align:start position:0%
+together with variable two that's sort
+ 
+
+ align:start position:0%
+together with variable two that's sort
+of just our normal notion of variance
+
+ align:start position:0%
+of just our normal notion of variance
+ 
+
+ align:start position:0%
+of just our normal notion of variance
+and there's also co-variance that is a
+
+ align:start position:0%
+and there's also co-variance that is a
+ 
+
+ align:start position:0%
+and there's also co-variance that is a
+measure of how these two variables move
+
+ align:start position:0%
+measure of how these two variables move
+ 
+
+ align:start position:0%
+measure of how these two variables move
+together we can actually write out and
+
+ align:start position:0%
+together we can actually write out and
+ 
+
+ align:start position:0%
+together we can actually write out and
+what the uh PDF
+
+ align:start position:0%
+what the uh PDF
+ 
+
+ align:start position:0%
+what the uh PDF
+probability density functions are in
+
+ align:start position:0%
+probability density functions are in
+ 
+
+ align:start position:0%
+probability density functions are in
+these joint cases and if you write it in
+
+ align:start position:0%
+these joint cases and if you write it in
+ 
+
+ align:start position:0%
+these joint cases and if you write it in
+Matrix form using this covariance Matrix
+
+ align:start position:0%
+Matrix form using this covariance Matrix
+ 
+
+ align:start position:0%
+Matrix form using this covariance Matrix
+and the MU
+
+ align:start position:0%
+and the MU
+ 
+
+ align:start position:0%
+and the MU
+Vector it looks almost exactly the same
+
+ align:start position:0%
+Vector it looks almost exactly the same
+ 
+
+ align:start position:0%
+Vector it looks almost exactly the same
+as the univariate case notice that
+
+ align:start position:0%
+as the univariate case notice that
+ 
+
+ align:start position:0%
+as the univariate case notice that
+instead of variance in the univariant
+
+ align:start position:0%
+instead of variance in the univariant
+ 
+
+ align:start position:0%
+instead of variance in the univariant
+case now we have the
+
+ align:start position:0%
+case now we have the
+ 
+
+ align:start position:0%
+case now we have the
+co-variance oops The covariance Matrix
+
+ align:start position:0%
+co-variance oops The covariance Matrix
+ 
+
+ align:start position:0%
+co-variance oops The covariance Matrix
+right and
+
+ align:start position:0%
+right and
+ 
+
+ align:start position:0%
+right and
+similarly instead of you know just X and
+
+ align:start position:0%
+similarly instead of you know just X and
+ 
+
+ align:start position:0%
+similarly instead of you know just X and
+U being univariate values I've got those
+
+ align:start position:0%
+U being univariate values I've got those
+ 
+
+ align:start position:0%
+U being univariate values I've got those
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+vectors but the
+
+ align:start position:0%
+vectors but the
+ 
+
+ align:start position:0%
+vectors but the
+PDF looks almost exactly the
+
+ align:start position:0%
+PDF looks almost exactly the
+ 
+
+ align:start position:0%
+PDF looks almost exactly the
+same and qualitatively you're
+
+ align:start position:0%
+same and qualitatively you're
+ 
+
+ align:start position:0%
+same and qualitatively you're
+getting an
+
+ align:start position:0%
+getting an
+ 
+
+ align:start position:0%
+getting an
+exponential drop off this e drop off
+
+ align:start position:0%
+exponential drop off this e drop off
+ 
+
+ align:start position:0%
+exponential drop off this e drop off
+with the square of the distance of a
+
+ align:start position:0%
+with the square of the distance of a
+ 
+
+ align:start position:0%
+with the square of the distance of a
+point from the mean right the normalized
+
+ align:start position:0%
+point from the mean right the normalized
+ 
+
+ align:start position:0%
+point from the mean right the normalized
+distance from the point so if we look
+
+ align:start position:0%
+distance from the point so if we look
+ 
+
+ align:start position:0%
+distance from the point so if we look
+back at the univariate the whole idea is
+
+ align:start position:0%
+back at the univariate the whole idea is
+ 
+
+ align:start position:0%
+back at the univariate the whole idea is
+I subtract off the mean when I
+
+ align:start position:0%
+I subtract off the mean when I
+ 
+
+ align:start position:0%
+I subtract off the mean when I
+standardize divide by the natural
+
+ align:start position:0%
+standardize divide by the natural
+ 
+
+ align:start position:0%
+standardize divide by the natural
+variation and that tells me the shape of
+
+ align:start position:0%
+variation and that tells me the shape of
+ 
+
+ align:start position:0%
+variation and that tells me the shape of
+the bell curve shape of the normal curve
+
+ align:start position:0%
+the bell curve shape of the normal curve
+ 
+
+ align:start position:0%
+the bell curve shape of the normal curve
+how fast things drop off and I can also
+
+ align:start position:0%
+how fast things drop off and I can also
+ 
+
+ align:start position:0%
+how fast things drop off and I can also
+for any particular multivariate U
+
+ align:start position:0%
+for any particular multivariate U
+ 
+
+ align:start position:0%
+for any particular multivariate U
+multivariate data point x that has you
+
+ align:start position:0%
+multivariate data point x that has you
+ 
+
+ align:start position:0%
+multivariate data point x that has you
+know its 10 parameters in it what's
+
+ align:start position:0%
+know its 10 parameters in it what's
+ 
+
+ align:start position:0%
+know its 10 parameters in it what's
+really cool is this formulation here of
+
+ align:start position:0%
+really cool is this formulation here of
+ 
+
+ align:start position:0%
+really cool is this formulation here of
+the distance of that X vector from the
+
+ align:start position:0%
+the distance of that X vector from the
+ 
+
+ align:start position:0%
+the distance of that X vector from the
+mean point the mean
+
+ align:start position:0%
+mean point the mean
+ 
+
+ align:start position:0%
+mean point the mean
+Vector squared that squared distance but
+
+ align:start position:0%
+Vector squared that squared distance but
+ 
+
+ align:start position:0%
+Vector squared that squared distance but
+weighted then or normalized to the
+
+ align:start position:0%
+weighted then or normalized to the
+ 
+
+ align:start position:0%
+weighted then or normalized to the
+Natural spread that natural spread or
+
+ align:start position:0%
+Natural spread that natural spread or
+ 
+
+ align:start position:0%
+Natural spread that natural spread or
+width of that cloud is just a distance
+
+ align:start position:0%
+width of that cloud is just a distance
+ 
+
+ align:start position:0%
+width of that cloud is just a distance
+measure a squared distance measure of
+
+ align:start position:0%
+measure a squared distance measure of
+ 
+
+ align:start position:0%
+measure a squared distance measure of
+each data point from the central moment
+
+ align:start position:0%
+each data point from the central moment
+ 
+
+ align:start position:0%
+each data point from the central moment
+of the central point of the distribution
+
+ align:start position:0%
+of the central point of the distribution
+ 
+
+ align:start position:0%
+of the central point of the distribution
+scaled to how much natural spread or
+
+ align:start position:0%
+scaled to how much natural spread or
+ 
+
+ align:start position:0%
+scaled to how much natural spread or
+scatter there is in the data
+
+ align:start position:0%
+scatter there is in the data
+ 
+
+ align:start position:0%
+scatter there is in the data
+okay so that's the PDF and now I can go
+
+ align:start position:0%
+okay so that's the PDF and now I can go
+ 
+
+ align:start position:0%
+okay so that's the PDF and now I can go
+in those are just the formulas for the
+
+ align:start position:0%
+in those are just the formulas for the
+ 
+
+ align:start position:0%
+in those are just the formulas for the
+samples in these cases what I can now go
+
+ align:start position:0%
+samples in these cases what I can now go
+ 
+
+ align:start position:0%
+samples in these cases what I can now go
+in and do
+
+ align:start position:0%
+in and do
+ 
+
+ align:start position:0%
+in and do
+is ask the question what is
+
+ align:start position:0%
+is ask the question what is
+ 
+
+ align:start position:0%
+is ask the question what is
+the distribution associated with that
+
+ align:start position:0%
+the distribution associated with that
+ 
+
+ align:start position:0%
+the distribution associated with that
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+metric and that distance metric is
+
+ align:start position:0%
+metric and that distance metric is
+ 
+
+ align:start position:0%
+metric and that distance metric is
+essentially if I expand out um that
+
+ align:start position:0%
+essentially if I expand out um that
+ 
+
+ align:start position:0%
+essentially if I expand out um that
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+formula it is a sum of squared distances
+
+ align:start position:0%
+formula it is a sum of squared distances
+ 
+
+ align:start position:0%
+formula it is a sum of squared distances
+normalized to to the uh the
+
+ align:start position:0%
+normalized to to the uh the
+ 
+
+ align:start position:0%
+normalized to to the uh the
+correlation which starts to sound like
+
+ align:start position:0%
+correlation which starts to sound like
+ 
+
+ align:start position:0%
+correlation which starts to sound like
+sum of
+
+ align:start position:0%
+sum of
+ 
+
+ align:start position:0%
+sum of
+squared unit normal
+
+ align:start position:0%
+squared unit normal
+ 
+
+ align:start position:0%
+squared unit normal
+variables which was our Ki squar
+
+ align:start position:0%
+variables which was our Ki squar
+ 
+
+ align:start position:0%
+variables which was our Ki squar
+distribution sum of squared
+
+ align:start position:0%
+distribution sum of squared
+ 
+
+ align:start position:0%
+distribution sum of squared
+normal so what's cool here is that the
+
+ align:start position:0%
+normal so what's cool here is that the
+ 
+
+ align:start position:0%
+normal so what's cool here is that the
+Ki squar
+
+ align:start position:0%
+Ki squar
+ 
+
+ align:start position:0%
+Ki squar
+distribution with P parameters P degrees
+
+ align:start position:0%
+distribution with P parameters P degrees
+ 
+
+ align:start position:0%
+distribution with P parameters P degrees
+of fre freedom is the right statistic
+
+ align:start position:0%
+of fre freedom is the right statistic
+ 
+
+ align:start position:0%
+of fre freedom is the right statistic
+for measuring How likely it is to see
+
+ align:start position:0%
+for measuring How likely it is to see
+ 
+
+ align:start position:0%
+for measuring How likely it is to see
+those distance that t^2 those distance
+
+ align:start position:0%
+those distance that t^2 those distance
+ 
+
+ align:start position:0%
+those distance that t^2 those distance
+metrics okay so one can actually have
+
+ align:start position:0%
+metrics okay so one can actually have
+ 
+
+ align:start position:0%
+metrics okay so one can actually have
+the PDF one can have the distribution
+
+ align:start position:0%
+the PDF one can have the distribution
+ 
+
+ align:start position:0%
+the PDF one can have the distribution
+for that PDF and based on that you can
+
+ align:start position:0%
+for that PDF and based on that you can
+ 
+
+ align:start position:0%
+for that PDF and based on that you can
+formulate or form a that statistic based
+
+ align:start position:0%
+formulate or form a that statistic based
+ 
+
+ align:start position:0%
+formulate or form a that statistic based
+on my actual data X and then I can have
+
+ align:start position:0%
+on my actual data X and then I can have
+ 
+
+ align:start position:0%
+on my actual data X and then I can have
+Alpha squared that I can pick my cut off
+
+ align:start position:0%
+Alpha squared that I can pick my cut off
+ 
+
+ align:start position:0%
+Alpha squared that I can pick my cut off
+points from appropriately oops I thought
+
+ align:start position:0%
+points from appropriately oops I thought
+ 
+
+ align:start position:0%
+points from appropriately oops I thought
+I had a PDF in here somewhere yeah well
+
+ align:start position:0%
+I had a PDF in here somewhere yeah well
+ 
+
+ align:start position:0%
+I had a PDF in here somewhere yeah well
+so when
+
+ align:start position:0%
+so when
+ 
+
+ align:start position:0%
+so when
+I'm making a control chart I use the
+
+ align:start position:0%
+I'm making a control chart I use the
+ 
+
+ align:start position:0%
+I'm making a control chart I use the
+same ideas that we saw before I have a
+
+ align:start position:0%
+same ideas that we saw before I have a
+ 
+
+ align:start position:0%
+same ideas that we saw before I have a
+false alarm rate in this case I'm going
+
+ align:start position:0%
+false alarm rate in this case I'm going
+ 
+
+ align:start position:0%
+false alarm rate in this case I'm going
+to aggregate all my data onto a single
+
+ align:start position:0%
+to aggregate all my data onto a single
+ 
+
+ align:start position:0%
+to aggregate all my data onto a single
+control chart so I can just use my
+
+ align:start position:0%
+control chart so I can just use my
+ 
+
+ align:start position:0%
+control chart so I can just use my
+aggregate Alpha and I pick the uh tail
+
+ align:start position:0%
+aggregate Alpha and I pick the uh tail
+ 
+
+ align:start position:0%
+aggregate Alpha and I pick the uh tail
+points on the kais squ distribution
+
+ align:start position:0%
+points on the kais squ distribution
+ 
+
+ align:start position:0%
+points on the kais squ distribution
+remember a Kai squar might have looked
+
+ align:start position:0%
+remember a Kai squar might have looked
+ 
+
+ align:start position:0%
+remember a Kai squar might have looked
+something like this and I might pick way
+
+ align:start position:0%
+something like this and I might pick way
+ 
+
+ align:start position:0%
+something like this and I might pick way
+out here as my Kai
+
+ align:start position:0%
+out here as my Kai
+ 
+
+ align:start position:0%
+out here as my Kai
+squar so that I've got my Alpha out
+
+ align:start position:0%
+squar so that I've got my Alpha out
+ 
+
+ align:start position:0%
+squar so that I've got my Alpha out
+there in the tail that picks my my cut
+
+ align:start position:0%
+there in the tail that picks my my cut
+ 
+
+ align:start position:0%
+there in the tail that picks my my cut
+off point for my upper control
+
+ align:start position:0%
+off point for my upper control
+ 
+
+ align:start position:0%
+off point for my upper control
+limit um
+
+ align:start position:0%
+limit um
+ 
+
+ align:start position:0%
+limit um
+generally uh you you can also do that
+
+ align:start position:0%
+generally uh you you can also do that
+ 
+
+ align:start position:0%
+generally uh you you can also do that
+for a lower control limit very often if
+
+ align:start position:0%
+for a lower control limit very often if
+ 
+
+ align:start position:0%
+for a lower control limit very often if
+you do some apply some of these formulas
+
+ align:start position:0%
+you do some apply some of these formulas
+ 
+
+ align:start position:0%
+you do some apply some of these formulas
+the lower control limit is is negative
+
+ align:start position:0%
+the lower control limit is is negative
+ 
+
+ align:start position:0%
+the lower control limit is is negative
+and you can't have negative squares so
+
+ align:start position:0%
+and you can't have negative squares so
+ 
+
+ align:start position:0%
+and you can't have negative squares so
+you pick zero as your your lower control
+
+ align:start position:0%
+you pick zero as your your lower control
+ 
+
+ align:start position:0%
+you pick zero as your your lower control
+limit and you're really only monitoring
+
+ align:start position:0%
+limit and you're really only monitoring
+ 
+
+ align:start position:0%
+limit and you're really only monitoring
+for data points that
+
+ align:start position:0%
+for data points that
+ 
+
+ align:start position:0%
+for data points that
+are larger than I've got more variation
+
+ align:start position:0%
+are larger than I've got more variation
+ 
+
+ align:start position:0%
+are larger than I've got more variation
+uh in my system than I
+
+ align:start position:0%
+uh in my system than I
+ 
+
+ align:start position:0%
+uh in my system than I
+expected so just to sort of close up on
+
+ align:start position:0%
+expected so just to sort of close up on
+ 
+
+ align:start position:0%
+expected so just to sort of close up on
+on this sort of univariate versus Ki
+
+ align:start position:0%
+on this sort of univariate versus Ki
+ 
+
+ align:start position:0%
+on this sort of univariate versus Ki
+squar
+
+ align:start position:0%
+squar
+ 
+
+ align:start position:0%
+squar
+chart here's an example sort of
+
+ align:start position:0%
+chart here's an example sort of
+ 
+
+ align:start position:0%
+chart here's an example sort of
+comparing the univariate case up here to
+
+ align:start position:0%
+comparing the univariate case up here to
+ 
+
+ align:start position:0%
+comparing the univariate case up here to
+the multivariate case down here and what
+
+ align:start position:0%
+the multivariate case down here and what
+ 
+
+ align:start position:0%
+the multivariate case down here and what
+I'm plotting here is again the scatter
+
+ align:start position:0%
+I'm plotting here is again the scatter
+ 
+
+ align:start position:0%
+I'm plotting here is again the scatter
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+data you might see there's a slight
+
+ align:start position:0%
+data you might see there's a slight
+ 
+
+ align:start position:0%
+data you might see there's a slight
+shaded oval case and all the blue data
+
+ align:start position:0%
+shaded oval case and all the blue data
+ 
+
+ align:start position:0%
+shaded oval case and all the blue data
+points are what I would do if I just
+
+ align:start position:0%
+points are what I would do if I just
+ 
+
+ align:start position:0%
+points are what I would do if I just
+projected those down to an X1 and X2 and
+
+ align:start position:0%
+projected those down to an X1 and X2 and
+ 
+
+ align:start position:0%
+projected those down to an X1 and X2 and
+did univariate control charting if I
+
+ align:start position:0%
+did univariate control charting if I
+ 
+
+ align:start position:0%
+did univariate control charting if I
+then had this little red dot
+
+ align:start position:0%
+then had this little red dot
+ 
+
+ align:start position:0%
+then had this little red dot
+that fell outside of the joint um
+
+ align:start position:0%
+that fell outside of the joint um
+ 
+
+ align:start position:0%
+that fell outside of the joint um
+confidence interval on my individual
+
+ align:start position:0%
+confidence interval on my individual
+ 
+
+ align:start position:0%
+confidence interval on my individual
+charts notice where it falls perfectly
+
+ align:start position:0%
+charts notice where it falls perfectly
+ 
+
+ align:start position:0%
+charts notice where it falls perfectly
+within the control limits nothing that
+
+ align:start position:0%
+within the control limits nothing that
+ 
+
+ align:start position:0%
+within the control limits nothing that
+tells me that that point is
+
+ align:start position:0%
+tells me that that point is
+ 
+
+ align:start position:0%
+tells me that that point is
+unusual but if I then plot that data
+
+ align:start position:0%
+unusual but if I then plot that data
+ 
+
+ align:start position:0%
+unusual but if I then plot that data
+point that red data point there uh on
+
+ align:start position:0%
+point that red data point there uh on
+ 
+
+ align:start position:0%
+point that red data point there uh on
+the kai squared chart I calculated the
+
+ align:start position:0%
+the kai squared chart I calculated the
+ 
+
+ align:start position:0%
+the kai squared chart I calculated the
+kai statistic that distance statistic
+
+ align:start position:0%
+kai statistic that distance statistic
+ 
+
+ align:start position:0%
+kai statistic that distance statistic
+that would trigger because its
+
+ align:start position:0%
+that would trigger because its
+ 
+
+ align:start position:0%
+that would trigger because its
+distance from from the mean is unusual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if I actually didn't
+
+ align:start position:0%
+now if I actually didn't
+ 
+
+ align:start position:0%
+now if I actually didn't
+know my true covariance Matrix but I had
+
+ align:start position:0%
+know my true covariance Matrix but I had
+ 
+
+ align:start position:0%
+know my true covariance Matrix but I had
+to estimate it I have to
+
+ align:start position:0%
+to estimate it I have to
+ 
+
+ align:start position:0%
+to estimate it I have to
+estimate Sigma with an S I'm I'm right
+
+ align:start position:0%
+estimate Sigma with an S I'm I'm right
+ 
+
+ align:start position:0%
+estimate Sigma with an S I'm I'm right
+back to this whole difference between a
+
+ align:start position:0%
+back to this whole difference between a
+ 
+
+ align:start position:0%
+back to this whole difference between a
+t and a unit normal so uh just to close
+
+ align:start position:0%
+t and a unit normal so uh just to close
+ 
+
+ align:start position:0%
+t and a unit normal so uh just to close
+this out we often talk about these as
+
+ align:start position:0%
+this out we often talk about these as
+ 
+
+ align:start position:0%
+this out we often talk about these as
+t^2 totaling t^2 statistics but it's
+
+ align:start position:0%
+t^2 totaling t^2 statistics but it's
+ 
+
+ align:start position:0%
+t^2 totaling t^2 statistics but it's
+it's exactly the same idea
+
+ align:start position:0%
+it's exactly the same idea
+ 
+
+ align:start position:0%
+it's exactly the same idea
+and it's got its own uh cff
+
+ align:start position:0%
+and it's got its own uh cff
+ 
+
+ align:start position:0%
+and it's got its own uh cff
+points okay so with that I think we've
+
+ align:start position:0%
+points okay so with that I think we've
+ 
+
+ align:start position:0%
+points okay so with that I think we've
+sort of pulled to a close on control
+
+ align:start position:0%
+sort of pulled to a close on control
+ 
+
+ align:start position:0%
+sort of pulled to a close on control
+charting for the for the at least for
+
+ align:start position:0%
+charting for the for the at least for
+ 
+
+ align:start position:0%
+charting for the for the at least for
+the time being uh next time we'll start
+
+ align:start position:0%
+the time being uh next time we'll start
+ 
+
+ align:start position:0%
+the time being uh next time we'll start
+diving in on yield modeling in different
+
+ align:start position:0%
+diving in on yield modeling in different
+ 
+
+ align:start position:0%
+diving in on yield modeling in different
+uses of some statistics but I think what
+
+ align:start position:0%
+uses of some statistics but I think what
+ 
+
+ align:start position:0%
+uses of some statistics but I think what
+you've got now is some exposure to ewma
+
+ align:start position:0%
+you've got now is some exposure to ewma
+ 
+
+ align:start position:0%
+you've got now is some exposure to ewma
+qm You'll play around with those with
+
+ align:start position:0%
+qm You'll play around with those with
+ 
+
+ align:start position:0%
+qm You'll play around with those with
+the three or four problems on this
+
+ align:start position:0%
+the three or four problems on this
+ 
+
+ align:start position:0%
+the three or four problems on this
+week's problem set um and start looking
+
+ align:start position:0%
+week's problem set um and start looking
+ 
+
+ align:start position:0%
+week's problem set um and start looking
+at the quizzes we'll have the first quiz
+
+ align:start position:0%
+at the quizzes we'll have the first quiz
+ 
+
+ align:start position:0%
+at the quizzes we'll have the first quiz
+a week from today in class
+
+ align:start position:0%
+a week from today in class
+ 
+
+ align:start position:0%
+a week from today in class
+so Professor I have a question yeah we
+
+ align:start position:0%
+so Professor I have a question yeah we
+ 
+
+ align:start position:0%
+so Professor I have a question yeah we
+go ahead and break I'll I'll I'll take
+
+ align:start position:0%
+go ahead and break I'll I'll I'll take
+ 
+
+ align:start position:0%
+go ahead and break I'll I'll I'll take
+your question while people are are are
+
+ align:start position:0%
+your question while people are are are
+ 
+
+ align:start position:0%
+your question while people are are are
+dispersing so so for the cont you tght
+
+ align:start position:0%
+dispersing so so for the cont you tght
+ 
+
+ align:start position:0%
+dispersing so so for the cont you tght
+us today are they going to be included
+
+ align:start position:0%
+us today are they going to be included
+ 
+
+ align:start position:0%
+us today are they going to be included
+in the quiz uh you might see a it's
+
+ align:start position:0%
+in the quiz uh you might see a it's
+ 
+
+ align:start position:0%
+in the quiz uh you might see a it's
+possible you'll see an ewma or a qome
+
+ align:start position:0%
+possible you'll see an ewma or a qome
+ 
+
+ align:start position:0%
+possible you'll see an ewma or a qome
+but uh they would only be fairly simple
+
+ align:start position:0%
+but uh they would only be fairly simple
+ 
+
+ align:start position:0%
+but uh they would only be fairly simple
+uh questions for those it's not likely
+
+ align:start position:0%
+uh questions for those it's not likely
+ 
+
+ align:start position:0%
+uh questions for those it's not likely
+you'll see a multivariant
+
+ align:start position:0%
+you'll see a multivariant
+ 
+
+ align:start position:0%
+you'll see a multivariant
+problem okay thank you
\ No newline at end of file
diff --git a/NvTZT0U01jc.txt b/NvTZT0U01jc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..85073619fd101a564725d3d041bddebef58be4bc
--- /dev/null
+++ b/NvTZT0U01jc.txt
@@ -0,0 +1,3307 @@
+align:start position:0%
+ 
+we discovered uh in the last several
+
+ align:start position:0%
+we discovered uh in the last several
+ 
+
+ align:start position:0%
+we discovered uh in the last several
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+is that this this plume of groundwater
+
+ align:start position:0%
+is that this this plume of groundwater
+ 
+
+ align:start position:0%
+is that this this plume of groundwater
+that's coming toward the lake and
+
+ align:start position:0%
+that's coming toward the lake and
+ 
+
+ align:start position:0%
+that's coming toward the lake and
+actually continuing on to the south
+
+ align:start position:0%
+actually continuing on to the south
+ 
+
+ align:start position:0%
+actually continuing on to the south
+we'll see that at the end of the trip
+
+ align:start position:0%
+we'll see that at the end of the trip
+ 
+
+ align:start position:0%
+we'll see that at the end of the trip
+is discharging it to what they call
+
+ align:start position:0%
+is discharging it to what they call
+ 
+
+ align:start position:0%
+is discharging it to what they call
+fisherman's cove right here
+
+ align:start position:0%
+fisherman's cove right here
+ 
+
+ align:start position:0%
+fisherman's cove right here
+all right and uh the way we discovered
+
+ align:start position:0%
+all right and uh the way we discovered
+ 
+
+ align:start position:0%
+all right and uh the way we discovered
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+was we were drilling wells somebody was
+
+ align:start position:0%
+was we were drilling wells somebody was
+ 
+
+ align:start position:0%
+was we were drilling wells somebody was
+asking earlier you know how do you do
+
+ align:start position:0%
+asking earlier you know how do you do
+ 
+
+ align:start position:0%
+asking earlier you know how do you do
+this well you drill well you sort of
+
+ align:start position:0%
+this well you drill well you sort of
+ 
+
+ align:start position:0%
+this well you drill well you sort of
+leapfrog your way down and
+
+ align:start position:0%
+leapfrog your way down and
+ 
+
+ align:start position:0%
+leapfrog your way down and
+suddenly there you are at the lake shore
+
+ align:start position:0%
+suddenly there you are at the lake shore
+ 
+
+ align:start position:0%
+suddenly there you are at the lake shore
+with your drill rig and you realize the
+
+ align:start position:0%
+with your drill rig and you realize the
+ 
+
+ align:start position:0%
+with your drill rig and you realize the
+next step is the lake
+
+ align:start position:0%
+next step is the lake
+ 
+
+ align:start position:0%
+next step is the lake
+so the thought was that the plume must
+
+ align:start position:0%
+so the thought was that the plume must
+ 
+
+ align:start position:0%
+so the thought was that the plume must
+be discharging into the like
+
+ align:start position:0%
+be discharging into the like
+ 
+
+ align:start position:0%
+be discharging into the like
+and so what we did is we went out
+
+ align:start position:0%
+and so what we did is we went out
+ 
+
+ align:start position:0%
+and so what we did is we went out
+into the lake itself a number of times
+
+ align:start position:0%
+into the lake itself a number of times
+ 
+
+ align:start position:0%
+into the lake itself a number of times
+over the last several years
+
+ align:start position:0%
+over the last several years
+ 
+
+ align:start position:0%
+over the last several years
+with a number of different devices
+
+ align:start position:0%
+with a number of different devices
+ 
+
+ align:start position:0%
+with a number of different devices
+driving devices like this one here is a
+
+ align:start position:0%
+driving devices like this one here is a
+ 
+
+ align:start position:0%
+driving devices like this one here is a
+good example
+
+ align:start position:0%
+good example
+ 
+
+ align:start position:0%
+good example
+a little temporary uh drive point it's a
+
+ align:start position:0%
+a little temporary uh drive point it's a
+ 
+
+ align:start position:0%
+a little temporary uh drive point it's a
+little multi-level sample like you saw
+
+ align:start position:0%
+little multi-level sample like you saw
+ 
+
+ align:start position:0%
+little multi-level sample like you saw
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+it's made out of steel instead so you
+
+ align:start position:0%
+it's made out of steel instead so you
+ 
+
+ align:start position:0%
+it's made out of steel instead so you
+can go out
+
+ align:start position:0%
+can go out
+ 
+
+ align:start position:0%
+can go out
+in the lake in waders or in a boat drive
+
+ align:start position:0%
+in the lake in waders or in a boat drive
+ 
+
+ align:start position:0%
+in the lake in waders or in a boat drive
+it in
+
+ align:start position:0%
+it in
+ 
+
+ align:start position:0%
+it in
+and then collect water samples out of
+
+ align:start position:0%
+and then collect water samples out of
+ 
+
+ align:start position:0%
+and then collect water samples out of
+the top of it and the idea being what's
+
+ align:start position:0%
+the top of it and the idea being what's
+ 
+
+ align:start position:0%
+the top of it and the idea being what's
+the water quality of the groundwater as
+
+ align:start position:0%
+the water quality of the groundwater as
+ 
+
+ align:start position:0%
+the water quality of the groundwater as
+it's coming into the lake
+
+ align:start position:0%
+it's coming into the lake
+ 
+
+ align:start position:0%
+it's coming into the lake
+right so we see it all the way to here
+
+ align:start position:0%
+right so we see it all the way to here
+ 
+
+ align:start position:0%
+right so we see it all the way to here
+what's the water quality look like
+
+ align:start position:0%
+what's the water quality look like
+ 
+
+ align:start position:0%
+what's the water quality look like
+another device we've used uh is
+
+ align:start position:0%
+another device we've used uh is
+ 
+
+ align:start position:0%
+another device we've used uh is
+something like this it's called the
+
+ align:start position:0%
+something like this it's called the
+ 
+
+ align:start position:0%
+something like this it's called the
+henry sampler it's a little tiny sampler
+
+ align:start position:0%
+henry sampler it's a little tiny sampler
+ 
+
+ align:start position:0%
+henry sampler it's a little tiny sampler
+let me just give you and
+
+ align:start position:0%
+let me just give you and
+ 
+
+ align:start position:0%
+let me just give you and
+show you how this works real easy
+
+ align:start position:0%
+show you how this works real easy
+ 
+
+ align:start position:0%
+show you how this works real easy
+it's kind of neat it's got a little tiny
+
+ align:start position:0%
+it's kind of neat it's got a little tiny
+ 
+
+ align:start position:0%
+it's kind of neat it's got a little tiny
+point on the end oh that's gross
+
+ align:start position:0%
+point on the end oh that's gross
+ 
+
+ align:start position:0%
+point on the end oh that's gross
+and it's got a little inner rod to give
+
+ align:start position:0%
+and it's got a little inner rod to give
+ 
+
+ align:start position:0%
+and it's got a little inner rod to give
+it some strength and you can see
+
+ align:start position:0%
+it some strength and you can see
+ 
+
+ align:start position:0%
+it some strength and you can see
+you'll see the end you know it's slotted
+
+ align:start position:0%
+you'll see the end you know it's slotted
+ 
+
+ align:start position:0%
+you'll see the end you know it's slotted
+on the end can you vouch for the rest of
+
+ align:start position:0%
+on the end can you vouch for the rest of
+ 
+
+ align:start position:0%
+on the end can you vouch for the rest of
+them that it's slotted on the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+when you shove it in like this and you
+
+ align:start position:0%
+when you shove it in like this and you
+ 
+
+ align:start position:0%
+when you shove it in like this and you
+pull out the little center rod like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can put the syringe on it
+
+ align:start position:0%
+and then you can put the syringe on it
+ 
+
+ align:start position:0%
+and then you can put the syringe on it
+or a pump of any kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you can get your water sample
+
+ align:start position:0%
+then you can get your water sample
+ 
+
+ align:start position:0%
+then you can get your water sample
+that's all there is to it
+
+ align:start position:0%
+that's all there is to it
+ 
+
+ align:start position:0%
+that's all there is to it
+that's a little crappy because it's
+
+ align:start position:0%
+that's a little crappy because it's
+ 
+
+ align:start position:0%
+that's a little crappy because it's
+obviously uh
+
+ align:start position:0%
+obviously uh
+ 
+
+ align:start position:0%
+obviously uh
+so so what we did is we went to um
+
+ align:start position:0%
+so so what we did is we went to um
+ 
+
+ align:start position:0%
+so so what we did is we went to um
+we went to dozens if not hundreds of
+
+ align:start position:0%
+we went to dozens if not hundreds of
+ 
+
+ align:start position:0%
+we went to dozens if not hundreds of
+locations here in the lake
+
+ align:start position:0%
+locations here in the lake
+ 
+
+ align:start position:0%
+locations here in the lake
+uh in this area and
+
+ align:start position:0%
+uh in this area and
+ 
+
+ align:start position:0%
+uh in this area and
+you see on page 15 we actually mapped
+
+ align:start position:0%
+you see on page 15 we actually mapped
+ 
+
+ align:start position:0%
+you see on page 15 we actually mapped
+out what the plume looks like coming out
+
+ align:start position:0%
+out what the plume looks like coming out
+ 
+
+ align:start position:0%
+out what the plume looks like coming out
+into the pond bottom
+
+ align:start position:0%
+into the pond bottom
+ 
+
+ align:start position:0%
+into the pond bottom
+right this is specific conductance i
+
+ align:start position:0%
+right this is specific conductance i
+ 
+
+ align:start position:0%
+right this is specific conductance i
+mentioned conductance before it's just a
+
+ align:start position:0%
+mentioned conductance before it's just a
+ 
+
+ align:start position:0%
+mentioned conductance before it's just a
+general measure of the inorganics in the
+
+ align:start position:0%
+general measure of the inorganics in the
+ 
+
+ align:start position:0%
+general measure of the inorganics in the
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+higher conductance more dissolved stuff
+
+ align:start position:0%
+higher conductance more dissolved stuff
+ 
+
+ align:start position:0%
+higher conductance more dissolved stuff
+in the water
+
+ align:start position:0%
+in the water
+ 
+
+ align:start position:0%
+in the water
+this is the conductance we measured all
+
+ align:start position:0%
+this is the conductance we measured all
+ 
+
+ align:start position:0%
+this is the conductance we measured all
+the little dots show you locations where
+
+ align:start position:0%
+the little dots show you locations where
+ 
+
+ align:start position:0%
+the little dots show you locations where
+they went out here with a little well
+
+ align:start position:0%
+they went out here with a little well
+ 
+
+ align:start position:0%
+they went out here with a little well
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+we actually had a boat and we had a
+
+ align:start position:0%
+we actually had a boat and we had a
+ 
+
+ align:start position:0%
+we actually had a boat and we had a
+barge at one point
+
+ align:start position:0%
+barge at one point
+ 
+
+ align:start position:0%
+barge at one point
+because it gets a little hard to work in
+
+ align:start position:0%
+because it gets a little hard to work in
+ 
+
+ align:start position:0%
+because it gets a little hard to work in
+water you know when it gets too deep
+
+ align:start position:0%
+water you know when it gets too deep
+ 
+
+ align:start position:0%
+water you know when it gets too deep
+um and we did that in three times 99
+
+ align:start position:0%
+um and we did that in three times 99
+ 
+
+ align:start position:0%
+um and we did that in three times 99
+2001 2003
+
+ align:start position:0%
+2001 2003
+ 
+
+ align:start position:0%
+2001 2003
+you'll notice there's a clear change in
+
+ align:start position:0%
+you'll notice there's a clear change in
+ 
+
+ align:start position:0%
+you'll notice there's a clear change in
+the nature of the map as you go with
+
+ align:start position:0%
+the nature of the map as you go with
+ 
+
+ align:start position:0%
+the nature of the map as you go with
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+see how it's it's high in 99 and then
+
+ align:start position:0%
+see how it's it's high in 99 and then
+ 
+
+ align:start position:0%
+see how it's it's high in 99 and then
+you seem to see a decrease in
+
+ align:start position:0%
+you seem to see a decrease in
+ 
+
+ align:start position:0%
+you seem to see a decrease in
+concentrations or conductance as you go
+
+ align:start position:0%
+concentrations or conductance as you go
+ 
+
+ align:start position:0%
+concentrations or conductance as you go
+later in the in the time
+
+ align:start position:0%
+later in the in the time
+ 
+
+ align:start position:0%
+later in the in the time
+what that is is that that trailing edge
+
+ align:start position:0%
+what that is is that that trailing edge
+ 
+
+ align:start position:0%
+what that is is that that trailing edge
+we were talking about the plume
+
+ align:start position:0%
+we were talking about the plume
+ 
+
+ align:start position:0%
+we were talking about the plume
+that natural flushing is actually in
+
+ align:start position:0%
+that natural flushing is actually in
+ 
+
+ align:start position:0%
+that natural flushing is actually in
+this time period began to arrive right
+
+ align:start position:0%
+this time period began to arrive right
+ 
+
+ align:start position:0%
+this time period began to arrive right
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+the tail end of the plume is leaving
+
+ align:start position:0%
+the tail end of the plume is leaving
+ 
+
+ align:start position:0%
+the tail end of the plume is leaving
+this neighborhood now
+
+ align:start position:0%
+this neighborhood now
+ 
+
+ align:start position:0%
+this neighborhood now
+and in fact we did some sampling in 2004
+
+ align:start position:0%
+and in fact we did some sampling in 2004
+ 
+
+ align:start position:0%
+and in fact we did some sampling in 2004
+and it's even more
+
+ align:start position:0%
+and it's even more
+ 
+
+ align:start position:0%
+and it's even more
+diminished so for many years the plume
+
+ align:start position:0%
+diminished so for many years the plume
+ 
+
+ align:start position:0%
+diminished so for many years the plume
+used to discharge here
+
+ align:start position:0%
+used to discharge here
+ 
+
+ align:start position:0%
+used to discharge here
+but now that they've shot off the plant
+
+ align:start position:0%
+but now that they've shot off the plant
+ 
+
+ align:start position:0%
+but now that they've shot off the plant
+it's gradually cleaning itself out and
+
+ align:start position:0%
+it's gradually cleaning itself out and
+ 
+
+ align:start position:0%
+it's gradually cleaning itself out and
+the water coming up into the pond here
+
+ align:start position:0%
+the water coming up into the pond here
+ 
+
+ align:start position:0%
+the water coming up into the pond here
+is obviously of a better quality than it
+
+ align:start position:0%
+is obviously of a better quality than it
+ 
+
+ align:start position:0%
+is obviously of a better quality than it
+used to be
+
+ align:start position:0%
+used to be
+ 
+
+ align:start position:0%
+used to be
+because you see that clearly indicated
+
+ align:start position:0%
+because you see that clearly indicated
+ 
+
+ align:start position:0%
+because you see that clearly indicated
+here we see that with boron
+
+ align:start position:0%
+here we see that with boron
+ 
+
+ align:start position:0%
+here we see that with boron
+we see with nitrate and so forth right
+
+ align:start position:0%
+we see with nitrate and so forth right
+ 
+
+ align:start position:0%
+we see with nitrate and so forth right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but turn the next page look at
+
+ align:start position:0%
+but turn the next page look at
+ 
+
+ align:start position:0%
+but turn the next page look at
+phosphorus
+
+ align:start position:0%
+phosphorus
+ 
+
+ align:start position:0%
+phosphorus
+same three views this is phosphorous
+
+ align:start position:0%
+same three views this is phosphorous
+ 
+
+ align:start position:0%
+same three views this is phosphorous
+all right and you'll see that the
+
+ align:start position:0%
+all right and you'll see that the
+ 
+
+ align:start position:0%
+all right and you'll see that the
+phosphorus high zone
+
+ align:start position:0%
+phosphorus high zone
+ 
+
+ align:start position:0%
+phosphorus high zone
+is right where we're standing right now
+
+ align:start position:0%
+is right where we're standing right now
+ 
+
+ align:start position:0%
+is right where we're standing right now
+on this bluff
+
+ align:start position:0%
+on this bluff
+ 
+
+ align:start position:0%
+on this bluff
+and you'll notice that it doesn't change
+
+ align:start position:0%
+and you'll notice that it doesn't change
+ 
+
+ align:start position:0%
+and you'll notice that it doesn't change
+at all to speak out the time
+
+ align:start position:0%
+at all to speak out the time
+ 
+
+ align:start position:0%
+at all to speak out the time
+see how it hasn't changed okay that's
+
+ align:start position:0%
+see how it hasn't changed okay that's
+ 
+
+ align:start position:0%
+see how it hasn't changed okay that's
+this whole business of phosphorus
+
+ align:start position:0%
+this whole business of phosphorus
+ 
+
+ align:start position:0%
+this whole business of phosphorus
+retardation
+
+ align:start position:0%
+retardation
+ 
+
+ align:start position:0%
+retardation
+the tail end of the plume is leaving but
+
+ align:start position:0%
+the tail end of the plume is leaving but
+ 
+
+ align:start position:0%
+the tail end of the plume is leaving but
+the phosphorus is like ink on a sponge
+
+ align:start position:0%
+the phosphorus is like ink on a sponge
+ 
+
+ align:start position:0%
+the phosphorus is like ink on a sponge
+it just doesn't want to rinse off
+
+ align:start position:0%
+it just doesn't want to rinse off
+ 
+
+ align:start position:0%
+it just doesn't want to rinse off
+so it's going to take many many many
+
+ align:start position:0%
+so it's going to take many many many
+ 
+
+ align:start position:0%
+so it's going to take many many many
+flushes for the phosphorus to be
+
+ align:start position:0%
+flushes for the phosphorus to be
+ 
+
+ align:start position:0%
+flushes for the phosphorus to be
+purged off the system and so long after
+
+ align:start position:0%
+purged off the system and so long after
+ 
+
+ align:start position:0%
+purged off the system and so long after
+the rest of the plume has left
+
+ align:start position:0%
+the rest of the plume has left
+ 
+
+ align:start position:0%
+the rest of the plume has left
+there'll be phosphate discharging to the
+
+ align:start position:0%
+there'll be phosphate discharging to the
+ 
+
+ align:start position:0%
+there'll be phosphate discharging to the
+lake at relatively high levels because
+
+ align:start position:0%
+lake at relatively high levels because
+ 
+
+ align:start position:0%
+lake at relatively high levels because
+99 of it's on the sediments and it has
+
+ align:start position:0%
+99 of it's on the sediments and it has
+ 
+
+ align:start position:0%
+99 of it's on the sediments and it has
+to flush off
+
+ align:start position:0%
+to flush off
+ 
+
+ align:start position:0%
+to flush off
+okay so the concern is that the
+
+ align:start position:0%
+okay so the concern is that the
+ 
+
+ align:start position:0%
+okay so the concern is that the
+phosphorous load to the lake is just
+
+ align:start position:0%
+phosphorous load to the lake is just
+ 
+
+ align:start position:0%
+phosphorous load to the lake is just
+going to go on for almost forever
+
+ align:start position:0%
+going to go on for almost forever
+ 
+
+ align:start position:0%
+going to go on for almost forever
+relatively speaking and the
+
+ align:start position:0%
+relatively speaking and the
+ 
+
+ align:start position:0%
+relatively speaking and the
+limonologists have said that's just too
+
+ align:start position:0%
+limonologists have said that's just too
+ 
+
+ align:start position:0%
+limonologists have said that's just too
+high a loading rate
+
+ align:start position:0%
+high a loading rate
+ 
+
+ align:start position:0%
+high a loading rate
+so the military was under the gun so to
+
+ align:start position:0%
+so the military was under the gun so to
+ 
+
+ align:start position:0%
+so the military was under the gun so to
+speak
+
+ align:start position:0%
+speak
+ 
+
+ align:start position:0%
+speak
+to um to try to cut down on the load of
+
+ align:start position:0%
+to um to try to cut down on the load of
+ 
+
+ align:start position:0%
+to um to try to cut down on the load of
+phosphate to the lake
+
+ align:start position:0%
+phosphate to the lake
+ 
+
+ align:start position:0%
+phosphate to the lake
+because they were responsible for like
+
+ align:start position:0%
+because they were responsible for like
+ 
+
+ align:start position:0%
+because they were responsible for like
+60 or 70 percent of it so they looked at
+
+ align:start position:0%
+60 or 70 percent of it so they looked at
+ 
+
+ align:start position:0%
+60 or 70 percent of it so they looked at
+a variety of options one was to
+
+ align:start position:0%
+a variety of options one was to
+ 
+
+ align:start position:0%
+a variety of options one was to
+provide soaring for all the homes okay
+
+ align:start position:0%
+provide soaring for all the homes okay
+ 
+
+ align:start position:0%
+provide soaring for all the homes okay
+in other words we'll let our phosphorus
+
+ align:start position:0%
+in other words we'll let our phosphorus
+ 
+
+ align:start position:0%
+in other words we'll let our phosphorus
+go in because it's too hard to get it
+
+ align:start position:0%
+go in because it's too hard to get it
+ 
+
+ align:start position:0%
+go in because it's too hard to get it
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+but we'll we'll take care of any new
+
+ align:start position:0%
+but we'll we'll take care of any new
+ 
+
+ align:start position:0%
+but we'll we'll take care of any new
+loads well it turns out that wasn't
+
+ align:start position:0%
+loads well it turns out that wasn't
+ 
+
+ align:start position:0%
+loads well it turns out that wasn't
+enough there are very few homes on the
+
+ align:start position:0%
+enough there are very few homes on the
+ 
+
+ align:start position:0%
+enough there are very few homes on the
+upgrading side of the lake
+
+ align:start position:0%
+upgrading side of the lake
+ 
+
+ align:start position:0%
+upgrading side of the lake
+it's mostly the military base they
+
+ align:start position:0%
+it's mostly the military base they
+ 
+
+ align:start position:0%
+it's mostly the military base they
+looked at putting in pumping wells
+
+ align:start position:0%
+looked at putting in pumping wells
+ 
+
+ align:start position:0%
+looked at putting in pumping wells
+and pumping but because phosphorus
+
+ align:start position:0%
+and pumping but because phosphorus
+ 
+
+ align:start position:0%
+and pumping but because phosphorus
+doesn't like to move you have to pump
+
+ align:start position:0%
+doesn't like to move you have to pump
+ 
+
+ align:start position:0%
+doesn't like to move you have to pump
+forever
+
+ align:start position:0%
+forever
+ 
+
+ align:start position:0%
+forever
+so they were looking for something that
+
+ align:start position:0%
+so they were looking for something that
+ 
+
+ align:start position:0%
+so they were looking for something that
+was a lot more passive when
+
+ align:start position:0%
+was a lot more passive when
+ 
+
+ align:start position:0%
+was a lot more passive when
+we mapped out this footprint they began
+
+ align:start position:0%
+we mapped out this footprint they began
+ 
+
+ align:start position:0%
+we mapped out this footprint they began
+to realize
+
+ align:start position:0%
+to realize
+ 
+
+ align:start position:0%
+to realize
+gee the area where most of the
+
+ align:start position:0%
+gee the area where most of the
+ 
+
+ align:start position:0%
+gee the area where most of the
+phosphorus is coming in it's not like a
+
+ align:start position:0%
+phosphorus is coming in it's not like a
+ 
+
+ align:start position:0%
+phosphorus is coming in it's not like a
+volatile organic or cancer-causing
+
+ align:start position:0%
+volatile organic or cancer-causing
+ 
+
+ align:start position:0%
+volatile organic or cancer-causing
+chemical where you have to get it all if
+
+ align:start position:0%
+chemical where you have to get it all if
+ 
+
+ align:start position:0%
+chemical where you have to get it all if
+they could knock down the load by 80
+
+ align:start position:0%
+they could knock down the load by 80
+ 
+
+ align:start position:0%
+they could knock down the load by 80
+percent they'd be
+
+ align:start position:0%
+percent they'd be
+ 
+
+ align:start position:0%
+percent they'd be
+way ahead and they noticed that the the
+
+ align:start position:0%
+way ahead and they noticed that the the
+ 
+
+ align:start position:0%
+way ahead and they noticed that the the
+footprint if you want to think of it
+
+ align:start position:0%
+footprint if you want to think of it
+ 
+
+ align:start position:0%
+footprint if you want to think of it
+that way the discharge area
+
+ align:start position:0%
+that way the discharge area
+ 
+
+ align:start position:0%
+that way the discharge area
+was relatively small so if they could
+
+ align:start position:0%
+was relatively small so if they could
+ 
+
+ align:start position:0%
+was relatively small so if they could
+put something down
+
+ align:start position:0%
+put something down
+ 
+
+ align:start position:0%
+put something down
+on the pawn bottom some sort of reactive
+
+ align:start position:0%
+on the pawn bottom some sort of reactive
+ 
+
+ align:start position:0%
+on the pawn bottom some sort of reactive
+media to capture like a sorbent
+
+ align:start position:0%
+media to capture like a sorbent
+ 
+
+ align:start position:0%
+media to capture like a sorbent
+they could capture the phosphorus right
+
+ align:start position:0%
+they could capture the phosphorus right
+ 
+
+ align:start position:0%
+they could capture the phosphorus right
+where it's coming out
+
+ align:start position:0%
+where it's coming out
+ 
+
+ align:start position:0%
+where it's coming out
+and and not let it get in the lake that
+
+ align:start position:0%
+and and not let it get in the lake that
+ 
+
+ align:start position:0%
+and and not let it get in the lake that
+way and if they could do something that
+
+ align:start position:0%
+way and if they could do something that
+ 
+
+ align:start position:0%
+way and if they could do something that
+was passive they wouldn't have to do
+
+ align:start position:0%
+was passive they wouldn't have to do
+ 
+
+ align:start position:0%
+was passive they wouldn't have to do
+anything more than that
+
+ align:start position:0%
+anything more than that
+ 
+
+ align:start position:0%
+anything more than that
+so the idea was to find something that
+
+ align:start position:0%
+so the idea was to find something that
+ 
+
+ align:start position:0%
+so the idea was to find something that
+they could lay out once and then walk
+
+ align:start position:0%
+they could lay out once and then walk
+ 
+
+ align:start position:0%
+they could lay out once and then walk
+away from
+
+ align:start position:0%
+away from
+ 
+
+ align:start position:0%
+away from
+right um and then it's not nothing wrong
+
+ align:start position:0%
+right um and then it's not nothing wrong
+ 
+
+ align:start position:0%
+right um and then it's not nothing wrong
+that's a great philosophy so um so what
+
+ align:start position:0%
+that's a great philosophy so um so what
+ 
+
+ align:start position:0%
+that's a great philosophy so um so what
+they did
+
+ align:start position:0%
+they did
+ 
+
+ align:start position:0%
+they did
+um in um this august
+
+ align:start position:0%
+um in um this august
+ 
+
+ align:start position:0%
+um in um this august
+so this just literally happened just a
+
+ align:start position:0%
+so this just literally happened just a
+ 
+
+ align:start position:0%
+so this just literally happened just a
+few weeks ago they came out here
+
+ align:start position:0%
+few weeks ago they came out here
+ 
+
+ align:start position:0%
+few weeks ago they came out here
+it's too hot we had a i ran a filter for
+
+ align:start position:0%
+it's too hot we had a i ran a filter for
+ 
+
+ align:start position:0%
+it's too hot we had a i ran a filter for
+the umass uh
+
+ align:start position:0%
+the umass uh
+ 
+
+ align:start position:0%
+the umass uh
+boston students uh in august and it was
+
+ align:start position:0%
+boston students uh in august and it was
+ 
+
+ align:start position:0%
+boston students uh in august and it was
+going on it was amazing because they got
+
+ align:start position:0%
+going on it was amazing because they got
+ 
+
+ align:start position:0%
+going on it was amazing because they got
+to watch it
+
+ align:start position:0%
+to watch it
+ 
+
+ align:start position:0%
+to watch it
+going in um in an area you can see the
+
+ align:start position:0%
+going in um in an area you can see the
+ 
+
+ align:start position:0%
+going in um in an area you can see the
+little pin flags out there
+
+ align:start position:0%
+little pin flags out there
+ 
+
+ align:start position:0%
+little pin flags out there
+in an area 40 feet wide from about right
+
+ align:start position:0%
+in an area 40 feet wide from about right
+ 
+
+ align:start position:0%
+in an area 40 feet wide from about right
+about here
+
+ align:start position:0%
+about here
+ 
+
+ align:start position:0%
+about here
+roughly where i'm standing here about 40
+
+ align:start position:0%
+roughly where i'm standing here about 40
+ 
+
+ align:start position:0%
+roughly where i'm standing here about 40
+feet and then 300 feet long
+
+ align:start position:0%
+feet and then 300 feet long
+ 
+
+ align:start position:0%
+feet and then 300 feet long
+they put out a cofferdam you know what a
+
+ align:start position:0%
+they put out a cofferdam you know what a
+ 
+
+ align:start position:0%
+they put out a cofferdam you know what a
+cofferdam is
+
+ align:start position:0%
+cofferdam is
+ 
+
+ align:start position:0%
+cofferdam is
+you know for engineering it was made out
+
+ align:start position:0%
+you know for engineering it was made out
+ 
+
+ align:start position:0%
+you know for engineering it was made out
+of big bladders that they inflated so
+
+ align:start position:0%
+of big bladders that they inflated so
+ 
+
+ align:start position:0%
+of big bladders that they inflated so
+they put out a copper dam
+
+ align:start position:0%
+they put out a copper dam
+ 
+
+ align:start position:0%
+they put out a copper dam
+and then they had two pumps three pumps
+
+ align:start position:0%
+and then they had two pumps three pumps
+ 
+
+ align:start position:0%
+and then they had two pumps three pumps
+that could pump a total of six thousand
+
+ align:start position:0%
+that could pump a total of six thousand
+ 
+
+ align:start position:0%
+that could pump a total of six thousand
+gallons a minute
+
+ align:start position:0%
+gallons a minute
+ 
+
+ align:start position:0%
+gallons a minute
+and they de-watered the pond up to the
+
+ align:start position:0%
+and they de-watered the pond up to the
+ 
+
+ align:start position:0%
+and they de-watered the pond up to the
+copper dams
+
+ align:start position:0%
+copper dams
+ 
+
+ align:start position:0%
+copper dams
+okay then they came in with excavators
+
+ align:start position:0%
+okay then they came in with excavators
+ 
+
+ align:start position:0%
+okay then they came in with excavators
+and they dug down
+
+ align:start position:0%
+and they dug down
+ 
+
+ align:start position:0%
+and they dug down
+three feet and they mixed into the
+
+ align:start position:0%
+three feet and they mixed into the
+ 
+
+ align:start position:0%
+three feet and they mixed into the
+natural sediments
+
+ align:start position:0%
+natural sediments
+ 
+
+ align:start position:0%
+natural sediments
+zero valence or elemental iron
+
+ align:start position:0%
+zero valence or elemental iron
+ 
+
+ align:start position:0%
+zero valence or elemental iron
+okay the idea being that the iron would
+
+ align:start position:0%
+okay the idea being that the iron would
+ 
+
+ align:start position:0%
+okay the idea being that the iron would
+rust
+
+ align:start position:0%
+rust
+ 
+
+ align:start position:0%
+rust
+turn into iron oxide and what do we say
+
+ align:start position:0%
+turn into iron oxide and what do we say
+ 
+
+ align:start position:0%
+turn into iron oxide and what do we say
+phosphorus likes to stick to
+
+ align:start position:0%
+phosphorus likes to stick to
+ 
+
+ align:start position:0%
+phosphorus likes to stick to
+iron oxide so as the groundwater passes
+
+ align:start position:0%
+iron oxide so as the groundwater passes
+ 
+
+ align:start position:0%
+iron oxide so as the groundwater passes
+up through this reactive blanket of iron
+
+ align:start position:0%
+up through this reactive blanket of iron
+ 
+
+ align:start position:0%
+up through this reactive blanket of iron
+it would be absorbed out by all this
+
+ align:start position:0%
+it would be absorbed out by all this
+ 
+
+ align:start position:0%
+it would be absorbed out by all this
+iron they added to the aquifer and never
+
+ align:start position:0%
+iron they added to the aquifer and never
+ 
+
+ align:start position:0%
+iron they added to the aquifer and never
+make it into the lake
+
+ align:start position:0%
+make it into the lake
+ 
+
+ align:start position:0%
+make it into the lake
+that's the idea that's why the shore is
+
+ align:start position:0%
+that's the idea that's why the shore is
+ 
+
+ align:start position:0%
+that's the idea that's why the shore is
+red
+
+ align:start position:0%
+red
+ 
+
+ align:start position:0%
+red
+it's the iron rusting this was used to
+
+ align:start position:0%
+it's the iron rusting this was used to
+ 
+
+ align:start position:0%
+it's the iron rusting this was used to
+be black
+
+ align:start position:0%
+be black
+ 
+
+ align:start position:0%
+be black
+so this is this is the iron rusting um
+
+ align:start position:0%
+so this is this is the iron rusting um
+ 
+
+ align:start position:0%
+so this is this is the iron rusting um
+on the pond bottom
+
+ align:start position:0%
+on the pond bottom
+ 
+
+ align:start position:0%
+on the pond bottom
+and sorting out the phosphorus in theory
+
+ align:start position:0%
+and sorting out the phosphorus in theory
+ 
+
+ align:start position:0%
+and sorting out the phosphorus in theory
+well we've all we have not the first
+
+ align:start position:0%
+well we've all we have not the first
+ 
+
+ align:start position:0%
+well we've all we have not the first
+post installation monitoring is only
+
+ align:start position:0%
+post installation monitoring is only
+ 
+
+ align:start position:0%
+post installation monitoring is only
+going to take place at the end of
+
+ align:start position:0%
+going to take place at the end of
+ 
+
+ align:start position:0%
+going to take place at the end of
+october
+
+ align:start position:0%
+october
+ 
+
+ align:start position:0%
+october
+okay now we've done some prelim we
+
+ align:start position:0%
+okay now we've done some prelim we
+ 
+
+ align:start position:0%
+okay now we've done some prelim we
+couldn't wait so we've done some
+
+ align:start position:0%
+couldn't wait so we've done some
+ 
+
+ align:start position:0%
+couldn't wait so we've done some
+preliminary sampling and
+
+ align:start position:0%
+preliminary sampling and
+ 
+
+ align:start position:0%
+preliminary sampling and
+we don't see phosphate in the water
+
+ align:start position:0%
+we don't see phosphate in the water
+ 
+
+ align:start position:0%
+we don't see phosphate in the water
+samples above the iron
+
+ align:start position:0%
+samples above the iron
+ 
+
+ align:start position:0%
+samples above the iron
+all right um what we did is um
+
+ align:start position:0%
+all right um what we did is um
+ 
+
+ align:start position:0%
+all right um what we did is um
+there was a concern that any kind of
+
+ align:start position:0%
+there was a concern that any kind of
+ 
+
+ align:start position:0%
+there was a concern that any kind of
+monitoring that we would do
+
+ align:start position:0%
+monitoring that we would do
+ 
+
+ align:start position:0%
+monitoring that we would do
+could potentially drag iron down to
+
+ align:start position:0%
+could potentially drag iron down to
+ 
+
+ align:start position:0%
+could potentially drag iron down to
+below the iron zone
+
+ align:start position:0%
+below the iron zone
+ 
+
+ align:start position:0%
+below the iron zone
+so if you were to try to drive things in
+
+ align:start position:0%
+so if you were to try to drive things in
+ 
+
+ align:start position:0%
+so if you were to try to drive things in
+after they put the iron in a little bit
+
+ align:start position:0%
+after they put the iron in a little bit
+ 
+
+ align:start position:0%
+after they put the iron in a little bit
+of iron would go down with your well
+
+ align:start position:0%
+of iron would go down with your well
+ 
+
+ align:start position:0%
+of iron would go down with your well
+point and then it would remediate the
+
+ align:start position:0%
+point and then it would remediate the
+ 
+
+ align:start position:0%
+point and then it would remediate the
+phosphorus and you'd never find it again
+
+ align:start position:0%
+phosphorus and you'd never find it again
+ 
+
+ align:start position:0%
+phosphorus and you'd never find it again
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we decided to instrument the si
+
+ align:start position:0%
+we decided to instrument the si
+ 
+
+ align:start position:0%
+we decided to instrument the si
+the site as they did the excavations so
+
+ align:start position:0%
+the site as they did the excavations so
+ 
+
+ align:start position:0%
+the site as they did the excavations so
+we put out four different kinds of
+
+ align:start position:0%
+we put out four different kinds of
+ 
+
+ align:start position:0%
+we put out four different kinds of
+instrumentation
+
+ align:start position:0%
+instrumentation
+ 
+
+ align:start position:0%
+instrumentation
+um let's see if i can point a lot of you
+
+ align:start position:0%
+um let's see if i can point a lot of you
+ 
+
+ align:start position:0%
+um let's see if i can point a lot of you
+can't see
+
+ align:start position:0%
+can't see
+ 
+
+ align:start position:0%
+can't see
+uh one of them is right there see that
+
+ align:start position:0%
+uh one of them is right there see that
+ 
+
+ align:start position:0%
+uh one of them is right there see that
+little green cap
+
+ align:start position:0%
+little green cap
+ 
+
+ align:start position:0%
+little green cap
+that's one of these guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's one of those like that little
+
+ align:start position:0%
+uh it's one of those like that little
+ 
+
+ align:start position:0%
+uh it's one of those like that little
+driven mls i showed you except it's made
+
+ align:start position:0%
+driven mls i showed you except it's made
+ 
+
+ align:start position:0%
+driven mls i showed you except it's made
+out of plastic
+
+ align:start position:0%
+out of plastic
+ 
+
+ align:start position:0%
+out of plastic
+we made out of plastic because we
+
+ align:start position:0%
+we made out of plastic because we
+ 
+
+ align:start position:0%
+we made out of plastic because we
+thought that anything steel would start
+
+ align:start position:0%
+thought that anything steel would start
+ 
+
+ align:start position:0%
+thought that anything steel would start
+to corrode like crazy
+
+ align:start position:0%
+to corrode like crazy
+ 
+
+ align:start position:0%
+to corrode like crazy
+inside here if i open this up it's a
+
+ align:start position:0%
+inside here if i open this up it's a
+ 
+
+ align:start position:0%
+inside here if i open this up it's a
+coil of little tubes
+
+ align:start position:0%
+coil of little tubes
+ 
+
+ align:start position:0%
+coil of little tubes
+so every one of those green guys that
+
+ align:start position:0%
+so every one of those green guys that
+ 
+
+ align:start position:0%
+so every one of those green guys that
+are along the shore are these little
+
+ align:start position:0%
+are along the shore are these little
+ 
+
+ align:start position:0%
+are along the shore are these little
+miniature multi-level samplers
+
+ align:start position:0%
+miniature multi-level samplers
+ 
+
+ align:start position:0%
+miniature multi-level samplers
+and the iron zone will go from about the
+
+ align:start position:0%
+and the iron zone will go from about the
+ 
+
+ align:start position:0%
+and the iron zone will go from about the
+surface down to about three feet so we
+
+ align:start position:0%
+surface down to about three feet so we
+ 
+
+ align:start position:0%
+surface down to about three feet so we
+always have one port below the iron
+
+ align:start position:0%
+always have one port below the iron
+ 
+
+ align:start position:0%
+always have one port below the iron
+so we can see phosphate down here and
+
+ align:start position:0%
+so we can see phosphate down here and
+ 
+
+ align:start position:0%
+so we can see phosphate down here and
+then we can see the phosphate disappear
+
+ align:start position:0%
+then we can see the phosphate disappear
+ 
+
+ align:start position:0%
+then we can see the phosphate disappear
+as the water comes up
+
+ align:start position:0%
+as the water comes up
+ 
+
+ align:start position:0%
+as the water comes up
+why does that make sense to everybody so
+
+ align:start position:0%
+why does that make sense to everybody so
+ 
+
+ align:start position:0%
+why does that make sense to everybody so
+we have a bunch of those out in fact i
+
+ align:start position:0%
+we have a bunch of those out in fact i
+ 
+
+ align:start position:0%
+we have a bunch of those out in fact i
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+you have a map maybe page you can't read
+
+ align:start position:0%
+you have a map maybe page you can't read
+ 
+
+ align:start position:0%
+you have a map maybe page you can't read
+the page numbers but the next map
+
+ align:start position:0%
+the page numbers but the next map
+ 
+
+ align:start position:0%
+the page numbers but the next map
+actually shows you where the instruments
+
+ align:start position:0%
+actually shows you where the instruments
+ 
+
+ align:start position:0%
+actually shows you where the instruments
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+that actually shows you the footprint
+
+ align:start position:0%
+that actually shows you the footprint
+ 
+
+ align:start position:0%
+that actually shows you the footprint
+the second kind of device we have
+
+ align:start position:0%
+the second kind of device we have
+ 
+
+ align:start position:0%
+the second kind of device we have
+i don't think any of them are visible
+
+ align:start position:0%
+i don't think any of them are visible
+ 
+
+ align:start position:0%
+i don't think any of them are visible
+from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't see them um
+
+ align:start position:0%
+i don't see them um
+ 
+
+ align:start position:0%
+i don't see them um
+anyway it doesn't really matter um well
+
+ align:start position:0%
+anyway it doesn't really matter um well
+ 
+
+ align:start position:0%
+anyway it doesn't really matter um well
+here's one right here you can't really
+
+ align:start position:0%
+here's one right here you can't really
+ 
+
+ align:start position:0%
+here's one right here you can't really
+see it
+
+ align:start position:0%
+see it
+ 
+
+ align:start position:0%
+see it
+you know those multi-level samplers we
+
+ align:start position:0%
+you know those multi-level samplers we
+ 
+
+ align:start position:0%
+you know those multi-level samplers we
+had in the gravel pit
+
+ align:start position:0%
+had in the gravel pit
+ 
+
+ align:start position:0%
+had in the gravel pit
+it occurred to us why not put some of
+
+ align:start position:0%
+it occurred to us why not put some of
+ 
+
+ align:start position:0%
+it occurred to us why not put some of
+those horizontally
+
+ align:start position:0%
+those horizontally
+ 
+
+ align:start position:0%
+those horizontally
+so when they excavated down three feet
+
+ align:start position:0%
+so when they excavated down three feet
+ 
+
+ align:start position:0%
+so when they excavated down three feet
+we laid one of those white plastic
+
+ align:start position:0%
+we laid one of those white plastic
+ 
+
+ align:start position:0%
+we laid one of those white plastic
+multi-level samplers
+
+ align:start position:0%
+multi-level samplers
+ 
+
+ align:start position:0%
+multi-level samplers
+out 40 feet with ports just like the
+
+ align:start position:0%
+out 40 feet with ports just like the
+ 
+
+ align:start position:0%
+out 40 feet with ports just like the
+vertical ones
+
+ align:start position:0%
+vertical ones
+ 
+
+ align:start position:0%
+vertical ones
+and they all come up to a road box on
+
+ align:start position:0%
+and they all come up to a road box on
+ 
+
+ align:start position:0%
+and they all come up to a road box on
+the shore here so we'll be able to pump
+
+ align:start position:0%
+the shore here so we'll be able to pump
+ 
+
+ align:start position:0%
+the shore here so we'll be able to pump
+those and get samples out underneath the
+
+ align:start position:0%
+those and get samples out underneath the
+ 
+
+ align:start position:0%
+those and get samples out underneath the
+iron there
+
+ align:start position:0%
+iron there
+ 
+
+ align:start position:0%
+iron there
+we also have what we call the fusion
+
+ align:start position:0%
+we also have what we call the fusion
+ 
+
+ align:start position:0%
+we also have what we call the fusion
+samplers
+
+ align:start position:0%
+samplers
+ 
+
+ align:start position:0%
+samplers
+out there same principle i showed you
+
+ align:start position:0%
+out there same principle i showed you
+ 
+
+ align:start position:0%
+out there same principle i showed you
+with the diffusion samplers in the
+
+ align:start position:0%
+with the diffusion samplers in the
+ 
+
+ align:start position:0%
+with the diffusion samplers in the
+gravel pit except these are made out of
+
+ align:start position:0%
+gravel pit except these are made out of
+ 
+
+ align:start position:0%
+gravel pit except these are made out of
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+60 milliliter bottles with a little
+
+ align:start position:0%
+60 milliliter bottles with a little
+ 
+
+ align:start position:0%
+60 milliliter bottles with a little
+nylon fabric on the end
+
+ align:start position:0%
+nylon fabric on the end
+ 
+
+ align:start position:0%
+nylon fabric on the end
+and we actually have chambers that these
+
+ align:start position:0%
+and we actually have chambers that these
+ 
+
+ align:start position:0%
+and we actually have chambers that these
+bottles sit in
+
+ align:start position:0%
+bottles sit in
+ 
+
+ align:start position:0%
+bottles sit in
+uh where they're in contact with the
+
+ align:start position:0%
+uh where they're in contact with the
+ 
+
+ align:start position:0%
+uh where they're in contact with the
+aquifer so what we're gonna do is we
+
+ align:start position:0%
+aquifer so what we're gonna do is we
+ 
+
+ align:start position:0%
+aquifer so what we're gonna do is we
+have a rack of these bottles
+
+ align:start position:0%
+have a rack of these bottles
+ 
+
+ align:start position:0%
+have a rack of these bottles
+at every like say five or six
+
+ align:start position:0%
+at every like say five or six
+ 
+
+ align:start position:0%
+at every like say five or six
+centimeters maybe yeah five or six
+
+ align:start position:0%
+centimeters maybe yeah five or six
+ 
+
+ align:start position:0%
+centimeters maybe yeah five or six
+centimeters
+
+ align:start position:0%
+centimeters
+ 
+
+ align:start position:0%
+centimeters
+we're gonna we lower those in we get
+
+ align:start position:0%
+we're gonna we lower those in we get
+ 
+
+ align:start position:0%
+we're gonna we lower those in we get
+diffusion over very
+
+ align:start position:0%
+diffusion over very
+ 
+
+ align:start position:0%
+diffusion over very
+short distances and then we can pull
+
+ align:start position:0%
+short distances and then we can pull
+ 
+
+ align:start position:0%
+short distances and then we can pull
+these bottles out and analyze them for
+
+ align:start position:0%
+these bottles out and analyze them for
+ 
+
+ align:start position:0%
+these bottles out and analyze them for
+phosphate you know everything is geared
+
+ align:start position:0%
+phosphate you know everything is geared
+ 
+
+ align:start position:0%
+phosphate you know everything is geared
+towards trying to prove
+
+ align:start position:0%
+towards trying to prove
+ 
+
+ align:start position:0%
+towards trying to prove
+or trying to be sure that the phosphorus
+
+ align:start position:0%
+or trying to be sure that the phosphorus
+ 
+
+ align:start position:0%
+or trying to be sure that the phosphorus
+that's in the ground water below the
+
+ align:start position:0%
+that's in the ground water below the
+ 
+
+ align:start position:0%
+that's in the ground water below the
+iron as it comes up through the iron it
+
+ align:start position:0%
+iron as it comes up through the iron it
+ 
+
+ align:start position:0%
+iron as it comes up through the iron it
+goes away
+
+ align:start position:0%
+goes away
+ 
+
+ align:start position:0%
+goes away
+they have a plan if their first plan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know in geologic time it'll all come off
+
+ align:start position:0%
+know in geologic time it'll all come off
+ 
+
+ align:start position:0%
+know in geologic time it'll all come off
+everything's on its way but by that
+
+ align:start position:0%
+everything's on its way but by that
+ 
+
+ align:start position:0%
+everything's on its way but by that
+point the cape will be gone
+
+ align:start position:0%
+point the cape will be gone
+ 
+
+ align:start position:0%
+point the cape will be gone
+you know because it's eroding away
+
+ align:start position:0%
+you know because it's eroding away
+ 
+
+ align:start position:0%
+you know because it's eroding away
+anyways uh the other thing too is
+
+ align:start position:0%
+anyways uh the other thing too is
+ 
+
+ align:start position:0%
+anyways uh the other thing too is
+apparently
+
+ align:start position:0%
+apparently
+ 
+
+ align:start position:0%
+apparently
+um i'm not a g chemist this is where i
+
+ align:start position:0%
+um i'm not a g chemist this is where i
+ 
+
+ align:start position:0%
+um i'm not a g chemist this is where i
+start to really he he knows more about
+
+ align:start position:0%
+start to really he he knows more about
+ 
+
+ align:start position:0%
+start to really he he knows more about
+it than i do
+
+ align:start position:0%
+it than i do
+ 
+
+ align:start position:0%
+it than i do
+uh pete does um
+
+ align:start position:0%
+uh pete does um
+ 
+
+ align:start position:0%
+uh pete does um
+apparently there's a fair amount of
+
+ align:start position:0%
+apparently there's a fair amount of
+ 
+
+ align:start position:0%
+apparently there's a fair amount of
+mineralization that can take place too
+
+ align:start position:0%
+mineralization that can take place too
+ 
+
+ align:start position:0%
+mineralization that can take place too
+so instead of just being a sort of a
+
+ align:start position:0%
+so instead of just being a sort of a
+ 
+
+ align:start position:0%
+so instead of just being a sort of a
+it's like it first absorbs on pretty
+
+ align:start position:0%
+it's like it first absorbs on pretty
+ 
+
+ align:start position:0%
+it's like it first absorbs on pretty
+loosely and then it begins to really
+
+ align:start position:0%
+loosely and then it begins to really
+ 
+
+ align:start position:0%
+loosely and then it begins to really
+work its way into the mineral matrix and
+
+ align:start position:0%
+work its way into the mineral matrix and
+ 
+
+ align:start position:0%
+work its way into the mineral matrix and
+then eventually you can actually get
+
+ align:start position:0%
+then eventually you can actually get
+ 
+
+ align:start position:0%
+then eventually you can actually get
+mineralization when you form things like
+
+ align:start position:0%
+mineralization when you form things like
+ 
+
+ align:start position:0%
+mineralization when you form things like
+appetite
+
+ align:start position:0%
+appetite
+ 
+
+ align:start position:0%
+appetite
+you actually get mineralization to form
+
+ align:start position:0%
+you actually get mineralization to form
+ 
+
+ align:start position:0%
+you actually get mineralization to form
+iron phosphate minerals
+
+ align:start position:0%
+iron phosphate minerals
+ 
+
+ align:start position:0%
+iron phosphate minerals
+which is gets much more solid so they
+
+ align:start position:0%
+which is gets much more solid so they
+ 
+
+ align:start position:0%
+which is gets much more solid so they
+think there's actually a fair amount of
+
+ align:start position:0%
+think there's actually a fair amount of
+ 
+
+ align:start position:0%
+think there's actually a fair amount of
+almost permanent removal for all
+
+ align:start position:0%
+almost permanent removal for all
+ 
+
+ align:start position:0%
+almost permanent removal for all
+practical purposes
+
+ align:start position:0%
+practical purposes
+ 
+
+ align:start position:0%
+practical purposes
+but the light can take a certain amount
+
+ align:start position:0%
+but the light can take a certain amount
+ 
+
+ align:start position:0%
+but the light can take a certain amount
+of phosphorus it's just this huge load
+
+ align:start position:0%
+of phosphorus it's just this huge load
+ 
+
+ align:start position:0%
+of phosphorus it's just this huge load
+for a short period of time is what's
+
+ align:start position:0%
+for a short period of time is what's
+ 
+
+ align:start position:0%
+for a short period of time is what's
+going to kill
+
+ align:start position:0%
+going to kill
+ 
+
+ align:start position:0%
+going to kill
+it's really important
+
+ align:start position:0%
+it's really important
+ 
+
+ align:start position:0%
+it's really important
+right the other thing they did is they
+
+ align:start position:0%
+right the other thing they did is they
+ 
+
+ align:start position:0%
+right the other thing they did is they
+um dosed the pond with alum aluminum
+
+ align:start position:0%
+um dosed the pond with alum aluminum
+ 
+
+ align:start position:0%
+um dosed the pond with alum aluminum
+oxide right
+
+ align:start position:0%
+oxide right
+ 
+
+ align:start position:0%
+oxide right
+to sequester the phosphorus that's in
+
+ align:start position:0%
+to sequester the phosphorus that's in
+ 
+
+ align:start position:0%
+to sequester the phosphorus that's in
+the sediment so that binds pretty
+
+ align:start position:0%
+the sediment so that binds pretty
+ 
+
+ align:start position:0%
+the sediment so that binds pretty
+strongly to the phosphorus
+
+ align:start position:0%
+strongly to the phosphorus
+ 
+
+ align:start position:0%
+strongly to the phosphorus
+the phosphorus no longer leeches up off
+
+ align:start position:0%
+the phosphorus no longer leeches up off
+ 
+
+ align:start position:0%
+the phosphorus no longer leeches up off
+of the bottom
+
+ align:start position:0%
+of the bottom
+ 
+
+ align:start position:0%
+of the bottom
+um now that was a big operation that was
+
+ align:start position:0%
+um now that was a big operation that was
+ 
+
+ align:start position:0%
+um now that was a big operation that was
+a big operation so they're trying a
+
+ align:start position:0%
+a big operation so they're trying a
+ 
+
+ align:start position:0%
+a big operation so they're trying a
+number of different ways to keep the
+
+ align:start position:0%
+number of different ways to keep the
+ 
+
+ align:start position:0%
+number of different ways to keep the
+water quality of the lake
+
+ align:start position:0%
+water quality of the lake
+ 
+
+ align:start position:0%
+water quality of the lake
+excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes yes yeah he gets an anaerobic
+
+ align:start position:0%
+yes yes yes yeah he gets an anaerobic
+ 
+
+ align:start position:0%
+yes yes yes yeah he gets an anaerobic
+hypolining and then you have
+
+ align:start position:0%
+hypolining and then you have
+ 
+
+ align:start position:0%
+hypolining and then you have
+high iron phosphate and it's when you
+
+ align:start position:0%
+high iron phosphate and it's when you
+ 
+
+ align:start position:0%
+high iron phosphate and it's when you
+have turnover you have these algal
+
+ align:start position:0%
+have turnover you have these algal
+ 
+
+ align:start position:0%
+have turnover you have these algal
+blooms
+
+ align:start position:0%
+blooms
+ 
+
+ align:start position:0%
+blooms
+there's a spring bloom and a fall bloom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah 60 feet yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so again the monitoring that we have
+
+ align:start position:0%
+so so again the monitoring that we have
+ 
+
+ align:start position:0%
+so so again the monitoring that we have
+going on are
+
+ align:start position:0%
+going on are
+ 
+
+ align:start position:0%
+going on are
+our vertical sampling this way we have a
+
+ align:start position:0%
+our vertical sampling this way we have a
+ 
+
+ align:start position:0%
+our vertical sampling this way we have a
+few multi-level samples that go out
+
+ align:start position:0%
+few multi-level samples that go out
+ 
+
+ align:start position:0%
+few multi-level samples that go out
+under the lake at different levels this
+
+ align:start position:0%
+under the lake at different levels this
+ 
+
+ align:start position:0%
+under the lake at different levels this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+we have these diffusion samples which i
+
+ align:start position:0%
+we have these diffusion samples which i
+ 
+
+ align:start position:0%
+we have these diffusion samples which i
+don't know if i explain that very well
+
+ align:start position:0%
+don't know if i explain that very well
+ 
+
+ align:start position:0%
+don't know if i explain that very well
+but they're sort of passive and you
+
+ align:start position:0%
+but they're sort of passive and you
+ 
+
+ align:start position:0%
+but they're sort of passive and you
+leave them there
+
+ align:start position:0%
+leave them there
+ 
+
+ align:start position:0%
+leave them there
+we did this because we were concerned
+
+ align:start position:0%
+we did this because we were concerned
+ 
+
+ align:start position:0%
+we did this because we were concerned
+that anytime you pump a water sample you
+
+ align:start position:0%
+that anytime you pump a water sample you
+ 
+
+ align:start position:0%
+that anytime you pump a water sample you
+disturb the flow
+
+ align:start position:0%
+disturb the flow
+ 
+
+ align:start position:0%
+disturb the flow
+and so these are set up in very close
+
+ align:start position:0%
+and so these are set up in very close
+ 
+
+ align:start position:0%
+and so these are set up in very close
+intervals these balls are all stacked so
+
+ align:start position:0%
+intervals these balls are all stacked so
+ 
+
+ align:start position:0%
+intervals these balls are all stacked so
+we can see very detailed gradients
+
+ align:start position:0%
+we can see very detailed gradients
+ 
+
+ align:start position:0%
+we can see very detailed gradients
+because we're trying to figure out where
+
+ align:start position:0%
+because we're trying to figure out where
+ 
+
+ align:start position:0%
+because we're trying to figure out where
+does all the reaction take place some of
+
+ align:start position:0%
+does all the reaction take place some of
+ 
+
+ align:start position:0%
+does all the reaction take place some of
+the chemists say
+
+ align:start position:0%
+the chemists say
+ 
+
+ align:start position:0%
+the chemists say
+the phosphorus is going to come all the
+
+ align:start position:0%
+the phosphorus is going to come all the
+ 
+
+ align:start position:0%
+the phosphorus is going to come all the
+way up through the elemental iron until
+
+ align:start position:0%
+way up through the elemental iron until
+ 
+
+ align:start position:0%
+way up through the elemental iron until
+it gets to the rusty part at the top
+
+ align:start position:0%
+it gets to the rusty part at the top
+ 
+
+ align:start position:0%
+it gets to the rusty part at the top
+and the barrier only had to be an inch
+
+ align:start position:0%
+and the barrier only had to be an inch
+ 
+
+ align:start position:0%
+and the barrier only had to be an inch
+thick but the bottom three feet is
+
+ align:start position:0%
+thick but the bottom three feet is
+ 
+
+ align:start position:0%
+thick but the bottom three feet is
+worthless others are saying no it'll
+
+ align:start position:0%
+worthless others are saying no it'll
+ 
+
+ align:start position:0%
+worthless others are saying no it'll
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+at depth and we don't know um
+
+ align:start position:0%
+at depth and we don't know um
+ 
+
+ align:start position:0%
+at depth and we don't know um
+so um anyway so that's
+
+ align:start position:0%
+so um anyway so that's
+ 
+
+ align:start position:0%
+so um anyway so that's
+those are the various monitoring methods
+
+ align:start position:0%
+those are the various monitoring methods
+ 
+
+ align:start position:0%
+those are the various monitoring methods
+except for one other
+
+ align:start position:0%
+except for one other
+ 
+
+ align:start position:0%
+except for one other
+the other method
\ No newline at end of file
diff --git a/O92M9n8uIGY.txt b/O92M9n8uIGY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9578a49773fa2bda07917499e27e4c2820ea66de
--- /dev/null
+++ b/O92M9n8uIGY.txt
@@ -0,0 +1,3426 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+First, welcome everybody
+and good afternoon.
+
+So the question is about
+the master equation.
+
+We know is that the
+most general master
+
+equation has to have
+the Lindblad form.
+
+And the Lindblad form
+has a jump operator
+
+which is providing dissipation.
+
+In its simplest
+case, a jump operator
+
+is just the sigma minus operator
+for spontaneous emission, which
+
+takes us from the excited
+state to the current state.
+
+And when we have the Linblad
+form, the jump operator
+
+and it's commission conjugate,
+like sigma plus, sigma minus,
+
+appear on the right-hand
+side of the master equation
+
+with the statistical operator
+here, here, and in the middle.
+
+There are plus-minus
+signs in factors of two.
+
+So I don't have a
+intuitive explanation
+
+where the factors come from.
+
+They come from the derivation.
+
+But you have a question
+about it, Nancy?
+
+AUDIENCE: So after
+writing the Linblad form,
+
+we get gamma [INAUDIBLE], which
+we are saying for the r dot
+
+vector, we were
+writing [INAUDIBLE].
+
+And we said that
+they are directly
+
+coming from the first one?
+
+PROFESSOR: Yes.
+
+So let's go right here.
+
+That's actually what we
+were going to discuss today.
+
+We want to discuss, today,
+solutions of the optical Bloch
+
+equations.
+
+And just to remind you, we
+derived a master equation
+
+for the density matrix.
+
+And this master equation,
+through the interaction
+
+with the reservoir,
+is acting a term
+
+to the Hamiltonian evolution.
+
+And this is showing right here.
+
+These are the interactions
+with the reservoir.
+
+And in the case of the
+optical Bloch equation
+
+and spontaneous
+emission, we have
+
+only one Lindblad
+operator, which
+
+is Lindblad operator,
+sigma minus,
+
+for spontaneous emission.
+
+So this here is
+the master equation
+
+for the two-level system
+interacting with a vacuum
+
+through spontaneous emission.
+
+And by substituting the
+two-level density matrix,
+
+has three non-trivial
+components-- sure, it's a 2
+
+by 2 matrix, but the
+craziest one-- and so
+
+we can transform from the matrix
+elements of the density matrix
+
+to three other coefficient,
+which come in very handy,
+
+because they allow a simple
+geometric interpretation.
+
+And this is the Bloch vector.
+
+And so the master equation,
+which is shown here,
+
+turns into a differential
+equation for the Bloch vector.
+
+And those two equations
+are identical,
+
+we've just done
+those substitution.
+
+But your question is now about--
+
+AUDIENCE: Plus gamma, because
+we have negative gamma over 2,
+
+which is from the
+first and last term.
+
+But the gamma term should
+be positive, right?
+
+PROFESSOR: This one here?
+
+AUDIENCE: No.
+
+PROFESSOR: This one?
+
+AUDIENCE: Yes.
+
+Because that's negative gamma
+over 2 times negative 2.
+
+PROFESSOR: No.
+
+I mean, first of all, this
+is a differential equation
+
+for r dot.
+
+OK.
+
+This is a differential
+equation for the Bloch vector.
+
+And we have here three
+different relaxation rates,
+
+which are gamma, gamma
+over 2, and gamma over 2.
+
+And they are all
+negative, because they
+
+are relaxation rates.
+
+This here is not
+a perfecter of r.
+
+It is sort of a constant.
+
+And it means, in the
+long time limit-- I mean,
+
+what happens if you have a
+system which spontaneously
+
+decay after a while?
+
+The r vector is not 0.
+
+The r vector is hanging down.
+
+The system is in
+its ground state.
+
+And this is exactly that.
+
+Wait.
+
+Am I r dot?
+
+Yes.
+
+The effect is the system,
+the differential equation,
+
+has to relax towards
+the equilibrium.
+
+You can actually
+re-write this equation,
+
+r dot equals a matrix times
+r minus r equilibrium.
+
+So here is the matrix of
+the optical Bloch equation.
+
+So if you re-write that that
+r dot is the matrix times r
+
+minus r equilibrium,
+then r equilibrium times
+
+the matrix gives
+something constant.
+
+And this is exactly this here.
+
+But it's a
+mathematical identity.
+
+Just look at it.
+
+There is no assumption.
+
+It's an exact re-writing
+of the equation.
+
+So it is this
+equation which will
+
+be in the focus of our
+attention not only today,
+
+but also when we talk
+about light forces.
+
+The first thing we
+did is we wanted
+
+to discuss the Mollow triplet.
+
+And just as a reminder,
+we have talked about,
+
+at the beginning
+of last class, we
+
+talked about the fluorescence.
+
+An atom is excited by
+mono-chromatic laser light.
+
+And at low intensity,
+a delta function
+
+emits exactly the same
+frequency of light
+
+which is provided
+by the laser light.
+
+So the incoming and
+outgoing photons
+
+have exactly the same frequency.
+
+And this is simply a consequence
+of energy conservation.
+
+But at higher intensity,
+we have sidebands.
+
+And we understand
+intuitively that we
+
+have sidebands because the
+system is Rabi oscillation.
+
+So same, classically,
+we have an emitter
+
+which has some modulation
+that creates sidebands.
+
+But is rather easy
+to understand is,
+
+by diagonalizing
+the 2 by 2 matrix,
+
+we find that we have a splitting
+of excited state with n photons
+
+and grounds it with
+n plus 1 photons.
+
+So we have sort of a
+plus and minus state.
+
+And if we look at the
+possible transitions,
+
+we immediately find
+the explanation
+
+for the Mollow triplet.
+
+There are three
+different frequencies
+
+which can be emitted
+in transitions
+
+between rest states.
+
+What is much more subtle,
+what cannot be obtained from
+
+a preterbative
+treatment, is the width,
+
+how wide are those peaks
+in the Mollow triplet.
+
+And there is tens
+and tens of pages
+
+in atom photo interaction.
+
+But at least, for
+two limiting cases,
+
+I could show you what the width
+of the peak is by first saying,
+
+if you have delta
+equals 0 and g equals
+
+0, the matrix, which
+determines the dynamics,
+
+has three eigenvalues,
+gamma over 2, gamma over 2,
+
+and gamma.
+
+And now, if we detune, we
+add a rotation along z.
+
+If you drive the system strong,
+it corresponds to rotation
+
+around x.
+
+You probably
+remember, from 8.421
+
+the spin in a magnetic field.
+
+It rotates.
+
+In a frame, rotating
+with omega, it
+
+rotates at the detuning delta.
+
+But if you drive it, we make
+it flip along the x-axis.
+
+So we find exactly that here.
+
+And then, it's an intuitive way
+to sort of matrix, if you want,
+
+solve the matrix mathematically.
+
+But intuitively, what happens
+is, if you have a z-rotation,
+
+we don't change in
+this eigenvalue.
+
+And the rotation is just
+aiding i omega-- omega
+
+is the rotation-- to x and
+y, because x and y are now
+
+rotating.
+
+So therefore, we obtained
+that, in the case of detuning
+
+the z-rotation, we have minus
+gamma, minus gamma over 2,
+
+minus gamma over 2.
+
+And here, what appears here
+is the rotation frequency.
+
+And then, if you rotate around
+the x-axis, then, of course,
+
+nothing happens, but what
+used to be the x-axis.
+
+So we get one eigenvalue
+with minus gamma over 2.
+
+But the y and z
+eigenvector are rotated.
+
+And hand-wavingly,
+I can tell you.
+
+But you can show
+it mathematically
+
+that this means the two
+new eigenvectors have
+
+the average of those
+two damping terms.
+
+And this is 3/4 gamma.
+
+So at least, for the two
+cases for large detuning
+
+and strong drive, I was, with
+a little bit of intuition,
+
+showing you and
+deriving for you where
+
+the non-trivial bits of the
+Mollow triplet comes from.
+
+So I hope you're,
+at least, impressed
+
+that these optical Bloch
+equations are powerful
+
+and allow us to make
+predictions which
+
+would be difficult
+to obtain otherwise.
+
+Any questions about that?
+
+About the Bloch vector,
+the differential equation,
+
+and the spectrum of
+the immediate light?
+
+OK, we want to now discuss one
+other aspect, which is actually
+
+fairly simple.
+
+We want to discuss
+steady state solution.
+
+For the steady state solution,
+we just go to the differential
+
+equation and say, the
+left-hand side is 0.
+
+That immediately gives us a
+solution for the Bloch vector.
+
+It gives us a Lorentzian.
+
+But for strong drive,
+it has a term here,
+
+which we will
+immediately realize
+
+that this gives us
+power broadening.
+
+And then the steady state
+Bloch vector is g delta,
+
+g gamma over 2, delta square
+plus gamma square over 4.
+
+So we can now use this
+solution for steady state
+
+and discuss everything we want
+what happens in steady state.
+
+So one question is, if
+you have an atom laser
+
+beam in steady state, how
+much light is absorbed?
+
+Well, the basic equation is,
+if you have a charged q which
+
+moves in an electric field,
+that means work is done.
+
+So therefore, the absorbed
+power is related to that.
+
+And we can now combine q dr/dt.
+
+And this is nothing
+else than the derivative
+
+of the dipole moment.
+
+And then we calculate
+the average.
+
+So with that, we find the
+result they the absorbed
+
+power is given by--
+just one second-- e0?
+
+Yeah.
+
+We express now e0 by
+the Rabi frequency.
+
+And h bar appears in omega.
+
+But the important thing is that
+we need now the dipole moment
+
+or the derivative of
+the dipole moment.
+
+And the dipole moment is
+given by the coherences
+
+of the density matrix.
+
+And that is, if you look
+at the substitution,
+
+is the x and y component of
+the optical Bloch vector.
+
+But now what we
+need, of course, we
+
+need only the component of
+the dipole moment, which
+
+gives a non-vanishing
+term with cosine omega t.
+
+That means, what we
+need is-- I mean,
+
+that's like an
+harmonic oscillator.
+
+The component of
+the motion which
+
+is responsible for
+absorption is the one
+
+which is in quadrature, which is
+assigned only the d-component.
+
+And that, you have to go
+back and look by inspection.
+
+But this is exactly what the
+y-component of the Bloch vector
+
+does for us.
+
+It will become important
+later on for optical forces.
+
+So we have the
+optical Bloch vector.
+
+We are in the rotating frame.
+
+And the one component,
+which is the x-component,
+
+is in phase with the light.
+
+And the y-phase is 90 degree
+out of phases in quadrature.
+
+And for absorption it's, of
+course, the in quadrature
+
+component which is
+relevant and which
+
+determines light scattering.
+
+OK, this is the absorbed light.
+
+And we don't measure
+power in watt,
+
+we measure power in the
+number of absorbed photons.
+
+This is the natural unit here.
+
+And for that, we have to divide
+the expression by h bar omega.
+
+And that means now that the
+number of photons absorbed
+
+per unit time is
+given by the Rabi
+
+frequency and the y-component
+of the Bloch vector.
+
+Well, we can ask
+another question
+
+and ask, what is the
+number of emitted photons?
+
+Well, the number
+of emitted photons
+
+is related to the population
+in the excited state.
+
+We take the population
+in the excited state
+
+and multiply with gamma.
+
+This is spontaneous emission
+out of the excited state.
+
+Now, the excited state can be--
+the excited state population,
+
+you have to look up
+at the substitution,
+
+but is related to
+the z-component
+
+of the optical Bloch vector.
+
+To remind you, the
+z-component is the difference
+
+of population between
+excited and ground state.
+
+But the sum of the two is one.
+
+So therefore, this is now
+the excited state population.
+
+And here is our
+steady state solution.
+
+Here is our steady state
+solution for the z-component.
+
+And by using that
+now, we find that we
+
+have the result with the
+Lorentzian denominator.
+
+And what we have here is
+gamma g square over 4.
+
+And now, of course,
+if you compare
+
+that with the
+solution for our y,
+
+for the number of absorbed
+photons, you find-- well,
+
+it shouldn't come
+as a big surprise--
+
+that the number of absorbed
+photon in steady state
+
+is equal to the number
+of emitted photon.
+
+So this is one case, one
+important part of the solution.
+
+And I should have shown
+that to you earlier.
+
+When we look at the
+two components, the x
+
+and y-component,
+the y-component is
+
+absorbed, if it is Lorentzian.
+
+Whereas, the x-component
+is dispersive.
+
+Just by inspection if these two
+expressions, here is a delta.
+
+And the delta makes the
+x-component anti-symmetric.
+
+And the y-component is symmetric
+with respect to the origin.
+
+So what we see here is
+we have a Lorentzian.
+
+The Lorentzian has a natural
+line broadening by gamma.
+
+So the full width
+at half maximum
+
+is gamma, but only in
+the limit of 0 drive.
+
+When we drive it, we have
+an additional broadening,
+
+which is called
+power broadening.
+
+So for absorption, the
+full width at half maximum
+
+is 2 times gamma square
+over 4 plus g square over 2.
+
+And this last term goes by
+the name power broadening
+
+or saturation broadening.
+
+Just to avoid common confusion,
+if you go to very high power,
+
+that least term
+doesn't play a role.
+
+How does the line width scale
+with power in power broadening?
+
+Linear in power?
+
+Quadratic in power?
+
+Square root of power?
+
+AUDIENCE: Square root?
+
+PROFESSOR: Square root of power.
+
+Yeah.
+
+So in that sense,
+yes, power broadening
+
+only goes to the
+square root of power.
+
+It's, in essence,
+the Rabi frequency.
+
+If you drive the system
+at the Rabi frequency,
+
+it gets power broadened
+by the Rabi frequency.
+
+And I think that's a pre-factor
+which is 2 or square root 2.
+
+But in essence, power broadening
+scales with the Rabi frequency.
+
+So let us quickly
+discuss the case
+
+when we go to very high power,
+very high Rabi frequency.
+
+At that moment, you can just see
+it in the solution on the page
+
+above.
+
+The z-component of the optical
+Bloch vector becomes 0.
+
+That means there is no
+population difference
+
+between excited and
+ground state anymore.
+
+We often describe the
+limit of high power
+
+by introducing a
+saturation parameter, which
+
+is defined here.
+
+Saturation is discussed
+in more details in Part 1
+
+of the course.
+
+But I want to relate
+it here to the solution
+
+with the optical Bloch vector.
+
+The z-component, which
+is the difference
+
+between ground and
+excited state population,
+
+now has a very simple
+form, 1 over 1 plus s.
+
+The population to be in
+the excited state is 1/2.
+
+That's what we get
+at infinite power.
+
+And then, if the
+power is finite,
+
+it is multiplied by
+s times s plus 1.
+
+In the power broadened line
+width is the natural line
+
+width, which gives
+the line width
+
+in the limit of
+low power, and then
+
+you multiply with the
+square root 1 plus s.
+
+So what does it mean to have
+a saturation parameter of 1?
+
+Well, if you just look
+how it was defined,
+
+if you have the ground and the
+excited state at a saturation
+
+parameter of-- first, at
+a saturation of infinite,
+
+you have 50-50 population.
+
+And at a saturation parameter
+of 1, you are 1/2 way to 50-50.
+
+That means you have
+3/4 population here
+
+and 1/4 population there.
+
+So at this case, the number of
+photons emitted per unit time,
+
+which is always given
+by this formula,
+
+becomes now gamma over 4.
+
+So at a saturation
+parameter of 1,
+
+the emission rate
+is gamma over 4.
+
+At a saturation
+parameter of infinity,
+
+the spontaneous emission
+rate is gamma over 2.
+
+Any questions about
+steady state solution?
+
+[INAUDIBLE]?
+
+AUDIENCE: So what
+we derived right now
+
+is a spontaneous emission rate.
+
+Does the optical Bloch
+equation say anything
+
+about the stimulated emission?
+
+Or is that the fact that it
+just doesn't have [INAUDIBLE]?
+
+PROFESSOR: Stimulated emission
+is built in the optical Bloch
+
+equations for negligible damping
+contained Rabi oscillation.
+
+And Rabi oscillation is
+the stimulated emission.
+
+So this is being built in.
+
+However, it seems to be
+a describing the drive
+
+field by a classical
+field by a Rabi frequency.
+
+We are not really
+accounting for the number
+
+of photons exchanged with that.
+
+So in a way, the
+driving field is always
+
+treated in the
+undepleted approximation.
+
+It's a C number.
+
+But in the drive through
+system, but of course,
+
+you can immediately lead
+from the Rabi oscillation
+
+the exchange of excitations
+between the atomic system
+
+and the drive field.
+
+So yes, the optical Bloch
+equations contains that,
+
+but not in the photon picture.
+
+AUDIENCE: If you have
+Rabi oscillations,
+
+you can kind of guess
+that, every time you
+
+go down you
+simulated the events.
+
+In space, say, you don't
+have Rabi oscillations.
+
+Can you still somehow
+extract the rate?
+
+PROFESSOR: I hope the question
+we answer will become crystal
+
+when we discuss quantum
+Monte Carlo simulations.
+
+AUDIENCE: OK.
+
+PROFESSOR: In quantum
+Monte Carlo simulation,
+
+we have an ensemble of atom.
+
+And the atoms all do
+Rabi oscillations.
+
+But in steady state,
+they do it out of phase.
+
+So you have atoms
+in your ensemble
+
+which, at a given time, absorb.
+
+And others emit in
+a stimulated way.
+
+And the effect cancels
+out in steady state.
+
+Other questions?
+
+Yes?
+
+AUDIENCE: So you're
+saying, in steady state,
+
+they kind of de-cohere.
+
+And you don't have any net
+change in those populations.
+
+Do you still get
+the triplet lines
+
+if you don't have a modulation
+of your intensity beam?
+
+PROFESSOR: Yes.
+
+Absolutely.
+
+The Mollow triplet is a
+feature in steady state.
+
+And maybe let me explain
+that, because it's
+
+an interesting discussion.
+
+What will happen is, in
+steady state in your ensemble,
+
+you don't have
+Rabi oscillations.
+
+But if you would
+look at one atom,
+
+you see Rabi oscillations.
+
+It's just when you average over
+all atoms in your ensemble,
+
+the phase of the Rabi
+oscillation has averaged out.
+
+So in other words, for
+instance, what would happen
+
+is the following.
+
+If you take a steady
+state solution
+
+and you ask, what is the dipole
+moment as a function of time
+
+in steady state, you
+will find that this is 0.
+
+So you would then
+ask, hey, where
+
+is the light emitted, because
+isn't the light emitted
+
+by a time-dependent
+dipole moment?
+
+What you really
+have to do is, when
+
+you want to study light
+emission in steady state,
+
+you can't look at
+expectation values
+
+because they're not changing
+as a function of time.
+
+What you have to do is you
+have to look at the correlation
+
+function.
+
+And the correlation
+function sort of
+
+tells you-- let me just use
+it for Rabi oscillation.
+
+If one atom is in the excited
+state, a Rabi period later,
+
+it would be again in
+the excited state.
+
+So although you are
+in steady state,
+
+you have correlations because,
+if you look at your ensemble
+
+and see there is a fluctuation
+where the atom is excited,
+
+you will actually find
+a co-related fluctuation
+
+a Rabi period later.
+
+So in steady state, when
+you want to study dynamics
+
+like the Mollow
+triplet, you should not
+
+look at the solution
+for the dipole.
+
+You should look for the
+solution of the correlation
+
+of the correlation function.
+
+And I made this cryptic
+remark on Wednesday
+
+that this correlation function
+follows the same differential
+
+equation as the
+expectation value.
+
+Therefore, when I try to
+discuss for you the line
+
+width of the Mollow
+triplet, I simply
+
+use the matrix for
+the Bloch vector
+
+knowing that it is the same
+matrix, the same differential
+
+equation which will describe
+this correlation function.
+
+But it is important here
+that, in steady state,
+
+the average values are 0,
+but we have fluctuations.
+
+And it is the
+fluctuations which emit
+
+the light, the fluctuations
+which emit the Mollow triplet.
+
+And fluctuations are described
+by quantities like this.
+
+So it's a little bit beyond what
+I want to discuss in the book,
+
+but atom photon indirection has
+a wonderful chapter on that.
+
+Other questions?
+
+There is another important case
+of the optical Bloch equation,
+
+which is the weak excitation
+limit, which is simple.
+
+But I've already asked you to
+look at it in your homework
+
+assignment.
+
+OK, let's now come to the
+third aspect of master equation
+
+solutions of optical
+Bloch or master equation.
+
+And these are damped
+vacuum Rabi oscillations.
+
+Yes.
+
+I really like this
+example in this chapter,
+
+so I hope-- well, I think
+we have many highlights,
+
+but this is a
+really nice example.
+
+I learned it from
+Professor [? Schwan ?]
+
+when he introduced it.
+
+And what I like
+about it is I can
+
+use it to show you what
+other Lindblad operators may
+
+be important.
+
+So you suddenly understand,
+in a bigger context,
+
+what the master equation is.
+
+And then we continue
+with an atomic cavity.
+
+And the damping is no longer
+by spontaneous emission.
+
+The damping is by photons
+sneaking out of the cavity.
+
+So we really learn
+something which
+
+is similar to optical
+Bloch equation,
+
+but in another context.
+
+And often, if you see two
+different realizations
+
+of similar physics,
+you maybe realize more
+
+what is more generic and
+what is special for instance
+
+of spontaneous emission,
+so I really like that.
+
+But also, I found
+that this example
+
+allows me to introduce to you
+the concept of the quantum Zeno
+
+effect and the concept
+of atypical elimination
+
+of coherences.
+
+So it's a wonderful
+example which connects us
+
+with a number of
+really neat concepts.
+
+So with that promise,
+let me remind you
+
+that, in the master
+equation, when we derived it,
+
+we got an exact expression
+when we did second order
+
+perturbation theory.
+
+And the structure which came
+was this double commutator
+
+between the interaction operator
+and the steady state operator.
+
+Just to remind you, in the
+interaction picture-- first
+
+in the non-interacting,
+in the normal picture,
+
+the derivative of the density
+matrix is a commutator with h.
+
+In the interaction
+picture, it's a commutator
+
+with v with the interaction.
+
+But when we iterate an
+equation to second order,
+
+we plot the first result
+into the equation.
+
+Then we get, in second
+order, this structure.
+
+And if I, by expanding
+the commutator,
+
+we obtain the
+following structure.
+
+And that gave rise
+to the Lindblad form
+
+of the master equation, which
+is rho dot equals a Hamiltonian
+
+part.
+
+But then we have now a
+sum, v, the interaction
+
+with the environment,
+can be a sum of mu
+
+dot b and b-- and so
+an external b field
+
+times magnetization and dipole
+moment times an electric field.
+
+It can have a number of terms.
+
+And therefore, in general, we
+have more than one Lindblad
+
+operator.
+
+But the structure
+is always given
+
+by this commutator in
+the following form.
+
+OK.
+
+So we have this
+general derivation.
+
+But until now, we
+have only looked
+
+at a system which
+is a simple atom.
+
+And the environment
+was the vacuum.
+
+So this is our environment.
+
+And also, the environment was
+always in the vacuum state.
+
+So these were our assumptions.
+
+And that means that the
+only Lindblad operator,
+
+the only jump
+operator in this sum
+
+is sigma minus for
+spontaneous emission.
+
+And by inserting
+this jump operator
+
+into the Lindblad form
+of the master equation,
+
+we find the optical
+Bloch equation.
+
+But now let's do cavity QED.
+
+And there are lots
+of experiments
+
+going on in the research
+group of Professor Vuletic.
+
+And in this situation,
+our system is actually not
+
+just the atoms, it's the
+atoms and a single mode
+
+of the cavity.
+
+This is our system.
+
+And the environment
+are all other modes.
+
+So in other words,
+the atoms interacting
+
+with a single mode of the
+cavity, this is our system.
+
+And the environment
+is now accessed
+
+by emitting-- the
+atom is emitting.
+
+Or there are photons
+leaking out of the cavity,
+
+because the cavity mirrors do
+not have 100.0% reflectivity.
+
+I will immediately reduce
+it to one Lindblad operator.
+
+But we could now say that this
+system, in its full glory,
+
+has four different
+Lindblad operators which
+
+provide dissipation,
+which provide coupling
+
+to the environment.
+
+The first one is simply
+what we had before,
+
+spontaneous emission.
+
+However, if we allow that
+the environment is thermal,
+
+we have to multiply.
+
+Well, whenever you have
+emission and you have already
+
+population in a
+mode, and thermal
+
+is a number of thermal photons
+in every mode, on average,
+
+then you have an extra bosonic
+or photonic stimulation term.
+
+That's stimulated emission,
+but not by the laser beam.
+
+It's now stimulated emission
+by a thermal occupation
+
+of all the other modes.
+
+So just assume,
+for that purpose,
+
+that you have a cavity here.
+
+But the cavity is now
+in a black body cavity.
+
+And everything, all
+modes in the vacuum,
+
+are no longer vacuum modes.
+
+They are occupied
+within thermal photons.
+
+Of course, if this
+is the case, we
+
+have also the opposite effect.
+
+You can see by
+unitality, namely,
+
+that we can have--
+oops, n should be--
+
+but that we have an
+absorption process.
+
+We absorb a photon from
+the thermal background.
+
+But now, we have
+two more processes.
+
+And this is photons
+leaking out of the cavity.
+
+When a photon leaks out of
+the cavity, this leakage
+
+is not coupled to the atom,
+it's coupled to the mode.
+
+We describe the mode
+by a mode operator, a.
+
+So now, the leakage
+out with the rate,
+
+kappa, is presented by that.
+
+But in the case of
+thermal photons,
+
+we have stimulation by
+the thermal photons.
+
+And also, if we have
+thermal photons,
+
+photons cannot only
+leak out of the cavity,
+
+they can also leak
+into the cavity.
+
+So we have assumed here that
+we have n thermal photons
+
+in each mode of the environment.
+
+So in other words, if you
+want to look at, for instance,
+
+Serge Haroche does experiment
+in the wonderful experiments
+
+in the microwave domain.
+
+He has cavities at, I think,
+gigahertz frequencies.
+
+And even at cryogenic
+temperature,
+
+there are occasional thermal
+photons in this mode.
+
+But you are now
+expert enough that you
+
+would know how to
+set up a master
+
+equation for that situation.
+
+But I want to discuss
+simple limiting cases.
+
+So I think you are
+glad to hear that we
+
+are choosing 0 thermal photons.
+
+So therefore, we assume we
+have a cavity in vacuum.
+
+And therefore, we only need the
+Lindblad operators, L1 and L2.
+
+And we want to describe the
+system which has only one
+
+x, which has, maximally,
+one excitation.
+
+We try to keep the
+density matrix small,
+
+so we only want to
+consider three states.
+
+So when I said there
+is one excitation,
+
+it is, of course,
+the state which
+
+has no photon in
+the excited state.
+
+The state two is we have the
+ground state and one photon.
+
+And those two states are
+coupled by the cavity.
+
+And since I really want to
+discuss the simplest case which
+
+already illustrates all
+the concepts I want to do
+
+is they are coupled by the
+vacuum Rabi oscillation.
+
+And we have discussed
+vacuum Rabi oscillation
+
+in part one of the course.
+
+But it's very simple.
+
+It's just two levels coupled.
+
+It's a 2 by 2 matrix,
+so this is something
+
+you are familiar with.
+
+But now, the master equation,
+the Lindblad operator
+
+bring in the third
+level, which is
+
+the ground state
+without photons.
+
+And this can happen in two ways.
+
+One is spontaneous emission.
+
+The excited state emits,
+but not into the cavity.
+
+It emits to the side.
+
+So spontaneous
+emission can take us
+
+down here, or when the
+excitation is in the cavity.
+
+We have one photon
+in the cavity,
+
+this photon can leak out.
+
+And the rate that is kappa.
+
+And since we have talked
+about spontaneous emission
+
+so much with the
+optical Bloch equation,
+
+we want to discuss now the case
+where gamma can be neglected.
+
+And we want to
+understand what happens
+
+when the only
+dissipation of the system
+
+comes by photons leaking
+out of the cavity.
+
+Any questions about the
+system and the motivation?
+
+So our system is now
+an atom with a cavity.
+
+The environment is a vacuum.
+
+But the process of
+dissipation relaxation
+
+is no longer
+spontaneous emission,
+
+it is the photon leaking
+out of the cavity.
+
+And this realizes
+different physics.
+
+And I hope, by experiencing
+these different physics,
+
+you have sort of a nicer
+picture what is dissipation
+
+in an open system
+and what is similar,
+
+but what is also different
+or spontaneous emission.
+
+[? Koren? ?]
+
+AUDIENCE: If you're considering
+only kappa, isn't there
+
+an equivalent process of
+order kappa that takes you
+
+to ground of two
+photons in the cavity?
+
+Don't you have to consider
+that state as well?
+
+That term would be of
+order kappa as well.
+
+PROFESSOR: So great.
+
+The question is I
+restrict the Hilbert
+
+space to maximally
+one excitation.
+
+So this is how we start out
+with our differential equation.
+
+AUDIENCE: Oh, this
+isn't in a thermal bath?
+
+I thought we were
+assuming we had a--
+
+PROFESSOR: Oh, sorry.
+
+I first made
+everything complicated.
+
+But then I said, now,
+let's make it simple.
+
+We assumed the
+thermal bath is 0.
+
+So we reduced--
+
+In a way, yes, I told you here
+are four Lindblad operators,
+
+and you can describe
+everything you want.
+
+But then I said, hey,
+two of them become 0,
+
+because we eliminate
+the thermal bath.
+
+And now I make the approximation
+that spontaneous emission
+
+is negligible.
+
+And now we are back
+to the situation
+
+which is nice for
+classroom discussion.
+
+We've only one
+term left, and this
+
+is the leaking of the
+photon out of the cavity.
+
+So I will show to
+you what happens.
+
+But ultimately, when we make
+the cavity better and better
+
+and kappa smaller and smaller,
+I will say, wait a moment.
+
+We now have to check that
+our solution is still
+
+consistent with our assumption
+that spontaneous emission can
+
+be neglected.
+
+So that's sort of
+what you want to do.
+
+Yes.
+
+Let's just get two more pages.
+
+OK.
+
+So what we want to
+do is we want to look
+
+for the dynamics of the system.
+
+We start out in state one.
+
+So we inject one excited
+atom into the cavity.
+
+And what we want
+to learn now is--
+
+and it has a lot of
+interesting physics in it--
+
+what will happen as a function
+of this new dissipation, kappa.
+
+Well, qualitatively, it
+should be pretty clear.
+
+If kappa is 0, we have
+vacuum Rabi oscillation
+
+between state one and state two.
+
+If you then put a little
+bit kappa into the system,
+
+you have a Rabi oscillation,
+but they are getting damped.
+
+And like in any oscillator,
+if you crank up the damping,
+
+you go into an
+overdamped regime.
+
+And this is exactly what
+the equations give us,
+
+Rabi oscillation, damped
+Rabi oscillation, and then
+
+overdamped regime.
+
+And actually, the most
+interesting regime for us
+
+will be the overdamped regime.
+
+That's something we
+haven't encountered.
+
+But let me just, before
+we go there, write down
+
+the master equation for you.
+
+So without the photon
+leaking out of the cavity,
+
+we have the following terms.
+
+Without the photon leaking
+out of the cavity, of course,
+
+state three is not involved.
+
+We simply have Rabi oscillation
+between state one and state
+
+two.
+
+And this is actually also like
+the optical Bloch equation.
+
+Without damping, it's simply
+the Jaynes-Cummings model.
+
+Minus, that's this.
+
+And for the coherences,
+we get omega 0
+
+rho 1, 1 minus rho 2, 2.
+
+But now, we put in
+the terms with kappa.
+
+The state, which is
+the state two, which
+
+is the ground state
+with the photon,
+
+has now a damping term, because
+the photon can leak out.
+
+We get, of course, an
+equation for the ground
+
+state, the population,
+the photon leaks out.
+
+And we populate state three.
+
+And the damping also
+affects the coherences.
+
+And the form of the master
+equation, the Lindblad form,
+
+gives us the following
+damping term.
+
+So there are two
+new concepts which
+
+I promised you to introduce.
+
+One is the idiopathic
+elimination of coherences.
+
+And the second one is
+the quantum Zeno effect.
+
+So first of all, if you look
+at the differential equation,
+
+and when kappa is small,
+in particular, kappa
+
+is smaller than 2 times
+the vacuum Rabi frequency,
+
+then the population to be in the
+excited state, which is rho 2,
+
+2, undergoes Rabi oscillation.
+
+And those Rabi oscillations,
+this population
+
+is damped by e to
+the minus kappa t.
+
+So what I want to discuss
+now is the overdamped case.
+
+And actually, before
+I derive it for you,
+
+I wanted to ask you
+some clicker question.
+
+I'm afraid I put the books
+out, but somebody put it away.
+
+So nobody took clickers?
+
+So why don't we just
+pass them around?
+
+And I can already
+formulate the question.
+
+I think you know by now
+that I have a preference
+
+to maybe ask you questions about
+really simple quantum physics.
+
+Quantum physics is sadly
+enough that nobody fully
+
+understands it.
+
+And we want to improve on that.
+
+So I want to test your intuition
+by looking at the situation.
+
+We have an excited
+state without photon.
+
+We have a ground state.
+
+So I want to test your
+intuition in the following way.
+
+We have Rabi oscillations
+between two levels.
+
+The case in the cavity is, it is
+Rabi oscillation between state
+
+two and state one,
+but it doesn't matter.
+
+You can also assume that
+it is Rabi oscillation
+
+between hyperfine levels.
+
+And the Rabi oscillation
+is driven by an RF field.
+
+And the one thing
+we introduce now
+
+is we introduce damping
+kappa to this level.
+
+But we start out
+the system with all
+
+of the population in this state.
+
+And in the overdamped case, when
+kappa is sufficiently strong,
+
+then we know an oscillator
+will be overdamped
+
+and will no longer oscillate.
+
+And in this situation,
+the probability
+
+to be in the initial
+state will decay.
+
+e to the minus kap-- e to the
+minus-- how should we call it?
+
+gamma t.
+
+So it decays with
+the decay rate kappa.
+
+And my question for you is,
+A, B and C, whether the decay
+
+rate, kappa, is proportional
+to the damping rate, gamma?
+
+Proportional to the
+inverse of gamma?
+
+Or independent of gamma?
+
+So we've exacted this system.
+
+The system has possibility
+of Rabi oscillation.
+
+I showed you the
+damped Rabi oscillation
+
+and in the limit of small kappa.
+
+But now you go to the
+overdamped regime.
+
+And my question is, if
+the system is overdamped,
+
+will this decay rate
+increase with kappa?
+
+Decrease with kappa?
+
+Or will it be independent
+of a damped regime?
+
+All right.
+
+OK.
+
+There's a clear neutrality.
+
+Let me not yet
+discuss the answer.
+
+Let me maybe try to give
+you another problem.
+
+And you should maybe figure
+out if those two problems
+
+are related.
+
+I want to ask you now
+something simpler.
+
+There are not three
+levels involved,
+
+there are two levels involved.
+
+But one of the level
+is broadened by kappa.
+
+Call it an unstable state.
+
+Because it can decay with
+the rate, kappa, and we
+
+often show something
+which is broadened.
+
+And now we have a matrix element
+between the discrete level
+
+and the broadened state,
+which I call omega.
+
+It's a matrix element
+or Rabi frequency.
+
+And now you should
+figure out what
+
+is the physical
+picture which describes
+
+the coupling of a discrete
+initial state to something
+
+which is broadened.
+
+It's now the transition rate
+from the original state.
+
+Does the original state decay
+with a collectivistic rate,
+
+which is omega?
+
+Or is it omega
+squared over kappa?
+
+Or is it none of the above?
+
+So coupling between two
+levels, very, very simple.
+
+But one level is broadened.
+
+OK.
+
+Yes, it's Fermi's Golden
+Rule, what I'm asking you.
+
+This is nothing else
+than Fermi's Golden Rule.
+
+We couple from one level into
+some continuum of states.
+
+If I take one state and
+smear it out over a width,
+
+kappa, the density of states,
+the density of modes which
+
+appears in Fermi's Golden
+Rule, is 1 over kappa.
+
+And Fermi's Golden Rule
+tells us that the coupling
+
+is the matrix element squared
+times the density of states,
+
+which is 1 over kappa.
+
+So this is nothing else
+than Fermi's Golden Rule.
+
+OK.
+
+Why don't we come back
+to the first question
+
+now where we have two
+discrete levels, maybe
+
+two hyperfine states, which are
+coupled by a Rabi frequency?
+
+But then one of the
+hyperfine states
+
+decays because there is
+some leakage, or we--
+
+I don't know-- we interrogate
+this state with laser
+
+beams or such.
+
+We make it unstable.
+
+We allow this state to
+decay to another state.
+
+And the question is, if we
+make the decay of that level
+
+stronger and stronger, does
+the decay of the initial state
+
+increase?
+
+Decrease?
+
+Or is of that?
+
+Good.
+
+So what you have learned here
+is that, actually, the more we
+
+damp the system on this
+side, the longer-lived
+
+is the initial state.
+
+But it's trivial.
+
+It's just Fermi's Golden Rule.
+
+When you couple into a
+level which is broadened,
+
+the coupling becomes weaker and
+weaker because, well, that's
+
+what Fermi's Golden
+Rule tells us.
+
+I want to now derive this
+situation for you for our atom
+
+in the cavity.
+
+And I will say that this is one
+example for the quantum Zeno
+
+effect.
+
+But let me already
+explain to you
+
+what the quantum Zeno effect is.
+
+Zeno is a Greek philosopher.
+
+And the Greek philosophers
+had some deep thoughts
+
+about the nature of time,
+the nature of motion.
+
+And I think, in the
+Greek philosophy-- sorry.
+
+I didn't go-- I mean, I don't
+have a strong background
+
+in philosophy, but
+I think the idea
+
+is that motion is when
+something moves around.
+
+But it takes some time to move.
+
+So if you observe
+it, it can't move,
+
+because every time you observe
+it, you localize something.
+
+That's the idea.
+
+If you see an arrow, the moment
+you observe it, it's localized.
+
+And if you localize something
+to often, it cannot move.
+
+And this is sort of
+what you can say here.
+
+The system wants to
+evolve to a second state.
+
+But kappa can actually
+be a measurement process.
+
+We can just shine a
+strong laser on this state
+
+and figure out has
+something arrived here.
+
+And the more often we look, the
+stronger our measurement is,
+
+the less the system can evolve.
+
+So a measurement of what
+arrives in this state
+
+slows down the
+dynamics to that state.
+
+And this is called the
+quantum Zeno effect.
+
+It also goes by the name
+of quantum Zeno paradox.
+
+But it's just quantum
+mechanics, it's not a paradox.
+
+In the popular world, it
+is sometimes paraphrased
+
+as if you observe the tea
+kettle, the water never boils.
+
+But you see now
+where it comes from.
+
+OK, so this is the
+quantum Zeno effect.
+
+And we want to now, by
+looking at the master
+
+equation for an
+atom in a cavity,
+
+I want to show you the
+limit that it really
+
+comes out of the
+master equation.
+
+Questions about that?
+
+OK, so this is the
+quantum Zeno effect.
+
+And well, one of the nicest
+papers on the quantum Zeno
+
+effect-- well, I'm biased here--
+but it was written by my group,
+
+because we used the
+Bose-Einstein condensate.
+
+We had an RF coupling to
+another hyperfine state.
+
+And then we used a laser beam
+and observed the population
+
+in the final state.
+
+And we saw that the
+effect of the RF drive
+
+became weaker and
+weaker and weaker,
+
+the stronger we made the
+measurement in the final state.
+
+And this is the reference.
+
+And our work was the first
+quantitative comparison.
+
+You can now do a
+measurement by just
+
+using a strong laser in,
+maybe, every millisecond or so.
+
+Or you can use a weaker
+laser beam continuously.
+
+So we showed in this work
+that the quantum Zeno effect
+
+is the same, whether you do
+a pulsed observation, which
+
+is a strong measurement, or
+continuous weak measurement.
+
+OK.
+
+But let's now, after
+this short interlude,
+
+go back to the master equation.
+
+So our job is now to
+solve this master equation
+
+for the limit of strong damping.
+
+And what we will
+find, actually, is
+
+we will find both the quantum
+Zeno effect and another tidbit.
+
+We will also find
+the Purcell effect,
+
+which is enhanced spontaneous
+emission to a cavity.
+
+Now the way how we solve
+this master equation
+
+in this limiting
+case is by the method
+
+of idiopathic elimination
+of coherences.
+
+And let me explain it to
+you with that equation.
+
+What we have here is the
+derivative of the coherences.
+
+And when you look at
+the right-hand side,
+
+the derivative of the coherences
+is kappa, a damping terms,
+
+times the coherence.
+
+Well, if you have
+an equation which
+
+says a dot equals minus
+strong damping times a,
+
+you have a very rapid
+exponential damping.
+
+The system immediately
+gets into an equilibrium.
+
+And the equilibrium is
+given by the first term.
+
+So if you have a situation that
+the population do not rapidly
+
+change, then this
+equation can be
+
+written that we have
+a very rapid damping.
+
+And ultimately, the
+coherences settle
+
+to an quasi-equilibrium
+value in a time 1
+
+over kappa, which is
+given by the first term.
+
+In other words, you
+set the time derivative
+
+of the left-hand side, 0.
+
+And then the coherences
+are expressed
+
+in terms of the slowly
+changing quantity, which
+
+are the populations.
+
+So let me repeat.
+
+If coherences are
+rapidly damped,
+
+we can neglect the
+time derivative
+
+of the left-hand side.
+
+And at any given
+moment, the coherences
+
+will be given by an expression
+which involves the population.
+
+And if the populations
+slowly change,
+
+the coherences
+will slowly change.
+
+Or in other words,
+the coherences
+
+follow the population.
+
+And the lag time is,
+at most, 1 over kappa.
+
+And we are in the
+limit of strong kappa.
+
+This principle of
+eliminating coherences and we
+
+simply get a master
+equation for population
+
+is called the idiopathic
+elimination of coherences.
+
+It's also called by Eric
+Hargan in his famous work
+
+about synergy by the principle
+that, if you have rapidly
+
+damped modes, they are
+slaved by the slow modes.
+
+In other words, the rapidly
+damped degrees of freedom
+
+follow the slow
+degrees of freedom.
+
+And this is what I just said,
+that the instantaneous value
+
+of the coherences is always
+given by the population.
+
+So let me just write that down
+and see where it takes us.
+
+So we have the
+situation that we want
+
+to now look at the
+case of strong damping.
+
+This is the overdamped case.
+
+And we use now the method
+of idiopathic elimination
+
+of coherences, because
+they are rapidly damped.
+
+And there is a
+wonderful discussion
+
+about this method in
+Atom-Photon interaction.
+
+It's the Exercise
+18 on page 601.
+
+So mathematically,
+what we assume
+
+is that the population
+vary slowly.
+
+For instance, they vary
+at the Rabi frequency.
+
+So therefore, we can say that
+over the rapid time evolution
+
+of the coherences-- rho
+1, 2 plus rho 2, 1--
+
+so this is the rapid time
+evolution of the coherences.
+
+But for times which are on
+the order of 1 over kappa,
+
+the population are not changing.
+
+The population change over
+the much longer time scale,
+
+which is the period of
+the Rabi oscillation.
+
+So therefore, for
+the short time scale,
+
+I can sort of pretend that
+this term is constant.
+
+And for obvious reasons, let
+me now call this constant term,
+
+or slowly varying term, it is,
+at least for short time scales,
+
+the equilibrium value.
+
+So the way how we
+should read it is
+
+that the coherences
+will very, very rapidly
+
+damp to this equilibrium value.
+
+And this equilibrium
+value was given
+
+by the population,
+which may slowly change.
+
+But that means, now, by
+eliminating coherences,
+
+we obtain a rate equation
+for the populations only.
+
+So therefore, if you
+neglect short transients
+
+over the short
+time 1 over kappa,
+
+the coherences are
+always given by
+
+this quasi-equilibrium
+value, which
+
+is expressed by the population.
+
+And therefore, we can go to
+our master equation, which
+
+was a master equation
+for the of diagram matrix
+
+elements of the density
+matrix, and we can now
+
+replace the coherences
+by an expression which
+
+involves only population.
+
+So we get now closed equations
+for only the population.
+
+I'm sort of emphasizing that
+because you may have asked
+
+yourself, when you have the
+rate equation a la Einstein,
+
+with the a and b
+coefficient, these are just
+
+rate equation for populations.
+
+But here, in our class, we've
+always talked about the density
+
+matrix, how important
+the coherences are.
+
+The coherences are important.
+
+Without coherences, you would
+never absorb or emit light.
+
+But if the coherences can
+be expressed by populations,
+
+you don't need a differential
+equation for them.
+
+OK.
+
+So with that now, we
+have our master equation
+
+for the population.
+
+And by just inserting
+that, we find this.
+
+And we were interested
+in the decay of rho 1, 1.
+
+Or this is also the population
+of the atom in the excited
+
+state.
+
+If we initially start
+where rho 1, 1 is large,
+
+we're interested in
+the initial decay,
+
+then the population in
+the ground state is small.
+
+And we find, indeed, that
+there is exponential decay
+
+of the initial distribution.
+
+And the decay rate,
+gamma z, gamma cavity,
+
+is given by this expression.
+
+So therefore, what we
+find is-- but you know it
+
+by now-- the effect that the
+stronger we damp the cavity,
+
+the smaller, the weaker, is
+the decay of the initial state.
+
+And I've already
+explained to you
+
+that one picture to explain
+that is that we have the excited
+
+state, we have the ground state.
+
+The ground state
+gets damped by kappa.
+
+And therefore, the
+time evolution,
+
+which is given by the vacuum
+Rabi oscillation, slows down.
+
+OK.
+
+Yes.
+
+Any questions?
+
+So we have now resolved
+for gamma cavity.
+
+We have a result
+how the atom decays
+
+in the presence of the cavity.
+
+And I want to rewrite this
+for you in a very nice way.
+
+Namely, I want to show
+you the famous result
+
+that, when an atom
+emits in a cavity,
+
+that the atom can decay faster
+than the spontaneous decay.
+
+Because if the cavity
+has a resonance,
+
+the cavity changes the
+vacuum around the atom.
+
+It increases the
+density of modes.
+
+And therefore, there
+is a stimulation
+
+of the atom into the cavity.
+
+So I don't have to
+do any other math
+
+than just rewriting our result
+of gamma cavity in other units,
+
+in other ways.
+
+And then we can compare it to
+the natural decay of an atom
+
+without the cavity.
+
+So what we want to
+do now is we want
+
+to take the cavity-induced
+decay of the excited state,
+
+and we want to compare with
+the natural decay rate, gamma.
+
+So I just have to rewrite
+things in a few units.
+
+The cavity-induced decay is
+the vacuum Rabi oscillation
+
+squared over kappa.
+
+So let me remind you that
+the Rabi frequency is always
+
+given by an dipole moment
+times electric field.
+
+It's a matrix element.
+
+Well, there's one of
+those factors of 2.
+
+And H bar keeps
+the units correct.
+
+And in the case of the
+vacuum Rabi oscillation,
+
+the electric field is the
+electric field, so to speak,
+
+of one photon in
+the cavity volume.
+
+And there is a factor
+of 2, so this is now
+
+the volume of the cavity.
+
+So therefore, the
+vacuum Rabi frequency
+
+is a dipole moment
+times 2 atomic resonance
+
+frequency epsilon 0 h bar v.
+
+And that means now-- and
+this is a nice result--
+
+that the cavity-induced decay
+is omega 0 square over kappa.
+
+And I just use the above
+result for omega 0.
+
+And for kappa, I
+introduce the Q factor
+
+of the cavity, which is
+the number of oscillations
+
+before it is damped.
+
+It's omega over kappa.
+
+And with that, I can rewrite
+the cavity-induced decay
+
+as 2d squared epsilon
+null H bar v times Q.
+
+And if you remember, from
+part 1 of the course,
+
+or standard textbook result,
+that spontaneous decay is
+
+a dipole moment squared times
+frequency to the power 3,
+
+then we obtain
+the famous result,
+
+which is called the
+Purcell factor, namely
+
+that the decay in
+the cavity, compared
+
+to the decay in free space,
+is proportional to the Q
+
+of the cavity.
+
+There is a numerical prefector.
+
+But then, what enters
+is the wavelength
+
+of the photon cubed
+over the volume.
+
+So the case of eta
+larger than 1--
+
+and it's actually interesting
+that this result is completely
+
+independent of
+atomic properties.
+
+So in other words, every
+atom you put in a cavity,
+
+no matter what its
+dipole moment is,
+
+it will decay with a rate
+which is Q times larger.
+
+There are many ways
+how to look at it.
+
+You can say, if the cavity
+consists of two mirrors,
+
+you create Q mirror
+images of your atom.
+
+And you have sort
+of an atom which
+
+has a Q times stronger
+dipole moment.
+
+And therefore, because the
+mirror images also radiate,
+
+and therefore you get
+a Q times faster decay.
+
+So this limit makes sense in
+many, many different pictures.
+
+And it's a general result
+that, if an atom emits
+
+in a cavity with finesse
+Q, you get a Q times
+
+enhancement of
+spontaneous decay.
+
+So this is called
+cavity-enhanced spontaneous
+
+emission.
+
+It goes back to Purcell in 1946.
+
+And you can see the
+whole field of cavity QED
+
+depends on this effect, that you
+can enhance spontaneous decay.
+
+Or it's the opposite.
+
+If an atom has a
+resonance frequency
+
+between two modes of the
+cavity, the spontaneous decay
+
+is inhibited.
+
+And this is sort of what
+is exploited in cavity QED.
+
+Let me just conclude
+here by saying
+
+that our assumptions
+have to be consistent.
+
+In our derivation,
+we neglected gamma.
+
+When I said the two
+Lindblad operators,
+
+we only look at the
+leakage out of the photon.
+
+We neglect spontaneous decay.
+
+So of course, this requires
+that eta is larger 1.
+
+So this is the consistent range
+of validity of our result.
+
+Secondly, we discussed
+the limit of overdamping,
+
+which requires that kappa has to
+be larger than the vacuum Rabi
+
+frequency.
+
+And therefore, the above
+result is valued for large Q.
+
+Q has to be sufficiently large,
+but cannot be larger than this
+
+value.
+
+Any questions?
+
+Nancy?
+
+AUDIENCE: For kappa, is that
+the loss in the cavity--
+
+is there any difference
+between the loss and the cavity
+
+because it's a cavity?
+
+Or the loss is into other
+modes of the cavity?
+
+PROFESSOR: Kappa is the loss.
+
+You can say kappa is the rate
+at which a photon in the cavity
+
+is lost.
+
+AUDIENCE: Is lost from
+the cavity totally?
+
+Or is lost into another
+mode inside the cavity?
+
+Is there any difference?
+
+Is v here just one
+mode inside the cavity.
+
+PROFESSOR: Well, we
+have not an element--
+
+OK, if the mirror
+has imperfections,
+
+we usually think of light
+leaking out of the mirror.
+
+If the mirror is absorbing
+because the coating has
+
+a tiny little bit
+of absorption, you
+
+know, from the beam
+splitter analogy,
+
+that a small absorption
+is equivalent here
+
+to a small transmission factor.
+
+Usually, we don't consider
+that the light transforms
+
+from one mode of the
+cavity to the other.
+
+It's either absorbed
+or leaking out.
+
+But if you assume that the
+mirrors are not super polished
+
+and they scatter
+light a little bit,
+
+then you would have a mechanism
+that the light in the cavity
+
+scatters into other modes.
+
+And all those losses
+are summarized
+
+in one coupling constant, kappa.
+
+Let me finish the class
+today and this week
+
+by showing to you the recent
+nature paper by the Innsbrook
+
+group.
+
+We've talked so much
+about Lindblad operators.
+
+And the Lindblad
+operators, the dissipation,
+
+tells us what is the
+effect of the environment.
+
+And usually, you would say,
+well, if you have an atom,
+
+and it interacts
+with the environment,
+
+what is the equilibrium state?
+
+Well, if you just
+have the vacuum,
+
+the atom goes to
+the ground state.
+
+And the ground state
+is the attractor,
+
+the stable state of the system.
+
+If you drive the system
+with one laser beam,
+
+the attractor state where
+the system goes into
+
+is the steady state solution
+of the optical Bloch equation.
+
+That all sounds a
+little bit boring.
+
+But in this paper, based on
+this theoretical suggestion
+
+of Peter Zola and an
+experimental realization
+
+with trapped ions at
+Innsbrook, they actually
+
+engineered an environment,
+engineered Lindblad operators
+
+in such a way that
+the system of two ions
+
+was relaxing into a Bell state.
+
+So you engineer
+now the environment
+
+that therm-- I wanted to say
+thermal equilibrium, no--
+
+the equilibrium state with the
+environment, the dissipation,
+
+leads to a Bell state.
+
+Well, it's a little bit
+complicated how it is done,
+
+but I just want to just look at
+a few highlighted key messages.
+
+So the idea is, here,
+engineering of dissipation,
+
+creating experimentally
+dissipative operators.
+
+We usually manipulate quantum
+system with Hamilton operators.
+
+But here, it is manipulated
+not by the H operator,
+
+but by the L operator.
+
+And so the idea here is to have
+an evolution of the density
+
+matrix, a linear mapping that
+the density matrix evolves
+
+in a certain way.
+
+I think you'll
+recognize partial trace.
+
+You'll recognize
+a few equations,
+
+a few results which
+we have discussed.
+
+And what you see here is
+exactly the Lindblad form.
+
+And what they did is, by
+using a number of laser
+
+beams in quantum operation,
+they designed operators, z,
+
+jump operators, Lindblad
+operators, in such a way
+
+that the system was damping
+out into a Bell state.
+
+So that seems a new
+frontier for research.
+
+It goes by the title that we
+can do quantum simulations,
+
+using trapped ions and
+cold atoms of Hamiltonians.
+
+But we can also quantum simulate
+very special environments.
+
+Maybe environments
+which it would
+
+be hard to find them
+in nature, but they
+
+are quantum-mechanically
+allowed possible environments.
+
+And they may have
+new features which
+
+have not been explored so far.
+
+I will add this
+paper to the website,
+
+if you want to
+read more about it.
+
+Any question?
+
+Then a reminder.
+
+No class next week.
+
+Monday is Patriot's Day.
+
+I'm out of town on
+Wednesday, but you
+
+have a homework to solve.
+
+I rather feel you should
+continue to have a homework
+
+assignment every
+week, because then you
+
+have more time at the end of
+the term for the term paper.
+
+I always have 10
+homework assignments.
+
+So when we spread
+them out more, there
+
+is less time left at the end
+of the semester for the term
+
+paper.
+
+So I decided, since we have
+covered enough material,
+
+we have a wonderful homework
+assignment for next week.
\ No newline at end of file
diff --git a/P7frcB_-g4w.txt b/P7frcB_-g4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d0d1915b48e4ab541e40f5bb6a94fc31794844be
--- /dev/null
+++ b/P7frcB_-g4w.txt
@@ -0,0 +1,7866 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hi
+
+ align:start position:0%
+ocw.mit.edu hi
+ 
+
+ align:start position:0%
+ocw.mit.edu hi
+everyone I am uh I'm Victor my full name
+
+ align:start position:0%
+everyone I am uh I'm Victor my full name
+ 
+
+ align:start position:0%
+everyone I am uh I'm Victor my full name
+is Victor Coston I'm a third- year PhD
+
+ align:start position:0%
+is Victor Coston I'm a third- year PhD
+ 
+
+ align:start position:0%
+is Victor Coston I'm a third- year PhD
+student I'm in uh cell and uh I work in
+
+ align:start position:0%
+student I'm in uh cell and uh I work in
+ 
+
+ align:start position:0%
+student I'm in uh cell and uh I work in
+systems I do mostly security and
+
+ align:start position:0%
+systems I do mostly security and
+ 
+
+ align:start position:0%
+systems I do mostly security and
+distributed systems and I'll be your
+
+ align:start position:0%
+distributed systems and I'll be your
+ 
+
+ align:start position:0%
+distributed systems and I'll be your
+algorithm ta for this term yay how many
+
+ align:start position:0%
+algorithm ta for this term yay how many
+ 
+
+ align:start position:0%
+algorithm ta for this term yay how many
+people went to lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yesterday all right are there any parts
+
+ align:start position:0%
+yesterday all right are there any parts
+ 
+
+ align:start position:0%
+yesterday all right are there any parts
+of the lecture that were particularly
+
+ align:start position:0%
+of the lecture that were particularly
+ 
+
+ align:start position:0%
+of the lecture that were particularly
+unclear that you guys want to go
+
+ align:start position:0%
+unclear that you guys want to go
+ 
+
+ align:start position:0%
+unclear that you guys want to go
+over so that I uh schedule what I talk
+
+ align:start position:0%
+over so that I uh schedule what I talk
+ 
+
+ align:start position:0%
+over so that I uh schedule what I talk
+about in such a way that I'll cover that
+
+ align:start position:0%
+about in such a way that I'll cover that
+ 
+
+ align:start position:0%
+about in such a way that I'll cover that
+more than the parts that are boring and
+
+ align:start position:0%
+more than the parts that are boring and
+ 
+
+ align:start position:0%
+more than the parts that are boring and
+obvious
+
+ align:start position:0%
+obvious
+ 
+
+ align:start position:0%
+obvious
+um can you explain complexity uh
+
+ align:start position:0%
+um can you explain complexity uh
+ 
+
+ align:start position:0%
+um can you explain complexity uh
+equations I took for2 like three years
+
+ align:start position:0%
+equations I took for2 like three years
+ 
+
+ align:start position:0%
+equations I took for2 like three years
+ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what
+
+ align:start position:0%
+okay what
+ 
+
+ align:start position:0%
+okay what
+else thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you some basic outlines for like writing
+
+ align:start position:0%
+you some basic outlines for like writing
+ 
+
+ align:start position:0%
+you some basic outlines for like writing
+proofs uh relevant to like the presets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else okay we're going to get started
+
+ align:start position:0%
+else okay we're going to get started
+ 
+
+ align:start position:0%
+else okay we're going to get started
+then so the hardest and I think most
+
+ align:start position:0%
+then so the hardest and I think most
+ 
+
+ align:start position:0%
+then so the hardest and I think most
+important part of U the whole whole
+
+ align:start position:0%
+important part of U the whole whole
+ 
+
+ align:start position:0%
+important part of U the whole whole
+course is learning how to deal with the
+
+ align:start position:0%
+course is learning how to deal with the
+ 
+
+ align:start position:0%
+course is learning how to deal with the
+ASM totic complexity so as ASM totic
+
+ align:start position:0%
+ASM totic complexity so as ASM totic
+ 
+
+ align:start position:0%
+ASM totic complexity so as ASM totic
+complexity is this very nice tool where
+
+ align:start position:0%
+complexity is this very nice tool where
+ 
+
+ align:start position:0%
+complexity is this very nice tool where
+you have a function that looks like
+
+ align:start position:0%
+you have a function that looks like
+ 
+
+ align:start position:0%
+you have a function that looks like
+this X
+
+ align:start position:0%
+this X
+ 
+
+ align:start position:0%
+this X
+Plus what do I have here 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have this guy which is quite long
+
+ align:start position:0%
+so you have this guy which is quite long
+ 
+
+ align:start position:0%
+so you have this guy which is quite long
+and horrible and would make your life
+
+ align:start position:0%
+and horrible and would make your life
+ 
+
+ align:start position:0%
+and horrible and would make your life
+miserable if you'd have to reason about
+
+ align:start position:0%
+miserable if you'd have to reason about
+ 
+
+ align:start position:0%
+miserable if you'd have to reason about
+it and you can say
+
+ align:start position:0%
+it and you can say
+ 
+
+ align:start position:0%
+it and you can say
+that this
+
+ align:start position:0%
+that this
+ 
+
+ align:start position:0%
+that this
+is Theta
+
+ align:start position:0%
+is Theta
+ 
+
+ align:start position:0%
+is Theta
+of n
+
+ align:start position:0%
+of n
+ 
+
+ align:start position:0%
+of n
+SED X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so everything that's here goes
+
+ align:start position:0%
+sorry so everything that's here goes
+ 
+
+ align:start position:0%
+sorry so everything that's here goes
+away and this constant Factor here goes
+
+ align:start position:0%
+away and this constant Factor here goes
+ 
+
+ align:start position:0%
+away and this constant Factor here goes
+away way and it's a nice and small
+
+ align:start position:0%
+away way and it's a nice and small
+ 
+
+ align:start position:0%
+away way and it's a nice and small
+function uh why is that the case first
+
+ align:start position:0%
+function uh why is that the case first
+ 
+
+ align:start position:0%
+function uh why is that the case first
+of all if I
+
+ align:start position:0%
+of all if I
+ 
+
+ align:start position:0%
+of all if I
+plot this function and since I don't
+
+ align:start position:0%
+plot this function and since I don't
+ 
+
+ align:start position:0%
+plot this function and since I don't
+have my projector you'll have to take my
+
+ align:start position:0%
+have my projector you'll have to take my
+ 
+
+ align:start position:0%
+have my projector you'll have to take my
+word for it I will get something that
+
+ align:start position:0%
+word for it I will get something that
+ 
+
+ align:start position:0%
+word for it I will get something that
+looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if I plot this function I will get
+
+ align:start position:0%
+this if I plot this function I will get
+ 
+
+ align:start position:0%
+this if I plot this function I will get
+something that looks like this this is a
+
+ align:start position:0%
+something that looks like this this is a
+ 
+
+ align:start position:0%
+something that looks like this this is a
+scale from0 to
+
+ align:start position:0%
+scale from0 to
+ 
+
+ align:start position:0%
+scale from0 to
+200 however if I make my
+
+ align:start position:0%
+200 however if I make my
+ 
+
+ align:start position:0%
+200 however if I make my
+scale 0 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+20,000 let's say 200,000 to make sure
+
+ align:start position:0%
+20,000 let's say 200,000 to make sure
+ 
+
+ align:start position:0%
+20,000 let's say 200,000 to make sure
+that it's going to be
+
+ align:start position:0%
+that it's going to be
+ 
+
+ align:start position:0%
+that it's going to be
+correct X squ looks like this and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function looks like
+
+ align:start position:0%
+function looks like
+ 
+
+ align:start position:0%
+function looks like
+this and as you make the scale bigger
+
+ align:start position:0%
+this and as you make the scale bigger
+ 
+
+ align:start position:0%
+this and as you make the scale bigger
+and bigger you can't even see this noise
+
+ align:start position:0%
+and bigger you can't even see this noise
+ 
+
+ align:start position:0%
+and bigger you can't even see this noise
+anymore the reason is that all the noise
+
+ align:start position:0%
+anymore the reason is that all the noise
+ 
+
+ align:start position:0%
+anymore the reason is that all the noise
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+in this term in the X to the power of
+
+ align:start position:0%
+in this term in the X to the power of
+ 
+
+ align:start position:0%
+in this term in the X to the power of
+1th term
+
+ align:start position:0%
+1th term
+ 
+
+ align:start position:0%
+1th term
+and as n Pretend This is n xn same thing
+
+ align:start position:0%
+and as n Pretend This is n xn same thing
+ 
+
+ align:start position:0%
+and as n Pretend This is n xn same thing
+so as the input to the function gets
+
+ align:start position:0%
+so as the input to the function gets
+ 
+
+ align:start position:0%
+so as the input to the function gets
+bigger and bigger this grows at a much
+
+ align:start position:0%
+bigger and bigger this grows at a much
+ 
+
+ align:start position:0%
+bigger and bigger this grows at a much
+faster rate than this so if what I care
+
+ align:start position:0%
+faster rate than this so if what I care
+ 
+
+ align:start position:0%
+faster rate than this so if what I care
+about is how the function grows I can
+
+ align:start position:0%
+about is how the function grows I can
+ 
+
+ align:start position:0%
+about is how the function grows I can
+ignore
+
+ align:start position:0%
+ignore
+ 
+
+ align:start position:0%
+ignore
+anything aside from the dominant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term do people remember this from
+
+ align:start position:0%
+term do people remember this from
+ 
+
+ align:start position:0%
+term do people remember this from
+lecture does this make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense okay if it doesn't that's great it
+
+ align:start position:0%
+sense okay if it doesn't that's great it
+ 
+
+ align:start position:0%
+sense okay if it doesn't that's great it
+means that I'm not wasting time covering
+
+ align:start position:0%
+means that I'm not wasting time covering
+ 
+
+ align:start position:0%
+means that I'm not wasting time covering
+it so we learned about three symbols or
+
+ align:start position:0%
+it so we learned about three symbols or
+ 
+
+ align:start position:0%
+it so we learned about three symbols or
+we will learn about three symbols when
+
+ align:start position:0%
+we will learn about three symbols when
+ 
+
+ align:start position:0%
+we will learn about three symbols when
+talking about the asmic complexity the
+
+ align:start position:0%
+talking about the asmic complexity the
+ 
+
+ align:start position:0%
+talking about the asmic complexity the
+three symbols are Theta o and
+
+ align:start position:0%
+three symbols are Theta o and
+ 
+
+ align:start position:0%
+three symbols are Theta o and
+Omega uh let's say this complicated
+
+ align:start position:0%
+Omega uh let's say this complicated
+ 
+
+ align:start position:0%
+Omega uh let's say this complicated
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is G and this nice simple function is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f if I say that g of X is Theta
+
+ align:start position:0%
+f if I say that g of X is Theta
+ 
+
+ align:start position:0%
+f if I say that g of X is Theta
+of F ofx that means two things it means
+
+ align:start position:0%
+of F ofx that means two things it means
+ 
+
+ align:start position:0%
+of F ofx that means two things it means
+I have a lower bound like I showed
+
+ align:start position:0%
+I have a lower bound like I showed
+ 
+
+ align:start position:0%
+I have a lower bound like I showed
+here and the lower bound looks something
+
+ align:start position:0%
+here and the lower bound looks something
+ 
+
+ align:start position:0%
+here and the lower bound looks something
+like X squ and it means that I also have
+
+ align:start position:0%
+like X squ and it means that I also have
+ 
+
+ align:start position:0%
+like X squ and it means that I also have
+a higher an upper Bound for it that also
+
+ align:start position:0%
+a higher an upper Bound for it that also
+ 
+
+ align:start position:0%
+a higher an upper Bound for it that also
+looks like X squ so the upper bound
+
+ align:start position:0%
+looks like X squ so the upper bound
+ 
+
+ align:start position:0%
+looks like X squ so the upper bound
+would be something like
+
+ align:start position:0%
+would be something like
+ 
+
+ align:start position:0%
+would be something like
+this and if I say this then I'm making a
+
+ align:start position:0%
+this and if I say this then I'm making a
+ 
+
+ align:start position:0%
+this and if I say this then I'm making a
+promise that the function stays between
+
+ align:start position:0%
+promise that the function stays between
+ 
+
+ align:start position:0%
+promise that the function stays between
+the lower bound and the upper bound and
+
+ align:start position:0%
+the lower bound and the upper bound and
+ 
+
+ align:start position:0%
+the lower bound and the upper bound and
+the bounds look sort of the same I can't
+
+ align:start position:0%
+the bounds look sort of the same I can't
+ 
+
+ align:start position:0%
+the bounds look sort of the same I can't
+really have X squ here and x squared
+
+ align:start position:0%
+really have X squ here and x squared
+ 
+
+ align:start position:0%
+really have X squ here and x squared
+here right that would be impossible so
+
+ align:start position:0%
+here right that would be impossible so
+ 
+
+ align:start position:0%
+here right that would be impossible so
+that's why I said they look the same
+
+ align:start position:0%
+that's why I said they look the same
+ 
+
+ align:start position:0%
+that's why I said they look the same
+they're not the
+
+ align:start position:0%
+they're not the
+ 
+
+ align:start position:0%
+they're not the
+same and they're not the same because
+
+ align:start position:0%
+same and they're not the same because
+ 
+
+ align:start position:0%
+same and they're not the same because
+they're allowed to differ by a constant
+
+ align:start position:0%
+they're allowed to differ by a constant
+ 
+
+ align:start position:0%
+they're allowed to differ by a constant
+Factor so if
+
+ align:start position:0%
+Factor so if
+ 
+
+ align:start position:0%
+Factor so if
+this is f and say this is f Prime F ofx
+
+ align:start position:0%
+this is f and say this is f Prime F ofx
+ 
+
+ align:start position:0%
+this is f and say this is f Prime F ofx
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+be X2 and we know for sure that this is
+
+ align:start position:0%
+be X2 and we know for sure that this is
+ 
+
+ align:start position:0%
+be X2 and we know for sure that this is
+going to be lower than this and frime of
+
+ align:start position:0%
+going to be lower than this and frime of
+ 
+
+ align:start position:0%
+going to be lower than this and frime of
+X might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be 1.2 * x^2 and because I have a 1.1
+
+ align:start position:0%
+be 1.2 * x^2 and because I have a 1.1
+ 
+
+ align:start position:0%
+be 1.2 * x^2 and because I have a 1.1
+here and I know that these get smaller
+
+ align:start position:0%
+here and I know that these get smaller
+ 
+
+ align:start position:0%
+here and I know that these get smaller
+and smaller in relation to this as the
+
+ align:start position:0%
+and smaller in relation to this as the
+ 
+
+ align:start position:0%
+and smaller in relation to this as the
+function uh as the inputs to the
+
+ align:start position:0%
+function uh as the inputs to the
+ 
+
+ align:start position:0%
+function uh as the inputs to the
+function get bigger I know that this is
+
+ align:start position:0%
+function get bigger I know that this is
+ 
+
+ align:start position:0%
+function get bigger I know that this is
+going to be the dominating factor and
+
+ align:start position:0%
+going to be the dominating factor and
+ 
+
+ align:start position:0%
+going to be the dominating factor and
+because this is bigger than this this
+
+ align:start position:0%
+because this is bigger than this this
+ 
+
+ align:start position:0%
+because this is bigger than this this
+function is going to eventually be
+
+ align:start position:0%
+function is going to eventually be
+ 
+
+ align:start position:0%
+function is going to eventually be
+larger than this function so I have a
+
+ align:start position:0%
+larger than this function so I have a
+ 
+
+ align:start position:0%
+larger than this function so I have a
+bound from above and I have a bound from
+
+ align:start position:0%
+bound from above and I have a bound from
+ 
+
+ align:start position:0%
+bound from above and I have a bound from
+below and the bounds look almost the
+
+ align:start position:0%
+below and the bounds look almost the
+ 
+
+ align:start position:0%
+below and the bounds look almost the
+same they're only different by a
+
+ align:start position:0%
+same they're only different by a
+ 
+
+ align:start position:0%
+same they're only different by a
+constant Factor this is
+
+ align:start position:0%
+constant Factor this is
+ 
+
+ align:start position:0%
+constant Factor this is
+Theta to make things spicier by the way
+
+ align:start position:0%
+Theta to make things spicier by the way
+ 
+
+ align:start position:0%
+Theta to make things spicier by the way
+Theta is really hard to pronounce as
+
+ align:start position:0%
+Theta is really hard to pronounce as
+ 
+
+ align:start position:0%
+Theta is really hard to pronounce as
+opposed to O So we usually say and write
+
+ align:start position:0%
+opposed to O So we usually say and write
+ 
+
+ align:start position:0%
+opposed to O So we usually say and write
+o instead of of theta we'll talk about
+
+ align:start position:0%
+o instead of of theta we'll talk about
+ 
+
+ align:start position:0%
+o instead of of theta we'll talk about
+what o really means in a bit but if you
+
+ align:start position:0%
+what o really means in a bit but if you
+ 
+
+ align:start position:0%
+what o really means in a bit but if you
+see o in a lot of places including our
+
+ align:start position:0%
+see o in a lot of places including our
+ 
+
+ align:start position:0%
+see o in a lot of places including our
+notes know that most of the time we
+
+ align:start position:0%
+notes know that most of the time we
+ 
+
+ align:start position:0%
+notes know that most of the time we
+actually mean Theta and sorry for that
+
+ align:start position:0%
+actually mean Theta and sorry for that
+ 
+
+ align:start position:0%
+actually mean Theta and sorry for that
+when do we know we actually
+
+ align:start position:0%
+when do we know we actually
+ 
+
+ align:start position:0%
+when do we know we actually
+mean uh you can ask us and we'll tell
+
+ align:start position:0%
+mean uh you can ask us and we'll tell
+ 
+
+ align:start position:0%
+mean uh you can ask us and we'll tell
+you fortunately it doesn't matter too
+
+ align:start position:0%
+you fortunately it doesn't matter too
+ 
+
+ align:start position:0%
+you fortunately it doesn't matter too
+much so we're trying to get an idea of
+
+ align:start position:0%
+much so we're trying to get an idea of
+ 
+
+ align:start position:0%
+much so we're trying to get an idea of
+how the functions look like in the
+
+ align:start position:0%
+how the functions look like in the
+ 
+
+ align:start position:0%
+how the functions look like in the
+bigger picture so most of the time it
+
+ align:start position:0%
+bigger picture so most of the time it
+ 
+
+ align:start position:0%
+bigger picture so most of the time it
+doesn't matter I'll give you an example
+
+ align:start position:0%
+doesn't matter I'll give you an example
+ 
+
+ align:start position:0%
+doesn't matter I'll give you an example
+though of where it matters and how it
+
+ align:start position:0%
+though of where it matters and how it
+ 
+
+ align:start position:0%
+though of where it matters and how it
+could matter
+
+ align:start position:0%
+could matter
+ 
+
+ align:start position:0%
+could matter
+so suppose I have another function that
+
+ align:start position:0%
+so suppose I have another function that
+ 
+
+ align:start position:0%
+so suppose I have another function that
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+like I keep doing that that looks like
+
+ align:start position:0%
+like I keep doing that that looks like
+ 
+
+ align:start position:0%
+like I keep doing that that looks like
+this so this is kind of ugly too uh this
+
+ align:start position:0%
+this so this is kind of ugly too uh this
+ 
+
+ align:start position:0%
+this so this is kind of ugly too uh this
+function is
+
+ align:start position:0%
+function is
+ 
+
+ align:start position:0%
+function is
+um G of X say x
+
+ align:start position:0%
+um G of X say x
+ 
+
+ align:start position:0%
+um G of X say x
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+1+ s of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+so I can't say anything about the lower
+
+ align:start position:0%
+so I can't say anything about the lower
+ 
+
+ align:start position:0%
+so I can't say anything about the lower
+bound of this this is going to hit zero
+
+ align:start position:0%
+bound of this this is going to hit zero
+ 
+
+ align:start position:0%
+bound of this this is going to hit zero
+at an infinite number of values right so
+
+ align:start position:0%
+at an infinite number of values right so
+ 
+
+ align:start position:0%
+at an infinite number of values right so
+I can't say that I can't have a nice
+
+ align:start position:0%
+I can't say that I can't have a nice
+ 
+
+ align:start position:0%
+I can't say that I can't have a nice
+lower Bound for it the lower Bound for
+
+ align:start position:0%
+lower Bound for it the lower Bound for
+ 
+
+ align:start position:0%
+lower Bound for it the lower Bound for
+it is zero but I'm pretty sure that it's
+
+ align:start position:0%
+it is zero but I'm pretty sure that it's
+ 
+
+ align:start position:0%
+it is zero but I'm pretty sure that it's
+never going to be bigger than 2x right
+
+ align:start position:0%
+never going to be bigger than 2x right
+ 
+
+ align:start position:0%
+never going to be bigger than 2x right
+and that's still worth something so
+
+ align:start position:0%
+and that's still worth something so
+ 
+
+ align:start position:0%
+and that's still worth something so
+there's this other function here that's
+
+ align:start position:0%
+there's this other function here that's
+ 
+
+ align:start position:0%
+there's this other function here that's
+supposed to be a line pretend it's a
+
+ align:start position:0%
+supposed to be a line pretend it's a
+ 
+
+ align:start position:0%
+supposed to be a line pretend it's a
+line F ofx = 2X and I know for sure that
+
+ align:start position:0%
+line F ofx = 2X and I know for sure that
+ 
+
+ align:start position:0%
+line F ofx = 2X and I know for sure that
+this this is never going to exceed these
+
+ align:start position:0%
+this this is never going to exceed these
+ 
+
+ align:start position:0%
+this this is never going to exceed these
+this and in that case where I only have
+
+ align:start position:0%
+this and in that case where I only have
+ 
+
+ align:start position:0%
+this and in that case where I only have
+one upper bound and I don't have a good
+
+ align:start position:0%
+one upper bound and I don't have a good
+ 
+
+ align:start position:0%
+one upper bound and I don't have a good
+lower bound I say that g ofx is order of
+
+ align:start position:0%
+lower bound I say that g ofx is order of
+ 
+
+ align:start position:0%
+lower bound I say that g ofx is order of
+F ofx and this is where this is what o
+
+ align:start position:0%
+F ofx and this is where this is what o
+ 
+
+ align:start position:0%
+F ofx and this is where this is what o
+really means it means I only have an
+
+ align:start position:0%
+really means it means I only have an
+ 
+
+ align:start position:0%
+really means it means I only have an
+upper bound and not a lower
+
+ align:start position:0%
+upper bound and not a lower
+ 
+
+ align:start position:0%
+upper bound and not a lower
+Bound in most of the cases when you're
+
+ align:start position:0%
+Bound in most of the cases when you're
+ 
+
+ align:start position:0%
+Bound in most of the cases when you're
+coding something you don't really care
+
+ align:start position:0%
+coding something you don't really care
+ 
+
+ align:start position:0%
+coding something you don't really care
+how how well your program can run if
+
+ align:start position:0%
+how how well your program can run if
+ 
+
+ align:start position:0%
+how how well your program can run if
+you're really lucky what you really care
+
+ align:start position:0%
+you're really lucky what you really care
+ 
+
+ align:start position:0%
+you're really lucky what you really care
+about is how does it run in the worst
+
+ align:start position:0%
+about is how does it run in the worst
+ 
+
+ align:start position:0%
+about is how does it run in the worst
+case or how does it run most of the time
+
+ align:start position:0%
+case or how does it run most of the time
+ 
+
+ align:start position:0%
+case or how does it run most of the time
+so suppose you're Google and you're
+
+ align:start position:0%
+so suppose you're Google and you're
+ 
+
+ align:start position:0%
+so suppose you're Google and you're
+writing your search engine H you have to
+
+ align:start position:0%
+writing your search engine H you have to
+ 
+
+ align:start position:0%
+writing your search engine H you have to
+return a result to the user in 200
+
+ align:start position:0%
+return a result to the user in 200
+ 
+
+ align:start position:0%
+return a result to the user in 200
+milliseconds because they did a study
+
+ align:start position:0%
+milliseconds because they did a study
+ 
+
+ align:start position:0%
+milliseconds because they did a study
+that shows that if you return the result
+
+ align:start position:0%
+that shows that if you return the result
+ 
+
+ align:start position:0%
+that shows that if you return the result
+in 400 milliseconds they lose some
+
+ align:start position:0%
+in 400 milliseconds they lose some
+ 
+
+ align:start position:0%
+in 400 milliseconds they lose some
+number of users which means they lose
+
+ align:start position:0%
+number of users which means they lose
+ 
+
+ align:start position:0%
+number of users which means they lose
+some number of billions a year so to
+
+ align:start position:0%
+some number of billions a year so to
+ 
+
+ align:start position:0%
+some number of billions a year so to
+them a guarantee that their algorithms
+
+ align:start position:0%
+them a guarantee that their algorithms
+ 
+
+ align:start position:0%
+them a guarantee that their algorithms
+complete in 200 milliseconds is pretty
+
+ align:start position:0%
+complete in 200 milliseconds is pretty
+ 
+
+ align:start position:0%
+complete in 200 milliseconds is pretty
+important because it means a ton of
+
+ align:start position:0%
+important because it means a ton of
+ 
+
+ align:start position:0%
+important because it means a ton of
+money so if you have a running time that
+
+ align:start position:0%
+money so if you have a running time that
+ 
+
+ align:start position:0%
+money so if you have a running time that
+looks like this that's okay as long as
+
+ align:start position:0%
+looks like this that's okay as long as
+ 
+
+ align:start position:0%
+looks like this that's okay as long as
+this is 200 milliseconds for the number
+
+ align:start position:0%
+this is 200 milliseconds for the number
+ 
+
+ align:start position:0%
+this is 200 milliseconds for the number
+of pages that Google
+
+ align:start position:0%
+of pages that Google
+ 
+
+ align:start position:0%
+of pages that Google
+indexes does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense okay no answer means yes so if it
+
+ align:start position:0%
+sense okay no answer means yes so if it
+ 
+
+ align:start position:0%
+sense okay no answer means yes so if it
+doesn't make sense please say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something okay I will draw another
+
+ align:start position:0%
+something okay I will draw another
+ 
+
+ align:start position:0%
+something okay I will draw another
+function again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+what so it's one plus s of
+
+ align:start position:0%
+what so it's one plus s of
+ 
+
+ align:start position:0%
+what so it's one plus s of
+X yeah sorry my handwriting is not very
+
+ align:start position:0%
+X yeah sorry my handwriting is not very
+ 
+
+ align:start position:0%
+X yeah sorry my handwriting is not very
+good it it doesn't really matter what it
+
+ align:start position:0%
+good it it doesn't really matter what it
+ 
+
+ align:start position:0%
+good it it doesn't really matter what it
+is it just needs to it needs to be
+
+ align:start position:0%
+is it just needs to it needs to be
+ 
+
+ align:start position:0%
+is it just needs to it needs to be
+signed so that it looks wavy like this
+
+ align:start position:0%
+signed so that it looks wavy like this
+ 
+
+ align:start position:0%
+signed so that it looks wavy like this
+so that I can make something that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complicated in the first example is it
+
+ align:start position:0%
+complicated in the first example is it
+ 
+
+ align:start position:0%
+complicated in the first example is it
+1.2 yes I wanted something that's higher
+
+ align:start position:0%
+1.2 yes I wanted something that's higher
+ 
+
+ align:start position:0%
+1.2 yes I wanted something that's higher
+than 1.1 so yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now that I got a break um does
+
+ align:start position:0%
+okay now that I got a break um does
+ 
+
+ align:start position:0%
+okay now that I got a break um does
+anyone else want to ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so I'm going to draw
+
+ align:start position:0%
+questions okay so I'm going to draw
+ 
+
+ align:start position:0%
+questions okay so I'm going to draw
+another function this one looks like
+
+ align:start position:0%
+another function this one looks like
+ 
+
+ align:start position:0%
+another function this one looks like
+this and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is f of x equals um 1 + sin of X I have
+
+ align:start position:0%
+is f of x equals um 1 + sin of X I have
+ 
+
+ align:start position:0%
+is f of x equals um 1 + sin of X I have
+to use the these signs to make them look
+
+ align:start position:0%
+to use the these signs to make them look
+ 
+
+ align:start position:0%
+to use the these signs to make them look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that times x to the power of what do I
+
+ align:start position:0%
+that times x to the power of what do I
+ 
+
+ align:start position:0%
+that times x to the power of what do I
+have there 15 plus x to the power of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1/4 so for this function I know for sure
+
+ align:start position:0%
+1/4 so for this function I know for sure
+ 
+
+ align:start position:0%
+1/4 so for this function I know for sure
+that it is greater than x to the power
+
+ align:start position:0%
+that it is greater than x to the power
+ 
+
+ align:start position:0%
+that it is greater than x to the power
+of 1/4 right so if this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I know for sure that it's greater
+
+ align:start position:0%
+um I know for sure that it's greater
+ 
+
+ align:start position:0%
+um I know for sure that it's greater
+than that also if I look at this and I
+
+ align:start position:0%
+than that also if I look at this and I
+ 
+
+ align:start position:0%
+than that also if I look at this and I
+know that sign is never bigger than one
+
+ align:start position:0%
+know that sign is never bigger than one
+ 
+
+ align:start position:0%
+know that sign is never bigger than one
+I know this whole thing is going to be
+
+ align:start position:0%
+I know this whole thing is going to be
+ 
+
+ align:start position:0%
+I know this whole thing is going to be
+at most two so if I have another
+
+ align:start position:0%
+at most two so if I have another
+ 
+
+ align:start position:0%
+at most two so if I have another
+function that
+
+ align:start position:0%
+function that
+ 
+
+ align:start position:0%
+function that
+says um frime of x equals say 3 * x ^ of
+
+ align:start position:0%
+says um frime of x equals say 3 * x ^ of
+ 
+
+ align:start position:0%
+says um frime of x equals say 3 * x ^ of
+1.5 I know that it's going to bound it
+
+ align:start position:0%
+1.5 I know that it's going to bound it
+ 
+
+ align:start position:0%
+1.5 I know that it's going to bound it
+from above so I have two
+
+ align:start position:0%
+from above so I have two
+ 
+
+ align:start position:0%
+from above so I have two
+bounds so it sort of looks like this
+
+ align:start position:0%
+bounds so it sort of looks like this
+ 
+
+ align:start position:0%
+bounds so it sort of looks like this
+case except when I I use Theta I have to
+
+ align:start position:0%
+case except when I I use Theta I have to
+ 
+
+ align:start position:0%
+case except when I I use Theta I have to
+make sure that the bounds are very
+
+ align:start position:0%
+make sure that the bounds are very
+ 
+
+ align:start position:0%
+make sure that the bounds are very
+similar they can only differ by a
+
+ align:start position:0%
+similar they can only differ by a
+ 
+
+ align:start position:0%
+similar they can only differ by a
+constant factor in this case my bounds
+
+ align:start position:0%
+constant factor in this case my bounds
+ 
+
+ align:start position:0%
+constant factor in this case my bounds
+differ by the exponent here which is
+
+ align:start position:0%
+differ by the exponent here which is
+ 
+
+ align:start position:0%
+differ by the exponent here which is
+more than a constant Factor so they're
+
+ align:start position:0%
+more than a constant Factor so they're
+ 
+
+ align:start position:0%
+more than a constant Factor so they're
+not the
+
+ align:start position:0%
+not the
+ 
+
+ align:start position:0%
+not the
+same so if I take my function which by
+
+ align:start position:0%
+same so if I take my function which by
+ 
+
+ align:start position:0%
+same so if I take my function which by
+the way is
+
+ align:start position:0%
+the way is
+ 
+
+ align:start position:0%
+the way is
+G if I want to say that um G to the x is
+
+ align:start position:0%
+G if I want to say that um G to the x is
+ 
+
+ align:start position:0%
+G if I want to say that um G to the x is
+Theta of something I can't
+
+ align:start position:0%
+Theta of something I can't
+ 
+
+ align:start position:0%
+Theta of something I can't
+because no matter what I put in here
+
+ align:start position:0%
+because no matter what I put in here
+ 
+
+ align:start position:0%
+because no matter what I put in here
+it's not going to be
+
+ align:start position:0%
+it's not going to be
+ 
+
+ align:start position:0%
+it's not going to be
+correct the lower bound is this the
+
+ align:start position:0%
+correct the lower bound is this the
+ 
+
+ align:start position:0%
+correct the lower bound is this the
+upper bound is
+
+ align:start position:0%
+upper bound is
+ 
+
+ align:start position:0%
+upper bound is
+this but what I can do is I can say that
+
+ align:start position:0%
+this but what I can do is I can say that
+ 
+
+ align:start position:0%
+this but what I can do is I can say that
+I know for sure that it is Theta of x to
+
+ align:start position:0%
+I know for sure that it is Theta of x to
+ 
+
+ align:start position:0%
+I know for sure that it is Theta of x to
+the power of 1/4 and by the way I can
+
+ align:start position:0%
+the power of 1/4 and by the way I can
+ 
+
+ align:start position:0%
+the power of 1/4 and by the way I can
+also say that it is order of x to the
+
+ align:start position:0%
+also say that it is order of x to the
+ 
+
+ align:start position:0%
+also say that it is order of x to the
+power of 1/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+15 so if you have weird running times
+
+ align:start position:0%
+15 so if you have weird running times
+ 
+
+ align:start position:0%
+15 so if you have weird running times
+that look like this then you can only
+
+ align:start position:0%
+that look like this then you can only
+ 
+
+ align:start position:0%
+that look like this then you can only
+use um o and
+
+ align:start position:0%
+use um o and
+ 
+
+ align:start position:0%
+use um o and
+Omega and with that being said we will
+
+ align:start position:0%
+Omega and with that being said we will
+ 
+
+ align:start position:0%
+Omega and with that being said we will
+use o for pretty much the rest of the
+
+ align:start position:0%
+use o for pretty much the rest of the
+ 
+
+ align:start position:0%
+use o for pretty much the rest of the
+scores and for most of the cases we will
+
+ align:start position:0%
+scores and for most of the cases we will
+ 
+
+ align:start position:0%
+scores and for most of the cases we will
+use it to mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta oh by the way these formulas look
+
+ align:start position:0%
+Theta oh by the way these formulas look
+ 
+
+ align:start position:0%
+Theta oh by the way these formulas look
+ugly and complicated because I wanted
+
+ align:start position:0%
+ugly and complicated because I wanted
+ 
+
+ align:start position:0%
+ugly and complicated because I wanted
+the graphs to look U complicated to
+
+ align:start position:0%
+the graphs to look U complicated to
+ 
+
+ align:start position:0%
+the graphs to look U complicated to
+illustrate the idea that uh ASM totic
+
+ align:start position:0%
+illustrate the idea that uh ASM totic
+ 
+
+ align:start position:0%
+illustrate the idea that uh ASM totic
+notation makes things look simpler the
+
+ align:start position:0%
+notation makes things look simpler the
+ 
+
+ align:start position:0%
+notation makes things look simpler the
+in this course the running times that
+
+ align:start position:0%
+in this course the running times that
+ 
+
+ align:start position:0%
+in this course the running times that
+you'll be dealing with are all look like
+
+ align:start position:0%
+you'll be dealing with are all look like
+ 
+
+ align:start position:0%
+you'll be dealing with are all look like
+this they will either be order one order
+
+ align:start position:0%
+this they will either be order one order
+ 
+
+ align:start position:0%
+this they will either be order one order
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+order n
+
+ align:start position:0%
+order n
+ 
+
+ align:start position:0%
+order n
+order and log
+
+ align:start position:0%
+order and log
+ 
+
+ align:start position:0%
+order and log
+n and Order N
+
+ align:start position:0%
+n and Order N
+ 
+
+ align:start position:0%
+n and Order N
+squared you might have a one or two
+
+ align:start position:0%
+squared you might have a one or two
+ 
+
+ align:start position:0%
+squared you might have a one or two
+cases where you get something else but
+
+ align:start position:0%
+cases where you get something else but
+ 
+
+ align:start position:0%
+cases where you get something else but
+most of the time if you have something
+
+ align:start position:0%
+most of the time if you have something
+ 
+
+ align:start position:0%
+most of the time if you have something
+else coming out of your recurrence it
+
+ align:start position:0%
+else coming out of your recurrence it
+ 
+
+ align:start position:0%
+else coming out of your recurrence it
+means you're doing it wrong
+
+ align:start position:0%
+means you're doing it wrong
+ 
+
+ align:start position:0%
+means you're doing it wrong
+so nice tip to have and you can see that
+
+ align:start position:0%
+so nice tip to have and you can see that
+ 
+
+ align:start position:0%
+so nice tip to have and you can see that
+I already started doing it I'm already
+
+ align:start position:0%
+I already started doing it I'm already
+ 
+
+ align:start position:0%
+I already started doing it I'm already
+using o instead of
+
+ align:start position:0%
+using o instead of
+ 
+
+ align:start position:0%
+using o instead of
+theta so I guess I'm getting into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Habit because whatever I put here is
+
+ align:start position:0%
+Habit because whatever I put here is
+ 
+
+ align:start position:0%
+Habit because whatever I put here is
+going to be wrong if I put x to the
+
+ align:start position:0%
+going to be wrong if I put x to the
+ 
+
+ align:start position:0%
+going to be wrong if I put x to the
+power of 1/5 this is wrong because I can
+
+ align:start position:0%
+power of 1/5 this is wrong because I can
+ 
+
+ align:start position:0%
+power of 1/5 this is wrong because I can
+have an upper bound that has X to the^
+
+ align:start position:0%
+have an upper bound that has X to the^
+ 
+
+ align:start position:0%
+have an upper bound that has X to the^
+of 1/5 in it but I can't have a bound
+
+ align:start position:0%
+of 1/5 in it but I can't have a bound
+ 
+
+ align:start position:0%
+of 1/5 in it but I can't have a bound
+like that because this function hits x
+
+ align:start position:0%
+like that because this function hits x
+ 
+
+ align:start position:0%
+like that because this function hits x
+to the power of 1/4 in infinitely many
+
+ align:start position:0%
+to the power of 1/4 in infinitely many
+ 
+
+ align:start position:0%
+to the power of 1/4 in infinitely many
+points if I try to do x to the power of
+
+ align:start position:0%
+points if I try to do x to the power of
+ 
+
+ align:start position:0%
+points if I try to do x to the power of
+1/4 same deal lower bound yes upper
+
+ align:start position:0%
+1/4 same deal lower bound yes upper
+ 
+
+ align:start position:0%
+1/4 same deal lower bound yes upper
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+no so whatever I put in here is going to
+
+ align:start position:0%
+no so whatever I put in here is going to
+ 
+
+ align:start position:0%
+no so whatever I put in here is going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+wrong thank you good
+
+ align:start position:0%
+wrong thank you good
+ 
+
+ align:start position:0%
+wrong thank you good
+question yes or4 uh 1.4 they're 1.4 and
+
+ align:start position:0%
+question yes or4 uh 1.4 they're 1.4 and
+ 
+
+ align:start position:0%
+question yes or4 uh 1.4 they're 1.4 and
+1.5 okay I thought you were saying one4
+
+ align:start position:0%
+1.5 okay I thought you were saying one4
+ 
+
+ align:start position:0%
+1.5 okay I thought you were saying one4
+and oh sorry 14 1.4 1.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.5 okay are we good so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far okay let's go through a couple of
+
+ align:start position:0%
+far okay let's go through a couple of
+ 
+
+ align:start position:0%
+far okay let's go through a couple of
+exercises so I'll give you a few
+
+ align:start position:0%
+exercises so I'll give you a few
+ 
+
+ align:start position:0%
+exercises so I'll give you a few
+functions yes theega is it's a lower
+
+ align:start position:0%
+functions yes theega is it's a lower
+ 
+
+ align:start position:0%
+functions yes theega is it's a lower
+bound already without multiplying by any
+
+ align:start position:0%
+bound already without multiplying by any
+ 
+
+ align:start position:0%
+bound already without multiplying by any
+constant or something is that what it is
+
+ align:start position:0%
+constant or something is that what it is
+ 
+
+ align:start position:0%
+constant or something is that what it is
+so for all of these what you put
+
+ align:start position:0%
+so for all of these what you put
+ 
+
+ align:start position:0%
+so for all of these what you put
+here is the simple is the simple form so
+
+ align:start position:0%
+here is the simple is the simple form so
+ 
+
+ align:start position:0%
+here is the simple is the simple form so
+your lower bound can be this function
+
+ align:start position:0%
+your lower bound can be this function
+ 
+
+ align:start position:0%
+your lower bound can be this function
+multiplied by any constant Factor Omega
+
+ align:start position:0%
+multiplied by any constant Factor Omega
+ 
+
+ align:start position:0%
+multiplied by any constant Factor Omega
+me lower um Omega means lower bound o
+
+ align:start position:0%
+me lower um Omega means lower bound o
+ 
+
+ align:start position:0%
+me lower um Omega means lower bound o
+means upper bound Theta means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other things to clear up before I
+
+ align:start position:0%
+any other things to clear up before I
+ 
+
+ align:start position:0%
+any other things to clear up before I
+ask
+
+ align:start position:0%
+ask
+ 
+
+ align:start position:0%
+ask
+questions so it's your turn before it's
+
+ align:start position:0%
+questions so it's your turn before it's
+ 
+
+ align:start position:0%
+questions so it's your turn before it's
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turn all right I'm going to go over a
+
+ align:start position:0%
+turn all right I'm going to go over a
+ 
+
+ align:start position:0%
+turn all right I'm going to go over a
+few functions and I want you guys to
+
+ align:start position:0%
+few functions and I want you guys to
+ 
+
+ align:start position:0%
+few functions and I want you guys to
+tell me what um to help me write them in
+
+ align:start position:0%
+tell me what um to help me write them in
+ 
+
+ align:start position:0%
+tell me what um to help me write them in
+asmic
+
+ align:start position:0%
+asmic
+ 
+
+ align:start position:0%
+asmic
+notation so I will
+
+ align:start position:0%
+notation so I will
+ 
+
+ align:start position:0%
+notation so I will
+have F of N and I want to know its sta
+
+ align:start position:0%
+have F of N and I want to know its sta
+ 
+
+ align:start position:0%
+have F of N and I want to know its sta
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+what so let's start with with f of Nal
+
+ align:start position:0%
+what so let's start with with f of Nal
+ 
+
+ align:start position:0%
+what so let's start with with f of Nal
+10 to the
+
+ align:start position:0%
+10 to the
+ 
+
+ align:start position:0%
+10 to the
+80 does anyone know why 10 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay that's the correct answer
+
+ align:start position:0%
+yes okay that's the correct answer
+ 
+
+ align:start position:0%
+yes okay that's the correct answer
+you're going ahead though I was
+
+ align:start position:0%
+you're going ahead though I was
+ 
+
+ align:start position:0%
+you're going ahead though I was
+wondering if I was wondering if you know
+
+ align:start position:0%
+wondering if I was wondering if you know
+ 
+
+ align:start position:0%
+wondering if I was wondering if you know
+why why why did I choose this does
+
+ align:start position:0%
+why why why did I choose this does
+ 
+
+ align:start position:0%
+why why why did I choose this does
+anyone know why I chose this
+
+ align:start position:0%
+anyone know why I chose this
+ 
+
+ align:start position:0%
+anyone know why I chose this
+yes uh I think that's
+
+ align:start position:0%
+yes uh I think that's
+ 
+
+ align:start position:0%
+yes uh I think that's
+100 you're getting close though it's
+
+ align:start position:0%
+100 you're getting close though it's
+ 
+
+ align:start position:0%
+100 you're getting close though it's
+something think it's a really big number
+
+ align:start position:0%
+something think it's a really big number
+ 
+
+ align:start position:0%
+something think it's a really big number
+it's a really big number all right so
+
+ align:start position:0%
+it's a really big number all right so
+ 
+
+ align:start position:0%
+it's a really big number all right so
+it's a really big number that's the
+
+ align:start position:0%
+it's a really big number that's the
+ 
+
+ align:start position:0%
+it's a really big number that's the
+estimated number of atoms in the
+
+ align:start position:0%
+estimated number of atoms in the
+ 
+
+ align:start position:0%
+estimated number of atoms in the
+universe so realistically any quantity
+
+ align:start position:0%
+universe so realistically any quantity
+ 
+
+ align:start position:0%
+universe so realistically any quantity
+that you deal with that will represent
+
+ align:start position:0%
+that you deal with that will represent
+ 
+
+ align:start position:0%
+that you deal with that will represent
+the real world is not going to be bigger
+
+ align:start position:0%
+the real world is not going to be bigger
+ 
+
+ align:start position:0%
+the real world is not going to be bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+this so if you want to get all
+
+ align:start position:0%
+this so if you want to get all
+ 
+
+ align:start position:0%
+this so if you want to get all
+philosophical you can say that for any
+
+ align:start position:0%
+philosophical you can say that for any
+ 
+
+ align:start position:0%
+philosophical you can say that for any
+algorithm that you write and any
+
+ align:start position:0%
+algorithm that you write and any
+ 
+
+ align:start position:0%
+algorithm that you write and any
+realistic input the running time will be
+
+ align:start position:0%
+realistic input the running time will be
+ 
+
+ align:start position:0%
+realistic input the running time will be
+Theta of one but if you do this we're
+
+ align:start position:0%
+Theta of one but if you do this we're
+ 
+
+ align:start position:0%
+Theta of one but if you do this we're
+not going to be happy with you on exams
+
+ align:start position:0%
+not going to be happy with you on exams
+ 
+
+ align:start position:0%
+not going to be happy with you on exams
+so let's choose another
+
+ align:start position:0%
+so let's choose another
+ 
+
+ align:start position:0%
+so let's choose another
+one 20 n to the power of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7th what's this an ASM totic notation
+
+ align:start position:0%
+7th what's this an ASM totic notation
+ 
+
+ align:start position:0%
+7th what's this an ASM totic notation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why yes order
+
+ align:start position:0%
+why yes order
+ 
+
+ align:start position:0%
+why yes order
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+okay that's same thing and to the seven
+
+ align:start position:0%
+okay that's same thing and to the seven
+ 
+
+ align:start position:0%
+okay that's same thing and to the seven
+thank you why is that because if you
+
+ align:start position:0%
+thank you why is that because if you
+ 
+
+ align:start position:0%
+thank you why is that because if you
+distribute the exponent s 20 to S just a
+
+ align:start position:0%
+distribute the exponent s 20 to S just a
+ 
+
+ align:start position:0%
+distribute the exponent s 20 to S just a
+Conant excellent 20 to the 7 time n to
+
+ align:start position:0%
+Conant excellent 20 to the 7 time n to
+ 
+
+ align:start position:0%
+Conant excellent 20 to the 7 time n to
+the 7 this is a constant so it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away okay and before I do another one I
+
+ align:start position:0%
+away okay and before I do another one I
+ 
+
+ align:start position:0%
+away okay and before I do another one I
+want to give you guys some help and
+
+ align:start position:0%
+want to give you guys some help and
+ 
+
+ align:start position:0%
+want to give you guys some help and
+remind you about logs how many people
+
+ align:start position:0%
+remind you about logs how many people
+ 
+
+ align:start position:0%
+remind you about logs how many people
+remember the laws of working with logs
+
+ align:start position:0%
+remember the laws of working with logs
+ 
+
+ align:start position:0%
+remember the laws of working with logs
+from algebra or some math
+
+ align:start position:0%
+from algebra or some math
+ 
+
+ align:start position:0%
+from algebra or some math
+class all right you guys will be helping
+
+ align:start position:0%
+class all right you guys will be helping
+ 
+
+ align:start position:0%
+class all right you guys will be helping
+me write them for everyone else so if I
+
+ align:start position:0%
+me write them for everyone else so if I
+ 
+
+ align:start position:0%
+me write them for everyone else so if I
+have log of n to the 100 and I want to
+
+ align:start position:0%
+have log of n to the 100 and I want to
+ 
+
+ align:start position:0%
+have log of n to the 100 and I want to
+get the Theta notation for it what is it
+
+ align:start position:0%
+get the Theta notation for it what is it
+ 
+
+ align:start position:0%
+get the Theta notation for it what is it
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent why is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case okay so when I have an exponent
+
+ align:start position:0%
+case okay so when I have an exponent
+ 
+
+ align:start position:0%
+case okay so when I have an exponent
+here I can pull it out in front of the
+
+ align:start position:0%
+here I can pull it out in front of the
+ 
+
+ align:start position:0%
+here I can pull it out in front of the
+log as a constant Factor so this is the
+
+ align:start position:0%
+log as a constant Factor so this is the
+ 
+
+ align:start position:0%
+log as a constant Factor so this is the
+same thing as
+
+ align:start position:0%
+same thing as
+ 
+
+ align:start position:0%
+same thing as
+100 log
+
+ align:start position:0%
+100 log
+ 
+
+ align:start position:0%
+100 log
+n okay now if I have a logarithm uh to
+
+ align:start position:0%
+n okay now if I have a logarithm uh to
+ 
+
+ align:start position:0%
+n okay now if I have a logarithm uh to
+the base uh using base five of
+
+ align:start position:0%
+the base uh using base five of
+ 
+
+ align:start position:0%
+the base uh using base five of
+n how about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this l n okay so this is can you say
+
+ align:start position:0%
+this l n okay so this is can you say
+ 
+
+ align:start position:0%
+this l n okay so this is can you say
+that again log okay so this is theeta of
+
+ align:start position:0%
+that again log okay so this is theeta of
+ 
+
+ align:start position:0%
+that again log okay so this is theeta of
+log n because it
+
+ align:start position:0%
+log n because it
+ 
+
+ align:start position:0%
+log n because it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+excellent log n
+
+ align:start position:0%
+excellent log n
+ 
+
+ align:start position:0%
+excellent log n
+over log
+
+ align:start position:0%
+over log
+ 
+
+ align:start position:0%
+over log
+five so exponents inside the logs turn
+
+ align:start position:0%
+five so exponents inside the logs turn
+ 
+
+ align:start position:0%
+five so exponents inside the logs turn
+into constant factors bases turn into
+
+ align:start position:0%
+into constant factors bases turn into
+ 
+
+ align:start position:0%
+into constant factors bases turn into
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+factors so if you have a an ugly
+
+ align:start position:0%
+factors so if you have a an ugly
+ 
+
+ align:start position:0%
+factors so if you have a an ugly
+expression inside the logarithm you can
+
+ align:start position:0%
+expression inside the logarithm you can
+ 
+
+ align:start position:0%
+expression inside the logarithm you can
+most of the time simplify it to
+
+ align:start position:0%
+most of the time simplify it to
+ 
+
+ align:start position:0%
+most of the time simplify it to
+something really nice and this
+
+ align:start position:0%
+something really nice and this
+ 
+
+ align:start position:0%
+something really nice and this
+contributes to the fact that um these
+
+ align:start position:0%
+contributes to the fact that um these
+ 
+
+ align:start position:0%
+contributes to the fact that um these
+are the only functions that you will see
+
+ align:start position:0%
+are the only functions that you will see
+ 
+
+ align:start position:0%
+are the only functions that you will see
+when the answer is cleaned up in asmic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation okay yes so when you're writing
+
+ align:start position:0%
+notation okay yes so when you're writing
+ 
+
+ align:start position:0%
+notation okay yes so when you're writing
+log are you assuming certain base then
+
+ align:start position:0%
+log are you assuming certain base then
+ 
+
+ align:start position:0%
+log are you assuming certain base then
+yes there is a certain base for logs uh
+
+ align:start position:0%
+yes there is a certain base for logs uh
+ 
+
+ align:start position:0%
+yes there is a certain base for logs uh
+we're all computer scientists right so
+
+ align:start position:0%
+we're all computer scientists right so
+ 
+
+ align:start position:0%
+we're all computer scientists right so
+what's the natural base for our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logarithms okay sweet uh math
+
+ align:start position:0%
+logarithms okay sweet uh math
+ 
+
+ align:start position:0%
+logarithms okay sweet uh math
+major no yeah I natural Bas okay yeah
+
+ align:start position:0%
+major no yeah I natural Bas okay yeah
+ 
+
+ align:start position:0%
+major no yeah I natural Bas okay yeah
+it's a math joke so for everyone else a
+
+ align:start position:0%
+it's a math joke so for everyone else a
+ 
+
+ align:start position:0%
+it's a math joke so for everyone else a
+natural logorithm is in Bas e for us CS
+
+ align:start position:0%
+natural logorithm is in Bas e for us CS
+ 
+
+ align:start position:0%
+natural logorithm is in Bas e for us CS
+people a natural base is two because
+
+ align:start position:0%
+people a natural base is two because
+ 
+
+ align:start position:0%
+people a natural base is two because
+that's how many values you have for a
+
+ align:start position:0%
+that's how many values you have for a
+ 
+
+ align:start position:0%
+that's how many values you have for a
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+so log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means log n is log base 2 of
+
+ align:start position:0%
+means log n is log base 2 of
+ 
+
+ align:start position:0%
+means log n is log base 2 of
+n uh the good news is that most of the
+
+ align:start position:0%
+n uh the good news is that most of the
+ 
+
+ align:start position:0%
+n uh the good news is that most of the
+time we're working with asmic notation
+
+ align:start position:0%
+time we're working with asmic notation
+ 
+
+ align:start position:0%
+time we're working with asmic notation
+so it doesn't really matter we can
+
+ align:start position:0%
+so it doesn't really matter we can
+ 
+
+ align:start position:0%
+so it doesn't really matter we can
+communicate with our math friends and we
+
+ align:start position:0%
+communicate with our math friends and we
+ 
+
+ align:start position:0%
+communicate with our math friends and we
+don't have to talk about
+
+ align:start position:0%
+don't have to talk about
+ 
+
+ align:start position:0%
+don't have to talk about
+this okay I need to get another
+
+ align:start position:0%
+this okay I need to get another
+ 
+
+ align:start position:0%
+this okay I need to get another
+complicated example and my memory fails
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so log see I'm using Ln to mean the
+
+ align:start position:0%
+okay so log see I'm using Ln to mean the
+ 
+
+ align:start position:0%
+okay so log see I'm using Ln to mean the
+math natural logarithm
+
+ align:start position:0%
+math natural logarithm
+ 
+
+ align:start position:0%
+math natural logarithm
+so we still have that somewhere in
+
+ align:start position:0%
+so we still have that somewhere in
+ 
+
+ align:start position:0%
+so we still have that somewhere in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+of log n to the base
+
+ align:start position:0%
+of log n to the base
+ 
+
+ align:start position:0%
+of log n to the base
+100 they made me add all these
+
+ align:start position:0%
+100 they made me add all these
+ 
+
+ align:start position:0%
+100 they made me add all these
+parentheses in the last section to be
+
+ align:start position:0%
+parentheses in the last section to be
+ 
+
+ align:start position:0%
+parentheses in the last section to be
+clear so I'm adding them now from the
+
+ align:start position:0%
+clear so I'm adding them now from the
+ 
+
+ align:start position:0%
+clear so I'm adding them now from the
+start who wants to help me clean this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up yes log l all right wow one
+
+ align:start position:0%
+up yes log l all right wow one
+ 
+
+ align:start position:0%
+up yes log l all right wow one
+step log log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay uh can you tell me why very
+
+ align:start position:0%
+n okay uh can you tell me why very
+ 
+
+ align:start position:0%
+n okay uh can you tell me why very
+quickly so we can simplify out the base
+
+ align:start position:0%
+quickly so we can simplify out the base
+ 
+
+ align:start position:0%
+quickly so we can simplify out the base
+and the exponent in there okay then base
+
+ align:start position:0%
+and the exponent in there okay then base
+ 
+
+ align:start position:0%
+and the exponent in there okay then base
+goes out exponent goes out log log of
+
+ align:start position:0%
+goes out exponent goes out log log of
+ 
+
+ align:start position:0%
+goes out exponent goes out log log of
+something is another class complexity
+
+ align:start position:0%
+something is another class complexity
+ 
+
+ align:start position:0%
+something is another class complexity
+that's not exactly up there but
+
+ align:start position:0%
+that's not exactly up there but
+ 
+
+ align:start position:0%
+that's not exactly up there but
+occasionally
+
+ align:start position:0%
+occasionally
+ 
+
+ align:start position:0%
+occasionally
+yep uh what does a theory students say
+
+ align:start position:0%
+yep uh what does a theory students say
+ 
+
+ align:start position:0%
+yep uh what does a theory students say
+when they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drowning log log log log some of you are
+
+ align:start position:0%
+drowning log log log log some of you are
+ 
+
+ align:start position:0%
+drowning log log log log some of you are
+laughing already you guys know this okay
+
+ align:start position:0%
+laughing already you guys know this okay
+ 
+
+ align:start position:0%
+laughing already you guys know this okay
+what if I want to make this a little bit
+
+ align:start position:0%
+what if I want to make this a little bit
+ 
+
+ align:start position:0%
+what if I want to make this a little bit
+harder and
+
+ align:start position:0%
+harder and
+ 
+
+ align:start position:0%
+harder and
+um I
+
+ align:start position:0%
+um I
+ 
+
+ align:start position:0%
+um I
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+log l five
+
+ align:start position:0%
+log l five
+ 
+
+ align:start position:0%
+log l five
+of log n to the
+
+ align:start position:0%
+of log n to the
+ 
+
+ align:start position:0%
+of log n to the
+100 you have to do a bit more work now
+
+ align:start position:0%
+100 you have to do a bit more work now
+ 
+
+ align:start position:0%
+100 you have to do a bit more work now
+you can't just use the tricks on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right anyone
+
+ align:start position:0%
+right anyone
+ 
+
+ align:start position:0%
+right anyone
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+yes okay it is still log log n but for a
+
+ align:start position:0%
+yes okay it is still log log n but for a
+ 
+
+ align:start position:0%
+yes okay it is still log log n but for a
+different reason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right almost okay maybe not so the base
+
+ align:start position:0%
+right almost okay maybe not so the base
+ 
+
+ align:start position:0%
+right almost okay maybe not so the base
+still goes out just like
+
+ align:start position:0%
+still goes out just like
+ 
+
+ align:start position:0%
+still goes out just like
+before but this guy now goes out here so
+
+ align:start position:0%
+before but this guy now goes out here so
+ 
+
+ align:start position:0%
+before but this guy now goes out here so
+I will have this be sort of
+
+ align:start position:0%
+I will have this be sort of
+ 
+
+ align:start position:0%
+I will have this be sort of
+like I notice that I'm not saying equal
+
+ align:start position:0%
+like I notice that I'm not saying equal
+ 
+
+ align:start position:0%
+like I notice that I'm not saying equal
+I'm saying like because I got rid of the
+
+ align:start position:0%
+I'm saying like because I got rid of the
+ 
+
+ align:start position:0%
+I'm saying like because I got rid of the
+base so it's like 100
+
+ align:start position:0%
+base so it's like 100
+ 
+
+ align:start position:0%
+base so it's like 100
+time log n which
+
+ align:start position:0%
+time log n which
+ 
+
+ align:start position:0%
+time log n which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+log 100
+
+ align:start position:0%
+log 100
+ 
+
+ align:start position:0%
+log 100
+plus log log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and this is a constant Factor this
+
+ align:start position:0%
+n and this is a constant Factor this
+ 
+
+ align:start position:0%
+n and this is a constant Factor this
+grows as n grows so this is going to
+
+ align:start position:0%
+grows as n grows so this is going to
+ 
+
+ align:start position:0%
+grows as n grows so this is going to
+become incredibly small as n becomes
+
+ align:start position:0%
+become incredibly small as n becomes
+ 
+
+ align:start position:0%
+become incredibly small as n becomes
+larger and larger so I can get rid of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay uh one more and this one's going to
+
+ align:start position:0%
+okay uh one more and this one's going to
+ 
+
+ align:start position:0%
+okay uh one more and this one's going to
+be less
+
+ align:start position:0%
+be less
+ 
+
+ align:start position:0%
+be less
+boring of 100 going from the last step
+
+ align:start position:0%
+boring of 100 going from the last step
+ 
+
+ align:start position:0%
+boring of 100 going from the last step
+how are you able to pop it
+
+ align:start position:0%
+how are you able to pop it
+ 
+
+ align:start position:0%
+how are you able to pop it
+out uh if my memory remember if my
+
+ align:start position:0%
+out uh if my memory remember if my
+ 
+
+ align:start position:0%
+out uh if my memory remember if my
+memory works I think log of a is log a
+
+ align:start position:0%
+memory works I think log of a is log a
+ 
+
+ align:start position:0%
+memory works I think log of a is log a
+plus log B am I right guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sweet
+
+ align:start position:0%
+sweet
+ 
+
+ align:start position:0%
+sweet
+good question I'm I wasn't sure but now
+
+ align:start position:0%
+good question I'm I wasn't sure but now
+ 
+
+ align:start position:0%
+good question I'm I wasn't sure but now
+that you asked everyone else help me
+
+ align:start position:0%
+that you asked everyone else help me
+ 
+
+ align:start position:0%
+that you asked everyone else help me
+make sure it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay I'm erasing so much because
+
+ align:start position:0%
+right okay I'm erasing so much because
+ 
+
+ align:start position:0%
+right okay I'm erasing so much because
+we're going to need more room for this
+
+ align:start position:0%
+we're going to need more room for this
+ 
+
+ align:start position:0%
+we're going to need more room for this
+so I have a log again but this time what
+
+ align:start position:0%
+so I have a log again but this time what
+ 
+
+ align:start position:0%
+so I have a log again but this time what
+I have inside the log is n choose n
+
+ align:start position:0%
+I have inside the log is n choose n
+ 
+
+ align:start position:0%
+I have inside the log is n choose n
+/2 does any Brave Sol wants to come up
+
+ align:start position:0%
+/2 does any Brave Sol wants to come up
+ 
+
+ align:start position:0%
+/2 does any Brave Sol wants to come up
+here and Sol this for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no you guys are going to make me ride
+
+ align:start position:0%
+no you guys are going to make me ride
+ 
+
+ align:start position:0%
+no you guys are going to make me ride
+for the entire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hour I off for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+help so this is is n factorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep n factorial Over N / 2 factorial
+
+ align:start position:0%
+yep n factorial Over N / 2 factorial
+ 
+
+ align:start position:0%
+yep n factorial Over N / 2 factorial
+times then / 2
+
+ align:start position:0%
+times then / 2
+ 
+
+ align:start position:0%
+times then / 2
+factorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close and I'll give out another hint
+
+ align:start position:0%
+close and I'll give out another hint
+ 
+
+ align:start position:0%
+close and I'll give out another hint
+which is that n factorial can be
+
+ align:start position:0%
+which is that n factorial can be
+ 
+
+ align:start position:0%
+which is that n factorial can be
+approximated as Square < TK of 2 pi n
+
+ align:start position:0%
+approximated as Square < TK of 2 pi n
+ 
+
+ align:start position:0%
+approximated as Square < TK of 2 pi n
+multiplied by n / e / n uh to the power
+
+ align:start position:0%
+multiplied by n / e / n uh to the power
+ 
+
+ align:start position:0%
+multiplied by n / e / n uh to the power
+of n but I think this will make you guys
+
+ align:start position:0%
+of n but I think this will make you guys
+ 
+
+ align:start position:0%
+of n but I think this will make you guys
+not want to come up and Sol this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I
+
+ align:start position:0%
+yes I
+ 
+
+ align:start position:0%
+yes I
+was is that it is that not it did I get
+
+ align:start position:0%
+was is that it is that not it did I get
+ 
+
+ align:start position:0%
+was is that it is that not it did I get
+it wrong okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I think that's an ASM totic that's
+
+ align:start position:0%
+I I think that's an ASM totic that's
+ 
+
+ align:start position:0%
+I I think that's an ASM totic that's
+that's what we'll I think we'll get to
+
+ align:start position:0%
+that's what we'll I think we'll get to
+ 
+
+ align:start position:0%
+that's what we'll I think we'll get to
+that but factorials grow
+
+ align:start position:0%
+that but factorials grow
+ 
+
+ align:start position:0%
+that but factorials grow
+exponentially so it should be something
+
+ align:start position:0%
+exponentially so it should be something
+ 
+
+ align:start position:0%
+exponentially so it should be something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this okay so we have that nice
+
+ align:start position:0%
+this okay so we have that nice
+ 
+
+ align:start position:0%
+this okay so we have that nice
+approximation does anyone want to work
+
+ align:start position:0%
+approximation does anyone want to work
+ 
+
+ align:start position:0%
+approximation does anyone want to work
+it out or will I have to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it keep that in mind when I'm grading
+
+ align:start position:0%
+it keep that in mind when I'm grading
+ 
+
+ align:start position:0%
+it keep that in mind when I'm grading
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+homework okay so it's log of square < TK
+
+ align:start position:0%
+homework okay so it's log of square < TK
+ 
+
+ align:start position:0%
+homework okay so it's log of square < TK
+2 pi n
+
+ align:start position:0%
+2 pi n
+ 
+
+ align:start position:0%
+2 pi n
+MTI power
+
+ align:start position:0%
+MTI power
+ 
+
+ align:start position:0%
+MTI power
+n I'm going to put these two together
+
+ align:start position:0%
+n I'm going to put these two together
+ 
+
+ align:start position:0%
+n I'm going to put these two together
+so 2
+
+ align:start position:0%
+so 2
+ 
+
+ align:start position:0%
+so 2
+pi and
+
+ align:start position:0%
+pi and
+ 
+
+ align:start position:0%
+pi and
+over there's an N / two there right so
+
+ align:start position:0%
+over there's an N / two there right so
+ 
+
+ align:start position:0%
+over there's an N / two there right so
+it's n / 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+etimes N /
+
+ align:start position:0%
+etimes N /
+ 
+
+ align:start position:0%
+etimes N /
+2 the Power of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Two okay I can get rid of this guy
+
+ align:start position:0%
+Two okay I can get rid of this guy
+ 
+
+ align:start position:0%
+Two okay I can get rid of this guy
+because it's a
+
+ align:start position:0%
+because it's a
+ 
+
+ align:start position:0%
+because it's a
+constant I can get no I can't get rid of
+
+ align:start position:0%
+constant I can get no I can't get rid of
+ 
+
+ align:start position:0%
+constant I can get no I can't get rid of
+this guy yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thein under the
+
+ align:start position:0%
+thein under the
+ 
+
+ align:start position:0%
+thein under the
+rad yep 2 pi and over two so this
+
+ align:start position:0%
+rad yep 2 pi and over two so this
+ 
+
+ align:start position:0%
+rad yep 2 pi and over two so this
+simplifies okay thank
+
+ align:start position:0%
+simplifies okay thank
+ 
+
+ align:start position:0%
+simplifies okay thank
+you sare the bottom and get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+andc expon okay can help me thanks so
+
+ align:start position:0%
+andc expon okay can help me thanks so
+ 
+
+ align:start position:0%
+andc expon okay can help me thanks so
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can distribute this exponent
+
+ align:start position:0%
+okay so we can distribute this exponent
+ 
+
+ align:start position:0%
+okay so we can distribute this exponent
+here to cancel this and then we get a
+
+ align:start position:0%
+here to cancel this and then we get a
+ 
+
+ align:start position:0%
+here to cancel this and then we get a
+square root of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi sorry my hand I think it's better
+
+ align:start position:0%
+Pi sorry my hand I think it's better
+ 
+
+ align:start position:0%
+Pi sorry my hand I think it's better
+than mine by quite a
+
+ align:start position:0%
+than mine by quite a
+ 
+
+ align:start position:0%
+than mine by quite a
+bit square root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of n oops and this is squ squ so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cancels yeah that's probably good so um
+
+ align:start position:0%
+cancels yeah that's probably good so um
+ 
+
+ align:start position:0%
+cancels yeah that's probably good so um
+since this is a n e to the n and n to e
+
+ align:start position:0%
+since this is a n e to the n and n to e
+ 
+
+ align:start position:0%
+since this is a n e to the n and n to e
+to the end well since they're to the end
+
+ align:start position:0%
+to the end well since they're to the end
+ 
+
+ align:start position:0%
+to the end well since they're to the end
+um both the N we can uh keep them as a
+
+ align:start position:0%
+um both the N we can uh keep them as a
+ 
+
+ align:start position:0%
+um both the N we can uh keep them as a
+single exponent cancel stuff so we just
+
+ align:start position:0%
+single exponent cancel stuff so we just
+ 
+
+ align:start position:0%
+single exponent cancel stuff so we just
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+uh square root of Pi n the * 2 the N
+
+ align:start position:0%
+uh square root of Pi n the * 2 the N
+ 
+
+ align:start position:0%
+uh square root of Pi n the * 2 the N
+over Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n can do some more cancelling and just
+
+ align:start position:0%
+n can do some more cancelling and just
+ 
+
+ align:start position:0%
+n can do some more cancelling and just
+get uh to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going to simplify this to the end over
+
+ align:start position:0%
+going to simplify this to the end over
+ 
+
+ align:start position:0%
+going to simplify this to the end over
+the square root
+
+ align:start position:0%
+the square root
+ 
+
+ align:start position:0%
+the square root
+of and uh we can take out the pi because
+
+ align:start position:0%
+of and uh we can take out the pi because
+ 
+
+ align:start position:0%
+of and uh we can take out the pi because
+it's an natural logorithm and it's a
+
+ align:start position:0%
+it's an natural logorithm and it's a
+ 
+
+ align:start position:0%
+it's an natural logorithm and it's a
+constant factor and this
+
+ align:start position:0%
+constant factor and this
+ 
+
+ align:start position:0%
+constant factor and this
+is log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then since it's a log of it's just a log
+
+ align:start position:0%
+then since it's a log of it's just a log
+ 
+
+ align:start position:0%
+then since it's a log of it's just a log
+of 2 the N so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh um say since it's a log you can take
+
+ align:start position:0%
+uh um say since it's a log you can take
+ 
+
+ align:start position:0%
+uh um say since it's a log you can take
+out you can turn into log of 2 the N
+
+ align:start position:0%
+out you can turn into log of 2 the N
+ 
+
+ align:start position:0%
+out you can turn into log of 2 the N
+minus log of squ n uh log of two to the
+
+ align:start position:0%
+minus log of squ n uh log of two to the
+ 
+
+ align:start position:0%
+minus log of squ n uh log of two to the
+N is a much greater complexity than
+
+ align:start position:0%
+N is a much greater complexity than
+ 
+
+ align:start position:0%
+N is a much greater complexity than
+square of n so we can sweet thank
+
+ align:start position:0%
+square of n so we can sweet thank
+ 
+
+ align:start position:0%
+square of n so we can sweet thank
+you so see complicated formula even more
+
+ align:start position:0%
+you so see complicated formula even more
+ 
+
+ align:start position:0%
+you so see complicated formula even more
+complicated formula came out to be one
+
+ align:start position:0%
+complicated formula came out to be one
+ 
+
+ align:start position:0%
+complicated formula came out to be one
+of the numbers that I promised it would
+
+ align:start position:0%
+of the numbers that I promised it would
+ 
+
+ align:start position:0%
+of the numbers that I promised it would
+come out to thanks for the help so you
+
+ align:start position:0%
+come out to thanks for the help so you
+ 
+
+ align:start position:0%
+come out to thanks for the help so you
+can get rid of the pi as soon as you
+
+ align:start position:0%
+can get rid of the pi as soon as you
+ 
+
+ align:start position:0%
+can get rid of the pi as soon as you
+want to and this is the last step I I
+
+ align:start position:0%
+want to and this is the last step I I
+ 
+
+ align:start position:0%
+want to and this is the last step I I
+just want to say it again to make sure
+
+ align:start position:0%
+just want to say it again to make sure
+ 
+
+ align:start position:0%
+just want to say it again to make sure
+everyone heard it so once you get here
+
+ align:start position:0%
+everyone heard it so once you get here
+ 
+
+ align:start position:0%
+everyone heard it so once you get here
+you get this order n
+
+ align:start position:0%
+you get this order n
+ 
+
+ align:start position:0%
+you get this order n
+minus log of square Ro TK of n which
+
+ align:start position:0%
+minus log of square Ro TK of n which
+ 
+
+ align:start position:0%
+minus log of square Ro TK of n which
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is order n minus one
+
+ align:start position:0%
+this is order n minus one
+ 
+
+ align:start position:0%
+this is order n minus one
+half log n and the log n is much smaller
+
+ align:start position:0%
+half log n and the log n is much smaller
+ 
+
+ align:start position:0%
+half log n and the log n is much smaller
+than n so this goes away completely and
+
+ align:start position:0%
+than n so this goes away completely and
+ 
+
+ align:start position:0%
+than n so this goes away completely and
+you get this as your final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer okay that's this make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense any questions
+
+ align:start position:0%
+sense any questions
+ 
+
+ align:start position:0%
+sense any questions
+anyone how many people are still paying
+
+ align:start position:0%
+anyone how many people are still paying
+ 
+
+ align:start position:0%
+anyone how many people are still paying
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+honestly wow
+
+ align:start position:0%
+honestly wow
+ 
+
+ align:start position:0%
+honestly wow
+nice you should come to all my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's talk about something we
+
+ align:start position:0%
+okay let's talk about something we
+ 
+
+ align:start position:0%
+okay let's talk about something we
+covered in class let's talk about Peak
+
+ align:start position:0%
+covered in class let's talk about Peak
+ 
+
+ align:start position:0%
+covered in class let's talk about Peak
+finding and we'll start with ond Peak
+
+ align:start position:0%
+finding and we'll start with ond Peak
+ 
+
+ align:start position:0%
+finding and we'll start with ond Peak
+finding and then we'll go to 2D pick
+
+ align:start position:0%
+finding and then we'll go to 2D pick
+ 
+
+ align:start position:0%
+finding and then we'll go to 2D pick
+finding so does anyone remember the
+
+ align:start position:0%
+finding so does anyone remember the
+ 
+
+ align:start position:0%
+finding so does anyone remember the
+pseudo code for the faster 1D pick
+
+ align:start position:0%
+pseudo code for the faster 1D pick
+ 
+
+ align:start position:0%
+pseudo code for the faster 1D pick
+finding by any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chance
+
+ align:start position:0%
+chance
+ 
+
+ align:start position:0%
+chance
+ond Peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finding I think everyone said they went
+
+ align:start position:0%
+finding I think everyone said they went
+ 
+
+ align:start position:0%
+finding I think everyone said they went
+to lecture so I don't have to explain
+
+ align:start position:0%
+to lecture so I don't have to explain
+ 
+
+ align:start position:0%
+to lecture so I don't have to explain
+what Peak finding is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's go for it so suppose I have a
+
+ align:start position:0%
+okay let's go for it so suppose I have a
+ 
+
+ align:start position:0%
+okay let's go for it so suppose I have a
+few numbers uh three let me write this
+
+ align:start position:0%
+few numbers uh three let me write this
+ 
+
+ align:start position:0%
+few numbers uh three let me write this
+three four five six
+
+ align:start position:0%
+three four five six
+ 
+
+ align:start position:0%
+three four five six
+7 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+54 so the pick finding problem says
+
+ align:start position:0%
+54 so the pick finding problem says
+ 
+
+ align:start position:0%
+54 so the pick finding problem says
+there's an array of numbers and I want
+
+ align:start position:0%
+there's an array of numbers and I want
+ 
+
+ align:start position:0%
+there's an array of numbers and I want
+to find the local Peak and the local
+
+ align:start position:0%
+to find the local Peak and the local
+ 
+
+ align:start position:0%
+to find the local Peak and the local
+Peak is a number that surrounded by
+
+ align:start position:0%
+Peak is a number that surrounded by
+ 
+
+ align:start position:0%
+Peak is a number that surrounded by
+numbers that are smaller or equal to it
+
+ align:start position:0%
+numbers that are smaller or equal to it
+ 
+
+ align:start position:0%
+numbers that are smaller or equal to it
+so there shouldn't be any larger numbers
+
+ align:start position:0%
+so there shouldn't be any larger numbers
+ 
+
+ align:start position:0%
+so there shouldn't be any larger numbers
+than it and I want to find a peak as
+
+ align:start position:0%
+than it and I want to find a peak as
+ 
+
+ align:start position:0%
+than it and I want to find a peak as
+quickly as I
+
+ align:start position:0%
+quickly as I
+ 
+
+ align:start position:0%
+quickly as I
+can so what's the faster algorithm that
+
+ align:start position:0%
+can so what's the faster algorithm that
+ 
+
+ align:start position:0%
+can so what's the faster algorithm that
+we talked about in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture yes okay you didn't answer right
+
+ align:start position:0%
+lecture yes okay you didn't answer right
+ 
+
+ align:start position:0%
+lecture yes okay you didn't answer right
+as much at least
+
+ align:start position:0%
+as much at least
+ 
+
+ align:start position:0%
+as much at least
+so yeah binary search okay it's exactly
+
+ align:start position:0%
+so yeah binary search okay it's exactly
+ 
+
+ align:start position:0%
+so yeah binary search okay it's exactly
+like binary search yep uh do help me
+
+ align:start position:0%
+like binary search yep uh do help me
+ 
+
+ align:start position:0%
+like binary search yep uh do help me
+write the pseudo code you can tell me
+
+ align:start position:0%
+write the pseudo code you can tell me
+ 
+
+ align:start position:0%
+write the pseudo code you can tell me
+what it
+
+ align:start position:0%
+what it
+ 
+
+ align:start position:0%
+what it
+is start midle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay start in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+middle if you if you write this on uh on
+
+ align:start position:0%
+middle if you if you write this on uh on
+ 
+
+ align:start position:0%
+middle if you if you write this on uh on
+your pet you might want to be a little
+
+ align:start position:0%
+your pet you might want to be a little
+ 
+
+ align:start position:0%
+your pet you might want to be a little
+bit more formal someone asked me about
+
+ align:start position:0%
+bit more formal someone asked me about
+ 
+
+ align:start position:0%
+bit more formal someone asked me about
+proofs I would say something like start
+
+ align:start position:0%
+proofs I would say something like start
+ 
+
+ align:start position:0%
+proofs I would say something like start
+by looking at the middle element of the
+
+ align:start position:0%
+by looking at the middle element of the
+ 
+
+ align:start position:0%
+by looking at the middle element of the
+array same thing
+
+ align:start position:0%
+array same thing
+ 
+
+ align:start position:0%
+array same thing
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+okay so let's pretend this is the
+
+ align:start position:0%
+okay so let's pretend this is the
+ 
+
+ align:start position:0%
+okay so let's pretend this is the
+middle now it
+
+ align:start position:0%
+middle now it
+ 
+
+ align:start position:0%
+middle now it
+is what do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do okay I'm looking at the right side I
+
+ align:start position:0%
+do okay I'm looking at the right side I
+ 
+
+ align:start position:0%
+do okay I'm looking at the right side I
+see a seven there so I know for sure
+
+ align:start position:0%
+see a seven there so I know for sure
+ 
+
+ align:start position:0%
+see a seven there so I know for sure
+that this is not a local Peak
+
+ align:start position:0%
+that this is not a local Peak
+ 
+
+ align:start position:0%
+that this is not a local Peak
+right what do I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now okay
+
+ align:start position:0%
+now okay
+ 
+
+ align:start position:0%
+now okay
+uh what if this would be small what if I
+
+ align:start position:0%
+uh what if this would be small what if I
+ 
+
+ align:start position:0%
+uh what if this would be small what if I
+would look at five
+
+ align:start position:0%
+would look at five
+ 
+
+ align:start position:0%
+would look at five
+first or shouldn't should I look at the
+
+ align:start position:0%
+first or shouldn't should I look at the
+ 
+
+ align:start position:0%
+first or shouldn't should I look at the
+other side too well you don't have to in
+
+ align:start position:0%
+other side too well you don't have to in
+ 
+
+ align:start position:0%
+other side too well you don't have to in
+this case but if you but if seven were
+
+ align:start position:0%
+this case but if you but if seven were
+ 
+
+ align:start position:0%
+this case but if you but if seven were
+smaller then you would go and look at
+
+ align:start position:0%
+smaller then you would go and look at
+ 
+
+ align:start position:0%
+smaller then you would go and look at
+the other side to check to see five was
+
+ align:start position:0%
+the other side to check to see five was
+ 
+
+ align:start position:0%
+the other side to check to see five was
+also smaller in that case You' already
+
+ align:start position:0%
+also smaller in that case You' already
+ 
+
+ align:start position:0%
+also smaller in that case You' already
+found it okay so I have to look at both
+
+ align:start position:0%
+found it okay so I have to look at both
+ 
+
+ align:start position:0%
+found it okay so I have to look at both
+sides and make sure if none of them is
+
+ align:start position:0%
+sides and make sure if none of them is
+ 
+
+ align:start position:0%
+sides and make sure if none of them is
+smaller then I sorry if none of them is
+
+ align:start position:0%
+smaller then I sorry if none of them is
+ 
+
+ align:start position:0%
+smaller then I sorry if none of them is
+bigger I found a peak if any of them is
+
+ align:start position:0%
+bigger I found a peak if any of them is
+ 
+
+ align:start position:0%
+bigger I found a peak if any of them is
+uh bigger then I can go whichever way I
+
+ align:start position:0%
+uh bigger then I can go whichever way I
+ 
+
+ align:start position:0%
+uh bigger then I can go whichever way I
+want so I saw my seven I'm going to cut
+
+ align:start position:0%
+want so I saw my seven I'm going to cut
+ 
+
+ align:start position:0%
+want so I saw my seven I'm going to cut
+this in half and now I look at this
+
+ align:start position:0%
+this in half and now I look at this
+ 
+
+ align:start position:0%
+this in half and now I look at this
+you're saying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so look at
+
+ align:start position:0%
+right so look at
+ 
+
+ align:start position:0%
+right so look at
+neighbors by the way can anyone
+
+ align:start position:0%
+neighbors by the way can anyone
+ 
+
+ align:start position:0%
+neighbors by the way can anyone
+understand my handwriting is it even
+
+ align:start position:0%
+understand my handwriting is it even
+ 
+
+ align:start position:0%
+understand my handwriting is it even
+worth bothering to
+
+ align:start position:0%
+worth bothering to
+ 
+
+ align:start position:0%
+worth bothering to
+write okay I see three nods I'm going to
+
+ align:start position:0%
+write okay I see three nods I'm going to
+ 
+
+ align:start position:0%
+write okay I see three nods I'm going to
+write for those three
+
+ align:start position:0%
+write for those three
+ 
+
+ align:start position:0%
+write for those three
+people look at years
+
+ align:start position:0%
+people look at years
+ 
+
+ align:start position:0%
+people look at years
+so okay thanks not feeling old at all
+
+ align:start position:0%
+so okay thanks not feeling old at all
+ 
+
+ align:start position:0%
+so okay thanks not feeling old at all
+okay look at neighbors uh figure out if
+
+ align:start position:0%
+okay look at neighbors uh figure out if
+ 
+
+ align:start position:0%
+okay look at neighbors uh figure out if
+you're a peak you're one of the people
+
+ align:start position:0%
+you're a peak you're one of the people
+ 
+
+ align:start position:0%
+you're a peak you're one of the people
+that said you can read it so now there's
+
+ align:start position:0%
+that said you can read it so now there's
+ 
+
+ align:start position:0%
+that said you can read it so now there's
+only two people that can read my
+
+ align:start position:0%
+only two people that can read my
+ 
+
+ align:start position:0%
+only two people that can read my
+handwriting and that I
+
+ align:start position:0%
+handwriting and that I
+ 
+
+ align:start position:0%
+handwriting and that I
+like uh look at the
+
+ align:start position:0%
+like uh look at the
+ 
+
+ align:start position:0%
+like uh look at the
+neighbors see if local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if not figure out which way to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in and I'll say if not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurse so what's the running time for
+
+ align:start position:0%
+recurse so what's the running time for
+ 
+
+ align:start position:0%
+recurse so what's the running time for
+this suppose I have n elements to start
+
+ align:start position:0%
+this suppose I have n elements to start
+ 
+
+ align:start position:0%
+this suppose I have n elements to start
+with that's my array size I will use T
+
+ align:start position:0%
+with that's my array size I will use T
+ 
+
+ align:start position:0%
+with that's my array size I will use T
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n as my running time so to figure out
+
+ align:start position:0%
+n as my running time so to figure out
+ 
+
+ align:start position:0%
+n as my running time so to figure out
+the running time for the whole algorithm
+
+ align:start position:0%
+the running time for the whole algorithm
+ 
+
+ align:start position:0%
+the running time for the whole algorithm
+I have to look at the running time for
+
+ align:start position:0%
+I have to look at the running time for
+ 
+
+ align:start position:0%
+I have to look at the running time for
+each step and add them up right what's
+
+ align:start position:0%
+each step and add them up right what's
+ 
+
+ align:start position:0%
+each step and add them up right what's
+the running time for the first step look
+
+ align:start position:0%
+the running time for the first step look
+ 
+
+ align:start position:0%
+the running time for the first step look
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+middle one one I I would not say it's
+
+ align:start position:0%
+middle one one I I would not say it's
+ 
+
+ align:start position:0%
+middle one one I I would not say it's
+zero I still have to look at it
+
+ align:start position:0%
+zero I still have to look at it
+ 
+
+ align:start position:0%
+zero I still have to look at it
+or to be on the safe side you say one
+
+ align:start position:0%
+or to be on the safe side you say one
+ 
+
+ align:start position:0%
+or to be on the safe side you say one
+Theta of one it's a
+
+ align:start position:0%
+Theta of one it's a
+ 
+
+ align:start position:0%
+Theta of one it's a
+constant okay now I have to look at the
+
+ align:start position:0%
+constant okay now I have to look at the
+ 
+
+ align:start position:0%
+constant okay now I have to look at the
+neighbors and I have to see if one of
+
+ align:start position:0%
+neighbors and I have to see if one of
+ 
+
+ align:start position:0%
+neighbors and I have to see if one of
+them is bigger or not how about that how
+
+ align:start position:0%
+them is bigger or not how about that how
+ 
+
+ align:start position:0%
+them is bigger or not how about that how
+much time is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I heard the constant okay very soft
+
+ align:start position:0%
+I heard the constant okay very soft
+ 
+
+ align:start position:0%
+I heard the constant okay very soft
+voice but I heard a constant there so
+
+ align:start position:0%
+voice but I heard a constant there so
+ 
+
+ align:start position:0%
+voice but I heard a constant there so
+I'm going to take it so this guy is a
+
+ align:start position:0%
+I'm going to take it so this guy is a
+ 
+
+ align:start position:0%
+I'm going to take it so this guy is a
+constant if it's a local pick I'm down
+
+ align:start position:0%
+constant if it's a local pick I'm down
+ 
+
+ align:start position:0%
+constant if it's a local pick I'm down
+if it's not a local pick what's the
+
+ align:start position:0%
+if it's not a local pick what's the
+ 
+
+ align:start position:0%
+if it's not a local pick what's the
+running time for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yep so I'm looking at this guy it's
+
+ align:start position:0%
+yep so I'm looking at this guy it's
+ 
+
+ align:start position:0%
+yep so I'm looking at this guy it's
+clearly not a peak so I'm going to look
+
+ align:start position:0%
+clearly not a peak so I'm going to look
+ 
+
+ align:start position:0%
+clearly not a peak so I'm going to look
+in the right side because I see a seven
+
+ align:start position:0%
+in the right side because I see a seven
+ 
+
+ align:start position:0%
+in the right side because I see a seven
+here that's bigger than a six so now I
+
+ align:start position:0%
+here that's bigger than a six so now I
+ 
+
+ align:start position:0%
+here that's bigger than a six so now I
+have the same problem except my array
+
+ align:start position:0%
+have the same problem except my array
+ 
+
+ align:start position:0%
+have the same problem except my array
+size just dropped to half so same
+
+ align:start position:0%
+size just dropped to half so same
+ 
+
+ align:start position:0%
+size just dropped to half so same
+problem because I already have a name
+
+ align:start position:0%
+problem because I already have a name
+ 
+
+ align:start position:0%
+problem because I already have a name
+for it except the input size is
+
+ align:start position:0%
+for it except the input size is
+ 
+
+ align:start position:0%
+for it except the input size is
+different so the running time for this
+
+ align:start position:0%
+different so the running time for this
+ 
+
+ align:start position:0%
+different so the running time for this
+entire step
+
+ align:start position:0%
+entire step
+ 
+
+ align:start position:0%
+entire step
+is Theta of 1 + T of n /2 so the running
+
+ align:start position:0%
+is Theta of 1 + T of n /2 so the running
+ 
+
+ align:start position:0%
+is Theta of 1 + T of n /2 so the running
+time for the whole thing
+
+ align:start position:0%
+time for the whole thing
+ 
+
+ align:start position:0%
+time for the whole thing
+is um I should have said Theta of 1 here
+
+ align:start position:0%
+is um I should have said Theta of 1 here
+ 
+
+ align:start position:0%
+is um I should have said Theta of 1 here
+sorry so Theta of 1 plus Theta of 1 + T
+
+ align:start position:0%
+sorry so Theta of 1 plus Theta of 1 + T
+ 
+
+ align:start position:0%
+sorry so Theta of 1 plus Theta of 1 + T
+of n / 2 so this is Theta of
+
+ align:start position:0%
+of n / 2 so this is Theta of
+ 
+
+ align:start position:0%
+of n / 2 so this is Theta of
+1+ T of n /
+
+ align:start position:0%
+1+ T of n /
+ 
+
+ align:start position:0%
+1+ T of n /
+2 so I wrote out my pseudo code looked
+
+ align:start position:0%
+2 so I wrote out my pseudo code looked
+ 
+
+ align:start position:0%
+2 so I wrote out my pseudo code looked
+at the running time for each step added
+
+ align:start position:0%
+at the running time for each step added
+ 
+
+ align:start position:0%
+at the running time for each step added
+them up now I have a recurrence and I
+
+ align:start position:0%
+them up now I have a recurrence and I
+ 
+
+ align:start position:0%
+them up now I have a recurrence and I
+have to solve it let's solve it we sort
+
+ align:start position:0%
+have to solve it let's solve it we sort
+ 
+
+ align:start position:0%
+have to solve it let's solve it we sort
+of glossed over that in lectures so
+
+ align:start position:0%
+of glossed over that in lectures so
+ 
+
+ align:start position:0%
+of glossed over that in lectures so
+we're going to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so T of n equals Theta of 1 + T of n
+
+ align:start position:0%
+now so T of n equals Theta of 1 + T of n
+ 
+
+ align:start position:0%
+now so T of n equals Theta of 1 + T of n
+/ 2 I'm going to expand this using the
+
+ align:start position:0%
+/ 2 I'm going to expand this using the
+ 
+
+ align:start position:0%
+/ 2 I'm going to expand this using the
+definition and and Theta of one is long
+
+ align:start position:0%
+definition and and Theta of one is long
+ 
+
+ align:start position:0%
+definition and and Theta of one is long
+so I'm going to call this C instead it's
+
+ align:start position:0%
+so I'm going to call this C instead it's
+ 
+
+ align:start position:0%
+so I'm going to call this C instead it's
+a constant right so C plus expanding
+
+ align:start position:0%
+a constant right so C plus expanding
+ 
+
+ align:start position:0%
+a constant right so C plus expanding
+this C + T of n / 4 I'm going to expand
+
+ align:start position:0%
+this C + T of n / 4 I'm going to expand
+ 
+
+ align:start position:0%
+this C + T of n / 4 I'm going to expand
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again anyone getting bir of
+
+ align:start position:0%
+again anyone getting bir of
+ 
+
+ align:start position:0%
+again anyone getting bir of
+this so if I expand it a lot of times
+
+ align:start position:0%
+this so if I expand it a lot of times
+ 
+
+ align:start position:0%
+this so if I expand it a lot of times
+I'm going to get I * C + T of n / by 2
+
+ align:start position:0%
+I'm going to get I * C + T of n / by 2
+ 
+
+ align:start position:0%
+I'm going to get I * C + T of n / by 2
+to the I and you can expand it as many
+
+ align:start position:0%
+to the I and you can expand it as many
+ 
+
+ align:start position:0%
+to the I and you can expand it as many
+times as you want until we see the
+
+ align:start position:0%
+times as you want until we see the
+ 
+
+ align:start position:0%
+times as you want until we see the
+pattern but this is the
+
+ align:start position:0%
+pattern but this is the
+ 
+
+ align:start position:0%
+pattern but this is the
+pattern so I have a recurrence what else
+
+ align:start position:0%
+pattern so I have a recurrence what else
+ 
+
+ align:start position:0%
+pattern so I have a recurrence what else
+do I need in order to get a function I
+
+ align:start position:0%
+do I need in order to get a function I
+ 
+
+ align:start position:0%
+do I need in order to get a function I
+need a base case so the problem size get
+
+ align:start position:0%
+need a base case so the problem size get
+ 
+
+ align:start position:0%
+need a base case so the problem size get
+smaller and smaller and smaller but at
+
+ align:start position:0%
+smaller and smaller and smaller but at
+ 
+
+ align:start position:0%
+smaller and smaller and smaller but at
+some point it becomes so small that I
+
+ align:start position:0%
+some point it becomes so small that I
+ 
+
+ align:start position:0%
+some point it becomes so small that I
+can solve it just by looking at it
+
+ align:start position:0%
+can solve it just by looking at it
+ 
+
+ align:start position:0%
+can solve it just by looking at it
+what's that case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I have an array of one
+
+ align:start position:0%
+okay so if I have an array of one
+ 
+
+ align:start position:0%
+okay so if I have an array of one
+element it's a peak right job
+
+ align:start position:0%
+element it's a peak right job
+ 
+
+ align:start position:0%
+element it's a peak right job
+done so T of one
+
+ align:start position:0%
+done so T of one
+ 
+
+ align:start position:0%
+done so T of one
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+constant so I want to write this in such
+
+ align:start position:0%
+constant so I want to write this in such
+ 
+
+ align:start position:0%
+constant so I want to write this in such
+a way that this
+
+ align:start position:0%
+a way that this
+ 
+
+ align:start position:0%
+a way that this
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+this so I want to figure out an I such
+
+ align:start position:0%
+this so I want to figure out an I such
+ 
+
+ align:start position:0%
+this so I want to figure out an I such
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah t of n / 2 to the I equals
+
+ align:start position:0%
+um yeah t of n / 2 to the I equals
+ 
+
+ align:start position:0%
+um yeah t of n / 2 to the I equals
+T of one and the easi way of doing that
+
+ align:start position:0%
+T of one and the easi way of doing that
+ 
+
+ align:start position:0%
+T of one and the easi way of doing that
+is to say that n / 2 to the I is 1 so I
+
+ align:start position:0%
+is to say that n / 2 to the I is 1 so I
+ 
+
+ align:start position:0%
+is to say that n / 2 to the I is 1 so I
+is the inverse of an
+
+ align:start position:0%
+is the inverse of an
+ 
+
+ align:start position:0%
+is the inverse of an
+exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone logarithm thank
+
+ align:start position:0%
+anyone logarithm thank
+ 
+
+ align:start position:0%
+anyone logarithm thank
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+n so I have I and I'm going to plug it
+
+ align:start position:0%
+n so I have I and I'm going to plug it
+ 
+
+ align:start position:0%
+n so I have I and I'm going to plug it
+back in here and I get constant
+
+ align:start position:0%
+back in here and I get constant
+ 
+
+ align:start position:0%
+back in here and I get constant
+times log
+
+ align:start position:0%
+times log
+ 
+
+ align:start position:0%
+times log
+n+ T of 1 which I know is Theta of
+
+ align:start position:0%
+n+ T of 1 which I know is Theta of
+ 
+
+ align:start position:0%
+n+ T of 1 which I know is Theta of
+one um I'm going to make this Theta of 1
+
+ align:start position:0%
+one um I'm going to make this Theta of 1
+ 
+
+ align:start position:0%
+one um I'm going to make this Theta of 1
+again so Theta of 1
+
+ align:start position:0%
+again so Theta of 1
+ 
+
+ align:start position:0%
+again so Theta of 1
+* log n+ plus Thea of 1 and I know that
+
+ align:start position:0%
+* log n+ plus Thea of 1 and I know that
+ 
+
+ align:start position:0%
+* log n+ plus Thea of 1 and I know that
+log n dominates a constant so this is
+
+ align:start position:0%
+log n dominates a constant so this is
+ 
+
+ align:start position:0%
+log n dominates a constant so this is
+going to be Theta of log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve okay how are we
+
+ align:start position:0%
+solve okay how are we
+ 
+
+ align:start position:0%
+solve okay how are we
+doing yes and second to last from the
+
+ align:start position:0%
+doing yes and second to last from the
+ 
+
+ align:start position:0%
+doing yes and second to last from the
+bottom I
+
+ align:start position:0%
+bottom I
+ 
+
+ align:start position:0%
+bottom I
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+I and second part of equation how
+
+ align:start position:0%
+I and second part of equation how
+ 
+
+ align:start position:0%
+I and second part of equation how
+you okay so uh in the jump from here to
+
+ align:start position:0%
+you okay so uh in the jump from here to
+ 
+
+ align:start position:0%
+you okay so uh in the jump from here to
+here where I said I equals log n
+
+ align:start position:0%
+here where I said I equals log n
+ 
+
+ align:start position:0%
+here where I said I equals log n
+right okay so I becomes log n c stays C
+
+ align:start position:0%
+right okay so I becomes log n c stays C
+ 
+
+ align:start position:0%
+right okay so I becomes log n c stays C
+you're wondering about this part
+
+ align:start position:0%
+you're wondering about this part
+ 
+
+ align:start position:0%
+you're wondering about this part
+right so if I is log n then 2 to the I
+
+ align:start position:0%
+right so if I is log n then 2 to the I
+ 
+
+ align:start position:0%
+right so if I is log n then 2 to the I
+is n so I have t of one which I have
+
+ align:start position:0%
+is n so I have t of one which I have
+ 
+
+ align:start position:0%
+is n so I have t of one which I have
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+I wanted to have this happen when I was
+
+ align:start position:0%
+I wanted to have this happen when I was
+ 
+
+ align:start position:0%
+I wanted to have this happen when I was
+solving for I here I set this guy to my
+
+ align:start position:0%
+solving for I here I set this guy to my
+ 
+
+ align:start position:0%
+solving for I here I set this guy to my
+base case so that I can get this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen the idea here is that you're
+
+ align:start position:0%
+happen the idea here is that you're
+ 
+
+ align:start position:0%
+happen the idea here is that you're
+expanding the recursion forever and you
+
+ align:start position:0%
+expanding the recursion forever and you
+ 
+
+ align:start position:0%
+expanding the recursion forever and you
+know that at some point you're going to
+
+ align:start position:0%
+know that at some point you're going to
+ 
+
+ align:start position:0%
+know that at some point you're going to
+have to stop when do you stop you stop
+
+ align:start position:0%
+have to stop when do you stop you stop
+ 
+
+ align:start position:0%
+have to stop when do you stop you stop
+at the base case so you force this to
+
+ align:start position:0%
+at the base case so you force this to
+ 
+
+ align:start position:0%
+at the base case so you force this to
+become the base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh let's do 2D Peak finding let's
+
+ align:start position:0%
+okay uh let's do 2D Peak finding let's
+ 
+
+ align:start position:0%
+okay uh let's do 2D Peak finding let's
+talk about it a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so 2D pick finding is exactly like
+
+ align:start position:0%
+bit so 2D pick finding is exactly like
+ 
+
+ align:start position:0%
+bit so 2D pick finding is exactly like
+1D Pi finding except you have a 2d
+
+ align:start position:0%
+1D Pi finding except you have a 2d
+ 
+
+ align:start position:0%
+1D Pi finding except you have a 2d
+Matrix instead of a 1D
+
+ align:start position:0%
+Matrix instead of a 1D
+ 
+
+ align:start position:0%
+Matrix instead of a 1D
+array
+
+ align:start position:0%
+array
+ 
+
+ align:start position:0%
+array
+uh let's see if I can do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so suppose this is our Matrix and
+
+ align:start position:0%
+right so suppose this is our Matrix and
+ 
+
+ align:start position:0%
+right so suppose this is our Matrix and
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+these are the rows suppose we have um M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rose and N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+columns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can anyone remind me what the
+
+ align:start position:0%
+okay can anyone remind me what the
+ 
+
+ align:start position:0%
+okay can anyone remind me what the
+pseudo code for for 2D Peak finding that
+
+ align:start position:0%
+pseudo code for for 2D Peak finding that
+ 
+
+ align:start position:0%
+pseudo code for for 2D Peak finding that
+we talked about in lecture so we had two
+
+ align:start position:0%
+we talked about in lecture so we had two
+ 
+
+ align:start position:0%
+we talked about in lecture so we had two
+attempts the first one was a clear
+
+ align:start position:0%
+attempts the first one was a clear
+ 
+
+ align:start position:0%
+attempts the first one was a clear
+failure it didn't work the second one
+
+ align:start position:0%
+failure it didn't work the second one
+ 
+
+ align:start position:0%
+failure it didn't work the second one
+worked and we talked about it running
+
+ align:start position:0%
+worked and we talked about it running
+ 
+
+ align:start position:0%
+worked and we talked about it running
+time a little bit and then FY asked you
+
+ align:start position:0%
+time a little bit and then FY asked you
+ 
+
+ align:start position:0%
+time a little bit and then FY asked you
+to think of a variation to the second
+
+ align:start position:0%
+to think of a variation to the second
+ 
+
+ align:start position:0%
+to think of a variation to the second
+one so let's do the straight up second
+
+ align:start position:0%
+one so let's do the straight up second
+ 
+
+ align:start position:0%
+one so let's do the straight up second
+uh version of the pseudo code without
+
+ align:start position:0%
+uh version of the pseudo code without
+ 
+
+ align:start position:0%
+uh version of the pseudo code without
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+variation so 2D pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm all right one person was not
+
+ align:start position:0%
+algorithm all right one person was not
+ 
+
+ align:start position:0%
+algorithm all right one person was not
+asleep in my section at the end of
+
+ align:start position:0%
+asleep in my section at the end of
+ 
+
+ align:start position:0%
+asleep in my section at the end of
+lecture I'm
+
+ align:start position:0%
+lecture I'm
+ 
+
+ align:start position:0%
+lecture I'm
+proud which one of
+
+ align:start position:0%
+proud which one of
+ 
+
+ align:start position:0%
+proud which one of
+us uh you had your hand up first though
+
+ align:start position:0%
+us uh you had your hand up first though
+ 
+
+ align:start position:0%
+us uh you had your hand up first though
+so you just
+
+ align:start position:0%
+so you just
+ 
+
+ align:start position:0%
+so you just
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak
+
+ align:start position:0%
+Peak
+ 
+
+ align:start position:0%
+Peak
+neighbors neighbors in the same
+
+ align:start position:0%
+neighbors neighbors in the same
+ 
+
+ align:start position:0%
+neighbors neighbors in the same
+row yeah yeah
+
+ align:start position:0%
+row yeah yeah
+ 
+
+ align:start position:0%
+row yeah yeah
+sorry row is the horizontal one right
+
+ align:start position:0%
+sorry row is the horizontal one right
+ 
+
+ align:start position:0%
+sorry row is the horizontal one right
+okay so what do you mean by find the
+
+ align:start position:0%
+okay so what do you mean by find the
+ 
+
+ align:start position:0%
+okay so what do you mean by find the
+peak
+
+ align:start position:0%
+peak
+ 
+
+ align:start position:0%
+peak
+here with the coln yes so find the peak
+
+ align:start position:0%
+here with the coln yes so find the peak
+ 
+
+ align:start position:0%
+here with the coln yes so find the peak
+using what we talked about before yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+find One D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peek so you're thinking ahead you're
+
+ align:start position:0%
+peek so you're thinking ahead you're
+ 
+
+ align:start position:0%
+peek so you're thinking ahead you're
+thinking of the variation that sh asked
+
+ align:start position:0%
+thinking of the variation that sh asked
+ 
+
+ align:start position:0%
+thinking of the variation that sh asked
+you guys to think about at home I'm glad
+
+ align:start position:0%
+you guys to think about at home I'm glad
+ 
+
+ align:start position:0%
+you guys to think about at home I'm glad
+you thought about it that's good but uh
+
+ align:start position:0%
+you thought about it that's good but uh
+ 
+
+ align:start position:0%
+you thought about it that's good but uh
+what's the one that we had in lecture I
+
+ align:start position:0%
+what's the one that we had in lecture I
+ 
+
+ align:start position:0%
+what's the one that we had in lecture I
+want to think about I don't want to give
+
+ align:start position:0%
+want to think about I don't want to give
+ 
+
+ align:start position:0%
+want to think about I don't want to give
+you guys the answer yet so what did we
+
+ align:start position:0%
+you guys the answer yet so what did we
+ 
+
+ align:start position:0%
+you guys the answer yet so what did we
+say we're going to do in
+
+ align:start position:0%
+say we're going to do in
+ 
+
+ align:start position:0%
+say we're going to do in
+lecture yes I think we just picked a
+
+ align:start position:0%
+lecture yes I think we just picked a
+ 
+
+ align:start position:0%
+lecture yes I think we just picked a
+spot check the neighbors and kept
+
+ align:start position:0%
+spot check the neighbors and kept
+ 
+
+ align:start position:0%
+spot check the neighbors and kept
+walking uphill if that makes sense every
+
+ align:start position:0%
+walking uphill if that makes sense every
+ 
+
+ align:start position:0%
+walking uphill if that makes sense every
+time we found a neighbor that was bigger
+
+ align:start position:0%
+time we found a neighbor that was bigger
+ 
+
+ align:start position:0%
+time we found a neighbor that was bigger
+move to that
+
+ align:start position:0%
+move to that
+ 
+
+ align:start position:0%
+move to that
+spot so this is this is the first
+
+ align:start position:0%
+spot so this is this is the first
+ 
+
+ align:start position:0%
+spot so this is this is the first
+algorithm that's slow it works you're
+
+ align:start position:0%
+algorithm that's slow it works you're
+ 
+
+ align:start position:0%
+algorithm that's slow it works you're
+going to get the correct answer but it's
+
+ align:start position:0%
+going to get the correct answer but it's
+ 
+
+ align:start position:0%
+going to get the correct answer but it's
+slow because if you have some uh handly
+
+ align:start position:0%
+slow because if you have some uh handly
+ 
+
+ align:start position:0%
+slow because if you have some uh handly
+crafted uh Matrix you can go like this
+
+ align:start position:0%
+crafted uh Matrix you can go like this
+ 
+
+ align:start position:0%
+crafted uh Matrix you can go like this
+and you're basically going through the
+
+ align:start position:0%
+and you're basically going through the
+ 
+
+ align:start position:0%
+and you're basically going through the
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+Matrix yes uh I think the second
+
+ align:start position:0%
+Matrix yes uh I think the second
+ 
+
+ align:start position:0%
+Matrix yes uh I think the second
+algorithm was find a look through the
+
+ align:start position:0%
+algorithm was find a look through the
+ 
+
+ align:start position:0%
+algorithm was find a look through the
+column for its maximum and then look to
+
+ align:start position:0%
+column for its maximum and then look to
+ 
+
+ align:start position:0%
+column for its maximum and then look to
+either side okay so instead of finding a
+
+ align:start position:0%
+either side okay so instead of finding a
+ 
+
+ align:start position:0%
+either side okay so instead of finding a
+1D Peak we're going to find the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value okay and this is correct and let's
+
+ align:start position:0%
+value okay and this is correct and let's
+ 
+
+ align:start position:0%
+value okay and this is correct and let's
+look at this running
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time does anyone want to help me so this
+
+ align:start position:0%
+time does anyone want to help me so this
+ 
+
+ align:start position:0%
+time does anyone want to help me so this
+is T
+
+ align:start position:0%
+is T
+ 
+
+ align:start position:0%
+is T
+of n m right and rows and
+
+ align:start position:0%
+of n m right and rows and
+ 
+
+ align:start position:0%
+of n m right and rows and
+columns so what's the running time for
+
+ align:start position:0%
+columns so what's the running time for
+ 
+
+ align:start position:0%
+columns so what's the running time for
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+step come on this is the easy one yes
+
+ align:start position:0%
+step come on this is the easy one yes
+ 
+
+ align:start position:0%
+step come on this is the easy one yes
+it's a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perfect okay what's the running time for
+
+ align:start position:0%
+perfect okay what's the running time for
+ 
+
+ align:start position:0%
+perfect okay what's the running time for
+finding a maximum out of n
+
+ align:start position:0%
+finding a maximum out of n
+ 
+
+ align:start position:0%
+finding a maximum out of n
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+perfect and suppose we do that
+
+ align:start position:0%
+perfect and suppose we do that
+ 
+
+ align:start position:0%
+perfect and suppose we do that
+here suppose these rows don't exist
+
+ align:start position:0%
+here suppose these rows don't exist
+ 
+
+ align:start position:0%
+here suppose these rows don't exist
+suppose this is my entire Matrix and I'm
+
+ align:start position:0%
+suppose this is my entire Matrix and I'm
+ 
+
+ align:start position:0%
+suppose this is my entire Matrix and I'm
+here and I found a maximum what do I do
+
+ align:start position:0%
+here and I found a maximum what do I do
+ 
+
+ align:start position:0%
+here and I found a maximum what do I do
+I look left I look right if both of them
+
+ align:start position:0%
+I look left I look right if both of them
+ 
+
+ align:start position:0%
+I look left I look right if both of them
+are smaller then it means I found my
+
+ align:start position:0%
+are smaller then it means I found my
+ 
+
+ align:start position:0%
+are smaller then it means I found my
+Peak because I know that number was a
+
+ align:start position:0%
+Peak because I know that number was a
+ 
+
+ align:start position:0%
+Peak because I know that number was a
+maximum in my column now if that's not
+
+ align:start position:0%
+maximum in my column now if that's not
+ 
+
+ align:start position:0%
+maximum in my column now if that's not
+the case if I find a number that's
+
+ align:start position:0%
+the case if I find a number that's
+ 
+
+ align:start position:0%
+the case if I find a number that's
+bigger I'll go in that direction does
+
+ align:start position:0%
+bigger I'll go in that direction does
+ 
+
+ align:start position:0%
+bigger I'll go in that direction does
+that un
+
+ align:start position:0%
+that un
+ 
+
+ align:start position:0%
+that un
+reasonable okay so maximum for my column
+
+ align:start position:0%
+reasonable okay so maximum for my column
+ 
+
+ align:start position:0%
+reasonable okay so maximum for my column
+and I'm going to go
+
+ align:start position:0%
+and I'm going to go
+ 
+
+ align:start position:0%
+and I'm going to go
+right so check neighbors and I have the
+
+ align:start position:0%
+right so check neighbors and I have the
+ 
+
+ align:start position:0%
+right so check neighbors and I have the
+same two conditions
+
+ align:start position:0%
+same two conditions
+ 
+
+ align:start position:0%
+same two conditions
+there if it's a peak then I'm
+
+ align:start position:0%
+there if it's a peak then I'm
+ 
+
+ align:start position:0%
+there if it's a peak then I'm
+happy otherwise
+
+ align:start position:0%
+happy otherwise
+ 
+
+ align:start position:0%
+happy otherwise
+recurse so what's the running time if I
+
+ align:start position:0%
+recurse so what's the running time if I
+ 
+
+ align:start position:0%
+recurse so what's the running time if I
+have to recurse how does the new problem
+
+ align:start position:0%
+have to recurse how does the new problem
+ 
+
+ align:start position:0%
+have to recurse how does the new problem
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like it's an identical problem I still
+
+ align:start position:0%
+like it's an identical problem I still
+ 
+
+ align:start position:0%
+like it's an identical problem I still
+have a matrix except what
+
+ align:start position:0%
+have a matrix except what
+ 
+
+ align:start position:0%
+have a matrix except what
+changed so suppose I got here and this
+
+ align:start position:0%
+changed so suppose I got here and this
+ 
+
+ align:start position:0%
+changed so suppose I got here and this
+is the middle of my Matrix and I see
+
+ align:start position:0%
+is the middle of my Matrix and I see
+ 
+
+ align:start position:0%
+is the middle of my Matrix and I see
+that this guy is bigger so I'm going to
+
+ align:start position:0%
+that this guy is bigger so I'm going to
+ 
+
+ align:start position:0%
+that this guy is bigger so I'm going to
+recurse to the right
+
+ align:start position:0%
+recurse to the right
+ 
+
+ align:start position:0%
+recurse to the right
+side what happened to my problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size okay sorry I'm not answering
+
+ align:start position:0%
+size okay sorry I'm not answering
+ 
+
+ align:start position:0%
+size okay sorry I'm not answering
+question but um should find Max not
+
+ align:start position:0%
+question but um should find Max not
+ 
+
+ align:start position:0%
+question but um should find Max not
+n let me see tell uh you are right thank
+
+ align:start position:0%
+n let me see tell uh you are right thank
+ 
+
+ align:start position:0%
+n let me see tell uh you are right thank
+you for paying
+
+ align:start position:0%
+you for paying
+ 
+
+ align:start position:0%
+you for paying
+attention there I am sweet that would
+
+ align:start position:0%
+attention there I am sweet that would
+ 
+
+ align:start position:0%
+attention there I am sweet that would
+have Tri me up later thanks for saving
+
+ align:start position:0%
+have Tri me up later thanks for saving
+ 
+
+ align:start position:0%
+have Tri me up later thanks for saving
+me okay so your question sorry so the
+
+ align:start position:0%
+me okay so your question sorry so the
+ 
+
+ align:start position:0%
+me okay so your question sorry so the
+question is if I have to
+
+ align:start position:0%
+question is if I have to
+ 
+
+ align:start position:0%
+question is if I have to
+recurse what's the running
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so I'm if I have to recurse I'm in
+
+ align:start position:0%
+time so I'm if I have to recurse I'm in
+ 
+
+ align:start position:0%
+time so I'm if I have to recurse I'm in
+this array that was originally n by
+
+ align:start position:0%
+this array that was originally n by
+ 
+
+ align:start position:0%
+this array that was originally n by
+m and I'm only going to look at the
+
+ align:start position:0%
+m and I'm only going to look at the
+ 
+
+ align:start position:0%
+m and I'm only going to look at the
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side how
+
+ align:start position:0%
+side how
+ 
+
+ align:start position:0%
+side how
+many these how many rows do I have in
+
+ align:start position:0%
+many these how many rows do I have in
+ 
+
+ align:start position:0%
+many these how many rows do I have in
+the new array start with a easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right same as
+
+ align:start position:0%
+one all right same as
+ 
+
+ align:start position:0%
+one all right same as
+before how many
+
+ align:start position:0%
+before how many
+ 
+
+ align:start position:0%
+before how many
+columns n/
+
+ align:start position:0%
+columns n/
+ 
+
+ align:start position:0%
+columns n/
+two sweet so the recursion for this is
+
+ align:start position:0%
+two sweet so the recursion for this is
+ 
+
+ align:start position:0%
+two sweet so the recursion for this is
+Theta of 1 plus Theta of
+
+ align:start position:0%
+Theta of 1 plus Theta of
+ 
+
+ align:start position:0%
+Theta of 1 plus Theta of
+M plus T
+
+ align:start position:0%
+M plus T
+ 
+
+ align:start position:0%
+M plus T
+of n / 2 and
+
+ align:start position:0%
+of n / 2 and
+ 
+
+ align:start position:0%
+of n / 2 and
+M uh I know that a constant can be
+
+ align:start position:0%
+M uh I know that a constant can be
+ 
+
+ align:start position:0%
+M uh I know that a constant can be
+absorbed by this other guy so it's Theta
+
+ align:start position:0%
+absorbed by this other guy so it's Theta
+ 
+
+ align:start position:0%
+absorbed by this other guy so it's Theta
+of M plus T of n / 2
+
+ align:start position:0%
+of M plus T of n / 2
+ 
+
+ align:start position:0%
+of M plus T of n / 2
+m how would I solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what's the first thing that we
+
+ align:start position:0%
+this what's the first thing that we
+ 
+
+ align:start position:0%
+this what's the first thing that we
+need yes figure out base case all right
+
+ align:start position:0%
+need yes figure out base case all right
+ 
+
+ align:start position:0%
+need yes figure out base case all right
+excellent base case what's the B what's
+
+ align:start position:0%
+excellent base case what's the B what's
+ 
+
+ align:start position:0%
+excellent base case what's the B what's
+the base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case T of one comma G of n m sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+sweet so if I only have one column
+
+ align:start position:0%
+sweet so if I only have one column
+ 
+
+ align:start position:0%
+sweet so if I only have one column
+then I can do I can find the maximum and
+
+ align:start position:0%
+then I can do I can find the maximum and
+ 
+
+ align:start position:0%
+then I can do I can find the maximum and
+I know for sure that's going to be a
+
+ align:start position:0%
+I know for sure that's going to be a
+ 
+
+ align:start position:0%
+I know for sure that's going to be a
+peak job done that's my base case so I'm
+
+ align:start position:0%
+peak job done that's my base case so I'm
+ 
+
+ align:start position:0%
+peak job done that's my base case so I'm
+going to reduce the problem size in half
+
+ align:start position:0%
+going to reduce the problem size in half
+ 
+
+ align:start position:0%
+going to reduce the problem size in half
+until I get to a single column then I
+
+ align:start position:0%
+until I get to a single column then I
+ 
+
+ align:start position:0%
+until I get to a single column then I
+find the peak there and I'm
+
+ align:start position:0%
+find the peak there and I'm
+ 
+
+ align:start position:0%
+find the peak there and I'm
+happy uh how would I solve this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence it's a one minute answer
+
+ align:start position:0%
+recurrence it's a one minute answer
+ 
+
+ align:start position:0%
+recurrence it's a one minute answer
+because I think that's exactly how much
+
+ align:start position:0%
+because I think that's exactly how much
+ 
+
+ align:start position:0%
+because I think that's exactly how much
+time we have as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come on guys this looks familiar
+
+ align:start position:0%
+come on guys this looks familiar
+ 
+
+ align:start position:0%
+come on guys this looks familiar
+yes exactly
+
+ align:start position:0%
+yes exactly
+ 
+
+ align:start position:0%
+yes exactly
+function exactly M never changes right
+
+ align:start position:0%
+function exactly M never changes right
+ 
+
+ align:start position:0%
+function exactly M never changes right
+so this is basically a function of n so
+
+ align:start position:0%
+so this is basically a function of n so
+ 
+
+ align:start position:0%
+so this is basically a function of n so
+if M never changes and I pretend that
+
+ align:start position:0%
+if M never changes and I pretend that
+ 
+
+ align:start position:0%
+if M never changes and I pretend that
+it's a constant this looks exactly like
+
+ align:start position:0%
+it's a constant this looks exactly like
+ 
+
+ align:start position:0%
+it's a constant this looks exactly like
+the recursion the recurrence that we Sol
+
+ align:start position:0%
+the recursion the recurrence that we Sol
+ 
+
+ align:start position:0%
+the recursion the recurrence that we Sol
+before T of N is a constant plus T of n
+
+ align:start position:0%
+before T of N is a constant plus T of n
+ 
+
+ align:start position:0%
+before T of N is a constant plus T of n
+uh over
+
+ align:start position:0%
+uh over
+ 
+
+ align:start position:0%
+uh over
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so I'm going to get that
+
+ align:start position:0%
+so I'm going to get that
+ 
+
+ align:start position:0%
+so I'm going to get that
+constant multiplied by log n which is
+
+ align:start position:0%
+constant multiplied by log n which is
+ 
+
+ align:start position:0%
+constant multiplied by log n which is
+the solution that I had before so the
+
+ align:start position:0%
+the solution that I had before so the
+ 
+
+ align:start position:0%
+the solution that I had before so the
+running time is Theta of M log
+
+ align:start position:0%
+running time is Theta of M log
+ 
+
+ align:start position:0%
+running time is Theta of M log
+n all right I think I have 30 seconds so
+
+ align:start position:0%
+n all right I think I have 30 seconds so
+ 
+
+ align:start position:0%
+n all right I think I have 30 seconds so
+what if I would choose what if I would
+
+ align:start position:0%
+what if I would choose what if I would
+ 
+
+ align:start position:0%
+what if I would choose what if I would
+try to do this algorithm instead it's
+
+ align:start position:0%
+try to do this algorithm instead it's
+ 
+
+ align:start position:0%
+try to do this algorithm instead it's
+another one minute question so I guess
+
+ align:start position:0%
+another one minute question so I guess
+ 
+
+ align:start position:0%
+another one minute question so I guess
+I'm cheating I'm taking time away sorry
+
+ align:start position:0%
+I'm cheating I'm taking time away sorry
+ 
+
+ align:start position:0%
+I'm cheating I'm taking time away sorry
+so what if I would be finding a One D
+
+ align:start position:0%
+so what if I would be finding a One D
+ 
+
+ align:start position:0%
+so what if I would be finding a One D
+Peak instead of finding a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum I'm looking at the running time
+
+ align:start position:0%
+maximum I'm looking at the running time
+ 
+
+ align:start position:0%
+maximum I'm looking at the running time
+because if the running time is going to
+
+ align:start position:0%
+because if the running time is going to
+ 
+
+ align:start position:0%
+because if the running time is going to
+be the same is not even worth thinking
+
+ align:start position:0%
+be the same is not even worth thinking
+ 
+
+ align:start position:0%
+be the same is not even worth thinking
+if it's correct or not if it's a more
+
+ align:start position:0%
+if it's correct or not if it's a more
+ 
+
+ align:start position:0%
+if it's correct or not if it's a more
+complicated algorithm with the same
+
+ align:start position:0%
+complicated algorithm with the same
+ 
+
+ align:start position:0%
+complicated algorithm with the same
+running time why care about it so is the
+
+ align:start position:0%
+running time why care about it so is the
+ 
+
+ align:start position:0%
+running time why care about it so is the
+running time going to be
+
+ align:start position:0%
+running time going to be
+ 
+
+ align:start position:0%
+running time going to be
+better okay I heard an OD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why all right so One D Pick is exactly
+
+ align:start position:0%
+why all right so One D Pick is exactly
+ 
+
+ align:start position:0%
+why all right so One D Pick is exactly
+what we have there thank you one D Pick
+
+ align:start position:0%
+what we have there thank you one D Pick
+ 
+
+ align:start position:0%
+what we have there thank you one D Pick
+is is exactly like you said log M so
+
+ align:start position:0%
+is is exactly like you said log M so
+ 
+
+ align:start position:0%
+is is exactly like you said log M so
+this constant here becomes this constant
+
+ align:start position:0%
+this constant here becomes this constant
+ 
+
+ align:start position:0%
+this constant here becomes this constant
+here so the algorithm would be a lot
+
+ align:start position:0%
+here so the algorithm would be a lot
+ 
+
+ align:start position:0%
+here so the algorithm would be a lot
+faster U as an order of magnitude idea
+
+ align:start position:0%
+faster U as an order of magnitude idea
+ 
+
+ align:start position:0%
+faster U as an order of magnitude idea
+if your M and N are 1 million each then
+
+ align:start position:0%
+if your M and N are 1 million each then
+ 
+
+ align:start position:0%
+if your M and N are 1 million each then
+log n is 20 so that's a 50 time x
+
+ align:start position:0%
+log n is 20 so that's a 50 time x
+ 
+
+ align:start position:0%
+log n is 20 so that's a 50 time x
+Improvement and these are real input
+
+ align:start position:0%
+Improvement and these are real input
+ 
+
+ align:start position:0%
+Improvement and these are real input
+sizes you might
+
+ align:start position:0%
+sizes you might
+ 
+
+ align:start position:0%
+sizes you might
+get and that's it thank you guys
\ No newline at end of file
diff --git a/PKbah48l3AU.txt b/PKbah48l3AU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b8bc7885e79a5c73843ee745d34085d13c96fd86
--- /dev/null
+++ b/PKbah48l3AU.txt
@@ -0,0 +1,8619 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well everyone's quieted down so
+
+ align:start position:0%
+okay well everyone's quieted down so
+ 
+
+ align:start position:0%
+okay well everyone's quieted down so
+that means we have to get started
+
+ align:start position:0%
+that means we have to get started
+ 
+
+ align:start position:0%
+that means we have to get started
+someone must say something here this
+
+ align:start position:0%
+someone must say something here this
+ 
+
+ align:start position:0%
+someone must say something here this
+will be our last our last conversation
+
+ align:start position:0%
+will be our last our last conversation
+ 
+
+ align:start position:0%
+will be our last our last conversation
+about optimization
+
+ align:start position:0%
+about optimization
+ 
+
+ align:start position:0%
+about optimization
+okay so we've discussed unconstrained
+
+ align:start position:0%
+okay so we've discussed unconstrained
+ 
+
+ align:start position:0%
+okay so we've discussed unconstrained
+optimization and then we're going to
+
+ align:start position:0%
+optimization and then we're going to
+ 
+
+ align:start position:0%
+optimization and then we're going to
+discuss slightly more complicated
+
+ align:start position:0%
+discuss slightly more complicated
+ 
+
+ align:start position:0%
+discuss slightly more complicated
+problem but you're gonna see it's it's
+
+ align:start position:0%
+problem but you're gonna see it's it's
+ 
+
+ align:start position:0%
+problem but you're gonna see it's it's
+really not that much more complicated
+
+ align:start position:0%
+really not that much more complicated
+ 
+
+ align:start position:0%
+really not that much more complicated
+constrained optimization these are the
+
+ align:start position:0%
+constrained optimization these are the
+ 
+
+ align:start position:0%
+constrained optimization these are the
+things we discussed before I don't want
+
+ align:start position:0%
+things we discussed before I don't want
+ 
+
+ align:start position:0%
+things we discussed before I don't want
+to spend much time recapping because I
+
+ align:start position:0%
+to spend much time recapping because I
+ 
+
+ align:start position:0%
+to spend much time recapping because I
+want to I want to take a minute and talk
+
+ align:start position:0%
+want to I want to take a minute and talk
+ 
+
+ align:start position:0%
+want to I want to take a minute and talk
+about the midterm exam okay all right so
+
+ align:start position:0%
+about the midterm exam okay all right so
+ 
+
+ align:start position:0%
+about the midterm exam okay all right so
+we have a quiz
+
+ align:start position:0%
+we have a quiz
+ 
+
+ align:start position:0%
+we have a quiz
+it's next Wednesday here's where it's
+
+ align:start position:0%
+it's next Wednesday here's where it's
+ 
+
+ align:start position:0%
+it's next Wednesday here's where it's
+gonna be located right here 66 head down
+
+ align:start position:0%
+gonna be located right here 66 head down
+ 
+
+ align:start position:0%
+gonna be located right here 66 head down
+Ames you're looking for Walker Memorial
+
+ align:start position:0%
+Ames you're looking for Walker Memorial
+ 
+
+ align:start position:0%
+Ames you're looking for Walker Memorial
+on the third floor okay unfortunately
+
+ align:start position:0%
+on the third floor okay unfortunately
+ 
+
+ align:start position:0%
+on the third floor okay unfortunately
+the time for the quiz is 7:00 to 9:00
+
+ align:start position:0%
+the time for the quiz is 7:00 to 9:00
+ 
+
+ align:start position:0%
+the time for the quiz is 7:00 to 9:00
+p.m. we really did try hard to get the
+
+ align:start position:0%
+p.m. we really did try hard to get the
+ 
+
+ align:start position:0%
+p.m. we really did try hard to get the
+scheduling office to give us something
+
+ align:start position:0%
+scheduling office to give us something
+ 
+
+ align:start position:0%
+scheduling office to give us something
+better but the only way to get a room
+
+ align:start position:0%
+better but the only way to get a room
+ 
+
+ align:start position:0%
+better but the only way to get a room
+that would fit everybody in was to do it
+
+ align:start position:0%
+that would fit everybody in was to do it
+ 
+
+ align:start position:0%
+that would fit everybody in was to do it
+at this time in Walker I really don't
+
+ align:start position:0%
+at this time in Walker I really don't
+ 
+
+ align:start position:0%
+at this time in Walker I really don't
+understand because I actually requested
+
+ align:start position:0%
+understand because I actually requested
+ 
+
+ align:start position:0%
+understand because I actually requested
+locations for the quizzes back in April
+
+ align:start position:0%
+locations for the quizzes back in April
+ 
+
+ align:start position:0%
+locations for the quizzes back in April
+and somehow I was I know too early maybe
+
+ align:start position:0%
+and somehow I was I know too early maybe
+ 
+
+ align:start position:0%
+and somehow I was I know too early maybe
+and got buried under a pile may be not
+
+ align:start position:0%
+and got buried under a pile may be not
+ 
+
+ align:start position:0%
+and got buried under a pile may be not
+important enough I don't know but it's
+
+ align:start position:0%
+important enough I don't know but it's
+ 
+
+ align:start position:0%
+important enough I don't know but it's
+gonna be from 7:00 to 9:00 next
+
+ align:start position:0%
+gonna be from 7:00 to 9:00 next
+ 
+
+ align:start position:0%
+gonna be from 7:00 to 9:00 next
+Wednesday right third floor there's not
+
+ align:start position:0%
+Wednesday right third floor there's not
+ 
+
+ align:start position:0%
+Wednesday right third floor there's not
+gonna be any class next Wednesday
+
+ align:start position:0%
+gonna be any class next Wednesday
+ 
+
+ align:start position:0%
+gonna be any class next Wednesday
+because you have a quiz instead to get a
+
+ align:start position:0%
+because you have a quiz instead to get a
+ 
+
+ align:start position:0%
+because you have a quiz instead to get a
+little extra time to relax or study
+
+ align:start position:0%
+little extra time to relax or study
+ 
+
+ align:start position:0%
+little extra time to relax or study
+prepare
+
+ align:start position:0%
+prepare
+ 
+
+ align:start position:0%
+prepare
+calm yourself before you go into the
+
+ align:start position:0%
+calm yourself before you go into the
+ 
+
+ align:start position:0%
+calm yourself before you go into the
+exam there's no homework this week okay
+
+ align:start position:0%
+exam there's no homework this week okay
+ 
+
+ align:start position:0%
+exam there's no homework this week okay
+so you can just use this time to focus
+
+ align:start position:0%
+so you can just use this time to focus
+ 
+
+ align:start position:0%
+so you can just use this time to focus
+on focus on the material we've discussed
+
+ align:start position:0%
+on focus on the material we've discussed
+ 
+
+ align:start position:0%
+on focus on the material we've discussed
+there's a practice exam from last year
+
+ align:start position:0%
+there's a practice exam from last year
+ 
+
+ align:start position:0%
+there's a practice exam from last year
+posted on the stellar site which you can
+
+ align:start position:0%
+posted on the stellar site which you can
+ 
+
+ align:start position:0%
+posted on the stellar site which you can
+utilize and study from I'll tell you
+
+ align:start position:0%
+utilize and study from I'll tell you
+ 
+
+ align:start position:0%
+utilize and study from I'll tell you
+this that practice exam a practice exam
+
+ align:start position:0%
+this that practice exam a practice exam
+ 
+
+ align:start position:0%
+this that practice exam a practice exam
+is hewed a little more towards some
+
+ align:start position:0%
+is hewed a little more towards some
+ 
+
+ align:start position:0%
+is hewed a little more towards some
+chemical engineering problems that
+
+ align:start position:0%
+chemical engineering problems that
+ 
+
+ align:start position:0%
+chemical engineering problems that
+motivate the numerix I found in the past
+
+ align:start position:0%
+motivate the numerix I found in the past
+ 
+
+ align:start position:0%
+motivate the numerix I found in the past
+that when problems like that are given
+
+ align:start position:0%
+that when problems like that are given
+ 
+
+ align:start position:0%
+that when problems like that are given
+on the exam sometimes there's a lot of
+
+ align:start position:0%
+on the exam sometimes there's a lot of
+ 
+
+ align:start position:0%
+on the exam sometimes there's a lot of
+reading that goes into understanding the
+
+ align:start position:0%
+reading that goes into understanding the
+ 
+
+ align:start position:0%
+reading that goes into understanding the
+engineering problem and that tends to
+
+ align:start position:0%
+engineering problem and that tends to
+ 
+
+ align:start position:0%
+engineering problem and that tends to
+set back the problem solving so I'll
+
+ align:start position:0%
+set back the problem solving so I'll
+ 
+
+ align:start position:0%
+set back the problem solving so I'll
+tell you that the
+
+ align:start position:0%
+tell you that the
+ 
+
+ align:start position:0%
+tell you that the
+is that you'll take on Wednesday will
+
+ align:start position:0%
+is that you'll take on Wednesday will
+ 
+
+ align:start position:0%
+is that you'll take on Wednesday will
+have less of the engineering associated
+
+ align:start position:0%
+have less of the engineering associated
+ 
+
+ align:start position:0%
+have less of the engineering associated
+with it and focus more on the numerical
+
+ align:start position:0%
+with it and focus more on the numerical
+ 
+
+ align:start position:0%
+with it and focus more on the numerical
+or computational science the underlying
+
+ align:start position:0%
+or computational science the underlying
+ 
+
+ align:start position:0%
+or computational science the underlying
+sorts of questions the way the questions
+
+ align:start position:0%
+sorts of questions the way the questions
+ 
+
+ align:start position:0%
+sorts of questions the way the questions
+are asked the kinds of responses you're
+
+ align:start position:0%
+are asked the kinds of responses you're
+ 
+
+ align:start position:0%
+are asked the kinds of responses you're
+expected to give by I'd say are very
+
+ align:start position:0%
+expected to give by I'd say are very
+ 
+
+ align:start position:0%
+expected to give by I'd say are very
+similar but we've tried to tune the
+
+ align:start position:0%
+similar but we've tried to tune the
+ 
+
+ align:start position:0%
+similar but we've tried to tune the
+exams so that it'll be less of a burden
+
+ align:start position:0%
+exams so that it'll be less of a burden
+ 
+
+ align:start position:0%
+exams so that it'll be less of a burden
+to understand the structure of the
+
+ align:start position:0%
+to understand the structure of the
+ 
+
+ align:start position:0%
+to understand the structure of the
+problem before describing how you solve
+
+ align:start position:0%
+problem before describing how you solve
+ 
+
+ align:start position:0%
+problem before describing how you solve
+it I think that's good it's
+
+ align:start position:0%
+it I think that's good it's
+ 
+
+ align:start position:0%
+it I think that's good it's
+comprehensive up to today okay so linear
+
+ align:start position:0%
+comprehensive up to today okay so linear
+ 
+
+ align:start position:0%
+comprehensive up to today okay so linear
+algebra systems of nonlinear equations
+
+ align:start position:0%
+algebra systems of nonlinear equations
+ 
+
+ align:start position:0%
+algebra systems of nonlinear equations
+and optimization are the quiz topics
+
+ align:start position:0%
+and optimization are the quiz topics
+ 
+
+ align:start position:0%
+and optimization are the quiz topics
+we're gonna switch on Friday to ordinary
+
+ align:start position:0%
+we're gonna switch on Friday to ordinary
+ 
+
+ align:start position:0%
+we're gonna switch on Friday to ordinary
+differential equations and initial value
+
+ align:start position:0%
+differential equations and initial value
+ 
+
+ align:start position:0%
+differential equations and initial value
+problems so you have two lectures on
+
+ align:start position:0%
+problems so you have two lectures on
+ 
+
+ align:start position:0%
+problems so you have two lectures on
+that but you won't have done any
+
+ align:start position:0%
+that but you won't have done any
+ 
+
+ align:start position:0%
+that but you won't have done any
+homework you probably don't know enough
+
+ align:start position:0%
+homework you probably don't know enough
+ 
+
+ align:start position:0%
+homework you probably don't know enough
+or practiced enough to answer any
+
+ align:start position:0%
+or practiced enough to answer any
+ 
+
+ align:start position:0%
+or practiced enough to answer any
+questions intelligently on the quiz
+
+ align:start position:0%
+questions intelligently on the quiz
+ 
+
+ align:start position:0%
+questions intelligently on the quiz
+don't expect that material to be on
+
+ align:start position:0%
+don't expect that material to be on
+ 
+
+ align:start position:0%
+don't expect that material to be on
+there it's not right it's gonna be these
+
+ align:start position:0%
+there it's not right it's gonna be these
+ 
+
+ align:start position:0%
+there it's not right it's gonna be these
+three topics are there any questions
+
+ align:start position:0%
+three topics are there any questions
+ 
+
+ align:start position:0%
+three topics are there any questions
+about this that I can answer crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah come come come prepared it
+
+ align:start position:0%
+okay so yeah come come come prepared it
+ 
+
+ align:start position:0%
+okay so yeah come come come prepared it
+might be cold it might be hot it leaks
+
+ align:start position:0%
+might be cold it might be hot it leaks
+ 
+
+ align:start position:0%
+might be cold it might be hot it leaks
+when it rains a little bit yeah it's not
+
+ align:start position:0%
+when it rains a little bit yeah it's not
+ 
+
+ align:start position:0%
+when it rains a little bit yeah it's not
+the not the greatest spot uh so come
+
+ align:start position:0%
+the not the greatest spot uh so come
+ 
+
+ align:start position:0%
+the not the greatest spot uh so come
+come come prepared that's true
+
+ align:start position:0%
+come come prepared that's true
+ 
+
+ align:start position:0%
+come come prepared that's true
+other questions things you want to know
+
+ align:start position:0%
+other questions things you want to know
+ 
+
+ align:start position:0%
+other questions things you want to know
+ooh good question so you can bring you
+
+ align:start position:0%
+ooh good question so you can bring you
+ 
+
+ align:start position:0%
+ooh good question so you can bring you
+can bring the book recommend it for the
+
+ align:start position:0%
+can bring the book recommend it for the
+ 
+
+ align:start position:0%
+can bring the book recommend it for the
+course you can bring your notes you can
+
+ align:start position:0%
+course you can bring your notes you can
+ 
+
+ align:start position:0%
+course you can bring your notes you can
+bring in calculator you need to bring
+
+ align:start position:0%
+bring in calculator you need to bring
+ 
+
+ align:start position:0%
+bring in calculator you need to bring
+some pencils will provide blue books for
+
+ align:start position:0%
+some pencils will provide blue books for
+ 
+
+ align:start position:0%
+some pencils will provide blue books for
+you okay to write your solutions to the
+
+ align:start position:0%
+you okay to write your solutions to the
+ 
+
+ align:start position:0%
+you okay to write your solutions to the
+exam in and so those are the materials
+
+ align:start position:0%
+exam in and so those are the materials
+ 
+
+ align:start position:0%
+exam in and so those are the materials
+good what else same question
+
+ align:start position:0%
+good what else same question
+ 
+
+ align:start position:0%
+good what else same question
+okay other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them okay so then let's jump into the
+
+ align:start position:0%
+them okay so then let's jump into the
+ 
+
+ align:start position:0%
+them okay so then let's jump into the
+topic of the day which is constrained
+
+ align:start position:0%
+topic of the day which is constrained
+ 
+
+ align:start position:0%
+topic of the day which is constrained
+optimization okay so these are problems
+
+ align:start position:0%
+optimization okay so these are problems
+ 
+
+ align:start position:0%
+optimization okay so these are problems
+of the sort right minimize an objective
+
+ align:start position:0%
+of the sort right minimize an objective
+ 
+
+ align:start position:0%
+of the sort right minimize an objective
+function f of X subject to the
+
+ align:start position:0%
+function f of X subject to the
+ 
+
+ align:start position:0%
+function f of X subject to the
+constraint right that X belongs to some
+
+ align:start position:0%
+constraint right that X belongs to some
+ 
+
+ align:start position:0%
+constraint right that X belongs to some
+set D or find the argument X that
+
+ align:start position:0%
+set D or find the argument X that
+ 
+
+ align:start position:0%
+set D or find the argument X that
+minimizes this function these are
+
+ align:start position:0%
+minimizes this function these are
+ 
+
+ align:start position:0%
+minimizes this function these are
+equivalent sorts of problems sometimes
+
+ align:start position:0%
+equivalent sorts of problems sometimes
+ 
+
+ align:start position:0%
+equivalent sorts of problems sometimes
+who want to know one or the other or
+
+ align:start position:0%
+who want to know one or the other or
+ 
+
+ align:start position:0%
+who want to know one or the other or
+both that's not a problem and
+
+ align:start position:0%
+both that's not a problem and
+ 
+
+ align:start position:0%
+both that's not a problem and
+graphically it looks like this here's F
+
+ align:start position:0%
+graphically it looks like this here's F
+ 
+
+ align:start position:0%
+graphically it looks like this here's F
+our objective function it's a nice
+
+ align:start position:0%
+our objective function it's a nice
+ 
+
+ align:start position:0%
+our objective function it's a nice
+convex bowl-shaped function here and we
+
+ align:start position:0%
+convex bowl-shaped function here and we
+ 
+
+ align:start position:0%
+convex bowl-shaped function here and we
+want to know the values of x1 and x2
+
+ align:start position:0%
+want to know the values of x1 and x2
+ 
+
+ align:start position:0%
+want to know the values of x1 and x2
+let's say that minimize this function
+
+ align:start position:0%
+let's say that minimize this function
+ 
+
+ align:start position:0%
+let's say that minimize this function
+subject to some constraint that
+
+ align:start position:0%
+subject to some constraint that
+ 
+
+ align:start position:0%
+subject to some constraint that
+constraint could be that x1 and x2 live
+
+ align:start position:0%
+constraint could be that x1 and x2 live
+ 
+
+ align:start position:0%
+constraint could be that x1 and x2 live
+inside this little blue circle could be
+
+ align:start position:0%
+inside this little blue circle could be
+ 
+
+ align:start position:0%
+inside this little blue circle could be
+D could be that x1 and x2 live on the
+
+ align:start position:0%
+D could be that x1 and x2 live on the
+ 
+
+ align:start position:0%
+D could be that x1 and x2 live on the
+surface of this circle right on the
+
+ align:start position:0%
+surface of this circle right on the
+ 
+
+ align:start position:0%
+surface of this circle right on the
+circumference of this circle that could
+
+ align:start position:0%
+circumference of this circle that could
+ 
+
+ align:start position:0%
+circumference of this circle that could
+be the constraint okay so these are the
+
+ align:start position:0%
+be the constraint okay so these are the
+ 
+
+ align:start position:0%
+be the constraint okay so these are the
+sorts of problems we want to solve D is
+
+ align:start position:0%
+sorts of problems we want to solve D is
+ 
+
+ align:start position:0%
+sorts of problems we want to solve D is
+called the feasible set right they can
+
+ align:start position:0%
+called the feasible set right they can
+ 
+
+ align:start position:0%
+called the feasible set right they can
+be described in terms of really two
+
+ align:start position:0%
+be described in terms of really two
+ 
+
+ align:start position:0%
+be described in terms of really two
+types of constraints one is what we call
+
+ align:start position:0%
+types of constraints one is what we call
+ 
+
+ align:start position:0%
+types of constraints one is what we call
+equality constraints so D can be the set
+
+ align:start position:0%
+equality constraints so D can be the set
+ 
+
+ align:start position:0%
+equality constraints so D can be the set
+of values X such that some non linear
+
+ align:start position:0%
+of values X such that some non linear
+ 
+
+ align:start position:0%
+of values X such that some non linear
+function C of X is equal to 0 ok so it's
+
+ align:start position:0%
+function C of X is equal to 0 ok so it's
+ 
+
+ align:start position:0%
+function C of X is equal to 0 ok so it's
+the set of points that satisfy this
+
+ align:start position:0%
+the set of points that satisfy this
+ 
+
+ align:start position:0%
+the set of points that satisfy this
+non-linear equation and among those
+
+ align:start position:0%
+non-linear equation and among those
+ 
+
+ align:start position:0%
+non-linear equation and among those
+points we want to know which one
+
+ align:start position:0%
+points we want to know which one
+ 
+
+ align:start position:0%
+points we want to know which one
+produces the minimum in the objective
+
+ align:start position:0%
+produces the minimum in the objective
+ 
+
+ align:start position:0%
+produces the minimum in the objective
+function or it could be an inequality
+
+ align:start position:0%
+function or it could be an inequality
+ 
+
+ align:start position:0%
+function or it could be an inequality
+constraint so D could be the set of
+
+ align:start position:0%
+constraint so D could be the set of
+ 
+
+ align:start position:0%
+constraint so D could be the set of
+points such that some nonlinear function
+
+ align:start position:0%
+points such that some nonlinear function
+ 
+
+ align:start position:0%
+points such that some nonlinear function
+H of X is by convention positive ok so H
+
+ align:start position:0%
+H of X is by convention positive ok so H
+ 
+
+ align:start position:0%
+H of X is by convention positive ok so H
+of X could represent for example the
+
+ align:start position:0%
+of X could represent for example the
+ 
+
+ align:start position:0%
+of X could represent for example the
+interior of a circle and C of X could
+
+ align:start position:0%
+interior of a circle and C of X could
+ 
+
+ align:start position:0%
+interior of a circle and C of X could
+represent the circumference of a circle
+
+ align:start position:0%
+represent the circumference of a circle
+ 
+
+ align:start position:0%
+represent the circumference of a circle
+right and we would have nonlinear
+
+ align:start position:0%
+right and we would have nonlinear
+ 
+
+ align:start position:0%
+right and we would have nonlinear
+equations that reflect those values of X
+
+ align:start position:0%
+equations that reflect those values of X
+ 
+
+ align:start position:0%
+equations that reflect those values of X
+that satisfy satisfied those sorts of
+
+ align:start position:0%
+that satisfy satisfied those sorts of
+ 
+
+ align:start position:0%
+that satisfy satisfied those sorts of
+geometries okay so equality constraint
+
+ align:start position:0%
+geometries okay so equality constraint
+ 
+
+ align:start position:0%
+geometries okay so equality constraint
+right points that lie on this circle
+
+ align:start position:0%
+right points that lie on this circle
+ 
+
+ align:start position:0%
+right points that lie on this circle
+inequality constraint points that lie
+
+ align:start position:0%
+inequality constraint points that lie
+ 
+
+ align:start position:0%
+inequality constraint points that lie
+within this circle the shape of the
+
+ align:start position:0%
+within this circle the shape of the
+ 
+
+ align:start position:0%
+within this circle the shape of the
+feasible set is constrained by the
+
+ align:start position:0%
+feasible set is constrained by the
+ 
+
+ align:start position:0%
+feasible set is constrained by the
+problem that you're actually interested
+
+ align:start position:0%
+problem that you're actually interested
+ 
+
+ align:start position:0%
+problem that you're actually interested
+in right so it's easy for me to draw
+
+ align:start position:0%
+in right so it's easy for me to draw
+ 
+
+ align:start position:0%
+in right so it's easy for me to draw
+circles in the plane because that's
+
+ align:start position:0%
+circles in the plane because that's
+ 
+
+ align:start position:0%
+circles in the plane because that's
+shape you're familiar with but actually
+
+ align:start position:0%
+shape you're familiar with but actually
+ 
+
+ align:start position:0%
+shape you're familiar with but actually
+it'll come from some sort of physical
+
+ align:start position:0%
+it'll come from some sort of physical
+ 
+
+ align:start position:0%
+it'll come from some sort of physical
+constraint on the engineering problem
+
+ align:start position:0%
+constraint on the engineering problem
+ 
+
+ align:start position:0%
+constraint on the engineering problem
+you're looking at like mole fractions
+
+ align:start position:0%
+you're looking at like mole fractions
+ 
+
+ align:start position:0%
+you're looking at like mole fractions
+need to be bigger than zero and smaller
+
+ align:start position:0%
+need to be bigger than zero and smaller
+ 
+
+ align:start position:0%
+need to be bigger than zero and smaller
+than one in temperatures an absolute
+
+ align:start position:0%
+than one in temperatures an absolute
+ 
+
+ align:start position:0%
+than one in temperatures an absolute
+value you have to be bigger than zero
+
+ align:start position:0%
+value you have to be bigger than zero
+ 
+
+ align:start position:0%
+value you have to be bigger than zero
+and smaller than some value because
+
+ align:start position:0%
+and smaller than some value because
+ 
+
+ align:start position:0%
+and smaller than some value because
+that's a safety factor on the process
+
+ align:start position:0%
+that's a safety factor on the process
+ 
+
+ align:start position:0%
+that's a safety factor on the process
+right so these are the set up right the
+
+ align:start position:0%
+right so these are the set up right the
+ 
+
+ align:start position:0%
+right so these are the set up right the
+constraints on various sorts of
+
+ align:start position:0%
+constraints on various sorts of
+ 
+
+ align:start position:0%
+constraints on various sorts of
+optimization problems that we're
+
+ align:start position:0%
+optimization problems that we're
+ 
+
+ align:start position:0%
+optimization problems that we're
+interested in it could also be true that
+
+ align:start position:0%
+interested in it could also be true that
+ 
+
+ align:start position:0%
+interested in it could also be true that
+we're interested in say optimization in
+
+ align:start position:0%
+we're interested in say optimization in
+ 
+
+ align:start position:0%
+we're interested in say optimization in
+the domain outside of this circle - it
+
+ align:start position:0%
+the domain outside of this circle - it
+ 
+
+ align:start position:0%
+the domain outside of this circle - it
+could be on the inside could be on the
+
+ align:start position:0%
+could be on the inside could be on the
+ 
+
+ align:start position:0%
+could be on the inside could be on the
+outside right that's also an inequality
+
+ align:start position:0%
+outside right that's also an inequality
+ 
+
+ align:start position:0%
+outside right that's also an inequality
+constrained sort of problem you know
+
+ align:start position:0%
+constrained sort of problem you know
+ 
+
+ align:start position:0%
+constrained sort of problem you know
+some of these already ok they're
+
+ align:start position:0%
+some of these already ok they're
+ 
+
+ align:start position:0%
+some of these already ok they're
+familiar to you so here's a classic one
+
+ align:start position:0%
+familiar to you so here's a classic one
+ 
+
+ align:start position:0%
+familiar to you so here's a classic one
+from mechanics right here's the total
+
+ align:start position:0%
+from mechanics right here's the total
+ 
+
+ align:start position:0%
+from mechanics right here's the total
+energy in a system for say a pendulum
+
+ align:start position:0%
+energy in a system for say a pendulum
+ 
+
+ align:start position:0%
+energy in a system for say a pendulum
+right so X is like the position of the
+
+ align:start position:0%
+right so X is like the position of the
+ 
+
+ align:start position:0%
+right so X is like the position of the
+tip of this pendulum and V is the
+
+ align:start position:0%
+tip of this pendulum and V is the
+ 
+
+ align:start position:0%
+tip of this pendulum and V is the
+velocity that it moves with this is the
+
+ align:start position:0%
+velocity that it moves with this is the
+ 
+
+ align:start position:0%
+velocity that it moves with this is the
+kinetic energy this is the potential
+
+ align:start position:0%
+kinetic energy this is the potential
+ 
+
+ align:start position:0%
+kinetic energy this is the potential
+energy and we know the pendulum will
+
+ align:start position:0%
+energy and we know the pendulum will
+ 
+
+ align:start position:0%
+energy and we know the pendulum will
+come to rest in a place where the energy
+
+ align:start position:0%
+come to rest in a place where the energy
+ 
+
+ align:start position:0%
+come to rest in a place where the energy
+is minimized right well the energy can
+
+ align:start position:0%
+is minimized right well the energy can
+ 
+
+ align:start position:0%
+is minimized right well the energy can
+only be minimized when the velocity here
+
+ align:start position:0%
+only be minimized when the velocity here
+ 
+
+ align:start position:0%
+only be minimized when the velocity here
+is zero because any nonzero velocity
+
+ align:start position:0%
+is zero because any nonzero velocity
+ 
+
+ align:start position:0%
+is zero because any nonzero velocity
+will always push the energy content up
+
+ align:start position:0%
+will always push the energy content up
+ 
+
+ align:start position:0%
+will always push the energy content up
+so it comes to rest right it doesn't
+
+ align:start position:0%
+so it comes to rest right it doesn't
+ 
+
+ align:start position:0%
+so it comes to rest right it doesn't
+move right and then there's some value
+
+ align:start position:0%
+move right and then there's some value
+ 
+
+ align:start position:0%
+move right and then there's some value
+of x at which the energy is minimized if
+
+ align:start position:0%
+of x at which the energy is minimized if
+ 
+
+ align:start position:0%
+of x at which the energy is minimized if
+there is no constraint that says that
+
+ align:start position:0%
+there is no constraint that says that
+ 
+
+ align:start position:0%
+there is no constraint that says that
+the pendulum is attached to some central
+
+ align:start position:0%
+the pendulum is attached to some central
+ 
+
+ align:start position:0%
+the pendulum is attached to some central
+axis then I can always make the energy
+
+ align:start position:0%
+axis then I can always make the energy
+ 
+
+ align:start position:0%
+axis then I can always make the energy
+smaller by making X more and more
+
+ align:start position:0%
+smaller by making X more and more
+ 
+
+ align:start position:0%
+smaller by making X more and more
+negative it just keeps falling right
+
+ align:start position:0%
+negative it just keeps falling right
+ 
+
+ align:start position:0%
+negative it just keeps falling right
+there is no stopping point but there's a
+
+ align:start position:0%
+there is no stopping point but there's a
+ 
+
+ align:start position:0%
+there is no stopping point but there's a
+constraint right the distance between
+
+ align:start position:0%
+constraint right the distance between
+ 
+
+ align:start position:0%
+constraint right the distance between
+the tip of the pendulum in this central
+
+ align:start position:0%
+the tip of the pendulum in this central
+ 
+
+ align:start position:0%
+the tip of the pendulum in this central
+point there is some fixed distance out
+
+ align:start position:0%
+point there is some fixed distance out
+ 
+
+ align:start position:0%
+point there is some fixed distance out
+so this is an equality constraint sort
+
+ align:start position:0%
+so this is an equality constraint sort
+ 
+
+ align:start position:0%
+so this is an equality constraint sort
+of problem and we have to choose from
+
+ align:start position:0%
+of problem and we have to choose from
+ 
+
+ align:start position:0%
+of problem and we have to choose from
+the set of V and X the values subject to
+
+ align:start position:0%
+the set of V and X the values subject to
+ 
+
+ align:start position:0%
+the set of V and X the values subject to
+this constraint that minimized the total
+
+ align:start position:0%
+this constraint that minimized the total
+ 
+
+ align:start position:0%
+this constraint that minimized the total
+energy and that's that's this
+
+ align:start position:0%
+energy and that's that's this
+ 
+
+ align:start position:0%
+energy and that's that's this
+configuration of the pendulum here so
+
+ align:start position:0%
+configuration of the pendulum here so
+ 
+
+ align:start position:0%
+configuration of the pendulum here so
+you know these sorts of problems already
+
+ align:start position:0%
+you know these sorts of problems already
+ 
+
+ align:start position:0%
+you know these sorts of problems already
+but we talked about this one right
+
+ align:start position:0%
+but we talked about this one right
+ 
+
+ align:start position:0%
+but we talked about this one right
+linear sorts of programs these are
+
+ align:start position:0%
+linear sorts of programs these are
+ 
+
+ align:start position:0%
+linear sorts of programs these are
+optimization problems where the
+
+ align:start position:0%
+optimization problems where the
+ 
+
+ align:start position:0%
+optimization problems where the
+objective function is linear in the
+
+ align:start position:0%
+objective function is linear in the
+ 
+
+ align:start position:0%
+objective function is linear in the
+design variables right so it's just the
+
+ align:start position:0%
+design variables right so it's just the
+ 
+
+ align:start position:0%
+design variables right so it's just the
+dot product between X and some vector C
+
+ align:start position:0%
+dot product between X and some vector C
+ 
+
+ align:start position:0%
+dot product between X and some vector C
+that weights the different design
+
+ align:start position:0%
+that weights the different design
+ 
+
+ align:start position:0%
+that weights the different design
+options against each other so we talked
+
+ align:start position:0%
+options against each other so we talked
+ 
+
+ align:start position:0%
+options against each other so we talked
+about ice cream guess this is all
+
+ align:start position:0%
+about ice cream guess this is all
+ 
+
+ align:start position:0%
+about ice cream guess this is all
+premium ice cream
+
+ align:start position:0%
+premium ice cream
+ 
+
+ align:start position:0%
+premium ice cream
+it comes in the small containers right
+
+ align:start position:0%
+it comes in the small containers right
+ 
+
+ align:start position:0%
+it comes in the small containers right
+subject to different constraints so
+
+ align:start position:0%
+subject to different constraints so
+ 
+
+ align:start position:0%
+subject to different constraints so
+those constraints can be things like oh
+
+ align:start position:0%
+those constraints can be things like oh
+ 
+
+ align:start position:0%
+those constraints can be things like oh
+x2 be positive because we can't make
+
+ align:start position:0%
+x2 be positive because we can't make
+ 
+
+ align:start position:0%
+x2 be positive because we can't make
+negative amounts of ice-cream and maybe
+
+ align:start position:0%
+negative amounts of ice-cream and maybe
+ 
+
+ align:start position:0%
+negative amounts of ice-cream and maybe
+we've done market research that tells us
+
+ align:start position:0%
+we've done market research that tells us
+ 
+
+ align:start position:0%
+we've done market research that tells us
+that the market can only tolerate
+
+ align:start position:0%
+that the market can only tolerate
+ 
+
+ align:start position:0%
+that the market can only tolerate
+certain ratios of different types of
+
+ align:start position:0%
+certain ratios of different types of
+ 
+
+ align:start position:0%
+certain ratios of different types of
+ice-cream and that maybe some set of
+
+ align:start position:0%
+ice-cream and that maybe some set of
+ 
+
+ align:start position:0%
+ice-cream and that maybe some set of
+linear equations that describe that
+
+ align:start position:0%
+linear equations that describe that
+ 
+
+ align:start position:0%
+linear equations that describe that
+market research that sort of bound the
+
+ align:start position:0%
+market research that sort of bound the
+ 
+
+ align:start position:0%
+market research that sort of bound the
+upper values of how much ice cream we
+
+ align:start position:0%
+upper values of how much ice cream we
+ 
+
+ align:start position:0%
+upper values of how much ice cream we
+can put out on the market then we try to
+
+ align:start position:0%
+can put out on the market then we try to
+ 
+
+ align:start position:0%
+can put out on the market then we try to
+choose the optimal blend of you know
+
+ align:start position:0%
+choose the optimal blend of you know
+ 
+
+ align:start position:0%
+choose the optimal blend of you know
+pina colada and strawberry - so okay
+
+ align:start position:0%
+pina colada and strawberry - so okay
+ 
+
+ align:start position:0%
+pina colada and strawberry - so okay
+those are linear programs okay this is
+
+ align:start position:0%
+those are linear programs okay this is
+ 
+
+ align:start position:0%
+those are linear programs okay this is
+an unqualified say minimize f of X
+
+ align:start position:0%
+an unqualified say minimize f of X
+ 
+
+ align:start position:0%
+an unqualified say minimize f of X
+subject to the constraint that C of X is
+
+ align:start position:0%
+subject to the constraint that C of X is
+ 
+
+ align:start position:0%
+subject to the constraint that C of X is
+0 and H of X is positive right so
+
+ align:start position:0%
+0 and H of X is positive right so
+ 
+
+ align:start position:0%
+0 and H of X is positive right so
+minimize it over the values of X that
+
+ align:start position:0%
+minimize it over the values of X that
+ 
+
+ align:start position:0%
+minimize it over the values of X that
+satisfy these two constraints
+
+ align:start position:0%
+satisfy these two constraints
+ 
+
+ align:start position:0%
+satisfy these two constraints
+there's an old approach discussed in the
+
+ align:start position:0%
+there's an old approach discussed in the
+ 
+
+ align:start position:0%
+there's an old approach discussed in the
+literature and it's not used I'm going
+
+ align:start position:0%
+literature and it's not used I'm going
+ 
+
+ align:start position:0%
+literature and it's not used I'm going
+to describe it to you and then I want
+
+ align:start position:0%
+to describe it to you and then I want
+ 
+
+ align:start position:0%
+to describe it to you and then I want
+you to try to figure out why it's not
+
+ align:start position:0%
+you to try to figure out why it's not
+ 
+
+ align:start position:0%
+you to try to figure out why it's not
+used okay and it's called the penalty
+
+ align:start position:0%
+used okay and it's called the penalty
+ 
+
+ align:start position:0%
+used okay and it's called the penalty
+method and the penalty method works this
+
+ align:start position:0%
+method and the penalty method works this
+ 
+
+ align:start position:0%
+method and the penalty method works this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+it says define a new objective function
+
+ align:start position:0%
+it says define a new objective function
+ 
+
+ align:start position:0%
+it says define a new objective function
+which is our old objective function plus
+
+ align:start position:0%
+which is our old objective function plus
+ 
+
+ align:start position:0%
+which is our old objective function plus
+some penalty for violating the
+
+ align:start position:0%
+some penalty for violating the
+ 
+
+ align:start position:0%
+some penalty for violating the
+constraints how does that penalty work
+
+ align:start position:0%
+constraints how does that penalty work
+ 
+
+ align:start position:0%
+constraints how does that penalty work
+so we know that we want values of X for
+
+ align:start position:0%
+so we know that we want values of X for
+ 
+
+ align:start position:0%
+so we know that we want values of X for
+which C of X is equal to 0 so if we add
+
+ align:start position:0%
+which C of X is equal to 0 so if we add
+ 
+
+ align:start position:0%
+which C of X is equal to 0 so if we add
+to our objective function the norm of C
+
+ align:start position:0%
+to our objective function the norm of C
+ 
+
+ align:start position:0%
+to our objective function the norm of C
+of X this is a positive quantity this is
+
+ align:start position:0%
+of X this is a positive quantity this is
+ 
+
+ align:start position:0%
+of X this is a positive quantity this is
+a positive quantity whenever X doesn't
+
+ align:start position:0%
+a positive quantity whenever X doesn't
+ 
+
+ align:start position:0%
+a positive quantity whenever X doesn't
+satisfy the constraint this positive
+
+ align:start position:0%
+satisfy the constraint this positive
+ 
+
+ align:start position:0%
+satisfy the constraint this positive
+quantity will be will give us a bigger
+
+ align:start position:0%
+quantity will be will give us a bigger
+ 
+
+ align:start position:0%
+quantity will be will give us a bigger
+value for this objective function f
+
+ align:start position:0%
+value for this objective function f
+ 
+
+ align:start position:0%
+value for this objective function f
+right then if C of X was equal to 0 so
+
+ align:start position:0%
+right then if C of X was equal to 0 so
+ 
+
+ align:start position:0%
+right then if C of X was equal to 0 so
+we penalize write points which don't
+
+ align:start position:0%
+we penalize write points which don't
+ 
+
+ align:start position:0%
+we penalize write points which don't
+satisfy the constraint and in the limit
+
+ align:start position:0%
+satisfy the constraint and in the limit
+ 
+
+ align:start position:0%
+satisfy the constraint and in the limit
+that this penalty factor mu here goes to
+
+ align:start position:0%
+that this penalty factor mu here goes to
+ 
+
+ align:start position:0%
+that this penalty factor mu here goes to
+0 the penalties get large okay so large
+
+ align:start position:0%
+0 the penalties get large okay so large
+ 
+
+ align:start position:0%
+0 the penalties get large okay so large
+that our solution will have to prefer
+
+ align:start position:0%
+that our solution will have to prefer
+ 
+
+ align:start position:0%
+that our solution will have to prefer
+right satisfying the constraints there's
+
+ align:start position:0%
+right satisfying the constraints there's
+ 
+
+ align:start position:0%
+right satisfying the constraints there's
+another penalty factor over here which
+
+ align:start position:0%
+another penalty factor over here which
+ 
+
+ align:start position:0%
+another penalty factor over here which
+is identical to this one but for the
+
+ align:start position:0%
+is identical to this one but for the
+ 
+
+ align:start position:0%
+is identical to this one but for the
+inequality constraint it's
+
+ align:start position:0%
+inequality constraint it's
+ 
+
+ align:start position:0%
+inequality constraint it's
+it says take a Heaviside step function
+
+ align:start position:0%
+it says take a Heaviside step function
+ 
+
+ align:start position:0%
+it says take a Heaviside step function
+right 4 which is equal to 1 right when
+
+ align:start position:0%
+right 4 which is equal to 1 right when
+ 
+
+ align:start position:0%
+right 4 which is equal to 1 right when
+the value of its argument is positive
+
+ align:start position:0%
+the value of its argument is positive
+ 
+
+ align:start position:0%
+the value of its argument is positive
+and it's equal to 0 when the value of
+
+ align:start position:0%
+and it's equal to 0 when the value of
+ 
+
+ align:start position:0%
+and it's equal to 0 when the value of
+its argument is negative right so
+
+ align:start position:0%
+its argument is negative right so
+ 
+
+ align:start position:0%
+its argument is negative right so
+whenever I violate my each of my
+
+ align:start position:0%
+whenever I violate my each of my
+ 
+
+ align:start position:0%
+whenever I violate my each of my
+inequality constraints H I of X right
+
+ align:start position:0%
+inequality constraints H I of X right
+ 
+
+ align:start position:0%
+inequality constraints H I of X right
+turn on this have a side step function
+
+ align:start position:0%
+turn on this have a side step function
+ 
+
+ align:start position:0%
+turn on this have a side step function
+make it equal to 1 and then multiply it
+
+ align:start position:0%
+make it equal to 1 and then multiply it
+ 
+
+ align:start position:0%
+make it equal to 1 and then multiply it
+by the value of the constraint squared a
+
+ align:start position:0%
+by the value of the constraint squared a
+ 
+
+ align:start position:0%
+by the value of the constraint squared a
+positive number right so this is the
+
+ align:start position:0%
+positive number right so this is the
+ 
+
+ align:start position:0%
+positive number right so this is the
+inequality constraint penalty and this
+
+ align:start position:0%
+inequality constraint penalty and this
+ 
+
+ align:start position:0%
+inequality constraint penalty and this
+is the Equality constraint penalty
+
+ align:start position:0%
+is the Equality constraint penalty
+ 
+
+ align:start position:0%
+is the Equality constraint penalty
+people don't use this though it makes
+
+ align:start position:0%
+people don't use this though it makes
+ 
+
+ align:start position:0%
+people don't use this though it makes
+sense right I take the limit that mu
+
+ align:start position:0%
+sense right I take the limit that mu
+ 
+
+ align:start position:0%
+sense right I take the limit that mu
+goes to 0 I'm gonna have to prefer
+
+ align:start position:0%
+goes to 0 I'm gonna have to prefer
+ 
+
+ align:start position:0%
+goes to 0 I'm gonna have to prefer
+solutions right that satisfy these
+
+ align:start position:0%
+solutions right that satisfy these
+ 
+
+ align:start position:0%
+solutions right that satisfy these
+constraints otherwise right if I don't
+
+ align:start position:0%
+constraints otherwise right if I don't
+ 
+
+ align:start position:0%
+constraints otherwise right if I don't
+satisfy these constraints I can always
+
+ align:start position:0%
+satisfy these constraints I can always
+ 
+
+ align:start position:0%
+satisfy these constraints I can always
+move closer to a solution that satisfies
+
+ align:start position:0%
+move closer to a solution that satisfies
+ 
+
+ align:start position:0%
+move closer to a solution that satisfies
+the constraint and I'll bring down right
+
+ align:start position:0%
+the constraint and I'll bring down right
+ 
+
+ align:start position:0%
+the constraint and I'll bring down right
+the value of this objective function
+
+ align:start position:0%
+the value of this objective function
+ 
+
+ align:start position:0%
+the value of this objective function
+I'll make it lower so I'll always prefer
+
+ align:start position:0%
+I'll make it lower so I'll always prefer
+ 
+
+ align:start position:0%
+I'll make it lower so I'll always prefer
+these lower value solutions but can you
+
+ align:start position:0%
+these lower value solutions but can you
+ 
+
+ align:start position:0%
+these lower value solutions but can you
+guys take a second and sort of talk to
+
+ align:start position:0%
+guys take a second and sort of talk to
+ 
+
+ align:start position:0%
+guys take a second and sort of talk to
+each other see if you can figure out why
+
+ align:start position:0%
+each other see if you can figure out why
+ 
+
+ align:start position:0%
+each other see if you can figure out why
+why one doesn't use this method why is
+
+ align:start position:0%
+why one doesn't use this method why is
+ 
+
+ align:start position:0%
+why one doesn't use this method why is
+this method a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I heard I heard the volume go up at
+
+ align:start position:0%
+okay I heard I heard the volume go up at
+ 
+
+ align:start position:0%
+okay I heard I heard the volume go up at
+some point which means either you switch
+
+ align:start position:0%
+some point which means either you switch
+ 
+
+ align:start position:0%
+some point which means either you switch
+topics and thought we're comfortable
+
+ align:start position:0%
+topics and thought we're comfortable
+ 
+
+ align:start position:0%
+topics and thought we're comfortable
+talking about that than this or maybe
+
+ align:start position:0%
+talking about that than this or maybe
+ 
+
+ align:start position:0%
+talking about that than this or maybe
+maybe you guys were coming to some
+
+ align:start position:0%
+maybe you guys were coming to some
+ 
+
+ align:start position:0%
+maybe you guys were coming to some
+conclusions or had some ideas about why
+
+ align:start position:0%
+conclusions or had some ideas about why
+ 
+
+ align:start position:0%
+conclusions or had some ideas about why
+this this might be a bad idea you want
+
+ align:start position:0%
+this this might be a bad idea you want
+ 
+
+ align:start position:0%
+this this might be a bad idea you want
+to join a volunteer some of what you
+
+ align:start position:0%
+to join a volunteer some of what you
+ 
+
+ align:start position:0%
+to join a volunteer some of what you
+were talking about yeah well that's that
+
+ align:start position:0%
+were talking about yeah well that's that
+ 
+
+ align:start position:0%
+were talking about yeah well that's that
+that's an interesting idea so yeah so if
+
+ align:start position:0%
+that's an interesting idea so yeah so if
+ 
+
+ align:start position:0%
+that's an interesting idea so yeah so if
+we have a non-convex optimization
+
+ align:start position:0%
+we have a non-convex optimization
+ 
+
+ align:start position:0%
+we have a non-convex optimization
+problem there could be some issues with
+
+ align:start position:0%
+problem there could be some issues with
+ 
+
+ align:start position:0%
+problem there could be some issues with
+f of X and maybe f of X runs away so
+
+ align:start position:0%
+f of X and maybe f of X runs away so
+ 
+
+ align:start position:0%
+f of X and maybe f of X runs away so
+fast that I can never make the penalty
+
+ align:start position:0%
+fast that I can never make the penalty
+ 
+
+ align:start position:0%
+fast that I can never make the penalty
+big enough to enforce the constraint
+
+ align:start position:0%
+big enough to enforce the constraint
+ 
+
+ align:start position:0%
+big enough to enforce the constraint
+that's that's actually a really
+
+ align:start position:0%
+that's that's actually a really
+ 
+
+ align:start position:0%
+that's that's actually a really
+interesting idea and I like I like the
+
+ align:start position:0%
+interesting idea and I like I like the
+ 
+
+ align:start position:0%
+interesting idea and I like I like the
+idea of comparing the magnitude of these
+
+ align:start position:0%
+idea of comparing the magnitude of these
+ 
+
+ align:start position:0%
+idea of comparing the magnitude of these
+two terms I think that's on the right
+
+ align:start position:0%
+two terms I think that's on the right
+ 
+
+ align:start position:0%
+two terms I think that's on the right
+track where there were there's some
+
+ align:start position:0%
+track where there were there's some
+ 
+
+ align:start position:0%
+track where there were there's some
+other ideas about why why you might not
+
+ align:start position:0%
+other ideas about why why you might not
+ 
+
+ align:start position:0%
+other ideas about why why you might not
+do this different ideas yeah well you
+
+ align:start position:0%
+do this different ideas yeah well you
+ 
+
+ align:start position:0%
+do this different ideas yeah well you
+know that that's an interesting idea
+
+ align:start position:0%
+know that that's an interesting idea
+ 
+
+ align:start position:0%
+know that that's an interesting idea
+but actually the two terms in the
+
+ align:start position:0%
+but actually the two terms in the
+ 
+
+ align:start position:0%
+but actually the two terms in the
+parentheses here are both positive right
+
+ align:start position:0%
+parentheses here are both positive right
+ 
+
+ align:start position:0%
+parentheses here are both positive right
+so they're only going to be minimized
+
+ align:start position:0%
+so they're only going to be minimized
+ 
+
+ align:start position:0%
+so they're only going to be minimized
+when I satisfy the constraints right so
+
+ align:start position:0%
+when I satisfy the constraints right so
+ 
+
+ align:start position:0%
+when I satisfy the constraints right so
+the local minimum of the of the terms in
+
+ align:start position:0%
+the local minimum of the of the terms in
+ 
+
+ align:start position:0%
+the local minimum of the of the terms in
+parentheses sit on the on or within the
+
+ align:start position:0%
+parentheses sit on the on or within the
+ 
+
+ align:start position:0%
+parentheses sit on the on or within the
+boundaries of the feasible set that
+
+ align:start position:0%
+boundaries of the feasible set that
+ 
+
+ align:start position:0%
+boundaries of the feasible set that
+we're looking at so by construction
+
+ align:start position:0%
+we're looking at so by construction
+ 
+
+ align:start position:0%
+we're looking at so by construction
+actually we're going to be able to
+
+ align:start position:0%
+actually we're going to be able to
+ 
+
+ align:start position:0%
+actually we're going to be able to
+satisfy them because the local minimum
+
+ align:start position:0%
+satisfy them because the local minimum
+ 
+
+ align:start position:0%
+satisfy them because the local minimum
+of these points that sits on these on
+
+ align:start position:0%
+of these points that sits on these on
+ 
+
+ align:start position:0%
+of these points that sits on these on
+these boundaries these terms are
+
+ align:start position:0%
+these boundaries these terms are
+ 
+
+ align:start position:0%
+these boundaries these terms are
+minimized okay by satisfying the
+
+ align:start position:0%
+minimized okay by satisfying the
+ 
+
+ align:start position:0%
+minimized okay by satisfying the
+constraints other ideas yeah what's that
+
+ align:start position:0%
+constraints other ideas yeah what's that
+ 
+
+ align:start position:0%
+constraints other ideas yeah what's that
+oh this is a good point right the
+
+ align:start position:0%
+oh this is a good point right the
+ 
+
+ align:start position:0%
+oh this is a good point right the
+iterates like this is an unconstrained
+
+ align:start position:0%
+iterates like this is an unconstrained
+ 
+
+ align:start position:0%
+iterates like this is an unconstrained
+optimization problem I'm just going to
+
+ align:start position:0%
+optimization problem I'm just going to
+ 
+
+ align:start position:0%
+optimization problem I'm just going to
+minimize this objective function it's
+
+ align:start position:0%
+minimize this objective function it's
+ 
+
+ align:start position:0%
+minimize this objective function it's
+like what her said right I can go
+
+ align:start position:0%
+like what her said right I can go
+ 
+
+ align:start position:0%
+like what her said right I can go
+anywhere I want in the domain I'm gonna
+
+ align:start position:0%
+anywhere I want in the domain I'm gonna
+ 
+
+ align:start position:0%
+anywhere I want in the domain I'm gonna
+minimize this objective function I'm
+
+ align:start position:0%
+minimize this objective function I'm
+ 
+
+ align:start position:0%
+minimize this objective function I'm
+gonna try and take the limit as mu goes
+
+ align:start position:0%
+gonna try and take the limit as mu goes
+ 
+
+ align:start position:0%
+gonna try and take the limit as mu goes
+to zero the interests don't have to be
+
+ align:start position:0%
+to zero the interests don't have to be
+ 
+
+ align:start position:0%
+to zero the interests don't have to be
+feasible maybe I can't even evaluate f
+
+ align:start position:0%
+feasible maybe I can't even evaluate f
+ 
+
+ align:start position:0%
+feasible maybe I can't even evaluate f
+of X if
+
+ align:start position:0%
+of X if
+ 
+
+ align:start position:0%
+of X if
+it's aren't feasible that's an excellent
+
+ align:start position:0%
+it's aren't feasible that's an excellent
+ 
+
+ align:start position:0%
+it's aren't feasible that's an excellent
+point right that could be an issue
+
+ align:start position:0%
+point right that could be an issue
+ 
+
+ align:start position:0%
+point right that could be an issue
+anything else there's some other ideas
+
+ align:start position:0%
+anything else there's some other ideas
+ 
+
+ align:start position:0%
+anything else there's some other ideas
+sure I think I think that's a good point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+short so you'll you'll see actually the
+
+ align:start position:0%
+short so you'll you'll see actually the
+ 
+
+ align:start position:0%
+short so you'll you'll see actually the
+way the right way to do this is to use
+
+ align:start position:0%
+way the right way to do this is to use
+ 
+
+ align:start position:0%
+way the right way to do this is to use
+what's called interior point methods
+
+ align:start position:0%
+what's called interior point methods
+ 
+
+ align:start position:0%
+what's called interior point methods
+which laid the inside the domain this is
+
+ align:start position:0%
+which laid the inside the domain this is
+ 
+
+ align:start position:0%
+which laid the inside the domain this is
+an excellent point there's another issue
+
+ align:start position:0%
+an excellent point there's another issue
+ 
+
+ align:start position:0%
+an excellent point there's another issue
+with this that's it's I think it's
+
+ align:start position:0%
+with this that's it's I think it's
+ 
+
+ align:start position:0%
+with this that's it's I think it's
+actually less subtle than some of these
+
+ align:start position:0%
+actually less subtle than some of these
+ 
+
+ align:start position:0%
+actually less subtle than some of these
+ideas which are all they're all correct
+
+ align:start position:0%
+ideas which are all they're all correct
+ 
+
+ align:start position:0%
+ideas which are all they're all correct
+actually these can be problems with this
+
+ align:start position:0%
+actually these can be problems with this
+ 
+
+ align:start position:0%
+actually these can be problems with this
+sort of penalty method as I take the
+
+ align:start position:0%
+sort of penalty method as I take the
+ 
+
+ align:start position:0%
+sort of penalty method as I take the
+limit that nu goes to zero the penalty
+
+ align:start position:0%
+limit that nu goes to zero the penalty
+ 
+
+ align:start position:0%
+limit that nu goes to zero the penalty
+function becomes large okay for all
+
+ align:start position:0%
+function becomes large okay for all
+ 
+
+ align:start position:0%
+function becomes large okay for all
+points outside the domain they can
+
+ align:start position:0%
+points outside the domain they can
+ 
+
+ align:start position:0%
+points outside the domain they can
+become larger than F right for those
+
+ align:start position:0%
+become larger than F right for those
+ 
+
+ align:start position:0%
+become larger than F right for those
+points and so there's some practical
+
+ align:start position:0%
+points and so there's some practical
+ 
+
+ align:start position:0%
+points and so there's some practical
+issues about comparing these two terms
+
+ align:start position:0%
+issues about comparing these two terms
+ 
+
+ align:start position:0%
+issues about comparing these two terms
+against each other right I may not have
+
+ align:start position:0%
+against each other right I may not have
+ 
+
+ align:start position:0%
+against each other right I may not have
+sufficient accuracy sufficient number of
+
+ align:start position:0%
+sufficient accuracy sufficient number of
+ 
+
+ align:start position:0%
+sufficient accuracy sufficient number of
+digits to accurately add these two terms
+
+ align:start position:0%
+digits to accurately add these two terms
+ 
+
+ align:start position:0%
+digits to accurately add these two terms
+together so I may prefer to find some
+
+ align:start position:0%
+together so I may prefer to find some
+ 
+
+ align:start position:0%
+together so I may prefer to find some
+point right that lives on the boundary
+
+ align:start position:0%
+point right that lives on the boundary
+ 
+
+ align:start position:0%
+point right that lives on the boundary
+of the domain as mu goes to zero but I
+
+ align:start position:0%
+of the domain as mu goes to zero but I
+ 
+
+ align:start position:0%
+of the domain as mu goes to zero but I
+can't guarantee you that it was a minima
+
+ align:start position:0%
+can't guarantee you that it was a minima
+ 
+
+ align:start position:0%
+can't guarantee you that it was a minima
+of F on that domain okay or within that
+
+ align:start position:0%
+of F on that domain okay or within that
+ 
+
+ align:start position:0%
+of F on that domain okay or within that
+feasible set so a lot of practical
+
+ align:start position:0%
+feasible set so a lot of practical
+ 
+
+ align:start position:0%
+feasible set so a lot of practical
+issues that suggest this is a bad idea
+
+ align:start position:0%
+issues that suggest this is a bad idea
+ 
+
+ align:start position:0%
+issues that suggest this is a bad idea
+this is an old idea people knew this was
+
+ align:start position:0%
+this is an old idea people knew this was
+ 
+
+ align:start position:0%
+this is an old idea people knew this was
+bad for a long time it seems natural
+
+ align:start position:0%
+bad for a long time it seems natural
+ 
+
+ align:start position:0%
+bad for a long time it seems natural
+though it seems like a good way to
+
+ align:start position:0%
+though it seems like a good way to
+ 
+
+ align:start position:0%
+though it seems like a good way to
+transform from these constrained
+
+ align:start position:0%
+transform from these constrained
+ 
+
+ align:start position:0%
+transform from these constrained
+optimization problems to something we
+
+ align:start position:0%
+optimization problems to something we
+ 
+
+ align:start position:0%
+optimization problems to something we
+know how to solve an unconstrained
+
+ align:start position:0%
+know how to solve an unconstrained
+ 
+
+ align:start position:0%
+know how to solve an unconstrained
+optimization problem but actually it
+
+ align:start position:0%
+optimization problem but actually it
+ 
+
+ align:start position:0%
+optimization problem but actually it
+turns out not to be such a great way to
+
+ align:start position:0%
+turns out not to be such a great way to
+ 
+
+ align:start position:0%
+turns out not to be such a great way to
+do it okay so let's talk about
+
+ align:start position:0%
+do it okay so let's talk about
+ 
+
+ align:start position:0%
+do it okay so let's talk about
+separating out these two different
+
+ align:start position:0%
+separating out these two different
+ 
+
+ align:start position:0%
+separating out these two different
+methods from each other where these two
+
+ align:start position:0%
+methods from each other where these two
+ 
+
+ align:start position:0%
+methods from each other where these two
+different two different problems let's
+
+ align:start position:0%
+different two different problems let's
+ 
+
+ align:start position:0%
+different two different problems let's
+talk first about equality constraints
+
+ align:start position:0%
+talk first about equality constraints
+ 
+
+ align:start position:0%
+talk first about equality constraints
+and then we'll talk about inequality
+
+ align:start position:0%
+and then we'll talk about inequality
+ 
+
+ align:start position:0%
+and then we'll talk about inequality
+constraints so a quality constrained
+
+ align:start position:0%
+constraints so a quality constrained
+ 
+
+ align:start position:0%
+constraints so a quality constrained
+optimization problems look like this
+
+ align:start position:0%
+optimization problems look like this
+ 
+
+ align:start position:0%
+optimization problems look like this
+right minimize f of X subject to C of x
+
+ align:start position:0%
+right minimize f of X subject to C of x
+ 
+
+ align:start position:0%
+right minimize f of X subject to C of x
+equals zero and let's make it even
+
+ align:start position:0%
+equals zero and let's make it even
+ 
+
+ align:start position:0%
+equals zero and let's make it even
+easier let's rather than having some
+
+ align:start position:0%
+easier let's rather than having some
+ 
+
+ align:start position:0%
+easier let's rather than having some
+vector of equality constraints let's
+
+ align:start position:0%
+vector of equality constraints let's
+ 
+
+ align:start position:0%
+vector of equality constraints let's
+just have a single equation that we have
+
+ align:start position:0%
+just have a single equation that we have
+ 
+
+ align:start position:0%
+just have a single equation that we have
+to satisfy for that equality constraint
+
+ align:start position:0%
+to satisfy for that equality constraint
+ 
+
+ align:start position:0%
+to satisfy for that equality constraint
+like the equation for a circle right
+
+ align:start position:0%
+like the equation for a circle right
+ 
+
+ align:start position:0%
+like the equation for a circle right
+solutions have to sit on the
+
+ align:start position:0%
+solutions have to sit on the
+ 
+
+ align:start position:0%
+solutions have to sit on the
+circumference of a circle okay so one
+
+ align:start position:0%
+circumference of a circle okay so one
+ 
+
+ align:start position:0%
+circumference of a circle okay so one
+equation that we have to satisfy you
+
+ align:start position:0%
+equation that we have to satisfy you
+ 
+
+ align:start position:0%
+equation that we have to satisfy you
+might ask again what are the necessary
+
+ align:start position:0%
+might ask again what are the necessary
+ 
+
+ align:start position:0%
+might ask again what are the necessary
+conditions for defining a minimum that's
+
+ align:start position:0%
+conditions for defining a minimum that's
+ 
+
+ align:start position:0%
+conditions for defining a minimum that's
+what we use when we had a quality or
+
+ align:start position:0%
+what we use when we had a quality or
+ 
+
+ align:start position:0%
+what we use when we had a quality or
+when we had unconstrained optimization
+
+ align:start position:0%
+when we had unconstrained optimization
+ 
+
+ align:start position:0%
+when we had unconstrained optimization
+first we had to define what what a
+
+ align:start position:0%
+first we had to define what what a
+ 
+
+ align:start position:0%
+first we had to define what what a
+minimum was right and we found that
+
+ align:start position:0%
+minimum was right and we found that
+ 
+
+ align:start position:0%
+minimum was right and we found that
+minima were critical points places were
+
+ align:start position:0%
+minima were critical points places were
+ 
+
+ align:start position:0%
+minima were critical points places were
+the gradient of the objective function
+
+ align:start position:0%
+the gradient of the objective function
+ 
+
+ align:start position:0%
+the gradient of the objective function
+worse was zero okay that doesn't have to
+
+ align:start position:0%
+worse was zero okay that doesn't have to
+ 
+
+ align:start position:0%
+worse was zero okay that doesn't have to
+be true anymore right now the minima has
+
+ align:start position:0%
+be true anymore right now the minima has
+ 
+
+ align:start position:0%
+be true anymore right now the minima has
+to live on this boundary right of some
+
+ align:start position:0%
+to live on this boundary right of some
+ 
+
+ align:start position:0%
+to live on this boundary right of some
+domain has to live in this set of points
+
+ align:start position:0%
+domain has to live in this set of points
+ 
+
+ align:start position:0%
+domain has to live in this set of points
+e of x equals zero and the gradient of F
+
+ align:start position:0%
+e of x equals zero and the gradient of F
+ 
+
+ align:start position:0%
+e of x equals zero and the gradient of F
+is not necessarily zero at that minimal
+
+ align:start position:0%
+is not necessarily zero at that minimal
+ 
+
+ align:start position:0%
+is not necessarily zero at that minimal
+point but you might guess right the
+
+ align:start position:0%
+point but you might guess right the
+ 
+
+ align:start position:0%
+point but you might guess right the
+Taylor expansions are the way to figure
+
+ align:start position:0%
+Taylor expansions are the way to figure
+ 
+
+ align:start position:0%
+Taylor expansions are the way to figure
+out okay Taylor expansions are the way
+
+ align:start position:0%
+out okay Taylor expansions are the way
+ 
+
+ align:start position:0%
+out okay Taylor expansions are the way
+to figure out the way to figure out what
+
+ align:start position:0%
+to figure out the way to figure out what
+ 
+
+ align:start position:0%
+to figure out the way to figure out what
+the appropriate conditions for a minima
+
+ align:start position:0%
+the appropriate conditions for a minima
+ 
+
+ align:start position:0%
+the appropriate conditions for a minima
+are so let's take f of X and let's
+
+ align:start position:0%
+are so let's take f of X and let's
+ 
+
+ align:start position:0%
+are so let's take f of X and let's
+expand it do a Taylor expansion in some
+
+ align:start position:0%
+expand it do a Taylor expansion in some
+ 
+
+ align:start position:0%
+expand it do a Taylor expansion in some
+direction D okay so we'll take a step
+
+ align:start position:0%
+direction D okay so we'll take a step
+ 
+
+ align:start position:0%
+direction D okay so we'll take a step
+away from X which is small in some
+
+ align:start position:0%
+away from X which is small in some
+ 
+
+ align:start position:0%
+away from X which is small in some
+direction D so f of X plus D is f of X
+
+ align:start position:0%
+direction D so f of X plus D is f of X
+ 
+
+ align:start position:0%
+direction D so f of X plus D is f of X
+plus G dot d all right the dot product
+
+ align:start position:0%
+plus G dot d all right the dot product
+ 
+
+ align:start position:0%
+plus G dot d all right the dot product
+between the gradient of F and D and at a
+
+ align:start position:0%
+between the gradient of F and D and at a
+ 
+
+ align:start position:0%
+between the gradient of F and D and at a
+minimum right either
+
+ align:start position:0%
+minimum right either
+ 
+
+ align:start position:0%
+minimum right either
+the gradient is 0 or the gradient is
+
+ align:start position:0%
+the gradient is 0 or the gradient is
+ 
+
+ align:start position:0%
+the gradient is 0 or the gradient is
+perpendicular to this direction we moved
+
+ align:start position:0%
+perpendicular to this direction we moved
+ 
+
+ align:start position:0%
+perpendicular to this direction we moved
+in D okay we know that because this term
+
+ align:start position:0%
+in D okay we know that because this term
+ 
+
+ align:start position:0%
+in D okay we know that because this term
+right this term is going to increase
+
+ align:start position:0%
+right this term is going to increase
+ 
+
+ align:start position:0%
+right this term is going to increase
+will change the value of f of X it'll
+
+ align:start position:0%
+will change the value of f of X it'll
+ 
+
+ align:start position:0%
+will change the value of f of X it'll
+either make it bigger or smaller
+
+ align:start position:0%
+either make it bigger or smaller
+ 
+
+ align:start position:0%
+either make it bigger or smaller
+depending on whether it's positive or
+
+ align:start position:0%
+depending on whether it's positive or
+ 
+
+ align:start position:0%
+depending on whether it's positive or
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+in either case it'll say that this point
+
+ align:start position:0%
+in either case it'll say that this point
+ 
+
+ align:start position:0%
+in either case it'll say that this point
+X can't be a minimum right unless this
+
+ align:start position:0%
+X can't be a minimum right unless this
+ 
+
+ align:start position:0%
+X can't be a minimum right unless this
+term is exactly equal to 0 in the limit
+
+ align:start position:0%
+term is exactly equal to 0 in the limit
+ 
+
+ align:start position:0%
+term is exactly equal to 0 in the limit
+that D becomes small so either the
+
+ align:start position:0%
+that D becomes small so either the
+ 
+
+ align:start position:0%
+that D becomes small so either the
+gradient is 0 or the gradient is
+
+ align:start position:0%
+gradient is 0 or the gradient is
+ 
+
+ align:start position:0%
+gradient is 0 or the gradient is
+orthogonal to this direction D we
+
+ align:start position:0%
+orthogonal to this direction D we
+ 
+
+ align:start position:0%
+orthogonal to this direction D we
+stepped in and D was arbitrary right we
+
+ align:start position:0%
+stepped in and D was arbitrary right we
+ 
+
+ align:start position:0%
+stepped in and D was arbitrary right we
+just said take a step in a direction D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take our equality constraint and
+
+ align:start position:0%
+let's take our equality constraint and
+ 
+
+ align:start position:0%
+let's take our equality constraint and
+do the sort of the same sort of Taylor
+
+ align:start position:0%
+do the sort of the same sort of Taylor
+ 
+
+ align:start position:0%
+do the sort of the same sort of Taylor
+expansion okay because we know right if
+
+ align:start position:0%
+expansion okay because we know right if
+ 
+
+ align:start position:0%
+expansion okay because we know right if
+we're searching for a minima along this
+
+ align:start position:0%
+we're searching for a minima along this
+ 
+
+ align:start position:0%
+we're searching for a minima along this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+see of X better be equal to zero it
+
+ align:start position:0%
+see of X better be equal to zero it
+ 
+
+ align:start position:0%
+see of X better be equal to zero it
+better satisfy the constraint and also
+
+ align:start position:0%
+better satisfy the constraint and also
+ 
+
+ align:start position:0%
+better satisfy the constraint and also
+see of X plus D right that little step
+
+ align:start position:0%
+see of X plus D right that little step
+ 
+
+ align:start position:0%
+see of X plus D right that little step
+in the direction D should also satisfy
+
+ align:start position:0%
+in the direction D should also satisfy
+ 
+
+ align:start position:0%
+in the direction D should also satisfy
+the constraint right we want to study
+
+ align:start position:0%
+the constraint right we want to study
+ 
+
+ align:start position:0%
+the constraint right we want to study
+only the feasible set of values so
+
+ align:start position:0%
+only the feasible set of values so
+ 
+
+ align:start position:0%
+only the feasible set of values so
+actually D wasn't arbitrary D had to
+
+ align:start position:0%
+actually D wasn't arbitrary D had to
+ 
+
+ align:start position:0%
+actually D wasn't arbitrary D had to
+satisfy this constraint then when I took
+
+ align:start position:0%
+satisfy this constraint then when I took
+ 
+
+ align:start position:0%
+satisfy this constraint then when I took
+this little step C of X plus D had to be
+
+ align:start position:0%
+this little step C of X plus D had to be
+ 
+
+ align:start position:0%
+this little step C of X plus D had to be
+equal to zero so again we'll take it now
+
+ align:start position:0%
+equal to zero so again we'll take it now
+ 
+
+ align:start position:0%
+equal to zero so again we'll take it now
+a Taylor expansion of C of X plus D
+
+ align:start position:0%
+a Taylor expansion of C of X plus D
+ 
+
+ align:start position:0%
+a Taylor expansion of C of X plus D
+which is C of X plus grad of C of X
+
+ align:start position:0%
+which is C of X plus grad of C of X
+ 
+
+ align:start position:0%
+which is C of X plus grad of C of X
+dotted with D okay and that implies
+
+ align:start position:0%
+dotted with D okay and that implies
+ 
+
+ align:start position:0%
+dotted with D okay and that implies
+write the D must be perpendicular to the
+
+ align:start position:0%
+write the D must be perpendicular to the
+ 
+
+ align:start position:0%
+write the D must be perpendicular to the
+gradient of C of X ok because C of X
+
+ align:start position:0%
+gradient of C of X ok because C of X
+ 
+
+ align:start position:0%
+gradient of C of X ok because C of X
+plus D has to be 0 and C of X has to be
+
+ align:start position:0%
+plus D has to be 0 and C of X has to be
+ 
+
+ align:start position:0%
+plus D has to be 0 and C of X has to be
+0 so the gradient of C of X dot d to
+
+ align:start position:0%
+0 so the gradient of C of X dot d to
+ 
+
+ align:start position:0%
+0 so the gradient of C of X dot d to
+leading order right has also got to be
+
+ align:start position:0%
+leading order right has also got to be
+ 
+
+ align:start position:0%
+leading order right has also got to be
+equal to 0 so D and the gradient in C
+
+ align:start position:0%
+equal to 0 so D and the gradient in C
+ 
+
+ align:start position:0%
+equal to 0 so D and the gradient in C
+are perpendicular and D and the gradient
+
+ align:start position:0%
+are perpendicular and D and the gradient
+ 
+
+ align:start position:0%
+are perpendicular and D and the gradient
+in G have to be perpendicular at a
+
+ align:start position:0%
+in G have to be perpendicular at a
+ 
+
+ align:start position:0%
+in G have to be perpendicular at a
+minimum that's going to define the
+
+ align:start position:0%
+minimum that's going to define the
+ 
+
+ align:start position:0%
+minimum that's going to define the
+minimum on this equality constraint set
+
+ align:start position:0%
+minimum on this equality constraint set
+ 
+
+ align:start position:0%
+minimum on this equality constraint set
+that makes sense right C's satisfies the
+
+ align:start position:0%
+that makes sense right C's satisfies the
+ 
+
+ align:start position:0%
+that makes sense right C's satisfies the
+constraint C plus D satisfies the
+
+ align:start position:0%
+constraint C plus D satisfies the
+ 
+
+ align:start position:0%
+constraint C plus D satisfies the
+constraint if this is true D has to be
+
+ align:start position:0%
+constraint if this is true D has to be
+ 
+
+ align:start position:0%
+constraint if this is true D has to be
+perpendicular to the gradient of C G has
+
+ align:start position:0%
+perpendicular to the gradient of C G has
+ 
+
+ align:start position:0%
+perpendicular to the gradient of C G has
+to be perpendicular to the gradient of D
+
+ align:start position:0%
+to be perpendicular to the gradient of D
+ 
+
+ align:start position:0%
+to be perpendicular to the gradient of D
+D is in some sense arbitrary still okay
+
+ align:start position:0%
+D is in some sense arbitrary still okay
+ 
+
+ align:start position:0%
+D is in some sense arbitrary still okay
+D has to satisfy condition that it's
+
+ align:start position:0%
+D has to satisfy condition that it's
+ 
+
+ align:start position:0%
+D has to satisfy condition that it's
+perpendicular to the gradient of C but
+
+ align:start position:0%
+perpendicular to the gradient of C but
+ 
+
+ align:start position:0%
+perpendicular to the gradient of C but
+who knows right there could be lots of
+
+ align:start position:0%
+who knows right there could be lots of
+ 
+
+ align:start position:0%
+who knows right there could be lots of
+vectors that are perpendicular to the
+
+ align:start position:0%
+vectors that are perpendicular to the
+ 
+
+ align:start position:0%
+vectors that are perpendicular to the
+gradient of C so the only generic
+
+ align:start position:0%
+gradient of C so the only generic
+ 
+
+ align:start position:0%
+gradient of C so the only generic
+relationship between these two we can
+
+ align:start position:0%
+relationship between these two we can
+ 
+
+ align:start position:0%
+relationship between these two we can
+formulate is G must be parallel to the
+
+ align:start position:0%
+formulate is G must be parallel to the
+ 
+
+ align:start position:0%
+formulate is G must be parallel to the
+gradient of C G's perpendicular to the
+
+ align:start position:0%
+gradient of C G's perpendicular to the
+ 
+
+ align:start position:0%
+gradient of C G's perpendicular to the
+gradient of C is perpendicular to be in
+
+ align:start position:0%
+gradient of C is perpendicular to be in
+ 
+
+ align:start position:0%
+gradient of C is perpendicular to be in
+the most generic way G and gradient of C
+
+ align:start position:0%
+the most generic way G and gradient of C
+ 
+
+ align:start position:0%
+the most generic way G and gradient of C
+should be parallel to each other because
+
+ align:start position:0%
+should be parallel to each other because
+ 
+
+ align:start position:0%
+should be parallel to each other because
+D I can select arbitrarily from all the
+
+ align:start position:0%
+D I can select arbitrarily from all the
+ 
+
+ align:start position:0%
+D I can select arbitrarily from all the
+vectors in of the same dimension as X ok
+
+ align:start position:0%
+vectors in of the same dimension as X ok
+ 
+
+ align:start position:0%
+vectors in of the same dimension as X ok
+if G is parallel to the gradient of C
+
+ align:start position:0%
+if G is parallel to the gradient of C
+ 
+
+ align:start position:0%
+if G is parallel to the gradient of C
+then I can write that G - write some
+
+ align:start position:0%
+then I can write that G - write some
+ 
+
+ align:start position:0%
+then I can write that G - write some
+scalar multiplied by the gradient of C
+
+ align:start position:0%
+scalar multiplied by the gradient of C
+ 
+
+ align:start position:0%
+scalar multiplied by the gradient of C
+is equal to 0 that's an equivalent
+
+ align:start position:0%
+is equal to 0 that's an equivalent
+ 
+
+ align:start position:0%
+is equal to 0 that's an equivalent
+statement that G is parallel to the
+
+ align:start position:0%
+statement that G is parallel to the
+ 
+
+ align:start position:0%
+statement that G is parallel to the
+gradient of C so that's a condition
+
+ align:start position:0%
+gradient of C so that's a condition
+ 
+
+ align:start position:0%
+gradient of C so that's a condition
+associated with points X that solve this
+
+ align:start position:0%
+associated with points X that solve this
+ 
+
+ align:start position:0%
+associated with points X that solve this
+equality constrained problem the other
+
+ align:start position:0%
+equality constrained problem the other
+ 
+
+ align:start position:0%
+equality constrained problem the other
+condition is that point
+
+ align:start position:0%
+condition is that point
+ 
+
+ align:start position:0%
+condition is that point
+sell us to satisfy the Equality
+
+ align:start position:0%
+sell us to satisfy the Equality
+ 
+
+ align:start position:0%
+sell us to satisfy the Equality
+constraint right but I introduced a new
+
+ align:start position:0%
+constraint right but I introduced a new
+ 
+
+ align:start position:0%
+constraint right but I introduced a new
+unknown this lambda which is called the
+
+ align:start position:0%
+unknown this lambda which is called the
+ 
+
+ align:start position:0%
+unknown this lambda which is called the
+Lagrange multiplier okay so I know I
+
+ align:start position:0%
+Lagrange multiplier okay so I know I
+ 
+
+ align:start position:0%
+Lagrange multiplier okay so I know I
+have one extra unknown but I have one
+
+ align:start position:0%
+have one extra unknown but I have one
+ 
+
+ align:start position:0%
+have one extra unknown but I have one
+extra equation let me give you a
+
+ align:start position:0%
+extra equation let me give you a
+ 
+
+ align:start position:0%
+extra equation let me give you a
+graphical depiction of this and then
+
+ align:start position:0%
+graphical depiction of this and then
+ 
+
+ align:start position:0%
+graphical depiction of this and then
+I'll write down the the formal equations
+
+ align:start position:0%
+I'll write down the the formal equations
+ 
+
+ align:start position:0%
+I'll write down the the formal equations
+again so let's suppose we want to
+
+ align:start position:0%
+again so let's suppose we want to
+ 
+
+ align:start position:0%
+again so let's suppose we want to
+minimize write this parabolic function
+
+ align:start position:0%
+minimize write this parabolic function
+ 
+
+ align:start position:0%
+minimize write this parabolic function
+subject to the constraint that the
+
+ align:start position:0%
+subject to the constraint that the
+ 
+
+ align:start position:0%
+subject to the constraint that the
+solution lives on the line okay so
+
+ align:start position:0%
+solution lives on the line okay so
+ 
+
+ align:start position:0%
+solution lives on the line okay so
+here's the contours of the function and
+
+ align:start position:0%
+here's the contours of the function and
+ 
+
+ align:start position:0%
+here's the contours of the function and
+the solution has to live on this line
+
+ align:start position:0%
+the solution has to live on this line
+ 
+
+ align:start position:0%
+the solution has to live on this line
+okay so I get to stand on this line and
+
+ align:start position:0%
+okay so I get to stand on this line and
+ 
+
+ align:start position:0%
+okay so I get to stand on this line and
+I get to walk and walk and walk until I
+
+ align:start position:0%
+I get to walk and walk and walk until I
+ 
+
+ align:start position:0%
+I get to walk and walk and walk until I
+can't walk downhill anymore and I got to
+
+ align:start position:0%
+can't walk downhill anymore and I got to
+ 
+
+ align:start position:0%
+can't walk downhill anymore and I got to
+turn and walk uphill again and you can
+
+ align:start position:0%
+turn and walk uphill again and you can
+ 
+
+ align:start position:0%
+turn and walk uphill again and you can
+see the point right where I can't walk
+
+ align:start position:0%
+see the point right where I can't walk
+ 
+
+ align:start position:0%
+see the point right where I can't walk
+downhill anymore it's the place where
+
+ align:start position:0%
+downhill anymore it's the place where
+ 
+
+ align:start position:0%
+downhill anymore it's the place where
+this constraint is parallel to the
+
+ align:start position:0%
+this constraint is parallel to the
+ 
+
+ align:start position:0%
+this constraint is parallel to the
+contour or where the gradient right of
+
+ align:start position:0%
+contour or where the gradient right of
+ 
+
+ align:start position:0%
+contour or where the gradient right of
+the objective function is parallel to
+
+ align:start position:0%
+the objective function is parallel to
+ 
+
+ align:start position:0%
+the objective function is parallel to
+the gradient of the constraint so you
+
+ align:start position:0%
+the gradient of the constraint so you
+ 
+
+ align:start position:0%
+the gradient of the constraint so you
+can you can actually find this point by
+
+ align:start position:0%
+can you can actually find this point by
+ 
+
+ align:start position:0%
+can you can actually find this point by
+imagining yourself moving along this
+
+ align:start position:0%
+imagining yourself moving along this
+ 
+
+ align:start position:0%
+imagining yourself moving along this
+landscape after I get to this point I
+
+ align:start position:0%
+landscape after I get to this point I
+ 
+
+ align:start position:0%
+landscape after I get to this point I
+start going uphill again right so that's
+
+ align:start position:0%
+start going uphill again right so that's
+ 
+
+ align:start position:0%
+start going uphill again right so that's
+the method of LaGrange multipliers
+
+ align:start position:0%
+the method of LaGrange multipliers
+ 
+
+ align:start position:0%
+the method of LaGrange multipliers
+minimize f of X subject to this
+
+ align:start position:0%
+minimize f of X subject to this
+ 
+
+ align:start position:0%
+minimize f of X subject to this
+constraint the solution is given by the
+
+ align:start position:0%
+constraint the solution is given by the
+ 
+
+ align:start position:0%
+constraint the solution is given by the
+point X at which the gradient is
+
+ align:start position:0%
+point X at which the gradient is
+ 
+
+ align:start position:0%
+point X at which the gradient is
+parallel to the gradient of C and at
+
+ align:start position:0%
+parallel to the gradient of C and at
+ 
+
+ align:start position:0%
+parallel to the gradient of C and at
+which C is equal to 0 and you solve the
+
+ align:start position:0%
+which C is equal to 0 and you solve the
+ 
+
+ align:start position:0%
+which C is equal to 0 and you solve the
+system of nonlinear equations for two
+
+ align:start position:0%
+system of nonlinear equations for two
+ 
+
+ align:start position:0%
+system of nonlinear equations for two
+unknowns one is X and the other is this
+
+ align:start position:0%
+unknowns one is X and the other is this
+ 
+
+ align:start position:0%
+unknowns one is X and the other is this
+unknown lambda right what is you know
+
+ align:start position:0%
+unknown lambda right what is you know
+ 
+
+ align:start position:0%
+unknown lambda right what is you know
+how far stretched is the gradient
+
+ align:start position:0%
+how far stretched is the gradient
+ 
+
+ align:start position:0%
+how far stretched is the gradient
+relative in F relative to the gradient
+
+ align:start position:0%
+relative in F relative to the gradient
+ 
+
+ align:start position:0%
+relative in F relative to the gradient
+in C so again we've turned the
+
+ align:start position:0%
+in C so again we've turned the
+ 
+
+ align:start position:0%
+in C so again we've turned the
+minimization problem into a system of
+
+ align:start position:0%
+minimization problem into a system of
+ 
+
+ align:start position:0%
+minimization problem into a system of
+non-linear equations in order to satisfy
+
+ align:start position:0%
+non-linear equations in order to satisfy
+ 
+
+ align:start position:0%
+non-linear equations in order to satisfy
+the Equality constraint we've had to
+
+ align:start position:0%
+the Equality constraint we've had to
+ 
+
+ align:start position:0%
+the Equality constraint we've had to
+introduce another unknown the Lagrange
+
+ align:start position:0%
+introduce another unknown the Lagrange
+ 
+
+ align:start position:0%
+introduce another unknown the Lagrange
+multiplier it turns out write this
+
+ align:start position:0%
+multiplier it turns out write this
+ 
+
+ align:start position:0%
+multiplier it turns out write this
+solution set X and lambda is a critical
+
+ align:start position:0%
+solution set X and lambda is a critical
+ 
+
+ align:start position:0%
+solution set X and lambda is a critical
+point of something called the Lagrangian
+
+ align:start position:0%
+point of something called the Lagrangian
+ 
+
+ align:start position:0%
+point of something called the Lagrangian
+right it's a function
+
+ align:start position:0%
+right it's a function
+ 
+
+ align:start position:0%
+right it's a function
+f of X minus lambda times C it's a
+
+ align:start position:0%
+f of X minus lambda times C it's a
+ 
+
+ align:start position:0%
+f of X minus lambda times C it's a
+critical point in X and lambda of this
+
+ align:start position:0%
+critical point in X and lambda of this
+ 
+
+ align:start position:0%
+critical point in X and lambda of this
+nonlinear function called the Lagrangian
+
+ align:start position:0%
+nonlinear function called the Lagrangian
+ 
+
+ align:start position:0%
+nonlinear function called the Lagrangian
+it's not a minimum of this function
+
+ align:start position:0%
+it's not a minimum of this function
+ 
+
+ align:start position:0%
+it's not a minimum of this function
+unfortunately it's a saddle point of the
+
+ align:start position:0%
+unfortunately it's a saddle point of the
+ 
+
+ align:start position:0%
+unfortunately it's a saddle point of the
+Lagrangian it turns out so we're trying
+
+ align:start position:0%
+Lagrangian it turns out so we're trying
+ 
+
+ align:start position:0%
+Lagrangian it turns out so we're trying
+to find a saddle point of the Lagrangian
+
+ align:start position:0%
+to find a saddle point of the Lagrangian
+ 
+
+ align:start position:0%
+to find a saddle point of the Lagrangian
+this makes sense yes okay we're going to
+
+ align:start position:0%
+this makes sense yes okay we're going to
+ 
+
+ align:start position:0%
+this makes sense yes okay we're going to
+be careful of course just like with
+
+ align:start position:0%
+be careful of course just like with
+ 
+
+ align:start position:0%
+be careful of course just like with
+unconstrained optimization we've still
+
+ align:start position:0%
+unconstrained optimization we've still
+ 
+
+ align:start position:0%
+unconstrained optimization we've still
+got a check that our solution is a
+
+ align:start position:0%
+got a check that our solution is a
+ 
+
+ align:start position:0%
+got a check that our solution is a
+minimum right
+
+ align:start position:0%
+minimum right
+ 
+
+ align:start position:0%
+minimum right
+we can't take for granted we can't can't
+
+ align:start position:0%
+we can't take for granted we can't can't
+ 
+
+ align:start position:0%
+we can't take for granted we can't can't
+suppose that our non-linear solver found
+
+ align:start position:0%
+suppose that our non-linear solver found
+ 
+
+ align:start position:0%
+suppose that our non-linear solver found
+a minimum when it solved this equation
+
+ align:start position:0%
+a minimum when it solved this equation
+ 
+
+ align:start position:0%
+a minimum when it solved this equation
+right other critical points can satisfy
+
+ align:start position:0%
+right other critical points can satisfy
+ 
+
+ align:start position:0%
+right other critical points can satisfy
+this equation too so we got to go back
+
+ align:start position:0%
+this equation too so we got to go back
+ 
+
+ align:start position:0%
+this equation too so we got to go back
+and try to check robustly whether
+
+ align:start position:0%
+and try to check robustly whether
+ 
+
+ align:start position:0%
+and try to check robustly whether
+whether it's actually a minimum but this
+
+ align:start position:0%
+whether it's actually a minimum but this
+ 
+
+ align:start position:0%
+whether it's actually a minimum but this
+is the method introduce an additional
+
+ align:start position:0%
+is the method introduce an additional
+ 
+
+ align:start position:0%
+is the method introduce an additional
+unknown the Lagrange multiplier because
+
+ align:start position:0%
+unknown the Lagrange multiplier because
+ 
+
+ align:start position:0%
+unknown the Lagrange multiplier because
+you can show geometrically that the
+
+ align:start position:0%
+you can show geometrically that the
+ 
+
+ align:start position:0%
+you can show geometrically that the
+gradient of the objective function
+
+ align:start position:0%
+gradient of the objective function
+ 
+
+ align:start position:0%
+gradient of the objective function
+should be parallel to the gradient of
+
+ align:start position:0%
+should be parallel to the gradient of
+ 
+
+ align:start position:0%
+should be parallel to the gradient of
+the constraint at the minimum does that
+
+ align:start position:0%
+the constraint at the minimum does that
+ 
+
+ align:start position:0%
+the constraint at the minimum does that
+make sense this picture makes sense okay
+
+ align:start position:0%
+make sense this picture makes sense okay
+ 
+
+ align:start position:0%
+make sense this picture makes sense okay
+so you know how to solve systems of
+
+ align:start position:0%
+so you know how to solve systems of
+ 
+
+ align:start position:0%
+so you know how to solve systems of
+nonlinear equations you know how to
+
+ align:start position:0%
+nonlinear equations you know how to
+ 
+
+ align:start position:0%
+nonlinear equations you know how to
+solve constrained optimization problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's F here's C right we can
+
+ align:start position:0%
+so here's F here's C right we can
+ 
+
+ align:start position:0%
+so here's F here's C right we can
+actually write out what these equations
+
+ align:start position:0%
+actually write out what these equations
+ 
+
+ align:start position:0%
+actually write out what these equations
+are so you can show that the gradient of
+
+ align:start position:0%
+are so you can show that the gradient of
+ 
+
+ align:start position:0%
+are so you can show that the gradient of
+X minus lambda gradient of C that's a
+
+ align:start position:0%
+X minus lambda gradient of C that's a
+ 
+
+ align:start position:0%
+X minus lambda gradient of C that's a
+vector to x1 minus lambda and 20 X 2
+
+ align:start position:0%
+vector to x1 minus lambda and 20 X 2
+ 
+
+ align:start position:0%
+vector to x1 minus lambda and 20 X 2
+plus lambda and C is the equation for
+
+ align:start position:0%
+plus lambda and C is the equation for
+ 
+
+ align:start position:0%
+plus lambda and C is the equation for
+this line down here so x1 minus x2 minus
+
+ align:start position:0%
+this line down here so x1 minus x2 minus
+ 
+
+ align:start position:0%
+this line down here so x1 minus x2 minus
+3 and that's all got to be equal to 0
+
+ align:start position:0%
+3 and that's all got to be equal to 0
+ 
+
+ align:start position:0%
+3 and that's all got to be equal to 0
+right in this case this is just the
+
+ align:start position:0%
+right in this case this is just the
+ 
+
+ align:start position:0%
+right in this case this is just the
+system of linear equations so you can
+
+ align:start position:0%
+system of linear equations so you can
+ 
+
+ align:start position:0%
+system of linear equations so you can
+actually solve directly for x1 x2 and
+
+ align:start position:0%
+actually solve directly for x1 x2 and
+ 
+
+ align:start position:0%
+actually solve directly for x1 x2 and
+lambda
+
+ align:start position:0%
+lambda
+ 
+
+ align:start position:0%
+lambda
+that's not too difficult to find the
+
+ align:start position:0%
+that's not too difficult to find the
+ 
+
+ align:start position:0%
+that's not too difficult to find the
+solution for all three of these things
+
+ align:start position:0%
+solution for all three of these things
+ 
+
+ align:start position:0%
+solution for all three of these things
+by hand
+
+ align:start position:0%
+by hand
+ 
+
+ align:start position:0%
+by hand
+ok but in general right these
+
+ align:start position:0%
+ok but in general right these
+ 
+
+ align:start position:0%
+ok but in general right these
+constraints can be nonlinear the
+
+ align:start position:0%
+constraints can be nonlinear the
+ 
+
+ align:start position:0%
+constraints can be nonlinear the
+objective function doesn't have to be
+
+ align:start position:0%
+objective function doesn't have to be
+ 
+
+ align:start position:0%
+objective function doesn't have to be
+quadratic those are the easiest cases to
+
+ align:start position:0%
+quadratic those are the easiest cases to
+ 
+
+ align:start position:0%
+quadratic those are the easiest cases to
+look at the same methodology applies so
+
+ align:start position:0%
+look at the same methodology applies so
+ 
+
+ align:start position:0%
+look at the same methodology applies so
+you should check that you're able to do
+
+ align:start position:0%
+you should check that you're able to do
+ 
+
+ align:start position:0%
+you should check that you're able to do
+this this is the simple responsible
+
+ align:start position:0%
+this this is the simple responsible
+ 
+
+ align:start position:0%
+this this is the simple responsible
+equality constraint problem you can do
+
+ align:start position:0%
+equality constraint problem you can do
+ 
+
+ align:start position:0%
+equality constraint problem you can do
+it by hand you should check that you're
+
+ align:start position:0%
+it by hand you should check that you're
+ 
+
+ align:start position:0%
+it by hand you should check that you're
+actually able to do it that you
+
+ align:start position:0%
+actually able to do it that you
+ 
+
+ align:start position:0%
+actually able to do it that you
+understand the steps that go into
+
+ align:start position:0%
+understand the steps that go into
+ 
+
+ align:start position:0%
+understand the steps that go into
+writing out these equations okay let's
+
+ align:start position:0%
+writing out these equations okay let's
+ 
+
+ align:start position:0%
+writing out these equations okay let's
+just take one step forward and look at
+
+ align:start position:0%
+just take one step forward and look at
+ 
+
+ align:start position:0%
+just take one step forward and look at
+the a less generic case one in which we
+
+ align:start position:0%
+the a less generic case one in which we
+ 
+
+ align:start position:0%
+the a less generic case one in which we
+have a vector valued function that gives
+
+ align:start position:0%
+have a vector valued function that gives
+ 
+
+ align:start position:0%
+have a vector valued function that gives
+thee that gives the Equality constraints
+
+ align:start position:0%
+thee that gives the Equality constraints
+ 
+
+ align:start position:0%
+thee that gives the Equality constraints
+instead so rather than one equation we
+
+ align:start position:0%
+instead so rather than one equation we
+ 
+
+ align:start position:0%
+instead so rather than one equation we
+have to satisfy there may be many okay
+
+ align:start position:0%
+have to satisfy there may be many okay
+ 
+
+ align:start position:0%
+have to satisfy there may be many okay
+it's possible right that the feasible
+
+ align:start position:0%
+it's possible right that the feasible
+ 
+
+ align:start position:0%
+it's possible right that the feasible
+set doesn't have any solutions in it
+
+ align:start position:0%
+set doesn't have any solutions in it
+ 
+
+ align:start position:0%
+set doesn't have any solutions in it
+right it's possible that there is no X
+
+ align:start position:0%
+right it's possible that there is no X
+ 
+
+ align:start position:0%
+right it's possible that there is no X
+that satisfies all of these constraints
+
+ align:start position:0%
+that satisfies all of these constraints
+ 
+
+ align:start position:0%
+that satisfies all of these constraints
+simultaneously that's a bad problem to
+
+ align:start position:0%
+simultaneously that's a bad problem to
+ 
+
+ align:start position:0%
+simultaneously that's a bad problem to
+have right you wouldn't you wouldn't
+
+ align:start position:0%
+have right you wouldn't you wouldn't
+ 
+
+ align:start position:0%
+have right you wouldn't you wouldn't
+like to have that problem very much but
+
+ align:start position:0%
+like to have that problem very much but
+ 
+
+ align:start position:0%
+like to have that problem very much but
+it's possible that that's the case but
+
+ align:start position:0%
+it's possible that that's the case but
+ 
+
+ align:start position:0%
+it's possible that that's the case but
+let's assume that there are solutions
+
+ align:start position:0%
+let's assume that there are solutions
+ 
+
+ align:start position:0%
+let's assume that there are solutions
+for the time being okay so there are X's
+
+ align:start position:0%
+for the time being okay so there are X's
+ 
+
+ align:start position:0%
+for the time being okay so there are X's
+that satisfy the Equality constraint
+
+ align:start position:0%
+that satisfy the Equality constraint
+ 
+
+ align:start position:0%
+that satisfy the Equality constraint
+let's see if we can figure out again
+
+ align:start position:0%
+let's see if we can figure out again
+ 
+
+ align:start position:0%
+let's see if we can figure out again
+what the necessary conditions for
+
+ align:start position:0%
+what the necessary conditions for
+ 
+
+ align:start position:0%
+what the necessary conditions for
+defining a minima are so it's same as
+
+ align:start position:0%
+defining a minima are so it's same as
+ 
+
+ align:start position:0%
+defining a minima are so it's same as
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+let's Taylor expand f of X in some going
+
+ align:start position:0%
+let's Taylor expand f of X in some going
+ 
+
+ align:start position:0%
+let's Taylor expand f of X in some going
+in some direction D and let's make D a
+
+ align:start position:0%
+in some direction D and let's make D a
+ 
+
+ align:start position:0%
+in some direction D and let's make D a
+nice small step so we can just treat the
+
+ align:start position:0%
+nice small step so we can just treat the
+ 
+
+ align:start position:0%
+nice small step so we can just treat the
+f of X plus D as a linearized function
+
+ align:start position:0%
+f of X plus D as a linearized function
+ 
+
+ align:start position:0%
+f of X plus D as a linearized function
+so you can see again that G has to be
+
+ align:start position:0%
+so you can see again that G has to be
+ 
+
+ align:start position:0%
+so you can see again that G has to be
+perpendicular to this direction D if
+
+ align:start position:0%
+perpendicular to this direction D if
+ 
+
+ align:start position:0%
+perpendicular to this direction D if
+we're gonna have a minima otherwise I
+
+ align:start position:0%
+we're gonna have a minima otherwise I
+ 
+
+ align:start position:0%
+we're gonna have a minima otherwise I
+could step in some direction D and I'll
+
+ align:start position:0%
+could step in some direction D and I'll
+ 
+
+ align:start position:0%
+could step in some direction D and I'll
+make I'll find either a smaller value of
+
+ align:start position:0%
+make I'll find either a smaller value of
+ 
+
+ align:start position:0%
+make I'll find either a smaller value of
+f of X plus D or a bigger value of f of
+
+ align:start position:0%
+f of X plus D or a bigger value of f of
+ 
+
+ align:start position:0%
+f of X plus D or a bigger value of f of
+X plus D okay so G has to be
+
+ align:start position:0%
+X plus D okay so G has to be
+ 
+
+ align:start position:0%
+X plus D okay so G has to be
+perpendicular to D and for the Equality
+
+ align:start position:0%
+perpendicular to D and for the Equality
+ 
+
+ align:start position:0%
+perpendicular to D and for the Equality
+constraints again they all have to
+
+ align:start position:0%
+constraints again they all have to
+ 
+
+ align:start position:0%
+constraints again they all have to
+satisfy right this equality constraint
+
+ align:start position:0%
+satisfy right this equality constraint
+ 
+
+ align:start position:0%
+satisfy right this equality constraint
+up there so C of X but C of X has to be
+
+ align:start position:0%
+up there so C of X but C of X has to be
+ 
+
+ align:start position:0%
+up there so C of X but C of X has to be
+equal to 0 and C of X plus D also has to
+
+ align:start position:0%
+equal to 0 and C of X plus D also has to
+ 
+
+ align:start position:0%
+equal to 0 and C of X plus D also has to
+be equal to 0 and so right if we take a
+
+ align:start position:0%
+be equal to 0 and so right if we take a
+ 
+
+ align:start position:0%
+be equal to 0 and so right if we take a
+Taylor expansion of C of x plus D about
+
+ align:start position:0%
+Taylor expansion of C of x plus D about
+ 
+
+ align:start position:0%
+Taylor expansion of C of x plus D about
+X right you'll get C of x plus D plus
+
+ align:start position:0%
+X right you'll get C of x plus D plus
+ 
+
+ align:start position:0%
+X right you'll get C of x plus D plus
+the Jacobian of C right all the partial
+
+ align:start position:0%
+the Jacobian of C right all the partial
+ 
+
+ align:start position:0%
+the Jacobian of C right all the partial
+derivatives of C with respect to X
+
+ align:start position:0%
+derivatives of C with respect to X
+ 
+
+ align:start position:0%
+derivatives of C with respect to X
+multiplied by D we know that C of x plus
+
+ align:start position:0%
+multiplied by D we know that C of x plus
+ 
+
+ align:start position:0%
+multiplied by D we know that C of x plus
+D is 0 and C of X is 0 so the directions
+
+ align:start position:0%
+D is 0 and C of X is 0 so the directions
+ 
+
+ align:start position:0%
+D is 0 and C of X is 0 so the directions
+D belong to what set of vectors the null
+
+ align:start position:0%
+D belong to what set of vectors the null
+ 
+
+ align:start position:0%
+D belong to what set of vectors the null
+space right so these directions have to
+
+ align:start position:0%
+space right so these directions have to
+ 
+
+ align:start position:0%
+space right so these directions have to
+live in the null space of the Jacobian
+
+ align:start position:0%
+live in the null space of the Jacobian
+ 
+
+ align:start position:0%
+live in the null space of the Jacobian
+of C
+
+ align:start position:0%
+of C
+ 
+
+ align:start position:0%
+of C
+so I can't step in any direction I have
+
+ align:start position:0%
+so I can't step in any direction I have
+ 
+
+ align:start position:0%
+so I can't step in any direction I have
+to step in directions that are in the
+
+ align:start position:0%
+to step in directions that are in the
+ 
+
+ align:start position:0%
+to step in directions that are in the
+null space of C G is perpendicular to D
+
+ align:start position:0%
+null space of C G is perpendicular to D
+ 
+
+ align:start position:0%
+null space of C G is perpendicular to D
+as well and D belongs to the null space
+
+ align:start position:0%
+as well and D belongs to the null space
+ 
+
+ align:start position:0%
+as well and D belongs to the null space
+of C in fact you know that D is
+
+ align:start position:0%
+of C in fact you know that D is
+ 
+
+ align:start position:0%
+of C in fact you know that D is
+perpendicular to each of the rows of the
+
+ align:start position:0%
+perpendicular to each of the rows of the
+ 
+
+ align:start position:0%
+perpendicular to each of the rows of the
+Jacobian right you know that I just do
+
+ align:start position:0%
+Jacobian right you know that I just do
+ 
+
+ align:start position:0%
+Jacobian right you know that I just do
+the matrix vector product right and so
+
+ align:start position:0%
+the matrix vector product right and so
+ 
+
+ align:start position:0%
+the matrix vector product right and so
+each element of this matrix vector
+
+ align:start position:0%
+each element of this matrix vector
+ 
+
+ align:start position:0%
+each element of this matrix vector
+product is the is the dot product of D
+
+ align:start position:0%
+product is the is the dot product of D
+ 
+
+ align:start position:0%
+product is the is the dot product of D
+with a different row of the Jacobian so
+
+ align:start position:0%
+with a different row of the Jacobian so
+ 
+
+ align:start position:0%
+with a different row of the Jacobian so
+those rows are set of vectors those rows
+
+ align:start position:0%
+those rows are set of vectors those rows
+ 
+
+ align:start position:0%
+those rows are set of vectors those rows
+describe the range of J transpose okay
+
+ align:start position:0%
+describe the range of J transpose okay
+ 
+
+ align:start position:0%
+describe the range of J transpose okay
+or the row space of J remember we talked
+
+ align:start position:0%
+or the row space of J remember we talked
+ 
+
+ align:start position:0%
+or the row space of J remember we talked
+about the four fundamental subspaces and
+
+ align:start position:0%
+about the four fundamental subspaces and
+ 
+
+ align:start position:0%
+about the four fundamental subspaces and
+I said we've almost never used those
+
+ align:start position:0%
+I said we've almost never used those
+ 
+
+ align:start position:0%
+I said we've almost never used those
+other ones but this is this is one time
+
+ align:start position:0%
+other ones but this is this is one time
+ 
+
+ align:start position:0%
+other ones but this is this is one time
+when we will so those rows belong to the
+
+ align:start position:0%
+when we will so those rows belong to the
+ 
+
+ align:start position:0%
+when we will so those rows belong to the
+range of J transpose or they belong to
+
+ align:start position:0%
+range of J transpose or they belong to
+ 
+
+ align:start position:0%
+range of J transpose or they belong to
+the left null space of J I need to find
+
+ align:start position:0%
+the left null space of J I need to find
+ 
+
+ align:start position:0%
+the left null space of J I need to find
+aji a gradient which is always
+
+ align:start position:0%
+aji a gradient which is always
+ 
+
+ align:start position:0%
+aji a gradient which is always
+perpendicular to D and I know D is
+
+ align:start position:0%
+perpendicular to D and I know D is
+ 
+
+ align:start position:0%
+perpendicular to D and I know D is
+always perpendicular to the rows of J so
+
+ align:start position:0%
+always perpendicular to the rows of J so
+ 
+
+ align:start position:0%
+always perpendicular to the rows of J so
+I can write GE as a linear superposition
+
+ align:start position:0%
+I can write GE as a linear superposition
+ 
+
+ align:start position:0%
+I can write GE as a linear superposition
+of the rows of J right as long as G is a
+
+ align:start position:0%
+of the rows of J right as long as G is a
+ 
+
+ align:start position:0%
+of the rows of J right as long as G is a
+linear superposition of the rows it'll
+
+ align:start position:0%
+linear superposition of the rows it'll
+ 
+
+ align:start position:0%
+linear superposition of the rows it'll
+always be perpendicular to D vectors
+
+ align:start position:0%
+always be perpendicular to D vectors
+ 
+
+ align:start position:0%
+always be perpendicular to D vectors
+from the null space of a matrix are
+
+ align:start position:0%
+from the null space of a matrix are
+ 
+
+ align:start position:0%
+from the null space of a matrix are
+orthogonal to vectors from the row space
+
+ align:start position:0%
+orthogonal to vectors from the row space
+ 
+
+ align:start position:0%
+orthogonal to vectors from the row space
+of that matrix it turns out and they're
+
+ align:start position:0%
+of that matrix it turns out and they're
+ 
+
+ align:start position:0%
+of that matrix it turns out and they're
+orthogonal for this reason okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it tells us right if JD is 0 right
+
+ align:start position:0%
+so it tells us right if JD is 0 right
+ 
+
+ align:start position:0%
+so it tells us right if JD is 0 right
+then D belongs to the null space G is
+
+ align:start position:0%
+then D belongs to the null space G is
+ 
+
+ align:start position:0%
+then D belongs to the null space G is
+perpendicular to D that means I could
+
+ align:start position:0%
+perpendicular to D that means I could
+ 
+
+ align:start position:0%
+perpendicular to D that means I could
+write G as a linear superposition of the
+
+ align:start position:0%
+write G as a linear superposition of the
+ 
+
+ align:start position:0%
+write G as a linear superposition of the
+rows of J so G belongs to the range of J
+
+ align:start position:0%
+rows of J so G belongs to the range of J
+ 
+
+ align:start position:0%
+rows of J so G belongs to the range of J
+transpose or belongs to the row space of
+
+ align:start position:0%
+transpose or belongs to the row space of
+ 
+
+ align:start position:0%
+transpose or belongs to the row space of
+J those are equivalent statements and
+
+ align:start position:0%
+J those are equivalent statements and
+ 
+
+ align:start position:0%
+J those are equivalent statements and
+therefore I should be able to write G as
+
+ align:start position:0%
+therefore I should be able to write G as
+ 
+
+ align:start position:0%
+therefore I should be able to write G as
+a linear superposition of the rows of J
+
+ align:start position:0%
+a linear superposition of the rows of J
+ 
+
+ align:start position:0%
+a linear superposition of the rows of J
+and one way to say that is I should be
+
+ align:start position:0%
+and one way to say that is I should be
+ 
+
+ align:start position:0%
+and one way to say that is I should be
+able to write G as J transpose
+
+ align:start position:0%
+able to write G as J transpose
+ 
+
+ align:start position:0%
+able to write G as J transpose
+times some other vector lambda that's an
+
+ align:start position:0%
+times some other vector lambda that's an
+ 
+
+ align:start position:0%
+times some other vector lambda that's an
+equivalent way of saying that G is a
+
+ align:start position:0%
+equivalent way of saying that G is a
+ 
+
+ align:start position:0%
+equivalent way of saying that G is a
+linear superposition of the rows of J I
+
+ align:start position:0%
+linear superposition of the rows of J I
+ 
+
+ align:start position:0%
+linear superposition of the rows of J I
+don't know the values of lambda so I
+
+ align:start position:0%
+don't know the values of lambda so I
+ 
+
+ align:start position:0%
+don't know the values of lambda so I
+introduced a new set of unknowns a set
+
+ align:start position:0%
+introduced a new set of unknowns a set
+ 
+
+ align:start position:0%
+introduced a new set of unknowns a set
+of LaGrange multipliers I need to my
+
+ align:start position:0%
+of LaGrange multipliers I need to my
+ 
+
+ align:start position:0%
+of LaGrange multipliers I need to my
+minima is going to be found when I
+
+ align:start position:0%
+minima is going to be found when I
+ 
+
+ align:start position:0%
+minima is going to be found when I
+satisfy this equation just like before
+
+ align:start position:0%
+satisfy this equation just like before
+ 
+
+ align:start position:0%
+satisfy this equation just like before
+and when I'm able to satisfy all of the
+
+ align:start position:0%
+and when I'm able to satisfy all of the
+ 
+
+ align:start position:0%
+and when I'm able to satisfy all of the
+equality constraints how many LaGrant
+
+ align:start position:0%
+equality constraints how many LaGrant
+ 
+
+ align:start position:0%
+equality constraints how many LaGrant
+appliers do I have here can you figure
+
+ align:start position:0%
+appliers do I have here can you figure
+ 
+
+ align:start position:0%
+appliers do I have here can you figure
+that out you can talk with your top of
+
+ align:start position:0%
+that out you can talk with your top of
+ 
+
+ align:start position:0%
+that out you can talk with your top of
+your neighbors if you want take a couple
+
+ align:start position:0%
+your neighbors if you want take a couple
+ 
+
+ align:start position:0%
+your neighbors if you want take a couple
+minutes tell me how many Lagrange
+
+ align:start position:0%
+minutes tell me how many Lagrange
+ 
+
+ align:start position:0%
+minutes tell me how many Lagrange
+multipliers how many elements are in
+
+ align:start position:0%
+multipliers how many elements are in
+ 
+
+ align:start position:0%
+multipliers how many elements are in
+this vector lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many elements are in lambda can you
+
+ align:start position:0%
+how many elements are in lambda can you
+ 
+
+ align:start position:0%
+how many elements are in lambda can you
+tell me - yes right it's the same as the
+
+ align:start position:0%
+tell me - yes right it's the same as the
+ 
+
+ align:start position:0%
+tell me - yes right it's the same as the
+number of equality constraints right J
+
+ align:start position:0%
+number of equality constraints right J
+ 
+
+ align:start position:0%
+number of equality constraints right J
+right came from the gradient of C okay
+
+ align:start position:0%
+right came from the gradient of C okay
+ 
+
+ align:start position:0%
+right came from the gradient of C okay
+it's the Jacobian of C so it has a
+
+ align:start position:0%
+it's the Jacobian of C so it has a
+ 
+
+ align:start position:0%
+it's the Jacobian of C so it has a
+number of columns equal to the number of
+
+ align:start position:0%
+number of columns equal to the number of
+ 
+
+ align:start position:0%
+number of columns equal to the number of
+elements in X because I'm taking partial
+
+ align:start position:0%
+elements in X because I'm taking partial
+ 
+
+ align:start position:0%
+elements in X because I'm taking partial
+derivatives with respect to each element
+
+ align:start position:0%
+derivatives with respect to each element
+ 
+
+ align:start position:0%
+derivatives with respect to each element
+of X and as a number of rows equal to
+
+ align:start position:0%
+of X and as a number of rows equal to
+ 
+
+ align:start position:0%
+of X and as a number of rows equal to
+the number of elements of C okay so J
+
+ align:start position:0%
+the number of elements of C okay so J
+ 
+
+ align:start position:0%
+the number of elements of C okay so J
+transpose I just transposed those
+
+ align:start position:0%
+transpose I just transposed those
+ 
+
+ align:start position:0%
+transpose I just transposed those
+dimensions and lambda right must have
+
+ align:start position:0%
+dimensions and lambda right must have
+ 
+
+ align:start position:0%
+dimensions and lambda right must have
+the same number of elements as C does in
+
+ align:start position:0%
+the same number of elements as C does in
+ 
+
+ align:start position:0%
+the same number of elements as C does in
+order to make this product make sense so
+
+ align:start position:0%
+order to make this product make sense so
+ 
+
+ align:start position:0%
+order to make this product make sense so
+I introduced a new number of unknowns
+
+ align:start position:0%
+I introduced a new number of unknowns
+ 
+
+ align:start position:0%
+I introduced a new number of unknowns
+it's equal to exactly the number of
+
+ align:start position:0%
+it's equal to exactly the number of
+ 
+
+ align:start position:0%
+it's equal to exactly the number of
+equality constraints that I had which is
+
+ align:start position:0%
+equality constraints that I had which is
+ 
+
+ align:start position:0%
+equality constraints that I had which is
+good because I'm going to make a system
+
+ align:start position:0%
+good because I'm going to make a system
+ 
+
+ align:start position:0%
+good because I'm going to make a system
+of equations right that says G of X
+
+ align:start position:0%
+of equations right that says G of X
+ 
+
+ align:start position:0%
+of equations right that says G of X
+minus J transpose lambda equals 0 and C
+
+ align:start position:0%
+minus J transpose lambda equals 0 and C
+ 
+
+ align:start position:0%
+minus J transpose lambda equals 0 and C
+of X equals 0 right and the number of
+
+ align:start position:0%
+of X equals 0 right and the number of
+ 
+
+ align:start position:0%
+of X equals 0 right and the number of
+equations here right it's the number of
+
+ align:start position:0%
+equations here right it's the number of
+ 
+
+ align:start position:0%
+equations here right it's the number of
+elements in X for this gradient and the
+
+ align:start position:0%
+elements in X for this gradient and the
+ 
+
+ align:start position:0%
+elements in X for this gradient and the
+number of elements in C for C and the
+
+ align:start position:0%
+number of elements in C for C and the
+ 
+
+ align:start position:0%
+number of elements in C for C and the
+number of unknowns is the number of
+
+ align:start position:0%
+number of unknowns is the number of
+ 
+
+ align:start position:0%
+number of unknowns is the number of
+elements in X and the number of elements
+
+ align:start position:0%
+elements in X and the number of elements
+ 
+
+ align:start position:0%
+elements in X and the number of elements
+in C associated with the LaGrant wealth
+
+ align:start position:0%
+in C associated with the LaGrant wealth
+ 
+
+ align:start position:0%
+in C associated with the LaGrant wealth
+layer so I have enough equations and
+
+ align:start position:0%
+layer so I have enough equations and
+ 
+
+ align:start position:0%
+layer so I have enough equations and
+unknowns to determine all of these
+
+ align:start position:0%
+unknowns to determine all of these
+ 
+
+ align:start position:0%
+unknowns to determine all of these
+things so whether I have one equality
+
+ align:start position:0%
+things so whether I have one equality
+ 
+
+ align:start position:0%
+things so whether I have one equality
+constraint or a million quality
+
+ align:start position:0%
+constraint or a million quality
+ 
+
+ align:start position:0%
+constraint or a million quality
+constraints right the problem is
+
+ align:start position:0%
+constraints right the problem is
+ 
+
+ align:start position:0%
+constraints right the problem is
+identical right we use the method of
+
+ align:start position:0%
+identical right we use the method of
+ 
+
+ align:start position:0%
+identical right we use the method of
+LaGrange multipliers we have to solve an
+
+ align:start position:0%
+LaGrange multipliers we have to solve an
+ 
+
+ align:start position:0%
+LaGrange multipliers we have to solve an
+Augmented system of equations for X and
+
+ align:start position:0%
+Augmented system of equations for X and
+ 
+
+ align:start position:0%
+Augmented system of equations for X and
+write this projection on the row space
+
+ align:start position:0%
+write this projection on the row space
+ 
+
+ align:start position:0%
+write this projection on the row space
+of J which tells us how the gradient is
+
+ align:start position:0%
+of J which tells us how the gradient is
+ 
+
+ align:start position:0%
+of J which tells us how the gradient is
+stretched or
+
+ align:start position:0%
+stretched or
+ 
+
+ align:start position:0%
+stretched or
+made up composed of elements of the row
+
+ align:start position:0%
+made up composed of elements of the row
+ 
+
+ align:start position:0%
+made up composed of elements of the row
+space of J these are the conditions
+
+ align:start position:0%
+space of J these are the conditions
+ 
+
+ align:start position:0%
+space of J these are the conditions
+associated with a minima in our
+
+ align:start position:0%
+associated with a minima in our
+ 
+
+ align:start position:0%
+associated with a minima in our
+objective function on this boundary
+
+ align:start position:0%
+objective function on this boundary
+ 
+
+ align:start position:0%
+objective function on this boundary
+dictated by the the Equality constraint
+
+ align:start position:0%
+dictated by the the Equality constraint
+ 
+
+ align:start position:0%
+dictated by the the Equality constraint
+and of course the solution set is a
+
+ align:start position:0%
+and of course the solution set is a
+ 
+
+ align:start position:0%
+and of course the solution set is a
+critical point of a Lagrangian which is
+
+ align:start position:0%
+critical point of a Lagrangian which is
+ 
+
+ align:start position:0%
+critical point of a Lagrangian which is
+f of X minus C dot lambda and it's not a
+
+ align:start position:0%
+f of X minus C dot lambda and it's not a
+ 
+
+ align:start position:0%
+f of X minus C dot lambda and it's not a
+minimum of it it's a critical point it's
+
+ align:start position:0%
+minimum of it it's a critical point it's
+ 
+
+ align:start position:0%
+minimum of it it's a critical point it's
+a saddle point it turns out of this
+
+ align:start position:0%
+a saddle point it turns out of this
+ 
+
+ align:start position:0%
+a saddle point it turns out of this
+Lagrangian okay so we got to check did
+
+ align:start position:0%
+Lagrangian okay so we got to check did
+ 
+
+ align:start position:0%
+Lagrangian okay so we got to check did
+we find a saddle point or not when we
+
+ align:start position:0%
+we find a saddle point or not when we
+ 
+
+ align:start position:0%
+we find a saddle point or not when we
+find a solution to this equation here
+
+ align:start position:0%
+find a solution to this equation here
+ 
+
+ align:start position:0%
+find a solution to this equation here
+okay but it's just a system of nonlinear
+
+ align:start position:0%
+okay but it's just a system of nonlinear
+ 
+
+ align:start position:0%
+okay but it's just a system of nonlinear
+equation so if we have some good initial
+
+ align:start position:0%
+equation so if we have some good initial
+ 
+
+ align:start position:0%
+equation so if we have some good initial
+guess what do we apply newton-raphson
+
+ align:start position:0%
+guess what do we apply newton-raphson
+ 
+
+ align:start position:0%
+guess what do we apply newton-raphson
+right converge rate towards the solution
+
+ align:start position:0%
+right converge rate towards the solution
+ 
+
+ align:start position:0%
+right converge rate towards the solution
+right if we don't have a good initial
+
+ align:start position:0%
+right if we don't have a good initial
+ 
+
+ align:start position:0%
+right if we don't have a good initial
+guess well you know we've discussed lots
+
+ align:start position:0%
+guess well you know we've discussed lots
+ 
+
+ align:start position:0%
+guess well you know we've discussed lots
+of methods we could employ like homotopy
+
+ align:start position:0%
+of methods we could employ like homotopy
+ 
+
+ align:start position:0%
+of methods we could employ like homotopy
+or continuation to try to develop good
+
+ align:start position:0%
+or continuation to try to develop good
+ 
+
+ align:start position:0%
+or continuation to try to develop good
+initial guesses for what the solution
+
+ align:start position:0%
+initial guesses for what the solution
+ 
+
+ align:start position:0%
+initial guesses for what the solution
+should be are there any questions about
+
+ align:start position:0%
+should be are there any questions about
+ 
+
+ align:start position:0%
+should be are there any questions about
+this good okay so this is you know so
+
+ align:start position:0%
+this good okay so this is you know so
+ 
+
+ align:start position:0%
+this good okay so this is you know so
+you go to MATLAB and you call F min con
+
+ align:start position:0%
+you go to MATLAB and you call F min con
+ 
+
+ align:start position:0%
+you go to MATLAB and you call F min con
+right do do a minimization problem to
+
+ align:start position:0%
+right do do a minimization problem to
+ 
+
+ align:start position:0%
+right do do a minimization problem to
+give us some constraints linear
+
+ align:start position:0%
+give us some constraints linear
+ 
+
+ align:start position:0%
+give us some constraints linear
+constraints non linear constraints it
+
+ align:start position:0%
+constraints non linear constraints it
+ 
+
+ align:start position:0%
+constraints non linear constraints it
+doesn't matter actually right the
+
+ align:start position:0%
+doesn't matter actually right the
+ 
+
+ align:start position:0%
+doesn't matter actually right the
+problem is the same for both of them
+
+ align:start position:0%
+problem is the same for both of them
+ 
+
+ align:start position:0%
+problem is the same for both of them
+it's just a little bit easier if I have
+
+ align:start position:0%
+it's just a little bit easier if I have
+ 
+
+ align:start position:0%
+it's just a little bit easier if I have
+linear constraints okay if this
+
+ align:start position:0%
+linear constraints okay if this
+ 
+
+ align:start position:0%
+linear constraints okay if this
+constraining function is a linear
+
+ align:start position:0%
+constraining function is a linear
+ 
+
+ align:start position:0%
+constraining function is a linear
+function then the Jacobian I know it's
+
+ align:start position:0%
+function then the Jacobian I know it's
+ 
+
+ align:start position:0%
+function then the Jacobian I know it's
+the coefficient matrix of this linear
+
+ align:start position:0%
+the coefficient matrix of this linear
+ 
+
+ align:start position:0%
+the coefficient matrix of this linear
+linear problem and I'll have to solve
+
+ align:start position:0%
+linear problem and I'll have to solve
+ 
+
+ align:start position:0%
+linear problem and I'll have to solve
+linear equations down here so the
+
+ align:start position:0%
+linear equations down here so the
+ 
+
+ align:start position:0%
+linear equations down here so the
+problem is a little bit it's a little
+
+ align:start position:0%
+problem is a little bit it's a little
+ 
+
+ align:start position:0%
+problem is a little bit it's a little
+bit simpler to solve so MATLAB sort of
+
+ align:start position:0%
+bit simpler to solve so MATLAB sort of
+ 
+
+ align:start position:0%
+bit simpler to solve so MATLAB sort of
+breaks these apart so it can use
+
+ align:start position:0%
+breaks these apart so it can use
+ 
+
+ align:start position:0%
+breaks these apart so it can use
+different techniques depending on which
+
+ align:start position:0%
+different techniques depending on which
+ 
+
+ align:start position:0%
+different techniques depending on which
+one which should a problem is posed but
+
+ align:start position:0%
+one which should a problem is posed but
+ 
+
+ align:start position:0%
+one which should a problem is posed but
+the solution method is the same it does
+
+ align:start position:0%
+the solution method is the same it does
+ 
+
+ align:start position:0%
+the solution method is the same it does
+the method of LaGrange multipliers to
+
+ align:start position:0%
+the method of LaGrange multipliers to
+ 
+
+ align:start position:0%
+the method of LaGrange multipliers to
+find the solution okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in equality constraints so interior
+
+ align:start position:0%
+in equality constraints so interior
+ 
+
+ align:start position:0%
+in equality constraints so interior
+point methods were mentioned and it
+
+ align:start position:0%
+point methods were mentioned and it
+ 
+
+ align:start position:0%
+point methods were mentioned and it
+turns out this is this is really the
+
+ align:start position:0%
+turns out this is this is really the
+ 
+
+ align:start position:0%
+turns out this is this is really the
+best way to go about solving generic
+
+ align:start position:0%
+best way to go about solving generic
+ 
+
+ align:start position:0%
+best way to go about solving generic
+inequality constrained problems so these
+
+ align:start position:0%
+inequality constrained problems so these
+ 
+
+ align:start position:0%
+inequality constrained problems so these
+are problems of the sort ranked minimize
+
+ align:start position:0%
+are problems of the sort ranked minimize
+ 
+
+ align:start position:0%
+are problems of the sort ranked minimize
+f of X subject to H of X is positive or
+
+ align:start position:0%
+f of X subject to H of X is positive or
+ 
+
+ align:start position:0%
+f of X subject to H of X is positive or
+at least not negative
+
+ align:start position:0%
+at least not negative
+ 
+
+ align:start position:0%
+at least not negative
+this is some non linear inequality that
+
+ align:start position:0%
+this is some non linear inequality that
+ 
+
+ align:start position:0%
+this is some non linear inequality that
+describes some domain and its boundary
+
+ align:start position:0%
+describes some domain and its boundary
+ 
+
+ align:start position:0%
+describes some domain and its boundary
+in which the solution has to live and
+
+ align:start position:0%
+in which the solution has to live and
+ 
+
+ align:start position:0%
+in which the solution has to live and
+what's done is to rewrite as an
+
+ align:start position:0%
+what's done is to rewrite as an
+ 
+
+ align:start position:0%
+what's done is to rewrite as an
+unconstrained optimization problem with
+
+ align:start position:0%
+unconstrained optimization problem with
+ 
+
+ align:start position:0%
+unconstrained optimization problem with
+the barrier that's incorporated okay
+
+ align:start position:0%
+the barrier that's incorporated okay
+ 
+
+ align:start position:0%
+the barrier that's incorporated okay
+this looks a lot like the penalty method
+
+ align:start position:0%
+this looks a lot like the penalty method
+ 
+
+ align:start position:0%
+this looks a lot like the penalty method
+but it's very different and I'll explain
+
+ align:start position:0%
+but it's very different and I'll explain
+ 
+
+ align:start position:0%
+but it's very different and I'll explain
+how right so instead we want to minimize
+
+ align:start position:0%
+how right so instead we want to minimize
+ 
+
+ align:start position:0%
+how right so instead we want to minimize
+this f of X minus mu times the sum of
+
+ align:start position:0%
+this f of X minus mu times the sum of
+ 
+
+ align:start position:0%
+this f of X minus mu times the sum of
+log of H each of these constraints okay
+
+ align:start position:0%
+log of H each of these constraints okay
+ 
+
+ align:start position:0%
+log of H each of these constraints okay
+if H is negative okay
+
+ align:start position:0%
+if H is negative okay
+ 
+
+ align:start position:0%
+if H is negative okay
+the log will be we'll take the log of a
+
+ align:start position:0%
+the log will be we'll take the log of a
+ 
+
+ align:start position:0%
+the log will be we'll take the log of a
+negative argument that's a problem
+
+ align:start position:0%
+negative argument that's a problem
+ 
+
+ align:start position:0%
+negative argument that's a problem
+computationally so the best we could do
+
+ align:start position:0%
+computationally so the best we could do
+ 
+
+ align:start position:0%
+computationally so the best we could do
+is approach the boundary where H is
+
+ align:start position:0%
+is approach the boundary where H is
+ 
+
+ align:start position:0%
+is approach the boundary where H is
+equal to zero right and as H goes to
+
+ align:start position:0%
+equal to zero right and as H goes to
+ 
+
+ align:start position:0%
+equal to zero right and as H goes to
+zero the law goes to minus infinity so
+
+ align:start position:0%
+zero the law goes to minus infinity so
+ 
+
+ align:start position:0%
+zero the law goes to minus infinity so
+this term tends to blow up because I got
+
+ align:start position:0%
+this term tends to blow up because I got
+ 
+
+ align:start position:0%
+this term tends to blow up because I got
+a minus sign in front of it right so
+
+ align:start position:0%
+a minus sign in front of it right so
+ 
+
+ align:start position:0%
+a minus sign in front of it right so
+this is sort of like a penalty but it's
+
+ align:start position:0%
+this is sort of like a penalty but it's
+ 
+
+ align:start position:0%
+this is sort of like a penalty but it's
+a little different because the factor in
+
+ align:start position:0%
+a little different because the factor in
+ 
+
+ align:start position:0%
+a little different because the factor in
+front I'm actually going to take the
+
+ align:start position:0%
+front I'm actually going to take the
+ 
+
+ align:start position:0%
+front I'm actually going to take the
+limit as mu goes to zero okay I'm gonna
+
+ align:start position:0%
+limit as mu goes to zero okay I'm gonna
+ 
+
+ align:start position:0%
+limit as mu goes to zero okay I'm gonna
+take the limit is this factor gets small
+
+ align:start position:0%
+take the limit is this factor gets small
+ 
+
+ align:start position:0%
+take the limit is this factor gets small
+rather than gets big okay the log will
+
+ align:start position:0%
+rather than gets big okay the log will
+ 
+
+ align:start position:0%
+rather than gets big okay the log will
+always get big as I approach the
+
+ align:start position:0%
+always get big as I approach the
+ 
+
+ align:start position:0%
+always get big as I approach the
+boundary of the domain right it'll blow
+
+ align:start position:0%
+boundary of the domain right it'll blow
+ 
+
+ align:start position:0%
+boundary of the domain right it'll blow
+up okay so that's not a problem but I
+
+ align:start position:0%
+up okay so that's not a problem but I
+ 
+
+ align:start position:0%
+up okay so that's not a problem but I
+can take the limit that nu gets smaller
+
+ align:start position:0%
+can take the limit that nu gets smaller
+ 
+
+ align:start position:0%
+can take the limit that nu gets smaller
+and smaller and this quantity here right
+
+ align:start position:0%
+and smaller and this quantity here right
+ 
+
+ align:start position:0%
+and smaller and this quantity here right
+will have less and less of an impact
+
+ align:start position:0%
+will have less and less of an impact
+ 
+
+ align:start position:0%
+will have less and less of an impact
+right on the shape of this new objective
+
+ align:start position:0%
+right on the shape of this new objective
+ 
+
+ align:start position:0%
+right on the shape of this new objective
+function as you get smaller and smaller
+
+ align:start position:0%
+function as you get smaller and smaller
+ 
+
+ align:start position:0%
+function as you get smaller and smaller
+right the impact will only be nearest
+
+ align:start position:0%
+right the impact will only be nearest
+ 
+
+ align:start position:0%
+right the impact will only be nearest
+the boundary that makes sense so you
+
+ align:start position:0%
+the boundary that makes sense so you
+ 
+
+ align:start position:0%
+the boundary that makes sense so you
+take the limit that mu approaches zero
+
+ align:start position:0%
+take the limit that mu approaches zero
+ 
+
+ align:start position:0%
+take the limit that mu approaches zero
+it's got to approach it from the
+
+ align:start position:0%
+it's got to approach it from the
+ 
+
+ align:start position:0%
+it's got to approach it from the
+positive side not the negative side so
+
+ align:start position:0%
+positive side not the negative side so
+ 
+
+ align:start position:0%
+positive side not the negative side so
+everything behaves well this is called
+
+ align:start position:0%
+everything behaves well this is called
+ 
+
+ align:start position:0%
+everything behaves well this is called
+an interior point method so we have to
+
+ align:start position:0%
+an interior point method so we have to
+ 
+
+ align:start position:0%
+an interior point method so we have to
+determine the minimum of this new
+
+ align:start position:0%
+determine the minimum of this new
+ 
+
+ align:start position:0%
+determine the minimum of this new
+objective function for progressively
+
+ align:start position:0%
+objective function for progressively
+ 
+
+ align:start position:0%
+objective function for progressively
+weaker barriers okay so we might start
+
+ align:start position:0%
+weaker barriers okay so we might start
+ 
+
+ align:start position:0%
+weaker barriers okay so we might start
+with some value of mu and we might
+
+ align:start position:0%
+with some value of mu and we might
+ 
+
+ align:start position:0%
+with some value of mu and we might
+reduce mu progressively right until we
+
+ align:start position:0%
+reduce mu progressively right until we
+ 
+
+ align:start position:0%
+reduce mu progressively right until we
+get me down small enough that we think
+
+ align:start position:0%
+get me down small enough that we think
+ 
+
+ align:start position:0%
+get me down small enough that we think
+we've converged to a solution so how do
+
+ align:start position:0%
+we've converged to a solution so how do
+ 
+
+ align:start position:0%
+we've converged to a solution so how do
+you do that reliably what's the
+
+ align:start position:0%
+you do that reliably what's the
+ 
+
+ align:start position:0%
+you do that reliably what's the
+procedure one uses to solve a problem
+
+ align:start position:0%
+procedure one uses to solve a problem
+ 
+
+ align:start position:0%
+procedure one uses to solve a problem
+successively for different parameter
+
+ align:start position:0%
+successively for different parameter
+ 
+
+ align:start position:0%
+successively for different parameter
+values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's a home attabi right you're
+
+ align:start position:0%
+yeah it's a home attabi right you're
+ 
+
+ align:start position:0%
+yeah it's a home attabi right you're
+just gonna change the value of this
+
+ align:start position:0%
+just gonna change the value of this
+ 
+
+ align:start position:0%
+just gonna change the value of this
+barrier parameter right and you're gonna
+
+ align:start position:0%
+barrier parameter right and you're gonna
+ 
+
+ align:start position:0%
+barrier parameter right and you're gonna
+find a minimum if you make a small
+
+ align:start position:0%
+find a minimum if you make a small
+ 
+
+ align:start position:0%
+find a minimum if you make a small
+change in the barrier prim that's gonna
+
+ align:start position:0%
+change in the barrier prim that's gonna
+ 
+
+ align:start position:0%
+change in the barrier prim that's gonna
+serve as an excellent initial guess for
+
+ align:start position:0%
+serve as an excellent initial guess for
+ 
+
+ align:start position:0%
+serve as an excellent initial guess for
+the next value right and so just can
+
+ align:start position:0%
+the next value right and so just can
+ 
+
+ align:start position:0%
+the next value right and so just can
+take these small steps right and the
+
+ align:start position:0%
+take these small steps right and the
+ 
+
+ align:start position:0%
+take these small steps right and the
+optimization routine is going to carry
+
+ align:start position:0%
+optimization routine is going to carry
+ 
+
+ align:start position:0%
+optimization routine is going to carry
+you towards the minimum in the limit
+
+ align:start position:0%
+you towards the minimum in the limit
+ 
+
+ align:start position:0%
+you towards the minimum in the limit
+that mu goes to zero so you do this with
+
+ align:start position:0%
+that mu goes to zero so you do this with
+ 
+
+ align:start position:0%
+that mu goes to zero so you do this with
+hama toffee here's an example of this
+
+ align:start position:0%
+hama toffee here's an example of this
+ 
+
+ align:start position:0%
+hama toffee here's an example of this
+sort of interior point method a trivial
+
+ align:start position:0%
+sort of interior point method a trivial
+ 
+
+ align:start position:0%
+sort of interior point method a trivial
+example right minimize X subject to X
+
+ align:start position:0%
+example right minimize X subject to X
+ 
+
+ align:start position:0%
+example right minimize X subject to X
+being positive we know the solution
+
+ align:start position:0%
+being positive we know the solution
+ 
+
+ align:start position:0%
+being positive we know the solution
+lives where x equals zero but let's
+
+ align:start position:0%
+lives where x equals zero but let's
+ 
+
+ align:start position:0%
+lives where x equals zero but let's
+write this as unconstrained optimization
+
+ align:start position:0%
+write this as unconstrained optimization
+ 
+
+ align:start position:0%
+write this as unconstrained optimization
+using a barrier so minimize X minus mu
+
+ align:start position:0%
+using a barrier so minimize X minus mu
+ 
+
+ align:start position:0%
+using a barrier so minimize X minus mu
+times log X here's X minus mu times log
+
+ align:start position:0%
+times log X here's X minus mu times log
+ 
+
+ align:start position:0%
+times log X here's X minus mu times log
+X so out here where X is big okay
+
+ align:start position:0%
+X so out here where X is big okay
+ 
+
+ align:start position:0%
+X so out here where X is big okay
+X wins over log X so everything starts
+
+ align:start position:0%
+X wins over log X so everything starts
+ 
+
+ align:start position:0%
+X wins over log X so everything starts
+to look linear but as X becomes smaller
+
+ align:start position:0%
+to look linear but as X becomes smaller
+ 
+
+ align:start position:0%
+to look linear but as X becomes smaller
+and smaller log X gets very negative so
+
+ align:start position:0%
+and smaller log X gets very negative so
+ 
+
+ align:start position:0%
+and smaller log X gets very negative so
+minus log X gets very positive and
+
+ align:start position:0%
+minus log X gets very positive and
+ 
+
+ align:start position:0%
+minus log X gets very positive and
+here's the log creeping back up and as I
+
+ align:start position:0%
+here's the log creeping back up and as I
+ 
+
+ align:start position:0%
+here's the log creeping back up and as I
+decrease Mew smaller and smaller you can
+
+ align:start position:0%
+decrease Mew smaller and smaller you can
+ 
+
+ align:start position:0%
+decrease Mew smaller and smaller you can
+see the minimum of this function is
+
+ align:start position:0%
+see the minimum of this function is
+ 
+
+ align:start position:0%
+see the minimum of this function is
+moving closer and closer and closer to
+
+ align:start position:0%
+moving closer and closer and closer to
+ 
+
+ align:start position:0%
+moving closer and closer and closer to
+zero right so if I take the limit that
+
+ align:start position:0%
+zero right so if I take the limit that
+ 
+
+ align:start position:0%
+zero right so if I take the limit that
+Mew decreases from some positive number
+
+ align:start position:0%
+Mew decreases from some positive number
+ 
+
+ align:start position:0%
+Mew decreases from some positive number
+towards zero
+
+ align:start position:0%
+towards zero
+ 
+
+ align:start position:0%
+towards zero
+eventually this minimum is going to
+
+ align:start position:0%
+eventually this minimum is going to
+ 
+
+ align:start position:0%
+eventually this minimum is going to
+converge right to the minimum of the
+
+ align:start position:0%
+converge right to the minimum of the
+ 
+
+ align:start position:0%
+converge right to the minimum of the
+constrained inequality constrained
+
+ align:start position:0%
+constrained inequality constrained
+ 
+
+ align:start position:0%
+constrained inequality constrained
+optimization problem makes sense okay
+
+ align:start position:0%
+optimization problem makes sense okay
+ 
+
+ align:start position:0%
+optimization problem makes sense okay
+okay so yeah so we want to do this you
+
+ align:start position:0%
+okay so yeah so we want to do this you
+ 
+
+ align:start position:0%
+okay so yeah so we want to do this you
+can choose any barrier function you want
+
+ align:start position:0%
+can choose any barrier function you want
+ 
+
+ align:start position:0%
+can choose any barrier function you want
+any any thoughts on why a logarithmic
+
+ align:start position:0%
+any any thoughts on why a logarithmic
+ 
+
+ align:start position:0%
+any any thoughts on why a logarithmic
+barrier is used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's okay so Mike - log is gonna
+
+ align:start position:0%
+okay that's okay so Mike - log is gonna
+ 
+
+ align:start position:0%
+okay that's okay so Mike - log is gonna
+be convex log as in convex but - log is
+
+ align:start position:0%
+be convex log as in convex but - log is
+ 
+
+ align:start position:0%
+be convex log as in convex but - log is
+going to be convex so that's good okay
+
+ align:start position:0%
+going to be convex so that's good okay
+ 
+
+ align:start position:0%
+going to be convex so that's good okay
+it's gonna if this function is convex
+
+ align:start position:0%
+it's gonna if this function is convex
+ 
+
+ align:start position:0%
+it's gonna if this function is convex
+and their combinations gonna be convex
+
+ align:start position:0%
+and their combinations gonna be convex
+ 
+
+ align:start position:0%
+and their combinations gonna be convex
+Oh we'll be okay
+
+ align:start position:0%
+Oh we'll be okay
+ 
+
+ align:start position:0%
+Oh we'll be okay
+but the gradient of the log is easy to
+
+ align:start position:0%
+but the gradient of the log is easy to
+ 
+
+ align:start position:0%
+but the gradient of the log is easy to
+compute right grad log H is one over H
+
+ align:start position:0%
+compute right grad log H is one over H
+ 
+
+ align:start position:0%
+compute right grad log H is one over H
+grad H so if I know H I know grad H it's
+
+ align:start position:0%
+grad H so if I know H I know grad H it's
+ 
+
+ align:start position:0%
+grad H so if I know H I know grad H it's
+easy for me to compute the gradient of
+
+ align:start position:0%
+easy for me to compute the gradient of
+ 
+
+ align:start position:0%
+easy for me to compute the gradient of
+log H we know we're gonna solve this
+
+ align:start position:0%
+log H we know we're gonna solve this
+ 
+
+ align:start position:0%
+log H we know we're gonna solve this
+unconstrained optimization problem where
+
+ align:start position:0%
+unconstrained optimization problem where
+ 
+
+ align:start position:0%
+unconstrained optimization problem where
+we need to take grad of this objective
+
+ align:start position:0%
+we need to take grad of this objective
+ 
+
+ align:start position:0%
+we need to take grad of this objective
+function equals zero so the calculations
+
+ align:start position:0%
+function equals zero so the calculations
+ 
+
+ align:start position:0%
+function equals zero so the calculations
+are easy right the log makes it easy
+
+ align:start position:0%
+are easy right the log makes it easy
+ 
+
+ align:start position:0%
+are easy right the log makes it easy
+like that the log is also like the most
+
+ align:start position:0%
+like that the log is also like the most
+ 
+
+ align:start position:0%
+like that the log is also like the most
+weekly singular function available to us
+
+ align:start position:0%
+weekly singular function available to us
+ 
+
+ align:start position:0%
+weekly singular function available to us
+right out of all the toolbox of all
+
+ align:start position:0%
+right out of all the toolbox of all
+ 
+
+ align:start position:0%
+right out of all the toolbox of all
+problems we can reach to the log has so
+
+ align:start position:0%
+problems we can reach to the log has so
+ 
+
+ align:start position:0%
+problems we can reach to the log has so
+the mildest sort of singularities
+
+ align:start position:0%
+the mildest sort of singularities
+ 
+
+ align:start position:0%
+the mildest sort of singularities
+singularities of both ends which is sort
+
+ align:start position:0%
+singularities of both ends which is sort
+ 
+
+ align:start position:0%
+singularities of both ends which is sort
+of funny but the mildest sort of
+
+ align:start position:0%
+of funny but the mildest sort of
+ 
+
+ align:start position:0%
+of funny but the mildest sort of
+singularities you have to cope with okay
+
+ align:start position:0%
+singularities you have to cope with okay
+ 
+
+ align:start position:0%
+singularities you have to cope with okay
+so we want to find the minimum of these
+
+ align:start position:0%
+so we want to find the minimum of these
+ 
+
+ align:start position:0%
+so we want to find the minimum of these
+unconstrained optimization problems
+
+ align:start position:0%
+unconstrained optimization problems
+ 
+
+ align:start position:0%
+unconstrained optimization problems
+where the gradient of f minus mu sum 1
+
+ align:start position:0%
+where the gradient of f minus mu sum 1
+ 
+
+ align:start position:0%
+where the gradient of f minus mu sum 1
+over h grad h is equal to 0 ok then we
+
+ align:start position:0%
+over h grad h is equal to 0 ok then we
+ 
+
+ align:start position:0%
+over h grad h is equal to 0 ok then we
+just do that for progressively smaller
+
+ align:start position:0%
+just do that for progressively smaller
+ 
+
+ align:start position:0%
+just do that for progressively smaller
+values of MU and will converge to a
+
+ align:start position:0%
+values of MU and will converge to a
+ 
+
+ align:start position:0%
+values of MU and will converge to a
+solution that's the interior point
+
+ align:start position:0%
+solution that's the interior point
+ 
+
+ align:start position:0%
+solution that's the interior point
+method you use homotopy right to study a
+
+ align:start position:0%
+method you use homotopy right to study a
+ 
+
+ align:start position:0%
+method you use homotopy right to study a
+sequence of barrier parameters or
+
+ align:start position:0%
+sequence of barrier parameters or
+ 
+
+ align:start position:0%
+sequence of barrier parameters or
+continuation to study sequence of
+
+ align:start position:0%
+continuation to study sequence of
+ 
+
+ align:start position:0%
+continuation to study sequence of
+barrier parameters you stop the hama
+
+ align:start position:0%
+barrier parameters you stop the hama
+ 
+
+ align:start position:0%
+barrier parameters you stop the hama
+toppy or continuation when what how are
+
+ align:start position:0%
+toppy or continuation when what how are
+ 
+
+ align:start position:0%
+toppy or continuation when what how are
+you gonna stop I got to make a new small
+
+ align:start position:0%
+you gonna stop I got to make a new small
+ 
+
+ align:start position:0%
+you gonna stop I got to make a new small
+right I want to go towards the limit mu
+
+ align:start position:0%
+right I want to go towards the limit mu
+ 
+
+ align:start position:0%
+right I want to go towards the limit mu
+equals 0 I can't actually get to mu
+
+ align:start position:0%
+equals 0 I can't actually get to mu
+ 
+
+ align:start position:0%
+equals 0 I can't actually get to mu
+equals you're alright I just going to
+
+ align:start position:0%
+equals you're alright I just going to
+ 
+
+ align:start position:0%
+equals you're alright I just going to
+approach it so how small do I need to
+
+ align:start position:0%
+approach it so how small do I need to
+ 
+
+ align:start position:0%
+approach it so how small do I need to
+make new before I quit it's an
+
+ align:start position:0%
+make new before I quit it's an
+ 
+
+ align:start position:0%
+make new before I quit it's an
+interesting question what do you think
+
+ align:start position:0%
+interesting question what do you think
+ 
+
+ align:start position:0%
+interesting question what do you think
+I'll take this answer first oh good so
+
+ align:start position:0%
+I'll take this answer first oh good so
+ 
+
+ align:start position:0%
+I'll take this answer first oh good so
+we might look at the solution and see is
+
+ align:start position:0%
+we might look at the solution and see is
+ 
+
+ align:start position:0%
+we might look at the solution and see is
+the solution becoming less and less
+
+ align:start position:0%
+the solution becoming less and less
+ 
+
+ align:start position:0%
+the solution becoming less and less
+sensitive to the choice of them you good
+
+ align:start position:0%
+sensitive to the choice of them you good
+ 
+
+ align:start position:0%
+sensitive to the choice of them you good
+did you have a did you another
+
+ align:start position:0%
+did you have a did you another
+ 
+
+ align:start position:0%
+did you have a did you another
+suggestion look is set a tolerance right
+
+ align:start position:0%
+suggestion look is set a tolerance right
+ 
+
+ align:start position:0%
+suggestion look is set a tolerance right
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm right rabbi right so you good so so
+
+ align:start position:0%
+hmm right rabbi right so you good so so
+ 
+
+ align:start position:0%
+hmm right rabbi right so you good so so
+there were two suggestions here one is
+
+ align:start position:0%
+there were two suggestions here one is
+ 
+
+ align:start position:0%
+there were two suggestions here one is
+one is along the lines of a step norm
+
+ align:start position:0%
+one is along the lines of a step norm
+ 
+
+ align:start position:0%
+one is along the lines of a step norm
+criteria right like I I checked my
+
+ align:start position:0%
+criteria right like I I checked my
+ 
+
+ align:start position:0%
+criteria right like I I checked my
+solution as I change mu and ask when
+
+ align:start position:0%
+solution as I change mu and ask when
+ 
+
+ align:start position:0%
+solution as I change mu and ask when
+does my solution seem relatively
+
+ align:start position:0%
+does my solution seem relatively
+ 
+
+ align:start position:0%
+does my solution seem relatively
+insensitive to MU right when the changes
+
+ align:start position:0%
+insensitive to MU right when the changes
+ 
+
+ align:start position:0%
+insensitive to MU right when the changes
+in these steps relative team you get
+
+ align:start position:0%
+in these steps relative team you get
+ 
+
+ align:start position:0%
+in these steps relative team you get
+sufficiently small right I might be
+
+ align:start position:0%
+sufficiently small right I might be
+ 
+
+ align:start position:0%
+sufficiently small right I might be
+willing to accept these solutions as
+
+ align:start position:0%
+willing to accept these solutions as
+ 
+
+ align:start position:0%
+willing to accept these solutions as
+reasonable solutions for the constrained
+
+ align:start position:0%
+reasonable solutions for the constrained
+ 
+
+ align:start position:0%
+reasonable solutions for the constrained
+optimization I can also go back and I
+
+ align:start position:0%
+optimization I can also go back and I
+ 
+
+ align:start position:0%
+optimization I can also go back and I
+can check sort of function norm right
+
+ align:start position:0%
+can check sort of function norm right
+ 
+
+ align:start position:0%
+can check sort of function norm right
+criteria right I can take the value of x
+
+ align:start position:0%
+criteria right I can take the value of x
+ 
+
+ align:start position:0%
+criteria right I can take the value of x
+I found as the minimum and I can ask
+
+ align:start position:0%
+I found as the minimum and I can ask
+ 
+
+ align:start position:0%
+I found as the minimum and I can ask
+right how good a job does it do
+
+ align:start position:0%
+right how good a job does it do
+ 
+
+ align:start position:0%
+right how good a job does it do
+satisfying right the original equations
+
+ align:start position:0%
+satisfying right the original equations
+ 
+
+ align:start position:0%
+satisfying right the original equations
+how far away am i from satisfying the
+
+ align:start position:0%
+how far away am i from satisfying the
+ 
+
+ align:start position:0%
+how far away am i from satisfying the
+inequality constraint how close am I to
+
+ align:start position:0%
+inequality constraint how close am I to
+ 
+
+ align:start position:0%
+inequality constraint how close am I to
+actually minimizing the function within
+
+ align:start position:0%
+actually minimizing the function within
+ 
+
+ align:start position:0%
+actually minimizing the function within
+that domain okay so we're running out of
+
+ align:start position:0%
+that domain okay so we're running out of
+ 
+
+ align:start position:0%
+that domain okay so we're running out of
+time here let me provide you with an
+
+ align:start position:0%
+time here let me provide you with an
+ 
+
+ align:start position:0%
+time here let me provide you with an
+example so let's minimize again I'd
+
+ align:start position:0%
+example so let's minimize again I'd
+ 
+
+ align:start position:0%
+example so let's minimize again I'd
+always pick this function because it's
+
+ align:start position:0%
+always pick this function because it's
+ 
+
+ align:start position:0%
+always pick this function because it's
+easy to visualize right a nice parabolic
+
+ align:start position:0%
+easy to visualize right a nice parabolic
+ 
+
+ align:start position:0%
+easy to visualize right a nice parabolic
+function it opens upwards and let's
+
+ align:start position:0%
+function it opens upwards and let's
+ 
+
+ align:start position:0%
+function it opens upwards and let's
+minimize it subject to the constraint
+
+ align:start position:0%
+minimize it subject to the constraint
+ 
+
+ align:start position:0%
+minimize it subject to the constraint
+right that H of X 1 and X 2 is equal to
+
+ align:start position:0%
+right that H of X 1 and X 2 is equal to
+ 
+
+ align:start position:0%
+right that H of X 1 and X 2 is equal to
+1 minus well the equation for a circle
+
+ align:start position:0%
+1 minus well the equation for a circle
+ 
+
+ align:start position:0%
+1 minus well the equation for a circle
+of radius 1 essentially the interior of
+
+ align:start position:0%
+of radius 1 essentially the interior of
+ 
+
+ align:start position:0%
+of radius 1 essentially the interior of
+that circle ok so here's the contours of
+
+ align:start position:0%
+that circle ok so here's the contours of
+ 
+
+ align:start position:0%
+that circle ok so here's the contours of
+the function and this red domain is the
+
+ align:start position:0%
+the function and this red domain is the
+ 
+
+ align:start position:0%
+the function and this red domain is the
+constraint we want to know the smallest
+
+ align:start position:0%
+constraint we want to know the smallest
+ 
+
+ align:start position:0%
+constraint we want to know the smallest
+value of f that lives in this domain all
+
+ align:start position:0%
+value of f that lives in this domain all
+ 
+
+ align:start position:0%
+value of f that lives in this domain all
+right so here's some MATLAB code you can
+
+ align:start position:0%
+right so here's some MATLAB code you can
+ 
+
+ align:start position:0%
+right so here's some MATLAB code you can
+try it out right and make a function the
+
+ align:start position:0%
+try it out right and make a function the
+ 
+
+ align:start position:0%
+try it out right and make a function the
+objective function f right it's x
+
+ align:start position:0%
+objective function f right it's x
+ 
+
+ align:start position:0%
+objective function f right it's x
+squared plus 10x X 1 squared plus 10x 2
+
+ align:start position:0%
+squared plus 10x X 1 squared plus 10x 2
+ 
+
+ align:start position:0%
+squared plus 10x X 1 squared plus 10x 2
+squared here's the gradient here's the
+
+ align:start position:0%
+squared here's the gradient here's the
+ 
+
+ align:start position:0%
+squared here's the gradient here's the
+Hessian ok here I calculate H here's the
+
+ align:start position:0%
+Hessian ok here I calculate H here's the
+ 
+
+ align:start position:0%
+Hessian ok here I calculate H here's the
+gradient in H here's the Hessian NH I
+
+ align:start position:0%
+gradient in H here's the Hessian NH I
+ 
+
+ align:start position:0%
+gradient in H here's the Hessian NH I
+get to define a new objective function V
+
+ align:start position:0%
+get to define a new objective function V
+ 
+
+ align:start position:0%
+get to define a new objective function V
+which is f minus nu log H this is the
+
+ align:start position:0%
+which is f minus nu log H this is the
+ 
+
+ align:start position:0%
+which is f minus nu log H this is the
+gradient in fee and this is the Hessian
+
+ align:start position:0%
+gradient in fee and this is the Hessian
+ 
+
+ align:start position:0%
+gradient in fee and this is the Hessian
+of fee oh man what a mess but actually
+
+ align:start position:0%
+of fee oh man what a mess but actually
+ 
+
+ align:start position:0%
+of fee oh man what a mess but actually
+not such a mess because the log makes it
+
+ align:start position:0%
+not such a mess because the log makes it
+ 
+
+ align:start position:0%
+not such a mess because the log makes it
+really easy to take these derivatives ok
+
+ align:start position:0%
+really easy to take these derivatives ok
+ 
+
+ align:start position:0%
+really easy to take these derivatives ok
+just just a lot of valley you know a lot
+
+ align:start position:0%
+just just a lot of valley you know a lot
+ 
+
+ align:start position:0%
+just just a lot of valley you know a lot
+of differential sort of calculus
+
+ align:start position:0%
+of differential sort of calculus
+ 
+
+ align:start position:0%
+of differential sort of calculus
+involved in working this out but this is
+
+ align:start position:0%
+involved in working this out but this is
+ 
+
+ align:start position:0%
+involved in working this out but this is
+the Hessian of fee and then I need some
+
+ align:start position:0%
+the Hessian of fee and then I need some
+ 
+
+ align:start position:0%
+the Hessian of fee and then I need some
+initial guess so I pick pick the center
+
+ align:start position:0%
+initial guess so I pick pick the center
+ 
+
+ align:start position:0%
+initial guess so I pick pick the center
+of my circle as an initial guess for the
+
+ align:start position:0%
+of my circle as an initial guess for the
+ 
+
+ align:start position:0%
+of my circle as an initial guess for the
+solution and I'm gonna loop over values
+
+ align:start position:0%
+solution and I'm gonna loop over values
+ 
+
+ align:start position:0%
+solution and I'm gonna loop over values
+of MU that get progressively smaller
+
+ align:start position:0%
+of MU that get progressively smaller
+ 
+
+ align:start position:0%
+of MU that get progressively smaller
+I'll just go down to ten to the minus
+
+ align:start position:0%
+I'll just go down to ten to the minus
+ 
+
+ align:start position:0%
+I'll just go down to ten to the minus
+two and stop for illustration purposes
+
+ align:start position:0%
+two and stop for illustration purposes
+ 
+
+ align:start position:0%
+two and stop for illustration purposes
+here but really we should be checking
+
+ align:start position:0%
+here but really we should be checking
+ 
+
+ align:start position:0%
+here but really we should be checking
+the solution as we go and deciding what
+
+ align:start position:0%
+the solution as we go and deciding what
+ 
+
+ align:start position:0%
+the solution as we go and deciding what
+values we want to stop with and then
+
+ align:start position:0%
+values we want to stop with and then
+ 
+
+ align:start position:0%
+values we want to stop with and then
+this loop here what's this do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's it do
+
+ align:start position:0%
+what's it do
+ 
+
+ align:start position:0%
+what's it do
+can you tell what's that yeah it's nuva
+
+ align:start position:0%
+can you tell what's that yeah it's nuva
+ 
+
+ align:start position:0%
+can you tell what's that yeah it's nuva
+raphson right X is X minus Hessian
+
+ align:start position:0%
+raphson right X is X minus Hessian
+ 
+
+ align:start position:0%
+raphson right X is X minus Hessian
+inverse times grad fee right so I just
+
+ align:start position:0%
+inverse times grad fee right so I just
+ 
+
+ align:start position:0%
+inverse times grad fee right so I just
+do newton-raphson I take my initial
+
+ align:start position:0%
+do newton-raphson I take my initial
+ 
+
+ align:start position:0%
+do newton-raphson I take my initial
+guess and I whip around with
+
+ align:start position:0%
+guess and I whip around with
+ 
+
+ align:start position:0%
+guess and I whip around with
+newton-raphson and when this loop
+
+ align:start position:0%
+newton-raphson and when this loop
+ 
+
+ align:start position:0%
+newton-raphson and when this loop
+finishes I reduce some U and it'll just
+
+ align:start position:0%
+finishes I reduce some U and it'll just
+ 
+
+ align:start position:0%
+finishes I reduce some U and it'll just
+use my previous guests as the initial
+
+ align:start position:0%
+use my previous guests as the initial
+ 
+
+ align:start position:0%
+use my previous guests as the initial
+guess for the next value of the loop
+
+ align:start position:0%
+guess for the next value of the loop
+ 
+
+ align:start position:0%
+guess for the next value of the loop
+until mu is sufficiently small okay
+
+ align:start position:0%
+until mu is sufficiently small okay
+ 
+
+ align:start position:0%
+until mu is sufficiently small okay
+interior point method here's what that
+
+ align:start position:0%
+interior point method here's what that
+ 
+
+ align:start position:0%
+interior point method here's what that
+solution path looks like okay so mu
+
+ align:start position:0%
+solution path looks like okay so mu
+ 
+
+ align:start position:0%
+solution path looks like okay so mu
+started at one and the barrier was here
+
+ align:start position:0%
+started at one and the barrier was here
+ 
+
+ align:start position:0%
+started at one and the barrier was here
+was close to the edge of the circle but
+
+ align:start position:0%
+was close to the edge of the circle but
+ 
+
+ align:start position:0%
+was close to the edge of the circle but
+not quite on it but as I reduced Mew
+
+ align:start position:0%
+not quite on it but as I reduced Mew
+ 
+
+ align:start position:0%
+not quite on it but as I reduced Mew
+further and further and further you can
+
+ align:start position:0%
+further and further and further you can
+ 
+
+ align:start position:0%
+further and further and further you can
+see the path the solution path that was
+
+ align:start position:0%
+see the path the solution path that was
+ 
+
+ align:start position:0%
+see the path the solution path that was
+followed works its way closer to the
+
+ align:start position:0%
+followed works its way closer to the
+ 
+
+ align:start position:0%
+followed works its way closer to the
+boundary of the circle and the minimum
+
+ align:start position:0%
+boundary of the circle and the minimum
+ 
+
+ align:start position:0%
+boundary of the circle and the minimum
+is found right here okay so it turns out
+
+ align:start position:0%
+is found right here okay so it turns out
+ 
+
+ align:start position:0%
+is found right here okay so it turns out
+the minimum of this function doesn't
+
+ align:start position:0%
+the minimum of this function doesn't
+ 
+
+ align:start position:0%
+the minimum of this function doesn't
+live in the domain it lives on the
+
+ align:start position:0%
+live in the domain it lives on the
+ 
+
+ align:start position:0%
+live in the domain it lives on the
+boundary of the domain recall that this
+
+ align:start position:0%
+boundary of the domain recall that this
+ 
+
+ align:start position:0%
+boundary of the domain recall that this
+point should be a point where the
+
+ align:start position:0%
+point should be a point where the
+ 
+
+ align:start position:0%
+point should be a point where the
+boundary of the domain is parallel to
+
+ align:start position:0%
+boundary of the domain is parallel to
+ 
+
+ align:start position:0%
+boundary of the domain is parallel to
+the contours of the function right since
+
+ align:start position:0%
+the contours of the function right since
+ 
+
+ align:start position:0%
+the contours of the function right since
+actually we didn't need the inequality
+
+ align:start position:0%
+actually we didn't need the inequality
+ 
+
+ align:start position:0%
+actually we didn't need the inequality
+constraint here we could have used the
+
+ align:start position:0%
+constraint here we could have used the
+ 
+
+ align:start position:0%
+constraint here we could have used the
+Equality constraint the Equality
+
+ align:start position:0%
+Equality constraint the Equality
+ 
+
+ align:start position:0%
+Equality constraint the Equality
+constraint problem has the same solution
+
+ align:start position:0%
+constraint problem has the same solution
+ 
+
+ align:start position:0%
+constraint problem has the same solution
+as the inequality constraint from and
+
+ align:start position:0%
+as the inequality constraint from and
+ 
+
+ align:start position:0%
+as the inequality constraint from and
+look that actually happened right here's
+
+ align:start position:0%
+look that actually happened right here's
+ 
+
+ align:start position:0%
+look that actually happened right here's
+the contours of the function the contour
+
+ align:start position:0%
+the contours of the function the contour
+ 
+
+ align:start position:0%
+the contours of the function the contour
+the function runs right along here and
+
+ align:start position:0%
+the function runs right along here and
+ 
+
+ align:start position:0%
+the function runs right along here and
+you can see it's looks like it's going
+
+ align:start position:0%
+you can see it's looks like it's going
+ 
+
+ align:start position:0%
+you can see it's looks like it's going
+to be tangent to the circle at this
+
+ align:start position:0%
+to be tangent to the circle at this
+ 
+
+ align:start position:0%
+to be tangent to the circle at this
+point so the interior point method
+
+ align:start position:0%
+point so the interior point method
+ 
+
+ align:start position:0%
+point so the interior point method
+actually solved an equality constraint
+
+ align:start position:0%
+actually solved an equality constraint
+ 
+
+ align:start position:0%
+actually solved an equality constraint
+problem in addition to an inequality
+
+ align:start position:0%
+problem in addition to an inequality
+ 
+
+ align:start position:0%
+problem in addition to an inequality
+constraint promises that's that's sort
+
+ align:start position:0%
+constraint promises that's that's sort
+ 
+
+ align:start position:0%
+constraint promises that's that's sort
+of cool that you can do it that way okay
+
+ align:start position:0%
+of cool that you can do it that way okay
+ 
+
+ align:start position:0%
+of cool that you can do it that way okay
+how about if I want to do a combination
+
+ align:start position:0%
+how about if I want to do a combination
+ 
+
+ align:start position:0%
+how about if I want to do a combination
+of equality and inequality constraints
+
+ align:start position:0%
+of equality and inequality constraints
+ 
+
+ align:start position:0%
+of equality and inequality constraints
+then what do I do yeah perfect right
+
+ align:start position:0%
+then what do I do yeah perfect right
+ 
+
+ align:start position:0%
+then what do I do yeah perfect right
+convert the Equality constraint into
+
+ align:start position:0%
+convert the Equality constraint into
+ 
+
+ align:start position:0%
+convert the Equality constraint into
+unknowns Lagrange multipliers instead
+
+ align:start position:0%
+unknowns Lagrange multipliers instead
+ 
+
+ align:start position:0%
+unknowns Lagrange multipliers instead
+right and then do the interior point
+
+ align:start position:0%
+right and then do the interior point
+ 
+
+ align:start position:0%
+right and then do the interior point
+method on the Lagrangian problem okay
+
+ align:start position:0%
+method on the Lagrangian problem okay
+ 
+
+ align:start position:0%
+method on the Lagrangian problem okay
+now you've got a combination of equality
+
+ align:start position:0%
+now you've got a combination of equality
+ 
+
+ align:start position:0%
+now you've got a combination of equality
+and inequality constraint this is
+
+ align:start position:0%
+and inequality constraint this is
+ 
+
+ align:start position:0%
+and inequality constraint this is
+exactly what MATLAB does
+
+ align:start position:0%
+exactly what MATLAB does
+ 
+
+ align:start position:0%
+exactly what MATLAB does
+okay so converts equality constraints
+
+ align:start position:0%
+okay so converts equality constraints
+ 
+
+ align:start position:0%
+okay so converts equality constraints
+into LeGrande multipliers in equality
+
+ align:start position:0%
+into LeGrande multipliers in equality
+ 
+
+ align:start position:0%
+into LeGrande multipliers in equality
+constraints that actually solves using
+
+ align:start position:0%
+constraints that actually solves using
+ 
+
+ align:start position:0%
+constraints that actually solves using
+interior point methods buried in that
+
+ align:start position:0%
+interior point methods buried in that
+ 
+
+ align:start position:0%
+interior point methods buried in that
+interior point method is some form of
+
+ align:start position:0%
+interior point method is some form of
+ 
+
+ align:start position:0%
+interior point method is some form of
+newton-raphson and steepest descent
+
+ align:start position:0%
+newton-raphson and steepest descent
+ 
+
+ align:start position:0%
+newton-raphson and steepest descent
+combined together like dogleg we talked
+
+ align:start position:0%
+combined together like dogleg we talked
+ 
+
+ align:start position:0%
+combined together like dogleg we talked
+about for unconstrained problems and
+
+ align:start position:0%
+about for unconstrained problems and
+ 
+
+ align:start position:0%
+about for unconstrained problems and
+it's going to do a continuation as it
+
+ align:start position:0%
+it's going to do a continuation as it
+ 
+
+ align:start position:0%
+it's going to do a continuation as it
+reduces the values of MU he'll have some
+
+ align:start position:0%
+reduces the values of MU he'll have some
+ 
+
+ align:start position:0%
+reduces the values of MU he'll have some
+heuristic for how it does that right
+
+ align:start position:0%
+heuristic for how it does that right
+ 
+
+ align:start position:0%
+heuristic for how it does that right
+it's going to use its previous solutions
+
+ align:start position:0%
+it's going to use its previous solutions
+ 
+
+ align:start position:0%
+it's going to use its previous solutions
+as initial guesses for the next
+
+ align:start position:0%
+as initial guesses for the next
+ 
+
+ align:start position:0%
+as initial guesses for the next
+iteration so these are very complicated
+
+ align:start position:0%
+iteration so these are very complicated
+ 
+
+ align:start position:0%
+iteration so these are very complicated
+problems but if you understand how to
+
+ align:start position:0%
+problems but if you understand how to
+ 
+
+ align:start position:0%
+problems but if you understand how to
+solve systems of nonlinear equations
+
+ align:start position:0%
+solve systems of nonlinear equations
+ 
+
+ align:start position:0%
+solve systems of nonlinear equations
+okay you think carefully about how to
+
+ align:start position:0%
+okay you think carefully about how to
+ 
+
+ align:start position:0%
+okay you think carefully about how to
+control numerical error in your
+
+ align:start position:0%
+control numerical error in your
+ 
+
+ align:start position:0%
+control numerical error in your
+algorithm you come to conclusion like
+
+ align:start position:0%
+algorithm you come to conclusion like
+ 
+
+ align:start position:0%
+algorithm you come to conclusion like
+this that you can you know you can you
+
+ align:start position:0%
+this that you can you know you can you
+ 
+
+ align:start position:0%
+this that you can you know you can you
+can do these sorts of Lagrange
+
+ align:start position:0%
+can do these sorts of Lagrange
+ 
+
+ align:start position:0%
+can do these sorts of Lagrange
+multiplier interior point methods solve
+
+ align:start position:0%
+multiplier interior point methods solve
+ 
+
+ align:start position:0%
+multiplier interior point methods solve
+a wide variety of problems with
+
+ align:start position:0%
+a wide variety of problems with
+ 
+
+ align:start position:0%
+a wide variety of problems with
+reasonable reliability okay any more
+
+ align:start position:0%
+reasonable reliability okay any more
+ 
+
+ align:start position:0%
+reasonable reliability okay any more
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no good well thank you and we'll see you
+
+ align:start position:0%
+no good well thank you and we'll see you
+ 
+
+ align:start position:0%
+no good well thank you and we'll see you
+on Friday
\ No newline at end of file
diff --git a/Pij6J0HsYFA.txt b/Pij6J0HsYFA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1f1dbe93f5b8e317953f44f9de33a2c370faf3a
--- /dev/null
+++ b/Pij6J0HsYFA.txt
@@ -0,0 +1,3074 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseware continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseware, at
+
+ocw.mit.edu.
+
+PROFESSOR JIM ERICSON:
+OK, to work.
+
+A word of warning: fasten
+your seat belts.
+
+Or, another way of saying it is,
+I'm going to open up the
+
+fire hose a little bit today.
+
+Last lecture, you might have
+thought this was a SHASS
+
+class, it's not like a
+philosophy class, and it was
+
+important to set the stage for
+what we're going to talk
+
+about, but we talked about
+very high level things.
+
+The notion of recipes, the
+notion of computation, why you
+
+want to do this, what you're
+going to learn.
+
+Today we're going to dive into
+the nitty-gritty, the nuts and
+
+bolts of the basics of
+computation, and in
+
+particular, what I'm going to do
+today is, I'm going to talk
+
+about operators and operands,
+which we did a little bit real
+
+last time, in particular how
+to create expressions, I'm
+
+going to talk about statements
+as the key building blocks for
+
+writing code, and I'm going to
+introduce simple sets of
+
+programs, in particular I'm
+going to talk about branching,
+
+conditionals, and iteration.
+
+So, a lot to do.
+
+OK?
+
+So, let me jump straight
+to it.
+
+At the end of last lecture, we
+started introducing some of
+
+the pieces you want to do.
+
+And I want to remind
+you of our goal.
+
+We're trying to describe
+processes.
+
+We want to have things that
+deduce new kinds of
+
+information.
+
+So we want to write programs
+to do that.
+
+If we're going to write
+programs, we need at least two
+
+things: we need some
+representation
+
+for fundamental data.
+
+And we saw last time two
+examples of that.
+
+And the second thing we're going
+to need, is we're going
+
+to need a way to give
+instructions to the computer
+
+to manipulate that data.
+
+We need to give it a description
+of the recipe.
+
+In terms of primitive
+data, what we saw
+
+were two kinds: Right?
+
+Numbers and strings.
+
+A little later on in the
+lecture we're going to
+
+introduce a third kind of value,
+but what we're going to
+
+see throughout the term is, no
+matter how complex a data
+
+structure we create, and we're
+going to create a variety of
+
+data structures, fundamentally
+all of them have their basis,
+
+their atomic level if you like,
+are going to be some
+
+combinations of numbers, of
+strings, and the third type,
+
+which are booleans, which I'm
+going to introduce a little
+
+later on in this lecture.
+
+And that kind of makes
+sense right?
+
+Numbers are there to do numeric
+things, strings are
+
+our fundamental way of
+representing textual
+
+information.
+
+And so we're going to see
+how to combine those
+
+things as we go along.
+
+Second thing we saw was, we saw
+that associated with every
+
+primitive value was a type.
+
+And these are kind of
+obvious, right?
+
+Strings are strings.
+
+For numbers, we had some
+variations; we had integers,
+
+we had floats.
+
+We'll introduce a few
+more as we go along.
+
+But those types are important,
+because they tell us something
+
+about what we want to do when we
+want to put them together.
+
+OK, but nonetheless, I want to
+stress we have both a value,
+
+yeah, and a type.
+
+All right.
+
+Once we have them, we
+want to start making
+
+combinations out of them.
+
+We want to put pieces
+together.
+
+And for that, we combine
+things in expressions.
+
+And what we saw as expressions
+are formed of
+
+operands and operators.
+
+And the simple things we did
+were the sort of things you'd
+
+expect from numerical things.
+
+Now I want to stress one
+other nuance here.
+
+Which is, and we're going to
+do some examples of this,
+
+initially we just typed in
+expressions into the
+
+interpreter; that is, directly
+into Python.
+
+And as I suggested last time,
+the interpreter is actually a
+
+program inside of the machine
+that is basically following
+
+the rules we're describing here
+to deduce the value and
+
+print it up.
+
+And if we type directly into
+the interpreter, it
+
+essentially does an
+eval and a print.
+
+It evaluates, and it prints.
+
+Most of the time, we're going to
+be doing expressions inside
+
+of some piece of code, inside
+of a script, which is the
+
+Python word for program.
+
+In there, I want to make this
+distinction, this nuance: the
+
+evaluator is still going to be
+taking those expressions and
+
+using its rules to get a value,
+but it's not going to
+
+print them back out.
+
+Why?
+
+Because typically, you're doing
+that to use it somewhere
+
+else in the program.
+
+It's going to be stored
+away in a variable.
+
+It's going to be stuck
+in a data structure.
+
+It's going to be used
+for a side effect.
+
+So, inside of code, or inside of
+a script, there's no print,
+
+unless we make it explicit.
+
+And that's a little bit down in
+the weeds, it's a detail,
+
+but one I want to stress.
+
+You need to, if you want
+something to be printed out
+
+inside your code, you need to
+tell the machine to do that.
+
+OK.
+
+So let's do some simple
+examples.
+
+We've already seen somebody's.
+
+I just want to remind you, if I
+wanted to, for example, type
+
+in an expression like that,
+notice the syntactical form,
+
+it's an expression, a number,
+followed by an operand,
+
+followed by another
+expression.
+
+And of course I get out the
+value I'd like there.
+
+Yes sir.
+
+Oh, you don't like leaning
+that far to the left?
+
+OK, if you're a Republican I'll
+be happy to shift this
+
+over a little bit.
+
+Wow, John, I got a laugh
+for a political
+
+joke, I'm in big trouble.
+
+That better?
+
+Oh damn, all right, I'll have
+to do it even more.
+
+OK, here we go, here we go,
+you see, I'm doing it down
+
+here, I can't see it, does
+that-- ah, I hear his sighs of
+
+relief, OK, good.
+
+There we go.
+
+Better.
+
+All right.
+
+One of the other things we
+showed last time is that
+
+operators are overloaded.
+
+And this is where you heard
+John and I disagree.
+
+I don't happen to like
+this, but he
+
+thinks it's an ok thing.
+
+In a particular-- if we, whoa,
+we don't do that, we do this--
+
+that is, give a combination of
+a number multiplication in a
+
+string, this will in fact give
+us back a new string with that
+
+many replicas, if you
+like, of the string
+
+concatenated together.
+
+All right?
+
+And if you want to do other
+things, for example, we can
+
+take two strings and add--
+whoops, sorry-- and add them
+
+together, we will get
+out, again, a
+
+concatenation of that string.
+
+And these will, we'll let you
+work through the variations,
+
+but these are the simple
+expressions we can use.
+
+Now, sometimes things get
+a little interesting.
+
+All right?
+
+What's the value of
+that expression?
+
+What do you think should happen
+if I evaluate that
+
+expression?
+
+Somebody with a hand up,
+so I can see it.
+
+What's going to happen?
+
+STUDENT: [UNINTELLIGIBLE]
+
+PROFESSOR JIM ERICSON:
+An error?
+
+Why?
+
+STUDENT: [UNINTELLIGIBLE]
+
+PROFESSOR JIM ERICSON: Great.
+
+OK.
+
+That means, let's check it.
+
+It certainly is.
+
+We bribe people.
+
+So I, ah, by the way, John's a
+Yankees fan, he throws like
+
+Johnny Damon, I'm a Red Sox fan,
+so we'll see if I, how
+
+about that?
+
+And I almost hit John along
+the way, great.
+
+My third right, exactly,
+what can I say?
+
+All right, so we're into bribing
+you as we go along
+
+here, and all right?
+
+You'll be badly overweight
+by the end of the term.
+
+Right, it's a syntactic error,
+because it doesn't know how to
+
+deal with this.
+
+But there's an important thing
+going on here, if I in fact
+
+wanted to combine those into a
+string, I should have told the
+
+machine to do that, and I can do
+that, by explicitly saying,
+
+take that, which is a number,
+and convert it into a string,
+
+and then-- bleah, I keep
+doing that-- then
+
+add it to that string.
+
+OK, so there's an important
+point here.
+
+We've got what's called
+type conversion.
+
+That is, if I want to combine
+two things together in a
+
+particular way, I need to make
+sure that I give it the kind
+
+of operand it expects.
+
+So STR, which I just typed up
+there, takes in parens, some
+
+input, and it converts it into
+a string, so that now I can
+
+use that where I was
+expecting a string.
+
+John.
+
+PROFESSOR JOHN GUTTAG: You've
+got a static semantic error in
+
+your syntax.
+
+PROFESSOR JIM ERICSON:
+Thank you.
+
+And I was going to come to that
+in a second, but thank
+
+you, John, for pointing it out.
+
+All right.
+
+Why is it a static
+semantic error?
+
+The syntax is OK in the sense
+of, it is an operand, an
+
+operator, an operand, so
+syntactically it's OK.
+
+The semantics was what caused
+the problem, because the
+
+operator was expecting
+a particular kind
+
+of structure there.
+
+There's a second thing going
+on here that I want to
+
+highlight, because it's
+really important.
+
+Yes indeed.
+
+OK, there we go.
+
+The second thing I want to
+highlight is, that what's
+
+going on, is that Python is
+doing some type checking.
+
+It caught the error, because
+it checked the types of the
+
+operands before it applied
+things, and it says,
+
+I'm going to stop.
+
+Now, you might have said, gee,
+why didn't it just assume that
+
+I wanted to in fact treat these
+as strings, and combine
+
+them together?
+
+Sounds like a reasonable
+thing to do.
+
+But it's a dangerous thing.
+
+Because in doing that, Python
+would then have a value that
+
+it could pass on into some other
+part of a computation,
+
+and if it wasn't what I wanted,
+I might be a long ways
+
+downstream in the computation
+before I actually hit some
+
+result that makes no sense.
+
+And tracing back where it came
+from can be really hard.
+
+So I actually want to have
+type checking as much
+
+as I can early on.
+
+And in fact, under type
+checking, different languages
+
+sometimes fall on a spectrum
+from weak to strong typing.
+
+Which basically says, how much
+type checking do they do?
+
+Now, you're going to hear John
+and I go back and forth a lot,
+
+as I said I'm an old time-- well
+I'm certainly old time,
+
+but I'm also an old time
+Lisp programmer.
+
+I love Lisp, but Lisp is
+certainly in the category of a
+
+very weakly typed language.
+
+It does not check the types
+of its arguments at all.
+
+Python is, I wouldn't say
+completely strong, but it's
+
+much closer to the strong
+end of the spectrum.
+
+It's going to do a lot of type
+checking for you before it
+
+actually passes things back.
+
+Nonetheless, I'm also going to
+argue that it's probably not
+
+as strongly typed as
+we might like.
+
+So, for example, there's
+an expression.
+
+Now, less than is just, if you
+haven't used it before, it's
+
+just the operator you'd expect,
+it's comparing two
+
+things and it's going to return
+either true or false
+
+depending on whether the first
+argument is less than the
+
+second argument.
+
+What's going to happen here?
+
+Again, I need a hand so I can
+know where to throw candy.
+
+I've also got on my
+reading glasses
+
+on, I can't see anything.
+
+Anybody.
+
+TAs don't count, they
+get their own candy.
+
+When it, yep.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR JIM ERICSON:
+Good question.
+
+Sounds like a reasonable
+guess, right?
+
+How in the world am I going to
+compare a string to a number?
+
+So, see how good my aim
+is, ah, not bad.
+
+All right.
+
+A good quest-- sorry, a
+good thought, but in
+
+fact, son of a gun.
+
+Or as my younger son would
+say, fudge knuckle.
+
+Yeah.
+
+All right?
+
+So, what in the world's
+going on here?
+
+This is a place--
+
+I don't know about you, John,
+I think this is actually
+
+really not good, because right,
+what this is doing is,
+
+it's allowing-- sorry, let me
+back up and say it-- it's got
+
+an overload on the less-than
+that allows you to compare
+
+basically the lexicographic
+ordering, or this sequence of
+
+ordering of symbols, including
+numbers inside of the machine.
+
+And this, in my mind, should
+have been an error.
+
+Why in the world would you
+want to compare that?
+
+Just to give you an example of
+that, for instance, I can do
+
+the following: all right, the
+number four is less than the
+
+string three, whereas the string
+four, oops, is not less
+
+than the string three.
+
+And this is a place where it's
+comparing strings and numbers
+
+in a strange way.
+
+So why am I showing you this?
+
+Partly to show you that it's
+kind of weird, but also to
+
+tell you that one of the things
+you want to do is
+
+exercise what I'm going to call
+some type discipline.
+
+Meaning, when you write code,
+you want to get into the habit
+
+of A, checking out operators or
+procedures to see what they
+
+do under different
+circumstances, either check
+
+them out or read the
+specifications of it, and two,
+
+when you write your own code,
+you want to be disciplined
+
+about what types of arguments
+or operands
+
+you apply to operators.
+
+Because this is something that
+could certainly have screwed
+
+you up if you didn't realize
+it did it, and you need to
+
+have that discipline
+to make sure it's
+
+doing the right thing.
+
+OK.
+
+One of the other things you're
+going to see is that some of
+
+the operators have
+odd meanings.
+
+And again, I think we looked--
+
+Yup?
+
+STUDENT: So, the string A is
+less than three, is false
+
+because they're comparing
+like ASCII values?
+
+PROFESSOR JIM ERICSON: Yes.
+
+I mean, I'm sorry.
+
+The answer is, I don't
+know if it's ASCII.
+
+John, do you know, are
+they doing ASCII
+
+encoding inside of here?
+
+I'm assuming so.
+
+Right.
+
+So, in case you didn't
+understand what the the
+
+question was, basically every
+symbol gets translated into a
+
+particular encoding, a string
+of bit, if you like, inside
+
+the machine, there's a
+particular one called ASCII,
+
+which is, if you like, an
+ordering of that, and that's
+
+what the machine's actually
+comparing inside of here,
+
+which is why in under ASCII
+encoding the numbers are going
+
+to appear after the characters,
+and you get the
+
+strange kind of thing going on.
+
+All right.
+
+I want a couple of other things,
+just to quickly remind
+
+you, and one of them is,
+remember, the operators do
+
+look at the types, so division,
+for example nine
+
+divided by five is one, because
+this is integer
+
+division, that is, it's the
+largest number of integer
+
+multiples of five to go into
+nine, and there would be a
+
+remainder associated with it,
+which is in fact four.
+
+And again, you've got
+to be careful about
+
+how you use the operators.
+
+Right, having done that, we
+can certainly get to more
+
+complicated things, so for
+example, suppose I look at
+
+that expression.
+
+Three plus four times five.
+
+All right.
+
+Now.
+
+There are two possible
+values here, I think.
+
+One is 23, the other's 35.
+
+Because this could be three plus
+four, times five, or it
+
+could be three, plus
+four times five.
+
+And of course, you know, when
+you look at code it doesn't
+
+pause in between them.
+
+But what I do?
+
+I just separated, do I do the
+addition first or do the
+
+multiplication first?
+
+Anybody know what happens
+In this case?
+
+Yeah, way up, oh God I'm going
+to have a hell of time
+
+throwing up there, way
+up at the back.
+
+STUDENT: Standard order of
+operations, I guess take the
+
+multiplication first,
+and add the three.
+
+PROFESSOR JIM ERICSON: Right.
+
+I'm going to try, if I don't
+make it, you know, just get
+
+somebody to pass back, whoa!
+
+I just hit somebody
+in the head.
+
+Thank you.
+
+Please pass it back
+to that guy.
+
+If you want candy, sit much
+closer down, and that way we
+
+can film you as well
+as we go along.
+
+Right.
+
+So the point is, there is
+something here called operator
+
+precedence, which is what
+the gentleman said.
+
+I'm not going to say much more
+about it, but basically what
+
+it says is, with all other
+things being equal, things
+
+like exponentiation are done
+before you do multiplication
+
+or division, which are done
+before you do things like
+
+addition and subtraction.
+
+And so, in fact, if I wanted
+the other version of it, in
+
+fact, if I do this right, it's
+going to give me 23 because it
+
+does the multiplication first,
+if I wanted the other version
+
+of it, I need to tell it that,
+by using, excuse me,
+
+parentheses.
+
+And in general, what I
+would say is, when
+
+in doubt, use parens.
+
+OK.
+
+Now, that just gives
+us expressions.
+
+We can start having complex
+expressions, you can imagine
+
+we can have things are lots of
+parens, and all sorts of
+
+things in it.
+
+Yes, question.
+
+STUDENT: What does it mean, the
+operator used, when you
+
+were calculating the remainder
+between nine and five?
+
+PROFESSOR JIM ERICSON: It's
+the percent sign.
+
+If you can't read it, I guess
+I'm going to have to blow that
+
+font up, aren't I,
+next time around.
+
+Yeah, it's a percent, so
+this percent sign will
+
+give you the remainder.
+
+OK.
+
+Second thing I need to do,
+though, is I need to, when I
+
+get those values, I want
+to hang on to them.
+
+I'd like to give them a name,
+so I can refer to them in
+
+other places.
+
+And so we saw that as well, the
+last piece we had here is
+
+the ability to create variables,
+which have their
+
+own values, and that's done
+using an assignment statement.
+
+So in particular, that is
+an assignment statement.
+
+It says, take the name x and
+create a binding for that name
+
+to the value of the
+sub-expression and in fact to
+
+do this, to stress a point,
+let's do that.
+
+It's not just a number,
+it's any expression.
+
+What Python will do, is it will
+evaluate that expression
+
+using the kinds of rules we
+talked about, and then it
+
+creates a binding for
+x to that value.
+
+And I want to stress this, we're
+going to come back to it
+
+later on in the term, so the
+way I'd like you to think
+
+about it for now, is that
+somewhere in the machine,
+
+there's a big space that
+contains all possible values.
+
+Right.
+
+It's a slight lie, it doesn't
+have all possible values, but
+
+you get the idea.
+
+It has, if you like,
+intellectually,
+
+all possible values.
+
+And when I create a binding, I'm
+taking a variable name, in
+
+this case x, stored somewhere in
+a table, and I'm creating a
+
+link or a pointer from that
+name to that value.
+
+This is a nuance.
+
+It's going to make a lot more
+sense later on when we
+
+introduce mutation into our
+language, but I want you to
+
+start thinking of it that way.
+
+Don't think of it as a specific
+box into which we're
+
+putting things; think of it
+as a link to a value.
+
+I could have, for example,
+another assignment statement,
+
+and that creates a binding from
+y into that same value,
+
+and one of the things as a
+conservist I can do is, I
+
+could have a statement like,
+let z be bound to
+
+the value of x.
+
+And I said it deliberately
+that way.
+
+That statement says, get the
+value of x, which is this
+
+link, and give z a pointer
+to the same place.
+
+To the value, not to x.
+
+OK, and we'll just plant that
+idea, we're going to come back
+
+to later on, as we carry on.
+
+OK.
+
+So if we have variables, one
+of the questions we can ask
+
+is, what's the type
+of the variable.
+
+And the answer is, it inherits
+it from its value.
+
+OK.
+
+Yes.
+
+So if somewhere in my code, I
+have that statement, that
+
+assignment statement,
+x now is a variable
+
+whose value is an integer.
+
+Unfortunately, at least in
+my mind, in Python, these
+
+variable bindings are
+dynamic, or the
+
+type, rather, is dynamic.
+
+Meaning, it changes depending on
+what the current value is.
+
+Or said a different way, if
+somewhere later on in the
+
+program I do this, x
+now has changed its
+
+type from INT to string.
+
+Now why should you care?
+
+OK, my view is, I
+don't like it.
+
+Especially in the presence
+of operator overload.
+
+Because I might have written
+some code in which I'm
+
+expecting that particular
+variable to
+
+have an integer value.
+
+If somewhere later on in the
+code it shifts to string, I
+
+might not be manipulating that
+and getting actual values out,
+
+but not what I wanted, and it's
+going to be really hard
+
+for me to chase it back.
+
+So one of the things I would
+like to suggest is that you
+
+develop some good style here,
+and in particular, don't
+
+change types arbitrarily.
+
+I can't spell today.
+
+Meaning, sometimes you need
+to do this, but in general
+
+there's-- at least in my view
+and I don't, John, would you
+
+agree?-- you just don't
+want to do this.
+
+You don't want to make
+those changes.
+
+It just leads to trouble
+down the road.
+
+OK.
+
+Now, last thing about variables,
+and then we're
+
+going to start pushing
+on this, is
+
+where can you use them?
+
+And the answer is, you can use
+a variable anywhere you can
+
+use the value.
+
+So, any place it's legal
+to use the value.
+
+OK.
+
+Now.
+
+This is just sort of bringing us
+back up to speed and adding
+
+a few more details in.
+
+What we really want to
+do now though is
+
+start using this stuff.
+
+So, operands.
+
+Let us take expressions, get
+values out, we can store them
+
+away in places, but ultimately
+we want to do something with
+
+them, so we need to now start
+talking about what are the
+
+things we can do inside of
+Python, or any programming
+
+language, to manipulate them.
+
+And for that, we're going
+to have statements.
+
+Statements are basically, if
+you want to think about it,
+
+legal, and I was about to use
+the word expression except
+
+I've misused that elsewhere, so
+legal commands that Python
+
+can interpret.
+
+You've already seen
+a couple of them.
+
+Print, assignment, certainly
+two obvious statements,
+
+they're commands to
+do something.
+
+Assignment is binding a name
+to a value, print is saying
+
+put it back out in the screen.
+
+Obviously if you have print as
+a way of putting things out,
+
+we expect to have ways of
+getting input in, we're going
+
+to see an example that
+in the second.
+
+And as we go through the next
+few lectures, we're going to
+
+add in more and more of
+these statements.
+
+But let's look at what we
+could do with this, OK?
+
+And to do this, I'm going to
+use some code that I've
+
+already typed in.
+
+So I'm hoping you can
+read that, and it's
+
+also in your handout.
+
+This is a little file I created,
+all right, and I'm
+
+going to start with a sequence
+of these things and walk them
+
+along, again I invite you to put
+comments on that handout
+
+so that you can follow what
+we're going to do.
+
+All right?
+
+So let's look at the
+first part of this.
+
+Right now, this is
+just a text file.
+
+OK.
+
+And I've highlighted in blue up
+there one of the pieces I'm
+
+going to start with.
+
+And what do I have?
+
+I have a sequence of commands;
+I've got an assignment
+
+statement, I've got another
+assignment statement, I've got
+
+a print statement, I've got an
+input statement, which we'll
+
+come back to in a second.
+
+And I want to basically try
+and use these things to do
+
+something with them.
+
+Second thing I want to note is,
+the little hash mark or
+
+the pound sign, that's
+identifying a comment.
+
+So what's a comment?
+
+It's words to you, or to the
+reader of the code, that are
+
+telling you what's going
+on inside of this code.
+
+OK?
+
+Now, these comments, frankly,
+are brain-damaged, or
+
+computationally challenged
+if you prefer.
+
+Meaning, why in the world do I
+have to tell the reader that
+
+I'm binding x to the
+value three?
+
+All right?
+
+I'm putting them in there
+to make a point.
+
+In general, good programming
+style says you put in comments
+
+that are going to be valuable
+in helping you as a reader
+
+understand what's going
+on inside of the code.
+
+It could be, what's the
+intuition behind
+
+this piece of code.
+
+It could be, preconditions
+I want to have on input.
+
+It could be, explanations of
+specific things you're doing.
+
+But you need to have those
+comments there.
+
+Now, this becomes a little bit
+of one of those motherhood and
+
+apple pie kinds of lectures.
+
+You know, your mother always
+told you to eat brussels
+
+sprouts because it
+was good for you.
+
+Well this is a brussels sprouts
+comment. everybody
+
+goes yeah, yeah, yeah,
+comments, of course.
+
+Of course we're going
+to do comments.
+
+And they never do.
+
+So my challenge to you, and I
+know Professor Guttag can do
+
+this, my challenge to you is, a
+year from now, come back and
+
+look at code you wrote here.
+
+Can you still understand what it
+was you were trying to do?
+
+I don't know, John, if
+you'd agree, right?
+
+If you can read the code a
+year later, even code you
+
+wrote yourself, it's a good
+sign that you put good
+
+comments in, right?
+
+Second good piece
+of style here is
+
+choice of variable names.
+
+These are lousy.
+
+Deliberately.
+
+OK?
+
+I'm just using simple things
+like x and y and z because I
+
+want to make it, just
+get through the
+
+lecture if you like.
+
+But in general, the choice of
+variable name is a great way
+
+of commenting your code.
+
+Use variable names
+that make sense.
+
+That little problem set
+zero that you did.
+
+You read in a couple
+of values, you
+
+probably stored them away.
+
+My bet is, you used simple
+names like x and y.
+
+A much better name would have
+been firstname, lastname, as
+
+the name of the variable to tell
+you what you were trying
+
+to capture there.
+
+OK.
+
+The other piece I want to say
+about variable names is, once
+
+I have that choice of variable
+name, I can use it, but in
+
+fact there are a few things that
+I can't use in terms of
+
+variable names.
+
+So, these are an important way
+of documenting, but there're
+
+some things excluded.
+
+And in particular, there are
+some key words that Python is
+
+going to use that have
+to be excluded.
+
+Let me highlight that.
+
+As I said, right now that's
+just text file.
+
+I'm going to save this away--
+yeah, not that way, I'm going
+
+to save this away-- with the
+subscript, or the suffix
+
+rather, py to make
+it a Python file.
+
+Yeah, and I know it's already
+there but I'm going to do it,
+
+and I get some wonderful
+colors.
+
+But these are important, OK?
+
+So notice what I have
+up there now.
+
+Comments appear in red.
+
+I can see those.
+
+There's a keyword, which I'm
+going to highlight right up
+
+here, print, which is in,
+I don't know what
+
+that color is, orange?
+
+There's a function in purple,
+there's a string in green, and
+
+in black I have the assignment
+statements.
+
+That print is a keyword.
+
+It's a command to Python
+to do something.
+
+As a consequence, I can't use
+it as a variable name.
+
+All right, think about
+it for a second.
+
+If I wanted to use print as a
+variable name, how do I get
+
+the system to decide gee, do
+I want print as a value for
+
+something, or do I want
+print as a command?
+
+So there's a sequence of these
+that are blocked out, and I--
+
+John, I think there are
+what, twenty-eight?
+
+Something like that,
+TAs, is that right?
+
+Twenty-eight keywords
+that are blocked?
+
+We'll find them as
+we go along--
+
+OK.
+
+Having done this now, I can
+simply go ahead and run this,
+
+and in fact if I go up here to
+run, you'll see I've got both
+
+an option to check the module,
+though in this case I'm just
+
+going to run it.
+
+Oh, notice what happened.
+
+It ran through that sequence of
+instructions, in particular
+
+it bound x to the value three,
+and then it took x times x,
+
+got the value of x multipied by
+x, which of course is nine,
+
+bound that to the value of x,
+and then it printed out the
+
+value, and now it's sitting
+here waiting for an input.
+
+You notice what it did, it
+printed out that little, right
+
+up here I'd said enter a number
+and that's what it's
+
+printed out, so I can enter a
+number and it prints it out.
+
+Great.
+
+Let's run it again.
+
+Actually for that, I can just
+use, if I'm lucky, function
+
+F5, which didn't work, so let me
+try it again., here we go.
+
+We're going to run that module.
+
+OK.
+
+Whoa.
+
+What happened?
+
+I said enter a number.
+
+I didn't.
+
+I gave it a string.
+
+And it still took it.
+
+And printed it up.
+
+Well, this is one of the places
+where I want to come
+
+back to that highlighting
+of what do things do?
+
+Even though my statement said
+enter a number, in particular,
+
+raw input here simply takes in a
+set of characters and treats
+
+it as a string.
+
+And then prints it back out.
+
+So if in fact I wanted to make
+sure this was a number, I
+
+should have done something like
+either try and convert it
+
+to a number, which of course
+failed here, or put in a check
+
+to say where it is.
+
+So it's a way of reminding you,
+I've got to be careful
+
+about the types of things
+that I put in.
+
+OK.
+
+This is still boring, so let's
+step on the accelerator.
+
+What I have now is the
+following: I can write
+
+expressions, do combinations of
+things to get out values, I
+
+can store them away, I
+can print them up.
+
+But literally all I can do at
+this stage is write what we
+
+would call a straight-line
+program, that is, a program in
+
+which we execute in which we
+execute the sequence of
+
+instructions one by one.
+
+Simply walk down that
+list. That's what we
+
+just did there, right?
+
+We just walked through that
+list. This is boring.
+
+In fact, you can do some nice
+things to prove what is the
+
+class of functions you can
+compute with straight-line
+
+programs, and what you'd see if
+you did that is, it's not
+
+particularly interesting.
+
+OK.
+
+Let's go back and think
+about our recipes.
+
+What we use as our
+motivation here.
+
+Even in real recipes, you
+have things like,
+
+if needed, add sugar.
+
+That's a decision.
+
+That's a conditional.
+
+That's a branch.
+
+That says, if something
+is true, do something.
+
+Otherwise, do something
+different.
+
+So to really add to this, we
+need to have branching
+
+programs. What I mean by that
+is, a branching program is
+
+something that can change the
+order of instructions based on
+
+some test. And that test is
+usually a value of a variable.
+
+OK.
+
+And these get a whole lot
+more interesting.
+
+So let's look at a little
+example, and this is going to,
+
+excuse me, both allow us
+introduce the syntax as well
+
+as what we want to have
+as the flow of
+
+control inside of here.
+
+So let me go back up here, and
+I'm going to comment out that
+
+region, and let's uncomment
+this region.
+
+I want to write a little
+piece of code.
+
+It's going to print out even or
+odd, depending on whether
+
+the value I put in, which is x
+in this case, is even or odd.
+
+Think about that.
+
+That says, if this thing has
+some particular value, I want
+
+to do one thing; otherwise,
+I want to
+
+do something different.
+
+And let's look at the
+syntax of this.
+
+This is the first of the
+conditionals that
+
+we're going to see.
+
+Notice the format.
+
+I'm going to go up there.
+
+The first statement right
+here, that's just an
+
+assignment statement, I'm
+giving some value to x.
+
+We could make it something
+different.
+
+And then, notice the
+structure here.
+
+The next three statements.
+
+First of all, IF is a keyword.
+which makes sense.
+
+It is followed, as you can see
+there, by some expression,
+
+followed by a colon.
+
+And in fact, that colon is
+important, so let me stress
+
+this over here.
+
+The colon is important It's
+defining the beginning of a
+
+block of instructions.
+
+Yes sir.
+
+STUDENT: [UNINTELLIGIBLE]
+
+PROFESSOR JIM ERICSON: Based on
+a test. Usually the value
+
+of a variable.
+
+OK, so let me go back
+to where I am.
+
+I'm looking at that
+piece of code.
+
+What that colon is saying is,
+I'm about to begin a sequence
+
+of instructions that I want
+to treat as a block.
+
+So it identifies a block
+of instructions.
+
+It's, and in particular, the
+colon is the start, and the
+
+carriage return is the end.
+
+Now what in the world
+does that mean?
+
+I'm doing a lot of words here,
+let me try and say this a
+
+little bit better.
+
+That code says the following:
+the IF says, I've got an
+
+expression, I'm going
+to evaluate it.
+
+If that value is true, I want
+to do a set of things.
+
+And that set of things is
+identified by the sequence of
+
+commands that are indented in,
+this one right here, following
+
+the colon but before I get
+back to the same place in
+
+terms of the indentation.
+
+If that test is not true, I want
+to skip this instruction,
+
+and there's a second keyword
+else, followed by a colon, and
+
+that tells me the thing
+I want to do in the
+
+case that it's false.
+
+So in fact if I run this,
+ah, and save it, and
+
+it prints out odd.
+
+So, what happened here?
+
+Well, let's look at the code.
+
+Right? x is initially
+bound to fifteen.
+
+I get to the IF.
+
+The IF says, evaluate that
+next expression.
+
+In that next expression, I'm
+actually taking advantage of
+
+the fact that I'm doing integer
+multiplication and
+
+division here.
+
+Right, that divide is, if x is
+an integer and two is an
+
+integer, what's it
+going to do?
+
+If x was even, x divided by two
+is going to be actually
+
+the half of x, right?
+
+If x is odd, that integer
+division is going to give me
+
+the number of multiples of two,
+that go into x, plus a
+
+remainder, which I'm going
+to throw away.
+
+In either case, I take that
+value and multiply back by
+
+two, if it was even I get back
+the original number, if it was
+
+odd, I'm not going to get back
+the original number, so I can
+
+just check to see if
+they're the same.
+
+OK, so a little nuance
+that I'm using there.
+
+So, the first thing that IF
+does, bleah that IF says is,
+
+evaluate that expression and
+if it's true, do the next
+
+thing, the thing after
+the colon.
+
+In this case it's not true, so
+it's going to skip down and
+
+evaluate the thing printed
+up the odd.
+
+OK.
+
+What-- yes.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR JIM ERICSON:
+Thank you.
+
+I was hoping somebody would
+ask that question.
+
+The question was, if you didn't
+hear, why do I have two
+
+equal signs?
+
+It's like I'm doing
+this, right?
+
+Anybody have a se--%uFFFD
+why don't I just
+
+use an equal sign?
+
+I want to know if something's
+equal to something.
+
+Yeah.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR JIM ERICSON:
+Absolutely.
+
+The equal sign is
+going to bind--
+
+Nice catch.
+
+John, this is so much
+fun, throwing candy.
+
+I've got to say, we've got
+to do this more often--
+
+Right.
+
+Let me, let me get
+to the point.
+
+What does an equal sign do?
+
+It is an assignment.
+
+It says, take this thing on the
+left and use it as a name
+
+to bind to the value
+on the right.
+
+It's not what I want here.
+
+Having already chosen to use
+equal as an assignment, I need
+
+something else to
+do comparison.
+
+And that's why I use
+double equals.
+
+Those two equal signs are
+saying, is this thing equal
+
+to, in value, the thing
+on the other side?
+
+OK.
+
+Now, having done that, again I
+want to stress this idea and
+
+I'm going to write it out one
+more time, that there's a
+
+particular format here.
+
+So we have if, and that is
+followed by, I'm going to use
+
+angle braces here just to
+indicates something goes in
+
+here, some test followed
+by a colon.
+
+That is followed by a block
+of instructions.
+
+And we have an ELSE, followed by
+a colon in some other block
+
+of instructions.
+
+And I want you to get used to
+this, that colon is important,
+
+it identifies the start, and
+then the set of indented
+
+things identify all the things
+at the same level, and when we
+
+reset back to the previous
+level, that's when we go back
+
+to where we were.
+
+OK.
+
+Now, that's a nice simple little
+test, let's look at a
+
+couple of other examples
+to get a sense of
+
+what this will do.
+
+OK, let me comment this out,
+and let's look at this next
+
+little piece of code.
+
+All right.
+
+I'm binding a z to be some
+value, and then I'm
+
+going to run this.
+
+Well, let's just run it
+and see what it does.
+
+Nothing.
+
+OK, so why?
+
+Well, let's look at it.
+
+I'm doing a test there to say,
+if the string x is less than
+
+the value of b, and x does not
+appear before b as strings,
+
+then I was going to do, oh, a
+couple of things, because
+
+they're at the same
+block level.
+
+Given that that wasn't
+true, it did nothing.
+
+Now, wait a minute, you say,
+where's the ELSE clause?
+
+And the answer is,
+I don't need one.
+
+All right, if this is purely a
+test of, if this is true do
+
+this otherwise I don't care, I
+don't need the ELSE clause in
+
+there to identify it.
+
+All right?
+
+Second thing I want to look at
+is, suppose I compare that the
+
+one below it.
+
+Oops, that I don't want to do.
+
+Comment that out, and let's
+uncomment this.
+
+Yeah, I've still got a binding
+for z and I'm giving it the
+
+same test, but notice now I've
+got the two same commands but
+
+they have different
+indentation.
+
+In this case, in fact I do
+get a different behavior.
+
+Why?
+
+Because that block identifies a
+set of things that I'm going
+
+to do if the test is true.
+
+If the test was not true, notice
+that that last command
+
+for print Mon is now back at the
+same level as the IF, so
+
+what this says is the IF does
+the test, having done the
+
+test, it decides I'm not going
+to do anything in the block
+
+below it, I'm going to skip
+down therefore to the next
+
+instruction at the same level
+as the IF, which gets me to
+
+the second print statement.
+
+OK.
+
+So now we're seeing some of
+these variations, let's see
+
+what else can we do here.
+
+So let me just to try something
+a little more
+
+interesting, and then we'll
+get to writing some simple
+
+programs. So I'm going to
+comment those out, and let's
+
+go down to this piece of
+code, and uncomment it.
+
+Ooh yes, that was brilliant.
+
+Let's try this again.
+
+And uncomment that, and
+uncomment it again.
+
+Right, so here's a little piece
+of code that's going to
+
+print out the smallest
+value of three.
+
+And notice what this
+is showing is that
+
+the IFs can be nested.
+
+All right, it's so if I looked
+at it, it's going to say that
+
+IF x is y-- sorry, IF x is less
+than y, THEN check to see
+
+IF x is less than z, and if
+that's true, print out x is
+
+the smallest. And notice the
+structure of it, if it's not
+
+true I'm going to go to that
+next ELSE, and print out that
+
+z is smallest. If the first test
+wasn't true, I'm going to
+
+skip that whole block and just
+go down and print out that y
+
+was smallest. So notice the
+nesting, I can flow my way
+
+through how those tests are
+actually going to take place.
+
+All right, so let's run this
+and see what happens.
+
+Great. y is smallest. OK.
+
+Is that code correct?
+
+Is that a tentative
+hand back there?
+
+Yeah.
+
+STUDENT: Let me compare
+y to [INAUDIBLE]
+
+PROFESSOR JIM ERICSON: Yeah,
+it's not doing all of the
+
+comparisons.
+
+All right, and let's just check
+this out, because I want
+
+to make a point of this, let's
+go back and do the following.
+
+Let's take y, change it to
+thirteen, let's run it, hmm.
+
+So what did I miss here?
+
+Two important points.
+
+First one, when I write a piece
+of code, especially code
+
+that has branches in it, when
+I design test cases for that
+
+piece of code, I should try and
+have a specific test case
+
+for each possible path
+through the code.
+
+And by just doing that, I just
+spotted, there's a bug here.
+
+And the bug was in my thinking,
+I did not look for
+
+all of the tests.
+
+So the way I can fix that, is,
+let me comment that out, and
+
+keep doing that, comment that
+out, let's uncomment this,
+
+notice the structure here.
+
+I now have multiple tests.
+
+So actually, let's just run
+it and then we'll talk
+
+about what it does.
+
+I run this, yeah, I have a
+syntax error, yes indeed,
+
+because I forgot to comment that
+one out, all right, and
+
+cue, we'll try it again.
+
+Ah-ha!
+
+And let's quickly look at
+the structure of this.
+
+This now has, gee, a funny
+thing, it says IF x is less
+
+than y AND x is less than
+z, then do something.
+
+And then it has a strange thing
+called ELIF, which is
+
+simply short for else/if in a
+second test. So the way to
+
+think about this in terms of
+flow is, it starts with that
+
+if and it says, check both
+of those things.
+
+And that fact that both of those
+things is the fact that
+
+we're using Boolean
+combination here.
+
+It is to say, we can take any
+logical expressions, combine
+
+them together with AND, OR,
+or NOT to make a complex
+
+expression, and use the value of
+that expression as my test.
+
+And that's literally what I've
+done there, right, I've got x
+
+less than y, that's a test, it
+returns a Boolean, which by
+
+the way is the other type, at
+least I would include here, it
+
+has only two values, which are
+true and false, and what that
+
+code says, if x is less than y,
+AND, logically, whatever I
+
+put up there, x is less than
+z, then the combination is
+
+true, and therefore I'm
+going to do something.
+
+So AND is if both arguments are
+true it's true, OR is if
+
+either argument it's true it's
+true, NOT is if the argument
+
+is not true it's true, and then
+the last piece, as I said
+
+is, I can now have a sequence
+of things I want to do.
+
+So if this is true do something
+else, otherwise test
+
+and see if this is true, do
+something else, as many as I
+
+like followed by the end.
+
+And ELSE, it says, here's
+what I want to do.
+
+OK.
+
+Now.
+
+Having added this in, I have
+branching instructions.
+
+I have simple branching
+programs. These are still
+
+awfully simple.
+
+OK?
+
+And they're awfully simple
+because, all I can do now, is
+
+decide whether to execute some
+piece of code or another.
+
+Said a different way, in the
+case of the straight-line
+
+programs, how long would it
+take to run a program?
+
+Well, basically, however many
+instructions I have, because
+
+I've got to do each
+one in order.
+
+With simple branching, how long
+is it going to take to
+
+run a piece of code?
+
+Well at most, I'm going to
+execute each instruction once.
+
+All right?
+
+Because the IFs are saying, if
+it's true do this, otherwise
+
+skip on it.
+
+Therefore, for simple branching
+programs, the length
+
+of time, the complexity
+the code, is what
+
+we would call constant.
+
+That is, it's at most the length
+of the actual number of
+
+instructions.
+
+It doesn't depend
+on the input.
+
+Real simple programs.
+
+Let's take another
+simple example.
+
+Suppose I want to compute
+the average age
+
+of all the MIT faculty.
+
+There's about a thousand
+of us.
+
+However I do that, I know that
+should inherently take more
+
+time than it takes to compute
+the average age of all the
+
+EECS faculty.
+
+There's only 125 of us.
+
+And that should take more time
+than what it takes to compute
+
+the average of John's and my
+ages, instructors in 600,
+
+because there's only
+two of us.
+
+All right, those pieces of
+code inherently involved
+
+something that does depend on
+the size of the input, or on
+
+the particular input.
+
+And that is a preface to an
+idea of computational
+
+complexity we're going
+to come back to.
+
+One of the things we want to
+help you do is identify the
+
+different classes of algorithms,
+what their costs
+
+are, and how you can map
+problems into the most
+
+efficient class to do
+the computation.
+
+OK.
+
+Now.
+
+Think for a second about
+computing the average age of
+
+the faculty.
+
+You can already kind of
+see what I want to do.
+
+I, somehow if, I want to walk
+through some sequence of data
+
+structures, gathering up or
+doing the same thing, adding
+
+ages in until I get a total
+age and then divide by the
+
+number faculty.
+
+How do I write a piece
+of code for that?
+
+Well, let's go back
+up to our original
+
+starting point of recipes.
+
+And I'm sure you don't remember,
+but one of the
+
+things I had in my recipe, is
+beat egg whites until stiff.
+
+OK.
+
+That until is an
+important word.
+
+It's actually defining a test.
+Let me rephrase it into
+
+garbled English that'll lead
+more naturally into what I
+
+want to do.
+
+While the egg whites are
+not stiff, beat them.
+
+That is a different
+kind of structure.
+
+It has a test in it, which is
+that while, while something is
+
+true, do something, but I
+want to keep doing it.
+
+And so for that, we need
+to add one last thing.
+
+Which is iteration.
+
+Or loops.
+
+We're going to see variations of
+this, we're going to see a
+
+variation of it called
+recursion, a little later on,
+
+but for now we're just going
+to talk about how do we do
+
+iterations.
+
+And I want to show you an
+example of this, to lead to
+
+both the syntax, and
+to the semantics.
+
+And let me comment that out,
+and let's go to this one.
+
+All right.
+
+What does this piece
+of code say?
+
+Not, what does it do, but
+what does it say.
+
+Well, the first three statements
+are just assignment
+
+statements.
+
+I'm binding x, y, and iters
+left to some values.
+
+And then notice the structure, I
+got a keyword WHILE, there's
+
+that color identifying it, and
+in parentheses I have a test.
+
+I'm expecting the value that
+test to be a Boolean.
+
+Followed by a colon.
+
+The colon's identifying
+a block of code.
+
+And what this is
+saying is, gee.
+
+Check to see if the variable
+iters left has a value
+
+greater than zero.
+
+If it does, then execute
+each of the
+
+instructions in that block.
+
+So I'm going to have an
+assignment of y, I'm going to
+
+have an assignment of iters
+left, I've got a comment that
+
+I had borrowed in order to do
+some debugging, and then what
+
+do I want it to do?
+
+I want it to go back around to
+the test. Once again, say, is
+
+that test true?
+
+If it is true, execute the
+sequence of instructions.
+
+So in fact we can block this
+out and see what it does.
+
+If I make a little chart here,
+I've got x, y, and iters left.
+
+x starts off as I think I set
+it up as, here I can't even
+
+read it, is x is three, y is
+zero, iters left is three.
+
+I can hand-simulate it.
+
+It says, is the value of iters
+left greater than zero?
+
+Yes it is.
+
+So, execute those two
+instructions.
+
+It says, take value of y and
+value of x, add them together,
+
+and create that as the
+new value of y.
+
+All right.
+
+That's the assigned statement.
+
+It says, take iters left,
+subtract one from it, and bind
+
+that as the new value
+of iters left.
+
+Having reached the end of the
+block, go back up and check
+
+the test. Is iters left
+greater than zero?
+
+Yes it is.
+
+So, evaluate the same sequence
+of instructions again. y plus
+
+x is six, that's my new value
+of y, two minus one is one,
+
+that's my new value of iters
+left, go back up.
+
+Is iters left greater
+than zero?
+
+Yes it is.
+
+So once more, thank God I didn't
+take 47 as an example,
+
+x plus y, subtract one from
+iters left, go back up to the
+
+test. Is iters left's value
+greater than zero?
+
+No, it is not.
+
+Therefore, skip the rest of that
+block of code and go to
+
+the next instruction, which
+is, ah, print out y.
+
+In fact, if we test this,
+son of a gun.
+
+Got a simple square
+procedure,.
+
+Right, It's just squaring an
+integer, is what it's doing.
+
+But notice the structure.
+
+Now I have the ability to create
+a loop, that is, to
+
+reuse the same pieces of
+code over and over
+
+again as I go around.
+
+And this adds, now, a lot
+of power to the kinds
+
+of code I can write.
+
+Notice some other things I want
+to highlight on this.
+
+All right?
+
+The first one is, that test
+has to involve-- shouldn't
+
+have to, but almost always is
+going to involve-- the value
+
+of some variable.
+
+What if I don't change the value
+of that variable inside
+
+of the code?
+
+Or, another way of saying it
+is, what if I did this?
+
+Comment it up.
+
+What happens if I
+run this sucker?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR JIM ERICSON: Yeah.
+
+It'll go forever.
+
+Absolutely, right?
+
+It's going to loop into
+an infinite loop--
+
+I think I can hit this close,
+ah, no I can't, boy what a
+
+terrible aim--
+
+All right, what has
+[UNINTELLIGIBLE PHRASE] try
+
+again, the point I'm trying to
+make here-- thank God we're at
+
+the end of this lecture, my
+tongue is falling apart-- the
+
+point I'm trying to make is,
+that test needs to involve
+
+some loop variable
+that is changing.
+
+Otherwise the test is always
+going to be true, we're going
+
+to go off here, but this would
+loop forever if I did that.
+
+All right.
+
+Second question: or maybe a
+better way of saying this, and
+
+the general format you're likely
+to see here is, a test
+
+involving a variable name,
+which must be initialized
+
+outside of the loop, and which
+interior to the loop gets
+
+changed, so that the test
+is going to change.
+
+Here's the second question.
+
+What value of inputs, what
+values of x will this run
+
+correctly for?
+
+Probably should be
+integers, right?
+
+Otherwise, this is going to be
+doing something strange, but
+
+all integers?
+
+All right, suppose I do this.
+
+It's my last example.
+
+Yeah, how about that, right?
+
+We knew this was trying to do
+squaring, so intellectually we
+
+know we can square -4, it
+ought to be 16, but what
+
+happens here?
+
+Double fudge knuckle.
+
+All right?
+
+It's going to run through the
+loop, accumulating the
+
+answers, but because I'm
+subtracting, it's just going
+
+to keep making x more and more
+negative as it goes along,
+
+again it's off into
+an infinite loop.
+
+Which is a way of reminding you
+that I need to think as I
+
+write the code about what are
+my expectations from the
+
+input, and how might
+I enforce them.
+
+In this case, I probably want
+to make sure I use absolute
+
+value of x before
+I carry it on.
+
+Yes ma'am.
+
+STUDENT: [UNINTELLIGIBLE]
+
+PROFESSOR JIM ERICSON: You're
+absolutely right, because I
+
+bind iters left to, um, yeah.
+
+Yes.
+
+Thank you.
+
+Boy, two candy for you.
+
+You caught me making an error.
+
+Yes.
+
+The point is, it's not going to
+work, and she caught both
+
+of them, impressive, it's not
+going to work because iters
+
+left is already negative, it's
+just going to skip the whole
+
+loop, and I'm in trouble, so
+thank you for catching that.
+
+All right.
+
+I was going to do one more
+example, but I've run you up
+
+to the end of the time.
+
+I'll leave the example on the
+handout, it shows you another
+
+version that we'll come
+back to next time.
+
+The key thing to notice is, I
+now have the ability to create
+
+iterations, which extends
+well I can do.
+
+And we'll see you next time.
\ No newline at end of file
diff --git a/Q2uUFNDuRFk.txt b/Q2uUFNDuRFk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..592d8d15d2e7551fbf07ed8c18d8784eca4228b3
--- /dev/null
+++ b/Q2uUFNDuRFk.txt
@@ -0,0 +1,387 @@
+align:start position:0%
+ 
+so it was very I'll say crucial for me
+
+ align:start position:0%
+so it was very I'll say crucial for me
+ 
+
+ align:start position:0%
+so it was very I'll say crucial for me
+to do this interview in both English and
+
+ align:start position:0%
+to do this interview in both English and
+ 
+
+ align:start position:0%
+to do this interview in both English and
+Creole because I see Creole languages
+
+ align:start position:0%
+Creole because I see Creole languages
+ 
+
+ align:start position:0%
+Creole because I see Creole languages
+like even in the case of Haiti
+
+ align:start position:0%
+like even in the case of Haiti
+ 
+
+ align:start position:0%
+like even in the case of Haiti
+especially because of Haiti as a
+
+ align:start position:0%
+especially because of Haiti as a
+ 
+
+ align:start position:0%
+especially because of Haiti as a
+particular revealing and clear test tube
+
+ align:start position:0%
+particular revealing and clear test tube
+ 
+
+ align:start position:0%
+particular revealing and clear test tube
+or key study to really show how language
+
+ align:start position:0%
+or key study to really show how language
+ 
+
+ align:start position:0%
+or key study to really show how language
+can be such a powerful tool either for
+
+ align:start position:0%
+can be such a powerful tool either for
+ 
+
+ align:start position:0%
+can be such a powerful tool either for
+illumination or for resistance either
+
+ align:start position:0%
+illumination or for resistance either
+ 
+
+ align:start position:0%
+illumination or for resistance either
+for oppression or for development so I I
+
+ align:start position:0%
+for oppression or for development so I I
+ 
+
+ align:start position:0%
+for oppression or for development so I I
+would love teachers who are watching
+
+ align:start position:0%
+would love teachers who are watching
+ 
+
+ align:start position:0%
+would love teachers who are watching
+this this video and we look at the
+
+ align:start position:0%
+this this video and we look at the
+ 
+
+ align:start position:0%
+this this video and we look at the
+course to see how they can adapt the
+
+ align:start position:0%
+course to see how they can adapt the
+ 
+
+ align:start position:0%
+course to see how they can adapt the
+content in order to address similar
+
+ align:start position:0%
+content in order to address similar
+ 
+
+ align:start position:0%
+content in order to address similar
+issues in the own community because I
+
+ align:start position:0%
+issues in the own community because I
+ 
+
+ align:start position:0%
+issues in the own community because I
+think that what you see happening in the
+
+ align:start position:0%
+think that what you see happening in the
+ 
+
+ align:start position:0%
+think that what you see happening in the
+Kazakh languages also happens in in the
+
+ align:start position:0%
+Kazakh languages also happens in in the
+ 
+
+ align:start position:0%
+Kazakh languages also happens in in the
+u.s. appengine in in Europe in Latin
+
+ align:start position:0%
+u.s. appengine in in Europe in Latin
+ 
+
+ align:start position:0%
+u.s. appengine in in Europe in Latin
+America in Africa where language is
+
+ align:start position:0%
+America in Africa where language is
+ 
+
+ align:start position:0%
+America in Africa where language is
+often in use of this technology for
+
+ align:start position:0%
+often in use of this technology for
+ 
+
+ align:start position:0%
+often in use of this technology for
+domination or resistance and I think
+
+ align:start position:0%
+domination or resistance and I think
+ 
+
+ align:start position:0%
+domination or resistance and I think
+this course gives the some basic
+
+ align:start position:0%
+this course gives the some basic
+ 
+
+ align:start position:0%
+this course gives the some basic
+analytical tools to be able to analyze
+
+ align:start position:0%
+analytical tools to be able to analyze
+ 
+
+ align:start position:0%
+analytical tools to be able to analyze
+these patterns and and for me it's also
+
+ align:start position:0%
+these patterns and and for me it's also
+ 
+
+ align:start position:0%
+these patterns and and for me it's also
+very important that teachers in Haiti
+
+ align:start position:0%
+very important that teachers in Haiti
+ 
+
+ align:start position:0%
+very important that teachers in Haiti
+and Suez in Haiti including say you know
+
+ align:start position:0%
+and Suez in Haiti including say you know
+ 
+
+ align:start position:0%
+and Suez in Haiti including say you know
+future leaders or policy makers get to
+
+ align:start position:0%
+future leaders or policy makers get to
+ 
+
+ align:start position:0%
+future leaders or policy makers get to
+understand the discourse and the
+
+ align:start position:0%
+understand the discourse and the
+ 
+
+ align:start position:0%
+understand the discourse and the
+readings and to understand that that
+
+ align:start position:0%
+readings and to understand that that
+ 
+
+ align:start position:0%
+readings and to understand that that
+Haiti could do so much better if if
+
+ align:start position:0%
+Haiti could do so much better if if
+ 
+
+ align:start position:0%
+Haiti could do so much better if if
+teachers students leaders had this
+
+ align:start position:0%
+teachers students leaders had this
+ 
+
+ align:start position:0%
+teachers students leaders had this
+awareness of how the old attitudes
+
+ align:start position:0%
+awareness of how the old attitudes
+ 
+
+ align:start position:0%
+awareness of how the old attitudes
+towards Creole versus French have played
+
+ align:start position:0%
+towards Creole versus French have played
+ 
+
+ align:start position:0%
+towards Creole versus French have played
+over centuries in keeping the country in
+
+ align:start position:0%
+over centuries in keeping the country in
+ 
+
+ align:start position:0%
+over centuries in keeping the country in
+the developed and if they could get a
+
+ align:start position:0%
+the developed and if they could get a
+ 
+
+ align:start position:0%
+the developed and if they could get a
+better sense of the importance of
+
+ align:start position:0%
+better sense of the importance of
+ 
+
+ align:start position:0%
+better sense of the importance of
+language in education development then I
+
+ align:start position:0%
+language in education development then I
+ 
+
+ align:start position:0%
+language in education development then I
+think the country would do so much
+
+ align:start position:0%
+think the country would do so much
+ 
+
+ align:start position:0%
+think the country would do so much
+better but for me it's a it's a it's a
+
+ align:start position:0%
+better but for me it's a it's a it's a
+ 
+
+ align:start position:0%
+better but for me it's a it's a it's a
+key bottleneck that we have to go pass
+
+ align:start position:0%
+key bottleneck that we have to go pass
+ 
+
+ align:start position:0%
+key bottleneck that we have to go pass
+in order to really be able to develop a
+
+ align:start position:0%
+in order to really be able to develop a
+ 
+
+ align:start position:0%
+in order to really be able to develop a
+nation is to be is to be able to
+
+ align:start position:0%
+nation is to be is to be able to
+ 
+
+ align:start position:0%
+nation is to be is to be able to
+understand the history and the nature of
+
+ align:start position:0%
+understand the history and the nature of
+ 
+
+ align:start position:0%
+understand the history and the nature of
+your national your ancestral language
+
+ align:start position:0%
+your national your ancestral language
+ 
+
+ align:start position:0%
+your national your ancestral language
+and to be able to use it in the most
+
+ align:start position:0%
+and to be able to use it in the most
+ 
+
+ align:start position:0%
+and to be able to use it in the most
+systematic and water and productive way
+
+ align:start position:0%
+systematic and water and productive way
+ 
+
+ align:start position:0%
+systematic and water and productive way
+if you cannot do that there is no way
+
+ align:start position:0%
+if you cannot do that there is no way
+ 
+
+ align:start position:0%
+if you cannot do that there is no way
+that you can develop a whole nation that
+
+ align:start position:0%
+that you can develop a whole nation that
+ 
+
+ align:start position:0%
+that you can develop a whole nation that
+speaks that language
\ No newline at end of file
diff --git a/QKO_2WQkZ0k.txt b/QKO_2WQkZ0k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b186f80934899942b0f762524ce5cb7472ec9588
--- /dev/null
+++ b/QKO_2WQkZ0k.txt
@@ -0,0 +1,2283 @@
+align:start position:0%
+ 
+pagerank is a measure of the importance
+
+ align:start position:0%
+pagerank is a measure of the importance
+ 
+
+ align:start position:0%
+pagerank is a measure of the importance
+of a web page
+
+ align:start position:0%
+of a web page
+ 
+
+ align:start position:0%
+of a web page
+but let me immediately correct my own
+
+ align:start position:0%
+but let me immediately correct my own
+ 
+
+ align:start position:0%
+but let me immediately correct my own
+confusion that i suffered from for some
+
+ align:start position:0%
+confusion that i suffered from for some
+ 
+
+ align:start position:0%
+confusion that i suffered from for some
+time until very recently which is that
+
+ align:start position:0%
+time until very recently which is that
+ 
+
+ align:start position:0%
+time until very recently which is that
+even though pagerank is used for ranking
+
+ align:start position:0%
+even though pagerank is used for ranking
+ 
+
+ align:start position:0%
+even though pagerank is used for ranking
+pages it's called pagerank after its
+
+ align:start position:0%
+pages it's called pagerank after its
+ 
+
+ align:start position:0%
+pages it's called pagerank after its
+effort after its discoverer developer
+
+ align:start position:0%
+effort after its discoverer developer
+ 
+
+ align:start position:0%
+effort after its discoverer developer
+larry page who is one of the co-founders
+
+ align:start position:0%
+larry page who is one of the co-founders
+ 
+
+ align:start position:0%
+larry page who is one of the co-founders
+along with serge brin of google
+
+ align:start position:0%
+along with serge brin of google
+ 
+
+ align:start position:0%
+along with serge brin of google
+so the motivation is that um when you at
+
+ align:start position:0%
+so the motivation is that um when you at
+ 
+
+ align:start position:0%
+so the motivation is that um when you at
+least before google when you did a
+
+ align:start position:0%
+least before google when you did a
+ 
+
+ align:start position:0%
+least before google when you did a
+standard retrieval on a web page using
+
+ align:start position:0%
+standard retrieval on a web page using
+ 
+
+ align:start position:0%
+standard retrieval on a web page using
+keyword search and similar kinds of
+
+ align:start position:0%
+keyword search and similar kinds of
+ 
+
+ align:start position:0%
+keyword search and similar kinds of
+criteria you'd get back millions of hits
+
+ align:start position:0%
+criteria you'd get back millions of hits
+ 
+
+ align:start position:0%
+criteria you'd get back millions of hits
+um most of which were really
+
+ align:start position:0%
+um most of which were really
+ 
+
+ align:start position:0%
+um most of which were really
+low quality and you weren't interested
+
+ align:start position:0%
+low quality and you weren't interested
+ 
+
+ align:start position:0%
+low quality and you weren't interested
+in and with a few useful pages buried in
+
+ align:start position:0%
+in and with a few useful pages buried in
+ 
+
+ align:start position:0%
+in and with a few useful pages buried in
+the millions and the question was uh all
+
+ align:start position:0%
+the millions and the question was uh all
+ 
+
+ align:start position:0%
+the millions and the question was uh all
+of these documents are indistinguishable
+
+ align:start position:0%
+of these documents are indistinguishable
+ 
+
+ align:start position:0%
+of these documents are indistinguishable
+in terms of keyword search and and
+
+ align:start position:0%
+in terms of keyword search and and
+ 
+
+ align:start position:0%
+in terms of keyword search and and
+textual patterns how do you figure out
+
+ align:start position:0%
+textual patterns how do you figure out
+ 
+
+ align:start position:0%
+textual patterns how do you figure out
+which of the important ones and the idea
+
+ align:start position:0%
+which of the important ones and the idea
+ 
+
+ align:start position:0%
+which of the important ones and the idea
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that page came up with was to use the
+
+ align:start position:0%
+that page came up with was to use the
+ 
+
+ align:start position:0%
+that page came up with was to use the
+web structure itself the structure of
+
+ align:start position:0%
+web structure itself the structure of
+ 
+
+ align:start position:0%
+web structure itself the structure of
+the world wide web to identify the
+
+ align:start position:0%
+the world wide web to identify the
+ 
+
+ align:start position:0%
+the world wide web to identify the
+important documents
+
+ align:start position:0%
+important documents
+ 
+
+ align:start position:0%
+important documents
+so we can think of the
+
+ align:start position:0%
+so we can think of the
+ 
+
+ align:start position:0%
+so we can think of the
+uh the whole internet as a graph
+
+ align:start position:0%
+uh the whole internet as a graph
+ 
+
+ align:start position:0%
+uh the whole internet as a graph
+where a user is
+
+ align:start position:0%
+where a user is
+ 
+
+ align:start position:0%
+where a user is
+on a page and we think of a url as a
+
+ align:start position:0%
+on a page and we think of a url as a
+ 
+
+ align:start position:0%
+on a page and we think of a url as a
+link to another page as a directed edge
+
+ align:start position:0%
+link to another page as a directed edge
+ 
+
+ align:start position:0%
+link to another page as a directed edge
+and users are kind of randomly traveling
+
+ align:start position:0%
+and users are kind of randomly traveling
+ 
+
+ align:start position:0%
+and users are kind of randomly traveling
+around in the world wide web they're at
+
+ align:start position:0%
+around in the world wide web they're at
+ 
+
+ align:start position:0%
+around in the world wide web they're at
+a page they randomly click a link to get
+
+ align:start position:0%
+a page they randomly click a link to get
+ 
+
+ align:start position:0%
+a page they randomly click a link to get
+to another page and they keep doing
+
+ align:start position:0%
+to another page and they keep doing
+ 
+
+ align:start position:0%
+to another page and they keep doing
+doing a walk on the web graph and every
+
+ align:start position:0%
+doing a walk on the web graph and every
+ 
+
+ align:start position:0%
+doing a walk on the web graph and every
+once in a while they're going to find
+
+ align:start position:0%
+once in a while they're going to find
+ 
+
+ align:start position:0%
+once in a while they're going to find
+that the thread that they're on is kind
+
+ align:start position:0%
+that the thread that they're on is kind
+ 
+
+ align:start position:0%
+that the thread that they're on is kind
+of losing steam where they find
+
+ align:start position:0%
+of losing steam where they find
+ 
+
+ align:start position:0%
+of losing steam where they find
+themselves in some kind of a cycle and
+
+ align:start position:0%
+themselves in some kind of a cycle and
+ 
+
+ align:start position:0%
+themselves in some kind of a cycle and
+they will randomly start over again
+
+ align:start position:0%
+they will randomly start over again
+ 
+
+ align:start position:0%
+they will randomly start over again
+at some other page
+
+ align:start position:0%
+at some other page
+ 
+
+ align:start position:0%
+at some other page
+and we want to argue or
+
+ align:start position:0%
+and we want to argue or
+ 
+
+ align:start position:0%
+and we want to argue or
+hypothesize that a page is more
+
+ align:start position:0%
+hypothesize that a page is more
+ 
+
+ align:start position:0%
+hypothesize that a page is more
+important when it's viewed a large
+
+ align:start position:0%
+important when it's viewed a large
+ 
+
+ align:start position:0%
+important when it's viewed a large
+fraction of the time by these random
+
+ align:start position:0%
+fraction of the time by these random
+ 
+
+ align:start position:0%
+fraction of the time by these random
+browsers and random users
+
+ align:start position:0%
+browsers and random users
+ 
+
+ align:start position:0%
+browsers and random users
+so to be formal we're going to take the
+
+ align:start position:0%
+so to be formal we're going to take the
+ 
+
+ align:start position:0%
+so to be formal we're going to take the
+entire world wide web trillions of
+
+ align:start position:0%
+entire world wide web trillions of
+ 
+
+ align:start position:0%
+entire world wide web trillions of
+vertices as a digraph
+
+ align:start position:0%
+vertices as a digraph
+ 
+
+ align:start position:0%
+vertices as a digraph
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's going to be an edge from one url
+
+ align:start position:0%
+there's going to be an edge from one url
+ 
+
+ align:start position:0%
+there's going to be an edge from one url
+to another from v to w if there's a link
+
+ align:start position:0%
+to another from v to w if there's a link
+ 
+
+ align:start position:0%
+to another from v to w if there's a link
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+uh the page v to
+
+ align:start position:0%
+uh the page v to
+ 
+
+ align:start position:0%
+uh the page v to
+uh the page w or the url w w might not
+
+ align:start position:0%
+uh the page w or the url w w might not
+ 
+
+ align:start position:0%
+uh the page w or the url w w might not
+even be a page it might be a document
+
+ align:start position:0%
+even be a page it might be a document
+ 
+
+ align:start position:0%
+even be a page it might be a document
+which means it doesn't have any links on
+
+ align:start position:0%
+which means it doesn't have any links on
+ 
+
+ align:start position:0%
+which means it doesn't have any links on
+it but for the the the real vertices are
+
+ align:start position:0%
+it but for the the the real vertices are
+ 
+
+ align:start position:0%
+it but for the the the real vertices are
+the web pages that have links on them
+
+ align:start position:0%
+the web pages that have links on them
+ 
+
+ align:start position:0%
+the web pages that have links on them
+okay that's the model uh and we're gonna
+
+ align:start position:0%
+okay that's the model uh and we're gonna
+ 
+
+ align:start position:0%
+okay that's the model uh and we're gonna
+make it into a random walk graph by
+
+ align:start position:0%
+make it into a random walk graph by
+ 
+
+ align:start position:0%
+make it into a random walk graph by
+saying that if you look at a
+
+ align:start position:0%
+saying that if you look at a
+ 
+
+ align:start position:0%
+saying that if you look at a
+url v a vertex v all of the edges out of
+
+ align:start position:0%
+url v a vertex v all of the edges out of
+ 
+
+ align:start position:0%
+url v a vertex v all of the edges out of
+it are equally likely it's a simple
+
+ align:start position:0%
+it are equally likely it's a simple
+ 
+
+ align:start position:0%
+it are equally likely it's a simple
+model and it might or might not work but
+
+ align:start position:0%
+model and it might or might not work but
+ 
+
+ align:start position:0%
+model and it might or might not work but
+in fact it did work pretty well that is
+
+ align:start position:0%
+in fact it did work pretty well that is
+ 
+
+ align:start position:0%
+in fact it did work pretty well that is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+model of the world wide web
+
+ align:start position:0%
+model of the world wide web
+ 
+
+ align:start position:0%
+model of the world wide web
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+a random walk graph
+
+ align:start position:0%
+a random walk graph
+ 
+
+ align:start position:0%
+a random walk graph
+so to be more precise the probability of
+
+ align:start position:0%
+so to be more precise the probability of
+ 
+
+ align:start position:0%
+so to be more precise the probability of
+the edge that goes from v to w
+
+ align:start position:0%
+the edge that goes from v to w
+ 
+
+ align:start position:0%
+the edge that goes from v to w
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one over the out degree of v that is all
+
+ align:start position:0%
+one over the out degree of v that is all
+ 
+
+ align:start position:0%
+one over the out degree of v that is all
+of the out degree of v edges leaving
+
+ align:start position:0%
+of the out degree of v edges leaving
+ 
+
+ align:start position:0%
+of the out degree of v edges leaving
+vertex v get equal weight
+
+ align:start position:0%
+vertex v get equal weight
+ 
+
+ align:start position:0%
+vertex v get equal weight
+now to model this aspect that the users
+
+ align:start position:0%
+now to model this aspect that the users
+ 
+
+ align:start position:0%
+now to model this aspect that the users
+start over again if they get bored or
+
+ align:start position:0%
+start over again if they get bored or
+ 
+
+ align:start position:0%
+start over again if they get bored or
+they get stuck
+
+ align:start position:0%
+they get stuck
+ 
+
+ align:start position:0%
+they get stuck
+we can formally add to the digraph a
+
+ align:start position:0%
+we can formally add to the digraph a
+ 
+
+ align:start position:0%
+we can formally add to the digraph a
+hypothetical super node
+
+ align:start position:0%
+hypothetical super node
+ 
+
+ align:start position:0%
+hypothetical super node
+um which and with the property that
+
+ align:start position:0%
+um which and with the property that
+ 
+
+ align:start position:0%
+um which and with the property that
+there's an edge from the super node to
+
+ align:start position:0%
+there's an edge from the super node to
+ 
+
+ align:start position:0%
+there's an edge from the super node to
+every other node with equally likelihood
+
+ align:start position:0%
+every other node with equally likelihood
+ 
+
+ align:start position:0%
+every other node with equally likelihood
+so once you're the super mode then
+
+ align:start position:0%
+so once you're the super mode then
+ 
+
+ align:start position:0%
+so once you're the super mode then
+following an edge is tantamount to
+
+ align:start position:0%
+following an edge is tantamount to
+ 
+
+ align:start position:0%
+following an edge is tantamount to
+saying pick a random page and start over
+
+ align:start position:0%
+saying pick a random page and start over
+ 
+
+ align:start position:0%
+saying pick a random page and start over
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to get to the super node we uh have no
+
+ align:start position:0%
+to get to the super node we uh have no
+ 
+
+ align:start position:0%
+to get to the super node we uh have no
+we have edges back from
+
+ align:start position:0%
+we have edges back from
+ 
+
+ align:start position:0%
+we have edges back from
+other nodes in the graph back to the
+
+ align:start position:0%
+other nodes in the graph back to the
+ 
+
+ align:start position:0%
+other nodes in the graph back to the
+super node now in the reading we said
+
+ align:start position:0%
+super node now in the reading we said
+ 
+
+ align:start position:0%
+super node now in the reading we said
+that uh we were going to have nodes back
+
+ align:start position:0%
+that uh we were going to have nodes back
+ 
+
+ align:start position:0%
+that uh we were going to have nodes back
+from uh from no terminal nodes that had
+
+ align:start position:0%
+from uh from no terminal nodes that had
+ 
+
+ align:start position:0%
+from uh from no terminal nodes that had
+no edges out for example a document or
+
+ align:start position:0%
+no edges out for example a document or
+ 
+
+ align:start position:0%
+no edges out for example a document or
+something like that that's actually not
+
+ align:start position:0%
+something like that that's actually not
+ 
+
+ align:start position:0%
+something like that that's actually not
+sufficient because uh for the
+
+ align:start position:0%
+sufficient because uh for the
+ 
+
+ align:start position:0%
+sufficient because uh for the
+for the pagerank to work in the
+
+ align:start position:0%
+for the pagerank to work in the
+ 
+
+ align:start position:0%
+for the pagerank to work in the
+theoretical way that we want it to
+
+ align:start position:0%
+theoretical way that we want it to
+ 
+
+ align:start position:0%
+theoretical way that we want it to
+because even if there is um no dead
+
+ align:start position:0%
+because even if there is um no dead
+ 
+
+ align:start position:0%
+because even if there is um no dead
+nodes you might be in a clump of nodes
+
+ align:start position:0%
+nodes you might be in a clump of nodes
+ 
+
+ align:start position:0%
+nodes you might be in a clump of nodes
+which you can't get out of and you'd
+
+ align:start position:0%
+which you can't get out of and you'd
+ 
+
+ align:start position:0%
+which you can't get out of and you'd
+want to be able to and even though none
+
+ align:start position:0%
+want to be able to and even though none
+ 
+
+ align:start position:0%
+want to be able to and even though none
+of them was a dead end because they all
+
+ align:start position:0%
+of them was a dead end because they all
+ 
+
+ align:start position:0%
+of them was a dead end because they all
+had arrows going out to each other and
+
+ align:start position:0%
+had arrows going out to each other and
+ 
+
+ align:start position:0%
+had arrows going out to each other and
+so you'd really want a node from an edge
+
+ align:start position:0%
+so you'd really want a node from an edge
+ 
+
+ align:start position:0%
+so you'd really want a node from an edge
+from a clump like that back to the super
+
+ align:start position:0%
+from a clump like that back to the super
+ 
+
+ align:start position:0%
+from a clump like that back to the super
+node to model starting over there
+
+ align:start position:0%
+node to model starting over there
+ 
+
+ align:start position:0%
+node to model starting over there
+the simplest way to do it really is to
+
+ align:start position:0%
+the simplest way to do it really is to
+ 
+
+ align:start position:0%
+the simplest way to do it really is to
+simply say that there's an edge to the
+
+ align:start position:0%
+simply say that there's an edge to the
+ 
+
+ align:start position:0%
+simply say that there's an edge to the
+super node from every vertex so where
+
+ align:start position:0%
+super node from every vertex so where
+ 
+
+ align:start position:0%
+super node from every vertex so where
+wherever you are you can randomly decide
+
+ align:start position:0%
+wherever you are you can randomly decide
+ 
+
+ align:start position:0%
+wherever you are you can randomly decide
+to start over but uh and
+
+ align:start position:0%
+to start over but uh and
+ 
+
+ align:start position:0%
+to start over but uh and
+paige uh and brynn and their co-authors
+
+ align:start position:0%
+paige uh and brynn and their co-authors
+ 
+
+ align:start position:0%
+paige uh and brynn and their co-authors
+in the original paper on page rank uh
+
+ align:start position:0%
+in the original paper on page rank uh
+ 
+
+ align:start position:0%
+in the original paper on page rank uh
+suggested that the edge back from a
+
+ align:start position:0%
+suggested that the edge back from a
+ 
+
+ align:start position:0%
+suggested that the edge back from a
+vertex to the super vertex might get a
+
+ align:start position:0%
+vertex to the super vertex might get a
+ 
+
+ align:start position:0%
+vertex to the super vertex might get a
+special probability it might be
+
+ align:start position:0%
+special probability it might be
+ 
+
+ align:start position:0%
+special probability it might be
+customized as opposed to being
+
+ align:start position:0%
+customized as opposed to being
+ 
+
+ align:start position:0%
+customized as opposed to being
+uh equally likely with all of the other
+
+ align:start position:0%
+uh equally likely with all of the other
+ 
+
+ align:start position:0%
+uh equally likely with all of the other
+uh edges leading a vertex in fact i
+
+ align:start position:0%
+uh edges leading a vertex in fact i
+ 
+
+ align:start position:0%
+uh edges leading a vertex in fact i
+think they decided that it there should
+
+ align:start position:0%
+think they decided that it there should
+ 
+
+ align:start position:0%
+think they decided that it there should
+be a 0.15 probability from each vertex
+
+ align:start position:0%
+be a 0.15 probability from each vertex
+ 
+
+ align:start position:0%
+be a 0.15 probability from each vertex
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+jumping at random to the super node
+
+ align:start position:0%
+jumping at random to the super node
+ 
+
+ align:start position:0%
+jumping at random to the super node
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+let's just illustrate this with an
+
+ align:start position:0%
+let's just illustrate this with an
+ 
+
+ align:start position:0%
+let's just illustrate this with an
+example this is a random walk graph that
+
+ align:start position:0%
+example this is a random walk graph that
+ 
+
+ align:start position:0%
+example this is a random walk graph that
+we've seen before modeling coin flipping
+
+ align:start position:0%
+we've seen before modeling coin flipping
+ 
+
+ align:start position:0%
+we've seen before modeling coin flipping
+and when i add the super node there's
+
+ align:start position:0%
+and when i add the super node there's
+ 
+
+ align:start position:0%
+and when i add the super node there's
+this one new uh
+
+ align:start position:0%
+this one new uh
+ 
+
+ align:start position:0%
+this one new uh
+vertex super and there's an edge from
+
+ align:start position:0%
+vertex super and there's an edge from
+ 
+
+ align:start position:0%
+vertex super and there's an edge from
+the super vertex to every other one of
+
+ align:start position:0%
+the super vertex to every other one of
+ 
+
+ align:start position:0%
+the super vertex to every other one of
+the vertices in the graph and from each
+
+ align:start position:0%
+the vertices in the graph and from each
+ 
+
+ align:start position:0%
+the vertices in the graph and from each
+vertex in the graph there is an edge
+
+ align:start position:0%
+vertex in the graph there is an edge
+ 
+
+ align:start position:0%
+vertex in the graph there is an edge
+going back i've illustrated that with
+
+ align:start position:0%
+going back i've illustrated that with
+ 
+
+ align:start position:0%
+going back i've illustrated that with
+two-way arrows
+
+ align:start position:0%
+two-way arrows
+ 
+
+ align:start position:0%
+two-way arrows
+so this is really
+
+ align:start position:0%
+so this is really
+ 
+
+ align:start position:0%
+so this is really
+an arrow with two arrowheads it
+
+ align:start position:0%
+an arrow with two arrowheads it
+ 
+
+ align:start position:0%
+an arrow with two arrowheads it
+represents an arrow in each direction
+
+ align:start position:0%
+represents an arrow in each direction
+ 
+
+ align:start position:0%
+represents an arrow in each direction
+now in the original paper actually uh
+
+ align:start position:0%
+now in the original paper actually uh
+ 
+
+ align:start position:0%
+now in the original paper actually uh
+paige didn't talk about a super vertex
+
+ align:start position:0%
+paige didn't talk about a super vertex
+ 
+
+ align:start position:0%
+paige didn't talk about a super vertex
+instead he talked about
+
+ align:start position:0%
+instead he talked about
+ 
+
+ align:start position:0%
+instead he talked about
+each vertex randomly jumping to another
+
+ align:start position:0%
+each vertex randomly jumping to another
+ 
+
+ align:start position:0%
+each vertex randomly jumping to another
+vertex but that would just get the whole
+
+ align:start position:0%
+vertex but that would just get the whole
+ 
+
+ align:start position:0%
+vertex but that would just get the whole
+state diagram completely clogged up with
+
+ align:start position:0%
+state diagram completely clogged up with
+ 
+
+ align:start position:0%
+state diagram completely clogged up with
+edges so it's more economical to have
+
+ align:start position:0%
+edges so it's more economical to have
+ 
+
+ align:start position:0%
+edges so it's more economical to have
+everybody jump to the super vertex
+
+ align:start position:0%
+everybody jump to the super vertex
+ 
+
+ align:start position:0%
+everybody jump to the super vertex
+and the super vertex jump back to
+
+ align:start position:0%
+and the super vertex jump back to
+ 
+
+ align:start position:0%
+and the super vertex jump back to
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+saves a significant number of edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+pagerank then is obtained by computing a
+
+ align:start position:0%
+pagerank then is obtained by computing a
+ 
+
+ align:start position:0%
+pagerank then is obtained by computing a
+stationary distribution for the world
+
+ align:start position:0%
+stationary distribution for the world
+ 
+
+ align:start position:0%
+stationary distribution for the world
+wide web
+
+ align:start position:0%
+wide web
+ 
+
+ align:start position:0%
+wide web
+so s bar is a vector of length trillions
+
+ align:start position:0%
+so s bar is a vector of length trillions
+ 
+
+ align:start position:0%
+so s bar is a vector of length trillions
+the chord chord the coordinates are
+
+ align:start position:0%
+the chord chord the coordinates are
+ 
+
+ align:start position:0%
+the chord chord the coordinates are
+indexed by the web pages
+
+ align:start position:0%
+indexed by the web pages
+ 
+
+ align:start position:0%
+indexed by the web pages
+and we want to calculate the stable
+
+ align:start position:0%
+and we want to calculate the stable
+ 
+
+ align:start position:0%
+and we want to calculate the stable
+distribution and then we simply define
+
+ align:start position:0%
+distribution and then we simply define
+ 
+
+ align:start position:0%
+distribution and then we simply define
+the pagerank of a page is its
+
+ align:start position:0%
+the pagerank of a page is its
+ 
+
+ align:start position:0%
+the pagerank of a page is its
+its probability of being there in the
+
+ align:start position:0%
+its probability of being there in the
+ 
+
+ align:start position:0%
+its probability of being there in the
+stationary distribution the v component
+
+ align:start position:0%
+stationary distribution the v component
+ 
+
+ align:start position:0%
+stationary distribution the v component
+of the stable of the stationary
+
+ align:start position:0%
+of the stable of the stationary
+ 
+
+ align:start position:0%
+of the stable of the stationary
+distribution s
+
+ align:start position:0%
+distribution s
+ 
+
+ align:start position:0%
+distribution s
+and of course we'll rank v above s when
+
+ align:start position:0%
+and of course we'll rank v above s when
+ 
+
+ align:start position:0%
+and of course we'll rank v above s when
+the probability of being in v
+
+ align:start position:0%
+the probability of being in v
+ 
+
+ align:start position:0%
+the probability of being in v
+is higher than the probability of being
+
+ align:start position:0%
+is higher than the probability of being
+ 
+
+ align:start position:0%
+is higher than the probability of being
+in w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way um
+
+ align:start position:0%
+by the way um
+ 
+
+ align:start position:0%
+by the way um
+i don't have the latest figures but uh
+
+ align:start position:0%
+i don't have the latest figures but uh
+ 
+
+ align:start position:0%
+i don't have the latest figures but uh
+there were
+
+ align:start position:0%
+there were
+ 
+
+ align:start position:0%
+there were
+uh i guess i've heard people have worked
+
+ align:start position:0%
+uh i guess i've heard people have worked
+ 
+
+ align:start position:0%
+uh i guess i've heard people have worked
+for google say and in some of the
+
+ align:start position:0%
+for google say and in some of the
+ 
+
+ align:start position:0%
+for google say and in some of the
+wikipedia articles that it takes a few
+
+ align:start position:0%
+wikipedia articles that it takes a few
+ 
+
+ align:start position:0%
+wikipedia articles that it takes a few
+weeks for the crawlers to
+
+ align:start position:0%
+weeks for the crawlers to
+ 
+
+ align:start position:0%
+weeks for the crawlers to
+create a new map of the web
+
+ align:start position:0%
+create a new map of the web
+ 
+
+ align:start position:0%
+create a new map of the web
+to create the new graph and then it
+
+ align:start position:0%
+to create the new graph and then it
+ 
+
+ align:start position:0%
+to create the new graph and then it
+takes um
+
+ align:start position:0%
+takes um
+ 
+
+ align:start position:0%
+takes um
+some number of hours i think under days
+
+ align:start position:0%
+some number of hours i think under days
+ 
+
+ align:start position:0%
+some number of hours i think under days
+to calculate the stationary distribution
+
+ align:start position:0%
+to calculate the stationary distribution
+ 
+
+ align:start position:0%
+to calculate the stationary distribution
+on the graph
+
+ align:start position:0%
+on the graph
+ 
+
+ align:start position:0%
+on the graph
+doing a lot of parallel computation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a useful feature about the uh using
+
+ align:start position:0%
+so a useful feature about the uh using
+ 
+
+ align:start position:0%
+so a useful feature about the uh using
+the the stationary distribution is that
+
+ align:start position:0%
+the the stationary distribution is that
+ 
+
+ align:start position:0%
+the the stationary distribution is that
+ways to hack uh the
+
+ align:start position:0%
+ways to hack uh the
+ 
+
+ align:start position:0%
+ways to hack uh the
+links in the world wide web to make a
+
+ align:start position:0%
+links in the world wide web to make a
+ 
+
+ align:start position:0%
+links in the world wide web to make a
+page look important are
+
+ align:start position:0%
+page look important are
+ 
+
+ align:start position:0%
+page look important are
+will not work very well against page
+
+ align:start position:0%
+will not work very well against page
+ 
+
+ align:start position:0%
+will not work very well against page
+rank so for example one way to look more
+
+ align:start position:0%
+rank so for example one way to look more
+ 
+
+ align:start position:0%
+rank so for example one way to look more
+important is to create a lot of nodes
+
+ align:start position:0%
+important is to create a lot of nodes
+ 
+
+ align:start position:0%
+important is to create a lot of nodes
+pointing to yourself fake nodes but
+
+ align:start position:0%
+pointing to yourself fake nodes but
+ 
+
+ align:start position:0%
+pointing to yourself fake nodes but
+that's not going to matter because the
+
+ align:start position:0%
+that's not going to matter because the
+ 
+
+ align:start position:0%
+that's not going to matter because the
+fake notes are not going to have much
+
+ align:start position:0%
+fake notes are not going to have much
+ 
+
+ align:start position:0%
+fake notes are not going to have much
+weight since they're fake and nobody's
+
+ align:start position:0%
+weight since they're fake and nobody's
+ 
+
+ align:start position:0%
+weight since they're fake and nobody's
+pointing to them so even though a large
+
+ align:start position:0%
+pointing to them so even though a large
+ 
+
+ align:start position:0%
+pointing to them so even though a large
+number of fake notes
+
+ align:start position:0%
+number of fake notes
+ 
+
+ align:start position:0%
+number of fake notes
+point to you
+
+ align:start position:0%
+point to you
+ 
+
+ align:start position:0%
+point to you
+their cumulative weight is low and
+
+ align:start position:0%
+their cumulative weight is low and
+ 
+
+ align:start position:0%
+their cumulative weight is low and
+they're not adding a lot to your own
+
+ align:start position:0%
+they're not adding a lot to your own
+ 
+
+ align:start position:0%
+they're not adding a lot to your own
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+likewise you could try taking links to
+
+ align:start position:0%
+likewise you could try taking links to
+ 
+
+ align:start position:0%
+likewise you could try taking links to
+important pages
+
+ align:start position:0%
+important pages
+ 
+
+ align:start position:0%
+important pages
+and try to make yourself look important
+
+ align:start position:0%
+and try to make yourself look important
+ 
+
+ align:start position:0%
+and try to make yourself look important
+that way but pagerank won't make you
+
+ align:start position:0%
+that way but pagerank won't make you
+ 
+
+ align:start position:0%
+that way but pagerank won't make you
+look important at all if none of those
+
+ align:start position:0%
+look important at all if none of those
+ 
+
+ align:start position:0%
+look important at all if none of those
+important nodes are pointing back
+
+ align:start position:0%
+important nodes are pointing back
+ 
+
+ align:start position:0%
+important nodes are pointing back
+so both of these simple-minded ways to
+
+ align:start position:0%
+so both of these simple-minded ways to
+ 
+
+ align:start position:0%
+so both of these simple-minded ways to
+try to look important by manipulating
+
+ align:start position:0%
+try to look important by manipulating
+ 
+
+ align:start position:0%
+try to look important by manipulating
+links won't improve your pagerank
+
+ align:start position:0%
+links won't improve your pagerank
+ 
+
+ align:start position:0%
+links won't improve your pagerank
+the supernode is playing a technical
+
+ align:start position:0%
+the supernode is playing a technical
+ 
+
+ align:start position:0%
+the supernode is playing a technical
+role
+
+ align:start position:0%
+role
+ 
+
+ align:start position:0%
+role
+in making sure that the stationary
+
+ align:start position:0%
+in making sure that the stationary
+ 
+
+ align:start position:0%
+in making sure that the stationary
+uh distribution exists so
+
+ align:start position:0%
+uh distribution exists so
+ 
+
+ align:start position:0%
+uh distribution exists so
+um uh it guarantees that there's a
+
+ align:start position:0%
+um uh it guarantees that there's a
+ 
+
+ align:start position:0%
+um uh it guarantees that there's a
+unique stationary distribution as bar by
+
+ align:start position:0%
+unique stationary distribution as bar by
+ 
+
+ align:start position:0%
+unique stationary distribution as bar by
+the way i sometimes use the word stable
+
+ align:start position:0%
+the way i sometimes use the word stable
+ 
+
+ align:start position:0%
+the way i sometimes use the word stable
+and sometimes stationary they're kind of
+
+ align:start position:0%
+and sometimes stationary they're kind of
+ 
+
+ align:start position:0%
+and sometimes stationary they're kind of
+synonyms um although i think officially
+
+ align:start position:0%
+synonyms um although i think officially
+ 
+
+ align:start position:0%
+synonyms um although i think officially
+we should stick to the word stationary
+
+ align:start position:0%
+we should stick to the word stationary
+ 
+
+ align:start position:0%
+we should stick to the word stationary
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+um when as i've mentioned before when a
+
+ align:start position:0%
+um when as i've mentioned before when a
+ 
+
+ align:start position:0%
+um when as i've mentioned before when a
+a digraph is strongly connected that is
+
+ align:start position:0%
+a digraph is strongly connected that is
+ 
+
+ align:start position:0%
+a digraph is strongly connected that is
+a sufficient condition for there to be a
+
+ align:start position:0%
+a sufficient condition for there to be a
+ 
+
+ align:start position:0%
+a sufficient condition for there to be a
+unique stable distribution that's
+
+ align:start position:0%
+unique stable distribution that's
+ 
+
+ align:start position:0%
+unique stable distribution that's
+actually proved in one of the exercises
+
+ align:start position:0%
+actually proved in one of the exercises
+ 
+
+ align:start position:0%
+actually proved in one of the exercises
+in the text at the end of the chapter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the supernode mechanism also
+
+ align:start position:0%
+the supernode mechanism also
+ 
+
+ align:start position:0%
+the supernode mechanism also
+ensures something even stronger that
+
+ align:start position:0%
+ensures something even stronger that
+ 
+
+ align:start position:0%
+ensures something even stronger that
+every initial distribution pay converges
+
+ align:start position:0%
+every initial distribution pay converges
+ 
+
+ align:start position:0%
+every initial distribution pay converges
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+stationary distribution to that unique
+
+ align:start position:0%
+stationary distribution to that unique
+ 
+
+ align:start position:0%
+stationary distribution to that unique
+stationary distribution state precisely
+
+ align:start position:0%
+stationary distribution state precisely
+ 
+
+ align:start position:0%
+stationary distribution state precisely
+mathematically
+
+ align:start position:0%
+mathematically
+ 
+
+ align:start position:0%
+mathematically
+if you start off at an arbitrary
+
+ align:start position:0%
+if you start off at an arbitrary
+ 
+
+ align:start position:0%
+if you start off at an arbitrary
+distribution of
+
+ align:start position:0%
+distribution of
+ 
+
+ align:start position:0%
+distribution of
+probabilities of being in different
+
+ align:start position:0%
+probabilities of being in different
+ 
+
+ align:start position:0%
+probabilities of being in different
+states p
+
+ align:start position:0%
+states p
+ 
+
+ align:start position:0%
+states p
+and you look at what happens to
+
+ align:start position:0%
+and you look at what happens to
+ 
+
+ align:start position:0%
+and you look at what happens to
+p after t steps remember that you get by
+
+ align:start position:0%
+p after t steps remember that you get by
+ 
+
+ align:start position:0%
+p after t steps remember that you get by
+multiplying the vector p by the matrix
+
+ align:start position:0%
+multiplying the vector p by the matrix
+ 
+
+ align:start position:0%
+multiplying the vector p by the matrix
+m raised to the power t
+
+ align:start position:0%
+m raised to the power t
+ 
+
+ align:start position:0%
+m raised to the power t
+and you take the limit as t approaches
+
+ align:start position:0%
+and you take the limit as t approaches
+ 
+
+ align:start position:0%
+and you take the limit as t approaches
+infinity that is to say
+
+ align:start position:0%
+infinity that is to say
+ 
+
+ align:start position:0%
+infinity that is to say
+what distribution do you approach as you
+
+ align:start position:0%
+what distribution do you approach as you
+ 
+
+ align:start position:0%
+what distribution do you approach as you
+do more and more updates
+
+ align:start position:0%
+do more and more updates
+ 
+
+ align:start position:0%
+do more and more updates
+and it turns out that that limit exists
+
+ align:start position:0%
+and it turns out that that limit exists
+ 
+
+ align:start position:0%
+and it turns out that that limit exists
+and it is that stationary distribution
+
+ align:start position:0%
+and it is that stationary distribution
+ 
+
+ align:start position:0%
+and it is that stationary distribution
+so it doesn't matter where you start
+
+ align:start position:0%
+so it doesn't matter where you start
+ 
+
+ align:start position:0%
+so it doesn't matter where you start
+you're going to wind up stable and as a
+
+ align:start position:0%
+you're going to wind up stable and as a
+ 
+
+ align:start position:0%
+you're going to wind up stable and as a
+matter of fact the convergence is rapid
+
+ align:start position:0%
+matter of fact the convergence is rapid
+ 
+
+ align:start position:0%
+matter of fact the convergence is rapid
+what that means is that you can actually
+
+ align:start position:0%
+what that means is that you can actually
+ 
+
+ align:start position:0%
+what that means is that you can actually
+calculate the stable distribution
+
+ align:start position:0%
+calculate the stable distribution
+ 
+
+ align:start position:0%
+calculate the stable distribution
+reasonably quickly because you don't
+
+ align:start position:0%
+reasonably quickly because you don't
+ 
+
+ align:start position:0%
+reasonably quickly because you don't
+need a very large t in order to arrive
+
+ align:start position:0%
+need a very large t in order to arrive
+ 
+
+ align:start position:0%
+need a very large t in order to arrive
+at a very good approximation to the
+
+ align:start position:0%
+at a very good approximation to the
+ 
+
+ align:start position:0%
+at a very good approximation to the
+stable distribution
+
+ align:start position:0%
+stable distribution
+ 
+
+ align:start position:0%
+stable distribution
+now the actual google
+
+ align:start position:0%
+now the actual google
+ 
+
+ align:start position:0%
+now the actual google
+rank uh and ranking is more complicated
+
+ align:start position:0%
+rank uh and ranking is more complicated
+ 
+
+ align:start position:0%
+rank uh and ranking is more complicated
+than just page rank pagerank was the
+
+ align:start position:0%
+than just page rank pagerank was the
+ 
+
+ align:start position:0%
+than just page rank pagerank was the
+original idea that got a lot of
+
+ align:start position:0%
+original idea that got a lot of
+ 
+
+ align:start position:0%
+original idea that got a lot of
+attention and in fact the latest
+
+ align:start position:0%
+attention and in fact the latest
+ 
+
+ align:start position:0%
+attention and in fact the latest
+information from google is that they
+
+ align:start position:0%
+information from google is that they
+ 
+
+ align:start position:0%
+information from google is that they
+think it gets over attention in the uh
+
+ align:start position:0%
+think it gets over attention in the uh
+ 
+
+ align:start position:0%
+think it gets over attention in the uh
+today in the modern world by too many
+
+ align:start position:0%
+today in the modern world by too many
+ 
+
+ align:start position:0%
+today in the modern world by too many
+commentators and and people trying to uh
+
+ align:start position:0%
+commentators and and people trying to uh
+ 
+
+ align:start position:0%
+commentators and and people trying to uh
+simulate ranking
+
+ align:start position:0%
+simulate ranking
+ 
+
+ align:start position:0%
+simulate ranking
+so the actual rank rules are a closely
+
+ align:start position:0%
+so the actual rank rules are a closely
+ 
+
+ align:start position:0%
+so the actual rank rules are a closely
+held trade secret for google by google
+
+ align:start position:0%
+held trade secret for google by google
+ 
+
+ align:start position:0%
+held trade secret for google by google
+they use text they use location they use
+
+ align:start position:0%
+they use text they use location they use
+ 
+
+ align:start position:0%
+they use text they use location they use
+payments because advertisers can pay to
+
+ align:start position:0%
+payments because advertisers can pay to
+ 
+
+ align:start position:0%
+payments because advertisers can pay to
+have their search results listed more
+
+ align:start position:0%
+have their search results listed more
+ 
+
+ align:start position:0%
+have their search results listed more
+prominently
+
+ align:start position:0%
+prominently
+ 
+
+ align:start position:0%
+prominently
+and lots of other criteria that have
+
+ align:start position:0%
+and lots of other criteria that have
+ 
+
+ align:start position:0%
+and lots of other criteria that have
+evolved over 15 years and they continue
+
+ align:start position:0%
+evolved over 15 years and they continue
+ 
+
+ align:start position:0%
+evolved over 15 years and they continue
+to evolve as people find ways to
+
+ align:start position:0%
+to evolve as people find ways to
+ 
+
+ align:start position:0%
+to evolve as people find ways to
+manipulate the ranking google revises
+
+ align:start position:0%
+manipulate the ranking google revises
+ 
+
+ align:start position:0%
+manipulate the ranking google revises
+its ranking criteria and algorithms but
+
+ align:start position:0%
+its ranking criteria and algorithms but
+ 
+
+ align:start position:0%
+its ranking criteria and algorithms but
+nevertheless pagerank continues to play
+
+ align:start position:0%
+nevertheless pagerank continues to play
+ 
+
+ align:start position:0%
+nevertheless pagerank continues to play
+a significant role in the whole story
\ No newline at end of file
diff --git a/QfYSZlfBV9A.txt b/QfYSZlfBV9A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..704e037837c15a6ccdd38ecd5c11c3d1b4a51d82
--- /dev/null
+++ b/QfYSZlfBV9A.txt
@@ -0,0 +1,15419 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome everyone
+
+ align:start position:0%
+welcome everyone
+ 
+
+ align:start position:0%
+welcome everyone
+um this uh optional informal uh
+
+ align:start position:0%
+um this uh optional informal uh
+ 
+
+ align:start position:0%
+um this uh optional informal uh
+discussion for um 8225
+
+ align:start position:0%
+discussion for um 8225
+ 
+
+ align:start position:0%
+discussion for um 8225
+sgs042 uh as hopefully you all know
+
+ align:start position:0%
+sgs042 uh as hopefully you all know
+ 
+
+ align:start position:0%
+sgs042 uh as hopefully you all know
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+just going to take our time just very
+
+ align:start position:0%
+just going to take our time just very
+ 
+
+ align:start position:0%
+just going to take our time just very
+informally
+
+ align:start position:0%
+informally
+ 
+
+ align:start position:0%
+informally
+um chat about really anything that's on
+
+ align:start position:0%
+um chat about really anything that's on
+ 
+
+ align:start position:0%
+um chat about really anything that's on
+your mind around the most recent
+
+ align:start position:0%
+your mind around the most recent
+ 
+
+ align:start position:0%
+your mind around the most recent
+material but in particular things that
+
+ align:start position:0%
+material but in particular things that
+ 
+
+ align:start position:0%
+material but in particular things that
+might have been
+
+ align:start position:0%
+might have been
+ 
+
+ align:start position:0%
+might have been
+um curious or puzzling or disturbing or
+
+ align:start position:0%
+um curious or puzzling or disturbing or
+ 
+
+ align:start position:0%
+um curious or puzzling or disturbing or
+whatever any of the above
+
+ align:start position:0%
+whatever any of the above
+ 
+
+ align:start position:0%
+whatever any of the above
+um that might have been
+
+ align:start position:0%
+um that might have been
+ 
+
+ align:start position:0%
+um that might have been
+um elicited in your mind upon watching
+
+ align:start position:0%
+um elicited in your mind upon watching
+ 
+
+ align:start position:0%
+um elicited in your mind upon watching
+the documentary film the day after
+
+ align:start position:0%
+the documentary film the day after
+ 
+
+ align:start position:0%
+the documentary film the day after
+Trinity
+
+ align:start position:0%
+Trinity
+ 
+
+ align:start position:0%
+Trinity
+um I actually watched the YouTube
+
+ align:start position:0%
+um I actually watched the YouTube
+ 
+
+ align:start position:0%
+um I actually watched the YouTube
+version with
+
+ align:start position:0%
+version with
+ 
+
+ align:start position:0%
+version with
+so my family over the weekend I didn't
+
+ align:start position:0%
+so my family over the weekend I didn't
+ 
+
+ align:start position:0%
+so my family over the weekend I didn't
+realize how poor the video quality was I
+
+ align:start position:0%
+realize how poor the video quality was I
+ 
+
+ align:start position:0%
+realize how poor the video quality was I
+apologize for that if you're watching on
+
+ align:start position:0%
+apologize for that if you're watching on
+ 
+
+ align:start position:0%
+apologize for that if you're watching on
+a small device maybe you didn't notice
+
+ align:start position:0%
+a small device maybe you didn't notice
+ 
+
+ align:start position:0%
+a small device maybe you didn't notice
+but if you were watching a super big
+
+ align:start position:0%
+but if you were watching a super big
+ 
+
+ align:start position:0%
+but if you were watching a super big
+crazy large TV you would have seen it
+
+ align:start position:0%
+crazy large TV you would have seen it
+ 
+
+ align:start position:0%
+crazy large TV you would have seen it
+was very blotchy visually but anyway
+
+ align:start position:0%
+was very blotchy visually but anyway
+ 
+
+ align:start position:0%
+was very blotchy visually but anyway
+hopefully it was nonetheless clear
+
+ align:start position:0%
+hopefully it was nonetheless clear
+ 
+
+ align:start position:0%
+hopefully it was nonetheless clear
+enough to uh to get the gist
+
+ align:start position:0%
+enough to uh to get the gist
+ 
+
+ align:start position:0%
+enough to uh to get the gist
+um and I have no sort of agenda for
+
+ align:start position:0%
+um and I have no sort of agenda for
+ 
+
+ align:start position:0%
+um and I have no sort of agenda for
+today I'm really just happy to go uh
+
+ align:start position:0%
+today I'm really just happy to go uh
+ 
+
+ align:start position:0%
+today I'm really just happy to go uh
+however whatever questions are on or
+
+ align:start position:0%
+however whatever questions are on or
+ 
+
+ align:start position:0%
+however whatever questions are on or
+comments or thoughts are on people's
+
+ align:start position:0%
+comments or thoughts are on people's
+ 
+
+ align:start position:0%
+comments or thoughts are on people's
+minds so anyone should feel free to jump
+
+ align:start position:0%
+minds so anyone should feel free to jump
+ 
+
+ align:start position:0%
+minds so anyone should feel free to jump
+in I think I expect we'll have a small
+
+ align:start position:0%
+in I think I expect we'll have a small
+ 
+
+ align:start position:0%
+in I think I expect we'll have a small
+enough group again we don't have to
+
+ align:start position:0%
+enough group again we don't have to
+ 
+
+ align:start position:0%
+enough group again we don't have to
+worry about breakout rooms we can just
+
+ align:start position:0%
+worry about breakout rooms we can just
+ 
+
+ align:start position:0%
+worry about breakout rooms we can just
+kind of manage the discussion hopefully
+
+ align:start position:0%
+kind of manage the discussion hopefully
+ 
+
+ align:start position:0%
+kind of manage the discussion hopefully
+pretty uh informally with the group this
+
+ align:start position:0%
+pretty uh informally with the group this
+ 
+
+ align:start position:0%
+pretty uh informally with the group this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+so I'm curious I mean just the floor is
+
+ align:start position:0%
+so I'm curious I mean just the floor is
+ 
+
+ align:start position:0%
+so I'm curious I mean just the floor is
+open were were there things that
+
+ align:start position:0%
+open were were there things that
+ 
+
+ align:start position:0%
+open were were there things that
+um surprised you from the film things
+
+ align:start position:0%
+um surprised you from the film things
+ 
+
+ align:start position:0%
+um surprised you from the film things
+that surprised you the film didn't you
+
+ align:start position:0%
+that surprised you the film didn't you
+ 
+
+ align:start position:0%
+that surprised you the film didn't you
+know Broach or cover and anything
+
+ align:start position:0%
+know Broach or cover and anything
+ 
+
+ align:start position:0%
+know Broach or cover and anything
+anything the whole the whole Topic's
+
+ align:start position:0%
+anything the whole the whole Topic's
+ 
+
+ align:start position:0%
+anything the whole the whole Topic's
+open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really interesting question that's
+
+ align:start position:0%
+really interesting question that's
+ 
+
+ align:start position:0%
+really interesting question that's
+that's a juicy one
+
+ align:start position:0%
+that's a juicy one
+ 
+
+ align:start position:0%
+that's a juicy one
+um and I should also say by the way I as
+
+ align:start position:0%
+um and I should also say by the way I as
+ 
+
+ align:start position:0%
+um and I should also say by the way I as
+you even more than usual I invite the
+
+ align:start position:0%
+you even more than usual I invite the
+ 
+
+ align:start position:0%
+you even more than usual I invite the
+Tas to jump in as well uh please don't
+
+ align:start position:0%
+Tas to jump in as well uh please don't
+ 
+
+ align:start position:0%
+Tas to jump in as well uh please don't
+be shy
+
+ align:start position:0%
+be shy
+ 
+
+ align:start position:0%
+be shy
+um but let me give you my my first crack
+
+ align:start position:0%
+um but let me give you my my first crack
+ 
+
+ align:start position:0%
+um but let me give you my my first crack
+at that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think a lot of people who were
+
+ align:start position:0%
+I think a lot of people who were
+ 
+
+ align:start position:0%
+I think a lot of people who were
+convinced to work on the project and the
+
+ align:start position:0%
+convinced to work on the project and the
+ 
+
+ align:start position:0%
+convinced to work on the project and the
+film gives a little hit to that they
+
+ align:start position:0%
+film gives a little hit to that they
+ 
+
+ align:start position:0%
+film gives a little hit to that they
+really were not given very much in
+
+ align:start position:0%
+really were not given very much in
+ 
+
+ align:start position:0%
+really were not given very much in
+advance to go on right they had to make
+
+ align:start position:0%
+advance to go on right they had to make
+ 
+
+ align:start position:0%
+advance to go on right they had to make
+a fairly snap decision uh in the middle
+
+ align:start position:0%
+a fairly snap decision uh in the middle
+ 
+
+ align:start position:0%
+a fairly snap decision uh in the middle
+of very you know dislocated times
+
+ align:start position:0%
+of very you know dislocated times
+ 
+
+ align:start position:0%
+of very you know dislocated times
+and often because of Secret City they
+
+ align:start position:0%
+and often because of Secret City they
+ 
+
+ align:start position:0%
+and often because of Secret City they
+couldn't be given a kind of full
+
+ align:start position:0%
+couldn't be given a kind of full
+ 
+
+ align:start position:0%
+couldn't be given a kind of full
+briefing ahead of time some of them
+
+ align:start position:0%
+briefing ahead of time some of them
+ 
+
+ align:start position:0%
+briefing ahead of time some of them
+didn't didn't have much idea of what was
+
+ align:start position:0%
+didn't didn't have much idea of what was
+ 
+
+ align:start position:0%
+didn't didn't have much idea of what was
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+and I my sense there's a lot of the
+
+ align:start position:0%
+and I my sense there's a lot of the
+ 
+
+ align:start position:0%
+and I my sense there's a lot of the
+folks who who did volunteer then to join
+
+ align:start position:0%
+folks who who did volunteer then to join
+ 
+
+ align:start position:0%
+folks who who did volunteer then to join
+the project
+
+ align:start position:0%
+the project
+ 
+
+ align:start position:0%
+the project
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+really we're deeply concerned about uh
+
+ align:start position:0%
+really we're deeply concerned about uh
+ 
+
+ align:start position:0%
+really we're deeply concerned about uh
+developments in Europe especially around
+
+ align:start position:0%
+developments in Europe especially around
+ 
+
+ align:start position:0%
+developments in Europe especially around
+uh what looked like the kind of
+
+ align:start position:0%
+uh what looked like the kind of
+ 
+
+ align:start position:0%
+uh what looked like the kind of
+unchecked uh military progress of the
+
+ align:start position:0%
+unchecked uh military progress of the
+ 
+
+ align:start position:0%
+unchecked uh military progress of the
+Nazis
+
+ align:start position:0%
+Nazis
+ 
+
+ align:start position:0%
+Nazis
+um so I think there was uh a sense that
+
+ align:start position:0%
+um so I think there was uh a sense that
+ 
+
+ align:start position:0%
+um so I think there was uh a sense that
+they that that they wanted to find some
+
+ align:start position:0%
+they that that they wanted to find some
+ 
+
+ align:start position:0%
+they that that they wanted to find some
+way to contribute
+
+ align:start position:0%
+way to contribute
+ 
+
+ align:start position:0%
+way to contribute
+to to the defense effort to the war
+
+ align:start position:0%
+to to the defense effort to the war
+ 
+
+ align:start position:0%
+to to the defense effort to the war
+effort
+
+ align:start position:0%
+effort
+ 
+
+ align:start position:0%
+effort
+um now that raises other questions which
+
+ align:start position:0%
+um now that raises other questions which
+ 
+
+ align:start position:0%
+um now that raises other questions which
+which are broached at least briefly in
+
+ align:start position:0%
+which are broached at least briefly in
+ 
+
+ align:start position:0%
+which are broached at least briefly in
+the film if if many people's principal
+
+ align:start position:0%
+the film if if many people's principal
+ 
+
+ align:start position:0%
+the film if if many people's principal
+motivation had to do with
+
+ align:start position:0%
+motivation had to do with
+ 
+
+ align:start position:0%
+motivation had to do with
+um Nazi Germany what happened between
+
+ align:start position:0%
+um Nazi Germany what happened between
+ 
+
+ align:start position:0%
+um Nazi Germany what happened between
+so-called VE Day the the ultimate defeat
+
+ align:start position:0%
+so-called VE Day the the ultimate defeat
+ 
+
+ align:start position:0%
+so-called VE Day the the ultimate defeat
+of the Nazis in April of 1945 uh and the
+
+ align:start position:0%
+of the Nazis in April of 1945 uh and the
+ 
+
+ align:start position:0%
+of the Nazis in April of 1945 uh and the
+and the uh sort of remainder of the
+
+ align:start position:0%
+and the uh sort of remainder of the
+ 
+
+ align:start position:0%
+and the uh sort of remainder of the
+project let alone the use of the weapons
+
+ align:start position:0%
+project let alone the use of the weapons
+ 
+
+ align:start position:0%
+project let alone the use of the weapons
+uh in against Japan so we can we should
+
+ align:start position:0%
+uh in against Japan so we can we should
+ 
+
+ align:start position:0%
+uh in against Japan so we can we should
+come back to that but nonetheless I
+
+ align:start position:0%
+come back to that but nonetheless I
+ 
+
+ align:start position:0%
+come back to that but nonetheless I
+think people felt strongly they wanted
+
+ align:start position:0%
+think people felt strongly they wanted
+ 
+
+ align:start position:0%
+think people felt strongly they wanted
+to do something uh many people did even
+
+ align:start position:0%
+to do something uh many people did even
+ 
+
+ align:start position:0%
+to do something uh many people did even
+very young people
+
+ align:start position:0%
+very young people
+ 
+
+ align:start position:0%
+very young people
+and this was a decision formed without
+
+ align:start position:0%
+and this was a decision formed without
+ 
+
+ align:start position:0%
+and this was a decision formed without
+full information right because often
+
+ align:start position:0%
+full information right because often
+ 
+
+ align:start position:0%
+full information right because often
+that literally couldn't be brief we I we
+
+ align:start position:0%
+that literally couldn't be brief we I we
+ 
+
+ align:start position:0%
+that literally couldn't be brief we I we
+talked last time about these
+
+ align:start position:0%
+talked last time about these
+ 
+
+ align:start position:0%
+talked last time about these
+um the so-called indoctrination course
+
+ align:start position:0%
+um the so-called indoctrination course
+ 
+
+ align:start position:0%
+um the so-called indoctrination course
+that Robert cerber gave once they
+
+ align:start position:0%
+that Robert cerber gave once they
+ 
+
+ align:start position:0%
+that Robert cerber gave once they
+actually arrived at Los Alamos uh for
+
+ align:start position:0%
+actually arrived at Los Alamos uh for
+ 
+
+ align:start position:0%
+actually arrived at Los Alamos uh for
+some of them that was he had to tell
+
+ align:start position:0%
+some of them that was he had to tell
+ 
+
+ align:start position:0%
+some of them that was he had to tell
+them oh we gathered here to build a bomb
+
+ align:start position:0%
+them oh we gathered here to build a bomb
+ 
+
+ align:start position:0%
+them oh we gathered here to build a bomb
+like he first had to say that because it
+
+ align:start position:0%
+like he first had to say that because it
+ 
+
+ align:start position:0%
+like he first had to say that because it
+wasn't might not have been obvious to
+
+ align:start position:0%
+wasn't might not have been obvious to
+ 
+
+ align:start position:0%
+wasn't might not have been obvious to
+everyone yet uh when they gathered I've
+
+ align:start position:0%
+everyone yet uh when they gathered I've
+ 
+
+ align:start position:0%
+everyone yet uh when they gathered I've
+just learned that extraordinary
+
+ align:start position:0%
+just learned that extraordinary
+ 
+
+ align:start position:0%
+just learned that extraordinary
+um there's a larger question though a
+
+ align:start position:0%
+um there's a larger question though a
+ 
+
+ align:start position:0%
+um there's a larger question though a
+larger thing that that a actually a good
+
+ align:start position:0%
+larger thing that that a actually a good
+ 
+
+ align:start position:0%
+larger thing that that a actually a good
+friend of mine historian Michael Gordon
+
+ align:start position:0%
+friend of mine historian Michael Gordon
+ 
+
+ align:start position:0%
+friend of mine historian Michael Gordon
+has written a really interesting short
+
+ align:start position:0%
+has written a really interesting short
+ 
+
+ align:start position:0%
+has written a really interesting short
+book about
+
+ align:start position:0%
+book about
+ 
+
+ align:start position:0%
+book about
+um the book is called five days in
+
+ align:start position:0%
+um the book is called five days in
+ 
+
+ align:start position:0%
+um the book is called five days in
+August which comes to another aspect of
+
+ align:start position:0%
+August which comes to another aspect of
+ 
+
+ align:start position:0%
+August which comes to another aspect of
+your question which is how did many
+
+ align:start position:0%
+your question which is how did many
+ 
+
+ align:start position:0%
+your question which is how did many
+people scientists on the project uh
+
+ align:start position:0%
+people scientists on the project uh
+ 
+
+ align:start position:0%
+people scientists on the project uh
+military officials political leaders uh
+
+ align:start position:0%
+military officials political leaders uh
+ 
+
+ align:start position:0%
+military officials political leaders uh
+any uh journalists other policy makers
+
+ align:start position:0%
+any uh journalists other policy makers
+ 
+
+ align:start position:0%
+any uh journalists other policy makers
+how did Hulk how did many different
+
+ align:start position:0%
+how did Hulk how did many different
+ 
+
+ align:start position:0%
+how did Hulk how did many different
+kinds of people
+
+ align:start position:0%
+kinds of people
+ 
+
+ align:start position:0%
+kinds of people
+come to think about the bomb once they
+
+ align:start position:0%
+come to think about the bomb once they
+ 
+
+ align:start position:0%
+come to think about the bomb once they
+learned about it
+
+ align:start position:0%
+learned about it
+ 
+
+ align:start position:0%
+learned about it
+and Michael's argument in brief let's
+
+ align:start position:0%
+and Michael's argument in brief let's
+ 
+
+ align:start position:0%
+and Michael's argument in brief let's
+see if I do justice to it again that
+
+ align:start position:0%
+see if I do justice to it again that
+ 
+
+ align:start position:0%
+see if I do justice to it again that
+some of the Tas knows but very very well
+
+ align:start position:0%
+some of the Tas knows but very very well
+ 
+
+ align:start position:0%
+some of the Tas knows but very very well
+so they should correct me but my
+
+ align:start position:0%
+so they should correct me but my
+ 
+
+ align:start position:0%
+so they should correct me but my
+recollection of my friend's book
+
+ align:start position:0%
+recollection of my friend's book
+ 
+
+ align:start position:0%
+recollection of my friend's book
+um is is more or less the following
+
+ align:start position:0%
+um is is more or less the following
+ 
+
+ align:start position:0%
+um is is more or less the following
+that the the bomb was treated by many
+
+ align:start position:0%
+that the the bomb was treated by many
+ 
+
+ align:start position:0%
+that the the bomb was treated by many
+many of these folks as not particularly
+
+ align:start position:0%
+many of these folks as not particularly
+ 
+
+ align:start position:0%
+many of these folks as not particularly
+unusual or special prior to its use
+
+ align:start position:0%
+unusual or special prior to its use
+ 
+
+ align:start position:0%
+unusual or special prior to its use
+uh and and my my favorite parts of
+
+ align:start position:0%
+uh and and my my favorite parts of
+ 
+
+ align:start position:0%
+uh and and my my favorite parts of
+Michael's book actually have to do with
+
+ align:start position:0%
+Michael's book actually have to do with
+ 
+
+ align:start position:0%
+Michael's book actually have to do with
+the mechanics of how the how the weapons
+
+ align:start position:0%
+the mechanics of how the how the weapons
+ 
+
+ align:start position:0%
+the mechanics of how the how the weapons
+were literally put together and then
+
+ align:start position:0%
+were literally put together and then
+ 
+
+ align:start position:0%
+were literally put together and then
+kind of armed for use uh in in
+
+ align:start position:0%
+kind of armed for use uh in in
+ 
+
+ align:start position:0%
+kind of armed for use uh in in
+um against Targets in Japan so on the
+
+ align:start position:0%
+um against Targets in Japan so on the
+ 
+
+ align:start position:0%
+um against Targets in Japan so on the
+island of tinian there's some some
+
+ align:start position:0%
+island of tinian there's some some
+ 
+
+ align:start position:0%
+island of tinian there's some some
+footage in the film
+
+ align:start position:0%
+footage in the film
+ 
+
+ align:start position:0%
+footage in the film
+of the kind of staging grounds on tinian
+
+ align:start position:0%
+of the kind of staging grounds on tinian
+ 
+
+ align:start position:0%
+of the kind of staging grounds on tinian
+and my understanding is it's not that
+
+ align:start position:0%
+and my understanding is it's not that
+ 
+
+ align:start position:0%
+and my understanding is it's not that
+President Truman the U.S President
+
+ align:start position:0%
+President Truman the U.S President
+ 
+
+ align:start position:0%
+President Truman the U.S President
+Truman gave direct orders every time to
+
+ align:start position:0%
+Truman gave direct orders every time to
+ 
+
+ align:start position:0%
+Truman gave direct orders every time to
+say drop a bomb now on Hiroshima drop a
+
+ align:start position:0%
+say drop a bomb now on Hiroshima drop a
+ 
+
+ align:start position:0%
+say drop a bomb now on Hiroshima drop a
+bomb now on Nagasaki there was no such
+
+ align:start position:0%
+bomb now on Nagasaki there was no such
+ 
+
+ align:start position:0%
+bomb now on Nagasaki there was no such
+order given not that specific
+
+ align:start position:0%
+order given not that specific
+ 
+
+ align:start position:0%
+order given not that specific
+the decision was made
+
+ align:start position:0%
+the decision was made
+ 
+
+ align:start position:0%
+the decision was made
+to use the weapons when they were
+
+ align:start position:0%
+to use the weapons when they were
+ 
+
+ align:start position:0%
+to use the weapons when they were
+available up to the discretion of the
+
+ align:start position:0%
+available up to the discretion of the
+ 
+
+ align:start position:0%
+available up to the discretion of the
+field commanders just like every other
+
+ align:start position:0%
+field commanders just like every other
+ 
+
+ align:start position:0%
+field commanders just like every other
+kind of weapons every other kind of
+
+ align:start position:0%
+kind of weapons every other kind of
+ 
+
+ align:start position:0%
+kind of weapons every other kind of
+bombing
+
+ align:start position:0%
+bombing
+ 
+
+ align:start position:0%
+bombing
+again as there was some uh footage in
+
+ align:start position:0%
+again as there was some uh footage in
+ 
+
+ align:start position:0%
+again as there was some uh footage in
+the film and others might you might
+
+ align:start position:0%
+the film and others might you might
+ 
+
+ align:start position:0%
+the film and others might you might
+already have known there had been uh
+
+ align:start position:0%
+already have known there had been uh
+ 
+
+ align:start position:0%
+already have known there had been uh
+campaigns of of um what was called
+
+ align:start position:0%
+campaigns of of um what was called
+ 
+
+ align:start position:0%
+campaigns of of um what was called
+incendiary bombing using certain kinds
+
+ align:start position:0%
+incendiary bombing using certain kinds
+ 
+
+ align:start position:0%
+incendiary bombing using certain kinds
+of conventional explosives that were
+
+ align:start position:0%
+of conventional explosives that were
+ 
+
+ align:start position:0%
+of conventional explosives that were
+especially likely to cause ground fires
+
+ align:start position:0%
+especially likely to cause ground fires
+ 
+
+ align:start position:0%
+especially likely to cause ground fires
+um against uh some cities in Europe but
+
+ align:start position:0%
+um against uh some cities in Europe but
+ 
+
+ align:start position:0%
+um against uh some cities in Europe but
+but many cities in Japan by the Ally Air
+
+ align:start position:0%
+but many cities in Japan by the Ally Air
+ 
+
+ align:start position:0%
+but many cities in Japan by the Ally Air
+Forces U.S particular
+
+ align:start position:0%
+Forces U.S particular
+ 
+
+ align:start position:0%
+Forces U.S particular
+uh and those weren't sort of separately
+
+ align:start position:0%
+uh and those weren't sort of separately
+ 
+
+ align:start position:0%
+uh and those weren't sort of separately
+ordered from on high they were field
+
+ align:start position:0%
+ordered from on high they were field
+ 
+
+ align:start position:0%
+ordered from on high they were field
+there was a chain of command in the
+
+ align:start position:0%
+there was a chain of command in the
+ 
+
+ align:start position:0%
+there was a chain of command in the
+field so to speak and up to their expert
+
+ align:start position:0%
+field so to speak and up to their expert
+ 
+
+ align:start position:0%
+field so to speak and up to their expert
+judgment uh where the conditions right
+
+ align:start position:0%
+judgment uh where the conditions right
+ 
+
+ align:start position:0%
+judgment uh where the conditions right
+is there a storm coming should they
+
+ align:start position:0%
+is there a storm coming should they
+ 
+
+ align:start position:0%
+is there a storm coming should they
+launch you know a series of bombing
+
+ align:start position:0%
+launch you know a series of bombing
+ 
+
+ align:start position:0%
+launch you know a series of bombing
+raids or not that was not a presidential
+
+ align:start position:0%
+raids or not that was not a presidential
+ 
+
+ align:start position:0%
+raids or not that was not a presidential
+level decision or even necessarily a
+
+ align:start position:0%
+level decision or even necessarily a
+ 
+
+ align:start position:0%
+level decision or even necessarily a
+general's level position that was kind
+
+ align:start position:0%
+general's level position that was kind
+ 
+
+ align:start position:0%
+general's level position that was kind
+of outsourced to the to the rank ranking
+
+ align:start position:0%
+of outsourced to the to the rank ranking
+ 
+
+ align:start position:0%
+of outsourced to the to the rank ranking
+officers in the field and what
+
+ align:start position:0%
+officers in the field and what
+ 
+
+ align:start position:0%
+officers in the field and what
+astonishes me what Michael found is that
+
+ align:start position:0%
+astonishes me what Michael found is that
+ 
+
+ align:start position:0%
+astonishes me what Michael found is that
+the in the earliest stages the nuclear
+
+ align:start position:0%
+the in the earliest stages the nuclear
+ 
+
+ align:start position:0%
+the in the earliest stages the nuclear
+weapons were treated like that they were
+
+ align:start position:0%
+weapons were treated like that they were
+ 
+
+ align:start position:0%
+weapons were treated like that they were
+they were plugged into an existing
+
+ align:start position:0%
+they were plugged into an existing
+ 
+
+ align:start position:0%
+they were plugged into an existing
+system of local decision making about
+
+ align:start position:0%
+system of local decision making about
+ 
+
+ align:start position:0%
+system of local decision making about
+when to use them under what
+
+ align:start position:0%
+when to use them under what
+ 
+
+ align:start position:0%
+when to use them under what
+circumstances and that Michael suggests
+
+ align:start position:0%
+circumstances and that Michael suggests
+ 
+
+ align:start position:0%
+circumstances and that Michael suggests
+shows that they were not treated as a
+
+ align:start position:0%
+shows that they were not treated as a
+ 
+
+ align:start position:0%
+shows that they were not treated as a
+sort of separate category early on they
+
+ align:start position:0%
+sort of separate category early on they
+ 
+
+ align:start position:0%
+sort of separate category early on they
+were treated like another weapon there
+
+ align:start position:0%
+were treated like another weapon there
+ 
+
+ align:start position:0%
+were treated like another weapon there
+have been many other kinds of weapons
+
+ align:start position:0%
+have been many other kinds of weapons
+ 
+
+ align:start position:0%
+have been many other kinds of weapons
+developed and deployed sort of from
+
+ align:start position:0%
+developed and deployed sort of from
+ 
+
+ align:start position:0%
+developed and deployed sort of from
+scratch in the course of the war and
+
+ align:start position:0%
+scratch in the course of the war and
+ 
+
+ align:start position:0%
+scratch in the course of the war and
+that these were kind of treated at least
+
+ align:start position:0%
+that these were kind of treated at least
+ 
+
+ align:start position:0%
+that these were kind of treated at least
+logistically or or
+
+ align:start position:0%
+logistically or or
+ 
+
+ align:start position:0%
+logistically or or
+um kind of bureaucratically
+
+ align:start position:0%
+um kind of bureaucratically
+ 
+
+ align:start position:0%
+um kind of bureaucratically
+like you know like yet another weapon to
+
+ align:start position:0%
+like you know like yet another weapon to
+ 
+
+ align:start position:0%
+like you know like yet another weapon to
+be deployed
+
+ align:start position:0%
+be deployed
+ 
+
+ align:start position:0%
+be deployed
+uh largely at the kind of discretion of
+
+ align:start position:0%
+uh largely at the kind of discretion of
+ 
+
+ align:start position:0%
+uh largely at the kind of discretion of
+the of the local
+
+ align:start position:0%
+the of the local
+ 
+
+ align:start position:0%
+the of the local
+um kind of field Commanders
+
+ align:start position:0%
+um kind of field Commanders
+ 
+
+ align:start position:0%
+um kind of field Commanders
+um and that
+
+ align:start position:0%
+um and that
+ 
+
+ align:start position:0%
+um and that
+the standing so they said there was a
+
+ align:start position:0%
+the standing so they said there was a
+ 
+
+ align:start position:0%
+the standing so they said there was a
+standing order at all it was use them
+
+ align:start position:0%
+standing order at all it was use them
+ 
+
+ align:start position:0%
+standing order at all it was use them
+when you got them it wasn't like drop
+
+ align:start position:0%
+when you got them it wasn't like drop
+ 
+
+ align:start position:0%
+when you got them it wasn't like drop
+one wait three days there was no such
+
+ align:start position:0%
+one wait three days there was no such
+ 
+
+ align:start position:0%
+one wait three days there was no such
+there was no such coordination of that
+
+ align:start position:0%
+there was no such coordination of that
+ 
+
+ align:start position:0%
+there was no such coordination of that
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+and in fact there was no third bomb
+
+ align:start position:0%
+and in fact there was no third bomb
+ 
+
+ align:start position:0%
+and in fact there was no third bomb
+ready the two were dropped the bomb
+
+ align:start position:0%
+ready the two were dropped the bomb
+ 
+
+ align:start position:0%
+ready the two were dropped the bomb
+dropped against Nagasaki was and they
+
+ align:start position:0%
+dropped against Nagasaki was and they
+ 
+
+ align:start position:0%
+dropped against Nagasaki was and they
+get a little bit of this in the film was
+
+ align:start position:0%
+get a little bit of this in the film was
+ 
+
+ align:start position:0%
+get a little bit of this in the film was
+uh the schedule was pushed up by the
+
+ align:start position:0%
+uh the schedule was pushed up by the
+ 
+
+ align:start position:0%
+uh the schedule was pushed up by the
+local field commanders because there was
+
+ align:start position:0%
+local field commanders because there was
+ 
+
+ align:start position:0%
+local field commanders because there was
+a worried about severe weather a kind of
+
+ align:start position:0%
+a worried about severe weather a kind of
+ 
+
+ align:start position:0%
+a worried about severe weather a kind of
+typhoon coming it would have threatened
+
+ align:start position:0%
+typhoon coming it would have threatened
+ 
+
+ align:start position:0%
+typhoon coming it would have threatened
+certain kinds of um uh you know aircraft
+
+ align:start position:0%
+certain kinds of um uh you know aircraft
+ 
+
+ align:start position:0%
+certain kinds of um uh you know aircraft
+runs
+
+ align:start position:0%
+runs
+ 
+
+ align:start position:0%
+runs
+so uh so and in fact nagasaka wasn't
+
+ align:start position:0%
+so uh so and in fact nagasaka wasn't
+ 
+
+ align:start position:0%
+so uh so and in fact nagasaka wasn't
+even the original Target City there was
+
+ align:start position:0%
+even the original Target City there was
+ 
+
+ align:start position:0%
+even the original Target City there was
+a decision made by the by the pilot in
+
+ align:start position:0%
+a decision made by the by the pilot in
+ 
+
+ align:start position:0%
+a decision made by the by the pilot in
+mid-flight to change path I think
+
+ align:start position:0%
+mid-flight to change path I think
+ 
+
+ align:start position:0%
+mid-flight to change path I think
+largely because of things like changing
+
+ align:start position:0%
+largely because of things like changing
+ 
+
+ align:start position:0%
+largely because of things like changing
+conditions in the weather and so on so
+
+ align:start position:0%
+conditions in the weather and so on so
+ 
+
+ align:start position:0%
+conditions in the weather and so on so
+these were not highly staged or high
+
+ align:start position:0%
+these were not highly staged or high
+ 
+
+ align:start position:0%
+these were not highly staged or high
+these are not highly
+
+ align:start position:0%
+these are not highly
+ 
+
+ align:start position:0%
+these are not highly
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+kind of carefully thought out and vetted
+
+ align:start position:0%
+kind of carefully thought out and vetted
+ 
+
+ align:start position:0%
+kind of carefully thought out and vetted
+individual decisions the decision was
+
+ align:start position:0%
+individual decisions the decision was
+ 
+
+ align:start position:0%
+individual decisions the decision was
+load them into the planes and drop them
+
+ align:start position:0%
+load them into the planes and drop them
+ 
+
+ align:start position:0%
+load them into the planes and drop them
+when you got him and they had two the
+
+ align:start position:0%
+when you got him and they had two the
+ 
+
+ align:start position:0%
+when you got him and they had two the
+the makings for a third not yet compiled
+
+ align:start position:0%
+the makings for a third not yet compiled
+ 
+
+ align:start position:0%
+the makings for a third not yet compiled
+weapon were literally on a boat making
+
+ align:start position:0%
+weapon were literally on a boat making
+ 
+
+ align:start position:0%
+weapon were literally on a boat making
+their way to tinian at the time that uh
+
+ align:start position:0%
+their way to tinian at the time that uh
+ 
+
+ align:start position:0%
+their way to tinian at the time that uh
+that Japan surrendered so they do is
+
+ align:start position:0%
+that Japan surrendered so they do is
+ 
+
+ align:start position:0%
+that Japan surrendered so they do is
+drop us drop them and one after the
+
+ align:start position:0%
+drop us drop them and one after the
+ 
+
+ align:start position:0%
+drop us drop them and one after the
+other much like the incendiary bombing
+
+ align:start position:0%
+other much like the incendiary bombing
+ 
+
+ align:start position:0%
+other much like the incendiary bombing
+rates have been you know kind of uh one
+
+ align:start position:0%
+rates have been you know kind of uh one
+ 
+
+ align:start position:0%
+rates have been you know kind of uh one
+after the other
+
+ align:start position:0%
+after the other
+ 
+
+ align:start position:0%
+after the other
+um and what what Michael and others have
+
+ align:start position:0%
+um and what what Michael and others have
+ 
+
+ align:start position:0%
+um and what what Michael and others have
+argued what made it seem what made the
+
+ align:start position:0%
+argued what made it seem what made the
+ 
+
+ align:start position:0%
+argued what made it seem what made the
+atomic weapon seem special was the fact
+
+ align:start position:0%
+atomic weapon seem special was the fact
+ 
+
+ align:start position:0%
+atomic weapon seem special was the fact
+that the fighting stopped which was not
+
+ align:start position:0%
+that the fighting stopped which was not
+ 
+
+ align:start position:0%
+that the fighting stopped which was not
+necessarily predicted uh no one thought
+
+ align:start position:0%
+necessarily predicted uh no one thought
+ 
+
+ align:start position:0%
+necessarily predicted uh no one thought
+you'd drop one and they'll stop or at
+
+ align:start position:0%
+you'd drop one and they'll stop or at
+ 
+
+ align:start position:0%
+you'd drop one and they'll stop or at
+least no one seems to have thought that
+
+ align:start position:0%
+least no one seems to have thought that
+ 
+
+ align:start position:0%
+least no one seems to have thought that
+no one thought if we time the other one
+
+ align:start position:0%
+no one thought if we time the other one
+ 
+
+ align:start position:0%
+no one thought if we time the other one
+very carefully that'll convince them
+
+ align:start position:0%
+very carefully that'll convince them
+ 
+
+ align:start position:0%
+very carefully that'll convince them
+there was no such calculation for the
+
+ align:start position:0%
+there was no such calculation for the
+ 
+
+ align:start position:0%
+there was no such calculation for the
+timing of of the second bomb that was
+
+ align:start position:0%
+timing of of the second bomb that was
+ 
+
+ align:start position:0%
+timing of of the second bomb that was
+used in this case against Nagasaki and
+
+ align:start position:0%
+used in this case against Nagasaki and
+ 
+
+ align:start position:0%
+used in this case against Nagasaki and
+they were prepared they were preparing
+
+ align:start position:0%
+they were prepared they were preparing
+ 
+
+ align:start position:0%
+they were prepared they were preparing
+to drop a third one and they would have
+
+ align:start position:0%
+to drop a third one and they would have
+ 
+
+ align:start position:0%
+to drop a third one and they would have
+dropped a fourth if they had one they
+
+ align:start position:0%
+dropped a fourth if they had one they
+ 
+
+ align:start position:0%
+dropped a fourth if they had one they
+just didn't literally didn't have the
+
+ align:start position:0%
+just didn't literally didn't have the
+ 
+
+ align:start position:0%
+just didn't literally didn't have the
+parts
+
+ align:start position:0%
+parts
+ 
+
+ align:start position:0%
+parts
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so Michael argues it was actually uh in
+
+ align:start position:0%
+so Michael argues it was actually uh in
+ 
+
+ align:start position:0%
+so Michael argues it was actually uh in
+response to the fact that unlike other
+
+ align:start position:0%
+response to the fact that unlike other
+ 
+
+ align:start position:0%
+response to the fact that unlike other
+military campaigns there was at least a
+
+ align:start position:0%
+military campaigns there was at least a
+ 
+
+ align:start position:0%
+military campaigns there was at least a
+coincidence in time this time around
+
+ align:start position:0%
+coincidence in time this time around
+ 
+
+ align:start position:0%
+coincidence in time this time around
+that Japan did surrender within days of
+
+ align:start position:0%
+that Japan did surrender within days of
+ 
+
+ align:start position:0%
+that Japan did surrender within days of
+the second bombing that then in kind of
+
+ align:start position:0%
+the second bombing that then in kind of
+ 
+
+ align:start position:0%
+the second bombing that then in kind of
+a post-hoc rationalization according to
+
+ align:start position:0%
+a post-hoc rationalization according to
+ 
+
+ align:start position:0%
+a post-hoc rationalization according to
+Michael kind of made people think that
+
+ align:start position:0%
+Michael kind of made people think that
+ 
+
+ align:start position:0%
+Michael kind of made people think that
+the atomic weapons were now somehow in
+
+ align:start position:0%
+the atomic weapons were now somehow in
+ 
+
+ align:start position:0%
+the atomic weapons were now somehow in
+the category of their own or different
+
+ align:start position:0%
+the category of their own or different
+ 
+
+ align:start position:0%
+the category of their own or different
+or special it was a long answer it's a
+
+ align:start position:0%
+or special it was a long answer it's a
+ 
+
+ align:start position:0%
+or special it was a long answer it's a
+very complicated question
+
+ align:start position:0%
+very complicated question
+ 
+
+ align:start position:0%
+very complicated question
+um I think a bunch of the scientists who
+
+ align:start position:0%
+um I think a bunch of the scientists who
+ 
+
+ align:start position:0%
+um I think a bunch of the scientists who
+work for example on Los Alamos scientist
+
+ align:start position:0%
+work for example on Los Alamos scientist
+ 
+
+ align:start position:0%
+work for example on Los Alamos scientist
+Engineers I think they thought this was
+
+ align:start position:0%
+Engineers I think they thought this was
+ 
+
+ align:start position:0%
+Engineers I think they thought this was
+different early on and some of their
+
+ align:start position:0%
+different early on and some of their
+ 
+
+ align:start position:0%
+different early on and some of their
+concerns we hear about less so in the
+
+ align:start position:0%
+concerns we hear about less so in the
+ 
+
+ align:start position:0%
+concerns we hear about less so in the
+film but other reminiscences and
+
+ align:start position:0%
+film but other reminiscences and
+ 
+
+ align:start position:0%
+film but other reminiscences and
+interviews and so on Memoir has been
+
+ align:start position:0%
+interviews and so on Memoir has been
+ 
+
+ align:start position:0%
+interviews and so on Memoir has been
+published is that they were often quite
+
+ align:start position:0%
+published is that they were often quite
+ 
+
+ align:start position:0%
+published is that they were often quite
+concerned that some of the
+
+ align:start position:0%
+concerned that some of the
+ 
+
+ align:start position:0%
+concerned that some of the
+uh army figures the military figures who
+
+ align:start position:0%
+uh army figures the military figures who
+ 
+
+ align:start position:0%
+uh army figures the military figures who
+also witnessed for example the Trinity
+
+ align:start position:0%
+also witnessed for example the Trinity
+ 
+
+ align:start position:0%
+also witnessed for example the Trinity
+test were not as shocked as the
+
+ align:start position:0%
+test were not as shocked as the
+ 
+
+ align:start position:0%
+test were not as shocked as the
+scientists were
+
+ align:start position:0%
+scientists were
+ 
+
+ align:start position:0%
+scientists were
+I think I mentioned very very briefly in
+
+ align:start position:0%
+I think I mentioned very very briefly in
+ 
+
+ align:start position:0%
+I think I mentioned very very briefly in
+my previous lecture
+
+ align:start position:0%
+my previous lecture
+ 
+
+ align:start position:0%
+my previous lecture
+that for the Trinity test in um
+
+ align:start position:0%
+that for the Trinity test in um
+ 
+
+ align:start position:0%
+that for the Trinity test in um
+Alamogordo New Mexico one of the things
+
+ align:start position:0%
+Alamogordo New Mexico one of the things
+ 
+
+ align:start position:0%
+Alamogordo New Mexico one of the things
+that really really seems to have left a
+
+ align:start position:0%
+that really really seems to have left a
+ 
+
+ align:start position:0%
+that really really seems to have left a
+visceral reaction to many of the folks
+
+ align:start position:0%
+visceral reaction to many of the folks
+ 
+
+ align:start position:0%
+visceral reaction to many of the folks
+who then were able to inspect the the
+
+ align:start position:0%
+who then were able to inspect the the
+ 
+
+ align:start position:0%
+who then were able to inspect the the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+soon called be called Ground Zero was
+
+ align:start position:0%
+soon called be called Ground Zero was
+ 
+
+ align:start position:0%
+soon called be called Ground Zero was
+that the the Heat and especially
+
+ align:start position:0%
+that the the Heat and especially
+ 
+
+ align:start position:0%
+that the the Heat and especially
+pressure of the blast had fused desert
+
+ align:start position:0%
+pressure of the blast had fused desert
+ 
+
+ align:start position:0%
+pressure of the blast had fused desert
+sand in the glass and that at least is
+
+ align:start position:0%
+sand in the glass and that at least is
+ 
+
+ align:start position:0%
+sand in the glass and that at least is
+some of these scientists later recalled
+
+ align:start position:0%
+some of these scientists later recalled
+ 
+
+ align:start position:0%
+some of these scientists later recalled
+that gave them a kind of visceral sense
+
+ align:start position:0%
+that gave them a kind of visceral sense
+ 
+
+ align:start position:0%
+that gave them a kind of visceral sense
+of the forces at play and then they were
+
+ align:start position:0%
+of the forces at play and then they were
+ 
+
+ align:start position:0%
+of the forces at play and then they were
+some of them report being equally
+
+ align:start position:0%
+some of them report being equally
+ 
+
+ align:start position:0%
+some of them report being equally
+viscerally upset that the generals
+
+ align:start position:0%
+viscerally upset that the generals
+ 
+
+ align:start position:0%
+viscerally upset that the generals
+weren't impressed by that so so some of
+
+ align:start position:0%
+weren't impressed by that so so some of
+ 
+
+ align:start position:0%
+weren't impressed by that so so some of
+the scientists seem to think we are
+
+ align:start position:0%
+the scientists seem to think we are
+ 
+
+ align:start position:0%
+the scientists seem to think we are
+playing with the forces that power the
+
+ align:start position:0%
+playing with the forces that power the
+ 
+
+ align:start position:0%
+playing with the forces that power the
+sun where we're dealing with
+
+ align:start position:0%
+sun where we're dealing with
+ 
+
+ align:start position:0%
+sun where we're dealing with
+extraordinarily powerful physical
+
+ align:start position:0%
+extraordinarily powerful physical
+ 
+
+ align:start position:0%
+extraordinarily powerful physical
+phenomena and so at least in their later
+
+ align:start position:0%
+phenomena and so at least in their later
+ 
+
+ align:start position:0%
+phenomena and so at least in their later
+Recollections they seem to have treated
+
+ align:start position:0%
+Recollections they seem to have treated
+ 
+
+ align:start position:0%
+Recollections they seem to have treated
+this as different not just another TNT
+
+ align:start position:0%
+this as different not just another TNT
+ 
+
+ align:start position:0%
+this as different not just another TNT
+bomb souped up and therefore they were
+
+ align:start position:0%
+bomb souped up and therefore they were
+ 
+
+ align:start position:0%
+bomb souped up and therefore they were
+concerned that others didn't treat it
+
+ align:start position:0%
+concerned that others didn't treat it
+ 
+
+ align:start position:0%
+concerned that others didn't treat it
+with a similar kind of differentness
+
+ align:start position:0%
+with a similar kind of differentness
+ 
+
+ align:start position:0%
+with a similar kind of differentness
+but I'm pretty convinced by Michael's
+
+ align:start position:0%
+but I'm pretty convinced by Michael's
+ 
+
+ align:start position:0%
+but I'm pretty convinced by Michael's
+argument more broadly if you look at the
+
+ align:start position:0%
+argument more broadly if you look at the
+ 
+
+ align:start position:0%
+argument more broadly if you look at the
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+political high-level political apparatus
+
+ align:start position:0%
+political high-level political apparatus
+ 
+
+ align:start position:0%
+political high-level political apparatus
+and the military planning and war
+
+ align:start position:0%
+and the military planning and war
+ 
+
+ align:start position:0%
+and the military planning and war
+department apparatus this was treated at
+
+ align:start position:0%
+department apparatus this was treated at
+ 
+
+ align:start position:0%
+department apparatus this was treated at
+least bureaucratically in terms of like
+
+ align:start position:0%
+least bureaucratically in terms of like
+ 
+
+ align:start position:0%
+least bureaucratically in terms of like
+standing orders as such much more like
+
+ align:start position:0%
+standing orders as such much more like
+ 
+
+ align:start position:0%
+standing orders as such much more like
+the next thing in the Arsenal to drop as
+
+ align:start position:0%
+the next thing in the Arsenal to drop as
+ 
+
+ align:start position:0%
+the next thing in the Arsenal to drop as
+opposed to some total separate category
+
+ align:start position:0%
+opposed to some total separate category
+ 
+
+ align:start position:0%
+opposed to some total separate category
+in itself
+
+ align:start position:0%
+in itself
+ 
+
+ align:start position:0%
+in itself
+if anyone else has any thoughts on that
+
+ align:start position:0%
+if anyone else has any thoughts on that
+ 
+
+ align:start position:0%
+if anyone else has any thoughts on that
+but that's my not very brief take on on
+
+ align:start position:0%
+but that's my not very brief take on on
+ 
+
+ align:start position:0%
+but that's my not very brief take on on
+that very juicy question it's a good
+
+ align:start position:0%
+that very juicy question it's a good
+ 
+
+ align:start position:0%
+that very juicy question it's a good
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's thank you Stephen that's
+
+ align:start position:0%
+right that's thank you Stephen that's
+ 
+
+ align:start position:0%
+right that's thank you Stephen that's
+also a really hard question it's a good
+
+ align:start position:0%
+also a really hard question it's a good
+ 
+
+ align:start position:0%
+also a really hard question it's a good
+important question a hard one
+
+ align:start position:0%
+important question a hard one
+ 
+
+ align:start position:0%
+important question a hard one
+um so and we I talked a little bit about
+
+ align:start position:0%
+um so and we I talked a little bit about
+ 
+
+ align:start position:0%
+um so and we I talked a little bit about
+this in a previous class session but
+
+ align:start position:0%
+this in a previous class session but
+ 
+
+ align:start position:0%
+this in a previous class session but
+it's um but it's worth revisiting
+
+ align:start position:0%
+it's um but it's worth revisiting
+ 
+
+ align:start position:0%
+it's um but it's worth revisiting
+so the short answer is many of these
+
+ align:start position:0%
+so the short answer is many of these
+ 
+
+ align:start position:0%
+so the short answer is many of these
+folks were aware as I say the scientists
+
+ align:start position:0%
+folks were aware as I say the scientists
+ 
+
+ align:start position:0%
+folks were aware as I say the scientists
+engineers let's say we're definitely
+
+ align:start position:0%
+engineers let's say we're definitely
+ 
+
+ align:start position:0%
+engineers let's say we're definitely
+aware that there was going to be
+
+ align:start position:0%
+aware that there was going to be
+ 
+
+ align:start position:0%
+aware that there was going to be
+Associated radiation and Fallout and
+
+ align:start position:0%
+Associated radiation and Fallout and
+ 
+
+ align:start position:0%
+Associated radiation and Fallout and
+that would not be good for people right
+
+ align:start position:0%
+that would not be good for people right
+ 
+
+ align:start position:0%
+that would not be good for people right
+they knew there was an inherent clear
+
+ align:start position:0%
+they knew there was an inherent clear
+ 
+
+ align:start position:0%
+they knew there was an inherent clear
+danger there was not like
+
+ align:start position:0%
+danger there was not like
+ 
+
+ align:start position:0%
+danger there was not like
+um you know TNT or other conventional
+
+ align:start position:0%
+um you know TNT or other conventional
+ 
+
+ align:start position:0%
+um you know TNT or other conventional
+explosives that really did strike many
+
+ align:start position:0%
+explosives that really did strike many
+ 
+
+ align:start position:0%
+explosives that really did strike many
+of them as being importantly different
+
+ align:start position:0%
+of them as being importantly different
+ 
+
+ align:start position:0%
+of them as being importantly different
+they did not have anything like the
+
+ align:start position:0%
+they did not have anything like the
+ 
+
+ align:start position:0%
+they did not have anything like the
+sophisticated
+
+ align:start position:0%
+sophisticated
+ 
+
+ align:start position:0%
+sophisticated
+large-scale statistically powerful you
+
+ align:start position:0%
+large-scale statistically powerful you
+ 
+
+ align:start position:0%
+large-scale statistically powerful you
+know controlled medical experimentation
+
+ align:start position:0%
+know controlled medical experimentation
+ 
+
+ align:start position:0%
+know controlled medical experimentation
+type results
+
+ align:start position:0%
+type results
+ 
+
+ align:start position:0%
+type results
+or body of knowledge that would develop
+
+ align:start position:0%
+or body of knowledge that would develop
+ 
+
+ align:start position:0%
+or body of knowledge that would develop
+um later so they didn't have I mean it
+
+ align:start position:0%
+um later so they didn't have I mean it
+ 
+
+ align:start position:0%
+um later so they didn't have I mean it
+would be on we shouldn't expect them to
+
+ align:start position:0%
+would be on we shouldn't expect them to
+ 
+
+ align:start position:0%
+would be on we shouldn't expect them to
+have the same knowledge about them
+
+ align:start position:0%
+have the same knowledge about them
+ 
+
+ align:start position:0%
+have the same knowledge about them
+human biological implications of Fallout
+
+ align:start position:0%
+human biological implications of Fallout
+ 
+
+ align:start position:0%
+human biological implications of Fallout
+as we as the community would later
+
+ align:start position:0%
+as we as the community would later
+ 
+
+ align:start position:0%
+as we as the community would later
+acquire largely from the use of these
+
+ align:start position:0%
+acquire largely from the use of these
+ 
+
+ align:start position:0%
+acquire largely from the use of these
+weapons and from other kinds of tests so
+
+ align:start position:0%
+weapons and from other kinds of tests so
+ 
+
+ align:start position:0%
+weapons and from other kinds of tests so
+they didn't know what would later be
+
+ align:start position:0%
+they didn't know what would later be
+ 
+
+ align:start position:0%
+they didn't know what would later be
+known they knew something
+
+ align:start position:0%
+known they knew something
+ 
+
+ align:start position:0%
+known they knew something
+they do enough to to treat it very
+
+ align:start position:0%
+they do enough to to treat it very
+ 
+
+ align:start position:0%
+they do enough to to treat it very
+relatively carefully
+
+ align:start position:0%
+relatively carefully
+ 
+
+ align:start position:0%
+relatively carefully
+it is yeah they're aware to it that
+
+ align:start position:0%
+it is yeah they're aware to it that
+ 
+
+ align:start position:0%
+it is yeah they're aware to it that
+that's at least a likely possibility on
+
+ align:start position:0%
+that's at least a likely possibility on
+ 
+
+ align:start position:0%
+that's at least a likely possibility on
+the other hand they were pretty Cavalier
+
+ align:start position:0%
+the other hand they were pretty Cavalier
+ 
+
+ align:start position:0%
+the other hand they were pretty Cavalier
+even with their own personal safety so
+
+ align:start position:0%
+even with their own personal safety so
+ 
+
+ align:start position:0%
+even with their own personal safety so
+for example uh one of my well I think I
+
+ align:start position:0%
+for example uh one of my well I think I
+ 
+
+ align:start position:0%
+for example uh one of my well I think I
+mentioned briefly one of my college
+
+ align:start position:0%
+mentioned briefly one of my college
+ 
+
+ align:start position:0%
+mentioned briefly one of my college
+professors who had just retired before I
+
+ align:start position:0%
+professors who had just retired before I
+ 
+
+ align:start position:0%
+professors who had just retired before I
+started college 10 000 years ago
+
+ align:start position:0%
+started college 10 000 years ago
+ 
+
+ align:start position:0%
+started college 10 000 years ago
+approximately uh he had served as a very
+
+ align:start position:0%
+approximately uh he had served as a very
+ 
+
+ align:start position:0%
+approximately uh he had served as a very
+young kid on the Manhattan Project I
+
+ align:start position:0%
+young kid on the Manhattan Project I
+ 
+
+ align:start position:0%
+young kid on the Manhattan Project I
+mean he was like a kid he was basically
+
+ align:start position:0%
+mean he was like a kid he was basically
+ 
+
+ align:start position:0%
+mean he was like a kid he was basically
+a very like a first-year grad student so
+
+ align:start position:0%
+a very like a first-year grad student so
+ 
+
+ align:start position:0%
+a very like a first-year grad student so
+even rtas are more advanced than this
+
+ align:start position:0%
+even rtas are more advanced than this
+ 
+
+ align:start position:0%
+even rtas are more advanced than this
+kid was when he joined the project uh
+
+ align:start position:0%
+kid was when he joined the project uh
+ 
+
+ align:start position:0%
+kid was when he joined the project uh
+and he would say you know they would
+
+ align:start position:0%
+and he would say you know they would
+ 
+
+ align:start position:0%
+and he would say you know they would
+carry little radioactive sources in
+
+ align:start position:0%
+carry little radioactive sources in
+ 
+
+ align:start position:0%
+carry little radioactive sources in
+there like in their like jacket or vest
+
+ align:start position:0%
+there like in their like jacket or vest
+ 
+
+ align:start position:0%
+there like in their like jacket or vest
+Pockets to to calibrate the local you
+
+ align:start position:0%
+Pockets to to calibrate the local you
+ 
+
+ align:start position:0%
+Pockets to to calibrate the local you
+know Machinery so they would put you
+
+ align:start position:0%
+know Machinery so they would put you
+ 
+
+ align:start position:0%
+know Machinery so they would put you
+know Alpha meters next to their gut I
+
+ align:start position:0%
+know Alpha meters next to their gut I
+ 
+
+ align:start position:0%
+know Alpha meters next to their gut I
+don't recommend you do that today like
+
+ align:start position:0%
+don't recommend you do that today like
+ 
+
+ align:start position:0%
+don't recommend you do that today like
+that so so there was a kind of
+
+ align:start position:0%
+that so so there was a kind of
+ 
+
+ align:start position:0%
+that so so there was a kind of
+cavalierness about radioactivity in
+
+ align:start position:0%
+cavalierness about radioactivity in
+ 
+
+ align:start position:0%
+cavalierness about radioactivity in
+general for a lot of these folks partly
+
+ align:start position:0%
+general for a lot of these folks partly
+ 
+
+ align:start position:0%
+general for a lot of these folks partly
+oh there's a war on you don't have time
+
+ align:start position:0%
+oh there's a war on you don't have time
+ 
+
+ align:start position:0%
+oh there's a war on you don't have time
+to be all special and careful but they
+
+ align:start position:0%
+to be all special and careful but they
+ 
+
+ align:start position:0%
+to be all special and careful but they
+didn't know what would later be better
+
+ align:start position:0%
+didn't know what would later be better
+ 
+
+ align:start position:0%
+didn't know what would later be better
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+and then partly for people who are
+
+ align:start position:0%
+and then partly for people who are
+ 
+
+ align:start position:0%
+and then partly for people who are
+working on the project
+
+ align:start position:0%
+working on the project
+ 
+
+ align:start position:0%
+working on the project
+who weren't themselves scientists or
+
+ align:start position:0%
+who weren't themselves scientists or
+ 
+
+ align:start position:0%
+who weren't themselves scientists or
+Engineers there was a really I think um
+
+ align:start position:0%
+Engineers there was a really I think um
+ 
+
+ align:start position:0%
+Engineers there was a really I think um
+very significant lack of effort to
+
+ align:start position:0%
+very significant lack of effort to
+ 
+
+ align:start position:0%
+very significant lack of effort to
+better inform those people about
+
+ align:start position:0%
+better inform those people about
+ 
+
+ align:start position:0%
+better inform those people about
+appropriate safety procedures that based
+
+ align:start position:0%
+appropriate safety procedures that based
+ 
+
+ align:start position:0%
+appropriate safety procedures that based
+on the knowledge that even was in hand
+
+ align:start position:0%
+on the knowledge that even was in hand
+ 
+
+ align:start position:0%
+on the knowledge that even was in hand
+at the time see what I mean and that's
+
+ align:start position:0%
+at the time see what I mean and that's
+ 
+
+ align:start position:0%
+at the time see what I mean and that's
+even before we get to and that's just
+
+ align:start position:0%
+even before we get to and that's just
+ 
+
+ align:start position:0%
+even before we get to and that's just
+for kind of
+
+ align:start position:0%
+for kind of
+ 
+
+ align:start position:0%
+for kind of
+radioactive emitters generally then we
+
+ align:start position:0%
+radioactive emitters generally then we
+ 
+
+ align:start position:0%
+radioactive emitters generally then we
+come to the question of Fallout
+
+ align:start position:0%
+come to the question of Fallout
+ 
+
+ align:start position:0%
+come to the question of Fallout
+specifically from what from the use of
+
+ align:start position:0%
+specifically from what from the use of
+ 
+
+ align:start position:0%
+specifically from what from the use of
+these weapons in a large human
+
+ align:start position:0%
+these weapons in a large human
+ 
+
+ align:start position:0%
+these weapons in a large human
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+and that again they knew enough that it
+
+ align:start position:0%
+and that again they knew enough that it
+ 
+
+ align:start position:0%
+and that again they knew enough that it
+was going to lead to they knew enough to
+
+ align:start position:0%
+was going to lead to they knew enough to
+ 
+
+ align:start position:0%
+was going to lead to they knew enough to
+start studying long-term effects they
+
+ align:start position:0%
+start studying long-term effects they
+ 
+
+ align:start position:0%
+start studying long-term effects they
+figured this would not be good for
+
+ align:start position:0%
+figured this would not be good for
+ 
+
+ align:start position:0%
+figured this would not be good for
+people they didn't have detailed
+
+ align:start position:0%
+people they didn't have detailed
+ 
+
+ align:start position:0%
+people they didn't have detailed
+information about the which cancers at
+
+ align:start position:0%
+information about the which cancers at
+ 
+
+ align:start position:0%
+information about the which cancers at
+what rates what kinds of you know
+
+ align:start position:0%
+what rates what kinds of you know
+ 
+
+ align:start position:0%
+what rates what kinds of you know
+demographics young children affected
+
+ align:start position:0%
+demographics young children affected
+ 
+
+ align:start position:0%
+demographics young children affected
+differently in older people a role of
+
+ align:start position:0%
+differently in older people a role of
+ 
+
+ align:start position:0%
+differently in older people a role of
+pre-existing conditions the kinds of
+
+ align:start position:0%
+pre-existing conditions the kinds of
+ 
+
+ align:start position:0%
+pre-existing conditions the kinds of
+things that kind of biostatisticians
+
+ align:start position:0%
+things that kind of biostatisticians
+ 
+
+ align:start position:0%
+things that kind of biostatisticians
+would would come to study much more
+
+ align:start position:0%
+would would come to study much more
+ 
+
+ align:start position:0%
+would would come to study much more
+carefully later
+
+ align:start position:0%
+carefully later
+ 
+
+ align:start position:0%
+carefully later
+so again that was a pretty long answer
+
+ align:start position:0%
+so again that was a pretty long answer
+ 
+
+ align:start position:0%
+so again that was a pretty long answer
+but they they they were not entirely
+
+ align:start position:0%
+but they they they were not entirely
+ 
+
+ align:start position:0%
+but they they they were not entirely
+ignorant of the dangers of radioactivity
+
+ align:start position:0%
+ignorant of the dangers of radioactivity
+ 
+
+ align:start position:0%
+ignorant of the dangers of radioactivity
+in general or some of the some of the
+
+ align:start position:0%
+in general or some of the some of the
+ 
+
+ align:start position:0%
+in general or some of the some of the
+likely
+
+ align:start position:0%
+likely
+ 
+
+ align:start position:0%
+likely
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh implications of of radioactive
+
+ align:start position:0%
+uh implications of of radioactive
+ 
+
+ align:start position:0%
+uh implications of of radioactive
+fallout from the use of these things in
+
+ align:start position:0%
+fallout from the use of these things in
+ 
+
+ align:start position:0%
+fallout from the use of these things in
+a city and they just you know they
+
+ align:start position:0%
+a city and they just you know they
+ 
+
+ align:start position:0%
+a city and they just you know they
+didn't know what what other people would
+
+ align:start position:0%
+didn't know what what other people would
+ 
+
+ align:start position:0%
+didn't know what what other people would
+learn in more detail later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a great one I'll just add again
+
+ align:start position:0%
+that's a great one I'll just add again
+ 
+
+ align:start position:0%
+that's a great one I'll just add again
+quickly thank you Tiffany on that point
+
+ align:start position:0%
+quickly thank you Tiffany on that point
+ 
+
+ align:start position:0%
+quickly thank you Tiffany on that point
+too uh coming back maybe just Stephen's
+
+ align:start position:0%
+too uh coming back maybe just Stephen's
+ 
+
+ align:start position:0%
+too uh coming back maybe just Stephen's
+question more directly
+
+ align:start position:0%
+question more directly
+ 
+
+ align:start position:0%
+question more directly
+uh then I didn't mean one directly for
+
+ align:start position:0%
+uh then I didn't mean one directly for
+ 
+
+ align:start position:0%
+uh then I didn't mean one directly for
+me than I did before there was a
+
+ align:start position:0%
+me than I did before there was a
+ 
+
+ align:start position:0%
+me than I did before there was a
+long-term study of people who were who
+
+ align:start position:0%
+long-term study of people who were who
+ 
+
+ align:start position:0%
+long-term study of people who were who
+were um in Hiroshima and Nagasaki at the
+
+ align:start position:0%
+were um in Hiroshima and Nagasaki at the
+ 
+
+ align:start position:0%
+were um in Hiroshima and Nagasaki at the
+time these web the bombs went off
+
+ align:start position:0%
+time these web the bombs went off
+ 
+
+ align:start position:0%
+time these web the bombs went off
+long-term longitudinal study uh largely
+
+ align:start position:0%
+long-term longitudinal study uh largely
+ 
+
+ align:start position:0%
+long-term longitudinal study uh largely
+under U.S auspices so Japan as you may
+
+ align:start position:0%
+under U.S auspices so Japan as you may
+ 
+
+ align:start position:0%
+under U.S auspices so Japan as you may
+know was occupied by the Allied Forces
+
+ align:start position:0%
+know was occupied by the Allied Forces
+ 
+
+ align:start position:0%
+know was occupied by the Allied Forces
+most of the U.S but the sort of allies
+
+ align:start position:0%
+most of the U.S but the sort of allies
+ 
+
+ align:start position:0%
+most of the U.S but the sort of allies
+of World War II
+
+ align:start position:0%
+of World War II
+ 
+
+ align:start position:0%
+of World War II
+for for uh the better part of a decade
+
+ align:start position:0%
+for for uh the better part of a decade
+ 
+
+ align:start position:0%
+for for uh the better part of a decade
+starting uh very soon after surrender so
+
+ align:start position:0%
+starting uh very soon after surrender so
+ 
+
+ align:start position:0%
+starting uh very soon after surrender so
+there were a lot of us-based long-term
+
+ align:start position:0%
+there were a lot of us-based long-term
+ 
+
+ align:start position:0%
+there were a lot of us-based long-term
+studies of the effects of the weapons on
+
+ align:start position:0%
+studies of the effects of the weapons on
+ 
+
+ align:start position:0%
+studies of the effects of the weapons on
+site
+
+ align:start position:0%
+site
+ 
+
+ align:start position:0%
+site
+um including a lot of these kind of
+
+ align:start position:0%
+um including a lot of these kind of
+ 
+
+ align:start position:0%
+um including a lot of these kind of
+biomedical uh kind of epidemiological
+
+ align:start position:0%
+biomedical uh kind of epidemiological
+ 
+
+ align:start position:0%
+biomedical uh kind of epidemiological
+type studies and yet it Still Remains
+
+ align:start position:0%
+type studies and yet it Still Remains
+ 
+
+ align:start position:0%
+type studies and yet it Still Remains
+deeply deeply
+
+ align:start position:0%
+deeply deeply
+ 
+
+ align:start position:0%
+deeply deeply
+um controversial
+
+ align:start position:0%
+um controversial
+ 
+
+ align:start position:0%
+um controversial
+how many deaths to attribute to the
+
+ align:start position:0%
+how many deaths to attribute to the
+ 
+
+ align:start position:0%
+how many deaths to attribute to the
+bombings
+
+ align:start position:0%
+bombings
+ 
+
+ align:start position:0%
+bombings
+partly because of different definitions
+
+ align:start position:0%
+partly because of different definitions
+ 
+
+ align:start position:0%
+partly because of different definitions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+who who was sort of exposed in what way
+
+ align:start position:0%
+who who was sort of exposed in what way
+ 
+
+ align:start position:0%
+who who was sort of exposed in what way
+partly to the usual difficulties
+
+ align:start position:0%
+partly to the usual difficulties
+ 
+
+ align:start position:0%
+partly to the usual difficulties
+statistically of saying would this many
+
+ align:start position:0%
+statistically of saying would this many
+ 
+
+ align:start position:0%
+statistically of saying would this many
+people have gotten lung cancer even if
+
+ align:start position:0%
+people have gotten lung cancer even if
+ 
+
+ align:start position:0%
+people have gotten lung cancer even if
+they hadn't been exposed to this kind of
+
+ align:start position:0%
+they hadn't been exposed to this kind of
+ 
+
+ align:start position:0%
+they hadn't been exposed to this kind of
+um you know basically pathogen for lack
+
+ align:start position:0%
+um you know basically pathogen for lack
+ 
+
+ align:start position:0%
+um you know basically pathogen for lack
+of better word radioactive source and
+
+ align:start position:0%
+of better word radioactive source and
+ 
+
+ align:start position:0%
+of better word radioactive source and
+also because a lot of the stuff remains
+
+ align:start position:0%
+also because a lot of the stuff remains
+ 
+
+ align:start position:0%
+also because a lot of the stuff remains
+classified or remain classified for a
+
+ align:start position:0%
+classified or remain classified for a
+ 
+
+ align:start position:0%
+classified or remain classified for a
+long long time anyway so we have the com
+
+ align:start position:0%
+long long time anyway so we have the com
+ 
+
+ align:start position:0%
+long long time anyway so we have the com
+one of the things we'll come to a bit in
+
+ align:start position:0%
+one of the things we'll come to a bit in
+ 
+
+ align:start position:0%
+one of the things we'll come to a bit in
+this class we've already got a little
+
+ align:start position:0%
+this class we've already got a little
+ 
+
+ align:start position:0%
+this class we've already got a little
+hint of it is the role of classification
+
+ align:start position:0%
+hint of it is the role of classification
+ 
+
+ align:start position:0%
+hint of it is the role of classification
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in making it difficult to draw certain
+
+ align:start position:0%
+in making it difficult to draw certain
+ 
+
+ align:start position:0%
+in making it difficult to draw certain
+kinds of conclusions from otherwise very
+
+ align:start position:0%
+kinds of conclusions from otherwise very
+ 
+
+ align:start position:0%
+kinds of conclusions from otherwise very
+complicated scientific and Technical
+
+ align:start position:0%
+complicated scientific and Technical
+ 
+
+ align:start position:0%
+complicated scientific and Technical
+projects uh in this case it was a lot of
+
+ align:start position:0%
+projects uh in this case it was a lot of
+ 
+
+ align:start position:0%
+projects uh in this case it was a lot of
+this stuff was was
+
+ align:start position:0%
+this stuff was was
+ 
+
+ align:start position:0%
+this stuff was was
+subjects who kind of born classified
+
+ align:start position:0%
+subjects who kind of born classified
+ 
+
+ align:start position:0%
+subjects who kind of born classified
+strictures which didn't help with kind
+
+ align:start position:0%
+strictures which didn't help with kind
+ 
+
+ align:start position:0%
+strictures which didn't help with kind
+of independent statisticians redoing the
+
+ align:start position:0%
+of independent statisticians redoing the
+ 
+
+ align:start position:0%
+of independent statisticians redoing the
+stats of the stuff that we would kind of
+
+ align:start position:0%
+stats of the stuff that we would kind of
+ 
+
+ align:start position:0%
+stats of the stuff that we would kind of
+take for granted in in uh kind of
+
+ align:start position:0%
+take for granted in in uh kind of
+ 
+
+ align:start position:0%
+take for granted in in uh kind of
+peer-reviewed scientific studies today
+
+ align:start position:0%
+peer-reviewed scientific studies today
+ 
+
+ align:start position:0%
+peer-reviewed scientific studies today
+so so literally today I'm sure I didn't
+
+ align:start position:0%
+so so literally today I'm sure I didn't
+ 
+
+ align:start position:0%
+so so literally today I'm sure I didn't
+look reasonable but I'm sure if anyone
+
+ align:start position:0%
+look reasonable but I'm sure if anyone
+ 
+
+ align:start position:0%
+look reasonable but I'm sure if anyone
+Google goes on Wikipedia it says how
+
+ align:start position:0%
+Google goes on Wikipedia it says how
+ 
+
+ align:start position:0%
+Google goes on Wikipedia it says how
+many casualties from the bombing of
+
+ align:start position:0%
+many casualties from the bombing of
+ 
+
+ align:start position:0%
+many casualties from the bombing of
+Hiroshima they were probably one of
+
+ align:start position:0%
+Hiroshima they were probably one of
+ 
+
+ align:start position:0%
+Hiroshima they were probably one of
+these like warning comment signs like
+
+ align:start position:0%
+these like warning comment signs like
+ 
+
+ align:start position:0%
+these like warning comment signs like
+people are flaming each other the
+
+ align:start position:0%
+people are flaming each other the
+ 
+
+ align:start position:0%
+people are flaming each other the
+editors don't agree because to this day
+
+ align:start position:0%
+editors don't agree because to this day
+ 
+
+ align:start position:0%
+editors don't agree because to this day
+75 years later asking what sounds like
+
+ align:start position:0%
+75 years later asking what sounds like
+ 
+
+ align:start position:0%
+75 years later asking what sounds like
+what what sounds like a countable
+
+ align:start position:0%
+what what sounds like a countable
+ 
+
+ align:start position:0%
+what what sounds like a countable
+straight seemingly straightforward
+
+ align:start position:0%
+straight seemingly straightforward
+ 
+
+ align:start position:0%
+straight seemingly straightforward
+question how many people were affected
+
+ align:start position:0%
+question how many people were affected
+ 
+
+ align:start position:0%
+question how many people were affected
+killed injured whatever is remarkably
+
+ align:start position:0%
+killed injured whatever is remarkably
+ 
+
+ align:start position:0%
+killed injured whatever is remarkably
+unstrate forward to to very
+
+ align:start position:0%
+unstrate forward to to very
+ 
+
+ align:start position:0%
+unstrate forward to to very
+well-intentioned experts let alone
+
+ align:start position:0%
+well-intentioned experts let alone
+ 
+
+ align:start position:0%
+well-intentioned experts let alone
+people who who are operating for more
+
+ align:start position:0%
+people who who are operating for more
+ 
+
+ align:start position:0%
+people who who are operating for more
+uh from further away from the from the
+
+ align:start position:0%
+uh from further away from the from the
+ 
+
+ align:start position:0%
+uh from further away from the from the
+original information so it gets really
+
+ align:start position:0%
+original information so it gets really
+ 
+
+ align:start position:0%
+original information so it gets really
+tricky to assess literally how many
+
+ align:start position:0%
+tricky to assess literally how many
+ 
+
+ align:start position:0%
+tricky to assess literally how many
+people's lives how many people were
+
+ align:start position:0%
+people's lives how many people were
+ 
+
+ align:start position:0%
+people's lives how many people were
+killed the immediate blast damage that
+
+ align:start position:0%
+killed the immediate blast damage that
+ 
+
+ align:start position:0%
+killed the immediate blast damage that
+actually was uh counted up pretty pretty
+
+ align:start position:0%
+actually was uh counted up pretty pretty
+ 
+
+ align:start position:0%
+actually was uh counted up pretty pretty
+compellingly clearly there's not much
+
+ align:start position:0%
+compellingly clearly there's not much
+ 
+
+ align:start position:0%
+compellingly clearly there's not much
+argument about who died within the first
+
+ align:start position:0%
+argument about who died within the first
+ 
+
+ align:start position:0%
+argument about who died within the first
+week but all these kind of long tail uh
+
+ align:start position:0%
+week but all these kind of long tail uh
+ 
+
+ align:start position:0%
+week but all these kind of long tail uh
+more kind of epidemiological type things
+
+ align:start position:0%
+more kind of epidemiological type things
+ 
+
+ align:start position:0%
+more kind of epidemiological type things
+remain actually quite tricky and and can
+
+ align:start position:0%
+remain actually quite tricky and and can
+ 
+
+ align:start position:0%
+remain actually quite tricky and and can
+Inspire some real
+
+ align:start position:0%
+Inspire some real
+ 
+
+ align:start position:0%
+Inspire some real
+um you know real Earnest debate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's it's a great Point Lulu and
+
+ align:start position:0%
+yeah it's it's a great Point Lulu and
+ 
+
+ align:start position:0%
+yeah it's it's a great Point Lulu and
+it's again It's Tricky I find it tricky
+
+ align:start position:0%
+it's again It's Tricky I find it tricky
+ 
+
+ align:start position:0%
+it's again It's Tricky I find it tricky
+myself
+
+ align:start position:0%
+myself
+ 
+
+ align:start position:0%
+myself
+um and and just biologically I'm closer
+
+ align:start position:0%
+um and and just biologically I'm closer
+ 
+
+ align:start position:0%
+um and and just biologically I'm closer
+to those times than most of the rest of
+
+ align:start position:0%
+to those times than most of the rest of
+ 
+
+ align:start position:0%
+to those times than most of the rest of
+you but not that much closer
+
+ align:start position:0%
+you but not that much closer
+ 
+
+ align:start position:0%
+you but not that much closer
+um I mean I grew up during the Cold War
+
+ align:start position:0%
+um I mean I grew up during the Cold War
+ 
+
+ align:start position:0%
+um I mean I grew up during the Cold War
+and thinking about I didn't have to do
+
+ align:start position:0%
+and thinking about I didn't have to do
+ 
+
+ align:start position:0%
+and thinking about I didn't have to do
+Duck and Cover drills during like h-bomb
+
+ align:start position:0%
+Duck and Cover drills during like h-bomb
+ 
+
+ align:start position:0%
+Duck and Cover drills during like h-bomb
+raids but you know like my parents did
+
+ align:start position:0%
+raids but you know like my parents did
+ 
+
+ align:start position:0%
+raids but you know like my parents did
+so I heard about it anyway but
+
+ align:start position:0%
+so I heard about it anyway but
+ 
+
+ align:start position:0%
+so I heard about it anyway but
+nonetheless it's hard it's it's hard to
+
+ align:start position:0%
+nonetheless it's hard it's it's hard to
+ 
+
+ align:start position:0%
+nonetheless it's hard it's it's hard to
+get my mind back to a time of of kind of
+
+ align:start position:0%
+get my mind back to a time of of kind of
+ 
+
+ align:start position:0%
+get my mind back to a time of of kind of
+Total War I mean thank goodness right
+
+ align:start position:0%
+Total War I mean thank goodness right
+ 
+
+ align:start position:0%
+Total War I mean thank goodness right
+but if you look at the casualty counts
+
+ align:start position:0%
+but if you look at the casualty counts
+ 
+
+ align:start position:0%
+but if you look at the casualty counts
+the fatality Counts from the incendiary
+
+ align:start position:0%
+the fatality Counts from the incendiary
+ 
+
+ align:start position:0%
+the fatality Counts from the incendiary
+bombings of Tokyo and Dresden
+
+ align:start position:0%
+bombings of Tokyo and Dresden
+ 
+
+ align:start position:0%
+bombings of Tokyo and Dresden
+they very likely exceeded at least the
+
+ align:start position:0%
+they very likely exceeded at least the
+ 
+
+ align:start position:0%
+they very likely exceeded at least the
+short-term casualty Counts from the
+
+ align:start position:0%
+short-term casualty Counts from the
+ 
+
+ align:start position:0%
+short-term casualty Counts from the
+bombings of Hiroshima nagasaka at least
+
+ align:start position:0%
+bombings of Hiroshima nagasaka at least
+ 
+
+ align:start position:0%
+bombings of Hiroshima nagasaka at least
+they were comparable meaning there are
+
+ align:start position:0%
+they were comparable meaning there are
+ 
+
+ align:start position:0%
+they were comparable meaning there are
+there were cities where hundreds of
+
+ align:start position:0%
+there were cities where hundreds of
+ 
+
+ align:start position:0%
+there were cities where hundreds of
+thousands of people were killed by
+
+ align:start position:0%
+thousands of people were killed by
+ 
+
+ align:start position:0%
+thousands of people were killed by
+dropping of weapons from aircraft
+
+ align:start position:0%
+dropping of weapons from aircraft
+ 
+
+ align:start position:0%
+dropping of weapons from aircraft
+multiple times in just the weeks a
+
+ align:start position:0%
+multiple times in just the weeks a
+ 
+
+ align:start position:0%
+multiple times in just the weeks a
+little months before these these these
+
+ align:start position:0%
+little months before these these these
+ 
+
+ align:start position:0%
+little months before these these these
+to our eyes new kinds of weapons were
+
+ align:start position:0%
+to our eyes new kinds of weapons were
+ 
+
+ align:start position:0%
+to our eyes new kinds of weapons were
+used in August at 45. so the scale of
+
+ align:start position:0%
+used in August at 45. so the scale of
+ 
+
+ align:start position:0%
+used in August at 45. so the scale of
+the human cost of Civilian of Total War
+
+ align:start position:0%
+the human cost of Civilian of Total War
+ 
+
+ align:start position:0%
+the human cost of Civilian of Total War
+where it's not people in uniform
+
+ align:start position:0%
+where it's not people in uniform
+ 
+
+ align:start position:0%
+where it's not people in uniform
+fighting on a battlefield but anyone
+
+ align:start position:0%
+fighting on a battlefield but anyone
+ 
+
+ align:start position:0%
+fighting on a battlefield but anyone
+who's within some geographical territory
+
+ align:start position:0%
+who's within some geographical territory
+ 
+
+ align:start position:0%
+who's within some geographical territory
+is suddenly considering kind of fair
+
+ align:start position:0%
+is suddenly considering kind of fair
+ 
+
+ align:start position:0%
+is suddenly considering kind of fair
+game as a Target that wasn't invented
+
+ align:start position:0%
+game as a Target that wasn't invented
+ 
+
+ align:start position:0%
+game as a Target that wasn't invented
+you know with the use of nuclear weapons
+
+ align:start position:0%
+you know with the use of nuclear weapons
+ 
+
+ align:start position:0%
+you know with the use of nuclear weapons
+and and the and the difference that
+
+ align:start position:0%
+and and the and the difference that
+ 
+
+ align:start position:0%
+and and the and the difference that
+sometimes people would would articulate
+
+ align:start position:0%
+sometimes people would would articulate
+ 
+
+ align:start position:0%
+sometimes people would would articulate
+soon afterwards whereas it took a
+
+ align:start position:0%
+soon afterwards whereas it took a
+ 
+
+ align:start position:0%
+soon afterwards whereas it took a
+thousand aircraft to level Tokyo and it
+
+ align:start position:0%
+thousand aircraft to level Tokyo and it
+ 
+
+ align:start position:0%
+thousand aircraft to level Tokyo and it
+took one to level Hiroshima so there was
+
+ align:start position:0%
+took one to level Hiroshima so there was
+ 
+
+ align:start position:0%
+took one to level Hiroshima so there was
+some people would start saying these
+
+ align:start position:0%
+some people would start saying these
+ 
+
+ align:start position:0%
+some people would start saying these
+really are different let's be careful
+
+ align:start position:0%
+really are different let's be careful
+ 
+
+ align:start position:0%
+really are different let's be careful
+let's think about this carefully others
+
+ align:start position:0%
+let's think about this carefully others
+ 
+
+ align:start position:0%
+let's think about this carefully others
+would say
+
+ align:start position:0%
+would say
+ 
+
+ align:start position:0%
+would say
+you know a hundred thousand people dead
+
+ align:start position:0%
+you know a hundred thousand people dead
+ 
+
+ align:start position:0%
+you know a hundred thousand people dead
+that's like last Thursday you know it's
+
+ align:start position:0%
+that's like last Thursday you know it's
+ 
+
+ align:start position:0%
+that's like last Thursday you know it's
+just a remarkable how what what's the
+
+ align:start position:0%
+just a remarkable how what what's the
+ 
+
+ align:start position:0%
+just a remarkable how what what's the
+comparison class let me go to that way
+
+ align:start position:0%
+comparison class let me go to that way
+ 
+
+ align:start position:0%
+comparison class let me go to that way
+what are you comparing it with and how
+
+ align:start position:0%
+what are you comparing it with and how
+ 
+
+ align:start position:0%
+what are you comparing it with and how
+do our own individual sensibilities
+
+ align:start position:0%
+do our own individual sensibilities
+ 
+
+ align:start position:0%
+do our own individual sensibilities
+shift uh compared to um what many folks
+
+ align:start position:0%
+shift uh compared to um what many folks
+ 
+
+ align:start position:0%
+shift uh compared to um what many folks
+were were kind of immersed in at the
+
+ align:start position:0%
+were were kind of immersed in at the
+ 
+
+ align:start position:0%
+were were kind of immersed in at the
+time and I don't say that to to to
+
+ align:start position:0%
+time and I don't say that to to to
+ 
+
+ align:start position:0%
+time and I don't say that to to to
+say there's no culpability I'm just
+
+ align:start position:0%
+say there's no culpability I'm just
+ 
+
+ align:start position:0%
+say there's no culpability I'm just
+saying it's astonishing to me that that
+
+ align:start position:0%
+saying it's astonishing to me that that
+ 
+
+ align:start position:0%
+saying it's astonishing to me that that
+might have seemed
+
+ align:start position:0%
+might have seemed
+ 
+
+ align:start position:0%
+might have seemed
+sort of unremarkable in its day given
+
+ align:start position:0%
+sort of unremarkable in its day given
+ 
+
+ align:start position:0%
+sort of unremarkable in its day given
+given three and a half four years of
+
+ align:start position:0%
+given three and a half four years of
+ 
+
+ align:start position:0%
+given three and a half four years of
+this really devastating civilian heavy
+
+ align:start position:0%
+this really devastating civilian heavy
+ 
+
+ align:start position:0%
+this really devastating civilian heavy
+civilian law so-called Total War
+
+ align:start position:0%
+civilian law so-called Total War
+ 
+
+ align:start position:0%
+civilian law so-called Total War
+um so so I just find that uh I mean
+
+ align:start position:0%
+um so so I just find that uh I mean
+ 
+
+ align:start position:0%
+um so so I just find that uh I mean
+thankfully I don't think I don't think
+
+ align:start position:0%
+thankfully I don't think I don't think
+ 
+
+ align:start position:0%
+thankfully I don't think I don't think
+we have that kind of experience in any
+
+ align:start position:0%
+we have that kind of experience in any
+ 
+
+ align:start position:0%
+we have that kind of experience in any
+of our lifetimes of that kind of um
+
+ align:start position:0%
+of our lifetimes of that kind of um
+ 
+
+ align:start position:0%
+of our lifetimes of that kind of um
+civilian loss of life in in Wartime
+
+ align:start position:0%
+civilian loss of life in in Wartime
+ 
+
+ align:start position:0%
+civilian loss of life in in Wartime
+nothing there's been plenty of bad
+
+ align:start position:0%
+nothing there's been plenty of bad
+ 
+
+ align:start position:0%
+nothing there's been plenty of bad
+things happen since but um so
+
+ align:start position:0%
+things happen since but um so
+ 
+
+ align:start position:0%
+things happen since but um so
+yeah anyway so so that just sort of the
+
+ align:start position:0%
+yeah anyway so so that just sort of the
+ 
+
+ align:start position:0%
+yeah anyway so so that just sort of the
+the scale of of Civilian human loss uh
+
+ align:start position:0%
+the scale of of Civilian human loss uh
+ 
+
+ align:start position:0%
+the scale of of Civilian human loss uh
+where you were you're you were deemed a
+
+ align:start position:0%
+where you were you're you were deemed a
+ 
+
+ align:start position:0%
+where you were you're you were deemed a
+legitimate Target if you happen to live
+
+ align:start position:0%
+legitimate Target if you happen to live
+ 
+
+ align:start position:0%
+legitimate Target if you happen to live
+in a city let alone if you were you know
+
+ align:start position:0%
+in a city let alone if you were you know
+ 
+
+ align:start position:0%
+in a city let alone if you were you know
+drafted let alone if you volunteered or
+
+ align:start position:0%
+drafted let alone if you volunteered or
+ 
+
+ align:start position:0%
+drafted let alone if you volunteered or
+or whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again I not not to get ahead of
+
+ align:start position:0%
+again I not not to get ahead of
+ 
+
+ align:start position:0%
+again I not not to get ahead of
+ourselves but for this coming Wednesdays
+
+ align:start position:0%
+ourselves but for this coming Wednesdays
+ 
+
+ align:start position:0%
+ourselves but for this coming Wednesdays
+class session we'll talk about and you
+
+ align:start position:0%
+class session we'll talk about and you
+ 
+
+ align:start position:0%
+class session we'll talk about and you
+get a hint to this in the film as well
+
+ align:start position:0%
+get a hint to this in the film as well
+ 
+
+ align:start position:0%
+get a hint to this in the film as well
+the you know the The Next Step that
+
+ align:start position:0%
+the you know the The Next Step that
+ 
+
+ align:start position:0%
+the you know the The Next Step that
+happened to have been taken in this
+
+ align:start position:0%
+happened to have been taken in this
+ 
+
+ align:start position:0%
+happened to have been taken in this
+thread of discussion was the development
+
+ align:start position:0%
+thread of discussion was the development
+ 
+
+ align:start position:0%
+thread of discussion was the development
+of uh hydrogen weapons
+
+ align:start position:0%
+of uh hydrogen weapons
+ 
+
+ align:start position:0%
+of uh hydrogen weapons
+which you know are roughly speaking a
+
+ align:start position:0%
+which you know are roughly speaking a
+ 
+
+ align:start position:0%
+which you know are roughly speaking a
+thousand plus times more destructive by
+
+ align:start position:0%
+thousand plus times more destructive by
+ 
+
+ align:start position:0%
+thousand plus times more destructive by
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+parameter you choose to measure then
+
+ align:start position:0%
+parameter you choose to measure then
+ 
+
+ align:start position:0%
+parameter you choose to measure then
+then the weapons that had already been
+
+ align:start position:0%
+then the weapons that had already been
+ 
+
+ align:start position:0%
+then the weapons that had already been
+used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right you know on the question of
+
+ align:start position:0%
+right right you know on the question of
+ 
+
+ align:start position:0%
+right right you know on the question of
+Niels boy it's a great Point Lucas and I
+
+ align:start position:0%
+Niels boy it's a great Point Lucas and I
+ 
+
+ align:start position:0%
+Niels boy it's a great Point Lucas and I
+think it's a it's a lot like somebody
+
+ align:start position:0%
+think it's a it's a lot like somebody
+ 
+
+ align:start position:0%
+think it's a it's a lot like somebody
+talked at least briefly about in a class
+
+ align:start position:0%
+talked at least briefly about in a class
+ 
+
+ align:start position:0%
+talked at least briefly about in a class
+session of maybe two classes ago on
+
+ align:start position:0%
+session of maybe two classes ago on
+ 
+
+ align:start position:0%
+session of maybe two classes ago on
+Einstein's you know very famous letter
+
+ align:start position:0%
+Einstein's you know very famous letter
+ 
+
+ align:start position:0%
+Einstein's you know very famous letter
+to to President Franklin Roosevelt as
+
+ align:start position:0%
+to to President Franklin Roosevelt as
+ 
+
+ align:start position:0%
+to to President Franklin Roosevelt as
+well these are these for a long time
+
+ align:start position:0%
+well these are these for a long time
+ 
+
+ align:start position:0%
+well these are these for a long time
+were held up by scientists as examples
+
+ align:start position:0%
+were held up by scientists as examples
+ 
+
+ align:start position:0%
+were held up by scientists as examples
+of you know these Nobel prize winning
+
+ align:start position:0%
+of you know these Nobel prize winning
+ 
+
+ align:start position:0%
+of you know these Nobel prize winning
+architects of modern physics were also
+
+ align:start position:0%
+architects of modern physics were also
+ 
+
+ align:start position:0%
+architects of modern physics were also
+Geniuses of The Human Condition and
+
+ align:start position:0%
+Geniuses of The Human Condition and
+ 
+
+ align:start position:0%
+Geniuses of The Human Condition and
+political Wizards I wish any of that
+
+ align:start position:0%
+political Wizards I wish any of that
+ 
+
+ align:start position:0%
+political Wizards I wish any of that
+were true and it's not to take away from
+
+ align:start position:0%
+were true and it's not to take away from
+ 
+
+ align:start position:0%
+were true and it's not to take away from
+either einsteiner board to say that
+
+ align:start position:0%
+either einsteiner board to say that
+ 
+
+ align:start position:0%
+either einsteiner board to say that
+those stories are are kind of
+
+ align:start position:0%
+those stories are are kind of
+ 
+
+ align:start position:0%
+those stories are are kind of
+not wishful thinking boar very earnestly
+
+ align:start position:0%
+not wishful thinking boar very earnestly
+ 
+
+ align:start position:0%
+not wishful thinking boar very earnestly
+tried to serve in exactly the capacity
+
+ align:start position:0%
+tried to serve in exactly the capacity
+ 
+
+ align:start position:0%
+tried to serve in exactly the capacity
+you you mentioned because you're quite
+
+ align:start position:0%
+you you mentioned because you're quite
+ 
+
+ align:start position:0%
+you you mentioned because you're quite
+right and the fact is he was
+
+ align:start position:0%
+right and the fact is he was
+ 
+
+ align:start position:0%
+right and the fact is he was
+completely and kind of predictably
+
+ align:start position:0%
+completely and kind of predictably
+ 
+
+ align:start position:0%
+completely and kind of predictably
+ineffective at it no one had any reason
+
+ align:start position:0%
+ineffective at it no one had any reason
+ 
+
+ align:start position:0%
+ineffective at it no one had any reason
+to listen to this mumbling Copenhagen
+
+ align:start position:0%
+to listen to this mumbling Copenhagen
+ 
+
+ align:start position:0%
+to listen to this mumbling Copenhagen
+guy who you know didn't seem to know
+
+ align:start position:0%
+guy who you know didn't seem to know
+ 
+
+ align:start position:0%
+guy who you know didn't seem to know
+anything about about uh how governments
+
+ align:start position:0%
+anything about about uh how governments
+ 
+
+ align:start position:0%
+anything about about uh how governments
+work so his his entries his efforts were
+
+ align:start position:0%
+work so his his entries his efforts were
+ 
+
+ align:start position:0%
+work so his his entries his efforts were
+he did make the efforts let's give him
+
+ align:start position:0%
+he did make the efforts let's give him
+ 
+
+ align:start position:0%
+he did make the efforts let's give him
+credit for that he was indeed he did see
+
+ align:start position:0%
+credit for that he was indeed he did see
+ 
+
+ align:start position:0%
+credit for that he was indeed he did see
+ahead I mean it was it was predictive as
+
+ align:start position:0%
+ahead I mean it was it was predictive as
+ 
+
+ align:start position:0%
+ahead I mean it was it was predictive as
+many people were of a kind of
+
+ align:start position:0%
+many people were of a kind of
+ 
+
+ align:start position:0%
+many people were of a kind of
+um arms race unless there was this
+
+ align:start position:0%
+um arms race unless there was this
+ 
+
+ align:start position:0%
+um arms race unless there was this
+narrow window of opportunity to try to
+
+ align:start position:0%
+narrow window of opportunity to try to
+ 
+
+ align:start position:0%
+narrow window of opportunity to try to
+avert an arms race uh Mutual suspicions
+
+ align:start position:0%
+avert an arms race uh Mutual suspicions
+ 
+
+ align:start position:0%
+avert an arms race uh Mutual suspicions
+uh and distrust growing
+
+ align:start position:0%
+uh and distrust growing
+ 
+
+ align:start position:0%
+uh and distrust growing
+but he I I think I think they were sort
+
+ align:start position:0%
+but he I I think I think they were sort
+ 
+
+ align:start position:0%
+but he I I think I think they were sort
+of very little chance of him having any
+
+ align:start position:0%
+of very little chance of him having any
+ 
+
+ align:start position:0%
+of very little chance of him having any
+actual success and it turns out he had
+
+ align:start position:0%
+actual success and it turns out he had
+ 
+
+ align:start position:0%
+actual success and it turns out he had
+approximately zero success so it's not
+
+ align:start position:0%
+approximately zero success so it's not
+ 
+
+ align:start position:0%
+approximately zero success so it's not
+default him for trying or for
+
+ align:start position:0%
+default him for trying or for
+ 
+
+ align:start position:0%
+default him for trying or for
+recognizing This was
+
+ align:start position:0%
+recognizing This was
+ 
+
+ align:start position:0%
+recognizing This was
+um a likely scenario but we we tend to
+
+ align:start position:0%
+um a likely scenario but we we tend to
+ 
+
+ align:start position:0%
+um a likely scenario but we we tend to
+hear about these stories by like
+
+ align:start position:0%
+hear about these stories by like
+ 
+
+ align:start position:0%
+hear about these stories by like
+biographers of Niels Bohr who who are
+
+ align:start position:0%
+biographers of Niels Bohr who who are
+ 
+
+ align:start position:0%
+biographers of Niels Bohr who who are
+enamorative the many extraordinary
+
+ align:start position:0%
+enamorative the many extraordinary
+ 
+
+ align:start position:0%
+enamorative the many extraordinary
+things that boar was able to do during
+
+ align:start position:0%
+things that boar was able to do during
+ 
+
+ align:start position:0%
+things that boar was able to do during
+his lifetime but if we if we if we ask
+
+ align:start position:0%
+his lifetime but if we if we if we ask
+ 
+
+ align:start position:0%
+his lifetime but if we if we if we ask
+the same question of you know historians
+
+ align:start position:0%
+the same question of you know historians
+ 
+
+ align:start position:0%
+the same question of you know historians
+of U.S foreign relations they'll say
+
+ align:start position:0%
+of U.S foreign relations they'll say
+ 
+
+ align:start position:0%
+of U.S foreign relations they'll say
+Niels who because it had literally zero
+
+ align:start position:0%
+Niels who because it had literally zero
+ 
+
+ align:start position:0%
+Niels who because it had literally zero
+impact you know from at least from where
+
+ align:start position:0%
+impact you know from at least from where
+ 
+
+ align:start position:0%
+impact you know from at least from where
+they're sitting on on the very very
+
+ align:start position:0%
+they're sitting on on the very very
+ 
+
+ align:start position:0%
+they're sitting on on the very very
+complicated relations between uh the U.S
+
+ align:start position:0%
+complicated relations between uh the U.S
+ 
+
+ align:start position:0%
+complicated relations between uh the U.S
+and Britain let alone
+
+ align:start position:0%
+and Britain let alone
+ 
+
+ align:start position:0%
+and Britain let alone
+U.S and Soviets anything else so so I
+
+ align:start position:0%
+U.S and Soviets anything else so so I
+ 
+
+ align:start position:0%
+U.S and Soviets anything else so so I
+guess I take these these these these
+
+ align:start position:0%
+guess I take these these these these
+ 
+
+ align:start position:0%
+guess I take these these these these
+episodes as examples that some of these
+
+ align:start position:0%
+episodes as examples that some of these
+ 
+
+ align:start position:0%
+episodes as examples that some of these
+physicists were indeed trying to think
+
+ align:start position:0%
+physicists were indeed trying to think
+ 
+
+ align:start position:0%
+physicists were indeed trying to think
+one or two steps ahead and they were not
+
+ align:start position:0%
+one or two steps ahead and they were not
+ 
+
+ align:start position:0%
+one or two steps ahead and they were not
+maybe they misjudged you know their own
+
+ align:start position:0%
+maybe they misjudged you know their own
+ 
+
+ align:start position:0%
+maybe they misjudged you know their own
+kind of likely uh influence
+
+ align:start position:0%
+kind of likely uh influence
+ 
+
+ align:start position:0%
+kind of likely uh influence
+um so they get credit in my mind for
+
+ align:start position:0%
+um so they get credit in my mind for
+ 
+
+ align:start position:0%
+um so they get credit in my mind for
+thinking about it at all and trying but
+
+ align:start position:0%
+thinking about it at all and trying but
+ 
+
+ align:start position:0%
+thinking about it at all and trying but
+but the the
+
+ align:start position:0%
+but the the
+ 
+
+ align:start position:0%
+but the the
+it's not much of a track record you know
+
+ align:start position:0%
+it's not much of a track record you know
+ 
+
+ align:start position:0%
+it's not much of a track record you know
+in hindsight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so great question you have a thank you
+
+ align:start position:0%
+so great question you have a thank you
+ 
+
+ align:start position:0%
+so great question you have a thank you
+really interesting so um the first
+
+ align:start position:0%
+really interesting so um the first
+ 
+
+ align:start position:0%
+really interesting so um the first
+impact was
+
+ align:start position:0%
+impact was
+ 
+
+ align:start position:0%
+impact was
+um it was it was not very many From Any
+
+ align:start position:0%
+um it was it was not very many From Any
+ 
+
+ align:start position:0%
+um it was it was not very many From Any
+Given campus so it wasn't like one
+
+ align:start position:0%
+Given campus so it wasn't like one
+ 
+
+ align:start position:0%
+Given campus so it wasn't like one
+Department was emptied out and in fact
+
+ align:start position:0%
+Department was emptied out and in fact
+ 
+
+ align:start position:0%
+Department was emptied out and in fact
+there was a at the time a very very
+
+ align:start position:0%
+there was a at the time a very very
+ 
+
+ align:start position:0%
+there was a at the time a very very
+strong concern on many many universities
+
+ align:start position:0%
+strong concern on many many universities
+ 
+
+ align:start position:0%
+strong concern on many many universities
+and college campus in the U.S to keep as
+
+ align:start position:0%
+and college campus in the U.S to keep as
+ 
+
+ align:start position:0%
+and college campus in the U.S to keep as
+many physicists on site as possible
+
+ align:start position:0%
+many physicists on site as possible
+ 
+
+ align:start position:0%
+many physicists on site as possible
+because they were involved in teaching
+
+ align:start position:0%
+because they were involved in teaching
+ 
+
+ align:start position:0%
+because they were involved in teaching
+what we would now consider basically
+
+ align:start position:0%
+what we would now consider basically
+ 
+
+ align:start position:0%
+what we would now consider basically
+classical physics
+
+ align:start position:0%
+classical physics
+ 
+
+ align:start position:0%
+classical physics
+um block sliding down planes and
+
+ align:start position:0%
+um block sliding down planes and
+ 
+
+ align:start position:0%
+um block sliding down planes and
+Elementary circuits and radio which was
+
+ align:start position:0%
+Elementary circuits and radio which was
+ 
+
+ align:start position:0%
+Elementary circuits and radio which was
+often done in physics departments not a
+
+ align:start position:0%
+often done in physics departments not a
+ 
+
+ align:start position:0%
+often done in physics departments not a
+separate electro engineering department
+
+ align:start position:0%
+separate electro engineering department
+ 
+
+ align:start position:0%
+separate electro engineering department
+many many places in time so there was a
+
+ align:start position:0%
+many many places in time so there was a
+ 
+
+ align:start position:0%
+many many places in time so there was a
+huge concern about literally they talked
+
+ align:start position:0%
+huge concern about literally they talked
+ 
+
+ align:start position:0%
+huge concern about literally they talked
+about rationing and stockpiling physics
+
+ align:start position:0%
+about rationing and stockpiling physics
+ 
+
+ align:start position:0%
+about rationing and stockpiling physics
+instructors to teach or sort of
+
+ align:start position:0%
+instructors to teach or sort of
+ 
+
+ align:start position:0%
+instructors to teach or sort of
+canonical college students but also to
+
+ align:start position:0%
+canonical college students but also to
+ 
+
+ align:start position:0%
+canonical college students but also to
+teach huge numbers of um Navy and army
+
+ align:start position:0%
+teach huge numbers of um Navy and army
+ 
+
+ align:start position:0%
+teach huge numbers of um Navy and army
+special students who were drafted
+
+ align:start position:0%
+special students who were drafted
+ 
+
+ align:start position:0%
+special students who were drafted
+sometimes often straight out of high
+
+ align:start position:0%
+sometimes often straight out of high
+ 
+
+ align:start position:0%
+sometimes often straight out of high
+school were not yet college students and
+
+ align:start position:0%
+school were not yet college students and
+ 
+
+ align:start position:0%
+school were not yet college students and
+were sent to many many campuses around
+
+ align:start position:0%
+were sent to many many campuses around
+ 
+
+ align:start position:0%
+were sent to many many campuses around
+the U.S
+
+ align:start position:0%
+the U.S
+ 
+
+ align:start position:0%
+the U.S
+um to for like crash course study very
+
+ align:start position:0%
+um to for like crash course study very
+ 
+
+ align:start position:0%
+um to for like crash course study very
+accelerated schedules to learn basically
+
+ align:start position:0%
+accelerated schedules to learn basically
+ 
+
+ align:start position:0%
+accelerated schedules to learn basically
+rudimentary physics like like for radio
+
+ align:start position:0%
+rudimentary physics like like for radio
+ 
+
+ align:start position:0%
+rudimentary physics like like for radio
+communication or you know or like citing
+
+ align:start position:0%
+communication or you know or like citing
+ 
+
+ align:start position:0%
+communication or you know or like citing
+or sound ranging it really was like
+
+ align:start position:0%
+or sound ranging it really was like
+ 
+
+ align:start position:0%
+or sound ranging it really was like
+classical physics and in fact physics
+
+ align:start position:0%
+classical physics and in fact physics
+ 
+
+ align:start position:0%
+classical physics and in fact physics
+departments were admonished not to waste
+
+ align:start position:0%
+departments were admonished not to waste
+ 
+
+ align:start position:0%
+departments were admonished not to waste
+their time teaching quantum mechanics or
+
+ align:start position:0%
+their time teaching quantum mechanics or
+ 
+
+ align:start position:0%
+their time teaching quantum mechanics or
+Nuclear Physics because that's not going
+
+ align:start position:0%
+Nuclear Physics because that's not going
+ 
+
+ align:start position:0%
+Nuclear Physics because that's not going
+to be of any importance during the war
+
+ align:start position:0%
+to be of any importance during the war
+ 
+
+ align:start position:0%
+to be of any importance during the war
+that kind of makes me smirk and they
+
+ align:start position:0%
+that kind of makes me smirk and they
+ 
+
+ align:start position:0%
+that kind of makes me smirk and they
+should put all their efforts teaching
+
+ align:start position:0%
+should put all their efforts teaching
+ 
+
+ align:start position:0%
+should put all their efforts teaching
+like classical e m uh and and Newtonian
+
+ align:start position:0%
+like classical e m uh and and Newtonian
+ 
+
+ align:start position:0%
+like classical e m uh and and Newtonian
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+um whether it's for you know how do you
+
+ align:start position:0%
+um whether it's for you know how do you
+ 
+
+ align:start position:0%
+um whether it's for you know how do you
+measure air pressure what's a barometer
+
+ align:start position:0%
+measure air pressure what's a barometer
+ 
+
+ align:start position:0%
+measure air pressure what's a barometer
+what you know how do you measure angles
+
+ align:start position:0%
+what you know how do you measure angles
+ 
+
+ align:start position:0%
+what you know how do you measure angles
+with a with a handheld
+
+ align:start position:0%
+with a with a handheld
+ 
+
+ align:start position:0%
+with a with a handheld
+um you know kind of siding device so I
+
+ align:start position:0%
+um you know kind of siding device so I
+ 
+
+ align:start position:0%
+um you know kind of siding device so I
+find that really fascinating so the the
+
+ align:start position:0%
+find that really fascinating so the the
+ 
+
+ align:start position:0%
+find that really fascinating so the the
+term that's often used
+
+ align:start position:0%
+term that's often used
+ 
+
+ align:start position:0%
+term that's often used
+you might have heard the second world
+
+ align:start position:0%
+you might have heard the second world
+ 
+
+ align:start position:0%
+you might have heard the second world
+war has often been called the physicists
+
+ align:start position:0%
+war has often been called the physicists
+ 
+
+ align:start position:0%
+war has often been called the physicists
+war and that term has usually been taken
+
+ align:start position:0%
+war and that term has usually been taken
+ 
+
+ align:start position:0%
+war and that term has usually been taken
+to me oh we know what that means it was
+
+ align:start position:0%
+to me oh we know what that means it was
+ 
+
+ align:start position:0%
+to me oh we know what that means it was
+all about radar and the sort of exotic
+
+ align:start position:0%
+all about radar and the sort of exotic
+ 
+
+ align:start position:0%
+all about radar and the sort of exotic
+uh weapons projects like uh the
+
+ align:start position:0%
+uh weapons projects like uh the
+ 
+
+ align:start position:0%
+uh weapons projects like uh the
+Manhattan Project
+
+ align:start position:0%
+Manhattan Project
+ 
+
+ align:start position:0%
+Manhattan Project
+and so I actually wrote about this
+
+ align:start position:0%
+and so I actually wrote about this
+ 
+
+ align:start position:0%
+and so I actually wrote about this
+recently it turns out the phrase was
+
+ align:start position:0%
+recently it turns out the phrase was
+ 
+
+ align:start position:0%
+recently it turns out the phrase was
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+um before the attack on Pearl Harbor
+
+ align:start position:0%
+um before the attack on Pearl Harbor
+ 
+
+ align:start position:0%
+um before the attack on Pearl Harbor
+before there was Los Alamos laboratory
+
+ align:start position:0%
+before there was Los Alamos laboratory
+ 
+
+ align:start position:0%
+before there was Los Alamos laboratory
+at a time when radar was still deeply
+
+ align:start position:0%
+at a time when radar was still deeply
+ 
+
+ align:start position:0%
+at a time when radar was still deeply
+classified the usage of the term if you
+
+ align:start position:0%
+classified the usage of the term if you
+ 
+
+ align:start position:0%
+classified the usage of the term if you
+do one of these Google engrams all these
+
+ align:start position:0%
+do one of these Google engrams all these
+ 
+
+ align:start position:0%
+do one of these Google engrams all these
+fun things we could do now searching in
+
+ align:start position:0%
+fun things we could do now searching in
+ 
+
+ align:start position:0%
+fun things we could do now searching in
+English language Corpus the phrase
+
+ align:start position:0%
+English language Corpus the phrase
+ 
+
+ align:start position:0%
+English language Corpus the phrase
+physicist Wars use it as spiked in 1943
+
+ align:start position:0%
+physicist Wars use it as spiked in 1943
+ 
+
+ align:start position:0%
+physicist Wars use it as spiked in 1943
+at which time anything about that and
+
+ align:start position:0%
+at which time anything about that and
+ 
+
+ align:start position:0%
+at which time anything about that and
+had project was deeply deeply classified
+
+ align:start position:0%
+had project was deeply deeply classified
+ 
+
+ align:start position:0%
+had project was deeply deeply classified
+they were not printing editorials about
+
+ align:start position:0%
+they were not printing editorials about
+ 
+
+ align:start position:0%
+they were not printing editorials about
+the nuclear weapons in the you know in
+
+ align:start position:0%
+the nuclear weapons in the you know in
+ 
+
+ align:start position:0%
+the nuclear weapons in the you know in
+the op-ed pages so the term business war
+
+ align:start position:0%
+the op-ed pages so the term business war
+ 
+
+ align:start position:0%
+the op-ed pages so the term business war
+was was used to respond to the fact that
+
+ align:start position:0%
+was was used to respond to the fact that
+ 
+
+ align:start position:0%
+was was used to respond to the fact that
+that uh that more and more young people
+
+ align:start position:0%
+that uh that more and more young people
+ 
+
+ align:start position:0%
+that uh that more and more young people
+mostly men mostly boys uh had to be
+
+ align:start position:0%
+mostly men mostly boys uh had to be
+ 
+
+ align:start position:0%
+mostly men mostly boys uh had to be
+trained in Crash Course settings on what
+
+ align:start position:0%
+trained in Crash Course settings on what
+ 
+
+ align:start position:0%
+trained in Crash Course settings on what
+we would call classical physics for
+
+ align:start position:0%
+we would call classical physics for
+ 
+
+ align:start position:0%
+we would call classical physics for
+practical purposes in the battlefield
+
+ align:start position:0%
+practical purposes in the battlefield
+ 
+
+ align:start position:0%
+practical purposes in the battlefield
+which by which they meant
+
+ align:start position:0%
+which by which they meant
+ 
+
+ align:start position:0%
+which by which they meant
+you know barometric pressure measure
+
+ align:start position:0%
+you know barometric pressure measure
+ 
+
+ align:start position:0%
+you know barometric pressure measure
+angles use siding on a gun and uh
+
+ align:start position:0%
+angles use siding on a gun and uh
+ 
+
+ align:start position:0%
+angles use siding on a gun and uh
+Elementary Electronics in circuits so
+
+ align:start position:0%
+Elementary Electronics in circuits so
+ 
+
+ align:start position:0%
+Elementary Electronics in circuits so
+the physicists were the meaning of the
+
+ align:start position:0%
+the physicists were the meaning of the
+ 
+
+ align:start position:0%
+the physicists were the meaning of the
+term actually changed quite dramatically
+
+ align:start position:0%
+term actually changed quite dramatically
+ 
+
+ align:start position:0%
+term actually changed quite dramatically
+after after this dramatic Revelation
+
+ align:start position:0%
+after after this dramatic Revelation
+ 
+
+ align:start position:0%
+after after this dramatic Revelation
+about these new previously secret
+
+ align:start position:0%
+about these new previously secret
+ 
+
+ align:start position:0%
+about these new previously secret
+weapons projects and the kind of impacts
+
+ align:start position:0%
+weapons projects and the kind of impacts
+ 
+
+ align:start position:0%
+weapons projects and the kind of impacts
+they had so there there were I mean so
+
+ align:start position:0%
+they had so there there were I mean so
+ 
+
+ align:start position:0%
+they had so there there were I mean so
+the so the physics classrooms were
+
+ align:start position:0%
+the so the physics classrooms were
+ 
+
+ align:start position:0%
+the so the physics classrooms were
+bulging faster than ever before they
+
+ align:start position:0%
+bulging faster than ever before they
+ 
+
+ align:start position:0%
+bulging faster than ever before they
+weren't getting drained out there were
+
+ align:start position:0%
+weren't getting drained out there were
+ 
+
+ align:start position:0%
+weren't getting drained out there were
+more people rushing to study Physics
+
+ align:start position:0%
+more people rushing to study Physics
+ 
+
+ align:start position:0%
+more people rushing to study Physics
+more more people who were put into
+
+ align:start position:0%
+more more people who were put into
+ 
+
+ align:start position:0%
+more more people who were put into
+physics classes whether they chose to or
+
+ align:start position:0%
+physics classes whether they chose to or
+ 
+
+ align:start position:0%
+physics classes whether they chose to or
+not and more and more people teaching
+
+ align:start position:0%
+not and more and more people teaching
+ 
+
+ align:start position:0%
+not and more and more people teaching
+physics in not just for Math and
+
+ align:start position:0%
+physics in not just for Math and
+ 
+
+ align:start position:0%
+physics in not just for Math and
+chemistry but from music anyone who had
+
+ align:start position:0%
+chemistry but from music anyone who had
+ 
+
+ align:start position:0%
+chemistry but from music anyone who had
+any kind of quantitative skills
+
+ align:start position:0%
+any kind of quantitative skills
+ 
+
+ align:start position:0%
+any kind of quantitative skills
+political science you know any
+
+ align:start position:0%
+political science you know any
+ 
+
+ align:start position:0%
+political science you know any
+statistics good now you know here's a
+
+ align:start position:0%
+statistics good now you know here's a
+ 
+
+ align:start position:0%
+statistics good now you know here's a
+crash course to relearn you know um
+
+ align:start position:0%
+crash course to relearn you know um
+ 
+
+ align:start position:0%
+crash course to relearn you know um
+calculus and you're going to teach Max
+
+ align:start position:0%
+calculus and you're going to teach Max
+ 
+
+ align:start position:0%
+calculus and you're going to teach Max
+equations next week and again anyone who
+
+ align:start position:0%
+equations next week and again anyone who
+ 
+
+ align:start position:0%
+equations next week and again anyone who
+is caught poaching that was there were
+
+ align:start position:0%
+is caught poaching that was there were
+ 
+
+ align:start position:0%
+is caught poaching that was there were
+stealing legitimate physics instructors
+
+ align:start position:0%
+stealing legitimate physics instructors
+ 
+
+ align:start position:0%
+stealing legitimate physics instructors
+from one campus uh were a subject to
+
+ align:start position:0%
+from one campus uh were a subject to
+ 
+
+ align:start position:0%
+from one campus uh were a subject to
+like public shaming so there was an
+
+ align:start position:0%
+like public shaming so there was an
+ 
+
+ align:start position:0%
+like public shaming so there was an
+effort to get to keep more and more
+
+ align:start position:0%
+effort to get to keep more and more
+ 
+
+ align:start position:0%
+effort to get to keep more and more
+physics instructors in the classrooms
+
+ align:start position:0%
+physics instructors in the classrooms
+ 
+
+ align:start position:0%
+physics instructors in the classrooms
+not to teach fancy fancy nuclear fission
+
+ align:start position:0%
+not to teach fancy fancy nuclear fission
+ 
+
+ align:start position:0%
+not to teach fancy fancy nuclear fission
+but rather these other topics
+
+ align:start position:0%
+but rather these other topics
+ 
+
+ align:start position:0%
+but rather these other topics
+um and that meant that when a couple
+
+ align:start position:0%
+um and that meant that when a couple
+ 
+
+ align:start position:0%
+um and that meant that when a couple
+slipped away it was I think lost kind of
+
+ align:start position:0%
+slipped away it was I think lost kind of
+ 
+
+ align:start position:0%
+slipped away it was I think lost kind of
+in the noise I have a feeling because
+
+ align:start position:0%
+in the noise I have a feeling because
+ 
+
+ align:start position:0%
+in the noise I have a feeling because
+there's so much tumult about these huge
+
+ align:start position:0%
+there's so much tumult about these huge
+ 
+
+ align:start position:0%
+there's so much tumult about these huge
+kind of throughput mit's Campus uh
+
+ align:start position:0%
+kind of throughput mit's Campus uh
+ 
+
+ align:start position:0%
+kind of throughput mit's Campus uh
+switched to basically 12-month
+
+ align:start position:0%
+switched to basically 12-month
+ 
+
+ align:start position:0%
+switched to basically 12-month
+instruction
+
+ align:start position:0%
+instruction
+ 
+
+ align:start position:0%
+instruction
+and we had I think at the height of this
+
+ align:start position:0%
+and we had I think at the height of this
+ 
+
+ align:start position:0%
+and we had I think at the height of this
+three times more or not three times it
+
+ align:start position:0%
+three times more or not three times it
+ 
+
+ align:start position:0%
+three times more or not three times it
+was like a three to two ratio so I guess
+
+ align:start position:0%
+was like a three to two ratio so I guess
+ 
+
+ align:start position:0%
+was like a three to two ratio so I guess
+one and a half times more so-called
+
+ align:start position:0%
+one and a half times more so-called
+ 
+
+ align:start position:0%
+one and a half times more so-called
+special students meaning full-time Army
+
+ align:start position:0%
+special students meaning full-time Army
+ 
+
+ align:start position:0%
+special students meaning full-time Army
+and Navy students assigned to MIT for
+
+ align:start position:0%
+and Navy students assigned to MIT for
+ 
+
+ align:start position:0%
+and Navy students assigned to MIT for
+like six week terms than MIT students so
+
+ align:start position:0%
+like six week terms than MIT students so
+ 
+
+ align:start position:0%
+like six week terms than MIT students so
+mit's own campus was was kind of taken
+
+ align:start position:0%
+mit's own campus was was kind of taken
+ 
+
+ align:start position:0%
+mit's own campus was was kind of taken
+over was put into high gear that was
+
+ align:start position:0%
+over was put into high gear that was
+ 
+
+ align:start position:0%
+over was put into high gear that was
+that was very common in many many other
+
+ align:start position:0%
+that was very common in many many other
+ 
+
+ align:start position:0%
+that was very common in many many other
+um liberal arts tiny liberal arts
+
+ align:start position:0%
+um liberal arts tiny liberal arts
+ 
+
+ align:start position:0%
+um liberal arts tiny liberal arts
+colleges big universities I think in
+
+ align:start position:0%
+colleges big universities I think in
+ 
+
+ align:start position:0%
+colleges big universities I think in
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+um these very very intensive kind of
+
+ align:start position:0%
+um these very very intensive kind of
+ 
+
+ align:start position:0%
+um these very very intensive kind of
+short-term uh crash course uh things in
+
+ align:start position:0%
+short-term uh crash course uh things in
+ 
+
+ align:start position:0%
+short-term uh crash course uh things in
+fact is I if I can find it in time I'll
+
+ align:start position:0%
+fact is I if I can find it in time I'll
+ 
+
+ align:start position:0%
+fact is I if I can find it in time I'll
+put it in the in the chat one of my
+
+ align:start position:0%
+put it in the in the chat one of my
+ 
+
+ align:start position:0%
+put it in the in the chat one of my
+favorite photos is actually of 10 to 50
+
+ align:start position:0%
+favorite photos is actually of 10 to 50
+ 
+
+ align:start position:0%
+favorite photos is actually of 10 to 50
+or I don't know if it's your beloved or
+
+ align:start position:0%
+or I don't know if it's your beloved or
+ 
+
+ align:start position:0%
+or I don't know if it's your beloved or
+you're hated you're a room many of you
+
+ align:start position:0%
+you're hated you're a room many of you
+ 
+
+ align:start position:0%
+you're hated you're a room many of you
+will probably know one of our big big
+
+ align:start position:0%
+will probably know one of our big big
+ 
+
+ align:start position:0%
+will probably know one of our big big
+lecture Halls 10 to 50. filled with
+
+ align:start position:0%
+lecture Halls 10 to 50. filled with
+ 
+
+ align:start position:0%
+lecture Halls 10 to 50. filled with
+young men in uniform taking one of these
+
+ align:start position:0%
+young men in uniform taking one of these
+ 
+
+ align:start position:0%
+young men in uniform taking one of these
+crash course classes in probably like
+
+ align:start position:0%
+crash course classes in probably like
+ 
+
+ align:start position:0%
+crash course classes in probably like
+Elementary circuits
+
+ align:start position:0%
+Elementary circuits
+ 
+
+ align:start position:0%
+Elementary circuits
+and it just just a Sea of Faces that all
+
+ align:start position:0%
+and it just just a Sea of Faces that all
+ 
+
+ align:start position:0%
+and it just just a Sea of Faces that all
+look the same in all the same uniforms
+
+ align:start position:0%
+look the same in all the same uniforms
+ 
+
+ align:start position:0%
+look the same in all the same uniforms
+just you know 400 people filling 10 to
+
+ align:start position:0%
+just you know 400 people filling 10 to
+ 
+
+ align:start position:0%
+just you know 400 people filling 10 to
+50 all in in their khakis that's that's
+
+ align:start position:0%
+50 all in in their khakis that's that's
+ 
+
+ align:start position:0%
+50 all in in their khakis that's that's
+what campus at MIT was was was like that
+
+ align:start position:0%
+what campus at MIT was was was like that
+ 
+
+ align:start position:0%
+what campus at MIT was was was like that
+was a predominant thing as opposed to uh
+
+ align:start position:0%
+was a predominant thing as opposed to uh
+ 
+
+ align:start position:0%
+was a predominant thing as opposed to uh
+hey where'd all these people go they
+
+ align:start position:0%
+hey where'd all these people go they
+ 
+
+ align:start position:0%
+hey where'd all these people go they
+must be doing something top secret
+
+ align:start position:0%
+must be doing something top secret
+ 
+
+ align:start position:0%
+must be doing something top secret
+uh Gary Europe and then Alex
+
+ align:start position:0%
+uh Gary Europe and then Alex
+ 
+
+ align:start position:0%
+uh Gary Europe and then Alex
+um I just wanted to share a a movie
+
+ align:start position:0%
+um I just wanted to share a a movie
+ 
+
+ align:start position:0%
+um I just wanted to share a a movie
+suggestion because you mentioned Dresden
+
+ align:start position:0%
+suggestion because you mentioned Dresden
+ 
+
+ align:start position:0%
+suggestion because you mentioned Dresden
+and it's a chilling movie but it's about
+
+ align:start position:0%
+and it's a chilling movie but it's about
+ 
+
+ align:start position:0%
+and it's a chilling movie but it's about
+how things can get normalized Bob
+
+ align:start position:0%
+how things can get normalized Bob
+ 
+
+ align:start position:0%
+how things can get normalized Bob
+McNamara who is the Secretary of Defense
+
+ align:start position:0%
+McNamara who is the Secretary of Defense
+ 
+
+ align:start position:0%
+McNamara who is the Secretary of Defense
+during the Vietnam war but was very
+
+ align:start position:0%
+during the Vietnam war but was very
+ 
+
+ align:start position:0%
+during the Vietnam war but was very
+involved in World War II uh with regard
+
+ align:start position:0%
+involved in World War II uh with regard
+ 
+
+ align:start position:0%
+involved in World War II uh with regard
+to the bombings in Tokyo the Tokyo fire
+
+ align:start position:0%
+to the bombings in Tokyo the Tokyo fire
+ 
+
+ align:start position:0%
+to the bombings in Tokyo the Tokyo fire
+bombing I got to know Bob very late in
+
+ align:start position:0%
+bombing I got to know Bob very late in
+ 
+
+ align:start position:0%
+bombing I got to know Bob very late in
+his life and I thought I'm going to hate
+
+ align:start position:0%
+his life and I thought I'm going to hate
+ 
+
+ align:start position:0%
+his life and I thought I'm going to hate
+this guy I I grew up just hating the
+
+ align:start position:0%
+this guy I I grew up just hating the
+ 
+
+ align:start position:0%
+this guy I I grew up just hating the
+whole idea of who the Secretary of
+
+ align:start position:0%
+whole idea of who the Secretary of
+ 
+
+ align:start position:0%
+whole idea of who the Secretary of
+Defense in the Vietnam War might be and
+
+ align:start position:0%
+Defense in the Vietnam War might be and
+ 
+
+ align:start position:0%
+Defense in the Vietnam War might be and
+he he was reflective about it and he
+
+ align:start position:0%
+he he was reflective about it and he
+ 
+
+ align:start position:0%
+he he was reflective about it and he
+made this movie when I knew him but he
+
+ align:start position:0%
+made this movie when I knew him but he
+ 
+
+ align:start position:0%
+made this movie when I knew him but he
+it's really worthwhile to watch the fog
+
+ align:start position:0%
+it's really worthwhile to watch the fog
+ 
+
+ align:start position:0%
+it's really worthwhile to watch the fog
+of War before yes one other story about
+
+ align:start position:0%
+of War before yes one other story about
+ 
+
+ align:start position:0%
+of War before yes one other story about
+normalizing my father was a Corporal
+
+ align:start position:0%
+normalizing my father was a Corporal
+ 
+
+ align:start position:0%
+normalizing my father was a Corporal
+never went to college and he was in
+
+ align:start position:0%
+never went to college and he was in
+ 
+
+ align:start position:0%
+never went to college and he was in
+tidion yeah and so the day after
+
+ align:start position:0%
+tidion yeah and so the day after
+ 
+
+ align:start position:0%
+tidion yeah and so the day after
+Nagasaki the general said to him Sammy
+
+ align:start position:0%
+Nagasaki the general said to him Sammy
+ 
+
+ align:start position:0%
+Nagasaki the general said to him Sammy
+you want to go up and see what we did
+
+ align:start position:0%
+you want to go up and see what we did
+ 
+
+ align:start position:0%
+you want to go up and see what we did
+yesterday so my dad flew over Nagasaki
+
+ align:start position:0%
+yesterday so my dad flew over Nagasaki
+ 
+
+ align:start position:0%
+yesterday so my dad flew over Nagasaki
+literally the day after
+
+ align:start position:0%
+literally the day after
+ 
+
+ align:start position:0%
+literally the day after
+30 or 40 years later if I had asked my
+
+ align:start position:0%
+30 or 40 years later if I had asked my
+ 
+
+ align:start position:0%
+30 or 40 years later if I had asked my
+dad about it and he was a good man I
+
+ align:start position:0%
+dad about it and he was a good man I
+ 
+
+ align:start position:0%
+dad about it and he was a good man I
+love I love him to this day
+
+ align:start position:0%
+love I love him to this day
+ 
+
+ align:start position:0%
+love I love him to this day
+um but he would say I'd say what do you
+
+ align:start position:0%
+um but he would say I'd say what do you
+ 
+
+ align:start position:0%
+um but he would say I'd say what do you
+think he said Gary we did what we needed
+
+ align:start position:0%
+think he said Gary we did what we needed
+ 
+
+ align:start position:0%
+think he said Gary we did what we needed
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+it was just a Corp role he was a radio
+
+ align:start position:0%
+it was just a Corp role he was a radio
+ 
+
+ align:start position:0%
+it was just a Corp role he was a radio
+mechanic yeah
+
+ align:start position:0%
+mechanic yeah
+ 
+
+ align:start position:0%
+mechanic yeah
+um but it just it got normalized I have
+
+ align:start position:0%
+um but it just it got normalized I have
+ 
+
+ align:start position:0%
+um but it just it got normalized I have
+a question for you David do you know why
+
+ align:start position:0%
+a question for you David do you know why
+ 
+
+ align:start position:0%
+a question for you David do you know why
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Jacob Beezer was the only man on both I
+
+ align:start position:0%
+Jacob Beezer was the only man on both I
+ 
+
+ align:start position:0%
+Jacob Beezer was the only man on both I
+don't know the answer but I knew his son
+
+ align:start position:0%
+don't know the answer but I knew his son
+ 
+
+ align:start position:0%
+don't know the answer but I knew his son
+I knew Jerry Beezer his son but Jacob
+
+ align:start position:0%
+I knew Jerry Beezer his son but Jacob
+ 
+
+ align:start position:0%
+I knew Jerry Beezer his son but Jacob
+beaser was the radar man on both flights
+
+ align:start position:0%
+beaser was the radar man on both flights
+ 
+
+ align:start position:0%
+beaser was the radar man on both flights
+and why did they do that he's the only
+
+ align:start position:0%
+and why did they do that he's the only
+ 
+
+ align:start position:0%
+and why did they do that he's the only
+person that was on both flights that's
+
+ align:start position:0%
+person that was on both flights that's
+ 
+
+ align:start position:0%
+person that was on both flights that's
+fascinating I didn't I didn't know that
+
+ align:start position:0%
+fascinating I didn't I didn't know that
+ 
+
+ align:start position:0%
+fascinating I didn't I didn't know that
+Gary so my guess I'm just guessing I'm
+
+ align:start position:0%
+Gary so my guess I'm just guessing I'm
+ 
+
+ align:start position:0%
+Gary so my guess I'm just guessing I'm
+spectating and Wikipedia might answer it
+
+ align:start position:0%
+spectating and Wikipedia might answer it
+ 
+
+ align:start position:0%
+spectating and Wikipedia might answer it
+you know quicker and maybe even more
+
+ align:start position:0%
+you know quicker and maybe even more
+ 
+
+ align:start position:0%
+you know quicker and maybe even more
+accurate than me my guess is that it was
+
+ align:start position:0%
+accurate than me my guess is that it was
+ 
+
+ align:start position:0%
+accurate than me my guess is that it was
+still you know it was kind of a
+
+ align:start position:0%
+still you know it was kind of a
+ 
+
+ align:start position:0%
+still you know it was kind of a
+shoestring operation that tinian I mean
+
+ align:start position:0%
+shoestring operation that tinian I mean
+ 
+
+ align:start position:0%
+shoestring operation that tinian I mean
+they were throwing this thing together
+
+ align:start position:0%
+they were throwing this thing together
+ 
+
+ align:start position:0%
+they were throwing this thing together
+they just barely gotten the kind of
+
+ align:start position:0%
+they just barely gotten the kind of
+ 
+
+ align:start position:0%
+they just barely gotten the kind of
+airstrip to dry you know that it was so
+
+ align:start position:0%
+airstrip to dry you know that it was so
+ 
+
+ align:start position:0%
+airstrip to dry you know that it was so
+last minute
+
+ align:start position:0%
+last minute
+ 
+
+ align:start position:0%
+last minute
+that my guess is it was just it could it
+
+ align:start position:0%
+that my guess is it was just it could it
+ 
+
+ align:start position:0%
+that my guess is it was just it could it
+could as well have been short staffed as
+
+ align:start position:0%
+could as well have been short staffed as
+ 
+
+ align:start position:0%
+could as well have been short staffed as
+any kind of strategic reason especially
+
+ align:start position:0%
+any kind of strategic reason especially
+ 
+
+ align:start position:0%
+any kind of strategic reason especially
+if it was it was a more kind of
+
+ align:start position:0%
+if it was it was a more kind of
+ 
+
+ align:start position:0%
+if it was it was a more kind of
+specialized role like the radar operator
+
+ align:start position:0%
+specialized role like the radar operator
+ 
+
+ align:start position:0%
+specialized role like the radar operator
+uh it wouldn't surprise me if he was the
+
+ align:start position:0%
+uh it wouldn't surprise me if he was the
+ 
+
+ align:start position:0%
+uh it wouldn't surprise me if he was the
+person who had been trained and was
+
+ align:start position:0%
+person who had been trained and was
+ 
+
+ align:start position:0%
+person who had been trained and was
+available I don't know if it was any
+
+ align:start position:0%
+available I don't know if it was any
+ 
+
+ align:start position:0%
+available I don't know if it was any
+more than that so it was Galaxy
+
+ align:start position:0%
+more than that so it was Galaxy
+ 
+
+ align:start position:0%
+more than that so it was Galaxy
+something else you had said oh yeah yeah
+
+ align:start position:0%
+something else you had said oh yeah yeah
+ 
+
+ align:start position:0%
+something else you had said oh yeah yeah
+so let me just say briefly because
+
+ align:start position:0%
+so let me just say briefly because
+ 
+
+ align:start position:0%
+so let me just say briefly because
+something the film didn't really uh get
+
+ align:start position:0%
+something the film didn't really uh get
+ 
+
+ align:start position:0%
+something the film didn't really uh get
+into a lot of the scholarship in the 40
+
+ align:start position:0%
+into a lot of the scholarship in the 40
+ 
+
+ align:start position:0%
+into a lot of the scholarship in the 40
+years since even the film came out let
+
+ align:start position:0%
+years since even the film came out let
+ 
+
+ align:start position:0%
+years since even the film came out let
+alone the 75 years since the events in
+
+ align:start position:0%
+alone the 75 years since the events in
+ 
+
+ align:start position:0%
+alone the 75 years since the events in
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+has really gone around and around
+
+ align:start position:0%
+has really gone around and around
+ 
+
+ align:start position:0%
+has really gone around and around
+frankly or or has been a very vigorous
+
+ align:start position:0%
+frankly or or has been a very vigorous
+ 
+
+ align:start position:0%
+frankly or or has been a very vigorous
+debate but put it that way about
+
+ align:start position:0%
+debate but put it that way about
+ 
+
+ align:start position:0%
+debate but put it that way about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+basically uh were the bombs needed
+
+ align:start position:0%
+basically uh were the bombs needed
+ 
+
+ align:start position:0%
+basically uh were the bombs needed
+that's kind of a second guessing after
+
+ align:start position:0%
+that's kind of a second guessing after
+ 
+
+ align:start position:0%
+that's kind of a second guessing after
+the fact or put a little more proact Pro
+
+ align:start position:0%
+the fact or put a little more proact Pro
+ 
+
+ align:start position:0%
+the fact or put a little more proact Pro
+perspectively what convinced people to
+
+ align:start position:0%
+perspectively what convinced people to
+ 
+
+ align:start position:0%
+perspectively what convinced people to
+give this standing order to use to use
+
+ align:start position:0%
+give this standing order to use to use
+ 
+
+ align:start position:0%
+give this standing order to use to use
+these weapons you know at all
+
+ align:start position:0%
+these weapons you know at all
+ 
+
+ align:start position:0%
+these weapons you know at all
+and the soon after the war I think it
+
+ align:start position:0%
+and the soon after the war I think it
+ 
+
+ align:start position:0%
+and the soon after the war I think it
+was 1947. the the then the person who
+
+ align:start position:0%
+was 1947. the the then the person who
+ 
+
+ align:start position:0%
+was 1947. the the then the person who
+had been Secretary of War during the
+
+ align:start position:0%
+had been Secretary of War during the
+ 
+
+ align:start position:0%
+had been Secretary of War during the
+second World War uh Henry Simpson
+
+ align:start position:0%
+second World War uh Henry Simpson
+ 
+
+ align:start position:0%
+second World War uh Henry Simpson
+published a famous famous article
+
+ align:start position:0%
+published a famous famous article
+ 
+
+ align:start position:0%
+published a famous famous article
+basically justifying the use of the
+
+ align:start position:0%
+basically justifying the use of the
+ 
+
+ align:start position:0%
+basically justifying the use of the
+nuclear weapons and he's saying it saved
+
+ align:start position:0%
+nuclear weapons and he's saying it saved
+ 
+
+ align:start position:0%
+nuclear weapons and he's saying it saved
+A Million Lives I and then became was it
+
+ align:start position:0%
+A Million Lives I and then became was it
+ 
+
+ align:start position:0%
+A Million Lives I and then became was it
+either a million fatalities or
+
+ align:start position:0%
+either a million fatalities or
+ 
+
+ align:start position:0%
+either a million fatalities or
+casualties by the way he said if the
+
+ align:start position:0%
+casualties by the way he said if the
+ 
+
+ align:start position:0%
+casualties by the way he said if the
+United States had to actually launch
+
+ align:start position:0%
+United States had to actually launch
+ 
+
+ align:start position:0%
+United States had to actually launch
+this planned in-person invasion of the
+
+ align:start position:0%
+this planned in-person invasion of the
+ 
+
+ align:start position:0%
+this planned in-person invasion of the
+Mainland of Japan if there were if there
+
+ align:start position:0%
+Mainland of Japan if there were if there
+ 
+
+ align:start position:0%
+Mainland of Japan if there were if there
+was no way to get to to secure a
+
+ align:start position:0%
+was no way to get to to secure a
+ 
+
+ align:start position:0%
+was no way to get to to secure a
+surrender in an end of the war other
+
+ align:start position:0%
+surrender in an end of the war other
+ 
+
+ align:start position:0%
+surrender in an end of the war other
+than a fully armed invasion of the
+
+ align:start position:0%
+than a fully armed invasion of the
+ 
+
+ align:start position:0%
+than a fully armed invasion of the
+Mainland which is what was indeed being
+
+ align:start position:0%
+Mainland which is what was indeed being
+ 
+
+ align:start position:0%
+Mainland which is what was indeed being
+planned
+
+ align:start position:0%
+planned
+ 
+
+ align:start position:0%
+planned
+by U.S mostly us Allied Forces
+
+ align:start position:0%
+by U.S mostly us Allied Forces
+ 
+
+ align:start position:0%
+by U.S mostly us Allied Forces
+then the casualty count both among U.S
+
+ align:start position:0%
+then the casualty count both among U.S
+ 
+
+ align:start position:0%
+then the casualty count both among U.S
+soldiers and among Japanese civilians
+
+ align:start position:0%
+soldiers and among Japanese civilians
+ 
+
+ align:start position:0%
+soldiers and among Japanese civilians
+would have been astronomical and they
+
+ align:start position:0%
+would have been astronomical and they
+ 
+
+ align:start position:0%
+would have been astronomical and they
+and he mentions that figure one million
+
+ align:start position:0%
+and he mentions that figure one million
+ 
+
+ align:start position:0%
+and he mentions that figure one million
+well other where to get the figure one
+
+ align:start position:0%
+well other where to get the figure one
+ 
+
+ align:start position:0%
+well other where to get the figure one
+million from it seems to have been
+
+ align:start position:0%
+million from it seems to have been
+ 
+
+ align:start position:0%
+million from it seems to have been
+invented in 1947. it seems not to have
+
+ align:start position:0%
+invented in 1947. it seems not to have
+ 
+
+ align:start position:0%
+invented in 1947. it seems not to have
+come from any classified or since
+
+ align:start position:0%
+come from any classified or since
+ 
+
+ align:start position:0%
+come from any classified or since
+Declassified military planning document
+
+ align:start position:0%
+Declassified military planning document
+ 
+
+ align:start position:0%
+Declassified military planning document
+ahead of time so so then the question
+
+ align:start position:0%
+ahead of time so so then the question
+ 
+
+ align:start position:0%
+ahead of time so so then the question
+has becomes would Innovation have been
+
+ align:start position:0%
+has becomes would Innovation have been
+ 
+
+ align:start position:0%
+has becomes would Innovation have been
+necessary were there other reasons to
+
+ align:start position:0%
+necessary were there other reasons to
+ 
+
+ align:start position:0%
+necessary were there other reasons to
+have thought of the space information
+
+ align:start position:0%
+have thought of the space information
+ 
+
+ align:start position:0%
+have thought of the space information
+available at the time that Japan might
+
+ align:start position:0%
+available at the time that Japan might
+ 
+
+ align:start position:0%
+available at the time that Japan might
+or might not have been getting closer to
+
+ align:start position:0%
+or might not have been getting closer to
+ 
+
+ align:start position:0%
+or might not have been getting closer to
+a surrender even prior to the use of the
+
+ align:start position:0%
+a surrender even prior to the use of the
+ 
+
+ align:start position:0%
+a surrender even prior to the use of the
+problems alone would an invasion have
+
+ align:start position:0%
+problems alone would an invasion have
+ 
+
+ align:start position:0%
+problems alone would an invasion have
+been needed and if an invasion were
+
+ align:start position:0%
+been needed and if an invasion were
+ 
+
+ align:start position:0%
+been needed and if an invasion were
+needed where do these casualty figures
+
+ align:start position:0%
+needed where do these casualty figures
+ 
+
+ align:start position:0%
+needed where do these casualty figures
+these projected figures have come from
+
+ align:start position:0%
+these projected figures have come from
+ 
+
+ align:start position:0%
+these projected figures have come from
+so I'll just say I don't have I don't
+
+ align:start position:0%
+so I'll just say I don't have I don't
+ 
+
+ align:start position:0%
+so I'll just say I don't have I don't
+know all the answers but I know people
+
+ align:start position:0%
+know all the answers but I know people
+ 
+
+ align:start position:0%
+know all the answers but I know people
+have poured over this very very
+
+ align:start position:0%
+have poured over this very very
+ 
+
+ align:start position:0%
+have poured over this very very
+carefully and say each of those
+
+ align:start position:0%
+carefully and say each of those
+ 
+
+ align:start position:0%
+carefully and say each of those
+questions is subject to let's say many
+
+ align:start position:0%
+questions is subject to let's say many
+ 
+
+ align:start position:0%
+questions is subject to let's say many
+compelling and quite different answers
+
+ align:start position:0%
+compelling and quite different answers
+ 
+
+ align:start position:0%
+compelling and quite different answers
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so many many U.S uh military officials
+
+ align:start position:0%
+so many many U.S uh military officials
+ 
+
+ align:start position:0%
+so many many U.S uh military officials
+as later came out in in Declassified
+
+ align:start position:0%
+as later came out in in Declassified
+ 
+
+ align:start position:0%
+as later came out in in Declassified
+doctors that were at the time quite
+
+ align:start position:0%
+doctors that were at the time quite
+ 
+
+ align:start position:0%
+doctors that were at the time quite
+Secret
+
+ align:start position:0%
+Secret
+ 
+
+ align:start position:0%
+Secret
+we're we're already raising skepticism
+
+ align:start position:0%
+we're we're already raising skepticism
+ 
+
+ align:start position:0%
+we're we're already raising skepticism
+about whether a a full you of invasion
+
+ align:start position:0%
+about whether a a full you of invasion
+ 
+
+ align:start position:0%
+about whether a a full you of invasion
+would be needed at all and then other
+
+ align:start position:0%
+would be needed at all and then other
+ 
+
+ align:start position:0%
+would be needed at all and then other
+people say oh but that was before the
+
+ align:start position:0%
+people say oh but that was before the
+ 
+
+ align:start position:0%
+people say oh but that was before the
+really uh quite horrible fighting in
+
+ align:start position:0%
+really uh quite horrible fighting in
+ 
+
+ align:start position:0%
+really uh quite horrible fighting in
+Okinawa which was in June so maybe there
+
+ align:start position:0%
+Okinawa which was in June so maybe there
+ 
+
+ align:start position:0%
+Okinawa which was in June so maybe there
+was a kind of fear a concern that the
+
+ align:start position:0%
+was a kind of fear a concern that the
+ 
+
+ align:start position:0%
+was a kind of fear a concern that the
+Japanese troops would actually not
+
+ align:start position:0%
+Japanese troops would actually not
+ 
+
+ align:start position:0%
+Japanese troops would actually not
+surrender even if they were clearly uh
+
+ align:start position:0%
+surrender even if they were clearly uh
+ 
+
+ align:start position:0%
+surrender even if they were clearly uh
+you know overwhelmed numerically so like
+
+ align:start position:0%
+you know overwhelmed numerically so like
+ 
+
+ align:start position:0%
+you know overwhelmed numerically so like
+did which military officials even
+
+ align:start position:0%
+did which military officials even
+ 
+
+ align:start position:0%
+did which military officials even
+thought we'd need that we the United
+
+ align:start position:0%
+thought we'd need that we the United
+ 
+
+ align:start position:0%
+thought we'd need that we the United
+States would need to mount an invasion
+
+ align:start position:0%
+States would need to mount an invasion
+ 
+
+ align:start position:0%
+States would need to mount an invasion
+that's already actually pretty
+
+ align:start position:0%
+that's already actually pretty
+ 
+
+ align:start position:0%
+that's already actually pretty
+complicated based on the documents that
+
+ align:start position:0%
+complicated based on the documents that
+ 
+
+ align:start position:0%
+complicated based on the documents that
+have since much later become available
+
+ align:start position:0%
+have since much later become available
+ 
+
+ align:start position:0%
+have since much later become available
+some people clearly wrote down Japan is
+
+ align:start position:0%
+some people clearly wrote down Japan is
+ 
+
+ align:start position:0%
+some people clearly wrote down Japan is
+on the brink of surrender anyway not you
+
+ align:start position:0%
+on the brink of surrender anyway not you
+ 
+
+ align:start position:0%
+on the brink of surrender anyway not you
+know prior to the use of the weapons
+
+ align:start position:0%
+know prior to the use of the weapons
+ 
+
+ align:start position:0%
+know prior to the use of the weapons
+prior to any Invasion other people said
+
+ align:start position:0%
+prior to any Invasion other people said
+ 
+
+ align:start position:0%
+prior to any Invasion other people said
+oh we thought they might surrender but
+
+ align:start position:0%
+oh we thought they might surrender but
+ 
+
+ align:start position:0%
+oh we thought they might surrender but
+now we're not so sure because of the
+
+ align:start position:0%
+now we're not so sure because of the
+ 
+
+ align:start position:0%
+now we're not so sure because of the
+really quite just horrific fighting the
+
+ align:start position:0%
+really quite just horrific fighting the
+ 
+
+ align:start position:0%
+really quite just horrific fighting the
+kind of dug in fighting especially at
+
+ align:start position:0%
+kind of dug in fighting especially at
+ 
+
+ align:start position:0%
+kind of dug in fighting especially at
+Okinawa late late not too long before
+
+ align:start position:0%
+Okinawa late late not too long before
+ 
+
+ align:start position:0%
+Okinawa late late not too long before
+the use of the nuclear weapons
+
+ align:start position:0%
+the use of the nuclear weapons
+ 
+
+ align:start position:0%
+the use of the nuclear weapons
+then there are all these questions like
+
+ align:start position:0%
+then there are all these questions like
+ 
+
+ align:start position:0%
+then there are all these questions like
+were the were there weapons used to end
+
+ align:start position:0%
+were the were there weapons used to end
+ 
+
+ align:start position:0%
+were the were there weapons used to end
+the war or to secure the post-war so was
+
+ align:start position:0%
+the war or to secure the post-war so was
+ 
+
+ align:start position:0%
+the war or to secure the post-war so was
+it signaling vis-a-vis rivalries with
+
+ align:start position:0%
+it signaling vis-a-vis rivalries with
+ 
+
+ align:start position:0%
+it signaling vis-a-vis rivalries with
+the Soviet Union which is a popular
+
+ align:start position:0%
+the Soviet Union which is a popular
+ 
+
+ align:start position:0%
+the Soviet Union which is a popular
+thesis or other things was it were they
+
+ align:start position:0%
+thesis or other things was it were they
+ 
+
+ align:start position:0%
+thesis or other things was it were they
+used for a kind of geopolitical strategy
+
+ align:start position:0%
+used for a kind of geopolitical strategy
+ 
+
+ align:start position:0%
+used for a kind of geopolitical strategy
+at least as much if not more than for
+
+ align:start position:0%
+at least as much if not more than for
+ 
+
+ align:start position:0%
+at least as much if not more than for
+direct kind of military strategy and
+
+ align:start position:0%
+direct kind of military strategy and
+ 
+
+ align:start position:0%
+direct kind of military strategy and
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+there are very compelling arguments
+
+ align:start position:0%
+there are very compelling arguments
+ 
+
+ align:start position:0%
+there are very compelling arguments
+based on lots and lots of documents on
+
+ align:start position:0%
+based on lots and lots of documents on
+ 
+
+ align:start position:0%
+based on lots and lots of documents on
+kind of not just both sides but a whole
+
+ align:start position:0%
+kind of not just both sides but a whole
+ 
+
+ align:start position:0%
+kind of not just both sides but a whole
+kind of spectrum of that it gets pretty
+
+ align:start position:0%
+kind of spectrum of that it gets pretty
+ 
+
+ align:start position:0%
+kind of spectrum of that it gets pretty
+murky pretty quickly
+
+ align:start position:0%
+murky pretty quickly
+ 
+
+ align:start position:0%
+murky pretty quickly
+so uh so there are waves of kind of re
+
+ align:start position:0%
+so uh so there are waves of kind of re
+ 
+
+ align:start position:0%
+so uh so there are waves of kind of re
+revisiting these questions about of what
+
+ align:start position:0%
+revisiting these questions about of what
+ 
+
+ align:start position:0%
+revisiting these questions about of what
+what military role do the weapons play
+
+ align:start position:0%
+what military role do the weapons play
+ 
+
+ align:start position:0%
+what military role do the weapons play
+and I'm not saying one or the other I
+
+ align:start position:0%
+and I'm not saying one or the other I
+ 
+
+ align:start position:0%
+and I'm not saying one or the other I
+actually I think it's complicated right
+
+ align:start position:0%
+actually I think it's complicated right
+ 
+
+ align:start position:0%
+actually I think it's complicated right
+but you can get these really interesting
+
+ align:start position:0%
+but you can get these really interesting
+ 
+
+ align:start position:0%
+but you can get these really interesting
+studies based on a lot more than what
+
+ align:start position:0%
+studies based on a lot more than what
+ 
+
+ align:start position:0%
+studies based on a lot more than what
+was publicly accessible uh in 1955 or
+
+ align:start position:0%
+was publicly accessible uh in 1955 or
+ 
+
+ align:start position:0%
+was publicly accessible uh in 1955 or
+even 1965 with the with much more
+
+ align:start position:0%
+even 1965 with the with much more
+ 
+
+ align:start position:0%
+even 1965 with the with much more
+passage of time and much more active use
+
+ align:start position:0%
+passage of time and much more active use
+ 
+
+ align:start position:0%
+passage of time and much more active use
+of Freedom of Information Act and
+
+ align:start position:0%
+of Freedom of Information Act and
+ 
+
+ align:start position:0%
+of Freedom of Information Act and
+declassification so on you know it's it
+
+ align:start position:0%
+declassification so on you know it's it
+ 
+
+ align:start position:0%
+declassification so on you know it's it
+it's pretty complicated
+
+ align:start position:0%
+it's pretty complicated
+ 
+
+ align:start position:0%
+it's pretty complicated
+um and so again that we go back to an
+
+ align:start position:0%
+um and so again that we go back to an
+ 
+
+ align:start position:0%
+um and so again that we go back to an
+early question where the bombs to the
+
+ align:start position:0%
+early question where the bombs to the
+ 
+
+ align:start position:0%
+early question where the bombs to the
+bombs and the war where they somehow
+
+ align:start position:0%
+bombs and the war where they somehow
+ 
+
+ align:start position:0%
+bombs and the war where they somehow
+special that incendiary bombings at
+
+ align:start position:0%
+special that incendiary bombings at
+ 
+
+ align:start position:0%
+special that incendiary bombings at
+leveled cities were not capable of
+
+ align:start position:0%
+leveled cities were not capable of
+ 
+
+ align:start position:0%
+leveled cities were not capable of
+ending the war but these special weapons
+
+ align:start position:0%
+ending the war but these special weapons
+ 
+
+ align:start position:0%
+ending the war but these special weapons
+were that was a popular interpretation
+
+ align:start position:0%
+were that was a popular interpretation
+ 
+
+ align:start position:0%
+were that was a popular interpretation
+very soon after the war when these
+
+ align:start position:0%
+very soon after the war when these
+ 
+
+ align:start position:0%
+very soon after the war when these
+things were revealed in such a dramatic
+
+ align:start position:0%
+things were revealed in such a dramatic
+ 
+
+ align:start position:0%
+things were revealed in such a dramatic
+way and then Generations since have gone
+
+ align:start position:0%
+way and then Generations since have gone
+ 
+
+ align:start position:0%
+way and then Generations since have gone
+back to the question and I think it's
+
+ align:start position:0%
+back to the question and I think it's
+ 
+
+ align:start position:0%
+back to the question and I think it's
+it's a little it's more complicated more
+
+ align:start position:0%
+it's a little it's more complicated more
+ 
+
+ align:start position:0%
+it's a little it's more complicated more
+subtle than some of the early pronounces
+
+ align:start position:0%
+subtle than some of the early pronounces
+ 
+
+ align:start position:0%
+subtle than some of the early pronounces
+either Pro or con
+
+ align:start position:0%
+either Pro or con
+ 
+
+ align:start position:0%
+either Pro or con
+uh and the people mentioned I could I'd
+
+ align:start position:0%
+uh and the people mentioned I could I'd
+ 
+
+ align:start position:0%
+uh and the people mentioned I could I'd
+be glad to share kind of reading lists
+
+ align:start position:0%
+be glad to share kind of reading lists
+ 
+
+ align:start position:0%
+be glad to share kind of reading lists
+of lots of things that dug into that
+
+ align:start position:0%
+of lots of things that dug into that
+ 
+
+ align:start position:0%
+of lots of things that dug into that
+since then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think the answer is neither and here's
+
+ align:start position:0%
+I think the answer is neither and here's
+ 
+
+ align:start position:0%
+I think the answer is neither and here's
+my understanding Alex but again I'm this
+
+ align:start position:0%
+my understanding Alex but again I'm this
+ 
+
+ align:start position:0%
+my understanding Alex but again I'm this
+is my uh I think it was raised as a
+
+ align:start position:0%
+is my uh I think it was raised as a
+ 
+
+ align:start position:0%
+is my uh I think it was raised as a
+serious question long before the test
+
+ align:start position:0%
+serious question long before the test
+ 
+
+ align:start position:0%
+serious question long before the test
+and settled to everyone's satisfaction
+
+ align:start position:0%
+and settled to everyone's satisfaction
+ 
+
+ align:start position:0%
+and settled to everyone's satisfaction
+before the test so I don't think it was
+
+ align:start position:0%
+before the test so I don't think it was
+ 
+
+ align:start position:0%
+before the test so I don't think it was
+only ever I think it was only a joke
+
+ align:start position:0%
+only ever I think it was only a joke
+ 
+
+ align:start position:0%
+only ever I think it was only a joke
+I think by the time of the test date
+
+ align:start position:0%
+I think by the time of the test date
+ 
+
+ align:start position:0%
+I think by the time of the test date
+people weren't worried about that the
+
+ align:start position:0%
+people weren't worried about that the
+ 
+
+ align:start position:0%
+people weren't worried about that the
+way they once had legitimately sat down
+
+ align:start position:0%
+way they once had legitimately sat down
+ 
+
+ align:start position:0%
+way they once had legitimately sat down
+and calculated they didn't just say gosh
+
+ align:start position:0%
+and calculated they didn't just say gosh
+ 
+
+ align:start position:0%
+and calculated they didn't just say gosh
+I wonder let's try it so I don't think
+
+ align:start position:0%
+I wonder let's try it so I don't think
+ 
+
+ align:start position:0%
+I wonder let's try it so I don't think
+it was a joke but I also think it was no
+
+ align:start position:0%
+it was a joke but I also think it was no
+ 
+
+ align:start position:0%
+it was a joke but I also think it was no
+longer a kind of live debated scientific
+
+ align:start position:0%
+longer a kind of live debated scientific
+ 
+
+ align:start position:0%
+longer a kind of live debated scientific
+question by by mid-july of 45.
+
+ align:start position:0%
+question by by mid-july of 45.
+ 
+
+ align:start position:0%
+question by by mid-july of 45.
+um I think they're you know my
+
+ align:start position:0%
+um I think they're you know my
+ 
+
+ align:start position:0%
+um I think they're you know my
+understanding is Enrico Fermi did was
+
+ align:start position:0%
+understanding is Enrico Fermi did was
+ 
+
+ align:start position:0%
+understanding is Enrico Fermi did was
+the one who articulated that question
+
+ align:start position:0%
+the one who articulated that question
+ 
+
+ align:start position:0%
+the one who articulated that question
+but not like the morning of I think
+
+ align:start position:0%
+but not like the morning of I think
+ 
+
+ align:start position:0%
+but not like the morning of I think
+there was enough time for enough people
+
+ align:start position:0%
+there was enough time for enough people
+ 
+
+ align:start position:0%
+there was enough time for enough people
+to to sit at that and check each other's
+
+ align:start position:0%
+to to sit at that and check each other's
+ 
+
+ align:start position:0%
+to to sit at that and check each other's
+calculations and really and not only
+
+ align:start position:0%
+calculations and really and not only
+ 
+
+ align:start position:0%
+calculations and really and not only
+physicists actually people know stuff
+
+ align:start position:0%
+physicists actually people know stuff
+ 
+
+ align:start position:0%
+physicists actually people know stuff
+like chemists and other people who had
+
+ align:start position:0%
+like chemists and other people who had
+ 
+
+ align:start position:0%
+like chemists and other people who had
+relevant expertise
+
+ align:start position:0%
+relevant expertise
+ 
+
+ align:start position:0%
+relevant expertise
+um I think there was there was a vetting
+
+ align:start position:0%
+um I think there was there was a vetting
+ 
+
+ align:start position:0%
+um I think there was there was a vetting
+of that question well before the test
+
+ align:start position:0%
+of that question well before the test
+ 
+
+ align:start position:0%
+of that question well before the test
+date
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so the short answer is yes but again
+
+ align:start position:0%
+yes so the short answer is yes but again
+ 
+
+ align:start position:0%
+yes so the short answer is yes but again
+I don't but but
+
+ align:start position:0%
+I don't but but
+ 
+
+ align:start position:0%
+I don't but but
+but you you phrased it very very well
+
+ align:start position:0%
+but you you phrased it very very well
+ 
+
+ align:start position:0%
+but you you phrased it very very well
+actually was there any indication the
+
+ align:start position:0%
+actually was there any indication the
+ 
+
+ align:start position:0%
+actually was there any indication the
+answer is yes not definitive indication
+
+ align:start position:0%
+answer is yes not definitive indication
+ 
+
+ align:start position:0%
+answer is yes not definitive indication
+that's why it's still you know you know
+
+ align:start position:0%
+that's why it's still you know you know
+ 
+
+ align:start position:0%
+that's why it's still you know you know
+the phrase war is hell like it's it's
+
+ align:start position:0%
+the phrase war is hell like it's it's
+ 
+
+ align:start position:0%
+the phrase war is hell like it's it's
+it's held for information as well as for
+
+ align:start position:0%
+it's held for information as well as for
+ 
+
+ align:start position:0%
+it's held for information as well as for
+all the more more obvious um reasons so
+
+ align:start position:0%
+all the more more obvious um reasons so
+ 
+
+ align:start position:0%
+all the more more obvious um reasons so
+here's what here's what I mean by that
+
+ align:start position:0%
+here's what here's what I mean by that
+ 
+
+ align:start position:0%
+here's what here's what I mean by that
+it has come to light since then that
+
+ align:start position:0%
+it has come to light since then that
+ 
+
+ align:start position:0%
+it has come to light since then that
+first of all uh some countries had
+
+ align:start position:0%
+first of all uh some countries had
+ 
+
+ align:start position:0%
+first of all uh some countries had
+cracked the Japanese encrypted cables so
+
+ align:start position:0%
+cracked the Japanese encrypted cables so
+ 
+
+ align:start position:0%
+cracked the Japanese encrypted cables so
+and and was leaking that information to
+
+ align:start position:0%
+and and was leaking that information to
+ 
+
+ align:start position:0%
+and and was leaking that information to
+Washington and London and and probably
+
+ align:start position:0%
+Washington and London and and probably
+ 
+
+ align:start position:0%
+Washington and London and and probably
+Moscow as well so some elements of the
+
+ align:start position:0%
+Moscow as well so some elements of the
+ 
+
+ align:start position:0%
+Moscow as well so some elements of the
+Japanese government which at this point
+
+ align:start position:0%
+Japanese government which at this point
+ 
+
+ align:start position:0%
+Japanese government which at this point
+was highly fractured and not really
+
+ align:start position:0%
+was highly fractured and not really
+ 
+
+ align:start position:0%
+was highly fractured and not really
+functioning very easily because Tokyo
+
+ align:start position:0%
+functioning very easily because Tokyo
+ 
+
+ align:start position:0%
+functioning very easily because Tokyo
+had been leveled some parts of the
+
+ align:start position:0%
+had been leveled some parts of the
+ 
+
+ align:start position:0%
+had been leveled some parts of the
+Japanese government were sending out
+
+ align:start position:0%
+Japanese government were sending out
+ 
+
+ align:start position:0%
+Japanese government were sending out
+feelers to try to see if a neutral third
+
+ align:start position:0%
+feelers to try to see if a neutral third
+ 
+
+ align:start position:0%
+feelers to try to see if a neutral third
+party could begin peace negotiations or
+
+ align:start position:0%
+party could begin peace negotiations or
+ 
+
+ align:start position:0%
+party could begin peace negotiations or
+you know negotiations and the fighting
+
+ align:start position:0%
+you know negotiations and the fighting
+ 
+
+ align:start position:0%
+you know negotiations and the fighting
+it's not clear that they had the
+
+ align:start position:0%
+it's not clear that they had the
+ 
+
+ align:start position:0%
+it's not clear that they had the
+authority to speak for the Emperor who
+
+ align:start position:0%
+authority to speak for the Emperor who
+ 
+
+ align:start position:0%
+authority to speak for the Emperor who
+was refusing to step down and that was
+
+ align:start position:0%
+was refusing to step down and that was
+ 
+
+ align:start position:0%
+was refusing to step down and that was
+part of this unconditional surrender
+
+ align:start position:0%
+part of this unconditional surrender
+ 
+
+ align:start position:0%
+part of this unconditional surrender
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so on so it's not clear
+
+ align:start position:0%
+so on so it's not clear
+ 
+
+ align:start position:0%
+so on so it's not clear
+if that represented sort of the what
+
+ align:start position:0%
+if that represented sort of the what
+ 
+
+ align:start position:0%
+if that represented sort of the what
+fraction of the then existing Japanese
+
+ align:start position:0%
+fraction of the then existing Japanese
+ 
+
+ align:start position:0%
+fraction of the then existing Japanese
+government that represented it's also
+
+ align:start position:0%
+government that represented it's also
+ 
+
+ align:start position:0%
+government that represented it's also
+not clear how far that ever got but
+
+ align:start position:0%
+not clear how far that ever got but
+ 
+
+ align:start position:0%
+not clear how far that ever got but
+there was some there indeed was some
+
+ align:start position:0%
+there was some there indeed was some
+ 
+
+ align:start position:0%
+there was some there indeed was some
+evidence that some highly placed members
+
+ align:start position:0%
+evidence that some highly placed members
+ 
+
+ align:start position:0%
+evidence that some highly placed members
+of the Japanese government before the
+
+ align:start position:0%
+of the Japanese government before the
+ 
+
+ align:start position:0%
+of the Japanese government before the
+bombings of Hiroshima Nagasaki were
+
+ align:start position:0%
+bombings of Hiroshima Nagasaki were
+ 
+
+ align:start position:0%
+bombings of Hiroshima Nagasaki were
+seeking to start basically um
+
+ align:start position:0%
+seeking to start basically um
+ 
+
+ align:start position:0%
+seeking to start basically um
+negotiations they were seeking a third
+
+ align:start position:0%
+negotiations they were seeking a third
+ 
+
+ align:start position:0%
+negotiations they were seeking a third
+party who might broker them and again
+
+ align:start position:0%
+party who might broker them and again
+ 
+
+ align:start position:0%
+party who might broker them and again
+that doesn't mean they were on the verge
+
+ align:start position:0%
+that doesn't mean they were on the verge
+ 
+
+ align:start position:0%
+that doesn't mean they were on the verge
+of surrender what seems to be more clear
+
+ align:start position:0%
+of surrender what seems to be more clear
+ 
+
+ align:start position:0%
+of surrender what seems to be more clear
+than anything else from these other
+
+ align:start position:0%
+than anything else from these other
+ 
+
+ align:start position:0%
+than anything else from these other
+Scholars not my own work but I've
+
+ align:start position:0%
+Scholars not my own work but I've
+ 
+
+ align:start position:0%
+Scholars not my own work but I've
+learned from other people who looked as
+
+ align:start position:0%
+learned from other people who looked as
+ 
+
+ align:start position:0%
+learned from other people who looked as
+much more carefully so it was just
+
+ align:start position:0%
+much more carefully so it was just
+ 
+
+ align:start position:0%
+much more carefully so it was just
+complete disarray
+
+ align:start position:0%
+complete disarray
+ 
+
+ align:start position:0%
+complete disarray
+um I mean Washington DC was not subject
+
+ align:start position:0%
+um I mean Washington DC was not subject
+ 
+
+ align:start position:0%
+um I mean Washington DC was not subject
+to that kind of bombardment and so there
+
+ align:start position:0%
+to that kind of bombardment and so there
+ 
+
+ align:start position:0%
+to that kind of bombardment and so there
+was something like a functioning chain
+
+ align:start position:0%
+was something like a functioning chain
+ 
+
+ align:start position:0%
+was something like a functioning chain
+of command and something like you know a
+
+ align:start position:0%
+of command and something like you know a
+ 
+
+ align:start position:0%
+of command and something like you know a
+fractious but still functioning you know
+
+ align:start position:0%
+fractious but still functioning you know
+ 
+
+ align:start position:0%
+fractious but still functioning you know
+kind of series of decision makers who
+
+ align:start position:0%
+kind of series of decision makers who
+ 
+
+ align:start position:0%
+kind of series of decision makers who
+could disagree but nonetheless act on
+
+ align:start position:0%
+could disagree but nonetheless act on
+ 
+
+ align:start position:0%
+could disagree but nonetheless act on
+behalf of a functioning government I
+
+ align:start position:0%
+behalf of a functioning government I
+ 
+
+ align:start position:0%
+behalf of a functioning government I
+think not much of that was functioning
+
+ align:start position:0%
+think not much of that was functioning
+ 
+
+ align:start position:0%
+think not much of that was functioning
+the same way in Japan by that point of
+
+ align:start position:0%
+the same way in Japan by that point of
+ 
+
+ align:start position:0%
+the same way in Japan by that point of
+the war because of things like the
+
+ align:start position:0%
+the war because of things like the
+ 
+
+ align:start position:0%
+the war because of things like the
+enormous disruptions from the from the
+
+ align:start position:0%
+enormous disruptions from the from the
+ 
+
+ align:start position:0%
+enormous disruptions from the from the
+incendiary bombing
+
+ align:start position:0%
+incendiary bombing
+ 
+
+ align:start position:0%
+incendiary bombing
+there were different factions as they're
+
+ align:start position:0%
+there were different factions as they're
+ 
+
+ align:start position:0%
+there were different factions as they're
+off as well might expect there were
+
+ align:start position:0%
+off as well might expect there were
+ 
+
+ align:start position:0%
+off as well might expect there were
+different factions of the US and in
+
+ align:start position:0%
+different factions of the US and in
+ 
+
+ align:start position:0%
+different factions of the US and in
+Britain there are different factions
+
+ align:start position:0%
+Britain there are different factions
+ 
+
+ align:start position:0%
+Britain there are different factions
+within Japan and it wasn't just kind of
+
+ align:start position:0%
+within Japan and it wasn't just kind of
+ 
+
+ align:start position:0%
+within Japan and it wasn't just kind of
+military civilian there were different
+
+ align:start position:0%
+military civilian there were different
+ 
+
+ align:start position:0%
+military civilian there were different
+kind of complicated
+
+ align:start position:0%
+kind of complicated
+ 
+
+ align:start position:0%
+kind of complicated
+um different kind of loyalties and and
+
+ align:start position:0%
+um different kind of loyalties and and
+ 
+
+ align:start position:0%
+um different kind of loyalties and and
+groups and so it was it's not clear who
+
+ align:start position:0%
+groups and so it was it's not clear who
+ 
+
+ align:start position:0%
+groups and so it was it's not clear who
+was speaking for whom and if they even
+
+ align:start position:0%
+was speaking for whom and if they even
+ 
+
+ align:start position:0%
+was speaking for whom and if they even
+were capable of having the equivalent of
+
+ align:start position:0%
+were capable of having the equivalent of
+ 
+
+ align:start position:0%
+were capable of having the equivalent of
+like a kind of full cabinet meeting the
+
+ align:start position:0%
+like a kind of full cabinet meeting the
+ 
+
+ align:start position:0%
+like a kind of full cabinet meeting the
+way we might expect in a U.S context so
+
+ align:start position:0%
+way we might expect in a U.S context so
+ 
+
+ align:start position:0%
+way we might expect in a U.S context so
+that's again so it's a great question
+
+ align:start position:0%
+that's again so it's a great question
+ 
+
+ align:start position:0%
+that's again so it's a great question
+Alex because and unfortunately the
+
+ align:start position:0%
+Alex because and unfortunately the
+ 
+
+ align:start position:0%
+Alex because and unfortunately the
+answer again is like oh gosh it's
+
+ align:start position:0%
+answer again is like oh gosh it's
+ 
+
+ align:start position:0%
+answer again is like oh gosh it's
+complicated so with the fullness of time
+
+ align:start position:0%
+complicated so with the fullness of time
+ 
+
+ align:start position:0%
+complicated so with the fullness of time
+evidence has come out that there were
+
+ align:start position:0%
+evidence has come out that there were
+ 
+
+ align:start position:0%
+evidence has come out that there were
+some parties looking to do some things
+
+ align:start position:0%
+some parties looking to do some things
+ 
+
+ align:start position:0%
+some parties looking to do some things
+what's not at all clear and maybe wasn't
+
+ align:start position:0%
+what's not at all clear and maybe wasn't
+ 
+
+ align:start position:0%
+what's not at all clear and maybe wasn't
+clear even at the time was in a sense
+
+ align:start position:0%
+clear even at the time was in a sense
+ 
+
+ align:start position:0%
+clear even at the time was in a sense
+who would that have carried the day who
+
+ align:start position:0%
+who would that have carried the day who
+ 
+
+ align:start position:0%
+who would that have carried the day who
+for who were they speaking on behalf of
+
+ align:start position:0%
+for who were they speaking on behalf of
+ 
+
+ align:start position:0%
+for who were they speaking on behalf of
+who had the authority at the time
+
+ align:start position:0%
+who had the authority at the time
+ 
+
+ align:start position:0%
+who had the authority at the time
+because I think that had gotten very
+
+ align:start position:0%
+because I think that had gotten very
+ 
+
+ align:start position:0%
+because I think that had gotten very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+um again let's just say non-trivial
+
+ align:start position:0%
+um again let's just say non-trivial
+ 
+
+ align:start position:0%
+um again let's just say non-trivial
+so it's a great it's a great great
+
+ align:start position:0%
+so it's a great it's a great great
+ 
+
+ align:start position:0%
+so it's a great it's a great great
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure yeah no the great question
+
+ align:start position:0%
+sure yeah no the great question
+ 
+
+ align:start position:0%
+sure yeah no the great question
+a lot lot has been written about the
+
+ align:start position:0%
+a lot lot has been written about the
+ 
+
+ align:start position:0%
+a lot lot has been written about the
+Oppenheimer um Affair let's say the
+
+ align:start position:0%
+Oppenheimer um Affair let's say the
+ 
+
+ align:start position:0%
+Oppenheimer um Affair let's say the
+Oppenheimer hearing
+
+ align:start position:0%
+Oppenheimer hearing
+ 
+
+ align:start position:0%
+Oppenheimer hearing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+over the years again people keep
+
+ align:start position:0%
+over the years again people keep
+ 
+
+ align:start position:0%
+over the years again people keep
+revisiting it as more and more becomes
+
+ align:start position:0%
+revisiting it as more and more becomes
+ 
+
+ align:start position:0%
+revisiting it as more and more becomes
+Declassified more people are interviewed
+
+ align:start position:0%
+Declassified more people are interviewed
+ 
+
+ align:start position:0%
+Declassified more people are interviewed
+and you know there's a lot this 100th
+
+ align:start position:0%
+and you know there's a lot this 100th
+ 
+
+ align:start position:0%
+and you know there's a lot this 100th
+anniversary of oppenheimer's birth was
+
+ align:start position:0%
+anniversary of oppenheimer's birth was
+ 
+
+ align:start position:0%
+anniversary of oppenheimer's birth was
+2004. and over the 12 months of his
+
+ align:start position:0%
+2004. and over the 12 months of his
+ 
+
+ align:start position:0%
+2004. and over the 12 months of his
+Centennial birth year there were 12 like
+
+ align:start position:0%
+Centennial birth year there were 12 like
+ 
+
+ align:start position:0%
+Centennial birth year there were 12 like
+like one per month 12 full-length
+
+ align:start position:0%
+like one per month 12 full-length
+ 
+
+ align:start position:0%
+like one per month 12 full-length
+biographies published just in that year
+
+ align:start position:0%
+biographies published just in that year
+ 
+
+ align:start position:0%
+biographies published just in that year
+at least 12 did I count that could have
+
+ align:start position:0%
+at least 12 did I count that could have
+ 
+
+ align:start position:0%
+at least 12 did I count that could have
+been more so I mean when I say there's
+
+ align:start position:0%
+been more so I mean when I say there's
+ 
+
+ align:start position:0%
+been more so I mean when I say there's
+like an Oppenheimer industry pouring
+
+ align:start position:0%
+like an Oppenheimer industry pouring
+ 
+
+ align:start position:0%
+like an Oppenheimer industry pouring
+over this that's that's what I mean huge
+
+ align:start position:0%
+over this that's that's what I mean huge
+ 
+
+ align:start position:0%
+over this that's that's what I mean huge
+huge um amount of study of this
+
+ align:start position:0%
+huge um amount of study of this
+ 
+
+ align:start position:0%
+huge um amount of study of this
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me just say briefly therefore
+
+ align:start position:0%
+let me just say briefly therefore
+ 
+
+ align:start position:0%
+let me just say briefly therefore
+instead of going on for hours
+
+ align:start position:0%
+instead of going on for hours
+ 
+
+ align:start position:0%
+instead of going on for hours
+um and again we'll talk a little bit
+
+ align:start position:0%
+um and again we'll talk a little bit
+ 
+
+ align:start position:0%
+um and again we'll talk a little bit
+about this also in Wednesday's class
+
+ align:start position:0%
+about this also in Wednesday's class
+ 
+
+ align:start position:0%
+about this also in Wednesday's class
+Oppenheimer uh you know ended the war
+
+ align:start position:0%
+Oppenheimer uh you know ended the war
+ 
+
+ align:start position:0%
+Oppenheimer uh you know ended the war
+um really as seen as as the person who
+
+ align:start position:0%
+um really as seen as as the person who
+ 
+
+ align:start position:0%
+um really as seen as as the person who
+built the bomb which is um you know
+
+ align:start position:0%
+built the bomb which is um you know
+ 
+
+ align:start position:0%
+built the bomb which is um you know
+not historically accurate the the
+
+ align:start position:0%
+not historically accurate the the
+ 
+
+ align:start position:0%
+not historically accurate the the
+Manhattan Project had 125 000 people and
+
+ align:start position:0%
+Manhattan Project had 125 000 people and
+ 
+
+ align:start position:0%
+Manhattan Project had 125 000 people and
+even the so-called Inner Circle was you
+
+ align:start position:0%
+even the so-called Inner Circle was you
+ 
+
+ align:start position:0%
+even the so-called Inner Circle was you
+know many many people not just one or
+
+ align:start position:0%
+know many many people not just one or
+ 
+
+ align:start position:0%
+know many many people not just one or
+two but he really became the kind of
+
+ align:start position:0%
+two but he really became the kind of
+ 
+
+ align:start position:0%
+two but he really became the kind of
+face of it and that became both for good
+
+ align:start position:0%
+face of it and that became both for good
+ 
+
+ align:start position:0%
+face of it and that became both for good
+and for ill I mean he was seen he was
+
+ align:start position:0%
+and for ill I mean he was seen he was
+ 
+
+ align:start position:0%
+and for ill I mean he was seen he was
+treated as a hero for for many people
+
+ align:start position:0%
+treated as a hero for for many people
+ 
+
+ align:start position:0%
+treated as a hero for for many people
+who thought that the bomb had ended the
+
+ align:start position:0%
+who thought that the bomb had ended the
+ 
+
+ align:start position:0%
+who thought that the bomb had ended the
+war and therefore saved lives which was
+
+ align:start position:0%
+war and therefore saved lives which was
+ 
+
+ align:start position:0%
+war and therefore saved lives which was
+a dominant interpretation uh soon after
+
+ align:start position:0%
+a dominant interpretation uh soon after
+ 
+
+ align:start position:0%
+a dominant interpretation uh soon after
+the war in the United States
+
+ align:start position:0%
+the war in the United States
+ 
+
+ align:start position:0%
+the war in the United States
+he was seen as this kind of Wizardly you
+
+ align:start position:0%
+he was seen as this kind of Wizardly you
+ 
+
+ align:start position:0%
+he was seen as this kind of Wizardly you
+know philosopher king like the film says
+
+ align:start position:0%
+know philosopher king like the film says
+ 
+
+ align:start position:0%
+know philosopher king like the film says
+who had made it happen uh despite all
+
+ align:start position:0%
+who had made it happen uh despite all
+ 
+
+ align:start position:0%
+who had made it happen uh despite all
+the odds
+
+ align:start position:0%
+the odds
+ 
+
+ align:start position:0%
+the odds
+I know they hadn't it also made some
+
+ align:start position:0%
+I know they hadn't it also made some
+ 
+
+ align:start position:0%
+I know they hadn't it also made some
+people think that he was uniquely
+
+ align:start position:0%
+people think that he was uniquely
+ 
+
+ align:start position:0%
+people think that he was uniquely
+dangerous if there is a kind of single
+
+ align:start position:0%
+dangerous if there is a kind of single
+ 
+
+ align:start position:0%
+dangerous if there is a kind of single
+Mastermind or a single set of secrets
+
+ align:start position:0%
+Mastermind or a single set of secrets
+ 
+
+ align:start position:0%
+Mastermind or a single set of secrets
+with which these things be made uh then
+
+ align:start position:0%
+with which these things be made uh then
+ 
+
+ align:start position:0%
+with which these things be made uh then
+then that invites the extra scrutiny
+
+ align:start position:0%
+then that invites the extra scrutiny
+ 
+
+ align:start position:0%
+then that invites the extra scrutiny
+right and there's something this is
+
+ align:start position:0%
+right and there's something this is
+ 
+
+ align:start position:0%
+right and there's something this is
+something we'll talk a bit more in
+
+ align:start position:0%
+something we'll talk a bit more in
+ 
+
+ align:start position:0%
+something we'll talk a bit more in
+Wednesday's class
+
+ align:start position:0%
+Wednesday's class
+ 
+
+ align:start position:0%
+Wednesday's class
+so there was a lot of scrutiny as the
+
+ align:start position:0%
+so there was a lot of scrutiny as the
+ 
+
+ align:start position:0%
+so there was a lot of scrutiny as the
+political assumptions and fortunes and
+
+ align:start position:0%
+political assumptions and fortunes and
+ 
+
+ align:start position:0%
+political assumptions and fortunes and
+kind of groups in or out of power within
+
+ align:start position:0%
+kind of groups in or out of power within
+ 
+
+ align:start position:0%
+kind of groups in or out of power within
+the US and elsewhere shifted after the
+
+ align:start position:0%
+the US and elsewhere shifted after the
+ 
+
+ align:start position:0%
+the US and elsewhere shifted after the
+war
+
+ align:start position:0%
+war
+ 
+
+ align:start position:0%
+war
+Oppenheimer you know kind of had made a
+
+ align:start position:0%
+Oppenheimer you know kind of had made a
+ 
+
+ align:start position:0%
+Oppenheimer you know kind of had made a
+lot of uh um enemies along the way
+
+ align:start position:0%
+lot of uh um enemies along the way
+ 
+
+ align:start position:0%
+lot of uh um enemies along the way
+because he was very smart and never ever
+
+ align:start position:0%
+because he was very smart and never ever
+ 
+
+ align:start position:0%
+because he was very smart and never ever
+ever shy about letting everyone know
+
+ align:start position:0%
+ever shy about letting everyone know
+ 
+
+ align:start position:0%
+ever shy about letting everyone know
+just how smart he was he could be
+
+ align:start position:0%
+just how smart he was he could be
+ 
+
+ align:start position:0%
+just how smart he was he could be
+terrifically cutting I mean just
+
+ align:start position:0%
+terrifically cutting I mean just
+ 
+
+ align:start position:0%
+terrifically cutting I mean just
+mercilessly mocking of people whom he
+
+ align:start position:0%
+mercilessly mocking of people whom he
+ 
+
+ align:start position:0%
+mercilessly mocking of people whom he
+considered intellectually inferior
+
+ align:start position:0%
+considered intellectually inferior
+ 
+
+ align:start position:0%
+considered intellectually inferior
+sometimes as students often of people
+
+ align:start position:0%
+sometimes as students often of people
+ 
+
+ align:start position:0%
+sometimes as students often of people
+who were outside of his immediate circle
+
+ align:start position:0%
+who were outside of his immediate circle
+ 
+
+ align:start position:0%
+who were outside of his immediate circle
+so he was mean to physics students he
+
+ align:start position:0%
+so he was mean to physics students he
+ 
+
+ align:start position:0%
+so he was mean to physics students he
+was horrible to people like the
+
+ align:start position:0%
+was horrible to people like the
+ 
+
+ align:start position:0%
+was horrible to people like the
+secretary of the Air Force which is not
+
+ align:start position:0%
+secretary of the Air Force which is not
+ 
+
+ align:start position:0%
+secretary of the Air Force which is not
+a smart thing by the way if you're ever
+
+ align:start position:0%
+a smart thing by the way if you're ever
+ 
+
+ align:start position:0%
+a smart thing by the way if you're ever
+in the position of mock the secretary of
+
+ align:start position:0%
+in the position of mock the secretary of
+ 
+
+ align:start position:0%
+in the position of mock the secretary of
+the Air Force let me advise you not to
+
+ align:start position:0%
+the Air Force let me advise you not to
+ 
+
+ align:start position:0%
+the Air Force let me advise you not to
+do it but whatever whether the person
+
+ align:start position:0%
+do it but whatever whether the person
+ 
+
+ align:start position:0%
+do it but whatever whether the person
+deserves it or not
+
+ align:start position:0%
+deserves it or not
+ 
+
+ align:start position:0%
+deserves it or not
+so that Oppenheimer kept making enemies
+
+ align:start position:0%
+so that Oppenheimer kept making enemies
+ 
+
+ align:start position:0%
+so that Oppenheimer kept making enemies
+basically he was in the spotlight and
+
+ align:start position:0%
+basically he was in the spotlight and
+ 
+
+ align:start position:0%
+basically he was in the spotlight and
+that gave him the opportunity to shoot
+
+ align:start position:0%
+that gave him the opportunity to shoot
+ 
+
+ align:start position:0%
+that gave him the opportunity to shoot
+his mouth off a lot and much like
+
+ align:start position:0%
+his mouth off a lot and much like
+ 
+
+ align:start position:0%
+his mouth off a lot and much like
+Galileo you know a couple centuries
+
+ align:start position:0%
+Galileo you know a couple centuries
+ 
+
+ align:start position:0%
+Galileo you know a couple centuries
+earlier he was often adopting positions
+
+ align:start position:0%
+earlier he was often adopting positions
+ 
+
+ align:start position:0%
+earlier he was often adopting positions
+that one might find the perfectly
+
+ align:start position:0%
+that one might find the perfectly
+ 
+
+ align:start position:0%
+that one might find the perfectly
+reasonable defensible but defending them
+
+ align:start position:0%
+reasonable defensible but defending them
+ 
+
+ align:start position:0%
+reasonable defensible but defending them
+in a often very aggressive and kind of
+
+ align:start position:0%
+in a often very aggressive and kind of
+ 
+
+ align:start position:0%
+in a often very aggressive and kind of
+mocking sort of way
+
+ align:start position:0%
+mocking sort of way
+ 
+
+ align:start position:0%
+mocking sort of way
+Galileo and the pope Oppenheimer the
+
+ align:start position:0%
+Galileo and the pope Oppenheimer the
+ 
+
+ align:start position:0%
+Galileo and the pope Oppenheimer the
+secretary Air Force right not actually
+
+ align:start position:0%
+secretary Air Force right not actually
+ 
+
+ align:start position:0%
+secretary Air Force right not actually
+so dissimilar in some ways so I better
+
+ align:start position:0%
+so dissimilar in some ways so I better
+ 
+
+ align:start position:0%
+so dissimilar in some ways so I better
+start get started collecting a slew of
+
+ align:start position:0%
+start get started collecting a slew of
+ 
+
+ align:start position:0%
+start get started collecting a slew of
+really quite emboldened uh political uh
+
+ align:start position:0%
+really quite emboldened uh political uh
+ 
+
+ align:start position:0%
+really quite emboldened uh political uh
+you know enemies
+
+ align:start position:0%
+you know enemies
+ 
+
+ align:start position:0%
+you know enemies
+and he started giving advice on
+
+ align:start position:0%
+and he started giving advice on
+ 
+
+ align:start position:0%
+and he started giving advice on
+strategic steps for the nuclear Arsenal
+
+ align:start position:0%
+strategic steps for the nuclear Arsenal
+ 
+
+ align:start position:0%
+strategic steps for the nuclear Arsenal
+that many of them didn't like either and
+
+ align:start position:0%
+that many of them didn't like either and
+ 
+
+ align:start position:0%
+that many of them didn't like either and
+we'll talk a bit about this and there's
+
+ align:start position:0%
+we'll talk a bit about this and there's
+ 
+
+ align:start position:0%
+we'll talk a bit about this and there's
+a hint of that in the film as well so so
+
+ align:start position:0%
+a hint of that in the film as well so so
+ 
+
+ align:start position:0%
+a hint of that in the film as well so so
+in less than a decade he had then made a
+
+ align:start position:0%
+in less than a decade he had then made a
+ 
+
+ align:start position:0%
+in less than a decade he had then made a
+long series of quite powerful people who
+
+ align:start position:0%
+long series of quite powerful people who
+ 
+
+ align:start position:0%
+long series of quite powerful people who
+were pretty pretty ticked off it
+
+ align:start position:0%
+were pretty pretty ticked off it
+ 
+
+ align:start position:0%
+were pretty pretty ticked off it
+uh and so in some sense his hearing was
+
+ align:start position:0%
+uh and so in some sense his hearing was
+ 
+
+ align:start position:0%
+uh and so in some sense his hearing was
+I don't know if it was over determined
+
+ align:start position:0%
+I don't know if it was over determined
+ 
+
+ align:start position:0%
+I don't know if it was over determined
+but it wasn't actually such a shock the
+
+ align:start position:0%
+but it wasn't actually such a shock the
+ 
+
+ align:start position:0%
+but it wasn't actually such a shock the
+fact of the hearing the fact that people
+
+ align:start position:0%
+fact of the hearing the fact that people
+ 
+
+ align:start position:0%
+fact of the hearing the fact that people
+wanted to get him what was left out of
+
+ align:start position:0%
+wanted to get him what was left out of
+ 
+
+ align:start position:0%
+wanted to get him what was left out of
+the film and this was largely came to
+
+ align:start position:0%
+the film and this was largely came to
+ 
+
+ align:start position:0%
+the film and this was largely came to
+light in in more recent scholarships
+
+ align:start position:0%
+light in in more recent scholarships
+ 
+
+ align:start position:0%
+light in in more recent scholarships
+since the early 2000s
+
+ align:start position:0%
+since the early 2000s
+ 
+
+ align:start position:0%
+since the early 2000s
+uh is that Oppenheimer
+
+ align:start position:0%
+uh is that Oppenheimer
+ 
+
+ align:start position:0%
+uh is that Oppenheimer
+you know frankly was trying to kind of
+
+ align:start position:0%
+you know frankly was trying to kind of
+ 
+
+ align:start position:0%
+you know frankly was trying to kind of
+hold on for a long time
+
+ align:start position:0%
+hold on for a long time
+ 
+
+ align:start position:0%
+hold on for a long time
+uh he
+
+ align:start position:0%
+uh he
+ 
+
+ align:start position:0%
+uh he
+he as we now know from declass from
+
+ align:start position:0%
+he as we now know from declass from
+ 
+
+ align:start position:0%
+he as we now know from declass from
+since Declassified documents he often
+
+ align:start position:0%
+since Declassified documents he often
+ 
+
+ align:start position:0%
+since Declassified documents he often
+kind of sold a bunch of his own students
+
+ align:start position:0%
+kind of sold a bunch of his own students
+ 
+
+ align:start position:0%
+kind of sold a bunch of his own students
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+um he was very desperate to protect his
+
+ align:start position:0%
+um he was very desperate to protect his
+ 
+
+ align:start position:0%
+um he was very desperate to protect his
+younger brother Frank who does feature a
+
+ align:start position:0%
+younger brother Frank who does feature a
+ 
+
+ align:start position:0%
+younger brother Frank who does feature a
+lot in the film Frank had been an
+
+ align:start position:0%
+lot in the film Frank had been an
+ 
+
+ align:start position:0%
+lot in the film Frank had been an
+explicit card carrying member of the
+
+ align:start position:0%
+explicit card carrying member of the
+ 
+
+ align:start position:0%
+explicit card carrying member of the
+Communist Party in the 30s not active
+
+ align:start position:0%
+Communist Party in the 30s not active
+ 
+
+ align:start position:0%
+Communist Party in the 30s not active
+but he joined the party as many many
+
+ align:start position:0%
+but he joined the party as many many
+ 
+
+ align:start position:0%
+but he joined the party as many many
+many many academics did in the US in the
+
+ align:start position:0%
+many many academics did in the US in the
+ 
+
+ align:start position:0%
+many many academics did in the US in the
+30s that wasn't so unusual
+
+ align:start position:0%
+30s that wasn't so unusual
+ 
+
+ align:start position:0%
+30s that wasn't so unusual
+but that made Frank an easy target
+
+ align:start position:0%
+but that made Frank an easy target
+ 
+
+ align:start position:0%
+but that made Frank an easy target
+and so it looks like not infrequently
+
+ align:start position:0%
+and so it looks like not infrequently
+ 
+
+ align:start position:0%
+and so it looks like not infrequently
+Robert Oppenheimer would kind of try to
+
+ align:start position:0%
+Robert Oppenheimer would kind of try to
+ 
+
+ align:start position:0%
+Robert Oppenheimer would kind of try to
+cut these deals he thought he could
+
+ align:start position:0%
+cut these deals he thought he could
+ 
+
+ align:start position:0%
+cut these deals he thought he could
+control the situation like don't bother
+
+ align:start position:0%
+control the situation like don't bother
+ 
+
+ align:start position:0%
+control the situation like don't bother
+my brother he's actually no harm but you
+
+ align:start position:0%
+my brother he's actually no harm but you
+ 
+
+ align:start position:0%
+my brother he's actually no harm but you
+want it but you know what those guys
+
+ align:start position:0%
+want it but you know what those guys
+ 
+
+ align:start position:0%
+want it but you know what those guys
+they're Reds as well and often those
+
+ align:start position:0%
+they're Reds as well and often those
+ 
+
+ align:start position:0%
+they're Reds as well and often those
+guys he'd point to where somebody's own
+
+ align:start position:0%
+guys he'd point to where somebody's own
+ 
+
+ align:start position:0%
+guys he'd point to where somebody's own
+former PhD students behind their backs
+
+ align:start position:0%
+former PhD students behind their backs
+ 
+
+ align:start position:0%
+former PhD students behind their backs
+so he was doing a lot of these things as
+
+ align:start position:0%
+so he was doing a lot of these things as
+ 
+
+ align:start position:0%
+so he was doing a lot of these things as
+we now know
+
+ align:start position:0%
+we now know
+ 
+
+ align:start position:0%
+we now know
+um that that that paint a more
+
+ align:start position:0%
+um that that that paint a more
+ 
+
+ align:start position:0%
+um that that that paint a more
+complicated frankly human picture than
+
+ align:start position:0%
+complicated frankly human picture than
+ 
+
+ align:start position:0%
+complicated frankly human picture than
+the kind of saintly martyr that often
+
+ align:start position:0%
+the kind of saintly martyr that often
+ 
+
+ align:start position:0%
+the kind of saintly martyr that often
+comes up even I think in this film
+
+ align:start position:0%
+comes up even I think in this film
+ 
+
+ align:start position:0%
+comes up even I think in this film
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+so his his own political
+
+ align:start position:0%
+so his his own political
+ 
+
+ align:start position:0%
+so his his own political
+skills were not quite as Sterling as he
+
+ align:start position:0%
+skills were not quite as Sterling as he
+ 
+
+ align:start position:0%
+skills were not quite as Sterling as he
+often thought his way of coping with
+
+ align:start position:0%
+often thought his way of coping with
+ 
+
+ align:start position:0%
+often thought his way of coping with
+fast-changing political wins were not
+
+ align:start position:0%
+fast-changing political wins were not
+ 
+
+ align:start position:0%
+fast-changing political wins were not
+what I think any of us would hope we
+
+ align:start position:0%
+what I think any of us would hope we
+ 
+
+ align:start position:0%
+what I think any of us would hope we
+would do if in that situation I don't
+
+ align:start position:0%
+would do if in that situation I don't
+ 
+
+ align:start position:0%
+would do if in that situation I don't
+know how how we would do but it didn't
+
+ align:start position:0%
+know how how we would do but it didn't
+ 
+
+ align:start position:0%
+know how how we would do but it didn't
+oh didn't always look great as we now
+
+ align:start position:0%
+oh didn't always look great as we now
+ 
+
+ align:start position:0%
+oh didn't always look great as we now
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+and it comes off as almost a kind of
+
+ align:start position:0%
+and it comes off as almost a kind of
+ 
+
+ align:start position:0%
+and it comes off as almost a kind of
+grasping at least in some of these
+
+ align:start position:0%
+grasping at least in some of these
+ 
+
+ align:start position:0%
+grasping at least in some of these
+scenarios so Oppenheimer becomes frankly
+
+ align:start position:0%
+scenarios so Oppenheimer becomes frankly
+ 
+
+ align:start position:0%
+scenarios so Oppenheimer becomes frankly
+more interesting and also just much more
+
+ align:start position:0%
+more interesting and also just much more
+ 
+
+ align:start position:0%
+more interesting and also just much more
+human there was a reason to write at
+
+ align:start position:0%
+human there was a reason to write at
+ 
+
+ align:start position:0%
+human there was a reason to write at
+least six of those 12 biographies in
+
+ align:start position:0%
+least six of those 12 biographies in
+ 
+
+ align:start position:0%
+least six of those 12 biographies in
+2004 and some there's a lot of
+
+ align:start position:0%
+2004 and some there's a lot of
+ 
+
+ align:start position:0%
+2004 and some there's a lot of
+Dimensions to this person and and a
+
+ align:start position:0%
+Dimensions to this person and and a
+ 
+
+ align:start position:0%
+Dimensions to this person and and a
+standing for for larger fast moving
+
+ align:start position:0%
+standing for for larger fast moving
+ 
+
+ align:start position:0%
+standing for for larger fast moving
+currents within certainly within the US
+
+ align:start position:0%
+currents within certainly within the US
+ 
+
+ align:start position:0%
+currents within certainly within the US
+and I think beyond that as well
+
+ align:start position:0%
+and I think beyond that as well
+ 
+
+ align:start position:0%
+and I think beyond that as well
+so um so so I I'd be glad to talk more
+
+ align:start position:0%
+so um so so I I'd be glad to talk more
+ 
+
+ align:start position:0%
+so um so so I I'd be glad to talk more
+about Oppenheimer but let me shift to
+
+ align:start position:0%
+about Oppenheimer but let me shift to
+ 
+
+ align:start position:0%
+about Oppenheimer but let me shift to
+teller Taylor was also a very early uh
+
+ align:start position:0%
+teller Taylor was also a very early uh
+ 
+
+ align:start position:0%
+teller Taylor was also a very early uh
+recruit very active at wartime Los
+
+ align:start position:0%
+recruit very active at wartime Los
+ 
+
+ align:start position:0%
+recruit very active at wartime Los
+Alamos and um
+
+ align:start position:0%
+Alamos and um
+ 
+
+ align:start position:0%
+Alamos and um
+already a very accomplished theoretical
+
+ align:start position:0%
+already a very accomplished theoretical
+ 
+
+ align:start position:0%
+already a very accomplished theoretical
+physicist they all kind of knew that
+
+ align:start position:0%
+physicist they all kind of knew that
+ 
+
+ align:start position:0%
+physicist they all kind of knew that
+generation they all knew each other it's
+
+ align:start position:0%
+generation they all knew each other it's
+ 
+
+ align:start position:0%
+generation they all knew each other it's
+a small community before them he's a he
+
+ align:start position:0%
+a small community before them he's a he
+ 
+
+ align:start position:0%
+a small community before them he's a he
+was an immigrant he was a Hungarian uh
+
+ align:start position:0%
+was an immigrant he was a Hungarian uh
+ 
+
+ align:start position:0%
+was an immigrant he was a Hungarian uh
+Jewish person who fled you know um
+
+ align:start position:0%
+Jewish person who fled you know um
+ 
+
+ align:start position:0%
+Jewish person who fled you know um
+fascism he'd been studying in Germany
+
+ align:start position:0%
+fascism he'd been studying in Germany
+ 
+
+ align:start position:0%
+fascism he'd been studying in Germany
+like many of them so he had very good
+
+ align:start position:0%
+like many of them so he had very good
+ 
+
+ align:start position:0%
+like many of them so he had very good
+reason to come to the United States in
+
+ align:start position:0%
+reason to come to the United States in
+ 
+
+ align:start position:0%
+reason to come to the United States in
+the 30s uh and and was hired here in
+
+ align:start position:0%
+the 30s uh and and was hired here in
+ 
+
+ align:start position:0%
+the 30s uh and and was hired here in
+that wave that we talked previously
+
+ align:start position:0%
+that wave that we talked previously
+ 
+
+ align:start position:0%
+that wave that we talked previously
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+and he was very accomplished in a
+
+ align:start position:0%
+and he was very accomplished in a
+ 
+
+ align:start position:0%
+and he was very accomplished in a
+particular very accomplished in nuclear
+
+ align:start position:0%
+particular very accomplished in nuclear
+ 
+
+ align:start position:0%
+particular very accomplished in nuclear
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+um kind of ahead of the curve on that he
+
+ align:start position:0%
+um kind of ahead of the curve on that he
+ 
+
+ align:start position:0%
+um kind of ahead of the curve on that he
+also I think because of his experiences
+
+ align:start position:0%
+also I think because of his experiences
+ 
+
+ align:start position:0%
+also I think because of his experiences
+with these very short-lived communist
+
+ align:start position:0%
+with these very short-lived communist
+ 
+
+ align:start position:0%
+with these very short-lived communist
+and socialist governments in Central
+
+ align:start position:0%
+and socialist governments in Central
+ 
+
+ align:start position:0%
+and socialist governments in Central
+Europe after the end of the first world
+
+ align:start position:0%
+Europe after the end of the first world
+ 
+
+ align:start position:0%
+Europe after the end of the first world
+war a bunch of these immigrants like
+
+ align:start position:0%
+war a bunch of these immigrants like
+ 
+
+ align:start position:0%
+war a bunch of these immigrants like
+teller had experienced what they
+
+ align:start position:0%
+teller had experienced what they
+ 
+
+ align:start position:0%
+teller had experienced what they
+considered just really scary kind of
+
+ align:start position:0%
+considered just really scary kind of
+ 
+
+ align:start position:0%
+considered just really scary kind of
+just chaos in their Reckoning right
+
+ align:start position:0%
+just chaos in their Reckoning right
+ 
+
+ align:start position:0%
+just chaos in their Reckoning right
+after the end of the first world war
+
+ align:start position:0%
+after the end of the first world war
+ 
+
+ align:start position:0%
+after the end of the first world war
+when they were basically late teens or
+
+ align:start position:0%
+when they were basically late teens or
+ 
+
+ align:start position:0%
+when they were basically late teens or
+early 20s a lot of them from
+
+ align:start position:0%
+early 20s a lot of them from
+ 
+
+ align:start position:0%
+early 20s a lot of them from
+self-proclaimed Communists or other
+
+ align:start position:0%
+self-proclaimed Communists or other
+ 
+
+ align:start position:0%
+self-proclaimed Communists or other
+socialists short-lived there was huge
+
+ align:start position:0%
+socialists short-lived there was huge
+ 
+
+ align:start position:0%
+socialists short-lived there was huge
+back and forth the far left the far
+
+ align:start position:0%
+back and forth the far left the far
+ 
+
+ align:start position:0%
+back and forth the far left the far
+right the far left far right militias in
+
+ align:start position:0%
+right the far left far right militias in
+ 
+
+ align:start position:0%
+right the far left far right militias in
+the streets hopefully hopefully nothing
+
+ align:start position:0%
+the streets hopefully hopefully nothing
+ 
+
+ align:start position:0%
+the streets hopefully hopefully nothing
+that any of us will experience uh soon
+
+ align:start position:0%
+that any of us will experience uh soon
+ 
+
+ align:start position:0%
+that any of us will experience uh soon
+or not so soon so teller was a devoted
+
+ align:start position:0%
+or not so soon so teller was a devoted
+ 
+
+ align:start position:0%
+or not so soon so teller was a devoted
+anti-communist before he landed on U.S
+
+ align:start position:0%
+anti-communist before he landed on U.S
+ 
+
+ align:start position:0%
+anti-communist before he landed on U.S
+Shore from I think really not because he
+
+ align:start position:0%
+Shore from I think really not because he
+ 
+
+ align:start position:0%
+Shore from I think really not because he
+read you know like um Marx and was
+
+ align:start position:0%
+read you know like um Marx and was
+ 
+
+ align:start position:0%
+read you know like um Marx and was
+horrified because he'd seen this blood
+
+ align:start position:0%
+horrified because he'd seen this blood
+ 
+
+ align:start position:0%
+horrified because he'd seen this blood
+in the streets kind of fights in the
+
+ align:start position:0%
+in the streets kind of fights in the
+ 
+
+ align:start position:0%
+in the streets kind of fights in the
+1919 teens
+
+ align:start position:0%
+1919 teens
+ 
+
+ align:start position:0%
+1919 teens
+so he was very and many of the folks who
+
+ align:start position:0%
+so he was very and many of the folks who
+ 
+
+ align:start position:0%
+so he was very and many of the folks who
+came with him from that era shared those
+
+ align:start position:0%
+came with him from that era shared those
+ 
+
+ align:start position:0%
+came with him from that era shared those
+sentiments so he was very kind of um we
+
+ align:start position:0%
+sentiments so he was very kind of um we
+ 
+
+ align:start position:0%
+sentiments so he was very kind of um we
+might say jingoistic his adopted home
+
+ align:start position:0%
+might say jingoistic his adopted home
+ 
+
+ align:start position:0%
+might say jingoistic his adopted home
+really should develop the most
+
+ align:start position:0%
+really should develop the most
+ 
+
+ align:start position:0%
+really should develop the most
+significant weapons we really should
+
+ align:start position:0%
+significant weapons we really should
+ 
+
+ align:start position:0%
+significant weapons we really should
+keep all these other kind of bad people
+
+ align:start position:0%
+keep all these other kind of bad people
+ 
+
+ align:start position:0%
+keep all these other kind of bad people
+at Bay was a rough paraphrase
+
+ align:start position:0%
+at Bay was a rough paraphrase
+ 
+
+ align:start position:0%
+at Bay was a rough paraphrase
+now he spent the war warriors at Los
+
+ align:start position:0%
+now he spent the war warriors at Los
+ 
+
+ align:start position:0%
+now he spent the war warriors at Los
+Alamos trying to argue that the fission
+
+ align:start position:0%
+Alamos trying to argue that the fission
+ 
+
+ align:start position:0%
+Alamos trying to argue that the fission
+bomb was small potatoes and why are we
+
+ align:start position:0%
+bomb was small potatoes and why are we
+ 
+
+ align:start position:0%
+bomb was small potatoes and why are we
+wasting our time with this we should
+
+ align:start position:0%
+wasting our time with this we should
+ 
+
+ align:start position:0%
+wasting our time with this we should
+actually be going for a fusion bomb of
+
+ align:start position:0%
+actually be going for a fusion bomb of
+ 
+
+ align:start position:0%
+actually be going for a fusion bomb of
+the sort we will talk briefly about on
+
+ align:start position:0%
+the sort we will talk briefly about on
+ 
+
+ align:start position:0%
+the sort we will talk briefly about on
+Wednesday
+
+ align:start position:0%
+Wednesday
+ 
+
+ align:start position:0%
+Wednesday
+so he kept butting heads with leadership
+
+ align:start position:0%
+so he kept butting heads with leadership
+ 
+
+ align:start position:0%
+so he kept butting heads with leadership
+because he thought they had the wrong
+
+ align:start position:0%
+because he thought they had the wrong
+ 
+
+ align:start position:0%
+because he thought they had the wrong
+priorities this was at a time when there
+
+ align:start position:0%
+priorities this was at a time when there
+ 
+
+ align:start position:0%
+priorities this was at a time when there
+were still like micrograms of plutonium
+
+ align:start position:0%
+were still like micrograms of plutonium
+ 
+
+ align:start position:0%
+were still like micrograms of plutonium
+on the planet no working device had been
+
+ align:start position:0%
+on the planet no working device had been
+ 
+
+ align:start position:0%
+on the planet no working device had been
+developed a little and tested and he's
+
+ align:start position:0%
+developed a little and tested and he's
+ 
+
+ align:start position:0%
+developed a little and tested and he's
+like what that's such a trivial task
+
+ align:start position:0%
+like what that's such a trivial task
+ 
+
+ align:start position:0%
+like what that's such a trivial task
+give me all the resources I want to
+
+ align:start position:0%
+give me all the resources I want to
+ 
+
+ align:start position:0%
+give me all the resources I want to
+build you know hydrogen
+
+ align:start position:0%
+build you know hydrogen
+ 
+
+ align:start position:0%
+build you know hydrogen
+he was very big strong fights about
+
+ align:start position:0%
+he was very big strong fights about
+ 
+
+ align:start position:0%
+he was very big strong fights about
+resources and priorities and so more or
+
+ align:start position:0%
+resources and priorities and so more or
+ 
+
+ align:start position:0%
+resources and priorities and so more or
+less kind of to appease him because he
+
+ align:start position:0%
+less kind of to appease him because he
+ 
+
+ align:start position:0%
+less kind of to appease him because he
+was a smart contributing member he was
+
+ align:start position:0%
+was a smart contributing member he was
+ 
+
+ align:start position:0%
+was a smart contributing member he was
+given a small little study group even
+
+ align:start position:0%
+given a small little study group even
+ 
+
+ align:start position:0%
+given a small little study group even
+during the War uh to work on Fusion
+
+ align:start position:0%
+during the War uh to work on Fusion
+ 
+
+ align:start position:0%
+during the War uh to work on Fusion
+weapons
+
+ align:start position:0%
+weapons
+ 
+
+ align:start position:0%
+weapons
+and I think even by his own Reckoning
+
+ align:start position:0%
+and I think even by his own Reckoning
+ 
+
+ align:start position:0%
+and I think even by his own Reckoning
+they got kind of nowhere but it was it
+
+ align:start position:0%
+they got kind of nowhere but it was it
+ 
+
+ align:start position:0%
+they got kind of nowhere but it was it
+was you know a study group to lay the
+
+ align:start position:0%
+was you know a study group to lay the
+ 
+
+ align:start position:0%
+was you know a study group to lay the
+seas in fact even before there was a Los
+
+ align:start position:0%
+seas in fact even before there was a Los
+ 
+
+ align:start position:0%
+seas in fact even before there was a Los
+Alamos laboratory he was arguing for
+
+ align:start position:0%
+Alamos laboratory he was arguing for
+ 
+
+ align:start position:0%
+Alamos laboratory he was arguing for
+delivery the very first discussion on
+
+ align:start position:0%
+delivery the very first discussion on
+ 
+
+ align:start position:0%
+delivery the very first discussion on
+Berkeley's campus with Oppenheimer and
+
+ align:start position:0%
+Berkeley's campus with Oppenheimer and
+ 
+
+ align:start position:0%
+Berkeley's campus with Oppenheimer and
+the rest that fission bombs would
+
+ align:start position:0%
+the rest that fission bombs would
+ 
+
+ align:start position:0%
+the rest that fission bombs would
+trivial we should be going right now
+
+ align:start position:0%
+trivial we should be going right now
+ 
+
+ align:start position:0%
+trivial we should be going right now
+from Summer 1942 into Fusion I mean that
+
+ align:start position:0%
+from Summer 1942 into Fusion I mean that
+ 
+
+ align:start position:0%
+from Summer 1942 into Fusion I mean that
+was his kind of eBay fix
+
+ align:start position:0%
+was his kind of eBay fix
+ 
+
+ align:start position:0%
+was his kind of eBay fix
+and after the war he becomes more and
+
+ align:start position:0%
+and after the war he becomes more and
+ 
+
+ align:start position:0%
+and after the war he becomes more and
+more uh he he's more and more listened
+
+ align:start position:0%
+more uh he he's more and more listened
+ 
+
+ align:start position:0%
+more uh he he's more and more listened
+to by the folks who are getting more and
+
+ align:start position:0%
+to by the folks who are getting more and
+ 
+
+ align:start position:0%
+to by the folks who are getting more and
+more impatient with Oppenheimer he's he
+
+ align:start position:0%
+more impatient with Oppenheimer he's he
+ 
+
+ align:start position:0%
+more impatient with Oppenheimer he's he
+seems like he has uh answers that many
+
+ align:start position:0%
+seems like he has uh answers that many
+ 
+
+ align:start position:0%
+seems like he has uh answers that many
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+um you know kind of Air Force leadership
+
+ align:start position:0%
+um you know kind of Air Force leadership
+ 
+
+ align:start position:0%
+um you know kind of Air Force leadership
+after the war actually does want to hear
+
+ align:start position:0%
+after the war actually does want to hear
+ 
+
+ align:start position:0%
+after the war actually does want to hear
+they want to hear about bigger Bobs that
+
+ align:start position:0%
+they want to hear about bigger Bobs that
+ 
+
+ align:start position:0%
+they want to hear about bigger Bobs that
+would be under the control of the Air
+
+ align:start position:0%
+would be under the control of the Air
+ 
+
+ align:start position:0%
+would be under the control of the Air
+Force that would be the reason the Air
+
+ align:start position:0%
+Force that would be the reason the Air
+ 
+
+ align:start position:0%
+Force that would be the reason the Air
+Force be the most important you know
+
+ align:start position:0%
+Force be the most important you know
+ 
+
+ align:start position:0%
+Force be the most important you know
+service branch and all these things get
+
+ align:start position:0%
+service branch and all these things get
+ 
+
+ align:start position:0%
+service branch and all these things get
+tied up in kind of rivalries within the
+
+ align:start position:0%
+tied up in kind of rivalries within the
+ 
+
+ align:start position:0%
+tied up in kind of rivalries within the
+U.S uh infrastructure so teller's star
+
+ align:start position:0%
+U.S uh infrastructure so teller's star
+ 
+
+ align:start position:0%
+U.S uh infrastructure so teller's star
+sort of Rises basically at least he has
+
+ align:start position:0%
+sort of Rises basically at least he has
+ 
+
+ align:start position:0%
+sort of Rises basically at least he has
+more people listening to him after the
+
+ align:start position:0%
+more people listening to him after the
+ 
+
+ align:start position:0%
+more people listening to him after the
+war including uh he's very influential
+
+ align:start position:0%
+war including uh he's very influential
+ 
+
+ align:start position:0%
+war including uh he's very influential
+not him alone he was a big mover and
+
+ align:start position:0%
+not him alone he was a big mover and
+ 
+
+ align:start position:0%
+not him alone he was a big mover and
+getting a whole second weapons
+
+ align:start position:0%
+getting a whole second weapons
+ 
+
+ align:start position:0%
+getting a whole second weapons
+laboratory established the Livermore
+
+ align:start position:0%
+laboratory established the Livermore
+ 
+
+ align:start position:0%
+laboratory established the Livermore
+National Laboratory which has opened its
+
+ align:start position:0%
+National Laboratory which has opened its
+ 
+
+ align:start position:0%
+National Laboratory which has opened its
+doors in September of 1952 with the
+
+ align:start position:0%
+doors in September of 1952 with the
+ 
+
+ align:start position:0%
+doors in September of 1952 with the
+express purpose of working full tilt on
+
+ align:start position:0%
+express purpose of working full tilt on
+ 
+
+ align:start position:0%
+express purpose of working full tilt on
+on Fusion weapons
+
+ align:start position:0%
+on Fusion weapons
+ 
+
+ align:start position:0%
+on Fusion weapons
+um this kind of thing so he he's moving
+
+ align:start position:0%
+um this kind of thing so he he's moving
+ 
+
+ align:start position:0%
+um this kind of thing so he he's moving
+in that he does he did testify as you
+
+ align:start position:0%
+in that he does he did testify as you
+ 
+
+ align:start position:0%
+in that he does he did testify as you
+heard in the film uh at oppenheimer's
+
+ align:start position:0%
+heard in the film uh at oppenheimer's
+ 
+
+ align:start position:0%
+heard in the film uh at oppenheimer's
+Security hearing in a way that really
+
+ align:start position:0%
+Security hearing in a way that really
+ 
+
+ align:start position:0%
+Security hearing in a way that really
+when the transcript was published
+
+ align:start position:0%
+when the transcript was published
+ 
+
+ align:start position:0%
+when the transcript was published
+uh was seen as really devastating by
+
+ align:start position:0%
+uh was seen as really devastating by
+ 
+
+ align:start position:0%
+uh was seen as really devastating by
+many many members of the physics
+
+ align:start position:0%
+many many members of the physics
+ 
+
+ align:start position:0%
+many many members of the physics
+Community he doesn't come out and
+
+ align:start position:0%
+Community he doesn't come out and
+ 
+
+ align:start position:0%
+Community he doesn't come out and
+explicitly call Oppenheimer a communist
+
+ align:start position:0%
+explicitly call Oppenheimer a communist
+ 
+
+ align:start position:0%
+explicitly call Oppenheimer a communist
+or um you know a directly security risk
+
+ align:start position:0%
+or um you know a directly security risk
+ 
+
+ align:start position:0%
+or um you know a directly security risk
+which other people were calling it
+
+ align:start position:0%
+which other people were calling it
+ 
+
+ align:start position:0%
+which other people were calling it
+fairly unfairly but he says Oppenheimer
+
+ align:start position:0%
+fairly unfairly but he says Oppenheimer
+ 
+
+ align:start position:0%
+fairly unfairly but he says Oppenheimer
+is a complicated person which was not
+
+ align:start position:0%
+is a complicated person which was not
+ 
+
+ align:start position:0%
+is a complicated person which was not
+meant to be a compliment and and the
+
+ align:start position:0%
+meant to be a compliment and and the
+ 
+
+ align:start position:0%
+meant to be a compliment and and the
+famous line which I'll get pretty close
+
+ align:start position:0%
+famous line which I'll get pretty close
+ 
+
+ align:start position:0%
+famous line which I'll get pretty close
+teller says under oath I wish that the
+
+ align:start position:0%
+teller says under oath I wish that the
+ 
+
+ align:start position:0%
+teller says under oath I wish that the
+that these that these big important
+
+ align:start position:0%
+that these that these big important
+ 
+
+ align:start position:0%
+that these that these big important
+tasks were in hands I understood better
+
+ align:start position:0%
+tasks were in hands I understood better
+ 
+
+ align:start position:0%
+tasks were in hands I understood better
+so therefore could trust more he says I
+
+ align:start position:0%
+so therefore could trust more he says I
+ 
+
+ align:start position:0%
+so therefore could trust more he says I
+basically don't trust Oppenheimer
+
+ align:start position:0%
+basically don't trust Oppenheimer
+ 
+
+ align:start position:0%
+basically don't trust Oppenheimer
+because he is this kind of complicated
+
+ align:start position:0%
+because he is this kind of complicated
+ 
+
+ align:start position:0%
+because he is this kind of complicated
+maybe scheming kind of person
+
+ align:start position:0%
+maybe scheming kind of person
+ 
+
+ align:start position:0%
+maybe scheming kind of person
+as a teller it gives us basically
+
+ align:start position:0%
+as a teller it gives us basically
+ 
+
+ align:start position:0%
+as a teller it gives us basically
+damning what scene is damning testimony
+
+ align:start position:0%
+damning what scene is damning testimony
+ 
+
+ align:start position:0%
+damning what scene is damning testimony
+for for decades you know he outlived off
+
+ align:start position:0%
+for for decades you know he outlived off
+ 
+
+ align:start position:0%
+for for decades you know he outlived off
+100 decades for decades people wouldn't
+
+ align:start position:0%
+100 decades for decades people wouldn't
+ 
+
+ align:start position:0%
+100 decades for decades people wouldn't
+shake his hand would he'd come to give a
+
+ align:start position:0%
+shake his hand would he'd come to give a
+ 
+
+ align:start position:0%
+shake his hand would he'd come to give a
+physics colloquium it really was had a a
+
+ align:start position:0%
+physics colloquium it really was had a a
+ 
+
+ align:start position:0%
+physics colloquium it really was had a a
+a generation long impact on how people
+
+ align:start position:0%
+a generation long impact on how people
+ 
+
+ align:start position:0%
+a generation long impact on how people
+thought of him nonetheless in other
+
+ align:start position:0%
+thought of him nonetheless in other
+ 
+
+ align:start position:0%
+thought of him nonetheless in other
+circles many others couldn't get enough
+
+ align:start position:0%
+circles many others couldn't get enough
+ 
+
+ align:start position:0%
+circles many others couldn't get enough
+and so he he continued to have influence
+
+ align:start position:0%
+and so he he continued to have influence
+ 
+
+ align:start position:0%
+and so he he continued to have influence
+among certain U.S Administrations
+
+ align:start position:0%
+among certain U.S Administrations
+ 
+
+ align:start position:0%
+among certain U.S Administrations
+well past the 80s I mean uh really
+
+ align:start position:0%
+well past the 80s I mean uh really
+ 
+
+ align:start position:0%
+well past the 80s I mean uh really
+decades after uh the 40s and 50s so you
+
+ align:start position:0%
+decades after uh the 40s and 50s so you
+ 
+
+ align:start position:0%
+decades after uh the 40s and 50s so you
+know he he
+
+ align:start position:0%
+know he he
+ 
+
+ align:start position:0%
+know he he
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+it's easy I mean much like it's easy to
+
+ align:start position:0%
+it's easy I mean much like it's easy to
+ 
+
+ align:start position:0%
+it's easy I mean much like it's easy to
+venerate people like Niels Bohr oh World
+
+ align:start position:0%
+venerate people like Niels Bohr oh World
+ 
+
+ align:start position:0%
+venerate people like Niels Bohr oh World
+Government if only he could have carried
+
+ align:start position:0%
+Government if only he could have carried
+ 
+
+ align:start position:0%
+Government if only he could have carried
+the day he was like well I don't think
+
+ align:start position:0%
+the day he was like well I don't think
+ 
+
+ align:start position:0%
+the day he was like well I don't think
+it works that way teller is I think
+
+ align:start position:0%
+it works that way teller is I think
+ 
+
+ align:start position:0%
+it works that way teller is I think
+often vilified Often by the same people
+
+ align:start position:0%
+often vilified Often by the same people
+ 
+
+ align:start position:0%
+often vilified Often by the same people
+who want to see Heroes like Einstein
+
+ align:start position:0%
+who want to see Heroes like Einstein
+ 
+
+ align:start position:0%
+who want to see Heroes like Einstein
+born and Oppenheimer all these people
+
+ align:start position:0%
+born and Oppenheimer all these people
+ 
+
+ align:start position:0%
+born and Oppenheimer all these people
+are complicated and the world is
+
+ align:start position:0%
+are complicated and the world is
+ 
+
+ align:start position:0%
+are complicated and the world is
+complicated and I I don't want to leave
+
+ align:start position:0%
+complicated and I I don't want to leave
+ 
+
+ align:start position:0%
+complicated and I I don't want to leave
+the impression that teller was somehow
+
+ align:start position:0%
+the impression that teller was somehow
+ 
+
+ align:start position:0%
+the impression that teller was somehow
+like a a masterful demon right which
+
+ align:start position:0%
+like a a masterful demon right which
+ 
+
+ align:start position:0%
+like a a masterful demon right which
+he's often been cast as he certainly had
+
+ align:start position:0%
+he's often been cast as he certainly had
+ 
+
+ align:start position:0%
+he's often been cast as he certainly had
+very very different ideas about the
+
+ align:start position:0%
+very very different ideas about the
+ 
+
+ align:start position:0%
+very very different ideas about the
+scientist responsibility and about the
+
+ align:start position:0%
+scientist responsibility and about the
+ 
+
+ align:start position:0%
+scientist responsibility and about the
+geopolitical stature of the U.S
+
+ align:start position:0%
+geopolitical stature of the U.S
+ 
+
+ align:start position:0%
+geopolitical stature of the U.S
+vis-a-vis changes in Europe especially
+
+ align:start position:0%
+vis-a-vis changes in Europe especially
+ 
+
+ align:start position:0%
+vis-a-vis changes in Europe especially
+and he was just dogged I mean he was
+
+ align:start position:0%
+and he was just dogged I mean he was
+ 
+
+ align:start position:0%
+and he was just dogged I mean he was
+just undetervable uh with this kind of
+
+ align:start position:0%
+just undetervable uh with this kind of
+ 
+
+ align:start position:0%
+just undetervable uh with this kind of
+focus on more and more bigger fancy
+
+ align:start position:0%
+focus on more and more bigger fancy
+ 
+
+ align:start position:0%
+focus on more and more bigger fancy
+weapons and let's make them available
+
+ align:start position:0%
+weapons and let's make them available
+ 
+
+ align:start position:0%
+weapons and let's make them available
+you know more and more quickly so that
+
+ align:start position:0%
+you know more and more quickly so that
+ 
+
+ align:start position:0%
+you know more and more quickly so that
+that became the kind of symbol of this
+
+ align:start position:0%
+that became the kind of symbol of this
+ 
+
+ align:start position:0%
+that became the kind of symbol of this
+larger split within the community
+
+ align:start position:0%
+larger split within the community
+ 
+
+ align:start position:0%
+larger split within the community
+uh between the kind of Oppenheimer camp
+
+ align:start position:0%
+uh between the kind of Oppenheimer camp
+ 
+
+ align:start position:0%
+uh between the kind of Oppenheimer camp
+and the teller Camp ironically teller
+
+ align:start position:0%
+and the teller Camp ironically teller
+ 
+
+ align:start position:0%
+and the teller Camp ironically teller
+was being surveilled by the FBI just as
+
+ align:start position:0%
+was being surveilled by the FBI just as
+ 
+
+ align:start position:0%
+was being surveilled by the FBI just as
+much as Oppenheimer was they didn't
+
+ align:start position:0%
+much as Oppenheimer was they didn't
+ 
+
+ align:start position:0%
+much as Oppenheimer was they didn't
+trust this strange weirdo European Jew
+
+ align:start position:0%
+trust this strange weirdo European Jew
+ 
+
+ align:start position:0%
+trust this strange weirdo European Jew
+who is this guy he came from places
+
+ align:start position:0%
+who is this guy he came from places
+ 
+
+ align:start position:0%
+who is this guy he came from places
+where they're Communists I mean the FBI
+
+ align:start position:0%
+where they're Communists I mean the FBI
+ 
+
+ align:start position:0%
+where they're Communists I mean the FBI
+was really an overdrive in this period I
+
+ align:start position:0%
+was really an overdrive in this period I
+ 
+
+ align:start position:0%
+was really an overdrive in this period I
+say chuckling now it wasn't so funny and
+
+ align:start position:0%
+say chuckling now it wasn't so funny and
+ 
+
+ align:start position:0%
+say chuckling now it wasn't so funny and
+there are these amazing passages in his
+
+ align:start position:0%
+there are these amazing passages in his
+ 
+
+ align:start position:0%
+there are these amazing passages in his
+once classified and tellers once
+
+ align:start position:0%
+once classified and tellers once
+ 
+
+ align:start position:0%
+once classified and tellers once
+classified file saying we don't trust
+
+ align:start position:0%
+classified file saying we don't trust
+ 
+
+ align:start position:0%
+classified file saying we don't trust
+this guy we don't know who he's talking
+
+ align:start position:0%
+this guy we don't know who he's talking
+ 
+
+ align:start position:0%
+this guy we don't know who he's talking
+to he's no more trustworthy than
+
+ align:start position:0%
+to he's no more trustworthy than
+ 
+
+ align:start position:0%
+to he's no more trustworthy than
+Oppenheimer so you know it's a kind of
+
+ align:start position:0%
+Oppenheimer so you know it's a kind of
+ 
+
+ align:start position:0%
+Oppenheimer so you know it's a kind of
+I don't want to say it's a shell game
+
+ align:start position:0%
+I don't want to say it's a shell game
+ 
+
+ align:start position:0%
+I don't want to say it's a shell game
+but it wasn't like he was seen as
+
+ align:start position:0%
+but it wasn't like he was seen as
+ 
+
+ align:start position:0%
+but it wasn't like he was seen as
+unproblematic he was seen as someone who
+
+ align:start position:0%
+unproblematic he was seen as someone who
+ 
+
+ align:start position:0%
+unproblematic he was seen as someone who
+said the things that some other powerful
+
+ align:start position:0%
+said the things that some other powerful
+ 
+
+ align:start position:0%
+said the things that some other powerful
+powerful people wanted to hear more at
+
+ align:start position:0%
+powerful people wanted to hear more at
+ 
+
+ align:start position:0%
+powerful people wanted to hear more at
+that time I think I think he was useful
+
+ align:start position:0%
+that time I think I think he was useful
+ 
+
+ align:start position:0%
+that time I think I think he was useful
+as I think he earnestly believed that
+
+ align:start position:0%
+as I think he earnestly believed that
+ 
+
+ align:start position:0%
+as I think he earnestly believed that
+but he was also useful to frankly other
+
+ align:start position:0%
+but he was also useful to frankly other
+ 
+
+ align:start position:0%
+but he was also useful to frankly other
+people who who really did understand a
+
+ align:start position:0%
+people who who really did understand a
+ 
+
+ align:start position:0%
+people who who really did understand a
+bit more of the kind of hard power you
+
+ align:start position:0%
+bit more of the kind of hard power you
+ 
+
+ align:start position:0%
+bit more of the kind of hard power you
+know um
+
+ align:start position:0%
+know um
+ 
+
+ align:start position:0%
+know um
+power plays of of Cold War politics
+
+ align:start position:0%
+power plays of of Cold War politics
+ 
+
+ align:start position:0%
+power plays of of Cold War politics
+so I think told is also has much much
+
+ align:start position:0%
+so I think told is also has much much
+ 
+
+ align:start position:0%
+so I think told is also has much much
+less attention paid to him in the in the
+
+ align:start position:0%
+less attention paid to him in the in the
+ 
+
+ align:start position:0%
+less attention paid to him in the in the
+secondary literature uh even though he
+
+ align:start position:0%
+secondary literature uh even though he
+ 
+
+ align:start position:0%
+secondary literature uh even though he
+lived a much longer life it was involved
+
+ align:start position:0%
+lived a much longer life it was involved
+ 
+
+ align:start position:0%
+lived a much longer life it was involved
+in many more kind of
+
+ align:start position:0%
+in many more kind of
+ 
+
+ align:start position:0%
+in many more kind of
+unusual events
+
+ align:start position:0%
+unusual events
+ 
+
+ align:start position:0%
+unusual events
+um but I I honestly think it's a
+
+ align:start position:0%
+um but I I honestly think it's a
+ 
+
+ align:start position:0%
+um but I I honestly think it's a
+lingering sense that he was somehow just
+
+ align:start position:0%
+lingering sense that he was somehow just
+ 
+
+ align:start position:0%
+lingering sense that he was somehow just
+the bad guy he's been cast I think in a
+
+ align:start position:0%
+the bad guy he's been cast I think in a
+ 
+
+ align:start position:0%
+the bad guy he's been cast I think in a
+kind of one-dimensional role that I that
+
+ align:start position:0%
+kind of one-dimensional role that I that
+ 
+
+ align:start position:0%
+kind of one-dimensional role that I that
+I think you know there's just been less
+
+ align:start position:0%
+I think you know there's just been less
+ 
+
+ align:start position:0%
+I think you know there's just been less
+attention paid to the Nuance that we
+
+ align:start position:0%
+attention paid to the Nuance that we
+ 
+
+ align:start position:0%
+attention paid to the Nuance that we
+might now get to try to do for someone
+
+ align:start position:0%
+might now get to try to do for someone
+ 
+
+ align:start position:0%
+might now get to try to do for someone
+like oppenheim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ER yeah yeah so we'll get we'll get a
+
+ align:start position:0%
+ER yeah yeah so we'll get we'll get a
+ 
+
+ align:start position:0%
+ER yeah yeah so we'll get we'll get a
+little into that it won't be the Chicago
+
+ align:start position:0%
+little into that it won't be the Chicago
+ 
+
+ align:start position:0%
+little into that it won't be the Chicago
+site uh but a little bit of that theme
+
+ align:start position:0%
+site uh but a little bit of that theme
+ 
+
+ align:start position:0%
+site uh but a little bit of that theme
+certainly comes up in the next film
+
+ align:start position:0%
+certainly comes up in the next film
+ 
+
+ align:start position:0%
+certainly comes up in the next film
+we'll watch basically a week from now
+
+ align:start position:0%
+we'll watch basically a week from now
+ 
+
+ align:start position:0%
+we'll watch basically a week from now
+and I'm going to figure out a way to
+
+ align:start position:0%
+and I'm going to figure out a way to
+ 
+
+ align:start position:0%
+and I'm going to figure out a way to
+make sure you can all see it through um
+
+ align:start position:0%
+make sure you can all see it through um
+ 
+
+ align:start position:0%
+make sure you can all see it through um
+the canvas site the film's called
+
+ align:start position:0%
+the canvas site the film's called
+ 
+
+ align:start position:0%
+the canvas site the film's called
+containment I think I mentioned it
+
+ align:start position:0%
+containment I think I mentioned it
+ 
+
+ align:start position:0%
+containment I think I mentioned it
+briefly um by by my friend and colleague
+
+ align:start position:0%
+briefly um by by my friend and colleague
+ 
+
+ align:start position:0%
+briefly um by by my friend and colleague
+and actually my former advisor
+
+ align:start position:0%
+and actually my former advisor
+ 
+
+ align:start position:0%
+and actually my former advisor
+Peter Gallison and some of his
+
+ align:start position:0%
+Peter Gallison and some of his
+ 
+
+ align:start position:0%
+Peter Gallison and some of his
+colleagues so it's much more recent view
+
+ align:start position:0%
+colleagues so it's much more recent view
+ 
+
+ align:start position:0%
+colleagues so it's much more recent view
+of some of the kind of nuclear legacies
+
+ align:start position:0%
+of some of the kind of nuclear legacies
+ 
+
+ align:start position:0%
+of some of the kind of nuclear legacies
+um in particular environmental and
+
+ align:start position:0%
+um in particular environmental and
+ 
+
+ align:start position:0%
+um in particular environmental and
+radiological
+
+ align:start position:0%
+radiological
+ 
+
+ align:start position:0%
+radiological
+um and not just of the wartime but of
+
+ align:start position:0%
+um and not just of the wartime but of
+ 
+
+ align:start position:0%
+um and not just of the wartime but of
+the of the kind of Cold War uh period
+
+ align:start position:0%
+the of the kind of Cold War uh period
+ 
+
+ align:start position:0%
+the of the kind of Cold War uh period
+ever since in some sense still going on
+
+ align:start position:0%
+ever since in some sense still going on
+ 
+
+ align:start position:0%
+ever since in some sense still going on
+so that uh you know how does one handle
+
+ align:start position:0%
+so that uh you know how does one handle
+ 
+
+ align:start position:0%
+so that uh you know how does one handle
+uh waste byproducts of of Civilian
+
+ align:start position:0%
+uh waste byproducts of of Civilian
+ 
+
+ align:start position:0%
+uh waste byproducts of of Civilian
+nuclear power let alone nuclear above
+
+ align:start position:0%
+nuclear power let alone nuclear above
+ 
+
+ align:start position:0%
+nuclear power let alone nuclear above
+ground nuclear testing when some of
+
+ align:start position:0%
+ground nuclear testing when some of
+ 
+
+ align:start position:0%
+ground nuclear testing when some of
+these very very deeply dangerous
+
+ align:start position:0%
+these very very deeply dangerous
+ 
+
+ align:start position:0%
+these very very deeply dangerous
+poisonous Isotopes have half-lives in
+
+ align:start position:0%
+poisonous Isotopes have half-lives in
+ 
+
+ align:start position:0%
+poisonous Isotopes have half-lives in
+the tens or even hundreds of thousands
+
+ align:start position:0%
+the tens or even hundreds of thousands
+ 
+
+ align:start position:0%
+the tens or even hundreds of thousands
+of years so this stuff isn't going away
+
+ align:start position:0%
+of years so this stuff isn't going away
+ 
+
+ align:start position:0%
+of years so this stuff isn't going away
+anytime soon uh to put in mildly and so
+
+ align:start position:0%
+anytime soon uh to put in mildly and so
+ 
+
+ align:start position:0%
+anytime soon uh to put in mildly and so
+that's the kind of thing that that the
+
+ align:start position:0%
+that's the kind of thing that that the
+ 
+
+ align:start position:0%
+that's the kind of thing that that the
+new film The more recent film
+
+ align:start position:0%
+new film The more recent film
+ 
+
+ align:start position:0%
+new film The more recent film
+kind of grapples with and we'll we'll
+
+ align:start position:0%
+kind of grapples with and we'll we'll
+ 
+
+ align:start position:0%
+kind of grapples with and we'll we'll
+watch that and we can have a similar
+
+ align:start position:0%
+watch that and we can have a similar
+ 
+
+ align:start position:0%
+watch that and we can have a similar
+session to talk about it uh next week
+
+ align:start position:0%
+session to talk about it uh next week
+ 
+
+ align:start position:0%
+session to talk about it uh next week
+I'll make sure we all have to
+
+ align:start position:0%
+I'll make sure we all have to
+ 
+
+ align:start position:0%
+I'll make sure we all have to
+details in email but yeah I mean
+
+ align:start position:0%
+details in email but yeah I mean
+ 
+
+ align:start position:0%
+details in email but yeah I mean
+again it's it's one of these things
+
+ align:start position:0%
+again it's it's one of these things
+ 
+
+ align:start position:0%
+again it's it's one of these things
+where people knew better at the time
+
+ align:start position:0%
+where people knew better at the time
+ 
+
+ align:start position:0%
+where people knew better at the time
+they didn't know as much as we know now
+
+ align:start position:0%
+they didn't know as much as we know now
+ 
+
+ align:start position:0%
+they didn't know as much as we know now
+but the the kind of cavalierness or even
+
+ align:start position:0%
+but the the kind of cavalierness or even
+ 
+
+ align:start position:0%
+but the the kind of cavalierness or even
+sometimes callousness I think with which
+
+ align:start position:0%
+sometimes callousness I think with which
+ 
+
+ align:start position:0%
+sometimes callousness I think with which
+some legitimately dangerous materials
+
+ align:start position:0%
+some legitimately dangerous materials
+ 
+
+ align:start position:0%
+some legitimately dangerous materials
+were handled in the 40s and 50s uh it's
+
+ align:start position:0%
+were handled in the 40s and 50s uh it's
+ 
+
+ align:start position:0%
+were handled in the 40s and 50s uh it's
+still um astonishing and it's not
+
+ align:start position:0%
+still um astonishing and it's not
+ 
+
+ align:start position:0%
+still um astonishing and it's not
+good to say the only place that was
+
+ align:start position:0%
+good to say the only place that was
+ 
+
+ align:start position:0%
+good to say the only place that was
+worse was was some parts of the Soviet
+
+ align:start position:0%
+worse was was some parts of the Soviet
+ 
+
+ align:start position:0%
+worse was was some parts of the Soviet
+Union I mean if that's a competition
+
+ align:start position:0%
+Union I mean if that's a competition
+ 
+
+ align:start position:0%
+Union I mean if that's a competition
+that's not great in terms of just the
+
+ align:start position:0%
+that's not great in terms of just the
+ 
+
+ align:start position:0%
+that's not great in terms of just the
+Cavalier uh disregard for local
+
+ align:start position:0%
+Cavalier uh disregard for local
+ 
+
+ align:start position:0%
+Cavalier uh disregard for local
+populations
+
+ align:start position:0%
+populations
+ 
+
+ align:start position:0%
+populations
+um that sort of the only place more
+
+ align:start position:0%
+um that sort of the only place more
+ 
+
+ align:start position:0%
+um that sort of the only place more
+poisonous from nuclear efforts than
+
+ align:start position:0%
+poisonous from nuclear efforts than
+ 
+
+ align:start position:0%
+poisonous from nuclear efforts than
+Hanford is the corresponding site in uh
+
+ align:start position:0%
+Hanford is the corresponding site in uh
+ 
+
+ align:start position:0%
+Hanford is the corresponding site in uh
+I forgot which one it is Tiffany by
+
+ align:start position:0%
+I forgot which one it is Tiffany by
+ 
+
+ align:start position:0%
+I forgot which one it is Tiffany by
+remember but one of these sites within
+
+ align:start position:0%
+remember but one of these sites within
+ 
+
+ align:start position:0%
+remember but one of these sites within
+the former Soviet Union with it also
+
+ align:start position:0%
+the former Soviet Union with it also
+ 
+
+ align:start position:0%
+the former Soviet Union with it also
+been doing enormously large-scale
+
+ align:start position:0%
+been doing enormously large-scale
+ 
+
+ align:start position:0%
+been doing enormously large-scale
+plutonium production so I think things
+
+ align:start position:0%
+plutonium production so I think things
+ 
+
+ align:start position:0%
+plutonium production so I think things
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right in fact my understanding is that
+
+ align:start position:0%
+right in fact my understanding is that
+ 
+
+ align:start position:0%
+right in fact my understanding is that
+he was exposed because he threw himself
+
+ align:start position:0%
+he was exposed because he threw himself
+ 
+
+ align:start position:0%
+he was exposed because he threw himself
+on top of it to knock him apart he
+
+ align:start position:0%
+on top of it to knock him apart he
+ 
+
+ align:start position:0%
+on top of it to knock him apart he
+basically threw like you like a soldier
+
+ align:start position:0%
+basically threw like you like a soldier
+ 
+
+ align:start position:0%
+basically threw like you like a soldier
+went on a grenade or something like that
+
+ align:start position:0%
+went on a grenade or something like that
+ 
+
+ align:start position:0%
+went on a grenade or something like that
+to save you know comrades that he he
+
+ align:start position:0%
+to save you know comrades that he he
+ 
+
+ align:start position:0%
+to save you know comrades that he he
+really threw his body on these now you
+
+ align:start position:0%
+really threw his body on these now you
+ 
+
+ align:start position:0%
+really threw his body on these now you
+know now joined uh um critical mass so
+
+ align:start position:0%
+know now joined uh um critical mass so
+ 
+
+ align:start position:0%
+know now joined uh um critical mass so
+he was so my mentor that I mentioned uh
+
+ align:start position:0%
+he was so my mentor that I mentioned uh
+ 
+
+ align:start position:0%
+he was so my mentor that I mentioned uh
+who had served as a young kid in
+
+ align:start position:0%
+who had served as a young kid in
+ 
+
+ align:start position:0%
+who had served as a young kid in
+Manhattan Project
+
+ align:start position:0%
+Manhattan Project
+ 
+
+ align:start position:0%
+Manhattan Project
+so the rest of his life my teacher wore
+
+ align:start position:0%
+so the rest of his life my teacher wore
+ 
+
+ align:start position:0%
+so the rest of his life my teacher wore
+sloten's belt buckle they've been
+
+ align:start position:0%
+sloten's belt buckle they've been
+ 
+
+ align:start position:0%
+sloten's belt buckle they've been
+buddies they were like total young kids
+
+ align:start position:0%
+buddies they were like total young kids
+ 
+
+ align:start position:0%
+buddies they were like total young kids
+together and uh at Los Alamos
+
+ align:start position:0%
+together and uh at Los Alamos
+ 
+
+ align:start position:0%
+together and uh at Los Alamos
+and slow so the accident happened soon
+
+ align:start position:0%
+and slow so the accident happened soon
+ 
+
+ align:start position:0%
+and slow so the accident happened soon
+after the war like weeks they were still
+
+ align:start position:0%
+after the war like weeks they were still
+ 
+
+ align:start position:0%
+after the war like weeks they were still
+working Full Tilt uh and and Leonard
+
+ align:start position:0%
+working Full Tilt uh and and Leonard
+ 
+
+ align:start position:0%
+working Full Tilt uh and and Leonard
+reason was still there my teacher and so
+
+ align:start position:0%
+reason was still there my teacher and so
+ 
+
+ align:start position:0%
+reason was still there my teacher and so
+uh slogan died within days of the
+
+ align:start position:0%
+uh slogan died within days of the
+ 
+
+ align:start position:0%
+uh slogan died within days of the
+exposure it was a very very intense
+
+ align:start position:0%
+exposure it was a very very intense
+ 
+
+ align:start position:0%
+exposure it was a very very intense
+exposure right in his in his gut which
+
+ align:start position:0%
+exposure right in his in his gut which
+ 
+
+ align:start position:0%
+exposure right in his in his gut which
+is not a good place to absorb lots of
+
+ align:start position:0%
+is not a good place to absorb lots of
+ 
+
+ align:start position:0%
+is not a good place to absorb lots of
+these things uh and so Leonard kept his
+
+ align:start position:0%
+these things uh and so Leonard kept his
+ 
+
+ align:start position:0%
+these things uh and so Leonard kept his
+uh got his belt buckle for the rest of
+
+ align:start position:0%
+uh got his belt buckle for the rest of
+ 
+
+ align:start position:0%
+uh got his belt buckle for the rest of
+his life that I only know the name
+
+ align:start position:0%
+his life that I only know the name
+ 
+
+ align:start position:0%
+his life that I only know the name
+because I heard about it when I was
+
+ align:start position:0%
+because I heard about it when I was
+ 
+
+ align:start position:0%
+because I heard about it when I was
+starting when I was about 18. but but
+
+ align:start position:0%
+starting when I was about 18. but but
+ 
+
+ align:start position:0%
+starting when I was about 18. but but
+but you're right house it's an amazing
+
+ align:start position:0%
+but you're right house it's an amazing
+ 
+
+ align:start position:0%
+but you're right house it's an amazing
+story about talk about Cavalier anything
+
+ align:start position:0%
+story about talk about Cavalier anything
+ 
+
+ align:start position:0%
+story about talk about Cavalier anything
+that like a kind of just shop level
+
+ align:start position:0%
+that like a kind of just shop level
+ 
+
+ align:start position:0%
+that like a kind of just shop level
+safety standards let alone
+
+ align:start position:0%
+safety standards let alone
+ 
+
+ align:start position:0%
+safety standards let alone
+you know treat these stuff treat these
+
+ align:start position:0%
+you know treat these stuff treat these
+ 
+
+ align:start position:0%
+you know treat these stuff treat these
+things with some level of kind of um awe
+
+ align:start position:0%
+things with some level of kind of um awe
+ 
+
+ align:start position:0%
+things with some level of kind of um awe
+and respect because of the forces of
+
+ align:start position:0%
+and respect because of the forces of
+ 
+
+ align:start position:0%
+and respect because of the forces of
+nature but just like don't prop stuff
+
+ align:start position:0%
+nature but just like don't prop stuff
+ 
+
+ align:start position:0%
+nature but just like don't prop stuff
+over with a screwdriver like come on you
+
+ align:start position:0%
+over with a screwdriver like come on you
+ 
+
+ align:start position:0%
+over with a screwdriver like come on you
+know just basic level of machine shop
+
+ align:start position:0%
+know just basic level of machine shop
+ 
+
+ align:start position:0%
+know just basic level of machine shop
+let alone uh Safe Handling of of nuclear
+
+ align:start position:0%
+let alone uh Safe Handling of of nuclear
+ 
+
+ align:start position:0%
+let alone uh Safe Handling of of nuclear
+materials so that does great that's
+
+ align:start position:0%
+materials so that does great that's
+ 
+
+ align:start position:0%
+materials so that does great that's
+another great example
+
+ align:start position:0%
+another great example
+ 
+
+ align:start position:0%
+another great example
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+any other questions these are great
+
+ align:start position:0%
+any other questions these are great
+ 
+
+ align:start position:0%
+any other questions these are great
+topics great questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it was it was definitely after it's a
+
+ align:start position:0%
+no it was it was definitely after it's a
+ 
+
+ align:start position:0%
+no it was it was definitely after it's a
+good question because I don't know the
+
+ align:start position:0%
+good question because I don't know the
+ 
+
+ align:start position:0%
+good question because I don't know the
+fine to tell some of the Tas might
+
+ align:start position:0%
+fine to tell some of the Tas might
+ 
+
+ align:start position:0%
+fine to tell some of the Tas might
+remember better from recent readings the
+
+ align:start position:0%
+remember better from recent readings the
+ 
+
+ align:start position:0%
+remember better from recent readings the
+rough story goes like this so there was
+
+ align:start position:0%
+rough story goes like this so there was
+ 
+
+ align:start position:0%
+rough story goes like this so there was
+um the soon after the end of the war and
+
+ align:start position:0%
+um the soon after the end of the war and
+ 
+
+ align:start position:0%
+um the soon after the end of the war and
+I guess I'll talk about this briefly on
+
+ align:start position:0%
+I guess I'll talk about this briefly on
+ 
+
+ align:start position:0%
+I guess I'll talk about this briefly on
+Wednesday
+
+ align:start position:0%
+Wednesday
+ 
+
+ align:start position:0%
+Wednesday
+um by I was signed into law I think
+
+ align:start position:0%
+um by I was signed into law I think
+ 
+
+ align:start position:0%
+um by I was signed into law I think
+August of 46 so
+
+ align:start position:0%
+August of 46 so
+ 
+
+ align:start position:0%
+August of 46 so
+roughly a year after after Japanese
+
+ align:start position:0%
+roughly a year after after Japanese
+ 
+
+ align:start position:0%
+roughly a year after after Japanese
+surrender the U.S passed the atomic
+
+ align:start position:0%
+surrender the U.S passed the atomic
+ 
+
+ align:start position:0%
+surrender the U.S passed the atomic
+energy Act uh and that was a sprawling
+
+ align:start position:0%
+energy Act uh and that was a sprawling
+ 
+
+ align:start position:0%
+energy Act uh and that was a sprawling
+piece of legislation that established
+
+ align:start position:0%
+piece of legislation that established
+ 
+
+ align:start position:0%
+piece of legislation that established
+the successor agency to the wartime
+
+ align:start position:0%
+the successor agency to the wartime
+ 
+
+ align:start position:0%
+the successor agency to the wartime
+Manhattan Project nominally civilian it
+
+ align:start position:0%
+Manhattan Project nominally civilian it
+ 
+
+ align:start position:0%
+Manhattan Project nominally civilian it
+it created what was called the atomic
+
+ align:start position:0%
+it created what was called the atomic
+ 
+
+ align:start position:0%
+it created what was called the atomic
+energy commission the aec
+
+ align:start position:0%
+energy commission the aec
+ 
+
+ align:start position:0%
+energy commission the aec
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh thank you and um and uh but it also
+
+ align:start position:0%
+uh thank you and um and uh but it also
+ 
+
+ align:start position:0%
+uh thank you and um and uh but it also
+made all things related to nuclear
+
+ align:start position:0%
+made all things related to nuclear
+ 
+
+ align:start position:0%
+made all things related to nuclear
+power born secret and and subject only
+
+ align:start position:0%
+power born secret and and subject only
+ 
+
+ align:start position:0%
+power born secret and and subject only
+basically to military or official
+
+ align:start position:0%
+basically to military or official
+ 
+
+ align:start position:0%
+basically to military or official
+government control in the U.S so it had
+
+ align:start position:0%
+government control in the U.S so it had
+ 
+
+ align:start position:0%
+government control in the U.S so it had
+a a kind of unintended consequence of
+
+ align:start position:0%
+a a kind of unintended consequence of
+ 
+
+ align:start position:0%
+a a kind of unintended consequence of
+hugely stifling a kind of private sector
+
+ align:start position:0%
+hugely stifling a kind of private sector
+ 
+
+ align:start position:0%
+hugely stifling a kind of private sector
+development of energy of of energy
+
+ align:start position:0%
+development of energy of of energy
+ 
+
+ align:start position:0%
+development of energy of of energy
+generation of reactors
+
+ align:start position:0%
+generation of reactors
+ 
+
+ align:start position:0%
+generation of reactors
+that was then uh amended a big Amendment
+
+ align:start position:0%
+that was then uh amended a big Amendment
+ 
+
+ align:start position:0%
+that was then uh amended a big Amendment
+to the atomic energy act and I think 53
+
+ align:start position:0%
+to the atomic energy act and I think 53
+ 
+
+ align:start position:0%
+to the atomic energy act and I think 53
+again others on the column I remember I
+
+ align:start position:0%
+again others on the column I remember I
+ 
+
+ align:start position:0%
+again others on the column I remember I
+think it's 1953.
+
+ align:start position:0%
+think it's 1953.
+ 
+
+ align:start position:0%
+think it's 1953.
+which which began to make certain kinds
+
+ align:start position:0%
+which which began to make certain kinds
+ 
+
+ align:start position:0%
+which which began to make certain kinds
+of we might call it private private
+
+ align:start position:0%
+of we might call it private private
+ 
+
+ align:start position:0%
+of we might call it private private
+Public Partnerships a kind of limited
+
+ align:start position:0%
+Public Partnerships a kind of limited
+ 
+
+ align:start position:0%
+Public Partnerships a kind of limited
+entrepreneurship possible in the power
+
+ align:start position:0%
+entrepreneurship possible in the power
+ 
+
+ align:start position:0%
+entrepreneurship possible in the power
+generation Market it still wasn't a free
+
+ align:start position:0%
+generation Market it still wasn't a free
+ 
+
+ align:start position:0%
+generation Market it still wasn't a free
+market but it was no longer a felony to
+
+ align:start position:0%
+market but it was no longer a felony to
+ 
+
+ align:start position:0%
+market but it was no longer a felony to
+to share certain kinds of you know
+
+ align:start position:0%
+to share certain kinds of you know
+ 
+
+ align:start position:0%
+to share certain kinds of you know
+documents of otherwise innocuous
+
+ align:start position:0%
+documents of otherwise innocuous
+ 
+
+ align:start position:0%
+documents of otherwise innocuous
+information seemingly innocuous not with
+
+ align:start position:0%
+information seemingly innocuous not with
+ 
+
+ align:start position:0%
+information seemingly innocuous not with
+no no kind of direct weapons potential
+
+ align:start position:0%
+no no kind of direct weapons potential
+ 
+
+ align:start position:0%
+no no kind of direct weapons potential
+so it starts you start getting a more
+
+ align:start position:0%
+so it starts you start getting a more
+ 
+
+ align:start position:0%
+so it starts you start getting a more
+active
+
+ align:start position:0%
+active
+ 
+
+ align:start position:0%
+active
+um kind of uh
+
+ align:start position:0%
+um kind of uh
+ 
+
+ align:start position:0%
+um kind of uh
+what's the word active um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry uh you know trying to build up a
+
+ align:start position:0%
+sorry uh you know trying to build up a
+ 
+
+ align:start position:0%
+sorry uh you know trying to build up a
+kind of uh working quasi-market private
+
+ align:start position:0%
+kind of uh working quasi-market private
+ 
+
+ align:start position:0%
+kind of uh working quasi-market private
+public partnership with major industrial
+
+ align:start position:0%
+public partnership with major industrial
+ 
+
+ align:start position:0%
+public partnership with major industrial
+contractors like General Electric like
+
+ align:start position:0%
+contractors like General Electric like
+ 
+
+ align:start position:0%
+contractors like General Electric like
+Westinghouse uh building
+
+ align:start position:0%
+Westinghouse uh building
+ 
+
+ align:start position:0%
+Westinghouse uh building
+um uh commercial react power reactors by
+
+ align:start position:0%
+um uh commercial react power reactors by
+ 
+
+ align:start position:0%
+um uh commercial react power reactors by
+the mid to late 50s it doesn't take off
+
+ align:start position:0%
+the mid to late 50s it doesn't take off
+ 
+
+ align:start position:0%
+the mid to late 50s it doesn't take off
+the way other new technologies you know
+
+ align:start position:0%
+the way other new technologies you know
+ 
+
+ align:start position:0%
+the way other new technologies you know
+have done in history because it still
+
+ align:start position:0%
+have done in history because it still
+ 
+
+ align:start position:0%
+have done in history because it still
+has a lot of um a lingering period of
+
+ align:start position:0%
+has a lot of um a lingering period of
+ 
+
+ align:start position:0%
+has a lot of um a lingering period of
+not clear quite how to get this right uh
+
+ align:start position:0%
+not clear quite how to get this right uh
+ 
+
+ align:start position:0%
+not clear quite how to get this right uh
+so so over the course of 50s there were
+
+ align:start position:0%
+so so over the course of 50s there were
+ 
+
+ align:start position:0%
+so so over the course of 50s there were
+power reactors actually coming online uh
+
+ align:start position:0%
+power reactors actually coming online uh
+ 
+
+ align:start position:0%
+power reactors actually coming online uh
+shipping Port News I think was the first
+
+ align:start position:0%
+shipping Port News I think was the first
+ 
+
+ align:start position:0%
+shipping Port News I think was the first
+or among the most famous somewhere in
+
+ align:start position:0%
+or among the most famous somewhere in
+ 
+
+ align:start position:0%
+or among the most famous somewhere in
+Pennsylvania for example
+
+ align:start position:0%
+Pennsylvania for example
+ 
+
+ align:start position:0%
+Pennsylvania for example
+um so they didn't become ubiquitous
+
+ align:start position:0%
+um so they didn't become ubiquitous
+ 
+
+ align:start position:0%
+um so they didn't become ubiquitous
+right away but they were coming into
+
+ align:start position:0%
+right away but they were coming into
+ 
+
+ align:start position:0%
+right away but they were coming into
+genuine civilian use you know in the
+
+ align:start position:0%
+genuine civilian use you know in the
+ 
+
+ align:start position:0%
+genuine civilian use you know in the
+outs groups of populated areas uh by the
+
+ align:start position:0%
+outs groups of populated areas uh by the
+ 
+
+ align:start position:0%
+outs groups of populated areas uh by the
+end of the 1950s for the submarines and
+
+ align:start position:0%
+end of the 1950s for the submarines and
+ 
+
+ align:start position:0%
+end of the 1950s for the submarines and
+things that was again I think a mid to
+
+ align:start position:0%
+things that was again I think a mid to
+ 
+
+ align:start position:0%
+things that was again I think a mid to
+late 50s development uh Admiral rickover
+
+ align:start position:0%
+late 50s development uh Admiral rickover
+ 
+
+ align:start position:0%
+late 50s development uh Admiral rickover
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Hyman rickover was I think the main
+
+ align:start position:0%
+Hyman rickover was I think the main
+ 
+
+ align:start position:0%
+Hyman rickover was I think the main
+moving force behind trying to um what
+
+ align:start position:0%
+moving force behind trying to um what
+ 
+
+ align:start position:0%
+moving force behind trying to um what
+was often called modernize the naval
+
+ align:start position:0%
+was often called modernize the naval
+ 
+
+ align:start position:0%
+was often called modernize the naval
+fleet including making uh reactor driven
+
+ align:start position:0%
+fleet including making uh reactor driven
+ 
+
+ align:start position:0%
+fleet including making uh reactor driven
+submarines that could stay underwater
+
+ align:start position:0%
+submarines that could stay underwater
+ 
+
+ align:start position:0%
+submarines that could stay underwater
+much longer for example let alone armed
+
+ align:start position:0%
+much longer for example let alone armed
+ 
+
+ align:start position:0%
+much longer for example let alone armed
+with nuclear weapons but just could
+
+ align:start position:0%
+with nuclear weapons but just could
+ 
+
+ align:start position:0%
+with nuclear weapons but just could
+could the could the power come largely
+
+ align:start position:0%
+could the could the power come largely
+ 
+
+ align:start position:0%
+could the could the power come largely
+from nuclear reactors on board uh for
+
+ align:start position:0%
+from nuclear reactors on board uh for
+ 
+
+ align:start position:0%
+from nuclear reactors on board uh for
+kind of strategic reasons wouldn't have
+
+ align:start position:0%
+kind of strategic reasons wouldn't have
+ 
+
+ align:start position:0%
+kind of strategic reasons wouldn't have
+to surface as frequently or things like
+
+ align:start position:0%
+to surface as frequently or things like
+ 
+
+ align:start position:0%
+to surface as frequently or things like
+that so again I think those are being
+
+ align:start position:0%
+that so again I think those are being
+ 
+
+ align:start position:0%
+that so again I think those are being
+developed largely uh in uh within the
+
+ align:start position:0%
+developed largely uh in uh within the
+ 
+
+ align:start position:0%
+developed largely uh in uh within the
+military so it didn't have the same kind
+
+ align:start position:0%
+military so it didn't have the same kind
+ 
+
+ align:start position:0%
+military so it didn't have the same kind
+of public private same level uh of of
+
+ align:start position:0%
+of public private same level uh of of
+ 
+
+ align:start position:0%
+of public private same level uh of of
+um friction but those were being again I
+
+ align:start position:0%
+um friction but those were being again I
+ 
+
+ align:start position:0%
+um friction but those were being again I
+don't know when the first one came into
+
+ align:start position:0%
+don't know when the first one came into
+ 
+
+ align:start position:0%
+don't know when the first one came into
+service probably by the early 60s at the
+
+ align:start position:0%
+service probably by the early 60s at the
+ 
+
+ align:start position:0%
+service probably by the early 60s at the
+latest certainly under active
+
+ align:start position:0%
+latest certainly under active
+ 
+
+ align:start position:0%
+latest certainly under active
+development and testing by the 50s late
+
+ align:start position:0%
+development and testing by the 50s late
+ 
+
+ align:start position:0%
+development and testing by the 50s late
+50s
+
+ align:start position:0%
+50s
+ 
+
+ align:start position:0%
+50s
+um and as we'll see in in Wednesday's
+
+ align:start position:0%
+um and as we'll see in in Wednesday's
+ 
+
+ align:start position:0%
+um and as we'll see in in Wednesday's
+class this also begins to coincide with
+
+ align:start position:0%
+class this also begins to coincide with
+ 
+
+ align:start position:0%
+class this also begins to coincide with
+growing concerns about
+
+ align:start position:0%
+growing concerns about
+ 
+
+ align:start position:0%
+growing concerns about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+about Fallout so about above ground
+
+ align:start position:0%
+about Fallout so about above ground
+ 
+
+ align:start position:0%
+about Fallout so about above ground
+nuclear weapons testing concerns about
+
+ align:start position:0%
+nuclear weapons testing concerns about
+ 
+
+ align:start position:0%
+nuclear weapons testing concerns about
+safety or otherwise of nuclear power
+
+ align:start position:0%
+safety or otherwise of nuclear power
+ 
+
+ align:start position:0%
+safety or otherwise of nuclear power
+generation uh was not the first topic of
+
+ align:start position:0%
+generation uh was not the first topic of
+ 
+
+ align:start position:0%
+generation uh was not the first topic of
+real kind of public consternation or or
+
+ align:start position:0%
+real kind of public consternation or or
+ 
+
+ align:start position:0%
+real kind of public consternation or or
+debate it really was about the Fallout
+
+ align:start position:0%
+debate it really was about the Fallout
+ 
+
+ align:start position:0%
+debate it really was about the Fallout
+coming back to questions that Stephen
+
+ align:start position:0%
+coming back to questions that Stephen
+ 
+
+ align:start position:0%
+coming back to questions that Stephen
+was asking earlier what happens when you
+
+ align:start position:0%
+was asking earlier what happens when you
+ 
+
+ align:start position:0%
+was asking earlier what happens when you
+blow a bunch of things of these things
+
+ align:start position:0%
+blow a bunch of things of these things
+ 
+
+ align:start position:0%
+blow a bunch of things of these things
+up in the atmosphere and stuff comes
+
+ align:start position:0%
+up in the atmosphere and stuff comes
+ 
+
+ align:start position:0%
+up in the atmosphere and stuff comes
+down uh and so we will hear a bit about
+
+ align:start position:0%
+down uh and so we will hear a bit about
+ 
+
+ align:start position:0%
+down uh and so we will hear a bit about
+that in Wednesday's class so so the
+
+ align:start position:0%
+that in Wednesday's class so so the
+ 
+
+ align:start position:0%
+that in Wednesday's class so so the
+first public efforts uh first widespread
+
+ align:start position:0%
+first public efforts uh first widespread
+ 
+
+ align:start position:0%
+first public efforts uh first widespread
+kind of anti-nuclear mobilizations
+
+ align:start position:0%
+kind of anti-nuclear mobilizations
+ 
+
+ align:start position:0%
+kind of anti-nuclear mobilizations
+we're really also starting by the late
+
+ align:start position:0%
+we're really also starting by the late
+ 
+
+ align:start position:0%
+we're really also starting by the late
+50s uh and they had these kind of fits
+
+ align:start position:0%
+50s uh and they had these kind of fits
+ 
+
+ align:start position:0%
+50s uh and they had these kind of fits
+and starts of temporarily successful
+
+ align:start position:0%
+and starts of temporarily successful
+ 
+
+ align:start position:0%
+and starts of temporarily successful
+treaties that would stop and then they'd
+
+ align:start position:0%
+treaties that would stop and then they'd
+ 
+
+ align:start position:0%
+treaties that would stop and then they'd
+go back and so so a lot of the kind of
+
+ align:start position:0%
+go back and so so a lot of the kind of
+ 
+
+ align:start position:0%
+go back and so so a lot of the kind of
+official um treaty space as well as more
+
+ align:start position:0%
+official um treaty space as well as more
+ 
+
+ align:start position:0%
+official um treaty space as well as more
+informal political organizing against
+
+ align:start position:0%
+informal political organizing against
+ 
+
+ align:start position:0%
+informal political organizing against
+certain aspects of nuclear uh
+
+ align:start position:0%
+certain aspects of nuclear uh
+ 
+
+ align:start position:0%
+certain aspects of nuclear uh
+Technologies now it's also growing over
+
+ align:start position:0%
+Technologies now it's also growing over
+ 
+
+ align:start position:0%
+Technologies now it's also growing over
+the course of 50s into the 1960s they've
+
+ align:start position:0%
+the course of 50s into the 1960s they've
+ 
+
+ align:start position:0%
+the course of 50s into the 1960s they've
+kind of grown up together
+
+ align:start position:0%
+kind of grown up together
+ 
+
+ align:start position:0%
+kind of grown up together
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+there were efforts by the way throughout
+
+ align:start position:0%
+there were efforts by the way throughout
+ 
+
+ align:start position:0%
+there were efforts by the way throughout
+the early and mid 50s to try to Modern
+
+ align:start position:0%
+the early and mid 50s to try to Modern
+ 
+
+ align:start position:0%
+the early and mid 50s to try to Modern
+so-called modernize the weapons side so
+
+ align:start position:0%
+so-called modernize the weapons side so
+ 
+
+ align:start position:0%
+so-called modernize the weapons side so
+to shrink down so both to make
+
+ align:start position:0%
+to shrink down so both to make
+ 
+
+ align:start position:0%
+to shrink down so both to make
+enormously humongous hydrogen weapons
+
+ align:start position:0%
+enormously humongous hydrogen weapons
+ 
+
+ align:start position:0%
+enormously humongous hydrogen weapons
+that were thousands as many thousands of
+
+ align:start position:0%
+that were thousands as many thousands of
+ 
+
+ align:start position:0%
+that were thousands as many thousands of
+times more powerful than the fission
+
+ align:start position:0%
+times more powerful than the fission
+ 
+
+ align:start position:0%
+times more powerful than the fission
+bombs of the war of the second world war
+
+ align:start position:0%
+bombs of the war of the second world war
+ 
+
+ align:start position:0%
+bombs of the war of the second world war
+but also to miniaturize them so that
+
+ align:start position:0%
+but also to miniaturize them so that
+ 
+
+ align:start position:0%
+but also to miniaturize them so that
+they would be more likely to be useful
+
+ align:start position:0%
+they would be more likely to be useful
+ 
+
+ align:start position:0%
+they would be more likely to be useful
+tactically not strategically
+
+ align:start position:0%
+tactically not strategically
+ 
+
+ align:start position:0%
+tactically not strategically
+strategically was the was the lingo
+
+ align:start position:0%
+strategically was the was the lingo
+ 
+
+ align:start position:0%
+strategically was the was the lingo
+Lucas you might know from talking with
+
+ align:start position:0%
+Lucas you might know from talking with
+ 
+
+ align:start position:0%
+Lucas you might know from talking with
+the folks in security studies strategic
+
+ align:start position:0%
+the folks in security studies strategic
+ 
+
+ align:start position:0%
+the folks in security studies strategic
+is the idea that is it based roughly
+
+ align:start position:0%
+is the idea that is it based roughly
+ 
+
+ align:start position:0%
+is the idea that is it based roughly
+speaking kind of symbolic would would it
+
+ align:start position:0%
+speaking kind of symbolic would would it
+ 
+
+ align:start position:0%
+speaking kind of symbolic would would it
+be impossible for any enemy to attack
+
+ align:start position:0%
+be impossible for any enemy to attack
+ 
+
+ align:start position:0%
+be impossible for any enemy to attack
+you because it could they be assured of
+
+ align:start position:0%
+you because it could they be assured of
+ 
+
+ align:start position:0%
+you because it could they be assured of
+immediate Annihilation because you have
+
+ align:start position:0%
+immediate Annihilation because you have
+ 
+
+ align:start position:0%
+immediate Annihilation because you have
+City leveling Megaton bombs so that was
+
+ align:start position:0%
+City leveling Megaton bombs so that was
+ 
+
+ align:start position:0%
+City leveling Megaton bombs so that was
+seen as strategic to have a kind of
+
+ align:start position:0%
+seen as strategic to have a kind of
+ 
+
+ align:start position:0%
+seen as strategic to have a kind of
+unsteady balance of power because no one
+
+ align:start position:0%
+unsteady balance of power because no one
+ 
+
+ align:start position:0%
+unsteady balance of power because no one
+would be dumb enough to trigger those
+
+ align:start position:0%
+would be dumb enough to trigger those
+ 
+
+ align:start position:0%
+would be dumb enough to trigger those
+enormous things for use then there's
+
+ align:start position:0%
+enormous things for use then there's
+ 
+
+ align:start position:0%
+enormous things for use then there's
+tactical weapons that people might
+
+ align:start position:0%
+tactical weapons that people might
+ 
+
+ align:start position:0%
+tactical weapons that people might
+actually plausibly use on a battlefield
+
+ align:start position:0%
+actually plausibly use on a battlefield
+ 
+
+ align:start position:0%
+actually plausibly use on a battlefield
+without the kind of you know high level
+
+ align:start position:0%
+without the kind of you know high level
+ 
+
+ align:start position:0%
+without the kind of you know high level
+uh uh hand ringing about oh my goodness
+
+ align:start position:0%
+uh uh hand ringing about oh my goodness
+ 
+
+ align:start position:0%
+uh uh hand ringing about oh my goodness
+it's Mega tonnage so people were making
+
+ align:start position:0%
+it's Mega tonnage so people were making
+ 
+
+ align:start position:0%
+it's Mega tonnage so people were making
+so-called Davy Crockett basically like
+
+ align:start position:0%
+so-called Davy Crockett basically like
+ 
+
+ align:start position:0%
+so-called Davy Crockett basically like
+shoulder-fired bazooka-sized nuclear
+
+ align:start position:0%
+shoulder-fired bazooka-sized nuclear
+ 
+
+ align:start position:0%
+shoulder-fired bazooka-sized nuclear
+weapons which were actually developed
+
+ align:start position:0%
+weapons which were actually developed
+ 
+
+ align:start position:0%
+weapons which were actually developed
+and deployed in the field technically
+
+ align:start position:0%
+and deployed in the field technically
+ 
+
+ align:start position:0%
+and deployed in the field technically
+never used but but certainly tested so
+
+ align:start position:0%
+never used but but certainly tested so
+ 
+
+ align:start position:0%
+never used but but certainly tested so
+those are both a miniaturization to make
+
+ align:start position:0%
+those are both a miniaturization to make
+ 
+
+ align:start position:0%
+those are both a miniaturization to make
+these things more ubiquitous in certain
+
+ align:start position:0%
+these things more ubiquitous in certain
+ 
+
+ align:start position:0%
+these things more ubiquitous in certain
+kinds of of uh tactical U.S military
+
+ align:start position:0%
+kinds of of uh tactical U.S military
+ 
+
+ align:start position:0%
+kinds of of uh tactical U.S military
+planning not only us but including West
+
+ align:start position:0%
+planning not only us but including West
+ 
+
+ align:start position:0%
+planning not only us but including West
+and then the kind of enormity the kind
+
+ align:start position:0%
+and then the kind of enormity the kind
+ 
+
+ align:start position:0%
+and then the kind of enormity the kind
+of monsters that will that that we'll
+
+ align:start position:0%
+of monsters that will that that we'll
+ 
+
+ align:start position:0%
+of monsters that will that that we'll
+talk a bit about uh in next class that
+
+ align:start position:0%
+talk a bit about uh in next class that
+ 
+
+ align:start position:0%
+talk a bit about uh in next class that
+were really um you know just made the
+
+ align:start position:0%
+were really um you know just made the
+ 
+
+ align:start position:0%
+were really um you know just made the
+the Hiroshima Nagasaki weapons look look
+
+ align:start position:0%
+the Hiroshima Nagasaki weapons look look
+ 
+
+ align:start position:0%
+the Hiroshima Nagasaki weapons look look
+small it was both these kind of fronts
+
+ align:start position:0%
+small it was both these kind of fronts
+ 
+
+ align:start position:0%
+small it was both these kind of fronts
+of development on the on the more
+
+ align:start position:0%
+of development on the on the more
+ 
+
+ align:start position:0%
+of development on the on the more
+weapons technology sides those were
+
+ align:start position:0%
+weapons technology sides those were
+ 
+
+ align:start position:0%
+weapons technology sides those were
+actively under under development
+
+ align:start position:0%
+actively under under development
+ 
+
+ align:start position:0%
+actively under under development
+throughout the 50s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah no that absolutely right and again
+
+ align:start position:0%
+yeah no that absolutely right and again
+ 
+
+ align:start position:0%
+yeah no that absolutely right and again
+we think back to that and yet that was
+
+ align:start position:0%
+we think back to that and yet that was
+ 
+
+ align:start position:0%
+we think back to that and yet that was
+not a sufficient to end the program much
+
+ align:start position:0%
+not a sufficient to end the program much
+ 
+
+ align:start position:0%
+not a sufficient to end the program much
+as the fact that poison gas first
+
+ align:start position:0%
+as the fact that poison gas first
+ 
+
+ align:start position:0%
+as the fact that poison gas first
+deployed in the first world war also you
+
+ align:start position:0%
+deployed in the first world war also you
+ 
+
+ align:start position:0%
+deployed in the first world war also you
+know the winds would change and you
+
+ align:start position:0%
+know the winds would change and you
+ 
+
+ align:start position:0%
+know the winds would change and you
+would not infrequently wound up casting
+
+ align:start position:0%
+would not infrequently wound up casting
+ 
+
+ align:start position:0%
+would not infrequently wound up casting
+your own troops inadvertently so the the
+
+ align:start position:0%
+your own troops inadvertently so the the
+ 
+
+ align:start position:0%
+your own troops inadvertently so the the
+the competing
+
+ align:start position:0%
+the competing
+ 
+
+ align:start position:0%
+the competing
+calculations about what's going to be a
+
+ align:start position:0%
+calculations about what's going to be a
+ 
+
+ align:start position:0%
+calculations about what's going to be a
+worthwhile device to to pursue uh
+
+ align:start position:0%
+worthwhile device to to pursue uh
+ 
+
+ align:start position:0%
+worthwhile device to to pursue uh
+unfortunately that was not unique either
+
+ align:start position:0%
+unfortunately that was not unique either
+ 
+
+ align:start position:0%
+unfortunately that was not unique either
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it's an idea that that so it comes
+
+ align:start position:0%
+yes it's an idea that that so it comes
+ 
+
+ align:start position:0%
+yes it's an idea that that so it comes
+and goes uh as as many of you may know
+
+ align:start position:0%
+and goes uh as as many of you may know
+ 
+
+ align:start position:0%
+and goes uh as as many of you may know
+where the US is for the time being uh is
+
+ align:start position:0%
+where the US is for the time being uh is
+ 
+
+ align:start position:0%
+where the US is for the time being uh is
+still subject to a um a Limited Test Ban
+
+ align:start position:0%
+still subject to a um a Limited Test Ban
+ 
+
+ align:start position:0%
+still subject to a um a Limited Test Ban
+Treaty which suggests that there can be
+
+ align:start position:0%
+Treaty which suggests that there can be
+ 
+
+ align:start position:0%
+Treaty which suggests that there can be
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I'm getting the wrong trade actually
+
+ align:start position:0%
+I'm getting the wrong trade actually
+ 
+
+ align:start position:0%
+I'm getting the wrong trade actually
+more recent treaty there was a a more
+
+ align:start position:0%
+more recent treaty there was a a more
+ 
+
+ align:start position:0%
+more recent treaty there was a a more
+complete test Bantry the U.S signed
+
+ align:start position:0%
+complete test Bantry the U.S signed
+ 
+
+ align:start position:0%
+complete test Bantry the U.S signed
+starting in 1992 was one of the last
+
+ align:start position:0%
+starting in 1992 was one of the last
+ 
+
+ align:start position:0%
+starting in 1992 was one of the last
+things that President George H.W bush
+
+ align:start position:0%
+things that President George H.W bush
+ 
+
+ align:start position:0%
+things that President George H.W bush
+signed uh before uh the before the
+
+ align:start position:0%
+signed uh before uh the before the
+ 
+
+ align:start position:0%
+signed uh before uh the before the
+Clinton administration
+
+ align:start position:0%
+Clinton administration
+ 
+
+ align:start position:0%
+Clinton administration
+so the U.S presently by our by treaty
+
+ align:start position:0%
+so the U.S presently by our by treaty
+ 
+
+ align:start position:0%
+so the U.S presently by our by treaty
+statute is not allowed to test new
+
+ align:start position:0%
+statute is not allowed to test new
+ 
+
+ align:start position:0%
+statute is not allowed to test new
+nuclear weapon designs and that led to
+
+ align:start position:0%
+nuclear weapon designs and that led to
+ 
+
+ align:start position:0%
+nuclear weapon designs and that led to
+an enormous multi-billion dollar project
+
+ align:start position:0%
+an enormous multi-billion dollar project
+ 
+
+ align:start position:0%
+an enormous multi-billion dollar project
+called stockpile stewardship to so there
+
+ align:start position:0%
+called stockpile stewardship to so there
+ 
+
+ align:start position:0%
+called stockpile stewardship to so there
+was testing allowed non-nuclear tests
+
+ align:start position:0%
+was testing allowed non-nuclear tests
+ 
+
+ align:start position:0%
+was testing allowed non-nuclear tests
+allowed to be performed to to maintain
+
+ align:start position:0%
+allowed to be performed to to maintain
+ 
+
+ align:start position:0%
+allowed to be performed to to maintain
+the Aging stock stockpiles of existing
+
+ align:start position:0%
+the Aging stock stockpiles of existing
+ 
+
+ align:start position:0%
+the Aging stock stockpiles of existing
+weapons epoxies dry out and change you
+
+ align:start position:0%
+weapons epoxies dry out and change you
+ 
+
+ align:start position:0%
+weapons epoxies dry out and change you
+know all the kind of convention
+
+ align:start position:0%
+know all the kind of convention
+ 
+
+ align:start position:0%
+know all the kind of convention
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+um don't have a shelf life of 10 000
+
+ align:start position:0%
+um don't have a shelf life of 10 000
+ 
+
+ align:start position:0%
+um don't have a shelf life of 10 000
+years so stockpile stewardship is meant
+
+ align:start position:0%
+years so stockpile stewardship is meant
+ 
+
+ align:start position:0%
+years so stockpile stewardship is meant
+to enable laboratory style testing for
+
+ align:start position:0%
+to enable laboratory style testing for
+ 
+
+ align:start position:0%
+to enable laboratory style testing for
+materials to maintain the existing
+
+ align:start position:0%
+materials to maintain the existing
+ 
+
+ align:start position:0%
+materials to maintain the existing
+Arsenal not to develop and perfect new
+
+ align:start position:0%
+Arsenal not to develop and perfect new
+ 
+
+ align:start position:0%
+Arsenal not to develop and perfect new
+weapons and so some of these areas get a
+
+ align:start position:0%
+weapons and so some of these areas get a
+ 
+
+ align:start position:0%
+weapons and so some of these areas get a
+little some critics at least say there's
+
+ align:start position:0%
+little some critics at least say there's
+ 
+
+ align:start position:0%
+little some critics at least say there's
+a little gray area some things that some
+
+ align:start position:0%
+a little gray area some things that some
+ 
+
+ align:start position:0%
+a little gray area some things that some
+people will say are being used for
+
+ align:start position:0%
+people will say are being used for
+ 
+
+ align:start position:0%
+people will say are being used for
+stockpiled stewardship might actually
+
+ align:start position:0%
+stockpiled stewardship might actually
+ 
+
+ align:start position:0%
+stockpiled stewardship might actually
+have implications to help with new
+
+ align:start position:0%
+have implications to help with new
+ 
+
+ align:start position:0%
+have implications to help with new
+designs it's again it it's an area where
+
+ align:start position:0%
+designs it's again it it's an area where
+ 
+
+ align:start position:0%
+designs it's again it it's an area where
+there's ongoing um debate and pushback
+
+ align:start position:0%
+there's ongoing um debate and pushback
+ 
+
+ align:start position:0%
+there's ongoing um debate and pushback
+largely uh you know away from Full
+
+ align:start position:0%
+largely uh you know away from Full
+ 
+
+ align:start position:0%
+largely uh you know away from Full
+public view because some of much of it
+
+ align:start position:0%
+public view because some of much of it
+ 
+
+ align:start position:0%
+public view because some of much of it
+Still Remains classified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah Amanda I agree that is a chilling
+
+ align:start position:0%
+yeah Amanda I agree that is a chilling
+ 
+
+ align:start position:0%
+yeah Amanda I agree that is a chilling
+part and that that as I said those lists
+
+ align:start position:0%
+part and that that as I said those lists
+ 
+
+ align:start position:0%
+part and that that as I said those lists
+were made in fact they were made I think
+
+ align:start position:0%
+were made in fact they were made I think
+ 
+
+ align:start position:0%
+were made in fact they were made I think
+by the so-called interim committee which
+
+ align:start position:0%
+by the so-called interim committee which
+ 
+
+ align:start position:0%
+by the so-called interim committee which
+included Oppenheimer and a couple other
+
+ align:start position:0%
+included Oppenheimer and a couple other
+ 
+
+ align:start position:0%
+included Oppenheimer and a couple other
+uh physicists as well as the Secretary
+
+ align:start position:0%
+uh physicists as well as the Secretary
+ 
+
+ align:start position:0%
+uh physicists as well as the Secretary
+of War and other military leaders it was
+
+ align:start position:0%
+of War and other military leaders it was
+ 
+
+ align:start position:0%
+of War and other military leaders it was
+a group of maybe a dozen people
+
+ align:start position:0%
+a group of maybe a dozen people
+ 
+
+ align:start position:0%
+a group of maybe a dozen people
+um and so for example there was a
+
+ align:start position:0%
+um and so for example there was a
+ 
+
+ align:start position:0%
+um and so for example there was a
+decision made early on I think by that
+
+ align:start position:0%
+decision made early on I think by that
+ 
+
+ align:start position:0%
+decision made early on I think by that
+group or at least the recommendation
+
+ align:start position:0%
+group or at least the recommendation
+ 
+
+ align:start position:0%
+group or at least the recommendation
+from that group uh not to bomb the city
+
+ align:start position:0%
+from that group uh not to bomb the city
+ 
+
+ align:start position:0%
+from that group uh not to bomb the city
+of Kyoto either by conventional means
+
+ align:start position:0%
+of Kyoto either by conventional means
+ 
+
+ align:start position:0%
+of Kyoto either by conventional means
+let alone by um with the newer weapons
+
+ align:start position:0%
+let alone by um with the newer weapons
+ 
+
+ align:start position:0%
+let alone by um with the newer weapons
+because I was seen as as two kind of
+
+ align:start position:0%
+because I was seen as as two kind of
+ 
+
+ align:start position:0%
+because I was seen as as two kind of
+culturally significant
+
+ align:start position:0%
+culturally significant
+ 
+
+ align:start position:0%
+culturally significant
+um it was you know a kind of Millennium
+
+ align:start position:0%
+um it was you know a kind of Millennium
+ 
+
+ align:start position:0%
+um it was you know a kind of Millennium
+old city of of uh of art culture and and
+
+ align:start position:0%
+old city of of uh of art culture and and
+ 
+
+ align:start position:0%
+old city of of uh of art culture and and
+um and kind of heritage
+
+ align:start position:0%
+um and kind of heritage
+ 
+
+ align:start position:0%
+um and kind of heritage
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+and that and that wasn't a kind of nukes
+
+ align:start position:0%
+and that and that wasn't a kind of nukes
+ 
+
+ align:start position:0%
+and that and that wasn't a kind of nukes
+versus incentives I was like don't
+
+ align:start position:0%
+versus incentives I was like don't
+ 
+
+ align:start position:0%
+versus incentives I was like don't
+please don't bomb that City
+
+ align:start position:0%
+please don't bomb that City
+ 
+
+ align:start position:0%
+please don't bomb that City
+the U.S uh uh committee advising the U.S
+
+ align:start position:0%
+the U.S uh uh committee advising the U.S
+ 
+
+ align:start position:0%
+the U.S uh uh committee advising the U.S
+military on that
+
+ align:start position:0%
+military on that
+ 
+
+ align:start position:0%
+military on that
+I think was it part of that same
+
+ align:start position:0%
+I think was it part of that same
+ 
+
+ align:start position:0%
+I think was it part of that same
+exercise say what cities would be
+
+ align:start position:0%
+exercise say what cities would be
+ 
+
+ align:start position:0%
+exercise say what cities would be
+so-called legitimate targets for use
+
+ align:start position:0%
+so-called legitimate targets for use
+ 
+
+ align:start position:0%
+so-called legitimate targets for use
+with the nuclear weapons versus other
+
+ align:start position:0%
+with the nuclear weapons versus other
+ 
+
+ align:start position:0%
+with the nuclear weapons versus other
+kinds of attack
+
+ align:start position:0%
+kinds of attack
+ 
+
+ align:start position:0%
+kinds of attack
+and I don't know that that means that
+
+ align:start position:0%
+and I don't know that that means that
+ 
+
+ align:start position:0%
+and I don't know that that means that
+they thought the bomb was special I
+
+ align:start position:0%
+they thought the bomb was special I
+ 
+
+ align:start position:0%
+they thought the bomb was special I
+think they thought it was new it is I I
+
+ align:start position:0%
+think they thought it was new it is I I
+ 
+
+ align:start position:0%
+think they thought it was new it is I I
+think that was the idea of like what for
+
+ align:start position:0%
+think that was the idea of like what for
+ 
+
+ align:start position:0%
+think that was the idea of like what for
+any new element of the in the collection
+
+ align:start position:0%
+any new element of the in the collection
+ 
+
+ align:start position:0%
+any new element of the in the collection
+so to speak you want to you know
+
+ align:start position:0%
+so to speak you want to you know
+ 
+
+ align:start position:0%
+so to speak you want to you know
+understand it's it's parameters its
+
+ align:start position:0%
+understand it's it's parameters its
+ 
+
+ align:start position:0%
+understand it's it's parameters its
+characteristics so I don't know that
+
+ align:start position:0%
+characteristics so I don't know that
+ 
+
+ align:start position:0%
+characteristics so I don't know that
+they that they thought it was somehow in
+
+ align:start position:0%
+they that they thought it was somehow in
+ 
+
+ align:start position:0%
+they that they thought it was somehow in
+a category unto itself I think my sense
+
+ align:start position:0%
+a category unto itself I think my sense
+ 
+
+ align:start position:0%
+a category unto itself I think my sense
+of that is that it's it's a new thing we
+
+ align:start position:0%
+of that is that it's it's a new thing we
+ 
+
+ align:start position:0%
+of that is that it's it's a new thing we
+want to learn about it because we intend
+
+ align:start position:0%
+want to learn about it because we intend
+ 
+
+ align:start position:0%
+want to learn about it because we intend
+to use it a lot more at least we have we
+
+ align:start position:0%
+to use it a lot more at least we have we
+ 
+
+ align:start position:0%
+to use it a lot more at least we have we
+have the option open that this will
+
+ align:start position:0%
+have the option open that this will
+ 
+
+ align:start position:0%
+have the option open that this will
+become a more a more common element of
+
+ align:start position:0%
+become a more a more common element of
+ 
+
+ align:start position:0%
+become a more a more common element of
+the of the Arsenal we'll talk a bit
+
+ align:start position:0%
+the of the Arsenal we'll talk a bit
+ 
+
+ align:start position:0%
+the of the Arsenal we'll talk a bit
+about that actually again on Wednesday
+
+ align:start position:0%
+about that actually again on Wednesday
+ 
+
+ align:start position:0%
+about that actually again on Wednesday
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+that they were even amidst the debates
+
+ align:start position:0%
+that they were even amidst the debates
+ 
+
+ align:start position:0%
+that they were even amidst the debates
+over whether or not the United States
+
+ align:start position:0%
+over whether or not the United States
+ 
+
+ align:start position:0%
+over whether or not the United States
+should pursue a hydrogen weapon so much
+
+ align:start position:0%
+should pursue a hydrogen weapon so much
+ 
+
+ align:start position:0%
+should pursue a hydrogen weapon so much
+more powerful the debate was rarely as
+
+ align:start position:0%
+more powerful the debate was rarely as
+ 
+
+ align:start position:0%
+more powerful the debate was rarely as
+we now know
+
+ align:start position:0%
+we now know
+ 
+
+ align:start position:0%
+we now know
+um nukes or no nukes it was fission
+
+ align:start position:0%
+um nukes or no nukes it was fission
+ 
+
+ align:start position:0%
+um nukes or no nukes it was fission
+versus fusion and one leading Reason Not
+
+ align:start position:0%
+versus fusion and one leading Reason Not
+ 
+
+ align:start position:0%
+versus fusion and one leading Reason Not
+that was before not to pursue Fusion
+
+ align:start position:0%
+that was before not to pursue Fusion
+ 
+
+ align:start position:0%
+that was before not to pursue Fusion
+weapons because it was it would it would
+
+ align:start position:0%
+weapons because it was it would it would
+ 
+
+ align:start position:0%
+weapons because it was it would it would
+slow down the production of lots more
+
+ align:start position:0%
+slow down the production of lots more
+ 
+
+ align:start position:0%
+slow down the production of lots more
+fission weapons because the idea at
+
+ align:start position:0%
+fission weapons because the idea at
+ 
+
+ align:start position:0%
+fission weapons because the idea at
+least among certain influential people
+
+ align:start position:0%
+least among certain influential people
+ 
+
+ align:start position:0%
+least among certain influential people
+including Oppenheimer was that the U.S
+
+ align:start position:0%
+including Oppenheimer was that the U.S
+ 
+
+ align:start position:0%
+including Oppenheimer was that the U.S
+should have hundreds if not thousands of
+
+ align:start position:0%
+should have hundreds if not thousands of
+ 
+
+ align:start position:0%
+should have hundreds if not thousands of
+these things already because at the time
+
+ align:start position:0%
+these things already because at the time
+ 
+
+ align:start position:0%
+these things already because at the time
+they were like very very few in a
+
+ align:start position:0%
+they were like very very few in a
+ 
+
+ align:start position:0%
+they were like very very few in a
+stockpile
+
+ align:start position:0%
+stockpile
+ 
+
+ align:start position:0%
+stockpile
+so so the concern wasn't these things
+
+ align:start position:0%
+so so the concern wasn't these things
+ 
+
+ align:start position:0%
+so so the concern wasn't these things
+were so terrible we should never use
+
+ align:start position:0%
+were so terrible we should never use
+ 
+
+ align:start position:0%
+were so terrible we should never use
+anything in this whole category again
+
+ align:start position:0%
+anything in this whole category again
+ 
+
+ align:start position:0%
+anything in this whole category again
+people have that concern but not not
+
+ align:start position:0%
+people have that concern but not not
+ 
+
+ align:start position:0%
+people have that concern but not not
+these groups behind the behind the fence
+
+ align:start position:0%
+these groups behind the behind the fence
+ 
+
+ align:start position:0%
+these groups behind the behind the fence
+advising we now know their concern was
+
+ align:start position:0%
+advising we now know their concern was
+ 
+
+ align:start position:0%
+advising we now know their concern was
+making these things which might not even
+
+ align:start position:0%
+making these things which might not even
+ 
+
+ align:start position:0%
+making these things which might not even
+work anyway will interrupt too much
+
+ align:start position:0%
+work anyway will interrupt too much
+ 
+
+ align:start position:0%
+work anyway will interrupt too much
+making the things that we now know more
+
+ align:start position:0%
+making the things that we now know more
+ 
+
+ align:start position:0%
+making the things that we now know more
+about because of these things like you
+
+ align:start position:0%
+about because of these things like you
+ 
+
+ align:start position:0%
+about because of these things like you
+know the usage against actual cities and
+
+ align:start position:0%
+know the usage against actual cities and
+ 
+
+ align:start position:0%
+know the usage against actual cities and
+the fact that they were
+
+ align:start position:0%
+the fact that they were
+ 
+
+ align:start position:0%
+the fact that they were
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+not previously destroyed targets you
+
+ align:start position:0%
+not previously destroyed targets you
+ 
+
+ align:start position:0%
+not previously destroyed targets you
+know environment so you could learn a
+
+ align:start position:0%
+know environment so you could learn a
+ 
+
+ align:start position:0%
+know environment so you could learn a
+lot from these post-bombing surveys
+
+ align:start position:0%
+lot from these post-bombing surveys
+ 
+
+ align:start position:0%
+lot from these post-bombing surveys
+I mean it's you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah anyway so that's a bit of a preview
+
+ align:start position:0%
+yeah anyway so that's a bit of a preview
+ 
+
+ align:start position:0%
+yeah anyway so that's a bit of a preview
+we will talk a bit about that in
+
+ align:start position:0%
+we will talk a bit about that in
+ 
+
+ align:start position:0%
+we will talk a bit about that in
+Wednesday's class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep yep yep no that's uh that's an
+
+ align:start position:0%
+yep yep yep no that's uh that's an
+ 
+
+ align:start position:0%
+yep yep yep no that's uh that's an
+excellent point
+
+ align:start position:0%
+excellent point
+ 
+
+ align:start position:0%
+excellent point
+good I think we'll we'll pause it was a
+
+ align:start position:0%
+good I think we'll we'll pause it was a
+ 
+
+ align:start position:0%
+good I think we'll we'll pause it was a
+really interesting discussion thank you
+
+ align:start position:0%
+really interesting discussion thank you
+ 
+
+ align:start position:0%
+really interesting discussion thank you
+all for for uh taking the time it was an
+
+ align:start position:0%
+all for for uh taking the time it was an
+ 
+
+ align:start position:0%
+all for for uh taking the time it was an
+option during a busy part of the term so
+
+ align:start position:0%
+option during a busy part of the term so
+ 
+
+ align:start position:0%
+option during a busy part of the term so
+I hope it was uh you know interesting
+
+ align:start position:0%
+I hope it was uh you know interesting
+ 
+
+ align:start position:0%
+I hope it was uh you know interesting
+and worthwhile discussion if you have
+
+ align:start position:0%
+and worthwhile discussion if you have
+ 
+
+ align:start position:0%
+and worthwhile discussion if you have
+other questions of course please don't
+
+ align:start position:0%
+other questions of course please don't
+ 
+
+ align:start position:0%
+other questions of course please don't
+hesitate I'll have my regular office
+
+ align:start position:0%
+hesitate I'll have my regular office
+ 
+
+ align:start position:0%
+hesitate I'll have my regular office
+hours on Wednesday morning uh feel free
+
+ align:start position:0%
+hours on Wednesday morning uh feel free
+ 
+
+ align:start position:0%
+hours on Wednesday morning uh feel free
+to email me to make a separate
+
+ align:start position:0%
+to email me to make a separate
+ 
+
+ align:start position:0%
+to email me to make a separate
+appointment of course at any time and
+
+ align:start position:0%
+appointment of course at any time and
+ 
+
+ align:start position:0%
+appointment of course at any time and
+otherwise we'll um we'll meet at our
+
+ align:start position:0%
+otherwise we'll um we'll meet at our
+ 
+
+ align:start position:0%
+otherwise we'll um we'll meet at our
+regular class time on Wednesday so stay
+
+ align:start position:0%
+regular class time on Wednesday so stay
+ 
+
+ align:start position:0%
+regular class time on Wednesday so stay
+well everyone see you soon
\ No newline at end of file
diff --git a/QstZW4N4SX8.txt b/QstZW4N4SX8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..48e5a334da756269fee3e4a9f5c78dc42b54f753
--- /dev/null
+++ b/QstZW4N4SX8.txt
@@ -0,0 +1,3433 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: --And go on with
+lectures 8 to 10.
+
+First I want to briefly
+review what we said
+
+about measurable functions.
+
+Again, I encourage you if you
+hate this material and you
+
+think it's only for
+mathematicians,
+
+please let me know.
+
+I don't know whether it's
+appropriate to cover it in
+
+this class either.
+
+I think it probably is because
+you need to know a little more
+
+mathematics when you deal with
+these Fourier transforms and
+
+Fourier series.
+
+When you're dealing with
+communication theory, then you
+
+need to know for signal
+processing
+
+and things like that.
+
+When you get into learning a
+little more, my sense at this
+
+point is it's much easier to
+learn a good deal more than it
+
+is to learn just a little bit
+more, because a little bit
+
+more you're always faced with
+all of these questions of what
+
+does this really mean.
+
+It turns out that if you put
+just a little bit of measure
+
+theory into your thinking, it
+makes all these problems very
+
+much simpler.
+
+So you remember we talked about
+what a measurable set
+
+was last time.
+
+What a measurable set is, is a
+set which you can essentially
+
+break up into a countable
+union of intervals, and
+
+something which is bounded by
+a countble set of intervals
+
+which have arbitrarily
+small measure.
+
+So you can take all of these
+sets of zero measure --
+
+countable sets, cantor sets, all
+of these things, and you
+
+can just throw all of those
+out from consideration.
+
+That's what makes measure theory
+useful and interesting
+
+and what simplifies things.
+
+So we then said that a function
+is measurable if each
+
+of these sets here -- if the
+set of times for which a is
+
+less than or equal to u of t is
+less than or equal to b --
+
+these things are these
+level sets here.
+
+It's a set of values, t, along
+this axis in which the
+
+function is nailed between any
+two of these points here.
+
+For a function to be measurable,
+all of these sets
+
+in here have to be measurable.
+
+We haven't given you any
+examples of sets which are not
+
+measurable, and therefore, we
+haven't given you any examples
+
+of functions which are
+not measurable.
+
+It's very, very difficult to
+construct such functions, and
+
+since it's so difficult to
+construct them, it's easier to
+
+just say that all of the
+functions we can think of are
+
+measurable.
+
+That includes an awful lot more
+functions than you ever
+
+deal with in engineering.
+
+If you ever make a serious
+mistake in your engineering
+
+work because of thinking that a
+function is measurable when
+
+it's not measurable, I
+will give you $1,000.
+
+I make that promise that you
+because I don't think it's
+
+ever happened in history, I
+don't think it ever will
+
+happen in history, and that's
+just how sure I am of it.
+
+Unless you try to deliberately
+make such a mistake in order
+
+to collect $1,000.
+
+Of course, that's not fair.
+
+Then we said the way we define
+this approximation to the
+
+integral, namely, we always
+defined it from underneath,
+
+and therefore, if we started to
+take these intervals here
+
+with epsilon and split them in
+half, the thing that happens
+
+is you always get extra
+components put in.
+
+So that as you make the scaling
+finer and finer, what
+
+happens is the approximation
+into the integral gets larger
+
+and larger.
+
+Because of that, if you're
+dealing with a non-negative
+
+function, the only two things
+that can happen, as you go to
+
+the limit of finer and finer
+scaling, is one, you come to a
+
+finite limit, and two, you come
+to an infinite limit.
+
+Nothing else can happen.
+
+You see that's remarkably simple
+as mathematics go.
+
+This is dealing with all of
+these functions you can ever
+
+think of, and those are the
+only two things that can
+
+happen here.
+
+So then we went on to say that
+a function as L1, if it's
+
+measurable, and if the integral
+of its magnitude is
+
+less than infinity, and
+so far we're still
+
+talking about real functions.
+
+If u of t is L1, then you can
+take the integral of u of t
+
+and you can split it
+up into two things.
+
+You can split it up into the set
+of times over which u of t
+
+is positive, and the
+set of times over
+
+which u of t is negative.
+
+The set of times over which u of
+t is equal to zero doesn't
+
+contribute to the integral
+at all so you can
+
+forget about that.
+
+This is well-defined as the
+function is measurable.
+
+What's now happening is that
+if the integral of this
+
+magnitude is less than infinity,
+then both this has
+
+to be less than infinity, and
+this has to be less than
+
+infinity, which says that so
+long as you're dealing with L1
+
+functions, you never have to
+worry about this nasty
+
+situation where the negative
+part of the function is
+
+infinite, the positive part of
+the function is infinite, and
+
+therefore, the difference, plus
+infinity, minus infinity
+
+doesn't make any sense at all.
+
+And instead of having an
+integral which is infinite or
+
+finite, you have a function
+which might just be undefined
+
+completely.
+
+Well this says that if the
+function is L1, you can't ever
+
+have any problem with integrals
+of this sort thing
+
+being undefined.
+
+So, and in fact, u of t is
+always integral and has a
+
+finite value in this case.
+
+Now, we say that a complex
+function is measurable if both
+
+the real part is measurable
+and the imaginary part is
+
+measurable.
+
+Therefore, you don't have to
+worry about complex functions
+
+as really being any more than
+twice as complicated as real
+
+functions, and conceptually
+they aren't any more
+
+complicated at all because you
+just treat them as two
+
+separate functions, and
+everything you know about real
+
+functions you now know about
+complex functions.
+
+Now, as far as Fourier theory
+is concerned --
+
+Fourier series, Fourier
+integrals, discrete time,
+
+Fourier transforms -- all of
+these things, if u of t is an
+
+L1 function, then u of t times e
+to the 2 pi ft has to be L1,
+
+and this has to be true for
+all possible values of f.
+
+Why is that?
+
+Well, it's just that the
+absolute value of u of t for
+
+any given t, is exactly the same
+as the absolute value of
+
+u of t times e to
+the 2 pi i ft.
+
+Namely, this is a quantity whose
+magnitude is always 1,
+
+and therefore, this quantity,
+this magnitude is equal to
+
+this magnitude.
+
+Therefore, when you integrate
+this magnitude, you get the
+
+same thing as when you integrate
+this magnitude.
+
+So, there's no problem here.
+
+So what that says, using this
+idea, too, of positive and
+
+negative parts, it says that the
+integral of u of t times e
+
+to the 2 pi i ft dt has to
+exist for all real f.
+
+That covers Fourier series
+and Fourier integral.
+
+We haven't talked about the
+Fourier integral yet, but it
+
+says that just by defining u of
+t to be L1, you avoid all
+
+of these problems of when these
+Fourier integrals exist
+
+and when they don't exist.
+
+They always exist.
+
+So let's talk about the Fourier
+transform then since
+
+we're backing into this
+slowly anyway.
+
+What you've learned in probably
+two or three classes
+
+by now is that the Fourier
+transform is
+
+defined in this way.
+
+Namely, the transform, a
+function of frequency, u hat
+
+of f, we use hats here instead
+of capital letters because we
+
+like to use capital letters
+for random variables.
+
+So that this transform here
+is the integral from minus
+
+infinity to infinity of the
+original function, we start
+
+with u of t times e to the
+minus 2 pi ift dt.
+
+Now, what's the nice
+part about this?
+
+The nice part about this is that
+if u of t is L1, then in
+
+fact this Fourier transform
+has to exist everywhere.
+
+Namely, what you've learned
+before in all of these classes
+
+says essentially that if these
+functions are well-behaved
+
+then these transforms exist.
+
+What you've learned about
+well-behaved is completely
+
+circular, namely, a function
+is well-behaved if the
+
+transform exists, and the
+transform exists if the
+
+function is well-behaved.
+
+You have no idea of what kinds
+of functions the Fourier
+
+transform exists and
+what kinds of
+
+functions it doesn't exist.
+
+There's another thing buried
+in here, in this transform
+
+relationship.
+
+Namely, the first thing is we're
+trying to define the
+
+transform function of frequency
+in terms of the
+
+function of time.
+
+Well and good.
+
+Then we try to define a function
+of time in terms of a
+
+function of frequency.
+
+What's hidden here is if you
+start with u of t, you then
+
+get a function of frequency,
+and this sort of implicitly
+
+says that you get back
+again the same
+
+thing you started with.
+
+That, in fact, is the most
+ticklish part of all of this.
+
+So that if we start with an L1
+function u of t, we wind up
+
+with a Fourier transform,
+u hat of f.
+
+Then u hat of f goes in here.
+
+We hope we might get back
+the sum transform here.
+
+The nasty thing, and one of the
+reasons we're going to get
+
+away from L1 in just a minute,
+is that if a function is L1,
+
+it's Fourier transform is
+not necessarily L1.
+
+What that means is that you
+have to learn all of this
+
+stuff about L1 functions, and
+then as soon as you take the
+
+Fourier transform, bingo, it's
+all gone up in a lot of smoke,
+
+and you have to start all over
+again saying something about
+
+what properties the transform
+might have.
+
+But anyway, it's nice to start
+with because when u of t is
+
+L1, we know that this function
+actually exists.
+
+It actually exists as
+a complex number.
+
+It exists as a complex
+number for every
+
+possible real f here.
+
+Namely, there aren't any if,
+and's, but's or maybe's here,
+
+there's nothing like L2
+convergence that we were
+
+talking about a little
+bit before.
+
+This just exists, period.
+
+There's something more here,
+that if this is L1, this not
+
+only exists but it's also a
+continuous function, and those
+
+don't prove that.
+
+If you've taken a course in
+analysis and you know what a
+
+complex function is and you're
+quite patient, you can sit
+
+down and actually show
+this yourselves, but
+
+it's a bit of a pain.
+
+So for a well-behaved function,
+the first integral
+
+exists for all f, the second
+exists for all t, and results
+
+in the original u of t.
+
+But then more specifically,
+if u of t is L1, the first
+
+integral exists for all f and
+it's a continuous function.
+
+It's also a bounded function, as
+we'll see in a little bit.
+
+If u hat of f is L1, the second
+integral exists for all
+
+t, and u of t is continuous.
+
+Therefore, if you assume at
+the output at the onset of
+
+things that both this is
+L1 and this is L1, then
+
+everything is also continuous
+and you have a very nice
+
+theory, which doesn't apply to
+too many of the things that
+
+you're interested in.
+
+And I'll explain why
+in a little bit.
+
+Anyway, for these well-behaved
+functions, we have all of
+
+these relationships that I'm
+sure you've learned in
+
+whatever linear systems
+course you've taken.
+
+Since you should know all of
+these things, I just want to
+
+briefly talk about them I mean
+this linearity idea is
+
+something you would
+just use without
+
+thinking about it, I think.
+
+In other words, if you'd never
+learned this and you were
+
+trying to work out a problem you
+would just use it anyway,
+
+because anything respectable has
+to have -- well, anything
+
+respectable, again,
+means anything
+
+which has this property.
+
+This conjugate property you can
+derive that easily from
+
+the Fourier transform
+relationships also, if you
+
+have a well-behaved function.
+
+This quantity here, this
+duality, is particularly
+
+interesting because it isn't
+really duality, it's something
+
+called hermitian duality.
+
+You start out with this formula
+here to go to there
+
+and you use almost the same
+formula to get back again.
+
+The only difference is instead
+of a minus 2 pi ift, you have
+
+a plus 2 pi ift.
+
+In other words, this is the
+conjugate of this, which is
+
+why this is called hermitian
+duality.
+
+But aside from that, everything
+you learn about the
+
+Fourier transform, you also
+automatically know about the
+
+inverse Fourier transform for
+these well-behaved functions.
+
+Otherwise you don't know whether
+the other one exists
+
+or not, and we'll certainly
+get into that.
+
+So, the duality is expressed
+this way, the Fourier
+
+transform of, bleah.
+
+If you take a function, u of
+t, and regard that as a
+
+Fourier transform, then --
+
+I always have trouble
+saying this.
+
+If you take a function, u of t,
+and then you regard that as
+
+a function of frequency --
+
+OK, that's this -- and then you
+regard it as a function of
+
+minus frequency, namely, you
+substitute minus f for t in
+
+whatever time function
+you start with.
+
+You start with a time function u
+of t, you substitute minus f
+
+for t, which gives you a
+function of frequency.
+
+The inverse Fourier transform
+of that is what you get by
+
+taking the Fourier transform
+of u of t, and then
+
+substituting t for f in it.
+
+It's much harder to
+say it than to do.
+
+This time shift, you've
+all seen that.
+
+If you shift a function in
+time, the only thing that
+
+happens is you get this
+rotating term in it.
+
+Same thing for a frequency
+shift.
+
+You want to have an interesting
+exercise, take
+
+time shift plus duality and
+derive the scaling and
+
+frequency from it -- it has to
+work, and of course, it does.
+
+Scaling --
+
+there's this relationship
+here.
+
+This one is always
+a funny one.
+
+It's a little strange because
+when you scale here, it's not
+
+too surprising that when you
+take a function and you squash
+
+it down that the Fourier
+transform
+
+gets squashed upwards.
+
+Because in a sense what you're
+doing when you squash a
+
+function down you're making
+everything happen faster than
+
+it did before, which means that
+all the frequencies in it
+
+are going to get higher
+than they are before.
+
+But also when you squash it
+down, the amount of energy in
+
+the function is going
+to go down.
+
+One of the most important
+properties that we're going to
+
+find and what you ought to know
+already is that when you
+
+take the energy in a function,
+you get the same answer as you
+
+get when you take the energy
+in the Fourier transform.
+
+Namely, you integrate u of f
+squared over frequency and you
+
+get the same as if you
+integrate u of t
+
+squared over time.
+
+That's an important check
+that you use on
+
+all sorts of things.
+
+The thing that happens now then
+when you're scaling is
+
+when you scale a function, u
+of t, you bring it down and
+
+you spread it out when
+you bring it down.
+
+The frequency function goes up
+so the energy in the time
+
+function goes down, the energy
+in the frequency function goes
+
+up, and you need something in
+order to keep the energy
+
+relationship working properly.
+
+This is what you need.
+
+Actually, if you derive
+this, the t
+
+just falls out naturally.
+
+So we get the same thing if we
+do scaling and frequency.
+
+I don't think I put that
+down but it's the same
+
+relationship.
+
+There's differentiation.
+
+Differentiation we won't talk
+about or use it a whole lot.
+
+All of these things turn out
+to be remarkably robust.
+
+When you're dealing with L1
+functions or L2 functions and
+
+you scale them or you shift
+them or do any of those
+
+things, if they're L1, they're
+still L1 after you're through,
+
+if they're L2, they're L2
+after you're through.
+
+If you differentiate
+a function, all
+
+those properties change.
+
+You can't be sure of
+anything anymore.
+
+There's convolution, which I'm
+sure you've derived many
+
+times, and which one of the
+exercises derives again.
+
+There's correlation, and what
+this sort of relationship says
+
+is taking products at the
+frequency domain is the same
+
+as going through this
+convolution relationship and
+
+the time domain.
+
+Of course, there's a dual
+relation to that, which you
+
+don't use very often but
+it still exists.
+
+Correlation is you actually get
+correlation by using one
+
+of the conjugate properties on
+the convolution and I'm sure
+
+you've all seen that.
+
+That's something you should
+all have been using and
+
+familiar with for a long time.
+
+Two special cases of the Fourier
+transform is that u of
+
+zero is what happens when you
+take the Fourier transform and
+
+you evaluate it at
+t equals zero.
+
+You get u of zero is just the
+integral of u hat of f.
+
+u hat of zero is just the
+integral of u of t.
+
+What do you use these for?
+
+Well the thing I use them for
+is this half the time when
+
+you're working out a problem
+it's obvious by inspection
+
+what this integral is or it's
+obvious by inspection what
+
+this integral is, and by doing
+that you can check whether you
+
+have all the constants
+right in the
+
+transform that you've taken.
+
+I don't know anybody who can
+take Fourier transforms
+
+without getting at least one
+constant wrong at least half
+
+the time they do it.
+
+I probably get one constant
+wrong about three-quarters of
+
+the time that I do it, and I'm
+sure I'll do it here in class
+
+a number of times.
+
+I hope you find it, but it's one
+of these things we all do.
+
+This is one of the best ways
+of finding out what you've
+
+done and going back
+and checking it.
+
+Parseval's Theorem, Parseval's
+Theorem is really just this
+
+convolution equation which
+we're applying
+
+at tau equals zero.
+
+You take the convolution, you
+apply it at tau equals zero
+
+and what do you get?
+
+You get the integral of u of t
+times some other conjugate --
+
+the conjugate of the other
+function is equal to the
+
+integral of u hat of
+f times the complex
+
+conjugate of v of f.
+
+Much more important than this
+is what happens if v happens
+
+to be the same as u, and that
+gives you the energy equation
+
+here, which is what I
+was talking about.
+
+It says the integral in a
+function you can find it two
+
+ways, either by looking
+at it in time or by
+
+looking at it in frequency.
+
+I urge you to always think
+about doing this whenever
+
+you're working problems, because
+often the Fourier
+
+integral it's very easy to find
+the integral and the and
+
+the time function is
+very difficult.
+
+A good example of this
+is sinc functions
+
+and rectangular functions.
+
+Anybody can take a rectangular
+function, square it and
+
+integrate it.
+
+It takes a good deal of skill
+if you don't use this
+
+relationship to take a sinc
+function, to square it and to
+
+integrate it.
+
+You can do it if you're skillful
+at integration, you
+
+might regard it as a challenge,
+but after you get
+
+done you realize that you've
+really wasted a lot of time
+
+because this is the right
+way of doing it here.
+
+Now, as I mentioned before,
+it's starting to look like
+
+Fourier series and Fourier
+integrals are much nicer when
+
+you have L1 functions, and they
+are, but L1 functions are
+
+not terribly useful
+as far as most
+
+communication functions go.
+
+In other words, not enough
+functions are L1 to provide
+
+suitable models for the
+communication systems that we
+
+want to look at.
+
+In fact, most of the models that
+we're going to look at,
+
+the functions that we're dealing
+with are L2 functions.
+
+One of the reasons for this is
+this sinc function, sine x
+
+over x function is not L1.
+
+A sinc function just goes down
+as 1 over t, and since it goes
+
+down as 1 over t, you take the
+absolute value of it and you
+
+integrate 1 over t and what do
+you get when you integrate it
+
+from minus infinity
+to infinity.
+
+A function that's 1 over t,
+well, if you really want to go
+
+through the trouble of
+integrating it, you can
+
+integrate it over limits and you
+get limits where you have
+
+to evaluate the limits on
+a logarithmic function.
+
+When you get all done
+with that you
+
+get an infinite value.
+
+And you can see this.
+
+You could take 1 over t and you
+just look at it, as you go
+
+further and further out it just
+gets bigger and bigger
+
+without limit.
+
+So, sinc t is not L1.
+
+Sinc function is a function
+we'd like to use.
+
+Any function with a
+discontinuity can't be the
+
+Fourier transform of
+any L1 function.
+
+In other words, we said that
+if you take the Fourier
+
+transform of an L1 function, one
+of the nice things about
+
+it is you get a continuous
+function.
+
+One of the nasty things
+about it is you get
+
+a continuous function.
+
+Since you get a continuous
+function it says that any time
+
+you want to deal with transforms
+which are not
+
+continuous, you can't be talking
+about time functions
+
+which are L1.
+
+One of the frequency functions
+we want to look at a great
+
+deal is a frequency function
+corresponding to a
+
+band-limited function.
+
+When you take a band-limited
+function you just chop it off
+
+at some frequency, and usually
+when you chop it off, you chop
+
+it off and get a
+discontinuity.
+
+When you chop it off and get a
+discountinuity, bingo, the
+
+time function you're dealing
+with cannot be L1.
+
+It has to dribble away
+much too slowly as
+
+time goes to infinity.
+
+That's an extraordinarily
+important thing to remember.
+
+Any time you get a function
+which is discontinuous in the
+
+frequency domain, the function
+cannot go to zero any faster
+
+in a time domain than 1 over
+t and vice versa in the
+
+frequency domain.
+
+L1 functions sometimes
+have infinite energy.
+
+In other words, sinc
+t is not L1 --
+
+well, that's not a good example
+because that's not L1,
+
+and it also has infinite energy,
+but you can just as
+
+easily find functions which drop
+off a little more slowly
+
+than sinc t, and which
+have infinite
+
+energy because they--.
+
+Excuse me.
+
+Sometimes you have functions
+which go off to infinity too
+
+fast as you approach time equals
+zero, things which are
+
+a little bit like impulses
+but not really.
+
+Impulses are awful and we'll
+talk about them in a minute,
+
+because they don't have finite
+energy as we said before.
+
+We have functions which just
+slowly go off to infinity and
+
+they are L2 but they
+aren't L1.
+
+Why do we care about those
+weird functions?
+
+We care about them, as I said
+before, because we would like
+
+to be able to make statements
+which are simple which we can
+
+believe in.
+
+In other words, you don't want
+to go through a course like
+
+this with a whole bunch of
+things that you have to leave.
+
+It's very nice to have some
+things that you really
+
+believe, and whether you believe
+them or not, it's nice
+
+to have theorems about them.
+
+Even if you don't believe the
+theorems, at least you have
+
+theorems so you can fool
+other people about
+
+it, if nothing else.
+
+Well, it turns out that L2
+functions are really the right
+
+class to look at here.
+
+Oh, I think I left out
+one of the most
+
+important things here.
+
+Maybe I put it down here.
+
+No, probably not.
+
+One of the reasons we want to
+deal with L2 functions is if
+
+you're dealing with compression,
+for example, and
+
+you take a function, if the
+function has infinite energy
+
+in it, then one of the things
+that happens is that any time
+
+you expand it into any kind of
+orthonormal expansion or
+
+orthongonal expansion, which
+we'll talk about later, you
+
+have coefficients, which
+have infinite energy.
+
+In other words, they have
+infinite values, or the sum
+
+squared of the coefficients
+is equal to infinity.
+
+When we try to compress those
+we're going to find that no
+
+matter how we do it our
+mean square error
+
+is going to be infinite.
+
+Yes, we will talk about that
+later when we get to talking
+
+about expansions.
+
+So for all those reasons L1
+isn't the right thing, L2 is
+
+the right thing.
+
+A function going from the reals
+into the complexes, in
+
+other words, a complex valued
+function is L2 if it's
+
+measurable, and if this
+integral is less than
+
+infinity, in other words, if
+that has finite energy.
+
+Primarily it means it has finite
+energy because all the
+
+functions you can think
+of are measurable.
+
+So it really says you're dealing
+with functions that
+
+have finite energy here.
+
+So, let's go on to Fourier
+transforms then.
+
+Interesting simple theorem.
+
+I think I stated this
+last time, also.
+
+If a function is L2 and its time
+limited, it's also L1.
+
+So we've already found that if
+functions are L1, they have
+
+Fourier transforms that exist.
+
+The reason for this is if you
+square u of t, take the
+
+magnitude squared of u of t for
+any given t, it has to be
+
+less than or equal to the
+sum of u of t plus 1.
+
+In fact, it has to be
+less than that.
+
+Why?
+
+How would you prove this
+if you had to prove it?
+
+Well, you say gee, this is
+two separate terms here.
+
+Why don't I look at two
+separate cases.
+
+The two separate cases are
+first, suppose u of t itself
+
+as a magnitude less than 1.
+
+If u of t has and magnitude less
+than 1 and you square it,
+
+you get something
+even smaller.
+
+So, any time u of t has a
+magnitude less than 1, u
+
+squared of t is less than
+or equal to u of t.
+
+Blah blah blah blah blah
+blah blah blah.
+
+If u of t --
+
+what did I do here?
+
+No wonder I couldn't explain
+this to you.
+
+Let's try it that way
+and see if it works.
+
+If you can prove something, turn
+it around and see if you
+
+can prove it then.
+
+Now, two cases.
+
+First one, let's suppose
+that u of t is less
+
+than or equal to 1.
+
+Well then, u of t is less
+than or equal to 1.
+
+And this is positive so this is
+less than or equal to that.
+
+Let's look at the other case.
+u of t is greater than or
+
+equal to 1, magnitude.
+
+Well then, it's less
+than or equal to u
+
+of t magnitude squared.
+
+So either way this is less
+than or equal to that.
+
+What that says is the integral
+over any finite limits of u of
+
+t dt is less than or equal
+to the integral of this.
+
+Well, the integral of this
+splits up into the integral
+
+magnitude u of t squared dt
+plus the integral of 1.
+
+Now, the integral of 1 over
+any finite limits is
+
+just b minus a.
+
+That's where the finite
+limits come in.
+
+Finite limits say you don't have
+to worry about this term
+
+because it's finite.
+
+So that says at any time you
+have an L2 function over a
+
+finite range, that function
+is also L1
+
+over that finite range.
+
+Which says that any time you
+take a Fourier transform of an
+
+L2 function, which is only
+non-zero over a finite range,
+
+bingo, it's L1 and you get all
+these nice properties.
+
+It has to exist, it has to be
+continuous, it has to be
+
+bounded, and all of
+that neat stuff.
+
+So for any L2 function u of t,
+what I'm going to try to do
+
+now, and I'm just copying what
+a guy by the name of
+
+Plancherel did a
+long time ago.
+
+The thing that Plancherel did
+was he said how do I know when
+
+a Fourier transform
+exists or not.
+
+I would like to make
+it exist for L2
+
+functions, how do I do it?
+
+Well, he said OK, the thing I'm
+going to do is to take the
+
+function u of t and I'm first
+going to truncate it.
+
+In fact, if you think in terms
+of Reimann integration and
+
+things like that, any time you
+take an integral from minus
+
+infinity to plus infinity,
+what do you mean by it?
+
+You mean the limit as you
+integrate the function over
+
+finite limits and then you let
+the limits go to infinity.
+
+So all we're doing is
+the same trick here.
+
+So we're going to take u of t,
+we're going to truncate it to
+
+some minus a to plus a over some
+finite range, no matter
+
+how big a happens to be.
+
+We're going to call the function
+b sub a of t, u of t
+
+truncated to these limits.
+
+In other words, u of t times a
+rectangular function evaluated
+
+at t over 2a.
+
+Now, can all of you look at this
+function and see that it
+
+just means truncate from
+minus a to plus a?
+
+No.
+
+Well, you should learn
+to do this.
+
+One of the ways to do it is
+to say OK, the rectangular
+
+function is defined as having
+the value 1 between minus 1/2
+
+and plus 1/2 and it's zero
+everywhere else.
+
+I think I said that before
+in class, didn't I?
+
+Certainly it's in the notes.
+
+Rectangle ft equals 1 for
+t less than or equal
+
+to 1/2, zero else.
+
+So with this definition you
+just evaluate what happens
+
+when t is equal to minus a, you
+get rectangle of minus a
+
+over 2a, which is minus 1/2.
+
+When t is equal to a, you're up
+to the other limit, so this
+
+function is 1 for t between
+minus a and plus a and zero
+
+everywhere else.
+
+Please get used to using this
+and become a little facile at
+
+sorting out what it means
+because it's a very handy way
+
+to avoid writing awkward
+things like this.
+
+So va of t by what we've said
+is both L2 and its L1.
+
+We started out with a function
+which is L2 and we truncated.
+
+Then according to this theorem
+here, this function va of t is
+
+now time limited.
+
+It's also L2, and therefore, by
+the theorem it's also L1.
+
+Therefore, it's continue and
+you can take the Fourier
+
+transform of it -- v hat a of
+f exists for all f and it's
+
+continuous.
+
+So this function is just the
+Fourier transform that you get
+
+when you truncate the function,
+which is what you
+
+would think of as a
+way to find the
+
+Fourier transform anyway.
+
+I mean if this is not a
+reasonable approximation to
+
+the Fourier transform a
+function, you haven't modeled
+
+the function very well.
+
+Because when a gets
+extraordinarily large, if
+
+there's anything of significance
+that happens
+
+before year ten to the minus 6
+or which happens after year
+
+ten to the plus 6, and you're
+dealing with electronic
+
+speeds, your models don't
+make any sense.
+
+So for anything of any interest,
+these functions here
+
+are going to start approximating
+u of t, and
+
+therefore we hope this will
+start approximating the
+
+Fourier transform of u of t.
+
+Who can make that more
+precise for me?
+
+What happens when u of
+t has finite energy?
+
+If it has finite energy it means
+that the integral of u
+
+of t magnitude squared over the
+
+infinite interval is finite.
+
+So you start integrating it
+over bigger and bigger
+
+minus a to plus a.
+
+What happens is as the minus
+a to plus a gets bigger and
+
+bigger and bigger, you're
+including more and more of the
+
+function, so that the integral
+of u of t squared over that
+
+bigger and bigger interval has
+to be getting closer and
+
+closer to the overall
+integral of u of t.
+
+Which says that the energy in u
+of t minus the a of t has to
+
+get very, very small
+as a gets large.
+
+That's one of the reasons why
+we like to deal with finite
+
+energy functions.
+
+By definition they cannot have
+a appreciable energy outside
+
+of very large limits.
+
+How large those large limits
+have to be depends on the
+
+function, but if you make them
+large enough you will always
+
+get negligible energy outside
+of those limits.
+
+So then we can take the Fourier
+transform of this
+
+function within those limits and
+we get something which we
+
+hope is going to be a reasonable
+approximation of
+
+the Fourier transform
+of u of t.
+
+That's what Plancherel said.
+
+Plancherel said if we have an
+L2 function, u of t, then
+
+there is an L2 function u hat
+of f, which is really the
+
+Fourier transform of u of t.
+
+Some people call this the
+Plancherel transform of u of t
+
+and say that indeed Plancherel
+was the one that invented
+
+Fourier transforms
+or Plancherel
+
+transforms for L2 functions.
+
+That's probably giving him a
+little too much credit, and
+
+Fourier somewhat less
+than due credit.
+
+But it was a neat theorem.
+
+What he said is that there is
+a function u hat of f, which
+
+we'll call the Fourier
+transform, which has the
+
+property that when you take the
+integral of the difference
+
+between u hat of f and the
+transform of b sub a of t,
+
+when you take the integral
+of this dt --
+
+in other words, when you
+evaluate the energy in the
+
+difference between u hat
+of f and v sub a of f,
+
+that goes to zero.
+
+Well this isn't a big deal.
+
+In other words, this is
+plausible, since this integral
+
+has to go to zero for an L2
+function, that's what we just
+
+said, then therefore, using the
+energy relation, this also
+
+has to go to zero.
+
+So is this another example where
+Plancherel just came
+
+along at the right time and he
+said something totally trivial
+
+and became famous
+because of it?
+
+I mean as I've urged all of
+you, work on problems that
+
+other people haven't
+worked on.
+
+If you're lucky, you
+will do something
+
+trivial and become famous.
+
+As another piece of philosophy,
+you become far
+
+more famous for doing something
+trivial than for
+
+doing something difficult,
+because everybody remembers
+
+something trivial.
+
+And if you do something
+difficult nobody even
+
+understands it.
+
+But no, it wasn't that because
+there's something hidden here.
+
+He says a function
+like this exists.
+
+In other words, the problem is
+these functions get closer and
+
+closer to something.
+
+They get closer and closer to
+each other as a gets bigger
+
+and bigger.
+
+You can show that because
+you have a
+
+handle on these functions.
+
+Whether they get closer and
+closer to a real bonafide
+
+function or not is
+another question.
+
+Back when you studied
+arithmetic, if you were in any
+
+kind of advanced class studying
+arithmetic, you
+
+studied the rational
+numbers and the
+
+real numbers you remember.
+
+And you remember the problem of
+what happens if you take a
+
+sequence of rational numbers
+which is approaching a limit.
+
+There's a big problem there
+because when you take a
+
+sequence of rational numbers
+that approaches a limit, the
+
+limit might not be rational.
+
+In other words, when you take
+sequences of things you can
+
+get out of the domain of the
+things you're working with.
+
+Now, we can't get out of the
+domain of being L2, but we
+
+might get out of domain of
+measurable functions, we might
+
+get out of the domain
+of functions at all.
+
+We can have all sorts of
+strange things happen.
+
+The nice thing here, which
+was really a theorem by
+
+[? Resenage ?]
+
+a long time ago.
+
+It says that when you take
+cosine sequences of L2
+
+functions, they converge
+to an L2 function.
+
+So that's really what's
+involved in here.
+
+So maybe this should be called
+the [? Resenage ?]
+
+transform, I don't know.
+
+But anyway, whatever this says,
+the theorem says, the
+
+first part of Plancherel's
+theorem says that this
+
+function exists and you get a
+handle on it by taking this
+
+transform, making a bigger and
+bigger, and it says it will
+
+converge to something in
+this energy sense.
+
+Bingo, when you're all done
+this goes to zero.
+
+We're going to denote this
+function as a limit and a mean
+
+of the Fourier transform.
+
+In other words, we do have a
+Fourier transform in the same
+
+sense that we had a Fourier
+series before.
+
+We didn't know weather the
+Fourier series would converge
+
+at every point, but we knew that
+it converged at enough
+
+points, namely, almost
+everywhere, everywhere but on
+
+a set of measure zero.
+
+It converges so that, in fact,
+you get this kind of
+
+relationship.
+
+Now, do you have to
+worry about that?
+
+No.
+
+Again, this is one of these
+very nice things that says
+
+there is a Fourier transform,
+you don't have to worry about
+
+what goes on at these oddball
+sets where the function has
+
+discountinuities and
+things like that.
+
+You can forget all of that.
+
+You can be as careless as you've
+ever been, and now you
+
+know that it all works out
+mathematically, so long as you
+
+stick to L2 functions.
+
+So, sticking to L2 functions
+says you can be a careless
+
+engineer, you can use lousy
+mathematics and you'll always
+
+get the right answer.
+
+So, it's nice for engineers,
+it's nice for me.
+
+I don't like to be careful
+all the time.
+
+I like to be careful once and
+then solve that and go on.
+
+Well, because of time frequency
+duality, you can do
+
+exactly the same thing in
+the frequency domain.
+
+So, you start out defining some
+b, which is bigger than
+
+zero which is arbitrarily large,
+you define a finite
+
+bandwidth approximation as w hat
+sub b of f is u hat of f.
+
+We now know that u
+hat of f exists
+
+and it's an L2 function.
+
+u hat of f times this
+rectangular function,
+
+that's f over 2b.
+
+In other words, it's u hat of f
+truncated to a big bandwidth
+
+minus b to plus b.
+
+Since w sub b of f
+is L1, as well as
+
+L2, this always exists.
+
+So long as you deal with a
+finite bandwidth, this
+
+quantity exists.
+
+It exists for all t and r.
+
+It's continuous.
+
+The second part of Plancherel's
+theorem then says
+
+that the limit as b goes to
+infinity of the integral of u
+
+of t minus this truncated
+function, magnitude squared
+
+the energy in that,
+goes to zero.
+
+This now is a little different
+than what we did before.
+
+It's easier in the sense that
+we don't have to worry about
+
+the existence of this function
+because we started out with
+
+this to start with.
+
+It's a little harder because
+we know that a function
+
+exists, but we don't know
+that it's u of t.
+
+So, in fact, poor old Plancherel
+had to do something
+
+other than just this very simple
+argument that says all
+
+the energy works out right.
+
+He had to also show that you
+really wind up with the right
+
+function when you get
+all through with it.
+
+But again, this is the same
+kind of energy convergence
+
+that we had before.
+
+Yeah?
+
+AUDIENCE: Could you discuss
+non-uniqueness?
+
+Clearly, [INAUDIBLE]
+
+u hat f to satisfy Plancherel
+1 and Plancherel 2.
+
+PROFESSOR: Yeah, in fact, any
+two functions which are L2
+
+equivalent.
+
+But you see the nice thing is
+when you take this finite
+
+bandwidth approximation
+there's only one.
+
+It's only when you get
+to the limit that all
+
+of this mess occurs.
+
+If you take these different
+possible functions, u hat of
+
+f, which just differ in these
+negligible sets of measure
+
+zero, those don't affect
+this integral.
+
+Sets of measure zero don't
+affect integrals at all.
+
+So the mathematicians deal
+with L2 theory by talking
+
+about equivalence classes
+of functions.
+
+I find it hard to think about
+equivalence classes of
+
+functions and partitioning the
+set of all functions into a
+
+bunch of equivalence classes.
+
+So I just sort of remember in
+the back of my mind that there
+
+are all these functions which
+differ in a strange way.
+
+We'll talk about that more when
+we get to the sampling
+
+theorem later today,
+because there it
+
+happens to be important.
+
+Here it's not really important,
+here we don't have
+
+to worry about it.
+
+Anyway, we can always get back
+to the u of t that we started
+
+with in this way.
+
+Now, this says that all L2
+functions have Fourier
+
+transforms in this
+very nice sense.
+
+In other words, at this point
+you don't have to worry about
+
+continuity, you don't have to
+worry about how fast things
+
+drop off, you don't have to
+worry about anything.
+
+So long as you have finite
+energy functions, this
+
+beautiful result always
+holds true.
+
+There always is a Fourier
+transform, it always has this
+
+nice property that it has the
+same energy as the function
+
+you started with.
+
+The only nasty thing, as Dave
+pointed out, is that, in fact,
+
+it might not be a unique
+function, but it's close
+
+enough to unique.
+
+It's unique in an engineering
+sense.
+
+The other thing is that L2 wave
+forms don't include some
+
+of your favorite wave forms.
+
+They don't include constants,
+they don't include sine waves,
+
+and they don't include Dirac
+impulse functions.
+
+All of them have infinite
+energy.
+
+I pointed out in class, spent
+quite a bit of time explaining
+
+why an impulse function had
+infinite energy by looking at
+
+it as a very narrow pulse of
+width epsilon and a height 1
+
+over epsilon, and showing that
+the energy in that is 1 over
+
+epsilon, and as epsilon goes
+to zero and the pulse gets
+
+narrower and narrower, bingo,
+the energy goes to infinity.
+
+Constants are the same way, they
+extend on and on forever.
+
+Therefore, they have infinite
+energy, except if the constant
+
+happens to be zero.
+
+Sine waves are the same way,
+they dribble on forever.
+
+So the question is are these
+good models of reality?
+
+The answer is they're good for
+some things and they're very
+
+bad for other things.
+
+The point in this course is
+that if you're looking for
+
+wave forms that are good models
+for either the kinds of
+
+functions that we're going to
+quantize, namely, source wave
+
+forms, or if you're looking for
+the kinds of things that
+
+we're going to transmit
+on channels, these
+
+are very lousy functions.
+
+They don't make any sense in
+a communication context.
+
+But anyway, where did these
+things come from?
+
+Constants and sine waves
+result from refusing to
+
+explicitly model when very
+
+long-lasting functions terminate.
+
+In other words, if you're
+looking at a carrier function
+
+in a communication's system,
+sine of 2 pi, f carrier times
+
+t, it just keeps on wiggling
+around forever.
+
+Since you want to talk about
+that over the complete time of
+
+interest, you don't want to say
+what the time of interest
+
+is, you don't want to admit to
+your employer that this thing
+
+is going to stop working after
+one month because you want to
+
+let him think that he's going
+to make a profit off of this
+
+forever, and you don't want to
+commit to putting it into use
+
+in one month when you know it's
+going to get delayed for
+
+a whole year.
+
+So you want to think of this as
+
+something which is permanent.
+
+You don't want to answer the
+question at what time does it
+
+start and at what time does it
+end, because for many of the
+
+questions you ask, you
+can just regard
+
+it as going on forever.
+
+You have the same thing
+with impulses.
+
+Impulses are always models
+of short pulses.
+
+If you put these short pulses
+through a filter, the only
+
+thing which is of interest
+in them is what
+
+their integral is.
+
+And since the only thing of
+interest is their integral,
+
+you call it an impulse and you
+don't worry about just how
+
+narrow it is, except that it
+has infinite energy and,
+
+therefore, whenever you start
+to deal with a situation in
+
+which energy is important, these
+becomes lousy models.
+
+So we can't use these
+when we're
+
+talking about L2 functions.
+
+That's the price we pay for
+dealing with L2 functions.
+
+But it's a small price because
+for almost all the things
+
+we'll be dealing with, it's the
+energy of the functions
+
+that are really important.
+
+So as communication wave forms,
+infinite energy wave
+
+forms make mean square error
+quantization results
+
+meaningless.
+
+In other words, when you sample
+these infinite energy
+
+wave forms you get results that
+don't make any sense, and
+
+they make those channel
+results meaningless.
+
+Therefore, from now on, whether
+I remember to say it
+
+or not, everything we deal with,
+unless we're looking at
+
+counter examples to something,
+is going to be an L2 function.
+
+Let's go on.
+
+I'm starting to feel like I'm
+back in our signals and
+
+systems course, because at this
+point I'm defining my
+
+third different kind
+of transform.
+
+Fortunately, this is the last
+transform we will have to talk
+
+about, so we're all
+done with this.
+
+The other nice thing is that
+the discrete time Fourier
+
+transform happens to be just the
+time frequency dual of the
+
+Fourier series.
+
+So that whether you've ever
+studied the dtft or not, you
+
+already know everything there
+is to know about it, because
+
+the only things there are to
+know about it are the results
+
+about Fourier series.
+
+So the theorem is really the
+same theorem that we had for
+
+Fourier series.
+
+Assume that you have a function
+of frequency, u hat
+
+of f -- before we had a function
+of time, now we have
+
+a function of frequency.
+
+Suppose it's defined over
+the interval minus w
+
+to plus w into c.
+
+In other words, a way we often
+say that a function is
+
+truncated is to say it goes
+from some interval into c.
+
+This is a complex function which
+is non-zero only for f
+
+in this finite bandwidth
+range.
+
+We want to assume that this
+is L2 and thus, we
+
+know it's also L1.
+
+Then we're going to take the
+Fourier coefficients.
+
+Before we thought of the
+Fourier coefficients as
+
+corresponding to what goes on at
+different frequencies, now
+
+we're going to regard them as
+time quantities, and we'll see
+
+exactly why later.
+
+So we'll define these
+as the Fourier
+
+coefficients of this function.
+
+So they're 1 over 2w times
+this integral here.
+
+You remember before when we
+dealt with the Fourier series,
+
+we went from minus t over
+2 to plus t over 2.
+
+Now we're going from
+minus w to plus w.
+
+Why?
+
+It's just convention, there's
+no real reason.
+
+So that what's happening here
+is that this is a Fourier
+
+series formula for a coefficient
+where we're
+
+substituting w for t over 2.
+
+We're putting a plus sign in
+the exponent instead of a
+
+minus sign.
+
+In other words, we're doing this
+hermitian duality bit.
+
+What's the other difference?
+
+We're interchanging time
+and frequency.
+
+Aside from that it's exactly
+the same theorem that we
+
+established -- well, that
+we stated before.
+
+So we know that this quantity
+here, since u hat of f is L1,
+
+this is finite and it exists
+-- that's just a finite
+
+complex number and nothing more
+-- for all integer k.
+
+Also, the convergence result
+when we go back, this is the
+
+formula we try to use to go
+back to the function we
+
+started with.
+
+It's just a finite
+approximation
+
+to the Fourier series.
+
+We're saying that as k zero gets
+larger and larger, this
+
+finite approximation approaches
+the function in
+
+energy sense.
+
+So this is exactly what you
+should mean by a Fourier
+
+series anyway.
+
+It's exactly what you
+should mean by a
+
+Fourier transform anyway.
+
+As you go to the limit with more
+and more terms you get
+
+something which is equal to what
+you started with, except
+
+on the set of measure zero.
+
+In other words, it converges
+everywhere where it matters.
+
+It converges to something
+in the sense that the
+
+energy is the same.
+
+I said that in such a way that
+makes it a little simpler than
+
+it really is.
+
+You can't always say that this
+converges in any nice way.
+
+Next time I'm going to show
+you a truly awful function
+
+which we'll use in the Fourier
+series instead of dtft, which
+
+is time limited and which is
+just incredibly messy and
+
+it'll show you why you have to
+be a little bit careful about
+
+stating these results.
+
+But you don't have to worry
+about it most of the time,
+
+because this theorem
+is still true.
+
+It's just that you have to be a
+little careful about how to
+
+interpret it because you don't
+know whether this is going to
+
+reach a limit or not.
+
+All you know is that this will
+be true, this energy
+
+difference goes to zero.
+
+Also, the energy in the function
+is equal to the
+
+energy in the coefficients.
+
+This was the thing that we
+found so useful with the
+
+Fourier series.
+
+It's why we can play this game
+that we play with mean square
+
+quantization error of taking a
+function and then turning it
+
+into a sequence of samples,
+trying to quantize the samples
+
+for minimum mean square error
+and associate the mean square
+
+error in the samples with
+the mean square
+
+error on the function.
+
+You can't do that with anything
+that I know of other
+
+than mean square error.
+
+If you want to deal with other
+kinds of quantization errors,
+
+you have a real problem
+going from
+
+coefficients to functions.
+
+And finally, for any set of
+numbers u sub k, if the sum is
+
+less than infinity, in other
+words, if you're dealing with
+
+a sequence of finite energy,
+there always is such a
+
+frequency function.
+
+Many people when they use the
+discrete time Fourier
+
+transform think of starting with
+the sequence and taking a
+
+sequence and saying well it's
+nice to think of this sequence
+
+in the frequency domain, and
+then they say a function f
+
+exists such that this is true,
+or they just say that this is
+
+equal to that without worrying
+about the convergence at all,
+
+which is more common.
+
+But since we've already gone
+through all of this for the
+
+Fourier series, we might as well
+say it right here also.
+
+So there's really nothing
+different here.
+
+But now the question is why
+do these u of k's --
+
+I mean why do we think of those
+as time coefficients?
+
+I mean what's really going
+on in this discrete
+
+time Fourier transform.
+
+At this point it just looks like
+a lot of mathematics and
+
+it's hard to interpret what
+any of these things mean.
+
+Well, the next thing I want
+to do is to go into
+
+the sampling theorem.
+
+The sampling theorem, in fact,
+is going to interpret for you
+
+what this discrete time Fourier
+transform is, because
+
+the sampling theorem and the
+discrete time Fourier
+
+transform are just intimately
+related, they're hand and
+
+glove with each other,
+and that's the next
+
+thing we want to do.
+
+But first we have to re-write
+this a little bit.
+
+We're going to say that this
+frequency function is the
+
+limit in the mean of this --
+
+this rectangular function is
+what we use just to make sure
+
+we're only talking about
+frequency between
+
+minus w and plus w.
+
+The limit in the mean, there's a
+little notational trick that
+
+we use so that we can think of
+this as just a limit instead
+
+of thinking of it as this
+crazy thing that we just
+
+derive, which is really
+not so crazy.
+
+That means we can talk about
+this transform without always
+
+rubbing our noses in all
+of this mess here.
+
+It just means that once in
+awhile we go back and think
+
+what does this really mean.
+
+It means convergence in energy
+rather than convergence
+
+point-wise, because we might
+not have convergence
+
+point-wise.
+
+So we're going to write this
+also as the limit in the mean
+
+of the sum over k of u of k.
+
+We're going to glop all
+of this together.
+
+This is just some function
+of k and a frequency.
+
+So we're going to call that phi
+sub k of f at some wave
+
+form, and the wave
+form is this.
+
+What happens if you look at the
+relationship between to
+
+phi k of f and phi
+k prime of f?
+
+Namely, if you look at two
+different functions.
+
+These two functions are
+orthongonal to each other for
+
+the same reason that the
+functions that the sinusoid
+
+you used in the Fourier series
+are orthongonal.
+
+Namely, you take this function,
+you multiply it by e
+
+to the minus 2 pi ik prime
+f over 2w times
+
+this rectangular function.
+
+You integrate from minus w
+to w and what do you get?
+
+You're just integrating
+a sinusoid --
+
+the whole thing is one
+big sinusoid --
+
+over one period of that sinusoid
+or multiple periods
+
+of the sinusoid.
+
+Actually, k minus k prime
+periods of the sinusoid.
+
+And when you integrate a
+sinusoid over a period, what
+
+do you get?
+
+You get zero.
+
+So it says that these functions
+are all orthongonal
+
+to each other.
+
+So, presto, we have another
+orthongonal expansion just
+
+like the Fourier series gave us
+an orthongonal expansion.
+
+And in fact, it's the same
+orthongonal expansion.
+
+Now the next thing to observe
+is that we have done the
+
+Fourier transform and we've also
+done the discrete time
+
+Fourier transform.
+
+In both of them we're dealing
+with some frequency function.
+
+Now we're dealing with some
+frequency function which is
+
+limited to minus w to plus
+w, but we have two
+
+expansions for it.
+
+We have the Fourier transform,
+so we can go to a function u
+
+of t, and we also have
+this discrete
+
+time Fourier transform.
+
+So u of t is equal to this
+Fourier transform here.
+
+Again, I should write limit in
+the mean here, but then I
+
+think about and I say
+do I have to write
+
+limit in the mean?
+
+No.
+
+I don't need a limit in the
+mean here because I'm
+
+integrating this over
+finite limits.
+
+Since I'm taking a function over
+finite limits, u hat of f
+
+is over these limits, is an L1
+function, therefore, this
+
+integral exists.
+
+This function is a continuous
+function.
+
+There aren't any sets of measure
+zero involved here.
+
+This is one specific function
+which is always the same.
+
+You know what it is exactly
+at every point.
+
+At every point t,
+this converges.
+
+So then what we're going to do,
+what the sampling theorem
+
+does is it relates this to
+what you get with a dtft.
+
+So the sampling theorem says
+let u hat of f be an L2
+
+function which goes from minus
+ww to c, and let u of t be
+
+this, namely, that, which we
+now know exists and is
+
+continuous.
+
+Define capital T as 1 over 2w.
+
+You don't have to do that if you
+don't want to, but it's a
+
+little easier to think in terms
+of some increment of
+
+time, T, here.
+
+Then u of t is continuous,
+L2 and bounded.
+
+It's bounded by u of t less
+than or equal to this.
+
+Why is that?
+
+It doesn't make any sense
+as I stated it.
+
+Now it makes sense.
+
+OK, its magnitude is bounded.
+
+Its magnitude is bounded because
+if you take u of t
+
+magnitude, it's equal to the
+magnitude of this which is
+
+less than or equal to the
+integral of the magnitude of
+
+this, which is equal to the
+integral of the magnitude of
+
+just u hat of f, which
+is what we have here.
+
+So all of that works nicely.
+
+So, u of t is a nice,
+well-defined function.
+
+Then the other part of it is
+that u of t is equal to the
+
+sum if its values at these
+sample points times sinc of t
+
+minus kt over t.
+
+Now you've probably seen this
+sampling theorem before.
+
+How many people haven't
+seen this before?
+
+I mean aside from the question
+of trying to do it --
+
+do it in a way that
+makes sense.
+
+OK, you've all seen it.
+
+So good.
+
+What it's saying is you can
+represent a function in terms
+
+of just knowing what
+its samples are.
+
+Or you can take the function,
+you can sample it, and when
+
+you sample it if you put these
+little sinc hats around all
+
+the samples, you get back
+to the function again.
+
+So you take all the samples,
+you then put these sincs
+
+around them, add them
+all up, and
+
+bingo, you got the function.
+
+Let's see why that's true.
+
+Here's the sinc function here.
+
+The important thing about sinc
+t, sine pi t over pi t, which
+
+you can see by just looking at
+the sine function, is it has
+
+the value 1 when t
+is equal to zero.
+
+I mean to get that value 1, you
+really have to go through
+
+a limiting operation here to
+think of sine pi t when t is
+
+very small as being
+approximately equal to pi t.
+
+When you divide pi t by pi t you
+get 1, so that's its value
+
+there and value around there.
+
+At every other sample point,
+namely, at t equals 1, sine of
+
+pi t is zero.
+
+At t equals 2, sine of pi
+t is equal to zero.
+
+So the sinc function is 1 at
+zero and is zero at every
+
+other integer point.
+
+Now to see why it's true and to
+understand what the dtft is
+
+all about, note that we have
+said that a frequency
+
+function, u hat of f, can be
+expressed as the sum over k --
+
+and I should use a limit in the
+mean here but I'm not --
+
+of uk times this transform
+relationship here.
+
+Well, these are these functions
+that we talked about
+
+awhile ago.
+
+They're these functions.
+
+They're the sinusoids, periodic
+sinusoids in k
+
+truncated in frequency.
+
+So we know that u hat of f is
+equal to that dtft expansion.
+
+If I take the inverse Fourier
+transform of that, I can take
+
+the inverse Fourier transform
+of all these functions and
+
+I'll get u of t is equal to the
+sum over k, of uk pk of t.
+
+I'm being careless about
+the mathematics here.
+
+I've been careful about
+it all along.
+
+The notes does it carefully,
+particularly in the appendix.
+
+I'm not going to worry
+about that here.
+
+If I take the function pk of
+f, which is this truncated
+
+sinusoid, and I take the inverse
+transform of that --
+
+take the transform of
+this, I get this.
+
+Can you see that just
+by inspection?
+
+If you were really hot on these
+things, if you just
+
+finished taking 6.003, you could
+probably see that by
+
+inspection.
+
+If you remember all of those
+relationships that we went
+
+through before, you can
+see it by inspection.
+
+The Fourier transform of erect
+function is a sinc function.
+
+This exponential here when you
+go into the time domain
+
+corresponds to a time shift,
+so that gives rise to this
+
+time shift here.
+
+The 1 over t is just one of
+these constants you have to
+
+keep straight, and which I would
+do just by integrating
+
+the things to see what I get.
+
+Finally, u of kt, if I look at
+this, is just 1 over t times u
+
+of k, because these functions
+here are these sinc functions,
+
+which are zero everywhere
+but on their own point.
+
+So if I look at u of kt, it's a
+sum over k of ck of kt, and
+
+ck of kt is only 1 when little
+t is equal to k times capital
+
+T, and therefore, I get
+that point there.
+
+Therefore, u of kt is just
+1 over t times u of k.
+
+That finishes the sampling
+theorem except for really
+
+tracing through all of these
+things about convergence, but
+
+it also tells you what the
+discrete time Fourier
+
+transform is.
+
+Because the discrete time
+Fourier transform is just
+
+scaled samples of u of t.
+
+In other words, you start out
+with this frequency function,
+
+you take the inverse Fourier
+transform of it, you get a
+
+time function.
+
+You take the samples of that,
+you scale them, and those are
+
+the coefficients in the
+discrete time Fourier
+
+transform, which is what you
+use discrete time Fourier
+
+transforms for.
+
+You think of sampling of
+function, then you represent
+
+the function in terms of those
+samples and then you want to
+
+go into the frequency domain as
+a way of dealing with the
+
+properties of those samples, and
+all you're doing is just
+
+going into the Fourier transform
+of u of t, and all
+
+of that works out.
+
+There's one bizarre thing here,
+and I'm going to talk
+
+about that more next time.
+
+That is that when you look at
+this time frequency limited
+
+function, u hat of f, u hat of
+f can be very badly behaved.
+
+You can have a frequency limited
+function which does
+
+all sorts of crazy things.
+
+Since it's frequency limited
+as inverse transform, it's
+
+beautifully behaved.
+
+It's just the sum of sinc
+functions -- it's bounded,
+
+it's continuous and
+everything else.
+
+When we go back into the
+frequency domain it is just as
+
+ugly as can be.
+
+So what we have in the sampling
+theorem, it comes out
+
+particularly clearly.
+
+Is that L1 functions in one
+domain are nice, continuous,
+
+beautiful functions which are
+not L1 in the other domain.
+
+So you sort of go from
+L1 to continuous.
+
+Now when we're dealing with
+L2 functions, they're not
+
+continuous, they're not anything
+else, but you always
+
+go from L2 to L2.
+
+In other words, you can't get
+out of the L2 domain, and
+
+therefore, when you're dealing
+with L2 functions, all you
+
+have to worry about is L2
+functions, because you always
+
+stay there no matter what.
+
+When we start talking about
+stochastic processes, we'll
+
+find out you always
+stay there also.
+
+In other words, you only have
+to know about one thing.
+
+We've seen here that to
+interpret what these Fourier
+
+transforms mean, it's nice to
+have a little idea about L1
+
+functions also because when we
+think of going to the limit,
+
+when we go to the limit we get
+something which is badly
+
+behaved, and for these finite
+time and finite frequency
+
+approximations, we have things
+which are beautifully behaved.
+
+I'm going to stop now so we
+can pass out the quizzes.
\ No newline at end of file
diff --git a/R6-LQbqUCI0.txt b/R6-LQbqUCI0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b92dcd4886a20d462434b6a276f769ce21d5f6e3
--- /dev/null
+++ b/R6-LQbqUCI0.txt
@@ -0,0 +1,4395 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so um we're going
+
+ align:start position:0%
+ocw.mit.edu all right so um we're going
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so um we're going
+to Now show some of the
+
+ align:start position:0%
+to Now show some of the
+ 
+
+ align:start position:0%
+to Now show some of the
+examples um and uh so again they're in
+
+ align:start position:0%
+examples um and uh so again they're in
+ 
+
+ align:start position:0%
+examples um and uh so again they're in
+our directory here examples we're now in
+
+ align:start position:0%
+our directory here examples we're now in
+ 
+
+ align:start position:0%
+our directory here examples we're now in
+the sort of section two so we're going
+
+ align:start position:0%
+the sort of section two so we're going
+ 
+
+ align:start position:0%
+the sort of section two so we're going
+to go to
+
+ align:start position:0%
+to go to
+ 
+
+ align:start position:0%
+to go to
+Applications and uh we have the section
+
+ align:start position:0%
+Applications and uh we have the section
+ 
+
+ align:start position:0%
+Applications and uh we have the section
+called perfect power
+
+ align:start position:0%
+called perfect power
+ 
+
+ align:start position:0%
+called perfect power
+law the actual example codes are all
+
+ align:start position:0%
+law the actual example codes are all
+ 
+
+ align:start position:0%
+law the actual example codes are all
+these ones called PPL 1 2 3 and four we
+
+ align:start position:0%
+these ones called PPL 1 2 3 and four we
+ 
+
+ align:start position:0%
+these ones called PPL 1 2 3 and four we
+have actually a lot of other functions
+
+ align:start position:0%
+have actually a lot of other functions
+ 
+
+ align:start position:0%
+have actually a lot of other functions
+in here which are actually really useful
+
+ align:start position:0%
+in here which are actually really useful
+ 
+
+ align:start position:0%
+in here which are actually really useful
+functions they're the functions that do
+
+ align:start position:0%
+functions they're the functions that do
+ 
+
+ align:start position:0%
+functions they're the functions that do
+all this stuff um and maybe they should
+
+ align:start position:0%
+all this stuff um and maybe they should
+ 
+
+ align:start position:0%
+all this stuff um and maybe they should
+actually get folded folded into the main
+
+ align:start position:0%
+actually get folded folded into the main
+ 
+
+ align:start position:0%
+actually get folded folded into the main
+deform distribution they're here right
+
+ align:start position:0%
+deform distribution they're here right
+ 
+
+ align:start position:0%
+deform distribution they're here right
+now um they probably could be cleaned up
+
+ align:start position:0%
+now um they probably could be cleaned up
+ 
+
+ align:start position:0%
+now um they probably could be cleaned up
+a little bit um as part of part of the
+
+ align:start position:0%
+a little bit um as part of part of the
+ 
+
+ align:start position:0%
+a little bit um as part of part of the
+homework but these are again very useful
+
+ align:start position:0%
+homework but these are again very useful
+ 
+
+ align:start position:0%
+homework but these are again very useful
+functions for allowing you to generate
+
+ align:start position:0%
+functions for allowing you to generate
+ 
+
+ align:start position:0%
+functions for allowing you to generate
+and fit these types of things all right
+
+ align:start position:0%
+and fit these types of things all right
+ 
+
+ align:start position:0%
+and fit these types of things all right
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+have already started my mat lab
+
+ align:start position:0%
+have already started my mat lab
+ 
+
+ align:start position:0%
+have already started my mat lab
+session and there we are and so we will
+
+ align:start position:0%
+session and there we are and so we will
+ 
+
+ align:start position:0%
+session and there we are and so we will
+do the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going along
+
+ align:start position:0%
+going along
+ 
+
+ align:start position:0%
+going along
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+figures all righty actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so if we go and look at what
+
+ align:start position:0%
+all right so if we go and look at what
+ 
+
+ align:start position:0%
+all right so if we go and look at what
+we did here so the first thing we did is
+
+ align:start position:0%
+we did here so the first thing we did is
+ 
+
+ align:start position:0%
+we did here so the first thing we did is
+um is we uh set our parameters for our
+
+ align:start position:0%
+um is we uh set our parameters for our
+ 
+
+ align:start position:0%
+um is we uh set our parameters for our
+power perfect power law fit so we set
+
+ align:start position:0%
+power perfect power law fit so we set
+ 
+
+ align:start position:0%
+power perfect power law fit so we set
+Alpha of 1.3 a dmax of a th000 then
+
+ align:start position:0%
+Alpha of 1.3 a dmax of a th000 then
+ 
+
+ align:start position:0%
+Alpha of 1.3 a dmax of a th000 then
+about you know approximately 30 bins we
+
+ align:start position:0%
+about you know approximately 30 bins we
+ 
+
+ align:start position:0%
+about you know approximately 30 bins we
+called our function here which is in
+
+ align:start position:0%
+called our function here which is in
+ 
+
+ align:start position:0%
+called our function here which is in
+this directory which is power law
+
+ align:start position:0%
+this directory which is power law
+ 
+
+ align:start position:0%
+this directory which is power law
+distribution which will create a power
+
+ align:start position:0%
+distribution which will create a power
+ 
+
+ align:start position:0%
+distribution which will create a power
+law distribution from these three
+
+ align:start position:0%
+law distribution from these three
+ 
+
+ align:start position:0%
+law distribution from these three
+parameters and then the first thing we
+
+ align:start position:0%
+parameters and then the first thing we
+ 
+
+ align:start position:0%
+parameters and then the first thing we
+did is just plot that distribution so we
+
+ align:start position:0%
+did is just plot that distribution so we
+ 
+
+ align:start position:0%
+did is just plot that distribution so we
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+here we go to figure one you can see
+
+ align:start position:0%
+here we go to figure one you can see
+ 
+
+ align:start position:0%
+here we go to figure one you can see
+there is that distribution so our
+
+ align:start position:0%
+there is that distribution so our
+ 
+
+ align:start position:0%
+there is that distribution so our
+perfect power law uh distribution with
+
+ align:start position:0%
+perfect power law uh distribution with
+ 
+
+ align:start position:0%
+perfect power law uh distribution with
+these parameters very nicely very nicely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done then uh then moving along we can
+
+ align:start position:0%
+done then uh then moving along we can
+ 
+
+ align:start position:0%
+done then uh then moving along we can
+compute this is how you compute the
+
+ align:start position:0%
+compute this is how you compute the
+ 
+
+ align:start position:0%
+compute this is how you compute the
+total number of vertices from the
+
+ align:start position:0%
+total number of vertices from the
+ 
+
+ align:start position:0%
+total number of vertices from the
+distribution we just sum the no total
+
+ align:start position:0%
+distribution we just sum the no total
+ 
+
+ align:start position:0%
+distribution we just sum the no total
+number of edges we can sum there and
+
+ align:start position:0%
+number of edges we can sum there and
+ 
+
+ align:start position:0%
+number of edges we can sum there and
+then we see that the total vertices was
+
+ align:start position:0%
+then we see that the total vertices was
+ 
+
+ align:start position:0%
+then we see that the total vertices was
+18, 187 84,000 edges with an edge to
+
+ align:start position:0%
+18, 187 84,000 edges with an edge to
+ 
+
+ align:start position:0%
+18, 187 84,000 edges with an edge to
+vertex ratio of
+
+ align:start position:0%
+vertex ratio of
+ 
+
+ align:start position:0%
+vertex ratio of
+4.6 we now have a function called edges
+
+ align:start position:0%
+4.6 we now have a function called edges
+ 
+
+ align:start position:0%
+4.6 we now have a function called edges
+from distribution so if I pass in the
+
+ align:start position:0%
+from distribution so if I pass in the
+ 
+
+ align:start position:0%
+from distribution so if I pass in the
+distribution essentially the degrees and
+
+ align:start position:0%
+distribution essentially the degrees and
+ 
+
+ align:start position:0%
+distribution essentially the degrees and
+the counts it will then generate a set
+
+ align:start position:0%
+the counts it will then generate a set
+ 
+
+ align:start position:0%
+the counts it will then generate a set
+of vertices that is consistent with that
+
+ align:start position:0%
+of vertices that is consistent with that
+ 
+
+ align:start position:0%
+of vertices that is consistent with that
+distribution all right and now I'm going
+
+ align:start position:0%
+distribution all right and now I'm going
+ 
+
+ align:start position:0%
+distribution all right and now I'm going
+to create some
+
+ align:start position:0%
+to create some
+ 
+
+ align:start position:0%
+to create some
+permutations basically uh of these
+
+ align:start position:0%
+permutations basically uh of these
+ 
+
+ align:start position:0%
+permutations basically uh of these
+vertices I'm going to create a I'm going
+
+ align:start position:0%
+vertices I'm going to create a I'm going
+ 
+
+ align:start position:0%
+vertices I'm going to create a I'm going
+to uh uh randomly permute The Edge order
+
+ align:start position:0%
+to uh uh randomly permute The Edge order
+ 
+
+ align:start position:0%
+to uh uh randomly permute The Edge order
+with these two sets here so if I B tally
+
+ align:start position:0%
+with these two sets here so if I B tally
+ 
+
+ align:start position:0%
+with these two sets here so if I B tally
+make a random permutation of the number
+
+ align:start position:0%
+make a random permutation of the number
+ 
+
+ align:start position:0%
+make a random permutation of the number
+of edges okay that allows me to permute
+
+ align:start position:0%
+of edges okay that allows me to permute
+ 
+
+ align:start position:0%
+of edges okay that allows me to permute
+the edges and I can also randomly
+
+ align:start position:0%
+the edges and I can also randomly
+ 
+
+ align:start position:0%
+the edges and I can also randomly
+permute the vertex labels themselves and
+
+ align:start position:0%
+permute the vertex labels themselves and
+ 
+
+ align:start position:0%
+permute the vertex labels themselves and
+then I can look at these different
+
+ align:start position:0%
+then I can look at these different
+ 
+
+ align:start position:0%
+then I can look at these different
+permutations to see what kind of graphs
+
+ align:start position:0%
+permutations to see what kind of graphs
+ 
+
+ align:start position:0%
+permutations to see what kind of graphs
+they've created so if I don't per
+
+ align:start position:0%
+they've created so if I don't per
+ 
+
+ align:start position:0%
+they've created so if I don't per
+permute the data I just have a Zer here
+
+ align:start position:0%
+permute the data I just have a Zer here
+ 
+
+ align:start position:0%
+permute the data I just have a Zer here
+okay I just pass in the vertices that
+
+ align:start position:0%
+okay I just pass in the vertices that
+ 
+
+ align:start position:0%
+okay I just pass in the vertices that
+were created I create a no non-permuted
+
+ align:start position:0%
+were created I create a no non-permuted
+ 
+
+ align:start position:0%
+were created I create a no non-permuted
+adjacency
+
+ align:start position:0%
+adjacency
+ 
+
+ align:start position:0%
+adjacency
+Matrix okay I can then look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and that just shows you this is the
+
+ align:start position:0%
+that and that just shows you this is the
+ 
+
+ align:start position:0%
+that and that just shows you this is the
+adjacency Matrix this isn't appli it
+
+ align:start position:0%
+adjacency Matrix this isn't appli it
+ 
+
+ align:start position:0%
+adjacency Matrix this isn't appli it
+just shows you that's I just created a
+
+ align:start position:0%
+just shows you that's I just created a
+ 
+
+ align:start position:0%
+just shows you that's I just created a
+Vertex that's entirely self- Loops not
+
+ align:start position:0%
+Vertex that's entirely self- Loops not
+ 
+
+ align:start position:0%
+Vertex that's entirely self- Loops not
+very interesting but nevertheless
+
+ align:start position:0%
+very interesting but nevertheless
+ 
+
+ align:start position:0%
+very interesting but nevertheless
+completely consistent with a perfect
+
+ align:start position:0%
+completely consistent with a perfect
+ 
+
+ align:start position:0%
+completely consistent with a perfect
+power law degree distribution
+
+ align:start position:0%
+power law degree distribution
+ 
+
+ align:start position:0%
+power law degree distribution
+so likewise if I just permute the
+
+ align:start position:0%
+so likewise if I just permute the
+ 
+
+ align:start position:0%
+so likewise if I just permute the
+edges so basically I take my permutation
+
+ align:start position:0%
+edges so basically I take my permutation
+ 
+
+ align:start position:0%
+edges so basically I take my permutation
+here and I just permute that okay this
+
+ align:start position:0%
+here and I just permute that okay this
+ 
+
+ align:start position:0%
+here and I just permute that okay this
+is just uh not permuting the vertex
+
+ align:start position:0%
+is just uh not permuting the vertex
+ 
+
+ align:start position:0%
+is just uh not permuting the vertex
+labels but just permuting the
+
+ align:start position:0%
+labels but just permuting the
+ 
+
+ align:start position:0%
+labels but just permuting the
+edges to the next figure here figure
+
+ align:start position:0%
+edges to the next figure here figure
+ 
+
+ align:start position:0%
+edges to the next figure here figure
+three all right and we get this
+
+ align:start position:0%
+three all right and we get this
+ 
+
+ align:start position:0%
+three all right and we get this
+distribution basically start vertex end
+
+ align:start position:0%
+distribution basically start vertex end
+ 
+
+ align:start position:0%
+distribution basically start vertex end
+vertex looks very random fairly random
+
+ align:start position:0%
+vertex looks very random fairly random
+ 
+
+ align:start position:0%
+vertex looks very random fairly random
+however you see the highest degree
+
+ align:start position:0%
+however you see the highest degree
+ 
+
+ align:start position:0%
+however you see the highest degree
+vertices are up here at 0 0 because
+
+ align:start position:0%
+vertices are up here at 0 0 because
+ 
+
+ align:start position:0%
+vertices are up here at 0 0 because
+that's the order in which the generator
+
+ align:start position:0%
+that's the order in which the generator
+ 
+
+ align:start position:0%
+that's the order in which the generator
+spits them out it gives you the highest
+
+ align:start position:0%
+spits them out it gives you the highest
+ 
+
+ align:start position:0%
+spits them out it gives you the highest
+degree vertices first and so although
+
+ align:start position:0%
+degree vertices first and so although
+ 
+
+ align:start position:0%
+degree vertices first and so although
+we've reconnected them with different
+
+ align:start position:0%
+we've reconnected them with different
+ 
+
+ align:start position:0%
+we've reconnected them with different
+edges okay you see that they still their
+
+ align:start position:0%
+edges okay you see that they still their
+ 
+
+ align:start position:0%
+edges okay you see that they still their
+vertex labels still have an in intrinsic
+
+ align:start position:0%
+vertex labels still have an in intrinsic
+ 
+
+ align:start position:0%
+vertex labels still have an in intrinsic
+order which is corresponding to vertex
+
+ align:start position:0%
+order which is corresponding to vertex
+ 
+
+ align:start position:0%
+order which is corresponding to vertex
+degree I should say this generates this
+
+ align:start position:0%
+degree I should say this generates this
+ 
+
+ align:start position:0%
+degree I should say this generates this
+naturally it's a very common way to
+
+ align:start position:0%
+naturally it's a very common way to
+ 
+
+ align:start position:0%
+naturally it's a very common way to
+if you have arbitrary vertices and you
+
+ align:start position:0%
+if you have arbitrary vertices and you
+ 
+
+ align:start position:0%
+if you have arbitrary vertices and you
+want to put them on an adjacency Matrix
+
+ align:start position:0%
+want to put them on an adjacency Matrix
+ 
+
+ align:start position:0%
+want to put them on an adjacency Matrix
+one of the first thing to do is just to
+
+ align:start position:0%
+one of the first thing to do is just to
+ 
+
+ align:start position:0%
+one of the first thing to do is just to
+reorder them according to degree you'll
+
+ align:start position:0%
+reorder them according to degree you'll
+ 
+
+ align:start position:0%
+reorder them according to degree you'll
+always get some kind of structure that
+
+ align:start position:0%
+always get some kind of structure that
+ 
+
+ align:start position:0%
+always get some kind of structure that
+emerges there and it's an often an
+
+ align:start position:0%
+emerges there and it's an often an
+ 
+
+ align:start position:0%
+emerges there and it's an often an
+easier way to kind of see what's going
+
+ align:start position:0%
+easier way to kind of see what's going
+ 
+
+ align:start position:0%
+easier way to kind of see what's going
+on there and as you can see from the
+
+ align:start position:0%
+on there and as you can see from the
+ 
+
+ align:start position:0%
+on there and as you can see from the
+previous data if you saw if you ordered
+
+ align:start position:0%
+previous data if you saw if you ordered
+ 
+
+ align:start position:0%
+previous data if you saw if you ordered
+things by degree and you saw this type
+
+ align:start position:0%
+things by degree and you saw this type
+ 
+
+ align:start position:0%
+things by degree and you saw this type
+of distribution be like aha that looks a
+
+ align:start position:0%
+of distribution be like aha that looks a
+ 
+
+ align:start position:0%
+of distribution be like aha that looks a
+lot like a power law distribution just
+
+ align:start position:0%
+lot like a power law distribution just
+ 
+
+ align:start position:0%
+lot like a power law distribution just
+from the kind of the the scatter of the
+
+ align:start position:0%
+from the kind of the the scatter of the
+ 
+
+ align:start position:0%
+from the kind of the the scatter of the
+dots
+
+ align:start position:0%
+dots
+ 
+
+ align:start position:0%
+dots
+so moving on here so now we're just
+
+ align:start position:0%
+so moving on here so now we're just
+ 
+
+ align:start position:0%
+so moving on here so now we're just
+going to permute the vertex labels so we
+
+ align:start position:0%
+going to permute the vertex labels so we
+ 
+
+ align:start position:0%
+going to permute the vertex labels so we
+are not permuting the edges just the
+
+ align:start position:0%
+are not permuting the edges just the
+ 
+
+ align:start position:0%
+are not permuting the edges just the
+vertex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+labels and so if you see
+
+ align:start position:0%
+labels and so if you see
+ 
+
+ align:start position:0%
+labels and so if you see
+here and then by permuting the vertex
+
+ align:start position:0%
+here and then by permuting the vertex
+ 
+
+ align:start position:0%
+here and then by permuting the vertex
+labels it looks random but fairly sparse
+
+ align:start position:0%
+labels it looks random but fairly sparse
+ 
+
+ align:start position:0%
+labels it looks random but fairly sparse
+that's because we still every single
+
+ align:start position:0%
+that's because we still every single
+ 
+
+ align:start position:0%
+that's because we still every single
+time you know we've moved the vertex
+
+ align:start position:0%
+time you know we've moved the vertex
+ 
+
+ align:start position:0%
+time you know we've moved the vertex
+labels around but all the edges
+
+ align:start position:0%
+labels around but all the edges
+ 
+
+ align:start position:0%
+labels around but all the edges
+associated with that vertex pair still
+
+ align:start position:0%
+associated with that vertex pair still
+ 
+
+ align:start position:0%
+associated with that vertex pair still
+will ship shipped around in sync we
+
+ align:start position:0%
+will ship shipped around in sync we
+ 
+
+ align:start position:0%
+will ship shipped around in sync we
+haven't done anything to break them up
+
+ align:start position:0%
+haven't done anything to break them up
+ 
+
+ align:start position:0%
+haven't done anything to break them up
+whereas before we broke up the edges but
+
+ align:start position:0%
+whereas before we broke up the edges but
+ 
+
+ align:start position:0%
+whereas before we broke up the edges but
+we didn't change the
+
+ align:start position:0%
+we didn't change the
+ 
+
+ align:start position:0%
+we didn't change the
+labels and so then the final one which
+
+ align:start position:0%
+labels and so then the final one which
+ 
+
+ align:start position:0%
+labels and so then the final one which
+is the one that we typically do when we
+
+ align:start position:0%
+is the one that we typically do when we
+ 
+
+ align:start position:0%
+is the one that we typically do when we
+want to create random is we permute both
+
+ align:start position:0%
+want to create random is we permute both
+ 
+
+ align:start position:0%
+want to create random is we permute both
+the vertices and the edges all right to
+
+ align:start position:0%
+the vertices and the edges all right to
+ 
+
+ align:start position:0%
+the vertices and the edges all right to
+create sort of a truly random looking uh
+
+ align:start position:0%
+create sort of a truly random looking uh
+ 
+
+ align:start position:0%
+create sort of a truly random looking uh
+adjacency Matrix and there you see you
+
+ align:start position:0%
+adjacency Matrix and there you see you
+ 
+
+ align:start position:0%
+adjacency Matrix and there you see you
+have something and now and now what you
+
+ align:start position:0%
+have something and now and now what you
+ 
+
+ align:start position:0%
+have something and now and now what you
+can also see here is these high degree
+
+ align:start position:0%
+can also see here is these high degree
+ 
+
+ align:start position:0%
+can also see here is these high degree
+vertices uh you know uh do stand out
+
+ align:start position:0%
+vertices uh you know uh do stand out
+ 
+
+ align:start position:0%
+vertices uh you know uh do stand out
+this is a very standard power law
+
+ align:start position:0%
+this is a very standard power law
+ 
+
+ align:start position:0%
+this is a very standard power law
+distribution you'll see these sort of
+
+ align:start position:0%
+distribution you'll see these sort of
+ 
+
+ align:start position:0%
+distribution you'll see these sort of
+dense rows and uh and and columns in
+
+ align:start position:0%
+dense rows and uh and and columns in
+ 
+
+ align:start position:0%
+dense rows and uh and and columns in
+there that are indicative of these very
+
+ align:start position:0%
+there that are indicative of these very
+ 
+
+ align:start position:0%
+there that are indicative of these very
+high degree nodes uh when we just when
+
+ align:start position:0%
+high degree nodes uh when we just when
+ 
+
+ align:start position:0%
+high degree nodes uh when we just when
+we didn't when we just permuted the
+
+ align:start position:0%
+we didn't when we just permuted the
+ 
+
+ align:start position:0%
+we didn't when we just permuted the
+edges but not the the the the vertices
+
+ align:start position:0%
+edges but not the the the the vertices
+ 
+
+ align:start position:0%
+edges but not the the the the vertices
+these high degree uh rows and columns
+
+ align:start position:0%
+these high degree uh rows and columns
+ 
+
+ align:start position:0%
+these high degree uh rows and columns
+all got shifted up into the corner of
+
+ align:start position:0%
+all got shifted up into the corner of
+ 
+
+ align:start position:0%
+all got shifted up into the corner of
+the plot so so again another way to sort
+
+ align:start position:0%
+the plot so so again another way to sort
+ 
+
+ align:start position:0%
+the plot so so again another way to sort
+of begin to look at the data in a way to
+
+ align:start position:0%
+of begin to look at the data in a way to
+ 
+
+ align:start position:0%
+of begin to look at the data in a way to
+sort of recognize structure H I think
+
+ align:start position:0%
+sort of recognize structure H I think
+ 
+
+ align:start position:0%
+sort of recognize structure H I think
+these adjacency matrices once you start
+
+ align:start position:0%
+these adjacency matrices once you start
+ 
+
+ align:start position:0%
+these adjacency matrices once you start
+looking at them you begin to certain get
+
+ align:start position:0%
+looking at them you begin to certain get
+ 
+
+ align:start position:0%
+looking at them you begin to certain get
+a comfort for them just as we do with
+
+ align:start position:0%
+a comfort for them just as we do with
+ 
+
+ align:start position:0%
+a comfort for them just as we do with
+other types of data we begin to learn
+
+ align:start position:0%
+other types of data we begin to learn
+ 
+
+ align:start position:0%
+other types of data we begin to learn
+what they what they look like um this is
+
+ align:start position:0%
+what they what they look like um this is
+ 
+
+ align:start position:0%
+what they what they look like um this is
+a very good way to look at the data
+
+ align:start position:0%
+a very good way to look at the data
+ 
+
+ align:start position:0%
+a very good way to look at the data
+because you can look at a fair amount if
+
+ align:start position:0%
+because you can look at a fair amount if
+ 
+
+ align:start position:0%
+because you can look at a fair amount if
+I were to actually plot the graph of
+
+ align:start position:0%
+I were to actually plot the graph of
+ 
+
+ align:start position:0%
+I were to actually plot the graph of
+18,000 vertices as a traditional graph
+
+ align:start position:0%
+18,000 vertices as a traditional graph
+ 
+
+ align:start position:0%
+18,000 vertices as a traditional graph
+with vertices and lines connecting them
+
+ align:start position:0%
+with vertices and lines connecting them
+ 
+
+ align:start position:0%
+with vertices and lines connecting them
+it would just be blue the entire screen
+
+ align:start position:0%
+it would just be blue the entire screen
+ 
+
+ align:start position:0%
+it would just be blue the entire screen
+would be blue there would be no way to
+
+ align:start position:0%
+would be blue there would be no way to
+ 
+
+ align:start position:0%
+would be blue there would be no way to
+properly uh position those vertices uh
+
+ align:start position:0%
+properly uh position those vertices uh
+ 
+
+ align:start position:0%
+properly uh position those vertices uh
+here you know this is 8 4,000 data
+
+ align:start position:0%
+here you know this is 8 4,000 data
+ 
+
+ align:start position:0%
+here you know this is 8 4,000 data
+points and I can still kind of see it a
+
+ align:start position:0%
+points and I can still kind of see it a
+ 
+
+ align:start position:0%
+points and I can still kind of see it a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit this is kind of the limit 100,000
+
+ align:start position:0%
+bit this is kind of the limit 100,000
+ 
+
+ align:start position:0%
+bit this is kind of the limit 100,000
+edges is kind of the limit of what you
+
+ align:start position:0%
+edges is kind of the limit of what you
+ 
+
+ align:start position:0%
+edges is kind of the limit of what you
+can put on any plot to really see it
+
+ align:start position:0%
+can put on any plot to really see it
+ 
+
+ align:start position:0%
+can put on any plot to really see it
+unless there's some sort of hidden
+
+ align:start position:0%
+unless there's some sort of hidden
+ 
+
+ align:start position:0%
+unless there's some sort of hidden
+structure that allows you to like you
+
+ align:start position:0%
+structure that allows you to like you
+ 
+
+ align:start position:0%
+structure that allows you to like you
+know really really you know move it all
+
+ align:start position:0%
+know really really you know move it all
+ 
+
+ align:start position:0%
+know really really you know move it all
+together um but you know the adjacency
+
+ align:start position:0%
+together um but you know the adjacency
+ 
+
+ align:start position:0%
+together um but you know the adjacency
+Matrix is a great way to look at fairly
+
+ align:start position:0%
+Matrix is a great way to look at fairly
+ 
+
+ align:start position:0%
+Matrix is a great way to look at fairly
+large uh
+
+ align:start position:0%
+large uh
+ 
+
+ align:start position:0%
+large uh
+graphs so when so the so we generally do
+
+ align:start position:0%
+graphs so when so the so we generally do
+ 
+
+ align:start position:0%
+graphs so when so the so we generally do
+that so this is just this is this is the
+
+ align:start position:0%
+that so this is just this is this is the
+ 
+
+ align:start position:0%
+that so this is just this is this is the
+procedure create you know your perfect
+
+ align:start position:0%
+procedure create you know your perfect
+ 
+
+ align:start position:0%
+procedure create you know your perfect
+power law distribution
+
+ align:start position:0%
+power law distribution
+ 
+
+ align:start position:0%
+power law distribution
+create some edges create some
+
+ align:start position:0%
+create some edges create some
+ 
+
+ align:start position:0%
+create some edges create some
+permutations and then permute it and
+
+ align:start position:0%
+permutations and then permute it and
+ 
+
+ align:start position:0%
+permutations and then permute it and
+then off you are you've just created a
+
+ align:start position:0%
+then off you are you've just created a
+ 
+
+ align:start position:0%
+then off you are you've just created a
+per randomized perfect Power log graph
+
+ align:start position:0%
+per randomized perfect Power log graph
+ 
+
+ align:start position:0%
+per randomized perfect Power log graph
+again this is a this is an example of a
+
+ align:start position:0%
+again this is a this is an example of a
+ 
+
+ align:start position:0%
+again this is a this is an example of a
+code where you probably might even just
+
+ align:start position:0%
+code where you probably might even just
+ 
+
+ align:start position:0%
+code where you probably might even just
+take this program and adjust it to suit
+
+ align:start position:0%
+take this program and adjust it to suit
+ 
+
+ align:start position:0%
+take this program and adjust it to suit
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+needs and then I think we did that and
+
+ align:start position:0%
+needs and then I think we did that and
+ 
+
+ align:start position:0%
+needs and then I think we did that and
+then finally we plotted the degree
+
+ align:start position:0%
+then finally we plotted the degree
+ 
+
+ align:start position:0%
+then finally we plotted the degree
+distribution of A3 just to see show you
+
+ align:start position:0%
+distribution of A3 just to see show you
+ 
+
+ align:start position:0%
+distribution of A3 just to see show you
+that I'm not lying and again the the
+
+ align:start position:0%
+that I'm not lying and again the the
+ 
+
+ align:start position:0%
+that I'm not lying and again the the
+triangle was the original and the blue
+
+ align:start position:0%
+triangle was the original and the blue
+ 
+
+ align:start position:0%
+triangle was the original and the blue
+was the thing and you see
+
+ align:start position:0%
+was the thing and you see
+ 
+
+ align:start position:0%
+was the thing and you see
+throughout all those permutations our
+
+ align:start position:0%
+throughout all those permutations our
+ 
+
+ align:start position:0%
+throughout all those permutations our
+degree distribution remain the same even
+
+ align:start position:0%
+degree distribution remain the same even
+ 
+
+ align:start position:0%
+degree distribution remain the same even
+though they look those would be
+
+ align:start position:0%
+though they look those would be
+ 
+
+ align:start position:0%
+though they look those would be
+completely different graphs their degree
+
+ align:start position:0%
+completely different graphs their degree
+ 
+
+ align:start position:0%
+completely different graphs their degree
+distributions are are
+
+ align:start position:0%
+distributions are are
+ 
+
+ align:start position:0%
+distributions are are
+identical all
+
+ align:start position:0%
+identical all
+ 
+
+ align:start position:0%
+identical all
+right so let's move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all righty so this is just showing
+
+ align:start position:0%
+here all righty so this is just showing
+ 
+
+ align:start position:0%
+here all righty so this is just showing
+so we actually rolled this up all into
+
+ align:start position:0%
+so we actually rolled this up all into
+ 
+
+ align:start position:0%
+so we actually rolled this up all into
+one function here for you Rand power law
+
+ align:start position:0%
+one function here for you Rand power law
+ 
+
+ align:start position:0%
+one function here for you Rand power law
+Matrix if you give it an alpha a dmax
+
+ align:start position:0%
+Matrix if you give it an alpha a dmax
+ 
+
+ align:start position:0%
+Matrix if you give it an alpha a dmax
+and an ND it will do those three steps
+
+ align:start position:0%
+and an ND it will do those three steps
+ 
+
+ align:start position:0%
+and an ND it will do those three steps
+for you that I had in the previous chart
+
+ align:start position:0%
+for you that I had in the previous chart
+ 
+
+ align:start position:0%
+for you that I had in the previous chart
+all in one thing and produce an
+
+ align:start position:0%
+all in one thing and produce an
+ 
+
+ align:start position:0%
+all in one thing and produce an
+adjacency Matrix that's uh that's a
+
+ align:start position:0%
+adjacency Matrix that's uh that's a
+ 
+
+ align:start position:0%
+adjacency Matrix that's uh that's a
+perfect power law based on these on
+
+ align:start position:0%
+perfect power law based on these on
+ 
+
+ align:start position:0%
+perfect power law based on these on
+these parameters and again you saw we
+
+ align:start position:0%
+these parameters and again you saw we
+ 
+
+ align:start position:0%
+these parameters and again you saw we
+have the same number of vertices that we
+
+ align:start position:0%
+have the same number of vertices that we
+ 
+
+ align:start position:0%
+have the same number of vertices that we
+saw and edges and ratio that we saw
+
+ align:start position:0%
+saw and edges and ratio that we saw
+ 
+
+ align:start position:0%
+saw and edges and ratio that we saw
+before so that's all the same uh now
+
+ align:start position:0%
+before so that's all the same uh now
+ 
+
+ align:start position:0%
+before so that's all the same uh now
+we're going to transform this data clean
+
+ align:start position:0%
+we're going to transform this data clean
+ 
+
+ align:start position:0%
+we're going to transform this data clean
+up this data by making it uh uh making
+
+ align:start position:0%
+up this data by making it uh uh making
+ 
+
+ align:start position:0%
+up this data by making it uh uh making
+it unweighted undirected we're going to
+
+ align:start position:0%
+it unweighted undirected we're going to
+ 
+
+ align:start position:0%
+it unweighted undirected we're going to
+eliminate self Loops we're going to take
+
+ align:start position:0%
+eliminate self Loops we're going to take
+ 
+
+ align:start position:0%
+eliminate self Loops we're going to take
+the upper triangular Port uh here's
+
+ align:start position:0%
+the upper triangular Port uh here's
+ 
+
+ align:start position:0%
+the upper triangular Port uh here's
+another one it's unweighted no self
+
+ align:start position:0%
+another one it's unweighted no self
+ 
+
+ align:start position:0%
+another one it's unweighted no self
+Loops different versions of them and
+
+ align:start position:0%
+Loops different versions of them and
+ 
+
+ align:start position:0%
+Loops different versions of them and
+then we do uh you can see what those
+
+ align:start position:0%
+then we do uh you can see what those
+ 
+
+ align:start position:0%
+then we do uh you can see what those
+that looks
+
+ align:start position:0%
+that looks
+ 
+
+ align:start position:0%
+that looks
+like so if we look at the first one here
+
+ align:start position:0%
+like so if we look at the first one here
+ 
+
+ align:start position:0%
+like so if we look at the first one here
+so this just shows the unweighted what
+
+ align:start position:0%
+so this just shows the unweighted what
+ 
+
+ align:start position:0%
+so this just shows the unweighted what
+unweighting just basically making the
+
+ align:start position:0%
+unweighting just basically making the
+ 
+
+ align:start position:0%
+unweighting just basically making the
+data unweighted does to the data set so
+
+ align:start position:0%
+data unweighted does to the data set so
+ 
+
+ align:start position:0%
+data unweighted does to the data set so
+this the the the triangles are the
+
+ align:start position:0%
+this the the the triangles are the
+ 
+
+ align:start position:0%
+this the the the triangles are the
+original data and just making it
+
+ align:start position:0%
+original data and just making it
+ 
+
+ align:start position:0%
+original data and just making it
+unweighted how it just distorts that
+
+ align:start position:0%
+unweighted how it just distorts that
+ 
+
+ align:start position:0%
+unweighted how it just distorts that
+that uh that data
+
+ align:start position:0%
+that uh that data
+ 
+
+ align:start position:0%
+that uh that data
+set we go
+
+ align:start position:0%
+set we go
+ 
+
+ align:start position:0%
+set we go
+here this just shows you what happens
+
+ align:start position:0%
+here this just shows you what happens
+ 
+
+ align:start position:0%
+here this just shows you what happens
+when you make it
+
+ align:start position:0%
+when you make it
+ 
+
+ align:start position:0%
+when you make it
+undirected so unweighted means we took
+
+ align:start position:0%
+undirected so unweighted means we took
+ 
+
+ align:start position:0%
+undirected so unweighted means we took
+everything everything all the any cases
+
+ align:start position:0%
+everything everything all the any cases
+ 
+
+ align:start position:0%
+everything everything all the any cases
+where we had vertices with more than one
+
+ align:start position:0%
+where we had vertices with more than one
+ 
+
+ align:start position:0%
+where we had vertices with more than one
+connection to them if something had five
+
+ align:start position:0%
+connection to them if something had five
+ 
+
+ align:start position:0%
+connection to them if something had five
+connections now it just gets one
+
+ align:start position:0%
+connections now it just gets one
+ 
+
+ align:start position:0%
+connections now it just gets one
+connection and so that was a fairly big
+
+ align:start position:0%
+connection and so that was a fairly big
+ 
+
+ align:start position:0%
+connection and so that was a fairly big
+distortion
+
+ align:start position:0%
+distortion
+ 
+
+ align:start position:0%
+distortion
+example is like if you you take a like a
+
+ align:start position:0%
+example is like if you you take a like a
+ 
+
+ align:start position:0%
+example is like if you you take a like a
+person's social network graph and if you
+
+ align:start position:0%
+person's social network graph and if you
+ 
+
+ align:start position:0%
+person's social network graph and if you
+were to make it
+
+ align:start position:0%
+were to make it
+ 
+
+ align:start position:0%
+were to make it
+unweighted what you're saying is that
+
+ align:start position:0%
+unweighted what you're saying is that
+ 
+
+ align:start position:0%
+unweighted what you're saying is that
+the fact that the connection you have
+
+ align:start position:0%
+the fact that the connection you have
+ 
+
+ align:start position:0%
+the fact that the connection you have
+with your spouse is identical to with
+
+ align:start position:0%
+with your spouse is identical to with
+ 
+
+ align:start position:0%
+with your spouse is identical to with
+someone that you emailed once or that
+
+ align:start position:0%
+someone that you emailed once or that
+ 
+
+ align:start position:0%
+someone that you emailed once or that
+you friended once right and I think we
+
+ align:start position:0%
+you friended once right and I think we
+ 
+
+ align:start position:0%
+you friended once right and I think we
+all agree that that's a fair amount of
+
+ align:start position:0%
+all agree that that's a fair amount of
+ 
+
+ align:start position:0%
+all agree that that's a fair amount of
+information that's lost there and so
+
+ align:start position:0%
+information that's lost there and so
+ 
+
+ align:start position:0%
+information that's lost there and so
+again encouraging folks to uh to uh to
+
+ align:start position:0%
+again encouraging folks to uh to uh to
+ 
+
+ align:start position:0%
+again encouraging folks to uh to uh to
+not to to be aware of that and to to
+
+ align:start position:0%
+not to to be aware of that and to to
+ 
+
+ align:start position:0%
+not to to be aware of that and to to
+sort of you know be careful of when
+
+ align:start position:0%
+sort of you know be careful of when
+ 
+
+ align:start position:0%
+sort of you know be careful of when
+they're doing again making it undirected
+
+ align:start position:0%
+they're doing again making it undirected
+ 
+
+ align:start position:0%
+they're doing again making it undirected
+just means we basically you know uh you
+
+ align:start position:0%
+just means we basically you know uh you
+ 
+
+ align:start position:0%
+just means we basically you know uh you
+know if if if if if I phone you a lot or
+
+ align:start position:0%
+know if if if if if I phone you a lot or
+ 
+
+ align:start position:0%
+know if if if if if I phone you a lot or
+I site you a lot in papers you know
+
+ align:start position:0%
+I site you a lot in papers you know
+ 
+
+ align:start position:0%
+I site you a lot in papers you know
+that's the same as you citing me a lot
+
+ align:start position:0%
+that's the same as you citing me a lot
+ 
+
+ align:start position:0%
+that's the same as you citing me a lot
+which you lose some information there um
+
+ align:start position:0%
+which you lose some information there um
+ 
+
+ align:start position:0%
+which you lose some information there um
+again and this just shows the kind of
+
+ align:start position:0%
+again and this just shows the kind of
+ 
+
+ align:start position:0%
+again and this just shows the kind of
+distortion that we get from just making
+
+ align:start position:0%
+distortion that we get from just making
+ 
+
+ align:start position:0%
+distortion that we get from just making
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undirected and then again this shows
+
+ align:start position:0%
+undirected and then again this shows
+ 
+
+ align:start position:0%
+undirected and then again this shows
+what happens when you do no so no self
+
+ align:start position:0%
+what happens when you do no so no self
+ 
+
+ align:start position:0%
+what happens when you do no so no self
+Loops well this there's not a lot of
+
+ align:start position:0%
+Loops well this there's not a lot of
+ 
+
+ align:start position:0%
+Loops well this there's not a lot of
+self Loops so we only have affected a
+
+ align:start position:0%
+self Loops so we only have affected a
+ 
+
+ align:start position:0%
+self Loops so we only have affected a
+few vertices here so in this
+
+ align:start position:0%
+few vertices here so in this
+ 
+
+ align:start position:0%
+few vertices here so in this
+case eliminating self Loops is not a
+
+ align:start position:0%
+case eliminating self Loops is not a
+ 
+
+ align:start position:0%
+case eliminating self Loops is not a
+terribly distorted doesn't really
+
+ align:start position:0%
+terribly distorted doesn't really
+ 
+
+ align:start position:0%
+terribly distorted doesn't really
+distort the data very much at all then
+
+ align:start position:0%
+distort the data very much at all then
+ 
+
+ align:start position:0%
+distort the data very much at all then
+finally this shows the cor the upper
+
+ align:start position:0%
+finally this shows the cor the upper
+ 
+
+ align:start position:0%
+finally this shows the cor the upper
+correlation Matrix so when we correlated
+
+ align:start position:0%
+correlation Matrix so when we correlated
+ 
+
+ align:start position:0%
+correlation Matrix so when we correlated
+the two basically multiplied the
+
+ align:start position:0%
+the two basically multiplied the
+ 
+
+ align:start position:0%
+the two basically multiplied the
+adjacent together again showing what we
+
+ align:start position:0%
+adjacent together again showing what we
+ 
+
+ align:start position:0%
+adjacent together again showing what we
+what we saw
+
+ align:start position:0%
+what we saw
+ 
+
+ align:start position:0%
+what we saw
+before all right moving on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah you get to see the plots that got
+
+ align:start position:0%
+ah you get to see the plots that got
+ 
+
+ align:start position:0%
+ah you get to see the plots that got
+eliminated from by
+
+ align:start position:0%
+eliminated from by
+ 
+
+ align:start position:0%
+eliminated from by
+PowerPoint mat lab has defeated
+
+ align:start position:0%
+PowerPoint mat lab has defeated
+ 
+
+ align:start position:0%
+PowerPoint mat lab has defeated
+PowerPoints attempts to deny you your
+
+ align:start position:0%
+PowerPoints attempts to deny you your
+ 
+
+ align:start position:0%
+PowerPoints attempts to deny you your
+education so um all right so again what
+
+ align:start position:0%
+education so um all right so again what
+ 
+
+ align:start position:0%
+education so um all right so again what
+we're doing here is we're uh we're uh
+
+ align:start position:0%
+we're doing here is we're uh we're uh
+ 
+
+ align:start position:0%
+we're doing here is we're uh we're uh
+we're creating a perfect power law all
+
+ align:start position:0%
+we're creating a perfect power law all
+ 
+
+ align:start position:0%
+we're creating a perfect power law all
+right this is a bigger one I wanted a
+
+ align:start position:0%
+right this is a bigger one I wanted a
+ 
+
+ align:start position:0%
+right this is a bigger one I wanted a
+lot of vertices so this time we had
+
+ align:start position:0%
+lot of vertices so this time we had
+ 
+
+ align:start position:0%
+lot of vertices so this time we had
+50,000 vertices 329,000 edges uh with a
+
+ align:start position:0%
+50,000 vertices 329,000 edges uh with a
+ 
+
+ align:start position:0%
+50,000 vertices 329,000 edges uh with a
+ratio of 6 and a half we create our
+
+ align:start position:0%
+ratio of 6 and a half we create our
+ 
+
+ align:start position:0%
+ratio of 6 and a half we create our
+vertices we randomize The Edge order Etc
+
+ align:start position:0%
+vertices we randomize The Edge order Etc
+ 
+
+ align:start position:0%
+vertices we randomize The Edge order Etc
+now we're going to randomly pick just a
+
+ align:start position:0%
+now we're going to randomly pick just a
+ 
+
+ align:start position:0%
+now we're going to randomly pick just a
+subsample of these and what do F samp
+
+ align:start position:0%
+subsample of these and what do F samp
+ 
+
+ align:start position:0%
+subsample of these and what do F samp
+set it it's 140th so I'm just going to
+
+ align:start position:0%
+set it it's 140th so I'm just going to
+ 
+
+ align:start position:0%
+set it it's 140th so I'm just going to
+take 1 140th of all the vertices okay
+
+ align:start position:0%
+take 1 140th of all the vertices okay
+ 
+
+ align:start position:0%
+take 1 140th of all the vertices okay
+now I'm going to go and compute that
+
+ align:start position:0%
+now I'm going to go and compute that
+ 
+
+ align:start position:0%
+now I'm going to go and compute that
+degree and I'm going to basically
+
+ align:start position:0%
+degree and I'm going to basically
+ 
+
+ align:start position:0%
+degree and I'm going to basically
+subsample all of these
+
+ align:start position:0%
+subsample all of these
+ 
+
+ align:start position:0%
+subsample all of these
+and later what you'll see so let's just
+
+ align:start position:0%
+and later what you'll see so let's just
+ 
+
+ align:start position:0%
+and later what you'll see so let's just
+take a look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this just shows that chart here
+
+ align:start position:0%
+that so this just shows that chart here
+ 
+
+ align:start position:0%
+that so this just shows that chart here
+so this is the original data again this
+
+ align:start position:0%
+so this is the original data again this
+ 
+
+ align:start position:0%
+so this is the original data again this
+is the vertex we're sorting by the
+
+ align:start position:0%
+is the vertex we're sorting by the
+ 
+
+ align:start position:0%
+is the vertex we're sorting by the
+vertices by degree here so this is the
+
+ align:start position:0%
+vertices by degree here so this is the
+ 
+
+ align:start position:0%
+vertices by degree here so this is the
+highest degree vertex these are the
+
+ align:start position:0%
+highest degree vertex these are the
+ 
+
+ align:start position:0%
+highest degree vertex these are the
+lowest uh degree
+
+ align:start position:0%
+lowest uh degree
+ 
+
+ align:start position:0%
+lowest uh degree
+vertex okay and and this each vertex is
+
+ align:start position:0%
+vertex okay and and this each vertex is
+ 
+
+ align:start position:0%
+vertex okay and and this each vertex is
+getting a DOT here so we have 50,000
+
+ align:start position:0%
+getting a DOT here so we have 50,000
+ 
+
+ align:start position:0%
+getting a DOT here so we have 50,000
+vertices they all get a DOT they all get
+
+ align:start position:0%
+vertices they all get a DOT they all get
+ 
+
+ align:start position:0%
+vertices they all get a DOT they all get
+a DOT here and we've only taken a 40th
+
+ align:start position:0%
+a DOT here and we've only taken a 40th
+ 
+
+ align:start position:0%
+a DOT here and we've only taken a 40th
+them and this just shows you here you
+
+ align:start position:0%
+them and this just shows you here you
+ 
+
+ align:start position:0%
+them and this just shows you here you
+know kind of what the if you if you only
+
+ align:start position:0%
+know kind of what the if you if you only
+ 
+
+ align:start position:0%
+know kind of what the if you if you only
+take a 40th of them and then compute
+
+ align:start position:0%
+take a 40th of them and then compute
+ 
+
+ align:start position:0%
+take a 40th of them and then compute
+their sample this is what you what you
+
+ align:start position:0%
+their sample this is what you what you
+ 
+
+ align:start position:0%
+their sample this is what you what you
+get now standard samply sampling Theory
+
+ align:start position:0%
+get now standard samply sampling Theory
+ 
+
+ align:start position:0%
+get now standard samply sampling Theory
+would say aha well I know how to correct
+
+ align:start position:0%
+would say aha well I know how to correct
+ 
+
+ align:start position:0%
+would say aha well I know how to correct
+for this the way I correct for this is I
+
+ align:start position:0%
+for this the way I correct for this is I
+ 
+
+ align:start position:0%
+for this the way I correct for this is I
+just multiply my sample data by 40 I
+
+ align:start position:0%
+just multiply my sample data by 40 I
+ 
+
+ align:start position:0%
+just multiply my sample data by 40 I
+only took 140 so that means you know
+
+ align:start position:0%
+only took 140 so that means you know
+ 
+
+ align:start position:0%
+only took 140 so that means you know
+whenever I measured it the the True
+
+ align:start position:0%
+whenever I measured it the the True
+ 
+
+ align:start position:0%
+whenever I measured it the the True
+Value should be 40 times higher so we
+
+ align:start position:0%
+Value should be 40 times higher so we
+ 
+
+ align:start position:0%
+Value should be 40 times higher so we
+can look at that in figure two so this
+
+ align:start position:0%
+can look at that in figure two so this
+ 
+
+ align:start position:0%
+can look at that in figure two so this
+is the true sample all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so again which we see for our high
+
+ align:start position:0%
+right so again which we see for our high
+ 
+
+ align:start position:0%
+right so again which we see for our high
+degree vertices here this is the highest
+
+ align:start position:0%
+degree vertices here this is the highest
+ 
+
+ align:start position:0%
+degree vertices here this is the highest
+degree vertix here again so this is the
+
+ align:start position:0%
+degree vertix here again so this is the
+ 
+
+ align:start position:0%
+degree vertix here again so this is the
+high degree vertices these are the low
+
+ align:start position:0%
+high degree vertices these are the low
+ 
+
+ align:start position:0%
+high degree vertices these are the low
+deegree vertices I don't know if I said
+
+ align:start position:0%
+deegree vertices I don't know if I said
+ 
+
+ align:start position:0%
+deegree vertices I don't know if I said
+that opposite when I mentioned it before
+
+ align:start position:0%
+that opposite when I mentioned it before
+ 
+
+ align:start position:0%
+that opposite when I mentioned it before
+this is the highest degree verx and you
+
+ align:start position:0%
+this is the highest degree verx and you
+ 
+
+ align:start position:0%
+this is the highest degree verx and you
+see that by sampling the data we're
+
+ align:start position:0%
+see that by sampling the data we're
+ 
+
+ align:start position:0%
+see that by sampling the data we're
+doing a very good job on the high degree
+
+ align:start position:0%
+doing a very good job on the high degree
+ 
+
+ align:start position:0%
+doing a very good job on the high degree
+vertices we're sampling them just fine
+
+ align:start position:0%
+vertices we're sampling them just fine
+ 
+
+ align:start position:0%
+vertices we're sampling them just fine
+and that's that's kind of why statistics
+
+ align:start position:0%
+and that's that's kind of why statistics
+ 
+
+ align:start position:0%
+and that's that's kind of why statistics
+works right you know you know if you if
+
+ align:start position:0%
+works right you know you know if you if
+ 
+
+ align:start position:0%
+works right you know you know if you if
+if something is really not rare and you
+
+ align:start position:0%
+if something is really not rare and you
+ 
+
+ align:start position:0%
+if something is really not rare and you
+sample you're going to get a you're
+
+ align:start position:0%
+sample you're going to get a you're
+ 
+
+ align:start position:0%
+sample you're going to get a you're
+going to get a good estimate however for
+
+ align:start position:0%
+going to get a good estimate however for
+ 
+
+ align:start position:0%
+going to get a good estimate however for
+these low degree vertices over here what
+
+ align:start position:0%
+these low degree vertices over here what
+ 
+
+ align:start position:0%
+these low degree vertices over here what
+you see by
+
+ align:start position:0%
+you see by
+ 
+
+ align:start position:0%
+you see by
+multiplying by 40 we're significantly
+
+ align:start position:0%
+multiplying by 40 we're significantly
+ 
+
+ align:start position:0%
+multiplying by 40 we're significantly
+overestimating their probability all
+
+ align:start position:0%
+overestimating their probability all
+ 
+
+ align:start position:0%
+overestimating their probability all
+right as I say this is the curve that
+
+ align:start position:0%
+right as I say this is the curve that
+ 
+
+ align:start position:0%
+right as I say this is the curve that
+proves that Optimist and pessimists are
+
+ align:start position:0%
+proves that Optimist and pessimists are
+ 
+
+ align:start position:0%
+proves that Optimist and pessimists are
+both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct there are so many rare thing if
+
+ align:start position:0%
+correct there are so many rare thing if
+ 
+
+ align:start position:0%
+correct there are so many rare thing if
+the world is a power law distribution
+
+ align:start position:0%
+the world is a power law distribution
+ 
+
+ align:start position:0%
+the world is a power law distribution
+means that there are so many rare events
+
+ align:start position:0%
+means that there are so many rare events
+ 
+
+ align:start position:0%
+means that there are so many rare events
+in the world some of them are going to
+
+ align:start position:0%
+in the world some of them are going to
+ 
+
+ align:start position:0%
+in the world some of them are going to
+happen to
+
+ align:start position:0%
+happen to
+ 
+
+ align:start position:0%
+happen to
+you so it means if you're an optimist go
+
+ align:start position:0%
+you so it means if you're an optimist go
+ 
+
+ align:start position:0%
+you so it means if you're an optimist go
+play the lottery all right if you're
+
+ align:start position:0%
+play the lottery all right if you're
+ 
+
+ align:start position:0%
+play the lottery all right if you're
+pessimist it means yeah lightning could
+
+ align:start position:0%
+pessimist it means yeah lightning could
+ 
+
+ align:start position:0%
+pessimist it means yeah lightning could
+hit you and you better just be you know
+
+ align:start position:0%
+hit you and you better just be you know
+ 
+
+ align:start position:0%
+hit you and you better just be you know
+stick and stay inside so there's just so
+
+ align:start position:0%
+stick and stay inside so there's just so
+ 
+
+ align:start position:0%
+stick and stay inside so there's just so
+many rare things that you know uh some
+
+ align:start position:0%
+many rare things that you know uh some
+ 
+
+ align:start position:0%
+many rare things that you know uh some
+of them are going to some really rare
+
+ align:start position:0%
+of them are going to some really rare
+ 
+
+ align:start position:0%
+of them are going to some really rare
+things are going to happen to you in
+
+ align:start position:0%
+things are going to happen to you in
+ 
+
+ align:start position:0%
+things are going to happen to you in
+your lifetime most likely those rare
+
+ align:start position:0%
+your lifetime most likely those rare
+ 
+
+ align:start position:0%
+your lifetime most likely those rare
+things though are very mundane you
+
+ align:start position:0%
+things though are very mundane you
+ 
+
+ align:start position:0%
+things though are very mundane you
+know so so but we can correct for this
+
+ align:start position:0%
+know so so but we can correct for this
+ 
+
+ align:start position:0%
+know so so but we can correct for this
+and so we have some some basically a way
+
+ align:start position:0%
+and so we have some some basically a way
+ 
+
+ align:start position:0%
+and so we have some some basically a way
+here of deriving calculations we compute
+
+ align:start position:0%
+here of deriving calculations we compute
+ 
+
+ align:start position:0%
+here of deriving calculations we compute
+the parameters of our distribution and
+
+ align:start position:0%
+the parameters of our distribution and
+ 
+
+ align:start position:0%
+the parameters of our distribution and
+through these two functions compute
+
+ align:start position:0%
+through these two functions compute
+ 
+
+ align:start position:0%
+through these two functions compute
+degree correction and apply degree
+
+ align:start position:0%
+degree correction and apply degree
+ 
+
+ align:start position:0%
+degree correction and apply degree
+correction we can actually go back and
+
+ align:start position:0%
+correction we can actually go back and
+ 
+
+ align:start position:0%
+correction we can actually go back and
+sort of say all right given that we
+
+ align:start position:0%
+sort of say all right given that we
+ 
+
+ align:start position:0%
+sort of say all right given that we
+believe the data is power law and we've
+
+ align:start position:0%
+believe the data is power law and we've
+ 
+
+ align:start position:0%
+believe the data is power law and we've
+sampled it can we then come up with a
+
+ align:start position:0%
+sampled it can we then come up with a
+ 
+
+ align:start position:0%
+sampled it can we then come up with a
+more uniform correction that basically
+
+ align:start position:0%
+more uniform correction that basically
+ 
+
+ align:start position:0%
+more uniform correction that basically
+gives us a better estimate that works at
+
+ align:start position:0%
+gives us a better estimate that works at
+ 
+
+ align:start position:0%
+gives us a better estimate that works at
+both the high and the low end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what you see here so
+
+ align:start position:0%
+and that's what you see here so
+ 
+
+ align:start position:0%
+and that's what you see here so
+basically we haven't changed the
+
+ align:start position:0%
+basically we haven't changed the
+ 
+
+ align:start position:0%
+basically we haven't changed the
+correction hasn't changed here but we've
+
+ align:start position:0%
+correction hasn't changed here but we've
+ 
+
+ align:start position:0%
+correction hasn't changed here but we've
+lowered we've downgraded these lower
+
+ align:start position:0%
+lowered we've downgraded these lower
+ 
+
+ align:start position:0%
+lowered we've downgraded these lower
+ones and essentially what we're doing is
+
+ align:start position:0%
+ones and essentially what we're doing is
+ 
+
+ align:start position:0%
+ones and essentially what we're doing is
+instead of just using the average as the
+
+ align:start position:0%
+instead of just using the average as the
+ 
+
+ align:start position:0%
+instead of just using the average as the
+statistic we're using the median so
+
+ align:start position:0%
+statistic we're using the median so
+ 
+
+ align:start position:0%
+statistic we're using the median so
+we're using essentially a quantile based
+
+ align:start position:0%
+we're using essentially a quantile based
+ 
+
+ align:start position:0%
+we're using essentially a quantile based
+uh uh uh uh correction here 50th percent
+
+ align:start position:0%
+uh uh uh uh correction here 50th percent
+ 
+
+ align:start position:0%
+uh uh uh uh correction here 50th percent
+quantile based correction here and that
+
+ align:start position:0%
+quantile based correction here and that
+ 
+
+ align:start position:0%
+quantile based correction here and that
+causes us to lower the estimates of
+
+ align:start position:0%
+causes us to lower the estimates of
+ 
+
+ align:start position:0%
+causes us to lower the estimates of
+these uh vertices and so there would be
+
+ align:start position:0%
+these uh vertices and so there would be
+ 
+
+ align:start position:0%
+these uh vertices and so there would be
+a better estimate in terms allow you to
+
+ align:start position:0%
+a better estimate in terms allow you to
+ 
+
+ align:start position:0%
+a better estimate in terms allow you to
+do do the sampling of that all right
+
+ align:start position:0%
+do do the sampling of that all right
+ 
+
+ align:start position:0%
+do do the sampling of that all right
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and our final demo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all righty so now what we're doing is
+
+ align:start position:0%
+all righty so now what we're doing is
+ 
+
+ align:start position:0%
+all righty so now what we're doing is
+doing power law fitting okay and so we
+
+ align:start position:0%
+doing power law fitting okay and so we
+ 
+
+ align:start position:0%
+doing power law fitting okay and so we
+have the routines for doing that so
+
+ align:start position:0%
+have the routines for doing that so
+ 
+
+ align:start position:0%
+have the routines for doing that so
+again here's our distribution it's a a
+
+ align:start position:0%
+again here's our distribution it's a a
+ 
+
+ align:start position:0%
+again here's our distribution it's a a
+power law of 1.3 we've set dmax to be
+
+ align:start position:0%
+power law of 1.3 we've set dmax to be
+ 
+
+ align:start position:0%
+power law of 1.3 we've set dmax to be
+2,000 and about 60-ish bins we create
+
+ align:start position:0%
+2,000 and about 60-ish bins we create
+ 
+
+ align:start position:0%
+2,000 and about 60-ish bins we create
+our power law distribution it has 50,000
+
+ align:start position:0%
+our power law distribution it has 50,000
+ 
+
+ align:start position:0%
+our power law distribution it has 50,000
+vertices 329,000 edges ratio so same as
+
+ align:start position:0%
+vertices 329,000 edges ratio so same as
+ 
+
+ align:start position:0%
+vertices 329,000 edges ratio so same as
+the one we did before
+
+ align:start position:0%
+the one we did before
+ 
+
+ align:start position:0%
+the one we did before
+we're going to make it
+
+ align:start position:0%
+we're going to make it
+ 
+
+ align:start position:0%
+we're going to make it
+undirected undirected unweighted
+
+ align:start position:0%
+undirected undirected unweighted
+ 
+
+ align:start position:0%
+undirected undirected unweighted
+undirected unweighted no self Loops so
+
+ align:start position:0%
+undirected unweighted no self Loops so
+ 
+
+ align:start position:0%
+undirected unweighted no self Loops so
+sort of standard Corrections that we
+
+ align:start position:0%
+sort of standard Corrections that we
+ 
+
+ align:start position:0%
+sort of standard Corrections that we
+do going to compute the degree
+
+ align:start position:0%
+do going to compute the degree
+ 
+
+ align:start position:0%
+do going to compute the degree
+distribution of that data and plot it or
+
+ align:start position:0%
+distribution of that data and plot it or
+ 
+
+ align:start position:0%
+distribution of that data and plot it or
+actually it there and now I'm going to
+
+ align:start position:0%
+actually it there and now I'm going to
+ 
+
+ align:start position:0%
+actually it there and now I'm going to
+then we have this function called Power
+
+ align:start position:0%
+then we have this function called Power
+ 
+
+ align:start position:0%
+then we have this function called Power
+law fit so if I compute this is I'm
+
+ align:start position:0%
+law fit so if I compute this is I'm
+ 
+
+ align:start position:0%
+law fit so if I compute this is I'm
+going to compute so I compute the degree
+
+ align:start position:0%
+going to compute so I compute the degree
+ 
+
+ align:start position:0%
+going to compute so I compute the degree
+distribution so have this function
+
+ align:start position:0%
+distribution so have this function
+ 
+
+ align:start position:0%
+distribution so have this function
+called outdegree which just gives us the
+
+ align:start position:0%
+called outdegree which just gives us the
+ 
+
+ align:start position:0%
+called outdegree which just gives us the
+distribution and I can find essentially
+
+ align:start position:0%
+distribution and I can find essentially
+ 
+
+ align:start position:0%
+distribution and I can find essentially
+the uh the number of values with the one
+
+ align:start position:0%
+the uh the number of values with the one
+ 
+
+ align:start position:0%
+the uh the number of values with the one
+and the one that are maximum so get our
+
+ align:start position:0%
+and the one that are maximum so get our
+ 
+
+ align:start position:0%
+and the one that are maximum so get our
+this is estimating our poor man's slope
+
+ align:start position:0%
+this is estimating our poor man's slope
+ 
+
+ align:start position:0%
+this is estimating our poor man's slope
+so we're Computing the slope we're
+
+ align:start position:0%
+so we're Computing the slope we're
+ 
+
+ align:start position:0%
+so we're Computing the slope we're
+counting the total number of of edges
+
+ align:start position:0%
+counting the total number of of edges
+ 
+
+ align:start position:0%
+counting the total number of of edges
+here and then we have this function
+
+ align:start position:0%
+here and then we have this function
+ 
+
+ align:start position:0%
+here and then we have this function
+called Power law fit basically we can
+
+ align:start position:0%
+called Power law fit basically we can
+ 
+
+ align:start position:0%
+called Power law fit basically we can
+plug in what the estimated Alpha is what
+
+ align:start position:0%
+plug in what the estimated Alpha is what
+ 
+
+ align:start position:0%
+plug in what the estimated Alpha is what
+the number of vertices is and the number
+
+ align:start position:0%
+the number of vertices is and the number
+ 
+
+ align:start position:0%
+the number of vertices is and the number
+of edges is to find our best fit
+
+ align:start position:0%
+of edges is to find our best fit
+ 
+
+ align:start position:0%
+of edges is to find our best fit
+distribution so this basically vers
+
+ align:start position:0%
+distribution so this basically vers
+ 
+
+ align:start position:0%
+distribution so this basically vers
+those two those formulas I showed you
+
+ align:start position:0%
+those two those formulas I showed you
+ 
+
+ align:start position:0%
+those two those formulas I showed you
+which is given a degree distribution
+
+ align:start position:0%
+which is given a degree distribution
+ 
+
+ align:start position:0%
+which is given a degree distribution
+that sums to a particular number of ver
+
+ align:start position:0%
+that sums to a particular number of ver
+ 
+
+ align:start position:0%
+that sums to a particular number of ver
+vertices and sums to a particular number
+
+ align:start position:0%
+vertices and sums to a particular number
+ 
+
+ align:start position:0%
+vertices and sums to a particular number
+of edges can you give me a new dmax and
+
+ align:start position:0%
+of edges can you give me a new dmax and
+ 
+
+ align:start position:0%
+of edges can you give me a new dmax and
+a new ND these sort of parameters that
+
+ align:start position:0%
+a new ND these sort of parameters that
+ 
+
+ align:start position:0%
+a new ND these sort of parameters that
+don't really have as much meaning to uh
+
+ align:start position:0%
+don't really have as much meaning to uh
+ 
+
+ align:start position:0%
+don't really have as much meaning to uh
+to to do that and so uh basically we use
+
+ align:start position:0%
+to to do that and so uh basically we use
+ 
+
+ align:start position:0%
+to to do that and so uh basically we use
+essentially a combination of three
+
+ align:start position:0%
+essentially a combination of three
+ 
+
+ align:start position:0%
+essentially a combination of three
+different techniques here because this
+
+ align:start position:0%
+different techniques here because this
+ 
+
+ align:start position:0%
+different techniques here because this
+is so nonlinear here and there's this
+
+ align:start position:0%
+is so nonlinear here and there's this
+ 
+
+ align:start position:0%
+is so nonlinear here and there's this
+basically remember I talked about
+
+ align:start position:0%
+basically remember I talked about
+ 
+
+ align:start position:0%
+basically remember I talked about
+integer bins and logarithmic bins well
+
+ align:start position:0%
+integer bins and logarithmic bins well
+ 
+
+ align:start position:0%
+integer bins and logarithmic bins well
+if you look at that plot it showed there
+
+ align:start position:0%
+if you look at that plot it showed there
+ 
+
+ align:start position:0%
+if you look at that plot it showed there
+was that sort of bending it's a very
+
+ align:start position:0%
+was that sort of bending it's a very
+ 
+
+ align:start position:0%
+was that sort of bending it's a very
+sort of nasty manifold uh the the
+
+ align:start position:0%
+sort of nasty manifold uh the the
+ 
+
+ align:start position:0%
+sort of nasty manifold uh the the
+surface of this function and it has a
+
+ align:start position:0%
+surface of this function and it has a
+ 
+
+ align:start position:0%
+surface of this function and it has a
+continuous part and a discrete part so
+
+ align:start position:0%
+continuous part and a discrete part so
+ 
+
+ align:start position:0%
+continuous part and a discrete part so
+what we do here is we do a essentially a
+
+ align:start position:0%
+what we do here is we do a essentially a
+ 
+
+ align:start position:0%
+what we do here is we do a essentially a
+a sampled search where we kind of
+
+ align:start position:0%
+a sampled search where we kind of
+ 
+
+ align:start position:0%
+a sampled search where we kind of
+randomly sample looking for a location
+
+ align:start position:0%
+randomly sample looking for a location
+ 
+
+ align:start position:0%
+randomly sample looking for a location
+we do a heuristic search which is sort
+
+ align:start position:0%
+we do a heuristic search which is sort
+ 
+
+ align:start position:0%
+we do a heuristic search which is sort
+of a kind of a simulated kneeling search
+
+ align:start position:0%
+of a kind of a simulated kneeling search
+ 
+
+ align:start position:0%
+of a kind of a simulated kneeling search
+and we also use bren's linear uh uh
+
+ align:start position:0%
+and we also use bren's linear uh uh
+ 
+
+ align:start position:0%
+and we also use bren's linear uh uh
+essentially A variation of Newton's
+
+ align:start position:0%
+essentially A variation of Newton's
+ 
+
+ align:start position:0%
+essentially A variation of Newton's
+method to all try and find the best set
+
+ align:start position:0%
+method to all try and find the best set
+ 
+
+ align:start position:0%
+method to all try and find the best set
+of parameters that will fit this data we
+
+ align:start position:0%
+of parameters that will fit this data we
+ 
+
+ align:start position:0%
+of parameters that will fit this data we
+never we rarely get an exact match but
+
+ align:start position:0%
+never we rarely get an exact match but
+ 
+
+ align:start position:0%
+never we rarely get an exact match but
+you can see here it's choosing different
+
+ align:start position:0%
+you can see here it's choosing different
+ 
+
+ align:start position:0%
+you can see here it's choosing different
+ones and this gives you the kind of how
+
+ align:start position:0%
+ones and this gives you the kind of how
+ 
+
+ align:start position:0%
+ones and this gives you the kind of how
+it's doing from the sample search this
+
+ align:start position:0%
+it's doing from the sample search this
+ 
+
+ align:start position:0%
+it's doing from the sample search this
+shows you the number of vertices and the
+
+ align:start position:0%
+shows you the number of vertices and the
+ 
+
+ align:start position:0%
+shows you the number of vertices and the
+number of edges it was able to achieve
+
+ align:start position:0%
+number of edges it was able to achieve
+ 
+
+ align:start position:0%
+number of edges it was able to achieve
+theistic search you know didn't do very
+
+ align:start position:0%
+theistic search you know didn't do very
+ 
+
+ align:start position:0%
+theistic search you know didn't do very
+well at all and then the Bren search did
+
+ align:start position:0%
+well at all and then the Bren search did
+ 
+
+ align:start position:0%
+well at all and then the Bren search did
+a pretty good job you know it and and it
+
+ align:start position:0%
+a pretty good job you know it and and it
+ 
+
+ align:start position:0%
+a pretty good job you know it and and it
+got got us a pretty so it Choice first
+
+ align:start position:0%
+got got us a pretty so it Choice first
+ 
+
+ align:start position:0%
+got got us a pretty so it Choice first
+thing it Choice it it actually actually
+
+ align:start position:0%
+thing it Choice it it actually actually
+ 
+
+ align:start position:0%
+thing it Choice it it actually actually
+it ended up comparing all of these and
+
+ align:start position:0%
+it ended up comparing all of these and
+ 
+
+ align:start position:0%
+it ended up comparing all of these and
+it ended up choosing the uh the sample
+
+ align:start position:0%
+it ended up choosing the uh the sample
+ 
+
+ align:start position:0%
+it ended up choosing the uh the sample
+search uh this one this first one it did
+
+ align:start position:0%
+search uh this one this first one it did
+ 
+
+ align:start position:0%
+search uh this one this first one it did
+it liked that best of all
+
+ align:start position:0%
+it liked that best of all
+ 
+
+ align:start position:0%
+it liked that best of all
+so we look at that
+
+ align:start position:0%
+so we look at that
+ 
+
+ align:start position:0%
+so we look at that
+here so figure two just was the original
+
+ align:start position:0%
+here so figure two just was the original
+ 
+
+ align:start position:0%
+here so figure two just was the original
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+data figure one shows you the manifold
+
+ align:start position:0%
+data figure one shows you the manifold
+ 
+
+ align:start position:0%
+data figure one shows you the manifold
+of this space and so plotted in this
+
+ align:start position:0%
+of this space and so plotted in this
+ 
+
+ align:start position:0%
+of this space and so plotted in this
+this coordinate system of n versus m the
+
+ align:start position:0%
+this coordinate system of n versus m the
+ 
+
+ align:start position:0%
+this coordinate system of n versus m the
+dot is the dot that it found it's
+
+ align:start position:0%
+dot is the dot that it found it's
+ 
+
+ align:start position:0%
+dot is the dot that it found it's
+actually here in this type in this tping
+
+ align:start position:0%
+actually here in this type in this tping
+ 
+
+ align:start position:0%
+actually here in this type in this tping
+these lines show the boundaries but you
+
+ align:start position:0%
+these lines show the boundaries but you
+ 
+
+ align:start position:0%
+these lines show the boundaries but you
+can see this sort of very nonlinear
+
+ align:start position:0%
+can see this sort of very nonlinear
+ 
+
+ align:start position:0%
+can see this sort of very nonlinear
+manifold here this is sort of the
+
+ align:start position:0%
+manifold here this is sort of the
+ 
+
+ align:start position:0%
+manifold here this is sort of the
+continuous regime this is the energer
+
+ align:start position:0%
+continuous regime this is the energer
+ 
+
+ align:start position:0%
+continuous regime this is the energer
+regime it cusps right at the transition
+
+ align:start position:0%
+regime it cusps right at the transition
+ 
+
+ align:start position:0%
+regime it cusps right at the transition
+again a very nasty function to try and
+
+ align:start position:0%
+again a very nasty function to try and
+ 
+
+ align:start position:0%
+again a very nasty function to try and
+uh try and invert and which is why we
+
+ align:start position:0%
+uh try and invert and which is why we
+ 
+
+ align:start position:0%
+uh try and invert and which is why we
+used all those different techniques to
+
+ align:start position:0%
+used all those different techniques to
+ 
+
+ align:start position:0%
+used all those different techniques to
+invert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and then so we did figure two and
+
+ align:start position:0%
+it and then so we did figure two and
+ 
+
+ align:start position:0%
+it and then so we did figure two and
+then figure three shows the results so
+
+ align:start position:0%
+then figure three shows the results so
+ 
+
+ align:start position:0%
+then figure three shows the results so
+um this black line shows the original
+
+ align:start position:0%
+um this black line shows the original
+ 
+
+ align:start position:0%
+um this black line shows the original
+model input that we provided so that was
+
+ align:start position:0%
+model input that we provided so that was
+ 
+
+ align:start position:0%
+model input that we provided so that was
+the the true model the circle shows the
+
+ align:start position:0%
+the the true model the circle shows the
+ 
+
+ align:start position:0%
+the the true model the circle shows the
+data after it was transformed we made it
+
+ align:start position:0%
+data after it was transformed we made it
+ 
+
+ align:start position:0%
+data after it was transformed we made it
+undirected unweighted with no self Loops
+
+ align:start position:0%
+undirected unweighted with no self Loops
+ 
+
+ align:start position:0%
+undirected unweighted with no self Loops
+that's this Alpha is this is our our
+
+ align:start position:0%
+that's this Alpha is this is our our
+ 
+
+ align:start position:0%
+that's this Alpha is this is our our
+poor man's Alpha which you can see is
+
+ align:start position:0%
+poor man's Alpha which you can see is
+ 
+
+ align:start position:0%
+poor man's Alpha which you can see is
+almost identical to the original model
+
+ align:start position:0%
+almost identical to the original model
+ 
+
+ align:start position:0%
+almost identical to the original model
+so the even you poor man's Alpha does a
+
+ align:start position:0%
+so the even you poor man's Alpha does a
+ 
+
+ align:start position:0%
+so the even you poor man's Alpha does a
+very good job of fitting in this case
+
+ align:start position:0%
+very good job of fitting in this case
+ 
+
+ align:start position:0%
+very good job of fitting in this case
+this shows the triangle shows the model
+
+ align:start position:0%
+this shows the triangle shows the model
+ 
+
+ align:start position:0%
+this shows the triangle shows the model
+fit so when we fit the data we came up
+
+ align:start position:0%
+fit so when we fit the data we came up
+ 
+
+ align:start position:0%
+fit so when we fit the data we came up
+with that best fit it CHS and we then
+
+ align:start position:0%
+with that best fit it CHS and we then
+ 
+
+ align:start position:0%
+with that best fit it CHS and we then
+created a new distribution this is what
+
+ align:start position:0%
+created a new distribution this is what
+ 
+
+ align:start position:0%
+created a new distribution this is what
+it looked like and then the plus sign
+
+ align:start position:0%
+it looked like and then the plus sign
+ 
+
+ align:start position:0%
+it looked like and then the plus sign
+shows us rebinning that data onto the
+
+ align:start position:0%
+shows us rebinning that data onto the
+ 
+
+ align:start position:0%
+shows us rebinning that data onto the
+bins from the model and you see that
+
+ align:start position:0%
+bins from the model and you see that
+ 
+
+ align:start position:0%
+bins from the model and you see that
+we've done a very nice job of recovering
+
+ align:start position:0%
+we've done a very nice job of recovering
+ 
+
+ align:start position:0%
+we've done a very nice job of recovering
+the original Power law distribution
+
+ align:start position:0%
+the original Power law distribution
+ 
+
+ align:start position:0%
+the original Power law distribution
+after even after we did that Distortion
+
+ align:start position:0%
+after even after we did that Distortion
+ 
+
+ align:start position:0%
+after even after we did that Distortion
+so again that sort of is the last
+
+ align:start position:0%
+so again that sort of is the last
+ 
+
+ align:start position:0%
+so again that sort of is the last
+example so I want to thank you and then
+
+ align:start position:0%
+example so I want to thank you and then
+ 
+
+ align:start position:0%
+example so I want to thank you and then
+for the homework um a lot of you did
+
+ align:start position:0%
+for the homework um a lot of you did
+ 
+
+ align:start position:0%
+for the homework um a lot of you did
+homework to which is great uh I think
+
+ align:start position:0%
+homework to which is great uh I think
+ 
+
+ align:start position:0%
+homework to which is great uh I think
+homework three wasn't such a great hit
+
+ align:start position:0%
+homework three wasn't such a great hit
+ 
+
+ align:start position:0%
+homework three wasn't such a great hit
+I'm going to definitely rethink that one
+
+ align:start position:0%
+I'm going to definitely rethink that one
+ 
+
+ align:start position:0%
+I'm going to definitely rethink that one
+um but the next homework does not
+
+ align:start position:0%
+um but the next homework does not
+ 
+
+ align:start position:0%
+um but the next homework does not
+require you to have done homework 3 if
+
+ align:start position:0%
+require you to have done homework 3 if
+ 
+
+ align:start position:0%
+require you to have done homework 3 if
+you did homework 2 um basically it's
+
+ align:start position:0%
+you did homework 2 um basically it's
+ 
+
+ align:start position:0%
+you did homework 2 um basically it's
+just saying computed de degree
+
+ align:start position:0%
+just saying computed de degree
+ 
+
+ align:start position:0%
+just saying computed de degree
+distribution okay and in fact you don't
+
+ align:start position:0%
+distribution okay and in fact you don't
+ 
+
+ align:start position:0%
+distribution okay and in fact you don't
+even need to have done homework 2 just
+
+ align:start position:0%
+even need to have done homework 2 just
+ 
+
+ align:start position:0%
+even need to have done homework 2 just
+you can compute a degree Distribution on
+
+ align:start position:0%
+you can compute a degree Distribution on
+ 
+
+ align:start position:0%
+you can compute a degree Distribution on
+your homework 2
+
+ align:start position:0%
+your homework 2
+ 
+
+ align:start position:0%
+your homework 2
+or you can compute a degree Distribution
+
+ align:start position:0%
+or you can compute a degree Distribution
+ 
+
+ align:start position:0%
+or you can compute a degree Distribution
+on any data set for example today is
+
+ align:start position:0%
+on any data set for example today is
+ 
+
+ align:start position:0%
+on any data set for example today is
+Halloween if you go trick- or retreating
+
+ align:start position:0%
+Halloween if you go trick- or retreating
+ 
+
+ align:start position:0%
+Halloween if you go trick- or retreating
+with your with with somebody yourself
+
+ align:start position:0%
+with your with with somebody yourself
+ 
+
+ align:start position:0%
+with your with with somebody yourself
+your children somebody else's children
+
+ align:start position:0%
+your children somebody else's children
+ 
+
+ align:start position:0%
+your children somebody else's children
+um you can uh you can uh maybe uh email
+
+ align:start position:0%
+um you can uh you can uh maybe uh email
+ 
+
+ align:start position:0%
+um you can uh you can uh maybe uh email
+me with the you know the histogram of
+
+ align:start position:0%
+me with the you know the histogram of
+ 
+
+ align:start position:0%
+me with the you know the histogram of
+your candy and plot it on a degree
+
+ align:start position:0%
+your candy and plot it on a degree
+ 
+
+ align:start position:0%
+your candy and plot it on a degree
+distribution uh and maybe compute the
+
+ align:start position:0%
+distribution uh and maybe compute the
+ 
+
+ align:start position:0%
+distribution uh and maybe compute the
+the poor man's Alpha coefficient from
+
+ align:start position:0%
+the poor man's Alpha coefficient from
+ 
+
+ align:start position:0%
+the poor man's Alpha coefficient from
+that and the other you know coefficients
+
+ align:start position:0%
+that and the other you know coefficients
+ 
+
+ align:start position:0%
+that and the other you know coefficients
+from that would be a fun exercise to do
+
+ align:start position:0%
+from that would be a fun exercise to do
+ 
+
+ align:start position:0%
+from that would be a fun exercise to do
+so that'll be the next homework I'll
+
+ align:start position:0%
+so that'll be the next homework I'll
+ 
+
+ align:start position:0%
+so that'll be the next homework I'll
+email that out in the next couple of
+
+ align:start position:0%
+email that out in the next couple of
+ 
+
+ align:start position:0%
+email that out in the next couple of
+days and so um uh look forward again if
+
+ align:start position:0%
+days and so um uh look forward again if
+ 
+
+ align:start position:0%
+days and so um uh look forward again if
+you send me the homework prior to um to
+
+ align:start position:0%
+you send me the homework prior to um to
+ 
+
+ align:start position:0%
+you send me the homework prior to um to
+next uh actually oh just reminder no
+
+ align:start position:0%
+next uh actually oh just reminder no
+ 
+
+ align:start position:0%
+next uh actually oh just reminder no
+class next week no class next week this
+
+ align:start position:0%
+class next week no class next week this
+ 
+
+ align:start position:0%
+class next week no class next week this
+room is being taken uh so but again if
+
+ align:start position:0%
+room is being taken uh so but again if
+ 
+
+ align:start position:0%
+room is being taken uh so but again if
+you email me the homework prior to this
+
+ align:start position:0%
+you email me the homework prior to this
+ 
+
+ align:start position:0%
+you email me the homework prior to this
+time next week I will give you feedback
+
+ align:start position:0%
+time next week I will give you feedback
+ 
+
+ align:start position:0%
+time next week I will give you feedback
+on it um can still send me the homework
+
+ align:start position:0%
+on it um can still send me the homework
+ 
+
+ align:start position:0%
+on it um can still send me the homework
+after that I just won't give you any
+
+ align:start position:0%
+after that I just won't give you any
+ 
+
+ align:start position:0%
+after that I just won't give you any
+feedback on it so thank you again and um
+
+ align:start position:0%
+feedback on it so thank you again and um
+ 
+
+ align:start position:0%
+feedback on it so thank you again and um
+um look forward to seeing you in 2 weeks
\ No newline at end of file
diff --git a/RVWsRDF0-p0.txt b/RVWsRDF0-p0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b18730f8de89c0fac6472cfe6750c2a8f189ffdd
--- /dev/null
+++ b/RVWsRDF0-p0.txt
@@ -0,0 +1,443 @@
+align:start position:0%
+ 
+I was just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thinking you know we're talking about
+
+ align:start position:0%
+thinking you know we're talking about
+ 
+
+ align:start position:0%
+thinking you know we're talking about
+cities and having
+
+ align:start position:0%
+cities and having
+ 
+
+ align:start position:0%
+cities and having
+problems how long have cities
+
+ align:start position:0%
+problems how long have cities
+ 
+
+ align:start position:0%
+problems how long have cities
+existed including the first settl
+
+ align:start position:0%
+existed including the first settl
+ 
+
+ align:start position:0%
+existed including the first settl
+permanent settlement say Jericho 8,000
+
+ align:start position:0%
+permanent settlement say Jericho 8,000
+ 
+
+ align:start position:0%
+permanent settlement say Jericho 8,000
+before Christ how many years do that to
+
+ align:start position:0%
+before Christ how many years do that to
+ 
+
+ align:start position:0%
+before Christ how many years do that to
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+20,000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years what are we now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2,200 added to
+
+ align:start position:0%
+2,200 added to
+ 
+
+ align:start position:0%
+2,200 added to
+8,000 10,000 years it took 2.6 million
+
+ align:start position:0%
+8,000 10,000 years it took 2.6 million
+ 
+
+ align:start position:0%
+8,000 10,000 years it took 2.6 million
+years for human beings to develop a
+
+ align:start position:0%
+years for human beings to develop a
+ 
+
+ align:start position:0%
+years for human beings to develop a
+brain large enough to to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think and we're talking about
+
+ align:start position:0%
+think and we're talking about
+ 
+
+ align:start position:0%
+think and we're talking about
+12,000 years
+
+ align:start position:0%
+12,000 years
+ 
+
+ align:start position:0%
+12,000 years
+which which was nothing in
+
+ align:start position:0%
+which which was nothing in
+ 
+
+ align:start position:0%
+which which was nothing in
+time and we expecting perfect answers to
+
+ align:start position:0%
+time and we expecting perfect answers to
+ 
+
+ align:start position:0%
+time and we expecting perfect answers to
+communal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+settlements so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relax we
+
+ align:start position:0%
+relax we
+ 
+
+ align:start position:0%
+relax we
+teach I say this because I'm an
+
+ align:start position:0%
+teach I say this because I'm an
+ 
+
+ align:start position:0%
+teach I say this because I'm an
+architect and have taught Design Studios
+
+ align:start position:0%
+architect and have taught Design Studios
+ 
+
+ align:start position:0%
+architect and have taught Design Studios
+endlessly we tend to idealize the world
+
+ align:start position:0%
+endlessly we tend to idealize the world
+ 
+
+ align:start position:0%
+endlessly we tend to idealize the world
+world that we and smooth the world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around I remember when I worked for on
+
+ align:start position:0%
+around I remember when I worked for on
+ 
+
+ align:start position:0%
+around I remember when I worked for on
+the image of the city research book with
+
+ align:start position:0%
+the image of the city research book with
+ 
+
+ align:start position:0%
+the image of the city research book with
+Kevin Lynch K Jerry keish his compatriot
+
+ align:start position:0%
+Kevin Lynch K Jerry keish his compatriot
+ 
+
+ align:start position:0%
+Kevin Lynch K Jerry keish his compatriot
+asked me to take a walk down Washington
+
+ align:start position:0%
+asked me to take a walk down Washington
+ 
+
+ align:start position:0%
+asked me to take a walk down Washington
+Street on a busy day and note just note
+
+ align:start position:0%
+Street on a busy day and note just note
+ 
+
+ align:start position:0%
+Street on a busy day and note just note
+all the things that I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saw I made the tabulation of all the
+
+ align:start position:0%
+saw I made the tabulation of all the
+ 
+
+ align:start position:0%
+saw I made the tabulation of all the
+things that I saw where the Sun was
+
+ align:start position:0%
+things that I saw where the Sun was
+ 
+
+ align:start position:0%
+things that I saw where the Sun was
+shining what noise there was what signs
+
+ align:start position:0%
+shining what noise there was what signs
+ 
+
+ align:start position:0%
+shining what noise there was what signs
+there were and so on and I came up and
+
+ align:start position:0%
+there were and so on and I came up and
+ 
+
+ align:start position:0%
+there were and so on and I came up and
+presented my work and said this is such
+
+ align:start position:0%
+presented my work and said this is such
+ 
+
+ align:start position:0%
+presented my work and said this is such
+an unbelievably confused Washington
+
+ align:start position:0%
+an unbelievably confused Washington
+ 
+
+ align:start position:0%
+an unbelievably confused Washington
+Street I don't know how anybody makes
+
+ align:start position:0%
+Street I don't know how anybody makes
+ 
+
+ align:start position:0%
+Street I don't know how anybody makes
+sense of
+
+ align:start position:0%
+sense of
+ 
+
+ align:start position:0%
+sense of
+it because at that time all Urban Design
+
+ align:start position:0%
+it because at that time all Urban Design
+ 
+
+ align:start position:0%
+it because at that time all Urban Design
+was was Victor gruen's work and how to
+
+ align:start position:0%
+was was Victor gruen's work and how to
+ 
+
+ align:start position:0%
+was was Victor gruen's work and how to
+make use modernism to cleans up conflict
+
+ align:start position:0%
+make use modernism to cleans up conflict
+ 
+
+ align:start position:0%
+make use modernism to cleans up conflict
+shopping centers had unified sign post
+
+ align:start position:0%
+shopping centers had unified sign post
+ 
+
+ align:start position:0%
+shopping centers had unified sign post
+control and uh here I was trying to say
+
+ align:start position:0%
+control and uh here I was trying to say
+ 
+
+ align:start position:0%
+control and uh here I was trying to say
+the real world is infinitely complex and
+
+ align:start position:0%
+the real world is infinitely complex and
+ 
+
+ align:start position:0%
+the real world is infinitely complex and
+yet because we have 10 to the 12
+
+ align:start position:0%
+yet because we have 10 to the 12
+ 
+
+ align:start position:0%
+yet because we have 10 to the 12
+neurons in our brain each connecting to
+
+ align:start position:0%
+neurons in our brain each connecting to
+ 
+
+ align:start position:0%
+neurons in our brain each connecting to
+5,000 other sites we have the
+
+ align:start position:0%
+5,000 other sites we have the
+ 
+
+ align:start position:0%
+5,000 other sites we have the
+electricity electronic system which can
+
+ align:start position:0%
+electricity electronic system which can
+ 
+
+ align:start position:0%
+electricity electronic system which can
+manage such complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think it's a message worth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remembering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe it'll become much clearer but I
+
+ align:start position:0%
+maybe it'll become much clearer but I
+ 
+
+ align:start position:0%
+maybe it'll become much clearer but I
+think working as you do as an urban
+
+ align:start position:0%
+think working as you do as an urban
+ 
+
+ align:start position:0%
+think working as you do as an urban
+designer in the midst of a dialectic of
+
+ align:start position:0%
+designer in the midst of a dialectic of
+ 
+
+ align:start position:0%
+designer in the midst of a dialectic of
+opposites is an intelligent place to be
\ No newline at end of file
diff --git a/RbAjBxvCsAU.txt b/RbAjBxvCsAU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17dbbf7db204322638d7a1a808913527e6bee6dc
--- /dev/null
+++ b/RbAjBxvCsAU.txt
@@ -0,0 +1,13864 @@
+align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+afternoon here we
+
+ align:start position:0%
+afternoon here we
+ 
+
+ align:start position:0%
+afternoon here we
+are March 19 lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+we are still in the process of studying
+
+ align:start position:0%
+we are still in the process of studying
+ 
+
+ align:start position:0%
+we are still in the process of studying
+mixtures the one wonderful word of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixtures and so let me just uh
+
+ align:start position:0%
+mixtures and so let me just uh
+ 
+
+ align:start position:0%
+mixtures and so let me just uh
+briefly see where we
+
+ align:start position:0%
+briefly see where we
+ 
+
+ align:start position:0%
+briefly see where we
+are you remember that we discussed
+
+ align:start position:0%
+are you remember that we discussed
+ 
+
+ align:start position:0%
+are you remember that we discussed
+um the properties of isobaric mixing
+
+ align:start position:0%
+um the properties of isobaric mixing
+ 
+
+ align:start position:0%
+um the properties of isobaric mixing
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+are uh measurable properties that allow
+
+ align:start position:0%
+are uh measurable properties that allow
+ 
+
+ align:start position:0%
+are uh measurable properties that allow
+us to
+
+ align:start position:0%
+us to
+ 
+
+ align:start position:0%
+us to
+infer uh the chemical potentials
+
+ align:start position:0%
+infer uh the chemical potentials
+ 
+
+ align:start position:0%
+infer uh the chemical potentials
+thanks to this uh expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we
+
+ align:start position:0%
+here we
+ 
+
+ align:start position:0%
+here we
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+discussed the intermolecular forces
+
+ align:start position:0%
+discussed the intermolecular forces
+ 
+
+ align:start position:0%
+discussed the intermolecular forces
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecules and for example the fact that
+
+ align:start position:0%
+molecules and for example the fact that
+ 
+
+ align:start position:0%
+molecules and for example the fact that
+in the gas or ideal gas
+
+ align:start position:0%
+in the gas or ideal gas
+ 
+
+ align:start position:0%
+in the gas or ideal gas
+regime
+
+ align:start position:0%
+regime
+ 
+
+ align:start position:0%
+regime
+molecules spend most most of their time
+
+ align:start position:0%
+molecules spend most most of their time
+ 
+
+ align:start position:0%
+molecules spend most most of their time
+far away from each other in spite of
+
+ align:start position:0%
+far away from each other in spite of
+ 
+
+ align:start position:0%
+far away from each other in spite of
+having an enormous amount of collisions
+
+ align:start position:0%
+having an enormous amount of collisions
+ 
+
+ align:start position:0%
+having an enormous amount of collisions
+per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second during which they do get
+
+ align:start position:0%
+second during which they do get
+ 
+
+ align:start position:0%
+second during which they do get
+close but the time they spend close is
+
+ align:start position:0%
+close but the time they spend close is
+ 
+
+ align:start position:0%
+close but the time they spend close is
+small with respect
+
+ align:start position:0%
+small with respect
+ 
+
+ align:start position:0%
+small with respect
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to uh the average and
+
+ align:start position:0%
+to uh the average and
+ 
+
+ align:start position:0%
+to uh the average and
+so since the properties are determined
+
+ align:start position:0%
+so since the properties are determined
+ 
+
+ align:start position:0%
+so since the properties are determined
+uh by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+average the effect of when of the
+
+ align:start position:0%
+average the effect of when of the
+ 
+
+ align:start position:0%
+average the effect of when of the
+intermolecular reaction
+
+ align:start position:0%
+intermolecular reaction
+ 
+
+ align:start position:0%
+intermolecular reaction
+interactions uh is
+
+ align:start position:0%
+interactions uh is
+ 
+
+ align:start position:0%
+interactions uh is
+relatively
+
+ align:start position:0%
+relatively
+ 
+
+ align:start position:0%
+relatively
+negligible and that's the ideal gas for
+
+ align:start position:0%
+negligible and that's the ideal gas for
+ 
+
+ align:start position:0%
+negligible and that's the ideal gas for
+regime we will see more about
+
+ align:start position:0%
+regime we will see more about
+ 
+
+ align:start position:0%
+regime we will see more about
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+today uh from another point of view
+
+ align:start position:0%
+today uh from another point of view
+ 
+
+ align:start position:0%
+today uh from another point of view
+which which uh we will see in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment we introduced a first ideal
+
+ align:start position:0%
+moment we introduced a first ideal
+ 
+
+ align:start position:0%
+moment we introduced a first ideal
+Behavior Uh model based on this idea of
+
+ align:start position:0%
+Behavior Uh model based on this idea of
+ 
+
+ align:start position:0%
+Behavior Uh model based on this idea of
+uh particles not
+
+ align:start position:0%
+uh particles not
+ 
+
+ align:start position:0%
+uh particles not
+interacting which is the ideal Gibs
+
+ align:start position:0%
+interacting which is the ideal Gibs
+ 
+
+ align:start position:0%
+interacting which is the ideal Gibs
+Dalton mixture
+
+ align:start position:0%
+Dalton mixture
+ 
+
+ align:start position:0%
+Dalton mixture
+model in which as you remember the idea
+
+ align:start position:0%
+model in which as you remember the idea
+ 
+
+ align:start position:0%
+model in which as you remember the idea
+is that that we uh represent the the
+
+ align:start position:0%
+is that that we uh represent the the
+ 
+
+ align:start position:0%
+is that that we uh represent the the
+properties of the
+
+ align:start position:0%
+properties of the
+ 
+
+ align:start position:0%
+properties of the
+mixture as
+
+ align:start position:0%
+mixture as
+ 
+
+ align:start position:0%
+mixture as
+equivalent to the properties of a
+
+ align:start position:0%
+equivalent to the properties of a
+ 
+
+ align:start position:0%
+equivalent to the properties of a
+composite system in
+
+ align:start position:0%
+composite system in
+ 
+
+ align:start position:0%
+composite system in
+which the various components are
+
+ align:start position:0%
+which the various components are
+ 
+
+ align:start position:0%
+which the various components are
+separate they occupy the same volum they
+
+ align:start position:0%
+separate they occupy the same volum they
+ 
+
+ align:start position:0%
+separate they occupy the same volum they
+are the same temperature and they are at
+
+ align:start position:0%
+are the same temperature and they are at
+ 
+
+ align:start position:0%
+are the same temperature and they are at
+the partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure according to this uh model if
+
+ align:start position:0%
+pressure according to this uh model if
+ 
+
+ align:start position:0%
+pressure according to this uh model if
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+if each of the substances
+
+ align:start position:0%
+if each of the substances
+ 
+
+ align:start position:0%
+if each of the substances
+behaves as an ideal gas so obeys the
+
+ align:start position:0%
+behaves as an ideal gas so obeys the
+ 
+
+ align:start position:0%
+behaves as an ideal gas so obeys the
+ideal gas PV equals RT
+
+ align:start position:0%
+ideal gas PV equals RT
+ 
+
+ align:start position:0%
+ideal gas PV equals RT
+um equation of
+
+ align:start position:0%
+um equation of
+ 
+
+ align:start position:0%
+um equation of
+State we found that the partial
+
+ align:start position:0%
+State we found that the partial
+ 
+
+ align:start position:0%
+State we found that the partial
+properties add up to the pressure of the
+
+ align:start position:0%
+properties add up to the pressure of the
+ 
+
+ align:start position:0%
+properties add up to the pressure of the
+mixture that's D dton law this
+
+ align:start position:0%
+mixture that's D dton law this
+ 
+
+ align:start position:0%
+mixture that's D dton law this
+here and the partial pressures are given
+
+ align:start position:0%
+here and the partial pressures are given
+ 
+
+ align:start position:0%
+here and the partial pressures are given
+by the pressure of the mixture times the
+
+ align:start position:0%
+by the pressure of the mixture times the
+ 
+
+ align:start position:0%
+by the pressure of the mixture times the
+mole
+
+ align:start position:0%
+mole
+ 
+
+ align:start position:0%
+mole
+fraction plus the chemical potential of
+
+ align:start position:0%
+fraction plus the chemical potential of
+ 
+
+ align:start position:0%
+fraction plus the chemical potential of
+the components in the mixture of each
+
+ align:start position:0%
+the components in the mixture of each
+ 
+
+ align:start position:0%
+the components in the mixture of each
+component is equal
+
+ align:start position:0%
+component is equal
+ 
+
+ align:start position:0%
+component is equal
+to this important expression that gives
+
+ align:start position:0%
+to this important expression that gives
+ 
+
+ align:start position:0%
+to this important expression that gives
+the that is the sum of the chemical
+
+ align:start position:0%
+the that is the sum of the chemical
+ 
+
+ align:start position:0%
+the that is the sum of the chemical
+potential of the pure component at the
+
+ align:start position:0%
+potential of the pure component at the
+ 
+
+ align:start position:0%
+potential of the pure component at the
+same temperature and pressure of the
+
+ align:start position:0%
+same temperature and pressure of the
+ 
+
+ align:start position:0%
+same temperature and pressure of the
+mixture plus RT the log of a mole
+
+ align:start position:0%
+mixture plus RT the log of a mole
+ 
+
+ align:start position:0%
+mixture plus RT the log of a mole
+fraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+then um proved also the amagat low
+
+ align:start position:0%
+then um proved also the amagat low
+ 
+
+ align:start position:0%
+then um proved also the amagat low
+additive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volumes uh whereby an ideal gas mixture
+
+ align:start position:0%
+volumes uh whereby an ideal gas mixture
+ 
+
+ align:start position:0%
+volumes uh whereby an ideal gas mixture
+is such that uh you can also view
+
+ align:start position:0%
+is such that uh you can also view
+ 
+
+ align:start position:0%
+is such that uh you can also view
+it as a composite of separate uh pure
+
+ align:start position:0%
+it as a composite of separate uh pure
+ 
+
+ align:start position:0%
+it as a composite of separate uh pure
+gases
+
+ align:start position:0%
+gases
+ 
+
+ align:start position:0%
+gases
+each all at the same temperature
+
+ align:start position:0%
+each all at the same temperature
+ 
+
+ align:start position:0%
+each all at the same temperature
+pressure but each occupying the
+
+ align:start position:0%
+pressure but each occupying the
+ 
+
+ align:start position:0%
+pressure but each occupying the
+the uh so-called proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume which is given but the volume
+
+ align:start position:0%
+volume which is given but the volume
+ 
+
+ align:start position:0%
+volume which is given but the volume
+that the they would occupy at the uh
+
+ align:start position:0%
+that the they would occupy at the uh
+ 
+
+ align:start position:0%
+that the they would occupy at the uh
+when pure in the same amount uh at the
+
+ align:start position:0%
+when pure in the same amount uh at the
+ 
+
+ align:start position:0%
+when pure in the same amount uh at the
+same temperature and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure then we discussed mixing
+
+ align:start position:0%
+pressure then we discussed mixing
+ 
+
+ align:start position:0%
+pressure then we discussed mixing
+spontaneous
+
+ align:start position:0%
+spontaneous
+ 
+
+ align:start position:0%
+spontaneous
+mixing what happens when we have
+
+ align:start position:0%
+mixing what happens when we have
+ 
+
+ align:start position:0%
+mixing what happens when we have
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+gases kept separate by partitions that
+
+ align:start position:0%
+gases kept separate by partitions that
+ 
+
+ align:start position:0%
+gases kept separate by partitions that
+are movable so they are all at the same
+
+ align:start position:0%
+are movable so they are all at the same
+ 
+
+ align:start position:0%
+are movable so they are all at the same
+temperature and
+
+ align:start position:0%
+temperature and
+ 
+
+ align:start position:0%
+temperature and
+pressure and without any external effect
+
+ align:start position:0%
+pressure and without any external effect
+ 
+
+ align:start position:0%
+pressure and without any external effect
+you see the weight is at the same level
+
+ align:start position:0%
+you see the weight is at the same level
+ 
+
+ align:start position:0%
+you see the weight is at the same level
+you just let them mix if you take the
+
+ align:start position:0%
+you just let them mix if you take the
+ 
+
+ align:start position:0%
+you just let them mix if you take the
+partitions away and let them
+
+ align:start position:0%
+partitions away and let them
+ 
+
+ align:start position:0%
+partitions away and let them
+mix we found that the mixing under these
+
+ align:start position:0%
+mix we found that the mixing under these
+ 
+
+ align:start position:0%
+mix we found that the mixing under these
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+yields the final temperature and the
+
+ align:start position:0%
+yields the final temperature and the
+ 
+
+ align:start position:0%
+yields the final temperature and the
+final pressure equal to the initial
+
+ align:start position:0%
+final pressure equal to the initial
+ 
+
+ align:start position:0%
+final pressure equal to the initial
+ones and the
+
+ align:start position:0%
+ones and the
+ 
+
+ align:start position:0%
+ones and the
+entropy increases by the so-called uh
+
+ align:start position:0%
+entropy increases by the so-called uh
+ 
+
+ align:start position:0%
+entropy increases by the so-called uh
+entropy of mixing which is given by this
+
+ align:start position:0%
+entropy of mixing which is given by this
+ 
+
+ align:start position:0%
+entropy of mixing which is given by this
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+minus the number of particles total
+
+ align:start position:0%
+minus the number of particles total
+ 
+
+ align:start position:0%
+minus the number of particles total
+number of particles the gas constant and
+
+ align:start position:0%
+number of particles the gas constant and
+ 
+
+ align:start position:0%
+number of particles the gas constant and
+the sum
+
+ align:start position:0%
+the sum
+ 
+
+ align:start position:0%
+the sum
+of Y log y
+
+ align:start position:0%
+of Y log y
+ 
+
+ align:start position:0%
+of Y log y
+so the mole fractions time the logarithm
+
+ align:start position:0%
+so the mole fractions time the logarithm
+ 
+
+ align:start position:0%
+so the mole fractions time the logarithm
+of the mole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fractions we also noticed
+
+ align:start position:0%
+fractions we also noticed
+ 
+
+ align:start position:0%
+fractions we also noticed
+that we could have done that mixing in a
+
+ align:start position:0%
+that we could have done that mixing in a
+ 
+
+ align:start position:0%
+that we could have done that mixing in a
+better way better from the thermodynamic
+
+ align:start position:0%
+better way better from the thermodynamic
+ 
+
+ align:start position:0%
+better way better from the thermodynamic
+point of view in other words
+
+ align:start position:0%
+point of view in other words
+ 
+
+ align:start position:0%
+point of view in other words
+reversibly in a weight process and we
+
+ align:start position:0%
+reversibly in a weight process and we
+ 
+
+ align:start position:0%
+reversibly in a weight process and we
+computed how much work we could uh oh so
+
+ align:start position:0%
+computed how much work we could uh oh so
+ 
+
+ align:start position:0%
+computed how much work we could uh oh so
+that for how much weight lifting we
+
+ align:start position:0%
+that for how much weight lifting we
+ 
+
+ align:start position:0%
+that for how much weight lifting we
+could get if we did that uh uh indeed
+
+ align:start position:0%
+could get if we did that uh uh indeed
+ 
+
+ align:start position:0%
+could get if we did that uh uh indeed
+reversibly and here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula and the last thing we discussed
+
+ align:start position:0%
+formula and the last thing we discussed
+ 
+
+ align:start position:0%
+formula and the last thing we discussed
+was a
+
+ align:start position:0%
+was a
+ 
+
+ align:start position:0%
+was a
+pictorial idea
+
+ align:start position:0%
+pictorial idea
+ 
+
+ align:start position:0%
+pictorial idea
+of how
+
+ align:start position:0%
+of how
+ 
+
+ align:start position:0%
+of how
+that extraction of thetic availability
+
+ align:start position:0%
+that extraction of thetic availability
+ 
+
+ align:start position:0%
+that extraction of thetic availability
+could uh could be done if we
+
+ align:start position:0%
+could uh could be done if we
+ 
+
+ align:start position:0%
+could uh could be done if we
+have uh semi- perable
+
+ align:start position:0%
+have uh semi- perable
+ 
+
+ align:start position:0%
+have uh semi- perable
+membranes so here we picture first of
+
+ align:start position:0%
+membranes so here we picture first of
+ 
+
+ align:start position:0%
+membranes so here we picture first of
+all the idea is that when we have a a
+
+ align:start position:0%
+all the idea is that when we have a a
+ 
+
+ align:start position:0%
+all the idea is that when we have a a
+gas um confined in a volume by a
+
+ align:start position:0%
+gas um confined in a volume by a
+ 
+
+ align:start position:0%
+gas um confined in a volume by a
+partition and on the other side of the
+
+ align:start position:0%
+partition and on the other side of the
+ 
+
+ align:start position:0%
+partition and on the other side of the
+partition there is volume I mean there
+
+ align:start position:0%
+partition there is volume I mean there
+ 
+
+ align:start position:0%
+partition there is volume I mean there
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+vacuum um the pressure of
+
+ align:start position:0%
+vacuum um the pressure of
+ 
+
+ align:start position:0%
+vacuum um the pressure of
+the molecules here on the Piston will
+
+ align:start position:0%
+the molecules here on the Piston will
+ 
+
+ align:start position:0%
+the molecules here on the Piston will
+tend to push it
+
+ align:start position:0%
+tend to push it
+ 
+
+ align:start position:0%
+tend to push it
+uh uh so as to increase uh the
+
+ align:start position:0%
+uh uh so as to increase uh the
+ 
+
+ align:start position:0%
+uh uh so as to increase uh the
+volume and that will lift the weight if
+
+ align:start position:0%
+volume and that will lift the weight if
+ 
+
+ align:start position:0%
+volume and that will lift the weight if
+properly
+
+ align:start position:0%
+properly
+ 
+
+ align:start position:0%
+properly
+connected similarly the black
+
+ align:start position:0%
+connected similarly the black
+ 
+
+ align:start position:0%
+connected similarly the black
+particles now the idea here is that in
+
+ align:start position:0%
+particles now the idea here is that in
+ 
+
+ align:start position:0%
+particles now the idea here is that in
+ideal G Gibs Dalton mixture Behavior the
+
+ align:start position:0%
+ideal G Gibs Dalton mixture Behavior the
+ 
+
+ align:start position:0%
+ideal G Gibs Dalton mixture Behavior the
+particles essentially even in the
+
+ align:start position:0%
+particles essentially even in the
+ 
+
+ align:start position:0%
+particles essentially even in the
+mixture ignore each other they don't
+
+ align:start position:0%
+mixture ignore each other they don't
+ 
+
+ align:start position:0%
+mixture ignore each other they don't
+they live in the entire volume even as
+
+ align:start position:0%
+they live in the entire volume even as
+ 
+
+ align:start position:0%
+they live in the entire volume even as
+if the others weren't
+
+ align:start position:0%
+if the others weren't
+ 
+
+ align:start position:0%
+if the others weren't
+there so for the gray particles to
+
+ align:start position:0%
+there so for the gray particles to
+ 
+
+ align:start position:0%
+there so for the gray particles to
+expand to to here whether there is a the
+
+ align:start position:0%
+expand to to here whether there is a the
+ 
+
+ align:start position:0%
+expand to to here whether there is a the
+black particles or not isn't really
+
+ align:start position:0%
+black particles or not isn't really
+ 
+
+ align:start position:0%
+black particles or not isn't really
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+so that is the idea that we can
+
+ align:start position:0%
+so that is the idea that we can
+ 
+
+ align:start position:0%
+so that is the idea that we can
+achieve with these semi-permeable
+
+ align:start position:0%
+achieve with these semi-permeable
+ 
+
+ align:start position:0%
+achieve with these semi-permeable
+membranes this one
+
+ align:start position:0%
+membranes this one
+ 
+
+ align:start position:0%
+membranes this one
+allows the black particles to go through
+
+ align:start position:0%
+allows the black particles to go through
+ 
+
+ align:start position:0%
+allows the black particles to go through
+but not the gray so the gray will push
+
+ align:start position:0%
+but not the gray so the gray will push
+ 
+
+ align:start position:0%
+but not the gray so the gray will push
+it to the right and pull up this weight
+
+ align:start position:0%
+it to the right and pull up this weight
+ 
+
+ align:start position:0%
+it to the right and pull up this weight
+this other membrane is
+
+ align:start position:0%
+this other membrane is
+ 
+
+ align:start position:0%
+this other membrane is
+permeable to the gray particles but not
+
+ align:start position:0%
+permeable to the gray particles but not
+ 
+
+ align:start position:0%
+permeable to the gray particles but not
+the black so the black will push it
+
+ align:start position:0%
+the black so the black will push it
+ 
+
+ align:start position:0%
+the black so the black will push it
+leftward and pull up this other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you asked uh do we have membranes
+
+ align:start position:0%
+okay you asked uh do we have membranes
+ 
+
+ align:start position:0%
+okay you asked uh do we have membranes
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+reality uh and yes we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do we have uh we can manufacture them we
+
+ align:start position:0%
+do we have uh we can manufacture them we
+ 
+
+ align:start position:0%
+do we have uh we can manufacture them we
+make we make we engineer uh
+
+ align:start position:0%
+make we make we engineer uh
+ 
+
+ align:start position:0%
+make we make we engineer uh
+materials these are some YouTube videos
+
+ align:start position:0%
+materials these are some YouTube videos
+ 
+
+ align:start position:0%
+materials these are some YouTube videos
+that you may want to to go and watch I'm
+
+ align:start position:0%
+that you may want to to go and watch I'm
+ 
+
+ align:start position:0%
+that you may want to to go and watch I'm
+not doing it
+
+ align:start position:0%
+not doing it
+ 
+
+ align:start position:0%
+not doing it
+here and uh so you you can essentially
+
+ align:start position:0%
+here and uh so you you can essentially
+ 
+
+ align:start position:0%
+here and uh so you you can essentially
+have a wall of uh
+
+ align:start position:0%
+have a wall of uh
+ 
+
+ align:start position:0%
+have a wall of uh
+materials with holes and if the holes
+
+ align:start position:0%
+materials with holes and if the holes
+ 
+
+ align:start position:0%
+materials with holes and if the holes
+are the proper size they can allow the
+
+ align:start position:0%
+are the proper size they can allow the
+ 
+
+ align:start position:0%
+are the proper size they can allow the
+passage of some particles and prevent
+
+ align:start position:0%
+passage of some particles and prevent
+ 
+
+ align:start position:0%
+passage of some particles and prevent
+the particles the the other particles to
+
+ align:start position:0%
+the particles the the other particles to
+ 
+
+ align:start position:0%
+the particles the the other particles to
+to pass so that is the way we achieve a
+
+ align:start position:0%
+to pass so that is the way we achieve a
+ 
+
+ align:start position:0%
+to pass so that is the way we achieve a
+semi perable uh
+
+ align:start position:0%
+semi perable uh
+ 
+
+ align:start position:0%
+semi perable uh
+membrane in nature also in
+
+ align:start position:0%
+membrane in nature also in
+ 
+
+ align:start position:0%
+membrane in nature also in
+biology this is very important on the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the surface of
+
+ align:start position:0%
+on the surface of
+ 
+
+ align:start position:0%
+on the surface of
+cells where you may have uh not you you
+
+ align:start position:0%
+cells where you may have uh not you you
+ 
+
+ align:start position:0%
+cells where you may have uh not you you
+may have active and passive
+
+ align:start position:0%
+may have active and passive
+ 
+
+ align:start position:0%
+may have active and passive
+transport active transport is a
+
+ align:start position:0%
+transport active transport is a
+ 
+
+ align:start position:0%
+transport active transport is a
+different story because it requires some
+
+ align:start position:0%
+different story because it requires some
+ 
+
+ align:start position:0%
+different story because it requires some
+energy uh for the um particles to
+
+ align:start position:0%
+energy uh for the um particles to
+ 
+
+ align:start position:0%
+energy uh for the um particles to
+move but also there is uh passive
+
+ align:start position:0%
+move but also there is uh passive
+ 
+
+ align:start position:0%
+move but also there is uh passive
+transport and the fact that membranes
+
+ align:start position:0%
+transport and the fact that membranes
+ 
+
+ align:start position:0%
+transport and the fact that membranes
+can be changed
+
+ align:start position:0%
+can be changed
+ 
+
+ align:start position:0%
+can be changed
+uh by the the cell uh depending on its
+
+ align:start position:0%
+uh by the the cell uh depending on its
+ 
+
+ align:start position:0%
+uh by the the cell uh depending on its
+need so for example if the cell needs to
+
+ align:start position:0%
+need so for example if the cell needs to
+ 
+
+ align:start position:0%
+need so for example if the cell needs to
+eat so to speak it could open little
+
+ align:start position:0%
+eat so to speak it could open little
+ 
+
+ align:start position:0%
+eat so to speak it could open little
+holes so that the say oxygen comes
+
+ align:start position:0%
+holes so that the say oxygen comes
+ 
+
+ align:start position:0%
+holes so that the say oxygen comes
+in uh if the cell needs to uh discharge
+
+ align:start position:0%
+in uh if the cell needs to uh discharge
+ 
+
+ align:start position:0%
+in uh if the cell needs to uh discharge
+maybe CO2 then it needs to open a little
+
+ align:start position:0%
+maybe CO2 then it needs to open a little
+ 
+
+ align:start position:0%
+maybe CO2 then it needs to open a little
+bigger holes so that the molecules these
+
+ align:start position:0%
+bigger holes so that the molecules these
+ 
+
+ align:start position:0%
+bigger holes so that the molecules these
+molecules can go out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I'll have another reference about U
+
+ align:start position:0%
+uh I'll have another reference about U
+ 
+
+ align:start position:0%
+uh I'll have another reference about U
+biological structures uh but I don't
+
+ align:start position:0%
+biological structures uh but I don't
+ 
+
+ align:start position:0%
+biological structures uh but I don't
+want to talk about them because I'm not
+
+ align:start position:0%
+want to talk about them because I'm not
+ 
+
+ align:start position:0%
+want to talk about them because I'm not
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+all expert on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this but so the world is is full of
+
+ align:start position:0%
+this but so the world is is full of
+ 
+
+ align:start position:0%
+this but so the world is is full of
+membranes and we will see more in in a
+
+ align:start position:0%
+membranes and we will see more in in a
+ 
+
+ align:start position:0%
+membranes and we will see more in in a
+few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moments now there is one uh historical
+
+ align:start position:0%
+moments now there is one uh historical
+ 
+
+ align:start position:0%
+moments now there is one uh historical
+topic that is maybe interesting just fun
+
+ align:start position:0%
+topic that is maybe interesting just fun
+ 
+
+ align:start position:0%
+topic that is maybe interesting just fun
+to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discuss it's called the Gibs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Paradox and we have the tools to Now
+
+ align:start position:0%
+Paradox and we have the tools to Now
+ 
+
+ align:start position:0%
+Paradox and we have the tools to Now
+understand what it means and essentially
+
+ align:start position:0%
+understand what it means and essentially
+ 
+
+ align:start position:0%
+understand what it means and essentially
+to resolve
+
+ align:start position:0%
+to resolve
+ 
+
+ align:start position:0%
+to resolve
+it the idea is this we just
+
+ align:start position:0%
+it the idea is this we just
+ 
+
+ align:start position:0%
+it the idea is this we just
+uh mentioned what happens when we have
+
+ align:start position:0%
+uh mentioned what happens when we have
+ 
+
+ align:start position:0%
+uh mentioned what happens when we have
+uh particles that mix so here suppose we
+
+ align:start position:0%
+uh particles that mix so here suppose we
+ 
+
+ align:start position:0%
+uh particles that mix so here suppose we
+are just a binary mixture only two types
+
+ align:start position:0%
+are just a binary mixture only two types
+ 
+
+ align:start position:0%
+are just a binary mixture only two types
+of particles the gray and the black and
+
+ align:start position:0%
+of particles the gray and the black and
+ 
+
+ align:start position:0%
+of particles the gray and the black and
+the spontaneous
+
+ align:start position:0%
+the spontaneous
+ 
+
+ align:start position:0%
+the spontaneous
+mixing occurs this
+
+ align:start position:0%
+mixing occurs this
+ 
+
+ align:start position:0%
+mixing occurs this
+way and if you compute the entropy of
+
+ align:start position:0%
+way and if you compute the entropy of
+ 
+
+ align:start position:0%
+way and if you compute the entropy of
+mixing this summation when you have only
+
+ align:start position:0%
+mixing this summation when you have only
+ 
+
+ align:start position:0%
+mixing this summation when you have only
+two uh types of particles becomes a some
+
+ align:start position:0%
+two uh types of particles becomes a some
+ 
+
+ align:start position:0%
+two uh types of particles becomes a some
+of just two terms and of course the mole
+
+ align:start position:0%
+of just two terms and of course the mole
+ 
+
+ align:start position:0%
+of just two terms and of course the mole
+fractions when you have two particles
+
+ align:start position:0%
+fractions when you have two particles
+ 
+
+ align:start position:0%
+fractions when you have two particles
+are not independent because one because
+
+ align:start position:0%
+are not independent because one because
+ 
+
+ align:start position:0%
+are not independent because one because
+they might they must add up to one so
+
+ align:start position:0%
+they might they must add up to one so
+ 
+
+ align:start position:0%
+they might they must add up to one so
+the mole fraction of the second type
+
+ align:start position:0%
+the mole fraction of the second type
+ 
+
+ align:start position:0%
+the mole fraction of the second type
+must be equal to one minus the mole
+
+ align:start position:0%
+must be equal to one minus the mole
+ 
+
+ align:start position:0%
+must be equal to one minus the mole
+fraction of the first type of
+
+ align:start position:0%
+fraction of the first type of
+ 
+
+ align:start position:0%
+fraction of the first type of
+particles in the particular case in
+
+ align:start position:0%
+particles in the particular case in
+ 
+
+ align:start position:0%
+particles in the particular case in
+which you have 50% of one and 50% of the
+
+ align:start position:0%
+which you have 50% of one and 50% of the
+ 
+
+ align:start position:0%
+which you have 50% of one and 50% of the
+other so the more fractions are 50% or 1
+
+ align:start position:0%
+other so the more fractions are 50% or 1
+ 
+
+ align:start position:0%
+other so the more fractions are 50% or 1
+half this entropy of
+
+ align:start position:0%
+half this entropy of
+ 
+
+ align:start position:0%
+half this entropy of
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+uh n R log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two now if we consider for example a
+
+ align:start position:0%
+two now if we consider for example a
+ 
+
+ align:start position:0%
+two now if we consider for example a
+case in which I
+
+ align:start position:0%
+case in which I
+ 
+
+ align:start position:0%
+case in which I
+have one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle okay if we express one particle
+
+ align:start position:0%
+particle okay if we express one particle
+ 
+
+ align:start position:0%
+particle okay if we express one particle
+in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moles uh that's one
+
+ align:start position:0%
+moles uh that's one
+ 
+
+ align:start position:0%
+moles uh that's one
+over the avado Ross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mole because in one mole you have these
+
+ align:start position:0%
+mole because in one mole you have these
+ 
+
+ align:start position:0%
+mole because in one mole you have these
+many particles
+
+ align:start position:0%
+many particles
+ 
+
+ align:start position:0%
+many particles
+6022 * 10
+
+ align:start position:0%
+6022 * 10
+ 
+
+ align:start position:0%
+6022 * 10
+23rd
+
+ align:start position:0%
+23rd
+ 
+
+ align:start position:0%
+23rd
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+NR in that case is equal to R
+
+ align:start position:0%
+NR in that case is equal to R
+ 
+
+ align:start position:0%
+NR in that case is equal to R
+over the avocados number
+
+ align:start position:0%
+over the avocados number
+ 
+
+ align:start position:0%
+over the avocados number
+and this is called the boltzman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant which is one of the physical
+
+ align:start position:0%
+constant which is one of the physical
+ 
+
+ align:start position:0%
+constant which is one of the physical
+constants so if we uh suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here uh we have
+
+ align:start position:0%
+here uh we have
+ 
+
+ align:start position:0%
+here uh we have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just one particle on one side and one
+
+ align:start position:0%
+just one particle on one side and one
+ 
+
+ align:start position:0%
+just one particle on one side and one
+particle on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so the total n is
+
+ align:start position:0%
+side so the total n is
+ 
+
+ align:start position:0%
+side so the total n is
+two it's it's actually two divided by
+
+ align:start position:0%
+two it's it's actually two divided by
+ 
+
+ align:start position:0%
+two it's it's actually two divided by
+av's
+
+ align:start position:0%
+av's
+ 
+
+ align:start position:0%
+av's
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+so that entropy of mixing is uh
+
+ align:start position:0%
+so that entropy of mixing is uh
+ 
+
+ align:start position:0%
+so that entropy of mixing is uh
+twice BS one constant log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is the the Gibs
+
+ align:start position:0%
+so what is the the Gibs
+ 
+
+ align:start position:0%
+so what is the the Gibs
+Paradox the Gibs Paradox runs as follows
+
+ align:start position:0%
+Paradox the Gibs Paradox runs as follows
+ 
+
+ align:start position:0%
+Paradox the Gibs Paradox runs as follows
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um there is a saying uh that
+
+ align:start position:0%
+um there is a saying uh that
+ 
+
+ align:start position:0%
+um there is a saying uh that
+uh I know it in
+
+ align:start position:0%
+uh I know it in
+ 
+
+ align:start position:0%
+uh I know it in
+uh in Latin NATA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non
+
+ align:start position:0%
+non
+ 
+
+ align:start position:0%
+non
+fit
+
+ align:start position:0%
+fit
+ 
+
+ align:start position:0%
+fit
+salum it means nature doesn't make
+
+ align:start position:0%
+salum it means nature doesn't make
+ 
+
+ align:start position:0%
+salum it means nature doesn't make
+jumps and this is a I think it goes back
+
+ align:start position:0%
+jumps and this is a I think it goes back
+ 
+
+ align:start position:0%
+jumps and this is a I think it goes back
+to Aristotle or maybe Li NS I mean
+
+ align:start position:0%
+to Aristotle or maybe Li NS I mean
+ 
+
+ align:start position:0%
+to Aristotle or maybe Li NS I mean
+everybody every every
+
+ align:start position:0%
+everybody every every
+ 
+
+ align:start position:0%
+everybody every every
+philosopher uh has uh touched on these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea so what what Gibbs I think the Gibs
+
+ align:start position:0%
+idea so what what Gibbs I think the Gibs
+ 
+
+ align:start position:0%
+idea so what what Gibbs I think the Gibs
+they call it I really don't know maybe
+
+ align:start position:0%
+they call it I really don't know maybe
+ 
+
+ align:start position:0%
+they call it I really don't know maybe
+when we should look it up about the
+
+ align:start position:0%
+when we should look it up about the
+ 
+
+ align:start position:0%
+when we should look it up about the
+history of these things is is
+
+ align:start position:0%
+history of these things is is
+ 
+
+ align:start position:0%
+history of these things is is
+interesting is a chapter in itself so
+
+ align:start position:0%
+interesting is a chapter in itself so
+ 
+
+ align:start position:0%
+interesting is a chapter in itself so
+I'm not an expert in that in that either
+
+ align:start position:0%
+I'm not an expert in that in that either
+ 
+
+ align:start position:0%
+I'm not an expert in that in that either
+but suppose that it was Gibbs who
+
+ align:start position:0%
+but suppose that it was Gibbs who
+ 
+
+ align:start position:0%
+but suppose that it was Gibbs who
+realized that all right suppose
+
+ align:start position:0%
+realized that all right suppose
+ 
+
+ align:start position:0%
+realized that all right suppose
+I I have um I'm coloring these
+
+ align:start position:0%
+I I have um I'm coloring these
+ 
+
+ align:start position:0%
+I I have um I'm coloring these
+particles with a d and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose the amount of
+
+ align:start position:0%
+suppose the amount of
+ 
+
+ align:start position:0%
+suppose the amount of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+distance in color is measured by this
+
+ align:start position:0%
+distance in color is measured by this
+ 
+
+ align:start position:0%
+distance in color is measured by this
+parameter Lambda so I say zero means the
+
+ align:start position:0%
+parameter Lambda so I say zero means the
+ 
+
+ align:start position:0%
+parameter Lambda so I say zero means the
+particles are the same color Lambda
+
+ align:start position:0%
+particles are the same color Lambda
+ 
+
+ align:start position:0%
+particles are the same color Lambda
+greater than zero it means that the
+
+ align:start position:0%
+greater than zero it means that the
+ 
+
+ align:start position:0%
+greater than zero it means that the
+particles are different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color all right so regardless of the
+
+ align:start position:0%
+color all right so regardless of the
+ 
+
+ align:start position:0%
+color all right so regardless of the
+color here we see that the result this
+
+ align:start position:0%
+color here we see that the result this
+ 
+
+ align:start position:0%
+color here we see that the result this
+result the entropy of mixing is the same
+
+ align:start position:0%
+result the entropy of mixing is the same
+ 
+
+ align:start position:0%
+result the entropy of mixing is the same
+regardless of how different the
+
+ align:start position:0%
+regardless of how different the
+ 
+
+ align:start position:0%
+regardless of how different the
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+ 
+are there is no detail about what the
+
+ align:start position:0%
+are there is no detail about what the
+ 
+
+ align:start position:0%
+are there is no detail about what the
+particles or the mass is it's just how
+
+ align:start position:0%
+particles or the mass is it's just how
+ 
+
+ align:start position:0%
+particles or the mass is it's just how
+many they
+
+ align:start position:0%
+many they
+ 
+
+ align:start position:0%
+many they
+are so the entropy of mixing is always
+
+ align:start position:0%
+are so the entropy of mixing is always
+ 
+
+ align:start position:0%
+are so the entropy of mixing is always
+given by this amount and are uh log of
+
+ align:start position:0%
+given by this amount and are uh log of
+ 
+
+ align:start position:0%
+given by this amount and are uh log of
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+except and so you would you say right as
+
+ align:start position:0%
+except and so you would you say right as
+ 
+
+ align:start position:0%
+except and so you would you say right as
+Lambda goes to zero I would
+
+ align:start position:0%
+Lambda goes to zero I would
+ 
+
+ align:start position:0%
+Lambda goes to zero I would
+expect that to also go
+
+ align:start position:0%
+expect that to also go
+ 
+
+ align:start position:0%
+expect that to also go
+uh continuously instead as you go to
+
+ align:start position:0%
+uh continuously instead as you go to
+ 
+
+ align:start position:0%
+uh continuously instead as you go to
+zero that jumps to
+
+ align:start position:0%
+zero that jumps to
+ 
+
+ align:start position:0%
+zero that jumps to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+we if we think in terms of the simple
+
+ align:start position:0%
+we if we think in terms of the simple
+ 
+
+ align:start position:0%
+we if we think in terms of the simple
+system model you remember
+
+ align:start position:0%
+system model you remember
+ 
+
+ align:start position:0%
+system model you remember
+that uh when we have a a pure substance
+
+ align:start position:0%
+that uh when we have a a pure substance
+ 
+
+ align:start position:0%
+that uh when we have a a pure substance
+putting a partition or removing it
+
+ align:start position:0%
+putting a partition or removing it
+ 
+
+ align:start position:0%
+putting a partition or removing it
+doesn't change the properties so that's
+
+ align:start position:0%
+doesn't change the properties so that's
+ 
+
+ align:start position:0%
+doesn't change the properties so that's
+one quick way since we have seen
+
+ align:start position:0%
+one quick way since we have seen
+ 
+
+ align:start position:0%
+one quick way since we have seen
+uh a lot before to show that if the
+
+ align:start position:0%
+uh a lot before to show that if the
+ 
+
+ align:start position:0%
+uh a lot before to show that if the
+particles are
+
+ align:start position:0%
+particles are
+ 
+
+ align:start position:0%
+particles are
+identical there will be removing the
+
+ align:start position:0%
+identical there will be removing the
+ 
+
+ align:start position:0%
+identical there will be removing the
+partition will not change any of the
+
+ align:start position:0%
+partition will not change any of the
+ 
+
+ align:start position:0%
+partition will not change any of the
+properties including
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy so there is no entropy of mixing
+
+ align:start position:0%
+entropy so there is no entropy of mixing
+ 
+
+ align:start position:0%
+entropy so there is no entropy of mixing
+in this case if you
+
+ align:start position:0%
+in this case if you
+ 
+
+ align:start position:0%
+in this case if you
+mix the same substance there is no
+
+ align:start position:0%
+mix the same substance there is no
+ 
+
+ align:start position:0%
+mix the same substance there is no
+entropy of mixing as soon as they become
+
+ align:start position:0%
+entropy of mixing as soon as they become
+ 
+
+ align:start position:0%
+entropy of mixing as soon as they become
+different there is entropy of mixing and
+
+ align:start position:0%
+different there is entropy of mixing and
+ 
+
+ align:start position:0%
+different there is entropy of mixing and
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+discontinuous so that's why the
+
+ align:start position:0%
+discontinuous so that's why the
+ 
+
+ align:start position:0%
+discontinuous so that's why the
+philosophers didn't like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea but in
+
+ align:start position:0%
+idea but in
+ 
+
+ align:start position:0%
+idea but in
+fact it all has to do with the fact that
+
+ align:start position:0%
+fact it all has to do with the fact that
+ 
+
+ align:start position:0%
+fact it all has to do with the fact that
+we are doing modeling of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+nature is the way we model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so if we have a possibility to
+
+ align:start position:0%
+it so if we have a possibility to
+ 
+
+ align:start position:0%
+it so if we have a possibility to
+distinguish the particles and
+
+ align:start position:0%
+distinguish the particles and
+ 
+
+ align:start position:0%
+distinguish the particles and
+therefore they are different for us
+
+ align:start position:0%
+therefore they are different for us
+ 
+
+ align:start position:0%
+therefore they are different for us
+then there is
+
+ align:start position:0%
+then there is
+ 
+
+ align:start position:0%
+then there is
+mixing and if there is entropy of mixing
+
+ align:start position:0%
+mixing and if there is entropy of mixing
+ 
+
+ align:start position:0%
+mixing and if there is entropy of mixing
+there is also the possibility to do
+
+ align:start position:0%
+there is also the possibility to do
+ 
+
+ align:start position:0%
+there is also the possibility to do
+work as we've seen we can we can do this
+
+ align:start position:0%
+work as we've seen we can we can do this
+ 
+
+ align:start position:0%
+work as we've seen we can we can do this
+work this U mixing uh properly and
+
+ align:start position:0%
+work this U mixing uh properly and
+ 
+
+ align:start position:0%
+work this U mixing uh properly and
+extract some work
+
+ align:start position:0%
+extract some work
+ 
+
+ align:start position:0%
+extract some work
+but if we don't have uh the possibility
+
+ align:start position:0%
+but if we don't have uh the possibility
+ 
+
+ align:start position:0%
+but if we don't have uh the possibility
+to recognize to identify to distinguish
+
+ align:start position:0%
+to recognize to identify to distinguish
+ 
+
+ align:start position:0%
+to recognize to identify to distinguish
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+particles that work is impossible for us
+
+ align:start position:0%
+particles that work is impossible for us
+ 
+
+ align:start position:0%
+particles that work is impossible for us
+so it has to do with the the way we
+
+ align:start position:0%
+so it has to do with the the way we
+ 
+
+ align:start position:0%
+so it has to do with the the way we
+model it or if you really want to go
+
+ align:start position:0%
+model it or if you really want to go
+ 
+
+ align:start position:0%
+model it or if you really want to go
+nature if the particles are truly
+
+ align:start position:0%
+nature if the particles are truly
+ 
+
+ align:start position:0%
+nature if the particles are truly
+indistinguishable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the sense quantum mechanics
+
+ align:start position:0%
+in the sense quantum mechanics
+ 
+
+ align:start position:0%
+in the sense quantum mechanics
+distinguishable
+
+ align:start position:0%
+distinguishable
+ 
+
+ align:start position:0%
+distinguishable
+indistinguishable fermion bosons and
+
+ align:start position:0%
+indistinguishable fermion bosons and
+ 
+
+ align:start position:0%
+indistinguishable fermion bosons and
+that kind of
+
+ align:start position:0%
+that kind of
+ 
+
+ align:start position:0%
+that kind of
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+then there is no way you can distinguish
+
+ align:start position:0%
+then there is no way you can distinguish
+ 
+
+ align:start position:0%
+then there is no way you can distinguish
+there is no way you can uh extract any
+
+ align:start position:0%
+there is no way you can uh extract any
+ 
+
+ align:start position:0%
+there is no way you can uh extract any
+work uh if the particles are
+
+ align:start position:0%
+work uh if the particles are
+ 
+
+ align:start position:0%
+work uh if the particles are
+distinguishable then it all depends
+
+ align:start position:0%
+distinguishable then it all depends
+ 
+
+ align:start position:0%
+distinguishable then it all depends
+on your model namely on your kind of
+
+ align:start position:0%
+on your model namely on your kind of
+ 
+
+ align:start position:0%
+on your model namely on your kind of
+tool that you are considering in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model so so that's essentially the
+
+ align:start position:0%
+model so so that's essentially the
+ 
+
+ align:start position:0%
+model so so that's essentially the
+resolution of the Paradox there's no
+
+ align:start position:0%
+resolution of the Paradox there's no
+ 
+
+ align:start position:0%
+resolution of the Paradox there's no
+Paradox it's it's it's through like this
+
+ align:start position:0%
+Paradox it's it's it's through like this
+ 
+
+ align:start position:0%
+Paradox it's it's it's through like this
+and the this continuity going from here
+
+ align:start position:0%
+and the this continuity going from here
+ 
+
+ align:start position:0%
+and the this continuity going from here
+to there
+
+ align:start position:0%
+to there
+ 
+
+ align:start position:0%
+to there
+is essentially embedded in uh in the our
+
+ align:start position:0%
+is essentially embedded in uh in the our
+ 
+
+ align:start position:0%
+is essentially embedded in uh in the our
+modeling or from the Practical point of
+
+ align:start position:0%
+modeling or from the Practical point of
+ 
+
+ align:start position:0%
+modeling or from the Practical point of
+view our ability to control the
+
+ align:start position:0%
+view our ability to control the
+ 
+
+ align:start position:0%
+view our ability to control the
+differences in
+
+ align:start position:0%
+differences in
+ 
+
+ align:start position:0%
+differences in
+particles because if the particles are
+
+ align:start position:0%
+particles because if the particles are
+ 
+
+ align:start position:0%
+particles because if the particles are
+different but we have no ways to uh
+
+ align:start position:0%
+different but we have no ways to uh
+ 
+
+ align:start position:0%
+different but we have no ways to uh
+control their differences and
+
+ align:start position:0%
+control their differences and
+ 
+
+ align:start position:0%
+control their differences and
+therefore uh
+
+ align:start position:0%
+therefore uh
+ 
+
+ align:start position:0%
+therefore uh
+build semi-permeable membranes
+
+ align:start position:0%
+build semi-permeable membranes
+ 
+
+ align:start position:0%
+build semi-permeable membranes
+that can
+
+ align:start position:0%
+that can
+ 
+
+ align:start position:0%
+that can
+select then obtaining that
+
+ align:start position:0%
+select then obtaining that
+ 
+
+ align:start position:0%
+select then obtaining that
+work is out of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reach
+
+ align:start position:0%
+reach
+ 
+
+ align:start position:0%
+reach
+okay so that's the Gibs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Paradox and since we are at it I want to
+
+ align:start position:0%
+Paradox and since we are at it I want to
+ 
+
+ align:start position:0%
+Paradox and since we are at it I want to
+take a little DET tour today
+
+ align:start position:0%
+take a little DET tour today
+ 
+
+ align:start position:0%
+take a little DET tour today
+uh uh also on some other topics that
+
+ align:start position:0%
+uh uh also on some other topics that
+ 
+
+ align:start position:0%
+uh uh also on some other topics that
+are important in statistics in
+
+ align:start position:0%
+are important in statistics in
+ 
+
+ align:start position:0%
+are important in statistics in
+information Theory and also in Quantum
+
+ align:start position:0%
+information Theory and also in Quantum
+ 
+
+ align:start position:0%
+information Theory and also in Quantum
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory so again look at this um box with
+
+ align:start position:0%
+Theory so again look at this um box with
+ 
+
+ align:start position:0%
+Theory so again look at this um box with
+particles different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles and suppose you make an
+
+ align:start position:0%
+particles and suppose you make an
+ 
+
+ align:start position:0%
+particles and suppose you make an
+experiment by having a little um
+
+ align:start position:0%
+experiment by having a little um
+ 
+
+ align:start position:0%
+experiment by having a little um
+window someplace like a control volume
+
+ align:start position:0%
+window someplace like a control volume
+ 
+
+ align:start position:0%
+window someplace like a control volume
+somewhere in that in that U uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+container where you can look if there is
+
+ align:start position:0%
+container where you can look if there is
+ 
+
+ align:start position:0%
+container where you can look if there is
+a particle in there there can be only
+
+ align:start position:0%
+a particle in there there can be only
+ 
+
+ align:start position:0%
+a particle in there there can be only
+one at a time it's a small control
+
+ align:start position:0%
+one at a time it's a small control
+ 
+
+ align:start position:0%
+one at a time it's a small control
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+you you write it down in your
+
+ align:start position:0%
+you you write it down in your
+ 
+
+ align:start position:0%
+you you write it down in your
+experimental uh uh
+
+ align:start position:0%
+experimental uh uh
+ 
+
+ align:start position:0%
+experimental uh uh
+notebook I say oh yeah I saw a molecule
+
+ align:start position:0%
+notebook I say oh yeah I saw a molecule
+ 
+
+ align:start position:0%
+notebook I say oh yeah I saw a molecule
+of nitrogen or I saw a molecule of
+
+ align:start position:0%
+of nitrogen or I saw a molecule of
+ 
+
+ align:start position:0%
+of nitrogen or I saw a molecule of
+oxygen or I saw a molecule of
+
+ align:start position:0%
+oxygen or I saw a molecule of
+ 
+
+ align:start position:0%
+oxygen or I saw a molecule of
+argon or I saw a molecule of
+
+ align:start position:0%
+argon or I saw a molecule of
+ 
+
+ align:start position:0%
+argon or I saw a molecule of
+CO2 if that's
+
+ align:start position:0%
+CO2 if that's
+ 
+
+ align:start position:0%
+CO2 if that's
+air this
+
+ align:start position:0%
+air this
+ 
+
+ align:start position:0%
+air this
+is uh the
+
+ align:start position:0%
+is uh the
+ 
+
+ align:start position:0%
+is uh the
+idea and if you are in a stable in a
+
+ align:start position:0%
+idea and if you are in a stable in a
+ 
+
+ align:start position:0%
+idea and if you are in a stable in a
+stable equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State um and
+
+ align:start position:0%
+State um and
+ 
+
+ align:start position:0%
+State um and
+therefore the probabilities
+
+ align:start position:0%
+therefore the probabilities
+ 
+
+ align:start position:0%
+therefore the probabilities
+that you find that you observe one of
+
+ align:start position:0%
+that you find that you observe one of
+ 
+
+ align:start position:0%
+that you find that you observe one of
+these molecules is
+
+ align:start position:0%
+these molecules is
+ 
+
+ align:start position:0%
+these molecules is
+proportional to the fraction of
+
+ align:start position:0%
+proportional to the fraction of
+ 
+
+ align:start position:0%
+proportional to the fraction of
+particles overall so it's the mole
+
+ align:start position:0%
+particles overall so it's the mole
+ 
+
+ align:start position:0%
+particles overall so it's the mole
+fraction so the mole fraction which by
+
+ align:start position:0%
+fraction so the mole fraction which by
+ 
+
+ align:start position:0%
+fraction so the mole fraction which by
+the way is a number like probability now
+
+ align:start position:0%
+the way is a number like probability now
+ 
+
+ align:start position:0%
+the way is a number like probability now
+it's a number between zero and one and
+
+ align:start position:0%
+it's a number between zero and one and
+ 
+
+ align:start position:0%
+it's a number between zero and one and
+it adds up to
+
+ align:start position:0%
+it adds up to
+ 
+
+ align:start position:0%
+it adds up to
+one so the mo fraction is the
+
+ align:start position:0%
+one so the mo fraction is the
+ 
+
+ align:start position:0%
+one so the mo fraction is the
+probability to get the particle of that
+
+ align:start position:0%
+probability to get the particle of that
+ 
+
+ align:start position:0%
+probability to get the particle of that
+type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a a measure if so if
+
+ align:start position:0%
+a a measure if so if
+ 
+
+ align:start position:0%
+a a measure if so if
+you if you are facing this situation
+
+ align:start position:0%
+you if you are facing this situation
+ 
+
+ align:start position:0%
+you if you are facing this situation
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities you are in an
+
+ align:start position:0%
+probabilities you are in an
+ 
+
+ align:start position:0%
+probabilities you are in an
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+situation you are uncertain uncertain
+
+ align:start position:0%
+situation you are uncertain uncertain
+ 
+
+ align:start position:0%
+situation you are uncertain uncertain
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+what will be the outcome of the next
+
+ align:start position:0%
+what will be the outcome of the next
+ 
+
+ align:start position:0%
+what will be the outcome of the next
+observation you cannot
+
+ align:start position:0%
+observation you cannot
+ 
+
+ align:start position:0%
+observation you cannot
+predict the next time that's what I will
+
+ align:start position:0%
+predict the next time that's what I will
+ 
+
+ align:start position:0%
+predict the next time that's what I will
+get but you can predict because you know
+
+ align:start position:0%
+get but you can predict because you know
+ 
+
+ align:start position:0%
+get but you can predict because you know
+the mo fractions with what frequency you
+
+ align:start position:0%
+the mo fractions with what frequency you
+ 
+
+ align:start position:0%
+the mo fractions with what frequency you
+will get these results upon repeated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measurement but when you are facing uh
+
+ align:start position:0%
+measurement but when you are facing uh
+ 
+
+ align:start position:0%
+measurement but when you are facing uh
+the next observation and uh you a big
+
+ align:start position:0%
+the next observation and uh you a big
+ 
+
+ align:start position:0%
+the next observation and uh you a big
+question mark in your in your mind and
+
+ align:start position:0%
+question mark in your in your mind and
+ 
+
+ align:start position:0%
+question mark in your in your mind and
+asking all right what will be the next
+
+ align:start position:0%
+asking all right what will be the next
+ 
+
+ align:start position:0%
+asking all right what will be the next
+outcome you are in a state of
+
+ align:start position:0%
+outcome you are in a state of
+ 
+
+ align:start position:0%
+outcome you are in a state of
+uncertainty and the the
+
+ align:start position:0%
+uncertainty and the the
+ 
+
+ align:start position:0%
+uncertainty and the the
+uncertainty can be
+
+ align:start position:0%
+uncertainty can be
+ 
+
+ align:start position:0%
+uncertainty can be
+measured by this measure of
+
+ align:start position:0%
+measured by this measure of
+ 
+
+ align:start position:0%
+measured by this measure of
+information is called the Shannon
+
+ align:start position:0%
+information is called the Shannon
+ 
+
+ align:start position:0%
+information is called the Shannon
+information entropy Shannon
+
+ align:start position:0%
+information entropy Shannon
+ 
+
+ align:start position:0%
+information entropy Shannon
+1948 uh said well if I uh look at the
+
+ align:start position:0%
+1948 uh said well if I uh look at the
+ 
+
+ align:start position:0%
+1948 uh said well if I uh look at the
+situation described by probabilities
+
+ align:start position:0%
+situation described by probabilities
+ 
+
+ align:start position:0%
+situation described by probabilities
+like these events and I want to find uh
+
+ align:start position:0%
+like these events and I want to find uh
+ 
+
+ align:start position:0%
+like these events and I want to find uh
+the most uh uh logical
+
+ align:start position:0%
+the most uh uh logical
+ 
+
+ align:start position:0%
+the most uh uh logical
+uh mathematical expression or or
+
+ align:start position:0%
+uh mathematical expression or or
+ 
+
+ align:start position:0%
+uh mathematical expression or or
+function of these probabilities that
+
+ align:start position:0%
+function of these probabilities that
+ 
+
+ align:start position:0%
+function of these probabilities that
+expresses my state of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty he set up some postulates
+
+ align:start position:0%
+uncertainty he set up some postulates
+ 
+
+ align:start position:0%
+uncertainty he set up some postulates
+some desiderata about this measurement
+
+ align:start position:0%
+some desiderata about this measurement
+ 
+
+ align:start position:0%
+some desiderata about this measurement
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+probabilities and uh the only function
+
+ align:start position:0%
+probabilities and uh the only function
+ 
+
+ align:start position:0%
+probabilities and uh the only function
+that satisfies those criteria is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one for
+
+ align:start position:0%
+one for
+ 
+
+ align:start position:0%
+one for
+example see if you are that is equal to
+
+ align:start position:0%
+example see if you are that is equal to
+ 
+
+ align:start position:0%
+example see if you are that is equal to
+zero if you have certainty so if if the
+
+ align:start position:0%
+zero if you have certainty so if if the
+ 
+
+ align:start position:0%
+zero if you have certainty so if if the
+probabilities are all zeros except one
+
+ align:start position:0%
+probabilities are all zeros except one
+ 
+
+ align:start position:0%
+probabilities are all zeros except one
+event that is equal to
+
+ align:start position:0%
+event that is equal to
+ 
+
+ align:start position:0%
+event that is equal to
+one so you have certainty so particles
+
+ align:start position:0%
+one so you have certainty so particles
+ 
+
+ align:start position:0%
+one so you have certainty so particles
+of only one Type M fraction is
+
+ align:start position:0%
+of only one Type M fraction is
+ 
+
+ align:start position:0%
+of only one Type M fraction is
+one okay uh well log of
+
+ align:start position:0%
+one okay uh well log of
+ 
+
+ align:start position:0%
+one okay uh well log of
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+zero and X log X for those that are zero
+
+ align:start position:0%
+zero and X log X for those that are zero
+ 
+
+ align:start position:0%
+zero and X log X for those that are zero
+is again zero because you remember that
+
+ align:start position:0%
+is again zero because you remember that
+ 
+
+ align:start position:0%
+is again zero because you remember that
+this functions uh P log
+
+ align:start position:0%
+this functions uh P log
+ 
+
+ align:start position:0%
+this functions uh P log
+P look this way between zero and one
+
+ align:start position:0%
+P look this way between zero and one
+ 
+
+ align:start position:0%
+P look this way between zero and one
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+function uh X log
+
+ align:start position:0%
+function uh X log
+ 
+
+ align:start position:0%
+function uh X log
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+okay so in that case of complete
+
+ align:start position:0%
+okay so in that case of complete
+ 
+
+ align:start position:0%
+okay so in that case of complete
+certainty the information entropy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero or on the opposite side if all
+
+ align:start position:0%
+zero or on the opposite side if all
+ 
+
+ align:start position:0%
+zero or on the opposite side if all
+particles have equal
+
+ align:start position:0%
+particles have equal
+ 
+
+ align:start position:0%
+particles have equal
+probability so all the uh Mo fractions
+
+ align:start position:0%
+probability so all the uh Mo fractions
+ 
+
+ align:start position:0%
+probability so all the uh Mo fractions
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+equal and in that case uh the
+
+ align:start position:0%
+equal and in that case uh the
+ 
+
+ align:start position:0%
+equal and in that case uh the
+entropy is equal to
+
+ align:start position:0%
+entropy is equal to
+ 
+
+ align:start position:0%
+entropy is equal to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+log of n of uh the number of of log of R
+
+ align:start position:0%
+log of n of uh the number of of log of R
+ 
+
+ align:start position:0%
+log of n of uh the number of of log of R
+in this case it's it's the number of
+
+ align:start position:0%
+in this case it's it's the number of
+ 
+
+ align:start position:0%
+in this case it's it's the number of
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles you can work it out you
+
+ align:start position:0%
+particles you can work it out you
+ 
+
+ align:start position:0%
+particles you can work it out you
+substitute each probability is one
+
+ align:start position:0%
+substitute each probability is one
+ 
+
+ align:start position:0%
+substitute each probability is one
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+R and that this summation gives a um log
+
+ align:start position:0%
+R and that this summation gives a um log
+ 
+
+ align:start position:0%
+R and that this summation gives a um log
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+R that's the maximum the most uncertain
+
+ align:start position:0%
+R that's the maximum the most uncertain
+ 
+
+ align:start position:0%
+R that's the maximum the most uncertain
+situation when they're all
+
+ align:start position:0%
+situation when they're all
+ 
+
+ align:start position:0%
+situation when they're all
+alike if you have instead a situation
+
+ align:start position:0%
+alike if you have instead a situation
+ 
+
+ align:start position:0%
+alike if you have instead a situation
+like uh for the molecules of
+
+ align:start position:0%
+like uh for the molecules of
+ 
+
+ align:start position:0%
+like uh for the molecules of
+air it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even and therefore some are more uh
+
+ align:start position:0%
+even and therefore some are more uh
+ 
+
+ align:start position:0%
+even and therefore some are more uh
+frequent than others so you could get
+
+ align:start position:0%
+frequent than others so you could get
+ 
+
+ align:start position:0%
+frequent than others so you could get
+you could guess some uh um some better
+
+ align:start position:0%
+you could guess some uh um some better
+ 
+
+ align:start position:0%
+you could guess some uh um some better
+than if everything was just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50% you can also
+
+ align:start position:0%
+50% you can also
+ 
+
+ align:start position:0%
+50% you can also
+view this is interesting also for us for
+
+ align:start position:0%
+view this is interesting also for us for
+ 
+
+ align:start position:0%
+view this is interesting also for us for
+the next step in the next definition
+
+ align:start position:0%
+the next step in the next definition
+ 
+
+ align:start position:0%
+the next step in the next definition
+of ideal
+
+ align:start position:0%
+of ideal
+ 
+
+ align:start position:0%
+of ideal
+solution you can also view this as a
+
+ align:start position:0%
+solution you can also view this as a
+ 
+
+ align:start position:0%
+solution you can also view this as a
+weighted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum weight on the mole
+
+ align:start position:0%
+sum weight on the mole
+ 
+
+ align:start position:0%
+sum weight on the mole
+fractions see I can view this as the
+
+ align:start position:0%
+fractions see I can view this as the
+ 
+
+ align:start position:0%
+fractions see I can view this as the
+summation the mole
+
+ align:start position:0%
+summation the mole
+ 
+
+ align:start position:0%
+summation the mole
+fraction times
+
+ align:start position:0%
+fraction times
+ 
+
+ align:start position:0%
+fraction times
+minus log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y now this term in parenthesis we
+
+ align:start position:0%
+Y now this term in parenthesis we
+ 
+
+ align:start position:0%
+Y now this term in parenthesis we
+could call it the
+
+ align:start position:0%
+could call it the
+ 
+
+ align:start position:0%
+could call it the
+surprise the
+
+ align:start position:0%
+surprise the
+ 
+
+ align:start position:0%
+surprise the
+surprise the surprise is a measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's high for the least probable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones so if I get H I could say that if I
+
+ align:start position:0%
+ones so if I get H I could say that if I
+ 
+
+ align:start position:0%
+ones so if I get H I could say that if I
+get a if I see a molecule of CO2
+
+ align:start position:0%
+get a if I see a molecule of CO2
+ 
+
+ align:start position:0%
+get a if I see a molecule of CO2
+there and I know that there are only 500
+
+ align:start position:0%
+there and I know that there are only 500
+ 
+
+ align:start position:0%
+there and I know that there are only 500
+ppms part per million so there is very
+
+ align:start position:0%
+ppms part per million so there is very
+ 
+
+ align:start position:0%
+ppms part per million so there is very
+low probability so if I see that one I'm
+
+ align:start position:0%
+low probability so if I see that one I'm
+ 
+
+ align:start position:0%
+low probability so if I see that one I'm
+kind of more surprised than if I see
+
+ align:start position:0%
+kind of more surprised than if I see
+ 
+
+ align:start position:0%
+kind of more surprised than if I see
+nitrogen or an
+
+ align:start position:0%
+nitrogen or an
+ 
+
+ align:start position:0%
+nitrogen or an
+oxygen argon also is a bit of a surprise
+
+ align:start position:0%
+oxygen argon also is a bit of a surprise
+ 
+
+ align:start position:0%
+oxygen argon also is a bit of a surprise
+because argon is less than
+
+ align:start position:0%
+because argon is less than
+ 
+
+ align:start position:0%
+because argon is less than
+1% so I need
+
+ align:start position:0%
+1% so I need
+ 
+
+ align:start position:0%
+1% so I need
+to uh do 100 trials to have on average
+
+ align:start position:0%
+to uh do 100 trials to have on average
+ 
+
+ align:start position:0%
+to uh do 100 trials to have on average
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+argon and uh here I need the uh
+
+ align:start position:0%
+argon and uh here I need the uh
+ 
+
+ align:start position:0%
+argon and uh here I need the uh
+2,000 trials to get one
+
+ align:start position:0%
+2,000 trials to get one
+ 
+
+ align:start position:0%
+2,000 trials to get one
+CO2 okay so that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surprise now in information Theory there
+
+ align:start position:0%
+surprise now in information Theory there
+ 
+
+ align:start position:0%
+surprise now in information Theory there
+is also this problem that is also
+
+ align:start position:0%
+is also this problem that is also
+ 
+
+ align:start position:0%
+is also this problem that is also
+relevant for uh
+
+ align:start position:0%
+relevant for uh
+ 
+
+ align:start position:0%
+relevant for uh
+measurements for example suppose that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you uh your device that finds the
+
+ align:start position:0%
+you uh your device that finds the
+ 
+
+ align:start position:0%
+you uh your device that finds the
+particle uh and characterizes the
+
+ align:start position:0%
+particle uh and characterizes the
+ 
+
+ align:start position:0%
+particle uh and characterizes the
+particle by uh the
+
+ align:start position:0%
+particle by uh the
+ 
+
+ align:start position:0%
+particle by uh the
+mass so when the when the particle is in
+
+ align:start position:0%
+mass so when the when the particle is in
+ 
+
+ align:start position:0%
+mass so when the when the particle is in
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+window your
+
+ align:start position:0%
+window your
+ 
+
+ align:start position:0%
+window your
+device uh maybe a spectrometer or
+
+ align:start position:0%
+device uh maybe a spectrometer or
+ 
+
+ align:start position:0%
+device uh maybe a spectrometer or
+whatever it tells you okay it was a mass
+
+ align:start position:0%
+whatever it tells you okay it was a mass
+ 
+
+ align:start position:0%
+whatever it tells you okay it was a mass
+a particle with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mass so in the end when you do a
+
+ align:start position:0%
+Mass so in the end when you do a
+ 
+
+ align:start position:0%
+Mass so in the end when you do a
+measurement like a repeated uh
+
+ align:start position:0%
+measurement like a repeated uh
+ 
+
+ align:start position:0%
+measurement like a repeated uh
+measurement procedure in the end you
+
+ align:start position:0%
+measurement procedure in the end you
+ 
+
+ align:start position:0%
+measurement procedure in the end you
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+find uh the average or the
+
+ align:start position:0%
+find uh the average or the
+ 
+
+ align:start position:0%
+find uh the average or the
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+mass that shows
+
+ align:start position:0%
+mass that shows
+ 
+
+ align:start position:0%
+mass that shows
+up and suppose that that's all that you
+
+ align:start position:0%
+up and suppose that that's all that you
+ 
+
+ align:start position:0%
+up and suppose that that's all that you
+can measure of your
+
+ align:start position:0%
+can measure of your
+ 
+
+ align:start position:0%
+can measure of your
+substance so all you can measure is the
+
+ align:start position:0%
+substance so all you can measure is the
+ 
+
+ align:start position:0%
+substance so all you can measure is the
+average value of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass if that's the only information I
+
+ align:start position:0%
+mass if that's the only information I
+ 
+
+ align:start position:0%
+mass if that's the only information I
+have about my system could I make an
+
+ align:start position:0%
+have about my system could I make an
+ 
+
+ align:start position:0%
+have about my system could I make an
+educated guess of what the probability
+
+ align:start position:0%
+educated guess of what the probability
+ 
+
+ align:start position:0%
+educated guess of what the probability
+uh distribution so therefore what the
+
+ align:start position:0%
+uh distribution so therefore what the
+ 
+
+ align:start position:0%
+uh distribution so therefore what the
+mole fractions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are and here
+
+ align:start position:0%
+are and here
+ 
+
+ align:start position:0%
+are and here
+comes U information Theory and again
+
+ align:start position:0%
+comes U information Theory and again
+ 
+
+ align:start position:0%
+comes U information Theory and again
+based on Shannon information
+
+ align:start position:0%
+based on Shannon information
+ 
+
+ align:start position:0%
+based on Shannon information
+entropy you say all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right in order to make the educated
+
+ align:start position:0%
+right in order to make the educated
+ 
+
+ align:start position:0%
+right in order to make the educated
+guess I should uh
+
+ align:start position:0%
+guess I should uh
+ 
+
+ align:start position:0%
+guess I should uh
+avoid any bias that is not contained in
+
+ align:start position:0%
+avoid any bias that is not contained in
+ 
+
+ align:start position:0%
+avoid any bias that is not contained in
+the information I have about the system
+
+ align:start position:0%
+the information I have about the system
+ 
+
+ align:start position:0%
+the information I have about the system
+so I should
+
+ align:start position:0%
+so I should
+ 
+
+ align:start position:0%
+so I should
+use the information I have the measured
+
+ align:start position:0%
+use the information I have the measured
+ 
+
+ align:start position:0%
+use the information I have the measured
+values but not extra
+
+ align:start position:0%
+values but not extra
+ 
+
+ align:start position:0%
+values but not extra
+stuff so I want to make the least biased
+
+ align:start position:0%
+stuff so I want to make the least biased
+ 
+
+ align:start position:0%
+stuff so I want to make the least biased
+guess and the least guy bias guess is is
+
+ align:start position:0%
+guess and the least guy bias guess is is
+ 
+
+ align:start position:0%
+guess and the least guy bias guess is is
+obtained by saying all right what is the
+
+ align:start position:0%
+obtained by saying all right what is the
+ 
+
+ align:start position:0%
+obtained by saying all right what is the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distribution that maximizes the shown
+
+ align:start position:0%
+distribution that maximizes the shown
+ 
+
+ align:start position:0%
+distribution that maximizes the shown
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+in other words it leaves me with the
+
+ align:start position:0%
+in other words it leaves me with the
+ 
+
+ align:start position:0%
+in other words it leaves me with the
+highest possible uncertainty compatible
+
+ align:start position:0%
+highest possible uncertainty compatible
+ 
+
+ align:start position:0%
+highest possible uncertainty compatible
+with that mean value that I I have
+
+ align:start position:0%
+with that mean value that I I have
+ 
+
+ align:start position:0%
+with that mean value that I I have
+observed in this way if uh I have not
+
+ align:start position:0%
+observed in this way if uh I have not
+ 
+
+ align:start position:0%
+observed in this way if uh I have not
+built in uh the probability distribution
+
+ align:start position:0%
+built in uh the probability distribution
+ 
+
+ align:start position:0%
+built in uh the probability distribution
+any extra
+
+ align:start position:0%
+any extra
+ 
+
+ align:start position:0%
+any extra
+information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and so mathematically this means you
+
+ align:start position:0%
+uh and so mathematically this means you
+ 
+
+ align:start position:0%
+uh and so mathematically this means you
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+maximize the on
+
+ align:start position:0%
+maximize the on
+ 
+
+ align:start position:0%
+maximize the on
+entropy subject to the constraint that
+
+ align:start position:0%
+entropy subject to the constraint that
+ 
+
+ align:start position:0%
+entropy subject to the constraint that
+your mean value be the non or measured
+
+ align:start position:0%
+your mean value be the non or measured
+ 
+
+ align:start position:0%
+your mean value be the non or measured
+value of course you also have to put the
+
+ align:start position:0%
+value of course you also have to put the
+ 
+
+ align:start position:0%
+value of course you also have to put the
+uh auxiliary constraint that
+
+ align:start position:0%
+uh auxiliary constraint that
+ 
+
+ align:start position:0%
+uh auxiliary constraint that
+probabilities must add up to
+
+ align:start position:0%
+probabilities must add up to
+ 
+
+ align:start position:0%
+probabilities must add up to
+one and if you solve
+
+ align:start position:0%
+one and if you solve
+ 
+
+ align:start position:0%
+one and if you solve
+this uh problem with the method of
+
+ align:start position:0%
+this uh problem with the method of
+ 
+
+ align:start position:0%
+this uh problem with the method of
+lrange
+
+ align:start position:0%
+lrange
+ 
+
+ align:start position:0%
+lrange
+multipliers I'm don't want to just go
+
+ align:start position:0%
+multipliers I'm don't want to just go
+ 
+
+ align:start position:0%
+multipliers I'm don't want to just go
+over that today but maybe later on on WE
+
+ align:start position:0%
+over that today but maybe later on on WE
+ 
+
+ align:start position:0%
+over that today but maybe later on on WE
+since we uh we we will uh will we'll
+
+ align:start position:0%
+since we uh we we will uh will we'll
+ 
+
+ align:start position:0%
+since we uh we we will uh will we'll
+review it uh uh in any case I presume
+
+ align:start position:0%
+review it uh uh in any case I presume
+ 
+
+ align:start position:0%
+review it uh uh in any case I presume
+that you have seen it somewhere else uh
+
+ align:start position:0%
+that you have seen it somewhere else uh
+ 
+
+ align:start position:0%
+that you have seen it somewhere else uh
+so the method simply says all right if
+
+ align:start position:0%
+so the method simply says all right if
+ 
+
+ align:start position:0%
+so the method simply says all right if
+you have a constraint maximization you
+
+ align:start position:0%
+you have a constraint maximization you
+ 
+
+ align:start position:0%
+you have a constraint maximization you
+must assign to each of the constraints a
+
+ align:start position:0%
+must assign to each of the constraints a
+ 
+
+ align:start position:0%
+must assign to each of the constraints a
+lrange multip a multiplier and under
+
+ align:start position:0%
+lrange multip a multiplier and under
+ 
+
+ align:start position:0%
+lrange multip a multiplier and under
+term in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplier uh then
+
+ align:start position:0%
+multiplier uh then
+ 
+
+ align:start position:0%
+multiplier uh then
+do an unconstrained maximization of the
+
+ align:start position:0%
+do an unconstrained maximization of the
+ 
+
+ align:start position:0%
+do an unconstrained maximization of the
+optimizing
+
+ align:start position:0%
+optimizing
+ 
+
+ align:start position:0%
+optimizing
+function uh minus the constraints
+
+ align:start position:0%
+function uh minus the constraints
+ 
+
+ align:start position:0%
+function uh minus the constraints
+multiplied by these
+
+ align:start position:0%
+multiplied by these
+ 
+
+ align:start position:0%
+multiplied by these
+multipliers and then once you obtain the
+
+ align:start position:0%
+multipliers and then once you obtain the
+ 
+
+ align:start position:0%
+multipliers and then once you obtain the
+solution of the unconstrained maximum in
+
+ align:start position:0%
+solution of the unconstrained maximum in
+ 
+
+ align:start position:0%
+solution of the unconstrained maximum in
+terms of these multipliers you will
+
+ align:start position:0%
+terms of these multipliers you will
+ 
+
+ align:start position:0%
+terms of these multipliers you will
+substitute back into the constraints and
+
+ align:start position:0%
+substitute back into the constraints and
+ 
+
+ align:start position:0%
+substitute back into the constraints and
+uh get the values for the multipliers
+
+ align:start position:0%
+uh get the values for the multipliers
+ 
+
+ align:start position:0%
+uh get the values for the multipliers
+all right that's
+
+ align:start position:0%
+all right that's
+ 
+
+ align:start position:0%
+all right that's
+a quick so I don't expect you to have
+
+ align:start position:0%
+a quick so I don't expect you to have
+ 
+
+ align:start position:0%
+a quick so I don't expect you to have
+learned it from from these words but in
+
+ align:start position:0%
+learned it from from these words but in
+ 
+
+ align:start position:0%
+learned it from from these words but in
+any case if you do the job here's the
+
+ align:start position:0%
+any case if you do the job here's the
+ 
+
+ align:start position:0%
+any case if you do the job here's the
+probability distribution that you
+
+ align:start position:0%
+probability distribution that you
+ 
+
+ align:start position:0%
+probability distribution that you
+get and
+
+ align:start position:0%
+get and
+ 
+
+ align:start position:0%
+get and
+uh if you
+
+ align:start position:0%
+uh if you
+ 
+
+ align:start position:0%
+uh if you
+substitute this probability back into
+
+ align:start position:0%
+substitute this probability back into
+ 
+
+ align:start position:0%
+substitute this probability back into
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+constraint this one that gives you the
+
+ align:start position:0%
+constraint this one that gives you the
+ 
+
+ align:start position:0%
+constraint this one that gives you the
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+M it uh gives you a
+
+ align:start position:0%
+M it uh gives you a
+ 
+
+ align:start position:0%
+M it uh gives you a
+relation between the Lambda M which is
+
+ align:start position:0%
+relation between the Lambda M which is
+ 
+
+ align:start position:0%
+relation between the Lambda M which is
+the lrange multiplier and the mean value
+
+ align:start position:0%
+the lrange multiplier and the mean value
+ 
+
+ align:start position:0%
+the lrange multiplier and the mean value
+so you get that the lrange multiplier
+
+ align:start position:0%
+so you get that the lrange multiplier
+ 
+
+ align:start position:0%
+so you get that the lrange multiplier
+depends on that mean value of the
+
+ align:start position:0%
+depends on that mean value of the
+ 
+
+ align:start position:0%
+depends on that mean value of the
+mass so this is the
+
+ align:start position:0%
+mass so this is the
+ 
+
+ align:start position:0%
+mass so this is the
+best or at least the least biased
+
+ align:start position:0%
+best or at least the least biased
+ 
+
+ align:start position:0%
+best or at least the least biased
+assignment of M fractions that you can
+
+ align:start position:0%
+assignment of M fractions that you can
+ 
+
+ align:start position:0%
+assignment of M fractions that you can
+do upon a measurement of only the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass we will see in a while that uh this
+
+ align:start position:0%
+mass we will see in a while that uh this
+ 
+
+ align:start position:0%
+mass we will see in a while that uh this
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distribution is very similar to what you
+
+ align:start position:0%
+distribution is very similar to what you
+ 
+
+ align:start position:0%
+distribution is very similar to what you
+obtain uh what you have for the
+
+ align:start position:0%
+obtain uh what you have for the
+ 
+
+ align:start position:0%
+obtain uh what you have for the
+description of stable equilibrium States
+
+ align:start position:0%
+description of stable equilibrium States
+ 
+
+ align:start position:0%
+description of stable equilibrium States
+within statistical mechanics and quantum
+
+ align:start position:0%
+within statistical mechanics and quantum
+ 
+
+ align:start position:0%
+within statistical mechanics and quantum
+theory it's called the canonical
+
+ align:start position:0%
+theory it's called the canonical
+ 
+
+ align:start position:0%
+theory it's called the canonical
+distribution If instead of mass you put
+
+ align:start position:0%
+distribution If instead of mass you put
+ 
+
+ align:start position:0%
+distribution If instead of mass you put
+energy and that allows or
+
+ align:start position:0%
+energy and that allows or
+ 
+
+ align:start position:0%
+energy and that allows or
+allowed uh
+
+ align:start position:0%
+allowed uh
+ 
+
+ align:start position:0%
+allowed uh
+researchers like uh
+
+ align:start position:0%
+researchers like uh
+ 
+
+ align:start position:0%
+researchers like uh
+James it's a big
+
+ align:start position:0%
+James it's a big
+ 
+
+ align:start position:0%
+James it's a big
+name who made uh
+
+ align:start position:0%
+name who made uh
+ 
+
+ align:start position:0%
+name who made uh
+these very neat connections between
+
+ align:start position:0%
+these very neat connections between
+ 
+
+ align:start position:0%
+these very neat connections between
+information Theory and statistical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanics or also uh if
+
+ align:start position:0%
+mechanics or also uh if
+ 
+
+ align:start position:0%
+mechanics or also uh if
+you if you if you still go to the
+
+ align:start position:0%
+you if you if you still go to the
+ 
+
+ align:start position:0%
+you if you if you still go to the
+library here at MIT there is a wonderful
+
+ align:start position:0%
+library here at MIT there is a wonderful
+ 
+
+ align:start position:0%
+library here at MIT there is a wonderful
+um set of video
+
+ align:start position:0%
+um set of video
+ 
+
+ align:start position:0%
+um set of video
+lectures by Professor myON
+
+ align:start position:0%
+lectures by Professor myON
+ 
+
+ align:start position:0%
+lectures by Professor myON
+tribus back in I think the 60s or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+70s uh where he does uh the information
+
+ align:start position:0%
+70s uh where he does uh the information
+ 
+
+ align:start position:0%
+70s uh where he does uh the information
+Theory point of view of thermodynamics
+
+ align:start position:0%
+Theory point of view of thermodynamics
+ 
+
+ align:start position:0%
+Theory point of view of thermodynamics
+so he develops the entire thermodynamics
+
+ align:start position:0%
+so he develops the entire thermodynamics
+ 
+
+ align:start position:0%
+so he develops the entire thermodynamics
+just by building up on uh information
+
+ align:start position:0%
+just by building up on uh information
+ 
+
+ align:start position:0%
+just by building up on uh information
+Theory
+
+ align:start position:0%
+Theory
+ 
+
+ align:start position:0%
+Theory
+concept and indeed
+
+ align:start position:0%
+concept and indeed
+ 
+
+ align:start position:0%
+concept and indeed
+there is uh a ground for doing it
+
+ align:start position:0%
+there is uh a ground for doing it
+ 
+
+ align:start position:0%
+there is uh a ground for doing it
+because the molecular view that we are
+
+ align:start position:0%
+because the molecular view that we are
+ 
+
+ align:start position:0%
+because the molecular view that we are
+discussing here and the tools developed
+
+ align:start position:0%
+discussing here and the tools developed
+ 
+
+ align:start position:0%
+discussing here and the tools developed
+by Shannon do pro do provide that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibility so I said that I wanted to
+
+ align:start position:0%
+possibility so I said that I wanted to
+ 
+
+ align:start position:0%
+possibility so I said that I wanted to
+make a little uh degression today
+
+ align:start position:0%
+make a little uh degression today
+ 
+
+ align:start position:0%
+make a little uh degression today
+so here is a degression in the
+
+ align:start position:0%
+so here is a degression in the
+ 
+
+ align:start position:0%
+so here is a degression in the
+degression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it has to
+
+ align:start position:0%
+uh it has to
+ 
+
+ align:start position:0%
+uh it has to
+do with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+treatment of a
+
+ align:start position:0%
+treatment of a
+ 
+
+ align:start position:0%
+treatment of a
+particle in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box okay so we take a
+
+ align:start position:0%
+box okay so we take a
+ 
+
+ align:start position:0%
+box okay so we take a
+box of uh sides L1 L2 and L3 in the
+
+ align:start position:0%
+box of uh sides L1 L2 and L3 in the
+ 
+
+ align:start position:0%
+box of uh sides L1 L2 and L3 in the
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+directions and we consider only one
+
+ align:start position:0%
+directions and we consider only one
+ 
+
+ align:start position:0%
+directions and we consider only one
+particle inside this
+
+ align:start position:0%
+particle inside this
+ 
+
+ align:start position:0%
+particle inside this
+box that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea of uh of this little uh survey of
+
+ align:start position:0%
+idea of uh of this little uh survey of
+ 
+
+ align:start position:0%
+idea of uh of this little uh survey of
+uh with some equations that are borrowed
+
+ align:start position:0%
+uh with some equations that are borrowed
+ 
+
+ align:start position:0%
+uh with some equations that are borrowed
+from quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+uh which you may be familiar or not but
+
+ align:start position:0%
+uh which you may be familiar or not but
+ 
+
+ align:start position:0%
+uh which you may be familiar or not but
+uh uh even if you are not it's okay this
+
+ align:start position:0%
+uh uh even if you are not it's okay this
+ 
+
+ align:start position:0%
+uh uh even if you are not it's okay this
+is a just a quick
+
+ align:start position:0%
+is a just a quick
+ 
+
+ align:start position:0%
+is a just a quick
+view that tells you how all these things
+
+ align:start position:0%
+view that tells you how all these things
+ 
+
+ align:start position:0%
+view that tells you how all these things
+are related so it might might be
+
+ align:start position:0%
+are related so it might might be
+ 
+
+ align:start position:0%
+are related so it might might be
+interesting um I will not ask for this
+
+ align:start position:0%
+interesting um I will not ask for this
+ 
+
+ align:start position:0%
+interesting um I will not ask for this
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+the oral exam of course and actually one
+
+ align:start position:0%
+the oral exam of course and actually one
+ 
+
+ align:start position:0%
+the oral exam of course and actually one
+day I will let you know
+
+ align:start position:0%
+day I will let you know
+ 
+
+ align:start position:0%
+day I will let you know
+which are of the many things that we
+
+ align:start position:0%
+which are of the many things that we
+ 
+
+ align:start position:0%
+which are of the many things that we
+cover the uh slides that uh are to be um
+
+ align:start position:0%
+cover the uh slides that uh are to be um
+ 
+
+ align:start position:0%
+cover the uh slides that uh are to be um
+I me are going to be part of the exam so
+
+ align:start position:0%
+I me are going to be part of the exam so
+ 
+
+ align:start position:0%
+I me are going to be part of the exam so
+that you can focus and because otherwise
+
+ align:start position:0%
+that you can focus and because otherwise
+ 
+
+ align:start position:0%
+that you can focus and because otherwise
+it's too much I I perfectly realize all
+
+ align:start position:0%
+it's too much I I perfectly realize all
+ 
+
+ align:start position:0%
+it's too much I I perfectly realize all
+right so uh the idea in quantum
+
+ align:start position:0%
+right so uh the idea in quantum
+ 
+
+ align:start position:0%
+right so uh the idea in quantum
+mechanics is that um in order to uh
+
+ align:start position:0%
+mechanics is that um in order to uh
+ 
+
+ align:start position:0%
+mechanics is that um in order to uh
+describe uh
+
+ align:start position:0%
+describe uh
+ 
+
+ align:start position:0%
+describe uh
+molecule like that or even
+
+ align:start position:0%
+molecule like that or even
+ 
+
+ align:start position:0%
+molecule like that or even
+simpler if you have a molecule on a
+
+ align:start position:0%
+simpler if you have a molecule on a
+ 
+
+ align:start position:0%
+simpler if you have a molecule on a
+one-dimensional box that we already
+
+ align:start position:0%
+one-dimensional box that we already
+ 
+
+ align:start position:0%
+one-dimensional box that we already
+mentioned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so suppose we have just
+
+ align:start position:0%
+uh so suppose we have just
+ 
+
+ align:start position:0%
+uh so suppose we have just
+onedimensional
+
+ align:start position:0%
+onedimensional
+ 
+
+ align:start position:0%
+onedimensional
+box in classical mechanics the particle
+
+ align:start position:0%
+box in classical mechanics the particle
+ 
+
+ align:start position:0%
+box in classical mechanics the particle
+is here and it goes uh back and forth
+
+ align:start position:0%
+is here and it goes uh back and forth
+ 
+
+ align:start position:0%
+is here and it goes uh back and forth
+It's Perfectly uh uh situated somewhere
+
+ align:start position:0%
+It's Perfectly uh uh situated somewhere
+ 
+
+ align:start position:0%
+It's Perfectly uh uh situated somewhere
+at every instant of time in uh quantum
+
+ align:start position:0%
+at every instant of time in uh quantum
+ 
+
+ align:start position:0%
+at every instant of time in uh quantum
+mechanics the story is different
+
+ align:start position:0%
+mechanics the story is different
+ 
+
+ align:start position:0%
+mechanics the story is different
+particle cannot be is not I mean the the
+
+ align:start position:0%
+particle cannot be is not I mean the the
+ 
+
+ align:start position:0%
+particle cannot be is not I mean the the
+idea of viewing the particle as
+
+ align:start position:0%
+idea of viewing the particle as
+ 
+
+ align:start position:0%
+idea of viewing the particle as
+localized is wrong it gives you some
+
+ align:start position:0%
+localized is wrong it gives you some
+ 
+
+ align:start position:0%
+localized is wrong it gives you some
+results that that are
+
+ align:start position:0%
+results that that are
+ 
+
+ align:start position:0%
+results that that are
+wrong so the idea of quantum mechanics
+
+ align:start position:0%
+wrong so the idea of quantum mechanics
+ 
+
+ align:start position:0%
+wrong so the idea of quantum mechanics
+is that you start from you have
+
+ align:start position:0%
+is that you start from you have
+ 
+
+ align:start position:0%
+is that you start from you have
+to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find a
+
+ align:start position:0%
+find a
+ 
+
+ align:start position:0%
+find a
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distribution which uh can be obtained by
+
+ align:start position:0%
+distribution which uh can be obtained by
+ 
+
+ align:start position:0%
+distribution which uh can be obtained by
+a function let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fe
+
+ align:start position:0%
+Fe
+ 
+
+ align:start position:0%
+Fe
+okay and this
+
+ align:start position:0%
+okay and this
+ 
+
+ align:start position:0%
+okay and this
+function uh is the uh
+
+ align:start position:0%
+function uh is the uh
+ 
+
+ align:start position:0%
+function uh is the uh
+solution of U an igen value problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh for
+
+ align:start position:0%
+and uh for
+ 
+
+ align:start position:0%
+and uh for
+example first of all this function can
+
+ align:start position:0%
+example first of all this function can
+ 
+
+ align:start position:0%
+example first of all this function can
+be also written as uh the
+
+ align:start position:0%
+be also written as uh the
+ 
+
+ align:start position:0%
+be also written as uh the
+factors so it's a product of a function
+
+ align:start position:0%
+factors so it's a product of a function
+ 
+
+ align:start position:0%
+factors so it's a product of a function
+of X and the function of uh
+
+ align:start position:0%
+of X and the function of uh
+ 
+
+ align:start position:0%
+of X and the function of uh
+time and the function of time uh
+
+ align:start position:0%
+time and the function of time uh
+ 
+
+ align:start position:0%
+time and the function of time uh
+remember uh it's
+
+ align:start position:0%
+remember uh it's
+ 
+
+ align:start position:0%
+remember uh it's
+minus uh H bar times the
+
+ align:start position:0%
+minus uh H bar times the
+ 
+
+ align:start position:0%
+minus uh H bar times the
+energy times time
+
+ align:start position:0%
+energy times time
+ 
+
+ align:start position:0%
+energy times time
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something it will it will come up uh
+
+ align:start position:0%
+something it will it will come up uh
+ 
+
+ align:start position:0%
+something it will it will come up uh
+somewhere uh over M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably not sure okay so the idea is
+
+ align:start position:0%
+probably not sure okay so the idea is
+ 
+
+ align:start position:0%
+probably not sure okay so the idea is
+that this function here the one that
+
+ align:start position:0%
+that this function here the one that
+ 
+
+ align:start position:0%
+that this function here the one that
+depends on
+
+ align:start position:0%
+depends on
+ 
+
+ align:start position:0%
+depends on
+X is the solution of an igen value uh
+
+ align:start position:0%
+X is the solution of an igen value uh
+ 
+
+ align:start position:0%
+X is the solution of an igen value uh
+problem uh
+
+ align:start position:0%
+problem uh
+ 
+
+ align:start position:0%
+problem uh
+and these
+
+ align:start position:0%
+and these
+ 
+
+ align:start position:0%
+and these
+functions are you can plot them as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows as we as we know uh um actually
+
+ align:start position:0%
+follows as we as we know uh um actually
+ 
+
+ align:start position:0%
+follows as we as we know uh um actually
+I think we have we have the expression
+
+ align:start position:0%
+I think we have we have the expression
+ 
+
+ align:start position:0%
+I think we have we have the expression
+it's something like square root of
+
+ align:start position:0%
+it's something like square root of
+ 
+
+ align:start position:0%
+it's something like square root of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um 2 over
+
+ align:start position:0%
+um 2 over
+ 
+
+ align:start position:0%
+um 2 over
+L where L is the side so this is from
+
+ align:start position:0%
+L where L is the side so this is from
+ 
+
+ align:start position:0%
+L where L is the side so this is from
+zero to
+
+ align:start position:0%
+zero to
+ 
+
+ align:start position:0%
+zero to
+L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times s of uh some
+
+ align:start position:0%
+times s of uh some
+ 
+
+ align:start position:0%
+times s of uh some
+J some maybe X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there are some other constants here
+
+ align:start position:0%
+and there are some other constants here
+ 
+
+ align:start position:0%
+and there are some other constants here
+that I now slips uh my uh
+
+ align:start position:0%
+that I now slips uh my uh
+ 
+
+ align:start position:0%
+that I now slips uh my uh
+memory and it's maybe
+
+ align:start position:0%
+memory and it's maybe
+ 
+
+ align:start position:0%
+memory and it's maybe
+uh maybe uh H over 2 m or something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that or maybe also an
+
+ align:start position:0%
+that or maybe also an
+ 
+
+ align:start position:0%
+that or maybe also an
+L uh there is also an L here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the idea is that this
+
+ align:start position:0%
+okay so the idea is that this
+ 
+
+ align:start position:0%
+okay so the idea is that this
+J is the integer
+
+ align:start position:0%
+J is the integer
+ 
+
+ align:start position:0%
+J is the integer
+numbers so there are many possible uh
+
+ align:start position:0%
+numbers so there are many possible uh
+ 
+
+ align:start position:0%
+numbers so there are many possible uh
+contributions each one of these for each
+
+ align:start position:0%
+contributions each one of these for each
+ 
+
+ align:start position:0%
+contributions each one of these for each
+J corresponds to a
+
+ align:start position:0%
+J corresponds to a
+ 
+
+ align:start position:0%
+J corresponds to a
+solution uh and to that solution
+
+ align:start position:0%
+solution uh and to that solution
+ 
+
+ align:start position:0%
+solution uh and to that solution
+corresponds
+
+ align:start position:0%
+corresponds
+ 
+
+ align:start position:0%
+corresponds
+also a uh an energy level so for example
+
+ align:start position:0%
+also a uh an energy level so for example
+ 
+
+ align:start position:0%
+also a uh an energy level so for example
+the the low lowest energy level
+
+ align:start position:0%
+the the low lowest energy level
+ 
+
+ align:start position:0%
+the the low lowest energy level
+corresponding to J is equal to
+
+ align:start position:0%
+corresponding to J is equal to
+ 
+
+ align:start position:0%
+corresponding to J is equal to
+1 is a function like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this then you may have the second energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level uh in
+
+ align:start position:0%
+level uh in
+ 
+
+ align:start position:0%
+level uh in
+which the
+
+ align:start position:0%
+which the
+ 
+
+ align:start position:0%
+which the
+function is something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and then J equal to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 right and so
+
+ align:start position:0%
+3 right and so
+ 
+
+ align:start position:0%
+3 right and so
+on corresponding to each of these
+
+ align:start position:0%
+on corresponding to each of these
+ 
+
+ align:start position:0%
+on corresponding to each of these
+JS there are
+
+ align:start position:0%
+JS there are
+ 
+
+ align:start position:0%
+JS there are
+energies or actually on the slide I'm
+
+ align:start position:0%
+energies or actually on the slide I'm
+ 
+
+ align:start position:0%
+energies or actually on the slide I'm
+calling them uh Epsilon J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and these energies are
+
+ align:start position:0%
+okay and these energies are
+ 
+
+ align:start position:0%
+okay and these energies are
+H squar over 2
+
+ align:start position:0%
+H squar over 2
+ 
+
+ align:start position:0%
+H squar over 2
+m multiplied by J 2 over L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 maybe there's a pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here because it needs to go to to to
+
+ align:start position:0%
+here because it needs to go to to to
+ 
+
+ align:start position:0%
+here because it needs to go to to to
+zero at zero and at L
+
+ align:start position:0%
+zero at zero and at L
+ 
+
+ align:start position:0%
+zero at zero and at L
+so okay so that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if this Epsilon one is the lowest
+
+ align:start position:0%
+that if this Epsilon one is the lowest
+ 
+
+ align:start position:0%
+that if this Epsilon one is the lowest
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level Epsilon
+
+ align:start position:0%
+level Epsilon
+ 
+
+ align:start position:0%
+level Epsilon
+2 is equal
+
+ align:start position:0%
+2 is equal
+ 
+
+ align:start position:0%
+2 is equal
+to uh it corresponds to J equals 2 so
+
+ align:start position:0%
+to uh it corresponds to J equals 2 so
+ 
+
+ align:start position:0%
+to uh it corresponds to J equals 2 so
+it's equals to j s is four times Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and Epsilon 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is 3 to the 2 so it's 9 * Epsilon
+
+ align:start position:0%
+is 3 to the 2 so it's 9 * Epsilon
+ 
+
+ align:start position:0%
+is 3 to the 2 so it's 9 * Epsilon
+1 and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so already this gives you the
+
+ align:start position:0%
+okay so already this gives you the
+ 
+
+ align:start position:0%
+okay so already this gives you the
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+levels now in an in an experiment that
+
+ align:start position:0%
+levels now in an in an experiment that
+ 
+
+ align:start position:0%
+levels now in an in an experiment that
+you do for example with uh
+
+ align:start position:0%
+you do for example with uh
+ 
+
+ align:start position:0%
+you do for example with uh
+spectroscopy on the
+
+ align:start position:0%
+spectroscopy on the
+ 
+
+ align:start position:0%
+spectroscopy on the
+particle uh you can measure the energy
+
+ align:start position:0%
+particle uh you can measure the energy
+ 
+
+ align:start position:0%
+particle uh you can measure the energy
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle and it and you're facing a
+
+ align:start position:0%
+particle and it and you're facing a
+ 
+
+ align:start position:0%
+particle and it and you're facing a
+situation like the one that we just done
+
+ align:start position:0%
+situation like the one that we just done
+ 
+
+ align:start position:0%
+situation like the one that we just done
+with the uh the mass of the particles
+
+ align:start position:0%
+with the uh the mass of the particles
+ 
+
+ align:start position:0%
+with the uh the mass of the particles
+that you don't know which one uh okay
+
+ align:start position:0%
+that you don't know which one uh okay
+ 
+
+ align:start position:0%
+that you don't know which one uh okay
+here it's a similar situation you do a
+
+ align:start position:0%
+here it's a similar situation you do a
+ 
+
+ align:start position:0%
+here it's a similar situation you do a
+measurement of energy and you don't know
+
+ align:start position:0%
+measurement of energy and you don't know
+ 
+
+ align:start position:0%
+measurement of energy and you don't know
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+one of the energies possible energies
+
+ align:start position:0%
+one of the energies possible energies
+ 
+
+ align:start position:0%
+one of the energies possible energies
+you get because the particle is not the
+
+ align:start position:0%
+you get because the particle is not the
+ 
+
+ align:start position:0%
+you get because the particle is not the
+definitely on this not always I mean
+
+ align:start position:0%
+definitely on this not always I mean
+ 
+
+ align:start position:0%
+definitely on this not always I mean
+most of the times it's in a
+
+ align:start position:0%
+most of the times it's in a
+ 
+
+ align:start position:0%
+most of the times it's in a
+superposition of energy levels so each
+
+ align:start position:0%
+superposition of energy levels so each
+ 
+
+ align:start position:0%
+superposition of energy levels so each
+one of them has a
+
+ align:start position:0%
+one of them has a
+ 
+
+ align:start position:0%
+one of them has a
+probability and the energy of uh of the
+
+ align:start position:0%
+probability and the energy of uh of the
+ 
+
+ align:start position:0%
+probability and the energy of uh of the
+particle is the weighted sum of these
+
+ align:start position:0%
+particle is the weighted sum of these
+ 
+
+ align:start position:0%
+particle is the weighted sum of these
+probabilities with with these
+
+ align:start position:0%
+probabilities with with these
+ 
+
+ align:start position:0%
+probabilities with with these
+probabilities of these energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+levels so the state
+
+ align:start position:0%
+levels so the state
+ 
+
+ align:start position:0%
+levels so the state
+of the particle is represented by a
+
+ align:start position:0%
+of the particle is represented by a
+ 
+
+ align:start position:0%
+of the particle is represented by a
+probability distribution which
+
+ align:start position:0%
+probability distribution which
+ 
+
+ align:start position:0%
+probability distribution which
+uh at least in the stable equilibrium
+
+ align:start position:0%
+uh at least in the stable equilibrium
+ 
+
+ align:start position:0%
+uh at least in the stable equilibrium
+States can be viewed as the uh
+
+ align:start position:0%
+States can be viewed as the uh
+ 
+
+ align:start position:0%
+States can be viewed as the uh
+probability of finding the energy levels
+
+ align:start position:0%
+probability of finding the energy levels
+ 
+
+ align:start position:0%
+probability of finding the energy levels
+among these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibilities that is for the particle
+
+ align:start position:0%
+possibilities that is for the particle
+ 
+
+ align:start position:0%
+possibilities that is for the particle
+in one uh dimensional box if you have a
+
+ align:start position:0%
+in one uh dimensional box if you have a
+ 
+
+ align:start position:0%
+in one uh dimensional box if you have a
+three dimensional box each Direction has
+
+ align:start position:0%
+three dimensional box each Direction has
+ 
+
+ align:start position:0%
+three dimensional box each Direction has
+a it
+
+ align:start position:0%
+a it
+ 
+
+ align:start position:0%
+a it
+own contribution and actually this
+
+ align:start position:0%
+own contribution and actually this
+ 
+
+ align:start position:0%
+own contribution and actually this
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+Factor so the
+
+ align:start position:0%
+Factor so the
+ 
+
+ align:start position:0%
+Factor so the
+three uh orthogonal translational
+
+ align:start position:0%
+three uh orthogonal translational
+ 
+
+ align:start position:0%
+three uh orthogonal translational
+degrees of freedom of the
+
+ align:start position:0%
+degrees of freedom of the
+ 
+
+ align:start position:0%
+degrees of freedom of the
+particle super superposed to in each
+
+ align:start position:0%
+particle super superposed to in each
+ 
+
+ align:start position:0%
+particle super superposed to in each
+other so it's like uh uh having three
+
+ align:start position:0%
+other so it's like uh uh having three
+ 
+
+ align:start position:0%
+other so it's like uh uh having three
+kind of uh of of of sub particles like
+
+ align:start position:0%
+kind of uh of of of sub particles like
+ 
+
+ align:start position:0%
+kind of uh of of of sub particles like
+in a perfect gas that uh sort of don't
+
+ align:start position:0%
+in a perfect gas that uh sort of don't
+ 
+
+ align:start position:0%
+in a perfect gas that uh sort of don't
+that ignore each other each each degree
+
+ align:start position:0%
+that ignore each other each each degree
+ 
+
+ align:start position:0%
+that ignore each other each each degree
+of Freedom lives by itself occupies uh
+
+ align:start position:0%
+of Freedom lives by itself occupies uh
+ 
+
+ align:start position:0%
+of Freedom lives by itself occupies uh
+its uh directional modes by itself
+
+ align:start position:0%
+its uh directional modes by itself
+ 
+
+ align:start position:0%
+its uh directional modes by itself
+without interacting with the other
+
+ align:start position:0%
+without interacting with the other
+ 
+
+ align:start position:0%
+without interacting with the other
+modes that's why this is such a simple
+
+ align:start position:0%
+modes that's why this is such a simple
+ 
+
+ align:start position:0%
+modes that's why this is such a simple
+uh uh extension of that just multiply so
+
+ align:start position:0%
+uh uh extension of that just multiply so
+ 
+
+ align:start position:0%
+uh uh extension of that just multiply so
+to speak or the the various uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions not only but
+
+ align:start position:0%
+functions not only but
+ 
+
+ align:start position:0%
+functions not only but
+from this one from these results you can
+
+ align:start position:0%
+from this one from these results you can
+ 
+
+ align:start position:0%
+from this one from these results you can
+also obtain the
+
+ align:start position:0%
+also obtain the
+ 
+
+ align:start position:0%
+also obtain the
+probability of finding um the prob
+
+ align:start position:0%
+probability of finding um the prob
+ 
+
+ align:start position:0%
+probability of finding um the prob
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+density of
+
+ align:start position:0%
+density of
+ 
+
+ align:start position:0%
+density of
+finding this uh uh particle if you make
+
+ align:start position:0%
+finding this uh uh particle if you make
+ 
+
+ align:start position:0%
+finding this uh uh particle if you make
+a position measurement finding it
+
+ align:start position:0%
+a position measurement finding it
+ 
+
+ align:start position:0%
+a position measurement finding it
+between X X and X Plus
+
+ align:start position:0%
+between X X and X Plus
+ 
+
+ align:start position:0%
+between X X and X Plus
+DX that's the PDF the probability
+
+ align:start position:0%
+DX that's the PDF the probability
+ 
+
+ align:start position:0%
+DX that's the PDF the probability
+density function it's given by the is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s the modulus of this one or also that
+
+ align:start position:0%
+s the modulus of this one or also that
+ 
+
+ align:start position:0%
+s the modulus of this one or also that
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think there is an I here that I am
+
+ align:start position:0%
+and I think there is an I here that I am
+ 
+
+ align:start position:0%
+and I think there is an I here that I am
+missing because this is supposed to be
+
+ align:start position:0%
+missing because this is supposed to be
+ 
+
+ align:start position:0%
+missing because this is supposed to be
+uh I is the square root of minus one
+
+ align:start position:0%
+uh I is the square root of minus one
+ 
+
+ align:start position:0%
+uh I is the square root of minus one
+okay so that means that when I do uh the
+
+ align:start position:0%
+okay so that means that when I do uh the
+ 
+
+ align:start position:0%
+okay so that means that when I do uh the
+complex conjugate of this one that be
+
+ align:start position:0%
+complex conjugate of this one that be
+ 
+
+ align:start position:0%
+complex conjugate of this one that be
+that I becomes minus I
+
+ align:start position:0%
+that I becomes minus I
+ 
+
+ align:start position:0%
+that I becomes minus I
+and so the modulus uh of V is equal to
+
+ align:start position:0%
+and so the modulus uh of V is equal to
+ 
+
+ align:start position:0%
+and so the modulus uh of V is equal to
+this one cancels and you're left
+
+ align:start position:0%
+this one cancels and you're left
+ 
+
+ align:start position:0%
+this one cancels and you're left
+with uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this which is the modulus of uh s
+
+ align:start position:0%
+this which is the modulus of uh s
+ 
+
+ align:start position:0%
+this which is the modulus of uh s
+squared and that is the probability
+
+ align:start position:0%
+squared and that is the probability
+ 
+
+ align:start position:0%
+squared and that is the probability
+density function so if you want to know
+
+ align:start position:0%
+density function so if you want to know
+ 
+
+ align:start position:0%
+density function so if you want to know
+how much is the probability in that
+
+ align:start position:0%
+how much is the probability in that
+ 
+
+ align:start position:0%
+how much is the probability in that
+interval you multiply by DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you want to know um the
+
+ align:start position:0%
+and if you want to know um the
+ 
+
+ align:start position:0%
+and if you want to know um the
+probability to go from to be from uh say
+
+ align:start position:0%
+probability to go from to be from uh say
+ 
+
+ align:start position:0%
+probability to go from to be from uh say
+from here to there you just do the
+
+ align:start position:0%
+from here to there you just do the
+ 
+
+ align:start position:0%
+from here to there you just do the
+integral from uh whatever X say X1 to X2
+
+ align:start position:0%
+integral from uh whatever X say X1 to X2
+ 
+
+ align:start position:0%
+integral from uh whatever X say X1 to X2
+to get to get the overall
+
+ align:start position:0%
+to get to get the overall
+ 
+
+ align:start position:0%
+to get to get the overall
+distribution so these
+
+ align:start position:0%
+distribution so these
+ 
+
+ align:start position:0%
+distribution so these
+functions are these ones that I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plotted I wish I had more space okay
+
+ align:start position:0%
+plotted I wish I had more space okay
+ 
+
+ align:start position:0%
+plotted I wish I had more space okay
+let's do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities are the
+
+ align:start position:0%
+probabilities are the
+ 
+
+ align:start position:0%
+probabilities are the
+square of these functions see this the
+
+ align:start position:0%
+square of these functions see this the
+ 
+
+ align:start position:0%
+square of these functions see this the
+way functions can go negative but the
+
+ align:start position:0%
+way functions can go negative but the
+ 
+
+ align:start position:0%
+way functions can go negative but the
+probability is essentially the
+
+ align:start position:0%
+probability is essentially the
+ 
+
+ align:start position:0%
+probability is essentially the
+square so take the square of this sign
+
+ align:start position:0%
+square so take the square of this sign
+ 
+
+ align:start position:0%
+square so take the square of this sign
+and become something like
+
+ align:start position:0%
+and become something like
+ 
+
+ align:start position:0%
+and become something like
+this the square of this other uh sign
+
+ align:start position:0%
+this the square of this other uh sign
+ 
+
+ align:start position:0%
+this the square of this other uh sign
+with it becomes something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay when the particle is in a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State uh it is not typically in just one
+
+ align:start position:0%
+State uh it is not typically in just one
+ 
+
+ align:start position:0%
+State uh it is not typically in just one
+of these energy
+
+ align:start position:0%
+of these energy
+ 
+
+ align:start position:0%
+of these energy
+levels it is in a probability
+
+ align:start position:0%
+levels it is in a probability
+ 
+
+ align:start position:0%
+levels it is in a probability
+distribution so each one of
+
+ align:start position:0%
+distribution so each one of
+ 
+
+ align:start position:0%
+distribution so each one of
+these um distributions in space is is
+
+ align:start position:0%
+these um distributions in space is is
+ 
+
+ align:start position:0%
+these um distributions in space is is
+weighted by a probability distribution
+
+ align:start position:0%
+weighted by a probability distribution
+ 
+
+ align:start position:0%
+weighted by a probability distribution
+so there will be a P1 it will be a P2 a
+
+ align:start position:0%
+so there will be a P1 it will be a P2 a
+ 
+
+ align:start position:0%
+so there will be a P1 it will be a P2 a
+P3 and so on so you have
+
+ align:start position:0%
+P3 and so on so you have
+ 
+
+ align:start position:0%
+P3 and so on so you have
+a weighted
+
+ align:start position:0%
+a weighted
+ 
+
+ align:start position:0%
+a weighted
+sum of these probabilities with which
+
+ align:start position:0%
+sum of these probabilities with which
+ 
+
+ align:start position:0%
+sum of these probabilities with which
+you can compute for
+
+ align:start position:0%
+you can compute for
+ 
+
+ align:start position:0%
+you can compute for
+example uh the
+
+ align:start position:0%
+example uh the
+ 
+
+ align:start position:0%
+example uh the
+um probability that your particles is
+
+ align:start position:0%
+um probability that your particles is
+ 
+
+ align:start position:0%
+um probability that your particles is
+between X and X Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX it's this area times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P1 plus this area time
+
+ align:start position:0%
+P1 plus this area time
+ 
+
+ align:start position:0%
+P1 plus this area time
+P2 plus that area time P3 up to to
+
+ align:start position:0%
+P2 plus that area time P3 up to to
+ 
+
+ align:start position:0%
+P2 plus that area time P3 up to to
+Infinity because you have to go up this
+
+ align:start position:0%
+Infinity because you have to go up this
+ 
+
+ align:start position:0%
+Infinity because you have to go up this
+J goes up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity and that's how you
+
+ align:start position:0%
+infinity and that's how you
+ 
+
+ align:start position:0%
+infinity and that's how you
+compute the actual stable equilibrium
+
+ align:start position:0%
+compute the actual stable equilibrium
+ 
+
+ align:start position:0%
+compute the actual stable equilibrium
+State probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution this is already we already
+
+ align:start position:0%
+distribution this is already we already
+ 
+
+ align:start position:0%
+distribution this is already we already
+mentioned the fact that when you do this
+
+ align:start position:0%
+mentioned the fact that when you do this
+ 
+
+ align:start position:0%
+mentioned the fact that when you do this
+job and you can compute therefore
+
+ align:start position:0%
+job and you can compute therefore
+ 
+
+ align:start position:0%
+job and you can compute therefore
+the uh the probability density
+
+ align:start position:0%
+the uh the probability density
+ 
+
+ align:start position:0%
+the uh the probability density
+for every for every X you will find that
+
+ align:start position:0%
+for every for every X you will find that
+ 
+
+ align:start position:0%
+for every for every X you will find that
+it will always go to zero uh at the
+
+ align:start position:0%
+it will always go to zero uh at the
+ 
+
+ align:start position:0%
+it will always go to zero uh at the
+edges because at the edges no matter how
+
+ align:start position:0%
+edges because at the edges no matter how
+ 
+
+ align:start position:0%
+edges because at the edges no matter how
+you weight it it's always zero so the
+
+ align:start position:0%
+you weight it it's always zero so the
+ 
+
+ align:start position:0%
+you weight it it's always zero so the
+sum of zero is
+
+ align:start position:0%
+sum of zero is
+ 
+
+ align:start position:0%
+sum of zero is
+zero whereas in the
+
+ align:start position:0%
+zero whereas in the
+ 
+
+ align:start position:0%
+zero whereas in the
+center uh it you'll have some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wiggles
+
+ align:start position:0%
+Wiggles
+ 
+
+ align:start position:0%
+Wiggles
+especially if the
+
+ align:start position:0%
+especially if the
+ 
+
+ align:start position:0%
+especially if the
+low energy levels are important as you
+
+ align:start position:0%
+low energy levels are important as you
+ 
+
+ align:start position:0%
+low energy levels are important as you
+go upwards this becomes so uh you may
+
+ align:start position:0%
+go upwards this becomes so uh you may
+ 
+
+ align:start position:0%
+go upwards this becomes so uh you may
+have if the quantum number goes um as it
+
+ align:start position:0%
+have if the quantum number goes um as it
+ 
+
+ align:start position:0%
+have if the quantum number goes um as it
+goes higher these Wiggles become more uh
+
+ align:start position:0%
+goes higher these Wiggles become more uh
+ 
+
+ align:start position:0%
+goes higher these Wiggles become more uh
+intense and then they add up and so the
+
+ align:start position:0%
+intense and then they add up and so the
+ 
+
+ align:start position:0%
+intense and then they add up and so the
+one cancels the others and so the zero
+
+ align:start position:0%
+one cancels the others and so the zero
+ 
+
+ align:start position:0%
+one cancels the others and so the zero
+you'll get only zero at the walls but
+
+ align:start position:0%
+you'll get only zero at the walls but
+ 
+
+ align:start position:0%
+you'll get only zero at the walls but
+not in the middle not in the bulk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are the energy
+
+ align:start position:0%
+okay so these are the energy
+ 
+
+ align:start position:0%
+okay so these are the energy
+levels here is the name for the
+
+ align:start position:0%
+levels here is the name for the
+ 
+
+ align:start position:0%
+levels here is the name for the
+probabilities that we simplified
+
+ align:start position:0%
+probabilities that we simplified
+ 
+
+ align:start position:0%
+probabilities that we simplified
+here in three dimensions you have three
+
+ align:start position:0%
+here in three dimensions you have three
+ 
+
+ align:start position:0%
+here in three dimensions you have three
+labels because you have one quantum
+
+ align:start position:0%
+labels because you have one quantum
+ 
+
+ align:start position:0%
+labels because you have one quantum
+number per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction and the typical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem that you face if you do energy
+
+ align:start position:0%
+problem that you face if you do energy
+ 
+
+ align:start position:0%
+problem that you face if you do energy
+measure measurements
+
+ align:start position:0%
+measure measurements
+ 
+
+ align:start position:0%
+measure measurements
+is well how do I what's my best guess
+
+ align:start position:0%
+is well how do I what's my best guess
+ 
+
+ align:start position:0%
+is well how do I what's my best guess
+for this probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution that's the information
+
+ align:start position:0%
+distribution that's the information
+ 
+
+ align:start position:0%
+distribution that's the information
+Theory point of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+view uh the thermodynamics point of view
+
+ align:start position:0%
+view uh the thermodynamics point of view
+ 
+
+ align:start position:0%
+view uh the thermodynamics point of view
+is all right probabilities if we accept
+
+ align:start position:0%
+is all right probabilities if we accept
+ 
+
+ align:start position:0%
+is all right probabilities if we accept
+that probabilities represent the state
+
+ align:start position:0%
+that probabilities represent the state
+ 
+
+ align:start position:0%
+that probabilities represent the state
+and if we accept that
+
+ align:start position:0%
+and if we accept that
+ 
+
+ align:start position:0%
+and if we accept that
+entropy uh is measured by a function
+
+ align:start position:0%
+entropy uh is measured by a function
+ 
+
+ align:start position:0%
+entropy uh is measured by a function
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this then we can use the maximum entropy
+
+ align:start position:0%
+this then we can use the maximum entropy
+ 
+
+ align:start position:0%
+this then we can use the maximum entropy
+principle which
+
+ align:start position:0%
+principle which
+ 
+
+ align:start position:0%
+principle which
+says for a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy my
+
+ align:start position:0%
+energy my
+ 
+
+ align:start position:0%
+energy my
+system uh has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um see of have an energy and an entropy
+
+ align:start position:0%
+um see of have an energy and an entropy
+ 
+
+ align:start position:0%
+um see of have an energy and an entropy
+an entropy
+
+ align:start position:0%
+an entropy
+ 
+
+ align:start position:0%
+an entropy
+diagram and for a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy I may have many different
+
+ align:start position:0%
+energy I may have many different
+ 
+
+ align:start position:0%
+energy I may have many different
+states but if I'm looking for the stable
+
+ align:start position:0%
+states but if I'm looking for the stable
+ 
+
+ align:start position:0%
+states but if I'm looking for the stable
+equilibrium State I know that it has to
+
+ align:start position:0%
+equilibrium State I know that it has to
+ 
+
+ align:start position:0%
+equilibrium State I know that it has to
+have the maximum entropy for that given
+
+ align:start position:0%
+have the maximum entropy for that given
+ 
+
+ align:start position:0%
+have the maximum entropy for that given
+energy so that's precisely the same
+
+ align:start position:0%
+energy so that's precisely the same
+ 
+
+ align:start position:0%
+energy so that's precisely the same
+problem that we've seen before maximize
+
+ align:start position:0%
+problem that we've seen before maximize
+ 
+
+ align:start position:0%
+problem that we've seen before maximize
+entropy and provided you accept that for
+
+ align:start position:0%
+entropy and provided you accept that for
+ 
+
+ align:start position:0%
+entropy and provided you accept that for
+fora for the entropy of the Quantum of
+
+ align:start position:0%
+fora for the entropy of the Quantum of
+ 
+
+ align:start position:0%
+fora for the entropy of the Quantum of
+the quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle then the mathematics of uh
+
+ align:start position:0%
+particle then the mathematics of uh
+ 
+
+ align:start position:0%
+particle then the mathematics of uh
+maximization is the same use lrange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multipliers now see since we know
+
+ align:start position:0%
+multipliers now see since we know
+ 
+
+ align:start position:0%
+multipliers now see since we know
+already the
+
+ align:start position:0%
+already the
+ 
+
+ align:start position:0%
+already the
+answer instead of call calling the
+
+ align:start position:0%
+answer instead of call calling the
+ 
+
+ align:start position:0%
+answer instead of call calling the
+lrange multiplier Lambda e
+
+ align:start position:0%
+lrange multiplier Lambda e
+ 
+
+ align:start position:0%
+lrange multiplier Lambda e
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+since later on WE recognize that that
+
+ align:start position:0%
+since later on WE recognize that that
+ 
+
+ align:start position:0%
+since later on WE recognize that that
+Lambda is the inverse of the temperature
+
+ align:start position:0%
+Lambda is the inverse of the temperature
+ 
+
+ align:start position:0%
+Lambda is the inverse of the temperature
+divided by the boltman constant we we
+
+ align:start position:0%
+divided by the boltman constant we we
+ 
+
+ align:start position:0%
+divided by the boltman constant we we
+already call it 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT and so you find this
+
+ align:start position:0%
+KT and so you find this
+ 
+
+ align:start position:0%
+KT and so you find this
+distribution so the
+
+ align:start position:0%
+distribution so the
+ 
+
+ align:start position:0%
+distribution so the
+probabilities are given by e to the
+
+ align:start position:0%
+probabilities are given by e to the
+ 
+
+ align:start position:0%
+probabilities are given by e to the
+minus the
+
+ align:start position:0%
+minus the
+ 
+
+ align:start position:0%
+minus the
+energy is energy
+
+ align:start position:0%
+energy is energy
+ 
+
+ align:start position:0%
+energy is energy
+values divided by or multiplied by the
+
+ align:start position:0%
+values divided by or multiplied by the
+ 
+
+ align:start position:0%
+values divided by or multiplied by the
+lrange multi
+
+ align:start position:0%
+lrange multi
+ 
+
+ align:start position:0%
+lrange multi
+mullier divided by this Q you can view
+
+ align:start position:0%
+mullier divided by this Q you can view
+ 
+
+ align:start position:0%
+mullier divided by this Q you can view
+it as a normalization factor it's
+
+ align:start position:0%
+it as a normalization factor it's
+ 
+
+ align:start position:0%
+it as a normalization factor it's
+essentially the summation of all these
+
+ align:start position:0%
+essentially the summation of all these
+ 
+
+ align:start position:0%
+essentially the summation of all these
+things at the
+
+ align:start position:0%
+things at the
+ 
+
+ align:start position:0%
+things at the
+numerator this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q a also see that since the energies the
+
+ align:start position:0%
+q a also see that since the energies the
+ 
+
+ align:start position:0%
+q a also see that since the energies the
+energy I values add
+
+ align:start position:0%
+energy I values add
+ 
+
+ align:start position:0%
+energy I values add
+up uh the exponential of sum is equal to
+
+ align:start position:0%
+up uh the exponential of sum is equal to
+ 
+
+ align:start position:0%
+up uh the exponential of sum is equal to
+the product of the exponentials so these
+
+ align:start position:0%
+the product of the exponentials so these
+ 
+
+ align:start position:0%
+the product of the exponentials so these
+probability distributions
+
+ align:start position:0%
+probability distributions
+ 
+
+ align:start position:0%
+probability distributions
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+into separate probability distributions
+
+ align:start position:0%
+into separate probability distributions
+ 
+
+ align:start position:0%
+into separate probability distributions
+for each of the directions of the
+
+ align:start position:0%
+for each of the directions of the
+ 
+
+ align:start position:0%
+for each of the directions of the
+box so so you can view the problem also
+
+ align:start position:0%
+box so so you can view the problem also
+ 
+
+ align:start position:0%
+box so so you can view the problem also
+just as you can solve it in One
+
+ align:start position:0%
+just as you can solve it in One
+ 
+
+ align:start position:0%
+just as you can solve it in One
+Direction per time and then simply
+
+ align:start position:0%
+Direction per time and then simply
+ 
+
+ align:start position:0%
+Direction per time and then simply
+multiply the results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these denominators or denominator for
+
+ align:start position:0%
+these denominators or denominator for
+ 
+
+ align:start position:0%
+these denominators or denominator for
+the overall is called the partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and uh it is yes it plays the
+
+ align:start position:0%
+function and uh it is yes it plays the
+ 
+
+ align:start position:0%
+function and uh it is yes it plays the
+role
+
+ align:start position:0%
+role
+ 
+
+ align:start position:0%
+role
+of the normalization factor so that
+
+ align:start position:0%
+of the normalization factor so that
+ 
+
+ align:start position:0%
+of the normalization factor so that
+uh uh when you sum the probabilities
+
+ align:start position:0%
+uh uh when you sum the probabilities
+ 
+
+ align:start position:0%
+uh uh when you sum the probabilities
+they add up to
+
+ align:start position:0%
+they add up to
+ 
+
+ align:start position:0%
+they add up to
+one but it also plays an interesting
+
+ align:start position:0%
+one but it also plays an interesting
+ 
+
+ align:start position:0%
+one but it also plays an interesting
+interesting role because uh uh uh
+
+ align:start position:0%
+interesting role because uh uh uh
+ 
+
+ align:start position:0%
+interesting role because uh uh uh
+essentially all you you you can extract
+
+ align:start position:0%
+essentially all you you you can extract
+ 
+
+ align:start position:0%
+essentially all you you you can extract
+everything if you know this partition
+
+ align:start position:0%
+everything if you know this partition
+ 
+
+ align:start position:0%
+everything if you know this partition
+function if you know this
+
+ align:start position:0%
+function if you know this
+ 
+
+ align:start position:0%
+function if you know this
+summation by playing with it in terms of
+
+ align:start position:0%
+summation by playing with it in terms of
+ 
+
+ align:start position:0%
+summation by playing with it in terms of
+taking some
+
+ align:start position:0%
+taking some
+ 
+
+ align:start position:0%
+taking some
+derivatives you can get uh everything of
+
+ align:start position:0%
+derivatives you can get uh everything of
+ 
+
+ align:start position:0%
+derivatives you can get uh everything of
+the distribution including the the
+
+ align:start position:0%
+the distribution including the the
+ 
+
+ align:start position:0%
+the distribution including the the
+probabilities
+
+ align:start position:0%
+probabilities
+ 
+
+ align:start position:0%
+probabilities
+themselves so if you take the the
+
+ align:start position:0%
+themselves so if you take the the
+ 
+
+ align:start position:0%
+themselves so if you take the the
+partial derivative of the logarithm of
+
+ align:start position:0%
+partial derivative of the logarithm of
+ 
+
+ align:start position:0%
+partial derivative of the logarithm of
+the partition function as written here
+
+ align:start position:0%
+the partition function as written here
+ 
+
+ align:start position:0%
+the partition function as written here
+and take the derivative with respect to
+
+ align:start position:0%
+and take the derivative with respect to
+ 
+
+ align:start position:0%
+and take the derivative with respect to
+the energy
+
+ align:start position:0%
+the energy
+ 
+
+ align:start position:0%
+the energy
+level you get the probability and
+
+ align:start position:0%
+level you get the probability and
+ 
+
+ align:start position:0%
+level you get the probability and
+multiply by KT and minus you get the
+
+ align:start position:0%
+multiply by KT and minus you get the
+ 
+
+ align:start position:0%
+multiply by KT and minus you get the
+probability of that energy of observing
+
+ align:start position:0%
+probability of that energy of observing
+ 
+
+ align:start position:0%
+probability of that energy of observing
+that energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+or you take this other derivative you
+
+ align:start position:0%
+or you take this other derivative you
+ 
+
+ align:start position:0%
+or you take this other derivative you
+take the derivative of Q respect to
+
+ align:start position:0%
+take the derivative of Q respect to
+ 
+
+ align:start position:0%
+take the derivative of Q respect to
+temperature because yes in a moment will
+
+ align:start position:0%
+temperature because yes in a moment will
+ 
+
+ align:start position:0%
+temperature because yes in a moment will
+recognize that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U this
+
+ align:start position:0%
+U this
+ 
+
+ align:start position:0%
+U this
+T is also this lrange
+
+ align:start position:0%
+T is also this lrange
+ 
+
+ align:start position:0%
+T is also this lrange
+multiplier satisfies our definition of
+
+ align:start position:0%
+multiplier satisfies our definition of
+ 
+
+ align:start position:0%
+multiplier satisfies our definition of
+temperature is the partial of s e with
+
+ align:start position:0%
+temperature is the partial of s e with
+ 
+
+ align:start position:0%
+temperature is the partial of s e with
+respect to
+
+ align:start position:0%
+respect to
+ 
+
+ align:start position:0%
+respect to
+S and so you identify it with the
+
+ align:start position:0%
+S and so you identify it with the
+ 
+
+ align:start position:0%
+S and so you identify it with the
+temperature uh so you take the log the
+
+ align:start position:0%
+temperature uh so you take the log the
+ 
+
+ align:start position:0%
+temperature uh so you take the log the
+partial of log Q respect respect to
+
+ align:start position:0%
+partial of log Q respect respect to
+ 
+
+ align:start position:0%
+partial of log Q respect respect to
+t uh you get the
+
+ align:start position:0%
+t uh you get the
+ 
+
+ align:start position:0%
+t uh you get the
+energy the mean energy the mean energy
+
+ align:start position:0%
+energy the mean energy the mean energy
+ 
+
+ align:start position:0%
+energy the mean energy the mean energy
+is the average value of the energy it's
+
+ align:start position:0%
+is the average value of the energy it's
+ 
+
+ align:start position:0%
+is the average value of the energy it's
+so it's the weighted sum of these energy
+
+ align:start position:0%
+so it's the weighted sum of these energy
+ 
+
+ align:start position:0%
+so it's the weighted sum of these energy
+levels weighted on the probability that
+
+ align:start position:0%
+levels weighted on the probability that
+ 
+
+ align:start position:0%
+levels weighted on the probability that
+represents that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state and also uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy also the entropy because the
+
+ align:start position:0%
+entropy also the entropy because the
+ 
+
+ align:start position:0%
+entropy also the entropy because the
+probabilties
+
+ align:start position:0%
+probabilties
+ 
+
+ align:start position:0%
+probabilties
+Factor the entropies add because the
+
+ align:start position:0%
+Factor the entropies add because the
+ 
+
+ align:start position:0%
+Factor the entropies add because the
+logarithm you remember the logarithm of
+
+ align:start position:0%
+logarithm you remember the logarithm of
+ 
+
+ align:start position:0%
+logarithm you remember the logarithm of
+the product is equal to the sum of the
+
+ align:start position:0%
+the product is equal to the sum of the
+ 
+
+ align:start position:0%
+the product is equal to the sum of the
+logarithms so you can write the overall
+
+ align:start position:0%
+logarithms so you can write the overall
+ 
+
+ align:start position:0%
+logarithms so you can write the overall
+entropy and split it in the entropies of
+
+ align:start position:0%
+entropy and split it in the entropies of
+ 
+
+ align:start position:0%
+entropy and split it in the entropies of
+the three directions of the
+
+ align:start position:0%
+the three directions of the
+ 
+
+ align:start position:0%
+the three directions of the
+box and each one of them can be obtained
+
+ align:start position:0%
+box and each one of them can be obtained
+ 
+
+ align:start position:0%
+box and each one of them can be obtained
+as a proper derivative of
+
+ align:start position:0%
+as a proper derivative of
+ 
+
+ align:start position:0%
+as a proper derivative of
+Q or if you already taken the derivative
+
+ align:start position:0%
+Q or if you already taken the derivative
+ 
+
+ align:start position:0%
+Q or if you already taken the derivative
+that give the energy you can write S as
+
+ align:start position:0%
+that give the energy you can write S as
+ 
+
+ align:start position:0%
+that give the energy you can write S as
+e/ t
+
+ align:start position:0%
+e/ t
+ 
+
+ align:start position:0%
+e/ t
+plus bman constant time times the
+
+ align:start position:0%
+plus bman constant time times the
+ 
+
+ align:start position:0%
+plus bman constant time times the
+logarithm of the partition
+
+ align:start position:0%
+logarithm of the partition
+ 
+
+ align:start position:0%
+logarithm of the partition
+function this is somehow uh close to
+
+ align:start position:0%
+function this is somehow uh close to
+ 
+
+ align:start position:0%
+function this is somehow uh close to
+the as close as you can get to the oiler
+
+ align:start position:0%
+the as close as you can get to the oiler
+ 
+
+ align:start position:0%
+the as close as you can get to the oiler
+free free energy or the free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because in fact some people call it call
+
+ align:start position:0%
+because in fact some people call it call
+ 
+
+ align:start position:0%
+because in fact some people call it call
+I mean you could also rewrite that as
+
+ align:start position:0%
+I mean you could also rewrite that as
+ 
+
+ align:start position:0%
+I mean you could also rewrite that as
+EI minus t SI I is equal to uh KB t log
+
+ align:start position:0%
+EI minus t SI I is equal to uh KB t log
+ 
+
+ align:start position:0%
+EI minus t SI I is equal to uh KB t log
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q probabbly with the minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now going
+
+ align:start position:0%
+so now going
+ 
+
+ align:start position:0%
+so now going
+back to these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities this probability
+
+ align:start position:0%
+probabilities this probability
+ 
+
+ align:start position:0%
+probabilities this probability
+distribution is the one that
+
+ align:start position:0%
+distribution is the one that
+ 
+
+ align:start position:0%
+distribution is the one that
+characterizes the stable equilibrium
+
+ align:start position:0%
+characterizes the stable equilibrium
+ 
+
+ align:start position:0%
+characterizes the stable equilibrium
+state it characterizes this
+
+ align:start position:0%
+state it characterizes this
+ 
+
+ align:start position:0%
+state it characterizes this
+state how about these other ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this canonical distribution the one
+
+ align:start position:0%
+so this canonical distribution the one
+ 
+
+ align:start position:0%
+so this canonical distribution the one
+maximum entropy one looks like
+
+ align:start position:0%
+maximum entropy one looks like
+ 
+
+ align:start position:0%
+maximum entropy one looks like
+this here for
+
+ align:start position:0%
+this here for
+ 
+
+ align:start position:0%
+this here for
+Simplicity I have drawn a system which
+
+ align:start position:0%
+Simplicity I have drawn a system which
+ 
+
+ align:start position:0%
+Simplicity I have drawn a system which
+doesn't have a
+
+ align:start position:0%
+doesn't have a
+ 
+
+ align:start position:0%
+doesn't have a
+uh this I value structure but it has
+
+ align:start position:0%
+uh this I value structure but it has
+ 
+
+ align:start position:0%
+uh this I value structure but it has
+energy levels that are equally spaced
+
+ align:start position:0%
+energy levels that are equally spaced
+ 
+
+ align:start position:0%
+energy levels that are equally spaced
+and there is only seven of them the
+
+ align:start position:0%
+and there is only seven of them the
+ 
+
+ align:start position:0%
+and there is only seven of them the
+lowest one one two 3 four five six seven
+
+ align:start position:0%
+lowest one one two 3 four five six seven
+ 
+
+ align:start position:0%
+lowest one one two 3 four five six seven
+okay equally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spaced we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already uh mentioned that they that for
+
+ align:start position:0%
+already uh mentioned that they that for
+ 
+
+ align:start position:0%
+already uh mentioned that they that for
+a system with an upper bound to the uh
+
+ align:start position:0%
+a system with an upper bound to the uh
+ 
+
+ align:start position:0%
+a system with an upper bound to the uh
+energy Spectrum this is an R
+
+ align:start position:0%
+energy Spectrum this is an R
+ 
+
+ align:start position:0%
+energy Spectrum this is an R
+here that would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Spectrum the the ersus diagram doesn't
+
+ align:start position:0%
+Spectrum the the ersus diagram doesn't
+ 
+
+ align:start position:0%
+Spectrum the the ersus diagram doesn't
+go up indefinitely but it bends and
+
+ align:start position:0%
+go up indefinitely but it bends and
+ 
+
+ align:start position:0%
+go up indefinitely but it bends and
+returns so that's that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so we have only seven energy levels
+
+ align:start position:0%
+case so we have only seven energy levels
+ 
+
+ align:start position:0%
+case so we have only seven energy levels
+and we can uh picture these
+
+ align:start position:0%
+and we can uh picture these
+ 
+
+ align:start position:0%
+and we can uh picture these
+probabilities by an instogram
+
+ align:start position:0%
+probabilities by an instogram
+ 
+
+ align:start position:0%
+probabilities by an instogram
+histogram so this is the max maximum
+
+ align:start position:0%
+histogram so this is the max maximum
+ 
+
+ align:start position:0%
+histogram so this is the max maximum
+entropy the canonical
+
+ align:start position:0%
+entropy the canonical
+ 
+
+ align:start position:0%
+entropy the canonical
+distribution for example this is a zero
+
+ align:start position:0%
+distribution for example this is a zero
+ 
+
+ align:start position:0%
+distribution for example this is a zero
+entropy a zero entropy state in what is
+
+ align:start position:0%
+entropy a zero entropy state in what is
+ 
+
+ align:start position:0%
+entropy a zero entropy state in what is
+one in which you are
+
+ align:start position:0%
+one in which you are
+ 
+
+ align:start position:0%
+one in which you are
+certain remember the the the entropy in
+
+ align:start position:0%
+certain remember the the the entropy in
+ 
+
+ align:start position:0%
+certain remember the the the entropy in
+in terms of probabilities represents
+
+ align:start position:0%
+in terms of probabilities represents
+ 
+
+ align:start position:0%
+in terms of probabilities represents
+your state of uncertainty well if I know
+
+ align:start position:0%
+your state of uncertainty well if I know
+ 
+
+ align:start position:0%
+your state of uncertainty well if I know
+that every time I measure I always find
+
+ align:start position:0%
+that every time I measure I always find
+ 
+
+ align:start position:0%
+that every time I measure I always find
+the particle in that energy level uh I
+
+ align:start position:0%
+the particle in that energy level uh I
+ 
+
+ align:start position:0%
+the particle in that energy level uh I
+have no uncertainty the entropy is zero
+
+ align:start position:0%
+have no uncertainty the entropy is zero
+ 
+
+ align:start position:0%
+have no uncertainty the entropy is zero
+and that is when uh I have zeros for
+
+ align:start position:0%
+and that is when uh I have zeros for
+ 
+
+ align:start position:0%
+and that is when uh I have zeros for
+all um Poss probabilities except one
+
+ align:start position:0%
+all um Poss probabilities except one
+ 
+
+ align:start position:0%
+all um Poss probabilities except one
+which is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one a point like
+
+ align:start position:0%
+one a point like
+ 
+
+ align:start position:0%
+one a point like
+here is one that has an intermediate
+
+ align:start position:0%
+here is one that has an intermediate
+ 
+
+ align:start position:0%
+here is one that has an intermediate
+probability between zero and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum you can
+
+ align:start position:0%
+maximum you can
+ 
+
+ align:start position:0%
+maximum you can
+concoct uh an infinite number of
+
+ align:start position:0%
+concoct uh an infinite number of
+ 
+
+ align:start position:0%
+concoct uh an infinite number of
+possibilities
+
+ align:start position:0%
+possibilities
+ 
+
+ align:start position:0%
+possibilities
+of different probabilities probability
+
+ align:start position:0%
+of different probabilities probability
+ 
+
+ align:start position:0%
+of different probabilities probability
+distributions that have the same entropy
+
+ align:start position:0%
+distributions that have the same entropy
+ 
+
+ align:start position:0%
+distributions that have the same entropy
+and of course the same
+
+ align:start position:0%
+and of course the same
+ 
+
+ align:start position:0%
+and of course the same
+energy here are the
+
+ align:start position:0%
+energy here are the
+ 
+
+ align:start position:0%
+energy here are the
+ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important okay when
+
+ align:start position:0%
+important okay when
+ 
+
+ align:start position:0%
+important okay when
+we when we are interested in describing
+
+ align:start position:0%
+we when we are interested in describing
+ 
+
+ align:start position:0%
+we when we are interested in describing
+non-equilibrium
+
+ align:start position:0%
+non-equilibrium
+ 
+
+ align:start position:0%
+non-equilibrium
+States what is important is
+
+ align:start position:0%
+States what is important is
+ 
+
+ align:start position:0%
+States what is important is
+to uh be able to understand or
+
+ align:start position:0%
+to uh be able to understand or
+ 
+
+ align:start position:0%
+to uh be able to understand or
+model how these states or these
+
+ align:start position:0%
+model how these states or these
+ 
+
+ align:start position:0%
+model how these states or these
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distributions evolve towards equilibrium
+
+ align:start position:0%
+distributions evolve towards equilibrium
+ 
+
+ align:start position:0%
+distributions evolve towards equilibrium
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+nature F salum
+
+ align:start position:0%
+nature F salum
+ 
+
+ align:start position:0%
+nature F salum
+but uh nature usually likes to go
+
+ align:start position:0%
+but uh nature usually likes to go
+ 
+
+ align:start position:0%
+but uh nature usually likes to go
+towards equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so there is a spontaneous uh
+
+ align:start position:0%
+and so there is a spontaneous uh
+ 
+
+ align:start position:0%
+and so there is a spontaneous uh
+tendency so there is a natural law that
+
+ align:start position:0%
+tendency so there is a natural law that
+ 
+
+ align:start position:0%
+tendency so there is a natural law that
+pushes a Pro system to uh even out or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+redistribute the energy load you can
+
+ align:start position:0%
+redistribute the energy load you can
+ 
+
+ align:start position:0%
+redistribute the energy load you can
+interpret these u in
+
+ align:start position:0%
+interpret these u in
+ 
+
+ align:start position:0%
+interpret these u in
+histograms as uh the probabilities you
+
+ align:start position:0%
+histograms as uh the probabilities you
+ 
+
+ align:start position:0%
+histograms as uh the probabilities you
+see is written here measure the degree
+
+ align:start position:0%
+see is written here measure the degree
+ 
+
+ align:start position:0%
+see is written here measure the degree
+of involvement
+
+ align:start position:0%
+of involvement
+ 
+
+ align:start position:0%
+of involvement
+of level of level EJ in sharing the mean
+
+ align:start position:0%
+of level of level EJ in sharing the mean
+ 
+
+ align:start position:0%
+of level of level EJ in sharing the mean
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+load you give some energy to the
+
+ align:start position:0%
+load you give some energy to the
+ 
+
+ align:start position:0%
+load you give some energy to the
+particle and the
+
+ align:start position:0%
+particle and the
+ 
+
+ align:start position:0%
+particle and the
+particle has to decide where to put it
+
+ align:start position:0%
+particle has to decide where to put it
+ 
+
+ align:start position:0%
+particle has to decide where to put it
+it can put it um in in translational
+
+ align:start position:0%
+it can put it um in in translational
+ 
+
+ align:start position:0%
+it can put it um in in translational
+mode but as we've seen here if the
+
+ align:start position:0%
+mode but as we've seen here if the
+ 
+
+ align:start position:0%
+mode but as we've seen here if the
+particle is confined the translational
+
+ align:start position:0%
+particle is confined the translational
+ 
+
+ align:start position:0%
+particle is confined the translational
+modes have this kind of energy levels so
+
+ align:start position:0%
+modes have this kind of energy levels so
+ 
+
+ align:start position:0%
+modes have this kind of energy levels so
+how much energy do I put in this mode
+
+ align:start position:0%
+how much energy do I put in this mode
+ 
+
+ align:start position:0%
+how much energy do I put in this mode
+and how much in that and how much in
+
+ align:start position:0%
+and how much in that and how much in
+ 
+
+ align:start position:0%
+and how much in that and how much in
+that if the particle also has a internal
+
+ align:start position:0%
+that if the particle also has a internal
+ 
+
+ align:start position:0%
+that if the particle also has a internal
+structure uh so for example it could uh
+
+ align:start position:0%
+structure uh so for example it could uh
+ 
+
+ align:start position:0%
+structure uh so for example it could uh
+vibrate or if it if it has a structure
+
+ align:start position:0%
+vibrate or if it if it has a structure
+ 
+
+ align:start position:0%
+vibrate or if it if it has a structure
+so that it can
+
+ align:start position:0%
+so that it can
+ 
+
+ align:start position:0%
+so that it can
+rotate can put also you get additional
+
+ align:start position:0%
+rotate can put also you get additional
+ 
+
+ align:start position:0%
+rotate can put also you get additional
+modes uh rotational
+
+ align:start position:0%
+modes uh rotational
+ 
+
+ align:start position:0%
+modes uh rotational
+modes uh and then you have electron iic
+
+ align:start position:0%
+modes uh and then you have electron iic
+ 
+
+ align:start position:0%
+modes uh and then you have electron iic
+modes all right so the particle uh has
+
+ align:start position:0%
+modes all right so the particle uh has
+ 
+
+ align:start position:0%
+modes all right so the particle uh has
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+decide how to distribute and uh uh
+
+ align:start position:0%
+decide how to distribute and uh uh
+ 
+
+ align:start position:0%
+decide how to distribute and uh uh
+distribute
+
+ align:start position:0%
+distribute
+ 
+
+ align:start position:0%
+distribute
+evenly so if it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unconstrained the the most even
+
+ align:start position:0%
+unconstrained the the most even
+ 
+
+ align:start position:0%
+unconstrained the the most even
+distribution is the maximum
+
+ align:start position:0%
+distribution is the maximum
+ 
+
+ align:start position:0%
+distribution is the maximum
+entropy the equilibrium one at
+
+ align:start position:0%
+entropy the equilibrium one at
+ 
+
+ align:start position:0%
+entropy the equilibrium one at
+equilibrium it will have distributed
+
+ align:start position:0%
+equilibrium it will have distributed
+ 
+
+ align:start position:0%
+equilibrium it will have distributed
+things so as to Max maximize the entropy
+
+ align:start position:0%
+things so as to Max maximize the entropy
+ 
+
+ align:start position:0%
+things so as to Max maximize the entropy
+so entropy also measures the uh degree
+
+ align:start position:0%
+so entropy also measures the uh degree
+ 
+
+ align:start position:0%
+so entropy also measures the uh degree
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sharing the highest degree of sharing is
+
+ align:start position:0%
+sharing the highest degree of sharing is
+ 
+
+ align:start position:0%
+sharing the highest degree of sharing is
+achieved here and the natural phenomena
+
+ align:start position:0%
+achieved here and the natural phenomena
+ 
+
+ align:start position:0%
+achieved here and the natural phenomena
+are in common have in common the idea
+
+ align:start position:0%
+are in common have in common the idea
+ 
+
+ align:start position:0%
+are in common have in common the idea
+that there is a spontaneous tendency to
+
+ align:start position:0%
+that there is a spontaneous tendency to
+ 
+
+ align:start position:0%
+that there is a spontaneous tendency to
+uh uh share uh the energy as evenly
+
+ align:start position:0%
+uh uh share uh the energy as evenly
+ 
+
+ align:start position:0%
+uh uh share uh the energy as evenly
+possible as possible
+
+ align:start position:0%
+possible as possible
+ 
+
+ align:start position:0%
+possible as possible
+uh among the uh available energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+levels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question about Dynamics is how do
+
+ align:start position:0%
+so the question about Dynamics is how do
+ 
+
+ align:start position:0%
+so the question about Dynamics is how do
+this thing evolve in time and here I
+
+ align:start position:0%
+this thing evolve in time and here I
+ 
+
+ align:start position:0%
+this thing evolve in time and here I
+have a slide with a
+
+ align:start position:0%
+have a slide with a
+ 
+
+ align:start position:0%
+have a slide with a
+some uh animation hopefully it should
+
+ align:start position:0%
+some uh animation hopefully it should
+ 
+
+ align:start position:0%
+some uh animation hopefully it should
+work let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see yeah okay so for example I started
+
+ align:start position:0%
+see yeah okay so for example I started
+ 
+
+ align:start position:0%
+see yeah okay so for example I started
+from very close to uh zero entropy and
+
+ align:start position:0%
+from very close to uh zero entropy and
+ 
+
+ align:start position:0%
+from very close to uh zero entropy and
+this is a smooth transition in which uh
+
+ align:start position:0%
+this is a smooth transition in which uh
+ 
+
+ align:start position:0%
+this is a smooth transition in which uh
+the particle while keeping the energy
+
+ align:start position:0%
+the particle while keeping the energy
+ 
+
+ align:start position:0%
+the particle while keeping the energy
+constant redistributes the probabilities
+
+ align:start position:0%
+constant redistributes the probabilities
+ 
+
+ align:start position:0%
+constant redistributes the probabilities
+until it eventually achieves the stable
+
+ align:start position:0%
+until it eventually achieves the stable
+ 
+
+ align:start position:0%
+until it eventually achieves the stable
+equilibrium canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+okay and also this one is another
+
+ align:start position:0%
+okay and also this one is another
+ 
+
+ align:start position:0%
+okay and also this one is another
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+started from an intermediate state with
+
+ align:start position:0%
+started from an intermediate state with
+ 
+
+ align:start position:0%
+started from an intermediate state with
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+initially uh full um energy levels and
+
+ align:start position:0%
+initially uh full um energy levels and
+ 
+
+ align:start position:0%
+initially uh full um energy levels and
+the the other ones get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+filled until in the end you get to the
+
+ align:start position:0%
+filled until in the end you get to the
+ 
+
+ align:start position:0%
+filled until in the end you get to the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state I rescued
+
+ align:start position:0%
+state I rescued
+ 
+
+ align:start position:0%
+state I rescued
+these view graphs from U
+
+ align:start position:0%
+these view graphs from U
+ 
+
+ align:start position:0%
+these view graphs from U
+work that I had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done for my PhD thesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1981 to devise a an equation of motion
+
+ align:start position:0%
+1981 to devise a an equation of motion
+ 
+
+ align:start position:0%
+1981 to devise a an equation of motion
+that would take any probability
+
+ align:start position:0%
+that would take any probability
+ 
+
+ align:start position:0%
+that would take any probability
+distribution of this sort and
+
+ align:start position:0%
+distribution of this sort and
+ 
+
+ align:start position:0%
+distribution of this sort and
+evolves uh it smoothly towards a stable
+
+ align:start position:0%
+evolves uh it smoothly towards a stable
+ 
+
+ align:start position:0%
+evolves uh it smoothly towards a stable
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and that's developed in the subject that
+
+ align:start position:0%
+and that's developed in the subject that
+ 
+
+ align:start position:0%
+and that's developed in the subject that
+um u i Now call it steepest entropy
+
+ align:start position:0%
+um u i Now call it steepest entropy
+ 
+
+ align:start position:0%
+um u i Now call it steepest entropy
+asent but also has to do with what I
+
+ align:start position:0%
+asent but also has to do with what I
+ 
+
+ align:start position:0%
+asent but also has to do with what I
+like to call the forlow of
+
+ align:start position:0%
+like to call the forlow of
+ 
+
+ align:start position:0%
+like to call the forlow of
+thermodynamics because essentially this
+
+ align:start position:0%
+thermodynamics because essentially this
+ 
+
+ align:start position:0%
+thermodynamics because essentially this
+kind of uh dynamical description of
+
+ align:start position:0%
+kind of uh dynamical description of
+ 
+
+ align:start position:0%
+kind of uh dynamical description of
+non-e equilibrium
+
+ align:start position:0%
+non-e equilibrium
+ 
+
+ align:start position:0%
+non-e equilibrium
+States is uh is is common of a large
+
+ align:start position:0%
+States is uh is is common of a large
+ 
+
+ align:start position:0%
+States is uh is is common of a large
+number of theories of on
+
+ align:start position:0%
+number of theories of on
+ 
+
+ align:start position:0%
+number of theories of on
+equilibrium there are some
+
+ align:start position:0%
+equilibrium there are some
+ 
+
+ align:start position:0%
+equilibrium there are some
+features
+
+ align:start position:0%
+features
+ 
+
+ align:start position:0%
+features
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+uh and there are some aspects some
+
+ align:start position:0%
+uh and there are some aspects some
+ 
+
+ align:start position:0%
+uh and there are some aspects some
+general aspects of this modeling
+
+ align:start position:0%
+general aspects of this modeling
+ 
+
+ align:start position:0%
+general aspects of this modeling
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ideas uh that are so uh common in spite
+
+ align:start position:0%
+ideas uh that are so uh common in spite
+ 
+
+ align:start position:0%
+ideas uh that are so uh common in spite
+of the different fields in which you
+
+ align:start position:0%
+of the different fields in which you
+ 
+
+ align:start position:0%
+of the different fields in which you
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+them uh uh that you can say that perhaps
+
+ align:start position:0%
+them uh uh that you can say that perhaps
+ 
+
+ align:start position:0%
+them uh uh that you can say that perhaps
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+represent uh another law
+
+ align:start position:0%
+represent uh another law
+ 
+
+ align:start position:0%
+represent uh another law
+of shouldn't say of nature but in our
+
+ align:start position:0%
+of shouldn't say of nature but in our
+ 
+
+ align:start position:0%
+of shouldn't say of nature but in our
+law another law of uh modeling nature
+
+ align:start position:0%
+law another law of uh modeling nature
+ 
+
+ align:start position:0%
+law another law of uh modeling nature
+correctly like the second law we have uh
+
+ align:start position:0%
+correctly like the second law we have uh
+ 
+
+ align:start position:0%
+correctly like the second law we have uh
+described as something that uh your
+
+ align:start position:0%
+described as something that uh your
+ 
+
+ align:start position:0%
+described as something that uh your
+model should not violate otherwise it is
+
+ align:start position:0%
+model should not violate otherwise it is
+ 
+
+ align:start position:0%
+model should not violate otherwise it is
+a bad model okay also the forth flow
+
+ align:start position:0%
+a bad model okay also the forth flow
+ 
+
+ align:start position:0%
+a bad model okay also the forth flow
+will be something that is similarly to
+
+ align:start position:0%
+will be something that is similarly to
+ 
+
+ align:start position:0%
+will be something that is similarly to
+be uh satisfied if your model has to
+
+ align:start position:0%
+be uh satisfied if your model has to
+ 
+
+ align:start position:0%
+be uh satisfied if your model has to
+provide a
+
+ align:start position:0%
+provide a
+ 
+
+ align:start position:0%
+provide a
+compatible description of how States
+
+ align:start position:0%
+compatible description of how States
+ 
+
+ align:start position:0%
+compatible description of how States
+evolve towards equilibrium uh in
+
+ align:start position:0%
+evolve towards equilibrium uh in
+ 
+
+ align:start position:0%
+evolve towards equilibrium uh in
+compatible with all we know
+
+ align:start position:0%
+compatible with all we know
+ 
+
+ align:start position:0%
+compatible with all we know
+about evidence of of physical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reality well little more because we
+
+ align:start position:0%
+reality well little more because we
+ 
+
+ align:start position:0%
+reality well little more because we
+haven't done we haven't finished the yet
+
+ align:start position:0%
+haven't done we haven't finished the yet
+ 
+
+ align:start position:0%
+haven't done we haven't finished the yet
+with the particle in the
+
+ align:start position:0%
+with the particle in the
+ 
+
+ align:start position:0%
+with the particle in the
+Box
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me uh take it um start again from
+
+ align:start position:0%
+um let me uh take it um start again from
+ 
+
+ align:start position:0%
+um let me uh take it um start again from
+the partition function
+
+ align:start position:0%
+the partition function
+ 
+
+ align:start position:0%
+the partition function
+Q of the onedimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case which is therefore this summation
+
+ align:start position:0%
+case which is therefore this summation
+ 
+
+ align:start position:0%
+case which is therefore this summation
+of e to the uh the energy levels over KT
+
+ align:start position:0%
+of e to the uh the energy levels over KT
+ 
+
+ align:start position:0%
+of e to the uh the energy levels over KT
+and here are the energy levels uh
+
+ align:start position:0%
+and here are the energy levels uh
+ 
+
+ align:start position:0%
+and here are the energy levels uh
+substituted directly so you see now in
+
+ align:start position:0%
+substituted directly so you see now in
+ 
+
+ align:start position:0%
+substituted directly so you see now in
+this expression what are the fixed the
+
+ align:start position:0%
+this expression what are the fixed the
+ 
+
+ align:start position:0%
+this expression what are the fixed the
+parameters I mean some are physical
+
+ align:start position:0%
+parameters I mean some are physical
+ 
+
+ align:start position:0%
+parameters I mean some are physical
+constants plank constant H uh bman
+
+ align:start position:0%
+constants plank constant H uh bman
+ 
+
+ align:start position:0%
+constants plank constant H uh bman
+constant KB m is the mass of your
+
+ align:start position:0%
+constant KB m is the mass of your
+ 
+
+ align:start position:0%
+constant KB m is the mass of your
+particle J is just the dummy variable in
+
+ align:start position:0%
+particle J is just the dummy variable in
+ 
+
+ align:start position:0%
+particle J is just the dummy variable in
+this summation there are only two
+
+ align:start position:0%
+this summation there are only two
+ 
+
+ align:start position:0%
+this summation there are only two
+parameters in this formula T which is
+
+ align:start position:0%
+parameters in this formula T which is
+ 
+
+ align:start position:0%
+parameters in this formula T which is
+the temperature and L which which is the
+
+ align:start position:0%
+the temperature and L which which is the
+ 
+
+ align:start position:0%
+the temperature and L which which is the
+side the size of of the box or the side
+
+ align:start position:0%
+side the size of of the box or the side
+ 
+
+ align:start position:0%
+side the size of of the box or the side
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box so Q is a function of two variables
+
+ align:start position:0%
+box so Q is a function of two variables
+ 
+
+ align:start position:0%
+box so Q is a function of two variables
+that means that as we like to do when we
+
+ align:start position:0%
+that means that as we like to do when we
+ 
+
+ align:start position:0%
+that means that as we like to do when we
+have functions we take the
+
+ align:start position:0%
+have functions we take the
+ 
+
+ align:start position:0%
+have functions we take the
+differentials so if I take the
+
+ align:start position:0%
+differentials so if I take the
+ 
+
+ align:start position:0%
+differentials so if I take the
+differential of the logarithm of this
+
+ align:start position:0%
+differential of the logarithm of this
+ 
+
+ align:start position:0%
+differential of the logarithm of this
+summation logar of
+
+ align:start position:0%
+summation logar of
+ 
+
+ align:start position:0%
+summation logar of
+q and u it takes a little while but uh
+
+ align:start position:0%
+q and u it takes a little while but uh
+ 
+
+ align:start position:0%
+q and u it takes a little while but uh
+you can do it that's just uh you can
+
+ align:start position:0%
+you can do it that's just uh you can
+ 
+
+ align:start position:0%
+you can do it that's just uh you can
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+um it can be written this
+
+ align:start position:0%
+um it can be written this
+ 
+
+ align:start position:0%
+um it can be written this
+way so of course it has a DT and a DL
+
+ align:start position:0%
+way so of course it has a DT and a DL
+ 
+
+ align:start position:0%
+way so of course it has a DT and a DL
+because the two variables are T and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L uh so once you have done it you may
+
+ align:start position:0%
+L uh so once you have done it you may
+ 
+
+ align:start position:0%
+L uh so once you have done it you may
+say um that the coefficient that
+
+ align:start position:0%
+say um that the coefficient that
+ 
+
+ align:start position:0%
+say um that the coefficient that
+multiplies DT is equal to the derivative
+
+ align:start position:0%
+multiplies DT is equal to the derivative
+ 
+
+ align:start position:0%
+multiplies DT is equal to the derivative
+of what you of of of the log of
+
+ align:start position:0%
+of what you of of of the log of
+ 
+
+ align:start position:0%
+of what you of of of the log of
+Q with respect to T and so you obtain
+
+ align:start position:0%
+Q with respect to T and so you obtain
+ 
+
+ align:start position:0%
+Q with respect to T and so you obtain
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+relation and this other one is equal to
+
+ align:start position:0%
+relation and this other one is equal to
+ 
+
+ align:start position:0%
+relation and this other one is equal to
+the derivative of uh uh log of Q with
+
+ align:start position:0%
+the derivative of uh uh log of Q with
+ 
+
+ align:start position:0%
+the derivative of uh uh log of Q with
+respect to
+
+ align:start position:0%
+respect to
+ 
+
+ align:start position:0%
+respect to
+L actually notice that if since it's DL
+
+ align:start position:0%
+L actually notice that if since it's DL
+ 
+
+ align:start position:0%
+L actually notice that if since it's DL
+over L this is also you the derivative
+
+ align:start position:0%
+over L this is also you the derivative
+ 
+
+ align:start position:0%
+over L this is also you the derivative
+of the log of
+
+ align:start position:0%
+of the log of
+ 
+
+ align:start position:0%
+of the log of
+L so we can so we obtain that the
+
+ align:start position:0%
+L so we can so we obtain that the
+ 
+
+ align:start position:0%
+L so we can so we obtain that the
+derivative of log of Q over uh log of L
+
+ align:start position:0%
+derivative of log of Q over uh log of L
+ 
+
+ align:start position:0%
+derivative of log of Q over uh log of L
+is equal to e subi over
+
+ align:start position:0%
+is equal to e subi over
+ 
+
+ align:start position:0%
+is equal to e subi over
+KT now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I don't find it in this slide but it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is a
+
+ align:start position:0%
+is is a
+ 
+
+ align:start position:0%
+is is a
+by if you go a couple of slides earlier
+
+ align:start position:0%
+by if you go a couple of slides earlier
+ 
+
+ align:start position:0%
+by if you go a couple of slides earlier
+you find it and you should correct me if
+
+ align:start position:0%
+you find it and you should correct me if
+ 
+
+ align:start position:0%
+you find it and you should correct me if
+I'm writing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong isi should be the weighted sum on
+
+ align:start position:0%
+wrong isi should be the weighted sum on
+ 
+
+ align:start position:0%
+wrong isi should be the weighted sum on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+probabilities of the energy
+
+ align:start position:0%
+probabilities of the energy
+ 
+
+ align:start position:0%
+probabilities of the energy
+levels of the single uh
+
+ align:start position:0%
+levels of the single uh
+ 
+
+ align:start position:0%
+levels of the single uh
+um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction so essentially
+
+ align:start position:0%
+Direction so essentially
+ 
+
+ align:start position:0%
+Direction so essentially
+it's the uh it's the partial energy see
+
+ align:start position:0%
+it's the uh it's the partial energy see
+ 
+
+ align:start position:0%
+it's the uh it's the partial energy see
+the the the overall
+
+ align:start position:0%
+the the the overall
+ 
+
+ align:start position:0%
+the the the overall
+energy is equal to the sum of the
+
+ align:start position:0%
+energy is equal to the sum of the
+ 
+
+ align:start position:0%
+energy is equal to the sum of the
+energies that the particle has in the
+
+ align:start position:0%
+energies that the particle has in the
+ 
+
+ align:start position:0%
+energies that the particle has in the
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+directions it's like
+
+ align:start position:0%
+directions it's like
+ 
+
+ align:start position:0%
+directions it's like
+additive they are independent
+
+ align:start position:0%
+additive they are independent
+ 
+
+ align:start position:0%
+additive they are independent
+modes independent lives that the
+
+ align:start position:0%
+modes independent lives that the
+ 
+
+ align:start position:0%
+modes independent lives that the
+particle has in the three Direction okay
+
+ align:start position:0%
+particle has in the three Direction okay
+ 
+
+ align:start position:0%
+particle has in the three Direction okay
+so here we're watching it just Just One
+
+ align:start position:0%
+so here we're watching it just Just One
+ 
+
+ align:start position:0%
+so here we're watching it just Just One
+Direction
+
+ align:start position:0%
+Direction
+ 
+
+ align:start position:0%
+Direction
+okay then another formula that we
+
+ align:start position:0%
+okay then another formula that we
+ 
+
+ align:start position:0%
+okay then another formula that we
+had couple of slides ago is this
+
+ align:start position:0%
+had couple of slides ago is this
+ 
+
+ align:start position:0%
+had couple of slides ago is this
+one the one that I also wrote uh here
+
+ align:start position:0%
+one the one that I also wrote uh here
+ 
+
+ align:start position:0%
+one the one that I also wrote uh here
+for the free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so if I take the differential of
+
+ align:start position:0%
+energy so if I take the differential of
+ 
+
+ align:start position:0%
+energy so if I take the differential of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one here is what I
+
+ align:start position:0%
+one here is what I
+ 
+
+ align:start position:0%
+one here is what I
+get again it takes a little bit of doing
+
+ align:start position:0%
+get again it takes a little bit of doing
+ 
+
+ align:start position:0%
+get again it takes a little bit of doing
+because I have to substit I have to take
+
+ align:start position:0%
+because I have to substit I have to take
+ 
+
+ align:start position:0%
+because I have to substit I have to take
+the differential of log of q but the
+
+ align:start position:0%
+the differential of log of q but the
+ 
+
+ align:start position:0%
+the differential of log of q but the
+differential of log of Q we just take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it we just took it and so here it is we
+
+ align:start position:0%
+it we just took it and so here it is we
+ 
+
+ align:start position:0%
+it we just took it and so here it is we
+substitute it there this one cancels
+
+ align:start position:0%
+substitute it there this one cancels
+ 
+
+ align:start position:0%
+substitute it there this one cancels
+with one of of the minus one / t^ s that
+
+ align:start position:0%
+with one of of the minus one / t^ s that
+ 
+
+ align:start position:0%
+with one of of the minus one / t^ s that
+comes from the derivative of this and so
+
+ align:start position:0%
+comes from the derivative of this and so
+ 
+
+ align:start position:0%
+comes from the derivative of this and so
+here is what I'm left with Ds 1 / TDE
+
+ align:start position:0%
+here is what I'm left with Ds 1 / TDE
+ 
+
+ align:start position:0%
+here is what I'm left with Ds 1 / TDE
+plus something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DL this is an ropy form of the
+
+ align:start position:0%
+DL this is an ropy form of the
+ 
+
+ align:start position:0%
+DL this is an ropy form of the
+fundamental relation for the stable
+
+ align:start position:0%
+fundamental relation for the stable
+ 
+
+ align:start position:0%
+fundamental relation for the stable
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state so this is the Gibbs relation you
+
+ align:start position:0%
+state so this is the Gibbs relation you
+ 
+
+ align:start position:0%
+state so this is the Gibbs relation you
+like to put it in energy form you just
+
+ align:start position:0%
+like to put it in energy form you just
+ 
+
+ align:start position:0%
+like to put it in energy form you just
+solve for de and here is it it's de is
+
+ align:start position:0%
+solve for de and here is it it's de is
+ 
+
+ align:start position:0%
+solve for de and here is it it's de is
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+TDS minus something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DL now if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you if you remember
+
+ align:start position:0%
+you if you remember
+ 
+
+ align:start position:0%
+you if you remember
+when we have a a sing a substance in the
+
+ align:start position:0%
+when we have a a sing a substance in the
+ 
+
+ align:start position:0%
+when we have a a sing a substance in the
+simple system model
+
+ align:start position:0%
+simple system model
+ 
+
+ align:start position:0%
+simple system model
+limit uh the Gibbs relation is that de
+
+ align:start position:0%
+limit uh the Gibbs relation is that de
+ 
+
+ align:start position:0%
+limit uh the Gibbs relation is that de
+is TDS minus
+
+ align:start position:0%
+is TDS minus
+ 
+
+ align:start position:0%
+is TDS minus
+pdv
+
+ align:start position:0%
+pdv
+ 
+
+ align:start position:0%
+pdv
+pdv okay volume is the parameter and
+
+ align:start position:0%
+pdv okay volume is the parameter and
+ 
+
+ align:start position:0%
+pdv okay volume is the parameter and
+pressure is the coefficient in the
+
+ align:start position:0%
+pressure is the coefficient in the
+ 
+
+ align:start position:0%
+pressure is the coefficient in the
+differential that measures uh the the
+
+ align:start position:0%
+differential that measures uh the the
+ 
+
+ align:start position:0%
+differential that measures uh the the
+partial of the energy with respect to
+
+ align:start position:0%
+partial of the energy with respect to
+ 
+
+ align:start position:0%
+partial of the energy with respect to
+volume at constant s all right so that
+
+ align:start position:0%
+volume at constant s all right so that
+ 
+
+ align:start position:0%
+volume at constant s all right so that
+prompts Us by just looking at this here
+
+ align:start position:0%
+prompts Us by just looking at this here
+ 
+
+ align:start position:0%
+prompts Us by just looking at this here
+we don't have volume because the volume
+
+ align:start position:0%
+we don't have volume because the volume
+ 
+
+ align:start position:0%
+we don't have volume because the volume
+there's no volume for this particle it
+
+ align:start position:0%
+there's no volume for this particle it
+ 
+
+ align:start position:0%
+there's no volume for this particle it
+is only the length of the Box the size
+
+ align:start position:0%
+is only the length of the Box the size
+ 
+
+ align:start position:0%
+is only the length of the Box the size
+of the box is the equivalent of the
+
+ align:start position:0%
+of the box is the equivalent of the
+ 
+
+ align:start position:0%
+of the box is the equivalent of the
+volume so we can
+
+ align:start position:0%
+volume so we can
+ 
+
+ align:start position:0%
+volume so we can
+Define the equivalent of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure I will call it don't know what
+
+ align:start position:0%
+pressure I will call it don't know what
+ 
+
+ align:start position:0%
+pressure I will call it don't know what
+name to to give but I will call it
+
+ align:start position:0%
+name to to give but I will call it
+ 
+
+ align:start position:0%
+name to to give but I will call it
+directional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure it has dimensions of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure and I
+
+ align:start position:0%
+pressure and I
+ 
+
+ align:start position:0%
+pressure and I
+say and I Define it uh as the partial
+
+ align:start position:0%
+say and I Define it uh as the partial
+ 
+
+ align:start position:0%
+say and I Define it uh as the partial
+the negative of the partial of the
+
+ align:start position:0%
+the negative of the partial of the
+ 
+
+ align:start position:0%
+the negative of the partial of the
+energy with respect to
+
+ align:start position:0%
+energy with respect to
+ 
+
+ align:start position:0%
+energy with respect to
+volume but
+
+ align:start position:0%
+volume but
+ 
+
+ align:start position:0%
+volume but
+done while changing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only the One
+
+ align:start position:0%
+only the One
+ 
+
+ align:start position:0%
+only the One
+Direction so you see see since I have a
+
+ align:start position:0%
+Direction so you see see since I have a
+ 
+
+ align:start position:0%
+Direction so you see see since I have a
+box now this size this
+
+ align:start position:0%
+box now this size this
+ 
+
+ align:start position:0%
+box now this size this
+shape there are three different ways in
+
+ align:start position:0%
+shape there are three different ways in
+ 
+
+ align:start position:0%
+shape there are three different ways in
+which I can change the
+
+ align:start position:0%
+which I can change the
+ 
+
+ align:start position:0%
+which I can change the
+volume one is to uh keep L2 and L3 fixed
+
+ align:start position:0%
+volume one is to uh keep L2 and L3 fixed
+ 
+
+ align:start position:0%
+volume one is to uh keep L2 and L3 fixed
+and make L1
+
+ align:start position:0%
+and make L1
+ 
+
+ align:start position:0%
+and make L1
+longer and then there are the other
+
+ align:start position:0%
+longer and then there are the other
+ 
+
+ align:start position:0%
+longer and then there are the other
+two okay so I'm changing the volume just
+
+ align:start position:0%
+two okay so I'm changing the volume just
+ 
+
+ align:start position:0%
+two okay so I'm changing the volume just
+by changing
+
+ align:start position:0%
+by changing
+ 
+
+ align:start position:0%
+by changing
+L1 that's the
+
+ align:start position:0%
+L1 that's the
+ 
+
+ align:start position:0%
+L1 that's the
+pressure assigned to Direction one
+
+ align:start position:0%
+pressure assigned to Direction one
+ 
+
+ align:start position:0%
+pressure assigned to Direction one
+how much how much the energy changes in
+
+ align:start position:0%
+how much how much the energy changes in
+ 
+
+ align:start position:0%
+how much how much the energy changes in
+the stable equilibrium at fixed s fixed
+
+ align:start position:0%
+the stable equilibrium at fixed s fixed
+ 
+
+ align:start position:0%
+the stable equilibrium at fixed s fixed
+L2 and L3 when I change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L1 okay so you can also rewrite it this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way and if you rewrite it this way
+
+ align:start position:0%
+way and if you rewrite it this way
+ 
+
+ align:start position:0%
+way and if you rewrite it this way
+because the volume I mean yeah I'll let
+
+ align:start position:0%
+because the volume I mean yeah I'll let
+ 
+
+ align:start position:0%
+because the volume I mean yeah I'll let
+you think about this this very
+
+ align:start position:0%
+you think about this this very
+ 
+
+ align:start position:0%
+you think about this this very
+simple um all right so the partial of e
+
+ align:start position:0%
+simple um all right so the partial of e
+ 
+
+ align:start position:0%
+simple um all right so the partial of e
+with respect to the the the logarithm of
+
+ align:start position:0%
+with respect to the the the logarithm of
+ 
+
+ align:start position:0%
+with respect to the the the logarithm of
+L1 is obtained
+
+ align:start position:0%
+L1 is obtained
+ 
+
+ align:start position:0%
+L1 is obtained
+here because from this
+
+ align:start position:0%
+here because from this
+ 
+
+ align:start position:0%
+here because from this
+differential this
+
+ align:start position:0%
+differential this
+ 
+
+ align:start position:0%
+differential this
+coefficient minus 2
+
+ align:start position:0%
+coefficient minus 2
+ 
+
+ align:start position:0%
+coefficient minus 2
+e is exactly the partial of e with
+
+ align:start position:0%
+e is exactly the partial of e with
+ 
+
+ align:start position:0%
+e is exactly the partial of e with
+respect to the logarithm d l over L is
+
+ align:start position:0%
+respect to the logarithm d l over L is
+ 
+
+ align:start position:0%
+respect to the logarithm d l over L is
+the logarithm of
+
+ align:start position:0%
+the logarithm of
+ 
+
+ align:start position:0%
+the logarithm of
+L okay so here what we find is that uh
+
+ align:start position:0%
+L okay so here what we find is that uh
+ 
+
+ align:start position:0%
+L okay so here what we find is that uh
+that pressure is two e over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V that is the closest we can get for the
+
+ align:start position:0%
+V that is the closest we can get for the
+ 
+
+ align:start position:0%
+V that is the closest we can get for the
+moment without additional assumption so
+
+ align:start position:0%
+moment without additional assumption so
+ 
+
+ align:start position:0%
+moment without additional assumption so
+we found that
+
+ align:start position:0%
+we found that
+ 
+
+ align:start position:0%
+we found that
+P or
+
+ align:start position:0%
+P or
+ 
+
+ align:start position:0%
+P or
+Pi say
+
+ align:start position:0%
+Pi say
+ 
+
+ align:start position:0%
+Pi say
+one times the
+
+ align:start position:0%
+one times the
+ 
+
+ align:start position:0%
+one times the
+volume is that the
+
+ align:start position:0%
+volume is that the
+ 
+
+ align:start position:0%
+volume is that the
+volume yeah is equal to 2 e
+
+ align:start position:0%
+volume yeah is equal to 2 e
+ 
+
+ align:start position:0%
+volume yeah is equal to 2 e
+i Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I in a
+
+ align:start position:0%
+I in a
+ 
+
+ align:start position:0%
+I in a
+moment if you add the information that
+
+ align:start position:0%
+moment if you add the information that
+ 
+
+ align:start position:0%
+moment if you add the information that
+uh eventually we will have that e subi
+
+ align:start position:0%
+uh eventually we will have that e subi
+ 
+
+ align:start position:0%
+uh eventually we will have that e subi
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+one2 of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT and you substitute up
+
+ align:start position:0%
+KT and you substitute up
+ 
+
+ align:start position:0%
+KT and you substitute up
+there you find
+
+ align:start position:0%
+there you find
+ 
+
+ align:start position:0%
+there you find
+that Pi V equals the two cancels equals
+
+ align:start position:0%
+that Pi V equals the two cancels equals
+ 
+
+ align:start position:0%
+that Pi V equals the two cancels equals
+KT K remember is the gas constant n r so
+
+ align:start position:0%
+KT K remember is the gas constant n r so
+ 
+
+ align:start position:0%
+KT K remember is the gas constant n r so
+you found that Pi V equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nrt that's the ideal gas equation of
+
+ align:start position:0%
+nrt that's the ideal gas equation of
+ 
+
+ align:start position:0%
+nrt that's the ideal gas equation of
+state it requires though this step which
+
+ align:start position:0%
+state it requires though this step which
+ 
+
+ align:start position:0%
+state it requires though this step which
+we didn't we don't get yet and it's not
+
+ align:start position:0%
+we didn't we don't get yet and it's not
+ 
+
+ align:start position:0%
+we didn't we don't get yet and it's not
+always but but at this stage without
+
+ align:start position:0%
+always but but at this stage without
+ 
+
+ align:start position:0%
+always but but at this stage without
+assumptions about uh uh how large the
+
+ align:start position:0%
+assumptions about uh uh how large the
+ 
+
+ align:start position:0%
+assumptions about uh uh how large the
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+is which is something that we we require
+
+ align:start position:0%
+is which is something that we we require
+ 
+
+ align:start position:0%
+is which is something that we we require
+to discuss to get to this result we have
+
+ align:start position:0%
+to discuss to get to this result we have
+ 
+
+ align:start position:0%
+to discuss to get to this result we have
+obtained essentially the equivalent the
+
+ align:start position:0%
+obtained essentially the equivalent the
+ 
+
+ align:start position:0%
+obtained essentially the equivalent the
+the equation of state and of course you
+
+ align:start position:0%
+the equation of state and of course you
+ 
+
+ align:start position:0%
+the equation of state and of course you
+have one such uh equation of State for
+
+ align:start position:0%
+have one such uh equation of State for
+ 
+
+ align:start position:0%
+have one such uh equation of State for
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+Direction you have you may have energy
+
+ align:start position:0%
+Direction you have you may have energy
+ 
+
+ align:start position:0%
+Direction you have you may have energy
+in uh in the X Y and Z Direction and so
+
+ align:start position:0%
+in uh in the X Y and Z Direction and so
+ 
+
+ align:start position:0%
+in uh in the X Y and Z Direction and so
+you have these directional pressures so
+
+ align:start position:0%
+you have these directional pressures so
+ 
+
+ align:start position:0%
+you have these directional pressures so
+you have three such relations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you also find that the since the
+
+ align:start position:0%
+here you also find that the since the
+ 
+
+ align:start position:0%
+here you also find that the since the
+energy sums I mean is additive
+
+ align:start position:0%
+energy sums I mean is additive
+ 
+
+ align:start position:0%
+energy sums I mean is additive
+the energy of the three directions adds
+
+ align:start position:0%
+the energy of the three directions adds
+ 
+
+ align:start position:0%
+the energy of the three directions adds
+up to the overall energy of your
+
+ align:start position:0%
+up to the overall energy of your
+ 
+
+ align:start position:0%
+up to the overall energy of your
+particle this relation between energy
+
+ align:start position:0%
+particle this relation between energy
+ 
+
+ align:start position:0%
+particle this relation between energy
+and pressures so you can also be written
+
+ align:start position:0%
+and pressures so you can also be written
+ 
+
+ align:start position:0%
+and pressures so you can also be written
+as the sum of these three uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressures times V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2
+
+ align:start position:0%
+/2
+ 
+
+ align:start position:0%
+/2
+and from the fact that the energy sums I
+
+ align:start position:0%
+and from the fact that the energy sums I
+ 
+
+ align:start position:0%
+and from the fact that the energy sums I
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also uh take the if I take the
+
+ align:start position:0%
+also uh take the if I take the
+ 
+
+ align:start position:0%
+also uh take the if I take the
+differential of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these so de is equal to the sum of the
+
+ align:start position:0%
+these so de is equal to the sum of the
+ 
+
+ align:start position:0%
+these so de is equal to the sum of the
+DI de I but the expressions for the de I
+
+ align:start position:0%
+DI de I but the expressions for the de I
+ 
+
+ align:start position:0%
+DI de I but the expressions for the de I
+is is here so the Gibs uh relations for
+
+ align:start position:0%
+is is here so the Gibs uh relations for
+ 
+
+ align:start position:0%
+is is here so the Gibs uh relations for
+the various directions are here I can
+
+ align:start position:0%
+the various directions are here I can
+ 
+
+ align:start position:0%
+the various directions are here I can
+sum them up to get the overall Gibs
+
+ align:start position:0%
+sum them up to get the overall Gibs
+ 
+
+ align:start position:0%
+sum them up to get the overall Gibs
+relation for my particle in the Box and
+
+ align:start position:0%
+relation for my particle in the Box and
+ 
+
+ align:start position:0%
+relation for my particle in the Box and
+so I have the equal
+
+ align:start position:0%
+so I have the equal
+ 
+
+ align:start position:0%
+so I have the equal
+TDS and instead of
+
+ align:start position:0%
+TDS and instead of
+ 
+
+ align:start position:0%
+TDS and instead of
+pdv we have three contributions one for
+
+ align:start position:0%
+pdv we have three contributions one for
+ 
+
+ align:start position:0%
+pdv we have three contributions one for
+each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction so this is in general the
+
+ align:start position:0%
+Direction so this is in general the
+ 
+
+ align:start position:0%
+Direction so this is in general the
+gives a relation for the particle in the
+
+ align:start position:0%
+gives a relation for the particle in the
+ 
+
+ align:start position:0%
+gives a relation for the particle in the
+box and it has it requires three
+
+ align:start position:0%
+box and it has it requires three
+ 
+
+ align:start position:0%
+box and it has it requires three
+pressures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we can uh uh make an observation
+
+ align:start position:0%
+now we can uh uh make an observation
+ 
+
+ align:start position:0%
+now we can uh uh make an observation
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function that we now recognized the the
+
+ align:start position:0%
+function that we now recognized the the
+ 
+
+ align:start position:0%
+function that we now recognized the the
+role
+
+ align:start position:0%
+role
+ 
+
+ align:start position:0%
+role
+uh is a
+
+ align:start position:0%
+uh is a
+ 
+
+ align:start position:0%
+uh is a
+summation okay so is a
+
+ align:start position:0%
+summation okay so is a
+ 
+
+ align:start position:0%
+summation okay so is a
+summation of various terms you can
+
+ align:start position:0%
+summation of various terms you can
+ 
+
+ align:start position:0%
+summation of various terms you can
+uh think think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+summation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the various terms consider them as a
+
+ align:start position:0%
+as the various terms consider them as a
+ 
+
+ align:start position:0%
+as the various terms consider them as a
+the terms in a histogram and then the
+
+ align:start position:0%
+the terms in a histogram and then the
+ 
+
+ align:start position:0%
+the terms in a histogram and then the
+summation is the is the area so this is
+
+ align:start position:0%
+summation is the is the area so this is
+ 
+
+ align:start position:0%
+summation is the is the area so this is
+like the first term like from 0er to one
+
+ align:start position:0%
+like the first term like from 0er to one
+ 
+
+ align:start position:0%
+like the first term like from 0er to one
+and from from here to two and three and
+
+ align:start position:0%
+and from from here to two and three and
+ 
+
+ align:start position:0%
+and from from here to two and three and
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on and so the summation
+
+ align:start position:0%
+on and so the summation
+ 
+
+ align:start position:0%
+on and so the summation
+gives you is essentially the area uh and
+
+ align:start position:0%
+gives you is essentially the area uh and
+ 
+
+ align:start position:0%
+gives you is essentially the area uh and
+this is the value of the element in the
+
+ align:start position:0%
+this is the value of the element in the
+ 
+
+ align:start position:0%
+this is the value of the element in the
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+okay the idea here is that you sometimes
+
+ align:start position:0%
+okay the idea here is that you sometimes
+ 
+
+ align:start position:0%
+okay the idea here is that you sometimes
+can approximate this
+
+ align:start position:0%
+can approximate this
+ 
+
+ align:start position:0%
+can approximate this
+summation as the integral of a
+
+ align:start position:0%
+summation as the integral of a
+ 
+
+ align:start position:0%
+summation as the integral of a
+curve and that approximation is
+
+ align:start position:0%
+curve and that approximation is
+ 
+
+ align:start position:0%
+curve and that approximation is
+good when the error that you make these
+
+ align:start position:0%
+good when the error that you make these
+ 
+
+ align:start position:0%
+good when the error that you make these
+differences here become small
+
+ align:start position:0%
+differences here become small
+ 
+
+ align:start position:0%
+differences here become small
+so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea it
+
+ align:start position:0%
+idea it
+ 
+
+ align:start position:0%
+idea it
+requires that U this these things be
+
+ align:start position:0%
+requires that U this these things be
+ 
+
+ align:start position:0%
+requires that U this these things be
+small uh somehow and that condition is
+
+ align:start position:0%
+small uh somehow and that condition is
+ 
+
+ align:start position:0%
+small uh somehow and that condition is
+written here it means that this um
+
+ align:start position:0%
+written here it means that this um
+ 
+
+ align:start position:0%
+written here it means that this um
+combination of terms must be smaller
+
+ align:start position:0%
+combination of terms must be smaller
+ 
+
+ align:start position:0%
+combination of terms must be smaller
+than one this is an
+
+ align:start position:0%
+than one this is an
+ 
+
+ align:start position:0%
+than one this is an
+dimensionless uh number which contains
+
+ align:start position:0%
+dimensionless uh number which contains
+ 
+
+ align:start position:0%
+dimensionless uh number which contains
+temperature and the square of the side
+
+ align:start position:0%
+temperature and the square of the side
+ 
+
+ align:start position:0%
+temperature and the square of the side
+and it has to be small if this is
+
+ align:start position:0%
+and it has to be small if this is
+ 
+
+ align:start position:0%
+and it has to be small if this is
+small you can approximate the summation
+
+ align:start position:0%
+small you can approximate the summation
+ 
+
+ align:start position:0%
+small you can approximate the summation
+with an integral and then this is a kind
+
+ align:start position:0%
+with an integral and then this is a kind
+ 
+
+ align:start position:0%
+with an integral and then this is a kind
+of integral that can be done because
+
+ align:start position:0%
+of integral that can be done because
+ 
+
+ align:start position:0%
+of integral that can be done because
+it's an integral from 0 to
+
+ align:start position:0%
+it's an integral from 0 to
+ 
+
+ align:start position:0%
+it's an integral from 0 to
+infinity and here is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result and this is the partition
+
+ align:start position:0%
+result and this is the partition
+ 
+
+ align:start position:0%
+result and this is the partition
+function for One Direction if you
+
+ align:start position:0%
+function for One Direction if you
+ 
+
+ align:start position:0%
+function for One Direction if you
+multiply the partition functions for the
+
+ align:start position:0%
+multiply the partition functions for the
+ 
+
+ align:start position:0%
+multiply the partition functions for the
+various
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions uh so you must multiply the
+
+ align:start position:0%
+directions uh so you must multiply the
+ 
+
+ align:start position:0%
+directions uh so you must multiply the
+three you get the partition function for
+
+ align:start position:0%
+three you get the partition function for
+ 
+
+ align:start position:0%
+three you get the partition function for
+the overall particle in the
+
+ align:start position:0%
+the overall particle in the
+ 
+
+ align:start position:0%
+the overall particle in the
+box and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you see here I have L uh
+
+ align:start position:0%
+uh you see here I have L uh
+ 
+
+ align:start position:0%
+uh you see here I have L uh
+I it's
+
+ align:start position:0%
+I it's
+ 
+
+ align:start position:0%
+I it's
+squared uh but actually
+
+ align:start position:0%
+squared uh but actually
+ 
+
+ align:start position:0%
+squared uh but actually
+it's to the 1/2 so you can take it
+
+ align:start position:0%
+it's to the 1/2 so you can take it
+ 
+
+ align:start position:0%
+it's to the 1/2 so you can take it
+outside
+
+ align:start position:0%
+outside
+ 
+
+ align:start position:0%
+outside
+also and when you multiply the three of
+
+ align:start position:0%
+also and when you multiply the three of
+ 
+
+ align:start position:0%
+also and when you multiply the three of
+them it becomes L1 * L2 * L3 which is
+
+ align:start position:0%
+them it becomes L1 * L2 * L3 which is
+ 
+
+ align:start position:0%
+them it becomes L1 * L2 * L3 which is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+volume of the
+
+ align:start position:0%
+volume of the
+ 
+
+ align:start position:0%
+volume of the
+box and so the partition function also
+
+ align:start position:0%
+box and so the partition function also
+ 
+
+ align:start position:0%
+box and so the partition function also
+here is a q to the
+
+ align:start position:0%
+here is a q to the
+ 
+
+ align:start position:0%
+here is a q to the
+2/3 but it's to the three halfes so you
+
+ align:start position:0%
+2/3 but it's to the three halfes so you
+ 
+
+ align:start position:0%
+2/3 but it's to the three halfes so you
+can take the V outside so essentially
+
+ align:start position:0%
+can take the V outside so essentially
+ 
+
+ align:start position:0%
+can take the V outside so essentially
+this says that the overall partition
+
+ align:start position:0%
+this says that the overall partition
+ 
+
+ align:start position:0%
+this says that the overall partition
+function depends on the volume
+
+ align:start position:0%
+function depends on the volume
+ 
+
+ align:start position:0%
+function depends on the volume
+only essentially in this limit you are
+
+ align:start position:0%
+only essentially in this limit you are
+ 
+
+ align:start position:0%
+only essentially in this limit you are
+uh losing the um
+
+ align:start position:0%
+uh losing the um
+ 
+
+ align:start position:0%
+uh losing the um
+effect of the details of the shape of
+
+ align:start position:0%
+effect of the details of the shape of
+ 
+
+ align:start position:0%
+effect of the details of the shape of
+the Box what
+
+ align:start position:0%
+the Box what
+ 
+
+ align:start position:0%
+the Box what
+counts is just the product of the three
+
+ align:start position:0%
+counts is just the product of the three
+ 
+
+ align:start position:0%
+counts is just the product of the three
+which is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume uh in
+
+ align:start position:0%
+volume uh in
+ 
+
+ align:start position:0%
+volume uh in
+fact in that limit
+
+ align:start position:0%
+fact in that limit
+ 
+
+ align:start position:0%
+fact in that limit
+uh if you if you take the formulas we
+
+ align:start position:0%
+uh if you if you take the formulas we
+ 
+
+ align:start position:0%
+uh if you if you take the formulas we
+have up up here for say for the energy e
+
+ align:start position:0%
+have up up here for say for the energy e
+ 
+
+ align:start position:0%
+have up up here for say for the energy e
+subi you have to take uh the log the
+
+ align:start position:0%
+subi you have to take uh the log the
+ 
+
+ align:start position:0%
+subi you have to take uh the log the
+partial of the logarithm with respect to
+
+ align:start position:0%
+partial of the logarithm with respect to
+ 
+
+ align:start position:0%
+partial of the logarithm with respect to
+T well here is Q take the
+
+ align:start position:0%
+T well here is Q take the
+ 
+
+ align:start position:0%
+T well here is Q take the
+logarithm with respect to
+
+ align:start position:0%
+logarithm with respect to
+ 
+
+ align:start position:0%
+logarithm with respect to
+T it's just 12 time
+
+ align:start position:0%
+T it's just 12 time
+ 
+
+ align:start position:0%
+T it's just 12 time
+KT that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result and
+
+ align:start position:0%
+result and
+ 
+
+ align:start position:0%
+result and
+therefore and is equal in all directions
+
+ align:start position:0%
+therefore and is equal in all directions
+ 
+
+ align:start position:0%
+therefore and is equal in all directions
+this is so-called equip
+
+ align:start position:0%
+this is so-called equip
+ 
+
+ align:start position:0%
+this is so-called equip
+partition theorem uh
+
+ align:start position:0%
+partition theorem uh
+ 
+
+ align:start position:0%
+partition theorem uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh the particle has decided in this
+
+ align:start position:0%
+uh the particle has decided in this
+ 
+
+ align:start position:0%
+uh the particle has decided in this
+limit to
+
+ align:start position:0%
+limit to
+ 
+
+ align:start position:0%
+limit to
+distribute equally the energy in the
+
+ align:start position:0%
+distribute equally the energy in the
+ 
+
+ align:start position:0%
+distribute equally the energy in the
+three translational
+
+ align:start position:0%
+three translational
+ 
+
+ align:start position:0%
+three translational
+modes and each one gets a half of KT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning that since the energy of the
+
+ align:start position:0%
+meaning that since the energy of the
+ 
+
+ align:start position:0%
+meaning that since the energy of the
+particle is the sum of the energies of
+
+ align:start position:0%
+particle is the sum of the energies of
+ 
+
+ align:start position:0%
+particle is the sum of the energies of
+the three
+
+ align:start position:0%
+the three
+ 
+
+ align:start position:0%
+the three
+directions e is equal to three halves of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT this a structureless
+
+ align:start position:0%
+KT this a structureless
+ 
+
+ align:start position:0%
+KT this a structureless
+particle and the so the specific heat
+
+ align:start position:0%
+particle and the so the specific heat
+ 
+
+ align:start position:0%
+particle and the so the specific heat
+which is the partial of e with respect
+
+ align:start position:0%
+which is the partial of e with respect
+ 
+
+ align:start position:0%
+which is the partial of e with respect
+to T is
+
+ align:start position:0%
+to T is
+ 
+
+ align:start position:0%
+to T is
+three2 K of the bement constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also these pressures become all uh equal
+
+ align:start position:0%
+also these pressures become all uh equal
+ 
+
+ align:start position:0%
+also these pressures become all uh equal
+to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another so if I take the Gibs relation
+
+ align:start position:0%
+another so if I take the Gibs relation
+ 
+
+ align:start position:0%
+another so if I take the Gibs relation
+and these pies are equal to one
+
+ align:start position:0%
+and these pies are equal to one
+ 
+
+ align:start position:0%
+and these pies are equal to one
+another uh I can write it this
+
+ align:start position:0%
+another uh I can write it this
+ 
+
+ align:start position:0%
+another uh I can write it this
+way and uh so I get uh uh so these three
+
+ align:start position:0%
+way and uh so I get uh uh so these three
+ 
+
+ align:start position:0%
+way and uh so I get uh uh so these three
+terms becomes
+
+ align:start position:0%
+terms becomes
+ 
+
+ align:start position:0%
+terms becomes
+KT which is here times the sum of the L
+
+ align:start position:0%
+KT which is here times the sum of the L
+ 
+
+ align:start position:0%
+KT which is here times the sum of the L
+over L this is the sum of the log of the
+
+ align:start position:0%
+over L this is the sum of the log of the
+ 
+
+ align:start position:0%
+over L this is the sum of the log of the
+of the logarithms so the it's the
+
+ align:start position:0%
+of the logarithms so the it's the
+ 
+
+ align:start position:0%
+of the logarithms so the it's the
+derivative of uh the volume over the
+
+ align:start position:0%
+derivative of uh the volume over the
+ 
+
+ align:start position:0%
+derivative of uh the volume over the
+volume it's D of log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v and so we have the GI
+
+ align:start position:0%
+v and so we have the GI
+ 
+
+ align:start position:0%
+v and so we have the GI
+relation but now if if we take the G
+
+ align:start position:0%
+relation but now if if we take the G
+ 
+
+ align:start position:0%
+relation but now if if we take the G
+relation and uh remember that what
+
+ align:start position:0%
+relation and uh remember that what
+ 
+
+ align:start position:0%
+relation and uh remember that what
+multiplies DV is what we call
+
+ align:start position:0%
+multiplies DV is what we call
+ 
+
+ align:start position:0%
+multiplies DV is what we call
+pressure here we find that therefore the
+
+ align:start position:0%
+pressure here we find that therefore the
+ 
+
+ align:start position:0%
+pressure here we find that therefore the
+pressure of the particle in the box is
+
+ align:start position:0%
+pressure of the particle in the box is
+ 
+
+ align:start position:0%
+pressure of the particle in the box is
+KT over V so we get PV is equal
+
+ align:start position:0%
+KT over V so we get PV is equal
+ 
+
+ align:start position:0%
+KT over V so we get PV is equal
+KT which is theal gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law we also get of course the expression
+
+ align:start position:0%
+law we also get of course the expression
+ 
+
+ align:start position:0%
+law we also get of course the expression
+for the entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a function of temperature which
+
+ align:start position:0%
+which is a function of temperature which
+ 
+
+ align:start position:0%
+which is a function of temperature which
+can be written as a function of
+
+ align:start position:0%
+can be written as a function of
+ 
+
+ align:start position:0%
+can be written as a function of
+temperature and volume
+
+ align:start position:0%
+temperature and volume
+ 
+
+ align:start position:0%
+temperature and volume
+only so we lost uh the information about
+
+ align:start position:0%
+only so we lost uh the information about
+ 
+
+ align:start position:0%
+only so we lost uh the information about
+the need to uh know the details of the
+
+ align:start position:0%
+the need to uh know the details of the
+ 
+
+ align:start position:0%
+the need to uh know the details of the
+box so that means that in that limit and
+
+ align:start position:0%
+box so that means that in that limit and
+ 
+
+ align:start position:0%
+box so that means that in that limit and
+this limit uh this condition that this
+
+ align:start position:0%
+this limit uh this condition that this
+ 
+
+ align:start position:0%
+this limit uh this condition that this
+is small can also be uh written this
+
+ align:start position:0%
+is small can also be uh written this
+ 
+
+ align:start position:0%
+is small can also be uh written this
+way that the temperature if you fix the
+
+ align:start position:0%
+way that the temperature if you fix the
+ 
+
+ align:start position:0%
+way that the temperature if you fix the
+volume it means that the temperature
+
+ align:start position:0%
+volume it means that the temperature
+ 
+
+ align:start position:0%
+volume it means that the temperature
+must be
+
+ align:start position:0%
+must be
+ 
+
+ align:start position:0%
+must be
+big enough so
+
+ align:start position:0%
+big enough so
+ 
+
+ align:start position:0%
+big enough so
+that these constants divided by the
+
+ align:start position:0%
+that these constants divided by the
+ 
+
+ align:start position:0%
+that these constants divided by the
+volume to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2/3 uh so that the temperature is much
+
+ align:start position:0%
+2/3 uh so that the temperature is much
+ 
+
+ align:start position:0%
+2/3 uh so that the temperature is much
+greater than this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number or you could also put it
+
+ align:start position:0%
+number or you could also put it
+ 
+
+ align:start position:0%
+number or you could also put it
+differently if you fix the temperature
+
+ align:start position:0%
+differently if you fix the temperature
+ 
+
+ align:start position:0%
+differently if you fix the temperature
+you need the volume to be big
+
+ align:start position:0%
+you need the volume to be big
+ 
+
+ align:start position:0%
+you need the volume to be big
+enough the system must be diluted enough
+
+ align:start position:0%
+enough the system must be diluted enough
+ 
+
+ align:start position:0%
+enough the system must be diluted enough
+so in these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limits
+
+ align:start position:0%
+limits
+ 
+
+ align:start position:0%
+limits
+um we find the ideal gas law and we find
+
+ align:start position:0%
+um we find the ideal gas law and we find
+ 
+
+ align:start position:0%
+um we find the ideal gas law and we find
+uh that
+
+ align:start position:0%
+uh that
+ 
+
+ align:start position:0%
+uh that
+the box of the same
+
+ align:start position:0%
+the box of the same
+ 
+
+ align:start position:0%
+the box of the same
+volume uh it could be very many
+
+ align:start position:0%
+volume uh it could be very many
+ 
+
+ align:start position:0%
+volume uh it could be very many
+different shapes have uh can have the
+
+ align:start position:0%
+different shapes have uh can have the
+ 
+
+ align:start position:0%
+different shapes have uh can have the
+same volume they all have the same
+
+ align:start position:0%
+same volume they all have the same
+ 
+
+ align:start position:0%
+same volume they all have the same
+properties that's why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in most practical situations this uh
+
+ align:start position:0%
+uh in most practical situations this uh
+ 
+
+ align:start position:0%
+uh in most practical situations this uh
+uh since this is
+
+ align:start position:0%
+uh since this is
+ 
+
+ align:start position:0%
+uh since this is
+satisfied except when you go to very low
+
+ align:start position:0%
+satisfied except when you go to very low
+ 
+
+ align:start position:0%
+satisfied except when you go to very low
+temperatures that's why we typically use
+
+ align:start position:0%
+temperatures that's why we typically use
+ 
+
+ align:start position:0%
+temperatures that's why we typically use
+just the volume as
+
+ align:start position:0%
+just the volume as
+ 
+
+ align:start position:0%
+just the volume as
+parameter because otherwise you would
+
+ align:start position:0%
+parameter because otherwise you would
+ 
+
+ align:start position:0%
+parameter because otherwise you would
+say all right you said the beginning you
+
+ align:start position:0%
+say all right you said the beginning you
+ 
+
+ align:start position:0%
+say all right you said the beginning you
+need to put the parameters in the
+
+ align:start position:0%
+need to put the parameters in the
+ 
+
+ align:start position:0%
+need to put the parameters in the
+fundamental relation but then you end up
+
+ align:start position:0%
+fundamental relation but then you end up
+ 
+
+ align:start position:0%
+fundamental relation but then you end up
+always putting only volume why well
+
+ align:start position:0%
+always putting only volume why well
+ 
+
+ align:start position:0%
+always putting only volume why well
+here's the reason because for most
+
+ align:start position:0%
+here's the reason because for most
+ 
+
+ align:start position:0%
+here's the reason because for most
+practical situation but not for small
+
+ align:start position:0%
+practical situation but not for small
+ 
+
+ align:start position:0%
+practical situation but not for small
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+uh volume is all that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counts
+
+ align:start position:0%
+counts
+ 
+
+ align:start position:0%
+counts
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+uh just a couple of
+
+ align:start position:0%
+uh just a couple of
+ 
+
+ align:start position:0%
+uh just a couple of
+minutes uh we are left uh I want to
+
+ align:start position:0%
+minutes uh we are left uh I want to
+ 
+
+ align:start position:0%
+minutes uh we are left uh I want to
+introduce this idea which is going to be
+
+ align:start position:0%
+introduce this idea which is going to be
+ 
+
+ align:start position:0%
+introduce this idea which is going to be
+our next step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember that we talked
+
+ align:start position:0%
+remember that we talked
+ 
+
+ align:start position:0%
+remember that we talked
+about the gas uh
+
+ align:start position:0%
+about the gas uh
+ 
+
+ align:start position:0%
+about the gas uh
+State uh as one in which the particles
+
+ align:start position:0%
+State uh as one in which the particles
+ 
+
+ align:start position:0%
+State uh as one in which the particles
+spend most of their times distant from
+
+ align:start position:0%
+spend most of their times distant from
+ 
+
+ align:start position:0%
+spend most of their times distant from
+one another in spite of their colliding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so in
+
+ align:start position:0%
+uh so in
+ 
+
+ align:start position:0%
+uh so in
+the ideal
+
+ align:start position:0%
+the ideal
+ 
+
+ align:start position:0%
+the ideal
+gas Gibbs Dalton
+
+ align:start position:0%
+gas Gibbs Dalton
+ 
+
+ align:start position:0%
+gas Gibbs Dalton
+mixture of Ideal
+
+ align:start position:0%
+mixture of Ideal
+ 
+
+ align:start position:0%
+mixture of Ideal
+gases we found that essentially the
+
+ align:start position:0%
+gases we found that essentially the
+ 
+
+ align:start position:0%
+gases we found that essentially the
+particles live in the space without
+
+ align:start position:0%
+particles live in the space without
+ 
+
+ align:start position:0%
+particles live in the space without
+seeing each other except when they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Collide and
+
+ align:start position:0%
+Collide and
+ 
+
+ align:start position:0%
+Collide and
+uh and that results to the
+
+ align:start position:0%
+uh and that results to the
+ 
+
+ align:start position:0%
+uh and that results to the
+fact that the entropy of mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the only
+
+ align:start position:0%
+is the only
+ 
+
+ align:start position:0%
+is the only
+effect uh that results upon mixing you
+
+ align:start position:0%
+effect uh that results upon mixing you
+ 
+
+ align:start position:0%
+effect uh that results upon mixing you
+mix
+
+ align:start position:0%
+mix
+ 
+
+ align:start position:0%
+mix
+gases at given uh the spontaneous
+
+ align:start position:0%
+gases at given uh the spontaneous
+ 
+
+ align:start position:0%
+gases at given uh the spontaneous
+process the temperature doesn't change
+
+ align:start position:0%
+process the temperature doesn't change
+ 
+
+ align:start position:0%
+process the temperature doesn't change
+the pressure doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change and the only thing that changes
+
+ align:start position:0%
+change and the only thing that changes
+ 
+
+ align:start position:0%
+change and the only thing that changes
+is the entropy is the mixing uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we need
+
+ align:start position:0%
+now we need
+ 
+
+ align:start position:0%
+now we need
+to Define also an ideal behavior for
+
+ align:start position:0%
+to Define also an ideal behavior for
+ 
+
+ align:start position:0%
+to Define also an ideal behavior for
+liquid phase now in liquid phase the
+
+ align:start position:0%
+liquid phase now in liquid phase the
+ 
+
+ align:start position:0%
+liquid phase now in liquid phase the
+particles do see each other actually
+
+ align:start position:0%
+particles do see each other actually
+ 
+
+ align:start position:0%
+particles do see each other actually
+they live most of the times close to one
+
+ align:start position:0%
+they live most of the times close to one
+ 
+
+ align:start position:0%
+they live most of the times close to one
+another so close
+
+ align:start position:0%
+another so close
+ 
+
+ align:start position:0%
+another so close
+to uh where this um um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermolecular potential has a min
+
+ align:start position:0%
+intermolecular potential has a min
+ 
+
+ align:start position:0%
+intermolecular potential has a min
+so for them that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+however we're going to Define an ideal
+
+ align:start position:0%
+however we're going to Define an ideal
+ 
+
+ align:start position:0%
+however we're going to Define an ideal
+solution Behavior one in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which uh the
+
+ align:start position:0%
+which uh the
+ 
+
+ align:start position:0%
+which uh the
+curves for the interaction
+
+ align:start position:0%
+curves for the interaction
+ 
+
+ align:start position:0%
+curves for the interaction
+between uh equal
+
+ align:start position:0%
+between uh equal
+ 
+
+ align:start position:0%
+between uh equal
+particles or different particles are all
+
+ align:start position:0%
+particles or different particles are all
+ 
+
+ align:start position:0%
+particles or different particles are all
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+similar so if they are all very
+
+ align:start position:0%
+similar so if they are all very
+ 
+
+ align:start position:0%
+similar so if they are all very
+similar the particle doesn't care what
+
+ align:start position:0%
+similar the particle doesn't care what
+ 
+
+ align:start position:0%
+similar the particle doesn't care what
+the neighbor
+
+ align:start position:0%
+the neighbor
+ 
+
+ align:start position:0%
+the neighbor
+is okay in this
+
+ align:start position:0%
+is okay in this
+ 
+
+ align:start position:0%
+is okay in this
+limit again when you mix
+
+ align:start position:0%
+limit again when you mix
+ 
+
+ align:start position:0%
+limit again when you mix
+stuff the only effect you don't get any
+
+ align:start position:0%
+stuff the only effect you don't get any
+ 
+
+ align:start position:0%
+stuff the only effect you don't get any
+energy of mixing or enthalpy of mixing
+
+ align:start position:0%
+energy of mixing or enthalpy of mixing
+ 
+
+ align:start position:0%
+energy of mixing or enthalpy of mixing
+you don't get any change of volume of
+
+ align:start position:0%
+you don't get any change of volume of
+ 
+
+ align:start position:0%
+you don't get any change of volume of
+mixing because the particle doesn't want
+
+ align:start position:0%
+mixing because the particle doesn't want
+ 
+
+ align:start position:0%
+mixing because the particle doesn't want
+to change their preferred distances
+
+ align:start position:0%
+to change their preferred distances
+ 
+
+ align:start position:0%
+to change their preferred distances
+which would
+
+ align:start position:0%
+which would
+ 
+
+ align:start position:0%
+which would
+imply enthalpy of mixing or uh volume of
+
+ align:start position:0%
+imply enthalpy of mixing or uh volume of
+ 
+
+ align:start position:0%
+imply enthalpy of mixing or uh volume of
+mixing which would imply uh stay
+
+ align:start position:0%
+mixing which would imply uh stay
+ 
+
+ align:start position:0%
+mixing which would imply uh stay
+changing the
+
+ align:start position:0%
+changing the
+ 
+
+ align:start position:0%
+changing the
+distance because essentially they
+
+ align:start position:0%
+distance because essentially they
+ 
+
+ align:start position:0%
+distance because essentially they
+uh they like each other in the same
+
+ align:start position:0%
+uh they like each other in the same
+ 
+
+ align:start position:0%
+uh they like each other in the same
+way uh the
+
+ align:start position:0%
+way uh the
+ 
+
+ align:start position:0%
+way uh the
+only effect upon mixing is the
+
+ align:start position:0%
+only effect upon mixing is the
+ 
+
+ align:start position:0%
+only effect upon mixing is the
+randomness so the entropy
+
+ align:start position:0%
+randomness so the entropy
+ 
+
+ align:start position:0%
+randomness so the entropy
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+okay and therefore in this model that we
+
+ align:start position:0%
+okay and therefore in this model that we
+ 
+
+ align:start position:0%
+okay and therefore in this model that we
+Define uh we will assume that the
+
+ align:start position:0%
+Define uh we will assume that the
+ 
+
+ align:start position:0%
+Define uh we will assume that the
+entropy of mixing of the single particle
+
+ align:start position:0%
+entropy of mixing of the single particle
+ 
+
+ align:start position:0%
+entropy of mixing of the single particle
+is related to the
+
+ align:start position:0%
+is related to the
+ 
+
+ align:start position:0%
+is related to the
+surprise uh and that is the only effect
+
+ align:start position:0%
+surprise uh and that is the only effect
+ 
+
+ align:start position:0%
+surprise uh and that is the only effect
+of this ideal situation that we're going
+
+ align:start position:0%
+of this ideal situation that we're going
+ 
+
+ align:start position:0%
+of this ideal situation that we're going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Define
+
+ align:start position:0%
+Define
+ 
+
+ align:start position:0%
+Define
+okay so with that we set the ground for
+
+ align:start position:0%
+okay so with that we set the ground for
+ 
+
+ align:start position:0%
+okay so with that we set the ground for
+the next uh lecture
\ No newline at end of file
diff --git a/RmdAWsvcsZw.txt b/RmdAWsvcsZw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17718d3a0444fb8e6979372065e8a605bc43393a
--- /dev/null
+++ b/RmdAWsvcsZw.txt
@@ -0,0 +1,10163 @@
+align:start position:0%
+ 
+so what we're going to do today is
+
+ align:start position:0%
+so what we're going to do today is
+ 
+
+ align:start position:0%
+so what we're going to do today is
+continue our discussion of modular uh
+
+ align:start position:0%
+continue our discussion of modular uh
+ 
+
+ align:start position:0%
+continue our discussion of modular uh
+computer software and specifically focus
+
+ align:start position:0%
+computer software and specifically focus
+ 
+
+ align:start position:0%
+computer software and specifically focus
+on a topic we started talking about the
+
+ align:start position:0%
+on a topic we started talking about the
+ 
+
+ align:start position:0%
+on a topic we started talking about the
+last time called soft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modularity and once we um figure out um
+
+ align:start position:0%
+modularity and once we um figure out um
+ 
+
+ align:start position:0%
+modularity and once we um figure out um
+you know finish our story with um um
+
+ align:start position:0%
+you know finish our story with um um
+ 
+
+ align:start position:0%
+you know finish our story with um um
+with regard to soft modularity and
+
+ align:start position:0%
+with regard to soft modularity and
+ 
+
+ align:start position:0%
+with regard to soft modularity and
+understand um exactly what this means
+
+ align:start position:0%
+understand um exactly what this means
+ 
+
+ align:start position:0%
+understand um exactly what this means
+we're we going to get to talk starting
+
+ align:start position:0%
+we're we going to get to talk starting
+ 
+
+ align:start position:0%
+we're we going to get to talk starting
+to talk about a different kind of
+
+ align:start position:0%
+to talk about a different kind of
+ 
+
+ align:start position:0%
+to talk about a different kind of
+modularity called uh enforced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modularity and enforced modularity is
+
+ align:start position:0%
+modularity and enforced modularity is
+ 
+
+ align:start position:0%
+modularity and enforced modularity is
+going to actually take us through um
+
+ align:start position:0%
+going to actually take us through um
+ 
+
+ align:start position:0%
+going to actually take us through um
+three lectures today um and the next two
+
+ align:start position:0%
+three lectures today um and the next two
+ 
+
+ align:start position:0%
+three lectures today um and the next two
+lectures um next week and the topic for
+
+ align:start position:0%
+lectures um next week and the topic for
+ 
+
+ align:start position:0%
+lectures um next week and the topic for
+today in terms of enforced modularity is
+
+ align:start position:0%
+today in terms of enforced modularity is
+ 
+
+ align:start position:0%
+today in terms of enforced modularity is
+a particular way of obtaining modularity
+
+ align:start position:0%
+a particular way of obtaining modularity
+ 
+
+ align:start position:0%
+a particular way of obtaining modularity
+in computer systems called client
+
+ align:start position:0%
+in computer systems called client
+ 
+
+ align:start position:0%
+in computer systems called client
+service organization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or some people call it client server
+
+ align:start position:0%
+or some people call it client server
+ 
+
+ align:start position:0%
+or some people call it client server
+Computing and um that's the plan for
+
+ align:start position:0%
+Computing and um that's the plan for
+ 
+
+ align:start position:0%
+Computing and um that's the plan for
+today so what we saw the last time was
+
+ align:start position:0%
+today so what we saw the last time was
+ 
+
+ align:start position:0%
+today so what we saw the last time was
+basically a lecture describing uh for
+
+ align:start position:0%
+basically a lecture describing uh for
+ 
+
+ align:start position:0%
+basically a lecture describing uh for
+the most part how linking worked and the
+
+ align:start position:0%
+the most part how linking worked and the
+ 
+
+ align:start position:0%
+the most part how linking worked and the
+idea in linking is that you
+
+ align:start position:0%
+idea in linking is that you
+ 
+
+ align:start position:0%
+idea in linking is that you
+have a number of software modules and
+
+ align:start position:0%
+have a number of software modules and
+ 
+
+ align:start position:0%
+have a number of software modules and
+your goal is to take all of them and to
+
+ align:start position:0%
+your goal is to take all of them and to
+ 
+
+ align:start position:0%
+your goal is to take all of them and to
+get an executable program out of them
+
+ align:start position:0%
+get an executable program out of them
+ 
+
+ align:start position:0%
+get an executable program out of them
+that you could then um that another
+
+ align:start position:0%
+that you could then um that another
+ 
+
+ align:start position:0%
+that you could then um that another
+program could load into memory and run
+
+ align:start position:0%
+program could load into memory and run
+ 
+
+ align:start position:0%
+program could load into memory and run
+and that was that task was being done
+
+ align:start position:0%
+and that was that task was being done
+ 
+
+ align:start position:0%
+and that was that task was being done
+by a piece of system software called a
+
+ align:start position:0%
+by a piece of system software called a
+ 
+
+ align:start position:0%
+by a piece of system software called a
+Linker and out pops an executable
+
+ align:start position:0%
+Linker and out pops an executable
+ 
+
+ align:start position:0%
+Linker and out pops an executable
+program um so at the end of lecture last
+
+ align:start position:0%
+program um so at the end of lecture last
+ 
+
+ align:start position:0%
+program um so at the end of lecture last
+time a couple of students asked me um
+
+ align:start position:0%
+time a couple of students asked me um
+ 
+
+ align:start position:0%
+time a couple of students asked me um
+two things one was why we were actually
+
+ align:start position:0%
+two things one was why we were actually
+ 
+
+ align:start position:0%
+two things one was why we were actually
+talking about this and the second more
+
+ align:start position:0%
+talking about this and the second more
+ 
+
+ align:start position:0%
+talking about this and the second more
+important question was why it wasn't in
+
+ align:start position:0%
+important question was why it wasn't in
+ 
+
+ align:start position:0%
+important question was why it wasn't in
+the notes and so let me answer the first
+
+ align:start position:0%
+the notes and so let me answer the first
+ 
+
+ align:start position:0%
+the notes and so let me answer the first
+question uh the question first um you
+
+ align:start position:0%
+question uh the question first um you
+ 
+
+ align:start position:0%
+question uh the question first um you
+know the plan in lectures is to do is to
+
+ align:start position:0%
+know the plan in lectures is to do is to
+ 
+
+ align:start position:0%
+know the plan in lectures is to do is to
+understand Concepts and computer systems
+
+ align:start position:0%
+understand Concepts and computer systems
+ 
+
+ align:start position:0%
+understand Concepts and computer systems
+with examples and often times we find
+
+ align:start position:0%
+with examples and often times we find
+ 
+
+ align:start position:0%
+with examples and often times we find
+examples that aren't actually in the
+
+ align:start position:0%
+examples that aren't actually in the
+ 
+
+ align:start position:0%
+examples that aren't actually in the
+notes and we use them a because if we
+
+ align:start position:0%
+notes and we use them a because if we
+ 
+
+ align:start position:0%
+notes and we use them a because if we
+don't use different examples there's
+
+ align:start position:0%
+don't use different examples there's
+ 
+
+ align:start position:0%
+don't use different examples there's
+sort of not as much incentive to show up
+
+ align:start position:0%
+sort of not as much incentive to show up
+ 
+
+ align:start position:0%
+sort of not as much incentive to show up
+um but often because some of the
+
+ align:start position:0%
+um but often because some of the
+ 
+
+ align:start position:0%
+um but often because some of the
+examples that work better in lecture
+
+ align:start position:0%
+examples that work better in lecture
+ 
+
+ align:start position:0%
+examples that work better in lecture
+don't actually work out um as clearly uh
+
+ align:start position:0%
+don't actually work out um as clearly uh
+ 
+
+ align:start position:0%
+don't actually work out um as clearly uh
+in the notes so we do tend to use uh
+
+ align:start position:0%
+in the notes so we do tend to use uh
+ 
+
+ align:start position:0%
+in the notes so we do tend to use uh
+different examples John to the first
+
+ align:start position:0%
+different examples John to the first
+ 
+
+ align:start position:0%
+different examples John to the first
+question why we actually looked at the
+
+ align:start position:0%
+question why we actually looked at the
+ 
+
+ align:start position:0%
+question why we actually looked at the
+Linker um first of all it's you know
+
+ align:start position:0%
+Linker um first of all it's you know
+ 
+
+ align:start position:0%
+Linker um first of all it's you know
+it's a common piece of software that
+
+ align:start position:0%
+it's a common piece of software that
+ 
+
+ align:start position:0%
+it's a common piece of software that
+pretty much every program that you run
+
+ align:start position:0%
+pretty much every program that you run
+ 
+
+ align:start position:0%
+pretty much every program that you run
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+goes through a process of linking but
+
+ align:start position:0%
+goes through a process of linking but
+ 
+
+ align:start position:0%
+goes through a process of linking but
+what it actually allowed us to do was
+
+ align:start position:0%
+what it actually allowed us to do was
+ 
+
+ align:start position:0%
+what it actually allowed us to do was
+illustrate two um main Concepts in
+
+ align:start position:0%
+illustrate two um main Concepts in
+ 
+
+ align:start position:0%
+illustrate two um main Concepts in
+naming having to do with the way in
+
+ align:start position:0%
+naming having to do with the way in
+ 
+
+ align:start position:0%
+naming having to do with the way in
+which um the name mathing algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worked and in the context of the Linker
+
+ align:start position:0%
+worked and in the context of the Linker
+ 
+
+ align:start position:0%
+worked and in the context of the Linker
+the problem was to take these symbols
+
+ align:start position:0%
+the problem was to take these symbols
+ 
+
+ align:start position:0%
+the problem was to take these symbols
+that you find in a program and um
+
+ align:start position:0%
+that you find in a program and um
+ 
+
+ align:start position:0%
+that you find in a program and um
+basically resolve them in other words
+
+ align:start position:0%
+basically resolve them in other words
+ 
+
+ align:start position:0%
+basically resolve them in other words
+find out where they're defined and where
+
+ align:start position:0%
+find out where they're defined and where
+ 
+
+ align:start position:0%
+find out where they're defined and where
+the instructions corresponding to those
+
+ align:start position:0%
+the instructions corresponding to those
+ 
+
+ align:start position:0%
+the instructions corresponding to those
+symbols or where the data corresponding
+
+ align:start position:0%
+symbols or where the data corresponding
+ 
+
+ align:start position:0%
+symbols or where the data corresponding
+to the the symbol was actually uh
+
+ align:start position:0%
+to the the symbol was actually uh
+ 
+
+ align:start position:0%
+to the the symbol was actually uh
+located and uh the concepts that we saw
+
+ align:start position:0%
+located and uh the concepts that we saw
+ 
+
+ align:start position:0%
+located and uh the concepts that we saw
+were uh two two different concepts uh
+
+ align:start position:0%
+were uh two two different concepts uh
+ 
+
+ align:start position:0%
+were uh two two different concepts uh
+the first was name mapping using a table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lookup where within each object file
+
+ align:start position:0%
+lookup where within each object file
+ 
+
+ align:start position:0%
+lookup where within each object file
+there was a symbol table that mapped
+
+ align:start position:0%
+there was a symbol table that mapped
+ 
+
+ align:start position:0%
+there was a symbol table that mapped
+between the symbols and found in that
+
+ align:start position:0%
+between the symbols and found in that
+ 
+
+ align:start position:0%
+between the symbols and found in that
+module to the location um where the
+
+ align:start position:0%
+module to the location um where the
+ 
+
+ align:start position:0%
+module to the location um where the
+symbols were defined further and another
+
+ align:start position:0%
+symbols were defined further and another
+ 
+
+ align:start position:0%
+symbols were defined further and another
+example which was of doing name mapping
+
+ align:start position:0%
+example which was of doing name mapping
+ 
+
+ align:start position:0%
+example which was of doing name mapping
+which was a process of search through a
+
+ align:start position:0%
+which was a process of search through a
+ 
+
+ align:start position:0%
+which was a process of search through a
+series of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contexts and in particular uh we looked
+
+ align:start position:0%
+contexts and in particular uh we looked
+ 
+
+ align:start position:0%
+contexts and in particular uh we looked
+at the problem of when you're in the
+
+ align:start position:0%
+at the problem of when you're in the
+ 
+
+ align:start position:0%
+at the problem of when you're in the
+context of um you know LD which GCC uses
+
+ align:start position:0%
+context of um you know LD which GCC uses
+ 
+
+ align:start position:0%
+context of um you know LD which GCC uses
+uh when it finds goes through a sequence
+
+ align:start position:0%
+uh when it finds goes through a sequence
+ 
+
+ align:start position:0%
+uh when it finds goes through a sequence
+of. o files as well as libraries in the
+
+ align:start position:0%
+of. o files as well as libraries in the
+ 
+
+ align:start position:0%
+of. o files as well as libraries in the
+command line what algorithm it actually
+
+ align:start position:0%
+command line what algorithm it actually
+ 
+
+ align:start position:0%
+command line what algorithm it actually
+uses to um resolve its symbols and I
+
+ align:start position:0%
+uses to um resolve its symbols and I
+ 
+
+ align:start position:0%
+uses to um resolve its symbols and I
+realized now that what I had left out on
+
+ align:start position:0%
+realized now that what I had left out on
+ 
+
+ align:start position:0%
+realized now that what I had left out on
+the board there was there was a couple
+
+ align:start position:0%
+the board there was there was a couple
+ 
+
+ align:start position:0%
+the board there was there was a couple
+of mistakes in the algorithm and I asked
+
+ align:start position:0%
+of mistakes in the algorithm and I asked
+ 
+
+ align:start position:0%
+of mistakes in the algorithm and I asked
+what the mistakes were and I realized I
+
+ align:start position:0%
+what the mistakes were and I realized I
+ 
+
+ align:start position:0%
+what the mistakes were and I realized I
+didn't actually fix and show you what
+
+ align:start position:0%
+didn't actually fix and show you what
+ 
+
+ align:start position:0%
+didn't actually fix and show you what
+the actual what the actual algorithm is
+
+ align:start position:0%
+the actual what the actual algorithm is
+ 
+
+ align:start position:0%
+the actual what the actual algorithm is
+correctly so I thought I'd spend a
+
+ align:start position:0%
+correctly so I thought I'd spend a
+ 
+
+ align:start position:0%
+correctly so I thought I'd spend a
+minute doing that so that you can you
+
+ align:start position:0%
+minute doing that so that you can you
+ 
+
+ align:start position:0%
+minute doing that so that you can you
+know if you have something wrong in your
+
+ align:start position:0%
+know if you have something wrong in your
+ 
+
+ align:start position:0%
+know if you have something wrong in your
+notes you can um fix that up because I
+
+ align:start position:0%
+notes you can um fix that up because I
+ 
+
+ align:start position:0%
+notes you can um fix that up because I
+realize I actually never said what the
+
+ align:start position:0%
+realize I actually never said what the
+ 
+
+ align:start position:0%
+realize I actually never said what the
+right thing was so if you recall the
+
+ align:start position:0%
+right thing was so if you recall the
+ 
+
+ align:start position:0%
+right thing was so if you recall the
+general problem was you have um GCC
+
+ align:start position:0%
+general problem was you have um GCC
+ 
+
+ align:start position:0%
+general problem was you have um GCC
+running on a set of. o files f1.0 all
+
+ align:start position:0%
+running on a set of. o files f1.0 all
+ 
+
+ align:start position:0%
+running on a set of. o files f1.0 all
+the way through fn. o and what we're
+
+ align:start position:0%
+the way through fn. o and what we're
+ 
+
+ align:start position:0%
+the way through fn. o and what we're
+trying to do is describe an algorithm
+
+ align:start position:0%
+trying to do is describe an algorithm
+ 
+
+ align:start position:0%
+trying to do is describe an algorithm
+where when you obtain the I object file
+
+ align:start position:0%
+where when you obtain the I object file
+ 
+
+ align:start position:0%
+where when you obtain the I object file
+and you you have a set of currently
+
+ align:start position:0%
+and you you have a set of currently
+ 
+
+ align:start position:0%
+and you you have a set of currently
+defined symbols and a set of currently
+
+ align:start position:0%
+defined symbols and a set of currently
+ 
+
+ align:start position:0%
+defined symbols and a set of currently
+undefined symbols how you can you know
+
+ align:start position:0%
+undefined symbols how you can you know
+ 
+
+ align:start position:0%
+undefined symbols how you can you know
+maintain three sets the set of object
+
+ align:start position:0%
+maintain three sets the set of object
+ 
+
+ align:start position:0%
+maintain three sets the set of object
+files that go into the executable the
+
+ align:start position:0%
+files that go into the executable the
+ 
+
+ align:start position:0%
+files that go into the executable the
+set of defined symbols that have been
+
+ align:start position:0%
+set of defined symbols that have been
+ 
+
+ align:start position:0%
+set of defined symbols that have been
+seen so far and the set of undefined
+
+ align:start position:0%
+seen so far and the set of undefined
+ 
+
+ align:start position:0%
+seen so far and the set of undefined
+symbols that have been seen so far and
+
+ align:start position:0%
+symbols that have been seen so far and
+ 
+
+ align:start position:0%
+symbols that have been seen so far and
+you want to keep updating
+
+ align:start position:0%
+you want to keep updating
+ 
+
+ align:start position:0%
+you want to keep updating
+that so one way to easily see what's
+
+ align:start position:0%
+that so one way to easily see what's
+ 
+
+ align:start position:0%
+that so one way to easily see what's
+going on is with a
+
+ align:start position:0%
+going on is with a
+ 
+
+ align:start position:0%
+going on is with a
+picture so up until now until you
+
+ align:start position:0%
+picture so up until now until you
+ 
+
+ align:start position:0%
+picture so up until now until you
+finished uh IUS one files let's say
+
+ align:start position:0%
+finished uh IUS one files let's say
+ 
+
+ align:start position:0%
+finished uh IUS one files let's say
+you've built up a set
+
+ align:start position:0%
+you've built up a set
+ 
+
+ align:start position:0%
+you've built up a set
+um U of all of the undefined symbols
+
+ align:start position:0%
+um U of all of the undefined symbols
+ 
+
+ align:start position:0%
+um U of all of the undefined symbols
+that have been encountered so
+
+ align:start position:0%
+that have been encountered so
+ 
+
+ align:start position:0%
+that have been encountered so
+far and likewise you have another set D
+
+ align:start position:0%
+far and likewise you have another set D
+ 
+
+ align:start position:0%
+far and likewise you have another set D
+of all of the symbols that have been
+
+ align:start position:0%
+of all of the symbols that have been
+ 
+
+ align:start position:0%
+of all of the symbols that have been
+defined so far that you've encountered
+
+ align:start position:0%
+defined so far that you've encountered
+ 
+
+ align:start position:0%
+defined so far that you've encountered
+and have been defined so far so D and U
+
+ align:start position:0%
+and have been defined so far so D and U
+ 
+
+ align:start position:0%
+and have been defined so far so D and U
+dynamically change as you go from left
+
+ align:start position:0%
+dynamically change as you go from left
+ 
+
+ align:start position:0%
+dynamically change as you go from left
+to right through the sequence of files
+
+ align:start position:0%
+to right through the sequence of files
+ 
+
+ align:start position:0%
+to right through the sequence of files
+now when you're on the I file there's a
+
+ align:start position:0%
+now when you're on the I file there's a
+ 
+
+ align:start position:0%
+now when you're on the I file there's a
+set of symbols that have been defined
+
+ align:start position:0%
+set of symbols that have been defined
+ 
+
+ align:start position:0%
+set of symbols that have been defined
+that are going to be defined in the I
+
+ align:start position:0%
+that are going to be defined in the I
+ 
+
+ align:start position:0%
+that are going to be defined in the I
+file and that set does not intersect
+
+ align:start position:0%
+file and that set does not intersect
+ 
+
+ align:start position:0%
+file and that set does not intersect
+with the set D because if it did then
+
+ align:start position:0%
+with the set D because if it did then
+ 
+
+ align:start position:0%
+with the set D because if it did then
+you have an overlapping defined symbol
+
+ align:start position:0%
+you have an overlapping defined symbol
+ 
+
+ align:start position:0%
+you have an overlapping defined symbol
+and that's an error so the interesting
+
+ align:start position:0%
+and that's an error so the interesting
+ 
+
+ align:start position:0%
+and that's an error so the interesting
+case is to look at this kind of an
+
+ align:start position:0%
+case is to look at this kind of an
+ 
+
+ align:start position:0%
+case is to look at this kind of an
+example where you have a set di of the
+
+ align:start position:0%
+example where you have a set di of the
+ 
+
+ align:start position:0%
+example where you have a set di of the
+symbols that were defined in the I
+
+ align:start position:0%
+symbols that were defined in the I
+ 
+
+ align:start position:0%
+symbols that were defined in the I
+file and likewise in the I file there
+
+ align:start position:0%
+file and likewise in the I file there
+ 
+
+ align:start position:0%
+file and likewise in the I file there
+are going to be a set of undefined
+
+ align:start position:0%
+are going to be a set of undefined
+ 
+
+ align:start position:0%
+are going to be a set of undefined
+symbols and clearly that set doesn't
+
+ align:start position:0%
+symbols and clearly that set doesn't
+ 
+
+ align:start position:0%
+symbols and clearly that set doesn't
+overlap with the set di because if it's
+
+ align:start position:0%
+overlap with the set di because if it's
+ 
+
+ align:start position:0%
+overlap with the set di because if it's
+undefined it can't be defined in the
+
+ align:start position:0%
+undefined it can't be defined in the
+ 
+
+ align:start position:0%
+undefined it can't be defined in the
+same file so that set in general looks
+
+ align:start position:0%
+same file so that set in general looks
+ 
+
+ align:start position:0%
+same file so that set in general looks
+something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this it has some symbols undefined in
+
+ align:start position:0%
+this it has some symbols undefined in
+ 
+
+ align:start position:0%
+this it has some symbols undefined in
+this object file that are also undefined
+
+ align:start position:0%
+this object file that are also undefined
+ 
+
+ align:start position:0%
+this object file that are also undefined
+previously
+
+ align:start position:0%
+previously
+ 
+
+ align:start position:0%
+previously
+some symbols that are undefined in this
+
+ align:start position:0%
+some symbols that are undefined in this
+ 
+
+ align:start position:0%
+some symbols that are undefined in this
+file that have been defined
+
+ align:start position:0%
+file that have been defined
+ 
+
+ align:start position:0%
+file that have been defined
+previously and some symbols that have
+
+ align:start position:0%
+previously and some symbols that have
+ 
+
+ align:start position:0%
+previously and some symbols that have
+been undefined here that you've really
+
+ align:start position:0%
+been undefined here that you've really
+ 
+
+ align:start position:0%
+been undefined here that you've really
+never seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before so you got to update two things
+
+ align:start position:0%
+before so you got to update two things
+ 
+
+ align:start position:0%
+before so you got to update two things
+so D gets updated pretty easily D just
+
+ align:start position:0%
+so D gets updated pretty easily D just
+ 
+
+ align:start position:0%
+so D gets updated pretty easily D just
+becomes D Union dii and if D
+
+ align:start position:0%
+becomes D Union dii and if D
+ 
+
+ align:start position:0%
+becomes D Union dii and if D
+intersection di is not null then you
+
+ align:start position:0%
+intersection di is not null then you
+ 
+
+ align:start position:0%
+intersection di is not null then you
+know there's an
+
+ align:start position:0%
+know there's an
+ 
+
+ align:start position:0%
+know there's an
+error and now you need to update U and
+
+ align:start position:0%
+error and now you need to update U and
+ 
+
+ align:start position:0%
+error and now you need to update U and
+there are many ways to do it that are
+
+ align:start position:0%
+there are many ways to do it that are
+ 
+
+ align:start position:0%
+there are many ways to do it that are
+more efficient than what we're going to
+
+ align:start position:0%
+more efficient than what we're going to
+ 
+
+ align:start position:0%
+more efficient than what we're going to
+write out but um it's pretty easy to see
+
+ align:start position:0%
+write out but um it's pretty easy to see
+ 
+
+ align:start position:0%
+write out but um it's pretty easy to see
+that you needs to get updated by
+
+ align:start position:0%
+that you needs to get updated by
+ 
+
+ align:start position:0%
+that you needs to get updated by
+unioning the current set with
+
+ align:start position:0%
+unioning the current set with
+ 
+
+ align:start position:0%
+unioning the current set with
+UI and so that kind of gives you this
+
+ align:start position:0%
+UI and so that kind of gives you this
+ 
+
+ align:start position:0%
+UI and so that kind of gives you this
+together with that but now you have to
+
+ align:start position:0%
+together with that but now you have to
+ 
+
+ align:start position:0%
+together with that but now you have to
+subtract out everything that's been
+
+ align:start position:0%
+subtract out everything that's been
+ 
+
+ align:start position:0%
+subtract out everything that's been
+defined already and since we updated D
+
+ align:start position:0%
+defined already and since we updated D
+ 
+
+ align:start position:0%
+defined already and since we updated D
+first we could do that very easily by
+
+ align:start position:0%
+first we could do that very easily by
+ 
+
+ align:start position:0%
+first we could do that very easily by
+just subtracting out the set of all
+
+ align:start position:0%
+just subtracting out the set of all
+ 
+
+ align:start position:0%
+just subtracting out the set of all
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+symbols and you run this through until
+
+ align:start position:0%
+symbols and you run this through until
+ 
+
+ align:start position:0%
+symbols and you run this through until
+the end and if you find that in the end
+
+ align:start position:0%
+the end and if you find that in the end
+ 
+
+ align:start position:0%
+the end and if you find that in the end
+U is not null then you know that um
+
+ align:start position:0%
+U is not null then you know that um
+ 
+
+ align:start position:0%
+U is not null then you know that um
+there's an undefined symbol so the
+
+ align:start position:0%
+there's an undefined symbol so the
+ 
+
+ align:start position:0%
+there's an undefined symbol so the
+linking doesn't actually work you can't
+
+ align:start position:0%
+linking doesn't actually work you can't
+ 
+
+ align:start position:0%
+linking doesn't actually work you can't
+produce an executable out of it with
+
+ align:start position:0%
+produce an executable out of it with
+ 
+
+ align:start position:0%
+produce an executable out of it with
+stat linking
+
+ align:start position:0%
+stat linking
+ 
+
+ align:start position:0%
+stat linking
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so when you do combine programs in
+
+ align:start position:0%
+okay so when you do combine programs in
+ 
+
+ align:start position:0%
+okay so when you do combine programs in
+this fashion to produce an
+
+ align:start position:0%
+this fashion to produce an
+ 
+
+ align:start position:0%
+this fashion to produce an
+executable there are all these different
+
+ align:start position:0%
+executable there are all these different
+ 
+
+ align:start position:0%
+executable there are all these different
+modules that have been brought together
+
+ align:start position:0%
+modules that have been brought together
+ 
+
+ align:start position:0%
+modules that have been brought together
+to run on um in an interpreter and you
+
+ align:start position:0%
+to run on um in an interpreter and you
+ 
+
+ align:start position:0%
+to run on um in an interpreter and you
+have to ask what kind of properties that
+
+ align:start position:0%
+have to ask what kind of properties that
+ 
+
+ align:start position:0%
+have to ask what kind of properties that
+program ends up having what kind of
+
+ align:start position:0%
+program ends up having what kind of
+ 
+
+ align:start position:0%
+program ends up having what kind of
+modularity do you get by combining these
+
+ align:start position:0%
+modularity do you get by combining these
+ 
+
+ align:start position:0%
+modularity do you get by combining these
+modules together in fashion it'll turn
+
+ align:start position:0%
+modules together in fashion it'll turn
+ 
+
+ align:start position:0%
+modules together in fashion it'll turn
+out that modularity is uh it's a form of
+
+ align:start position:0%
+out that modularity is uh it's a form of
+ 
+
+ align:start position:0%
+out that modularity is uh it's a form of
+modularity called
+
+ align:start position:0%
+modularity called
+ 
+
+ align:start position:0%
+modularity called
+soft modularity and to understand why
+
+ align:start position:0%
+soft modularity and to understand why
+ 
+
+ align:start position:0%
+soft modularity and to understand why
+you have to understand what the
+
+ align:start position:0%
+you have to understand what the
+ 
+
+ align:start position:0%
+you have to understand what the
+interfaces between the different modules
+
+ align:start position:0%
+interfaces between the different modules
+ 
+
+ align:start position:0%
+interfaces between the different modules
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like but basically when you look at a c
+
+ align:start position:0%
+like but basically when you look at a c
+ 
+
+ align:start position:0%
+like but basically when you look at a c
+program and we saw an example last time
+
+ align:start position:0%
+program and we saw an example last time
+ 
+
+ align:start position:0%
+program and we saw an example last time
+of how these modules work together um
+
+ align:start position:0%
+of how these modules work together um
+ 
+
+ align:start position:0%
+of how these modules work together um
+the different modules interact with one
+
+ align:start position:0%
+the different modules interact with one
+ 
+
+ align:start position:0%
+the different modules interact with one
+another through procedures and
+
+ align:start position:0%
+another through procedures and
+ 
+
+ align:start position:0%
+another through procedures and
+procedures between modules have
+
+ align:start position:0%
+procedures between modules have
+ 
+
+ align:start position:0%
+procedures between modules have
+something that I'll call a procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contract and really to understand the
+
+ align:start position:0%
+contract and really to understand the
+ 
+
+ align:start position:0%
+contract and really to understand the
+property of the modularity that you get
+
+ align:start position:0%
+property of the modularity that you get
+ 
+
+ align:start position:0%
+property of the modularity that you get
+from procedural contract we need to
+
+ align:start position:0%
+from procedural contract we need to
+ 
+
+ align:start position:0%
+from procedural contract we need to
+understand a little bit about what
+
+ align:start position:0%
+understand a little bit about what
+ 
+
+ align:start position:0%
+understand a little bit about what
+happens underneath the covers when um
+
+ align:start position:0%
+happens underneath the covers when um
+ 
+
+ align:start position:0%
+happens underneath the covers when um
+you know a caller of a procedure invokes
+
+ align:start position:0%
+you know a caller of a procedure invokes
+ 
+
+ align:start position:0%
+you know a caller of a procedure invokes
+a call E of a procedure and this is
+
+ align:start position:0%
+a call E of a procedure and this is
+ 
+
+ align:start position:0%
+a call E of a procedure and this is
+actually material
+
+ align:start position:0%
+actually material
+ 
+
+ align:start position:0%
+actually material
+from4 so if you um you know if you
+
+ align:start position:0%
+from4 so if you um you know if you
+ 
+
+ align:start position:0%
+from4 so if you um you know if you
+forgotten I'll refresh your memory a
+
+ align:start position:0%
+forgotten I'll refresh your memory a
+ 
+
+ align:start position:0%
+forgotten I'll refresh your memory a
+little bit about it
+
+ align:start position:0%
+little bit about it
+ 
+
+ align:start position:0%
+little bit about it
+um so very abstractly if you look at uh
+
+ align:start position:0%
+um so very abstractly if you look at uh
+ 
+
+ align:start position:0%
+um so very abstractly if you look at uh
+a computer you know it's got a processor
+
+ align:start position:0%
+a computer you know it's got a processor
+ 
+
+ align:start position:0%
+a computer you know it's got a processor
+in it that's
+
+ align:start position:0%
+in it that's
+ 
+
+ align:start position:0%
+in it that's
+running um that actually executes
+
+ align:start position:0%
+running um that actually executes
+ 
+
+ align:start position:0%
+running um that actually executes
+instructions and it has a chunk of
+
+ align:start position:0%
+instructions and it has a chunk of
+ 
+
+ align:start position:0%
+instructions and it has a chunk of
+memory and in that memory there's a
+
+ align:start position:0%
+memory and in that memory there's a
+ 
+
+ align:start position:0%
+memory and in that memory there's a
+portion of memory that um corresponds to
+
+ align:start position:0%
+portion of memory that um corresponds to
+ 
+
+ align:start position:0%
+portion of memory that um corresponds to
+the stack which is really where
+
+ align:start position:0%
+the stack which is really where
+ 
+
+ align:start position:0%
+the stack which is really where
+procedures um the interesting stuff with
+
+ align:start position:0%
+procedures um the interesting stuff with
+ 
+
+ align:start position:0%
+procedures um the interesting stuff with
+procedures gets uh implemented and we
+
+ align:start position:0%
+procedures gets uh implemented and we
+ 
+
+ align:start position:0%
+procedures gets uh implemented and we
+also have a bunch of registers so you
+
+ align:start position:0%
+also have a bunch of registers so you
+ 
+
+ align:start position:0%
+also have a bunch of registers so you
+know inside the processor and um you
+
+ align:start position:0%
+know inside the processor and um you
+ 
+
+ align:start position:0%
+know inside the processor and um you
+have a special variable here called the
+
+ align:start position:0%
+have a special variable here called the
+ 
+
+ align:start position:0%
+have a special variable here called the
+stack pointer which keeps track of um
+
+ align:start position:0%
+stack pointer which keeps track of um
+ 
+
+ align:start position:0%
+stack pointer which keeps track of um
+where the current head of the stack is
+
+ align:start position:0%
+where the current head of the stack is
+ 
+
+ align:start position:0%
+where the current head of the stack is
+that you can then start pulling um
+
+ align:start position:0%
+that you can then start pulling um
+ 
+
+ align:start position:0%
+that you can then start pulling um
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+off the journey plan is is a caller the
+
+ align:start position:0%
+off the journey plan is is a caller the
+ 
+
+ align:start position:0%
+off the journey plan is is a caller the
+caller and the colleag interact with one
+
+ align:start position:0%
+caller and the colleag interact with one
+ 
+
+ align:start position:0%
+caller and the colleag interact with one
+another by means
+
+ align:start position:0%
+another by means
+ 
+
+ align:start position:0%
+another by means
+of so when a caller wants to invoke um
+
+ align:start position:0%
+of so when a caller wants to invoke um
+ 
+
+ align:start position:0%
+of so when a caller wants to invoke um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+colle what it does is it takes the
+
+ align:start position:0%
+colle what it does is it takes the
+ 
+
+ align:start position:0%
+colle what it does is it takes the
+arguments to the procedure and pushes
+
+ align:start position:0%
+arguments to the procedure and pushes
+ 
+
+ align:start position:0%
+arguments to the procedure and pushes
+them onto the stack one after another
+
+ align:start position:0%
+them onto the stack one after another
+ 
+
+ align:start position:0%
+them onto the stack one after another
+then the last thing it does is to tell
+
+ align:start position:0%
+then the last thing it does is to tell
+ 
+
+ align:start position:0%
+then the last thing it does is to tell
+the coli where it should return control
+
+ align:start position:0%
+the coli where it should return control
+ 
+
+ align:start position:0%
+the coli where it should return control
+after the procedure function has
+
+ align:start position:0%
+after the procedure function has
+ 
+
+ align:start position:0%
+after the procedure function has
+actually been executed and that's the
+
+ align:start position:0%
+actually been executed and that's the
+ 
+
+ align:start position:0%
+actually been executed and that's the
+the last thing that's pushed on top of
+
+ align:start position:0%
+the last thing that's pushed on top of
+ 
+
+ align:start position:0%
+the last thing that's pushed on top of
+the stack is the is the
+
+ align:start position:0%
+the stack is the is the
+ 
+
+ align:start position:0%
+the stack is the is the
+uh so then after it does that the caller
+
+ align:start position:0%
+uh so then after it does that the caller
+ 
+
+ align:start position:0%
+uh so then after it does that the caller
+then jumps to a location where the
+
+ align:start position:0%
+then jumps to a location where the
+ 
+
+ align:start position:0%
+then jumps to a location where the
+coli's module is located and then
+
+ align:start position:0%
+coli's module is located and then
+ 
+
+ align:start position:0%
+coli's module is located and then
+control passes to the
+
+ align:start position:0%
+control passes to the
+ 
+
+ align:start position:0%
+control passes to the
+coli what the collie then does is it
+
+ align:start position:0%
+coli what the collie then does is it
+ 
+
+ align:start position:0%
+coli what the collie then does is it
+pops you know it finds out what the
+
+ align:start position:0%
+pops you know it finds out what the
+ 
+
+ align:start position:0%
+pops you know it finds out what the
+return address is pops the arguments one
+
+ align:start position:0%
+return address is pops the arguments one
+ 
+
+ align:start position:0%
+return address is pops the arguments one
+after another and then goes ahead and
+
+ align:start position:0%
+after another and then goes ahead and
+ 
+
+ align:start position:0%
+after another and then goes ahead and
+runs the function and then at the end of
+
+ align:start position:0%
+runs the function and then at the end of
+ 
+
+ align:start position:0%
+runs the function and then at the end of
+that it looks at the return address and
+
+ align:start position:0%
+that it looks at the return address and
+ 
+
+ align:start position:0%
+that it looks at the return address and
+pass control back and before it does
+
+ align:start position:0%
+pass control back and before it does
+ 
+
+ align:start position:0%
+pass control back and before it does
+that it actually puts the answer and by
+
+ align:start position:0%
+that it actually puts the answer and by
+ 
+
+ align:start position:0%
+that it actually puts the answer and by
+convention and you know let's assume
+
+ align:start position:0%
+convention and you know let's assume
+ 
+
+ align:start position:0%
+convention and you know let's assume
+that it puts the answer in some in a
+
+ align:start position:0%
+that it puts the answer in some in a
+ 
+
+ align:start position:0%
+that it puts the answer in some in a
+special register and that's part of the
+
+ align:start position:0%
+special register and that's part of the
+ 
+
+ align:start position:0%
+special register and that's part of the
+contract as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well and um once the caller gets control
+
+ align:start position:0%
+well and um once the caller gets control
+ 
+
+ align:start position:0%
+well and um once the caller gets control
+back from the Ki it can proceed as
+
+ align:start position:0%
+back from the Ki it can proceed as
+ 
+
+ align:start position:0%
+back from the Ki it can proceed as
+before now the important thing about
+
+ align:start position:0%
+before now the important thing about
+ 
+
+ align:start position:0%
+before now the important thing about
+this way of interacting between caller
+
+ align:start position:0%
+this way of interacting between caller
+ 
+
+ align:start position:0%
+this way of interacting between caller
+and Ki with procedures stack is that
+
+ align:start position:0%
+and Ki with procedures stack is that
+ 
+
+ align:start position:0%
+and Ki with procedures stack is that
+this contract has to obey an invariant
+
+ align:start position:0%
+this contract has to obey an invariant
+ 
+
+ align:start position:0%
+this contract has to obey an invariant
+or a dis discipline called the stack
+
+ align:start position:0%
+or a dis discipline called the stack
+ 
+
+ align:start position:0%
+or a dis discipline called the stack
+discipline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the essence of the stack discipline
+
+ align:start position:0%
+and the essence of the stack discipline
+ 
+
+ align:start position:0%
+and the essence of the stack discipline
+is that the colleag should leave the
+
+ align:start position:0%
+is that the colleag should leave the
+ 
+
+ align:start position:0%
+is that the colleag should leave the
+stack exactly the way the caller left it
+
+ align:start position:0%
+stack exactly the way the caller left it
+ 
+
+ align:start position:0%
+stack exactly the way the caller left it
+when it invoked the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+colleag so which means that the caller
+
+ align:start position:0%
+colleag so which means that the caller
+ 
+
+ align:start position:0%
+colleag so which means that the caller
+had set up a bunch of arguments on it
+
+ align:start position:0%
+had set up a bunch of arguments on it
+ 
+
+ align:start position:0%
+had set up a bunch of arguments on it
+and put the return um address on it um
+
+ align:start position:0%
+and put the return um address on it um
+ 
+
+ align:start position:0%
+and put the return um address on it um
+the colle should really leave things as
+
+ align:start position:0%
+the colle should really leave things as
+ 
+
+ align:start position:0%
+the colle should really leave things as
+is and in fact the col is not allowed to
+
+ align:start position:0%
+is and in fact the col is not allowed to
+ 
+
+ align:start position:0%
+is and in fact the col is not allowed to
+touch anything it should leave
+
+ align:start position:0%
+touch anything it should leave
+ 
+
+ align:start position:0%
+touch anything it should leave
+everything as is pretty much except for
+
+ align:start position:0%
+everything as is pretty much except for
+ 
+
+ align:start position:0%
+everything as is pretty much except for
+the register that has the answer and as
+
+ align:start position:0%
+the register that has the answer and as
+ 
+
+ align:start position:0%
+the register that has the answer and as
+long as this discipline is maintained
+
+ align:start position:0%
+long as this discipline is maintained
+ 
+
+ align:start position:0%
+long as this discipline is maintained
+and that invariant is maintained across
+
+ align:start position:0%
+and that invariant is maintained across
+ 
+
+ align:start position:0%
+and that invariant is maintained across
+procedure invocations this model of
+
+ align:start position:0%
+procedure invocations this model of
+ 
+
+ align:start position:0%
+procedure invocations this model of
+using Stacks is extremely powerful you
+
+ align:start position:0%
+using Stacks is extremely powerful you
+ 
+
+ align:start position:0%
+using Stacks is extremely powerful you
+could Implement all sorts of procedures
+
+ align:start position:0%
+could Implement all sorts of procedures
+ 
+
+ align:start position:0%
+could Implement all sorts of procedures
+nested procedure I mean recursive
+
+ align:start position:0%
+nested procedure I mean recursive
+ 
+
+ align:start position:0%
+nested procedure I mean recursive
+procedures mutually recursive procedures
+
+ align:start position:0%
+procedures mutually recursive procedures
+ 
+
+ align:start position:0%
+procedures mutually recursive procedures
+and so on because um you know each of
+
+ align:start position:0%
+and so on because um you know each of
+ 
+
+ align:start position:0%
+and so on because um you know each of
+these invocations of a procedure has a
+
+ align:start position:0%
+these invocations of a procedure has a
+ 
+
+ align:start position:0%
+these invocations of a procedure has a
+certain portion of the stack um that
+
+ align:start position:0%
+certain portion of the stack um that
+ 
+
+ align:start position:0%
+certain portion of the stack um that
+corresponds to an activation frame and
+
+ align:start position:0%
+corresponds to an activation frame and
+ 
+
+ align:start position:0%
+corresponds to an activation frame and
+as long as this discipline is maintained
+
+ align:start position:0%
+as long as this discipline is maintained
+ 
+
+ align:start position:0%
+as long as this discipline is maintained
+you can be quite complicated you can do
+
+ align:start position:0%
+you can be quite complicated you can do
+ 
+
+ align:start position:0%
+you can be quite complicated you can do
+quite complicated and interesting
+
+ align:start position:0%
+quite complicated and interesting
+ 
+
+ align:start position:0%
+quite complicated and interesting
+combinations of
+
+ align:start position:0%
+combinations of
+ 
+
+ align:start position:0%
+combinations of
+modules but the problem is that
+
+ align:start position:0%
+modules but the problem is that
+ 
+
+ align:start position:0%
+modules but the problem is that
+that mod it depends crucially on the
+
+ align:start position:0%
+that mod it depends crucially on the
+ 
+
+ align:start position:0%
+that mod it depends crucially on the
+stack discipline being maintained and
+
+ align:start position:0%
+stack discipline being maintained and
+ 
+
+ align:start position:0%
+stack discipline being maintained and
+any violation of it CIF can disrupt the
+
+ align:start position:0%
+any violation of it CIF can disrupt the
+ 
+
+ align:start position:0%
+any violation of it CIF can disrupt the
+collar and bring it
+
+ align:start position:0%
+collar and bring it
+ 
+
+ align:start position:0%
+collar and bring it
+down there are many ways in which this
+
+ align:start position:0%
+down there are many ways in which this
+ 
+
+ align:start position:0%
+down there are many ways in which this
+this discipline could be violated and
+
+ align:start position:0%
+this discipline could be violated and
+ 
+
+ align:start position:0%
+this discipline could be violated and
+the easiest one uh is that there's some
+
+ align:start position:0%
+the easiest one uh is that there's some
+ 
+
+ align:start position:0%
+the easiest one uh is that there's some
+error or bug in the collie and the
+
+ align:start position:0%
+error or bug in the collie and the
+ 
+
+ align:start position:0%
+error or bug in the collie and the
+collie corrupts the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stack or the collie corrupts the stack
+
+ align:start position:0%
+stack or the collie corrupts the stack
+ 
+
+ align:start position:0%
+stack or the collie corrupts the stack
+pointer so it actually returns control
+
+ align:start position:0%
+pointer so it actually returns control
+ 
+
+ align:start position:0%
+pointer so it actually returns control
+but the stack pointer points somewhere
+
+ align:start position:0%
+but the stack pointer points somewhere
+ 
+
+ align:start position:0%
+but the stack pointer points somewhere
+else else and um you know some bad
+
+ align:start position:0%
+else else and um you know some bad
+ 
+
+ align:start position:0%
+else else and um you know some bad
+instruction runs or you know you have
+
+ align:start position:0%
+instruction runs or you know you have
+ 
+
+ align:start position:0%
+instruction runs or you know you have
+you have a
+
+ align:start position:0%
+you have a
+ 
+
+ align:start position:0%
+you have a
+problem now another problem is that the
+
+ align:start position:0%
+problem now another problem is that the
+ 
+
+ align:start position:0%
+problem now another problem is that the
+collie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crashes for instance there's a divide by
+
+ align:start position:0%
+crashes for instance there's a divide by
+ 
+
+ align:start position:0%
+crashes for instance there's a divide by
+zero or there's some other violation
+
+ align:start position:0%
+zero or there's some other violation
+ 
+
+ align:start position:0%
+zero or there's some other violation
+that causes the col to crash and then
+
+ align:start position:0%
+that causes the col to crash and then
+ 
+
+ align:start position:0%
+that causes the col to crash and then
+the CER comes coming down you know comes
+
+ align:start position:0%
+the CER comes coming down you know comes
+ 
+
+ align:start position:0%
+the CER comes coming down you know comes
+crashing down as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a bunch of other reasons but
+
+ align:start position:0%
+and there's a bunch of other reasons but
+ 
+
+ align:start position:0%
+and there's a bunch of other reasons but
+all of them have to do with the stack
+
+ align:start position:0%
+all of them have to do with the stack
+ 
+
+ align:start position:0%
+all of them have to do with the stack
+discipline being violated or with the
+
+ align:start position:0%
+discipline being violated or with the
+ 
+
+ align:start position:0%
+discipline being violated or with the
+collie crashing and control never
+
+ align:start position:0%
+collie crashing and control never
+ 
+
+ align:start position:0%
+collie crashing and control never
+returning to the Coller um which means
+
+ align:start position:0%
+returning to the Coller um which means
+ 
+
+ align:start position:0%
+returning to the Coller um which means
+that the caller and the collie share
+
+ align:start position:0%
+that the caller and the collie share
+ 
+
+ align:start position:0%
+that the caller and the collie share
+fate you know if something bad happens
+
+ align:start position:0%
+fate you know if something bad happens
+ 
+
+ align:start position:0%
+fate you know if something bad happens
+to the person who's called sorry to
+
+ align:start position:0%
+to the person who's called sorry to
+ 
+
+ align:start position:0%
+to the person who's called sorry to
+which is called the collie then the
+
+ align:start position:0%
+which is called the collie then the
+ 
+
+ align:start position:0%
+which is called the collie then the
+caller struggles as well and doesn't
+
+ align:start position:0%
+caller struggles as well and doesn't
+ 
+
+ align:start position:0%
+caller struggles as well and doesn't
+really isn't able to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continue so Cally this is referred to at
+
+ align:start position:0%
+continue so Cally this is referred to at
+ 
+
+ align:start position:0%
+continue so Cally this is referred to at
+as fate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sharing and the resulting modularity is
+
+ align:start position:0%
+sharing and the resulting modularity is
+ 
+
+ align:start position:0%
+sharing and the resulting modularity is
+soft because any fault or error in the
+
+ align:start position:0%
+soft because any fault or error in the
+ 
+
+ align:start position:0%
+soft because any fault or error in the
+affects the collar the collar isn't um
+
+ align:start position:0%
+affects the collar the collar isn't um
+ 
+
+ align:start position:0%
+affects the collar the collar isn't um
+there isn't any kind of a firewall where
+
+ align:start position:0%
+there isn't any kind of a firewall where
+ 
+
+ align:start position:0%
+there isn't any kind of a firewall where
+errors in the coli are you know are
+
+ align:start position:0%
+errors in the coli are you know are
+ 
+
+ align:start position:0%
+errors in the coli are you know are
+insulated from errors in the collar
+
+ align:start position:0%
+insulated from errors in the collar
+ 
+
+ align:start position:0%
+insulated from errors in the collar
+there's sort of no shielding between the
+
+ align:start position:0%
+there's sort of no shielding between the
+ 
+
+ align:start position:0%
+there's sort of no shielding between the
+collar and Ki and why am I why is this
+
+ align:start position:0%
+collar and Ki and why am I why is this
+ 
+
+ align:start position:0%
+collar and Ki and why am I why is this
+thing going like all right um so there's
+
+ align:start position:0%
+thing going like all right um so there's
+ 
+
+ align:start position:0%
+thing going like all right um so there's
+no insulation between caller and Ki and
+
+ align:start position:0%
+no insulation between caller and Ki and
+ 
+
+ align:start position:0%
+no insulation between caller and Ki and
+um the resulting modularity is not as um
+
+ align:start position:0%
+um the resulting modularity is not as um
+ 
+
+ align:start position:0%
+um the resulting modularity is not as um
+hard as we would like it to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be so this is the problem uh we'd like
+
+ align:start position:0%
+be so this is the problem uh we'd like
+ 
+
+ align:start position:0%
+be so this is the problem uh we'd like
+to solve today and the first solution
+
+ align:start position:0%
+to solve today and the first solution
+ 
+
+ align:start position:0%
+to solve today and the first solution
+we're going to um discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a way of organizing callers and Coles
+
+ align:start position:0%
+is a way of organizing callers and Coles
+ 
+
+ align:start position:0%
+is a way of organizing callers and Coles
+into an organization called client
+
+ align:start position:0%
+into an organization called client
+ 
+
+ align:start position:0%
+into an organization called client
+service organization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the main idea is going to actually
+
+ align:start position:0%
+and the main idea is going to actually
+ 
+
+ align:start position:0%
+and the main idea is going to actually
+involve a different abstraction for by
+
+ align:start position:0%
+involve a different abstraction for by
+ 
+
+ align:start position:0%
+involve a different abstraction for by
+which callers and colleages communicate
+
+ align:start position:0%
+which callers and colleages communicate
+ 
+
+ align:start position:0%
+which callers and colleages communicate
+with one another from the abstractions
+
+ align:start position:0%
+with one another from the abstractions
+ 
+
+ align:start position:0%
+with one another from the abstractions
+we've seen already we've already seen
+
+ align:start position:0%
+we've seen already we've already seen
+ 
+
+ align:start position:0%
+we've seen already we've already seen
+the memory abstraction where um you
+
+ align:start position:0%
+the memory abstraction where um you
+ 
+
+ align:start position:0%
+the memory abstraction where um you
+could read write values to a name and
+
+ align:start position:0%
+could read write values to a name and
+ 
+
+ align:start position:0%
+could read write values to a name and
+another person could read from it and
+
+ align:start position:0%
+another person could read from it and
+ 
+
+ align:start position:0%
+another person could read from it and
+we've already seen the interpreted
+
+ align:start position:0%
+we've already seen the interpreted
+ 
+
+ align:start position:0%
+we've already seen the interpreted
+abstraction it'll turn out we're going
+
+ align:start position:0%
+abstraction it'll turn out we're going
+ 
+
+ align:start position:0%
+abstraction it'll turn out we're going
+to use a slightly a different
+
+ align:start position:0%
+to use a slightly a different
+ 
+
+ align:start position:0%
+to use a slightly a different
+abstraction communication path
+
+ align:start position:0%
+abstraction communication path
+ 
+
+ align:start position:0%
+abstraction communication path
+abstraction to implement um The Client
+
+ align:start position:0%
+abstraction to implement um The Client
+ 
+
+ align:start position:0%
+abstraction to implement um The Client
+Service
+
+ align:start position:0%
+Service
+ 
+
+ align:start position:0%
+Service
+organization and the idea is the
+
+ align:start position:0%
+organization and the idea is the
+ 
+
+ align:start position:0%
+organization and the idea is the
+following your program is going to be
+
+ align:start position:0%
+following your program is going to be
+ 
+
+ align:start position:0%
+following your program is going to be
+decomposed um into clients and services
+
+ align:start position:0%
+decomposed um into clients and services
+ 
+
+ align:start position:0%
+decomposed um into clients and services
+and you might have many clients and many
+
+ align:start position:0%
+and you might have many clients and many
+ 
+
+ align:start position:0%
+and you might have many clients and many
+services and you know you could have
+
+ align:start position:0%
+services and you know you could have
+ 
+
+ align:start position:0%
+services and you know you could have
+client which is a client of one service
+
+ align:start position:0%
+client which is a client of one service
+ 
+
+ align:start position:0%
+client which is a client of one service
+and a service turn is a client of yet
+
+ align:start position:0%
+and a service turn is a client of yet
+ 
+
+ align:start position:0%
+and a service turn is a client of yet
+another service Cascade things um like
+
+ align:start position:0%
+another service Cascade things um like
+ 
+
+ align:start position:0%
+another service Cascade things um like
+that but any pairwise interaction is
+
+ align:start position:0%
+that but any pairwise interaction is
+ 
+
+ align:start position:0%
+that but any pairwise interaction is
+going to be between a client and a
+
+ align:start position:0%
+going to be between a client and a
+ 
+
+ align:start position:0%
+going to be between a client and a
+service and think of you know mapping
+
+ align:start position:0%
+service and think of you know mapping
+ 
+
+ align:start position:0%
+service and think of you know mapping
+that example onto here think of the uh
+
+ align:start position:0%
+that example onto here think of the uh
+ 
+
+ align:start position:0%
+that example onto here think of the uh
+Coli for example being the service and
+
+ align:start position:0%
+Coli for example being the service and
+ 
+
+ align:start position:0%
+Coli for example being the service and
+the caller being the client so the
+
+ align:start position:0%
+the caller being the client so the
+ 
+
+ align:start position:0%
+the caller being the client so the
+caller wants some work done so it's the
+
+ align:start position:0%
+caller wants some work done so it's the
+ 
+
+ align:start position:0%
+caller wants some work done so it's the
+client and it invokes the service the
+
+ align:start position:0%
+client and it invokes the service the
+ 
+
+ align:start position:0%
+client and it invokes the service the
+colleague to get that work
+
+ align:start position:0%
+colleague to get that work
+ 
+
+ align:start position:0%
+colleague to get that work
+done and the plan is going to be that
+
+ align:start position:0%
+done and the plan is going to be that
+ 
+
+ align:start position:0%
+done and the plan is going to be that
+the client and the service are going to
+
+ align:start position:0%
+the client and the service are going to
+ 
+
+ align:start position:0%
+the client and the service are going to
+run on different computers physically
+
+ align:start position:0%
+run on different computers physically
+ 
+
+ align:start position:0%
+run on different computers physically
+different computers and we're going to
+
+ align:start position:0%
+different computers and we're going to
+ 
+
+ align:start position:0%
+different computers and we're going to
+connect the computers up with a
+
+ align:start position:0%
+connect the computers up with a
+ 
+
+ align:start position:0%
+connect the computers up with a
+wire and the idea is the moment you do
+
+ align:start position:0%
+wire and the idea is the moment you do
+ 
+
+ align:start position:0%
+wire and the idea is the moment you do
+that um the crash of a call E doesn't
+
+ align:start position:0%
+that um the crash of a call E doesn't
+ 
+
+ align:start position:0%
+that um the crash of a call E doesn't
+actually bring the caller coming down
+
+ align:start position:0%
+actually bring the caller coming down
+ 
+
+ align:start position:0%
+actually bring the caller coming down
+because it's running on a completely
+
+ align:start position:0%
+because it's running on a completely
+ 
+
+ align:start position:0%
+because it's running on a completely
+different processor the stack is not
+
+ align:start position:0%
+different processor the stack is not
+ 
+
+ align:start position:0%
+different processor the stack is not
+shared the memory is not shared um you
+
+ align:start position:0%
+shared the memory is not shared um you
+ 
+
+ align:start position:0%
+shared the memory is not shared um you
+know the stack pointers are not shared
+
+ align:start position:0%
+know the stack pointers are not shared
+ 
+
+ align:start position:0%
+know the stack pointers are not shared
+there's really no
+
+ align:start position:0%
+there's really no
+ 
+
+ align:start position:0%
+there's really no
+problem with regard to col crash
+
+ align:start position:0%
+problem with regard to col crash
+ 
+
+ align:start position:0%
+problem with regard to col crash
+bringing the callar
+
+ align:start position:0%
+bringing the callar
+ 
+
+ align:start position:0%
+bringing the callar
+down of course we now need a way by
+
+ align:start position:0%
+down of course we now need a way by
+ 
+
+ align:start position:0%
+down of course we now need a way by
+which the client can communicate its
+
+ align:start position:0%
+which the client can communicate its
+ 
+
+ align:start position:0%
+which the client can communicate its
+arguments to the service and the service
+
+ align:start position:0%
+arguments to the service and the service
+ 
+
+ align:start position:0%
+arguments to the service and the service
+can communicate its arguments back to
+
+ align:start position:0%
+can communicate its arguments back to
+ 
+
+ align:start position:0%
+can communicate its arguments back to
+the client previously we did the first
+
+ align:start position:0%
+the client previously we did the first
+ 
+
+ align:start position:0%
+the client previously we did the first
+one the arguments were communicated by
+
+ align:start position:0%
+one the arguments were communicated by
+ 
+
+ align:start position:0%
+one the arguments were communicated by
+putting them on the Shar on the on the
+
+ align:start position:0%
+putting them on the Shar on the on the
+ 
+
+ align:start position:0%
+putting them on the Shar on the on the
+memory using memory on the stack and
+
+ align:start position:0%
+memory using memory on the stack and
+ 
+
+ align:start position:0%
+memory using memory on the stack and
+um the answers were coming back to us
+
+ align:start position:0%
+um the answers were coming back to us
+ 
+
+ align:start position:0%
+um the answers were coming back to us
+with from register we don't have that
+
+ align:start position:0%
+with from register we don't have that
+ 
+
+ align:start position:0%
+with from register we don't have that
+shared State anymore so we're going to
+
+ align:start position:0%
+shared State anymore so we're going to
+ 
+
+ align:start position:0%
+shared State anymore so we're going to
+have to implement that um using messages
+
+ align:start position:0%
+have to implement that um using messages
+ 
+
+ align:start position:0%
+have to implement that um using messages
+and we're going to take these messages
+
+ align:start position:0%
+and we're going to take these messages
+ 
+
+ align:start position:0%
+and we're going to take these messages
+use the communication path abstraction
+
+ align:start position:0%
+use the communication path abstraction
+ 
+
+ align:start position:0%
+use the communication path abstraction
+and send messages from the client to the
+
+ align:start position:0%
+and send messages from the client to the
+ 
+
+ align:start position:0%
+and send messages from the client to the
+service so imagine that time flows down
+
+ align:start position:0%
+service so imagine that time flows down
+ 
+
+ align:start position:0%
+service so imagine that time flows down
+downwards starting from when the client
+
+ align:start position:0%
+downwards starting from when the client
+ 
+
+ align:start position:0%
+downwards starting from when the client
+invokes the
+
+ align:start position:0%
+invokes the
+ 
+
+ align:start position:0%
+invokes the
+service you know a message is sent from
+
+ align:start position:0%
+service you know a message is sent from
+ 
+
+ align:start position:0%
+service you know a message is sent from
+this C sends a message to the service
+
+ align:start position:0%
+this C sends a message to the service
+ 
+
+ align:start position:0%
+this C sends a message to the service
+saying you know here's all the arguments
+
+ align:start position:0%
+saying you know here's all the arguments
+ 
+
+ align:start position:0%
+saying you know here's all the arguments
+and here's the procedure that I want you
+
+ align:start position:0%
+and here's the procedure that I want you
+ 
+
+ align:start position:0%
+and here's the procedure that I want you
+to run and it takes that information up
+
+ align:start position:0%
+to run and it takes that information up
+ 
+
+ align:start position:0%
+to run and it takes that information up
+somehow packages it up into a message
+
+ align:start position:0%
+somehow packages it up into a message
+ 
+
+ align:start position:0%
+somehow packages it up into a message
+and call send okay and the assumption is
+
+ align:start position:0%
+and call send okay and the assumption is
+ 
+
+ align:start position:0%
+and call send okay and the assumption is
+that the client somehow already knows
+
+ align:start position:0%
+that the client somehow already knows
+ 
+
+ align:start position:0%
+that the client somehow already knows
+something about the name of the service
+
+ align:start position:0%
+something about the name of the service
+ 
+
+ align:start position:0%
+something about the name of the service
+or the location of the service um you
+
+ align:start position:0%
+or the location of the service um you
+ 
+
+ align:start position:0%
+or the location of the service um you
+know that's outside of the scope of the
+
+ align:start position:0%
+know that's outside of the scope of the
+ 
+
+ align:start position:0%
+know that's outside of the scope of the
+current discussion um let's pretend
+
+ align:start position:0%
+current discussion um let's pretend
+ 
+
+ align:start position:0%
+current discussion um let's pretend
+somebody tells you that here's where the
+
+ align:start position:0%
+somebody tells you that here's where the
+ 
+
+ align:start position:0%
+somebody tells you that here's where the
+service is running that can you know run
+
+ align:start position:0%
+service is running that can you know run
+ 
+
+ align:start position:0%
+service is running that can you know run
+this function for you so takes the take
+
+ align:start position:0%
+this function for you so takes the take
+ 
+
+ align:start position:0%
+this function for you so takes the take
+the arguments and the name of the
+
+ align:start position:0%
+the arguments and the name of the
+ 
+
+ align:start position:0%
+the arguments and the name of the
+procedure packages it up to a message
+
+ align:start position:0%
+procedure packages it up to a message
+ 
+
+ align:start position:0%
+procedure packages it up to a message
+and sends it across when the service
+
+ align:start position:0%
+and sends it across when the service
+ 
+
+ align:start position:0%
+and sends it across when the service
+gets the message it validates the
+
+ align:start position:0%
+gets the message it validates the
+ 
+
+ align:start position:0%
+gets the message it validates the
+message to make sure that it's the right
+
+ align:start position:0%
+message to make sure that it's the right
+ 
+
+ align:start position:0%
+message to make sure that it's the right
+sizes and you know it's not too big and
+
+ align:start position:0%
+sizes and you know it's not too big and
+ 
+
+ align:start position:0%
+sizes and you know it's not too big and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+on and then it takes this message and
+
+ align:start position:0%
+on and then it takes this message and
+ 
+
+ align:start position:0%
+on and then it takes this message and
+then does some processing on that
+
+ align:start position:0%
+then does some processing on that
+ 
+
+ align:start position:0%
+then does some processing on that
+message the technical term for it is
+
+ align:start position:0%
+message the technical term for it is
+ 
+
+ align:start position:0%
+message the technical term for it is
+going to be called unmarshaling because
+
+ align:start position:0%
+going to be called unmarshaling because
+ 
+
+ align:start position:0%
+going to be called unmarshaling because
+when we took these arguments and put
+
+ align:start position:0%
+when we took these arguments and put
+ 
+
+ align:start position:0%
+when we took these arguments and put
+into a message that procedure that
+
+ align:start position:0%
+into a message that procedure that
+ 
+
+ align:start position:0%
+into a message that procedure that
+process is called marshalling uh the
+
+ align:start position:0%
+process is called marshalling uh the
+ 
+
+ align:start position:0%
+process is called marshalling uh the
+service is going to unmarshal this
+
+ align:start position:0%
+service is going to unmarshal this
+ 
+
+ align:start position:0%
+service is going to unmarshal this
+message and obtain the actual arguments
+
+ align:start position:0%
+message and obtain the actual arguments
+ 
+
+ align:start position:0%
+message and obtain the actual arguments
+in the name of the procedure and then
+
+ align:start position:0%
+in the name of the procedure and then
+ 
+
+ align:start position:0%
+in the name of the procedure and then
+it's going to run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I don't know if it's one L or two
+
+ align:start position:0%
+it I don't know if it's one L or two
+ 
+
+ align:start position:0%
+it I don't know if it's one L or two
+L's non Marshal and then it's going to
+
+ align:start position:0%
+L's non Marshal and then it's going to
+ 
+
+ align:start position:0%
+L's non Marshal and then it's going to
+run the procedure that's named here it's
+
+ align:start position:0%
+run the procedure that's named here it's
+ 
+
+ align:start position:0%
+run the procedure that's named here it's
+going to find the answer and then when
+
+ align:start position:0%
+going to find the answer and then when
+ 
+
+ align:start position:0%
+going to find the answer and then when
+it gets the answer it does the same
+
+ align:start position:0%
+it gets the answer it does the same
+ 
+
+ align:start position:0%
+it gets the answer it does the same
+thing back it puts it back in a message
+
+ align:start position:0%
+thing back it puts it back in a message
+ 
+
+ align:start position:0%
+thing back it puts it back in a message
+and sends it across to the client and
+
+ align:start position:0%
+and sends it across to the client and
+ 
+
+ align:start position:0%
+and sends it across to the client and
+now the client's waiting for this
+
+ align:start position:0%
+now the client's waiting for this
+ 
+
+ align:start position:0%
+now the client's waiting for this
+message because it had sent off this um
+
+ align:start position:0%
+message because it had sent off this um
+ 
+
+ align:start position:0%
+message because it had sent off this um
+message to the service to run this thing
+
+ align:start position:0%
+message to the service to run this thing
+ 
+
+ align:start position:0%
+message to the service to run this thing
+uh it gets this answer back it does the
+
+ align:start position:0%
+uh it gets this answer back it does the
+ 
+
+ align:start position:0%
+uh it gets this answer back it does the
+same thing it you know takes the message
+
+ align:start position:0%
+same thing it you know takes the message
+ 
+
+ align:start position:0%
+same thing it you know takes the message
+and then it recovers the answer from it
+
+ align:start position:0%
+and then it recovers the answer from it
+ 
+
+ align:start position:0%
+and then it recovers the answer from it
+and then it runs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continues so this is the basic idea in
+
+ align:start position:0%
+continues so this is the basic idea in
+ 
+
+ align:start position:0%
+continues so this is the basic idea in
+client server
+
+ align:start position:0%
+client server
+ 
+
+ align:start position:0%
+client server
+organization and the way in which we
+
+ align:start position:0%
+organization and the way in which we
+ 
+
+ align:start position:0%
+organization and the way in which we
+solve this problem is that these two
+
+ align:start position:0%
+solve this problem is that these two
+ 
+
+ align:start position:0%
+solve this problem is that these two
+problems are solved because the colleag
+
+ align:start position:0%
+problems are solved because the colleag
+ 
+
+ align:start position:0%
+problems are solved because the colleag
+can't really corrupt the stack or the
+
+ align:start position:0%
+can't really corrupt the stack or the
+ 
+
+ align:start position:0%
+can't really corrupt the stack or the
+stack pointer or anything else that in
+
+ align:start position:0%
+stack pointer or anything else that in
+ 
+
+ align:start position:0%
+stack pointer or anything else that in
+this model would have affected the
+
+ align:start position:0%
+this model would have affected the
+ 
+
+ align:start position:0%
+this model would have affected the
+caller and because we put them two
+
+ align:start position:0%
+caller and because we put them two
+ 
+
+ align:start position:0%
+caller and because we put them two
+physically different computers and
+
+ align:start position:0%
+physically different computers and
+ 
+
+ align:start position:0%
+physically different computers and
+hooked them up with a you know let's say
+
+ align:start position:0%
+hooked them up with a you know let's say
+ 
+
+ align:start position:0%
+hooked them up with a you know let's say
+wire um the service crashing does not
+
+ align:start position:0%
+wire um the service crashing does not
+ 
+
+ align:start position:0%
+wire um the service crashing does not
+actually bring the client if the service
+
+ align:start position:0%
+actually bring the client if the service
+ 
+
+ align:start position:0%
+actually bring the client if the service
+decides that it you know it crashes then
+
+ align:start position:0%
+decides that it you know it crashes then
+ 
+
+ align:start position:0%
+decides that it you know it crashes then
+the client actually doesn't come
+
+ align:start position:0%
+the client actually doesn't come
+ 
+
+ align:start position:0%
+the client actually doesn't come
+crashing down of course the client has
+
+ align:start position:0%
+crashing down of course the client has
+ 
+
+ align:start position:0%
+crashing down of course the client has
+to somehow have a plan by which it knows
+
+ align:start position:0%
+to somehow have a plan by which it knows
+ 
+
+ align:start position:0%
+to somehow have a plan by which it knows
+that the service is still you know whe
+
+ align:start position:0%
+that the service is still you know whe
+ 
+
+ align:start position:0%
+that the service is still you know whe
+for example the client has to know
+
+ align:start position:0%
+for example the client has to know
+ 
+
+ align:start position:0%
+for example the client has to know
+whether the service is crashed or
+
+ align:start position:0%
+whether the service is crashed or
+ 
+
+ align:start position:0%
+whether the service is crashed or
+whether the service is just taking a
+
+ align:start position:0%
+whether the service is just taking a
+ 
+
+ align:start position:0%
+whether the service is just taking a
+long time to run something um that's
+
+ align:start position:0%
+long time to run something um that's
+ 
+
+ align:start position:0%
+long time to run something um that's
+something we have to address and we will
+
+ align:start position:0%
+something we have to address and we will
+ 
+
+ align:start position:0%
+something we have to address and we will
+in a bit but as long as the client's
+
+ align:start position:0%
+in a bit but as long as the client's
+ 
+
+ align:start position:0%
+in a bit but as long as the client's
+able to do that a service going away
+
+ align:start position:0%
+able to do that a service going away
+ 
+
+ align:start position:0%
+able to do that a service going away
+crashing is not really going to bring
+
+ align:start position:0%
+crashing is not really going to bring
+ 
+
+ align:start position:0%
+crashing is not really going to bring
+the color of the client um down with
+
+ align:start position:0%
+the color of the client um down with
+ 
+
+ align:start position:0%
+the color of the client um down with
+it so some properties of this
+
+ align:start position:0%
+it so some properties of this
+ 
+
+ align:start position:0%
+it so some properties of this
+organization are first of all that it's
+
+ align:start position:0%
+organization are first of all that it's
+ 
+
+ align:start position:0%
+organization are first of all that it's
+modular it has essentially the same
+
+ align:start position:0%
+modular it has essentially the same
+ 
+
+ align:start position:0%
+modular it has essentially the same
+modularity as as we had with procedures
+
+ align:start position:0%
+modularity as as we had with procedures
+ 
+
+ align:start position:0%
+modularity as as we had with procedures
+because if you had enough computers you
+
+ align:start position:0%
+because if you had enough computers you
+ 
+
+ align:start position:0%
+because if you had enough computers you
+could all of the different procedures on
+
+ align:start position:0%
+could all of the different procedures on
+ 
+
+ align:start position:0%
+could all of the different procedures on
+different computers you know all of the
+
+ align:start position:0%
+different computers you know all of the
+ 
+
+ align:start position:0%
+different computers you know all of the
+colar col relationships and you can
+
+ align:start position:0%
+colar col relationships and you can
+ 
+
+ align:start position:0%
+colar col relationships and you can
+preserve essentially the same modularity
+
+ align:start position:0%
+preserve essentially the same modularity
+ 
+
+ align:start position:0%
+preserve essentially the same modularity
+that you had um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before moreover this modularity has a
+
+ align:start position:0%
+before moreover this modularity has a
+ 
+
+ align:start position:0%
+before moreover this modularity has a
+different adjective in front of it
+
+ align:start position:0%
+different adjective in front of it
+ 
+
+ align:start position:0%
+different adjective in front of it
+different from soft this modularity is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enforced what that means is not only are
+
+ align:start position:0%
+enforced what that means is not only are
+ 
+
+ align:start position:0%
+enforced what that means is not only are
+you not only is it a modular
+
+ align:start position:0%
+you not only is it a modular
+ 
+
+ align:start position:0%
+you not only is it a modular
+organization it's one where errors of
+
+ align:start position:0%
+organization it's one where errors of
+ 
+
+ align:start position:0%
+organization it's one where errors of
+you know for example um things where one
+
+ align:start position:0%
+you know for example um things where one
+ 
+
+ align:start position:0%
+you know for example um things where one
+module fails or crashes this not bring
+
+ align:start position:0%
+module fails or crashes this not bring
+ 
+
+ align:start position:0%
+module fails or crashes this not bring
+the other one come crashing down so the
+
+ align:start position:0%
+the other one come crashing down so the
+ 
+
+ align:start position:0%
+the other one come crashing down so the
+modularity is more enforced than when
+
+ align:start position:0%
+modularity is more enforced than when
+ 
+
+ align:start position:0%
+modularity is more enforced than when
+they were both running on the same
+
+ align:start position:0%
+they were both running on the same
+ 
+
+ align:start position:0%
+they were both running on the same
+computer using Pro the procedure
+
+ align:start position:0%
+computer using Pro the procedure
+ 
+
+ align:start position:0%
+computer using Pro the procedure
+interface and the third property of this
+
+ align:start position:0%
+interface and the third property of this
+ 
+
+ align:start position:0%
+interface and the third property of this
+kind of modularity is something I've
+
+ align:start position:0%
+kind of modularity is something I've
+ 
+
+ align:start position:0%
+kind of modularity is something I've
+already mentioned it relies
+
+ align:start position:0%
+already mentioned it relies
+ 
+
+ align:start position:0%
+already mentioned it relies
+on the message abstraction um actually
+
+ align:start position:0%
+on the message abstraction um actually
+ 
+
+ align:start position:0%
+on the message abstraction um actually
+the communication path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+abstraction um the client and service
+
+ align:start position:0%
+abstraction um the client and service
+ 
+
+ align:start position:0%
+abstraction um the client and service
+communicate with each other through
+
+ align:start position:0%
+communicate with each other through
+ 
+
+ align:start position:0%
+communicate with each other through
+messages and these aren't AR messages
+
+ align:start position:0%
+messages and these aren't AR messages
+ 
+
+ align:start position:0%
+messages and these aren't AR messages
+you can't just sort of take an you know
+
+ align:start position:0%
+you can't just sort of take an you know
+ 
+
+ align:start position:0%
+you can't just sort of take an you know
+a random string of bites and send it to
+
+ align:start position:0%
+a random string of bites and send it to
+ 
+
+ align:start position:0%
+a random string of bites and send it to
+the service um it's actually messages
+
+ align:start position:0%
+the service um it's actually messages
+ 
+
+ align:start position:0%
+the service um it's actually messages
+that correspond to a particular format
+
+ align:start position:0%
+that correspond to a particular format
+ 
+
+ align:start position:0%
+that correspond to a particular format
+and these are agreed upon in advance so
+
+ align:start position:0%
+and these are agreed upon in advance so
+ 
+
+ align:start position:0%
+and these are agreed upon in advance so
+that way the service isn't surprised and
+
+ align:start position:0%
+that way the service isn't surprised and
+ 
+
+ align:start position:0%
+that way the service isn't surprised and
+the client isn't surprised when um you
+
+ align:start position:0%
+the client isn't surprised when um you
+ 
+
+ align:start position:0%
+the client isn't surprised when um you
+know messages that don't conform to that
+
+ align:start position:0%
+know messages that don't conform to that
+ 
+
+ align:start position:0%
+know messages that don't conform to that
+pattern arrive I mean you know exactly
+
+ align:start position:0%
+pattern arrive I mean you know exactly
+ 
+
+ align:start position:0%
+pattern arrive I mean you know exactly
+what kind of message is going to arrive
+
+ align:start position:0%
+what kind of message is going to arrive
+ 
+
+ align:start position:0%
+what kind of message is going to arrive
+and anything that doesn't conform to
+
+ align:start position:0%
+and anything that doesn't conform to
+ 
+
+ align:start position:0%
+and anything that doesn't conform to
+what's agreed upon in advance is
+
+ align:start position:0%
+what's agreed upon in advance is
+ 
+
+ align:start position:0%
+what's agreed upon in advance is
+rejected but you basically make it so
+
+ align:start position:0%
+rejected but you basically make it so
+ 
+
+ align:start position:0%
+rejected but you basically make it so
+that you explicitly declare the nature
+
+ align:start position:0%
+that you explicitly declare the nature
+ 
+
+ align:start position:0%
+that you explicitly declare the nature
+of these messages much like you did the
+
+ align:start position:0%
+of these messages much like you did the
+ 
+
+ align:start position:0%
+of these messages much like you did the
+nature of the procedural
+
+ align:start position:0%
+nature of the procedural
+ 
+
+ align:start position:0%
+nature of the procedural
+interface but now because you physically
+
+ align:start position:0%
+interface but now because you physically
+ 
+
+ align:start position:0%
+interface but now because you physically
+separated it you have a more enforced
+
+ align:start position:0%
+separated it you have a more enforced
+ 
+
+ align:start position:0%
+separated it you have a more enforced
+modularity than in the previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model of course nothing comes for free
+
+ align:start position:0%
+model of course nothing comes for free
+ 
+
+ align:start position:0%
+model of course nothing comes for free
+it's not like you've got this enforced
+
+ align:start position:0%
+it's not like you've got this enforced
+ 
+
+ align:start position:0%
+it's not like you've got this enforced
+modularity and you have all of these
+
+ align:start position:0%
+modularity and you have all of these
+ 
+
+ align:start position:0%
+modularity and you have all of these
+nice properties that you did before um
+
+ align:start position:0%
+nice properties that you did before um
+ 
+
+ align:start position:0%
+nice properties that you did before um
+of um you know here you had a nice
+
+ align:start position:0%
+of um you know here you had a nice
+ 
+
+ align:start position:0%
+of um you know here you had a nice
+property that the colag could has the
+
+ align:start position:0%
+property that the colag could has the
+ 
+
+ align:start position:0%
+property that the colag could has the
+property that either it when it runs and
+
+ align:start position:0%
+property that either it when it runs and
+ 
+
+ align:start position:0%
+property that either it when it runs and
+it returns to you you know exactly what
+
+ align:start position:0%
+it returns to you you know exactly what
+ 
+
+ align:start position:0%
+it returns to you you know exactly what
+happened and if it doesn't return you
+
+ align:start position:0%
+happened and if it doesn't return you
+ 
+
+ align:start position:0%
+happened and if it doesn't return you
+know that you know you usually come
+
+ align:start position:0%
+know that you know you usually come
+ 
+
+ align:start position:0%
+know that you know you usually come
+crashing down if the collie doesn't
+
+ align:start position:0%
+crashing down if the collie doesn't
+ 
+
+ align:start position:0%
+crashing down if the collie doesn't
+return it means that control never comes
+
+ align:start position:0%
+return it means that control never comes
+ 
+
+ align:start position:0%
+return it means that control never comes
+back to the caller so it's not like the
+
+ align:start position:0%
+back to the caller so it's not like the
+ 
+
+ align:start position:0%
+back to the caller so it's not like the
+caller has to is left wondering what
+
+ align:start position:0%
+caller has to is left wondering what
+ 
+
+ align:start position:0%
+caller has to is left wondering what
+really happened because the caller
+
+ align:start position:0%
+really happened because the caller
+ 
+
+ align:start position:0%
+really happened because the caller
+doesn't get control
+
+ align:start position:0%
+doesn't get control
+ 
+
+ align:start position:0%
+doesn't get control
+again here you have a problem if the
+
+ align:start position:0%
+again here you have a problem if the
+ 
+
+ align:start position:0%
+again here you have a problem if the
+caller if the service if the colleag the
+
+ align:start position:0%
+caller if the service if the colleag the
+ 
+
+ align:start position:0%
+caller if the service if the colleag the
+service doesn't return back to the
+
+ align:start position:0%
+service doesn't return back to the
+ 
+
+ align:start position:0%
+service doesn't return back to the
+client the client actually doesn't know
+
+ align:start position:0%
+client the client actually doesn't know
+ 
+
+ align:start position:0%
+client the client actually doesn't know
+what's going on um when when you have
+
+ align:start position:0%
+what's going on um when when you have
+ 
+
+ align:start position:0%
+what's going on um when when you have
+two machines two computers connected
+
+ align:start position:0%
+two machines two computers connected
+ 
+
+ align:start position:0%
+two machines two computers connected
+over wire or over a network it's
+
+ align:start position:0%
+over wire or over a network it's
+ 
+
+ align:start position:0%
+over wire or over a network it's
+extremely hard to distinguish between a
+
+ align:start position:0%
+extremely hard to distinguish between a
+ 
+
+ align:start position:0%
+extremely hard to distinguish between a
+service running really really really
+
+ align:start position:0%
+service running really really really
+ 
+
+ align:start position:0%
+service running really really really
+slow and a service that's gone
+
+ align:start position:0%
+slow and a service that's gone
+ 
+
+ align:start position:0%
+slow and a service that's gone
+away and we'll revisit this few time a
+
+ align:start position:0%
+away and we'll revisit this few time a
+ 
+
+ align:start position:0%
+away and we'll revisit this few time a
+few different times in this course but
+
+ align:start position:0%
+few different times in this course but
+ 
+
+ align:start position:0%
+few different times in this course but
+it's going to be essentially impossible
+
+ align:start position:0%
+it's going to be essentially impossible
+ 
+
+ align:start position:0%
+it's going to be essentially impossible
+for us to tell for sure um although
+
+ align:start position:0%
+for us to tell for sure um although
+ 
+
+ align:start position:0%
+for us to tell for sure um although
+we're going to very hard it's going to
+
+ align:start position:0%
+we're going to very hard it's going to
+ 
+
+ align:start position:0%
+we're going to very hard it's going to
+be really hard for us to tell for sure
+
+ align:start position:0%
+be really hard for us to tell for sure
+ 
+
+ align:start position:0%
+be really hard for us to tell for sure
+whether something exactly happened and
+
+ align:start position:0%
+whether something exactly happened and
+ 
+
+ align:start position:0%
+whether something exactly happened and
+if the service didn't return we don't
+
+ align:start position:0%
+if the service didn't return we don't
+ 
+
+ align:start position:0%
+if the service didn't return we don't
+really know for sure without much more
+
+ align:start position:0%
+really know for sure without much more
+ 
+
+ align:start position:0%
+really know for sure without much more
+Machinery whether it was just that the
+
+ align:start position:0%
+Machinery whether it was just that the
+ 
+
+ align:start position:0%
+Machinery whether it was just that the
+service is still running or whether it's
+
+ align:start position:0%
+service is still running or whether it's
+ 
+
+ align:start position:0%
+service is still running or whether it's
+crashed and you know we're just
+
+ align:start position:0%
+crashed and you know we're just
+ 
+
+ align:start position:0%
+crashed and you know we're just
+waiting and so this organization
+
+ align:start position:0%
+waiting and so this organization
+ 
+
+ align:start position:0%
+waiting and so this organization
+requires u a timer at the client and
+
+ align:start position:0%
+requires u a timer at the client and
+ 
+
+ align:start position:0%
+requires u a timer at the client and
+there are many names given to this timer
+
+ align:start position:0%
+there are many names given to this timer
+ 
+
+ align:start position:0%
+there are many names given to this timer
+I mean people call them keep Alives or
+
+ align:start position:0%
+I mean people call them keep Alives or
+ 
+
+ align:start position:0%
+I mean people call them keep Alives or
+people um call them with various names
+
+ align:start position:0%
+people um call them with various names
+ 
+
+ align:start position:0%
+people um call them with various names
+I'm going to call it a watchdog
+
+ align:start position:0%
+I'm going to call it a watchdog
+ 
+
+ align:start position:0%
+I'm going to call it a watchdog
+timer where the client has to keep track
+
+ align:start position:0%
+timer where the client has to keep track
+ 
+
+ align:start position:0%
+timer where the client has to keep track
+using a watchdog or some kind of a timer
+
+ align:start position:0%
+using a watchdog or some kind of a timer
+ 
+
+ align:start position:0%
+using a watchdog or some kind of a timer
+um of the service and if the service
+
+ align:start position:0%
+um of the service and if the service
+ 
+
+ align:start position:0%
+um of the service and if the service
+doesn't return within a certain period
+
+ align:start position:0%
+doesn't return within a certain period
+ 
+
+ align:start position:0%
+doesn't return within a certain period
+of time um the client has to time out
+
+ align:start position:0%
+of time um the client has to time out
+ 
+
+ align:start position:0%
+of time um the client has to time out
+and say well the service didn't return
+
+ align:start position:0%
+and say well the service didn't return
+ 
+
+ align:start position:0%
+and say well the service didn't return
+and I'm not quite sure what happened it
+
+ align:start position:0%
+and I'm not quite sure what happened it
+ 
+
+ align:start position:0%
+and I'm not quite sure what happened it
+might be that the procedure I wanted
+
+ align:start position:0%
+might be that the procedure I wanted
+ 
+
+ align:start position:0%
+might be that the procedure I wanted
+executed ran but I didn't get the answer
+
+ align:start position:0%
+executed ran but I didn't get the answer
+ 
+
+ align:start position:0%
+executed ran but I didn't get the answer
+or it might be that you know the
+
+ align:start position:0%
+or it might be that you know the
+ 
+
+ align:start position:0%
+or it might be that you know the
+procedure didn't get executed at all and
+
+ align:start position:0%
+procedure didn't get executed at all and
+ 
+
+ align:start position:0%
+procedure didn't get executed at all and
+I have to deal with it and you might
+
+ align:start position:0%
+I have to deal with it and you might
+ 
+
+ align:start position:0%
+I have to deal with it and you might
+deal with it by retrying the procedure
+
+ align:start position:0%
+deal with it by retrying the procedure
+ 
+
+ align:start position:0%
+deal with it by retrying the procedure
+or you might contact another service
+
+ align:start position:0%
+or you might contact another service
+ 
+
+ align:start position:0%
+or you might contact another service
+which provides the same function it but
+
+ align:start position:0%
+which provides the same function it but
+ 
+
+ align:start position:0%
+which provides the same function it but
+the client has to deal with all of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so fundamental to this client
+
+ align:start position:0%
+that so fundamental to this client
+ 
+
+ align:start position:0%
+that so fundamental to this client
+organization is a no is the notion um of
+
+ align:start position:0%
+organization is a no is the notion um of
+ 
+
+ align:start position:0%
+organization is a no is the notion um of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+timeout and we didn't have that here
+
+ align:start position:0%
+timeout and we didn't have that here
+ 
+
+ align:start position:0%
+timeout and we didn't have that here
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+here if the colleag decides that it's
+
+ align:start position:0%
+here if the colleag decides that it's
+ 
+
+ align:start position:0%
+here if the colleag decides that it's
+just going to continue on and not return
+
+ align:start position:0%
+just going to continue on and not return
+ 
+
+ align:start position:0%
+just going to continue on and not return
+the caller never gets control back so it
+
+ align:start position:0%
+the caller never gets control back so it
+ 
+
+ align:start position:0%
+the caller never gets control back so it
+doesn't have this decision to make there
+
+ align:start position:0%
+doesn't have this decision to make there
+ 
+
+ align:start position:0%
+doesn't have this decision to make there
+is no such notion of a watch do that we
+
+ align:start position:0%
+is no such notion of a watch do that we
+ 
+
+ align:start position:0%
+is no such notion of a watch do that we
+have to worry about in this other
+
+ align:start position:0%
+have to worry about in this other
+ 
+
+ align:start position:0%
+have to worry about in this other
+organization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another nice property of this client
+
+ align:start position:0%
+so another nice property of this client
+ 
+
+ align:start position:0%
+so another nice property of this client
+service organization is that so far
+
+ align:start position:0%
+service organization is that so far
+ 
+
+ align:start position:0%
+service organization is that so far
+we've presented it in the context of the
+
+ align:start position:0%
+we've presented it in the context of the
+ 
+
+ align:start position:0%
+we've presented it in the context of the
+client and the service being modularized
+
+ align:start position:0%
+client and the service being modularized
+ 
+
+ align:start position:0%
+client and the service being modularized
+from each other and we've enforced
+
+ align:start position:0%
+from each other and we've enforced
+ 
+
+ align:start position:0%
+from each other and we've enforced
+modularity between the client and the
+
+ align:start position:0%
+modularity between the client and the
+ 
+
+ align:start position:0%
+modularity between the client and the
+service but in fact there's another nice
+
+ align:start position:0%
+service but in fact there's another nice
+ 
+
+ align:start position:0%
+service but in fact there's another nice
+property to it which is that a client
+
+ align:start position:0%
+property to it which is that a client
+ 
+
+ align:start position:0%
+property to it which is that a client
+service organization allows us to design
+
+ align:start position:0%
+service organization allows us to design
+ 
+
+ align:start position:0%
+service organization allows us to design
+modules and Design Systems where clients
+
+ align:start position:0%
+modules and Design Systems where clients
+ 
+
+ align:start position:0%
+modules and Design Systems where clients
+get modularized from each other the
+
+ align:start position:0%
+get modularized from each other the
+ 
+
+ align:start position:0%
+get modularized from each other the
+clients we can achieve soft modularity
+
+ align:start position:0%
+clients we can achieve soft modularity
+ 
+
+ align:start position:0%
+clients we can achieve soft modularity
+by protecting clients from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each the idea here is if you have many
+
+ align:start position:0%
+each the idea here is if you have many
+ 
+
+ align:start position:0%
+each the idea here is if you have many
+clients all of which want to use a given
+
+ align:start position:0%
+clients all of which want to use a given
+ 
+
+ align:start position:0%
+clients all of which want to use a given
+service for example U there's some
+
+ align:start position:0%
+service for example U there's some
+ 
+
+ align:start position:0%
+service for example U there's some
+there's a service that's let's say uh
+
+ align:start position:0%
+there's a service that's let's say uh
+ 
+
+ align:start position:0%
+there's a service that's let's say uh
+implemented by your bank and what it
+
+ align:start position:0%
+implemented by your bank and what it
+ 
+
+ align:start position:0%
+implemented by your bank and what it
+does is it's the service that deals with
+
+ align:start position:0%
+does is it's the service that deals with
+ 
+
+ align:start position:0%
+does is it's the service that deals with
+managing your accounts and you can move
+
+ align:start position:0%
+managing your accounts and you can move
+ 
+
+ align:start position:0%
+managing your accounts and you can move
+money between accounts and it'll tell
+
+ align:start position:0%
+money between accounts and it'll tell
+ 
+
+ align:start position:0%
+money between accounts and it'll tell
+you your account balance and so
+
+ align:start position:0%
+you your account balance and so
+ 
+
+ align:start position:0%
+you your account balance and so
+on you can Implement that as one service
+
+ align:start position:0%
+on you can Implement that as one service
+ 
+
+ align:start position:0%
+on you can Implement that as one service
+and many many clients can share the same
+
+ align:start position:0%
+and many many clients can share the same
+ 
+
+ align:start position:0%
+and many many clients can share the same
+service now all of the clients trust the
+
+ align:start position:0%
+service now all of the clients trust the
+ 
+
+ align:start position:0%
+service now all of the clients trust the
+service because I mean if you're a
+
+ align:start position:0%
+service because I mean if you're a
+ 
+
+ align:start position:0%
+service because I mean if you're a
+customer of a bank you're you know and
+
+ align:start position:0%
+customer of a bank you're you know and
+ 
+
+ align:start position:0%
+customer of a bank you're you know and
+you're using your browser to to look for
+
+ align:start position:0%
+you're using your browser to to look for
+ 
+
+ align:start position:0%
+you're using your browser to to look for
+your account balance that means you sort
+
+ align:start position:0%
+your account balance that means you sort
+ 
+
+ align:start position:0%
+your account balance that means you sort
+of trust the bank and all of the clients
+
+ align:start position:0%
+of trust the bank and all of the clients
+ 
+
+ align:start position:0%
+of trust the bank and all of the clients
+trust the service but the clients sure
+
+ align:start position:0%
+trust the service but the clients sure
+ 
+
+ align:start position:0%
+trust the service but the clients sure
+don't trust each
+
+ align:start position:0%
+don't trust each
+ 
+
+ align:start position:0%
+don't trust each
+other and the nice thing about this
+
+ align:start position:0%
+other and the nice thing about this
+ 
+
+ align:start position:0%
+other and the nice thing about this
+organization is that you can use the
+
+ align:start position:0%
+organization is that you can use the
+ 
+
+ align:start position:0%
+organization is that you can use the
+service um in the form of an
+
+ align:start position:0%
+service um in the form of an
+ 
+
+ align:start position:0%
+service um in the form of an
+intermediary that allows the clients to
+
+ align:start position:0%
+intermediary that allows the clients to
+ 
+
+ align:start position:0%
+intermediary that allows the clients to
+be separated from each other
+
+ align:start position:0%
+be separated from each other
+ 
+
+ align:start position:0%
+be separated from each other
+um Each of which can use the service but
+
+ align:start position:0%
+um Each of which can use the service but
+ 
+
+ align:start position:0%
+um Each of which can use the service but
+the clients don't have to trust each
+
+ align:start position:0%
+the clients don't have to trust each
+ 
+
+ align:start position:0%
+the clients don't have to trust each
+other and clients don't really have to
+
+ align:start position:0%
+other and clients don't really have to
+ 
+
+ align:start position:0%
+other and clients don't really have to
+um you know know about each other's uh
+
+ align:start position:0%
+um you know know about each other's uh
+ 
+
+ align:start position:0%
+um you know know about each other's uh
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+and this idea of using a a service to
+
+ align:start position:0%
+and this idea of using a a service to
+ 
+
+ align:start position:0%
+and this idea of using a a service to
+modularize clients from each other uh is
+
+ align:start position:0%
+modularize clients from each other uh is
+ 
+
+ align:start position:0%
+modularize clients from each other uh is
+called a trusted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermediary there's many examples of
+
+ align:start position:0%
+intermediary there's many examples of
+ 
+
+ align:start position:0%
+intermediary there's many examples of
+trusted intermediaries that um we'll see
+
+ align:start position:0%
+trusted intermediaries that um we'll see
+ 
+
+ align:start position:0%
+trusted intermediaries that um we'll see
+in this in this course in fact
+
+ align:start position:0%
+in this in this course in fact
+ 
+
+ align:start position:0%
+in this in this course in fact
+tomorrow's recitation on the X Windows
+
+ align:start position:0%
+tomorrow's recitation on the X Windows
+ 
+
+ align:start position:0%
+tomorrow's recitation on the X Windows
+system has a system where your computer
+
+ align:start position:0%
+system has a system where your computer
+ 
+
+ align:start position:0%
+system has a system where your computer
+display is going to be managed by a
+
+ align:start position:0%
+display is going to be managed by a
+ 
+
+ align:start position:0%
+display is going to be managed by a
+service called the by the X window
+
+ align:start position:0%
+service called the by the X window
+ 
+
+ align:start position:0%
+service called the by the X window
+system and there are many clients that
+
+ align:start position:0%
+system and there are many clients that
+ 
+
+ align:start position:0%
+system and there are many clients that
+are going to use that service and the
+
+ align:start position:0%
+are going to use that service and the
+ 
+
+ align:start position:0%
+are going to use that service and the
+clients actually you know don't actually
+
+ align:start position:0%
+clients actually you know don't actually
+ 
+
+ align:start position:0%
+clients actually you know don't actually
+trust each other and they don't really
+
+ align:start position:0%
+trust each other and they don't really
+ 
+
+ align:start position:0%
+trust each other and they don't really
+they want to get modularized away from
+
+ align:start position:0%
+they want to get modularized away from
+ 
+
+ align:start position:0%
+they want to get modularized away from
+each other and the X Windows system as a
+
+ align:start position:0%
+each other and the X Windows system as a
+ 
+
+ align:start position:0%
+each other and the X Windows system as a
+trusted intermediary deals with that it
+
+ align:start position:0%
+trusted intermediary deals with that it
+ 
+
+ align:start position:0%
+trusted intermediary deals with that it
+manages this resource your display and
+
+ align:start position:0%
+manages this resource your display and
+ 
+
+ align:start position:0%
+manages this resource your display and
+it arranges for the clients to be
+
+ align:start position:0%
+it arranges for the clients to be
+ 
+
+ align:start position:0%
+it arranges for the clients to be
+designed each independent from the
+
+ align:start position:0%
+designed each independent from the
+ 
+
+ align:start position:0%
+designed each independent from the
+other and in general uh we're going to
+
+ align:start position:0%
+other and in general uh we're going to
+ 
+
+ align:start position:0%
+other and in general uh we're going to
+see in the next few lectures many
+
+ align:start position:0%
+see in the next few lectures many
+ 
+
+ align:start position:0%
+see in the next few lectures many
+examples of your operating system being
+
+ align:start position:0%
+examples of your operating system being
+ 
+
+ align:start position:0%
+examples of your operating system being
+a trusted intermediary um arranging for
+
+ align:start position:0%
+a trusted intermediary um arranging for
+ 
+
+ align:start position:0%
+a trusted intermediary um arranging for
+many different clients to use some
+
+ align:start position:0%
+many different clients to use some
+ 
+
+ align:start position:0%
+many different clients to use some
+resource on your computer like the
+
+ align:start position:0%
+resource on your computer like the
+ 
+
+ align:start position:0%
+resource on your computer like the
+processor or the memory and or the disk
+
+ align:start position:0%
+processor or the memory and or the disk
+ 
+
+ align:start position:0%
+processor or the memory and or the disk
+and our architecture for the operating
+
+ align:start position:0%
+and our architecture for the operating
+ 
+
+ align:start position:0%
+and our architecture for the operating
+system is going to end up being in the
+
+ align:start position:0%
+system is going to end up being in the
+ 
+
+ align:start position:0%
+system is going to end up being in the
+form of these trusted intermediaries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so far we've seen what the what
+
+ align:start position:0%
+so so far we've seen what the what
+ 
+
+ align:start position:0%
+so so far we've seen what the what
+client service organization means it
+
+ align:start position:0%
+client service organization means it
+ 
+
+ align:start position:0%
+client service organization means it
+means you have a client and a service
+
+ align:start position:0%
+means you have a client and a service
+ 
+
+ align:start position:0%
+means you have a client and a service
+and they communicate with messages using
+
+ align:start position:0%
+and they communicate with messages using
+ 
+
+ align:start position:0%
+and they communicate with messages using
+the communication path abstraction of
+
+ align:start position:0%
+the communication path abstraction of
+ 
+
+ align:start position:0%
+the communication path abstraction of
+send and receive um and we've seen some
+
+ align:start position:0%
+send and receive um and we've seen some
+ 
+
+ align:start position:0%
+send and receive um and we've seen some
+properties of client service
+
+ align:start position:0%
+properties of client service
+ 
+
+ align:start position:0%
+properties of client service
+organization but I haven't actually told
+
+ align:start position:0%
+organization but I haven't actually told
+ 
+
+ align:start position:0%
+organization but I haven't actually told
+you how to implement any of this stuff
+
+ align:start position:0%
+you how to implement any of this stuff
+ 
+
+ align:start position:0%
+you how to implement any of this stuff
+and so that's what we're going to do the
+
+ align:start position:0%
+and so that's what we're going to do the
+ 
+
+ align:start position:0%
+and so that's what we're going to do the
+rest of rest of today um and in fact
+
+ align:start position:0%
+rest of rest of today um and in fact
+ 
+
+ align:start position:0%
+rest of rest of today um and in fact
+we're going to continue with different
+
+ align:start position:0%
+we're going to continue with different
+ 
+
+ align:start position:0%
+we're going to continue with different
+ways of implementing um various forms of
+
+ align:start position:0%
+ways of implementing um various forms of
+ 
+
+ align:start position:0%
+ways of implementing um various forms of
+client service many times uh in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course so there are many ways to
+
+ align:start position:0%
+course so there are many ways to
+ 
+
+ align:start position:0%
+course so there are many ways to
+implement client service organization
+
+ align:start position:0%
+implement client service organization
+ 
+
+ align:start position:0%
+implement client service organization
+and all of them have to do with all of
+
+ align:start position:0%
+and all of them have to do with all of
+ 
+
+ align:start position:0%
+and all of them have to do with all of
+them involve different ways in which
+
+ align:start position:0%
+them involve different ways in which
+ 
+
+ align:start position:0%
+them involve different ways in which
+messages are sent between client and
+
+ align:start position:0%
+messages are sent between client and
+ 
+
+ align:start position:0%
+messages are sent between client and
+service
+
+ align:start position:0%
+service
+ 
+
+ align:start position:0%
+service
+a common way and a pretty standard way
+
+ align:start position:0%
+a common way and a pretty standard way
+ 
+
+ align:start position:0%
+a common way and a pretty standard way
+of implementing it is something called a
+
+ align:start position:0%
+of implementing it is something called a
+ 
+
+ align:start position:0%
+of implementing it is something called a
+remote procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call there are many examples of remote
+
+ align:start position:0%
+call there are many examples of remote
+ 
+
+ align:start position:0%
+call there are many examples of remote
+procedure call systems I mean the the
+
+ align:start position:0%
+procedure call systems I mean the the
+ 
+
+ align:start position:0%
+procedure call systems I mean the the
+one of the most U common ones is
+
+ align:start position:0%
+one of the most U common ones is
+ 
+
+ align:start position:0%
+one of the most U common ones is
+something called the sun remote
+
+ align:start position:0%
+something called the sun remote
+ 
+
+ align:start position:0%
+something called the sun remote
+procedure call system or sun RPC um
+
+ align:start position:0%
+procedure call system or sun RPC um
+ 
+
+ align:start position:0%
+procedure call system or sun RPC um
+that's one example um there are many
+
+ align:start position:0%
+that's one example um there are many
+ 
+
+ align:start position:0%
+that's one example um there are many
+other examples as well well a more
+
+ align:start position:0%
+other examples as well well a more
+ 
+
+ align:start position:0%
+other examples as well well a more
+modern
+
+ align:start position:0%
+modern
+ 
+
+ align:start position:0%
+modern
+example which some of you may have heard
+
+ align:start position:0%
+example which some of you may have heard
+ 
+
+ align:start position:0%
+example which some of you may have heard
+of is a a relatively new system about 5
+
+ align:start position:0%
+of is a a relatively new system about 5
+ 
+
+ align:start position:0%
+of is a a relatively new system about 5
+years old called XML
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RPC so if you've heard of buzzwords like
+
+ align:start position:0%
+RPC so if you've heard of buzzwords like
+ 
+
+ align:start position:0%
+RPC so if you've heard of buzzwords like
+web services and you know busino
+
+ align:start position:0%
+web services and you know busino
+ 
+
+ align:start position:0%
+web services and you know busino
+business interactions or busines to
+
+ align:start position:0%
+business interactions or busines to
+ 
+
+ align:start position:0%
+business interactions or busines to
+business um applications these things
+
+ align:start position:0%
+business um applications these things
+ 
+
+ align:start position:0%
+business um applications these things
+use something called XML RPC and you
+
+ align:start position:0%
+use something called XML RPC and you
+ 
+
+ align:start position:0%
+use something called XML RPC and you
+know there's the there's a lot of
+
+ align:start position:0%
+know there's the there's a lot of
+ 
+
+ align:start position:0%
+know there's the there's a lot of
+different three-letter acronyms and
+
+ align:start position:0%
+different three-letter acronyms and
+ 
+
+ align:start position:0%
+different three-letter acronyms and
+four-letter acronyms um this has led to
+
+ align:start position:0%
+four-letter acronyms um this has led to
+ 
+
+ align:start position:0%
+four-letter acronyms um this has led to
+something called soap which stands for
+
+ align:start position:0%
+something called soap which stands for
+ 
+
+ align:start position:0%
+something called soap which stands for
+the simple object access protocol um so
+
+ align:start position:0%
+the simple object access protocol um so
+ 
+
+ align:start position:0%
+the simple object access protocol um so
+there are many different ways of
+
+ align:start position:0%
+there are many different ways of
+ 
+
+ align:start position:0%
+there are many different ways of
+implementing uh RPC systems and you know
+
+ align:start position:0%
+implementing uh RPC systems and you know
+ 
+
+ align:start position:0%
+implementing uh RPC systems and you know
+on until last year or a couple of years
+
+ align:start position:0%
+on until last year or a couple of years
+ 
+
+ align:start position:0%
+on until last year or a couple of years
+ago we used to talk about sunrpc as an
+
+ align:start position:0%
+ago we used to talk about sunrpc as an
+ 
+
+ align:start position:0%
+ago we used to talk about sunrpc as an
+example in this in this class but I
+
+ align:start position:0%
+example in this in this class but I
+ 
+
+ align:start position:0%
+example in this in this class but I
+decided that's so 20th centuries so
+
+ align:start position:0%
+decided that's so 20th centuries so
+ 
+
+ align:start position:0%
+decided that's so 20th centuries so
+we're going to talk about XML RPC today
+
+ align:start position:0%
+we're going to talk about XML RPC today
+ 
+
+ align:start position:0%
+we're going to talk about XML RPC today
+um you know it has the property that's
+
+ align:start position:0%
+um you know it has the property that's
+ 
+
+ align:start position:0%
+um you know it has the property that's
+much more inefficient um but that's sort
+
+ align:start position:0%
+much more inefficient um but that's sort
+ 
+
+ align:start position:0%
+much more inefficient um but that's sort
+of keep keeping with the fact that
+
+ align:start position:0%
+of keep keeping with the fact that
+ 
+
+ align:start position:0%
+of keep keeping with the fact that
+computers have become faster we don't
+
+ align:start position:0%
+computers have become faster we don't
+ 
+
+ align:start position:0%
+computers have become faster we don't
+really have to worry in many cases about
+
+ align:start position:0%
+really have to worry in many cases about
+ 
+
+ align:start position:0%
+really have to worry in many cases about
+efficiency so we're going to talk a
+
+ align:start position:0%
+efficiency so we're going to talk a
+ 
+
+ align:start position:0%
+efficiency so we're going to talk a
+little bit about um how xmlrpc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works so let me first show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you program written what a client
+
+ align:start position:0%
+you program written what a client
+ 
+
+ align:start position:0%
+you program written what a client
+written with um this kind of RPC looks
+
+ align:start position:0%
+written with um this kind of RPC looks
+ 
+
+ align:start position:0%
+written with um this kind of RPC looks
+like um in jav it's going to show you a
+
+ align:start position:0%
+like um in jav it's going to show you a
+ 
+
+ align:start position:0%
+like um in jav it's going to show you a
+a code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right had to work hard to make sure
+
+ align:start position:0%
+all right had to work hard to make sure
+ 
+
+ align:start position:0%
+all right had to work hard to make sure
+it would fit on
+
+ align:start position:0%
+it would fit on
+ 
+
+ align:start position:0%
+it would fit on
+this okay um all right the way this
+
+ align:start position:0%
+this okay um all right the way this
+ 
+
+ align:start position:0%
+this okay um all right the way this
+thing works is actually very very
+
+ align:start position:0%
+thing works is actually very very
+ 
+
+ align:start position:0%
+thing works is actually very very
+simple um this uses uh something called
+
+ align:start position:0%
+simple um this uses uh something called
+ 
+
+ align:start position:0%
+simple um this uses uh something called
+the xmlc library that for Java that was
+
+ align:start position:0%
+the xmlc library that for Java that was
+ 
+
+ align:start position:0%
+the xmlc library that for Java that was
+written by um the Apache people tool and
+
+ align:start position:0%
+written by um the Apache people tool and
+ 
+
+ align:start position:0%
+written by um the Apache people tool and
+once you incorporate that Library your
+
+ align:start position:0%
+once you incorporate that Library your
+ 
+
+ align:start position:0%
+once you incorporate that Library your
+program becomes completely easy so let
+
+ align:start position:0%
+program becomes completely easy so let
+ 
+
+ align:start position:0%
+program becomes completely easy so let
+me just walk you through this what the
+
+ align:start position:0%
+me just walk you through this what the
+ 
+
+ align:start position:0%
+me just walk you through this what the
+the high level idea here is that it's
+
+ align:start position:0%
+the high level idea here is that it's
+ 
+
+ align:start position:0%
+the high level idea here is that it's
+sending um you know it's transferring
+
+ align:start position:0%
+sending um you know it's transferring
+ 
+
+ align:start position:0%
+sending um you know it's transferring
+money account to the other um you know
+
+ align:start position:0%
+money account to the other um you know
+ 
+
+ align:start position:0%
+money account to the other um you know
+through a that's run by the bank so the
+
+ align:start position:0%
+through a that's run by the bank so the
+ 
+
+ align:start position:0%
+through a that's run by the bank so the
+first line of this thing here um you
+
+ align:start position:0%
+first line of this thing here um you
+ 
+
+ align:start position:0%
+first line of this thing here um you
+know creates an xmlrpc object um an
+
+ align:start position:0%
+know creates an xmlrpc object um an
+ 
+
+ align:start position:0%
+know creates an xmlrpc object um an
+xmlrpc client object and what you give
+
+ align:start position:0%
+xmlrpc client object and what you give
+ 
+
+ align:start position:0%
+xmlrpc client object and what you give
+it is actually the name of the service
+
+ align:start position:0%
+it is actually the name of the service
+ 
+
+ align:start position:0%
+it is actually the name of the service
+so somebody has to tell you the name of
+
+ align:start position:0%
+so somebody has to tell you the name of
+ 
+
+ align:start position:0%
+so somebody has to tell you the name of
+the service and I don't want to get into
+
+ align:start position:0%
+the service and I don't want to get into
+ 
+
+ align:start position:0%
+the service and I don't want to get into
+the details of everything everything
+
+ align:start position:0%
+the details of everything everything
+ 
+
+ align:start position:0%
+the details of everything everything
+here but the basic idea is your back
+
+ align:start position:0%
+here but the basic idea is your back
+ 
+
+ align:start position:0%
+here but the basic idea is your back
+name.com colon 8080 is the name the DNS
+
+ align:start position:0%
+name.com colon 8080 is the name the DNS
+ 
+
+ align:start position:0%
+name.com colon 8080 is the name the DNS
+name at which the service runs and a
+
+ align:start position:0%
+name at which the service runs and a
+ 
+
+ align:start position:0%
+name at which the service runs and a
+port the thing about xmlrpc is that it
+
+ align:start position:0%
+port the thing about xmlrpc is that it
+ 
+
+ align:start position:0%
+port the thing about xmlrpc is that it
+runs over HTTP which is what you use to
+
+ align:start position:0%
+runs over HTTP which is what you use to
+ 
+
+ align:start position:0%
+runs over HTTP which is what you use to
+transfer objects um on the web and
+
+ align:start position:0%
+transfer objects um on the web and
+ 
+
+ align:start position:0%
+transfer objects um on the web and
+underneath I'll talk about how it's
+
+ align:start position:0%
+underneath I'll talk about how it's
+ 
+
+ align:start position:0%
+underneath I'll talk about how it's
+implemented underneath this is
+
+ align:start position:0%
+implemented underneath this is
+ 
+
+ align:start position:0%
+implemented underneath this is
+implemented using a standard method in
+
+ align:start position:0%
+implemented using a standard method in
+ 
+
+ align:start position:0%
+implemented using a standard method in
+HTTP called a post which allows a client
+
+ align:start position:0%
+HTTP called a post which allows a client
+ 
+
+ align:start position:0%
+HTTP called a post which allows a client
+normally HTTP has a get where you
+
+ align:start position:0%
+normally HTTP has a get where you
+ 
+
+ align:start position:0%
+normally HTTP has a get where you
+retrieve stuff but it also has a post
+
+ align:start position:0%
+retrieve stuff but it also has a post
+ 
+
+ align:start position:0%
+retrieve stuff but it also has a post
+that many of you are familiar with where
+
+ align:start position:0%
+that many of you are familiar with where
+ 
+
+ align:start position:0%
+that many of you are familiar with where
+the client can push some stuff to the
+
+ align:start position:0%
+the client can push some stuff to the
+ 
+
+ align:start position:0%
+the client can push some stuff to the
+service to the server and it just uses
+
+ align:start position:0%
+service to the server and it just uses
+ 
+
+ align:start position:0%
+service to the server and it just uses
+post um what's going on very easy you
+
+ align:start position:0%
+post um what's going on very easy you
+ 
+
+ align:start position:0%
+post um what's going on very easy you
+create a vector of um parameters and you
+
+ align:start position:0%
+create a vector of um parameters and you
+ 
+
+ align:start position:0%
+create a vector of um parameters and you
+fill that uh Vector in with you know in
+
+ align:start position:0%
+fill that uh Vector in with you know in
+ 
+
+ align:start position:0%
+fill that uh Vector in with you know in
+this case your account number um you
+
+ align:start position:0%
+this case your account number um you
+ 
+
+ align:start position:0%
+this case your account number um you
+know let's say here the idea is that you
+
+ align:start position:0%
+know let's say here the idea is that you
+ 
+
+ align:start position:0%
+know let's say here the idea is that you
+know your comp you know this sort of
+
+ align:start position:0%
+know your comp you know this sort of
+ 
+
+ align:start position:0%
+know your comp you know this sort of
+thing is very popular at big companies
+
+ align:start position:0%
+thing is very popular at big companies
+ 
+
+ align:start position:0%
+thing is very popular at big companies
+like Ford or Cisco which have thousands
+
+ align:start position:0%
+like Ford or Cisco which have thousands
+ 
+
+ align:start position:0%
+like Ford or Cisco which have thousands
+of suppliers and um they're always
+
+ align:start position:0%
+of suppliers and um they're always
+ 
+
+ align:start position:0%
+of suppliers and um they're always
+worried about and they never actually
+
+ align:start position:0%
+worried about and they never actually
+ 
+
+ align:start position:0%
+worried about and they never actually
+maintain a lot of inventory of their own
+
+ align:start position:0%
+maintain a lot of inventory of their own
+ 
+
+ align:start position:0%
+maintain a lot of inventory of their own
+so they're always trying to figure out
+
+ align:start position:0%
+so they're always trying to figure out
+ 
+
+ align:start position:0%
+so they're always trying to figure out
+the latest cost of any of their supplies
+
+ align:start position:0%
+the latest cost of any of their supplies
+ 
+
+ align:start position:0%
+the latest cost of any of their supplies
+and they using this web service like
+
+ align:start position:0%
+and they using this web service like
+ 
+
+ align:start position:0%
+and they using this web service like
+interface in fact this you know this is
+
+ align:start position:0%
+interface in fact this you know this is
+ 
+
+ align:start position:0%
+interface in fact this you know this is
+called also called a web service
+
+ align:start position:0%
+called also called a web service
+ 
+
+ align:start position:0%
+called also called a web service
+interface to communicate with their
+
+ align:start position:0%
+interface to communicate with their
+ 
+
+ align:start position:0%
+interface to communicate with their
+suppliers to always have
+
+ align:start position:0%
+suppliers to always have
+ 
+
+ align:start position:0%
+suppliers to always have
+latest whether their suppliers have any
+
+ align:start position:0%
+latest whether their suppliers have any
+ 
+
+ align:start position:0%
+latest whether their suppliers have any
+given item in stock and how much it
+
+ align:start position:0%
+given item in stock and how much it
+ 
+
+ align:start position:0%
+given item in stock and how much it
+costs and so let's pretend you've done
+
+ align:start position:0%
+costs and so let's pretend you've done
+ 
+
+ align:start position:0%
+costs and so let's pretend you've done
+that in your company and um you know
+
+ align:start position:0%
+that in your company and um you know
+ 
+
+ align:start position:0%
+that in your company and um you know
+you're trying to pay off um you know
+
+ align:start position:0%
+you're trying to pay off um you know
+ 
+
+ align:start position:0%
+you're trying to pay off um you know
+you're taking your supplier's account
+
+ align:start position:0%
+you're taking your supplier's account
+ 
+
+ align:start position:0%
+you're taking your supplier's account
+number and pay some money to him okay so
+
+ align:start position:0%
+number and pay some money to him okay so
+ 
+
+ align:start position:0%
+number and pay some money to him okay so
+in this case um whatever dollars is that
+
+ align:start position:0%
+in this case um whatever dollars is that
+ 
+
+ align:start position:0%
+in this case um whatever dollars is that
+is that argument um so you create your
+
+ align:start position:0%
+is that argument um so you create your
+ 
+
+ align:start position:0%
+is that argument um so you create your
+parameters and all you do at the end is
+
+ align:start position:0%
+parameters and all you do at the end is
+ 
+
+ align:start position:0%
+parameters and all you do at the end is
+you use this xmlrpc client object and
+
+ align:start position:0%
+you use this xmlrpc client object and
+ 
+
+ align:start position:0%
+you use this xmlrpc client object and
+invoke a it's it presents to you called
+
+ align:start position:0%
+invoke a it's it presents to you called
+ 
+
+ align:start position:0%
+invoke a it's it presents to you called
+execute and you give it two arguments
+
+ align:start position:0%
+execute and you give it two arguments
+ 
+
+ align:start position:0%
+execute and you give it two arguments
+the second argument is the parameters
+
+ align:start position:0%
+the second argument is the parameters
+ 
+
+ align:start position:0%
+the second argument is the parameters
+and the first argument is the name of
+
+ align:start position:0%
+and the first argument is the name of
+ 
+
+ align:start position:0%
+and the first argument is the name of
+the procedure that you wish to run on
+
+ align:start position:0%
+the procedure that you wish to run on
+ 
+
+ align:start position:0%
+the procedure that you wish to run on
+the service okay um that's in this case
+
+ align:start position:0%
+the service okay um that's in this case
+ 
+
+ align:start position:0%
+the service okay um that's in this case
+called money transfer so corresponding
+
+ align:start position:0%
+called money transfer so corresponding
+ 
+
+ align:start position:0%
+called money transfer so corresponding
+to this somewhat longer is a piece of
+
+ align:start position:0%
+to this somewhat longer is a piece of
+ 
+
+ align:start position:0%
+to this somewhat longer is a piece of
+code running on the service which
+
+ align:start position:0%
+code running on the service which
+ 
+
+ align:start position:0%
+code running on the service which
+implements the server side of it uh
+
+ align:start position:0%
+implements the server side of it uh
+ 
+
+ align:start position:0%
+implements the server side of it uh
+which has a basic basically it obtains
+
+ align:start position:0%
+which has a basic basically it obtains
+ 
+
+ align:start position:0%
+which has a basic basically it obtains
+the you know the gives message from the
+
+ align:start position:0%
+the you know the gives message from the
+ 
+
+ align:start position:0%
+the you know the gives message from the
+network calls an object that will
+
+ align:start position:0%
+network calls an object that will
+ 
+
+ align:start position:0%
+network calls an object that will
+unmarshal the arguments and then it'll
+
+ align:start position:0%
+unmarshal the arguments and then it'll
+ 
+
+ align:start position:0%
+unmarshal the arguments and then it'll
+execute money transfer all of which all
+
+ align:start position:0%
+execute money transfer all of which all
+ 
+
+ align:start position:0%
+execute money transfer all of which all
+done essent there's little that actually
+
+ align:start position:0%
+done essent there's little that actually
+ 
+
+ align:start position:0%
+done essent there's little that actually
+has to run on the service it's just a
+
+ align:start position:0%
+has to run on the service it's just a
+ 
+
+ align:start position:0%
+has to run on the service it's just a
+little bit longer than this
+
+ align:start position:0%
+little bit longer than this
+ 
+
+ align:start position:0%
+little bit longer than this
+um now this line here is a little is
+
+ align:start position:0%
+um now this line here is a little is
+ 
+
+ align:start position:0%
+um now this line here is a little is
+important that's the line on which you
+
+ align:start position:0%
+important that's the line on which you
+ 
+
+ align:start position:0%
+important that's the line on which you
+get your result in this case the result
+
+ align:start position:0%
+get your result in this case the result
+ 
+
+ align:start position:0%
+get your result in this case the result
+is a string you know it might tell you
+
+ align:start position:0%
+is a string you know it might tell you
+ 
+
+ align:start position:0%
+is a string you know it might tell you
+that I was I finished transferring X
+
+ align:start position:0%
+that I was I finished transferring X
+ 
+
+ align:start position:0%
+that I was I finished transferring X
+from this account to that account um or
+
+ align:start position:0%
+from this account to that account um or
+ 
+
+ align:start position:0%
+from this account to that account um or
+it might tell you I couldn't transfer
+
+ align:start position:0%
+it might tell you I couldn't transfer
+ 
+
+ align:start position:0%
+it might tell you I couldn't transfer
+and you know there was some kind of an
+
+ align:start position:0%
+and you know there was some kind of an
+ 
+
+ align:start position:0%
+and you know there was some kind of an
+error or um you might actually not get
+
+ align:start position:0%
+error or um you might actually not get
+ 
+
+ align:start position:0%
+error or um you might actually not get
+any answer in which case the library
+
+ align:start position:0%
+any answer in which case the library
+ 
+
+ align:start position:0%
+any answer in which case the library
+would actually in this case the
+
+ align:start position:0%
+would actually in this case the
+ 
+
+ align:start position:0%
+would actually in this case the
+underlying library that implements this
+
+ align:start position:0%
+underlying library that implements this
+ 
+
+ align:start position:0%
+underlying library that implements this
+remote procedure call would throw an
+
+ align:start position:0%
+remote procedure call would throw an
+ 
+
+ align:start position:0%
+remote procedure call would throw an
+exception that your code has to deal
+
+ align:start position:0%
+exception that your code has to deal
+ 
+
+ align:start position:0%
+exception that your code has to deal
+with and how you deal with it is a
+
+ align:start position:0%
+with and how you deal with it is a
+ 
+
+ align:start position:0%
+with and how you deal with it is a
+little tricky U because you don't quite
+
+ align:start position:0%
+little tricky U because you don't quite
+ 
+
+ align:start position:0%
+little tricky U because you don't quite
+know and we'll see this in a moment you
+
+ align:start position:0%
+know and we'll see this in a moment you
+ 
+
+ align:start position:0%
+know and we'll see this in a moment you
+don't quite know what happened when you
+
+ align:start position:0%
+don't quite know what happened when you
+ 
+
+ align:start position:0%
+don't quite know what happened when you
+know you didn't get an answer back from
+
+ align:start position:0%
+know you didn't get an answer back from
+ 
+
+ align:start position:0%
+know you didn't get an answer back from
+the service you don't know if service
+
+ align:start position:0%
+the service you don't know if service
+ 
+
+ align:start position:0%
+the service you don't know if service
+actually got your transfer request and
+
+ align:start position:0%
+actually got your transfer request and
+ 
+
+ align:start position:0%
+actually got your transfer request and
+you know crashed after that and you know
+
+ align:start position:0%
+you know crashed after that and you know
+ 
+
+ align:start position:0%
+you know crashed after that and you know
+it got the request it actually
+
+ align:start position:0%
+it got the request it actually
+ 
+
+ align:start position:0%
+it got the request it actually
+implemented the transfer and then
+
+ align:start position:0%
+implemented the transfer and then
+ 
+
+ align:start position:0%
+implemented the transfer and then
+crashed it just didn't send your
+
+ align:start position:0%
+crashed it just didn't send your
+ 
+
+ align:start position:0%
+crashed it just didn't send your
+response back so you're not quite sure
+
+ align:start position:0%
+response back so you're not quite sure
+ 
+
+ align:start position:0%
+response back so you're not quite sure
+whether you need to retry the request or
+
+ align:start position:0%
+whether you need to retry the request or
+ 
+
+ align:start position:0%
+whether you need to retry the request or
+not okay uh we'll actually see how to
+
+ align:start position:0%
+not okay uh we'll actually see how to
+ 
+
+ align:start position:0%
+not okay uh we'll actually see how to
+deal with the these issues um in in in a
+
+ align:start position:0%
+deal with the these issues um in in in a
+ 
+
+ align:start position:0%
+deal with the these issues um in in in a
+few
+
+ align:start position:0%
+few
+ 
+
+ align:start position:0%
+few
+minutes now there was one thing that's
+
+ align:start position:0%
+minutes now there was one thing that's
+ 
+
+ align:start position:0%
+minutes now there was one thing that's
+really important that about this line of
+
+ align:start position:0%
+really important that about this line of
+ 
+
+ align:start position:0%
+really important that about this line of
+code this line xmlrpc execute money
+
+ align:start position:0%
+code this line xmlrpc execute money
+ 
+
+ align:start position:0%
+code this line xmlrpc execute money
+transfer block that line of code
+
+ align:start position:0%
+transfer block that line of code
+ 
+
+ align:start position:0%
+transfer block that line of code
+actually is not something that runs on
+
+ align:start position:0%
+actually is not something that runs on
+ 
+
+ align:start position:0%
+actually is not something that runs on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+service okay it's a local procedure call
+
+ align:start position:0%
+service okay it's a local procedure call
+ 
+
+ align:start position:0%
+service okay it's a local procedure call
+xmlrpc execute is a local procedure call
+
+ align:start position:0%
+xmlrpc execute is a local procedure call
+ 
+
+ align:start position:0%
+xmlrpc execute is a local procedure call
+okay and that procedure is an example of
+
+ align:start position:0%
+okay and that procedure is an example of
+ 
+
+ align:start position:0%
+okay and that procedure is an example of
+something called a stub because what it
+
+ align:start position:0%
+something called a stub because what it
+ 
+
+ align:start position:0%
+something called a stub because what it
+is is a stub that to this caller fakes
+
+ align:start position:0%
+is is a stub that to this caller fakes
+ 
+
+ align:start position:0%
+is is a stub that to this caller fakes
+out the fact that there's a service
+
+ align:start position:0%
+out the fact that there's a service
+ 
+
+ align:start position:0%
+out the fact that there's a service
+somewhere else I mean it doesn't it it
+
+ align:start position:0%
+somewhere else I mean it doesn't it it
+ 
+
+ align:start position:0%
+somewhere else I mean it doesn't it it
+prevents the caller from having to deal
+
+ align:start position:0%
+prevents the caller from having to deal
+ 
+
+ align:start position:0%
+prevents the caller from having to deal
+with taking the arguments and putting it
+
+ align:start position:0%
+with taking the arguments and putting it
+ 
+
+ align:start position:0%
+with taking the arguments and putting it
+in a message and sending it to the other
+
+ align:start position:0%
+in a message and sending it to the other
+ 
+
+ align:start position:0%
+in a message and sending it to the other
+side um the caller just calls a Lo
+
+ align:start position:0%
+side um the caller just calls a Lo
+ 
+
+ align:start position:0%
+side um the caller just calls a Lo
+procedure um giving it suitable
+
+ align:start position:0%
+procedure um giving it suitable
+ 
+
+ align:start position:0%
+procedure um giving it suitable
+arguments that change for this function
+
+ align:start position:0%
+arguments that change for this function
+ 
+
+ align:start position:0%
+arguments that change for this function
+now to do the work of sending a message
+
+ align:start position:0%
+now to do the work of sending a message
+ 
+
+ align:start position:0%
+now to do the work of sending a message
+across the network but this is a local
+
+ align:start position:0%
+across the network but this is a local
+ 
+
+ align:start position:0%
+across the network but this is a local
+call so what happens underneath
+
+ align:start position:0%
+call so what happens underneath
+ 
+
+ align:start position:0%
+call so what happens underneath
+underneath in the library once you call
+
+ align:start position:0%
+underneath in the library once you call
+ 
+
+ align:start position:0%
+underneath in the library once you call
+exml RPC do execute in this example
+
+ align:start position:0%
+exml RPC do execute in this example
+ 
+
+ align:start position:0%
+exml RPC do execute in this example
+somebody does the work that Library does
+
+ align:start position:0%
+somebody does the work that Library does
+ 
+
+ align:start position:0%
+somebody does the work that Library does
+the work of taking the different
+
+ align:start position:0%
+the work of taking the different
+ 
+
+ align:start position:0%
+the work of taking the different
+arguments that have been presented to it
+
+ align:start position:0%
+arguments that have been presented to it
+ 
+
+ align:start position:0%
+arguments that have been presented to it
+and converting them into a message
+
+ align:start position:0%
+and converting them into a message
+ 
+
+ align:start position:0%
+and converting them into a message
+marshalling all of the stuff into a
+
+ align:start position:0%
+marshalling all of the stuff into a
+ 
+
+ align:start position:0%
+marshalling all of the stuff into a
+message and then shipping that message
+
+ align:start position:0%
+message and then shipping that message
+ 
+
+ align:start position:0%
+message and then shipping that message
+off to the server and that has to go
+
+ align:start position:0%
+off to the server and that has to go
+ 
+
+ align:start position:0%
+off to the server and that has to go
+into some kind of a format on the wire
+
+ align:start position:0%
+into some kind of a format on the wire
+ 
+
+ align:start position:0%
+into some kind of a format on the wire
+right ultimately on this wire connecting
+
+ align:start position:0%
+right ultimately on this wire connecting
+ 
+
+ align:start position:0%
+right ultimately on this wire connecting
+the client to the service there's format
+
+ align:start position:0%
+the client to the service there's format
+ 
+
+ align:start position:0%
+the client to the service there's format
+and I already mentioned that this runs
+
+ align:start position:0%
+and I already mentioned that this runs
+ 
+
+ align:start position:0%
+and I already mentioned that this runs
+on top of HTTP and so we can actually
+
+ align:start position:0%
+on top of HTTP and so we can actually
+ 
+
+ align:start position:0%
+on top of HTTP and so we can actually
+look at um what that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so post here is the method
+
+ align:start position:0%
+right okay so post here is the method
+ 
+
+ align:start position:0%
+right okay so post here is the method
+that you use in HTTP um the SL rpc2 is
+
+ align:start position:0%
+that you use in HTTP um the SL rpc2 is
+ 
+
+ align:start position:0%
+that you use in HTTP um the SL rpc2 is
+actually the same thing that was used in
+
+ align:start position:0%
+actually the same thing that was used in
+ 
+
+ align:start position:0%
+actually the same thing that was used in
+if you remember the previous uh uh from
+
+ align:start position:0%
+if you remember the previous uh uh from
+ 
+
+ align:start position:0%
+if you remember the previous uh uh from
+the previous screenshot um when we did
+
+ align:start position:0%
+the previous screenshot um when we did
+ 
+
+ align:start position:0%
+the previous screenshot um when we did
+the new to when we did the new call to
+
+ align:start position:0%
+the new to when we did the new call to
+ 
+
+ align:start position:0%
+the new to when we did the new call to
+get a new XML RPC client we gave it a
+
+ align:start position:0%
+get a new XML RPC client we gave it a
+ 
+
+ align:start position:0%
+get a new XML RPC client we gave it a
+server name and a port number but we
+
+ align:start position:0%
+server name and a port number but we
+ 
+
+ align:start position:0%
+server name and a port number but we
+also gave it something called rpc2 now
+
+ align:start position:0%
+also gave it something called rpc2 now
+ 
+
+ align:start position:0%
+also gave it something called rpc2 now
+that's just like a file on the other
+
+ align:start position:0%
+that's just like a file on the other
+ 
+
+ align:start position:0%
+that's just like a file on the other
+side it says there are many different
+
+ align:start position:0%
+side it says there are many different
+ 
+
+ align:start position:0%
+side it says there are many different
+RPC programs running on your service and
+
+ align:start position:0%
+RPC programs running on your service and
+ 
+
+ align:start position:0%
+RPC programs running on your service and
+I want rpc2 to run I mean I could have
+
+ align:start position:0%
+I want rpc2 to run I mean I could have
+ 
+
+ align:start position:0%
+I want rpc2 to run I mean I could have
+named it anything um I
+
+ align:start position:0%
+named it anything um I
+ 
+
+ align:start position:0%
+named it anything um I
+wanted and you know that's a lot like
+
+ align:start position:0%
+wanted and you know that's a lot like
+ 
+
+ align:start position:0%
+wanted and you know that's a lot like
+giving the file name on a URL and then
+
+ align:start position:0%
+giving the file name on a URL and then
+ 
+
+ align:start position:0%
+giving the file name on a URL and then
+you uh go on you give it the host name
+
+ align:start position:0%
+you uh go on you give it the host name
+ 
+
+ align:start position:0%
+you uh go on you give it the host name
+this is a lot like an HTTP header the
+
+ align:start position:0%
+this is a lot like an HTTP header the
+ 
+
+ align:start position:0%
+this is a lot like an HTTP header the
+interesting new stuff here is um in the
+
+ align:start position:0%
+interesting new stuff here is um in the
+ 
+
+ align:start position:0%
+interesting new stuff here is um in the
+XML Arguments for those who are not
+
+ align:start position:0%
+XML Arguments for those who are not
+ 
+
+ align:start position:0%
+XML Arguments for those who are not
+familiar with XML you know it's just a
+
+ align:start position:0%
+familiar with XML you know it's just a
+ 
+
+ align:start position:0%
+familiar with XML you know it's just a
+method of send a way of sending things
+
+ align:start position:0%
+method of send a way of sending things
+ 
+
+ align:start position:0%
+method of send a way of sending things
+that have attributes and values
+
+ align:start position:0%
+that have attributes and values
+ 
+
+ align:start position:0%
+that have attributes and values
+associated with them so every message
+
+ align:start position:0%
+associated with them so every message
+ 
+
+ align:start position:0%
+associated with them so every message
+has is in the has the format that it's
+
+ align:start position:0%
+has is in the has the format that it's
+ 
+
+ align:start position:0%
+has is in the has the format that it's
+attributes and values and they can be
+
+ align:start position:0%
+attributes and values and they can be
+ 
+
+ align:start position:0%
+attributes and values and they can be
+nested within each other um the only
+
+ align:start position:0%
+nested within each other um the only
+ 
+
+ align:start position:0%
+nested within each other um the only
+interesting thing is here U this
+
+ align:start position:0%
+interesting thing is here U this
+ 
+
+ align:start position:0%
+interesting thing is here U this
+particular XML RPC system supports a few
+
+ align:start position:0%
+particular XML RPC system supports a few
+ 
+
+ align:start position:0%
+particular XML RPC system supports a few
+different data formats you can do
+
+ align:start position:0%
+different data formats you can do
+ 
+
+ align:start position:0%
+different data formats you can do
+integers and you characters and strings
+
+ align:start position:0%
+integers and you characters and strings
+ 
+
+ align:start position:0%
+integers and you characters and strings
+and doubles and floats and a few
+
+ align:start position:0%
+and doubles and floats and a few
+ 
+
+ align:start position:0%
+and doubles and floats and a few
+different things like that and I4 just
+
+ align:start position:0%
+different things like that and I4 just
+ 
+
+ align:start position:0%
+different things like that and I4 just
+means it's a 32-bit integer and you can
+
+ align:start position:0%
+means it's a 32-bit integer and you can
+ 
+
+ align:start position:0%
+means it's a 32-bit integer and you can
+give it you know three numbers the from
+
+ align:start position:0%
+give it you know three numbers the from
+ 
+
+ align:start position:0%
+give it you know three numbers the from
+your account number the you know your
+
+ align:start position:0%
+your account number the you know your
+ 
+
+ align:start position:0%
+your account number the you know your
+supplier's account number and the amount
+
+ align:start position:0%
+supplier's account number and the amount
+ 
+
+ align:start position:0%
+supplier's account number and the amount
+of money that you want to
+
+ align:start position:0%
+of money that you want to
+ 
+
+ align:start position:0%
+of money that you want to
+transfer the good thing is all of this
+
+ align:start position:0%
+transfer the good thing is all of this
+ 
+
+ align:start position:0%
+transfer the good thing is all of this
+stuff is done underneath the covers and
+
+ align:start position:0%
+stuff is done underneath the covers and
+ 
+
+ align:start position:0%
+stuff is done underneath the covers and
+you don't actually have to deal with it
+
+ align:start position:0%
+you don't actually have to deal with it
+ 
+
+ align:start position:0%
+you don't actually have to deal with it
+if you're writing the client or you're
+
+ align:start position:0%
+if you're writing the client or you're
+ 
+
+ align:start position:0%
+if you're writing the client or you're
+writing the service all this work
+
+ align:start position:0%
+writing the service all this work
+ 
+
+ align:start position:0%
+writing the service all this work
+happens underneath so it greatly
+
+ align:start position:0%
+happens underneath so it greatly
+ 
+
+ align:start position:0%
+happens underneath so it greatly
+simplifies uh your ability to take um
+
+ align:start position:0%
+simplifies uh your ability to take um
+ 
+
+ align:start position:0%
+simplifies uh your ability to take um
+you know Implement client service
+
+ align:start position:0%
+you know Implement client service
+ 
+
+ align:start position:0%
+you know Implement client service
+programs with clients Services being
+
+ align:start position:0%
+programs with clients Services being
+ 
+
+ align:start position:0%
+programs with clients Services being
+separated from one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+okay so so far we've made it look a lot
+
+ align:start position:0%
+okay so so far we've made it look a lot
+ 
+
+ align:start position:0%
+okay so so far we've made it look a lot
+except for this little timer that you
+
+ align:start position:0%
+except for this little timer that you
+ 
+
+ align:start position:0%
+except for this little timer that you
+have to maintain um we made look a lot
+
+ align:start position:0%
+have to maintain um we made look a lot
+ 
+
+ align:start position:0%
+have to maintain um we made look a lot
+like a remote procedure call is like a
+
+ align:start position:0%
+like a remote procedure call is like a
+ 
+
+ align:start position:0%
+like a remote procedure call is like a
+procedure problem in fact the code here
+
+ align:start position:0%
+procedure problem in fact the code here
+ 
+
+ align:start position:0%
+procedure problem in fact the code here
+I mean the only difference was we
+
+ align:start position:0%
+I mean the only difference was we
+ 
+
+ align:start position:0%
+I mean the only difference was we
+replace what was previously what would
+
+ align:start position:0%
+replace what was previously what would
+ 
+
+ align:start position:0%
+replace what was previously what would
+have been money transferred with
+
+ align:start position:0%
+have been money transferred with
+ 
+
+ align:start position:0%
+have been money transferred with
+argument we replaced with a stub call
+
+ align:start position:0%
+argument we replaced with a stub call
+ 
+
+ align:start position:0%
+argument we replaced with a stub call
+taking the name of the procedure we want
+
+ align:start position:0%
+taking the name of the procedure we want
+ 
+
+ align:start position:0%
+taking the name of the procedure we want
+to run on the service with the so it
+
+ align:start position:0%
+to run on the service with the so it
+ 
+
+ align:start position:0%
+to run on the service with the so it
+looks a lot like a
+
+ align:start position:0%
+looks a lot like a
+ 
+
+ align:start position:0%
+looks a lot like a
+procedure that actually is a pretty
+
+ align:start position:0%
+procedure that actually is a pretty
+ 
+
+ align:start position:0%
+procedure that actually is a pretty
+deceptive thing and in fact a hint at
+
+ align:start position:0%
+deceptive thing and in fact a hint at
+ 
+
+ align:start position:0%
+deceptive thing and in fact a hint at
+that is you can get from the fact that
+
+ align:start position:0%
+that is you can get from the fact that
+ 
+
+ align:start position:0%
+that is you can get from the fact that
+at the bottom of this thing up there um
+
+ align:start position:0%
+at the bottom of this thing up there um
+ 
+
+ align:start position:0%
+at the bottom of this thing up there um
+there are there's a line that says you
+
+ align:start position:0%
+there are there's a line that says you
+ 
+
+ align:start position:0%
+there are there's a line that says you
+have to deal with xmlrpc exception and
+
+ align:start position:0%
+have to deal with xmlrpc exception and
+ 
+
+ align:start position:0%
+have to deal with xmlrpc exception and
+that's the kind of exception you get
+
+ align:start position:0%
+that's the kind of exception you get
+ 
+
+ align:start position:0%
+that's the kind of exception you get
+when the underlying RPC Library decides
+
+ align:start position:0%
+when the underlying RPC Library decides
+ 
+
+ align:start position:0%
+when the underlying RPC Library decides
+that it hasn't heard an answer from the
+
+ align:start position:0%
+that it hasn't heard an answer from the
+ 
+
+ align:start position:0%
+that it hasn't heard an answer from the
+service in a while and throws an
+
+ align:start position:0%
+service in a while and throws an
+ 
+
+ align:start position:0%
+service in a while and throws an
+exception and your code has to deal with
+
+ align:start position:0%
+exception and your code has to deal with
+ 
+
+ align:start position:0%
+exception and your code has to deal with
+it now you're never going to get that
+
+ align:start position:0%
+it now you're never going to get that
+ 
+
+ align:start position:0%
+it now you're never going to get that
+kind of exception from a regular
+
+ align:start position:0%
+kind of exception from a regular
+ 
+
+ align:start position:0%
+kind of exception from a regular
+procedure it's not going to say I didn't
+
+ align:start position:0%
+procedure it's not going to say I didn't
+ 
+
+ align:start position:0%
+procedure it's not going to say I didn't
+hear back from the caller from the
+
+ align:start position:0%
+hear back from the caller from the
+ 
+
+ align:start position:0%
+hear back from the caller from the
+colleag do something see that's a
+
+ align:start position:0%
+colleag do something see that's a
+ 
+
+ align:start position:0%
+colleag do something see that's a
+different that's that's a new mode a new
+
+ align:start position:0%
+different that's that's a new mode a new
+ 
+
+ align:start position:0%
+different that's that's a new mode a new
+exception mode that you didn't
+
+ align:start position:0%
+exception mode that you didn't
+ 
+
+ align:start position:0%
+exception mode that you didn't
+previously have to deal with I mean you
+
+ align:start position:0%
+previously have to deal with I mean you
+ 
+
+ align:start position:0%
+previously have to deal with I mean you
+have to deal with other kinds of
+
+ align:start position:0%
+have to deal with other kinds of
+ 
+
+ align:start position:0%
+have to deal with other kinds of
+exceptions but not this
+
+ align:start position:0%
+exceptions but not this
+ 
+
+ align:start position:0%
+exceptions but not this
+one so an RPC is notal is not the same
+
+ align:start position:0%
+one so an RPC is notal is not the same
+ 
+
+ align:start position:0%
+one so an RPC is notal is not the same
+as a procedure call and in fact it's a
+
+ align:start position:0%
+as a procedure call and in fact it's a
+ 
+
+ align:start position:0%
+as a procedure call and in fact it's a
+little unfortunate
+
+ align:start position:0%
+little unfortunate
+ 
+
+ align:start position:0%
+little unfortunate
+that um in most historical reasons uh
+
+ align:start position:0%
+that um in most historical reasons uh
+ 
+
+ align:start position:0%
+that um in most historical reasons uh
+we're stuck a little bit with the name
+
+ align:start position:0%
+we're stuck a little bit with the name
+ 
+
+ align:start position:0%
+we're stuck a little bit with the name
+mode procedure call in fact increasingly
+
+ align:start position:0%
+mode procedure call in fact increasingly
+ 
+
+ align:start position:0%
+mode procedure call in fact increasingly
+more and more RPC systems um don't look
+
+ align:start position:0%
+more and more RPC systems um don't look
+ 
+
+ align:start position:0%
+more and more RPC systems um don't look
+like procedure calls at all in terms of
+
+ align:start position:0%
+like procedure calls at all in terms of
+ 
+
+ align:start position:0%
+like procedure calls at all in terms of
+the semantics um but we're sort of stuck
+
+ align:start position:0%
+the semantics um but we're sort of stuck
+ 
+
+ align:start position:0%
+the semantics um but we're sort of stuck
+with the name and people continue to
+
+ align:start position:0%
+with the name and people continue to
+ 
+
+ align:start position:0%
+with the name and people continue to
+have um you know kinds of remote
+
+ align:start position:0%
+have um you know kinds of remote
+ 
+
+ align:start position:0%
+have um you know kinds of remote
+procedure calls and they use the same
+
+ align:start position:0%
+procedure calls and they use the same
+ 
+
+ align:start position:0%
+procedure calls and they use the same
+name for
+
+ align:start position:0%
+name for
+ 
+
+ align:start position:0%
+name for
+it and the first main difference arises
+
+ align:start position:0%
+it and the first main difference arises
+ 
+
+ align:start position:0%
+it and the first main difference arises
+from the fact
+
+ align:start position:0%
+from the fact
+ 
+
+ align:start position:0%
+from the fact
+that there is no fate sharing between
+
+ align:start position:0%
+that there is no fate sharing between
+ 
+
+ align:start position:0%
+that there is no fate sharing between
+client and service it's the service
+
+ align:start position:0%
+client and service it's the service
+ 
+
+ align:start position:0%
+client and service it's the service
+crashes the client doesn't cck already
+
+ align:start position:0%
+crashes the client doesn't cck already
+ 
+
+ align:start position:0%
+crashes the client doesn't cck already
+you have a big difference between um a
+
+ align:start position:0%
+you have a big difference between um a
+ 
+
+ align:start position:0%
+you have a big difference between um a
+regular procedure and previously I
+
+ align:start position:0%
+regular procedure and previously I
+ 
+
+ align:start position:0%
+regular procedure and previously I
+presented this as a an advantage because
+
+ align:start position:0%
+presented this as a an advantage because
+ 
+
+ align:start position:0%
+presented this as a an advantage because
+you know if you have faith sharing then
+
+ align:start position:0%
+you know if you have faith sharing then
+ 
+
+ align:start position:0%
+you know if you have faith sharing then
+the color is always at the mercy of the
+
+ align:start position:0%
+the color is always at the mercy of the
+ 
+
+ align:start position:0%
+the color is always at the mercy of the
+colleague but because you have no faith
+
+ align:start position:0%
+colleague but because you have no faith
+ 
+
+ align:start position:0%
+colleague but because you have no faith
+sharing you have other problems um to
+
+ align:start position:0%
+sharing you have other problems um to
+ 
+
+ align:start position:0%
+sharing you have other problems um to
+deal with and in particular all of these
+
+ align:start position:0%
+deal with and in particular all of these
+ 
+
+ align:start position:0%
+deal with and in particular all of these
+stem from the fact that it's extremely
+
+ align:start position:0%
+stem from the fact that it's extremely
+ 
+
+ align:start position:0%
+stem from the fact that it's extremely
+hard to distinguish between a failure
+
+ align:start position:0%
+hard to distinguish between a failure
+ 
+
+ align:start position:0%
+hard to distinguish between a failure
+versus extremely slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it will turn out that we'll revisit
+
+ align:start position:0%
+and it will turn out that we'll revisit
+ 
+
+ align:start position:0%
+and it will turn out that we'll revisit
+this over and over again we talk when we
+
+ align:start position:0%
+this over and over again we talk when we
+ 
+
+ align:start position:0%
+this over and over again we talk when we
+talk about networks um and reliable
+
+ align:start position:0%
+talk about networks um and reliable
+ 
+
+ align:start position:0%
+talk about networks um and reliable
+transmission over networks we'll deal
+
+ align:start position:0%
+transmission over networks we'll deal
+ 
+
+ align:start position:0%
+transmission over networks we'll deal
+with it and then we're going to talk
+
+ align:start position:0%
+with it and then we're going to talk
+ 
+
+ align:start position:0%
+with it and then we're going to talk
+about fall tolerance um and we're going
+
+ align:start position:0%
+about fall tolerance um and we're going
+ 
+
+ align:start position:0%
+about fall tolerance um and we're going
+to talk about an idea called atomicity
+
+ align:start position:0%
+to talk about an idea called atomicity
+ 
+
+ align:start position:0%
+to talk about an idea called atomicity
+and then we're going to talk about
+
+ align:start position:0%
+and then we're going to talk about
+ 
+
+ align:start position:0%
+and then we're going to talk about
+something called transactions and
+
+ align:start position:0%
+something called transactions and
+ 
+
+ align:start position:0%
+something called transactions and
+they're all going to deal with this
+
+ align:start position:0%
+they're all going to deal with this
+ 
+
+ align:start position:0%
+they're all going to deal with this
+problem that it's going to be very hard
+
+ align:start position:0%
+problem that it's going to be very hard
+ 
+
+ align:start position:0%
+problem that it's going to be very hard
+for us to tell when you ask somebody to
+
+ align:start position:0%
+for us to tell when you ask somebody to
+ 
+
+ align:start position:0%
+for us to tell when you ask somebody to
+do a piece of work whether they did it
+
+ align:start position:0%
+do a piece of work whether they did it
+ 
+
+ align:start position:0%
+do a piece of work whether they did it
+fully or did not okay and this is going
+
+ align:start position:0%
+fully or did not okay and this is going
+ 
+
+ align:start position:0%
+fully or did not okay and this is going
+to be a repeated theme a theme that
+
+ align:start position:0%
+to be a repeated theme a theme that
+ 
+
+ align:start position:0%
+to be a repeated theme a theme that
+going to repeatedly see in in the course
+
+ align:start position:0%
+going to repeatedly see in in the course
+ 
+
+ align:start position:0%
+going to repeatedly see in in the course
+but to complicate why this is hard uh
+
+ align:start position:0%
+but to complicate why this is hard uh
+ 
+
+ align:start position:0%
+but to complicate why this is hard uh
+let me explain three possible things
+
+ align:start position:0%
+let me explain three possible things
+ 
+
+ align:start position:0%
+let me explain three possible things
+that could happen when you have a client
+
+ align:start position:0%
+that could happen when you have a client
+ 
+
+ align:start position:0%
+that could happen when you have a client
+talk to a service and um what kind of
+
+ align:start position:0%
+talk to a service and um what kind of
+ 
+
+ align:start position:0%
+talk to a service and um what kind of
+semantics you want from a client service
+
+ align:start position:0%
+semantics you want from a client service
+ 
+
+ align:start position:0%
+semantics you want from a client service
+interaction they all stem from the fact
+
+ align:start position:0%
+interaction they all stem from the fact
+ 
+
+ align:start position:0%
+interaction they all stem from the fact
+that this is extremely hard to
+
+ align:start position:0%
+that this is extremely hard to
+ 
+
+ align:start position:0%
+that this is extremely hard to
+determine the first semantics that you
+
+ align:start position:0%
+determine the first semantics that you
+ 
+
+ align:start position:0%
+determine the first semantics that you
+might want is the ideal sems the client
+
+ align:start position:0%
+might want is the ideal sems the client
+ 
+
+ align:start position:0%
+might want is the ideal sems the client
+talks to the service and either the
+
+ align:start position:0%
+talks to the service and either the
+ 
+
+ align:start position:0%
+talks to the service and either the
+service answers with a response or it
+
+ align:start position:0%
+service answers with a response or it
+ 
+
+ align:start position:0%
+service answers with a response or it
+doesn't okay and that's something called
+
+ align:start position:0%
+doesn't okay and that's something called
+ 
+
+ align:start position:0%
+doesn't okay and that's something called
+exactly once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+semantics so in this example here
+
+ align:start position:0%
+semantics so in this example here
+ 
+
+ align:start position:0%
+semantics so in this example here
+underneath the library May time out and
+
+ align:start position:0%
+underneath the library May time out and
+ 
+
+ align:start position:0%
+underneath the library May time out and
+it may wish to retransmit or it may wish
+
+ align:start position:0%
+it may wish to retransmit or it may wish
+ 
+
+ align:start position:0%
+it may wish to retransmit or it may wish
+to throw an exception and the caller
+
+ align:start position:0%
+to throw an exception and the caller
+ 
+
+ align:start position:0%
+to throw an exception and the caller
+caller may you know the client may want
+
+ align:start position:0%
+caller may you know the client may want
+ 
+
+ align:start position:0%
+caller may you know the client may want
+to send the request again but in ideal
+
+ align:start position:0%
+to send the request again but in ideal
+ 
+
+ align:start position:0%
+to send the request again but in ideal
+hits you want one time you want exactly
+
+ align:start position:0%
+hits you want one time you want exactly
+ 
+
+ align:start position:0%
+hits you want one time you want exactly
+once this amount of money to be moved
+
+ align:start position:0%
+once this amount of money to be moved
+ 
+
+ align:start position:0%
+once this amount of money to be moved
+from Bank account one to bank account
+
+ align:start position:0%
+from Bank account one to bank account
+ 
+
+ align:start position:0%
+from Bank account one to bank account
+two right you certainly don't want you
+
+ align:start position:0%
+two right you certainly don't want you
+ 
+
+ align:start position:0%
+two right you certainly don't want you
+know your amount of money to be moved
+
+ align:start position:0%
+know your amount of money to be moved
+ 
+
+ align:start position:0%
+know your amount of money to be moved
+twice to your
+
+ align:start position:0%
+twice to your
+ 
+
+ align:start position:0%
+twice to your
+supplier it will turn out this is ideal
+
+ align:start position:0%
+supplier it will turn out this is ideal
+ 
+
+ align:start position:0%
+supplier it will turn out this is ideal
+and it's going to be you know pretty
+
+ align:start position:0%
+and it's going to be you know pretty
+ 
+
+ align:start position:0%
+and it's going to be you know pretty
+difficult and extremely hard to to um
+
+ align:start position:0%
+difficult and extremely hard to to um
+ 
+
+ align:start position:0%
+difficult and extremely hard to to um
+achieve exactly once the mandat and
+
+ align:start position:0%
+achieve exactly once the mandat and
+ 
+
+ align:start position:0%
+achieve exactly once the mandat and
+we're going to try hard to different
+
+ align:start position:0%
+we're going to try hard to different
+ 
+
+ align:start position:0%
+we're going to try hard to different
+methods in the course but this it's not
+
+ align:start position:0%
+methods in the course but this it's not
+ 
+
+ align:start position:0%
+methods in the course but this it's not
+an easy problem at all it stems from the
+
+ align:start position:0%
+an easy problem at all it stems from the
+ 
+
+ align:start position:0%
+an easy problem at all it stems from the
+fact that it's very hard to know
+
+ align:start position:0%
+fact that it's very hard to know
+ 
+
+ align:start position:0%
+fact that it's very hard to know
+that so we might give up a little bit
+
+ align:start position:0%
+that so we might give up a little bit
+ 
+
+ align:start position:0%
+that so we might give up a little bit
+and say okay I don't I can't really get
+
+ align:start position:0%
+and say okay I don't I can't really get
+ 
+
+ align:start position:0%
+and say okay I don't I can't really get
+exactly once sematics very easily but
+
+ align:start position:0%
+exactly once sematics very easily but
+ 
+
+ align:start position:0%
+exactly once sematics very easily but
+let me try for at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once so what this means is that I will
+
+ align:start position:0%
+once so what this means is that I will
+ 
+
+ align:start position:0%
+once so what this means is that I will
+keep the client will keep retrying or
+
+ align:start position:0%
+keep the client will keep retrying or
+ 
+
+ align:start position:0%
+keep the client will keep retrying or
+the library will keep retrying and you
+
+ align:start position:0%
+the library will keep retrying and you
+ 
+
+ align:start position:0%
+the library will keep retrying and you
+can decompose it in either way until it
+
+ align:start position:0%
+can decompose it in either way until it
+ 
+
+ align:start position:0%
+can decompose it in either way until it
+is sure that the that this call
+
+ align:start position:0%
+is sure that the that this call
+ 
+
+ align:start position:0%
+is sure that the that this call
+succeeded at least once now it might
+
+ align:start position:0%
+succeeded at least once now it might
+ 
+
+ align:start position:0%
+succeeded at least once now it might
+have succeeded more than once you know
+
+ align:start position:0%
+have succeeded more than once you know
+ 
+
+ align:start position:0%
+have succeeded more than once you know
+the service you know was very slow and
+
+ align:start position:0%
+the service you know was very slow and
+ 
+
+ align:start position:0%
+the service you know was very slow and
+then it times out you try it again the
+
+ align:start position:0%
+then it times out you try it again the
+ 
+
+ align:start position:0%
+then it times out you try it again the
+service says oh okay I see a request I
+
+ align:start position:0%
+service says oh okay I see a request I
+ 
+
+ align:start position:0%
+service says oh okay I see a request I
+do it again but it's at least once
+
+ align:start position:0%
+do it again but it's at least once
+ 
+
+ align:start position:0%
+do it again but it's at least once
+okay now at least once is not nice
+
+ align:start position:0%
+okay now at least once is not nice
+ 
+
+ align:start position:0%
+okay now at least once is not nice
+semantics if you're using at least one
+
+ align:start position:0%
+semantics if you're using at least one
+ 
+
+ align:start position:0%
+semantics if you're using at least one
+semantics in your code here right
+
+ align:start position:0%
+semantics in your code here right
+ 
+
+ align:start position:0%
+semantics in your code here right
+because I mean your supplier might end
+
+ align:start position:0%
+because I mean your supplier might end
+ 
+
+ align:start position:0%
+because I mean your supplier might end
+up with $7 million instead of $1 million
+
+ align:start position:0%
+up with $7 million instead of $1 million
+ 
+
+ align:start position:0%
+up with $7 million instead of $1 million
+but at least once is okay if the service
+
+ align:start position:0%
+but at least once is okay if the service
+ 
+
+ align:start position:0%
+but at least once is okay if the service
+has a certain kind of semantic called
+
+ align:start position:0%
+has a certain kind of semantic called
+ 
+
+ align:start position:0%
+has a certain kind of semantic called
+item Port
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+semantics what that means is that when
+
+ align:start position:0%
+semantics what that means is that when
+ 
+
+ align:start position:0%
+semantics what that means is that when
+you do an operation more than once the
+
+ align:start position:0%
+you do an operation more than once the
+ 
+
+ align:start position:0%
+you do an operation more than once the
+answers are the same as if you really
+
+ align:start position:0%
+answers are the same as if you really
+ 
+
+ align:start position:0%
+answers are the same as if you really
+want as a simple example if this wasn't
+
+ align:start position:0%
+want as a simple example if this wasn't
+ 
+
+ align:start position:0%
+want as a simple example if this wasn't
+a transfer of money but just you
+
+ align:start position:0%
+a transfer of money but just you
+ 
+
+ align:start position:0%
+a transfer of money but just you
+checking your bank account balance it
+
+ align:start position:0%
+checking your bank account balance it
+ 
+
+ align:start position:0%
+checking your bank account balance it
+doesn't really matter that you do it 100
+
+ align:start position:0%
+doesn't really matter that you do it 100
+ 
+
+ align:start position:0%
+doesn't really matter that you do it 100
+times as long as one of them succeeds
+
+ align:start position:0%
+times as long as one of them succeeds
+ 
+
+ align:start position:0%
+times as long as one of them succeeds
+and you get back balance you're fine I
+
+ align:start position:0%
+and you get back balance you're fine I
+ 
+
+ align:start position:0%
+and you get back balance you're fine I
+mean doing it seven times does not
+
+ align:start position:0%
+mean doing it seven times does not
+ 
+
+ align:start position:0%
+mean doing it seven times does not
+really change anything does not move
+
+ align:start position:0%
+really change anything does not move
+ 
+
+ align:start position:0%
+really change anything does not move
+extra money anywhere else um you know so
+
+ align:start position:0%
+extra money anywhere else um you know so
+ 
+
+ align:start position:0%
+extra money anywhere else um you know so
+that's an example of an item poent um
+
+ align:start position:0%
+that's an example of an item poent um
+ 
+
+ align:start position:0%
+that's an example of an item poent um
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+which um you know works out well with at
+
+ align:start position:0%
+which um you know works out well with at
+ 
+
+ align:start position:0%
+which um you know works out well with at
+least one semantics and at least one
+
+ align:start position:0%
+least one semantics and at least one
+ 
+
+ align:start position:0%
+least one semantics and at least one
+semantics is much easier to obtain than
+
+ align:start position:0%
+semantics is much easier to obtain than
+ 
+
+ align:start position:0%
+semantics is much easier to obtain than
+exactly once semantics
+
+ align:start position:0%
+exactly once semantics
+ 
+
+ align:start position:0%
+exactly once semantics
+and the Third Kind of semantics U is
+
+ align:start position:0%
+and the Third Kind of semantics U is
+ 
+
+ align:start position:0%
+and the Third Kind of semantics U is
+something which you know coners or at
+
+ align:start position:0%
+something which you know coners or at
+ 
+
+ align:start position:0%
+something which you know coners or at
+most wants
+
+ align:start position:0%
+most wants
+ 
+
+ align:start position:0%
+most wants
+semantics that means zero or more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times and here the challenge is really
+
+ align:start position:0%
+times and here the challenge is really
+ 
+
+ align:start position:0%
+times and here the challenge is really
+figuring out did it really work at least
+
+ align:start position:0%
+figuring out did it really work at least
+ 
+
+ align:start position:0%
+figuring out did it really work at least
+once or not did it work exactly I mean
+
+ align:start position:0%
+once or not did it work exactly I mean
+ 
+
+ align:start position:0%
+once or not did it work exactly I mean
+at most once or not so if you don't get
+
+ align:start position:0%
+at most once or not so if you don't get
+ 
+
+ align:start position:0%
+at most once or not so if you don't get
+a response back then um you know you
+
+ align:start position:0%
+a response back then um you know you
+ 
+
+ align:start position:0%
+a response back then um you know you
+time out and it might be that it didn't
+
+ align:start position:0%
+time out and it might be that it didn't
+ 
+
+ align:start position:0%
+time out and it might be that it didn't
+succeed at all and you say that's fine
+
+ align:start position:0%
+succeed at all and you say that's fine
+ 
+
+ align:start position:0%
+succeed at all and you say that's fine
+I'll deal with it um separately and if
+
+ align:start position:0%
+I'll deal with it um separately and if
+ 
+
+ align:start position:0%
+I'll deal with it um separately and if
+you get a response back then you know
+
+ align:start position:0%
+you get a response back then you know
+ 
+
+ align:start position:0%
+you get a response back then you know
+that it worked it turns out even that is
+
+ align:start position:0%
+that it worked it turns out even that is
+ 
+
+ align:start position:0%
+that it worked it turns out even that is
+going to be a little bit tricky to
+
+ align:start position:0%
+going to be a little bit tricky to
+ 
+
+ align:start position:0%
+going to be a little bit tricky to
+implement but these are the kinds of
+
+ align:start position:0%
+implement but these are the kinds of
+ 
+
+ align:start position:0%
+implement but these are the kinds of
+schematics you could get you could
+
+ align:start position:0%
+schematics you could get you could
+ 
+
+ align:start position:0%
+schematics you could get you could
+expect from your RPC
+
+ align:start position:0%
+expect from your RPC
+ 
+
+ align:start position:0%
+expect from your RPC
+system now actually to first order most
+
+ align:start position:0%
+system now actually to first order most
+ 
+
+ align:start position:0%
+system now actually to first order most
+RPC systems like XML RPC don't really
+
+ align:start position:0%
+RPC systems like XML RPC don't really
+ 
+
+ align:start position:0%
+RPC systems like XML RPC don't really
+deal with any of this in a particular
+
+ align:start position:0%
+deal with any of this in a particular
+ 
+
+ align:start position:0%
+deal with any of this in a particular
+They Don't Really provide any well-
+
+ align:start position:0%
+They Don't Really provide any well-
+ 
+
+ align:start position:0%
+They Don't Really provide any well-
+defined semantics it's usually for the
+
+ align:start position:0%
+defined semantics it's usually for the
+ 
+
+ align:start position:0%
+defined semantics it's usually for the
+clients sitting on top and the services
+
+ align:start position:0%
+clients sitting on top and the services
+ 
+
+ align:start position:0%
+clients sitting on top and the services
+to determine what kind of semantics they
+
+ align:start position:0%
+to determine what kind of semantics they
+ 
+
+ align:start position:0%
+to determine what kind of semantics they
+need and Implement that um at a at a
+
+ align:start position:0%
+need and Implement that um at a at a
+ 
+
+ align:start position:0%
+need and Implement that um at a at a
+higher layer at least with most of these
+
+ align:start position:0%
+higher layer at least with most of these
+ 
+
+ align:start position:0%
+higher layer at least with most of these
+standard protocols but but many of them
+
+ align:start position:0%
+standard protocols but but many of them
+ 
+
+ align:start position:0%
+standard protocols but but many of them
+are well equipped to deal with at least
+
+ align:start position:0%
+are well equipped to deal with at least
+ 
+
+ align:start position:0%
+are well equipped to deal with at least
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+um and you know through the course we'll
+
+ align:start position:0%
+um and you know through the course we'll
+ 
+
+ align:start position:0%
+um and you know through the course we'll
+see me different ways in which we'll
+
+ align:start position:0%
+see me different ways in which we'll
+ 
+
+ align:start position:0%
+see me different ways in which we'll
+accomplish um these different goals
+
+ align:start position:0%
+accomplish um these different goals
+ 
+
+ align:start position:0%
+accomplish um these different goals
+these different schematics that we want
+
+ align:start position:0%
+these different schematics that we want
+ 
+
+ align:start position:0%
+these different schematics that we want
+from our RPC like system from from our
+
+ align:start position:0%
+from our RPC like system from from our
+ 
+
+ align:start position:0%
+from our RPC like system from from our
+different RPC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems now there's another difference
+
+ align:start position:0%
+systems now there's another difference
+ 
+
+ align:start position:0%
+systems now there's another difference
+between regular procedure calls and um
+
+ align:start position:0%
+between regular procedure calls and um
+ 
+
+ align:start position:0%
+between regular procedure calls and um
+remote procedure calls or more generally
+
+ align:start position:0%
+remote procedure calls or more generally
+ 
+
+ align:start position:0%
+remote procedure calls or more generally
+from client service
+
+ align:start position:0%
+from client service
+ 
+
+ align:start position:0%
+from client service
+computer remember um in the uh second
+
+ align:start position:0%
+computer remember um in the uh second
+ 
+
+ align:start position:0%
+computer remember um in the uh second
+lecture I told you that you know you can
+
+ align:start position:0%
+lecture I told you that you know you can
+ 
+
+ align:start position:0%
+lecture I told you that you know you can
+always get more band with and you can
+
+ align:start position:0%
+always get more band with and you can
+ 
+
+ align:start position:0%
+always get more band with and you can
+always get more processing than to law
+
+ align:start position:0%
+always get more processing than to law
+ 
+
+ align:start position:0%
+always get more processing than to law
+but one thing you can't actually change
+
+ align:start position:0%
+but one thing you can't actually change
+ 
+
+ align:start position:0%
+but one thing you can't actually change
+is the latency between two computers
+
+ align:start position:0%
+is the latency between two computers
+ 
+
+ align:start position:0%
+is the latency between two computers
+connected by a wi connected by a network
+
+ align:start position:0%
+connected by a wi connected by a network
+ 
+
+ align:start position:0%
+connected by a wi connected by a network
+and the speed of light isn't
+
+ align:start position:0%
+and the speed of light isn't
+ 
+
+ align:start position:0%
+and the speed of light isn't
+changing what that means is that with
+
+ align:start position:0%
+changing what that means is that with
+ 
+
+ align:start position:0%
+changing what that means is that with
+time the number of instructions that you
+
+ align:start position:0%
+time the number of instructions that you
+ 
+
+ align:start position:0%
+time the number of instructions that you
+can run when you have a computer two
+
+ align:start position:0%
+can run when you have a computer two
+ 
+
+ align:start position:0%
+can run when you have a computer two
+computers separated by a wire there's a
+
+ align:start position:0%
+computers separated by a wire there's a
+ 
+
+ align:start position:0%
+computers separated by a wire there's a
+certain delay between them no matter
+
+ align:start position:0%
+certain delay between them no matter
+ 
+
+ align:start position:0%
+certain delay between them no matter
+what you do so there's a certain delay
+
+ align:start position:0%
+what you do so there's a certain delay
+ 
+
+ align:start position:0%
+what you do so there's a certain delay
+to do a procedure call that's a remote
+
+ align:start position:0%
+to do a procedure call that's a remote
+ 
+
+ align:start position:0%
+to do a procedure call that's a remote
+procedure call you know take certain
+
+ align:start position:0%
+procedure call you know take certain
+ 
+
+ align:start position:0%
+procedure call you know take certain
+delay to send a message and to get a
+
+ align:start position:0%
+delay to send a message and to get a
+ 
+
+ align:start position:0%
+delay to send a message and to get a
+response back even as computers get
+
+ align:start position:0%
+response back even as computers get
+ 
+
+ align:start position:0%
+response back even as computers get
+faster and faster and faster that
+
+ align:start position:0%
+faster and faster and faster that
+ 
+
+ align:start position:0%
+faster and faster and faster that
+changing at all but the problem is that
+
+ align:start position:0%
+changing at all but the problem is that
+ 
+
+ align:start position:0%
+changing at all but the problem is that
+the number of instructions you can run
+
+ align:start position:0%
+the number of instructions you can run
+ 
+
+ align:start position:0%
+the number of instructions you can run
+within that duration is increasing with
+
+ align:start position:0%
+within that duration is increasing with
+ 
+
+ align:start position:0%
+within that duration is increasing with
+time because it's a fixed amount of time
+
+ align:start position:0%
+time because it's a fixed amount of time
+ 
+
+ align:start position:0%
+time because it's a fixed amount of time
+and the number of instructions you could
+
+ align:start position:0%
+and the number of instructions you could
+ 
+
+ align:start position:0%
+and the number of instructions you could
+run locally on a computer uh increases
+
+ align:start position:0%
+run locally on a computer uh increases
+ 
+
+ align:start position:0%
+run locally on a computer uh increases
+um with
+
+ align:start position:0%
+um with
+ 
+
+ align:start position:0%
+um with
+time so that has led people to be more
+
+ align:start position:0%
+time so that has led people to be more
+ 
+
+ align:start position:0%
+time so that has led people to be more
+aggressive about what they do in a
+
+ align:start position:0%
+aggressive about what they do in a
+ 
+
+ align:start position:0%
+aggressive about what they do in a
+remote procedure call what people have
+
+ align:start position:0%
+remote procedure call what people have
+ 
+
+ align:start position:0%
+remote procedure call what people have
+said is wait it doesn't make sense for
+
+ align:start position:0%
+said is wait it doesn't make sense for
+ 
+
+ align:start position:0%
+said is wait it doesn't make sense for
+me me to for a client to issue a
+
+ align:start position:0%
+me me to for a client to issue a
+ 
+
+ align:start position:0%
+me me to for a client to issue a
+procedure call invocation to a service
+
+ align:start position:0%
+procedure call invocation to a service
+ 
+
+ align:start position:0%
+procedure call invocation to a service
+and then just sit and wait like in a
+
+ align:start position:0%
+and then just sit and wait like in a
+ 
+
+ align:start position:0%
+and then just sit and wait like in a
+regular procedure call the answer I mean
+
+ align:start position:0%
+regular procedure call the answer I mean
+ 
+
+ align:start position:0%
+regular procedure call the answer I mean
+you know I'm just sitting there tring my
+
+ align:start position:0%
+you know I'm just sitting there tring my
+ 
+
+ align:start position:0%
+you know I'm just sitting there tring my
+thumbs and this thing is you know gone
+
+ align:start position:0%
+thumbs and this thing is you know gone
+ 
+
+ align:start position:0%
+thumbs and this thing is you know gone
+away and you know I'm waiting for it to
+
+ align:start position:0%
+away and you know I'm waiting for it to
+ 
+
+ align:start position:0%
+away and you know I'm waiting for it to
+respond I could be doing
+
+ align:start position:0%
+respond I could be doing
+ 
+
+ align:start position:0%
+respond I could be doing
+work so that's LED people to changing
+
+ align:start position:0%
+work so that's LED people to changing
+ 
+
+ align:start position:0%
+work so that's LED people to changing
+the synchronous model
+
+ align:start position:0%
+the synchronous model
+ 
+
+ align:start position:0%
+the synchronous model
+of um of RPC of a procedure call
+
+ align:start position:0%
+of um of RPC of a procedure call
+ 
+
+ align:start position:0%
+of um of RPC of a procedure call
+interface to do thing called an
+
+ align:start position:0%
+interface to do thing called an
+ 
+
+ align:start position:0%
+interface to do thing called an
+asynchronous procedure call interface
+
+ align:start position:0%
+asynchronous procedure call interface
+ 
+
+ align:start position:0%
+asynchronous procedure call interface
+and all you know things like xmlrpc and
+
+ align:start position:0%
+and all you know things like xmlrpc and
+ 
+
+ align:start position:0%
+and all you know things like xmlrpc and
+its follow on the difference between
+
+ align:start position:0%
+its follow on the difference between
+ 
+
+ align:start position:0%
+its follow on the difference between
+soap and XML RPC is that um I can
+
+ align:start position:0%
+soap and XML RPC is that um I can
+ 
+
+ align:start position:0%
+soap and XML RPC is that um I can
+understand this and this Builds on xmlc
+
+ align:start position:0%
+understand this and this Builds on xmlc
+ 
+
+ align:start position:0%
+understand this and this Builds on xmlc
+and it seems like very few people
+
+ align:start position:0%
+and it seems like very few people
+ 
+
+ align:start position:0%
+and it seems like very few people
+understand so um I mean
+
+ align:start position:0%
+understand so um I mean
+ 
+
+ align:start position:0%
+understand so um I mean
+I um there's a lot of people who have
+
+ align:start position:0%
+I um there's a lot of people who have
+ 
+
+ align:start position:0%
+I um there's a lot of people who have
+given up on trying to understand the
+
+ align:start position:0%
+given up on trying to understand the
+ 
+
+ align:start position:0%
+given up on trying to understand the
+specification but XML RPC turns out to
+
+ align:start position:0%
+specification but XML RPC turns out to
+ 
+
+ align:start position:0%
+specification but XML RPC turns out to
+be a really simple seven or 10 page
+
+ align:start position:0%
+be a really simple seven or 10 page
+ 
+
+ align:start position:0%
+be a really simple seven or 10 page
+document that's very easy to understand
+
+ align:start position:0%
+document that's very easy to understand
+ 
+
+ align:start position:0%
+document that's very easy to understand
+a lot of people use it um but anyway all
+
+ align:start position:0%
+a lot of people use it um but anyway all
+ 
+
+ align:start position:0%
+a lot of people use it um but anyway all
+of these Systems Support air synchronous
+
+ align:start position:0%
+of these Systems Support air synchronous
+ 
+
+ align:start position:0%
+of these Systems Support air synchronous
+RP see the idea here is that the client
+
+ align:start position:0%
+RP see the idea here is that the client
+ 
+
+ align:start position:0%
+RP see the idea here is that the client
+sends call indicator remote request to
+
+ align:start position:0%
+sends call indicator remote request to
+ 
+
+ align:start position:0%
+sends call indicator remote request to
+the service and then it goes about doing
+
+ align:start position:0%
+the service and then it goes about doing
+ 
+
+ align:start position:0%
+the service and then it goes about doing
+its work when the service responds with
+
+ align:start position:0%
+its work when the service responds with
+ 
+
+ align:start position:0%
+its work when the service responds with
+an answer it responds with not just the
+
+ align:start position:0%
+an answer it responds with not just the
+ 
+
+ align:start position:0%
+an answer it responds with not just the
+answer but also something that tells the
+
+ align:start position:0%
+answer but also something that tells the
+ 
+
+ align:start position:0%
+answer but also something that tells the
+client which service request which
+
+ align:start position:0%
+client which service request which
+ 
+
+ align:start position:0%
+client which service request which
+procedure call request it's responding
+
+ align:start position:0%
+procedure call request it's responding
+ 
+
+ align:start position:0%
+procedure call request it's responding
+to and when that response comes back the
+
+ align:start position:0%
+to and when that response comes back the
+ 
+
+ align:start position:0%
+to and when that response comes back the
+client can handle
+
+ align:start position:0%
+client can handle
+ 
+
+ align:start position:0%
+client can handle
+it now the way in which you have to
+
+ align:start position:0%
+it now the way in which you have to
+ 
+
+ align:start position:0%
+it now the way in which you have to
+implement this or the way in which you
+
+ align:start position:0%
+implement this or the way in which you
+ 
+
+ align:start position:0%
+implement this or the way in which you
+have to design this is that associated
+
+ align:start position:0%
+have to design this is that associated
+ 
+
+ align:start position:0%
+have to design this is that associated
+with every procedure called request you
+
+ align:start position:0%
+with every procedure called request you
+ 
+
+ align:start position:0%
+with every procedure called request you
+also have to associate what's called
+
+ align:start position:0%
+also have to associate what's called
+ 
+
+ align:start position:0%
+also have to associate what's called
+called A Handler because you're going to
+
+ align:start position:0%
+called A Handler because you're going to
+ 
+
+ align:start position:0%
+called A Handler because you're going to
+issue this request to the service and
+
+ align:start position:0%
+issue this request to the service and
+ 
+
+ align:start position:0%
+issue this request to the service and
+then go about doing your work when the
+
+ align:start position:0%
+then go about doing your work when the
+ 
+
+ align:start position:0%
+then go about doing your work when the
+answer comes back the RPC Library
+
+ align:start position:0%
+answer comes back the RPC Library
+ 
+
+ align:start position:0%
+answer comes back the RPC Library
+underneath has to the communication
+
+ align:start position:0%
+underneath has to the communication
+ 
+
+ align:start position:0%
+underneath has to the communication
+library has to know who gets this answer
+
+ align:start position:0%
+library has to know who gets this answer
+ 
+
+ align:start position:0%
+library has to know who gets this answer
+because you might have issued many such
+
+ align:start position:0%
+because you might have issued many such
+ 
+
+ align:start position:0%
+because you might have issued many such
+service requests so who gets this answer
+
+ align:start position:0%
+service requests so who gets this answer
+ 
+
+ align:start position:0%
+service requests so who gets this answer
+so you associate with every request a
+
+ align:start position:0%
+so you associate with every request a
+ 
+
+ align:start position:0%
+so you associate with every request a
+call back a Handler which then is called
+
+ align:start position:0%
+call back a Handler which then is called
+ 
+
+ align:start position:0%
+call back a Handler which then is called
+back and that Handler runs dealing with
+
+ align:start position:0%
+back and that Handler runs dealing with
+ 
+
+ align:start position:0%
+back and that Handler runs dealing with
+the answer that comes from
+
+ align:start position:0%
+the answer that comes from
+ 
+
+ align:start position:0%
+the answer that comes from
+and so that actually allows you to be a
+
+ align:start position:0%
+and so that actually allows you to be a
+ 
+
+ align:start position:0%
+and so that actually allows you to be a
+little more decoupled than we were with
+
+ align:start position:0%
+little more decoupled than we were with
+ 
+
+ align:start position:0%
+little more decoupled than we were with
+remote procedure College even more
+
+ align:start position:0%
+remote procedure College even more
+ 
+
+ align:start position:0%
+remote procedure College even more
+decoupled The Client Services even more
+
+ align:start position:0%
+decoupled The Client Services even more
+ 
+
+ align:start position:0%
+decoupled The Client Services even more
+because the c is now no longer waiting
+
+ align:start position:0%
+because the c is now no longer waiting
+ 
+
+ align:start position:0%
+because the c is now no longer waiting
+for the service to turn an answer to
+
+ align:start position:0%
+for the service to turn an answer to
+ 
+
+ align:start position:0%
+for the service to turn an answer to
+it so that's the first way in which
+
+ align:start position:0%
+it so that's the first way in which
+ 
+
+ align:start position:0%
+it so that's the first way in which
+people have extended it the second way
+
+ align:start position:0%
+people have extended it the second way
+ 
+
+ align:start position:0%
+people have extended it the second way
+in which people have extended it is
+
+ align:start position:0%
+in which people have extended it is
+ 
+
+ align:start position:0%
+in which people have extended it is
+using this intermediary idea that we
+
+ align:start position:0%
+using this intermediary idea that we
+ 
+
+ align:start position:0%
+using this intermediary idea that we
+talked about before where the service is
+
+ align:start position:0%
+talked about before where the service is
+ 
+
+ align:start position:0%
+talked about before where the service is
+a trusted
+
+ align:start position:0%
+a trusted
+ 
+
+ align:start position:0%
+a trusted
+intermediary to use this intermediary
+
+ align:start position:0%
+intermediary to use this intermediary
+ 
+
+ align:start position:0%
+intermediary to use this intermediary
+idea to
+
+ align:start position:0%
+idea to
+ 
+
+ align:start position:0%
+idea to
+actually make design remote um message
+
+ align:start position:0%
+actually make design remote um message
+ 
+
+ align:start position:0%
+actually make design remote um message
+based commun systems communication
+
+ align:start position:0%
+based commun systems communication
+ 
+
+ align:start position:0%
+based commun systems communication
+systems where the Cent service don't
+
+ align:start position:0%
+systems where the Cent service don't
+ 
+
+ align:start position:0%
+systems where the Cent service don't
+actually have to be up and running at
+
+ align:start position:0%
+actually have to be up and running at
+ 
+
+ align:start position:0%
+actually have to be up and running at
+the same time so you could actually the
+
+ align:start position:0%
+the same time so you could actually the
+ 
+
+ align:start position:0%
+the same time so you could actually the
+client could send a request
+
+ align:start position:0%
+client could send a request
+ 
+
+ align:start position:0%
+client could send a request
+out to the service but the service is
+
+ align:start position:0%
+out to the service but the service is
+ 
+
+ align:start position:0%
+out to the service but the service is
+actually not up and running so the idea
+
+ align:start position:0%
+actually not up and running so the idea
+ 
+
+ align:start position:0%
+actually not up and running so the idea
+is there's an intermediary that acts as
+
+ align:start position:0%
+is there's an intermediary that acts as
+ 
+
+ align:start position:0%
+is there's an intermediary that acts as
+a broker on behalf of the service and
+
+ align:start position:0%
+a broker on behalf of the service and
+ 
+
+ align:start position:0%
+a broker on behalf of the service and
+buffers the message and then when the
+
+ align:start position:0%
+buffers the message and then when the
+ 
+
+ align:start position:0%
+buffers the message and then when the
+service comes up the service knows to
+
+ align:start position:0%
+service comes up the service knows to
+ 
+
+ align:start position:0%
+service comes up the service knows to
+pull the message from this intermediary
+
+ align:start position:0%
+pull the message from this intermediary
+ 
+
+ align:start position:0%
+pull the message from this intermediary
+that's buer messages for it and then it
+
+ align:start position:0%
+that's buer messages for it and then it
+ 
+
+ align:start position:0%
+that's buer messages for it and then it
+processes the message and then push the
+
+ align:start position:0%
+processes the message and then push the
+ 
+
+ align:start position:0%
+processes the message and then push the
+answer back to the intermediary which
+
+ align:start position:0%
+answer back to the intermediary which
+ 
+
+ align:start position:0%
+answer back to the intermediary which
+then stores the message to some other
+
+ align:start position:0%
+then stores the message to some other
+ 
+
+ align:start position:0%
+then stores the message to some other
+intermediary perhaps and then the client
+
+ align:start position:0%
+intermediary perhaps and then the client
+ 
+
+ align:start position:0%
+intermediary perhaps and then the client
+knows to get the answer from that
+
+ align:start position:0%
+knows to get the answer from that
+ 
+
+ align:start position:0%
+knows to get the answer from that
+intermediate so now we can actually have
+
+ align:start position:0%
+intermediate so now we can actually have
+ 
+
+ align:start position:0%
+intermediate so now we can actually have
+clients and services that interact with
+
+ align:start position:0%
+clients and services that interact with
+ 
+
+ align:start position:0%
+clients and services that interact with
+each other um without actually having to
+
+ align:start position:0%
+each other um without actually having to
+ 
+
+ align:start position:0%
+each other um without actually having to
+be up and running at the same time there
+
+ align:start position:0%
+be up and running at the same time there
+ 
+
+ align:start position:0%
+be up and running at the same time there
+are many examples of this and the notes
+
+ align:start position:0%
+are many examples of this and the notes
+ 
+
+ align:start position:0%
+are many examples of this and the notes
+talk about um various ways of doing
+
+ align:start position:0%
+talk about um various ways of doing
+ 
+
+ align:start position:0%
+talk about um various ways of doing
+intermed various examples of
+
+ align:start position:0%
+intermed various examples of
+ 
+
+ align:start position:0%
+intermed various examples of
+intermediate based
+
+ align:start position:0%
+intermediate based
+ 
+
+ align:start position:0%
+intermediate based
+communication so the Gen summ of what
+
+ align:start position:0%
+communication so the Gen summ of what
+ 
+
+ align:start position:0%
+communication so the Gen summ of what
+we've talked about so far is is that we
+
+ align:start position:0%
+we've talked about so far is is that we
+ 
+
+ align:start position:0%
+we've talked about so far is is that we
+looked at different ways of achieving
+
+ align:start position:0%
+looked at different ways of achieving
+ 
+
+ align:start position:0%
+looked at different ways of achieving
+modularity talked about soft modularity
+
+ align:start position:0%
+modularity talked about soft modularity
+ 
+
+ align:start position:0%
+modularity talked about soft modularity
+last time and today about particular way
+
+ align:start position:0%
+last time and today about particular way
+ 
+
+ align:start position:0%
+last time and today about particular way
+of enforcing modularity using client
+
+ align:start position:0%
+of enforcing modularity using client
+ 
+
+ align:start position:0%
+of enforcing modularity using client
+service organization and the next few
+
+ align:start position:0%
+service organization and the next few
+ 
+
+ align:start position:0%
+service organization and the next few
+lectures we're going to solve a big
+
+ align:start position:0%
+lectures we're going to solve a big
+ 
+
+ align:start position:0%
+lectures we're going to solve a big
+weakness of the current system which is
+
+ align:start position:0%
+weakness of the current system which is
+ 
+
+ align:start position:0%
+weakness of the current system which is
+that you need many different computers
+
+ align:start position:0%
+that you need many different computers
+ 
+
+ align:start position:0%
+that you need many different computers
+so we're going to take these ideas and
+
+ align:start position:0%
+so we're going to take these ideas and
+ 
+
+ align:start position:0%
+so we're going to take these ideas and
+Implement them all on one computer see
+
+ align:start position:0%
+Implement them all on one computer see
+ 
+
+ align:start position:0%
+Implement them all on one computer see
+you next week on Tuesday
\ No newline at end of file
diff --git a/Rv3xYk85Lq0.txt b/Rv3xYk85Lq0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..90b5d3b5368bb06b212c24b12c648efc4bf5d39f
--- /dev/null
+++ b/Rv3xYk85Lq0.txt
@@ -0,0 +1,11688 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last time we started talking about
+
+ align:start position:0%
+last time we started talking about
+ 
+
+ align:start position:0%
+last time we started talking about
+metric spaces being compact on euclidean
+
+ align:start position:0%
+metric spaces being compact on euclidean
+ 
+
+ align:start position:0%
+metric spaces being compact on euclidean
+space in particular where we showed on
+
+ align:start position:0%
+space in particular where we showed on
+ 
+
+ align:start position:0%
+space in particular where we showed on
+RN that sequentially compact was the
+
+ align:start position:0%
+RN that sequentially compact was the
+ 
+
+ align:start position:0%
+RN that sequentially compact was the
+same as closed and bounded which was the
+
+ align:start position:0%
+same as closed and bounded which was the
+ 
+
+ align:start position:0%
+same as closed and bounded which was the
+same as topologically Compact and notice
+
+ align:start position:0%
+same as topologically Compact and notice
+ 
+
+ align:start position:0%
+same as topologically Compact and notice
+that in these two theorems we use some
+
+ align:start position:0%
+that in these two theorems we use some
+ 
+
+ align:start position:0%
+that in these two theorems we use some
+very important propositions that we've
+
+ align:start position:0%
+very important propositions that we've
+ 
+
+ align:start position:0%
+very important propositions that we've
+learned from real analysis
+
+ align:start position:0%
+learned from real analysis
+ 
+
+ align:start position:0%
+learned from real analysis
+to prove that coast and bounded implied
+
+ align:start position:0%
+to prove that coast and bounded implied
+ 
+
+ align:start position:0%
+to prove that coast and bounded implied
+sequentially compact we had to use the
+
+ align:start position:0%
+sequentially compact we had to use the
+ 
+
+ align:start position:0%
+sequentially compact we had to use the
+bolzanovirus trust serum which
+
+ align:start position:0%
+bolzanovirus trust serum which
+ 
+
+ align:start position:0%
+bolzanovirus trust serum which
+essentially states exactly the condition
+
+ align:start position:0%
+essentially states exactly the condition
+ 
+
+ align:start position:0%
+essentially states exactly the condition
+of sequentially compactness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to use closed and bounded to show
+
+ align:start position:0%
+and to use closed and bounded to show
+ 
+
+ align:start position:0%
+and to use closed and bounded to show
+topologically compact we had to use the
+
+ align:start position:0%
+topologically compact we had to use the
+ 
+
+ align:start position:0%
+topologically compact we had to use the
+heineboreal theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we trapped our compact set inside
+
+ align:start position:0%
+where we trapped our compact set inside
+ 
+
+ align:start position:0%
+where we trapped our compact set inside
+of a closed Cube and we know that that
+
+ align:start position:0%
+of a closed Cube and we know that that
+ 
+
+ align:start position:0%
+of a closed Cube and we know that that
+closed cube is going to be compact
+
+ align:start position:0%
+closed cube is going to be compact
+ 
+
+ align:start position:0%
+closed cube is going to be compact
+but we don't always have these closed
+
+ align:start position:0%
+but we don't always have these closed
+ 
+
+ align:start position:0%
+but we don't always have these closed
+cubes on Metric spaces right what does
+
+ align:start position:0%
+cubes on Metric spaces right what does
+ 
+
+ align:start position:0%
+cubes on Metric spaces right what does
+it mean for there to be a cube of
+
+ align:start position:0%
+it mean for there to be a cube of
+ 
+
+ align:start position:0%
+it mean for there to be a cube of
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+um and in fact in general these
+
+ align:start position:0%
+um and in fact in general these
+ 
+
+ align:start position:0%
+um and in fact in general these
+implications are not going to be
+
+ align:start position:0%
+implications are not going to be
+ 
+
+ align:start position:0%
+implications are not going to be
+precisely true and small area from last
+
+ align:start position:0%
+precisely true and small area from last
+ 
+
+ align:start position:0%
+precisely true and small area from last
+time last time I stated that
+
+ align:start position:0%
+time last time I stated that
+ 
+
+ align:start position:0%
+time last time I stated that
+sequentially compact was the same as
+
+ align:start position:0%
+sequentially compact was the same as
+ 
+
+ align:start position:0%
+sequentially compact was the same as
+closed and bounded on Metric spaces this
+
+ align:start position:0%
+closed and bounded on Metric spaces this
+ 
+
+ align:start position:0%
+closed and bounded on Metric spaces this
+is not the case
+
+ align:start position:0%
+is not the case
+ 
+
+ align:start position:0%
+is not the case
+um sorry about that
+
+ align:start position:0%
+um sorry about that
+ 
+
+ align:start position:0%
+um sorry about that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we are using bosonavirus shots to prove
+
+ align:start position:0%
+we are using bosonavirus shots to prove
+ 
+
+ align:start position:0%
+we are using bosonavirus shots to prove
+this theorem
+
+ align:start position:0%
+this theorem
+ 
+
+ align:start position:0%
+this theorem
+and we need it to show the other
+
+ align:start position:0%
+and we need it to show the other
+ 
+
+ align:start position:0%
+and we need it to show the other
+implication if it was always the same
+
+ align:start position:0%
+implication if it was always the same
+ 
+
+ align:start position:0%
+implication if it was always the same
+then all three of these would always be
+
+ align:start position:0%
+then all three of these would always be
+ 
+
+ align:start position:0%
+then all three of these would always be
+true and it's not metric spaces were
+
+ align:start position:0%
+true and it's not metric spaces were
+ 
+
+ align:start position:0%
+true and it's not metric spaces were
+closed and bounded implies topologically
+
+ align:start position:0%
+closed and bounded implies topologically
+ 
+
+ align:start position:0%
+closed and bounded implies topologically
+compact have the high Noble property and
+
+ align:start position:0%
+compact have the high Noble property and
+ 
+
+ align:start position:0%
+compact have the high Noble property and
+not every metric space has this property
+
+ align:start position:0%
+not every metric space has this property
+ 
+
+ align:start position:0%
+not every metric space has this property
+but what we're going to show today
+
+ align:start position:0%
+but what we're going to show today
+ 
+
+ align:start position:0%
+but what we're going to show today
+is that if we're not on RN if we're on a
+
+ align:start position:0%
+is that if we're not on RN if we're on a
+ 
+
+ align:start position:0%
+is that if we're not on RN if we're on a
+general metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we still have
+
+ align:start position:0%
+we still have
+ 
+
+ align:start position:0%
+we still have
+the following implications we already
+
+ align:start position:0%
+the following implications we already
+ 
+
+ align:start position:0%
+the following implications we already
+know that sequentially Compact and
+
+ align:start position:0%
+know that sequentially Compact and
+ 
+
+ align:start position:0%
+know that sequentially Compact and
+topologically compact implies closed and
+
+ align:start position:0%
+topologically compact implies closed and
+ 
+
+ align:start position:0%
+topologically compact implies closed and
+bounded which is a very helpful thing
+
+ align:start position:0%
+bounded which is a very helpful thing
+ 
+
+ align:start position:0%
+bounded which is a very helpful thing
+right if you want to show that a metric
+
+ align:start position:0%
+right if you want to show that a metric
+ 
+
+ align:start position:0%
+right if you want to show that a metric
+space is it isn't compact you just have
+
+ align:start position:0%
+space is it isn't compact you just have
+ 
+
+ align:start position:0%
+space is it isn't compact you just have
+to show that it's not closed or at least
+
+ align:start position:0%
+to show that it's not closed or at least
+ 
+
+ align:start position:0%
+to show that it's not closed or at least
+not bounded
+
+ align:start position:0%
+not bounded
+ 
+
+ align:start position:0%
+not bounded
+but we're still going to have the
+
+ align:start position:0%
+but we're still going to have the
+ 
+
+ align:start position:0%
+but we're still going to have the
+following implication what we're going
+
+ align:start position:0%
+following implication what we're going
+ 
+
+ align:start position:0%
+following implication what we're going
+to show today we're going to show that
+
+ align:start position:0%
+to show today we're going to show that
+ 
+
+ align:start position:0%
+to show today we're going to show that
+sequentially compact
+
+ align:start position:0%
+sequentially compact
+ 
+
+ align:start position:0%
+sequentially compact
+it's the same as topologically compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact we're going to show two more
+
+ align:start position:0%
+in fact we're going to show two more
+ 
+
+ align:start position:0%
+in fact we're going to show two more
+properties that emphasize the importance
+
+ align:start position:0%
+properties that emphasize the importance
+ 
+
+ align:start position:0%
+properties that emphasize the importance
+of compact metric spaces in general it's
+
+ align:start position:0%
+of compact metric spaces in general it's
+ 
+
+ align:start position:0%
+of compact metric spaces in general it's
+going to be a very proof intensive day
+
+ align:start position:0%
+going to be a very proof intensive day
+ 
+
+ align:start position:0%
+going to be a very proof intensive day
+but I hope you stick with it through me
+
+ align:start position:0%
+but I hope you stick with it through me
+ 
+
+ align:start position:0%
+but I hope you stick with it through me
+sorry stick with it with me
+
+ align:start position:0%
+sorry stick with it with me
+ 
+
+ align:start position:0%
+sorry stick with it with me
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so yeah that's our goal for today before
+
+ align:start position:0%
+so yeah that's our goal for today before
+ 
+
+ align:start position:0%
+so yeah that's our goal for today before
+we show sequentially compact implies
+
+ align:start position:0%
+we show sequentially compact implies
+ 
+
+ align:start position:0%
+we show sequentially compact implies
+topologically Compact and thus and
+
+ align:start position:0%
+topologically Compact and thus and
+ 
+
+ align:start position:0%
+topologically Compact and thus and
+furthermore the opposite direction first
+
+ align:start position:0%
+furthermore the opposite direction first
+ 
+
+ align:start position:0%
+furthermore the opposite direction first
+we're going to start by proving some
+
+ align:start position:0%
+we're going to start by proving some
+ 
+
+ align:start position:0%
+we're going to start by proving some
+lemmas about sequential compactness to
+
+ align:start position:0%
+lemmas about sequential compactness to
+ 
+
+ align:start position:0%
+lemmas about sequential compactness to
+make our job just a little bit easier in
+
+ align:start position:0%
+make our job just a little bit easier in
+ 
+
+ align:start position:0%
+make our job just a little bit easier in
+the long term and in fact these summers
+
+ align:start position:0%
+the long term and in fact these summers
+ 
+
+ align:start position:0%
+the long term and in fact these summers
+are going to be used throughout the rest
+
+ align:start position:0%
+are going to be used throughout the rest
+ 
+
+ align:start position:0%
+are going to be used throughout the rest
+of the class so please pay attention
+
+ align:start position:0%
+of the class so please pay attention
+ 
+
+ align:start position:0%
+of the class so please pay attention
+so first we have what is known as
+
+ align:start position:0%
+so first we have what is known as
+ 
+
+ align:start position:0%
+so first we have what is known as
+dilemma the little big number Lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're here I'm just not writing out
+
+ align:start position:0%
+we're here I'm just not writing out
+ 
+
+ align:start position:0%
+we're here I'm just not writing out
+number but the idea is given our metrics
+
+ align:start position:0%
+number but the idea is given our metrics
+ 
+
+ align:start position:0%
+number but the idea is given our metrics
+base X
+
+ align:start position:0%
+base X
+ 
+
+ align:start position:0%
+base X
+is sequentially compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I have an open cover of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call this our uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+then there exists
+ 
+
+ align:start position:0%
+then there exists
+in R bigger than zero such that for all
+
+ align:start position:0%
+in R bigger than zero such that for all
+ 
+
+ align:start position:0%
+in R bigger than zero such that for all
+x and x
+
+ align:start position:0%
+x and x
+ 
+
+ align:start position:0%
+x and x
+the ball of radius R round X
+
+ align:start position:0%
+the ball of radius R round X
+ 
+
+ align:start position:0%
+the ball of radius R round X
+is contained in one of the uis for some
+
+ align:start position:0%
+is contained in one of the uis for some
+ 
+
+ align:start position:0%
+is contained in one of the uis for some
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's draw a picture of what I'm
+
+ align:start position:0%
+now let's draw a picture of what I'm
+ 
+
+ align:start position:0%
+now let's draw a picture of what I'm
+actually describing here because this
+
+ align:start position:0%
+actually describing here because this
+ 
+
+ align:start position:0%
+actually describing here because this
+quantifier logic can be a little bit
+
+ align:start position:0%
+quantifier logic can be a little bit
+ 
+
+ align:start position:0%
+quantifier logic can be a little bit
+confusing the first time you see it
+
+ align:start position:0%
+confusing the first time you see it
+ 
+
+ align:start position:0%
+confusing the first time you see it
+so here let's just draw a little blob
+
+ align:start position:0%
+so here let's just draw a little blob
+ 
+
+ align:start position:0%
+so here let's just draw a little blob
+for a metric SpaceX
+
+ align:start position:0%
+for a metric SpaceX
+ 
+
+ align:start position:0%
+for a metric SpaceX
+and what we're going to do is find an
+
+ align:start position:0%
+and what we're going to do is find an
+ 
+
+ align:start position:0%
+and what we're going to do is find an
+open cover of this by the UI so I'll
+
+ align:start position:0%
+open cover of this by the UI so I'll
+ 
+
+ align:start position:0%
+open cover of this by the UI so I'll
+draw these by circles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are our uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there we go
+
+ align:start position:0%
+okay there we go
+ 
+
+ align:start position:0%
+okay there we go
+and now for every x in x we claim that
+
+ align:start position:0%
+and now for every x in x we claim that
+ 
+
+ align:start position:0%
+and now for every x in x we claim that
+there exists a ball of radius r
+
+ align:start position:0%
+there exists a ball of radius r
+ 
+
+ align:start position:0%
+there exists a ball of radius r
+around X
+
+ align:start position:0%
+around X
+ 
+
+ align:start position:0%
+around X
+such that it's contained in only one of
+
+ align:start position:0%
+such that it's contained in only one of
+ 
+
+ align:start position:0%
+such that it's contained in only one of
+these open sets
+
+ align:start position:0%
+these open sets
+ 
+
+ align:start position:0%
+these open sets
+or sorry not only one that it's fully
+
+ align:start position:0%
+or sorry not only one that it's fully
+ 
+
+ align:start position:0%
+or sorry not only one that it's fully
+contained in one of these sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and this might ring out to you as
+
+ align:start position:0%
+um and this might ring out to you as
+ 
+
+ align:start position:0%
+um and this might ring out to you as
+being true if you want to prove
+
+ align:start position:0%
+being true if you want to prove
+ 
+
+ align:start position:0%
+being true if you want to prove
+topologically compact it's the same as
+
+ align:start position:0%
+topologically compact it's the same as
+ 
+
+ align:start position:0%
+topologically compact it's the same as
+sequentially compact what we're going to
+
+ align:start position:0%
+sequentially compact what we're going to
+ 
+
+ align:start position:0%
+sequentially compact what we're going to
+do in the long term is assume that we're
+
+ align:start position:0%
+do in the long term is assume that we're
+ 
+
+ align:start position:0%
+do in the long term is assume that we're
+sequentially compact take an open cover
+
+ align:start position:0%
+sequentially compact take an open cover
+ 
+
+ align:start position:0%
+sequentially compact take an open cover
+and use this R to construct our
+
+ align:start position:0%
+and use this R to construct our
+ 
+
+ align:start position:0%
+and use this R to construct our
+conclusion
+
+ align:start position:0%
+conclusion
+ 
+
+ align:start position:0%
+conclusion
+first we have to prove the steps
+
+ align:start position:0%
+first we have to prove the steps
+ 
+
+ align:start position:0%
+first we have to prove the steps
+and the proof
+
+ align:start position:0%
+and the proof
+ 
+
+ align:start position:0%
+and the proof
+is going to be as pretty usual for
+
+ align:start position:0%
+is going to be as pretty usual for
+ 
+
+ align:start position:0%
+is going to be as pretty usual for
+sequential compactness our proof is
+
+ align:start position:0%
+sequential compactness our proof is
+ 
+
+ align:start position:0%
+sequential compactness our proof is
+going to be by contradiction
+
+ align:start position:0%
+going to be by contradiction
+ 
+
+ align:start position:0%
+going to be by contradiction
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+use contradiction assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean for this statement to
+
+ align:start position:0%
+what does it mean for this statement to
+ 
+
+ align:start position:0%
+what does it mean for this statement to
+be not true well it means that for every
+
+ align:start position:0%
+be not true well it means that for every
+ 
+
+ align:start position:0%
+be not true well it means that for every
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+bigger than zero there exists some X
+
+ align:start position:0%
+bigger than zero there exists some X
+ 
+
+ align:start position:0%
+bigger than zero there exists some X
+in x
+
+ align:start position:0%
+in x
+ 
+
+ align:start position:0%
+in x
+such that the ball of radius R around an
+
+ align:start position:0%
+such that the ball of radius R around an
+ 
+
+ align:start position:0%
+such that the ball of radius R around an
+X is not contained in any of the uis
+
+ align:start position:0%
+X is not contained in any of the uis
+ 
+
+ align:start position:0%
+X is not contained in any of the uis
+it's covered It's contained in a cover
+
+ align:start position:0%
+it's covered It's contained in a cover
+ 
+
+ align:start position:0%
+it's covered It's contained in a cover
+of the uis it's just not fully contained
+
+ align:start position:0%
+of the uis it's just not fully contained
+ 
+
+ align:start position:0%
+of the uis it's just not fully contained
+in one of them at least
+
+ align:start position:0%
+in one of them at least
+ 
+
+ align:start position:0%
+in one of them at least
+and what we're going to do is use this
+
+ align:start position:0%
+and what we're going to do is use this
+ 
+
+ align:start position:0%
+and what we're going to do is use this
+to construct a sequence and take the
+
+ align:start position:0%
+to construct a sequence and take the
+ 
+
+ align:start position:0%
+to construct a sequence and take the
+convergent subsequence and reach
+
+ align:start position:0%
+convergent subsequence and reach
+ 
+
+ align:start position:0%
+convergent subsequence and reach
+contradiction so choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each
+
+ align:start position:0%
+for each
+ 
+
+ align:start position:0%
+for each
+r equal to 1 over n
+
+ align:start position:0%
+r equal to 1 over n
+ 
+
+ align:start position:0%
+r equal to 1 over n
+choose x n
+
+ align:start position:0%
+choose x n
+ 
+
+ align:start position:0%
+choose x n
+to satisfy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the above property so we're going to
+
+ align:start position:0%
+the above property so we're going to
+ 
+
+ align:start position:0%
+the above property so we're going to
+choose the points in our sequence to be
+
+ align:start position:0%
+choose the points in our sequence to be
+ 
+
+ align:start position:0%
+choose the points in our sequence to be
+the xn or at least one of the xn such
+
+ align:start position:0%
+the xn or at least one of the xn such
+ 
+
+ align:start position:0%
+the xn or at least one of the xn such
+that the ball of radius r or the ball of
+
+ align:start position:0%
+that the ball of radius r or the ball of
+ 
+
+ align:start position:0%
+that the ball of radius r or the ball of
+radius one over n around X is not
+
+ align:start position:0%
+radius one over n around X is not
+ 
+
+ align:start position:0%
+radius one over n around X is not
+contained in any of the uis and we know
+
+ align:start position:0%
+contained in any of the uis and we know
+ 
+
+ align:start position:0%
+contained in any of the uis and we know
+that this is going to be true because 1
+
+ align:start position:0%
+that this is going to be true because 1
+ 
+
+ align:start position:0%
+that this is going to be true because 1
+over n is going to be bigger than zero
+
+ align:start position:0%
+over n is going to be bigger than zero
+ 
+
+ align:start position:0%
+over n is going to be bigger than zero
+so what are we going to do with the
+
+ align:start position:0%
+so what are we going to do with the
+ 
+
+ align:start position:0%
+so what are we going to do with the
+sequence what we're going to start by
+
+ align:start position:0%
+sequence what we're going to start by
+ 
+
+ align:start position:0%
+sequence what we're going to start by
+taking a convergent subsequence right
+
+ align:start position:0%
+taking a convergent subsequence right
+ 
+
+ align:start position:0%
+taking a convergent subsequence right
+we're going to use the fact that we're
+
+ align:start position:0%
+we're going to use the fact that we're
+ 
+
+ align:start position:0%
+we're going to use the fact that we're
+sequentially compact
+
+ align:start position:0%
+sequentially compact
+ 
+
+ align:start position:0%
+sequentially compact
+and this trend will carry on throughout
+
+ align:start position:0%
+and this trend will carry on throughout
+ 
+
+ align:start position:0%
+and this trend will carry on throughout
+the day so
+
+ align:start position:0%
+the day so
+ 
+
+ align:start position:0%
+the day so
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a convergent subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call it X and K converging to X of
+
+ align:start position:0%
+let's call it X and K converging to X of
+ 
+
+ align:start position:0%
+let's call it X and K converging to X of
+course that's what we usually Let It Be
+
+ align:start position:0%
+course that's what we usually Let It Be
+ 
+
+ align:start position:0%
+course that's what we usually Let It Be
+okay so what are we going to do we want
+
+ align:start position:0%
+okay so what are we going to do we want
+ 
+
+ align:start position:0%
+okay so what are we going to do we want
+to reach the contradiction that there is
+
+ align:start position:0%
+to reach the contradiction that there is
+ 
+
+ align:start position:0%
+to reach the contradiction that there is
+in fact a ball of radius R round one of
+
+ align:start position:0%
+in fact a ball of radius R round one of
+ 
+
+ align:start position:0%
+in fact a ball of radius R round one of
+these X's contained in a UI how do we do
+
+ align:start position:0%
+these X's contained in a UI how do we do
+ 
+
+ align:start position:0%
+these X's contained in a UI how do we do
+that well first we notice that X has to
+
+ align:start position:0%
+that well first we notice that X has to
+ 
+
+ align:start position:0%
+that well first we notice that X has to
+be in one of the uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is in u i naught for some I naught
+
+ align:start position:0%
+X is in u i naught for some I naught
+ 
+
+ align:start position:0%
+X is in u i naught for some I naught
+and this is true given that it's an open
+
+ align:start position:0%
+and this is true given that it's an open
+ 
+
+ align:start position:0%
+and this is true given that it's an open
+cover of our space
+
+ align:start position:0%
+cover of our space
+ 
+
+ align:start position:0%
+cover of our space
+and therefore because we're because the
+
+ align:start position:0%
+and therefore because we're because the
+ 
+
+ align:start position:0%
+and therefore because we're because the
+UI not is open
+
+ align:start position:0%
+UI not is open
+ 
+
+ align:start position:0%
+UI not is open
+there exists an R naught bigger than
+
+ align:start position:0%
+there exists an R naught bigger than
+ 
+
+ align:start position:0%
+there exists an R naught bigger than
+zero such that the ball of radius R
+
+ align:start position:0%
+zero such that the ball of radius R
+ 
+
+ align:start position:0%
+zero such that the ball of radius R
+naught
+
+ align:start position:0%
+naught
+ 
+
+ align:start position:0%
+naught
+is contained in u i naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now we want to find a subset of
+
+ align:start position:0%
+right now we want to find a subset of
+ 
+
+ align:start position:0%
+right now we want to find a subset of
+this such that we reach our
+
+ align:start position:0%
+this such that we reach our
+ 
+
+ align:start position:0%
+this such that we reach our
+contradiction so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+choose
+
+ align:start position:0%
+choose
+ 
+
+ align:start position:0%
+choose
+and sufficiently large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one over n
+
+ align:start position:0%
+one over n
+ 
+
+ align:start position:0%
+one over n
+is less than R naught over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh did you do
+
+ align:start position:0%
+uh did you do
+ 
+
+ align:start position:0%
+uh did you do
+the distance from X to x n
+
+ align:start position:0%
+the distance from X to x n
+ 
+
+ align:start position:0%
+the distance from X to x n
+is less than R naught over two
+
+ align:start position:0%
+is less than R naught over two
+ 
+
+ align:start position:0%
+is less than R naught over two
+and we're going to use this to create a
+
+ align:start position:0%
+and we're going to use this to create a
+ 
+
+ align:start position:0%
+and we're going to use this to create a
+subset of BR naught of x
+
+ align:start position:0%
+subset of BR naught of x
+ 
+
+ align:start position:0%
+subset of BR naught of x
+so how do we do that well we consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ball of radius 1 over n
+
+ align:start position:0%
+the ball of radius 1 over n
+ 
+
+ align:start position:0%
+the ball of radius 1 over n
+around X
+
+ align:start position:0%
+around X
+ 
+
+ align:start position:0%
+around X
+or sorry around x n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for all Y in this set
+
+ align:start position:0%
+so for all Y in this set
+ 
+
+ align:start position:0%
+so for all Y in this set
+we notice that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the distance from X
+
+ align:start position:0%
+the distance from X
+ 
+
+ align:start position:0%
+the distance from X
+to y
+
+ align:start position:0%
+to y
+ 
+
+ align:start position:0%
+to y
+is less than or equal to the distance
+
+ align:start position:0%
+is less than or equal to the distance
+ 
+
+ align:start position:0%
+is less than or equal to the distance
+from X to x n
+
+ align:start position:0%
+from X to x n
+ 
+
+ align:start position:0%
+from X to x n
+plus the distance
+
+ align:start position:0%
+plus the distance
+ 
+
+ align:start position:0%
+plus the distance
+from y to xn this is by the triangle
+
+ align:start position:0%
+from y to xn this is by the triangle
+ 
+
+ align:start position:0%
+from y to xn this is by the triangle
+inequality this term is going to be less
+
+ align:start position:0%
+inequality this term is going to be less
+ 
+
+ align:start position:0%
+inequality this term is going to be less
+than 1 over sorry R naught Over N so R
+
+ align:start position:0%
+than 1 over sorry R naught Over N so R
+ 
+
+ align:start position:0%
+than 1 over sorry R naught Over N so R
+naught over two it's less than one over
+
+ align:start position:0%
+naught over two it's less than one over
+ 
+
+ align:start position:0%
+naught over two it's less than one over
+n Which is less than R naught over two
+
+ align:start position:0%
+n Which is less than R naught over two
+ 
+
+ align:start position:0%
+n Which is less than R naught over two
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+one over uh something that's less than
+
+ align:start position:0%
+one over uh something that's less than
+ 
+
+ align:start position:0%
+one over uh something that's less than
+one over n Which is less than R naught
+
+ align:start position:0%
+one over n Which is less than R naught
+ 
+
+ align:start position:0%
+one over n Which is less than R naught
+over two
+
+ align:start position:0%
+over two
+ 
+
+ align:start position:0%
+over two
+so this is R naught which tells us that
+
+ align:start position:0%
+so this is R naught which tells us that
+ 
+
+ align:start position:0%
+so this is R naught which tells us that
+the ball of radius 1 over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around x n
+
+ align:start position:0%
+around x n
+ 
+
+ align:start position:0%
+around x n
+is fully contained and the ball of
+
+ align:start position:0%
+is fully contained and the ball of
+ 
+
+ align:start position:0%
+is fully contained and the ball of
+radius R naught around x n sorry not x n
+
+ align:start position:0%
+radius R naught around x n sorry not x n
+ 
+
+ align:start position:0%
+radius R naught around x n sorry not x n
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+which is fully contained and UI naught
+
+ align:start position:0%
+which is fully contained and UI naught
+ 
+
+ align:start position:0%
+which is fully contained and UI naught
+which is our contradiction right because
+
+ align:start position:0%
+which is our contradiction right because
+ 
+
+ align:start position:0%
+which is our contradiction right because
+we claimed at the very beginning that
+
+ align:start position:0%
+we claimed at the very beginning that
+ 
+
+ align:start position:0%
+we claimed at the very beginning that
+none of these balls are going to be
+
+ align:start position:0%
+none of these balls are going to be
+ 
+
+ align:start position:0%
+none of these balls are going to be
+contained in any or fully contained in
+
+ align:start position:0%
+contained in any or fully contained in
+ 
+
+ align:start position:0%
+contained in any or fully contained in
+any of the uis
+
+ align:start position:0%
+any of the uis
+ 
+
+ align:start position:0%
+any of the uis
+so this is still the big number Lemma as
+
+ align:start position:0%
+so this is still the big number Lemma as
+ 
+
+ align:start position:0%
+so this is still the big number Lemma as
+a small note the largest such R such
+
+ align:start position:0%
+a small note the largest such R such
+ 
+
+ align:start position:0%
+a small note the largest such R such
+that this property holds is known as the
+
+ align:start position:0%
+that this property holds is known as the
+ 
+
+ align:start position:0%
+that this property holds is known as the
+big number and this comes up in a number
+
+ align:start position:0%
+big number and this comes up in a number
+ 
+
+ align:start position:0%
+big number and this comes up in a number
+of other applications we're just not
+
+ align:start position:0%
+of other applications we're just not
+ 
+
+ align:start position:0%
+of other applications we're just not
+going to be talking about them today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now we have a way of refining our open
+
+ align:start position:0%
+now we have a way of refining our open
+ 
+
+ align:start position:0%
+now we have a way of refining our open
+cover to refine our open cover to the
+
+ align:start position:0%
+cover to refine our open cover to the
+ 
+
+ align:start position:0%
+cover to refine our open cover to the
+set of open balls of all the same radius
+
+ align:start position:0%
+set of open balls of all the same radius
+ 
+
+ align:start position:0%
+set of open balls of all the same radius
+but what we need to do is reach a
+
+ align:start position:0%
+but what we need to do is reach a
+ 
+
+ align:start position:0%
+but what we need to do is reach a
+what we need to do
+
+ align:start position:0%
+what we need to do
+ 
+
+ align:start position:0%
+what we need to do
+is get finitely many of these open balls
+
+ align:start position:0%
+is get finitely many of these open balls
+ 
+
+ align:start position:0%
+is get finitely many of these open balls
+for open cover
+
+ align:start position:0%
+for open cover
+ 
+
+ align:start position:0%
+for open cover
+and as such we're going to define a new
+
+ align:start position:0%
+and as such we're going to define a new
+ 
+
+ align:start position:0%
+and as such we're going to define a new
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+so definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the term is known as totally bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a or I should say metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call it X
+
+ align:start position:0%
+let's call it X
+ 
+
+ align:start position:0%
+let's call it X
+is totally bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+for all Epsilon bigger than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists y1
+
+ align:start position:0%
+there exists y1
+ 
+
+ align:start position:0%
+there exists y1
+through y k
+
+ align:start position:0%
+through y k
+ 
+
+ align:start position:0%
+through y k
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+the union of balls of radius Epsilon
+
+ align:start position:0%
+the union of balls of radius Epsilon
+ 
+
+ align:start position:0%
+the union of balls of radius Epsilon
+around the finitely many y I's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contains X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a very similar picture to this
+
+ align:start position:0%
+so it's a very similar picture to this
+ 
+
+ align:start position:0%
+so it's a very similar picture to this
+only where I have all the same radius r
+
+ align:start position:0%
+only where I have all the same radius r
+ 
+
+ align:start position:0%
+only where I have all the same radius r
+instead of our regular open cover
+
+ align:start position:0%
+instead of our regular open cover
+ 
+
+ align:start position:0%
+instead of our regular open cover
+and what we're going to do is show that
+
+ align:start position:0%
+and what we're going to do is show that
+ 
+
+ align:start position:0%
+and what we're going to do is show that
+sequential compactness implies totally
+
+ align:start position:0%
+sequential compactness implies totally
+ 
+
+ align:start position:0%
+sequential compactness implies totally
+bounded
+
+ align:start position:0%
+bounded
+ 
+
+ align:start position:0%
+bounded
+this is another Lemma of ours
+
+ align:start position:0%
+this is another Lemma of ours
+ 
+
+ align:start position:0%
+this is another Lemma of ours
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequentially bound sorry sequentially
+
+ align:start position:0%
+sequentially bound sorry sequentially
+ 
+
+ align:start position:0%
+sequentially bound sorry sequentially
+compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies totally bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as metric spaces
+
+ align:start position:0%
+as metric spaces
+ 
+
+ align:start position:0%
+as metric spaces
+so if your metric space is sequentially
+
+ align:start position:0%
+so if your metric space is sequentially
+ 
+
+ align:start position:0%
+so if your metric space is sequentially
+compact then it's going to be totally
+
+ align:start position:0%
+compact then it's going to be totally
+ 
+
+ align:start position:0%
+compact then it's going to be totally
+bounded
+
+ align:start position:0%
+bounded
+ 
+
+ align:start position:0%
+bounded
+let's prove this proof
+
+ align:start position:0%
+let's prove this proof
+ 
+
+ align:start position:0%
+let's prove this proof
+again our proof is going to be by
+
+ align:start position:0%
+again our proof is going to be by
+ 
+
+ align:start position:0%
+again our proof is going to be by
+contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume that it's not totally bounded
+
+ align:start position:0%
+assume that it's not totally bounded
+ 
+
+ align:start position:0%
+assume that it's not totally bounded
+then for all Epsilon bigger than zero
+
+ align:start position:0%
+then for all Epsilon bigger than zero
+ 
+
+ align:start position:0%
+then for all Epsilon bigger than zero
+there exists or sorry I should say
+
+ align:start position:0%
+there exists or sorry I should say
+ 
+
+ align:start position:0%
+there exists or sorry I should say
+there does not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon balls
+
+ align:start position:0%
+Epsilon balls
+ 
+
+ align:start position:0%
+Epsilon balls
+that coverage base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean to be not existent
+
+ align:start position:0%
+what does it mean to be not existent
+ 
+
+ align:start position:0%
+what does it mean to be not existent
+right what does it mean for there to not
+
+ align:start position:0%
+right what does it mean for there to not
+ 
+
+ align:start position:0%
+right what does it mean for there to not
+exist finally many Epsilon balls well
+
+ align:start position:0%
+exist finally many Epsilon balls well
+ 
+
+ align:start position:0%
+exist finally many Epsilon balls well
+this means that there are infinitely
+
+ align:start position:0%
+this means that there are infinitely
+ 
+
+ align:start position:0%
+this means that there are infinitely
+many of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it takes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon balls
+
+ align:start position:0%
+Epsilon balls
+ 
+
+ align:start position:0%
+Epsilon balls
+to cover X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what we're going to do with this
+
+ align:start position:0%
+now what we're going to do with this
+ 
+
+ align:start position:0%
+now what we're going to do with this
+we're once again going to construct a
+
+ align:start position:0%
+we're once again going to construct a
+ 
+
+ align:start position:0%
+we're once again going to construct a
+sequence and take a convergent
+
+ align:start position:0%
+sequence and take a convergent
+ 
+
+ align:start position:0%
+sequence and take a convergent
+subsequence but we need to somehow use
+
+ align:start position:0%
+subsequence but we need to somehow use
+ 
+
+ align:start position:0%
+subsequence but we need to somehow use
+the fact that there it takes infinitely
+
+ align:start position:0%
+the fact that there it takes infinitely
+ 
+
+ align:start position:0%
+the fact that there it takes infinitely
+many Epsilon balls to cover X
+
+ align:start position:0%
+many Epsilon balls to cover X
+ 
+
+ align:start position:0%
+many Epsilon balls to cover X
+well let's just start by taking any X
+
+ align:start position:0%
+well let's just start by taking any X
+ 
+
+ align:start position:0%
+well let's just start by taking any X
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+be an X
+
+ align:start position:0%
+be an X
+ 
+
+ align:start position:0%
+be an X
+and now we want to construct an x two
+
+ align:start position:0%
+and now we want to construct an x two
+ 
+
+ align:start position:0%
+and now we want to construct an x two
+such that there's no koshy subsequence
+
+ align:start position:0%
+such that there's no koshy subsequence
+ 
+
+ align:start position:0%
+such that there's no koshy subsequence
+of the X ends so let's take X2
+
+ align:start position:0%
+of the X ends so let's take X2
+ 
+
+ align:start position:0%
+of the X ends so let's take X2
+to be an X not including the ball of
+
+ align:start position:0%
+to be an X not including the ball of
+ 
+
+ align:start position:0%
+to be an X not including the ball of
+radius Epsilon around X1
+
+ align:start position:0%
+radius Epsilon around X1
+ 
+
+ align:start position:0%
+radius Epsilon around X1
+now let's do this let's continue this
+
+ align:start position:0%
+now let's do this let's continue this
+ 
+
+ align:start position:0%
+now let's do this let's continue this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+let X N be an X not including
+
+ align:start position:0%
+let X N be an X not including
+ 
+
+ align:start position:0%
+let X N be an X not including
+the union of balls of radius Epsilon
+
+ align:start position:0%
+the union of balls of radius Epsilon
+ 
+
+ align:start position:0%
+the union of balls of radius Epsilon
+around x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why are we doing this we want to
+
+ align:start position:0%
+now why are we doing this we want to
+ 
+
+ align:start position:0%
+now why are we doing this we want to
+create a sequence of points such that
+
+ align:start position:0%
+create a sequence of points such that
+ 
+
+ align:start position:0%
+create a sequence of points such that
+every the distance between every point
+
+ align:start position:0%
+every the distance between every point
+ 
+
+ align:start position:0%
+every the distance between every point
+is bigger than Epsilon which we have
+
+ align:start position:0%
+is bigger than Epsilon which we have
+ 
+
+ align:start position:0%
+is bigger than Epsilon which we have
+immediately from this
+
+ align:start position:0%
+immediately from this
+ 
+
+ align:start position:0%
+immediately from this
+the distance from x i to x j is always
+
+ align:start position:0%
+the distance from x i to x j is always
+ 
+
+ align:start position:0%
+the distance from x i to x j is always
+bigger than Epsilon by construction
+
+ align:start position:0%
+bigger than Epsilon by construction
+ 
+
+ align:start position:0%
+bigger than Epsilon by construction
+because if it wasn't less than Epsilon
+
+ align:start position:0%
+because if it wasn't less than Epsilon
+ 
+
+ align:start position:0%
+because if it wasn't less than Epsilon
+then it would be contained in the ball
+
+ align:start position:0%
+then it would be contained in the ball
+ 
+
+ align:start position:0%
+then it would be contained in the ball
+of radius Epsilon around one of the
+
+ align:start position:0%
+of radius Epsilon around one of the
+ 
+
+ align:start position:0%
+of radius Epsilon around one of the
+other X I's
+
+ align:start position:0%
+other X I's
+ 
+
+ align:start position:0%
+other X I's
+so what does this tell us
+
+ align:start position:0%
+so what does this tell us
+ 
+
+ align:start position:0%
+so what does this tell us
+this tells us that our sequence can
+
+ align:start position:0%
+this tells us that our sequence can
+ 
+
+ align:start position:0%
+this tells us that our sequence can
+never be koshy right if our sequence was
+
+ align:start position:0%
+never be koshy right if our sequence was
+ 
+
+ align:start position:0%
+never be koshy right if our sequence was
+koshy or a subsequence was koshy
+
+ align:start position:0%
+koshy or a subsequence was koshy
+ 
+
+ align:start position:0%
+koshy or a subsequence was koshy
+then the distance between subsequent
+
+ align:start position:0%
+then the distance between subsequent
+ 
+
+ align:start position:0%
+then the distance between subsequent
+points has to be able to get less than
+
+ align:start position:0%
+points has to be able to get less than
+ 
+
+ align:start position:0%
+points has to be able to get less than
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+which is not the case
+
+ align:start position:0%
+which is not the case
+ 
+
+ align:start position:0%
+which is not the case
+so what we notice
+
+ align:start position:0%
+so what we notice
+ 
+
+ align:start position:0%
+so what we notice
+is that there are no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+koshy subsequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the sequence x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is going to be our
+
+ align:start position:0%
+and this is going to be our
+ 
+
+ align:start position:0%
+and this is going to be our
+contradiction why
+
+ align:start position:0%
+contradiction why
+ 
+
+ align:start position:0%
+contradiction why
+because this is a sequence in a
+
+ align:start position:0%
+because this is a sequence in a
+ 
+
+ align:start position:0%
+because this is a sequence in a
+sequentially compact metrics base so we
+
+ align:start position:0%
+sequentially compact metrics base so we
+ 
+
+ align:start position:0%
+sequentially compact metrics base so we
+know that there has to exist a
+
+ align:start position:0%
+know that there has to exist a
+ 
+
+ align:start position:0%
+know that there has to exist a
+convergent subsequence but being
+
+ align:start position:0%
+convergent subsequence but being
+ 
+
+ align:start position:0%
+convergent subsequence but being
+convergent implies that it's going to be
+
+ align:start position:0%
+convergent implies that it's going to be
+ 
+
+ align:start position:0%
+convergent implies that it's going to be
+koshy we've shown this on the second day
+
+ align:start position:0%
+koshy we've shown this on the second day
+ 
+
+ align:start position:0%
+koshy we've shown this on the second day
+in our general theory of metric spaces
+
+ align:start position:0%
+in our general theory of metric spaces
+ 
+
+ align:start position:0%
+in our general theory of metric spaces
+so what we've shown is that
+
+ align:start position:0%
+so what we've shown is that
+ 
+
+ align:start position:0%
+so what we've shown is that
+there should be a koshy subsequence but
+
+ align:start position:0%
+there should be a koshy subsequence but
+ 
+
+ align:start position:0%
+there should be a koshy subsequence but
+there is no koshy subsequence so this is
+
+ align:start position:0%
+there is no koshy subsequence so this is
+ 
+
+ align:start position:0%
+there is no koshy subsequence so this is
+our contradiction
+
+ align:start position:0%
+our contradiction
+ 
+
+ align:start position:0%
+our contradiction
+and that concludes the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these two lemmas the lebeg number
+
+ align:start position:0%
+and these two lemmas the lebeg number
+ 
+
+ align:start position:0%
+and these two lemmas the lebeg number
+Lema and this one right here are going
+
+ align:start position:0%
+Lema and this one right here are going
+ 
+
+ align:start position:0%
+Lema and this one right here are going
+to be all we need to show that
+
+ align:start position:0%
+to be all we need to show that
+ 
+
+ align:start position:0%
+to be all we need to show that
+sequentially compact implies
+
+ align:start position:0%
+sequentially compact implies
+ 
+
+ align:start position:0%
+sequentially compact implies
+topologically compact
+
+ align:start position:0%
+topologically compact
+ 
+
+ align:start position:0%
+topologically compact
+so let's start that proof serum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequentially compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the same
+
+ align:start position:0%
+is the same
+ 
+
+ align:start position:0%
+is the same
+as topologically compact as metric
+
+ align:start position:0%
+as topologically compact as metric
+ 
+
+ align:start position:0%
+as topologically compact as metric
+spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's start the proof proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume
+
+ align:start position:0%
+assume
+ 
+
+ align:start position:0%
+assume
+sequentially compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Inlet
+
+ align:start position:0%
+Inlet
+ 
+
+ align:start position:0%
+Inlet
+UI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be an open cover of the metrics base X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we then know by the little big
+
+ align:start position:0%
+what we then know by the little big
+ 
+
+ align:start position:0%
+what we then know by the little big
+number Lema is that there exists an R
+
+ align:start position:0%
+number Lema is that there exists an R
+ 
+
+ align:start position:0%
+number Lema is that there exists an R
+bigger than zero such that balls of
+
+ align:start position:0%
+bigger than zero such that balls of
+ 
+
+ align:start position:0%
+bigger than zero such that balls of
+radius R are contained in one of the uis
+
+ align:start position:0%
+radius R are contained in one of the uis
+ 
+
+ align:start position:0%
+radius R are contained in one of the uis
+so therefore
+
+ align:start position:0%
+so therefore
+ 
+
+ align:start position:0%
+so therefore
+by the big number Lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+and R bigger than zero such that balls
+
+ align:start position:0%
+and R bigger than zero such that balls
+ 
+
+ align:start position:0%
+and R bigger than zero such that balls
+of radius all around X
+
+ align:start position:0%
+of radius all around X
+ 
+
+ align:start position:0%
+of radius all around X
+are contained in u i for some I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+IE for every X there exists some I such
+
+ align:start position:0%
+IE for every X there exists some I such
+ 
+
+ align:start position:0%
+IE for every X there exists some I such
+that this is true
+
+ align:start position:0%
+that this is true
+ 
+
+ align:start position:0%
+that this is true
+and now how do we go from this to
+
+ align:start position:0%
+and now how do we go from this to
+ 
+
+ align:start position:0%
+and now how do we go from this to
+finitely many of these uis well here we
+
+ align:start position:0%
+finitely many of these uis well here we
+ 
+
+ align:start position:0%
+finitely many of these uis well here we
+use the following Nama we know that it's
+
+ align:start position:0%
+use the following Nama we know that it's
+ 
+
+ align:start position:0%
+use the following Nama we know that it's
+totally bounded so given this R bigger
+
+ align:start position:0%
+totally bounded so given this R bigger
+ 
+
+ align:start position:0%
+totally bounded so given this R bigger
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+let R be equal to Epsilon and the
+
+ align:start position:0%
+let R be equal to Epsilon and the
+ 
+
+ align:start position:0%
+let R be equal to Epsilon and the
+definition of totally bounded
+
+ align:start position:0%
+definition of totally bounded
+ 
+
+ align:start position:0%
+definition of totally bounded
+and then we know that there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y1
+
+ align:start position:0%
+y1
+ 
+
+ align:start position:0%
+y1
+through y k
+
+ align:start position:0%
+through y k
+ 
+
+ align:start position:0%
+through y k
+such that X
+
+ align:start position:0%
+such that X
+ 
+
+ align:start position:0%
+such that X
+is contained
+
+ align:start position:0%
+is contained
+ 
+
+ align:start position:0%
+is contained
+in balls of radius in the union of balls
+
+ align:start position:0%
+in balls of radius in the union of balls
+ 
+
+ align:start position:0%
+in balls of radius in the union of balls
+of radius R around y i
+
+ align:start position:0%
+of radius R around y i
+ 
+
+ align:start position:0%
+of radius R around y i
+from I equals 1 to K
+
+ align:start position:0%
+from I equals 1 to K
+ 
+
+ align:start position:0%
+from I equals 1 to K
+but we want to go from this to a finite
+
+ align:start position:0%
+but we want to go from this to a finite
+ 
+
+ align:start position:0%
+but we want to go from this to a finite
+cover from we want to go from this to a
+
+ align:start position:0%
+cover from we want to go from this to a
+ 
+
+ align:start position:0%
+cover from we want to go from this to a
+finite sub cover
+
+ align:start position:0%
+finite sub cover
+ 
+
+ align:start position:0%
+finite sub cover
+but what we notice
+
+ align:start position:0%
+but what we notice
+ 
+
+ align:start position:0%
+but what we notice
+is that each of these ball of radius R
+
+ align:start position:0%
+is that each of these ball of radius R
+ 
+
+ align:start position:0%
+is that each of these ball of radius R
+is contained in one of the uis
+
+ align:start position:0%
+is contained in one of the uis
+ 
+
+ align:start position:0%
+is contained in one of the uis
+so right now this is going to be
+
+ align:start position:0%
+so right now this is going to be
+ 
+
+ align:start position:0%
+so right now this is going to be
+contained in the union of uij where I J
+
+ align:start position:0%
+contained in the union of uij where I J
+ 
+
+ align:start position:0%
+contained in the union of uij where I J
+is the one such that the balls of radius
+
+ align:start position:0%
+is the one such that the balls of radius
+ 
+
+ align:start position:0%
+is the one such that the balls of radius
+are around y i
+
+ align:start position:0%
+are around y i
+ 
+
+ align:start position:0%
+are around y i
+is contained in the ball sorry is
+
+ align:start position:0%
+is contained in the ball sorry is
+ 
+
+ align:start position:0%
+is contained in the ball sorry is
+contained in uij
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we're done
+
+ align:start position:0%
+and then we're done
+ 
+
+ align:start position:0%
+and then we're done
+with the forward Direction
+
+ align:start position:0%
+with the forward Direction
+ 
+
+ align:start position:0%
+with the forward Direction
+right because we've gone from an open
+
+ align:start position:0%
+right because we've gone from an open
+ 
+
+ align:start position:0%
+right because we've gone from an open
+cover of our sequentially compact metric
+
+ align:start position:0%
+cover of our sequentially compact metric
+ 
+
+ align:start position:0%
+cover of our sequentially compact metric
+space and reached a finite subcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that shows a sequentially compact
+
+ align:start position:0%
+so that shows a sequentially compact
+ 
+
+ align:start position:0%
+so that shows a sequentially compact
+implies topologically compact
+
+ align:start position:0%
+implies topologically compact
+ 
+
+ align:start position:0%
+implies topologically compact
+the other direction is going to be
+
+ align:start position:0%
+the other direction is going to be
+ 
+
+ align:start position:0%
+the other direction is going to be
+mildly harder but is still going to be
+
+ align:start position:0%
+mildly harder but is still going to be
+ 
+
+ align:start position:0%
+mildly harder but is still going to be
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's still going to be essentially we've
+
+ align:start position:0%
+it's still going to be essentially we've
+ 
+
+ align:start position:0%
+it's still going to be essentially we've
+been doing this entire time we're going
+
+ align:start position:0%
+been doing this entire time we're going
+ 
+
+ align:start position:0%
+been doing this entire time we're going
+to assume that it's not sequentially
+
+ align:start position:0%
+to assume that it's not sequentially
+ 
+
+ align:start position:0%
+to assume that it's not sequentially
+compact construct a sequence and take
+
+ align:start position:0%
+compact construct a sequence and take
+ 
+
+ align:start position:0%
+compact construct a sequence and take
+the convergent subsequence and reach a
+
+ align:start position:0%
+the convergent subsequence and reach a
+ 
+
+ align:start position:0%
+the convergent subsequence and reach a
+contradiction somehow
+
+ align:start position:0%
+contradiction somehow
+ 
+
+ align:start position:0%
+contradiction somehow
+okay so suppose
+
+ align:start position:0%
+okay so suppose
+ 
+
+ align:start position:0%
+okay so suppose
+topologically compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I'm holding it backwards Let Me
+
+ align:start position:0%
+oh I'm holding it backwards Let Me
+ 
+
+ align:start position:0%
+oh I'm holding it backwards Let Me
+rewrite this compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I suppose for the sake of
+
+ align:start position:0%
+and I suppose for the sake of
+ 
+
+ align:start position:0%
+and I suppose for the sake of
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the sake of contradiction
+
+ align:start position:0%
+for the sake of contradiction
+ 
+
+ align:start position:0%
+for the sake of contradiction
+were not sequentially compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we're going to do
+
+ align:start position:0%
+what we're going to do
+ 
+
+ align:start position:0%
+what we're going to do
+is or sorry let me first stage what does
+
+ align:start position:0%
+is or sorry let me first stage what does
+ 
+
+ align:start position:0%
+is or sorry let me first stage what does
+it mean to be not sequentially compact
+
+ align:start position:0%
+it mean to be not sequentially compact
+ 
+
+ align:start position:0%
+it mean to be not sequentially compact
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call it XM of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with no convergent subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our goal is to go from this to an open
+
+ align:start position:0%
+our goal is to go from this to an open
+ 
+
+ align:start position:0%
+our goal is to go from this to an open
+cover of our space and show that there
+
+ align:start position:0%
+cover of our space and show that there
+ 
+
+ align:start position:0%
+cover of our space and show that there
+is no finite subcover to reach our
+
+ align:start position:0%
+is no finite subcover to reach our
+ 
+
+ align:start position:0%
+is no finite subcover to reach our
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+well how do we do that well first we
+
+ align:start position:0%
+well how do we do that well first we
+ 
+
+ align:start position:0%
+well how do we do that well first we
+need to note some facts about convergent
+
+ align:start position:0%
+need to note some facts about convergent
+ 
+
+ align:start position:0%
+need to note some facts about convergent
+subsequences
+
+ align:start position:0%
+subsequences
+ 
+
+ align:start position:0%
+subsequences
+firstly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+none of the
+
+ align:start position:0%
+none of the
+ 
+
+ align:start position:0%
+none of the
+X eyes actually I guess I should say
+
+ align:start position:0%
+X eyes actually I guess I should say
+ 
+
+ align:start position:0%
+X eyes actually I guess I should say
+firstly just note that none of the X I
+
+ align:start position:0%
+firstly just note that none of the X I
+ 
+
+ align:start position:0%
+firstly just note that none of the X I
+can appear infinitely many times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually yeah I'm going to call this
+
+ align:start position:0%
+actually yeah I'm going to call this
+ 
+
+ align:start position:0%
+actually yeah I'm going to call this
+firstly
+
+ align:start position:0%
+firstly
+ 
+
+ align:start position:0%
+firstly
+why is this true well if any of the X
+
+ align:start position:0%
+why is this true well if any of the X
+ 
+
+ align:start position:0%
+why is this true well if any of the X
+I's appeared infinitely many times then
+
+ align:start position:0%
+I's appeared infinitely many times then
+ 
+
+ align:start position:0%
+I's appeared infinitely many times then
+that would mean that we could just take
+
+ align:start position:0%
+that would mean that we could just take
+ 
+
+ align:start position:0%
+that would mean that we could just take
+a very trivial subsequence of X I's and
+
+ align:start position:0%
+a very trivial subsequence of X I's and
+ 
+
+ align:start position:0%
+a very trivial subsequence of X I's and
+that will converge to x i
+
+ align:start position:0%
+that will converge to x i
+ 
+
+ align:start position:0%
+that will converge to x i
+so we know that none of them appears
+
+ align:start position:0%
+so we know that none of them appears
+ 
+
+ align:start position:0%
+so we know that none of them appears
+infinitely many times so we can just
+
+ align:start position:0%
+infinitely many times so we can just
+ 
+
+ align:start position:0%
+infinitely many times so we can just
+assume that each one appears finitely
+
+ align:start position:0%
+assume that each one appears finitely
+ 
+
+ align:start position:0%
+assume that each one appears finitely
+many times
+
+ align:start position:0%
+many times
+ 
+
+ align:start position:0%
+many times
+but furthermore
+
+ align:start position:0%
+but furthermore
+ 
+
+ align:start position:0%
+but furthermore
+we know that for all Epsilon bigger than
+
+ align:start position:0%
+we know that for all Epsilon bigger than
+ 
+
+ align:start position:0%
+we know that for all Epsilon bigger than
+nope that's not what I meant to say
+
+ align:start position:0%
+nope that's not what I meant to say
+ 
+
+ align:start position:0%
+nope that's not what I meant to say
+we know that there exists an Epsilon n
+
+ align:start position:0%
+we know that there exists an Epsilon n
+ 
+
+ align:start position:0%
+we know that there exists an Epsilon n
+bigger than zero
+
+ align:start position:0%
+bigger than zero
+ 
+
+ align:start position:0%
+bigger than zero
+such that the ball of radius Epsilon n
+
+ align:start position:0%
+such that the ball of radius Epsilon n
+ 
+
+ align:start position:0%
+such that the ball of radius Epsilon n
+around x n
+
+ align:start position:0%
+around x n
+ 
+
+ align:start position:0%
+around x n
+is simply the set
+
+ align:start position:0%
+is simply the set
+ 
+
+ align:start position:0%
+is simply the set
+xn where here I mean the single point x
+
+ align:start position:0%
+xn where here I mean the single point x
+ 
+
+ align:start position:0%
+xn where here I mean the single point x
+ad
+
+ align:start position:0%
+ad
+ 
+
+ align:start position:0%
+ad
+so I guess to be extra clear I'll write
+
+ align:start position:0%
+so I guess to be extra clear I'll write
+ 
+
+ align:start position:0%
+so I guess to be extra clear I'll write
+this as XJ
+
+ align:start position:0%
+this as XJ
+ 
+
+ align:start position:0%
+this as XJ
+and XJ
+
+ align:start position:0%
+and XJ
+ 
+
+ align:start position:0%
+and XJ
+why is this true well suppose for the
+
+ align:start position:0%
+why is this true well suppose for the
+ 
+
+ align:start position:0%
+why is this true well suppose for the
+sake of contradiction that for every
+
+ align:start position:0%
+sake of contradiction that for every
+ 
+
+ align:start position:0%
+sake of contradiction that for every
+Epsilon bigger than zero there exists uh
+
+ align:start position:0%
+Epsilon bigger than zero there exists uh
+ 
+
+ align:start position:0%
+Epsilon bigger than zero there exists uh
+some X I in a ball of radius Epsilon
+
+ align:start position:0%
+some X I in a ball of radius Epsilon
+ 
+
+ align:start position:0%
+some X I in a ball of radius Epsilon
+around XJ
+
+ align:start position:0%
+around XJ
+ 
+
+ align:start position:0%
+around XJ
+well then that what that would tell us
+
+ align:start position:0%
+well then that what that would tell us
+ 
+
+ align:start position:0%
+well then that what that would tell us
+is that we could take a convergent
+
+ align:start position:0%
+is that we could take a convergent
+ 
+
+ align:start position:0%
+is that we could take a convergent
+subsequence which will converge to x j
+
+ align:start position:0%
+subsequence which will converge to x j
+ 
+
+ align:start position:0%
+subsequence which will converge to x j
+we just choose closer and closer points
+
+ align:start position:0%
+we just choose closer and closer points
+ 
+
+ align:start position:0%
+we just choose closer and closer points
+to x j
+
+ align:start position:0%
+to x j
+ 
+
+ align:start position:0%
+to x j
+so we know that there must exist some
+
+ align:start position:0%
+so we know that there must exist some
+ 
+
+ align:start position:0%
+so we know that there must exist some
+Epsilon n such that this is the case
+
+ align:start position:0%
+Epsilon n such that this is the case
+ 
+
+ align:start position:0%
+Epsilon n such that this is the case
+so we're going to use this to create our
+
+ align:start position:0%
+so we're going to use this to create our
+ 
+
+ align:start position:0%
+so we're going to use this to create our
+open cover
+
+ align:start position:0%
+open cover
+ 
+
+ align:start position:0%
+open cover
+we're going to let these
+
+ align:start position:0%
+we're going to let these
+ 
+
+ align:start position:0%
+we're going to let these
+be the open cover of u j so let's call
+
+ align:start position:0%
+be the open cover of u j so let's call
+ 
+
+ align:start position:0%
+be the open cover of u j so let's call
+them u i or UJS
+
+ align:start position:0%
+them u i or UJS
+ 
+
+ align:start position:0%
+them u i or UJS
+yeah from J equals 1 to Infinity
+
+ align:start position:0%
+yeah from J equals 1 to Infinity
+ 
+
+ align:start position:0%
+yeah from J equals 1 to Infinity
+but this isn't quite an open cover we
+
+ align:start position:0%
+but this isn't quite an open cover we
+ 
+
+ align:start position:0%
+but this isn't quite an open cover we
+don't know that we've fully covered x
+
+ align:start position:0%
+don't know that we've fully covered x
+ 
+
+ align:start position:0%
+don't know that we've fully covered x
+yet so what we're going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that U not
+
+ align:start position:0%
+is that U not
+ 
+
+ align:start position:0%
+is that U not
+be equal to X
+
+ align:start position:0%
+be equal to X
+ 
+
+ align:start position:0%
+be equal to X
+not including any of the terms in our
+
+ align:start position:0%
+not including any of the terms in our
+ 
+
+ align:start position:0%
+not including any of the terms in our
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why does this make sense
+
+ align:start position:0%
+now why does this make sense
+ 
+
+ align:start position:0%
+now why does this make sense
+or sorry why is this an open set
+
+ align:start position:0%
+or sorry why is this an open set
+ 
+
+ align:start position:0%
+or sorry why is this an open set
+well we know
+
+ align:start position:0%
+well we know
+ 
+
+ align:start position:0%
+well we know
+that the complement of this set contains
+
+ align:start position:0%
+that the complement of this set contains
+ 
+
+ align:start position:0%
+that the complement of this set contains
+all of its limit points which means that
+
+ align:start position:0%
+all of its limit points which means that
+ 
+
+ align:start position:0%
+all of its limit points which means that
+it's going to be closed
+
+ align:start position:0%
+it's going to be closed
+ 
+
+ align:start position:0%
+it's going to be closed
+as you've shown on your second problem
+
+ align:start position:0%
+as you've shown on your second problem
+ 
+
+ align:start position:0%
+as you've shown on your second problem
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+so what this tells us is that the
+
+ align:start position:0%
+so what this tells us is that the
+ 
+
+ align:start position:0%
+so what this tells us is that the
+complement of the complement is
+
+ align:start position:0%
+complement of the complement is
+ 
+
+ align:start position:0%
+complement of the complement is
+therefore going to be open so U naught
+
+ align:start position:0%
+therefore going to be open so U naught
+ 
+
+ align:start position:0%
+therefore going to be open so U naught
+is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore we've reached an open cover of
+
+ align:start position:0%
+therefore we've reached an open cover of
+ 
+
+ align:start position:0%
+therefore we've reached an open cover of
+our metric Space X we have that X
+
+ align:start position:0%
+our metric Space X we have that X
+ 
+
+ align:start position:0%
+our metric Space X we have that X
+is contained Oh wrong direction
+
+ align:start position:0%
+is contained Oh wrong direction
+ 
+
+ align:start position:0%
+is contained Oh wrong direction
+contained in U naught
+
+ align:start position:0%
+contained in U naught
+ 
+
+ align:start position:0%
+contained in U naught
+Union the infinite Union of uis or uj's
+
+ align:start position:0%
+Union the infinite Union of uis or uj's
+ 
+
+ align:start position:0%
+Union the infinite Union of uis or uj's
+J equals
+
+ align:start position:0%
+J equals
+ 
+
+ align:start position:0%
+J equals
+1 to Infinity
+
+ align:start position:0%
+1 to Infinity
+ 
+
+ align:start position:0%
+1 to Infinity
+now from here we want to reach a finite
+
+ align:start position:0%
+now from here we want to reach a finite
+ 
+
+ align:start position:0%
+now from here we want to reach a finite
+subcover
+
+ align:start position:0%
+subcover
+ 
+
+ align:start position:0%
+subcover
+but notice that every
+
+ align:start position:0%
+but notice that every
+ 
+
+ align:start position:0%
+but notice that every
+Friday sub cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every subcover is going to be emitting
+
+ align:start position:0%
+every subcover is going to be emitting
+ 
+
+ align:start position:0%
+every subcover is going to be emitting
+infinitely many points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because every Friday sub cover is
+
+ align:start position:0%
+right because every Friday sub cover is
+ 
+
+ align:start position:0%
+right because every Friday sub cover is
+going to have finitely many of these UJS
+
+ align:start position:0%
+going to have finitely many of these UJS
+ 
+
+ align:start position:0%
+going to have finitely many of these UJS
+but what that tells you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that infinitely many of them sorry
+
+ align:start position:0%
+is that infinitely many of them sorry
+ 
+
+ align:start position:0%
+is that infinitely many of them sorry
+let me double check what I want to be
+
+ align:start position:0%
+let me double check what I want to be
+ 
+
+ align:start position:0%
+let me double check what I want to be
+saying here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because it's going to Omit
+
+ align:start position:0%
+yeah because it's going to Omit
+ 
+
+ align:start position:0%
+yeah because it's going to Omit
+infinitely many points this tells us
+
+ align:start position:0%
+infinitely many points this tells us
+ 
+
+ align:start position:0%
+infinitely many points this tells us
+that X
+
+ align:start position:0%
+that X
+ 
+
+ align:start position:0%
+that X
+or sorry
+
+ align:start position:0%
+or sorry
+ 
+
+ align:start position:0%
+or sorry
+there is no finite subcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is our contradiction because we're
+
+ align:start position:0%
+which is our contradiction because we're
+ 
+
+ align:start position:0%
+which is our contradiction because we're
+assuming topologically compact
+
+ align:start position:0%
+assuming topologically compact
+ 
+
+ align:start position:0%
+assuming topologically compact
+so we've shown the topologically compact
+
+ align:start position:0%
+so we've shown the topologically compact
+ 
+
+ align:start position:0%
+so we've shown the topologically compact
+implies sequentially Compact and that
+
+ align:start position:0%
+implies sequentially Compact and that
+ 
+
+ align:start position:0%
+implies sequentially Compact and that
+concludes the other direction of our
+
+ align:start position:0%
+concludes the other direction of our
+ 
+
+ align:start position:0%
+concludes the other direction of our
+proof and thus we're done
+
+ align:start position:0%
+proof and thus we're done
+ 
+
+ align:start position:0%
+proof and thus we're done
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is essentially what we've set off
+
+ align:start position:0%
+this is essentially what we've set off
+ 
+
+ align:start position:0%
+this is essentially what we've set off
+to do from the very beginning which is
+
+ align:start position:0%
+to do from the very beginning which is
+ 
+
+ align:start position:0%
+to do from the very beginning which is
+very motivated by Metric spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but as you may guess from the fact that
+
+ align:start position:0%
+but as you may guess from the fact that
+ 
+
+ align:start position:0%
+but as you may guess from the fact that
+sequentially compact implies
+
+ align:start position:0%
+sequentially compact implies
+ 
+
+ align:start position:0%
+sequentially compact implies
+topologically com sorry from the fact
+
+ align:start position:0%
+topologically com sorry from the fact
+ 
+
+ align:start position:0%
+topologically com sorry from the fact
+that sequentially compact implies
+
+ align:start position:0%
+that sequentially compact implies
+ 
+
+ align:start position:0%
+that sequentially compact implies
+totally bounded there's quite a bit more
+
+ align:start position:0%
+totally bounded there's quite a bit more
+ 
+
+ align:start position:0%
+totally bounded there's quite a bit more
+that we can actually be assuming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we're going to show for the rest
+
+ align:start position:0%
+so what we're going to show for the rest
+ 
+
+ align:start position:0%
+so what we're going to show for the rest
+of today is two more equivalent
+
+ align:start position:0%
+of today is two more equivalent
+ 
+
+ align:start position:0%
+of today is two more equivalent
+definitions of compactiveness on a
+
+ align:start position:0%
+definitions of compactiveness on a
+ 
+
+ align:start position:0%
+definitions of compactiveness on a
+metric space
+
+ align:start position:0%
+metric space
+ 
+
+ align:start position:0%
+metric space
+and I'll again reiterate these are for a
+
+ align:start position:0%
+and I'll again reiterate these are for a
+ 
+
+ align:start position:0%
+and I'll again reiterate these are for a
+metric space not inherently
+
+ align:start position:0%
+metric space not inherently
+ 
+
+ align:start position:0%
+metric space not inherently
+a topological space as you might see in
+
+ align:start position:0%
+a topological space as you might see in
+ 
+
+ align:start position:0%
+a topological space as you might see in
+18901 but this is the definition of
+
+ align:start position:0%
+18901 but this is the definition of
+ 
+
+ align:start position:0%
+18901 but this is the definition of
+compactness or equivalent definitions of
+
+ align:start position:0%
+compactness or equivalent definitions of
+ 
+
+ align:start position:0%
+compactness or equivalent definitions of
+compactness for a metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but before I do that I want to First
+
+ align:start position:0%
+but before I do that I want to First
+ 
+
+ align:start position:0%
+but before I do that I want to First
+State some lemmas
+
+ align:start position:0%
+State some lemmas
+ 
+
+ align:start position:0%
+State some lemmas
+or some corollaries of these facts that
+
+ align:start position:0%
+or some corollaries of these facts that
+ 
+
+ align:start position:0%
+or some corollaries of these facts that
+we've shown so far because they're
+
+ align:start position:0%
+we've shown so far because they're
+ 
+
+ align:start position:0%
+we've shown so far because they're
+deeply important
+
+ align:start position:0%
+deeply important
+ 
+
+ align:start position:0%
+deeply important
+compactness has some very deep results
+
+ align:start position:0%
+compactness has some very deep results
+ 
+
+ align:start position:0%
+compactness has some very deep results
+and I know that this is going to be a
+
+ align:start position:0%
+and I know that this is going to be a
+ 
+
+ align:start position:0%
+and I know that this is going to be a
+very proof intensive class so I want to
+
+ align:start position:0%
+very proof intensive class so I want to
+ 
+
+ align:start position:0%
+very proof intensive class so I want to
+first start by stating some facts that
+
+ align:start position:0%
+first start by stating some facts that
+ 
+
+ align:start position:0%
+first start by stating some facts that
+are a little bit easier to prove but
+
+ align:start position:0%
+are a little bit easier to prove but
+ 
+
+ align:start position:0%
+are a little bit easier to prove but
+also mildly intuitive
+
+ align:start position:0%
+also mildly intuitive
+ 
+
+ align:start position:0%
+also mildly intuitive
+so first recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a function f from X to Y where X and Y
+
+ align:start position:0%
+a function f from X to Y where X and Y
+ 
+
+ align:start position:0%
+a function f from X to Y where X and Y
+metric spaces
+
+ align:start position:0%
+metric spaces
+ 
+
+ align:start position:0%
+metric spaces
+is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+for every U open
+
+ align:start position:0%
+for every U open
+ 
+
+ align:start position:0%
+for every U open
+in y
+
+ align:start position:0%
+in y
+ 
+
+ align:start position:0%
+in y
+F inverse of U
+
+ align:start position:0%
+F inverse of U
+ 
+
+ align:start position:0%
+F inverse of U
+is open in x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry you know I didn't fully write it
+
+ align:start position:0%
+sorry you know I didn't fully write it
+ 
+
+ align:start position:0%
+sorry you know I didn't fully write it
+out but I at least had to verbally F
+
+ align:start position:0%
+out but I at least had to verbally F
+ 
+
+ align:start position:0%
+out but I at least had to verbally F
+inverse of U is going to be open in X
+
+ align:start position:0%
+inverse of U is going to be open in X
+ 
+
+ align:start position:0%
+inverse of U is going to be open in X
+this is the definition of continuous and
+
+ align:start position:0%
+this is the definition of continuous and
+ 
+
+ align:start position:0%
+this is the definition of continuous and
+we're going to do is therefore show
+
+ align:start position:0%
+we're going to do is therefore show
+ 
+
+ align:start position:0%
+we're going to do is therefore show
+llama
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if K is a compact compact subset of X
+
+ align:start position:0%
+if K is a compact compact subset of X
+ 
+
+ align:start position:0%
+if K is a compact compact subset of X
+we're here the double sub the double
+
+ align:start position:0%
+we're here the double sub the double
+ 
+
+ align:start position:0%
+we're here the double sub the double
+subsets implies compact
+
+ align:start position:0%
+subsets implies compact
+ 
+
+ align:start position:0%
+subsets implies compact
+so recall that notation
+
+ align:start position:0%
+so recall that notation
+ 
+
+ align:start position:0%
+so recall that notation
+we're going to note that F of K
+
+ align:start position:0%
+we're going to note that F of K
+ 
+
+ align:start position:0%
+we're going to note that F of K
+is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why
+
+ align:start position:0%
+and why
+ 
+
+ align:start position:0%
+and why
+here f
+
+ align:start position:0%
+here f
+ 
+
+ align:start position:0%
+here f
+is a continuous map from X to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is our first statement that
+
+ align:start position:0%
+so this is our first statement that
+ 
+
+ align:start position:0%
+so this is our first statement that
+we're going to prove today
+
+ align:start position:0%
+we're going to prove today
+ 
+
+ align:start position:0%
+we're going to prove today
+or sorry the first statement that we're
+
+ align:start position:0%
+or sorry the first statement that we're
+ 
+
+ align:start position:0%
+or sorry the first statement that we're
+going to prove right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we want to somehow reach an open
+
+ align:start position:0%
+well we want to somehow reach an open
+ 
+
+ align:start position:0%
+well we want to somehow reach an open
+cover from
+
+ align:start position:0%
+cover from
+ 
+
+ align:start position:0%
+cover from
+of K
+
+ align:start position:0%
+of K
+ 
+
+ align:start position:0%
+of K
+so let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u i
+
+ align:start position:0%
+u i
+ 
+
+ align:start position:0%
+u i
+be an open cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+F of K
+
+ align:start position:0%
+F of K
+ 
+
+ align:start position:0%
+F of K
+in y
+
+ align:start position:0%
+in y
+ 
+
+ align:start position:0%
+in y
+then what do we know
+
+ align:start position:0%
+then what do we know
+ 
+
+ align:start position:0%
+then what do we know
+well what this will imply is that F
+
+ align:start position:0%
+well what this will imply is that F
+ 
+
+ align:start position:0%
+well what this will imply is that F
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+of UI
+
+ align:start position:0%
+of UI
+ 
+
+ align:start position:0%
+of UI
+will be a finite sorry not finite will
+
+ align:start position:0%
+will be a finite sorry not finite will
+ 
+
+ align:start position:0%
+will be a finite sorry not finite will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+an open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cover
+
+ align:start position:0%
+cover
+ 
+
+ align:start position:0%
+cover
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the fact that the inverse image is cover
+
+ align:start position:0%
+the fact that the inverse image is cover
+ 
+
+ align:start position:0%
+the fact that the inverse image is cover
+K is by the very definition of f of K
+
+ align:start position:0%
+K is by the very definition of f of K
+ 
+
+ align:start position:0%
+K is by the very definition of f of K
+but how do we know that they're open
+
+ align:start position:0%
+but how do we know that they're open
+ 
+
+ align:start position:0%
+but how do we know that they're open
+well this is from the fact that it's
+
+ align:start position:0%
+well this is from the fact that it's
+ 
+
+ align:start position:0%
+well this is from the fact that it's
+continuous these are the inverse images
+
+ align:start position:0%
+continuous these are the inverse images
+ 
+
+ align:start position:0%
+continuous these are the inverse images
+of open sets
+
+ align:start position:0%
+of open sets
+ 
+
+ align:start position:0%
+of open sets
+and so what we know is that we can reach
+
+ align:start position:0%
+and so what we know is that we can reach
+ 
+
+ align:start position:0%
+and so what we know is that we can reach
+a finite subcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a finite sub cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+F inverse UI
+
+ align:start position:0%
+F inverse UI
+ 
+
+ align:start position:0%
+F inverse UI
+from let's say I equals one decay
+
+ align:start position:0%
+from let's say I equals one decay
+ 
+
+ align:start position:0%
+from let's say I equals one decay
+and what we're going to do is map this
+
+ align:start position:0%
+and what we're going to do is map this
+ 
+
+ align:start position:0%
+and what we're going to do is map this
+back to F of K notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that then f
+
+ align:start position:0%
+that then f
+ 
+
+ align:start position:0%
+that then f
+of f inverse of u i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+UI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is therefore going to give us our
+
+ align:start position:0%
+which is therefore going to give us our
+ 
+
+ align:start position:0%
+which is therefore going to give us our
+open sorry how should I say this
+
+ align:start position:0%
+open sorry how should I say this
+ 
+
+ align:start position:0%
+open sorry how should I say this
+how should I say this this is not
+
+ align:start position:0%
+how should I say this this is not
+ 
+
+ align:start position:0%
+how should I say this this is not
+necessarily directly true
+
+ align:start position:0%
+necessarily directly true
+ 
+
+ align:start position:0%
+necessarily directly true
+what I mean to say
+
+ align:start position:0%
+what I mean to say
+ 
+
+ align:start position:0%
+what I mean to say
+is that the new I
+
+ align:start position:0%
+is that the new I
+ 
+
+ align:start position:0%
+is that the new I
+from I equals 1 to K
+
+ align:start position:0%
+from I equals 1 to K
+ 
+
+ align:start position:0%
+from I equals 1 to K
+is a open cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f of K
+
+ align:start position:0%
+of f of K
+ 
+
+ align:start position:0%
+of f of K
+how do you know this
+
+ align:start position:0%
+how do you know this
+ 
+
+ align:start position:0%
+how do you know this
+well we know that the uis are such that
+
+ align:start position:0%
+well we know that the uis are such that
+ 
+
+ align:start position:0%
+well we know that the uis are such that
+oh sorry the F inverse of uis cover K so
+
+ align:start position:0%
+oh sorry the F inverse of uis cover K so
+ 
+
+ align:start position:0%
+oh sorry the F inverse of uis cover K so
+therefore the images of them must cover
+
+ align:start position:0%
+therefore the images of them must cover
+ 
+
+ align:start position:0%
+therefore the images of them must cover
+F of K
+
+ align:start position:0%
+F of K
+ 
+
+ align:start position:0%
+F of K
+and so we've gone from an open cover of
+
+ align:start position:0%
+and so we've gone from an open cover of
+ 
+
+ align:start position:0%
+and so we've gone from an open cover of
+f of K to a finite subcover which shows
+
+ align:start position:0%
+f of K to a finite subcover which shows
+ 
+
+ align:start position:0%
+f of K to a finite subcover which shows
+that is compact in y
+
+ align:start position:0%
+that is compact in y
+ 
+
+ align:start position:0%
+that is compact in y
+so that enter proof that shows that the
+
+ align:start position:0%
+so that enter proof that shows that the
+ 
+
+ align:start position:0%
+so that enter proof that shows that the
+image of compact sets is going to be
+
+ align:start position:0%
+image of compact sets is going to be
+ 
+
+ align:start position:0%
+image of compact sets is going to be
+compact under continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and using this and the fact that we have
+
+ align:start position:0%
+and using this and the fact that we have
+ 
+
+ align:start position:0%
+and using this and the fact that we have
+sequential compactness is going to allow
+
+ align:start position:0%
+sequential compactness is going to allow
+ 
+
+ align:start position:0%
+sequential compactness is going to allow
+us to State some very helpful lemmas
+
+ align:start position:0%
+us to State some very helpful lemmas
+ 
+
+ align:start position:0%
+us to State some very helpful lemmas
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+Lemma or sorry not llama Corollary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a map f
+
+ align:start position:0%
+a map f
+ 
+
+ align:start position:0%
+a map f
+from X to let's say the real numbers
+
+ align:start position:0%
+from X to let's say the real numbers
+ 
+
+ align:start position:0%
+from X to let's say the real numbers
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a max
+
+ align:start position:0%
+has a max
+ 
+
+ align:start position:0%
+has a max
+Andy min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+achieved on compact sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+by which I mean for every compact subset
+
+ align:start position:0%
+by which I mean for every compact subset
+ 
+
+ align:start position:0%
+by which I mean for every compact subset
+of X the image of it to R is going to
+
+ align:start position:0%
+of X the image of it to R is going to
+ 
+
+ align:start position:0%
+of X the image of it to R is going to
+have a maximum and a minimum achieved
+
+ align:start position:0%
+have a maximum and a minimum achieved
+ 
+
+ align:start position:0%
+have a maximum and a minimum achieved
+in the proof is very short at this point
+
+ align:start position:0%
+in the proof is very short at this point
+ 
+
+ align:start position:0%
+in the proof is very short at this point
+we know that F of K
+
+ align:start position:0%
+we know that F of K
+ 
+
+ align:start position:0%
+we know that F of K
+is going to be compact in r
+
+ align:start position:0%
+is going to be compact in r
+ 
+
+ align:start position:0%
+is going to be compact in r
+which implies that it's going to be
+
+ align:start position:0%
+which implies that it's going to be
+ 
+
+ align:start position:0%
+which implies that it's going to be
+closed and bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed and bounded which you can think
+
+ align:start position:0%
+closed and bounded which you can think
+ 
+
+ align:start position:0%
+closed and bounded which you can think
+of as sequentially compact in the same
+
+ align:start position:0%
+of as sequentially compact in the same
+ 
+
+ align:start position:0%
+of as sequentially compact in the same
+way implies that we can find a maximum
+
+ align:start position:0%
+way implies that we can find a maximum
+ 
+
+ align:start position:0%
+way implies that we can find a maximum
+and a minimum of f of K
+
+ align:start position:0%
+and a minimum of f of K
+ 
+
+ align:start position:0%
+and a minimum of f of K
+this is essentially just the extreme
+
+ align:start position:0%
+this is essentially just the extreme
+ 
+
+ align:start position:0%
+this is essentially just the extreme
+value theorem but it's much more General
+
+ align:start position:0%
+value theorem but it's much more General
+ 
+
+ align:start position:0%
+value theorem but it's much more General
+than the extreme value theorem before
+
+ align:start position:0%
+than the extreme value theorem before
+ 
+
+ align:start position:0%
+than the extreme value theorem before
+the extreme value theorem was a map from
+
+ align:start position:0%
+the extreme value theorem was a map from
+ 
+
+ align:start position:0%
+the extreme value theorem was a map from
+the real numbers or at least a compact
+
+ align:start position:0%
+the real numbers or at least a compact
+ 
+
+ align:start position:0%
+the real numbers or at least a compact
+subset Like A to B to the real numbers
+
+ align:start position:0%
+subset Like A to B to the real numbers
+ 
+
+ align:start position:0%
+subset Like A to B to the real numbers
+now all of a sudden we have the extreme
+
+ align:start position:0%
+now all of a sudden we have the extreme
+ 
+
+ align:start position:0%
+now all of a sudden we have the extreme
+value theorem for for metric spaces
+
+ align:start position:0%
+value theorem for for metric spaces
+ 
+
+ align:start position:0%
+value theorem for for metric spaces
+this fact is extremely helpful
+
+ align:start position:0%
+this fact is extremely helpful
+ 
+
+ align:start position:0%
+this fact is extremely helpful
+um I cannot iterate how important it's
+
+ align:start position:0%
+um I cannot iterate how important it's
+ 
+
+ align:start position:0%
+um I cannot iterate how important it's
+going to be in the long term if you keep
+
+ align:start position:0%
+going to be in the long term if you keep
+ 
+
+ align:start position:0%
+going to be in the long term if you keep
+taking analysis courses but the fact
+
+ align:start position:0%
+taking analysis courses but the fact
+ 
+
+ align:start position:0%
+taking analysis courses but the fact
+that images of compact sets are going to
+
+ align:start position:0%
+that images of compact sets are going to
+ 
+
+ align:start position:0%
+that images of compact sets are going to
+be compact is very very helpful
+
+ align:start position:0%
+be compact is very very helpful
+ 
+
+ align:start position:0%
+be compact is very very helpful
+and helps us with finding a maximum and
+
+ align:start position:0%
+and helps us with finding a maximum and
+ 
+
+ align:start position:0%
+and helps us with finding a maximum and
+a minimum in fact one other way to think
+
+ align:start position:0%
+a minimum in fact one other way to think
+ 
+
+ align:start position:0%
+a minimum in fact one other way to think
+of this theorem is just to take a
+
+ align:start position:0%
+of this theorem is just to take a
+ 
+
+ align:start position:0%
+of this theorem is just to take a
+sequence that converges to the maximum
+
+ align:start position:0%
+sequence that converges to the maximum
+ 
+
+ align:start position:0%
+sequence that converges to the maximum
+and converges to the minimum and there
+
+ align:start position:0%
+and converges to the minimum and there
+ 
+
+ align:start position:0%
+and converges to the minimum and there
+has to be a convergent subsequence of
+
+ align:start position:0%
+has to be a convergent subsequence of
+ 
+
+ align:start position:0%
+has to be a convergent subsequence of
+that sequence because it's sequentially
+
+ align:start position:0%
+that sequence because it's sequentially
+ 
+
+ align:start position:0%
+that sequence because it's sequentially
+compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+besides this
+
+ align:start position:0%
+besides this
+ 
+
+ align:start position:0%
+besides this
+I also want to note
+
+ align:start position:0%
+I also want to note
+ 
+
+ align:start position:0%
+I also want to note
+Corollary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Maps f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F from X to R
+
+ align:start position:0%
+F from X to R
+ 
+
+ align:start position:0%
+F from X to R
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to be bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the second corollary right
+
+ align:start position:0%
+this is the second corollary right
+ 
+
+ align:start position:0%
+this is the second corollary right
+before we were using closeness right now
+
+ align:start position:0%
+before we were using closeness right now
+ 
+
+ align:start position:0%
+before we were using closeness right now
+we're using boundedness
+
+ align:start position:0%
+we're using boundedness
+ 
+
+ align:start position:0%
+we're using boundedness
+so this is very helpful
+
+ align:start position:0%
+so this is very helpful
+ 
+
+ align:start position:0%
+so this is very helpful
+um just in order to be able to
+
+ align:start position:0%
+um just in order to be able to
+ 
+
+ align:start position:0%
+um just in order to be able to
+conceptualize what's happening
+
+ align:start position:0%
+conceptualize what's happening
+ 
+
+ align:start position:0%
+conceptualize what's happening
+so the proof is already complete by
+
+ align:start position:0%
+so the proof is already complete by
+ 
+
+ align:start position:0%
+so the proof is already complete by
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+so I will stop there for the moment
+
+ align:start position:0%
+so I will stop there for the moment
+ 
+
+ align:start position:0%
+so I will stop there for the moment
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+now we have one more CRM that I want to
+
+ align:start position:0%
+now we have one more CRM that I want to
+ 
+
+ align:start position:0%
+now we have one more CRM that I want to
+show that will
+
+ align:start position:0%
+show that will
+ 
+
+ align:start position:0%
+show that will
+have some implications
+
+ align:start position:0%
+have some implications
+ 
+
+ align:start position:0%
+have some implications
+for or that will be conceptually helpful
+
+ align:start position:0%
+for or that will be conceptually helpful
+ 
+
+ align:start position:0%
+for or that will be conceptually helpful
+but before I do that I'm going to drink
+
+ align:start position:0%
+but before I do that I'm going to drink
+ 
+
+ align:start position:0%
+but before I do that I'm going to drink
+some water
+
+ align:start position:0%
+some water
+ 
+
+ align:start position:0%
+some water
+the next theorem is known as cantor's
+
+ align:start position:0%
+the next theorem is known as cantor's
+ 
+
+ align:start position:0%
+the next theorem is known as cantor's
+intersection theorem it's one that tells
+
+ align:start position:0%
+intersection theorem it's one that tells
+ 
+
+ align:start position:0%
+intersection theorem it's one that tells
+us things about nested sequences of
+
+ align:start position:0%
+us things about nested sequences of
+ 
+
+ align:start position:0%
+us things about nested sequences of
+compact sets
+
+ align:start position:0%
+compact sets
+ 
+
+ align:start position:0%
+compact sets
+and it's helpful conceptually it's used
+
+ align:start position:0%
+and it's helpful conceptually it's used
+ 
+
+ align:start position:0%
+and it's helpful conceptually it's used
+all the time in fact if you were to take
+
+ align:start position:0%
+all the time in fact if you were to take
+ 
+
+ align:start position:0%
+all the time in fact if you were to take
+a complex analysis class it's one of the
+
+ align:start position:0%
+a complex analysis class it's one of the
+ 
+
+ align:start position:0%
+a complex analysis class it's one of the
+first things that's used to show
+
+ align:start position:0%
+first things that's used to show
+ 
+
+ align:start position:0%
+first things that's used to show
+convergence of line integrals
+
+ align:start position:0%
+convergence of line integrals
+ 
+
+ align:start position:0%
+convergence of line integrals
+for holomorphic functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+this is known as cantor's intersection
+
+ align:start position:0%
+this is known as cantor's intersection
+ 
+
+ align:start position:0%
+this is known as cantor's intersection
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K1
+
+ align:start position:0%
+K1
+ 
+
+ align:start position:0%
+K1
+containing K2 contained in K3 so on and
+
+ align:start position:0%
+containing K2 contained in K3 so on and
+ 
+
+ align:start position:0%
+containing K2 contained in K3 so on and
+so forth each compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each done empty
+
+ align:start position:0%
+each done empty
+ 
+
+ align:start position:0%
+each done empty
+and compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by compact I mean topologically or
+
+ align:start position:0%
+by compact I mean topologically or
+ 
+
+ align:start position:0%
+by compact I mean topologically or
+sequentially which we know that that's a
+
+ align:start position:0%
+sequentially which we know that that's a
+ 
+
+ align:start position:0%
+sequentially which we know that that's a
+simple fact that
+
+ align:start position:0%
+simple fact that
+ 
+
+ align:start position:0%
+simple fact that
+let me reiterate
+
+ align:start position:0%
+let me reiterate
+ 
+
+ align:start position:0%
+let me reiterate
+by non-empty and compact I mean
+
+ align:start position:0%
+by non-empty and compact I mean
+ 
+
+ align:start position:0%
+by non-empty and compact I mean
+subsequentially are topologically
+
+ align:start position:0%
+subsequentially are topologically
+ 
+
+ align:start position:0%
+subsequentially are topologically
+because they're the equivalent on a
+
+ align:start position:0%
+because they're the equivalent on a
+ 
+
+ align:start position:0%
+because they're the equivalent on a
+metrics base and here I'm assuming that
+
+ align:start position:0%
+metrics base and here I'm assuming that
+ 
+
+ align:start position:0%
+metrics base and here I'm assuming that
+the compact subsets are in a metric
+
+ align:start position:0%
+the compact subsets are in a metric
+ 
+
+ align:start position:0%
+the compact subsets are in a metric
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+the kis from I equals 1 to Infinity
+
+ align:start position:0%
+the kis from I equals 1 to Infinity
+ 
+
+ align:start position:0%
+the kis from I equals 1 to Infinity
+is non-empty
+
+ align:start position:0%
+is non-empty
+ 
+
+ align:start position:0%
+is non-empty
+how do we prove this
+
+ align:start position:0%
+how do we prove this
+ 
+
+ align:start position:0%
+how do we prove this
+well we prove this by taking a sequence
+
+ align:start position:0%
+well we prove this by taking a sequence
+ 
+
+ align:start position:0%
+well we prove this by taking a sequence
+of terms in kis
+
+ align:start position:0%
+of terms in kis
+ 
+
+ align:start position:0%
+of terms in kis
+so proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let x i
+
+ align:start position:0%
+let x i
+ 
+
+ align:start position:0%
+let x i
+B and K i for all I
+
+ align:start position:0%
+B and K i for all I
+ 
+
+ align:start position:0%
+B and K i for all I
+and we know that there exists such an x
+
+ align:start position:0%
+and we know that there exists such an x
+ 
+
+ align:start position:0%
+and we know that there exists such an x
+i because they're not empty so right off
+
+ align:start position:0%
+i because they're not empty so right off
+ 
+
+ align:start position:0%
+i because they're not empty so right off
+the bat we're using the hypothesis
+
+ align:start position:0%
+the bat we're using the hypothesis
+ 
+
+ align:start position:0%
+the bat we're using the hypothesis
+and what we want to note is then that
+
+ align:start position:0%
+and what we want to note is then that
+ 
+
+ align:start position:0%
+and what we want to note is then that
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+or sorry let's focus on K1 for now
+
+ align:start position:0%
+or sorry let's focus on K1 for now
+ 
+
+ align:start position:0%
+or sorry let's focus on K1 for now
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+x i is in K1
+
+ align:start position:0%
+x i is in K1
+ 
+
+ align:start position:0%
+x i is in K1
+for all I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this follows from the fact that it's a
+
+ align:start position:0%
+this follows from the fact that it's a
+ 
+
+ align:start position:0%
+this follows from the fact that it's a
+nested sequence of compact sets
+
+ align:start position:0%
+nested sequence of compact sets
+ 
+
+ align:start position:0%
+nested sequence of compact sets
+so therefore
+
+ align:start position:0%
+so therefore
+ 
+
+ align:start position:0%
+so therefore
+there exists a convergent
+
+ align:start position:0%
+there exists a convergent
+ 
+
+ align:start position:0%
+there exists a convergent
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and K
+
+ align:start position:0%
+X and K
+ 
+
+ align:start position:0%
+X and K
+converging to some a and K1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you can continue to show
+
+ align:start position:0%
+and what you can continue to show
+ 
+
+ align:start position:0%
+and what you can continue to show
+is that it's going to continue to
+
+ align:start position:0%
+is that it's going to continue to
+ 
+
+ align:start position:0%
+is that it's going to continue to
+convergence to a in every Ki
+
+ align:start position:0%
+convergence to a in every Ki
+ 
+
+ align:start position:0%
+convergence to a in every Ki
+so secondly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X I from I equal to 2 to Infinity as
+
+ align:start position:0%
+X I from I equal to 2 to Infinity as
+ 
+
+ align:start position:0%
+X I from I equal to 2 to Infinity as
+opposed to including one
+
+ align:start position:0%
+opposed to including one
+ 
+
+ align:start position:0%
+opposed to including one
+is going to be a subset of K2
+
+ align:start position:0%
+is going to be a subset of K2
+ 
+
+ align:start position:0%
+is going to be a subset of K2
+and therefore there exists a convergent
+
+ align:start position:0%
+and therefore there exists a convergent
+ 
+
+ align:start position:0%
+and therefore there exists a convergent
+subsequence and the convergent
+
+ align:start position:0%
+subsequence and the convergent
+ 
+
+ align:start position:0%
+subsequence and the convergent
+subsequence has a unique limit point
+
+ align:start position:0%
+subsequence has a unique limit point
+ 
+
+ align:start position:0%
+subsequence has a unique limit point
+right this is what we said on the second
+
+ align:start position:0%
+right this is what we said on the second
+ 
+
+ align:start position:0%
+right this is what we said on the second
+day convergence sequences have
+
+ align:start position:0%
+day convergence sequences have
+ 
+
+ align:start position:0%
+day convergence sequences have
+equivalent or have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't want to say this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have the same limit points so therefore
+
+ align:start position:0%
+have the same limit points so therefore
+ 
+
+ align:start position:0%
+have the same limit points so therefore
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+will be in K2
+
+ align:start position:0%
+will be in K2
+ 
+
+ align:start position:0%
+will be in K2
+and we can continue this process over
+
+ align:start position:0%
+and we can continue this process over
+ 
+
+ align:start position:0%
+and we can continue this process over
+and over again ending up with a single
+
+ align:start position:0%
+and over again ending up with a single
+ 
+
+ align:start position:0%
+and over again ending up with a single
+point at least in all of the kis
+
+ align:start position:0%
+point at least in all of the kis
+ 
+
+ align:start position:0%
+point at least in all of the kis
+so this concludes our proof
+
+ align:start position:0%
+so this concludes our proof
+ 
+
+ align:start position:0%
+so this concludes our proof
+and this is used in complex analysis as
+
+ align:start position:0%
+and this is used in complex analysis as
+ 
+
+ align:start position:0%
+and this is used in complex analysis as
+I stated to
+
+ align:start position:0%
+I stated to
+ 
+
+ align:start position:0%
+I stated to
+go from
+
+ align:start position:0%
+go from
+ 
+
+ align:start position:0%
+go from
+a sequence of triangles that say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say we have the sequence of
+
+ align:start position:0%
+so let's say we have the sequence of
+ 
+
+ align:start position:0%
+so let's say we have the sequence of
+triangles and we know that there exists
+
+ align:start position:0%
+triangles and we know that there exists
+ 
+
+ align:start position:0%
+triangles and we know that there exists
+a point in every one of them
+
+ align:start position:0%
+a point in every one of them
+ 
+
+ align:start position:0%
+a point in every one of them
+we can keep reiterating this pattern and
+
+ align:start position:0%
+we can keep reiterating this pattern and
+ 
+
+ align:start position:0%
+we can keep reiterating this pattern and
+end up with a point in the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we know that the limits of the
+
+ align:start position:0%
+so we know that the limits of the
+ 
+
+ align:start position:0%
+so we know that the limits of the
+intersection is going to be non-empty
+
+ align:start position:0%
+intersection is going to be non-empty
+ 
+
+ align:start position:0%
+intersection is going to be non-empty
+so that's how it's used in complex
+
+ align:start position:0%
+so that's how it's used in complex
+ 
+
+ align:start position:0%
+so that's how it's used in complex
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+we can't discuss this more fully now
+
+ align:start position:0%
+we can't discuss this more fully now
+ 
+
+ align:start position:0%
+we can't discuss this more fully now
+because it requires a discussion so that
+
+ align:start position:0%
+because it requires a discussion so that
+ 
+
+ align:start position:0%
+because it requires a discussion so that
+takes numerous days of complex analysis
+
+ align:start position:0%
+takes numerous days of complex analysis
+ 
+
+ align:start position:0%
+takes numerous days of complex analysis
+to prove but you know if you take
+
+ align:start position:0%
+to prove but you know if you take
+ 
+
+ align:start position:0%
+to prove but you know if you take
+complex analysis this will be one of the
+
+ align:start position:0%
+complex analysis this will be one of the
+ 
+
+ align:start position:0%
+complex analysis this will be one of the
+first things you see
+
+ align:start position:0%
+first things you see
+ 
+
+ align:start position:0%
+first things you see
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what we're going to do with this new
+
+ align:start position:0%
+so what we're going to do with this new
+ 
+
+ align:start position:0%
+so what we're going to do with this new
+theorem what we're going to define a new
+
+ align:start position:0%
+theorem what we're going to define a new
+ 
+
+ align:start position:0%
+theorem what we're going to define a new
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a collection of closed sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice here that I'm assuming closed and
+
+ align:start position:0%
+notice here that I'm assuming closed and
+ 
+
+ align:start position:0%
+notice here that I'm assuming closed and
+not compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh or has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the finite intersection property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersection property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite subsection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E if I take friendly many of the
+
+ align:start position:0%
+I.E if I take friendly many of the
+ 
+
+ align:start position:0%
+I.E if I take friendly many of the
+closets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to assume that it has
+
+ align:start position:0%
+we're going to assume that it has
+ 
+
+ align:start position:0%
+we're going to assume that it has
+non-empty end intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know that this is already going to be
+
+ align:start position:0%
+we know that this is already going to be
+ 
+
+ align:start position:0%
+we know that this is already going to be
+true for compact sets because the
+
+ align:start position:0%
+true for compact sets because the
+ 
+
+ align:start position:0%
+true for compact sets because the
+infinite intersection of them is not
+
+ align:start position:0%
+infinite intersection of them is not
+ 
+
+ align:start position:0%
+infinite intersection of them is not
+empty but this statement is a little bit
+
+ align:start position:0%
+empty but this statement is a little bit
+ 
+
+ align:start position:0%
+empty but this statement is a little bit
+more General and that we're only
+
+ align:start position:0%
+more General and that we're only
+ 
+
+ align:start position:0%
+more General and that we're only
+assuming that it's going to be closed
+
+ align:start position:0%
+assuming that it's going to be closed
+ 
+
+ align:start position:0%
+assuming that it's going to be closed
+and so we're assuming that every finite
+
+ align:start position:0%
+and so we're assuming that every finite
+ 
+
+ align:start position:0%
+and so we're assuming that every finite
+subcollection has non-empty intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we're going to show is that in
+
+ align:start position:0%
+and so we're going to show is that in
+ 
+
+ align:start position:0%
+and so we're going to show is that in
+fact there's a relationship between the
+
+ align:start position:0%
+fact there's a relationship between the
+ 
+
+ align:start position:0%
+fact there's a relationship between the
+finite intersection property
+
+ align:start position:0%
+finite intersection property
+ 
+
+ align:start position:0%
+finite intersection property
+and topologically and sequentially
+
+ align:start position:0%
+and topologically and sequentially
+ 
+
+ align:start position:0%
+and topologically and sequentially
+compact that's going to be a huge
+
+ align:start position:0%
+compact that's going to be a huge
+ 
+
+ align:start position:0%
+compact that's going to be a huge
+theorem for today it's going to take a
+
+ align:start position:0%
+theorem for today it's going to take a
+ 
+
+ align:start position:0%
+theorem for today it's going to take a
+little bit to prove
+
+ align:start position:0%
+little bit to prove
+ 
+
+ align:start position:0%
+little bit to prove
+but will be deeply powerful once we're
+
+ align:start position:0%
+but will be deeply powerful once we're
+ 
+
+ align:start position:0%
+but will be deeply powerful once we're
+done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our theorem
+
+ align:start position:0%
+our theorem
+ 
+
+ align:start position:0%
+our theorem
+is that the following are equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the following are equivalent which I'll
+
+ align:start position:0%
+the following are equivalent which I'll
+ 
+
+ align:start position:0%
+the following are equivalent which I'll
+write out more fully in case you haven't
+
+ align:start position:0%
+write out more fully in case you haven't
+ 
+
+ align:start position:0%
+write out more fully in case you haven't
+seen this abbreviation before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a metric Space X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+X is
+
+ align:start position:0%
+X is
+ 
+
+ align:start position:0%
+X is
+topologically compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topologically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+X is sequentially compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which makes sense we've already shown
+
+ align:start position:0%
+which makes sense we've already shown
+ 
+
+ align:start position:0%
+which makes sense we've already shown
+this implication
+
+ align:start position:0%
+this implication
+ 
+
+ align:start position:0%
+this implication
+but we're going to show two more
+
+ align:start position:0%
+but we're going to show two more
+ 
+
+ align:start position:0%
+but we're going to show two more
+properties right now
+
+ align:start position:0%
+properties right now
+ 
+
+ align:start position:0%
+properties right now
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+X is totally bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which you've already shown sequentially
+
+ align:start position:0%
+which you've already shown sequentially
+ 
+
+ align:start position:0%
+which you've already shown sequentially
+compact implies totally bounded but
+
+ align:start position:0%
+compact implies totally bounded but
+ 
+
+ align:start position:0%
+compact implies totally bounded but
+there's one more thing we need to
+
+ align:start position:0%
+there's one more thing we need to
+ 
+
+ align:start position:0%
+there's one more thing we need to
+include
+
+ align:start position:0%
+include
+ 
+
+ align:start position:0%
+include
+we need to include that is koshy
+
+ align:start position:0%
+we need to include that is koshy
+ 
+
+ align:start position:0%
+we need to include that is koshy
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally our fourth property
+
+ align:start position:0%
+and finally our fourth property
+ 
+
+ align:start position:0%
+and finally our fourth property
+is going to be the following which all
+
+ align:start position:0%
+is going to be the following which all
+ 
+
+ align:start position:0%
+is going to be the following which all
+state out clearly because it's one of
+
+ align:start position:0%
+state out clearly because it's one of
+ 
+
+ align:start position:0%
+state out clearly because it's one of
+the more confusing ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every collection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of closed sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of close-up sets of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the finite intersection property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has non-empty intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the difference is that we know that
+
+ align:start position:0%
+here the difference is that we know that
+ 
+
+ align:start position:0%
+here the difference is that we know that
+every finite subcollection has non-empty
+
+ align:start position:0%
+every finite subcollection has non-empty
+ 
+
+ align:start position:0%
+every finite subcollection has non-empty
+intersection but what this theorem is
+
+ align:start position:0%
+intersection but what this theorem is
+ 
+
+ align:start position:0%
+intersection but what this theorem is
+telling you is that the intersection of
+
+ align:start position:0%
+telling you is that the intersection of
+ 
+
+ align:start position:0%
+telling you is that the intersection of
+all of the closed subsets if they have
+
+ align:start position:0%
+all of the closed subsets if they have
+ 
+
+ align:start position:0%
+all of the closed subsets if they have
+the final intersection property is also
+
+ align:start position:0%
+the final intersection property is also
+ 
+
+ align:start position:0%
+the final intersection property is also
+going to be non-empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what we're going to do is show that
+
+ align:start position:0%
+now what we're going to do is show that
+ 
+
+ align:start position:0%
+now what we're going to do is show that
+one is true if and only if four is true
+
+ align:start position:0%
+one is true if and only if four is true
+ 
+
+ align:start position:0%
+one is true if and only if four is true
+we've all already showed let me write
+
+ align:start position:0%
+we've all already showed let me write
+ 
+
+ align:start position:0%
+we've all already showed let me write
+this summer fully we've already shown
+
+ align:start position:0%
+this summer fully we've already shown
+ 
+
+ align:start position:0%
+this summer fully we've already shown
+that one is true if and only if two is
+
+ align:start position:0%
+that one is true if and only if two is
+ 
+
+ align:start position:0%
+that one is true if and only if two is
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+what we're now going to do is show that
+
+ align:start position:0%
+what we're now going to do is show that
+ 
+
+ align:start position:0%
+what we're now going to do is show that
+one is true if and only if 4 is true
+
+ align:start position:0%
+one is true if and only if 4 is true
+ 
+
+ align:start position:0%
+one is true if and only if 4 is true
+and then show
+
+ align:start position:0%
+and then show
+ 
+
+ align:start position:0%
+and then show
+that 2 is true if and only a 3 is true
+
+ align:start position:0%
+that 2 is true if and only a 3 is true
+ 
+
+ align:start position:0%
+that 2 is true if and only a 3 is true
+because we've already shown sequentially
+
+ align:start position:0%
+because we've already shown sequentially
+ 
+
+ align:start position:0%
+because we've already shown sequentially
+compact implies totally bounded so we
+
+ align:start position:0%
+compact implies totally bounded so we
+ 
+
+ align:start position:0%
+compact implies totally bounded so we
+would just have to show koshy
+
+ align:start position:0%
+would just have to show koshy
+ 
+
+ align:start position:0%
+would just have to show koshy
+completeness
+
+ align:start position:0%
+completeness
+ 
+
+ align:start position:0%
+completeness
+and then that's going to be the end of
+
+ align:start position:0%
+and then that's going to be the end of
+ 
+
+ align:start position:0%
+and then that's going to be the end of
+today we're going to show these four
+
+ align:start position:0%
+today we're going to show these four
+ 
+
+ align:start position:0%
+today we're going to show these four
+properties of compact sets and then
+
+ align:start position:0%
+properties of compact sets and then
+ 
+
+ align:start position:0%
+properties of compact sets and then
+we're going to end today's discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's start with showing that one is
+
+ align:start position:0%
+so let's start with showing that one is
+ 
+
+ align:start position:0%
+so let's start with showing that one is
+true implies 4 is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the proof is going to start with
+
+ align:start position:0%
+so the proof is going to start with
+ 
+
+ align:start position:0%
+so the proof is going to start with
+finding or supposing for the sake of
+
+ align:start position:0%
+finding or supposing for the sake of
+ 
+
+ align:start position:0%
+finding or supposing for the sake of
+contradiction there exists a collection
+
+ align:start position:0%
+contradiction there exists a collection
+ 
+
+ align:start position:0%
+contradiction there exists a collection
+of closed sets with the final
+
+ align:start position:0%
+of closed sets with the final
+ 
+
+ align:start position:0%
+of closed sets with the final
+intersection property but with empty
+
+ align:start position:0%
+intersection property but with empty
+ 
+
+ align:start position:0%
+intersection property but with empty
+intersection so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+c i
+
+ align:start position:0%
+c i
+ 
+
+ align:start position:0%
+c i
+equals 1 to Infinity
+
+ align:start position:0%
+equals 1 to Infinity
+ 
+
+ align:start position:0%
+equals 1 to Infinity
+closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the finite
+
+ align:start position:0%
+the finite
+ 
+
+ align:start position:0%
+the finite
+intersection property
+
+ align:start position:0%
+intersection property
+ 
+
+ align:start position:0%
+intersection property
+I.E intersection of finite sub
+
+ align:start position:0%
+I.E intersection of finite sub
+ 
+
+ align:start position:0%
+I.E intersection of finite sub
+collections is going to be non-empty
+
+ align:start position:0%
+collections is going to be non-empty
+ 
+
+ align:start position:0%
+collections is going to be non-empty
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and the intersection of all the CIS is
+
+ align:start position:0%
+and the intersection of all the CIS is
+ 
+
+ align:start position:0%
+and the intersection of all the CIS is
+that's going to be our assumption for
+
+ align:start position:0%
+that's going to be our assumption for
+ 
+
+ align:start position:0%
+that's going to be our assumption for
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+well knowing that the intersection of
+
+ align:start position:0%
+well knowing that the intersection of
+ 
+
+ align:start position:0%
+well knowing that the intersection of
+these cosets is going to be empty what
+
+ align:start position:0%
+these cosets is going to be empty what
+ 
+
+ align:start position:0%
+these cosets is going to be empty what
+do we know about the complements
+
+ align:start position:0%
+do we know about the complements
+ 
+
+ align:start position:0%
+do we know about the complements
+well then we know that X which is the
+
+ align:start position:0%
+well then we know that X which is the
+ 
+
+ align:start position:0%
+well then we know that X which is the
+complement of the empty set is going to
+
+ align:start position:0%
+complement of the empty set is going to
+ 
+
+ align:start position:0%
+complement of the empty set is going to
+be the complement of the intersection of
+
+ align:start position:0%
+be the complement of the intersection of
+ 
+
+ align:start position:0%
+be the complement of the intersection of
+CIS
+
+ align:start position:0%
+CIS
+ 
+
+ align:start position:0%
+CIS
+but then we know by De Morgan's laws
+
+ align:start position:0%
+but then we know by De Morgan's laws
+ 
+
+ align:start position:0%
+but then we know by De Morgan's laws
+which we introduced on the second day in
+
+ align:start position:0%
+which we introduced on the second day in
+ 
+
+ align:start position:0%
+which we introduced on the second day in
+general theory
+
+ align:start position:0%
+general theory
+ 
+
+ align:start position:0%
+general theory
+it's going to be the Union
+
+ align:start position:0%
+it's going to be the Union
+ 
+
+ align:start position:0%
+it's going to be the Union
+of the complements of Ci's from I equals
+
+ align:start position:0%
+of the complements of Ci's from I equals
+ 
+
+ align:start position:0%
+of the complements of Ci's from I equals
+1 to Infinity
+
+ align:start position:0%
+1 to Infinity
+ 
+
+ align:start position:0%
+1 to Infinity
+what do we know that
+
+ align:start position:0%
+what do we know that
+ 
+
+ align:start position:0%
+what do we know that
+was a complement of a closed set is
+
+ align:start position:0%
+was a complement of a closed set is
+ 
+
+ align:start position:0%
+was a complement of a closed set is
+going to be open so what we've gone from
+
+ align:start position:0%
+going to be open so what we've gone from
+ 
+
+ align:start position:0%
+going to be open so what we've gone from
+is this collection of closed sets to an
+
+ align:start position:0%
+is this collection of closed sets to an
+ 
+
+ align:start position:0%
+is this collection of closed sets to an
+open cover of x
+
+ align:start position:0%
+open cover of x
+ 
+
+ align:start position:0%
+open cover of x
+therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a finite subcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given by let's say the union from I
+
+ align:start position:0%
+given by let's say the union from I
+ 
+
+ align:start position:0%
+given by let's say the union from I
+equals 1 to K of C i complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know what we're going to show is then
+
+ align:start position:0%
+I know what we're going to show is then
+ 
+
+ align:start position:0%
+I know what we're going to show is then
+that it fails to have the final
+
+ align:start position:0%
+that it fails to have the final
+ 
+
+ align:start position:0%
+that it fails to have the final
+intersection property
+
+ align:start position:0%
+intersection property
+ 
+
+ align:start position:0%
+intersection property
+so notice then
+
+ align:start position:0%
+so notice then
+ 
+
+ align:start position:0%
+so notice then
+that the intersection
+
+ align:start position:0%
+that the intersection
+ 
+
+ align:start position:0%
+that the intersection
+of CI from I equals
+
+ align:start position:0%
+of CI from I equals
+ 
+
+ align:start position:0%
+of CI from I equals
+1 to K
+
+ align:start position:0%
+1 to K
+ 
+
+ align:start position:0%
+1 to K
+is going to be the same as
+
+ align:start position:0%
+is going to be the same as
+ 
+
+ align:start position:0%
+is going to be the same as
+the union of the complements
+
+ align:start position:0%
+the union of the complements
+ 
+
+ align:start position:0%
+the union of the complements
+from I equals 1 to K
+
+ align:start position:0%
+from I equals 1 to K
+ 
+
+ align:start position:0%
+from I equals 1 to K
+which we know is X
+
+ align:start position:0%
+which we know is X
+ 
+
+ align:start position:0%
+which we know is X
+so what this tells us is that the
+
+ align:start position:0%
+so what this tells us is that the
+ 
+
+ align:start position:0%
+so what this tells us is that the
+complement of this
+
+ align:start position:0%
+complement of this
+ 
+
+ align:start position:0%
+complement of this
+sorry that's not what I meant to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me reiterate
+
+ align:start position:0%
+let me reiterate
+ 
+
+ align:start position:0%
+let me reiterate
+what we know then is that
+
+ align:start position:0%
+what we know then is that
+ 
+
+ align:start position:0%
+what we know then is that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+X yeah X is equal to
+
+ align:start position:0%
+X yeah X is equal to
+ 
+
+ align:start position:0%
+X yeah X is equal to
+the union of c i complement from I
+
+ align:start position:0%
+the union of c i complement from I
+ 
+
+ align:start position:0%
+the union of c i complement from I
+equals one
+
+ align:start position:0%
+equals one
+ 
+
+ align:start position:0%
+equals one
+to K which is of course equal to the
+
+ align:start position:0%
+to K which is of course equal to the
+ 
+
+ align:start position:0%
+to K which is of course equal to the
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+from n equals one
+
+ align:start position:0%
+from n equals one
+ 
+
+ align:start position:0%
+from n equals one
+okay see from I equals one to K
+
+ align:start position:0%
+okay see from I equals one to K
+ 
+
+ align:start position:0%
+okay see from I equals one to K
+c i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complement so we've gone from the union
+
+ align:start position:0%
+complement so we've gone from the union
+ 
+
+ align:start position:0%
+complement so we've gone from the union
+of the complements to the complement of
+
+ align:start position:0%
+of the complements to the complement of
+ 
+
+ align:start position:0%
+of the complements to the complement of
+the intersection
+
+ align:start position:0%
+the intersection
+ 
+
+ align:start position:0%
+the intersection
+and then this implies
+
+ align:start position:0%
+and then this implies
+ 
+
+ align:start position:0%
+and then this implies
+that the intersection from I equals 1 to
+
+ align:start position:0%
+that the intersection from I equals 1 to
+ 
+
+ align:start position:0%
+that the intersection from I equals 1 to
+K of CI must be the empty set which is a
+
+ align:start position:0%
+K of CI must be the empty set which is a
+ 
+
+ align:start position:0%
+K of CI must be the empty set which is a
+contradiction because we're assuming
+
+ align:start position:0%
+contradiction because we're assuming
+ 
+
+ align:start position:0%
+contradiction because we're assuming
+that it has the final intersection
+
+ align:start position:0%
+that it has the final intersection
+ 
+
+ align:start position:0%
+that it has the final intersection
+property which again means that every
+
+ align:start position:0%
+property which again means that every
+ 
+
+ align:start position:0%
+property which again means that every
+finite subcollection has a non-empty
+
+ align:start position:0%
+finite subcollection has a non-empty
+ 
+
+ align:start position:0%
+finite subcollection has a non-empty
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+so this is our contradiction and we've
+
+ align:start position:0%
+so this is our contradiction and we've
+ 
+
+ align:start position:0%
+so this is our contradiction and we've
+shown that topologically compact implies
+
+ align:start position:0%
+shown that topologically compact implies
+ 
+
+ align:start position:0%
+shown that topologically compact implies
+that every collection of closed sets has
+
+ align:start position:0%
+that every collection of closed sets has
+ 
+
+ align:start position:0%
+that every collection of closed sets has
+with the final intersection property has
+
+ align:start position:0%
+with the final intersection property has
+ 
+
+ align:start position:0%
+with the final intersection property has
+non-empty intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the proof of the other direction is
+
+ align:start position:0%
+the proof of the other direction is
+ 
+
+ align:start position:0%
+the proof of the other direction is
+going to be very similar
+
+ align:start position:0%
+going to be very similar
+ 
+
+ align:start position:0%
+going to be very similar
+we're going to show that it's
+
+ align:start position:0%
+we're going to show that it's
+ 
+
+ align:start position:0%
+we're going to show that it's
+topologically compact given property
+
+ align:start position:0%
+topologically compact given property
+ 
+
+ align:start position:0%
+topologically compact given property
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+so we're going to show that four
+
+ align:start position:0%
+so we're going to show that four
+ 
+
+ align:start position:0%
+so we're going to show that four
+implies one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are an open cover
+
+ align:start position:0%
+are an open cover
+ 
+
+ align:start position:0%
+are an open cover
+of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we want to go from then
+
+ align:start position:0%
+when we want to go from then
+ 
+
+ align:start position:0%
+when we want to go from then
+is we want to use this to find
+
+ align:start position:0%
+is we want to use this to find
+ 
+
+ align:start position:0%
+is we want to use this to find
+information about closed sets so that we
+
+ align:start position:0%
+information about closed sets so that we
+ 
+
+ align:start position:0%
+information about closed sets so that we
+can apply property for Well what we'll
+
+ align:start position:0%
+can apply property for Well what we'll
+ 
+
+ align:start position:0%
+can apply property for Well what we'll
+do is let UI complement
+
+ align:start position:0%
+do is let UI complement
+ 
+
+ align:start position:0%
+do is let UI complement
+TI which are going to be closed
+
+ align:start position:0%
+TI which are going to be closed
+ 
+
+ align:start position:0%
+TI which are going to be closed
+how do you know that they're closed
+
+ align:start position:0%
+how do you know that they're closed
+ 
+
+ align:start position:0%
+how do you know that they're closed
+because the complement is going to be
+
+ align:start position:0%
+because the complement is going to be
+ 
+
+ align:start position:0%
+because the complement is going to be
+the uis which are open so that implies
+
+ align:start position:0%
+the uis which are open so that implies
+ 
+
+ align:start position:0%
+the uis which are open so that implies
+that it's closed
+
+ align:start position:0%
+that it's closed
+ 
+
+ align:start position:0%
+that it's closed
+and so we're going to note or what we're
+
+ align:start position:0%
+and so we're going to note or what we're
+ 
+
+ align:start position:0%
+and so we're going to note or what we're
+going to show is that the Ci's have
+
+ align:start position:0%
+going to show is that the Ci's have
+ 
+
+ align:start position:0%
+going to show is that the Ci's have
+finite intersection
+
+ align:start position:0%
+finite intersection
+ 
+
+ align:start position:0%
+finite intersection
+so how's the final intersection property
+
+ align:start position:0%
+so how's the final intersection property
+ 
+
+ align:start position:0%
+so how's the final intersection property
+well notice then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume for the sake of contradiction
+
+ align:start position:0%
+assume for the sake of contradiction
+ 
+
+ align:start position:0%
+assume for the sake of contradiction
+that they don't have the fine
+
+ align:start position:0%
+that they don't have the fine
+ 
+
+ align:start position:0%
+that they don't have the fine
+intersection property
+
+ align:start position:0%
+intersection property
+ 
+
+ align:start position:0%
+intersection property
+for the sake of contradiction
+
+ align:start position:0%
+for the sake of contradiction
+ 
+
+ align:start position:0%
+for the sake of contradiction
+that the intersection of ci1
+
+ align:start position:0%
+that the intersection of ci1
+ 
+
+ align:start position:0%
+that the intersection of ci1
+c i k is empty
+
+ align:start position:0%
+c i k is empty
+ 
+
+ align:start position:0%
+c i k is empty
+I.E it doesn't have the final
+
+ align:start position:0%
+I.E it doesn't have the final
+ 
+
+ align:start position:0%
+I.E it doesn't have the final
+intersection property
+
+ align:start position:0%
+intersection property
+ 
+
+ align:start position:0%
+intersection property
+well then
+
+ align:start position:0%
+well then
+ 
+
+ align:start position:0%
+well then
+what we'll have is that the union from I
+
+ align:start position:0%
+what we'll have is that the union from I
+ 
+
+ align:start position:0%
+what we'll have is that the union from I
+equals one
+
+ align:start position:0%
+equals one
+ 
+
+ align:start position:0%
+equals one
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+of the uis
+
+ align:start position:0%
+of the uis
+ 
+
+ align:start position:0%
+of the uis
+is equal to the intersection of the CI K
+
+ align:start position:0%
+is equal to the intersection of the CI K
+ 
+
+ align:start position:0%
+is equal to the intersection of the CI K
+cim from n equals 1 to K complement
+
+ align:start position:0%
+cim from n equals 1 to K complement
+ 
+
+ align:start position:0%
+cim from n equals 1 to K complement
+complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is of course then the complement
+
+ align:start position:0%
+which is of course then the complement
+ 
+
+ align:start position:0%
+which is of course then the complement
+of the intersection of the cosets which
+
+ align:start position:0%
+of the intersection of the cosets which
+ 
+
+ align:start position:0%
+of the intersection of the cosets which
+is X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um do I want to read to this proof
+
+ align:start position:0%
+um do I want to read to this proof
+ 
+
+ align:start position:0%
+um do I want to read to this proof
+I will redo this proof I want to rewrite
+
+ align:start position:0%
+I will redo this proof I want to rewrite
+ 
+
+ align:start position:0%
+I will redo this proof I want to rewrite
+this out more carefully because we have
+
+ align:start position:0%
+this out more carefully because we have
+ 
+
+ align:start position:0%
+this out more carefully because we have
+two nested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradictions so firstly
+
+ align:start position:0%
+contradictions so firstly
+ 
+
+ align:start position:0%
+contradictions so firstly
+assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the sake of contradiction
+
+ align:start position:0%
+for the sake of contradiction
+ 
+
+ align:start position:0%
+for the sake of contradiction
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there is no finite subcover of the uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite subcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E uh we're assuming for the sake of
+
+ align:start position:0%
+I.E uh we're assuming for the sake of
+ 
+
+ align:start position:0%
+I.E uh we're assuming for the sake of
+contradiction that X is not
+
+ align:start position:0%
+contradiction that X is not
+ 
+
+ align:start position:0%
+contradiction that X is not
+topologically compact
+
+ align:start position:0%
+topologically compact
+ 
+
+ align:start position:0%
+topologically compact
+furthermore we're going to assume
+
+ align:start position:0%
+furthermore we're going to assume
+ 
+
+ align:start position:0%
+furthermore we're going to assume
+for the sake of contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you guys have or don't have the final
+
+ align:start position:0%
+do you guys have or don't have the final
+ 
+
+ align:start position:0%
+do you guys have or don't have the final
+intersection property
+
+ align:start position:0%
+intersection property
+ 
+
+ align:start position:0%
+intersection property
+therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we want to show that they do
+
+ align:start position:0%
+because we want to show that they do
+ 
+
+ align:start position:0%
+because we want to show that they do
+have the final intersection property
+
+ align:start position:0%
+have the final intersection property
+ 
+
+ align:start position:0%
+have the final intersection property
+so the intersection from n equals 1 to K
+
+ align:start position:0%
+so the intersection from n equals 1 to K
+ 
+
+ align:start position:0%
+so the intersection from n equals 1 to K
+of C i n
+
+ align:start position:0%
+of C i n
+ 
+
+ align:start position:0%
+of C i n
+is empty that's what we're going to
+
+ align:start position:0%
+is empty that's what we're going to
+ 
+
+ align:start position:0%
+is empty that's what we're going to
+assume well then what do we know we know
+
+ align:start position:0%
+assume well then what do we know we know
+ 
+
+ align:start position:0%
+assume well then what do we know we know
+then that the union of the uis uin from
+
+ align:start position:0%
+then that the union of the uis uin from
+ 
+
+ align:start position:0%
+then that the union of the uis uin from
+n equals 1 to Infinity not Infinity to K
+
+ align:start position:0%
+n equals 1 to Infinity not Infinity to K
+ 
+
+ align:start position:0%
+n equals 1 to Infinity not Infinity to K
+intersection of the complements
+
+ align:start position:0%
+intersection of the complements
+ 
+
+ align:start position:0%
+intersection of the complements
+complement from
+
+ align:start position:0%
+complement from
+ 
+
+ align:start position:0%
+complement from
+n equals 1 to K
+
+ align:start position:0%
+n equals 1 to K
+ 
+
+ align:start position:0%
+n equals 1 to K
+but then this is going to be all of X
+
+ align:start position:0%
+but then this is going to be all of X
+ 
+
+ align:start position:0%
+but then this is going to be all of X
+right because it's a complement of the
+
+ align:start position:0%
+right because it's a complement of the
+ 
+
+ align:start position:0%
+right because it's a complement of the
+empty set
+
+ align:start position:0%
+empty set
+ 
+
+ align:start position:0%
+empty set
+and that's a contradiction because we're
+
+ align:start position:0%
+and that's a contradiction because we're
+ 
+
+ align:start position:0%
+and that's a contradiction because we're
+assuming that there's no finite subcover
+
+ align:start position:0%
+assuming that there's no finite subcover
+ 
+
+ align:start position:0%
+assuming that there's no finite subcover
+of the uis
+
+ align:start position:0%
+of the uis
+ 
+
+ align:start position:0%
+of the uis
+so what we know then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that the Ci's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have the finite intersection property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E the intersection of all of the CIS
+
+ align:start position:0%
+I.E the intersection of all of the CIS
+ 
+
+ align:start position:0%
+I.E the intersection of all of the CIS
+from I equals 1 to Infinity
+
+ align:start position:0%
+from I equals 1 to Infinity
+ 
+
+ align:start position:0%
+from I equals 1 to Infinity
+is non-empty
+
+ align:start position:0%
+is non-empty
+ 
+
+ align:start position:0%
+is non-empty
+so what do we know we know then that the
+
+ align:start position:0%
+so what do we know we know then that the
+ 
+
+ align:start position:0%
+so what do we know we know then that the
+complement of these is going to be not
+
+ align:start position:0%
+complement of these is going to be not
+ 
+
+ align:start position:0%
+complement of these is going to be not
+all of X so we know that X
+
+ align:start position:0%
+all of X so we know that X
+ 
+
+ align:start position:0%
+all of X so we know that X
+which is the complement of the empty set
+
+ align:start position:0%
+which is the complement of the empty set
+ 
+
+ align:start position:0%
+which is the complement of the empty set
+is not going to be equal to
+
+ align:start position:0%
+is not going to be equal to
+ 
+
+ align:start position:0%
+is not going to be equal to
+the complement of the intersection of
+
+ align:start position:0%
+the complement of the intersection of
+ 
+
+ align:start position:0%
+the complement of the intersection of
+the CIS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I equals one
+
+ align:start position:0%
+I equals one
+ 
+
+ align:start position:0%
+I equals one
+to Infinity which is of course the union
+
+ align:start position:0%
+to Infinity which is of course the union
+ 
+
+ align:start position:0%
+to Infinity which is of course the union
+of the uis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is a contradiction because
+
+ align:start position:0%
+but this is a contradiction because
+ 
+
+ align:start position:0%
+but this is a contradiction because
+we've assumed from the very beginning
+
+ align:start position:0%
+we've assumed from the very beginning
+ 
+
+ align:start position:0%
+we've assumed from the very beginning
+that the uis are an open cover of X so
+
+ align:start position:0%
+that the uis are an open cover of X so
+ 
+
+ align:start position:0%
+that the uis are an open cover of X so
+what we've shown is that our open cover
+
+ align:start position:0%
+what we've shown is that our open cover
+ 
+
+ align:start position:0%
+what we've shown is that our open cover
+is not in fact an open cover which is
+
+ align:start position:0%
+is not in fact an open cover which is
+ 
+
+ align:start position:0%
+is not in fact an open cover which is
+our contradiction
+
+ align:start position:0%
+our contradiction
+ 
+
+ align:start position:0%
+our contradiction
+so we've shown so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one implies four which implies one
+
+ align:start position:0%
+that one implies four which implies one
+ 
+
+ align:start position:0%
+that one implies four which implies one
+and one
+
+ align:start position:0%
+and one
+ 
+
+ align:start position:0%
+and one
+implies two
+
+ align:start position:0%
+implies two
+ 
+
+ align:start position:0%
+implies two
+which implies one so now what we need to
+
+ align:start position:0%
+which implies one so now what we need to
+ 
+
+ align:start position:0%
+which implies one so now what we need to
+show is that 2 is the same as 3. I.E
+
+ align:start position:0%
+show is that 2 is the same as 3. I.E
+ 
+
+ align:start position:0%
+show is that 2 is the same as 3. I.E
+sequentially compact is the same as
+
+ align:start position:0%
+sequentially compact is the same as
+ 
+
+ align:start position:0%
+sequentially compact is the same as
+totally bounded and cushy complete
+
+ align:start position:0%
+totally bounded and cushy complete
+ 
+
+ align:start position:0%
+totally bounded and cushy complete
+now one of these directions has already
+
+ align:start position:0%
+now one of these directions has already
+ 
+
+ align:start position:0%
+now one of these directions has already
+been done for us we've already shown
+
+ align:start position:0%
+been done for us we've already shown
+ 
+
+ align:start position:0%
+been done for us we've already shown
+that totally bounded is a comp is a
+
+ align:start position:0%
+that totally bounded is a comp is a
+ 
+
+ align:start position:0%
+that totally bounded is a comp is a
+consequence of sequentially compact but
+
+ align:start position:0%
+consequence of sequentially compact but
+ 
+
+ align:start position:0%
+consequence of sequentially compact but
+we now need to show is that it's koshy
+
+ align:start position:0%
+we now need to show is that it's koshy
+ 
+
+ align:start position:0%
+we now need to show is that it's koshy
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+so we're going to first show that 2
+
+ align:start position:0%
+so we're going to first show that 2
+ 
+
+ align:start position:0%
+so we're going to first show that 2
+implies 3.
+
+ align:start position:0%
+implies 3.
+ 
+
+ align:start position:0%
+implies 3.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let
+
+ align:start position:0%
+so let
+ 
+
+ align:start position:0%
+so let
+x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a koshy sequence of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i e
+
+ align:start position:0%
+i e
+ 
+
+ align:start position:0%
+i e
+for all Epsilon bigger than zero there
+
+ align:start position:0%
+for all Epsilon bigger than zero there
+ 
+
+ align:start position:0%
+for all Epsilon bigger than zero there
+exists an n in the natural numbers
+
+ align:start position:0%
+exists an n in the natural numbers
+ 
+
+ align:start position:0%
+exists an n in the natural numbers
+such that for all and an M bigger than
+
+ align:start position:0%
+such that for all and an M bigger than
+ 
+
+ align:start position:0%
+such that for all and an M bigger than
+or equal to n
+
+ align:start position:0%
+or equal to n
+ 
+
+ align:start position:0%
+or equal to n
+the distance between x n and XM
+
+ align:start position:0%
+the distance between x n and XM
+ 
+
+ align:start position:0%
+the distance between x n and XM
+is less than Epsilon we're going to use
+
+ align:start position:0%
+is less than Epsilon we're going to use
+ 
+
+ align:start position:0%
+is less than Epsilon we're going to use
+this to our advantage
+
+ align:start position:0%
+this to our advantage
+ 
+
+ align:start position:0%
+this to our advantage
+so furthermore what we know is that by
+
+ align:start position:0%
+so furthermore what we know is that by
+ 
+
+ align:start position:0%
+so furthermore what we know is that by
+sequential compactness there's going to
+
+ align:start position:0%
+sequential compactness there's going to
+ 
+
+ align:start position:0%
+sequential compactness there's going to
+exist a convergent subsequence of the X
+
+ align:start position:0%
+exist a convergent subsequence of the X
+ 
+
+ align:start position:0%
+exist a convergent subsequence of the X
+I's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say it converges to X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what we're going to show then is
+
+ align:start position:0%
+and what we're going to show then is
+ 
+
+ align:start position:0%
+and what we're going to show then is
+that in fact X I will converge to X
+
+ align:start position:0%
+that in fact X I will converge to X
+ 
+
+ align:start position:0%
+that in fact X I will converge to X
+we're going to show that the limit point
+
+ align:start position:0%
+we're going to show that the limit point
+ 
+
+ align:start position:0%
+we're going to show that the limit point
+of the Koji sequence is in fact going to
+
+ align:start position:0%
+of the Koji sequence is in fact going to
+ 
+
+ align:start position:0%
+of the Koji sequence is in fact going to
+be in our metric space
+
+ align:start position:0%
+be in our metric space
+ 
+
+ align:start position:0%
+be in our metric space
+to do that let me move to actually I can
+
+ align:start position:0%
+to do that let me move to actually I can
+ 
+
+ align:start position:0%
+to do that let me move to actually I can
+fit this in here
+
+ align:start position:0%
+fit this in here
+ 
+
+ align:start position:0%
+fit this in here
+notice then
+
+ align:start position:0%
+notice then
+ 
+
+ align:start position:0%
+notice then
+for all n
+
+ align:start position:0%
+for all n
+ 
+
+ align:start position:0%
+for all n
+bigger than or equal to n for all n K
+
+ align:start position:0%
+bigger than or equal to n for all n K
+ 
+
+ align:start position:0%
+bigger than or equal to n for all n K
+and N bigger than or equal to n so look
+
+ align:start position:0%
+and N bigger than or equal to n so look
+ 
+
+ align:start position:0%
+and N bigger than or equal to n so look
+at the distance from X to xn and this
+
+ align:start position:0%
+at the distance from X to xn and this
+ 
+
+ align:start position:0%
+at the distance from X to xn and this
+will be less than or equal to the
+
+ align:start position:0%
+will be less than or equal to the
+ 
+
+ align:start position:0%
+will be less than or equal to the
+distance from X to X and K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus the distance from X and K
+
+ align:start position:0%
+plus the distance from X and K
+ 
+
+ align:start position:0%
+plus the distance from X and K
+to x n
+
+ align:start position:0%
+to x n
+ 
+
+ align:start position:0%
+to x n
+and we know that this term is going to
+
+ align:start position:0%
+and we know that this term is going to
+ 
+
+ align:start position:0%
+and we know that this term is going to
+be less than Epsilon over 2.
+
+ align:start position:0%
+be less than Epsilon over 2.
+ 
+
+ align:start position:0%
+be less than Epsilon over 2.
+or sorry we should assume Epsilon over 2
+
+ align:start position:0%
+or sorry we should assume Epsilon over 2
+ 
+
+ align:start position:0%
+or sorry we should assume Epsilon over 2
+from the beginning
+
+ align:start position:0%
+from the beginning
+ 
+
+ align:start position:0%
+from the beginning
+but furthermore we know that X and K
+
+ align:start position:0%
+but furthermore we know that X and K
+ 
+
+ align:start position:0%
+but furthermore we know that X and K
+converges to X so we can assume that
+
+ align:start position:0%
+converges to X so we can assume that
+ 
+
+ align:start position:0%
+converges to X so we can assume that
+this one is less than Epsilon over 2
+
+ align:start position:0%
+this one is less than Epsilon over 2
+ 
+
+ align:start position:0%
+this one is less than Epsilon over 2
+which is Epsilon so we've shown that x n
+
+ align:start position:0%
+which is Epsilon so we've shown that x n
+ 
+
+ align:start position:0%
+which is Epsilon so we've shown that x n
+is so what we've shown
+
+ align:start position:0%
+is so what we've shown
+ 
+
+ align:start position:0%
+is so what we've shown
+therefore is that X I will converge to X
+
+ align:start position:0%
+therefore is that X I will converge to X
+ 
+
+ align:start position:0%
+therefore is that X I will converge to X
+and so we've shown that every cauchy
+
+ align:start position:0%
+and so we've shown that every cauchy
+ 
+
+ align:start position:0%
+and so we've shown that every cauchy
+sequence has a conver is convergent so
+
+ align:start position:0%
+sequence has a conver is convergent so
+ 
+
+ align:start position:0%
+sequence has a conver is convergent so
+we've shown cushy completeness
+
+ align:start position:0%
+we've shown cushy completeness
+ 
+
+ align:start position:0%
+we've shown cushy completeness
+which is what we wanted to show we
+
+ align:start position:0%
+which is what we wanted to show we
+ 
+
+ align:start position:0%
+which is what we wanted to show we
+wanted to show that sequential
+
+ align:start position:0%
+wanted to show that sequential
+ 
+
+ align:start position:0%
+wanted to show that sequential
+compactness was the same as totally
+
+ align:start position:0%
+compactness was the same as totally
+ 
+
+ align:start position:0%
+compactness was the same as totally
+bounded and koshy complete which
+
+ align:start position:0%
+bounded and koshy complete which
+ 
+
+ align:start position:0%
+bounded and koshy complete which
+concludes the first part of our proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second part the second direction is
+
+ align:start position:0%
+the second part the second direction is
+ 
+
+ align:start position:0%
+the second part the second direction is
+going to be quite a bit harder because
+
+ align:start position:0%
+going to be quite a bit harder because
+ 
+
+ align:start position:0%
+going to be quite a bit harder because
+we want to show that every sequence has
+
+ align:start position:0%
+we want to show that every sequence has
+ 
+
+ align:start position:0%
+we want to show that every sequence has
+a convergent subsequence assuming
+
+ align:start position:0%
+a convergent subsequence assuming
+ 
+
+ align:start position:0%
+a convergent subsequence assuming
+totally bounded in koshy complete which
+
+ align:start position:0%
+totally bounded in koshy complete which
+ 
+
+ align:start position:0%
+totally bounded in koshy complete which
+is going to require quite a bit of work
+
+ align:start position:0%
+is going to require quite a bit of work
+ 
+
+ align:start position:0%
+is going to require quite a bit of work
+um or at least quite a bit of mental
+
+ align:start position:0%
+um or at least quite a bit of mental
+ 
+
+ align:start position:0%
+um or at least quite a bit of mental
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+even if on the chalkboard it's not so
+
+ align:start position:0%
+even if on the chalkboard it's not so
+ 
+
+ align:start position:0%
+even if on the chalkboard it's not so
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+it's a little bit confusing how we go
+
+ align:start position:0%
+it's a little bit confusing how we go
+ 
+
+ align:start position:0%
+it's a little bit confusing how we go
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+totally bounded and koshy complete
+
+ align:start position:0%
+totally bounded and koshy complete
+ 
+
+ align:start position:0%
+totally bounded and koshy complete
+to a convergent subsequence
+
+ align:start position:0%
+to a convergent subsequence
+ 
+
+ align:start position:0%
+to a convergent subsequence
+okay we now want to show that property 4
+
+ align:start position:0%
+okay we now want to show that property 4
+ 
+
+ align:start position:0%
+okay we now want to show that property 4
+implies property one
+
+ align:start position:0%
+implies property one
+ 
+
+ align:start position:0%
+implies property one
+and this will conclude our proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how are we going to do this well
+
+ align:start position:0%
+okay how are we going to do this well
+ 
+
+ align:start position:0%
+okay how are we going to do this well
+we're going to assume that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is totally bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and cushy complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we want to show sequential
+
+ align:start position:0%
+and we want to show sequential
+ 
+
+ align:start position:0%
+and we want to show sequential
+compactness
+
+ align:start position:0%
+compactness
+ 
+
+ align:start position:0%
+compactness
+how do we do that well we're going to
+
+ align:start position:0%
+how do we do that well we're going to
+ 
+
+ align:start position:0%
+how do we do that well we're going to
+start with a arbitrary sequence in x
+
+ align:start position:0%
+start with a arbitrary sequence in x
+ 
+
+ align:start position:0%
+start with a arbitrary sequence in x
+so let
+
+ align:start position:0%
+so let
+ 
+
+ align:start position:0%
+so let
+x i
+
+ align:start position:0%
+x i
+ 
+
+ align:start position:0%
+x i
+be an arbitrary
+
+ align:start position:0%
+be an arbitrary
+ 
+
+ align:start position:0%
+be an arbitrary
+sequence in x
+
+ align:start position:0%
+sequence in x
+ 
+
+ align:start position:0%
+sequence in x
+and we want to show that there exists a
+
+ align:start position:0%
+and we want to show that there exists a
+ 
+
+ align:start position:0%
+and we want to show that there exists a
+convergent subsequence which is going to
+
+ align:start position:0%
+convergent subsequence which is going to
+ 
+
+ align:start position:0%
+convergent subsequence which is going to
+be a little bit difficult
+
+ align:start position:0%
+be a little bit difficult
+ 
+
+ align:start position:0%
+be a little bit difficult
+okay to do so what we're going to do is
+
+ align:start position:0%
+okay to do so what we're going to do is
+ 
+
+ align:start position:0%
+okay to do so what we're going to do is
+start with totally bounded we're going
+
+ align:start position:0%
+start with totally bounded we're going
+ 
+
+ align:start position:0%
+start with totally bounded we're going
+to note
+
+ align:start position:0%
+to note
+ 
+
+ align:start position:0%
+to note
+that for all n bigger than or equal to
+
+ align:start position:0%
+that for all n bigger than or equal to
+ 
+
+ align:start position:0%
+that for all n bigger than or equal to
+for all and the natural numbers
+
+ align:start position:0%
+for all and the natural numbers
+ 
+
+ align:start position:0%
+for all and the natural numbers
+we have that there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists finally many y1 or in fact
+
+ align:start position:0%
+there exists finally many y1 or in fact
+ 
+
+ align:start position:0%
+there exists finally many y1 or in fact
+I'll notate this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y n one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through y r of n n
+
+ align:start position:0%
+through y r of n n
+ 
+
+ align:start position:0%
+through y r of n n
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the balls of radius 1 over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around y
+
+ align:start position:0%
+around y
+ 
+
+ align:start position:0%
+around y
+I of n
+
+ align:start position:0%
+I of n
+ 
+
+ align:start position:0%
+I of n
+we cover X
+
+ align:start position:0%
+we cover X
+ 
+
+ align:start position:0%
+we cover X
+this is our assumption from totally
+
+ align:start position:0%
+this is our assumption from totally
+ 
+
+ align:start position:0%
+this is our assumption from totally
+boundedness here R of n is just a
+
+ align:start position:0%
+boundedness here R of n is just a
+ 
+
+ align:start position:0%
+boundedness here R of n is just a
+function of r uh if it's a function r
+
+ align:start position:0%
+function of r uh if it's a function r
+ 
+
+ align:start position:0%
+function of r uh if it's a function r
+that depends on N because the number of
+
+ align:start position:0%
+that depends on N because the number of
+ 
+
+ align:start position:0%
+that depends on N because the number of
+finally many terms
+
+ align:start position:0%
+finally many terms
+ 
+
+ align:start position:0%
+finally many terms
+um can depend on n
+
+ align:start position:0%
+um can depend on n
+ 
+
+ align:start position:0%
+um can depend on n
+so we in other words we don't know
+
+ align:start position:0%
+so we in other words we don't know
+ 
+
+ align:start position:0%
+so we in other words we don't know
+exactly how many finally many terms we
+
+ align:start position:0%
+exactly how many finally many terms we
+ 
+
+ align:start position:0%
+exactly how many finally many terms we
+have but the more important thing to
+
+ align:start position:0%
+have but the more important thing to
+ 
+
+ align:start position:0%
+have but the more important thing to
+note is that we have finally many of
+
+ align:start position:0%
+note is that we have finally many of
+ 
+
+ align:start position:0%
+note is that we have finally many of
+these for every single n which is our
+
+ align:start position:0%
+these for every single n which is our
+ 
+
+ align:start position:0%
+these for every single n which is our
+sub superscript
+
+ align:start position:0%
+sub superscript
+ 
+
+ align:start position:0%
+sub superscript
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what are we going to do with this
+
+ align:start position:0%
+what are we going to do with this
+ 
+
+ align:start position:0%
+what are we going to do with this
+well we're going to go from this to
+
+ align:start position:0%
+well we're going to go from this to
+ 
+
+ align:start position:0%
+well we're going to go from this to
+okay we want to go from this to a koshy
+
+ align:start position:0%
+okay we want to go from this to a koshy
+ 
+
+ align:start position:0%
+okay we want to go from this to a koshy
+subsequence of the X I's and once we
+
+ align:start position:0%
+subsequence of the X I's and once we
+ 
+
+ align:start position:0%
+subsequence of the X I's and once we
+know that it's koshy we're going to know
+
+ align:start position:0%
+know that it's koshy we're going to know
+ 
+
+ align:start position:0%
+know that it's koshy we're going to know
+that it's convergent
+
+ align:start position:0%
+that it's convergent
+ 
+
+ align:start position:0%
+that it's convergent
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know that there must exist one
+
+ align:start position:0%
+we know that there must exist one
+ 
+
+ align:start position:0%
+we know that there must exist one
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do I want to see this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh to do
+
+ align:start position:0%
+uh to do
+ 
+
+ align:start position:0%
+uh to do
+yeah let's let S1
+
+ align:start position:0%
+yeah let's let S1
+ 
+
+ align:start position:0%
+yeah let's let S1
+be the set of these points y1 and
+
+ align:start position:0%
+be the set of these points y1 and
+ 
+
+ align:start position:0%
+be the set of these points y1 and
+through y r of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we know is that given that x i is
+
+ align:start position:0%
+what we know is that given that x i is
+ 
+
+ align:start position:0%
+what we know is that given that x i is
+an infinitely long sequence in X that
+
+ align:start position:0%
+an infinitely long sequence in X that
+ 
+
+ align:start position:0%
+an infinitely long sequence in X that
+one of that one of the balls of radius r
+
+ align:start position:0%
+one of that one of the balls of radius r
+ 
+
+ align:start position:0%
+one of that one of the balls of radius r
+or balls of radius one over n around
+
+ align:start position:0%
+or balls of radius one over n around
+ 
+
+ align:start position:0%
+or balls of radius one over n around
+these points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry I should call this SN
+
+ align:start position:0%
+sorry I should call this SN
+ 
+
+ align:start position:0%
+sorry I should call this SN
+we know that around the balls of radius
+
+ align:start position:0%
+we know that around the balls of radius
+ 
+
+ align:start position:0%
+we know that around the balls of radius
+1 over n around one of these points has
+
+ align:start position:0%
+1 over n around one of these points has
+ 
+
+ align:start position:0%
+1 over n around one of these points has
+to contain infinitely many of the terms
+
+ align:start position:0%
+to contain infinitely many of the terms
+ 
+
+ align:start position:0%
+to contain infinitely many of the terms
+this is by the pigeonhole principle
+
+ align:start position:0%
+this is by the pigeonhole principle
+ 
+
+ align:start position:0%
+this is by the pigeonhole principle
+so therefore
+
+ align:start position:0%
+so therefore
+ 
+
+ align:start position:0%
+so therefore
+there exists an x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh sorry I should say there exists a
+
+ align:start position:0%
+oh sorry I should say there exists a
+ 
+
+ align:start position:0%
+oh sorry I should say there exists a
+ball of radius one
+
+ align:start position:0%
+ball of radius one
+ 
+
+ align:start position:0%
+ball of radius one
+around some y i of one
+
+ align:start position:0%
+around some y i of one
+ 
+
+ align:start position:0%
+around some y i of one
+containing infinitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing
+
+ align:start position:0%
+containing
+ 
+
+ align:start position:0%
+containing
+infinitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what we're going to do is choose our
+
+ align:start position:0%
+and what we're going to do is choose our
+ 
+
+ align:start position:0%
+and what we're going to do is choose our
+first point in our sequence to be one of
+
+ align:start position:0%
+first point in our sequence to be one of
+ 
+
+ align:start position:0%
+first point in our sequence to be one of
+these points
+
+ align:start position:0%
+these points
+ 
+
+ align:start position:0%
+these points
+so let
+
+ align:start position:0%
+so let
+ 
+
+ align:start position:0%
+so let
+Z1 be the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just out of just just out of assumption
+
+ align:start position:0%
+just out of just just out of assumption
+ 
+
+ align:start position:0%
+just out of just just out of assumption
+and what we're going to do is continue
+
+ align:start position:0%
+and what we're going to do is continue
+ 
+
+ align:start position:0%
+and what we're going to do is continue
+constructing these Eis well we know then
+
+ align:start position:0%
+constructing these Eis well we know then
+ 
+
+ align:start position:0%
+constructing these Eis well we know then
+furthermore is that there exists a ball
+
+ align:start position:0%
+furthermore is that there exists a ball
+ 
+
+ align:start position:0%
+furthermore is that there exists a ball
+of radius one
+
+ align:start position:0%
+of radius one
+ 
+
+ align:start position:0%
+of radius one
+of why I to
+
+ align:start position:0%
+of why I to
+ 
+
+ align:start position:0%
+of why I to
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+sorry one half
+
+ align:start position:0%
+sorry one half
+ 
+
+ align:start position:0%
+sorry one half
+such that the intersection of these two
+
+ align:start position:0%
+such that the intersection of these two
+ 
+
+ align:start position:0%
+such that the intersection of these two
+ball of radius 1 over 2 around y
+
+ align:start position:0%
+ball of radius 1 over 2 around y
+ 
+
+ align:start position:0%
+ball of radius 1 over 2 around y
+I2
+
+ align:start position:0%
+I2
+ 
+
+ align:start position:0%
+I2
+intersection the ball of radius one
+
+ align:start position:0%
+intersection the ball of radius one
+ 
+
+ align:start position:0%
+intersection the ball of radius one
+y j one
+
+ align:start position:0%
+y j one
+ 
+
+ align:start position:0%
+y j one
+has infinitely many
+
+ align:start position:0%
+has infinitely many
+ 
+
+ align:start position:0%
+has infinitely many
+x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we know that this is true
+
+ align:start position:0%
+how do we know that this is true
+ 
+
+ align:start position:0%
+how do we know that this is true
+well we know that infinitely many of
+
+ align:start position:0%
+well we know that infinitely many of
+ 
+
+ align:start position:0%
+well we know that infinitely many of
+them already lie in this ball and so we
+
+ align:start position:0%
+them already lie in this ball and so we
+ 
+
+ align:start position:0%
+them already lie in this ball and so we
+already know if we take the intersection
+
+ align:start position:0%
+already know if we take the intersection
+ 
+
+ align:start position:0%
+already know if we take the intersection
+of this with all the other balls of
+
+ align:start position:0%
+of this with all the other balls of
+ 
+
+ align:start position:0%
+of this with all the other balls of
+radius one half there has to be
+
+ align:start position:0%
+radius one half there has to be
+ 
+
+ align:start position:0%
+radius one half there has to be
+infinitely many there and to see this
+
+ align:start position:0%
+infinitely many there and to see this
+ 
+
+ align:start position:0%
+infinitely many there and to see this
+I'll draw a little bit more of a picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+is our metrics base X and we start with
+
+ align:start position:0%
+is our metrics base X and we start with
+ 
+
+ align:start position:0%
+is our metrics base X and we start with
+covering it with balls of radius one
+
+ align:start position:0%
+covering it with balls of radius one
+ 
+
+ align:start position:0%
+covering it with balls of radius one
+which all draw pretty big just so that
+
+ align:start position:0%
+which all draw pretty big just so that
+ 
+
+ align:start position:0%
+which all draw pretty big just so that
+we don't have to make a bunch of small
+
+ align:start position:0%
+we don't have to make a bunch of small
+ 
+
+ align:start position:0%
+we don't have to make a bunch of small
+pictures so here are the balls of radius
+
+ align:start position:0%
+pictures so here are the balls of radius
+ 
+
+ align:start position:0%
+pictures so here are the balls of radius
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we know then is that one of these
+
+ align:start position:0%
+well we know then is that one of these
+ 
+
+ align:start position:0%
+well we know then is that one of these
+let's say this one
+
+ align:start position:0%
+let's say this one
+ 
+
+ align:start position:0%
+let's say this one
+contains infinitely many terms
+
+ align:start position:0%
+contains infinitely many terms
+ 
+
+ align:start position:0%
+contains infinitely many terms
+so we choose our Z1
+
+ align:start position:0%
+so we choose our Z1
+ 
+
+ align:start position:0%
+so we choose our Z1
+to be here
+
+ align:start position:0%
+to be here
+ 
+
+ align:start position:0%
+to be here
+furthermore we have the intersection of
+
+ align:start position:0%
+furthermore we have the intersection of
+ 
+
+ align:start position:0%
+furthermore we have the intersection of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+with balls of radius one half so I'll
+
+ align:start position:0%
+with balls of radius one half so I'll
+ 
+
+ align:start position:0%
+with balls of radius one half so I'll
+make these a little bit smaller
+
+ align:start position:0%
+make these a little bit smaller
+ 
+
+ align:start position:0%
+make these a little bit smaller
+sorry that's not quite good let me
+
+ align:start position:0%
+sorry that's not quite good let me
+ 
+
+ align:start position:0%
+sorry that's not quite good let me
+yeah these will be our my balls of
+
+ align:start position:0%
+yeah these will be our my balls of
+ 
+
+ align:start position:0%
+yeah these will be our my balls of
+radius one half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would I know then is that the
+
+ align:start position:0%
+would I know then is that the
+ 
+
+ align:start position:0%
+would I know then is that the
+intersection of the balls of radius one
+
+ align:start position:0%
+intersection of the balls of radius one
+ 
+
+ align:start position:0%
+intersection of the balls of radius one
+half and the ball is of radius one
+
+ align:start position:0%
+half and the ball is of radius one
+ 
+
+ align:start position:0%
+half and the ball is of radius one
+there's only going to be finally many of
+
+ align:start position:0%
+there's only going to be finally many of
+ 
+
+ align:start position:0%
+there's only going to be finally many of
+them by assumption and the fact that
+
+ align:start position:0%
+them by assumption and the fact that
+ 
+
+ align:start position:0%
+them by assumption and the fact that
+there are finally many of them implies
+
+ align:start position:0%
+there are finally many of them implies
+ 
+
+ align:start position:0%
+there are finally many of them implies
+that there exists infinitely many of
+
+ align:start position:0%
+that there exists infinitely many of
+ 
+
+ align:start position:0%
+that there exists infinitely many of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+that lie in one of these balls one of
+
+ align:start position:0%
+that lie in one of these balls one of
+ 
+
+ align:start position:0%
+that lie in one of these balls one of
+these balls of radius one half
+
+ align:start position:0%
+these balls of radius one half
+ 
+
+ align:start position:0%
+these balls of radius one half
+intersected one of the balls of radius
+
+ align:start position:0%
+intersected one of the balls of radius
+ 
+
+ align:start position:0%
+intersected one of the balls of radius
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so what we can do is choose Z2
+
+ align:start position:0%
+so what we can do is choose Z2
+ 
+
+ align:start position:0%
+so what we can do is choose Z2
+to be in this intersection of them and
+
+ align:start position:0%
+to be in this intersection of them and
+ 
+
+ align:start position:0%
+to be in this intersection of them and
+we're going to reiterate this process
+
+ align:start position:0%
+we're going to reiterate this process
+ 
+
+ align:start position:0%
+we're going to reiterate this process
+we're going to assume that Z3 is one of
+
+ align:start position:0%
+we're going to assume that Z3 is one of
+ 
+
+ align:start position:0%
+we're going to assume that Z3 is one of
+the infinitely many points in the
+
+ align:start position:0%
+the infinitely many points in the
+ 
+
+ align:start position:0%
+the infinitely many points in the
+intersection of balls of radius one
+
+ align:start position:0%
+intersection of balls of radius one
+ 
+
+ align:start position:0%
+intersection of balls of radius one
+third one half and one
+
+ align:start position:0%
+third one half and one
+ 
+
+ align:start position:0%
+third one half and one
+and so on and so forth and what we hope
+
+ align:start position:0%
+and so on and so forth and what we hope
+ 
+
+ align:start position:0%
+and so on and so forth and what we hope
+to show
+
+ align:start position:0%
+to show
+ 
+
+ align:start position:0%
+to show
+is that this sequence is going to be
+
+ align:start position:0%
+is that this sequence is going to be
+ 
+
+ align:start position:0%
+is that this sequence is going to be
+cushy
+
+ align:start position:0%
+cushy
+ 
+
+ align:start position:0%
+cushy
+but that's not at this point going to be
+
+ align:start position:0%
+but that's not at this point going to be
+ 
+
+ align:start position:0%
+but that's not at this point going to be
+too hard to do
+
+ align:start position:0%
+too hard to do
+ 
+
+ align:start position:0%
+too hard to do
+because okay let me write this somewhere
+
+ align:start position:0%
+because okay let me write this somewhere
+ 
+
+ align:start position:0%
+because okay let me write this somewhere
+fully we're going to choose z k to be in
+
+ align:start position:0%
+fully we're going to choose z k to be in
+ 
+
+ align:start position:0%
+fully we're going to choose z k to be in
+the intersection
+
+ align:start position:0%
+the intersection
+ 
+
+ align:start position:0%
+the intersection
+of balls of radius
+
+ align:start position:0%
+of balls of radius
+ 
+
+ align:start position:0%
+of balls of radius
+NK
+
+ align:start position:0%
+NK
+ 
+
+ align:start position:0%
+NK
+of n from n equals 1 to K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah balls of radius one to K
+
+ align:start position:0%
+yeah balls of radius one to K
+ 
+
+ align:start position:0%
+yeah balls of radius one to K
+and now we want to show that this
+
+ align:start position:0%
+and now we want to show that this
+ 
+
+ align:start position:0%
+and now we want to show that this
+sequence is going to be koshy well
+
+ align:start position:0%
+sequence is going to be koshy well
+ 
+
+ align:start position:0%
+sequence is going to be koshy well
+what's the distance or choose
+
+ align:start position:0%
+what's the distance or choose
+ 
+
+ align:start position:0%
+what's the distance or choose
+for all Epsilon bigger than zero
+
+ align:start position:0%
+for all Epsilon bigger than zero
+ 
+
+ align:start position:0%
+for all Epsilon bigger than zero
+choose n in the natural numbers
+
+ align:start position:0%
+choose n in the natural numbers
+ 
+
+ align:start position:0%
+choose n in the natural numbers
+such that 1 over n is less than Epsilon
+
+ align:start position:0%
+such that 1 over n is less than Epsilon
+ 
+
+ align:start position:0%
+such that 1 over n is less than Epsilon
+then what do we know well for all n and
+
+ align:start position:0%
+then what do we know well for all n and
+ 
+
+ align:start position:0%
+then what do we know well for all n and
+M bigger than or equal to n
+
+ align:start position:0%
+M bigger than or equal to n
+ 
+
+ align:start position:0%
+M bigger than or equal to n
+we know then that z n and z m
+
+ align:start position:0%
+we know then that z n and z m
+ 
+
+ align:start position:0%
+we know then that z n and z m
+are both going to be contained in the
+
+ align:start position:0%
+are both going to be contained in the
+ 
+
+ align:start position:0%
+are both going to be contained in the
+ball of radius one over n of one of the
+
+ align:start position:0%
+ball of radius one over n of one of the
+ 
+
+ align:start position:0%
+ball of radius one over n of one of the
+Y I's I won't describe which one because
+
+ align:start position:0%
+Y I's I won't describe which one because
+ 
+
+ align:start position:0%
+Y I's I won't describe which one because
+it's a little bit annoying but we know
+
+ align:start position:0%
+it's a little bit annoying but we know
+ 
+
+ align:start position:0%
+it's a little bit annoying but we know
+that they both must lie in one over n
+
+ align:start position:0%
+that they both must lie in one over n
+ 
+
+ align:start position:0%
+that they both must lie in one over n
+because they're in this intersection of
+
+ align:start position:0%
+because they're in this intersection of
+ 
+
+ align:start position:0%
+because they're in this intersection of
+all these terms so what we know then
+
+ align:start position:0%
+all these terms so what we know then
+ 
+
+ align:start position:0%
+all these terms so what we know then
+is at the distance from ZN to Z M must
+
+ align:start position:0%
+is at the distance from ZN to Z M must
+ 
+
+ align:start position:0%
+is at the distance from ZN to Z M must
+be less than one over n or less than or
+
+ align:start position:0%
+be less than one over n or less than or
+ 
+
+ align:start position:0%
+be less than one over n or less than or
+equal to 1 over n
+
+ align:start position:0%
+equal to 1 over n
+ 
+
+ align:start position:0%
+equal to 1 over n
+Which is less than Epsilon which implies
+
+ align:start position:0%
+Which is less than Epsilon which implies
+ 
+
+ align:start position:0%
+Which is less than Epsilon which implies
+that the zis must be koshy so therefore
+
+ align:start position:0%
+that the zis must be koshy so therefore
+ 
+
+ align:start position:0%
+that the zis must be koshy so therefore
+the Z i's are koshy
+
+ align:start position:0%
+the Z i's are koshy
+ 
+
+ align:start position:0%
+the Z i's are koshy
+and by koshy completeness
+
+ align:start position:0%
+and by koshy completeness
+ 
+
+ align:start position:0%
+and by koshy completeness
+we know that there exists a limit point
+
+ align:start position:0%
+we know that there exists a limit point
+ 
+
+ align:start position:0%
+we know that there exists a limit point
+z i converges to some Z in x
+
+ align:start position:0%
+z i converges to some Z in x
+ 
+
+ align:start position:0%
+z i converges to some Z in x
+but recall again that our Z i's are
+
+ align:start position:0%
+but recall again that our Z i's are
+ 
+
+ align:start position:0%
+but recall again that our Z i's are
+constructed from our original sequence
+
+ align:start position:0%
+constructed from our original sequence
+ 
+
+ align:start position:0%
+constructed from our original sequence
+they're convergent they're a subsequence
+
+ align:start position:0%
+they're convergent they're a subsequence
+ 
+
+ align:start position:0%
+they're convergent they're a subsequence
+of our original sequence
+
+ align:start position:0%
+of our original sequence
+ 
+
+ align:start position:0%
+of our original sequence
+so what we've shown is that there is a
+
+ align:start position:0%
+so what we've shown is that there is a
+ 
+
+ align:start position:0%
+so what we've shown is that there is a
+convergent subsequence of our sequence
+
+ align:start position:0%
+convergent subsequence of our sequence
+ 
+
+ align:start position:0%
+convergent subsequence of our sequence
+in x and this is exactly what we sought
+
+ align:start position:0%
+in x and this is exactly what we sought
+ 
+
+ align:start position:0%
+in x and this is exactly what we sought
+out to show and this shows that totally
+
+ align:start position:0%
+out to show and this shows that totally
+ 
+
+ align:start position:0%
+out to show and this shows that totally
+bounded and koshy complete implies
+
+ align:start position:0%
+bounded and koshy complete implies
+ 
+
+ align:start position:0%
+bounded and koshy complete implies
+sequentially compact
+
+ align:start position:0%
+sequentially compact
+ 
+
+ align:start position:0%
+sequentially compact
+and this is the end of our four-part
+
+ align:start position:0%
+and this is the end of our four-part
+ 
+
+ align:start position:0%
+and this is the end of our four-part
+proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again to reiterate we've shown that
+
+ align:start position:0%
+so again to reiterate we've shown that
+ 
+
+ align:start position:0%
+so again to reiterate we've shown that
+topologically compact is the same as
+
+ align:start position:0%
+topologically compact is the same as
+ 
+
+ align:start position:0%
+topologically compact is the same as
+sequentially compact where here we use
+
+ align:start position:0%
+sequentially compact where here we use
+ 
+
+ align:start position:0%
+sequentially compact where here we use
+the big numberlema and totally
+
+ align:start position:0%
+the big numberlema and totally
+ 
+
+ align:start position:0%
+the big numberlema and totally
+boundedness
+
+ align:start position:0%
+boundedness
+ 
+
+ align:start position:0%
+boundedness
+then from here we show that sequentially
+
+ align:start position:0%
+then from here we show that sequentially
+ 
+
+ align:start position:0%
+then from here we show that sequentially
+compact is the same as totally bounded
+
+ align:start position:0%
+compact is the same as totally bounded
+ 
+
+ align:start position:0%
+compact is the same as totally bounded
+and koshy complete
+
+ align:start position:0%
+and koshy complete
+ 
+
+ align:start position:0%
+and koshy complete
+takoshi complete didn't take too much
+
+ align:start position:0%
+takoshi complete didn't take too much
+ 
+
+ align:start position:0%
+takoshi complete didn't take too much
+more work that was pretty short the
+
+ align:start position:0%
+more work that was pretty short the
+ 
+
+ align:start position:0%
+more work that was pretty short the
+other direction required quite a bit of
+
+ align:start position:0%
+other direction required quite a bit of
+ 
+
+ align:start position:0%
+other direction required quite a bit of
+maneuvering to get that convergent
+
+ align:start position:0%
+maneuvering to get that convergent
+ 
+
+ align:start position:0%
+maneuvering to get that convergent
+subsequence but again the notes contain
+
+ align:start position:0%
+subsequence but again the notes contain
+ 
+
+ align:start position:0%
+subsequence but again the notes contain
+this more fully if you want to read
+
+ align:start position:0%
+this more fully if you want to read
+ 
+
+ align:start position:0%
+this more fully if you want to read
+through it slowly and at your own pace
+
+ align:start position:0%
+through it slowly and at your own pace
+ 
+
+ align:start position:0%
+through it slowly and at your own pace
+but lastly we showed and furthermore
+
+ align:start position:0%
+but lastly we showed and furthermore
+ 
+
+ align:start position:0%
+but lastly we showed and furthermore
+lastly we showed that one is the same as
+
+ align:start position:0%
+lastly we showed that one is the same as
+ 
+
+ align:start position:0%
+lastly we showed that one is the same as
+four we're topologically compact is the
+
+ align:start position:0%
+four we're topologically compact is the
+ 
+
+ align:start position:0%
+four we're topologically compact is the
+same as closed subsets with the final
+
+ align:start position:0%
+same as closed subsets with the final
+ 
+
+ align:start position:0%
+same as closed subsets with the final
+intersection property having non-empty
+
+ align:start position:0%
+intersection property having non-empty
+ 
+
+ align:start position:0%
+intersection property having non-empty
+intersection and now let's think
+
+ align:start position:0%
+intersection and now let's think
+ 
+
+ align:start position:0%
+intersection and now let's think
+carefully about how each of these proofs
+
+ align:start position:0%
+carefully about how each of these proofs
+ 
+
+ align:start position:0%
+carefully about how each of these proofs
+went because they each have their own
+
+ align:start position:0%
+went because they each have their own
+ 
+
+ align:start position:0%
+went because they each have their own
+purpose in a proof
+
+ align:start position:0%
+purpose in a proof
+ 
+
+ align:start position:0%
+purpose in a proof
+about metric spaces
+
+ align:start position:0%
+about metric spaces
+ 
+
+ align:start position:0%
+about metric spaces
+to show that one was the same as four we
+
+ align:start position:0%
+to show that one was the same as four we
+ 
+
+ align:start position:0%
+to show that one was the same as four we
+looked at open covers right we took the
+
+ align:start position:0%
+looked at open covers right we took the
+ 
+
+ align:start position:0%
+looked at open covers right we took the
+open cover definition and looked at
+
+ align:start position:0%
+open cover definition and looked at
+ 
+
+ align:start position:0%
+open cover definition and looked at
+complements of closed sets and being
+
+ align:start position:0%
+complements of closed sets and being
+ 
+
+ align:start position:0%
+complements of closed sets and being
+open and complements of open sets being
+
+ align:start position:0%
+open and complements of open sets being
+ 
+
+ align:start position:0%
+open and complements of open sets being
+closed and we used all these different
+
+ align:start position:0%
+closed and we used all these different
+ 
+
+ align:start position:0%
+closed and we used all these different
+properties like that and that makes a
+
+ align:start position:0%
+properties like that and that makes a
+ 
+
+ align:start position:0%
+properties like that and that makes a
+lot of sense because both definitions
+
+ align:start position:0%
+lot of sense because both definitions
+ 
+
+ align:start position:0%
+lot of sense because both definitions
+are in terms of closed and open sets but
+
+ align:start position:0%
+are in terms of closed and open sets but
+ 
+
+ align:start position:0%
+are in terms of closed and open sets but
+the show is sequentially compact was the
+
+ align:start position:0%
+the show is sequentially compact was the
+ 
+
+ align:start position:0%
+the show is sequentially compact was the
+same as totally boundated Koshi complete
+
+ align:start position:0%
+same as totally boundated Koshi complete
+ 
+
+ align:start position:0%
+same as totally boundated Koshi complete
+we use definitions of sequential
+
+ align:start position:0%
+we use definitions of sequential
+ 
+
+ align:start position:0%
+we use definitions of sequential
+compactness right because it's so much
+
+ align:start position:0%
+compactness right because it's so much
+ 
+
+ align:start position:0%
+compactness right because it's so much
+easier to look at convergent
+
+ align:start position:0%
+easier to look at convergent
+ 
+
+ align:start position:0%
+easier to look at convergent
+subsequences and such when you're
+
+ align:start position:0%
+subsequences and such when you're
+ 
+
+ align:start position:0%
+subsequences and such when you're
+looking at sequential compactness so we
+
+ align:start position:0%
+looking at sequential compactness so we
+ 
+
+ align:start position:0%
+looking at sequential compactness so we
+could have proven that one implies three
+
+ align:start position:0%
+could have proven that one implies three
+ 
+
+ align:start position:0%
+could have proven that one implies three
+but it would have been a little bit more
+
+ align:start position:0%
+but it would have been a little bit more
+ 
+
+ align:start position:0%
+but it would have been a little bit more
+difficult and a little bit harder to
+
+ align:start position:0%
+difficult and a little bit harder to
+ 
+
+ align:start position:0%
+difficult and a little bit harder to
+maneuver around and in fact that's why
+
+ align:start position:0%
+maneuver around and in fact that's why
+ 
+
+ align:start position:0%
+maneuver around and in fact that's why
+I've shown these four properties today
+
+ align:start position:0%
+I've shown these four properties today
+ 
+
+ align:start position:0%
+I've shown these four properties today
+because if you're in a class where
+
+ align:start position:0%
+because if you're in a class where
+ 
+
+ align:start position:0%
+because if you're in a class where
+you're proving facts about metric spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you need to show you need to use the
+
+ align:start position:0%
+you need to show you need to use the
+ 
+
+ align:start position:0%
+you need to show you need to use the
+property that makes the most sense to
+
+ align:start position:0%
+property that makes the most sense to
+ 
+
+ align:start position:0%
+property that makes the most sense to
+use in a given moment for instance on
+
+ align:start position:0%
+use in a given moment for instance on
+ 
+
+ align:start position:0%
+use in a given moment for instance on
+your problem set you're going to be
+
+ align:start position:0%
+your problem set you're going to be
+ 
+
+ align:start position:0%
+your problem set you're going to be
+asked to show that the union of finitely
+
+ align:start position:0%
+asked to show that the union of finitely
+ 
+
+ align:start position:0%
+asked to show that the union of finitely
+many compact sets is going to be compact
+
+ align:start position:0%
+many compact sets is going to be compact
+ 
+
+ align:start position:0%
+many compact sets is going to be compact
+how do you know that this is going to be
+
+ align:start position:0%
+how do you know that this is going to be
+ 
+
+ align:start position:0%
+how do you know that this is going to be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+well you can use sequential compactness
+
+ align:start position:0%
+well you can use sequential compactness
+ 
+
+ align:start position:0%
+well you can use sequential compactness
+you can use topological compactness you
+
+ align:start position:0%
+you can use topological compactness you
+ 
+
+ align:start position:0%
+you can use topological compactness you
+can use any of these four properties
+
+ align:start position:0%
+can use any of these four properties
+ 
+
+ align:start position:0%
+can use any of these four properties
+that you still wish to choose But be
+
+ align:start position:0%
+that you still wish to choose But be
+ 
+
+ align:start position:0%
+that you still wish to choose But be
+sure to think carefully about which one
+
+ align:start position:0%
+sure to think carefully about which one
+ 
+
+ align:start position:0%
+sure to think carefully about which one
+because one of them might be a little
+
+ align:start position:0%
+because one of them might be a little
+ 
+
+ align:start position:0%
+because one of them might be a little
+bit easier so I won't discredit you if
+
+ align:start position:0%
+bit easier so I won't discredit you if
+ 
+
+ align:start position:0%
+bit easier so I won't discredit you if
+you use any of the other ones
+
+ align:start position:0%
+you use any of the other ones
+ 
+
+ align:start position:0%
+you use any of the other ones
+and this is true in general when you're
+
+ align:start position:0%
+and this is true in general when you're
+ 
+
+ align:start position:0%
+and this is true in general when you're
+going into proofs about metric spaces
+
+ align:start position:0%
+going into proofs about metric spaces
+ 
+
+ align:start position:0%
+going into proofs about metric spaces
+having the intuition from one definition
+
+ align:start position:0%
+having the intuition from one definition
+ 
+
+ align:start position:0%
+having the intuition from one definition
+to the other is deeply important and
+
+ align:start position:0%
+to the other is deeply important and
+ 
+
+ align:start position:0%
+to the other is deeply important and
+very useful to know
+
+ align:start position:0%
+very useful to know
+ 
+
+ align:start position:0%
+very useful to know
+so that will conclude today's lecture on
+
+ align:start position:0%
+so that will conclude today's lecture on
+ 
+
+ align:start position:0%
+so that will conclude today's lecture on
+next Thursday we're going to prove some
+
+ align:start position:0%
+next Thursday we're going to prove some
+ 
+
+ align:start position:0%
+next Thursday we're going to prove some
+new facts about compact spaces and in
+
+ align:start position:0%
+new facts about compact spaces and in
+ 
+
+ align:start position:0%
+new facts about compact spaces and in
+particular what we're going to show or
+
+ align:start position:0%
+particular what we're going to show or
+ 
+
+ align:start position:0%
+particular what we're going to show or
+talk about is the history of compact
+
+ align:start position:0%
+talk about is the history of compact
+ 
+
+ align:start position:0%
+talk about is the history of compact
+metric spaces and why they were
+
+ align:start position:0%
+metric spaces and why they were
+ 
+
+ align:start position:0%
+metric spaces and why they were
+developed in the first place which comes
+
+ align:start position:0%
+developed in the first place which comes
+ 
+
+ align:start position:0%
+developed in the first place which comes
+from what is known as the dirichlet
+
+ align:start position:0%
+from what is known as the dirichlet
+ 
+
+ align:start position:0%
+from what is known as the dirichlet
+problem but I'll leave that discussion
+
+ align:start position:0%
+problem but I'll leave that discussion
+ 
+
+ align:start position:0%
+problem but I'll leave that discussion
+until next Thursday until then have a
+
+ align:start position:0%
+until next Thursday until then have a
+ 
+
+ align:start position:0%
+until next Thursday until then have a
+great weekend thank you
\ No newline at end of file
diff --git a/S1PUUyVdC9M.txt b/S1PUUyVdC9M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a98d37e11ad7d66fe1d6c0c4e5f2295fb2e05b4f
--- /dev/null
+++ b/S1PUUyVdC9M.txt
@@ -0,0 +1,111 @@
+Now let's turn our attention to the second
+class of instructions: load (LD) and store
+
+(ST), which allow the CPU to access values
+in memory.
+
+Note that since the Beta is a load-store architecture
+these instructions are the *only* mechanism
+
+for accessing memory values.
+
+The LD and ST instructions use the same instruction
+template as the ALU-with-constant instructions.
+
+To access memory, we'll need a memory address,
+which is computed by adding the value of the
+
+"ra" register to the sign-extended 16-bit
+constant from the low-order 16 bits of the
+
+instruction.
+
+This computation is exactly the one performed
+by the ADDC instruction - so we'll reuse that
+
+hardware - and the sum is sent to main memory
+as the byte address of the location to be
+
+accessed.
+
+For the LD instruction, the data returned
+by main memory is written to the "rc" register.
+
+The store instruction (ST) performs the same
+address calculation as LD, then reads the
+
+data value from the "rc" register and sends
+both to main memory.
+
+The ST instruction is special in several ways:
+it's the only instruction that needs to read
+
+the value of the "rc" register, so we'll need
+to adjust the datapath hardware slightly to
+
+accommodate that need.
+
+And since "rc" is serving as a source operand,
+it appears as the first operand in the symbolic
+
+form of the instruction, followed by "const"
+and "ra" which are specifying the destination
+
+address.
+
+ST is the only instruction that does *not*
+write a result into the register file at end
+
+of the instruction.
+
+Here's the example we saw earlier, where we
+needed to load the value of the variable x
+
+from memory, multiply it by 37 and write the
+result back to the memory location that holds
+
+the value of the variable y.
+
+Now that we have actual Beta instructions,
+we've expressed the computation as a sequence
+
+of three instructions.
+
+To access the value of variable x, the LD
+instruction adds the contents of R31 to the
+
+constant 0x1008, which sums to 0x1008, the
+address we need to access.
+
+The ST instruction specifies a similar address
+calculation to write into the location for
+
+the variable y.
+
+The address calculation performed by LD and
+ST works well when the locations we need to
+
+access have addresses that fit into the 16-bit
+constant field.
+
+What happens when we need to access locations
+at addresses higher than 0x7FFF?
+
+Then we need to treat those addresses as we
+would any large constant, and store those
+
+large addresses in main memory so they can
+be loaded into a register to be used by LD
+
+and ST.
+
+Okay, but what if the number of large constants
+we need to store is greater than will fit
+
+in low memory, i.e., the addresses we can
+access directly?
+
+To solve this problem, the Beta includes a
+"load relative" (LDR) instruction, which we'll
+
+see in the lecture on the Beta implementation.
\ No newline at end of file
diff --git a/SPDZbn6QC4c.txt b/SPDZbn6QC4c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c11cc957ca297622e3924a1bf8555e694a92ddb
--- /dev/null
+++ b/SPDZbn6QC4c.txt
@@ -0,0 +1,1635 @@
+align:start position:0%
+ 
+at this point i'm going to talk about
+
+ align:start position:0%
+at this point i'm going to talk about
+ 
+
+ align:start position:0%
+at this point i'm going to talk about
+the third element of the garage case we
+
+ align:start position:0%
+the third element of the garage case we
+ 
+
+ align:start position:0%
+the third element of the garage case we
+already started with the idea of what
+
+ align:start position:0%
+already started with the idea of what
+ 
+
+ align:start position:0%
+already started with the idea of what
+the deterministic engineering design was
+
+ align:start position:0%
+the deterministic engineering design was
+ 
+
+ align:start position:0%
+the deterministic engineering design was
+then we saw how that analysis led to a
+
+ align:start position:0%
+then we saw how that analysis led to a
+ 
+
+ align:start position:0%
+then we saw how that analysis led to a
+wrong estimate of the value and in fact
+
+ align:start position:0%
+wrong estimate of the value and in fact
+ 
+
+ align:start position:0%
+wrong estimate of the value and in fact
+the wrong design once we accounted for
+
+ align:start position:0%
+the wrong design once we accounted for
+ 
+
+ align:start position:0%
+the wrong design once we accounted for
+the reality of uncertainty
+
+ align:start position:0%
+the reality of uncertainty
+ 
+
+ align:start position:0%
+the reality of uncertainty
+now let's think how we can be proactive
+
+ align:start position:0%
+now let's think how we can be proactive
+ 
+
+ align:start position:0%
+now let's think how we can be proactive
+about this design and we're going to do
+
+ align:start position:0%
+about this design and we're going to do
+ 
+
+ align:start position:0%
+about this design and we're going to do
+that by introducing flexibility what
+
+ align:start position:0%
+that by introducing flexibility what
+ 
+
+ align:start position:0%
+that by introducing flexibility what
+does that mean
+
+ align:start position:0%
+does that mean
+ 
+
+ align:start position:0%
+does that mean
+the flexibility is the ability to adjust
+
+ align:start position:0%
+the flexibility is the ability to adjust
+ 
+
+ align:start position:0%
+the flexibility is the ability to adjust
+the project to the actual needs
+
+ align:start position:0%
+the project to the actual needs
+ 
+
+ align:start position:0%
+the project to the actual needs
+according to the future how the future
+
+ align:start position:0%
+according to the future how the future
+ 
+
+ align:start position:0%
+according to the future how the future
+develops in particular it means that if
+
+ align:start position:0%
+develops in particular it means that if
+ 
+
+ align:start position:0%
+develops in particular it means that if
+the future is very positive in terms of
+
+ align:start position:0%
+the future is very positive in terms of
+ 
+
+ align:start position:0%
+the future is very positive in terms of
+demand and you'd like to have greater
+
+ align:start position:0%
+demand and you'd like to have greater
+ 
+
+ align:start position:0%
+demand and you'd like to have greater
+capacity that you have the capability of
+
+ align:start position:0%
+capacity that you have the capability of
+ 
+
+ align:start position:0%
+capacity that you have the capability of
+adding that if needed
+
+ align:start position:0%
+adding that if needed
+ 
+
+ align:start position:0%
+adding that if needed
+uh we it also presumes that we are
+
+ align:start position:0%
+uh we it also presumes that we are
+ 
+
+ align:start position:0%
+uh we it also presumes that we are
+managing this project we just don't
+
+ align:start position:0%
+managing this project we just don't
+ 
+
+ align:start position:0%
+managing this project we just don't
+create it then say there it's off on its
+
+ align:start position:0%
+create it then say there it's off on its
+ 
+
+ align:start position:0%
+create it then say there it's off on its
+own it's on autopilot no we have a
+
+ align:start position:0%
+own it's on autopilot no we have a
+ 
+
+ align:start position:0%
+own it's on autopilot no we have a
+system and we manage it appropriately so
+
+ align:start position:0%
+system and we manage it appropriately so
+ 
+
+ align:start position:0%
+system and we manage it appropriately so
+it's very important to understand that
+
+ align:start position:0%
+it's very important to understand that
+ 
+
+ align:start position:0%
+it's very important to understand that
+if we want to deliver the value of a
+
+ align:start position:0%
+if we want to deliver the value of a
+ 
+
+ align:start position:0%
+if we want to deliver the value of a
+design it's not only what we do at the
+
+ align:start position:0%
+design it's not only what we do at the
+ 
+
+ align:start position:0%
+design it's not only what we do at the
+beginning but how we manage the project
+
+ align:start position:0%
+beginning but how we manage the project
+ 
+
+ align:start position:0%
+beginning but how we manage the project
+as it encounters different situations
+
+ align:start position:0%
+as it encounters different situations
+ 
+
+ align:start position:0%
+as it encounters different situations
+and has to deal with different
+
+ align:start position:0%
+and has to deal with different
+ 
+
+ align:start position:0%
+and has to deal with different
+possibilities and opportunities
+
+ align:start position:0%
+possibilities and opportunities
+ 
+
+ align:start position:0%
+possibilities and opportunities
+how do we do this for the garage
+
+ align:start position:0%
+how do we do this for the garage
+ 
+
+ align:start position:0%
+how do we do this for the garage
+for the garage case what we do is we
+
+ align:start position:0%
+for the garage case what we do is we
+ 
+
+ align:start position:0%
+for the garage case what we do is we
+enable the addition of more capacity
+
+ align:start position:0%
+enable the addition of more capacity
+ 
+
+ align:start position:0%
+enable the addition of more capacity
+that is it has to have the strength to
+
+ align:start position:0%
+that is it has to have the strength to
+ 
+
+ align:start position:0%
+that is it has to have the strength to
+carry more loads it has if you want fat
+
+ align:start position:0%
+carry more loads it has if you want fat
+ 
+
+ align:start position:0%
+carry more loads it has if you want fat
+columns with more strength of them it
+
+ align:start position:0%
+columns with more strength of them it
+ 
+
+ align:start position:0%
+columns with more strength of them it
+has to have bigger foundations to carry
+
+ align:start position:0%
+has to have bigger foundations to carry
+ 
+
+ align:start position:0%
+has to have bigger foundations to carry
+the loads on the soil and it has to have
+
+ align:start position:0%
+the loads on the soil and it has to have
+ 
+
+ align:start position:0%
+the loads on the soil and it has to have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+building system that you can easily add
+
+ align:start position:0%
+building system that you can easily add
+ 
+
+ align:start position:0%
+building system that you can easily add
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+in this case a precast
+
+ align:start position:0%
+in this case a precast
+ 
+
+ align:start position:0%
+in this case a precast
+situation you build it off-site can
+
+ align:start position:0%
+situation you build it off-site can
+ 
+
+ align:start position:0%
+situation you build it off-site can
+bring it in and can expand it
+
+ align:start position:0%
+bring it in and can expand it
+ 
+
+ align:start position:0%
+bring it in and can expand it
+with a minimal closure of the garage
+
+ align:start position:0%
+with a minimal closure of the garage
+ 
+
+ align:start position:0%
+with a minimal closure of the garage
+during the expansion period so
+
+ align:start position:0%
+during the expansion period so
+ 
+
+ align:start position:0%
+during the expansion period so
+that you have the ability to add floors
+
+ align:start position:0%
+that you have the ability to add floors
+ 
+
+ align:start position:0%
+that you have the ability to add floors
+and what happens
+
+ align:start position:0%
+and what happens
+ 
+
+ align:start position:0%
+and what happens
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+let's think about how we're going to
+
+ align:start position:0%
+let's think about how we're going to
+ 
+
+ align:start position:0%
+let's think about how we're going to
+analyze this with the simulation process
+
+ align:start position:0%
+analyze this with the simulation process
+ 
+
+ align:start position:0%
+analyze this with the simulation process
+here is a spreadsheet of it and this is
+
+ align:start position:0%
+here is a spreadsheet of it and this is
+ 
+
+ align:start position:0%
+here is a spreadsheet of it and this is
+the one for four floors now what we have
+
+ align:start position:0%
+the one for four floors now what we have
+ 
+
+ align:start position:0%
+the one for four floors now what we have
+here i'll won't explain in the detail
+
+ align:start position:0%
+here i'll won't explain in the detail
+ 
+
+ align:start position:0%
+here i'll won't explain in the detail
+how it works but i'll give you the idea
+
+ align:start position:0%
+how it works but i'll give you the idea
+ 
+
+ align:start position:0%
+how it works but i'll give you the idea
+of it is that we have a forecast here
+
+ align:start position:0%
+of it is that we have a forecast here
+ 
+
+ align:start position:0%
+of it is that we have a forecast here
+and this is a simulated forecast that is
+
+ align:start position:0%
+and this is a simulated forecast that is
+ 
+
+ align:start position:0%
+and this is a simulated forecast that is
+sometimes the top number of the forecast
+
+ align:start position:0%
+sometimes the top number of the forecast
+ 
+
+ align:start position:0%
+sometimes the top number of the forecast
+will be uh up sometimes it'll be down
+
+ align:start position:0%
+will be uh up sometimes it'll be down
+ 
+
+ align:start position:0%
+will be uh up sometimes it'll be down
+it'll be up and down over time
+
+ align:start position:0%
+it'll be up and down over time
+ 
+
+ align:start position:0%
+it'll be up and down over time
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's what we observe then we think
+
+ align:start position:0%
+that's what we observe then we think
+ 
+
+ align:start position:0%
+that's what we observe then we think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how we would exercise the flexibility
+
+ align:start position:0%
+how we would exercise the flexibility
+ 
+
+ align:start position:0%
+how we would exercise the flexibility
+that's available
+
+ align:start position:0%
+that's available
+ 
+
+ align:start position:0%
+that's available
+in terms of intelligent management so
+
+ align:start position:0%
+in terms of intelligent management so
+ 
+
+ align:start position:0%
+in terms of intelligent management so
+if the demand is not increasing we do
+
+ align:start position:0%
+if the demand is not increasing we do
+ 
+
+ align:start position:0%
+if the demand is not increasing we do
+not add the capability if the
+
+ align:start position:0%
+not add the capability if the
+ 
+
+ align:start position:0%
+not add the capability if the
+extra floors in particular if the demand
+
+ align:start position:0%
+extra floors in particular if the demand
+ 
+
+ align:start position:0%
+extra floors in particular if the demand
+however does increase
+
+ align:start position:0%
+however does increase
+ 
+
+ align:start position:0%
+however does increase
+then it looks like we'd be valuable to
+
+ align:start position:0%
+then it looks like we'd be valuable to
+ 
+
+ align:start position:0%
+then it looks like we'd be valuable to
+have more floors on it we add them so in
+
+ align:start position:0%
+have more floors on it we add them so in
+ 
+
+ align:start position:0%
+have more floors on it we add them so in
+we've embedded in here uh through what's
+
+ align:start position:0%
+we've embedded in here uh through what's
+ 
+
+ align:start position:0%
+we've embedded in here uh through what's
+called if statements that looks at
+
+ align:start position:0%
+called if statements that looks at
+ 
+
+ align:start position:0%
+called if statements that looks at
+what's been happening and what would be
+
+ align:start position:0%
+what's been happening and what would be
+ 
+
+ align:start position:0%
+what's been happening and what would be
+the intelligent thing to do and for each
+
+ align:start position:0%
+the intelligent thing to do and for each
+ 
+
+ align:start position:0%
+the intelligent thing to do and for each
+simulation that we run we
+
+ align:start position:0%
+simulation that we run we
+ 
+
+ align:start position:0%
+simulation that we run we
+factor that in and
+
+ align:start position:0%
+factor that in and
+ 
+
+ align:start position:0%
+factor that in and
+calculate the value so we do this for
+
+ align:start position:0%
+calculate the value so we do this for
+ 
+
+ align:start position:0%
+calculate the value so we do this for
+thousands of times a couple thousand in
+
+ align:start position:0%
+thousands of times a couple thousand in
+ 
+
+ align:start position:0%
+thousands of times a couple thousand in
+this particular analysis and we look at
+
+ align:start position:0%
+this particular analysis and we look at
+ 
+
+ align:start position:0%
+this particular analysis and we look at
+sometimes you expand because it's
+
+ align:start position:0%
+sometimes you expand because it's
+ 
+
+ align:start position:0%
+sometimes you expand because it's
+desirable sometimes you do not expand we
+
+ align:start position:0%
+desirable sometimes you do not expand we
+ 
+
+ align:start position:0%
+desirable sometimes you do not expand we
+look at the combination and figure out
+
+ align:start position:0%
+look at the combination and figure out
+ 
+
+ align:start position:0%
+look at the combination and figure out
+the overall expected value
+
+ align:start position:0%
+the overall expected value
+ 
+
+ align:start position:0%
+the overall expected value
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where does that lead us it leads us as
+
+ align:start position:0%
+where does that lead us it leads us as
+ 
+
+ align:start position:0%
+where does that lead us it leads us as
+we look at all the possibilities
+
+ align:start position:0%
+we look at all the possibilities
+ 
+
+ align:start position:0%
+we look at all the possibilities
+one story two story and so forth with
+
+ align:start position:0%
+one story two story and so forth with
+ 
+
+ align:start position:0%
+one story two story and so forth with
+and without the flexibility that the
+
+ align:start position:0%
+and without the flexibility that the
+ 
+
+ align:start position:0%
+and without the flexibility that the
+optimal design in this particular case
+
+ align:start position:0%
+optimal design in this particular case
+ 
+
+ align:start position:0%
+optimal design in this particular case
+with these numbers is not six stories
+
+ align:start position:0%
+with these numbers is not six stories
+ 
+
+ align:start position:0%
+with these numbers is not six stories
+which was a deterministic sign not the
+
+ align:start position:0%
+which was a deterministic sign not the
+ 
+
+ align:start position:0%
+which was a deterministic sign not the
+five stories which is the
+
+ align:start position:0%
+five stories which is the
+ 
+
+ align:start position:0%
+five stories which is the
+risk averse avoiding the downside
+
+ align:start position:0%
+risk averse avoiding the downside
+ 
+
+ align:start position:0%
+risk averse avoiding the downside
+approach where you recognize the
+
+ align:start position:0%
+approach where you recognize the
+ 
+
+ align:start position:0%
+approach where you recognize the
+uncertainty but it's four stories but
+
+ align:start position:0%
+uncertainty but it's four stories but
+ 
+
+ align:start position:0%
+uncertainty but it's four stories but
+four stories with the ability to expand
+
+ align:start position:0%
+four stories with the ability to expand
+ 
+
+ align:start position:0%
+four stories with the ability to expand
+when needed so observe what's happening
+
+ align:start position:0%
+when needed so observe what's happening
+ 
+
+ align:start position:0%
+when needed so observe what's happening
+you've built it smaller so it didn't
+
+ align:start position:0%
+you've built it smaller so it didn't
+ 
+
+ align:start position:0%
+you've built it smaller so it didn't
+cost as much as having five or six
+
+ align:start position:0%
+cost as much as having five or six
+ 
+
+ align:start position:0%
+cost as much as having five or six
+stories even though you had strong
+
+ align:start position:0%
+stories even though you had strong
+ 
+
+ align:start position:0%
+stories even though you had strong
+foundations
+
+ align:start position:0%
+foundations
+ 
+
+ align:start position:0%
+foundations
+so it's less exposure to the downside
+
+ align:start position:0%
+so it's less exposure to the downside
+ 
+
+ align:start position:0%
+so it's less exposure to the downside
+but you build it so that you get five
+
+ align:start position:0%
+but you build it so that you get five
+ 
+
+ align:start position:0%
+but you build it so that you get five
+six seven or eight stories if the demand
+
+ align:start position:0%
+six seven or eight stories if the demand
+ 
+
+ align:start position:0%
+six seven or eight stories if the demand
+occurred
+
+ align:start position:0%
+occurred
+ 
+
+ align:start position:0%
+occurred
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here is the summary of the design
+
+ align:start position:0%
+here is the summary of the design
+ 
+
+ align:start position:0%
+here is the summary of the design
+results so that on the one hand we have
+
+ align:start position:0%
+results so that on the one hand we have
+ 
+
+ align:start position:0%
+results so that on the one hand we have
+the different
+
+ align:start position:0%
+the different
+ 
+
+ align:start position:0%
+the different
+possibilities and their performance over
+
+ align:start position:0%
+possibilities and their performance over
+ 
+
+ align:start position:0%
+possibilities and their performance over
+time and we have the value at the end
+
+ align:start position:0%
+time and we have the value at the end
+ 
+
+ align:start position:0%
+time and we have the value at the end
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what we observe here is that the
+
+ align:start position:0%
+what we observe here is that the
+ 
+
+ align:start position:0%
+what we observe here is that the
+four-story building is the most
+
+ align:start position:0%
+four-story building is the most
+ 
+
+ align:start position:0%
+four-story building is the most
+productive one
+
+ align:start position:0%
+productive one
+ 
+
+ align:start position:0%
+productive one
+and we might have thought that the
+
+ align:start position:0%
+and we might have thought that the
+ 
+
+ align:start position:0%
+and we might have thought that the
+deterministic design with a value of six
+
+ align:start position:0%
+deterministic design with a value of six
+ 
+
+ align:start position:0%
+deterministic design with a value of six
+million was better but that result is a
+
+ align:start position:0%
+million was better but that result is a
+ 
+
+ align:start position:0%
+million was better but that result is a
+sham because given this uncertainty we
+
+ align:start position:0%
+sham because given this uncertainty we
+ 
+
+ align:start position:0%
+sham because given this uncertainty we
+will never get that result as the
+
+ align:start position:0%
+will never get that result as the
+ 
+
+ align:start position:0%
+will never get that result as the
+expected value its expected value will
+
+ align:start position:0%
+expected value its expected value will
+ 
+
+ align:start position:0%
+expected value its expected value will
+be lower and in fact in the case of uns
+
+ align:start position:0%
+be lower and in fact in the case of uns
+ 
+
+ align:start position:0%
+be lower and in fact in the case of uns
+the reality case with the uncertainty is
+
+ align:start position:0%
+the reality case with the uncertainty is
+ 
+
+ align:start position:0%
+the reality case with the uncertainty is
+we'll get only about three million with
+
+ align:start position:0%
+we'll get only about three million with
+ 
+
+ align:start position:0%
+we'll get only about three million with
+it as the value as compared to what we
+
+ align:start position:0%
+it as the value as compared to what we
+ 
+
+ align:start position:0%
+it as the value as compared to what we
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's think about what's happening here
+
+ align:start position:0%
+let's think about what's happening here
+ 
+
+ align:start position:0%
+let's think about what's happening here
+we built it smaller less cost of the
+
+ align:start position:0%
+we built it smaller less cost of the
+ 
+
+ align:start position:0%
+we built it smaller less cost of the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+less possibility of loss on the other
+
+ align:start position:0%
+less possibility of loss on the other
+ 
+
+ align:start position:0%
+less possibility of loss on the other
+hand we can build it up as much as seems
+
+ align:start position:0%
+hand we can build it up as much as seems
+ 
+
+ align:start position:0%
+hand we can build it up as much as seems
+appropriate in the particular conditions
+
+ align:start position:0%
+appropriate in the particular conditions
+ 
+
+ align:start position:0%
+appropriate in the particular conditions
+without a we have favorable demand and
+
+ align:start position:0%
+without a we have favorable demand and
+ 
+
+ align:start position:0%
+without a we have favorable demand and
+we can make more of value so
+
+ align:start position:0%
+we can make more of value so
+ 
+
+ align:start position:0%
+we can make more of value so
+let's look about
+
+ align:start position:0%
+let's look about
+ 
+
+ align:start position:0%
+let's look about
+what it is how we think about this
+
+ align:start position:0%
+what it is how we think about this
+ 
+
+ align:start position:0%
+what it is how we think about this
+overall for this particular design case
+
+ align:start position:0%
+overall for this particular design case
+ 
+
+ align:start position:0%
+overall for this particular design case
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we need to have a multi-dimensional
+
+ align:start position:0%
+we need to have a multi-dimensional
+ 
+
+ align:start position:0%
+we need to have a multi-dimensional
+evaluation
+
+ align:start position:0%
+evaluation
+ 
+
+ align:start position:0%
+evaluation
+why multi-dimensional
+
+ align:start position:0%
+why multi-dimensional
+ 
+
+ align:start position:0%
+why multi-dimensional
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+since we have a distribution one number
+
+ align:start position:0%
+since we have a distribution one number
+ 
+
+ align:start position:0%
+since we have a distribution one number
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+value for it is not describing what's
+
+ align:start position:0%
+value for it is not describing what's
+ 
+
+ align:start position:0%
+value for it is not describing what's
+happening you care not only about the
+
+ align:start position:0%
+happening you care not only about the
+ 
+
+ align:start position:0%
+happening you care not only about the
+average you care about how bad can get
+
+ align:start position:0%
+average you care about how bad can get
+ 
+
+ align:start position:0%
+average you care about how bad can get
+how good can it get what's the
+
+ align:start position:0%
+how good can it get what's the
+ 
+
+ align:start position:0%
+how good can it get what's the
+possibilities in this particular case
+
+ align:start position:0%
+possibilities in this particular case
+ 
+
+ align:start position:0%
+possibilities in this particular case
+that we see that the uh the several
+
+ align:start position:0%
+that we see that the uh the several
+ 
+
+ align:start position:0%
+that we see that the uh the several
+factors that we're looking at in terms
+
+ align:start position:0%
+factors that we're looking at in terms
+ 
+
+ align:start position:0%
+factors that we're looking at in terms
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+initial investment
+
+ align:start position:0%
+initial investment
+ 
+
+ align:start position:0%
+initial investment
+that we how much money do we have to put
+
+ align:start position:0%
+that we how much money do we have to put
+ 
+
+ align:start position:0%
+that we how much money do we have to put
+down to start the process it is lower
+
+ align:start position:0%
+down to start the process it is lower
+ 
+
+ align:start position:0%
+down to start the process it is lower
+for the flexible design because we build
+
+ align:start position:0%
+for the flexible design because we build
+ 
+
+ align:start position:0%
+for the flexible design because we build
+it smaller
+
+ align:start position:0%
+it smaller
+ 
+
+ align:start position:0%
+it smaller
+so what's the expected value of it it's
+
+ align:start position:0%
+so what's the expected value of it it's
+ 
+
+ align:start position:0%
+so what's the expected value of it it's
+very much larger than otherwise because
+
+ align:start position:0%
+very much larger than otherwise because
+ 
+
+ align:start position:0%
+very much larger than otherwise because
+we can take advantage of the good things
+
+ align:start position:0%
+we can take advantage of the good things
+ 
+
+ align:start position:0%
+we can take advantage of the good things
+and avoid the bad things
+
+ align:start position:0%
+and avoid the bad things
+ 
+
+ align:start position:0%
+and avoid the bad things
+and con
+
+ align:start position:0%
+and con
+ 
+
+ align:start position:0%
+and con
+in in that same way the maximum value we
+
+ align:start position:0%
+in in that same way the maximum value we
+ 
+
+ align:start position:0%
+in in that same way the maximum value we
+can get is larger the minimum value that
+
+ align:start position:0%
+can get is larger the minimum value that
+ 
+
+ align:start position:0%
+can get is larger the minimum value that
+we might be forced to accept is smaller
+
+ align:start position:0%
+we might be forced to accept is smaller
+ 
+
+ align:start position:0%
+we might be forced to accept is smaller
+so that it's good in all cases
+
+ align:start position:0%
+so that it's good in all cases
+ 
+
+ align:start position:0%
+so that it's good in all cases
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+everything is better why how did that
+
+ align:start position:0%
+everything is better why how did that
+ 
+
+ align:start position:0%
+everything is better why how did that
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+that is we have not had a technological
+
+ align:start position:0%
+that is we have not had a technological
+ 
+
+ align:start position:0%
+that is we have not had a technological
+breakthrough in this case it is not a
+
+ align:start position:0%
+breakthrough in this case it is not a
+ 
+
+ align:start position:0%
+breakthrough in this case it is not a
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+sophisticated or advanced design it is
+
+ align:start position:0%
+sophisticated or advanced design it is
+ 
+
+ align:start position:0%
+sophisticated or advanced design it is
+because we have changed the
+
+ align:start position:0%
+because we have changed the
+ 
+
+ align:start position:0%
+because we have changed the
+design approach from we've changed the
+
+ align:start position:0%
+design approach from we've changed the
+ 
+
+ align:start position:0%
+design approach from we've changed the
+framing of the problem that instead of
+
+ align:start position:0%
+framing of the problem that instead of
+ 
+
+ align:start position:0%
+framing of the problem that instead of
+going to saying we're designing it for a
+
+ align:start position:0%
+going to saying we're designing it for a
+ 
+
+ align:start position:0%
+going to saying we're designing it for a
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+view of the future we folk and instead
+
+ align:start position:0%
+view of the future we folk and instead
+ 
+
+ align:start position:0%
+view of the future we folk and instead
+of focusing on this mythical and this
+
+ align:start position:0%
+of focusing on this mythical and this
+ 
+
+ align:start position:0%
+of focusing on this mythical and this
+fairy tale future that in fact will not
+
+ align:start position:0%
+fairy tale future that in fact will not
+ 
+
+ align:start position:0%
+fairy tale future that in fact will not
+be the exact case
+
+ align:start position:0%
+be the exact case
+ 
+
+ align:start position:0%
+be the exact case
+we change from that to managing the
+
+ align:start position:0%
+we change from that to managing the
+ 
+
+ align:start position:0%
+we change from that to managing the
+realistic uncertainties of the life by
+
+ align:start position:0%
+realistic uncertainties of the life by
+ 
+
+ align:start position:0%
+realistic uncertainties of the life by
+having the flexible design and therefore
+
+ align:start position:0%
+having the flexible design and therefore
+ 
+
+ align:start position:0%
+having the flexible design and therefore
+can adjust to the conditions and in that
+
+ align:start position:0%
+can adjust to the conditions and in that
+ 
+
+ align:start position:0%
+can adjust to the conditions and in that
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+have an overall better
+
+ align:start position:0%
+have an overall better
+ 
+
+ align:start position:0%
+have an overall better
+solution now in this case the flexible
+
+ align:start position:0%
+solution now in this case the flexible
+ 
+
+ align:start position:0%
+solution now in this case the flexible
+design was better on four counts that as
+
+ align:start position:0%
+design was better on four counts that as
+ 
+
+ align:start position:0%
+design was better on four counts that as
+i mentioned that may not always happen
+
+ align:start position:0%
+i mentioned that may not always happen
+ 
+
+ align:start position:0%
+i mentioned that may not always happen
+sometimes the situation is not so
+
+ align:start position:0%
+sometimes the situation is not so
+ 
+
+ align:start position:0%
+sometimes the situation is not so
+uniquely favorable but it's the kind of
+
+ align:start position:0%
+uniquely favorable but it's the kind of
+ 
+
+ align:start position:0%
+uniquely favorable but it's the kind of
+thing could happen because it's built in
+
+ align:start position:0%
+thing could happen because it's built in
+ 
+
+ align:start position:0%
+thing could happen because it's built in
+to the way of approaching it is less
+
+ align:start position:0%
+to the way of approaching it is less
+ 
+
+ align:start position:0%
+to the way of approaching it is less
+downside more upside
+
+ align:start position:0%
+downside more upside
+ 
+
+ align:start position:0%
+downside more upside
+lower cost than beginning overall it's a
+
+ align:start position:0%
+lower cost than beginning overall it's a
+ 
+
+ align:start position:0%
+lower cost than beginning overall it's a
+win-win at less cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/TZSBHuy8yhQ.txt b/TZSBHuy8yhQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..deeb7fb1c5f466c4c25fb0e5a9d1fd080a41e6d8
--- /dev/null
+++ b/TZSBHuy8yhQ.txt
@@ -0,0 +1,15979 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right welcome back to
+
+ align:start position:0%
+ocw.mit.edu all right welcome back to
+ 
+
+ align:start position:0%
+ocw.mit.edu all right welcome back to
+6890 uh today we continue our team of
+
+ align:start position:0%
+6890 uh today we continue our team of
+ 
+
+ align:start position:0%
+6890 uh today we continue our team of
+reductions NP hardness reductions from
+
+ align:start position:0%
+reductions NP hardness reductions from
+ 
+
+ align:start position:0%
+reductions NP hardness reductions from
+three partition uh yesterday we saw a
+
+ align:start position:0%
+three partition uh yesterday we saw a
+ 
+
+ align:start position:0%
+three partition uh yesterday we saw a
+couple of different reductions from
+
+ align:start position:0%
+couple of different reductions from
+ 
+
+ align:start position:0%
+couple of different reductions from
+three partition and then a bunch of
+
+ align:start position:0%
+three partition and then a bunch of
+ 
+
+ align:start position:0%
+three partition and then a bunch of
+reductions from those problems uh
+
+ align:start position:0%
+reductions from those problems uh
+ 
+
+ align:start position:0%
+reductions from those problems uh
+various puzzles uh the last one we
+
+ align:start position:0%
+various puzzles uh the last one we
+ 
+
+ align:start position:0%
+various puzzles uh the last one we
+covered was packing squares into a
+
+ align:start position:0%
+covered was packing squares into a
+ 
+
+ align:start position:0%
+covered was packing squares into a
+square this is just a reminder visually
+
+ align:start position:0%
+square this is just a reminder visually
+ 
+
+ align:start position:0%
+square this is just a reminder visually
+what it looks like uh but we're going to
+
+ align:start position:0%
+what it looks like uh but we're going to
+ 
+
+ align:start position:0%
+what it looks like uh but we're going to
+just take this result as given and our
+
+ align:start position:0%
+just take this result as given and our
+ 
+
+ align:start position:0%
+just take this result as given and our
+first MP hardness reduction will be from
+
+ align:start position:0%
+first MP hardness reduction will be from
+ 
+
+ align:start position:0%
+first MP hardness reduction will be from
+packing squares into a square and then
+
+ align:start position:0%
+packing squares into a square and then
+ 
+
+ align:start position:0%
+packing squares into a square and then
+we will see a bunch of possibly as many
+
+ align:start position:0%
+we will see a bunch of possibly as many
+ 
+
+ align:start position:0%
+we will see a bunch of possibly as many
+as eight reductions uh from three
+
+ align:start position:0%
+as eight reductions uh from three
+ 
+
+ align:start position:0%
+as eight reductions uh from three
+partition so uh without further Ado
+
+ align:start position:0%
+partition so uh without further Ado
+ 
+
+ align:start position:0%
+partition so uh without further Ado
+let's get started um the first problem
+
+ align:start position:0%
+let's get started um the first problem
+ 
+
+ align:start position:0%
+let's get started um the first problem
+we're going to talk about uh is Edge
+
+ align:start position:0%
+we're going to talk about uh is Edge
+ 
+
+ align:start position:0%
+we're going to talk about uh is Edge
+unfolding polyhedra this is a um
+
+ align:start position:0%
+unfolding polyhedra this is a um
+ 
+
+ align:start position:0%
+unfolding polyhedra this is a um
+geometric folding problem so if you're
+
+ align:start position:0%
+geometric folding problem so if you're
+ 
+
+ align:start position:0%
+geometric folding problem so if you're
+interested in more you can uh take
+
+ align:start position:0%
+interested in more you can uh take
+ 
+
+ align:start position:0%
+interested in more you can uh take
+6849 um but here's a simple if you've
+
+ align:start position:0%
+6849 um but here's a simple if you've
+ 
+
+ align:start position:0%
+6849 um but here's a simple if you've
+ever made a cube out of paper probably
+
+ align:start position:0%
+ever made a cube out of paper probably
+ 
+
+ align:start position:0%
+ever made a cube out of paper probably
+you cut out uh a cross shape and then
+
+ align:start position:0%
+you cut out uh a cross shape and then
+ 
+
+ align:start position:0%
+you cut out uh a cross shape and then
+folded it into the cube there but if you
+
+ align:start position:0%
+folded it into the cube there but if you
+ 
+
+ align:start position:0%
+folded it into the cube there but if you
+want to know how should I what shape
+
+ align:start position:0%
+want to know how should I what shape
+ 
+
+ align:start position:0%
+want to know how should I what shape
+should I cut out to make a cube then you
+
+ align:start position:0%
+should I cut out to make a cube then you
+ 
+
+ align:start position:0%
+should I cut out to make a cube then you
+want to know where should I cut which
+
+ align:start position:0%
+want to know where should I cut which
+ 
+
+ align:start position:0%
+want to know where should I cut which
+edges of the cube should I cut they're
+
+ align:start position:0%
+edges of the cube should I cut they're
+ 
+
+ align:start position:0%
+edges of the cube should I cut they're
+drawn in red here so that when I unfold
+
+ align:start position:0%
+drawn in red here so that when I unfold
+ 
+
+ align:start position:0%
+drawn in red here so that when I unfold
+it I get one connected piece without
+
+ align:start position:0%
+it I get one connected piece without
+ 
+
+ align:start position:0%
+it I get one connected piece without
+overlap um so for surfaces that are
+
+ align:start position:0%
+overlap um so for surfaces that are
+ 
+
+ align:start position:0%
+overlap um so for surfaces that are
+topologically a sphere uh you want to
+
+ align:start position:0%
+topologically a sphere uh you want to
+ 
+
+ align:start position:0%
+topologically a sphere uh you want to
+cut along a spanning tree of the edges
+
+ align:start position:0%
+cut along a spanning tree of the edges
+ 
+
+ align:start position:0%
+cut along a spanning tree of the edges
+um and for a cube that will always work
+
+ align:start position:0%
+um and for a cube that will always work
+ 
+
+ align:start position:0%
+um and for a cube that will always work
+but for some polyhedra like these two
+
+ align:start position:0%
+but for some polyhedra like these two
+ 
+
+ align:start position:0%
+but for some polyhedra like these two
+when you unfold you get overlap and in
+
+ align:start position:0%
+when you unfold you get overlap and in
+ 
+
+ align:start position:0%
+when you unfold you get overlap and in
+fact no matter which spanning tree of
+
+ align:start position:0%
+fact no matter which spanning tree of
+ 
+
+ align:start position:0%
+fact no matter which spanning tree of
+the edges you take for either of these
+
+ align:start position:0%
+the edges you take for either of these
+ 
+
+ align:start position:0%
+the edges you take for either of these
+two polyhedra
+
+ align:start position:0%
+two polyhedra
+ 
+
+ align:start position:0%
+two polyhedra
+uh you are guaranteed to fail you cannot
+
+ align:start position:0%
+uh you are guaranteed to fail you cannot
+ 
+
+ align:start position:0%
+uh you are guaranteed to fail you cannot
+make these out of one piece of paper uh
+
+ align:start position:0%
+make these out of one piece of paper uh
+ 
+
+ align:start position:0%
+make these out of one piece of paper uh
+by folding and get an exact cover uh so
+
+ align:start position:0%
+by folding and get an exact cover uh so
+ 
+
+ align:start position:0%
+by folding and get an exact cover uh so
+that's bad news and these are old
+
+ align:start position:0%
+that's bad news and these are old
+ 
+
+ align:start position:0%
+that's bad news and these are old
+results these are back in
+
+ align:start position:0%
+results these are back in
+ 
+
+ align:start position:0%
+results these are back in
+1998 um but it remained an open problem
+
+ align:start position:0%
+1998 um but it remained an open problem
+ 
+
+ align:start position:0%
+1998 um but it remained an open problem
+are there how many other examples are
+
+ align:start position:0%
+are there how many other examples are
+ 
+
+ align:start position:0%
+are there how many other examples are
+there if I give you a polyhedron I want
+
+ align:start position:0%
+there if I give you a polyhedron I want
+ 
+
+ align:start position:0%
+there if I give you a polyhedron I want
+to know is there an edge unfolding we
+
+ align:start position:0%
+to know is there an edge unfolding we
+ 
+
+ align:start position:0%
+to know is there an edge unfolding we
+only cut along the edges uh what's the
+
+ align:start position:0%
+only cut along the edges uh what's the
+ 
+
+ align:start position:0%
+only cut along the edges uh what's the
+complexity of that and the answer is
+
+ align:start position:0%
+complexity of that and the answer is
+ 
+
+ align:start position:0%
+complexity of that and the answer is
+it's NP
+
+ align:start position:0%
+it's NP
+ 
+
+ align:start position:0%
+it's NP
+complete um strongly NP complete
+
+ align:start position:0%
+complete um strongly NP complete
+ 
+
+ align:start position:0%
+complete um strongly NP complete
+slightly stronger this is not obviously
+
+ align:start position:0%
+slightly stronger this is not obviously
+ 
+
+ align:start position:0%
+slightly stronger this is not obviously
+a number problem but uh in Geometry you
+
+ align:start position:0%
+a number problem but uh in Geometry you
+ 
+
+ align:start position:0%
+a number problem but uh in Geometry you
+have this issue of what are the
+
+ align:start position:0%
+have this issue of what are the
+ 
+
+ align:start position:0%
+have this issue of what are the
+coordinates of the vertices so the
+
+ align:start position:0%
+coordinates of the vertices so the
+ 
+
+ align:start position:0%
+coordinates of the vertices so the
+coordinates could be exponentially large
+
+ align:start position:0%
+coordinates could be exponentially large
+ 
+
+ align:start position:0%
+coordinates could be exponentially large
+or they could just be polom large here
+
+ align:start position:0%
+or they could just be polom large here
+ 
+
+ align:start position:0%
+or they could just be polom large here
+they only need to be polom large so
+
+ align:start position:0%
+they only need to be polom large so
+ 
+
+ align:start position:0%
+they only need to be polom large so
+strongly mty complete this is a
+
+ align:start position:0%
+strongly mty complete this is a
+ 
+
+ align:start position:0%
+strongly mty complete this is a
+complicated proof uh so I'm just going
+
+ align:start position:0%
+complicated proof uh so I'm just going
+ 
+
+ align:start position:0%
+complicated proof uh so I'm just going
+to sketch the idea of how it works um at
+
+ align:start position:0%
+to sketch the idea of how it works um at
+ 
+
+ align:start position:0%
+to sketch the idea of how it works um at
+the beginning like most proofs there's
+
+ align:start position:0%
+the beginning like most proofs there's
+ 
+
+ align:start position:0%
+the beginning like most proofs there's
+some kind of like overall infrastructure
+
+ align:start position:0%
+some kind of like overall infrastructure
+ 
+
+ align:start position:0%
+some kind of like overall infrastructure
+that holds all the pieces together this
+
+ align:start position:0%
+that holds all the pieces together this
+ 
+
+ align:start position:0%
+that holds all the pieces together this
+is one part of that well this is the
+
+ align:start position:0%
+is one part of that well this is the
+ 
+
+ align:start position:0%
+is one part of that well this is the
+main infrastructure structure in this uh
+
+ align:start position:0%
+main infrastructure structure in this uh
+ 
+
+ align:start position:0%
+main infrastructure structure in this uh
+reduction there's some stuff around the
+
+ align:start position:0%
+reduction there's some stuff around the
+ 
+
+ align:start position:0%
+reduction there's some stuff around the
+side this is mainly to make the Surface
+
+ align:start position:0%
+side this is mainly to make the Surface
+ 
+
+ align:start position:0%
+side this is mainly to make the Surface
+uh topologically a sphere um the the
+
+ align:start position:0%
+uh topologically a sphere um the the
+ 
+
+ align:start position:0%
+uh topologically a sphere um the the
+focus is on uh a square face here with
+
+ align:start position:0%
+focus is on uh a square face here with
+ 
+
+ align:start position:0%
+focus is on uh a square face here with
+has a little slit in it and there's a
+
+ align:start position:0%
+has a little slit in it and there's a
+ 
+
+ align:start position:0%
+has a little slit in it and there's a
+tower coming out it's drawn uh Edge on
+
+ align:start position:0%
+tower coming out it's drawn uh Edge on
+ 
+
+ align:start position:0%
+tower coming out it's drawn uh Edge on
+here this is the part we actually care
+
+ align:start position:0%
+here this is the part we actually care
+ 
+
+ align:start position:0%
+here this is the part we actually care
+about uh I think actually it will be
+
+ align:start position:0%
+about uh I think actually it will be
+ 
+
+ align:start position:0%
+about uh I think actually it will be
+redrawn here so we'll really just be
+
+ align:start position:0%
+redrawn here so we'll really just be
+ 
+
+ align:start position:0%
+redrawn here so we'll really just be
+thinking about this and then there's
+
+ align:start position:0%
+thinking about this and then there's
+ 
+
+ align:start position:0%
+thinking about this and then there's
+some stuff that wraps it around and
+
+ align:start position:0%
+some stuff that wraps it around and
+ 
+
+ align:start position:0%
+some stuff that wraps it around and
+makes it a sphere without changing
+
+ align:start position:0%
+makes it a sphere without changing
+ 
+
+ align:start position:0%
+makes it a sphere without changing
+unfolding
+
+ align:start position:0%
+unfolding
+ 
+
+ align:start position:0%
+unfolding
+so don't worry too much about that
+
+ align:start position:0%
+so don't worry too much about that
+ 
+
+ align:start position:0%
+so don't worry too much about that
+mainly we have this giant uh think of it
+
+ align:start position:0%
+mainly we have this giant uh think of it
+ 
+
+ align:start position:0%
+mainly we have this giant uh think of it
+as an obstacle because we're not allowed
+
+ align:start position:0%
+as an obstacle because we're not allowed
+ 
+
+ align:start position:0%
+as an obstacle because we're not allowed
+to overlap when we unfold this thing so
+
+ align:start position:0%
+to overlap when we unfold this thing so
+ 
+
+ align:start position:0%
+to overlap when we unfold this thing so
+this shape can't be cut up because it
+
+ align:start position:0%
+this shape can't be cut up because it
+ 
+
+ align:start position:0%
+this shape can't be cut up because it
+has no edges except for here so this
+
+ align:start position:0%
+has no edges except for here so this
+ 
+
+ align:start position:0%
+has no edges except for here so this
+part can move around uh it turns out it
+
+ align:start position:0%
+part can move around uh it turns out it
+ 
+
+ align:start position:0%
+part can move around uh it turns out it
+will stay in there but it might just
+
+ align:start position:0%
+will stay in there but it might just
+ 
+
+ align:start position:0%
+will stay in there but it might just
+move up so we can make a little bit of
+
+ align:start position:0%
+move up so we can make a little bit of
+ 
+
+ align:start position:0%
+move up so we can make a little bit of
+space here uh there's there's this hole
+
+ align:start position:0%
+space here uh there's there's this hole
+ 
+
+ align:start position:0%
+space here uh there's there's this hole
+uh of this face and then there's this
+
+ align:start position:0%
+uh of this face and then there's this
+ 
+
+ align:start position:0%
+uh of this face and then there's this
+Tower that's sticking out into the third
+
+ align:start position:0%
+Tower that's sticking out into the third
+ 
+
+ align:start position:0%
+Tower that's sticking out into the third
+dimension and we need to somehow unfold
+
+ align:start position:0%
+dimension and we need to somehow unfold
+ 
+
+ align:start position:0%
+dimension and we need to somehow unfold
+that thing and fit it in here doesn't
+
+ align:start position:0%
+that thing and fit it in here doesn't
+ 
+
+ align:start position:0%
+that thing and fit it in here doesn't
+look possible uh because this is not
+
+ align:start position:0%
+look possible uh because this is not
+ 
+
+ align:start position:0%
+look possible uh because this is not
+quite drawn to scale um this is going to
+
+ align:start position:0%
+quite drawn to scale um this is going to
+ 
+
+ align:start position:0%
+quite drawn to scale um this is going to
+be super long so a lot of the stuff here
+
+ align:start position:0%
+be super long so a lot of the stuff here
+ 
+
+ align:start position:0%
+be super long so a lot of the stuff here
+is just going to be stuffed up the
+
+ align:start position:0%
+is just going to be stuffed up the
+ 
+
+ align:start position:0%
+is just going to be stuffed up the
+chimney so to speak um uh but also on
+
+ align:start position:0%
+chimney so to speak um uh but also on
+ 
+
+ align:start position:0%
+chimney so to speak um uh but also on
+the surface there's more stuff going on
+
+ align:start position:0%
+the surface there's more stuff going on
+ 
+
+ align:start position:0%
+the surface there's more stuff going on
+so let's zoom into this thing uh if we
+
+ align:start position:0%
+so let's zoom into this thing uh if we
+ 
+
+ align:start position:0%
+so let's zoom into this thing uh if we
+unfold that Tower into a plus sign uh
+
+ align:start position:0%
+unfold that Tower into a plus sign uh
+ 
+
+ align:start position:0%
+unfold that Tower into a plus sign uh
+most of it is lots of tiny um stuff
+
+ align:start position:0%
+most of it is lots of tiny um stuff
+ 
+
+ align:start position:0%
+most of it is lots of tiny um stuff
+called atoms which uh we will get to and
+
+ align:start position:0%
+called atoms which uh we will get to and
+ 
+
+ align:start position:0%
+called atoms which uh we will get to and
+then the kind of the interesting part
+
+ align:start position:0%
+then the kind of the interesting part
+ 
+
+ align:start position:0%
+then the kind of the interesting part
+from a three part partition standpoint
+
+ align:start position:0%
+from a three part partition standpoint
+ 
+
+ align:start position:0%
+from a three part partition standpoint
+or sorry from a square packing
+
+ align:start position:0%
+or sorry from a square packing
+ 
+
+ align:start position:0%
+or sorry from a square packing
+standpoint is there are some square
+
+ align:start position:0%
+standpoint is there are some square
+ 
+
+ align:start position:0%
+standpoint is there are some square
+faces and because we're Edge cutting uh
+
+ align:start position:0%
+faces and because we're Edge cutting uh
+ 
+
+ align:start position:0%
+faces and because we're Edge cutting uh
+our surface those squares will remain
+
+ align:start position:0%
+our surface those squares will remain
+ 
+
+ align:start position:0%
+our surface those squares will remain
+squares there's no edges on them so uh
+
+ align:start position:0%
+squares there's no edges on them so uh
+ 
+
+ align:start position:0%
+squares there's no edges on them so uh
+those guys somehow have to move around
+
+ align:start position:0%
+those guys somehow have to move around
+ 
+
+ align:start position:0%
+those guys somehow have to move around
+when you unfold and it's not drawn this
+
+ align:start position:0%
+when you unfold and it's not drawn this
+ 
+
+ align:start position:0%
+when you unfold and it's not drawn this
+way but the squares are large enough uh
+
+ align:start position:0%
+way but the squares are large enough uh
+ 
+
+ align:start position:0%
+way but the squares are large enough uh
+that they can't fit up the chimney okay
+
+ align:start position:0%
+that they can't fit up the chimney okay
+ 
+
+ align:start position:0%
+that they can't fit up the chimney okay
+this chimney is actually pretty narrow
+
+ align:start position:0%
+this chimney is actually pretty narrow
+ 
+
+ align:start position:0%
+this chimney is actually pretty narrow
+constant width and those guys are all
+
+ align:start position:0%
+constant width and those guys are all
+ 
+
+ align:start position:0%
+constant width and those guys are all
+really big so this other stuff can move
+
+ align:start position:0%
+really big so this other stuff can move
+ 
+
+ align:start position:0%
+really big so this other stuff can move
+up the chimney the squares will have to
+
+ align:start position:0%
+up the chimney the squares will have to
+ 
+
+ align:start position:0%
+up the chimney the squares will have to
+stay in this square and that's how we're
+
+ align:start position:0%
+stay in this square and that's how we're
+ 
+
+ align:start position:0%
+stay in this square and that's how we're
+going to get packing squares into
+
+ align:start position:0%
+going to get packing squares into
+ 
+
+ align:start position:0%
+going to get packing squares into
+squares okay now the challenge is what
+
+ align:start position:0%
+squares okay now the challenge is what
+ 
+
+ align:start position:0%
+squares okay now the challenge is what
+we want to be able to do is move the
+
+ align:start position:0%
+we want to be able to do is move the
+ 
+
+ align:start position:0%
+we want to be able to do is move the
+squares around freely um but in reality
+
+ align:start position:0%
+squares around freely um but in reality
+ 
+
+ align:start position:0%
+squares around freely um but in reality
+we need to make a connected 2D shape so
+
+ align:start position:0%
+we need to make a connected 2D shape so
+ 
+
+ align:start position:0%
+we need to make a connected 2D shape so
+somehow we need to connect together
+
+ align:start position:0%
+somehow we need to connect together
+ 
+
+ align:start position:0%
+somehow we need to connect together
+these squares by some stuff that's the
+
+ align:start position:0%
+these squares by some stuff that's the
+ 
+
+ align:start position:0%
+these squares by some stuff that's the
+mystery atoms uh so that basically we
+
+ align:start position:0%
+mystery atoms uh so that basically we
+ 
+
+ align:start position:0%
+mystery atoms uh so that basically we
+for any Square packing we can uh arrange
+
+ align:start position:0%
+for any Square packing we can uh arrange
+ 
+
+ align:start position:0%
+for any Square packing we can uh arrange
+to have those faces in that rough
+
+ align:start position:0%
+to have those faces in that rough
+ 
+
+ align:start position:0%
+to have those faces in that rough
+Arrangement and then the other stuff
+
+ align:start position:0%
+Arrangement and then the other stuff
+ 
+
+ align:start position:0%
+Arrangement and then the other stuff
+somehow connects everything together and
+
+ align:start position:0%
+somehow connects everything together and
+ 
+
+ align:start position:0%
+somehow connects everything together and
+whatever doesn't fit in here goes up the
+
+ align:start position:0%
+whatever doesn't fit in here goes up the
+ 
+
+ align:start position:0%
+whatever doesn't fit in here goes up the
+chimney so that's the plan uh if we zoom
+
+ align:start position:0%
+chimney so that's the plan uh if we zoom
+ 
+
+ align:start position:0%
+chimney so that's the plan uh if we zoom
+in uh right so this is sort of the the
+
+ align:start position:0%
+in uh right so this is sort of the the
+ 
+
+ align:start position:0%
+in uh right so this is sort of the the
+diagram of that plan imagine you have
+
+ align:start position:0%
+diagram of that plan imagine you have
+ 
+
+ align:start position:0%
+diagram of that plan imagine you have
+some placement of the squares um and
+
+ align:start position:0%
+some placement of the squares um and
+ 
+
+ align:start position:0%
+some placement of the squares um and
+we're going to try to connect all the
+
+ align:start position:0%
+we're going to try to connect all the
+ 
+
+ align:start position:0%
+we're going to try to connect all the
+pieces together uh maybe to some common
+
+ align:start position:0%
+pieces together uh maybe to some common
+ 
+
+ align:start position:0%
+pieces together uh maybe to some common
+root in the lower left corner first
+
+ align:start position:0%
+root in the lower left corner first
+ 
+
+ align:start position:0%
+root in the lower left corner first
+we're just going to draw some L's
+
+ align:start position:0%
+we're just going to draw some L's
+ 
+
+ align:start position:0%
+we're just going to draw some L's
+conceptually to connect them all to here
+
+ align:start position:0%
+conceptually to connect them all to here
+ 
+
+ align:start position:0%
+conceptually to connect them all to here
+um those cross which is not allowed but
+
+ align:start position:0%
+um those cross which is not allowed but
+ 
+
+ align:start position:0%
+um those cross which is not allowed but
+then we're going to reroute the L's to
+
+ align:start position:0%
+then we're going to reroute the L's to
+ 
+
+ align:start position:0%
+then we're going to reroute the L's to
+go around the uh so to get up to this
+
+ align:start position:0%
+go around the uh so to get up to this
+ 
+
+ align:start position:0%
+go around the uh so to get up to this
+box we're going to go around all of the
+
+ align:start position:0%
+box we're going to go around all of the
+ 
+
+ align:start position:0%
+box we're going to go around all of the
+other boxes below it um and in this way
+
+ align:start position:0%
+other boxes below it um and in this way
+ 
+
+ align:start position:0%
+other boxes below it um and in this way
+we get a non-crossing Arrangement if we
+
+ align:start position:0%
+we get a non-crossing Arrangement if we
+ 
+
+ align:start position:0%
+we get a non-crossing Arrangement if we
+zoom in even closer these I've drawn as
+
+ align:start position:0%
+zoom in even closer these I've drawn as
+ 
+
+ align:start position:0%
+zoom in even closer these I've drawn as
+lines but really they're little strips
+
+ align:start position:0%
+lines but really they're little strips
+ 
+
+ align:start position:0%
+lines but really they're little strips
+of paper and they may do weird things
+
+ align:start position:0%
+of paper and they may do weird things
+ 
+
+ align:start position:0%
+of paper and they may do weird things
+like zigzag back and forth how that
+
+ align:start position:0%
+like zigzag back and forth how that
+ 
+
+ align:start position:0%
+like zigzag back and forth how that
+happens we'll see in a moment um but
+
+ align:start position:0%
+happens we'll see in a moment um but
+ 
+
+ align:start position:0%
+happens we'll see in a moment um but
+this is to convince you that at least if
+
+ align:start position:0%
+this is to convince you that at least if
+ 
+
+ align:start position:0%
+this is to convince you that at least if
+we could place squares and they're not
+
+ align:start position:0%
+we could place squares and they're not
+ 
+
+ align:start position:0%
+we could place squares and they're not
+like right touching each other so we're
+
+ align:start position:0%
+like right touching each other so we're
+ 
+
+ align:start position:0%
+like right touching each other so we're
+going to shrink each square a tiny bit
+
+ align:start position:0%
+going to shrink each square a tiny bit
+ 
+
+ align:start position:0%
+going to shrink each square a tiny bit
+which I won't get into the details but
+
+ align:start position:0%
+which I won't get into the details but
+ 
+
+ align:start position:0%
+which I won't get into the details but
+if if the if they're integer squares
+
+ align:start position:0%
+if if the if they're integer squares
+ 
+
+ align:start position:0%
+if if the if they're integer squares
+let's say then we'll shrink them maybe
+
+ align:start position:0%
+let's say then we'll shrink them maybe
+ 
+
+ align:start position:0%
+let's say then we'll shrink them maybe
+by minus one over n or something polom
+
+ align:start position:0%
+by minus one over n or something polom
+ 
+
+ align:start position:0%
+by minus one over n or something polom
+small um and then that that gives us a
+
+ align:start position:0%
+small um and then that that gives us a
+ 
+
+ align:start position:0%
+small um and then that that gives us a
+little bit of room to Route all of these
+
+ align:start position:0%
+little bit of room to Route all of these
+ 
+
+ align:start position:0%
+little bit of room to Route all of these
+paths if we make them like 1 over n^ s
+
+ align:start position:0%
+paths if we make them like 1 over n^ s
+ 
+
+ align:start position:0%
+paths if we make them like 1 over n^ s
+or 1 over n cubed in thickness still
+
+ align:start position:0%
+or 1 over n cubed in thickness still
+ 
+
+ align:start position:0%
+or 1 over n cubed in thickness still
+polinomial so still strongly empty hard
+
+ align:start position:0%
+polinomial so still strongly empty hard
+ 
+
+ align:start position:0%
+polinomial so still strongly empty hard
+um so uh if we have a square pack
+
+ align:start position:0%
+um so uh if we have a square pack
+ 
+
+ align:start position:0%
+um so uh if we have a square pack
+we can connect them all up in this way
+
+ align:start position:0%
+we can connect them all up in this way
+ 
+
+ align:start position:0%
+we can connect them all up in this way
+if we have these magical atoms that can
+
+ align:start position:0%
+if we have these magical atoms that can
+ 
+
+ align:start position:0%
+if we have these magical atoms that can
+do whatever we want uh freely and that's
+
+ align:start position:0%
+do whatever we want uh freely and that's
+ 
+
+ align:start position:0%
+do whatever we want uh freely and that's
+the um so in a little more detail in
+
+ align:start position:0%
+the um so in a little more detail in
+ 
+
+ align:start position:0%
+the um so in a little more detail in
+this picture um the we imagine the atoms
+
+ align:start position:0%
+this picture um the we imagine the atoms
+ 
+
+ align:start position:0%
+this picture um the we imagine the atoms
+is somehow being connected together in a
+
+ align:start position:0%
+is somehow being connected together in a
+ 
+
+ align:start position:0%
+is somehow being connected together in a
+chain potentially and then when they
+
+ align:start position:0%
+chain potentially and then when they
+ 
+
+ align:start position:0%
+chain potentially and then when they
+unfold this is the fun part so um we
+
+ align:start position:0%
+unfold this is the fun part so um we
+ 
+
+ align:start position:0%
+unfold this is the fun part so um we
+maybe for connectivity purposes maybe
+
+ align:start position:0%
+maybe for connectivity purposes maybe
+ 
+
+ align:start position:0%
+maybe for connectivity purposes maybe
+first we want to visit B1 then we want a
+
+ align:start position:0%
+first we want to visit B1 then we want a
+ 
+
+ align:start position:0%
+first we want to visit B1 then we want a
+visit B2 and so on
+
+ align:start position:0%
+visit B2 and so on
+ 
+
+ align:start position:0%
+visit B2 and so on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that corresponds to some traversal
+
+ align:start position:0%
+and that corresponds to some traversal
+ 
+
+ align:start position:0%
+and that corresponds to some traversal
+on the surface of this uh plus sign or
+
+ align:start position:0%
+on the surface of this uh plus sign or
+ 
+
+ align:start position:0%
+on the surface of this uh plus sign or
+the the tower that's sticking out uh and
+
+ align:start position:0%
+the the tower that's sticking out uh and
+ 
+
+ align:start position:0%
+the the tower that's sticking out uh and
+then in 2D when we unfold it we have a
+
+ align:start position:0%
+then in 2D when we unfold it we have a
+ 
+
+ align:start position:0%
+then in 2D when we unfold it we have a
+different thing in mind of whether we
+
+ align:start position:0%
+different thing in mind of whether we
+ 
+
+ align:start position:0%
+different thing in mind of whether we
+want it to go left or right so there's
+
+ align:start position:0%
+want it to go left or right so there's
+ 
+
+ align:start position:0%
+want it to go left or right so there's
+moving left or right intrinsically on
+
+ align:start position:0%
+moving left or right intrinsically on
+ 
+
+ align:start position:0%
+moving left or right intrinsically on
+the surface and then there's moving left
+
+ align:start position:0%
+the surface and then there's moving left
+ 
+
+ align:start position:0%
+the surface and then there's moving left
+and right in the unfolding so two
+
+ align:start position:0%
+and right in the unfolding so two
+ 
+
+ align:start position:0%
+and right in the unfolding so two
+separate things and conveniently this
+
+ align:start position:0%
+separate things and conveniently this
+ 
+
+ align:start position:0%
+separate things and conveniently this
+one structure is one of these boxes this
+
+ align:start position:0%
+one structure is one of these boxes this
+ 
+
+ align:start position:0%
+one structure is one of these boxes this
+is what we call the atom can do all of
+
+ align:start position:0%
+is what we call the atom can do all of
+ 
+
+ align:start position:0%
+is what we call the atom can do all of
+those things uh certainly not obvious
+
+ align:start position:0%
+those things uh certainly not obvious
+ 
+
+ align:start position:0%
+those things uh certainly not obvious
+from the picture it's just a little
+
+ align:start position:0%
+from the picture it's just a little
+ 
+
+ align:start position:0%
+from the picture it's just a little
+bumpy Square uh but you just trial the
+
+ align:start position:0%
+bumpy Square uh but you just trial the
+ 
+
+ align:start position:0%
+bumpy Square uh but you just trial the
+cases these are three of the cases not
+
+ align:start position:0%
+cases these are three of the cases not
+ 
+
+ align:start position:0%
+cases these are three of the cases not
+obvious but there turn out to be 10 if
+
+ align:start position:0%
+obvious but there turn out to be 10 if
+ 
+
+ align:start position:0%
+obvious but there turn out to be 10 if
+after you remove uh Reflections and
+
+ align:start position:0%
+after you remove uh Reflections and
+ 
+
+ align:start position:0%
+after you remove uh Reflections and
+rotations um there's a few things going
+
+ align:start position:0%
+rotations um there's a few things going
+ 
+
+ align:start position:0%
+rotations um there's a few things going
+on but the main thing going on is
+
+ align:start position:0%
+on but the main thing going on is
+ 
+
+ align:start position:0%
+on but the main thing going on is
+whether you're going left or right in
+
+ align:start position:0%
+whether you're going left or right in
+ 
+
+ align:start position:0%
+whether you're going left or right in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh get just get this straight whether
+
+ align:start position:0%
+uh get just get this straight whether
+ 
+
+ align:start position:0%
+uh get just get this straight whether
+you're going left or right in
+
+ align:start position:0%
+you're going left or right in
+ 
+
+ align:start position:0%
+you're going left or right in
+intrinsically on the surface surface and
+
+ align:start position:0%
+intrinsically on the surface surface and
+ 
+
+ align:start position:0%
+intrinsically on the surface surface and
+whether you're going left or right or
+
+ align:start position:0%
+whether you're going left or right or
+ 
+
+ align:start position:0%
+whether you're going left or right or
+straight u in the unfolding so here you
+
+ align:start position:0%
+straight u in the unfolding so here you
+ 
+
+ align:start position:0%
+straight u in the unfolding so here you
+can see you're turning left in the
+
+ align:start position:0%
+can see you're turning left in the
+ 
+
+ align:start position:0%
+can see you're turning left in the
+unfolding you're going straight in the
+
+ align:start position:0%
+unfolding you're going straight in the
+ 
+
+ align:start position:0%
+unfolding you're going straight in the
+unfolding and you're turning left in the
+
+ align:start position:0%
+unfolding and you're turning left in the
+ 
+
+ align:start position:0%
+unfolding and you're turning left in the
+unfolding so the second coordinate is L
+
+ align:start position:0%
+unfolding so the second coordinate is L
+ 
+
+ align:start position:0%
+unfolding so the second coordinate is L
+S and L what's less obvious is if you
+
+ align:start position:0%
+S and L what's less obvious is if you
+ 
+
+ align:start position:0%
+S and L what's less obvious is if you
+fold this up and you you get the atom
+
+ align:start position:0%
+fold this up and you you get the atom
+ 
+
+ align:start position:0%
+fold this up and you you get the atom
+structure but the thing that you attach
+
+ align:start position:0%
+structure but the thing that you attach
+ 
+
+ align:start position:0%
+structure but the thing that you attach
+to here is on on the folded structure
+
+ align:start position:0%
+to here is on on the folded structure
+ 
+
+ align:start position:0%
+to here is on on the folded structure
+either to the left or to the left or to
+
+ align:start position:0%
+either to the left or to the left or to
+ 
+
+ align:start position:0%
+either to the left or to the left or to
+the right uh so you just check all these
+
+ align:start position:0%
+the right uh so you just check all these
+ 
+
+ align:start position:0%
+the right uh so you just check all these
+things and then this is like a universal
+
+ align:start position:0%
+things and then this is like a universal
+ 
+
+ align:start position:0%
+things and then this is like a universal
+glue that can connect together the
+
+ align:start position:0%
+glue that can connect together the
+ 
+
+ align:start position:0%
+glue that can connect together the
+squares however you want both on the
+
+ align:start position:0%
+squares however you want both on the
+ 
+
+ align:start position:0%
+squares however you want both on the
+surface uh where they have to be
+
+ align:start position:0%
+surface uh where they have to be
+ 
+
+ align:start position:0%
+surface uh where they have to be
+connected originally and in the
+
+ align:start position:0%
+connected originally and in the
+ 
+
+ align:start position:0%
+connected originally and in the
+unfolding uh where you want to match
+
+ align:start position:0%
+unfolding uh where you want to match
+ 
+
+ align:start position:0%
+unfolding uh where you want to match
+some Square packing so a little bit of
+
+ align:start position:0%
+some Square packing so a little bit of
+ 
+
+ align:start position:0%
+some Square packing so a little bit of
+hand waving there lots of hand waving
+
+ align:start position:0%
+hand waving there lots of hand waving
+ 
+
+ align:start position:0%
+hand waving there lots of hand waving
+but in the end you get empty strong
+
+ align:start position:0%
+but in the end you get empty strong
+ 
+
+ align:start position:0%
+but in the end you get empty strong
+empty completeness of edge unfolding
+
+ align:start position:0%
+empty completeness of edge unfolding
+ 
+
+ align:start position:0%
+empty completeness of edge unfolding
+polyhedra uh any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right perfectly clear then um let's
+
+ align:start position:0%
+all right perfectly clear then um let's
+ 
+
+ align:start position:0%
+all right perfectly clear then um let's
+move to another puzzle this is called
+
+ align:start position:0%
+move to another puzzle this is called
+ 
+
+ align:start position:0%
+move to another puzzle this is called
+the snake Cube puzzle or the kubra
+
+ align:start position:0%
+the snake Cube puzzle or the kubra
+ 
+
+ align:start position:0%
+the snake Cube puzzle or the kubra
+puzzle um here is one instantiation of
+
+ align:start position:0%
+puzzle um here is one instantiation of
+ 
+
+ align:start position:0%
+puzzle um here is one instantiation of
+it so we have um it's a chain of
+
+ align:start position:0%
+it so we have um it's a chain of
+ 
+
+ align:start position:0%
+it so we have um it's a chain of
+blocks I try to unfold in a way that I
+
+ align:start position:0%
+blocks I try to unfold in a way that I
+ 
+
+ align:start position:0%
+blocks I try to unfold in a way that I
+can put it back together because it's
+
+ align:start position:0%
+can put it back together because it's
+ 
+
+ align:start position:0%
+can put it back together because it's
+actually quite tricky to solve um it's a
+
+ align:start position:0%
+actually quite tricky to solve um it's a
+ 
+
+ align:start position:0%
+actually quite tricky to solve um it's a
+chain of blocks and there's an elastic
+
+ align:start position:0%
+chain of blocks and there's an elastic
+ 
+
+ align:start position:0%
+chain of blocks and there's an elastic
+through the centers uh going through the
+
+ align:start position:0%
+through the centers uh going through the
+ 
+
+ align:start position:0%
+through the centers uh going through the
+center of the faces and so the result is
+
+ align:start position:0%
+center of the faces and so the result is
+ 
+
+ align:start position:0%
+center of the faces and so the result is
+uh you can't really pull the squares
+
+ align:start position:0%
+uh you can't really pull the squares
+ 
+
+ align:start position:0%
+uh you can't really pull the squares
+apart it's a pretty tight elastic but
+
+ align:start position:0%
+apart it's a pretty tight elastic but
+ 
+
+ align:start position:0%
+apart it's a pretty tight elastic but
+you can spin because from the elastics
+
+ align:start position:0%
+you can spin because from the elastics
+ 
+
+ align:start position:0%
+you can spin because from the elastics
+point of view these are all equally
+
+ align:start position:0%
+point of view these are all equally
+ 
+
+ align:start position:0%
+point of view these are all equally
+happy so you're basically told that and
+
+ align:start position:0%
+happy so you're basically told that and
+ 
+
+ align:start position:0%
+happy so you're basically told that and
+I I could also spin here but it doesn't
+
+ align:start position:0%
+I I could also spin here but it doesn't
+ 
+
+ align:start position:0%
+I I could also spin here but it doesn't
+do anything if I stop at a 90° angle so
+
+ align:start position:0%
+do anything if I stop at a 90° angle so
+ 
+
+ align:start position:0%
+do anything if I stop at a 90° angle so
+I'm forced to be straight here and then
+
+ align:start position:0%
+I'm forced to be straight here and then
+ 
+
+ align:start position:0%
+I'm forced to be straight here and then
+I'm forced to have a 90d turn and then
+
+ align:start position:0%
+I'm forced to have a 90d turn and then
+ 
+
+ align:start position:0%
+I'm forced to have a 90d turn and then
+I'm forced to go straight and then have
+
+ align:start position:0%
+I'm forced to go straight and then have
+ 
+
+ align:start position:0%
+I'm forced to go straight and then have
+a 90 degre turn and then go straight and
+
+ align:start position:0%
+a 90 degre turn and then go straight and
+ 
+
+ align:start position:0%
+a 90 degre turn and then go straight and
+then have a 90 degre turn uh here I have
+
+ align:start position:0%
+then have a 90 degre turn uh here I have
+ 
+
+ align:start position:0%
+then have a 90 degre turn uh here I have
+a a few 90 90° turns in a row and that's
+
+ align:start position:0%
+a a few 90 90° turns in a row and that's
+ 
+
+ align:start position:0%
+a a few 90 90° turns in a row and that's
+the general structure and can I still
+
+ align:start position:0%
+the general structure and can I still
+ 
+
+ align:start position:0%
+the general structure and can I still
+solve it maybe uh the goal is to get
+
+ align:start position:0%
+solve it maybe uh the goal is to get
+ 
+
+ align:start position:0%
+solve it maybe uh the goal is to get
+into a cube okay and there are a bunch
+
+ align:start position:0%
+into a cube okay and there are a bunch
+ 
+
+ align:start position:0%
+into a cube okay and there are a bunch
+of different versions plastic wood
+
+ align:start position:0%
+of different versions plastic wood
+ 
+
+ align:start position:0%
+of different versions plastic wood
+whatever this one is not solved and so I
+
+ align:start position:0%
+whatever this one is not solved and so I
+ 
+
+ align:start position:0%
+whatever this one is not solved and so I
+will not do so well but you get an idea
+
+ align:start position:0%
+will not do so well but you get an idea
+ 
+
+ align:start position:0%
+will not do so well but you get an idea
+of what it looks like in its sort of
+
+ align:start position:0%
+of what it looks like in its sort of
+ 
+
+ align:start position:0%
+of what it looks like in its sort of
+Flat state I can make it into a kind of
+
+ align:start position:0%
+Flat state I can make it into a kind of
+ 
+
+ align:start position:0%
+Flat state I can make it into a kind of
+staircase uh so in general this this
+
+ align:start position:0%
+staircase uh so in general this this
+ 
+
+ align:start position:0%
+staircase uh so in general this this
+puzzle is specified by sequence of
+
+ align:start position:0%
+puzzle is specified by sequence of
+ 
+
+ align:start position:0%
+puzzle is specified by sequence of
+lengths of straits and then in between
+
+ align:start position:0%
+lengths of straits and then in between
+ 
+
+ align:start position:0%
+lengths of straits and then in between
+those lengths are the 90° turns Okay so
+
+ align:start position:0%
+those lengths are the 90° turns Okay so
+ 
+
+ align:start position:0%
+those lengths are the 90° turns Okay so
+so that's the puzzle pretty simple
+
+ align:start position:0%
+so that's the puzzle pretty simple
+ 
+
+ align:start position:0%
+so that's the puzzle pretty simple
+specification and your goal is to fold
+
+ align:start position:0%
+specification and your goal is to fold
+ 
+
+ align:start position:0%
+specification and your goal is to fold
+into a cube you know how big the cube is
+
+ align:start position:0%
+into a cube you know how big the cube is
+ 
+
+ align:start position:0%
+into a cube you know how big the cube is
+you just take the number of little cubes
+
+ align:start position:0%
+you just take the number of little cubes
+ 
+
+ align:start position:0%
+you just take the number of little cubes
+and take the cube root um
+
+ align:start position:0%
+and take the cube root um
+ 
+
+ align:start position:0%
+and take the cube root um
+so uh this puzzle maybe goes uh is at
+
+ align:start position:0%
+so uh this puzzle maybe goes uh is at
+ 
+
+ align:start position:0%
+so uh this puzzle maybe goes uh is at
+least uh 1990 but could be older we
+
+ align:start position:0%
+least uh 1990 but could be older we
+ 
+
+ align:start position:0%
+least uh 1990 but could be older we
+don't know exactly um and this puzzle is
+
+ align:start position:0%
+don't know exactly um and this puzzle is
+ 
+
+ align:start position:0%
+don't know exactly um and this puzzle is
+also MP complete um and this proof is
+
+ align:start position:0%
+also MP complete um and this proof is
+ 
+
+ align:start position:0%
+also MP complete um and this proof is
+also complicated so we won't see all the
+
+ align:start position:0%
+also complicated so we won't see all the
+ 
+
+ align:start position:0%
+also complicated so we won't see all the
+details but this one we'll probably see
+
+ align:start position:0%
+details but this one we'll probably see
+ 
+
+ align:start position:0%
+details but this one we'll probably see
+a little bit clearer um this is a proof
+
+ align:start position:0%
+a little bit clearer um this is a proof
+ 
+
+ align:start position:0%
+a little bit clearer um this is a proof
+by in in particular the three of us and
+
+ align:start position:0%
+by in in particular the three of us and
+ 
+
+ align:start position:0%
+by in in particular the three of us and
+and Marty in the back so for all four of
+
+ align:start position:0%
+and Marty in the back so for all four of
+ 
+
+ align:start position:0%
+and Marty in the back so for all four of
+us um and let's see so this doesn't look
+
+ align:start position:0%
+us um and let's see so this doesn't look
+ 
+
+ align:start position:0%
+us um and let's see so this doesn't look
+like a cube uh so let's before we try to
+
+ align:start position:0%
+like a cube uh so let's before we try to
+ 
+
+ align:start position:0%
+like a cube uh so let's before we try to
+solve the problem of folding into a cube
+
+ align:start position:0%
+solve the problem of folding into a cube
+ 
+
+ align:start position:0%
+solve the problem of folding into a cube
+shape let's suppose um I give you one of
+
+ align:start position:0%
+shape let's suppose um I give you one of
+ 
+
+ align:start position:0%
+shape let's suppose um I give you one of
+these chains and I want to can it fold
+
+ align:start position:0%
+these chains and I want to can it fold
+ 
+
+ align:start position:0%
+these chains and I want to can it fold
+into this shape let's say this is the
+
+ align:start position:0%
+into this shape let's say this is the
+ 
+
+ align:start position:0%
+into this shape let's say this is the
+target so it's a big box down here I
+
+ align:start position:0%
+target so it's a big box down here I
+ 
+
+ align:start position:0%
+target so it's a big box down here I
+think we call the Hub and then there are
+
+ align:start position:0%
+think we call the Hub and then there are
+ 
+
+ align:start position:0%
+think we call the Hub and then there are
+these spokes
+
+ align:start position:0%
+these spokes
+ 
+
+ align:start position:0%
+these spokes
+or just big boxes long boxes sticking
+
+ align:start position:0%
+or just big boxes long boxes sticking
+ 
+
+ align:start position:0%
+or just big boxes long boxes sticking
+out of the Hub there's a there's a hole
+
+ align:start position:0%
+out of the Hub there's a there's a hole
+ 
+
+ align:start position:0%
+out of the Hub there's a there's a hole
+here there's they're connected to the
+
+ align:start position:0%
+here there's they're connected to the
+ 
+
+ align:start position:0%
+here there's they're connected to the
+main structure and you want to fold
+
+ align:start position:0%
+main structure and you want to fold
+ 
+
+ align:start position:0%
+main structure and you want to fold
+that and uh let's see so the the the big
+
+ align:start position:0%
+that and uh let's see so the the the big
+ 
+
+ align:start position:0%
+that and uh let's see so the the the big
+idea we're reducing from three partition
+
+ align:start position:0%
+idea we're reducing from three partition
+ 
+
+ align:start position:0%
+idea we're reducing from three partition
+here we're going to represent a number
+
+ align:start position:0%
+here we're going to represent a number
+ 
+
+ align:start position:0%
+here we're going to represent a number
+AI as uh a zigzag well not sorry I
+
+ align:start position:0%
+AI as uh a zigzag well not sorry I
+ 
+
+ align:start position:0%
+AI as uh a zigzag well not sorry I
+shouldn't call it a zigzag uh but we
+
+ align:start position:0%
+shouldn't call it a zigzag uh but we
+ 
+
+ align:start position:0%
+shouldn't call it a zigzag uh but we
+have a really long bar then a length one
+
+ align:start position:0%
+have a really long bar then a length one
+ 
+
+ align:start position:0%
+have a really long bar then a length one
+bar and then a really long bar and a
+
+ align:start position:0%
+bar and then a really long bar and a
+ 
+
+ align:start position:0%
+bar and then a really long bar and a
+length one bar I'm drawing sort of the
+
+ align:start position:0%
+length one bar I'm drawing sort of the
+ 
+
+ align:start position:0%
+length one bar I'm drawing sort of the
+thinned version this is really a little
+
+ align:start position:0%
+thinned version this is really a little
+ 
+
+ align:start position:0%
+thinned version this is really a little
+Cube this is a little Cube these are
+
+ align:start position:0%
+Cube this is a little Cube these are
+ 
+
+ align:start position:0%
+Cube this is a little Cube these are
+lots of Cubes uh huge number of Cubes
+
+ align:start position:0%
+lots of Cubes uh huge number of Cubes
+ 
+
+ align:start position:0%
+lots of Cubes uh huge number of Cubes
+okay uh so that's really really big um
+
+ align:start position:0%
+okay uh so that's really really big um
+ 
+
+ align:start position:0%
+okay uh so that's really really big um
+so big that the only place it could fit
+
+ align:start position:0%
+so big that the only place it could fit
+ 
+
+ align:start position:0%
+so big that the only place it could fit
+is down one of these spokes so of course
+
+ align:start position:0%
+is down one of these spokes so of course
+ 
+
+ align:start position:0%
+is down one of these spokes so of course
+the idea is that these represent our
+
+ align:start position:0%
+the idea is that these represent our
+ 
+
+ align:start position:0%
+the idea is that these represent our
+triples whose sum is equal to
+
+ align:start position:0%
+triples whose sum is equal to
+ 
+
+ align:start position:0%
+triples whose sum is equal to
+T um and so we have to take these things
+
+ align:start position:0%
+T um and so we have to take these things
+ 
+
+ align:start position:0%
+T um and so we have to take these things
+and because these are are so short you
+
+ align:start position:0%
+and because these are are so short you
+ 
+
+ align:start position:0%
+and because these are are so short you
+can't like go out of one Hub and like
+
+ align:start position:0%
+can't like go out of one Hub and like
+ 
+
+ align:start position:0%
+can't like go out of one Hub and like
+jump to the next one because there's a a
+
+ align:start position:0%
+jump to the next one because there's a a
+ 
+
+ align:start position:0%
+jump to the next one because there's a a
+non a gap there that's bigger than one
+
+ align:start position:0%
+non a gap there that's bigger than one
+ 
+
+ align:start position:0%
+non a gap there that's bigger than one
+so once you commit to having one of
+
+ align:start position:0%
+so once you commit to having one of
+ 
+
+ align:start position:0%
+so once you commit to having one of
+these long bars into one of these
+
+ align:start position:0%
+these long bars into one of these
+ 
+
+ align:start position:0%
+these long bars into one of these
+Pockets then all of them have to go into
+
+ align:start position:0%
+Pockets then all of them have to go into
+ 
+
+ align:start position:0%
+Pockets then all of them have to go into
+the pocket so this is a in general big
+
+ align:start position:0%
+the pocket so this is a in general big
+ 
+
+ align:start position:0%
+the pocket so this is a in general big
+issue with three partition proofs is you
+
+ align:start position:0%
+issue with three partition proofs is you
+ 
+
+ align:start position:0%
+issue with three partition proofs is you
+want to represent the number AI in some
+
+ align:start position:0%
+want to represent the number AI in some
+ 
+
+ align:start position:0%
+want to represent the number AI in some
+way that cannot be uh it's not divisible
+
+ align:start position:0%
+way that cannot be uh it's not divisible
+ 
+
+ align:start position:0%
+way that cannot be uh it's not divisible
+if you could take I Ai and split it into
+
+ align:start position:0%
+if you could take I Ai and split it into
+ 
+
+ align:start position:0%
+if you could take I Ai and split it into
+two parts then the packing problem
+
+ align:start position:0%
+two parts then the packing problem
+ 
+
+ align:start position:0%
+two parts then the packing problem
+becomes trivial youl split everything
+
+ align:start position:0%
+becomes trivial youl split everything
+ 
+
+ align:start position:0%
+becomes trivial youl split everything
+into units or something um so we have to
+
+ align:start position:0%
+into units or something um so we have to
+ 
+
+ align:start position:0%
+into units or something um so we have to
+make sure AI remains a single Chunk we
+
+ align:start position:0%
+make sure AI remains a single Chunk we
+ 
+
+ align:start position:0%
+make sure AI remains a single Chunk we
+are of course encoding AI in un here
+
+ align:start position:0%
+are of course encoding AI in un here
+ 
+
+ align:start position:0%
+are of course encoding AI in un here
+because we have one Long Bar per each AI
+
+ align:start position:0%
+because we have one Long Bar per each AI
+ 
+
+ align:start position:0%
+because we have one Long Bar per each AI
+but for three partition un is okay um
+
+ align:start position:0%
+but for three partition un is okay um
+ 
+
+ align:start position:0%
+but for three partition un is okay um
+there's some things going on here a
+
+ align:start position:0%
+there's some things going on here a
+ 
+
+ align:start position:0%
+there's some things going on here a
+little bit weird uh so you see this
+
+ align:start position:0%
+little bit weird uh so you see this
+ 
+
+ align:start position:0%
+little bit weird uh so you see this
+thing is occupying the full length and
+
+ align:start position:0%
+thing is occupying the full length and
+ 
+
+ align:start position:0%
+thing is occupying the full length and
+the length here is going to be eight
+
+ align:start position:0%
+the length here is going to be eight
+ 
+
+ align:start position:0%
+the length here is going to be eight
+times the target sum instead of just the
+
+ align:start position:0%
+times the target sum instead of just the
+ 
+
+ align:start position:0%
+times the target sum instead of just the
+target sum and we're multiplying this by
+
+ align:start position:0%
+target sum and we're multiplying this by
+ 
+
+ align:start position:0%
+target sum and we're multiplying this by
+eight so those are equal we're fine
+
+ align:start position:0%
+eight so those are equal we're fine
+ 
+
+ align:start position:0%
+eight so those are equal we're fine
+there there's a reason for the eight
+
+ align:start position:0%
+there there's a reason for the eight
+ 
+
+ align:start position:0%
+there there's a reason for the eight
+which we will get to okay now um like
+
+ align:start position:0%
+which we will get to okay now um like
+ 
+
+ align:start position:0%
+which we will get to okay now um like
+the previous proof The Edge unfolding
+
+ align:start position:0%
+the previous proof The Edge unfolding
+ 
+
+ align:start position:0%
+the previous proof The Edge unfolding
+polyhedra we have these great units and
+
+ align:start position:0%
+polyhedra we have these great units and
+ 
+
+ align:start position:0%
+polyhedra we have these great units and
+we just like them to be free floating
+
+ align:start position:0%
+we just like them to be free floating
+ 
+
+ align:start position:0%
+we just like them to be free floating
+and if you if you generalize this puzzle
+
+ align:start position:0%
+and if you if you generalize this puzzle
+ 
+
+ align:start position:0%
+and if you if you generalize this puzzle
+a little bit and say well actually uh I
+
+ align:start position:0%
+a little bit and say well actually uh I
+ 
+
+ align:start position:0%
+a little bit and say well actually uh I
+don't just have one chain I have two
+
+ align:start position:0%
+don't just have one chain I have two
+ 
+
+ align:start position:0%
+don't just have one chain I have two
+chains and or I have n chains and
+
+ align:start position:0%
+chains and or I have n chains and
+ 
+
+ align:start position:0%
+chains and or I have n chains and
+together collectively they have to fold
+
+ align:start position:0%
+together collectively they have to fold
+ 
+
+ align:start position:0%
+together collectively they have to fold
+into this shape then we're done except
+
+ align:start position:0%
+into this shape then we're done except
+ 
+
+ align:start position:0%
+into this shape then we're done except
+you would remove the Box the big uh the
+
+ align:start position:0%
+you would remove the Box the big uh the
+ 
+
+ align:start position:0%
+you would remove the Box the big uh the
+box over
+
+ align:start position:0%
+box over
+ 
+
+ align:start position:0%
+box over
+here uh because then these guys just
+
+ align:start position:0%
+here uh because then these guys just
+ 
+
+ align:start position:0%
+here uh because then these guys just
+somehow have to be assigned to these
+
+ align:start position:0%
+somehow have to be assigned to these
+ 
+
+ align:start position:0%
+somehow have to be assigned to these
+little pockets and we're happy okay um
+
+ align:start position:0%
+little pockets and we're happy okay um
+ 
+
+ align:start position:0%
+little pockets and we're happy okay um
+all of these numbers although again not
+
+ align:start position:0%
+all of these numbers although again not
+ 
+
+ align:start position:0%
+all of these numbers although again not
+drawn to scale all of these numbers are
+
+ align:start position:0%
+drawn to scale all of these numbers are
+ 
+
+ align:start position:0%
+drawn to scale all of these numbers are
+much smaller than huge so you can't like
+
+ align:start position:0%
+much smaller than huge so you can't like
+ 
+
+ align:start position:0%
+much smaller than huge so you can't like
+take this guy and put it here even
+
+ align:start position:0%
+take this guy and put it here even
+ 
+
+ align:start position:0%
+take this guy and put it here even
+though in this picture it looks like you
+
+ align:start position:0%
+though in this picture it looks like you
+ 
+
+ align:start position:0%
+though in this picture it looks like you
+might be able to all right so uh the
+
+ align:start position:0%
+might be able to all right so uh the
+ 
+
+ align:start position:0%
+might be able to all right so uh the
+issue is now we want to connect this
+
+ align:start position:0%
+issue is now we want to connect this
+ 
+
+ align:start position:0%
+issue is now we want to connect this
+together into one big chain we have
+
+ align:start position:0%
+together into one big chain we have
+ 
+
+ align:start position:0%
+together into one big chain we have
+these units for each eye uh we have one
+
+ align:start position:0%
+these units for each eye uh we have one
+ 
+
+ align:start position:0%
+these units for each eye uh we have one
+of these units that's cool uh and we
+
+ align:start position:0%
+of these units that's cool uh and we
+ 
+
+ align:start position:0%
+of these units that's cool uh and we
+want to attach them together in a way
+
+ align:start position:0%
+want to attach them together in a way
+ 
+
+ align:start position:0%
+want to attach them together in a way
+that is super flexible just like the
+
+ align:start position:0%
+that is super flexible just like the
+ 
+
+ align:start position:0%
+that is super flexible just like the
+atoms we had before um now we're going
+
+ align:start position:0%
+atoms we had before um now we're going
+ 
+
+ align:start position:0%
+atoms we had before um now we're going
+to use something which we call the
+
+ align:start position:0%
+to use something which we call the
+ 
+
+ align:start position:0%
+to use something which we call the
+zigzag that's why I didn't want to call
+
+ align:start position:0%
+zigzag that's why I didn't want to call
+ 
+
+ align:start position:0%
+zigzag that's why I didn't want to call
+this a zigzag um this is all unit
+
+ align:start position:0%
+this a zigzag um this is all unit
+ 
+
+ align:start position:0%
+this a zigzag um this is all unit
+segments so you have 90 degree turn 90°
+
+ align:start position:0%
+segments so you have 90 degree turn 90°
+ 
+
+ align:start position:0%
+segments so you have 90 degree turn 90°
+turn 90° turn 90 degre turn no straights
+
+ align:start position:0%
+turn 90° turn 90 degre turn no straights
+ 
+
+ align:start position:0%
+turn 90° turn 90 degre turn no straights
+this turns out to be Universal in a
+
+ align:start position:0%
+this turns out to be Universal in a
+ 
+
+ align:start position:0%
+this turns out to be Universal in a
+strong sense it can fold into
+
+ align:start position:0%
+strong sense it can fold into
+ 
+
+ align:start position:0%
+strong sense it can fold into
+anything um and so we can use it to
+
+ align:start position:0%
+anything um and so we can use it to
+ 
+
+ align:start position:0%
+anything um and so we can use it to
+connect these parts together so what
+
+ align:start position:0%
+connect these parts together so what
+ 
+
+ align:start position:0%
+connect these parts together so what
+we're going to do is have
+
+ align:start position:0%
+we're going to do is have
+ 
+
+ align:start position:0%
+we're going to do is have
+uh the A1 Gadget then we're going to
+
+ align:start position:0%
+uh the A1 Gadget then we're going to
+ 
+
+ align:start position:0%
+uh the A1 Gadget then we're going to
+have a whole bunch of zigzags so you can
+
+ align:start position:0%
+have a whole bunch of zigzags so you can
+ 
+
+ align:start position:0%
+have a whole bunch of zigzags so you can
+go wherever you need to go then we'll
+
+ align:start position:0%
+go wherever you need to go then we'll
+ 
+
+ align:start position:0%
+go wherever you need to go then we'll
+have the A2 Gadget and then we'll have a
+
+ align:start position:0%
+have the A2 Gadget and then we'll have a
+ 
+
+ align:start position:0%
+have the A2 Gadget and then we'll have a
+the universal zigzag Gadget uh for a
+
+ align:start position:0%
+the universal zigzag Gadget uh for a
+ 
+
+ align:start position:0%
+the universal zigzag Gadget uh for a
+long length of it and then the A3 and
+
+ align:start position:0%
+long length of it and then the A3 and
+ 
+
+ align:start position:0%
+long length of it and then the A3 and
+then alternating between zigzags and the
+
+ align:start position:0%
+then alternating between zigzags and the
+ 
+
+ align:start position:0%
+then alternating between zigzags and the
+AI and at the end we'll have enough
+
+ align:start position:0%
+AI and at the end we'll have enough
+ 
+
+ align:start position:0%
+AI and at the end we'll have enough
+zigzag uh that we can fill all this sort
+
+ align:start position:0%
+zigzag uh that we can fill all this sort
+ 
+
+ align:start position:0%
+zigzag uh that we can fill all this sort
+of extra garbage space but we will use
+
+ align:start position:0%
+of extra garbage space but we will use
+ 
+
+ align:start position:0%
+of extra garbage space but we will use
+this garbage space in order to Route
+
+ align:start position:0%
+this garbage space in order to Route
+ 
+
+ align:start position:0%
+this garbage space in order to Route
+around so maybe a1's going to go here
+
+ align:start position:0%
+around so maybe a1's going to go here
+ 
+
+ align:start position:0%
+around so maybe a1's going to go here
+and so we do the this thing
+
+ align:start position:0%
+and so we do the this thing
+ 
+
+ align:start position:0%
+and so we do the this thing
+this um yeah looks like some kind of
+
+ align:start position:0%
+this um yeah looks like some kind of
+ 
+
+ align:start position:0%
+this um yeah looks like some kind of
+cooker uh we go back and forth like that
+
+ align:start position:0%
+cooker uh we go back and forth like that
+ 
+
+ align:start position:0%
+cooker uh we go back and forth like that
+uh then we'll have the zigzag we say
+
+ align:start position:0%
+uh then we'll have the zigzag we say
+ 
+
+ align:start position:0%
+uh then we'll have the zigzag we say
+Okay I want to go over here next and
+
+ align:start position:0%
+Okay I want to go over here next and
+ 
+
+ align:start position:0%
+Okay I want to go over here next and
+then we'll do A2 there and then we'll
+
+ align:start position:0%
+then we'll do A2 there and then we'll
+ 
+
+ align:start position:0%
+then we'll do A2 there and then we'll
+route over here and because this is in
+
+ align:start position:0%
+route over here and because this is in
+ 
+
+ align:start position:0%
+route over here and because this is in
+3D Crossings are not an issue I can just
+
+ align:start position:0%
+3D Crossings are not an issue I can just
+ 
+
+ align:start position:0%
+3D Crossings are not an issue I can just
+go out into the third dimension um we
+
+ align:start position:0%
+go out into the third dimension um we
+ 
+
+ align:start position:0%
+go out into the third dimension um we
+don't need much of a third dimension
+
+ align:start position:0%
+don't need much of a third dimension
+ 
+
+ align:start position:0%
+don't need much of a third dimension
+Eight is Enough uh you can just enough
+
+ align:start position:0%
+Eight is Enough uh you can just enough
+ 
+
+ align:start position:0%
+Eight is Enough uh you can just enough
+to go over each
+
+ align:start position:0%
+to go over each
+ 
+
+ align:start position:0%
+to go over each
+other okay and then at the end uh we're
+
+ align:start position:0%
+other okay and then at the end uh we're
+ 
+
+ align:start position:0%
+other okay and then at the end uh we're
+going to fill in all the space with this
+
+ align:start position:0%
+going to fill in all the space with this
+ 
+
+ align:start position:0%
+going to fill in all the space with this
+zigzag so let's talk about the
+
+ align:start position:0%
+zigzag so let's talk about the
+ 
+
+ align:start position:0%
+zigzag so let's talk about the
+zigzag uh what we claim there a couple
+
+ align:start position:0%
+zigzag uh what we claim there a couple
+ 
+
+ align:start position:0%
+zigzag uh what we claim there a couple
+different senses in which it's
+
+ align:start position:0%
+different senses in which it's
+ 
+
+ align:start position:0%
+different senses in which it's
+Universal um but the the key idea are
+
+ align:start position:0%
+Universal um but the the key idea are
+ 
+
+ align:start position:0%
+Universal um but the the key idea are
+these sets of gadgets uh so we're
+
+ align:start position:0%
+these sets of gadgets uh so we're
+ 
+
+ align:start position:0%
+these sets of gadgets uh so we're
+drawing here a 2X twox
+
+ align:start position:0%
+drawing here a 2X twox
+ 
+
+ align:start position:0%
+drawing here a 2X twox
+two uh cube made up out of you know uh
+
+ align:start position:0%
+two uh cube made up out of you know uh
+ 
+
+ align:start position:0%
+two uh cube made up out of you know uh
+eight little
+
+ align:start position:0%
+eight little
+ 
+
+ align:start position:0%
+eight little
+cubes and uh if you look at the uh what
+
+ align:start position:0%
+cubes and uh if you look at the uh what
+ 
+
+ align:start position:0%
+cubes and uh if you look at the uh what
+we've drawn here is the elastic that
+
+ align:start position:0%
+we've drawn here is the elastic that
+ 
+
+ align:start position:0%
+we've drawn here is the elastic that
+goes through the centers of the cubes
+
+ align:start position:0%
+goes through the centers of the cubes
+ 
+
+ align:start position:0%
+goes through the centers of the cubes
+and notice it turns 90° at every at
+
+ align:start position:0%
+and notice it turns 90° at every at
+ 
+
+ align:start position:0%
+and notice it turns 90° at every at
+every voxel at every little Cube um so
+
+ align:start position:0%
+every voxel at every little Cube um so
+ 
+
+ align:start position:0%
+every voxel at every little Cube um so
+that's this is part of these are zigzag
+
+ align:start position:0%
+that's this is part of these are zigzag
+ 
+
+ align:start position:0%
+that's this is part of these are zigzag
+constructions so um what we want to say
+
+ align:start position:0%
+constructions so um what we want to say
+ 
+
+ align:start position:0%
+constructions so um what we want to say
+is that if you sort of uh so one sense
+
+ align:start position:0%
+is that if you sort of uh so one sense
+ 
+
+ align:start position:0%
+is that if you sort of uh so one sense
+of universality is that the zigzag uh
+
+ align:start position:0%
+of universality is that the zigzag uh
+ 
+
+ align:start position:0%
+of universality is that the zigzag uh
+structure can fold into any polycube
+
+ align:start position:0%
+structure can fold into any polycube
+ 
+
+ align:start position:0%
+structure can fold into any polycube
+structure poly cube is the 3D
+
+ align:start position:0%
+structure poly cube is the 3D
+ 
+
+ align:start position:0%
+structure poly cube is the 3D
+generalization of polyomino that we saw
+
+ align:start position:0%
+generalization of polyomino that we saw
+ 
+
+ align:start position:0%
+generalization of polyomino that we saw
+last time um from polyomino
+
+ align:start position:0%
+last time um from polyomino
+ 
+
+ align:start position:0%
+last time um from polyomino
+packing uh that's not true but if you
+
+ align:start position:0%
+packing uh that's not true but if you
+ 
+
+ align:start position:0%
+packing uh that's not true but if you
+take any poly Cube structure and you
+
+ align:start position:0%
+take any poly Cube structure and you
+ 
+
+ align:start position:0%
+take any poly Cube structure and you
+just scale it by a factor of two so you
+
+ align:start position:0%
+just scale it by a factor of two so you
+ 
+
+ align:start position:0%
+just scale it by a factor of two so you
+replace every cube with a 2X two x two
+
+ align:start position:0%
+replace every cube with a 2X two x two
+ 
+
+ align:start position:0%
+replace every cube with a 2X two x two
+grid like this picture then it's still
+
+ align:start position:0%
+grid like this picture then it's still
+ 
+
+ align:start position:0%
+grid like this picture then it's still
+not true but it's better um so what's
+
+ align:start position:0%
+not true but it's better um so what's
+ 
+
+ align:start position:0%
+not true but it's better um so what's
+true at that point is if you take any
+
+ align:start position:0%
+true at that point is if you take any
+ 
+
+ align:start position:0%
+true at that point is if you take any
+path of 2x two x two cubes this is what
+
+ align:start position:0%
+path of 2x two x two cubes this is what
+ 
+
+ align:start position:0%
+path of 2x two x two cubes this is what
+we would call a hamiltonian shape
+
+ align:start position:0%
+we would call a hamiltonian shape
+ 
+
+ align:start position:0%
+we would call a hamiltonian shape
+because there's one path that visits
+
+ align:start position:0%
+because there's one path that visits
+ 
+
+ align:start position:0%
+because there's one path that visits
+everything with no Collision so it has
+
+ align:start position:0%
+everything with no Collision so it has
+ 
+
+ align:start position:0%
+everything with no Collision so it has
+to be a path that does not hit itself in
+
+ align:start position:0%
+to be a path that does not hit itself in
+ 
+
+ align:start position:0%
+to be a path that does not hit itself in
+3D um then you can follow these Gadgets
+
+ align:start position:0%
+3D um then you can follow these Gadgets
+ 
+
+ align:start position:0%
+3D um then you can follow these Gadgets
+in order to make any turns you need to
+
+ align:start position:0%
+in order to make any turns you need to
+ 
+
+ align:start position:0%
+in order to make any turns you need to
+do or you can go straight uh everything
+
+ align:start position:0%
+do or you can go straight uh everything
+ 
+
+ align:start position:0%
+do or you can go straight uh everything
+is possible uh we'll talk a little bit
+
+ align:start position:0%
+is possible uh we'll talk a little bit
+ 
+
+ align:start position:0%
+is possible uh we'll talk a little bit
+more about that in a moment so 2x2 x two
+
+ align:start position:0%
+more about that in a moment so 2x2 x two
+ 
+
+ align:start position:0%
+more about that in a moment so 2x2 x two
+refinement meaning scaling everything by
+
+ align:start position:0%
+refinement meaning scaling everything by
+ 
+
+ align:start position:0%
+refinement meaning scaling everything by
+a factor of two uh allows the zigzag to
+
+ align:start position:0%
+a factor of two uh allows the zigzag to
+ 
+
+ align:start position:0%
+a factor of two uh allows the zigzag to
+make any hamiltonian shape scaled by two
+
+ align:start position:0%
+make any hamiltonian shape scaled by two
+ 
+
+ align:start position:0%
+make any hamiltonian shape scaled by two
+um but that's hamiltonian shapes now
+
+ align:start position:0%
+um but that's hamiltonian shapes now
+ 
+
+ align:start position:0%
+um but that's hamiltonian shapes now
+conveniently there's this theorem which
+
+ align:start position:0%
+conveniently there's this theorem which
+ 
+
+ align:start position:0%
+conveniently there's this theorem which
+is used a lot in computational geometry
+
+ align:start position:0%
+is used a lot in computational geometry
+ 
+
+ align:start position:0%
+is used a lot in computational geometry
+and we use it in this hardness proof uh
+
+ align:start position:0%
+and we use it in this hardness proof uh
+ 
+
+ align:start position:0%
+and we use it in this hardness proof uh
+that if you take any shape and you
+
+ align:start position:0%
+that if you take any shape and you
+ 
+
+ align:start position:0%
+that if you take any shape and you
+refine it by 2x 2 by two or you scale by
+
+ align:start position:0%
+refine it by 2x 2 by two or you scale by
+ 
+
+ align:start position:0%
+refine it by 2x 2 by two or you scale by
+a factor of two then it becomes
+
+ align:start position:0%
+a factor of two then it becomes
+ 
+
+ align:start position:0%
+a factor of two then it becomes
+hamiltonian by a similar kind of Gadget
+
+ align:start position:0%
+hamiltonian by a similar kind of Gadget
+ 
+
+ align:start position:0%
+hamiltonian by a similar kind of Gadget
+construction although it's easier if you
+
+ align:start position:0%
+construction although it's easier if you
+ 
+
+ align:start position:0%
+construction although it's easier if you
+just want hamiltonian paths you don't
+
+ align:start position:0%
+just want hamiltonian paths you don't
+ 
+
+ align:start position:0%
+just want hamiltonian paths you don't
+care about where you where you're
+
+ align:start position:0%
+care about where you where you're
+ 
+
+ align:start position:0%
+care about where you where you're
+turning and where you're not turning uh
+
+ align:start position:0%
+turning and where you're not turning uh
+ 
+
+ align:start position:0%
+turning and where you're not turning uh
+so that's a pretty easy proof left as an
+
+ align:start position:0%
+so that's a pretty easy proof left as an
+ 
+
+ align:start position:0%
+so that's a pretty easy proof left as an
+exercise to you um and sort of an aside
+
+ align:start position:0%
+exercise to you um and sort of an aside
+ 
+
+ align:start position:0%
+exercise to you um and sort of an aside
+from this this issue so we take any
+
+ align:start position:0%
+from this this issue so we take any
+ 
+
+ align:start position:0%
+from this this issue so we take any
+shape we 2 by two by two refine it we
+
+ align:start position:0%
+shape we 2 by two by two refine it we
+ 
+
+ align:start position:0%
+shape we 2 by two by two refine it we
+make it hamiltonian then we 2 by two
+
+ align:start position:0%
+make it hamiltonian then we 2 by two
+ 
+
+ align:start position:0%
+make it hamiltonian then we 2 by two
+refine it again in total 4x4x4
+
+ align:start position:0%
+refine it again in total 4x4x4
+ 
+
+ align:start position:0%
+refine it again in total 4x4x4
+refinement and then uh zigzag path can
+
+ align:start position:0%
+refinement and then uh zigzag path can
+ 
+
+ align:start position:0%
+refinement and then uh zigzag path can
+make that poly Cube shape this is for
+
+ align:start position:0%
+make that poly Cube shape this is for
+ 
+
+ align:start position:0%
+make that poly Cube shape this is for
+any poly Cube so that's cool now uh I'll
+
+ align:start position:0%
+any poly Cube so that's cool now uh I'll
+ 
+
+ align:start position:0%
+any poly Cube so that's cool now uh I'll
+mention here in this proof one of the
+
+ align:start position:0%
+mention here in this proof one of the
+ 
+
+ align:start position:0%
+mention here in this proof one of the
+issues um which we'll see a bunch of
+
+ align:start position:0%
+issues um which we'll see a bunch of
+ 
+
+ align:start position:0%
+issues um which we'll see a bunch of
+times I'm just going to mention it here
+
+ align:start position:0%
+times I'm just going to mention it here
+ 
+
+ align:start position:0%
+times I'm just going to mention it here
+is uh we have a parody issue because the
+
+ align:start position:0%
+is uh we have a parody issue because the
+ 
+
+ align:start position:0%
+is uh we have a parody issue because the
+uh the cubicle grid
+
+ align:start position:0%
+uh the cubicle grid
+ 
+
+ align:start position:0%
+uh the cubicle grid
+is uh two colorable right you can
+
+ align:start position:0%
+is uh two colorable right you can
+ 
+
+ align:start position:0%
+is uh two colorable right you can
+checkerboard the the 3D grid of squares
+
+ align:start position:0%
+checkerboard the the 3D grid of squares
+ 
+
+ align:start position:0%
+checkerboard the the 3D grid of squares
+um and so what that means is every time
+
+ align:start position:0%
+um and so what that means is every time
+ 
+
+ align:start position:0%
+um and so what that means is every time
+you go from one Cube on the grid to
+
+ align:start position:0%
+you go from one Cube on the grid to
+ 
+
+ align:start position:0%
+you go from one Cube on the grid to
+another Cube on the grid you're
+
+ align:start position:0%
+another Cube on the grid you're
+ 
+
+ align:start position:0%
+another Cube on the grid you're
+switching parody so if you checkerboard
+
+ align:start position:0%
+switching parody so if you checkerboard
+ 
+
+ align:start position:0%
+switching parody so if you checkerboard
+the 3D space uh black and white it was
+
+ align:start position:0%
+the 3D space uh black and white it was
+ 
+
+ align:start position:0%
+the 3D space uh black and white it was
+going from white to black then black to
+
+ align:start position:0%
+going from white to black then black to
+ 
+
+ align:start position:0%
+going from white to black then black to
+white then black to white then oh sorry
+
+ align:start position:0%
+white then black to white then oh sorry
+ 
+
+ align:start position:0%
+white then black to white then oh sorry
+alternating black and white um and
+
+ align:start position:0%
+alternating black and white um and
+ 
+
+ align:start position:0%
+alternating black and white um and
+easier to do than to say and um so
+
+ align:start position:0%
+easier to do than to say and um so
+ 
+
+ align:start position:0%
+easier to do than to say and um so
+that's a constraint so for example it is
+
+ align:start position:0%
+that's a constraint so for example it is
+ 
+
+ align:start position:0%
+that's a constraint so for example it is
+impossible to in a 2 by two by two thing
+
+ align:start position:0%
+impossible to in a 2 by two by two thing
+ 
+
+ align:start position:0%
+impossible to in a 2 by two by two thing
+to uh let's see
+
+ align:start position:0%
+to uh let's see
+ 
+
+ align:start position:0%
+to uh let's see
+enter from this Cube the front Cube and
+
+ align:start position:0%
+enter from this Cube the front Cube and
+ 
+
+ align:start position:0%
+enter from this Cube the front Cube and
+exit from this one uh just by a counting
+
+ align:start position:0%
+exit from this one uh just by a counting
+ 
+
+ align:start position:0%
+exit from this one uh just by a counting
+argument so you start let's say this is
+
+ align:start position:0%
+argument so you start let's say this is
+ 
+
+ align:start position:0%
+argument so you start let's say this is
+a Black Cube this one also a black Cube
+
+ align:start position:0%
+a Black Cube this one also a black Cube
+ 
+
+ align:start position:0%
+a Black Cube this one also a black Cube
+and so you start black and then you
+
+ align:start position:0%
+and so you start black and then you
+ 
+
+ align:start position:0%
+and so you start black and then you
+alternate black white black white and
+
+ align:start position:0%
+alternate black white black white and
+ 
+
+ align:start position:0%
+alternate black white black white and
+there's eight things to visit and you
+
+ align:start position:0%
+there's eight things to visit and you
+ 
+
+ align:start position:0%
+there's eight things to visit and you
+want to end black that's not possible
+
+ align:start position:0%
+want to end black that's not possible
+ 
+
+ align:start position:0%
+want to end black that's not possible
+you have to end white so if you enter on
+
+ align:start position:0%
+you have to end white so if you enter on
+ 
+
+ align:start position:0%
+you have to end white so if you enter on
+a black Cube you will leave on a white
+
+ align:start position:0%
+a black Cube you will leave on a white
+ 
+
+ align:start position:0%
+a black Cube you will leave on a white
+Cube and if you enter on a white Cube
+
+ align:start position:0%
+Cube and if you enter on a white Cube
+ 
+
+ align:start position:0%
+Cube and if you enter on a white Cube
+you leave on a black Cube so um that's a
+
+ align:start position:0%
+you leave on a black Cube so um that's a
+ 
+
+ align:start position:0%
+you leave on a black Cube so um that's a
+constraint doesn't really get in the way
+
+ align:start position:0%
+constraint doesn't really get in the way
+ 
+
+ align:start position:0%
+constraint doesn't really get in the way
+here but it's something you have to keep
+
+ align:start position:0%
+here but it's something you have to keep
+ 
+
+ align:start position:0%
+here but it's something you have to keep
+track of and the theorem wouldn't be
+
+ align:start position:0%
+track of and the theorem wouldn't be
+ 
+
+ align:start position:0%
+track of and the theorem wouldn't be
+what you'd like to say is well I can
+
+ align:start position:0%
+what you'd like to say is well I can
+ 
+
+ align:start position:0%
+what you'd like to say is well I can
+enter from any Cube and leave from any
+
+ align:start position:0%
+enter from any Cube and leave from any
+ 
+
+ align:start position:0%
+enter from any Cube and leave from any
+Cube and uh you could actually prove
+
+ align:start position:0%
+Cube and uh you could actually prove
+ 
+
+ align:start position:0%
+Cube and uh you could actually prove
+that by induction except the base case
+
+ align:start position:0%
+that by induction except the base case
+ 
+
+ align:start position:0%
+that by induction except the base case
+would be wrong so this is something to
+
+ align:start position:0%
+would be wrong so this is something to
+ 
+
+ align:start position:0%
+would be wrong so this is something to
+be careful about this is the base case
+
+ align:start position:0%
+be careful about this is the base case
+ 
+
+ align:start position:0%
+be careful about this is the base case
+this is one Cube can I enter from
+
+ align:start position:0%
+this is one Cube can I enter from
+ 
+
+ align:start position:0%
+this is one Cube can I enter from
+anywhere one 2X 2 by two super Cube can
+
+ align:start position:0%
+anywhere one 2X 2 by two super Cube can
+ 
+
+ align:start position:0%
+anywhere one 2X 2 by two super Cube can
+I enter anywhere leave anywhere the
+
+ align:start position:0%
+I enter anywhere leave anywhere the
+ 
+
+ align:start position:0%
+I enter anywhere leave anywhere the
+answer is no but I can enter and exit
+
+ align:start position:0%
+answer is no but I can enter and exit
+ 
+
+ align:start position:0%
+answer is no but I can enter and exit
+anywhere that have the right parity so
+
+ align:start position:0%
+anywhere that have the right parity so
+ 
+
+ align:start position:0%
+anywhere that have the right parity so
+if the entrance Cube and the exit cubes
+
+ align:start position:0%
+if the entrance Cube and the exit cubes
+ 
+
+ align:start position:0%
+if the entrance Cube and the exit cubes
+have opposite parity then this is
+
+ align:start position:0%
+have opposite parity then this is
+ 
+
+ align:start position:0%
+have opposite parity then this is
+actually all of the cases uh these four
+
+ align:start position:0%
+actually all of the cases uh these four
+ 
+
+ align:start position:0%
+actually all of the cases uh these four
+are where the entrance and exit Cube are
+
+ align:start position:0%
+are where the entrance and exit Cube are
+ 
+
+ align:start position:0%
+are where the entrance and exit Cube are
+um adjacent to each other and these uh
+
+ align:start position:0%
+um adjacent to each other and these uh
+ 
+
+ align:start position:0%
+um adjacent to each other and these uh
+two cases are where they're opposite
+
+ align:start position:0%
+two cases are where they're opposite
+ 
+
+ align:start position:0%
+two cases are where they're opposite
+from each other not touching um and
+
+ align:start position:0%
+from each other not touching um and
+ 
+
+ align:start position:0%
+from each other not touching um and
+that's all the cases with with all the
+
+ align:start position:0%
+that's all the cases with with all the
+ 
+
+ align:start position:0%
+that's all the cases with with all the
+rotations and Reflections um so once you
+
+ align:start position:0%
+rotations and Reflections um so once you
+ 
+
+ align:start position:0%
+rotations and Reflections um so once you
+prove that the base case is actually
+
+ align:start position:0%
+prove that the base case is actually
+ 
+
+ align:start position:0%
+prove that the base case is actually
+really easy to do by induction you just
+
+ align:start position:0%
+really easy to do by induction you just
+ 
+
+ align:start position:0%
+really easy to do by induction you just
+are essentially pasting all of these
+
+ align:start position:0%
+are essentially pasting all of these
+ 
+
+ align:start position:0%
+are essentially pasting all of these
+things together to make any
+
+ align:start position:0%
+things together to make any
+ 
+
+ align:start position:0%
+things together to make any
+path uh and then we can make any
+
+ align:start position:0%
+path uh and then we can make any
+ 
+
+ align:start position:0%
+path uh and then we can make any
+hamiltonian shape then further
+
+ align:start position:0%
+hamiltonian shape then further
+ 
+
+ align:start position:0%
+hamiltonian shape then further
+refinement we can any shape becomes
+
+ align:start position:0%
+refinement we can any shape becomes
+ 
+
+ align:start position:0%
+refinement we can any shape becomes
+hamiltonian so that's how we prove
+
+ align:start position:0%
+hamiltonian so that's how we prove
+ 
+
+ align:start position:0%
+hamiltonian so that's how we prove
+zigzags are Universal and this uh
+
+ align:start position:0%
+zigzags are Universal and this uh
+ 
+
+ align:start position:0%
+zigzags are Universal and this uh
+connects together uh all of these
+
+ align:start position:0%
+connects together uh all of these
+ 
+
+ align:start position:0%
+connects together uh all of these
+gadgets so there's really two Gadgets in
+
+ align:start position:0%
+gadgets so there's really two Gadgets in
+ 
+
+ align:start position:0%
+gadgets so there's really two Gadgets in
+this proof the AI gadgets there's n of n
+
+ align:start position:0%
+this proof the AI gadgets there's n of n
+ 
+
+ align:start position:0%
+this proof the AI gadgets there's n of n
+copies of that and the zigzag Gadget
+
+ align:start position:0%
+copies of that and the zigzag Gadget
+ 
+
+ align:start position:0%
+copies of that and the zigzag Gadget
+there's n copies of that as well and
+
+ align:start position:0%
+there's n copies of that as well and
+ 
+
+ align:start position:0%
+there's n copies of that as well and
+that now there are some details to check
+
+ align:start position:0%
+that now there are some details to check
+ 
+
+ align:start position:0%
+that now there are some details to check
+here of course that the zigzag gadgets
+
+ align:start position:0%
+here of course that the zigzag gadgets
+ 
+
+ align:start position:0%
+here of course that the zigzag gadgets
+can actually uh navigate around uh and
+
+ align:start position:0%
+can actually uh navigate around uh and
+ 
+
+ align:start position:0%
+can actually uh navigate around uh and
+not across each other with height eight
+
+ align:start position:0%
+not across each other with height eight
+ 
+
+ align:start position:0%
+not across each other with height eight
+um and that at the end you can fill all
+
+ align:start position:0%
+um and that at the end you can fill all
+ 
+
+ align:start position:0%
+um and that at the end you can fill all
+the blank space if you're just organized
+
+ align:start position:0%
+the blank space if you're just organized
+ 
+
+ align:start position:0%
+the blank space if you're just organized
+about you Traverse each of the AIS uh
+
+ align:start position:0%
+about you Traverse each of the AIS uh
+ 
+
+ align:start position:0%
+about you Traverse each of the AIS uh
+and where you put the blank space I
+
+ align:start position:0%
+and where you put the blank space I
+ 
+
+ align:start position:0%
+and where you put the blank space I
+think we just leave some Headroom so you
+
+ align:start position:0%
+think we just leave some Headroom so you
+ 
+
+ align:start position:0%
+think we just leave some Headroom so you
+can just go up walk over to where all
+
+ align:start position:0%
+can just go up walk over to where all
+ 
+
+ align:start position:0%
+can just go up walk over to where all
+the blank space is just sered to a scan
+
+ align:start position:0%
+the blank space is just sered to a scan
+ 
+
+ align:start position:0%
+the blank space is just sered to a scan
+line traversal wherever there's Blank
+
+ align:start position:0%
+line traversal wherever there's Blank
+ 
+
+ align:start position:0%
+line traversal wherever there's Blank
+Space you eat it up with your zigzag at
+
+ align:start position:0%
+Space you eat it up with your zigzag at
+ 
+
+ align:start position:0%
+Space you eat it up with your zigzag at
+the end so all what this does is it lets
+
+ align:start position:0%
+the end so all what this does is it lets
+ 
+
+ align:start position:0%
+the end so all what this does is it lets
+the AIS move around completely freely uh
+
+ align:start position:0%
+the AIS move around completely freely uh
+ 
+
+ align:start position:0%
+the AIS move around completely freely uh
+there's no there shouldn't be any
+
+ align:start position:0%
+there's no there shouldn't be any
+ 
+
+ align:start position:0%
+there's no there shouldn't be any
+constraints on how the AIS are assigned
+
+ align:start position:0%
+constraints on how the AIS are assigned
+ 
+
+ align:start position:0%
+constraints on how the AIS are assigned
+to these uh Pockets because we want
+
+ align:start position:0%
+to these uh Pockets because we want
+ 
+
+ align:start position:0%
+to these uh Pockets because we want
+every solution to the three partition
+
+ align:start position:0%
+every solution to the three partition
+ 
+
+ align:start position:0%
+every solution to the three partition
+instance to work here and the zigzags
+
+ align:start position:0%
+instance to work here and the zigzags
+ 
+
+ align:start position:0%
+instance to work here and the zigzags
+let us do that because they're so
+
+ align:start position:0%
+let us do that because they're so
+ 
+
+ align:start position:0%
+let us do that because they're so
+Universal
+
+ align:start position:0%
+Universal
+ 
+
+ align:start position:0%
+Universal
+cool so I think that's what I wanted to
+
+ align:start position:0%
+cool so I think that's what I wanted to
+ 
+
+ align:start position:0%
+cool so I think that's what I wanted to
+say about this proof let me double check
+
+ align:start position:0%
+say about this proof let me double check
+ 
+
+ align:start position:0%
+say about this proof let me double check
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+notes uh there was one other thing uh
+
+ align:start position:0%
+notes uh there was one other thing uh
+ 
+
+ align:start position:0%
+notes uh there was one other thing uh
+which I found a little funny uh
+
+ align:start position:0%
+which I found a little funny uh
+ 
+
+ align:start position:0%
+which I found a little funny uh
+rereading this paper is why eight
+
+ align:start position:0%
+rereading this paper is why eight
+ 
+
+ align:start position:0%
+rereading this paper is why eight
+because uh we know everything has to
+
+ align:start position:0%
+because uh we know everything has to
+ 
+
+ align:start position:0%
+because uh we know everything has to
+scale up by a factor of four but uh and
+
+ align:start position:0%
+scale up by a factor of four but uh and
+ 
+
+ align:start position:0%
+scale up by a factor of four but uh and
+that's that's all we're doing in some
+
+ align:start position:0%
+that's that's all we're doing in some
+ 
+
+ align:start position:0%
+that's that's all we're doing in some
+sense but we do make these uh we scale
+
+ align:start position:0%
+sense but we do make these uh we scale
+ 
+
+ align:start position:0%
+sense but we do make these uh we scale
+all the AIS by a factor of eight
+
+ align:start position:0%
+all the AIS by a factor of eight
+ 
+
+ align:start position:0%
+all the AIS by a factor of eight
+not a big deal but there's a reason for
+
+ align:start position:0%
+not a big deal but there's a reason for
+ 
+
+ align:start position:0%
+not a big deal but there's a reason for
+eight um if we just did
+
+ align:start position:0%
+eight um if we just did
+ 
+
+ align:start position:0%
+eight um if we just did
+four uh and
+
+ align:start position:0%
+four uh and
+ 
+
+ align:start position:0%
+four uh and
+say yeah um so we want to go uh so this
+
+ align:start position:0%
+say yeah um so we want to go uh so this
+ 
+
+ align:start position:0%
+say yeah um so we want to go uh so this
+thing gets mapped onto here and we go
+
+ align:start position:0%
+thing gets mapped onto here and we go
+ 
+
+ align:start position:0%
+thing gets mapped onto here and we go
+out and back and out and back if we just
+
+ align:start position:0%
+out and back and out and back if we just
+ 
+
+ align:start position:0%
+out and back and out and back if we just
+did it four times we would be arriving
+
+ align:start position:0%
+did it four times we would be arriving
+ 
+
+ align:start position:0%
+did it four times we would be arriving
+at basically the same position in the
+
+ align:start position:0%
+at basically the same position in the
+ 
+
+ align:start position:0%
+at basically the same position in the
+4x4x4 block or sorry we would be
+
+ align:start position:0%
+4x4x4 block or sorry we would be
+ 
+
+ align:start position:0%
+4x4x4 block or sorry we would be
+arriving at the same 4x4x4 block that we
+
+ align:start position:0%
+arriving at the same 4x4x4 block that we
+ 
+
+ align:start position:0%
+arriving at the same 4x4x4 block that we
+started from that's not good because we
+
+ align:start position:0%
+started from that's not good because we
+ 
+
+ align:start position:0%
+started from that's not good because we
+can only visit a block once so this is
+
+ align:start position:0%
+can only visit a block once so this is
+ 
+
+ align:start position:0%
+can only visit a block once so this is
+sort of an interface issue between the
+
+ align:start position:0%
+sort of an interface issue between the
+ 
+
+ align:start position:0%
+sort of an interface issue between the
+zigzag which is nice and Universal you
+
+ align:start position:0%
+zigzag which is nice and Universal you
+ 
+
+ align:start position:0%
+zigzag which is nice and Universal you
+can always paste two of these chains
+
+ align:start position:0%
+can always paste two of these chains
+ 
+
+ align:start position:0%
+can always paste two of these chains
+together no problem whereas with this
+
+ align:start position:0%
+together no problem whereas with this
+ 
+
+ align:start position:0%
+together no problem whereas with this
+thing which is not Universal it folds
+
+ align:start position:0%
+thing which is not Universal it folds
+ 
+
+ align:start position:0%
+thing which is not Universal it folds
+into basically the shape um that's it so
+
+ align:start position:0%
+into basically the shape um that's it so
+ 
+
+ align:start position:0%
+into basically the shape um that's it so
+uh we need to make sure that um I mean
+
+ align:start position:0%
+uh we need to make sure that um I mean
+ 
+
+ align:start position:0%
+uh we need to make sure that um I mean
+we can universally do whatever we want
+
+ align:start position:0%
+we can universally do whatever we want
+ 
+
+ align:start position:0%
+we can universally do whatever we want
+in here but we need to make sure that
+
+ align:start position:0%
+in here but we need to make sure that
+ 
+
+ align:start position:0%
+in here but we need to make sure that
+when we connect between this zigzag
+
+ align:start position:0%
+when we connect between this zigzag
+ 
+
+ align:start position:0%
+when we connect between this zigzag
+structure and then we paste in one of
+
+ align:start position:0%
+structure and then we paste in one of
+ 
+
+ align:start position:0%
+structure and then we paste in one of
+these and then we come back that we do
+
+ align:start position:0%
+these and then we come back that we do
+ 
+
+ align:start position:0%
+these and then we come back that we do
+that in a valid way from the perspective
+
+ align:start position:0%
+that in a valid way from the perspective
+ 
+
+ align:start position:0%
+that in a valid way from the perspective
+Ive of this big chunk so the the factor
+
+ align:start position:0%
+Ive of this big chunk so the the factor
+ 
+
+ align:start position:0%
+Ive of this big chunk so the the factor
+of eight makes sure that we if we leave
+
+ align:start position:0%
+of eight makes sure that we if we leave
+ 
+
+ align:start position:0%
+of eight makes sure that we if we leave
+from one 4x4x4 Chunk we come back on a
+
+ align:start position:0%
+from one 4x4x4 Chunk we come back on a
+ 
+
+ align:start position:0%
+from one 4x4x4 Chunk we come back on a
+different one and then it's easy to
+
+ align:start position:0%
+different one and then it's easy to
+ 
+
+ align:start position:0%
+different one and then it's easy to
+paste all the paths
+
+ align:start position:0%
+paste all the paths
+ 
+
+ align:start position:0%
+paste all the paths
+together so that is uh hths yeah I don't
+
+ align:start position:0%
+together so that is uh hths yeah I don't
+ 
+
+ align:start position:0%
+together so that is uh hths yeah I don't
+quite see that this proves that snake
+
+ align:start position:0%
+quite see that this proves that snake
+ 
+
+ align:start position:0%
+quite see that this proves that snake
+cube is empty right ah yeah there's one
+
+ align:start position:0%
+cube is empty right ah yeah there's one
+ 
+
+ align:start position:0%
+cube is empty right ah yeah there's one
+more issue which is uh this was folding
+
+ align:start position:0%
+more issue which is uh this was folding
+ 
+
+ align:start position:0%
+more issue which is uh this was folding
+this shape but we want to fold a cube
+
+ align:start position:0%
+this shape but we want to fold a cube
+ 
+
+ align:start position:0%
+this shape but we want to fold a cube
+yeah this is uh this is the an part of
+
+ align:start position:0%
+yeah this is uh this is the an part of
+ 
+
+ align:start position:0%
+yeah this is uh this is the an part of
+the proof it's very hard to draw um this
+
+ align:start position:0%
+the proof it's very hard to draw um this
+ 
+
+ align:start position:0%
+the proof it's very hard to draw um this
+is my attempt at drawing it and
+
+ align:start position:0%
+is my attempt at drawing it and
+ 
+
+ align:start position:0%
+is my attempt at drawing it and
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so uh I will sketch the idea uh I'll
+
+ align:start position:0%
+so uh I will sketch the idea uh I'll
+ 
+
+ align:start position:0%
+so uh I will sketch the idea uh I'll
+tell you the the first part is
+
+ align:start position:0%
+tell you the the first part is
+ 
+
+ align:start position:0%
+tell you the the first part is
+conceptually easy again hard to draw um
+
+ align:start position:0%
+conceptually easy again hard to draw um
+ 
+
+ align:start position:0%
+conceptually easy again hard to draw um
+the issue is forcing this chain of
+
+ align:start position:0%
+the issue is forcing this chain of
+ 
+
+ align:start position:0%
+the issue is forcing this chain of
+blocks to do anything and one key idea
+
+ align:start position:0%
+blocks to do anything and one key idea
+ 
+
+ align:start position:0%
+blocks to do anything and one key idea
+is if you want to fold let's say a k by
+
+ align:start position:0%
+is if you want to fold let's say a k by
+ 
+
+ align:start position:0%
+is if you want to fold let's say a k by
+K by K box if you have a straight path
+
+ align:start position:0%
+K by K box if you have a straight path
+ 
+
+ align:start position:0%
+K by K box if you have a straight path
+of length
+
+ align:start position:0%
+of length
+ 
+
+ align:start position:0%
+of length
+K uh there AR very many places you can
+
+ align:start position:0%
+K uh there AR very many places you can
+ 
+
+ align:start position:0%
+K uh there AR very many places you can
+put that I mean there I guess there are
+
+ align:start position:0%
+put that I mean there I guess there are
+ 
+
+ align:start position:0%
+put that I mean there I guess there are
+still Cas orders K squared of them um
+
+ align:start position:0%
+still Cas orders K squared of them um
+ 
+
+ align:start position:0%
+still Cas orders K squared of them um
+but you you have to start and end at the
+
+ align:start position:0%
+but you you have to start and end at the
+ 
+
+ align:start position:0%
+but you you have to start and end at the
+beginning and end of the of the overall
+
+ align:start position:0%
+beginning and end of the of the overall
+ 
+
+ align:start position:0%
+beginning and end of the of the overall
+Cube if you have a full length of
+
+ align:start position:0%
+Cube if you have a full length of
+ 
+
+ align:start position:0%
+Cube if you have a full length of
+straight so the first step we do is take
+
+ align:start position:0%
+straight so the first step we do is take
+ 
+
+ align:start position:0%
+straight so the first step we do is take
+your oh sorry the this is the first step
+
+ align:start position:0%
+your oh sorry the this is the first step
+ 
+
+ align:start position:0%
+your oh sorry the this is the first step
+it's upside down because we're doing
+
+ align:start position:0%
+it's upside down because we're doing
+ 
+
+ align:start position:0%
+it's upside down because we're doing
+things in reverse order so first thing
+
+ align:start position:0%
+things in reverse order so first thing
+ 
+
+ align:start position:0%
+things in reverse order so first thing
+we do is we take a Target Cube and we're
+
+ align:start position:0%
+we do is we take a Target Cube and we're
+ 
+
+ align:start position:0%
+we do is we take a Target Cube and we're
+basically going to have a lot of really
+
+ align:start position:0%
+basically going to have a lot of really
+ 
+
+ align:start position:0%
+basically going to have a lot of really
+long guys will force you to in in a row
+
+ align:start position:0%
+long guys will force you to in in a row
+ 
+
+ align:start position:0%
+long guys will force you to in in a row
+and you see that in these kinds of
+
+ align:start position:0%
+and you see that in these kinds of
+ 
+
+ align:start position:0%
+and you see that in these kinds of
+puzzles you tend to have uh Straits of
+
+ align:start position:0%
+puzzles you tend to have uh Straits of
+ 
+
+ align:start position:0%
+puzzles you tend to have uh Straits of
+length three like this this um these are
+
+ align:start position:0%
+length three like this this um these are
+ 
+
+ align:start position:0%
+length three like this this um these are
+three threes in a row and we're making a
+
+ align:start position:0%
+three threes in a row and we're making a
+ 
+
+ align:start position:0%
+three threes in a row and we're making a
+3x3x3 Cub so that sort of has that has
+
+ align:start position:0%
+3x3x3 Cub so that sort of has that has
+ 
+
+ align:start position:0%
+3x3x3 Cub so that sort of has that has
+to live in well it can do weird things
+
+ align:start position:0%
+to live in well it can do weird things
+ 
+
+ align:start position:0%
+to live in well it can do weird things
+but it's relatively restricted maybe you
+
+ align:start position:0%
+but it's relatively restricted maybe you
+ 
+
+ align:start position:0%
+but it's relatively restricted maybe you
+can do something like this but then
+
+ align:start position:0%
+can do something like this but then
+ 
+
+ align:start position:0%
+can do something like this but then
+these must be the edges of the cube in
+
+ align:start position:0%
+these must be the edges of the cube in
+ 
+
+ align:start position:0%
+these must be the edges of the cube in
+that case so we have a bunch of those
+
+ align:start position:0%
+that case so we have a bunch of those
+ 
+
+ align:start position:0%
+that case so we have a bunch of those
+and lots of care and we end up reducing
+
+ align:start position:0%
+and lots of care and we end up reducing
+ 
+
+ align:start position:0%
+and lots of care and we end up reducing
+the cube to a box meaning we cover all
+
+ align:start position:0%
+the cube to a box meaning we cover all
+ 
+
+ align:start position:0%
+the cube to a box meaning we cover all
+of the cube we're forced to cover all of
+
+ align:start position:0%
+of the cube we're forced to cover all of
+ 
+
+ align:start position:0%
+of the cube we're forced to cover all of
+the cube and leave exactly a box behind
+
+ align:start position:0%
+the cube and leave exactly a box behind
+ 
+
+ align:start position:0%
+the cube and leave exactly a box behind
+sort of like what we did when we were
+
+ align:start position:0%
+sort of like what we did when we were
+ 
+
+ align:start position:0%
+sort of like what we did when we were
+doing squares into square we'd put a
+
+ align:start position:0%
+doing squares into square we'd put a
+ 
+
+ align:start position:0%
+doing squares into square we'd put a
+bunch of big boxes that were relatively
+
+ align:start position:0%
+bunch of big boxes that were relatively
+ 
+
+ align:start position:0%
+bunch of big boxes that were relatively
+constrained and it just left a empty
+
+ align:start position:0%
+constrained and it just left a empty
+ 
+
+ align:start position:0%
+constrained and it just left a empty
+space which is a box here it's actually
+
+ align:start position:0%
+space which is a box here it's actually
+ 
+
+ align:start position:0%
+space which is a box here it's actually
+forced
+
+ align:start position:0%
+forced
+ 
+
+ align:start position:0%
+forced
+exactly then once we have a box so the
+
+ align:start position:0%
+exactly then once we have a box so the
+ 
+
+ align:start position:0%
+exactly then once we have a box so the
+Box will be this wide and it will go
+
+ align:start position:0%
+Box will be this wide and it will go
+ 
+
+ align:start position:0%
+Box will be this wide and it will go
+over this way um and but it won't have
+
+ align:start position:0%
+over this way um and but it won't have
+ 
+
+ align:start position:0%
+over this way um and but it won't have
+this sort of fine feature stuff this
+
+ align:start position:0%
+this sort of fine feature stuff this
+ 
+
+ align:start position:0%
+this sort of fine feature stuff this
+will just all be filled in as a box then
+
+ align:start position:0%
+will just all be filled in as a box then
+ 
+
+ align:start position:0%
+will just all be filled in as a box then
+uh this step that's drawn is to carve
+
+ align:start position:0%
+uh this step that's drawn is to carve
+ 
+
+ align:start position:0%
+uh this step that's drawn is to carve
+out this uh Hub and spoke shape uh and
+
+ align:start position:0%
+out this uh Hub and spoke shape uh and
+ 
+
+ align:start position:0%
+out this uh Hub and spoke shape uh and
+that's based on a structure like this
+
+ align:start position:0%
+that's based on a structure like this
+ 
+
+ align:start position:0%
+that's based on a structure like this
+where you have a a huge thing and then a
+
+ align:start position:0%
+where you have a a huge thing and then a
+ 
+
+ align:start position:0%
+where you have a a huge thing and then a
+relatively short thing of length about
+
+ align:start position:0%
+relatively short thing of length about
+ 
+
+ align:start position:0%
+relatively short thing of length about
+8T and then we go down and then
+
+ align:start position:0%
+8T and then we go down and then
+ 
+
+ align:start position:0%
+8T and then we go down and then
+immediately back up and then over and
+
+ align:start position:0%
+immediately back up and then over and
+ 
+
+ align:start position:0%
+immediately back up and then over and
+down and up and and so on
+
+ align:start position:0%
+down and up and and so on
+ 
+
+ align:start position:0%
+down and up and and so on
+and you that roughly carves out this
+
+ align:start position:0%
+and you that roughly carves out this
+ 
+
+ align:start position:0%
+and you that roughly carves out this
+structure now you have to be careful
+
+ align:start position:0%
+structure now you have to be careful
+ 
+
+ align:start position:0%
+structure now you have to be careful
+that this is actually unique
+
+ align:start position:0%
+that this is actually unique
+ 
+
+ align:start position:0%
+that this is actually unique
+uh but we have some this is why we only
+
+ align:start position:0%
+uh but we have some this is why we only
+ 
+
+ align:start position:0%
+uh but we have some this is why we only
+want the height of this box to be eight
+
+ align:start position:0%
+want the height of this box to be eight
+ 
+
+ align:start position:0%
+want the height of this box to be eight
+because then you can't go out of plane
+
+ align:start position:0%
+because then you can't go out of plane
+ 
+
+ align:start position:0%
+because then you can't go out of plane
+very much and this while this is short
+
+ align:start position:0%
+very much and this while this is short
+ 
+
+ align:start position:0%
+very much and this while this is short
+it's longer than eight if T is bigger
+
+ align:start position:0%
+it's longer than eight if T is bigger
+ 
+
+ align:start position:0%
+it's longer than eight if T is bigger
+than one so um you can't have this spoke
+
+ align:start position:0%
+than one so um you can't have this spoke
+ 
+
+ align:start position:0%
+than one so um you can't have this spoke
+go up so it does have to live in a
+
+ align:start position:0%
+go up so it does have to live in a
+ 
+
+ align:start position:0%
+go up so it does have to live in a
+plane uh sounds right and this is much
+
+ align:start position:0%
+plane uh sounds right and this is much
+ 
+
+ align:start position:0%
+plane uh sounds right and this is much
+smaller than huge so you can't fold it
+
+ align:start position:0%
+smaller than huge so you can't fold it
+ 
+
+ align:start position:0%
+smaller than huge so you can't fold it
+some other way uh so that's pretty much
+
+ align:start position:0%
+some other way uh so that's pretty much
+ 
+
+ align:start position:0%
+some other way uh so that's pretty much
+forced and then we have to get rid of
+
+ align:start position:0%
+forced and then we have to get rid of
+ 
+
+ align:start position:0%
+forced and then we have to get rid of
+the other uh seven planes which we do
+
+ align:start position:0%
+the other uh seven planes which we do
+ 
+
+ align:start position:0%
+the other uh seven planes which we do
+with really long guys so uh
+
+ align:start position:0%
+with really long guys so uh
+ 
+
+ align:start position:0%
+with really long guys so uh
+unfortunately we don't have all of that
+
+ align:start position:0%
+unfortunately we don't have all of that
+ 
+
+ align:start position:0%
+unfortunately we don't have all of that
+drawn so it's especially hard to see but
+
+ align:start position:0%
+drawn so it's especially hard to see but
+ 
+
+ align:start position:0%
+drawn so it's especially hard to see but
+this is a rough idea of how you start
+
+ align:start position:0%
+this is a rough idea of how you start
+ 
+
+ align:start position:0%
+this is a rough idea of how you start
+with a box and you do uh these sort of
+
+ align:start position:0%
+with a box and you do uh these sort of
+ 
+
+ align:start position:0%
+with a box and you do uh these sort of
+infrastructure gadgets to just carve out
+
+ align:start position:0%
+infrastructure gadgets to just carve out
+ 
+
+ align:start position:0%
+infrastructure gadgets to just carve out
+the shape you want and then it's then
+
+ align:start position:0%
+the shape you want and then it's then
+ 
+
+ align:start position:0%
+the shape you want and then it's then
+you go into the interesting part of the
+
+ align:start position:0%
+you go into the interesting part of the
+ 
+
+ align:start position:0%
+you go into the interesting part of the
+chain this is all at the beginning of
+
+ align:start position:0%
+chain this is all at the beginning of
+ 
+
+ align:start position:0%
+chain this is all at the beginning of
+the chain and it's you show it's forced
+
+ align:start position:0%
+the chain and it's you show it's forced
+ 
+
+ align:start position:0%
+the chain and it's you show it's forced
+to do all this and then we start say
+
+ align:start position:0%
+to do all this and then we start say
+ 
+
+ align:start position:0%
+to do all this and then we start say
+here with some zigzag and then an AI
+
+ align:start position:0%
+here with some zigzag and then an AI
+ 
+
+ align:start position:0%
+here with some zigzag and then an AI
+Gadget and so on yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy right so um you do see here I would
+
+ align:start position:0%
+easy right so um you do see here I would
+ 
+
+ align:start position:0%
+easy right so um you do see here I would
+say a very uh algorithmic approach I
+
+ align:start position:0%
+say a very uh algorithmic approach I
+ 
+
+ align:start position:0%
+say a very uh algorithmic approach I
+mean this idea of showing that uh
+
+ align:start position:0%
+mean this idea of showing that uh
+ 
+
+ align:start position:0%
+mean this idea of showing that uh
+zigzags are Universal they can make any
+
+ align:start position:0%
+zigzags are Universal they can make any
+ 
+
+ align:start position:0%
+zigzags are Universal they can make any
+shape this is something we do in
+
+ align:start position:0%
+shape this is something we do in
+ 
+
+ align:start position:0%
+shape this is something we do in
+computational Geometry all the time we
+
+ align:start position:0%
+computational Geometry all the time we
+ 
+
+ align:start position:0%
+computational Geometry all the time we
+Pro that these folding structures fold
+
+ align:start position:0%
+Pro that these folding structures fold
+ 
+
+ align:start position:0%
+Pro that these folding structures fold
+into whatever we want so we uh and we
+
+ align:start position:0%
+into whatever we want so we uh and we
+ 
+
+ align:start position:0%
+into whatever we want so we uh and we
+hadn't proved this one before but we
+
+ align:start position:0%
+hadn't proved this one before but we
+ 
+
+ align:start position:0%
+hadn't proved this one before but we
+were armed with a lot of algorithmic
+
+ align:start position:0%
+were armed with a lot of algorithmic
+ 
+
+ align:start position:0%
+were armed with a lot of algorithmic
+tools to do this and that led us do this
+
+ align:start position:0%
+tools to do this and that led us do this
+ 
+
+ align:start position:0%
+tools to do this and that led us do this
+reduction so lower bounds in our case is
+
+ align:start position:0%
+reduction so lower bounds in our case is
+ 
+
+ align:start position:0%
+reduction so lower bounds in our case is
+really all about designing the right
+
+ align:start position:0%
+really all about designing the right
+ 
+
+ align:start position:0%
+really all about designing the right
+algorithms uh to give you powerful
+
+ align:start position:0%
+algorithms uh to give you powerful
+ 
+
+ align:start position:0%
+algorithms uh to give you powerful
+gadgets like this that's why this is the
+
+ align:start position:0%
+gadgets like this that's why this is the
+ 
+
+ align:start position:0%
+gadgets like this that's why this is the
+class called algorithmic Lower
+
+ align:start position:0%
+class called algorithmic Lower
+ 
+
+ align:start position:0%
+class called algorithmic Lower
+bounds um other questions about snake
+
+ align:start position:0%
+bounds um other questions about snake
+ 
+
+ align:start position:0%
+bounds um other questions about snake
+cubes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Adam uh I think we want it to be a
+
+ align:start position:0%
+Adam uh I think we want it to be a
+ 
+
+ align:start position:0%
+Adam uh I think we want it to be a
+multiple of
+
+ align:start position:0%
+multiple of
+ 
+
+ align:start position:0%
+multiple of
+four uh so that it's compatible with the
+
+ align:start position:0%
+four uh so that it's compatible with the
+ 
+
+ align:start position:0%
+four uh so that it's compatible with the
+grid six yeah that seems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cleaner that way we can predict if we
+
+ align:start position:0%
+cleaner that way we can predict if we
+ 
+
+ align:start position:0%
+cleaner that way we can predict if we
+leave on this 4x4x4 thing we know which
+
+ align:start position:0%
+leave on this 4x4x4 thing we know which
+ 
+
+ align:start position:0%
+leave on this 4x4x4 thing we know which
+one will come back on whereas if it's
+
+ align:start position:0%
+one will come back on whereas if it's
+ 
+
+ align:start position:0%
+one will come back on whereas if it's
+could be in a half grid position that
+
+ align:start position:0%
+could be in a half grid position that
+ 
+
+ align:start position:0%
+could be in a half grid position that
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+messy other
+
+ align:start position:0%
+messy other
+ 
+
+ align:start position:0%
+messy other
+questions I you might be able to make
+
+ align:start position:0%
+questions I you might be able to make
+ 
+
+ align:start position:0%
+questions I you might be able to make
+that to work but the advantage of
+
+ align:start position:0%
+that to work but the advantage of
+ 
+
+ align:start position:0%
+that to work but the advantage of
+hardness proofs because it's not a real
+
+ align:start position:0%
+hardness proofs because it's not a real
+ 
+
+ align:start position:0%
+hardness proofs because it's not a real
+algorithm I mean it's not an algorithm
+
+ align:start position:0%
+algorithm I mean it's not an algorithm
+ 
+
+ align:start position:0%
+algorithm I mean it's not an algorithm
+you want to run the point is to show
+
+ align:start position:0%
+you want to run the point is to show
+ 
+
+ align:start position:0%
+you want to run the point is to show
+this problem is hard you can be
+
+ align:start position:0%
+this problem is hard you can be
+ 
+
+ align:start position:0%
+this problem is hard you can be
+inefficient in lots of places as long as
+
+ align:start position:0%
+inefficient in lots of places as long as
+ 
+
+ align:start position:0%
+inefficient in lots of places as long as
+it's still polinomial it doesn't really
+
+ align:start position:0%
+it's still polinomial it doesn't really
+ 
+
+ align:start position:0%
+it's still polinomial it doesn't really
+matter except for drawing the pictures
+
+ align:start position:0%
+matter except for drawing the pictures
+ 
+
+ align:start position:0%
+matter except for drawing the pictures
+that's one place where it
+
+ align:start position:0%
+that's one place where it
+ 
+
+ align:start position:0%
+that's one place where it
+matters all right that's snake cubes uh
+
+ align:start position:0%
+matters all right that's snake cubes uh
+ 
+
+ align:start position:0%
+matters all right that's snake cubes uh
+going to go on to another packing
+
+ align:start position:0%
+going to go on to another packing
+ 
+
+ align:start position:0%
+going to go on to another packing
+problem so we've seen rectangles into
+
+ align:start position:0%
+problem so we've seen rectangles into
+ 
+
+ align:start position:0%
+problem so we've seen rectangles into
+squares squares into squares how about
+
+ align:start position:0%
+squares squares into squares how about
+ 
+
+ align:start position:0%
+squares squares into squares how about
+circles into
+
+ align:start position:0%
+circles into
+ 
+
+ align:start position:0%
+circles into
+squares um so this is a real life puzzle
+
+ align:start position:0%
+squares um so this is a real life puzzle
+ 
+
+ align:start position:0%
+squares um so this is a real life puzzle
+uh where you have these uh I think
+
+ align:start position:0%
+uh where you have these uh I think
+ 
+
+ align:start position:0%
+uh where you have these uh I think
+they're waterjet cut or laser cut uh
+
+ align:start position:0%
+they're waterjet cut or laser cut uh
+ 
+
+ align:start position:0%
+they're waterjet cut or laser cut uh
+metal discs and you have to fit them
+
+ align:start position:0%
+metal discs and you have to fit them
+ 
+
+ align:start position:0%
+metal discs and you have to fit them
+into this box uh so these are real life
+
+ align:start position:0%
+into this box uh so these are real life
+ 
+
+ align:start position:0%
+into this box uh so these are real life
+puzzles that's one motivation uh there's
+
+ align:start position:0%
+puzzles that's one motivation uh there's
+ 
+
+ align:start position:0%
+puzzles that's one motivation uh there's
+a stronger motivation for studying this
+
+ align:start position:0%
+a stronger motivation for studying this
+ 
+
+ align:start position:0%
+a stronger motivation for studying this
+problem because it's related to
+
+ align:start position:0%
+problem because it's related to
+ 
+
+ align:start position:0%
+problem because it's related to
+computational origami there's this
+
+ align:start position:0%
+computational origami there's this
+ 
+
+ align:start position:0%
+computational origami there's this
+method called the tree method of or
+
+ align:start position:0%
+method called the tree method of or
+ 
+
+ align:start position:0%
+method called the tree method of or
+origami design uh if you're interested
+
+ align:start position:0%
+origami design uh if you're interested
+ 
+
+ align:start position:0%
+origami design uh if you're interested
+in it you can take 6849 or read Robert
+
+ align:start position:0%
+in it you can take 6849 or read Robert
+ 
+
+ align:start position:0%
+in it you can take 6849 or read Robert
+Lang's book uh origami design secrets
+
+ align:start position:0%
+Lang's book uh origami design secrets
+ 
+
+ align:start position:0%
+Lang's book uh origami design secrets
+and basically it lets you fold things
+
+ align:start position:0%
+and basically it lets you fold things
+ 
+
+ align:start position:0%
+and basically it lets you fold things
+like this um that's at a high level you
+
+ align:start position:0%
+like this um that's at a high level you
+ 
+
+ align:start position:0%
+like this um that's at a high level you
+and a key key component of it is to pack
+
+ align:start position:0%
+and a key key component of it is to pack
+ 
+
+ align:start position:0%
+and a key key component of it is to pack
+discs into a square the square is your
+
+ align:start position:0%
+discs into a square the square is your
+ 
+
+ align:start position:0%
+discs into a square the square is your
+piece of paper the discs correspond to
+
+ align:start position:0%
+piece of paper the discs correspond to
+ 
+
+ align:start position:0%
+piece of paper the discs correspond to
+sort of the limbs of your creature and
+
+ align:start position:0%
+sort of the limbs of your creature and
+ 
+
+ align:start position:0%
+sort of the limbs of your creature and
+uh you can't use the same piece of paper
+
+ align:start position:0%
+uh you can't use the same piece of paper
+ 
+
+ align:start position:0%
+uh you can't use the same piece of paper
+to represent this Limb and this limb so
+
+ align:start position:0%
+to represent this Limb and this limb so
+ 
+
+ align:start position:0%
+to represent this Limb and this limb so
+the discs have to be disjoint so it's
+
+ align:start position:0%
+the discs have to be disjoint so it's
+ 
+
+ align:start position:0%
+the discs have to be disjoint so it's
+all about pack those discs into given
+
+ align:start position:0%
+all about pack those discs into given
+ 
+
+ align:start position:0%
+all about pack those discs into given
+square and uh yeah so that's at a high
+
+ align:start position:0%
+square and uh yeah so that's at a high
+ 
+
+ align:start position:0%
+square and uh yeah so that's at a high
+level why we care about dis packing and
+
+ align:start position:0%
+level why we care about dis packing and
+ 
+
+ align:start position:0%
+level why we care about dis packing and
+people have thought about dis packing a
+
+ align:start position:0%
+people have thought about dis packing a
+ 
+
+ align:start position:0%
+people have thought about dis packing a
+lot um but surprisingly it hadn't been
+
+ align:start position:0%
+lot um but surprisingly it hadn't been
+ 
+
+ align:start position:0%
+lot um but surprisingly it hadn't been
+proved hard until uh four years ago so
+
+ align:start position:0%
+proved hard until uh four years ago so
+ 
+
+ align:start position:0%
+proved hard until uh four years ago so
+um this proof is also complicated so uh
+
+ align:start position:0%
+um this proof is also complicated so uh
+ 
+
+ align:start position:0%
+um this proof is also complicated so uh
+and it involves a lot of geometry and
+
+ align:start position:0%
+and it involves a lot of geometry and
+ 
+
+ align:start position:0%
+and it involves a lot of geometry and
+trigonometry and some calculus and fun
+
+ align:start position:0%
+trigonometry and some calculus and fun
+ 
+
+ align:start position:0%
+trigonometry and some calculus and fun
+stuff so I'm going to give you a sketch
+
+ align:start position:0%
+stuff so I'm going to give you a sketch
+ 
+
+ align:start position:0%
+stuff so I'm going to give you a sketch
+of it and you should be believable that
+
+ align:start position:0%
+of it and you should be believable that
+ 
+
+ align:start position:0%
+of it and you should be believable that
+this works but the details again are
+
+ align:start position:0%
+this works but the details again are
+ 
+
+ align:start position:0%
+this works but the details again are
+messy um for starters let's say that
+
+ align:start position:0%
+messy um for starters let's say that
+ 
+
+ align:start position:0%
+messy um for starters let's say that
+we're packing discs into a equilateral
+
+ align:start position:0%
+we're packing discs into a equilateral
+ 
+
+ align:start position:0%
+we're packing discs into a equilateral
+triangle this is much easier to work
+
+ align:start position:0%
+triangle this is much easier to work
+ 
+
+ align:start position:0%
+triangle this is much easier to work
+with I'll go to a square in a second so
+
+ align:start position:0%
+with I'll go to a square in a second so
+ 
+
+ align:start position:0%
+with I'll go to a square in a second so
+uh if I have this equilateral triangle
+
+ align:start position:0%
+uh if I have this equilateral triangle
+ 
+
+ align:start position:0%
+uh if I have this equilateral triangle
+what I'm going to do is first I'm going
+
+ align:start position:0%
+what I'm going to do is first I'm going
+ 
+
+ align:start position:0%
+what I'm going to do is first I'm going
+to give you a bunch of discs that are
+
+ align:start position:0%
+to give you a bunch of discs that are
+ 
+
+ align:start position:0%
+to give you a bunch of discs that are
+forced to pack in this nice uh
+
+ align:start position:0%
+forced to pack in this nice uh
+ 
+
+ align:start position:0%
+forced to pack in this nice uh
+triangular grid Arrangement uh leaving
+
+ align:start position:0%
+triangular grid Arrangement uh leaving
+ 
+
+ align:start position:0%
+triangular grid Arrangement uh leaving
+these uh dark
+
+ align:start position:0%
+these uh dark
+ 
+
+ align:start position:0%
+these uh dark
+holes and I'm going to give you more
+
+ align:start position:0%
+holes and I'm going to give you more
+ 
+
+ align:start position:0%
+holes and I'm going to give you more
+discs and so the the more discs have to
+
+ align:start position:0%
+discs and so the the more discs have to
+ 
+
+ align:start position:0%
+discs and so the the more discs have to
+go into those holes and these are
+
+ align:start position:0%
+go into those holes and these are
+ 
+
+ align:start position:0%
+go into those holes and these are
+actually kissing discs they're touching
+
+ align:start position:0%
+actually kissing discs they're touching
+ 
+
+ align:start position:0%
+actually kissing discs they're touching
+uh so you can only put uh every disc you
+
+ align:start position:0%
+uh so you can only put uh every disc you
+ 
+
+ align:start position:0%
+uh so you can only put uh every disc you
+put from now on will be in one of these
+
+ align:start position:0%
+put from now on will be in one of these
+ 
+
+ align:start position:0%
+put from now on will be in one of these
+holes and I'm just going to do this in
+
+ align:start position:0%
+holes and I'm just going to do this in
+ 
+
+ align:start position:0%
+holes and I'm just going to do this in
+big enough so that I have at least n
+
+ align:start position:0%
+big enough so that I have at least n
+ 
+
+ align:start position:0%
+big enough so that I have at least n
+over three holes each hole is going to
+
+ align:start position:0%
+over three holes each hole is going to
+ 
+
+ align:start position:0%
+over three holes each hole is going to
+represent a bin that I'm trying to put a
+
+ align:start position:0%
+represent a bin that I'm trying to put a
+ 
+
+ align:start position:0%
+represent a bin that I'm trying to put a
+triple of numbers into and then uh here
+
+ align:start position:0%
+triple of numbers into and then uh here
+ 
+
+ align:start position:0%
+triple of numbers into and then uh here
+is the construction for uh I guess this
+
+ align:start position:0%
+is the construction for uh I guess this
+ 
+
+ align:start position:0%
+is the construction for uh I guess this
+would be a three partition Gadget uh we
+
+ align:start position:0%
+would be a three partition Gadget uh we
+ 
+
+ align:start position:0%
+would be a three partition Gadget uh we
+want to get that slight type of the AI
+
+ align:start position:0%
+want to get that slight type of the AI
+ 
+
+ align:start position:0%
+want to get that slight type of the AI
+plus AJ plus a
+
+ align:start position:0%
+plus AJ plus a
+ 
+
+ align:start position:0%
+plus AJ plus a
+is less than equal to T um and so these
+
+ align:start position:0%
+is less than equal to T um and so these
+ 
+
+ align:start position:0%
+is less than equal to T um and so these
+are the three discs representing AI AJ
+
+ align:start position:0%
+are the three discs representing AI AJ
+ 
+
+ align:start position:0%
+are the three discs representing AI AJ
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a and there's an extra disc in the
+
+ align:start position:0%
+a and there's an extra disc in the
+ 
+
+ align:start position:0%
+a and there's an extra disc in the
+center and what's drawn here is
+
+ align:start position:0%
+center and what's drawn here is
+ 
+
+ align:start position:0%
+center and what's drawn here is
+everything is maybe tight and as
+
+ align:start position:0%
+everything is maybe tight and as
+ 
+
+ align:start position:0%
+everything is maybe tight and as
+touching but we're going to shrink these
+
+ align:start position:0%
+touching but we're going to shrink these
+ 
+
+ align:start position:0%
+touching but we're going to shrink these
+discs a little bit uh or rather I'm
+
+ align:start position:0%
+discs a little bit uh or rather I'm
+ 
+
+ align:start position:0%
+discs a little bit uh or rather I'm
+going to shrink uh yeah I guess I'll
+
+ align:start position:0%
+going to shrink uh yeah I guess I'll
+ 
+
+ align:start position:0%
+going to shrink uh yeah I guess I'll
+shrink well get this right I'm going to
+
+ align:start position:0%
+shrink well get this right I'm going to
+ 
+
+ align:start position:0%
+shrink well get this right I'm going to
+shrink this disc a little bit and I'm
+
+ align:start position:0%
+shrink this disc a little bit and I'm
+ 
+
+ align:start position:0%
+shrink this disc a little bit and I'm
+going to make these ones a little bit
+
+ align:start position:0%
+going to make these ones a little bit
+ 
+
+ align:start position:0%
+going to make these ones a little bit
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+according to the AI values um so this
+
+ align:start position:0%
+according to the AI values um so this
+ 
+
+ align:start position:0%
+according to the AI values um so this
+one will be proportional to AK larger
+
+ align:start position:0%
+one will be proportional to AK larger
+ 
+
+ align:start position:0%
+one will be proportional to AK larger
+than the disc that would perfectly fit
+
+ align:start position:0%
+than the disc that would perfectly fit
+ 
+
+ align:start position:0%
+than the disc that would perfectly fit
+here if this one was maximally sized and
+
+ align:start position:0%
+here if this one was maximally sized and
+ 
+
+ align:start position:0%
+here if this one was maximally sized and
+so that's going to force this guy to
+
+ align:start position:0%
+so that's going to force this guy to
+ 
+
+ align:start position:0%
+so that's going to force this guy to
+move away well he's a little bit shrunk
+
+ align:start position:0%
+move away well he's a little bit shrunk
+ 
+
+ align:start position:0%
+move away well he's a little bit shrunk
+so maybe he doesn't have to move away um
+
+ align:start position:0%
+so maybe he doesn't have to move away um
+ 
+
+ align:start position:0%
+so maybe he doesn't have to move away um
+but this Center disc when it's shrunk
+
+ align:start position:0%
+but this Center disc when it's shrunk
+ 
+
+ align:start position:0%
+but this Center disc when it's shrunk
+down it has a little bit of flexibility
+
+ align:start position:0%
+down it has a little bit of flexibility
+ 
+
+ align:start position:0%
+down it has a little bit of flexibility
+it could move more this way if this disc
+
+ align:start position:0%
+it could move more this way if this disc
+ 
+
+ align:start position:0%
+it could move more this way if this disc
+is smaller it will move more this way it
+
+ align:start position:0%
+is smaller it will move more this way it
+ 
+
+ align:start position:0%
+is smaller it will move more this way it
+can move more this way more this way and
+
+ align:start position:0%
+can move more this way more this way and
+ 
+
+ align:start position:0%
+can move more this way more this way and
+in general you show that um these so
+
+ align:start position:0%
+in general you show that um these so
+ 
+
+ align:start position:0%
+in general you show that um these so
+these guys are sort of placing demands
+
+ align:start position:0%
+these guys are sort of placing demands
+ 
+
+ align:start position:0%
+these guys are sort of placing demands
+by being a little bit bigger they need
+
+ align:start position:0%
+by being a little bit bigger they need
+ 
+
+ align:start position:0%
+by being a little bit bigger they need
+to push out uh and this one is a little
+
+ align:start position:0%
+to push out uh and this one is a little
+ 
+
+ align:start position:0%
+to push out uh and this one is a little
+bit smaller and its size is just a
+
+ align:start position:0%
+bit smaller and its size is just a
+ 
+
+ align:start position:0%
+bit smaller and its size is just a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+T and so it's going to move around and
+
+ align:start position:0%
+T and so it's going to move around and
+ 
+
+ align:start position:0%
+T and so it's going to move around and
+the claim is uh it has a valid position
+
+ align:start position:0%
+the claim is uh it has a valid position
+ 
+
+ align:start position:0%
+the claim is uh it has a valid position
+if and only if a i plus AJ plus a k is
+
+ align:start position:0%
+if and only if a i plus AJ plus a k is
+ 
+
+ align:start position:0%
+if and only if a i plus AJ plus a k is
+less than equal to T I have written down
+
+ align:start position:0%
+less than equal to T I have written down
+ 
+
+ align:start position:0%
+less than equal to T I have written down
+a little bit of the
+
+ align:start position:0%
+a little bit of the
+ 
+
+ align:start position:0%
+a little bit of the
+details um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to choose some big number
+
+ align:start position:0%
+so we're going to choose some big number
+ 
+
+ align:start position:0%
+so we're going to choose some big number
+capital N maybe it's like n to the 100
+
+ align:start position:0%
+capital N maybe it's like n to the 100
+ 
+
+ align:start position:0%
+capital N maybe it's like n to the 100
+little n to the 100 something like that
+
+ align:start position:0%
+little n to the 100 something like that
+ 
+
+ align:start position:0%
+little n to the 100 something like that
+and we'll shrink the big disc by that
+
+ align:start position:0%
+and we'll shrink the big disc by that
+ 
+
+ align:start position:0%
+and we'll shrink the big disc by that
+amount uh I'm going to scale everything
+
+ align:start position:0%
+amount uh I'm going to scale everything
+ 
+
+ align:start position:0%
+amount uh I'm going to scale everything
+so that t equals 1 um that will simplify
+
+ align:start position:0%
+so that t equals 1 um that will simplify
+ 
+
+ align:start position:0%
+so that t equals 1 um that will simplify
+things a little bit so just shrink
+
+ align:start position:0%
+things a little bit so just shrink
+ 
+
+ align:start position:0%
+things a little bit so just shrink
+everything uh all the values down divide
+
+ align:start position:0%
+everything uh all the values down divide
+ 
+
+ align:start position:0%
+everything uh all the values down divide
+everything by T AI is in the T
+
+ align:start position:0%
+everything by T AI is in the T
+ 
+
+ align:start position:0%
+everything by T AI is in the T
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+then I think we're going
+
+ align:start position:0%
+then I think we're going
+ 
+
+ align:start position:0%
+then I think we're going
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+shrink the AI
+
+ align:start position:0%
+shrink the AI
+ 
+
+ align:start position:0%
+shrink the AI
+disc
+
+ align:start position:0%
+disc
+ 
+
+ align:start position:0%
+disc
+by Min -1 Over N sared plus AI Over N
+
+ align:start position:0%
+by Min -1 Over N sared plus AI Over N
+ 
+
+ align:start position:0%
+by Min -1 Over N sared plus AI Over N
+this is a funny notion of shrink uh I'm
+
+ align:start position:0%
+this is a funny notion of shrink uh I'm
+ 
+
+ align:start position:0%
+this is a funny notion of shrink uh I'm
+going to first make it smaller by 1 over
+
+ align:start position:0%
+going to first make it smaller by 1 over
+ 
+
+ align:start position:0%
+going to first make it smaller by 1 over
+n^2 and then I'm going to grow it by AI
+
+ align:start position:0%
+n^2 and then I'm going to grow it by AI
+ 
+
+ align:start position:0%
+n^2 and then I'm going to grow it by AI
+Over N um this term I believe is to
+
+ align:start position:0%
+Over N um this term I believe is to
+ 
+
+ align:start position:0%
+Over N um this term I believe is to
+uh get rid of smaller things in the
+
+ align:start position:0%
+uh get rid of smaller things in the
+ 
+
+ align:start position:0%
+uh get rid of smaller things in the
+tailor expansion so discs are annoying
+
+ align:start position:0%
+tailor expansion so discs are annoying
+ 
+
+ align:start position:0%
+tailor expansion so discs are annoying
+because they're circular uh because
+
+ align:start position:0%
+because they're circular uh because
+ 
+
+ align:start position:0%
+because they're circular uh because
+they're quadratic curves and so you get
+
+ align:start position:0%
+they're quadratic curves and so you get
+ 
+
+ align:start position:0%
+they're quadratic curves and so you get
+uh you know it's it's an awkward shape
+
+ align:start position:0%
+uh you know it's it's an awkward shape
+ 
+
+ align:start position:0%
+uh you know it's it's an awkward shape
+to deal with um and you're worried about
+
+ align:start position:0%
+to deal with um and you're worried about
+ 
+
+ align:start position:0%
+to deal with um and you're worried about
+how how I move this Center relative to
+
+ align:start position:0%
+how how I move this Center relative to
+ 
+
+ align:start position:0%
+how how I move this Center relative to
+how I move the other centers and whether
+
+ align:start position:0%
+how I move the other centers and whether
+ 
+
+ align:start position:0%
+how I move the other centers and whether
+they're hitting each other and whether
+
+ align:start position:0%
+they're hitting each other and whether
+ 
+
+ align:start position:0%
+they're hitting each other and whether
+they're hitting each other is a
+
+ align:start position:0%
+they're hitting each other is a
+ 
+
+ align:start position:0%
+they're hitting each other is a
+quadratic constraint you have to measure
+
+ align:start position:0%
+quadratic constraint you have to measure
+ 
+
+ align:start position:0%
+quadratic constraint you have to measure
+the distance between these two points it
+
+ align:start position:0%
+the distance between these two points it
+ 
+
+ align:start position:0%
+the distance between these two points it
+should be greater than or equal to the
+
+ align:start position:0%
+should be greater than or equal to the
+ 
+
+ align:start position:0%
+should be greater than or equal to the
+sum of the
+
+ align:start position:0%
+sum of the
+ 
+
+ align:start position:0%
+sum of the
+radi uh so that's tough to work with so
+
+ align:start position:0%
+radi uh so that's tough to work with so
+ 
+
+ align:start position:0%
+radi uh so that's tough to work with so
+to simplify things we take first
+
+ align:start position:0%
+to simplify things we take first
+ 
+
+ align:start position:0%
+to simplify things we take first
+derivatives and say well to the first
+
+ align:start position:0%
+derivatives and say well to the first
+ 
+
+ align:start position:0%
+derivatives and say well to the first
+order what's happening when I move these
+
+ align:start position:0%
+order what's happening when I move these
+ 
+
+ align:start position:0%
+order what's happening when I move these
+discs around and uh when you take first
+
+ align:start position:0%
+discs around and uh when you take first
+ 
+
+ align:start position:0%
+discs around and uh when you take first
+derivatives you get an approximation to
+
+ align:start position:0%
+derivatives you get an approximation to
+ 
+
+ align:start position:0%
+derivatives you get an approximation to
+the truth and the second derivative
+
+ align:start position:0%
+the truth and the second derivative
+ 
+
+ align:start position:0%
+the truth and the second derivative
+tells you a little bit more of the truth
+
+ align:start position:0%
+tells you a little bit more of the truth
+ 
+
+ align:start position:0%
+tells you a little bit more of the truth
+and uh if you've ever done Taylor uh
+
+ align:start position:0%
+and uh if you've ever done Taylor uh
+ 
+
+ align:start position:0%
+and uh if you've ever done Taylor uh
+series you know you get something like 1
+
+ align:start position:0%
+series you know you get something like 1
+ 
+
+ align:start position:0%
+series you know you get something like 1
+over n something * 1 n plus something
+
+ align:start position:0%
+over n something * 1 n plus something
+ 
+
+ align:start position:0%
+over n something * 1 n plus something
+Time 1 n^ 2 and so on um and so if if we
+
+ align:start position:0%
+Time 1 n^ 2 and so on um and so if if we
+ 
+
+ align:start position:0%
+Time 1 n^ 2 and so on um and so if if we
+just subtract off this term make these
+
+ align:start position:0%
+just subtract off this term make these
+ 
+
+ align:start position:0%
+just subtract off this term make these
+discs a little bit smaller than they
+
+ align:start position:0%
+discs a little bit smaller than they
+ 
+
+ align:start position:0%
+discs a little bit smaller than they
+need to be uh that lets you deal with
+
+ align:start position:0%
+need to be uh that lets you deal with
+ 
+
+ align:start position:0%
+need to be uh that lets you deal with
+all those terms all at once so it lets
+
+ align:start position:0%
+all those terms all at once so it lets
+ 
+
+ align:start position:0%
+all those terms all at once so it lets
+us focus on the lead term uh and to the
+
+ align:start position:0%
+us focus on the lead term uh and to the
+ 
+
+ align:start position:0%
+us focus on the lead term uh and to the
+first order the claim is what happens is
+
+ align:start position:0%
+first order the claim is what happens is
+ 
+
+ align:start position:0%
+first order the claim is what happens is
+well we made this disc smaller by one
+
+ align:start position:0%
+well we made this disc smaller by one
+ 
+
+ align:start position:0%
+well we made this disc smaller by one
+remember one is T we made the other guys
+
+ align:start position:0%
+remember one is T we made the other guys
+ 
+
+ align:start position:0%
+remember one is T we made the other guys
+larger by AI so um that's going to work
+
+ align:start position:0%
+larger by AI so um that's going to work
+ 
+
+ align:start position:0%
+larger by AI so um that's going to work
+out exactly when the sum of the three I
+
+ align:start position:0%
+out exactly when the sum of the three I
+ 
+
+ align:start position:0%
+out exactly when the sum of the three I
+is less than equal to one then this will
+
+ align:start position:0%
+is less than equal to one then this will
+ 
+
+ align:start position:0%
+is less than equal to one then this will
+all have room and that's true to the
+
+ align:start position:0%
+all have room and that's true to the
+ 
+
+ align:start position:0%
+all have room and that's true to the
+first order and you have to do this ugly
+
+ align:start position:0%
+first order and you have to do this ugly
+ 
+
+ align:start position:0%
+first order and you have to do this ugly
+business to make it true exactly so I
+
+ align:start position:0%
+business to make it true exactly so I
+ 
+
+ align:start position:0%
+business to make it true exactly so I
+think without going into vector algebra
+
+ align:start position:0%
+think without going into vector algebra
+ 
+
+ align:start position:0%
+think without going into vector algebra
+this is the intuition of what's going
+
+ align:start position:0%
+this is the intuition of what's going
+ 
+
+ align:start position:0%
+this is the intuition of what's going
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+and that's that
+
+ align:start position:0%
+and that's that
+ 
+
+ align:start position:0%
+and that's that
+proof any questions the point here is to
+
+ align:start position:0%
+proof any questions the point here is to
+ 
+
+ align:start position:0%
+proof any questions the point here is to
+expose you to lots of different ways to
+
+ align:start position:0%
+expose you to lots of different ways to
+ 
+
+ align:start position:0%
+expose you to lots of different ways to
+represent numbers and uh three partition
+
+ align:start position:0%
+represent numbers and uh three partition
+ 
+
+ align:start position:0%
+represent numbers and uh three partition
+and uh a lot of the times it comes up in
+
+ align:start position:0%
+and uh a lot of the times it comes up in
+ 
+
+ align:start position:0%
+and uh a lot of the times it comes up in
+geometric settings but so far we've seen
+
+ align:start position:0%
+geometric settings but so far we've seen
+ 
+
+ align:start position:0%
+geometric settings but so far we've seen
+rather different ways to represent it
+
+ align:start position:0%
+rather different ways to represent it
+ 
+
+ align:start position:0%
+rather different ways to represent it
+we'll see graph theory in a moment um
+
+ align:start position:0%
+we'll see graph theory in a moment um
+ 
+
+ align:start position:0%
+we'll see graph theory in a moment um
+probably next up is games and puzzles so
+
+ align:start position:0%
+probably next up is games and puzzles so
+ 
+
+ align:start position:0%
+probably next up is games and puzzles so
+let's play some
+
+ align:start position:0%
+let's play some
+ 
+
+ align:start position:0%
+let's play some
+games uh oh I have a right there was one
+
+ align:start position:0%
+games uh oh I have a right there was one
+ 
+
+ align:start position:0%
+games uh oh I have a right there was one
+more part of this proof I forgot uh what
+
+ align:start position:0%
+more part of this proof I forgot uh what
+ 
+
+ align:start position:0%
+more part of this proof I forgot uh what
+if you're packing into a square this is
+
+ align:start position:0%
+if you're packing into a square this is
+ 
+
+ align:start position:0%
+if you're packing into a square this is
+particularly important for origami this
+
+ align:start position:0%
+particularly important for origami this
+ 
+
+ align:start position:0%
+particularly important for origami this
+paper appeared in an origami conference
+
+ align:start position:0%
+paper appeared in an origami conference
+ 
+
+ align:start position:0%
+paper appeared in an origami conference
+so uh we needed to solve the case of
+
+ align:start position:0%
+so uh we needed to solve the case of
+ 
+
+ align:start position:0%
+so uh we needed to solve the case of
+square packing this is more Awkward um
+
+ align:start position:0%
+square packing this is more Awkward um
+ 
+
+ align:start position:0%
+square packing this is more Awkward um
+the idea uh because you can't make a
+
+ align:start position:0%
+the idea uh because you can't make a
+ 
+
+ align:start position:0%
+the idea uh because you can't make a
+nice regular grid on a you know Square
+
+ align:start position:0%
+nice regular grid on a you know Square
+ 
+
+ align:start position:0%
+nice regular grid on a you know Square
+grid packing is not very efficient for
+
+ align:start position:0%
+grid packing is not very efficient for
+ 
+
+ align:start position:0%
+grid packing is not very efficient for
+discs um but if you have these four
+
+ align:start position:0%
+discs um but if you have these four
+ 
+
+ align:start position:0%
+discs um but if you have these four
+really big discs I should mention here
+
+ align:start position:0%
+really big discs I should mention here
+ 
+
+ align:start position:0%
+really big discs I should mention here
+the the goal is for the disc to fit uh
+
+ align:start position:0%
+the the goal is for the disc to fit uh
+ 
+
+ align:start position:0%
+the the goal is for the disc to fit uh
+the centers of the disc to fit inside
+
+ align:start position:0%
+the centers of the disc to fit inside
+ 
+
+ align:start position:0%
+the centers of the disc to fit inside
+the square that turns out to be the
+
+ align:start position:0%
+the square that turns out to be the
+ 
+
+ align:start position:0%
+the square that turns out to be the
+right constraint from the origami
+
+ align:start position:0%
+right constraint from the origami
+ 
+
+ align:start position:0%
+right constraint from the origami
+perspective um so we make these four big
+
+ align:start position:0%
+perspective um so we make these four big
+ 
+
+ align:start position:0%
+perspective um so we make these four big
+discs they have to be at the corners
+
+ align:start position:0%
+discs they have to be at the corners
+ 
+
+ align:start position:0%
+discs they have to be at the corners
+then we make this big disc it has to be
+
+ align:start position:0%
+then we make this big disc it has to be
+ 
+
+ align:start position:0%
+then we make this big disc it has to be
+in the center these are all perfectly
+
+ align:start position:0%
+in the center these are all perfectly
+ 
+
+ align:start position:0%
+in the center these are all perfectly
+touching uh then we add these four discs
+
+ align:start position:0%
+touching uh then we add these four discs
+ 
+
+ align:start position:0%
+touching uh then we add these four discs
+and it forces a particular Arrangement
+
+ align:start position:0%
+and it forces a particular Arrangement
+ 
+
+ align:start position:0%
+and it forces a particular Arrangement
+here which is a little awkward to
+
+ align:start position:0%
+here which is a little awkward to
+ 
+
+ align:start position:0%
+here which is a little awkward to
+compute but you can uh
+
+ align:start position:0%
+compute but you can uh
+ 
+
+ align:start position:0%
+compute but you can uh
+and yes we do that four times then for
+
+ align:start position:0%
+and yes we do that four times then for
+ 
+
+ align:start position:0%
+and yes we do that four times then for
+each of these constructions this is the
+
+ align:start position:0%
+each of these constructions this is the
+ 
+
+ align:start position:0%
+each of these constructions this is the
+shape that we want we want these kind of
+
+ align:start position:0%
+shape that we want we want these kind of
+ 
+
+ align:start position:0%
+shape that we want we want these kind of
+equilateral triangle is uh gaps I say is
+
+ align:start position:0%
+equilateral triangle is uh gaps I say is
+ 
+
+ align:start position:0%
+equilateral triangle is uh gaps I say is
+because they're not straight sides
+
+ align:start position:0%
+because they're not straight sides
+ 
+
+ align:start position:0%
+because they're not straight sides
+they're Arc sides but it is per the
+
+ align:start position:0%
+they're Arc sides but it is per the
+ 
+
+ align:start position:0%
+they're Arc sides but it is per the
+centers form an equilateral triangle
+
+ align:start position:0%
+centers form an equilateral triangle
+ 
+
+ align:start position:0%
+centers form an equilateral triangle
+perfectly uh then we recurse so wherever
+
+ align:start position:0%
+perfectly uh then we recurse so wherever
+ 
+
+ align:start position:0%
+perfectly uh then we recurse so wherever
+we have a gap like that which is this
+
+ align:start position:0%
+we have a gap like that which is this
+ 
+
+ align:start position:0%
+we have a gap like that which is this
+thing uh then we add this Center guy and
+
+ align:start position:0%
+thing uh then we add this Center guy and
+ 
+
+ align:start position:0%
+thing uh then we add this Center guy and
+then we add these four discs again just
+
+ align:start position:0%
+then we add these four discs again just
+ 
+
+ align:start position:0%
+then we add these four discs again just
+like over here three times now of course
+
+ align:start position:0%
+like over here three times now of course
+ 
+
+ align:start position:0%
+like over here three times now of course
+we can't force the disc to go here but
+
+ align:start position:0%
+we can't force the disc to go here but
+ 
+
+ align:start position:0%
+we can't force the disc to go here but
+um they will
+
+ align:start position:0%
+um they will
+ 
+
+ align:start position:0%
+um they will
+uh this is a very symmetric construction
+
+ align:start position:0%
+uh this is a very symmetric construction
+ 
+
+ align:start position:0%
+uh this is a very symmetric construction
+so we're going to do this symmetrically
+
+ align:start position:0%
+so we're going to do this symmetrically
+ 
+
+ align:start position:0%
+so we're going to do this symmetrically
+on all the things uh the other challenge
+
+ align:start position:0%
+on all the things uh the other challenge
+ 
+
+ align:start position:0%
+on all the things uh the other challenge
+is we left these rather large gaps here
+
+ align:start position:0%
+is we left these rather large gaps here
+ 
+
+ align:start position:0%
+is we left these rather large gaps here
+I mean relative to these tiny discs
+
+ align:start position:0%
+I mean relative to these tiny discs
+ 
+
+ align:start position:0%
+I mean relative to these tiny discs
+which are all fit inside that Gap um
+
+ align:start position:0%
+which are all fit inside that Gap um
+ 
+
+ align:start position:0%
+which are all fit inside that Gap um
+this is pretty big gap so we also have
+
+ align:start position:0%
+this is pretty big gap so we also have
+ 
+
+ align:start position:0%
+this is pretty big gap so we also have
+to make these gaps unusable by adding a
+
+ align:start position:0%
+to make these gaps unusable by adding a
+ 
+
+ align:start position:0%
+to make these gaps unusable by adding a
+maximal disc and then adding maximal
+
+ align:start position:0%
+maximal disc and then adding maximal
+ 
+
+ align:start position:0%
+maximal disc and then adding maximal
+disc and just recursively adding maximal
+
+ align:start position:0%
+disc and just recursively adding maximal
+ 
+
+ align:start position:0%
+disc and just recursively adding maximal
+disc until the gaps that are left are
+
+ align:start position:0%
+disc until the gaps that are left are
+ 
+
+ align:start position:0%
+disc until the gaps that are left are
+tinier than all the ones that we're
+
+ align:start position:0%
+tinier than all the ones that we're
+ 
+
+ align:start position:0%
+tinier than all the ones that we're
+going to produce in this recursion this
+
+ align:start position:0%
+going to produce in this recursion this
+ 
+
+ align:start position:0%
+going to produce in this recursion this
+recursion as depth like log n so we get
+
+ align:start position:0%
+recursion as depth like log n so we get
+ 
+
+ align:start position:0%
+recursion as depth like log n so we get
+in the end we get uh roughly n of these
+
+ align:start position:0%
+in the end we get uh roughly n of these
+ 
+
+ align:start position:0%
+in the end we get uh roughly n of these
+things or n over three if we have extras
+
+ align:start position:0%
+things or n over three if we have extras
+ 
+
+ align:start position:0%
+things or n over three if we have extras
+we'll just throw in maximal discs and
+
+ align:start position:0%
+we'll just throw in maximal discs and
+ 
+
+ align:start position:0%
+we'll just throw in maximal discs and
+make them
+
+ align:start position:0%
+make them
+ 
+
+ align:start position:0%
+make them
+unusable uh so that's
+
+ align:start position:0%
+unusable uh so that's
+ 
+
+ align:start position:0%
+unusable uh so that's
+it uh so this is a lot harder because
+
+ align:start position:0%
+it uh so this is a lot harder because
+ 
+
+ align:start position:0%
+it uh so this is a lot harder because
+you have to fill in all of these gaps
+
+ align:start position:0%
+you have to fill in all of these gaps
+ 
+
+ align:start position:0%
+you have to fill in all of these gaps
+and make sure everything is going to be
+
+ align:start position:0%
+and make sure everything is going to be
+ 
+
+ align:start position:0%
+and make sure everything is going to be
+happy and no disc can go in the wrong
+
+ align:start position:0%
+happy and no disc can go in the wrong
+ 
+
+ align:start position:0%
+happy and no disc can go in the wrong
+place but if you sort of do it in the
+
+ align:start position:0%
+place but if you sort of do it in the
+ 
+
+ align:start position:0%
+place but if you sort of do it in the
+right order you can be convinced at
+
+ align:start position:0%
+right order you can be convinced at
+ 
+
+ align:start position:0%
+right order you can be convinced at
+every stage your dis has to go where
+
+ align:start position:0%
+every stage your dis has to go where
+ 
+
+ align:start position:0%
+every stage your dis has to go where
+you're putting it except at the very end
+
+ align:start position:0%
+you're putting it except at the very end
+ 
+
+ align:start position:0%
+you're putting it except at the very end
+where you have Freedom the freedom you
+
+ align:start position:0%
+where you have Freedom the freedom you
+ 
+
+ align:start position:0%
+where you have Freedom the freedom you
+have is where the AIS go which pocket
+
+ align:start position:0%
+have is where the AIS go which pocket
+ 
+
+ align:start position:0%
+have is where the AIS go which pocket
+they belong to that's the only Freedom
+
+ align:start position:0%
+they belong to that's the only Freedom
+ 
+
+ align:start position:0%
+they belong to that's the only Freedom
+you have it's the only Freedom we want
+
+ align:start position:0%
+you have it's the only Freedom we want
+ 
+
+ align:start position:0%
+you have it's the only Freedom we want
+you to
+
+ align:start position:0%
+you to
+ 
+
+ align:start position:0%
+you to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+okay so that was dis packing next is
+
+ align:start position:0%
+okay so that was dis packing next is
+ 
+
+ align:start position:0%
+okay so that was dis packing next is
+Click Mania how many people have played
+
+ align:start position:0%
+Click Mania how many people have played
+ 
+
+ align:start position:0%
+Click Mania how many people have played
+click Mania a few good it's not
+
+ align:start position:0%
+click Mania a few good it's not
+ 
+
+ align:start position:0%
+click Mania a few good it's not
+completely obscure yet um so here here I
+
+ align:start position:0%
+completely obscure yet um so here here I
+ 
+
+ align:start position:0%
+completely obscure yet um so here here I
+have the real thing I think this is
+
+ align:start position:0%
+have the real thing I think this is
+ 
+
+ align:start position:0%
+have the real thing I think this is
+called click Next Generation and I want
+
+ align:start position:0%
+called click Next Generation and I want
+ 
+
+ align:start position:0%
+called click Next Generation and I want
+to start a new game so I don't have a
+
+ align:start position:0%
+to start a new game so I don't have a
+ 
+
+ align:start position:0%
+to start a new game so I don't have a
+really bad score uh so the idea is
+
+ align:start position:0%
+really bad score uh so the idea is
+ 
+
+ align:start position:0%
+really bad score uh so the idea is
+you're going to click on a group a
+
+ align:start position:0%
+you're going to click on a group a
+ 
+
+ align:start position:0%
+you're going to click on a group a
+connected group of one color that group
+
+ align:start position:0%
+connected group of one color that group
+ 
+
+ align:start position:0%
+connected group of one color that group
+is destroyed and then Things Fall
+
+ align:start position:0%
+is destroyed and then Things Fall
+ 
+
+ align:start position:0%
+is destroyed and then Things Fall
+vertically uh so column by
+
+ align:start position:0%
+vertically uh so column by
+ 
+
+ align:start position:0%
+vertically uh so column by
+column rules clear uh your goal is to
+
+ align:start position:0%
+column rules clear uh your goal is to
+ 
+
+ align:start position:0%
+column rules clear uh your goal is to
+remove all of the
+
+ align:start position:0%
+remove all of the
+ 
+
+ align:start position:0%
+remove all of the
+blocks uh which I probably won't succeed
+
+ align:start position:0%
+blocks uh which I probably won't succeed
+ 
+
+ align:start position:0%
+blocks uh which I probably won't succeed
+in doing I haven't played in a long
+
+ align:start position:0%
+in doing I haven't played in a long
+ 
+
+ align:start position:0%
+in doing I haven't played in a long
+time but let's I would like to show you
+
+ align:start position:0%
+time but let's I would like to show you
+ 
+
+ align:start position:0%
+time but let's I would like to show you
+one other rule but I may fail to do
+
+ align:start position:0%
+one other rule but I may fail to do
+ 
+
+ align:start position:0%
+one other rule but I may fail to do
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progress uh this kind of checkerboarding
+
+ align:start position:0%
+progress uh this kind of checkerboarding
+ 
+
+ align:start position:0%
+progress uh this kind of checkerboarding
+not so
+
+ align:start position:0%
+not so
+ 
+
+ align:start position:0%
+not so
+good don't do that when you play uh also
+
+ align:start position:0%
+good don't do that when you play uh also
+ 
+
+ align:start position:0%
+good don't do that when you play uh also
+very bad okay uh the one rule which I
+
+ align:start position:0%
+very bad okay uh the one rule which I
+ 
+
+ align:start position:0%
+very bad okay uh the one rule which I
+won't demonstrate here uh is if you
+
+ align:start position:0%
+won't demonstrate here uh is if you
+ 
+
+ align:start position:0%
+won't demonstrate here uh is if you
+clear a column then these guys just sort
+
+ align:start position:0%
+clear a column then these guys just sort
+ 
+
+ align:start position:0%
+clear a column then these guys just sort
+of eat the column they just move closer
+
+ align:start position:0%
+of eat the column they just move closer
+ 
+
+ align:start position:0%
+of eat the column they just move closer
+to each other I think usually the Right
+
+ align:start position:0%
+to each other I think usually the Right
+ 
+
+ align:start position:0%
+to each other I think usually the Right
+Moves to the left one one step okay so
+
+ align:start position:0%
+Moves to the left one one step okay so
+ 
+
+ align:start position:0%
+Moves to the left one one step okay so
+that's uh here here's a successful
+
+ align:start position:0%
+that's uh here here's a successful
+ 
+
+ align:start position:0%
+that's uh here here's a successful
+execution from The Click Mania website
+
+ align:start position:0%
+execution from The Click Mania website
+ 
+
+ align:start position:0%
+execution from The Click Mania website
+um but I have done it a few times just
+
+ align:start position:0%
+um but I have done it a few times just
+ 
+
+ align:start position:0%
+um but I have done it a few times just
+haven't in a long time the Only Rule is
+
+ align:start position:0%
+haven't in a long time the Only Rule is
+ 
+
+ align:start position:0%
+haven't in a long time the Only Rule is
+you C the group that you click on the
+
+ align:start position:0%
+you C the group that you click on the
+ 
+
+ align:start position:0%
+you C the group that you click on the
+connected uh color chunk has to be of
+
+ align:start position:0%
+connected uh color chunk has to be of
+ 
+
+ align:start position:0%
+connected uh color chunk has to be of
+size greater than one otherwise you
+
+ align:start position:0%
+size greater than one otherwise you
+ 
+
+ align:start position:0%
+size greater than one otherwise you
+could just keep clicking on everything
+
+ align:start position:0%
+could just keep clicking on everything
+ 
+
+ align:start position:0%
+could just keep clicking on everything
+uh so that's why the checkerboarding is
+
+ align:start position:0%
+uh so that's why the checkerboarding is
+ 
+
+ align:start position:0%
+uh so that's why the checkerboarding is
+bad because there you have single
+
+ align:start position:0%
+bad because there you have single
+ 
+
+ align:start position:0%
+bad because there you have single
+Singleton
+
+ align:start position:0%
+Singleton
+ 
+
+ align:start position:0%
+Singleton
+guys so you may have some Singleton guys
+
+ align:start position:0%
+guys so you may have some Singleton guys
+ 
+
+ align:start position:0%
+guys so you may have some Singleton guys
+but if you're careful you sometimes can
+
+ align:start position:0%
+but if you're careful you sometimes can
+ 
+
+ align:start position:0%
+but if you're careful you sometimes can
+get rid of them question is when can you
+
+ align:start position:0%
+get rid of them question is when can you
+ 
+
+ align:start position:0%
+get rid of them question is when can you
+uh and and the answer is it's NP
+
+ align:start position:0%
+uh and and the answer is it's NP
+ 
+
+ align:start position:0%
+uh and and the answer is it's NP
+complete so this was actually uh my
+
+ align:start position:0%
+complete so this was actually uh my
+ 
+
+ align:start position:0%
+complete so this was actually uh my
+first NP hardness proof I think ever
+
+ align:start position:0%
+first NP hardness proof I think ever
+ 
+
+ align:start position:0%
+first NP hardness proof I think ever
+definitely of a game um I think ever so
+
+ align:start position:0%
+definitely of a game um I think ever so
+ 
+
+ align:start position:0%
+definitely of a game um I think ever so
+there's a few results here one is that
+
+ align:start position:0%
+there's a few results here one is that
+ 
+
+ align:start position:0%
+there's a few results here one is that
+if you have a single column that case we
+
+ align:start position:0%
+if you have a single column that case we
+ 
+
+ align:start position:0%
+if you have a single column that case we
+can solve a single row single row
+
+ align:start position:0%
+can solve a single row single row
+ 
+
+ align:start position:0%
+can solve a single row single row
+actually behaves the same as a single
+
+ align:start position:0%
+actually behaves the same as a single
+ 
+
+ align:start position:0%
+actually behaves the same as a single
+column uh because even though they're
+
+ align:start position:0%
+column uh because even though they're
+ 
+
+ align:start position:0%
+column uh because even though they're
+asymmetric in general for when it's one
+
+ align:start position:0%
+asymmetric in general for when it's one
+ 
+
+ align:start position:0%
+asymmetric in general for when it's one
+they're the same and if you happen to
+
+ align:start position:0%
+they're the same and if you happen to
+ 
+
+ align:start position:0%
+they're the same and if you happen to
+know context free grammars then uh here
+
+ align:start position:0%
+know context free grammars then uh here
+ 
+
+ align:start position:0%
+know context free grammars then uh here
+is the answer it's not obvious that this
+
+ align:start position:0%
+is the answer it's not obvious that this
+ 
+
+ align:start position:0%
+is the answer it's not obvious that this
+is the answer but this is saying
+
+ align:start position:0%
+is the answer but this is saying
+ 
+
+ align:start position:0%
+is the answer but this is saying
+something like well it could be you
+
+ align:start position:0%
+something like well it could be you
+ 
+
+ align:start position:0%
+something like well it could be you
+already solved the game that's the empty
+
+ align:start position:0%
+already solved the game that's the empty
+ 
+
+ align:start position:0%
+already solved the game that's the empty
+string or it could be you have a
+
+ align:start position:0%
+string or it could be you have a
+ 
+
+ align:start position:0%
+string or it could be you have a
+solvable game followed by solvable game
+
+ align:start position:0%
+solvable game followed by solvable game
+ 
+
+ align:start position:0%
+solvable game followed by solvable game
+you could just sort of do them
+
+ align:start position:0%
+you could just sort of do them
+ 
+
+ align:start position:0%
+you could just sort of do them
+separately and if you're careful they
+
+ align:start position:0%
+separately and if you're careful they
+ 
+
+ align:start position:0%
+separately and if you're careful they
+won't mess each other up and then you
+
+ align:start position:0%
+won't mess each other up and then you
+ 
+
+ align:start position:0%
+won't mess each other up and then you
+solve the overall game or it could be
+
+ align:start position:0%
+solve the overall game or it could be
+ 
+
+ align:start position:0%
+solve the overall game or it could be
+you have a solvable game and you have uh
+
+ align:start position:0%
+you have a solvable game and you have uh
+ 
+
+ align:start position:0%
+you have a solvable game and you have uh
+the same color one block of the same
+
+ align:start position:0%
+the same color one block of the same
+ 
+
+ align:start position:0%
+the same color one block of the same
+color on either side that would also be
+
+ align:start position:0%
+color on either side that would also be
+ 
+
+ align:start position:0%
+color on either side that would also be
+solvable because you could just solve
+
+ align:start position:0%
+solvable because you could just solve
+ 
+
+ align:start position:0%
+solvable because you could just solve
+the center thing then these two guys
+
+ align:start position:0%
+the center thing then these two guys
+ 
+
+ align:start position:0%
+the center thing then these two guys
+come together and then you click that
+
+ align:start position:0%
+come together and then you click that
+ 
+
+ align:start position:0%
+come together and then you click that
+group of size two uh or this could also
+
+ align:start position:0%
+group of size two uh or this could also
+ 
+
+ align:start position:0%
+group of size two uh or this could also
+happen where you solve two things and
+
+ align:start position:0%
+happen where you solve two things and
+ 
+
+ align:start position:0%
+happen where you solve two things and
+then three blocks come together and you
+
+ align:start position:0%
+then three blocks come together and you
+ 
+
+ align:start position:0%
+then three blocks come together and you
+could also Imagine other rules but it
+
+ align:start position:0%
+could also Imagine other rules but it
+ 
+
+ align:start position:0%
+could also Imagine other rules but it
+turns out these are enough rules to
+
+ align:start position:0%
+turns out these are enough rules to
+ 
+
+ align:start position:0%
+turns out these are enough rules to
+capture all solvable puzzles for one row
+
+ align:start position:0%
+capture all solvable puzzles for one row
+ 
+
+ align:start position:0%
+capture all solvable puzzles for one row
+or column but that's not a hardness
+
+ align:start position:0%
+or column but that's not a hardness
+ 
+
+ align:start position:0%
+or column but that's not a hardness
+proof so we won't talk about it um we
+
+ align:start position:0%
+proof so we won't talk about it um we
+ 
+
+ align:start position:0%
+proof so we won't talk about it um we
+have two NP hardness results one is for
+
+ align:start position:0%
+have two NP hardness results one is for
+ 
+
+ align:start position:0%
+have two NP hardness results one is for
+two columns and five colors and the
+
+ align:start position:0%
+two columns and five colors and the
+ 
+
+ align:start position:0%
+two columns and five colors and the
+other one is a hardness proof for five
+
+ align:start position:0%
+other one is a hardness proof for five
+ 
+
+ align:start position:0%
+other one is a hardness proof for five
+columns and three
+
+ align:start position:0%
+columns and three
+ 
+
+ align:start position:0%
+columns and three
+colors um and these are the proofs
+
+ align:start position:0%
+colors um and these are the proofs
+ 
+
+ align:start position:0%
+colors um and these are the proofs
+uh this one is three partition this one
+
+ align:start position:0%
+uh this one is three partition this one
+ 
+
+ align:start position:0%
+uh this one is three partition this one
+is threat so we might talk about that in
+
+ align:start position:0%
+is threat so we might talk about that in
+ 
+
+ align:start position:0%
+is threat so we might talk about that in
+the threat section of the class but I'm
+
+ align:start position:0%
+the threat section of the class but I'm
+ 
+
+ align:start position:0%
+the threat section of the class but I'm
+going to focus here on the three
+
+ align:start position:0%
+going to focus here on the three
+ 
+
+ align:start position:0%
+going to focus here on the three
+partition two columns five colors open
+
+ align:start position:0%
+partition two columns five colors open
+ 
+
+ align:start position:0%
+partition two columns five colors open
+problem um is whether two colors you can
+
+ align:start position:0%
+problem um is whether two colors you can
+ 
+
+ align:start position:0%
+problem um is whether two colors you can
+get any hardness question um is it
+
+ align:start position:0%
+get any hardness question um is it
+ 
+
+ align:start position:0%
+get any hardness question um is it
+obvious that s to SS is a no it's not
+
+ align:start position:0%
+obvious that s to SS is a no it's not
+ 
+
+ align:start position:0%
+obvious that s to SS is a no it's not
+obvious that s to SS is valid because
+
+ align:start position:0%
+obvious that s to SS is valid because
+ 
+
+ align:start position:0%
+obvious that s to SS is valid because
+you worry that when you solve one of
+
+ align:start position:0%
+you worry that when you solve one of
+ 
+
+ align:start position:0%
+you worry that when you solve one of
+them you might eat a group from the
+
+ align:start position:0%
+them you might eat a group from the
+ 
+
+ align:start position:0%
+them you might eat a group from the
+right hand side uh but you can prove
+
+ align:start position:0%
+right hand side uh but you can prove
+ 
+
+ align:start position:0%
+right hand side uh but you can prove
+it's always possible I don't remember
+
+ align:start position:0%
+it's always possible I don't remember
+ 
+
+ align:start position:0%
+it's always possible I don't remember
+how that proof works but you can check
+
+ align:start position:0%
+how that proof works but you can check
+ 
+
+ align:start position:0%
+how that proof works but you can check
+the paper um yeah if you look at the if
+
+ align:start position:0%
+the paper um yeah if you look at the if
+ 
+
+ align:start position:0%
+the paper um yeah if you look at the if
+you ever go to the course website and
+
+ align:start position:0%
+you ever go to the course website and
+ 
+
+ align:start position:0%
+you ever go to the course website and
+look watch this lecture or click around
+
+ align:start position:0%
+look watch this lecture or click around
+ 
+
+ align:start position:0%
+look watch this lecture or click around
+the slides of this lecture it has links
+
+ align:start position:0%
+the slides of this lecture it has links
+ 
+
+ align:start position:0%
+the slides of this lecture it has links
+to all the papers that I'm talking about
+
+ align:start position:0%
+to all the papers that I'm talking about
+ 
+
+ align:start position:0%
+to all the papers that I'm talking about
+so if you ever want to know more details
+
+ align:start position:0%
+so if you ever want to know more details
+ 
+
+ align:start position:0%
+so if you ever want to know more details
+just go there link is right there you
+
+ align:start position:0%
+just go there link is right there you
+ 
+
+ align:start position:0%
+just go there link is right there you
+don't have to type in all these names
+
+ align:start position:0%
+don't have to type in all these names
+ 
+
+ align:start position:0%
+don't have to type in all these names
+and Google for
+
+ align:start position:0%
+and Google for
+ 
+
+ align:start position:0%
+and Google for
+it cool so uh this is my attempt at
+
+ align:start position:0%
+it cool so uh this is my attempt at
+ 
+
+ align:start position:0%
+it cool so uh this is my attempt at
+drawing the hardness proof this uh uh
+
+ align:start position:0%
+drawing the hardness proof this uh uh
+ 
+
+ align:start position:0%
+drawing the hardness proof this uh uh
+this was challenging and I should say
+
+ align:start position:0%
+this was challenging and I should say
+ 
+
+ align:start position:0%
+this was challenging and I should say
+it's not drawn to
+
+ align:start position:0%
+it's not drawn to
+ 
+
+ align:start position:0%
+it's not drawn to
+scale um so it's not exactly right but
+
+ align:start position:0%
+scale um so it's not exactly right but
+ 
+
+ align:start position:0%
+scale um so it's not exactly right but
+it gives you a flavor of what happens
+
+ align:start position:0%
+it gives you a flavor of what happens
+ 
+
+ align:start position:0%
+it gives you a flavor of what happens
+and I believe all the braces are correct
+
+ align:start position:0%
+and I believe all the braces are correct
+ 
+
+ align:start position:0%
+and I believe all the braces are correct
+uh but it just wouldn't fit on the
+
+ align:start position:0%
+uh but it just wouldn't fit on the
+ 
+
+ align:start position:0%
+uh but it just wouldn't fit on the
+screen if we drew everything properly to
+
+ align:start position:0%
+screen if we drew everything properly to
+ 
+
+ align:start position:0%
+screen if we drew everything properly to
+scale um
+
+ align:start position:0%
+scale um
+ 
+
+ align:start position:0%
+scale um
+so reduction from three partition we
+
+ align:start position:0%
+so reduction from three partition we
+ 
+
+ align:start position:0%
+so reduction from three partition we
+have n numbers A1 through a n integers
+
+ align:start position:0%
+have n numbers A1 through a n integers
+ 
+
+ align:start position:0%
+have n numbers A1 through a n integers
+we're going to scale everything up we're
+
+ align:start position:0%
+we're going to scale everything up we're
+ 
+
+ align:start position:0%
+we're going to scale everything up we're
+going to scale the AIS and T by a factor
+
+ align:start position:0%
+going to scale the AIS and T by a factor
+ 
+
+ align:start position:0%
+going to scale the AIS and T by a factor
+of B B is 4/3 n i don't totally know why
+
+ align:start position:0%
+of B B is 4/3 n i don't totally know why
+ 
+
+ align:start position:0%
+of B B is 4/3 n i don't totally know why
+but you know it's it's n plus the number
+
+ align:start position:0%
+but you know it's it's n plus the number
+ 
+
+ align:start position:0%
+but you know it's it's n plus the number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+groups um I'm guessing a larger number
+
+ align:start position:0%
+groups um I'm guessing a larger number
+ 
+
+ align:start position:0%
+groups um I'm guessing a larger number
+would also work but that's uh definitely
+
+ align:start position:0%
+would also work but that's uh definitely
+ 
+
+ align:start position:0%
+would also work but that's uh definitely
+enough okay so basically the there's two
+
+ align:start position:0%
+enough okay so basically the there's two
+ 
+
+ align:start position:0%
+enough okay so basically the there's two
+columns remember always going to stay in
+
+ align:start position:0%
+columns remember always going to stay in
+ 
+
+ align:start position:0%
+columns remember always going to stay in
+two columns it never increases um there
+
+ align:start position:0%
+two columns it never increases um there
+ 
+
+ align:start position:0%
+two columns it never increases um there
+are some clickable blocks uh clickable
+
+ align:start position:0%
+are some clickable blocks uh clickable
+ 
+
+ align:start position:0%
+are some clickable blocks uh clickable
+groups which correspond to the AIS so
+
+ align:start position:0%
+groups which correspond to the AIS so
+ 
+
+ align:start position:0%
+groups which correspond to the AIS so
+for every AI you're gonna have exactly
+
+ align:start position:0%
+for every AI you're gonna have exactly
+ 
+
+ align:start position:0%
+for every AI you're gonna have exactly
+one block which is B time AI by
+
+ align:start position:0%
+one block which is B time AI by
+ 
+
+ align:start position:0%
+one block which is B time AI by
+one uh these h i don't draw the lines
+
+ align:start position:0%
+one uh these h i don't draw the lines
+ 
+
+ align:start position:0%
+one uh these h i don't draw the lines
+when they're in the same connected
+
+ align:start position:0%
+when they're in the same connected
+ 
+
+ align:start position:0%
+when they're in the same connected
+component but technically these are
+
+ align:start position:0%
+component but technically these are
+ 
+
+ align:start position:0%
+component but technically these are
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+squares um there's also some clickable
+
+ align:start position:0%
+squares um there's also some clickable
+ 
+
+ align:start position:0%
+squares um there's also some clickable
+things up here uh that's those are not
+
+ align:start position:0%
+things up here uh that's those are not
+ 
+
+ align:start position:0%
+things up here uh that's those are not
+too essential they're basically to
+
+ align:start position:0%
+too essential they're basically to
+ 
+
+ align:start position:0%
+too essential they're basically to
+spread out these Red
+
+ align:start position:0%
+spread out these Red
+ 
+
+ align:start position:0%
+spread out these Red
+Blocks there are n over3 Red Blocks here
+
+ align:start position:0%
+Blocks there are n over3 Red Blocks here
+ 
+
+ align:start position:0%
+Blocks there are n over3 Red Blocks here
+and there n over3 Red Blocks here you
+
+ align:start position:0%
+and there n over3 Red Blocks here you
+ 
+
+ align:start position:0%
+and there n over3 Red Blocks here you
+will never win the game unless you
+
+ align:start position:0%
+will never win the game unless you
+ 
+
+ align:start position:0%
+will never win the game unless you
+destroy these Red Blocks so uh for
+
+ align:start position:0%
+destroy these Red Blocks so uh for
+ 
+
+ align:start position:0%
+destroy these Red Blocks so uh for
+example you could click all these blue
+
+ align:start position:0%
+example you could click all these blue
+ 
+
+ align:start position:0%
+example you could click all these blue
+things make the red together and then
+
+ align:start position:0%
+things make the red together and then
+ 
+
+ align:start position:0%
+things make the red together and then
+destroy the red but that's not a good
+
+ align:start position:0%
+destroy the red but that's not a good
+ 
+
+ align:start position:0%
+destroy the red but that's not a good
+idea um because these These are only
+
+ align:start position:0%
+idea um because these These are only
+ 
+
+ align:start position:0%
+idea um because these These are only
+this is a very small space uh this is a
+
+ align:start position:0%
+this is a very small space uh this is a
+ 
+
+ align:start position:0%
+this is a very small space uh this is a
+relatively large gap I know it doesn't
+
+ align:start position:0%
+relatively large gap I know it doesn't
+ 
+
+ align:start position:0%
+relatively large gap I know it doesn't
+look like it but this is only n over3
+
+ align:start position:0%
+look like it but this is only n over3
+ 
+
+ align:start position:0%
+look like it but this is only n over3
+total the gap between these two things
+
+ align:start position:0%
+total the gap between these two things
+ 
+
+ align:start position:0%
+total the gap between these two things
+is B * T which is way bigger than n
+
+ align:start position:0%
+is B * T which is way bigger than n
+ 
+
+ align:start position:0%
+is B * T which is way bigger than n
+over3 okay so there's big gaps between
+
+ align:start position:0%
+over3 okay so there's big gaps between
+ 
+
+ align:start position:0%
+over3 okay so there's big gaps between
+these red guys uh so what you're
+
+ align:start position:0%
+these red guys uh so what you're
+ 
+
+ align:start position:0%
+these red guys uh so what you're
+basically going to do is make this
+
+ align:start position:0%
+basically going to do is make this
+ 
+
+ align:start position:0%
+basically going to do is make this
+column fall down until the first red guy
+
+ align:start position:0%
+column fall down until the first red guy
+ 
+
+ align:start position:0%
+column fall down until the first red guy
+aligns with this one then you delete
+
+ align:start position:0%
+aligns with this one then you delete
+ 
+
+ align:start position:0%
+aligns with this one then you delete
+those two then you're going to make it
+
+ align:start position:0%
+those two then you're going to make it
+ 
+
+ align:start position:0%
+those two then you're going to make it
+fall down farther until this red guy
+
+ align:start position:0%
+fall down farther until this red guy
+ 
+
+ align:start position:0%
+fall down farther until this red guy
+hits this one and then you can delete
+
+ align:start position:0%
+hits this one and then you can delete
+ 
+
+ align:start position:0%
+hits this one and then you can delete
+those two just two at a time then we're
+
+ align:start position:0%
+those two just two at a time then we're
+ 
+
+ align:start position:0%
+those two just two at a time then we're
+going to bring it down till the third
+
+ align:start position:0%
+going to bring it down till the third
+ 
+
+ align:start position:0%
+going to bring it down till the third
+guy hits the third guy and then the
+
+ align:start position:0%
+guy hits the third guy and then the
+ 
+
+ align:start position:0%
+guy hits the third guy and then the
+fourth guy hits the fourth guy then the
+
+ align:start position:0%
+fourth guy hits the fourth guy then the
+ 
+
+ align:start position:0%
+fourth guy hits the fourth guy then the
+reds are
+
+ align:start position:0%
+reds are
+ 
+
+ align:start position:0%
+reds are
+gone uh before I get to how that happens
+
+ align:start position:0%
+gone uh before I get to how that happens
+ 
+
+ align:start position:0%
+gone uh before I get to how that happens
+let me tell you what happens when the
+
+ align:start position:0%
+let me tell you what happens when the
+ 
+
+ align:start position:0%
+let me tell you what happens when the
+reds are gone uh when the reds are gone
+
+ align:start position:0%
+reds are gone uh when the reds are gone
+ 
+
+ align:start position:0%
+reds are gone uh when the reds are gone
+I mean if there are any purples left
+
+ align:start position:0%
+I mean if there are any purples left
+ 
+
+ align:start position:0%
+I mean if there are any purples left
+turns out there won't be but you could
+
+ align:start position:0%
+turns out there won't be but you could
+ 
+
+ align:start position:0%
+turns out there won't be but you could
+click them all then you could click all
+
+ align:start position:0%
+click them all then you could click all
+ 
+
+ align:start position:0%
+click them all then you could click all
+the blue then you're done on the right
+
+ align:start position:0%
+the blue then you're done on the right
+ 
+
+ align:start position:0%
+the blue then you're done on the right
+column so right column was finishable no
+
+ align:start position:0%
+column so right column was finishable no
+ 
+
+ align:start position:0%
+column so right column was finishable no
+problem uh once you've gotten rid of the
+
+ align:start position:0%
+problem uh once you've gotten rid of the
+ 
+
+ align:start position:0%
+problem uh once you've gotten rid of the
+red now this the left column is a mostly
+
+ align:start position:0%
+red now this the left column is a mostly
+ 
+
+ align:start position:0%
+red now this the left column is a mostly
+checkerboard and if you remove the red
+
+ align:start position:0%
+checkerboard and if you remove the red
+ 
+
+ align:start position:0%
+checkerboard and if you remove the red
+uh pixels you're left with exactly a
+
+ align:start position:0%
+uh pixels you're left with exactly a
+ 
+
+ align:start position:0%
+uh pixels you're left with exactly a
+checkerboard except here the topmost red
+
+ align:start position:0%
+checkerboard except here the topmost red
+ 
+
+ align:start position:0%
+checkerboard except here the topmost red
+guy there's it's white on either side
+
+ align:start position:0%
+guy there's it's white on either side
+ 
+
+ align:start position:0%
+guy there's it's white on either side
+and in general everything below this
+
+ align:start position:0%
+and in general everything below this
+ 
+
+ align:start position:0%
+and in general everything below this
+point is the same as everything above
+
+ align:start position:0%
+point is the same as everything above
+ 
+
+ align:start position:0%
+point is the same as everything above
+this point upside down down and so then
+
+ align:start position:0%
+this point upside down down and so then
+ 
+
+ align:start position:0%
+this point upside down down and so then
+you can always just click on the center
+
+ align:start position:0%
+you can always just click on the center
+ 
+
+ align:start position:0%
+you can always just click on the center
+Center Center Center I guess you have to
+
+ align:start position:0%
+Center Center Center I guess you have to
+ 
+
+ align:start position:0%
+Center Center Center I guess you have to
+move your mouse down as that happens but
+
+ align:start position:0%
+move your mouse down as that happens but
+ 
+
+ align:start position:0%
+move your mouse down as that happens but
+uh you will then destroy the black and
+
+ align:start position:0%
+uh you will then destroy the black and
+ 
+
+ align:start position:0%
+uh you will then destroy the black and
+white part total is five colors we've
+
+ align:start position:0%
+white part total is five colors we've
+ 
+
+ align:start position:0%
+white part total is five colors we've
+got red purple blue black and
+
+ align:start position:0%
+got red purple blue black and
+ 
+
+ align:start position:0%
+got red purple blue black and
+white okay uh now this is my attempt at
+
+ align:start position:0%
+white okay uh now this is my attempt at
+ 
+
+ align:start position:0%
+white okay uh now this is my attempt at
+showing you uh how we get the red things
+
+ align:start position:0%
+showing you uh how we get the red things
+ 
+
+ align:start position:0%
+showing you uh how we get the red things
+to align but the the idea is simple uh
+
+ align:start position:0%
+to align but the the idea is simple uh
+ 
+
+ align:start position:0%
+to align but the the idea is simple uh
+these the initial Gap from this guy to
+
+ align:start position:0%
+these the initial Gap from this guy to
+ 
+
+ align:start position:0%
+these the initial Gap from this guy to
+this guy and then the Gap henceforth
+
+ align:start position:0%
+this guy and then the Gap henceforth
+ 
+
+ align:start position:0%
+this guy and then the Gap henceforth
+from this one to this one to this one is
+
+ align:start position:0%
+from this one to this one to this one is
+ 
+
+ align:start position:0%
+from this one to this one to this one is
+always B * t plus some constant uh the
+
+ align:start position:0%
+always B * t plus some constant uh the
+ 
+
+ align:start position:0%
+always B * t plus some constant uh the
+constants are just annoying um so
+
+ align:start position:0%
+constants are just annoying um so
+ 
+
+ align:start position:0%
+constants are just annoying um so
+they're not essential the idea is well
+
+ align:start position:0%
+they're not essential the idea is well
+ 
+
+ align:start position:0%
+they're not essential the idea is well
+I've got to bring this down B * T so in
+
+ align:start position:0%
+I've got to bring this down B * T so in
+ 
+
+ align:start position:0%
+I've got to bring this down B * T so in
+order to do that I'm going to click on
+
+ align:start position:0%
+order to do that I'm going to click on
+ 
+
+ align:start position:0%
+order to do that I'm going to click on
+some purple things whose total size is B
+
+ align:start position:0%
+some purple things whose total size is B
+ 
+
+ align:start position:0%
+some purple things whose total size is B
+* T in other words the sum of the AIS
+
+ align:start position:0%
+* T in other words the sum of the AIS
+ 
+
+ align:start position:0%
+* T in other words the sum of the AIS
+that I'm clicking on should be equal to
+
+ align:start position:0%
+that I'm clicking on should be equal to
+ 
+
+ align:start position:0%
+that I'm clicking on should be equal to
+t uh and we happen to know that will be
+
+ align:start position:0%
+t uh and we happen to know that will be
+ 
+
+ align:start position:0%
+t uh and we happen to know that will be
+three things but uh that's not essential
+
+ align:start position:0%
+three things but uh that's not essential
+ 
+
+ align:start position:0%
+three things but uh that's not essential
+here we can just use the simple version
+
+ align:start position:0%
+here we can just use the simple version
+ 
+
+ align:start position:0%
+here we can just use the simple version
+of three partition where you're asking
+
+ align:start position:0%
+of three partition where you're asking
+ 
+
+ align:start position:0%
+of three partition where you're asking
+for sets that happen to sum to t uh and
+
+ align:start position:0%
+for sets that happen to sum to t uh and
+ 
+
+ align:start position:0%
+for sets that happen to sum to t uh and
+because everything is scaled up so big
+
+ align:start position:0%
+because everything is scaled up so big
+ 
+
+ align:start position:0%
+because everything is scaled up so big
+by these factors of B I mean these gaps
+
+ align:start position:0%
+by these factors of B I mean these gaps
+ 
+
+ align:start position:0%
+by these factors of B I mean these gaps
+you have to even to get in in the right
+
+ align:start position:0%
+you have to even to get in in the right
+ 
+
+ align:start position:0%
+you have to even to get in in the right
+proximity you have to choose AIS that
+
+ align:start position:0%
+proximity you have to choose AIS that
+ 
+
+ align:start position:0%
+proximity you have to choose AIS that
+sum to exactly
+
+ align:start position:0%
+sum to exactly
+ 
+
+ align:start position:0%
+sum to exactly
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+um yes so the constants are annoying
+
+ align:start position:0%
+um yes so the constants are annoying
+ 
+
+ align:start position:0%
+um yes so the constants are annoying
+because uh you want to make sure so here
+
+ align:start position:0%
+because uh you want to make sure so here
+ 
+
+ align:start position:0%
+because uh you want to make sure so here
+here's an example here are are in this
+
+ align:start position:0%
+here's an example here are are in this
+ 
+
+ align:start position:0%
+here's an example here are are in this
+particular picture the height of one of
+
+ align:start position:0%
+particular picture the height of one of
+ 
+
+ align:start position:0%
+particular picture the height of one of
+these things is six and so I click on
+
+ align:start position:0%
+these things is six and so I click on
+ 
+
+ align:start position:0%
+these things is six and so I click on
+one purple thing of size four and one
+
+ align:start position:0%
+one purple thing of size four and one
+ 
+
+ align:start position:0%
+one purple thing of size four and one
+purple thing of size two in reality
+
+ align:start position:0%
+purple thing of size two in reality
+ 
+
+ align:start position:0%
+purple thing of size two in reality
+these numbers would be much bigger but
+
+ align:start position:0%
+these numbers would be much bigger but
+ 
+
+ align:start position:0%
+these numbers would be much bigger but
+for the picture that works then Things
+
+ align:start position:0%
+for the picture that works then Things
+ 
+
+ align:start position:0%
+for the picture that works then Things
+fall and we get this picture um and
+
+ align:start position:0%
+fall and we get this picture um and
+ 
+
+ align:start position:0%
+fall and we get this picture um and
+these red things are almost align but
+
+ align:start position:0%
+these red things are almost align but
+ 
+
+ align:start position:0%
+these red things are almost align but
+they're off by two so I click on this
+
+ align:start position:0%
+they're off by two so I click on this
+ 
+
+ align:start position:0%
+they're off by two so I click on this
+little one by two block and then they're
+
+ align:start position:0%
+little one by two block and then they're
+ 
+
+ align:start position:0%
+little one by two block and then they're
+aligned then I can click on the red
+
+ align:start position:0%
+aligned then I can click on the red
+ 
+
+ align:start position:0%
+aligned then I can click on the red
+thing um I also click on this blue thing
+
+ align:start position:0%
+thing um I also click on this blue thing
+ 
+
+ align:start position:0%
+thing um I also click on this blue thing
+to sort of advance to the next red thing
+
+ align:start position:0%
+to sort of advance to the next red thing
+ 
+
+ align:start position:0%
+to sort of advance to the next red thing
+and then these guys fall and I get this
+
+ align:start position:0%
+and then these guys fall and I get this
+ 
+
+ align:start position:0%
+and then these guys fall and I get this
+picture I could click on the white but
+
+ align:start position:0%
+picture I could click on the white but
+ 
+
+ align:start position:0%
+picture I could click on the white but
+it won't matter that's just I can do
+
+ align:start position:0%
+it won't matter that's just I can do
+ 
+
+ align:start position:0%
+it won't matter that's just I can do
+that all at the end later now my goal is
+
+ align:start position:0%
+that all at the end later now my goal is
+ 
+
+ align:start position:0%
+that all at the end later now my goal is
+to get this red thing to Here Again The
+
+ align:start position:0%
+to get this red thing to Here Again The
+ 
+
+ align:start position:0%
+to get this red thing to Here Again The
+Gap is exactly
+
+ align:start position:0%
+Gap is exactly
+ 
+
+ align:start position:0%
+Gap is exactly
+five so um I click on let's say two or
+
+ align:start position:0%
+five so um I click on let's say two or
+ 
+
+ align:start position:0%
+five so um I click on let's say two or
+sorry six uh let's say I click on two
+
+ align:start position:0%
+sorry six uh let's say I click on two
+ 
+
+ align:start position:0%
+sorry six uh let's say I click on two
+things of size three um and so then
+
+ align:start position:0%
+things of size three um and so then
+ 
+
+ align:start position:0%
+things of size three um and so then
+everything falls then the Red's a line
+
+ align:start position:0%
+everything falls then the Red's a line
+ 
+
+ align:start position:0%
+everything falls then the Red's a line
+then I delete it I also delete the blue
+
+ align:start position:0%
+then I delete it I also delete the blue
+ 
+
+ align:start position:0%
+then I delete it I also delete the blue
+thing to
+
+ align:start position:0%
+thing to
+ 
+
+ align:start position:0%
+thing to
+advance uh and I think that that works
+
+ align:start position:0%
+advance uh and I think that that works
+ 
+
+ align:start position:0%
+advance uh and I think that that works
+yeah question sure that it's always the
+
+ align:start position:0%
+yeah question sure that it's always the
+ 
+
+ align:start position:0%
+yeah question sure that it's always the
+leading red block that has to go with
+
+ align:start position:0%
+leading red block that has to go with
+ 
+
+ align:start position:0%
+leading red block that has to go with
+the um tra red block right so it could
+
+ align:start position:0%
+the um tra red block right so it could
+ 
+
+ align:start position:0%
+the um tra red block right so it could
+be you take some other block other red
+
+ align:start position:0%
+be you take some other block other red
+ 
+
+ align:start position:0%
+be you take some other block other red
+block and align it with this one um that
+
+ align:start position:0%
+block and align it with this one um that
+ 
+
+ align:start position:0%
+block and align it with this one um that
+is mostly a worry from a construction
+
+ align:start position:0%
+is mostly a worry from a construction
+ 
+
+ align:start position:0%
+is mostly a worry from a construction
+standpoint um if you did that you might
+
+ align:start position:0%
+standpoint um if you did that you might
+ 
+
+ align:start position:0%
+standpoint um if you did that you might
+get stuck uh but I claim if I do that
+
+ align:start position:0%
+get stuck uh but I claim if I do that
+ 
+
+ align:start position:0%
+get stuck uh but I claim if I do that
+it's it's never a problem to do that
+
+ align:start position:0%
+it's it's never a problem to do that
+ 
+
+ align:start position:0%
+it's it's never a problem to do that
+because this length is this total uh
+
+ align:start position:0%
+because this length is this total uh
+ 
+
+ align:start position:0%
+because this length is this total uh
+extent of these red guys is relatively
+
+ align:start position:0%
+extent of these red guys is relatively
+ 
+
+ align:start position:0%
+extent of these red guys is relatively
+small the whole length here is n sorry
+
+ align:start position:0%
+small the whole length here is n sorry
+ 
+
+ align:start position:0%
+small the whole length here is n sorry
+it's it's 3 * n over3
+
+ align:start position:0%
+it's it's 3 * n over3
+ 
+
+ align:start position:0%
+it's it's 3 * n over3
+whole length is n whereas all these AIS
+
+ align:start position:0%
+whole length is n whereas all these AIS
+ 
+
+ align:start position:0%
+whole length is n whereas all these AIS
+are scaled by a factor of much bigger
+
+ align:start position:0%
+are scaled by a factor of much bigger
+ 
+
+ align:start position:0%
+are scaled by a factor of much bigger
+than n well not a huge amount bigger but
+
+ align:start position:0%
+than n well not a huge amount bigger but
+ 
+
+ align:start position:0%
+than n well not a huge amount bigger but
+bigger than n so even to get in vaguely
+
+ align:start position:0%
+bigger than n so even to get in vaguely
+ 
+
+ align:start position:0%
+bigger than n so even to get in vaguely
+the this is why I was saying what to get
+
+ align:start position:0%
+the this is why I was saying what to get
+ 
+
+ align:start position:0%
+the this is why I was saying what to get
+this red block or any of these Red
+
+ align:start position:0%
+this red block or any of these Red
+ 
+
+ align:start position:0%
+this red block or any of these Red
+Blocks near this one uh because these
+
+ align:start position:0%
+Blocks near this one uh because these
+ 
+
+ align:start position:0%
+Blocks near this one uh because these
+things are scaled so huge uh you to get
+
+ align:start position:0%
+things are scaled so huge uh you to get
+ 
+
+ align:start position:0%
+things are scaled so huge uh you to get
+one close is the same as getting all of
+
+ align:start position:0%
+one close is the same as getting all of
+ 
+
+ align:start position:0%
+one close is the same as getting all of
+them close so for if you happen to
+
+ align:start position:0%
+them close so for if you happen to
+ 
+
+ align:start position:0%
+them close so for if you happen to
+succeed in a way that gets the Reds to
+
+ align:start position:0%
+succeed in a way that gets the Reds to
+ 
+
+ align:start position:0%
+succeed in a way that gets the Reds to
+align in out of order that would still
+
+ align:start position:0%
+align in out of order that would still
+ 
+
+ align:start position:0%
+align in out of order that would still
+give a valid solution to three part
+
+ align:start position:0%
+give a valid solution to three part
+ 
+
+ align:start position:0%
+give a valid solution to three part
+that's the point because we SC
+
+ align:start position:0%
+that's the point because we SC
+ 
+
+ align:start position:0%
+that's the point because we SC
+everything so huge um
+
+ align:start position:0%
+everything so huge um
+ 
+
+ align:start position:0%
+everything so huge um
+the to do the other direction say if you
+
+ align:start position:0%
+the to do the other direction say if you
+ 
+
+ align:start position:0%
+the to do the other direction say if you
+have a solution to three partition then
+
+ align:start position:0%
+have a solution to three partition then
+ 
+
+ align:start position:0%
+have a solution to three partition then
+there's a solution to this instance
+
+ align:start position:0%
+there's a solution to this instance
+ 
+
+ align:start position:0%
+there's a solution to this instance
+there we do it in order so that we're in
+
+ align:start position:0%
+there we do it in order so that we're in
+ 
+
+ align:start position:0%
+there we do it in order so that we're in
+control and make sure every all the
+
+ align:start position:0%
+control and make sure every all the
+ 
+
+ align:start position:0%
+control and make sure every all the
+constants add up right and that's that's
+
+ align:start position:0%
+constants add up right and that's that's
+ 
+
+ align:start position:0%
+constants add up right and that's that's
+sort of the annoying part of this proof
+
+ align:start position:0%
+sort of the annoying part of this proof
+ 
+
+ align:start position:0%
+sort of the annoying part of this proof
+but this is a relatively easy proof
+
+ align:start position:0%
+but this is a relatively easy proof
+ 
+
+ align:start position:0%
+but this is a relatively easy proof
+except for these little additive
+
+ align:start position:0%
+except for these little additive
+ 
+
+ align:start position:0%
+except for these little additive
+constants to make sure everything lines
+
+ align:start position:0%
+constants to make sure everything lines
+ 
+
+ align:start position:0%
+constants to make sure everything lines
+up it would be great if I could just put
+
+ align:start position:0%
+up it would be great if I could just put
+ 
+
+ align:start position:0%
+up it would be great if I could just put
+these Reds on top of each other but then
+
+ align:start position:0%
+these Reds on top of each other but then
+ 
+
+ align:start position:0%
+these Reds on top of each other but then
+they're one group and you delete them
+
+ align:start position:0%
+they're one group and you delete them
+ 
+
+ align:start position:0%
+they're one group and you delete them
+all at once so I have to put these
+
+ align:start position:0%
+all at once so I have to put these
+ 
+
+ align:start position:0%
+all at once so I have to put these
+things in between they have to be length
+
+ align:start position:0%
+things in between they have to be length
+ 
+
+ align:start position:0%
+things in between they have to be length
+two so I can destroy them when I need
+
+ align:start position:0%
+two so I can destroy them when I need
+ 
+
+ align:start position:0%
+two so I can destroy them when I need
+whenever I want to and so all these
+
+ align:start position:0%
+whenever I want to and so all these
+ 
+
+ align:start position:0%
+whenever I want to and so all these
+additive constants kind of get in the
+
+ align:start position:0%
+additive constants kind of get in the
+ 
+
+ align:start position:0%
+additive constants kind of get in the
+way but um it's not too
+
+ align:start position:0%
+way but um it's not too
+ 
+
+ align:start position:0%
+way but um it's not too
+bad other questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof that's click
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mania cool next is
+
+ align:start position:0%
+Mania cool next is
+ 
+
+ align:start position:0%
+Mania cool next is
+Tetris as advertised in the original um
+
+ align:start position:0%
+Tetris as advertised in the original um
+ 
+
+ align:start position:0%
+Tetris as advertised in the original um
+first first lecture uh so if you haven't
+
+ align:start position:0%
+first first lecture uh so if you haven't
+ 
+
+ align:start position:0%
+first first lecture uh so if you haven't
+played
+
+ align:start position:0%
+played
+ 
+
+ align:start position:0%
+played
+Tetris here is the I hope you've played
+
+ align:start position:0%
+Tetris here is the I hope you've played
+ 
+
+ align:start position:0%
+Tetris here is the I hope you've played
+Tetris I played a lot as a kid uh you
+
+ align:start position:0%
+Tetris I played a lot as a kid uh you
+ 
+
+ align:start position:0%
+Tetris I played a lot as a kid uh you
+have these tetromino blocks you can
+
+ align:start position:0%
+have these tetromino blocks you can
+ 
+
+ align:start position:0%
+have these tetromino blocks you can
+rotate them and then you can Force drop
+
+ align:start position:0%
+rotate them and then you can Force drop
+ 
+
+ align:start position:0%
+rotate them and then you can Force drop
+them or you can slowly drop them and do
+
+ align:start position:0%
+them or you can slowly drop them and do
+ 
+
+ align:start position:0%
+them or you can slowly drop them and do
+weird things like that uh you know sort
+
+ align:start position:0%
+weird things like that uh you know sort
+ 
+
+ align:start position:0%
+weird things like that uh you know sort
+of last minute
+
+ align:start position:0%
+of last minute
+ 
+
+ align:start position:0%
+of last minute
+moves uh let
+
+ align:start position:0%
+moves uh let
+ 
+
+ align:start position:0%
+moves uh let
+see I don't think that's yeah the
+
+ align:start position:0%
+see I don't think that's yeah the
+ 
+
+ align:start position:0%
+see I don't think that's yeah the
+rotation centers are always a bit funny
+
+ align:start position:0%
+rotation centers are always a bit funny
+ 
+
+ align:start position:0%
+rotation centers are always a bit funny
+so you can do cool things uh so let's
+
+ align:start position:0%
+so you can do cool things uh so let's
+ 
+
+ align:start position:0%
+so you can do cool things uh so let's
+let's have some
+
+ align:start position:0%
+let's have some
+ 
+
+ align:start position:0%
+let's have some
+fun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I'll just play Tetris for the rest of
+
+ align:start position:0%
+uh I'll just play Tetris for the rest of
+ 
+
+ align:start position:0%
+uh I'll just play Tetris for the rest of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+class okay uh so important rule is when
+
+ align:start position:0%
+class okay uh so important rule is when
+ 
+
+ align:start position:0%
+class okay uh so important rule is when
+you complete a line then that line
+
+ align:start position:0%
+you complete a line then that line
+ 
+
+ align:start position:0%
+you complete a line then that line
+disappears although in the proof we will
+
+ align:start position:0%
+disappears although in the proof we will
+ 
+
+ align:start position:0%
+disappears although in the proof we will
+prevent that from happening uh it is a
+
+ align:start position:0%
+prevent that from happening uh it is a
+ 
+
+ align:start position:0%
+prevent that from happening uh it is a
+rule of the game that's
+
+ align:start position:0%
+rule of the game that's
+ 
+
+ align:start position:0%
+rule of the game that's
+annoying also annoying
+
+ align:start position:0%
+annoying also annoying
+ 
+
+ align:start position:0%
+annoying also annoying
+okay well you get the idea you're super
+
+ align:start position:0%
+okay well you get the idea you're super
+ 
+
+ align:start position:0%
+okay well you get the idea you're super
+impressed by my Tetris
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skills all right so um cool I used to
+
+ align:start position:0%
+skills all right so um cool I used to
+ 
+
+ align:start position:0%
+skills all right so um cool I used to
+play it on Game Boy but uh and then NES
+
+ align:start position:0%
+play it on Game Boy but uh and then NES
+ 
+
+ align:start position:0%
+play it on Game Boy but uh and then NES
+you can play it on the Green
+
+ align:start position:0%
+you can play it on the Green
+ 
+
+ align:start position:0%
+you can play it on the Green
+Building um this happened in 2012
+
+ align:start position:0%
+Building um this happened in 2012
+ 
+
+ align:start position:0%
+Building um this happened in 2012
+finally after it was dreamed for many
+
+ align:start position:0%
+finally after it was dreamed for many
+ 
+
+ align:start position:0%
+finally after it was dreamed for many
+years uh I am a Tetris Master according
+
+ align:start position:0%
+years uh I am a Tetris Master according
+ 
+
+ align:start position:0%
+years uh I am a Tetris Master according
+to the Harvard Tetra Society uh this was
+
+ align:start position:0%
+to the Harvard Tetra Society uh this was
+ 
+
+ align:start position:0%
+to the Harvard Tetra Society uh this was
+for proving and I didn't have to play a
+
+ align:start position:0%
+for proving and I didn't have to play a
+ 
+
+ align:start position:0%
+for proving and I didn't have to play a
+game to as you can tell uh for proving
+
+ align:start position:0%
+game to as you can tell uh for proving
+ 
+
+ align:start position:0%
+game to as you can tell uh for proving
+NP completeness and maximization of
+
+ align:start position:0%
+NP completeness and maximization of
+ 
+
+ align:start position:0%
+NP completeness and maximization of
+lines tetrises pieces plate or
+
+ align:start position:0%
+lines tetrises pieces plate or
+ 
+
+ align:start position:0%
+lines tetrises pieces plate or
+minimization of square height we masters
+
+ align:start position:0%
+minimization of square height we masters
+ 
+
+ align:start position:0%
+minimization of square height we masters
+of the Harvard tet Society hereby confer
+
+ align:start position:0%
+of the Harvard tet Society hereby confer
+ 
+
+ align:start position:0%
+of the Harvard tet Society hereby confer
+the title of tetras Master Eric D demain
+
+ align:start position:0%
+the title of tetras Master Eric D demain
+ 
+
+ align:start position:0%
+the title of tetras Master Eric D demain
+on the 16th day of the 12th month in the
+
+ align:start position:0%
+on the 16th day of the 12th month in the
+ 
+
+ align:start position:0%
+on the 16th day of the 12th month in the
+year 17 anot tetri which is since the
+
+ align:start position:0%
+year 17 anot tetri which is since the
+ 
+
+ align:start position:0%
+year 17 anot tetri which is since the
+invention of
+
+ align:start position:0%
+invention of
+ 
+
+ align:start position:0%
+invention of
+Tetris okay uh this is a proof done
+
+ align:start position:0%
+Tetris okay uh this is a proof done
+ 
+
+ align:start position:0%
+Tetris okay uh this is a proof done
+early in my career at MIT uh with two
+
+ align:start position:0%
+early in my career at MIT uh with two
+ 
+
+ align:start position:0%
+early in my career at MIT uh with two
+MIT students uh David Lanell and Susan
+
+ align:start position:0%
+MIT students uh David Lanell and Susan
+ 
+
+ align:start position:0%
+MIT students uh David Lanell and Susan
+hoen bger um now professors at other
+
+ align:start position:0%
+hoen bger um now professors at other
+ 
+
+ align:start position:0%
+hoen bger um now professors at other
+schools this was a first attempt at a
+
+ align:start position:0%
+schools this was a first attempt at a
+ 
+
+ align:start position:0%
+schools this was a first attempt at a
+proof we had many attempts at appr proof
+
+ align:start position:0%
+proof we had many attempts at appr proof
+ 
+
+ align:start position:0%
+proof we had many attempts at appr proof
+many of which all of which were wrong
+
+ align:start position:0%
+many of which all of which were wrong
+ 
+
+ align:start position:0%
+many of which all of which were wrong
+except the last one um yeah anyway you
+
+ align:start position:0%
+except the last one um yeah anyway you
+ 
+
+ align:start position:0%
+except the last one um yeah anyway you
+could try to see what's wrong with that
+
+ align:start position:0%
+could try to see what's wrong with that
+ 
+
+ align:start position:0%
+could try to see what's wrong with that
+proof but uh here is a a working proof
+
+ align:start position:0%
+proof but uh here is a a working proof
+ 
+
+ align:start position:0%
+proof but uh here is a a working proof
+this is actually not the first working
+
+ align:start position:0%
+this is actually not the first working
+ 
+
+ align:start position:0%
+this is actually not the first working
+proof we had uh you so there's me David
+
+ align:start position:0%
+proof we had uh you so there's me David
+ 
+
+ align:start position:0%
+proof we had uh you so there's me David
+and Susan and then uh we published a
+
+ align:start position:0%
+and Susan and then uh we published a
+ 
+
+ align:start position:0%
+and Susan and then uh we published a
+much harder version of the proof with
+
+ align:start position:0%
+much harder version of the proof with
+ 
+
+ align:start position:0%
+much harder version of the proof with
+like 500 cases and then these three guys
+
+ align:start position:0%
+like 500 cases and then these three guys
+ 
+
+ align:start position:0%
+like 500 cases and then these three guys
+read our paper and said hey I think we
+
+ align:start position:0%
+read our paper and said hey I think we
+ 
+
+ align:start position:0%
+read our paper and said hey I think we
+can simplify it like this and then we
+
+ align:start position:0%
+can simplify it like this and then we
+ 
+
+ align:start position:0%
+can simplify it like this and then we
+wrote joint Journal version so um
+
+ align:start position:0%
+wrote joint Journal version so um
+ 
+
+ align:start position:0%
+wrote joint Journal version so um
+reduction is from three partition
+
+ align:start position:0%
+reduction is from three partition
+ 
+
+ align:start position:0%
+reduction is from three partition
+surprise um this is so I should say what
+
+ align:start position:0%
+surprise um this is so I should say what
+ 
+
+ align:start position:0%
+surprise um this is so I should say what
+does Tetris mean from a computational
+
+ align:start position:0%
+does Tetris mean from a computational
+ 
+
+ align:start position:0%
+does Tetris mean from a computational
+complexity standpoint there are multiple
+
+ align:start position:0%
+complexity standpoint there are multiple
+ 
+
+ align:start position:0%
+complexity standpoint there are multiple
+interpretations our interpretation is I
+
+ align:start position:0%
+interpretations our interpretation is I
+ 
+
+ align:start position:0%
+interpretations our interpretation is I
+give you an initial board because you've
+
+ align:start position:0%
+give you an initial board because you've
+ 
+
+ align:start position:0%
+give you an initial board because you've
+already been playing for a while here's
+
+ align:start position:0%
+already been playing for a while here's
+ 
+
+ align:start position:0%
+already been playing for a while here's
+what you're what you have and then I
+
+ align:start position:0%
+what you're what you have and then I
+ 
+
+ align:start position:0%
+what you're what you have and then I
+give you the entire sequence of pieces
+
+ align:start position:0%
+give you the entire sequence of pieces
+ 
+
+ align:start position:0%
+give you the entire sequence of pieces
+that's going to come and I want to know
+
+ align:start position:0%
+that's going to come and I want to know
+ 
+
+ align:start position:0%
+that's going to come and I want to know
+can you survive maximize a number of
+
+ align:start position:0%
+can you survive maximize a number of
+ 
+
+ align:start position:0%
+can you survive maximize a number of
+lines uh this is not yet the the
+
+ align:start position:0%
+lines uh this is not yet the the
+ 
+
+ align:start position:0%
+lines uh this is not yet the the
+approximability part of the class but we
+
+ align:start position:0%
+approximability part of the class but we
+ 
+
+ align:start position:0%
+approximability part of the class but we
+get some really easy inapproximability
+
+ align:start position:0%
+get some really easy inapproximability
+ 
+
+ align:start position:0%
+get some really easy inapproximability
+results so I will mention them for now
+
+ align:start position:0%
+results so I will mention them for now
+ 
+
+ align:start position:0%
+results so I will mention them for now
+it's just can you survive the the
+
+ align:start position:0%
+it's just can you survive the the
+ 
+
+ align:start position:0%
+it's just can you survive the the
+ceiling is like here a couple couple uh
+
+ align:start position:0%
+ceiling is like here a couple couple uh
+ 
+
+ align:start position:0%
+ceiling is like here a couple couple uh
+rows above this initial picture so
+
+ align:start position:0%
+rows above this initial picture so
+ 
+
+ align:start position:0%
+rows above this initial picture so
+you're almost dead so it's like every
+
+ align:start position:0%
+you're almost dead so it's like every
+ 
+
+ align:start position:0%
+you're almost dead so it's like every
+second counts all right your goal is to
+
+ align:start position:0%
+second counts all right your goal is to
+ 
+
+ align:start position:0%
+second counts all right your goal is to
+fill up these Chambers these
+
+ align:start position:0%
+fill up these Chambers these
+ 
+
+ align:start position:0%
+fill up these Chambers these
+bins uh exactly with no holes so if you
+
+ align:start position:0%
+bins uh exactly with no holes so if you
+ 
+
+ align:start position:0%
+bins uh exactly with no holes so if you
+can do it at the end I'm going to give
+
+ align:start position:0%
+can do it at the end I'm going to give
+ 
+
+ align:start position:0%
+can do it at the end I'm going to give
+you a t and then a whole bunch of
+
+ align:start position:0%
+you a t and then a whole bunch of
+ 
+
+ align:start position:0%
+you a t and then a whole bunch of
+straits and then you you can win the
+
+ align:start position:0%
+straits and then you you can win the
+ 
+
+ align:start position:0%
+straits and then you you can win the
+game all right so uh so we have n over3
+
+ align:start position:0%
+game all right so uh so we have n over3
+ 
+
+ align:start position:0%
+game all right so uh so we have n over3
+of these buckets each one is roughly T
+
+ align:start position:0%
+of these buckets each one is roughly T
+ 
+
+ align:start position:0%
+of these buckets each one is roughly T
+tall uh there's some additive constant
+
+ align:start position:0%
+tall uh there's some additive constant
+ 
+
+ align:start position:0%
+tall uh there's some additive constant
+to deal with some stuff but uh there's T
+
+ align:start position:0%
+to deal with some stuff but uh there's T
+ 
+
+ align:start position:0%
+to deal with some stuff but uh there's T
+notches each of these is basically
+
+ align:start position:0%
+notches each of these is basically
+ 
+
+ align:start position:0%
+notches each of these is basically
+counting one unit of an
+
+ align:start position:0%
+counting one unit of an
+ 
+
+ align:start position:0%
+counting one unit of an
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+okay uh yeah the point is if you don't
+
+ align:start position:0%
+okay uh yeah the point is if you don't
+ 
+
+ align:start position:0%
+okay uh yeah the point is if you don't
+open this thing where the is going to go
+
+ align:start position:0%
+open this thing where the is going to go
+ 
+
+ align:start position:0%
+open this thing where the is going to go
+and you will only be able to open this
+
+ align:start position:0%
+and you will only be able to open this
+ 
+
+ align:start position:0%
+and you will only be able to open this
+thing if this is full and this is full
+
+ align:start position:0%
+thing if this is full and this is full
+ 
+
+ align:start position:0%
+thing if this is full and this is full
+and this is full and this is full so
+
+ align:start position:0%
+and this is full and this is full so
+ 
+
+ align:start position:0%
+and this is full and this is full so
+you've got to get these perfect so that
+
+ align:start position:0%
+you've got to get these perfect so that
+ 
+
+ align:start position:0%
+you've got to get these perfect so that
+at the top you can open this and and
+
+ align:start position:0%
+at the top you can open this and and
+ 
+
+ align:start position:0%
+at the top you can open this and and
+then clear
+
+ align:start position:0%
+then clear
+ 
+
+ align:start position:0%
+then clear
+everything okay uh so here are the
+
+ align:start position:0%
+everything okay uh so here are the
+ 
+
+ align:start position:0%
+everything okay uh so here are the
+gadgets from the piece pers perspective
+
+ align:start position:0%
+gadgets from the piece pers perspective
+ 
+
+ align:start position:0%
+gadgets from the piece pers perspective
+that was the initial configuration of
+
+ align:start position:0%
+that was the initial configuration of
+ 
+
+ align:start position:0%
+that was the initial configuration of
+course there are no AIS yet so the piece
+
+ align:start position:0%
+course there are no AIS yet so the piece
+ 
+
+ align:start position:0%
+course there are no AIS yet so the piece
+sequence has to encode the AIS in uny
+
+ align:start position:0%
+sequence has to encode the AIS in uny
+ 
+
+ align:start position:0%
+sequence has to encode the AIS in uny
+because you there are only a constant
+
+ align:start position:0%
+because you there are only a constant
+ 
+
+ align:start position:0%
+because you there are only a constant
+number of different tetromino pieces uh
+
+ align:start position:0%
+number of different tetromino pieces uh
+ 
+
+ align:start position:0%
+number of different tetromino pieces uh
+so you have to encode well I guess you
+
+ align:start position:0%
+so you have to encode well I guess you
+ 
+
+ align:start position:0%
+so you have to encode well I guess you
+could try to encode in binary it's very
+
+ align:start position:0%
+could try to encode in binary it's very
+ 
+
+ align:start position:0%
+could try to encode in binary it's very
+hard to add uh when you're working with
+
+ align:start position:0%
+hard to add uh when you're working with
+ 
+
+ align:start position:0%
+hard to add uh when you're working with
+chromas unless you do it in uny so um
+
+ align:start position:0%
+chromas unless you do it in uny so um
+ 
+
+ align:start position:0%
+chromas unless you do it in uny so um
+here's the idea we have an initial setup
+
+ align:start position:0%
+here's the idea we have an initial setup
+ 
+
+ align:start position:0%
+here's the idea we have an initial setup
+like this it will always have this
+
+ align:start position:0%
+like this it will always have this
+ 
+
+ align:start position:0%
+like this it will always have this
+little thing in the corner and so to say
+
+ align:start position:0%
+little thing in the corner and so to say
+ 
+
+ align:start position:0%
+little thing in the corner and so to say
+hey new AI is starting we're going to
+
+ align:start position:0%
+hey new AI is starting we're going to
+ 
+
+ align:start position:0%
+hey new AI is starting we're going to
+give you uh might call this a right word
+
+ align:start position:0%
+give you uh might call this a right word
+ 
+
+ align:start position:0%
+give you uh might call this a right word
+pointing L if you look from the barrel
+
+ align:start position:0%
+pointing L if you look from the barrel
+ 
+
+ align:start position:0%
+pointing L if you look from the barrel
+of the gun then it goes to the right um
+
+ align:start position:0%
+of the gun then it goes to the right um
+ 
+
+ align:start position:0%
+of the gun then it goes to the right um
+so that makes a nice flat face here
+
+ align:start position:0%
+so that makes a nice flat face here
+ 
+
+ align:start position:0%
+so that makes a nice flat face here
+because the next piece that's coming is
+
+ align:start position:0%
+because the next piece that's coming is
+ 
+
+ align:start position:0%
+because the next piece that's coming is
+a 2X two square so what you're going to
+
+ align:start position:0%
+a 2X two square so what you're going to
+ 
+
+ align:start position:0%
+a 2X two square so what you're going to
+do is let it drop all the way and then
+
+ align:start position:0%
+do is let it drop all the way and then
+ 
+
+ align:start position:0%
+do is let it drop all the way and then
+at the very last second you slide it to
+
+ align:start position:0%
+at the very last second you slide it to
+ 
+
+ align:start position:0%
+at the very last second you slide it to
+the right okay uh and in general we're
+
+ align:start position:0%
+the right okay uh and in general we're
+ 
+
+ align:start position:0%
+the right okay uh and in general we're
+going to represent AI by this pattern
+
+ align:start position:0%
+going to represent AI by this pattern
+ 
+
+ align:start position:0%
+going to represent AI by this pattern
+Square left L Square to the power AI
+
+ align:start position:0%
+Square left L Square to the power AI
+ 
+
+ align:start position:0%
+Square left L Square to the power AI
+like we're going to repeat that AI times
+
+ align:start position:0%
+like we're going to repeat that AI times
+ 
+
+ align:start position:0%
+like we're going to repeat that AI times
+so here I've repeated it twice and then
+
+ align:start position:0%
+so here I've repeated it twice and then
+ 
+
+ align:start position:0%
+so here I've repeated it twice and then
+dot dot dot okay that is encoding AI in
+
+ align:start position:0%
+dot dot dot okay that is encoding AI in
+ 
+
+ align:start position:0%
+dot dot dot okay that is encoding AI in
+un or I don't know if there's something
+
+ align:start position:0%
+un or I don't know if there's something
+ 
+
+ align:start position:0%
+un or I don't know if there's something
+smaller than un where you use three
+
+ align:start position:0%
+smaller than un where you use three
+ 
+
+ align:start position:0%
+smaller than un where you use three
+objects to represent one one unit but uh
+
+ align:start position:0%
+objects to represent one one unit but uh
+ 
+
+ align:start position:0%
+objects to represent one one unit but uh
+there you go and then at the end the at
+
+ align:start position:0%
+there you go and then at the end the at
+ 
+
+ align:start position:0%
+there you go and then at the end the at
+the end of the AI we're going to sort of
+
+ align:start position:0%
+the end of the AI we're going to sort of
+ 
+
+ align:start position:0%
+the end of the AI we're going to sort of
+finish things off and reset to this
+
+ align:start position:0%
+finish things off and reset to this
+ 
+
+ align:start position:0%
+finish things off and reset to this
+original kind of configuration by saying
+
+ align:start position:0%
+original kind of configuration by saying
+ 
+
+ align:start position:0%
+original kind of configuration by saying
+Square uh and
+
+ align:start position:0%
+Square uh and
+ 
+
+ align:start position:0%
+Square uh and
+straight okay so the square Nestles in
+
+ align:start position:0%
+straight okay so the square Nestles in
+ 
+
+ align:start position:0%
+straight okay so the square Nestles in
+there we get a straight uh and if all
+
+ align:start position:0%
+there we get a straight uh and if all
+ 
+
+ align:start position:0%
+there we get a straight uh and if all
+goes according to plan what you've done
+
+ align:start position:0%
+goes according to plan what you've done
+ 
+
+ align:start position:0%
+goes according to plan what you've done
+is filled up basically AI units of this
+
+ align:start position:0%
+is filled up basically AI units of this
+ 
+
+ align:start position:0%
+is filled up basically AI units of this
+thing and maybe plus one but we know
+
+ align:start position:0%
+thing and maybe plus one but we know
+ 
+
+ align:start position:0%
+thing and maybe plus one but we know
+there's only three AIS going into each
+
+ align:start position:0%
+there's only three AIS going into each
+ 
+
+ align:start position:0%
+there's only three AIS going into each
+bucket so we can deal with a plus add of
+
+ align:start position:0%
+bucket so we can deal with a plus add of
+ 
+
+ align:start position:0%
+bucket so we can deal with a plus add of
+three that's no big deal um
+
+ align:start position:0%
+three that's no big deal um
+ 
+
+ align:start position:0%
+three that's no big deal um
+and that's good so now you have a choice
+
+ align:start position:0%
+and that's good so now you have a choice
+ 
+
+ align:start position:0%
+and that's good so now you have a choice
+you have this long sequence of pieces
+
+ align:start position:0%
+you have this long sequence of pieces
+ 
+
+ align:start position:0%
+you have this long sequence of pieces
+representing AI in general the P
+
+ align:start position:0%
+representing AI in general the P
+ 
+
+ align:start position:0%
+representing AI in general the P
+sequence is the P sequence for A1 P
+
+ align:start position:0%
+sequence is the P sequence for A1 P
+ 
+
+ align:start position:0%
+sequence is the P sequence for A1 P
+sequence for A2 P sequence for A3 the
+
+ align:start position:0%
+sequence for A2 P sequence for A3 the
+ 
+
+ align:start position:0%
+sequence for A2 P sequence for A3 the
+intent is you put all of these pieces
+
+ align:start position:0%
+intent is you put all of these pieces
+ 
+
+ align:start position:0%
+intent is you put all of these pieces
+into one column one of these buckets uh
+
+ align:start position:0%
+into one column one of these buckets uh
+ 
+
+ align:start position:0%
+into one column one of these buckets uh
+the claim is you can you can't again
+
+ align:start position:0%
+the claim is you can you can't again
+ 
+
+ align:start position:0%
+the claim is you can you can't again
+this is divisibility issue the big issue
+
+ align:start position:0%
+this is divisibility issue the big issue
+ 
+
+ align:start position:0%
+this is divisibility issue the big issue
+is can we divide AI into two parts put
+
+ align:start position:0%
+is can we divide AI into two parts put
+ 
+
+ align:start position:0%
+is can we divide AI into two parts put
+part of it in one bucket part of it in
+
+ align:start position:0%
+part of it in one bucket part of it in
+ 
+
+ align:start position:0%
+part of it in one bucket part of it in
+another bucket that would not give us a
+
+ align:start position:0%
+another bucket that would not give us a
+ 
+
+ align:start position:0%
+another bucket that would not give us a
+solution to three partition but the
+
+ align:start position:0%
+solution to three partition but the
+ 
+
+ align:start position:0%
+solution to three partition but the
+claim is you can't and the proof of this
+
+ align:start position:0%
+claim is you can't and the proof of this
+ 
+
+ align:start position:0%
+claim is you can't and the proof of this
+claim is not too hard for this proof it
+
+ align:start position:0%
+claim is not too hard for this proof it
+ 
+
+ align:start position:0%
+claim is not too hard for this proof it
+was much more tedious for the original
+
+ align:start position:0%
+was much more tedious for the original
+ 
+
+ align:start position:0%
+was much more tedious for the original
+proof uh but basically you try
+
+ align:start position:0%
+proof uh but basically you try
+ 
+
+ align:start position:0%
+proof uh but basically you try
+everything else and show that you doomed
+
+ align:start position:0%
+everything else and show that you doomed
+ 
+
+ align:start position:0%
+everything else and show that you doomed
+uh so every other possible move um so
+
+ align:start position:0%
+uh so every other possible move um so
+ 
+
+ align:start position:0%
+uh so every other possible move um so
+one type of bad move so we um when you
+
+ align:start position:0%
+one type of bad move so we um when you
+ 
+
+ align:start position:0%
+one type of bad move so we um when you
+when you do um this thing of putting in
+
+ align:start position:0%
+when you do um this thing of putting in
+ 
+
+ align:start position:0%
+when you do um this thing of putting in
+the rightward facing L remember there's
+
+ align:start position:0%
+the rightward facing L remember there's
+ 
+
+ align:start position:0%
+the rightward facing L remember there's
+only rightward facing L's there's only n
+
+ align:start position:0%
+only rightward facing L's there's only n
+ 
+
+ align:start position:0%
+only rightward facing L's there's only n
+of them one per
+
+ align:start position:0%
+of them one per
+ 
+
+ align:start position:0%
+of them one per
+AI so that's the only sort of nice piece
+
+ align:start position:0%
+AI so that's the only sort of nice piece
+ 
+
+ align:start position:0%
+AI so that's the only sort of nice piece
+we call this priming a bucket uh because
+
+ align:start position:0%
+we call this priming a bucket uh because
+ 
+
+ align:start position:0%
+we call this priming a bucket uh because
+now it has a nice flat bottom and so
+
+ align:start position:0%
+now it has a nice flat bottom and so
+ 
+
+ align:start position:0%
+now it has a nice flat bottom and so
+these pieces fit nicely especially the
+
+ align:start position:0%
+these pieces fit nicely especially the
+ 
+
+ align:start position:0%
+these pieces fit nicely especially the
+squares so one issue is what if you have
+
+ align:start position:0%
+squares so one issue is what if you have
+ 
+
+ align:start position:0%
+squares so one issue is what if you have
+an unprimed bucket it still has this
+
+ align:start position:0%
+an unprimed bucket it still has this
+ 
+
+ align:start position:0%
+an unprimed bucket it still has this
+stuff over on the left and you try to
+
+ align:start position:0%
+stuff over on the left and you try to
+ 
+
+ align:start position:0%
+stuff over on the left and you try to
+just insert into it cuz uh first A1
+
+ align:start position:0%
+just insert into it cuz uh first A1
+ 
+
+ align:start position:0%
+just insert into it cuz uh first A1
+comes you prime one of the buckets
+
+ align:start position:0%
+comes you prime one of the buckets
+ 
+
+ align:start position:0%
+comes you prime one of the buckets
+what if you switch Midstream and try to
+
+ align:start position:0%
+what if you switch Midstream and try to
+ 
+
+ align:start position:0%
+what if you switch Midstream and try to
+move the rest into an unprimed bucket
+
+ align:start position:0%
+move the rest into an unprimed bucket
+ 
+
+ align:start position:0%
+move the rest into an unprimed bucket
+claim is you die you look at the squares
+
+ align:start position:0%
+claim is you die you look at the squares
+ 
+
+ align:start position:0%
+claim is you die you look at the squares
+you say well it could go here or here or
+
+ align:start position:0%
+you say well it could go here or here or
+ 
+
+ align:start position:0%
+you say well it could go here or here or
+or higher and they're all bad uh this
+
+ align:start position:0%
+or higher and they're all bad uh this
+ 
+
+ align:start position:0%
+or higher and they're all bad uh this
+one means you'll never fill this stuff
+
+ align:start position:0%
+one means you'll never fill this stuff
+ 
+
+ align:start position:0%
+one means you'll never fill this stuff
+uh so you're basically going to run out
+
+ align:start position:0%
+uh so you're basically going to run out
+ 
+
+ align:start position:0%
+uh so you're basically going to run out
+of area something's going to have to go
+
+ align:start position:0%
+of area something's going to have to go
+ 
+
+ align:start position:0%
+of area something's going to have to go
+into the sky uh if you put this here
+
+ align:start position:0%
+into the sky uh if you put this here
+ 
+
+ align:start position:0%
+into the sky uh if you put this here
+you'll never get anything here you put
+
+ align:start position:0%
+you'll never get anything here you put
+ 
+
+ align:start position:0%
+you'll never get anything here you put
+that there you'll never get anything
+
+ align:start position:0%
+that there you'll never get anything
+ 
+
+ align:start position:0%
+that there you'll never get anything
+here because squares won't fit anymore
+
+ align:start position:0%
+here because squares won't fit anymore
+ 
+
+ align:start position:0%
+here because squares won't fit anymore
+so on uh L's can't go pass through that
+
+ align:start position:0%
+so on uh L's can't go pass through that
+ 
+
+ align:start position:0%
+so on uh L's can't go pass through that
+thing okay similarly if you try to put a
+
+ align:start position:0%
+thing okay similarly if you try to put a
+ 
+
+ align:start position:0%
+thing okay similarly if you try to put a
+straightaway in something bad happens I
+
+ align:start position:0%
+straightaway in something bad happens I
+ 
+
+ align:start position:0%
+straightaway in something bad happens I
+don't quite remember what the bad thing
+
+ align:start position:0%
+don't quite remember what the bad thing
+ 
+
+ align:start position:0%
+don't quite remember what the bad thing
+is here uh but that
+
+ align:start position:0%
+is here uh but that
+ 
+
+ align:start position:0%
+is here uh but that
+looks right you can once you cover one
+
+ align:start position:0%
+looks right you can once you cover one
+ 
+
+ align:start position:0%
+looks right you can once you cover one
+you can't cover the other yeah it's not
+
+ align:start position:0%
+you can't cover the other yeah it's not
+ 
+
+ align:start position:0%
+you can't cover the other yeah it's not
+even obvious you can cover this one but
+
+ align:start position:0%
+even obvious you can cover this one but
+ 
+
+ align:start position:0%
+even obvious you can cover this one but
+I think with some clever rotation you
+
+ align:start position:0%
+I think with some clever rotation you
+ 
+
+ align:start position:0%
+I think with some clever rotation you
+can ah Tetris is a little weird in that
+
+ align:start position:0%
+can ah Tetris is a little weird in that
+ 
+
+ align:start position:0%
+can ah Tetris is a little weird in that
+respect um and then with the leftward
+
+ align:start position:0%
+respect um and then with the leftward
+ 
+
+ align:start position:0%
+respect um and then with the leftward
+facing L's you can try all the things
+
+ align:start position:0%
+facing L's you can try all the things
+ 
+
+ align:start position:0%
+facing L's you can try all the things
+and again you're
+
+ align:start position:0%
+and again you're
+ 
+
+ align:start position:0%
+and again you're
+toast okay so that's one type of bad
+
+ align:start position:0%
+toast okay so that's one type of bad
+ 
+
+ align:start position:0%
+toast okay so that's one type of bad
+thing where you switch mid stream from
+
+ align:start position:0%
+thing where you switch mid stream from
+ 
+
+ align:start position:0%
+thing where you switch mid stream from
+one of you you start putting an AI into
+
+ align:start position:0%
+one of you you start putting an AI into
+ 
+
+ align:start position:0%
+one of you you start putting an AI into
+a bucket and then you try to put it into
+
+ align:start position:0%
+a bucket and then you try to put it into
+ 
+
+ align:start position:0%
+a bucket and then you try to put it into
+a bucket that's currently unprimed um
+
+ align:start position:0%
+a bucket that's currently unprimed um
+ 
+
+ align:start position:0%
+a bucket that's currently unprimed um
+the so
+
+ align:start position:0%
+the so
+ 
+
+ align:start position:0%
+the so
+uh what's left is if you stick to one
+
+ align:start position:0%
+uh what's left is if you stick to one
+ 
+
+ align:start position:0%
+uh what's left is if you stick to one
+bucket uh do you have to play like we
+
+ align:start position:0%
+bucket uh do you have to play like we
+ 
+
+ align:start position:0%
+bucket uh do you have to play like we
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+play and so in the sequence of pieces
+
+ align:start position:0%
+play and so in the sequence of pieces
+ 
+
+ align:start position:0%
+play and so in the sequence of pieces
+after you've when you haven't placed
+
+ align:start position:0%
+after you've when you haven't placed
+ 
+
+ align:start position:0%
+after you've when you haven't placed
+anything well maybe you try to prime it
+
+ align:start position:0%
+anything well maybe you try to prime it
+ 
+
+ align:start position:0%
+anything well maybe you try to prime it
+in a different way and then that opens
+
+ align:start position:0%
+in a different way and then that opens
+ 
+
+ align:start position:0%
+in a different way and then that opens
+up something else because then you'd
+
+ align:start position:0%
+up something else because then you'd
+ 
+
+ align:start position:0%
+up something else because then you'd
+have to go through that entire analysis
+
+ align:start position:0%
+have to go through that entire analysis
+ 
+
+ align:start position:0%
+have to go through that entire analysis
+from the last slide again uh for however
+
+ align:start position:0%
+from the last slide again uh for however
+ 
+
+ align:start position:0%
+from the last slide again uh for however
+the unprimed bucket might look but it
+
+ align:start position:0%
+the unprimed bucket might look but it
+ 
+
+ align:start position:0%
+the unprimed bucket might look but it
+turns out however you do it uh you're
+
+ align:start position:0%
+turns out however you do it uh you're
+ 
+
+ align:start position:0%
+turns out however you do it uh you're
+toast you've you've hidden some Square
+
+ align:start position:0%
+toast you've you've hidden some Square
+ 
+
+ align:start position:0%
+toast you've you've hidden some Square
+which you won't be able to uh open up
+
+ align:start position:0%
+which you won't be able to uh open up
+ 
+
+ align:start position:0%
+which you won't be able to uh open up
+unless you do it the right way and once
+
+ align:start position:0%
+unless you do it the right way and once
+ 
+
+ align:start position:0%
+unless you do it the right way and once
+you've done that piece you check that
+
+ align:start position:0%
+you've done that piece you check that
+ 
+
+ align:start position:0%
+you've done that piece you check that
+the next piece has only one place to go
+
+ align:start position:0%
+the next piece has only one place to go
+ 
+
+ align:start position:0%
+the next piece has only one place to go
+uh obviously if it's to the left then
+
+ align:start position:0%
+uh obviously if it's to the left then
+ 
+
+ align:start position:0%
+uh obviously if it's to the left then
+those are not good uh and then the next
+
+ align:start position:0%
+those are not good uh and then the next
+ 
+
+ align:start position:0%
+those are not good uh and then the next
+piece and so on so you check all these
+
+ align:start position:0%
+piece and so on so you check all these
+ 
+
+ align:start position:0%
+piece and so on so you check all these
+things and you conclude there's really
+
+ align:start position:0%
+things and you conclude there's really
+ 
+
+ align:start position:0%
+things and you conclude there's really
+only one way to play this sequence
+
+ align:start position:0%
+only one way to play this sequence
+ 
+
+ align:start position:0%
+only one way to play this sequence
+except for the flexibility of when a new
+
+ align:start position:0%
+except for the flexibility of when a new
+ 
+
+ align:start position:0%
+except for the flexibility of when a new
+AI stream comes which bucket do I put it
+
+ align:start position:0%
+AI stream comes which bucket do I put it
+ 
+
+ align:start position:0%
+AI stream comes which bucket do I put it
+in we're assuming here infinite
+
+ align:start position:0%
+in we're assuming here infinite
+ 
+
+ align:start position:0%
+in we're assuming here infinite
+dexterity so you can slide to the left
+
+ align:start position:0%
+dexterity so you can slide to the left
+ 
+
+ align:start position:0%
+dexterity so you can slide to the left
+and right pick the bucket you want and
+
+ align:start position:0%
+and right pick the bucket you want and
+ 
+
+ align:start position:0%
+and right pick the bucket you want and
+then let it
+
+ align:start position:0%
+then let it
+ 
+
+ align:start position:0%
+then let it
+fall questions yeah so you set up the
+
+ align:start position:0%
+fall questions yeah so you set up the
+ 
+
+ align:start position:0%
+fall questions yeah so you set up the
+you set up the infrastructure so that if
+
+ align:start position:0%
+you set up the infrastructure so that if
+ 
+
+ align:start position:0%
+you set up the infrastructure so that if
+you leave even one space unfilled and
+
+ align:start position:0%
+you leave even one space unfilled and
+ 
+
+ align:start position:0%
+you leave even one space unfilled and
+you're going to die before
+
+ align:start position:0%
+you're going to die before
+ 
+
+ align:start position:0%
+you're going to die before
+you yes um
+
+ align:start position:0%
+you yes um
+ 
+
+ align:start position:0%
+you yes um
+so the idea is that if you leave any
+
+ align:start position:0%
+so the idea is that if you leave any
+ 
+
+ align:start position:0%
+so the idea is that if you leave any
+Square out here you will be in trouble
+
+ align:start position:0%
+Square out here you will be in trouble
+ 
+
+ align:start position:0%
+Square out here you will be in trouble
+um and I there are probably many ways to
+
+ align:start position:0%
+um and I there are probably many ways to
+ 
+
+ align:start position:0%
+um and I there are probably many ways to
+do this and I forget exactly what we do
+
+ align:start position:0%
+do this and I forget exactly what we do
+ 
+
+ align:start position:0%
+do this and I forget exactly what we do
+in the paper I think the easy one would
+
+ align:start position:0%
+in the paper I think the easy one would
+ 
+
+ align:start position:0%
+in the paper I think the easy one would
+be that if you put any square up here
+
+ align:start position:0%
+be that if you put any square up here
+ 
+
+ align:start position:0%
+be that if you put any square up here
+you die so you're right at the limit of
+
+ align:start position:0%
+you die so you're right at the limit of
+ 
+
+ align:start position:0%
+you die so you're right at the limit of
+the game if anything doesn't go into a
+
+ align:start position:0%
+the game if anything doesn't go into a
+ 
+
+ align:start position:0%
+the game if anything doesn't go into a
+bucket you're in trouble and then it's
+
+ align:start position:0%
+bucket you're in trouble and then it's
+ 
+
+ align:start position:0%
+bucket you're in trouble and then it's
+just a volume argument so you've got all
+
+ align:start position:0%
+just a volume argument so you've got all
+ 
+
+ align:start position:0%
+just a volume argument so you've got all
+these pieces the total volume of them is
+
+ align:start position:0%
+these pieces the total volume of them is
+ 
+
+ align:start position:0%
+these pieces the total volume of them is
+exactly the sum of the bucket sizes so
+
+ align:start position:0%
+exactly the sum of the bucket sizes so
+ 
+
+ align:start position:0%
+exactly the sum of the bucket sizes so
+if you leave any blank blank space that
+
+ align:start position:0%
+if you leave any blank blank space that
+ 
+
+ align:start position:0%
+if you leave any blank blank space that
+means that the material that was there
+
+ align:start position:0%
+means that the material that was there
+ 
+
+ align:start position:0%
+means that the material that was there
+is going to somehow end up on the top
+
+ align:start position:0%
+is going to somehow end up on the top
+ 
+
+ align:start position:0%
+is going to somehow end up on the top
+row and then you're
+
+ align:start position:0%
+row and then you're
+ 
+
+ align:start position:0%
+row and then you're
+dead I don't remember if that's exactly
+
+ align:start position:0%
+dead I don't remember if that's exactly
+ 
+
+ align:start position:0%
+dead I don't remember if that's exactly
+what we did but that certainly seems to
+
+ align:start position:0%
+what we did but that certainly seems to
+ 
+
+ align:start position:0%
+what we did but that certainly seems to
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+Adam if you place something too high but
+
+ align:start position:0%
+Adam if you place something too high but
+ 
+
+ align:start position:0%
+Adam if you place something too high but
+at the same time finish a line do you
+
+ align:start position:0%
+at the same time finish a line do you
+ 
+
+ align:start position:0%
+at the same time finish a line do you
+die
+
+ align:start position:0%
+die
+ 
+
+ align:start position:0%
+die
+and um could we force our way through
+
+ align:start position:0%
+and um could we force our way through
+ 
+
+ align:start position:0%
+and um could we force our way through
+the lock
+
+ align:start position:0%
+the lock
+ 
+
+ align:start position:0%
+the lock
+early I believe in real Tetris if you
+
+ align:start position:0%
+early I believe in real Tetris if you
+ 
+
+ align:start position:0%
+early I believe in real Tetris if you
+clear a line that happens before you
+
+ align:start position:0%
+clear a line that happens before you
+ 
+
+ align:start position:0%
+clear a line that happens before you
+potentially die I don't think that's an
+
+ align:start position:0%
+potentially die I don't think that's an
+ 
+
+ align:start position:0%
+potentially die I don't think that's an
+issue here because you won't be able to
+
+ align:start position:0%
+issue here because you won't be able to
+ 
+
+ align:start position:0%
+issue here because you won't be able to
+clear anything until the T piece so I
+
+ align:start position:0%
+clear anything until the T piece so I
+ 
+
+ align:start position:0%
+clear anything until the T piece so I
+think you use the argument I said uh up
+
+ align:start position:0%
+think you use the argument I said uh up
+ 
+
+ align:start position:0%
+think you use the argument I said uh up
+to here if there are no other T's in the
+
+ align:start position:0%
+to here if there are no other T's in the
+ 
+
+ align:start position:0%
+to here if there are no other T's in the
+construction so uh any other piece you
+
+ align:start position:0%
+construction so uh any other piece you
+ 
+
+ align:start position:0%
+construction so uh any other piece you
+try to put in here I think will get you
+
+ align:start position:0%
+try to put in here I think will get you
+ 
+
+ align:start position:0%
+try to put in here I think will get you
+Above This row and then you die so so
+
+ align:start position:0%
+Above This row and then you die so so
+ 
+
+ align:start position:0%
+Above This row and then you die so so
+that's essentially unusable space until
+
+ align:start position:0%
+that's essentially unusable space until
+ 
+
+ align:start position:0%
+that's essentially unusable space until
+the T and then up until that point you
+
+ align:start position:0%
+the T and then up until that point you
+ 
+
+ align:start position:0%
+the T and then up until that point you
+have to exactly fill all this stuff yeah
+
+ align:start position:0%
+have to exactly fill all this stuff yeah
+ 
+
+ align:start position:0%
+have to exactly fill all this stuff yeah
+so if we ignore filling the lower stuff
+
+ align:start position:0%
+so if we ignore filling the lower stuff
+ 
+
+ align:start position:0%
+so if we ignore filling the lower stuff
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+um uh main gadgets and just uh stick
+
+ align:start position:0%
+um uh main gadgets and just uh stick
+ 
+
+ align:start position:0%
+um uh main gadgets and just uh stick
+something up high and try to fill just
+
+ align:start position:0%
+something up high and try to fill just
+ 
+
+ align:start position:0%
+something up high and try to fill just
+the tops of each of them um so that with
+
+ align:start position:0%
+the tops of each of them um so that with
+ 
+
+ align:start position:0%
+the tops of each of them um so that with
+um an L or something we can clear one
+
+ align:start position:0%
+um an L or something we can clear one
+ 
+
+ align:start position:0%
+um an L or something we can clear one
+space of the oh I see you could try to
+
+ align:start position:0%
+space of the oh I see you could try to
+ 
+
+ align:start position:0%
+space of the oh I see you could try to
+put an L like that or like
+
+ align:start position:0%
+put an L like that or like
+ 
+
+ align:start position:0%
+put an L like that or like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah but if the row clears first all
+
+ align:start position:0%
+uh yeah but if the row clears first all
+ 
+
+ align:start position:0%
+uh yeah but if the row clears first all
+right then now I have to look up the
+
+ align:start position:0%
+right then now I have to look up the
+ 
+
+ align:start position:0%
+right then now I have to look up the
+rules I guess uh
+
+ align:start position:0%
+rules I guess uh
+ 
+
+ align:start position:0%
+rules I guess uh
+yeah I think it might be okay because
+
+ align:start position:0%
+yeah I think it might be okay because
+ 
+
+ align:start position:0%
+yeah I think it might be okay because
+then there's no way ever to fill the
+
+ align:start position:0%
+then there's no way ever to fill the
+ 
+
+ align:start position:0%
+then there's no way ever to fill the
+next part right let's talk about this
+
+ align:start position:0%
+next part right let's talk about this
+ 
+
+ align:start position:0%
+next part right let's talk about this
+offline I think there's something to
+
+ align:start position:0%
+offline I think there's something to
+ 
+
+ align:start position:0%
+offline I think there's something to
+check here which hopefully we did in the
+
+ align:start position:0%
+check here which hopefully we did in the
+ 
+
+ align:start position:0%
+check here which hopefully we did in the
+paper but I've by now forgotten yeah uh
+
+ align:start position:0%
+paper but I've by now forgotten yeah uh
+ 
+
+ align:start position:0%
+paper but I've by now forgotten yeah uh
+just for fun if you succeed at the end
+
+ align:start position:0%
+just for fun if you succeed at the end
+ 
+
+ align:start position:0%
+just for fun if you succeed at the end
+you get all of these right word facing
+
+ align:start position:0%
+you get all of these right word facing
+ 
+
+ align:start position:0%
+you get all of these right word facing
+L's then you get the T those lines clear
+
+ align:start position:0%
+L's then you get the T those lines clear
+ 
+
+ align:start position:0%
+L's then you get the T those lines clear
+and then you get all the eyes and it's
+
+ align:start position:0%
+and then you get all the eyes and it's
+ 
+
+ align:start position:0%
+and then you get all the eyes and it's
+so satisfying all those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tetrises and then if you're um so Tetris
+
+ align:start position:0%
+tetrises and then if you're um so Tetris
+ 
+
+ align:start position:0%
+tetrises and then if you're um so Tetris
+is when you get four rows in one one
+
+ align:start position:0%
+is when you get four rows in one one
+ 
+
+ align:start position:0%
+is when you get four rows in one one
+move which can only be done with the
+
+ align:start position:0%
+move which can only be done with the
+ 
+
+ align:start position:0%
+move which can only be done with the
+Straits um so this is if you survive
+
+ align:start position:0%
+Straits um so this is if you survive
+ 
+
+ align:start position:0%
+Straits um so this is if you survive
+then you clear a whole bunch of uh
+
+ align:start position:0%
+then you clear a whole bunch of uh
+ 
+
+ align:start position:0%
+then you clear a whole bunch of uh
+columns but if you want to make it
+
+ align:start position:0%
+columns but if you want to make it
+ 
+
+ align:start position:0%
+columns but if you want to make it
+really embarrassing then you put this
+
+ align:start position:0%
+really embarrassing then you put this
+ 
+
+ align:start position:0%
+really embarrassing then you put this
+entire construction over a nice big wall
+
+ align:start position:0%
+entire construction over a nice big wall
+ 
+
+ align:start position:0%
+entire construction over a nice big wall
+or but big empty space and you put a
+
+ align:start position:0%
+or but big empty space and you put a
+ 
+
+ align:start position:0%
+or but big empty space and you put a
+whole bunch of pieces at the end uh like
+
+ align:start position:0%
+whole bunch of pieces at the end uh like
+ 
+
+ align:start position:0%
+whole bunch of pieces at the end uh like
+let's say L's all of the same
+
+ align:start position:0%
+let's say L's all of the same
+ 
+
+ align:start position:0%
+let's say L's all of the same
+orientation or something those are
+
+ align:start position:0%
+orientation or something those are
+ 
+
+ align:start position:0%
+orientation or something those are
+really easy to pack so if you want to
+
+ align:start position:0%
+really easy to pack so if you want to
+ 
+
+ align:start position:0%
+really easy to pack so if you want to
+maximize your score and you don't solve
+
+ align:start position:0%
+maximize your score and you don't solve
+ 
+
+ align:start position:0%
+maximize your score and you don't solve
+this thing then you're really going to
+
+ align:start position:0%
+this thing then you're really going to
+ 
+
+ align:start position:0%
+this thing then you're really going to
+lose bad because if you do solve this
+
+ align:start position:0%
+lose bad because if you do solve this
+ 
+
+ align:start position:0%
+lose bad because if you do solve this
+thing you're going to get tons of points
+
+ align:start position:0%
+thing you're going to get tons of points
+ 
+
+ align:start position:0%
+thing you're going to get tons of points
+by just playing in here
+
+ align:start position:0%
+by just playing in here
+ 
+
+ align:start position:0%
+by just playing in here
+forever so n the one minus Epsilon of
+
+ align:start position:0%
+forever so n the one minus Epsilon of
+ 
+
+ align:start position:0%
+forever so n the one minus Epsilon of
+the game is down here um and if you
+
+ align:start position:0%
+the game is down here um and if you
+ 
+
+ align:start position:0%
+the game is down here um and if you
+can't solve this thing at the top then
+
+ align:start position:0%
+can't solve this thing at the top then
+ 
+
+ align:start position:0%
+can't solve this thing at the top then
+you're getting a score of basically zero
+
+ align:start position:0%
+you're getting a score of basically zero
+ 
+
+ align:start position:0%
+you're getting a score of basically zero
+I mean you do place a few pieces but
+
+ align:start position:0%
+I mean you do place a few pieces but
+ 
+
+ align:start position:0%
+I mean you do place a few pieces but
+very small compared to the number of
+
+ align:start position:0%
+very small compared to the number of
+ 
+
+ align:start position:0%
+very small compared to the number of
+things down here you place like n the
+
+ align:start position:0%
+things down here you place like n the
+ 
+
+ align:start position:0%
+things down here you place like n the
+Epsilon pieces whereas if you do succeed
+
+ align:start position:0%
+Epsilon pieces whereas if you do succeed
+ 
+
+ align:start position:0%
+Epsilon pieces whereas if you do succeed
+then you uh get to place all n Pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by uh this is just the initial
+
+ align:start position:0%
+by uh this is just the initial
+ 
+
+ align:start position:0%
+by uh this is just the initial
+configuration or which floating Square
+
+ align:start position:0%
+configuration or which floating Square
+ 
+
+ align:start position:0%
+configuration or which floating Square
+this thing sare oh this one that is
+
+ align:start position:0%
+this thing sare oh this one that is
+ 
+
+ align:start position:0%
+this thing sare oh this one that is
+possible to construct I
+
+ align:start position:0%
+possible to construct I
+ 
+
+ align:start position:0%
+possible to construct I
+believe uh this is a challenge there a
+
+ align:start position:0%
+believe uh this is a challenge there a
+ 
+
+ align:start position:0%
+believe uh this is a challenge there a
+whole industry of making cool initial
+
+ align:start position:0%
+whole industry of making cool initial
+ 
+
+ align:start position:0%
+whole industry of making cool initial
+patterns by playing a lot of things uh I
+
+ align:start position:0%
+patterns by playing a lot of things uh I
+ 
+
+ align:start position:0%
+patterns by playing a lot of things uh I
+agree that's not obvious but I think it
+
+ align:start position:0%
+agree that's not obvious but I think it
+ 
+
+ align:start position:0%
+agree that's not obvious but I think it
+can be built um um um and so what we get
+
+ align:start position:0%
+can be built um um um and so what we get
+ 
+
+ align:start position:0%
+can be built um um um and so what we get
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+approximate uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tetris let's say the number of pieces
+
+ align:start position:0%
+Tetris let's say the number of pieces
+ 
+
+ align:start position:0%
+Tetris let's say the number of pieces
+that you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play uh less than an N to the 1us
+
+ align:start position:0%
+play uh less than an N to the 1us
+ 
+
+ align:start position:0%
+play uh less than an N to the 1us
+Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factor is NP
+
+ align:start position:0%
+factor is NP
+ 
+
+ align:start position:0%
+factor is NP
+hard that's what we just showed or
+
+ align:start position:0%
+hard that's what we just showed or
+ 
+
+ align:start position:0%
+hard that's what we just showed or
+sketched
+
+ align:start position:0%
+sketched
+ 
+
+ align:start position:0%
+sketched
+um so this is an example of an
+
+ align:start position:0%
+um so this is an example of an
+ 
+
+ align:start position:0%
+um so this is an example of an
+inapproximability result this is a
+
+ align:start position:0%
+inapproximability result this is a
+ 
+
+ align:start position:0%
+inapproximability result this is a
+relatively easy one we just need to
+
+ align:start position:0%
+relatively easy one we just need to
+ 
+
+ align:start position:0%
+relatively easy one we just need to
+assume P does not equal NP and we get
+
+ align:start position:0%
+assume P does not equal NP and we get
+ 
+
+ align:start position:0%
+assume P does not equal NP and we get
+that you really can't approximate within
+
+ align:start position:0%
+that you really can't approximate within
+ 
+
+ align:start position:0%
+that you really can't approximate within
+any very good Factor sort of All or
+
+ align:start position:0%
+any very good Factor sort of All or
+ 
+
+ align:start position:0%
+any very good Factor sort of All or
+Nothing in this game um later in the
+
+ align:start position:0%
+Nothing in this game um later in the
+ 
+
+ align:start position:0%
+Nothing in this game um later in the
+class we'll see much more
+
+ align:start position:0%
+class we'll see much more
+ 
+
+ align:start position:0%
+class we'll see much more
+subtle in approximability
+
+ align:start position:0%
+subtle in approximability
+ 
+
+ align:start position:0%
+subtle in approximability
+results okay other questions hopefully
+
+ align:start position:0%
+results okay other questions hopefully
+ 
+
+ align:start position:0%
+results okay other questions hopefully
+no more
+
+ align:start position:0%
+no more
+ 
+
+ align:start position:0%
+no more
+issues um there are a lot of other open
+
+ align:start position:0%
+issues um there are a lot of other open
+ 
+
+ align:start position:0%
+issues um there are a lot of other open
+problems about Tetris uh you mentioned
+
+ align:start position:0%
+problems about Tetris uh you mentioned
+ 
+
+ align:start position:0%
+problems about Tetris uh you mentioned
+construction uh what if the board is
+
+ align:start position:0%
+construction uh what if the board is
+ 
+
+ align:start position:0%
+construction uh what if the board is
+empty seems like quite a challenging
+
+ align:start position:0%
+empty seems like quite a challenging
+ 
+
+ align:start position:0%
+empty seems like quite a challenging
+problem constant number of rows or
+
+ align:start position:0%
+problem constant number of rows or
+ 
+
+ align:start position:0%
+problem constant number of rows or
+columns here we assume that both
+
+ align:start position:0%
+columns here we assume that both
+ 
+
+ align:start position:0%
+columns here we assume that both
+dimensions are arbitrarily large it's
+
+ align:start position:0%
+dimensions are arbitrarily large it's
+ 
+
+ align:start position:0%
+dimensions are arbitrarily large it's
+part of the input uh but these seem very
+
+ align:start position:0%
+part of the input uh but these seem very
+ 
+
+ align:start position:0%
+part of the input uh but these seem very
+annoying uh interesting if you just have
+
+ align:start position:0%
+annoying uh interesting if you just have
+ 
+
+ align:start position:0%
+annoying uh interesting if you just have
+Straits I imagine Tetris is pretty easy
+
+ align:start position:0%
+Straits I imagine Tetris is pretty easy
+ 
+
+ align:start position:0%
+Straits I imagine Tetris is pretty easy
+uh so how many of the tetris pieces do
+
+ align:start position:0%
+uh so how many of the tetris pieces do
+ 
+
+ align:start position:0%
+uh so how many of the tetris pieces do
+you need to get a hardness proof or can
+
+ align:start position:0%
+you need to get a hardness proof or can
+ 
+
+ align:start position:0%
+you need to get a hardness proof or can
+are there certain small combinations
+
+ align:start position:0%
+are there certain small combinations
+ 
+
+ align:start position:0%
+are there certain small combinations
+that are easy uh we need this ability to
+
+ align:start position:0%
+that are easy uh we need this ability to
+ 
+
+ align:start position:0%
+that are easy uh we need this ability to
+slide at the last minute be nice if you
+
+ align:start position:0%
+slide at the last minute be nice if you
+ 
+
+ align:start position:0%
+slide at the last minute be nice if you
+could just always be hitting space bar
+
+ align:start position:0%
+could just always be hitting space bar
+ 
+
+ align:start position:0%
+could just always be hitting space bar
+and always drop your pieces from
+
+ align:start position:0%
+and always drop your pieces from
+ 
+
+ align:start position:0%
+and always drop your pieces from
+positive Infinity we don't know whether
+
+ align:start position:0%
+positive Infinity we don't know whether
+ 
+
+ align:start position:0%
+positive Infinity we don't know whether
+that problem is empty complete that
+
+ align:start position:0%
+that problem is empty complete that
+ 
+
+ align:start position:0%
+that problem is empty complete that
+might be the most tractable but it's uh
+
+ align:start position:0%
+might be the most tractable but it's uh
+ 
+
+ align:start position:0%
+might be the most tractable but it's uh
+proof would have to be a little
+
+ align:start position:0%
+proof would have to be a little
+ 
+
+ align:start position:0%
+proof would have to be a little
+different two-player Tetris online
+
+ align:start position:0%
+different two-player Tetris online
+ 
+
+ align:start position:0%
+different two-player Tetris online
+Tetris where you don't know the pieces
+
+ align:start position:0%
+Tetris where you don't know the pieces
+ 
+
+ align:start position:0%
+Tetris where you don't know the pieces
+in advance that's something we might get
+
+ align:start position:0%
+in advance that's something we might get
+ 
+
+ align:start position:0%
+in advance that's something we might get
+to later in the class but these are all
+
+ align:start position:0%
+to later in the class but these are all
+ 
+
+ align:start position:0%
+to later in the class but these are all
+open okay um so next topic is in graph
+
+ align:start position:0%
+open okay um so next topic is in graph
+ 
+
+ align:start position:0%
+open okay um so next topic is in graph
+Theory so suppose you have a graph
+
+ align:start position:0%
+Theory so suppose you have a graph
+ 
+
+ align:start position:0%
+Theory so suppose you have a graph
+vertices and edges you want to draw it
+
+ align:start position:0%
+vertices and edges you want to draw it
+ 
+
+ align:start position:0%
+vertices and edges you want to draw it
+in the plane uh no two vertices touching
+
+ align:start position:0%
+in the plane uh no two vertices touching
+ 
+
+ align:start position:0%
+in the plane uh no two vertices touching
+no vertex on an edge that's regular
+
+ align:start position:0%
+no vertex on an edge that's regular
+ 
+
+ align:start position:0%
+no vertex on an edge that's regular
+notional drawing
+
+ align:start position:0%
+notional drawing
+ 
+
+ align:start position:0%
+notional drawing
+but edges are allowed to cross if you're
+
+ align:start position:0%
+but edges are allowed to cross if you're
+ 
+
+ align:start position:0%
+but edges are allowed to cross if you're
+lucky graph is planer don't need any
+
+ align:start position:0%
+lucky graph is planer don't need any
+ 
+
+ align:start position:0%
+lucky graph is planer don't need any
+Crossings there's this notion of one
+
+ align:start position:0%
+Crossings there's this notion of one
+ 
+
+ align:start position:0%
+Crossings there's this notion of one
+planarity which goes back to the 80s
+
+ align:start position:0%
+planarity which goes back to the 80s
+ 
+
+ align:start position:0%
+planarity which goes back to the 80s
+where every Edge can cross at most one
+
+ align:start position:0%
+where every Edge can cross at most one
+ 
+
+ align:start position:0%
+where every Edge can cross at most one
+other Edge uh so this is an example of a
+
+ align:start position:0%
+other Edge uh so this is an example of a
+ 
+
+ align:start position:0%
+other Edge uh so this is an example of a
+one planer drawing some edges don't
+
+ align:start position:0%
+one planer drawing some edges don't
+ 
+
+ align:start position:0%
+one planer drawing some edges don't
+cross anything but but any Edge that has
+
+ align:start position:0%
+cross anything but but any Edge that has
+ 
+
+ align:start position:0%
+cross anything but but any Edge that has
+a Crossing only has
+
+ align:start position:0%
+a Crossing only has
+ 
+
+ align:start position:0%
+a Crossing only has
+one okay so uh this is n be
+
+ align:start position:0%
+one okay so uh this is n be
+ 
+
+ align:start position:0%
+one okay so uh this is n be
+complete uh no notion of strong here
+
+ align:start position:0%
+complete uh no notion of strong here
+ 
+
+ align:start position:0%
+complete uh no notion of strong here
+there's no numbers uh this is from 2007
+
+ align:start position:0%
+there's no numbers uh this is from 2007
+ 
+
+ align:start position:0%
+there's no numbers uh this is from 2007
+and a reduction from three
+
+ align:start position:0%
+and a reduction from three
+ 
+
+ align:start position:0%
+and a reduction from three
+partition so uh here are two gadgets
+
+ align:start position:0%
+partition so uh here are two gadgets
+ 
+
+ align:start position:0%
+partition so uh here are two gadgets
+this is a double well okay we'll get to
+
+ align:start position:0%
+this is a double well okay we'll get to
+ 
+
+ align:start position:0%
+this is a double well okay we'll get to
+this one in a moment um here's a gadget
+
+ align:start position:0%
+this one in a moment um here's a gadget
+ 
+
+ align:start position:0%
+this one in a moment um here's a gadget
+which is the complete graph on six
+
+ align:start position:0%
+which is the complete graph on six
+ 
+
+ align:start position:0%
+which is the complete graph on six
+vertices k6 and uh the idea is that
+
+ align:start position:0%
+vertices k6 and uh the idea is that
+ 
+
+ align:start position:0%
+vertices k6 and uh the idea is that
+we're going to plug this in instead of a
+
+ align:start position:0%
+we're going to plug this in instead of a
+ 
+
+ align:start position:0%
+we're going to plug this in instead of a
+single Bold Edge so wherever there's a
+
+ align:start position:0%
+single Bold Edge so wherever there's a
+ 
+
+ align:start position:0%
+single Bold Edge so wherever there's a
+Bold Edge here what it really means is
+
+ align:start position:0%
+Bold Edge here what it really means is
+ 
+
+ align:start position:0%
+Bold Edge here what it really means is
+this gadget okay this is meant to be an
+
+ align:start position:0%
+this gadget okay this is meant to be an
+ 
+
+ align:start position:0%
+this gadget okay this is meant to be an
+uncrossable edge because usually an can
+
+ align:start position:0%
+uncrossable edge because usually an can
+ 
+
+ align:start position:0%
+uncrossable edge because usually an can
+take up to one Crossing what we're going
+
+ align:start position:0%
+take up to one Crossing what we're going
+ 
+
+ align:start position:0%
+take up to one Crossing what we're going
+to replace this edge with this thing
+
+ align:start position:0%
+to replace this edge with this thing
+ 
+
+ align:start position:0%
+to replace this edge with this thing
+which has a bunch of Crossings in it no
+
+ align:start position:0%
+which has a bunch of Crossings in it no
+ 
+
+ align:start position:0%
+which has a bunch of Crossings in it no
+matter how you draw it k6 is very
+
+ align:start position:0%
+matter how you draw it k6 is very
+ 
+
+ align:start position:0%
+matter how you draw it k6 is very
+symmetric so it's not too hard to argue
+
+ align:start position:0%
+symmetric so it's not too hard to argue
+ 
+
+ align:start position:0%
+symmetric so it's not too hard to argue
+about the different drawings but you see
+
+ align:start position:0%
+about the different drawings but you see
+ 
+
+ align:start position:0%
+about the different drawings but you see
+a Crossing there a Crossing there and a
+
+ align:start position:0%
+a Crossing there a Crossing there and a
+ 
+
+ align:start position:0%
+a Crossing there a Crossing there and a
+Crossing there and in general if you
+
+ align:start position:0%
+Crossing there and in general if you
+ 
+
+ align:start position:0%
+Crossing there and in general if you
+look at any path from this vertex to
+
+ align:start position:0%
+look at any path from this vertex to
+ 
+
+ align:start position:0%
+look at any path from this vertex to
+this vertex uh you visit a Crossing
+
+ align:start position:0%
+this vertex uh you visit a Crossing
+ 
+
+ align:start position:0%
+this vertex uh you visit a Crossing
+there's no way to get uh wait what about
+
+ align:start position:0%
+there's no way to get uh wait what about
+ 
+
+ align:start position:0%
+there's no way to get uh wait what about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one uh what do I mean if I if I attempt
+
+ align:start position:0%
+one uh what do I mean if I if I attempt
+ 
+
+ align:start position:0%
+one uh what do I mean if I if I attempt
+to draw an Edge through here I will hit
+
+ align:start position:0%
+to draw an Edge through here I will hit
+ 
+
+ align:start position:0%
+to draw an Edge through here I will hit
+an edge that has a Crossing on it that's
+
+ align:start position:0%
+an edge that has a Crossing on it that's
+ 
+
+ align:start position:0%
+an edge that has a Crossing on it that's
+what I want so in other words it's not
+
+ align:start position:0%
+what I want so in other words it's not
+ 
+
+ align:start position:0%
+what I want so in other words it's not
+possible to draw an edge across here and
+
+ align:start position:0%
+possible to draw an edge across here and
+ 
+
+ align:start position:0%
+possible to draw an edge across here and
+still be one planer so this effectively
+
+ align:start position:0%
+still be one planer so this effectively
+ 
+
+ align:start position:0%
+still be one planer so this effectively
+becomes an uncrossable edge this is
+
+ align:start position:0%
+becomes an uncrossable edge this is
+ 
+
+ align:start position:0%
+becomes an uncrossable edge this is
+notation this is super useful when you
+
+ align:start position:0%
+notation this is super useful when you
+ 
+
+ align:start position:0%
+notation this is super useful when you
+have a complicated construction if you
+
+ align:start position:0%
+have a complicated construction if you
+ 
+
+ align:start position:0%
+have a complicated construction if you
+do if you use the right notation it's
+
+ align:start position:0%
+do if you use the right notation it's
+ 
+
+ align:start position:0%
+do if you use the right notation it's
+not necessarily so complicated if we
+
+ align:start position:0%
+not necessarily so complicated if we
+ 
+
+ align:start position:0%
+not necessarily so complicated if we
+drew this everywhere in these pictures
+
+ align:start position:0%
+drew this everywhere in these pictures
+ 
+
+ align:start position:0%
+drew this everywhere in these pictures
+it would be really hard to see what's
+
+ align:start position:0%
+it would be really hard to see what's
+ 
+
+ align:start position:0%
+it would be really hard to see what's
+going on so we use this this visual idea
+
+ align:start position:0%
+going on so we use this this visual idea
+ 
+
+ align:start position:0%
+going on so we use this this visual idea
+that this is a symbol for that and then
+
+ align:start position:0%
+that this is a symbol for that and then
+ 
+
+ align:start position:0%
+that this is a symbol for that and then
+we can draw really simple pictures
+
+ align:start position:0%
+we can draw really simple pictures
+ 
+
+ align:start position:0%
+we can draw really simple pictures
+relatively simple pictures this is
+
+ align:start position:0%
+relatively simple pictures this is
+ 
+
+ align:start position:0%
+relatively simple pictures this is
+what's called a double wheel uh it's got
+
+ align:start position:0%
+what's called a double wheel uh it's got
+ 
+
+ align:start position:0%
+what's called a double wheel uh it's got
+a lot of spokes in the center and a
+
+ align:start position:0%
+a lot of spokes in the center and a
+ 
+
+ align:start position:0%
+a lot of spokes in the center and a
+cycle around there and then just another
+
+ align:start position:0%
+cycle around there and then just another
+ 
+
+ align:start position:0%
+cycle around there and then just another
+one around
+
+ align:start position:0%
+one around
+ 
+
+ align:start position:0%
+one around
+there and we're going to have two of
+
+ align:start position:0%
+there and we're going to have two of
+ 
+
+ align:start position:0%
+there and we're going to have two of
+them there's going to be exactly two of
+
+ align:start position:0%
+them there's going to be exactly two of
+ 
+
+ align:start position:0%
+them there's going to be exactly two of
+these gadgets one of size some of the
+
+ align:start position:0%
+these gadgets one of size some of the
+ 
+
+ align:start position:0%
+these gadgets one of size some of the
+A's the other of size
+
+ align:start position:0%
+A's the other of size
+ 
+
+ align:start position:0%
+A's the other of size
+n okay so in this picture we have six
+
+ align:start position:0%
+n okay so in this picture we have six
+ 
+
+ align:start position:0%
+n okay so in this picture we have six
+AIS and the sum of all of them is
+
+ align:start position:0%
+AIS and the sum of all of them is
+ 
+
+ align:start position:0%
+AIS and the sum of all of them is
+however many spokes are on that wheel
+
+ align:start position:0%
+however many spokes are on that wheel
+ 
+
+ align:start position:0%
+however many spokes are on that wheel
+okay um and then this is the actual
+
+ align:start position:0%
+okay um and then this is the actual
+ 
+
+ align:start position:0%
+okay um and then this is the actual
+construction so this is these are this
+
+ align:start position:0%
+construction so this is these are this
+ 
+
+ align:start position:0%
+construction so this is these are this
+is the AI
+
+ align:start position:0%
+is the AI
+ 
+
+ align:start position:0%
+is the AI
+Gadget um so let's look at this one this
+
+ align:start position:0%
+Gadget um so let's look at this one this
+ 
+
+ align:start position:0%
+Gadget um so let's look at this one this
+is uh when AI equals 3 going to have a
+
+ align:start position:0%
+is uh when AI equals 3 going to have a
+ 
+
+ align:start position:0%
+is uh when AI equals 3 going to have a
+vertex of degree 3 + 1 this path is a
+
+ align:start position:0%
+vertex of degree 3 + 1 this path is a
+ 
+
+ align:start position:0%
+vertex of degree 3 + 1 this path is a
+path of length two and it goes to this
+
+ align:start position:0%
+path of length two and it goes to this
+ 
+
+ align:start position:0%
+path of length two and it goes to this
+vertex the center of the smaller wheel
+
+ align:start position:0%
+vertex the center of the smaller wheel
+ 
+
+ align:start position:0%
+vertex the center of the smaller wheel
+of the N wheel um and then these the
+
+ align:start position:0%
+of the N wheel um and then these the
+ 
+
+ align:start position:0%
+of the N wheel um and then these the
+other three paths again are of length
+
+ align:start position:0%
+other three paths again are of length
+ 
+
+ align:start position:0%
+other three paths again are of length
+two and they connect to uh the center of
+
+ align:start position:0%
+two and they connect to uh the center of
+ 
+
+ align:start position:0%
+two and they connect to uh the center of
+of the sum of the
+
+ align:start position:0%
+of the sum of the
+ 
+
+ align:start position:0%
+of the sum of the
+AI uh Gadget so this is intended to
+
+ align:start position:0%
+AI uh Gadget so this is intended to
+ 
+
+ align:start position:0%
+AI uh Gadget so this is intended to
+represent the number three now there's a
+
+ align:start position:0%
+represent the number three now there's a
+ 
+
+ align:start position:0%
+represent the number three now there's a
+little bit more going on which is we
+
+ align:start position:0%
+little bit more going on which is we
+ 
+
+ align:start position:0%
+little bit more going on which is we
+added a Bold Edge here and a Bold Edge
+
+ align:start position:0%
+added a Bold Edge here and a Bold Edge
+ 
+
+ align:start position:0%
+added a Bold Edge here and a Bold Edge
+here in this case uh here's a case
+
+ align:start position:0%
+here in this case uh here's a case
+ 
+
+ align:start position:0%
+here in this case uh here's a case
+you're curious in this case n over3 is
+
+ align:start position:0%
+you're curious in this case n over3 is
+ 
+
+ align:start position:0%
+you're curious in this case n over3 is
+two so in general we have the sum of all
+
+ align:start position:0%
+two so in general we have the sum of all
+ 
+
+ align:start position:0%
+two so in general we have the sum of all
+we have all the AIS basically laid out
+
+ align:start position:0%
+we have all the AIS basically laid out
+ 
+
+ align:start position:0%
+we have all the AIS basically laid out
+here in some order and what we're trying
+
+ align:start position:0%
+here in some order and what we're trying
+ 
+
+ align:start position:0%
+here in some order and what we're trying
+to do is partition them into groups of
+
+ align:start position:0%
+to do is partition them into groups of
+ 
+
+ align:start position:0%
+to do is partition them into groups of
+size T so so here T is whatever this
+
+ align:start position:0%
+size T so so here T is whatever this
+ 
+
+ align:start position:0%
+size T so so here T is whatever this
+number is and so we add these
+
+ align:start position:0%
+number is and so we add these
+ 
+
+ align:start position:0%
+number is and so we add these
+uncrossable edges to say well an AI
+
+ align:start position:0%
+uncrossable edges to say well an AI
+ 
+
+ align:start position:0%
+uncrossable edges to say well an AI
+cannot go partly in this bin and partly
+
+ align:start position:0%
+cannot go partly in this bin and partly
+ 
+
+ align:start position:0%
+cannot go partly in this bin and partly
+in this bin it's got to choose which
+
+ align:start position:0%
+in this bin it's got to choose which
+ 
+
+ align:start position:0%
+in this bin it's got to choose which
+side of all of these bold lines it's on
+
+ align:start position:0%
+side of all of these bold lines it's on
+ 
+
+ align:start position:0%
+side of all of these bold lines it's on
+and so for each AI you choose in this
+
+ align:start position:0%
+and so for each AI you choose in this
+ 
+
+ align:start position:0%
+and so for each AI you choose in this
+case there's only two bins but in
+
+ align:start position:0%
+case there's only two bins but in
+ 
+
+ align:start position:0%
+case there's only two bins but in
+general there' be several bands each uh
+
+ align:start position:0%
+general there' be several bands each uh
+ 
+
+ align:start position:0%
+general there' be several bands each uh
+delineated by a Bold Edge from the end
+
+ align:start position:0%
+delineated by a Bold Edge from the end
+ 
+
+ align:start position:0%
+delineated by a Bold Edge from the end
+of the thing to uh the end of the thing
+
+ align:start position:0%
+of the thing to uh the end of the thing
+ 
+
+ align:start position:0%
+of the thing to uh the end of the thing
+over there um I mean this looks a little
+
+ align:start position:0%
+over there um I mean this looks a little
+ 
+
+ align:start position:0%
+over there um I mean this looks a little
+bit weird like okay how do the AI choose
+
+ align:start position:0%
+bit weird like okay how do the AI choose
+ 
+
+ align:start position:0%
+bit weird like okay how do the AI choose
+which side they're on here well they
+
+ align:start position:0%
+which side they're on here well they
+ 
+
+ align:start position:0%
+which side they're on here well they
+just choose whichever side they're on if
+
+ align:start position:0%
+just choose whichever side they're on if
+ 
+
+ align:start position:0%
+just choose whichever side they're on if
+they're on the b in the bottom chunk
+
+ align:start position:0%
+they're on the b in the bottom chunk
+ 
+
+ align:start position:0%
+they're on the b in the bottom chunk
+over here then they'll just connect to
+
+ align:start position:0%
+over here then they'll just connect to
+ 
+
+ align:start position:0%
+over here then they'll just connect to
+the bottom chunk over here so in the top
+
+ align:start position:0%
+the bottom chunk over here so in the top
+ 
+
+ align:start position:0%
+the bottom chunk over here so in the top
+chunk over here they'll connect to the
+
+ align:start position:0%
+chunk over here they'll connect to the
+ 
+
+ align:start position:0%
+chunk over here they'll connect to the
+corresponding chunk over
+
+ align:start position:0%
+corresponding chunk over
+ 
+
+ align:start position:0%
+corresponding chunk over
+there uh this is basically to force the
+
+ align:start position:0%
+there uh this is basically to force the
+ 
+
+ align:start position:0%
+there uh this is basically to force the
+AIS to start on the outside of this
+
+ align:start position:0%
+AIS to start on the outside of this
+ 
+
+ align:start position:0%
+AIS to start on the outside of this
+construction so you uh there's a lot of
+
+ align:start position:0%
+construction so you uh there's a lot of
+ 
+
+ align:start position:0%
+construction so you uh there's a lot of
+again there's a lot of cases here to
+
+ align:start position:0%
+again there's a lot of cases here to
+ 
+
+ align:start position:0%
+again there's a lot of cases here to
+worry about about other ways you might
+
+ align:start position:0%
+worry about about other ways you might
+ 
+
+ align:start position:0%
+worry about about other ways you might
+draw this maybe you take this entire
+
+ align:start position:0%
+draw this maybe you take this entire
+ 
+
+ align:start position:0%
+draw this maybe you take this entire
+picture and stuff it into this little
+
+ align:start position:0%
+picture and stuff it into this little
+ 
+
+ align:start position:0%
+picture and stuff it into this little
+triangle but they all end up with lots
+
+ align:start position:0%
+triangle but they all end up with lots
+ 
+
+ align:start position:0%
+triangle but they all end up with lots
+of Crossings on a single edge if you did
+
+ align:start position:0%
+of Crossings on a single edge if you did
+ 
+
+ align:start position:0%
+of Crossings on a single edge if you did
+that then you have to go you have to
+
+ align:start position:0%
+that then you have to go you have to
+ 
+
+ align:start position:0%
+that then you have to go you have to
+cross this Edge many times for
+
+ align:start position:0%
+cross this Edge many times for
+ 
+
+ align:start position:0%
+cross this Edge many times for
+example uh think we convinced ourselves
+
+ align:start position:0%
+example uh think we convinced ourselves
+ 
+
+ align:start position:0%
+example uh think we convinced ourselves
+that with a single wheel without this
+
+ align:start position:0%
+that with a single wheel without this
+ 
+
+ align:start position:0%
+that with a single wheel without this
+extra thing uh the
+
+ align:start position:0%
+extra thing uh the
+ 
+
+ align:start position:0%
+extra thing uh the
+construction I think we're not certain
+
+ align:start position:0%
+construction I think we're not certain
+ 
+
+ align:start position:0%
+construction I think we're not certain
+about whether construction works there's
+
+ align:start position:0%
+about whether construction works there's
+ 
+
+ align:start position:0%
+about whether construction works there's
+definitely more cases to consider so at
+
+ align:start position:0%
+definitely more cases to consider so at
+ 
+
+ align:start position:0%
+definitely more cases to consider so at
+the very least simplifies things by
+
+ align:start position:0%
+the very least simplifies things by
+ 
+
+ align:start position:0%
+the very least simplifies things by
+adding the second wheel it would also
+
+ align:start position:0%
+adding the second wheel it would also
+ 
+
+ align:start position:0%
+adding the second wheel it would also
+mean you'd have to have multiple edges
+
+ align:start position:0%
+mean you'd have to have multiple edges
+ 
+
+ align:start position:0%
+mean you'd have to have multiple edges
+here between the same two vertices so
+
+ align:start position:0%
+here between the same two vertices so
+ 
+
+ align:start position:0%
+here between the same two vertices so
+maybe that's why they did the the double
+
+ align:start position:0%
+maybe that's why they did the the double
+ 
+
+ align:start position:0%
+maybe that's why they did the the double
+wheel so that you have this padel length
+
+ align:start position:0%
+wheel so that you have this padel length
+ 
+
+ align:start position:0%
+wheel so that you have this padel length
+to connecting the same thing instead of
+
+ align:start position:0%
+to connecting the same thing instead of
+ 
+
+ align:start position:0%
+to connecting the same thing instead of
+the exact same Edge anyway uh so again
+
+ align:start position:0%
+the exact same Edge anyway uh so again
+ 
+
+ align:start position:0%
+the exact same Edge anyway uh so again
+you have to prove there's essentially
+
+ align:start position:0%
+you have to prove there's essentially
+ 
+
+ align:start position:0%
+you have to prove there's essentially
+only one planer embedding for the uh
+
+ align:start position:0%
+only one planer embedding for the uh
+ 
+
+ align:start position:0%
+only one planer embedding for the uh
+each of these wheels and for these
+
+ align:start position:0%
+each of these wheels and for these
+ 
+
+ align:start position:0%
+each of these wheels and for these
+things to connect them together and so
+
+ align:start position:0%
+things to connect them together and so
+ 
+
+ align:start position:0%
+things to connect them together and so
+the AIS have the freedom of which bucket
+
+ align:start position:0%
+the AIS have the freedom of which bucket
+ 
+
+ align:start position:0%
+the AIS have the freedom of which bucket
+they go into but um because each of
+
+ align:start position:0%
+they go into but um because each of
+ 
+
+ align:start position:0%
+they go into but um because each of
+these edges can only be crossed once
+
+ align:start position:0%
+these edges can only be crossed once
+ 
+
+ align:start position:0%
+these edges can only be crossed once
+each unit of each AI can only only one
+
+ align:start position:0%
+each unit of each AI can only only one
+ 
+
+ align:start position:0%
+each unit of each AI can only only one
+unit can occupy each of these cells so
+
+ align:start position:0%
+unit can occupy each of these cells so
+ 
+
+ align:start position:0%
+unit can occupy each of these cells so
+you get three
+
+ align:start position:0%
+you get three
+ 
+
+ align:start position:0%
+you get three
+partition cool yet another way to
+
+ align:start position:0%
+partition cool yet another way to
+ 
+
+ align:start position:0%
+partition cool yet another way to
+represent numbers in
+
+ align:start position:0%
+represent numbers in
+ 
+
+ align:start position:0%
+represent numbers in
+un question don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understand ah so okay so the these These
+
+ align:start position:0%
+understand ah so okay so the these These
+ 
+
+ align:start position:0%
+understand ah so okay so the these These
+are the AIS A1 is 2 A2 is three A3 is 3
+
+ align:start position:0%
+are the AIS A1 is 2 A2 is three A3 is 3
+ 
+
+ align:start position:0%
+are the AIS A1 is 2 A2 is three A3 is 3
+A4 is three A5 is four and A6 is five
+
+ align:start position:0%
+A4 is three A5 is four and A6 is five
+ 
+
+ align:start position:0%
+A4 is three A5 is four and A6 is five
+and they are represented by this thing
+
+ align:start position:0%
+and they are represented by this thing
+ 
+
+ align:start position:0%
+and they are represented by this thing
+is a two this thing is a three this
+
+ align:start position:0%
+is a two this thing is a three this
+ 
+
+ align:start position:0%
+is a two this thing is a three this
+thing is a three this thing is a four
+
+ align:start position:0%
+thing is a three this thing is a four
+ 
+
+ align:start position:0%
+thing is a three this thing is a four
+and this is a five and that should be
+
+ align:start position:0%
+and this is a five and that should be
+ 
+
+ align:start position:0%
+and this is a five and that should be
+the same sequence I think I missed this
+
+ align:start position:0%
+the same sequence I think I missed this
+ 
+
+ align:start position:0%
+the same sequence I think I missed this
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+good okay that was one
+
+ align:start position:0%
+good okay that was one
+ 
+
+ align:start position:0%
+good okay that was one
+planarity oh boy four minutes which
+
+ align:start position:0%
+planarity oh boy four minutes which
+ 
+
+ align:start position:0%
+planarity oh boy four minutes which
+proofs to cover
+
+ align:start position:0%
+proofs to cover
+ 
+
+ align:start position:0%
+proofs to cover
+um I will wave my hands at this one uh
+
+ align:start position:0%
+um I will wave my hands at this one uh
+ 
+
+ align:start position:0%
+um I will wave my hands at this one uh
+this is a chain of blocks with with
+
+ align:start position:0%
+this is a chain of blocks with with
+ 
+
+ align:start position:0%
+this is a chain of blocks with with
+hinges on them uh and it has colors on
+
+ align:start position:0%
+hinges on them uh and it has colors on
+ 
+
+ align:start position:0%
+hinges on them uh and it has colors on
+it your goal is to form a particular
+
+ align:start position:0%
+it your goal is to form a particular
+ 
+
+ align:start position:0%
+it your goal is to form a particular
+pattern of colors um I find it
+
+ align:start position:0%
+pattern of colors um I find it
+ 
+
+ align:start position:0%
+pattern of colors um I find it
+interesting this is our hardness proof
+
+ align:start position:0%
+interesting this is our hardness proof
+ 
+
+ align:start position:0%
+interesting this is our hardness proof
+uh it's interesting in that it's a lot
+
+ align:start position:0%
+uh it's interesting in that it's a lot
+ 
+
+ align:start position:0%
+uh it's interesting in that it's a lot
+of the proofs you've seen it's all about
+
+ align:start position:0%
+of the proofs you've seen it's all about
+ 
+
+ align:start position:0%
+of the proofs you've seen it's all about
+making the AI being a straight line here
+
+ align:start position:0%
+making the AI being a straight line here
+ 
+
+ align:start position:0%
+making the AI being a straight line here
+that's not a big deal we've uh sort of
+
+ align:start position:0%
+that's not a big deal we've uh sort of
+ 
+
+ align:start position:0%
+that's not a big deal we've uh sort of
+drawn out uh this is again a kind of
+
+ align:start position:0%
+drawn out uh this is again a kind of
+ 
+
+ align:start position:0%
+drawn out uh this is again a kind of
+universal construction you can build in
+
+ align:start position:0%
+universal construction you can build in
+ 
+
+ align:start position:0%
+universal construction you can build in
+any polyomino with it it's all about the
+
+ align:start position:0%
+any polyomino with it it's all about the
+ 
+
+ align:start position:0%
+any polyomino with it it's all about the
+colors and so the idea is that the AIS
+
+ align:start position:0%
+colors and so the idea is that the AIS
+ 
+
+ align:start position:0%
+colors and so the idea is that the AIS
+are represented by how long of a blue
+
+ align:start position:0%
+are represented by how long of a blue
+ 
+
+ align:start position:0%
+are represented by how long of a blue
+segment you have here in the overall
+
+ align:start position:0%
+segment you have here in the overall
+ 
+
+ align:start position:0%
+segment you have here in the overall
+chain of pieces and uh these are the
+
+ align:start position:0%
+chain of pieces and uh these are the
+ 
+
+ align:start position:0%
+chain of pieces and uh these are the
+buckets and so you just come in at some
+
+ align:start position:0%
+buckets and so you just come in at some
+ 
+
+ align:start position:0%
+buckets and so you just come in at some
+point and fill in however big your AI is
+
+ align:start position:0%
+point and fill in however big your AI is
+ 
+
+ align:start position:0%
+point and fill in however big your AI is
+and then leave uh and there's just
+
+ align:start position:0%
+and then leave uh and there's just
+ 
+
+ align:start position:0%
+and then leave uh and there's just
+enough blue to cover all the blue so you
+
+ align:start position:0%
+enough blue to cover all the blue so you
+ 
+
+ align:start position:0%
+enough blue to cover all the blue so you
+better not waste it uh but all the other
+
+ align:start position:0%
+better not waste it uh but all the other
+ 
+
+ align:start position:0%
+better not waste it uh but all the other
+stuff you you have a lot of flexibility
+
+ align:start position:0%
+stuff you you have a lot of flexibility
+ 
+
+ align:start position:0%
+stuff you you have a lot of flexibility
+so it's all about just uh kind of
+
+ align:start position:0%
+so it's all about just uh kind of
+ 
+
+ align:start position:0%
+so it's all about just uh kind of
+filling these amorphous blobs that have
+
+ align:start position:0%
+filling these amorphous blobs that have
+ 
+
+ align:start position:0%
+filling these amorphous blobs that have
+exactly the right area to fill all these
+
+ align:start position:0%
+exactly the right area to fill all these
+ 
+
+ align:start position:0%
+exactly the right area to fill all these
+blue regions and there's three times
+
+ align:start position:0%
+blue regions and there's three times
+ 
+
+ align:start position:0%
+blue regions and there's three times
+you're allowed to visit and that gives
+
+ align:start position:0%
+you're allowed to visit and that gives
+ 
+
+ align:start position:0%
+you're allowed to visit and that gives
+you three partitions so I won't it's
+
+ align:start position:0%
+you three partitions so I won't it's
+ 
+
+ align:start position:0%
+you three partitions so I won't it's
+hard especially without a physical model
+
+ align:start position:0%
+hard especially without a physical model
+ 
+
+ align:start position:0%
+hard especially without a physical model
+to understand what the rules are of this
+
+ align:start position:0%
+to understand what the rules are of this
+ 
+
+ align:start position:0%
+to understand what the rules are of this
+game but gives you some idea of another
+
+ align:start position:0%
+game but gives you some idea of another
+ 
+
+ align:start position:0%
+game but gives you some idea of another
+way to represent three
+
+ align:start position:0%
+way to represent three
+ 
+
+ align:start position:0%
+way to represent three
+partition um next you may have seen this
+
+ align:start position:0%
+partition um next you may have seen this
+ 
+
+ align:start position:0%
+partition um next you may have seen this
+kind of object is called a carpers ruler
+
+ align:start position:0%
+kind of object is called a carpers ruler
+ 
+
+ align:start position:0%
+kind of object is called a carpers ruler
+or rule uh it's got hinges it's got
+
+ align:start position:0%
+or rule uh it's got hinges it's got
+ 
+
+ align:start position:0%
+or rule uh it's got hinges it's got
+rigid bars and usually when you're not
+
+ align:start position:0%
+rigid bars and usually when you're not
+ 
+
+ align:start position:0%
+rigid bars and usually when you're not
+using it one of I mean you can measure
+
+ align:start position:0%
+using it one of I mean you can measure
+ 
+
+ align:start position:0%
+using it one of I mean you can measure
+lengths that's that's the ruler part and
+
+ align:start position:0%
+lengths that's that's the ruler part and
+ 
+
+ align:start position:0%
+lengths that's that's the ruler part and
+when you're not using it it folds into
+
+ align:start position:0%
+when you're not using it it folds into
+ 
+
+ align:start position:0%
+when you're not using it it folds into
+this nice compact form it's great and
+
+ align:start position:0%
+this nice compact form it's great and
+ 
+
+ align:start position:0%
+this nice compact form it's great and
+everyone used these until the invention
+
+ align:start position:0%
+everyone used these until the invention
+ 
+
+ align:start position:0%
+everyone used these until the invention
+of the retractable one though they still
+
+ align:start position:0%
+of the retractable one though they still
+ 
+
+ align:start position:0%
+of the retractable one though they still
+use these a lot in Europe um so has unit
+
+ align:start position:0%
+use these a lot in Europe um so has unit
+ 
+
+ align:start position:0%
+use these a lot in Europe um so has unit
+length in this case but what if you have
+
+ align:start position:0%
+length in this case but what if you have
+ 
+
+ align:start position:0%
+length in this case but what if you have
+a really annoying uh Carpenters Rule and
+
+ align:start position:0%
+a really annoying uh Carpenters Rule and
+ 
+
+ align:start position:0%
+a really annoying uh Carpenters Rule and
+the lengths are not all
+
+ align:start position:0%
+the lengths are not all
+ 
+
+ align:start position:0%
+the lengths are not all
+equal uh and you have this nice box
+
+ align:start position:0%
+equal uh and you have this nice box
+ 
+
+ align:start position:0%
+equal uh and you have this nice box
+which is unit length or you know some
+
+ align:start position:0%
+which is unit length or you know some
+ 
+
+ align:start position:0%
+which is unit length or you know some
+length youd like to fit your rule ruler
+
+ align:start position:0%
+length youd like to fit your rule ruler
+ 
+
+ align:start position:0%
+length youd like to fit your rule ruler
+into that one-dimensional box Let's
+
+ align:start position:0%
+into that one-dimensional box Let's
+ 
+
+ align:start position:0%
+into that one-dimensional box Let's
+ignore the thickness here okay then this
+
+ align:start position:0%
+ignore the thickness here okay then this
+ 
+
+ align:start position:0%
+ignore the thickness here okay then this
+problem is hard uh it is weak NP hard
+
+ align:start position:0%
+problem is hard uh it is weak NP hard
+ 
+
+ align:start position:0%
+problem is hard uh it is weak NP hard
+you can solve it in pseudo poomi time so
+
+ align:start position:0%
+you can solve it in pseudo poomi time so
+ 
+
+ align:start position:0%
+you can solve it in pseudo poomi time so
+this is what this is like one of the
+
+ align:start position:0%
+this is what this is like one of the
+ 
+
+ align:start position:0%
+this is what this is like one of the
+very few problems we'll see of this type
+
+ align:start position:0%
+very few problems we'll see of this type
+ 
+
+ align:start position:0%
+very few problems we'll see of this type
+uh and this is the proof it's one of the
+
+ align:start position:0%
+uh and this is the proof it's one of the
+ 
+
+ align:start position:0%
+uh and this is the proof it's one of the
+simplest proofs uh from reduction from
+
+ align:start position:0%
+simplest proofs uh from reduction from
+ 
+
+ align:start position:0%
+simplest proofs uh from reduction from
+partition which is two partition which
+
+ align:start position:0%
+partition which is two partition which
+ 
+
+ align:start position:0%
+partition which is two partition which
+is divide your numbers into two groups
+
+ align:start position:0%
+is divide your numbers into two groups
+ 
+
+ align:start position:0%
+is divide your numbers into two groups
+and I apologize here in this book of
+
+ align:start position:0%
+and I apologize here in this book of
+ 
+
+ align:start position:0%
+and I apologize here in this book of
+ours we use x instead of a so those are
+
+ align:start position:0%
+ours we use x instead of a so those are
+ 
+
+ align:start position:0%
+ours we use x instead of a so those are
+AIS so you're given some AIS and the
+
+ align:start position:0%
+AIS so you're given some AIS and the
+ 
+
+ align:start position:0%
+AIS so you're given some AIS and the
+idea is well if I would like to
+
+ align:start position:0%
+idea is well if I would like to
+ 
+
+ align:start position:0%
+idea is well if I would like to
+partition the AIS into two groups of
+
+ align:start position:0%
+partition the AIS into two groups of
+ 
+
+ align:start position:0%
+partition the AIS into two groups of
+equal sums like so that's the same as
+
+ align:start position:0%
+equal sums like so that's the same as
+ 
+
+ align:start position:0%
+equal sums like so that's the same as
+saying well some of the AIS or the XIs
+
+ align:start position:0%
+saying well some of the AIS or the XIs
+ 
+
+ align:start position:0%
+saying well some of the AIS or the XIs
+are going to go left some of them are
+
+ align:start position:0%
+are going to go left some of them are
+ 
+
+ align:start position:0%
+are going to go left some of them are
+going to go right and whether I fold
+
+ align:start position:0%
+going to go right and whether I fold
+ 
+
+ align:start position:0%
+going to go right and whether I fold
+something where I could either leave it
+
+ align:start position:0%
+something where I could either leave it
+ 
+
+ align:start position:0%
+something where I could either leave it
+at 180 degre or I could fold it to 0
+
+ align:start position:0%
+at 180 degre or I could fold it to 0
+ 
+
+ align:start position:0%
+at 180 degre or I could fold it to 0
+degrees that's sort of my binary choice
+
+ align:start position:0%
+degrees that's sort of my binary choice
+ 
+
+ align:start position:0%
+degrees that's sort of my binary choice
+if I'm going to go into a
+
+ align:start position:0%
+if I'm going to go into a
+ 
+
+ align:start position:0%
+if I'm going to go into a
+one-dimensional box if I fold it I
+
+ align:start position:0%
+one-dimensional box if I fold it I
+ 
+
+ align:start position:0%
+one-dimensional box if I fold it I
+change direction if I don't fold it I
+
+ align:start position:0%
+change direction if I don't fold it I
+ 
+
+ align:start position:0%
+change direction if I don't fold it I
+stay in the same direction but that what
+
+ align:start position:0%
+stay in the same direction but that what
+ 
+
+ align:start position:0%
+stay in the same direction but that what
+that really means is uh by some running
+
+ align:start position:0%
+that really means is uh by some running
+ 
+
+ align:start position:0%
+that really means is uh by some running
+sumti thing I can choose for each AI
+
+ align:start position:0%
+sumti thing I can choose for each AI
+ 
+
+ align:start position:0%
+sumti thing I can choose for each AI
+whether it goes left or right okay and
+
+ align:start position:0%
+whether it goes left or right okay and
+ 
+
+ align:start position:0%
+whether it goes left or right okay and
+then this is going to if this happens
+
+ align:start position:0%
+then this is going to if this happens
+ 
+
+ align:start position:0%
+then this is going to if this happens
+what it means is my starting point is
+
+ align:start position:0%
+what it means is my starting point is
+ 
+
+ align:start position:0%
+what it means is my starting point is
+equal to my ending point now it could be
+
+ align:start position:0%
+equal to my ending point now it could be
+ 
+
+ align:start position:0%
+equal to my ending point now it could be
+in between I go left and right and who
+
+ align:start position:0%
+in between I go left and right and who
+ 
+
+ align:start position:0%
+in between I go left and right and who
+knows what happens but the point is if
+
+ align:start position:0%
+knows what happens but the point is if
+ 
+
+ align:start position:0%
+knows what happens but the point is if
+they sum up to the lefts equal the
+
+ align:start position:0%
+they sum up to the lefts equal the
+ 
+
+ align:start position:0%
+they sum up to the lefts equal the
+rights then the starting point will be
+
+ align:start position:0%
+rights then the starting point will be
+ 
+
+ align:start position:0%
+rights then the starting point will be
+uh horizontally aligned with my ending
+
+ align:start position:0%
+uh horizontally aligned with my ending
+ 
+
+ align:start position:0%
+uh horizontally aligned with my ending
+point so that's not the problem the
+
+ align:start position:0%
+point so that's not the problem the
+ 
+
+ align:start position:0%
+point so that's not the problem the
+problem is to fit into a box of a given
+
+ align:start position:0%
+problem is to fit into a box of a given
+ 
+
+ align:start position:0%
+problem is to fit into a box of a given
+size so this says nothing about the box
+
+ align:start position:0%
+size so this says nothing about the box
+ 
+
+ align:start position:0%
+size so this says nothing about the box
+but if you do this very simple
+
+ align:start position:0%
+but if you do this very simple
+ 
+
+ align:start position:0%
+but if you do this very simple
+construction which is add a super long
+
+ align:start position:0%
+construction which is add a super long
+ 
+
+ align:start position:0%
+construction which is add a super long
+length and then add half of that at the
+
+ align:start position:0%
+length and then add half of that at the
+ 
+
+ align:start position:0%
+length and then add half of that at the
+beginning and then at the end you add
+
+ align:start position:0%
+beginning and then at the end you add
+ 
+
+ align:start position:0%
+beginning and then at the end you add
+half of the long length and then the
+
+ align:start position:0%
+half of the long length and then the
+ 
+
+ align:start position:0%
+half of the long length and then the
+super long length then and your goal is
+
+ align:start position:0%
+super long length then and your goal is
+ 
+
+ align:start position:0%
+super long length then and your goal is
+to fit it in a box of equal to the super
+
+ align:start position:0%
+to fit it in a box of equal to the super
+ 
+
+ align:start position:0%
+to fit it in a box of equal to the super
+long length that will be possible if and
+
+ align:start position:0%
+long length that will be possible if and
+ 
+
+ align:start position:0%
+long length that will be possible if and
+only if these are aligned if they're not
+
+ align:start position:0%
+only if these are aligned if they're not
+ 
+
+ align:start position:0%
+only if these are aligned if they're not
+aligned then if you go halfway left or
+
+ align:start position:0%
+aligned then if you go halfway left or
+ 
+
+ align:start position:0%
+aligned then if you go halfway left or
+right and then add the super long length
+
+ align:start position:0%
+right and then add the super long length
+ 
+
+ align:start position:0%
+right and then add the super long length
+if it's not aligned with this one then
+
+ align:start position:0%
+if it's not aligned with this one then
+ 
+
+ align:start position:0%
+if it's not aligned with this one then
+you'll be a little bit too big and you
+
+ align:start position:0%
+you'll be a little bit too big and you
+ 
+
+ align:start position:0%
+you'll be a little bit too big and you
+won't fit in the Box okay so that
+
+ align:start position:0%
+won't fit in the Box okay so that
+ 
+
+ align:start position:0%
+won't fit in the Box okay so that
+represents two
+
+ align:start position:0%
+represents two
+ 
+
+ align:start position:0%
+represents two
+partition cool 20 seconds one more proof
+
+ align:start position:0%
+partition cool 20 seconds one more proof
+ 
+
+ align:start position:0%
+partition cool 20 seconds one more proof
+um so here's another problem map folding
+
+ align:start position:0%
+um so here's another problem map folding
+ 
+
+ align:start position:0%
+um so here's another problem map folding
+uh you've probably done this before
+
+ align:start position:0%
+uh you've probably done this before
+ 
+
+ align:start position:0%
+uh you've probably done this before
+easiest way to refold a road map is
+
+ align:start position:0%
+easiest way to refold a road map is
+ 
+
+ align:start position:0%
+easiest way to refold a road map is
+differently uh but generally what we're
+
+ align:start position:0%
+differently uh but generally what we're
+ 
+
+ align:start position:0%
+differently uh but generally what we're
+interested in here is just very simple
+
+ align:start position:0%
+interested in here is just very simple
+ 
+
+ align:start position:0%
+interested in here is just very simple
+fold fold along one line then fold along
+
+ align:start position:0%
+fold fold along one line then fold along
+ 
+
+ align:start position:0%
+fold fold along one line then fold along
+another line and so on okay so uh this
+
+ align:start position:0%
+another line and so on okay so uh this
+ 
+
+ align:start position:0%
+another line and so on okay so uh this
+is NP hard if I give you a crease
+
+ align:start position:0%
+is NP hard if I give you a crease
+ 
+
+ align:start position:0%
+is NP hard if I give you a crease
+pattern this doesn't look much like a
+
+ align:start position:0%
+pattern this doesn't look much like a
+ 
+
+ align:start position:0%
+pattern this doesn't look much like a
+map but uh we can talk about that if I
+
+ align:start position:0%
+map but uh we can talk about that if I
+ 
+
+ align:start position:0%
+map but uh we can talk about that if I
+give you a a map a polygon and some
+
+ align:start position:0%
+give you a a map a polygon and some
+ 
+
+ align:start position:0%
+give you a a map a polygon and some
+creases on it and I want to fold all of
+
+ align:start position:0%
+creases on it and I want to fold all of
+ 
+
+ align:start position:0%
+creases on it and I want to fold all of
+these creases this is possible if and
+
+ align:start position:0%
+these creases this is possible if and
+ 
+
+ align:start position:0%
+these creases this is possible if and
+only if uh two partition is solvable
+
+ align:start position:0%
+only if uh two partition is solvable
+ 
+
+ align:start position:0%
+only if uh two partition is solvable
+notice these lengths ah here we used A's
+
+ align:start position:0%
+notice these lengths ah here we used A's
+ 
+
+ align:start position:0%
+notice these lengths ah here we used A's
+that's smart of us so these are the AIS
+
+ align:start position:0%
+that's smart of us so these are the AIS
+ 
+
+ align:start position:0%
+that's smart of us so these are the AIS
+down the distances between these creases
+
+ align:start position:0%
+down the distances between these creases
+ 
+
+ align:start position:0%
+down the distances between these creases
+consecutive creases and again the idea
+
+ align:start position:0%
+consecutive creases and again the idea
+ 
+
+ align:start position:0%
+consecutive creases and again the idea
+is well I could fold each one or not and
+
+ align:start position:0%
+is well I could fold each one or not and
+ 
+
+ align:start position:0%
+is well I could fold each one or not and
+just like the Carpenters rule I can fold
+
+ align:start position:0%
+just like the Carpenters rule I can fold
+ 
+
+ align:start position:0%
+just like the Carpenters rule I can fold
+or not and if I'm clever and I do it
+
+ align:start position:0%
+or not and if I'm clever and I do it
+ 
+
+ align:start position:0%
+or not and if I'm clever and I do it
+with the right choice then this end
+
+ align:start position:0%
+with the right choice then this end
+ 
+
+ align:start position:0%
+with the right choice then this end
+point will be uh vertically aligned has
+
+ align:start position:0%
+point will be uh vertically aligned has
+ 
+
+ align:start position:0%
+point will be uh vertically aligned has
+the same y-coordinate as this end
+
+ align:start position:0%
+the same y-coordinate as this end
+ 
+
+ align:start position:0%
+the same y-coordinate as this end
+point okay and if I do that then and
+
+ align:start position:0%
+point okay and if I do that then and
+ 
+
+ align:start position:0%
+point okay and if I do that then and
+again we've added half of the super long
+
+ align:start position:0%
+again we've added half of the super long
+ 
+
+ align:start position:0%
+again we've added half of the super long
+length and then the super long length
+
+ align:start position:0%
+length and then the super long length
+ 
+
+ align:start position:0%
+length and then the super long length
+here there's also half of the super long
+
+ align:start position:0%
+here there's also half of the super long
+ 
+
+ align:start position:0%
+here there's also half of the super long
+length and the super long length there
+
+ align:start position:0%
+length and the super long length there
+ 
+
+ align:start position:0%
+length and the super long length there
+and now I can fold these two folds so
+
+ align:start position:0%
+and now I can fold these two folds so
+ 
+
+ align:start position:0%
+and now I can fold these two folds so
+when I fold one it's going to go here
+
+ align:start position:0%
+when I fold one it's going to go here
+ 
+
+ align:start position:0%
+when I fold one it's going to go here
+and it won't hit anything if and only if
+
+ align:start position:0%
+and it won't hit anything if and only if
+ 
+
+ align:start position:0%
+and it won't hit anything if and only if
+I solve two
+
+ align:start position:0%
+I solve two
+ 
+
+ align:start position:0%
+I solve two
+partition right if again this this is
+
+ align:start position:0%
+partition right if again this this is
+ 
+
+ align:start position:0%
+partition right if again this this is
+the box that I'm trying to fit
+
+ align:start position:0%
+the box that I'm trying to fit
+ 
+
+ align:start position:0%
+the box that I'm trying to fit
+everything into and this is the thing
+
+ align:start position:0%
+everything into and this is the thing
+ 
+
+ align:start position:0%
+everything into and this is the thing
+that I'm trying to shift up and down to
+
+ align:start position:0%
+that I'm trying to shift up and down to
+ 
+
+ align:start position:0%
+that I'm trying to shift up and down to
+be perfectly aligned with that if I can
+
+ align:start position:0%
+be perfectly aligned with that if I can
+ 
+
+ align:start position:0%
+be perfectly aligned with that if I can
+perfectly align it then I fold
+
+ align:start position:0%
+perfectly align it then I fold
+ 
+
+ align:start position:0%
+perfectly align it then I fold
+this Miss then fold this and it's out
+
+ align:start position:0%
+this Miss then fold this and it's out
+ 
+
+ align:start position:0%
+this Miss then fold this and it's out
+again and then I can finish these other
+
+ align:start position:0%
+again and then I can finish these other
+ 
+
+ align:start position:0%
+again and then I can finish these other
+creases that I haven't folded yet okay
+
+ align:start position:0%
+creases that I haven't folded yet okay
+ 
+
+ align:start position:0%
+creases that I haven't folded yet okay
+so it's all about when do you execute
+
+ align:start position:0%
+so it's all about when do you execute
+ 
+
+ align:start position:0%
+so it's all about when do you execute
+these two folds and so I'm going to do
+
+ align:start position:0%
+these two folds and so I'm going to do
+ 
+
+ align:start position:0%
+these two folds and so I'm going to do
+some of the horizontal folds so that
+
+ align:start position:0%
+some of the horizontal folds so that
+ 
+
+ align:start position:0%
+some of the horizontal folds so that
+things fit nicely then I'll do the two
+
+ align:start position:0%
+things fit nicely then I'll do the two
+ 
+
+ align:start position:0%
+things fit nicely then I'll do the two
+vertical folds then I'll do the rest of
+
+ align:start position:0%
+vertical folds then I'll do the rest of
+ 
+
+ align:start position:0%
+vertical folds then I'll do the rest of
+the horizontal folds and that will work
+
+ align:start position:0%
+the horizontal folds and that will work
+ 
+
+ align:start position:0%
+the horizontal folds and that will work
+if and only if two partition is solvable
+
+ align:start position:0%
+if and only if two partition is solvable
+ 
+
+ align:start position:0%
+if and only if two partition is solvable
+now this may look like a weird map
+
+ align:start position:0%
+now this may look like a weird map
+ 
+
+ align:start position:0%
+now this may look like a weird map
+but it turns out if you have a regular
+
+ align:start position:0%
+but it turns out if you have a regular
+ 
+
+ align:start position:0%
+but it turns out if you have a regular
+rectangular
+
+ align:start position:0%
+rectangular
+ 
+
+ align:start position:0%
+rectangular
+map uh not maybe a regular one and you
+
+ align:start position:0%
+map uh not maybe a regular one and you
+ 
+
+ align:start position:0%
+map uh not maybe a regular one and you
+have uh some diagonal folds
+
+ align:start position:0%
+have uh some diagonal folds
+ 
+
+ align:start position:0%
+have uh some diagonal folds
+45° then that will basically force you
+
+ align:start position:0%
+45° then that will basically force you
+ 
+
+ align:start position:0%
+45° then that will basically force you
+to fold oops
+
+ align:start position:0%
+to fold oops
+ 
+
+ align:start position:0%
+to fold oops
+uh didn't Mo myself enough the
+
+ align:start position:0%
+uh didn't Mo myself enough the
+ 
+
+ align:start position:0%
+uh didn't Mo myself enough the
+room that will force you to fold
+
+ align:start position:0%
+room that will force you to fold
+ 
+
+ align:start position:0%
+room that will force you to fold
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again uh one two and then
+
+ align:start position:0%
+again uh one two and then
+ 
+
+ align:start position:0%
+again uh one two and then
+here okay so you can put in diagonal
+
+ align:start position:0%
+here okay so you can put in diagonal
+ 
+
+ align:start position:0%
+here okay so you can put in diagonal
+folds to force you to fold into this
+
+ align:start position:0%
+folds to force you to fold into this
+ 
+
+ align:start position:0%
+folds to force you to fold into this
+initial structure and then add folds on
+
+ align:start position:0%
+initial structure and then add folds on
+ 
+
+ align:start position:0%
+initial structure and then add folds on
+top of that so it's like composing two
+
+ align:start position:0%
+top of that so it's like composing two
+ 
+
+ align:start position:0%
+top of that so it's like composing two
+gadgets then you add horizontal and
+
+ align:start position:0%
+gadgets then you add horizontal and
+ 
+
+ align:start position:0%
+gadgets then you add horizontal and
+vertical folds just like that picture
+
+ align:start position:0%
+vertical folds just like that picture
+ 
+
+ align:start position:0%
+vertical folds just like that picture
+and then you'll have a rectangular map
+
+ align:start position:0%
+and then you'll have a rectangular map
+ 
+
+ align:start position:0%
+and then you'll have a rectangular map
+with horizontal vertical and diagonal
+
+ align:start position:0%
+with horizontal vertical and diagonal
+ 
+
+ align:start position:0%
+with horizontal vertical and diagonal
+creases that you can fold all the
+
+ align:start position:0%
+creases that you can fold all the
+ 
+
+ align:start position:0%
+creases that you can fold all the
+increases by simple folds if and only if
+
+ align:start position:0%
+increases by simple folds if and only if
+ 
+
+ align:start position:0%
+increases by simple folds if and only if
+to partition is solvable open problem is
+
+ align:start position:0%
+to partition is solvable open problem is
+ 
+
+ align:start position:0%
+to partition is solvable open problem is
+this strongly NP hard we don't know is
+
+ align:start position:0%
+this strongly NP hard we don't know is
+ 
+
+ align:start position:0%
+this strongly NP hard we don't know is
+there pseud polinomial algorithm
+
+ align:start position:0%
+there pseud polinomial algorithm
+ 
+
+ align:start position:0%
+there pseud polinomial algorithm
+obviously we don't know um it's quite
+
+ align:start position:0%
+obviously we don't know um it's quite
+ 
+
+ align:start position:0%
+obviously we don't know um it's quite
+tantalizing uh but this is basically why
+
+ align:start position:0%
+tantalizing uh but this is basically why
+ 
+
+ align:start position:0%
+tantalizing uh but this is basically why
+Maps don't have diagonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faults and that's it for today
\ No newline at end of file
diff --git a/VuG2JNcRXYg.txt b/VuG2JNcRXYg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eda6a8d5e990c48f263da50b600a7bd8a027504f
--- /dev/null
+++ b/VuG2JNcRXYg.txt
@@ -0,0 +1,4651 @@
+align:start position:0%
+ 
+so we're going to talk about State
+
+ align:start position:0%
+so we're going to talk about State
+ 
+
+ align:start position:0%
+so we're going to talk about State
+machines which is a topic that you're
+
+ align:start position:0%
+machines which is a topic that you're
+ 
+
+ align:start position:0%
+machines which is a topic that you're
+going to see on many further courses
+
+ align:start position:0%
+going to see on many further courses
+ 
+
+ align:start position:0%
+going to see on many further courses
+because State machines model
+
+ align:start position:0%
+because State machines model
+ 
+
+ align:start position:0%
+because State machines model
+step-by-step
+
+ align:start position:0%
+step-by-step
+ 
+
+ align:start position:0%
+step-by-step
+processes uh and of course if you think
+
+ align:start position:0%
+processes uh and of course if you think
+ 
+
+ align:start position:0%
+processes uh and of course if you think
+about a computation the normal way you
+
+ align:start position:0%
+about a computation the normal way you
+ 
+
+ align:start position:0%
+about a computation the normal way you
+think about it is that it's doing
+
+ align:start position:0%
+think about it is that it's doing
+ 
+
+ align:start position:0%
+think about it is that it's doing
+instructions step by step one after
+
+ align:start position:0%
+instructions step by step one after
+ 
+
+ align:start position:0%
+instructions step by step one after
+another until it finally reaches
+
+ align:start position:0%
+another until it finally reaches
+ 
+
+ align:start position:0%
+another until it finally reaches
+termination uh likewise uh various
+
+ align:start position:0%
+termination uh likewise uh various
+ 
+
+ align:start position:0%
+termination uh likewise uh various
+digital circuits move through stages or
+
+ align:start position:0%
+digital circuits move through stages or
+ 
+
+ align:start position:0%
+digital circuits move through stages or
+States until they produce a final answer
+
+ align:start position:0%
+States until they produce a final answer
+ 
+
+ align:start position:0%
+States until they produce a final answer
+uh so State machines come up in at least
+
+ align:start position:0%
+uh so State machines come up in at least
+ 
+
+ align:start position:0%
+uh so State machines come up in at least
+those circumstances and many others now
+
+ align:start position:0%
+those circumstances and many others now
+ 
+
+ align:start position:0%
+those circumstances and many others now
+the general model of State machine
+
+ align:start position:0%
+the general model of State machine
+ 
+
+ align:start position:0%
+the general model of State machine
+involves the idea that you can give it
+
+ align:start position:0%
+involves the idea that you can give it
+ 
+
+ align:start position:0%
+involves the idea that you can give it
+input and it responds to them but we
+
+ align:start position:0%
+input and it responds to them but we
+ 
+
+ align:start position:0%
+input and it responds to them but we
+don't really need that for our purposes
+
+ align:start position:0%
+don't really need that for our purposes
+ 
+
+ align:start position:0%
+don't really need that for our purposes
+um so let's look at our example of a
+
+ align:start position:0%
+um so let's look at our example of a
+ 
+
+ align:start position:0%
+um so let's look at our example of a
+state machine here's Maybe here's a
+
+ align:start position:0%
+state machine here's Maybe here's a
+ 
+
+ align:start position:0%
+state machine here's Maybe here's a
+particular simple one uh this is a the a
+
+ align:start position:0%
+particular simple one uh this is a the a
+ 
+
+ align:start position:0%
+particular simple one uh this is a the a
+description of a state machine that
+
+ align:start position:0%
+description of a state machine that
+ 
+
+ align:start position:0%
+description of a state machine that
+counts to 99 so the circles are
+
+ align:start position:0%
+counts to 99 so the circles are
+ 
+
+ align:start position:0%
+counts to 99 so the circles are
+indicating what its states are we've
+
+ align:start position:0%
+indicating what its states are we've
+ 
+
+ align:start position:0%
+indicating what its states are we've
+named them uh from zero through 99 and
+
+ align:start position:0%
+named them uh from zero through 99 and
+ 
+
+ align:start position:0%
+named them uh from zero through 99 and
+then there's a final State called
+
+ align:start position:0%
+then there's a final State called
+ 
+
+ align:start position:0%
+then there's a final State called
+overflow and that funny uh Arc is an
+
+ align:start position:0%
+overflow and that funny uh Arc is an
+ 
+
+ align:start position:0%
+overflow and that funny uh Arc is an
+indication that if you're about to if
+
+ align:start position:0%
+indication that if you're about to if
+ 
+
+ align:start position:0%
+indication that if you're about to if
+you're in overflow mode and you make
+
+ align:start position:0%
+you're in overflow mode and you make
+ 
+
+ align:start position:0%
+you're in overflow mode and you make
+another step by following the arc you
+
+ align:start position:0%
+another step by following the arc you
+ 
+
+ align:start position:0%
+another step by following the arc you
+get back to overflow mode but if you're
+
+ align:start position:0%
+get back to overflow mode but if you're
+ 
+
+ align:start position:0%
+get back to overflow mode but if you're
+in zero you can make a step to one and
+
+ align:start position:0%
+in zero you can make a step to one and
+ 
+
+ align:start position:0%
+in zero you can make a step to one and
+if you're in one you can make a step to
+
+ align:start position:0%
+if you're in one you can make a step to
+ 
+
+ align:start position:0%
+if you're in one you can make a step to
+two and so on so starting off um at the
+
+ align:start position:0%
+two and so on so starting off um at the
+ 
+
+ align:start position:0%
+two and so on so starting off um at the
+start State um which is generally
+
+ align:start position:0%
+start State um which is generally
+ 
+
+ align:start position:0%
+start State um which is generally
+indicated by uh that double Mark so to
+
+ align:start position:0%
+indicated by uh that double Mark so to
+ 
+
+ align:start position:0%
+indicated by uh that double Mark so to
+indicate where to start then the
+
+ align:start position:0%
+indicate where to start then the
+ 
+
+ align:start position:0%
+indicate where to start then the
+description of this machine consistent
+
+ align:start position:0%
+description of this machine consistent
+ 
+
+ align:start position:0%
+description of this machine consistent
+in in complete description is a set of
+
+ align:start position:0%
+in in complete description is a set of
+ 
+
+ align:start position:0%
+in in complete description is a set of
+states which are pictured as 0 through
+
+ align:start position:0%
+states which are pictured as 0 through
+ 
+
+ align:start position:0%
+states which are pictured as 0 through
+99 plus overflow a set of transitions
+
+ align:start position:0%
+99 plus overflow a set of transitions
+ 
+
+ align:start position:0%
+99 plus overflow a set of transitions
+which are indicated by the arrows which
+
+ align:start position:0%
+which are indicated by the arrows which
+ 
+
+ align:start position:0%
+which are indicated by the arrows which
+is how one state can move to another
+
+ align:start position:0%
+is how one state can move to another
+ 
+
+ align:start position:0%
+is how one state can move to another
+state uh and the transitions can be
+
+ align:start position:0%
+state uh and the transitions can be
+ 
+
+ align:start position:0%
+state uh and the transitions can be
+summarized by saying that they're of the
+
+ align:start position:0%
+summarized by saying that they're of the
+ 
+
+ align:start position:0%
+summarized by saying that they're of the
+form I to I + 1 for I between 0 and 99
+
+ align:start position:0%
+form I to I + 1 for I between 0 and 99
+ 
+
+ align:start position:0%
+form I to I + 1 for I between 0 and 99
+and then there's a 90 9 transition to
+
+ align:start position:0%
+and then there's a 90 9 transition to
+ 
+
+ align:start position:0%
+and then there's a 90 9 transition to
+overflow and once you're in overflow you
+
+ align:start position:0%
+overflow and once you're in overflow you
+ 
+
+ align:start position:0%
+overflow and once you're in overflow you
+stay in overflow so the picture at the
+
+ align:start position:0%
+stay in overflow so the picture at the
+ 
+
+ align:start position:0%
+stay in overflow so the picture at the
+top is saying exactly the same thing as
+
+ align:start position:0%
+top is saying exactly the same thing as
+ 
+
+ align:start position:0%
+top is saying exactly the same thing as
+we've said here uh in mathematical
+
+ align:start position:0%
+we've said here uh in mathematical
+ 
+
+ align:start position:0%
+we've said here uh in mathematical
+notation explicitly describing what the
+
+ align:start position:0%
+notation explicitly describing what the
+ 
+
+ align:start position:0%
+notation explicitly describing what the
+transitions are so so this is a machine
+
+ align:start position:0%
+transitions are so so this is a machine
+ 
+
+ align:start position:0%
+transitions are so so this is a machine
+that if if you really built something
+
+ align:start position:0%
+that if if you really built something
+ 
+
+ align:start position:0%
+that if if you really built something
+that behaved this way it wouldn't be
+
+ align:start position:0%
+that behaved this way it wouldn't be
+ 
+
+ align:start position:0%
+that behaved this way it wouldn't be
+much use because once it's overflowed
+
+ align:start position:0%
+much use because once it's overflowed
+ 
+
+ align:start position:0%
+much use because once it's overflowed
+it's dead because it stays there uh real
+
+ align:start position:0%
+it's dead because it stays there uh real
+ 
+
+ align:start position:0%
+it's dead because it stays there uh real
+machine to be useful would have a reset
+
+ align:start position:0%
+machine to be useful would have a reset
+ 
+
+ align:start position:0%
+machine to be useful would have a reset
+transition which took overflow back to
+
+ align:start position:0%
+transition which took overflow back to
+ 
+
+ align:start position:0%
+transition which took overflow back to
+zero but uh this illustrates uh the
+
+ align:start position:0%
+zero but uh this illustrates uh the
+ 
+
+ align:start position:0%
+zero but uh this illustrates uh the
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+idea so let's look at a fun example from
+
+ align:start position:0%
+idea so let's look at a fun example from
+ 
+
+ align:start position:0%
+idea so let's look at a fun example from
+a Die Hard movie I forgotten which one
+
+ align:start position:0%
+a Die Hard movie I forgotten which one
+ 
+
+ align:start position:0%
+a Die Hard movie I forgotten which one
+it was um but there was one with Bruce
+
+ align:start position:0%
+it was um but there was one with Bruce
+ 
+
+ align:start position:0%
+it was um but there was one with Bruce
+Willis and Samuel Jackson playing a
+
+ align:start position:0%
+Willis and Samuel Jackson playing a
+ 
+
+ align:start position:0%
+Willis and Samuel Jackson playing a
+detective and a a friend that he meets
+
+ align:start position:0%
+detective and a a friend that he meets
+ 
+
+ align:start position:0%
+detective and a a friend that he meets
+who helps him deal with a Madman as is
+
+ align:start position:0%
+who helps him deal with a Madman as is
+ 
+
+ align:start position:0%
+who helps him deal with a Madman as is
+the case in all these movies this time
+
+ align:start position:0%
+the case in all these movies this time
+ 
+
+ align:start position:0%
+the case in all these movies this time
+the madman's name is Simon and what
+
+ align:start position:0%
+the madman's name is Simon and what
+ 
+
+ align:start position:0%
+the madman's name is Simon and what
+Simon says to them as they stand behind
+
+ align:start position:0%
+Simon says to them as they stand behind
+ 
+
+ align:start position:0%
+Simon says to them as they stand behind
+the fountain in the park shown on the
+
+ align:start position:0%
+the fountain in the park shown on the
+ 
+
+ align:start position:0%
+the fountain in the park shown on the
+previous slide is that on the fountain
+
+ align:start position:0%
+previous slide is that on the fountain
+ 
+
+ align:start position:0%
+previous slide is that on the fountain
+there should be two jugs do you see them
+
+ align:start position:0%
+there should be two jugs do you see them
+ 
+
+ align:start position:0%
+there should be two jugs do you see them
+a 5 gallon and a three gallon fill one
+
+ align:start position:0%
+a 5 gallon and a three gallon fill one
+ 
+
+ align:start position:0%
+a 5 gallon and a three gallon fill one
+of these jugs with exactly four gallons
+
+ align:start position:0%
+of these jugs with exactly four gallons
+ 
+
+ align:start position:0%
+of these jugs with exactly four gallons
+of water and place it on the scale and
+
+ align:start position:0%
+of water and place it on the scale and
+ 
+
+ align:start position:0%
+of water and place it on the scale and
+the timer will stop the timer and the
+
+ align:start position:0%
+the timer will stop the timer and the
+ 
+
+ align:start position:0%
+the timer will stop the timer and the
+scale are not shown in that picture but
+
+ align:start position:0%
+scale are not shown in that picture but
+ 
+
+ align:start position:0%
+scale are not shown in that picture but
+there's a scale and a timer nearby you
+
+ align:start position:0%
+there's a scale and a timer nearby you
+ 
+
+ align:start position:0%
+there's a scale and a timer nearby you
+must be precise 1 oun more or less will
+
+ align:start position:0%
+must be precise 1 oun more or less will
+ 
+
+ align:start position:0%
+must be precise 1 oun more or less will
+result in detonation if you're still
+
+ align:start position:0%
+result in detonation if you're still
+ 
+
+ align:start position:0%
+result in detonation if you're still
+alive in five minutes we'll
+
+ align:start position:0%
+alive in five minutes we'll
+ 
+
+ align:start position:0%
+alive in five minutes we'll
+speak okay so let's think about
+
+ align:start position:0%
+speak okay so let's think about
+ 
+
+ align:start position:0%
+speak okay so let's think about
+formalizing this as a state machine to
+
+ align:start position:0%
+formalizing this as a state machine to
+ 
+
+ align:start position:0%
+formalizing this as a state machine to
+see what's going on and so the but first
+
+ align:start position:0%
+see what's going on and so the but first
+ 
+
+ align:start position:0%
+see what's going on and so the but first
+of all to understand the uh the the the
+
+ align:start position:0%
+of all to understand the uh the the the
+ 
+
+ align:start position:0%
+of all to understand the uh the the the
+specification informally what there is
+
+ align:start position:0%
+specification informally what there is
+ 
+
+ align:start position:0%
+specification informally what there is
+is a three gallon jug and a five gallon
+
+ align:start position:0%
+is a three gallon jug and a five gallon
+ 
+
+ align:start position:0%
+is a three gallon jug and a five gallon
+jug uh that it's capable of holding
+
+ align:start position:0%
+jug uh that it's capable of holding
+ 
+
+ align:start position:0%
+jug uh that it's capable of holding
+water and an unlimited supply of water
+
+ align:start position:0%
+water and an unlimited supply of water
+ 
+
+ align:start position:0%
+water and an unlimited supply of water
+that you can get from The
+
+ align:start position:0%
+that you can get from The
+ 
+
+ align:start position:0%
+that you can get from The
+Fountain and the basic moves that you
+
+ align:start position:0%
+Fountain and the basic moves that you
+ 
+
+ align:start position:0%
+Fountain and the basic moves that you
+can make so with this setup the kind of
+
+ align:start position:0%
+can make so with this setup the kind of
+ 
+
+ align:start position:0%
+can make so with this setup the kind of
+moves that you can make would be say you
+
+ align:start position:0%
+moves that you can make would be say you
+ 
+
+ align:start position:0%
+moves that you can make would be say you
+fill up the three gallon jug with water
+
+ align:start position:0%
+fill up the three gallon jug with water
+ 
+
+ align:start position:0%
+fill up the three gallon jug with water
+uh and then you could pour the three
+
+ align:start position:0%
+uh and then you could pour the three
+ 
+
+ align:start position:0%
+uh and then you could pour the three
+gallon jug into the five gallon jug so
+
+ align:start position:0%
+gallon jug into the five gallon jug so
+ 
+
+ align:start position:0%
+gallon jug into the five gallon jug so
+the three gallon jug was empty and the 5
+
+ align:start position:0%
+the three gallon jug was empty and the 5
+ 
+
+ align:start position:0%
+the three gallon jug was empty and the 5
+gallon jug you knew had exactly three
+
+ align:start position:0%
+gallon jug you knew had exactly three
+ 
+
+ align:start position:0%
+gallon jug you knew had exactly three
+gallons in it um uh and then you can do
+
+ align:start position:0%
+gallons in it um uh and then you can do
+ 
+
+ align:start position:0%
+gallons in it um uh and then you can do
+other things like empty a jug and fill a
+
+ align:start position:0%
+other things like empty a jug and fill a
+ 
+
+ align:start position:0%
+other things like empty a jug and fill a
+jug um and empty them into each other so
+
+ align:start position:0%
+jug um and empty them into each other so
+ 
+
+ align:start position:0%
+jug um and empty them into each other so
+let's model this as a state machine and
+
+ align:start position:0%
+let's model this as a state machine and
+ 
+
+ align:start position:0%
+let's model this as a state machine and
+the first decision we need to make is
+
+ align:start position:0%
+the first decision we need to make is
+ 
+
+ align:start position:0%
+the first decision we need to make is
+what's the state going to be well the
+
+ align:start position:0%
+what's the state going to be well the
+ 
+
+ align:start position:0%
+what's the state going to be well the
+state the obvious model for the state is
+
+ align:start position:0%
+state the obvious model for the state is
+ 
+
+ align:start position:0%
+state the obvious model for the state is
+the amount of water in each of the jugs
+
+ align:start position:0%
+the amount of water in each of the jugs
+ 
+
+ align:start position:0%
+the amount of water in each of the jugs
+so B is the amount of in the big jug and
+
+ align:start position:0%
+so B is the amount of in the big jug and
+ 
+
+ align:start position:0%
+so B is the amount of in the big jug and
+L is the amount in the little jug and
+
+ align:start position:0%
+L is the amount in the little jug and
+ 
+
+ align:start position:0%
+L is the amount in the little jug and
+what we know about B and L is that
+
+ align:start position:0%
+what we know about B and L is that
+ 
+
+ align:start position:0%
+what we know about B and L is that
+they're going to be some amount between
+
+ align:start position:0%
+they're going to be some amount between
+ 
+
+ align:start position:0%
+they're going to be some amount between
+zero and five for B and zero and three
+
+ align:start position:0%
+zero and five for B and zero and three
+ 
+
+ align:start position:0%
+zero and five for B and zero and three
+for L where we're going to quickly
+
+ align:start position:0%
+for L where we're going to quickly
+ 
+
+ align:start position:0%
+for L where we're going to quickly
+realize that we need them to be integers
+
+ align:start position:0%
+realize that we need them to be integers
+ 
+
+ align:start position:0%
+realize that we need them to be integers
+but off hand we can allow them to be
+
+ align:start position:0%
+but off hand we can allow them to be
+ 
+
+ align:start position:0%
+but off hand we can allow them to be
+real numbers because uh after all you
+
+ align:start position:0%
+real numbers because uh after all you
+ 
+
+ align:start position:0%
+real numbers because uh after all you
+could just pour some arbitrary amount of
+
+ align:start position:0%
+could just pour some arbitrary amount of
+ 
+
+ align:start position:0%
+could just pour some arbitrary amount of
+water into the big jug any amount that
+
+ align:start position:0%
+water into the big jug any amount that
+ 
+
+ align:start position:0%
+water into the big jug any amount that
+it'll hold between zero and five
+
+ align:start position:0%
+it'll hold between zero and five
+ 
+
+ align:start position:0%
+it'll hold between zero and five
+although that'll be dangerous because as
+
+ align:start position:0%
+although that'll be dangerous because as
+ 
+
+ align:start position:0%
+although that'll be dangerous because as
+soon as you do that uh you're going to
+
+ align:start position:0%
+soon as you do that uh you're going to
+ 
+
+ align:start position:0%
+soon as you do that uh you're going to
+lose track of exactly how much is in
+
+ align:start position:0%
+lose track of exactly how much is in
+ 
+
+ align:start position:0%
+lose track of exactly how much is in
+there and you won't know when you have
+
+ align:start position:0%
+there and you won't know when you have
+ 
+
+ align:start position:0%
+there and you won't know when you have
+four gallons or not so let's formalize
+
+ align:start position:0%
+four gallons or not so let's formalize
+ 
+
+ align:start position:0%
+four gallons or not so let's formalize
+the possible moves that we can have so
+
+ align:start position:0%
+the possible moves that we can have so
+ 
+
+ align:start position:0%
+the possible moves that we can have so
+first of all the start state is 0
+
+ align:start position:0%
+first of all the start state is 0
+ 
+
+ align:start position:0%
+first of all the start state is 0
+because we start with both jugs empty
+
+ align:start position:0%
+because we start with both jugs empty
+ 
+
+ align:start position:0%
+because we start with both jugs empty
+and then what are the possible
+
+ align:start position:0%
+and then what are the possible
+ 
+
+ align:start position:0%
+and then what are the possible
+transitions of how B&L moves well let's
+
+ align:start position:0%
+transitions of how B&L moves well let's
+ 
+
+ align:start position:0%
+transitions of how B&L moves well let's
+see the the fill the little jug move
+
+ align:start position:0%
+see the the fill the little jug move
+ 
+
+ align:start position:0%
+see the the fill the little jug move
+amounts to saying that if you have an
+
+ align:start position:0%
+amounts to saying that if you have an
+ 
+
+ align:start position:0%
+amounts to saying that if you have an
+amount a b in big and L in little then
+
+ align:start position:0%
+amount a b in big and L in little then
+ 
+
+ align:start position:0%
+amount a b in big and L in little then
+you can make a transition called fill
+
+ align:start position:0%
+you can make a transition called fill
+ 
+
+ align:start position:0%
+you can make a transition called fill
+the little jug into B in big still
+
+ align:start position:0%
+the little jug into B in big still
+ 
+
+ align:start position:0%
+the little jug into B in big still
+unchanged and three in little for L less
+
+ align:start position:0%
+unchanged and three in little for L less
+ 
+
+ align:start position:0%
+unchanged and three in little for L less
+than three I'm going to forbid the
+
+ align:start position:0%
+than three I'm going to forbid the
+ 
+
+ align:start position:0%
+than three I'm going to forbid the
+vacuous move where you the little jug is
+
+ align:start position:0%
+vacuous move where you the little jug is
+ 
+
+ align:start position:0%
+vacuous move where you the little jug is
+already F full and you try to fill it
+
+ align:start position:0%
+already F full and you try to fill it
+ 
+
+ align:start position:0%
+already F full and you try to fill it
+that doesn't count so L has to be less
+
+ align:start position:0%
+that doesn't count so L has to be less
+ 
+
+ align:start position:0%
+that doesn't count so L has to be less
+than three and you can make it three by
+
+ align:start position:0%
+than three and you can make it three by
+ 
+
+ align:start position:0%
+than three and you can make it three by
+filling the little jug similarly you can
+
+ align:start position:0%
+filling the little jug similarly you can
+ 
+
+ align:start position:0%
+filling the little jug similarly you can
+fill the big jug if B is less than five
+
+ align:start position:0%
+fill the big jug if B is less than five
+ 
+
+ align:start position:0%
+fill the big jug if B is less than five
+then you can turn it into five by
+
+ align:start position:0%
+then you can turn it into five by
+ 
+
+ align:start position:0%
+then you can turn it into five by
+filling it and then you can empty the
+
+ align:start position:0%
+filling it and then you can empty the
+ 
+
+ align:start position:0%
+filling it and then you can empty the
+little jug which is easy if you go from
+
+ align:start position:0%
+little jug which is easy if you go from
+ 
+
+ align:start position:0%
+little jug which is easy if you go from
+BL you go to be zero and likewise you
+
+ align:start position:0%
+BL you go to be zero and likewise you
+ 
+
+ align:start position:0%
+BL you go to be zero and likewise you
+can empty the big jug those are the easy
+
+ align:start position:0%
+can empty the big jug those are the easy
+ 
+
+ align:start position:0%
+can empty the big jug those are the easy
+moves a slightly more complicated move
+
+ align:start position:0%
+moves a slightly more complicated move
+ 
+
+ align:start position:0%
+moves a slightly more complicated move
+is pour the big jug into the little jug
+
+ align:start position:0%
+is pour the big jug into the little jug
+ 
+
+ align:start position:0%
+is pour the big jug into the little jug
+well if there's no Overflow what that
+
+ align:start position:0%
+well if there's no Overflow what that
+ 
+
+ align:start position:0%
+well if there's no Overflow what that
+means is that there's l in the little
+
+ align:start position:0%
+means is that there's l in the little
+ 
+
+ align:start position:0%
+means is that there's l in the little
+jug and B in the big jug and after
+
+ align:start position:0%
+jug and B in the big jug and after
+ 
+
+ align:start position:0%
+jug and B in the big jug and after
+you've poured the big jug into the
+
+ align:start position:0%
+you've poured the big jug into the
+ 
+
+ align:start position:0%
+you've poured the big jug into the
+little jug there's B plus l in the in
+
+ align:start position:0%
+little jug there's B plus l in the in
+ 
+
+ align:start position:0%
+little jug there's B plus l in the in
+the little one and nothing in the big
+
+ align:start position:0%
+the little one and nothing in the big
+ 
+
+ align:start position:0%
+the little one and nothing in the big
+one but let's be careful here about what
+
+ align:start position:0%
+one but let's be careful here about what
+ 
+
+ align:start position:0%
+one but let's be careful here about what
+exactly we're doing math we're not sort
+
+ align:start position:0%
+exactly we're doing math we're not sort
+ 
+
+ align:start position:0%
+exactly we're doing math we're not sort
+of we're trying to get away from the
+
+ align:start position:0%
+of we're trying to get away from the
+ 
+
+ align:start position:0%
+of we're trying to get away from the
+metaphor so what does no overflow means
+
+ align:start position:0%
+metaphor so what does no overflow means
+ 
+
+ align:start position:0%
+metaphor so what does no overflow means
+simply means that b plus L will fit B
+
+ align:start position:0%
+simply means that b plus L will fit B
+ 
+
+ align:start position:0%
+simply means that b plus L will fit B
+plus L is less than or equal to three
+
+ align:start position:0%
+plus L is less than or equal to three
+ 
+
+ align:start position:0%
+plus L is less than or equal to three
+all right uh what's the other case of
+
+ align:start position:0%
+all right uh what's the other case of
+ 
+
+ align:start position:0%
+all right uh what's the other case of
+pouring the big jug into the little jug
+
+ align:start position:0%
+pouring the big jug into the little jug
+ 
+
+ align:start position:0%
+pouring the big jug into the little jug
+well that's when B plus L won't fit in
+
+ align:start position:0%
+well that's when B plus L won't fit in
+ 
+
+ align:start position:0%
+well that's when B plus L won't fit in
+which case you pour into the little jug
+
+ align:start position:0%
+which case you pour into the little jug
+ 
+
+ align:start position:0%
+which case you pour into the little jug
+it's got l so you pour in 3 minus L to
+
+ align:start position:0%
+it's got l so you pour in 3 minus L to
+ 
+
+ align:start position:0%
+it's got l so you pour in 3 minus L to
+fill it up and then what's left in B is
+
+ align:start position:0%
+fill it up and then what's left in B is
+ 
+
+ align:start position:0%
+fill it up and then what's left in B is
+B minus the 3 minus little L that you
+
+ align:start position:0%
+B minus the 3 minus little L that you
+ 
+
+ align:start position:0%
+B minus the 3 minus little L that you
+poured so that's the otherwise case when
+
+ align:start position:0%
+poured so that's the otherwise case when
+ 
+
+ align:start position:0%
+poured so that's the otherwise case when
+there is Overflow and similarly there
+
+ align:start position:0%
+there is Overflow and similarly there
+ 
+
+ align:start position:0%
+there is Overflow and similarly there
+are moves for pouring the little jug
+
+ align:start position:0%
+are moves for pouring the little jug
+ 
+
+ align:start position:0%
+are moves for pouring the little jug
+into the big jug so that then is a
+
+ align:start position:0%
+into the big jug so that then is a
+ 
+
+ align:start position:0%
+into the big jug so that then is a
+formal specification of the DI hard
+
+ align:start position:0%
+formal specification of the DI hard
+ 
+
+ align:start position:0%
+formal specification of the DI hard
+machine and the moves that we're going
+
+ align:start position:0%
+machine and the moves that we're going
+ 
+
+ align:start position:0%
+machine and the moves that we're going
+to allow now you could allow other moves
+
+ align:start position:0%
+to allow now you could allow other moves
+ 
+
+ align:start position:0%
+to allow now you could allow other moves
+like randomly pouring out a little water
+
+ align:start position:0%
+like randomly pouring out a little water
+ 
+
+ align:start position:0%
+like randomly pouring out a little water
+or randomly filling up a little water
+
+ align:start position:0%
+or randomly filling up a little water
+ 
+
+ align:start position:0%
+or randomly filling up a little water
+but if you did that again you lose track
+
+ align:start position:0%
+but if you did that again you lose track
+ 
+
+ align:start position:0%
+but if you did that again you lose track
+of how much water is in the jug so these
+
+ align:start position:0%
+of how much water is in the jug so these
+ 
+
+ align:start position:0%
+of how much water is in the jug so these
+are the only safe moves and they're the
+
+ align:start position:0%
+are the only safe moves and they're the
+ 
+
+ align:start position:0%
+are the only safe moves and they're the
+only ones we're going to model all right
+
+ align:start position:0%
+only ones we're going to model all right
+ 
+
+ align:start position:0%
+only ones we're going to model all right
+so let's go back to Simon's challenge he
+
+ align:start position:0%
+so let's go back to Simon's challenge he
+ 
+
+ align:start position:0%
+so let's go back to Simon's challenge he
+wants to disarm the Bomb by getting
+
+ align:start position:0%
+wants to disarm the Bomb by getting
+ 
+
+ align:start position:0%
+wants to disarm the Bomb by getting
+exactly four gallons of water on the SC
+
+ align:start position:0%
+exactly four gallons of water on the SC
+ 
+
+ align:start position:0%
+exactly four gallons of water on the SC
+in a jug and measure it on the scale or
+
+ align:start position:0%
+in a jug and measure it on the scale or
+ 
+
+ align:start position:0%
+in a jug and measure it on the scale or
+things will blow up and how do you do it
+
+ align:start position:0%
+things will blow up and how do you do it
+ 
+
+ align:start position:0%
+things will blow up and how do you do it
+well why don't you take a moment to
+
+ align:start position:0%
+well why don't you take a moment to
+ 
+
+ align:start position:0%
+well why don't you take a moment to
+think about it before I proceed to the
+
+ align:start position:0%
+think about it before I proceed to the
+ 
+
+ align:start position:0%
+think about it before I proceed to the
+next set of slides or before you let me
+
+ align:start position:0%
+next set of slides or before you let me
+ 
+
+ align:start position:0%
+next set of slides or before you let me
+proceed but just to understand the rules
+
+ align:start position:0%
+proceed but just to understand the rules
+ 
+
+ align:start position:0%
+proceed but just to understand the rules
+again and watch them work here's how um
+
+ align:start position:0%
+again and watch them work here's how um
+ 
+
+ align:start position:0%
+again and watch them work here's how um
+we're going to start off with both jugs
+
+ align:start position:0%
+we're going to start off with both jugs
+ 
+
+ align:start position:0%
+we're going to start off with both jugs
+empty so we start off in state 00 0 and
+
+ align:start position:0%
+empty so we start off in state 00 0 and
+ 
+
+ align:start position:0%
+empty so we start off in state 00 0 and
+the first move is going to be to fill
+
+ align:start position:0%
+the first move is going to be to fill
+ 
+
+ align:start position:0%
+the first move is going to be to fill
+the big jug which takes us to State
+
+ align:start position:0%
+the big jug which takes us to State
+ 
+
+ align:start position:0%
+the big jug which takes us to State
+5 where the big jug has five and the
+
+ align:start position:0%
+5 where the big jug has five and the
+ 
+
+ align:start position:0%
+5 where the big jug has five and the
+little jug is still empty then we're
+
+ align:start position:0%
+little jug is still empty then we're
+ 
+
+ align:start position:0%
+little jug is still empty then we're
+going to pour from the big into the
+
+ align:start position:0%
+going to pour from the big into the
+ 
+
+ align:start position:0%
+going to pour from the big into the
+little so now the little jug has three
+
+ align:start position:0%
+little so now the little jug has three
+ 
+
+ align:start position:0%
+little so now the little jug has three
+we're filling up the little one that
+
+ align:start position:0%
+we're filling up the little one that
+ 
+
+ align:start position:0%
+we're filling up the little one that
+leaves two in the big
+
+ align:start position:0%
+leaves two in the big
+ 
+
+ align:start position:0%
+leaves two in the big
+jug um now we're going to empty the
+
+ align:start position:0%
+jug um now we're going to empty the
+ 
+
+ align:start position:0%
+jug um now we're going to empty the
+little one and we still have two left in
+
+ align:start position:0%
+little one and we still have two left in
+ 
+
+ align:start position:0%
+little one and we still have two left in
+the big
+
+ align:start position:0%
+the big
+ 
+
+ align:start position:0%
+the big
+one and now we're going to pour from the
+
+ align:start position:0%
+one and now we're going to pour from the
+ 
+
+ align:start position:0%
+one and now we're going to pour from the
+big one into the little one so the
+
+ align:start position:0%
+big one into the little one so the
+ 
+
+ align:start position:0%
+big one into the little one so the
+little one has two gallons and the big
+
+ align:start position:0%
+little one has two gallons and the big
+ 
+
+ align:start position:0%
+little one has two gallons and the big
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+empty now we fill the big jug and
+
+ align:start position:0%
+empty now we fill the big jug and
+ 
+
+ align:start position:0%
+empty now we fill the big jug and
+there's still two gallons in the little
+
+ align:start position:0%
+there's still two gallons in the little
+ 
+
+ align:start position:0%
+there's still two gallons in the little
+one and five gallons in the big one now
+
+ align:start position:0%
+one and five gallons in the big one now
+ 
+
+ align:start position:0%
+one and five gallons in the big one now
+we pour off from the five gallon jug
+
+ align:start position:0%
+we pour off from the five gallon jug
+ 
+
+ align:start position:0%
+we pour off from the five gallon jug
+into until the one gallon jug is full
+
+ align:start position:0%
+into until the one gallon jug is full
+ 
+
+ align:start position:0%
+into until the one gallon jug is full
+that's removing the one gallon that the
+
+ align:start position:0%
+that's removing the one gallon that the
+ 
+
+ align:start position:0%
+that's removing the one gallon that the
+three gallon jug still has capacity for
+
+ align:start position:0%
+three gallon jug still has capacity for
+ 
+
+ align:start position:0%
+three gallon jug still has capacity for
+we're reduced to full three gallons in
+
+ align:start position:0%
+we're reduced to full three gallons in
+ 
+
+ align:start position:0%
+we're reduced to full three gallons in
+the little jug and four gallons our
+
+ align:start position:0%
+the little jug and four gallons our
+ 
+
+ align:start position:0%
+the little jug and four gallons our
+Target in the big jug and so we've
+
+ align:start position:0%
+Target in the big jug and so we've
+ 
+
+ align:start position:0%
+Target in the big jug and so we've
+accomplished it and we're done so the
+
+ align:start position:0%
+accomplished it and we're done so the
+ 
+
+ align:start position:0%
+accomplished it and we're done so the
+bomb doesn't go off all right so the
+
+ align:start position:0%
+bomb doesn't go off all right so the
+ 
+
+ align:start position:0%
+bomb doesn't go off all right so the
+point of this exercise is really just to
+
+ align:start position:0%
+point of this exercise is really just to
+ 
+
+ align:start position:0%
+point of this exercise is really just to
+practice how the moves work and what the
+
+ align:start position:0%
+practice how the moves work and what the
+ 
+
+ align:start position:0%
+practice how the moves work and what the
+states are but the question that I want
+
+ align:start position:0%
+states are but the question that I want
+ 
+
+ align:start position:0%
+states are but the question that I want
+to raise is uh suppose that we want to
+
+ align:start position:0%
+to raise is uh suppose that we want to
+ 
+
+ align:start position:0%
+to raise is uh suppose that we want to
+have a die hard once and for all
+
+ align:start position:0%
+have a die hard once and for all
+ 
+
+ align:start position:0%
+have a die hard once and for all
+scenario in which we're tired of the
+
+ align:start position:0%
+scenario in which we're tired of the
+ 
+
+ align:start position:0%
+scenario in which we're tired of the
+remakes of these movies and we propos
+
+ align:start position:0%
+remakes of these movies and we propos
+ 
+
+ align:start position:0%
+remakes of these movies and we propos
+that in the next movie um that Simon if
+
+ align:start position:0%
+that in the next movie um that Simon if
+ 
+
+ align:start position:0%
+that in the next movie um that Simon if
+he's still around offers an alternative
+
+ align:start position:0%
+he's still around offers an alternative
+ 
+
+ align:start position:0%
+he's still around offers an alternative
+challenge where instead of a three
+
+ align:start position:0%
+challenge where instead of a three
+ 
+
+ align:start position:0%
+challenge where instead of a three
+gallon and a five gallon jug there's a
+
+ align:start position:0%
+gallon and a five gallon jug there's a
+ 
+
+ align:start position:0%
+gallon and a five gallon jug there's a
+three gallon jug and a nine gallon jug
+
+ align:start position:0%
+three gallon jug and a nine gallon jug
+ 
+
+ align:start position:0%
+three gallon jug and a nine gallon jug
+and now the question is can you get four
+
+ align:start position:0%
+and now the question is can you get four
+ 
+
+ align:start position:0%
+and now the question is can you get four
+gallons into the big jug by pouring back
+
+ align:start position:0%
+gallons into the big jug by pouring back
+ 
+
+ align:start position:0%
+gallons into the big jug by pouring back
+and forth with rules like these or can't
+
+ align:start position:0%
+and forth with rules like these or can't
+ 
+
+ align:start position:0%
+and forth with rules like these or can't
+you and can you prove it well my guess
+
+ align:start position:0%
+you and can you prove it well my guess
+ 
+
+ align:start position:0%
+you and can you prove it well my guess
+is that you probably can figure out
+
+ align:start position:0%
+is that you probably can figure out
+ 
+
+ align:start position:0%
+is that you probably can figure out
+what's going on because what's happening
+
+ align:start position:0%
+what's going on because what's happening
+ 
+
+ align:start position:0%
+what's going on because what's happening
+is if you start off with nothing in
+
+ align:start position:0%
+is if you start off with nothing in
+ 
+
+ align:start position:0%
+is if you start off with nothing in
+either jug and you do these moves of
+
+ align:start position:0%
+either jug and you do these moves of
+ 
+
+ align:start position:0%
+either jug and you do these moves of
+filling up a jug or pouring one jug into
+
+ align:start position:0%
+filling up a jug or pouring one jug into
+ 
+
+ align:start position:0%
+filling up a jug or pouring one jug into
+another you'll discover that the amount
+
+ align:start position:0%
+another you'll discover that the amount
+ 
+
+ align:start position:0%
+another you'll discover that the amount
+of water in any jug is always divisible
+
+ align:start position:0%
+of water in any jug is always divisible
+ 
+
+ align:start position:0%
+of water in any jug is always divisible
+by three this is a preserved invariant
+
+ align:start position:0%
+by three this is a preserved invariant
+ 
+
+ align:start position:0%
+by three this is a preserved invariant
+any state that you can get to starting
+
+ align:start position:0%
+any state that you can get to starting
+ 
+
+ align:start position:0%
+any state that you can get to starting
+off from 0 three will divide the number
+
+ align:start position:0%
+off from 0 three will divide the number
+ 
+
+ align:start position:0%
+off from 0 three will divide the number
+of gallons in each jug we could state it
+
+ align:start position:0%
+of gallons in each jug we could state it
+ 
+
+ align:start position:0%
+of gallons in each jug we could state it
+this way there's a property of states
+
+ align:start position:0%
+this way there's a property of states
+ 
+
+ align:start position:0%
+this way there's a property of states
+property of B and L which is the state
+
+ align:start position:0%
+property of B and L which is the state
+ 
+
+ align:start position:0%
+property of B and L which is the state
+which is that 3 divides B that vertical
+
+ align:start position:0%
+which is that 3 divides B that vertical
+ 
+
+ align:start position:0%
+which is that 3 divides B that vertical
+uh line is is a Shand for the symbol
+
+ align:start position:0%
+uh line is is a Shand for the symbol
+ 
+
+ align:start position:0%
+uh line is is a Shand for the symbol
+divides so three divides b or B is a
+
+ align:start position:0%
+divides so three divides b or B is a
+ 
+
+ align:start position:0%
+divides so three divides b or B is a
+multiple of three 3 divides L synonym L
+
+ align:start position:0%
+multiple of three 3 divides L synonym L
+ 
+
+ align:start position:0%
+multiple of three 3 divides L synonym L
+is a multiple of three and the claim is
+
+ align:start position:0%
+is a multiple of three and the claim is
+ 
+
+ align:start position:0%
+is a multiple of three and the claim is
+that that's always going to be
+
+ align:start position:0%
+that that's always going to be
+ 
+
+ align:start position:0%
+that that's always going to be
+true so in case that's not obvious you
+
+ align:start position:0%
+true so in case that's not obvious you
+ 
+
+ align:start position:0%
+true so in case that's not obvious you
+might not have all the rules in your
+
+ align:start position:0%
+might not have all the rules in your
+ 
+
+ align:start position:0%
+might not have all the rules in your
+head but let's just take an ex look at
+
+ align:start position:0%
+head but let's just take an ex look at
+ 
+
+ align:start position:0%
+head but let's just take an ex look at
+one of the more complicated rules this
+
+ align:start position:0%
+one of the more complicated rules this
+ 
+
+ align:start position:0%
+one of the more complicated rules this
+was the rule where you're pouring the
+
+ align:start position:0%
+was the rule where you're pouring the
+ 
+
+ align:start position:0%
+was the rule where you're pouring the
+big J into the little jug up till the
+
+ align:start position:0%
+big J into the little jug up till the
+ 
+
+ align:start position:0%
+big J into the little jug up till the
+until the little jug is full um and that
+
+ align:start position:0%
+until the little jug is full um and that
+ 
+
+ align:start position:0%
+until the little jug is full um and that
+transition is that if you're in state b
+
+ align:start position:0%
+transition is that if you're in state b
+ 
+
+ align:start position:0%
+transition is that if you're in state b
+l you move to B minus 3 minus L and
+
+ align:start position:0%
+l you move to B minus 3 minus L and
+ 
+
+ align:start position:0%
+l you move to B minus 3 minus L and
+three and if you look at this now
+
+ align:start position:0%
+three and if you look at this now
+ 
+
+ align:start position:0%
+three and if you look at this now
+clearly if three divides both B and L
+
+ align:start position:0%
+clearly if three divides both B and L
+ 
+
+ align:start position:0%
+clearly if three divides both B and L
+both components of the state you're at
+
+ align:start position:0%
+both components of the state you're at
+ 
+
+ align:start position:0%
+both components of the state you're at
+then in the new state well three
+
+ align:start position:0%
+then in the new state well three
+ 
+
+ align:start position:0%
+then in the new state well three
+obviously divides the contents of the
+
+ align:start position:0%
+obviously divides the contents of the
+ 
+
+ align:start position:0%
+obviously divides the contents of the
+little jug which is three but three also
+
+ align:start position:0%
+little jug which is three but three also
+ 
+
+ align:start position:0%
+little jug which is three but three also
+divides the contents of the big jug
+
+ align:start position:0%
+divides the contents of the big jug
+ 
+
+ align:start position:0%
+divides the contents of the big jug
+which is a multiple of three namely B
+
+ align:start position:0%
+which is a multiple of three namely B
+ 
+
+ align:start position:0%
+which is a multiple of three namely B
+minus 3 which is a multiple of 3 minus W
+
+ align:start position:0%
+minus 3 which is a multiple of 3 minus W
+ 
+
+ align:start position:0%
+minus 3 which is a multiple of 3 minus W
+which is a multiple of three when you
+
+ align:start position:0%
+which is a multiple of three when you
+ 
+
+ align:start position:0%
+which is a multiple of three when you
+take a linear combination of multiples
+
+ align:start position:0%
+take a linear combination of multiples
+ 
+
+ align:start position:0%
+take a linear combination of multiples
+of three you get a multiple of three and
+
+ align:start position:0%
+of three you get a multiple of three and
+ 
+
+ align:start position:0%
+of three you get a multiple of three and
+you look at all the other Transitions
+
+ align:start position:0%
+you look at all the other Transitions
+ 
+
+ align:start position:0%
+you look at all the other Transitions
+and they check equally well if you're in
+
+ align:start position:0%
+and they check equally well if you're in
+ 
+
+ align:start position:0%
+and they check equally well if you're in
+a state BL and you move to a new state B
+
+ align:start position:0%
+a state BL and you move to a new state B
+ 
+
+ align:start position:0%
+a state BL and you move to a new state B
+Prime L
+
+ align:start position:0%
+Prime L
+ 
+
+ align:start position:0%
+Prime L
+Prime if 3 divides B and L then 3
+
+ align:start position:0%
+Prime if 3 divides B and L then 3
+ 
+
+ align:start position:0%
+Prime if 3 divides B and L then 3
+divides B Prime and L Prime so this is
+
+ align:start position:0%
+divides B Prime and L Prime so this is
+ 
+
+ align:start position:0%
+divides B Prime and L Prime so this is
+what's called a preserved invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course the Cory is that in the
+
+ align:start position:0%
+and of course the Cory is that in the
+ 
+
+ align:start position:0%
+and of course the Cory is that in the
+Die Hard once and for all game with the
+
+ align:start position:0%
+Die Hard once and for all game with the
+ 
+
+ align:start position:0%
+Die Hard once and for all game with the
+three jug three gallon jug and the nine
+
+ align:start position:0%
+three jug three gallon jug and the nine
+ 
+
+ align:start position:0%
+three jug three gallon jug and the nine
+gallon jug you can't get to any state of
+
+ align:start position:0%
+gallon jug you can't get to any state of
+ 
+
+ align:start position:0%
+gallon jug you can't get to any state of
+the form 4X because four is not
+
+ align:start position:0%
+the form 4X because four is not
+ 
+
+ align:start position:0%
+the form 4X because four is not
+divisible by three and therefore Bruce
+
+ align:start position:0%
+divisible by three and therefore Bruce
+ 
+
+ align:start position:0%
+divisible by three and therefore Bruce
+is going to
+
+ align:start position:0%
+is going to
+ 
+
+ align:start position:0%
+is going to
+die now what we've Illustrated here is
+
+ align:start position:0%
+die now what we've Illustrated here is
+ 
+
+ align:start position:0%
+die now what we've Illustrated here is
+an argument that's known as Floyd's
+
+ align:start position:0%
+an argument that's known as Floyd's
+ 
+
+ align:start position:0%
+an argument that's known as Floyd's
+invariant principle and it's really
+
+ align:start position:0%
+invariant principle and it's really
+ 
+
+ align:start position:0%
+invariant principle and it's really
+nothing but induction reformulated for
+
+ align:start position:0%
+nothing but induction reformulated for
+ 
+
+ align:start position:0%
+nothing but induction reformulated for
+State machines the uh statement of
+
+ align:start position:0%
+State machines the uh statement of
+ 
+
+ align:start position:0%
+State machines the uh statement of
+Floyd's invariant principle is that
+
+ align:start position:0%
+Floyd's invariant principle is that
+ 
+
+ align:start position:0%
+Floyd's invariant principle is that
+we're going to define a preserved
+
+ align:start position:0%
+we're going to define a preserved
+ 
+
+ align:start position:0%
+we're going to define a preserved
+invariant is a property of states and a
+
+ align:start position:0%
+invariant is a property of states and a
+ 
+
+ align:start position:0%
+invariant is a property of states and a
+preserved invariant means it has the
+
+ align:start position:0%
+preserved invariant means it has the
+ 
+
+ align:start position:0%
+preserved invariant means it has the
+property that if you're in a state that
+
+ align:start position:0%
+property that if you're in a state that
+ 
+
+ align:start position:0%
+property that if you're in a state that
+has property p and it's possible to make
+
+ align:start position:0%
+has property p and it's possible to make
+ 
+
+ align:start position:0%
+has property p and it's possible to make
+a single transition to a state R then R
+
+ align:start position:0%
+a single transition to a state R then R
+ 
+
+ align:start position:0%
+a single transition to a state R then R
+will also have property P this is just
+
+ align:start position:0%
+will also have property P this is just
+ 
+
+ align:start position:0%
+will also have property P this is just
+like the induction step you have to
+
+ align:start position:0%
+like the induction step you have to
+ 
+
+ align:start position:0%
+like the induction step you have to
+prove that P of n implies P of n plus
+
+ align:start position:0%
+prove that P of n implies P of n plus
+ 
+
+ align:start position:0%
+prove that P of n implies P of n plus
+one so if you have a preserved
+
+ align:start position:0%
+one so if you have a preserved
+ 
+
+ align:start position:0%
+one so if you have a preserved
+invariant uh then uh
+
+ align:start position:0%
+invariant uh then uh
+ 
+
+ align:start position:0%
+invariant uh then uh
+if the property holds at the start State
+
+ align:start position:0%
+if the property holds at the start State
+ 
+
+ align:start position:0%
+if the property holds at the start State
+then it's obvious uh that the property
+
+ align:start position:0%
+then it's obvious uh that the property
+ 
+
+ align:start position:0%
+then it's obvious uh that the property
+will hold for all of the states that you
+
+ align:start position:0%
+will hold for all of the states that you
+ 
+
+ align:start position:0%
+will hold for all of the states that you
+can possibly get to uh that P of R will
+
+ align:start position:0%
+can possibly get to uh that P of R will
+ 
+
+ align:start position:0%
+can possibly get to uh that P of R will
+hold for all reachable states you can
+
+ align:start position:0%
+hold for all reachable states you can
+ 
+
+ align:start position:0%
+hold for all reachable states you can
+prove this by induction on the number of
+
+ align:start position:0%
+prove this by induction on the number of
+ 
+
+ align:start position:0%
+prove this by induction on the number of
+states but I think it's clear that if
+
+ align:start position:0%
+states but I think it's clear that if
+ 
+
+ align:start position:0%
+states but I think it's clear that if
+you have a property that you begin with
+
+ align:start position:0%
+you have a property that you begin with
+ 
+
+ align:start position:0%
+you have a property that you begin with
+and it doesn't change making a step it's
+
+ align:start position:0%
+and it doesn't change making a step it's
+ 
+
+ align:start position:0%
+and it doesn't change making a step it's
+never going to change and that's all
+
+ align:start position:0%
+never going to change and that's all
+ 
+
+ align:start position:0%
+never going to change and that's all
+that Floyd's invariant principle states
+
+ align:start position:0%
+that Floyd's invariant principle states
+ 
+
+ align:start position:0%
+that Floyd's invariant principle states
+so in particular uh since the prop
+
+ align:start position:0%
+so in particular uh since the prop
+ 
+
+ align:start position:0%
+so in particular uh since the prop
+property P holds in all reachable states
+
+ align:start position:0%
+property P holds in all reachable states
+ 
+
+ align:start position:0%
+property P holds in all reachable states
+if there is any final state which which
+
+ align:start position:0%
+if there is any final state which which
+ 
+
+ align:start position:0%
+if there is any final state which which
+the machine reaches then p is going to
+
+ align:start position:0%
+the machine reaches then p is going to
+ 
+
+ align:start position:0%
+the machine reaches then p is going to
+hold in that state and what we saw was
+
+ align:start position:0%
+hold in that state and what we saw was
+ 
+
+ align:start position:0%
+hold in that state and what we saw was
+that incidentally we're using the word
+
+ align:start position:0%
+that incidentally we're using the word
+ 
+
+ align:start position:0%
+that incidentally we're using the word
+preserved invariant to distinguish the
+
+ align:start position:0%
+preserved invariant to distinguish the
+ 
+
+ align:start position:0%
+preserved invariant to distinguish the
+definition here from uh another usage
+
+ align:start position:0%
+definition here from uh another usage
+ 
+
+ align:start position:0%
+definition here from uh another usage
+that's co-opted the word invariant to
+
+ align:start position:0%
+that's co-opted the word invariant to
+ 
+
+ align:start position:0%
+that's co-opted the word invariant to
+mean a property that's true in all
+
+ align:start position:0%
+mean a property that's true in all
+ 
+
+ align:start position:0%
+mean a property that's true in all
+states uh and while it's nice to know
+
+ align:start position:0%
+states uh and while it's nice to know
+ 
+
+ align:start position:0%
+states uh and while it's nice to know
+that some property is true in all states
+
+ align:start position:0%
+that some property is true in all states
+ 
+
+ align:start position:0%
+that some property is true in all states
+uh the way you prove that is by having
+
+ align:start position:0%
+uh the way you prove that is by having
+ 
+
+ align:start position:0%
+uh the way you prove that is by having
+having a preserved invariant so you want
+
+ align:start position:0%
+having a preserved invariant so you want
+ 
+
+ align:start position:0%
+having a preserved invariant so you want
+to distinguish the two technically if
+
+ align:start position:0%
+to distinguish the two technically if
+ 
+
+ align:start position:0%
+to distinguish the two technically if
+you look at this the predicate that's
+
+ align:start position:0%
+you look at this the predicate that's
+ 
+
+ align:start position:0%
+you look at this the predicate that's
+always false is a preserved invariant
+
+ align:start position:0%
+always false is a preserved invariant
+ 
+
+ align:start position:0%
+always false is a preserved invariant
+because uh of the condition as usual the
+
+ align:start position:0%
+because uh of the condition as usual the
+ 
+
+ align:start position:0%
+because uh of the condition as usual the
+way implication works if the antecedent
+
+ align:start position:0%
+way implication works if the antecedent
+ 
+
+ align:start position:0%
+way implication works if the antecedent
+is false then the entire implication is
+
+ align:start position:0%
+is false then the entire implication is
+ 
+
+ align:start position:0%
+is false then the entire implication is
+true so if you're always false then it's
+
+ align:start position:0%
+true so if you're always false then it's
+ 
+
+ align:start position:0%
+true so if you're always false then it's
+always the case that if false held in a
+
+ align:start position:0%
+always the case that if false held in a
+ 
+
+ align:start position:0%
+always the case that if false held in a
+state which it never does then it has to
+
+ align:start position:0%
+state which it never does then it has to
+ 
+
+ align:start position:0%
+state which it never does then it has to
+hold in any state you can get to so the
+
+ align:start position:0%
+hold in any state you can get to so the
+ 
+
+ align:start position:0%
+hold in any state you can get to so the
+that implication is true so just
+
+ align:start position:0%
+that implication is true so just
+ 
+
+ align:start position:0%
+that implication is true so just
+remember that preserved invariants that
+
+ align:start position:0%
+remember that preserved invariants that
+ 
+
+ align:start position:0%
+remember that preserved invariants that
+are constantly false uh exist uh they
+
+ align:start position:0%
+are constantly false uh exist uh they
+ 
+
+ align:start position:0%
+are constantly false uh exist uh they
+are good preserved invariants but
+
+ align:start position:0%
+are good preserved invariants but
+ 
+
+ align:start position:0%
+are good preserved invariants but
+they're not what other people would call
+
+ align:start position:0%
+they're not what other people would call
+ 
+
+ align:start position:0%
+they're not what other people would call
+an invariant we use preserved invariants
+
+ align:start position:0%
+an invariant we use preserved invariants
+ 
+
+ align:start position:0%
+an invariant we use preserved invariants
+to prove that a property is true in all
+
+ align:start position:0%
+to prove that a property is true in all
+ 
+
+ align:start position:0%
+to prove that a property is true in all
+states it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methodology so let's do one more example
+
+ align:start position:0%
+methodology so let's do one more example
+ 
+
+ align:start position:0%
+methodology so let's do one more example
+to wrap this up suppose I have a robot
+
+ align:start position:0%
+to wrap this up suppose I have a robot
+ 
+
+ align:start position:0%
+to wrap this up suppose I have a robot
+on a grid and the integer grid and we
+
+ align:start position:0%
+on a grid and the integer grid and we
+ 
+
+ align:start position:0%
+on a grid and the integer grid and we
+can think then of the coordinates of the
+
+ align:start position:0%
+can think then of the coordinates of the
+ 
+
+ align:start position:0%
+can think then of the coordinates of the
+integer as a pair of the coordinates of
+
+ align:start position:0%
+integer as a pair of the coordinates of
+ 
+
+ align:start position:0%
+integer as a pair of the coordinates of
+the robot as the coordinates of the
+
+ align:start position:0%
+the robot as the coordinates of the
+ 
+
+ align:start position:0%
+the robot as the coordinates of the
+square that it's in a pair of non-
+
+ align:start position:0%
+square that it's in a pair of non-
+ 
+
+ align:start position:0%
+square that it's in a pair of non-
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+integers now the way this robot can move
+
+ align:start position:0%
+integers now the way this robot can move
+ 
+
+ align:start position:0%
+integers now the way this robot can move
+is it can make a diagonal move in one
+
+ align:start position:0%
+is it can make a diagonal move in one
+ 
+
+ align:start position:0%
+is it can make a diagonal move in one
+step so it can move one step to the
+
+ align:start position:0%
+step so it can move one step to the
+ 
+
+ align:start position:0%
+step so it can move one step to the
+northeast or Southeast or Northwest or
+
+ align:start position:0%
+northeast or Southeast or Northwest or
+ 
+
+ align:start position:0%
+northeast or Southeast or Northwest or
+Southwest and that's it and the question
+
+ align:start position:0%
+Southwest and that's it and the question
+ 
+
+ align:start position:0%
+Southwest and that's it and the question
+that I want to ask is suppose you start
+
+ align:start position:0%
+that I want to ask is suppose you start
+ 
+
+ align:start position:0%
+that I want to ask is suppose you start
+the robot off at the origin at
+
+ align:start position:0%
+the robot off at the origin at
+ 
+
+ align:start position:0%
+the robot off at the origin at
+0 is there some way that it can wander
+
+ align:start position:0%
+0 is there some way that it can wander
+ 
+
+ align:start position:0%
+0 is there some way that it can wander
+around following its moves and get to a
+
+ align:start position:0%
+around following its moves and get to a
+ 
+
+ align:start position:0%
+around following its moves and get to a
+net state where it's moved Square over
+
+ align:start position:0%
+net state where it's moved Square over
+ 
+
+ align:start position:0%
+net state where it's moved Square over
+that is it gets to the square uh
+
+ align:start position:0%
+that is it gets to the square uh
+ 
+
+ align:start position:0%
+that is it gets to the square uh
+01 and uh the answer to that is settled
+
+ align:start position:0%
+01 and uh the answer to that is settled
+ 
+
+ align:start position:0%
+01 and uh the answer to that is settled
+Again by a preserved invariant I don't
+
+ align:start position:0%
+Again by a preserved invariant I don't
+ 
+
+ align:start position:0%
+Again by a preserved invariant I don't
+know whether it's obvious to you yet but
+
+ align:start position:0%
+know whether it's obvious to you yet but
+ 
+
+ align:start position:0%
+know whether it's obvious to you yet but
+it will be in a moment I'm claiming you
+
+ align:start position:0%
+it will be in a moment I'm claiming you
+ 
+
+ align:start position:0%
+it will be in a moment I'm claiming you
+can't get to the square 01 and the
+
+ align:start position:0%
+can't get to the square 01 and the
+ 
+
+ align:start position:0%
+can't get to the square 01 and the
+reason is that there's a preserved
+
+ align:start position:0%
+reason is that there's a preserved
+ 
+
+ align:start position:0%
+reason is that there's a preserved
+invariant of that set of robot moves
+
+ align:start position:0%
+invariant of that set of robot moves
+ 
+
+ align:start position:0%
+invariant of that set of robot moves
+namely the sum of the coordinates is
+
+ align:start position:0%
+namely the sum of the coordinates is
+ 
+
+ align:start position:0%
+namely the sum of the coordinates is
+even is an invariant if the sum of the
+
+ align:start position:0%
+even is an invariant if the sum of the
+ 
+
+ align:start position:0%
+even is an invariant if the sum of the
+coordinates is even it stays even and
+
+ align:start position:0%
+coordinates is even it stays even and
+ 
+
+ align:start position:0%
+coordinates is even it stays even and
+why is that well any move uh adds plus
+
+ align:start position:0%
+why is that well any move uh adds plus
+ 
+
+ align:start position:0%
+why is that well any move uh adds plus
+or minus one to the coordinates of both
+
+ align:start position:0%
+or minus one to the coordinates of both
+ 
+
+ align:start position:0%
+or minus one to the coordinates of both
+X and Y um maybe uh X and Y uh both go
+
+ align:start position:0%
+X and Y um maybe uh X and Y uh both go
+ 
+
+ align:start position:0%
+X and Y um maybe uh X and Y uh both go
+up by one in which case the sum of X and
+
+ align:start position:0%
+up by one in which case the sum of X and
+ 
+
+ align:start position:0%
+up by one in which case the sum of X and
+Y increases by two so if it was even it
+
+ align:start position:0%
+Y increases by two so if it was even it
+ 
+
+ align:start position:0%
+Y increases by two so if it was even it
+stays even or they both go down by one
+
+ align:start position:0%
+stays even or they both go down by one
+ 
+
+ align:start position:0%
+stays even or they both go down by one
+or maybe one goes up and the other goes
+
+ align:start position:0%
+or maybe one goes up and the other goes
+ 
+
+ align:start position:0%
+or maybe one goes up and the other goes
+down in which case the sum doesn't
+
+ align:start position:0%
+down in which case the sum doesn't
+ 
+
+ align:start position:0%
+down in which case the sum doesn't
+change in every case um uh if X Plus y
+
+ align:start position:0%
+change in every case um uh if X Plus y
+ 
+
+ align:start position:0%
+change in every case um uh if X Plus y
+was even it stays even and as a matter
+
+ align:start position:0%
+was even it stays even and as a matter
+ 
+
+ align:start position:0%
+was even it stays even and as a matter
+of fact if it was odd it stays odd moves
+
+ align:start position:0%
+of fact if it was odd it stays odd moves
+ 
+
+ align:start position:0%
+of fact if it was odd it stays odd moves
+actually preserve the parity of X Plus y
+
+ align:start position:0%
+actually preserve the parity of X Plus y
+ 
+
+ align:start position:0%
+actually preserve the parity of X Plus y
+but the invariant is that x + y is even
+
+ align:start position:0%
+but the invariant is that x + y is even
+ 
+
+ align:start position:0%
+but the invariant is that x + y is even
+now what else is the case well 0 0 uh 0
+
+ align:start position:0%
+now what else is the case well 0 0 uh 0
+ 
+
+ align:start position:0%
+now what else is the case well 0 0 uh 0
+plus 0 is z which is even and so we're
+
+ align:start position:0%
+plus 0 is z which is even and so we're
+ 
+
+ align:start position:0%
+plus 0 is z which is even and so we're
+in a Floyd invariant principle case
+
+ align:start position:0%
+in a Floyd invariant principle case
+ 
+
+ align:start position:0%
+in a Floyd invariant principle case
+where uh all the positions you can get
+
+ align:start position:0%
+where uh all the positions you can get
+ 
+
+ align:start position:0%
+where uh all the positions you can get
+to from the origin 0 0 which has an even
+
+ align:start position:0%
+to from the origin 0 0 which has an even
+ 
+
+ align:start position:0%
+to from the origin 0 0 which has an even
+sum have to have an even sum and since
+
+ align:start position:0%
+sum have to have an even sum and since
+ 
+
+ align:start position:0%
+sum have to have an even sum and since
+uh 1+0 is odd you can't get to that
+
+ align:start position:0%
+uh 1+0 is odd you can't get to that
+ 
+
+ align:start position:0%
+uh 1+0 is odd you can't get to that
+square one Z it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reachable so the parody and variant of
+
+ align:start position:0%
+reachable so the parody and variant of
+ 
+
+ align:start position:0%
+reachable so the parody and variant of
+the diagonally moving robot will set us
+
+ align:start position:0%
+the diagonally moving robot will set us
+ 
+
+ align:start position:0%
+the diagonally moving robot will set us
+up for uh an analysis of the 15 puzzle
+
+ align:start position:0%
+up for uh an analysis of the 15 puzzle
+ 
+
+ align:start position:0%
+up for uh an analysis of the 15 puzzle
+game that's this logo that we've had on
+
+ align:start position:0%
+game that's this logo that we've had on
+ 
+
+ align:start position:0%
+game that's this logo that we've had on
+every slide in 6042 so far with six
+
+ align:start position:0%
+every slide in 6042 so far with six
+ 
+
+ align:start position:0%
+every slide in 6042 so far with six
+blank 42 on the diagonal uh this is a
+
+ align:start position:0%
+blank 42 on the diagonal uh this is a
+ 
+
+ align:start position:0%
+blank 42 on the diagonal uh this is a
+game where there are these little
+
+ align:start position:0%
+game where there are these little
+ 
+
+ align:start position:0%
+game where there are these little
+numbered SL tiles that slide into the
+
+ align:start position:0%
+numbered SL tiles that slide into the
+ 
+
+ align:start position:0%
+numbered SL tiles that slide into the
+blank square and the question is how to
+
+ align:start position:0%
+blank square and the question is how to
+ 
+
+ align:start position:0%
+blank square and the question is how to
+permute um how to get from one
+
+ align:start position:0%
+permute um how to get from one
+ 
+
+ align:start position:0%
+permute um how to get from one
+permutation of the numbers to another uh
+
+ align:start position:0%
+permutation of the numbers to another uh
+ 
+
+ align:start position:0%
+permutation of the numbers to another uh
+and it turns out that the analysis of
+
+ align:start position:0%
+and it turns out that the analysis of
+ 
+
+ align:start position:0%
+and it turns out that the analysis of
+that game depends on a parody invariant
+
+ align:start position:0%
+that game depends on a parody invariant
+ 
+
+ align:start position:0%
+that game depends on a parody invariant
+uh reminiscent of well slightly more
+
+ align:start position:0%
+uh reminiscent of well slightly more
+ 
+
+ align:start position:0%
+uh reminiscent of well slightly more
+sophisticated than the diagonally moving
+
+ align:start position:0%
+sophisticated than the diagonally moving
+ 
+
+ align:start position:0%
+sophisticated than the diagonally moving
+robot let's look at one more example of
+
+ align:start position:0%
+robot let's look at one more example of
+ 
+
+ align:start position:0%
+robot let's look at one more example of
+uh using the invariant to verify y a
+
+ align:start position:0%
+uh using the invariant to verify y a
+ 
+
+ align:start position:0%
+uh using the invariant to verify y a
+little algorithm that actually will be
+
+ align:start position:0%
+little algorithm that actually will be
+ 
+
+ align:start position:0%
+little algorithm that actually will be
+quite important uh as the course
+
+ align:start position:0%
+quite important uh as the course
+ 
+
+ align:start position:0%
+quite important uh as the course
+progresses and that is fast
+
+ align:start position:0%
+progresses and that is fast
+ 
+
+ align:start position:0%
+progresses and that is fast
+exponentiation so in this setup um a is
+
+ align:start position:0%
+exponentiation so in this setup um a is
+ 
+
+ align:start position:0%
+exponentiation so in this setup um a is
+a real number and B is a non- negative
+
+ align:start position:0%
+a real number and B is a non- negative
+ 
+
+ align:start position:0%
+a real number and B is a non- negative
+integer and I want to compute the be
+
+ align:start position:0%
+integer and I want to compute the be
+ 
+
+ align:start position:0%
+integer and I want to compute the be
+power of a let's say uh B was uh uh 128
+
+ align:start position:0%
+power of a let's say uh B was uh uh 128
+ 
+
+ align:start position:0%
+power of a let's say uh B was uh uh 128
+and I want to compute the 128th power of
+
+ align:start position:0%
+and I want to compute the 128th power of
+ 
+
+ align:start position:0%
+and I want to compute the 128th power of
+some real number a well I can multiply a
+
+ align:start position:0%
+some real number a well I can multiply a
+ 
+
+ align:start position:0%
+some real number a well I can multiply a
+by itself 127 times that would work fine
+
+ align:start position:0%
+by itself 127 times that would work fine
+ 
+
+ align:start position:0%
+by itself 127 times that would work fine
+but if you think about it suppose I
+
+ align:start position:0%
+but if you think about it suppose I
+ 
+
+ align:start position:0%
+but if you think about it suppose I
+square a and then I Square it again and
+
+ align:start position:0%
+square a and then I Square it again and
+ 
+
+ align:start position:0%
+square a and then I Square it again and
+I Square it again then in about eight
+
+ align:start position:0%
+I Square it again then in about eight
+ 
+
+ align:start position:0%
+I Square it again then in about eight
+squarings instead of 99 multiplications
+
+ align:start position:0%
+squarings instead of 99 multiplications
+ 
+
+ align:start position:0%
+squarings instead of 99 multiplications
+I'm going to get to a to the
+
+ align:start position:0%
+I'm going to get to a to the
+ 
+
+ align:start position:0%
+I'm going to get to a to the
+128 U now if B is not a power of two you
+
+ align:start position:0%
+128 U now if B is not a power of two you
+ 
+
+ align:start position:0%
+128 U now if B is not a power of two you
+adjust it slightly uh and using that
+
+ align:start position:0%
+adjust it slightly uh and using that
+ 
+
+ align:start position:0%
+adjust it slightly uh and using that
+idea you can compute the uh be power of
+
+ align:start position:0%
+idea you can compute the uh be power of
+ 
+
+ align:start position:0%
+idea you can compute the uh be power of
+a much more rapidly than if you just
+
+ align:start position:0%
+a much more rapidly than if you just
+ 
+
+ align:start position:0%
+a much more rapidly than if you just
+naively multiplied out B minus1 times so
+
+ align:start position:0%
+naively multiplied out B minus1 times so
+ 
+
+ align:start position:0%
+naively multiplied out B minus1 times so
+let's look at the pseudo code for this
+
+ align:start position:0%
+let's look at the pseudo code for this
+ 
+
+ align:start position:0%
+let's look at the pseudo code for this
+algorithm uh here uh X YZ and R are
+
+ align:start position:0%
+algorithm uh here uh X YZ and R are
+ 
+
+ align:start position:0%
+algorithm uh here uh X YZ and R are
+temporary registers um uh Y and Z hold
+
+ align:start position:0%
+temporary registers um uh Y and Z hold
+ 
+
+ align:start position:0%
+temporary registers um uh Y and Z hold
+uh uh YZ and R all hold integers and X
+
+ align:start position:0%
+uh uh YZ and R all hold integers and X
+ 
+
+ align:start position:0%
+uh uh YZ and R all hold integers and X
+holds this real number a uh and you can
+
+ align:start position:0%
+holds this real number a uh and you can
+ 
+
+ align:start position:0%
+holds this real number a uh and you can
+read the code um if you wish but in fact
+
+ align:start position:0%
+read the code um if you wish but in fact
+ 
+
+ align:start position:0%
+read the code um if you wish but in fact
+I'm going to immediately jump to the
+
+ align:start position:0%
+I'm going to immediately jump to the
+ 
+
+ align:start position:0%
+I'm going to immediately jump to the
+slightly more abstract and easier to
+
+ align:start position:0%
+slightly more abstract and easier to
+ 
+
+ align:start position:0%
+slightly more abstract and easier to
+understand version of it as a state
+
+ align:start position:0%
+understand version of it as a state
+ 
+
+ align:start position:0%
+understand version of it as a state
+machine so what matters about this fast
+
+ align:start position:0%
+machine so what matters about this fast
+ 
+
+ align:start position:0%
+machine so what matters about this fast
+exponentiation algorithm as a state
+
+ align:start position:0%
+exponentiation algorithm as a state
+ 
+
+ align:start position:0%
+exponentiation algorithm as a state
+machine is that first of all um there
+
+ align:start position:0%
+machine is that first of all um there
+ 
+
+ align:start position:0%
+machine is that first of all um there
+are three states uh two real numbers
+
+ align:start position:0%
+are three states uh two real numbers
+ 
+
+ align:start position:0%
+are three states uh two real numbers
+numbers and uh a non- negative
+
+ align:start position:0%
+numbers and uh a non- negative
+ 
+
+ align:start position:0%
+numbers and uh a non- negative
+integer um and the start state is going
+
+ align:start position:0%
+integer um and the start state is going
+ 
+
+ align:start position:0%
+integer um and the start state is going
+to be that the number a is in the first
+
+ align:start position:0%
+to be that the number a is in the first
+ 
+
+ align:start position:0%
+to be that the number a is in the first
+register or in the first location first
+
+ align:start position:0%
+register or in the first location first
+ 
+
+ align:start position:0%
+register or in the first location first
+coordinate of the states one is the real
+
+ align:start position:0%
+coordinate of the states one is the real
+ 
+
+ align:start position:0%
+coordinate of the states one is the real
+number in the second coordinate and B
+
+ align:start position:0%
+number in the second coordinate and B
+ 
+
+ align:start position:0%
+number in the second coordinate and B
+the target exponent uh is the non-
+
+ align:start position:0%
+the target exponent uh is the non-
+ 
+
+ align:start position:0%
+the target exponent uh is the non-
+negative integer in the third
+
+ align:start position:0%
+negative integer in the third
+ 
+
+ align:start position:0%
+negative integer in the third
+component um the transitions are going
+
+ align:start position:0%
+component um the transitions are going
+ 
+
+ align:start position:0%
+component um the transitions are going
+to be as follows here's a simple one uh
+
+ align:start position:0%
+to be as follows here's a simple one uh
+ 
+
+ align:start position:0%
+to be as follows here's a simple one uh
+if I have an amount X in the first
+
+ align:start position:0%
+if I have an amount X in the first
+ 
+
+ align:start position:0%
+if I have an amount X in the first
+location y in the second location Z in
+
+ align:start position:0%
+location y in the second location Z in
+ 
+
+ align:start position:0%
+location y in the second location Z in
+the third then if Z is if Z is positive
+
+ align:start position:0%
+the third then if Z is if Z is positive
+ 
+
+ align:start position:0%
+the third then if Z is if Z is positive
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+even then I'm going to square X leave y
+
+ align:start position:0%
+even then I'm going to square X leave y
+ 
+
+ align:start position:0%
+even then I'm going to square X leave y
+alone and divide Z by
+
+ align:start position:0%
+alone and divide Z by
+ 
+
+ align:start position:0%
+alone and divide Z by
+two and that's the new state that I get
+
+ align:start position:0%
+two and that's the new state that I get
+ 
+
+ align:start position:0%
+two and that's the new state that I get
+at on the other hand if Z is odd and
+
+ align:start position:0%
+at on the other hand if Z is odd and
+ 
+
+ align:start position:0%
+at on the other hand if Z is odd and
+positive then I'm going to square X
+
+ align:start position:0%
+positive then I'm going to square X
+ 
+
+ align:start position:0%
+positive then I'm going to square X
+multiply y by X and again take the
+
+ align:start position:0%
+multiply y by X and again take the
+ 
+
+ align:start position:0%
+multiply y by X and again take the
+quotient of Z divide Z by
+
+ align:start position:0%
+quotient of Z divide Z by
+ 
+
+ align:start position:0%
+quotient of Z divide Z by
+two okay why does this state machine do
+
+ align:start position:0%
+two okay why does this state machine do
+ 
+
+ align:start position:0%
+two okay why does this state machine do
+fast exponentiation why is it correct
+
+ align:start position:0%
+fast exponentiation why is it correct
+ 
+
+ align:start position:0%
+fast exponentiation why is it correct
+and the Insight is that there's a
+
+ align:start position:0%
+and the Insight is that there's a
+ 
+
+ align:start position:0%
+and the Insight is that there's a
+preserved invariant of this machine and
+
+ align:start position:0%
+preserved invariant of this machine and
+ 
+
+ align:start position:0%
+preserved invariant of this machine and
+the preserved invariant is that y * x to
+
+ align:start position:0%
+the preserved invariant is that y * x to
+ 
+
+ align:start position:0%
+the preserved invariant is that y * x to
+the Z is always a to the B so let's see
+
+ align:start position:0%
+the Z is always a to the B so let's see
+ 
+
+ align:start position:0%
+the Z is always a to the B so let's see
+how to verify that that uh y x to the Z
+
+ align:start position:0%
+how to verify that that uh y x to the Z
+ 
+
+ align:start position:0%
+how to verify that that uh y x to the Z
+is equal to a to the B well let's just
+
+ align:start position:0%
+is equal to a to the B well let's just
+ 
+
+ align:start position:0%
+is equal to a to the B well let's just
+look at uh maybe the slightly more
+
+ align:start position:0%
+look at uh maybe the slightly more
+ 
+
+ align:start position:0%
+look at uh maybe the slightly more
+interesting of the two transition rules
+
+ align:start position:0%
+interesting of the two transition rules
+ 
+
+ align:start position:0%
+interesting of the two transition rules
+which is when Z is positive in odd uh
+
+ align:start position:0%
+which is when Z is positive in odd uh
+ 
+
+ align:start position:0%
+which is when Z is positive in odd uh
+the XYZ State moves to a new State uh
+
+ align:start position:0%
+the XYZ State moves to a new State uh
+ 
+
+ align:start position:0%
+the XYZ State moves to a new State uh
+indicated in green where the new value
+
+ align:start position:0%
+indicated in green where the new value
+ 
+
+ align:start position:0%
+indicated in green where the new value
+of x is X squ the new value of y is XY
+
+ align:start position:0%
+of x is X squ the new value of y is XY
+ 
+
+ align:start position:0%
+of x is X squ the new value of y is XY
+and the new value of Z is z minus 1
+
+ align:start position:0%
+and the new value of Z is z minus 1
+ 
+
+ align:start position:0%
+and the new value of Z is z minus 1
+over2 remember you went to the quotient
+
+ align:start position:0%
+over2 remember you went to the quotient
+ 
+
+ align:start position:0%
+over2 remember you went to the quotient
+of Z ided two and when Z is odd that
+
+ align:start position:0%
+of Z ided two and when Z is odd that
+ 
+
+ align:start position:0%
+of Z ided two and when Z is odd that
+means Z it's literally Z minus1 /2 well
+
+ align:start position:0%
+means Z it's literally Z minus1 /2 well
+ 
+
+ align:start position:0%
+means Z it's literally Z minus1 /2 well
+do the new values satisfy the invariant
+
+ align:start position:0%
+do the new values satisfy the invariant
+ 
+
+ align:start position:0%
+do the new values satisfy the invariant
+if if I plug in the green values uh of
+
+ align:start position:0%
+if if I plug in the green values uh of
+ 
+
+ align:start position:0%
+if if I plug in the green values uh of
+x^2 for y and XY for x uh for sorry X2
+
+ align:start position:0%
+x^2 for y and XY for x uh for sorry X2
+ 
+
+ align:start position:0%
+x^2 for y and XY for x uh for sorry X2
+for X XY for y and z-1 over2 for Z well
+
+ align:start position:0%
+for X XY for y and z-1 over2 for Z well
+ 
+
+ align:start position:0%
+for X XY for y and z-1 over2 for Z well
+let's see what happens um if I uh uh
+
+ align:start position:0%
+let's see what happens um if I uh uh
+ 
+
+ align:start position:0%
+let's see what happens um if I uh uh
+take uh the new value of y which is XY
+
+ align:start position:0%
+take uh the new value of y which is XY
+ 
+
+ align:start position:0%
+take uh the new value of y which is XY
+um and I multiply it by the new value of
+
+ align:start position:0%
+um and I multiply it by the new value of
+ 
+
+ align:start position:0%
+um and I multiply it by the new value of
+x which is X2 raised to the new value of
+
+ align:start position:0%
+x which is X2 raised to the new value of
+ 
+
+ align:start position:0%
+x which is X2 raised to the new value of
+Z which is z minus1 / 2 uh let's do a
+
+ align:start position:0%
+Z which is z minus1 / 2 uh let's do a
+ 
+
+ align:start position:0%
+Z which is z minus1 / 2 uh let's do a
+little algebra simplification of that
+
+ align:start position:0%
+little algebra simplification of that
+ 
+
+ align:start position:0%
+little algebra simplification of that
+well the x^2 to the z-1 / 2 becomes X
+
+ align:start position:0%
+well the x^2 to the z-1 / 2 becomes X
+ 
+
+ align:start position:0%
+well the x^2 to the z-1 / 2 becomes X
+the Z minus1 uh and I'm just carrying
+
+ align:start position:0%
+the Z minus1 uh and I'm just carrying
+ 
+
+ align:start position:0%
+the Z minus1 uh and I'm just carrying
+over the XY uh and then that simplifies
+
+ align:start position:0%
+over the XY uh and then that simplifies
+ 
+
+ align:start position:0%
+over the XY uh and then that simplifies
+to Simply uh y * x * X the Z minus1 or
+
+ align:start position:0%
+to Simply uh y * x * X the Z minus1 or
+ 
+
+ align:start position:0%
+to Simply uh y * x * X the Z minus1 or
+YX to the Z which we assumed was equal
+
+ align:start position:0%
+YX to the Z which we assumed was equal
+ 
+
+ align:start position:0%
+YX to the Z which we assumed was equal
+to a to the B so sure enough the new
+
+ align:start position:0%
+to a to the B so sure enough the new
+ 
+
+ align:start position:0%
+to a to the B so sure enough the new
+values of X Y and Z satisfy the
+
+ align:start position:0%
+values of X Y and Z satisfy the
+ 
+
+ align:start position:0%
+values of X Y and Z satisfy the
+invariant it is a preserved invariant
+
+ align:start position:0%
+invariant it is a preserved invariant
+ 
+
+ align:start position:0%
+invariant it is a preserved invariant
+and an even simpler argument applies to
+
+ align:start position:0%
+and an even simpler argument applies to
+ 
+
+ align:start position:0%
+and an even simpler argument applies to
+the other the transition when Z is
+
+ align:start position:0%
+the other the transition when Z is
+ 
+
+ align:start position:0%
+the other the transition when Z is
+positive and even so we verified that
+
+ align:start position:0%
+positive and even so we verified that
+ 
+
+ align:start position:0%
+positive and even so we verified that
+this is a preserved invariant now at the
+
+ align:start position:0%
+this is a preserved invariant now at the
+ 
+
+ align:start position:0%
+this is a preserved invariant now at the
+start uh remember we start off with uh
+
+ align:start position:0%
+start uh remember we start off with uh
+ 
+
+ align:start position:0%
+start uh remember we start off with uh
+the real number a in register X the real
+
+ align:start position:0%
+the real number a in register X the real
+ 
+
+ align:start position:0%
+the real number a in register X the real
+number B in Z and the real number one in
+
+ align:start position:0%
+number B in Z and the real number one in
+ 
+
+ align:start position:0%
+number B in Z and the real number one in
+Y which is the accumulator and uh 1 * a
+
+ align:start position:0%
+Y which is the accumulator and uh 1 * a
+ 
+
+ align:start position:0%
+Y which is the accumulator and uh 1 * a
+the B is equal to a to the B so this is
+
+ align:start position:0%
+the B is equal to a to the B so this is
+ 
+
+ align:start position:0%
+the B is equal to a to the B so this is
+a this preserved invariant is true of
+
+ align:start position:0%
+a this preserved invariant is true of
+ 
+
+ align:start position:0%
+a this preserved invariant is true of
+the start State and that means by Floyds
+
+ align:start position:0%
+the start State and that means by Floyds
+ 
+
+ align:start position:0%
+the start State and that means by Floyds
+variant principle that it is true at
+
+ align:start position:0%
+variant principle that it is true at
+ 
+
+ align:start position:0%
+variant principle that it is true at
+this the final state if and when the
+
+ align:start position:0%
+this the final state if and when the
+ 
+
+ align:start position:0%
+this the final state if and when the
+thing stops well when does this machine
+
+ align:start position:0%
+thing stops well when does this machine
+ 
+
+ align:start position:0%
+thing stops well when does this machine
+stop as long as Z is positive it can
+
+ align:start position:0%
+stop as long as Z is positive it can
+ 
+
+ align:start position:0%
+stop as long as Z is positive it can
+keep moving so it gets stuck when Z is
+
+ align:start position:0%
+keep moving so it gets stuck when Z is
+ 
+
+ align:start position:0%
+keep moving so it gets stuck when Z is
+zero what happens if it ever gets to Z a
+
+ align:start position:0%
+zero what happens if it ever gets to Z a
+ 
+
+ align:start position:0%
+zero what happens if it ever gets to Z a
+zero if it gets stuck then the
+
+ align:start position:0%
+zero if it gets stuck then the
+ 
+
+ align:start position:0%
+zero if it gets stuck then the
+invariance says that YX to the 0 has to
+
+ align:start position:0%
+invariance says that YX to the 0 has to
+ 
+
+ align:start position:0%
+invariance says that YX to the 0 has to
+equal to a to the B but of course YX to
+
+ align:start position:0%
+equal to a to the B but of course YX to
+ 
+
+ align:start position:0%
+equal to a to the B but of course YX to
+the 0 is nothing but Y and what we
+
+ align:start position:0%
+the 0 is nothing but Y and what we
+ 
+
+ align:start position:0%
+the 0 is nothing but Y and what we
+conclude is that sure enough this
+
+ align:start position:0%
+conclude is that sure enough this
+ 
+
+ align:start position:0%
+conclude is that sure enough this
+machine leaves the desired exponential
+
+ align:start position:0%
+machine leaves the desired exponential
+ 
+
+ align:start position:0%
+machine leaves the desired exponential
+value in the register Y which is where
+
+ align:start position:0%
+value in the register Y which is where
+ 
+
+ align:start position:0%
+value in the register Y which is where
+we get the answer and that's why this
+
+ align:start position:0%
+we get the answer and that's why this
+ 
+
+ align:start position:0%
+we get the answer and that's why this
+algorithm is
+
+ align:start position:0%
+algorithm is
+ 
+
+ align:start position:0%
+algorithm is
+correct uh now another aspect of uh of
+
+ align:start position:0%
+correct uh now another aspect of uh of
+ 
+
+ align:start position:0%
+correct uh now another aspect of uh of
+what's going on here uh is proving that
+
+ align:start position:0%
+what's going on here uh is proving that
+ 
+
+ align:start position:0%
+what's going on here uh is proving that
+the algorithm does terminate so let me
+
+ align:start position:0%
+the algorithm does terminate so let me
+ 
+
+ align:start position:0%
+the algorithm does terminate so let me
+just say a word that Floyd uh
+
+ align:start position:0%
+just say a word that Floyd uh
+ 
+
+ align:start position:0%
+just say a word that Floyd uh
+distinguished sort of these two aspects
+
+ align:start position:0%
+distinguished sort of these two aspects
+ 
+
+ align:start position:0%
+distinguished sort of these two aspects
+of program correctness that typically
+
+ align:start position:0%
+of program correctness that typically
+ 
+
+ align:start position:0%
+of program correctness that typically
+come up one is showing that if you get
+
+ align:start position:0%
+come up one is showing that if you get
+ 
+
+ align:start position:0%
+come up one is showing that if you get
+an answer it's correct and that's what
+
+ align:start position:0%
+an answer it's correct and that's what
+ 
+
+ align:start position:0%
+an answer it's correct and that's what
+we just did if this machine stops if it
+
+ align:start position:0%
+we just did if this machine stops if it
+ 
+
+ align:start position:0%
+we just did if this machine stops if it
+ever gets to the case where Z is zero
+
+ align:start position:0%
+ever gets to the case where Z is zero
+ 
+
+ align:start position:0%
+ever gets to the case where Z is zero
+then y has the right answer but we
+
+ align:start position:0%
+then y has the right answer but we
+ 
+
+ align:start position:0%
+then y has the right answer but we
+haven't proved that it stops so we've
+
+ align:start position:0%
+haven't proved that it stops so we've
+ 
+
+ align:start position:0%
+haven't proved that it stops so we've
+shown that it's partially correct like a
+
+ align:start position:0%
+shown that it's partially correct like a
+ 
+
+ align:start position:0%
+shown that it's partially correct like a
+partial function uh it might not be
+
+ align:start position:0%
+partial function uh it might not be
+ 
+
+ align:start position:0%
+partial function uh it might not be
+defined everywhere we haven't shown that
+
+ align:start position:0%
+defined everywhere we haven't shown that
+ 
+
+ align:start position:0%
+defined everywhere we haven't shown that
+yet but when it is defined it gives the
+
+ align:start position:0%
+yet but when it is defined it gives the
+ 
+
+ align:start position:0%
+yet but when it is defined it gives the
+right answer then the other aspect of
+
+ align:start position:0%
+right answer then the other aspect of
+ 
+
+ align:start position:0%
+right answer then the other aspect of
+correctness is termination showing in
+
+ align:start position:0%
+correctness is termination showing in
+ 
+
+ align:start position:0%
+correctness is termination showing in
+effect that the function is total that
+
+ align:start position:0%
+effect that the function is total that
+ 
+
+ align:start position:0%
+effect that the function is total that
+the program always does stop well in
+
+ align:start position:0%
+the program always does stop well in
+ 
+
+ align:start position:0%
+the program always does stop well in
+this case there's an easy way to see why
+
+ align:start position:0%
+this case there's an easy way to see why
+ 
+
+ align:start position:0%
+this case there's an easy way to see why
+it always stops because at every
+
+ align:start position:0%
+it always stops because at every
+ 
+
+ align:start position:0%
+it always stops because at every
+transition um Z is being haved or more Z
+
+ align:start position:0%
+transition um Z is being haved or more Z
+ 
+
+ align:start position:0%
+transition um Z is being haved or more Z
+is a uh a non- negative integer valued
+
+ align:start position:0%
+is a uh a non- negative integer valued
+ 
+
+ align:start position:0%
+is a uh a non- negative integer valued
+variable and uh since we're having it or
+
+ align:start position:0%
+variable and uh since we're having it or
+ 
+
+ align:start position:0%
+variable and uh since we're having it or
+Mak it even smaller than half of it at
+
+ align:start position:0%
+Mak it even smaller than half of it at
+ 
+
+ align:start position:0%
+Mak it even smaller than half of it at
+every step it means that since it starts
+
+ align:start position:0%
+every step it means that since it starts
+ 
+
+ align:start position:0%
+every step it means that since it starts
+with the value z uh it can't get smaller
+
+ align:start position:0%
+with the value z uh it can't get smaller
+ 
+
+ align:start position:0%
+with the value z uh it can't get smaller
+more than log to the base 2 of B times
+
+ align:start position:0%
+more than log to the base 2 of B times
+ 
+
+ align:start position:0%
+more than log to the base 2 of B times
+because by then it would have hit zero
+
+ align:start position:0%
+because by then it would have hit zero
+ 
+
+ align:start position:0%
+because by then it would have hit zero
+and so we can be sure that this machine
+
+ align:start position:0%
+and so we can be sure that this machine
+ 
+
+ align:start position:0%
+and so we can be sure that this machine
+makes it most log to the base two of B
+
+ align:start position:0%
+makes it most log to the base two of B
+ 
+
+ align:start position:0%
+makes it most log to the base two of B
+transitions uh and then it has to get
+
+ align:start position:0%
+transitions uh and then it has to get
+ 
+
+ align:start position:0%
+transitions uh and then it has to get
+stuck at the only place that it can
+
+ align:start position:0%
+stuck at the only place that it can
+ 
+
+ align:start position:0%
+stuck at the only place that it can
+stuck which is when Z equals zero um and
+
+ align:start position:0%
+stuck which is when Z equals zero um and
+ 
+
+ align:start position:0%
+stuck which is when Z equals zero um and
+there is a picture of my uh uh friend
+
+ align:start position:0%
+there is a picture of my uh uh friend
+ 
+
+ align:start position:0%
+there is a picture of my uh uh friend
+and early colleague Bob Floyd uh whom I
+
+ align:start position:0%
+and early colleague Bob Floyd uh whom I
+ 
+
+ align:start position:0%
+and early colleague Bob Floyd uh whom I
+met at the very beginning of my career
+
+ align:start position:0%
+met at the very beginning of my career
+ 
+
+ align:start position:0%
+met at the very beginning of my career
+at uh Carnegie melon University we
+
+ align:start position:0%
+at uh Carnegie melon University we
+ 
+
+ align:start position:0%
+at uh Carnegie melon University we
+worked together for about one year
+
+ align:start position:0%
+worked together for about one year
+ 
+
+ align:start position:0%
+worked together for about one year
+before he went off to Stanford and you
+
+ align:start position:0%
+before he went off to Stanford and you
+ 
+
+ align:start position:0%
+before he went off to Stanford and you
+can read uh much more about his life in
+
+ align:start position:0%
+can read uh much more about his life in
+ 
+
+ align:start position:0%
+can read uh much more about his life in
+a a warm and in and and detailed eulogy
+
+ align:start position:0%
+a a warm and in and and detailed eulogy
+ 
+
+ align:start position:0%
+a a warm and in and and detailed eulogy
+written by his best friend Don kth uh
+
+ align:start position:0%
+written by his best friend Don kth uh
+ 
+
+ align:start position:0%
+written by his best friend Don kth uh
+Floyd won the touring award uh for his
+
+ align:start position:0%
+Floyd won the touring award uh for his
+ 
+
+ align:start position:0%
+Floyd won the touring award uh for his
+major contributions both to program
+
+ align:start position:0%
+major contributions both to program
+ 
+
+ align:start position:0%
+major contributions both to program
+correctness and to programming language
+
+ align:start position:0%
+correctness and to programming language
+ 
+
+ align:start position:0%
+correctness and to programming language
+parsing
\ No newline at end of file
diff --git a/WCCpss6udNs.txt b/WCCpss6udNs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab6853180ede1c57afc15a49fa96a55577e2a766
--- /dev/null
+++ b/WCCpss6udNs.txt
@@ -0,0 +1,9691 @@
+align:start position:0%
+ 
+So last time
+
+ align:start position:0%
+So last time
+ 
+
+ align:start position:0%
+So last time
+uh last time we talked about the basic
+
+ align:start position:0%
+uh last time we talked about the basic
+ 
+
+ align:start position:0%
+uh last time we talked about the basic
+algebraic operation for limit of
+
+ align:start position:0%
+algebraic operation for limit of
+ 
+
+ align:start position:0%
+algebraic operation for limit of
+sequences. We talked about the mono
+
+ align:start position:0%
+sequences. We talked about the mono
+ 
+
+ align:start position:0%
+sequences. We talked about the mono
+convergence theorem. So the mono
+
+ align:start position:0%
+convergence theorem. So the mono
+ 
+
+ align:start position:0%
+convergence theorem. So the mono
+convergence theorem was that you had a
+
+ align:start position:0%
+convergence theorem was that you had a
+ 
+
+ align:start position:0%
+convergence theorem was that you had a
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+that was increasing or it could be
+
+ align:start position:0%
+that was increasing or it could be
+ 
+
+ align:start position:0%
+that was increasing or it could be
+decreasing. So either it was increasing
+
+ align:start position:0%
+decreasing. So either it was increasing
+ 
+
+ align:start position:0%
+decreasing. So either it was increasing
+this meant that the next element was
+
+ align:start position:0%
+this meant that the next element was
+ 
+
+ align:start position:0%
+this meant that the next element was
+bigger equal to the previous and then
+
+ align:start position:0%
+bigger equal to the previous and then
+ 
+
+ align:start position:0%
+bigger equal to the previous and then
+they were all assumed to be bounded.
+
+ align:start position:0%
+they were all assumed to be bounded.
+ 
+
+ align:start position:0%
+they were all assumed to be bounded.
+If you had such a sequence or similarly
+
+ align:start position:0%
+If you had such a sequence or similarly
+ 
+
+ align:start position:0%
+If you had such a sequence or similarly
+if you had a sequence so this was the
+
+ align:start position:0%
+if you had a sequence so this was the
+ 
+
+ align:start position:0%
+if you had a sequence so this was the
+increasing case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there was a similar decreasing case
+
+ align:start position:0%
+then there was a similar decreasing case
+ 
+
+ align:start position:0%
+then there was a similar decreasing case
+where the the the
+
+ align:start position:0%
+where the the the
+ 
+
+ align:start position:0%
+where the the the
+previous is bigger equal to the next one
+
+ align:start position:0%
+previous is bigger equal to the next one
+ 
+
+ align:start position:0%
+previous is bigger equal to the next one
+and then they are assumed to be bounded
+
+ align:start position:0%
+and then they are assumed to be bounded
+ 
+
+ align:start position:0%
+and then they are assumed to be bounded
+from below.
+
+ align:start position:0%
+from below.
+ 
+
+ align:start position:0%
+from below.
+So this was decreasing.
+
+ align:start position:0%
+So this was decreasing.
+ 
+
+ align:start position:0%
+So this was decreasing.
+So monotum convergent theorem was that
+
+ align:start position:0%
+So monotum convergent theorem was that
+ 
+
+ align:start position:0%
+So monotum convergent theorem was that
+if you had a bounded increasing sequence
+
+ align:start position:0%
+if you had a bounded increasing sequence
+ 
+
+ align:start position:0%
+if you had a bounded increasing sequence
+or a bounded decreasing sequence in
+
+ align:start position:0%
+or a bounded decreasing sequence in
+ 
+
+ align:start position:0%
+or a bounded decreasing sequence in
+either case
+
+ align:start position:0%
+either case
+ 
+
+ align:start position:0%
+either case
+uh uh the sequence is convergent
+
+ align:start position:0%
+uh uh the sequence is convergent
+ 
+
+ align:start position:0%
+uh uh the sequence is convergent
+and it's converging in the first case in
+
+ align:start position:0%
+and it's converging in the first case in
+ 
+
+ align:start position:0%
+and it's converging in the first case in
+this case here a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's converg to the soup
+
+ align:start position:0%
+um it's converg to the soup
+ 
+
+ align:start position:0%
+um it's converg to the soup
+of the xm to the in case Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And in the case B it converts to the in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case case B. So that was the mono
+
+ align:start position:0%
+case case B. So that was the mono
+ 
+
+ align:start position:0%
+case case B. So that was the mono
+convergence theorem.
+
+ align:start position:0%
+convergence theorem.
+ 
+
+ align:start position:0%
+convergence theorem.
+And the third thing we talk about and
+
+ align:start position:0%
+And the third thing we talk about and
+ 
+
+ align:start position:0%
+And the third thing we talk about and
+that's where we will continue today is
+
+ align:start position:0%
+that's where we will continue today is
+ 
+
+ align:start position:0%
+that's where we will continue today is
+uh is cruise sequence. So we talked
+
+ align:start position:0%
+uh is cruise sequence. So we talked
+ 
+
+ align:start position:0%
+uh is cruise sequence. So we talked
+about push sequence.
+
+ align:start position:0%
+about push sequence.
+ 
+
+ align:start position:0%
+about push sequence.
+So let me and we prove a few things
+
+ align:start position:0%
+So let me and we prove a few things
+ 
+
+ align:start position:0%
+So let me and we prove a few things
+about cruise sequence but we want to
+
+ align:start position:0%
+about cruise sequence but we want to
+ 
+
+ align:start position:0%
+about cruise sequence but we want to
+examine that all today. So let me remind
+
+ align:start position:0%
+examine that all today. So let me remind
+ 
+
+ align:start position:0%
+examine that all today. So let me remind
+you what a cruise sequence is. So a
+
+ align:start position:0%
+you what a cruise sequence is. So a
+ 
+
+ align:start position:0%
+you what a cruise sequence is. So a
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is said to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh if for all epsilon greater than zero
+
+ align:start position:0%
+Uh if for all epsilon greater than zero
+ 
+
+ align:start position:0%
+Uh if for all epsilon greater than zero
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist n such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if little n is bigger equal to the
+
+ align:start position:0%
+if little n is bigger equal to the
+ 
+
+ align:start position:0%
+if little n is bigger equal to the
+capital n then Um sorry if little n and
+
+ align:start position:0%
+capital n then Um sorry if little n and
+ 
+
+ align:start position:0%
+capital n then Um sorry if little n and
+little m.
+
+ align:start position:0%
+little m.
+ 
+
+ align:start position:0%
+little m.
+So if n and m m and n are big or equal
+
+ align:start position:0%
+So if n and m m and n are big or equal
+ 
+
+ align:start position:0%
+So if n and m m and n are big or equal
+then they are
+
+ align:start position:0%
+then they are
+ 
+
+ align:start position:0%
+then they are
+epsilon close together
+
+ align:start position:0%
+epsilon close together
+ 
+
+ align:start position:0%
+epsilon close together
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+and x m the distance between them.
+
+ align:start position:0%
+and x m the distance between them.
+ 
+
+ align:start position:0%
+and x m the distance between them.
+So this was a cus sequence and it just
+
+ align:start position:0%
+So this was a cus sequence and it just
+ 
+
+ align:start position:0%
+So this was a cus sequence and it just
+meant quis sequence just meant that the
+
+ align:start position:0%
+meant quis sequence just meant that the
+ 
+
+ align:start position:0%
+meant quis sequence just meant that the
+tail right of the sequence bunchs
+
+ align:start position:0%
+tail right of the sequence bunchs
+ 
+
+ align:start position:0%
+tail right of the sequence bunchs
+together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, uh, let me just prove I think we
+
+ align:start position:0%
+Now, uh, let me just prove I think we
+ 
+
+ align:start position:0%
+Now, uh, let me just prove I think we
+maybe talk about this, but let me but
+
+ align:start position:0%
+maybe talk about this, but let me but
+ 
+
+ align:start position:0%
+maybe talk about this, but let me but
+I'm going to let me
+
+ align:start position:0%
+I'm going to let me
+ 
+
+ align:start position:0%
+I'm going to let me
+just a little theorem here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um if
+
+ align:start position:0%
+Um if
+ 
+
+ align:start position:0%
+Um if
+if uh xn
+
+ align:start position:0%
+if uh xn
+ 
+
+ align:start position:0%
+if uh xn
+is a cruci sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then uh xn is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the proof of this is a proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now in the definition of it being a
+
+ align:start position:0%
+So now in the definition of it being a
+ 
+
+ align:start position:0%
+So now in the definition of it being a
+frequency you can take epsilon to be
+
+ align:start position:0%
+frequency you can take epsilon to be
+ 
+
+ align:start position:0%
+frequency you can take epsilon to be
+equal to one. So if you take take
+
+ align:start position:0%
+equal to one. So if you take take
+ 
+
+ align:start position:0%
+equal to one. So if you take take
+epsilon equal to 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of being
+
+ align:start position:0%
+of being
+ 
+
+ align:start position:0%
+of being
+accuracy sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that there exist there
+
+ align:start position:0%
+So this means that there exist there
+ 
+
+ align:start position:0%
+So this means that there exist there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist some n
+
+ align:start position:0%
+there exist some n
+ 
+
+ align:start position:0%
+there exist some n
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if little n and little m are bigger
+
+ align:start position:0%
+uh if little n and little m are bigger
+ 
+
+ align:start position:0%
+uh if little n and little m are bigger
+than this n then the difference between
+
+ align:start position:0%
+than this n then the difference between
+ 
+
+ align:start position:0%
+than this n then the difference between
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+is less than one. Right? This is the
+
+ align:start position:0%
+is less than one. Right? This is the
+ 
+
+ align:start position:0%
+is less than one. Right? This is the
+definition where I just apply it to
+
+ align:start position:0%
+definition where I just apply it to
+ 
+
+ align:start position:0%
+definition where I just apply it to
+epsilon equal to one. We have this but
+
+ align:start position:0%
+epsilon equal to one. We have this but
+ 
+
+ align:start position:0%
+epsilon equal to one. We have this but
+of course in particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular we can set say m equal to
+
+ align:start position:0%
+in particular we can set say m equal to
+ 
+
+ align:start position:0%
+in particular we can set say m equal to
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you have that x all the other
+
+ align:start position:0%
+and then you have that x all the other
+ 
+
+ align:start position:0%
+and then you have that x all the other
+ones. This means that for all
+
+ align:start position:0%
+ones. This means that for all
+ 
+
+ align:start position:0%
+ones. This means that for all
+then for all
+
+ align:start position:0%
+then for all
+ 
+
+ align:start position:0%
+then for all
+um little n bigger than capital n if
+
+ align:start position:0%
+um little n bigger than capital n if
+ 
+
+ align:start position:0%
+um little n bigger than capital n if
+you're looking at this
+
+ align:start position:0%
+you're looking at this
+ 
+
+ align:start position:0%
+you're looking at this
+difference here then this is less than
+
+ align:start position:0%
+difference here then this is less than
+ 
+
+ align:start position:0%
+difference here then this is less than
+one I'm only applying this now I'm just
+
+ align:start position:0%
+one I'm only applying this now I'm just
+ 
+
+ align:start position:0%
+one I'm only applying this now I'm just
+choosing just one single m and I'm
+
+ align:start position:0%
+choosing just one single m and I'm
+ 
+
+ align:start position:0%
+choosing just one single m and I'm
+choosing it to be equal to that capital
+
+ align:start position:0%
+choosing it to be equal to that capital
+ 
+
+ align:start position:0%
+choosing it to be equal to that capital
+so you have that And so this means that
+
+ align:start position:0%
+so you have that And so this means that
+ 
+
+ align:start position:0%
+so you have that And so this means that
+that now you see that if you take now so
+
+ align:start position:0%
+that now you see that if you take now so
+ 
+
+ align:start position:0%
+that now you see that if you take now so
+so if you take
+
+ align:start position:0%
+so if you take
+ 
+
+ align:start position:0%
+so if you take
+uh x so now suppose that little n
+
+ align:start position:0%
+uh x so now suppose that little n
+ 
+
+ align:start position:0%
+uh x so now suppose that little n
+so so for
+
+ align:start position:0%
+so so for
+ 
+
+ align:start position:0%
+so so for
+little n bigger than capital n if you if
+
+ align:start position:0%
+little n bigger than capital n if you if
+ 
+
+ align:start position:0%
+little n bigger than capital n if you if
+you look at little n
+
+ align:start position:0%
+you look at little n
+ 
+
+ align:start position:0%
+you look at little n
+then you have this
+
+ align:start position:0%
+then you have this
+ 
+
+ align:start position:0%
+then you have this
+so or
+
+ align:start position:0%
+so or
+ 
+
+ align:start position:0%
+so or
+for or little n big or equal to capital
+
+ align:start position:0%
+for or little n big or equal to capital
+ 
+
+ align:start position:0%
+for or little n big or equal to capital
+n. Then you have that the norm of little
+
+ align:start position:0%
+n. Then you have that the norm of little
+ 
+
+ align:start position:0%
+n. Then you have that the norm of little
+n. Well, you can write little n as as um
+
+ align:start position:0%
+n. Well, you can write little n as as um
+ 
+
+ align:start position:0%
+n. Well, you can write little n as as um
+as a difference.
+
+ align:start position:0%
+as a difference.
+ 
+
+ align:start position:0%
+as a difference.
+You can write little n
+
+ align:start position:0%
+You can write little n
+ 
+
+ align:start position:0%
+You can write little n
+like you can subtract it first and then
+
+ align:start position:0%
+like you can subtract it first and then
+ 
+
+ align:start position:0%
+like you can subtract it first and then
+add it again. So this is clearly the
+
+ align:start position:0%
+add it again. So this is clearly the
+ 
+
+ align:start position:0%
+add it again. So this is clearly the
+same.
+
+ align:start position:0%
+same.
+ 
+
+ align:start position:0%
+same.
+And now you can just
+
+ align:start position:0%
+And now you can just
+ 
+
+ align:start position:0%
+And now you can just
+So you have the sum of two things. You
+
+ align:start position:0%
+So you have the sum of two things. You
+ 
+
+ align:start position:0%
+So you have the sum of two things. You
+can think about this in here as one
+
+ align:start position:0%
+can think about this in here as one
+ 
+
+ align:start position:0%
+can think about this in here as one
+number and this is another number. So
+
+ align:start position:0%
+number and this is another number. So
+ 
+
+ align:start position:0%
+number and this is another number. So
+this is now less than x n minus x
+
+ align:start position:0%
+this is now less than x n minus x
+ 
+
+ align:start position:0%
+this is now less than x n minus x
+capital n plus the norm of x capital n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this here was because little n was
+
+ align:start position:0%
+And this here was because little n was
+ 
+
+ align:start position:0%
+And this here was because little n was
+bigger than capital n. This here is
+
+ align:start position:0%
+bigger than capital n. This here is
+ 
+
+ align:start position:0%
+bigger than capital n. This here is
+bounded by one. So this is less than one
+
+ align:start position:0%
+bounded by one. So this is less than one
+ 
+
+ align:start position:0%
+bounded by one. So this is less than one
+plus the norm.
+
+ align:start position:0%
+plus the norm.
+ 
+
+ align:start position:0%
+plus the norm.
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+So you see that for all the the little
+
+ align:start position:0%
+So you see that for all the the little
+ 
+
+ align:start position:0%
+So you see that for all the the little
+ends that are bigger than capture all of
+
+ align:start position:0%
+ends that are bigger than capture all of
+ 
+
+ align:start position:0%
+ends that are bigger than capture all of
+those there is a uniform arch right and
+
+ align:start position:0%
+those there is a uniform arch right and
+ 
+
+ align:start position:0%
+those there is a uniform arch right and
+so this means that if you're now just
+
+ align:start position:0%
+so this means that if you're now just
+ 
+
+ align:start position:0%
+so this means that if you're now just
+taking them the maximum
+
+ align:start position:0%
+taking them the maximum
+ 
+
+ align:start position:0%
+taking them the maximum
+of uh the norm of x1 the norm of x2
+
+ align:start position:0%
+of uh the norm of x1 the norm of x2
+ 
+
+ align:start position:0%
+of uh the norm of x1 the norm of x2
+up to the norm of xn
+
+ align:start position:0%
+up to the norm of xn
+ 
+
+ align:start position:0%
+up to the norm of xn
+uh minus uh sorry xn minus one
+
+ align:start position:0%
+uh minus uh sorry xn minus one
+ 
+
+ align:start position:0%
+uh minus uh sorry xn minus one
+and then x capital n
+
+ align:start position:0%
+and then x capital n
+ 
+
+ align:start position:0%
+and then x capital n
++ one. If you take the maximum of this
+
+ align:start position:0%
++ one. If you take the maximum of this
+ 
+
+ align:start position:0%
++ one. If you take the maximum of this
+and call this m then clearly for all n
+
+ align:start position:0%
+and call this m then clearly for all n
+ 
+
+ align:start position:0%
+and call this m then clearly for all n
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clearly you have for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have that x n is lesser equal to n
+
+ align:start position:0%
+you have that x n is lesser equal to n
+ 
+
+ align:start position:0%
+you have that x n is lesser equal to n
+right because if n little n is bigger
+
+ align:start position:0%
+right because if n little n is bigger
+ 
+
+ align:start position:0%
+right because if n little n is bigger
+than capital n then it's bounded by
+
+ align:start position:0%
+than capital n then it's bounded by
+ 
+
+ align:start position:0%
+than capital n then it's bounded by
+capital M because it's it's a maximum in
+
+ align:start position:0%
+capital M because it's it's a maximum in
+ 
+
+ align:start position:0%
+capital M because it's it's a maximum in
+particular of this and on the other one
+
+ align:start position:0%
+particular of this and on the other one
+ 
+
+ align:start position:0%
+particular of this and on the other one
+that's sort of obvious.
+
+ align:start position:0%
+that's sort of obvious.
+ 
+
+ align:start position:0%
+that's sort of obvious.
+Okay. So so it means that if you have a
+
+ align:start position:0%
+Okay. So so it means that if you have a
+ 
+
+ align:start position:0%
+Okay. So so it means that if you have a
+cushy sequence it's automatically
+
+ align:start position:0%
+cushy sequence it's automatically
+ 
+
+ align:start position:0%
+cushy sequence it's automatically
+bounded. Okay.
+
+ align:start position:0%
+bounded. Okay.
+ 
+
+ align:start position:0%
+bounded. Okay.
+Now we have the
+
+ align:start position:0%
+Now we have the
+ 
+
+ align:start position:0%
+Now we have the
+convergence theorem. So next we want to
+
+ align:start position:0%
+convergence theorem. So next we want to
+ 
+
+ align:start position:0%
+convergence theorem. So next we want to
+discuss
+
+ align:start position:0%
+discuss
+ 
+
+ align:start position:0%
+discuss
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the following that uh any
+
+ align:start position:0%
+So this is the following that uh any
+ 
+
+ align:start position:0%
+So this is the following that uh any
+any precision principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So remember that last time we
+
+ align:start position:0%
+Okay. So remember that last time we
+ 
+
+ align:start position:0%
+Okay. So remember that last time we
+proved the following. So so recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we showed the converse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So namely we prove the following
+
+ align:start position:0%
+So namely we prove the following
+ 
+
+ align:start position:0%
+So namely we prove the following
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to prove that if
+
+ align:start position:0%
+to prove that if
+ 
+
+ align:start position:0%
+to prove that if
+that any
+
+ align:start position:0%
+that any
+ 
+
+ align:start position:0%
+that any
+convergent sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a cushy sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the cushy convergence theorem is
+
+ align:start position:0%
+and so the cushy convergence theorem is
+ 
+
+ align:start position:0%
+and so the cushy convergence theorem is
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Now uh so we'll come back to the proof
+
+ align:start position:0%
+Now uh so we'll come back to the proof
+ 
+
+ align:start position:0%
+Now uh so we'll come back to the proof
+in just a little bit
+
+ align:start position:0%
+in just a little bit
+ 
+
+ align:start position:0%
+in just a little bit
+but before that let me talk about some
+
+ align:start position:0%
+but before that let me talk about some
+ 
+
+ align:start position:0%
+but before that let me talk about some
+applications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the first one we we sort of
+
+ align:start position:0%
+and so the first one we we sort of
+ 
+
+ align:start position:0%
+and so the first one we we sort of
+started talking a little bit um last
+
+ align:start position:0%
+started talking a little bit um last
+ 
+
+ align:start position:0%
+started talking a little bit um last
+time and this is uh the contracting
+
+ align:start position:0%
+time and this is uh the contracting
+ 
+
+ align:start position:0%
+time and this is uh the contracting
+mapping the so contracting And that in
+
+ align:start position:0%
+mapping the so contracting And that in
+ 
+
+ align:start position:0%
+mapping the so contracting And that in
+itself have a number of applications. So
+
+ align:start position:0%
+itself have a number of applications. So
+ 
+
+ align:start position:0%
+itself have a number of applications. So
+contracting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for that I need some I need to uh
+
+ align:start position:0%
+and for that I need some I need to uh
+ 
+
+ align:start position:0%
+and for that I need some I need to uh
+call some definitions.
+
+ align:start position:0%
+call some definitions.
+ 
+
+ align:start position:0%
+call some definitions.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+so a map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a map t from r e to r
+
+ align:start position:0%
+a map t from r e to r
+ 
+
+ align:start position:0%
+a map t from r e to r
+uh is set to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a contracting map.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some constant C positive C is positive
+
+ align:start position:0%
+some constant C positive C is positive
+ 
+
+ align:start position:0%
+some constant C positive C is positive
+and the key point is it's it will have
+
+ align:start position:0%
+and the key point is it's it will have
+ 
+
+ align:start position:0%
+and the key point is it's it will have
+to be positive. So that but the key
+
+ align:start position:0%
+to be positive. So that but the key
+ 
+
+ align:start position:0%
+to be positive. So that but the key
+point is that this constant has to be
+
+ align:start position:0%
+point is that this constant has to be
+ 
+
+ align:start position:0%
+point is that this constant has to be
+strictly less than one. And then
+
+ align:start position:0%
+strictly less than one. And then
+ 
+
+ align:start position:0%
+strictly less than one. And then
+contracting mapping just means that if
+
+ align:start position:0%
+contracting mapping just means that if
+ 
+
+ align:start position:0%
+contracting mapping just means that if
+you looking at the difference
+
+ align:start position:0%
+you looking at the difference
+ 
+
+ align:start position:0%
+you looking at the difference
+between the images
+
+ align:start position:0%
+between the images
+ 
+
+ align:start position:0%
+between the images
+then they are closer together. This
+
+ align:start position:0%
+then they are closer together. This
+ 
+
+ align:start position:0%
+then they are closer together. This
+they're strictly closer together
+
+ align:start position:0%
+they're strictly closer together
+ 
+
+ align:start position:0%
+they're strictly closer together
+than than the points that they are
+
+ align:start position:0%
+than than the points that they are
+ 
+
+ align:start position:0%
+than than the points that they are
+images of.
+
+ align:start position:0%
+images of.
+ 
+
+ align:start position:0%
+images of.
+Okay. So this is a contracting map
+
+ align:start position:0%
+Okay. So this is a contracting map
+ 
+
+ align:start position:0%
+Okay. So this is a contracting map
+right then. So the contracting mapping
+
+ align:start position:0%
+right then. So the contracting mapping
+ 
+
+ align:start position:0%
+right then. So the contracting mapping
+again this here inequality is it say
+
+ align:start position:0%
+again this here inequality is it say
+ 
+
+ align:start position:0%
+again this here inequality is it say
+that under the map the images are
+
+ align:start position:0%
+that under the map the images are
+ 
+
+ align:start position:0%
+that under the map the images are
+squeezed more together.
+
+ align:start position:0%
+squeezed more together.
+ 
+
+ align:start position:0%
+squeezed more together.
+So now
+
+ align:start position:0%
+So now
+ 
+
+ align:start position:0%
+So now
+that's one concept. The other one we
+
+ align:start position:0%
+that's one concept. The other one we
+ 
+
+ align:start position:0%
+that's one concept. The other one we
+need is that for fixed points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the other concept is fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So So X here is a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for MF.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+See if if it is
+
+ align:start position:0%
+See if if it is
+ 
+
+ align:start position:0%
+See if if it is
+if under the map the the points uh
+
+ align:start position:0%
+if under the map the the points uh
+ 
+
+ align:start position:0%
+if under the map the the points uh
+remain unchanged. So T of X is equal to
+
+ align:start position:0%
+remain unchanged. So T of X is equal to
+ 
+
+ align:start position:0%
+remain unchanged. So T of X is equal to
+X. So this is what it needs to be. Yeah.
+
+ align:start position:0%
+X. So this is what it needs to be. Yeah.
+ 
+
+ align:start position:0%
+X. So this is what it needs to be. Yeah.
+>> But that it's not the same C for X and
+
+ align:start position:0%
+>> But that it's not the same C for X and
+ 
+
+ align:start position:0%
+>> But that it's not the same C for X and
+Y. It is the same scene. It is.
+
+ align:start position:0%
+Y. It is the same scene. It is.
+ 
+
+ align:start position:0%
+Y. It is the same scene. It is.
+>> Yeah, it's the same scene.
+
+ align:start position:0%
+>> Yeah, it's the same scene.
+ 
+
+ align:start position:0%
+>> Yeah, it's the same scene.
+>> And we'll come back to this in just a
+
+ align:start position:0%
+>> And we'll come back to this in just a
+ 
+
+ align:start position:0%
+>> And we'll come back to this in just a
+second, but but it but it it is supposed
+
+ align:start position:0%
+second, but but it but it it is supposed
+ 
+
+ align:start position:0%
+second, but but it but it it is supposed
+to be the same scene.
+
+ align:start position:0%
+to be the same scene.
+ 
+
+ align:start position:0%
+to be the same scene.
+You can weaken that a little bit. Uh but
+
+ align:start position:0%
+You can weaken that a little bit. Uh but
+ 
+
+ align:start position:0%
+You can weaken that a little bit. Uh but
+essentially, I mean, you sort of, you
+
+ align:start position:0%
+essentially, I mean, you sort of, you
+ 
+
+ align:start position:0%
+essentially, I mean, you sort of, you
+know, at least we'll talk about this in
+
+ align:start position:0%
+know, at least we'll talk about this in
+ 
+
+ align:start position:0%
+know, at least we'll talk about this in
+just a second, but it it's important
+
+ align:start position:0%
+just a second, but it it's important
+ 
+
+ align:start position:0%
+just a second, but it it's important
+just think about it that it's a
+
+ align:start position:0%
+just think about it that it's a
+ 
+
+ align:start position:0%
+just think about it that it's a
+requirement that it's the same seat for
+
+ align:start position:0%
+requirement that it's the same seat for
+ 
+
+ align:start position:0%
+requirement that it's the same seat for
+all. And the key point is that this C is
+
+ align:start position:0%
+all. And the key point is that this C is
+ 
+
+ align:start position:0%
+all. And the key point is that this C is
+strictly less than one. Okay. So this is
+
+ align:start position:0%
+strictly less than one. Okay. So this is
+ 
+
+ align:start position:0%
+strictly less than one. Okay. So this is
+a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now um so now the first
+
+ align:start position:0%
+And now um so now the first
+ 
+
+ align:start position:0%
+And now um so now the first
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have a lema here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh if t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is a contracting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then um there's at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at most one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there cannot be more than one fix. Okay.
+
+ align:start position:0%
+there cannot be more than one fix. Okay.
+ 
+
+ align:start position:0%
+there cannot be more than one fix. Okay.
+So let's prove that. a pro.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So yeah, so I'm going to So suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and Y are fixed points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to show
+
+ align:start position:0%
+and I want to show
+ 
+
+ align:start position:0%
+and I want to show
+that X is equal to Y.
+
+ align:start position:0%
+that X is equal to Y.
+ 
+
+ align:start position:0%
+that X is equal to Y.
+So I'm looking at the
+
+ align:start position:0%
+So I'm looking at the
+ 
+
+ align:start position:0%
+So I'm looking at the
+images.
+
+ align:start position:0%
+images.
+ 
+
+ align:start position:0%
+images.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's continue.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'm looking at the images under F. So
+
+ align:start position:0%
+So I'm looking at the images under F. So
+ 
+
+ align:start position:0%
+So I'm looking at the images under F. So
+I'm looking at So I take T of X
+
+ align:start position:0%
+I'm looking at So I take T of X
+ 
+
+ align:start position:0%
+I'm looking at So I take T of X
+and I'm looking at the difference
+
+ align:start position:0%
+and I'm looking at the difference
+ 
+
+ align:start position:0%
+and I'm looking at the difference
+between T of X and T of Y
+
+ align:start position:0%
+between T of X and T of Y
+ 
+
+ align:start position:0%
+between T of X and T of Y
+and I want to estimate that difference.
+
+ align:start position:0%
+and I want to estimate that difference.
+ 
+
+ align:start position:0%
+and I want to estimate that difference.
+Well, on one hand T X is supposed to be
+
+ align:start position:0%
+Well, on one hand T X is supposed to be
+ 
+
+ align:start position:0%
+Well, on one hand T X is supposed to be
+a fixed point. So T of X is the same as
+
+ align:start position:0%
+a fixed point. So T of X is the same as
+ 
+
+ align:start position:0%
+a fixed point. So T of X is the same as
+X and likewise for Y. So this here is
+
+ align:start position:0%
+X and likewise for Y. So this here is
+ 
+
+ align:start position:0%
+X and likewise for Y. So this here is
+the same. So T of X is the same as X. T
+
+ align:start position:0%
+the same. So T of X is the same as X. T
+ 
+
+ align:start position:0%
+the same. So T of X is the same as X. T
+Y is supposed to be the same as Y. So I
+
+ align:start position:0%
+Y is supposed to be the same as Y. So I
+ 
+
+ align:start position:0%
+Y is supposed to be the same as Y. So I
+have this. On the other hand, it's a
+
+ align:start position:0%
+have this. On the other hand, it's a
+ 
+
+ align:start position:0%
+have this. On the other hand, it's a
+contracting map. So this here is less or
+
+ align:start position:0%
+contracting map. So this here is less or
+ 
+
+ align:start position:0%
+contracting map. So this here is less or
+equal to C
+
+ align:start position:0%
+equal to C
+ 
+
+ align:start position:0%
+equal to C
+times the norm of X - Y.
+
+ align:start position:0%
+times the norm of X - Y.
+ 
+
+ align:start position:0%
+times the norm of X - Y.
+Right? But now C here remember C is
+
+ align:start position:0%
+Right? But now C here remember C is
+ 
+
+ align:start position:0%
+Right? But now C here remember C is
+strictly less than one.
+
+ align:start position:0%
+strictly less than one.
+ 
+
+ align:start position:0%
+strictly less than one.
+So you can only have an inequality like
+
+ align:start position:0%
+So you can only have an inequality like
+ 
+
+ align:start position:0%
+So you can only have an inequality like
+this, right? If this number here is
+
+ align:start position:0%
+this, right? If this number here is
+ 
+
+ align:start position:0%
+this, right? If this number here is
+zero, right? when c is strictly less
+
+ align:start position:0%
+zero, right? when c is strictly less
+ 
+
+ align:start position:0%
+zero, right? when c is strictly less
+than one. So this here implies that x -
+
+ align:start position:0%
+than one. So this here implies that x -
+ 
+
+ align:start position:0%
+than one. So this here implies that x -
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+the distance is zero and so of course
+
+ align:start position:0%
+the distance is zero and so of course
+ 
+
+ align:start position:0%
+the distance is zero and so of course
+this means that x is equal to y.
+
+ align:start position:0%
+this means that x is equal to y.
+ 
+
+ align:start position:0%
+this means that x is equal to y.
+>> Okay. So that's what we want to prove.
+
+ align:start position:0%
+>> Okay. So that's what we want to prove.
+ 
+
+ align:start position:0%
+>> Okay. So that's what we want to prove.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. I'm sorry that was uh yeah it
+
+ align:start position:0%
+>> Yeah. I'm sorry that was uh yeah it
+ 
+
+ align:start position:0%
+>> Yeah. I'm sorry that was uh yeah it
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+because otherwise you know it's it
+
+ align:start position:0%
+because otherwise you know it's it
+ 
+
+ align:start position:0%
+because otherwise you know it's it
+wouldn't be if x is equal to y would be
+
+ align:start position:0%
+wouldn't be if x is equal to y would be
+ 
+
+ align:start position:0%
+wouldn't be if x is equal to y would be
+so should be let's change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a contracting map have at most
+
+ align:start position:0%
+okay so a contracting map have at most
+ 
+
+ align:start position:0%
+okay so a contracting map have at most
+one fix one
+
+ align:start position:0%
+one fix one
+ 
+
+ align:start position:0%
+one fix one
+okay now let's
+
+ align:start position:0%
+okay now let's
+ 
+
+ align:start position:0%
+okay now let's
+uh so so so let me Just so you're going
+
+ align:start position:0%
+uh so so so let me Just so you're going
+ 
+
+ align:start position:0%
+uh so so so let me Just so you're going
+to do this. So um
+
+ align:start position:0%
+to do this. So um
+ 
+
+ align:start position:0%
+to do this. So um
+um I have harassed the graders to give
+
+ align:start position:0%
+um I have harassed the graders to give
+ 
+
+ align:start position:0%
+um I have harassed the graders to give
+you back the homework. I uh it should be
+
+ align:start position:0%
+you back the homework. I uh it should be
+ 
+
+ align:start position:0%
+you back the homework. I uh it should be
+back today. I mean otherwise they're in
+
+ align:start position:0%
+back today. I mean otherwise they're in
+ 
+
+ align:start position:0%
+back today. I mean otherwise they're in
+trouble. So hopefully but but but and
+
+ align:start position:0%
+trouble. So hopefully but but but and
+ 
+
+ align:start position:0%
+trouble. So hopefully but but but and
+the assignment for next week is already
+
+ align:start position:0%
+the assignment for next week is already
+ 
+
+ align:start position:0%
+the assignment for next week is already
+posted.
+
+ align:start position:0%
+posted.
+ 
+
+ align:start position:0%
+posted.
+And and here's
+
+ align:start position:0%
+And and here's
+ 
+
+ align:start position:0%
+And and here's
+here's um
+
+ align:start position:0%
+here's um
+ 
+
+ align:start position:0%
+here's um
+so this is on the next so I I will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's um here's something on pet
+
+ align:start position:0%
+so here's um here's something on pet
+ 
+
+ align:start position:0%
+so here's um here's something on pet
+stream
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think it's uh
+
+ align:start position:0%
+and I think it's uh
+ 
+
+ align:start position:0%
+and I think it's uh
+okay uh yeah I forget which one it is
+
+ align:start position:0%
+okay uh yeah I forget which one it is
+ 
+
+ align:start position:0%
+okay uh yeah I forget which one it is
+but anyway on on the third pet
+
+ align:start position:0%
+but anyway on on the third pet
+ 
+
+ align:start position:0%
+but anyway on on the third pet
+You will be asked to prove the following
+
+ align:start position:0%
+You will be asked to prove the following
+ 
+
+ align:start position:0%
+You will be asked to prove the following
+that if uh t here
+
+ align:start position:0%
+that if uh t here
+ 
+
+ align:start position:0%
+that if uh t here
+is a contracting map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and x here is any point
+
+ align:start position:0%
+and x here is any point
+ 
+
+ align:start position:0%
+and x here is any point
+any point in the domain of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then if you form the sequence a n so a1
+
+ align:start position:0%
+Then if you form the sequence a n so a1
+ 
+
+ align:start position:0%
+Then if you form the sequence a n so a1
+say that's just x
+
+ align:start position:0%
+say that's just x
+ 
+
+ align:start position:0%
+say that's just x
+a2 uh let's let's call it a sorry let's
+
+ align:start position:0%
+a2 uh let's let's call it a sorry let's
+ 
+
+ align:start position:0%
+a2 uh let's let's call it a sorry let's
+let's call it a z is x
+
+ align:start position:0%
+let's call it a z is x
+ 
+
+ align:start position:0%
+let's call it a z is x
+uh a1 here
+
+ align:start position:0%
+uh a1 here
+ 
+
+ align:start position:0%
+uh a1 here
+is t of x t of a is zero so this is t of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a2
+
+ align:start position:0%
+and a2
+ 
+
+ align:start position:0%
+and a2
+is t of a1. So this is the same as t of
+
+ align:start position:0%
+is t of a1. So this is the same as t of
+ 
+
+ align:start position:0%
+is t of a1. So this is the same as t of
+this. So this is t
+
+ align:start position:0%
+this. So this is t
+ 
+
+ align:start position:0%
+this. So this is t
+* t of x which I'm will write like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh a3 so we continue this way a3 is
+
+ align:start position:0%
+and uh a3 so we continue this way a3 is
+ 
+
+ align:start position:0%
+and uh a3 so we continue this way a3 is
+t of a2. So that is
+
+ align:start position:0%
+t of a2. So that is
+ 
+
+ align:start position:0%
+t of a2. So that is
+t applied three times. So t g
+
+ align:start position:0%
+t applied three times. So t g
+ 
+
+ align:start position:0%
+t applied three times. So t g
+t g t g t g t g t g t g t g t g t g t g
+
+ align:start position:0%
+t g t g t g t g t g t g t g t g t g t g
+ 
+
+ align:start position:0%
+t g t g t g t g t g t g t g t g t g t g
+t g t g t g t g t g t g t g t g t g t g
+
+ align:start position:0%
+t g t g t g t g t g t g t g t g t g t g
+ 
+
+ align:start position:0%
+t g t g t g t g t g t g t g t g t g t g
+of x and I'm going to write this as g c
+
+ align:start position:0%
+of x and I'm going to write this as g c
+ 
+
+ align:start position:0%
+of x and I'm going to write this as g c
+2 of x
+
+ align:start position:0%
+2 of x
+ 
+
+ align:start position:0%
+2 of x
+and and so on. So a n is going to be t
+
+ align:start position:0%
+and and so on. So a n is going to be t
+ 
+
+ align:start position:0%
+and and so on. So a n is going to be t
+of a sorry it's t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a n + one
+
+ align:start position:0%
+a n + one
+ 
+
+ align:start position:0%
+a n + one
+is going to be t of a n. So that's the
+
+ align:start position:0%
+is going to be t of a n. So that's the
+ 
+
+ align:start position:0%
+is going to be t of a n. So that's the
+same as uh t to the power n + one
+
+ align:start position:0%
+same as uh t to the power n + one
+ 
+
+ align:start position:0%
+same as uh t to the power n + one
+of x.
+
+ align:start position:0%
+of x.
+ 
+
+ align:start position:0%
+of x.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So if you have a contracting map and you
+
+ align:start position:0%
+So if you have a contracting map and you
+ 
+
+ align:start position:0%
+So if you have a contracting map and you
+just start with any point you want and
+
+ align:start position:0%
+just start with any point you want and
+ 
+
+ align:start position:0%
+just start with any point you want and
+now you form a sequence that is based on
+
+ align:start position:0%
+now you form a sequence that is based on
+ 
+
+ align:start position:0%
+now you form a sequence that is based on
+that point and uh and the nth element is
+
+ align:start position:0%
+that point and uh and the nth element is
+ 
+
+ align:start position:0%
+that point and uh and the nth element is
+just where you have applied the map n
+
+ align:start position:0%
+just where you have applied the map n
+ 
+
+ align:start position:0%
+just where you have applied the map n
+times to the original point. So if you
+
+ align:start position:0%
+times to the original point. So if you
+ 
+
+ align:start position:0%
+times to the original point. So if you
+form that sequence then you will prove
+
+ align:start position:0%
+form that sequence then you will prove
+ 
+
+ align:start position:0%
+form that sequence then you will prove
+uh you will show
+
+ align:start position:0%
+uh you will show
+ 
+
+ align:start position:0%
+uh you will show
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+in the homework you will show that this
+
+ align:start position:0%
+in the homework you will show that this
+ 
+
+ align:start position:0%
+in the homework you will show that this
+sequence so this set
+
+ align:start position:0%
+sequence so this set
+ 
+
+ align:start position:0%
+sequence so this set
+three and I I will just do a
+
+ align:start position:0%
+three and I I will just do a
+ 
+
+ align:start position:0%
+three and I I will just do a
+special case of it that you will start
+
+ align:start position:0%
+special case of it that you will start
+ 
+
+ align:start position:0%
+special case of it that you will start
+with but we'll just do this now
+
+ align:start position:0%
+with but we'll just do this now
+ 
+
+ align:start position:0%
+with but we'll just do this now
+and then the rest to you to you know I
+
+ align:start position:0%
+and then the rest to you to you know I
+ 
+
+ align:start position:0%
+and then the rest to you to you know I
+leave you for the homework but but on
+
+ align:start position:0%
+leave you for the homework but but on
+ 
+
+ align:start position:0%
+leave you for the homework but but on
+piece of three you prove that this a is
+
+ align:start position:0%
+piece of three you prove that this a is
+ 
+
+ align:start position:0%
+piece of three you prove that this a is
+a secret
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what is the the key starting point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+starting point for this
+
+ align:start position:0%
+starting point for this
+ 
+
+ align:start position:0%
+starting point for this
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+because you're there you know you're
+
+ align:start position:0%
+because you're there you know you're
+ 
+
+ align:start position:0%
+because you're there you know you're
+already uh well started on on p three is
+
+ align:start position:0%
+already uh well started on on p three is
+ 
+
+ align:start position:0%
+already uh well started on on p three is
+a key starting point for this is to
+
+ align:start position:0%
+a key starting point for this is to
+ 
+
+ align:start position:0%
+a key starting point for this is to
+prove that it's a cruise sequence so I
+
+ align:start position:0%
+prove that it's a cruise sequence so I
+ 
+
+ align:start position:0%
+prove that it's a cruise sequence so I
+want to estimate
+
+ align:start position:0%
+want to estimate
+ 
+
+ align:start position:0%
+want to estimate
+so this is not enough right I mean I
+
+ align:start position:0%
+so this is not enough right I mean I
+ 
+
+ align:start position:0%
+so this is not enough right I mean I
+need to prove what I need to show is
+
+ align:start position:0%
+need to prove what I need to show is
+ 
+
+ align:start position:0%
+need to prove what I need to show is
+remember I need to prove that when
+
+ align:start position:0%
+remember I need to prove that when
+ 
+
+ align:start position:0%
+remember I need to prove that when
+little m and little m
+
+ align:start position:0%
+little m and little m
+ 
+
+ align:start position:0%
+little m and little m
+are sufficiently large then I want to
+
+ align:start position:0%
+are sufficiently large then I want to
+ 
+
+ align:start position:0%
+are sufficiently large then I want to
+estimate the distance between these two
+
+ align:start position:0%
+estimate the distance between these two
+ 
+
+ align:start position:0%
+estimate the distance between these two
+and show that they're bunched together,
+
+ align:start position:0%
+and show that they're bunched together,
+ 
+
+ align:start position:0%
+and show that they're bunched together,
+right? That's what we need to prove.
+
+ align:start position:0%
+right? That's what we need to prove.
+ 
+
+ align:start position:0%
+right? That's what we need to prove.
+Prove this precision. I I won't quite do
+
+ align:start position:0%
+Prove this precision. I I won't quite do
+ 
+
+ align:start position:0%
+Prove this precision. I I won't quite do
+this, but I do a special case that is a
+
+ align:start position:0%
+this, but I do a special case that is a
+ 
+
+ align:start position:0%
+this, but I do a special case that is a
+key starting point. And that is the
+
+ align:start position:0%
+key starting point. And that is the
+ 
+
+ align:start position:0%
+key starting point. And that is the
+where I'm looking at this thing here.
+
+ align:start position:0%
+where I'm looking at this thing here.
+ 
+
+ align:start position:0%
+where I'm looking at this thing here.
+I'm looking at two consecutive element
+
+ align:start position:0%
+I'm looking at two consecutive element
+ 
+
+ align:start position:0%
+I'm looking at two consecutive element
+in the sequence and I'm estimating the
+
+ align:start position:0%
+in the sequence and I'm estimating the
+ 
+
+ align:start position:0%
+in the sequence and I'm estimating the
+distance. That's not enough to prove
+
+ align:start position:0%
+distance. That's not enough to prove
+ 
+
+ align:start position:0%
+distance. That's not enough to prove
+that C sequence, right? Because I need
+
+ align:start position:0%
+that C sequence, right? Because I need
+ 
+
+ align:start position:0%
+that C sequence, right? Because I need
+to prove that for all n and m
+
+ align:start position:0%
+to prove that for all n and m
+ 
+
+ align:start position:0%
+to prove that for all n and m
+sufficiently large. And I'm just proving
+
+ align:start position:0%
+sufficiently large. And I'm just proving
+ 
+
+ align:start position:0%
+sufficiently large. And I'm just proving
+here that for any ns sufficiently large
+
+ align:start position:0%
+here that for any ns sufficiently large
+ 
+
+ align:start position:0%
+here that for any ns sufficiently large
+if I'm looking at the neighbor then that
+
+ align:start position:0%
+if I'm looking at the neighbor then that
+ 
+
+ align:start position:0%
+if I'm looking at the neighbor then that
+this is very small but but but you can
+
+ align:start position:0%
+this is very small but but but you can
+ 
+
+ align:start position:0%
+this is very small but but but you can
+use the estimates that we will now prove
+
+ align:start position:0%
+use the estimates that we will now prove
+ 
+
+ align:start position:0%
+use the estimates that we will now prove
+to prove that it is in fact a sequence.
+
+ align:start position:0%
+to prove that it is in fact a sequence.
+ 
+
+ align:start position:0%
+to prove that it is in fact a sequence.
+So in order to estimate this right I'm
+
+ align:start position:0%
+So in order to estimate this right I'm
+ 
+
+ align:start position:0%
+So in order to estimate this right I'm
+can think about this thing here
+
+ align:start position:0%
+can think about this thing here
+ 
+
+ align:start position:0%
+can think about this thing here
+as t as a to the n + one this here is
+
+ align:start position:0%
+as t as a to the n + one this here is
+ 
+
+ align:start position:0%
+as t as a to the n + one this here is
+just t of a to n and a n itself this is
+
+ align:start position:0%
+just t of a to n and a n itself this is
+ 
+
+ align:start position:0%
+just t of a to n and a n itself this is
+t of the previous element right this is
+
+ align:start position:0%
+t of the previous element right this is
+ 
+
+ align:start position:0%
+t of the previous element right this is
+how we define them so this means that
+
+ align:start position:0%
+how we define them so this means that
+ 
+
+ align:start position:0%
+how we define them so this means that
+this thing here so again I could just
+
+ align:start position:0%
+this thing here so again I could just
+ 
+
+ align:start position:0%
+this thing here so again I could just
+write this in here. So this thing is
+
+ align:start position:0%
+write this in here. So this thing is
+ 
+
+ align:start position:0%
+write this in here. So this thing is
+equal to a n minus t of a n minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now I can use that contracting map
+
+ align:start position:0%
+and now I can use that contracting map
+ 
+
+ align:start position:0%
+and now I can use that contracting map
+right because now I have these two gez
+
+ align:start position:0%
+right because now I have these two gez
+ 
+
+ align:start position:0%
+right because now I have these two gez
+here so I can use that contracting map
+
+ align:start position:0%
+here so I can use that contracting map
+ 
+
+ align:start position:0%
+here so I can use that contracting map
+so I get less or equal to and then a n
+
+ align:start position:0%
+so I get less or equal to and then a n
+ 
+
+ align:start position:0%
+so I get less or equal to and then a n
+minus a n minus one
+
+ align:start position:0%
+minus a n minus one
+ 
+
+ align:start position:0%
+minus a n minus one
+and so you see that that's the Next the
+
+ align:start position:0%
+and so you see that that's the Next the
+ 
+
+ align:start position:0%
+and so you see that that's the Next the
+distance between the next pair is
+
+ align:start position:0%
+distance between the next pair is
+ 
+
+ align:start position:0%
+distance between the next pair is
+because C is strictly less than one. It
+
+ align:start position:0%
+because C is strictly less than one. It
+ 
+
+ align:start position:0%
+because C is strictly less than one. It
+has decreased with some factor. Right?
+
+ align:start position:0%
+has decreased with some factor. Right?
+ 
+
+ align:start position:0%
+has decreased with some factor. Right?
+And so now the the the key starting
+
+ align:start position:0%
+And so now the the the key starting
+ 
+
+ align:start position:0%
+And so now the the the key starting
+point is that if you just iterate this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now if I iterate this, so I'm looking
+
+ align:start position:0%
+So now if I iterate this, so I'm looking
+ 
+
+ align:start position:0%
+So now if I iterate this, so I'm looking
+at a n + 1 minus a n
+
+ align:start position:0%
+at a n + 1 minus a n
+ 
+
+ align:start position:0%
+at a n + 1 minus a n
+and I now have that this thing here is
+
+ align:start position:0%
+and I now have that this thing here is
+ 
+
+ align:start position:0%
+and I now have that this thing here is
+less than c a n minus a n minus one. But
+
+ align:start position:0%
+less than c a n minus a n minus one. But
+ 
+
+ align:start position:0%
+less than c a n minus a n minus one. But
+now I'm writing forget about the c for a
+
+ align:start position:0%
+now I'm writing forget about the c for a
+ 
+
+ align:start position:0%
+now I'm writing forget about the c for a
+second. I'm just writing this thing
+
+ align:start position:0%
+second. I'm just writing this thing
+ 
+
+ align:start position:0%
+second. I'm just writing this thing
+here. So I do the same thing again. I
+
+ align:start position:0%
+here. So I do the same thing again. I
+ 
+
+ align:start position:0%
+here. So I do the same thing again. I
+write this here as the image of a n
+
+ align:start position:0%
+write this here as the image of a n
+ 
+
+ align:start position:0%
+write this here as the image of a n
+minus one and I write this n minus one
+
+ align:start position:0%
+minus one and I write this n minus one
+ 
+
+ align:start position:0%
+minus one and I write this n minus one
+as the image of the previous one. So n
+
+ align:start position:0%
+as the image of the previous one. So n
+ 
+
+ align:start position:0%
+as the image of the previous one. So n
+minus two right and now so I write this
+
+ align:start position:0%
+minus two right and now so I write this
+ 
+
+ align:start position:0%
+minus two right and now so I write this
+so c here I just have to carry along for
+
+ align:start position:0%
+so c here I just have to carry along for
+ 
+
+ align:start position:0%
+so c here I just have to carry along for
+the right and then I have t a n minus
+
+ align:start position:0%
+the right and then I have t a n minus
+ 
+
+ align:start position:0%
+the right and then I have t a n minus
+one minus t a n minus 2.
+
+ align:start position:0%
+one minus t a n minus 2.
+ 
+
+ align:start position:0%
+one minus t a n minus 2.
+And now forget about this just use this
+
+ align:start position:0%
+And now forget about this just use this
+ 
+
+ align:start position:0%
+And now forget about this just use this
+contracting mapping. So then this is
+
+ align:start position:0%
+contracting mapping. So then this is
+ 
+
+ align:start position:0%
+contracting mapping. So then this is
+less than equal to and then the C here I
+
+ align:start position:0%
+less than equal to and then the C here I
+ 
+
+ align:start position:0%
+less than equal to and then the C here I
+to carry along. But then there's another
+
+ align:start position:0%
+to carry along. But then there's another
+ 
+
+ align:start position:0%
+to carry along. But then there's another
+C that pops out. Right? So this is times
+
+ align:start position:0%
+C that pops out. Right? So this is times
+ 
+
+ align:start position:0%
+C that pops out. Right? So this is times
+C that pops out because of the
+
+ align:start position:0%
+C that pops out because of the
+ 
+
+ align:start position:0%
+C that pops out because of the
+contracting mapping and then a N minus
+
+ align:start position:0%
+contracting mapping and then a N minus
+ 
+
+ align:start position:0%
+contracting mapping and then a N minus
+one minus A N minus 2. And so you see
+
+ align:start position:0%
+one minus A N minus 2. And so you see
+ 
+
+ align:start position:0%
+one minus A N minus 2. And so you see
+that you have written this as c^ squ a n
+
+ align:start position:0%
+that you have written this as c^ squ a n
+ 
+
+ align:start position:0%
+that you have written this as c^ squ a n
+minus 2 - one minus a n minus 2. And so
+
+ align:start position:0%
+minus 2 - one minus a n minus 2. And so
+ 
+
+ align:start position:0%
+minus 2 - one minus a n minus 2. And so
+now you continue it and so you see that
+
+ align:start position:0%
+now you continue it and so you see that
+ 
+
+ align:start position:0%
+now you continue it and so you see that
+the further out you get right. So you
+
+ align:start position:0%
+the further out you get right. So you
+ 
+
+ align:start position:0%
+the further out you get right. So you
+continue this all the way down to that
+
+ align:start position:0%
+continue this all the way down to that
+ 
+
+ align:start position:0%
+continue this all the way down to that
+you're getting that this element is the
+
+ align:start position:0%
+you're getting that this element is the
+ 
+
+ align:start position:0%
+you're getting that this element is the
+initial point and and this one is the
+
+ align:start position:0%
+initial point and and this one is the
+ 
+
+ align:start position:0%
+initial point and and this one is the
+first ele you know a1. This is a z and
+
+ align:start position:0%
+first ele you know a1. This is a z and
+ 
+
+ align:start position:0%
+first ele you know a1. This is a z and
+this is a1 right
+
+ align:start position:0%
+this is a1 right
+ 
+
+ align:start position:0%
+this is a1 right
+and so you see that you're getting
+
+ align:start position:0%
+and so you see that you're getting
+ 
+
+ align:start position:0%
+and so you see that you're getting
+something which is like a a c to some
+
+ align:start position:0%
+something which is like a a c to some
+ 
+
+ align:start position:0%
+something which is like a a c to some
+power n times the distance that you
+
+ align:start position:0%
+power n times the distance that you
+ 
+
+ align:start position:0%
+power n times the distance that you
+started with right so this is bounded by
+
+ align:start position:0%
+started with right so this is bounded by
+ 
+
+ align:start position:0%
+started with right so this is bounded by
+uh something like c to the n * a 1 - a z
+
+ align:start position:0%
+uh something like c to the n * a 1 - a z
+ 
+
+ align:start position:0%
+uh something like c to the n * a 1 - a z
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+and so that's a key starting point. So
+
+ align:start position:0%
+and so that's a key starting point. So
+ 
+
+ align:start position:0%
+and so that's a key starting point. So
+if you going very very far out remember
+
+ align:start position:0%
+if you going very very far out remember
+ 
+
+ align:start position:0%
+if you going very very far out remember
+that this number is smaller than one. So
+
+ align:start position:0%
+that this number is smaller than one. So
+ 
+
+ align:start position:0%
+that this number is smaller than one. So
+this here will become incredibly small
+
+ align:start position:0%
+this here will become incredibly small
+ 
+
+ align:start position:0%
+this here will become incredibly small
+when n is large. Right? And so this is
+
+ align:start position:0%
+when n is large. Right? And so this is
+ 
+
+ align:start position:0%
+when n is large. Right? And so this is
+the key starting point uh to prove that
+
+ align:start position:0%
+the key starting point uh to prove that
+ 
+
+ align:start position:0%
+the key starting point uh to prove that
+to prove that if you take a contracting
+
+ align:start position:0%
+to prove that if you take a contracting
+ 
+
+ align:start position:0%
+to prove that if you take a contracting
+map start with any point and you form
+
+ align:start position:0%
+map start with any point and you form
+ 
+
+ align:start position:0%
+map start with any point and you form
+this sequence here then it's a sequence.
+
+ align:start position:0%
+this sequence here then it's a sequence.
+ 
+
+ align:start position:0%
+this sequence here then it's a sequence.
+So now
+
+ align:start position:0%
+So now
+ 
+
+ align:start position:0%
+So now
+so and I leave the rest for the
+
+ align:start position:0%
+so and I leave the rest for the
+ 
+
+ align:start position:0%
+so and I leave the rest for the
+homework. Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's prove the
+
+ align:start position:0%
+now let's prove the
+ 
+
+ align:start position:0%
+now let's prove the
+contracting mapping theorem
+
+ align:start position:0%
+contracting mapping theorem
+ 
+
+ align:start position:0%
+contracting mapping theorem
+using the cush convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cushion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will not prove the contracting Not going
+
+ align:start position:0%
+will not prove the contracting Not going
+ 
+
+ align:start position:0%
+will not prove the contracting Not going
+to serve.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So what is a contracting mapping
+
+ align:start position:0%
+Okay. So what is a contracting mapping
+ 
+
+ align:start position:0%
+Okay. So what is a contracting mapping
+theorem? The contracting mapping theorem
+
+ align:start position:0%
+theorem? The contracting mapping theorem
+ 
+
+ align:start position:0%
+theorem? The contracting mapping theorem
+is that if t here is a contracting map.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So T g from R to R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maps R into R gives a contracting map.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+then T has a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We already know that such a fixed point
+
+ align:start position:0%
+We already know that such a fixed point
+ 
+
+ align:start position:0%
+We already know that such a fixed point
+is unique, right? We already proved that
+
+ align:start position:0%
+is unique, right? We already proved that
+ 
+
+ align:start position:0%
+is unique, right? We already proved that
+it can at most be one fixed point.
+
+ align:start position:0%
+it can at most be one fixed point.
+ 
+
+ align:start position:0%
+it can at most be one fixed point.
+Okay, so let's try to prove that. So
+
+ align:start position:0%
+Okay, so let's try to prove that. So
+ 
+
+ align:start position:0%
+Okay, so let's try to prove that. So
+we're going to use like this result from
+
+ align:start position:0%
+we're going to use like this result from
+ 
+
+ align:start position:0%
+we're going to use like this result from
+PC.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So I start with I start with any point
+
+ align:start position:0%
+So I start with I start with any point
+ 
+
+ align:start position:0%
+So I start with I start with any point
+X. You pick any point you want and then
+
+ align:start position:0%
+X. You pick any point you want and then
+ 
+
+ align:start position:0%
+X. You pick any point you want and then
+we form the sequence
+
+ align:start position:0%
+we form the sequence
+ 
+
+ align:start position:0%
+we form the sequence
+where you apply this uh uh end time to
+
+ align:start position:0%
+where you apply this uh uh end time to
+ 
+
+ align:start position:0%
+where you apply this uh uh end time to
+X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now we have that. So, so then we have we
+
+ align:start position:0%
+Now we have that. So, so then we have we
+ 
+
+ align:start position:0%
+Now we have that. So, so then we have we
+have so this is this pie set from P
+
+ align:start position:0%
+have so this is this pie set from P
+ 
+
+ align:start position:0%
+have so this is this pie set from P
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a
+
+ align:start position:0%
+that a
+ 
+
+ align:start position:0%
+that a
+is a sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay. But then the but then from the
+
+ align:start position:0%
+Okay. But then the but then from the
+ 
+
+ align:start position:0%
+Okay. But then the but then from the
+from Kushik convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh we have that am
+
+ align:start position:0%
+uh we have that am
+ 
+
+ align:start position:0%
+uh we have that am
+is converging right that this here is
+
+ align:start position:0%
+is converging right that this here is
+ 
+
+ align:start position:0%
+is converging right that this here is
+this here is a cushy sequence but the
+
+ align:start position:0%
+this here is a cushy sequence but the
+ 
+
+ align:start position:0%
+this here is a cushy sequence but the
+cus convergence I'm saying that any
+
+ align:start position:0%
+cus convergence I'm saying that any
+ 
+
+ align:start position:0%
+cus convergence I'm saying that any
+cushy sequence is actually convergent so
+
+ align:start position:0%
+cushy sequence is actually convergent so
+ 
+
+ align:start position:0%
+cushy sequence is actually convergent so
+this here converts to some a
+
+ align:start position:0%
+this here converts to some a
+ 
+
+ align:start position:0%
+this here converts to some a
+okay and now the idea is that we want to
+
+ align:start position:0%
+okay and now the idea is that we want to
+ 
+
+ align:start position:0%
+okay and now the idea is that we want to
+show so want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+a is a fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's
+
+ align:start position:0%
+So that's
+ 
+
+ align:start position:0%
+So that's
+this is a kind of uh it's a you know
+
+ align:start position:0%
+this is a kind of uh it's a you know
+ 
+
+ align:start position:0%
+this is a kind of uh it's a you know
+it's it's it's the contracting mapping
+
+ align:start position:0%
+it's it's it's the contracting mapping
+ 
+
+ align:start position:0%
+it's it's it's the contracting mapping
+is actually extremely powerful
+
+ align:start position:0%
+is actually extremely powerful
+ 
+
+ align:start position:0%
+is actually extremely powerful
+uh it can be used to again can be used
+
+ align:start position:0%
+uh it can be used to again can be used
+ 
+
+ align:start position:0%
+uh it can be used to again can be used
+to solve
+
+ align:start position:0%
+to solve
+ 
+
+ align:start position:0%
+to solve
+uh you know uh what's called o ordinary
+
+ align:start position:0%
+uh you know uh what's called o ordinary
+ 
+
+ align:start position:0%
+uh you know uh what's called o ordinary
+differential equations.
+
+ align:start position:0%
+differential equations.
+ 
+
+ align:start position:0%
+differential equations.
+And we talk a little bit about that at
+
+ align:start position:0%
+And we talk a little bit about that at
+ 
+
+ align:start position:0%
+And we talk a little bit about that at
+some later point in the class. And but
+
+ align:start position:0%
+some later point in the class. And but
+ 
+
+ align:start position:0%
+some later point in the class. And but
+it can also be used to solve uh PDS
+
+ align:start position:0%
+it can also be used to solve uh PDS
+ 
+
+ align:start position:0%
+it can also be used to solve uh PDS
+which is more complicated partial
+
+ align:start position:0%
+which is more complicated partial
+ 
+
+ align:start position:0%
+which is more complicated partial
+differential equation and in all kind of
+
+ align:start position:0%
+differential equation and in all kind of
+ 
+
+ align:start position:0%
+differential equation and in all kind of
+other areas of math. Um and um
+
+ align:start position:0%
+other areas of math. Um and um
+ 
+
+ align:start position:0%
+other areas of math. Um and um
+okay so now we want to prove that this a
+
+ align:start position:0%
+okay so now we want to prove that this a
+ 
+
+ align:start position:0%
+okay so now we want to prove that this a
+here is a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+have and and we we will come back in
+
+ align:start position:0%
+have and and we we will come back in
+ 
+
+ align:start position:0%
+have and and we we will come back in
+just a minute we'll through something
+
+ align:start position:0%
+just a minute we'll through something
+ 
+
+ align:start position:0%
+just a minute we'll through something
+um related to this but but let me just
+
+ align:start position:0%
+um related to this but but let me just
+ 
+
+ align:start position:0%
+um related to this but but let me just
+very simple uh so I talking about a n
+
+ align:start position:0%
+very simple uh so I talking about a n
+ 
+
+ align:start position:0%
+very simple uh so I talking about a n
+here I know that it's converted to a I
+
+ align:start position:0%
+here I know that it's converted to a I
+ 
+
+ align:start position:0%
+here I know that it's converted to a I
+then look at the sequence t of a
+
+ align:start position:0%
+then look at the sequence t of a
+ 
+
+ align:start position:0%
+then look at the sequence t of a
+Well, t of a n that was a n was wrong,
+
+ align:start position:0%
+Well, t of a n that was a n was wrong,
+ 
+
+ align:start position:0%
+Well, t of a n that was a n was wrong,
+right? It was just one further out of
+
+ align:start position:0%
+right? It was just one further out of
+ 
+
+ align:start position:0%
+right? It was just one further out of
+the sequence, right? But so since a
+
+ align:start position:0%
+the sequence, right? But so since a
+ 
+
+ align:start position:0%
+the sequence, right? But so since a
+converge, this means of course that
+
+ align:start position:0%
+converge, this means of course that
+ 
+
+ align:start position:0%
+converge, this means of course that
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+since a n converts to a n, this means
+
+ align:start position:0%
+since a n converts to a n, this means
+ 
+
+ align:start position:0%
+since a n converts to a n, this means
+that this here will also converge to a
+
+ align:start position:0%
+that this here will also converge to a
+ 
+
+ align:start position:0%
+that this here will also converge to a
+n. So since this here a n + one as n
+
+ align:start position:0%
+n. So since this here a n + one as n
+ 
+
+ align:start position:0%
+n. So since this here a n + one as n
+become very large for converge to
+
+ align:start position:0%
+become very large for converge to
+ 
+
+ align:start position:0%
+become very large for converge to
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if you're looking at t
+
+ align:start position:0%
+if you're looking at t
+ 
+
+ align:start position:0%
+if you're looking at t
+of a n
+
+ align:start position:0%
+of a n
+ 
+
+ align:start position:0%
+of a n
+so you want to estimate now
+
+ align:start position:0%
+so you want to estimate now
+ 
+
+ align:start position:0%
+so you want to estimate now
+uh so what I want to prove is right so
+
+ align:start position:0%
+uh so what I want to prove is right so
+ 
+
+ align:start position:0%
+uh so what I want to prove is right so
+now I'm looking at this distance so I
+
+ align:start position:0%
+now I'm looking at this distance so I
+ 
+
+ align:start position:0%
+now I'm looking at this distance so I
+want to show
+
+ align:start position:0%
+want to show
+ 
+
+ align:start position:0%
+want to show
+So want to show we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that C of A right is equal to A. That's
+
+ align:start position:0%
+that C of A right is equal to A. That's
+ 
+
+ align:start position:0%
+that C of A right is equal to A. That's
+what we want to do.
+
+ align:start position:0%
+what we want to do.
+ 
+
+ align:start position:0%
+what we want to do.
+And so if I'm looking at T of A N,
+
+ align:start position:0%
+And so if I'm looking at T of A N,
+ 
+
+ align:start position:0%
+And so if I'm looking at T of A N,
+right? T of A N, this here was A N +
+
+ align:start position:0%
+right? T of A N, this here was A N +
+ 
+
+ align:start position:0%
+right? T of A N, this here was A N +
+one. And so if I'm looking at t of a n
+
+ align:start position:0%
+one. And so if I'm looking at t of a n
+ 
+
+ align:start position:0%
+one. And so if I'm looking at t of a n
+plus uh a n minus uh t of a
+
+ align:start position:0%
+plus uh a n minus uh t of a
+ 
+
+ align:start position:0%
+plus uh a n minus uh t of a
+right because it is a contracting map
+
+ align:start position:0%
+right because it is a contracting map
+ 
+
+ align:start position:0%
+right because it is a contracting map
+this thing here is bounded is lesser
+
+ align:start position:0%
+this thing here is bounded is lesser
+ 
+
+ align:start position:0%
+this thing here is bounded is lesser
+equal to c a n minus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is also equal to a n + 1 - g of
+
+ align:start position:0%
+and this is also equal to a n + 1 - g of
+ 
+
+ align:start position:0%
+and this is also equal to a n + 1 - g of
+That was just the definition of the a +
+
+ align:start position:0%
+That was just the definition of the a +
+ 
+
+ align:start position:0%
+That was just the definition of the a +
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+So now I have that a m converts to a. So
+
+ align:start position:0%
+So now I have that a m converts to a. So
+ 
+
+ align:start position:0%
+So now I have that a m converts to a. So
+this means that this here converts to
+
+ align:start position:0%
+this means that this here converts to
+ 
+
+ align:start position:0%
+this means that this here converts to
+zero. Right? Since so now since
+
+ align:start position:0%
+zero. Right? Since so now since
+ 
+
+ align:start position:0%
+zero. Right? Since so now since
+a n converts to a then you have that a n
+
+ align:start position:0%
+a n converts to a then you have that a n
+ 
+
+ align:start position:0%
+a n converts to a then you have that a n
+minus a you can think about this as a
+
+ align:start position:0%
+minus a you can think about this as a
+ 
+
+ align:start position:0%
+minus a you can think about this as a
+sequence that converts to zero.
+
+ align:start position:0%
+sequence that converts to zero.
+ 
+
+ align:start position:0%
+sequence that converts to zero.
+But this inequality here say that since
+
+ align:start position:0%
+But this inequality here say that since
+ 
+
+ align:start position:0%
+But this inequality here say that since
+this goes to zero this in here must also
+
+ align:start position:0%
+this goes to zero this in here must also
+ 
+
+ align:start position:0%
+this goes to zero this in here must also
+go to zero. So you see that therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a n + one minus t of a
+
+ align:start position:0%
+a n + one minus t of a
+ 
+
+ align:start position:0%
+a n + one minus t of a
+goes to zero. Right? So but this but
+
+ align:start position:0%
+goes to zero. Right? So but this but
+ 
+
+ align:start position:0%
+goes to zero. Right? So but this but
+that this here goes to zero. This just
+
+ align:start position:0%
+that this here goes to zero. This just
+ 
+
+ align:start position:0%
+that this here goes to zero. This just
+means that a n + one this much converge
+
+ align:start position:0%
+means that a n + one this much converge
+ 
+
+ align:start position:0%
+means that a n + one this much converge
+to t of a
+
+ align:start position:0%
+to t of a
+ 
+
+ align:start position:0%
+to t of a
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+But this sequence already converts to a.
+
+ align:start position:0%
+But this sequence already converts to a.
+ 
+
+ align:start position:0%
+But this sequence already converts to a.
+There can only be one limit. Right? So
+
+ align:start position:0%
+There can only be one limit. Right? So
+ 
+
+ align:start position:0%
+There can only be one limit. Right? So
+we already had that a m + one converts
+
+ align:start position:0%
+we already had that a m + one converts
+ 
+
+ align:start position:0%
+we already had that a m + one converts
+to a. But then these two numbers must be
+
+ align:start position:0%
+to a. But then these two numbers must be
+ 
+
+ align:start position:0%
+to a. But then these two numbers must be
+the same. Right? So the conclusion here
+
+ align:start position:0%
+the same. Right? So the conclusion here
+ 
+
+ align:start position:0%
+the same. Right? So the conclusion here
+is that that a must be equal to g of a.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So from the cus convergence theorem
+
+ align:start position:0%
+So from the cus convergence theorem
+ 
+
+ align:start position:0%
+So from the cus convergence theorem
+then you get the contracting mapping
+
+ align:start position:0%
+then you get the contracting mapping
+ 
+
+ align:start position:0%
+then you get the contracting mapping
+thems
+
+ align:start position:0%
+thems
+ 
+
+ align:start position:0%
+thems
+and and we already proved that there was
+
+ align:start position:0%
+and and we already proved that there was
+ 
+
+ align:start position:0%
+and and we already proved that there was
+you get a fixed point and we already
+
+ align:start position:0%
+you get a fixed point and we already
+ 
+
+ align:start position:0%
+you get a fixed point and we already
+knew that there was at most one fix
+
+ align:start position:0%
+knew that there was at most one fix
+ 
+
+ align:start position:0%
+knew that there was at most one fix
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+and so so and so this is a very powerful
+
+ align:start position:0%
+and so so and so this is a very powerful
+ 
+
+ align:start position:0%
+and so so and so this is a very powerful
+idea because for many things
+
+ align:start position:0%
+idea because for many things
+ 
+
+ align:start position:0%
+idea because for many things
+it's almost impossible to find the
+
+ align:start position:0%
+it's almost impossible to find the
+ 
+
+ align:start position:0%
+it's almost impossible to find the
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+fix point. But what you do is that
+
+ align:start position:0%
+fix point. But what you do is that
+ 
+
+ align:start position:0%
+fix point. But what you do is that
+you're starting with some right. So in
+
+ align:start position:0%
+you're starting with some right. So in
+ 
+
+ align:start position:0%
+you're starting with some right. So in
+this case you just said you pick any X
+
+ align:start position:0%
+this case you just said you pick any X
+ 
+
+ align:start position:0%
+this case you just said you pick any X
+and then you just apply the map enough
+
+ align:start position:0%
+and then you just apply the map enough
+ 
+
+ align:start position:0%
+and then you just apply the map enough
+times. Right? Sometimes you would start
+
+ align:start position:0%
+times. Right? Sometimes you would start
+ 
+
+ align:start position:0%
+times. Right? Sometimes you would start
+with a you can't
+
+ align:start position:0%
+with a you can't
+ 
+
+ align:start position:0%
+with a you can't
+find a fix point but you can find
+
+ align:start position:0%
+find a fix point but you can find
+ 
+
+ align:start position:0%
+find a fix point but you can find
+something pretty close to the fix point
+
+ align:start position:0%
+something pretty close to the fix point
+ 
+
+ align:start position:0%
+something pretty close to the fix point
+and then then you iterate from there on
+
+ align:start position:0%
+and then then you iterate from there on
+ 
+
+ align:start position:0%
+and then then you iterate from there on
+and we'll see we'll see just in a
+
+ align:start position:0%
+and we'll see we'll see just in a
+ 
+
+ align:start position:0%
+and we'll see we'll see just in a
+second. which I already talked about
+
+ align:start position:0%
+second. which I already talked about
+ 
+
+ align:start position:0%
+second. which I already talked about
+that this applied to the existence
+
+ align:start position:0%
+that this applied to the existence
+ 
+
+ align:start position:0%
+that this applied to the existence
+of solutions to OD and to PD. And now
+
+ align:start position:0%
+of solutions to OD and to PD. And now
+ 
+
+ align:start position:0%
+of solutions to OD and to PD. And now
+let me illustrate this last point.
+
+ align:start position:0%
+let me illustrate this last point.
+ 
+
+ align:start position:0%
+let me illustrate this last point.
+Another example and this come backs to
+
+ align:start position:0%
+Another example and this come backs to
+ 
+
+ align:start position:0%
+Another example and this come backs to
+your question uh about you know is this
+
+ align:start position:0%
+your question uh about you know is this
+ 
+
+ align:start position:0%
+your question uh about you know is this
+the same but but do think about it as
+
+ align:start position:0%
+the same but but do think about it as
+ 
+
+ align:start position:0%
+the same but but do think about it as
+being the same for all X and Y. But you
+
+ align:start position:0%
+being the same for all X and Y. But you
+ 
+
+ align:start position:0%
+being the same for all X and Y. But you
+could have some kind of local statement
+
+ align:start position:0%
+could have some kind of local statement
+ 
+
+ align:start position:0%
+could have some kind of local statement
+where it was true for X and Y in some
+
+ align:start position:0%
+where it was true for X and Y in some
+ 
+
+ align:start position:0%
+where it was true for X and Y in some
+small range and that would be enough to
+
+ align:start position:0%
+small range and that would be enough to
+ 
+
+ align:start position:0%
+small range and that would be enough to
+guarantee you a fix point. But but but
+
+ align:start position:0%
+guarantee you a fix point. But but but
+ 
+
+ align:start position:0%
+guarantee you a fix point. But but but
+in general just I mean it's the same in
+
+ align:start position:0%
+in general just I mean it's the same in
+ 
+
+ align:start position:0%
+in general just I mean it's the same in
+the definition it's supposed to be the
+
+ align:start position:0%
+the definition it's supposed to be the
+ 
+
+ align:start position:0%
+the definition it's supposed to be the
+same for all x and y but so let me
+
+ align:start position:0%
+same for all x and y but so let me
+ 
+
+ align:start position:0%
+same for all x and y but so let me
+explain that
+
+ align:start position:0%
+explain that
+ 
+
+ align:start position:0%
+explain that
+in what's called Newton method.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is Newton measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the idea is that you have a
+
+ align:start position:0%
+and so the idea is that you have a
+ 
+
+ align:start position:0%
+and so the idea is that you have a
+function you have some function here f
+
+ align:start position:0%
+function you have some function here f
+ 
+
+ align:start position:0%
+function you have some function here f
+maybe it doesn't look like a function
+
+ align:start position:0%
+maybe it doesn't look like a function
+ 
+
+ align:start position:0%
+maybe it doesn't look like a function
+but it's supposed to this is f ofx
+
+ align:start position:0%
+but it's supposed to this is f ofx
+ 
+
+ align:start position:0%
+but it's supposed to this is f ofx
+and you want to find where this or you
+
+ align:start position:0%
+and you want to find where this or you
+ 
+
+ align:start position:0%
+and you want to find where this or you
+want to find points where this function
+
+ align:start position:0%
+want to find points where this function
+ 
+
+ align:start position:0%
+want to find points where this function
+vanishes. Okay.
+
+ align:start position:0%
+vanishes. Okay.
+ 
+
+ align:start position:0%
+vanishes. Okay.
+And so so the method is sort of a
+
+ align:start position:0%
+And so so the method is sort of a
+ 
+
+ align:start position:0%
+And so so the method is sort of a
+numerical method to find such a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know just you know if if this
+
+ align:start position:0%
+you know just you know if if this
+ 
+
+ align:start position:0%
+you know just you know if if this
+function was very simple like a linear
+
+ align:start position:0%
+function was very simple like a linear
+ 
+
+ align:start position:0%
+function was very simple like a linear
+function or quadratic function then of
+
+ align:start position:0%
+function or quadratic function then of
+ 
+
+ align:start position:0%
+function or quadratic function then of
+course it would be easy to find but
+
+ align:start position:0%
+course it would be easy to find but
+ 
+
+ align:start position:0%
+course it would be easy to find but
+maybe this is a very complicated
+
+ align:start position:0%
+maybe this is a very complicated
+ 
+
+ align:start position:0%
+maybe this is a very complicated
+function and so you wouldn't be you
+
+ align:start position:0%
+function and so you wouldn't be you
+ 
+
+ align:start position:0%
+function and so you wouldn't be you
+wouldn't necessarily be able to say
+
+ align:start position:0%
+wouldn't necessarily be able to say
+ 
+
+ align:start position:0%
+wouldn't necessarily be able to say
+exactly what the point is
+
+ align:start position:0%
+exactly what the point is
+ 
+
+ align:start position:0%
+exactly what the point is
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the idea is that so Newton method
+
+ align:start position:0%
+the idea is that so Newton method
+ 
+
+ align:start position:0%
+the idea is that so Newton method
+Newton method is that Newton's methods
+
+ align:start position:0%
+Newton method is that Newton's methods
+ 
+
+ align:start position:0%
+Newton method is that Newton's methods
+require that you start with a good guess
+
+ align:start position:0%
+require that you start with a good guess
+ 
+
+ align:start position:0%
+require that you start with a good guess
+and but this is the idea of the Newton
+
+ align:start position:0%
+and but this is the idea of the Newton
+ 
+
+ align:start position:0%
+and but this is the idea of the Newton
+method.
+
+ align:start position:0%
+method.
+ 
+
+ align:start position:0%
+method.
+So here's the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we're looking at a function like
+
+ align:start position:0%
+that we're looking at a function like
+ 
+
+ align:start position:0%
+that we're looking at a function like
+this. I'm going to assume that this is
+
+ align:start position:0%
+this. I'm going to assume that this is
+ 
+
+ align:start position:0%
+this. I'm going to assume that this is
+um that is not zero. So it's actually
+
+ align:start position:0%
+um that is not zero. So it's actually
+ 
+
+ align:start position:0%
+um that is not zero. So it's actually
+monotom is either increasing or
+
+ align:start position:0%
+monotom is either increasing or
+ 
+
+ align:start position:0%
+monotom is either increasing or
+decreasing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I I'm assuming that there's nowhere
+
+ align:start position:0%
+So I I'm assuming that there's nowhere
+ 
+
+ align:start position:0%
+So I I'm assuming that there's nowhere
+where the the fractional vanishes.
+
+ align:start position:0%
+where the the fractional vanishes.
+ 
+
+ align:start position:0%
+where the the fractional vanishes.
+And then I defined a map t of x to be
+
+ align:start position:0%
+And then I defined a map t of x to be
+ 
+
+ align:start position:0%
+And then I defined a map t of x to be
+equal to x
+
+ align:start position:0%
+equal to x
+ 
+
+ align:start position:0%
+equal to x
+minus uh f ofx
+
+ align:start position:0%
+minus uh f ofx
+ 
+
+ align:start position:0%
+minus uh f ofx
+frime of x. This seems kind of uh quite
+
+ align:start position:0%
+frime of x. This seems kind of uh quite
+ 
+
+ align:start position:0%
+frime of x. This seems kind of uh quite
+it seems uh yeah seems far away from
+
+ align:start position:0%
+it seems uh yeah seems far away from
+ 
+
+ align:start position:0%
+it seems uh yeah seems far away from
+now. But if you define it like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now let me take the derivative of this.
+
+ align:start position:0%
+Now let me take the derivative of this.
+ 
+
+ align:start position:0%
+Now let me take the derivative of this.
+If I take the derivative of this now
+
+ align:start position:0%
+If I take the derivative of this now
+ 
+
+ align:start position:0%
+If I take the derivative of this now
+then I get that this in here the
+
+ align:start position:0%
+then I get that this in here the
+ 
+
+ align:start position:0%
+then I get that this in here the
+derivative of x that's just one. The
+
+ align:start position:0%
+derivative of x that's just one. The
+ 
+
+ align:start position:0%
+derivative of x that's just one. The
+derivative of this in here
+
+ align:start position:0%
+derivative of this in here
+ 
+
+ align:start position:0%
+derivative of this in here
+um it's the this is a closing. So it's f
+
+ align:start position:0%
+um it's the this is a closing. So it's f
+ 
+
+ align:start position:0%
+um it's the this is a closing. So it's f
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+uh times
+
+ align:start position:0%
+uh times
+ 
+
+ align:start position:0%
+uh times
+my derivative of this time frime and
+
+ align:start position:0%
+my derivative of this time frime and
+ 
+
+ align:start position:0%
+my derivative of this time frime and
+then f prime squ minus
+
+ align:start position:0%
+then f prime squ minus
+ 
+
+ align:start position:0%
+then f prime squ minus
+and then uh f fp prime like that right
+
+ align:start position:0%
+and then uh f fp prime like that right
+ 
+
+ align:start position:0%
+and then uh f fp prime like that right
+that's a quotion for taking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you see that you can write this
+
+ align:start position:0%
+and so you see that you can write this
+ 
+
+ align:start position:0%
+and so you see that you can write this
+if you split this up into two this has
+
+ align:start position:0%
+if you split this up into two this has
+ 
+
+ align:start position:0%
+if you split this up into two this has
+one you split it up to two this has
+
+ align:start position:0%
+one you split it up to two this has
+ 
+
+ align:start position:0%
+one you split it up to two this has
+frime
+
+ align:start position:0%
+frime
+ 
+
+ align:start position:0%
+frime
+2 / frime squ and then this here becomes
+
+ align:start position:0%
+2 / frime squ and then this here becomes
+ 
+
+ align:start position:0%
+2 / frime squ and then this here becomes
+plus and then I'm writing it as f f
+
+ align:start position:0%
+plus and then I'm writing it as f f
+ 
+
+ align:start position:0%
+plus and then I'm writing it as f f
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+fr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you see that this here cancel
+
+ align:start position:0%
+and so you see that this here cancel
+ 
+
+ align:start position:0%
+and so you see that this here cancel
+with that so these are cancel so you
+
+ align:start position:0%
+with that so these are cancel so you
+ 
+
+ align:start position:0%
+with that so these are cancel so you
+have that the derivative of this map
+
+ align:start position:0%
+have that the derivative of this map
+ 
+
+ align:start position:0%
+have that the derivative of this map
+is just f of x
+
+ align:start position:0%
+is just f of x
+ 
+
+ align:start position:0%
+is just f of x
+uh frime prime of x frime of x²
+
+ align:start position:0%
+uh frime prime of x frime of x²
+ 
+
+ align:start position:0%
+uh frime prime of x frime of x²
+that's the derivative
+
+ align:start position:0%
+that's the derivative
+ 
+
+ align:start position:0%
+that's the derivative
+and now of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I'm using the mean magnet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then I have that uh derivative.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then I have that t of x minus t of y. By
+
+ align:start position:0%
+Then I have that t of x minus t of y. By
+ 
+
+ align:start position:0%
+Then I have that t of x minus t of y. By
+the mean man theorem say that this thing
+
+ align:start position:0%
+the mean man theorem say that this thing
+ 
+
+ align:start position:0%
+the mean man theorem say that this thing
+here is the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's actually like wer theorem or
+
+ align:start position:0%
+it's actually like wer theorem or
+ 
+
+ align:start position:0%
+it's actually like wer theorem or
+whatever but but you can also think
+
+ align:start position:0%
+whatever but but you can also think
+ 
+
+ align:start position:0%
+whatever but but you can also think
+about this is the derivative at
+
+ align:start position:0%
+about this is the derivative at
+ 
+
+ align:start position:0%
+about this is the derivative at
+somewhere in between x and y times the
+
+ align:start position:0%
+somewhere in between x and y times the
+ 
+
+ align:start position:0%
+somewhere in between x and y times the
+difference between x and y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so We see that if we already knew. So if
+
+ align:start position:0%
+so We see that if we already knew. So if
+ 
+
+ align:start position:0%
+so We see that if we already knew. So if
+we can show if we knew
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the derivative
+
+ align:start position:0%
+that the derivative
+ 
+
+ align:start position:0%
+that the derivative
+was bounded everywhere was bounded by
+
+ align:start position:0%
+was bounded everywhere was bounded by
+ 
+
+ align:start position:0%
+was bounded everywhere was bounded by
+some C little C that was less than one.
+
+ align:start position:0%
+some C little C that was less than one.
+ 
+
+ align:start position:0%
+some C little C that was less than one.
+If you had that then of course then you
+
+ align:start position:0%
+If you had that then of course then you
+ 
+
+ align:start position:0%
+If you had that then of course then you
+just take absolute value of this. So
+
+ align:start position:0%
+just take absolute value of this. So
+ 
+
+ align:start position:0%
+just take absolute value of this. So
+then you had the t of x minus t of y the
+
+ align:start position:0%
+then you had the t of x minus t of y the
+ 
+
+ align:start position:0%
+then you had the t of x minus t of y the
+absolute value was was equal to t prime
+
+ align:start position:0%
+absolute value was was equal to t prime
+ 
+
+ align:start position:0%
+absolute value was was equal to t prime
+in this intermediate point x - y but in
+
+ align:start position:0%
+in this intermediate point x - y but in
+ 
+
+ align:start position:0%
+in this intermediate point x - y but in
+this intermediate point we're assuming
+
+ align:start position:0%
+this intermediate point we're assuming
+ 
+
+ align:start position:0%
+this intermediate point we're assuming
+that everywhere the derivative is lesser
+
+ align:start position:0%
+that everywhere the derivative is lesser
+ 
+
+ align:start position:0%
+that everywhere the derivative is lesser
+equal to c. So this here is now this is
+
+ align:start position:0%
+equal to c. So this here is now this is
+ 
+
+ align:start position:0%
+equal to c. So this here is now this is
+lesser equal to c. So c x - y and we're
+
+ align:start position:0%
+lesser equal to c. So c x - y and we're
+ 
+
+ align:start position:0%
+lesser equal to c. So c x - y and we're
+assuming that c is strictly less than
+
+ align:start position:0%
+assuming that c is strictly less than
+ 
+
+ align:start position:0%
+assuming that c is strictly less than
+one. So you see that this here if we
+
+ align:start position:0%
+one. So you see that this here if we
+ 
+
+ align:start position:0%
+one. So you see that this here if we
+knew that the derivative of t was
+
+ align:start position:0%
+knew that the derivative of t was
+ 
+
+ align:start position:0%
+knew that the derivative of t was
+strictly less than one everywhere then
+
+ align:start position:0%
+strictly less than one everywhere then
+ 
+
+ align:start position:0%
+strictly less than one everywhere then
+we would know that this map was
+
+ align:start position:0%
+we would know that this map was
+ 
+
+ align:start position:0%
+we would know that this map was
+contracting that.
+
+ align:start position:0%
+contracting that.
+ 
+
+ align:start position:0%
+contracting that.
+Okay. But but of course you know what we
+
+ align:start position:0%
+Okay. But but of course you know what we
+ 
+
+ align:start position:0%
+Okay. But but of course you know what we
+have for the derivative is we have this
+
+ align:start position:0%
+have for the derivative is we have this
+ 
+
+ align:start position:0%
+have for the derivative is we have this
+in here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now but now the idea is that if
+
+ align:start position:0%
+And so now but now the idea is that if
+ 
+
+ align:start position:0%
+And so now but now the idea is that if
+you start with a really good guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you start with a so so the idea is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so idea
+
+ align:start position:0%
+so so idea
+ 
+
+ align:start position:0%
+so so idea
+the idea of with Newton method
+
+ align:start position:0%
+the idea of with Newton method
+ 
+
+ align:start position:0%
+the idea of with Newton method
+is start with a good this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this and I'm not going to make that
+
+ align:start position:0%
+like this and I'm not going to make that
+ 
+
+ align:start position:0%
+like this and I'm not going to make that
+too precise.
+
+ align:start position:0%
+too precise.
+ 
+
+ align:start position:0%
+too precise.
+I'm putting it in quotation marks but
+
+ align:start position:0%
+I'm putting it in quotation marks but
+ 
+
+ align:start position:0%
+I'm putting it in quotation marks but
+the idea is that you want to so good
+
+ align:start position:0%
+the idea is that you want to so good
+ 
+
+ align:start position:0%
+the idea is that you want to so good
+guesses remember that what we want is we
+
+ align:start position:0%
+guesses remember that what we want is we
+ 
+
+ align:start position:0%
+guesses remember that what we want is we
+want to find a point we're interested in
+
+ align:start position:0%
+want to find a point we're interested in
+ 
+
+ align:start position:0%
+want to find a point we're interested in
+this point here where this function here
+
+ align:start position:0%
+this point here where this function here
+ 
+
+ align:start position:0%
+this point here where this function here
+we're interested in a point where the
+
+ align:start position:0%
+we're interested in a point where the
+ 
+
+ align:start position:0%
+we're interested in a point where the
+function vanishes right so starting with
+
+ align:start position:0%
+function vanishes right so starting with
+ 
+
+ align:start position:0%
+function vanishes right so starting with
+a good guess means that you're starting
+
+ align:start position:0%
+a good guess means that you're starting
+ 
+
+ align:start position:0%
+a good guess means that you're starting
+you may not start where the function
+
+ align:start position:0%
+you may not start where the function
+ 
+
+ align:start position:0%
+you may not start where the function
+vanishes but you're starting somewhere
+
+ align:start position:0%
+vanishes but you're starting somewhere
+ 
+
+ align:start position:0%
+vanishes but you're starting somewhere
+where where the values is really small,
+
+ align:start position:0%
+where where the values is really small,
+ 
+
+ align:start position:0%
+where where the values is really small,
+right? That would be a good guess,
+
+ align:start position:0%
+right? That would be a good guess,
+ 
+
+ align:start position:0%
+right? That would be a good guess,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And so start with a good guess meaning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that f at that point
+
+ align:start position:0%
+that f at that point
+ 
+
+ align:start position:0%
+that f at that point
+is is is small
+
+ align:start position:0%
+is is is small
+ 
+
+ align:start position:0%
+is is is small
+is is very small.
+
+ align:start position:0%
+is is very small.
+ 
+
+ align:start position:0%
+is is very small.
+Now, of course, you're going to ask what
+
+ align:start position:0%
+Now, of course, you're going to ask what
+ 
+
+ align:start position:0%
+Now, of course, you're going to ask what
+do you mean by very small? So very small
+
+ align:start position:0%
+do you mean by very small? So very small
+ 
+
+ align:start position:0%
+do you mean by very small? So very small
+here is going to mean that the value.
+
+ align:start position:0%
+here is going to mean that the value.
+ 
+
+ align:start position:0%
+here is going to mean that the value.
+So so now we have right from this here.
+
+ align:start position:0%
+So so now we have right from this here.
+ 
+
+ align:start position:0%
+So so now we have right from this here.
+So we have that we have that the
+
+ align:start position:0%
+So we have that we have that the
+ 
+
+ align:start position:0%
+So we have that we have that the
+derivative here of this map here
+
+ align:start position:0%
+derivative here of this map here
+ 
+
+ align:start position:0%
+derivative here of this map here
+was equal to these two terms cancel out.
+
+ align:start position:0%
+was equal to these two terms cancel out.
+ 
+
+ align:start position:0%
+was equal to these two terms cancel out.
+So this is f of x f prime of x
+
+ align:start position:0%
+So this is f of x f prime of x
+ 
+
+ align:start position:0%
+So this is f of x f prime of x
+uh frime
+
+ align:start position:0%
+uh frime
+ 
+
+ align:start position:0%
+uh frime
+of x².
+
+ align:start position:0%
+of x².
+ 
+
+ align:start position:0%
+of x².
+So starting with a good guess means that
+
+ align:start position:0%
+So starting with a good guess means that
+ 
+
+ align:start position:0%
+So starting with a good guess means that
+this thing here is really really small
+
+ align:start position:0%
+this thing here is really really small
+ 
+
+ align:start position:0%
+this thing here is really really small
+and in fact I want it to be small
+
+ align:start position:0%
+and in fact I want it to be small
+ 
+
+ align:start position:0%
+and in fact I want it to be small
+compared with this. Right? So if this
+
+ align:start position:0%
+compared with this. Right? So if this
+ 
+
+ align:start position:0%
+compared with this. Right? So if this
+here is really small compared with that
+
+ align:start position:0%
+here is really small compared with that
+ 
+
+ align:start position:0%
+here is really small compared with that
+then I can guarantee that the absolute
+
+ align:start position:0%
+then I can guarantee that the absolute
+ 
+
+ align:start position:0%
+then I can guarantee that the absolute
+value of this is smaller than one.
+
+ align:start position:0%
+value of this is smaller than one.
+ 
+
+ align:start position:0%
+value of this is smaller than one.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And so you see that if you start with a
+
+ align:start position:0%
+And so you see that if you start with a
+ 
+
+ align:start position:0%
+And so you see that if you start with a
+really good guess then it would be a
+
+ align:start position:0%
+really good guess then it would be a
+ 
+
+ align:start position:0%
+really good guess then it would be a
+contracting mapping right and then of
+
+ align:start position:0%
+contracting mapping right and then of
+ 
+
+ align:start position:0%
+contracting mapping right and then of
+course you need to prove that so you're
+
+ align:start position:0%
+course you need to prove that so you're
+ 
+
+ align:start position:0%
+course you need to prove that so you're
+forming the sequence right and you need
+
+ align:start position:0%
+forming the sequence right and you need
+ 
+
+ align:start position:0%
+forming the sequence right and you need
+to prove somehow you need to estimate
+
+ align:start position:0%
+to prove somehow you need to estimate
+ 
+
+ align:start position:0%
+to prove somehow you need to estimate
+that you need to be able to say that
+
+ align:start position:0%
+that you need to be able to say that
+ 
+
+ align:start position:0%
+that you need to be able to say that
+that once you form the sequence you you
+
+ align:start position:0%
+that once you form the sequence you you
+ 
+
+ align:start position:0%
+that once you form the sequence you you
+know the next thing that is spitting out
+
+ align:start position:0%
+know the next thing that is spitting out
+ 
+
+ align:start position:0%
+know the next thing that is spitting out
+is also a good guess right so that you
+
+ align:start position:0%
+is also a good guess right so that you
+ 
+
+ align:start position:0%
+is also a good guess right so that you
+stay in this range of good guess, right?
+
+ align:start position:0%
+stay in this range of good guess, right?
+ 
+
+ align:start position:0%
+stay in this range of good guess, right?
+And if it has this property, then it
+
+ align:start position:0%
+And if it has this property, then it
+ 
+
+ align:start position:0%
+And if it has this property, then it
+would be a contracting map and you would
+
+ align:start position:0%
+would be a contracting map and you would
+ 
+
+ align:start position:0%
+would be a contracting map and you would
+guarantee to get a fixed point, right?
+
+ align:start position:0%
+guarantee to get a fixed point, right?
+ 
+
+ align:start position:0%
+guarantee to get a fixed point, right?
+But and but that's all the Newton
+
+ align:start position:0%
+But and but that's all the Newton
+ 
+
+ align:start position:0%
+But and but that's all the Newton
+methods say, right? So you need to kind
+
+ align:start position:0%
+methods say, right? So you need to kind
+ 
+
+ align:start position:0%
+methods say, right? So you need to kind
+of justify why if you start with a good
+
+ align:start position:0%
+of justify why if you start with a good
+ 
+
+ align:start position:0%
+of justify why if you start with a good
+guess, why you keep as you're iterating
+
+ align:start position:0%
+guess, why you keep as you're iterating
+ 
+
+ align:start position:0%
+guess, why you keep as you're iterating
+this process, why you keep in the range
+
+ align:start position:0%
+this process, why you keep in the range
+ 
+
+ align:start position:0%
+this process, why you keep in the range
+of good guesses.
+
+ align:start position:0%
+of good guesses.
+ 
+
+ align:start position:0%
+of good guesses.
+But but but you know the news method
+
+ align:start position:0%
+But but but you know the news method
+ 
+
+ align:start position:0%
+But but but you know the news method
+doesn't doesn't tell you anything about
+
+ align:start position:0%
+doesn't doesn't tell you anything about
+ 
+
+ align:start position:0%
+doesn't doesn't tell you anything about
+that but but but it require that to be a
+
+ align:start position:0%
+that but but but it require that to be a
+ 
+
+ align:start position:0%
+that but but but it require that to be a
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+and so okay so it's a contracting map
+
+ align:start position:0%
+and so okay so it's a contracting map
+ 
+
+ align:start position:0%
+and so okay so it's a contracting map
+this T is a contracting map right if if
+
+ align:start position:0%
+this T is a contracting map right if if
+ 
+
+ align:start position:0%
+this T is a contracting map right if if
+I can start with a good guess and when I
+
+ align:start position:0%
+I can start with a good guess and when I
+ 
+
+ align:start position:0%
+I can start with a good guess and when I
+do this when I form so I start with this
+
+ align:start position:0%
+do this when I form so I start with this
+ 
+
+ align:start position:0%
+do this when I form so I start with this
+good guess and then I'm looking at that
+
+ align:start position:0%
+good guess and then I'm looking at that
+ 
+
+ align:start position:0%
+good guess and then I'm looking at that
+the next thing is this t of x and then I
+
+ align:start position:0%
+the next thing is this t of x and then I
+ 
+
+ align:start position:0%
+the next thing is this t of x and then I
+t^ squ of x
+
+ align:start position:0%
+t^ squ of x
+ 
+
+ align:start position:0%
+t^ squ of x
+right then and I want all of these to
+
+ align:start position:0%
+right then and I want all of these to
+ 
+
+ align:start position:0%
+right then and I want all of these to
+also be good guesses and then I'm saying
+
+ align:start position:0%
+also be good guesses and then I'm saying
+ 
+
+ align:start position:0%
+also be good guesses and then I'm saying
+that as n goes to infinity this here is
+
+ align:start position:0%
+that as n goes to infinity this here is
+ 
+
+ align:start position:0%
+that as n goes to infinity this here is
+cons
+
+ align:start position:0%
+cons
+ 
+
+ align:start position:0%
+cons
+is going to converge to this fixed point
+
+ align:start position:0%
+is going to converge to this fixed point
+ 
+
+ align:start position:0%
+is going to converge to this fixed point
+I guess I called it x well this is the
+
+ align:start position:0%
+I guess I called it x well this is the
+ 
+
+ align:start position:0%
+I guess I called it x well this is the
+fix point
+
+ align:start position:0%
+fix point
+ 
+
+ align:start position:0%
+fix point
+fix point
+
+ align:start position:0%
+fix point
+ 
+
+ align:start position:0%
+fix point
+for for t
+
+ align:start position:0%
+for for t
+ 
+
+ align:start position:0%
+for for t
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+so now we we we started with a function
+
+ align:start position:0%
+so now we we we started with a function
+ 
+
+ align:start position:0%
+so now we we we started with a function
+and what we were interested in, we
+
+ align:start position:0%
+and what we were interested in, we
+ 
+
+ align:start position:0%
+and what we were interested in, we
+wanted to find a root. So, x0 where this
+
+ align:start position:0%
+wanted to find a root. So, x0 where this
+ 
+
+ align:start position:0%
+wanted to find a root. So, x0 where this
+function vanishes, right? And I
+
+ align:start position:0%
+function vanishes, right? And I
+ 
+
+ align:start position:0%
+function vanishes, right? And I
+constructed a contracting map. But now I
+
+ align:start position:0%
+constructed a contracting map. But now I
+ 
+
+ align:start position:0%
+constructed a contracting map. But now I
+need to relate this contracting map or
+
+ align:start position:0%
+need to relate this contracting map or
+ 
+
+ align:start position:0%
+need to relate this contracting map or
+the fixed point for the contracting to
+
+ align:start position:0%
+the fixed point for the contracting to
+ 
+
+ align:start position:0%
+the fixed point for the contracting to
+the original problem. So, what is a
+
+ align:start position:0%
+the original problem. So, what is a
+ 
+
+ align:start position:0%
+the original problem. So, what is a
+fixed point for the contracting map?
+
+ align:start position:0%
+fixed point for the contracting map?
+ 
+
+ align:start position:0%
+fixed point for the contracting map?
+So the map here
+
+ align:start position:0%
+So the map here
+ 
+
+ align:start position:0%
+So the map here
+the map we defined
+
+ align:start position:0%
+the map we defined
+ 
+
+ align:start position:0%
+the map we defined
+was g of x is equal to x - fx
+
+ align:start position:0%
+was g of x is equal to x - fx
+ 
+
+ align:start position:0%
+was g of x is equal to x - fx
+over frime of x
+
+ align:start position:0%
+over frime of x
+ 
+
+ align:start position:0%
+over frime of x
+but a fixed point fixed point. So if x0
+
+ align:start position:0%
+but a fixed point fixed point. So if x0
+ 
+
+ align:start position:0%
+but a fixed point fixed point. So if x0
+is a fixed point
+
+ align:start position:0%
+is a fixed point
+ 
+
+ align:start position:0%
+is a fixed point
+then this means that uh this here is the
+
+ align:start position:0%
+then this means that uh this here is the
+ 
+
+ align:start position:0%
+then this means that uh this here is the
+same as x0 minus f of x0
+
+ align:start position:0%
+same as x0 minus f of x0
+ 
+
+ align:start position:0%
+same as x0 minus f of x0
+frime of x0
+
+ align:start position:0%
+frime of x0
+ 
+
+ align:start position:0%
+frime of x0
+and now you can just write. So therefore
+
+ align:start position:0%
+and now you can just write. So therefore
+ 
+
+ align:start position:0%
+and now you can just write. So therefore
+this implies that f of x0 minus f of x0
+
+ align:start position:0%
+this implies that f of x0 minus f of x0
+ 
+
+ align:start position:0%
+this implies that f of x0 minus f of x0
+over frime of x0 this here you subtract
+
+ align:start position:0%
+over frime of x0 this here you subtract
+ 
+
+ align:start position:0%
+over frime of x0 this here you subtract
+x0 on both sides and this is equal to
+
+ align:start position:0%
+x0 on both sides and this is equal to
+ 
+
+ align:start position:0%
+x0 on both sides and this is equal to
+zero but that of course means that
+
+ align:start position:0%
+zero but that of course means that
+ 
+
+ align:start position:0%
+zero but that of course means that
+denominator must be zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a fixed point is indeed a point where
+
+ align:start position:0%
+So a fixed point is indeed a point where
+ 
+
+ align:start position:0%
+So a fixed point is indeed a point where
+f of x0
+
+ align:start position:0%
+f of x0
+ 
+
+ align:start position:0%
+f of x0
+is equal to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+um, so now we want to prove the C
+
+ align:start position:0%
+um, so now we want to prove the C
+ 
+
+ align:start position:0%
+um, so now we want to prove the C
+convergence,
+
+ align:start position:0%
+convergence,
+ 
+
+ align:start position:0%
+convergence,
+but we're going to cheat just a little
+
+ align:start position:0%
+but we're going to cheat just a little
+ 
+
+ align:start position:0%
+but we're going to cheat just a little
+bit because we are going to deduce it
+
+ align:start position:0%
+bit because we are going to deduce it
+ 
+
+ align:start position:0%
+bit because we are going to deduce it
+from another theorem that I will prove
+
+ align:start position:0%
+from another theorem that I will prove
+ 
+
+ align:start position:0%
+from another theorem that I will prove
+next time.
+
+ align:start position:0%
+next time.
+ 
+
+ align:start position:0%
+next time.
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to prove the component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's we'll prove next time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, what is a bosano?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the person theorem. So the person
+
+ align:start position:0%
+So the person theorem. So the person
+ 
+
+ align:start position:0%
+So the person theorem. So the person
+theorem says that every bounded sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's a coal is
+
+ align:start position:0%
+So that's a coal is
+ 
+
+ align:start position:0%
+So that's a coal is
+okay.
+
+ align:start position:0%
+okay.
+ 
+
+ align:start position:0%
+okay.
+Now let's try to so I assume this again
+
+ align:start position:0%
+Now let's try to so I assume this again
+ 
+
+ align:start position:0%
+Now let's try to so I assume this again
+I'll prove this next time. So let's but
+
+ align:start position:0%
+I'll prove this next time. So let's but
+ 
+
+ align:start position:0%
+I'll prove this next time. So let's but
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+This is to prove the cush
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the device. I show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kids.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> That's fall off.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So remember the cushy convergence here
+
+ align:start position:0%
+So remember the cushy convergence here
+ 
+
+ align:start position:0%
+So remember the cushy convergence here
+I'm saying that if you have a C sequence
+
+ align:start position:0%
+I'm saying that if you have a C sequence
+ 
+
+ align:start position:0%
+I'm saying that if you have a C sequence
+then it is converted. So suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XN is a C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I want to prove that it's
+
+ align:start position:0%
+Okay, I want to prove that it's
+ 
+
+ align:start position:0%
+Okay, I want to prove that it's
+convergent.
+
+ align:start position:0%
+convergent.
+ 
+
+ align:start position:0%
+convergent.
+But I already we already showed we
+
+ align:start position:0%
+But I already we already showed we
+ 
+
+ align:start position:0%
+But I already we already showed we
+already show
+
+ align:start position:0%
+already show
+ 
+
+ align:start position:0%
+already show
+we already proven
+
+ align:start position:0%
+we already proven
+ 
+
+ align:start position:0%
+we already proven
+show that any C sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh any C sequence
+
+ align:start position:0%
+uh any C sequence
+ 
+
+ align:start position:0%
+uh any C sequence
+shown that XN any C sequence is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is this earlier.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now by therefore by the biosium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the pano biosium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a converted subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's a converted subsequent x and
+
+ align:start position:0%
+So there's a converted subsequent x and
+ 
+
+ align:start position:0%
+So there's a converted subsequent x and
+k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So So now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have that uh you have that this
+
+ align:start position:0%
+you have that uh you have that this
+ 
+
+ align:start position:0%
+you have that uh you have that this
+subsequence here convert to some x
+
+ align:start position:0%
+subsequence here convert to some x
+ 
+
+ align:start position:0%
+subsequence here convert to some x
+and now I want to show that the original
+
+ align:start position:0%
+and now I want to show that the original
+ 
+
+ align:start position:0%
+and now I want to show that the original
+sequence converts to x.
+
+ align:start position:0%
+sequence converts to x.
+ 
+
+ align:start position:0%
+sequence converts to x.
+So uh so give so since
+
+ align:start position:0%
+So uh so give so since
+ 
+
+ align:start position:0%
+So uh so give so since
+xn is accus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+given uh epsilon greater than zero.
+
+ align:start position:0%
+given uh epsilon greater than zero.
+ 
+
+ align:start position:0%
+given uh epsilon greater than zero.
+There exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist uh capital n. So that so
+
+ align:start position:0%
+there exist uh capital n. So that so
+ 
+
+ align:start position:0%
+there exist uh capital n. So that so
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+m and n are bigger than capital n then
+
+ align:start position:0%
+m and n are bigger than capital n then
+ 
+
+ align:start position:0%
+m and n are bigger than capital n then
+uh x n minus xm
+
+ align:start position:0%
+uh x n minus xm
+ 
+
+ align:start position:0%
+uh x n minus xm
+is less than epsilon
+
+ align:start position:0%
+is less than epsilon
+ 
+
+ align:start position:0%
+is less than epsilon
+using the epsilon
+
+ align:start position:0%
+using the epsilon
+ 
+
+ align:start position:0%
+using the epsilon
+in the definition of being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now I and this let's call this the
+
+ align:start position:0%
+but now I and this let's call this the
+ 
+
+ align:start position:0%
+but now I and this let's call this the
+exist n let's call it n1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now since
+
+ align:start position:0%
+So now since
+ 
+
+ align:start position:0%
+So now since
+x and k
+
+ align:start position:0%
+x and k
+ 
+
+ align:start position:0%
+x and k
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+to x there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for that epsilon there exist
+
+ align:start position:0%
+for that epsilon there exist
+ 
+
+ align:start position:0%
+for that epsilon there exist
+uh n2 uh k2 n2. Yeah. So that if uh if k
+
+ align:start position:0%
+uh n2 uh k2 n2. Yeah. So that if uh if k
+ 
+
+ align:start position:0%
+uh n2 uh k2 n2. Yeah. So that if uh if k
+here is bigger than n_sub_2
+
+ align:start position:0%
+here is bigger than n_sub_2
+ 
+
+ align:start position:0%
+here is bigger than n_sub_2
+then uh x n k - x
+
+ align:start position:0%
+then uh x n k - x
+ 
+
+ align:start position:0%
+then uh x n k - x
+is less than ep 2.
+
+ align:start position:0%
+is less than ep 2.
+ 
+
+ align:start position:0%
+is less than ep 2.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now,
+
+ align:start position:0%
+So now,
+ 
+
+ align:start position:0%
+So now,
+so now you just take, so now we take um
+
+ align:start position:0%
+so now you just take, so now we take um
+ 
+
+ align:start position:0%
+so now you just take, so now we take um
+we take um n to be equal to
+
+ align:start position:0%
+we take um n to be equal to
+ 
+
+ align:start position:0%
+we take um n to be equal to
+um the maximum
+
+ align:start position:0%
+um the maximum
+ 
+
+ align:start position:0%
+um the maximum
+of uh n1
+
+ align:start position:0%
+of uh n1
+ 
+
+ align:start position:0%
+of uh n1
+and n sorry and n
+
+ align:start position:0%
+and n sorry and n
+ 
+
+ align:start position:0%
+and n sorry and n
+two. This is the one that corresponds to
+
+ align:start position:0%
+two. This is the one that corresponds to
+ 
+
+ align:start position:0%
+two. This is the one that corresponds to
+right. So this is where where k is
+
+ align:start position:0%
+right. So this is where where k is
+ 
+
+ align:start position:0%
+right. So this is where where k is
+taking equal to this n2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if we take n like that and you're
+
+ align:start position:0%
+So if we take n like that and you're
+ 
+
+ align:start position:0%
+So if we take n like that and you're
+looking at uh n bigger equal to n and
+
+ align:start position:0%
+looking at uh n bigger equal to n and
+ 
+
+ align:start position:0%
+looking at uh n bigger equal to n and
+you now want to estimate this thing here
+
+ align:start position:0%
+you now want to estimate this thing here
+ 
+
+ align:start position:0%
+you now want to estimate this thing here
+then you can think about this difference
+
+ align:start position:0%
+then you can think about this difference
+ 
+
+ align:start position:0%
+then you can think about this difference
+here as x - x n2
+
+ align:start position:0%
+here as x - x n2
+ 
+
+ align:start position:0%
+here as x - x n2
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+uh sorry x n
+
+ align:start position:0%
+uh sorry x n
+ 
+
+ align:start position:0%
+uh sorry x n
+like this minus plus uh x
+
+ align:start position:0%
+like this minus plus uh x
+ 
+
+ align:start position:0%
+like this minus plus uh x
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+uh x uh x n - uh x
+
+ align:start position:0%
+uh x uh x n - uh x
+ 
+
+ align:start position:0%
+uh x uh x n - uh x
+uh n / x terms like like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this here is now in this. So this is
+
+ align:start position:0%
+and this here is now in this. So this is
+ 
+
+ align:start position:0%
+and this here is now in this. So this is
+now in this uh subsequence and so one of
+
+ align:start position:0%
+now in this uh subsequence and so one of
+ 
+
+ align:start position:0%
+now in this uh subsequence and so one of
+them this is less than epsilon / two and
+
+ align:start position:0%
+them this is less than epsilon / two and
+ 
+
+ align:start position:0%
+them this is less than epsilon / two and
+this here is less than epsilon / two and
+
+ align:start position:0%
+this here is less than epsilon / two and
+ 
+
+ align:start position:0%
+this here is less than epsilon / two and
+so you get that this difference here was
+
+ align:start position:0%
+so you get that this difference here was
+ 
+
+ align:start position:0%
+so you get that this difference here was
+less than epilon. Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so this is why the balsano vastra
+
+ align:start position:0%
+now so this is why the balsano vastra
+ 
+
+ align:start position:0%
+now so this is why the balsano vastra
+theorem implies a cush convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now the next thing is that I
+
+ align:start position:0%
+Okay. So now the next thing is that I
+ 
+
+ align:start position:0%
+Okay. So now the next thing is that I
+want to give another
+
+ align:start position:0%
+want to give another
+ 
+
+ align:start position:0%
+want to give another
+uh application of so of the kus
+
+ align:start position:0%
+uh application of so of the kus
+ 
+
+ align:start position:0%
+uh application of so of the kus
+convergence. So here's another
+
+ align:start position:0%
+convergence. So here's another
+ 
+
+ align:start position:0%
+convergence. So here's another
+application of the cus convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So one one application was to the
+
+ align:start position:0%
+So one one application was to the
+ 
+
+ align:start position:0%
+So one one application was to the
+contracting mapping theorem. But here's
+
+ align:start position:0%
+contracting mapping theorem. But here's
+ 
+
+ align:start position:0%
+contracting mapping theorem. But here's
+another application of the of the cushy
+
+ align:start position:0%
+another application of the of the cushy
+ 
+
+ align:start position:0%
+another application of the of the cushy
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem.
+
+ align:start position:0%
+theorem.
+ 
+
+ align:start position:0%
+theorem.
+So this is the extreme value theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now before I I um before I explain that,
+
+ align:start position:0%
+Now before I I um before I explain that,
+ 
+
+ align:start position:0%
+Now before I I um before I explain that,
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+introduce uh this notion of a function
+
+ align:start position:0%
+introduce uh this notion of a function
+ 
+
+ align:start position:0%
+introduce uh this notion of a function
+being continuous
+
+ align:start position:0%
+being continuous
+ 
+
+ align:start position:0%
+being continuous
+in a rigorous way. So what does it mean
+
+ align:start position:0%
+in a rigorous way. So what does it mean
+ 
+
+ align:start position:0%
+in a rigorous way. So what does it mean
+for a function to be continuous?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f say from r to r it could be a subset
+
+ align:start position:0%
+f say from r to r it could be a subset
+ 
+
+ align:start position:0%
+f say from r to r it could be a subset
+of r
+
+ align:start position:0%
+of r
+ 
+
+ align:start position:0%
+of r
+all of them is set to be continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to being continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0 at some points x0.
+
+ align:start position:0%
+at x0 at some points x0.
+ 
+
+ align:start position:0%
+at x0 at some points x0.
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+epsilon greater than zero there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist delta greater than zero such
+
+ align:start position:0%
+there exist delta greater than zero such
+ 
+
+ align:start position:0%
+there exist delta greater than zero such
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if x minus x0
+
+ align:start position:0%
+if x minus x0
+ 
+
+ align:start position:0%
+if x minus x0
+is smaller than delta then the images
+
+ align:start position:0%
+is smaller than delta then the images
+ 
+
+ align:start position:0%
+is smaller than delta then the images
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+within epsilon.
+
+ align:start position:0%
+within epsilon.
+ 
+
+ align:start position:0%
+within epsilon.
+each other.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you think about it, so if you have
+
+ align:start position:0%
+So if you think about it, so if you have
+ 
+
+ align:start position:0%
+So if you think about it, so if you have
+like the function, this is a function
+
+ align:start position:0%
+like the function, this is a function
+ 
+
+ align:start position:0%
+like the function, this is a function
+you you
+
+ align:start position:0%
+you you
+ 
+
+ align:start position:0%
+you you
+to say that it's continuous at some x0
+
+ align:start position:0%
+to say that it's continuous at some x0
+ 
+
+ align:start position:0%
+to say that it's continuous at some x0
+means that if this thing here is this
+
+ align:start position:0%
+means that if this thing here is this
+ 
+
+ align:start position:0%
+means that if this thing here is this
+here is now f of x0.
+
+ align:start position:0%
+here is now f of x0.
+ 
+
+ align:start position:0%
+here is now f of x0.
+If you take a little interval around
+
+ align:start position:0%
+If you take a little interval around
+ 
+
+ align:start position:0%
+If you take a little interval around
+here, this is a epsilon interval around
+
+ align:start position:0%
+here, this is a epsilon interval around
+ 
+
+ align:start position:0%
+here, this is a epsilon interval around
+here. Then there should be some delta
+
+ align:start position:0%
+here. Then there should be some delta
+ 
+
+ align:start position:0%
+here. Then there should be some delta
+interval around here. So that if you're
+
+ align:start position:0%
+interval around here. So that if you're
+ 
+
+ align:start position:0%
+interval around here. So that if you're
+looking at images here, then it will map
+
+ align:start position:0%
+looking at images here, then it will map
+ 
+
+ align:start position:0%
+looking at images here, then it will map
+into here.
+
+ align:start position:0%
+into here.
+ 
+
+ align:start position:0%
+into here.
+Right? That's what it means to be
+
+ align:start position:0%
+Right? That's what it means to be
+ 
+
+ align:start position:0%
+Right? That's what it means to be
+continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? So this is continuous at a point
+
+ align:start position:0%
+Okay? So this is continuous at a point
+ 
+
+ align:start position:0%
+Okay? So this is continuous at a point
+and a function is set to be continuous
+
+ align:start position:0%
+and a function is set to be continuous
+ 
+
+ align:start position:0%
+and a function is set to be continuous
+if it's continuous at all points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is set to be continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If it is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at all.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now we have a little theorem here
+
+ align:start position:0%
+And so now we have a little theorem here
+ 
+
+ align:start position:0%
+And so now we have a little theorem here
+and this is often useful way of thinking
+
+ align:start position:0%
+and this is often useful way of thinking
+ 
+
+ align:start position:0%
+and this is often useful way of thinking
+about continuity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if
+
+ align:start position:0%
+So if
+ 
+
+ align:start position:0%
+So if
+f is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say f let's just say it doesn't
+
+ align:start position:0%
+So let's say f let's just say it doesn't
+ 
+
+ align:start position:0%
+So let's say f let's just say it doesn't
+need to be all of r. You just have to be
+
+ align:start position:0%
+need to be all of r. You just have to be
+ 
+
+ align:start position:0%
+need to be all of r. You just have to be
+careful that everything that you talk
+
+ align:start position:0%
+careful that everything that you talk
+ 
+
+ align:start position:0%
+careful that everything that you talk
+about is in the domain. But let's just
+
+ align:start position:0%
+about is in the domain. But let's just
+ 
+
+ align:start position:0%
+about is in the domain. But let's just
+say that f is a function from r to r is
+
+ align:start position:0%
+say that f is a function from r to r is
+ 
+
+ align:start position:0%
+say that f is a function from r to r is
+continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if f is is continuous
+
+ align:start position:0%
+So if f is is continuous
+ 
+
+ align:start position:0%
+So if f is is continuous
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+xn is a sequence that converts to x
+
+ align:start position:0%
+xn is a sequence that converts to x
+ 
+
+ align:start position:0%
+xn is a sequence that converts to x
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then the images so f of xn this is
+
+ align:start position:0%
+then the images so f of xn this is
+ 
+
+ align:start position:0%
+then the images so f of xn this is
+another sequence those converge to f of
+
+ align:start position:0%
+another sequence those converge to f of
+ 
+
+ align:start position:0%
+another sequence those converge to f of
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is this This is a usual way of
+
+ align:start position:0%
+this is this This is a usual way of
+ 
+
+ align:start position:0%
+this is this This is a usual way of
+thinking about it being continuous.
+
+ align:start position:0%
+thinking about it being continuous.
+ 
+
+ align:start position:0%
+thinking about it being continuous.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+and so now so now why is this the case?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+f is continuous,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only leaf that is continuous at is
+
+ align:start position:0%
+the only leaf that is continuous at is
+ 
+
+ align:start position:0%
+the only leaf that is continuous at is
+x.
+
+ align:start position:0%
+x.
+ 
+
+ align:start position:0%
+x.
+So since it continue at x, this means
+
+ align:start position:0%
+So since it continue at x, this means
+ 
+
+ align:start position:0%
+So since it continue at x, this means
+that for all epsilon you're given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Given epsilon greater than zero there
+
+ align:start position:0%
+Given epsilon greater than zero there
+ 
+
+ align:start position:0%
+Given epsilon greater than zero there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist delta greater than zero such
+
+ align:start position:0%
+there exist delta greater than zero such
+ 
+
+ align:start position:0%
+there exist delta greater than zero such
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+uh x - y
+
+ align:start position:0%
+uh x - y
+ 
+
+ align:start position:0%
+uh x - y
+this is this this x here that you think
+
+ align:start position:0%
+this is this this x here that you think
+ 
+
+ align:start position:0%
+this is this this x here that you think
+about fixed if x if you have another
+
+ align:start position:0%
+about fixed if x if you have another
+ 
+
+ align:start position:0%
+about fixed if x if you have another
+point that is within delta
+
+ align:start position:0%
+point that is within delta
+ 
+
+ align:start position:0%
+point that is within delta
+And uh the images f of x - f of y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is just that is continuous at that
+
+ align:start position:0%
+this is just that is continuous at that
+ 
+
+ align:start position:0%
+this is just that is continuous at that
+one point x. Okay.
+
+ align:start position:0%
+one point x. Okay.
+ 
+
+ align:start position:0%
+one point x. Okay.
+Now since
+
+ align:start position:0%
+Now since
+ 
+
+ align:start position:0%
+Now since
+since um xn converts to x right since xn
+
+ align:start position:0%
+since um xn converts to x right since xn
+ 
+
+ align:start position:0%
+since um xn converts to x right since xn
+converts to x this means that if you use
+
+ align:start position:0%
+converts to x this means that if you use
+ 
+
+ align:start position:0%
+converts to x this means that if you use
+this delta here in the definition of uh
+
+ align:start position:0%
+this delta here in the definition of uh
+ 
+
+ align:start position:0%
+this delta here in the definition of uh
+convergence then uh there exist
+
+ align:start position:0%
+convergence then uh there exist
+ 
+
+ align:start position:0%
+convergence then uh there exist
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital n such that If x if sorry if
+
+ align:start position:0%
+capital n such that If x if sorry if
+ 
+
+ align:start position:0%
+capital n such that If x if sorry if
+little n is bigger than capital n then x
+
+ align:start position:0%
+little n is bigger than capital n then x
+ 
+
+ align:start position:0%
+little n is bigger than capital n then x
+n minus x
+
+ align:start position:0%
+n minus x
+ 
+
+ align:start position:0%
+n minus x
+is less than delta.
+
+ align:start position:0%
+is less than delta.
+ 
+
+ align:start position:0%
+is less than delta.
+But now you see that if little n is
+
+ align:start position:0%
+But now you see that if little n is
+ 
+
+ align:start position:0%
+But now you see that if little n is
+bigger than capital n then these lies
+
+ align:start position:0%
+bigger than capital n then these lies
+ 
+
+ align:start position:0%
+bigger than capital n then these lies
+this close to x. But then this say that
+
+ align:start position:0%
+this close to x. But then this say that
+ 
+
+ align:start position:0%
+this close to x. But then this say that
+the images. So therefore the images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of xn
+
+ align:start position:0%
+f of xn
+ 
+
+ align:start position:0%
+f of xn
+minus f of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than epsilon. And this was just
+
+ align:start position:0%
+is less than epsilon. And this was just
+ 
+
+ align:start position:0%
+is less than epsilon. And this was just
+as long as little n was bigger than
+
+ align:start position:0%
+as long as little n was bigger than
+ 
+
+ align:start position:0%
+as long as little n was bigger than
+capital n. That's exactly proving that
+
+ align:start position:0%
+capital n. That's exactly proving that
+ 
+
+ align:start position:0%
+capital n. That's exactly proving that
+this sequence converts to that. Right?
+
+ align:start position:0%
+this sequence converts to that. Right?
+ 
+
+ align:start position:0%
+this sequence converts to that. Right?
+So that's okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now let's prove the extreme value. I
+
+ align:start position:0%
+Now let's prove the extreme value. I
+ 
+
+ align:start position:0%
+Now let's prove the extreme value. I
+need to state that first.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And there's two versions
+
+ align:start position:0%
+And there's two versions
+ 
+
+ align:start position:0%
+And there's two versions
+uh of it.
+
+ align:start position:0%
+uh of it.
+ 
+
+ align:start position:0%
+uh of it.
+So extreme guys.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you take a function f on some
+
+ align:start position:0%
+So you take a function f on some
+ 
+
+ align:start position:0%
+So you take a function f on some
+interval a and b a real number.
+
+ align:start position:0%
+interval a and b a real number.
+ 
+
+ align:start position:0%
+interval a and b a real number.
+They're both included.
+
+ align:start position:0%
+They're both included.
+ 
+
+ align:start position:0%
+They're both included.
+And f here is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's continuous at all points.
+
+ align:start position:0%
+It's continuous at all points.
+ 
+
+ align:start position:0%
+It's continuous at all points.
+It needs to be continuous at all points
+
+ align:start position:0%
+It needs to be continuous at all points
+ 
+
+ align:start position:0%
+It needs to be continuous at all points
+and this interval needs to contain the
+
+ align:start position:0%
+and this interval needs to contain the
+ 
+
+ align:start position:0%
+and this interval needs to contain the
+ins.
+
+ align:start position:0%
+ins.
+ 
+
+ align:start position:0%
+ins.
+So if this is continuous then
+
+ align:start position:0%
+So if this is continuous then
+ 
+
+ align:start position:0%
+So if this is continuous then
+the soup of f is achieved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at some
+
+ align:start position:0%
+at some
+ 
+
+ align:start position:0%
+at some
+uh x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So meaning that soup
+
+ align:start position:0%
+So meaning that soup
+ 
+
+ align:start position:0%
+So meaning that soup
+of f over this interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to the value
+
+ align:start position:0%
+is equal to the value
+ 
+
+ align:start position:0%
+is equal to the value
+um let's say let's call it x capital m
+
+ align:start position:0%
+um let's say let's call it x capital m
+ 
+
+ align:start position:0%
+um let's say let's call it x capital m
+yeah capital m for max
+
+ align:start position:0%
+yeah capital m for max
+ 
+
+ align:start position:0%
+yeah capital m for max
+at some point in particular the soup is
+
+ align:start position:0%
+at some point in particular the soup is
+ 
+
+ align:start position:0%
+at some point in particular the soup is
+finite right the soup is finite and it's
+
+ align:start position:0%
+finite right the soup is finite and it's
+ 
+
+ align:start position:0%
+finite right the soup is finite and it's
+not really a soup it's a max Right? And
+
+ align:start position:0%
+not really a soup it's a max Right? And
+ 
+
+ align:start position:0%
+not really a soup it's a max Right? And
+so likewise it also said that moreover
+
+ align:start position:0%
+so likewise it also said that moreover
+ 
+
+ align:start position:0%
+so likewise it also said that moreover
+just the same thing and you could in the
+
+ align:start position:0%
+just the same thing and you could in the
+ 
+
+ align:start position:0%
+just the same thing and you could in the
+usual way you could obtain it from this
+
+ align:start position:0%
+usual way you could obtain it from this
+ 
+
+ align:start position:0%
+usual way you could obtain it from this
+by looking at the function minus f if
+
+ align:start position:0%
+by looking at the function minus f if
+ 
+
+ align:start position:0%
+by looking at the function minus f if
+you wanted or you could just prove it
+
+ align:start position:0%
+you wanted or you could just prove it
+ 
+
+ align:start position:0%
+you wanted or you could just prove it
+directly with the same that we're going
+
+ align:start position:0%
+directly with the same that we're going
+ 
+
+ align:start position:0%
+directly with the same that we're going
+to give here. Moreover, uh the in
+
+ align:start position:0%
+to give here. Moreover, uh the in
+ 
+
+ align:start position:0%
+to give here. Moreover, uh the in
+of f over this interval
+
+ align:start position:0%
+of f over this interval
+ 
+
+ align:start position:0%
+of f over this interval
+is equal to the value at some point. So
+
+ align:start position:0%
+is equal to the value at some point. So
+ 
+
+ align:start position:0%
+is equal to the value at some point. So
+it's not, you know, it's not just a in
+
+ align:start position:0%
+it's not, you know, it's not just a in
+ 
+
+ align:start position:0%
+it's not, you know, it's not just a in
+it actually is a minimum where x little
+
+ align:start position:0%
+it actually is a minimum where x little
+ 
+
+ align:start position:0%
+it actually is a minimum where x little
+m is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now let's try to prove that. And
+
+ align:start position:0%
+And so now let's try to prove that. And
+ 
+
+ align:start position:0%
+And so now let's try to prove that. And
+so this is going to use this theorem
+
+ align:start position:0%
+so this is going to use this theorem
+ 
+
+ align:start position:0%
+so this is going to use this theorem
+that we proved this theorem and then
+
+ align:start position:0%
+that we proved this theorem and then
+ 
+
+ align:start position:0%
+that we proved this theorem and then
+it's going to use uh the kushi conver
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um okay so and I'm just going to
+
+ align:start position:0%
+So um okay so and I'm just going to
+ 
+
+ align:start position:0%
+So um okay so and I'm just going to
+prove like just because the two the two
+
+ align:start position:0%
+prove like just because the two the two
+ 
+
+ align:start position:0%
+prove like just because the two the two
+there's two parts to the extreme values
+
+ align:start position:0%
+there's two parts to the extreme values
+ 
+
+ align:start position:0%
+there's two parts to the extreme values
+the this with a soup and that's this
+
+ align:start position:0%
+the this with a soup and that's this
+ 
+
+ align:start position:0%
+the this with a soup and that's this
+with in but the proof uh you know with
+
+ align:start position:0%
+with in but the proof uh you know with
+ 
+
+ align:start position:0%
+with in but the proof uh you know with
+obvious modification
+
+ align:start position:0%
+obvious modification
+ 
+
+ align:start position:0%
+obvious modification
+they're same
+
+ align:start position:0%
+they're same
+ 
+
+ align:start position:0%
+they're same
+okay so I'm just going to focus on the
+
+ align:start position:0%
+okay so I'm just going to focus on the
+ 
+
+ align:start position:0%
+okay so I'm just going to focus on the
+soup.
+
+ align:start position:0%
+soup.
+ 
+
+ align:start position:0%
+soup.
+So, so I so I want to prove so looking
+
+ align:start position:0%
+So, so I so I want to prove so looking
+ 
+
+ align:start position:0%
+So, so I so I want to prove so looking
+at the soup of this function I pro the
+
+ align:start position:0%
+at the soup of this function I pro the
+ 
+
+ align:start position:0%
+at the soup of this function I pro the
+soup could be infinity. Okay. So,
+
+ align:start position:0%
+soup could be infinity. Okay. So,
+ 
+
+ align:start position:0%
+soup could be infinity. Okay. So,
+usually we like soup to be finite but
+
+ align:start position:0%
+usually we like soup to be finite but
+ 
+
+ align:start position:0%
+usually we like soup to be finite but
+let me allow this that if if there is no
+
+ align:start position:0%
+let me allow this that if if there is no
+ 
+
+ align:start position:0%
+let me allow this that if if there is no
+upper bound then I will write infinity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in any case I um there exist
+
+ align:start position:0%
+So in any case I um there exist
+ 
+
+ align:start position:0%
+So in any case I um there exist
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+so that xn
+
+ align:start position:0%
+so that xn
+ 
+
+ align:start position:0%
+so that xn
+so that f there exist a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this domain here so that the f of xn
+
+ align:start position:0%
+in this domain here so that the f of xn
+ 
+
+ align:start position:0%
+in this domain here so that the f of xn
+converge to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+>> Okay. I'm allowing here and we don't
+
+ align:start position:0%
+>> Okay. I'm allowing here and we don't
+ 
+
+ align:start position:0%
+>> Okay. I'm allowing here and we don't
+usually like this but I allow this here
+
+ align:start position:0%
+usually like this but I allow this here
+ 
+
+ align:start position:0%
+usually like this but I allow this here
+to be infinite. If it's infinite then I
+
+ align:start position:0%
+to be infinite. If it's infinite then I
+ 
+
+ align:start position:0%
+to be infinite. If it's infinite then I
+just mean that there's a sequence where
+
+ align:start position:0%
+just mean that there's a sequence where
+ 
+
+ align:start position:0%
+just mean that there's a sequence where
+the value of these become larger and
+
+ align:start position:0%
+the value of these become larger and
+ 
+
+ align:start position:0%
+the value of these become larger and
+larger than
+
+ align:start position:0%
+larger than
+ 
+
+ align:start position:0%
+larger than
+right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I have that but now you see this here
+
+ align:start position:0%
+So I have that but now you see this here
+ 
+
+ align:start position:0%
+So I have that but now you see this here
+is in this range. So this is a bounded
+
+ align:start position:0%
+is in this range. So this is a bounded
+ 
+
+ align:start position:0%
+is in this range. So this is a bounded
+this is a boundary. So note that xn So
+
+ align:start position:0%
+this is a boundary. So note that xn So
+ 
+
+ align:start position:0%
+this is a boundary. So note that xn So
+note
+
+ align:start position:0%
+note
+ 
+
+ align:start position:0%
+note
+that xn is a boundary sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So then I'm using not kushi conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I use the banana vas. So it's a
+
+ align:start position:0%
+but I use the banana vas. So it's a
+ 
+
+ align:start position:0%
+but I use the banana vas. So it's a
+bounded sequence. which I know that they
+
+ align:start position:0%
+bounded sequence. which I know that they
+ 
+
+ align:start position:0%
+bounded sequence. which I know that they
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a good exercise to see that this
+
+ align:start position:0%
+it's a good exercise to see that this
+ 
+
+ align:start position:0%
+it's a good exercise to see that this
+sequence in itself you know you can just
+
+ align:start position:0%
+sequence in itself you know you can just
+ 
+
+ align:start position:0%
+sequence in itself you know you can just
+draw a little picture and you'll
+
+ align:start position:0%
+draw a little picture and you'll
+ 
+
+ align:start position:0%
+draw a little picture and you'll
+convince yourself that it this sequence
+
+ align:start position:0%
+convince yourself that it this sequence
+ 
+
+ align:start position:0%
+convince yourself that it this sequence
+it in itself may not be convergent. But
+
+ align:start position:0%
+it in itself may not be convergent. But
+ 
+
+ align:start position:0%
+it in itself may not be convergent. But
+after you pass to a subsequence, you you
+
+ align:start position:0%
+after you pass to a subsequence, you you
+ 
+
+ align:start position:0%
+after you pass to a subsequence, you you
+can find a converging subsequence.
+
+ align:start position:0%
+can find a converging subsequence.
+ 
+
+ align:start position:0%
+can find a converging subsequence.
+So it converge. So this here converge
+
+ align:start position:0%
+So it converge. So this here converge
+ 
+
+ align:start position:0%
+So it converge. So this here converge
+and it converts to something in this
+
+ align:start position:0%
+and it converts to something in this
+ 
+
+ align:start position:0%
+and it converts to something in this
+interval, right? And that's important.
+
+ align:start position:0%
+interval, right? And that's important.
+ 
+
+ align:start position:0%
+interval, right? And that's important.
+So it converts to some to some x and I
+
+ align:start position:0%
+So it converts to some to some x and I
+ 
+
+ align:start position:0%
+So it converts to some to some x and I
+call this x capital m.
+
+ align:start position:0%
+call this x capital m.
+ 
+
+ align:start position:0%
+call this x capital m.
+Okay. So converging and the key point
+
+ align:start position:0%
+Okay. So converging and the key point
+ 
+
+ align:start position:0%
+Okay. So converging and the key point
+here is that this thing here is lying in
+
+ align:start position:0%
+here is that this thing here is lying in
+ 
+
+ align:start position:0%
+here is that this thing here is lying in
+this interval and and the function is
+
+ align:start position:0%
+this interval and and the function is
+ 
+
+ align:start position:0%
+this interval and and the function is
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+in particular at this point. Right? So
+
+ align:start position:0%
+in particular at this point. Right? So
+ 
+
+ align:start position:0%
+in particular at this point. Right? So
+if this had not included the end point
+
+ align:start position:0%
+if this had not included the end point
+ 
+
+ align:start position:0%
+if this had not included the end point
+it converts to one of the end point but
+
+ align:start position:0%
+it converts to one of the end point but
+ 
+
+ align:start position:0%
+it converts to one of the end point but
+the function would not be defined there.
+
+ align:start position:0%
+the function would not be defined there.
+ 
+
+ align:start position:0%
+the function would not be defined there.
+So you wouldn't be able to conclude the
+
+ align:start position:0%
+So you wouldn't be able to conclude the
+ 
+
+ align:start position:0%
+So you wouldn't be able to conclude the
+extreme direct but anyway. So should we
+
+ align:start position:0%
+extreme direct but anyway. So should we
+ 
+
+ align:start position:0%
+extreme direct but anyway. So should we
+include the end point here?
+
+ align:start position:0%
+include the end point here?
+ 
+
+ align:start position:0%
+include the end point here?
+Then now we have
+
+ align:start position:0%
+Then now we have
+ 
+
+ align:start position:0%
+Then now we have
+now we have that from this theorem that
+
+ align:start position:0%
+now we have that from this theorem that
+ 
+
+ align:start position:0%
+now we have that from this theorem that
+is right here we have that since this
+
+ align:start position:0%
+is right here we have that since this
+ 
+
+ align:start position:0%
+is right here we have that since this
+sequence converts to that we have that
+
+ align:start position:0%
+sequence converts to that we have that
+ 
+
+ align:start position:0%
+sequence converts to that we have that
+the images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+to sorry to the image of
+
+ align:start position:0%
+to sorry to the image of
+ 
+
+ align:start position:0%
+to sorry to the image of
+X capital N right
+
+ align:start position:0%
+X capital N right
+ 
+
+ align:start position:0%
+X capital N right
+but on the other hand this sequence here
+
+ align:start position:0%
+but on the other hand this sequence here
+ 
+
+ align:start position:0%
+but on the other hand this sequence here
+was a subsequence of a sequence that
+
+ align:start position:0%
+was a subsequence of a sequence that
+ 
+
+ align:start position:0%
+was a subsequence of a sequence that
+converts to the soup. Right? But if you
+
+ align:start position:0%
+converts to the soup. Right? But if you
+ 
+
+ align:start position:0%
+converts to the soup. Right? But if you
+take a sequence that converts to
+
+ align:start position:0%
+take a sequence that converts to
+ 
+
+ align:start position:0%
+take a sequence that converts to
+whatever number, then any subsequence
+
+ align:start position:0%
+whatever number, then any subsequence
+ 
+
+ align:start position:0%
+whatever number, then any subsequence
+will convert to the same number. So this
+
+ align:start position:0%
+will convert to the same number. So this
+ 
+
+ align:start position:0%
+will convert to the same number. So this
+here also
+
+ align:start position:0%
+here also
+ 
+
+ align:start position:0%
+here also
+converts to to
+
+ align:start position:0%
+converts to to
+ 
+
+ align:start position:0%
+converts to to
+the soup
+
+ align:start position:0%
+the soup
+ 
+
+ align:start position:0%
+the soup
+to soup.
+
+ align:start position:0%
+to soup.
+ 
+
+ align:start position:0%
+to soup.
+And so this means that these two numbers
+
+ align:start position:0%
+And so this means that these two numbers
+ 
+
+ align:start position:0%
+And so this means that these two numbers
+here must be the same.
+
+ align:start position:0%
+here must be the same.
+ 
+
+ align:start position:0%
+here must be the same.
+And so you should just you know it would
+
+ align:start position:0%
+And so you should just you know it would
+ 
+
+ align:start position:0%
+And so you should just you know it would
+take you just a second to convince
+
+ align:start position:0%
+take you just a second to convince
+ 
+
+ align:start position:0%
+take you just a second to convince
+yourself that everything is fine if you
+
+ align:start position:0%
+yourself that everything is fine if you
+ 
+
+ align:start position:0%
+yourself that everything is fine if you
+know if a I didn't know that the soup
+
+ align:start position:0%
+know if a I didn't know that the soup
+ 
+
+ align:start position:0%
+know if a I didn't know that the soup
+was a finite number but infinite right
+
+ align:start position:0%
+was a finite number but infinite right
+ 
+
+ align:start position:0%
+was a finite number but infinite right
+that it's that is still fine but but
+
+ align:start position:0%
+that it's that is still fine but but
+ 
+
+ align:start position:0%
+that it's that is still fine but but
+it's that should also take a minute to
+
+ align:start position:0%
+it's that should also take a minute to
+ 
+
+ align:start position:0%
+it's that should also take a minute to
+convince yourself about that. So that
+
+ align:start position:0%
+convince yourself about that. So that
+ 
+
+ align:start position:0%
+convince yourself about that. So that
+that proves the extreme value theorem
+
+ align:start position:0%
+that proves the extreme value theorem
+ 
+
+ align:start position:0%
+that proves the extreme value theorem
+right that the if you take a function
+
+ align:start position:0%
+right that the if you take a function
+ 
+
+ align:start position:0%
+right that the if you take a function
+that is continuous
+
+ align:start position:0%
+that is continuous
+ 
+
+ align:start position:0%
+that is continuous
+and defined on an interval where the
+
+ align:start position:0%
+and defined on an interval where the
+ 
+
+ align:start position:0%
+and defined on an interval where the
+interval include both end points then uh
+
+ align:start position:0%
+interval include both end points then uh
+ 
+
+ align:start position:0%
+interval include both end points then uh
+the s the soup is achieved. So the soup
+
+ align:start position:0%
+the s the soup is achieved. So the soup
+ 
+
+ align:start position:0%
+the s the soup is achieved. So the soup
+is really a max and the in by very
+
+ align:start position:0%
+is really a max and the in by very
+ 
+
+ align:start position:0%
+is really a max and the in by very
+similar proof the inom is also achieved
+
+ align:start position:0%
+similar proof the inom is also achieved
+ 
+
+ align:start position:0%
+similar proof the inom is also achieved
+and so both the min and max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Okay. So that was the So yeah, that's
+
+ align:start position:0%
+>> Okay. So that was the So yeah, that's
+ 
+
+ align:start position:0%
+>> Okay. So that was the So yeah, that's
+right. So you're saying just so it was
+
+ align:start position:0%
+right. So you're saying just so it was
+ 
+
+ align:start position:0%
+right. So you're saying just so it was
+clear enough that it was a boundary
+
+ align:start position:0%
+clear enough that it was a boundary
+ 
+
+ align:start position:0%
+clear enough that it was a boundary
+sequence because it lying in this
+
+ align:start position:0%
+sequence because it lying in this
+ 
+
+ align:start position:0%
+sequence because it lying in this
+bounded interval, right? So it's a
+
+ align:start position:0%
+bounded interval, right? So it's a
+ 
+
+ align:start position:0%
+bounded interval, right? So it's a
+boundary sequence. Are you asking why
+
+ align:start position:0%
+boundary sequence. Are you asking why
+ 
+
+ align:start position:0%
+boundary sequence. Are you asking why
+such a bound sequence exist?
+
+ align:start position:0%
+such a bound sequence exist?
+ 
+
+ align:start position:0%
+such a bound sequence exist?
+>> So okay. So, so I just so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have you have this function,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? So, so like this. So, you you
+
+ align:start position:0%
+right? So, so like this. So, you you
+ 
+
+ align:start position:0%
+right? So, so like this. So, you you
+take the soup of f over this in term
+
+ align:start position:0%
+take the soup of f over this in term
+ 
+
+ align:start position:0%
+take the soup of f over this in term
+and so this means that that if you take
+
+ align:start position:0%
+and so this means that that if you take
+ 
+
+ align:start position:0%
+and so this means that that if you take
+any any epsilon and you subtract it from
+
+ align:start position:0%
+any any epsilon and you subtract it from
+ 
+
+ align:start position:0%
+any any epsilon and you subtract it from
+the two, right? Then actually there must
+
+ align:start position:0%
+the two, right? Then actually there must
+ 
+
+ align:start position:0%
+the two, right? Then actually there must
+exist a x depending on this epsilon
+
+ align:start position:0%
+exist a x depending on this epsilon
+ 
+
+ align:start position:0%
+exist a x depending on this epsilon
+there must exist so that the value at
+
+ align:start position:0%
+there must exist so that the value at
+ 
+
+ align:start position:0%
+there must exist so that the value at
+this x is larger than this right and so
+
+ align:start position:0%
+this x is larger than this right and so
+ 
+
+ align:start position:0%
+this x is larger than this right and so
+you could imagine instead of epsilon
+
+ align:start position:0%
+you could imagine instead of epsilon
+ 
+
+ align:start position:0%
+you could imagine instead of epsilon
+here take looking at a sequence like
+
+ align:start position:0%
+here take looking at a sequence like
+ 
+
+ align:start position:0%
+here take looking at a sequence like
+this and then this gives you a sequence
+
+ align:start position:0%
+this and then this gives you a sequence
+ 
+
+ align:start position:0%
+this and then this gives you a sequence
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+and so right so that would be how and
+
+ align:start position:0%
+and so right so that would be how and
+ 
+
+ align:start position:0%
+and so right so that would be how and
+the same when you do
+
+ align:start position:0%
+the same when you do
+ 
+
+ align:start position:0%
+the same when you do
+and so once you have it it's bound
+
+ align:start position:0%
+and so once you have it it's bound
+ 
+
+ align:start position:0%
+and so once you have it it's bound
+sequence because it's lie between A and
+
+ align:start position:0%
+sequence because it's lie between A and
+ 
+
+ align:start position:0%
+sequence because it's lie between A and
+B, right? You're using the Banana Vest
+
+ align:start position:0%
+B, right? You're using the Banana Vest
+ 
+
+ align:start position:0%
+B, right? You're using the Banana Vest
+theorem that we prove next time to get a
+
+ align:start position:0%
+theorem that we prove next time to get a
+ 
+
+ align:start position:0%
+theorem that we prove next time to get a
+convergent subsequence and then you
+
+ align:start position:0%
+convergent subsequence and then you
+ 
+
+ align:start position:0%
+convergent subsequence and then you
+apply the theorem this theorem here to
+
+ align:start position:0%
+apply the theorem this theorem here to
+ 
+
+ align:start position:0%
+apply the theorem this theorem here to
+get that in that case the maximum and
+
+ align:start position:0%
+get that in that case the maximum and
+ 
+
+ align:start position:0%
+get that in that case the maximum and
+likewise for the minimum that they
+
+ align:start position:0%
+likewise for the minimum that they
+ 
+
+ align:start position:0%
+likewise for the minimum that they
+achieved.
+
+ align:start position:0%
+achieved.
+ 
+
+ align:start position:0%
+achieved.
+Any questions?
\ No newline at end of file
diff --git a/XWFocLnBdhM.txt b/XWFocLnBdhM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b29c222269be06b62df6110e6639e5815b66f71e
--- /dev/null
+++ b/XWFocLnBdhM.txt
@@ -0,0 +1,795 @@
+align:start position:0%
+ 
+earlier in this course we talked about
+
+ align:start position:0%
+earlier in this course we talked about
+ 
+
+ align:start position:0%
+earlier in this course we talked about
+the changing role of labor unions and
+
+ align:start position:0%
+the changing role of labor unions and
+ 
+
+ align:start position:0%
+the changing role of labor unions and
+how the decline in Union membership has
+
+ align:start position:0%
+how the decline in Union membership has
+ 
+
+ align:start position:0%
+how the decline in Union membership has
+contributed to the breakdown of the
+
+ align:start position:0%
+contributed to the breakdown of the
+ 
+
+ align:start position:0%
+contributed to the breakdown of the
+social contract to understand this
+
+ align:start position:0%
+social contract to understand this
+ 
+
+ align:start position:0%
+social contract to understand this
+better let's look at how union
+
+ align:start position:0%
+better let's look at how union
+ 
+
+ align:start position:0%
+better let's look at how union
+membership rates have changed since
+
+ align:start position:0%
+membership rates have changed since
+ 
+
+ align:start position:0%
+membership rates have changed since
+their peak in the 1950s when almost
+
+ align:start position:0%
+their peak in the 1950s when almost
+ 
+
+ align:start position:0%
+their peak in the 1950s when almost
+onethird of all employees belong to a
+
+ align:start position:0%
+onethird of all employees belong to a
+ 
+
+ align:start position:0%
+onethird of all employees belong to a
+union by the early 1980s around the time
+
+ align:start position:0%
+union by the early 1980s around the time
+ 
+
+ align:start position:0%
+union by the early 1980s around the time
+when we begin to see the real effects of
+
+ align:start position:0%
+when we begin to see the real effects of
+ 
+
+ align:start position:0%
+when we begin to see the real effects of
+the breakdown of the social contract
+
+ align:start position:0%
+the breakdown of the social contract
+ 
+
+ align:start position:0%
+the breakdown of the social contract
+union membership was already declining
+
+ align:start position:0%
+union membership was already declining
+ 
+
+ align:start position:0%
+union membership was already declining
+and from then until now it declined even
+
+ align:start position:0%
+and from then until now it declined even
+ 
+
+ align:start position:0%
+and from then until now it declined even
+more dramatically in 2013 only 11% of
+
+ align:start position:0%
+more dramatically in 2013 only 11% of
+ 
+
+ align:start position:0%
+more dramatically in 2013 only 11% of
+129 million working individuals in the
+
+ align:start position:0%
+129 million working individuals in the
+ 
+
+ align:start position:0%
+129 million working individuals in the
+US had a union on a job and collective
+
+ align:start position:0%
+US had a union on a job and collective
+ 
+
+ align:start position:0%
+US had a union on a job and collective
+bargaining at work now in the private
+
+ align:start position:0%
+bargaining at work now in the private
+ 
+
+ align:start position:0%
+bargaining at work now in the private
+sector which employs most working
+
+ align:start position:0%
+sector which employs most working
+ 
+
+ align:start position:0%
+sector which employs most working
+individuals in the US this percentage is
+
+ align:start position:0%
+individuals in the US this percentage is
+ 
+
+ align:start position:0%
+individuals in the US this percentage is
+even lower barely 7% of these workers in
+
+ align:start position:0%
+even lower barely 7% of these workers in
+ 
+
+ align:start position:0%
+even lower barely 7% of these workers in
+fast food health care or technology for
+
+ align:start position:0%
+fast food health care or technology for
+ 
+
+ align:start position:0%
+fast food health care or technology for
+example barely 7% have a union at work
+
+ align:start position:0%
+example barely 7% have a union at work
+ 
+
+ align:start position:0%
+example barely 7% have a union at work
+now labor leaders and Scholars who study
+
+ align:start position:0%
+now labor leaders and Scholars who study
+ 
+
+ align:start position:0%
+now labor leaders and Scholars who study
+employment in labor unions argue that a
+
+ align:start position:0%
+employment in labor unions argue that a
+ 
+
+ align:start position:0%
+employment in labor unions argue that a
+number of factors have contributed to
+
+ align:start position:0%
+number of factors have contributed to
+ 
+
+ align:start position:0%
+number of factors have contributed to
+this decline in unions some argue for
+
+ align:start position:0%
+this decline in unions some argue for
+ 
+
+ align:start position:0%
+this decline in unions some argue for
+example that the structure of the
+
+ align:start position:0%
+example that the structure of the
+ 
+
+ align:start position:0%
+example that the structure of the
+economy plays a role as growth in
+
+ align:start position:0%
+economy plays a role as growth in
+ 
+
+ align:start position:0%
+economy plays a role as growth in
+non-union sectors concentrated in
+
+ align:start position:0%
+non-union sectors concentrated in
+ 
+
+ align:start position:0%
+non-union sectors concentrated in
+service Industries has outstripped
+
+ align:start position:0%
+service Industries has outstripped
+ 
+
+ align:start position:0%
+service Industries has outstripped
+growth in Industries like construction
+
+ align:start position:0%
+growth in Industries like construction
+ 
+
+ align:start position:0%
+growth in Industries like construction
+and Manufacturing where unions
+
+ align:start position:0%
+and Manufacturing where unions
+ 
+
+ align:start position:0%
+and Manufacturing where unions
+historically have been strong others
+
+ align:start position:0%
+historically have been strong others
+ 
+
+ align:start position:0%
+historically have been strong others
+point to the increased difficulty of
+
+ align:start position:0%
+point to the increased difficulty of
+ 
+
+ align:start position:0%
+point to the increased difficulty of
+organizing new membership and in
+
+ align:start position:0%
+organizing new membership and in
+ 
+
+ align:start position:0%
+organizing new membership and in
+particular to the legal obstacles that
+
+ align:start position:0%
+particular to the legal obstacles that
+ 
+
+ align:start position:0%
+particular to the legal obstacles that
+exist in implementing new agreements at
+
+ align:start position:0%
+exist in implementing new agreements at
+ 
+
+ align:start position:0%
+exist in implementing new agreements at
+work Recent research has found that only
+
+ align:start position:0%
+work Recent research has found that only
+ 
+
+ align:start position:0%
+work Recent research has found that only
+one in seven workplaces where workers
+
+ align:start position:0%
+one in seven workplaces where workers
+ 
+
+ align:start position:0%
+one in seven workplaces where workers
+have organized an election and voted for
+
+ align:start position:0%
+have organized an election and voted for
+ 
+
+ align:start position:0%
+have organized an election and voted for
+a union will actually see a contract in
+
+ align:start position:0%
+a union will actually see a contract in
+ 
+
+ align:start position:0%
+a union will actually see a contract in
+the year following their vote and often
+
+ align:start position:0%
+the year following their vote and often
+ 
+
+ align:start position:0%
+the year following their vote and often
+times these types of elections are
+
+ align:start position:0%
+times these types of elections are
+ 
+
+ align:start position:0%
+times these types of elections are
+contentious
+
+ align:start position:0%
+contentious
+ 
+
+ align:start position:0%
+contentious
+and in workplaces where employers have
+
+ align:start position:0%
+and in workplaces where employers have
+ 
+
+ align:start position:0%
+and in workplaces where employers have
+been charged with trying to discourage
+
+ align:start position:0%
+been charged with trying to discourage
+ 
+
+ align:start position:0%
+been charged with trying to discourage
+Union activity through unfair labor
+
+ align:start position:0%
+Union activity through unfair labor
+ 
+
+ align:start position:0%
+Union activity through unfair labor
+practices the odds go down by nearly a
+
+ align:start position:0%
+practices the odds go down by nearly a
+ 
+
+ align:start position:0%
+practices the odds go down by nearly a
+third in addition to these economic and
+
+ align:start position:0%
+third in addition to these economic and
+ 
+
+ align:start position:0%
+third in addition to these economic and
+legal challenges labor leaders and
+
+ align:start position:0%
+legal challenges labor leaders and
+ 
+
+ align:start position:0%
+legal challenges labor leaders and
+Scholars also point to increased
+
+ align:start position:0%
+Scholars also point to increased
+ 
+
+ align:start position:0%
+Scholars also point to increased
+anti-union activity not only by
+
+ align:start position:0%
+anti-union activity not only by
+ 
+
+ align:start position:0%
+anti-union activity not only by
+employers but increasingly by policy
+
+ align:start position:0%
+employers but increasingly by policy
+ 
+
+ align:start position:0%
+employers but increasingly by policy
+makers as we've seen in States like
+
+ align:start position:0%
+makers as we've seen in States like
+ 
+
+ align:start position:0%
+makers as we've seen in States like
+Wisconsin and Indiana or rolling back
+
+ align:start position:0%
+Wisconsin and Indiana or rolling back
+ 
+
+ align:start position:0%
+Wisconsin and Indiana or rolling back
+workers rights to organize and
+
+ align:start position:0%
+workers rights to organize and
+ 
+
+ align:start position:0%
+workers rights to organize and
+collective bargaining agreements so over
+
+ align:start position:0%
+collective bargaining agreements so over
+ 
+
+ align:start position:0%
+collective bargaining agreements so over
+the past three decades there's really
+
+ align:start position:0%
+the past three decades there's really
+ 
+
+ align:start position:0%
+the past three decades there's really
+been a shift not only in how many people
+
+ align:start position:0%
+been a shift not only in how many people
+ 
+
+ align:start position:0%
+been a shift not only in how many people
+experience labor unions on the job but
+
+ align:start position:0%
+experience labor unions on the job but
+ 
+
+ align:start position:0%
+experience labor unions on the job but
+in the way that we think about labor
+
+ align:start position:0%
+in the way that we think about labor
+ 
+
+ align:start position:0%
+in the way that we think about labor
+unions and in this course we've talked
+
+ align:start position:0%
+unions and in this course we've talked
+ 
+
+ align:start position:0%
+unions and in this course we've talked
+about the social contract and what it
+
+ align:start position:0%
+about the social contract and what it
+ 
+
+ align:start position:0%
+about the social contract and what it
+means at work this idea that what's good
+
+ align:start position:0%
+means at work this idea that what's good
+ 
+
+ align:start position:0%
+means at work this idea that what's good
+for workers is good for businesses and
+
+ align:start position:0%
+for workers is good for businesses and
+ 
+
+ align:start position:0%
+for workers is good for businesses and
+although we have examples of many good
+
+ align:start position:0%
+although we have examples of many good
+ 
+
+ align:start position:0%
+although we have examples of many good
+employers as discussed by Professor Zay
+
+ align:start position:0%
+employers as discussed by Professor Zay
+ 
+
+ align:start position:0%
+employers as discussed by Professor Zay
+Upton in her video many employers act as
+
+ align:start position:0%
+Upton in her video many employers act as
+ 
+
+ align:start position:0%
+Upton in her video many employers act as
+though this idea is no longer the case
+
+ align:start position:0%
+though this idea is no longer the case
+ 
+
+ align:start position:0%
+though this idea is no longer the case
+that what's good good for workers is not
+
+ align:start position:0%
+that what's good good for workers is not
+ 
+
+ align:start position:0%
+that what's good good for workers is not
+necessarily good for businesses and that
+
+ align:start position:0%
+necessarily good for businesses and that
+ 
+
+ align:start position:0%
+necessarily good for businesses and that
+unions do not have a role in improving
+
+ align:start position:0%
+unions do not have a role in improving
+ 
+
+ align:start position:0%
+unions do not have a role in improving
+the way that firms work at the same time
+
+ align:start position:0%
+the way that firms work at the same time
+ 
+
+ align:start position:0%
+the way that firms work at the same time
+declining wages less job security and
+
+ align:start position:0%
+declining wages less job security and
+ 
+
+ align:start position:0%
+declining wages less job security and
+increased costs related to things like
+
+ align:start position:0%
+increased costs related to things like
+ 
+
+ align:start position:0%
+increased costs related to things like
+health care and student loans are making
+
+ align:start position:0%
+health care and student loans are making
+ 
+
+ align:start position:0%
+health care and student loans are making
+it more difficult for working
+
+ align:start position:0%
+it more difficult for working
+ 
+
+ align:start position:0%
+it more difficult for working
+individuals all of this adds up to a
+
+ align:start position:0%
+individuals all of this adds up to a
+ 
+
+ align:start position:0%
+individuals all of this adds up to a
+difficult environment not only for labor
+
+ align:start position:0%
+difficult environment not only for labor
+ 
+
+ align:start position:0%
+difficult environment not only for labor
+unions but also for individuals who try
+
+ align:start position:0%
+unions but also for individuals who try
+ 
+
+ align:start position:0%
+unions but also for individuals who try
+to protect their rights on the job the
+
+ align:start position:0%
+to protect their rights on the job the
+ 
+
+ align:start position:0%
+to protect their rights on the job the
+good news however is that over the past
+
+ align:start position:0%
+good news however is that over the past
+ 
+
+ align:start position:0%
+good news however is that over the past
+two decades we've had a flurry of
+
+ align:start position:0%
+two decades we've had a flurry of
+ 
+
+ align:start position:0%
+two decades we've had a flurry of
+activity in organizing around economic
+
+ align:start position:0%
+activity in organizing around economic
+ 
+
+ align:start position:0%
+activity in organizing around economic
+Justice in ways that are bringing
+
+ align:start position:0%
+Justice in ways that are bringing
+ 
+
+ align:start position:0%
+Justice in ways that are bringing
+employees voices front and center these
+
+ align:start position:0%
+employees voices front and center these
+ 
+
+ align:start position:0%
+employees voices front and center these
+include new strategies of labor unions
+
+ align:start position:0%
+include new strategies of labor unions
+ 
+
+ align:start position:0%
+include new strategies of labor unions
+to expand their membership and include
+
+ align:start position:0%
+to expand their membership and include
+ 
+
+ align:start position:0%
+to expand their membership and include
+more working people the growth of worker
+
+ align:start position:0%
+more working people the growth of worker
+ 
+
+ align:start position:0%
+more working people the growth of worker
+centers and labor associations outside
+
+ align:start position:0%
+centers and labor associations outside
+ 
+
+ align:start position:0%
+centers and labor associations outside
+this realm and the strengthening of
+
+ align:start position:0%
+this realm and the strengthening of
+ 
+
+ align:start position:0%
+this realm and the strengthening of
+employment policy through Economic
+
+ align:start position:0%
+employment policy through Economic
+ 
+
+ align:start position:0%
+employment policy through Economic
+Development we've also seen a growing
+
+ align:start position:0%
+Development we've also seen a growing
+ 
+
+ align:start position:0%
+Development we've also seen a growing
+number of social movements that are
+
+ align:start position:0%
+number of social movements that are
+ 
+
+ align:start position:0%
+number of social movements that are
+highlighting the ways in which the
+
+ align:start position:0%
+highlighting the ways in which the
+ 
+
+ align:start position:0%
+highlighting the ways in which the
+social contract can be reestablished at
+
+ align:start position:0%
+social contract can be reestablished at
+ 
+
+ align:start position:0%
+social contract can be reestablished at
+work in the next video we'll talk about
+
+ align:start position:0%
+work in the next video we'll talk about
+ 
+
+ align:start position:0%
+work in the next video we'll talk about
+each of these in a bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detail for
\ No newline at end of file
diff --git a/XsYXACeIklU.txt b/XsYXACeIklU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1b6e45d5688a1156ff7db03d26ab3903886a14c
--- /dev/null
+++ b/XsYXACeIklU.txt
@@ -0,0 +1,2517 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOHN TSITSIKLIS: Today we're
+going to finish our discussion
+
+of the Poisson process.
+
+We're going to see a few of
+its properties, do a few
+
+interesting problems, some more
+interesting than others.
+
+So go through a few examples and
+then we're going to talk
+
+about some quite strange things
+that happen with the
+
+Poisson process.
+
+So the first thing is to
+remember what the Poisson
+
+processes is.
+
+It's a model, let's say, of
+arrivals of customers that
+
+are, in some sense, quote
+unquote, completely random,
+
+that is a customer can arrive
+at any point in time.
+
+All points in time are
+equally likely.
+
+And different points in time
+are sort of independent of
+
+other points in time.
+
+So the fact that I got an
+arrival now doesn't tell me
+
+anything about whether there's
+going to be an arrival at some
+
+other time.
+
+In some sense, it's a continuous
+time version of the
+
+Bernoulli process.
+
+So the best way to think about
+the Poisson process is that we
+
+divide time into extremely
+tiny slots.
+
+And in each time slot, there's
+an independent possibility of
+
+having an arrival.
+
+Different time slots are
+independent of each other.
+
+On the other hand, when the slot
+is tiny, the probability
+
+for obtaining an arrival during
+that tiny slot is
+
+itself going to be tiny.
+
+So we capture these properties
+into a formal definition what
+
+the Poisson process is.
+
+We have a probability mass
+function for the number of
+
+arrivals, k, during an interval
+of a given length.
+
+So this is the sort of basic
+description of the
+
+distribution of the number
+of arrivals.
+
+So tau is fixed.
+
+And k is the parameter.
+
+So when we add over all k's, the
+sum of these probabilities
+
+has to be equal to 1.
+
+There's a time homogeneity
+assumption, which is hidden in
+
+this, namely, the only thing
+that matters is the duration
+
+of the time interval, not where
+the time interval sits
+
+on the real axis.
+
+Then we have an independence
+assumption.
+
+Intervals that are disjoint are
+statistically independent
+
+from each other.
+
+So any information you give me
+about arrivals during this
+
+time interval doesn't change my
+beliefs about what's going
+
+to happen during another
+time interval.
+
+So this is a generalization
+of the idea that we had in
+
+Bernoulli processes that
+different time slots are
+
+independent of each other.
+
+And then to specify this
+function, the distribution of
+
+the number of arrivals, we
+sort of go in stages.
+
+We first specify this function
+for the case where the time
+
+interval is very small.
+
+And I'm telling you what those
+probabilities will be.
+
+And based on these then, we do
+some calculations and to find
+
+the formula for the distribution
+of the number of
+
+arrivals for intervals of
+a general duration.
+
+So for a small duration, delta,
+the probability of
+
+obtaining 1 arrival
+is lambda delta.
+
+The remaining probability is
+assigned to the event that we
+
+get to no arrivals during
+that interval.
+
+The probability of obtaining
+more than 1 arrival in a tiny
+
+interval is essentially 0.
+
+And when we say essentially,
+it's means modular, terms that
+
+of order delta squared.
+
+And when delta is very small,
+anything which is delta
+
+squared can be ignored.
+
+So up to delta squared terms,
+that's what happened during a
+
+little interval.
+
+Now if we know the probability
+distribution for the number of
+
+arrivals in a little interval.
+
+We can use this to get the
+distribution for the number of
+
+arrivals over several
+intervals.
+
+How do we do that?
+
+The big interval is composed
+of many little intervals.
+
+Each little interval is
+independent from any other
+
+little interval, so is it is
+as if we have a sequence of
+
+Bernoulli trials.
+
+Each Bernoulli trial is
+associated with a little
+
+interval and has a small
+probability of obtaining a
+
+success or an arrival during
+that mini-slot.
+
+On the other hand, when delta
+is small, and you take a big
+
+interval and chop it
+up, you get a large
+
+number of little intervals.
+
+So what we essentially have here
+is a Bernoulli process,
+
+in which is the number of
+trials is huge but the
+
+probability of success during
+any given trial is tiny.
+
+The average number of trials
+ends up being proportional to
+
+the length of the interval.
+
+If you have twice as large an
+interval, it's as if you're
+
+having twice as many over these
+mini-trials, so the
+
+expected number of arrivals will
+increase proportionately.
+
+There's also this parameter
+lambda, which we interpret as
+
+expected number of arrivals
+per unit time.
+
+And it comes in those
+probabilities here.
+
+When you double lambda, this
+means that a little interval
+
+is twice as likely to
+get an arrival.
+
+So you would expect
+to get twice as
+
+many arrivals as well.
+
+That's why the expected number
+of arrivals during an interval
+
+of length tau also scales
+proportional to
+
+this parameter lambda.
+
+Somewhat unexpectedly, it turns
+out that the variance of
+
+the number of arrivals is also
+the same as the mean.
+
+This is a peculiarity
+that happens
+
+in the Poisson process.
+
+So this is one way of thinking
+about Poisson process, in
+
+terms of little intervals, each
+one of which has a tiny
+
+probability of success.
+
+And we think of the distribution
+associated with
+
+that process as being
+described by
+
+this particular PMF.
+
+So this is the PMF for the
+number of arrivals during an
+
+interval of a fixed
+duration, tau.
+
+It's a PMF that extends all
+over the entire range of
+
+non-negative integers.
+
+So the number of arrivals you
+can get during an interval for
+
+certain length can
+be anything.
+
+You can get as many arrivals
+as you want.
+
+Of course the probability of
+getting a zillion arrivals is
+
+going to be tiny.
+
+But in principle, this
+is possible.
+
+And that's because an interval,
+even if it's a fixed
+
+length, consists of an infinite
+number of mini-slots
+
+in some sense.
+
+You can divide, chop
+it up, into as many
+
+mini-slots as you want.
+
+So in principle, it's
+possible that every
+
+mini-slot gets an arrival.
+
+In principle, it's possible to
+get an arbitrarily large
+
+number of arrivals.
+
+So this particular formula here
+is not very intuitive
+
+when you look at it.
+
+But it's a legitimate PMF.
+
+And it's called the
+Poisson PMF.
+
+It's the PMF that describes
+the number of arrivals.
+
+So that's one way of thinking
+about the Poisson process,
+
+where the basic object of
+interest would be this PMF and
+
+you try to work with it.
+
+There's another way of thinking
+about what happens in
+
+the Poisson process.
+
+And this has to do with letting
+things evolve in time.
+
+You start at time 0.
+
+There's going to be a time at
+which the first arrival
+
+occurs, and call that time T1.
+
+This time turns out to have an
+exponential distribution with
+
+parameter lambda.
+
+Once you get an arrival,
+it's as if the
+
+process starts fresh.
+
+The best way to understand why
+this is the case is by
+
+thinking in terms of
+the analogy with
+
+the Bernoulli process.
+
+If you believe that statement
+for the Bernoulli process,
+
+since this is a limiting case,
+it should also be true.
+
+So starting from this time,
+we're going to wait a random
+
+amount of time until we get the
+second arrival This random
+
+amount of time, let's
+call it T2.
+
+This time, T2 is also going
+to have an exponential
+
+distribution with the same
+parameter, lambda.
+
+And these two are going to be
+independent of each other.
+
+OK?
+
+So the Poisson process has all
+the same memorylessness
+
+properties that the Bernoulli
+process has.
+
+What's another way of thinking
+of this property?
+
+So think of a process where
+you have a light bulb.
+
+The time at the light bulb burns
+out, you can model it by
+
+an exponential random
+variable.
+
+And suppose that they tell you
+that so far, we're are sitting
+
+at some time, T. And I tell you
+that the light bulb has
+
+not yet burned out.
+
+What does this tell you about
+the future of the light bulb?
+
+Is the fact that they didn't
+burn out, so far, is it good
+
+news or is it bad news?
+
+Would you rather keep this light
+bulb that has worked for
+
+t times steps and is still OK?
+
+Or would you rather use a new
+light bulb that starts new at
+
+that point in time?
+
+Because of the memorylessness
+property, the past of that
+
+light bulb doesn't matter.
+
+So the future of this light bulb
+is statistically the same
+
+as the future of a
+new light bulb.
+
+For both of them, the time until
+they burn out is going
+
+to be described an exponential
+distribution.
+
+So one way that people described
+the situation is to
+
+say that used is exactly
+as good as a new.
+
+So a used on is no worse
+than a new one.
+
+A used one is no better
+than a new one.
+
+So a used light bulb that
+hasn't yet burnt out is
+
+exactly as good as
+a new light bulb.
+
+So that's another way of
+thinking about the
+
+memorylessness that we have
+in the Poisson process.
+
+Back to this picture.
+
+The time until the second
+arrival is the sum of two
+
+independent exponential
+random variables.
+
+So, in principle, you can use
+the convolution formula to
+
+find the distribution of T1
+plus T2, and that would be
+
+what we call Y2, the time until
+the second arrival.
+
+But there's also a direct
+way of obtaining to the
+
+distribution of Y2, and this is
+the calculation that we did
+
+last time on the blackboard.
+
+And actually, we did
+it more generally.
+
+We found the time until the
+case arrival occurs.
+
+It has a closed form formula,
+which is called the Erlang
+
+distribution with k degrees
+of freedom.
+
+So let's see what's
+going on here.
+
+It's a distribution
+Of what kind?
+
+It's a continuous
+distribution.
+
+It's a probability
+density function.
+
+This is because the time is a
+continuous random variable.
+
+Time is continuous.
+
+Arrivals can happen
+at any time.
+
+So we're talking
+about the PDF.
+
+This k is just the parameter
+of the distribution.
+
+We're talking about the
+k-th arrival, so
+
+k is a fixed number.
+
+Lambda is another parameter of
+the distribution, which is the
+
+arrival rate So it's a PDF over
+the Y's, whereas lambda
+
+and k are parameters of
+the distribution.
+
+OK.
+
+So this was what we knew
+from last time.
+
+Just to get some practice, let
+us do a problem that's not too
+
+difficult, but just to see how
+we use the various formulas
+
+that we have.
+
+So Poisson was a mathematician,
+but Poisson
+
+also means fish in French.
+
+So Poisson goes fishing.
+
+And let's assume that fish
+are caught according
+
+to a Poisson process.
+
+That's not too bad
+an assumption.
+
+At any given point in time, you
+have a little probability
+
+that a fish would be caught.
+
+And whether you catch one now
+is sort of independent about
+
+whether at some later time a
+fish will be caught or not.
+
+So let's just make
+this assumption.
+
+And suppose that the rules of
+the game are that you--
+
+Fish are being called it the
+certain rate of 0.6 per hour.
+
+You fish for 2 hours,
+no matter what.
+
+And then there are two
+possibilities.
+
+If I have caught a fish,
+I stop and go home.
+
+So if some fish have been
+caught, so there's at least 1
+
+arrival during this interval,
+I go home.
+
+Or if nothing has being caught,
+I continue fishing
+
+until I catch something.
+
+And then I go home.
+
+So that's the description of
+what is going to happen.
+
+And now let's starts asking
+questions of all sorts.
+
+What is the probability that
+I'm going to be fishing for
+
+more than 2 hours?
+
+I will be fishing for more than
+2 hours, if and only if
+
+no fish were caught during those
+2 hours, in which case,
+
+I will have to continue.
+
+Therefore, this is just
+this quantity.
+
+The probability of catching
+2 fish in--
+
+of catching 0 fish in the next
+2 hours, and according to the
+
+formula that we have, this is
+going to be e to the minus
+
+lambda times how much
+time we have.
+
+There's another way of
+thinking about this.
+
+The probability that I fish for
+more than 2 hours is the
+
+probability that the first catch
+happens after time 2,
+
+which would be the integral
+from 2 to infinity of the
+
+density of the first
+arrival time.
+
+And that density is
+an exponential.
+
+So you do the integral of an
+exponential, and, of course,
+
+you would get the same answer.
+
+OK.
+
+That's easy.
+
+So what's the probability of
+fishing for more than 2 but
+
+less than 5 hours?
+
+What does it take for
+this to happen?
+
+For this to happen, we need to
+catch 0 fish from time 0 to 2
+
+and catch the first fish
+sometime between 2 and 5.
+
+So if you--
+
+one way of thinking about what's
+happening here might be
+
+to say that there's a
+Poisson process that
+
+keeps going on forever.
+
+But as soon as I catch the
+first fish, instead of
+
+continuing fishing and obtaining
+those other fish I
+
+just go home right now.
+
+Now the fact that I go home
+before time 5 means that, if I
+
+were to stay until time
+5, I would have
+
+caught at least 1 fish.
+
+I might have caught
+more than 1.
+
+So the event of interest here
+is that the first catch
+
+happens between times 2 and 5.
+
+So one way of calculating
+this quantity would be--
+
+Its the probability that the
+first catch happens between
+
+times 2 and 5.
+
+Another way to deal with it
+is to say, this is the
+
+probability that I caught 0 fish
+in the first 2 hours and
+
+then the probability that I
+catch at least 1 fish during
+
+the next 3 hours.
+
+This.
+
+What is this?
+
+The probability of 0 fish in
+the next 3 hours is the
+
+probability of 0 fish
+during this time.
+
+1 minus this is the probability
+of catching at
+
+least 1 fish, of having
+at least 1 arrival,
+
+between times 2 and 5.
+
+If there's at least 1 arrival
+between times 2 and 5, then I
+
+would have gone home
+by time 5.
+
+So both of these, if you plug-in
+numbers and all that,
+
+of course, are going to give
+you the same answer.
+
+Now next, what's the probability
+that I catch at
+
+least 2 fish?
+
+In which scenario are we?
+
+Under this scenario, I go home
+when I catch my first fish.
+
+So in order to catch
+at least 2 fish, it
+
+must be in this case.
+
+So this is the same as the event
+that I catch at least 2
+
+fish during the first
+2 time steps.
+
+So it's going to be the
+probability from 2 to
+
+infinity, the probability that
+I catch 2 fish, or that I
+
+catch 3 fish, or I catch
+more than that.
+
+So it's this quantity.
+
+k is the number of fish
+that I catch.
+
+At least 2, so k goes
+from 2 to infinity.
+
+These are the probabilities of
+catching a number k of fish
+
+during this interval.
+
+And if you want a simpler form
+without an infinite sum, this
+
+would be 1 minus the probability
+of catching 0
+
+fish, minus the probability of
+catching 1 fish, during a time
+
+interval of length 2.
+
+Another way to think of it.
+
+I'm going to catch 2 fish, at
+least 2 fish, if and only if
+
+the second fish caught in this
+process happens before time 2.
+
+So that's another way of
+thinking about the same event.
+
+So it's going to be the
+probability that the random
+
+variable Y2, the arrival time
+over the second fish, is less
+
+than or equal to 2.
+
+OK.
+
+The next one is a
+little trickier.
+
+Here we need to do a little
+bit of divide and conquer.
+
+Overall, in this expedition,
+what the expected number of
+
+fish to be caught?
+
+One way to think about it is
+to try to use the total
+
+expectations theorem.
+
+And think of expected number of
+fish, given this scenario,
+
+or expected number of fish,
+given this scenario.
+
+That's a little more complicated
+than the way I'm
+
+going to do it.
+
+The way I'm going to do is
+to think as follows--
+
+Expected number of fish is the
+expected number of fish caught
+
+between times 0 and 2 plus
+expected number of fish caught
+
+after time 2.
+
+So what's the expected number
+caught between time 0 and 2?
+
+This is lambda t.
+
+So lambda is 0.6 times 2.
+
+This is the expected number of
+fish that are caught between
+
+times 0 and 2.
+
+Now let's think about the
+expected number of fish caught
+
+afterwards.
+
+How many fish are being
+caught afterwards?
+
+Well it depends on
+the scenario.
+
+If we're in this scenario,
+we've gone home
+
+and we catch 0.
+
+If we're in this scenario, then
+we continue fishing until
+
+we catch one.
+
+So the expected number of fish
+to be caught after time 2 is
+
+going to be the probability
+of this scenario times 1.
+
+And the probability of that
+scenario is the probability
+
+that they call it's 0 fish
+during the first 2 time steps
+
+times 1, which is the number of
+fish I'm going to catch if
+
+I continue.
+
+The expected total fishing time
+we can calculate exactly
+
+the same way.
+
+I'm jumping to the last one.
+
+My total fishing time has a
+period of 2 time steps.
+
+I'm going to fish for 2 time
+steps no matter what.
+
+And then if I caught 0 fish,
+which happens with this
+
+probability, my expected time
+is going to be the expected
+
+time from here onwards, which is
+the expected value of this
+
+geometric random variable
+with parameter lambda.
+
+So the expected time
+is 1 over lambda.
+
+And in our case this,
+is 1/0.6.
+
+Finally, if I tell you that I
+have been fishing for 4 hours
+
+and nothing has been caught so
+far, how much do you expect
+
+this quantity to be?
+
+Here is the story that, again,
+that for the Poisson process
+
+used is as good as new.
+
+The process does not
+have any memory.
+
+Given what happens in the past
+doesn't matter for the future.
+
+It's as if the process starts
+new at this point in time.
+
+So this one is going to be,
+again, the same exponentially
+
+distributed random
+variable with the
+
+same parameter lambda.
+
+So expected time until an
+arrival comes is an
+
+exponential distribut --
+
+has an exponential distribution
+with parameter
+
+lambda, no matter what has
+happened in the past.
+
+Starting from now and looking
+into the future, it's as if
+
+the process has just started.
+
+So it's going to be 1 over
+lambda, which is 1/0.6.
+
+OK.
+
+Now our next example is going
+to be a little more
+
+complicated or subtle.
+
+But before we get to the
+example, let's refresh our
+
+memory about what we discussed
+last time about merging
+
+Poisson independent
+Poisson processes.
+
+Instead of drawing the picture
+that way, another way we could
+
+draw it could be this.
+
+We have a Poisson process with
+rate lambda1, and a Poisson
+
+process with rate lambda2.
+
+They have, each one of these,
+have their arrivals.
+
+And then we form the
+merged process.
+
+And the merged process records
+an arrival whenever there's an
+
+arrival in either of
+the two processes.
+
+This process in that process are
+assumed to be independent
+
+of each other.
+
+Now different times in this
+process and that process are
+
+independent of each other.
+
+So what happens in these two
+time intervals is independent
+
+from what happens in these
+two time intervals.
+
+These two time intervals to
+determine what happens here.
+
+These two time intervals
+determine what happens there.
+
+So because these are independent
+from these, this
+
+means that this is also
+independent from that.
+
+So the independence assumption
+is satisfied
+
+for the merged process.
+
+And the merged process turns out
+to be a Poisson process.
+
+And if you want to find the
+arrival rate for that process,
+
+you argue as follows.
+
+During a little interval of
+length delta, we have
+
+probability lambda1
+delta of having an
+
+arrival in this process.
+
+We have probability lambda2
+delta of an arrival in this
+
+process, plus second
+order terms in
+
+delta, which we're ignoring.
+
+And then you do the calculation
+and you find that
+
+in this process, you're going
+to have an arrival
+
+probability, which is lambda1
+plus lambda2, again ignoring
+
+second order in delta--
+
+terms that are second
+order in delta.
+
+So the merged process is a
+Poisson process whose arrival
+
+rate is the sum of the
+arrival rates of
+
+the individual processes.
+
+And the calculation we did at
+the end of the last lecture--
+
+If I tell you that the new
+arrival happened here, where
+
+did that arrival come from?
+
+Did it come from here
+or from there?
+
+If the lambda1 is equal to
+lambda2, then by symmetry you
+
+would say that it's equally
+likely to have come from here
+
+or to come from there.
+
+But if this lambda is much
+bigger than that lambda, the
+
+fact that they saw an arrival
+is more likely to have come
+
+from there.
+
+And the formula that captures
+this is the following.
+
+This is the probability that my
+arrival has come from this
+
+particular stream rather than
+that particular stream.
+
+So when an arrival comes and you
+ask, what is the origin of
+
+that arrival?
+
+It's as if I'm flipping a
+coin with these odds.
+
+And depending on outcome of that
+coin, I'm going to tell
+
+you came from there or
+it came from there.
+
+So the origin of an arrival
+is either this
+
+stream or that stream.
+
+And this is the probability that
+the origin of the arrival
+
+is that one.
+
+Now if we look at 2 different
+arrivals, and we ask about
+
+their origins--
+
+So let's think about the origin
+of this arrival and
+
+compare it with the origin
+that arrival.
+
+The origin of this arrival
+is random.
+
+It could be right be either
+this or that.
+
+And this is the relevant
+probability.
+
+The origin of that arrival
+is random.
+
+It could be either here or is
+there, and again, with the
+
+same relevant probability.
+
+Question.
+
+The origin of this arrival, is
+it dependent or independent
+
+from the origin that arrival?
+
+And here's how the
+argument goes.
+
+Separate times are
+independent.
+
+Whatever has happened in the
+process during this set of
+
+times is independent from
+whatever happened in the
+
+process during that
+set of times.
+
+Because different times have
+nothing to do with each other,
+
+the origin of this, of an
+arrival here, has nothing to
+
+do with the origin of
+an arrival there.
+
+So the origins of different
+arrivals are also independent
+
+random variables.
+
+So if I tell you that--
+
+yeah.
+
+OK.
+
+So it as if that each time that
+you have an arrival in
+
+the merge process, it's as if
+you're flipping a coin to
+
+determine where did that arrival
+came from and these
+
+coins are independent
+of each other.
+
+OK.
+
+OK.
+
+Now we're going to use this--
+
+what we know about merged
+processes to solve the problem
+
+that would be harder to do, if
+you were not using ideas from
+
+Poisson processes.
+
+So the formulation of the
+problem has nothing to do with
+
+the Poisson process.
+
+The formulation is
+the following.
+
+We have 3 light-bulbs.
+
+And each light bulb is
+independent and is going to
+
+die out at the time that's
+exponentially distributed.
+
+So 3 light bulbs.
+
+They start their lives and
+then at some point
+
+they die or burn out.
+
+So let's think of this as X,
+this as Y, and this as Z.
+
+And we're interested in the
+time until the last
+
+light-bulb burns out.
+
+So we're interested in the
+maximum of the 3 random
+
+variables, X, Y, and Z. And in
+particular, we want to find
+
+the expected value
+of this maximum.
+
+OK.
+
+So you can do derived
+distribution, use the expected
+
+value rule, anything you want.
+
+You can get this answer using
+the tools that you already
+
+have in your hands.
+
+But now let us see how we can
+connect to this picture with a
+
+Poisson picture and come up
+with the answer in a very
+
+simple way.
+
+What is an exponential
+random variable?
+
+An exponential random variable
+is the first act in the long
+
+play that involves a whole
+Poisson process.
+
+So an exponential random
+variable is the first act of a
+
+Poisson movie.
+
+Same thing here.
+
+You can think of this random
+variable as being part of some
+
+Poisson process that
+has been running.
+
+So it's part of this
+bigger picture.
+
+We're still interested in
+the maximum of the 3.
+
+The other arrivals are not going
+to affect our answers.
+
+It's just, conceptually
+speaking, we can think of the
+
+exponential random variable as
+being embedded in a bigger
+
+Poisson picture.
+
+So we have 3 Poisson process
+that are running in parallel.
+
+Let us split the expected time
+until the last burnout into
+
+pieces, which is time until the
+first burnout, time from
+
+the first until the second,
+and time from the
+
+second until the third.
+
+And find the expected values of
+each one of these pieces.
+
+What can we say about the
+expected value of this?
+
+This is the first arrival
+out of all of
+
+these 3 Poisson processes.
+
+It's the first event that
+happens when you look at all
+
+of these processes
+simultaneously.
+
+So 3 Poisson processes
+running in parallel.
+
+We're interested in the time
+until one of them, any one of
+
+them, gets in arrival.
+
+Rephrase.
+
+We merged the 3 Poisson
+processes, and we ask for the
+
+time until we observe an arrival
+in the merged process.
+
+When 1 of the 3 gets an arrival
+for the first time,
+
+the merged process gets
+its first arrival.
+
+So what's the expected
+value of this time
+
+until the first burnout?
+
+It's going to be the
+expected value of a
+
+Poisson random variable.
+
+So the first burnout is going
+to have an expected
+
+value, which is--
+
+OK.
+
+It's a Poisson process.
+
+The merged process of the 3 has
+a collective arrival rate,
+
+which is 3 times lambda.
+
+So this is the parameter over
+the exponential distribution
+
+that describes the time until
+the first arrival in the
+
+merged process.
+
+And the expected value
+of this random
+
+variable is 1 over that.
+
+When you have an exponential
+random variable with parameter
+
+lambda, the expected value
+of that random
+
+variable is 1 over lambda.
+
+Here we're talking about the
+first arrival time in a
+
+process with rate 3 lambda.
+
+The expected time until
+the first arrival
+
+is 1 over (3 lambda).
+
+Alright.
+
+So at this time, this bulb, this
+arrival happened, this
+
+bulb has been burned.
+
+So we don't care about
+that bulb anymore.
+
+We start at this time,
+and we look forward.
+
+This bulb has been burned.
+
+So let's just look forward
+from now on.
+
+What have we got?
+
+We have two bulbs that
+are burning.
+
+We have a Poisson process that's
+the bigger picture of
+
+what could happen to that light
+bulb, if we were to keep
+
+replacing it.
+
+Another Poisson process.
+
+These two processes are,
+again, independent.
+
+From this time until that time,
+how long does it take?
+
+It's the time until either
+this process records an
+
+arrival or that process
+records and arrival.
+
+That's the same as the time
+that the merged process of
+
+these two records an arrival.
+
+So we're talking about the
+expected time until the first
+
+arrival in a merged process.
+
+The merged process is Poisson.
+
+It's Poisson with
+rate 2 lambda.
+
+So that extra time is
+going to take--
+
+the expected value is going to
+be 1 over the (rate of that
+
+Poisson process).
+
+So 1 over (2 lambda) is
+the expected value
+
+of this random variable.
+
+So at this point, this bulb
+now is also burned.
+
+So we start looking
+from this time on.
+
+That part of the picture
+disappears.
+
+Starting from this time, what's
+the expected value
+
+until that remaining light-bulb
+burns out?
+
+Well, as we said before, in
+a Poisson process or with
+
+exponential random variables,
+we have memorylessness.
+
+A used bulb is as good
+as a new one.
+
+So it's as if we're starting
+from scratch here.
+
+So this is going to be an
+exponential random variable
+
+with parameter lambda.
+
+And the expected value of it is
+going to be 1 over lambda.
+
+So the beauty of approaching
+this problem in this
+
+particular way is, of course,
+that we manage to do
+
+everything without any calculus
+at all, without
+
+striking an integral, without
+trying to calculate
+
+expectations in any form.
+
+Most of the non-trivial problems
+that you encounter in
+
+the Poisson world basically
+involve tricks of these kind.
+
+You have a question and you try
+to rephrase it, trying to
+
+think in terms of what might
+happen in the Poisson setting,
+
+use memorylessness, use merging,
+et cetera, et cetera.
+
+Now we talked about merging.
+
+It turns out that the splitting
+of Poisson processes
+
+also works in a nice way.
+
+The story here is exactly
+the same as for
+
+the Bernoulli process.
+
+So I'm having a Poisson
+process.
+
+And each time, with some rate
+lambda, and each time that an
+
+arrival comes, I'm going to send
+it to that stream and the
+
+record an arrival here with some
+probability P. And I'm
+
+going to send it to the other
+stream with some probability 1
+
+minus P. So either of this
+will happen or that will
+
+happen, depending on
+the outcome of the
+
+coin flip that I do.
+
+Each time that then arrival
+occurs, I flip a coin and I
+
+decide whether to record
+it here or there.
+
+This is called splitting
+a Poisson
+
+process into two pieces.
+
+What kind of process
+do we get here?
+
+If you look at the little
+interval for length delta,
+
+what's the probability
+that this little
+
+interval gets an arrival?
+
+It's the probability that this
+one gets an arrival, which is
+
+lambda delta times the
+probability that after I get
+
+an arrival my coin flip came out
+to be that way, so that it
+
+sends me there.
+
+So this means that this little
+interval is going to have
+
+probability lambda delta P. Or
+maybe more suggestively, I
+
+should write it as lambda
+P times delta.
+
+So every little interval has
+a probability of an arrival
+
+proportional to delta.
+
+The proportionality factor is
+lambda P. So lambda P is the
+
+rate of that process.
+
+And then you go through the
+mental exercise that you went
+
+through for the Bernoulli
+process to argue that a
+
+different intervals here are
+independent and so on.
+
+And that completes checking that
+this process is going to
+
+be a Poisson process.
+
+So when you split a Poisson
+process by doing independent
+
+coin flips each time that
+something happens, the
+
+processes that you get is again
+a Poisson process, but
+
+of course with a reduced rate.
+
+So instead of the word
+splitting, sometimes people
+
+also use the words
+thinning-out.
+
+That is, out of the arrivals
+that came, you keep a few but
+
+throw away a few.
+
+OK.
+
+So now the last topic over
+this lecture is a quite
+
+curious phenomenon that
+goes under the
+
+name of random incidents.
+
+So here's the story.
+
+Buses have been running
+on Mass Ave. from time
+
+immemorial.
+
+And the bus company that runs
+the buses claims that they
+
+come as a Poisson process with
+some rate, let's say, of 4
+
+buses per hour.
+
+So that the expected time
+between bus arrivals is going
+
+to be 15 minutes.
+
+OK.
+
+Alright.
+
+So people have been complaining
+that they have
+
+been showing up there.
+
+They think the buses are
+taking too long.
+
+So you are asked
+to investigate.
+
+Is the company--
+
+Does it operate according
+to its promises or not.
+
+So you send an undercover agent
+to go and check the
+
+interarrival times
+of the buses.
+
+Are they 15 minutes?
+
+Or are they longer?
+
+So you put your dark glasses
+and you show up at the bus
+
+stop at some random time.
+
+And you go and ask the guy in
+the falafel truck, how long
+
+has it been since the
+last arrival?
+
+So of course that guy works
+for the FBI, right?
+
+So they tell you, well, it's
+been, let's say, 12 minutes
+
+since the last bus arrival.
+
+And then you say,
+"Oh, 12 minutes.
+
+Average time is 15.
+
+So a bus should be coming
+any time now."
+
+Is that correct?
+
+No, you wouldn't
+think that way.
+
+It's a Poisson process.
+
+It doesn't matter how long
+it has been since
+
+the last bus arrival.
+
+So you don't go through
+that fallacy.
+
+Instead of predicting how long
+it's going to be, you just sit
+
+down there and wait and
+measure the time.
+
+And you find that this is,
+let's say, 11 minutes.
+
+And you go to your boss and
+report, "Well, it took--
+
+I went there and the time from
+the previous bus to the next
+
+one was 23 minutes.
+
+It's more than the 15
+that they said."
+
+So go and do that again.
+
+You go day after day.
+
+You keep these statistics of the
+length of this interval.
+
+And you tell your boss it's
+a lot more than 15.
+
+It tends to be more
+like 30 or so.
+
+So the bus company
+is cheating us.
+
+Does the bus company really run
+Poisson buses at the rate
+
+that they have promised?
+
+Well let's analyze the situation
+here and figure out
+
+what the length of
+this interval
+
+should be, on the average.
+
+The naive argument is that
+this interval is an
+
+interarrival time.
+
+And interarrival times, on the
+average, are 15 minutes, if
+
+the company runs indeed Poisson
+processes with these
+
+interarrival times.
+
+But actually the situation is
+a little more subtle because
+
+this is not a typical
+interarrival interval.
+
+This interarrival interval
+consists of two pieces.
+
+Let's call them T1
+and T1 prime.
+
+What can you tell me about those
+two random variables?
+
+What kind of random
+variable is T1?
+
+Starting from this time, with
+the Poisson process, the past
+
+doesn't matter.
+
+It's the time until an
+arrival happens.
+
+So T1 is going to be an
+exponential random variable
+
+with parameter lambda.
+
+So in particular, the expected
+value of T1 is
+
+going to be 15 by itself.
+
+How about the random
+variable T1 prime.
+
+What kind of random
+variable is it?
+
+This is like the first arrival
+in a Poisson process that runs
+
+backwards in time.
+
+What kind of process is a
+Poisson process running
+
+backwards in time?
+
+Let's think of coin flips.
+
+Suppose you have a movie
+of coin flips.
+
+And for some accident, that
+fascinating movie, you happen
+
+to watch it backwards.
+
+Will it look any different
+statistically?
+
+No.
+
+It's going to be just the
+sequence of random coin flips.
+
+So a Bernoulli process that's
+runs in reverse time is
+
+statistically identical
+to a Bernoulli
+
+process in forward time.
+
+The Poisson process is a
+limit of the Bernoulli.
+
+So, same story with the
+Poisson process.
+
+If you run it backwards in
+time it looks the same.
+
+So looking backwards in time,
+this is a Poisson process.
+
+And T1 prime is the time until
+the first arrival in this
+
+backward process.
+
+So T1 prime is also going to
+be an exponential random
+
+variable with the same
+parameter, lambda.
+
+And the expected value
+of T1 prime is 15.
+
+Conclusion is that the expected
+length of this
+
+interval is going to
+be 30 minutes.
+
+And the fact that this agent
+found the average to be
+
+something like 30 does not
+contradict the claims of the
+
+bus company that they're running
+Poisson buses with a
+
+rate of lambda equal to 4.
+
+OK.
+
+So maybe the company can this
+way-- they can defend
+
+themselves in court.
+
+But there's something
+puzzling here.
+
+How long is the interarrival
+time?
+
+Is it 15?
+
+Or is it 30?
+
+On the average.
+
+The issue is what do we
+mean by a typical
+
+interarrival time.
+
+When we say typical, we mean
+some kind of average.
+
+But average over what?
+
+And here's two different ways
+of thinking about averages.
+
+You number the buses.
+
+And you have bus number 100.
+
+You have bus number 101,
+bus number 102, bus
+
+number 110, and so on.
+
+One way of thinking about
+averages is that you pick a
+
+bus number at random.
+
+I pick, let's say, that bus,
+all buses being sort of
+
+equally likely to be picked.
+
+And I measure this interarrival
+time.
+
+So for a typical bus.
+
+Then, starting from here until
+there, the expected time has
+
+to be 1 over lambda, for
+the Poisson process.
+
+But what we did in
+this experiment
+
+was something different.
+
+We didn't pick a
+bus at random.
+
+We picked a time at random.
+
+And if the picture is, let's
+say, this way, I'm much more
+
+likely to pick this interval
+and therefore this
+
+interarrival time, rather
+than that interval.
+
+Because, this interval
+corresponds to very few times.
+
+So if I'm picking a time at
+random and, in some sense,
+
+let's say, uniform, so that all
+times are equally likely,
+
+I'm much more likely to fall
+inside a big interval rather
+
+than a small interval.
+
+So a person who shows up at the
+bus stop at a random time.
+
+They're selecting an interval in
+a biased way, with the bias
+
+favor of longer intervals.
+
+And that's why what they observe
+is a random variable
+
+that has a larger expected
+value then the ordinary
+
+expected value.
+
+So the subtlety here is to
+realize that we're talking
+
+between two different kinds
+of experiments.
+
+Picking a bus number at random
+verses picking an interval at
+
+random with a bias in favor
+of longer intervals.
+
+Lots of paradoxes that one
+can cook up using Poisson
+
+processes and random processes
+in general often have to do
+
+with the story of this kind.
+
+The phenomenon that we had in
+this particular example also
+
+shows up in general, whenever
+you have other kinds of
+
+arrival processes.
+
+So the Poisson process is the
+simplest arrival process there
+
+is, where the interarrival
+times are
+
+exponential random variables.
+
+There's a larger class
+of models.
+
+They're called renewal
+processes, in which, again, we
+
+have a sequence of successive
+arrivals, interarrival times
+
+are identically distributed and
+independent, but they may
+
+come from a general
+distribution.
+
+So to make the same point of the
+previous example but in a
+
+much simpler setting, suppose
+that bus interarrival times
+
+are either 5 or 10
+minutes apart.
+
+So you get some intervals
+that are of length 5.
+
+You get some that are
+of length 10.
+
+And suppose that these
+are equally likely.
+
+So we have -- not exactly --
+
+In the long run, we have as many
+5 minute intervals as we
+
+have 10 minute intervals.
+
+So the average interarrival
+time is 7 and 1/2.
+
+But if a person shows up at a
+random time, what are they
+
+going to see?
+
+Do we have as many 5s as 10s?
+
+But every 10 covers twice
+as much space.
+
+So if I show up at a random
+time, I have probability 2/3
+
+falling inside an interval
+of duration 10.
+
+And I have one 1/3 probability
+of falling inside an interval
+
+of duration 5.
+
+That's because, out of the whole
+real line, 2/3 of it is
+
+covered by intervals
+of length 10, just
+
+because they're longer.
+
+1/3 is covered by the
+smaller intervals.
+
+Now if I fall inside an interval
+of length 10 and I
+
+measure the length of the
+interval that I fell into,
+
+that's going to be 10.
+
+But if I fall inside an interval
+of length 5 and I
+
+measure how long it is,
+I'm going to get a 5.
+
+And that, of course, is going
+to be different than 7.5.
+
+OK.
+
+And which number should
+be bigger?
+
+It's the second number that's
+bigger because this one is
+
+biased in favor of the
+longer intervals.
+
+So that's, again, another
+illustration of the different
+
+results that you get when you
+have this random incidence
+
+phenomenon.
+
+So the bottom line, again, is
+that if you talk about a
+
+typical interarrival time, one
+must be very precise in
+
+specifying what we
+mean typical.
+
+So typical means
+sort of random.
+
+But to use the word random,
+you must specify very
+
+precisely what is the random
+experiment that you are using.
+
+And if you're not careful, you
+can get into apparent puzzles,
+
+such as the following.
+
+Suppose somebody tells you the
+average family size is 4, but
+
+the average person lives
+in a family of size 6.
+
+Is that compatible?
+
+Family size is 4 on the average,
+but typical people
+
+live, on the average, in
+families of size 6.
+
+Well yes.
+
+There's no contradiction here.
+
+We're talking about two
+different experiments.
+
+In one experiment, I pick a
+family at random, and I tell
+
+you the average family is 4.
+
+In another experiment, I pick a
+person at random and I tell
+
+you that this person, on the
+average, will be in their
+
+family of size 6.
+
+And what is the catch here?
+
+That if I pick a person at
+random, large families are
+
+more likely to be picked.
+
+So there's a bias in favor
+of large families.
+
+Or if you want to survey, let's
+say, are trains crowded
+
+in your city?
+
+Or are buses crowded?
+
+One choice is to pick a bus
+at random and inspect
+
+how crowded it is.
+
+Another choice is to pick a
+typical person and ask them,
+
+"Did you ride the bus today?
+
+Was it's crowded?" Well suppose
+that in this city
+
+there's one bus that's extremely
+crowded and all the
+
+other buses are completely
+empty.
+
+If you ask a person. "Was your
+bus crowded?" They will tell
+
+you, "Yes, my bus was crowded."
+There's no witness
+
+from the empty buses to testify
+in their favor.
+
+So by sampling people instead
+of sampling buses, you're
+
+going to get different result.
+
+And in the process industry, if
+your job is to inspect and
+
+check cookies, you will be
+faced with a big dilemma.
+
+Do you want to find out how many
+chocolate chips there are
+
+on a typical cookie?
+
+Are you going to interview
+cookies or are you going to
+
+interview chocolate chips and
+ask them how many other chips
+
+where there on your cookie?
+
+And you're going to
+get different
+
+answers in these cases.
+
+So moral is, one has to be
+very precise on how you
+
+formulate the sampling procedure
+that you have.
+
+And you'll get different
+answers.
\ No newline at end of file
diff --git a/YAo1sd4kuOQ.txt b/YAo1sd4kuOQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6399b1e0193c79a28cb2c3109fcf093ee0d32258
--- /dev/null
+++ b/YAo1sd4kuOQ.txt
@@ -0,0 +1,8099 @@
+align:start position:0%
+ 
+so the first topic that I want to
+
+ align:start position:0%
+so the first topic that I want to
+ 
+
+ align:start position:0%
+so the first topic that I want to
+discuss in this course is extrema graph
+
+ align:start position:0%
+discuss in this course is extrema graph
+ 
+
+ align:start position:0%
+discuss in this course is extrema graph
+theory and in particular there's a whole
+
+ align:start position:0%
+theory and in particular there's a whole
+ 
+
+ align:start position:0%
+theory and in particular there's a whole
+class of problems which have to do with
+
+ align:start position:0%
+class of problems which have to do with
+ 
+
+ align:start position:0%
+class of problems which have to do with
+what happens if you forbid specific sub
+
+ align:start position:0%
+what happens if you forbid specific sub
+ 
+
+ align:start position:0%
+what happens if you forbid specific sub
+graph and ask you what's the maximum
+
+ align:start position:0%
+graph and ask you what's the maximum
+ 
+
+ align:start position:0%
+graph and ask you what's the maximum
+number of edges that can appear in your
+
+ align:start position:0%
+number of edges that can appear in your
+ 
+
+ align:start position:0%
+number of edges that can appear in your
+graph in particular and this is the
+
+ align:start position:0%
+graph in particular and this is the
+ 
+
+ align:start position:0%
+graph in particular and this is the
+question that we saw at the end of last
+
+ align:start position:0%
+question that we saw at the end of last
+ 
+
+ align:start position:0%
+question that we saw at the end of last
+lecture which tells theorem essentially
+
+ align:start position:0%
+lecture which tells theorem essentially
+ 
+
+ align:start position:0%
+lecture which tells theorem essentially
+asks if you know that your graph has no
+
+ align:start position:0%
+asks if you know that your graph has no
+ 
+
+ align:start position:0%
+asks if you know that your graph has no
+triangles what's the maximum number of
+
+ align:start position:0%
+triangles what's the maximum number of
+ 
+
+ align:start position:0%
+triangles what's the maximum number of
+edges it can have i ment else theorem
+
+ align:start position:0%
+edges it can have i ment else theorem
+ 
+
+ align:start position:0%
+edges it can have i ment else theorem
+tells us that the extreme example is
+
+ align:start position:0%
+tells us that the extreme example is
+ 
+
+ align:start position:0%
+tells us that the extreme example is
+when your graph consists of putting half
+
+ align:start position:0%
+when your graph consists of putting half
+ 
+
+ align:start position:0%
+when your graph consists of putting half
+the vertices on one side half the
+
+ align:start position:0%
+the vertices on one side half the
+ 
+
+ align:start position:0%
+the vertices on one side half the
+vertices on the other side and putting
+
+ align:start position:0%
+vertices on the other side and putting
+ 
+
+ align:start position:0%
+vertices on the other side and putting
+in all the edges between so this is a
+
+ align:start position:0%
+in all the edges between so this is a
+ 
+
+ align:start position:0%
+in all the edges between so this is a
+complete bipartite graph for these
+
+ align:start position:0%
+complete bipartite graph for these
+ 
+
+ align:start position:0%
+complete bipartite graph for these
+partitions we denote complete bipartite
+
+ align:start position:0%
+partitions we denote complete bipartite
+ 
+
+ align:start position:0%
+partitions we denote complete bipartite
+graphs like that and mentos theorem
+
+ align:start position:0%
+graphs like that and mentos theorem
+ 
+
+ align:start position:0%
+graphs like that and mentos theorem
+tells us that this graph among triangle
+
+ align:start position:0%
+tells us that this graph among triangle
+ 
+
+ align:start position:0%
+tells us that this graph among triangle
+free graphs has the most number of edges
+
+ align:start position:0%
+free graphs has the most number of edges
+ 
+
+ align:start position:0%
+free graphs has the most number of edges
+triangle free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and vertices Haas at most so the number
+
+ align:start position:0%
+and vertices Haas at most so the number
+ 
+
+ align:start position:0%
+and vertices Haas at most so the number
+of edges there is N squared divided by
+
+ align:start position:0%
+of edges there is N squared divided by
+ 
+
+ align:start position:0%
+of edges there is N squared divided by
+four round down that many edges and from
+
+ align:start position:0%
+four round down that many edges and from
+ 
+
+ align:start position:0%
+four round down that many edges and from
+this example this bound is tight so when
+
+ align:start position:0%
+this example this bound is tight so when
+ 
+
+ align:start position:0%
+this example this bound is tight so when
+helstem gives us a completely
+
+ align:start position:0%
+helstem gives us a completely
+ 
+
+ align:start position:0%
+helstem gives us a completely
+satisfactory answer to the question of
+
+ align:start position:0%
+satisfactory answer to the question of
+ 
+
+ align:start position:0%
+satisfactory answer to the question of
+what's the maximum number of edges in a
+
+ align:start position:0%
+what's the maximum number of edges in a
+ 
+
+ align:start position:0%
+what's the maximum number of edges in a
+graph without triangles and I want to
+
+ align:start position:0%
+graph without triangles and I want to
+ 
+
+ align:start position:0%
+graph without triangles and I want to
+begin by showing you a few different
+
+ align:start position:0%
+begin by showing you a few different
+ 
+
+ align:start position:0%
+begin by showing you a few different
+proofs of mental serum with illustrating
+
+ align:start position:0%
+proofs of mental serum with illustrating
+ 
+
+ align:start position:0%
+proofs of mental serum with illustrating
+some different techniques in graph
+
+ align:start position:0%
+some different techniques in graph
+ 
+
+ align:start position:0%
+some different techniques in graph
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+so we'll see quite a few proofs in
+
+ align:start position:0%
+so we'll see quite a few proofs in
+ 
+
+ align:start position:0%
+so we'll see quite a few proofs in
+today's lecture the first one begins
+
+ align:start position:0%
+today's lecture the first one begins
+ 
+
+ align:start position:0%
+today's lecture the first one begins
+well here's the setup I have G and
+
+ align:start position:0%
+well here's the setup I have G and
+ 
+
+ align:start position:0%
+well here's the setup I have G and
+vertex graph and let me denote the
+
+ align:start position:0%
+vertex graph and let me denote the
+ 
+
+ align:start position:0%
+vertex graph and let me denote the
+vertices and edges of G by if I have an
+
+ align:start position:0%
+vertices and edges of G by if I have an
+ 
+
+ align:start position:0%
+vertices and edges of G by if I have an
+edge in G between vertices x and y then
+
+ align:start position:0%
+edge in G between vertices x and y then
+ 
+
+ align:start position:0%
+edge in G between vertices x and y then
+note that they cannot have any common
+
+ align:start position:0%
+note that they cannot have any common
+ 
+
+ align:start position:0%
+note that they cannot have any common
+neighbors because I would see a triangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what can we say about the degrees of
+
+ align:start position:0%
+so what can we say about the degrees of
+ 
+
+ align:start position:0%
+so what can we say about the degrees of
+the two endpoints of this edge they
+
+ align:start position:0%
+the two endpoints of this edge they
+ 
+
+ align:start position:0%
+the two endpoints of this edge they
+cannot add up to they cannot add up to
+
+ align:start position:0%
+cannot add up to they cannot add up to
+ 
+
+ align:start position:0%
+cannot add up to they cannot add up to
+more than n so in particular exactly the
+
+ align:start position:0%
+more than n so in particular exactly the
+ 
+
+ align:start position:0%
+more than n so in particular exactly the
+degrees of these two endpoints is at
+
+ align:start position:0%
+degrees of these two endpoints is at
+ 
+
+ align:start position:0%
+degrees of these two endpoints is at
+most n whenever XY edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so now let me consider the
+
+ align:start position:0%
+well okay so now let me consider the
+ 
+
+ align:start position:0%
+well okay so now let me consider the
+quantity which is the sum of the squared
+
+ align:start position:0%
+quantity which is the sum of the squared
+ 
+
+ align:start position:0%
+quantity which is the sum of the squared
+degrees on one hand I claim that this
+
+ align:start position:0%
+degrees on one hand I claim that this
+ 
+
+ align:start position:0%
+degrees on one hand I claim that this
+sum is equal to this quantity here where
+
+ align:start position:0%
+sum is equal to this quantity here where
+ 
+
+ align:start position:0%
+sum is equal to this quantity here where
+I sum over all edges and the reason is
+
+ align:start position:0%
+I sum over all edges and the reason is
+ 
+
+ align:start position:0%
+I sum over all edges and the reason is
+we'll look at the sum suppose imagine
+
+ align:start position:0%
+we'll look at the sum suppose imagine
+ 
+
+ align:start position:0%
+we'll look at the sum suppose imagine
+writing out all the summons how many
+
+ align:start position:0%
+writing out all the summons how many
+ 
+
+ align:start position:0%
+writing out all the summons how many
+times does each DX come up each DX
+
+ align:start position:0%
+times does each DX come up each DX
+ 
+
+ align:start position:0%
+times does each DX come up each DX
+appears one for each edge accessing so
+
+ align:start position:0%
+appears one for each edge accessing so
+ 
+
+ align:start position:0%
+appears one for each edge accessing so
+appears exactly the x times but we saw
+
+ align:start position:0%
+appears exactly the x times but we saw
+ 
+
+ align:start position:0%
+appears exactly the x times but we saw
+from up here that each summon is at most
+
+ align:start position:0%
+from up here that each summon is at most
+ 
+
+ align:start position:0%
+from up here that each summon is at most
+n so this sum here is that most a men on
+
+ align:start position:0%
+n so this sum here is that most a men on
+ 
+
+ align:start position:0%
+n so this sum here is that most a men on
+the other hand let's consider the
+
+ align:start position:0%
+the other hand let's consider the
+ 
+
+ align:start position:0%
+the other hand let's consider the
+quantity which is just the sum of the
+
+ align:start position:0%
+quantity which is just the sum of the
+ 
+
+ align:start position:0%
+quantity which is just the sum of the
+degrees and you know sometimes known as
+
+ align:start position:0%
+degrees and you know sometimes known as
+ 
+
+ align:start position:0%
+degrees and you know sometimes known as
+the handshaking lemma that the sums of
+
+ align:start position:0%
+the handshaking lemma that the sums of
+ 
+
+ align:start position:0%
+the handshaking lemma that the sums of
+degrees is just twice the number of
+
+ align:start position:0%
+degrees is just twice the number of
+ 
+
+ align:start position:0%
+degrees is just twice the number of
+edges each edge is considered twice in
+
+ align:start position:0%
+edges each edge is considered twice in
+ 
+
+ align:start position:0%
+edges each edge is considered twice in
+this sum well now we apply the Cauchy
+
+ align:start position:0%
+this sum well now we apply the Cauchy
+ 
+
+ align:start position:0%
+this sum well now we apply the Cauchy
+Schwarz inequality which as you'll see
+
+ align:start position:0%
+Schwarz inequality which as you'll see
+ 
+
+ align:start position:0%
+Schwarz inequality which as you'll see
+many times in this course although you
+
+ align:start position:0%
+many times in this course although you
+ 
+
+ align:start position:0%
+many times in this course although you
+might think of it as a fairly simple
+
+ align:start position:0%
+might think of it as a fairly simple
+ 
+
+ align:start position:0%
+might think of it as a fairly simple
+inequality it's extremely powerful and
+
+ align:start position:0%
+inequality it's extremely powerful and
+ 
+
+ align:start position:0%
+inequality it's extremely powerful and
+it will come up pretty much throughout
+
+ align:start position:0%
+it will come up pretty much throughout
+ 
+
+ align:start position:0%
+it will come up pretty much throughout
+this course by the Cauchy Schwarz
+
+ align:start position:0%
+this course by the Cauchy Schwarz
+ 
+
+ align:start position:0%
+this course by the Cauchy Schwarz
+inequality you compare these two
+
+ align:start position:0%
+inequality you compare these two
+ 
+
+ align:start position:0%
+inequality you compare these two
+quantities I find that we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this inequality over here relating the
+
+ align:start position:0%
+this inequality over here relating the
+ 
+
+ align:start position:0%
+this inequality over here relating the
+sums of the degrees and square of the
+
+ align:start position:0%
+sums of the degrees and square of the
+ 
+
+ align:start position:0%
+sums of the degrees and square of the
+sum of the degrees but we saw on one
+
+ align:start position:0%
+sum of the degrees but we saw on one
+ 
+
+ align:start position:0%
+sum of the degrees but we saw on one
+hand the left hand side is for M Squared
+
+ align:start position:0%
+hand the left hand side is for M Squared
+ 
+
+ align:start position:0%
+hand the left hand side is for M Squared
+and we also saw the right hand side is
+
+ align:start position:0%
+and we also saw the right hand side is
+ 
+
+ align:start position:0%
+and we also saw the right hand side is
+that most M N squared putting them
+
+ align:start position:0%
+that most M N squared putting them
+ 
+
+ align:start position:0%
+that most M N squared putting them
+together we see that M is that most N
+
+ align:start position:0%
+together we see that M is that most N
+ 
+
+ align:start position:0%
+together we see that M is that most N
+squared over four and of course because
+
+ align:start position:0%
+squared over four and of course because
+ 
+
+ align:start position:0%
+squared over four and of course because
+it's an integer it's at most the floor
+
+ align:start position:0%
+it's an integer it's at most the floor
+ 
+
+ align:start position:0%
+it's an integer it's at most the floor
+of this number and that's a proof of
+
+ align:start position:0%
+of this number and that's a proof of
+ 
+
+ align:start position:0%
+of this number and that's a proof of
+mental stare what can you tell me about
+
+ align:start position:0%
+mental stare what can you tell me about
+ 
+
+ align:start position:0%
+mental stare what can you tell me about
+the Equality case in this proof I'll let
+
+ align:start position:0%
+the Equality case in this proof I'll let
+ 
+
+ align:start position:0%
+the Equality case in this proof I'll let
+you think about that but let me show you
+
+ align:start position:0%
+you think about that but let me show you
+ 
+
+ align:start position:0%
+you think about that but let me show you
+some other proofs in other words are
+
+ align:start position:0%
+some other proofs in other words are
+ 
+
+ align:start position:0%
+some other proofs in other words are
+there graphs with the same number of
+
+ align:start position:0%
+there graphs with the same number of
+ 
+
+ align:start position:0%
+there graphs with the same number of
+edges as the graph shown up there that
+
+ align:start position:0%
+edges as the graph shown up there that
+ 
+
+ align:start position:0%
+edges as the graph shown up there that
+is also triangle frequent it's not a
+
+ align:start position:0%
+is also triangle frequent it's not a
+ 
+
+ align:start position:0%
+is also triangle frequent it's not a
+unique example okay so let me show you a
+
+ align:start position:0%
+unique example okay so let me show you a
+ 
+
+ align:start position:0%
+unique example okay so let me show you a
+different proof of Mancow still in this
+
+ align:start position:0%
+different proof of Mancow still in this
+ 
+
+ align:start position:0%
+different proof of Mancow still in this
+proof so we begin with a step that seems
+
+ align:start position:0%
+proof so we begin with a step that seems
+ 
+
+ align:start position:0%
+proof so we begin with a step that seems
+a little tricky let's let a be a subset
+
+ align:start position:0%
+a little tricky let's let a be a subset
+ 
+
+ align:start position:0%
+a little tricky let's let a be a subset
+of vertices such that a is a largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gee remember independent set is subset
+
+ align:start position:0%
+gee remember independent set is subset
+ 
+
+ align:start position:0%
+gee remember independent set is subset
+of vertices with no edges inside you may
+
+ align:start position:0%
+of vertices with no edges inside you may
+ 
+
+ align:start position:0%
+of vertices with no edges inside you may
+have many independent sets all having
+
+ align:start position:0%
+have many independent sets all having
+ 
+
+ align:start position:0%
+have many independent sets all having
+the same maximum size take one of them
+
+ align:start position:0%
+the same maximum size take one of them
+ 
+
+ align:start position:0%
+the same maximum size take one of them
+why should you do this step sometimes
+
+ align:start position:0%
+why should you do this step sometimes
+ 
+
+ align:start position:0%
+why should you do this step sometimes
+magic happens
+
+ align:start position:0%
+magic happens
+ 
+
+ align:start position:0%
+magic happens
+let's consider some vertex there's some
+
+ align:start position:0%
+let's consider some vertex there's some
+ 
+
+ align:start position:0%
+let's consider some vertex there's some
+vertex let's say X and look at it
+
+ align:start position:0%
+vertex let's say X and look at it
+ 
+
+ align:start position:0%
+vertex let's say X and look at it
+neighborhood the neighborhood must be an
+
+ align:start position:0%
+neighborhood the neighborhood must be an
+ 
+
+ align:start position:0%
+neighborhood the neighborhood must be an
+independent set otherwise I get a
+
+ align:start position:0%
+independent set otherwise I get a
+ 
+
+ align:start position:0%
+independent set otherwise I get a
+triangle and as a result the degree of
+
+ align:start position:0%
+triangle and as a result the degree of
+ 
+
+ align:start position:0%
+triangle and as a result the degree of
+every vertex is at most the size of the
+
+ align:start position:0%
+every vertex is at most the size of the
+ 
+
+ align:start position:0%
+every vertex is at most the size of the
+largest so now let the complement so I
+
+ align:start position:0%
+largest so now let the complement so I
+ 
+
+ align:start position:0%
+largest so now let the complement so I
+have a every Edge has to intersect P the
+
+ align:start position:0%
+have a every Edge has to intersect P the
+ 
+
+ align:start position:0%
+have a every Edge has to intersect P the
+edge cannot be entirely containing a
+
+ align:start position:0%
+edge cannot be entirely containing a
+ 
+
+ align:start position:0%
+edge cannot be entirely containing a
+because a has no edges so the number of
+
+ align:start position:0%
+because a has no edges so the number of
+ 
+
+ align:start position:0%
+because a has no edges so the number of
+edges of G is at most I count over
+
+ align:start position:0%
+edges of G is at most I count over
+ 
+
+ align:start position:0%
+edges of G is at most I count over
+vertices in B the degree may be an over
+
+ align:start position:0%
+vertices in B the degree may be an over
+ 
+
+ align:start position:0%
+vertices in B the degree may be an over
+count so the edges containing B I count
+
+ align:start position:0%
+count so the edges containing B I count
+ 
+
+ align:start position:0%
+count so the edges containing B I count
+twice but that's okay so this is an
+
+ align:start position:0%
+twice but that's okay so this is an
+ 
+
+ align:start position:0%
+twice but that's okay so this is an
+upper bound on a number of edges but I
+
+ align:start position:0%
+upper bound on a number of edges but I
+ 
+
+ align:start position:0%
+upper bound on a number of edges but I
+also know that every vertex in the graph
+
+ align:start position:0%
+also know that every vertex in the graph
+ 
+
+ align:start position:0%
+also know that every vertex in the graph
+has degree at most the size of a so
+
+ align:start position:0%
+has degree at most the size of a so
+ 
+
+ align:start position:0%
+has degree at most the size of a so
+each someone is at most the size of a
+
+ align:start position:0%
+each someone is at most the size of a
+ 
+
+ align:start position:0%
+each someone is at most the size of a
+and I have the terms now by the a MGM
+
+ align:start position:0%
+and I have the terms now by the a MGM
+ 
+
+ align:start position:0%
+and I have the terms now by the a MGM
+inequality and the sizes of a and B add
+
+ align:start position:0%
+inequality and the sizes of a and B add
+ 
+
+ align:start position:0%
+inequality and the sizes of a and B add
+up to the entire vertex set and squared
+
+ align:start position:0%
+up to the entire vertex set and squared
+ 
+
+ align:start position:0%
+up to the entire vertex set and squared
+over 4 so that gives you another proof
+
+ align:start position:0%
+over 4 so that gives you another proof
+ 
+
+ align:start position:0%
+over 4 so that gives you another proof
+of men house theorem what does this
+
+ align:start position:0%
+of men house theorem what does this
+ 
+
+ align:start position:0%
+of men house theorem what does this
+proof tell us about the Equality case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know something I always want you to
+
+ align:start position:0%
+you know something I always want you to
+ 
+
+ align:start position:0%
+you know something I always want you to
+keep in mind when we do proofs is
+
+ align:start position:0%
+keep in mind when we do proofs is
+ 
+
+ align:start position:0%
+keep in mind when we do proofs is
+especially if we have a type example
+
+ align:start position:0%
+especially if we have a type example
+ 
+
+ align:start position:0%
+especially if we have a type example
+like that and later on and the course
+
+ align:start position:0%
+like that and later on and the course
+ 
+
+ align:start position:0%
+like that and later on and the course
+will almost never have good examples
+
+ align:start position:0%
+will almost never have good examples
+ 
+
+ align:start position:0%
+will almost never have good examples
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so this is still early on in the course
+
+ align:start position:0%
+so this is still early on in the course
+ 
+
+ align:start position:0%
+so this is still early on in the course
+we're still very clean examples is to
+
+ align:start position:0%
+we're still very clean examples is to
+ 
+
+ align:start position:0%
+we're still very clean examples is to
+keep the extremal example in mind and
+
+ align:start position:0%
+keep the extremal example in mind and
+ 
+
+ align:start position:0%
+keep the extremal example in mind and
+every step in your proof it should be
+
+ align:start position:0%
+every step in your proof it should be
+ 
+
+ align:start position:0%
+every step in your proof it should be
+tight for that example otherwise
+
+ align:start position:0%
+tight for that example otherwise
+ 
+
+ align:start position:0%
+tight for that example otherwise
+something went wrong with your proof
+
+ align:start position:0%
+something went wrong with your proof
+ 
+
+ align:start position:0%
+something went wrong with your proof
+let's think about the inequalities and
+
+ align:start position:0%
+let's think about the inequalities and
+ 
+
+ align:start position:0%
+let's think about the inequalities and
+equality we must have that so looking at
+
+ align:start position:0%
+equality we must have that so looking at
+ 
+
+ align:start position:0%
+equality we must have that so looking at
+this inequality so there are no edges in
+
+ align:start position:0%
+this inequality so there are no edges in
+ 
+
+ align:start position:0%
+this inequality so there are no edges in
+B we also have that by data every vertex
+
+ align:start position:0%
+B we also have that by data every vertex
+ 
+
+ align:start position:0%
+B we also have that by data every vertex
+in B is complete 2a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally a and B should have the same
+
+ align:start position:0%
+and finally a and B should have the same
+ 
+
+ align:start position:0%
+and finally a and B should have the same
+size so it is exactly the configuration
+
+ align:start position:0%
+size so it is exactly the configuration
+ 
+
+ align:start position:0%
+size so it is exactly the configuration
+shown up there now when n is odd we're
+
+ align:start position:0%
+shown up there now when n is odd we're
+ 
+
+ align:start position:0%
+shown up there now when n is odd we're
+rounding down by one so you can lose a
+
+ align:start position:0%
+rounding down by one so you can lose a
+ 
+
+ align:start position:0%
+rounding down by one so you can lose a
+little bit and then you can check that
+
+ align:start position:0%
+little bit and then you can check that
+ 
+
+ align:start position:0%
+little bit and then you can check that
+actually what we described up there is
+
+ align:start position:0%
+actually what we described up there is
+ 
+
+ align:start position:0%
+actually what we described up there is
+also the unique example okay so so that
+
+ align:start position:0%
+also the unique example okay so so that
+ 
+
+ align:start position:0%
+also the unique example okay so so that
+graphic complete bipartite graph with
+
+ align:start position:0%
+graphic complete bipartite graph with
+ 
+
+ align:start position:0%
+graphic complete bipartite graph with
+two equal parts is the unique maximal
+
+ align:start position:0%
+two equal parts is the unique maximal
+ 
+
+ align:start position:0%
+two equal parts is the unique maximal
+example number of edges in a triangle
+
+ align:start position:0%
+example number of edges in a triangle
+ 
+
+ align:start position:0%
+example number of edges in a triangle
+free graph okay great so once we know
+
+ align:start position:0%
+free graph okay great so once we know
+ 
+
+ align:start position:0%
+free graph okay great so once we know
+what the answer is for triangle free of
+
+ align:start position:0%
+what the answer is for triangle free of
+ 
+
+ align:start position:0%
+what the answer is for triangle free of
+course we should ask further questions
+
+ align:start position:0%
+course we should ask further questions
+ 
+
+ align:start position:0%
+course we should ask further questions
+instead of forbidding a triangle what if
+
+ align:start position:0%
+instead of forbidding a triangle what if
+ 
+
+ align:start position:0%
+instead of forbidding a triangle what if
+we forbid other graphs so and what are
+
+ align:start position:0%
+we forbid other graphs so and what are
+ 
+
+ align:start position:0%
+we forbid other graphs so and what are
+some natural next steps to take instead
+
+ align:start position:0%
+some natural next steps to take instead
+ 
+
+ align:start position:0%
+some natural next steps to take instead
+of triangles we can ask what about if we
+
+ align:start position:0%
+of triangles we can ask what about if we
+ 
+
+ align:start position:0%
+of triangles we can ask what about if we
+prepared a K for a clique of four
+
+ align:start position:0%
+prepared a K for a clique of four
+ 
+
+ align:start position:0%
+prepared a K for a clique of four
+vertices or in general what if we forbid
+
+ align:start position:0%
+vertices or in general what if we forbid
+ 
+
+ align:start position:0%
+vertices or in general what if we forbid
+a click on the fixed number of vertices
+
+ align:start position:0%
+a click on the fixed number of vertices
+ 
+
+ align:start position:0%
+a click on the fixed number of vertices
+so what is the maximum edges there's a
+
+ align:start position:0%
+so what is the maximum edges there's a
+ 
+
+ align:start position:0%
+so what is the maximum edges there's a
+good reason why index an R plus one so
+
+ align:start position:0%
+good reason why index an R plus one so
+ 
+
+ align:start position:0%
+good reason why index an R plus one so
+for example if we're interested in K for
+
+ align:start position:0%
+for example if we're interested in K for
+ 
+
+ align:start position:0%
+for example if we're interested in K for
+free so what might be a good candidate
+
+ align:start position:0%
+free so what might be a good candidate
+ 
+
+ align:start position:0%
+free so what might be a good candidate
+for a graph with lots of edges that has
+
+ align:start position:0%
+for a graph with lots of edges that has
+ 
+
+ align:start position:0%
+for a graph with lots of edges that has
+no K for certainly that example we saw
+
+ align:start position:0%
+no K for certainly that example we saw
+ 
+
+ align:start position:0%
+no K for certainly that example we saw
+it does does not have K force because it
+
+ align:start position:0%
+it does does not have K force because it
+ 
+
+ align:start position:0%
+it does does not have K force because it
+doesn't have any triangles or we can do
+
+ align:start position:0%
+doesn't have any triangles or we can do
+ 
+
+ align:start position:0%
+doesn't have any triangles or we can do
+even better instead of taking two parts
+
+ align:start position:0%
+even better instead of taking two parts
+ 
+
+ align:start position:0%
+even better instead of taking two parts
+you can take more parts for K for if I
+
+ align:start position:0%
+you can take more parts for K for if I
+ 
+
+ align:start position:0%
+you can take more parts for K for if I
+take three parts each one n over three
+
+ align:start position:0%
+take three parts each one n over three
+ 
+
+ align:start position:0%
+take three parts each one n over three
+number of vertices of course if and it's
+
+ align:start position:0%
+number of vertices of course if and it's
+ 
+
+ align:start position:0%
+number of vertices of course if and it's
+not divisible by three round up and
+
+ align:start position:0%
+not divisible by three round up and
+ 
+
+ align:start position:0%
+not divisible by three round up and
+round down and putting all the edges
+
+ align:start position:0%
+round down and putting all the edges
+ 
+
+ align:start position:0%
+round down and putting all the edges
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+different parts you can see this graph
+
+ align:start position:0%
+different parts you can see this graph
+ 
+
+ align:start position:0%
+different parts you can see this graph
+here has no k4 okay so that's an example
+
+ align:start position:0%
+here has no k4 okay so that's an example
+ 
+
+ align:start position:0%
+here has no k4 okay so that's an example
+of a k4 free graph there's a half the
+
+ align:start position:0%
+of a k4 free graph there's a half the
+ 
+
+ align:start position:0%
+of a k4 free graph there's a half the
+maximum possible number of edges so is
+
+ align:start position:0%
+maximum possible number of edges so is
+ 
+
+ align:start position:0%
+maximum possible number of edges so is
+this the best that we can do so it turns
+
+ align:start position:0%
+this the best that we can do so it turns
+ 
+
+ align:start position:0%
+this the best that we can do so it turns
+out the answer is yes and that's the
+
+ align:start position:0%
+out the answer is yes and that's the
+ 
+
+ align:start position:0%
+out the answer is yes and that's the
+next theorem that we'll see but just to
+
+ align:start position:0%
+next theorem that we'll see but just to
+ 
+
+ align:start position:0%
+next theorem that we'll see but just to
+give it a name so we're going to call
+
+ align:start position:0%
+give it a name so we're going to call
+ 
+
+ align:start position:0%
+give it a name so we're going to call
+graphs like these to run graphs okay so
+
+ align:start position:0%
+graphs like these to run graphs okay so
+ 
+
+ align:start position:0%
+graphs like these to run graphs okay so
+next theorem is proved by Qur'an
+
+ align:start position:0%
+next theorem is proved by Qur'an
+ 
+
+ align:start position:0%
+next theorem is proved by Qur'an
+Torrance term so turn on graph go to
+
+ align:start position:0%
+Torrance term so turn on graph go to
+ 
+
+ align:start position:0%
+Torrance term so turn on graph go to
+node T and sub T sub n R it is a
+
+ align:start position:0%
+node T and sub T sub n R it is a
+ 
+
+ align:start position:0%
+node T and sub T sub n R it is a
+complete our part I graph such that
+
+ align:start position:0%
+complete our part I graph such that
+ 
+
+ align:start position:0%
+complete our part I graph such that
+there are n vertices whose parts sizes
+
+ align:start position:0%
+there are n vertices whose parts sizes
+ 
+
+ align:start position:0%
+there are n vertices whose parts sizes
+are all nearly the same up to at most
+
+ align:start position:0%
+are all nearly the same up to at most
+ 
+
+ align:start position:0%
+are all nearly the same up to at most
+one difference this is an example
+
+ align:start position:0%
+one difference this is an example
+ 
+
+ align:start position:0%
+one difference this is an example
+general maybe you have our part and just
+
+ align:start position:0%
+general maybe you have our part and just
+ 
+
+ align:start position:0%
+general maybe you have our part and just
+between different parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's not too hard to calculate the
+
+ align:start position:0%
+so it's not too hard to calculate the
+ 
+
+ align:start position:0%
+so it's not too hard to calculate the
+number of edges in such a graph and
+
+ align:start position:0%
+number of edges in such a graph and
+ 
+
+ align:start position:0%
+number of edges in such a graph and
+Torrens theorem tells us that that is
+
+ align:start position:0%
+Torrens theorem tells us that that is
+ 
+
+ align:start position:0%
+Torrens theorem tells us that that is
+the extreme example you cannot do better
+
+ align:start position:0%
+the extreme example you cannot do better
+ 
+
+ align:start position:0%
+the extreme example you cannot do better
+in terms of getting more edges at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a generalization of meant helps
+
+ align:start position:0%
+it's a generalization of meant helps
+ 
+
+ align:start position:0%
+it's a generalization of meant helps
+term and you can think about if the
+
+ align:start position:0%
+term and you can think about if the
+ 
+
+ align:start position:0%
+term and you can think about if the
+proofs that we did for men tells them
+
+ align:start position:0%
+proofs that we did for men tells them
+ 
+
+ align:start position:0%
+proofs that we did for men tells them
+and generalizes to Torrance term and
+
+ align:start position:0%
+and generalizes to Torrance term and
+ 
+
+ align:start position:0%
+and generalizes to Torrance term and
+it's actually not entirely clear how to
+
+ align:start position:0%
+it's actually not entirely clear how to
+ 
+
+ align:start position:0%
+it's actually not entirely clear how to
+do it so let me present for you three
+
+ align:start position:0%
+do it so let me present for you three
+ 
+
+ align:start position:0%
+do it so let me present for you three
+three different proofs of Torrance
+
+ align:start position:0%
+three different proofs of Torrance
+ 
+
+ align:start position:0%
+three different proofs of Torrance
+theorem so some of them you can think
+
+ align:start position:0%
+theorem so some of them you can think
+ 
+
+ align:start position:0%
+theorem so some of them you can think
+about are they related to the proofs of
+
+ align:start position:0%
+about are they related to the proofs of
+ 
+
+ align:start position:0%
+about are they related to the proofs of
+mint house term that we did and they all
+
+ align:start position:0%
+mint house term that we did and they all
+ 
+
+ align:start position:0%
+mint house term that we did and they all
+are going to look somewhat different but
+
+ align:start position:0%
+are going to look somewhat different but
+ 
+
+ align:start position:0%
+are going to look somewhat different but
+maybe superficially the first proof we
+
+ align:start position:0%
+maybe superficially the first proof we
+ 
+
+ align:start position:0%
+maybe superficially the first proof we
+will use induction courtesies so this is
+
+ align:start position:0%
+will use induction courtesies so this is
+ 
+
+ align:start position:0%
+will use induction courtesies so this is
+one of very few times in this course
+
+ align:start position:0%
+one of very few times in this course
+ 
+
+ align:start position:0%
+one of very few times in this course
+where we will see induction so of course
+
+ align:start position:0%
+where we will see induction so of course
+ 
+
+ align:start position:0%
+where we will see induction so of course
+induction is a powerful technique in
+
+ align:start position:0%
+induction is a powerful technique in
+ 
+
+ align:start position:0%
+induction is a powerful technique in
+combinatorics but for almost the rest of
+
+ align:start position:0%
+combinatorics but for almost the rest of
+ 
+
+ align:start position:0%
+combinatorics but for almost the rest of
+the course we're not gonna have clean
+
+ align:start position:0%
+the course we're not gonna have clean
+ 
+
+ align:start position:0%
+the course we're not gonna have clean
+examples and when we do have clean
+
+ align:start position:0%
+examples and when we do have clean
+ 
+
+ align:start position:0%
+examples and when we do have clean
+examples to work with somehow increasing
+
+ align:start position:0%
+examples to work with somehow increasing
+ 
+
+ align:start position:0%
+examples to work with somehow increasing
+n by one doesn't buy you all that much
+
+ align:start position:0%
+n by one doesn't buy you all that much
+ 
+
+ align:start position:0%
+n by one doesn't buy you all that much
+here you know there are very clean
+
+ align:start position:0%
+here you know there are very clean
+ 
+
+ align:start position:0%
+here you know there are very clean
+examples very clean answers and
+
+ align:start position:0%
+examples very clean answers and
+ 
+
+ align:start position:0%
+examples very clean answers and
+induction works out quite well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when n is small persue should always
+
+ align:start position:0%
+when n is small persue should always
+ 
+
+ align:start position:0%
+when n is small persue should always
+address that can come up with many funny
+
+ align:start position:0%
+address that can come up with many funny
+ 
+
+ align:start position:0%
+address that can come up with many funny
+proofs if you don't address small so any
+
+ align:start position:0%
+proofs if you don't address small so any
+ 
+
+ align:start position:0%
+proofs if you don't address small so any
+small this promise
+
+ align:start position:0%
+small this promise
+ 
+
+ align:start position:0%
+small this promise
+trivial and it's the most are you can
+
+ align:start position:0%
+trivial and it's the most are you can
+ 
+
+ align:start position:0%
+trivial and it's the most are you can
+have the complete graph on our vertices
+
+ align:start position:0%
+have the complete graph on our vertices
+ 
+
+ align:start position:0%
+have the complete graph on our vertices
+and then we're good so let's assume that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're not in this case and also by
+
+ align:start position:0%
+we're not in this case and also by
+ 
+
+ align:start position:0%
+we're not in this case and also by
+induction hypothesis let's assume that
+
+ align:start position:0%
+induction hypothesis let's assume that
+ 
+
+ align:start position:0%
+induction hypothesis let's assume that
+it is true for all graphs fewer than n
+
+ align:start position:0%
+it is true for all graphs fewer than n
+ 
+
+ align:start position:0%
+it is true for all graphs fewer than n
+vertices and let G be a graph that is K
+
+ align:start position:0%
+vertices and let G be a graph that is K
+ 
+
+ align:start position:0%
+vertices and let G be a graph that is K
+sub R plus 1 3 on n vertices and also
+
+ align:start position:0%
+sub R plus 1 3 on n vertices and also
+ 
+
+ align:start position:0%
+sub R plus 1 3 on n vertices and also
+let's assume a maximum example to begin
+
+ align:start position:0%
+let's assume a maximum example to begin
+ 
+
+ align:start position:0%
+let's assume a maximum example to begin
+with so let's assume that the G that you
+
+ align:start position:0%
+with so let's assume that the G that you
+ 
+
+ align:start position:0%
+with so let's assume that the G that you
+chose has already the maximum possible
+
+ align:start position:0%
+chose has already the maximum possible
+ 
+
+ align:start position:0%
+chose has already the maximum possible
+number of edges they're only finally
+
+ align:start position:0%
+number of edges they're only finally
+ 
+
+ align:start position:0%
+number of edges they're only finally
+such an example so pick one that already
+
+ align:start position:0%
+such an example so pick one that already
+ 
+
+ align:start position:0%
+such an example so pick one that already
+has the maximum number of edges and
+
+ align:start position:0%
+has the maximum number of edges and
+ 
+
+ align:start position:0%
+has the maximum number of edges and
+let's think about what properties this
+
+ align:start position:0%
+let's think about what properties this
+ 
+
+ align:start position:0%
+let's think about what properties this
+graph G has I claim that G must already
+
+ align:start position:0%
+graph G has I claim that G must already
+ 
+
+ align:start position:0%
+graph G has I claim that G must already
+contain a click on our vertices so think
+
+ align:start position:0%
+contain a click on our vertices so think
+ 
+
+ align:start position:0%
+contain a click on our vertices so think
+about that if G does not contain your
+
+ align:start position:0%
+about that if G does not contain your
+ 
+
+ align:start position:0%
+about that if G does not contain your
+click on our vertices then I can add in
+
+ align:start position:0%
+click on our vertices then I can add in
+ 
+
+ align:start position:0%
+click on our vertices then I can add in
+more edges and I can still maintain the
+
+ align:start position:0%
+more edges and I can still maintain the
+ 
+
+ align:start position:0%
+more edges and I can still maintain the
+property of being K sub R plus 1 so I
+
+ align:start position:0%
+property of being K sub R plus 1 so I
+ 
+
+ align:start position:0%
+property of being K sub R plus 1 so I
+can assume that G must contain a K sub R
+
+ align:start position:0%
+can assume that G must contain a K sub R
+ 
+
+ align:start position:0%
+can assume that G must contain a K sub R
+so let's look at one of these case of
+
+ align:start position:0%
+so let's look at one of these case of
+ 
+
+ align:start position:0%
+so let's look at one of these case of
+ours so let M be the vertices so our
+
+ align:start position:0%
+ours so let M be the vertices so our
+ 
+
+ align:start position:0%
+ours so let M be the vertices so our
+clique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gee we have some a and the compliments
+
+ align:start position:0%
+gee we have some a and the compliments
+ 
+
+ align:start position:0%
+gee we have some a and the compliments
+that let me call that be alright look at
+
+ align:start position:0%
+that let me call that be alright look at
+ 
+
+ align:start position:0%
+that let me call that be alright look at
+the vertex in B how many neighbors can
+
+ align:start position:0%
+the vertex in B how many neighbors can
+ 
+
+ align:start position:0%
+the vertex in B how many neighbors can
+have in a it cannot be complete to a
+
+ align:start position:0%
+have in a it cannot be complete to a
+ 
+
+ align:start position:0%
+have in a it cannot be complete to a
+otherwise I would have an R plus 1 click
+
+ align:start position:0%
+otherwise I would have an R plus 1 click
+ 
+
+ align:start position:0%
+otherwise I would have an R plus 1 click
+so every vertex in B has at most R minus
+
+ align:start position:0%
+so every vertex in B has at most R minus
+ 
+
+ align:start position:0%
+so every vertex in B has at most R minus
+1 neighbors a so let's count all the
+
+ align:start position:0%
+1 neighbors a so let's count all the
+ 
+
+ align:start position:0%
+1 neighbors a so let's count all the
+edges the number of edges in G is that
+
+ align:start position:0%
+edges the number of edges in G is that
+ 
+
+ align:start position:0%
+edges the number of edges in G is that
+most or first which to account for the
+
+ align:start position:0%
+most or first which to account for the
+ 
+
+ align:start position:0%
+most or first which to account for the
+edges inside a and they are R choose two
+
+ align:start position:0%
+edges inside a and they are R choose two
+ 
+
+ align:start position:0%
+edges inside a and they are R choose two
+of them and then the edges between a and
+
+ align:start position:0%
+of them and then the edges between a and
+ 
+
+ align:start position:0%
+of them and then the edges between a and
+B for every vertex in B they are at most
+
+ align:start position:0%
+B for every vertex in B they are at most
+ 
+
+ align:start position:0%
+B for every vertex in B they are at most
+R minus 1 vertices going to a to each
+
+ align:start position:0%
+R minus 1 vertices going to a to each
+ 
+
+ align:start position:0%
+R minus 1 vertices going to a to each
+vertex and finally the edge set well we
+
+ align:start position:0%
+vertex and finally the edge set well we
+ 
+
+ align:start position:0%
+vertex and finally the edge set well we
+can say something more about these
+
+ align:start position:0%
+can say something more about these
+ 
+
+ align:start position:0%
+can say something more about these
+quantities we know that the size of B is
+
+ align:start position:0%
+quantities we know that the size of B is
+ 
+
+ align:start position:0%
+quantities we know that the size of B is
+exactly n minus R but what can we say
+
+ align:start position:0%
+exactly n minus R but what can we say
+ 
+
+ align:start position:0%
+exactly n minus R but what can we say
+about the number of edges in B we can
+
+ align:start position:0%
+about the number of edges in B we can
+ 
+
+ align:start position:0%
+about the number of edges in B we can
+use induction hypothesis P is also R
+
+ align:start position:0%
+use induction hypothesis P is also R
+ 
+
+ align:start position:0%
+use induction hypothesis P is also R
+plus 1 click free so the number of edges
+
+ align:start position:0%
+plus 1 click free so the number of edges
+ 
+
+ align:start position:0%
+plus 1 click free so the number of edges
+is that most the number of edges in the
+
+ align:start position:0%
+is that most the number of edges in the
+ 
+
+ align:start position:0%
+is that most the number of edges in the
+corresponding Terron graph now at this
+
+ align:start position:0%
+corresponding Terron graph now at this
+ 
+
+ align:start position:0%
+corresponding Terron graph now at this
+point you can do a calculation well I
+
+ align:start position:0%
+point you can do a calculation well I
+ 
+
+ align:start position:0%
+point you can do a calculation well I
+mean you should expect that the answer
+
+ align:start position:0%
+mean you should expect that the answer
+ 
+
+ align:start position:0%
+mean you should expect that the answer
+we're looking for is I mean this should
+
+ align:start position:0%
+we're looking for is I mean this should
+ 
+
+ align:start position:0%
+we're looking for is I mean this should
+be equal to the number of edges
+
+ align:start position:0%
+be equal to the number of edges
+ 
+
+ align:start position:0%
+be equal to the number of edges
+in the toronto f so you can either do a
+
+ align:start position:0%
+in the toronto f so you can either do a
+ 
+
+ align:start position:0%
+in the toronto f so you can either do a
+calculation to figure this out or
+
+ align:start position:0%
+calculation to figure this out or
+ 
+
+ align:start position:0%
+calculation to figure this out or
+remember what i said earlier that keep
+
+ align:start position:0%
+remember what i said earlier that keep
+ 
+
+ align:start position:0%
+remember what i said earlier that keep
+the type example in mind and everything
+
+ align:start position:0%
+the type example in mind and everything
+ 
+
+ align:start position:0%
+the type example in mind and everything
+should check out for a height example so
+
+ align:start position:0%
+should check out for a height example so
+ 
+
+ align:start position:0%
+should check out for a height example so
+in particular if you are in a situation
+
+ align:start position:0%
+in particular if you are in a situation
+ 
+
+ align:start position:0%
+in particular if you are in a situation
+of a complete multi-part a graph with
+
+ align:start position:0%
+of a complete multi-part a graph with
+ 
+
+ align:start position:0%
+of a complete multi-part a graph with
+equal size or nearly equal sized parts
+
+ align:start position:0%
+equal size or nearly equal sized parts
+ 
+
+ align:start position:0%
+equal size or nearly equal sized parts
+what is a a is one vertex from each part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you take out one vertex from each
+
+ align:start position:0%
+so you take out one vertex from each
+ 
+
+ align:start position:0%
+so you take out one vertex from each
+part and read off this calculation for
+
+ align:start position:0%
+part and read off this calculation for
+ 
+
+ align:start position:0%
+part and read off this calculation for
+this graph over here and then you see
+
+ align:start position:0%
+this graph over here and then you see
+ 
+
+ align:start position:0%
+this graph over here and then you see
+that that is indeed equality so you
+
+ align:start position:0%
+that that is indeed equality so you
+ 
+
+ align:start position:0%
+that that is indeed equality so you
+should check out you don't need to do
+
+ align:start position:0%
+should check out you don't need to do
+ 
+
+ align:start position:0%
+should check out you don't need to do
+any actual calculations ok any questions
+
+ align:start position:0%
+any actual calculations ok any questions
+ 
+
+ align:start position:0%
+any actual calculations ok any questions
+about the proofs we've done so far all
+
+ align:start position:0%
+about the proofs we've done so far all
+ 
+
+ align:start position:0%
+about the proofs we've done so far all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+let me show you a another proof of
+
+ align:start position:0%
+let me show you a another proof of
+ 
+
+ align:start position:0%
+let me show you a another proof of
+Tehran's theorem so this proof is as a
+
+ align:start position:0%
+Tehran's theorem so this proof is as a
+ 
+
+ align:start position:0%
+Tehran's theorem so this proof is as a
+name so it's called Z cough
+
+ align:start position:0%
+name so it's called Z cough
+ 
+
+ align:start position:0%
+name so it's called Z cough
+symmetrization the capacity
+
+ align:start position:0%
+symmetrization the capacity
+ 
+
+ align:start position:0%
+symmetrization the capacity
+unfortunately only having a name that's
+
+ align:start position:0%
+unfortunately only having a name that's
+ 
+
+ align:start position:0%
+unfortunately only having a name that's
+hard to beat in terms of alphabetical
+
+ align:start position:0%
+hard to beat in terms of alphabetical
+ 
+
+ align:start position:0%
+hard to beat in terms of alphabetical
+watering if you and I were to write a
+
+ align:start position:0%
+watering if you and I were to write a
+ 
+
+ align:start position:0%
+watering if you and I were to write a
+paper I wouldn't be the last often ok so
+
+ align:start position:0%
+paper I wouldn't be the last often ok so
+ 
+
+ align:start position:0%
+paper I wouldn't be the last often ok so
+what's this about so let G be the graph
+
+ align:start position:0%
+what's this about so let G be the graph
+ 
+
+ align:start position:0%
+what's this about so let G be the graph
+again as before we're going to take a
+
+ align:start position:0%
+again as before we're going to take a
+ 
+
+ align:start position:0%
+again as before we're going to take a
+maximal example
+
+ align:start position:0%
+maximal example
+ 
+
+ align:start position:0%
+maximal example
+so be the end vertex graph that is free
+
+ align:start position:0%
+so be the end vertex graph that is free
+ 
+
+ align:start position:0%
+so be the end vertex graph that is free
+of clicks on R plus 1 vertices and has
+
+ align:start position:0%
+of clicks on R plus 1 vertices and has
+ 
+
+ align:start position:0%
+of clicks on R plus 1 vertices and has
+already the maximum number of edges so
+
+ align:start position:0%
+already the maximum number of edges so
+ 
+
+ align:start position:0%
+already the maximum number of edges so
+here's a property I want to prove about
+
+ align:start position:0%
+here's a property I want to prove about
+ 
+
+ align:start position:0%
+here's a property I want to prove about
+this graph I claim that if you look at
+
+ align:start position:0%
+this graph I claim that if you look at
+ 
+
+ align:start position:0%
+this graph I claim that if you look at
+the complement of the graph of this
+
+ align:start position:0%
+the complement of the graph of this
+ 
+
+ align:start position:0%
+the complement of the graph of this
+extremal example
+
+ align:start position:0%
+extremal example
+ 
+
+ align:start position:0%
+extremal example
+it must be an equivalence relation so
+
+ align:start position:0%
+it must be an equivalence relation so
+ 
+
+ align:start position:0%
+it must be an equivalence relation so
+more precisely claim that if XY is a non
+
+ align:start position:0%
+more precisely claim that if XY is a non
+ 
+
+ align:start position:0%
+more precisely claim that if XY is a non
+edge and Y Z is a non edge then X Z must
+
+ align:start position:0%
+edge and Y Z is a non edge then X Z must
+ 
+
+ align:start position:0%
+edge and Y Z is a non edge then X Z must
+also be a long edge so in other words
+
+ align:start position:0%
+also be a long edge so in other words
+ 
+
+ align:start position:0%
+also be a long edge so in other words
+non edges form equivalence relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again you should always think about
+
+ align:start position:0%
+and again you should always think about
+ 
+
+ align:start position:0%
+and again you should always think about
+the extreme example it is true for the
+
+ align:start position:0%
+the extreme example it is true for the
+ 
+
+ align:start position:0%
+the extreme example it is true for the
+extremo example because the compliment
+
+ align:start position:0%
+extremo example because the compliment
+ 
+
+ align:start position:0%
+extremo example because the compliment
+are a bunch of clicks so it is an
+
+ align:start position:0%
+are a bunch of clicks so it is an
+ 
+
+ align:start position:0%
+are a bunch of clicks so it is an
+equivalence relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's prove this claim so let's
+
+ align:start position:0%
+okay so let's prove this claim so let's
+ 
+
+ align:start position:0%
+okay so let's prove this claim so let's
+assume that the conclusion is not true
+
+ align:start position:0%
+assume that the conclusion is not true
+ 
+
+ align:start position:0%
+assume that the conclusion is not true
+so suppose for the contrary that we have
+
+ align:start position:0%
+so suppose for the contrary that we have
+ 
+
+ align:start position:0%
+so suppose for the contrary that we have
+XY and Y Z being non edges but XZ is an
+
+ align:start position:0%
+XY and Y Z being non edges but XZ is an
+ 
+
+ align:start position:0%
+XY and Y Z being non edges but XZ is an
+edge so let's think about what happens
+
+ align:start position:0%
+edge so let's think about what happens
+ 
+
+ align:start position:0%
+edge so let's think about what happens
+to the degrees of knowledge isn't
+
+ align:start position:0%
+to the degrees of knowledge isn't
+ 
+
+ align:start position:0%
+to the degrees of knowledge isn't
+vertices so I claim that if the degree
+
+ align:start position:0%
+vertices so I claim that if the degree
+ 
+
+ align:start position:0%
+vertices so I claim that if the degree
+of Y or smaller than the degree of X
+
+ align:start position:0%
+of Y or smaller than the degree of X
+ 
+
+ align:start position:0%
+of Y or smaller than the degree of X
+then I can do something to the graph
+
+ align:start position:0%
+then I can do something to the graph
+ 
+
+ align:start position:0%
+then I can do something to the graph
+that violates the maximality of the
+
+ align:start position:0%
+that violates the maximality of the
+ 
+
+ align:start position:0%
+that violates the maximality of the
+number of edges namely I can replace Y
+
+ align:start position:0%
+number of edges namely I can replace Y
+ 
+
+ align:start position:0%
+number of edges namely I can replace Y
+by a chrome of X so I chop off Y from
+
+ align:start position:0%
+by a chrome of X so I chop off Y from
+ 
+
+ align:start position:0%
+by a chrome of X so I chop off Y from
+the graph and I look at X and I chrome
+
+ align:start position:0%
+the graph and I look at X and I chrome
+ 
+
+ align:start position:0%
+the graph and I look at X and I chrome
+it so calling it means taking some X
+
+ align:start position:0%
+it so calling it means taking some X
+ 
+
+ align:start position:0%
+it so calling it means taking some X
+Prime and a join X Prime to all the same
+
+ align:start position:0%
+Prime and a join X Prime to all the same
+ 
+
+ align:start position:0%
+Prime and a join X Prime to all the same
+neighbors as X so Chrome X into some
+
+ align:start position:0%
+neighbors as X so Chrome X into some
+ 
+
+ align:start position:0%
+neighbors as X so Chrome X into some
+other vertex X Prime now when you do
+
+ align:start position:0%
+other vertex X Prime now when you do
+ 
+
+ align:start position:0%
+other vertex X Prime now when you do
+this I claim that you also get a graph
+
+ align:start position:0%
+this I claim that you also get a graph
+ 
+
+ align:start position:0%
+this I claim that you also get a graph
+that is free of K sub R plus 1 so we
+
+ align:start position:0%
+that is free of K sub R plus 1 so we
+ 
+
+ align:start position:0%
+that is free of K sub R plus 1 so we
+also obtain
+
+ align:start position:0%
+also obtain
+ 
+
+ align:start position:0%
+also obtain
+a case up or plus one free graph case
+
+ align:start position:0%
+a case up or plus one free graph case
+ 
+
+ align:start position:0%
+a case up or plus one free graph case
+why is that if you were to have an R
+
+ align:start position:0%
+why is that if you were to have an R
+ 
+
+ align:start position:0%
+why is that if you were to have an R
+plus 1 Creek well it shouldn't have both
+
+ align:start position:0%
+plus 1 Creek well it shouldn't have both
+ 
+
+ align:start position:0%
+plus 1 Creek well it shouldn't have both
+X and X chrome because there's no edge
+
+ align:start position:0%
+X and X chrome because there's no edge
+ 
+
+ align:start position:0%
+X and X chrome because there's no edge
+between them so it only has one of X and
+
+ align:start position:0%
+between them so it only has one of X and
+ 
+
+ align:start position:0%
+between them so it only has one of X and
+X cloned but then that would have been a
+
+ align:start position:0%
+X cloned but then that would have been a
+ 
+
+ align:start position:0%
+X cloned but then that would have been a
+creek in the original graph however what
+
+ align:start position:0%
+creek in the original graph however what
+ 
+
+ align:start position:0%
+creek in the original graph however what
+about the number of edges that we obtain
+
+ align:start position:0%
+about the number of edges that we obtain
+ 
+
+ align:start position:0%
+about the number of edges that we obtain
+after this transformation if X had more
+
+ align:start position:0%
+after this transformation if X had more
+ 
+
+ align:start position:0%
+after this transformation if X had more
+outgoing edges a higher degree than Y
+
+ align:start position:0%
+outgoing edges a higher degree than Y
+ 
+
+ align:start position:0%
+outgoing edges a higher degree than Y
+then crowning X to replace Y increases
+
+ align:start position:0%
+then crowning X to replace Y increases
+ 
+
+ align:start position:0%
+then crowning X to replace Y increases
+the number of edges we obtain a graph
+
+ align:start position:0%
+the number of edges we obtain a graph
+ 
+
+ align:start position:0%
+the number of edges we obtain a graph
+that is also K sub R plus 1 and G which
+
+ align:start position:0%
+that is also K sub R plus 1 and G which
+ 
+
+ align:start position:0%
+that is also K sub R plus 1 and G which
+is not possible because we assume that G
+
+ align:start position:0%
+is not possible because we assume that G
+ 
+
+ align:start position:0%
+is not possible because we assume that G
+started with a maximum number of edges
+
+ align:start position:0%
+started with a maximum number of edges
+ 
+
+ align:start position:0%
+started with a maximum number of edges
+so therefore the degree of Y is that
+
+ align:start position:0%
+so therefore the degree of Y is that
+ 
+
+ align:start position:0%
+so therefore the degree of Y is that
+most the degree of X basically for every
+
+ align:start position:0%
+most the degree of X basically for every
+ 
+
+ align:start position:0%
+most the degree of X basically for every
+edge XY likewise we also have that
+
+ align:start position:0%
+edge XY likewise we also have that
+ 
+
+ align:start position:0%
+edge XY likewise we also have that
+there's no edge between y and z so the
+
+ align:start position:0%
+there's no edge between y and z so the
+ 
+
+ align:start position:0%
+there's no edge between y and z so the
+degree of y is we have wise and Easter
+
+ align:start position:0%
+degree of y is we have wise and Easter
+ 
+
+ align:start position:0%
+degree of y is we have wise and Easter
+the queer backs now so we have wives at
+
+ align:start position:0%
+the queer backs now so we have wives at
+ 
+
+ align:start position:0%
+the queer backs now so we have wives at
+least now Y has a lot of outgoing edges
+
+ align:start position:0%
+least now Y has a lot of outgoing edges
+ 
+
+ align:start position:0%
+least now Y has a lot of outgoing edges
+so now let's replace both x and z by
+
+ align:start position:0%
+so now let's replace both x and z by
+ 
+
+ align:start position:0%
+so now let's replace both x and z by
+Chrome's of Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as before we obtain some graph I will
+
+ align:start position:0%
+as before we obtain some graph I will
+ 
+
+ align:start position:0%
+as before we obtain some graph I will
+call G Prime and G Prime
+
+ align:start position:0%
+call G Prime and G Prime
+ 
+
+ align:start position:0%
+call G Prime and G Prime
+same reason as before is K sub R plus 1
+
+ align:start position:0%
+same reason as before is K sub R plus 1
+ 
+
+ align:start position:0%
+same reason as before is K sub R plus 1
+3 right if you had a case of R plus 1
+
+ align:start position:0%
+3 right if you had a case of R plus 1
+ 
+
+ align:start position:0%
+3 right if you had a case of R plus 1
+then the same clique should have shown
+
+ align:start position:0%
+then the same clique should have shown
+ 
+
+ align:start position:0%
+then the same clique should have shown
+up in G so so G prime does not have R
+
+ align:start position:0%
+up in G so so G prime does not have R
+ 
+
+ align:start position:0%
+up in G so so G prime does not have R
+plus 1 clicks either but what about the
+
+ align:start position:0%
+plus 1 clicks either but what about the
+ 
+
+ align:start position:0%
+plus 1 clicks either but what about the
+number of edges in G prime so the number
+
+ align:start position:0%
+number of edges in G prime so the number
+ 
+
+ align:start position:0%
+number of edges in G prime so the number
+of edges in G prime well we started with
+
+ align:start position:0%
+of edges in G prime well we started with
+ 
+
+ align:start position:0%
+of edges in G prime well we started with
+G we deleted X and Z so we deleted this
+
+ align:start position:0%
+G we deleted X and Z so we deleted this
+ 
+
+ align:start position:0%
+G we deleted X and Z so we deleted this
+many edges here were crucially using the
+
+ align:start position:0%
+many edges here were crucially using the
+ 
+
+ align:start position:0%
+many edges here were crucially using the
+fact that there is an edge between X and
+
+ align:start position:0%
+fact that there is an edge between X and
+ 
+
+ align:start position:0%
+fact that there is an edge between X and
+Z but now we also add it back in a bunch
+
+ align:start position:0%
+Z but now we also add it back in a bunch
+ 
+
+ align:start position:0%
+Z but now we also add it back in a bunch
+of edges coming from the chrome of Y and
+
+ align:start position:0%
+of edges coming from the chrome of Y and
+ 
+
+ align:start position:0%
+of edges coming from the chrome of Y and
+there are 2 times the Y edges added back
+
+ align:start position:0%
+there are 2 times the Y edges added back
+ 
+
+ align:start position:0%
+there are 2 times the Y edges added back
+in and see because Y has degree at least
+
+ align:start position:0%
+in and see because Y has degree at least
+ 
+
+ align:start position:0%
+in and see because Y has degree at least
+that of both X and Z we obtained that
+
+ align:start position:0%
+that of both X and Z we obtained that
+ 
+
+ align:start position:0%
+that of both X and Z we obtained that
+this number of edges is strictly bigger
+
+ align:start position:0%
+this number of edges is strictly bigger
+ 
+
+ align:start position:0%
+this number of edges is strictly bigger
+than that of G which contradicts the
+
+ align:start position:0%
+than that of G which contradicts the
+ 
+
+ align:start position:0%
+than that of G which contradicts the
+maximality of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so at this point we know that the
+
+ align:start position:0%
+so at this point we know that the
+ 
+
+ align:start position:0%
+so at this point we know that the
+complement of G must be an equivalence
+
+ align:start position:0%
+complement of G must be an equivalence
+ 
+
+ align:start position:0%
+complement of G must be an equivalence
+relation so the complement is a bunch of
+
+ align:start position:0%
+relation so the complement is a bunch of
+ 
+
+ align:start position:0%
+relation so the complement is a bunch of
+clicks and that's that's a lot of
+
+ align:start position:0%
+clicks and that's that's a lot of
+ 
+
+ align:start position:0%
+clicks and that's that's a lot of
+information right so that's almost the
+
+ align:start position:0%
+information right so that's almost the
+ 
+
+ align:start position:0%
+information right so that's almost the
+best thing we can hope for is a
+
+ align:start position:0%
+best thing we can hope for is a
+ 
+
+ align:start position:0%
+best thing we can hope for is a
+structural information we're not quite
+
+ align:start position:0%
+structural information we're not quite
+ 
+
+ align:start position:0%
+structural information we're not quite
+done yet and why is that almost there
+
+ align:start position:0%
+done yet and why is that almost there
+ 
+
+ align:start position:0%
+done yet and why is that almost there
+we're not quite done yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we need to figure out the sizes
+
+ align:start position:0%
+okay so we need to figure out the sizes
+ 
+
+ align:start position:0%
+okay so we need to figure out the sizes
+of the individual parts so we need to
+
+ align:start position:0%
+of the individual parts so we need to
+ 
+
+ align:start position:0%
+of the individual parts so we need to
+figure out the sizes of individual parts
+
+ align:start position:0%
+figure out the sizes of individual parts
+ 
+
+ align:start position:0%
+figure out the sizes of individual parts
+and also note that you cannot have too
+
+ align:start position:0%
+and also note that you cannot have too
+ 
+
+ align:start position:0%
+and also note that you cannot have too
+many parts so at this point after the
+
+ align:start position:0%
+many parts so at this point after the
+ 
+
+ align:start position:0%
+many parts so at this point after the
+claim we know that G is a complete
+
+ align:start position:0%
+claim we know that G is a complete
+ 
+
+ align:start position:0%
+claim we know that G is a complete
+multi-part a graph it has and most are
+
+ align:start position:0%
+multi-part a graph it has and most are
+ 
+
+ align:start position:0%
+multi-part a graph it has and most are
+parts if it had R plus one parts I would
+
+ align:start position:0%
+parts if it had R plus one parts I would
+ 
+
+ align:start position:0%
+parts if it had R plus one parts I would
+see a clique and R plus 1 vertices if so
+
+ align:start position:0%
+see a clique and R plus 1 vertices if so
+ 
+
+ align:start position:0%
+see a clique and R plus 1 vertices if so
+and finally I need to show the rest is
+
+ align:start position:0%
+and finally I need to show the rest is
+ 
+
+ align:start position:0%
+and finally I need to show the rest is
+fairly routine I need to show what the
+
+ align:start position:0%
+fairly routine I need to show what the
+ 
+
+ align:start position:0%
+fairly routine I need to show what the
+part sizes have to be to maximize the
+
+ align:start position:0%
+part sizes have to be to maximize the
+ 
+
+ align:start position:0%
+part sizes have to be to maximize the
+number of edges and basically if you had
+
+ align:start position:0%
+number of edges and basically if you had
+ 
+
+ align:start position:0%
+number of edges and basically if you had
+some two parts so consider exactly our
+
+ align:start position:0%
+some two parts so consider exactly our
+ 
+
+ align:start position:0%
+some two parts so consider exactly our
+parts are all empty parts is some two
+
+ align:start position:0%
+parts are all empty parts is some two
+ 
+
+ align:start position:0%
+parts are all empty parts is some two
+parts half the number of vertices
+
+ align:start position:0%
+parts half the number of vertices
+ 
+
+ align:start position:0%
+parts half the number of vertices
+differing by more than one then what I
+
+ align:start position:0%
+differing by more than one then what I
+ 
+
+ align:start position:0%
+differing by more than one then what I
+can do is so if you had one part much
+
+ align:start position:0%
+can do is so if you had one part much
+ 
+
+ align:start position:0%
+can do is so if you had one part much
+bigger than the other part and imagine
+
+ align:start position:0%
+bigger than the other part and imagine
+ 
+
+ align:start position:0%
+bigger than the other part and imagine
+moving one vertex from one part to the
+
+ align:start position:0%
+moving one vertex from one part to the
+ 
+
+ align:start position:0%
+moving one vertex from one part to the
+other part and should convince yourself
+
+ align:start position:0%
+other part and should convince yourself
+ 
+
+ align:start position:0%
+other part and should convince yourself
+that this operation should strictly
+
+ align:start position:0%
+that this operation should strictly
+ 
+
+ align:start position:0%
+that this operation should strictly
+increase the number of edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving vertices should strictly increase
+
+ align:start position:0%
+moving vertices should strictly increase
+ 
+
+ align:start position:0%
+moving vertices should strictly increase
+the number of edges of G and putting
+
+ align:start position:0%
+the number of edges of G and putting
+ 
+
+ align:start position:0%
+the number of edges of G and putting
+this all together we see that the
+
+ align:start position:0%
+this all together we see that the
+ 
+
+ align:start position:0%
+this all together we see that the
+extremal example necessarily has to be a
+
+ align:start position:0%
+extremal example necessarily has to be a
+ 
+
+ align:start position:0%
+extremal example necessarily has to be a
+current graph namely a complete our part
+
+ align:start position:0%
+current graph namely a complete our part
+ 
+
+ align:start position:0%
+current graph namely a complete our part
+i graph where all the parts have the
+
+ align:start position:0%
+i graph where all the parts have the
+ 
+
+ align:start position:0%
+i graph where all the parts have the
+same size up to almost one difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions so the question is
+
+ align:start position:0%
+okay any questions so the question is
+ 
+
+ align:start position:0%
+okay any questions so the question is
+can the zhukov symmetrization have been
+
+ align:start position:0%
+can the zhukov symmetrization have been
+ 
+
+ align:start position:0%
+can the zhukov symmetrization have been
+confused for any other types of problem
+
+ align:start position:0%
+confused for any other types of problem
+ 
+
+ align:start position:0%
+confused for any other types of problem
+I do have something else in mind but I
+
+ align:start position:0%
+I do have something else in mind but I
+ 
+
+ align:start position:0%
+I do have something else in mind but I
+don't want to discuss it now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any more questions okay and you see that
+
+ align:start position:0%
+any more questions okay and you see that
+ 
+
+ align:start position:0%
+any more questions okay and you see that
+in both proofs were if you look at this
+
+ align:start position:0%
+in both proofs were if you look at this
+ 
+
+ align:start position:0%
+in both proofs were if you look at this
+proof as well you see that the tauren
+
+ align:start position:0%
+proof as well you see that the tauren
+ 
+
+ align:start position:0%
+proof as well you see that the tauren
+graph is the unique extra measure I want
+
+ align:start position:0%
+graph is the unique extra measure I want
+ 
+
+ align:start position:0%
+graph is the unique extra measure I want
+to give you a third proof that has a
+
+ align:start position:0%
+to give you a third proof that has a
+ 
+
+ align:start position:0%
+to give you a third proof that has a
+somewhat different flavor so these two
+
+ align:start position:0%
+somewhat different flavor so these two
+ 
+
+ align:start position:0%
+somewhat different flavor so these two
+proofs they're both somewhat
+
+ align:start position:0%
+proofs they're both somewhat
+ 
+
+ align:start position:0%
+proofs they're both somewhat
+combinatorial in flavor so I'm doing
+
+ align:start position:0%
+combinatorial in flavor so I'm doing
+ 
+
+ align:start position:0%
+combinatorial in flavor so I'm doing
+some arguments either looking at you
+
+ align:start position:0%
+some arguments either looking at you
+ 
+
+ align:start position:0%
+some arguments either looking at you
+know in this case you click and arguing
+
+ align:start position:0%
+know in this case you click and arguing
+ 
+
+ align:start position:0%
+know in this case you click and arguing
+what happens outside of it and over
+
+ align:start position:0%
+what happens outside of it and over
+ 
+
+ align:start position:0%
+what happens outside of it and over
+there again looking at Maximo example
+
+ align:start position:0%
+there again looking at Maximo example
+ 
+
+ align:start position:0%
+there again looking at Maximo example
+but the third proof I want to show is
+
+ align:start position:0%
+but the third proof I want to show is
+ 
+
+ align:start position:0%
+but the third proof I want to show is
+more of a probabilistic proof so this
+
+ align:start position:0%
+more of a probabilistic proof so this
+ 
+
+ align:start position:0%
+more of a probabilistic proof so this
+highlights an important method in
+
+ align:start position:0%
+highlights an important method in
+ 
+
+ align:start position:0%
+highlights an important method in
+combinatorics known as the probabilistic
+
+ align:start position:0%
+combinatorics known as the probabilistic
+ 
+
+ align:start position:0%
+combinatorics known as the probabilistic
+method where we start with a problem
+
+ align:start position:0%
+method where we start with a problem
+ 
+
+ align:start position:0%
+method where we start with a problem
+that comes with no randomness but we
+
+ align:start position:0%
+that comes with no randomness but we
+ 
+
+ align:start position:0%
+that comes with no randomness but we
+introduce some randomness to make the
+
+ align:start position:0%
+introduce some randomness to make the
+ 
+
+ align:start position:0%
+introduce some randomness to make the
+problem amenable and it's a very pretty
+
+ align:start position:0%
+problem amenable and it's a very pretty
+ 
+
+ align:start position:0%
+problem amenable and it's a very pretty
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we start again with G being and n
+
+ align:start position:0%
+so we start again with G being and n
+ 
+
+ align:start position:0%
+so we start again with G being and n
+vertex K sub R plus one free well ommm
+
+ align:start position:0%
+vertex K sub R plus one free well ommm
+ 
+
+ align:start position:0%
+vertex K sub R plus one free well ommm
+edges and what I want to do is to
+
+ align:start position:0%
+edges and what I want to do is to
+ 
+
+ align:start position:0%
+edges and what I want to do is to
+randomly sort the vertex set consider a
+
+ align:start position:0%
+randomly sort the vertex set consider a
+ 
+
+ align:start position:0%
+randomly sort the vertex set consider a
+random order so I put all the vertices
+
+ align:start position:0%
+random order so I put all the vertices
+ 
+
+ align:start position:0%
+random order so I put all the vertices
+on the line where the vertices are
+
+ align:start position:0%
+on the line where the vertices are
+ 
+
+ align:start position:0%
+on the line where the vertices are
+chosen in random order and you see some
+
+ align:start position:0%
+chosen in random order and you see some
+ 
+
+ align:start position:0%
+chosen in random order and you see some
+of the edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me show you how to find a click and
+
+ align:start position:0%
+let me show you how to find a click and
+ 
+
+ align:start position:0%
+let me show you how to find a click and
+essentially we do it in not so smart way
+
+ align:start position:0%
+essentially we do it in not so smart way
+ 
+
+ align:start position:0%
+essentially we do it in not so smart way
+namely I basically pick all the vertices
+
+ align:start position:0%
+namely I basically pick all the vertices
+ 
+
+ align:start position:0%
+namely I basically pick all the vertices
+in some greedy like manner where I
+
+ align:start position:0%
+in some greedy like manner where I
+ 
+
+ align:start position:0%
+in some greedy like manner where I
+include a vertex in my set if it is
+
+ align:start position:0%
+include a vertex in my set if it is
+ 
+
+ align:start position:0%
+include a vertex in my set if it is
+adjacent to all earlier vertices if if
+
+ align:start position:0%
+adjacent to all earlier vertices if if
+ 
+
+ align:start position:0%
+adjacent to all earlier vertices if if
+all of its neighbors so I include V if V
+
+ align:start position:0%
+all of its neighbors so I include V if V
+ 
+
+ align:start position:0%
+all of its neighbors so I include V if V
+is the earliest vertex
+
+ align:start position:0%
+is the earliest vertex
+ 
+
+ align:start position:0%
+is the earliest vertex
+among its neighbors okay so earliest
+
+ align:start position:0%
+among its neighbors okay so earliest
+ 
+
+ align:start position:0%
+among its neighbors okay so earliest
+means the leftmost go from left to right
+
+ align:start position:0%
+means the leftmost go from left to right
+ 
+
+ align:start position:0%
+means the leftmost go from left to right
+so in this case up here look at the
+
+ align:start position:0%
+so in this case up here look at the
+ 
+
+ align:start position:0%
+so in this case up here look at the
+first vertex well first of all taxes
+
+ align:start position:0%
+first vertex well first of all taxes
+ 
+
+ align:start position:0%
+first vertex well first of all taxes
+should always be in your set this vertex
+
+ align:start position:0%
+should always be in your set this vertex
+ 
+
+ align:start position:0%
+should always be in your set this vertex
+has one neighbors to the right that's
+
+ align:start position:0%
+has one neighbors to the right that's
+ 
+
+ align:start position:0%
+has one neighbors to the right that's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and no sorry that's not what I want to
+
+ align:start position:0%
+and no sorry that's not what I want to
+ 
+
+ align:start position:0%
+and no sorry that's not what I want to
+do so I actually do you mean when I was
+
+ align:start position:0%
+do so I actually do you mean when I was
+ 
+
+ align:start position:0%
+do so I actually do you mean when I was
+initially V is adjacent to all the
+
+ align:start position:0%
+initially V is adjacent to all the
+ 
+
+ align:start position:0%
+initially V is adjacent to all the
+earlier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices in this order but so for
+
+ align:start position:0%
+vertices in this order but so for
+ 
+
+ align:start position:0%
+vertices in this order but so for
+example this vertex it's okay and I'm
+
+ align:start position:0%
+example this vertex it's okay and I'm
+ 
+
+ align:start position:0%
+example this vertex it's okay and I'm
+also going to include this vertex here
+
+ align:start position:0%
+also going to include this vertex here
+ 
+
+ align:start position:0%
+also going to include this vertex here
+yes it has both of its nativist earlier
+
+ align:start position:0%
+yes it has both of its nativist earlier
+ 
+
+ align:start position:0%
+yes it has both of its nativist earlier
+vertices are in in both the earlier
+
+ align:start position:0%
+vertices are in in both the earlier
+ 
+
+ align:start position:0%
+vertices are in in both the earlier
+vertices are adjacent to the third
+
+ align:start position:0%
+vertices are adjacent to the third
+ 
+
+ align:start position:0%
+vertices are adjacent to the third
+vertex and I think that's it now this
+
+ align:start position:0%
+vertex and I think that's it now this
+ 
+
+ align:start position:0%
+vertex and I think that's it now this
+set X I claim two things one that X has
+
+ align:start position:0%
+set X I claim two things one that X has
+ 
+
+ align:start position:0%
+set X I claim two things one that X has
+to be a clique so clean the X has to be
+
+ align:start position:0%
+to be a clique so clean the X has to be
+ 
+
+ align:start position:0%
+to be a clique so clean the X has to be
+a clique because every vertex in X is
+
+ align:start position:0%
+a clique because every vertex in X is
+ 
+
+ align:start position:0%
+a clique because every vertex in X is
+two jacent to the earlier vertices in
+
+ align:start position:0%
+two jacent to the earlier vertices in
+ 
+
+ align:start position:0%
+two jacent to the earlier vertices in
+particular all the vertices in X are
+
+ align:start position:0%
+particular all the vertices in X are
+ 
+
+ align:start position:0%
+particular all the vertices in X are
+joined to each other on the other hand
+
+ align:start position:0%
+joined to each other on the other hand
+ 
+
+ align:start position:0%
+joined to each other on the other hand
+how big is X at least in expectation so
+
+ align:start position:0%
+how big is X at least in expectation so
+ 
+
+ align:start position:0%
+how big is X at least in expectation so
+for every vertex I want to understand
+
+ align:start position:0%
+for every vertex I want to understand
+ 
+
+ align:start position:0%
+for every vertex I want to understand
+the probability that this V is included
+
+ align:start position:0%
+the probability that this V is included
+ 
+
+ align:start position:0%
+the probability that this V is included
+in X all right so V has a bunch of non
+
+ align:start position:0%
+in X all right so V has a bunch of non
+ 
+
+ align:start position:0%
+in X all right so V has a bunch of non
+neighbors and the property of being
+
+ align:start position:0%
+neighbors and the property of being
+ 
+
+ align:start position:0%
+neighbors and the property of being
+included in X is that all of its non
+
+ align:start position:0%
+included in X is that all of its non
+ 
+
+ align:start position:0%
+included in X is that all of its non
+neighbors up here after B so the
+
+ align:start position:0%
+neighbors up here after B so the
+ 
+
+ align:start position:0%
+neighbors up here after B so the
+probability that V little B is in the
+
+ align:start position:0%
+probability that V little B is in the
+ 
+
+ align:start position:0%
+probability that V little B is in the
+set X its equal to the probability that
+
+ align:start position:0%
+set X its equal to the probability that
+ 
+
+ align:start position:0%
+set X its equal to the probability that
+B appears before all its no neighbors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all we and it's now neighbors they're
+
+ align:start position:0%
+all we and it's now neighbors they're
+ 
+
+ align:start position:0%
+all we and it's now neighbors they're
+sorted uniformly so the probability that
+
+ align:start position:0%
+sorted uniformly so the probability that
+ 
+
+ align:start position:0%
+sorted uniformly so the probability that
+this occurs is exactly one over one plus
+
+ align:start position:0%
+this occurs is exactly one over one plus
+ 
+
+ align:start position:0%
+this occurs is exactly one over one plus
+the number of non neighbors which is n
+
+ align:start position:0%
+the number of non neighbors which is n
+ 
+
+ align:start position:0%
+the number of non neighbors which is n
+minus the degree of P okay but we know
+
+ align:start position:0%
+minus the degree of P okay but we know
+ 
+
+ align:start position:0%
+minus the degree of P okay but we know
+that this graph G has no cliques of size
+
+ align:start position:0%
+that this graph G has no cliques of size
+ 
+
+ align:start position:0%
+that this graph G has no cliques of size
+R plus one so if we consider the
+
+ align:start position:0%
+R plus one so if we consider the
+ 
+
+ align:start position:0%
+R plus one so if we consider the
+expected number of size of X on one hand
+
+ align:start position:0%
+expected number of size of X on one hand
+ 
+
+ align:start position:0%
+expected number of size of X on one hand
+it has a most part because G 3 on the
+
+ align:start position:0%
+it has a most part because G 3 on the
+ 
+
+ align:start position:0%
+it has a most part because G 3 on the
+other hand by linearity of expectations
+
+ align:start position:0%
+other hand by linearity of expectations
+ 
+
+ align:start position:0%
+other hand by linearity of expectations
+for each vertex is included with some
+
+ align:start position:0%
+for each vertex is included with some
+ 
+
+ align:start position:0%
+for each vertex is included with some
+probability so the size of X in
+
+ align:start position:0%
+probability so the size of X in
+ 
+
+ align:start position:0%
+probability so the size of X in
+expectation is just the sum of all of
+
+ align:start position:0%
+expectation is just the sum of all of
+ 
+
+ align:start position:0%
+expectation is just the sum of all of
+these individual inclusion probabilities
+
+ align:start position:0%
+these individual inclusion probabilities
+ 
+
+ align:start position:0%
+these individual inclusion probabilities
+which individually we've computed above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that now by convexity I can
+
+ align:start position:0%
+like that now by convexity I can
+ 
+
+ align:start position:0%
+like that now by convexity I can
+conclude that this quantity this sum
+
+ align:start position:0%
+conclude that this quantity this sum
+ 
+
+ align:start position:0%
+conclude that this quantity this sum
+here is at least the content without
+
+ align:start position:0%
+here is at least the content without
+ 
+
+ align:start position:0%
+here is at least the content without
+would have been obtained if all the
+
+ align:start position:0%
+would have been obtained if all the
+ 
+
+ align:start position:0%
+would have been obtained if all the
+degrees were equal to each other and if
+
+ align:start position:0%
+degrees were equal to each other and if
+ 
+
+ align:start position:0%
+degrees were equal to each other and if
+you rearrange this equation this
+
+ align:start position:0%
+you rearrange this equation this
+ 
+
+ align:start position:0%
+you rearrange this equation this
+inequality we obtain most one minus one
+
+ align:start position:0%
+inequality we obtain most one minus one
+ 
+
+ align:start position:0%
+inequality we obtain most one minus one
+over R times N squared over two and if
+
+ align:start position:0%
+over R times N squared over two and if
+ 
+
+ align:start position:0%
+over R times N squared over two and if
+you compare this number to the number of
+
+ align:start position:0%
+you compare this number to the number of
+ 
+
+ align:start position:0%
+you compare this number to the number of
+edges in the current graph okay so you
+
+ align:start position:0%
+edges in the current graph okay so you
+ 
+
+ align:start position:0%
+edges in the current graph okay so you
+see that this is basically the number of
+
+ align:start position:0%
+see that this is basically the number of
+ 
+
+ align:start position:0%
+see that this is basically the number of
+edges and this gives you a proof and
+
+ align:start position:0%
+edges and this gives you a proof and
+ 
+
+ align:start position:0%
+edges and this gives you a proof and
+it's divisible by R and in fact the
+
+ align:start position:0%
+it's divisible by R and in fact the
+ 
+
+ align:start position:0%
+it's divisible by R and in fact the
+number of edges in the Terim graph is
+
+ align:start position:0%
+number of edges in the Terim graph is
+ 
+
+ align:start position:0%
+number of edges in the Terim graph is
+exactly this number here if this
+
+ align:start position:0%
+exactly this number here if this
+ 
+
+ align:start position:0%
+exactly this number here if this
+divisibility because condition is true
+
+ align:start position:0%
+divisibility because condition is true
+ 
+
+ align:start position:0%
+divisibility because condition is true
+if it's not you need to do a little bit
+
+ align:start position:0%
+if it's not you need to do a little bit
+ 
+
+ align:start position:0%
+if it's not you need to do a little bit
+more work because we were a little bit
+
+ align:start position:0%
+more work because we were a little bit
+ 
+
+ align:start position:0%
+more work because we were a little bit
+lost here this step right so you should
+
+ align:start position:0%
+lost here this step right so you should
+ 
+
+ align:start position:0%
+lost here this step right so you should
+see that this quantity here is minimized
+
+ align:start position:0%
+see that this quantity here is minimized
+ 
+
+ align:start position:0%
+see that this quantity here is minimized
+when all the degrees are roughly equal
+
+ align:start position:0%
+when all the degrees are roughly equal
+ 
+
+ align:start position:0%
+when all the degrees are roughly equal
+to each other and you make them as close
+
+ align:start position:0%
+to each other and you make them as close
+ 
+
+ align:start position:0%
+to each other and you make them as close
+to switch to each other as possible okay
+
+ align:start position:0%
+to switch to each other as possible okay
+ 
+
+ align:start position:0%
+to switch to each other as possible okay
+so with a little bit more work you can
+
+ align:start position:0%
+so with a little bit more work you can
+ 
+
+ align:start position:0%
+so with a little bit more work you can
+get the exact version of Tehran's
+
+ align:start position:0%
+get the exact version of Tehran's
+ 
+
+ align:start position:0%
+get the exact version of Tehran's
+theorem up there but at least what we've
+
+ align:start position:0%
+theorem up there but at least what we've
+ 
+
+ align:start position:0%
+theorem up there but at least what we've
+shown yes from here we've shown that the
+
+ align:start position:0%
+shown yes from here we've shown that the
+ 
+
+ align:start position:0%
+shown yes from here we've shown that the
+number of edges the number of edges is
+
+ align:start position:0%
+number of edges the number of edges is
+ 
+
+ align:start position:0%
+number of edges the number of edges is
+and most this quantity which for most
+
+ align:start position:0%
+and most this quantity which for most
+ 
+
+ align:start position:0%
+and most this quantity which for most
+purposes is basically as good as Torrens
+
+ align:start position:0%
+purposes is basically as good as Torrens
+ 
+
+ align:start position:0%
+purposes is basically as good as Torrens
+theorem okay any questions about this
+
+ align:start position:0%
+theorem okay any questions about this
+ 
+
+ align:start position:0%
+theorem okay any questions about this
+proof yet it's a probabilistic method
+
+ align:start position:0%
+proof yet it's a probabilistic method
+ 
+
+ align:start position:0%
+proof yet it's a probabilistic method
+proof so we're introducing some
+
+ align:start position:0%
+proof so we're introducing some
+ 
+
+ align:start position:0%
+proof so we're introducing some
+randomness into the problem that
+
+ align:start position:0%
+randomness into the problem that
+ 
+
+ align:start position:0%
+randomness into the problem that
+originally had no randomness in it okay
+
+ align:start position:0%
+originally had no randomness in it okay
+ 
+
+ align:start position:0%
+originally had no randomness in it okay
+great so let's take a very quick two
+
+ align:start position:0%
+great so let's take a very quick two
+ 
+
+ align:start position:0%
+great so let's take a very quick two
+minute break and then when we come back
+
+ align:start position:0%
+minute break and then when we come back
+ 
+
+ align:start position:0%
+minute break and then when we come back
+I want to show you that even though
+
+ align:start position:0%
+I want to show you that even though
+ 
+
+ align:start position:0%
+I want to show you that even though
+we've shown so many different proofs of
+
+ align:start position:0%
+we've shown so many different proofs of
+ 
+
+ align:start position:0%
+we've shown so many different proofs of
+Quran stir
+
+ align:start position:0%
+Quran stir
+ 
+
+ align:start position:0%
+Quran stir
+and Telstra might think okay this is a
+
+ align:start position:0%
+and Telstra might think okay this is a
+ 
+
+ align:start position:0%
+and Telstra might think okay this is a
+pretty simple thing even if I tweak the
+
+ align:start position:0%
+pretty simple thing even if I tweak the
+ 
+
+ align:start position:0%
+pretty simple thing even if I tweak the
+problem just a little bit there are so
+
+ align:start position:0%
+problem just a little bit there are so
+ 
+
+ align:start position:0%
+problem just a little bit there are so
+many things that we do not understand
+
+ align:start position:0%
+many things that we do not understand
+ 
+
+ align:start position:0%
+many things that we do not understand
+and many important open problems in
+
+ align:start position:0%
+and many important open problems in
+ 
+
+ align:start position:0%
+and many important open problems in
+combinatorics that are variants of
+
+ align:start position:0%
+combinatorics that are variants of
+ 
+
+ align:start position:0%
+combinatorics that are variants of
+Turin's theorem so let's take a quick
+
+ align:start position:0%
+Turin's theorem so let's take a quick
+ 
+
+ align:start position:0%
+Turin's theorem so let's take a quick
+break okay so so far we've been talking
+
+ align:start position:0%
+break okay so so far we've been talking
+ 
+
+ align:start position:0%
+break okay so so far we've been talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+Tehran's theorem or generally big
+
+ align:start position:0%
+Tehran's theorem or generally big
+ 
+
+ align:start position:0%
+Tehran's theorem or generally big
+problem of if you forbid a certain
+
+ align:start position:0%
+problem of if you forbid a certain
+ 
+
+ align:start position:0%
+problem of if you forbid a certain
+structure forbid a certain sub graph
+
+ align:start position:0%
+structure forbid a certain sub graph
+ 
+
+ align:start position:0%
+structure forbid a certain sub graph
+what is the maximum number of edges
+
+ align:start position:0%
+what is the maximum number of edges
+ 
+
+ align:start position:0%
+what is the maximum number of edges
+we're going to spend the next few
+
+ align:start position:0%
+we're going to spend the next few
+ 
+
+ align:start position:0%
+we're going to spend the next few
+lectures discussing more problems of
+
+ align:start position:0%
+lectures discussing more problems of
+ 
+
+ align:start position:0%
+lectures discussing more problems of
+that form and it turns out for the
+
+ align:start position:0%
+that form and it turns out for the
+ 
+
+ align:start position:0%
+that form and it turns out for the
+questions that we've the answers we've
+
+ align:start position:0%
+questions that we've the answers we've
+ 
+
+ align:start position:0%
+questions that we've the answers we've
+just seen they're deceptively simple and
+
+ align:start position:0%
+just seen they're deceptively simple and
+ 
+
+ align:start position:0%
+just seen they're deceptively simple and
+for almost any other situation we don't
+
+ align:start position:0%
+for almost any other situation we don't
+ 
+
+ align:start position:0%
+for almost any other situation we don't
+really know the exact answer and for
+
+ align:start position:0%
+really know the exact answer and for
+ 
+
+ align:start position:0%
+really know the exact answer and for
+many questions we don't know anything
+
+ align:start position:0%
+many questions we don't know anything
+ 
+
+ align:start position:0%
+many questions we don't know anything
+close to the truth I mean particularly I
+
+ align:start position:0%
+close to the truth I mean particularly I
+ 
+
+ align:start position:0%
+close to the truth I mean particularly I
+want to show you one variant of this
+
+ align:start position:0%
+want to show you one variant of this
+ 
+
+ align:start position:0%
+want to show you one variant of this
+problem namely what happens instead of
+
+ align:start position:0%
+problem namely what happens instead of
+ 
+
+ align:start position:0%
+problem namely what happens instead of
+looking at graphs if you look at hyper
+
+ align:start position:0%
+looking at graphs if you look at hyper
+ 
+
+ align:start position:0%
+looking at graphs if you look at hyper
+graphs and there that's a major open
+
+ align:start position:0%
+graphs and there that's a major open
+ 
+
+ align:start position:0%
+graphs and there that's a major open
+problem in combinatorics what the truth
+
+ align:start position:0%
+problem in combinatorics what the truth
+ 
+
+ align:start position:0%
+problem in combinatorics what the truth
+should be so here is an open problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is what happens to Tehran's
+
+ align:start position:0%
+which is what happens to Tehran's
+ 
+
+ align:start position:0%
+which is what happens to Tehran's
+theorem for three scared by the word
+
+ align:start position:0%
+theorem for three scared by the word
+ 
+
+ align:start position:0%
+theorem for three scared by the word
+hyper graph we actually think of graphs
+
+ align:start position:0%
+hyper graph we actually think of graphs
+ 
+
+ align:start position:0%
+hyper graph we actually think of graphs
+as having edges consisting of pairs of
+
+ align:start position:0%
+as having edges consisting of pairs of
+ 
+
+ align:start position:0%
+as having edges consisting of pairs of
+vertices a hyper graph is simply a
+
+ align:start position:0%
+vertices a hyper graph is simply a
+ 
+
+ align:start position:0%
+vertices a hyper graph is simply a
+structure where three uniform hyper
+
+ align:start position:0%
+structure where three uniform hyper
+ 
+
+ align:start position:0%
+structure where three uniform hyper
+graph the edges are triples triples of
+
+ align:start position:0%
+graph the edges are triples triples of
+ 
+
+ align:start position:0%
+graph the edges are triples triples of
+vertices so question is what is the
+
+ align:start position:0%
+vertices so question is what is the
+ 
+
+ align:start position:0%
+vertices so question is what is the
+maximum number of triples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a graph without or for mental Sturm
+
+ align:start position:0%
+in a graph without or for mental Sturm
+ 
+
+ align:start position:0%
+in a graph without or for mental Sturm
+we asked what happens without a triangle
+
+ align:start position:0%
+we asked what happens without a triangle
+ 
+
+ align:start position:0%
+we asked what happens without a triangle
+for three uniform basic question you can
+
+ align:start position:0%
+for three uniform basic question you can
+ 
+
+ align:start position:0%
+for three uniform basic question you can
+ask is what about forbidding a
+
+ align:start position:0%
+ask is what about forbidding a
+ 
+
+ align:start position:0%
+ask is what about forbidding a
+tetrahedron so suppose you don't have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four vertices such that every triple
+
+ align:start position:0%
+four vertices such that every triple
+ 
+
+ align:start position:0%
+four vertices such that every triple
+inside the four vertices is an edge
+
+ align:start position:0%
+inside the four vertices is an edge
+ 
+
+ align:start position:0%
+inside the four vertices is an edge
+what's the maximum number of edges you
+
+ align:start position:0%
+what's the maximum number of edges you
+ 
+
+ align:start position:0%
+what's the maximum number of edges you
+can have awaiting it's not so easy to
+
+ align:start position:0%
+can have awaiting it's not so easy to
+ 
+
+ align:start position:0%
+can have awaiting it's not so easy to
+come up with good examples so two runs
+
+ align:start position:0%
+come up with good examples so two runs
+ 
+
+ align:start position:0%
+come up with good examples so two runs
+to pick a bipartite graph complete
+
+ align:start position:0%
+to pick a bipartite graph complete
+ 
+
+ align:start position:0%
+to pick a bipartite graph complete
+bipartite graph well here it's not so
+
+ align:start position:0%
+bipartite graph well here it's not so
+ 
+
+ align:start position:0%
+bipartite graph well here it's not so
+easy to come up with examples but there
+
+ align:start position:0%
+easy to come up with examples but there
+ 
+
+ align:start position:0%
+easy to come up with examples but there
+are some examples and in fact Iran
+
+ align:start position:0%
+are some examples and in fact Iran
+ 
+
+ align:start position:0%
+are some examples and in fact Iran
+suggested the following construction
+
+ align:start position:0%
+suggested the following construction
+ 
+
+ align:start position:0%
+suggested the following construction
+namely you divide the set of vertices as
+
+ align:start position:0%
+namely you divide the set of vertices as
+ 
+
+ align:start position:0%
+namely you divide the set of vertices as
+before two three go for the equal sized
+
+ align:start position:0%
+before two three go for the equal sized
+ 
+
+ align:start position:0%
+before two three go for the equal sized
+parts and let me take all triples that
+
+ align:start position:0%
+parts and let me take all triples that
+ 
+
+ align:start position:0%
+parts and let me take all triples that
+look like one of the following forms
+
+ align:start position:0%
+look like one of the following forms
+ 
+
+ align:start position:0%
+look like one of the following forms
+either three vertices one in each vertex
+
+ align:start position:0%
+either three vertices one in each vertex
+ 
+
+ align:start position:0%
+either three vertices one in each vertex
+set or a triple looking like that two
+
+ align:start position:0%
+set or a triple looking like that two
+ 
+
+ align:start position:0%
+set or a triple looking like that two
+vertex in one set one in the next set
+
+ align:start position:0%
+vertex in one set one in the next set
+ 
+
+ align:start position:0%
+vertex in one set one in the next set
+we're going cyclically like that so I
+
+ align:start position:0%
+we're going cyclically like that so I
+ 
+
+ align:start position:0%
+we're going cyclically like that so I
+include all triples one of these forms
+
+ align:start position:0%
+include all triples one of these forms
+ 
+
+ align:start position:0%
+include all triples one of these forms
+and you should check that this
+
+ align:start position:0%
+and you should check that this
+ 
+
+ align:start position:0%
+and you should check that this
+construction has no cave has no
+
+ align:start position:0%
+construction has no cave has no
+ 
+
+ align:start position:0%
+construction has no cave has no
+tetrahedron if they had a tetrahedron it
+
+ align:start position:0%
+tetrahedron if they had a tetrahedron it
+ 
+
+ align:start position:0%
+tetrahedron if they had a tetrahedron it
+would have had at least two vertices in
+
+ align:start position:0%
+would have had at least two vertices in
+ 
+
+ align:start position:0%
+would have had at least two vertices in
+one part also then where the other two
+
+ align:start position:0%
+one part also then where the other two
+ 
+
+ align:start position:0%
+one part also then where the other two
+vertices can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then how many edges does it have the
+
+ align:start position:0%
+so then how many edges does it have the
+ 
+
+ align:start position:0%
+so then how many edges does it have the
+exact number is not so important but
+
+ align:start position:0%
+exact number is not so important but
+ 
+
+ align:start position:0%
+exact number is not so important but
+what's important is that the edge
+
+ align:start position:0%
+what's important is that the edge
+ 
+
+ align:start position:0%
+what's important is that the edge
+density of all the possible triples the
+
+ align:start position:0%
+density of all the possible triples the
+ 
+
+ align:start position:0%
+density of all the possible triples the
+fraction of edges that are containing
+
+ align:start position:0%
+fraction of edges that are containing
+ 
+
+ align:start position:0%
+fraction of edges that are containing
+this construction is 5 9 and it is
+
+ align:start position:0%
+this construction is 5 9 and it is
+ 
+
+ align:start position:0%
+this construction is 5 9 and it is
+conjectured that this is open however
+
+ align:start position:0%
+conjectured that this is open however
+ 
+
+ align:start position:0%
+conjectured that this is open however
+we're quite far from proving this number
+
+ align:start position:0%
+we're quite far from proving this number
+ 
+
+ align:start position:0%
+we're quite far from proving this number
+so the best upper bound that that is
+
+ align:start position:0%
+so the best upper bound that that is
+ 
+
+ align:start position:0%
+so the best upper bound that that is
+currently available and it's found quite
+
+ align:start position:0%
+currently available and it's found quite
+ 
+
+ align:start position:0%
+currently available and it's found quite
+recently using this fairly new method in
+
+ align:start position:0%
+recently using this fairly new method in
+ 
+
+ align:start position:0%
+recently using this fairly new method in
+graph theory called flag algebras
+
+ align:start position:0%
+graph theory called flag algebras
+ 
+
+ align:start position:0%
+graph theory called flag algebras
+essentially a computerised way to try to
+
+ align:start position:0%
+essentially a computerised way to try to
+ 
+
+ align:start position:0%
+essentially a computerised way to try to
+prove such inequalities and the best
+
+ align:start position:0%
+prove such inequalities and the best
+ 
+
+ align:start position:0%
+prove such inequalities and the best
+upper bound is something like 0.56 2 and
+
+ align:start position:0%
+upper bound is something like 0.56 2 and
+ 
+
+ align:start position:0%
+upper bound is something like 0.56 2 and
+it's a major open problem to either
+
+ align:start position:0%
+it's a major open problem to either
+ 
+
+ align:start position:0%
+it's a major open problem to either
+prove or disprove that this construction
+
+ align:start position:0%
+prove or disprove that this construction
+ 
+
+ align:start position:0%
+prove or disprove that this construction
+here is the optimal one so you see even
+
+ align:start position:0%
+here is the optimal one so you see even
+ 
+
+ align:start position:0%
+here is the optimal one so you see even
+though I present there's so many proofs
+
+ align:start position:0%
+though I present there's so many proofs
+ 
+
+ align:start position:0%
+though I present there's so many proofs
+of mental state materials during my at
+
+ align:start position:0%
+of mental state materials during my at
+ 
+
+ align:start position:0%
+of mental state materials during my at
+this point hopefully they should all be
+
+ align:start position:0%
+this point hopefully they should all be
+ 
+
+ align:start position:0%
+this point hopefully they should all be
+you know seem quite simple in retrospect
+
+ align:start position:0%
+you know seem quite simple in retrospect
+ 
+
+ align:start position:0%
+you know seem quite simple in retrospect
+it's deceptive its deceptive and even if
+
+ align:start position:0%
+it's deceptive its deceptive and even if
+ 
+
+ align:start position:0%
+it's deceptive its deceptive and even if
+I change and tweak the problem just a
+
+ align:start position:0%
+I change and tweak the problem just a
+ 
+
+ align:start position:0%
+I change and tweak the problem just a
+little bit going to three uniform hyper
+
+ align:start position:0%
+little bit going to three uniform hyper
+ 
+
+ align:start position:0%
+little bit going to three uniform hyper
+graphs instead of graphs we really have
+
+ align:start position:0%
+graphs instead of graphs we really have
+ 
+
+ align:start position:0%
+graphs instead of graphs we really have
+no idea what's going on it's question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so great the question is why do I
+
+ align:start position:0%
+okay so great the question is why do I
+ 
+
+ align:start position:0%
+okay so great the question is why do I
+say it's a pretty big gap so we know
+
+ align:start position:0%
+say it's a pretty big gap so we know
+ 
+
+ align:start position:0%
+say it's a pretty big gap so we know
+that there has to be some proportion of
+
+ align:start position:0%
+that there has to be some proportion of
+ 
+
+ align:start position:0%
+that there has to be some proportion of
+the total number of triples so well you
+
+ align:start position:0%
+the total number of triples so well you
+ 
+
+ align:start position:0%
+the total number of triples so well you
+have two numbers and out there they
+
+ align:start position:0%
+have two numbers and out there they
+ 
+
+ align:start position:0%
+have two numbers and out there they
+think I mean to me they seem pretty far
+
+ align:start position:0%
+think I mean to me they seem pretty far
+ 
+
+ align:start position:0%
+think I mean to me they seem pretty far
+apart it's not it's not some lower water
+
+ align:start position:0%
+apart it's not it's not some lower water
+ 
+
+ align:start position:0%
+apart it's not it's not some lower water
+gap so this is a first-order gap any
+
+ align:start position:0%
+gap so this is a first-order gap any
+ 
+
+ align:start position:0%
+gap so this is a first-order gap any
+more questions but it's true that later
+
+ align:start position:0%
+more questions but it's true that later
+ 
+
+ align:start position:0%
+more questions but it's true that later
+in the course we'll see gaps that are
+
+ align:start position:0%
+in the course we'll see gaps that are
+ 
+
+ align:start position:0%
+in the course we'll see gaps that are
+much bigger know we'll see gaps where it
+
+ align:start position:0%
+much bigger know we'll see gaps where it
+ 
+
+ align:start position:0%
+much bigger know we'll see gaps where it
+is like a polynomial on one side and a
+
+ align:start position:0%
+is like a polynomial on one side and a
+ 
+
+ align:start position:0%
+is like a polynomial on one side and a
+power of Exponential's on the other side
+
+ align:start position:0%
+power of Exponential's on the other side
+ 
+
+ align:start position:0%
+power of Exponential's on the other side
+and there I agree that's much worse so
+
+ align:start position:0%
+and there I agree that's much worse so
+ 
+
+ align:start position:0%
+and there I agree that's much worse so
+the gap is much bigger here it's just
+
+ align:start position:0%
+the gap is much bigger here it's just
+ 
+
+ align:start position:0%
+the gap is much bigger here it's just
+two numbers but you know in the worst
+
+ align:start position:0%
+two numbers but you know in the worst
+ 
+
+ align:start position:0%
+two numbers but you know in the worst
+case that can be two numbers anything
+
+ align:start position:0%
+case that can be two numbers anything
+ 
+
+ align:start position:0%
+case that can be two numbers anything
+any more questions
+
+ align:start position:0%
+any more questions
+ 
+
+ align:start position:0%
+any more questions
+okay so throughout this course I'll try
+
+ align:start position:0%
+okay so throughout this course I'll try
+ 
+
+ align:start position:0%
+okay so throughout this course I'll try
+to bring out some open problems and
+
+ align:start position:0%
+to bring out some open problems and
+ 
+
+ align:start position:0%
+to bring out some open problems and
+there are they are lost so I'll tell you
+
+ align:start position:0%
+there are they are lost so I'll tell you
+ 
+
+ align:start position:0%
+there are they are lost so I'll tell you
+what we do understand but most things we
+
+ align:start position:0%
+what we do understand but most things we
+ 
+
+ align:start position:0%
+what we do understand but most things we
+do not understand and hopefully you know
+
+ align:start position:0%
+do not understand and hopefully you know
+ 
+
+ align:start position:0%
+do not understand and hopefully you know
+some of you all go and try to understand
+
+ align:start position:0%
+some of you all go and try to understand
+ 
+
+ align:start position:0%
+some of you all go and try to understand
+them better so the next time I teach the
+
+ align:start position:0%
+them better so the next time I teach the
+ 
+
+ align:start position:0%
+them better so the next time I teach the
+course I can have something new to
+
+ align:start position:0%
+course I can have something new to
+ 
+
+ align:start position:0%
+course I can have something new to
+present okay so then we've so now that
+
+ align:start position:0%
+present okay so then we've so now that
+ 
+
+ align:start position:0%
+present okay so then we've so now that
+we've addressed the question of what's
+
+ align:start position:0%
+we've addressed the question of what's
+ 
+
+ align:start position:0%
+we've addressed the question of what's
+the maximum number of edges if you
+
+ align:start position:0%
+the maximum number of edges if you
+ 
+
+ align:start position:0%
+the maximum number of edges if you
+forbid a triangle or a clique the next
+
+ align:start position:0%
+forbid a triangle or a clique the next
+ 
+
+ align:start position:0%
+forbid a triangle or a clique the next
+natural thing to ask is what about if
+
+ align:start position:0%
+natural thing to ask is what about if
+ 
+
+ align:start position:0%
+natural thing to ask is what about if
+you forbid a general H so give me a
+
+ align:start position:0%
+you forbid a general H so give me a
+ 
+
+ align:start position:0%
+you forbid a general H so give me a
+graph H and what's the maximum number of
+
+ align:start position:0%
+graph H and what's the maximum number of
+ 
+
+ align:start position:0%
+graph H and what's the maximum number of
+edges if you're forbidden to do some
+
+ align:start position:0%
+edges if you're forbidden to do some
+ 
+
+ align:start position:0%
+edges if you're forbidden to do some
+notation so the extreme what the note by
+
+ align:start position:0%
+notation so the extreme what the note by
+ 
+
+ align:start position:0%
+notation so the extreme what the note by
+e^x and this is also called the Courant
+
+ align:start position:0%
+e^x and this is also called the Courant
+ 
+
+ align:start position:0%
+e^x and this is also called the Courant
+number sometimes because Curran serum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hope you call it the extremal number or
+
+ align:start position:0%
+hope you call it the extremal number or
+ 
+
+ align:start position:0%
+hope you call it the extremal number or
+frequently so this number here is
+
+ align:start position:0%
+frequently so this number here is
+ 
+
+ align:start position:0%
+frequently so this number here is
+defined to be the maximum number of
+
+ align:start position:0%
+defined to be the maximum number of
+ 
+
+ align:start position:0%
+defined to be the maximum number of
+edges in an vertex graph containing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to just clarify a piece of
+
+ align:start position:0%
+I want to just clarify a piece of
+ 
+
+ align:start position:0%
+I want to just clarify a piece of
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+so when I say a sub graph so what do I
+
+ align:start position:0%
+so when I say a sub graph so what do I
+ 
+
+ align:start position:0%
+so when I say a sub graph so what do I
+mean so there are several notions of
+
+ align:start position:0%
+mean so there are several notions of
+ 
+
+ align:start position:0%
+mean so there are several notions of
+different kinds of sub graphs and the
+
+ align:start position:0%
+different kinds of sub graphs and the
+ 
+
+ align:start position:0%
+different kinds of sub graphs and the
+couple that come up
+
+ align:start position:0%
+couple that come up
+ 
+
+ align:start position:0%
+couple that come up
+somewhat frequently one is sub graph and
+
+ align:start position:0%
+somewhat frequently one is sub graph and
+ 
+
+ align:start position:0%
+somewhat frequently one is sub graph and
+then there's something called induced
+
+ align:start position:0%
+then there's something called induced
+ 
+
+ align:start position:0%
+then there's something called induced
+sub graph so probably easiest if I just
+
+ align:start position:0%
+sub graph so probably easiest if I just
+ 
+
+ align:start position:0%
+sub graph so probably easiest if I just
+show you an example suppose my H is the
+
+ align:start position:0%
+show you an example suppose my H is the
+ 
+
+ align:start position:0%
+show you an example suppose my H is the
+fourth cycle so an example of H being a
+
+ align:start position:0%
+fourth cycle so an example of H being a
+ 
+
+ align:start position:0%
+fourth cycle so an example of H being a
+sub graph is suppose I have this graph
+
+ align:start position:0%
+sub graph is suppose I have this graph
+ 
+
+ align:start position:0%
+sub graph is suppose I have this graph
+here so H is a sub graph of this graph
+
+ align:start position:0%
+here so H is a sub graph of this graph
+ 
+
+ align:start position:0%
+here so H is a sub graph of this graph
+here in many different ways but in
+
+ align:start position:0%
+here in many different ways but in
+ 
+
+ align:start position:0%
+here in many different ways but in
+particular like that but you see there
+
+ align:start position:0%
+particular like that but you see there
+ 
+
+ align:start position:0%
+particular like that but you see there
+are some more edges that are among the
+
+ align:start position:0%
+are some more edges that are among the
+ 
+
+ align:start position:0%
+are some more edges that are among the
+vertices but that's okay so sub graph
+
+ align:start position:0%
+vertices but that's okay so sub graph
+ 
+
+ align:start position:0%
+vertices but that's okay so sub graph
+only requires you to have a subset of
+
+ align:start position:0%
+only requires you to have a subset of
+ 
+
+ align:start position:0%
+only requires you to have a subset of
+vertices and a subset of edges whereas
+
+ align:start position:0%
+vertices and a subset of edges whereas
+ 
+
+ align:start position:0%
+vertices and a subset of edges whereas
+induced subgraphs this is not an example
+
+ align:start position:0%
+induced subgraphs this is not an example
+ 
+
+ align:start position:0%
+induced subgraphs this is not an example
+of induced sub graph so an induced sub
+
+ align:start position:0%
+of induced sub graph so an induced sub
+ 
+
+ align:start position:0%
+of induced sub graph so an induced sub
+graph means that you take the set of
+
+ align:start position:0%
+graph means that you take the set of
+ 
+
+ align:start position:0%
+graph means that you take the set of
+vertices and you look at all the edges
+
+ align:start position:0%
+vertices and you look at all the edges
+ 
+
+ align:start position:0%
+vertices and you look at all the edges
+in the big graph
+
+ align:start position:0%
+in the big graph
+ 
+
+ align:start position:0%
+in the big graph
+among your set of vertices so that's an
+
+ align:start position:0%
+among your set of vertices so that's an
+ 
+
+ align:start position:0%
+among your set of vertices so that's an
+induced sub graph so here the fourth
+
+ align:start position:0%
+induced sub graph so here the fourth
+ 
+
+ align:start position:0%
+induced sub graph so here the fourth
+cycle is an induced sub graph but not
+
+ align:start position:0%
+cycle is an induced sub graph but not
+ 
+
+ align:start position:0%
+cycle is an induced sub graph but not
+induced sub graph over here so I just
+
+ align:start position:0%
+induced sub graph over here so I just
+ 
+
+ align:start position:0%
+induced sub graph over here so I just
+want to make that distinction clear and
+
+ align:start position:0%
+want to make that distinction clear and
+ 
+
+ align:start position:0%
+want to make that distinction clear and
+for now in this chapter we'll only talk
+
+ align:start position:0%
+for now in this chapter we'll only talk
+ 
+
+ align:start position:0%
+for now in this chapter we'll only talk
+about sub graphs not induced necessarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's recap what happened
+
+ align:start position:0%
+all right so let's recap what happened
+ 
+
+ align:start position:0%
+all right so let's recap what happened
+for Terron still so Turin's theorem told
+
+ align:start position:0%
+for Terron still so Turin's theorem told
+ 
+
+ align:start position:0%
+for Terron still so Turin's theorem told
+us that the extremal number of these
+
+ align:start position:0%
+us that the extremal number of these
+ 
+
+ align:start position:0%
+us that the extremal number of these
+cliques well we know very precisely to
+
+ align:start position:0%
+cliques well we know very precisely to
+ 
+
+ align:start position:0%
+cliques well we know very precisely to
+be the number of edges in the tauren
+
+ align:start position:0%
+be the number of edges in the tauren
+ 
+
+ align:start position:0%
+be the number of edges in the tauren
+graph and in particular we saw from the
+
+ align:start position:0%
+graph and in particular we saw from the
+ 
+
+ align:start position:0%
+graph and in particular we saw from the
+last proof and also similarly if you
+
+ align:start position:0%
+last proof and also similarly if you
+ 
+
+ align:start position:0%
+last proof and also similarly if you
+just do a calculation that it is almost
+
+ align:start position:0%
+just do a calculation that it is almost
+ 
+
+ align:start position:0%
+just do a calculation that it is almost
+this quantity over here and it's
+
+ align:start position:0%
+this quantity over here and it's
+ 
+
+ align:start position:0%
+this quantity over here and it's
+basically that content so you can the
+
+ align:start position:0%
+basically that content so you can the
+ 
+
+ align:start position:0%
+basically that content so you can the
+number of edges in the strong graph is
+
+ align:start position:0%
+number of edges in the strong graph is
+ 
+
+ align:start position:0%
+number of edges in the strong graph is
+asymptotically that quantity up to and
+
+ align:start position:0%
+asymptotically that quantity up to and
+ 
+
+ align:start position:0%
+asymptotically that quantity up to and
+the basic question is what about general
+
+ align:start position:0%
+the basic question is what about general
+ 
+
+ align:start position:0%
+the basic question is what about general
+itch so if I give you some arbitrary
+
+ align:start position:0%
+itch so if I give you some arbitrary
+ 
+
+ align:start position:0%
+itch so if I give you some arbitrary
+graph H what can you tell me about the
+
+ align:start position:0%
+graph H what can you tell me about the
+ 
+
+ align:start position:0%
+graph H what can you tell me about the
+maximum number of edges in the graph
+
+ align:start position:0%
+maximum number of edges in the graph
+ 
+
+ align:start position:0%
+maximum number of edges in the graph
+forbidding this H as a sub graph and it
+
+ align:start position:0%
+forbidding this H as a sub graph and it
+ 
+
+ align:start position:0%
+forbidding this H as a sub graph and it
+turns out for most Atrus we have a
+
+ align:start position:0%
+turns out for most Atrus we have a
+ 
+
+ align:start position:0%
+turns out for most Atrus we have a
+pretty good understanding and perhaps
+
+ align:start position:0%
+pretty good understanding and perhaps
+ 
+
+ align:start position:0%
+pretty good understanding and perhaps
+quite surprisingly because you can
+
+ align:start position:0%
+quite surprisingly because you can
+ 
+
+ align:start position:0%
+quite surprisingly because you can
+imagine this problem looks like it might
+
+ align:start position:0%
+imagine this problem looks like it might
+ 
+
+ align:start position:0%
+imagine this problem looks like it might
+get quite complicated or all the proof
+
+ align:start position:0%
+get quite complicated or all the proof
+ 
+
+ align:start position:0%
+get quite complicated or all the proof
+that we've done are very specific to
+
+ align:start position:0%
+that we've done are very specific to
+ 
+
+ align:start position:0%
+that we've done are very specific to
+cliques but it turns out that we already
+
+ align:start position:0%
+cliques but it turns out that we already
+ 
+
+ align:start position:0%
+cliques but it turns out that we already
+understand a lot and the critical
+
+ align:start position:0%
+understand a lot and the critical
+ 
+
+ align:start position:0%
+understand a lot and the critical
+parameter that governs how this quantity
+
+ align:start position:0%
+parameter that governs how this quantity
+ 
+
+ align:start position:0%
+parameter that governs how this quantity
+behaves is the chromatic number of H
+
+ align:start position:0%
+behaves is the chromatic number of H
+ 
+
+ align:start position:0%
+behaves is the chromatic number of H
+so if you tell me the chromatic number
+
+ align:start position:0%
+so if you tell me the chromatic number
+ 
+
+ align:start position:0%
+so if you tell me the chromatic number
+of H I can already tell you quite a lot
+
+ align:start position:0%
+of H I can already tell you quite a lot
+ 
+
+ align:start position:0%
+of H I can already tell you quite a lot
+so just to remind you the chromatic
+
+ align:start position:0%
+so just to remind you the chromatic
+ 
+
+ align:start position:0%
+so just to remind you the chromatic
+number of a graph is the minimum number
+
+ align:start position:0%
+number of a graph is the minimum number
+ 
+
+ align:start position:0%
+number of a graph is the minimum number
+of colors you need to properly cover the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H I H is the minimum number of colors
+
+ align:start position:0%
+H I H is the minimum number of colors
+ 
+
+ align:start position:0%
+H I H is the minimum number of colors
+needed to color the vertices of H so
+
+ align:start position:0%
+needed to color the vertices of H so
+ 
+
+ align:start position:0%
+needed to color the vertices of H so
+that no two adjacent vertices have the
+
+ align:start position:0%
+that no two adjacent vertices have the
+ 
+
+ align:start position:0%
+that no two adjacent vertices have the
+same color so for instance if I give you
+
+ align:start position:0%
+same color so for instance if I give you
+ 
+
+ align:start position:0%
+same color so for instance if I give you
+a clique R plus 1 vertices so all the
+
+ align:start position:0%
+a clique R plus 1 vertices so all the
+ 
+
+ align:start position:0%
+a clique R plus 1 vertices so all the
+vertices must receive different colors
+
+ align:start position:0%
+vertices must receive different colors
+ 
+
+ align:start position:0%
+vertices must receive different colors
+because every pair of vertices adjacent
+
+ align:start position:0%
+because every pair of vertices adjacent
+ 
+
+ align:start position:0%
+because every pair of vertices adjacent
+so the chromatic number is R plus 1 the
+
+ align:start position:0%
+so the chromatic number is R plus 1 the
+ 
+
+ align:start position:0%
+so the chromatic number is R plus 1 the
+chromatic number of the tauren graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's our chromatic number of the Chiron
+
+ align:start position:0%
+it's our chromatic number of the Chiron
+ 
+
+ align:start position:0%
+it's our chromatic number of the Chiron
+graphics are I can color each part in
+
+ align:start position:0%
+graphics are I can color each part in
+ 
+
+ align:start position:0%
+graphics are I can color each part in
+this complete bipartite graph using a
+
+ align:start position:0%
+this complete bipartite graph using a
+ 
+
+ align:start position:0%
+this complete bipartite graph using a
+different color and that's the best I
+
+ align:start position:0%
+different color and that's the best I
+ 
+
+ align:start position:0%
+different color and that's the best I
+can do now if I have one graph being a
+
+ align:start position:0%
+can do now if I have one graph being a
+ 
+
+ align:start position:0%
+can do now if I have one graph being a
+sub graph of another graph what can you
+
+ align:start position:0%
+sub graph of another graph what can you
+ 
+
+ align:start position:0%
+sub graph of another graph what can you
+tell me about the relationships between
+
+ align:start position:0%
+tell me about the relationships between
+ 
+
+ align:start position:0%
+tell me about the relationships between
+their chromatic numbers if H there's a
+
+ align:start position:0%
+their chromatic numbers if H there's a
+ 
+
+ align:start position:0%
+their chromatic numbers if H there's a
+sub graph of G so what can you tell me
+
+ align:start position:0%
+sub graph of G so what can you tell me
+ 
+
+ align:start position:0%
+sub graph of G so what can you tell me
+about relationship between their
+
+ align:start position:0%
+about relationship between their
+ 
+
+ align:start position:0%
+about relationship between their
+chromatic numbers most high FG and why
+
+ align:start position:0%
+chromatic numbers most high FG and why
+ 
+
+ align:start position:0%
+chromatic numbers most high FG and why
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever coloring you do for G
+
+ align:start position:0%
+whatever coloring you do for G
+ 
+
+ align:start position:0%
+whatever coloring you do for G
+use the same coloring and that's a
+
+ align:start position:0%
+use the same coloring and that's a
+ 
+
+ align:start position:0%
+use the same coloring and that's a
+proper coloring for HS well so the
+
+ align:start position:0%
+proper coloring for HS well so the
+ 
+
+ align:start position:0%
+proper coloring for HS well so the
+chromatic number of H might be smaller
+
+ align:start position:0%
+chromatic number of H might be smaller
+ 
+
+ align:start position:0%
+chromatic number of H might be smaller
+but certainly cannot be bigger than that
+
+ align:start position:0%
+but certainly cannot be bigger than that
+ 
+
+ align:start position:0%
+but certainly cannot be bigger than that
+of G so in particular if you have a
+
+ align:start position:0%
+of G so in particular if you have a
+ 
+
+ align:start position:0%
+of G so in particular if you have a
+graph H with chromatic number or plus 1
+
+ align:start position:0%
+graph H with chromatic number or plus 1
+ 
+
+ align:start position:0%
+graph H with chromatic number or plus 1
+then this Terron graph is always H 3 H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+requires 4 colors it cannot be embedded
+
+ align:start position:0%
+requires 4 colors it cannot be embedded
+ 
+
+ align:start position:0%
+requires 4 colors it cannot be embedded
+into the complete multi-part a graph on
+
+ align:start position:0%
+into the complete multi-part a graph on
+ 
+
+ align:start position:0%
+into the complete multi-part a graph on
+three parts so the turn graph is also an
+
+ align:start position:0%
+three parts so the turn graph is also an
+ 
+
+ align:start position:0%
+three parts so the turn graph is also an
+example of an H free graph with lots of
+
+ align:start position:0%
+example of an H free graph with lots of
+ 
+
+ align:start position:0%
+example of an H free graph with lots of
+edges and this tells us that the
+
+ align:start position:0%
+edges and this tells us that the
+ 
+
+ align:start position:0%
+edges and this tells us that the
+extremal number of H is at least that of
+
+ align:start position:0%
+extremal number of H is at least that of
+ 
+
+ align:start position:0%
+extremal number of H is at least that of
+the store number fine
+
+ align:start position:0%
+the store number fine
+ 
+
+ align:start position:0%
+the store number fine
+as one as the chromatic number minus one
+
+ align:start position:0%
+as one as the chromatic number minus one
+ 
+
+ align:start position:0%
+as one as the chromatic number minus one
+okay so that's some lower bound
+
+ align:start position:0%
+okay so that's some lower bound
+ 
+
+ align:start position:0%
+okay so that's some lower bound
+construction we saw earlier no we know
+
+ align:start position:0%
+construction we saw earlier no we know
+ 
+
+ align:start position:0%
+construction we saw earlier no we know
+what the asymptotic is it's like for the
+
+ align:start position:0%
+what the asymptotic is it's like for the
+ 
+
+ align:start position:0%
+what the asymptotic is it's like for the
+number of edges n goes to infinity and
+
+ align:start position:0%
+number of edges n goes to infinity and
+ 
+
+ align:start position:0%
+number of edges n goes to infinity and
+now the question is is this the right
+
+ align:start position:0%
+now the question is is this the right
+ 
+
+ align:start position:0%
+now the question is is this the right
+answer is it possible that we completely
+
+ align:start position:0%
+answer is it possible that we completely
+ 
+
+ align:start position:0%
+answer is it possible that we completely
+missed some construction that might
+
+ align:start position:0%
+missed some construction that might
+ 
+
+ align:start position:0%
+missed some construction that might
+produce a lot more edges and it turns
+
+ align:start position:0%
+produce a lot more edges and it turns
+ 
+
+ align:start position:0%
+produce a lot more edges and it turns
+out and I think this should be somewhat
+
+ align:start position:0%
+out and I think this should be somewhat
+ 
+
+ align:start position:0%
+out and I think this should be somewhat
+surprising because so far I feel like I
+
+ align:start position:0%
+surprising because so far I feel like I
+ 
+
+ align:start position:0%
+surprising because so far I feel like I
+haven't really told you anything oh
+
+ align:start position:0%
+haven't really told you anything oh
+ 
+
+ align:start position:0%
+haven't really told you anything oh
+that's surprising yet really mysterious
+
+ align:start position:0%
+that's surprising yet really mysterious
+ 
+
+ align:start position:0%
+that's surprising yet really mysterious
+from but it turns out that this is more
+
+ align:start position:0%
+from but it turns out that this is more
+ 
+
+ align:start position:0%
+from but it turns out that this is more
+or less the right answer so you cannot
+
+ align:start position:0%
+or less the right answer so you cannot
+ 
+
+ align:start position:0%
+or less the right answer so you cannot
+do much better than the tauren graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that for every graph H okay so if I fix
+
+ align:start position:0%
+that for every graph H okay so if I fix
+ 
+
+ align:start position:0%
+that for every graph H okay so if I fix
+H then the limit as n goes to infinity
+
+ align:start position:0%
+H then the limit as n goes to infinity
+ 
+
+ align:start position:0%
+H then the limit as n goes to infinity
+of the extremal number as a fraction of
+
+ align:start position:0%
+of the extremal number as a fraction of
+ 
+
+ align:start position:0%
+of the extremal number as a fraction of
+total number of pairs so here this is
+
+ align:start position:0%
+total number of pairs so here this is
+ 
+
+ align:start position:0%
+total number of pairs so here this is
+the edge density so this quantity here
+
+ align:start position:0%
+the edge density so this quantity here
+ 
+
+ align:start position:0%
+the edge density so this quantity here
+is equal to 1 minus Chi of H so 1 minus
+
+ align:start position:0%
+is equal to 1 minus Chi of H so 1 minus
+ 
+
+ align:start position:0%
+is equal to 1 minus Chi of H so 1 minus
+1 over Chi of H minus 1 so knowing the
+
+ align:start position:0%
+1 over Chi of H minus 1 so knowing the
+ 
+
+ align:start position:0%
+1 over Chi of H minus 1 so knowing the
+chromatic number in some sense
+
+ align:start position:0%
+chromatic number in some sense
+ 
+
+ align:start position:0%
+chromatic number in some sense
+completely determines how big the
+
+ align:start position:0%
+completely determines how big the
+ 
+
+ align:start position:0%
+completely determines how big the
+extremal number should be and you see
+
+ align:start position:0%
+extremal number should be and you see
+ 
+
+ align:start position:0%
+extremal number should be and you see
+that so far everything we've proved
+
+ align:start position:0%
+that so far everything we've proved
+ 
+
+ align:start position:0%
+that so far everything we've proved
+Tehran's theorem and house term agree
+
+ align:start position:0%
+Tehran's theorem and house term agree
+ 
+
+ align:start position:0%
+Tehran's theorem and house term agree
+with this formula here but if I give you
+
+ align:start position:0%
+with this formula here but if I give you
+ 
+
+ align:start position:0%
+with this formula here but if I give you
+some H may be quite complicated and
+
+ align:start position:0%
+some H may be quite complicated and
+ 
+
+ align:start position:0%
+some H may be quite complicated and
+those previous proofs don't work but
+
+ align:start position:0%
+those previous proofs don't work but
+ 
+
+ align:start position:0%
+those previous proofs don't work but
+still you know the first water has some
+
+ align:start position:0%
+still you know the first water has some
+ 
+
+ align:start position:0%
+still you know the first water has some
+tonics but there's still more to say but
+
+ align:start position:0%
+tonics but there's still more to say but
+ 
+
+ align:start position:0%
+tonics but there's still more to say but
+first let me just run through some
+
+ align:start position:0%
+first let me just run through some
+ 
+
+ align:start position:0%
+first let me just run through some
+examples for sanity check so if H is
+
+ align:start position:0%
+examples for sanity check so if H is
+ 
+
+ align:start position:0%
+examples for sanity check so if H is
+triangle H chromatic number and this
+
+ align:start position:0%
+triangle H chromatic number and this
+ 
+
+ align:start position:0%
+triangle H chromatic number and this
+limit so if H is the triangle chromatic
+
+ align:start position:0%
+limit so if H is the triangle chromatic
+ 
+
+ align:start position:0%
+limit so if H is the triangle chromatic
+number 3 is 1/2 and that's indeed the
+
+ align:start position:0%
+number 3 is 1/2 and that's indeed the
+ 
+
+ align:start position:0%
+number 3 is 1/2 and that's indeed the
+case that's what we did with mental
+
+ align:start position:0%
+case that's what we did with mental
+ 
+
+ align:start position:0%
+case that's what we did with mental
+Sturm if H is a clique of four vertices
+
+ align:start position:0%
+Sturm if H is a clique of four vertices
+ 
+
+ align:start position:0%
+Sturm if H is a clique of four vertices
+then the chromatic number is four and
+
+ align:start position:0%
+then the chromatic number is four and
+ 
+
+ align:start position:0%
+then the chromatic number is four and
+the answer is two-thirds and also that
+
+ align:start position:0%
+the answer is two-thirds and also that
+ 
+
+ align:start position:0%
+the answer is two-thirds and also that
+agrees with two runs to Greece with
+
+ align:start position:0%
+agrees with two runs to Greece with
+ 
+
+ align:start position:0%
+agrees with two runs to Greece with
+Tehran's theorem but I can give you some
+
+ align:start position:0%
+Tehran's theorem but I can give you some
+ 
+
+ align:start position:0%
+Tehran's theorem but I can give you some
+fairly complicated looking each so for
+
+ align:start position:0%
+fairly complicated looking each so for
+ 
+
+ align:start position:0%
+fairly complicated looking each so for
+example H might be the Peterson graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so every good graph theory course should
+
+ align:start position:0%
+so every good graph theory course should
+ 
+
+ align:start position:0%
+so every good graph theory course should
+feature Peterson graph at least once
+
+ align:start position:0%
+feature Peterson graph at least once
+ 
+
+ align:start position:0%
+feature Peterson graph at least once
+somewhere so that's the Peterson graph
+
+ align:start position:0%
+somewhere so that's the Peterson graph
+ 
+
+ align:start position:0%
+somewhere so that's the Peterson graph
+what's the chromatic number of the
+
+ align:start position:0%
+what's the chromatic number of the
+ 
+
+ align:start position:0%
+what's the chromatic number of the
+Peterson graph that's kind of a tricky
+
+ align:start position:0%
+Peterson graph that's kind of a tricky
+ 
+
+ align:start position:0%
+Peterson graph that's kind of a tricky
+question the last time I taught this
+
+ align:start position:0%
+question the last time I taught this
+ 
+
+ align:start position:0%
+question the last time I taught this
+course I even got the answer wrong so it
+
+ align:start position:0%
+course I even got the answer wrong so it
+ 
+
+ align:start position:0%
+course I even got the answer wrong so it
+turns out you can three color the
+
+ align:start position:0%
+turns out you can three color the
+ 
+
+ align:start position:0%
+turns out you can three color the
+Peterson graph okay so it's completely
+
+ align:start position:0%
+Peterson graph okay so it's completely
+ 
+
+ align:start position:0%
+Peterson graph okay so it's completely
+not obvious how to do this perfume oh
+
+ align:start position:0%
+not obvious how to do this perfume oh
+ 
+
+ align:start position:0%
+not obvious how to do this perfume oh
+there are only so many vertices if you
+
+ align:start position:0%
+there are only so many vertices if you
+ 
+
+ align:start position:0%
+there are only so many vertices if you
+stir it long enough you can you can see
+
+ align:start position:0%
+stir it long enough you can you can see
+ 
+
+ align:start position:0%
+stir it long enough you can you can see
+what happens but let me just show you a
+
+ align:start position:0%
+what happens but let me just show you a
+ 
+
+ align:start position:0%
+what happens but let me just show you a
+three coloring at the Peterson graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+third color okay so that's a three
+
+ align:start position:0%
+third color okay so that's a three
+ 
+
+ align:start position:0%
+third color okay so that's a three
+coloring of the Peterson graph that's
+
+ align:start position:0%
+coloring of the Peterson graph that's
+ 
+
+ align:start position:0%
+coloring of the Peterson graph that's
+chromatic number three it's not - okay
+
+ align:start position:0%
+chromatic number three it's not - okay
+ 
+
+ align:start position:0%
+chromatic number three it's not - okay
+so why is it now - it's not bipartite as
+
+ align:start position:0%
+so why is it now - it's not bipartite as
+ 
+
+ align:start position:0%
+so why is it now - it's not bipartite as
+a five cycle which cannot be two colored
+
+ align:start position:0%
+a five cycle which cannot be two colored
+ 
+
+ align:start position:0%
+a five cycle which cannot be two colored
+so then the limit is one half and here I
+
+ align:start position:0%
+so then the limit is one half and here I
+ 
+
+ align:start position:0%
+so then the limit is one half and here I
+we can apply this theorem as a durstone
+
+ align:start position:0%
+we can apply this theorem as a durstone
+ 
+
+ align:start position:0%
+we can apply this theorem as a durstone
+small image and I think it should be
+
+ align:start position:0%
+small image and I think it should be
+ 
+
+ align:start position:0%
+small image and I think it should be
+somewhat surprising because the Peterson
+
+ align:start position:0%
+somewhat surprising because the Peterson
+ 
+
+ align:start position:0%
+somewhat surprising because the Peterson
+graph looks quite complicated if you try
+
+ align:start position:0%
+graph looks quite complicated if you try
+ 
+
+ align:start position:0%
+graph looks quite complicated if you try
+to forbid this graph in some big G it
+
+ align:start position:0%
+to forbid this graph in some big G it
+ 
+
+ align:start position:0%
+to forbid this graph in some big G it
+seems like it's kind of hard to do but
+
+ align:start position:0%
+seems like it's kind of hard to do but
+ 
+
+ align:start position:0%
+seems like it's kind of hard to do but
+it turns out the chromatic number
+
+ align:start position:0%
+it turns out the chromatic number
+ 
+
+ align:start position:0%
+it turns out the chromatic number
+completely governs the behavior of the
+
+ align:start position:0%
+completely governs the behavior of the
+ 
+
+ align:start position:0%
+completely governs the behavior of the
+extremal numbers but it turns out that's
+
+ align:start position:0%
+extremal numbers but it turns out that's
+ 
+
+ align:start position:0%
+extremal numbers but it turns out that's
+not the entire story because well this
+
+ align:start position:0%
+not the entire story because well this
+ 
+
+ align:start position:0%
+not the entire story because well this
+is quite a good deal and I said it gives
+
+ align:start position:0%
+is quite a good deal and I said it gives
+ 
+
+ align:start position:0%
+is quite a good deal and I said it gives
+you the first water asymptotics actually
+
+ align:start position:0%
+you the first water asymptotics actually
+ 
+
+ align:start position:0%
+you the first water asymptotics actually
+that's a lie it doesn't always give you
+
+ align:start position:0%
+that's a lie it doesn't always give you
+ 
+
+ align:start position:0%
+that's a lie it doesn't always give you
+the first water asymptotics and when is
+
+ align:start position:0%
+the first water asymptotics and when is
+ 
+
+ align:start position:0%
+the first water asymptotics and when is
+either strong shamone mesh not effective
+
+ align:start position:0%
+either strong shamone mesh not effective
+ 
+
+ align:start position:0%
+either strong shamone mesh not effective
+or rather it's not the complete it's not
+
+ align:start position:0%
+or rather it's not the complete it's not
+ 
+
+ align:start position:0%
+or rather it's not the complete it's not
+the final answer well you can say what
+
+ align:start position:0%
+the final answer well you can say what
+ 
+
+ align:start position:0%
+the final answer well you can say what
+about this little okay so that so we're
+
+ align:start position:0%
+about this little okay so that so we're
+ 
+
+ align:start position:0%
+about this little okay so that so we're
+still trying
+
+ align:start position:0%
+still trying
+ 
+
+ align:start position:0%
+still trying
+understand you know there is a limit and
+
+ align:start position:0%
+understand you know there is a limit and
+ 
+
+ align:start position:0%
+understand you know there is a limit and
+you can understand the one is the how
+
+ align:start position:0%
+you can understand the one is the how
+ 
+
+ align:start position:0%
+you can understand the one is the how
+quickly there's a converge to this
+
+ align:start position:0%
+quickly there's a converge to this
+ 
+
+ align:start position:0%
+quickly there's a converge to this
+number here okay so that's certainly a
+
+ align:start position:0%
+number here okay so that's certainly a
+ 
+
+ align:start position:0%
+number here okay so that's certainly a
+valid question but more importantly
+
+ align:start position:0%
+valid question but more importantly
+ 
+
+ align:start position:0%
+valid question but more importantly
+though if your graph is bipartite and
+
+ align:start position:0%
+though if your graph is bipartite and
+ 
+
+ align:start position:0%
+though if your graph is bipartite and
+all this theorem tells you is that the
+
+ align:start position:0%
+all this theorem tells you is that the
+ 
+
+ align:start position:0%
+all this theorem tells you is that the
+limit is equal to zero which somehow is
+
+ align:start position:0%
+limit is equal to zero which somehow is
+ 
+
+ align:start position:0%
+limit is equal to zero which somehow is
+not the most satisfying answer you want
+
+ align:start position:0%
+not the most satisfying answer you want
+ 
+
+ align:start position:0%
+not the most satisfying answer you want
+to know the first word there asymptotics
+
+ align:start position:0%
+to know the first word there asymptotics
+ 
+
+ align:start position:0%
+to know the first word there asymptotics
+I mean this still tells you something
+
+ align:start position:0%
+I mean this still tells you something
+ 
+
+ align:start position:0%
+I mean this still tells you something
+shamone master tells you that the
+
+ align:start position:0%
+shamone master tells you that the
+ 
+
+ align:start position:0%
+shamone master tells you that the
+extremal number is N squared of course
+
+ align:start position:0%
+extremal number is N squared of course
+ 
+
+ align:start position:0%
+extremal number is N squared of course
+you are a curious mathematician and you
+
+ align:start position:0%
+you are a curious mathematician and you
+ 
+
+ align:start position:0%
+you are a curious mathematician and you
+want to know really what is the
+
+ align:start position:0%
+want to know really what is the
+ 
+
+ align:start position:0%
+want to know really what is the
+asymptotics is it like n to the
+
+ align:start position:0%
+asymptotics is it like n to the
+ 
+
+ align:start position:0%
+asymptotics is it like n to the
+three-halves
+
+ align:start position:0%
+three-halves
+ 
+
+ align:start position:0%
+three-halves
+it's like n to the 4/3 you know what it
+
+ align:start position:0%
+it's like n to the 4/3 you know what it
+ 
+
+ align:start position:0%
+it's like n to the 4/3 you know what it
+this is not satisfying and it turns out
+
+ align:start position:0%
+this is not satisfying and it turns out
+ 
+
+ align:start position:0%
+this is not satisfying and it turns out
+from most bipartite graphs H it is a
+
+ align:start position:0%
+from most bipartite graphs H it is a
+ 
+
+ align:start position:0%
+from most bipartite graphs H it is a
+very difficult problem that we still do
+
+ align:start position:0%
+very difficult problem that we still do
+ 
+
+ align:start position:0%
+very difficult problem that we still do
+not know the answer to even what is the
+
+ align:start position:0%
+not know the answer to even what is the
+ 
+
+ align:start position:0%
+not know the answer to even what is the
+order of the asymptotics
+
+ align:start position:0%
+order of the asymptotics
+ 
+
+ align:start position:0%
+order of the asymptotics
+so the next few lectures what I want to
+
+ align:start position:0%
+so the next few lectures what I want to
+ 
+
+ align:start position:0%
+so the next few lectures what I want to
+do is to show you some techniques that
+
+ align:start position:0%
+do is to show you some techniques that
+ 
+
+ align:start position:0%
+do is to show you some techniques that
+will allow you to prove some upper
+
+ align:start position:0%
+will allow you to prove some upper
+ 
+
+ align:start position:0%
+will allow you to prove some upper
+bounds for this extremal number in the
+
+ align:start position:0%
+bounds for this extremal number in the
+ 
+
+ align:start position:0%
+bounds for this extremal number in the
+case when H is bipartite that shows you
+
+ align:start position:0%
+case when H is bipartite that shows you
+ 
+
+ align:start position:0%
+case when H is bipartite that shows you
+that the exponent can be less than two
+
+ align:start position:0%
+that the exponent can be less than two
+ 
+
+ align:start position:0%
+that the exponent can be less than two
+and I will also show you some
+
+ align:start position:0%
+and I will also show you some
+ 
+
+ align:start position:0%
+and I will also show you some
+constructions that sometimes but in the
+
+ align:start position:0%
+constructions that sometimes but in the
+ 
+
+ align:start position:0%
+constructions that sometimes but in the
+very few cases matches the upper bound
+
+ align:start position:0%
+very few cases matches the upper bound
+ 
+
+ align:start position:0%
+very few cases matches the upper bound
+so there are very few examples of graphs
+
+ align:start position:0%
+so there are very few examples of graphs
+ 
+
+ align:start position:0%
+so there are very few examples of graphs
+H from which we know the first order
+
+ align:start position:0%
+H from which we know the first order
+ 
+
+ align:start position:0%
+H from which we know the first order
+asymptotics and for most graph H it is
+
+ align:start position:0%
+asymptotics and for most graph H it is
+ 
+
+ align:start position:0%
+asymptotics and for most graph H it is
+their major open problems in common
+
+ align:start position:0%
+their major open problems in common
+ 
+
+ align:start position:0%
+their major open problems in common
+network and there's some really old ones
+
+ align:start position:0%
+network and there's some really old ones
+ 
+
+ align:start position:0%
+network and there's some really old ones
+which any solution might be quite
+
+ align:start position:0%
+which any solution might be quite
+ 
+
+ align:start position:0%
+which any solution might be quite
+exciting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will not show you a proof of
+
+ align:start position:0%
+I will not show you a proof of
+ 
+
+ align:start position:0%
+I will not show you a proof of
+Adderstone small image now we will see
+
+ align:start position:0%
+Adderstone small image now we will see
+ 
+
+ align:start position:0%
+Adderstone small image now we will see
+that later in the term once we've
+
+ align:start position:0%
+that later in the term once we've
+ 
+
+ align:start position:0%
+that later in the term once we've
+developed some more machinery although
+
+ align:start position:0%
+developed some more machinery although
+ 
+
+ align:start position:0%
+developed some more machinery although
+so later on in the term we'll see a
+
+ align:start position:0%
+so later on in the term we'll see a
+ 
+
+ align:start position:0%
+so later on in the term we'll see a
+proof using the so-called similarities
+
+ align:start position:0%
+proof using the so-called similarities
+ 
+
+ align:start position:0%
+proof using the so-called similarities
+regularity lemma which I've mentioned a
+
+ align:start position:0%
+regularity lemma which I've mentioned a
+ 
+
+ align:start position:0%
+regularity lemma which I've mentioned a
+few times in the first lecture although
+
+ align:start position:0%
+few times in the first lecture although
+ 
+
+ align:start position:0%
+few times in the first lecture although
+you don't actually need such heavy
+
+ align:start position:0%
+you don't actually need such heavy
+ 
+
+ align:start position:0%
+you don't actually need such heavy
+machinery so there is so the original
+
+ align:start position:0%
+machinery so there is so the original
+ 
+
+ align:start position:0%
+machinery so there is so the original
+proofs of errors in snow and stone first
+
+ align:start position:0%
+proofs of errors in snow and stone first
+ 
+
+ align:start position:0%
+proofs of errors in snow and stone first
+proved this result for H being a
+
+ align:start position:0%
+proved this result for H being a
+ 
+
+ align:start position:0%
+proved this result for H being a
+complete multi-part a graph and smaller
+
+ align:start position:0%
+complete multi-part a graph and smaller
+ 
+
+ align:start position:0%
+complete multi-part a graph and smaller
+which observed that knowing H for a
+
+ align:start position:0%
+which observed that knowing H for a
+ 
+
+ align:start position:0%
+which observed that knowing H for a
+complete multi-part I graph actually
+
+ align:start position:0%
+complete multi-part I graph actually
+ 
+
+ align:start position:0%
+complete multi-part I graph actually
+implies this result in general so you
+
+ align:start position:0%
+implies this result in general so you
+ 
+
+ align:start position:0%
+implies this result in general so you
+will not find a paper with all three of
+
+ align:start position:0%
+will not find a paper with all three of
+ 
+
+ align:start position:0%
+will not find a paper with all three of
+them in being authors so later on in the
+
+ align:start position:0%
+them in being authors so later on in the
+ 
+
+ align:start position:0%
+them in being authors so later on in the
+course once we've developed the
+
+ align:start position:0%
+course once we've developed the
+ 
+
+ align:start position:0%
+course once we've developed the
+machinery of graph regularity Lamas I
+
+ align:start position:0%
+machinery of graph regularity Lamas I
+ 
+
+ align:start position:0%
+machinery of graph regularity Lamas I
+will show you how you can deduce order
+
+ align:start position:0%
+will show you how you can deduce order
+ 
+
+ align:start position:0%
+will show you how you can deduce order
+stone simonova CH from Tehran's theorem
+
+ align:start position:0%
+stone simonova CH from Tehran's theorem
+ 
+
+ align:start position:0%
+stone simonova CH from Tehran's theorem
+somehow you use Tehran's theorem and
+
+ align:start position:0%
+somehow you use Tehran's theorem and
+ 
+
+ align:start position:0%
+somehow you use Tehran's theorem and
+bootstrap it to address stone Shimano
+
+ align:start position:0%
+bootstrap it to address stone Shimano
+ 
+
+ align:start position:0%
+bootstrap it to address stone Shimano
+venture so that should seem somewhat
+
+ align:start position:0%
+venture so that should seem somewhat
+ 
+
+ align:start position:0%
+venture so that should seem somewhat
+magical right so on one hand you have
+
+ align:start position:0%
+magical right so on one hand you have
+ 
+
+ align:start position:0%
+magical right so on one hand you have
+clicks and the other hand you have
+
+ align:start position:0%
+clicks and the other hand you have
+ 
+
+ align:start position:0%
+clicks and the other hand you have
+things that somehow don't have clicks
+
+ align:start position:0%
+things that somehow don't have clicks
+ 
+
+ align:start position:0%
+things that somehow don't have clicks
+they don't really look like clicks but
+
+ align:start position:0%
+they don't really look like clicks but
+ 
+
+ align:start position:0%
+they don't really look like clicks but
+you can still bootstrap one to the other
+
+ align:start position:0%
+you can still bootstrap one to the other
+ 
+
+ align:start position:0%
+you can still bootstrap one to the other
+and so after we develop some machinery
+
+ align:start position:0%
+and so after we develop some machinery
+ 
+
+ align:start position:0%
+and so after we develop some machinery
+won't do that but the earths are
+
+ align:start position:0%
+won't do that but the earths are
+ 
+
+ align:start position:0%
+won't do that but the earths are
+combinatorial proof which doesn't use
+
+ align:start position:0%
+combinatorial proof which doesn't use
+ 
+
+ align:start position:0%
+combinatorial proof which doesn't use
+any of this heavy machinery so you can I
+
+ align:start position:0%
+any of this heavy machinery so you can I
+ 
+
+ align:start position:0%
+any of this heavy machinery so you can I
+won't discuss it in this lecture but you
+
+ align:start position:0%
+won't discuss it in this lecture but you
+ 
+
+ align:start position:0%
+won't discuss it in this lecture but you
+can look it up and it's it's quite nice
+
+ align:start position:0%
+can look it up and it's it's quite nice
+ 
+
+ align:start position:0%
+can look it up and it's it's quite nice
+it has some combinatorial techniques and
+
+ align:start position:0%
+it has some combinatorial techniques and
+ 
+
+ align:start position:0%
+it has some combinatorial techniques and
+some double counting arguments I want to
+
+ align:start position:0%
+some double counting arguments I want to
+ 
+
+ align:start position:0%
+some double counting arguments I want to
+okay so going forward I want to show you
+
+ align:start position:0%
+okay so going forward I want to show you
+ 
+
+ align:start position:0%
+okay so going forward I want to show you
+some questions
+
+ align:start position:0%
+some questions
+ 
+
+ align:start position:0%
+some questions
+mostly questions but some answers as
+
+ align:start position:0%
+mostly questions but some answers as
+ 
+
+ align:start position:0%
+mostly questions but some answers as
+well so questions such as what is the
+
+ align:start position:0%
+well so questions such as what is the
+ 
+
+ align:start position:0%
+well so questions such as what is the
+extremal number of so what are some of
+
+ align:start position:0%
+extremal number of so what are some of
+ 
+
+ align:start position:0%
+extremal number of so what are some of
+the basic bipartite graphs one of them
+
+ align:start position:0%
+the basic bipartite graphs one of them
+ 
+
+ align:start position:0%
+the basic bipartite graphs one of them
+is just a complete bipartite graph so
+
+ align:start position:0%
+is just a complete bipartite graph so
+ 
+
+ align:start position:0%
+is just a complete bipartite graph so
+this for the 0 and k which problem and
+
+ align:start position:0%
+this for the 0 and k which problem and
+ 
+
+ align:start position:0%
+this for the 0 and k which problem and
+for some values of s and T we know the
+
+ align:start position:0%
+for some values of s and T we know the
+ 
+
+ align:start position:0%
+for some values of s and T we know the
+answer but for most values we have no
+
+ align:start position:0%
+answer but for most values we have no
+ 
+
+ align:start position:0%
+answer but for most values we have no
+idea what the answer is for
+
+ align:start position:0%
+idea what the answer is for
+ 
+
+ align:start position:0%
+idea what the answer is for
+4k4 for we do not know what is the
+
+ align:start position:0%
+4k4 for we do not know what is the
+ 
+
+ align:start position:0%
+4k4 for we do not know what is the
+correct exponent so even fairly small
+
+ align:start position:0%
+correct exponent so even fairly small
+ 
+
+ align:start position:0%
+correct exponent so even fairly small
+cases so this is all to show you that
+
+ align:start position:0%
+cases so this is all to show you that
+ 
+
+ align:start position:0%
+cases so this is all to show you that
+you know these simple proofs that we did
+
+ align:start position:0%
+you know these simple proofs that we did
+ 
+
+ align:start position:0%
+you know these simple proofs that we did
+today they are perhaps too deceptively
+
+ align:start position:0%
+today they are perhaps too deceptively
+ 
+
+ align:start position:0%
+today they are perhaps too deceptively
+simple even if you change the question a
+
+ align:start position:0%
+simple even if you change the question a
+ 
+
+ align:start position:0%
+simple even if you change the question a
+little bit we don't understand a lot so
+
+ align:start position:0%
+little bit we don't understand a lot so
+ 
+
+ align:start position:0%
+little bit we don't understand a lot so
+so questions like this will occupy the
+
+ align:start position:0%
+so questions like this will occupy the
+ 
+
+ align:start position:0%
+so questions like this will occupy the
+next several lectures and I also show
+
+ align:start position:0%
+next several lectures and I also show
+ 
+
+ align:start position:0%
+next several lectures and I also show
+you some constructions and there are
+
+ align:start position:0%
+you some constructions and there are
+ 
+
+ align:start position:0%
+you some constructions and there are
+some constructions that used nice
+
+ align:start position:0%
+some constructions that used nice
+ 
+
+ align:start position:0%
+some constructions that used nice
+algebraic ideas and some probabilistic
+
+ align:start position:0%
+algebraic ideas and some probabilistic
+ 
+
+ align:start position:0%
+algebraic ideas and some probabilistic
+idea so have see ideas coming from many
+
+ align:start position:0%
+idea so have see ideas coming from many
+ 
+
+ align:start position:0%
+idea so have see ideas coming from many
+different sources I want to close off by
+
+ align:start position:0%
+different sources I want to close off by
+ 
+
+ align:start position:0%
+different sources I want to close off by
+just a cultural remark so in this course
+
+ align:start position:0%
+just a cultural remark so in this course
+ 
+
+ align:start position:0%
+just a cultural remark so in this course
+especially the the first half will
+
+ align:start position:0%
+especially the the first half will
+ 
+
+ align:start position:0%
+especially the the first half will
+encounter a lot of Hungarian names we
+
+ align:start position:0%
+encounter a lot of Hungarian names we
+ 
+
+ align:start position:0%
+encounter a lot of Hungarian names we
+already thought a couple of them and I
+
+ align:start position:0%
+already thought a couple of them and I
+ 
+
+ align:start position:0%
+already thought a couple of them and I
+just want to give you a very quick
+
+ align:start position:0%
+just want to give you a very quick
+ 
+
+ align:start position:0%
+just want to give you a very quick
+tutorial on how to pronounce Hungarian
+
+ align:start position:0%
+tutorial on how to pronounce Hungarian
+ 
+
+ align:start position:0%
+tutorial on how to pronounce Hungarian
+names because for cultural purposes now
+
+ align:start position:0%
+names because for cultural purposes now
+ 
+
+ align:start position:0%
+names because for cultural purposes now
+in the past when I taught this class
+
+ align:start position:0%
+in the past when I taught this class
+ 
+
+ align:start position:0%
+in the past when I taught this class
+there were no Hungarian speakers but I
+
+ align:start position:0%
+there were no Hungarian speakers but I
+ 
+
+ align:start position:0%
+there were no Hungarian speakers but I
+think we do have at least one Hungarian
+
+ align:start position:0%
+think we do have at least one Hungarian
+ 
+
+ align:start position:0%
+think we do have at least one Hungarian
+speaker in the room so I want you but
+
+ align:start position:0%
+speaker in the room so I want you but
+ 
+
+ align:start position:0%
+speaker in the room so I want you but
+but you are native Hungarian speaker so
+
+ align:start position:0%
+but you are native Hungarian speaker so
+ 
+
+ align:start position:0%
+but you are native Hungarian speaker so
+you should tell us okay so can you
+
+ align:start position:0%
+you should tell us okay so can you
+ 
+
+ align:start position:0%
+you should tell us okay so can you
+pronounce help us pronounce these names
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this shamone yep
+
+ align:start position:0%
+this shamone yep
+ 
+
+ align:start position:0%
+this shamone yep
+so the one I'll just tell you two things
+
+ align:start position:0%
+so the one I'll just tell you two things
+ 
+
+ align:start position:0%
+so the one I'll just tell you two things
+about Hungarian names one of them is
+
+ align:start position:0%
+about Hungarian names one of them is
+ 
+
+ align:start position:0%
+about Hungarian names one of them is
+that the S it's pronounced like Shh and
+
+ align:start position:0%
+that the S it's pronounced like Shh and
+ 
+
+ align:start position:0%
+that the S it's pronounced like Shh and
+another thing that comes up is s Z which
+
+ align:start position:0%
+another thing that comes up is s Z which
+ 
+
+ align:start position:0%
+another thing that comes up is s Z which
+we saw in samurai D so this was
+
+ align:start position:0%
+we saw in samurai D so this was
+ 
+
+ align:start position:0%
+we saw in samurai D so this was
+pronounced like s forget the Z others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another thing about a dish that you
+
+ align:start position:0%
+another thing about a dish that you
+ 
+
+ align:start position:0%
+another thing about a dish that you
+should know is that what is this accent
+
+ align:start position:0%
+should know is that what is this accent
+ 
+
+ align:start position:0%
+should know is that what is this accent
+it is not a double dot tag you would
+
+ align:start position:0%
+it is not a double dot tag you would
+ 
+
+ align:start position:0%
+it is not a double dot tag you would
+type it as / H just a few cultural
+
+ align:start position:0%
+type it as / H just a few cultural
+ 
+
+ align:start position:0%
+type it as / H just a few cultural
+remarks about about names okay great so
+
+ align:start position:0%
+remarks about about names okay great so
+ 
+
+ align:start position:0%
+remarks about about names okay great so
+we'll end today and then next time we'll
+
+ align:start position:0%
+we'll end today and then next time we'll
+ 
+
+ align:start position:0%
+we'll end today and then next time we'll
+start looking at other extremal numbers
+
+ align:start position:0%
+start looking at other extremal numbers
+ 
+
+ align:start position:0%
+start looking at other extremal numbers
+for more bipartite graphs
\ No newline at end of file
diff --git a/YwKqzngTcLw.txt b/YwKqzngTcLw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bbaaaf6e12071d98849ef8009906c0b7cac7ce98
--- /dev/null
+++ b/YwKqzngTcLw.txt
@@ -0,0 +1,834 @@
+SPEAKER: The following content
+is provided under a Creative
+
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOCELYN: Hi.
+
+Jocelyn here.
+
+And today we're going to go over
+fall 2009's final exam,
+
+problem 10.
+
+As always we're going to start
+by reading the question.
+
+You have 333 milliliters of
+alkaline solution at a pH
+
+equal to 9.9.
+
+You wish to neutralize this
+by reacting it with 222
+
+milliliters of acid.
+
+What must be the value of
+the pH of the acid?
+
+So first off let's write down
+the information that was given
+
+and the information that
+he's asking for.
+
+So we have 333 milliliters
+of a solution
+
+with pH equal to 9.9.
+
+And he's asking you what must
+the pH be if you want to put
+
+in 222 milliliters in order to
+completely neutralize that
+
+basic solution.
+
+And the key here
+is to recognize
+
+what neutralize means.
+
+And a neutralization is when you
+take acid, or protons, and
+
+base and it reacts to
+form water, thus
+
+creating a neutral solution.
+
+So the next step would probably
+be to figure out how
+
+much excess hydroxide we
+have in this solution.
+
+And then we can figure out how
+much hydrogen we need to react
+
+with that hydroxide and to
+form water in order to
+
+completely neutralize
+this solution.
+
+So first step is to
+find out what our
+
+concentration of OH minus is.
+
+And we do that by remembering
+a few things
+
+about acid/base solutions.
+
+Right?
+
+We know that if you have the pH
+plus the pOH it equals 14.
+
+And this is from the equilibrium
+constant of this
+
+neutralization reaction.
+
+And then we can figure out what
+the pOH is because we're
+
+given the pH of our
+initial solution--
+
+9.9--
+
+and that equals 4.01.
+
+Now using the definition of
+pOH, which is that the pOH
+
+equals the negative log of the
+concentration of the OH minus,
+
+we can rearrange that and
+get that our OH minus
+
+concentration equals 10
+to the negative pOH.
+
+Right?
+
+Just using our log
+rules there.
+
+So this gives us that our
+current concentration of the
+
+hydroxide ion is 10 to
+the negative 4.1.
+
+That gives us the concentration
+of the
+
+hydroxide, but what we really
+want to know, if we're going
+
+to use our neutralization
+reaction here, is we want to
+
+know how many moles
+of hydroxide we
+
+have in that solution.
+
+And we can just do that
+with stoichiometry.
+
+Right?
+
+The concentration is
+in moles per liter.
+
+And we know--
+
+so our moles hydroxide equals
+our concentration, which is 10
+
+to the negative 4.1
+moles per liter.
+
+Times--
+
+if we want to get rid of that
+liter unit we multiply it by
+
+our volume, which is 333
+milliliters, converting it
+
+from milliliters to liters.
+
+And this gives us 2.65 times 10
+to the negative 5 moles of
+
+OH minus in solution.
+
+So that's just the first
+step of this problem.
+
+Now that we have the number of
+moles of OH minus we need to
+
+find the number of moles of H
+plus necessary to react with
+
+this excess hydroxide, and then
+we will be able to find
+
+the concentration of hydrogen,
+or protons,
+
+in that second solution.
+
+So first off we're going to
+look at our neutralization
+
+reaction over here and realize
+that it's a one-to-one
+
+stoichiometric ratio.
+
+That means in order to react
+with 2.65 times 10 to the
+
+negative 5 moles of hydroxide,
+we need the same number of
+
+moles of hydrogen.
+
+So over here I'm going to say
+that this also equals the
+
+moles of H plus needed.
+
+All right.
+
+Now that we have our moles H
+plus needed, we need to do the
+
+same process here
+but in reverse.
+
+So first we need to find the
+concentration of protons that
+
+we have. So given that we want
+to only have 222 milliliters
+
+of this solution, right?
+
+So we have--
+
+and we just divide that by
+our volume, 0.222 liters.
+
+Right?
+
+Because we divide by 1,000 to
+convert from milliliters.
+
+And that equals 1.19
+times 10 to the
+
+negative 4 moles per liter.
+
+So this is another problem where
+you could get the answer
+
+but not actually be answering
+the question.
+
+Right?
+
+Because this is the
+concentration of protons that
+
+we need, but now we need
+to convert that to pH.
+
+So moving over here we'll just
+write the final steps.
+
+We know the definition of pH
+is the negative log of the
+
+concentration.
+
+And so because we know the
+concentration of protons we
+
+know that the--
+
+we just need to plug this into
+our calculator and we get our
+
+answer, which is a pH of 3.92.
+
+Put a box around that one
+because it's our correct final
+
+answer, and you'll
+be good to go for
+
+this part of the problem.
+
+Now moving on to part b we are
+asked, name the conjugate base
+
+of each of the following.
+
+So we'll just start
+part b right here.
+
+And the first thing to recognize
+is what does a
+
+conjugate base mean.
+
+And in an acid/base pair, or
+when you have a kind of
+
+dissociation of an acid, in the
+most simple terms we can
+
+think about it just
+losing a proton.
+
+In the leftover molecule, that's
+the conjugate base
+
+right there.
+
+So in this problem we're asked
+if the molecule loses a
+
+proton, what is the resulting
+molecule?
+
+Ion, basically.
+
+So part i we have HPO4, and
+that will dissociate to
+
+hydrogen phosphate ion.
+
+Simple enough.
+
+This is your conjugate base.
+
+So that's your answer
+for part i.
+
+Moving to part ii.
+
+We have CH3NH3 plus.
+
+So it's kind of like an ammonia
+ion but not quite--
+
+sorry, ammonium.
+
+And we know that this
+dissociates by losing a
+
+hydrogen off of the nitrogen,
+because that's where the
+
+positive charge is.
+
+It makes more sense there.
+
+And we get--
+
+sorry, keeping the same
+order as above--
+
+a proton plus.
+
+And this would be your
+conjugate base.
+
+If you were a little bit
+confused on this one it might
+
+help to draw the Lewis
+structure, and you would see
+
+that the formal charge does
+actually reside on nitrogen
+
+and, therefore, it makes
+sense that the nitrogen
+
+would lose a proton.
+
+In addition, if you think about
+the ammonia/ammonium ion
+
+relationship you know that you
+have NH3 going to NH4.
+
+And in this case we just have
+one of the hydrogens replaced
+
+with a methyl group, and so you
+can make the analogy there
+
+that, oh, the hydrogen
+would come from the
+
+nitrogen in that case.
+
+All right.
+
+So hopefully this was pretty
+straightforward.
+
+As long as you're comfortable
+with what a conjugate base is
+
+and what the dissociation
+reactions look like for acids.
+
+So now on part c we are asked
+to classify each of the
+
+following as a Lewis acid
+or a Lewis base.
+
+Now first we need to remember
+what a Lewis acid and
+
+a Lewis base are.
+
+So if you remember from lecture
+or in your reading, we
+
+know that a Lewis acid is an
+electron-pair acceptor and a
+
+Lewis base is an electron-pair
+donor.
+
+These definitions are just a
+little more general than the
+
+classic proton acceptor
+or proton donor.
+
+The first part is asking us
+about the cyanide ion.
+
+And to kind of clarify it for
+yourself and because we're
+
+asked about Lewis acids and
+bases, which are to deal with
+
+electron pairs, it might
+be helpful to
+
+draw the Lewis structure.
+
+So for this molecule a good
+Lewis structure looks like
+
+this, and it has a net
+negative charge.
+
+And you can see that we have a
+couple of lone electron pairs
+
+there that aren't involved
+in bonding.
+
+And because it has a net
+negative charge you can
+
+imagine that these electron
+pairs would want to kind of
+
+grab onto something else that's
+a little bit more
+
+electron positive.
+
+And because of that we
+know that this is
+
+actually a Lewis base.
+
+It acts as a base and would grab
+something like a proton
+
+and thus become more, I don't
+know, stable in some cases.
+
+All right.
+
+Moving to part 2.
+
+We are asked about water, which
+is a molecule that we
+
+deal a lot with in acid/base
+chemistry.
+
+Again, you might be able to
+answer this right off the bat,
+
+but we're going to look at
+the Lewis structure here.
+
+Water has two lone pairs.
+
+So that means it could very
+well act as a Lewis base.
+
+Hopefully that makes a
+little bit of sense.
+
+Right?
+
+Because these electrons can go
+and grab something like a
+
+proton and form the hydronium
+ion with a positive charge,
+
+thus acting as a Lewis base.
+
+It's important to remember
+that even though we're
+
+creating an acid in the
+hydronium ion, this water
+
+molecule in converting to the
+acid acts as a Lewis base.
+
+However, we also know that water
+can lose a hydrogen and
+
+accepts those electrons to form
+the hydroxide ion, and
+
+thus acts as a Lewis acid.
+
+So in the case of water either
+Lewis acid or Lewis base was a
+
+correct answer in this case.
+
+Now moving on to part d.
+
+We will go over here, I think.
+
+I'm sorry.
+
+d, not b.
+
+Again, it's going to be
+about acids and bases.
+
+Consider the effect each of the
+following substances has
+
+on the ionization of the
+weak base ammonia.
+
+For each state whether the
+substance, one, suppresses
+
+ionization, two, enhances
+ionization, or, three, has no
+
+effect on the ionization
+of ammonia.
+
+In each instance give a reason
+for your choice.
+
+Going back to the first part of
+this question we see that
+
+it's asking us about the
+ionization of ammonia.
+
+A good place to start from here
+would be to write down
+
+the reaction, just so we have
+that on our paper, in our
+
+mind, ready to think about it.
+
+So we have ammonia--
+
+and aqueous means that
+it's in water, right?
+
+And that is reacting
+with water to form
+
+the ammonium ion--
+
+sorry--
+
+by adding a proton and
+a hydroxide ion.
+
+OK.
+
+So this is the reaction
+we're asked about.
+
+Now we need to look at each of
+the three substances listed
+
+and decide how it affects
+this ionization.
+
+So number i, we have KOH.
+
+Again, a good place to start
+is to write what happens to
+
+potassium hydroxide when
+it goes into water.
+
+And we know that KOH is
+a strong base and will
+
+dissociate into potassium
+plus hydroxide.
+
+So we see that it produces
+hydroxide.
+
+And this should indicate to
+you that, well, it has the
+
+same product as one of
+the products of the
+
+ionization of ammonia.
+
+And if we remember back a
+little bit before this
+
+section, we know that if you
+have the same ion in solution
+
+it will definitely affect the
+solubility, or ionization.
+
+So that's one way to think about
+it, is that I now have a
+
+common ion effect that will,
+because there's more hydroxide
+
+in solution now, it will push
+this reaction, this
+
+equilibrium, back to the left.
+
+Another way to think
+about that is
+
+Le Chatelier's Principle.
+
+Kind of the same thing, although
+it's a little bit
+
+more versatile, I think, so
+pretty easy to think about.
+
+Right?
+
+If you add a product
+your reaction will
+
+shift to the left.
+
+If you add a reactant
+your reaction will
+
+shift to the right.
+
+So here we're adding a product,
+our reaction will
+
+shift to the left.
+
+Same as a common ion effect,
+these two combine to decrease,
+
+or both suggest that we will
+decrease, ionization.
+
+Moving to the second part
+of this problem.
+
+We're asked about hydrogen
+chloride.
+
+Again, let's look at what
+that does in water.
+
+We know that it's a strong acid,
+so it will dissociate
+
+into hydrogen, or protons,
+and chloride.
+
+Now this one's a little bit
+trickier because we don't have
+
+either of these ions in our
+initial ionization reaction,
+
+but if we think about the fact
+that ammonia is a weak base we
+
+can write an additional
+ionization reaction.
+
+So that additional would be
+ammonia reacting with a proton
+
+to form ammonium.
+
+Right?
+
+So this is another way
+that the ammonia
+
+molecule would be ionized.
+
+And we can see that if we add
+protons from this acidic
+
+molecule there we will increase
+the ionization,
+
+because it will allow the
+ammonia to work more as a base
+
+because of this reaction here.
+
+So we are increasing
+ionization.
+
+Another way to think about this
+is completely valid and
+
+kind of the same thing, but if
+we look at this ionization
+
+reaction here where the
+hydrogen chloride is
+
+dissociating into protons and
+chlorides we can recognize
+
+that these protons will then
+react with the hydroxide that
+
+is produced in the initial
+ionization reaction.
+
+This will result in a decrease
+of hydroxide
+
+in solution, right?
+
+And so by Le Chatelier's
+Principle we know that a
+
+decrease in a product causes the
+reaction to shift towards
+
+the product, to make
+more hydroxide.
+
+So that's just another way of
+thinking about the same
+
+process, and it results in the
+same conclusion that addition
+
+of hydrogen chloride increases
+the ionization of ammonia.
+
+OK.
+
+Moving to part iii.
+
+We have ammonium chloride, and
+this will dissociate into
+
+ammonium and chloride.
+
+And even if you're not sure how
+much it will dissociate,
+
+it will still dissociate
+to some amount.
+
+So it will have at least a
+little bit of an effect on our
+
+initial ionization reaction.
+
+So here we see the dissociation
+produces ammonium
+
+ions, and just like the first
+case that is one of the
+
+products in our ionization
+reaction.
+
+And so Le Chatelier's Principle,
+common ion effect,
+
+whatever you want to call it,
+tells us that it will shift
+
+the equilibrium to the left
+and decrease ionization.
+
+So with that we're done with
+problem 10 from the final.
+
+It had a lot to do with
+acid/bases, so hopefully you
+
+feel more comfortable with
+them after this.
\ No newline at end of file
diff --git a/YwZYSTQs-Hk.txt b/YwZYSTQs-Hk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82fedd03cd87dfe8b279ab6001ccb1fdb1a8a313
--- /dev/null
+++ b/YwZYSTQs-Hk.txt
@@ -0,0 +1,1787 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+what I'd like you to do is use leas
+
+ align:start position:0%
+what I'd like you to do is use leas
+ 
+
+ align:start position:0%
+what I'd like you to do is use leas
+squares to fit a line to the following
+
+ align:start position:0%
+squares to fit a line to the following
+ 
+
+ align:start position:0%
+squares to fit a line to the following
+data which includes three points the
+
+ align:start position:0%
+data which includes three points the
+ 
+
+ align:start position:0%
+data which includes three points the
+point 01 the point 21 and the point 34
+
+ align:start position:0%
+point 01 the point 21 and the point 34
+ 
+
+ align:start position:0%
+point 01 the point 21 and the point 34
+and I've drawn a rough picture of where
+
+ align:start position:0%
+and I've drawn a rough picture of where
+ 
+
+ align:start position:0%
+and I've drawn a rough picture of where
+these points are on a graph and I'll
+
+ align:start position:0%
+these points are on a graph and I'll
+ 
+
+ align:start position:0%
+these points are on a graph and I'll
+I'll be talking a little bit about that
+
+ align:start position:0%
+I'll be talking a little bit about that
+ 
+
+ align:start position:0%
+I'll be talking a little bit about that
+after you give a uh try this problem so
+
+ align:start position:0%
+after you give a uh try this problem so
+ 
+
+ align:start position:0%
+after you give a uh try this problem so
+why don't you try to solve the problem
+
+ align:start position:0%
+why don't you try to solve the problem
+ 
+
+ align:start position:0%
+why don't you try to solve the problem
+based on the technique you learned in
+
+ align:start position:0%
+based on the technique you learned in
+ 
+
+ align:start position:0%
+based on the technique you learned in
+class and then bring the video back up
+
+ align:start position:0%
+class and then bring the video back up
+ 
+
+ align:start position:0%
+class and then bring the video back up
+I'll show you again what you're actually
+
+ align:start position:0%
+I'll show you again what you're actually
+ 
+
+ align:start position:0%
+I'll show you again what you're actually
+doing and then I will also solve the
+
+ align:start position:0%
+doing and then I will also solve the
+ 
+
+ align:start position:0%
+doing and then I will also solve the
+problem and you can see uh you can
+
+ align:start position:0%
+problem and you can see uh you can
+ 
+
+ align:start position:0%
+problem and you can see uh you can
+compare your answer to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mine okay welcome back so the first
+
+ align:start position:0%
+mine okay welcome back so the first
+ 
+
+ align:start position:0%
+mine okay welcome back so the first
+thing I want to do when we're talking
+
+ align:start position:0%
+thing I want to do when we're talking
+ 
+
+ align:start position:0%
+thing I want to do when we're talking
+about least squares to fit a line to
+
+ align:start position:0%
+about least squares to fit a line to
+ 
+
+ align:start position:0%
+about least squares to fit a line to
+these data what I'd like to do is I'm
+
+ align:start position:0%
+these data what I'd like to do is I'm
+ 
+
+ align:start position:0%
+these data what I'd like to do is I'm
+going to draw a line on here and we're
+
+ align:start position:0%
+going to draw a line on here and we're
+ 
+
+ align:start position:0%
+going to draw a line on here and we're
+going to talk talk about what the Le
+
+ align:start position:0%
+going to talk talk about what the Le
+ 
+
+ align:start position:0%
+going to talk talk about what the Le
+squares actually is trying to do and so
+
+ align:start position:0%
+squares actually is trying to do and so
+ 
+
+ align:start position:0%
+squares actually is trying to do and so
+I'm going to draw this line say
+
+ align:start position:0%
+I'm going to draw this line say
+ 
+
+ align:start position:0%
+I'm going to draw this line say
+something like this and that's my first
+
+ align:start position:0%
+something like this and that's my first
+ 
+
+ align:start position:0%
+something like this and that's my first
+guess on what might be the uh the actual
+
+ align:start position:0%
+guess on what might be the uh the actual
+ 
+
+ align:start position:0%
+guess on what might be the uh the actual
+leas squares line for these data and if
+
+ align:start position:0%
+leas squares line for these data and if
+ 
+
+ align:start position:0%
+leas squares line for these data and if
+you recall what you're actually trying
+
+ align:start position:0%
+you recall what you're actually trying
+ 
+
+ align:start position:0%
+you recall what you're actually trying
+to do is you're trying to minimize a
+
+ align:start position:0%
+to do is you're trying to minimize a
+ 
+
+ align:start position:0%
+to do is you're trying to minimize a
+certain quantity and the Quant quantity
+
+ align:start position:0%
+certain quantity and the Quant quantity
+ 
+
+ align:start position:0%
+certain quantity and the Quant quantity
+you're trying to minimize is the
+
+ align:start position:0%
+you're trying to minimize is the
+ 
+
+ align:start position:0%
+you're trying to minimize is the
+difference between the the actual value
+
+ align:start position:0%
+difference between the the actual value
+ 
+
+ align:start position:0%
+difference between the the actual value
+you get and the expected value you get
+
+ align:start position:0%
+you get and the expected value you get
+ 
+
+ align:start position:0%
+you get and the expected value you get
+the square of that so this is one thing
+
+ align:start position:0%
+the square of that so this is one thing
+ 
+
+ align:start position:0%
+the square of that so this is one thing
+we're we're going to square so even
+
+ align:start position:0%
+we're we're going to square so even
+ 
+
+ align:start position:0%
+we're we're going to square so even
+pictorially we could say we have
+
+ align:start position:0%
+pictorially we could say we have
+ 
+
+ align:start position:0%
+pictorially we could say we have
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+that's that contributes some
+
+ align:start position:0%
+that's that contributes some
+ 
+
+ align:start position:0%
+that's that contributes some
+area Okay and then this is another thing
+
+ align:start position:0%
+area Okay and then this is another thing
+ 
+
+ align:start position:0%
+area Okay and then this is another thing
+it's a difference between the expected
+
+ align:start position:0%
+it's a difference between the expected
+ 
+
+ align:start position:0%
+it's a difference between the expected
+value in y and the actual value you
+
+ align:start position:0%
+value in y and the actual value you
+ 
+
+ align:start position:0%
+value in y and the actual value you
+get and so let me try and make that
+
+ align:start position:0%
+get and so let me try and make that
+ 
+
+ align:start position:0%
+get and so let me try and make that
+square because we square that value and
+
+ align:start position:0%
+square because we square that value and
+ 
+
+ align:start position:0%
+square because we square that value and
+then this last one is pretty small it's
+
+ align:start position:0%
+then this last one is pretty small it's
+ 
+
+ align:start position:0%
+then this last one is pretty small it's
+the difference between the expected
+
+ align:start position:0%
+the difference between the expected
+ 
+
+ align:start position:0%
+the difference between the expected
+value and the actual value is very small
+
+ align:start position:0%
+value and the actual value is very small
+ 
+
+ align:start position:0%
+value and the actual value is very small
+over in this this case from the picture
+
+ align:start position:0%
+over in this this case from the picture
+ 
+
+ align:start position:0%
+over in this this case from the picture
+I drew and so what you're trying to do
+
+ align:start position:0%
+I drew and so what you're trying to do
+ 
+
+ align:start position:0%
+I drew and so what you're trying to do
+is you're trying to find the line that
+
+ align:start position:0%
+is you're trying to find the line that
+ 
+
+ align:start position:0%
+is you're trying to find the line that
+minimizes the area of the sum of these
+
+ align:start position:0%
+minimizes the area of the sum of these
+ 
+
+ align:start position:0%
+minimizes the area of the sum of these
+three in this case three squares so if I
+
+ align:start position:0%
+three in this case three squares so if I
+ 
+
+ align:start position:0%
+three in this case three squares so if I
+you know if I tip the line down further
+
+ align:start position:0%
+you know if I tip the line down further
+ 
+
+ align:start position:0%
+you know if I tip the line down further
+here but I kept it kept it fixed there
+
+ align:start position:0%
+here but I kept it kept it fixed there
+ 
+
+ align:start position:0%
+here but I kept it kept it fixed there
+the area of this Square would get bigger
+
+ align:start position:0%
+the area of this Square would get bigger
+ 
+
+ align:start position:0%
+the area of this Square would get bigger
+because the the distance this distance
+
+ align:start position:0%
+because the the distance this distance
+ 
+
+ align:start position:0%
+because the the distance this distance
+would get bigger but of course the area
+
+ align:start position:0%
+would get bigger but of course the area
+ 
+
+ align:start position:0%
+would get bigger but of course the area
+of this Square would get smaller and so
+
+ align:start position:0%
+of this Square would get smaller and so
+ 
+
+ align:start position:0%
+of this Square would get smaller and so
+you're trying to figure out a way to
+
+ align:start position:0%
+you're trying to figure out a way to
+ 
+
+ align:start position:0%
+you're trying to figure out a way to
+optimize uh in this case minimize the
+
+ align:start position:0%
+optimize uh in this case minimize the
+ 
+
+ align:start position:0%
+optimize uh in this case minimize the
+area of these these
+
+ align:start position:0%
+area of these these
+ 
+
+ align:start position:0%
+area of these these
+sorry the sum of the areas of these
+
+ align:start position:0%
+sorry the sum of the areas of these
+ 
+
+ align:start position:0%
+sorry the sum of the areas of these
+squares by figuring out where to put the
+
+ align:start position:0%
+squares by figuring out where to put the
+ 
+
+ align:start position:0%
+squares by figuring out where to put the
+the line now I mentioned I would fix if
+
+ align:start position:0%
+the line now I mentioned I would fix if
+ 
+
+ align:start position:0%
+the line now I mentioned I would fix if
+I could fix this here and move it up and
+
+ align:start position:0%
+I could fix this here and move it up and
+ 
+
+ align:start position:0%
+I could fix this here and move it up and
+down and that would change the that
+
+ align:start position:0%
+down and that would change the that
+ 
+
+ align:start position:0%
+down and that would change the that
+would change the slope but fix the
+
+ align:start position:0%
+would change the slope but fix the
+ 
+
+ align:start position:0%
+would change the slope but fix the
+intercept but I could also move the
+
+ align:start position:0%
+intercept but I could also move the
+ 
+
+ align:start position:0%
+intercept but I could also move the
+intercept up and down and and uh I could
+
+ align:start position:0%
+intercept up and down and and uh I could
+ 
+
+ align:start position:0%
+intercept up and down and and uh I could
+slide the line up and down and that
+
+ align:start position:0%
+slide the line up and down and that
+ 
+
+ align:start position:0%
+slide the line up and down and that
+would fix the slope but uh vary The
+
+ align:start position:0%
+would fix the slope but uh vary The
+ 
+
+ align:start position:0%
+would fix the slope but uh vary The
+Intercept or I could do both and
+
+ align:start position:0%
+Intercept or I could do both and
+ 
+
+ align:start position:0%
+Intercept or I could do both and
+ultimately that's what you're doing
+
+ align:start position:0%
+ultimately that's what you're doing
+ 
+
+ align:start position:0%
+ultimately that's what you're doing
+you're trying to find the best Y
+
+ align:start position:0%
+you're trying to find the best Y
+ 
+
+ align:start position:0%
+you're trying to find the best Y
+intercept and the best slope at the same
+
+ align:start position:0%
+intercept and the best slope at the same
+ 
+
+ align:start position:0%
+intercept and the best slope at the same
+time and that's why you learned this
+
+ align:start position:0%
+time and that's why you learned this
+ 
+
+ align:start position:0%
+time and that's why you learned this
+process in multivariable calculus
+
+ align:start position:0%
+process in multivariable calculus
+ 
+
+ align:start position:0%
+process in multivariable calculus
+because you were trying to you're trying
+
+ align:start position:0%
+because you were trying to you're trying
+ 
+
+ align:start position:0%
+because you were trying to you're trying
+to optimize something that has two
+
+ align:start position:0%
+to optimize something that has two
+ 
+
+ align:start position:0%
+to optimize something that has two
+quantities that you can change you can
+
+ align:start position:0%
+quantities that you can change you can
+ 
+
+ align:start position:0%
+quantities that you can change you can
+change slope and you can change the Y
+
+ align:start position:0%
+change slope and you can change the Y
+ 
+
+ align:start position:0%
+change slope and you can change the Y
+intercept so that's why you learned it
+
+ align:start position:0%
+intercept so that's why you learned it
+ 
+
+ align:start position:0%
+intercept so that's why you learned it
+now instead of uh in single variable
+
+ align:start position:0%
+now instead of uh in single variable
+ 
+
+ align:start position:0%
+now instead of uh in single variable
+calculus now if we come over here I
+
+ align:start position:0%
+calculus now if we come over here I
+ 
+
+ align:start position:0%
+calculus now if we come over here I
+wrote down ahead of time what the
+
+ align:start position:0%
+wrote down ahead of time what the
+ 
+
+ align:start position:0%
+wrote down ahead of time what the
+equations are you get when you when you
+
+ align:start position:0%
+equations are you get when you when you
+ 
+
+ align:start position:0%
+equations are you get when you when you
+optimize uh when you're trying to
+
+ align:start position:0%
+optimize uh when you're trying to
+ 
+
+ align:start position:0%
+optimize uh when you're trying to
+optimize the least squares line so you
+
+ align:start position:0%
+optimize the least squares line so you
+ 
+
+ align:start position:0%
+optimize the least squares line so you
+write down you know the function as a
+
+ align:start position:0%
+write down you know the function as a
+ 
+
+ align:start position:0%
+write down you know the function as a
+function of a and b and you take the
+
+ align:start position:0%
+function of a and b and you take the
+ 
+
+ align:start position:0%
+function of a and b and you take the
+derivative with respect to a and you set
+
+ align:start position:0%
+derivative with respect to a and you set
+ 
+
+ align:start position:0%
+derivative with respect to a and you set
+it equal to zero you get the first
+
+ align:start position:0%
+it equal to zero you get the first
+ 
+
+ align:start position:0%
+it equal to zero you get the first
+equation when you take the derivative
+
+ align:start position:0%
+equation when you take the derivative
+ 
+
+ align:start position:0%
+equation when you take the derivative
+with respect to B and you set it equal
+
+ align:start position:0%
+with respect to B and you set it equal
+ 
+
+ align:start position:0%
+with respect to B and you set it equal
+to zero you get the second equation and
+
+ align:start position:0%
+to zero you get the second equation and
+ 
+
+ align:start position:0%
+to zero you get the second equation and
+so I'm just going to fill in the details
+
+ align:start position:0%
+so I'm just going to fill in the details
+ 
+
+ align:start position:0%
+so I'm just going to fill in the details
+and then tell you what the solution is
+
+ align:start position:0%
+and then tell you what the solution is
+ 
+
+ align:start position:0%
+and then tell you what the solution is
+and then I'm going to mention um a
+
+ align:start position:0%
+and then I'm going to mention um a
+ 
+
+ align:start position:0%
+and then I'm going to mention um a
+little more sophisticated thing we can
+
+ align:start position:0%
+little more sophisticated thing we can
+ 
+
+ align:start position:0%
+little more sophisticated thing we can
+do or I guess maybe the next level of uh
+
+ align:start position:0%
+do or I guess maybe the next level of uh
+ 
+
+ align:start position:0%
+do or I guess maybe the next level of uh
+of Le squares we can do that's not a
+
+ align:start position:0%
+of Le squares we can do that's not a
+ 
+
+ align:start position:0%
+of Le squares we can do that's not a
+linear problem so I'll do that last so
+
+ align:start position:0%
+linear problem so I'll do that last so
+ 
+
+ align:start position:0%
+linear problem so I'll do that last so
+what I want to do is I've put all the
+
+ align:start position:0%
+what I want to do is I've put all the
+ 
+
+ align:start position:0%
+what I want to do is I've put all the
+values I need over here on the right so
+
+ align:start position:0%
+values I need over here on the right so
+ 
+
+ align:start position:0%
+values I need over here on the right so
+all the values we need are on the right
+
+ align:start position:0%
+all the values we need are on the right
+ 
+
+ align:start position:0%
+all the values we need are on the right
+we're going to need the sum of all the X
+
+ align:start position:0%
+we're going to need the sum of all the X
+ 
+
+ align:start position:0%
+we're going to need the sum of all the X
+eyes and that's five the sum of all the
+
+ align:start position:0%
+eyes and that's five the sum of all the
+ 
+
+ align:start position:0%
+eyes and that's five the sum of all the
+Y eyes is six sum of the x i squares is
+
+ align:start position:0%
+Y eyes is six sum of the x i squares is
+ 
+
+ align:start position:0%
+Y eyes is six sum of the x i squares is
+13 and the sum of the x i Yi products is
+
+ align:start position:0%
+13 and the sum of the x i Yi products is
+ 
+
+ align:start position:0%
+13 and the sum of the x i Yi products is
+14 now where are these coming from
+
+ align:start position:0%
+14 now where are these coming from
+ 
+
+ align:start position:0%
+14 now where are these coming from
+remember what is x i and what is Yi if
+
+ align:start position:0%
+remember what is x i and what is Yi if
+ 
+
+ align:start position:0%
+remember what is x i and what is Yi if
+we come back over
+
+ align:start position:0%
+we come back over
+ 
+
+ align:start position:0%
+we come back over
+here this is X1 y1 X2 Y2 X3 Y3 okay so
+
+ align:start position:0%
+here this is X1 y1 X2 Y2 X3 Y3 okay so
+ 
+
+ align:start position:0%
+here this is X1 y1 X2 Y2 X3 Y3 okay so
+that's sort of how we get if we switch
+
+ align:start position:0%
+that's sort of how we get if we switch
+ 
+
+ align:start position:0%
+that's sort of how we get if we switch
+the if we switch the whole pairs around
+
+ align:start position:0%
+the if we switch the whole pairs around
+ 
+
+ align:start position:0%
+the if we switch the whole pairs around
+it doesn't matter matter obviously if we
+
+ align:start position:0%
+it doesn't matter matter obviously if we
+ 
+
+ align:start position:0%
+it doesn't matter matter obviously if we
+switched X and Y values together it does
+
+ align:start position:0%
+switched X and Y values together it does
+ 
+
+ align:start position:0%
+switched X and Y values together it does
+matter and that you see actually from
+
+ align:start position:0%
+matter and that you see actually from
+ 
+
+ align:start position:0%
+matter and that you see actually from
+the equation does matter right here you
+
+ align:start position:0%
+the equation does matter right here you
+ 
+
+ align:start position:0%
+the equation does matter right here you
+have a product of them so let me write
+
+ align:start position:0%
+have a product of them so let me write
+ 
+
+ align:start position:0%
+have a product of them so let me write
+this out and again we're solving for A
+
+ align:start position:0%
+this out and again we're solving for A
+ 
+
+ align:start position:0%
+this out and again we're solving for A
+and B so in this case a is the slope and
+
+ align:start position:0%
+and B so in this case a is the slope and
+ 
+
+ align:start position:0%
+and B so in this case a is the slope and
+B is The Intercept right so let me write
+
+ align:start position:0%
+B is The Intercept right so let me write
+ 
+
+ align:start position:0%
+B is The Intercept right so let me write
+everything in so we actually get that we
+
+ align:start position:0%
+everything in so we actually get that we
+ 
+
+ align:start position:0%
+everything in so we actually get that we
+want to solve the following system 13 a
+
+ align:start position:0%
+want to solve the following system 13 a
+ 
+
+ align:start position:0%
+want to solve the following system 13 a
++ 5 b is equal to 14
+
+ align:start position:0%
++ 5 b is equal to 14
+ 
+
+ align:start position:0%
++ 5 b is equal to 14
+make sure I put in everything correctly
+
+ align:start position:0%
+make sure I put in everything correctly
+ 
+
+ align:start position:0%
+make sure I put in everything correctly
+and then the second one is uh 5 a plus n
+
+ align:start position:0%
+and then the second one is uh 5 a plus n
+ 
+
+ align:start position:0%
+and then the second one is uh 5 a plus n
+in this case is three because there were
+
+ align:start position:0%
+in this case is three because there were
+ 
+
+ align:start position:0%
+in this case is three because there were
+three points plus
+
+ align:start position:0%
+three points plus
+ 
+
+ align:start position:0%
+three points plus
+3B is equal to 6 okay this is a system
+
+ align:start position:0%
+3B is equal to 6 okay this is a system
+ 
+
+ align:start position:0%
+3B is equal to 6 okay this is a system
+of equations it has two equations and
+
+ align:start position:0%
+of equations it has two equations and
+ 
+
+ align:start position:0%
+of equations it has two equations and
+two unknowns and if you solve this I
+
+ align:start position:0%
+two unknowns and if you solve this I
+ 
+
+ align:start position:0%
+two unknowns and if you solve this I
+should look at my notes because I didn't
+
+ align:start position:0%
+should look at my notes because I didn't
+ 
+
+ align:start position:0%
+should look at my notes because I didn't
+memorize it and I'm not going to do all
+
+ align:start position:0%
+memorize it and I'm not going to do all
+ 
+
+ align:start position:0%
+memorize it and I'm not going to do all
+the algebra if you go to solve this what
+
+ align:start position:0%
+the algebra if you go to solve this what
+ 
+
+ align:start position:0%
+the algebra if you go to solve this what
+you actually get is that a is equal to
+
+ align:start position:0%
+you actually get is that a is equal to
+ 
+
+ align:start position:0%
+you actually get is that a is equal to
+67 and B is equal to 47 so you get that
+
+ align:start position:0%
+67 and B is equal to 47 so you get that
+ 
+
+ align:start position:0%
+67 and B is equal to 47 so you get that
+the line let me write it here you get a
+
+ align:start position:0%
+the line let me write it here you get a
+ 
+
+ align:start position:0%
+the line let me write it here you get a
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+67th and B is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+47th okay and so what that tells you is
+
+ align:start position:0%
+47th okay and so what that tells you is
+ 
+
+ align:start position:0%
+47th okay and so what that tells you is
+if you come back over here the line we
+
+ align:start position:0%
+if you come back over here the line we
+ 
+
+ align:start position:0%
+if you come back over here the line we
+actually want I'll write the solution
+
+ align:start position:0%
+actually want I'll write the solution
+ 
+
+ align:start position:0%
+actually want I'll write the solution
+right here the line we actually want is
+
+ align:start position:0%
+right here the line we actually want is
+ 
+
+ align:start position:0%
+right here the line we actually want is
+the line Y = 67
+
+ align:start position:0%
+the line Y = 67
+ 
+
+ align:start position:0%
+the line Y = 67
+x + 47 that is our least squares line
+
+ align:start position:0%
+x + 47 that is our least squares line
+ 
+
+ align:start position:0%
+x + 47 that is our least squares line
+that is our
+
+ align:start position:0%
+that is our
+ 
+
+ align:start position:0%
+that is our
+solution okay so that is actually
+
+ align:start position:0%
+solution okay so that is actually
+ 
+
+ align:start position:0%
+solution okay so that is actually
+solving for a line to fit these data you
+
+ align:start position:0%
+solving for a line to fit these data you
+ 
+
+ align:start position:0%
+solving for a line to fit these data you
+get the following solution but I want to
+
+ align:start position:0%
+get the following solution but I want to
+ 
+
+ align:start position:0%
+get the following solution but I want to
+point out and what we're going to do
+
+ align:start position:0%
+point out and what we're going to do
+ 
+
+ align:start position:0%
+point out and what we're going to do
+after this video there will be a a
+
+ align:start position:0%
+after this video there will be a a
+ 
+
+ align:start position:0%
+after this video there will be a a
+challenge problem to have you actually
+
+ align:start position:0%
+challenge problem to have you actually
+ 
+
+ align:start position:0%
+challenge problem to have you actually
+finish this I want to point out that you
+
+ align:start position:0%
+finish this I want to point out that you
+ 
+
+ align:start position:0%
+finish this I want to point out that you
+can actually also fit a higher degree
+
+ align:start position:0%
+can actually also fit a higher degree
+ 
+
+ align:start position:0%
+can actually also fit a higher degree
+polinomial to these data for instance
+
+ align:start position:0%
+polinomial to these data for instance
+ 
+
+ align:start position:0%
+polinomial to these data for instance
+you could try and use the technique of
+
+ align:start position:0%
+you could try and use the technique of
+ 
+
+ align:start position:0%
+you could try and use the technique of
+leas squares to fit a parabola to these
+
+ align:start position:0%
+leas squares to fit a parabola to these
+ 
+
+ align:start position:0%
+leas squares to fit a parabola to these
+data and let me point out what the
+
+ align:start position:0%
+data and let me point out what the
+ 
+
+ align:start position:0%
+data and let me point out what the
+function would look like in this case
+
+ align:start position:0%
+function would look like in this case
+ 
+
+ align:start position:0%
+function would look like in this case
+Okay so this is this is for the
+
+ align:start position:0%
+Okay so this is this is for the
+ 
+
+ align:start position:0%
+Okay so this is this is for the
+challenge
+
+ align:start position:0%
+challenge
+ 
+
+ align:start position:0%
+challenge
+problem for the challenge problem it now
+
+ align:start position:0%
+problem for the challenge problem it now
+ 
+
+ align:start position:0%
+problem for the challenge problem it now
+will be a function of three variables so
+
+ align:start position:0%
+will be a function of three variables so
+ 
+
+ align:start position:0%
+will be a function of three variables so
+it will look something like this we'll
+
+ align:start position:0%
+it will look something like this we'll
+ 
+
+ align:start position:0%
+it will look something like this we'll
+say a comma B comma C and the point we
+
+ align:start position:0%
+say a comma B comma C and the point we
+ 
+
+ align:start position:0%
+say a comma B comma C and the point we
+that we'll be wanting to minimize or the
+
+ align:start position:0%
+that we'll be wanting to minimize or the
+ 
+
+ align:start position:0%
+that we'll be wanting to minimize or the
+function will'll be wanting to minimize
+
+ align:start position:0%
+function will'll be wanting to minimize
+ 
+
+ align:start position:0%
+function will'll be wanting to minimize
+we're summing over I again from 1 to
+
+ align:start position:0%
+we're summing over I again from 1 to
+ 
+
+ align:start position:0%
+we're summing over I again from 1 to
+three I didn't write that down above but
+
+ align:start position:0%
+three I didn't write that down above but
+ 
+
+ align:start position:0%
+three I didn't write that down above but
+it was fairly obvious that that was what
+
+ align:start position:0%
+it was fairly obvious that that was what
+ 
+
+ align:start position:0%
+it was fairly obvious that that was what
+we were summing over the following thing
+
+ align:start position:0%
+we were summing over the following thing
+ 
+
+ align:start position:0%
+we were summing over the following thing
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have Yi
+
+ align:start position:0%
+have Yi
+ 
+
+ align:start position:0%
+have Yi
+minus this big quantity a x i 2 + b x i
+
+ align:start position:0%
+minus this big quantity a x i 2 + b x i
+ 
+
+ align:start position:0%
+minus this big quantity a x i 2 + b x i
++ C and we Square the whole thing and so
+
+ align:start position:0%
++ C and we Square the whole thing and so
+ 
+
+ align:start position:0%
++ C and we Square the whole thing and so
+what this is actually giving you is just
+
+ align:start position:0%
+what this is actually giving you is just
+ 
+
+ align:start position:0%
+what this is actually giving you is just
+as in the picture before this is giving
+
+ align:start position:0%
+as in the picture before this is giving
+ 
+
+ align:start position:0%
+as in the picture before this is giving
+you the difference between the expected
+
+ align:start position:0%
+you the difference between the expected
+ 
+
+ align:start position:0%
+you the difference between the expected
+value and the actual value so this is
+
+ align:start position:0%
+value and the actual value so this is
+ 
+
+ align:start position:0%
+value and the actual value so this is
+your actual y value and based on the
+
+ align:start position:0%
+your actual y value and based on the
+ 
+
+ align:start position:0%
+your actual y value and based on the
+parabola you're looking for what's in
+
+ align:start position:0%
+parabola you're looking for what's in
+ 
+
+ align:start position:0%
+parabola you're looking for what's in
+parth es is your expected y
+
+ align:start position:0%
+parth es is your expected y
+ 
+
+ align:start position:0%
+parth es is your expected y
+value right so this is actually this
+
+ align:start position:0%
+value right so this is actually this
+ 
+
+ align:start position:0%
+value right so this is actually this
+would actually be my Parabola when I
+
+ align:start position:0%
+would actually be my Parabola when I
+ 
+
+ align:start position:0%
+would actually be my Parabola when I
+evaluated at XI I get a number I get a
+
+ align:start position:0%
+evaluated at XI I get a number I get a
+ 
+
+ align:start position:0%
+evaluated at XI I get a number I get a
+value and that value will be on the
+
+ align:start position:0%
+value and that value will be on the
+ 
+
+ align:start position:0%
+value and that value will be on the
+parabola this will be the yvalue
+
+ align:start position:0%
+parabola this will be the yvalue
+ 
+
+ align:start position:0%
+parabola this will be the yvalue
+associated to the x value from the data
+
+ align:start position:0%
+associated to the x value from the data
+ 
+
+ align:start position:0%
+associated to the x value from the data
+so this is the actual value this is the
+
+ align:start position:0%
+so this is the actual value this is the
+ 
+
+ align:start position:0%
+so this is the actual value this is the
+expected value we take the difference
+
+ align:start position:0%
+expected value we take the difference
+ 
+
+ align:start position:0%
+expected value we take the difference
+and square it and because we want to
+
+ align:start position:0%
+and square it and because we want to
+ 
+
+ align:start position:0%
+and square it and because we want to
+minimize how we're going to solve this
+
+ align:start position:0%
+minimize how we're going to solve this
+ 
+
+ align:start position:0%
+minimize how we're going to solve this
+problem and this is what you'll have to
+
+ align:start position:0%
+problem and this is what you'll have to
+ 
+
+ align:start position:0%
+problem and this is what you'll have to
+do is just like with with the line uh
+
+ align:start position:0%
+do is just like with with the line uh
+ 
+
+ align:start position:0%
+do is just like with with the line uh
+situation you're going to take the
+
+ align:start position:0%
+situation you're going to take the
+ 
+
+ align:start position:0%
+situation you're going to take the
+derivative of this function with respect
+
+ align:start position:0%
+derivative of this function with respect
+ 
+
+ align:start position:0%
+derivative of this function with respect
+to each of these three variables
+
+ align:start position:0%
+to each of these three variables
+ 
+
+ align:start position:0%
+to each of these three variables
+separately so you'll take F sub a and
+
+ align:start position:0%
+separately so you'll take F sub a and
+ 
+
+ align:start position:0%
+separately so you'll take F sub a and
+then you'll set that equal to zero and
+
+ align:start position:0%
+then you'll set that equal to zero and
+ 
+
+ align:start position:0%
+then you'll set that equal to zero and
+then you'll take F subb you'll set that
+
+ align:start position:0%
+then you'll take F subb you'll set that
+ 
+
+ align:start position:0%
+then you'll take F subb you'll set that
+equal to zero and then you'll take F Sub
+
+ align:start position:0%
+equal to zero and then you'll take F Sub
+ 
+
+ align:start position:0%
+equal to zero and then you'll take F Sub
+C and you'll set that equal to zero
+
+ align:start position:0%
+C and you'll set that equal to zero
+ 
+
+ align:start position:0%
+C and you'll set that equal to zero
+again we set them all equal to zero
+
+ align:start position:0%
+again we set them all equal to zero
+ 
+
+ align:start position:0%
+again we set them all equal to zero
+because this is really an optimization
+
+ align:start position:0%
+because this is really an optimization
+ 
+
+ align:start position:0%
+because this is really an optimization
+problem we want to minimize something
+
+ align:start position:0%
+problem we want to minimize something
+ 
+
+ align:start position:0%
+problem we want to minimize something
+want to minimize this
+
+ align:start position:0%
+want to minimize this
+ 
+
+ align:start position:0%
+want to minimize this
+quantity so you take each of those three
+
+ align:start position:0%
+quantity so you take each of those three
+ 
+
+ align:start position:0%
+quantity so you take each of those three
+derivatives partial derivatives set them
+
+ align:start position:0%
+derivatives partial derivatives set them
+ 
+
+ align:start position:0%
+derivatives partial derivatives set them
+equal to zero and you have a system of
+
+ align:start position:0%
+equal to zero and you have a system of
+ 
+
+ align:start position:0%
+equal to zero and you have a system of
+three equations with three variables and
+
+ align:start position:0%
+three equations with three variables and
+ 
+
+ align:start position:0%
+three equations with three variables and
+you know how to solve such a system by
+
+ align:start position:0%
+you know how to solve such a system by
+ 
+
+ align:start position:0%
+you know how to solve such a system by
+using matrices for instance that would
+
+ align:start position:0%
+using matrices for instance that would
+ 
+
+ align:start position:0%
+using matrices for instance that would
+be one way to solve such a system and so
+
+ align:start position:0%
+be one way to solve such a system and so
+ 
+
+ align:start position:0%
+be one way to solve such a system and so
+then you can actually come up with a
+
+ align:start position:0%
+then you can actually come up with a
+ 
+
+ align:start position:0%
+then you can actually come up with a
+formula uh for the the sort of Parabola
+
+ align:start position:0%
+formula uh for the the sort of Parabola
+ 
+
+ align:start position:0%
+formula uh for the the sort of Parabola
+of best fit you could think of it as and
+
+ align:start position:0%
+of best fit you could think of it as and
+ 
+
+ align:start position:0%
+of best fit you could think of it as and
+so I'm going to stop there because I
+
+ align:start position:0%
+so I'm going to stop there because I
+ 
+
+ align:start position:0%
+so I'm going to stop there because I
+think from here you guys will do it but
+
+ align:start position:0%
+think from here you guys will do it but
+ 
+
+ align:start position:0%
+think from here you guys will do it but
+I just want to point out this is where
+
+ align:start position:0%
+I just want to point out this is where
+ 
+
+ align:start position:0%
+I just want to point out this is where
+you're going to be starting this next
+
+ align:start position:0%
+you're going to be starting this next
+ 
+
+ align:start position:0%
+you're going to be starting this next
+sort of challenge problem to find the
+
+ align:start position:0%
+sort of challenge problem to find the
+ 
+
+ align:start position:0%
+sort of challenge problem to find the
+quadratic of best fit for these three
+
+ align:start position:0%
+quadratic of best fit for these three
+ 
+
+ align:start position:0%
+quadratic of best fit for these three
+data points so that's where I'll end it
\ No newline at end of file
diff --git a/ZQu2B3GyI_k.txt b/ZQu2B3GyI_k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d55c6d9006cfec1ac009ef9f6c0df9642d38cd84
--- /dev/null
+++ b/ZQu2B3GyI_k.txt
@@ -0,0 +1,15219 @@
+align:start position:0%
+ 
+fortunately I have a
+
+ align:start position:0%
+fortunately I have a
+ 
+
+ align:start position:0%
+fortunately I have a
+today dr. Adam Wright who will be doing
+
+ align:start position:0%
+today dr. Adam Wright who will be doing
+ 
+
+ align:start position:0%
+today dr. Adam Wright who will be doing
+an interview style session and will
+
+ align:start position:0%
+an interview style session and will
+ 
+
+ align:start position:0%
+an interview style session and will
+answer questions for you this is Adams
+
+ align:start position:0%
+answer questions for you this is Adams
+ 
+
+ align:start position:0%
+answer questions for you this is Adams
+sort of bread and butter is exactly how
+
+ align:start position:0%
+sort of bread and butter is exactly how
+ 
+
+ align:start position:0%
+sort of bread and butter is exactly how
+to translate this kind of technology
+
+ align:start position:0%
+to translate this kind of technology
+ 
+
+ align:start position:0%
+to translate this kind of technology
+into into the clinic he's currently in
+
+ align:start position:0%
+into into the clinic he's currently in
+ 
+
+ align:start position:0%
+into into the clinic he's currently in
+the partner system at the Brigham I
+
+ align:start position:0%
+the partner system at the Brigham I
+ 
+
+ align:start position:0%
+the partner system at the Brigham I
+guess but he's about to become a traitor
+
+ align:start position:0%
+guess but he's about to become a traitor
+ 
+
+ align:start position:0%
+guess but he's about to become a traitor
+and leave us in Boston and and occupy a
+
+ align:start position:0%
+and leave us in Boston and and occupy a
+ 
+
+ align:start position:0%
+and leave us in Boston and and occupy a
+position at Vanderbilt University
+
+ align:start position:0%
+position at Vanderbilt University
+ 
+
+ align:start position:0%
+position at Vanderbilt University
+so for which we wish him luck but I'm
+
+ align:start position:0%
+so for which we wish him luck but I'm
+ 
+
+ align:start position:0%
+so for which we wish him luck but I'm
+glad that we caught him before he leaves
+
+ align:start position:0%
+glad that we caught him before he leaves
+ 
+
+ align:start position:0%
+glad that we caught him before he leaves
+the summer okay
+
+ align:start position:0%
+the summer okay
+ 
+
+ align:start position:0%
+the summer okay
+so quite frankly I wish that I could
+
+ align:start position:0%
+so quite frankly I wish that I could
+ 
+
+ align:start position:0%
+so quite frankly I wish that I could
+tell you a much happier story than the
+
+ align:start position:0%
+tell you a much happier story than the
+ 
+
+ align:start position:0%
+tell you a much happier story than the
+one that you're going to hear from me
+
+ align:start position:0%
+one that you're going to hear from me
+ 
+
+ align:start position:0%
+one that you're going to hear from me
+during the prepared part of my talk and
+
+ align:start position:0%
+during the prepared part of my talk and
+ 
+
+ align:start position:0%
+during the prepared part of my talk and
+maybe Adam will will cheer us up and
+
+ align:start position:0%
+maybe Adam will will cheer us up and
+ 
+
+ align:start position:0%
+maybe Adam will will cheer us up and
+make us more optimistic based on on on
+
+ align:start position:0%
+make us more optimistic based on on on
+ 
+
+ align:start position:0%
+make us more optimistic based on on on
+his experience so you may have noticed
+
+ align:start position:0%
+his experience so you may have noticed
+ 
+
+ align:start position:0%
+his experience so you may have noticed
+that AI is hot so hims for example is
+
+ align:start position:0%
+that AI is hot so hims for example is
+ 
+
+ align:start position:0%
+that AI is hot so hims for example is
+the health information management system
+
+ align:start position:0%
+the health information management system
+ 
+
+ align:start position:0%
+the health information management system
+Society it's a big they hold annual
+
+ align:start position:0%
+Society it's a big they hold annual
+ 
+
+ align:start position:0%
+Society it's a big they hold annual
+meetings and and consist of a lot of
+
+ align:start position:0%
+meetings and and consist of a lot of
+ 
+
+ align:start position:0%
+meetings and and consist of a lot of
+vendors and a lot of academics and it's
+
+ align:start position:0%
+vendors and a lot of academics and it's
+ 
+
+ align:start position:0%
+vendors and a lot of academics and it's
+one of these huge tradeshow kinds of
+
+ align:start position:0%
+one of these huge tradeshow kinds of
+ 
+
+ align:start position:0%
+one of these huge tradeshow kinds of
+things with balloons hanging over booths
+
+ align:start position:0%
+things with balloons hanging over booths
+ 
+
+ align:start position:0%
+things with balloons hanging over booths
+and big big open spaces and so for
+
+ align:start position:0%
+and big big open spaces and so for
+ 
+
+ align:start position:0%
+and big big open spaces and so for
+example they are now talking about AI
+
+ align:start position:0%
+example they are now talking about AI
+ 
+
+ align:start position:0%
+example they are now talking about AI
+powered healthcare on the other hand
+
+ align:start position:0%
+powered healthcare on the other hand
+ 
+
+ align:start position:0%
+powered healthcare on the other hand
+it's important to remember this graph so
+
+ align:start position:0%
+it's important to remember this graph so
+ 
+
+ align:start position:0%
+it's important to remember this graph so
+this is the sort of technology adoption
+
+ align:start position:0%
+this is the sort of technology adoption
+ 
+
+ align:start position:0%
+this is the sort of technology adoption
+graph and it's called the height cycle
+
+ align:start position:0%
+graph and it's called the height cycle
+ 
+
+ align:start position:0%
+graph and it's called the height cycle
+and what you see here is that our MD
+
+ align:start position:0%
+and what you see here is that our MD
+ 
+
+ align:start position:0%
+and what you see here is that our MD
+produces some wonderful interesting idea
+
+ align:start position:0%
+produces some wonderful interesting idea
+ 
+
+ align:start position:0%
+produces some wonderful interesting idea
+and then all of a sudden people get
+
+ align:start position:0%
+and then all of a sudden people get
+ 
+
+ align:start position:0%
+and then all of a sudden people get
+excited about it so who are the people
+
+ align:start position:0%
+excited about it so who are the people
+ 
+
+ align:start position:0%
+excited about it so who are the people
+that get most excited about it it's the
+
+ align:start position:0%
+that get most excited about it it's the
+ 
+
+ align:start position:0%
+that get most excited about it it's the
+people who think they're going to make a
+
+ align:start position:0%
+people who think they're going to make a
+ 
+
+ align:start position:0%
+people who think they're going to make a
+fortune from it and these are the so
+
+ align:start position:0%
+fortune from it and these are the so
+ 
+
+ align:start position:0%
+fortune from it and these are the so
+called vulture capitalists
+
+ align:start position:0%
+called vulture capitalists
+ 
+
+ align:start position:0%
+called vulture capitalists
+you're capitalists and so the venture
+
+ align:start position:0%
+you're capitalists and so the venture
+ 
+
+ align:start position:0%
+you're capitalists and so the venture
+capitalists come in and they encourage
+
+ align:start position:0%
+capitalists come in and they encourage
+ 
+
+ align:start position:0%
+capitalists come in and they encourage
+people like us to go out and found
+
+ align:start position:0%
+people like us to go out and found
+ 
+
+ align:start position:0%
+people like us to go out and found
+companies or if if not us then our
+
+ align:start position:0%
+companies or if if not us then our
+ 
+
+ align:start position:0%
+companies or if if not us then our
+students to go found companies and
+
+ align:start position:0%
+students to go found companies and
+ 
+
+ align:start position:0%
+students to go found companies and
+figure out how to turn this nascent idea
+
+ align:start position:0%
+figure out how to turn this nascent idea
+ 
+
+ align:start position:0%
+figure out how to turn this nascent idea
+into some important money-making
+
+ align:start position:0%
+into some important money-making
+ 
+
+ align:start position:0%
+into some important money-making
+enterprise now the secret of venture
+
+ align:start position:0%
+enterprise now the secret of venture
+ 
+
+ align:start position:0%
+enterprise now the secret of venture
+capital is that they know that about 90%
+
+ align:start position:0%
+capital is that they know that about 90%
+ 
+
+ align:start position:0%
+capital is that they know that about 90%
+of the companies that they fund are
+
+ align:start position:0%
+of the companies that they fund are
+ 
+
+ align:start position:0%
+of the companies that they fund are
+going to tank they're going to do very
+
+ align:start position:0%
+going to tank they're going to do very
+ 
+
+ align:start position:0%
+going to tank they're going to do very
+badly and so as a result what they hope
+
+ align:start position:0%
+badly and so as a result what they hope
+ 
+
+ align:start position:0%
+badly and so as a result what they hope
+for and what they expect and what the
+
+ align:start position:0%
+for and what they expect and what the
+ 
+
+ align:start position:0%
+for and what they expect and what the
+good ones actually get is that that one
+
+ align:start position:0%
+good ones actually get is that that one
+ 
+
+ align:start position:0%
+good ones actually get is that that one
+in ten that becomes successful makes so
+
+ align:start position:0%
+in ten that becomes successful makes so
+ 
+
+ align:start position:0%
+in ten that becomes successful makes so
+much money that it makes up for all of
+
+ align:start position:0%
+much money that it makes up for all of
+ 
+
+ align:start position:0%
+much money that it makes up for all of
+the investment that they poured into the
+
+ align:start position:0%
+the investment that they poured into the
+ 
+
+ align:start position:0%
+the investment that they poured into the
+nine out of ten that do badly so I
+
+ align:start position:0%
+nine out of ten that do badly so I
+ 
+
+ align:start position:0%
+nine out of ten that do badly so I
+actually remember in the 1990s I was
+
+ align:start position:0%
+actually remember in the 1990s I was
+ 
+
+ align:start position:0%
+actually remember in the 1990s I was
+helping a group pitch a company to
+
+ align:start position:0%
+helping a group pitch a company to
+ 
+
+ align:start position:0%
+helping a group pitch a company to
+kleiner perkins which is the big event
+
+ align:start position:0%
+kleiner perkins which is the big event
+ 
+
+ align:start position:0%
+kleiner perkins which is the big event
+one of the big venture capital funds in
+
+ align:start position:0%
+one of the big venture capital funds in
+ 
+
+ align:start position:0%
+one of the big venture capital funds in
+Silicon Valley and we walked into their
+
+ align:start position:0%
+Silicon Valley and we walked into their
+ 
+
+ align:start position:0%
+Silicon Valley and we walked into their
+boardroom and they had a copy of the San
+
+ align:start position:0%
+boardroom and they had a copy of the San
+ 
+
+ align:start position:0%
+boardroom and they had a copy of the San
+Jose Mercury News which is the local
+
+ align:start position:0%
+Jose Mercury News which is the local
+ 
+
+ align:start position:0%
+Jose Mercury News which is the local
+newspaper for Silicon Valley on their
+
+ align:start position:0%
+newspaper for Silicon Valley on their
+ 
+
+ align:start position:0%
+newspaper for Silicon Valley on their
+table and they were just beaming because
+
+ align:start position:0%
+table and they were just beaming because
+ 
+
+ align:start position:0%
+table and they were just beaming because
+there was an article that said that in
+
+ align:start position:0%
+there was an article that said that in
+ 
+
+ align:start position:0%
+there was an article that said that in
+the past year the two best and the two
+
+ align:start position:0%
+the past year the two best and the two
+ 
+
+ align:start position:0%
+the past year the two best and the two
+worst investments in Silicon Valley had
+
+ align:start position:0%
+worst investments in Silicon Valley had
+ 
+
+ align:start position:0%
+worst investments in Silicon Valley had
+been by their company right but that's
+
+ align:start position:0%
+been by their company right but that's
+ 
+
+ align:start position:0%
+been by their company right but that's
+pretty good right if you're if you get
+
+ align:start position:0%
+pretty good right if you're if you get
+ 
+
+ align:start position:0%
+pretty good right if you're if you get
+two winners and two really bad losers
+
+ align:start position:0%
+two winners and two really bad losers
+ 
+
+ align:start position:0%
+two winners and two really bad losers
+you're making tons and tons of money so
+
+ align:start position:0%
+you're making tons and tons of money so
+ 
+
+ align:start position:0%
+you're making tons and tons of money so
+they were in a good mood and they funded
+
+ align:start position:0%
+they were in a good mood and they funded
+ 
+
+ align:start position:0%
+they were in a good mood and they funded
+us we didn't make them any money so what
+
+ align:start position:0%
+us we didn't make them any money so what
+ 
+
+ align:start position:0%
+us we didn't make them any money so what
+you see on this curve is that there's a
+
+ align:start position:0%
+you see on this curve is that there's a
+ 
+
+ align:start position:0%
+you see on this curve is that there's a
+kind of a set of rising expectations
+
+ align:start position:0%
+kind of a set of rising expectations
+ 
+
+ align:start position:0%
+kind of a set of rising expectations
+that comes from the development of these
+
+ align:start position:0%
+that comes from the development of these
+ 
+
+ align:start position:0%
+that comes from the development of these
+technologies and you have some early
+
+ align:start position:0%
+technologies and you have some early
+ 
+
+ align:start position:0%
+technologies and you have some early
+adopters
+
+ align:start position:0%
+adopters
+ 
+
+ align:start position:0%
+adopters
+and you have the newspapers writing
+
+ align:start position:0%
+and you have the newspapers writing
+ 
+
+ align:start position:0%
+and you have the newspapers writing
+about how this is the revolution and
+
+ align:start position:0%
+about how this is the revolution and
+ 
+
+ align:start position:0%
+about how this is the revolution and
+everything will be different from here
+
+ align:start position:0%
+everything will be different from here
+ 
+
+ align:start position:0%
+everything will be different from here
+on out and then you have some additional
+
+ align:start position:0%
+on out and then you have some additional
+ 
+
+ align:start position:0%
+on out and then you have some additional
+activity beyond early adopters and then
+
+ align:start position:0%
+activity beyond early adopters and then
+ 
+
+ align:start position:0%
+activity beyond early adopters and then
+people start looking at this and going
+
+ align:start position:0%
+people start looking at this and going
+ 
+
+ align:start position:0%
+people start looking at this and going
+well it really isn't as good as as it's
+
+ align:start position:0%
+well it really isn't as good as as it's
+ 
+
+ align:start position:0%
+well it really isn't as good as as it's
+cracked up to be and then you have the
+
+ align:start position:0%
+cracked up to be and then you have the
+ 
+
+ align:start position:0%
+cracked up to be and then you have the
+steep decline where there's some
+
+ align:start position:0%
+steep decline where there's some
+ 
+
+ align:start position:0%
+steep decline where there's some
+consolidation and some failures and
+
+ align:start position:0%
+consolidation and some failures and
+ 
+
+ align:start position:0%
+consolidation and some failures and
+people have to go back to venture
+
+ align:start position:0%
+people have to go back to venture
+ 
+
+ align:start position:0%
+people have to go back to venture
+capital to try to get more money in
+
+ align:start position:0%
+capital to try to get more money in
+ 
+
+ align:start position:0%
+capital to try to get more money in
+order to keep their companies going and
+
+ align:start position:0%
+order to keep their companies going and
+ 
+
+ align:start position:0%
+order to keep their companies going and
+then there's a kind of trough where
+
+ align:start position:0%
+then there's a kind of trough where
+ 
+
+ align:start position:0%
+then there's a kind of trough where
+people go oh well this was another of
+
+ align:start position:0%
+people go oh well this was another of
+ 
+
+ align:start position:0%
+people go oh well this was another of
+these failed kind of technological
+
+ align:start position:0%
+these failed kind of technological
+ 
+
+ align:start position:0%
+these failed kind of technological
+innovations and then gradually you start
+
+ align:start position:0%
+innovations and then gradually you start
+ 
+
+ align:start position:0%
+innovations and then gradually you start
+reaching what if this author calls the
+
+ align:start position:0%
+reaching what if this author calls the
+ 
+
+ align:start position:0%
+reaching what if this author calls the
+slope of enlightenment where people
+
+ align:start position:0%
+slope of enlightenment where people
+ 
+
+ align:start position:0%
+slope of enlightenment where people
+realize that okay it's not really as bad
+
+ align:start position:0%
+realize that okay it's not really as bad
+ 
+
+ align:start position:0%
+realize that okay it's not really as bad
+as we thought it was when it didn't meet
+
+ align:start position:0%
+as we thought it was when it didn't meet
+ 
+
+ align:start position:0%
+as we thought it was when it didn't meet
+our lofty expectations and then
+
+ align:start position:0%
+our lofty expectations and then
+ 
+
+ align:start position:0%
+our lofty expectations and then
+gradually if it's successful then you
+
+ align:start position:0%
+gradually if it's successful then you
+ 
+
+ align:start position:0%
+gradually if it's successful then you
+get multiple generations of the product
+
+ align:start position:0%
+get multiple generations of the product
+ 
+
+ align:start position:0%
+get multiple generations of the product
+and it does achieve adoption the
+
+ align:start position:0%
+and it does achieve adoption the
+ 
+
+ align:start position:0%
+and it does achieve adoption the
+adoption almost never reaches the peak
+
+ align:start position:0%
+adoption almost never reaches the peak
+ 
+
+ align:start position:0%
+adoption almost never reaches the peak
+that it was expected to reach at the
+
+ align:start position:0%
+that it was expected to reach at the
+ 
+
+ align:start position:0%
+that it was expected to reach at the
+time of the the top of the hike cycle
+
+ align:start position:0%
+time of the the top of the hike cycle
+ 
+
+ align:start position:0%
+time of the the top of the hike cycle
+but it becomes useful becomes profitable
+
+ align:start position:0%
+but it becomes useful becomes profitable
+ 
+
+ align:start position:0%
+but it becomes useful becomes profitable
+it becomes productive now I've been
+
+ align:start position:0%
+it becomes productive now I've been
+ 
+
+ align:start position:0%
+it becomes productive now I've been
+around long enough to see a number of
+
+ align:start position:0%
+around long enough to see a number of
+ 
+
+ align:start position:0%
+around long enough to see a number of
+these cycles go by so in the 1980s for
+
+ align:start position:0%
+these cycles go by so in the 1980s for
+ 
+
+ align:start position:0%
+these cycles go by so in the 1980s for
+example at a time that was now jokingly
+
+ align:start position:0%
+example at a time that was now jokingly
+ 
+
+ align:start position:0%
+example at a time that was now jokingly
+referred to as a isomer where people
+
+ align:start position:0%
+referred to as a isomer where people
+ 
+
+ align:start position:0%
+referred to as a isomer where people
+were building expert systems and these
+
+ align:start position:0%
+were building expert systems and these
+ 
+
+ align:start position:0%
+were building expert systems and these
+expert systems were going to just
+
+ align:start position:0%
+expert systems were going to just
+ 
+
+ align:start position:0%
+expert systems were going to just
+revolutionize everything I remember
+
+ align:start position:0%
+revolutionize everything I remember
+ 
+
+ align:start position:0%
+revolutionize everything I remember
+going to a conference where the Campbell
+
+ align:start position:0%
+going to a conference where the Campbell
+ 
+
+ align:start position:0%
+going to a conference where the Campbell
+Soup Company had built an expert system
+
+ align:start position:0%
+Soup Company had built an expert system
+ 
+
+ align:start position:0%
+Soup Company had built an expert system
+that that was based on the expertise of
+
+ align:start position:0%
+that that was based on the expertise of
+ 
+
+ align:start position:0%
+that that was based on the expertise of
+some old-timers who were retiring and
+
+ align:start position:0%
+some old-timers who were retiring and
+ 
+
+ align:start position:0%
+some old-timers who were retiring and
+what this expert system did is it told
+
+ align:start position:0%
+what this expert system did is it told
+ 
+
+ align:start position:0%
+what this expert system did is it told
+you how to clean the vats of soup you
+
+ align:start position:0%
+you how to clean the vats of soup you
+ 
+
+ align:start position:0%
+you how to clean the vats of soup you
+know these giant million gallon things
+
+ align:start position:0%
+know these giant million gallon things
+ 
+
+ align:start position:0%
+know these giant million gallon things
+where they make sue
+
+ align:start position:0%
+where they make sue
+ 
+
+ align:start position:0%
+where they make sue
+when you're switching from making one
+
+ align:start position:0%
+when you're switching from making one
+ 
+
+ align:start position:0%
+when you're switching from making one
+kind of soup to another so you know if
+
+ align:start position:0%
+kind of soup to another so you know if
+ 
+
+ align:start position:0%
+kind of soup to another so you know if
+you're making beef consommé and you
+
+ align:start position:0%
+you're making beef consommé and you
+ 
+
+ align:start position:0%
+you're making beef consommé and you
+switch to making beef barley soup you
+
+ align:start position:0%
+switch to making beef barley soup you
+ 
+
+ align:start position:0%
+switch to making beef barley soup you
+don't need to clean the VAT at all
+
+ align:start position:0%
+don't need to clean the VAT at all
+ 
+
+ align:start position:0%
+don't need to clean the VAT at all
+whereas if you're switching from you
+
+ align:start position:0%
+whereas if you're switching from you
+ 
+
+ align:start position:0%
+whereas if you're switching from you
+know something like clam chowder to a
+
+ align:start position:0%
+know something like clam chowder to a
+ 
+
+ align:start position:0%
+know something like clam chowder to a
+consomme then you need to clean it
+
+ align:start position:0%
+consomme then you need to clean it
+ 
+
+ align:start position:0%
+consomme then you need to clean it
+really well and so this was exactly the
+
+ align:start position:0%
+really well and so this was exactly the
+ 
+
+ align:start position:0%
+really well and so this was exactly the
+kind of thing that they were doing and
+
+ align:start position:0%
+kind of thing that they were doing and
+ 
+
+ align:start position:0%
+kind of thing that they were doing and
+there were literally literally thousands
+
+ align:start position:0%
+there were literally literally thousands
+ 
+
+ align:start position:0%
+there were literally literally thousands
+of these applications being built and at
+
+ align:start position:0%
+of these applications being built and at
+ 
+
+ align:start position:0%
+of these applications being built and at
+the top of the hype cycle all kinds of
+
+ align:start position:0%
+the top of the hype cycle all kinds of
+ 
+
+ align:start position:0%
+the top of the hype cycle all kinds of
+companies like Campbell Soup and the
+
+ align:start position:0%
+companies like Campbell Soup and the
+ 
+
+ align:start position:0%
+companies like Campbell Soup and the
+airlines and everybody was investing
+
+ align:start position:0%
+airlines and everybody was investing
+ 
+
+ align:start position:0%
+airlines and everybody was investing
+huge amounts of money into this and then
+
+ align:start position:0%
+huge amounts of money into this and then
+ 
+
+ align:start position:0%
+huge amounts of money into this and then
+there was a kind of failure of
+
+ align:start position:0%
+there was a kind of failure of
+ 
+
+ align:start position:0%
+there was a kind of failure of
+expectations these didn't turn out to be
+
+ align:start position:0%
+expectations these didn't turn out to be
+ 
+
+ align:start position:0%
+expectations these didn't turn out to be
+as good as people thought they were
+
+ align:start position:0%
+as good as people thought they were
+ 
+
+ align:start position:0%
+as good as people thought they were
+going to be or as valuable as people
+
+ align:start position:0%
+going to be or as valuable as people
+ 
+
+ align:start position:0%
+going to be or as valuable as people
+thought they were going to be and then
+
+ align:start position:0%
+thought they were going to be and then
+ 
+
+ align:start position:0%
+thought they were going to be and then
+all of a sudden came AI winter so AI
+
+ align:start position:0%
+all of a sudden came AI winter so AI
+ 
+
+ align:start position:0%
+all of a sudden came AI winter so AI
+winter followed AI summer there was no
+
+ align:start position:0%
+winter followed AI summer there was no
+ 
+
+ align:start position:0%
+winter followed AI summer there was no
+AI fall except in a different sense of
+
+ align:start position:0%
+AI fall except in a different sense of
+ 
+
+ align:start position:0%
+AI fall except in a different sense of
+the word fall and and all of a sudden
+
+ align:start position:0%
+the word fall and and all of a sudden
+ 
+
+ align:start position:0%
+the word fall and and all of a sudden
+funding dried up and and the whole thing
+
+ align:start position:0%
+funding dried up and and the whole thing
+ 
+
+ align:start position:0%
+funding dried up and and the whole thing
+was declared a failure but in fact today
+
+ align:start position:0%
+was declared a failure but in fact today
+ 
+
+ align:start position:0%
+was declared a failure but in fact today
+if you go out there and you look at you
+
+ align:start position:0%
+if you go out there and you look at you
+ 
+
+ align:start position:0%
+if you go out there and you look at you
+know Microsoft Excel has an expert
+
+ align:start position:0%
+know Microsoft Excel has an expert
+ 
+
+ align:start position:0%
+know Microsoft Excel has an expert
+system based help system bundled inside
+
+ align:start position:0%
+system based help system bundled inside
+ 
+
+ align:start position:0%
+system based help system bundled inside
+it and there are tons of such
+
+ align:start position:0%
+it and there are tons of such
+ 
+
+ align:start position:0%
+it and there are tons of such
+applications it's just that now they're
+
+ align:start position:0%
+applications it's just that now they're
+ 
+
+ align:start position:0%
+applications it's just that now they're
+no longer considered cutting-edge
+
+ align:start position:0%
+no longer considered cutting-edge
+ 
+
+ align:start position:0%
+no longer considered cutting-edge
+applications of artificial intelligence
+
+ align:start position:0%
+applications of artificial intelligence
+ 
+
+ align:start position:0%
+applications of artificial intelligence
+they're simply considered you know
+
+ align:start position:0%
+they're simply considered you know
+ 
+
+ align:start position:0%
+they're simply considered you know
+routine practice so they they've become
+
+ align:start position:0%
+routine practice so they they've become
+ 
+
+ align:start position:0%
+routine practice so they they've become
+incorporated without the hype into all
+
+ align:start position:0%
+incorporated without the hype into all
+ 
+
+ align:start position:0%
+incorporated without the hype into all
+kinds of existing products and and
+
+ align:start position:0%
+kinds of existing products and and
+ 
+
+ align:start position:0%
+kinds of existing products and and
+they're serving a very useful role but
+
+ align:start position:0%
+they're serving a very useful role but
+ 
+
+ align:start position:0%
+they're serving a very useful role but
+they didn't make those venture capital
+
+ align:start position:0%
+they didn't make those venture capital
+ 
+
+ align:start position:0%
+they didn't make those venture capital
+firms the tons of money that they had
+
+ align:start position:0%
+firms the tons of money that they had
+ 
+
+ align:start position:0%
+firms the tons of money that they had
+hoped to make there was a similar boom
+
+ align:start position:0%
+hoped to make there was a similar boom
+ 
+
+ align:start position:0%
+hoped to make there was a similar boom
+and bust cycle in the 2000s around the
+
+ align:start position:0%
+and bust cycle in the 2000s around the
+ 
+
+ align:start position:0%
+and bust cycle in the 2000s around the
+creation of the world wide web and
+
+ align:start position:0%
+creation of the world wide web and
+ 
+
+ align:start position:0%
+creation of the world wide web and
+e-commerce
+
+ align:start position:0%
+e-commerce
+ 
+
+ align:start position:0%
+e-commerce
+okay so ecommerce again there was this
+
+ align:start position:0%
+okay so ecommerce again there was this
+ 
+
+ align:start position:0%
+okay so ecommerce again there was this
+unbelievably inflated set of
+
+ align:start position:0%
+unbelievably inflated set of
+ 
+
+ align:start position:0%
+unbelievably inflated set of
+expectations and then around the year
+
+ align:start position:0%
+expectations and then around the year
+ 
+
+ align:start position:0%
+expectations and then around the year
+2000 there was a
+
+ align:start position:0%
+2000 there was a
+ 
+
+ align:start position:0%
+2000 there was a
+big crash where all of a sudden you know
+
+ align:start position:0%
+big crash where all of a sudden you know
+ 
+
+ align:start position:0%
+big crash where all of a sudden you know
+people realized that the value in these
+
+ align:start position:0%
+people realized that the value in these
+ 
+
+ align:start position:0%
+people realized that the value in these
+applications was not as high as what
+
+ align:start position:0%
+applications was not as high as what
+ 
+
+ align:start position:0%
+applications was not as high as what
+they expected it to be nevertheless you
+
+ align:start position:0%
+they expected it to be nevertheless you
+ 
+
+ align:start position:0%
+they expected it to be nevertheless you
+know Amazon is doing just fine and there
+
+ align:start position:0%
+know Amazon is doing just fine and there
+ 
+
+ align:start position:0%
+know Amazon is doing just fine and there
+are plenty of online e-commerce sites
+
+ align:start position:0%
+are plenty of online e-commerce sites
+ 
+
+ align:start position:0%
+are plenty of online e-commerce sites
+that are in perfectly good operating
+
+ align:start position:0%
+that are in perfectly good operating
+ 
+
+ align:start position:0%
+that are in perfectly good operating
+order today and but it's no longer the
+
+ align:start position:0%
+order today and but it's no longer the
+ 
+
+ align:start position:0%
+order today and but it's no longer the
+same hype about this technology it's
+
+ align:start position:0%
+same hype about this technology it's
+ 
+
+ align:start position:0%
+same hype about this technology it's
+just become an accepted part of the way
+
+ align:start position:0%
+just become an accepted part of the way
+ 
+
+ align:start position:0%
+just become an accepted part of the way
+that you do business and almost
+
+ align:start position:0%
+that you do business and almost
+ 
+
+ align:start position:0%
+that you do business and almost
+everything yeah they were either rule
+
+ align:start position:0%
+everything yeah they were either rule
+ 
+
+ align:start position:0%
+everything yeah they were either rule
+based or pattern-matching systems there
+
+ align:start position:0%
+based or pattern-matching systems there
+ 
+
+ align:start position:0%
+based or pattern-matching systems there
+were two basic kinds I think a week from
+
+ align:start position:0%
+were two basic kinds I think a week from
+ 
+
+ align:start position:0%
+were two basic kinds I think a week from
+today I'm going to talk about some of
+
+ align:start position:0%
+today I'm going to talk about some of
+ 
+
+ align:start position:0%
+today I'm going to talk about some of
+that and how it relates to modern
+
+ align:start position:0%
+that and how it relates to modern
+ 
+
+ align:start position:0%
+that and how it relates to modern
+machine learning so we'll see some
+
+ align:start position:0%
+machine learning so we'll see some
+ 
+
+ align:start position:0%
+machine learning so we'll see some
+examples okay well a cautionary tale is
+
+ align:start position:0%
+examples okay well a cautionary tale is
+ 
+
+ align:start position:0%
+examples okay well a cautionary tale is
+is IBM's Watson health so I assume most
+
+ align:start position:0%
+is IBM's Watson health so I assume most
+ 
+
+ align:start position:0%
+is IBM's Watson health so I assume most
+of you remember when Watson hit the big
+
+ align:start position:0%
+of you remember when Watson hit the big
+ 
+
+ align:start position:0%
+of you remember when Watson hit the big
+time by beating the Jeopardy champions
+
+ align:start position:0%
+time by beating the Jeopardy champions
+ 
+
+ align:start position:0%
+time by beating the Jeopardy champions
+this was back in the early 2010's or
+
+ align:start position:0%
+this was back in the early 2010's or
+ 
+
+ align:start position:0%
+this was back in the early 2010's or
+something I don't remember exactly which
+
+ align:start position:0%
+something I don't remember exactly which
+ 
+
+ align:start position:0%
+something I don't remember exactly which
+year and they had in fact built a really
+
+ align:start position:0%
+year and they had in fact built a really
+ 
+
+ align:start position:0%
+year and they had in fact built a really
+impressive set of technologies that went
+
+ align:start position:0%
+impressive set of technologies that went
+ 
+
+ align:start position:0%
+impressive set of technologies that went
+out and read all kinds of online sources
+
+ align:start position:0%
+out and read all kinds of online sources
+ 
+
+ align:start position:0%
+out and read all kinds of online sources
+and distilled them into a kind of
+
+ align:start position:0%
+and distilled them into a kind of
+ 
+
+ align:start position:0%
+and distilled them into a kind of
+representation that they could very
+
+ align:start position:0%
+representation that they could very
+ 
+
+ align:start position:0%
+representation that they could very
+quickly look up things when they were
+
+ align:start position:0%
+quickly look up things when they were
+ 
+
+ align:start position:0%
+quickly look up things when they were
+challenged with the Jeopardy question
+
+ align:start position:0%
+challenged with the Jeopardy question
+ 
+
+ align:start position:0%
+challenged with the Jeopardy question
+and then it had a sophisticated set of
+
+ align:start position:0%
+and then it had a sophisticated set of
+ 
+
+ align:start position:0%
+and then it had a sophisticated set of
+algorithms that would try to find the
+
+ align:start position:0%
+algorithms that would try to find the
+ 
+
+ align:start position:0%
+algorithms that would try to find the
+best answer for some question and they
+
+ align:start position:0%
+best answer for some question and they
+ 
+
+ align:start position:0%
+best answer for some question and they
+even had all kinds of bizarre
+
+ align:start position:0%
+even had all kinds of bizarre
+ 
+
+ align:start position:0%
+even had all kinds of bizarre
+special-purpose things I remember there
+
+ align:start position:0%
+special-purpose things I remember there
+ 
+
+ align:start position:0%
+special-purpose things I remember there
+was a probabilistic model that figured
+
+ align:start position:0%
+was a probabilistic model that figured
+ 
+
+ align:start position:0%
+was a probabilistic model that figured
+out where the Daily Double
+
+ align:start position:0%
+out where the Daily Double
+ 
+
+ align:start position:0%
+out where the Daily Double
+squares were most likely to be on the
+
+ align:start position:0%
+squares were most likely to be on the
+ 
+
+ align:start position:0%
+squares were most likely to be on the
+Jeopardy board and then they did a
+
+ align:start position:0%
+Jeopardy board and then they did a
+ 
+
+ align:start position:0%
+Jeopardy board and then they did a
+utility theoretic calculation to figure
+
+ align:start position:0%
+utility theoretic calculation to figure
+ 
+
+ align:start position:0%
+utility theoretic calculation to figure
+out if they did hit the Daily Double
+
+ align:start position:0%
+out if they did hit the Daily Double
+ 
+
+ align:start position:0%
+out if they did hit the Daily Double
+what was the optimum amount of money to
+
+ align:start position:0%
+what was the optimum amount of money to
+ 
+
+ align:start position:0%
+what was the optimum amount of money to
+bet based on on the machines performance
+
+ align:start position:0%
+bet based on on the machines performance
+ 
+
+ align:start position:0%
+bet based on on the machines performance
+in order to optimize
+
+ align:start position:0%
+in order to optimize
+ 
+
+ align:start position:0%
+in order to optimize
+they decided that humans typically don't
+
+ align:start position:0%
+they decided that humans typically don't
+ 
+
+ align:start position:0%
+they decided that humans typically don't
+bet enough when they have a chance in on
+
+ align:start position:0%
+bet enough when they have a chance in on
+ 
+
+ align:start position:0%
+bet enough when they have a chance in on
+The Daily Double
+
+ align:start position:0%
+The Daily Double
+ 
+
+ align:start position:0%
+The Daily Double
+so there was a lot of very special
+
+ align:start position:0%
+so there was a lot of very special
+ 
+
+ align:start position:0%
+so there was a lot of very special
+purpose stuff done for this so this was
+
+ align:start position:0%
+purpose stuff done for this so this was
+ 
+
+ align:start position:0%
+purpose stuff done for this so this was
+a huge publicity bonanza and IBM decided
+
+ align:start position:0%
+a huge publicity bonanza and IBM decided
+ 
+
+ align:start position:0%
+a huge publicity bonanza and IBM decided
+that next they were going to tackle
+
+ align:start position:0%
+that next they were going to tackle
+ 
+
+ align:start position:0%
+that next they were going to tackle
+medicine and so they were going to take
+
+ align:start position:0%
+medicine and so they were going to take
+ 
+
+ align:start position:0%
+medicine and so they were going to take
+this technology and apply it to medicine
+
+ align:start position:0%
+this technology and apply it to medicine
+ 
+
+ align:start position:0%
+this technology and apply it to medicine
+they were going to read all of the
+
+ align:start position:0%
+they were going to read all of the
+ 
+
+ align:start position:0%
+they were going to read all of the
+medical journals and all of the medical
+
+ align:start position:0%
+medical journals and all of the medical
+ 
+
+ align:start position:0%
+medical journals and all of the medical
+electronic medical records that they
+
+ align:start position:0%
+electronic medical records that they
+ 
+
+ align:start position:0%
+electronic medical records that they
+could get their hands on and somehow
+
+ align:start position:0%
+could get their hands on and somehow
+ 
+
+ align:start position:0%
+could get their hands on and somehow
+this technology would again distill the
+
+ align:start position:0%
+this technology would again distill the
+ 
+
+ align:start position:0%
+this technology would again distill the
+right information so that they could
+
+ align:start position:0%
+right information so that they could
+ 
+
+ align:start position:0%
+right information so that they could
+answer questions like a Jeopardy
+
+ align:start position:0%
+answer questions like a Jeopardy
+ 
+
+ align:start position:0%
+answer questions like a Jeopardy
+question except not stated in its funny
+
+ align:start position:0%
+question except not stated in its funny
+ 
+
+ align:start position:0%
+question except not stated in its funny
+backward way where you might say okay
+
+ align:start position:0%
+backward way where you might say okay
+ 
+
+ align:start position:0%
+backward way where you might say okay
+for this patient what is the optimum
+
+ align:start position:0%
+for this patient what is the optimum
+ 
+
+ align:start position:0%
+for this patient what is the optimum
+therapy and it would go out and use the
+
+ align:start position:0%
+therapy and it would go out and use the
+ 
+
+ align:start position:0%
+therapy and it would go out and use the
+same technology to figure that out now
+
+ align:start position:0%
+same technology to figure that out now
+ 
+
+ align:start position:0%
+same technology to figure that out now
+that was a perfectly reasonable thing to
+
+ align:start position:0%
+that was a perfectly reasonable thing to
+ 
+
+ align:start position:0%
+that was a perfectly reasonable thing to
+try the the problem they ran into was
+
+ align:start position:0%
+try the the problem they ran into was
+ 
+
+ align:start position:0%
+try the the problem they ran into was
+this hype cycle that the people who made
+
+ align:start position:0%
+this hype cycle that the people who made
+ 
+
+ align:start position:0%
+this hype cycle that the people who made
+this publicly known were their marketing
+
+ align:start position:0%
+this publicly known were their marketing
+ 
+
+ align:start position:0%
+this publicly known were their marketing
+people and not their technical people
+
+ align:start position:0%
+people and not their technical people
+ 
+
+ align:start position:0%
+people and not their technical people
+and the marketing people over-promised
+
+ align:start position:0%
+and the marketing people over-promised
+ 
+
+ align:start position:0%
+and the marketing people over-promised
+like crazy okay they said surely this is
+
+ align:start position:0%
+like crazy okay they said surely this is
+ 
+
+ align:start position:0%
+like crazy okay they said surely this is
+just gonna solve all these problems and
+
+ align:start position:0%
+just gonna solve all these problems and
+ 
+
+ align:start position:0%
+just gonna solve all these problems and
+we won't need any more research in this
+
+ align:start position:0%
+we won't need any more research in this
+ 
+
+ align:start position:0%
+we won't need any more research in this
+area because man we got it III mean I'm
+
+ align:start position:0%
+area because man we got it III mean I'm
+ 
+
+ align:start position:0%
+area because man we got it III mean I'm
+overstating it even from the marketing
+
+ align:start position:0%
+overstating it even from the marketing
+ 
+
+ align:start position:0%
+overstating it even from the marketing
+point of view and so Watson for oncology
+
+ align:start position:0%
+point of view and so Watson for oncology
+ 
+
+ align:start position:0%
+point of view and so Watson for oncology
+used this cloud-based supercomputer to
+
+ align:start position:0%
+used this cloud-based supercomputer to
+ 
+
+ align:start position:0%
+used this cloud-based supercomputer to
+digest massive amounts of data and and
+
+ align:start position:0%
+digest massive amounts of data and and
+ 
+
+ align:start position:0%
+digest massive amounts of data and and
+that data included all kinds of
+
+ align:start position:0%
+that data included all kinds of
+ 
+
+ align:start position:0%
+that data included all kinds of
+different different things so I'm gonna
+
+ align:start position:0%
+different different things so I'm gonna
+ 
+
+ align:start position:0%
+different different things so I'm gonna
+go into a little bit of detail about
+
+ align:start position:0%
+go into a little bit of detail about
+ 
+
+ align:start position:0%
+go into a little bit of detail about
+what some of their problems were this is
+
+ align:start position:0%
+what some of their problems were this is
+ 
+
+ align:start position:0%
+what some of their problems were this is
+from an article in in this this journal
+
+ align:start position:0%
+from an article in in this this journal
+ 
+
+ align:start position:0%
+from an article in in this this journal
+stat news which did an investigative
+
+ align:start position:0%
+stat news which did an investigative
+ 
+
+ align:start position:0%
+stat news which did an investigative
+piece on on what happened with Watson
+
+ align:start position:0%
+piece on on what happened with Watson
+ 
+
+ align:start position:0%
+piece on on what happened with Watson
+and so you know they say what I just
+
+ align:start position:0%
+and so you know they say what I just
+ 
+
+ align:start position:0%
+and so you know they say what I just
+said breathlessly promoting its
+
+ align:start position:0%
+said breathlessly promoting its
+ 
+
+ align:start position:0%
+said breathlessly promoting its
+signature brands IBM sought to capture
+
+ align:start position:0%
+signature brands IBM sought to capture
+ 
+
+ align:start position:0%
+signature brands IBM sought to capture
+the world's imagination and quickly
+
+ align:start position:0%
+the world's imagination and quickly
+ 
+
+ align:start position:0%
+the world's imagination and quickly
+zeroed in on a high-profile target which
+
+ align:start position:0%
+zeroed in on a high-profile target which
+ 
+
+ align:start position:0%
+zeroed in on a high-profile target which
+cancer so this was gonna solve the
+
+ align:start position:0%
+cancer so this was gonna solve the
+ 
+
+ align:start position:0%
+cancer so this was gonna solve the
+problem of some patient shows up is
+
+ align:start position:0%
+problem of some patient shows up is
+ 
+
+ align:start position:0%
+problem of some patient shows up is
+diagnosed with cancer and you want to
+
+ align:start position:0%
+diagnosed with cancer and you want to
+ 
+
+ align:start position:0%
+diagnosed with cancer and you want to
+know how to treat this person so this
+
+ align:start position:0%
+know how to treat this person so this
+ 
+
+ align:start position:0%
+know how to treat this person so this
+would use all of the literature and all
+
+ align:start position:0%
+would use all of the literature and all
+ 
+
+ align:start position:0%
+would use all of the literature and all
+of everything that it had gathered from
+
+ align:start position:0%
+of everything that it had gathered from
+ 
+
+ align:start position:0%
+of everything that it had gathered from
+previous treatments of previous patients
+
+ align:start position:0%
+previous treatments of previous patients
+ 
+
+ align:start position:0%
+previous treatments of previous patients
+and it would give you the optimal
+
+ align:start position:0%
+and it would give you the optimal
+ 
+
+ align:start position:0%
+and it would give you the optimal
+solution now it has not been a success
+
+ align:start position:0%
+solution now it has not been a success
+ 
+
+ align:start position:0%
+solution now it has not been a success
+there were a few dozen hospitals that
+
+ align:start position:0%
+there were a few dozen hospitals that
+ 
+
+ align:start position:0%
+there were a few dozen hospitals that
+have adopted the system very few of them
+
+ align:start position:0%
+have adopted the system very few of them
+ 
+
+ align:start position:0%
+have adopted the system very few of them
+in the United States more of them abroad
+
+ align:start position:0%
+in the United States more of them abroad
+ 
+
+ align:start position:0%
+in the United States more of them abroad
+and the foreigners complained that its
+
+ align:start position:0%
+and the foreigners complained that its
+ 
+
+ align:start position:0%
+and the foreigners complained that its
+advice is biased toward American
+
+ align:start position:0%
+advice is biased toward American
+ 
+
+ align:start position:0%
+advice is biased toward American
+patients and American approaches to me
+
+ align:start position:0%
+patients and American approaches to me
+ 
+
+ align:start position:0%
+patients and American approaches to me
+the biggest problem is that they haven't
+
+ align:start position:0%
+the biggest problem is that they haven't
+ 
+
+ align:start position:0%
+the biggest problem is that they haven't
+actually published anything that
+
+ align:start position:0%
+actually published anything that
+ 
+
+ align:start position:0%
+actually published anything that
+validates in a scientific sense that
+
+ align:start position:0%
+validates in a scientific sense that
+ 
+
+ align:start position:0%
+validates in a scientific sense that
+this is a good idea that it's getting
+
+ align:start position:0%
+this is a good idea that it's getting
+ 
+
+ align:start position:0%
+this is a good idea that it's getting
+the right answers and my guess is the
+
+ align:start position:0%
+the right answers and my guess is the
+ 
+
+ align:start position:0%
+the right answers and my guess is the
+reason for this is because it's not
+
+ align:start position:0%
+reason for this is because it's not
+ 
+
+ align:start position:0%
+reason for this is because it's not
+getting the right answers a lot of the
+
+ align:start position:0%
+getting the right answers a lot of the
+ 
+
+ align:start position:0%
+getting the right answers a lot of the
+time but that doesn't prevent marketing
+
+ align:start position:0%
+time but that doesn't prevent marketing
+ 
+
+ align:start position:0%
+time but that doesn't prevent marketing
+from from selling it the other problem
+
+ align:start position:0%
+from from selling it the other problem
+ 
+
+ align:start position:0%
+from from selling it the other problem
+is that they made a deal with Memorial
+
+ align:start position:0%
+is that they made a deal with Memorial
+ 
+
+ align:start position:0%
+is that they made a deal with Memorial
+sloan-kettering which is one of the
+
+ align:start position:0%
+sloan-kettering which is one of the
+ 
+
+ align:start position:0%
+sloan-kettering which is one of the
+leading cancer hospitals in the country
+
+ align:start position:0%
+leading cancer hospitals in the country
+ 
+
+ align:start position:0%
+leading cancer hospitals in the country
+to say we're gonna work with you guys
+
+ align:start position:0%
+to say we're gonna work with you guys
+ 
+
+ align:start position:0%
+to say we're gonna work with you guys
+and and your oncologists in order to
+
+ align:start position:0%
+and and your oncologists in order to
+ 
+
+ align:start position:0%
+and and your oncologists in order to
+figure out what really is the right
+
+ align:start position:0%
+figure out what really is the right
+ 
+
+ align:start position:0%
+figure out what really is the right
+answer and so I think they tried to do
+
+ align:start position:0%
+answer and so I think they tried to do
+ 
+
+ align:start position:0%
+answer and so I think they tried to do
+what their marketing says that they're
+
+ align:start position:0%
+what their marketing says that they're
+ 
+
+ align:start position:0%
+what their marketing says that they're
+doing which is to really derive the
+
+ align:start position:0%
+doing which is to really derive the
+ 
+
+ align:start position:0%
+doing which is to really derive the
+right answer from reading all of the
+
+ align:start position:0%
+right answer from reading all of the
+ 
+
+ align:start position:0%
+right answer from reading all of the
+literature and looking at past cases but
+
+ align:start position:0%
+literature and looking at past cases but
+ 
+
+ align:start position:0%
+literature and looking at past cases but
+I don't think that worked well enough
+
+ align:start position:0%
+I don't think that worked well enough
+ 
+
+ align:start position:0%
+I don't think that worked well enough
+and so what they wound up doing is
+
+ align:start position:0%
+and so what they wound up doing is
+ 
+
+ align:start position:0%
+and so what they wound up doing is
+turning to real oncologists saying what
+
+ align:start position:0%
+turning to real oncologists saying what
+ 
+
+ align:start position:0%
+turning to real oncologists saying what
+would you do under these circumstances
+
+ align:start position:0%
+would you do under these circumstances
+ 
+
+ align:start position:0%
+would you do under these circumstances
+and so what they wound up building is
+
+ align:start position:0%
+and so what they wound up building is
+ 
+
+ align:start position:0%
+and so what they wound up building is
+something like a rule based system that
+
+ align:start position:0%
+something like a rule based system that
+ 
+
+ align:start position:0%
+something like a rule based system that
+says if you see the following symptoms
+
+ align:start position:0%
+says if you see the following symptoms
+ 
+
+ align:start position:0%
+says if you see the following symptoms
+and you have the following genetic
+
+ align:start position:0%
+and you have the following genetic
+ 
+
+ align:start position:0%
+and you have the following genetic
+defects then this is the right treatment
+
+ align:start position:0%
+defects then this is the right treatment
+ 
+
+ align:start position:0%
+defects then this is the right treatment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so the promise that this was going
+
+ align:start position:0%
+and so the promise that this was going
+ 
+
+ align:start position:0%
+and so the promise that this was going
+to be a machine learning system that
+
+ align:start position:0%
+to be a machine learning system that
+ 
+
+ align:start position:0%
+to be a machine learning system that
+revolutionized cancer care by finding
+
+ align:start position:0%
+revolutionized cancer care by finding
+ 
+
+ align:start position:0%
+revolutionized cancer care by finding
+the optimal treatment really is not what
+
+ align:start position:0%
+the optimal treatment really is not what
+ 
+
+ align:start position:0%
+the optimal treatment really is not what
+they what they provided and as the
+
+ align:start position:0%
+they what they provided and as the
+ 
+
+ align:start position:0%
+they what they provided and as the
+article says the system doesn't really
+
+ align:start position:0%
+article says the system doesn't really
+ 
+
+ align:start position:0%
+article says the system doesn't really
+create new knowledge
+
+ align:start position:0%
+create new knowledge
+ 
+
+ align:start position:0%
+create new knowledge
+and so it's AI only in the sense of
+
+ align:start position:0%
+and so it's AI only in the sense of
+ 
+
+ align:start position:0%
+and so it's AI only in the sense of
+providing a search engine that when it
+
+ align:start position:0%
+providing a search engine that when it
+ 
+
+ align:start position:0%
+providing a search engine that when it
+makes a recommendation can point you to
+
+ align:start position:0%
+makes a recommendation can point you to
+ 
+
+ align:start position:0%
+makes a recommendation can point you to
+articles that are a reasonable
+
+ align:start position:0%
+articles that are a reasonable
+ 
+
+ align:start position:0%
+articles that are a reasonable
+reflection of what it's recommending
+
+ align:start position:0%
+reflection of what it's recommending
+ 
+
+ align:start position:0%
+reflection of what it's recommending
+well I'm gonna stop going through this
+
+ align:start position:0%
+well I'm gonna stop going through this
+ 
+
+ align:start position:0%
+well I'm gonna stop going through this
+litany but you'll see it in in the
+
+ align:start position:0%
+litany but you'll see it in in the
+ 
+
+ align:start position:0%
+litany but you'll see it in in the
+slides which we'll post they had a big
+
+ align:start position:0%
+slides which we'll post they had a big
+ 
+
+ align:start position:0%
+slides which we'll post they had a big
+contract with MD Anderson which is
+
+ align:start position:0%
+contract with MD Anderson which is
+ 
+
+ align:start position:0%
+contract with MD Anderson which is
+another leading Cancer Center in the
+
+ align:start position:0%
+another leading Cancer Center in the
+ 
+
+ align:start position:0%
+another leading Cancer Center in the
+United States and the Anderson spent
+
+ align:start position:0%
+United States and the Anderson spent
+ 
+
+ align:start position:0%
+United States and the Anderson spent
+about sixty million dollars on this
+
+ align:start position:0%
+about sixty million dollars on this
+ 
+
+ align:start position:0%
+about sixty million dollars on this
+contract implementing it and they pulled
+
+ align:start position:0%
+contract implementing it and they pulled
+ 
+
+ align:start position:0%
+contract implementing it and they pulled
+the plug on it because they decided that
+
+ align:start position:0%
+the plug on it because they decided that
+ 
+
+ align:start position:0%
+the plug on it because they decided that
+it just wasn't wasn't doing the job now
+
+ align:start position:0%
+it just wasn't wasn't doing the job now
+ 
+
+ align:start position:0%
+it just wasn't wasn't doing the job now
+by contrast there was a much more
+
+ align:start position:0%
+by contrast there was a much more
+ 
+
+ align:start position:0%
+by contrast there was a much more
+successful attempt years ago which was
+
+ align:start position:0%
+successful attempt years ago which was
+ 
+
+ align:start position:0%
+successful attempt years ago which was
+less driven by marketing and more driven
+
+ align:start position:0%
+less driven by marketing and more driven
+ 
+
+ align:start position:0%
+less driven by marketing and more driven
+by medical need and the idea here was
+
+ align:start position:0%
+by medical need and the idea here was
+ 
+
+ align:start position:0%
+by medical need and the idea here was
+CPOE stands for computerized physician
+
+ align:start position:0%
+CPOE stands for computerized physician
+ 
+
+ align:start position:0%
+CPOE stands for computerized physician
+order entry
+
+ align:start position:0%
+order entry
+ 
+
+ align:start position:0%
+order entry
+the idea behind CPOE was that if you
+
+ align:start position:0%
+the idea behind CPOE was that if you
+ 
+
+ align:start position:0%
+the idea behind CPOE was that if you
+want to affect the behavior of
+
+ align:start position:0%
+want to affect the behavior of
+ 
+
+ align:start position:0%
+want to affect the behavior of
+clinicians in ordering tests or drugs or
+
+ align:start position:0%
+clinicians in ordering tests or drugs or
+ 
+
+ align:start position:0%
+clinicians in ordering tests or drugs or
+procedures what you want to do is to
+
+ align:start position:0%
+procedures what you want to do is to
+ 
+
+ align:start position:0%
+procedures what you want to do is to
+make sure that they are interacting with
+
+ align:start position:0%
+make sure that they are interacting with
+ 
+
+ align:start position:0%
+make sure that they are interacting with
+the computer so that when they order for
+
+ align:start position:0%
+the computer so that when they order for
+ 
+
+ align:start position:0%
+the computer so that when they order for
+example some insanely expensive drug the
+
+ align:start position:0%
+example some insanely expensive drug the
+ 
+
+ align:start position:0%
+example some insanely expensive drug the
+system can come back and say hey do you
+
+ align:start position:0%
+system can come back and say hey do you
+ 
+
+ align:start position:0%
+system can come back and say hey do you
+realize that there's a drug that costs
+
+ align:start position:0%
+realize that there's a drug that costs
+ 
+
+ align:start position:0%
+realize that there's a drug that costs
+1/100 as much which according to the
+
+ align:start position:0%
+1/100 as much which according to the
+ 
+
+ align:start position:0%
+1/100 as much which according to the
+clinical trials that we have on record
+
+ align:start position:0%
+clinical trials that we have on record
+ 
+
+ align:start position:0%
+clinical trials that we have on record
+is just as effective as the one that
+
+ align:start position:0%
+is just as effective as the one that
+ 
+
+ align:start position:0%
+is just as effective as the one that
+you've ordered and so for example here
+
+ align:start position:0%
+you've ordered and so for example here
+ 
+
+ align:start position:0%
+you've ordered and so for example here
+at the Beth Israel many years ago they
+
+ align:start position:0%
+at the Beth Israel many years ago they
+ 
+
+ align:start position:0%
+at the Beth Israel many years ago they
+implemented a system like that and in
+
+ align:start position:0%
+implemented a system like that and in
+ 
+
+ align:start position:0%
+implemented a system like that and in
+the first year they showed that they
+
+ align:start position:0%
+the first year they showed that they
+ 
+
+ align:start position:0%
+the first year they showed that they
+saved something like 16 million dollars
+
+ align:start position:0%
+saved something like 16 million dollars
+ 
+
+ align:start position:0%
+saved something like 16 million dollars
+in the pharmacy just by ordering cheaper
+
+ align:start position:0%
+in the pharmacy just by ordering cheaper
+ 
+
+ align:start position:0%
+in the pharmacy just by ordering cheaper
+variants of drugs that could have been
+
+ align:start position:0%
+variants of drugs that could have been
+ 
+
+ align:start position:0%
+variants of drugs that could have been
+very expensive and they also found that
+
+ align:start position:0%
+very expensive and they also found that
+ 
+
+ align:start position:0%
+very expensive and they also found that
+the doctors who were doing the ordering
+
+ align:start position:0%
+the doctors who were doing the ordering
+ 
+
+ align:start position:0%
+the doctors who were doing the ordering
+were perfectly satisfied with that
+
+ align:start position:0%
+were perfectly satisfied with that
+ 
+
+ align:start position:0%
+were perfectly satisfied with that
+because they just didn't know how
+
+ align:start position:0%
+because they just didn't know how
+ 
+
+ align:start position:0%
+because they just didn't know how
+expensive these drugs were you know
+
+ align:start position:0%
+expensive these drugs were you know
+ 
+
+ align:start position:0%
+expensive these drugs were you know
+that's not one of the things that they
+
+ align:start position:0%
+that's not one of the things that they
+ 
+
+ align:start position:0%
+that's not one of the things that they
+pay attention
+
+ align:start position:0%
+pay attention
+ 
+
+ align:start position:0%
+pay attention
+- so there are many applications like
+
+ align:start position:0%
+- so there are many applications like
+ 
+
+ align:start position:0%
+- so there are many applications like
+that that are driven by this and again
+
+ align:start position:0%
+that that are driven by this and again
+ 
+
+ align:start position:0%
+that that are driven by this and again
+here are some statistics you can reduce
+
+ align:start position:0%
+here are some statistics you can reduce
+ 
+
+ align:start position:0%
+here are some statistics you can reduce
+error rates by half you can reduce
+
+ align:start position:0%
+error rates by half you can reduce
+ 
+
+ align:start position:0%
+error rates by half you can reduce
+severe medication errors by 88% you can
+
+ align:start position:0%
+severe medication errors by 88% you can
+ 
+
+ align:start position:0%
+severe medication errors by 88% you can
+have a 70% reduction in antibiotic
+
+ align:start position:0%
+have a 70% reduction in antibiotic
+ 
+
+ align:start position:0%
+have a 70% reduction in antibiotic
+related adverse drug events you can
+
+ align:start position:0%
+related adverse drug events you can
+ 
+
+ align:start position:0%
+related adverse drug events you can
+reduce length of stay which is another
+
+ align:start position:0%
+reduce length of stay which is another
+ 
+
+ align:start position:0%
+reduce length of stay which is another
+big goal that people go after and at
+
+ align:start position:0%
+big goal that people go after and at
+ 
+
+ align:start position:0%
+big goal that people go after and at
+least if you're an optimist
+
+ align:start position:0%
+least if you're an optimist
+ 
+
+ align:start position:0%
+least if you're an optimist
+you can believe these extrapolations
+
+ align:start position:0%
+you can believe these extrapolations
+ 
+
+ align:start position:0%
+you can believe these extrapolations
+that say well we could prevent 3 million
+
+ align:start position:0%
+that say well we could prevent 3 million
+ 
+
+ align:start position:0%
+that say well we could prevent 3 million
+adverse drug events at big city
+
+ align:start position:0%
+adverse drug events at big city
+ 
+
+ align:start position:0%
+adverse drug events at big city
+hospitals in the United States if
+
+ align:start position:0%
+hospitals in the United States if
+ 
+
+ align:start position:0%
+hospitals in the United States if
+everybody used systems like this so the
+
+ align:start position:0%
+everybody used systems like this so the
+ 
+
+ align:start position:0%
+everybody used systems like this so the
+benefits are that it prompts with
+
+ align:start position:0%
+benefits are that it prompts with
+ 
+
+ align:start position:0%
+benefits are that it prompts with
+warnings against possible drug
+
+ align:start position:0%
+warnings against possible drug
+ 
+
+ align:start position:0%
+warnings against possible drug
+interactions allergies or overdoses
+
+ align:start position:0%
+interactions allergies or overdoses
+ 
+
+ align:start position:0%
+interactions allergies or overdoses
+it can be kept up to date by some sort
+
+ align:start position:0%
+it can be kept up to date by some sort
+ 
+
+ align:start position:0%
+it can be kept up to date by some sort
+of mechanism where people read the
+
+ align:start position:0%
+of mechanism where people read the
+ 
+
+ align:start position:0%
+of mechanism where people read the
+literature and keep updating the
+
+ align:start position:0%
+literature and keep updating the
+ 
+
+ align:start position:0%
+literature and keep updating the
+databases that this is driven from and
+
+ align:start position:0%
+databases that this is driven from and
+ 
+
+ align:start position:0%
+databases that this is driven from and
+you know it can do sort of mechanical
+
+ align:start position:0%
+you know it can do sort of mechanical
+ 
+
+ align:start position:0%
+you know it can do sort of mechanical
+things like eliminate confusion about
+
+ align:start position:0%
+things like eliminate confusion about
+ 
+
+ align:start position:0%
+things like eliminate confusion about
+drug names that sound similar stuff like
+
+ align:start position:0%
+drug names that sound similar stuff like
+ 
+
+ align:start position:0%
+drug names that sound similar stuff like
+that and so the Leapfrog Group which
+
+ align:start position:0%
+that and so the Leapfrog Group which
+ 
+
+ align:start position:0%
+that and so the Leapfrog Group which
+does a lot of meta analyses and studies
+
+ align:start position:0%
+does a lot of meta analyses and studies
+ 
+
+ align:start position:0%
+does a lot of meta analyses and studies
+of what's effective really is behind
+
+ align:start position:0%
+of what's effective really is behind
+ 
+
+ align:start position:0%
+of what's effective really is behind
+this and and pushing it very strongly
+
+ align:start position:0%
+this and and pushing it very strongly
+ 
+
+ align:start position:0%
+this and and pushing it very strongly
+potential future benefits of course are
+
+ align:start position:0%
+potential future benefits of course are
+ 
+
+ align:start position:0%
+potential future benefits of course are
+that if the kinds of machine learning
+
+ align:start position:0%
+that if the kinds of machine learning
+ 
+
+ align:start position:0%
+that if the kinds of machine learning
+techniques that we talked about become
+
+ align:start position:0%
+techniques that we talked about become
+ 
+
+ align:start position:0%
+techniques that we talked about become
+widely used then these systems can be
+
+ align:start position:0%
+widely used then these systems can be
+ 
+
+ align:start position:0%
+widely used then these systems can be
+updated automatically rather than by
+
+ align:start position:0%
+updated automatically rather than by
+ 
+
+ align:start position:0%
+updated automatically rather than by
+manual review and you can gain the
+
+ align:start position:0%
+manual review and you can gain the
+ 
+
+ align:start position:0%
+manual review and you can gain the
+advantages of immediate feedback as new
+
+ align:start position:0%
+advantages of immediate feedback as new
+ 
+
+ align:start position:0%
+advantages of immediate feedback as new
+information becomes available now the
+
+ align:start position:0%
+information becomes available now the
+ 
+
+ align:start position:0%
+information becomes available now the
+adoption of CPOE was recommended by the
+
+ align:start position:0%
+adoption of CPOE was recommended by the
+ 
+
+ align:start position:0%
+adoption of CPOE was recommended by the
+National Academy of Medicine they wanted
+
+ align:start position:0%
+National Academy of Medicine they wanted
+ 
+
+ align:start position:0%
+National Academy of Medicine they wanted
+every hospital to use this by by 1999
+
+ align:start position:0%
+every hospital to use this by by 1999
+ 
+
+ align:start position:0%
+every hospital to use this by by 1999
+and of course it hasn't happens
+
+ align:start position:0%
+and of course it hasn't happens
+ 
+
+ align:start position:0%
+and of course it hasn't happens
+I couldn't find current data but 2014
+
+ align:start position:0%
+I couldn't find current data but 2014
+ 
+
+ align:start position:0%
+I couldn't find current data but 2014
+data shows that CPOE for example for
+
+ align:start position:0%
+data shows that CPOE for example for
+ 
+
+ align:start position:0%
+data shows that CPOE for example for
+medication orders is only being used in
+
+ align:start position:0%
+medication orders is only being used in
+ 
+
+ align:start position:0%
+medication orders is only being used in
+about 25 percent of the hospitals and at
+
+ align:start position:0%
+about 25 percent of the hospitals and at
+ 
+
+ align:start position:0%
+about 25 percent of the hospitals and at
+that time people were extrapolating and
+
+ align:start position:0%
+that time people were extrapolating and
+ 
+
+ align:start position:0%
+that time people were extrapolating and
+saying well it's not going to reach 80
+
+ align:start position:0%
+saying well it's not going to reach 80
+ 
+
+ align:start position:0%
+saying well it's not going to reach 80
+percent penetration until the Year 2029
+
+ align:start position:0%
+percent penetration until the Year 2029
+ 
+
+ align:start position:0%
+percent penetration until the Year 2029
+so it's a very slow adoption cycle right
+
+ align:start position:0%
+so it's a very slow adoption cycle right
+ 
+
+ align:start position:0%
+so it's a very slow adoption cycle right
+maybe it's gotten better the other
+
+ align:start position:0%
+maybe it's gotten better the other
+ 
+
+ align:start position:0%
+maybe it's gotten better the other
+problem and one of the reasons for
+
+ align:start position:0%
+problem and one of the reasons for
+ 
+
+ align:start position:0%
+problem and one of the reasons for
+resistance is that it puts additional
+
+ align:start position:0%
+resistance is that it puts additional
+ 
+
+ align:start position:0%
+resistance is that it puts additional
+stresses on people so for example this
+
+ align:start position:0%
+stresses on people so for example this
+ 
+
+ align:start position:0%
+stresses on people so for example this
+is a study of how pharmacists spend
+
+ align:start position:0%
+is a study of how pharmacists spend
+ 
+
+ align:start position:0%
+is a study of how pharmacists spend
+their time and so clinical clinical time
+
+ align:start position:0%
+their time and so clinical clinical time
+ 
+
+ align:start position:0%
+their time and so clinical clinical time
+is useful that's when they're consulting
+
+ align:start position:0%
+is useful that's when they're consulting
+ 
+
+ align:start position:0%
+is useful that's when they're consulting
+with doctors helping them figure out
+
+ align:start position:0%
+with doctors helping them figure out
+ 
+
+ align:start position:0%
+with doctors helping them figure out
+appropriate dosage for patients or
+
+ align:start position:0%
+appropriate dosage for patients or
+ 
+
+ align:start position:0%
+appropriate dosage for patients or
+they're talking to patients explaining
+
+ align:start position:0%
+they're talking to patients explaining
+ 
+
+ align:start position:0%
+they're talking to patients explaining
+to them how to take their medications
+
+ align:start position:0%
+to them how to take their medications
+ 
+
+ align:start position:0%
+to them how to take their medications
+what side effects to watch out for etc
+
+ align:start position:0%
+what side effects to watch out for etc
+ 
+
+ align:start position:0%
+what side effects to watch out for etc
+these distributive tasks it's a funny
+
+ align:start position:0%
+these distributive tasks it's a funny
+ 
+
+ align:start position:0%
+these distributive tasks it's a funny
+term mean the non clinical part of what
+
+ align:start position:0%
+term mean the non clinical part of what
+ 
+
+ align:start position:0%
+term mean the non clinical part of what
+they're doing and what you see is that
+
+ align:start position:0%
+they're doing and what you see is that
+ 
+
+ align:start position:0%
+they're doing and what you see is that
+hospitals that have adopted CPOE they
+
+ align:start position:0%
+hospitals that have adopted CPOE they
+ 
+
+ align:start position:0%
+hospitals that have adopted CPOE they
+wind up spending a little bit more time
+
+ align:start position:0%
+wind up spending a little bit more time
+ 
+
+ align:start position:0%
+wind up spending a little bit more time
+on the distributive tasks and a little
+
+ align:start position:0%
+on the distributive tasks and a little
+ 
+
+ align:start position:0%
+on the distributive tasks and a little
+bit less time on the clinical tasks
+
+ align:start position:0%
+bit less time on the clinical tasks
+ 
+
+ align:start position:0%
+bit less time on the clinical tasks
+which is probably not in the right
+
+ align:start position:0%
+which is probably not in the right
+ 
+
+ align:start position:0%
+which is probably not in the right
+direction in terms of what the
+
+ align:start position:0%
+direction in terms of what the
+ 
+
+ align:start position:0%
+direction in terms of what the
+pharmacists were hoping for out of
+
+ align:start position:0%
+pharmacists were hoping for out of
+ 
+
+ align:start position:0%
+pharmacists were hoping for out of
+systems like this now people have
+
+ align:start position:0%
+systems like this now people have
+ 
+
+ align:start position:0%
+systems like this now people have
+studied the diffusion of new medical
+
+ align:start position:0%
+studied the diffusion of new medical
+ 
+
+ align:start position:0%
+studied the diffusion of new medical
+technologies and I think I'll just show
+
+ align:start position:0%
+technologies and I think I'll just show
+ 
+
+ align:start position:0%
+technologies and I think I'll just show
+you the graph so this is this is in
+
+ align:start position:0%
+you the graph so this is this is in
+ 
+
+ align:start position:0%
+you the graph so this is this is in
+England but this is the adoption for
+
+ align:start position:0%
+England but this is the adoption for
+ 
+
+ align:start position:0%
+England but this is the adoption for
+statins so from the time they were
+
+ align:start position:0%
+statins so from the time they were
+ 
+
+ align:start position:0%
+statins so from the time they were
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+statins is a drug that keeps your
+
+ align:start position:0%
+statins is a drug that keeps your
+ 
+
+ align:start position:0%
+statins is a drug that keeps your
+cholesterol low from the time they were
+
+ align:start position:0%
+cholesterol low from the time they were
+ 
+
+ align:start position:0%
+cholesterol low from the time they were
+introduced until they were being used
+
+ align:start position:0%
+introduced until they were being used
+ 
+
+ align:start position:0%
+introduced until they were being used
+essentially at a hundred percent of
+
+ align:start position:0%
+essentially at a hundred percent of
+ 
+
+ align:start position:0%
+essentially at a hundred percent of
+places was about five and a half six
+
+ align:start position:0%
+places was about five and a half six
+ 
+
+ align:start position:0%
+places was about five and a half six
+years okay
+
+ align:start position:0%
+years okay
+ 
+
+ align:start position:0%
+years okay
+so reasonably fast if you look at the
+
+ align:start position:0%
+so reasonably fast if you look at the
+ 
+
+ align:start position:0%
+so reasonably fast if you look at the
+adoption of magnetic resonance imaging
+
+ align:start position:0%
+adoption of magnetic resonance imaging
+ 
+
+ align:start position:0%
+adoption of magnetic resonance imaging
+technology
+
+ align:start position:0%
+technology
+ 
+
+ align:start position:0%
+technology
+it took five years for it to have any
+
+ align:start position:0%
+it took five years for it to have any
+ 
+
+ align:start position:0%
+it took five years for it to have any
+adoption whatsoever and that's because
+
+ align:start position:0%
+adoption whatsoever and that's because
+ 
+
+ align:start position:0%
+adoption whatsoever and that's because
+it was insanely expensive and so there
+
+ align:start position:0%
+it was insanely expensive and so there
+ 
+
+ align:start position:0%
+it was insanely expensive and so there
+were all kinds of limitations you know
+
+ align:start position:0%
+were all kinds of limitations you know
+ 
+
+ align:start position:0%
+were all kinds of limitations you know
+even in Massachusetts you had to get
+
+ align:start position:0%
+even in Massachusetts you had to get
+ 
+
+ align:start position:0%
+even in Massachusetts you had to get
+permission from some state committee to
+
+ align:start position:0%
+permission from some state committee to
+ 
+
+ align:start position:0%
+permission from some state committee to
+buy a new MRI machine and if another
+
+ align:start position:0%
+buy a new MRI machine and if another
+ 
+
+ align:start position:0%
+buy a new MRI machine and if another
+hospital in your town already had one
+
+ align:start position:0%
+hospital in your town already had one
+ 
+
+ align:start position:0%
+hospital in your town already had one
+then they would say well you shouldn't
+
+ align:start position:0%
+then they would say well you shouldn't
+ 
+
+ align:start position:0%
+then they would say well you shouldn't
+buy one because you should be able to
+
+ align:start position:0%
+buy one because you should be able to
+ 
+
+ align:start position:0%
+buy one because you should be able to
+use this other hospitals MRI machine
+
+ align:start position:0%
+use this other hospitals MRI machine
+ 
+
+ align:start position:0%
+use this other hospitals MRI machine
+same thing happened with CT but as soon
+
+ align:start position:0%
+same thing happened with CT but as soon
+ 
+
+ align:start position:0%
+same thing happened with CT but as soon
+as those limitations were lifted boom
+
+ align:start position:0%
+as those limitations were lifted boom
+ 
+
+ align:start position:0%
+as those limitations were lifted boom
+you know it went up and then continues
+
+ align:start position:0%
+you know it went up and then continues
+ 
+
+ align:start position:0%
+you know it went up and then continues
+to go up
+
+ align:start position:0%
+to go up
+ 
+
+ align:start position:0%
+to go up
+whereas stents I actually don't know why
+
+ align:start position:0%
+whereas stents I actually don't know why
+ 
+
+ align:start position:0%
+whereas stents I actually don't know why
+they were delayed by that long but this
+
+ align:start position:0%
+they were delayed by that long but this
+ 
+
+ align:start position:0%
+they were delayed by that long but this
+is for people with blockages and
+
+ align:start position:0%
+is for people with blockages and
+ 
+
+ align:start position:0%
+is for people with blockages and
+coronary arteries or other arteries you
+
+ align:start position:0%
+coronary arteries or other arteries you
+ 
+
+ align:start position:0%
+coronary arteries or other arteries you
+can put in a little mesh tube that just
+
+ align:start position:0%
+can put in a little mesh tube that just
+ 
+
+ align:start position:0%
+can put in a little mesh tube that just
+keeps that artery open and that adoption
+
+ align:start position:0%
+keeps that artery open and that adoption
+ 
+
+ align:start position:0%
+keeps that artery open and that adoption
+was incredibly quick okay so different
+
+ align:start position:0%
+was incredibly quick okay so different
+ 
+
+ align:start position:0%
+was incredibly quick okay so different
+things get adopted at different rates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the last topic I want to talk about
+
+ align:start position:0%
+now the last topic I want to talk about
+ 
+
+ align:start position:0%
+now the last topic I want to talk about
+before I yeah so according to those
+
+ align:start position:0%
+before I yeah so according to those
+ 
+
+ align:start position:0%
+before I yeah so according to those
+authors in the case of Stan's there were
+
+ align:start position:0%
+authors in the case of Stan's there were
+ 
+
+ align:start position:0%
+authors in the case of Stan's there were
+some champions of the idea of stenting
+
+ align:start position:0%
+some champions of the idea of stenting
+ 
+
+ align:start position:0%
+some champions of the idea of stenting
+who went around and convinced their
+
+ align:start position:0%
+who went around and convinced their
+ 
+
+ align:start position:0%
+who went around and convinced their
+colleagues that this was the right
+
+ align:start position:0%
+colleagues that this was the right
+ 
+
+ align:start position:0%
+colleagues that this was the right
+technology to use and so there was just
+
+ align:start position:0%
+technology to use and so there was just
+ 
+
+ align:start position:0%
+technology to use and so there was just
+an explosive growth in it in the other
+
+ align:start position:0%
+an explosive growth in it in the other
+ 
+
+ align:start position:0%
+an explosive growth in it in the other
+technologies you know for in the MRI
+
+ align:start position:0%
+technologies you know for in the MRI
+ 
+
+ align:start position:0%
+technologies you know for in the MRI
+case money mattered a lot because
+
+ align:start position:0%
+case money mattered a lot because
+ 
+
+ align:start position:0%
+case money mattered a lot because
+they're so expensive stents are
+
+ align:start position:0%
+they're so expensive stents are
+ 
+
+ align:start position:0%
+they're so expensive stents are
+relatively cheap and in the in the case
+
+ align:start position:0%
+relatively cheap and in the in the case
+ 
+
+ align:start position:0%
+relatively cheap and in the in the case
+of statins those are also relatively
+
+ align:start position:0%
+of statins those are also relatively
+ 
+
+ align:start position:0%
+of statins those are also relatively
+cheap or they've become cheap since they
+
+ align:start position:0%
+cheap or they've become cheap since they
+ 
+
+ align:start position:0%
+cheap or they've become cheap since they
+went off patent originally they were
+
+ align:start position:0%
+went off patent originally they were
+ 
+
+ align:start position:0%
+went off patent originally they were
+they were much more expensive but but
+
+ align:start position:0%
+they were much more expensive but but
+ 
+
+ align:start position:0%
+they were much more expensive but but
+there are still adoption problems so for
+
+ align:start position:0%
+there are still adoption problems so for
+ 
+
+ align:start position:0%
+there are still adoption problems so for
+example there was a recommendation I
+
+ align:start position:0%
+example there was a recommendation I
+ 
+
+ align:start position:0%
+example there was a recommendation I
+think about 15 maybe even 20 years ago
+
+ align:start position:0%
+think about 15 maybe even 20 years ago
+ 
+
+ align:start position:0%
+think about 15 maybe even 20 years ago
+that said that anybody who has had a
+
+ align:start position:0%
+that said that anybody who has had a
+ 
+
+ align:start position:0%
+that said that anybody who has had a
+heart attack or coronary artery disease
+
+ align:start position:0%
+heart attack or coronary artery disease
+ 
+
+ align:start position:0%
+heart attack or coronary artery disease
+should be taking beta blockers and I
+
+ align:start position:0%
+should be taking beta blockers and I
+ 
+
+ align:start position:0%
+should be taking beta blockers and I
+don't remember what the adoption rate is
+
+ align:start position:0%
+don't remember what the adoption rate is
+ 
+
+ align:start position:0%
+don't remember what the adoption rate is
+today but it's it's only on the order of
+
+ align:start position:0%
+today but it's it's only on the order of
+ 
+
+ align:start position:0%
+today but it's it's only on the order of
+a half and so why this is a dirt cheap
+
+ align:start position:0%
+a half and so why this is a dirt cheap
+ 
+
+ align:start position:0%
+a half and so why this is a dirt cheap
+drug for reasons not quite understood it
+
+ align:start position:0%
+drug for reasons not quite understood it
+ 
+
+ align:start position:0%
+drug for reasons not quite understood it
+reduces the probability of having a
+
+ align:start position:0%
+reduces the probability of having a
+ 
+
+ align:start position:0%
+reduces the probability of having a
+second heart attack by about 35% so it's
+
+ align:start position:0%
+second heart attack by about 35% so it's
+ 
+
+ align:start position:0%
+second heart attack by about 35% so it's
+a really cheap protective way of keeping
+
+ align:start position:0%
+a really cheap protective way of keeping
+ 
+
+ align:start position:0%
+a really cheap protective way of keeping
+people healthier and yet it just hasn't
+
+ align:start position:0%
+people healthier and yet it just hasn't
+ 
+
+ align:start position:0%
+people healthier and yet it just hasn't
+suffused practice as much as as people
+
+ align:start position:0%
+suffused practice as much as as people
+ 
+
+ align:start position:0%
+suffused practice as much as as people
+think it should have all right okay so
+
+ align:start position:0%
+think it should have all right okay so
+ 
+
+ align:start position:0%
+think it should have all right okay so
+how do we assure the quality of these
+
+ align:start position:0%
+how do we assure the quality of these
+ 
+
+ align:start position:0%
+how do we assure the quality of these
+technologies before we forced along the
+
+ align:start position:0%
+technologies before we forced along the
+ 
+
+ align:start position:0%
+technologies before we forced along the
+world and this is tricky so Johnny
+
+ align:start position:0%
+world and this is tricky so Johnny
+ 
+
+ align:start position:0%
+world and this is tricky so Johnny
+Anita's a Stanford professor has made an
+
+ align:start position:0%
+Anita's a Stanford professor has made an
+ 
+
+ align:start position:0%
+Anita's a Stanford professor has made an
+extremely successful career out of
+
+ align:start position:0%
+extremely successful career out of
+ 
+
+ align:start position:0%
+extremely successful career out of
+pointing out that most biomedical
+
+ align:start position:0%
+pointing out that most biomedical
+ 
+
+ align:start position:0%
+pointing out that most biomedical
+research is crap
+
+ align:start position:0%
+research is crap
+ 
+
+ align:start position:0%
+research is crap
+it can't be reproduced and there are
+
+ align:start position:0%
+it can't be reproduced and there are
+ 
+
+ align:start position:0%
+it can't be reproduced and there are
+some famous publications that that show
+
+ align:start position:0%
+some famous publications that that show
+ 
+
+ align:start position:0%
+some famous publications that that show
+that people have taken some area of
+
+ align:start position:0%
+that people have taken some area of
+ 
+
+ align:start position:0%
+that people have taken some area of
+biomedicine and they've looked at a
+
+ align:start position:0%
+biomedicine and they've looked at a
+ 
+
+ align:start position:0%
+biomedicine and they've looked at a
+bunch of well-respected published
+
+ align:start position:0%
+bunch of well-respected published
+ 
+
+ align:start position:0%
+bunch of well-respected published
+studies and they've gone to the lab and
+
+ align:start position:0%
+studies and they've gone to the lab and
+ 
+
+ align:start position:0%
+studies and they've gone to the lab and
+they've tried to replicate those studies
+
+ align:start position:0%
+they've tried to replicate those studies
+ 
+
+ align:start position:0%
+they've tried to replicate those studies
+and half the time or three-quarters of
+
+ align:start position:0%
+and half the time or three-quarters of
+ 
+
+ align:start position:0%
+and half the time or three-quarters of
+the time they fail to do so you go oh my
+
+ align:start position:0%
+the time they fail to do so you go oh my
+ 
+
+ align:start position:0%
+the time they fail to do so you go oh my
+god this is horrible
+
+ align:start position:0%
+god this is horrible
+ 
+
+ align:start position:0%
+god this is horrible
+right it is horrible yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worse than that so it's not that there
+
+ align:start position:0%
+worse than that so it's not that there
+ 
+
+ align:start position:0%
+worse than that so it's not that there
+are slight differences it's that for
+
+ align:start position:0%
+are slight differences it's that for
+ 
+
+ align:start position:0%
+are slight differences it's that for
+example a result that was shown to be
+
+ align:start position:0%
+example a result that was shown to be
+ 
+
+ align:start position:0%
+example a result that was shown to be
+statistically significant
+
+ align:start position:0%
+statistically significant
+ 
+
+ align:start position:0%
+statistically significant
+in one study when they repeat the study
+
+ align:start position:0%
+in one study when they repeat the study
+ 
+
+ align:start position:0%
+in one study when they repeat the study
+is no longer statistically significant
+
+ align:start position:0%
+is no longer statistically significant
+ 
+
+ align:start position:0%
+is no longer statistically significant
+okay that's bad
+
+ align:start position:0%
+okay that's bad
+ 
+
+ align:start position:0%
+okay that's bad
+if if you base policy on on that kind of
+
+ align:start position:0%
+if if you base policy on on that kind of
+ 
+
+ align:start position:0%
+if if you base policy on on that kind of
+decision so you need EES has a
+
+ align:start position:0%
+decision so you need EES has a
+ 
+
+ align:start position:0%
+decision so you need EES has a
+suggestion which would probably help a
+
+ align:start position:0%
+suggestion which would probably help a
+ 
+
+ align:start position:0%
+suggestion which would probably help a
+lot and that is basically make known to
+
+ align:start position:0%
+lot and that is basically make known to
+ 
+
+ align:start position:0%
+lot and that is basically make known to
+everybody all the studies that have
+
+ align:start position:0%
+everybody all the studies that have
+ 
+
+ align:start position:0%
+everybody all the studies that have
+failed so the problem is that if you
+
+ align:start position:0%
+failed so the problem is that if you
+ 
+
+ align:start position:0%
+failed so the problem is that if you
+give me a big data set and I start
+
+ align:start position:0%
+give me a big data set and I start
+ 
+
+ align:start position:0%
+give me a big data set and I start
+mining this data set I'm gonna find tons
+
+ align:start position:0%
+mining this data set I'm gonna find tons
+ 
+
+ align:start position:0%
+mining this data set I'm gonna find tons
+and tons of interesting correlations in
+
+ align:start position:0%
+and tons of interesting correlations in
+ 
+
+ align:start position:0%
+and tons of interesting correlations in
+this data okay and as soon as I get one
+
+ align:start position:0%
+this data okay and as soon as I get one
+ 
+
+ align:start position:0%
+this data okay and as soon as I get one
+that has a good p-value my students and
+
+ align:start position:0%
+that has a good p-value my students and
+ 
+
+ align:start position:0%
+that has a good p-value my students and
+I go hmm fantastic time to publish right
+
+ align:start position:0%
+I go hmm fantastic time to publish right
+ 
+
+ align:start position:0%
+I go hmm fantastic time to publish right
+now consider the fact that I'm not the
+
+ align:start position:0%
+now consider the fact that I'm not the
+ 
+
+ align:start position:0%
+now consider the fact that I'm not the
+only person in this role so you know
+
+ align:start position:0%
+only person in this role so you know
+ 
+
+ align:start position:0%
+only person in this role so you know
+David's group is doing the same thing
+
+ align:start position:0%
+David's group is doing the same thing
+ 
+
+ align:start position:0%
+David's group is doing the same thing
+and jong-gu togs and Regina barzil ace
+
+ align:start position:0%
+and jong-gu togs and Regina barzil ace
+ 
+
+ align:start position:0%
+and jong-gu togs and Regina barzil ace
+and all of our colleagues at every other
+
+ align:start position:0%
+and all of our colleagues at every other
+ 
+
+ align:start position:0%
+and all of our colleagues at every other
+major University and Hospital in the
+
+ align:start position:0%
+major University and Hospital in the
+ 
+
+ align:start position:0%
+major University and Hospital in the
+United States and so there may be
+
+ align:start position:0%
+United States and so there may be
+ 
+
+ align:start position:0%
+United States and so there may be
+hundreds of people who are mining this
+
+ align:start position:0%
+hundreds of people who are mining this
+ 
+
+ align:start position:0%
+hundreds of people who are mining this
+data and each of us has slightly
+
+ align:start position:0%
+data and each of us has slightly
+ 
+
+ align:start position:0%
+data and each of us has slightly
+different ways of doing it we select our
+
+ align:start position:0%
+different ways of doing it we select our
+ 
+
+ align:start position:0%
+different ways of doing it we select our
+cases differently we pre-process the
+
+ align:start position:0%
+cases differently we pre-process the
+ 
+
+ align:start position:0%
+cases differently we pre-process the
+data differently we apply different
+
+ align:start position:0%
+data differently we apply different
+ 
+
+ align:start position:0%
+data differently we apply different
+learning algorithms to them to them but
+
+ align:start position:0%
+learning algorithms to them to them but
+ 
+
+ align:start position:0%
+learning algorithms to them to them but
+just by random chance some of us
+
+ align:start position:0%
+just by random chance some of us
+ 
+
+ align:start position:0%
+just by random chance some of us
+are going to find interesting results
+
+ align:start position:0%
+are going to find interesting results
+ 
+
+ align:start position:0%
+are going to find interesting results
+interesting patterns and of course those
+
+ align:start position:0%
+interesting patterns and of course those
+ 
+
+ align:start position:0%
+interesting patterns and of course those
+are the ones that get published because
+
+ align:start position:0%
+are the ones that get published because
+ 
+
+ align:start position:0%
+are the ones that get published because
+if you don't find an interesting result
+
+ align:start position:0%
+if you don't find an interesting result
+ 
+
+ align:start position:0%
+if you don't find an interesting result
+you're not going to submit it to a
+
+ align:start position:0%
+you're not going to submit it to a
+ 
+
+ align:start position:0%
+you're not going to submit it to a
+journal and say you know I looked for
+
+ align:start position:0%
+journal and say you know I looked for
+ 
+
+ align:start position:0%
+journal and say you know I looked for
+the following fact phenomenon and I was
+
+ align:start position:0%
+the following fact phenomenon and I was
+ 
+
+ align:start position:0%
+the following fact phenomenon and I was
+unable to find it because the journal
+
+ align:start position:0%
+unable to find it because the journal
+ 
+
+ align:start position:0%
+unable to find it because the journal
+says well that's not interesting to
+
+ align:start position:0%
+says well that's not interesting to
+ 
+
+ align:start position:0%
+says well that's not interesting to
+anybody and so so Ian Edie's is
+
+ align:start position:0%
+anybody and so so Ian Edie's is
+ 
+
+ align:start position:0%
+anybody and so so Ian Edie's is
+recommending that basically every study
+
+ align:start position:0%
+recommending that basically every study
+ 
+
+ align:start position:0%
+recommending that basically every study
+that anybody undertakes should be
+
+ align:start position:0%
+that anybody undertakes should be
+ 
+
+ align:start position:0%
+that anybody undertakes should be
+registered and if you don't get a
+
+ align:start position:0%
+registered and if you don't get a
+ 
+
+ align:start position:0%
+registered and if you don't get a
+significant result that should be known
+
+ align:start position:0%
+significant result that should be known
+ 
+
+ align:start position:0%
+significant result that should be known
+and this would allow us to make at least
+
+ align:start position:0%
+and this would allow us to make at least
+ 
+
+ align:start position:0%
+and this would allow us to make at least
+some reasonable estimate of whether the
+
+ align:start position:0%
+some reasonable estimate of whether the
+ 
+
+ align:start position:0%
+some reasonable estimate of whether the
+significant results that were gotten are
+
+ align:start position:0%
+significant results that were gotten are
+ 
+
+ align:start position:0%
+significant results that were gotten are
+just the statistical outliers that
+
+ align:start position:0%
+just the statistical outliers that
+ 
+
+ align:start position:0%
+just the statistical outliers that
+happen to reach p equal point oh five or
+
+ align:start position:0%
+happen to reach p equal point oh five or
+ 
+
+ align:start position:0%
+happen to reach p equal point oh five or
+whatever your threshold is or whether
+
+ align:start position:0%
+whatever your threshold is or whether
+ 
+
+ align:start position:0%
+whatever your threshold is or whether
+it's a real effect because not that many
+
+ align:start position:0%
+it's a real effect because not that many
+ 
+
+ align:start position:0%
+it's a real effect because not that many
+people have been trying this yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it could be any of those it could be
+
+ align:start position:0%
+it could be any of those it could be
+ 
+
+ align:start position:0%
+it could be any of those it could be
+that you know your hospital has some
+
+ align:start position:0%
+that you know your hospital has some
+ 
+
+ align:start position:0%
+that you know your hospital has some
+biased data collection and so you find
+
+ align:start position:0%
+biased data collection and so you find
+ 
+
+ align:start position:0%
+biased data collection and so you find
+in effect my hospital doesn't and so I
+
+ align:start position:0%
+in effect my hospital doesn't and so I
+ 
+
+ align:start position:0%
+in effect my hospital doesn't and so I
+don't find it it could be that we just
+
+ align:start position:0%
+don't find it it could be that we just
+ 
+
+ align:start position:0%
+don't find it it could be that we just
+randomly subsampled a different sample
+
+ align:start position:0%
+randomly subsampled a different sample
+ 
+
+ align:start position:0%
+randomly subsampled a different sample
+of the population
+
+ align:start position:0%
+of the population
+ 
+
+ align:start position:0%
+of the population
+okay so it's very interesting last year
+
+ align:start position:0%
+okay so it's very interesting last year
+ 
+
+ align:start position:0%
+okay so it's very interesting last year
+I was invited to a meeting by Jeff
+
+ align:start position:0%
+I was invited to a meeting by Jeff
+ 
+
+ align:start position:0%
+I was invited to a meeting by Jeff
+Drazen who's the executive editor of the
+
+ align:start position:0%
+Drazen who's the executive editor of the
+ 
+
+ align:start position:0%
+Drazen who's the executive editor of the
+New England Journal and he's thinking
+
+ align:start position:0%
+New England Journal and he's thinking
+ 
+
+ align:start position:0%
+New England Journal and he's thinking
+about has not decided but he's thinking
+
+ align:start position:0%
+about has not decided but he's thinking
+ 
+
+ align:start position:0%
+about has not decided but he's thinking
+about a policy for the New England
+
+ align:start position:0%
+about a policy for the New England
+ 
+
+ align:start position:0%
+about a policy for the New England
+Journal which is like the top Medical
+
+ align:start position:0%
+Journal which is like the top Medical
+ 
+
+ align:start position:0%
+Journal which is like the top Medical
+Journal that says that he will not
+
+ align:start position:0%
+Journal that says that he will not
+ 
+
+ align:start position:0%
+Journal that says that he will not
+publish any result unless it's been
+
+ align:start position:0%
+publish any result unless it's been
+ 
+
+ align:start position:0%
+publish any result unless it's been
+replicated on two independent data sets
+
+ align:start position:0%
+replicated on two independent data sets
+ 
+
+ align:start position:0%
+replicated on two independent data sets
+right so that's interesting and that's
+
+ align:start position:0%
+right so that's interesting and that's
+ 
+
+ align:start position:0%
+right so that's interesting and that's
+an attempt to fight back against this
+
+ align:start position:0%
+an attempt to fight back against this
+ 
+
+ align:start position:0%
+an attempt to fight back against this
+problem it's a different solution than
+
+ align:start position:0%
+problem it's a different solution than
+ 
+
+ align:start position:0%
+problem it's a different solution than
+what what you need is is recommending so
+
+ align:start position:0%
+what what you need is is recommending so
+ 
+
+ align:start position:0%
+what what you need is is recommending so
+this was a study by Enrico Carrara and
+
+ align:start position:0%
+this was a study by Enrico Carrara and
+ 
+
+ align:start position:0%
+this was a study by Enrico Carrara and
+he's talking about what it means to
+
+ align:start position:0%
+he's talking about what it means to
+ 
+
+ align:start position:0%
+he's talking about what it means to
+replicate and again I'm not going to go
+
+ align:start position:0%
+replicate and again I'm not going to go
+ 
+
+ align:start position:0%
+replicate and again I'm not going to go
+through all this but there's a notion of
+
+ align:start position:0%
+through all this but there's a notion of
+ 
+
+ align:start position:0%
+through all this but there's a notion of
+replication might mean exact replication
+
+ align:start position:0%
+replication might mean exact replication
+ 
+
+ align:start position:0%
+replication might mean exact replication
+ie you do exactly the same thing on
+
+ align:start position:0%
+ie you do exactly the same thing on
+ 
+
+ align:start position:0%
+ie you do exactly the same thing on
+exactly the same kind of data but in a
+
+ align:start position:0%
+exactly the same kind of data but in a
+ 
+
+ align:start position:0%
+exactly the same kind of data but in a
+different data set and then partial
+
+ align:start position:0%
+different data set and then partial
+ 
+
+ align:start position:0%
+different data set and then partial
+replication conceptual replication which
+
+ align:start position:0%
+replication conceptual replication which
+ 
+
+ align:start position:0%
+replication conceptual replication which
+says you follow the same procedures but
+
+ align:start position:0%
+says you follow the same procedures but
+ 
+
+ align:start position:0%
+says you follow the same procedures but
+in a different environment and then
+
+ align:start position:0%
+in a different environment and then
+ 
+
+ align:start position:0%
+in a different environment and then
+quasi replication either partial or
+
+ align:start position:0%
+quasi replication either partial or
+ 
+
+ align:start position:0%
+quasi replication either partial or
+conceptual and these have various
+
+ align:start position:0%
+conceptual and these have various
+ 
+
+ align:start position:0%
+conceptual and these have various
+characteristics that you can look at
+
+ align:start position:0%
+characteristics that you can look at
+ 
+
+ align:start position:0%
+characteristics that you can look at
+it's an interesting framework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is not a new idea the first
+
+ align:start position:0%
+so this is not a new idea the first
+ 
+
+ align:start position:0%
+so this is not a new idea the first
+edition of this book evaluation methods
+
+ align:start position:0%
+edition of this book evaluation methods
+ 
+
+ align:start position:0%
+edition of this book evaluation methods
+and biomedical informatics was called
+
+ align:start position:0%
+and biomedical informatics was called
+ 
+
+ align:start position:0%
+and biomedical informatics was called
+evaluation methods in medical
+
+ align:start position:0%
+evaluation methods in medical
+ 
+
+ align:start position:0%
+evaluation methods in medical
+informatics by the same authors and was
+
+ align:start position:0%
+informatics by the same authors and was
+ 
+
+ align:start position:0%
+informatics by the same authors and was
+published a long time ago I can't
+
+ align:start position:0%
+published a long time ago I can't
+ 
+
+ align:start position:0%
+published a long time ago I can't
+remember this one is relatively recent
+
+ align:start position:0%
+remember this one is relatively recent
+ 
+
+ align:start position:0%
+remember this one is relatively recent
+and so they do a multi-hundred page very
+
+ align:start position:0%
+and so they do a multi-hundred page very
+ 
+
+ align:start position:0%
+and so they do a multi-hundred page very
+detailed evaluation of exactly how one
+
+ align:start position:0%
+detailed evaluation of exactly how one
+ 
+
+ align:start position:0%
+detailed evaluation of exactly how one
+should evaluate clinical systems like
+
+ align:start position:0%
+should evaluate clinical systems like
+ 
+
+ align:start position:0%
+should evaluate clinical systems like
+this and it's very careful and very
+
+ align:start position:0%
+this and it's very careful and very
+ 
+
+ align:start position:0%
+this and it's very careful and very
+cautious but it's also very conservative
+
+ align:start position:0%
+cautious but it's also very conservative
+ 
+
+ align:start position:0%
+cautious but it's also very conservative
+so for example one of the things that
+
+ align:start position:0%
+so for example one of the things that
+ 
+
+ align:start position:0%
+so for example one of the things that
+they recommend is that the people doing
+
+ align:start position:0%
+they recommend is that the people doing
+ 
+
+ align:start position:0%
+they recommend is that the people doing
+the evaluation should not be the people
+
+ align:start position:0%
+the evaluation should not be the people
+ 
+
+ align:start position:0%
+the evaluation should not be the people
+who developed the technique because
+
+ align:start position:0%
+who developed the technique because
+ 
+
+ align:start position:0%
+who developed the technique because
+there's innately bias and you know I
+
+ align:start position:0%
+there's innately bias and you know I
+ 
+
+ align:start position:0%
+there's innately bias and you know I
+want my technique to succeed and so they
+
+ align:start position:0%
+want my technique to succeed and so they
+ 
+
+ align:start position:0%
+want my technique to succeed and so they
+say hand it off to somebody else who
+
+ align:start position:0%
+say hand it off to somebody else who
+ 
+
+ align:start position:0%
+say hand it off to somebody else who
+doesn't have that same vested interest
+
+ align:start position:0%
+doesn't have that same vested interest
+ 
+
+ align:start position:0%
+doesn't have that same vested interest
+and then you're going to get a more
+
+ align:start position:0%
+and then you're going to get a more
+ 
+
+ align:start position:0%
+and then you're going to get a more
+careful evaluation so Steve Paola and I
+
+ align:start position:0%
+careful evaluation so Steve Paola and I
+ 
+
+ align:start position:0%
+careful evaluation so Steve Paola and I
+wrote a response to one of their early
+
+ align:start position:0%
+wrote a response to one of their early
+ 
+
+ align:start position:0%
+wrote a response to one of their early
+papers recommending this that said well
+
+ align:start position:0%
+papers recommending this that said well
+ 
+
+ align:start position:0%
+papers recommending this that said well
+that's so conservative that it sort of
+
+ align:start position:0%
+that's so conservative that it sort of
+ 
+
+ align:start position:0%
+that's so conservative that it sort of
+throws the baby out with the bathwater
+
+ align:start position:0%
+throws the baby out with the bathwater
+ 
+
+ align:start position:0%
+throws the baby out with the bathwater
+because if you make it so difficult to
+
+ align:start position:0%
+because if you make it so difficult to
+ 
+
+ align:start position:0%
+because if you make it so difficult to
+do an evaluation you'll never get
+
+ align:start position:0%
+do an evaluation you'll never get
+ 
+
+ align:start position:0%
+do an evaluation you'll never get
+anything past it and so we proposed
+
+ align:start position:0%
+anything past it and so we proposed
+ 
+
+ align:start position:0%
+anything past it and so we proposed
+instead a kind of staged evaluation that
+
+ align:start position:0%
+instead a kind of staged evaluation that
+ 
+
+ align:start position:0%
+instead a kind of staged evaluation that
+says first of all you should do
+
+ align:start position:0%
+says first of all you should do
+ 
+
+ align:start position:0%
+says first of all you should do
+regression testing so that every time
+
+ align:start position:0%
+regression testing so that every time
+ 
+
+ align:start position:0%
+regression testing so that every time
+you use these agile development methods
+
+ align:start position:0%
+you use these agile development methods
+ 
+
+ align:start position:0%
+you use these agile development methods
+you should have the set of cases that
+
+ align:start position:0%
+you should have the set of cases that
+ 
+
+ align:start position:0%
+you should have the set of cases that
+your program has worked on before you
+
+ align:start position:0%
+your program has worked on before you
+ 
+
+ align:start position:0%
+your program has worked on before you
+should automatically rerun them and see
+
+ align:start position:0%
+should automatically rerun them and see
+ 
+
+ align:start position:0%
+should automatically rerun them and see
+which ones you've made better and which
+
+ align:start position:0%
+which ones you've made better and which
+ 
+
+ align:start position:0%
+which ones you've made better and which
+ones you've made worse and that'll give
+
+ align:start position:0%
+ones you've made worse and that'll give
+ 
+
+ align:start position:0%
+ones you've made worse and that'll give
+you some insight into whether what
+
+ align:start position:0%
+you some insight into whether what
+ 
+
+ align:start position:0%
+you some insight into whether what
+you're doing is reasonable and then you
+
+ align:start position:0%
+you're doing is reasonable and then you
+ 
+
+ align:start position:0%
+you're doing is reasonable and then you
+might also build tools that look at
+
+ align:start position:0%
+might also build tools that look at
+ 
+
+ align:start position:0%
+might also build tools that look at
+automating ways of looking for
+
+ align:start position:0%
+automating ways of looking for
+ 
+
+ align:start position:0%
+automating ways of looking for
+inconsistencies in the models that
+
+ align:start position:0%
+inconsistencies in the models that
+ 
+
+ align:start position:0%
+inconsistencies in the models that
+you're you're building then you have
+
+ align:start position:0%
+you're you're building then you have
+ 
+
+ align:start position:0%
+you're you're building then you have
+retrospective review judged by
+
+ align:start position:0%
+retrospective review judged by
+ 
+
+ align:start position:0%
+retrospective review judged by
+clinicians so you run a program that you
+
+ align:start position:0%
+clinicians so you run a program that you
+ 
+
+ align:start position:0%
+clinicians so you run a program that you
+like over a hold by
+
+ align:start position:0%
+like over a hold by
+ 
+
+ align:start position:0%
+like over a hold by
+existing data like what you're doing
+
+ align:start position:0%
+existing data like what you're doing
+ 
+
+ align:start position:0%
+existing data like what you're doing
+with mimic or with market scan and then
+
+ align:start position:0%
+with mimic or with market scan and then
+ 
+
+ align:start position:0%
+with mimic or with market scan and then
+you do it prospectively but without
+
+ align:start position:0%
+you do it prospectively but without
+ 
+
+ align:start position:0%
+you do it prospectively but without
+actually affecting patients so you do it
+
+ align:start position:0%
+actually affecting patients so you do it
+ 
+
+ align:start position:0%
+actually affecting patients so you do it
+in real time as the data is coming in
+
+ align:start position:0%
+in real time as the data is coming in
+ 
+
+ align:start position:0%
+in real time as the data is coming in
+but you don't tell anybody what the
+
+ align:start position:0%
+but you don't tell anybody what the
+ 
+
+ align:start position:0%
+but you don't tell anybody what the
+program results in you just ask them to
+
+ align:start position:0%
+program results in you just ask them to
+ 
+
+ align:start position:0%
+program results in you just ask them to
+evaluate in retrospect to see whether it
+
+ align:start position:0%
+evaluate in retrospect to see whether it
+ 
+
+ align:start position:0%
+evaluate in retrospect to see whether it
+was right and you might say well what's
+
+ align:start position:0%
+was right and you might say well what's
+ 
+
+ align:start position:0%
+was right and you might say well what's
+the difference between collecting the
+
+ align:start position:0%
+the difference between collecting the
+ 
+
+ align:start position:0%
+the difference between collecting the
+data in real time and collecting the
+
+ align:start position:0%
+data in real time and collecting the
+ 
+
+ align:start position:0%
+data in real time and collecting the
+data retrospectively and historically
+
+ align:start position:0%
+data retrospectively and historically
+ 
+
+ align:start position:0%
+data retrospectively and historically
+the answer is there is a difference so
+
+ align:start position:0%
+the answer is there is a difference so
+ 
+
+ align:start position:0%
+the answer is there is a difference so
+circumstances differ the mechanisms that
+
+ align:start position:0%
+circumstances differ the mechanisms that
+ 
+
+ align:start position:0%
+circumstances differ the mechanisms that
+you have for collecting the data differ
+
+ align:start position:0%
+you have for collecting the data differ
+ 
+
+ align:start position:0%
+you have for collecting the data differ
+so this turns out to be an important
+
+ align:start position:0%
+so this turns out to be an important
+ 
+
+ align:start position:0%
+so this turns out to be an important
+issue and then you can run a prospective
+
+ align:start position:0%
+issue and then you can run a prospective
+ 
+
+ align:start position:0%
+issue and then you can run a prospective
+controlled trial
+
+ align:start position:0%
+controlled trial
+ 
+
+ align:start position:0%
+controlled trial
+where you're interested in evaluating
+
+ align:start position:0%
+where you're interested in evaluating
+ 
+
+ align:start position:0%
+where you're interested in evaluating
+both the answer that you get from the
+
+ align:start position:0%
+both the answer that you get from the
+ 
+
+ align:start position:0%
+both the answer that you get from the
+program and ultimately the effect on
+
+ align:start position:0%
+program and ultimately the effect on
+ 
+
+ align:start position:0%
+program and ultimately the effect on
+health outcomes so if I have a decision
+
+ align:start position:0%
+health outcomes so if I have a decision
+ 
+
+ align:start position:0%
+health outcomes so if I have a decision
+support system the ultimate proof of the
+
+ align:start position:0%
+support system the ultimate proof of the
+ 
+
+ align:start position:0%
+support system the ultimate proof of the
+pudding is if I run that decision
+
+ align:start position:0%
+pudding is if I run that decision
+ 
+
+ align:start position:0%
+pudding is if I run that decision
+support system I give advice to
+
+ align:start position:0%
+support system I give advice to
+ 
+
+ align:start position:0%
+support system I give advice to
+clinicians the clinicians change their
+
+ align:start position:0%
+clinicians the clinicians change their
+ 
+
+ align:start position:0%
+clinicians the clinicians change their
+behavior sometimes and the patients get
+
+ align:start position:0%
+behavior sometimes and the patients get
+ 
+
+ align:start position:0%
+behavior sometimes and the patients get
+a better outcome then I'm convinced that
+
+ align:start position:0%
+a better outcome then I'm convinced that
+ 
+
+ align:start position:0%
+a better outcome then I'm convinced that
+this is really useful but you have to
+
+ align:start position:0%
+this is really useful but you have to
+ 
+
+ align:start position:0%
+this is really useful but you have to
+get there slowly because you don't want
+
+ align:start position:0%
+get there slowly because you don't want
+ 
+
+ align:start position:0%
+get there slowly because you don't want
+to give them worse outcomes that's
+
+ align:start position:0%
+to give them worse outcomes that's
+ 
+
+ align:start position:0%
+to give them worse outcomes that's
+unethical and probably illegal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you want to compare this to the
+
+ align:start position:0%
+and you want to compare this to the
+ 
+
+ align:start position:0%
+and you want to compare this to the
+performance of unaided doctors so the
+
+ align:start position:0%
+performance of unaided doctors so the
+ 
+
+ align:start position:0%
+performance of unaided doctors so the
+Food and Drug Administration has been
+
+ align:start position:0%
+Food and Drug Administration has been
+ 
+
+ align:start position:0%
+Food and Drug Administration has been
+dealing with this issue for many many
+
+ align:start position:0%
+dealing with this issue for many many
+ 
+
+ align:start position:0%
+dealing with this issue for many many
+years I remember talking to them in
+
+ align:start position:0%
+years I remember talking to them in
+ 
+
+ align:start position:0%
+years I remember talking to them in
+about 1976 when they were reading about
+
+ align:start position:0%
+about 1976 when they were reading about
+ 
+
+ align:start position:0%
+about 1976 when they were reading about
+the very first expert system programs
+
+ align:start position:0%
+the very first expert system programs
+ 
+
+ align:start position:0%
+the very first expert system programs
+for diagnosis and therapy selection and
+
+ align:start position:0%
+for diagnosis and therapy selection and
+ 
+
+ align:start position:0%
+for diagnosis and therapy selection and
+they said well how should we regulate
+
+ align:start position:0%
+they said well how should we regulate
+ 
+
+ align:start position:0%
+they said well how should we regulate
+these and my response at the time was
+
+ align:start position:0%
+these and my response at the time was
+ 
+
+ align:start position:0%
+these and my response at the time was
+god help us keep your hands off right
+
+ align:start position:0%
+god help us keep your hands off right
+ 
+
+ align:start position:0%
+god help us keep your hands off right
+because if you regulate it then you're
+
+ align:start position:0%
+because if you regulate it then you're
+ 
+
+ align:start position:0%
+because if you regulate it then you're
+gonna slow down progress and in any case
+
+ align:start position:0%
+gonna slow down progress and in any case
+ 
+
+ align:start position:0%
+gonna slow down progress and in any case
+none of these programs are being used
+
+ align:start position:0%
+none of these programs are being used
+ 
+
+ align:start position:0%
+none of these programs are being used
+these programs that are being developed
+
+ align:start position:0%
+these programs that are being developed
+ 
+
+ align:start position:0%
+these programs that are being developed
+as experimental programs in experimental
+
+ align:start position:0%
+as experimental programs in experimental
+ 
+
+ align:start position:0%
+as experimental programs in experimental
+settings they're not coming anywhere
+
+ align:start position:0%
+settings they're not coming anywhere
+ 
+
+ align:start position:0%
+settings they're not coming anywhere
+close to being used on real patients and
+
+ align:start position:0%
+close to being used on real patients and
+ 
+
+ align:start position:0%
+close to being used on real patients and
+so there's not a regulatory issue and
+
+ align:start position:0%
+so there's not a regulatory issue and
+ 
+
+ align:start position:0%
+so there's not a regulatory issue and
+about every five years FDA has revisited
+
+ align:start position:0%
+about every five years FDA has revisited
+ 
+
+ align:start position:0%
+about every five years FDA has revisited
+that question and they have continued to
+
+ align:start position:0%
+that question and they have continued to
+ 
+
+ align:start position:0%
+that question and they have continued to
+make essentially the same decision based
+
+ align:start position:0%
+make essentially the same decision based
+ 
+
+ align:start position:0%
+make essentially the same decision based
+on the rationale that for example they
+
+ align:start position:0%
+on the rationale that for example they
+ 
+
+ align:start position:0%
+on the rationale that for example they
+don't regulate books if I write a
+
+ align:start position:0%
+don't regulate books if I write a
+ 
+
+ align:start position:0%
+don't regulate books if I write a
+textbook that explains something about
+
+ align:start position:0%
+textbook that explains something about
+ 
+
+ align:start position:0%
+textbook that explains something about
+medicine the FDA is not going to see
+
+ align:start position:0%
+medicine the FDA is not going to see
+ 
+
+ align:start position:0%
+medicine the FDA is not going to see
+whether it's correct or not and the
+
+ align:start position:0%
+whether it's correct or not and the
+ 
+
+ align:start position:0%
+whether it's correct or not and the
+reason is because the expectation is
+
+ align:start position:0%
+reason is because the expectation is
+ 
+
+ align:start position:0%
+reason is because the expectation is
+that the textbook is making
+
+ align:start position:0%
+that the textbook is making
+ 
+
+ align:start position:0%
+that the textbook is making
+recommendations so to speak to clinical
+
+ align:start position:0%
+recommendations so to speak to clinical
+ 
+
+ align:start position:0%
+recommendations so to speak to clinical
+practitioners who are responsible
+
+ align:start position:0%
+practitioners who are responsible
+ 
+
+ align:start position:0%
+practitioners who are responsible
+experts themselves and so the ultimate
+
+ align:start position:0%
+experts themselves and so the ultimate
+ 
+
+ align:start position:0%
+experts themselves and so the ultimate
+responsibility for how they behave rests
+
+ align:start position:0%
+responsibility for how they behave rests
+ 
+
+ align:start position:0%
+responsibility for how they behave rests
+with them and not with the textbook and
+
+ align:start position:0%
+with them and not with the textbook and
+ 
+
+ align:start position:0%
+with them and not with the textbook and
+they said we're gonna treat these
+
+ align:start position:0%
+they said we're gonna treat these
+ 
+
+ align:start position:0%
+they said we're gonna treat these
+computer programs as if they were
+
+ align:start position:0%
+computer programs as if they were
+ 
+
+ align:start position:0%
+computer programs as if they were
+dynamic textbooks rather than colleagues
+
+ align:start position:0%
+dynamic textbooks rather than colleagues
+ 
+
+ align:start position:0%
+dynamic textbooks rather than colleagues
+who are acting independently and giving
+
+ align:start position:0%
+who are acting independently and giving
+ 
+
+ align:start position:0%
+who are acting independently and giving
+advice now as soon as you try to give
+
+ align:start position:0%
+advice now as soon as you try to give
+ 
+
+ align:start position:0%
+advice now as soon as you try to give
+that advice not to a professional but to
+
+ align:start position:0%
+that advice not to a professional but to
+ 
+
+ align:start position:0%
+that advice not to a professional but to
+a patient then you are immediately under
+
+ align:start position:0%
+a patient then you are immediately under
+ 
+
+ align:start position:0%
+a patient then you are immediately under
+the regulatory auspices of FDA because
+
+ align:start position:0%
+the regulatory auspices of FDA because
+ 
+
+ align:start position:0%
+the regulatory auspices of FDA because
+now there is no professional
+
+ align:start position:0%
+now there is no professional
+ 
+
+ align:start position:0%
+now there is no professional
+intermediate that can evaluate the
+
+ align:start position:0%
+intermediate that can evaluate the
+ 
+
+ align:start position:0%
+intermediate that can evaluate the
+quality of that advice so what FDA has
+
+ align:start position:0%
+quality of that advice so what FDA has
+ 
+
+ align:start position:0%
+quality of that advice so what FDA has
+done it just in the past year is they
+
+ align:start position:0%
+done it just in the past year is they
+ 
+
+ align:start position:0%
+done it just in the past year is they
+said that we're going to treat these AI
+
+ align:start position:0%
+said that we're going to treat these AI
+ 
+
+ align:start position:0%
+said that we're going to treat these AI
+based quote-unquote devices as medical
+
+ align:start position:0%
+based quote-unquote devices as medical
+ 
+
+ align:start position:0%
+based quote-unquote devices as medical
+devices and we're going to apply the
+
+ align:start position:0%
+devices and we're going to apply the
+ 
+
+ align:start position:0%
+devices and we're going to apply the
+same regulatory requirements that we
+
+ align:start position:0%
+same regulatory requirements that we
+ 
+
+ align:start position:0%
+same regulatory requirements that we
+have for these devices except we don't
+
+ align:start position:0%
+have for these devices except we don't
+ 
+
+ align:start position:0%
+have for these devices except we don't
+really know how to do this and so
+
+ align:start position:0%
+really know how to do this and so
+ 
+
+ align:start position:0%
+really know how to do this and so
+there's a kind of experiment going on
+
+ align:start position:0%
+there's a kind of experiment going on
+ 
+
+ align:start position:0%
+there's a kind of experiment going on
+right now where they're saying okay
+
+ align:start position:0%
+right now where they're saying okay
+ 
+
+ align:start position:0%
+right now where they're saying okay
+we're submit applications for review of
+
+ align:start position:0%
+we're submit applications for review of
+ 
+
+ align:start position:0%
+we're submit applications for review of
+these devices to us we will review them
+
+ align:start position:0%
+these devices to us we will review them
+ 
+
+ align:start position:0%
+these devices to us we will review them
+and we will use these criteria product
+
+ align:start position:0%
+and we will use these criteria product
+ 
+
+ align:start position:0%
+and we will use these criteria product
+quality patient safety clinical
+
+ align:start position:0%
+quality patient safety clinical
+ 
+
+ align:start position:0%
+quality patient safety clinical
+responsibility cybersecurity
+
+ align:start position:0%
+responsibility cybersecurity
+ 
+
+ align:start position:0%
+responsibility cybersecurity
+responsibility and a so-called proactive
+
+ align:start position:0%
+responsibility and a so-called proactive
+ 
+
+ align:start position:0%
+responsibility and a so-called proactive
+culture in the organization that's
+
+ align:start position:0%
+culture in the organization that's
+ 
+
+ align:start position:0%
+culture in the organization that's
+developing them in order to make a
+
+ align:start position:0%
+developing them in order to make a
+ 
+
+ align:start position:0%
+developing them in order to make a
+judgement of whether or not to let you
+
+ align:start position:0%
+judgement of whether or not to let you
+ 
+
+ align:start position:0%
+judgement of whether or not to let you
+proceed with marketing one of these
+
+ align:start position:0%
+proceed with marketing one of these
+ 
+
+ align:start position:0%
+proceed with marketing one of these
+things so if you look there are in fact
+
+ align:start position:0%
+things so if you look there are in fact
+ 
+
+ align:start position:0%
+things so if you look there are in fact
+about ten devices quote unquote these
+
+ align:start position:0%
+about ten devices quote unquote these
+ 
+
+ align:start position:0%
+about ten devices quote unquote these
+are all software that have been approved
+
+ align:start position:0%
+are all software that have been approved
+ 
+
+ align:start position:0%
+are all software that have been approved
+so far by FDA and almost all of them are
+
+ align:start position:0%
+so far by FDA and almost all of them are
+ 
+
+ align:start position:0%
+so far by FDA and almost all of them are
+imaging devices they're they're things
+
+ align:start position:0%
+imaging devices they're they're things
+ 
+
+ align:start position:0%
+imaging devices they're they're things
+that do convolutional networks over one
+
+ align:start position:0%
+that do convolutional networks over one
+ 
+
+ align:start position:0%
+that do convolutional networks over one
+thing or another and so here are just a
+
+ align:start position:0%
+thing or another and so here are just a
+ 
+
+ align:start position:0%
+thing or another and so here are just a
+few examples
+
+ align:start position:0%
+few examples
+ 
+
+ align:start position:0%
+few examples
+Imogen has osteo detect which analyzes
+
+ align:start position:0%
+Imogen has osteo detect which analyzes
+ 
+
+ align:start position:0%
+Imogen has osteo detect which analyzes
+two dimensional x-ray images for signs
+
+ align:start position:0%
+two dimensional x-ray images for signs
+ 
+
+ align:start position:0%
+two dimensional x-ray images for signs
+of distal radius fracture so if you
+
+ align:start position:0%
+of distal radius fracture so if you
+ 
+
+ align:start position:0%
+of distal radius fracture so if you
+break your wrist then this system will
+
+ align:start position:0%
+break your wrist then this system will
+ 
+
+ align:start position:0%
+break your wrist then this system will
+look at the x-ray and and decide whether
+
+ align:start position:0%
+look at the x-ray and and decide whether
+ 
+
+ align:start position:0%
+look at the x-ray and and decide whether
+or not you've done that
+
+ align:start position:0%
+or not you've done that
+ 
+
+ align:start position:0%
+or not you've done that
+here's one from idx which looks at the
+
+ align:start position:0%
+here's one from idx which looks at the
+ 
+
+ align:start position:0%
+here's one from idx which looks at the
+photographs of your retina and decides
+
+ align:start position:0%
+photographs of your retina and decides
+ 
+
+ align:start position:0%
+photographs of your retina and decides
+whether you have diabetic retinopathy
+
+ align:start position:0%
+whether you have diabetic retinopathy
+ 
+
+ align:start position:0%
+whether you have diabetic retinopathy
+and actually they've published a lot of
+
+ align:start position:0%
+and actually they've published a lot of
+ 
+
+ align:start position:0%
+and actually they've published a lot of
+papers that show that they can also
+
+ align:start position:0%
+papers that show that they can also
+ 
+
+ align:start position:0%
+papers that show that they can also
+identify heart disease and stroke risk
+
+ align:start position:0%
+identify heart disease and stroke risk
+ 
+
+ align:start position:0%
+identify heart disease and stroke risk
+and various other things from those same
+
+ align:start position:0%
+and various other things from those same
+ 
+
+ align:start position:0%
+and various other things from those same
+photographs so FDA has granted them
+
+ align:start position:0%
+photographs so FDA has granted them
+ 
+
+ align:start position:0%
+photographs so FDA has granted them
+approval to market this thing
+
+ align:start position:0%
+approval to market this thing
+ 
+
+ align:start position:0%
+approval to market this thing
+another one is vis which
+
+ align:start position:0%
+another one is vis which
+ 
+
+ align:start position:0%
+another one is vis which
+automatically analyzes CT scans for ER
+
+ align:start position:0%
+automatically analyzes CT scans for ER
+ 
+
+ align:start position:0%
+automatically analyzes CT scans for ER
+patients and is looking for blockages in
+
+ align:start position:0%
+patients and is looking for blockages in
+ 
+
+ align:start position:0%
+patients and is looking for blockages in
+major brain blood vessels so this can
+
+ align:start position:0%
+major brain blood vessels so this can
+ 
+
+ align:start position:0%
+major brain blood vessels so this can
+obviously lead to a stroke and this is
+
+ align:start position:0%
+obviously lead to a stroke and this is
+ 
+
+ align:start position:0%
+obviously lead to a stroke and this is
+an automated technique that does that
+
+ align:start position:0%
+an automated technique that does that
+ 
+
+ align:start position:0%
+an automated technique that does that
+and here's another one
+
+ align:start position:0%
+and here's another one
+ 
+
+ align:start position:0%
+and here's another one
+our Duras measures and tracks tumors or
+
+ align:start position:0%
+our Duras measures and tracks tumors or
+ 
+
+ align:start position:0%
+our Duras measures and tracks tumors or
+potential cancers in radiology images so
+
+ align:start position:0%
+potential cancers in radiology images so
+ 
+
+ align:start position:0%
+potential cancers in radiology images so
+these are the the ones that have been
+
+ align:start position:0%
+these are the the ones that have been
+ 
+
+ align:start position:0%
+these are the the ones that have been
+approved and then I just wanted to
+
+ align:start position:0%
+approved and then I just wanted to
+ 
+
+ align:start position:0%
+approved and then I just wanted to
+remind you that there's actually plenty
+
+ align:start position:0%
+remind you that there's actually plenty
+ 
+
+ align:start position:0%
+remind you that there's actually plenty
+of literature about this kind of stuff
+
+ align:start position:0%
+of literature about this kind of stuff
+ 
+
+ align:start position:0%
+of literature about this kind of stuff
+so the book on the left actually comes
+
+ align:start position:0%
+so the book on the left actually comes
+ 
+
+ align:start position:0%
+so the book on the left actually comes
+out next week and I got to read a
+
+ align:start position:0%
+out next week and I got to read a
+ 
+
+ align:start position:0%
+out next week and I got to read a
+preprint of it by Eric Topol who's one
+
+ align:start position:0%
+preprint of it by Eric Topol who's one
+ 
+
+ align:start position:0%
+preprint of it by Eric Topol who's one
+of these doctors who writes a lot about
+
+ align:start position:0%
+of these doctors who writes a lot about
+ 
+
+ align:start position:0%
+of these doctors who writes a lot about
+the future of Medicine
+
+ align:start position:0%
+the future of Medicine
+ 
+
+ align:start position:0%
+the future of Medicine
+and he actually goes through tons and
+
+ align:start position:0%
+and he actually goes through tons and
+ 
+
+ align:start position:0%
+and he actually goes through tons and
+tons of examples of not only the systems
+
+ align:start position:0%
+tons of examples of not only the systems
+ 
+
+ align:start position:0%
+tons of examples of not only the systems
+that have been approved by FDA but also
+
+ align:start position:0%
+that have been approved by FDA but also
+ 
+
+ align:start position:0%
+that have been approved by FDA but also
+things that are in the works that he's
+
+ align:start position:0%
+things that are in the works that he's
+ 
+
+ align:start position:0%
+things that are in the works that he's
+very optimistic that these will again
+
+ align:start position:0%
+very optimistic that these will again
+ 
+
+ align:start position:0%
+very optimistic that these will again
+revolutionize the practice of medicine
+
+ align:start position:0%
+revolutionize the practice of medicine
+ 
+
+ align:start position:0%
+revolutionize the practice of medicine
+Bob Walker who wrote the book on the
+
+ align:start position:0%
+Bob Walker who wrote the book on the
+ 
+
+ align:start position:0%
+Bob Walker who wrote the book on the
+left a couple of years ago is a little
+
+ align:start position:0%
+left a couple of years ago is a little
+ 
+
+ align:start position:0%
+left a couple of years ago is a little
+bit more cautious because he's chief of
+
+ align:start position:0%
+bit more cautious because he's chief of
+ 
+
+ align:start position:0%
+bit more cautious because he's chief of
+medicine at UC San Francisco and he
+
+ align:start position:0%
+medicine at UC San Francisco and he
+ 
+
+ align:start position:0%
+medicine at UC San Francisco and he
+wrote this book in response to them
+
+ align:start position:0%
+wrote this book in response to them
+ 
+
+ align:start position:0%
+wrote this book in response to them
+almost killing a kid by giving him a 39
+
+ align:start position:0%
+almost killing a kid by giving him a 39
+ 
+
+ align:start position:0%
+almost killing a kid by giving him a 39
+X overdose of a medication they didn't
+
+ align:start position:0%
+X overdose of a medication they didn't
+ 
+
+ align:start position:0%
+X overdose of a medication they didn't
+quite succeed in killing the kids so it
+
+ align:start position:0%
+quite succeed in killing the kids so it
+ 
+
+ align:start position:0%
+quite succeed in killing the kids so it
+turned out okay but he was really
+
+ align:start position:0%
+turned out okay but he was really
+ 
+
+ align:start position:0%
+turned out okay but he was really
+concerned about how this wonderful
+
+ align:start position:0%
+concerned about how this wonderful
+ 
+
+ align:start position:0%
+concerned about how this wonderful
+technology led to such a disastrous
+
+ align:start position:0%
+technology led to such a disastrous
+ 
+
+ align:start position:0%
+technology led to such a disastrous
+outcome and so he spent a year studying
+
+ align:start position:0%
+outcome and so he spent a year studying
+ 
+
+ align:start position:0%
+outcome and so he spent a year studying
+how these systems are being used and
+
+ align:start position:0%
+how these systems are being used and
+ 
+
+ align:start position:0%
+how these systems are being used and
+write some more cautionary tale okay so
+
+ align:start position:0%
+write some more cautionary tale okay so
+ 
+
+ align:start position:0%
+write some more cautionary tale okay so
+let me turn to Adam who as I said is a
+
+ align:start position:0%
+let me turn to Adam who as I said is a
+ 
+
+ align:start position:0%
+let me turn to Adam who as I said is a
+professor at at the Brigham in Harvard
+
+ align:start position:0%
+professor at at the Brigham in Harvard
+ 
+
+ align:start position:0%
+professor at at the Brigham in Harvard
+Medical School and please come and join
+
+ align:start position:0%
+Medical School and please come and join
+ 
+
+ align:start position:0%
+Medical School and please come and join
+me and we can have a conversation so my
+
+ align:start position:0%
+me and we can have a conversation so my
+ 
+
+ align:start position:0%
+me and we can have a conversation so my
+name is Adam Wright I'm an associate
+
+ align:start position:0%
+name is Adam Wright I'm an associate
+ 
+
+ align:start position:0%
+name is Adam Wright I'm an associate
+professor of medicine at Harvard Medical
+
+ align:start position:0%
+professor of medicine at Harvard Medical
+ 
+
+ align:start position:0%
+professor of medicine at Harvard Medical
+School and that
+
+ align:start position:0%
+School and that
+ 
+
+ align:start position:0%
+School and that
+I lead a research program and I teach
+
+ align:start position:0%
+I lead a research program and I teach
+ 
+
+ align:start position:0%
+I lead a research program and I teach
+the introduction to biomedical
+
+ align:start position:0%
+the introduction to biomedical
+ 
+
+ align:start position:0%
+the introduction to biomedical
+informatics at courses at the Medical
+
+ align:start position:0%
+informatics at courses at the Medical
+ 
+
+ align:start position:0%
+informatics at courses at the Medical
+School so if you're interested in the
+
+ align:start position:0%
+School so if you're interested in the
+ 
+
+ align:start position:0%
+School so if you're interested in the
+topics that Pete was talking about today
+
+ align:start position:0%
+topics that Pete was talking about today
+ 
+
+ align:start position:0%
+topics that Pete was talking about today
+you should definitely consider cross
+
+ align:start position:0%
+you should definitely consider cross
+ 
+
+ align:start position:0%
+you should definitely consider cross
+registering and BMI 701 or 702 at the
+
+ align:start position:0%
+registering and BMI 701 or 702 at the
+ 
+
+ align:start position:0%
+registering and BMI 701 or 702 at the
+medical school we certainly always could
+
+ align:start position:0%
+medical school we certainly always could
+ 
+
+ align:start position:0%
+medical school we certainly always could
+use a few more enthusiastic
+
+ align:start position:0%
+use a few more enthusiastic
+ 
+
+ align:start position:0%
+use a few more enthusiastic
+technically-minded machine learning
+
+ align:start position:0%
+technically-minded machine learning
+ 
+
+ align:start position:0%
+technically-minded machine learning
+experts in our in our course and then I
+
+ align:start position:0%
+experts in our in our course and then I
+ 
+
+ align:start position:0%
+experts in our in our course and then I
+have a operational job at partners
+
+ align:start position:0%
+have a operational job at partners
+ 
+
+ align:start position:0%
+have a operational job at partners
+partners is the health system that
+
+ align:start position:0%
+partners is the health system that
+ 
+
+ align:start position:0%
+partners is the health system that
+includes Mass General Hospital and the
+
+ align:start position:0%
+includes Mass General Hospital and the
+ 
+
+ align:start position:0%
+includes Mass General Hospital and the
+Brigham and the nessam community
+
+ align:start position:0%
+Brigham and the nessam community
+ 
+
+ align:start position:0%
+Brigham and the nessam community
+hospitals and I work on partners II care
+
+ align:start position:0%
+hospitals and I work on partners II care
+ 
+
+ align:start position:0%
+hospitals and I work on partners II care
+which is our kind of cool brand name for
+
+ align:start position:0%
+which is our kind of cool brand name for
+ 
+
+ align:start position:0%
+which is our kind of cool brand name for
+it for epic so epic is a HR these are
+
+ align:start position:0%
+it for epic so epic is a HR these are
+ 
+
+ align:start position:0%
+it for epic so epic is a HR these are
+partners and I helped oversee the
+
+ align:start position:0%
+partners and I helped oversee the
+ 
+
+ align:start position:0%
+partners and I helped oversee the
+clinical decision support there so we
+
+ align:start position:0%
+clinical decision support there so we
+ 
+
+ align:start position:0%
+clinical decision support there so we
+have a decision support team I am the
+
+ align:start position:0%
+have a decision support team I am the
+ 
+
+ align:start position:0%
+have a decision support team I am the
+clinical lead for monitoring and
+
+ align:start position:0%
+clinical lead for monitoring and
+ 
+
+ align:start position:0%
+clinical lead for monitoring and
+evaluation and so I help make sure that
+
+ align:start position:0%
+evaluation and so I help make sure that
+ 
+
+ align:start position:0%
+evaluation and so I help make sure that
+our decision support systems of the the
+
+ align:start position:0%
+our decision support systems of the the
+ 
+
+ align:start position:0%
+our decision support systems of the the
+type that Pete's talking about working
+
+ align:start position:0%
+type that Pete's talking about working
+ 
+
+ align:start position:0%
+type that Pete's talking about working
+correctly so that's my job at the
+
+ align:start position:0%
+correctly so that's my job at the
+ 
+
+ align:start position:0%
+correctly so that's my job at the
+Brigham and Partners cool and and I
+
+ align:start position:0%
+Brigham and Partners cool and and I
+ 
+
+ align:start position:0%
+Brigham and Partners cool and and I
+appreciate it very much thanks I
+
+ align:start position:0%
+appreciate it very much thanks I
+ 
+
+ align:start position:0%
+appreciate it very much thanks I
+appreciate invitation it's fun to be
+
+ align:start position:0%
+appreciate invitation it's fun to be
+ 
+
+ align:start position:0%
+appreciate invitation it's fun to be
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so Adam first obvious question is so
+
+ align:start position:0%
+so Adam first obvious question is so
+ 
+
+ align:start position:0%
+so Adam first obvious question is so
+what kind of decision support systems
+
+ align:start position:0%
+what kind of decision support systems
+ 
+
+ align:start position:0%
+what kind of decision support systems
+have you guys actually put in place
+
+ align:start position:0%
+have you guys actually put in place
+ 
+
+ align:start position:0%
+have you guys actually put in place
+absolutely so I mean you know we've had
+
+ align:start position:0%
+absolutely so I mean you know we've had
+ 
+
+ align:start position:0%
+absolutely so I mean you know we've had
+a long history at the Brigham and
+
+ align:start position:0%
+a long history at the Brigham and
+ 
+
+ align:start position:0%
+a long history at the Brigham and
+partners of using decision support
+
+ align:start position:0%
+partners of using decision support
+ 
+
+ align:start position:0%
+partners of using decision support
+historically we developed our own
+
+ align:start position:0%
+historically we developed our own
+ 
+
+ align:start position:0%
+historically we developed our own
+electronic health record which was a
+
+ align:start position:0%
+electronic health record which was a
+ 
+
+ align:start position:0%
+electronic health record which was a
+little bit unusual about three years ago
+
+ align:start position:0%
+little bit unusual about three years ago
+ 
+
+ align:start position:0%
+little bit unusual about three years ago
+we switched from our self-developed
+
+ align:start position:0%
+we switched from our self-developed
+ 
+
+ align:start position:0%
+we switched from our self-developed
+system to epic which is a very widely
+
+ align:start position:0%
+system to epic which is a very widely
+ 
+
+ align:start position:0%
+system to epic which is a very widely
+used a commercial electronic health
+
+ align:start position:0%
+used a commercial electronic health
+ 
+
+ align:start position:0%
+used a commercial electronic health
+record and to the point that you gave
+
+ align:start position:0%
+record and to the point that you gave
+ 
+
+ align:start position:0%
+record and to the point that you gave
+we've really started with a lot of
+
+ align:start position:0%
+we've really started with a lot of
+ 
+
+ align:start position:0%
+we've really started with a lot of
+medication related decision support so
+
+ align:start position:0%
+medication related decision support so
+ 
+
+ align:start position:0%
+medication related decision support so
+that's things like drug interaction
+
+ align:start position:0%
+that's things like drug interaction
+ 
+
+ align:start position:0%
+that's things like drug interaction
+alerting so you prescribe two drugs that
+
+ align:start position:0%
+alerting so you prescribe two drugs that
+ 
+
+ align:start position:0%
+alerting so you prescribe two drugs that
+might interact with each other and we
+
+ align:start position:0%
+might interact with each other and we
+ 
+
+ align:start position:0%
+might interact with each other and we
+use a table you know no machine learning
+
+ align:start position:0%
+use a table you know no machine learning
+ 
+
+ align:start position:0%
+use a table you know no machine learning
+and complicated that says we think this
+
+ align:start position:0%
+and complicated that says we think this
+ 
+
+ align:start position:0%
+and complicated that says we think this
+drug might interact with this we raise
+
+ align:start position:0%
+drug might interact with this we raise
+ 
+
+ align:start position:0%
+drug might interact with this we raise
+an alert to the doctor and the
+
+ align:start position:0%
+an alert to the doctor and the
+ 
+
+ align:start position:0%
+an alert to the doctor and the
+pharmacist and they make a decision
+
+ align:start position:0%
+pharmacist and they make a decision
+ 
+
+ align:start position:0%
+pharmacist and they make a decision
+using their expertise as as the limited
+
+ align:start position:0%
+using their expertise as as the limited
+ 
+
+ align:start position:0%
+using their expertise as as the limited
+intermediary but we're going to continue
+
+ align:start position:0%
+intermediary but we're going to continue
+ 
+
+ align:start position:0%
+intermediary but we're going to continue
+with that prescription
+
+ align:start position:0%
+with that prescription
+ 
+
+ align:start position:0%
+with that prescription
+let's have some dosing support allergy
+
+ align:start position:0%
+let's have some dosing support allergy
+ 
+
+ align:start position:0%
+let's have some dosing support allergy
+checking and things like that so our
+
+ align:start position:0%
+checking and things like that so our
+ 
+
+ align:start position:0%
+checking and things like that so our
+first kind of set of decision support
+
+ align:start position:0%
+first kind of set of decision support
+ 
+
+ align:start position:0%
+first kind of set of decision support
+really was around medications and then
+
+ align:start position:0%
+really was around medications and then
+ 
+
+ align:start position:0%
+really was around medications and then
+we turned to kind of a broader set of
+
+ align:start position:0%
+we turned to kind of a broader set of
+ 
+
+ align:start position:0%
+we turned to kind of a broader set of
+things like preventive care reminders so
+
+ align:start position:0%
+things like preventive care reminders so
+ 
+
+ align:start position:0%
+things like preventive care reminders so
+identifying patients that are overdue
+
+ align:start position:0%
+identifying patients that are overdue
+ 
+
+ align:start position:0%
+identifying patients that are overdue
+for a mammogram or a pap smear or the
+
+ align:start position:0%
+for a mammogram or a pap smear or the
+ 
+
+ align:start position:0%
+for a mammogram or a pap smear or the
+might benefit from a statin or something
+
+ align:start position:0%
+might benefit from a statin or something
+ 
+
+ align:start position:0%
+might benefit from a statin or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+or a beta blocker in the case of acute
+
+ align:start position:0%
+or a beta blocker in the case of acute
+ 
+
+ align:start position:0%
+or a beta blocker in the case of acute
+marital friction and we make suggestions
+
+ align:start position:0%
+marital friction and we make suggestions
+ 
+
+ align:start position:0%
+marital friction and we make suggestions
+to the doctor or to other members of the
+
+ align:start position:0%
+to the doctor or to other members of the
+ 
+
+ align:start position:0%
+to the doctor or to other members of the
+care team to do those things again those
+
+ align:start position:0%
+care team to do those things again those
+ 
+
+ align:start position:0%
+care team to do those things again those
+historically have largely been
+
+ align:start position:0%
+historically have largely been
+ 
+
+ align:start position:0%
+historically have largely been
+rule-based
+
+ align:start position:0%
+rule-based
+ 
+
+ align:start position:0%
+rule-based
+so some experts sat down and wrote
+
+ align:start position:0%
+so some experts sat down and wrote
+ 
+
+ align:start position:0%
+so some experts sat down and wrote
+boolean if-then rules using variables
+
+ align:start position:0%
+boolean if-then rules using variables
+ 
+
+ align:start position:0%
+boolean if-then rules using variables
+that are in a patient's chart we have
+
+ align:start position:0%
+that are in a patient's chart we have
+ 
+
+ align:start position:0%
+that are in a patient's chart we have
+increasingly though started trying to
+
+ align:start position:0%
+increasingly though started trying to
+ 
+
+ align:start position:0%
+increasingly though started trying to
+use some predictive models for things
+
+ align:start position:0%
+use some predictive models for things
+ 
+
+ align:start position:0%
+use some predictive models for things
+like readmission or with their patients
+
+ align:start position:0%
+like readmission or with their patients
+ 
+
+ align:start position:0%
+like readmission or with their patients
+at risk of falling down in the hospital
+
+ align:start position:0%
+at risk of falling down in the hospital
+ 
+
+ align:start position:0%
+at risk of falling down in the hospital
+a big problem that patients often
+
+ align:start position:0%
+a big problem that patients often
+ 
+
+ align:start position:0%
+a big problem that patients often
+encounter is they're in the hospital you
+
+ align:start position:0%
+encounter is they're in the hospital you
+ 
+
+ align:start position:0%
+encounter is they're in the hospital you
+know they're kind of delirious the
+
+ align:start position:0%
+know they're kind of delirious the
+ 
+
+ align:start position:0%
+know they're kind of delirious the
+hospital is a weird place and start to
+
+ align:start position:0%
+hospital is a weird place and start to
+ 
+
+ align:start position:0%
+hospital is a weird place and start to
+get it to go to the bathroom they trip
+
+ align:start position:0%
+get it to go to the bathroom they trip
+ 
+
+ align:start position:0%
+get it to go to the bathroom they trip
+on there you know IV tubing and then
+
+ align:start position:0%
+on there you know IV tubing and then
+ 
+
+ align:start position:0%
+on there you know IV tubing and then
+they fall and are injured and so we
+
+ align:start position:0%
+they fall and are injured and so we
+ 
+
+ align:start position:0%
+they fall and are injured and so we
+would like to prevent that from
+
+ align:start position:0%
+would like to prevent that from
+ 
+
+ align:start position:0%
+would like to prevent that from
+happening cuz it's obviously kind of a
+
+ align:start position:0%
+happening cuz it's obviously kind of a
+ 
+
+ align:start position:0%
+happening cuz it's obviously kind of a
+bad thing happen to you what's here in
+
+ align:start position:0%
+bad thing happen to you what's here in
+ 
+
+ align:start position:0%
+bad thing happen to you what's here in
+the hospital and so we have some machine
+
+ align:start position:0%
+the hospital and so we have some machine
+ 
+
+ align:start position:0%
+the hospital and so we have some machine
+learning based tools for predicting
+
+ align:start position:0%
+learning based tools for predicting
+ 
+
+ align:start position:0%
+learning based tools for predicting
+patients that are at risk for Falls and
+
+ align:start position:0%
+patients that are at risk for Falls and
+ 
+
+ align:start position:0%
+patients that are at risk for Falls and
+then there is a set of you know
+
+ align:start position:0%
+then there is a set of you know
+ 
+
+ align:start position:0%
+then there is a set of you know
+interventions like putting the bed rails
+
+ align:start position:0%
+interventions like putting the bed rails
+ 
+
+ align:start position:0%
+interventions like putting the bed rails
+up or putting an alarm that buzzes when
+
+ align:start position:0%
+up or putting an alarm that buzzes when
+ 
+
+ align:start position:0%
+up or putting an alarm that buzzes when
+they're if they get out of bed or in
+
+ align:start position:0%
+they're if they get out of bed or in
+ 
+
+ align:start position:0%
+they're if they get out of bed or in
+more extreme cases having a sitter like
+
+ align:start position:0%
+more extreme cases having a sitter like
+ 
+
+ align:start position:0%
+more extreme cases having a sitter like
+a person who actually sits in the room
+
+ align:start position:0%
+a person who actually sits in the room
+ 
+
+ align:start position:0%
+a person who actually sits in the room
+with them and tries to keep them from
+
+ align:start position:0%
+with them and tries to keep them from
+ 
+
+ align:start position:0%
+with them and tries to keep them from
+getting up or assists them to the
+
+ align:start position:0%
+getting up or assists them to the
+ 
+
+ align:start position:0%
+getting up or assists them to the
+bathroom and we call someone who can
+
+ align:start position:0%
+bathroom and we call someone who can
+ 
+
+ align:start position:0%
+bathroom and we call someone who can
+assist them to the bathroom so we have
+
+ align:start position:0%
+assist them to the bathroom so we have
+ 
+
+ align:start position:0%
+assist them to the bathroom so we have
+increasingly started using those machine
+
+ align:start position:0%
+increasingly started using those machine
+ 
+
+ align:start position:0%
+increasingly started using those machine
+learning tools some of which we get from
+
+ align:start position:0%
+learning tools some of which we get from
+ 
+
+ align:start position:0%
+learning tools some of which we get from
+third parties like from our electronic
+
+ align:start position:0%
+third parties like from our electronic
+ 
+
+ align:start position:0%
+third parties like from our electronic
+health record vendor and some of which
+
+ align:start position:0%
+health record vendor and some of which
+ 
+
+ align:start position:0%
+health record vendor and some of which
+we sort of train ourselves on our own
+
+ align:start position:0%
+we sort of train ourselves on our own
+ 
+
+ align:start position:0%
+we sort of train ourselves on our own
+data that's a newer pursuit for us is
+
+ align:start position:0%
+data that's a newer pursuit for us is
+ 
+
+ align:start position:0%
+data that's a newer pursuit for us is
+this machine learning so when you have
+
+ align:start position:0%
+this machine learning so when you have
+ 
+
+ align:start position:0%
+this machine learning so when you have
+something like a risk model how do you
+
+ align:start position:0%
+something like a risk model how do you
+ 
+
+ align:start position:0%
+something like a risk model how do you
+decide where to set the threshold you
+
+ align:start position:0%
+decide where to set the threshold you
+ 
+
+ align:start position:0%
+decide where to set the threshold you
+know if I'm at 53 percent risk of
+
+ align:start position:0%
+know if I'm at 53 percent risk of
+ 
+
+ align:start position:0%
+know if I'm at 53 percent risk of
+falling yeah should you get a sitter to
+
+ align:start position:0%
+falling yeah should you get a sitter to
+ 
+
+ align:start position:0%
+falling yeah should you get a sitter to
+sit by my age it's complicated right I
+
+ align:start position:0%
+sit by my age it's complicated right I
+ 
+
+ align:start position:0%
+sit by my age it's complicated right I
+mean I would like to say that what we do
+
+ align:start position:0%
+mean I would like to say that what we do
+ 
+
+ align:start position:0%
+mean I would like to say that what we do
+is sort of a full kind of you know
+
+ align:start position:0%
+is sort of a full kind of you know
+ 
+
+ align:start position:0%
+is sort of a full kind of you know
+utility analysis right where we say we
+
+ align:start position:0%
+utility analysis right where we say we
+ 
+
+ align:start position:0%
+utility analysis right where we say we
+pay a sitter this much per hour and the
+
+ align:start position:0%
+pay a sitter this much per hour and the
+ 
+
+ align:start position:0%
+pay a sitter this much per hour and the
+risk of falling is this much and the
+
+ align:start position:0%
+risk of falling is this much and the
+ 
+
+ align:start position:0%
+risk of falling is this much and the
+cost of a fall you know most patients
+
+ align:start position:0%
+cost of a fall you know most patients
+ 
+
+ align:start position:0%
+cost of a fall you know most patients
+who fall aren't hurt but some are and so
+
+ align:start position:0%
+who fall aren't hurt but some are and so
+ 
+
+ align:start position:0%
+who fall aren't hurt but some are and so
+you would sort of calculate the you know
+
+ align:start position:0%
+you would sort of calculate the you know
+ 
+
+ align:start position:0%
+you would sort of calculate the you know
+the cost benefit of each of those things
+
+ align:start position:0%
+the cost benefit of each of those things
+ 
+
+ align:start position:0%
+the cost benefit of each of those things
+and you know sort of figure out where on
+
+ align:start position:0%
+and you know sort of figure out where on
+ 
+
+ align:start position:0%
+and you know sort of figure out where on
+the ROC curve if you want to put place
+
+ align:start position:0%
+the ROC curve if you want to put place
+ 
+
+ align:start position:0%
+the ROC curve if you want to put place
+yourself in practice I think we often
+
+ align:start position:0%
+yourself in practice I think we often
+ 
+
+ align:start position:0%
+yourself in practice I think we often
+just play it by ear in part because a
+
+ align:start position:0%
+just play it by ear in part because a
+ 
+
+ align:start position:0%
+just play it by ear in part because a
+lot of our things are intended to be
+
+ align:start position:0%
+lot of our things are intended to be
+ 
+
+ align:start position:0%
+lot of our things are intended to be
+suggestions right so so our threshold
+
+ align:start position:0%
+suggestions right so so our threshold
+ 
+
+ align:start position:0%
+suggestions right so so our threshold
+for saying to the doctor hey this
+
+ align:start position:0%
+for saying to the doctor hey this
+ 
+
+ align:start position:0%
+for saying to the doctor hey this
+patient is that elevated risk for fall
+
+ align:start position:0%
+patient is that elevated risk for fall
+ 
+
+ align:start position:0%
+patient is that elevated risk for fall
+consider doing something is pretty low
+
+ align:start position:0%
+consider doing something is pretty low
+ 
+
+ align:start position:0%
+consider doing something is pretty low
+if the system works a automatically
+
+ align:start position:0%
+if the system works a automatically
+ 
+
+ align:start position:0%
+if the system works a automatically
+ordering a sitter we might set it higher
+
+ align:start position:0%
+ordering a sitter we might set it higher
+ 
+
+ align:start position:0%
+ordering a sitter we might set it higher
+I would say that's an area
+
+ align:start position:0%
+I would say that's an area
+ 
+
+ align:start position:0%
+I would say that's an area
+of of research I would also say that one
+
+ align:start position:0%
+of of research I would also say that one
+ 
+
+ align:start position:0%
+of of research I would also say that one
+challenge we have we often set and
+
+ align:start position:0%
+challenge we have we often set and
+ 
+
+ align:start position:0%
+challenge we have we often set and
+forget these kinds of systems right and
+
+ align:start position:0%
+forget these kinds of systems right and
+ 
+
+ align:start position:0%
+forget these kinds of systems right and
+so there's you know kind of feature
+
+ align:start position:0%
+so there's you know kind of feature
+ 
+
+ align:start position:0%
+so there's you know kind of feature
+drift in patience change over time we
+
+ align:start position:0%
+drift in patience change over time we
+ 
+
+ align:start position:0%
+drift in patience change over time we
+probably should do a better job of then
+
+ align:start position:0%
+probably should do a better job of then
+ 
+
+ align:start position:0%
+probably should do a better job of then
+looking back to see how well they're
+
+ align:start position:0%
+looking back to see how well they're
+ 
+
+ align:start position:0%
+looking back to see how well they're
+actually working and making tweaks to
+
+ align:start position:0%
+actually working and making tweaks to
+ 
+
+ align:start position:0%
+actually working and making tweaks to
+the thresholds but these are of course
+
+ align:start position:0%
+the thresholds but these are of course
+ 
+
+ align:start position:0%
+the thresholds but these are of course
+very complicated decisions
+
+ align:start position:0%
+very complicated decisions
+ 
+
+ align:start position:0%
+very complicated decisions
+really I remember fifty years ago
+
+ align:start position:0%
+really I remember fifty years ago
+ 
+
+ align:start position:0%
+really I remember fifty years ago
+talking to some people in the Air Force
+
+ align:start position:0%
+talking to some people in the Air Force
+ 
+
+ align:start position:0%
+talking to some people in the Air Force
+yeah about how much should they invest
+
+ align:start position:0%
+yeah about how much should they invest
+ 
+
+ align:start position:0%
+yeah about how much should they invest
+invest in safety measures and and they
+
+ align:start position:0%
+invest in safety measures and and they
+ 
+
+ align:start position:0%
+invest in safety measures and and they
+had a utility theoretic model that said
+
+ align:start position:0%
+had a utility theoretic model that said
+ 
+
+ align:start position:0%
+had a utility theoretic model that said
+ok how much does it cost to replace a
+
+ align:start position:0%
+ok how much does it cost to replace a
+ 
+
+ align:start position:0%
+ok how much does it cost to replace a
+pilot if you kill him yeah yeah yeah
+
+ align:start position:0%
+pilot if you kill him yeah yeah yeah
+ 
+
+ align:start position:0%
+pilot if you kill him yeah yeah yeah
+yeah and this was not publicized a lot I
+
+ align:start position:0%
+yeah and this was not publicized a lot I
+ 
+
+ align:start position:0%
+yeah and this was not publicized a lot I
+mean we do calculate things like quality
+
+ align:start position:0%
+mean we do calculate things like quality
+ 
+
+ align:start position:0%
+mean we do calculate things like quality
+adjusted life years and disability
+
+ align:start position:0%
+adjusted life years and disability
+ 
+
+ align:start position:0%
+adjusted life years and disability
+adjusted life years so there is in all
+
+ align:start position:0%
+adjusted life years so there is in all
+ 
+
+ align:start position:0%
+adjusted life years so there is in all
+of medicine right is people that deploy
+
+ align:start position:0%
+of medicine right is people that deploy
+ 
+
+ align:start position:0%
+of medicine right is people that deploy
+resources kind of in this calculus and I
+
+ align:start position:0%
+resources kind of in this calculus and I
+ 
+
+ align:start position:0%
+resources kind of in this calculus and I
+think we tend to a sign of really high
+
+ align:start position:0%
+think we tend to a sign of really high
+ 
+
+ align:start position:0%
+think we tend to a sign of really high
+weight to patient harm right because
+
+ align:start position:0%
+weight to patient harm right because
+ 
+
+ align:start position:0%
+weight to patient harm right because
+patient harm is the if you think about
+
+ align:start position:0%
+patient harm is the if you think about
+ 
+
+ align:start position:0%
+patient harm is the if you think about
+the kind of the the oath the doctors
+
+ align:start position:0%
+the kind of the the oath the doctors
+ 
+
+ align:start position:0%
+the kind of the the oath the doctors
+swear right first do no harm like the
+
+ align:start position:0%
+swear right first do no harm like the
+ 
+
+ align:start position:0%
+swear right first do no harm like the
+worst thing we can do is harm you in the
+
+ align:start position:0%
+worst thing we can do is harm you in the
+ 
+
+ align:start position:0%
+worst thing we can do is harm you in the
+hospital so I think we have a pretty
+
+ align:start position:0%
+hospital so I think we have a pretty
+ 
+
+ align:start position:0%
+hospital so I think we have a pretty
+strong aversion to do that but it's hard
+
+ align:start position:0%
+strong aversion to do that but it's hard
+ 
+
+ align:start position:0%
+strong aversion to do that but it's hard
+to it's very hard to weigh these things
+
+ align:start position:0%
+to it's very hard to weigh these things
+ 
+
+ align:start position:0%
+to it's very hard to weigh these things
+I think one of the challenges we often
+
+ align:start position:0%
+I think one of the challenges we often
+ 
+
+ align:start position:0%
+I think one of the challenges we often
+run into is that different doctors would
+
+ align:start position:0%
+run into is that different doctors would
+ 
+
+ align:start position:0%
+run into is that different doctors would
+make different decisions right so if you
+
+ align:start position:0%
+make different decisions right so if you
+ 
+
+ align:start position:0%
+make different decisions right so if you
+put the same patient in front of 10
+
+ align:start position:0%
+put the same patient in front of 10
+ 
+
+ align:start position:0%
+put the same patient in front of 10
+doctors and said does this patient need
+
+ align:start position:0%
+doctors and said does this patient need
+ 
+
+ align:start position:0%
+doctors and said does this patient need
+a sitter maybe half would say yes and
+
+ align:start position:0%
+a sitter maybe half would say yes and
+ 
+
+ align:start position:0%
+a sitter maybe half would say yes and
+half would say no and so it's especially
+
+ align:start position:0%
+half would say no and so it's especially
+ 
+
+ align:start position:0%
+half would say no and so it's especially
+hard to know what to do with a decision
+
+ align:start position:0%
+hard to know what to do with a decision
+ 
+
+ align:start position:0%
+hard to know what to do with a decision
+support system if the humans can't agree
+
+ align:start position:0%
+support system if the humans can't agree
+ 
+
+ align:start position:0%
+support system if the humans can't agree
+on what you should do in the so the
+
+ align:start position:0%
+on what you should do in the so the
+ 
+
+ align:start position:0%
+on what you should do in the so the
+other thing we talked about on the phone
+
+ align:start position:0%
+other thing we talked about on the phone
+ 
+
+ align:start position:0%
+other thing we talked about on the phone
+yesterday is I was concerned a few years
+
+ align:start position:0%
+yesterday is I was concerned a few years
+ 
+
+ align:start position:0%
+yesterday is I was concerned a few years
+ago I was visiting one of these August
+
+ align:start position:0%
+ago I was visiting one of these August
+ 
+
+ align:start position:0%
+ago I was visiting one of these August
+Boston area hospitals and and asked to
+
+ align:start position:0%
+Boston area hospitals and and asked to
+ 
+
+ align:start position:0%
+Boston area hospitals and and asked to
+see a an example of somebody interacting
+
+ align:start position:0%
+see a an example of somebody interacting
+ 
+
+ align:start position:0%
+see a an example of somebody interacting
+with this computerized physician order
+
+ align:start position:0%
+with this computerized physician order
+ 
+
+ align:start position:0%
+with this computerized physician order
+entry system and the the senior resident
+
+ align:start position:0%
+entry system and the the senior resident
+ 
+
+ align:start position:0%
+entry system and the the senior resident
+who was taking me around went up to the
+
+ align:start position:0%
+who was taking me around went up to the
+ 
+
+ align:start position:0%
+who was taking me around went up to the
+computer and said well I think I
+
+ align:start position:0%
+computer and said well I think I
+ 
+
+ align:start position:0%
+computer and said well I think I
+remember how to use this and I said wait
+
+ align:start position:0%
+remember how to use this and I said wait
+ 
+
+ align:start position:0%
+remember how to use this and I said wait
+a minute
+
+ align:start position:0%
+a minute
+ 
+
+ align:start position:0%
+a minute
+this is something you were expected to
+
+ align:start position:0%
+this is something you were expected to
+ 
+
+ align:start position:0%
+this is something you were expected to
+use daily
+
+ align:start position:0%
+use daily
+ 
+
+ align:start position:0%
+use daily
+but in reality what happens is that it's
+
+ align:start position:0%
+but in reality what happens is that it's
+ 
+
+ align:start position:0%
+but in reality what happens is that it's
+not the senior doctors or even the
+
+ align:start position:0%
+not the senior doctors or even the
+ 
+
+ align:start position:0%
+not the senior doctors or even the
+medium senior doctors it's it's the
+
+ align:start position:0%
+medium senior doctors it's it's the
+ 
+
+ align:start position:0%
+medium senior doctors it's it's the
+interns on the junior residents who
+
+ align:start position:0%
+interns on the junior residents who
+ 
+
+ align:start position:0%
+interns on the junior residents who
+actually use the system's Easter yeah
+
+ align:start position:0%
+actually use the system's Easter yeah
+ 
+
+ align:start position:0%
+actually use the system's Easter yeah
+and the concern I had was that it takes
+
+ align:start position:0%
+and the concern I had was that it takes
+ 
+
+ align:start position:0%
+and the concern I had was that it takes
+a junior resident with a lot of guts to
+
+ align:start position:0%
+a junior resident with a lot of guts to
+ 
+
+ align:start position:0%
+a junior resident with a lot of guts to
+go up to the you know chief of your
+
+ align:start position:0%
+go up to the you know chief of your
+ 
+
+ align:start position:0%
+go up to the you know chief of your
+service and say dr. X even though you
+
+ align:start position:0%
+service and say dr. X even though you
+ 
+
+ align:start position:0%
+service and say dr. X even though you
+asked me to order this drug for this
+
+ align:start position:0%
+asked me to order this drug for this
+ 
+
+ align:start position:0%
+asked me to order this drug for this
+patient the computer is arguing back
+
+ align:start position:0%
+patient the computer is arguing back
+ 
+
+ align:start position:0%
+patient the computer is arguing back
+that you should use this other one
+
+ align:start position:0%
+that you should use this other one
+ 
+
+ align:start position:0%
+that you should use this other one
+instead yeah it does and in fact I
+
+ align:start position:0%
+instead yeah it does and in fact I
+ 
+
+ align:start position:0%
+instead yeah it does and in fact I
+actually thought about this a little
+
+ align:start position:0%
+actually thought about this a little
+ 
+
+ align:start position:0%
+actually thought about this a little
+more after we chatted about it and we've
+
+ align:start position:0%
+more after we chatted about it and we've
+ 
+
+ align:start position:0%
+more after we chatted about it and we've
+heard from residents that people said to
+
+ align:start position:0%
+heard from residents that people said to
+ 
+
+ align:start position:0%
+heard from residents that people said to
+them if you dare page me with an epic
+
+ align:start position:0%
+them if you dare page me with an epic
+ 
+
+ align:start position:0%
+them if you dare page me with an epic
+suggestion in the middle of the night
+
+ align:start position:0%
+suggestion in the middle of the night
+ 
+
+ align:start position:0%
+suggestion in the middle of the night
+I'll never talk to you again so you know
+
+ align:start position:0%
+I'll never talk to you again so you know
+ 
+
+ align:start position:0%
+I'll never talk to you again so you know
+just override all of those alerts so I
+
+ align:start position:0%
+just override all of those alerts so I
+ 
+
+ align:start position:0%
+just override all of those alerts so I
+think that you know one of the
+
+ align:start position:0%
+think that you know one of the
+ 
+
+ align:start position:0%
+think that you know one of the
+challenges says and there's some you
+
+ align:start position:0%
+challenges says and there's some you
+ 
+
+ align:start position:0%
+challenges says and there's some you
+know as a cool billionaire on our part
+
+ align:start position:0%
+know as a cool billionaire on our part
+ 
+
+ align:start position:0%
+know as a cool billionaire on our part
+is that a lot of these alerts we give
+
+ align:start position:0%
+is that a lot of these alerts we give
+ 
+
+ align:start position:0%
+is that a lot of these alerts we give
+are you know to have a PPV of like you
+
+ align:start position:0%
+are you know to have a PPV of like you
+ 
+
+ align:start position:0%
+are you know to have a PPV of like you
+know ten or twenty percent right you
+
+ align:start position:0%
+know ten or twenty percent right you
+ 
+
+ align:start position:0%
+know ten or twenty percent right you
+know they are usually wrong it's we
+
+ align:start position:0%
+know they are usually wrong it's we
+ 
+
+ align:start position:0%
+know they are usually wrong it's we
+think it's really important so we really
+
+ align:start position:0%
+think it's really important so we really
+ 
+
+ align:start position:0%
+think it's really important so we really
+raised these or it's a lot but people
+
+ align:start position:0%
+raised these or it's a lot but people
+ 
+
+ align:start position:0%
+raised these or it's a lot but people
+experience this kind of alert fatigue or
+
+ align:start position:0%
+experience this kind of alert fatigue or
+ 
+
+ align:start position:0%
+experience this kind of alert fatigue or
+what people call alarm fatigue you see
+
+ align:start position:0%
+what people call alarm fatigue you see
+ 
+
+ align:start position:0%
+what people call alarm fatigue you see
+this in cockpits too but people get too
+
+ align:start position:0%
+this in cockpits too but people get too
+ 
+
+ align:start position:0%
+this in cockpits too but people get too
+many alerts and they start ignoring the
+
+ align:start position:0%
+many alerts and they start ignoring the
+ 
+
+ align:start position:0%
+many alerts and they start ignoring the
+alert so they assume that they're wrong
+
+ align:start position:0%
+alert so they assume that they're wrong
+ 
+
+ align:start position:0%
+alert so they assume that they're wrong
+they tell the resident not to page them
+
+ align:start position:0%
+they tell the resident not to page them
+ 
+
+ align:start position:0%
+they tell the resident not to page them
+in the moment I know no matter what the
+
+ align:start position:0%
+in the moment I know no matter what the
+ 
+
+ align:start position:0%
+in the moment I know no matter what the
+computer says so I do think that we have
+
+ align:start position:0%
+computer says so I do think that we have
+ 
+
+ align:start position:0%
+computer says so I do think that we have
+some some responsibility to improve the
+
+ align:start position:0%
+some some responsibility to improve the
+ 
+
+ align:start position:0%
+some some responsibility to improve the
+accuracy of these alerts and I do think
+
+ align:start position:0%
+accuracy of these alerts and I do think
+ 
+
+ align:start position:0%
+accuracy of these alerts and I do think
+you know machine learning could help us
+
+ align:start position:0%
+you know machine learning could help us
+ 
+
+ align:start position:0%
+you know machine learning could help us
+we're actually just having a meeting
+
+ align:start position:0%
+we're actually just having a meeting
+ 
+
+ align:start position:0%
+we're actually just having a meeting
+about a pneumococcal vaccination alert
+
+ align:start position:0%
+about a pneumococcal vaccination alert
+ 
+
+ align:start position:0%
+about a pneumococcal vaccination alert
+system it helps people remember to
+
+ align:start position:0%
+system it helps people remember to
+ 
+
+ align:start position:0%
+system it helps people remember to
+prescribe this facts they should help
+
+ align:start position:0%
+prescribe this facts they should help
+ 
+
+ align:start position:0%
+prescribe this facts they should help
+you not get pneumonia and it takes four
+
+ align:start position:0%
+you not get pneumonia and it takes four
+ 
+
+ align:start position:0%
+you not get pneumonia and it takes four
+or five variables into account and we
+
+ align:start position:0%
+or five variables into account and we
+ 
+
+ align:start position:0%
+or five variables into account and we
+started looking at the cases when people
+
+ align:start position:0%
+started looking at the cases when people
+ 
+
+ align:start position:0%
+started looking at the cases when people
+would override the alert and they were
+
+ align:start position:0%
+would override the alert and they were
+ 
+
+ align:start position:0%
+would override the alert and they were
+mostly appropriate right so the patient
+
+ align:start position:0%
+mostly appropriate right so the patient
+ 
+
+ align:start position:0%
+mostly appropriate right so the patient
+is you know in a really extreme state
+
+ align:start position:0%
+is you know in a really extreme state
+ 
+
+ align:start position:0%
+is you know in a really extreme state
+right now or conversely the patient is
+
+ align:start position:0%
+right now or conversely the patient is
+ 
+
+ align:start position:0%
+right now or conversely the patient is
+close to the end of life and they're not
+
+ align:start position:0%
+close to the end of life and they're not
+ 
+
+ align:start position:0%
+close to the end of life and they're not
+going to benefit from this vaccination
+
+ align:start position:0%
+going to benefit from this vaccination
+ 
+
+ align:start position:0%
+going to benefit from this vaccination
+or patient has a phobia of needles the
+
+ align:start position:0%
+or patient has a phobia of needles the
+ 
+
+ align:start position:0%
+or patient has a phobia of needles the
+patient has an insurance problem and we
+
+ align:start position:0%
+patient has an insurance problem and we
+ 
+
+ align:start position:0%
+patient has an insurance problem and we
+think there's probably more like 30 or
+
+ align:start position:0%
+think there's probably more like 30 or
+ 
+
+ align:start position:0%
+think there's probably more like 30 or
+40 variables that you would need to take
+
+ align:start position:0%
+40 variables that you would need to take
+ 
+
+ align:start position:0%
+40 variables that you would need to take
+into account to make that really
+
+ align:start position:0%
+into account to make that really
+ 
+
+ align:start position:0%
+into account to make that really
+accurate and so the question is many of
+
+ align:start position:0%
+accurate and so the question is many of
+ 
+
+ align:start position:0%
+accurate and so the question is many of
+that many variables
+
+ align:start position:0%
+that many variables
+ 
+
+ align:start position:0%
+that many variables
+can a human develop and maintain that
+
+ align:start position:0%
+can a human develop and maintain that
+ 
+
+ align:start position:0%
+can a human develop and maintain that
+logic
+
+ align:start position:0%
+logic
+ 
+
+ align:start position:0%
+logic
+or would we be better off trying to use
+
+ align:start position:0%
+or would we be better off trying to use
+ 
+
+ align:start position:0%
+or would we be better off trying to use
+a machine learning system to do that
+
+ align:start position:0%
+a machine learning system to do that
+ 
+
+ align:start position:0%
+a machine learning system to do that
+would that really work or not it's so so
+
+ align:start position:0%
+would that really work or not it's so so
+ 
+
+ align:start position:0%
+would that really work or not it's so so
+how far are we from being able to use
+
+ align:start position:0%
+how far are we from being able to use
+ 
+
+ align:start position:0%
+how far are we from being able to use
+the machine learning system to do that
+
+ align:start position:0%
+the machine learning system to do that
+ 
+
+ align:start position:0%
+the machine learning system to do that
+yeah I think that the biggest challenge
+
+ align:start position:0%
+yeah I think that the biggest challenge
+ 
+
+ align:start position:0%
+yeah I think that the biggest challenge
+honestly relates to this group available
+
+ align:start position:0%
+honestly relates to this group available
+ 
+
+ align:start position:0%
+honestly relates to this group available
+in accuracy of the data in our systems
+
+ align:start position:0%
+in accuracy of the data in our systems
+ 
+
+ align:start position:0%
+in accuracy of the data in our systems
+so epoch which is the EHR that we're
+
+ align:start position:0%
+so epoch which is the EHR that we're
+ 
+
+ align:start position:0%
+so epoch which is the EHR that we're
+using and Cerner and all scripts and
+
+ align:start position:0%
+using and Cerner and all scripts and
+ 
+
+ align:start position:0%
+using and Cerner and all scripts and
+mostly major systems have various ways
+
+ align:start position:0%
+mostly major systems have various ways
+ 
+
+ align:start position:0%
+mostly major systems have various ways
+to run even kind of sophisticated
+
+ align:start position:0%
+to run even kind of sophisticated
+ 
+
+ align:start position:0%
+to run even kind of sophisticated
+machine learning models either inside of
+
+ align:start position:0%
+machine learning models either inside of
+ 
+
+ align:start position:0%
+machine learning models either inside of
+the system or sort of kind of bolted on
+
+ align:start position:0%
+the system or sort of kind of bolted on
+ 
+
+ align:start position:0%
+the system or sort of kind of bolted on
+to the system than feeding model
+
+ align:start position:0%
+to the system than feeding model
+ 
+
+ align:start position:0%
+to the system than feeding model
+inferences back into their to the system
+
+ align:start position:0%
+inferences back into their to the system
+ 
+
+ align:start position:0%
+inferences back into their to the system
+when I was giving that example in
+
+ align:start position:0%
+when I was giving that example in
+ 
+
+ align:start position:0%
+when I was giving that example in
+pneumococcal vaccination one of the
+
+ align:start position:0%
+pneumococcal vaccination one of the
+ 
+
+ align:start position:0%
+pneumococcal vaccination one of the
+major problems is that there's not
+
+ align:start position:0%
+major problems is that there's not
+ 
+
+ align:start position:0%
+major problems is that there's not
+always a really good structured way in
+
+ align:start position:0%
+always a really good structured way in
+ 
+
+ align:start position:0%
+always a really good structured way in
+the system that we indicate that a
+
+ align:start position:0%
+the system that we indicate that a
+ 
+
+ align:start position:0%
+the system that we indicate that a
+patient is at the end of life and
+
+ align:start position:0%
+patient is at the end of life and
+ 
+
+ align:start position:0%
+patient is at the end of life and
+receiving comfort measures only or the
+
+ align:start position:0%
+receiving comfort measures only or the
+ 
+
+ align:start position:0%
+receiving comfort measures only or the
+patient is in a really extreme state
+
+ align:start position:0%
+patient is in a really extreme state
+ 
+
+ align:start position:0%
+patient is in a really extreme state
+that we're in the middle of the code
+
+ align:start position:0%
+that we're in the middle of the code
+ 
+
+ align:start position:0%
+that we're in the middle of the code
+blue and that we need to sort of pause
+
+ align:start position:0%
+blue and that we need to sort of pause
+ 
+
+ align:start position:0%
+blue and that we need to sort of pause
+for a second it's not given you know
+
+ align:start position:0%
+for a second it's not given you know
+ 
+
+ align:start position:0%
+for a second it's not given you know
+these kind of friendly preventive care
+
+ align:start position:0%
+these kind of friendly preventive care
+ 
+
+ align:start position:0%
+these kind of friendly preventive care
+suggestions and so I would actually say
+
+ align:start position:0%
+suggestions and so I would actually say
+ 
+
+ align:start position:0%
+suggestions and so I would actually say
+that the biggest barrier to really good
+
+ align:start position:0%
+that the biggest barrier to really good
+ 
+
+ align:start position:0%
+that the biggest barrier to really good
+machine learning based decision support
+
+ align:start position:0%
+machine learning based decision support
+ 
+
+ align:start position:0%
+machine learning based decision support
+is just the the lack of good reliably
+
+ align:start position:0%
+is just the the lack of good reliably
+ 
+
+ align:start position:0%
+is just the the lack of good reliably
+documented coded useable features I
+
+ align:start position:0%
+documented coded useable features I
+ 
+
+ align:start position:0%
+documented coded useable features I
+think that the second challenge on
+
+ align:start position:0%
+think that the second challenge on
+ 
+
+ align:start position:0%
+think that the second challenge on
+Hugh's work flow right you said sort of
+
+ align:start position:0%
+Hugh's work flow right you said sort of
+ 
+
+ align:start position:0%
+Hugh's work flow right you said sort of
+you know it's sometimes hard to know in
+
+ align:start position:0%
+you know it's sometimes hard to know in
+ 
+
+ align:start position:0%
+you know it's sometimes hard to know in
+the hospital who a patient's doctor is
+
+ align:start position:0%
+the hospital who a patient's doctor is
+ 
+
+ align:start position:0%
+the hospital who a patient's doctor is
+right the patient is admitted and on the
+
+ align:start position:0%
+right the patient is admitted and on the
+ 
+
+ align:start position:0%
+right the patient is admitted and on the
+care team is an intern a junior resident
+
+ align:start position:0%
+care team is an intern a junior resident
+ 
+
+ align:start position:0%
+care team is an intern a junior resident
+and a fellow and attending several
+
+ align:start position:0%
+and a fellow and attending several
+ 
+
+ align:start position:0%
+and a fellow and attending several
+specialists a couple of nurses and who
+
+ align:start position:0%
+specialists a couple of nurses and who
+ 
+
+ align:start position:0%
+specialists a couple of nurses and who
+should get that message or who should
+
+ align:start position:0%
+should get that message or who should
+ 
+
+ align:start position:0%
+should get that message or who should
+get that page workflow is second my this
+
+ align:start position:0%
+get that page workflow is second my this
+ 
+
+ align:start position:0%
+get that page workflow is second my this
+is where I think a you may sister I have
+
+ align:start position:0%
+is where I think a you may sister I have
+ 
+
+ align:start position:0%
+is where I think a you may sister I have
+some optimism I actually think that the
+
+ align:start position:0%
+some optimism I actually think that the
+ 
+
+ align:start position:0%
+some optimism I actually think that the
+technical ability of our EHR software to
+
+ align:start position:0%
+technical ability of our EHR software to
+ 
+
+ align:start position:0%
+technical ability of our EHR software to
+run these models is is better than it
+
+ align:start position:0%
+run these models is is better than it
+ 
+
+ align:start position:0%
+run these models is is better than it
+was three or five years ago and it's
+
+ align:start position:0%
+was three or five years ago and it's
+ 
+
+ align:start position:0%
+was three or five years ago and it's
+actually usually not the barrier we've
+
+ align:start position:0%
+actually usually not the barrier we've
+ 
+
+ align:start position:0%
+actually usually not the barrier we've
+done so there there were attempts again
+
+ align:start position:0%
+done so there there were attempts again
+ 
+
+ align:start position:0%
+done so there there were attempts again
+20 years ago to create kind of formal
+
+ align:start position:0%
+20 years ago to create kind of formal
+ 
+
+ align:start position:0%
+20 years ago to create kind of formal
+rules about who gets notified under what
+
+ align:start position:0%
+rules about who gets notified under what
+ 
+
+ align:start position:0%
+rules about who gets notified under what
+circumstances I remember one of the
+
+ align:start position:0%
+circumstances I remember one of the
+ 
+
+ align:start position:0%
+circumstances I remember one of the
+doctors I worked with at Tufts Medical
+
+ align:start position:0%
+doctors I worked with at Tufts Medical
+ 
+
+ align:start position:0%
+doctors I worked with at Tufts Medical
+Center was going crazy because that when
+
+ align:start position:0%
+Center was going crazy because that when
+ 
+
+ align:start position:0%
+Center was going crazy because that when
+they implemented a new lab information
+
+ align:start position:0%
+they implemented a new lab information
+ 
+
+ align:start position:0%
+they implemented a new lab information
+system it would alert on every other lab
+
+ align:start position:0%
+system it would alert on every other lab
+ 
+
+ align:start position:0%
+system it would alert on every other lab
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is crazy but there were other
+
+ align:start position:0%
+this is crazy but there were other
+ 
+
+ align:start position:0%
+this is crazy but there were other
+hospitals that said well let's be a
+
+ align:start position:0%
+hospitals that said well let's be a
+ 
+
+ align:start position:0%
+hospitals that said well let's be a
+little more sophisticated about when
+
+ align:start position:0%
+little more sophisticated about when
+ 
+
+ align:start position:0%
+little more sophisticated about when
+it's necessary to alert and then if
+
+ align:start position:0%
+it's necessary to alert and then if
+ 
+
+ align:start position:0%
+it's necessary to alert and then if
+somebody doesn't respond to an alert
+
+ align:start position:0%
+somebody doesn't respond to an alert
+ 
+
+ align:start position:0%
+somebody doesn't respond to an alert
+within a very short period of time then
+
+ align:start position:0%
+within a very short period of time then
+ 
+
+ align:start position:0%
+within a very short period of time then
+we escalate it to somebody higher up or
+
+ align:start position:0%
+we escalate it to somebody higher up or
+ 
+
+ align:start position:0%
+we escalate it to somebody higher up or
+somebody else on the care team and that
+
+ align:start position:0%
+somebody else on the care team and that
+ 
+
+ align:start position:0%
+somebody else on the care team and that
+seemed like a reasonable idea to me but
+
+ align:start position:0%
+seemed like a reasonable idea to me but
+ 
+
+ align:start position:0%
+seemed like a reasonable idea to me but
+are there things like that in place now
+
+ align:start position:0%
+are there things like that in place now
+ 
+
+ align:start position:0%
+are there things like that in place now
+there are it works very differently the
+
+ align:start position:0%
+there are it works very differently the
+ 
+
+ align:start position:0%
+there are it works very differently the
+inpatient and the outpatient setting
+
+ align:start position:0%
+inpatient and the outpatient setting
+ 
+
+ align:start position:0%
+inpatient and the outpatient setting
+right the inpatient setting were writing
+
+ align:start position:0%
+right the inpatient setting were writing
+ 
+
+ align:start position:0%
+right the inpatient setting were writing
+very kind of acute care to a patient and
+
+ align:start position:0%
+very kind of acute care to a patient and
+ 
+
+ align:start position:0%
+very kind of acute care to a patient and
+so we have processes where people sort
+
+ align:start position:0%
+so we have processes where people sort
+ 
+
+ align:start position:0%
+so we have processes where people sort
+of sign in and out of the the care team
+
+ align:start position:0%
+of sign in and out of the the care team
+ 
+
+ align:start position:0%
+of sign in and out of the the care team
+and in fact these sort of prevalence of
+
+ align:start position:0%
+and in fact these sort of prevalence of
+ 
+
+ align:start position:0%
+and in fact these sort of prevalence of
+these automated messages is an incentive
+
+ align:start position:0%
+these automated messages is an incentive
+ 
+
+ align:start position:0%
+these automated messages is an incentive
+to sort of do that well right so if I go
+
+ align:start position:0%
+to sort of do that well right so if I go
+ 
+
+ align:start position:0%
+to sort of do that well right so if I go
+home I better sign myself out of that
+
+ align:start position:0%
+home I better sign myself out of that
+ 
+
+ align:start position:0%
+home I better sign myself out of that
+patient otherwise I'm gonna get all
+
+ align:start position:0%
+patient otherwise I'm gonna get all
+ 
+
+ align:start position:0%
+patient otherwise I'm gonna get all
+these pages all night about them and the
+
+ align:start position:0%
+these pages all night about them and the
+ 
+
+ align:start position:0%
+these pages all night about them and the
+system sort of well you don't always
+
+ align:start position:0%
+system sort of well you don't always
+ 
+
+ align:start position:0%
+system sort of well you don't always
+make sure that somebody is they're
+
+ align:start position:0%
+make sure that somebody is they're
+ 
+
+ align:start position:0%
+make sure that somebody is they're
+responding a provider it becomes a
+
+ align:start position:0%
+responding a provider it becomes a
+ 
+
+ align:start position:0%
+responding a provider it becomes a
+little thorny er in the outpatient
+
+ align:start position:0%
+little thorny er in the outpatient
+ 
+
+ align:start position:0%
+little thorny er in the outpatient
+setting right because a lot of e to the
+
+ align:start position:0%
+setting right because a lot of e to the
+ 
+
+ align:start position:0%
+setting right because a lot of e to the
+academic doctors at the Brigham only
+
+ align:start position:0%
+academic doctors at the Brigham only
+ 
+
+ align:start position:0%
+academic doctors at the Brigham only
+have clinic you know half a day a week
+
+ align:start position:0%
+have clinic you know half a day a week
+ 
+
+ align:start position:0%
+have clinic you know half a day a week
+and so the question is if an abnormal
+
+ align:start position:0%
+and so the question is if an abnormal
+ 
+
+ align:start position:0%
+and so the question is if an abnormal
+result comes back should I send it to
+
+ align:start position:0%
+result comes back should I send it to
+ 
+
+ align:start position:0%
+result comes back should I send it to
+that doctor should I send it to the
+
+ align:start position:0%
+that doctor should I send it to the
+ 
+
+ align:start position:0%
+that doctor should I send it to the
+person sort of on-call in that clinic
+
+ align:start position:0%
+person sort of on-call in that clinic
+ 
+
+ align:start position:0%
+person sort of on-call in that clinic
+should I send it to the to the head of
+
+ align:start position:0%
+should I send it to the to the head of
+ 
+
+ align:start position:0%
+should I send it to the to the head of
+the clinic there are also these sort of
+
+ align:start position:0%
+the clinic there are also these sort of
+ 
+
+ align:start position:0%
+the clinic there are also these sort of
+edge cases that sort of mess us up a lot
+
+ align:start position:0%
+edge cases that sort of mess us up a lot
+ 
+
+ align:start position:0%
+edge cases that sort of mess us up a lot
+right and so a classic one is a patient
+
+ align:start position:0%
+right and so a classic one is a patient
+ 
+
+ align:start position:0%
+right and so a classic one is a patient
+is in the hospital I've ordered some lab
+
+ align:start position:0%
+is in the hospital I've ordered some lab
+ 
+
+ align:start position:0%
+is in the hospital I've ordered some lab
+tests they're looking well so I
+
+ align:start position:0%
+tests they're looking well so I
+ 
+
+ align:start position:0%
+tests they're looking well so I
+discharged the patient the test is still
+
+ align:start position:0%
+discharged the patient the test is still
+ 
+
+ align:start position:0%
+discharged the patient the test is still
+pending at the time the patient is
+
+ align:start position:0%
+pending at the time the patient is
+ 
+
+ align:start position:0%
+pending at the time the patient is
+discharged and now who does that go to
+
+ align:start position:0%
+discharged and now who does that go to
+ 
+
+ align:start position:0%
+discharged and now who does that go to
+like it to go to the patient's primary
+
+ align:start position:0%
+like it to go to the patient's primary
+ 
+
+ align:start position:0%
+like it to go to the patient's primary
+care doctor do they have a primary care
+
+ align:start position:0%
+care doctor do they have a primary care
+ 
+
+ align:start position:0%
+care doctor do they have a primary care
+doctor should it go to the person who
+
+ align:start position:0%
+doctor should it go to the person who
+ 
+
+ align:start position:0%
+doctor should it go to the person who
+ordered the tests that person may be on
+
+ align:start position:0%
+ordered the tests that person may be on
+ 
+
+ align:start position:0%
+ordered the tests that person may be on
+vacation now if it's a test that kind of
+
+ align:start position:0%
+vacation now if it's a test that kind of
+ 
+
+ align:start position:0%
+vacation now if it's a test that kind of
+takes him he wants to come back so he
+
+ align:start position:0%
+takes him he wants to come back so he
+ 
+
+ align:start position:0%
+takes him he wants to come back so he
+still circled with all those tea pads
+
+ align:start position:0%
+still circled with all those tea pads
+ 
+
+ align:start position:0%
+still circled with all those tea pads
+tests pending a district we still circle
+
+ align:start position:0%
+tests pending a district we still circle
+ 
+
+ align:start position:0%
+tests pending a district we still circle
+with some someone's edge cases but I
+
+ align:start position:0%
+with some someone's edge cases but I
+ 
+
+ align:start position:0%
+with some someone's edge cases but I
+think in the core we're pretty good at
+
+ align:start position:0%
+think in the core we're pretty good at
+ 
+
+ align:start position:0%
+think in the core we're pretty good at
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of the things we talked about is
+
+ align:start position:0%
+so one of the things we talked about is
+ 
+
+ align:start position:0%
+so one of the things we talked about is
+an experience I've had and you've
+
+ align:start position:0%
+an experience I've had and you've
+ 
+
+ align:start position:0%
+an experience I've had and you've
+probably had that for example a few
+
+ align:start position:0%
+probably had that for example a few
+ 
+
+ align:start position:0%
+probably had that for example a few
+years ago I was working with the people
+
+ align:start position:0%
+years ago I was working with the people
+ 
+
+ align:start position:0%
+years ago I was working with the people
+who run the clinical labs at Mass
+
+ align:start position:0%
+who run the clinical labs at Mass
+ 
+
+ align:start position:0%
+who run the clinical labs at Mass
+General and they run some ancient
+
+ align:start position:0%
+General and they run some ancient
+ 
+
+ align:start position:0%
+General and they run some ancient
+laboratory information systems that as
+
+ align:start position:0%
+laboratory information systems that as
+ 
+
+ align:start position:0%
+laboratory information systems that as
+you said can add and subtract but
+
+ align:start position:0%
+you said can add and subtract but
+ 
+
+ align:start position:0%
+you said can add and subtract but
+multiply or divide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't support negative numbers only
+
+ align:start position:0%
+it doesn't support negative numbers only
+ 
+
+ align:start position:0%
+it doesn't support negative numbers only
+unsigned integers so there are these
+
+ align:start position:0%
+unsigned integers so there are these
+ 
+
+ align:start position:0%
+unsigned integers so there are these
+wonderful legacy systems around that
+
+ align:start position:0%
+wonderful legacy systems around that
+ 
+
+ align:start position:0%
+wonderful legacy systems around that
+that really create horrendous problems
+
+ align:start position:0%
+that really create horrendous problems
+ 
+
+ align:start position:0%
+that really create horrendous problems
+because if you try to build anything I
+
+ align:start position:0%
+because if you try to build anything I
+ 
+
+ align:start position:0%
+because if you try to build anything I
+mean even a risk prediction calculator
+
+ align:start position:0%
+mean even a risk prediction calculator
+ 
+
+ align:start position:0%
+mean even a risk prediction calculator
+it really helps to be able to divide
+
+ align:start position:0%
+it really helps to be able to divide
+ 
+
+ align:start position:0%
+it really helps to be able to divide
+sure was multiplying and so we've
+
+ align:start position:0%
+sure was multiplying and so we've
+ 
+
+ align:start position:0%
+sure was multiplying and so we've
+struggled in that project and I'm sure
+
+ align:start position:0%
+struggled in that project and I'm sure
+ 
+
+ align:start position:0%
+struggled in that project and I'm sure
+you've had similar experiences with how
+
+ align:start position:0%
+you've had similar experiences with how
+ 
+
+ align:start position:0%
+you've had similar experiences with how
+do we incorporate a decision support
+
+ align:start position:0%
+do we incorporate a decision support
+ 
+
+ align:start position:0%
+do we incorporate a decision support
+system into some of this Cree Heald
+
+ align:start position:0%
+system into some of this Cree Heald
+ 
+
+ align:start position:0%
+system into some of this Cree Heald
+technology that that just doesn't
+
+ align:start position:0%
+technology that that just doesn't
+ 
+
+ align:start position:0%
+technology that that just doesn't
+support it yeah so what what's the right
+
+ align:start position:0%
+support it yeah so what what's the right
+ 
+
+ align:start position:0%
+support it yeah so what what's the right
+approach there are a lot of
+
+ align:start position:0%
+approach there are a lot of
+ 
+
+ align:start position:0%
+approach there are a lot of
+architectures and they all have pros and
+
+ align:start position:0%
+architectures and they all have pros and
+ 
+
+ align:start position:0%
+architectures and they all have pros and
+cons I'm not sure if any one of them is
+
+ align:start position:0%
+cons I'm not sure if any one of them is
+ 
+
+ align:start position:0%
+cons I'm not sure if any one of them is
+sort of the right approach I think we
+
+ align:start position:0%
+sort of the right approach I think we
+ 
+
+ align:start position:0%
+sort of the right approach I think we
+often do favor using the sort of you
+
+ align:start position:0%
+often do favor using the sort of you
+ 
+
+ align:start position:0%
+often do favor using the sort of you
+know creaky old technology or the new
+
+ align:start position:0%
+know creaky old technology or the new
+ 
+
+ align:start position:0%
+know creaky old technology or the new
+technology right so epic has a built-in
+
+ align:start position:0%
+technology right so epic has a built-in
+ 
+
+ align:start position:0%
+technology right so epic has a built-in
+rule engine that laboratory system you
+
+ align:start position:0%
+rule engine that laboratory system you
+ 
+
+ align:start position:0%
+rule engine that laboratory system you
+talked about has a basic calculation
+
+ align:start position:0%
+talked about has a basic calculation
+ 
+
+ align:start position:0%
+talked about has a basic calculation
+engine with some significant limitations
+
+ align:start position:0%
+engine with some significant limitations
+ 
+
+ align:start position:0%
+engine with some significant limitations
+to it so where we can we often will try
+
+ align:start position:0%
+to it so where we can we often will try
+ 
+
+ align:start position:0%
+to it so where we can we often will try
+to build rules internally using these
+
+ align:start position:0%
+to build rules internally using these
+ 
+
+ align:start position:0%
+to build rules internally using these
+systems those tend to sort of have
+
+ align:start position:0%
+systems those tend to sort of have
+ 
+
+ align:start position:0%
+systems those tend to sort of have
+real-time availability of data the best
+
+ align:start position:0%
+real-time availability of data the best
+ 
+
+ align:start position:0%
+real-time availability of data the best
+ability to sort of push a little to be
+
+ align:start position:0%
+ability to sort of push a little to be
+ 
+
+ align:start position:0%
+ability to sort of push a little to be
+the person right in their workflow and
+
+ align:start position:0%
+the person right in their workflow and
+ 
+
+ align:start position:0%
+the person right in their workflow and
+make those alerts actionable in cases
+
+ align:start position:0%
+make those alerts actionable in cases
+ 
+
+ align:start position:0%
+make those alerts actionable in cases
+where we can't do that I like for
+
+ align:start position:0%
+where we can't do that I like for
+ 
+
+ align:start position:0%
+where we can't do that I like for
+example models it's too complex to
+
+ align:start position:0%
+example models it's too complex to
+ 
+
+ align:start position:0%
+example models it's too complex to
+execute in the system one thing that
+
+ align:start position:0%
+execute in the system one thing that
+ 
+
+ align:start position:0%
+execute in the system one thing that
+we've often done is sort of run that
+
+ align:start position:0%
+we've often done is sort of run that
+ 
+
+ align:start position:0%
+we've often done is sort of run that
+model against our data warehouse so we
+
+ align:start position:0%
+model against our data warehouse so we
+ 
+
+ align:start position:0%
+model against our data warehouse so we
+have a data warehouse that extracts the
+
+ align:start position:0%
+have a data warehouse that extracts the
+ 
+
+ align:start position:0%
+have a data warehouse that extracts the
+data from the electronic health record
+
+ align:start position:0%
+data from the electronic health record
+ 
+
+ align:start position:0%
+data from the electronic health record
+every night at midnight and so if we
+
+ align:start position:0%
+every night at midnight and so if we
+ 
+
+ align:start position:0%
+every night at midnight and so if we
+don't need real-time data it's possible
+
+ align:start position:0%
+don't need real-time data it's possible
+ 
+
+ align:start position:0%
+don't need real-time data it's possible
+to run the extract the data run a model
+
+ align:start position:0%
+to run the extract the data run a model
+ 
+
+ align:start position:0%
+to run the extract the data run a model
+and then actually write a risk score or
+
+ align:start position:0%
+and then actually write a risk score or
+ 
+
+ align:start position:0%
+and then actually write a risk score or
+a flag back into the patient's record
+
+ align:start position:0%
+a flag back into the patient's record
+ 
+
+ align:start position:0%
+a flag back into the patient's record
+that can then be shown to the clinician
+
+ align:start position:0%
+that can then be shown to the clinician
+ 
+
+ align:start position:0%
+that can then be shown to the clinician
+or used to drive an alert or something
+
+ align:start position:0%
+or used to drive an alert or something
+ 
+
+ align:start position:0%
+or used to drive an alert or something
+like that that works really well except
+
+ align:start position:0%
+like that that works really well except
+ 
+
+ align:start position:0%
+like that that works really well except
+that a lot of things that happen
+
+ align:start position:0%
+that a lot of things that happen
+ 
+
+ align:start position:0%
+that a lot of things that happen
+particularly an inpatient setting like
+
+ align:start position:0%
+particularly an inpatient setting like
+ 
+
+ align:start position:0%
+particularly an inpatient setting like
+predicting except this depend on
+
+ align:start position:0%
+predicting except this depend on
+ 
+
+ align:start position:0%
+predicting except this depend on
+real-time data anything that would mean
+
+ align:start position:0%
+real-time data anything that would mean
+ 
+
+ align:start position:0%
+real-time data anything that would mean
+right away and so we run into the
+
+ align:start position:0%
+right away and so we run into the
+ 
+
+ align:start position:0%
+right away and so we run into the
+challenge where that particular approach
+
+ align:start position:0%
+challenge where that particular approach
+ 
+
+ align:start position:0%
+challenge where that particular approach
+only works you know kind of on a 24-hour
+
+ align:start position:0%
+only works you know kind of on a 24-hour
+ 
+
+ align:start position:0%
+only works you know kind of on a 24-hour
+kind of retrospective basis we have also
+
+ align:start position:0%
+kind of retrospective basis we have also
+ 
+
+ align:start position:0%
+kind of retrospective basis we have also
+developed systems that depend on
+
+ align:start position:0%
+developed systems that depend on
+ 
+
+ align:start position:0%
+developed systems that depend on
+messages so there's this hl7 as
+
+ align:start position:0%
+messages so there's this hl7 as
+ 
+
+ align:start position:0%
+messages so there's this hl7 as
+standard format for exchanging data with
+
+ align:start position:0%
+standard format for exchanging data with
+ 
+
+ align:start position:0%
+standard format for exchanging data with
+the north priming health record various
+
+ align:start position:0%
+the north priming health record various
+ 
+
+ align:start position:0%
+the north priming health record various
+versions and profiles at hl7 but you can
+
+ align:start position:0%
+versions and profiles at hl7 but you can
+ 
+
+ align:start position:0%
+versions and profiles at hl7 but you can
+sort of set up an infrastructure that
+
+ align:start position:0%
+sort of set up an infrastructure that
+ 
+
+ align:start position:0%
+sort of set up an infrastructure that
+sits outside of the EHR and gets
+
+ align:start position:0%
+sits outside of the EHR and gets
+ 
+
+ align:start position:0%
+sits outside of the EHR and gets
+messages and real-time from the EHR and
+
+ align:start position:0%
+messages and real-time from the EHR and
+ 
+
+ align:start position:0%
+messages and real-time from the EHR and
+makes inferences and sort of sends
+
+ align:start position:0%
+makes inferences and sort of sends
+ 
+
+ align:start position:0%
+makes inferences and sort of sends
+messages back into the EHR increasingly
+
+ align:start position:0%
+messages back into the EHR increasingly
+ 
+
+ align:start position:0%
+messages back into the EHR increasingly
+EHRs also do support sort of kind of web
+
+ align:start position:0%
+EHRs also do support sort of kind of web
+ 
+
+ align:start position:0%
+EHRs also do support sort of kind of web
+service approaches right so that you can
+
+ align:start position:0%
+service approaches right so that you can
+ 
+
+ align:start position:0%
+service approaches right so that you can
+register a hook and say call my hook
+
+ align:start position:0%
+register a hook and say call my hook
+ 
+
+ align:start position:0%
+register a hook and say call my hook
+whenever this thing happens or you can
+
+ align:start position:0%
+whenever this thing happens or you can
+ 
+
+ align:start position:0%
+whenever this thing happens or you can
+pull the HR to get data out and use
+
+ align:start position:0%
+pull the HR to get data out and use
+ 
+
+ align:start position:0%
+pull the HR to get data out and use
+another web service to write data back
+
+ align:start position:0%
+another web service to write data back
+ 
+
+ align:start position:0%
+another web service to write data back
+in that's worked really well for us you
+
+ align:start position:0%
+in that's worked really well for us you
+ 
+
+ align:start position:0%
+in that's worked really well for us you
+can also sort of ask the EHR to sort of
+
+ align:start position:0%
+can also sort of ask the EHR to sort of
+ 
+
+ align:start position:0%
+can also sort of ask the EHR to sort of
+embed an app that you develop so people
+
+ align:start position:0%
+embed an app that you develop so people
+ 
+
+ align:start position:0%
+embed an app that you develop so people
+here may have heard or should hear at
+
+ align:start position:0%
+here may have heard or should hear at
+ 
+
+ align:start position:0%
+here may have heard or should hear at
+some point about smart on fire which is
+
+ align:start position:0%
+some point about smart on fire which is
+ 
+
+ align:start position:0%
+some point about smart on fire which is
+a open kind of API that allows you to
+
+ align:start position:0%
+a open kind of API that allows you to
+ 
+
+ align:start position:0%
+a open kind of API that allows you to
+sort of develop an application and embed
+
+ align:start position:0%
+sort of develop an application and embed
+ 
+
+ align:start position:0%
+sort of develop an application and embed
+that application into an electronic
+
+ align:start position:0%
+that application into an electronic
+ 
+
+ align:start position:0%
+that application into an electronic
+health record we've increasingly been
+
+ align:start position:0%
+health record we've increasingly been
+ 
+
+ align:start position:0%
+health record we've increasingly been
+building some of those those
+
+ align:start position:0%
+building some of those those
+ 
+
+ align:start position:0%
+building some of those those
+applications the downside right now the
+
+ align:start position:0%
+applications the downside right now the
+ 
+
+ align:start position:0%
+applications the downside right now the
+smart apps is that they're really good
+
+ align:start position:0%
+smart apps is that they're really good
+ 
+
+ align:start position:0%
+smart apps is that they're really good
+for sort of reading data out of the
+
+ align:start position:0%
+for sort of reading data out of the
+ 
+
+ align:start position:0%
+for sort of reading data out of the
+record and sort of visualizing or
+
+ align:start position:0%
+record and sort of visualizing or
+ 
+
+ align:start position:0%
+record and sort of visualizing or
+displaying it but they don't always have
+
+ align:start position:0%
+displaying it but they don't always have
+ 
+
+ align:start position:0%
+displaying it but they don't always have
+a lot of capability to sort of write
+
+ align:start position:0%
+a lot of capability to sort of write
+ 
+
+ align:start position:0%
+a lot of capability to sort of write
+data back into the record or take
+
+ align:start position:0%
+data back into the record or take
+ 
+
+ align:start position:0%
+data back into the record or take
+actions most of the HR vendors also have
+
+ align:start position:0%
+actions most of the HR vendors also have
+ 
+
+ align:start position:0%
+actions most of the HR vendors also have
+a proprietary approach like an app store
+
+ align:start position:0%
+a proprietary approach like an app store
+ 
+
+ align:start position:0%
+a proprietary approach like an app store
+so epic calls there's the app orchard
+
+ align:start position:0%
+so epic calls there's the app orchard
+ 
+
+ align:start position:0%
+so epic calls there's the app orchard
+and almost the EHRs have something
+
+ align:start position:0%
+and almost the EHRs have something
+ 
+
+ align:start position:0%
+and almost the EHRs have something
+similar where you can join a developer
+
+ align:start position:0%
+similar where you can join a developer
+ 
+
+ align:start position:0%
+similar where you can join a developer
+program and sort of build an application
+
+ align:start position:0%
+program and sort of build an application
+ 
+
+ align:start position:0%
+program and sort of build an application
+and those are often more full-featured
+
+ align:start position:0%
+and those are often more full-featured
+ 
+
+ align:start position:0%
+and those are often more full-featured
+they can may be proprietary so if you
+
+ align:start position:0%
+they can may be proprietary so if you
+ 
+
+ align:start position:0%
+they can may be proprietary so if you
+build one epic app you have to then
+
+ align:start position:0%
+build one epic app you have to then
+ 
+
+ align:start position:0%
+build one epic app you have to then
+build a Cerner happen in all scripts and
+
+ align:start position:0%
+build a Cerner happen in all scripts and
+ 
+
+ align:start position:0%
+build a Cerner happen in all scripts and
+eClinicalWorks after separately there
+
+ align:start position:0%
+eClinicalWorks after separately there
+ 
+
+ align:start position:0%
+eClinicalWorks after separately there
+are often heavy fees for joining those
+
+ align:start position:0%
+are often heavy fees for joining those
+ 
+
+ align:start position:0%
+are often heavy fees for joining those
+programs although the EHR vendors epic
+
+ align:start position:0%
+programs although the EHR vendors epic
+ 
+
+ align:start position:0%
+programs although the EHR vendors epic
+in particular have lowered their prices
+
+ align:start position:0%
+in particular have lowered their prices
+ 
+
+ align:start position:0%
+in particular have lowered their prices
+a lot and the federal government the
+
+ align:start position:0%
+a lot and the federal government the
+ 
+
+ align:start position:0%
+a lot and the federal government the
+Office of the National Coordinator for
+
+ align:start position:0%
+Office of the National Coordinator for
+ 
+
+ align:start position:0%
+Office of the National Coordinator for
+health IT just about a week and a half
+
+ align:start position:0%
+health IT just about a week and a half
+ 
+
+ align:start position:0%
+health IT just about a week and a half
+ago released some new regulations which
+
+ align:start position:0%
+ago released some new regulations which
+ 
+
+ align:start position:0%
+ago released some new regulations which
+really limit the rate at which vendors
+
+ align:start position:0%
+really limit the rate at which vendors
+ 
+
+ align:start position:0%
+really limit the rate at which vendors
+can charge application developers for
+
+ align:start position:0%
+can charge application developers for
+ 
+
+ align:start position:0%
+can charge application developers for
+API access basically to almost nothing
+
+ align:start position:0%
+API access basically to almost nothing
+ 
+
+ align:start position:0%
+API access basically to almost nothing
+except for kind of incremental
+
+ align:start position:0%
+except for kind of incremental
+ 
+
+ align:start position:0%
+except for kind of incremental
+computation costs our special support
+
+ align:start position:0%
+computation costs our special support
+ 
+
+ align:start position:0%
+computation costs our special support
+and so I think that may change
+
+ align:start position:0%
+and so I think that may change
+ 
+
+ align:start position:0%
+and so I think that may change
+everything now with that regulation has
+
+ align:start position:0%
+everything now with that regulation has
+ 
+
+ align:start position:0%
+everything now with that regulation has
+been promulgated so we'll see so
+
+ align:start position:0%
+been promulgated so we'll see so
+ 
+
+ align:start position:0%
+been promulgated so we'll see so
+contrary to my pessimistic beginning the
+
+ align:start position:0%
+contrary to my pessimistic beginning the
+ 
+
+ align:start position:0%
+contrary to my pessimistic beginning the
+this actually is the thing that makes me
+
+ align:start position:0%
+this actually is the thing that makes me
+ 
+
+ align:start position:0%
+this actually is the thing that makes me
+most optimistic
+
+ align:start position:0%
+most optimistic
+ 
+
+ align:start position:0%
+most optimistic
+that even five years ago if you looked
+
+ align:start position:0%
+that even five years ago if you looked
+ 
+
+ align:start position:0%
+that even five years ago if you looked
+at many of these systems they they
+
+ align:start position:0%
+at many of these systems they they
+ 
+
+ align:start position:0%
+at many of these systems they they
+essentially locked you out I remember in
+
+ align:start position:0%
+essentially locked you out I remember in
+ 
+
+ align:start position:0%
+essentially locked you out I remember in
+the early 2000s I was at the University
+
+ align:start position:0%
+the early 2000s I was at the University
+ 
+
+ align:start position:0%
+the early 2000s I was at the University
+of Pittsburgh where they had they had
+
+ align:start position:0%
+of Pittsburgh where they had they had
+ 
+
+ align:start position:0%
+of Pittsburgh where they had they had
+one of the first centers that was doing
+
+ align:start position:0%
+one of the first centers that was doing
+ 
+
+ align:start position:0%
+one of the first centers that was doing
+heart lung transplants and so there
+
+ align:start position:0%
+heart lung transplants and so there
+ 
+
+ align:start position:0%
+heart lung transplants and so there
+people had built a special application
+
+ align:start position:0%
+people had built a special application
+ 
+
+ align:start position:0%
+people had built a special application
+for supporting heart-lung transplant
+
+ align:start position:0%
+for supporting heart-lung transplant
+ 
+
+ align:start position:0%
+for supporting heart-lung transplant
+patients in their own home made
+
+ align:start position:0%
+patients in their own home made
+ 
+
+ align:start position:0%
+patients in their own home made
+electronic medical record system and
+
+ align:start position:0%
+electronic medical record system and
+ 
+
+ align:start position:0%
+electronic medical record system and
+then UPMC went to Cerner at the time and
+
+ align:start position:0%
+then UPMC went to Cerner at the time and
+ 
+
+ align:start position:0%
+then UPMC went to Cerner at the time and
+I remember I was at some meeting where
+
+ align:start position:0%
+I remember I was at some meeting where
+ 
+
+ align:start position:0%
+I remember I was at some meeting where
+the doctors who ran this heart-lung
+
+ align:start position:0%
+the doctors who ran this heart-lung
+ 
+
+ align:start position:0%
+the doctors who ran this heart-lung
+transplant unit were talking to the
+
+ align:start position:0%
+transplant unit were talking to the
+ 
+
+ align:start position:0%
+transplant unit were talking to the
+Cerner people and saying you know how
+
+ align:start position:0%
+Cerner people and saying you know how
+ 
+
+ align:start position:0%
+Cerner people and saying you know how
+could we get something to support our
+
+ align:start position:0%
+could we get something to support our
+ 
+
+ align:start position:0%
+could we get something to support our
+special needs for our patients and
+
+ align:start position:0%
+special needs for our patients and
+ 
+
+ align:start position:0%
+special needs for our patients and
+Cerner's answer was well you know
+
+ align:start position:0%
+Cerner's answer was well you know
+ 
+
+ align:start position:0%
+Cerner's answer was well you know
+commercially it doesn't make sense for
+
+ align:start position:0%
+commercially it doesn't make sense for
+ 
+
+ align:start position:0%
+commercially it doesn't make sense for
+us to do this because at the time there
+
+ align:start position:0%
+us to do this because at the time there
+ 
+
+ align:start position:0%
+us to do this because at the time there
+were like four hospitals in the country
+
+ align:start position:0%
+were like four hospitals in the country
+ 
+
+ align:start position:0%
+were like four hospitals in the country
+that did this and so it's not a big a
+
+ align:start position:0%
+that did this and so it's not a big a
+ 
+
+ align:start position:0%
+that did this and so it's not a big a
+big moneymaker and so their offer was
+
+ align:start position:0%
+big moneymaker and so their offer was
+ 
+
+ align:start position:0%
+big moneymaker and so their offer was
+while you pay us an extra three million
+
+ align:start position:0%
+while you pay us an extra three million
+ 
+
+ align:start position:0%
+while you pay us an extra three million
+dollars and within three years we will
+
+ align:start position:0%
+dollars and within three years we will
+ 
+
+ align:start position:0%
+dollars and within three years we will
+develop the appropriate software for you
+
+ align:start position:0%
+develop the appropriate software for you
+ 
+
+ align:start position:0%
+develop the appropriate software for you
+so that that's just crazy right I mean
+
+ align:start position:0%
+so that that's just crazy right I mean
+ 
+
+ align:start position:0%
+so that that's just crazy right I mean
+that's a totally untenable way of going
+
+ align:start position:0%
+that's a totally untenable way of going
+ 
+
+ align:start position:0%
+that's a totally untenable way of going
+about things and now that there are
+
+ align:start position:0%
+about things and now that there are
+ 
+
+ align:start position:0%
+about things and now that there are
+systemic ways for you either to embed
+
+ align:start position:0%
+systemic ways for you either to embed
+ 
+
+ align:start position:0%
+systemic ways for you either to embed
+your own code into one of these systems
+
+ align:start position:0%
+your own code into one of these systems
+ 
+
+ align:start position:0%
+your own code into one of these systems
+or at least to have a well documented
+
+ align:start position:0%
+or at least to have a well documented
+ 
+
+ align:start position:0%
+or at least to have a well documented
+reasonable way of feeding data out and
+
+ align:start position:0%
+reasonable way of feeding data out and
+ 
+
+ align:start position:0%
+reasonable way of feeding data out and
+then feeding results back into the
+
+ align:start position:0%
+then feeding results back into the
+ 
+
+ align:start position:0%
+then feeding results back into the
+system that makes it possible to do the
+
+ align:start position:0%
+system that makes it possible to do the
+ 
+
+ align:start position:0%
+system that makes it possible to do the
+special-purpose applications like this
+
+ align:start position:0%
+special-purpose applications like this
+ 
+
+ align:start position:0%
+special-purpose applications like this
+or experimental applications or all
+
+ align:start position:0%
+or experimental applications or all
+ 
+
+ align:start position:0%
+or experimental applications or all
+kinds of novel things so that's great
+
+ align:start position:0%
+kinds of novel things so that's great
+ 
+
+ align:start position:0%
+kinds of novel things so that's great
+that's what we're optimistic about but I
+
+ align:start position:0%
+that's what we're optimistic about but I
+ 
+
+ align:start position:0%
+that's what we're optimistic about but I
+think it's it's worth adding that
+
+ align:start position:0%
+think it's it's worth adding that
+ 
+
+ align:start position:0%
+think it's it's worth adding that
+there's sort of two barriers you have to
+
+ align:start position:0%
+there's sort of two barriers you have to
+ 
+
+ align:start position:0%
+there's sort of two barriers you have to
+get through right one is epic has to
+
+ align:start position:0%
+get through right one is epic has to
+ 
+
+ align:start position:0%
+get through right one is epic has to
+sort of let you into their app work
+
+ align:start position:0%
+sort of let you into their app work
+ 
+
+ align:start position:0%
+sort of let you into their app work
+shirt which is sort of the barrier that
+
+ align:start position:0%
+shirt which is sort of the barrier that
+ 
+
+ align:start position:0%
+shirt which is sort of the barrier that
+is increasingly lower and then you need
+
+ align:start position:0%
+is increasingly lower and then you need
+ 
+
+ align:start position:0%
+is increasingly lower and then you need
+to find a hospital or a healthcare
+
+ align:start position:0%
+to find a hospital or a healthcare
+ 
+
+ align:start position:0%
+to find a hospital or a healthcare
+provider that wants to use your app
+
+ align:start position:0%
+provider that wants to use your app
+ 
+
+ align:start position:0%
+provider that wants to use your app
+right you know so you kind of have to
+
+ align:start position:0%
+right you know so you kind of have to
+ 
+
+ align:start position:0%
+right you know so you kind of have to
+clear both of those
+
+ align:start position:0%
+clear both of those
+ 
+
+ align:start position:0%
+clear both of those
+I think it's increasingly possible you
+
+ align:start position:0%
+I think it's increasingly possible you
+ 
+
+ align:start position:0%
+I think it's increasingly possible you
+got smart people here at MIT or at the
+
+ align:start position:0%
+got smart people here at MIT or at the
+ 
+
+ align:start position:0%
+got smart people here at MIT or at the
+hospitals and we have in Boston sort of
+
+ align:start position:0%
+hospitals and we have in Boston sort of
+ 
+
+ align:start position:0%
+hospitals and we have in Boston sort of
+always sort of wanted to build these
+
+ align:start position:0%
+always sort of wanted to build these
+ 
+
+ align:start position:0%
+always sort of wanted to build these
+apps and I would say five years ago we
+
+ align:start position:0%
+apps and I would say five years ago we
+ 
+
+ align:start position:0%
+apps and I would say five years ago we
+would have told people sorry it's not
+
+ align:start position:0%
+would have told people sorry it's not
+ 
+
+ align:start position:0%
+would have told people sorry it's not
+possible and today we're usually to tell
+
+ align:start position:0%
+possible and today we're usually to tell
+ 
+
+ align:start position:0%
+possible and today we're usually to tell
+people that if there's clinical interest
+
+ align:start position:0%
+people that if there's clinical interest
+ 
+
+ align:start position:0%
+people that if there's clinical interest
+in that technical part will fall into
+
+ align:start position:0%
+in that technical part will fall into
+ 
+
+ align:start position:0%
+in that technical part will fall into
+place that's exciting for us yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's a lot of different ways
+
+ align:start position:0%
+yeah there's a lot of different ways
+ 
+
+ align:start position:0%
+yeah there's a lot of different ways
+that we sort of share these applications
+
+ align:start position:0%
+that we sort of share these applications
+ 
+
+ align:start position:0%
+that we sort of share these applications
+right so a lot of us are researchers so
+
+ align:start position:0%
+right so a lot of us are researchers so
+ 
+
+ align:start position:0%
+right so a lot of us are researchers so
+we will you know released an open-source
+
+ align:start position:0%
+we will you know released an open-source
+ 
+
+ align:start position:0%
+we will you know released an open-source
+version of the application or you know
+
+ align:start position:0%
+version of the application or you know
+ 
+
+ align:start position:0%
+version of the application or you know
+write a paper and say this is available
+
+ align:start position:0%
+write a paper and say this is available
+ 
+
+ align:start position:0%
+write a paper and say this is available
+and what sort of shared with you the app
+
+ align:start position:0%
+and what sort of shared with you the app
+ 
+
+ align:start position:0%
+and what sort of shared with you the app
+orchard is particularly focused on
+
+ align:start position:0%
+orchard is particularly focused on
+ 
+
+ align:start position:0%
+orchard is particularly focused on
+applications that you want to sell so
+
+ align:start position:0%
+applications that you want to sell so
+ 
+
+ align:start position:0%
+applications that you want to sell so
+our hospital hasn't decided that we
+
+ align:start position:0%
+our hospital hasn't decided that we
+ 
+
+ align:start position:0%
+our hospital hasn't decided that we
+wanted to sell any applications we've
+
+ align:start position:0%
+wanted to sell any applications we've
+ 
+
+ align:start position:0%
+wanted to sell any applications we've
+given a lot of applications away epic
+
+ align:start position:0%
+given a lot of applications away epic
+ 
+
+ align:start position:0%
+given a lot of applications away epic
+also has something called the community
+
+ align:start position:0%
+also has something called the community
+ 
+
+ align:start position:0%
+also has something called the community
+library which is like the aperture but
+
+ align:start position:0%
+library which is like the aperture but
+ 
+
+ align:start position:0%
+library which is like the aperture but
+it's free instead of costing money and
+
+ align:start position:0%
+it's free instead of costing money and
+ 
+
+ align:start position:0%
+it's free instead of costing money and
+so we released a ton of stuff through
+
+ align:start position:0%
+so we released a ton of stuff through
+ 
+
+ align:start position:0%
+so we released a ton of stuff through
+the community library to the point that
+
+ align:start position:0%
+the community library to the point that
+ 
+
+ align:start position:0%
+the community library to the point that
+I was sort of poking out before one of
+
+ align:start position:0%
+I was sort of poking out before one of
+ 
+
+ align:start position:0%
+I was sort of poking out before one of
+the challenges is that if we build a
+
+ align:start position:0%
+the challenges is that if we build a
+ 
+
+ align:start position:0%
+the challenges is that if we build a
+smart on fire app we're able to sort of
+
+ align:start position:0%
+smart on fire app we're able to sort of
+ 
+
+ align:start position:0%
+smart on fire app we're able to sort of
+share that publicly we can post that on
+
+ align:start position:0%
+share that publicly we can post that on
+ 
+
+ align:start position:0%
+share that publicly we can post that on
+the web on github in any video you can
+
+ align:start position:0%
+the web on github in any video you can
+ 
+
+ align:start position:0%
+the web on github in any video you can
+use it epic has a position that they're
+
+ align:start position:0%
+use it epic has a position that they're
+ 
+
+ align:start position:0%
+use it epic has a position that they're
+api's are proprietary and they represent
+
+ align:start position:0%
+api's are proprietary and they represent
+ 
+
+ align:start position:0%
+api's are proprietary and they represent
+epics valuable intellectual property or
+
+ align:start position:0%
+epics valuable intellectual property or
+ 
+
+ align:start position:0%
+epics valuable intellectual property or
+trade secrets and so we're only allowed
+
+ align:start position:0%
+trade secrets and so we're only allowed
+ 
+
+ align:start position:0%
+trade secrets and so we're only allowed
+to share those apps through the the epic
+
+ align:start position:0%
+to share those apps through the the epic
+ 
+
+ align:start position:0%
+to share those apps through the the epic
+ecosystem and so we often now when we
+
+ align:start position:0%
+ecosystem and so we often now when we
+ 
+
+ align:start position:0%
+ecosystem and so we often now when we
+get a grant but most of my work is it is
+
+ align:start position:0%
+get a grant but most of my work is it is
+ 
+
+ align:start position:0%
+get a grant but most of my work is it is
+through grants we'll have an ethics I
+
+ align:start position:0%
+through grants we'll have an ethics I
+ 
+
+ align:start position:0%
+through grants we'll have an ethics I
+eat and we'll share that through the
+
+ align:start position:0%
+eat and we'll share that through the
+ 
+
+ align:start position:0%
+eat and we'll share that through the
+community why you bringing all of a
+
+ align:start position:0%
+community why you bringing all of a
+ 
+
+ align:start position:0%
+community why you bringing all of a
+Cerner site and share it through
+
+ align:start position:0%
+Cerner site and share it through
+ 
+
+ align:start position:0%
+Cerner site and share it through
+Cerner's equivalent but I think until
+
+ align:start position:0%
+Cerner's equivalent but I think until
+ 
+
+ align:start position:0%
+Cerner's equivalent but I think until
+the capability of the open API is like
+
+ align:start position:0%
+the capability of the open API is like
+ 
+
+ align:start position:0%
+the capability of the open API is like
+smart on fire reaches the same level as
+
+ align:start position:0%
+smart on fire reaches the same level as
+ 
+
+ align:start position:0%
+smart on fire reaches the same level as
+that proprietary api's we're still
+
+ align:start position:0%
+that proprietary api's we're still
+ 
+
+ align:start position:0%
+that proprietary api's we're still
+somewhat walked into having to build
+
+ align:start position:0%
+somewhat walked into having to build
+ 
+
+ align:start position:0%
+somewhat walked into having to build
+different versions and distribute three
+
+ align:start position:0%
+different versions and distribute three
+ 
+
+ align:start position:0%
+different versions and distribute three
+each HR under separate channel it's
+
+ align:start position:0%
+each HR under separate channel it's
+ 
+
+ align:start position:0%
+each HR under separate channel it's
+really really good question and so what
+
+ align:start position:0%
+really really good question and so what
+ 
+
+ align:start position:0%
+really really good question and so what
+what what's lacking in things like smart
+
+ align:start position:0%
+what what's lacking in things like smart
+ 
+
+ align:start position:0%
+what what's lacking in things like smart
+on fire that you get from the native
+
+ align:start position:0%
+on fire that you get from the native
+ 
+
+ align:start position:0%
+on fire that you get from the native
+interfaces so I mean it's very
+
+ align:start position:0%
+interfaces so I mean it's very
+ 
+
+ align:start position:0%
+interfaces so I mean it's very
+situational right so so for example
+
+ align:start position:0%
+situational right so so for example
+ 
+
+ align:start position:0%
+situational right so so for example
+certain you know and some EHR
+
+ align:start position:0%
+certain you know and some EHR
+ 
+
+ align:start position:0%
+certain you know and some EHR
+implementations this Marmon fire will
+
+ align:start position:0%
+implementations this Marmon fire will
+ 
+
+ align:start position:0%
+implementations this Marmon fire will
+give you lists of the patient's current
+
+ align:start position:0%
+give you lists of the patient's current
+ 
+
+ align:start position:0%
+give you lists of the patient's current
+medications but may not give you
+
+ align:start position:0%
+medications but may not give you
+ 
+
+ align:start position:0%
+medications but may not give you
+historical medications or will tell you
+
+ align:start position:0%
+historical medications or will tell you
+ 
+
+ align:start position:0%
+historical medications or will tell you
+that the medicine is ordered but it
+
+ align:start position:0%
+that the medicine is ordered but it
+ 
+
+ align:start position:0%
+that the medicine is ordered but it
+won't tell you whether it's been
+
+ align:start position:0%
+won't tell you whether it's been
+ 
+
+ align:start position:0%
+won't tell you whether it's been
+administered so one half the battle is
+
+ align:start position:0%
+administered so one half the battle is
+ 
+
+ align:start position:0%
+administered so one half the battle is
+less complete data the other one is that
+
+ align:start position:0%
+less complete data the other one is that
+ 
+
+ align:start position:0%
+less complete data the other one is that
+the most EHRs are not implementing at
+
+ align:start position:0%
+the most EHRs are not implementing at
+ 
+
+ align:start position:0%
+the most EHRs are not implementing at
+this point the sort of right back
+
+ align:start position:0%
+this point the sort of right back
+ 
+
+ align:start position:0%
+this point the sort of right back
+capabilities or the actionable
+
+ align:start position:0%
+capabilities or the actionable
+ 
+
+ align:start position:0%
+capabilities or the actionable
+capabilities that smart on fire is sort
+
+ align:start position:0%
+capabilities that smart on fire is sort
+ 
+
+ align:start position:0%
+capabilities that smart on fire is sort
+of working on and it released some
+
+ align:start position:0%
+of working on and it released some
+ 
+
+ align:start position:0%
+of working on and it released some
+standards for us so if we want to build
+
+ align:start position:0%
+standards for us so if we want to build
+ 
+
+ align:start position:0%
+standards for us so if we want to build
+an application sort of shows how a page
+
+ align:start position:0%
+an application sort of shows how a page
+ 
+
+ align:start position:0%
+an application sort of shows how a page
+fits on a growth curve that's fine if we
+
+ align:start position:0%
+fits on a growth curve that's fine if we
+ 
+
+ align:start position:0%
+fits on a growth curve that's fine if we
+went balloon applications suggest
+
+ align:start position:0%
+went balloon applications suggest
+ 
+
+ align:start position:0%
+went balloon applications suggest
+ordering medicines that can be really
+
+ align:start position:0%
+ordering medicines that can be really
+ 
+
+ align:start position:0%
+ordering medicines that can be really
+challenging where is the internal API so
+
+ align:start position:0%
+challenging where is the internal API so
+ 
+
+ align:start position:0%
+challenging where is the internal API so
+the vendors provide typically have both
+
+ align:start position:0%
+the vendors provide typically have both
+ 
+
+ align:start position:0%
+the vendors provide typically have both
+read and write capabilities do the
+
+ align:start position:0%
+read and write capabilities do the
+ 
+
+ align:start position:0%
+read and write capabilities do the
+vendors worry about I guess two related
+
+ align:start position:0%
+vendors worry about I guess two related
+ 
+
+ align:start position:0%
+vendors worry about I guess two related
+things one is sort of cognitive overload
+
+ align:start position:0%
+things one is sort of cognitive overload
+ 
+
+ align:start position:0%
+things one is sort of cognitive overload
+because if you build a thousand smart on
+
+ align:start position:0%
+because if you build a thousand smart on
+ 
+
+ align:start position:0%
+because if you build a thousand smart on
+fire apps and they all start firing for
+
+ align:start position:0%
+fire apps and they all start firing for
+ 
+
+ align:start position:0%
+fire apps and they all start firing for
+these impatience you're gonna be back in
+
+ align:start position:0%
+these impatience you're gonna be back in
+ 
+
+ align:start position:0%
+these impatience you're gonna be back in
+the same situation of over alerting and
+
+ align:start position:0%
+the same situation of over alerting and
+ 
+
+ align:start position:0%
+the same situation of over alerting and
+the other question is is are they
+
+ align:start position:0%
+the other question is is are they
+ 
+
+ align:start position:0%
+the other question is is are they
+worried about liability since if you're
+
+ align:start position:0%
+worried about liability since if you're
+ 
+
+ align:start position:0%
+worried about liability since if you're
+using their system to display
+
+ align:start position:0%
+using their system to display
+ 
+
+ align:start position:0%
+using their system to display
+recommendations and those
+
+ align:start position:0%
+recommendations and those
+ 
+
+ align:start position:0%
+recommendations and those
+recommendations turn out to be wrong and
+
+ align:start position:0%
+recommendations turn out to be wrong and
+ 
+
+ align:start position:0%
+recommendations turn out to be wrong and
+harmful impatient then somebody will
+
+ align:start position:0%
+harmful impatient then somebody will
+ 
+
+ align:start position:0%
+harmful impatient then somebody will
+reach out to them legally because they
+
+ align:start position:0%
+reach out to them legally because they
+ 
+
+ align:start position:0%
+reach out to them legally because they
+have a lot of money absolutely they're
+
+ align:start position:0%
+have a lot of money absolutely they're
+ 
+
+ align:start position:0%
+have a lot of money absolutely they're
+worried about both of those related
+
+ align:start position:0%
+worried about both of those related
+ 
+
+ align:start position:0%
+worried about both of those related
+particularly to the second one they're
+
+ align:start position:0%
+particularly to the second one they're
+ 
+
+ align:start position:0%
+particularly to the second one they're
+also worried about sort of you know
+
+ align:start position:0%
+also worried about sort of you know
+ 
+
+ align:start position:0%
+also worried about sort of you know
+corruption or integrity of the data
+
+ align:start position:0%
+corruption or integrity of the data
+ 
+
+ align:start position:0%
+corruption or integrity of the data
+right so somehow if I can write a
+
+ align:start position:0%
+right so somehow if I can write a
+ 
+
+ align:start position:0%
+right so somehow if I can write a
+medication order directly to the
+
+ align:start position:0%
+medication order directly to the
+ 
+
+ align:start position:0%
+medication order directly to the
+database and it may bypass certain
+
+ align:start position:0%
+database and it may bypass certain
+ 
+
+ align:start position:0%
+database and it may bypass certain
+checks that would be done normally and
+
+ align:start position:0%
+checks that would be done normally and
+ 
+
+ align:start position:0%
+checks that would be done normally and
+and I can potentially enter a wrong or
+
+ align:start position:0%
+and I can potentially enter a wrong or
+ 
+
+ align:start position:0%
+and I can potentially enter a wrong or
+dangerous order the other thing that
+
+ align:start position:0%
+dangerous order the other thing that
+ 
+
+ align:start position:0%
+dangerous order the other thing that
+we're increasingly hearing is sort of
+
+ align:start position:0%
+we're increasingly hearing is sort of
+ 
+
+ align:start position:0%
+we're increasingly hearing is sort of
+concerns about kind of protection of
+
+ align:start position:0%
+concerns about kind of protection of
+ 
+
+ align:start position:0%
+concerns about kind of protection of
+data sort of Cambridge analytic a style
+
+ align:start position:0%
+data sort of Cambridge analytic a style
+ 
+
+ align:start position:0%
+data sort of Cambridge analytic a style
+worries right so if I as a epic patient
+
+ align:start position:0%
+worries right so if I as a epic patient
+ 
+
+ align:start position:0%
+worries right so if I as a epic patient
+authorize you know the you know words
+
+ align:start position:0%
+authorize you know the you know words
+ 
+
+ align:start position:0%
+authorize you know the you know words
+with friends app to like see my medical
+
+ align:start position:0%
+with friends app to like see my medical
+ 
+
+ align:start position:0%
+with friends app to like see my medical
+record and then they post that on the
+
+ align:start position:0%
+record and then they post that on the
+ 
+
+ align:start position:0%
+record and then they post that on the
+web or sort of monetize it in some sort
+
+ align:start position:0%
+web or sort of monetize it in some sort
+ 
+
+ align:start position:0%
+web or sort of monetize it in some sort
+of tricky way what liability if any does
+
+ align:start position:0%
+of tricky way what liability if any does
+ 
+
+ align:start position:0%
+of tricky way what liability if any does
+my health care provider organization or
+
+ align:start position:0%
+my health care provider organization or
+ 
+
+ align:start position:0%
+my health care provider organization or
+my the HR vendor have for that and and
+
+ align:start position:0%
+my the HR vendor have for that and and
+ 
+
+ align:start position:0%
+my the HR vendor have for that and and
+the new regulations are extremely strict
+
+ align:start position:0%
+the new regulations are extremely strict
+ 
+
+ align:start position:0%
+the new regulations are extremely strict
+right they say that if a patient asks
+
+ align:start position:0%
+right they say that if a patient asks
+ 
+
+ align:start position:0%
+right they say that if a patient asks
+you to and authorizes an act to access
+
+ align:start position:0%
+you to and authorizes an act to access
+ 
+
+ align:start position:0%
+you to and authorizes an act to access
+their record you may not block that
+
+ align:start position:0%
+their record you may not block that
+ 
+
+ align:start position:0%
+their record you may not block that
+access even if you could say that I have
+
+ align:start position:0%
+access even if you could say that I have
+ 
+
+ align:start position:0%
+access even if you could say that I have
+to be a bad actor so that's I think an
+
+ align:start position:0%
+to be a bad actor so that's I think an
+ 
+
+ align:start position:0%
+to be a bad actor so that's I think an
+area of liability that is just beginning
+
+ align:start position:0%
+area of liability that is just beginning
+ 
+
+ align:start position:0%
+area of liability that is just beginning
+to be sorted out and it is I think some
+
+ align:start position:0%
+to be sorted out and it is I think some
+ 
+
+ align:start position:0%
+to be sorted out and it is I think some
+cause for concern but at the same time
+
+ align:start position:0%
+cause for concern but at the same time
+ 
+
+ align:start position:0%
+cause for concern but at the same time
+you could imagine universe where I think
+
+ align:start position:0%
+you could imagine universe where I think
+ 
+
+ align:start position:0%
+you could imagine universe where I think
+there are conservative healthcare
+
+ align:start position:0%
+there are conservative healthcare
+ 
+
+ align:start position:0%
+there are conservative healthcare
+organizations they would choose to never
+
+ align:start position:0%
+organizations they would choose to never
+ 
+
+ align:start position:0%
+organizations they would choose to never
+authorize any application to avoid risk
+
+ align:start position:0%
+authorize any application to avoid risk
+ 
+
+ align:start position:0%
+authorize any application to avoid risk
+so how you balance that is it's not yet
+
+ align:start position:0%
+so how you balance that is it's not yet
+ 
+
+ align:start position:0%
+so how you balance that is it's not yet
+solved well or and to avoid leakage so I
+
+ align:start position:0%
+solved well or and to avoid leakage so I
+ 
+
+ align:start position:0%
+solved well or and to avoid leakage so I
+remember years ago there was a lot of
+
+ align:start position:0%
+remember years ago there was a lot of
+ 
+
+ align:start position:0%
+remember years ago there was a lot of
+reluctance even among Boston area
+
+ align:start position:0%
+reluctance even among Boston area
+ 
+
+ align:start position:0%
+reluctance even among Boston area
+hospitals to share data because they
+
+ align:start position:0%
+hospitals to share data because they
+ 
+
+ align:start position:0%
+hospitals to share data because they
+were worried that another hospital could
+
+ align:start position:0%
+were worried that another hospital could
+ 
+
+ align:start position:0%
+were worried that another hospital could
+cherry-pick their most lucrative
+
+ align:start position:0%
+cherry-pick their most lucrative
+ 
+
+ align:start position:0%
+cherry-pick their most lucrative
+patients by figuring out something about
+
+ align:start position:0%
+patients by figuring out something about
+ 
+
+ align:start position:0%
+patients by figuring out something about
+them so I'm sure that that hasn't gone
+
+ align:start position:0%
+them so I'm sure that that hasn't gone
+ 
+
+ align:start position:0%
+them so I'm sure that that hasn't gone
+away as a concern yeah okay we're gonna
+
+ align:start position:0%
+away as a concern yeah okay we're gonna
+ 
+
+ align:start position:0%
+away as a concern yeah okay we're gonna
+try to remember to repeat the questions
+
+ align:start position:0%
+try to remember to repeat the questions
+ 
+
+ align:start position:0%
+try to remember to repeat the questions
+you're asking okay because of the
+
+ align:start position:0%
+you're asking okay because of the
+ 
+
+ align:start position:0%
+you're asking okay because of the
+recording yeah so the question is how
+
+ align:start position:0%
+recording yeah so the question is how
+ 
+
+ align:start position:0%
+recording yeah so the question is how
+does a third party vendor deploy an
+
+ align:start position:0%
+does a third party vendor deploy an
+ 
+
+ align:start position:0%
+does a third party vendor deploy an
+application or a machine learning model
+
+ align:start position:0%
+application or a machine learning model
+ 
+
+ align:start position:0%
+application or a machine learning model
+or something like that and so with epic
+
+ align:start position:0%
+or something like that and so with epic
+ 
+
+ align:start position:0%
+or something like that and so with epic
+there's always a relationship between
+
+ align:start position:0%
+there's always a relationship between
+ 
+
+ align:start position:0%
+there's always a relationship between
+the vendor of the application and the
+
+ align:start position:0%
+the vendor of the application and the
+ 
+
+ align:start position:0%
+the vendor of the application and the
+healthcare provider organization and so
+
+ align:start position:0%
+healthcare provider organization and so
+ 
+
+ align:start position:0%
+healthcare provider organization and so
+we could work together directly so if
+
+ align:start position:0%
+we could work together directly so if
+ 
+
+ align:start position:0%
+we could work together directly so if
+you had an app that the Brigham wanted
+
+ align:start position:0%
+you had an app that the Brigham wanted
+ 
+
+ align:start position:0%
+you had an app that the Brigham wanted
+to use you could share that app with us
+
+ align:start position:0%
+to use you could share that app with us
+ 
+
+ align:start position:0%
+to use you could share that app with us
+in a number of ways so epic supports
+
+ align:start position:0%
+in a number of ways so epic supports
+ 
+
+ align:start position:0%
+in a number of ways so epic supports
+this this thing called predictive
+
+ align:start position:0%
+this this thing called predictive
+ 
+
+ align:start position:0%
+this this thing called predictive
+modeling markup language or PMML so if
+
+ align:start position:0%
+modeling markup language or PMML so if
+ 
+
+ align:start position:0%
+modeling markup language or PMML so if
+you train a model you can export a P in
+
+ align:start position:0%
+you train a model you can export a P in
+ 
+
+ align:start position:0%
+you train a model you can export a P in
+the male model I can import it into epic
+
+ align:start position:0%
+the male model I can import it into epic
+ 
+
+ align:start position:0%
+the male model I can import it into epic
+and and run it natively or you can
+
+ align:start position:0%
+and and run it natively or you can
+ 
+
+ align:start position:0%
+and and run it natively or you can
+produce a web service that I call out to
+
+ align:start position:0%
+produce a web service that I call out to
+ 
+
+ align:start position:0%
+produce a web service that I call out to
+and sort of it gives me an answer we
+
+ align:start position:0%
+and sort of it gives me an answer we
+ 
+
+ align:start position:0%
+and sort of it gives me an answer we
+could work together directly however
+
+ align:start position:0%
+could work together directly however
+ 
+
+ align:start position:0%
+could work together directly however
+there are some limitations and what I'm
+
+ align:start position:0%
+there are some limitations and what I'm
+ 
+
+ align:start position:0%
+there are some limitations and what I'm
+allowed to sort of tell you or share
+
+ align:start position:0%
+allowed to sort of tell you or share
+ 
+
+ align:start position:0%
+allowed to sort of tell you or share
+with you about epics data model and epic
+
+ align:start position:0%
+with you about epics data model and epic
+ 
+
+ align:start position:0%
+with you about epics data model and epic
+whatever seems to be their their
+
+ align:start position:0%
+whatever seems to be their their
+ 
+
+ align:start position:0%
+whatever seems to be their their
+intellectual property and so it is
+
+ align:start position:0%
+intellectual property and so it is
+ 
+
+ align:start position:0%
+intellectual property and so it is
+facilitated by you joining this program
+
+ align:start position:0%
+facilitated by you joining this program
+ 
+
+ align:start position:0%
+facilitated by you joining this program
+because if you join this program you get
+
+ align:start position:0%
+because if you join this program you get
+ 
+
+ align:start position:0%
+because if you join this program you get
+access to documentation you would
+
+ align:start position:0%
+access to documentation you would
+ 
+
+ align:start position:0%
+access to documentation you would
+otherwise not have access to you may get
+
+ align:start position:0%
+otherwise not have access to you may get
+ 
+
+ align:start position:0%
+otherwise not have access to you may get
+access to a test harness or a test
+
+ align:start position:0%
+access to a test harness or a test
+ 
+
+ align:start position:0%
+access to a test harness or a test
+system that lets you sort of validate
+
+ align:start position:0%
+system that lets you sort of validate
+ 
+
+ align:start position:0%
+system that lets you sort of validate
+your work however people who join the
+
+ align:start position:0%
+your work however people who join the
+ 
+
+ align:start position:0%
+your work however people who join the
+program often think that means that I
+
+ align:start position:0%
+program often think that means that I
+ 
+
+ align:start position:0%
+program often think that means that I
+can then just run my app at every
+
+ align:start position:0%
+can then just run my app at every
+ 
+
+ align:start position:0%
+can then just run my app at every
+customer right but with epic in
+
+ align:start position:0%
+customer right but with epic in
+ 
+
+ align:start position:0%
+customer right but with epic in
+particular you have to then make a deal
+
+ align:start position:0%
+particular you have to then make a deal
+ 
+
+ align:start position:0%
+particular you have to then make a deal
+with me to use it at the program and
+
+ align:start position:0%
+with me to use it at the program and
+ 
+
+ align:start position:0%
+with me to use it at the program and
+make a deal with you know my colleague
+
+ align:start position:0%
+make a deal with you know my colleague
+ 
+
+ align:start position:0%
+make a deal with you know my colleague
+to use it at Stanford other EHR vendors
+
+ align:start position:0%
+to use it at Stanford other EHR vendors
+ 
+
+ align:start position:0%
+to use it at Stanford other EHR vendors
+have developed a more sort of
+
+ align:start position:0%
+have developed a more sort of
+ 
+
+ align:start position:0%
+have developed a more sort of
+centralized model where you can actually
+
+ align:start position:0%
+centralized model where you can actually
+ 
+
+ align:start position:0%
+centralized model where you can actually
+sort of release it in
+
+ align:start position:0%
+sort of release it in
+ 
+
+ align:start position:0%
+sort of release it in
+salad and I can pay for it directly
+
+ align:start position:0%
+salad and I can pay for it directly
+ 
+
+ align:start position:0%
+salad and I can pay for it directly
+through through the app store and
+
+ align:start position:0%
+through through the app store and
+ 
+
+ align:start position:0%
+through through the app store and
+integrate it I think that last mile
+
+ align:start position:0%
+integrate it I think that last mile
+ 
+
+ align:start position:0%
+integrate it I think that last mile
+piece hasn't really been standardized
+
+ align:start position:0%
+piece hasn't really been standardized
+ 
+
+ align:start position:0%
+piece hasn't really been standardized
+yet yeah we just want to not stop us
+
+ align:start position:0%
+yet yeah we just want to not stop us
+ 
+
+ align:start position:0%
+yet yeah we just want to not stop us
+from doing that the only real
+
+ align:start position:0%
+from doing that the only real
+ 
+
+ align:start position:0%
+from doing that the only real
+restriction is that epic would limit my
+
+ align:start position:0%
+restriction is that epic would limit my
+ 
+
+ align:start position:0%
+restriction is that epic would limit my
+ability to tell you stuff about epics
+
+ align:start position:0%
+ability to tell you stuff about epics
+ 
+
+ align:start position:0%
+ability to tell you stuff about epics
+guts and so you would need a relatively
+
+ align:start position:0%
+guts and so you would need a relatively
+ 
+
+ align:start position:0%
+guts and so you would need a relatively
+sophisticated healthcare provider
+
+ align:start position:0%
+sophisticated healthcare provider
+ 
+
+ align:start position:0%
+sophisticated healthcare provider
+organization who could map between some
+
+ align:start position:0%
+organization who could map between some
+ 
+
+ align:start position:0%
+organization who could map between some
+sort of kind of platonic date of
+
+ align:start position:0%
+sort of kind of platonic date of
+ 
+
+ align:start position:0%
+sort of kind of platonic date of
+clinical data model and epics internal
+
+ align:start position:0%
+clinical data model and epics internal
+ 
+
+ align:start position:0%
+clinical data model and epics internal
+data model but if you had that you could
+
+ align:start position:0%
+data model but if you had that you could
+ 
+
+ align:start position:0%
+data model but if you had that you could
+any minute the freedom we have this AI
+
+ align:start position:0%
+any minute the freedom we have this AI
+ 
+
+ align:start position:0%
+any minute the freedom we have this AI
+hub innovation program and we're
+
+ align:start position:0%
+hub innovation program and we're
+ 
+
+ align:start position:0%
+hub innovation program and we're
+probably working with 50 to 100 startups
+
+ align:start position:0%
+probably working with 50 to 100 startups
+ 
+
+ align:start position:0%
+probably working with 50 to 100 startups
+of doing work like that some of whom are
+
+ align:start position:0%
+of doing work like that some of whom are
+ 
+
+ align:start position:0%
+of doing work like that some of whom are
+members of the epic aperture and some
+
+ align:start position:0%
+members of the epic aperture and some
+ 
+
+ align:start position:0%
+members of the epic aperture and some
+who choose not to University in the epic
+
+ align:start position:0%
+who choose not to University in the epic
+ 
+
+ align:start position:0%
+who choose not to University in the epic
+aperture it's we're saying that joining
+
+ align:start position:0%
+aperture it's we're saying that joining
+ 
+
+ align:start position:0%
+aperture it's we're saying that joining
+the aperture during these programs
+
+ align:start position:0%
+the aperture during these programs
+ 
+
+ align:start position:0%
+the aperture during these programs
+entails revenue sharing with that
+
+ align:start position:0%
+entails revenue sharing with that
+ 
+
+ align:start position:0%
+entails revenue sharing with that
+backhand and some complexity that may go
+
+ align:start position:0%
+backhand and some complexity that may go
+ 
+
+ align:start position:0%
+backhand and some complexity that may go
+way down with these new regulations but
+
+ align:start position:0%
+way down with these new regulations but
+ 
+
+ align:start position:0%
+way down with these new regulations but
+right now some organizations have chosen
+
+ align:start position:0%
+right now some organizations have chosen
+ 
+
+ align:start position:0%
+right now some organizations have chosen
+not to not to partner with the vendors
+
+ align:start position:0%
+not to not to partner with the vendors
+ 
+
+ align:start position:0%
+not to not to partner with the vendors
+more directly without their fight
+
+ align:start position:0%
+more directly without their fight
+ 
+
+ align:start position:0%
+more directly without their fight
+organization so on the quality side of
+
+ align:start position:0%
+organization so on the quality side of
+ 
+
+ align:start position:0%
+organization so on the quality side of
+that question if you do develop an
+
+ align:start position:0%
+that question if you do develop an
+ 
+
+ align:start position:0%
+that question if you do develop an
+application and field it at the Brigham
+
+ align:start position:0%
+application and field it at the Brigham
+ 
+
+ align:start position:0%
+application and field it at the Brigham
+will that will Stanford be interested in
+
+ align:start position:0%
+will that will Stanford be interested in
+ 
+
+ align:start position:0%
+will that will Stanford be interested in
+in taking it or are they going to be
+
+ align:start position:0%
+in taking it or are they going to be
+ 
+
+ align:start position:0%
+in taking it or are they going to be
+concerned about the fact that somehow
+
+ align:start position:0%
+concerned about the fact that somehow
+ 
+
+ align:start position:0%
+concerned about the fact that somehow
+you fit it to the patient population in
+
+ align:start position:0%
+you fit it to the patient population in
+ 
+
+ align:start position:0%
+you fit it to the patient population in
+Boston and it won't be appropriate to
+
+ align:start position:0%
+Boston and it won't be appropriate to
+ 
+
+ align:start position:0%
+Boston and it won't be appropriate to
+their data yeah I think that's a
+
+ align:start position:0%
+their data yeah I think that's a
+ 
+
+ align:start position:0%
+their data yeah I think that's a
+fundamental question right as to what
+
+ align:start position:0%
+fundamental question right as to what
+ 
+
+ align:start position:0%
+fundamental question right as to what
+extent do these models generalize right
+
+ align:start position:0%
+extent do these models generalize right
+ 
+
+ align:start position:0%
+extent do these models generalize right
+can you train a model at one place to
+
+ align:start position:0%
+can you train a model at one place to
+ 
+
+ align:start position:0%
+can you train a model at one place to
+transfer it to it to another place we
+
+ align:start position:0%
+transfer it to it to another place we
+ 
+
+ align:start position:0%
+transfer it to it to another place we
+generally seem that many of them
+
+ align:start position:0%
+generally seem that many of them
+ 
+
+ align:start position:0%
+generally seem that many of them
+transfer pretty well right so if they
+
+ align:start position:0%
+transfer pretty well right so if they
+ 
+
+ align:start position:0%
+transfer pretty well right so if they
+really have more to do with kind of core
+
+ align:start position:0%
+really have more to do with kind of core
+ 
+
+ align:start position:0%
+really have more to do with kind of core
+human physiology that can be pretty
+
+ align:start position:0%
+human physiology that can be pretty
+ 
+
+ align:start position:0%
+human physiology that can be pretty
+similar between organizations if they're
+
+ align:start position:0%
+similar between organizations if they're
+ 
+
+ align:start position:0%
+similar between organizations if they're
+sort of really bound up in a particular
+
+ align:start position:0%
+sort of really bound up in a particular
+ 
+
+ align:start position:0%
+sort of really bound up in a particular
+workflow right they do you know they
+
+ align:start position:0%
+workflow right they do you know they
+ 
+
+ align:start position:0%
+workflow right they do you know they
+assume that you're doing this task this
+
+ align:start position:0%
+assume that you're doing this task this
+ 
+
+ align:start position:0%
+assume that you're doing this task this
+task this task in this order they tend
+
+ align:start position:0%
+task this task in this order they tend
+ 
+
+ align:start position:0%
+task this task in this order they tend
+to transfer really very poorly so I
+
+ align:start position:0%
+to transfer really very poorly so I
+ 
+
+ align:start position:0%
+to transfer really very poorly so I
+would say that our general approach has
+
+ align:start position:0%
+would say that our general approach has
+ 
+
+ align:start position:0%
+would say that our general approach has
+been to take a model that somebody has
+
+ align:start position:0%
+been to take a model that somebody has
+ 
+
+ align:start position:0%
+been to take a model that somebody has
+sort of run at retrospectively on our
+
+ align:start position:0%
+sort of run at retrospectively on our
+ 
+
+ align:start position:0%
+sort of run at retrospectively on our
+data warehouse and see if it's accurate
+
+ align:start position:0%
+data warehouse and see if it's accurate
+ 
+
+ align:start position:0%
+data warehouse and see if it's accurate
+and if it is we might go forward with it
+
+ align:start position:0%
+and if it is we might go forward with it
+ 
+
+ align:start position:0%
+and if it is we might go forward with it
+if it's not we would try to retrain it
+
+ align:start position:0%
+if it's not we would try to retrain it
+ 
+
+ align:start position:0%
+if it's not we would try to retrain it
+on our data and then see how much
+
+ align:start position:0%
+on our data and then see how much
+ 
+
+ align:start position:0%
+on our data and then see how much
+improvement we get by retraining it and
+
+ align:start position:0%
+improvement we get by retraining it and
+ 
+
+ align:start position:0%
+improvement we get by retraining it and
+so have you in fact imported such
+
+ align:start position:0%
+so have you in fact imported such
+ 
+
+ align:start position:0%
+so have you in fact imported such
+model yeah yeah we provides five or six
+
+ align:start position:0%
+model yeah yeah we provides five or six
+ 
+
+ align:start position:0%
+model yeah yeah we provides five or six
+models we just started using some of
+
+ align:start position:0%
+models we just started using some of
+ 
+
+ align:start position:0%
+models we just started using some of
+them at the Brigham are just kind of
+
+ align:start position:0%
+them at the Brigham are just kind of
+ 
+
+ align:start position:0%
+them at the Brigham are just kind of
+signed a license to begin using them and
+
+ align:start position:0%
+signed a license to begin using them and
+ 
+
+ align:start position:0%
+signed a license to begin using them and
+I think in our experiences that yeah
+
+ align:start position:0%
+I think in our experiences that yeah
+ 
+
+ align:start position:0%
+I think in our experiences that yeah
+absolutely so the question is we get a
+
+ align:start position:0%
+absolutely so the question is we get a
+ 
+
+ align:start position:0%
+absolutely so the question is we get a
+risks or we deploy new risk or it says
+
+ align:start position:0%
+risks or we deploy new risk or it says
+ 
+
+ align:start position:0%
+risks or we deploy new risk or it says
+patients a fall Langer patients who've
+
+ align:start position:0%
+patients a fall Langer patients who've
+ 
+
+ align:start position:0%
+patients a fall Langer patients who've
+had them sepsis or something like that
+
+ align:start position:0%
+had them sepsis or something like that
+ 
+
+ align:start position:0%
+had them sepsis or something like that
+you know we tend to do several levels of
+
+ align:start position:0%
+you know we tend to do several levels of
+ 
+
+ align:start position:0%
+you know we tend to do several levels of
+evaluation right so so the first level
+
+ align:start position:0%
+evaluation right so so the first level
+ 
+
+ align:start position:0%
+evaluation right so so the first level
+is when we show the score what do people
+
+ align:start position:0%
+is when we show the score what do people
+ 
+
+ align:start position:0%
+is when we show the score what do people
+do right if we typically we don't just
+
+ align:start position:0%
+do right if we typically we don't just
+ 
+
+ align:start position:0%
+do right if we typically we don't just
+show a score we make a recommendation we
+
+ align:start position:0%
+show a score we make a recommendation we
+ 
+
+ align:start position:0%
+show a score we make a recommendation we
+say based on the score we think you
+
+ align:start position:0%
+say based on the score we think you
+ 
+
+ align:start position:0%
+say based on the score we think you
+should order a lactate to see if the
+
+ align:start position:0%
+should order a lactate to see if the
+ 
+
+ align:start position:0%
+should order a lactate to see if the
+patient is at risk of having sepsis
+
+ align:start position:0%
+patient is at risk of having sepsis
+ 
+
+ align:start position:0%
+patient is at risk of having sepsis
+first we like to see if people do what
+
+ align:start position:0%
+first we like to see if people do what
+ 
+
+ align:start position:0%
+first we like to see if people do what
+we say right so we think it's a good
+
+ align:start position:0%
+we say right so we think it's a good
+ 
+
+ align:start position:0%
+we say right so we think it's a good
+sign if people sort of follow the
+
+ align:start position:0%
+sign if people sort of follow the
+ 
+
+ align:start position:0%
+sign if people sort of follow the
+suggestions but ultimately you know we
+
+ align:start position:0%
+suggestions but ultimately you know we
+ 
+
+ align:start position:0%
+suggestions but ultimately you know we
+view ourselves as sort of clinical trial
+
+ align:start position:0%
+view ourselves as sort of clinical trial
+ 
+
+ align:start position:0%
+view ourselves as sort of clinical trial
+lists right so we deploy this model with
+
+ align:start position:0%
+lists right so we deploy this model with
+ 
+
+ align:start position:0%
+lists right so we deploy this model with
+an intent to move something right to
+
+ align:start position:0%
+an intent to move something right to
+ 
+
+ align:start position:0%
+an intent to move something right to
+reduce the rate of sepsis or to reduce
+
+ align:start position:0%
+reduce the rate of sepsis or to reduce
+ 
+
+ align:start position:0%
+reduce the rate of sepsis or to reduce
+the rate of mortality in sepsis and said
+
+ align:start position:0%
+the rate of mortality in sepsis and said
+ 
+
+ align:start position:0%
+the rate of mortality in sepsis and said
+we would try to sort of measure it if
+
+ align:start position:0%
+we would try to sort of measure it if
+ 
+
+ align:start position:0%
+we would try to sort of measure it if
+nothing else do it before and after City
+
+ align:start position:0%
+nothing else do it before and after City
+ 
+
+ align:start position:0%
+nothing else do it before and after City
+right measure the rates before implement
+
+ align:start position:0%
+right measure the rates before implement
+ 
+
+ align:start position:0%
+right measure the rates before implement
+this intervention and measure the rates
+
+ align:start position:0%
+this intervention and measure the rates
+ 
+
+ align:start position:0%
+this intervention and measure the rates
+after in cases where we're sort of less
+
+ align:start position:0%
+after in cases where we're sort of less
+ 
+
+ align:start position:0%
+after in cases where we're sort of less
+sure we really care about the results
+
+ align:start position:0%
+sure we really care about the results
+ 
+
+ align:start position:0%
+sure we really care about the results
+we'll even do a randomized trial right
+
+ align:start position:0%
+we'll even do a randomized trial right
+ 
+
+ align:start position:0%
+we'll even do a randomized trial right
+so look if half of the units will get a
+
+ align:start position:0%
+so look if half of the units will get a
+ 
+
+ align:start position:0%
+so look if half of the units will get a
+the alert half the units won't get the
+
+ align:start position:0%
+the alert half the units won't get the
+ 
+
+ align:start position:0%
+the alert half the units won't get the
+alert unless you compare the effect on a
+
+ align:start position:0%
+alert unless you compare the effect on a
+ 
+
+ align:start position:0%
+alert unless you compare the effect on a
+clinical outcome and see what that what
+
+ align:start position:0%
+clinical outcome and see what that what
+ 
+
+ align:start position:0%
+clinical outcome and see what that what
+the difference is it our opinion unless
+
+ align:start position:0%
+the difference is it our opinion unless
+ 
+
+ align:start position:0%
+the difference is it our opinion unless
+we can show and sort of an effect on
+
+ align:start position:0%
+we can show and sort of an effect on
+ 
+
+ align:start position:0%
+we can show and sort of an effect on
+these clinical measures we shouldn't be
+
+ align:start position:0%
+these clinical measures we shouldn't be
+ 
+
+ align:start position:0%
+these clinical measures we shouldn't be
+bothering people right you know Pete
+
+ align:start position:0%
+bothering people right you know Pete
+ 
+
+ align:start position:0%
+bothering people right you know Pete
+made this point that you know what's the
+
+ align:start position:0%
+made this point that you know what's the
+ 
+
+ align:start position:0%
+made this point that you know what's the
+purpose of have that you know if we have
+
+ align:start position:0%
+purpose of have that you know if we have
+ 
+
+ align:start position:0%
+purpose of have that you know if we have
+a thousand alerts everyone will be
+
+ align:start position:0%
+a thousand alerts everyone will be
+ 
+
+ align:start position:0%
+a thousand alerts everyone will be
+overwhelmed so we should only keep
+
+ align:start position:0%
+overwhelmed so we should only keep
+ 
+
+ align:start position:0%
+overwhelmed so we should only keep
+alerts on it for each other they're
+
+ align:start position:0%
+alerts on it for each other they're
+ 
+
+ align:start position:0%
+alerts on it for each other they're
+making a real clinical difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+checks are there papers of like some of
+
+ align:start position:0%
+checks are there papers of like some of
+ 
+
+ align:start position:0%
+checks are there papers of like some of
+these deployments uh it sorry tart
+
+ align:start position:0%
+these deployments uh it sorry tart
+ 
+
+ align:start position:0%
+these deployments uh it sorry tart
+intend to publish everything right and I
+
+ align:start position:0%
+intend to publish everything right and I
+ 
+
+ align:start position:0%
+intend to publish everything right and I
+think we're behind but I'd say you don't
+
+ align:start position:0%
+think we're behind but I'd say you don't
+ 
+
+ align:start position:0%
+think we're behind but I'd say you don't
+we publish everything we off we have
+
+ align:start position:0%
+we publish everything we off we have
+ 
+
+ align:start position:0%
+we publish everything we off we have
+some things that we finish that we
+
+ align:start position:0%
+some things that we finish that we
+ 
+
+ align:start position:0%
+some things that we finish that we
+haven't published yet they're sort of
+
+ align:start position:0%
+haven't published yet they're sort of
+ 
+
+ align:start position:0%
+haven't published yet they're sort of
+the next thing to sort of come out yeah
+
+ align:start position:0%
+the next thing to sort of come out yeah
+ 
+
+ align:start position:0%
+the next thing to sort of come out yeah
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+oh yeah so the question is do we ever
+
+ align:start position:0%
+oh yeah so the question is do we ever
+ 
+
+ align:start position:0%
+oh yeah so the question is do we ever
+check to see how often the model
+
+ align:start position:0%
+check to see how often the model
+ 
+
+ align:start position:0%
+check to see how often the model
+recommendation matches what the doctor
+
+ align:start position:0%
+recommendation matches what the doctor
+ 
+
+ align:start position:0%
+recommendation matches what the doctor
+does and so there's sort of two ways we
+
+ align:start position:0%
+does and so there's sort of two ways we
+ 
+
+ align:start position:0%
+does and so there's sort of two ways we
+do that we'll often retrospectively test
+
+ align:start position:0%
+do that we'll often retrospectively test
+ 
+
+ align:start position:0%
+do that we'll often retrospectively test
+the model back and so I think peach
+
+ align:start position:0%
+the model back and so I think peach
+ 
+
+ align:start position:0%
+the model back and so I think peach
+aired a paper from Cerner where they
+
+ align:start position:0%
+aired a paper from Cerner where they
+ 
+
+ align:start position:0%
+aired a paper from Cerner where they
+looked at these sort of suggestions that
+
+ align:start position:0%
+looked at these sort of suggestions that
+ 
+
+ align:start position:0%
+looked at these sort of suggestions that
+they made to order the lactates or to do
+
+ align:start position:0%
+they made to order the lactates or to do
+ 
+
+ align:start position:0%
+they made to order the lactates or to do
+other sort of sepsis works definitely
+
+ align:start position:0%
+other sort of sepsis works definitely
+ 
+
+ align:start position:0%
+other sort of sepsis works definitely
+look to see whether the recommendations
+
+ align:start position:0%
+look to see whether the recommendations
+ 
+
+ align:start position:0%
+look to see whether the recommendations
+that they made matched what the doctors
+
+ align:start position:0%
+that they made matched what the doctors
+ 
+
+ align:start position:0%
+that they made matched what the doctors
+had actually done and they they showed
+
+ align:start position:0%
+had actually done and they they showed
+ 
+
+ align:start position:0%
+had actually done and they they showed
+that they in many cases did so that
+
+ align:start position:0%
+that they in many cases did so that
+ 
+
+ align:start position:0%
+that they in many cases did so that
+would be the first thing that we do is
+
+ align:start position:0%
+would be the first thing that we do is
+ 
+
+ align:start position:0%
+would be the first thing that we do is
+before we even turn the model on will
+
+ align:start position:0%
+before we even turn the model on will
+ 
+
+ align:start position:0%
+before we even turn the model on will
+run it in sort of silent mode and see if
+
+ align:start position:0%
+run it in sort of silent mode and see if
+ 
+
+ align:start position:0%
+run it in sort of silent mode and see if
+the doctor does what we suggest now the
+
+ align:start position:0%
+the doctor does what we suggest now the
+ 
+
+ align:start position:0%
+the doctor does what we suggest now the
+doctor is not a perfect supervision
+
+ align:start position:0%
+doctor is not a perfect supervision
+ 
+
+ align:start position:0%
+doctor is not a perfect supervision
+right because the doctor may neglect to
+
+ align:start position:0%
+right because the doctor may neglect to
+ 
+
+ align:start position:0%
+right because the doctor may neglect to
+do something that would be good to do so
+
+ align:start position:0%
+do something that would be good to do so
+ 
+
+ align:start position:0%
+do something that would be good to do so
+then when we turn it on we actually look
+
+ align:start position:0%
+then when we turn it on we actually look
+ 
+
+ align:start position:0%
+then when we turn it on we actually look
+to see whether the doctor takes the
+
+ align:start position:0%
+to see whether the doctor takes the
+ 
+
+ align:start position:0%
+to see whether the doctor takes the
+action that we suggested and if we're
+
+ align:start position:0%
+action that we suggested and if we're
+ 
+
+ align:start position:0%
+action that we suggested and if we're
+doing it in this randomized mode we
+
+ align:start position:0%
+doing it in this randomized mode we
+ 
+
+ align:start position:0%
+doing it in this randomized mode we
+would then look to see whether the
+
+ align:start position:0%
+would then look to see whether the
+ 
+
+ align:start position:0%
+would then look to see whether the
+doctor takes the action we suggested
+
+ align:start position:0%
+doctor takes the action we suggested
+ 
+
+ align:start position:0%
+doctor takes the action we suggested
+more often in the case where we show the
+
+ align:start position:0%
+more often in the case where we show the
+ 
+
+ align:start position:0%
+more often in the case where we show the
+alert than where we generate the alert
+
+ align:start position:0%
+alert than where we generate the alert
+ 
+
+ align:start position:0%
+alert than where we generate the alert
+but sort of just log it and don't don't
+
+ align:start position:0%
+but sort of just log it and don't don't
+ 
+
+ align:start position:0%
+but sort of just log it and don't don't
+show it yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you mentioned how there's that sort
+
+ align:start position:0%
+so you mentioned how there's that sort
+ 
+
+ align:start position:0%
+so you mentioned how there's that sort
+of like right you said that kids have
+
+ align:start position:0%
+of like right you said that kids have
+ 
+
+ align:start position:0%
+of like right you said that kids have
+like my very limited understanding of
+
+ align:start position:0%
+like my very limited understanding of
+ 
+
+ align:start position:0%
+like my very limited understanding of
+like is that if you're flying like say
+
+ align:start position:0%
+like is that if you're flying like say
+ 
+
+ align:start position:0%
+like is that if you're flying like say
+below 10,000 people arms get turned off
+
+ align:start position:0%
+below 10,000 people arms get turned off
+ 
+
+ align:start position:0%
+below 10,000 people arms get turned off
+yep I don't know if there seems to be
+
+ align:start position:0%
+yep I don't know if there seems to be
+ 
+
+ align:start position:0%
+yep I don't know if there seems to be
+yes just because the technology workflow
+
+ align:start position:0%
+yes just because the technology workflow
+ 
+
+ align:start position:0%
+yes just because the technology workflow
+is not good sure enough what kind of
+
+ align:start position:0%
+is not good sure enough what kind of
+ 
+
+ align:start position:0%
+is not good sure enough what kind of
+question about the incentives between
+
+ align:start position:0%
+question about the incentives between
+ 
+
+ align:start position:0%
+question about the incentives between
+you know we try rights as we often don't
+
+ align:start position:0%
+you know we try rights as we often don't
+ 
+
+ align:start position:0%
+you know we try rights as we often don't
+know about the situations in a
+
+ align:start position:0%
+know about the situations in a
+ 
+
+ align:start position:0%
+know about the situations in a
+structured way the EHR so most of our
+
+ align:start position:0%
+structured way the EHR so most of our
+ 
+
+ align:start position:0%
+structured way the EHR so most of our
+alerts are suppressed in the operating
+
+ align:start position:0%
+alerts are suppressed in the operating
+ 
+
+ align:start position:0%
+alerts are suppressed in the operating
+room right so being an answer when a
+
+ align:start position:0%
+room right so being an answer when a
+ 
+
+ align:start position:0%
+room right so being an answer when a
+patient is on anesthesia you know their
+
+ align:start position:0%
+patient is on anesthesia you know their
+ 
+
+ align:start position:0%
+patient is on anesthesia you know their
+physiology is being sort of manually
+
+ align:start position:0%
+physiology is being sort of manually
+ 
+
+ align:start position:0%
+physiology is being sort of manually
+controlled by a doctor and so we often
+
+ align:start position:0%
+controlled by a doctor and so we often
+ 
+
+ align:start position:0%
+controlled by a doctor and so we often
+suppress the alert um in those
+
+ align:start position:0%
+suppress the alert um in those
+ 
+
+ align:start position:0%
+suppress the alert um in those
+situations I guess I didn't say to say
+
+ align:start position:0%
+situations I guess I didn't say to say
+ 
+
+ align:start position:0%
+situations I guess I didn't say to say
+the question but the question was do we
+
+ align:start position:0%
+the question but the question was do we
+ 
+
+ align:start position:0%
+the question but the question was do we
+try to take situations into account or
+
+ align:start position:0%
+try to take situations into account or
+ 
+
+ align:start position:0%
+try to take situations into account or
+how much can we we didn't use to know
+
+ align:start position:0%
+how much can we we didn't use to know
+ 
+
+ align:start position:0%
+how much can we we didn't use to know
+that a code blue was going on because we
+
+ align:start position:0%
+that a code blue was going on because we
+ 
+
+ align:start position:0%
+that a code blue was going on because we
+used to do almost or a code blue
+
+ align:start position:0%
+used to do almost or a code blue
+ 
+
+ align:start position:0%
+used to do almost or a code blue
+documentation on paper we now use this
+
+ align:start position:0%
+documentation on paper we now use this
+ 
+
+ align:start position:0%
+documentation on paper we now use this
+code narrator right so we can tell when
+
+ align:start position:0%
+code narrator right so we can tell when
+ 
+
+ align:start position:0%
+code narrator right so we can tell when
+a code blue starts when a code blue ends
+
+ align:start position:0%
+a code blue starts when a code blue ends
+ 
+
+ align:start position:0%
+a code blue starts when a code blue ends
+a Code Blue is like a cardiac arrest the
+
+ align:start position:0%
+a Code Blue is like a cardiac arrest the
+ 
+
+ align:start position:0%
+a Code Blue is like a cardiac arrest the
+resuscitation of the patient and so we
+
+ align:start position:0%
+resuscitation of the patient and so we
+ 
+
+ align:start position:0%
+resuscitation of the patient and so we
+actually do increasingly turn a lot of
+
+ align:start position:0%
+actually do increasingly turn a lot of
+ 
+
+ align:start position:0%
+actually do increasingly turn a lot of
+alerting off during a code blue I get an
+
+ align:start position:0%
+alerting off during a code blue I get an
+ 
+
+ align:start position:0%
+alerting off during a code blue I get an
+email or a page whenever a doctor
+
+ align:start position:0%
+email or a page whenever a doctor
+ 
+
+ align:start position:0%
+email or a page whenever a doctor
+overrides an alert and like writes a
+
+ align:start position:0%
+overrides an alert and like writes a
+ 
+
+ align:start position:0%
+overrides an alert and like writes a
+cranky message and they'll often say
+
+ align:start position:0%
+cranky message and they'll often say
+ 
+
+ align:start position:0%
+cranky message and they'll often say
+something like you know this patient is
+
+ align:start position:0%
+something like you know this patient is
+ 
+
+ align:start position:0%
+something like you know this patient is
+dying of the you know of a myocardial
+
+ align:start position:0%
+dying of the you know of a myocardial
+ 
+
+ align:start position:0%
+dying of the you know of a myocardial
+infarction right now and you're
+
+ align:start position:0%
+infarction right now and you're
+ 
+
+ align:start position:0%
+infarction right now and you're
+bothering me about this influenza
+
+ align:start position:0%
+bothering me about this influenza
+ 
+
+ align:start position:0%
+bothering me about this influenza
+vaccination and then what I'll do is
+
+ align:start position:0%
+vaccination and then what I'll do is
+ 
+
+ align:start position:0%
+vaccination and then what I'll do is
+I'll go back you know seriously I
+
+ align:start position:0%
+I'll go back you know seriously I
+ 
+
+ align:start position:0%
+I'll go back you know seriously I
+thought yesterday and so what authors
+
+ align:start position:0%
+thought yesterday and so what authors
+ 
+
+ align:start position:0%
+thought yesterday and so what authors
+I'll go back and look in the record and
+
+ align:start position:0%
+I'll go back and look in the record and
+ 
+
+ align:start position:0%
+I'll go back and look in the record and
+say what signs did I have this patient
+
+ align:start position:0%
+say what signs did I have this patient
+ 
+
+ align:start position:0%
+say what signs did I have this patient
+sort of in extremis and in that
+
+ align:start position:0%
+sort of in extremis and in that
+ 
+
+ align:start position:0%
+sort of in extremis and in that
+particular case it was a patient who
+
+ align:start position:0%
+particular case it was a patient who
+ 
+
+ align:start position:0%
+particular case it was a patient who
+came into the IDI and my very little
+
+ align:start position:0%
+came into the IDI and my very little
+ 
+
+ align:start position:0%
+came into the IDI and my very little
+documentation had been started and so
+
+ align:start position:0%
+documentation had been started and so
+ 
+
+ align:start position:0%
+documentation had been started and so
+there actually were very few signs that
+
+ align:start position:0%
+there actually were very few signs that
+ 
+
+ align:start position:0%
+there actually were very few signs that
+the patient was in the sort of acute
+
+ align:start position:0%
+the patient was in the sort of acute
+ 
+
+ align:start position:0%
+the patient was in the sort of acute
+state I think you know some day couldn't
+
+ align:start position:0%
+state I think you know some day couldn't
+ 
+
+ align:start position:0%
+state I think you know some day couldn't
+be smarter about integrating monitor
+
+ align:start position:0%
+be smarter about integrating monitor
+ 
+
+ align:start position:0%
+be smarter about integrating monitor
+data and device data to figure that out
+
+ align:start position:0%
+data and device data to figure that out
+ 
+
+ align:start position:0%
+data and device data to figure that out
+but at that point we didn't have a good
+
+ align:start position:0%
+but at that point we didn't have a good
+ 
+
+ align:start position:0%
+but at that point we didn't have a good
+structured data a woman in the chart
+
+ align:start position:0%
+structured data a woman in the chart
+ 
+
+ align:start position:0%
+structured data a woman in the chart
+that said this patient is like so ill
+
+ align:start position:0%
+that said this patient is like so ill
+ 
+
+ align:start position:0%
+that said this patient is like so ill
+that it's offensive to suggest the
+
+ align:start position:0%
+that it's offensive to suggest the
+ 
+
+ align:start position:0%
+that it's offensive to suggest the
+influenza vaccination right now so now
+
+ align:start position:0%
+influenza vaccination right now so now
+ 
+
+ align:start position:0%
+influenza vaccination right now so now
+there are hospitals that have started
+
+ align:start position:0%
+there are hospitals that have started
+ 
+
+ align:start position:0%
+there are hospitals that have started
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+thing with things like acquiring data
+
+ align:start position:0%
+thing with things like acquiring data
+ 
+
+ align:start position:0%
+thing with things like acquiring data
+from the ambulance as the patient is
+
+ align:start position:0%
+from the ambulance as the patient is
+ 
+
+ align:start position:0%
+from the ambulance as the patient is
+coming in so that the IDI is already
+
+ align:start position:0%
+coming in so that the IDI is already
+ 
+
+ align:start position:0%
+coming in so that the IDI is already
+primed with preliminary data and in that
+
+ align:start position:0%
+primed with preliminary data and in that
+ 
+
+ align:start position:0%
+primed with preliminary data and in that
+circumstance you could tell so this is
+
+ align:start position:0%
+circumstance you could tell so this is
+ 
+
+ align:start position:0%
+circumstance you could tell so this is
+the interoperability challenge right so
+
+ align:start position:0%
+the interoperability challenge right so
+ 
+
+ align:start position:0%
+the interoperability challenge right so
+we actually get the run achieve all the
+
+ align:start position:0%
+we actually get the run achieve all the
+ 
+
+ align:start position:0%
+we actually get the run achieve all the
+amulets data to us it comes in as a PDF
+
+ align:start position:0%
+amulets data to us it comes in as a PDF
+ 
+
+ align:start position:0%
+amulets data to us it comes in as a PDF
+that's transmitted from the ambulance
+
+ align:start position:0%
+that's transmitted from the ambulance
+ 
+
+ align:start position:0%
+that's transmitted from the ambulance
+emergency management system to our EHR
+
+ align:start position:0%
+emergency management system to our EHR
+ 
+
+ align:start position:0%
+emergency management system to our EHR
+and so it's not coming in in a way that
+
+ align:start position:0%
+and so it's not coming in in a way that
+ 
+
+ align:start position:0%
+and so it's not coming in in a way that
+we can sort of read it well but your
+
+ align:start position:0%
+we can sort of read it well but your
+ 
+
+ align:start position:0%
+we can sort of read it well but your
+point exactly if we were better at
+
+ align:start position:0%
+point exactly if we were better at
+ 
+
+ align:start position:0%
+point exactly if we were better at
+interoperability I've also talked to
+
+ align:start position:0%
+interoperability I've also talked to
+ 
+
+ align:start position:0%
+interoperability I've also talked to
+hospitals who you know use things like
+
+ align:start position:0%
+hospitals who you know use things like
+ 
+
+ align:start position:0%
+hospitals who you know use things like
+you know video cameras and people's
+
+ align:start position:0%
+you know video cameras and people's
+ 
+
+ align:start position:0%
+you know video cameras and people's
+badges but there's 50 people hovering
+
+ align:start position:0%
+badges but there's 50 people hovering
+ 
+
+ align:start position:0%
+badges but there's 50 people hovering
+around a patient that's a sign that
+
+ align:start position:0%
+around a patient that's a sign that
+ 
+
+ align:start position:0%
+around a patient that's a sign that
+something bad is happening so we might
+
+ align:start position:0%
+something bad is happening so we might
+ 
+
+ align:start position:0%
+something bad is happening so we might
+be able to use something like that but
+
+ align:start position:0%
+be able to use something like that but
+ 
+
+ align:start position:0%
+be able to use something like that but
+yeah where we'd like to be better at
+
+ align:start position:0%
+yeah where we'd like to be better at
+ 
+
+ align:start position:0%
+yeah where we'd like to be better at
+that so what why did hl7 version 3 not
+
+ align:start position:0%
+that so what why did hl7 version 3 not
+ 
+
+ align:start position:0%
+that so what why did hl7 version 3 not
+solve all these this is a good
+
+ align:start position:0%
+solve all these this is a good
+ 
+
+ align:start position:0%
+solve all these this is a good
+philosophical question come to BMI 701
+
+ align:start position:0%
+philosophical question come to BMI 701
+ 
+
+ align:start position:0%
+philosophical question come to BMI 701
+and 702 and we'll talk about it and
+
+ align:start position:0%
+and 702 and we'll talk about it and
+ 
+
+ align:start position:0%
+and 702 and we'll talk about it and
+Hertz hl7 version 2 fees questions
+
+ align:start position:0%
+Hertz hl7 version 2 fees questions
+ 
+
+ align:start position:0%
+Hertz hl7 version 2 fees questions
+version 2 is a very practical standard
+
+ align:start position:0%
+version 2 is a very practical standard
+ 
+
+ align:start position:0%
+version 2 is a very practical standard
+version 3 was a very deeply
+
+ align:start position:0%
+version 3 was a very deeply
+ 
+
+ align:start position:0%
+version 3 was a very deeply
+philosophical standard as Perosh
+
+ align:start position:0%
+philosophical standard as Perosh
+ 
+
+ align:start position:0%
+philosophical standard as Perosh
+aspirational that never quite caught on
+
+ align:start position:0%
+aspirational that never quite caught on
+ 
+
+ align:start position:0%
+aspirational that never quite caught on
+it did in pieces I mean smart if I there
+
+ align:start position:0%
+it did in pieces I mean smart if I there
+ 
+
+ align:start position:0%
+it did in pieces I mean smart if I there
+is a simplification of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes sir danke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I mean there's calibration right so
+
+ align:start position:0%
+yeah I mean there's calibration right so
+ 
+
+ align:start position:0%
+yeah I mean there's calibration right so
+we can say this model works particularly
+
+ align:start position:0%
+we can say this model works particularly
+ 
+
+ align:start position:0%
+we can say this model works particularly
+well in these patients or not as well in
+
+ align:start position:0%
+well in these patients or not as well in
+ 
+
+ align:start position:0%
+well in these patients or not as well in
+these patients there are some you know
+
+ align:start position:0%
+these patients there are some you know
+ 
+
+ align:start position:0%
+these patients there are some you know
+very simple equations or models that we
+
+ align:start position:0%
+very simple equations or models that we
+ 
+
+ align:start position:0%
+very simple equations or models that we
+use for example where we use a different
+
+ align:start position:0%
+use for example where we use a different
+ 
+
+ align:start position:0%
+use for example where we use a different
+model in African American patients
+
+ align:start position:0%
+model in African American patients
+ 
+
+ align:start position:0%
+model in African American patients
+versus even on African American patients
+
+ align:start position:0%
+versus even on African American patients
+ 
+
+ align:start position:0%
+versus even on African American patients
+because there's some data that says this
+
+ align:start position:0%
+because there's some data that says this
+ 
+
+ align:start position:0%
+because there's some data that says this
+model is better calibrated in this
+
+ align:start position:0%
+model is better calibrated in this
+ 
+
+ align:start position:0%
+model is better calibrated in this
+subgroup of patients versus another I do
+
+ align:start position:0%
+subgroup of patients versus another I do
+ 
+
+ align:start position:0%
+subgroup of patients versus another I do
+think though to your point that there's
+
+ align:start position:0%
+think though to your point that there's
+ 
+
+ align:start position:0%
+think though to your point that there's
+a suggestion you know an inference from
+
+ align:start position:0%
+a suggestion you know an inference from
+ 
+
+ align:start position:0%
+a suggestion you know an inference from
+a model this patient is that at risk of
+
+ align:start position:0%
+a model this patient is that at risk of
+ 
+
+ align:start position:0%
+a model this patient is that at risk of
+a fall and then there's this whole set
+
+ align:start position:0%
+a fall and then there's this whole set
+ 
+
+ align:start position:0%
+a fall and then there's this whole set
+of you know kind of value judgments and
+
+ align:start position:0%
+of you know kind of value judgments and
+ 
+
+ align:start position:0%
+of you know kind of value judgments and
+beliefs and knowledge and understanding
+
+ align:start position:0%
+beliefs and knowledge and understanding
+ 
+
+ align:start position:0%
+beliefs and knowledge and understanding
+of a patient's circumstances that are
+
+ align:start position:0%
+of a patient's circumstances that are
+ 
+
+ align:start position:0%
+of a patient's circumstances that are
+very human and I think that that's
+
+ align:start position:0%
+very human and I think that that's
+ 
+
+ align:start position:0%
+very human and I think that that's
+largely why we deliver these suggestions
+
+ align:start position:0%
+largely why we deliver these suggestions
+ 
+
+ align:start position:0%
+largely why we deliver these suggestions
+to in doctor to a nurse and then that
+
+ align:start position:0%
+to in doctor to a nurse and then that
+ 
+
+ align:start position:0%
+to in doctor to a nurse and then that
+human uses that information plus their
+
+ align:start position:0%
+human uses that information plus their
+ 
+
+ align:start position:0%
+human uses that information plus their
+expertise and their relationship and
+
+ align:start position:0%
+expertise and their relationship and
+ 
+
+ align:start position:0%
+expertise and their relationship and
+their experience to make a suggestion
+
+ align:start position:0%
+their experience to make a suggestion
+ 
+
+ align:start position:0%
+their experience to make a suggestion
+rather than you know just having the
+
+ align:start position:0%
+rather than you know just having the
+ 
+
+ align:start position:0%
+rather than you know just having the
+computer adjust the knob on the
+
+ align:start position:0%
+computer adjust the knob on the
+ 
+
+ align:start position:0%
+computer adjust the knob on the
+ventilator itself question that people
+
+ align:start position:0%
+ventilator itself question that people
+ 
+
+ align:start position:0%
+ventilator itself question that people
+always ask me and if you should ask me
+
+ align:start position:0%
+always ask me and if you should ask me
+ 
+
+ align:start position:0%
+always ask me and if you should ask me
+is when we eventually not need that that
+
+ align:start position:0%
+is when we eventually not need that that
+ 
+
+ align:start position:0%
+is when we eventually not need that that
+human and I think I'm more optimistic
+
+ align:start position:0%
+human and I think I'm more optimistic
+ 
+
+ align:start position:0%
+human and I think I'm more optimistic
+than some people that there are cases
+
+ align:start position:0%
+than some people that there are cases
+ 
+
+ align:start position:0%
+than some people that there are cases
+where the computer is good enough or the
+
+ align:start position:0%
+where the computer is good enough or the
+ 
+
+ align:start position:0%
+where the computer is good enough or the
+human is poor enough that it would be
+
+ align:start position:0%
+human is poor enough that it would be
+ 
+
+ align:start position:0%
+human is poor enough that it would be
+safe to sort of have a close to closed
+
+ align:start position:0%
+safe to sort of have a close to closed
+ 
+
+ align:start position:0%
+safe to sort of have a close to closed
+loop however I think those cases are not
+
+ align:start position:0%
+loop however I think those cases are not
+ 
+
+ align:start position:0%
+loop however I think those cases are not
+the norm I think that there'll be more
+
+ align:start position:0%
+the norm I think that there'll be more
+ 
+
+ align:start position:0%
+the norm I think that there'll be more
+cases where where human doctors are
+
+ align:start position:0%
+cases where where human doctors are
+ 
+
+ align:start position:0%
+cases where where human doctors are
+still very much very much needed so I
+
+ align:start position:0%
+still very much very much needed so I
+ 
+
+ align:start position:0%
+still very much very much needed so I
+just add that there are tasks where
+
+ align:start position:0%
+just add that there are tasks where
+ 
+
+ align:start position:0%
+just add that there are tasks where
+where patients are fungible in the words
+
+ align:start position:0%
+where patients are fungible in the words
+ 
+
+ align:start position:0%
+where patients are fungible in the words
+that I used a few lectures ago so for
+
+ align:start position:0%
+that I used a few lectures ago so for
+ 
+
+ align:start position:0%
+that I used a few lectures ago so for
+example a lot of hospitals are
+
+ align:start position:0%
+example a lot of hospitals are
+ 
+
+ align:start position:0%
+example a lot of hospitals are
+developing models that predict whether a
+
+ align:start position:0%
+developing models that predict whether a
+ 
+
+ align:start position:0%
+developing models that predict whether a
+patient will show up for their optional
+
+ align:start position:0%
+patient will show up for their optional
+ 
+
+ align:start position:0%
+patient will show up for their optional
+surgery and because then if they can do
+
+ align:start position:0%
+surgery and because then if they can do
+ 
+
+ align:start position:0%
+surgery and because then if they can do
+a better job of over-scheduling the
+
+ align:start position:0%
+a better job of over-scheduling the
+ 
+
+ align:start position:0%
+a better job of over-scheduling the
+operating room in the same way that the
+
+ align:start position:0%
+operating room in the same way that the
+ 
+
+ align:start position:0%
+operating room in the same way that the
+airline's over oversell seats because
+
+ align:start position:0%
+airline's over oversell seats because
+ 
+
+ align:start position:0%
+airline's over oversell seats because
+statistically you could win doing that
+
+ align:start position:0%
+statistically you could win doing that
+ 
+
+ align:start position:0%
+statistically you could win doing that
+those are very safe predictions because
+
+ align:start position:0%
+those are very safe predictions because
+ 
+
+ align:start position:0%
+those are very safe predictions because
+the worst thing that happens is you get
+
+ align:start position:0%
+the worst thing that happens is you get
+ 
+
+ align:start position:0%
+the worst thing that happens is you get
+delayed but it's not going to have a
+
+ align:start position:0%
+delayed but it's not going to have a
+ 
+
+ align:start position:0%
+delayed but it's not going to have a
+harmful outcome on upon an individual
+
+ align:start position:0%
+harmful outcome on upon an individual
+ 
+
+ align:start position:0%
+harmful outcome on upon an individual
+patient University there are people that
+
+ align:start position:0%
+patient University there are people that
+ 
+
+ align:start position:0%
+patient University there are people that
+are working on machine learning systems
+
+ align:start position:0%
+are working on machine learning systems
+ 
+
+ align:start position:0%
+are working on machine learning systems
+for dosing insulin or adjusting people's
+
+ align:start position:0%
+for dosing insulin or adjusting people's
+ 
+
+ align:start position:0%
+for dosing insulin or adjusting people's
+ventilator settings and
+
+ align:start position:0%
+ventilator settings and
+ 
+
+ align:start position:0%
+ventilator settings and
+those are a high area yeah alright last
+
+ align:start position:0%
+those are a high area yeah alright last
+ 
+
+ align:start position:0%
+those are a high area yeah alright last
+question because we have to wrap up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+retraining yeah absolutely so the
+
+ align:start position:0%
+retraining yeah absolutely so the
+ 
+
+ align:start position:0%
+retraining yeah absolutely so the
+question is the kind of set and forget
+
+ align:start position:0%
+question is the kind of set and forget
+ 
+
+ align:start position:0%
+question is the kind of set and forget
+right we build the model of the Model T
+
+ align:start position:0%
+right we build the model of the Model T
+ 
+
+ align:start position:0%
+right we build the model of the Model T
+become stale should we update the model
+
+ align:start position:0%
+become stale should we update the model
+ 
+
+ align:start position:0%
+become stale should we update the model
+and how do we decide to do that I mean
+
+ align:start position:0%
+and how do we decide to do that I mean
+ 
+
+ align:start position:0%
+and how do we decide to do that I mean
+we're using you know it depends what you
+
+ align:start position:0%
+we're using you know it depends what you
+ 
+
+ align:start position:0%
+we're using you know it depends what you
+define as a model we're using tables and
+
+ align:start position:0%
+define as a model we're using tables and
+ 
+
+ align:start position:0%
+define as a model we're using tables and
+rules that we develop since the 1970s I
+
+ align:start position:0%
+rules that we develop since the 1970s I
+ 
+
+ align:start position:0%
+rules that we develop since the 1970s I
+think we have a pretty high desire to
+
+ align:start position:0%
+think we have a pretty high desire to
+ 
+
+ align:start position:0%
+think we have a pretty high desire to
+sort of purely revisit those it's a
+
+ align:start position:0%
+sort of purely revisit those it's a
+ 
+
+ align:start position:0%
+sort of purely revisit those it's a
+problem in the field in France it's
+
+ align:start position:0%
+problem in the field in France it's
+ 
+
+ align:start position:0%
+problem in the field in France it's
+called knowledge management or knowledge
+
+ align:start position:0%
+called knowledge management or knowledge
+ 
+
+ align:start position:0%
+called knowledge management or knowledge
+engineering right how do we sort of
+
+ align:start position:0%
+engineering right how do we sort of
+ 
+
+ align:start position:0%
+engineering right how do we sort of
+remember which of our knowledge bases
+
+ align:start position:0%
+remember which of our knowledge bases
+ 
+
+ align:start position:0%
+remember which of our knowledge bases
+need to be started check again or
+
+ align:start position:0%
+need to be started check again or
+ 
+
+ align:start position:0%
+need to be started check again or
+updated and we'll often you know just as
+
+ align:start position:0%
+updated and we'll often you know just as
+ 
+
+ align:start position:0%
+updated and we'll often you know just as
+a standard retrain a model we
+
+ align:start position:0%
+a standard retrain a model we
+ 
+
+ align:start position:0%
+a standard retrain a model we
+re-evaluated knowledge base every six
+
+ align:start position:0%
+re-evaluated knowledge base every six
+ 
+
+ align:start position:0%
+re-evaluated knowledge base every six
+months or every year because it's both
+
+ align:start position:0%
+months or every year because it's both
+ 
+
+ align:start position:0%
+months or every year because it's both
+harmful to patients if this stuff's out
+
+ align:start position:0%
+harmful to patients if this stuff's out
+ 
+
+ align:start position:0%
+harmful to patients if this stuff's out
+of date and it also makes us look stupid
+
+ align:start position:0%
+of date and it also makes us look stupid
+ 
+
+ align:start position:0%
+of date and it also makes us look stupid
+right so if you know there's a new paper
+
+ align:start position:0%
+right so if you know there's a new paper
+ 
+
+ align:start position:0%
+right so if you know there's a new paper
+that comes out and says beta blockers
+
+ align:start position:0%
+that comes out and says beta blockers
+ 
+
+ align:start position:0%
+that comes out and says beta blockers
+are terrible poison and then we keep
+
+ align:start position:0%
+are terrible poison and then we keep
+ 
+
+ align:start position:0%
+are terrible poison and then we keep
+suggesting them then people no longer
+
+ align:start position:0%
+suggesting them then people no longer
+ 
+
+ align:start position:0%
+suggesting them then people no longer
+believe suggestions we make that said we
+
+ align:start position:0%
+believe suggestions we make that said we
+ 
+
+ align:start position:0%
+believe suggestions we make that said we
+still make mistakes right I mean things
+
+ align:start position:0%
+still make mistakes right I mean things
+ 
+
+ align:start position:0%
+still make mistakes right I mean things
+happen all the time a lot of my work has
+
+ align:start position:0%
+happen all the time a lot of my work has
+ 
+
+ align:start position:0%
+happen all the time a lot of my work has
+focused on malfunctions in these systems
+
+ align:start position:0%
+focused on malfunctions in these systems
+ 
+
+ align:start position:0%
+focused on malfunctions in these systems
+and so it's an example you know if
+
+ align:start position:0%
+and so it's an example you know if
+ 
+
+ align:start position:0%
+and so it's an example you know if
+apparently the pharmacy might change the
+
+ align:start position:0%
+apparently the pharmacy might change the
+ 
+
+ align:start position:0%
+apparently the pharmacy might change the
+code or ID number for a medicine or a
+
+ align:start position:0%
+code or ID number for a medicine or a
+ 
+
+ align:start position:0%
+code or ID number for a medicine or a
+new medicine might come on the market
+
+ align:start position:0%
+new medicine might come on the market
+ 
+
+ align:start position:0%
+new medicine might come on the market
+and we have to make sure to continually
+
+ align:start position:0%
+and we have to make sure to continually
+ 
+
+ align:start position:0%
+and we have to make sure to continually
+update the knowledge base so that we're
+
+ align:start position:0%
+update the knowledge base so that we're
+ 
+
+ align:start position:0%
+update the knowledge base so that we're
+not suggesting an old medicine or
+
+ align:start position:0%
+not suggesting an old medicine or
+ 
+
+ align:start position:0%
+not suggesting an old medicine or
+overlooking fact the patient's already
+
+ align:start position:0%
+overlooking fact the patient's already
+ 
+
+ align:start position:0%
+overlooking fact the patient's already
+been prescribed a new medicine and so we
+
+ align:start position:0%
+been prescribed a new medicine and so we
+ 
+
+ align:start position:0%
+been prescribed a new medicine and so we
+tried to do that prospectively or
+
+ align:start position:0%
+tried to do that prospectively or
+ 
+
+ align:start position:0%
+tried to do that prospectively or
+practically but then we also tried to
+
+ align:start position:0%
+practically but then we also tried to
+ 
+
+ align:start position:0%
+practically but then we also tried to
+listen to feedback from users and fix
+
+ align:start position:0%
+listen to feedback from users and fix
+ 
+
+ align:start position:0%
+listen to feedback from users and fix
+things as we go school and just one one
+
+ align:start position:0%
+things as we go school and just one one
+ 
+
+ align:start position:0%
+things as we go school and just one one
+more comment on that so some things are
+
+ align:start position:0%
+more comment on that so some things are
+ 
+
+ align:start position:0%
+more comment on that so some things are
+done in real time there was a system
+
+ align:start position:0%
+done in real time there was a system
+ 
+
+ align:start position:0%
+done in real time there was a system
+many years ago at Intermountain health
+
+ align:start position:0%
+many years ago at Intermountain health
+ 
+
+ align:start position:0%
+many years ago at Intermountain health
+in Salt Lake City where they were
+
+ align:start position:0%
+in Salt Lake City where they were
+ 
+
+ align:start position:0%
+in Salt Lake City where they were
+looking at what bugs were growing out of
+
+ align:start position:0%
+looking at what bugs were growing out of
+ 
+
+ align:start position:0%
+looking at what bugs were growing out of
+microbiology samples in the laboratory
+
+ align:start position:0%
+microbiology samples in the laboratory
+ 
+
+ align:start position:0%
+microbiology samples in the laboratory
+and of course that can change on an hour
+
+ align:start position:0%
+and of course that can change on an hour
+ 
+
+ align:start position:0%
+and of course that can change on an hour
+by hour or day to day basis and so they
+
+ align:start position:0%
+by hour or day to day basis and so they
+ 
+
+ align:start position:0%
+by hour or day to day basis and so they
+were updating those systems that warn
+
+ align:start position:0%
+were updating those systems that warn
+ 
+
+ align:start position:0%
+were updating those systems that warn
+you about the possibility of that kind
+
+ align:start position:0%
+you about the possibility of that kind
+ 
+
+ align:start position:0%
+you about the possibility of that kind
+of infection in real time by taking
+
+ align:start position:0%
+of infection in real time by taking
+ 
+
+ align:start position:0%
+of infection in real time by taking
+feeds directly from the laboratory all
+
+ align:start position:0%
+feeds directly from the laboratory all
+ 
+
+ align:start position:0%
+feeds directly from the laboratory all
+right thank you very much
+
+ align:start position:0%
+right thank you very much
+ 
+
+ align:start position:0%
+right thank you very much
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/_OkTw766oCs.txt b/_OkTw766oCs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..645570eba7c73a4c50ebec8fbb0bd805a05cacd4
--- /dev/null
+++ b/_OkTw766oCs.txt
@@ -0,0 +1,8755 @@
+align:start position:0%
+ 
+this is 1401
+
+ align:start position:0%
+this is 1401
+ 
+
+ align:start position:0%
+this is 1401
+i'm john gruber and uh this is uh
+
+ align:start position:0%
+i'm john gruber and uh this is uh
+ 
+
+ align:start position:0%
+i'm john gruber and uh this is uh
+microeconomics
+
+ align:start position:0%
+microeconomics
+ 
+
+ align:start position:0%
+microeconomics
+um today i want to i want to cover three
+
+ align:start position:0%
+um today i want to i want to cover three
+ 
+
+ align:start position:0%
+um today i want to i want to cover three
+things i want to talk about the course
+
+ align:start position:0%
+things i want to talk about the course
+ 
+
+ align:start position:0%
+things i want to talk about the course
+details
+
+ align:start position:0%
+details
+ 
+
+ align:start position:0%
+details
+uh i want about what is microeconomics
+
+ align:start position:0%
+uh i want about what is microeconomics
+ 
+
+ align:start position:0%
+uh i want about what is microeconomics
+and then i'll talk start our
+
+ align:start position:0%
+and then i'll talk start our
+ 
+
+ align:start position:0%
+and then i'll talk start our
+start uh the substance of the course by
+
+ align:start position:0%
+start uh the substance of the course by
+ 
+
+ align:start position:0%
+start uh the substance of the course by
+talking about supply and demand
+
+ align:start position:0%
+talking about supply and demand
+ 
+
+ align:start position:0%
+talking about supply and demand
+a couple of points about the course the
+
+ align:start position:0%
+a couple of points about the course the
+ 
+
+ align:start position:0%
+a couple of points about the course the
+course will have a distinct sort of
+
+ align:start position:0%
+course will have a distinct sort of
+ 
+
+ align:start position:0%
+course will have a distinct sort of
+policy
+
+ align:start position:0%
+policy
+ 
+
+ align:start position:0%
+policy
+angle to it i sort of do economic policy
+
+ align:start position:0%
+angle to it i sort of do economic policy
+ 
+
+ align:start position:0%
+angle to it i sort of do economic policy
+is government policy is my thing
+
+ align:start position:0%
+is government policy is my thing
+ 
+
+ align:start position:0%
+is government policy is my thing
+so i i think it's what makes economics
+
+ align:start position:0%
+so i i think it's what makes economics
+ 
+
+ align:start position:0%
+so i i think it's what makes economics
+exciting and it sort of offers
+
+ align:start position:0%
+exciting and it sort of offers
+ 
+
+ align:start position:0%
+exciting and it sort of offers
+i think an interesting angle to
+
+ align:start position:0%
+i think an interesting angle to
+ 
+
+ align:start position:0%
+i think an interesting angle to
+understand why we're learning what we're
+
+ align:start position:0%
+understand why we're learning what we're
+ 
+
+ align:start position:0%
+understand why we're learning what we're
+learning i think sometimes in an intro
+
+ align:start position:0%
+learning i think sometimes in an intro
+ 
+
+ align:start position:0%
+learning i think sometimes in an intro
+class it's sort of hard to understand
+
+ align:start position:0%
+class it's sort of hard to understand
+ 
+
+ align:start position:0%
+class it's sort of hard to understand
+why the heck you're doing things um
+
+ align:start position:0%
+why the heck you're doing things um
+ 
+
+ align:start position:0%
+why the heck you're doing things um
+however that's just sort of a slight
+
+ align:start position:0%
+however that's just sort of a slight
+ 
+
+ align:start position:0%
+however that's just sort of a slight
+flavor if you're really more interested
+
+ align:start position:0%
+flavor if you're really more interested
+ 
+
+ align:start position:0%
+flavor if you're really more interested
+in this i teach a whole course called
+
+ align:start position:0%
+in this i teach a whole course called
+ 
+
+ align:start position:0%
+in this i teach a whole course called
+1441. i'm not teaching it this year
+
+ align:start position:0%
+1441. i'm not teaching it this year
+ 
+
+ align:start position:0%
+1441. i'm not teaching it this year
+but it'll be taught by a visitor in the
+
+ align:start position:0%
+but it'll be taught by a visitor in the
+ 
+
+ align:start position:0%
+but it'll be taught by a visitor in the
+spring uh kristen butcher from wellesley
+
+ align:start position:0%
+spring uh kristen butcher from wellesley
+ 
+
+ align:start position:0%
+spring uh kristen butcher from wellesley
+and i'll be teaching it next year
+
+ align:start position:0%
+and i'll be teaching it next year
+ 
+
+ align:start position:0%
+and i'll be teaching it next year
+that dies much more into these policy
+
+ align:start position:0%
+that dies much more into these policy
+ 
+
+ align:start position:0%
+that dies much more into these policy
+issues so i'm going to sort of use
+
+ align:start position:0%
+issues so i'm going to sort of use
+ 
+
+ align:start position:0%
+issues so i'm going to sort of use
+government policy sort of an organizing
+
+ align:start position:0%
+government policy sort of an organizing
+ 
+
+ align:start position:0%
+government policy sort of an organizing
+theme but it won't be sort of the
+
+ align:start position:0%
+theme but it won't be sort of the
+ 
+
+ align:start position:0%
+theme but it won't be sort of the
+dominant theme of the class
+
+ align:start position:0%
+dominant theme of the class
+ 
+
+ align:start position:0%
+dominant theme of the class
+finally three points about my teaching
+
+ align:start position:0%
+finally three points about my teaching
+ 
+
+ align:start position:0%
+finally three points about my teaching
+style um i don't write everything in the
+
+ align:start position:0%
+style um i don't write everything in the
+ 
+
+ align:start position:0%
+style um i don't write everything in the
+board we're not in high school anymore
+
+ align:start position:0%
+board we're not in high school anymore
+ 
+
+ align:start position:0%
+board we're not in high school anymore
+you're actually responsible for what i
+
+ align:start position:0%
+you're actually responsible for what i
+ 
+
+ align:start position:0%
+you're actually responsible for what i
+say not what i write uh
+
+ align:start position:0%
+say not what i write uh
+ 
+
+ align:start position:0%
+say not what i write uh
+partly that's because my handwriting is
+
+ align:start position:0%
+partly that's because my handwriting is
+ 
+
+ align:start position:0%
+partly that's because my handwriting is
+brutal um as you can tell already
+
+ align:start position:0%
+brutal um as you can tell already
+ 
+
+ align:start position:0%
+brutal um as you can tell already
+um uh so what that means is please
+
+ align:start position:0%
+um uh so what that means is please
+ 
+
+ align:start position:0%
+um uh so what that means is please
+please do not be afraid to ask me what
+
+ align:start position:0%
+please do not be afraid to ask me what
+ 
+
+ align:start position:0%
+please do not be afraid to ask me what
+the hell i just wrote on the board
+
+ align:start position:0%
+the hell i just wrote on the board
+ 
+
+ align:start position:0%
+the hell i just wrote on the board
+okay there's no shame in that don't just
+
+ align:start position:0%
+okay there's no shame in that don't just
+ 
+
+ align:start position:0%
+okay there's no shame in that don't just
+lean to your neighbor and say what the
+
+ align:start position:0%
+lean to your neighbor and say what the
+ 
+
+ align:start position:0%
+lean to your neighbor and say what the
+hell is writing the board like
+
+ align:start position:0%
+hell is writing the board like
+ 
+
+ align:start position:0%
+hell is writing the board like
+ask me because if you can't read it i'm
+
+ align:start position:0%
+ask me because if you can't read it i'm
+ 
+
+ align:start position:0%
+ask me because if you can't read it i'm
+sure someone else can't read it so feel
+
+ align:start position:0%
+sure someone else can't read it so feel
+ 
+
+ align:start position:0%
+sure someone else can't read it so feel
+free to ask
+
+ align:start position:0%
+free to ask
+ 
+
+ align:start position:0%
+free to ask
+and in general please feel free to
+
+ align:start position:0%
+and in general please feel free to
+ 
+
+ align:start position:0%
+and in general please feel free to
+engage with questions in this class
+
+ align:start position:0%
+engage with questions in this class
+ 
+
+ align:start position:0%
+engage with questions in this class
+the other point of my teaching style is
+
+ align:start position:0%
+the other point of my teaching style is
+ 
+
+ align:start position:0%
+the other point of my teaching style is
+i talk way too fast
+
+ align:start position:0%
+i talk way too fast
+ 
+
+ align:start position:0%
+i talk way too fast
+and the longer i go there's a
+
+ align:start position:0%
+and the longer i go there's a
+ 
+
+ align:start position:0%
+and the longer i go there's a
+mathematical function which is the
+
+ align:start position:0%
+mathematical function which is the
+ 
+
+ align:start position:0%
+mathematical function which is the
+longer i go without interruption the
+
+ align:start position:0%
+longer i go without interruption the
+ 
+
+ align:start position:0%
+longer i go without interruption the
+faster i speak
+
+ align:start position:0%
+faster i speak
+ 
+
+ align:start position:0%
+faster i speak
+until i just spin off okay so basically
+
+ align:start position:0%
+until i just spin off okay so basically
+ 
+
+ align:start position:0%
+until i just spin off okay so basically
+please ask questions if anything's not
+
+ align:start position:0%
+please ask questions if anything's not
+ 
+
+ align:start position:0%
+please ask questions if anything's not
+clear or you just want to
+
+ align:start position:0%
+clear or you just want to
+ 
+
+ align:start position:0%
+clear or you just want to
+ask questions about some related tangent
+
+ align:start position:0%
+ask questions about some related tangent
+ 
+
+ align:start position:0%
+ask questions about some related tangent
+or whatever please feel free to do so
+
+ align:start position:0%
+or whatever please feel free to do so
+ 
+
+ align:start position:0%
+or whatever please feel free to do so
+you might think how would that work in a
+
+ align:start position:0%
+you might think how would that work in a
+ 
+
+ align:start position:0%
+you might think how would that work in a
+class this big there's always way too
+
+ align:start position:0%
+class this big there's always way too
+ 
+
+ align:start position:0%
+class this big there's always way too
+few questions
+
+ align:start position:0%
+few questions
+ 
+
+ align:start position:0%
+few questions
+even a class is big so never be afraid
+
+ align:start position:0%
+even a class is big so never be afraid
+ 
+
+ align:start position:0%
+even a class is big so never be afraid
+that like it'll slow me down or whatever
+
+ align:start position:0%
+that like it'll slow me down or whatever
+ 
+
+ align:start position:0%
+that like it'll slow me down or whatever
+i ask a question we have plenty of time
+
+ align:start position:0%
+i ask a question we have plenty of time
+ 
+
+ align:start position:0%
+i ask a question we have plenty of time
+on the class
+
+ align:start position:0%
+on the class
+ 
+
+ align:start position:0%
+on the class
+and you'll be doing your classmates a
+
+ align:start position:0%
+and you'll be doing your classmates a
+ 
+
+ align:start position:0%
+and you'll be doing your classmates a
+favor because it'll slow me down
+
+ align:start position:0%
+favor because it'll slow me down
+ 
+
+ align:start position:0%
+favor because it'll slow me down
+um finally last point i have this
+
+ align:start position:0%
+um finally last point i have this
+ 
+
+ align:start position:0%
+um finally last point i have this
+terrible tendency to use the term
+
+ align:start position:0%
+terrible tendency to use the term
+ 
+
+ align:start position:0%
+terrible tendency to use the term
+guys in a gender-neutral way so this
+
+ align:start position:0%
+guys in a gender-neutral way so this
+ 
+
+ align:start position:0%
+guys in a gender-neutral way so this
+class i like to see looks like it's a
+
+ align:start position:0%
+class i like to see looks like it's a
+ 
+
+ align:start position:0%
+class i like to see looks like it's a
+fairly healthy representation both males
+
+ align:start position:0%
+fairly healthy representation both males
+ 
+
+ align:start position:0%
+fairly healthy representation both males
+and females when i say guys i don't mean
+
+ align:start position:0%
+and females when i say guys i don't mean
+ 
+
+ align:start position:0%
+and females when i say guys i don't mean
+men i mean people
+
+ align:start position:0%
+men i mean people
+ 
+
+ align:start position:0%
+men i mean people
+i mean people so don't take it women
+
+ align:start position:0%
+i mean people so don't take it women
+ 
+
+ align:start position:0%
+i mean people so don't take it women
+don't take it personally
+
+ align:start position:0%
+don't take it personally
+ 
+
+ align:start position:0%
+don't take it personally
+guys means economic agents it means
+
+ align:start position:0%
+guys means economic agents it means
+ 
+
+ align:start position:0%
+guys means economic agents it means
+people it doesn't mean men it's just the
+
+ align:start position:0%
+people it doesn't mean men it's just the
+ 
+
+ align:start position:0%
+people it doesn't mean men it's just the
+way just a bad tendency drives my life
+
+ align:start position:0%
+way just a bad tendency drives my life
+ 
+
+ align:start position:0%
+way just a bad tendency drives my life
+crazy but
+
+ align:start position:0%
+crazy but
+ 
+
+ align:start position:0%
+crazy but
+i've decided better to just apologize up
+
+ align:start position:0%
+i've decided better to just apologize up
+ 
+
+ align:start position:0%
+i've decided better to just apologize up
+front than try to
+
+ align:start position:0%
+front than try to
+ 
+
+ align:start position:0%
+front than try to
+try to fix it throughout which is
+
+ align:start position:0%
+try to fix it throughout which is
+ 
+
+ align:start position:0%
+try to fix it throughout which is
+impossible okay
+
+ align:start position:0%
+impossible okay
+ 
+
+ align:start position:0%
+impossible okay
+so let's talk about what is
+
+ align:start position:0%
+so let's talk about what is
+ 
+
+ align:start position:0%
+so let's talk about what is
+microeconomics okay
+
+ align:start position:0%
+microeconomics okay
+ 
+
+ align:start position:0%
+microeconomics okay
+so fundamentally microeconomics
+
+ align:start position:0%
+so fundamentally microeconomics
+ 
+
+ align:start position:0%
+so fundamentally microeconomics
+how people took ap high school econ
+
+ align:start position:0%
+how people took ap high school econ
+ 
+
+ align:start position:0%
+how people took ap high school econ
+okay um how many people
+
+ align:start position:0%
+okay um how many people
+ 
+
+ align:start position:0%
+okay um how many people
+for how many for how many was it taught
+
+ align:start position:0%
+for how many for how many was it taught
+ 
+
+ align:start position:0%
+for how many for how many was it taught
+really well
+
+ align:start position:0%
+really well
+ 
+
+ align:start position:0%
+really well
+okay that's about that right that's why
+
+ align:start position:0%
+okay that's about that right that's why
+ 
+
+ align:start position:0%
+okay that's about that right that's why
+i did my high school online class that's
+
+ align:start position:0%
+i did my high school online class that's
+ 
+
+ align:start position:0%
+i did my high school online class that's
+the answer i wanted to hear
+
+ align:start position:0%
+the answer i wanted to hear
+ 
+
+ align:start position:0%
+the answer i wanted to hear
+um uh okay so uh tell your friends still
+
+ align:start position:0%
+um uh okay so uh tell your friends still
+ 
+
+ align:start position:0%
+um uh okay so uh tell your friends still
+in high school
+
+ align:start position:0%
+in high school
+ 
+
+ align:start position:0%
+in high school
+we're taking its lecon if your high
+
+ align:start position:0%
+we're taking its lecon if your high
+ 
+
+ align:start position:0%
+we're taking its lecon if your high
+school econ teacher isn't great tell
+
+ align:start position:0%
+school econ teacher isn't great tell
+ 
+
+ align:start position:0%
+school econ teacher isn't great tell
+them to go on edx and take the class
+
+ align:start position:0%
+them to go on edx and take the class
+ 
+
+ align:start position:0%
+them to go on edx and take the class
+uh and and help out your friends still
+
+ align:start position:0%
+uh and and help out your friends still
+ 
+
+ align:start position:0%
+uh and and help out your friends still
+in high school
+
+ align:start position:0%
+in high school
+ 
+
+ align:start position:0%
+in high school
+okay so um what is microeconomics
+
+ align:start position:0%
+okay so um what is microeconomics
+ 
+
+ align:start position:0%
+okay so um what is microeconomics
+microeconomics is the study of how
+
+ align:start position:0%
+microeconomics is the study of how
+ 
+
+ align:start position:0%
+microeconomics is the study of how
+individuals and firms
+
+ align:start position:0%
+individuals and firms
+ 
+
+ align:start position:0%
+individuals and firms
+make decisions in a world of scarcity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scarcity is what drives microeconomics
+
+ align:start position:0%
+scarcity is what drives microeconomics
+ 
+
+ align:start position:0%
+scarcity is what drives microeconomics
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+basically what microeconomics is is a
+
+ align:start position:0%
+basically what microeconomics is is a
+ 
+
+ align:start position:0%
+basically what microeconomics is is a
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+of constrained optimization exercises
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where economic agents be they firms or
+
+ align:start position:0%
+where economic agents be they firms or
+ 
+
+ align:start position:0%
+where economic agents be they firms or
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+try to make themselves as well off as
+
+ align:start position:0%
+try to make themselves as well off as
+ 
+
+ align:start position:0%
+try to make themselves as well off as
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+given their constraints yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i will but not as much as i should uh
+
+ align:start position:0%
+i will but not as much as i should uh
+ 
+
+ align:start position:0%
+i will but not as much as i should uh
+essentially we have another course in
+
+ align:start position:0%
+essentially we have another course in
+ 
+
+ align:start position:0%
+essentially we have another course in
+the department called 1413
+
+ align:start position:0%
+the department called 1413
+ 
+
+ align:start position:0%
+the department called 1413
+behavioral economics which gets in that
+
+ align:start position:0%
+behavioral economics which gets in that
+ 
+
+ align:start position:0%
+behavioral economics which gets in that
+much more i will sprinkle it throughout
+
+ align:start position:0%
+much more i will sprinkle it throughout
+ 
+
+ align:start position:0%
+much more i will sprinkle it throughout
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+but not as much as i actually believe in
+
+ align:start position:0%
+but not as much as i actually believe in
+ 
+
+ align:start position:0%
+but not as much as i actually believe in
+it uh in other words the
+
+ align:start position:0%
+it uh in other words the
+ 
+
+ align:start position:0%
+it uh in other words the
+way we think about economics is it's
+
+ align:start position:0%
+way we think about economics is it's
+ 
+
+ align:start position:0%
+way we think about economics is it's
+best to sort of get the basics down
+
+ align:start position:0%
+best to sort of get the basics down
+ 
+
+ align:start position:0%
+best to sort of get the basics down
+before you start worrying about the
+
+ align:start position:0%
+before you start worrying about the
+ 
+
+ align:start position:0%
+before you start worrying about the
+deviations
+
+ align:start position:0%
+deviations
+ 
+
+ align:start position:0%
+deviations
+find better to climb the tree before you
+
+ align:start position:0%
+find better to climb the tree before you
+ 
+
+ align:start position:0%
+find better to climb the tree before you
+start going out in the branches
+
+ align:start position:0%
+start going out in the branches
+ 
+
+ align:start position:0%
+start going out in the branches
+um okay so basically um
+
+ align:start position:0%
+um okay so basically um
+ 
+
+ align:start position:0%
+um okay so basically um
+what this course is then about is it's
+
+ align:start position:0%
+what this course is then about is it's
+ 
+
+ align:start position:0%
+what this course is then about is it's
+about trade-offs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's about how do you given that you're
+
+ align:start position:0%
+it's about how do you given that you're
+ 
+
+ align:start position:0%
+it's about how do you given that you're
+constrained how do you trade off things
+
+ align:start position:0%
+constrained how do you trade off things
+ 
+
+ align:start position:0%
+constrained how do you trade off things
+to make yourself as well off as possible
+
+ align:start position:0%
+to make yourself as well off as possible
+ 
+
+ align:start position:0%
+to make yourself as well off as possible
+and behind this notion of trade-offs is
+
+ align:start position:0%
+and behind this notion of trade-offs is
+ 
+
+ align:start position:0%
+and behind this notion of trade-offs is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+i'll say about a hundred times this is
+
+ align:start position:0%
+i'll say about a hundred times this is
+ 
+
+ align:start position:0%
+i'll say about a hundred times this is
+the most important thing in the course
+
+ align:start position:0%
+the most important thing in the course
+ 
+
+ align:start position:0%
+the most important thing in the course
+so just ignore that
+
+ align:start position:0%
+so just ignore that
+ 
+
+ align:start position:0%
+so just ignore that
+but this is one of the most important
+
+ align:start position:0%
+but this is one of the most important
+ 
+
+ align:start position:0%
+but this is one of the most important
+things i'll say one of the most
+
+ align:start position:0%
+things i'll say one of the most
+ 
+
+ align:start position:0%
+things i'll say one of the most
+important things in the course
+
+ align:start position:0%
+important things in the course
+ 
+
+ align:start position:0%
+important things in the course
+is the notion of opportunity cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opportunity cost is a very important
+
+ align:start position:0%
+opportunity cost is a very important
+ 
+
+ align:start position:0%
+opportunity cost is a very important
+concept
+
+ align:start position:0%
+concept
+ 
+
+ align:start position:0%
+concept
+that uh we teach sort of the first
+
+ align:start position:0%
+that uh we teach sort of the first
+ 
+
+ align:start position:0%
+that uh we teach sort of the first
+concept we teach
+
+ align:start position:0%
+concept we teach
+ 
+
+ align:start position:0%
+concept we teach
+um which is that every action
+
+ align:start position:0%
+um which is that every action
+ 
+
+ align:start position:0%
+um which is that every action
+or every inaction has a cost
+
+ align:start position:0%
+or every inaction has a cost
+ 
+
+ align:start position:0%
+or every inaction has a cost
+and that you could have been doing
+
+ align:start position:0%
+and that you could have been doing
+ 
+
+ align:start position:0%
+and that you could have been doing
+something else instead okay
+
+ align:start position:0%
+something else instead okay
+ 
+
+ align:start position:0%
+something else instead okay
+so if you buy a shirt you could have
+
+ align:start position:0%
+so if you buy a shirt you could have
+ 
+
+ align:start position:0%
+so if you buy a shirt you could have
+bought pants
+
+ align:start position:0%
+bought pants
+ 
+
+ align:start position:0%
+bought pants
+if you sit at home and watch tv you
+
+ align:start position:0%
+if you sit at home and watch tv you
+ 
+
+ align:start position:0%
+if you sit at home and watch tv you
+could have been out working
+
+ align:start position:0%
+could have been out working
+ 
+
+ align:start position:0%
+could have been out working
+everything you do has the next best
+
+ align:start position:0%
+everything you do has the next best
+ 
+
+ align:start position:0%
+everything you do has the next best
+alternative you could have done instead
+
+ align:start position:0%
+alternative you could have done instead
+ 
+
+ align:start position:0%
+alternative you could have done instead
+and that is called the opportunity cost
+
+ align:start position:0%
+and that is called the opportunity cost
+ 
+
+ align:start position:0%
+and that is called the opportunity cost
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's a critical concept in
+
+ align:start position:0%
+and that's a critical concept in
+ 
+
+ align:start position:0%
+and that's a critical concept in
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+and that is why in some sense we are
+
+ align:start position:0%
+and that is why in some sense we are
+ 
+
+ align:start position:0%
+and that is why in some sense we are
+called referred to casually as the
+
+ align:start position:0%
+called referred to casually as the
+ 
+
+ align:start position:0%
+called referred to casually as the
+dismal science
+
+ align:start position:0%
+dismal science
+ 
+
+ align:start position:0%
+dismal science
+economics referred to as the dismal
+
+ align:start position:0%
+economics referred to as the dismal
+ 
+
+ align:start position:0%
+economics referred to as the dismal
+science first of all i'm flattered we're
+
+ align:start position:0%
+science first of all i'm flattered we're
+ 
+
+ align:start position:0%
+science first of all i'm flattered we're
+considered a science
+
+ align:start position:0%
+considered a science
+ 
+
+ align:start position:0%
+considered a science
+uh or called the dismal science because
+
+ align:start position:0%
+uh or called the dismal science because
+ 
+
+ align:start position:0%
+uh or called the dismal science because
+our whole point is that
+
+ align:start position:0%
+our whole point is that
+ 
+
+ align:start position:0%
+our whole point is that
+nothing is free there's always a
+
+ align:start position:0%
+nothing is free there's always a
+ 
+
+ align:start position:0%
+nothing is free there's always a
+trade-off there's always an opportunity
+
+ align:start position:0%
+trade-off there's always an opportunity
+ 
+
+ align:start position:0%
+trade-off there's always an opportunity
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+anything you do you could be doing
+
+ align:start position:0%
+anything you do you could be doing
+ 
+
+ align:start position:0%
+anything you do you could be doing
+something else instead
+
+ align:start position:0%
+something else instead
+ 
+
+ align:start position:0%
+something else instead
+okay and your constrained optimization
+
+ align:start position:0%
+okay and your constrained optimization
+ 
+
+ align:start position:0%
+okay and your constrained optimization
+means you're gonna have to pass up one
+
+ align:start position:0%
+means you're gonna have to pass up one
+ 
+
+ align:start position:0%
+means you're gonna have to pass up one
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+uh to do another now some may call it
+
+ align:start position:0%
+uh to do another now some may call it
+ 
+
+ align:start position:0%
+uh to do another now some may call it
+dismal
+
+ align:start position:0%
+dismal
+ 
+
+ align:start position:0%
+dismal
+but as a former mit undergraduate i call
+
+ align:start position:0%
+but as a former mit undergraduate i call
+ 
+
+ align:start position:0%
+but as a former mit undergraduate i call
+it fun and this is why i think mit
+
+ align:start position:0%
+it fun and this is why i think mit
+ 
+
+ align:start position:0%
+it fun and this is why i think mit
+is the perfect place to be teaching
+
+ align:start position:0%
+is the perfect place to be teaching
+ 
+
+ align:start position:0%
+is the perfect place to be teaching
+economics because mit
+
+ align:start position:0%
+economics because mit
+ 
+
+ align:start position:0%
+economics because mit
+engineering is all about constrained
+
+ align:start position:0%
+engineering is all about constrained
+ 
+
+ align:start position:0%
+engineering is all about constrained
+optimization that's what engineering is
+
+ align:start position:0%
+optimization that's what engineering is
+ 
+
+ align:start position:0%
+optimization that's what engineering is
+and economics is just the engine it's
+
+ align:start position:0%
+and economics is just the engine it's
+ 
+
+ align:start position:0%
+and economics is just the engine it's
+just the principles you learn
+
+ align:start position:0%
+just the principles you learn
+ 
+
+ align:start position:0%
+just the principles you learn
+you learn engineering um uh applied in
+
+ align:start position:0%
+you learn engineering um uh applied in
+ 
+
+ align:start position:0%
+you learn engineering um uh applied in
+different contexts
+
+ align:start position:0%
+different contexts
+ 
+
+ align:start position:0%
+different contexts
+so there's if we think about the 2007
+
+ align:start position:0%
+so there's if we think about the 2007
+ 
+
+ align:start position:0%
+so there's if we think about the 2007
+contest that still exists with the
+
+ align:start position:0%
+contest that still exists with the
+ 
+
+ align:start position:0%
+contest that still exists with the
+robots
+
+ align:start position:0%
+robots
+ 
+
+ align:start position:0%
+robots
+2007. yeah okay the 2007 contest those
+
+ align:start position:0%
+2007. yeah okay the 2007 contest those
+ 
+
+ align:start position:0%
+2007. yeah okay the 2007 contest those
+you know is a contest where you're given
+
+ align:start position:0%
+you know is a contest where you're given
+ 
+
+ align:start position:0%
+you know is a contest where you're given
+a limited set of materials
+
+ align:start position:0%
+a limited set of materials
+ 
+
+ align:start position:0%
+a limited set of materials
+and you have to build a robot that does
+
+ align:start position:0%
+and you have to build a robot that does
+ 
+
+ align:start position:0%
+and you have to build a robot that does
+some tasks like pushing ping-pong balls
+
+ align:start position:0%
+some tasks like pushing ping-pong balls
+ 
+
+ align:start position:0%
+some tasks like pushing ping-pong balls
+off a table or something like that
+
+ align:start position:0%
+off a table or something like that
+ 
+
+ align:start position:0%
+off a table or something like that
+okay that's just constrained
+
+ align:start position:0%
+okay that's just constrained
+ 
+
+ align:start position:0%
+okay that's just constrained
+optimization it's got nothing to do with
+
+ align:start position:0%
+optimization it's got nothing to do with
+ 
+
+ align:start position:0%
+optimization it's got nothing to do with
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+but it's constrained optimization so
+
+ align:start position:0%
+but it's constrained optimization so
+ 
+
+ align:start position:0%
+but it's constrained optimization so
+just think of
+
+ align:start position:0%
+just think of
+ 
+
+ align:start position:0%
+just think of
+um just think of uh microeconomics
+
+ align:start position:0%
+um just think of uh microeconomics
+ 
+
+ align:start position:0%
+um just think of uh microeconomics
+as like engineering but actually
+
+ align:start position:0%
+as like engineering but actually
+ 
+
+ align:start position:0%
+as like engineering but actually
+interesting okay
+
+ align:start position:0%
+interesting okay
+ 
+
+ align:start position:0%
+interesting okay
+so think of microeconomics as
+
+ align:start position:0%
+so think of microeconomics as
+ 
+
+ align:start position:0%
+so think of microeconomics as
+engineering but instead of building
+
+ align:start position:0%
+engineering but instead of building
+ 
+
+ align:start position:0%
+engineering but instead of building
+something to push a ping pong ball off
+
+ align:start position:0%
+something to push a ping pong ball off
+ 
+
+ align:start position:0%
+something to push a ping pong ball off
+tables
+
+ align:start position:0%
+tables
+ 
+
+ align:start position:0%
+tables
+you actually build people's lives and
+
+ align:start position:0%
+you actually build people's lives and
+ 
+
+ align:start position:0%
+you actually build people's lives and
+businesses and
+
+ align:start position:0%
+businesses and
+ 
+
+ align:start position:0%
+businesses and
+understand the decisions that drive our
+
+ align:start position:0%
+understand the decisions that drive our
+ 
+
+ align:start position:0%
+understand the decisions that drive our
+economy okay
+
+ align:start position:0%
+economy okay
+ 
+
+ align:start position:0%
+economy okay
+so the same principles that you could
+
+ align:start position:0%
+so the same principles that you could
+ 
+
+ align:start position:0%
+so the same principles that you could
+think of for engineering classes but
+
+ align:start position:0%
+think of for engineering classes but
+ 
+
+ align:start position:0%
+think of for engineering classes but
+applied to people's lives
+
+ align:start position:0%
+applied to people's lives
+ 
+
+ align:start position:0%
+applied to people's lives
+and that's why in fact modern economics
+
+ align:start position:0%
+and that's why in fact modern economics
+ 
+
+ align:start position:0%
+and that's why in fact modern economics
+was born in this room either this room
+
+ align:start position:0%
+was born in this room either this room
+ 
+
+ align:start position:0%
+was born in this room either this room
+or 26-100
+
+ align:start position:0%
+or 26-100
+ 
+
+ align:start position:0%
+or 26-100
+okay by paul samuelson in the 1940s and
+
+ align:start position:0%
+okay by paul samuelson in the 1940s and
+ 
+
+ align:start position:0%
+okay by paul samuelson in the 1940s and
+50s
+
+ align:start position:0%
+50s
+ 
+
+ align:start position:0%
+50s
+who wrote the fundamental textbook that
+
+ align:start position:0%
+who wrote the fundamental textbook that
+ 
+
+ align:start position:0%
+who wrote the fundamental textbook that
+gave birth to modern economics
+
+ align:start position:0%
+gave birth to modern economics
+ 
+
+ align:start position:0%
+gave birth to modern economics
+because he was here and applied the kind
+
+ align:start position:0%
+because he was here and applied the kind
+ 
+
+ align:start position:0%
+because he was here and applied the kind
+of engineering principles
+
+ align:start position:0%
+of engineering principles
+ 
+
+ align:start position:0%
+of engineering principles
+of mit to actually develop the field of
+
+ align:start position:0%
+of mit to actually develop the field of
+ 
+
+ align:start position:0%
+of mit to actually develop the field of
+modern economics
+
+ align:start position:0%
+modern economics
+ 
+
+ align:start position:0%
+modern economics
+what we learned today was developed at
+
+ align:start position:0%
+what we learned today was developed at
+ 
+
+ align:start position:0%
+what we learned today was developed at
+mit so it's a great place to be learning
+
+ align:start position:0%
+mit so it's a great place to be learning
+ 
+
+ align:start position:0%
+mit so it's a great place to be learning
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+now with that as background okay any
+
+ align:start position:0%
+now with that as background okay any
+ 
+
+ align:start position:0%
+now with that as background okay any
+questions about that
+
+ align:start position:0%
+questions about that
+ 
+
+ align:start position:0%
+questions about that
+about what is microeconomics okay
+
+ align:start position:0%
+about what is microeconomics okay
+ 
+
+ align:start position:0%
+about what is microeconomics okay
+with that as background let's turn to
+
+ align:start position:0%
+with that as background let's turn to
+ 
+
+ align:start position:0%
+with that as background let's turn to
+our for the first
+
+ align:start position:0%
+our for the first
+ 
+
+ align:start position:0%
+our for the first
+model we'll talk about this semester
+
+ align:start position:0%
+model we'll talk about this semester
+ 
+
+ align:start position:0%
+model we'll talk about this semester
+which is the supply and demand model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+supply and demand now the way we're
+
+ align:start position:0%
+supply and demand now the way we're
+ 
+
+ align:start position:0%
+supply and demand now the way we're
+going to proceed in this course
+
+ align:start position:0%
+going to proceed in this course
+ 
+
+ align:start position:0%
+going to proceed in this course
+is going to drive you crazy because
+
+ align:start position:0%
+is going to drive you crazy because
+ 
+
+ align:start position:0%
+is going to drive you crazy because
+we're going to proceed
+
+ align:start position:0%
+we're going to proceed
+ 
+
+ align:start position:0%
+we're going to proceed
+by teaching very s as the very first
+
+ align:start position:0%
+by teaching very s as the very first
+ 
+
+ align:start position:0%
+by teaching very s as the very first
+question pointed out by teaching
+
+ align:start position:0%
+question pointed out by teaching
+ 
+
+ align:start position:0%
+question pointed out by teaching
+very simplified models okay we're gonna
+
+ align:start position:0%
+very simplified models okay we're gonna
+ 
+
+ align:start position:0%
+very simplified models okay we're gonna
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+what is a model a model is technically a
+
+ align:start position:0%
+what is a model a model is technically a
+ 
+
+ align:start position:0%
+what is a model a model is technically a
+description between any two or more
+
+ align:start position:0%
+description between any two or more
+ 
+
+ align:start position:0%
+description between any two or more
+economic variables or any two or more
+
+ align:start position:0%
+economic variables or any two or more
+ 
+
+ align:start position:0%
+economic variables or any two or more
+variables okay
+
+ align:start position:0%
+variables okay
+ 
+
+ align:start position:0%
+variables okay
+but unlike the models used in all your
+
+ align:start position:0%
+but unlike the models used in all your
+ 
+
+ align:start position:0%
+but unlike the models used in all your
+other classes
+
+ align:start position:0%
+other classes
+ 
+
+ align:start position:0%
+other classes
+these aren't laws by and large they're
+
+ align:start position:0%
+these aren't laws by and large they're
+ 
+
+ align:start position:0%
+these aren't laws by and large they're
+models so we don't have a relationship
+
+ align:start position:0%
+models so we don't have a relationship
+ 
+
+ align:start position:0%
+models so we don't have a relationship
+between energy and mass which you can
+
+ align:start position:0%
+between energy and mass which you can
+ 
+
+ align:start position:0%
+between energy and mass which you can
+write down to law and we're done
+
+ align:start position:0%
+write down to law and we're done
+ 
+
+ align:start position:0%
+write down to law and we're done
+we have models which are never 100 true
+
+ align:start position:0%
+we have models which are never 100 true
+ 
+
+ align:start position:0%
+we have models which are never 100 true
+but always pretty true pretty being
+
+ align:start position:0%
+but always pretty true pretty being
+ 
+
+ align:start position:0%
+but always pretty true pretty being
+somewhere between
+
+ align:start position:0%
+somewhere between
+ 
+
+ align:start position:0%
+somewhere between
+10 and 95 percent true okay so basically
+
+ align:start position:0%
+10 and 95 percent true okay so basically
+ 
+
+ align:start position:0%
+10 and 95 percent true okay so basically
+the idea is to make a trade-off we want
+
+ align:start position:0%
+the idea is to make a trade-off we want
+ 
+
+ align:start position:0%
+the idea is to make a trade-off we want
+to write down
+
+ align:start position:0%
+to write down
+ 
+
+ align:start position:0%
+to write down
+in our models a set of simplifying
+
+ align:start position:0%
+in our models a set of simplifying
+ 
+
+ align:start position:0%
+in our models a set of simplifying
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+that allow us with a relatively small
+
+ align:start position:0%
+that allow us with a relatively small
+ 
+
+ align:start position:0%
+that allow us with a relatively small
+set of steps
+
+ align:start position:0%
+set of steps
+ 
+
+ align:start position:0%
+set of steps
+to capture relatively broad phenomena
+
+ align:start position:0%
+to capture relatively broad phenomena
+ 
+
+ align:start position:0%
+to capture relatively broad phenomena
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so there's essentially a trade-off on
+
+ align:start position:0%
+so there's essentially a trade-off on
+ 
+
+ align:start position:0%
+so there's essentially a trade-off on
+the one hand we'd like a model
+
+ align:start position:0%
+the one hand we'd like a model
+ 
+
+ align:start position:0%
+the one hand we'd like a model
+that captures as well as possible the
+
+ align:start position:0%
+that captures as well as possible the
+ 
+
+ align:start position:0%
+that captures as well as possible the
+phenomenon the real world
+
+ align:start position:0%
+phenomenon the real world
+ 
+
+ align:start position:0%
+phenomenon the real world
+like equals nc squared but we want to do
+
+ align:start position:0%
+like equals nc squared but we want to do
+ 
+
+ align:start position:0%
+like equals nc squared but we want to do
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in the most tractable possible way so
+
+ align:start position:0%
+in the most tractable possible way so
+ 
+
+ align:start position:0%
+in the most tractable possible way so
+that we can teach it from first
+
+ align:start position:0%
+that we can teach it from first
+ 
+
+ align:start position:0%
+that we can teach it from first
+principles and not
+
+ align:start position:0%
+principles and not
+ 
+
+ align:start position:0%
+principles and not
+you know don't need don't need an hour
+
+ align:start position:0%
+you know don't need don't need an hour
+ 
+
+ align:start position:0%
+you know don't need don't need an hour
+to teach every single uh
+
+ align:start position:0%
+to teach every single uh
+ 
+
+ align:start position:0%
+to teach every single uh
+every single insight we have okay so
+
+ align:start position:0%
+every single insight we have okay so
+ 
+
+ align:start position:0%
+every single insight we have okay so
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+in economics we tend to resolve that by
+
+ align:start position:0%
+in economics we tend to resolve that by
+ 
+
+ align:start position:0%
+in economics we tend to resolve that by
+erroring on the side of
+
+ align:start position:0%
+erroring on the side of
+ 
+
+ align:start position:0%
+erroring on the side of
+tractability that is why i can teach you
+
+ align:start position:0%
+tractability that is why i can teach you
+ 
+
+ align:start position:0%
+tractability that is why i can teach you
+the entire field of microeconomics
+
+ align:start position:0%
+the entire field of microeconomics
+ 
+
+ align:start position:0%
+the entire field of microeconomics
+which is really sort of macro is kind of
+
+ align:start position:0%
+which is really sort of macro is kind of
+ 
+
+ align:start position:0%
+which is really sort of macro is kind of
+a fun application micro's really
+
+ align:start position:0%
+a fun application micro's really
+ 
+
+ align:start position:0%
+a fun application micro's really
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+okay i could teach you the fire field of
+
+ align:start position:0%
+okay i could teach you the fire field of
+ 
+
+ align:start position:0%
+okay i could teach you the fire field of
+microeconomics at a semester because
+
+ align:start position:0%
+microeconomics at a semester because
+ 
+
+ align:start position:0%
+microeconomics at a semester because
+we're going to make a whole huge set
+
+ align:start position:0%
+we're going to make a whole huge set
+ 
+
+ align:start position:0%
+we're going to make a whole huge set
+of simplifying assumptions to make
+
+ align:start position:0%
+of simplifying assumptions to make
+ 
+
+ align:start position:0%
+of simplifying assumptions to make
+things tractable
+
+ align:start position:0%
+things tractable
+ 
+
+ align:start position:0%
+things tractable
+but the key thing is that you will be
+
+ align:start position:0%
+but the key thing is that you will be
+ 
+
+ align:start position:0%
+but the key thing is that you will be
+amazed at what these models will be able
+
+ align:start position:0%
+amazed at what these models will be able
+ 
+
+ align:start position:0%
+amazed at what these models will be able
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+with a fairly simple set of models we'll
+
+ align:start position:0%
+with a fairly simple set of models we'll
+ 
+
+ align:start position:0%
+with a fairly simple set of models we'll
+be able to offer insights and explain a
+
+ align:start position:0%
+be able to offer insights and explain a
+ 
+
+ align:start position:0%
+be able to offer insights and explain a
+whole huge variety of phenomena
+
+ align:start position:0%
+whole huge variety of phenomena
+ 
+
+ align:start position:0%
+whole huge variety of phenomena
+never perfectly but always pretty well
+
+ align:start position:0%
+never perfectly but always pretty well
+ 
+
+ align:start position:0%
+never perfectly but always pretty well
+generally pretty well
+
+ align:start position:0%
+generally pretty well
+ 
+
+ align:start position:0%
+generally pretty well
+okay and so that is essentially the
+
+ align:start position:0%
+okay and so that is essentially the
+ 
+
+ align:start position:0%
+okay and so that is essentially the
+trade-off we're going to try to do
+
+ align:start position:0%
+trade-off we're going to try to do
+ 
+
+ align:start position:0%
+trade-off we're going to try to do
+uh this semester so the line i like is
+
+ align:start position:0%
+uh this semester so the line i like is
+ 
+
+ align:start position:0%
+uh this semester so the line i like is
+this the statistician george box
+
+ align:start position:0%
+this the statistician george box
+ 
+
+ align:start position:0%
+this the statistician george box
+said that all models are wrong but some
+
+ align:start position:0%
+said that all models are wrong but some
+ 
+
+ align:start position:0%
+said that all models are wrong but some
+are useful
+
+ align:start position:0%
+are useful
+ 
+
+ align:start position:0%
+are useful
+now obviously it doesn't apply to models
+
+ align:start position:0%
+now obviously it doesn't apply to models
+ 
+
+ align:start position:0%
+now obviously it doesn't apply to models
+models in the hard sciences but in the
+
+ align:start position:0%
+models in the hard sciences but in the
+ 
+
+ align:start position:0%
+models in the hard sciences but in the
+social sciences that's true
+
+ align:start position:0%
+social sciences that's true
+ 
+
+ align:start position:0%
+social sciences that's true
+and basically i'm going to write down a
+
+ align:start position:0%
+and basically i'm going to write down a
+ 
+
+ align:start position:0%
+and basically i'm going to write down a
+set of models like that
+
+ align:start position:0%
+set of models like that
+ 
+
+ align:start position:0%
+set of models like that
+now with every model i write down i'm
+
+ align:start position:0%
+now with every model i write down i'm
+ 
+
+ align:start position:0%
+now with every model i write down i'm
+going to try i would my goal is to have
+
+ align:start position:0%
+going to try i would my goal is to have
+ 
+
+ align:start position:0%
+going to try i would my goal is to have
+you understand it at three levels
+
+ align:start position:0%
+you understand it at three levels
+ 
+
+ align:start position:0%
+you understand it at three levels
+the first and most important level is
+
+ align:start position:0%
+the first and most important level is
+ 
+
+ align:start position:0%
+the first and most important level is
+the intuitive level
+
+ align:start position:0%
+the intuitive level
+ 
+
+ align:start position:0%
+the intuitive level
+okay the level which you sort of
+
+ align:start position:0%
+okay the level which you sort of
+ 
+
+ align:start position:0%
+okay the level which you sort of
+understand i call it passing the mom
+
+ align:start position:0%
+understand i call it passing the mom
+ 
+
+ align:start position:0%
+understand i call it passing the mom
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+you can go home and explain it to your
+
+ align:start position:0%
+you can go home and explain it to your
+ 
+
+ align:start position:0%
+you can go home and explain it to your
+mom at thanksgiving or at the end of the
+
+ align:start position:0%
+mom at thanksgiving or at the end of the
+ 
+
+ align:start position:0%
+mom at thanksgiving or at the end of the
+semester
+
+ align:start position:0%
+semester
+ 
+
+ align:start position:0%
+semester
+okay no offense to dads just call it the
+
+ align:start position:0%
+okay no offense to dads just call it the
+ 
+
+ align:start position:0%
+okay no offense to dads just call it the
+mom test
+
+ align:start position:0%
+mom test
+ 
+
+ align:start position:0%
+mom test
+okay so basically that's the intuitive
+
+ align:start position:0%
+okay so basically that's the intuitive
+ 
+
+ align:start position:0%
+okay so basically that's the intuitive
+level you really understand it way that
+
+ align:start position:0%
+level you really understand it way that
+ 
+
+ align:start position:0%
+level you really understand it way that
+you could explain it
+
+ align:start position:0%
+you could explain it
+ 
+
+ align:start position:0%
+you could explain it
+the second is graphical we were going to
+
+ align:start position:0%
+the second is graphical we were going to
+ 
+
+ align:start position:0%
+the second is graphical we were going to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+most of our models here will develop in
+
+ align:start position:0%
+most of our models here will develop in
+ 
+
+ align:start position:0%
+most of our models here will develop in
+a graphical framework
+
+ align:start position:0%
+a graphical framework
+ 
+
+ align:start position:0%
+a graphical framework
+okay using xy graphs that we're really
+
+ align:start position:0%
+okay using xy graphs that we're really
+ 
+
+ align:start position:0%
+okay using xy graphs that we're really
+weak
+
+ align:start position:0%
+weak
+ 
+
+ align:start position:0%
+weak
+in economics we think delivers a lot of
+
+ align:start position:0%
+in economics we think delivers a lot of
+ 
+
+ align:start position:0%
+in economics we think delivers a lot of
+shorthand power
+
+ align:start position:0%
+shorthand power
+ 
+
+ align:start position:0%
+shorthand power
+and the third is mathematical okay the
+
+ align:start position:0%
+and the third is mathematical okay the
+ 
+
+ align:start position:0%
+and the third is mathematical okay the
+mathematical is probably the least
+
+ align:start position:0%
+mathematical is probably the least
+ 
+
+ align:start position:0%
+mathematical is probably the least
+important but it's the easiest to test
+
+ align:start position:0%
+important but it's the easiest to test
+ 
+
+ align:start position:0%
+important but it's the easiest to test
+you on
+
+ align:start position:0%
+you on
+ 
+
+ align:start position:0%
+you on
+so we're gonna need to know things
+
+ align:start position:0%
+so we're gonna need to know things
+ 
+
+ align:start position:0%
+so we're gonna need to know things
+mathematically uh as well
+
+ align:start position:0%
+mathematically uh as well
+ 
+
+ align:start position:0%
+mathematically uh as well
+okay um so let's start
+
+ align:start position:0%
+okay um so let's start
+ 
+
+ align:start position:0%
+okay um so let's start
+um by considering the supply and demand
+
+ align:start position:0%
+um by considering the supply and demand
+ 
+
+ align:start position:0%
+um by considering the supply and demand
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+by using the famous example uh brought
+
+ align:start position:0%
+by using the famous example uh brought
+ 
+
+ align:start position:0%
+by using the famous example uh brought
+up by adam smith
+
+ align:start position:0%
+up by adam smith
+ 
+
+ align:start position:0%
+up by adam smith
+adam smith is sort of considered the
+
+ align:start position:0%
+adam smith is sort of considered the
+ 
+
+ align:start position:0%
+adam smith is sort of considered the
+father of economics and paul sam's the
+
+ align:start position:0%
+father of economics and paul sam's the
+ 
+
+ align:start position:0%
+father of economics and paul sam's the
+father of modern economics adam smith
+
+ align:start position:0%
+father of modern economics adam smith
+ 
+
+ align:start position:0%
+father of modern economics adam smith
+the father of all economics
+
+ align:start position:0%
+the father of all economics
+ 
+
+ align:start position:0%
+the father of all economics
+his 1776 book the wealth of nations
+
+ align:start position:0%
+his 1776 book the wealth of nations
+ 
+
+ align:start position:0%
+his 1776 book the wealth of nations
+did an incredible job of actually laying
+
+ align:start position:0%
+did an incredible job of actually laying
+ 
+
+ align:start position:0%
+did an incredible job of actually laying
+out the entire core of the economics
+
+ align:start position:0%
+out the entire core of the economics
+ 
+
+ align:start position:0%
+out the entire core of the economics
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+uh no math just words but kind of he
+
+ align:start position:0%
+uh no math just words but kind of he
+ 
+
+ align:start position:0%
+uh no math just words but kind of he
+just nailed it
+
+ align:start position:0%
+just nailed it
+ 
+
+ align:start position:0%
+just nailed it
+and um he started one of his most famous
+
+ align:start position:0%
+and um he started one of his most famous
+ 
+
+ align:start position:0%
+and um he started one of his most famous
+examples was the water diamond paradox
+
+ align:start position:0%
+examples was the water diamond paradox
+ 
+
+ align:start position:0%
+examples was the water diamond paradox
+okay he said think about water and
+
+ align:start position:0%
+okay he said think about water and
+ 
+
+ align:start position:0%
+okay he said think about water and
+diamonds so start with water
+
+ align:start position:0%
+diamonds so start with water
+ 
+
+ align:start position:0%
+diamonds so start with water
+nothing is more important for life than
+
+ align:start position:0%
+nothing is more important for life than
+ 
+
+ align:start position:0%
+nothing is more important for life than
+water it's the building block of all of
+
+ align:start position:0%
+water it's the building block of all of
+ 
+
+ align:start position:0%
+water it's the building block of all of
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+okay even when we look for life on other
+
+ align:start position:0%
+okay even when we look for life on other
+ 
+
+ align:start position:0%
+okay even when we look for life on other
+planets we start by looking for water
+
+ align:start position:0%
+planets we start by looking for water
+ 
+
+ align:start position:0%
+planets we start by looking for water
+now think of diamonds one of the more
+
+ align:start position:0%
+now think of diamonds one of the more
+ 
+
+ align:start position:0%
+now think of diamonds one of the more
+frivolous things you can buy
+
+ align:start position:0%
+frivolous things you can buy
+ 
+
+ align:start position:0%
+frivolous things you can buy
+certainly irrelevant to uh leading a
+
+ align:start position:0%
+certainly irrelevant to uh leading a
+ 
+
+ align:start position:0%
+certainly irrelevant to uh leading a
+successful or happy or productive life
+
+ align:start position:0%
+successful or happy or productive life
+ 
+
+ align:start position:0%
+successful or happy or productive life
+or any life
+
+ align:start position:0%
+or any life
+ 
+
+ align:start position:0%
+or any life
+okay yet for most of us
+
+ align:start position:0%
+okay yet for most of us
+ 
+
+ align:start position:0%
+okay yet for most of us
+water's free and diamonds are super
+
+ align:start position:0%
+water's free and diamonds are super
+ 
+
+ align:start position:0%
+water's free and diamonds are super
+expensive okay
+
+ align:start position:0%
+expensive okay
+ 
+
+ align:start position:0%
+expensive okay
+how can this be adam smith asked well
+
+ align:start position:0%
+how can this be adam smith asked well
+ 
+
+ align:start position:0%
+how can this be adam smith asked well
+the answer he posed
+
+ align:start position:0%
+the answer he posed
+ 
+
+ align:start position:0%
+the answer he posed
+is that what i first described was just
+
+ align:start position:0%
+is that what i first described was just
+ 
+
+ align:start position:0%
+is that what i first described was just
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+that is we demand lots of water we
+
+ align:start position:0%
+that is we demand lots of water we
+ 
+
+ align:start position:0%
+that is we demand lots of water we
+demand fewer diamonds
+
+ align:start position:0%
+demand fewer diamonds
+ 
+
+ align:start position:0%
+demand fewer diamonds
+but we have to match that with the
+
+ align:start position:0%
+but we have to match that with the
+ 
+
+ align:start position:0%
+but we have to match that with the
+concept of supply
+
+ align:start position:0%
+concept of supply
+ 
+
+ align:start position:0%
+concept of supply
+okay and the supply of water is almost
+
+ align:start position:0%
+okay and the supply of water is almost
+ 
+
+ align:start position:0%
+okay and the supply of water is almost
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+while the supply of diamonds maybe not
+
+ align:start position:0%
+while the supply of diamonds maybe not
+ 
+
+ align:start position:0%
+while the supply of diamonds maybe not
+naturally maybe it's through
+
+ align:start position:0%
+naturally maybe it's through
+ 
+
+ align:start position:0%
+naturally maybe it's through
+uh decisions of various businesses but
+
+ align:start position:0%
+uh decisions of various businesses but
+ 
+
+ align:start position:0%
+uh decisions of various businesses but
+it's somewhat limited
+
+ align:start position:0%
+it's somewhat limited
+ 
+
+ align:start position:0%
+it's somewhat limited
+okay so basically um
+
+ align:start position:0%
+okay so basically um
+ 
+
+ align:start position:0%
+okay so basically um
+what what he developed is what we call
+
+ align:start position:0%
+what what he developed is what we call
+ 
+
+ align:start position:0%
+what what he developed is what we call
+the supply and demand scissors
+
+ align:start position:0%
+the supply and demand scissors
+ 
+
+ align:start position:0%
+the supply and demand scissors
+that you can't just think of supply or
+
+ align:start position:0%
+that you can't just think of supply or
+ 
+
+ align:start position:0%
+that you can't just think of supply or
+demand in isolation you have to put them
+
+ align:start position:0%
+demand in isolation you have to put them
+ 
+
+ align:start position:0%
+demand in isolation you have to put them
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+if you want to explain the real world
+
+ align:start position:0%
+if you want to explain the real world
+ 
+
+ align:start position:0%
+if you want to explain the real world
+phenomena we see like the fact that
+
+ align:start position:0%
+phenomena we see like the fact that
+ 
+
+ align:start position:0%
+phenomena we see like the fact that
+water's cheap
+
+ align:start position:0%
+water's cheap
+ 
+
+ align:start position:0%
+water's cheap
+and uh diamonds are expensive so let's
+
+ align:start position:0%
+and uh diamonds are expensive so let's
+ 
+
+ align:start position:0%
+and uh diamonds are expensive so let's
+just talk
+
+ align:start position:0%
+just talk
+ 
+
+ align:start position:0%
+just talk
+let's talk about an example so there's
+
+ align:start position:0%
+let's talk about an example so there's
+ 
+
+ align:start position:0%
+let's talk about an example so there's
+one graph that was handed out in the
+
+ align:start position:0%
+one graph that was handed out in the
+ 
+
+ align:start position:0%
+one graph that was handed out in the
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+okay um which is let's talk about the
+
+ align:start position:0%
+okay um which is let's talk about the
+ 
+
+ align:start position:0%
+okay um which is let's talk about the
+market for roses
+
+ align:start position:0%
+market for roses
+ 
+
+ align:start position:0%
+market for roses
+okay um so
+
+ align:start position:0%
+okay um so
+ 
+
+ align:start position:0%
+okay um so
+in the market for roses we have
+
+ align:start position:0%
+in the market for roses we have
+ 
+
+ align:start position:0%
+in the market for roses we have
+a demand curve and a supply curve so
+
+ align:start position:0%
+a demand curve and a supply curve so
+ 
+
+ align:start position:0%
+a demand curve and a supply curve so
+what we have here this is the kind of xy
+
+ align:start position:0%
+what we have here this is the kind of xy
+ 
+
+ align:start position:0%
+what we have here this is the kind of xy
+graph we're going to look at all
+
+ align:start position:0%
+graph we're going to look at all
+ 
+
+ align:start position:0%
+graph we're going to look at all
+throughout the semester
+
+ align:start position:0%
+throughout the semester
+ 
+
+ align:start position:0%
+throughout the semester
+okay on the x-axis is the quantity of
+
+ align:start position:0%
+okay on the x-axis is the quantity of
+ 
+
+ align:start position:0%
+okay on the x-axis is the quantity of
+roses
+
+ align:start position:0%
+roses
+ 
+
+ align:start position:0%
+roses
+on the y-axis is the price of roses
+
+ align:start position:0%
+on the y-axis is the price of roses
+ 
+
+ align:start position:0%
+on the y-axis is the price of roses
+the blue downward sloping line is the
+
+ align:start position:0%
+the blue downward sloping line is the
+ 
+
+ align:start position:0%
+the blue downward sloping line is the
+demand curve
+
+ align:start position:0%
+demand curve
+ 
+
+ align:start position:0%
+demand curve
+now what i'm going to do here i'm just
+
+ align:start position:0%
+now what i'm going to do here i'm just
+ 
+
+ align:start position:0%
+now what i'm going to do here i'm just
+giving you an overview we're going to we
+
+ align:start position:0%
+giving you an overview we're going to we
+ 
+
+ align:start position:0%
+giving you an overview we're going to we
+are going over the next six
+
+ align:start position:0%
+are going over the next six
+ 
+
+ align:start position:0%
+are going over the next six
+like five or six lectures dive into
+
+ align:start position:0%
+like five or six lectures dive into
+ 
+
+ align:start position:0%
+like five or six lectures dive into
+where this demand curve comes from
+
+ align:start position:0%
+where this demand curve comes from
+ 
+
+ align:start position:0%
+where this demand curve comes from
+okay we'll go to first principles and
+
+ align:start position:0%
+okay we'll go to first principles and
+ 
+
+ align:start position:0%
+okay we'll go to first principles and
+build it back up but for now we know
+
+ align:start position:0%
+build it back up but for now we know
+ 
+
+ align:start position:0%
+build it back up but for now we know
+about demand curve
+
+ align:start position:0%
+about demand curve
+ 
+
+ align:start position:0%
+about demand curve
+is it simply represents the relationship
+
+ align:start position:0%
+is it simply represents the relationship
+ 
+
+ align:start position:0%
+is it simply represents the relationship
+between the price of a good and how much
+
+ align:start position:0%
+between the price of a good and how much
+ 
+
+ align:start position:0%
+between the price of a good and how much
+people want it
+
+ align:start position:0%
+people want it
+ 
+
+ align:start position:0%
+people want it
+therefore we assume it is downward
+
+ align:start position:0%
+therefore we assume it is downward
+ 
+
+ align:start position:0%
+therefore we assume it is downward
+sloping at higher prices people want
+
+ align:start position:0%
+sloping at higher prices people want
+ 
+
+ align:start position:0%
+sloping at higher prices people want
+less of the good
+
+ align:start position:0%
+less of the good
+ 
+
+ align:start position:0%
+less of the good
+and we'll just we'll derive where that
+
+ align:start position:0%
+and we'll just we'll derive where that
+ 
+
+ align:start position:0%
+and we'll just we'll derive where that
+comes from shortly starting next lecture
+
+ align:start position:0%
+comes from shortly starting next lecture
+ 
+
+ align:start position:0%
+comes from shortly starting next lecture
+but for now i think it's pretty
+
+ align:start position:0%
+but for now i think it's pretty
+ 
+
+ align:start position:0%
+but for now i think it's pretty
+intuitive that if the price of roads is
+
+ align:start position:0%
+intuitive that if the price of roads is
+ 
+
+ align:start position:0%
+intuitive that if the price of roads is
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+people want fewer of them and that's why
+
+ align:start position:0%
+people want fewer of them and that's why
+ 
+
+ align:start position:0%
+people want fewer of them and that's why
+it's downward sloping
+
+ align:start position:0%
+it's downward sloping
+ 
+
+ align:start position:0%
+it's downward sloping
+okay that basically as the price of
+
+ align:start position:0%
+okay that basically as the price of
+ 
+
+ align:start position:0%
+okay that basically as the price of
+roses goes up
+
+ align:start position:0%
+roses goes up
+ 
+
+ align:start position:0%
+roses goes up
+people want fewer roses the yellow curve
+
+ align:start position:0%
+people want fewer roses the yellow curve
+ 
+
+ align:start position:0%
+people want fewer roses the yellow curve
+is the supply curve now after we've
+
+ align:start position:0%
+is the supply curve now after we've
+ 
+
+ align:start position:0%
+is the supply curve now after we've
+derived the demand curve we'll then go
+
+ align:start position:0%
+derived the demand curve we'll then go
+ 
+
+ align:start position:0%
+derived the demand curve we'll then go
+and spend about
+
+ align:start position:0%
+and spend about
+ 
+
+ align:start position:0%
+and spend about
+12 lectures to ride the supply curve
+
+ align:start position:0%
+12 lectures to ride the supply curve
+ 
+
+ align:start position:0%
+12 lectures to ride the supply curve
+that's a bit harder but once again we'll
+
+ align:start position:0%
+that's a bit harder but once again we'll
+ 
+
+ align:start position:0%
+that's a bit harder but once again we'll
+start from first principles and build it
+
+ align:start position:0%
+start from first principles and build it
+ 
+
+ align:start position:0%
+start from first principles and build it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+for now you just need to know is that's
+
+ align:start position:0%
+for now you just need to know is that's
+ 
+
+ align:start position:0%
+for now you just need to know is that's
+how much firms are willing to supply
+
+ align:start position:0%
+how much firms are willing to supply
+ 
+
+ align:start position:0%
+how much firms are willing to supply
+given the price
+
+ align:start position:0%
+given the price
+ 
+
+ align:start position:0%
+given the price
+so basically as the price goes up firms
+
+ align:start position:0%
+so basically as the price goes up firms
+ 
+
+ align:start position:0%
+so basically as the price goes up firms
+want to produce more roses
+
+ align:start position:0%
+want to produce more roses
+ 
+
+ align:start position:0%
+want to produce more roses
+okay the higher price means you make
+
+ align:start position:0%
+okay the higher price means you make
+ 
+
+ align:start position:0%
+okay the higher price means you make
+more money so you want to produce more
+
+ align:start position:0%
+more money so you want to produce more
+ 
+
+ align:start position:0%
+more money so you want to produce more
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+this is a slightly less intuitive than
+
+ align:start position:0%
+this is a slightly less intuitive than
+ 
+
+ align:start position:0%
+this is a slightly less intuitive than
+demand but we'll derive it and explain
+
+ align:start position:0%
+demand but we'll derive it and explain
+ 
+
+ align:start position:0%
+demand but we'll derive it and explain
+how it can be
+
+ align:start position:0%
+how it can be
+ 
+
+ align:start position:0%
+how it can be
+but for now just go with the basic
+
+ align:start position:0%
+but for now just go with the basic
+ 
+
+ align:start position:0%
+but for now just go with the basic
+intuition that if you're making
+
+ align:start position:0%
+intuition that if you're making
+ 
+
+ align:start position:0%
+intuition that if you're making
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and you can sell in the market for a
+
+ align:start position:0%
+and you can sell in the market for a
+ 
+
+ align:start position:0%
+and you can sell in the market for a
+higher price you're going to want to
+
+ align:start position:0%
+higher price you're going to want to
+ 
+
+ align:start position:0%
+higher price you're going to want to
+make more of it
+
+ align:start position:0%
+make more of it
+ 
+
+ align:start position:0%
+make more of it
+okay and that leads the upward sloping
+
+ align:start position:0%
+okay and that leads the upward sloping
+ 
+
+ align:start position:0%
+okay and that leads the upward sloping
+supply curve
+
+ align:start position:0%
+supply curve
+ 
+
+ align:start position:0%
+supply curve
+where the points meet is the market
+
+ align:start position:0%
+where the points meet is the market
+ 
+
+ align:start position:0%
+where the points meet is the market
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+where supply and demand meets is the
+
+ align:start position:0%
+where supply and demand meets is the
+ 
+
+ align:start position:0%
+where supply and demand meets is the
+market equilibrium okay
+
+ align:start position:0%
+market equilibrium okay
+ 
+
+ align:start position:0%
+market equilibrium okay
+in the that is the point where both
+
+ align:start position:0%
+in the that is the point where both
+ 
+
+ align:start position:0%
+in the that is the point where both
+consumers
+
+ align:start position:0%
+consumers
+ 
+
+ align:start position:0%
+consumers
+and producers are happy to make a
+
+ align:start position:0%
+and producers are happy to make a
+ 
+
+ align:start position:0%
+and producers are happy to make a
+transaction
+
+ align:start position:0%
+transaction
+ 
+
+ align:start position:0%
+transaction
+consumers are happy because they are on
+
+ align:start position:0%
+consumers are happy because they are on
+ 
+
+ align:start position:0%
+consumers are happy because they are on
+their demand curve is the point
+
+ align:start position:0%
+their demand curve is the point
+ 
+
+ align:start position:0%
+their demand curve is the point
+600 is the point three dollars and six
+
+ align:start position:0%
+600 is the point three dollars and six
+ 
+
+ align:start position:0%
+600 is the point three dollars and six
+hundred roses
+
+ align:start position:0%
+hundred roses
+ 
+
+ align:start position:0%
+hundred roses
+that is they are willing to buy six
+
+ align:start position:0%
+that is they are willing to buy six
+ 
+
+ align:start position:0%
+that is they are willing to buy six
+hundred rows at three dollars
+
+ align:start position:0%
+hundred rows at three dollars
+ 
+
+ align:start position:0%
+hundred rows at three dollars
+okay producers are happy because on
+
+ align:start position:0%
+okay producers are happy because on
+ 
+
+ align:start position:0%
+okay producers are happy because on
+their supply curve is the same point
+
+ align:start position:0%
+their supply curve is the same point
+ 
+
+ align:start position:0%
+their supply curve is the same point
+they are willing to supply 600 rows of
+
+ align:start position:0%
+they are willing to supply 600 rows of
+ 
+
+ align:start position:0%
+they are willing to supply 600 rows of
+three dollars that is the one point
+
+ align:start position:0%
+three dollars that is the one point
+ 
+
+ align:start position:0%
+three dollars that is the one point
+where consumers are happy and producers
+
+ align:start position:0%
+where consumers are happy and producers
+ 
+
+ align:start position:0%
+where consumers are happy and producers
+are happy therefore it's the equilibrium
+
+ align:start position:0%
+are happy therefore it's the equilibrium
+ 
+
+ align:start position:0%
+are happy therefore it's the equilibrium
+highly non-technical but that's the
+
+ align:start position:0%
+highly non-technical but that's the
+ 
+
+ align:start position:0%
+highly non-technical but that's the
+basic intuition
+
+ align:start position:0%
+basic intuition
+ 
+
+ align:start position:0%
+basic intuition
+okay the point at which they're both
+
+ align:start position:0%
+okay the point at which they're both
+ 
+
+ align:start position:0%
+okay the point at which they're both
+willing to make that transaction the
+
+ align:start position:0%
+willing to make that transaction the
+ 
+
+ align:start position:0%
+willing to make that transaction the
+point that they're both satisfied with
+
+ align:start position:0%
+point that they're both satisfied with
+ 
+
+ align:start position:0%
+point that they're both satisfied with
+that transaction
+
+ align:start position:0%
+that transaction
+ 
+
+ align:start position:0%
+that transaction
+is the equilibrium which in this case is
+
+ align:start position:0%
+is the equilibrium which in this case is
+ 
+
+ align:start position:0%
+is the equilibrium which in this case is
+three dollars per rose and 600 roses
+
+ align:start position:0%
+three dollars per rose and 600 roses
+ 
+
+ align:start position:0%
+three dollars per rose and 600 roses
+now this raises lots of questions where
+
+ align:start position:0%
+now this raises lots of questions where
+ 
+
+ align:start position:0%
+now this raises lots of questions where
+do the curves come from
+
+ align:start position:0%
+do the curves come from
+ 
+
+ align:start position:0%
+do the curves come from
+how does equilibrium get achieved um why
+
+ align:start position:0%
+how does equilibrium get achieved um why
+ 
+
+ align:start position:0%
+how does equilibrium get achieved um why
+the heck do we give roses
+
+ align:start position:0%
+the heck do we give roses
+ 
+
+ align:start position:0%
+the heck do we give roses
+these are a bunch of questions we will
+
+ align:start position:0%
+these are a bunch of questions we will
+ 
+
+ align:start position:0%
+these are a bunch of questions we will
+um we will all
+
+ align:start position:0%
+um we will all
+ 
+
+ align:start position:0%
+um we will all
+we will come to all these questions over
+
+ align:start position:0%
+we will come to all these questions over
+ 
+
+ align:start position:0%
+we will come to all these questions over
+the next set of lectures
+
+ align:start position:0%
+the next set of lectures
+ 
+
+ align:start position:0%
+the next set of lectures
+but the basic thing is to understand
+
+ align:start position:0%
+but the basic thing is to understand
+ 
+
+ align:start position:0%
+but the basic thing is to understand
+this intuition of adam smith's supply
+
+ align:start position:0%
+this intuition of adam smith's supply
+ 
+
+ align:start position:0%
+this intuition of adam smith's supply
+and demand model
+
+ align:start position:0%
+and demand model
+ 
+
+ align:start position:0%
+and demand model
+okay questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now um this model
+
+ align:start position:0%
+okay now um this model
+ 
+
+ align:start position:0%
+okay now um this model
+also raises another important
+
+ align:start position:0%
+also raises another important
+ 
+
+ align:start position:0%
+also raises another important
+distinction that will focus on the
+
+ align:start position:0%
+distinction that will focus on the
+ 
+
+ align:start position:0%
+distinction that will focus on the
+semester and it's easy to get mixed up
+
+ align:start position:0%
+semester and it's easy to get mixed up
+ 
+
+ align:start position:0%
+semester and it's easy to get mixed up
+so i want you to if you're ever unclear
+
+ align:start position:0%
+so i want you to if you're ever unclear
+ 
+
+ align:start position:0%
+so i want you to if you're ever unclear
+i want you to ask me about it
+
+ align:start position:0%
+i want you to ask me about it
+ 
+
+ align:start position:0%
+i want you to ask me about it
+and that's distinguishing between
+
+ align:start position:0%
+and that's distinguishing between
+ 
+
+ align:start position:0%
+and that's distinguishing between
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive versus normative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analyses positive versus normative
+
+ align:start position:0%
+analyses positive versus normative
+ 
+
+ align:start position:0%
+analyses positive versus normative
+positive analysis is the study of the
+
+ align:start position:0%
+positive analysis is the study of the
+ 
+
+ align:start position:0%
+positive analysis is the study of the
+way things
+
+ align:start position:0%
+way things
+ 
+
+ align:start position:0%
+way things
+are while normative analyses are this is
+
+ align:start position:0%
+are while normative analyses are this is
+ 
+
+ align:start position:0%
+are while normative analyses are this is
+the study of the way things should be
+
+ align:start position:0%
+the study of the way things should be
+ 
+
+ align:start position:0%
+the study of the way things should be
+okay positive analysis to study the way
+
+ align:start position:0%
+okay positive analysis to study the way
+ 
+
+ align:start position:0%
+okay positive analysis to study the way
+things are while normative analysis
+
+ align:start position:0%
+things are while normative analysis
+ 
+
+ align:start position:0%
+things are while normative analysis
+is to study the way things should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me give you a great example which is
+
+ align:start position:0%
+let me give you a great example which is
+ 
+
+ align:start position:0%
+let me give you a great example which is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ebay auctions okay
+
+ align:start position:0%
+ebay auctions okay
+ 
+
+ align:start position:0%
+ebay auctions okay
+auctions are a terrific example they're
+
+ align:start position:0%
+auctions are a terrific example they're
+ 
+
+ align:start position:0%
+auctions are a terrific example they're
+like the textbook example of the
+
+ align:start position:0%
+like the textbook example of the
+ 
+
+ align:start position:0%
+like the textbook example of the
+competitive market
+
+ align:start position:0%
+competitive market
+ 
+
+ align:start position:0%
+competitive market
+you can see it in your head demand comes
+
+ align:start position:0%
+you can see it in your head demand comes
+ 
+
+ align:start position:0%
+you can see it in your head demand comes
+a bunch of people going on and bidding
+
+ align:start position:0%
+a bunch of people going on and bidding
+ 
+
+ align:start position:0%
+a bunch of people going on and bidding
+people who want it more bid more so you
+
+ align:start position:0%
+people who want it more bid more so you
+ 
+
+ align:start position:0%
+people who want it more bid more so you
+actually get a demand curve
+
+ align:start position:0%
+actually get a demand curve
+ 
+
+ align:start position:0%
+actually get a demand curve
+the higher the price the fewer people
+
+ align:start position:0%
+the higher the price the fewer people
+ 
+
+ align:start position:0%
+the higher the price the fewer people
+are getting you're getting to bid
+
+ align:start position:0%
+are getting you're getting to bid
+ 
+
+ align:start position:0%
+are getting you're getting to bid
+supply is how much how many units of it
+
+ align:start position:0%
+supply is how much how many units of it
+ 
+
+ align:start position:0%
+supply is how much how many units of it
+are for sale on ebay
+
+ align:start position:0%
+are for sale on ebay
+ 
+
+ align:start position:0%
+are for sale on ebay
+you you bid until those two meet and
+
+ align:start position:0%
+you you bid until those two meet and
+ 
+
+ align:start position:0%
+you you bid until those two meet and
+then you have
+
+ align:start position:0%
+then you have
+ 
+
+ align:start position:0%
+then you have
+a market equilibrium at that bidded
+
+ align:start position:0%
+a market equilibrium at that bidded
+ 
+
+ align:start position:0%
+a market equilibrium at that bidded
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+okay now one um
+
+ align:start position:0%
+okay now one um
+ 
+
+ align:start position:0%
+okay now one um
+one example of an ebay auction that got
+
+ align:start position:0%
+one example of an ebay auction that got
+ 
+
+ align:start position:0%
+one example of an ebay auction that got
+a lot of attention a number of years ago
+
+ align:start position:0%
+a lot of attention a number of years ago
+ 
+
+ align:start position:0%
+a lot of attention a number of years ago
+early in the days of ebay was someone
+
+ align:start position:0%
+early in the days of ebay was someone
+ 
+
+ align:start position:0%
+early in the days of ebay was someone
+offered their kidney for auction
+
+ align:start position:0%
+offered their kidney for auction
+ 
+
+ align:start position:0%
+offered their kidney for auction
+they said look i got two kidneys you
+
+ align:start position:0%
+they said look i got two kidneys you
+ 
+
+ align:start position:0%
+they said look i got two kidneys you
+only need one to live there people out
+
+ align:start position:0%
+only need one to live there people out
+ 
+
+ align:start position:0%
+only need one to live there people out
+there need a kidney
+
+ align:start position:0%
+there need a kidney
+ 
+
+ align:start position:0%
+there need a kidney
+i'm putting my kidney on ebay for
+
+ align:start position:0%
+i'm putting my kidney on ebay for
+ 
+
+ align:start position:0%
+i'm putting my kidney on ebay for
+auction um
+
+ align:start position:0%
+auction um
+ 
+
+ align:start position:0%
+auction um
+and what happened bidding went nuts it
+
+ align:start position:0%
+and what happened bidding went nuts it
+ 
+
+ align:start position:0%
+and what happened bidding went nuts it
+started at 25 000
+
+ align:start position:0%
+started at 25 000
+ 
+
+ align:start position:0%
+started at 25 000
+it climbed to 5 million before the
+
+ align:start position:0%
+it climbed to 5 million before the
+ 
+
+ align:start position:0%
+it climbed to 5 million before the
+auction was shut down and ebay decided
+
+ align:start position:0%
+auction was shut down and ebay decided
+ 
+
+ align:start position:0%
+auction was shut down and ebay decided
+they wouldn't
+
+ align:start position:0%
+they wouldn't
+ 
+
+ align:start position:0%
+they wouldn't
+allow you to sell your body on ebay
+
+ align:start position:0%
+allow you to sell your body on ebay
+ 
+
+ align:start position:0%
+allow you to sell your body on ebay
+bodily parts on ebay okay
+
+ align:start position:0%
+bodily parts on ebay okay
+ 
+
+ align:start position:0%
+bodily parts on ebay okay
+so this raises two questions
+
+ align:start position:0%
+so this raises two questions
+ 
+
+ align:start position:0%
+so this raises two questions
+the first is the positive question why
+
+ align:start position:0%
+the first is the positive question why
+ 
+
+ align:start position:0%
+the first is the positive question why
+did the price go so high
+
+ align:start position:0%
+did the price go so high
+ 
+
+ align:start position:0%
+did the price go so high
+so what's the answer to that what's the
+
+ align:start position:0%
+so what's the answer to that what's the
+ 
+
+ align:start position:0%
+so what's the answer to that what's the
+answer to the positive question
+
+ align:start position:0%
+answer to the positive question
+ 
+
+ align:start position:0%
+answer to the positive question
+okay let's look good but let's let's
+
+ align:start position:0%
+okay let's look good but let's let's
+ 
+
+ align:start position:0%
+okay let's look good but let's let's
+raise hands and
+
+ align:start position:0%
+raise hands and
+ 
+
+ align:start position:0%
+raise hands and
+give ants that's part of it yeah
+
+ align:start position:0%
+give ants that's part of it yeah
+ 
+
+ align:start position:0%
+give ants that's part of it yeah
+supply high demand demand is incredibly
+
+ align:start position:0%
+supply high demand demand is incredibly
+ 
+
+ align:start position:0%
+supply high demand demand is incredibly
+high because i die without it
+
+ align:start position:0%
+high because i die without it
+ 
+
+ align:start position:0%
+high because i die without it
+supply is low because like not a lot of
+
+ align:start position:0%
+supply is low because like not a lot of
+ 
+
+ align:start position:0%
+supply is low because like not a lot of
+us are willing to sell their kitties on
+
+ align:start position:0%
+us are willing to sell their kitties on
+ 
+
+ align:start position:0%
+us are willing to sell their kitties on
+ebay
+
+ align:start position:0%
+ebay
+ 
+
+ align:start position:0%
+ebay
+okay so low supply high demand led to a
+
+ align:start position:0%
+okay so low supply high demand led to a
+ 
+
+ align:start position:0%
+okay so low supply high demand led to a
+high price
+
+ align:start position:0%
+high price
+ 
+
+ align:start position:0%
+high price
+adam smith at work that's the positive
+
+ align:start position:0%
+adam smith at work that's the positive
+ 
+
+ align:start position:0%
+adam smith at work that's the positive
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+okay but this raises the north but then
+
+ align:start position:0%
+okay but this raises the north but then
+ 
+
+ align:start position:0%
+okay but this raises the north but then
+there's the normative question
+
+ align:start position:0%
+there's the normative question
+ 
+
+ align:start position:0%
+there's the normative question
+which is should you be allowed to sell
+
+ align:start position:0%
+which is should you be allowed to sell
+ 
+
+ align:start position:0%
+which is should you be allowed to sell
+your kidneys on ebay
+
+ align:start position:0%
+your kidneys on ebay
+ 
+
+ align:start position:0%
+your kidneys on ebay
+that's the normative question the
+
+ align:start position:0%
+that's the normative question the
+ 
+
+ align:start position:0%
+that's the normative question the
+positive question is what happens if you
+
+ align:start position:0%
+positive question is what happens if you
+ 
+
+ align:start position:0%
+positive question is what happens if you
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+the normative question is should you now
+
+ align:start position:0%
+the normative question is should you now
+ 
+
+ align:start position:0%
+the normative question is should you now
+the standard economics answer to start
+
+ align:start position:0%
+the standard economics answer to start
+ 
+
+ align:start position:0%
+the standard economics answer to start
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+of course you should we're in a world
+
+ align:start position:0%
+of course you should we're in a world
+ 
+
+ align:start position:0%
+of course you should we're in a world
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+thousands of people die every year
+
+ align:start position:0%
+thousands of people die every year
+ 
+
+ align:start position:0%
+thousands of people die every year
+because there's a waiting list for a
+
+ align:start position:0%
+because there's a waiting list for a
+ 
+
+ align:start position:0%
+because there's a waiting list for a
+kidney transplant
+
+ align:start position:0%
+kidney transplant
+ 
+
+ align:start position:0%
+kidney transplant
+okay and these are people who would
+
+ align:start position:0%
+okay and these are people who would
+ 
+
+ align:start position:0%
+okay and these are people who would
+happily pay a lot of money to stay alive
+
+ align:start position:0%
+happily pay a lot of money to stay alive
+ 
+
+ align:start position:0%
+happily pay a lot of money to stay alive
+i presume
+
+ align:start position:0%
+i presume
+ 
+
+ align:start position:0%
+i presume
+okay meanwhile there's
+
+ align:start position:0%
+okay meanwhile there's
+ 
+
+ align:start position:0%
+okay meanwhile there's
+hundreds of millions of people walking
+
+ align:start position:0%
+hundreds of millions of people walking
+ 
+
+ align:start position:0%
+hundreds of millions of people walking
+around with two kidneys
+
+ align:start position:0%
+around with two kidneys
+ 
+
+ align:start position:0%
+around with two kidneys
+who only need one and many of these
+
+ align:start position:0%
+who only need one and many of these
+ 
+
+ align:start position:0%
+who only need one and many of these
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+are poor and lives could be changed by
+
+ align:start position:0%
+are poor and lives could be changed by
+ 
+
+ align:start position:0%
+are poor and lives could be changed by
+being paid a million dollars for their
+
+ align:start position:0%
+being paid a million dollars for their
+ 
+
+ align:start position:0%
+being paid a million dollars for their
+kidney
+
+ align:start position:0%
+kidney
+ 
+
+ align:start position:0%
+kidney
+and might be happy to take the risk that
+
+ align:start position:0%
+and might be happy to take the risk that
+ 
+
+ align:start position:0%
+and might be happy to take the risk that
+their other that one kidney will be fine
+
+ align:start position:0%
+their other that one kidney will be fine
+ 
+
+ align:start position:0%
+their other that one kidney will be fine
+as it is for most everyone for most of
+
+ align:start position:0%
+as it is for most everyone for most of
+ 
+
+ align:start position:0%
+as it is for most everyone for most of
+their life
+
+ align:start position:0%
+their life
+ 
+
+ align:start position:0%
+their life
+in return for having the life-changing
+
+ align:start position:0%
+in return for having the life-changing
+ 
+
+ align:start position:0%
+in return for having the life-changing
+payment from a stranger
+
+ align:start position:0%
+payment from a stranger
+ 
+
+ align:start position:0%
+payment from a stranger
+so economists say look here's a
+
+ align:start position:0%
+so economists say look here's a
+ 
+
+ align:start position:0%
+so economists say look here's a
+transaction to make both parties better
+
+ align:start position:0%
+transaction to make both parties better
+ 
+
+ align:start position:0%
+transaction to make both parties better
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+the person who gets the kidney gets to
+
+ align:start position:0%
+the person who gets the kidney gets to
+ 
+
+ align:start position:0%
+the person who gets the kidney gets to
+stay alive and they're what they are
+
+ align:start position:0%
+stay alive and they're what they are
+ 
+
+ align:start position:0%
+stay alive and they're what they are
+willing to pay a huge amount for that
+
+ align:start position:0%
+willing to pay a huge amount for that
+ 
+
+ align:start position:0%
+willing to pay a huge amount for that
+the person who sells the kidney in most
+
+ align:start position:0%
+the person who sells the kidney in most
+ 
+
+ align:start position:0%
+the person who sells the kidney in most
+probability is
+
+ align:start position:0%
+probability is
+ 
+
+ align:start position:0%
+probability is
+fine because almost all of us can make
+
+ align:start position:0%
+fine because almost all of us can make
+ 
+
+ align:start position:0%
+fine because almost all of us can make
+it through life fine with one kidney
+
+ align:start position:0%
+it through life fine with one kidney
+ 
+
+ align:start position:0%
+it through life fine with one kidney
+and get a life-changing amount of money
+
+ align:start position:0%
+and get a life-changing amount of money
+ 
+
+ align:start position:0%
+and get a life-changing amount of money
+that could allow them to pursue their
+
+ align:start position:0%
+that could allow them to pursue their
+ 
+
+ align:start position:0%
+that could allow them to pursue their
+dreams in various ways
+
+ align:start position:0%
+dreams in various ways
+ 
+
+ align:start position:0%
+dreams in various ways
+okay so that's the standard argument
+
+ align:start position:0%
+okay so that's the standard argument
+ 
+
+ align:start position:0%
+okay so that's the standard argument
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+yeah you should be able to sell your
+
+ align:start position:0%
+yeah you should be able to sell your
+ 
+
+ align:start position:0%
+yeah you should be able to sell your
+kidneys on ebay
+
+ align:start position:0%
+kidneys on ebay
+ 
+
+ align:start position:0%
+kidneys on ebay
+okay so the question is why not
+
+ align:start position:0%
+okay so the question is why not
+ 
+
+ align:start position:0%
+okay so the question is why not
+why would we want to stop this
+
+ align:start position:0%
+why would we want to stop this
+ 
+
+ align:start position:0%
+why would we want to stop this
+transaction what are the counter
+
+ align:start position:0%
+transaction what are the counter
+ 
+
+ align:start position:0%
+transaction what are the counter
+arguments
+
+ align:start position:0%
+arguments
+ 
+
+ align:start position:0%
+arguments
+to that let's raise our rates yeah
+
+ align:start position:0%
+to that let's raise our rates yeah
+ 
+
+ align:start position:0%
+to that let's raise our rates yeah
+like i i think maybe the issue was like
+
+ align:start position:0%
+like i i think maybe the issue was like
+ 
+
+ align:start position:0%
+like i i think maybe the issue was like
+because it was ebay there's like no way
+
+ align:start position:0%
+because it was ebay there's like no way
+ 
+
+ align:start position:0%
+because it was ebay there's like no way
+to regulate it
+
+ align:start position:0%
+to regulate it
+ 
+
+ align:start position:0%
+to regulate it
+or like you don't like necessarily know
+
+ align:start position:0%
+or like you don't like necessarily know
+ 
+
+ align:start position:0%
+or like you don't like necessarily know
+like people could be like selling fake
+
+ align:start position:0%
+like people could be like selling fake
+ 
+
+ align:start position:0%
+like people could be like selling fake
+kidneys per se
+
+ align:start position:0%
+kidneys per se
+ 
+
+ align:start position:0%
+kidneys per se
+right so the first type of problem comes
+
+ align:start position:0%
+right so the first type of problem comes
+ 
+
+ align:start position:0%
+right so the first type of problem comes
+out of the category we call
+
+ align:start position:0%
+out of the category we call
+ 
+
+ align:start position:0%
+out of the category we call
+market failures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+market failures are reasons why the
+
+ align:start position:0%
+market failures are reasons why the
+ 
+
+ align:start position:0%
+market failures are reasons why the
+market doesn't work in the wonderful way
+
+ align:start position:0%
+market doesn't work in the wonderful way
+ 
+
+ align:start position:0%
+market doesn't work in the wonderful way
+economists like to think it should
+
+ align:start position:0%
+economists like to think it should
+ 
+
+ align:start position:0%
+economists like to think it should
+so for example this answer puts up that
+
+ align:start position:0%
+so for example this answer puts up that
+ 
+
+ align:start position:0%
+so for example this answer puts up that
+could be the problem
+
+ align:start position:0%
+could be the problem
+ 
+
+ align:start position:0%
+could be the problem
+of um fraud
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay people might not be able to tell
+
+ align:start position:0%
+okay people might not be able to tell
+ 
+
+ align:start position:0%
+okay people might not be able to tell
+if they're getting a legit kidney or not
+
+ align:start position:0%
+if they're getting a legit kidney or not
+ 
+
+ align:start position:0%
+if they're getting a legit kidney or not
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there could be the example of imperfect
+
+ align:start position:0%
+there could be the example of imperfect
+ 
+
+ align:start position:0%
+there could be the example of imperfect
+information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you know what the odds are that you
+
+ align:start position:0%
+do you know what the odds are that you
+ 
+
+ align:start position:0%
+do you know what the odds are that you
+can spend the rest of your life with
+
+ align:start position:0%
+can spend the rest of your life with
+ 
+
+ align:start position:0%
+can spend the rest of your life with
+only one kidney
+
+ align:start position:0%
+only one kidney
+ 
+
+ align:start position:0%
+only one kidney
+i don't either okay we ought to know
+
+ align:start position:0%
+i don't either okay we ought to know
+ 
+
+ align:start position:0%
+i don't either okay we ought to know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+before we start selling our kidneys okay
+
+ align:start position:0%
+before we start selling our kidneys okay
+ 
+
+ align:start position:0%
+before we start selling our kidneys okay
+there could be a perfect information
+
+ align:start position:0%
+there could be a perfect information
+ 
+
+ align:start position:0%
+there could be a perfect information
+okay these are the kinds of this is one
+
+ align:start position:0%
+okay these are the kinds of this is one
+ 
+
+ align:start position:0%
+okay these are the kinds of this is one
+type of problem which is the market
+
+ align:start position:0%
+type of problem which is the market
+ 
+
+ align:start position:0%
+type of problem which is the market
+maybe the market may fail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like okay current system also helps
+
+ align:start position:0%
+like okay current system also helps
+ 
+
+ align:start position:0%
+like okay current system also helps
+people who are
+
+ align:start position:0%
+people who are
+ 
+
+ align:start position:0%
+people who are
+poor and have failed kidney um
+
+ align:start position:0%
+poor and have failed kidney um
+ 
+
+ align:start position:0%
+poor and have failed kidney um
+and which would be which are people to
+
+ align:start position:0%
+and which would be which are people to
+ 
+
+ align:start position:0%
+and which would be which are people to
+be completely screwed underwater
+
+ align:start position:0%
+be completely screwed underwater
+ 
+
+ align:start position:0%
+be completely screwed underwater
+the set a second problem is what we call
+
+ align:start position:0%
+the set a second problem is what we call
+ 
+
+ align:start position:0%
+the set a second problem is what we call
+equity
+
+ align:start position:0%
+equity
+ 
+
+ align:start position:0%
+equity
+or fairness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equity or fairness which is
+
+ align:start position:0%
+equity or fairness which is
+ 
+
+ align:start position:0%
+equity or fairness which is
+we would end up with a world where only
+
+ align:start position:0%
+we would end up with a world where only
+ 
+
+ align:start position:0%
+we would end up with a world where only
+rich people would get kidneys
+
+ align:start position:0%
+rich people would get kidneys
+ 
+
+ align:start position:0%
+rich people would get kidneys
+okay currently there's a bunch of
+
+ align:start position:0%
+okay currently there's a bunch of
+ 
+
+ align:start position:0%
+okay currently there's a bunch of
+voluntary donors and people who are in
+
+ align:start position:0%
+voluntary donors and people who are in
+ 
+
+ align:start position:0%
+voluntary donors and people who are in
+accidents who have kidneys left over
+
+ align:start position:0%
+accidents who have kidneys left over
+ 
+
+ align:start position:0%
+accidents who have kidneys left over
+okay and those go to a people on the
+
+ align:start position:0%
+okay and those go to a people on the
+ 
+
+ align:start position:0%
+okay and those go to a people on the
+base of where they are in a waiting list
+
+ align:start position:0%
+base of where they are in a waiting list
+ 
+
+ align:start position:0%
+base of where they are in a waiting list
+actually a prioritized waiting list it's
+
+ align:start position:0%
+actually a prioritized waiting list it's
+ 
+
+ align:start position:0%
+actually a prioritized waiting list it's
+kind of a cool
+
+ align:start position:0%
+kind of a cool
+ 
+
+ align:start position:0%
+kind of a cool
+one of my colleagues nikhil agarwal if
+
+ align:start position:0%
+one of my colleagues nikhil agarwal if
+ 
+
+ align:start position:0%
+one of my colleagues nikhil agarwal if
+you think about
+
+ align:start position:0%
+you think about
+ 
+
+ align:start position:0%
+you think about
+i'll talk a lot this semester about the
+
+ align:start position:0%
+i'll talk a lot this semester about the
+ 
+
+ align:start position:0%
+i'll talk a lot this semester about the
+imperialistic view of economics all the
+
+ align:start position:0%
+imperialistic view of economics all the
+ 
+
+ align:start position:0%
+imperialistic view of economics all the
+cool things we can study
+
+ align:start position:0%
+cool things we can study
+ 
+
+ align:start position:0%
+cool things we can study
+so he actually uses economic models to
+
+ align:start position:0%
+so he actually uses economic models to
+ 
+
+ align:start position:0%
+so he actually uses economic models to
+study the optimal way to allocate organs
+
+ align:start position:0%
+study the optimal way to allocate organs
+ 
+
+ align:start position:0%
+study the optimal way to allocate organs
+to individuals right now it's just done
+
+ align:start position:0%
+to individuals right now it's just done
+ 
+
+ align:start position:0%
+to individuals right now it's just done
+based on a waiting list
+
+ align:start position:0%
+based on a waiting list
+ 
+
+ align:start position:0%
+based on a waiting list
+but but it may be that someone further
+
+ align:start position:0%
+but but it may be that someone further
+ 
+
+ align:start position:0%
+but but it may be that someone further
+down the waiting list needs it more than
+
+ align:start position:0%
+down the waiting list needs it more than
+ 
+
+ align:start position:0%
+down the waiting list needs it more than
+so and higher up the waiting list
+
+ align:start position:0%
+so and higher up the waiting list
+ 
+
+ align:start position:0%
+so and higher up the waiting list
+because they're more critical or
+
+ align:start position:0%
+because they're more critical or
+ 
+
+ align:start position:0%
+because they're more critical or
+whatever so there's various
+
+ align:start position:0%
+whatever so there's various
+ 
+
+ align:start position:0%
+whatever so there's various
+optimum ways to allocate but certainly
+
+ align:start position:0%
+optimum ways to allocate but certainly
+ 
+
+ align:start position:0%
+optimum ways to allocate but certainly
+although it allocate wouldn't be the
+
+ align:start position:0%
+although it allocate wouldn't be the
+ 
+
+ align:start position:0%
+although it allocate wouldn't be the
+rich guy gets it first
+
+ align:start position:0%
+rich guy gets it first
+ 
+
+ align:start position:0%
+rich guy gets it first
+that would be unlikely to be what
+
+ align:start position:0%
+that would be unlikely to be what
+ 
+
+ align:start position:0%
+that would be unlikely to be what
+society would necessarily want
+
+ align:start position:0%
+society would necessarily want
+ 
+
+ align:start position:0%
+society would necessarily want
+so there's an equity concern with that
+
+ align:start position:0%
+so there's an equity concern with that
+ 
+
+ align:start position:0%
+so there's an equity concern with that
+what else
+
+ align:start position:0%
+what else
+ 
+
+ align:start position:0%
+what else
+what other sorts yeah really
+
+ align:start position:0%
+what other sorts yeah really
+ 
+
+ align:start position:0%
+what other sorts yeah really
+since you know you can make money off of
+
+ align:start position:0%
+since you know you can make money off of
+ 
+
+ align:start position:0%
+since you know you can make money off of
+selling kidneys and you take advantage
+
+ align:start position:0%
+selling kidneys and you take advantage
+ 
+
+ align:start position:0%
+selling kidneys and you take advantage
+of people
+
+ align:start position:0%
+of people
+ 
+
+ align:start position:0%
+of people
+and it's very bad black market for
+
+ align:start position:0%
+and it's very bad black market for
+ 
+
+ align:start position:0%
+and it's very bad black market for
+kidneys
+
+ align:start position:0%
+kidneys
+ 
+
+ align:start position:0%
+kidneys
+right so there's sort of a third it's
+
+ align:start position:0%
+right so there's sort of a third it's
+ 
+
+ align:start position:0%
+right so there's sort of a third it's
+related to fraud but there's sort of a
+
+ align:start position:0%
+related to fraud but there's sort of a
+ 
+
+ align:start position:0%
+related to fraud but there's sort of a
+third class of failures
+
+ align:start position:0%
+third class of failures
+ 
+
+ align:start position:0%
+third class of failures
+that gets into the question about mis
+
+ align:start position:0%
+that gets into the question about mis
+ 
+
+ align:start position:0%
+that gets into the question about mis
+behavioral economics we talked that was
+
+ align:start position:0%
+behavioral economics we talked that was
+ 
+
+ align:start position:0%
+behavioral economics we talked that was
+raised earlier
+
+ align:start position:0%
+raised earlier
+ 
+
+ align:start position:0%
+raised earlier
+which we could just call so failing
+
+ align:start position:0%
+which we could just call so failing
+ 
+
+ align:start position:0%
+which we could just call so failing
+behavioral
+
+ align:start position:0%
+behavioral
+ 
+
+ align:start position:0%
+behavioral
+it's called behavioral economics for one
+
+ align:start position:0%
+it's called behavioral economics for one
+ 
+
+ align:start position:0%
+it's called behavioral economics for one
+of a better term which is essentially
+
+ align:start position:0%
+of a better term which is essentially
+ 
+
+ align:start position:0%
+of a better term which is essentially
+people don't always make decisions in
+
+ align:start position:0%
+people don't always make decisions in
+ 
+
+ align:start position:0%
+people don't always make decisions in
+the perfectly rational logical way we
+
+ align:start position:0%
+the perfectly rational logical way we
+ 
+
+ align:start position:0%
+the perfectly rational logical way we
+will model them as doing so this
+
+ align:start position:0%
+will model them as doing so this
+ 
+
+ align:start position:0%
+will model them as doing so this
+semester
+
+ align:start position:0%
+semester
+ 
+
+ align:start position:0%
+semester
+people make mistakes that's a word we
+
+ align:start position:0%
+people make mistakes that's a word we
+ 
+
+ align:start position:0%
+people make mistakes that's a word we
+hate using economics we hate saying
+
+ align:start position:0%
+hate using economics we hate saying
+ 
+
+ align:start position:0%
+hate using economics we hate saying
+mistakes ooh boo
+
+ align:start position:0%
+mistakes ooh boo
+ 
+
+ align:start position:0%
+mistakes ooh boo
+mistakes nobody makes mistakes we're all
+
+ align:start position:0%
+mistakes nobody makes mistakes we're all
+ 
+
+ align:start position:0%
+mistakes nobody makes mistakes we're all
+perfect little economic beings but we
+
+ align:start position:0%
+perfect little economic beings but we
+ 
+
+ align:start position:0%
+perfect little economic beings but we
+know that's not true
+
+ align:start position:0%
+know that's not true
+ 
+
+ align:start position:0%
+know that's not true
+increasingly over the past several
+
+ align:start position:0%
+increasingly over the past several
+ 
+
+ align:start position:0%
+increasingly over the past several
+decades economists have started
+
+ align:start position:0%
+decades economists have started
+ 
+
+ align:start position:0%
+decades economists have started
+incorporating insights from psychology
+
+ align:start position:0%
+incorporating insights from psychology
+ 
+
+ align:start position:0%
+incorporating insights from psychology
+into our models to not just say people
+
+ align:start position:0%
+into our models to not just say people
+ 
+
+ align:start position:0%
+into our models to not just say people
+make mistakes that's a lackadaisical but
+
+ align:start position:0%
+make mistakes that's a lackadaisical but
+ 
+
+ align:start position:0%
+make mistakes that's a lackadaisical but
+to rigorously model the nature of those
+
+ align:start position:0%
+to rigorously model the nature of those
+ 
+
+ align:start position:0%
+to rigorously model the nature of those
+mistakes
+
+ align:start position:0%
+mistakes
+ 
+
+ align:start position:0%
+mistakes
+and understand how mistakes can actually
+
+ align:start position:0%
+and understand how mistakes can actually
+ 
+
+ align:start position:0%
+and understand how mistakes can actually
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+due to virus cognitive biases and other
+
+ align:start position:0%
+due to virus cognitive biases and other
+ 
+
+ align:start position:0%
+due to virus cognitive biases and other
+things in this world you can imagine
+
+ align:start position:0%
+things in this world you can imagine
+ 
+
+ align:start position:0%
+things in this world you can imagine
+people could
+
+ align:start position:0%
+people could
+ 
+
+ align:start position:0%
+people could
+make mistakes they could be they could
+
+ align:start position:0%
+make mistakes they could be they could
+ 
+
+ align:start position:0%
+make mistakes they could be they could
+not really sit down and quite understand
+
+ align:start position:0%
+not really sit down and quite understand
+ 
+
+ align:start position:0%
+not really sit down and quite understand
+what they're doing
+
+ align:start position:0%
+what they're doing
+ 
+
+ align:start position:0%
+what they're doing
+and they could have selling their kidney
+
+ align:start position:0%
+and they could have selling their kidney
+ 
+
+ align:start position:0%
+and they could have selling their kidney
+when it's really not in their own
+
+ align:start position:0%
+when it's really not in their own
+ 
+
+ align:start position:0%
+when it's really not in their own
+long-term interest
+
+ align:start position:0%
+long-term interest
+ 
+
+ align:start position:0%
+long-term interest
+yeah example be like if there's like a
+
+ align:start position:0%
+yeah example be like if there's like a
+ 
+
+ align:start position:0%
+yeah example be like if there's like a
+family that's like an extreme poverty
+
+ align:start position:0%
+family that's like an extreme poverty
+ 
+
+ align:start position:0%
+family that's like an extreme poverty
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+even though they only have one kidney
+
+ align:start position:0%
+even though they only have one kidney
+ 
+
+ align:start position:0%
+even though they only have one kidney
+they might sell the other one just to
+
+ align:start position:0%
+they might sell the other one just to
+ 
+
+ align:start position:0%
+they might sell the other one just to
+give them money for the family per se
+
+ align:start position:0%
+give them money for the family per se
+ 
+
+ align:start position:0%
+give them money for the family per se
+well i mean in subsets that would be
+
+ align:start position:0%
+well i mean in subsets that would be
+ 
+
+ align:start position:0%
+well i mean in subsets that would be
+once again
+
+ align:start position:0%
+once again
+ 
+
+ align:start position:0%
+once again
+in a if we took this factor out we took
+
+ align:start position:0%
+in a if we took this factor out we took
+ 
+
+ align:start position:0%
+in a if we took this factor out we took
+if we took
+
+ align:start position:0%
+if we took
+ 
+
+ align:start position:0%
+if we took
+if we took if the market worked well
+
+ align:start position:0%
+if we took if the market worked well
+ 
+
+ align:start position:0%
+if we took if the market worked well
+there's no behavioral effects we'd say
+
+ align:start position:0%
+there's no behavioral effects we'd say
+ 
+
+ align:start position:0%
+there's no behavioral effects we'd say
+well you know what that's their decision
+
+ align:start position:0%
+well you know what that's their decision
+ 
+
+ align:start position:0%
+well you know what that's their decision
+you know if they otherwise they starve
+
+ align:start position:0%
+you know if they otherwise they starve
+ 
+
+ align:start position:0%
+you know if they otherwise they starve
+who are you to say
+
+ align:start position:0%
+who are you to say
+ 
+
+ align:start position:0%
+who are you to say
+okay but once you choose this say well
+
+ align:start position:0%
+okay but once you choose this say well
+ 
+
+ align:start position:0%
+okay but once you choose this say well
+wait a second maybe they're not
+
+ align:start position:0%
+wait a second maybe they're not
+ 
+
+ align:start position:0%
+wait a second maybe they're not
+evaluating the trade-offs correctly
+
+ align:start position:0%
+evaluating the trade-offs correctly
+ 
+
+ align:start position:0%
+evaluating the trade-offs correctly
+even if there's no fraud even if there's
+
+ align:start position:0%
+even if there's no fraud even if there's
+ 
+
+ align:start position:0%
+even if there's no fraud even if there's
+perfect information they may not know
+
+ align:start position:0%
+perfect information they may not know
+ 
+
+ align:start position:0%
+perfect information they may not know
+how to process that information
+
+ align:start position:0%
+how to process that information
+ 
+
+ align:start position:0%
+how to process that information
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+okay but that is not standard economics
+
+ align:start position:0%
+okay but that is not standard economics
+ 
+
+ align:start position:0%
+okay but that is not standard economics
+that's not what we'll spend a lot of
+
+ align:start position:0%
+that's not what we'll spend a lot of
+ 
+
+ align:start position:0%
+that's not what we'll spend a lot of
+time in the semester but it's obviously
+
+ align:start position:0%
+time in the semester but it's obviously
+ 
+
+ align:start position:0%
+time in the semester but it's obviously
+realistic
+
+ align:start position:0%
+realistic
+ 
+
+ align:start position:0%
+realistic
+okay so those are a bunch of good
+
+ align:start position:0%
+okay so those are a bunch of good
+ 
+
+ align:start position:0%
+okay so those are a bunch of good
+comments great comments
+
+ align:start position:0%
+comments great comments
+ 
+
+ align:start position:0%
+comments great comments
+and that yeah they're also an inelastic
+
+ align:start position:0%
+and that yeah they're also an inelastic
+ 
+
+ align:start position:0%
+and that yeah they're also an inelastic
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+such that people will always need
+
+ align:start position:0%
+such that people will always need
+ 
+
+ align:start position:0%
+such that people will always need
+kidneys that won't turn out to be a pro
+
+ align:start position:0%
+kidneys that won't turn out to be a pro
+ 
+
+ align:start position:0%
+kidneys that won't turn out to be a pro
+that doesn't turn out to be a problem
+
+ align:start position:0%
+that doesn't turn out to be a problem
+ 
+
+ align:start position:0%
+that doesn't turn out to be a problem
+okay we'll come back that's a great
+
+ align:start position:0%
+okay we'll come back that's a great
+ 
+
+ align:start position:0%
+okay we'll come back that's a great
+comeback though we talk about the shape
+
+ align:start position:0%
+comeback though we talk about the shape
+ 
+
+ align:start position:0%
+comeback though we talk about the shape
+and demand curves
+
+ align:start position:0%
+and demand curves
+ 
+
+ align:start position:0%
+and demand curves
+if you want to return to that question a
+
+ align:start position:0%
+if you want to return to that question a
+ 
+
+ align:start position:0%
+if you want to return to that question a
+few lectures but that doesn't actually
+
+ align:start position:0%
+few lectures but that doesn't actually
+ 
+
+ align:start position:0%
+few lectures but that doesn't actually
+cause a problem
+
+ align:start position:0%
+cause a problem
+ 
+
+ align:start position:0%
+cause a problem
+it's just that's more of a positive
+
+ align:start position:0%
+it's just that's more of a positive
+ 
+
+ align:start position:0%
+it's just that's more of a positive
+thing about why the price is so high but
+
+ align:start position:0%
+thing about why the price is so high but
+ 
+
+ align:start position:0%
+thing about why the price is so high but
+it's not a normative issue about whether
+
+ align:start position:0%
+it's not a normative issue about whether
+ 
+
+ align:start position:0%
+it's not a normative issue about whether
+you should allow it or not
+
+ align:start position:0%
+you should allow it or not
+ 
+
+ align:start position:0%
+you should allow it or not
+okay so basically these are exactly
+
+ align:start position:0%
+okay so basically these are exactly
+ 
+
+ align:start position:0%
+okay so basically these are exactly
+this isn't to me honestly i spend my
+
+ align:start position:0%
+this isn't to me honestly i spend my
+ 
+
+ align:start position:0%
+this isn't to me honestly i spend my
+life thinking a lot about these things i
+
+ align:start position:0%
+life thinking a lot about these things i
+ 
+
+ align:start position:0%
+life thinking a lot about these things i
+think these are really interesting
+
+ align:start position:0%
+think these are really interesting
+ 
+
+ align:start position:0%
+think these are really interesting
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+but you can't get to the nordic issues
+
+ align:start position:0%
+but you can't get to the nordic issues
+ 
+
+ align:start position:0%
+but you can't get to the nordic issues
+without the positive analysis
+
+ align:start position:0%
+without the positive analysis
+ 
+
+ align:start position:0%
+without the positive analysis
+usually the positive analysis to
+
+ align:start position:0%
+usually the positive analysis to
+ 
+
+ align:start position:0%
+usually the positive analysis to
+understand the economic framework
+
+ align:start position:0%
+understand the economic framework
+ 
+
+ align:start position:0%
+understand the economic framework
+before you start jumping you're drawing
+
+ align:start position:0%
+before you start jumping you're drawing
+ 
+
+ align:start position:0%
+before you start jumping you're drawing
+conclusions that's no fun we all want to
+
+ align:start position:0%
+conclusions that's no fun we all want to
+ 
+
+ align:start position:0%
+conclusions that's no fun we all want to
+jump to draw conclusions
+
+ align:start position:0%
+jump to draw conclusions
+ 
+
+ align:start position:0%
+jump to draw conclusions
+saying this should happen it shouldn't
+
+ align:start position:0%
+saying this should happen it shouldn't
+ 
+
+ align:start position:0%
+saying this should happen it shouldn't
+happen you can't do that we have to be
+
+ align:start position:0%
+happen you can't do that we have to be
+ 
+
+ align:start position:0%
+happen you can't do that we have to be
+disciplined
+
+ align:start position:0%
+disciplined
+ 
+
+ align:start position:0%
+disciplined
+we have to start with the fundamental
+
+ align:start position:0%
+we have to start with the fundamental
+ 
+
+ align:start position:0%
+we have to start with the fundamental
+economic framework
+
+ align:start position:0%
+economic framework
+ 
+
+ align:start position:0%
+economic framework
+okay and basically the bottom line you
+
+ align:start position:0%
+okay and basically the bottom line you
+ 
+
+ align:start position:0%
+okay and basically the bottom line you
+know i said i'll teach this course with
+
+ align:start position:0%
+know i said i'll teach this course with
+ 
+
+ align:start position:0%
+know i said i'll teach this course with
+a policy bent
+
+ align:start position:0%
+a policy bent
+ 
+
+ align:start position:0%
+a policy bent
+but you have to recognize that economics
+
+ align:start position:0%
+but you have to recognize that economics
+ 
+
+ align:start position:0%
+but you have to recognize that economics
+at its core is a right-wing science
+
+ align:start position:0%
+at its core is a right-wing science
+ 
+
+ align:start position:0%
+at its core is a right-wing science
+economics at its core is all about how
+
+ align:start position:0%
+economics at its core is all about how
+ 
+
+ align:start position:0%
+economics at its core is all about how
+the market knows best
+
+ align:start position:0%
+the market knows best
+ 
+
+ align:start position:0%
+the market knows best
+okay and that basically governments only
+
+ align:start position:0%
+okay and that basically governments only
+ 
+
+ align:start position:0%
+okay and that basically governments only
+mess things up
+
+ align:start position:0%
+mess things up
+ 
+
+ align:start position:0%
+mess things up
+that's sort of the basic a lot of what
+
+ align:start position:0%
+that's sort of the basic a lot of what
+ 
+
+ align:start position:0%
+that's sort of the basic a lot of what
+we'll learn this semester as semester
+
+ align:start position:0%
+we'll learn this semester as semester
+ 
+
+ align:start position:0%
+we'll learn this semester as semester
+goes on and we'll talk about what's
+
+ align:start position:0%
+goes on and we'll talk about what's
+ 
+
+ align:start position:0%
+goes on and we'll talk about what's
+wrong with that view
+
+ align:start position:0%
+wrong with that view
+ 
+
+ align:start position:0%
+wrong with that view
+and how governments can improve things
+
+ align:start position:0%
+and how governments can improve things
+ 
+
+ align:start position:0%
+and how governments can improve things
+indeed i teach a whole course about the
+
+ align:start position:0%
+indeed i teach a whole course about the
+ 
+
+ align:start position:0%
+indeed i teach a whole course about the
+proper role of government
+
+ align:start position:0%
+proper role of government
+ 
+
+ align:start position:0%
+proper role of government
+economy but the standard of economics is
+
+ align:start position:0%
+economy but the standard of economics is
+ 
+
+ align:start position:0%
+economy but the standard of economics is
+the market knows best
+
+ align:start position:0%
+the market knows best
+ 
+
+ align:start position:0%
+the market knows best
+okay and that leads us to the last thing
+
+ align:start position:0%
+okay and that leads us to the last thing
+ 
+
+ align:start position:0%
+okay and that leads us to the last thing
+i want to talk about
+
+ align:start position:0%
+i want to talk about
+ 
+
+ align:start position:0%
+i want to talk about
+which is basically how freely should an
+
+ align:start position:0%
+which is basically how freely should an
+ 
+
+ align:start position:0%
+which is basically how freely should an
+economy function let's step back to the
+
+ align:start position:0%
+economy function let's step back to the
+ 
+
+ align:start position:0%
+economy function let's step back to the
+giant picture
+
+ align:start position:0%
+giant picture
+ 
+
+ align:start position:0%
+giant picture
+let's step back from a market for roses
+
+ align:start position:0%
+let's step back from a market for roses
+ 
+
+ align:start position:0%
+let's step back from a market for roses
+to the entire economy
+
+ align:start position:0%
+to the entire economy
+ 
+
+ align:start position:0%
+to the entire economy
+how freely should a market should an
+
+ align:start position:0%
+how freely should a market should an
+ 
+
+ align:start position:0%
+how freely should a market should an
+economy function
+
+ align:start position:0%
+economy function
+ 
+
+ align:start position:0%
+economy function
+we have what's known as a capitalistic
+
+ align:start position:0%
+we have what's known as a capitalistic
+ 
+
+ align:start position:0%
+we have what's known as a capitalistic
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+in a capitalistic economy firms that
+
+ align:start position:0%
+in a capitalistic economy firms that
+ 
+
+ align:start position:0%
+in a capitalistic economy firms that
+individuals decide what to produce and
+
+ align:start position:0%
+individuals decide what to produce and
+ 
+
+ align:start position:0%
+individuals decide what to produce and
+consume
+
+ align:start position:0%
+consume
+ 
+
+ align:start position:0%
+consume
+may be subject to some rules of the road
+
+ align:start position:0%
+may be subject to some rules of the road
+ 
+
+ align:start position:0%
+may be subject to some rules of the road
+set by the government there's some
+
+ align:start position:0%
+set by the government there's some
+ 
+
+ align:start position:0%
+set by the government there's some
+minimal rules of the road
+
+ align:start position:0%
+minimal rules of the road
+ 
+
+ align:start position:0%
+minimal rules of the road
+to try to avoid fraud or misinformation
+
+ align:start position:0%
+to try to avoid fraud or misinformation
+ 
+
+ align:start position:0%
+to try to avoid fraud or misinformation
+but otherwise we let the dice roll
+
+ align:start position:0%
+but otherwise we let the dice roll
+ 
+
+ align:start position:0%
+but otherwise we let the dice roll
+firms and consumers decide sort of what
+
+ align:start position:0%
+firms and consumers decide sort of what
+ 
+
+ align:start position:0%
+firms and consumers decide sort of what
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+what to do now this has led to
+
+ align:start position:0%
+what to do now this has led to
+ 
+
+ align:start position:0%
+what to do now this has led to
+tremendous growth
+
+ align:start position:0%
+tremendous growth
+ 
+
+ align:start position:0%
+tremendous growth
+okay america was not a wealthy nation it
+
+ align:start position:0%
+okay america was not a wealthy nation it
+ 
+
+ align:start position:0%
+okay america was not a wealthy nation it
+was not very wealthy nation
+
+ align:start position:0%
+was not very wealthy nation
+ 
+
+ align:start position:0%
+was not very wealthy nation
+a hundred years ago 150 years ago it's
+
+ align:start position:0%
+a hundred years ago 150 years ago it's
+ 
+
+ align:start position:0%
+a hundred years ago 150 years ago it's
+led to tremendous growth where we are
+
+ align:start position:0%
+led to tremendous growth where we are
+ 
+
+ align:start position:0%
+led to tremendous growth where we are
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the most powerful still the most
+
+ align:start position:0%
+the most powerful still the most
+ 
+
+ align:start position:0%
+the most powerful still the most
+powerful and wealthiest nation in the
+
+ align:start position:0%
+powerful and wealthiest nation in the
+ 
+
+ align:start position:0%
+powerful and wealthiest nation in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+okay largely driven by the
+
+ align:start position:0%
+okay largely driven by the
+ 
+
+ align:start position:0%
+okay largely driven by the
+capitalist nation capitalistic nature of
+
+ align:start position:0%
+capitalist nation capitalistic nature of
+ 
+
+ align:start position:0%
+capitalist nation capitalistic nature of
+our economy
+
+ align:start position:0%
+our economy
+ 
+
+ align:start position:0%
+our economy
+on the other hand we are a nation with
+
+ align:start position:0%
+on the other hand we are a nation with
+ 
+
+ align:start position:0%
+on the other hand we are a nation with
+tremendous inequality
+
+ align:start position:0%
+tremendous inequality
+ 
+
+ align:start position:0%
+tremendous inequality
+we are by far the most unequal major
+
+ align:start position:0%
+we are by far the most unequal major
+ 
+
+ align:start position:0%
+we are by far the most unequal major
+nation in the world okay
+
+ align:start position:0%
+nation in the world okay
+ 
+
+ align:start position:0%
+nation in the world okay
+the top one percent of americans has a
+
+ align:start position:0%
+the top one percent of americans has a
+ 
+
+ align:start position:0%
+the top one percent of americans has a
+much higher share of our income
+
+ align:start position:0%
+much higher share of our income
+ 
+
+ align:start position:0%
+much higher share of our income
+than in any other large country in the
+
+ align:start position:0%
+than in any other large country in the
+ 
+
+ align:start position:0%
+than in any other large country in the
+world any other large developed country
+
+ align:start position:0%
+world any other large developed country
+ 
+
+ align:start position:0%
+world any other large developed country
+in the world
+
+ align:start position:0%
+in the world
+ 
+
+ align:start position:0%
+in the world
+the bottom 99 has less of our income
+
+ align:start position:0%
+the bottom 99 has less of our income
+ 
+
+ align:start position:0%
+the bottom 99 has less of our income
+corresponding than anywhere else so it's
+
+ align:start position:0%
+corresponding than anywhere else so it's
+ 
+
+ align:start position:0%
+corresponding than anywhere else so it's
+led to major inequality
+
+ align:start position:0%
+led to major inequality
+ 
+
+ align:start position:0%
+led to major inequality
+and it's led to other problems it turns
+
+ align:start position:0%
+and it's led to other problems it turns
+ 
+
+ align:start position:0%
+and it's led to other problems it turns
+out that the government can
+
+ align:start position:0%
+out that the government can
+ 
+
+ align:start position:0%
+out that the government can
+appropriately set the rules the road to
+
+ align:start position:0%
+appropriately set the rules the road to
+ 
+
+ align:start position:0%
+appropriately set the rules the road to
+avoid things like fraud
+
+ align:start position:0%
+avoid things like fraud
+ 
+
+ align:start position:0%
+avoid things like fraud
+as we saw with enron if you remember
+
+ align:start position:0%
+as we saw with enron if you remember
+ 
+
+ align:start position:0%
+as we saw with enron if you remember
+back to that or a lot of what happened
+
+ align:start position:0%
+back to that or a lot of what happened
+ 
+
+ align:start position:0%
+back to that or a lot of what happened
+during the financial meltdown
+
+ align:start position:0%
+during the financial meltdown
+ 
+
+ align:start position:0%
+during the financial meltdown
+it turns out it's hard to get people
+
+ align:start position:0%
+it turns out it's hard to get people
+ 
+
+ align:start position:0%
+it turns out it's hard to get people
+perfect information etc
+
+ align:start position:0%
+perfect information etc
+ 
+
+ align:start position:0%
+perfect information etc
+so we've seen the problems we've grown
+
+ align:start position:0%
+so we've seen the problems we've grown
+ 
+
+ align:start position:0%
+so we've seen the problems we've grown
+very wealthy as a nation
+
+ align:start position:0%
+very wealthy as a nation
+ 
+
+ align:start position:0%
+very wealthy as a nation
+but we've introduced a whole set of
+
+ align:start position:0%
+but we've introduced a whole set of
+ 
+
+ align:start position:0%
+but we've introduced a whole set of
+problems through the system
+
+ align:start position:0%
+problems through the system
+ 
+
+ align:start position:0%
+problems through the system
+now the other extreme is what's called
+
+ align:start position:0%
+now the other extreme is what's called
+ 
+
+ align:start position:0%
+now the other extreme is what's called
+the command economy
+
+ align:start position:0%
+the command economy
+ 
+
+ align:start position:0%
+the command economy
+rather than a capitalist economy is
+
+ align:start position:0%
+rather than a capitalist economy is
+ 
+
+ align:start position:0%
+rather than a capitalist economy is
+what's called a command economy
+
+ align:start position:0%
+what's called a command economy
+ 
+
+ align:start position:0%
+what's called a command economy
+okay in this case the government makes
+
+ align:start position:0%
+okay in this case the government makes
+ 
+
+ align:start position:0%
+okay in this case the government makes
+all the production and consumption
+
+ align:start position:0%
+all the production and consumption
+ 
+
+ align:start position:0%
+all the production and consumption
+decisions the government needs to set
+
+ align:start position:0%
+decisions the government needs to set
+ 
+
+ align:start position:0%
+decisions the government needs to set
+the rules the road the government
+
+ align:start position:0%
+the rules the road the government
+ 
+
+ align:start position:0%
+the rules the road the government
+owns the road the government says we're
+
+ align:start position:0%
+owns the road the government says we're
+ 
+
+ align:start position:0%
+owns the road the government says we're
+going to produce this many
+
+ align:start position:0%
+going to produce this many
+ 
+
+ align:start position:0%
+going to produce this many
+cars this year okay and people
+
+ align:start position:0%
+cars this year okay and people
+ 
+
+ align:start position:0%
+cars this year okay and people
+can get them in some way it could be a
+
+ align:start position:0%
+can get them in some way it could be a
+ 
+
+ align:start position:0%
+can get them in some way it could be a
+lottery could be waiting in line however
+
+ align:start position:0%
+lottery could be waiting in line however
+ 
+
+ align:start position:0%
+lottery could be waiting in line however
+we decide to allocate them
+
+ align:start position:0%
+we decide to allocate them
+ 
+
+ align:start position:0%
+we decide to allocate them
+we're not going to let the market
+
+ align:start position:0%
+we're not going to let the market
+ 
+
+ align:start position:0%
+we're not going to let the market
+allocate them we the government will
+
+ align:start position:0%
+allocate them we the government will
+ 
+
+ align:start position:0%
+allocate them we the government will
+allocate them well okay how many get
+
+ align:start position:0%
+allocate them well okay how many get
+ 
+
+ align:start position:0%
+allocate them well okay how many get
+produced
+
+ align:start position:0%
+produced
+ 
+
+ align:start position:0%
+produced
+and who gets them okay and this was the
+
+ align:start position:0%
+and who gets them okay and this was the
+ 
+
+ align:start position:0%
+and who gets them okay and this was the
+model the soviet union that i grew up
+
+ align:start position:0%
+model the soviet union that i grew up
+ 
+
+ align:start position:0%
+model the soviet union that i grew up
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+okay this was the pre-1989 soviet union
+
+ align:start position:0%
+okay this was the pre-1989 soviet union
+ 
+
+ align:start position:0%
+okay this was the pre-1989 soviet union
+okay the government decided how many
+
+ align:start position:0%
+okay the government decided how many
+ 
+
+ align:start position:0%
+okay the government decided how many
+shirts cars cds every i mean it's sort
+
+ align:start position:0%
+shirts cars cds every i mean it's sort
+ 
+
+ align:start position:0%
+shirts cars cds every i mean it's sort
+of bizarre to think about literally
+
+ align:start position:0%
+of bizarre to think about literally
+ 
+
+ align:start position:0%
+of bizarre to think about literally
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+the government decided how much to
+
+ align:start position:0%
+the government decided how much to
+ 
+
+ align:start position:0%
+the government decided how much to
+produce and by and large the government
+
+ align:start position:0%
+produce and by and large the government
+ 
+
+ align:start position:0%
+produce and by and large the government
+decided who got it
+
+ align:start position:0%
+decided who got it
+ 
+
+ align:start position:0%
+decided who got it
+partly through corruption that is the
+
+ align:start position:0%
+partly through corruption that is the
+ 
+
+ align:start position:0%
+partly through corruption that is the
+party p the party members
+
+ align:start position:0%
+party p the party members
+ 
+
+ align:start position:0%
+party p the party members
+party leaders got it first and often
+
+ align:start position:0%
+party leaders got it first and often
+ 
+
+ align:start position:0%
+party leaders got it first and often
+just through waiting in line
+
+ align:start position:0%
+just through waiting in line
+ 
+
+ align:start position:0%
+just through waiting in line
+for the remaining application now in
+
+ align:start position:0%
+for the remaining application now in
+ 
+
+ align:start position:0%
+for the remaining application now in
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+this ensured equity by making sure that
+
+ align:start position:0%
+this ensured equity by making sure that
+ 
+
+ align:start position:0%
+this ensured equity by making sure that
+everybody is shot at things
+
+ align:start position:0%
+everybody is shot at things
+ 
+
+ align:start position:0%
+everybody is shot at things
+in practice it didn't work well at all
+
+ align:start position:0%
+in practice it didn't work well at all
+ 
+
+ align:start position:0%
+in practice it didn't work well at all
+and actually was what dragged down
+
+ align:start position:0%
+and actually was what dragged down
+ 
+
+ align:start position:0%
+and actually was what dragged down
+the collapse of the old soviet economy
+
+ align:start position:0%
+the collapse of the old soviet economy
+ 
+
+ align:start position:0%
+the collapse of the old soviet economy
+was that the command model
+
+ align:start position:0%
+was that the command model
+ 
+
+ align:start position:0%
+was that the command model
+simply doesn't work partly there's just
+
+ align:start position:0%
+simply doesn't work partly there's just
+ 
+
+ align:start position:0%
+simply doesn't work partly there's just
+too many opportunities for corruption
+
+ align:start position:0%
+too many opportunities for corruption
+ 
+
+ align:start position:0%
+too many opportunities for corruption
+when the government controls everything
+
+ align:start position:0%
+when the government controls everything
+ 
+
+ align:start position:0%
+when the government controls everything
+that means there's no checks and
+
+ align:start position:0%
+that means there's no checks and
+ 
+
+ align:start position:0%
+that means there's no checks and
+balances
+
+ align:start position:0%
+balances
+ 
+
+ align:start position:0%
+balances
+on the the the the opportunity for
+
+ align:start position:0%
+on the the the the opportunity for
+ 
+
+ align:start position:0%
+on the the the the opportunity for
+enormous corruption
+
+ align:start position:0%
+enormous corruption
+ 
+
+ align:start position:0%
+enormous corruption
+the capitalist economy puts some natural
+
+ align:start position:0%
+the capitalist economy puts some natural
+ 
+
+ align:start position:0%
+the capitalist economy puts some natural
+checks and balances on that
+
+ align:start position:0%
+checks and balances on that
+ 
+
+ align:start position:0%
+checks and balances on that
+and partly because it turns out that
+
+ align:start position:0%
+and partly because it turns out that
+ 
+
+ align:start position:0%
+and partly because it turns out that
+it's hard to control human nature
+
+ align:start position:0%
+it's hard to control human nature
+ 
+
+ align:start position:0%
+it's hard to control human nature
+and adam smith had it right adam smith
+
+ align:start position:0%
+and adam smith had it right adam smith
+ 
+
+ align:start position:0%
+and adam smith had it right adam smith
+talks about the invisible hand
+
+ align:start position:0%
+talks about the invisible hand
+ 
+
+ align:start position:0%
+talks about the invisible hand
+of the capitalist economy the invisible
+
+ align:start position:0%
+of the capitalist economy the invisible
+ 
+
+ align:start position:0%
+of the capitalist economy the invisible
+hand is
+
+ align:start position:0%
+hand is
+ 
+
+ align:start position:0%
+hand is
+basically the notion that the capitalist
+
+ align:start position:0%
+basically the notion that the capitalist
+ 
+
+ align:start position:0%
+basically the notion that the capitalist
+economy will manage distribute things
+
+ align:start position:0%
+economy will manage distribute things
+ 
+
+ align:start position:0%
+economy will manage distribute things
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+in proportion what people want okay and
+
+ align:start position:0%
+in proportion what people want okay and
+ 
+
+ align:start position:0%
+in proportion what people want okay and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+where peak folks want to be they folks
+
+ align:start position:0%
+where peak folks want to be they folks
+ 
+
+ align:start position:0%
+where peak folks want to be they folks
+who want a certain kind of car are going
+
+ align:start position:0%
+who want a certain kind of car are going
+ 
+
+ align:start position:0%
+who want a certain kind of car are going
+to want to get to that kind of car
+
+ align:start position:0%
+to want to get to that kind of car
+ 
+
+ align:start position:0%
+to want to get to that kind of car
+and the government has it wrong they're
+
+ align:start position:0%
+and the government has it wrong they're
+ 
+
+ align:start position:0%
+and the government has it wrong they're
+going to get upset and it's going to
+
+ align:start position:0%
+going to get upset and it's going to
+ 
+
+ align:start position:0%
+going to get upset and it's going to
+lead to a less functional economy
+
+ align:start position:0%
+lead to a less functional economy
+ 
+
+ align:start position:0%
+lead to a less functional economy
+okay so basically um
+
+ align:start position:0%
+okay so basically um
+ 
+
+ align:start position:0%
+okay so basically um
+adam smith's view is that the invisible
+
+ align:start position:0%
+adam smith's view is that the invisible
+ 
+
+ align:start position:0%
+adam smith's view is that the invisible
+hand view is that consumers
+
+ align:start position:0%
+hand view is that consumers
+ 
+
+ align:start position:0%
+hand view is that consumers
+and firms serving their own best
+
+ align:start position:0%
+and firms serving their own best
+ 
+
+ align:start position:0%
+and firms serving their own best
+interest
+
+ align:start position:0%
+interest
+ 
+
+ align:start position:0%
+interest
+will do what is best for society okay so
+
+ align:start position:0%
+will do what is best for society okay so
+ 
+
+ align:start position:0%
+will do what is best for society okay so
+the fundamental core of the capitalistic
+
+ align:start position:0%
+the fundamental core of the capitalistic
+ 
+
+ align:start position:0%
+the fundamental core of the capitalistic
+view
+
+ align:start position:0%
+view
+ 
+
+ align:start position:0%
+view
+is the consumers and firms serving their
+
+ align:start position:0%
+is the consumers and firms serving their
+ 
+
+ align:start position:0%
+is the consumers and firms serving their
+own best interests
+
+ align:start position:0%
+own best interests
+ 
+
+ align:start position:0%
+own best interests
+will do what ends up being best for
+
+ align:start position:0%
+will do what ends up being best for
+ 
+
+ align:start position:0%
+will do what ends up being best for
+society and that's essentially the model
+
+ align:start position:0%
+society and that's essentially the model
+ 
+
+ align:start position:0%
+society and that's essentially the model
+we'll learn to start in this course
+
+ align:start position:0%
+we'll learn to start in this course
+ 
+
+ align:start position:0%
+we'll learn to start in this course
+yeah um in that definition are we
+
+ align:start position:0%
+yeah um in that definition are we
+ 
+
+ align:start position:0%
+yeah um in that definition are we
+defining the best for society as you're
+
+ align:start position:0%
+defining the best for society as you're
+ 
+
+ align:start position:0%
+defining the best for society as you're
+like like everybody has the most money
+
+ align:start position:0%
+like like everybody has the most money
+ 
+
+ align:start position:0%
+like like everybody has the most money
+or like everyone has the best health or
+
+ align:start position:0%
+or like everyone has the best health or
+ 
+
+ align:start position:0%
+or like everyone has the best health or
+the best and from living like
+
+ align:start position:0%
+the best and from living like
+ 
+
+ align:start position:0%
+the best and from living like
+what is the best great great question
+
+ align:start position:0%
+what is the best great great question
+ 
+
+ align:start position:0%
+what is the best great great question
+we're going to spend a lot of the
+
+ align:start position:0%
+we're going to spend a lot of the
+ 
+
+ align:start position:0%
+we're going to spend a lot of the
+semester talking about that
+
+ align:start position:0%
+semester talking about that
+ 
+
+ align:start position:0%
+semester talking about that
+for now we're going to find best for
+
+ align:start position:0%
+for now we're going to find best for
+ 
+
+ align:start position:0%
+for now we're going to find best for
+society as the most
+
+ align:start position:0%
+society as the most
+ 
+
+ align:start position:0%
+society as the most
+stuff gets produced and consumed okay
+
+ align:start position:0%
+stuff gets produced and consumed okay
+ 
+
+ align:start position:0%
+stuff gets produced and consumed okay
+that's how we're going to find it
+
+ align:start position:0%
+that's how we're going to find it
+ 
+
+ align:start position:0%
+that's how we're going to find it
+obviously you've raised a set of issues
+
+ align:start position:0%
+obviously you've raised a set of issues
+ 
+
+ align:start position:0%
+obviously you've raised a set of issues
+about what about pollution what about
+
+ align:start position:0%
+about what about pollution what about
+ 
+
+ align:start position:0%
+about what about pollution what about
+health
+
+ align:start position:0%
+health
+ 
+
+ align:start position:0%
+health
+etc we're going to come to those but for
+
+ align:start position:0%
+etc we're going to come to those but for
+ 
+
+ align:start position:0%
+etc we're going to come to those but for
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+two thirds of the course best for
+
+ align:start position:0%
+two thirds of the course best for
+ 
+
+ align:start position:0%
+two thirds of the course best for
+society means
+
+ align:start position:0%
+society means
+ 
+
+ align:start position:0%
+society means
+what we're going to call maximum surplus
+
+ align:start position:0%
+what we're going to call maximum surplus
+ 
+
+ align:start position:0%
+what we're going to call maximum surplus
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+the most stuff gets produced that people
+
+ align:start position:0%
+the most stuff gets produced that people
+ 
+
+ align:start position:0%
+the most stuff gets produced that people
+value okay
+
+ align:start position:0%
+value okay
+ 
+
+ align:start position:0%
+value okay
+so that's that's how we're going to do
+
+ align:start position:0%
+so that's that's how we're going to do
+ 
+
+ align:start position:0%
+so that's that's how we're going to do
+it and in his view the visual hand does
+
+ align:start position:0%
+it and in his view the visual hand does
+ 
+
+ align:start position:0%
+it and in his view the visual hand does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and by and large by and large it's a
+
+ align:start position:0%
+and by and large by and large it's a
+ 
+
+ align:start position:0%
+and by and large by and large it's a
+very helpful framework
+
+ align:start position:0%
+very helpful framework
+ 
+
+ align:start position:0%
+very helpful framework
+to turn to okay however at least the
+
+ align:start position:0%
+to turn to okay however at least the
+ 
+
+ align:start position:0%
+to turn to okay however at least the
+outcomes that
+
+ align:start position:0%
+outcomes that
+ 
+
+ align:start position:0%
+outcomes that
+can lead to outcomes that are not very
+
+ align:start position:0%
+can lead to outcomes that are not very
+ 
+
+ align:start position:0%
+can lead to outcomes that are not very
+fair so the way we're going to proceed
+
+ align:start position:0%
+fair so the way we're going to proceed
+ 
+
+ align:start position:0%
+fair so the way we're going to proceed
+in this course
+
+ align:start position:0%
+in this course
+ 
+
+ align:start position:0%
+in this course
+is we're going to start by talking about
+
+ align:start position:0%
+is we're going to start by talking about
+ 
+
+ align:start position:0%
+is we're going to start by talking about
+how adam smith's magic works
+
+ align:start position:0%
+how adam smith's magic works
+ 
+
+ align:start position:0%
+how adam smith's magic works
+how does the magic happen how does
+
+ align:start position:0%
+how does the magic happen how does
+ 
+
+ align:start position:0%
+how does the magic happen how does
+individuals and firms act in their own
+
+ align:start position:0%
+individuals and firms act in their own
+ 
+
+ align:start position:0%
+individuals and firms act in their own
+self-interest
+
+ align:start position:0%
+self-interest
+ 
+
+ align:start position:0%
+self-interest
+without caring about anybody else end up
+
+ align:start position:0%
+without caring about anybody else end up
+ 
+
+ align:start position:0%
+without caring about anybody else end up
+yielding
+
+ align:start position:0%
+yielding
+ 
+
+ align:start position:0%
+yielding
+the largest si possible the the largest
+
+ align:start position:0%
+the largest si possible the the largest
+ 
+
+ align:start position:0%
+the largest si possible the the largest
+possible productive economy
+
+ align:start position:0%
+possible productive economy
+ 
+
+ align:start position:0%
+possible productive economy
+okay how does that happen okay and we're
+
+ align:start position:0%
+okay how does that happen okay and we're
+ 
+
+ align:start position:0%
+okay how does that happen okay and we're
+going to talk about that
+
+ align:start position:0%
+going to talk about that
+ 
+
+ align:start position:0%
+going to talk about that
+we'll start with demand which is how do
+
+ align:start position:0%
+we'll start with demand which is how do
+ 
+
+ align:start position:0%
+we'll start with demand which is how do
+consumers decide what they want
+
+ align:start position:0%
+consumers decide what they want
+ 
+
+ align:start position:0%
+consumers decide what they want
+given their resources we'll talk about
+
+ align:start position:0%
+given their resources we'll talk about
+ 
+
+ align:start position:0%
+given their resources we'll talk about
+the principle of utility maximization
+
+ align:start position:0%
+the principle of utility maximization
+ 
+
+ align:start position:0%
+the principle of utility maximization
+the idea that i have utility function
+
+ align:start position:0%
+the idea that i have utility function
+ 
+
+ align:start position:0%
+the idea that i have utility function
+that i can math mathematically write
+
+ align:start position:0%
+that i can math mathematically write
+ 
+
+ align:start position:0%
+that i can math mathematically write
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+what i want i'll have a budget
+
+ align:start position:0%
+what i want i'll have a budget
+ 
+
+ align:start position:0%
+what i want i'll have a budget
+constraint which is the resource i have
+
+ align:start position:0%
+constraint which is the resource i have
+ 
+
+ align:start position:0%
+constraint which is the resource i have
+and the ones do constrained optimization
+
+ align:start position:0%
+and the ones do constrained optimization
+ 
+
+ align:start position:0%
+and the ones do constrained optimization
+we'll say give them what i want and the
+
+ align:start position:0%
+we'll say give them what i want and the
+ 
+
+ align:start position:0%
+we'll say give them what i want and the
+resource i have
+
+ align:start position:0%
+resource i have
+ 
+
+ align:start position:0%
+resource i have
+what decisions do i make boom we get the
+
+ align:start position:0%
+what decisions do i make boom we get the
+ 
+
+ align:start position:0%
+what decisions do i make boom we get the
+demand curve then we'll turn to supply
+
+ align:start position:0%
+demand curve then we'll turn to supply
+ 
+
+ align:start position:0%
+demand curve then we'll turn to supply
+and we'll talk about how do firms decide
+
+ align:start position:0%
+and we'll talk about how do firms decide
+ 
+
+ align:start position:0%
+and we'll talk about how do firms decide
+what to produce
+
+ align:start position:0%
+what to produce
+ 
+
+ align:start position:0%
+what to produce
+that's much more complicated because
+
+ align:start position:0%
+that's much more complicated because
+ 
+
+ align:start position:0%
+that's much more complicated because
+firms have to decide what inputs to use
+
+ align:start position:0%
+firms have to decide what inputs to use
+ 
+
+ align:start position:0%
+firms have to decide what inputs to use
+and what outputs to produce and we'll
+
+ align:start position:0%
+and what outputs to produce and we'll
+ 
+
+ align:start position:0%
+and what outputs to produce and we'll
+talk about how firms operate
+
+ align:start position:0%
+talk about how firms operate
+ 
+
+ align:start position:0%
+talk about how firms operate
+can operate in very different markets
+
+ align:start position:0%
+can operate in very different markets
+ 
+
+ align:start position:0%
+can operate in very different markets
+there's a competitive market that
+
+ align:start position:0%
+there's a competitive market that
+ 
+
+ align:start position:0%
+there's a competitive market that
+smith envisioned but that doesn't always
+
+ align:start position:0%
+smith envisioned but that doesn't always
+ 
+
+ align:start position:0%
+smith envisioned but that doesn't always
+work sometimes we get monopoly markets
+
+ align:start position:0%
+work sometimes we get monopoly markets
+ 
+
+ align:start position:0%
+work sometimes we get monopoly markets
+okay where one firm dominates and you
+
+ align:start position:0%
+okay where one firm dominates and you
+ 
+
+ align:start position:0%
+okay where one firm dominates and you
+can actually end up outcomes which
+
+ align:start position:0%
+can actually end up outcomes which
+ 
+
+ align:start position:0%
+can actually end up outcomes which
+aren't the best possible outcome even
+
+ align:start position:0%
+aren't the best possible outcome even
+ 
+
+ align:start position:0%
+aren't the best possible outcome even
+with the invisible hand
+
+ align:start position:0%
+with the invisible hand
+ 
+
+ align:start position:0%
+with the invisible hand
+okay so we'll talk about different kinds
+
+ align:start position:0%
+okay so we'll talk about different kinds
+ 
+
+ align:start position:0%
+okay so we'll talk about different kinds
+of markets then we'll put it together to
+
+ align:start position:0%
+of markets then we'll put it together to
+ 
+
+ align:start position:0%
+of markets then we'll put it together to
+get market equilibrium
+
+ align:start position:0%
+get market equilibrium
+ 
+
+ align:start position:0%
+get market equilibrium
+and talk about sort of smith's
+
+ align:start position:0%
+and talk about sort of smith's
+ 
+
+ align:start position:0%
+and talk about sort of smith's
+principles and then from there we'll
+
+ align:start position:0%
+principles and then from there we'll
+ 
+
+ align:start position:0%
+principles and then from there we'll
+talk about how it
+
+ align:start position:0%
+talk about how it
+ 
+
+ align:start position:0%
+talk about how it
+breaks down in reality different change
+
+ align:start position:0%
+breaks down in reality different change
+ 
+
+ align:start position:0%
+breaks down in reality different change
+in reality how there are various market
+
+ align:start position:0%
+in reality how there are various market
+ 
+
+ align:start position:0%
+in reality how there are various market
+failures
+
+ align:start position:0%
+failures
+ 
+
+ align:start position:0%
+failures
+that can get in the way why we have to
+
+ align:start position:0%
+that can get in the way why we have to
+ 
+
+ align:start position:0%
+that can get in the way why we have to
+care about equity and what implications
+
+ align:start position:0%
+care about equity and what implications
+ 
+
+ align:start position:0%
+care about equity and what implications
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+about behavioral economics about a set
+
+ align:start position:0%
+about behavioral economics about a set
+ 
+
+ align:start position:0%
+about behavioral economics about a set
+of other factors
+
+ align:start position:0%
+of other factors
+ 
+
+ align:start position:0%
+of other factors
+okay so that's basically how we're going
+
+ align:start position:0%
+okay so that's basically how we're going
+ 
+
+ align:start position:0%
+okay so that's basically how we're going
+to proceed uh this semester
+
+ align:start position:0%
+to proceed uh this semester
+ 
+
+ align:start position:0%
+to proceed uh this semester
+as i said the lectures are important but
+
+ align:start position:0%
+as i said the lectures are important but
+ 
+
+ align:start position:0%
+as i said the lectures are important but
+the rest stations are as well
+
+ align:start position:0%
+the rest stations are as well
+ 
+
+ align:start position:0%
+the rest stations are as well
+once we're sort of in steady state the
+
+ align:start position:0%
+once we're sort of in steady state the
+ 
+
+ align:start position:0%
+once we're sort of in steady state the
+rest station is about half
+
+ align:start position:0%
+rest station is about half
+ 
+
+ align:start position:0%
+rest station is about half
+uh working half new material and half
+
+ align:start position:0%
+uh working half new material and half
+ 
+
+ align:start position:0%
+uh working half new material and half
+working through problems
+
+ align:start position:0%
+working through problems
+ 
+
+ align:start position:0%
+working through problems
+to help you prepare for the next problem
+
+ align:start position:0%
+to help you prepare for the next problem
+ 
+
+ align:start position:0%
+to help you prepare for the next problem
+set so the problem sets are going to
+
+ align:start position:0%
+set so the problem sets are going to
+ 
+
+ align:start position:0%
+set so the problem sets are going to
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+is the problem set that's assigned will
+
+ align:start position:0%
+is the problem set that's assigned will
+ 
+
+ align:start position:0%
+is the problem set that's assigned will
+cover material that's taught
+
+ align:start position:0%
+cover material that's taught
+ 
+
+ align:start position:0%
+cover material that's taught
+up to that date so for example problem
+
+ align:start position:0%
+up to that date so for example problem
+ 
+
+ align:start position:0%
+up to that date so for example problem
+set one is to be assigned next friday
+
+ align:start position:0%
+set one is to be assigned next friday
+ 
+
+ align:start position:0%
+set one is to be assigned next friday
+that will cover everything you've
+
+ align:start position:0%
+that will cover everything you've
+ 
+
+ align:start position:0%
+that will cover everything you've
+learned up through next wednesday
+
+ align:start position:0%
+learned up through next wednesday
+ 
+
+ align:start position:0%
+learned up through next wednesday
+okay therefore in section on next friday
+
+ align:start position:0%
+okay therefore in section on next friday
+ 
+
+ align:start position:0%
+okay therefore in section on next friday
+we'll do a practice problem
+
+ align:start position:0%
+we'll do a practice problem
+ 
+
+ align:start position:0%
+we'll do a practice problem
+which will help which you should
+
+ align:start position:0%
+which will help which you should
+ 
+
+ align:start position:0%
+which will help which you should
+understand because we'll cover things
+
+ align:start position:0%
+understand because we'll cover things
+ 
+
+ align:start position:0%
+understand because we'll cover things
+we've taught in class
+
+ align:start position:0%
+we've taught in class
+ 
+
+ align:start position:0%
+we've taught in class
+and he'll prepare you for the problem
+
+ align:start position:0%
+and he'll prepare you for the problem
+ 
+
+ align:start position:0%
+and he'll prepare you for the problem
+set and we'll do that every week
+
+ align:start position:0%
+set and we'll do that every week
+ 
+
+ align:start position:0%
+set and we'll do that every week
+that about half the sections the other
+
+ align:start position:0%
+that about half the sections the other
+ 
+
+ align:start position:0%
+that about half the sections the other
+half the section will be new material
+
+ align:start position:0%
+half the section will be new material
+ 
+
+ align:start position:0%
+half the section will be new material
+okay this friday the section friday is
+
+ align:start position:0%
+okay this friday the section friday is
+ 
+
+ align:start position:0%
+okay this friday the section friday is
+all new material
+
+ align:start position:0%
+all new material
+ 
+
+ align:start position:0%
+all new material
+we're doing fridays cover the
+
+ align:start position:0%
+we're doing fridays cover the
+ 
+
+ align:start position:0%
+we're doing fridays cover the
+mathematics i don't like doing math
+
+ align:start position:0%
+mathematics i don't like doing math
+ 
+
+ align:start position:0%
+mathematics i don't like doing math
+i always get it wrong okay so i leave
+
+ align:start position:0%
+i always get it wrong okay so i leave
+ 
+
+ align:start position:0%
+i always get it wrong okay so i leave
+math for the tas who are smarter than i
+
+ align:start position:0%
+math for the tas who are smarter than i
+ 
+
+ align:start position:0%
+math for the tas who are smarter than i
+am
+
+ align:start position:0%
+am
+ 
+
+ align:start position:0%
+am
+okay so this friday we're doing the
+
+ align:start position:0%
+okay so this friday we're doing the
+ 
+
+ align:start position:0%
+okay so this friday we're doing the
+mathematics of supply and demand
+
+ align:start position:0%
+mathematics of supply and demand
+ 
+
+ align:start position:0%
+mathematics of supply and demand
+and how you take the intuition here and
+
+ align:start position:0%
+and how you take the intuition here and
+ 
+
+ align:start position:0%
+and how you take the intuition here and
+the simple graphics and actually turn it
+
+ align:start position:0%
+the simple graphics and actually turn it
+ 
+
+ align:start position:0%
+the simple graphics and actually turn it
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+mathematical representations which is
+
+ align:start position:0%
+mathematical representations which is
+ 
+
+ align:start position:0%
+mathematical representations which is
+what you need for the problem sets
+
+ align:start position:0%
+what you need for the problem sets
+ 
+
+ align:start position:0%
+what you need for the problem sets
+that this friday then we'll come back on
+
+ align:start position:0%
+that this friday then we'll come back on
+ 
+
+ align:start position:0%
+that this friday then we'll come back on
+monday and start talking about
+
+ align:start position:0%
+monday and start talking about
+ 
+
+ align:start position:0%
+monday and start talking about
+uh what's underneath the demand curve
+
+ align:start position:0%
+uh what's underneath the demand curve
+ 
+
+ align:start position:0%
+uh what's underneath the demand curve
+all right any other questions
+
+ align:start position:0%
+all right any other questions
+ 
+
+ align:start position:0%
+all right any other questions
+okay i'll see you on monday
\ No newline at end of file
diff --git a/__tGxUu5BTc.txt b/__tGxUu5BTc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..161c88f26567f6afd3606243883114df56d3ad0a
--- /dev/null
+++ b/__tGxUu5BTc.txt
@@ -0,0 +1,3018 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Let's start.
+
+Any questions?
+
+We've been gradually building
+up thermodynamics, culminating
+
+in what I call the most
+important fundamental relation,
+
+which was the E is
+T dS plus Ji dxi.
+
+And essentially
+we said that this
+
+was some statement of
+conservation of energy.
+
+where there's a heat component
+that goes into the system,
+
+and there's a work component.
+
+And actually, we ended up
+breaking the work component
+
+into a mechanical part
+and a chemical part,
+
+which we wrote as
+mu alpha dN alpha.
+
+I guess if I don't
+write the sums,
+
+the summation
+convention is assumed.
+
+Now, this gave us an idea of
+what a thermodynamic system is,
+
+in the sense of how many
+coordinates do we need in order
+
+to place the system
+in equilibrium
+
+somewhere in some
+coordinate space.
+
+And we said that we can just
+count the number of variables
+
+that we have on this side.
+
+And indeed, for
+the case of energy,
+
+the natural set of variables
+would be S, x, and N.
+
+And given some place in
+the coordinate system that
+
+is S, x, and N, you
+could find a point that
+
+corresponds to that
+thermodynamic equilibrium
+
+state.
+
+Now, having gotten this
+fundamental relation,
+
+we can manipulate and write
+it in different fashion.
+
+And in particular,
+for example, you
+
+can write the S is dE by
+dT, minus Ji dxi over T,
+
+minus mu alpha dN alpha over
+T. So you could in principle
+
+express everything rather than
+in terms of entropy-- which
+
+in some circumstances may not
+be the right variable-- in terms
+
+of the energy content of
+the system and the variables
+
+that you need in order to
+make work type of changes
+
+on the system.
+
+And we saw that other
+versions of it is possible.
+
+So for example, we
+could rearrange.
+
+Rather than looking
+at E, we could
+
+look at E minus TS, the
+quantity that we call F.
+
+And then dF would look very
+much like the original equation.
+
+Rather than T dS, we
+would get minus S dT.
+
+And clearly, for
+this quantity F,
+
+the natural variables
+are T, x, and N.
+
+And there were other
+types of these functions
+
+that we construct.
+
+So basically at this stage, we
+have a formula that tells us
+
+how to navigate our way
+in this space of things
+
+that are in equilibrium.
+
+And by taking various
+derivatives of equilibrium
+
+functions with
+respect to each other,
+
+we can express other ones.
+
+And via this methodology, we can
+relate to many different things
+
+to each other and have
+mathematical relations
+
+between physical observables.
+
+So following up on
+that, we then ask
+
+what are some other mathematical
+forms that we can look at.
+
+And one set of forms
+followed from extensivity.
+
+And we saw that if we were
+under circumstances such
+
+that we were to multiply all
+of the extensive variables
+
+by some factor-- 2, 3,
+whatever-- and the energy
+
+content would increase
+by that same factor,
+
+then we could in fact
+integrate the equation
+
+and drop the d's and
+write it in this fashion--
+
+TS Jx plus mu N, regarding
+these as kind of vectors.
+
+And importantly, that told us
+that the intensive variables
+
+were not independent
+of each other.
+
+And you had relationship that
+you-- S dT plus Ji xi dJi
+
+plus N alpha d mu alpha is 0.
+
+And last time, I
+did one calculation
+
+using this Gibbs-Duhem
+relation that I repeat.
+
+And that was for a gas isotherm.
+
+Isotherm corresponds
+to dT goes to 0.
+
+And the analogue of hydrostatic
+work for a gas was minus P
+
+for J. So this becomes
+minus V dP plus N d mu.
+
+If you have one
+component, it goes to 0.
+
+And we said that this
+gives us the relationship
+
+along an isotherm.
+
+So for a fixed T, d
+mu by dP is V over N.
+
+I'll come back to that shortly.
+
+Towards the end
+of last lecture, I
+
+mentioned that we
+can get a number
+
+of other so-called
+Maxwell relations
+
+by noting that mixed
+second derivatives are
+
+independent of the order
+of taking derivatives.
+
+So that if you have some df
+of x and y written as df by dx
+
+at constant y dx, plus df
+by dy at constant x dy,
+
+then the order of the
+second derivatives, which
+
+would be obtained
+by taking either
+
+a derivative of the
+first term with respect
+
+to y or the second term
+with respect to x--
+
+doesn't matter which order.
+
+So let's start with
+our initial equation.
+
+And for simplicity,
+let's think of cases
+
+where we have a fixed
+number of particles
+
+so that we can write
+dE as T dS plus Ji dxi.
+
+So this looks like this dF
+that I wrote before for you.
+
+And I can identify temperature
+as dE by dS at constant x,
+
+and each one of the forces Ji
+as dE by dxi at constant S.
+
+And all of the J's that are
+not equal to i kept fixed.
+
+And then, since the
+second derivative
+
+is irrespective of order, I
+can form the second derivative
+
+with respect to the combination
+S xi into a different fashion.
+
+I can either take a derivative
+over here-- I already
+
+have derivative with
+respect to S giving me T,
+
+so I will get dT by dxi,
+essentially at constant S--
+
+or I can take the
+derivative of this object.
+
+I already have the x derivative,
+so I take the S derivative.
+
+So I have dJi with respect
+to S at constant x.
+
+So this is an example
+of the Maxwell relation.
+
+And just to remind
+you, we can always
+
+invert these derivatives.
+
+So I can invert this
+and say that actually,
+
+if I had wondered how
+the entropy changes
+
+as a function of a force such
+as pressure at constant x,
+
+it would be related to how
+the corresponding displacement
+
+to the force changes as a
+function of temperature.
+
+So you would have a relationship
+between some observable
+
+such as how the length
+of a wire changes
+
+if you change
+temperature rapidly,
+
+and how the entropy would change
+as a function of pressure,
+
+or corresponding force,
+whatever it may be.
+
+Now, what I would like to
+remind you is that the best
+
+way to sort of derive
+these relationships
+
+is to reconstruct
+what kind of second
+
+derivative or mixed
+derivative you
+
+want to have to give
+you the right result.
+
+So for example, say
+somebody told me
+
+that I want to calculate
+something similar-- dS by dJ,
+
+let's say at
+constant temperature.
+
+How do I calculate that?
+
+A nice way to calculate
+that is if I somehow
+
+manipulate so that S appears
+as a first derivative.
+
+Now, S does not appear as
+a first derivative here,
+
+but certainly appears as
+a first derivative here.
+
+So who says I have to take
+E as a function of state?
+
+I can look at the
+second derivative of F.
+
+So if I look at F,
+which is E minus TS--
+
+and actually, I don't
+even need to know
+
+what the name of this entity is,
+whether it's F, G, et cetera.
+
+All I know is that it will
+convert this to minus S dT--
+
+the TS that I don't want,
+so that S appears now
+
+as a first derivative.
+
+Now I want to take a
+derivative of S with respect
+
+to J. If I just stop here, the
+next term that I would have
+
+is Ji dxi.
+
+And the natural way that I would
+construct a second derivative
+
+would give me dS
+with respect to xi.
+
+But I want the S
+with respect to Ji.
+
+So I say, OK, I'll do
+this function instead.
+
+As I said, I don't
+really care what
+
+the name of these functions is.
+
+This will get
+converted to xi dJ.
+
+Now I can say there is
+this first derivative-- d o
+
+minus S with respect
+to Ji at constant T
+
+is the same thing as d
+of minus y with respect
+
+to T at constant J. So I can
+get rid of the minus sign
+
+if I want, and I have
+the answer that I want.
+
+It is dxi by dT at constant
+J-- at constant-- yeah, T-- J.
+
+And you can go and construct
+anything else that you like.
+
+Let me, for example,
+try to construct
+
+this entity we
+already calculated.
+
+So let's see.
+
+What can I say about d mu by
+dP at constant temperature,
+
+and I want to calculate
+that via a Maxwell relation?
+
+So what do I know?
+
+I know that dE is
+T dS minus pdV.
+
+Good.
+
+Oh, I want to have
+mu in the play,
+
+so now I have to add mu dN.
+
+That's good, because I have
+mu as a first derivative.
+
+I have it over here.
+
+But I have P as a
+first derivative,
+
+whereas I want P to appear as
+the work element, something
+
+like dP.
+
+So what I will do is I will
+make this d of E plus pV.
+
+This converts this to
+plus V dP plus mu dN.
+
+That's fine, except that
+when I do things now,
+
+I would have calculated
+things at constant S.
+
+And I want to calculate
+things at constant T.
+
+That's not really important.
+
+I do a minus ST. This
+becomes minus S dT.
+
+And then I have a
+function of state--
+
+I don't care what
+it's called-- that has
+
+the right format for me
+to identify that d mu
+
+by dP at constant N and T,
+along an isotherm of a fixed
+
+number of particles,
+is the same thing as dV
+
+by dN at constant PN T. So
+that's my Maxwell relation.
+
+So why didn't I get this result?
+
+Did I make a mistake?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Louder.
+
+AUDIENCE: Is this valid
+for extensive systems?
+
+PROFESSOR: Yes, this is
+valid for extensive system.
+
+I used extensively in
+the relation of this.
+
+And here, I never
+used extensivity.
+
+But if I have a system that
+I tell you its pressure
+
+and temperature, how
+is its volume related
+
+to the number of particles?
+
+I have a box in this room.
+
+I tell you pressure and
+temperature are fixed.
+
+If I make the box twice as big,
+number of particles, volume
+
+will go twice as big.
+
+So if I were to
+apply extensivity,
+
+I would have to conclude that
+this is the same thing as V
+
+over N, and I would
+be in agreement
+
+with what I had before.
+
+Any questions?
+
+Yes.
+
+AUDIENCE: What about the
+constraint of constant PN T
+
+[INAUDIBLE]?
+
+PROFESSOR: OK.
+
+Actually, constraint
+of constant PN T
+
+is important because
+we said that said there
+
+it is a kind of
+Gibbs-Duhem relation.
+
+And the Gibbs-Duhem
+relation tells me
+
+for the case of the gas that
+the S dT minus V dP plus N d mu
+
+is 0.
+
+And that constraint
+is the one that
+
+tells me that once you have
+set P and T, which are the two
+
+variables that I have specified
+here, you also know mu.
+
+That is, you know all
+the intensive quantities.
+
+So once you set PN T-- the
+constraints over there--
+
+really, the only thing
+that you don't know
+
+is how big the system is.
+
+And that's what's the condition
+that I used over here.
+
+But it is only-- so
+let me re-emphasize
+
+it this way-- I
+will write dV by dN
+
+is the same thing as V over
+N, only if I have PN T here.
+
+If I had here PN S, for example,
+I wouldn't be able to use this.
+
+I was going to
+build this equation
+
+to say, look at the
+elements of this.
+
+This part we got
+from the first law,
+
+the temperature we got
+from the zeroth law,
+
+and this we got from the
+second law, which is correct,
+
+but it leaves out
+something, which
+
+is that what the second
+law had was things
+
+going some particular direction.
+
+And in particular, we had
+that for the certain changes
+
+that I won't repeat, the change
+in entropy to be positive.
+
+So when you are in
+equilibrium, you
+
+have this relationship between
+equilibrium state functions.
+
+But in fact, the second
+law of thermodynamics
+
+tells you a little
+bit more than that.
+
+So the next item that
+we are going to look at
+
+is, what are the
+consequences of having
+
+underlying this equality
+between functions
+
+of state some kind of an
+inequality about certain things
+
+being possible and things
+not being possible?
+
+And that relates to
+stability conditions.
+
+And I find it easier to
+again introduce to you these
+
+stability conditions by thinking
+of a mechanical analogue.
+
+So let's imagine that you
+have some kind of a spring,
+
+and that this spring has some
+kind of a potential energy
+
+that I will call phi as a
+function of the extension x.
+
+And let's say that it's
+some non-linear function
+
+such as this.
+
+There is no reason why we
+should use a hook and spring,
+
+but something like this.
+
+Now, we also discussed
+last time what
+
+happens if I were to pull
+on this with some force J.
+
+So I pull on this.
+
+As a result, presumably
+it will no longer
+
+be sitting at x, because
+what I need to do
+
+is to minimize something else--
+the function that we call H--
+
+which was the potential
+energy of the spring
+
+plus the entity that
+was exerting the force.
+
+So if I were to make it
+in the vertical direction,
+
+you can imagine this as
+being the potential energy
+
+of the mass that was
+pulling on the spring.
+
+So what that means is
+that in the presence of J,
+
+what I need to do is
+to find the x that
+
+minimizes this expression.
+
+Once essentially the kinetic
+energy has disappeared,
+
+my spring stops oscillating
+and goes to a particular value.
+
+And mathematically,
+that corresponds
+
+to subtracting a linear
+function from this.
+
+Actually, what
+will it look like?
+
+Let's not make this go flat,
+but go up in some linear fashion
+
+so that at least I can
+draw something like this.
+
+So what I need to do
+is to minimize this.
+
+So I find that for
+a given J, I have
+
+to solve d phi dx equals J.
+But especially if you have
+
+a spring that has the kind of
+potential that I drew for you,
+
+you start increasing
+the-- so basically,
+
+what it says is that
+you end up at the place
+
+where the slope is
+equal to the derivative
+
+of the potential function.
+
+What happens if you start
+increasing this slope,
+
+if it is a non-linear type
+of thing, at some point
+
+you can see it's impossible.
+
+Essentially, it's like
+a very flat noodle.
+
+You pull on it too much and then
+it starts to expand forever.
+
+So essentially, this thing that
+we are looking for a minimum,
+
+ultimately also
+means that you need
+
+to have a condition on
+the second derivative.
+
+d2 phi by dx squared better
+be positive actually,
+
+I have to take d2
+H y dx squared.
+
+I took one derivative
+to identify
+
+where the location of
+the best solution is.
+
+If I take a second
+derivative, this
+
+became essentially the
+J. J is a constant.
+
+It only depends on
+the potential energy.
+
+So it says independent of
+the force that you apply.
+
+You know that if the shape of
+the potential energy is given,
+
+the only places
+that are accessible
+
+are the kinds of
+places where you
+
+take the second
+derivative and the second
+
+has a particular sign.
+
+So this portion of the
+curve is in principle
+
+physically accessible.
+
+The portion that corresponds
+to essentially changing
+
+the curvature and going the
+other way, there's no way,
+
+there's no force
+that you can put
+
+that would be able to access
+those kinds of displacements.
+
+So there is this
+convexity condition.
+
+This was for one variable.
+
+Now suppose you have multiple
+variables-- x2, x3, et cetera.
+
+So you will have
+the potential energy
+
+as a function of many variables.
+
+And the condition that you have
+is that the second derivative
+
+of the potential with respect
+to all variables, which forms--
+
+and if there are n variables,
+this would be an n by n matrix.
+
+This matrix is
+positive definite.
+
+What that means is
+that if you think
+
+of this as defining for you
+the bottom of a potential,
+
+in whatever direction
+you go, this
+
+would describe the change
+of potential for you.
+
+The first order
+change you already
+
+set to 0 because of the force J.
+The second order change better
+
+be positive.
+
+So this is the condition that
+you would have for stability,
+
+quite generally mechanically.
+
+And again, this
+came from the fact
+
+that if you were
+to exert a force,
+
+you would change the energy
+by something like J delta
+
+x, which is certainly the
+same thing that we have here.
+
+This is just one component
+that I have been focusing on.
+
+And so ultimately,
+I'm going to try
+
+to generalize that to this form.
+
+But one thing that I don't
+quite like in this form
+
+is that I'm focusing too
+much on the displacements.
+
+This is written appropriately
+using this form.
+
+And we have seen over
+here that whether or not
+
+I express things in terms
+of the displacements
+
+or in terms of entropy,
+temperature, conjugate forces,
+
+et cetera, these are
+all equivalent ways
+
+of describing the
+equilibrium system.
+
+So I'm going to do a
+slight manipulation of this
+
+to make that symmetry between
+forces and displacements
+
+apparent.
+
+So the generalization
+of this expression
+
+that we have over
+here is that once I
+
+know the potential
+energy, the force
+
+in this multi-component
+space is df by dxi.
+
+So in this multi-component
+space, I have some J,
+
+and there's a corresponding x.
+
+They're related by this.
+
+Now, if I were to
+make a change in J,
+
+there will be a change in the
+position of the equilibrium.
+
+And I can get that by
+doing a corresponding cange
+
+in the derivative.
+
+The corresponding
+change in the derivative
+
+is the second derivative
+of phi with respect
+
+to xi xj delta xj, sum
+over J. So what I'm saying
+
+is that this is a
+condition that relates
+
+the position to the forces.
+
+If I make a slight
+change in the force,
+
+there will be a corresponding
+slight change in the position.
+
+And the changes in the
+position and the force given
+
+by this equilibrium condition
+are related by this formula.
+
+Now, you can see that that
+sum is already present here.
+
+So I can rewrite
+the expression that
+
+is over here using that
+formula as delta xi delta
+
+Ji, sum over i--
+better be positive.
+
+So this expression is slightly
+different and better way
+
+of writing essentially the same
+convexity condition, stability
+
+condition, but in a
+manner that treats
+
+the displacements and
+the forces equivalently.
+
+And I'm going to
+apply that to this
+
+and say that in
+general, there will
+
+be more ways of
+manipulating the energy
+
+of a thermodynamic system, and
+that having the system reach
+
+to equilibrium requires
+the generalization of this
+
+as a delta T delta S, plus
+sum over i delta Ji delta xi,
+
+plus sum over alpha,
+delta mu alpha,
+
+delta N alpha-- to be positive.
+
+And you may say I didn't
+really derive this for you
+
+because I started from
+mechanical equilibrium
+
+and stability condition
+and generalized
+
+to the thermodynamic one.
+
+But really, if you go back
+and I use this condition
+
+and do manipulations that
+are compatible to this,
+
+you will come up with exactly
+this stability condition.
+
+And I have that in the notes.
+
+It is somewhat more
+mathematically complicated
+
+than this, because the
+derivatives involve
+
+additional factors
+of 1 over T. And you
+
+have to do slightly more
+work, but you will ultimately
+
+come with the same expression.
+
+OK?
+
+You say, why is that of any use?
+
+It is possible
+that you've already
+
+seen a particular use
+of this expression.
+
+Let's look at the case
+of a gas-- one component.
+
+You would say that the
+condition that we have
+
+is that delta T delta S minus
+delta P delta V plus delta mu
+
+delta N has to be positive.
+
+Let's even be simpler.
+
+Look at the case
+where delta T is 0,
+
+delta N equals to 0, which
+means that I have a fixed
+
+amount of gas at a
+particular temperature.
+
+So I could have,
+for example, a box
+
+in this room which
+is in equilibrium
+
+at the same temperature as
+the temperature of the room.
+
+But its volume I'm
+allowed to adjust
+
+so that the pressure changes.
+
+So in that process, at a
+particular temperature,
+
+I will be finding a particular
+curve in the pressure volume
+
+space.
+
+And the reason that I
+drew this particular way
+
+is because I have the condition
+that minus dP dV better
+
+be positive, so that if I
+have P as a function of V,
+
+then I know that dP
+is dP by dV delta V.
+
+And if the product
+dP dV is positive,
+
+then this derivative dP
+by dV has to be negative.
+
+This has to be a
+decreasing function.
+
+And another way
+of saying that is
+
+that the compressibility--
+kappa T, which is minus 1
+
+over V, the inverse of this
+dV by dP at constant T--
+
+has to be positive.
+
+So this is a curve where
+dP by dV is negative.
+
+Fine, you say.
+
+Nothing surprising about that.
+
+Well, it turns out that
+if you cool the gas,
+
+the shape of this
+isotherm can change.
+
+It can get started.
+
+And there is a critical
+isotherm at which
+
+you see a condition such
+as this, where there's
+
+a point where the curve
+comes with 0 slope.
+
+So you say that for that
+particular critical isotherm
+
+occurring at TC, if I were
+to make this expansion,
+
+the first term in
+this expansion is 0.
+
+You say, OK, let's continue and
+write down the second term--
+
+1/2 d2 P by dV squared
+at constant P times
+
+delta V squared.
+
+Now the problem is
+that if I multiply this
+
+by delta V-- which would have
+made this into delta V squared
+
+and then this into
+delta V cubed--
+
+I have a problem
+because delta V can
+
+be both positive or negative.
+
+I can go one direction
+or the other direction.
+
+And a term that is a
+cubic can change sign--
+
+can sometimes be positive,
+can sometimes be negative,
+
+depending on the sign of that.
+
+And that is disallowed
+by this condition.
+
+So that would say that if
+an analytical expression
+
+for the expansion exists, the
+second derivative has to be 0.
+
+And then you would have
+to go to the next term-- d
+
+cubed P dV cubed.
+
+And then delta V-- you would
+normally write delta V cubed,
+
+but then I've multiplied by
+delta V on the other side.
+
+We'd have delta V to the fourth.
+
+Delta V to the fourth you would
+say is definitely positive.
+
+Then I can get things done
+by having to make sure
+
+that the third
+derivative is negative.
+
+And you say, OK, exactly
+what have you done here?
+
+What you have done
+here is you've
+
+drawn a curve that
+locally looks like a cubic
+
+with the appropriate sign.
+
+And so that's certainly
+true that if you
+
+have an isotherm there the
+compressibility diverges,
+
+you have a condition
+on second derivatives.
+
+And you probably have used this
+for calculating critical points
+
+of van der Waals
+and other gases.
+
+And we will do that ourselves.
+
+But it's actually not the
+right way to go about,
+
+because when you go and look
+at things experimentally
+
+with sufficient detail, you find
+that these curves at this point
+
+are not analytic.
+
+They don't admit a
+Taylor expansion.
+
+So while this
+condition is correct,
+
+that the shape should
+be something like this,
+
+it is neither cubic
+nor a fifth power,
+
+but some kind of a
+non-analytic curve.
+
+AUDIENCE: Could you
+repeat last statement?
+
+PROFESSOR: That
+statement, in order
+
+to fully understand
+and appreciate,
+
+you have to come
+to next term, where
+
+we talk about phase transitions.
+
+But the statement
+is that the shape
+
+of the function in the
+vicinity of something like this
+
+is delta P is
+proportional to delta V
+
+to some other gamma that is
+neither 3 nor 5 nor an integer.
+
+It is some number
+that experimentally
+
+has been determined to be of
+the order of, I don't know, 4.7.
+
+And why it is 4.7 you have to
+do a lot of interesting field
+
+theory to understand.
+
+And hopefully, you'll come next
+semester and I'll explain it.
+
+AUDIENCE: So your point is
+that gamma is not [INAUDIBLE].
+
+PROFESSOR: Gamma is not-- so
+the statement is, in order
+
+for me to write this
+curve as something delta V
+
+plus some other thing--
+delta V Squared--
+
+plus some other
+thing-- delta V cubed--
+
+which we do all the time,
+there is an inherent assumption
+
+that an analytical expansion
+is possible around this point.
+
+Whereas if I gave you a
+function y that is x to the 5/3,
+
+around x of 0, you cannot
+write a Taylor series for it.
+
+OK?
+
+Essentially, this
+stability condition
+
+tells you a lot of things about
+signs of response functions.
+
+In the case of
+mechanical cases, it
+
+is really that if
+you have a spring,
+
+you better have a force
+constant that is positive,
+
+so that when you pull on it,
+the change in displacement
+
+has the right sign.
+
+It wants to be contracted.
+
+And similarly here,
+you are essentially
+
+compressing the gas.
+
+There's a thermal analogue of
+that sine which is worth making
+
+sure we know.
+
+Let's look at the
+case where we have
+
+a fixed number of particles.
+
+And then what we would
+have is that our dE
+
+is T dS plus Ji dxi.
+
+I am free to choose
+any set of variables.
+
+The interesting set of
+variables-- well, OK.
+
+So then stability implies
+that delta T delta
+
+S plus delta Ji delta xi with
+the sum over i is positive.
+
+Now, I can take a look
+at this expression
+
+and choose any set of variables
+to express these changes
+
+in terms of.
+
+So I'm going to choose for my
+variables temperature and xi.
+
+You see, the way that
+I've written it here,
+
+S, T, J, x appear
+completely equivalently.
+
+I could have chosen
+to express things
+
+in terms of S and
+J, T and J, S and x.
+
+But I choose to use T and x.
+
+All right, so what
+does that mean?
+
+It means that I write my
+delta S in terms of dS
+
+by dT at constant x dT,
+plus dS by dxi at constant T
+
+and other xj not
+equal to i, delta xi.
+
+I also need an expression
+for delta Ji here.
+
+so my delta Ji
+would be dJi by dT
+
+at constant x, delta T,
+plus dJi with respect
+
+to xj at constant T, an
+appropriate set of J's,
+
+delta xi-- delta xj.
+
+Sum over J implicit here.
+
+I substitute these--
+delta S and delta J--
+
+in the general form of
+the stability condition
+
+to get constraints
+applicable to combinations
+
+involving delta T and delta x.
+
+So I have to multiply
+delta S with delta T.
+
+I have to multiply delta
+Ji with delta xi here.
+
+Yes?
+
+AUDIENCE: So here,
+J is not equal to i.
+
+And then which one is J?
+
+[INAUDIBLE]
+
+PROFESSOR: OK.
+
+So let's say that I have S
+that is a function of-- I
+
+have x1 and x2.
+
+So here, I would
+have derivatives
+
+dS by dx1 times delta x1.
+
+I would have derivatives
+dS by dx2 times delta x2.
+
+In both cases, T is kept fixed.
+
+In this case, additionally,
+x2 is kept fixed.
+
+In this case, additionally,
+x1 is kept fixed.
+
+That's all.
+
+OK?
+
+So let's do that multiplication.
+
+We multiply a delta T here and
+we get dS by dT at constant x,
+
+delta T squared.
+
+We get here a term which is
+delta T delta xi, multiplying
+
+dS by dxi at constant
+T, and the others
+
+that I don't bother to write.
+
+But I note that I will
+get another term that
+
+is delta xi delta t from the
+second term, whose coefficient
+
+is dJi by dT at constant x.
+
+And I group those
+two terms together.
+
+And finally, we have
+the last term here,
+
+which is delta xi delta
+xj, dJi by dxj, constant T.
+
+And the constraint for all
+of these stability conditions
+
+that I have written,
+I have to be
+
+in the minimum of a potential.
+
+Any deviation that
+I make better lead
+
+to an increase in this
+combination, which
+
+is kind of equivalent
+to being at the minimum
+
+of some kind of
+potential energy.
+
+If you do some
+manipulations, this
+
+is also equivalent to
+being at the maximum
+
+of some entropy function.
+
+Now, let's look at that
+manipulation a little bit.
+
+Now, I happen to know
+that this form will
+
+simplify a little bit.
+
+And that's why I chose this
+combination of variables.
+
+And the simplification
+that will happen
+
+is that this entity is 0.
+
+So let me show you
+why that entity is 0.
+
+And that relies on one of
+these Maxwell relationships
+
+that I had.
+
+So let's find the
+Maxwell relation that
+
+is applicable to dS by
+dxi at constant T, which
+
+is what I have over here.
+
+OK, let's again start with
+dE being T dS plus ji dxi.
+
+I'm at fixed number
+of particles.
+
+I don't need to write
+the other term-- UDN.
+
+Unfortunately here, S is
+not the first derivative.
+
+So what I will do is I
+will look at E minus TS.
+
+That's going to turn
+this into minus S dT.
+
+Good.
+
+Ji dxi is exactly what I want
+because this will tell me
+
+something about the
+derivative in this fashion.
+
+dS by dxi at constant
+T is equal to what?
+
+It's taking the things
+in this fashion,
+
+which is dJi by
+dT at constant x.
+
+Good.
+
+So I can see that the sum
+total of these two terms is 0.
+
+And that's exactly
+what I have here.
+
+So this is 0 by
+Maxwell relation.
+
+OK?
+
+OK
+
+So having set that to
+0, I have two terms.
+
+One of them is this entity
+that goes with delta T squared.
+
+And the other is this entity--
+sum over i and J, delta xi,
+
+delta xj, dJi, dxj,
+constant T. And this--
+
+for any choice of delta x's
+and delta T's-- for any choice,
+
+it better be positive.
+
+So in particular,
+given this nice form
+
+that I have over
+here, I can certainly
+
+choose all of the delta x's
+to be 0, because I do things
+
+at constant displacement.
+
+And then what I have
+is that the whole thing
+
+is proportional to delta T
+squared and some coefficient.
+
+So that coefficient
+better be positive.
+
+So entropy should always
+be an increasing function
+
+of temperature at
+constant displacement.
+
+And the consequence of that is
+that heat capacities measure
+
+at constant displacement.
+
+So this is the
+heat capacity-- Cx.
+
+The general definition is
+you put some amount of heat
+
+into the system at
+constant displacement.
+
+So I have to specify
+the procedure
+
+by which heat is
+applied to the system
+
+and see how much this
+temperature changes.
+
+I can in principle do this
+sufficiently stability
+
+so I can measure precisely
+the changes in temperature
+
+infinitesimally.
+
+And then I can use
+the relationship
+
+between dQ and reversible
+heat-- so dS at constant x dT.
+
+And dS by dT at constant
+x is precisely the entity
+
+that we have looked
+at-- to be positive.
+
+So in the same way that a spring
+is stable-- if you pull on it,
+
+its extension should
+increase a little bit.
+
+And so the coefficient
+that relates
+
+the change in
+displacement corresponding
+
+to the change in force has
+to be positive for stability.
+
+Heat capacities must have
+this positivity in the sense
+
+that if you add
+heat to a system,
+
+its temperature should go up.
+
+It it went the other way, it
+would actually also violate
+
+the second law of
+thermodynamics.
+
+Yes?
+
+AUDIENCE: I'm a bit confused
+about the J notation
+
+that we used.
+
+The initial equation
+that we start
+
+has only-- it deals with i,
+but where does J come from?
+
+PROFESSOR: This equation.
+
+Which equation?
+
+Up here?
+
+AUDIENCE: So index J is
+just a dummy variable?
+
+[INAUDIBLE] that dE
+equals T dS equals Ji dSi.
+
+PROFESSOR: OK.
+
+Fine.
+
+So let's start from here.
+
+And part of the confusion is
+that I'm not really consistent.
+
+Whenever I write an
+index that is repeated,
+
+there is a so-called
+summation convention
+
+that you may have seen
+in quantum mechanics
+
+and other courses which
+says that the index that
+
+is repeated twice
+is summed over.
+
+So when I write ai bi, using
+the summation convention, what
+
+I mean is, sum over all
+possible values of i, ai, bi.
+
+So what I meant
+here is that there
+
+may be multiple ways of
+doing work on the system.
+
+So there could be pressure,
+there could be spring,
+
+there could be magnetic work.
+
+And if I do mechanical
+work on the system,
+
+the change in energy is the
+sum total of all different ways
+
+to do mechanical
+works, plus the heat
+
+that is supplied to the system.
+
+So that's statement number one.
+
+Now, I did something
+else here, which
+
+is that when I take a derivative
+of a function that depends
+
+on multiple variables-- so
+f depends on x1, x2, x3,
+
+xn-- then if I look
+at the change in this,
+
+any one of these
+variables can change
+
+by an amount that is dxi.
+
+And if the second
+variable changes,
+
+there is a corresponding
+contribution,
+
+which is df with respect
+to the second variable.
+
+And I have to add all of
+these things together.
+
+So if I'm again
+inconsistent, this
+
+is really what I
+mean, that when you
+
+do a change in a function
+of multiple variables,
+
+you would write it
+as dxi, df by dxi.
+
+If you use the
+summation convention,
+
+I have to really sum
+over all possibilities.
+
+Now, suppose I took one of
+these things, like df by dx3.
+
+So it's one of the
+derivatives here.
+
+And I took another derivative,
+or I looked at the change
+
+in this function.
+
+This function depends also
+on variables x1 through xn.
+
+So I have to look at the sum
+over all changes with respect
+
+to xj of df by dx3 delta xj.
+
+So you can see that
+automatically, I
+
+have kind of assumed
+some of these things
+
+as I write things rapidly.
+
+And if it is not clear, you have
+to spend a little bit of time
+
+writing things more in
+detail, because it's
+
+after all kind of
+simple algebra.
+
+Yes, did I make another mistake?
+
+Yes?
+
+AUDIENCE: Oh, not
+a mistake, just--
+
+PROFESSOR: Yes?
+
+AUDIENCE: When you were
+talking about mechanicals,
+
+you had a non-linear spring.
+
+You start pulling on it.
+
+At some point, it
+just increases.
+
+PROFESSOR: If it is a non-linear
+spring, yes, that's right.
+
+AUDIENCE: Can you provide
+example of thermodynamic system
+
+which, upon some
+threshold action upon it,
+
+becomes unstable?
+
+PROFESSOR: OK.
+
+I think I more or
+less had that example.
+
+Let's try to develop it
+a little bit further.
+
+So I said that typically, if
+I look at the pressure volume
+
+isotherms of a gas, it
+looks something like this.
+
+And I told you that
+there is actually
+
+some kind of a critical isotherm
+that looks something like this.
+
+And you may ask,
+well, what do things
+
+look below that for
+lower temperatures?
+
+And again, you
+probably know this,
+
+is that this is the
+temperature below which
+
+you have a transition to
+liquid gas coexistence.
+
+And so the isotherms
+would look like that.
+
+Now, it turns out that while
+these are true equilibrium
+
+things-- you would have
+to wait sufficiently long
+
+so that the system
+explores these isotherms--
+
+it is also possible
+in certain systems
+
+to do things a little
+bit more rapidly.
+
+And then when you
+go below, you will
+
+see a kind of remnant of that
+isotherm which kind of looks
+
+like this.
+
+So that isotherm would
+have portions of it
+
+that don't satisfy these
+conditions of stability.
+
+And the reason that you still
+get some remnant of it--
+
+not quite the entire thing.
+
+You get actually
+some portion here,
+
+some portion here-- is because
+you do things very rapidly
+
+and the system
+does not have time
+
+to explore the
+entire equilibrium.
+
+So that's one example
+that I can think
+
+of where some remnants
+of something that
+
+is like that non-linear
+noodle takes place.
+
+But even the non-linear
+noodle, you cannot really see
+
+in equilibrium.
+
+You can only see it
+when you're pulling it.
+
+And you can see that
+it is being extended.
+
+There is no equilibrium that
+you can see that has that.
+
+So if I want to find an analogue
+of that non-linear noodle
+
+showing instability, I'd better
+find some near-equilibrium
+
+condition.
+
+And this is the near-equilibrium
+condition that I can think of.
+
+There are a number of cases.
+
+And essentially, you've
+probably heard hysteresis
+
+in magnets and things like that.
+
+And by definition,
+hysteresis means
+
+that for the same
+set of conditions,
+
+you see multiple
+different states.
+
+So not both of them can
+be or multiple of them
+
+can be in equilibrium.
+
+And over some
+sufficient time scale,
+
+you would go from one
+behavior to another behavior.
+
+But if you explore the vicinity
+of the curves that correspond
+
+to these hysteretic
+behavior, you
+
+would see the signatures
+of these kinds
+
+of thermodynamic instabilities.
+
+There was one other part
+of this that maybe I
+
+will write a little bit
+in more detail, given
+
+the questions that were.
+
+Asked It is here I looked
+at this general condition
+
+for the case where
+the delta x's were 0.
+
+Let's look at the same
+thing for the case
+
+where delta T equals
+to 0, because then I
+
+have the condition that
+the Ji by the xj, delta xi,
+
+delta xj should be positive.
+
+And this was done at constant T.
+
+And to be more explicit, there
+is a sum over i and J in here.
+
+So if I'm doing things
+at constant temperature,
+
+I really have the analogue
+of the instability condition.
+
+What I have here, it is
+the same thing as this one.
+
+And if you think about this
+in a little bit more detail--
+
+let's say I have
+something like a gas.
+
+We have two ways of
+doing work on the system.
+
+I have dJ1 by dx1.
+
+I have dJ2 by dx2.
+
+I have dJ1 by dx2.
+
+I have dj2 by dx1.
+
+Essentially, this object,
+there are four of them.
+
+And those four I can put
+into something like this.
+
+And the statement
+that I have written
+
+is that this 2 by
+2 matrix, if it
+
+acts on the displacement delta
+x1 delta x2 on the right,
+
+and then gets contracted on the
+left by the same vector delta
+
+x1, delta x2, for any
+choice of the vector delta
+
+x1 delta x2, this
+better be positive.
+
+This is for two, but in
+general, this expression
+
+is going to be valid
+for any number.
+
+Now, what are the constraints
+that a matrix must satisfy
+
+so that irrespective of the
+choice of this displacement,
+
+you will get a positive result?
+
+Mathematically, that's caused
+a positive definite matrix.
+
+So one of the conditions that
+is certainly immediately obvious
+
+is that if I choose the case
+where delta x2 is 0, then
+
+the diagonal term
+that corresponds
+
+to that entity
+better be positive.
+
+So a matrix is positive
+definite if for every one
+
+of the diagonal elements,
+I have this condition.
+
+So this is actually something
+that we already saw.
+
+In the case of the
+gas, this would
+
+be something like minus dP by
+dV at constant temperature--
+
+be positive.
+
+This is the nature of
+these isotherms always
+
+going one way that
+I was drawing.
+
+AUDIENCE: Question.
+
+PROFESSOR: Yes.
+
+AUDIENCE: You're not summing
+over alpha now, are you?
+
+Or are you--
+
+PROFESSOR: Yes, I'm not.
+
+And I don't know how
+to write. [LAUGHS]
+
+Let's call it delta J1, x1.
+
+So all diagonal elements
+must be positive,
+
+but that's not enough.
+
+So I can write a matrix that
+has only positive elements
+
+along the diagonal, but
+off-diagonal elements such
+
+that the combination
+will give you
+
+negative values of
+this culmination
+
+for appropriate choices
+of delta x1 and delta x2.
+
+The thing that
+you really need is
+
+that all eigenvalues
+must be positive.
+
+It is not that easy to
+write down mathematically
+
+in general what that means
+in terms of multiple response
+
+functions.
+
+That's why this
+form of writing is
+
+much more compact and effective.
+
+It basically says, no matter
+what combination of elements
+
+you choose, you are at the
+bottom of the potential.
+
+You should not be able
+to go away from it.
+
+AUDIENCE: So the
+second statement
+
+is necessary and
+sufficient condition?
+
+PROFESSOR: This statement is
+necessary but not sufficient.
+
+This statement is
+equivalent to the meaning
+
+of what is a positive
+definite matrix.
+
+It is sufficient.
+
+Yes?
+
+AUDIENCE: Is there any
+physical interpretation
+
+to diagonalizing that matrix?
+
+PROFESSOR: It depends on
+the kind of the formations
+
+that you make.
+
+Like if I was really
+thinking about a gas
+
+where I allow some exchange
+with the surface or something
+
+else so that delta
+N is not equal to 0,
+
+the general form of this
+matrix in the case where
+
+I have pressure volume would
+be something like this.
+
+I would have minus dP by dV.
+
+I would have d mu by dN.
+
+I would have dP by dN.
+
+I would have d mu by dV.
+
+And I would have to make sure
+that this matrix is positive
+
+definite, so I know certainly
+that the compressibility
+
+by itself has to be positive.
+
+d mu by dN also
+has to be positive.
+
+But if I allow
+changes both in volume
+
+and the number of
+particles, then because
+
+of these off-diagonal terms,
+I have additional constraints.
+
+So for appropriate
+changes, it is
+
+sufficient to look at
+the diagonal terms.
+
+But for the entire set of
+possible transformations,
+
+it's not.
+
+Yes?
+
+AUDIENCE: If you look at
+different ways to do the work
+
+on the system-- so in
+this case, change volume,
+
+change number of particles,
+if you're saying forces have
+
+different dimensions, and
+if diagonalization of these
+
+metrics corresponds to inventing
+some new ways of acting
+
+on the system which are a linear
+combination of old ways like
+
+change volume a little
+and change particles--
+
+PROFESSOR: Change the
+number of particles, yes.
+
+AUDIENCE: Those are pretty
+weird manipulations,
+
+in terms of how to
+physically explain
+
+what is diagonalization matrix.
+
+PROFESSOR: OK.
+
+There is a question
+of dimensions,
+
+and there's a
+question of amount.
+
+So maybe what you
+are worried about
+
+is that if I make one them
+volume and the other pressure,
+
+one is extensive,
+one is intensive,
+
+and the response
+functions would have
+
+to carry something that
+is proportional to size.
+
+But then there are
+other conditions,
+
+let's say, where all of the
+variables are intensive.
+
+And then it's moving
+around in the space that
+
+is characterized, let's say, by
+pressure and chemical potential
+
+from one point to another point.
+
+And there is some generalized
+response that you would have,
+
+depending on which
+direction you go to.
+
+So essentially,
+I could certainly
+
+characterize various
+thermodynamic functions
+
+in this space P mu.
+
+And what I know is that I cannot
+write any function in this
+
+two-parameter space that
+would be consistent with
+
+the thermodynamic
+principles of stability.
+
+I have to have some
+kind of convexity.
+
+So certainly, what
+typically-- let's say again,
+
+going back to my favorite
+example here-- what people do
+
+and what we will
+do later on is we
+
+specify that you have
+some particular pressure
+
+and volume of an
+interacting gas.
+
+And there is no way
+that we can calculate
+
+the thermodynamic properties
+of that system exactly.
+
+We try to construct
+a free energy
+
+as a function of
+these variables.
+
+And that free energy
+will be approximate based
+
+on some ideas.
+
+And then we will see that that
+free energy that I construct
+
+in some places will violate
+the conditions of stability.
+
+And then I know that that free
+energy that I constructed,
+
+let's say on the assumption
+that the box that I have
+
+is uniformly covered
+by some material,
+
+that assumption is violated.
+
+And maybe what has happened
+is that part of the volume
+
+is a liquid and part
+of the volume is gas.
+
+So we will do precisely
+that exercise later on.
+
+We will choose a
+pair of variables.
+
+We will try to construct a
+free energy function out.
+
+We make the assumption that
+the box is uniformly occupied
+
+with the gas at some density.
+
+Based on that, we estimate its
+energy, entropy, et cetera.
+
+We construct a free
+energy function out.
+
+And then we will see that
+that energy function violates
+
+the compressibility
+condition at some point.
+
+So we know that, oh,
+we made a mistake.
+
+The assumption that it is
+uniformly occupying this box
+
+is wrong.
+
+All right, any other questions?
+
+Yes?
+
+AUDIENCE: One of the
+things that confuses me
+
+about thermodynamics
+in general is
+
+the limits of its applicability.
+
+We think of it as
+being very general,
+
+applying to many
+different systems.
+
+For example, if we
+had two bar magnets
+
+and we had the north pole
+close to the south pole
+
+of the other one, and I
+thought of the magnetic field
+
+in between, is it
+conceivable to think
+
+of that as a
+thermodynamic system?
+
+PROFESSOR: You can
+think of the magnet
+
+as a thermodynamic system.
+
+And you can certainly
+look at two of them,
+
+including the electromagnetic
+field that surrounds them.
+
+And there would be
+some conditions,
+
+like if you were to jiggle
+these things with respect
+
+to each other-- and you would
+maintain the entire thing
+
+in a box that prevented escape
+of electromagnetic waves
+
+or heat to the outside--
+that eventually
+
+this jiggling of the two magnets
+will lead to their coming
+
+to equilibrium but at
+a higher temperature.
+
+So this is what I'm saying.
+
+So imagine that you have-- let's
+for simplicity think of, again,
+
+one big magnet that
+you don't move,
+
+and one small magnet here that
+you externally jiggle around.
+
+And then you remove
+the source of work.
+
+You wait for a while.
+
+And then you find
+that after a while,
+
+this thing comes
+to an equilibrium.
+
+You ask, where did that
+kinetic energy go to?
+
+You had some kinetic energy
+that you had set into this,
+
+and the kinetic
+energy disappeared.
+
+And I assume that
+there are conditions
+
+that the kinetic energy could
+not have escaped from this box.
+
+So the only thing that
+could have happened
+
+is that that kinetic
+energy heated up
+
+the air of the box, the
+magnet, or whatever you have.
+
+So thermodynamics is applicable
+in that sense to your system.
+
+Now, if you ask me, is
+it applicable to having
+
+a single electron spin
+that is polarized because
+
+of the magnetic field
+and some condition
+
+that I set it to oscillate,
+then it's not applicable,
+
+because then I know some
+quantum mechanical rules that
+
+govern this.
+
+There may be in
+some circumstances
+
+some conservation law that says
+this with oscillate forever.
+
+If it doesn't oscillate
+forever, there's
+
+presumably a
+transition matrix that
+
+says it will admit a particular
+photon of a particular energy.
+
+And I have to ask what
+happened to that photon.
+
+So what we will see later
+on is that thermodynamics
+
+is very powerful, but it's
+not a fundamental theory
+
+in this sense that
+the quantum mechanics
+
+that governs the spins.
+
+And the reason that this works
+for the case of the magnet
+
+is because the magnet has
+billions of spins in it--
+
+billions and billions
+of spins, or whatever.
+
+So it is the of large
+numbers that ultimately
+
+allows you to translate
+the rules of motion
+
+into a well-defined
+theory that is
+
+consistent with thermodynamics.
+
+AUDIENCE: I know that my
+question seemed off-topic.
+
+But the reason why I asked
+about this particular system
+
+is because I would
+think that it doesn't
+
+have a positive compressibility.
+
+Like if you pull the two
+magnets apart very slowly,
+
+the force pulling them
+together decreases
+
+instead of increasing
+like with the rubber band.
+
+PROFESSOR: OK.
+
+It may be that you have to
+add additional agents in order
+
+to make the whole system work.
+
+So it may be that the
+picture that I had in mind
+
+was that you have
+the magnet that
+
+is being pushed up and down.
+
+And I really do put
+a number of springs
+
+that make sure there exists
+an equilibrium position.
+
+If there is no mechanical
+equilibrium position,
+
+then the story is not whether
+or not to thermodynamic applies.
+
+It's a question of whether or
+not there is an equilibrium.
+
+So in order for me to
+talk about thermodynamics
+
+I need to know that there
+is an eventual equilibrium.
+
+and that's why I actually recast
+the answer to your question,
+
+eventually getting rid of
+the kinetic energy of this
+
+so that I have a system
+that is in equilibrium.
+
+If there are things that
+are not in equilibrium,
+
+all bets are off.
+
+Thermodynamics is the science of
+things that are in equilibrium.
+
+Other questions?
+
+All right, so there is only one
+minor part of our description--
+
+rapid survey of
+thermodynamics-- that is left.
+
+And that's the third
+law of thermodynamics
+
+and that has to do something
+with the behavior of things
+
+as you go towards
+the limit of the zero
+
+of thermodynamic temperature.
+
+And I think we will spend maybe
+10, 15 minutes next lecture
+
+talking about the third
+law of thermodynamics.
+
+Probably from my
+perspective, that
+
+is enough time with
+respect towards the time
+
+we spend on the other
+laws of thermodynamics,
+
+because as I will
+emphasize to you also,
+
+the third law of
+thermodynamics is in some sense
+
+less valid than the others.
+
+It's certainly correct
+and it is valid.
+
+It is just that its validity
+rests on other things than what
+
+I was emphasizing
+right now, which
+
+is the large number
+of degrees of freedom.
+
+You could have a large
+number of degrees
+
+of freedom in a world
+that is governed
+
+by classic laws of physics, and
+the third law of thermodynamics
+
+would be violated.
+
+So it is a condition
+that we live
+
+in a world that is governed by
+quantum mechanics that tells us
+
+about the third law, as
+we will discuss next time.
\ No newline at end of file
diff --git a/b04CichdN5g.txt b/b04CichdN5g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..63449604ad29c444d8321f58cf60f70761021b5f
--- /dev/null
+++ b/b04CichdN5g.txt
@@ -0,0 +1,987 @@
+align:start position:0%
+ 
+la
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good morning
+
+ align:start position:0%
+good morning
+ 
+
+ align:start position:0%
+good morning
+students morning Mr Su can anyone tell
+
+ align:start position:0%
+students morning Mr Su can anyone tell
+ 
+
+ align:start position:0%
+students morning Mr Su can anyone tell
+me the answer please I I can is
+
+ align:start position:0%
+me the answer please I I can is
+ 
+
+ align:start position:0%
+me the answer please I I can is
+everything clear yes perfectly clear are
+
+ align:start position:0%
+everything clear yes perfectly clear are
+ 
+
+ align:start position:0%
+everything clear yes perfectly clear are
+there any other
+
+ align:start position:0%
+there any other
+ 
+
+ align:start position:0%
+there any other
+questions no no questions I will see you
+
+ align:start position:0%
+questions no no questions I will see you
+ 
+
+ align:start position:0%
+questions no no questions I will see you
+on Tuesday thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you wait a minute that's not what
+
+ align:start position:0%
+you wait a minute that's not what
+ 
+
+ align:start position:0%
+you wait a minute that's not what
+happens in real life
+
+ align:start position:0%
+happens in real life
+ 
+
+ align:start position:0%
+happens in real life
+actual MIT undergraduates often come to
+
+ align:start position:0%
+actual MIT undergraduates often come to
+ 
+
+ align:start position:0%
+actual MIT undergraduates often come to
+class on 3 hours of
+
+ align:start position:0%
+class on 3 hours of
+ 
+
+ align:start position:0%
+class on 3 hours of
+sleep can anyone tell me the answer
+
+ align:start position:0%
+sleep can anyone tell me the answer
+ 
+
+ align:start position:0%
+sleep can anyone tell me the answer
+please sometimes they're afraid to
+
+ align:start position:0%
+please sometimes they're afraid to
+ 
+
+ align:start position:0%
+please sometimes they're afraid to
+volunteer what might be the wrong answer
+
+ align:start position:0%
+volunteer what might be the wrong answer
+ 
+
+ align:start position:0%
+volunteer what might be the wrong answer
+learn in lecture by considering a simple
+
+ align:start position:0%
+learn in lecture by considering a simple
+ 
+
+ align:start position:0%
+learn in lecture by considering a simple
+example they're not always paying
+
+ align:start position:0%
+example they're not always paying
+ 
+
+ align:start position:0%
+example they're not always paying
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+what and they might not understand what
+
+ align:start position:0%
+what and they might not understand what
+ 
+
+ align:start position:0%
+what and they might not understand what
+you thought you explained well is
+
+ align:start position:0%
+you thought you explained well is
+ 
+
+ align:start position:0%
+you thought you explained well is
+everything clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how can you be a successful ta at
+
+ align:start position:0%
+so how can you be a successful ta at
+ 
+
+ align:start position:0%
+so how can you be a successful ta at
+MIT try thinking of your class as a
+
+ align:start position:0%
+MIT try thinking of your class as a
+ 
+
+ align:start position:0%
+MIT try thinking of your class as a
+popular website that visitors come back
+
+ align:start position:0%
+popular website that visitors come back
+ 
+
+ align:start position:0%
+popular website that visitors come back
+to again and again what makes a website
+
+ align:start position:0%
+to again and again what makes a website
+ 
+
+ align:start position:0%
+to again and again what makes a website
+userfriendly user friendly to me means
+
+ align:start position:0%
+userfriendly user friendly to me means
+ 
+
+ align:start position:0%
+userfriendly user friendly to me means
+that um in order to complete the task at
+
+ align:start position:0%
+that um in order to complete the task at
+ 
+
+ align:start position:0%
+that um in order to complete the task at
+hand the website is designed in a way
+
+ align:start position:0%
+hand the website is designed in a way
+ 
+
+ align:start position:0%
+hand the website is designed in a way
+that's logical yeah um I feel like
+
+ align:start position:0%
+that's logical yeah um I feel like
+ 
+
+ align:start position:0%
+that's logical yeah um I feel like
+format just a clean simple format is
+
+ align:start position:0%
+format just a clean simple format is
+ 
+
+ align:start position:0%
+format just a clean simple format is
+really nice it's not cluttered and messy
+
+ align:start position:0%
+really nice it's not cluttered and messy
+ 
+
+ align:start position:0%
+really nice it's not cluttered and messy
+the most important things for a
+
+ align:start position:0%
+the most important things for a
+ 
+
+ align:start position:0%
+the most important things for a
+userfriendly website is a clear
+
+ align:start position:0%
+userfriendly website is a clear
+ 
+
+ align:start position:0%
+userfriendly website is a clear
+interface simple categories and a search
+
+ align:start position:0%
+interface simple categories and a search
+ 
+
+ align:start position:0%
+interface simple categories and a search
+option and an accessible language so
+
+ align:start position:0%
+option and an accessible language so
+ 
+
+ align:start position:0%
+option and an accessible language so
+being able to find things very
+
+ align:start position:0%
+being able to find things very
+ 
+
+ align:start position:0%
+being able to find things very
+efficiently and quickly is definitely
+
+ align:start position:0%
+efficiently and quickly is definitely
+ 
+
+ align:start position:0%
+efficiently and quickly is definitely
+pretty important I I think it's more
+
+ align:start position:0%
+pretty important I I think it's more
+ 
+
+ align:start position:0%
+pretty important I I think it's more
+user friendly when you can actually
+
+ align:start position:0%
+user friendly when you can actually
+ 
+
+ align:start position:0%
+user friendly when you can actually
+understand what you what they want you
+
+ align:start position:0%
+understand what you what they want you
+ 
+
+ align:start position:0%
+understand what you what they want you
+to do and where things are being able to
+
+ align:start position:0%
+to do and where things are being able to
+ 
+
+ align:start position:0%
+to do and where things are being able to
+find the right things um in a way that's
+
+ align:start position:0%
+find the right things um in a way that's
+ 
+
+ align:start position:0%
+find the right things um in a way that's
+easy in other words a userfriendly
+
+ align:start position:0%
+easy in other words a userfriendly
+ 
+
+ align:start position:0%
+easy in other words a userfriendly
+website should be designed uh with the
+
+ align:start position:0%
+website should be designed uh with the
+ 
+
+ align:start position:0%
+website should be designed uh with the
+with the thinking that to make the user
+
+ align:start position:0%
+with the thinking that to make the user
+ 
+
+ align:start position:0%
+with the thinking that to make the user
+feel happy and easy instead of making
+
+ align:start position:0%
+feel happy and easy instead of making
+ 
+
+ align:start position:0%
+feel happy and easy instead of making
+the computer Engineers to feel happy at
+
+ align:start position:0%
+the computer Engineers to feel happy at
+ 
+
+ align:start position:0%
+the computer Engineers to feel happy at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+easy what if the engineer is a teacher
+
+ align:start position:0%
+easy what if the engineer is a teacher
+ 
+
+ align:start position:0%
+easy what if the engineer is a teacher
+and the user a
+
+ align:start position:0%
+and the user a
+ 
+
+ align:start position:0%
+and the user a
+student the main principle of
+
+ align:start position:0%
+student the main principle of
+ 
+
+ align:start position:0%
+student the main principle of
+accessibility should be the same a
+
+ align:start position:0%
+accessibility should be the same a
+ 
+
+ align:start position:0%
+accessibility should be the same a
+website should be simple clean and also
+
+ align:start position:0%
+website should be simple clean and also
+ 
+
+ align:start position:0%
+website should be simple clean and also
+like should have where you want to go
+
+ align:start position:0%
+like should have where you want to go
+ 
+
+ align:start position:0%
+like should have where you want to go
+right away and a teacher should be able
+
+ align:start position:0%
+right away and a teacher should be able
+ 
+
+ align:start position:0%
+right away and a teacher should be able
+to judge where the students need what
+
+ align:start position:0%
+to judge where the students need what
+ 
+
+ align:start position:0%
+to judge where the students need what
+the students needs where the students
+
+ align:start position:0%
+the students needs where the students
+ 
+
+ align:start position:0%
+the students needs where the students
+want to go and adapt in that way I guess
+
+ align:start position:0%
+want to go and adapt in that way I guess
+ 
+
+ align:start position:0%
+want to go and adapt in that way I guess
+like the search button would be asking
+
+ align:start position:0%
+like the search button would be asking
+ 
+
+ align:start position:0%
+like the search button would be asking
+the ti asking the professor for more
+
+ align:start position:0%
+the ti asking the professor for more
+ 
+
+ align:start position:0%
+the ti asking the professor for more
+information it's not necessarily that
+
+ align:start position:0%
+information it's not necessarily that
+ 
+
+ align:start position:0%
+information it's not necessarily that
+everyone is going to be your friend but
+
+ align:start position:0%
+everyone is going to be your friend but
+ 
+
+ align:start position:0%
+everyone is going to be your friend but
+it's more
+
+ align:start position:0%
+it's more
+ 
+
+ align:start position:0%
+it's more
+about being easy to understand in terms
+
+ align:start position:0%
+about being easy to understand in terms
+ 
+
+ align:start position:0%
+about being easy to understand in terms
+of having a clear interface just a
+
+ align:start position:0%
+of having a clear interface just a
+ 
+
+ align:start position:0%
+of having a clear interface just a
+simple structure of the class something
+
+ align:start position:0%
+simple structure of the class something
+ 
+
+ align:start position:0%
+simple structure of the class something
+students can expect like the lecture
+
+ align:start position:0%
+students can expect like the lecture
+ 
+
+ align:start position:0%
+students can expect like the lecture
+goes the lectures go the same way the
+
+ align:start position:0%
+goes the lectures go the same way the
+ 
+
+ align:start position:0%
+goes the lectures go the same way the
+recitation go the same way and something
+
+ align:start position:0%
+recitation go the same way and something
+ 
+
+ align:start position:0%
+recitation go the same way and something
+that students can expect so organization
+
+ align:start position:0%
+that students can expect so organization
+ 
+
+ align:start position:0%
+that students can expect so organization
+and predictability are key to the
+
+ align:start position:0%
+and predictability are key to the
+ 
+
+ align:start position:0%
+and predictability are key to the
+userfriendly class but um planning that
+
+ align:start position:0%
+userfriendly class but um planning that
+ 
+
+ align:start position:0%
+userfriendly class but um planning that
+way in The Logical session where you
+
+ align:start position:0%
+way in The Logical session where you
+ 
+
+ align:start position:0%
+way in The Logical session where you
+like review the things that are
+
+ align:start position:0%
+like review the things that are
+ 
+
+ align:start position:0%
+like review the things that are
+necessary and then um going into problem
+
+ align:start position:0%
+necessary and then um going into problem
+ 
+
+ align:start position:0%
+necessary and then um going into problem
+practice problems and then going into um
+
+ align:start position:0%
+practice problems and then going into um
+ 
+
+ align:start position:0%
+practice problems and then going into um
+going over what were the right answers I
+
+ align:start position:0%
+going over what were the right answers I
+ 
+
+ align:start position:0%
+going over what were the right answers I
+thought that was like pretty user
+
+ align:start position:0%
+thought that was like pretty user
+ 
+
+ align:start position:0%
+thought that was like pretty user
+friendly for a student cuz um it was a
+
+ align:start position:0%
+friendly for a student cuz um it was a
+ 
+
+ align:start position:0%
+friendly for a student cuz um it was a
+good review and then get practice so
+
+ align:start position:0%
+good review and then get practice so
+ 
+
+ align:start position:0%
+good review and then get practice so
+it's like logical for today's recitation
+
+ align:start position:0%
+it's like logical for today's recitation
+ 
+
+ align:start position:0%
+it's like logical for today's recitation
+we're going to do the TA acts as a guide
+
+ align:start position:0%
+we're going to do the TA acts as a guide
+ 
+
+ align:start position:0%
+we're going to do the TA acts as a guide
+for the students it's important
+
+ align:start position:0%
+for the students it's important
+ 
+
+ align:start position:0%
+for the students it's important
+to ex well explain the learning
+
+ align:start position:0%
+to ex well explain the learning
+ 
+
+ align:start position:0%
+to ex well explain the learning
+objectives of the class earlier on have
+
+ align:start position:0%
+objectives of the class earlier on have
+ 
+
+ align:start position:0%
+objectives of the class earlier on have
+just like an air of confidence and be
+
+ align:start position:0%
+just like an air of confidence and be
+ 
+
+ align:start position:0%
+just like an air of confidence and be
+able to direct the recitation a very big
+
+ align:start position:0%
+able to direct the recitation a very big
+ 
+
+ align:start position:0%
+able to direct the recitation a very big
+expectation in a recitation is for the
+
+ align:start position:0%
+expectation in a recitation is for the
+ 
+
+ align:start position:0%
+expectation in a recitation is for the
+TA to provide us with the big picture of
+
+ align:start position:0%
+TA to provide us with the big picture of
+ 
+
+ align:start position:0%
+TA to provide us with the big picture of
+the concepts you know the TA is
+
+ align:start position:0%
+the concepts you know the TA is
+ 
+
+ align:start position:0%
+the concepts you know the TA is
+approachable and supportive you need to
+
+ align:start position:0%
+approachable and supportive you need to
+ 
+
+ align:start position:0%
+approachable and supportive you need to
+feel that you can approach them and ask
+
+ align:start position:0%
+feel that you can approach them and ask
+ 
+
+ align:start position:0%
+feel that you can approach them and ask
+questions without any problem and
+
+ align:start position:0%
+questions without any problem and
+ 
+
+ align:start position:0%
+questions without any problem and
+knowledgeable the most important thing
+
+ align:start position:0%
+knowledgeable the most important thing
+ 
+
+ align:start position:0%
+knowledgeable the most important thing
+for um a TA is that they have to have a
+
+ align:start position:0%
+for um a TA is that they have to have a
+ 
+
+ align:start position:0%
+for um a TA is that they have to have a
+very solid understanding of what's going
+
+ align:start position:0%
+very solid understanding of what's going
+ 
+
+ align:start position:0%
+very solid understanding of what's going
+on um in the material but is knowledge
+
+ align:start position:0%
+on um in the material but is knowledge
+ 
+
+ align:start position:0%
+on um in the material but is knowledge
+enough unfortunately it's not enough to
+
+ align:start position:0%
+enough unfortunately it's not enough to
+ 
+
+ align:start position:0%
+enough unfortunately it's not enough to
+Simply Be knowledgeable about the
+
+ align:start position:0%
+Simply Be knowledgeable about the
+ 
+
+ align:start position:0%
+Simply Be knowledgeable about the
+subject it's the way you presented the
+
+ align:start position:0%
+subject it's the way you presented the
+ 
+
+ align:start position:0%
+subject it's the way you presented the
+way it communicated they're all very
+
+ align:start position:0%
+way it communicated they're all very
+ 
+
+ align:start position:0%
+way it communicated they're all very
+smart I know they all know what they're
+
+ align:start position:0%
+smart I know they all know what they're
+ 
+
+ align:start position:0%
+smart I know they all know what they're
+talking about so it's just how they can
+
+ align:start position:0%
+talking about so it's just how they can
+ 
+
+ align:start position:0%
+talking about so it's just how they can
+communicate that to us so what is good
+
+ align:start position:0%
+communicate that to us so what is good
+ 
+
+ align:start position:0%
+communicate that to us so what is good
+communication in the userfriendly
+
+ align:start position:0%
+communication in the userfriendly
+ 
+
+ align:start position:0%
+communication in the userfriendly
+classroom the biggest thing that came
+
+ align:start position:0%
+classroom the biggest thing that came
+ 
+
+ align:start position:0%
+classroom the biggest thing that came
+across my mind was definitely like how
+
+ align:start position:0%
+across my mind was definitely like how
+ 
+
+ align:start position:0%
+across my mind was definitely like how
+they uh answered questions and like the
+
+ align:start position:0%
+they uh answered questions and like the
+ 
+
+ align:start position:0%
+they uh answered questions and like the
+feedback they got from the students and
+
+ align:start position:0%
+feedback they got from the students and
+ 
+
+ align:start position:0%
+feedback they got from the students and
+how they responded to that it's not the
+
+ align:start position:0%
+how they responded to that it's not the
+ 
+
+ align:start position:0%
+how they responded to that it's not the
+same when they read a paper and they
+
+ align:start position:0%
+same when they read a paper and they
+ 
+
+ align:start position:0%
+same when they read a paper and they
+just write the problem in the board and
+
+ align:start position:0%
+just write the problem in the board and
+ 
+
+ align:start position:0%
+just write the problem in the board and
+solve the problem than explaining why is
+
+ align:start position:0%
+solve the problem than explaining why is
+ 
+
+ align:start position:0%
+solve the problem than explaining why is
+it going like this or why is it working
+
+ align:start position:0%
+it going like this or why is it working
+ 
+
+ align:start position:0%
+it going like this or why is it working
+like this I think um just the
+
+ align:start position:0%
+like this I think um just the
+ 
+
+ align:start position:0%
+like this I think um just the
+willingness to clarify is very very
+
+ align:start position:0%
+willingness to clarify is very very
+ 
+
+ align:start position:0%
+willingness to clarify is very very
+important being patient and being able
+
+ align:start position:0%
+important being patient and being able
+ 
+
+ align:start position:0%
+important being patient and being able
+to explain the same concept in different
+
+ align:start position:0%
+to explain the same concept in different
+ 
+
+ align:start position:0%
+to explain the same concept in different
+ways and they can actually explain it to
+
+ align:start position:0%
+ways and they can actually explain it to
+ 
+
+ align:start position:0%
+ways and they can actually explain it to
+you at a basic undergrad level in the
+
+ align:start position:0%
+you at a basic undergrad level in the
+ 
+
+ align:start position:0%
+you at a basic undergrad level in the
+next videos we will learn communication
+
+ align:start position:0%
+next videos we will learn communication
+ 
+
+ align:start position:0%
+next videos we will learn communication
+skills and strategies to meet students
+
+ align:start position:0%
+skills and strategies to meet students
+ 
+
+ align:start position:0%
+skills and strategies to meet students
+expectations and create a userfriendly
+
+ align:start position:0%
+expectations and create a userfriendly
+ 
+
+ align:start position:0%
+expectations and create a userfriendly
+classroom
\ No newline at end of file
diff --git a/b0VqqwHLqcI.txt b/b0VqqwHLqcI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..39fb2348e54c32fd76bcadd6cc2ae0aeaf9a26d7
--- /dev/null
+++ b/b0VqqwHLqcI.txt
@@ -0,0 +1,19752 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu let's talk about the uh V
+
+ align:start position:0%
+ocw.mit.edu let's talk about the uh V
+ 
+
+ align:start position:0%
+ocw.mit.edu let's talk about the uh V
+model here we are interesting we have a
+
+ align:start position:0%
+model here we are interesting we have a
+ 
+
+ align:start position:0%
+model here we are interesting we have a
+little bit of a lag here so the um life
+
+ align:start position:0%
+little bit of a lag here so the um life
+ 
+
+ align:start position:0%
+little bit of a lag here so the um life
+cycle management essentially is our last
+
+ align:start position:0%
+cycle management essentially is our last
+ 
+
+ align:start position:0%
+cycle management essentially is our last
+topic for today and that sort of
+
+ align:start position:0%
+topic for today and that sort of
+ 
+
+ align:start position:0%
+topic for today and that sort of
+completes the the V and then
+
+ align:start position:0%
+completes the the V and then
+ 
+
+ align:start position:0%
+completes the the V and then
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+manufacturing so what I'd like to cover
+
+ align:start position:0%
+manufacturing so what I'd like to cover
+ 
+
+ align:start position:0%
+manufacturing so what I'd like to cover
+today is essentially a definition of
+
+ align:start position:0%
+today is essentially a definition of
+ 
+
+ align:start position:0%
+today is essentially a definition of
+management what does it include what do
+
+ align:start position:0%
+management what does it include what do
+ 
+
+ align:start position:0%
+management what does it include what do
+we mean by that and then focus on the
+
+ align:start position:0%
+we mean by that and then focus on the
+ 
+
+ align:start position:0%
+we mean by that and then focus on the
+life cycle properties also known as the
+
+ align:start position:0%
+life cycle properties also known as the
+ 
+
+ align:start position:0%
+life cycle properties also known as the
+IL um discuss a little bit where they
+
+ align:start position:0%
+IL um discuss a little bit where they
+ 
+
+ align:start position:0%
+IL um discuss a little bit where they
+come from how much we know about them
+
+ align:start position:0%
+come from how much we know about them
+ 
+
+ align:start position:0%
+come from how much we know about them
+then the bulk of the discussion is going
+
+ align:start position:0%
+then the bulk of the discussion is going
+ 
+
+ align:start position:0%
+then the bulk of the discussion is going
+to be a case study called
+
+ align:start position:0%
+to be a case study called
+ 
+
+ align:start position:0%
+to be a case study called
+reconfiguration communication satellite
+
+ align:start position:0%
+reconfiguration communication satellite
+ 
+
+ align:start position:0%
+reconfiguration communication satellite
+constellations and this sort of explains
+
+ align:start position:0%
+constellations and this sort of explains
+ 
+
+ align:start position:0%
+constellations and this sort of explains
+the idea that a system once you brought
+
+ align:start position:0%
+the idea that a system once you brought
+ 
+
+ align:start position:0%
+the idea that a system once you brought
+a system into operation that's not the
+
+ align:start position:0%
+a system into operation that's not the
+ 
+
+ align:start position:0%
+a system into operation that's not the
+end of the story that system is going to
+
+ align:start position:0%
+end of the story that system is going to
+ 
+
+ align:start position:0%
+end of the story that system is going to
+continue to live and change and be
+
+ align:start position:0%
+continue to live and change and be
+ 
+
+ align:start position:0%
+continue to live and change and be
+modified over its life uh I'll try to
+
+ align:start position:0%
+modified over its life uh I'll try to
+ 
+
+ align:start position:0%
+modified over its life uh I'll try to
+summarize some of the key concepts of
+
+ align:start position:0%
+summarize some of the key concepts of
+ 
+
+ align:start position:0%
+summarize some of the key concepts of
+the whole semester and then I have like
+
+ align:start position:0%
+the whole semester and then I have like
+ 
+
+ align:start position:0%
+the whole semester and then I have like
+one slide on career and study
+
+ align:start position:0%
+one slide on career and study
+ 
+
+ align:start position:0%
+one slide on career and study
+recommendations if you want to go
+
+ align:start position:0%
+recommendations if you want to go
+ 
+
+ align:start position:0%
+recommendations if you want to go
+further into systems
+
+ align:start position:0%
+further into systems
+ 
+
+ align:start position:0%
+further into systems
+engineering um so life cycle
+
+ align:start position:0%
+engineering um so life cycle
+ 
+
+ align:start position:0%
+engineering um so life cycle
+management um so this is my definition
+
+ align:start position:0%
+management um so this is my definition
+ 
+
+ align:start position:0%
+management um so this is my definition
+of what life cycle management is it's
+
+ align:start position:0%
+of what life cycle management is it's
+ 
+
+ align:start position:0%
+of what life cycle management is it's
+essentially the active engagement of
+
+ align:start position:0%
+essentially the active engagement of
+ 
+
+ align:start position:0%
+essentially the active engagement of
+it's the active engagement of all the
+
+ align:start position:0%
+it's the active engagement of all the
+ 
+
+ align:start position:0%
+it's the active engagement of all the
+stakeholders with the system between the
+
+ align:start position:0%
+stakeholders with the system between the
+ 
+
+ align:start position:0%
+stakeholders with the system between the
+time when it starts to operates you've
+
+ align:start position:0%
+time when it starts to operates you've
+ 
+
+ align:start position:0%
+time when it starts to operates you've
+done the commissioning you've done the
+
+ align:start position:0%
+done the commissioning you've done the
+ 
+
+ align:start position:0%
+done the commissioning you've done the
+operations until you decide to
+
+ align:start position:0%
+operations until you decide to
+ 
+
+ align:start position:0%
+operations until you decide to
+decommission retire the system so it's
+
+ align:start position:0%
+decommission retire the system so it's
+ 
+
+ align:start position:0%
+decommission retire the system so it's
+the during the whole operational life
+
+ align:start position:0%
+the during the whole operational life
+ 
+
+ align:start position:0%
+the during the whole operational life
+and what you want to do is you want to
+
+ align:start position:0%
+and what you want to do is you want to
+ 
+
+ align:start position:0%
+and what you want to do is you want to
+maximize the value that you gain from
+
+ align:start position:0%
+maximize the value that you gain from
+ 
+
+ align:start position:0%
+maximize the value that you gain from
+the system's existence and so uh life
+
+ align:start position:0%
+the system's existence and so uh life
+ 
+
+ align:start position:0%
+the system's existence and so uh life
+cycle management starts from the very
+
+ align:start position:0%
+cycle management starts from the very
+ 
+
+ align:start position:0%
+cycle management starts from the very
+very very start and so I listed here
+
+ align:start position:0%
+very very start and so I listed here
+ 
+
+ align:start position:0%
+very very start and so I listed here
+some activities that are included in
+
+ align:start position:0%
+some activities that are included in
+ 
+
+ align:start position:0%
+some activities that are included in
+life cycle management so obviously daily
+
+ align:start position:0%
+life cycle management so obviously daily
+ 
+
+ align:start position:0%
+life cycle management so obviously daily
+operations you know monitoring is the
+
+ align:start position:0%
+operations you know monitoring is the
+ 
+
+ align:start position:0%
+operations you know monitoring is the
+system working uh as expected uh
+
+ align:start position:0%
+system working uh as expected uh
+ 
+
+ align:start position:0%
+system working uh as expected uh
+training and certification of The
+
+ align:start position:0%
+training and certification of The
+ 
+
+ align:start position:0%
+training and certification of The
+Operators sometimes you know in long
+
+ align:start position:0%
+Operators sometimes you know in long
+ 
+
+ align:start position:0%
+Operators sometimes you know in long
+lived systems the people that were the
+
+ align:start position:0%
+lived systems the people that were the
+ 
+
+ align:start position:0%
+lived systems the people that were the
+early operators generation one are not
+
+ align:start position:0%
+early operators generation one are not
+ 
+
+ align:start position:0%
+early operators generation one are not
+necessarily the people who are going to
+
+ align:start position:0%
+necessarily the people who are going to
+ 
+
+ align:start position:0%
+necessarily the people who are going to
+operate for the whole life so you have
+
+ align:start position:0%
+operate for the whole life so you have
+ 
+
+ align:start position:0%
+operate for the whole life so you have
+to you know you have to have new people
+
+ align:start position:0%
+to you know you have to have new people
+ 
+
+ align:start position:0%
+to you know you have to have new people
+operate the maybe one of the most
+
+ align:start position:0%
+operate the maybe one of the most
+ 
+
+ align:start position:0%
+operate the maybe one of the most
+extreme examples of that is an airplane
+
+ align:start position:0%
+extreme examples of that is an airplane
+ 
+
+ align:start position:0%
+extreme examples of that is an airplane
+known as the B-52 have you heard of this
+
+ align:start position:0%
+known as the B-52 have you heard of this
+ 
+
+ align:start position:0%
+known as the B-52 have you heard of this
+this airplane might be the first
+
+ align:start position:0%
+this airplane might be the first
+ 
+
+ align:start position:0%
+this airplane might be the first
+airplane that actually has a 100-year
+
+ align:start position:0%
+airplane that actually has a 100-year
+ 
+
+ align:start position:0%
+airplane that actually has a 100-year
+operational life and there are
+
+ align:start position:0%
+operational life and there are
+ 
+
+ align:start position:0%
+operational life and there are
+apparently maybe you uh Air Force guys
+
+ align:start position:0%
+apparently maybe you uh Air Force guys
+ 
+
+ align:start position:0%
+apparently maybe you uh Air Force guys
+at MIT you can confirm this that there's
+
+ align:start position:0%
+at MIT you can confirm this that there's
+ 
+
+ align:start position:0%
+at MIT you can confirm this that there's
+actually like you know the the
+
+ align:start position:0%
+actually like you know the the
+ 
+
+ align:start position:0%
+actually like you know the the
+grandfather was the first you know
+
+ align:start position:0%
+grandfather was the first you know
+ 
+
+ align:start position:0%
+grandfather was the first you know
+generation and there's like third
+
+ align:start position:0%
+generation and there's like third
+ 
+
+ align:start position:0%
+generation and there's like third
+generation Pilots now flying on the B-52
+
+ align:start position:0%
+generation Pilots now flying on the B-52
+ 
+
+ align:start position:0%
+generation Pilots now flying on the B-52
+that's what I've been told is that have
+
+ align:start position:0%
+that's what I've been told is that have
+ 
+
+ align:start position:0%
+that's what I've been told is that have
+you did you hear this as
+
+ align:start position:0%
+you did you hear this as
+ 
+
+ align:start position:0%
+you did you hear this as
+well yeah that's that's
+
+ align:start position:0%
+well yeah that's that's
+ 
+
+ align:start position:0%
+well yeah that's that's
+correct do you know some of these people
+
+ align:start position:0%
+correct do you know some of these people
+ 
+
+ align:start position:0%
+correct do you know some of these people
+no I've never actually worked on uh that
+
+ align:start position:0%
+no I've never actually worked on uh that
+ 
+
+ align:start position:0%
+no I've never actually worked on uh that
+airframe okay but anyway so that's what
+
+ align:start position:0%
+airframe okay but anyway so that's what
+ 
+
+ align:start position:0%
+airframe okay but anyway so that's what
+I mean by training and certification not
+
+ align:start position:0%
+I mean by training and certification not
+ 
+
+ align:start position:0%
+I mean by training and certification not
+just of the initial operators but you
+
+ align:start position:0%
+just of the initial operators but you
+ 
+
+ align:start position:0%
+just of the initial operators but you
+know over multiple Generations then the
+
+ align:start position:0%
+know over multiple Generations then the
+ 
+
+ align:start position:0%
+know over multiple Generations then the
+third thing here is servicing and
+
+ align:start position:0%
+third thing here is servicing and
+ 
+
+ align:start position:0%
+third thing here is servicing and
+servicing comes in two flavors are
+
+ align:start position:0%
+servicing comes in two flavors are
+ 
+
+ align:start position:0%
+servicing comes in two flavors are
+preventive maintenance you know regular
+
+ align:start position:0%
+preventive maintenance you know regular
+ 
+
+ align:start position:0%
+preventive maintenance you know regular
+maintenance uh and then corrective
+
+ align:start position:0%
+maintenance uh and then corrective
+ 
+
+ align:start position:0%
+maintenance uh and then corrective
+maintenance which we also call repair uh
+
+ align:start position:0%
+maintenance which we also call repair uh
+ 
+
+ align:start position:0%
+maintenance which we also call repair uh
+dealing with small and large failures
+
+ align:start position:0%
+dealing with small and large failures
+ 
+
+ align:start position:0%
+dealing with small and large failures
+recalls anomalies big this is a big deal
+
+ align:start position:0%
+recalls anomalies big this is a big deal
+ 
+
+ align:start position:0%
+recalls anomalies big this is a big deal
+in the automotive industry as we know uh
+
+ align:start position:0%
+in the automotive industry as we know uh
+ 
+
+ align:start position:0%
+in the automotive industry as we know uh
+increasingly protecting the system from
+
+ align:start position:0%
+increasingly protecting the system from
+ 
+
+ align:start position:0%
+increasingly protecting the system from
+either random or targeted attacks cyber
+
+ align:start position:0%
+either random or targeted attacks cyber
+ 
+
+ align:start position:0%
+either random or targeted attacks cyber
+physical right
+
+ align:start position:0%
+physical right
+ 
+
+ align:start position:0%
+physical right
+physical security but also cyber
+
+ align:start position:0%
+physical security but also cyber
+ 
+
+ align:start position:0%
+physical security but also cyber
+security is becoming a huge topic uh
+
+ align:start position:0%
+security is becoming a huge topic uh
+ 
+
+ align:start position:0%
+security is becoming a huge topic uh
+sharing And archiving the data that's
+
+ align:start position:0%
+sharing And archiving the data that's
+ 
+
+ align:start position:0%
+sharing And archiving the data that's
+being produced by the system more and
+
+ align:start position:0%
+being produced by the system more and
+ 
+
+ align:start position:0%
+being produced by the system more and
+more systems produce large amounts of
+
+ align:start position:0%
+more systems produce large amounts of
+ 
+
+ align:start position:0%
+more systems produce large amounts of
+data well what do you do with it how do
+
+ align:start position:0%
+data well what do you do with it how do
+ 
+
+ align:start position:0%
+data well what do you do with it how do
+you store that data um upgrading and
+
+ align:start position:0%
+you store that data um upgrading and
+ 
+
+ align:start position:0%
+you store that data um upgrading and
+retrofitting the system as needed so
+
+ align:start position:0%
+retrofitting the system as needed so
+ 
+
+ align:start position:0%
+retrofitting the system as needed so
+retrofitting means we're physically
+
+ align:start position:0%
+retrofitting means we're physically
+ 
+
+ align:start position:0%
+retrofitting means we're physically
+changing the configuration of the system
+
+ align:start position:0%
+changing the configuration of the system
+ 
+
+ align:start position:0%
+changing the configuration of the system
+right over its life to add new
+
+ align:start position:0%
+right over its life to add new
+ 
+
+ align:start position:0%
+right over its life to add new
+capabilities um and uh upgrading
+
+ align:start position:0%
+capabilities um and uh upgrading
+ 
+
+ align:start position:0%
+capabilities um and uh upgrading
+upgrading can be done sometimes without
+
+ align:start position:0%
+upgrading can be done sometimes without
+ 
+
+ align:start position:0%
+upgrading can be done sometimes without
+having to change the hardware right so
+
+ align:start position:0%
+having to change the hardware right so
+ 
+
+ align:start position:0%
+having to change the hardware right so
+you're doing like a software upgrade or
+
+ align:start position:0%
+you're doing like a software upgrade or
+ 
+
+ align:start position:0%
+you're doing like a software upgrade or
+software update software patching all of
+
+ align:start position:0%
+software update software patching all of
+ 
+
+ align:start position:0%
+software update software patching all of
+this would would go under upgrades
+
+ align:start position:0%
+this would would go under upgrades
+ 
+
+ align:start position:0%
+this would would go under upgrades
+um cross strapping the system with other
+
+ align:start position:0%
+um cross strapping the system with other
+ 
+
+ align:start position:0%
+um cross strapping the system with other
+systems in a Federation of systems so
+
+ align:start position:0%
+systems in a Federation of systems so
+ 
+
+ align:start position:0%
+systems in a Federation of systems so
+what I mean by this is a system May uh
+
+ align:start position:0%
+what I mean by this is a system May uh
+ 
+
+ align:start position:0%
+what I mean by this is a system May uh
+have been designed just to operate on
+
+ align:start position:0%
+have been designed just to operate on
+ 
+
+ align:start position:0%
+have been designed just to operate on
+its own but now you're connecting it
+
+ align:start position:0%
+its own but now you're connecting it
+ 
+
+ align:start position:0%
+its own but now you're connecting it
+with another system this happened in for
+
+ align:start position:0%
+with another system this happened in for
+ 
+
+ align:start position:0%
+with another system this happened in for
+example the electrical grid right the
+
+ align:start position:0%
+example the electrical grid right the
+ 
+
+ align:start position:0%
+example the electrical grid right the
+the early electrical grids were local
+
+ align:start position:0%
+the early electrical grids were local
+ 
+
+ align:start position:0%
+the early electrical grids were local
+Regional power grids and now we've
+
+ align:start position:0%
+Regional power grids and now we've
+ 
+
+ align:start position:0%
+Regional power grids and now we've
+connected them in the US we we have
+
+ align:start position:0%
+connected them in the US we we have
+ 
+
+ align:start position:0%
+connected them in the US we we have
+three major grids the Eastern the
+
+ align:start position:0%
+three major grids the Eastern the
+ 
+
+ align:start position:0%
+three major grids the Eastern the
+Western and then Texas has its own grid
+
+ align:start position:0%
+Western and then Texas has its own grid
+ 
+
+ align:start position:0%
+Western and then Texas has its own grid
+Texas does a lot of its own stuff it's
+
+ align:start position:0%
+Texas does a lot of its own stuff it's
+ 
+
+ align:start position:0%
+Texas does a lot of its own stuff it's
+called aircut and then here in Europe uh
+
+ align:start position:0%
+called aircut and then here in Europe uh
+ 
+
+ align:start position:0%
+called aircut and then here in Europe uh
+you know the European electrical grid is
+
+ align:start position:0%
+you know the European electrical grid is
+ 
+
+ align:start position:0%
+you know the European electrical grid is
+now Continental wide and it used to be
+
+ align:start position:0%
+now Continental wide and it used to be
+ 
+
+ align:start position:0%
+now Continental wide and it used to be
+and of course that that has big big
+
+ align:start position:0%
+and of course that that has big big
+ 
+
+ align:start position:0%
+and of course that that has big big
+implications for operations um reducing
+
+ align:start position:0%
+implications for operations um reducing
+ 
+
+ align:start position:0%
+implications for operations um reducing
+the resource consumption and
+
+ align:start position:0%
+the resource consumption and
+ 
+
+ align:start position:0%
+the resource consumption and
+environmental burden of the system over
+
+ align:start position:0%
+environmental burden of the system over
+ 
+
+ align:start position:0%
+environmental burden of the system over
+time and then finally decommissioning
+
+ align:start position:0%
+time and then finally decommissioning
+ 
+
+ align:start position:0%
+time and then finally decommissioning
+the system when it's time to to do so
+
+ align:start position:0%
+the system when it's time to to do so
+ 
+
+ align:start position:0%
+the system when it's time to to do so
+and you know in many systems this is a
+
+ align:start position:0%
+and you know in many systems this is a
+ 
+
+ align:start position:0%
+and you know in many systems this is a
+big uh challenge is to finding when is
+
+ align:start position:0%
+big uh challenge is to finding when is
+ 
+
+ align:start position:0%
+big uh challenge is to finding when is
+the right time to uh decommission the
+
+ align:start position:0%
+the right time to uh decommission the
+ 
+
+ align:start position:0%
+the right time to uh decommission the
+system and that's often the case when
+
+ align:start position:0%
+system and that's often the case when
+ 
+
+ align:start position:0%
+system and that's often the case when
+you know the operating cost exceeds the
+
+ align:start position:0%
+you know the operating cost exceeds the
+ 
+
+ align:start position:0%
+you know the operating cost exceeds the
+value that the system delivers so this
+
+ align:start position:0%
+value that the system delivers so this
+ 
+
+ align:start position:0%
+value that the system delivers so this
+is a pretty long list here and um a lot
+
+ align:start position:0%
+is a pretty long list here and um a lot
+ 
+
+ align:start position:0%
+is a pretty long list here and um a lot
+of a lot of tasks a lot of decisions to
+
+ align:start position:0%
+of a lot of tasks a lot of decisions to
+ 
+
+ align:start position:0%
+of a lot of tasks a lot of decisions to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+made um any questions about this list
+
+ align:start position:0%
+made um any questions about this list
+ 
+
+ align:start position:0%
+made um any questions about this list
+it's I don't think it's complete but um
+
+ align:start position:0%
+it's I don't think it's complete but um
+ 
+
+ align:start position:0%
+it's I don't think it's complete but um
+this this is this is a lot of things you
+
+ align:start position:0%
+this this is this is a lot of things you
+ 
+
+ align:start position:0%
+this this is this is a lot of things you
+need to take care of during operations
+
+ align:start position:0%
+need to take care of during operations
+ 
+
+ align:start position:0%
+need to take care of during operations
+here's a a more a more graphical view of
+
+ align:start position:0%
+here's a a more a more graphical view of
+ 
+
+ align:start position:0%
+here's a a more a more graphical view of
+this so this is my sketch of the systems
+
+ align:start position:0%
+this so this is my sketch of the systems
+ 
+
+ align:start position:0%
+this so this is my sketch of the systems
+engineering life cycle so this is part
+
+ align:start position:0%
+engineering life cycle so this is part
+ 
+
+ align:start position:0%
+engineering life cycle so this is part
+one right con conceptual design con
+
+ align:start position:0%
+one right con conceptual design con
+ 
+
+ align:start position:0%
+one right con conceptual design con
+conception design and implementation you
+
+ align:start position:0%
+conception design and implementation you
+ 
+
+ align:start position:0%
+conception design and implementation you
+start the life cycle you do something
+
+ align:start position:0%
+start the life cycle you do something
+ 
+
+ align:start position:0%
+start the life cycle you do something
+like a system requirements review
+
+ align:start position:0%
+like a system requirements review
+ 
+
+ align:start position:0%
+like a system requirements review
+understand the mission the requirements
+
+ align:start position:0%
+understand the mission the requirements
+ 
+
+ align:start position:0%
+understand the mission the requirements
+the constraints you you do conceptual
+
+ align:start position:0%
+the constraints you you do conceptual
+ 
+
+ align:start position:0%
+the constraints you you do conceptual
+design that's where you do creativity
+
+ align:start position:0%
+design that's where you do creativity
+ 
+
+ align:start position:0%
+design that's where you do creativity
+architecting trade studies at the PDR
+
+ align:start position:0%
+architecting trade studies at the PDR
+ 
+
+ align:start position:0%
+architecting trade studies at the PDR
+you choose your so in this case you know
+
+ align:start position:0%
+you choose your so in this case you know
+ 
+
+ align:start position:0%
+you choose your so in this case you know
+we're going to go for this triangle
+
+ align:start position:0%
+we're going to go for this triangle
+ 
+
+ align:start position:0%
+we're going to go for this triangle
+concept and then you design all the
+
+ align:start position:0%
+concept and then you design all the
+ 
+
+ align:start position:0%
+concept and then you design all the
+details within it that's where we do
+
+ align:start position:0%
+details within it that's where we do
+ 
+
+ align:start position:0%
+details within it that's where we do
+modeling simulation
+
+ align:start position:0%
+modeling simulation
+ 
+
+ align:start position:0%
+modeling simulation
+experiments uh mdo uh and we iterate uh
+
+ align:start position:0%
+experiments uh mdo uh and we iterate uh
+ 
+
+ align:start position:0%
+experiments uh mdo uh and we iterate uh
+sometimes you have to iterate this this
+
+ align:start position:0%
+sometimes you have to iterate this this
+ 
+
+ align:start position:0%
+sometimes you have to iterate this this
+dashed iteration means abandoning the
+
+ align:start position:0%
+dashed iteration means abandoning the
+ 
+
+ align:start position:0%
+dashed iteration means abandoning the
+concept you chose and go for a different
+
+ align:start position:0%
+concept you chose and go for a different
+ 
+
+ align:start position:0%
+concept you chose and go for a different
+concept that's usually undesirable at
+
+ align:start position:0%
+concept that's usually undesirable at
+ 
+
+ align:start position:0%
+concept that's usually undesirable at
+the after the CDR we implement the
+
+ align:start position:0%
+the after the CDR we implement the
+ 
+
+ align:start position:0%
+the after the CDR we implement the
+system we turn information to matter and
+
+ align:start position:0%
+system we turn information to matter and
+ 
+
+ align:start position:0%
+system we turn information to matter and
+this all happens in a technological
+
+ align:start position:0%
+this all happens in a technological
+ 
+
+ align:start position:0%
+this all happens in a technological
+economic social context so then the
+
+ align:start position:0%
+economic social context so then the
+ 
+
+ align:start position:0%
+economic social context so then the
+second the second part of it you know
+
+ align:start position:0%
+second the second part of it you know
+ 
+
+ align:start position:0%
+second the second part of it you know
+which in many systems you know if this
+
+ align:start position:0%
+which in many systems you know if this
+ 
+
+ align:start position:0%
+which in many systems you know if this
+if this is 10 years this could be 30
+
+ align:start position:0%
+if this is 10 years this could be 30
+ 
+
+ align:start position:0%
+if this is 10 years this could be 30
+years or more uh is the actual
+
+ align:start position:0%
+years or more uh is the actual
+ 
+
+ align:start position:0%
+years or more uh is the actual
+operational phase so the system has now
+
+ align:start position:0%
+operational phase so the system has now
+ 
+
+ align:start position:0%
+operational phase so the system has now
+been tested validated verified and
+
+ align:start position:0%
+been tested validated verified and
+ 
+
+ align:start position:0%
+been tested validated verified and
+deployed and now uh you know we we
+
+ align:start position:0%
+deployed and now uh you know we we
+ 
+
+ align:start position:0%
+deployed and now uh you know we we
+operate the system things break we need
+
+ align:start position:0%
+operate the system things break we need
+ 
+
+ align:start position:0%
+operate the system things break we need
+to service it and then I have this um
+
+ align:start position:0%
+to service it and then I have this um
+ 
+
+ align:start position:0%
+to service it and then I have this um
+you see there's two versions of the
+
+ align:start position:0%
+you see there's two versions of the
+ 
+
+ align:start position:0%
+you see there's two versions of the
+system one is solid and the other one is
+
+ align:start position:0%
+system one is solid and the other one is
+ 
+
+ align:start position:0%
+system one is solid and the other one is
+kind of faint that's a virtual version
+
+ align:start position:0%
+kind of faint that's a virtual version
+ 
+
+ align:start position:0%
+kind of faint that's a virtual version
+of the system so one of the big Concepts
+
+ align:start position:0%
+of the system so one of the big Concepts
+ 
+
+ align:start position:0%
+of the system so one of the big Concepts
+that's being pushed now in certainly in
+
+ align:start position:0%
+that's being pushed now in certainly in
+ 
+
+ align:start position:0%
+that's being pushed now in certainly in
+the US uh by the dod but also other
+
+ align:start position:0%
+the US uh by the dod but also other
+ 
+
+ align:start position:0%
+the US uh by the dod but also other
+places is the idea of a digital twin
+
+ align:start position:0%
+places is the idea of a digital twin
+ 
+
+ align:start position:0%
+places is the idea of a digital twin
+right the the idea of a digital twin is
+
+ align:start position:0%
+right the the idea of a digital twin is
+ 
+
+ align:start position:0%
+right the the idea of a digital twin is
+that there's the physical system right
+
+ align:start position:0%
+that there's the physical system right
+ 
+
+ align:start position:0%
+that there's the physical system right
+that exists and then there's a digital
+
+ align:start position:0%
+that exists and then there's a digital
+ 
+
+ align:start position:0%
+that exists and then there's a digital
+version a digital twin of that system
+
+ align:start position:0%
+version a digital twin of that system
+ 
+
+ align:start position:0%
+version a digital twin of that system
+somewhere on a on a computer that
+
+ align:start position:0%
+somewhere on a on a computer that
+ 
+
+ align:start position:0%
+somewhere on a on a computer that
+mirrors exactly what the real system is
+
+ align:start position:0%
+mirrors exactly what the real system is
+ 
+
+ align:start position:0%
+mirrors exactly what the real system is
+doing so if something breaks on the
+
+ align:start position:0%
+doing so if something breaks on the
+ 
+
+ align:start position:0%
+doing so if something breaks on the
+physical system well that same component
+
+ align:start position:0%
+physical system well that same component
+ 
+
+ align:start position:0%
+physical system well that same component
+fails in the digital twin and then
+
+ align:start position:0%
+fails in the digital twin and then
+ 
+
+ align:start position:0%
+fails in the digital twin and then
+before you actually do a repair or any
+
+ align:start position:0%
+before you actually do a repair or any
+ 
+
+ align:start position:0%
+before you actually do a repair or any
+actions you execute those actions on the
+
+ align:start position:0%
+actions you execute those actions on the
+ 
+
+ align:start position:0%
+actions you execute those actions on the
+digital twin to see whether the system
+
+ align:start position:0%
+digital twin to see whether the system
+ 
+
+ align:start position:0%
+digital twin to see whether the system
+will operate properly and um and so this
+
+ align:start position:0%
+will operate properly and um and so this
+ 
+
+ align:start position:0%
+will operate properly and um and so this
+is this is kind of the the the latest
+
+ align:start position:0%
+is this is kind of the the the latest
+ 
+
+ align:start position:0%
+is this is kind of the the the latest
+this thinking is that for any system we
+
+ align:start position:0%
+this thinking is that for any system we
+ 
+
+ align:start position:0%
+this thinking is that for any system we
+should have a digital twin uh during
+
+ align:start position:0%
+should have a digital twin uh during
+ 
+
+ align:start position:0%
+should have a digital twin uh during
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+upgrading the system so in this case
+
+ align:start position:0%
+upgrading the system so in this case
+ 
+
+ align:start position:0%
+upgrading the system so in this case
+we're we're adding things to it we're
+
+ align:start position:0%
+we're we're adding things to it we're
+ 
+
+ align:start position:0%
+we're we're adding things to it we're
+connecting it you know and at some point
+
+ align:start position:0%
+connecting it you know and at some point
+ 
+
+ align:start position:0%
+connecting it you know and at some point
+the system does degrade because for
+
+ align:start position:0%
+the system does degrade because for
+ 
+
+ align:start position:0%
+the system does degrade because for
+example you know materials age they get
+
+ align:start position:0%
+example you know materials age they get
+ 
+
+ align:start position:0%
+example you know materials age they get
+brittle uh technology becomes
+
+ align:start position:0%
+brittle uh technology becomes
+ 
+
+ align:start position:0%
+brittle uh technology becomes
+obsolete you know it gets harder and
+
+ align:start position:0%
+obsolete you know it gets harder and
+ 
+
+ align:start position:0%
+obsolete you know it gets harder and
+harder to maintain spare parts are uh
+
+ align:start position:0%
+harder to maintain spare parts are uh
+ 
+
+ align:start position:0%
+harder to maintain spare parts are uh
+the the suppliers of the original spare
+
+ align:start position:0%
+the the suppliers of the original spare
+ 
+
+ align:start position:0%
+the the suppliers of the original spare
+parts went out of business so these
+
+ align:start position:0%
+parts went out of business so these
+ 
+
+ align:start position:0%
+parts went out of business so these
+really old Legacy systems can be very
+
+ align:start position:0%
+really old Legacy systems can be very
+ 
+
+ align:start position:0%
+really old Legacy systems can be very
+expensive to operate and then at some
+
+ align:start position:0%
+expensive to operate and then at some
+ 
+
+ align:start position:0%
+expensive to operate and then at some
+point you liquidate and uh and it's the
+
+ align:start position:0%
+point you liquidate and uh and it's the
+ 
+
+ align:start position:0%
+point you liquidate and uh and it's the
+end of the life cycle so I've already
+
+ align:start position:0%
+end of the life cycle so I've already
+ 
+
+ align:start position:0%
+end of the life cycle so I've already
+told you about one example for this
+
+ align:start position:0%
+told you about one example for this
+ 
+
+ align:start position:0%
+told you about one example for this
+which is uh the space shuttle and uh so
+
+ align:start position:0%
+which is uh the space shuttle and uh so
+ 
+
+ align:start position:0%
+which is uh the space shuttle and uh so
+I'm not going to belabor this again but
+
+ align:start position:0%
+I'm not going to belabor this again but
+ 
+
+ align:start position:0%
+I'm not going to belabor this again but
+I think it's a it's a great opportunity
+
+ align:start position:0%
+I think it's a it's a great opportunity
+ 
+
+ align:start position:0%
+I think it's a it's a great opportunity
+to learn the space shuttle had a 10-year
+
+ align:start position:0%
+to learn the space shuttle had a 10-year
+ 
+
+ align:start position:0%
+to learn the space shuttle had a 10-year
+design life uh roughly from 1971 until
+
+ align:start position:0%
+design life uh roughly from 1971 until
+ 
+
+ align:start position:0%
+design life uh roughly from 1971 until
+81 first flight and then we operated the
+
+ align:start position:0%
+81 first flight and then we operated the
+ 
+
+ align:start position:0%
+81 first flight and then we operated the
+shuttle for 30 years and we had a total
+
+ align:start position:0%
+shuttle for 30 years and we had a total
+ 
+
+ align:start position:0%
+shuttle for 30 years and we had a total
+of 135 launches during that time we
+
+ align:start position:0%
+of 135 launches during that time we
+ 
+
+ align:start position:0%
+of 135 launches during that time we
+spent 1992 billion uh dollars on the
+
+ align:start position:0%
+spent 1992 billion uh dollars on the
+ 
+
+ align:start position:0%
+spent 1992 billion uh dollars on the
+shuttle program and if you average that
+
+ align:start position:0%
+shuttle program and if you average that
+ 
+
+ align:start position:0%
+shuttle program and if you average that
+it's 1.5 billion per flight which is a
+
+ align:start position:0%
+it's 1.5 billion per flight which is a
+ 
+
+ align:start position:0%
+it's 1.5 billion per flight which is a
+lot more than uh than was planned but
+
+ align:start position:0%
+lot more than uh than was planned but
+ 
+
+ align:start position:0%
+lot more than uh than was planned but
+just yesterday here at the epfl we had
+
+ align:start position:0%
+just yesterday here at the epfl we had
+ 
+
+ align:start position:0%
+just yesterday here at the epfl we had
+the uh annual meeting of the um Swiss
+
+ align:start position:0%
+the uh annual meeting of the um Swiss
+ 
+
+ align:start position:0%
+the uh annual meeting of the um Swiss
+Space Center and one of the uh
+
+ align:start position:0%
+Space Center and one of the uh
+ 
+
+ align:start position:0%
+Space Center and one of the uh
+astronauts here Cloe nicolier gave and
+
+ align:start position:0%
+astronauts here Cloe nicolier gave and
+ 
+
+ align:start position:0%
+astronauts here Cloe nicolier gave and
+and his colleague uh professor meron
+
+ align:start position:0%
+and his colleague uh professor meron
+ 
+
+ align:start position:0%
+and his colleague uh professor meron
+gave a great talk about uh the Hubble
+
+ align:start position:0%
+gave a great talk about uh the Hubble
+ 
+
+ align:start position:0%
+gave a great talk about uh the Hubble
+and the servicing of the Hubble and you
+
+ align:start position:0%
+and the servicing of the Hubble and you
+ 
+
+ align:start position:0%
+and the servicing of the Hubble and you
+know the the amazing things we've
+
+ align:start position:0%
+know the the amazing things we've
+ 
+
+ align:start position:0%
+know the the amazing things we've
+learned through it and uh uh you guys at
+
+ align:start position:0%
+learned through it and uh uh you guys at
+ 
+
+ align:start position:0%
+learned through it and uh uh you guys at
+MIT Jeff Hoffman was part of uh at least
+
+ align:start position:0%
+MIT Jeff Hoffman was part of uh at least
+ 
+
+ align:start position:0%
+MIT Jeff Hoffman was part of uh at least
+the first servicing Mission as well so
+
+ align:start position:0%
+the first servicing Mission as well so
+ 
+
+ align:start position:0%
+the first servicing Mission as well so
+there's you know incredible things that
+
+ align:start position:0%
+there's you know incredible things that
+ 
+
+ align:start position:0%
+there's you know incredible things that
+were done by the shuttle and uh and so I
+
+ align:start position:0%
+were done by the shuttle and uh and so I
+ 
+
+ align:start position:0%
+were done by the shuttle and uh and so I
+think we we need to acknowledge that not
+
+ align:start position:0%
+think we we need to acknowledge that not
+ 
+
+ align:start position:0%
+think we we need to acknowledge that not
+just the fact that uh it was very
+
+ align:start position:0%
+just the fact that uh it was very
+ 
+
+ align:start position:0%
+just the fact that uh it was very
+expensive it accomplished great things
+
+ align:start position:0%
+expensive it accomplished great things
+ 
+
+ align:start position:0%
+expensive it accomplished great things
+during its life but you know if we had a
+
+ align:start position:0%
+during its life but you know if we had a
+ 
+
+ align:start position:0%
+during its life but you know if we had a
+chance to do it again would we would we
+
+ align:start position:0%
+chance to do it again would we would we
+ 
+
+ align:start position:0%
+chance to do it again would we would we
+come up with the exact same system would
+
+ align:start position:0%
+come up with the exact same system would
+ 
+
+ align:start position:0%
+come up with the exact same system would
+we make all the same design decisions
+
+ align:start position:0%
+we make all the same design decisions
+ 
+
+ align:start position:0%
+we make all the same design decisions
+you know we lost two of them probably
+
+ align:start position:0%
+you know we lost two of them probably
+ 
+
+ align:start position:0%
+you know we lost two of them probably
+not we would probably do something
+
+ align:start position:0%
+not we would probably do something
+ 
+
+ align:start position:0%
+not we would probably do something
+something different um so here's what we
+
+ align:start position:0%
+something different um so here's what we
+ 
+
+ align:start position:0%
+something different um so here's what we
+wanted and then finally we got a much
+
+ align:start position:0%
+wanted and then finally we got a much
+ 
+
+ align:start position:0%
+wanted and then finally we got a much
+more complex system in the end and
+
+ align:start position:0%
+more complex system in the end and
+ 
+
+ align:start position:0%
+more complex system in the end and
+particularly uh my sense is that a lot
+
+ align:start position:0%
+particularly uh my sense is that a lot
+ 
+
+ align:start position:0%
+particularly uh my sense is that a lot
+of the things that made the shuttle
+
+ align:start position:0%
+of the things that made the shuttle
+ 
+
+ align:start position:0%
+of the things that made the shuttle
+expensive to operate during its life
+
+ align:start position:0%
+expensive to operate during its life
+ 
+
+ align:start position:0%
+expensive to operate during its life
+were things related to U maintainability
+
+ align:start position:0%
+were things related to U maintainability
+ 
+
+ align:start position:0%
+were things related to U maintainability
+right reliability and so forth so the
+
+ align:start position:0%
+right reliability and so forth so the
+ 
+
+ align:start position:0%
+right reliability and so forth so the
+life cycle properties which I want to
+
+ align:start position:0%
+life cycle properties which I want to
+ 
+
+ align:start position:0%
+life cycle properties which I want to
+talk about next so the I I just going to
+
+ align:start position:0%
+talk about next so the I I just going to
+ 
+
+ align:start position:0%
+talk about next so the I I just going to
+repeat the question so you guys can hear
+
+ align:start position:0%
+repeat the question so you guys can hear
+ 
+
+ align:start position:0%
+repeat the question so you guys can hear
+as well so the question was about uh
+
+ align:start position:0%
+as well so the question was about uh
+ 
+
+ align:start position:0%
+as well so the question was about uh
+reusability so the the shuttle was re
+
+ align:start position:0%
+reusability so the the shuttle was re
+ 
+
+ align:start position:0%
+reusability so the the shuttle was re
+the Orbiter was fully reusable uh the
+
+ align:start position:0%
+the Orbiter was fully reusable uh the
+ 
+
+ align:start position:0%
+the Orbiter was fully reusable uh the
+external fuel tank was not reusable
+
+ align:start position:0%
+external fuel tank was not reusable
+ 
+
+ align:start position:0%
+external fuel tank was not reusable
+right and then the solid rocket boosters
+
+ align:start position:0%
+right and then the solid rocket boosters
+ 
+
+ align:start position:0%
+right and then the solid rocket boosters
+were partially reusable because they had
+
+ align:start position:0%
+were partially reusable because they had
+ 
+
+ align:start position:0%
+were partially reusable because they had
+to be stripped down you know and and and
+
+ align:start position:0%
+to be stripped down you know and and and
+ 
+
+ align:start position:0%
+to be stripped down you know and and and
+rebuilt essentially for every launch the
+
+ align:start position:0%
+rebuilt essentially for every launch the
+ 
+
+ align:start position:0%
+rebuilt essentially for every launch the
+idea of you know blue origin and then
+
+ align:start position:0%
+idea of you know blue origin and then
+ 
+
+ align:start position:0%
+idea of you know blue origin and then
+SpaceX stage one you know flying it back
+
+ align:start position:0%
+SpaceX stage one you know flying it back
+ 
+
+ align:start position:0%
+SpaceX stage one you know flying it back
+to the to the launch site is absolutely
+
+ align:start position:0%
+to the to the launch site is absolutely
+ 
+
+ align:start position:0%
+to the to the launch site is absolutely
+the fact that if you can make it
+
+ align:start position:0%
+the fact that if you can make it
+ 
+
+ align:start position:0%
+the fact that if you can make it
+reusable then you should you can
+
+ align:start position:0%
+reusable then you should you can
+ 
+
+ align:start position:0%
+reusable then you should you can
+amortize the capex in that element over
+
+ align:start position:0%
+amortize the capex in that element over
+ 
+
+ align:start position:0%
+amortize the capex in that element over
+multiple flights and it should drop you
+
+ align:start position:0%
+multiple flights and it should drop you
+ 
+
+ align:start position:0%
+multiple flights and it should drop you
+know the cost by you know a factor of
+
+ align:start position:0%
+know the cost by you know a factor of
+ 
+
+ align:start position:0%
+know the cost by you know a factor of
+five or 10 or more now the devils in the
+
+ align:start position:0%
+five or 10 or more now the devils in the
+ 
+
+ align:start position:0%
+five or 10 or more now the devils in the
+details right so if you start and
+
+ align:start position:0%
+details right so if you start and
+ 
+
+ align:start position:0%
+details right so if you start and
+restart an engine multiple times you
+
+ align:start position:0%
+restart an engine multiple times you
+ 
+
+ align:start position:0%
+restart an engine multiple times you
+have a big transient every time so did
+
+ align:start position:0%
+have a big transient every time so did
+ 
+
+ align:start position:0%
+have a big transient every time so did
+was the system in fact designed to
+
+ align:start position:0%
+was the system in fact designed to
+ 
+
+ align:start position:0%
+was the system in fact designed to
+withstand these transients can it handle
+
+ align:start position:0%
+withstand these transients can it handle
+ 
+
+ align:start position:0%
+withstand these transients can it handle
+multiple starts uh what does it do to
+
+ align:start position:0%
+multiple starts uh what does it do to
+ 
+
+ align:start position:0%
+multiple starts uh what does it do to
+the materials and so forth and and so to
+
+ align:start position:0%
+the materials and so forth and and so to
+ 
+
+ align:start position:0%
+the materials and so forth and and so to
+really model this ahead of time and then
+
+ align:start position:0%
+really model this ahead of time and then
+ 
+
+ align:start position:0%
+really model this ahead of time and then
+test it over these Cycles is the key so
+
+ align:start position:0%
+test it over these Cycles is the key so
+ 
+
+ align:start position:0%
+test it over these Cycles is the key so
+in the shuttle the big problems the two
+
+ align:start position:0%
+in the shuttle the big problems the two
+ 
+
+ align:start position:0%
+in the shuttle the big problems the two
+major subsystems in the shuttle in the
+
+ align:start position:0%
+major subsystems in the shuttle in the
+ 
+
+ align:start position:0%
+major subsystems in the shuttle in the
+Orbiter in particular that that made it
+
+ align:start position:0%
+Orbiter in particular that that made it
+ 
+
+ align:start position:0%
+Orbiter in particular that that made it
+expensive uh and the difference between
+
+ align:start position:0%
+expensive uh and the difference between
+ 
+
+ align:start position:0%
+expensive uh and the difference between
+the top picture and the bottom picture
+
+ align:start position:0%
+the top picture and the bottom picture
+ 
+
+ align:start position:0%
+the top picture and the bottom picture
+was a the TPS the thermal protection
+
+ align:start position:0%
+was a the TPS the thermal protection
+ 
+
+ align:start position:0%
+was a the TPS the thermal protection
+system you know every uh every tile has
+
+ align:start position:0%
+system you know every uh every tile has
+ 
+
+ align:start position:0%
+system you know every uh every tile has
+a had a different curvature and geometry
+
+ align:start position:0%
+a had a different curvature and geometry
+ 
+
+ align:start position:0%
+a had a different curvature and geometry
+so really inspecting every tile uh
+
+ align:start position:0%
+so really inspecting every tile uh
+ 
+
+ align:start position:0%
+so really inspecting every tile uh
+replacing tiles making sure that the TPS
+
+ align:start position:0%
+replacing tiles making sure that the TPS
+ 
+
+ align:start position:0%
+replacing tiles making sure that the TPS
+was CU just one weakness in the TPS
+
+ align:start position:0%
+was CU just one weakness in the TPS
+ 
+
+ align:start position:0%
+was CU just one weakness in the TPS
+could you know basically be fatal on
+
+ align:start position:0%
+could you know basically be fatal on
+ 
+
+ align:start position:0%
+could you know basically be fatal on
+re-entry and so TPS was very difficult
+
+ align:start position:0%
+re-entry and so TPS was very difficult
+ 
+
+ align:start position:0%
+re-entry and so TPS was very difficult
+and uh you know as opposed to an
+
+ align:start position:0%
+and uh you know as opposed to an
+ 
+
+ align:start position:0%
+and uh you know as opposed to an
+ablative heat shield that you just
+
+ align:start position:0%
+ablative heat shield that you just
+ 
+
+ align:start position:0%
+ablative heat shield that you just
+sacrific the heat shield uh completely
+
+ align:start position:0%
+sacrific the heat shield uh completely
+ 
+
+ align:start position:0%
+sacrific the heat shield uh completely
+and then the other was the main engine
+
+ align:start position:0%
+and then the other was the main engine
+ 
+
+ align:start position:0%
+and then the other was the main engine
+the shuttle main engine originally the
+
+ align:start position:0%
+the shuttle main engine originally the
+ 
+
+ align:start position:0%
+the shuttle main engine originally the
+idea was to only do very deep
+
+ align:start position:0%
+idea was to only do very deep
+ 
+
+ align:start position:0%
+idea was to only do very deep
+inspections and disassembly disassembly
+
+ align:start position:0%
+inspections and disassembly disassembly
+ 
+
+ align:start position:0%
+inspections and disassembly disassembly
+of the shuttle main engine after the
+
+ align:start position:0%
+of the shuttle main engine after the
+ 
+
+ align:start position:0%
+of the shuttle main engine after the
+first few test flights and then fly
+
+ align:start position:0%
+first few test flights and then fly
+ 
+
+ align:start position:0%
+first few test flights and then fly
+multiple times without having to really
+
+ align:start position:0%
+multiple times without having to really
+ 
+
+ align:start position:0%
+multiple times without having to really
+reinspect or you know disassemble the
+
+ align:start position:0%
+reinspect or you know disassemble the
+ 
+
+ align:start position:0%
+reinspect or you know disassemble the
+engines so they they did the disassembly
+
+ align:start position:0%
+engines so they they did the disassembly
+ 
+
+ align:start position:0%
+engines so they they did the disassembly
+of the engines after the test flights
+
+ align:start position:0%
+of the engines after the test flights
+ 
+
+ align:start position:0%
+of the engines after the test flights
+and then they just kept doing it for
+
+ align:start position:0%
+and then they just kept doing it for
+ 
+
+ align:start position:0%
+and then they just kept doing it for
+every flight where the or original
+
+ align:start position:0%
+every flight where the or original
+ 
+
+ align:start position:0%
+every flight where the or original
+intent was to only do it for the test
+
+ align:start position:0%
+intent was to only do it for the test
+ 
+
+ align:start position:0%
+intent was to only do it for the test
+flights and so the main shuttle main
+
+ align:start position:0%
+flights and so the main shuttle main
+ 
+
+ align:start position:0%
+flights and so the main shuttle main
+engines were the second big cost driver
+
+ align:start position:0%
+engines were the second big cost driver
+ 
+
+ align:start position:0%
+engines were the second big cost driver
+in operations so in in reusability is is
+
+ align:start position:0%
+in operations so in in reusability is is
+ 
+
+ align:start position:0%
+in operations so in in reusability is is
+a great idea but to the degree to which
+
+ align:start position:0%
+a great idea but to the degree to which
+ 
+
+ align:start position:0%
+a great idea but to the degree to which
+reusability actually happens in reality
+
+ align:start position:0%
+reusability actually happens in reality
+ 
+
+ align:start position:0%
+reusability actually happens in reality
+that's you know that's really about
+
+ align:start position:0%
+that's you know that's really about
+ 
+
+ align:start position:0%
+that's you know that's really about
+detailed design decisions you
+
+ align:start position:0%
+detailed design decisions you
+ 
+
+ align:start position:0%
+detailed design decisions you
+make okay so uh let me move on then
+
+ align:start position:0%
+make okay so uh let me move on then
+ 
+
+ align:start position:0%
+make okay so uh let me move on then
+um I want to mention is you know when it
+
+ align:start position:0%
+um I want to mention is you know when it
+ 
+
+ align:start position:0%
+um I want to mention is you know when it
+comes to really understanding um life
+
+ align:start position:0%
+comes to really understanding um life
+ 
+
+ align:start position:0%
+comes to really understanding um life
+cycle proes I do want to point you to
+
+ align:start position:0%
+cycle proes I do want to point you to
+ 
+
+ align:start position:0%
+cycle proes I do want to point you to
+the 15 28 the 15288 standard which is um
+
+ align:start position:0%
+the 15 28 the 15288 standard which is um
+ 
+
+ align:start position:0%
+the 15 28 the 15288 standard which is um
+the iso 15288 standard which has
+
+ align:start position:0%
+the iso 15288 standard which has
+ 
+
+ align:start position:0%
+the iso 15288 standard which has
+a fairly complete list of system life
+
+ align:start position:0%
+a fairly complete list of system life
+ 
+
+ align:start position:0%
+a fairly complete list of system life
+cycle processes so this is essentially
+
+ align:start position:0%
+cycle processes so this is essentially
+ 
+
+ align:start position:0%
+cycle processes so this is essentially
+the system and software engineering
+
+ align:start position:0%
+the system and software engineering
+ 
+
+ align:start position:0%
+the system and software engineering
+system life cycle process standard that
+
+ align:start position:0%
+system life cycle process standard that
+ 
+
+ align:start position:0%
+system life cycle process standard that
+has a whole range of processes that are
+
+ align:start position:0%
+has a whole range of processes that are
+ 
+
+ align:start position:0%
+has a whole range of processes that are
+that are described in quite some detail
+
+ align:start position:0%
+that are described in quite some detail
+ 
+
+ align:start position:0%
+that are described in quite some detail
+and they're not just the technical
+
+ align:start position:0%
+and they're not just the technical
+ 
+
+ align:start position:0%
+and they're not just the technical
+processes shown here on the right side
+
+ align:start position:0%
+processes shown here on the right side
+ 
+
+ align:start position:0%
+processes shown here on the right side
+uh we focused a lot on those technical
+
+ align:start position:0%
+uh we focused a lot on those technical
+ 
+
+ align:start position:0%
+uh we focused a lot on those technical
+processes in this class the stakeholders
+
+ align:start position:0%
+processes in this class the stakeholders
+ 
+
+ align:start position:0%
+processes in this class the stakeholders
+the requirements the architectural
+
+ align:start position:0%
+the requirements the architectural
+ 
+
+ align:start position:0%
+the requirements the architectural
+design which is essentially the
+
+ align:start position:0%
+design which is essentially the
+ 
+
+ align:start position:0%
+design which is essentially the
+conceptual design but there's also the
+
+ align:start position:0%
+conceptual design but there's also the
+ 
+
+ align:start position:0%
+conceptual design but there's also the
+project processes right executing the
+
+ align:start position:0%
+project processes right executing the
+ 
+
+ align:start position:0%
+project processes right executing the
+projects agreement processes so this
+
+ align:start position:0%
+projects agreement processes so this
+ 
+
+ align:start position:0%
+projects agreement processes so this
+would be negotiating uh contracts you
+
+ align:start position:0%
+would be negotiating uh contracts you
+ 
+
+ align:start position:0%
+would be negotiating uh contracts you
+know Supply contracts acquisition
+
+ align:start position:0%
+know Supply contracts acquisition
+ 
+
+ align:start position:0%
+know Supply contracts acquisition
+contracts and then all the
+
+ align:start position:0%
+contracts and then all the
+ 
+
+ align:start position:0%
+contracts and then all the
+organizational things you need to do to
+
+ align:start position:0%
+organizational things you need to do to
+ 
+
+ align:start position:0%
+organizational things you need to do to
+create the right organization to execute
+
+ align:start position:0%
+create the right organization to execute
+ 
+
+ align:start position:0%
+create the right organization to execute
+these projects so what's nice about the
+
+ align:start position:0%
+these projects so what's nice about the
+ 
+
+ align:start position:0%
+these projects so what's nice about the
+uh 15288 standard is that it's it's a
+
+ align:start position:0%
+uh 15288 standard is that it's it's a
+ 
+
+ align:start position:0%
+uh 15288 standard is that it's it's a
+pretty broad
+
+ align:start position:0%
+pretty broad
+ 
+
+ align:start position:0%
+pretty broad
+standard okay so let me talk about the
+
+ align:start position:0%
+standard okay so let me talk about the
+ 
+
+ align:start position:0%
+standard okay so let me talk about the
+Iles of the life cycle properties in
+
+ align:start position:0%
+Iles of the life cycle properties in
+ 
+
+ align:start position:0%
+Iles of the life cycle properties in
+particular uh what they are and how uh
+
+ align:start position:0%
+particular uh what they are and how uh
+ 
+
+ align:start position:0%
+particular uh what they are and how uh
+we can describe them and how especially
+
+ align:start position:0%
+we can describe them and how especially
+ 
+
+ align:start position:0%
+we can describe them and how especially
+how they relate to each other and so the
+
+ align:start position:0%
+how they relate to each other and so the
+ 
+
+ align:start position:0%
+how they relate to each other and so the
+paper there two papers that underly this
+
+ align:start position:0%
+paper there two papers that underly this
+ 
+
+ align:start position:0%
+paper there two papers that underly this
+lecture that you can read to get some
+
+ align:start position:0%
+lecture that you can read to get some
+ 
+
+ align:start position:0%
+lecture that you can read to get some
+more detail and this is one of them so
+
+ align:start position:0%
+more detail and this is one of them so
+ 
+
+ align:start position:0%
+more detail and this is one of them so
+this paper is called investigating the
+
+ align:start position:0%
+this paper is called investigating the
+ 
+
+ align:start position:0%
+this paper is called investigating the
+relationships and semantic sets among
+
+ align:start position:0%
+relationships and semantic sets among
+ 
+
+ align:start position:0%
+relationships and semantic sets among
+life cycle properties and we we
+
+ align:start position:0%
+life cycle properties and we we
+ 
+
+ align:start position:0%
+life cycle properties and we we
+published this about 3 years ago in Del
+
+ align:start position:0%
+published this about 3 years ago in Del
+ 
+
+ align:start position:0%
+published this about 3 years ago in Del
+at the uh seisan conference so um the
+
+ align:start position:0%
+at the uh seisan conference so um the
+ 
+
+ align:start position:0%
+at the uh seisan conference so um the
+the background here is the following is
+
+ align:start position:0%
+the background here is the following is
+ 
+
+ align:start position:0%
+the background here is the following is
+that you know as as you've seen complex
+
+ align:start position:0%
+that you know as as you've seen complex
+ 
+
+ align:start position:0%
+that you know as as you've seen complex
+Engineering Systems live for decades or
+
+ align:start position:0%
+Engineering Systems live for decades or
+ 
+
+ align:start position:0%
+Engineering Systems live for decades or
+some of them even for centuries and the
+
+ align:start position:0%
+some of them even for centuries and the
+ 
+
+ align:start position:0%
+some of them even for centuries and the
+the IL by Ides we mean properties of
+
+ align:start position:0%
+the IL by Ides we mean properties of
+ 
+
+ align:start position:0%
+the IL by Ides we mean properties of
+systems that are that are not the
+
+ align:start position:0%
+systems that are that are not the
+ 
+
+ align:start position:0%
+systems that are that are not the
+primary functional properties in
+
+ align:start position:0%
+primary functional properties in
+ 
+
+ align:start position:0%
+primary functional properties in
+software engineering they're often
+
+ align:start position:0%
+software engineering they're often
+ 
+
+ align:start position:0%
+software engineering they're often
+called nonfunctional properties and the
+
+ align:start position:0%
+called nonfunctional properties and the
+ 
+
+ align:start position:0%
+called nonfunctional properties and the
+the thing that's tricky about the Ides
+
+ align:start position:0%
+the thing that's tricky about the Ides
+ 
+
+ align:start position:0%
+the thing that's tricky about the Ides
+is that you often only can observe them
+
+ align:start position:0%
+is that you often only can observe them
+ 
+
+ align:start position:0%
+is that you often only can observe them
+during operations so you know you can
+
+ align:start position:0%
+during operations so you know you can
+ 
+
+ align:start position:0%
+during operations so you know you can
+test systems in the short term you can
+
+ align:start position:0%
+test systems in the short term you can
+ 
+
+ align:start position:0%
+test systems in the short term you can
+you can see does it work does it fulfill
+
+ align:start position:0%
+you can see does it work does it fulfill
+ 
+
+ align:start position:0%
+you can see does it work does it fulfill
+its function but whether certain ilities
+
+ align:start position:0%
+its function but whether certain ilities
+ 
+
+ align:start position:0%
+its function but whether certain ilities
+are present it often only shows itself
+
+ align:start position:0%
+are present it often only shows itself
+ 
+
+ align:start position:0%
+are present it often only shows itself
+over time um and and so um most of the
+
+ align:start position:0%
+over time um and and so um most of the
+ 
+
+ align:start position:0%
+over time um and and so um most of the
+research that's been done in sort of
+
+ align:start position:0%
+research that's been done in sort of
+ 
+
+ align:start position:0%
+research that's been done in sort of
+quantifying the ilities has been looking
+
+ align:start position:0%
+quantifying the ilities has been looking
+ 
+
+ align:start position:0%
+quantifying the ilities has been looking
+at these properties one at a time so the
+
+ align:start position:0%
+at these properties one at a time so the
+ 
+
+ align:start position:0%
+at these properties one at a time so the
+questions we wanted wanted to go here uh
+
+ align:start position:0%
+questions we wanted wanted to go here uh
+ 
+
+ align:start position:0%
+questions we wanted wanted to go here uh
+wanted to answer is you know is which of
+
+ align:start position:0%
+wanted to answer is you know is which of
+ 
+
+ align:start position:0%
+wanted to answer is you know is which of
+these life cycle properties are more
+
+ align:start position:0%
+these life cycle properties are more
+ 
+
+ align:start position:0%
+these life cycle properties are more
+prevalent than others you know the top
+
+ align:start position:0%
+prevalent than others you know the top
+ 
+
+ align:start position:0%
+prevalent than others you know the top
+20 and then especially what's the
+
+ align:start position:0%
+20 and then especially what's the
+ 
+
+ align:start position:0%
+20 and then especially what's the
+relationship among life cycle properties
+
+ align:start position:0%
+relationship among life cycle properties
+ 
+
+ align:start position:0%
+relationship among life cycle properties
+do they form what we call semantic sets
+
+ align:start position:0%
+do they form what we call semantic sets
+ 
+
+ align:start position:0%
+do they form what we call semantic sets
+and then you know how could you use this
+
+ align:start position:0%
+and then you know how could you use this
+ 
+
+ align:start position:0%
+and then you know how could you use this
+information and so here we're going to
+
+ align:start position:0%
+information and so here we're going to
+ 
+
+ align:start position:0%
+information and so here we're going to
+do this using two different methods the
+
+ align:start position:0%
+do this using two different methods the
+ 
+
+ align:start position:0%
+do this using two different methods the
+first method is what I call prevalence
+
+ align:start position:0%
+first method is what I call prevalence
+ 
+
+ align:start position:0%
+first method is what I call prevalence
+analysis we're going to look in the
+
+ align:start position:0%
+analysis we're going to look in the
+ 
+
+ align:start position:0%
+analysis we're going to look in the
+literature and on the internet how
+
+ align:start position:0%
+literature and on the internet how
+ 
+
+ align:start position:0%
+literature and on the internet how
+frequently these life cycle properties
+
+ align:start position:0%
+frequently these life cycle properties
+ 
+
+ align:start position:0%
+frequently these life cycle properties
+show up are mentioned how much we know
+
+ align:start position:0%
+show up are mentioned how much we know
+ 
+
+ align:start position:0%
+show up are mentioned how much we know
+about them and then the second method is
+
+ align:start position:0%
+about them and then the second method is
+ 
+
+ align:start position:0%
+about them and then the second method is
+a cognitive method where we ask people
+
+ align:start position:0%
+a cognitive method where we ask people
+ 
+
+ align:start position:0%
+a cognitive method where we ask people
+to uh give their understanding of these
+
+ align:start position:0%
+to uh give their understanding of these
+ 
+
+ align:start position:0%
+to uh give their understanding of these
+life cycle properties and put them in
+
+ align:start position:0%
+life cycle properties and put them in
+ 
+
+ align:start position:0%
+life cycle properties and put them in
+into a hierarchy and then we'll compare
+
+ align:start position:0%
+into a hierarchy and then we'll compare
+ 
+
+ align:start position:0%
+into a hierarchy and then we'll compare
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+results so um here are essentially the
+
+ align:start position:0%
+results so um here are essentially the
+ 
+
+ align:start position:0%
+results so um here are essentially the
+results from the prevalence analysis and
+
+ align:start position:0%
+results from the prevalence analysis and
+ 
+
+ align:start position:0%
+results from the prevalence analysis and
+this is ranked according to uh the
+
+ align:start position:0%
+this is ranked according to uh the
+ 
+
+ align:start position:0%
+this is ranked according to uh the
+number of Journal articles uh this is
+
+ align:start position:0%
+number of Journal articles uh this is
+ 
+
+ align:start position:0%
+number of Journal articles uh this is
+scientific Papers written where this
+
+ align:start position:0%
+scientific Papers written where this
+ 
+
+ align:start position:0%
+scientific Papers written where this
+particular keyw like quality or
+
+ align:start position:0%
+particular keyw like quality or
+ 
+
+ align:start position:0%
+particular keyw like quality or
+reliability shows up in the title or in
+
+ align:start position:0%
+reliability shows up in the title or in
+ 
+
+ align:start position:0%
+reliability shows up in the title or in
+the abstract of the paper and you can
+
+ align:start position:0%
+the abstract of the paper and you can
+ 
+
+ align:start position:0%
+the abstract of the paper and you can
+see this is in units of thousands okay
+
+ align:start position:0%
+see this is in units of thousands okay
+ 
+
+ align:start position:0%
+see this is in units of thousands okay
+so quality is number one right quality
+
+ align:start position:0%
+so quality is number one right quality
+ 
+
+ align:start position:0%
+so quality is number one right quality
+is number one the most most scientific
+
+ align:start position:0%
+is number one the most most scientific
+ 
+
+ align:start position:0%
+is number one the most most scientific
+Papers written about quality and you can
+
+ align:start position:0%
+Papers written about quality and you can
+ 
+
+ align:start position:0%
+Papers written about quality and you can
+see it's almost a million Journal
+
+ align:start position:0%
+see it's almost a million Journal
+ 
+
+ align:start position:0%
+see it's almost a million Journal
+articles this is I'll show this to you
+
+ align:start position:0%
+articles this is I'll show this to you
+ 
+
+ align:start position:0%
+articles this is I'll show this to you
+over time but since 1884 is the first
+
+ align:start position:0%
+over time but since 1884 is the first
+ 
+
+ align:start position:0%
+over time but since 1884 is the first
+year okay and the databases that were
+
+ align:start position:0%
+year okay and the databases that were
+ 
+
+ align:start position:0%
+year okay and the databases that were
+used for this are called it's compendex
+
+ align:start position:0%
+used for this are called it's compendex
+ 
+
+ align:start position:0%
+used for this are called it's compendex
+and inspec uh these are actually
+
+ align:start position:0%
+and inspec uh these are actually
+ 
+
+ align:start position:0%
+and inspec uh these are actually
+combined if you go to a website called
+
+ align:start position:0%
+combined if you go to a website called
+ 
+
+ align:start position:0%
+combined if you go to a website called
+engineering Village . this is you know
+
+ align:start position:0%
+engineering Village . this is you know
+ 
+
+ align:start position:0%
+engineering Village . this is you know
+sort of a master database for scientific
+
+ align:start position:0%
+sort of a master database for scientific
+ 
+
+ align:start position:0%
+sort of a master database for scientific
+papers in engineering U that that was
+
+ align:start position:0%
+papers in engineering U that that was
+ 
+
+ align:start position:0%
+papers in engineering U that that was
+the basis for this uh number two
+
+ align:start position:0%
+the basis for this uh number two
+ 
+
+ align:start position:0%
+the basis for this uh number two
+reliability number three safety then
+
+ align:start position:0%
+reliability number three safety then
+ 
+
+ align:start position:0%
+reliability number three safety then
+flexibility robustness and so forth and
+
+ align:start position:0%
+flexibility robustness and so forth and
+ 
+
+ align:start position:0%
+flexibility robustness and so forth and
+the other bar the gray bar is if you
+
+ align:start position:0%
+the other bar the gray bar is if you
+ 
+
+ align:start position:0%
+the other bar the gray bar is if you
+Google essentially for uh this
+
+ align:start position:0%
+Google essentially for uh this
+ 
+
+ align:start position:0%
+Google essentially for uh this
+particular keyword and you know keep in
+
+ align:start position:0%
+particular keyword and you know keep in
+ 
+
+ align:start position:0%
+particular keyword and you know keep in
+mind this was done about 5 years ago
+
+ align:start position:0%
+mind this was done about 5 years ago
+ 
+
+ align:start position:0%
+mind this was done about 5 years ago
+this is the number the millions of hits
+
+ align:start position:0%
+this is the number the millions of hits
+ 
+
+ align:start position:0%
+this is the number the millions of hits
+that you will get and um so you know
+
+ align:start position:0%
+that you will get and um so you know
+ 
+
+ align:start position:0%
+that you will get and um so you know
+there's a factor of a thousand
+
+ align:start position:0%
+there's a factor of a thousand
+ 
+
+ align:start position:0%
+there's a factor of a thousand
+difference here between Journal articles
+
+ align:start position:0%
+difference here between Journal articles
+ 
+
+ align:start position:0%
+difference here between Journal articles
+and hits on the internet but still you
+
+ align:start position:0%
+and hits on the internet but still you
+ 
+
+ align:start position:0%
+and hits on the internet but still you
+can sort of compare uh the two and so in
+
+ align:start position:0%
+can sort of compare uh the two and so in
+ 
+
+ align:start position:0%
+can sort of compare uh the two and so in
+some sense the black bar is you know the
+
+ align:start position:0%
+some sense the black bar is you know the
+ 
+
+ align:start position:0%
+some sense the black bar is you know the
+the the totality of scientific knowledge
+
+ align:start position:0%
+the the totality of scientific knowledge
+ 
+
+ align:start position:0%
+the the totality of scientific knowledge
+about this life cycle property and then
+
+ align:start position:0%
+about this life cycle property and then
+ 
+
+ align:start position:0%
+about this life cycle property and then
+the gray bar would be you know the U
+
+ align:start position:0%
+the gray bar would be you know the U
+ 
+
+ align:start position:0%
+the gray bar would be you know the U
+amount of information or uses usage of
+
+ align:start position:0%
+amount of information or uses usage of
+ 
+
+ align:start position:0%
+amount of information or uses usage of
+that knowledge at least as far as it's
+
+ align:start position:0%
+that knowledge at least as far as it's
+ 
+
+ align:start position:0%
+that knowledge at least as far as it's
+represented on the internet and what's
+
+ align:start position:0%
+represented on the internet and what's
+ 
+
+ align:start position:0%
+represented on the internet and what's
+interesting is you know in some cases
+
+ align:start position:0%
+interesting is you know in some cases
+ 
+
+ align:start position:0%
+interesting is you know in some cases
+the the the black bar is smaller than uh
+
+ align:start position:0%
+the the the black bar is smaller than uh
+ 
+
+ align:start position:0%
+the the the black bar is smaller than uh
+the gray bar which means that common
+
+ align:start position:0%
+the gray bar which means that common
+ 
+
+ align:start position:0%
+the gray bar which means that common
+usage is leading so sustainability would
+
+ align:start position:0%
+usage is leading so sustainability would
+ 
+
+ align:start position:0%
+usage is leading so sustainability would
+be an example everybody talks about
+
+ align:start position:0%
+be an example everybody talks about
+ 
+
+ align:start position:0%
+be an example everybody talks about
+sustainability you know companies have
+
+ align:start position:0%
+sustainability you know companies have
+ 
+
+ align:start position:0%
+sustainability you know companies have
+you know they say our system is
+
+ align:start position:0%
+you know they say our system is
+ 
+
+ align:start position:0%
+you know they say our system is
+sustainable because you know it uses
+
+ align:start position:0%
+sustainable because you know it uses
+ 
+
+ align:start position:0%
+sustainable because you know it uses
+less resources it produces less
+
+ align:start position:0%
+less resources it produces less
+ 
+
+ align:start position:0%
+less resources it produces less
+emissions but the actual amount of uh
+
+ align:start position:0%
+emissions but the actual amount of uh
+ 
+
+ align:start position:0%
+emissions but the actual amount of uh
+scientific knowledge the actual amount
+
+ align:start position:0%
+scientific knowledge the actual amount
+ 
+
+ align:start position:0%
+scientific knowledge the actual amount
+of research as to what really is
+
+ align:start position:0%
+of research as to what really is
+ 
+
+ align:start position:0%
+of research as to what really is
+sustainability and how do you design for
+
+ align:start position:0%
+sustainability and how do you design for
+ 
+
+ align:start position:0%
+sustainability and how do you design for
+it is actually smaller than the usage
+
+ align:start position:0%
+it is actually smaller than the usage
+ 
+
+ align:start position:0%
+it is actually smaller than the usage
+and then there's areas where it's the
+
+ align:start position:0%
+and then there's areas where it's the
+ 
+
+ align:start position:0%
+and then there's areas where it's the
+opposite like for example modularity
+
+ align:start position:0%
+opposite like for example modularity
+ 
+
+ align:start position:0%
+opposite like for example modularity
+right you see that in modularity um so
+
+ align:start position:0%
+right you see that in modularity um so
+ 
+
+ align:start position:0%
+right you see that in modularity um so
+in a relative sense academic interest is
+
+ align:start position:0%
+in a relative sense academic interest is
+ 
+
+ align:start position:0%
+in a relative sense academic interest is
+leading there's quite a literature on
+
+ align:start position:0%
+leading there's quite a literature on
+ 
+
+ align:start position:0%
+leading there's quite a literature on
+modularity in mathematics you know
+
+ align:start position:0%
+modularity in mathematics you know
+ 
+
+ align:start position:0%
+modularity in mathematics you know
+modularity in software modularity and
+
+ align:start position:0%
+modularity in software modularity and
+ 
+
+ align:start position:0%
+modularity in software modularity and
+design but most people you know
+
+ align:start position:0%
+design but most people you know
+ 
+
+ align:start position:0%
+design but most people you know
+modularity per se is not so interesting
+
+ align:start position:0%
+modularity per se is not so interesting
+ 
+
+ align:start position:0%
+modularity per se is not so interesting
+and so exciting to you know the general
+
+ align:start position:0%
+and so exciting to you know the general
+ 
+
+ align:start position:0%
+and so exciting to you know the general
+public so keep in mind that for some
+
+ align:start position:0%
+public so keep in mind that for some
+ 
+
+ align:start position:0%
+public so keep in mind that for some
+ilities uh there's an imbalance
+
+ align:start position:0%
+ilities uh there's an imbalance
+ 
+
+ align:start position:0%
+ilities uh there's an imbalance
+essentially between our our
+
+ align:start position:0%
+essentially between our our
+ 
+
+ align:start position:0%
+essentially between our our
+understanding of the scientific
+
+ align:start position:0%
+understanding of the scientific
+ 
+
+ align:start position:0%
+understanding of the scientific
+knowledge our understanding to be design
+
+ align:start position:0%
+knowledge our understanding to be design
+ 
+
+ align:start position:0%
+knowledge our understanding to be design
+how to design for it and you know how
+
+ align:start position:0%
+how to design for it and you know how
+ 
+
+ align:start position:0%
+how to design for it and you know how
+frequently at least that keyword is
+
+ align:start position:0%
+frequently at least that keyword is
+ 
+
+ align:start position:0%
+frequently at least that keyword is
+used um now here this is a little bit
+
+ align:start position:0%
+used um now here this is a little bit
+ 
+
+ align:start position:0%
+used um now here this is a little bit
+more uh this is a little bit harder to
+
+ align:start position:0%
+more uh this is a little bit harder to
+ 
+
+ align:start position:0%
+more uh this is a little bit harder to
+see this is essentially looking at these
+
+ align:start position:0%
+see this is essentially looking at these
+ 
+
+ align:start position:0%
+see this is essentially looking at these
+life cycle properties over over time so
+
+ align:start position:0%
+life cycle properties over over time so
+ 
+
+ align:start position:0%
+life cycle properties over over time so
+what this graph shows you is starting
+
+ align:start position:0%
+what this graph shows you is starting
+ 
+
+ align:start position:0%
+what this graph shows you is starting
+here in
+
+ align:start position:0%
+here in
+ 
+
+ align:start position:0%
+here in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+cumulatively uh the number of Journal
+
+ align:start position:0%
+cumulatively uh the number of Journal
+ 
+
+ align:start position:0%
+cumulatively uh the number of Journal
+articles published about each life cycle
+
+ align:start position:0%
+articles published about each life cycle
+ 
+
+ align:start position:0%
+articles published about each life cycle
+property and uh roughly the way you can
+
+ align:start position:0%
+property and uh roughly the way you can
+ 
+
+ align:start position:0%
+property and uh roughly the way you can
+think about this is that there's some
+
+ align:start position:0%
+think about this is that there's some
+ 
+
+ align:start position:0%
+think about this is that there's some
+life cycle property the top four five
+
+ align:start position:0%
+life cycle property the top four five
+ 
+
+ align:start position:0%
+life cycle property the top four five
+that we've been actually working on for
+
+ align:start position:0%
+that we've been actually working on for
+ 
+
+ align:start position:0%
+that we've been actually working on for
+a long time even safety you know there's
+
+ align:start position:0%
+a long time even safety you know there's
+ 
+
+ align:start position:0%
+a long time even safety you know there's
+some interesting articles in the 1890s
+
+ align:start position:0%
+some interesting articles in the 1890s
+ 
+
+ align:start position:0%
+some interesting articles in the 1890s
+about safety for example in mines you
+
+ align:start position:0%
+about safety for example in mines you
+ 
+
+ align:start position:0%
+about safety for example in mines you
+know coal mines there's an article about
+
+ align:start position:0%
+know coal mines there's an article about
+ 
+
+ align:start position:0%
+know coal mines there's an article about
+how does the impact of lighting better
+
+ align:start position:0%
+how does the impact of lighting better
+ 
+
+ align:start position:0%
+how does the impact of lighting better
+Lighting on safety and productivity in
+
+ align:start position:0%
+Lighting on safety and productivity in
+ 
+
+ align:start position:0%
+Lighting on safety and productivity in
+mines 1890 okay and so they showed that
+
+ align:start position:0%
+mines 1890 okay and so they showed that
+ 
+
+ align:start position:0%
+mines 1890 okay and so they showed that
+just providing better lighting actually
+
+ align:start position:0%
+just providing better lighting actually
+ 
+
+ align:start position:0%
+just providing better lighting actually
+has a dual benefit pure accidents pure
+
+ align:start position:0%
+has a dual benefit pure accidents pure
+ 
+
+ align:start position:0%
+has a dual benefit pure accidents pure
+fatalities and better production output
+
+ align:start position:0%
+fatalities and better production output
+ 
+
+ align:start position:0%
+fatalities and better production output
+and so you know that that's and this was
+
+ align:start position:0%
+and so you know that that's and this was
+ 
+
+ align:start position:0%
+and so you know that that's and this was
+a scientific study that was done by you
+
+ align:start position:0%
+a scientific study that was done by you
+ 
+
+ align:start position:0%
+a scientific study that was done by you
+know comparing data in different minds
+
+ align:start position:0%
+know comparing data in different minds
+ 
+
+ align:start position:0%
+know comparing data in different minds
+and and actually performing some
+
+ align:start position:0%
+and and actually performing some
+ 
+
+ align:start position:0%
+and and actually performing some
+experiments um then you have a group of
+
+ align:start position:0%
+experiments um then you have a group of
+ 
+
+ align:start position:0%
+experiments um then you have a group of
+life cycle properties that we only
+
+ align:start position:0%
+life cycle properties that we only
+ 
+
+ align:start position:0%
+life cycle properties that we only
+started really thinking about and
+
+ align:start position:0%
+started really thinking about and
+ 
+
+ align:start position:0%
+started really thinking about and
+Publishing about I would say around
+
+ align:start position:0%
+Publishing about I would say around
+ 
+
+ align:start position:0%
+Publishing about I would say around
+World War II such as usability uh
+
+ align:start position:0%
+World War II such as usability uh
+ 
+
+ align:start position:0%
+World War II such as usability uh
+maintainability and my interpretation of
+
+ align:start position:0%
+maintainability and my interpretation of
+ 
+
+ align:start position:0%
+maintainability and my interpretation of
+this is that especially during World War
+
+ align:start position:0%
+this is that especially during World War
+ 
+
+ align:start position:0%
+this is that especially during World War
+II a big difference made Logistics you
+
+ align:start position:0%
+II a big difference made Logistics you
+ 
+
+ align:start position:0%
+II a big difference made Logistics you
+know how how easy was it was it to use
+
+ align:start position:0%
+know how how easy was it was it to use
+ 
+
+ align:start position:0%
+know how how easy was it was it to use
+uh different weapons uh how easy was it
+
+ align:start position:0%
+uh different weapons uh how easy was it
+ 
+
+ align:start position:0%
+uh different weapons uh how easy was it
+to maintain
+
+ align:start position:0%
+to maintain
+ 
+
+ align:start position:0%
+to maintain
+equipment uh it became a huge
+
+ align:start position:0%
+equipment uh it became a huge
+ 
+
+ align:start position:0%
+equipment uh it became a huge
+determining factor in the outcome of the
+
+ align:start position:0%
+determining factor in the outcome of the
+ 
+
+ align:start position:0%
+determining factor in the outcome of the
+war you know for example in North Africa
+
+ align:start position:0%
+war you know for example in North Africa
+ 
+
+ align:start position:0%
+war you know for example in North Africa
+and the North African theater uh you
+
+ align:start position:0%
+and the North African theater uh you
+ 
+
+ align:start position:0%
+and the North African theater uh you
+know tanks uh trucks uh being exposed to
+
+ align:start position:0%
+know tanks uh trucks uh being exposed to
+ 
+
+ align:start position:0%
+know tanks uh trucks uh being exposed to
+you know the sand and and so forth so
+
+ align:start position:0%
+you know the sand and and so forth so
+ 
+
+ align:start position:0%
+you know the sand and and so forth so
+people really started thinking about the
+
+ align:start position:0%
+people really started thinking about the
+ 
+
+ align:start position:0%
+people really started thinking about the
+military started thinking heavily About
+
+ align:start position:0%
+military started thinking heavily About
+ 
+
+ align:start position:0%
+military started thinking heavily About
+You Know M the importance of
+
+ align:start position:0%
+You Know M the importance of
+ 
+
+ align:start position:0%
+You Know M the importance of
+maintainability in the design of these
+
+ align:start position:0%
+maintainability in the design of these
+ 
+
+ align:start position:0%
+maintainability in the design of these
+systems and after the war then a lot of
+
+ align:start position:0%
+systems and after the war then a lot of
+ 
+
+ align:start position:0%
+systems and after the war then a lot of
+these Concepts like usability and
+
+ align:start position:0%
+these Concepts like usability and
+ 
+
+ align:start position:0%
+these Concepts like usability and
+maintain ility started spreading into
+
+ align:start position:0%
+maintain ility started spreading into
+ 
+
+ align:start position:0%
+maintain ility started spreading into
+General civilian life and products and
+
+ align:start position:0%
+General civilian life and products and
+ 
+
+ align:start position:0%
+General civilian life and products and
+so forth and then the third uh the third
+
+ align:start position:0%
+so forth and then the third uh the third
+ 
+
+ align:start position:0%
+so forth and then the third uh the third
+uh period or the third type of illes are
+
+ align:start position:0%
+uh period or the third type of illes are
+ 
+
+ align:start position:0%
+uh period or the third type of illes are
+the the newer ones that we've done
+
+ align:start position:0%
+the the newer ones that we've done
+ 
+
+ align:start position:0%
+the the newer ones that we've done
+research on just since the 70s in the
+
+ align:start position:0%
+research on just since the 70s in the
+ 
+
+ align:start position:0%
+research on just since the 70s in the
+last 30 years so here in this category I
+
+ align:start position:0%
+last 30 years so here in this category I
+ 
+
+ align:start position:0%
+last 30 years so here in this category I
+would put things like
+
+ align:start position:0%
+would put things like
+ 
+
+ align:start position:0%
+would put things like
+sustainability uh recyclability
+
+ align:start position:0%
+sustainability uh recyclability
+ 
+
+ align:start position:0%
+sustainability uh recyclability
+evolvability even interoperability which
+
+ align:start position:0%
+evolvability even interoperability which
+ 
+
+ align:start position:0%
+evolvability even interoperability which
+means the ability of systems to connect
+
+ align:start position:0%
+means the ability of systems to connect
+ 
+
+ align:start position:0%
+means the ability of systems to connect
+together and work across system
+
+ align:start position:0%
+together and work across system
+ 
+
+ align:start position:0%
+together and work across system
+boundaries those are pretty recent uh
+
+ align:start position:0%
+boundaries those are pretty recent uh
+ 
+
+ align:start position:0%
+boundaries those are pretty recent uh
+life cycle properties and we're still
+
+ align:start position:0%
+life cycle properties and we're still
+ 
+
+ align:start position:0%
+life cycle properties and we're still
+actively researching
+
+ align:start position:0%
+actively researching
+ 
+
+ align:start position:0%
+actively researching
+them so another way to show this is by
+
+ align:start position:0%
+them so another way to show this is by
+ 
+
+ align:start position:0%
+them so another way to show this is by
+essentially making a network of these
+
+ align:start position:0%
+essentially making a network of these
+ 
+
+ align:start position:0%
+essentially making a network of these
+life cycle properties and so the way
+
+ align:start position:0%
+life cycle properties and so the way
+ 
+
+ align:start position:0%
+life cycle properties and so the way
+this is still all using this prevalence
+
+ align:start position:0%
+this is still all using this prevalence
+ 
+
+ align:start position:0%
+this is still all using this prevalence
+data essentially what you see here is a
+
+ align:start position:0%
+data essentially what you see here is a
+ 
+
+ align:start position:0%
+data essentially what you see here is a
+network diagram that has these life
+
+ align:start position:0%
+network diagram that has these life
+ 
+
+ align:start position:0%
+network diagram that has these life
+cycle properties in a network
+
+ align:start position:0%
+cycle properties in a network
+ 
+
+ align:start position:0%
+cycle properties in a network
+relationship let me just explain um the
+
+ align:start position:0%
+relationship let me just explain um the
+ 
+
+ align:start position:0%
+relationship let me just explain um the
+so the size of the nodes relates to uh
+
+ align:start position:0%
+so the size of the nodes relates to uh
+ 
+
+ align:start position:0%
+so the size of the nodes relates to uh
+how many you know how much knowledge we
+
+ align:start position:0%
+how many you know how much knowledge we
+ 
+
+ align:start position:0%
+how many you know how much knowledge we
+have essentially the the height of the
+
+ align:start position:0%
+have essentially the the height of the
+ 
+
+ align:start position:0%
+have essentially the the height of the
+bars that we saw earlier and then the
+
+ align:start position:0%
+bars that we saw earlier and then the
+ 
+
+ align:start position:0%
+bars that we saw earlier and then the
+strength the thickness of the line
+
+ align:start position:0%
+strength the thickness of the line
+ 
+
+ align:start position:0%
+strength the thickness of the line
+relates to the strength of Rel how
+
+ align:start position:0%
+relates to the strength of Rel how
+ 
+
+ align:start position:0%
+relates to the strength of Rel how
+closely are these two ilities related
+
+ align:start position:0%
+closely are these two ilities related
+ 
+
+ align:start position:0%
+closely are these two ilities related
+and the way this is calculated is using
+
+ align:start position:0%
+and the way this is calculated is using
+ 
+
+ align:start position:0%
+and the way this is calculated is using
+a so-called Tut tupal correlation so you
+
+ align:start position:0%
+a so-called Tut tupal correlation so you
+ 
+
+ align:start position:0%
+a so-called Tut tupal correlation so you
+take essentially articles that have you
+
+ align:start position:0%
+take essentially articles that have you
+ 
+
+ align:start position:0%
+take essentially articles that have you
+look at articles that have for example
+
+ align:start position:0%
+look at articles that have for example
+ 
+
+ align:start position:0%
+look at articles that have for example
+reliability and maintainability in the
+
+ align:start position:0%
+reliability and maintainability in the
+ 
+
+ align:start position:0%
+reliability and maintainability in the
+same article right and then you divide
+
+ align:start position:0%
+same article right and then you divide
+ 
+
+ align:start position:0%
+same article right and then you divide
+that by the total number of articles on
+
+ align:start position:0%
+that by the total number of articles on
+ 
+
+ align:start position:0%
+that by the total number of articles on
+reliability and or maintainability and
+
+ align:start position:0%
+reliability and or maintainability and
+ 
+
+ align:start position:0%
+reliability and or maintainability and
+that's a ratio between zero and one and
+
+ align:start position:0%
+that's a ratio between zero and one and
+ 
+
+ align:start position:0%
+that's a ratio between zero and one and
+then this graph was produced with a
+
+ align:start position:0%
+then this graph was produced with a
+ 
+
+ align:start position:0%
+then this graph was produced with a
+cutof strength of 0.1 right so if
+
+ align:start position:0%
+cutof strength of 0.1 right so if
+ 
+
+ align:start position:0%
+cutof strength of 0.1 right so if
+there's more than 10% of of Articles
+
+ align:start position:0%
+there's more than 10% of of Articles
+ 
+
+ align:start position:0%
+there's more than 10% of of Articles
+list these two properties together then
+
+ align:start position:0%
+list these two properties together then
+ 
+
+ align:start position:0%
+list these two properties together then
+there will be a line here and the
+
+ align:start position:0%
+there will be a line here and the
+ 
+
+ align:start position:0%
+there will be a line here and the
+stronger the line the thicker the line
+
+ align:start position:0%
+stronger the line the thicker the line
+ 
+
+ align:start position:0%
+stronger the line the thicker the line
+is the more closely the more often these
+
+ align:start position:0%
+is the more closely the more often these
+ 
+
+ align:start position:0%
+is the more closely the more often these
+concepts are co- mentioned in the same
+
+ align:start position:0%
+concepts are co- mentioned in the same
+ 
+
+ align:start position:0%
+concepts are co- mentioned in the same
+in the same article or the same piece of
+
+ align:start position:0%
+in the same article or the same piece of
+ 
+
+ align:start position:0%
+in the same article or the same piece of
+work so it reflects the strength of
+
+ align:start position:0%
+work so it reflects the strength of
+ 
+
+ align:start position:0%
+work so it reflects the strength of
+relationship now what's interesting is
+
+ align:start position:0%
+relationship now what's interesting is
+ 
+
+ align:start position:0%
+relationship now what's interesting is
+you know when you first look at this you
+
+ align:start position:0%
+you know when you first look at this you
+ 
+
+ align:start position:0%
+you know when you first look at this you
+you know you don't see much but after
+
+ align:start position:0%
+you know you don't see much but after
+ 
+
+ align:start position:0%
+you know you don't see much but after
+you look at this for a while you start
+
+ align:start position:0%
+you look at this for a while you start
+ 
+
+ align:start position:0%
+you look at this for a while you start
+to realize a few things first of all in
+
+ align:start position:0%
+to realize a few things first of all in
+ 
+
+ align:start position:0%
+to realize a few things first of all in
+the center of the graph we have the
+
+ align:start position:0%
+the center of the graph we have the
+ 
+
+ align:start position:0%
+the center of the graph we have the
+classic ilities of engineering quality
+
+ align:start position:0%
+classic ilities of engineering quality
+ 
+
+ align:start position:0%
+classic ilities of engineering quality
+safety reliability and I would argue
+
+ align:start position:0%
+safety reliability and I would argue
+ 
+
+ align:start position:0%
+safety reliability and I would argue
+flexibility as well those are the top
+
+ align:start position:0%
+flexibility as well those are the top
+ 
+
+ align:start position:0%
+flexibility as well those are the top
+four that we saw before and then around
+
+ align:start position:0%
+four that we saw before and then around
+ 
+
+ align:start position:0%
+four that we saw before and then around
+the periphery of the graph we have newer
+
+ align:start position:0%
+the periphery of the graph we have newer
+ 
+
+ align:start position:0%
+the periphery of the graph we have newer
+life cycle properties that are more
+
+ align:start position:0%
+life cycle properties that are more
+ 
+
+ align:start position:0%
+life cycle properties that are more
+recent we haven't really uh thought
+
+ align:start position:0%
+recent we haven't really uh thought
+ 
+
+ align:start position:0%
+recent we haven't really uh thought
+about them too much we don't fully know
+
+ align:start position:0%
+about them too much we don't fully know
+ 
+
+ align:start position:0%
+about them too much we don't fully know
+how to design for them yet and if you
+
+ align:start position:0%
+how to design for them yet and if you
+ 
+
+ align:start position:0%
+how to design for them yet and if you
+look at them in groups I will argue that
+
+ align:start position:0%
+look at them in groups I will argue that
+ 
+
+ align:start position:0%
+look at them in groups I will argue that
+there are three major groups here so the
+
+ align:start position:0%
+there are three major groups here so the
+ 
+
+ align:start position:0%
+there are three major groups here so the
+first group in the upper left is things
+
+ align:start position:0%
+first group in the upper left is things
+ 
+
+ align:start position:0%
+first group in the upper left is things
+like maintainability durability
+
+ align:start position:0%
+like maintainability durability
+ 
+
+ align:start position:0%
+like maintainability durability
+reliability quality and so forth so this
+
+ align:start position:0%
+reliability quality and so forth so this
+ 
+
+ align:start position:0%
+reliability quality and so forth so this
+is all about is the system made well
+
+ align:start position:0%
+is all about is the system made well
+ 
+
+ align:start position:0%
+is all about is the system made well
+with high quality particularly early in
+
+ align:start position:0%
+with high quality particularly early in
+ 
+
+ align:start position:0%
+with high quality particularly early in
+its life right then we have a a group
+
+ align:start position:0%
+its life right then we have a a group
+ 
+
+ align:start position:0%
+its life right then we have a a group
+here on the right and this is about is
+
+ align:start position:0%
+here on the right and this is about is
+ 
+
+ align:start position:0%
+here on the right and this is about is
+the system easy to change is it easy to
+
+ align:start position:0%
+the system easy to change is it easy to
+ 
+
+ align:start position:0%
+the system easy to change is it easy to
+change the system configuration
+
+ align:start position:0%
+change the system configuration
+ 
+
+ align:start position:0%
+change the system configuration
+flexibility
+
+ align:start position:0%
+flexibility
+ 
+
+ align:start position:0%
+flexibility
+extensibility uh modularity and
+
+ align:start position:0%
+extensibility uh modularity and
+ 
+
+ align:start position:0%
+extensibility uh modularity and
+scalability uh
+
+ align:start position:0%
+scalability uh
+ 
+
+ align:start position:0%
+scalability uh
+interoperability those are all different
+
+ align:start position:0%
+interoperability those are all different
+ 
+
+ align:start position:0%
+interoperability those are all different
+subf flavers if you want of being able
+
+ align:start position:0%
+subf flavers if you want of being able
+ 
+
+ align:start position:0%
+subf flavers if you want of being able
+to modify the system over its life and
+
+ align:start position:0%
+to modify the system over its life and
+ 
+
+ align:start position:0%
+to modify the system over its life and
+so that's group abilities that that goes
+
+ align:start position:0%
+so that's group abilities that that goes
+ 
+
+ align:start position:0%
+so that's group abilities that that goes
+together and then the third one is you
+
+ align:start position:0%
+together and then the third one is you
+ 
+
+ align:start position:0%
+together and then the third one is you
+know resilience robustness quality um
+
+ align:start position:0%
+know resilience robustness quality um
+ 
+
+ align:start position:0%
+know resilience robustness quality um
+safety um and so this is really related
+
+ align:start position:0%
+safety um and so this is really related
+ 
+
+ align:start position:0%
+safety um and so this is really related
+to Performance of the system under
+
+ align:start position:0%
+to Performance of the system under
+ 
+
+ align:start position:0%
+to Performance of the system under
+different types of uncertainty you know
+
+ align:start position:0%
+different types of uncertainty you know
+ 
+
+ align:start position:0%
+different types of uncertainty you know
+either uh environmental variability or
+
+ align:start position:0%
+either uh environmental variability or
+ 
+
+ align:start position:0%
+either uh environmental variability or
+failures in the system and the ability
+
+ align:start position:0%
+failures in the system and the ability
+ 
+
+ align:start position:0%
+failures in the system and the ability
+of the system to withstand or at least
+
+ align:start position:0%
+of the system to withstand or at least
+ 
+
+ align:start position:0%
+of the system to withstand or at least
+perform you know have good residual
+
+ align:start position:0%
+perform you know have good residual
+ 
+
+ align:start position:0%
+perform you know have good residual
+performance even in the face of failures
+
+ align:start position:0%
+performance even in the face of failures
+ 
+
+ align:start position:0%
+performance even in the face of failures
+so that's I think an important way to
+
+ align:start position:0%
+so that's I think an important way to
+ 
+
+ align:start position:0%
+so that's I think an important way to
+think about it and when you're writing
+
+ align:start position:0%
+think about it and when you're writing
+ 
+
+ align:start position:0%
+think about it and when you're writing
+requirements for systems like the system
+
+ align:start position:0%
+requirements for systems like the system
+ 
+
+ align:start position:0%
+requirements for systems like the system
+should be resilient then this helps you
+
+ align:start position:0%
+should be resilient then this helps you
+ 
+
+ align:start position:0%
+should be resilient then this helps you
+understand well what are the other
+
+ align:start position:0%
+understand well what are the other
+ 
+
+ align:start position:0%
+understand well what are the other
+properties that are linked to it and
+
+ align:start position:0%
+properties that are linked to it and
+ 
+
+ align:start position:0%
+properties that are linked to it and
+that maybe support that okay any any
+
+ align:start position:0%
+that maybe support that okay any any
+ 
+
+ align:start position:0%
+that maybe support that okay any any
+questions uh here or at MIT about uh
+
+ align:start position:0%
+questions uh here or at MIT about uh
+ 
+
+ align:start position:0%
+questions uh here or at MIT about uh
+this is sort of method one is get data
+
+ align:start position:0%
+this is sort of method one is get data
+ 
+
+ align:start position:0%
+this is sort of method one is get data
+about these life cycle properties and
+
+ align:start position:0%
+about these life cycle properties and
+ 
+
+ align:start position:0%
+about these life cycle properties and
+put them in relation to each other any
+
+ align:start position:0%
+put them in relation to each other any
+ 
+
+ align:start position:0%
+put them in relation to each other any
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yanna are there any questions there yeah
+
+ align:start position:0%
+Yanna are there any questions there yeah
+ 
+
+ align:start position:0%
+Yanna are there any questions there yeah
+I have a question so is this chart that
+
+ align:start position:0%
+I have a question so is this chart that
+ 
+
+ align:start position:0%
+I have a question so is this chart that
+you have up now actually used in the
+
+ align:start position:0%
+you have up now actually used in the
+ 
+
+ align:start position:0%
+you have up now actually used in the
+initial design and like conception
+
+ align:start position:0%
+initial design and like conception
+ 
+
+ align:start position:0%
+initial design and like conception
+conops to like try to tease out the
+
+ align:start position:0%
+conops to like try to tease out the
+ 
+
+ align:start position:0%
+conops to like try to tease out the
+interdependencies or is it too abstract
+
+ align:start position:0%
+interdependencies or is it too abstract
+ 
+
+ align:start position:0%
+interdependencies or is it too abstract
+and just more of a educational
+
+ align:start position:0%
+and just more of a educational
+ 
+
+ align:start position:0%
+and just more of a educational
+tool it's really at this point you know
+
+ align:start position:0%
+tool it's really at this point you know
+ 
+
+ align:start position:0%
+tool it's really at this point you know
+this is fairly recent this was just done
+
+ align:start position:0%
+this is fairly recent this was just done
+ 
+
+ align:start position:0%
+this is fairly recent this was just done
+in the last few years so this I don't
+
+ align:start position:0%
+in the last few years so this I don't
+ 
+
+ align:start position:0%
+in the last few years so this I don't
+think this has fully penetrated system
+
+ align:start position:0%
+think this has fully penetrated system
+ 
+
+ align:start position:0%
+think this has fully penetrated system
+engineering practice yet but the point
+
+ align:start position:0%
+engineering practice yet but the point
+ 
+
+ align:start position:0%
+engineering practice yet but the point
+the point that I I want to make here is
+
+ align:start position:0%
+the point that I I want to make here is
+ 
+
+ align:start position:0%
+the point that I I want to make here is
+that there's a huge there's a huge gap
+
+ align:start position:0%
+that there's a huge there's a huge gap
+ 
+
+ align:start position:0%
+that there's a huge there's a huge gap
+right now between when people in the you
+
+ align:start position:0%
+right now between when people in the you
+ 
+
+ align:start position:0%
+right now between when people in the you
+know in briefings you know either at the
+
+ align:start position:0%
+know in briefings you know either at the
+ 
+
+ align:start position:0%
+know in briefings you know either at the
+the Pentagon or you know at a corporate
+
+ align:start position:0%
+the Pentagon or you know at a corporate
+ 
+
+ align:start position:0%
+the Pentagon or you know at a corporate
+headquarters say you know we want a
+
+ align:start position:0%
+headquarters say you know we want a
+ 
+
+ align:start position:0%
+headquarters say you know we want a
+sustainable product or we want a you
+
+ align:start position:0%
+sustainable product or we want a you
+ 
+
+ align:start position:0%
+sustainable product or we want a you
+know we're a software company we're do
+
+ align:start position:0%
+know we're a software company we're do
+ 
+
+ align:start position:0%
+know we're a software company we're do
+we do Optical networking and we want we
+
+ align:start position:0%
+we do Optical networking and we want we
+ 
+
+ align:start position:0%
+we do Optical networking and we want we
+want to have the most resilient design
+
+ align:start position:0%
+want to have the most resilient design
+ 
+
+ align:start position:0%
+want to have the most resilient design
+of the IND history you know they'll put
+
+ align:start position:0%
+of the IND history you know they'll put
+ 
+
+ align:start position:0%
+of the IND history you know they'll put
+that as a goal for the project the
+
+ align:start position:0%
+that as a goal for the project the
+ 
+
+ align:start position:0%
+that as a goal for the project the
+question then is well okay that's fine
+
+ align:start position:0%
+question then is well okay that's fine
+ 
+
+ align:start position:0%
+question then is well okay that's fine
+but what does that really mean what does
+
+ align:start position:0%
+but what does that really mean what does
+ 
+
+ align:start position:0%
+but what does that really mean what does
+it really mean resilient you have to
+
+ align:start position:0%
+it really mean resilient you have to
+ 
+
+ align:start position:0%
+it really mean resilient you have to
+operationalize that definition such that
+
+ align:start position:0%
+operationalize that definition such that
+ 
+
+ align:start position:0%
+operationalize that definition such that
+you can derive from it lower level
+
+ align:start position:0%
+you can derive from it lower level
+ 
+
+ align:start position:0%
+you can derive from it lower level
+requirements that you can actually go
+
+ align:start position:0%
+requirements that you can actually go
+ 
+
+ align:start position:0%
+requirements that you can actually go
+and designed to that you can test for so
+
+ align:start position:0%
+and designed to that you can test for so
+ 
+
+ align:start position:0%
+and designed to that you can test for so
+um what what what this helps you to do
+
+ align:start position:0%
+um what what what this helps you to do
+ 
+
+ align:start position:0%
+um what what what this helps you to do
+is understand what are what are maybe
+
+ align:start position:0%
+is understand what are what are maybe
+ 
+
+ align:start position:0%
+is understand what are what are maybe
+supporting that what are supporting um
+
+ align:start position:0%
+supporting that what are supporting um
+ 
+
+ align:start position:0%
+supporting that what are supporting um
+elements that will that will will be
+
+ align:start position:0%
+elements that will that will will be
+ 
+
+ align:start position:0%
+elements that will that will will be
+related to resilience you know what are
+
+ align:start position:0%
+related to resilience you know what are
+ 
+
+ align:start position:0%
+related to resilience you know what are
+what are what are supporting Concepts
+
+ align:start position:0%
+what are what are supporting Concepts
+ 
+
+ align:start position:0%
+what are what are supporting Concepts
+supporting life cycle properties that
+
+ align:start position:0%
+supporting life cycle properties that
+ 
+
+ align:start position:0%
+supporting life cycle properties that
+that this property that you're looking
+
+ align:start position:0%
+that this property that you're looking
+ 
+
+ align:start position:0%
+that this property that you're looking
+for uh is linked to right so it's it's
+
+ align:start position:0%
+for uh is linked to right so it's it's
+ 
+
+ align:start position:0%
+for uh is linked to right so it's it's
+an evolution you know we we know how to
+
+ align:start position:0%
+an evolution you know we we know how to
+ 
+
+ align:start position:0%
+an evolution you know we we know how to
+design now for you know speed and Energy
+
+ align:start position:0%
+design now for you know speed and Energy
+ 
+
+ align:start position:0%
+design now for you know speed and Energy
+Efficiency and you know the sort of
+
+ align:start position:0%
+Efficiency and you know the sort of
+ 
+
+ align:start position:0%
+Efficiency and you know the sort of
+things that were really hard to do 20 30
+
+ align:start position:0%
+things that were really hard to do 20 30
+ 
+
+ align:start position:0%
+things that were really hard to do 20 30
+50 years ago it's pretty standard
+
+ align:start position:0%
+50 years ago it's pretty standard
+ 
+
+ align:start position:0%
+50 years ago it's pretty standard
+practice now you know how do you design
+
+ align:start position:0%
+practice now you know how do you design
+ 
+
+ align:start position:0%
+practice now you know how do you design
+for optimal interoperability we don't
+
+ align:start position:0%
+for optimal interoperability we don't
+ 
+
+ align:start position:0%
+for optimal interoperability we don't
+quite know yet but we're we're finding
+
+ align:start position:0%
+quite know yet but we're we're finding
+ 
+
+ align:start position:0%
+quite know yet but we're we're finding
+our way and so uh believe is that you
+
+ align:start position:0%
+our way and so uh believe is that you
+ 
+
+ align:start position:0%
+our way and so uh believe is that you
+know those especially the life cycle
+
+ align:start position:0%
+know those especially the life cycle
+ 
+
+ align:start position:0%
+know those especially the life cycle
+properties on the outer periphery of
+
+ align:start position:0%
+properties on the outer periphery of
+ 
+
+ align:start position:0%
+properties on the outer periphery of
+this chart the those are the ones that
+
+ align:start position:0%
+this chart the those are the ones that
+ 
+
+ align:start position:0%
+this chart the those are the ones that
+that need more work and those are the
+
+ align:start position:0%
+that need more work and those are the
+ 
+
+ align:start position:0%
+that need more work and those are the
+ones that were really learning how to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operationalize does that make
+
+ align:start position:0%
+operationalize does that make
+ 
+
+ align:start position:0%
+operationalize does that make
+sense uh yeah thanks that makes
+
+ align:start position:0%
+sense uh yeah thanks that makes
+ 
+
+ align:start position:0%
+sense uh yeah thanks that makes
+sense okay good so uh let me talk about
+
+ align:start position:0%
+sense okay good so uh let me talk about
+ 
+
+ align:start position:0%
+sense okay good so uh let me talk about
+method two so this was basically uh
+
+ align:start position:0%
+method two so this was basically uh
+ 
+
+ align:start position:0%
+method two so this was basically uh
+trying to get to how how do people how
+
+ align:start position:0%
+trying to get to how how do people how
+ 
+
+ align:start position:0%
+trying to get to how how do people how
+do humans there sem semantics means the
+
+ align:start position:0%
+do humans there sem semantics means the
+ 
+
+ align:start position:0%
+do humans there sem semantics means the
+meaning of words right semantics is the
+
+ align:start position:0%
+meaning of words right semantics is the
+ 
+
+ align:start position:0%
+meaning of words right semantics is the
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+
+ align:start position:0%
+science of the meaning of words how do
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+they what how do they interpret these
+ 
+
+ align:start position:0%
+they what how do they interpret these
+life cycle properties and um and so here
+
+ align:start position:0%
+life cycle properties and um and so here
+ 
+
+ align:start position:0%
+life cycle properties and um and so here
+humans have a deep and possibly varied
+
+ align:start position:0%
+humans have a deep and possibly varied
+ 
+
+ align:start position:0%
+humans have a deep and possibly varied
+understanding of the semantics of these
+
+ align:start position:0%
+understanding of the semantics of these
+ 
+
+ align:start position:0%
+understanding of the semantics of these
+life cycle properties so what was done
+
+ align:start position:0%
+life cycle properties so what was done
+ 
+
+ align:start position:0%
+life cycle properties so what was done
+here was that a list of 15 life cycle
+
+ align:start position:0%
+here was that a list of 15 life cycle
+ 
+
+ align:start position:0%
+here was that a list of 15 life cycle
+properties many of them are overlapping
+
+ align:start position:0%
+properties many of them are overlapping
+ 
+
+ align:start position:0%
+properties many of them are overlapping
+with the ones you saw earlier were
+
+ align:start position:0%
+with the ones you saw earlier were
+ 
+
+ align:start position:0%
+with the ones you saw earlier were
+presented um and then the challenge was
+
+ align:start position:0%
+presented um and then the challenge was
+ 
+
+ align:start position:0%
+presented um and then the challenge was
+to the the question that these uh four
+
+ align:start position:0%
+to the the question that these uh four
+ 
+
+ align:start position:0%
+to the the question that these uh four
+groups 12 12 participants four groups
+
+ align:start position:0%
+groups 12 12 participants four groups
+ 
+
+ align:start position:0%
+groups 12 12 participants four groups
+had to say is there a hierarchy here you
+
+ align:start position:0%
+had to say is there a hierarchy here you
+ 
+
+ align:start position:0%
+had to say is there a hierarchy here you
+know are some higher level life cycle
+
+ align:start position:0%
+know are some higher level life cycle
+ 
+
+ align:start position:0%
+know are some higher level life cycle
+properties are some of them lower level
+
+ align:start position:0%
+properties are some of them lower level
+ 
+
+ align:start position:0%
+properties are some of them lower level
+properties that support these so there
+
+ align:start position:0%
+properties that support these so there
+ 
+
+ align:start position:0%
+properties that support these so there
+was round one find the parent child
+
+ align:start position:0%
+was round one find the parent child
+ 
+
+ align:start position:0%
+was round one find the parent child
+relationships described these interviews
+
+ align:start position:0%
+relationships described these interviews
+ 
+
+ align:start position:0%
+relationships described these interviews
+and then a second round so here's
+
+ align:start position:0%
+and then a second round so here's
+ 
+
+ align:start position:0%
+and then a second round so here's
+essentially um what was what was the
+
+ align:start position:0%
+essentially um what was what was the
+ 
+
+ align:start position:0%
+essentially um what was what was the
+results of the first round so four
+
+ align:start position:0%
+results of the first round so four
+ 
+
+ align:start position:0%
+results of the first round so four
+different groups so each of them
+
+ align:start position:0%
+different groups so each of them
+ 
+
+ align:start position:0%
+different groups so each of them
+basically uh came up with its own
+
+ align:start position:0%
+basically uh came up with its own
+ 
+
+ align:start position:0%
+basically uh came up with its own
+version of a hierarchy they didn't talk
+
+ align:start position:0%
+version of a hierarchy they didn't talk
+ 
+
+ align:start position:0%
+version of a hierarchy they didn't talk
+to each other they were firewalled from
+
+ align:start position:0%
+to each other they were firewalled from
+ 
+
+ align:start position:0%
+to each other they were firewalled from
+each other and in all cases this notion
+
+ align:start position:0%
+each other and in all cases this notion
+ 
+
+ align:start position:0%
+each other and in all cases this notion
+of value robustness came out on top so
+
+ align:start position:0%
+of value robustness came out on top so
+ 
+
+ align:start position:0%
+of value robustness came out on top so
+value robustness means the system should
+
+ align:start position:0%
+value robustness means the system should
+ 
+
+ align:start position:0%
+value robustness means the system should
+deliver value right to the stakeholders
+
+ align:start position:0%
+deliver value right to the stakeholders
+ 
+
+ align:start position:0%
+deliver value right to the stakeholders
+despite uh failures you know
+
+ align:start position:0%
+despite uh failures you know
+ 
+
+ align:start position:0%
+despite uh failures you know
+environmental changes so value delivery
+
+ align:start position:0%
+environmental changes so value delivery
+ 
+
+ align:start position:0%
+environmental changes so value delivery
+of the system is the top the most
+
+ align:start position:0%
+of the system is the top the most
+ 
+
+ align:start position:0%
+of the system is the top the most
+important thing then what's different
+
+ align:start position:0%
+important thing then what's different
+ 
+
+ align:start position:0%
+important thing then what's different
+here is you know how do you achieve that
+
+ align:start position:0%
+here is you know how do you achieve that
+ 
+
+ align:start position:0%
+here is you know how do you achieve that
+uh so for example you see group one had
+
+ align:start position:0%
+uh so for example you see group one had
+ 
+
+ align:start position:0%
+uh so for example you see group one had
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+robustness uh and changeability so
+
+ align:start position:0%
+robustness uh and changeability so
+ 
+
+ align:start position:0%
+robustness uh and changeability so
+robustness typically means even if you
+
+ align:start position:0%
+robustness typically means even if you
+ 
+
+ align:start position:0%
+robustness typically means even if you
+don't make any changes to the system it
+
+ align:start position:0%
+don't make any changes to the system it
+ 
+
+ align:start position:0%
+don't make any changes to the system it
+should continue you know it should be
+
+ align:start position:0%
+should continue you know it should be
+ 
+
+ align:start position:0%
+should continue you know it should be
+survivable it should be
+
+ align:start position:0%
+survivable it should be
+ 
+
+ align:start position:0%
+survivable it should be
+versatile uh changeable means to
+
+ align:start position:0%
+versatile uh changeable means to
+ 
+
+ align:start position:0%
+versatile uh changeable means to
+actually modify the system over its life
+
+ align:start position:0%
+actually modify the system over its life
+ 
+
+ align:start position:0%
+actually modify the system over its life
+and then we have lower level properties
+
+ align:start position:0%
+and then we have lower level properties
+ 
+
+ align:start position:0%
+and then we have lower level properties
+like modularity or reconfigurability and
+
+ align:start position:0%
+like modularity or reconfigurability and
+ 
+
+ align:start position:0%
+like modularity or reconfigurability and
+you know there were differences between
+
+ align:start position:0%
+you know there were differences between
+ 
+
+ align:start position:0%
+you know there were differences between
+the groups but um not not as big as you
+
+ align:start position:0%
+the groups but um not not as big as you
+ 
+
+ align:start position:0%
+the groups but um not not as big as you
+might think so in the second round as a
+
+ align:start position:0%
+might think so in the second round as a
+ 
+
+ align:start position:0%
+might think so in the second round as a
+result of the second round then this um
+
+ align:start position:0%
+result of the second round then this um
+ 
+
+ align:start position:0%
+result of the second round then this um
+so-called means to ends hierarchy was
+
+ align:start position:0%
+so-called means to ends hierarchy was
+ 
+
+ align:start position:0%
+so-called means to ends hierarchy was
+constructed so means means you know
+
+ align:start position:0%
+constructed so means means you know
+ 
+
+ align:start position:0%
+constructed so means means you know
+these are the enabling life cycle
+
+ align:start position:0%
+these are the enabling life cycle
+ 
+
+ align:start position:0%
+these are the enabling life cycle
+properties and ends means this is the
+
+ align:start position:0%
+properties and ends means this is the
+ 
+
+ align:start position:0%
+properties and ends means this is the
+final soort of this is really what you
+
+ align:start position:0%
+final soort of this is really what you
+ 
+
+ align:start position:0%
+final soort of this is really what you
+want to achieve and so this was the
+
+ align:start position:0%
+want to achieve and so this was the
+ 
+
+ align:start position:0%
+want to achieve and so this was the
+result of that uh so again at the top we
+
+ align:start position:0%
+result of that uh so again at the top we
+ 
+
+ align:start position:0%
+result of that uh so again at the top we
+have this notion of value robustness and
+
+ align:start position:0%
+have this notion of value robustness and
+ 
+
+ align:start position:0%
+have this notion of value robustness and
+this is achieved by a combination of
+
+ align:start position:0%
+this is achieved by a combination of
+ 
+
+ align:start position:0%
+this is achieved by a combination of
+survivability robustness and
+
+ align:start position:0%
+survivability robustness and
+ 
+
+ align:start position:0%
+survivability robustness and
+changeability and then these in turn are
+
+ align:start position:0%
+changeability and then these in turn are
+ 
+
+ align:start position:0%
+changeability and then these in turn are
+achieved by lower level life cycle
+
+ align:start position:0%
+achieved by lower level life cycle
+ 
+
+ align:start position:0%
+achieved by lower level life cycle
+properties and then at the lowest level
+
+ align:start position:0%
+properties and then at the lowest level
+ 
+
+ align:start position:0%
+properties and then at the lowest level
+we have things like interoperability
+
+ align:start position:0%
+we have things like interoperability
+ 
+
+ align:start position:0%
+we have things like interoperability
+modularity reconfigurability and so
+
+ align:start position:0%
+modularity reconfigurability and so
+ 
+
+ align:start position:0%
+modularity reconfigurability and so
+forth okay and the the difference
+
+ align:start position:0%
+forth okay and the the difference
+ 
+
+ align:start position:0%
+forth okay and the the difference
+between the solid line and the dash
+
+ align:start position:0%
+between the solid line and the dash
+ 
+
+ align:start position:0%
+between the solid line and the dash
+lines here is that if it's a solid line
+
+ align:start position:0%
+lines here is that if it's a solid line
+ 
+
+ align:start position:0%
+lines here is that if it's a solid line
+and these are directed
+
+ align:start position:0%
+and these are directed
+ 
+
+ align:start position:0%
+and these are directed
+arrows that means that three three or
+
+ align:start position:0%
+arrows that means that three three or
+ 
+
+ align:start position:0%
+arrows that means that three three or
+four out of four groups right so the
+
+ align:start position:0%
+four out of four groups right so the
+ 
+
+ align:start position:0%
+four out of four groups right so the
+majority of groups had this as a
+
+ align:start position:0%
+majority of groups had this as a
+ 
+
+ align:start position:0%
+majority of groups had this as a
+particular CH parent child relationship
+
+ align:start position:0%
+particular CH parent child relationship
+ 
+
+ align:start position:0%
+particular CH parent child relationship
+and if it's a dash line it means only
+
+ align:start position:0%
+and if it's a dash line it means only
+ 
+
+ align:start position:0%
+and if it's a dash line it means only
+two out of four and if it's only one out
+
+ align:start position:0%
+two out of four and if it's only one out
+ 
+
+ align:start position:0%
+two out of four and if it's only one out
+of four it's not shown here okay so this
+
+ align:start position:0%
+of four it's not shown here okay so this
+ 
+
+ align:start position:0%
+of four it's not shown here okay so this
+is kind of a combined results across the
+
+ align:start position:0%
+is kind of a combined results across the
+ 
+
+ align:start position:0%
+is kind of a combined results across the
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+groups so so um you know what do we take
+
+ align:start position:0%
+groups so so um you know what do we take
+ 
+
+ align:start position:0%
+groups so so um you know what do we take
+from this so first of all life cycle
+
+ align:start position:0%
+from this so first of all life cycle
+ 
+
+ align:start position:0%
+from this so first of all life cycle
+properties are absolutely critical you
+
+ align:start position:0%
+properties are absolutely critical you
+ 
+
+ align:start position:0%
+properties are absolutely critical you
+you'll find this in in in mission
+
+ align:start position:0%
+you'll find this in in in mission
+ 
+
+ align:start position:0%
+you'll find this in in in mission
+statements you know you'll find it in
+
+ align:start position:0%
+statements you know you'll find it in
+ 
+
+ align:start position:0%
+statements you know you'll find it in
+even in advertising right a lot of
+
+ align:start position:0%
+even in advertising right a lot of
+ 
+
+ align:start position:0%
+even in advertising right a lot of
+companies say we have we have a robust
+
+ align:start position:0%
+companies say we have we have a robust
+ 
+
+ align:start position:0%
+companies say we have we have a robust
+solution we have a sustainable system we
+
+ align:start position:0%
+solution we have a sustainable system we
+ 
+
+ align:start position:0%
+solution we have a sustainable system we
+have resilient networks so it it really
+
+ align:start position:0%
+have resilient networks so it it really
+ 
+
+ align:start position:0%
+have resilient networks so it it really
+is a huge huge selling point it's very
+
+ align:start position:0%
+is a huge huge selling point it's very
+ 
+
+ align:start position:0%
+is a huge huge selling point it's very
+critical what I encourage you to do as
+
+ align:start position:0%
+critical what I encourage you to do as
+ 
+
+ align:start position:0%
+critical what I encourage you to do as
+system Engineers is take a critical look
+
+ align:start position:0%
+system Engineers is take a critical look
+ 
+
+ align:start position:0%
+system Engineers is take a critical look
+at this and say well what does that how
+
+ align:start position:0%
+at this and say well what does that how
+ 
+
+ align:start position:0%
+at this and say well what does that how
+resilient is resilient you know how many
+
+ align:start position:0%
+resilient is resilient you know how many
+ 
+
+ align:start position:0%
+resilient is resilient you know how many
+subsequent failures you know of the
+
+ align:start position:0%
+subsequent failures you know of the
+ 
+
+ align:start position:0%
+subsequent failures you know of the
+system can you tolerate uh
+
+ align:start position:0%
+system can you tolerate uh
+ 
+
+ align:start position:0%
+system can you tolerate uh
+sustainability what does it mean in
+
+ align:start position:0%
+sustainability what does it mean in
+ 
+
+ align:start position:0%
+sustainability what does it mean in
+terms of you know kilowatt hours per
+
+ align:start position:0%
+terms of you know kilowatt hours per
+ 
+
+ align:start position:0%
+terms of you know kilowatt hours per
+hour of usage you have to get down to
+
+ align:start position:0%
+hour of usage you have to get down to
+ 
+
+ align:start position:0%
+hour of usage you have to get down to
+the details to start quantifying what
+
+ align:start position:0%
+the details to start quantifying what
+ 
+
+ align:start position:0%
+the details to start quantifying what
+these life cycle properties mean and
+
+ align:start position:0%
+these life cycle properties mean and
+ 
+
+ align:start position:0%
+these life cycle properties mean and
+compare them among
+
+ align:start position:0%
+compare them among
+ 
+
+ align:start position:0%
+compare them among
+systems uh despite differ differences
+
+ align:start position:0%
+systems uh despite differ differences
+ 
+
+ align:start position:0%
+systems uh despite differ differences
+this these two methods that we just
+
+ align:start position:0%
+this these two methods that we just
+ 
+
+ align:start position:0%
+this these two methods that we just
+looked at so one is the prevalence
+
+ align:start position:0%
+looked at so one is the prevalence
+ 
+
+ align:start position:0%
+looked at so one is the prevalence
+analysis and the other one is the um you
+
+ align:start position:0%
+analysis and the other one is the um you
+ 
+
+ align:start position:0%
+analysis and the other one is the um you
+know the the human semantic exercise
+
+ align:start position:0%
+know the the human semantic exercise
+ 
+
+ align:start position:0%
+know the the human semantic exercise
+despite differences the high level
+
+ align:start position:0%
+despite differences the high level
+ 
+
+ align:start position:0%
+despite differences the high level
+conclusions were similar so some ilities
+
+ align:start position:0%
+conclusions were similar so some ilities
+ 
+
+ align:start position:0%
+conclusions were similar so some ilities
+are closely related to each other and
+
+ align:start position:0%
+are closely related to each other and
+ 
+
+ align:start position:0%
+are closely related to each other and
+form semantic sets meaning they're
+
+ align:start position:0%
+form semantic sets meaning they're
+ 
+
+ align:start position:0%
+form semantic sets meaning they're
+they're tied together by both synonymy
+
+ align:start position:0%
+they're tied together by both synonymy
+ 
+
+ align:start position:0%
+they're tied together by both synonymy
+or polyi relationships synonymy means
+
+ align:start position:0%
+or polyi relationships synonymy means
+ 
+
+ align:start position:0%
+or polyi relationships synonymy means
+they essentially mean the same they're
+
+ align:start position:0%
+they essentially mean the same they're
+ 
+
+ align:start position:0%
+they essentially mean the same they're
+synonymous they essentially mean the
+
+ align:start position:0%
+synonymous they essentially mean the
+ 
+
+ align:start position:0%
+synonymous they essentially mean the
+same thing polyi means it is one word
+
+ align:start position:0%
+same thing polyi means it is one word
+ 
+
+ align:start position:0%
+same thing polyi means it is one word
+but it means can mean have possible sub
+
+ align:start position:0%
+but it means can mean have possible sub
+ 
+
+ align:start position:0%
+but it means can mean have possible sub
+meanings right so so uh the idea of
+
+ align:start position:0%
+meanings right so so uh the idea of
+ 
+
+ align:start position:0%
+meanings right so so uh the idea of
+groups of of semantic sets and um those
+
+ align:start position:0%
+groups of of semantic sets and um those
+ 
+
+ align:start position:0%
+groups of of semantic sets and um those
+uh those groups essentially are
+
+ align:start position:0%
+uh those groups essentially are
+ 
+
+ align:start position:0%
+uh those groups essentially are
+robustness so this is the ability of the
+
+ align:start position:0%
+robustness so this is the ability of the
+ 
+
+ align:start position:0%
+robustness so this is the ability of the
+system to perform its job despite either
+
+ align:start position:0%
+system to perform its job despite either
+ 
+
+ align:start position:0%
+system to perform its job despite either
+internal or exogenous disturbances right
+
+ align:start position:0%
+internal or exogenous disturbances right
+ 
+
+ align:start position:0%
+internal or exogenous disturbances right
+that's robustness flexible or changeable
+
+ align:start position:0%
+that's robustness flexible or changeable
+ 
+
+ align:start position:0%
+that's robustness flexible or changeable
+which means that um you can modify the
+
+ align:start position:0%
+which means that um you can modify the
+ 
+
+ align:start position:0%
+which means that um you can modify the
+system easily you know if you operate
+
+ align:start position:0%
+system easily you know if you operate
+ 
+
+ align:start position:0%
+system easily you know if you operate
+the system for a while and then you
+
+ align:start position:0%
+the system for a while and then you
+ 
+
+ align:start position:0%
+the system for a while and then you
+realize ah I I need the system to do
+
+ align:start position:0%
+realize ah I I need the system to do
+ 
+
+ align:start position:0%
+realize ah I I need the system to do
+something else or I need to ad adapt it
+
+ align:start position:0%
+something else or I need to ad adapt it
+ 
+
+ align:start position:0%
+something else or I need to ad adapt it
+or make it bigger or make it smaller or
+
+ align:start position:0%
+or make it bigger or make it smaller or
+ 
+
+ align:start position:0%
+or make it bigger or make it smaller or
+add some functions so you would modify
+
+ align:start position:0%
+add some functions so you would modify
+ 
+
+ align:start position:0%
+add some functions so you would modify
+the system and that's flexibility or
+
+ align:start position:0%
+the system and that's flexibility or
+ 
+
+ align:start position:0%
+the system and that's flexibility or
+changeability and then resilient and
+
+ align:start position:0%
+changeability and then resilient and
+ 
+
+ align:start position:0%
+changeability and then resilient and
+survivable is very specifically the
+
+ align:start position:0%
+survivable is very specifically the
+ 
+
+ align:start position:0%
+survivable is very specifically the
+ability of the system to continue
+
+ align:start position:0%
+ability of the system to continue
+ 
+
+ align:start position:0%
+ability of the system to continue
+performing despite uh failures or
+
+ align:start position:0%
+performing despite uh failures or
+ 
+
+ align:start position:0%
+performing despite uh failures or
+attacks right that's what resilience
+
+ align:start position:0%
+attacks right that's what resilience
+ 
+
+ align:start position:0%
+attacks right that's what resilience
+really means and so those seem to be the
+
+ align:start position:0%
+really means and so those seem to be the
+ 
+
+ align:start position:0%
+really means and so those seem to be the
+big three semantic clusters that we see
+
+ align:start position:0%
+big three semantic clusters that we see
+ 
+
+ align:start position:0%
+big three semantic clusters that we see
+in life cycle properties and then the
+
+ align:start position:0%
+in life cycle properties and then the
+ 
+
+ align:start position:0%
+in life cycle properties and then the
+the third Point here is there appears to
+
+ align:start position:0%
+the third Point here is there appears to
+ 
+
+ align:start position:0%
+the third Point here is there appears to
+be a hierarchy of life cycle properties
+
+ align:start position:0%
+be a hierarchy of life cycle properties
+ 
+
+ align:start position:0%
+be a hierarchy of life cycle properties
+with two or three levels where we have
+
+ align:start position:0%
+with two or three levels where we have
+ 
+
+ align:start position:0%
+with two or three levels where we have
+lower level properties of systems like
+
+ align:start position:0%
+lower level properties of systems like
+ 
+
+ align:start position:0%
+lower level properties of systems like
+modularity for example really your
+
+ align:start position:0%
+modularity for example really your
+ 
+
+ align:start position:0%
+modularity for example really your
+customer probably does not care about
+
+ align:start position:0%
+customer probably does not care about
+ 
+
+ align:start position:0%
+customer probably does not care about
+modularity right if you advertise the
+
+ align:start position:0%
+modularity right if you advertise the
+ 
+
+ align:start position:0%
+modularity right if you advertise the
+modularity of the product you know some
+
+ align:start position:0%
+modularity of the product you know some
+ 
+
+ align:start position:0%
+modularity of the product you know some
+of the more educated uh you know some of
+
+ align:start position:0%
+of the more educated uh you know some of
+ 
+
+ align:start position:0%
+of the more educated uh you know some of
+the more technically Savvy customers
+
+ align:start position:0%
+the more technically Savvy customers
+ 
+
+ align:start position:0%
+the more technically Savvy customers
+they may understand what that means but
+
+ align:start position:0%
+they may understand what that means but
+ 
+
+ align:start position:0%
+they may understand what that means but
+most of your customers really won't
+
+ align:start position:0%
+most of your customers really won't
+ 
+
+ align:start position:0%
+most of your customers really won't
+appreciate modularity because it's kind
+
+ align:start position:0%
+appreciate modularity because it's kind
+ 
+
+ align:start position:0%
+appreciate modularity because it's kind
+of a low-level form oriented technical
+
+ align:start position:0%
+of a low-level form oriented technical
+ 
+
+ align:start position:0%
+of a low-level form oriented technical
+property of the system but what what
+
+ align:start position:0%
+property of the system but what what
+ 
+
+ align:start position:0%
+property of the system but what what
+they will appreciate is the ability of
+
+ align:start position:0%
+they will appreciate is the ability of
+ 
+
+ align:start position:0%
+they will appreciate is the ability of
+the system to be reconfigured or adapted
+
+ align:start position:0%
+the system to be reconfigured or adapted
+ 
+
+ align:start position:0%
+the system to be reconfigured or adapted
+for different uses right so
+
+ align:start position:0%
+for different uses right so
+ 
+
+ align:start position:0%
+for different uses right so
+interoperability modularity Etc are
+
+ align:start position:0%
+interoperability modularity Etc are
+ 
+
+ align:start position:0%
+interoperability modularity Etc are
+lower level life cycle properties that
+
+ align:start position:0%
+lower level life cycle properties that
+ 
+
+ align:start position:0%
+lower level life cycle properties that
+act as enablers of the higher level life
+
+ align:start position:0%
+act as enablers of the higher level life
+ 
+
+ align:start position:0%
+act as enablers of the higher level life
+cycle properties okay and so future work
+
+ align:start position:0%
+cycle properties okay and so future work
+ 
+
+ align:start position:0%
+cycle properties okay and so future work
+uh future work in this area is to both
+
+ align:start position:0%
+uh future work in this area is to both
+ 
+
+ align:start position:0%
+uh future work in this area is to both
+um to you know to apply the these
+
+ align:start position:0%
+um to you know to apply the these
+ 
+
+ align:start position:0%
+um to you know to apply the these
+methods to a broader set abilities
+
+ align:start position:0%
+methods to a broader set abilities
+ 
+
+ align:start position:0%
+methods to a broader set abilities
+larger group of test subjects you know
+
+ align:start position:0%
+larger group of test subjects you know
+ 
+
+ align:start position:0%
+larger group of test subjects you know
+more data but also from a practical
+
+ align:start position:0%
+more data but also from a practical
+ 
+
+ align:start position:0%
+more data but also from a practical
+standpoint to to operationalize better
+
+ align:start position:0%
+standpoint to to operationalize better
+ 
+
+ align:start position:0%
+standpoint to to operationalize better
+how do we write requirements how do we
+
+ align:start position:0%
+how do we write requirements how do we
+ 
+
+ align:start position:0%
+how do we write requirements how do we
+actually design for these life cycle
+
+ align:start position:0%
+actually design for these life cycle
+ 
+
+ align:start position:0%
+actually design for these life cycle
+properties like resilience you know
+
+ align:start position:0%
+properties like resilience you know
+ 
+
+ align:start position:0%
+properties like resilience you know
+flexibility changeability how do you
+
+ align:start position:0%
+flexibility changeability how do you
+ 
+
+ align:start position:0%
+flexibility changeability how do you
+really design it so go from the keyword
+
+ align:start position:0%
+really design it so go from the keyword
+ 
+
+ align:start position:0%
+really design it so go from the keyword
+to real engineering by operationalizing
+
+ align:start position:0%
+to real engineering by operationalizing
+ 
+
+ align:start position:0%
+to real engineering by operationalizing
+the the the subattributes or factor of
+
+ align:start position:0%
+the the the subattributes or factor of
+ 
+
+ align:start position:0%
+the the the subattributes or factor of
+these systems okay so that's uh quick
+
+ align:start position:0%
+these systems okay so that's uh quick
+ 
+
+ align:start position:0%
+these systems okay so that's uh quick
+summary of life you know I could go on
+
+ align:start position:0%
+summary of life you know I could go on
+ 
+
+ align:start position:0%
+summary of life you know I could go on
+for hours about this uh this is I'm very
+
+ align:start position:0%
+for hours about this uh this is I'm very
+ 
+
+ align:start position:0%
+for hours about this uh this is I'm very
+passionate about this topic and I will
+
+ align:start position:0%
+passionate about this topic and I will
+ 
+
+ align:start position:0%
+passionate about this topic and I will
+say that um you know people who have
+
+ align:start position:0%
+say that um you know people who have
+ 
+
+ align:start position:0%
+say that um you know people who have
+dealt with large complex systems you
+
+ align:start position:0%
+dealt with large complex systems you
+ 
+
+ align:start position:0%
+dealt with large complex systems you
+know whether you're operating the
+
+ align:start position:0%
+know whether you're operating the
+ 
+
+ align:start position:0%
+know whether you're operating the
+transportation system of a city or you
+
+ align:start position:0%
+transportation system of a city or you
+ 
+
+ align:start position:0%
+transportation system of a city or you
+know in Airline operations or you know
+
+ align:start position:0%
+know in Airline operations or you know
+ 
+
+ align:start position:0%
+know in Airline operations or you know
+you're running the it infrastructure of
+
+ align:start position:0%
+you're running the it infrastructure of
+ 
+
+ align:start position:0%
+you're running the it infrastructure of
+a major
+
+ align:start position:0%
+a major
+ 
+
+ align:start position:0%
+a major
+corporation these words uh
+
+ align:start position:0%
+corporation these words uh
+ 
+
+ align:start position:0%
+corporation these words uh
+these words are real these words are you
+
+ align:start position:0%
+these words are real these words are you
+ 
+
+ align:start position:0%
+these words are real these words are you
+know real dollars real challenges this
+
+ align:start position:0%
+know real dollars real challenges this
+ 
+
+ align:start position:0%
+know real dollars real challenges this
+is really where the action is in in a
+
+ align:start position:0%
+is really where the action is in in a
+ 
+
+ align:start position:0%
+is really where the action is in in a
+lot of these large complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems okay any any comments or
+
+ align:start position:0%
+systems okay any any comments or
+ 
+
+ align:start position:0%
+systems okay any any comments or
+questions about uh life cycle properties
+
+ align:start position:0%
+questions about uh life cycle properties
+ 
+
+ align:start position:0%
+questions about uh life cycle properties
+how what they are how they relate to
+
+ align:start position:0%
+how what they are how they relate to
+ 
+
+ align:start position:0%
+how what they are how they relate to
+each other why they're important bulker
+
+ align:start position:0%
+each other why they're important bulker
+ 
+
+ align:start position:0%
+each other why they're important bulker
+did you want to maybe say something okay
+
+ align:start position:0%
+did you want to maybe say something okay
+ 
+
+ align:start position:0%
+did you want to maybe say something okay
+all right so let me talk about uh try to
+
+ align:start position:0%
+all right so let me talk about uh try to
+ 
+
+ align:start position:0%
+all right so let me talk about uh try to
+make this a little more real uh let me
+
+ align:start position:0%
+make this a little more real uh let me
+ 
+
+ align:start position:0%
+make this a little more real uh let me
+talk about a case study very specific
+
+ align:start position:0%
+talk about a case study very specific
+ 
+
+ align:start position:0%
+talk about a case study very specific
+case study about uh communication
+
+ align:start position:0%
+case study about uh communication
+ 
+
+ align:start position:0%
+case study about uh communication
+satellite constellations and this is the
+
+ align:start position:0%
+satellite constellations and this is the
+ 
+
+ align:start position:0%
+satellite constellations and this is the
+second paper uh that underlies today's
+
+ align:start position:0%
+second paper uh that underlies today's
+ 
+
+ align:start position:0%
+second paper uh that underlies today's
+lecture and so let me give you a little
+
+ align:start position:0%
+lecture and so let me give you a little
+ 
+
+ align:start position:0%
+lecture and so let me give you a little
+context for this first uh so this this
+
+ align:start position:0%
+context for this first uh so this this
+ 
+
+ align:start position:0%
+context for this first uh so this this
+uh work here was originally published uh
+
+ align:start position:0%
+uh work here was originally published uh
+ 
+
+ align:start position:0%
+uh work here was originally published uh
+about a decade ago in March 2004 and
+
+ align:start position:0%
+about a decade ago in March 2004 and
+ 
+
+ align:start position:0%
+about a decade ago in March 2004 and
+that was a few years after um idium and
+
+ align:start position:0%
+that was a few years after um idium and
+ 
+
+ align:start position:0%
+that was a few years after um idium and
+Global star these are the two well-known
+
+ align:start position:0%
+Global star these are the two well-known
+ 
+
+ align:start position:0%
+Global star these are the two well-known
+communication satellite constellations
+
+ align:start position:0%
+communication satellite constellations
+ 
+
+ align:start position:0%
+communication satellite constellations
+had had been launched and I have to give
+
+ align:start position:0%
+had had been launched and I have to give
+ 
+
+ align:start position:0%
+had had been launched and I have to give
+you a little context when I first came
+
+ align:start position:0%
+you a little context when I first came
+ 
+
+ align:start position:0%
+you a little context when I first came
+to MIT in the mid 1990s there was a huge
+
+ align:start position:0%
+to MIT in the mid 1990s there was a huge
+ 
+
+ align:start position:0%
+to MIT in the mid 1990s there was a huge
+interest in this area of satellite
+
+ align:start position:0%
+interest in this area of satellite
+ 
+
+ align:start position:0%
+interest in this area of satellite
+constellations you know commercially
+
+ align:start position:0%
+constellations you know commercially
+ 
+
+ align:start position:0%
+constellations you know commercially
+scientifically um you know in fact you
+
+ align:start position:0%
+scientifically um you know in fact you
+ 
+
+ align:start position:0%
+scientifically um you know in fact you
+know the the impression was there were
+
+ align:start position:0%
+know the the impression was there were
+ 
+
+ align:start position:0%
+know the the impression was there were
+so many applications for satellite
+
+ align:start position:0%
+so many applications for satellite
+ 
+
+ align:start position:0%
+so many applications for satellite
+constellations filed that you know we're
+
+ align:start position:0%
+constellations filed that you know we're
+ 
+
+ align:start position:0%
+constellations filed that you know we're
+going to have so many satellites up
+
+ align:start position:0%
+going to have so many satellites up
+ 
+
+ align:start position:0%
+going to have so many satellites up
+there you won't even see the sun anymore
+
+ align:start position:0%
+there you won't even see the sun anymore
+ 
+
+ align:start position:0%
+there you won't even see the sun anymore
+right it was just like thousands and
+
+ align:start position:0%
+right it was just like thousands and
+ 
+
+ align:start position:0%
+right it was just like thousands and
+thousands of satellites and irium and
+
+ align:start position:0%
+thousands of satellites and irium and
+ 
+
+ align:start position:0%
+thousands of satellites and irium and
+Global star were really the first two
+
+ align:start position:0%
+Global star were really the first two
+ 
+
+ align:start position:0%
+Global star were really the first two
+constellations that were fully developed
+
+ align:start position:0%
+constellations that were fully developed
+ 
+
+ align:start position:0%
+constellations that were fully developed
+launched and both of them uh failed
+
+ align:start position:0%
+launched and both of them uh failed
+ 
+
+ align:start position:0%
+launched and both of them uh failed
+commercially within a really short time
+
+ align:start position:0%
+commercially within a really short time
+ 
+
+ align:start position:0%
+commercially within a really short time
+a couple years and so after this
+
+ align:start position:0%
+a couple years and so after this
+ 
+
+ align:start position:0%
+a couple years and so after this
+happened the whole market and interest
+
+ align:start position:0%
+happened the whole market and interest
+ 
+
+ align:start position:0%
+happened the whole market and interest
+in Satellite constellations
+
+ align:start position:0%
+in Satellite constellations
+ 
+
+ align:start position:0%
+in Satellite constellations
+collapsed uh for a long time uh until
+
+ align:start position:0%
+collapsed uh for a long time uh until
+ 
+
+ align:start position:0%
+collapsed uh for a long time uh until
+about you know few years ago two or 3
+
+ align:start position:0%
+about you know few years ago two or 3
+ 
+
+ align:start position:0%
+about you know few years ago two or 3
+years ago now you know people talk about
+
+ align:start position:0%
+years ago now you know people talk about
+ 
+
+ align:start position:0%
+years ago now you know people talk about
+these constellations again you know uh
+
+ align:start position:0%
+these constellations again you know uh
+ 
+
+ align:start position:0%
+these constellations again you know uh
+constellations of cube sets uh uh
+
+ align:start position:0%
+constellations of cube sets uh uh
+ 
+
+ align:start position:0%
+constellations of cube sets uh uh
+iridium next you know there's sort of a
+
+ align:start position:0%
+iridium next you know there's sort of a
+ 
+
+ align:start position:0%
+iridium next you know there's sort of a
+new enthusiasm new wave of enthusiasm
+
+ align:start position:0%
+new enthusiasm new wave of enthusiasm
+ 
+
+ align:start position:0%
+new enthusiasm new wave of enthusiasm
+for constellation so um so this this
+
+ align:start position:0%
+for constellation so um so this this
+ 
+
+ align:start position:0%
+for constellation so um so this this
+paper and this case that I want to tell
+
+ align:start position:0%
+paper and this case that I want to tell
+ 
+
+ align:start position:0%
+paper and this case that I want to tell
+you about is really about the first
+
+ align:start position:0%
+you about is really about the first
+ 
+
+ align:start position:0%
+you about is really about the first
+wave and in terms of the Ides what I the
+
+ align:start position:0%
+wave and in terms of the Ides what I the
+ 
+
+ align:start position:0%
+wave and in terms of the Ides what I the
+the one that I'm that I'm um that I like
+
+ align:start position:0%
+the one that I'm that I'm um that I like
+ 
+
+ align:start position:0%
+the one that I'm that I'm um that I like
+to explain to you about here is
+
+ align:start position:0%
+to explain to you about here is
+ 
+
+ align:start position:0%
+to explain to you about here is
+flexibility and scalability rather than
+
+ align:start position:0%
+flexibility and scalability rather than
+ 
+
+ align:start position:0%
+flexibility and scalability rather than
+thinking about a system
+
+ align:start position:0%
+thinking about a system
+ 
+
+ align:start position:0%
+thinking about a system
+something that you design and build all
+
+ align:start position:0%
+something that you design and build all
+ 
+
+ align:start position:0%
+something that you design and build all
+at once how do you design a system such
+
+ align:start position:0%
+at once how do you design a system such
+ 
+
+ align:start position:0%
+at once how do you design a system such
+that you can gradually deploy it we call
+
+ align:start position:0%
+that you can gradually deploy it we call
+ 
+
+ align:start position:0%
+that you can gradually deploy it we call
+that stage deployment approach and
+
+ align:start position:0%
+that stage deployment approach and
+ 
+
+ align:start position:0%
+that stage deployment approach and
+what's the benefit of that okay so
+
+ align:start position:0%
+what's the benefit of that okay so
+ 
+
+ align:start position:0%
+what's the benefit of that okay so
+here's some uh pictures uh you see on
+
+ align:start position:0%
+here's some uh pictures uh you see on
+ 
+
+ align:start position:0%
+here's some uh pictures uh you see on
+the right side this is what the original
+
+ align:start position:0%
+the right side this is what the original
+ 
+
+ align:start position:0%
+the right side this is what the original
+aridium satellites look like they
+
+ align:start position:0%
+aridium satellites look like they
+ 
+
+ align:start position:0%
+aridium satellites look like they
+actually use uh phased array antennas uh
+
+ align:start position:0%
+actually use uh phased array antennas uh
+ 
+
+ align:start position:0%
+actually use uh phased array antennas uh
+they actually both use phased array
+
+ align:start position:0%
+they actually both use phased array
+ 
+
+ align:start position:0%
+they actually both use phased array
+antennas so you have individual elements
+
+ align:start position:0%
+antennas so you have individual elements
+ 
+
+ align:start position:0%
+antennas so you have individual elements
+here and by differentially phasing the
+
+ align:start position:0%
+here and by differentially phasing the
+ 
+
+ align:start position:0%
+here and by differentially phasing the
+signal you can actually steer the beam
+
+ align:start position:0%
+signal you can actually steer the beam
+ 
+
+ align:start position:0%
+signal you can actually steer the beam
+so this was a very new technology at the
+
+ align:start position:0%
+so this was a very new technology at the
+ 
+
+ align:start position:0%
+so this was a very new technology at the
+time and then the global Star Satellite
+
+ align:start position:0%
+time and then the global Star Satellite
+ 
+
+ align:start position:0%
+time and then the global Star Satellite
+uh shown at the lower um the lower
+
+ align:start position:0%
+uh shown at the lower um the lower
+ 
+
+ align:start position:0%
+uh shown at the lower um the lower
+picture here's a little bit of data uh
+
+ align:start position:0%
+picture here's a little bit of data uh
+ 
+
+ align:start position:0%
+picture here's a little bit of data uh
+both of these were launched in the late
+
+ align:start position:0%
+both of these were launched in the late
+ 
+
+ align:start position:0%
+both of these were launched in the late
+1990s uh idium has 66 satellites Global
+
+ align:start position:0%
+1990s uh idium has 66 satellites Global
+ 
+
+ align:start position:0%
+1990s uh idium has 66 satellites Global
+star 48 uh idium is a polar
+
+ align:start position:0%
+star 48 uh idium is a polar
+ 
+
+ align:start position:0%
+star 48 uh idium is a polar
+constellation so the satellites go
+
+ align:start position:0%
+constellation so the satellites go
+ 
+
+ align:start position:0%
+constellation so the satellites go
+almost directly over the poles um global
+
+ align:start position:0%
+almost directly over the poles um global
+ 
+
+ align:start position:0%
+almost directly over the poles um global
+star is a walker constellation so it's
+
+ align:start position:0%
+star is a walker constellation so it's
+ 
+
+ align:start position:0%
+star is a walker constellation so it's
+inclined doesn't quite give you full
+
+ align:start position:0%
+inclined doesn't quite give you full
+ 
+
+ align:start position:0%
+inclined doesn't quite give you full
+Global coverage it's about plus orus 70°
+
+ align:start position:0%
+Global coverage it's about plus orus 70°
+ 
+
+ align:start position:0%
+Global coverage it's about plus orus 70°
+so you can't use Global star at the
+
+ align:start position:0%
+so you can't use Global star at the
+ 
+
+ align:start position:0%
+so you can't use Global star at the
+poles uh the altitudes are a bit
+
+ align:start position:0%
+poles uh the altitudes are a bit
+ 
+
+ align:start position:0%
+poles uh the altitudes are a bit
+different too idium is at 780 km while
+
+ align:start position:0%
+different too idium is at 780 km while
+ 
+
+ align:start position:0%
+different too idium is at 780 km while
+uh Global star is at 1,400 which um um
+
+ align:start position:0%
+uh Global star is at 1,400 which um um
+ 
+
+ align:start position:0%
+uh Global star is at 1,400 which um um
+who's I know at least one or two of you
+
+ align:start position:0%
+who's I know at least one or two of you
+ 
+
+ align:start position:0%
+who's I know at least one or two of you
+are working on the Van Allen the Van
+
+ align:start position:0%
+are working on the Van Allen the Van
+ 
+
+ align:start position:0%
+are working on the Van Allen the Van
+Allen belt mission right the cube sets
+
+ align:start position:0%
+Allen belt mission right the cube sets
+ 
+
+ align:start position:0%
+Allen belt mission right the cube sets
+to measure the Van Allen belts somebody
+
+ align:start position:0%
+to measure the Van Allen belts somebody
+ 
+
+ align:start position:0%
+to measure the Van Allen belts somebody
+mentioned that today who was that no did
+
+ align:start position:0%
+mentioned that today who was that no did
+ 
+
+ align:start position:0%
+mentioned that today who was that no did
+I hear that
+
+ align:start position:0%
+I hear that
+ 
+
+ align:start position:0%
+I hear that
+wrong it was mentioned right so who is
+
+ align:start position:0%
+wrong it was mentioned right so who is
+ 
+
+ align:start position:0%
+wrong it was mentioned right so who is
+that oh no and he's not here huh you see
+
+ align:start position:0%
+that oh no and he's not here huh you see
+ 
+
+ align:start position:0%
+that oh no and he's not here huh you see
+so 1400 kilomet you're actually pushing
+
+ align:start position:0%
+so 1400 kilomet you're actually pushing
+ 
+
+ align:start position:0%
+so 1400 kilomet you're actually pushing
+you're starting to push the lower edges
+
+ align:start position:0%
+you're starting to push the lower edges
+ 
+
+ align:start position:0%
+you're starting to push the lower edges
+of the Van Allen belt so one of the big
+
+ align:start position:0%
+of the Van Allen belt so one of the big
+ 
+
+ align:start position:0%
+of the Van Allen belt so one of the big
+you know in in in some sense it's easier
+
+ align:start position:0%
+you know in in in some sense it's easier
+ 
+
+ align:start position:0%
+you know in in in some sense it's easier
+to be higher because you need fewer
+
+ align:start position:0%
+to be higher because you need fewer
+ 
+
+ align:start position:0%
+to be higher because you need fewer
+satellites to cover the whole Earth
+
+ align:start position:0%
+satellites to cover the whole Earth
+ 
+
+ align:start position:0%
+satellites to cover the whole Earth
+Earth but the higher you go the more
+
+ align:start position:0%
+Earth but the higher you go the more
+ 
+
+ align:start position:0%
+Earth but the higher you go the more
+exposed you are to the radiation
+
+ align:start position:0%
+exposed you are to the radiation
+ 
+
+ align:start position:0%
+exposed you are to the radiation
+environment you get closer to the Van
+
+ align:start position:0%
+environment you get closer to the Van
+ 
+
+ align:start position:0%
+environment you get closer to the Van
+Allen belt so that's the big tradeoff
+
+ align:start position:0%
+Allen belt so that's the big tradeoff
+ 
+
+ align:start position:0%
+Allen belt so that's the big tradeoff
+there you know the mass of these
+
+ align:start position:0%
+there you know the mass of these
+ 
+
+ align:start position:0%
+there you know the mass of these
+satellites they're between you know 450
+
+ align:start position:0%
+satellites they're between you know 450
+ 
+
+ align:start position:0%
+satellites they're between you know 450
+and 700 kg transmitter power around 400
+
+ align:start position:0%
+and 700 kg transmitter power around 400
+ 
+
+ align:start position:0%
+and 700 kg transmitter power around 400
+watts you know which is not that much if
+
+ align:start position:0%
+watts you know which is not that much if
+ 
+
+ align:start position:0%
+watts you know which is not that much if
+you think about it right that's four
+
+ align:start position:0%
+you think about it right that's four
+ 
+
+ align:start position:0%
+you think about it right that's four
+very strong light bulbs uh the old style
+
+ align:start position:0%
+very strong light bulbs uh the old style
+ 
+
+ align:start position:0%
+very strong light bulbs uh the old style
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+buls um um and then what's very
+
+ align:start position:0%
+buls um um and then what's very
+ 
+
+ align:start position:0%
+buls um um and then what's very
+different again is the multi- access
+
+ align:start position:0%
+different again is the multi- access
+ 
+
+ align:start position:0%
+different again is the multi- access
+scheme so idium used uh time Division
+
+ align:start position:0%
+scheme so idium used uh time Division
+ 
+
+ align:start position:0%
+scheme so idium used uh time Division
+multiplexing and Global star which was
+
+ align:start position:0%
+multiplexing and Global star which was
+ 
+
+ align:start position:0%
+multiplexing and Global star which was
+supported by Qualcomm used essentially
+
+ align:start position:0%
+supported by Qualcomm used essentially
+ 
+
+ align:start position:0%
+supported by Qualcomm used essentially
+CDMA so you don't chop your frequency
+
+ align:start position:0%
+CDMA so you don't chop your frequency
+ 
+
+ align:start position:0%
+CDMA so you don't chop your frequency
+band into separate channels you use the
+
+ align:start position:0%
+band into separate channels you use the
+ 
+
+ align:start position:0%
+band into separate channels you use the
+whole the whole frequency band and then
+
+ align:start position:0%
+whole the whole frequency band and then
+ 
+
+ align:start position:0%
+whole the whole frequency band and then
+you then you use U pseudo random access
+
+ align:start position:0%
+you then you use U pseudo random access
+ 
+
+ align:start position:0%
+you then you use U pseudo random access
+codes to essentially uh deconvolve the
+
+ align:start position:0%
+codes to essentially uh deconvolve the
+ 
+
+ align:start position:0%
+codes to essentially uh deconvolve the
+signal uh for each
+
+ align:start position:0%
+signal uh for each
+ 
+
+ align:start position:0%
+signal uh for each
+Channel um the number of channels about
+
+ align:start position:0%
+Channel um the number of channels about
+ 
+
+ align:start position:0%
+Channel um the number of channels about
+72,000 about
+
+ align:start position:0%
+72,000 about
+ 
+
+ align:start position:0%
+72,000 about
+120,000 duplex channels so that you can
+
+ align:start position:0%
+120,000 duplex channels so that you can
+ 
+
+ align:start position:0%
+120,000 duplex channels so that you can
+actually duplex means you can carry on a
+
+ align:start position:0%
+actually duplex means you can carry on a
+ 
+
+ align:start position:0%
+actually duplex means you can carry on a
+two-way conversation as opposed to just
+
+ align:start position:0%
+two-way conversation as opposed to just
+ 
+
+ align:start position:0%
+two-way conversation as opposed to just
+a asynchronous and then you can see the
+
+ align:start position:0%
+a asynchronous and then you can see the
+ 
+
+ align:start position:0%
+a asynchronous and then you can see the
+data rates quite low right per Channel
+
+ align:start position:0%
+data rates quite low right per Channel
+ 
+
+ align:start position:0%
+data rates quite low right per Channel
+4.8 uh kilobits per second 2.4 4.8 9.6
+
+ align:start position:0%
+4.8 uh kilobits per second 2.4 4.8 9.6
+ 
+
+ align:start position:0%
+4.8 uh kilobits per second 2.4 4.8 9.6
+for Global star it's enough for uh
+
+ align:start position:0%
+for Global star it's enough for uh
+ 
+
+ align:start position:0%
+for Global star it's enough for uh
+having a conversation and total system
+
+ align:start position:0%
+having a conversation and total system
+ 
+
+ align:start position:0%
+having a conversation and total system
+cost idium was about uh $5.7 billion and
+
+ align:start position:0%
+cost idium was about uh $5.7 billion and
+ 
+
+ align:start position:0%
+cost idium was about uh $5.7 billion and
+glas star about 3.3 three not including
+
+ align:start position:0%
+glas star about 3.3 three not including
+ 
+
+ align:start position:0%
+glas star about 3.3 three not including
+the cost of the ground stations both
+
+ align:start position:0%
+the cost of the ground stations both
+ 
+
+ align:start position:0%
+the cost of the ground stations both
+went bankrupt relatively quickly after
+
+ align:start position:0%
+went bankrupt relatively quickly after
+ 
+
+ align:start position:0%
+went bankrupt relatively quickly after
+they launched however they've been
+
+ align:start position:0%
+they launched however they've been
+ 
+
+ align:start position:0%
+they launched however they've been
+operating really since then right since
+
+ align:start position:0%
+operating really since then right since
+ 
+
+ align:start position:0%
+operating really since then right since
+this time idium next is currently under
+
+ align:start position:0%
+this time idium next is currently under
+ 
+
+ align:start position:0%
+this time idium next is currently under
+development and is scheduled to launch
+
+ align:start position:0%
+development and is scheduled to launch
+ 
+
+ align:start position:0%
+development and is scheduled to launch
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+2017 uh Global star is publicly traded
+
+ align:start position:0%
+2017 uh Global star is publicly traded
+ 
+
+ align:start position:0%
+2017 uh Global star is publicly traded
+and actually valued as a company at $
+
+ align:start position:0%
+and actually valued as a company at $
+ 
+
+ align:start position:0%
+and actually valued as a company at $
+1.9 billion so they're actually both you
+
+ align:start position:0%
+1.9 billion so they're actually both you
+ 
+
+ align:start position:0%
+1.9 billion so they're actually both you
+you could almost argue that they they
+
+ align:start position:0%
+you could almost argue that they they
+ 
+
+ align:start position:0%
+you could almost argue that they they
+were at a decade ahead of their time and
+
+ align:start position:0%
+were at a decade ahead of their time and
+ 
+
+ align:start position:0%
+were at a decade ahead of their time and
+um and I want to tell you a little bit
+
+ align:start position:0%
+um and I want to tell you a little bit
+ 
+
+ align:start position:0%
+um and I want to tell you a little bit
+about the story of especially idium so
+
+ align:start position:0%
+about the story of especially idium so
+ 
+
+ align:start position:0%
+about the story of especially idium so
+here's a couple of um these are press
+
+ align:start position:0%
+here's a couple of um these are press
+ 
+
+ align:start position:0%
+here's a couple of um these are press
+releases or things that have been
+
+ align:start position:0%
+releases or things that have been
+ 
+
+ align:start position:0%
+releases or things that have been
+written in the Press so look at this one
+
+ align:start position:0%
+written in the Press so look at this one
+ 
+
+ align:start position:0%
+written in the Press so look at this one
+26th of June 1990 Motorola unveils New
+
+ align:start position:0%
+26th of June 1990 Motorola unveils New
+ 
+
+ align:start position:0%
+26th of June 1990 Motorola unveils New
+Concept for Global personal
+
+ align:start position:0%
+Concept for Global personal
+ 
+
+ align:start position:0%
+Concept for Global personal
+communication base is a constellation of
+
+ align:start position:0%
+communication base is a constellation of
+ 
+
+ align:start position:0%
+communication base is a constellation of
+lower low earth orbit cellular
+
+ align:start position:0%
+lower low earth orbit cellular
+ 
+
+ align:start position:0%
+lower low earth orbit cellular
+satellites August 18th 1999 9 years
+
+ align:start position:0%
+satellites August 18th 1999 9 years
+ 
+
+ align:start position:0%
+satellites August 18th 1999 9 years
+later last week rum LLC filed bankruptcy
+
+ align:start position:0%
+later last week rum LLC filed bankruptcy
+ 
+
+ align:start position:0%
+later last week rum LLC filed bankruptcy
+court protection lost Investments are
+
+ align:start position:0%
+court protection lost Investments are
+ 
+
+ align:start position:0%
+court protection lost Investments are
+estimated at 5 billion okay so question
+
+ align:start position:0%
+estimated at 5 billion okay so question
+ 
+
+ align:start position:0%
+estimated at 5 billion okay so question
+is why did it happen because the
+
+ align:start position:0%
+is why did it happen because the
+ 
+
+ align:start position:0%
+is why did it happen because the
+technology actually worked quite well it
+
+ align:start position:0%
+technology actually worked quite well it
+ 
+
+ align:start position:0%
+technology actually worked quite well it
+was not a technological failure it was a
+
+ align:start position:0%
+was not a technological failure it was a
+ 
+
+ align:start position:0%
+was not a technological failure it was a
+business failure but I would argue a
+
+ align:start position:0%
+business failure but I would argue a
+ 
+
+ align:start position:0%
+business failure but I would argue a
+systems failure to think about the
+
+ align:start position:0%
+systems failure to think about the
+ 
+
+ align:start position:0%
+systems failure to think about the
+problem differently so the the
+
+ align:start position:0%
+problem differently so the the
+ 
+
+ align:start position:0%
+problem differently so the the
+fundamental challenge is to to properly
+
+ align:start position:0%
+fundamental challenge is to to properly
+ 
+
+ align:start position:0%
+fundamental challenge is to to properly
+size the capacity of a lart system so if
+
+ align:start position:0%
+size the capacity of a lart system so if
+ 
+
+ align:start position:0%
+size the capacity of a lart system so if
+you're designing you know a car factory
+
+ align:start position:0%
+you're designing you know a car factory
+ 
+
+ align:start position:0%
+you're designing you know a car factory
+a new power system a you know and it's
+
+ align:start position:0%
+a new power system a you know and it's
+ 
+
+ align:start position:0%
+a new power system a you know and it's
+for a future uner demand it's very
+
+ align:start position:0%
+for a future uner demand it's very
+ 
+
+ align:start position:0%
+for a future uner demand it's very
+difficult to do this because uncert
+
+ align:start position:0%
+difficult to do this because uncert
+ 
+
+ align:start position:0%
+difficult to do this because uncert
+demand is uncertain so is it better to
+
+ align:start position:0%
+demand is uncertain so is it better to
+ 
+
+ align:start position:0%
+demand is uncertain so is it better to
+oversize the system or are you
+
+ align:start position:0%
+oversize the system or are you
+ 
+
+ align:start position:0%
+oversize the system or are you
+conservative and you make it smaller uh
+
+ align:start position:0%
+conservative and you make it smaller uh
+ 
+
+ align:start position:0%
+conservative and you make it smaller uh
+Market assumptions can change right in
+
+ align:start position:0%
+Market assumptions can change right in
+ 
+
+ align:start position:0%
+Market assumptions can change right in
+those seven to eight years and uh
+
+ align:start position:0%
+those seven to eight years and uh
+ 
+
+ align:start position:0%
+those seven to eight years and uh
+between so essentially the V right
+
+ align:start position:0%
+between so essentially the V right
+ 
+
+ align:start position:0%
+between so essentially the V right
+getting back to the V each of those two
+
+ align:start position:0%
+getting back to the V each of those two
+ 
+
+ align:start position:0%
+getting back to the V each of those two
+systems idium and and global are it took
+
+ align:start position:0%
+systems idium and and global are it took
+ 
+
+ align:start position:0%
+systems idium and and global are it took
+them essentially a decade almost 10
+
+ align:start position:0%
+them essentially a decade almost 10
+ 
+
+ align:start position:0%
+them essentially a decade almost 10
+years right to go across the whole V and
+
+ align:start position:0%
+years right to go across the whole V and
+ 
+
+ align:start position:0%
+years right to go across the whole V and
+when you make you know your requirements
+
+ align:start position:0%
+when you make you know your requirements
+ 
+
+ align:start position:0%
+when you make you know your requirements
+your stakeholders all the stuff in the
+
+ align:start position:0%
+your stakeholders all the stuff in the
+ 
+
+ align:start position:0%
+your stakeholders all the stuff in the
+upper left portion of the V when there's
+
+ align:start position:0%
+upper left portion of the V when there's
+ 
+
+ align:start position:0%
+upper left portion of the V when there's
+there's so many years that elapse
+
+ align:start position:0%
+there's so many years that elapse
+ 
+
+ align:start position:0%
+there's so many years that elapse
+between when you make those assumptions
+
+ align:start position:0%
+between when you make those assumptions
+ 
+
+ align:start position:0%
+between when you make those assumptions
+you write those requirements and when
+
+ align:start position:0%
+you write those requirements and when
+ 
+
+ align:start position:0%
+you write those requirements and when
+you actually go to market a lot of
+
+ align:start position:0%
+you actually go to market a lot of
+ 
+
+ align:start position:0%
+you actually go to market a lot of
+things can change and that's
+
+ align:start position:0%
+things can change and that's
+ 
+
+ align:start position:0%
+things can change and that's
+fundamentally the challenge
+
+ align:start position:0%
+fundamentally the challenge
+ 
+
+ align:start position:0%
+fundamentally the challenge
+here uh just to illustrate this for you
+
+ align:start position:0%
+here uh just to illustrate this for you
+ 
+
+ align:start position:0%
+here uh just to illustrate this for you
+um showing some data
+
+ align:start position:0%
+um showing some data
+ 
+
+ align:start position:0%
+um showing some data
+this is uh cellular this is not
+
+ align:start position:0%
+this is uh cellular this is not
+ 
+
+ align:start position:0%
+this is uh cellular this is not
+space-based this is on the ground
+
+ align:start position:0%
+space-based this is on the ground
+ 
+
+ align:start position:0%
+space-based this is on the ground
+cellular subscribers for mobile phones
+
+ align:start position:0%
+cellular subscribers for mobile phones
+ 
+
+ align:start position:0%
+cellular subscribers for mobile phones
+it it's I know this is hard for your
+
+ align:start position:0%
+it it's I know this is hard for your
+ 
+
+ align:start position:0%
+it it's I know this is hard for your
+generation to sort of understand this
+
+ align:start position:0%
+generation to sort of understand this
+ 
+
+ align:start position:0%
+generation to sort of understand this
+but we actually didn't have mobile
+
+ align:start position:0%
+but we actually didn't have mobile
+ 
+
+ align:start position:0%
+but we actually didn't have mobile
+phones or they were these clunky bricks
+
+ align:start position:0%
+phones or they were these clunky bricks
+ 
+
+ align:start position:0%
+phones or they were these clunky bricks
+you know in your car you know it's it's
+
+ align:start position:0%
+you know in your car you know it's it's
+ 
+
+ align:start position:0%
+you know in your car you know it's it's
+really um remarkable what's happened so
+
+ align:start position:0%
+really um remarkable what's happened so
+ 
+
+ align:start position:0%
+really um remarkable what's happened so
+look at this data in 1991 right which is
+
+ align:start position:0%
+look at this data in 1991 right which is
+ 
+
+ align:start position:0%
+look at this data in 1991 right which is
+when when the system was just being
+
+ align:start position:0%
+when when the system was just being
+ 
+
+ align:start position:0%
+when when the system was just being
+developed there were less than 10
+
+ align:start position:0%
+developed there were less than 10
+ 
+
+ align:start position:0%
+developed there were less than 10
+million mobile phone users in the US it
+
+ align:start position:0%
+million mobile phone users in the US it
+ 
+
+ align:start position:0%
+million mobile phone users in the US it
+just wasn't it was very expensive it was
+
+ align:start position:0%
+just wasn't it was very expensive it was
+ 
+
+ align:start position:0%
+just wasn't it was very expensive it was
+just not not widely uh that technology
+
+ align:start position:0%
+just not not widely uh that technology
+ 
+
+ align:start position:0%
+just not not widely uh that technology
+hadn't been the networks weren't there
+
+ align:start position:0%
+hadn't been the networks weren't there
+ 
+
+ align:start position:0%
+hadn't been the networks weren't there
+you know um so the the the green Bars
+
+ align:start position:0%
+you know um so the the the green Bars
+ 
+
+ align:start position:0%
+you know um so the the the green Bars
+were the forecast that was done in 1991
+
+ align:start position:0%
+were the forecast that was done in 1991
+ 
+
+ align:start position:0%
+were the forecast that was done in 1991
+as to how quickly the mobile user Market
+
+ align:start position:0%
+as to how quickly the mobile user Market
+ 
+
+ align:start position:0%
+as to how quickly the mobile user Market
+would evolve in the US so their
+
+ align:start position:0%
+would evolve in the US so their
+ 
+
+ align:start position:0%
+would evolve in the US so their
+prediction was that by 2000 a decade
+
+ align:start position:0%
+prediction was that by 2000 a decade
+ 
+
+ align:start position:0%
+prediction was that by 2000 a decade
+later there'd be just shy of 40 million
+
+ align:start position:0%
+later there'd be just shy of 40 million
+ 
+
+ align:start position:0%
+later there'd be just shy of 40 million
+users
+
+ align:start position:0%
+users
+ 
+
+ align:start position:0%
+users
+okay now the dark blue bar is the actual
+
+ align:start position:0%
+okay now the dark blue bar is the actual
+ 
+
+ align:start position:0%
+okay now the dark blue bar is the actual
+Evolution so actually by 2000 you know
+
+ align:start position:0%
+Evolution so actually by 2000 you know
+ 
+
+ align:start position:0%
+Evolution so actually by 2000 you know
+the US now has 310 or so million
+
+ align:start position:0%
+the US now has 310 or so million
+ 
+
+ align:start position:0%
+the US now has 310 or so million
+inhabitants um so by 2000 there were 120
+
+ align:start position:0%
+inhabitants um so by 2000 there were 120
+ 
+
+ align:start position:0%
+inhabitants um so by 2000 there were 120
+million users so the forecast that was
+
+ align:start position:0%
+million users so the forecast that was
+ 
+
+ align:start position:0%
+million users so the forecast that was
+done 10 years earlier was off by a
+
+ align:start position:0%
+done 10 years earlier was off by a
+ 
+
+ align:start position:0%
+done 10 years earlier was off by a
+factor of three the ground the
+
+ align:start position:0%
+factor of three the ground the
+ 
+
+ align:start position:0%
+factor of three the ground the
+terrestrial mobile
+
+ align:start position:0%
+terrestrial mobile
+ 
+
+ align:start position:0%
+terrestrial mobile
+networks uh veloped three times faster
+
+ align:start position:0%
+networks uh veloped three times faster
+ 
+
+ align:start position:0%
+networks uh veloped three times faster
+than had been predicted now that's great
+
+ align:start position:0%
+than had been predicted now that's great
+ 
+
+ align:start position:0%
+than had been predicted now that's great
+for the terrestrial people right the
+
+ align:start position:0%
+for the terrestrial people right the
+ 
+
+ align:start position:0%
+for the terrestrial people right the
+AT&T and Comcast not not Comcast
+
+ align:start position:0%
+AT&T and Comcast not not Comcast
+ 
+
+ align:start position:0%
+AT&T and Comcast not not Comcast
+Qualcomm Etc but the problem is of
+
+ align:start position:0%
+Qualcomm Etc but the problem is of
+ 
+
+ align:start position:0%
+Qualcomm Etc but the problem is of
+course that because you know groundbased
+
+ align:start position:0%
+course that because you know groundbased
+ 
+
+ align:start position:0%
+course that because you know groundbased
+Communications was so much easier a lot
+
+ align:start position:0%
+Communications was so much easier a lot
+ 
+
+ align:start position:0%
+Communications was so much easier a lot
+of the market that had been anticipated
+
+ align:start position:0%
+of the market that had been anticipated
+ 
+
+ align:start position:0%
+of the market that had been anticipated
+for the satellite based Communications
+
+ align:start position:0%
+for the satellite based Communications
+ 
+
+ align:start position:0%
+for the satellite based Communications
+was essentially uh eaten Away by uh you
+
+ align:start position:0%
+was essentially uh eaten Away by uh you
+ 
+
+ align:start position:0%
+was essentially uh eaten Away by uh you
+know by this competitor by the
+
+ align:start position:0%
+know by this competitor by the
+ 
+
+ align:start position:0%
+know by this competitor by the
+groundbased competitor go ahead may I
+
+ align:start position:0%
+groundbased competitor go ahead may I
+ 
+
+ align:start position:0%
+groundbased competitor go ahead may I
+intervene here just so that uh yeah okay
+
+ align:start position:0%
+intervene here just so that uh yeah okay
+ 
+
+ align:start position:0%
+intervene here just so that uh yeah okay
+uh can you still hear it are you still
+
+ align:start position:0%
+uh can you still hear it are you still
+ 
+
+ align:start position:0%
+uh can you still hear it are you still
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+us yes yes you are okay vulker wants to
+
+ align:start position:0%
+us yes yes you are okay vulker wants to
+ 
+
+ align:start position:0%
+us yes yes you are okay vulker wants to
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something actually the figures that you
+
+ align:start position:0%
+something actually the figures that you
+ 
+
+ align:start position:0%
+something actually the figures that you
+showed o about American Statics and for
+
+ align:start position:0%
+showed o about American Statics and for
+ 
+
+ align:start position:0%
+showed o about American Statics and for
+once Americans did not look over the
+
+ align:start position:0%
+once Americans did not look over the
+ 
+
+ align:start position:0%
+once Americans did not look over the
+pond because at that time in Europe the
+
+ align:start position:0%
+pond because at that time in Europe the
+ 
+
+ align:start position:0%
+pond because at that time in Europe the
+GSM systems came really strong and very
+
+ align:start position:0%
+GSM systems came really strong and very
+ 
+
+ align:start position:0%
+GSM systems came really strong and very
+quickly in the early '90s you could
+
+ align:start position:0%
+quickly in the early '90s you could
+ 
+
+ align:start position:0%
+quickly in the early '90s you could
+already have your sim card and your
+
+ align:start position:0%
+already have your sim card and your
+ 
+
+ align:start position:0%
+already have your sim card and your
+telephone yourself and back in America
+
+ align:start position:0%
+telephone yourself and back in America
+ 
+
+ align:start position:0%
+telephone yourself and back in America
+then you could only buy the telephone
+
+ align:start position:0%
+then you could only buy the telephone
+ 
+
+ align:start position:0%
+then you could only buy the telephone
+with all the SIM card in you had to buy
+
+ align:start position:0%
+with all the SIM card in you had to buy
+ 
+
+ align:start position:0%
+with all the SIM card in you had to buy
+the whole system and so as the system
+
+ align:start position:0%
+the whole system and so as the system
+ 
+
+ align:start position:0%
+the whole system and so as the system
+was controlled by the large companies
+
+ align:start position:0%
+was controlled by the large companies
+ 
+
+ align:start position:0%
+was controlled by the large companies
+and not by the users the large companies
+
+ align:start position:0%
+and not by the users the large companies
+ 
+
+ align:start position:0%
+and not by the users the large companies
+Motorola thought that they could impose
+
+ align:start position:0%
+Motorola thought that they could impose
+ 
+
+ align:start position:0%
+Motorola thought that they could impose
+their satellite system on the market and
+
+ align:start position:0%
+their satellite system on the market and
+ 
+
+ align:start position:0%
+their satellite system on the market and
+in this case contrary to the uh uh video
+
+ align:start position:0%
+in this case contrary to the uh uh video
+ 
+
+ align:start position:0%
+in this case contrary to the uh uh video
+recorders Hi-Fi systems earlier uh
+
+ align:start position:0%
+recorders Hi-Fi systems earlier uh
+ 
+
+ align:start position:0%
+recorders Hi-Fi systems earlier uh
+Europe went much f faster in America and
+
+ align:start position:0%
+Europe went much f faster in America and
+ 
+
+ align:start position:0%
+Europe went much f faster in America and
+actually the European GSM Market cell
+
+ align:start position:0%
+actually the European GSM Market cell
+ 
+
+ align:start position:0%
+actually the European GSM Market cell
+phones as you know them went much
+
+ align:start position:0%
+phones as you know them went much
+ 
+
+ align:start position:0%
+phones as you know them went much
+quicker and then Nokia which is actually
+
+ align:start position:0%
+quicker and then Nokia which is actually
+ 
+
+ align:start position:0%
+quicker and then Nokia which is actually
+European overtook and it took probably
+
+ align:start position:0%
+European overtook and it took probably
+ 
+
+ align:start position:0%
+European overtook and it took probably
+the next decade for Americans to catch
+
+ align:start position:0%
+the next decade for Americans to catch
+ 
+
+ align:start position:0%
+the next decade for Americans to catch
+up so finally here this was then a
+
+ align:start position:0%
+up so finally here this was then a
+ 
+
+ align:start position:0%
+up so finally here this was then a
+combination that people had a product
+
+ align:start position:0%
+combination that people had a product
+ 
+
+ align:start position:0%
+combination that people had a product
+and they just didn't get in the US so
+
+ align:start position:0%
+and they just didn't get in the US so
+ 
+
+ align:start position:0%
+and they just didn't get in the US so
+they were limited to their own market
+
+ align:start position:0%
+they were limited to their own market
+ 
+
+ align:start position:0%
+they were limited to their own market
+and not to sell their products to the
+
+ align:start position:0%
+and not to sell their products to the
+ 
+
+ align:start position:0%
+and not to sell their products to the
+rest of the world as they had done in
+
+ align:start position:0%
+rest of the world as they had done in
+ 
+
+ align:start position:0%
+rest of the world as they had done in
+the past yeah good point so and in in
+
+ align:start position:0%
+the past yeah good point so and in in
+ 
+
+ align:start position:0%
+the past yeah good point so and in in
+fact you know one of the one of the
+
+ align:start position:0%
+fact you know one of the one of the
+ 
+
+ align:start position:0%
+fact you know one of the one of the
+things that um
+
+ align:start position:0%
+things that um
+ 
+
+ align:start position:0%
+things that um
+that um I think both Global star and
+
+ align:start position:0%
+that um I think both Global star and
+ 
+
+ align:start position:0%
+that um I think both Global star and
+aridium had to do and this was a very
+
+ align:start position:0%
+aridium had to do and this was a very
+ 
+
+ align:start position:0%
+aridium had to do and this was a very
+late decision like just in the last
+
+ align:start position:0%
+late decision like just in the last
+ 
+
+ align:start position:0%
+late decision like just in the last
+couple years here before launch 97 98 is
+
+ align:start position:0%
+couple years here before launch 97 98 is
+ 
+
+ align:start position:0%
+couple years here before launch 97 98 is
+to make their their handset dual use
+
+ align:start position:0%
+to make their their handset dual use
+ 
+
+ align:start position:0%
+to make their their handset dual use
+right that if you were in an in an area
+
+ align:start position:0%
+right that if you were in an in an area
+ 
+
+ align:start position:0%
+right that if you were in an in an area
+where there was a cellular network the
+
+ align:start position:0%
+where there was a cellular network the
+ 
+
+ align:start position:0%
+where there was a cellular network the
+phone would switch to that because that
+
+ align:start position:0%
+phone would switch to that because that
+ 
+
+ align:start position:0%
+phone would switch to that because that
+would be cheaper and if if you didn't
+
+ align:start position:0%
+would be cheaper and if if you didn't
+ 
+
+ align:start position:0%
+would be cheaper and if if you didn't
+have cell your network access it would
+
+ align:start position:0%
+have cell your network access it would
+ 
+
+ align:start position:0%
+have cell your network access it would
+automatically try to communicate to the
+
+ align:start position:0%
+automatically try to communicate to the
+ 
+
+ align:start position:0%
+automatically try to communicate to the
+satellite so there was a lot of there
+
+ align:start position:0%
+satellite so there was a lot of there
+ 
+
+ align:start position:0%
+satellite so there was a lot of there
+were a lot lot of uh issues that came up
+
+ align:start position:0%
+were a lot lot of uh issues that came up
+ 
+
+ align:start position:0%
+were a lot lot of uh issues that came up
+by essentially the markets I think in in
+
+ align:start position:0%
+by essentially the markets I think in in
+ 
+
+ align:start position:0%
+by essentially the markets I think in in
+in in Europe your point wker about the
+
+ align:start position:0%
+in in Europe your point wker about the
+ 
+
+ align:start position:0%
+in in Europe your point wker about the
+GSM and in the US just developing quite
+
+ align:start position:0%
+GSM and in the US just developing quite
+ 
+
+ align:start position:0%
+GSM and in the US just developing quite
+differently than had been
+
+ align:start position:0%
+differently than had been
+ 
+
+ align:start position:0%
+differently than had been
+anticipated okay so I want to give you a
+
+ align:start position:0%
+anticipated okay so I want to give you a
+ 
+
+ align:start position:0%
+anticipated okay so I want to give you a
+little bit about sort of Economics of in
+
+ align:start position:0%
+little bit about sort of Economics of in
+ 
+
+ align:start position:0%
+little bit about sort of Economics of in
+the end a lot of this is driven by uh by
+
+ align:start position:0%
+the end a lot of this is driven by uh by
+ 
+
+ align:start position:0%
+the end a lot of this is driven by uh by
+money by economics and so this is you
+
+ align:start position:0%
+money by economics and so this is you
+ 
+
+ align:start position:0%
+money by economics and so this is you
+know satellite economics
+
+ align:start position:0%
+know satellite economics
+ 
+
+ align:start position:0%
+know satellite economics
+101 um the key question here is how much
+
+ align:start position:0%
+101 um the key question here is how much
+ 
+
+ align:start position:0%
+101 um the key question here is how much
+how expensive is it what's what's the
+
+ align:start position:0%
+how expensive is it what's what's the
+ 
+
+ align:start position:0%
+how expensive is it what's what's the
+cost and then what is the price that you
+
+ align:start position:0%
+cost and then what is the price that you
+ 
+
+ align:start position:0%
+cost and then what is the price that you
+can charge for one minute of service
+
+ align:start position:0%
+can charge for one minute of service
+ 
+
+ align:start position:0%
+can charge for one minute of service
+right one minute of one unit of
+
+ align:start position:0%
+right one minute of one unit of
+ 
+
+ align:start position:0%
+right one minute of one unit of
+service and so look at this equation
+
+ align:start position:0%
+service and so look at this equation
+ 
+
+ align:start position:0%
+service and so look at this equation
+here here this is cpf stands for cost
+
+ align:start position:0%
+here here this is cpf stands for cost
+ 
+
+ align:start position:0%
+here here this is cpf stands for cost
+per function um and so in the numerator
+
+ align:start position:0%
+per function um and so in the numerator
+ 
+
+ align:start position:0%
+per function um and so in the numerator
+we have the life cycle cost which is
+
+ align:start position:0%
+we have the life cycle cost which is
+ 
+
+ align:start position:0%
+we have the life cycle cost which is
+your initial
+
+ align:start position:0%
+your initial
+ 
+
+ align:start position:0%
+your initial
+investment uh and then we uh we
+
+ align:start position:0%
+investment uh and then we uh we
+ 
+
+ align:start position:0%
+investment uh and then we uh we
+essentially capitalize that with some
+
+ align:start position:0%
+essentially capitalize that with some
+ 
+
+ align:start position:0%
+essentially capitalize that with some
+interest rate K plus then for each year
+
+ align:start position:0%
+interest rate K plus then for each year
+ 
+
+ align:start position:0%
+interest rate K plus then for each year
+of of operation you have the operational
+
+ align:start position:0%
+of of operation you have the operational
+ 
+
+ align:start position:0%
+of of operation you have the operational
+cost for that year that you have to add
+
+ align:start position:0%
+cost for that year that you have to add
+ 
+
+ align:start position:0%
+cost for that year that you have to add
+so that's your initial you know that's
+
+ align:start position:0%
+so that's your initial you know that's
+ 
+
+ align:start position:0%
+so that's your initial you know that's
+your development cost your manufacturing
+
+ align:start position:0%
+your development cost your manufacturing
+ 
+
+ align:start position:0%
+your development cost your manufacturing
+cost for the satellites including the
+
+ align:start position:0%
+cost for the satellites including the
+ 
+
+ align:start position:0%
+cost for the satellites including the
+launch cost and then the Ops cost would
+
+ align:start position:0%
+launch cost and then the Ops cost would
+ 
+
+ align:start position:0%
+launch cost and then the Ops cost would
+be operating your ground stations your
+
+ align:start position:0%
+be operating your ground stations your
+ 
+
+ align:start position:0%
+be operating your ground stations your
+networks any replenishment cost they
+
+ align:start position:0%
+networks any replenishment cost they
+ 
+
+ align:start position:0%
+networks any replenishment cost they
+would be in your Ops cost and then you
+
+ align:start position:0%
+would be in your Ops cost and then you
+ 
+
+ align:start position:0%
+would be in your Ops cost and then you
+divide this by what's called here the
+
+ align:start position:0%
+divide this by what's called here the
+ 
+
+ align:start position:0%
+divide this by what's called here the
+number of billable minutes that doesn't
+
+ align:start position:0%
+number of billable minutes that doesn't
+ 
+
+ align:start position:0%
+number of billable minutes that doesn't
+mean you're actually going to build
+
+ align:start position:0%
+mean you're actually going to build
+ 
+
+ align:start position:0%
+mean you're actually going to build
+people it means just the are potentially
+
+ align:start position:0%
+people it means just the are potentially
+ 
+
+ align:start position:0%
+people it means just the are potentially
+billable minutes so that's the capacity
+
+ align:start position:0%
+billable minutes so that's the capacity
+ 
+
+ align:start position:0%
+billable minutes so that's the capacity
+of the system C Subs times you know 3
+
+ align:start position:0%
+of the system C Subs times you know 3
+ 
+
+ align:start position:0%
+of the system C Subs times you know 3
+365 days * 24 hours * 60 Minutes times
+
+ align:start position:0%
+365 days * 24 hours * 60 Minutes times
+ 
+
+ align:start position:0%
+365 days * 24 hours * 60 Minutes times
+uh what's the load Factor so the load
+
+ align:start position:0%
+uh what's the load Factor so the load
+ 
+
+ align:start position:0%
+uh what's the load Factor so the load
+factor is essentially the the capacity
+
+ align:start position:0%
+factor is essentially the the capacity
+ 
+
+ align:start position:0%
+factor is essentially the the capacity
+utilization of the system that you
+
+ align:start position:0%
+utilization of the system that you
+ 
+
+ align:start position:0%
+utilization of the system that you
+anticipate okay so that's that's the
+
+ align:start position:0%
+anticipate okay so that's that's the
+ 
+
+ align:start position:0%
+anticipate okay so that's that's the
+basic equation for calculating uh cpf
+
+ align:start position:0%
+basic equation for calculating uh cpf
+ 
+
+ align:start position:0%
+basic equation for calculating uh cpf
+cost per function plug in some numbers
+
+ align:start position:0%
+cost per function plug in some numbers
+ 
+
+ align:start position:0%
+cost per function plug in some numbers
+here these are the numbers that had been
+
+ align:start position:0%
+here these are the numbers that had been
+ 
+
+ align:start position:0%
+here these are the numbers that had been
+assumed you know a $3 billion investment
+
+ align:start position:0%
+assumed you know a $3 billion investment
+ 
+
+ align:start position:0%
+assumed you know a $3 billion investment
+5% interest rate $300 million per year
+
+ align:start position:0%
+5% interest rate $300 million per year
+ 
+
+ align:start position:0%
+5% interest rate $300 million per year
+of Ops cost 15year life cycle this is
+
+ align:start position:0%
+of Ops cost 15year life cycle this is
+ 
+
+ align:start position:0%
+of Ops cost 15year life cycle this is
+the capital T over 15 years 100,000
+
+ align:start position:0%
+the capital T over 15 years 100,000
+ 
+
+ align:start position:0%
+the capital T over 15 years 100,000
+channels that's your capacity number of
+
+ align:start position:0%
+channels that's your capacity number of
+ 
+
+ align:start position:0%
+channels that's your capacity number of
+users in this case uh so the the the
+
+ align:start position:0%
+users in this case uh so the the the
+ 
+
+ align:start position:0%
+users in this case uh so the the the
+load factor is simply the number of
+
+ align:start position:0%
+load factor is simply the number of
+ 
+
+ align:start position:0%
+load factor is simply the number of
+users times the average activity per
+
+ align:start position:0%
+users times the average activity per
+ 
+
+ align:start position:0%
+users times the average activity per
+user in this case assumed to be 100 uh
+
+ align:start position:0%
+user in this case assumed to be 100 uh
+ 
+
+ align:start position:0%
+user in this case assumed to be 100 uh
+1,00 minutes per year but 100 minutes
+
+ align:start position:0%
+1,00 minutes per year but 100 minutes
+ 
+
+ align:start position:0%
+1,00 minutes per year but 100 minutes
+per month okay uh so that gets you um
+
+ align:start position:0%
+per month okay uh so that gets you um
+ 
+
+ align:start position:0%
+per month okay uh so that gets you um
+that gets you a cpf of 20 cents per
+
+ align:start position:0%
+that gets you a cpf of 20 cents per
+ 
+
+ align:start position:0%
+that gets you a cpf of 20 cents per
+minute and based on that you can you can
+
+ align:start position:0%
+minute and based on that you can you can
+ 
+
+ align:start position:0%
+minute and based on that you can you can
+uh you know the business case was made
+
+ align:start position:0%
+uh you know the business case was made
+ 
+
+ align:start position:0%
+uh you know the business case was made
+made based on these kind of numbers um
+
+ align:start position:0%
+made based on these kind of numbers um
+ 
+
+ align:start position:0%
+made based on these kind of numbers um
+and and so 3 million users these are 3
+
+ align:start position:0%
+and and so 3 million users these are 3
+ 
+
+ align:start position:0%
+and and so 3 million users these are 3
+million subscribers right not 3 million
+
+ align:start position:0%
+million subscribers right not 3 million
+ 
+
+ align:start position:0%
+million subscribers right not 3 million
+users at the same time that number would
+
+ align:start position:0%
+users at the same time that number would
+ 
+
+ align:start position:0%
+users at the same time that number would
+be much smaller that number can't be
+
+ align:start position:0%
+be much smaller that number can't be
+ 
+
+ align:start position:0%
+be much smaller that number can't be
+bigger than 100,000 because that's your
+
+ align:start position:0%
+bigger than 100,000 because that's your
+ 
+
+ align:start position:0%
+bigger than 100,000 because that's your
+capacity so for example if you if you
+
+ align:start position:0%
+capacity so for example if you if you
+ 
+
+ align:start position:0%
+capacity so for example if you if you
+run if if you run a fitness club right
+
+ align:start position:0%
+run if if you run a fitness club right
+ 
+
+ align:start position:0%
+run if if you run a fitness club right
+uh at any given time in your Fitness
+
+ align:start position:0%
+uh at any given time in your Fitness
+ 
+
+ align:start position:0%
+uh at any given time in your Fitness
+club you can maybe have I don't know 50
+
+ align:start position:0%
+club you can maybe have I don't know 50
+ 
+
+ align:start position:0%
+club you can maybe have I don't know 50
+or 100 people actually working out right
+
+ align:start position:0%
+or 100 people actually working out right
+ 
+
+ align:start position:0%
+or 100 people actually working out right
+but your number of customers or
+
+ align:start position:0%
+but your number of customers or
+ 
+
+ align:start position:0%
+but your number of customers or
+subscribers should be you know a th000
+
+ align:start position:0%
+subscribers should be you know a th000
+ 
+
+ align:start position:0%
+subscribers should be you know a th000
+or 2,000 and if they all show up at the
+
+ align:start position:0%
+or 2,000 and if they all show up at the
+ 
+
+ align:start position:0%
+or 2,000 and if they all show up at the
+same time you're in big trouble right so
+
+ align:start position:0%
+same time you're in big trouble right so
+ 
+
+ align:start position:0%
+same time you're in big trouble right so
+that's the big that's the difference
+
+ align:start position:0%
+that's the big that's the difference
+ 
+
+ align:start position:0%
+that's the big that's the difference
+between number of users or number of
+
+ align:start position:0%
+between number of users or number of
+ 
+
+ align:start position:0%
+between number of users or number of
+subscribers and number of active users
+
+ align:start position:0%
+subscribers and number of active users
+ 
+
+ align:start position:0%
+subscribers and number of active users
+at any given time that's that's a big
+
+ align:start position:0%
+at any given time that's that's a big
+ 
+
+ align:start position:0%
+at any given time that's that's a big
+part of um man in these kind of systems
+
+ align:start position:0%
+part of um man in these kind of systems
+ 
+
+ align:start position:0%
+part of um man in these kind of systems
+however uh what actually happened is the
+
+ align:start position:0%
+however uh what actually happened is the
+ 
+
+ align:start position:0%
+however uh what actually happened is the
+number of actual users grew much much
+
+ align:start position:0%
+number of actual users grew much much
+ 
+
+ align:start position:0%
+number of actual users grew much much
+slower so if you plug in some different
+
+ align:start position:0%
+slower so if you plug in some different
+ 
+
+ align:start position:0%
+slower so if you plug in some different
+num let's keep all the numbers the same
+
+ align:start position:0%
+num let's keep all the numbers the same
+ 
+
+ align:start position:0%
+num let's keep all the numbers the same
+except for the subscriber base the
+
+ align:start position:0%
+except for the subscriber base the
+ 
+
+ align:start position:0%
+except for the subscriber base the
+number of users in this case we're going
+
+ align:start position:0%
+number of users in this case we're going
+ 
+
+ align:start position:0%
+number of users in this case we're going
+to assume 50,000 users instead of the 3
+
+ align:start position:0%
+to assume 50,000 users instead of the 3
+ 
+
+ align:start position:0%
+to assume 50,000 users instead of the 3
+million this is closer to what they had
+
+ align:start position:0%
+million this is closer to what they had
+ 
+
+ align:start position:0%
+million this is closer to what they had
+after you know about a year of operation
+
+ align:start position:0%
+after you know about a year of operation
+ 
+
+ align:start position:0%
+after you know about a year of operation
+now your cpf goes to $12 per minute
+
+ align:start position:0%
+now your cpf goes to $12 per minute
+ 
+
+ align:start position:0%
+now your cpf goes to $12 per minute
+which is non-competitive is right except
+
+ align:start position:0%
+which is non-competitive is right except
+ 
+
+ align:start position:0%
+which is non-competitive is right except
+for some extremely you know like
+
+ align:start position:0%
+for some extremely you know like
+ 
+
+ align:start position:0%
+for some extremely you know like
+military applications or you know making
+
+ align:start position:0%
+military applications or you know making
+ 
+
+ align:start position:0%
+military applications or you know making
+some emergency phone calls on an oil rig
+
+ align:start position:0%
+some emergency phone calls on an oil rig
+ 
+
+ align:start position:0%
+some emergency phone calls on an oil rig
+you know on the ocean you know most
+
+ align:start position:0%
+you know on the ocean you know most
+ 
+
+ align:start position:0%
+you know on the ocean you know most
+people at the time now and at the time
+
+ align:start position:0%
+people at the time now and at the time
+ 
+
+ align:start position:0%
+people at the time now and at the time
+would never pay this uh uh for for one
+
+ align:start position:0%
+would never pay this uh uh for for one
+ 
+
+ align:start position:0%
+would never pay this uh uh for for one
+minute of
+
+ align:start position:0%
+minute of
+ 
+
+ align:start position:0%
+minute of
+service and so um that was the
+
+ align:start position:0%
+service and so um that was the
+ 
+
+ align:start position:0%
+service and so um that was the
+fundamental problem is that the user
+
+ align:start position:0%
+fundamental problem is that the user
+ 
+
+ align:start position:0%
+fundamental problem is that the user
+base did not materialize as fast as
+
+ align:start position:0%
+base did not materialize as fast as
+ 
+
+ align:start position:0%
+base did not materialize as fast as
+planned therefore this cost per function
+
+ align:start position:0%
+planned therefore this cost per function
+ 
+
+ align:start position:0%
+planned therefore this cost per function
+was way higher and they did charge you
+
+ align:start position:0%
+was way higher and they did charge you
+ 
+
+ align:start position:0%
+was way higher and they did charge you
+know $3 to5 per minute of usage of the
+
+ align:start position:0%
+know $3 to5 per minute of usage of the
+ 
+
+ align:start position:0%
+know $3 to5 per minute of usage of the
+system which uh you know as you try to
+
+ align:start position:0%
+system which uh you know as you try to
+ 
+
+ align:start position:0%
+system which uh you know as you try to
+squeeze your existing users more uh
+
+ align:start position:0%
+squeeze your existing users more uh
+ 
+
+ align:start position:0%
+squeeze your existing users more uh
+you're not going to get the the ramp up
+
+ align:start position:0%
+you're not going to get the the ramp up
+ 
+
+ align:start position:0%
+you're not going to get the the ramp up
+and the scale up in the system that you
+
+ align:start position:0%
+and the scale up in the system that you
+ 
+
+ align:start position:0%
+and the scale up in the system that you
+need that was the fundamental problem
+
+ align:start position:0%
+need that was the fundamental problem
+ 
+
+ align:start position:0%
+need that was the fundamental problem
+with with the economics of these
+
+ align:start position:0%
+with with the economics of these
+ 
+
+ align:start position:0%
+with with the economics of these
+systems so let me talk a little bit
+
+ align:start position:0%
+systems so let me talk a little bit
+ 
+
+ align:start position:0%
+systems so let me talk a little bit
+about you know the design decisions the
+
+ align:start position:0%
+about you know the design decisions the
+ 
+
+ align:start position:0%
+about you know the design decisions the
+conceptual design uh of what this design
+
+ align:start position:0%
+conceptual design uh of what this design
+ 
+
+ align:start position:0%
+conceptual design uh of what this design
+space looks like so fundamental um oh
+
+ align:start position:0%
+space looks like so fundamental um oh
+ 
+
+ align:start position:0%
+space looks like so fundamental um oh
+the other thing I should mention to you
+
+ align:start position:0%
+the other thing I should mention to you
+ 
+
+ align:start position:0%
+the other thing I should mention to you
+what was interesting is both after the
+
+ align:start position:0%
+what was interesting is both after the
+ 
+
+ align:start position:0%
+what was interesting is both after the
+bankruptcy both of radium and Global
+
+ align:start position:0%
+bankruptcy both of radium and Global
+ 
+
+ align:start position:0%
+bankruptcy both of radium and Global
+Star both of the chief Engineers for
+
+ align:start position:0%
+Star both of the chief Engineers for
+ 
+
+ align:start position:0%
+Star both of the chief Engineers for
+both of these systems uh took Refuge at
+
+ align:start position:0%
+both of these systems uh took Refuge at
+ 
+
+ align:start position:0%
+both of these systems uh took Refuge at
+MIT essentially they came like uh Joel
+
+ align:start position:0%
+MIT essentially they came like uh Joel
+ 
+
+ align:start position:0%
+MIT essentially they came like uh Joel
+shandal who was the uh chief engineer
+
+ align:start position:0%
+shandal who was the uh chief engineer
+ 
+
+ align:start position:0%
+shandal who was the uh chief engineer
+for Global star great guy both very
+
+ align:start position:0%
+for Global star great guy both very
+ 
+
+ align:start position:0%
+for Global star great guy both very
+competent people uh came to MIT still
+
+ align:start position:0%
+competent people uh came to MIT still
+ 
+
+ align:start position:0%
+competent people uh came to MIT still
+there he's still a professor there and
+
+ align:start position:0%
+there he's still a professor there and
+ 
+
+ align:start position:0%
+there he's still a professor there and
+then Ray Leopold was one of the three
+
+ align:start position:0%
+then Ray Leopold was one of the three
+ 
+
+ align:start position:0%
+then Ray Leopold was one of the three
+architects for idium also came to MIT
+
+ align:start position:0%
+architects for idium also came to MIT
+ 
+
+ align:start position:0%
+architects for idium also came to MIT
+during this time so I had extensive
+
+ align:start position:0%
+during this time so I had extensive
+ 
+
+ align:start position:0%
+during this time so I had extensive
+discussions with them and what you see
+
+ align:start position:0%
+discussions with them and what you see
+ 
+
+ align:start position:0%
+discussions with them and what you see
+here on slide 25 is one result of those
+
+ align:start position:0%
+here on slide 25 is one result of those
+ 
+
+ align:start position:0%
+here on slide 25 is one result of those
+discussions which is you know the the
+
+ align:start position:0%
+discussions which is you know the the
+ 
+
+ align:start position:0%
+discussions which is you know the the
+key design decisions that they had to
+
+ align:start position:0%
+key design decisions that they had to
+ 
+
+ align:start position:0%
+key design decisions that they had to
+make uh fundamentally there's uh you
+
+ align:start position:0%
+make uh fundamentally there's uh you
+ 
+
+ align:start position:0%
+make uh fundamentally there's uh you
+won't be surprised to see this this is
+
+ align:start position:0%
+won't be surprised to see this this is
+ 
+
+ align:start position:0%
+won't be surprised to see this this is
+the magic number seven right seven key
+
+ align:start position:0%
+the magic number seven right seven key
+ 
+
+ align:start position:0%
+the magic number seven right seven key
+design decisions when you design a
+
+ align:start position:0%
+design decisions when you design a
+ 
+
+ align:start position:0%
+design decisions when you design a
+satellite constellation for
+
+ align:start position:0%
+satellite constellation for
+ 
+
+ align:start position:0%
+satellite constellation for
+communication purposes constellation
+
+ align:start position:0%
+communication purposes constellation
+ 
+
+ align:start position:0%
+communication purposes constellation
+type polar or Walker orbital altitude
+
+ align:start position:0%
+type polar or Walker orbital altitude
+ 
+
+ align:start position:0%
+type polar or Walker orbital altitude
+minimum elevation angle above the
+
+ align:start position:0%
+minimum elevation angle above the
+ 
+
+ align:start position:0%
+minimum elevation angle above the
+Horizon that you can
+
+ align:start position:0%
+Horizon that you can
+ 
+
+ align:start position:0%
+Horizon that you can
+communicate satellite transmit power the
+
+ align:start position:0%
+communicate satellite transmit power the
+ 
+
+ align:start position:0%
+communicate satellite transmit power the
+size of your primary antenna your
+
+ align:start position:0%
+size of your primary antenna your
+ 
+
+ align:start position:0%
+size of your primary antenna your
+multiax scheme so this is time division
+
+ align:start position:0%
+multiax scheme so this is time division
+ 
+
+ align:start position:0%
+multiax scheme so this is time division
+or uh code Division multiplexing and
+
+ align:start position:0%
+or uh code Division multiplexing and
+ 
+
+ align:start position:0%
+or uh code Division multiplexing and
+then the last one is about the network
+
+ align:start position:0%
+then the last one is about the network
+ 
+
+ align:start position:0%
+then the last one is about the network
+architecture do you have inters
+
+ align:start position:0%
+architecture do you have inters
+ 
+
+ align:start position:0%
+architecture do you have inters
+satellite links yes or no inters
+
+ align:start position:0%
+satellite links yes or no inters
+ 
+
+ align:start position:0%
+satellite links yes or no inters
+satellite links means satellites can
+
+ align:start position:0%
+satellite links means satellites can
+ 
+
+ align:start position:0%
+satellite links means satellites can
+talk to each other
+
+ align:start position:0%
+talk to each other
+ 
+
+ align:start position:0%
+talk to each other
+uh and iridium chose that um Global star
+
+ align:start position:0%
+uh and iridium chose that um Global star
+ 
+
+ align:start position:0%
+uh and iridium chose that um Global star
+did not so in global star the global
+
+ align:start position:0%
+did not so in global star the global
+ 
+
+ align:start position:0%
+did not so in global star the global
+star satellites cannot talk to each
+
+ align:start position:0%
+star satellites cannot talk to each
+ 
+
+ align:start position:0%
+star satellites cannot talk to each
+other directly in space they can only
+
+ align:start position:0%
+other directly in space they can only
+ 
+
+ align:start position:0%
+other directly in space they can only
+talk it's a bent pipe system through a
+
+ align:start position:0%
+talk it's a bent pipe system through a
+ 
+
+ align:start position:0%
+talk it's a bent pipe system through a
+ground
+
+ align:start position:0%
+ground
+ 
+
+ align:start position:0%
+ground
+station okay so if you this is like the
+
+ align:start position:0%
+station okay so if you this is like the
+ 
+
+ align:start position:0%
+station okay so if you this is like the
+morphological Matrix that you learned
+
+ align:start position:0%
+morphological Matrix that you learned
+ 
+
+ align:start position:0%
+morphological Matrix that you learned
+about you just pick uh design decisions
+
+ align:start position:0%
+about you just pick uh design decisions
+ 
+
+ align:start position:0%
+about you just pick uh design decisions
+in this morphological Matrix and you
+
+ align:start position:0%
+in this morphological Matrix and you
+ 
+
+ align:start position:0%
+in this morphological Matrix and you
+come up with an architecture in fact a
+
+ align:start position:0%
+come up with an architecture in fact a
+ 
+
+ align:start position:0%
+come up with an architecture in fact a
+full factorial search of the space base
+
+ align:start position:0%
+full factorial search of the space base
+ 
+
+ align:start position:0%
+full factorial search of the space base
+would reveal 1440 different satellite
+
+ align:start position:0%
+would reveal 1440 different satellite
+ 
+
+ align:start position:0%
+would reveal 1440 different satellite
+architectures um so what's your that's
+
+ align:start position:0%
+architectures um so what's your that's
+ 
+
+ align:start position:0%
+architectures um so what's your that's
+on the input side what's the output
+
+ align:start position:0%
+on the input side what's the output
+ 
+
+ align:start position:0%
+on the input side what's the output
+Vector what do you care about in terms
+
+ align:start position:0%
+Vector what do you care about in terms
+ 
+
+ align:start position:0%
+Vector what do you care about in terms
+of output of the system well first of
+
+ align:start position:0%
+of output of the system well first of
+ 
+
+ align:start position:0%
+of output of the system well first of
+all performance um so the performance of
+
+ align:start position:0%
+all performance um so the performance of
+ 
+
+ align:start position:0%
+all performance um so the performance of
+this is for voice Communications it in a
+
+ align:start position:0%
+this is for voice Communications it in a
+ 
+
+ align:start position:0%
+this is for voice Communications it in a
+sense it applies to data Communications
+
+ align:start position:0%
+sense it applies to data Communications
+ 
+
+ align:start position:0%
+sense it applies to data Communications
+as well is your data rate per channel
+
+ align:start position:0%
+as well is your data rate per channel
+ 
+
+ align:start position:0%
+as well is your data rate per channel
+right 4.8 uh kbps your bit error rate
+
+ align:start position:0%
+right 4.8 uh kbps your bit error rate
+ 
+
+ align:start position:0%
+right 4.8 uh kbps your bit error rate
+like what's the average number of bits
+
+ align:start position:0%
+like what's the average number of bits
+ 
+
+ align:start position:0%
+like what's the average number of bits
+that are wrong 10 Theus 3 that's
+
+ align:start position:0%
+that are wrong 10 Theus 3 that's
+ 
+
+ align:start position:0%
+that are wrong 10 Theus 3 that's
+actually a pretty uh not a very that's
+
+ align:start position:0%
+actually a pretty uh not a very that's
+ 
+
+ align:start position:0%
+actually a pretty uh not a very that's
+not a very stringent requirement and the
+
+ align:start position:0%
+not a very stringent requirement and the
+ 
+
+ align:start position:0%
+not a very stringent requirement and the
+reason is you're just this is for voice
+
+ align:start position:0%
+reason is you're just this is for voice
+ 
+
+ align:start position:0%
+reason is you're just this is for voice
+communication this is not for sending
+
+ align:start position:0%
+communication this is not for sending
+ 
+
+ align:start position:0%
+communication this is not for sending
+you know commands to a spacecraft going
+
+ align:start position:0%
+you know commands to a spacecraft going
+ 
+
+ align:start position:0%
+you know commands to a spacecraft going
+to Mars if you send commands it would
+
+ align:start position:0%
+to Mars if you send commands it would
+ 
+
+ align:start position:0%
+to Mars if you send commands it would
+have to be you know 10 theus1 or 10- 9
+
+ align:start position:0%
+have to be you know 10 theus1 or 10- 9
+ 
+
+ align:start position:0%
+have to be you know 10 theus1 or 10- 9
+much much better bit error rate but this
+
+ align:start position:0%
+much much better bit error rate but this
+ 
+
+ align:start position:0%
+much much better bit error rate but this
+is okay for for voice and then the link
+
+ align:start position:0%
+is okay for for voice and then the link
+ 
+
+ align:start position:0%
+is okay for for voice and then the link
+fading margin 16 uh DB this is the
+
+ align:start position:0%
+fading margin 16 uh DB this is the
+ 
+
+ align:start position:0%
+fading margin 16 uh DB this is the
+strength of the signal uh which will
+
+ align:start position:0%
+strength of the signal uh which will
+ 
+
+ align:start position:0%
+strength of the signal uh which will
+which will dictate whether or not you
+
+ align:start position:0%
+which will dictate whether or not you
+ 
+
+ align:start position:0%
+which will dictate whether or not you
+can use the phone under trees or in
+
+ align:start position:0%
+can use the phone under trees or in
+ 
+
+ align:start position:0%
+can use the phone under trees or in
+buildings uh so you want this number to
+
+ align:start position:0%
+buildings uh so you want this number to
+ 
+
+ align:start position:0%
+buildings uh so you want this number to
+be higher but the higher it is you know
+
+ align:start position:0%
+be higher but the higher it is you know
+ 
+
+ align:start position:0%
+be higher but the higher it is you know
+given the power you have on the
+
+ align:start position:0%
+given the power you have on the
+ 
+
+ align:start position:0%
+given the power you have on the
+satellites the fewer channels you have
+
+ align:start position:0%
+satellites the fewer channels you have
+ 
+
+ align:start position:0%
+satellites the fewer channels you have
+so there's tradeoffs so what was done
+
+ align:start position:0%
+so there's tradeoffs so what was done
+ 
+
+ align:start position:0%
+so there's tradeoffs so what was done
+here is to keep the performance fixed
+
+ align:start position:0%
+here is to keep the performance fixed
+ 
+
+ align:start position:0%
+here is to keep the performance fixed
+and so that you can compare
+
+ align:start position:0%
+and so that you can compare
+ 
+
+ align:start position:0%
+and so that you can compare
+architectures you know compare apples to
+
+ align:start position:0%
+architectures you know compare apples to
+ 
+
+ align:start position:0%
+architectures you know compare apples to
+apples then we have capacity which is
+
+ align:start position:0%
+apples then we have capacity which is
+ 
+
+ align:start position:0%
+apples then we have capacity which is
+the number of simultaneous uh duplex
+
+ align:start position:0%
+the number of simultaneous uh duplex
+ 
+
+ align:start position:0%
+the number of simultaneous uh duplex
+channels and then finally the life cycle
+
+ align:start position:0%
+channels and then finally the life cycle
+ 
+
+ align:start position:0%
+channels and then finally the life cycle
+cost of the system which includes
+
+ align:start position:0%
+cost of the system which includes
+ 
+
+ align:start position:0%
+cost of the system which includes
+research development test and evaluation
+
+ align:start position:0%
+research development test and evaluation
+ 
+
+ align:start position:0%
+research development test and evaluation
+satellite construction and tests launch
+
+ align:start position:0%
+satellite construction and tests launch
+ 
+
+ align:start position:0%
+satellite construction and tests launch
+and orbital insertion and then the
+
+ align:start position:0%
+and orbital insertion and then the
+ 
+
+ align:start position:0%
+and orbital insertion and then the
+operations and replenishment so if a
+
+ align:start position:0%
+operations and replenishment so if a
+ 
+
+ align:start position:0%
+operations and replenishment so if a
+satellite fails in orbit either you have
+
+ align:start position:0%
+satellite fails in orbit either you have
+ 
+
+ align:start position:0%
+satellite fails in orbit either you have
+to already have prepositioned the spare
+
+ align:start position:0%
+to already have prepositioned the spare
+ 
+
+ align:start position:0%
+to already have prepositioned the spare
+or you're going to launch you're going
+
+ align:start position:0%
+or you're going to launch you're going
+ 
+
+ align:start position:0%
+or you're going to launch you're going
+to launch a replacement and this
+
+ align:start position:0%
+to launch a replacement and this
+ 
+
+ align:start position:0%
+to launch a replacement and this
+actually happen uh in both cases for
+
+ align:start position:0%
+actually happen uh in both cases for
+ 
+
+ align:start position:0%
+actually happen uh in both cases for
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+constellations so um
+
+ align:start position:0%
+constellations so um
+ 
+
+ align:start position:0%
+constellations so um
+in order to then you know connect the
+
+ align:start position:0%
+in order to then you know connect the
+ 
+
+ align:start position:0%
+in order to then you know connect the
+input to the output you need to build a
+
+ align:start position:0%
+input to the output you need to build a
+ 
+
+ align:start position:0%
+input to the output you need to build a
+simulator or a model of the system and
+
+ align:start position:0%
+simulator or a model of the system and
+ 
+
+ align:start position:0%
+simulator or a model of the system and
+this is a high level view of what that
+
+ align:start position:0%
+this is a high level view of what that
+ 
+
+ align:start position:0%
+this is a high level view of what that
+model looks like so we take our input
+
+ align:start position:0%
+model looks like so we take our input
+ 
+
+ align:start position:0%
+model looks like so we take our input
+our design decisions and certain
+
+ align:start position:0%
+our design decisions and certain
+ 
+
+ align:start position:0%
+our design decisions and certain
+Constance that we assume a constant
+
+ align:start position:0%
+Constance that we assume a constant
+ 
+
+ align:start position:0%
+Constance that we assume a constant
+vector and Cascade this information you
+
+ align:start position:0%
+vector and Cascade this information you
+ 
+
+ align:start position:0%
+vector and Cascade this information you
+know for the constellation module takes
+
+ align:start position:0%
+know for the constellation module takes
+ 
+
+ align:start position:0%
+know for the constellation module takes
+the altitude and the minimum elevation
+
+ align:start position:0%
+the altitude and the minimum elevation
+ 
+
+ align:start position:0%
+the altitude and the minimum elevation
+angle and produces uh T is the number of
+
+ align:start position:0%
+angle and produces uh T is the number of
+ 
+
+ align:start position:0%
+angle and produces uh T is the number of
+satellites and ke is the number of
+
+ align:start position:0%
+satellites and ke is the number of
+ 
+
+ align:start position:0%
+satellites and ke is the number of
+orbital planes so this is sort of
+
+ align:start position:0%
+orbital planes so this is sort of
+ 
+
+ align:start position:0%
+orbital planes so this is sort of
+orbital Dynamics the spacecraft module
+
+ align:start position:0%
+orbital Dynamics the spacecraft module
+ 
+
+ align:start position:0%
+orbital Dynamics the spacecraft module
+calculates the satellite Mass um the
+
+ align:start position:0%
+calculates the satellite Mass um the
+ 
+
+ align:start position:0%
+calculates the satellite Mass um the
+satellite Network um you know builds
+
+ align:start position:0%
+satellite Network um you know builds
+ 
+
+ align:start position:0%
+satellite Network um you know builds
+essentially the communication
+
+ align:start position:0%
+essentially the communication
+ 
+
+ align:start position:0%
+essentially the communication
+communication Pathways the link budget
+
+ align:start position:0%
+communication Pathways the link budget
+ 
+
+ align:start position:0%
+communication Pathways the link budget
+will calculate the capacity of the
+
+ align:start position:0%
+will calculate the capacity of the
+ 
+
+ align:start position:0%
+will calculate the capacity of the
+system you know given given those
+
+ align:start position:0%
+system you know given given those
+ 
+
+ align:start position:0%
+system you know given given those
+performance constraints the launch
+
+ align:start position:0%
+performance constraints the launch
+ 
+
+ align:start position:0%
+performance constraints the launch
+module will determine uh how many
+
+ align:start position:0%
+module will determine uh how many
+ 
+
+ align:start position:0%
+module will determine uh how many
+launches do you need from where and then
+
+ align:start position:0%
+launches do you need from where and then
+ 
+
+ align:start position:0%
+launches do you need from where and then
+the cost module basically calculates the
+
+ align:start position:0%
+the cost module basically calculates the
+ 
+
+ align:start position:0%
+the cost module basically calculates the
+total cost of the system the life cycle
+
+ align:start position:0%
+total cost of the system the life cycle
+ 
+
+ align:start position:0%
+total cost of the system the life cycle
+cost and finally you get essentially a
+
+ align:start position:0%
+cost and finally you get essentially a
+ 
+
+ align:start position:0%
+cost and finally you get essentially a
+tradeoff of life cycle cost versus
+
+ align:start position:0%
+tradeoff of life cycle cost versus
+ 
+
+ align:start position:0%
+tradeoff of life cycle cost versus
+capacity of the
+
+ align:start position:0%
+capacity of the
+ 
+
+ align:start position:0%
+capacity of the
+system um let me just show you some you
+
+ align:start position:0%
+system um let me just show you some you
+ 
+
+ align:start position:0%
+system um let me just show you some you
+know you say well that's tying together
+
+ align:start position:0%
+know you say well that's tying together
+ 
+
+ align:start position:0%
+know you say well that's tying together
+a lot of information into a
+
+ align:start position:0%
+a lot of information into a
+ 
+
+ align:start position:0%
+a lot of information into a
+multidisciplinary model so what kind of
+
+ align:start position:0%
+multidisciplinary model so what kind of
+ 
+
+ align:start position:0%
+multidisciplinary model so what kind of
+information do you have you have a mix
+
+ align:start position:0%
+information do you have you have a mix
+ 
+
+ align:start position:0%
+information do you have you have a mix
+really of physics-based models so this
+
+ align:start position:0%
+really of physics-based models so this
+ 
+
+ align:start position:0%
+really of physics-based models so this
+is a very well-known equation the EB
+
+ align:start position:0%
+is a very well-known equation the EB
+ 
+
+ align:start position:0%
+is a very well-known equation the EB
+knot this is the energy bit over noise
+
+ align:start position:0%
+knot this is the energy bit over noise
+ 
+
+ align:start position:0%
+knot this is the energy bit over noise
+ratio this is a closed form you know
+
+ align:start position:0%
+ratio this is a closed form you know
+ 
+
+ align:start position:0%
+ratio this is a closed form you know
+physics based equation that tells you
+
+ align:start position:0%
+physics based equation that tells you
+ 
+
+ align:start position:0%
+physics based equation that tells you
+how much energy is there per bit uh
+
+ align:start position:0%
+how much energy is there per bit uh
+ 
+
+ align:start position:0%
+how much energy is there per bit uh
+what's the signal to noise ratio on a
+
+ align:start position:0%
+what's the signal to noise ratio on a
+ 
+
+ align:start position:0%
+what's the signal to noise ratio on a
+per bit basis and this is a function of
+
+ align:start position:0%
+per bit basis and this is a function of
+ 
+
+ align:start position:0%
+per bit basis and this is a function of
+you know transmitter power receiver and
+
+ align:start position:0%
+you know transmitter power receiver and
+ 
+
+ align:start position:0%
+you know transmitter power receiver and
+transmission gains various losses in the
+
+ align:start position:0%
+transmission gains various losses in the
+ 
+
+ align:start position:0%
+transmission gains various losses in the
+system and then some of the equations
+
+ align:start position:0%
+system and then some of the equations
+ 
+
+ align:start position:0%
+system and then some of the equations
+are some of the information is empirical
+
+ align:start position:0%
+are some of the information is empirical
+ 
+
+ align:start position:0%
+are some of the information is empirical
+for example the relationship between
+
+ align:start position:0%
+for example the relationship between
+ 
+
+ align:start position:0%
+for example the relationship between
+spacecraft wet mass and payo power you
+
+ align:start position:0%
+spacecraft wet mass and payo power you
+ 
+
+ align:start position:0%
+spacecraft wet mass and payo power you
+know if you wanted to have a closed form
+
+ align:start position:0%
+know if you wanted to have a closed form
+ 
+
+ align:start position:0%
+know if you wanted to have a closed form
+or you wanted to have more detail you
+
+ align:start position:0%
+or you wanted to have more detail you
+ 
+
+ align:start position:0%
+or you wanted to have more detail you
+would have to almost build like a cad
+
+ align:start position:0%
+would have to almost build like a cad
+ 
+
+ align:start position:0%
+would have to almost build like a cad
+model right a separate model you'd have
+
+ align:start position:0%
+model right a separate model you'd have
+ 
+
+ align:start position:0%
+model right a separate model you'd have
+for each of these 1440 architectures
+
+ align:start position:0%
+for each of these 1440 architectures
+ 
+
+ align:start position:0%
+for each of these 1440 architectures
+you'd have to manually construct an
+
+ align:start position:0%
+you'd have to manually construct an
+ 
+
+ align:start position:0%
+you'd have to manually construct an
+individual um detailed design and that's
+
+ align:start position:0%
+individual um detailed design and that's
+ 
+
+ align:start position:0%
+individual um detailed design and that's
+not feasible so what you do instead is
+
+ align:start position:0%
+not feasible so what you do instead is
+ 
+
+ align:start position:0%
+not feasible so what you do instead is
+you use some prior data and you can see
+
+ align:start position:0%
+you use some prior data and you can see
+ 
+
+ align:start position:0%
+you use some prior data and you can see
+here uh a a scaling relationship it's
+
+ align:start position:0%
+here uh a a scaling relationship it's
+ 
+
+ align:start position:0%
+here uh a a scaling relationship it's
+not perfect but we we can um you know we
+
+ align:start position:0%
+not perfect but we we can um you know we
+ 
+
+ align:start position:0%
+not perfect but we we can um you know we
+have air bars we know how good it is
+
+ align:start position:0%
+have air bars we know how good it is
+ 
+
+ align:start position:0%
+have air bars we know how good it is
+satellite Mass satellite uh wet mass as
+
+ align:start position:0%
+satellite Mass satellite uh wet mass as
+ 
+
+ align:start position:0%
+satellite Mass satellite uh wet mass as
+a function of transmitter power and in
+
+ align:start position:0%
+a function of transmitter power and in
+ 
+
+ align:start position:0%
+a function of transmitter power and in
+this case propellant Mass okay so two
+
+ align:start position:0%
+this case propellant Mass okay so two
+ 
+
+ align:start position:0%
+this case propellant Mass okay so two
+kinds of
+
+ align:start position:0%
+kinds of
+ 
+
+ align:start position:0%
+kinds of
+equations bench marking uh so once you
+
+ align:start position:0%
+equations bench marking uh so once you
+ 
+
+ align:start position:0%
+equations bench marking uh so once you
+have this model you need to ask the
+
+ align:start position:0%
+have this model you need to ask the
+ 
+
+ align:start position:0%
+have this model you need to ask the
+question how can I trust this model does
+
+ align:start position:0%
+question how can I trust this model does
+ 
+
+ align:start position:0%
+question how can I trust this model does
+it give me reasonable reasonable answers
+
+ align:start position:0%
+it give me reasonable reasonable answers
+ 
+
+ align:start position:0%
+it give me reasonable reasonable answers
+and in this case uh benchmarking is the
+
+ align:start position:0%
+and in this case uh benchmarking is the
+ 
+
+ align:start position:0%
+and in this case uh benchmarking is the
+process of validating simulation by
+
+ align:start position:0%
+process of validating simulation by
+ 
+
+ align:start position:0%
+process of validating simulation by
+comparing the predicted response against
+
+ align:start position:0%
+comparing the predicted response against
+ 
+
+ align:start position:0%
+comparing the predicted response against
+reality so just quickly here showing you
+
+ align:start position:0%
+reality so just quickly here showing you
+ 
+
+ align:start position:0%
+reality so just quickly here showing you
+four kinds of data so one of the
+
+ align:start position:0%
+four kinds of data so one of the
+ 
+
+ align:start position:0%
+four kinds of data so one of the
+simultaneous channels of the
+
+ align:start position:0%
+simultaneous channels of the
+ 
+
+ align:start position:0%
+simultaneous channels of the
+constellation this is the prediction of
+
+ align:start position:0%
+constellation this is the prediction of
+ 
+
+ align:start position:0%
+constellation this is the prediction of
+capacity uh you can see it's pretty good
+
+ align:start position:0%
+capacity uh you can see it's pretty good
+ 
+
+ align:start position:0%
+capacity uh you can see it's pretty good
+uh in this case the model is actually a
+
+ align:start position:0%
+uh in this case the model is actually a
+ 
+
+ align:start position:0%
+uh in this case the model is actually a
+little conservative so the blue bars are
+
+ align:start position:0%
+little conservative so the blue bars are
+ 
+
+ align:start position:0%
+little conservative so the blue bars are
+the actual or planned capacities the red
+
+ align:start position:0%
+the actual or planned capacities the red
+ 
+
+ align:start position:0%
+the actual or planned capacities the red
+ones or magenta is simulated and you can
+
+ align:start position:0%
+ones or magenta is simulated and you can
+ 
+
+ align:start position:0%
+ones or magenta is simulated and you can
+see that the simulation underpredicts
+
+ align:start position:0%
+see that the simulation underpredicts
+ 
+
+ align:start position:0%
+see that the simulation underpredicts
+slightly the true capacity of the system
+
+ align:start position:0%
+slightly the true capacity of the system
+ 
+
+ align:start position:0%
+slightly the true capacity of the system
+um life cycle cost you saw that idium
+
+ align:start position:0%
+um life cycle cost you saw that idium
+ 
+
+ align:start position:0%
+um life cycle cost you saw that idium
+was just a bit more than 5 billion uh
+
+ align:start position:0%
+was just a bit more than 5 billion uh
+ 
+
+ align:start position:0%
+was just a bit more than 5 billion uh
+global star was between three and four
+
+ align:start position:0%
+global star was between three and four
+ 
+
+ align:start position:0%
+global star was between three and four
+and so uh here we're in the right
+
+ align:start position:0%
+and so uh here we're in the right
+ 
+
+ align:start position:0%
+and so uh here we're in the right
+Ballpark and then in terms of satellite
+
+ align:start position:0%
+Ballpark and then in terms of satellite
+ 
+
+ align:start position:0%
+Ballpark and then in terms of satellite
+mass and the number of satellites in the
+
+ align:start position:0%
+mass and the number of satellites in the
+ 
+
+ align:start position:0%
+mass and the number of satellites in the
+constellation required we match that
+
+ align:start position:0%
+constellation required we match that
+ 
+
+ align:start position:0%
+constellation required we match that
+very closely and the reason for this is
+
+ align:start position:0%
+very closely and the reason for this is
+ 
+
+ align:start position:0%
+very closely and the reason for this is
+fundamentally this is just geometry
+
+ align:start position:0%
+fundamentally this is just geometry
+ 
+
+ align:start position:0%
+fundamentally this is just geometry
+right if if I tell you the altitude and
+
+ align:start position:0%
+right if if I tell you the altitude and
+ 
+
+ align:start position:0%
+right if if I tell you the altitude and
+the minimum elevation angle and I'm
+
+ align:start position:0%
+the minimum elevation angle and I'm
+ 
+
+ align:start position:0%
+the minimum elevation angle and I'm
+telling you I need I need Global
+
+ align:start position:0%
+telling you I need I need Global
+ 
+
+ align:start position:0%
+telling you I need I need Global
+coverage and I want dual redundancy so
+
+ align:start position:0%
+coverage and I want dual redundancy so
+ 
+
+ align:start position:0%
+coverage and I want dual redundancy so
+you can always see at least two
+
+ align:start position:0%
+you can always see at least two
+ 
+
+ align:start position:0%
+you can always see at least two
+satellites it's just geometry to figure
+
+ align:start position:0%
+satellites it's just geometry to figure
+ 
+
+ align:start position:0%
+satellites it's just geometry to figure
+out how many satellites and how many
+
+ align:start position:0%
+out how many satellites and how many
+ 
+
+ align:start position:0%
+out how many satellites and how many
+orbital planes you need and that's why
+
+ align:start position:0%
+orbital planes you need and that's why
+ 
+
+ align:start position:0%
+orbital planes you need and that's why
+the model or the simulation and reality
+
+ align:start position:0%
+the model or the simulation and reality
+ 
+
+ align:start position:0%
+the model or the simulation and reality
+match very very closely so this gives
+
+ align:start position:0%
+match very very closely so this gives
+ 
+
+ align:start position:0%
+match very very closely so this gives
+you know some confidence that that that
+
+ align:start position:0%
+you know some confidence that that that
+ 
+
+ align:start position:0%
+you know some confidence that that that
+these results that this model is is
+
+ align:start position:0%
+these results that this model is is
+ 
+
+ align:start position:0%
+these results that this model is is
+reasonable so what you can do with it is
+
+ align:start position:0%
+reasonable so what you can do with it is
+ 
+
+ align:start position:0%
+reasonable so what you can do with it is
+now what we call Trade space exploration
+
+ align:start position:0%
+now what we call Trade space exploration
+ 
+
+ align:start position:0%
+now what we call Trade space exploration
+which is in a sense what you did uh what
+
+ align:start position:0%
+which is in a sense what you did uh what
+ 
+
+ align:start position:0%
+which is in a sense what you did uh what
+you did for the canat competition so
+
+ align:start position:0%
+you did for the canat competition so
+ 
+
+ align:start position:0%
+you did for the canat competition so
+this this picture here this graph shows
+
+ align:start position:0%
+this this picture here this graph shows
+ 
+
+ align:start position:0%
+this this picture here this graph shows
+you the life cyle cost right over those
+
+ align:start position:0%
+you the life cyle cost right over those
+ 
+
+ align:start position:0%
+you the life cyle cost right over those
+15 years versus global capacity of the
+
+ align:start position:0%
+15 years versus global capacity of the
+ 
+
+ align:start position:0%
+15 years versus global capacity of the
+system each of these blue dots
+
+ align:start position:0%
+system each of these blue dots
+ 
+
+ align:start position:0%
+system each of these blue dots
+represents one of those 1440
+
+ align:start position:0%
+represents one of those 1440
+ 
+
+ align:start position:0%
+represents one of those 1440
+architectures and you can even see on
+
+ align:start position:0%
+architectures and you can even see on
+ 
+
+ align:start position:0%
+architectures and you can even see on
+this uh where iridium actual versus
+
+ align:start position:0%
+this uh where iridium actual versus
+ 
+
+ align:start position:0%
+this uh where iridium actual versus
+simulated Falls and where Global star
+
+ align:start position:0%
+simulated Falls and where Global star
+ 
+
+ align:start position:0%
+simulated Falls and where Global star
+actual versus simulated Falls so both of
+
+ align:start position:0%
+actual versus simulated Falls so both of
+ 
+
+ align:start position:0%
+actual versus simulated Falls so both of
+them were actually off the Pito Frontier
+
+ align:start position:0%
+them were actually off the Pito Frontier
+ 
+
+ align:start position:0%
+them were actually off the Pito Frontier
+which was interesting and led to quite
+
+ align:start position:0%
+which was interesting and led to quite
+ 
+
+ align:start position:0%
+which was interesting and led to quite
+some discussions and uh you can the pero
+
+ align:start position:0%
+some discussions and uh you can the pero
+ 
+
+ align:start position:0%
+some discussions and uh you can the pero
+Frontier in itself is a of course very
+
+ align:start position:0%
+Frontier in itself is a of course very
+ 
+
+ align:start position:0%
+Frontier in itself is a of course very
+useful uh one of the reasons that idium
+
+ align:start position:0%
+useful uh one of the reasons that idium
+ 
+
+ align:start position:0%
+useful uh one of the reasons that idium
+is not on the Pito Frontier is that
+
+ align:start position:0%
+is not on the Pito Frontier is that
+ 
+
+ align:start position:0%
+is not on the Pito Frontier is that
+fundamentally polar constellations are
+
+ align:start position:0%
+fundamentally polar constellations are
+ 
+
+ align:start position:0%
+fundamentally polar constellations are
+inefficient and if you think about it
+
+ align:start position:0%
+inefficient and if you think about it
+ 
+
+ align:start position:0%
+inefficient and if you think about it
+when the satellites are crossing over
+
+ align:start position:0%
+when the satellites are crossing over
+ 
+
+ align:start position:0%
+when the satellites are crossing over
+the PO uh they're very close to each
+
+ align:start position:0%
+the PO uh they're very close to each
+ 
+
+ align:start position:0%
+the PO uh they're very close to each
+other and they're actually not Crossing
+
+ align:start position:0%
+other and they're actually not Crossing
+ 
+
+ align:start position:0%
+other and they're actually not Crossing
+exactly over the poles or you you could
+
+ align:start position:0%
+exactly over the poles or you you could
+ 
+
+ align:start position:0%
+exactly over the poles or you you could
+actually Collide right so you you offset
+
+ align:start position:0%
+actually Collide right so you you offset
+ 
+
+ align:start position:0%
+actually Collide right so you you offset
+them slightly to avoid collisions but
+
+ align:start position:0%
+them slightly to avoid collisions but
+ 
+
+ align:start position:0%
+them slightly to avoid collisions but
+um uh some of the satellites actually
+
+ align:start position:0%
+um uh some of the satellites actually
+ 
+
+ align:start position:0%
+um uh some of the satellites actually
+get get turned off when they cost the PO
+
+ align:start position:0%
+get get turned off when they cost the PO
+ 
+
+ align:start position:0%
+get get turned off when they cost the PO
+so you're not utilizing your assets
+
+ align:start position:0%
+so you're not utilizing your assets
+ 
+
+ align:start position:0%
+so you're not utilizing your assets
+super efficiently in a polar
+
+ align:start position:0%
+super efficiently in a polar
+ 
+
+ align:start position:0%
+super efficiently in a polar
+constellation which is one of the
+
+ align:start position:0%
+constellation which is one of the
+ 
+
+ align:start position:0%
+constellation which is one of the
+reasons why they're not on Theo front
+
+ align:start position:0%
+reasons why they're not on Theo front
+ 
+
+ align:start position:0%
+reasons why they're not on Theo front
+now the way you would use this in a
+
+ align:start position:0%
+now the way you would use this in a
+ 
+
+ align:start position:0%
+now the way you would use this in a
+traditional system engineering approach
+
+ align:start position:0%
+traditional system engineering approach
+ 
+
+ align:start position:0%
+traditional system engineering approach
+which is traditional system engineering
+
+ align:start position:0%
+which is traditional system engineering
+ 
+
+ align:start position:0%
+which is traditional system engineering
+approach means give me the requirement
+
+ align:start position:0%
+approach means give me the requirement
+ 
+
+ align:start position:0%
+approach means give me the requirement
+right write down the requirement and
+
+ align:start position:0%
+right write down the requirement and
+ 
+
+ align:start position:0%
+right write down the requirement and
+then find the minimum cost system for
+
+ align:start position:0%
+then find the minimum cost system for
+ 
+
+ align:start position:0%
+then find the minimum cost system for
+that requirement so a requirement could
+
+ align:start position:0%
+that requirement so a requirement could
+ 
+
+ align:start position:0%
+that requirement so a requirement could
+be you know we need a capacity of of you
+
+ align:start position:0%
+be you know we need a capacity of of you
+ 
+
+ align:start position:0%
+be you know we need a capacity of of you
+know 50,000 for example and then you
+
+ align:start position:0%
+know 50,000 for example and then you
+ 
+
+ align:start position:0%
+know 50,000 for example and then you
+find this intersection with the pedo
+
+ align:start position:0%
+find this intersection with the pedo
+ 
+
+ align:start position:0%
+find this intersection with the pedo
+front and that's the system you that's
+
+ align:start position:0%
+front and that's the system you that's
+ 
+
+ align:start position:0%
+front and that's the system you that's
+the minimum life cycle cost design that
+
+ align:start position:0%
+the minimum life cycle cost design that
+ 
+
+ align:start position:0%
+the minimum life cycle cost design that
+gives you that capacity right and that's
+
+ align:start position:0%
+gives you that capacity right and that's
+ 
+
+ align:start position:0%
+gives you that capacity right and that's
+the system you take and that's what you
+
+ align:start position:0%
+the system you take and that's what you
+ 
+
+ align:start position:0%
+the system you take and that's what you
+go and build and that's essentially what
+
+ align:start position:0%
+go and build and that's essentially what
+ 
+
+ align:start position:0%
+go and build and that's essentially what
+they did the problem with this if
+
+ align:start position:0%
+they did the problem with this if
+ 
+
+ align:start position:0%
+they did the problem with this if
+there's High uncertainty is the true
+
+ align:start position:0%
+there's High uncertainty is the true
+ 
+
+ align:start position:0%
+there's High uncertainty is the true
+requirement is kind of unknown right the
+
+ align:start position:0%
+requirement is kind of unknown right the
+ 
+
+ align:start position:0%
+requirement is kind of unknown right the
+market will tell us in the future what
+
+ align:start position:0%
+market will tell us in the future what
+ 
+
+ align:start position:0%
+market will tell us in the future what
+the true capacity should be so how do
+
+ align:start position:0%
+the true capacity should be so how do
+ 
+
+ align:start position:0%
+the true capacity should be so how do
+you deal with this well you could be oh
+
+ align:start position:0%
+you deal with this well you could be oh
+ 
+
+ align:start position:0%
+you deal with this well you could be oh
+we we're going to be on the safe side
+
+ align:start position:0%
+we we're going to be on the safe side
+ 
+
+ align:start position:0%
+we we're going to be on the safe side
+right we're going to be um uh we're
+
+ align:start position:0%
+right we're going to be um uh we're
+ 
+
+ align:start position:0%
+right we're going to be um uh we're
+going to oversize so if the true demand
+
+ align:start position:0%
+going to oversize so if the true demand
+ 
+
+ align:start position:0%
+going to oversize so if the true demand
+the true capacity that you would need is
+
+ align:start position:0%
+the true capacity that you would need is
+ 
+
+ align:start position:0%
+the true capacity that you would need is
+higher than what you've had your your
+
+ align:start position:0%
+higher than what you've had your your
+ 
+
+ align:start position:0%
+higher than what you've had your your
+system is going to be under capacity
+
+ align:start position:0%
+system is going to be under capacity
+ 
+
+ align:start position:0%
+system is going to be under capacity
+right your system is going to be
+
+ align:start position:0%
+right your system is going to be
+ 
+
+ align:start position:0%
+right your system is going to be
+undersized for what it should be and so
+
+ align:start position:0%
+undersized for what it should be and so
+ 
+
+ align:start position:0%
+undersized for what it should be and so
+what happens in practice uh what do you
+
+ align:start position:0%
+what happens in practice uh what do you
+ 
+
+ align:start position:0%
+what happens in practice uh what do you
+think happens in an underc capacity
+
+ align:start position:0%
+think happens in an underc capacity
+ 
+
+ align:start position:0%
+think happens in an underc capacity
+situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say your system is too small relative to
+
+ align:start position:0%
+say your system is too small relative to
+ 
+
+ align:start position:0%
+say your system is too small relative to
+the market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demand you're not capturing as much as
+
+ align:start position:0%
+demand you're not capturing as much as
+ 
+
+ align:start position:0%
+demand you're not capturing as much as
+you can meaning a competitor will
+
+ align:start position:0%
+you can meaning a competitor will
+ 
+
+ align:start position:0%
+you can meaning a competitor will
+probably capture it I mean I guess you
+
+ align:start position:0%
+probably capture it I mean I guess you
+ 
+
+ align:start position:0%
+probably capture it I mean I guess you
+can you can change your price policy but
+
+ align:start position:0%
+can you can change your price policy but
+ 
+
+ align:start position:0%
+can you can change your price policy but
+fundamentally you're missing out on
+
+ align:start position:0%
+fundamentally you're missing out on
+ 
+
+ align:start position:0%
+fundamentally you're missing out on
+Market opportunity right the other
+
+ align:start position:0%
+Market opportunity right the other
+ 
+
+ align:start position:0%
+Market opportunity right the other
+situation which is actually what
+
+ align:start position:0%
+situation which is actually what
+ 
+
+ align:start position:0%
+situation which is actually what
+happened is that the demand is much less
+
+ align:start position:0%
+happened is that the demand is much less
+ 
+
+ align:start position:0%
+happened is that the demand is much less
+than you anticipated your system is
+
+ align:start position:0%
+than you anticipated your system is
+ 
+
+ align:start position:0%
+than you anticipated your system is
+oversized and remember once you launch a
+
+ align:start position:0%
+oversized and remember once you launch a
+ 
+
+ align:start position:0%
+oversized and remember once you launch a
+satellite constellation it's not like a
+
+ align:start position:0%
+satellite constellation it's not like a
+ 
+
+ align:start position:0%
+satellite constellation it's not like a
+fleet of taxis right where you just park
+
+ align:start position:0%
+fleet of taxis right where you just park
+ 
+
+ align:start position:0%
+fleet of taxis right where you just park
+them in a in a in a in a parking lot uh
+
+ align:start position:0%
+them in a in a in a in a parking lot uh
+ 
+
+ align:start position:0%
+them in a in a in a in a parking lot uh
+you've already the fixed cost is very
+
+ align:start position:0%
+you've already the fixed cost is very
+ 
+
+ align:start position:0%
+you've already the fixed cost is very
+high so um if if if demand is below
+
+ align:start position:0%
+high so um if if if demand is below
+ 
+
+ align:start position:0%
+high so um if if if demand is below
+capacity you have this all this
+
+ align:start position:0%
+capacity you have this all this
+ 
+
+ align:start position:0%
+capacity you have this all this
+investment here life cycle cost has been
+
+ align:start position:0%
+investment here life cycle cost has been
+ 
+
+ align:start position:0%
+investment here life cycle cost has been
+wasted right because you're oversiz the
+
+ align:start position:0%
+wasted right because you're oversiz the
+ 
+
+ align:start position:0%
+wasted right because you're oversiz the
+system and and the challenge is that the
+
+ align:start position:0%
+system and and the challenge is that the
+ 
+
+ align:start position:0%
+system and and the challenge is that the
+true requirement is kind of like this
+
+ align:start position:0%
+true requirement is kind of like this
+ 
+
+ align:start position:0%
+true requirement is kind of like this
+there's this probability density
+
+ align:start position:0%
+there's this probability density
+ 
+
+ align:start position:0%
+there's this probability density
+function right there's a it's a
+
+ align:start position:0%
+function right there's a it's a
+ 
+
+ align:start position:0%
+function right there's a it's a
+probabilistic requirement essentially
+
+ align:start position:0%
+probabilistic requirement essentially
+ 
+
+ align:start position:0%
+probabilistic requirement essentially
+and and there's no set of experiments
+
+ align:start position:0%
+and and there's no set of experiments
+ 
+
+ align:start position:0%
+and and there's no set of experiments
+because it's aloric uncertainty it's not
+
+ align:start position:0%
+because it's aloric uncertainty it's not
+ 
+
+ align:start position:0%
+because it's aloric uncertainty it's not
+epistemic uncertainty there's no set of
+
+ align:start position:0%
+epistemic uncertainty there's no set of
+ 
+
+ align:start position:0%
+epistemic uncertainty there's no set of
+experiments you could do today that will
+
+ align:start position:0%
+experiments you could do today that will
+ 
+
+ align:start position:0%
+experiments you could do today that will
+help you refine the requirement now they
+
+ align:start position:0%
+help you refine the requirement now they
+ 
+
+ align:start position:0%
+help you refine the requirement now they
+did do Market studies uh and but again
+
+ align:start position:0%
+did do Market studies uh and but again
+ 
+
+ align:start position:0%
+did do Market studies uh and but again
+those Market studies were years ahead of
+
+ align:start position:0%
+those Market studies were years ahead of
+ 
+
+ align:start position:0%
+those Market studies were years ahead of
+when the actual system was launched so
+
+ align:start position:0%
+when the actual system was launched so
+ 
+
+ align:start position:0%
+when the actual system was launched so
+they were unreliable fundamentally so um
+
+ align:start position:0%
+they were unreliable fundamentally so um
+ 
+
+ align:start position:0%
+they were unreliable fundamentally so um
+what I'm arguing here is in this kind of
+
+ align:start position:0%
+what I'm arguing here is in this kind of
+ 
+
+ align:start position:0%
+what I'm arguing here is in this kind of
+system where you have large
+
+ align:start position:0%
+system where you have large
+ 
+
+ align:start position:0%
+system where you have large
+uncertainties as to the true requirement
+
+ align:start position:0%
+uncertainties as to the true requirement
+ 
+
+ align:start position:0%
+uncertainties as to the true requirement
+you shouldn't just guess and then put
+
+ align:start position:0%
+you shouldn't just guess and then put
+ 
+
+ align:start position:0%
+you shouldn't just guess and then put
+billions of dollars on a guess this is
+
+ align:start position:0%
+billions of dollars on a guess this is
+ 
+
+ align:start position:0%
+billions of dollars on a guess this is
+like playing in the casino right
+
+ align:start position:0%
+like playing in the casino right
+ 
+
+ align:start position:0%
+like playing in the casino right
+essentially what you should do is think
+
+ align:start position:0%
+essentially what you should do is think
+ 
+
+ align:start position:0%
+essentially what you should do is think
+about the problem differently and in
+
+ align:start position:0%
+about the problem differently and in
+ 
+
+ align:start position:0%
+about the problem differently and in
+this case the answer is stage deployment
+
+ align:start position:0%
+this case the answer is stage deployment
+ 
+
+ align:start position:0%
+this case the answer is stage deployment
+or one of the aners is stage deployment
+
+ align:start position:0%
+or one of the aners is stage deployment
+ 
+
+ align:start position:0%
+or one of the aners is stage deployment
+so you build the system such that it can
+
+ align:start position:0%
+so you build the system such that it can
+ 
+
+ align:start position:0%
+so you build the system such that it can
+uh adapt itself to the uncertain demand
+
+ align:start position:0%
+uh adapt itself to the uncertain demand
+ 
+
+ align:start position:0%
+uh adapt itself to the uncertain demand
+so uh you build initially a smaller more
+
+ align:start position:0%
+so uh you build initially a smaller more
+ 
+
+ align:start position:0%
+so uh you build initially a smaller more
+affordable system but and then the
+
+ align:start position:0%
+affordable system but and then the
+ 
+
+ align:start position:0%
+affordable system but and then the
+system has already built into it the
+
+ align:start position:0%
+system has already built into it the
+ 
+
+ align:start position:0%
+system has already built into it the
+flexibility or scalability to expand if
+
+ align:start position:0%
+flexibility or scalability to expand if
+ 
+
+ align:start position:0%
+flexibility or scalability to expand if
+needed but only if
+
+ align:start position:0%
+needed but only if
+ 
+
+ align:start position:0%
+needed but only if
+needed and there are two major uh
+
+ align:start position:0%
+needed and there are two major uh
+ 
+
+ align:start position:0%
+needed and there are two major uh
+economic advantages to that one is that
+
+ align:start position:0%
+economic advantages to that one is that
+ 
+
+ align:start position:0%
+economic advantages to that one is that
+you don't need to spend all the capital
+
+ align:start position:0%
+you don't need to spend all the capital
+ 
+
+ align:start position:0%
+you don't need to spend all the capital
+up front right so you're deferring
+
+ align:start position:0%
+up front right so you're deferring
+ 
+
+ align:start position:0%
+up front right so you're deferring
+capital investment and you retain the
+
+ align:start position:0%
+capital investment and you retain the
+ 
+
+ align:start position:0%
+capital investment and you retain the
+decision freedom to reconfig
+
+ align:start position:0%
+decision freedom to reconfig
+ 
+
+ align:start position:0%
+decision freedom to reconfig
+or not and that's typically what we call
+
+ align:start position:0%
+or not and that's typically what we call
+ 
+
+ align:start position:0%
+or not and that's typically what we call
+a real option You' created a real option
+
+ align:start position:0%
+a real option You' created a real option
+ 
+
+ align:start position:0%
+a real option You' created a real option
+uh for the
+
+ align:start position:0%
+uh for the
+ 
+
+ align:start position:0%
+uh for the
+future so the question then is well how
+
+ align:start position:0%
+future so the question then is well how
+ 
+
+ align:start position:0%
+future so the question then is well how
+valuable is that you know is it
+
+ align:start position:0%
+valuable is that you know is it
+ 
+
+ align:start position:0%
+valuable is that you know is it
+worthwhile doing this stage deployment
+
+ align:start position:0%
+worthwhile doing this stage deployment
+ 
+
+ align:start position:0%
+worthwhile doing this stage deployment
+approach so um there's probably
+
+ align:start position:0%
+approach so um there's probably
+ 
+
+ align:start position:0%
+approach so um there's probably
+different ways of doing this and I just
+
+ align:start position:0%
+different ways of doing this and I just
+ 
+
+ align:start position:0%
+different ways of doing this and I just
+want to share with you and this is from
+
+ align:start position:0%
+want to share with you and this is from
+ 
+
+ align:start position:0%
+want to share with you and this is from
+the paper how this was done so step one
+
+ align:start position:0%
+the paper how this was done so step one
+ 
+
+ align:start position:0%
+the paper how this was done so step one
+is you partition Your Design Vector so
+
+ align:start position:0%
+is you partition Your Design Vector so
+ 
+
+ align:start position:0%
+is you partition Your Design Vector so
+you basically decide which which part of
+
+ align:start position:0%
+you basically decide which which part of
+ 
+
+ align:start position:0%
+you basically decide which which part of
+the system is flexible cuz you can't
+
+ align:start position:0%
+the system is flexible cuz you can't
+ 
+
+ align:start position:0%
+the system is flexible cuz you can't
+make everything flexible typically what
+
+ align:start position:0%
+make everything flexible typically what
+ 
+
+ align:start position:0%
+make everything flexible typically what
+part is flexible and what part is fixed
+
+ align:start position:0%
+part is flexible and what part is fixed
+ 
+
+ align:start position:0%
+part is flexible and what part is fixed
+is the base you can't change it so in
+
+ align:start position:0%
+is the base you can't change it so in
+ 
+
+ align:start position:0%
+is the base you can't change it so in
+this case uh excuse me the idea is that
+
+ align:start position:0%
+this case uh excuse me the idea is that
+ 
+
+ align:start position:0%
+this case uh excuse me the idea is that
+the satellites themselves the design of
+
+ align:start position:0%
+the satellites themselves the design of
+ 
+
+ align:start position:0%
+the satellites themselves the design of
+the satellites their transmitter power
+
+ align:start position:0%
+the satellites their transmitter power
+ 
+
+ align:start position:0%
+the satellites their transmitter power
+their protocols their antenna size the
+
+ align:start position:0%
+their protocols their antenna size the
+ 
+
+ align:start position:0%
+their protocols their antenna size the
+network architecture should be fixed
+
+ align:start position:0%
+network architecture should be fixed
+ 
+
+ align:start position:0%
+network architecture should be fixed
+right because those things are difficult
+
+ align:start position:0%
+right because those things are difficult
+ 
+
+ align:start position:0%
+right because those things are difficult
+to change uh but we're going to allow
+
+ align:start position:0%
+to change uh but we're going to allow
+ 
+
+ align:start position:0%
+to change uh but we're going to allow
+the astrodynamics the actual shape of
+
+ align:start position:0%
+the astrodynamics the actual shape of
+ 
+
+ align:start position:0%
+the astrodynamics the actual shape of
+the constellation to be flexible so keep
+
+ align:start position:0%
+the constellation to be flexible so keep
+ 
+
+ align:start position:0%
+the constellation to be flexible so keep
+the satellites the same only change
+
+ align:start position:0%
+the satellites the same only change
+ 
+
+ align:start position:0%
+the satellites the same only change
+their arrangement in space so what you
+
+ align:start position:0%
+their arrangement in space so what you
+ 
+
+ align:start position:0%
+their arrangement in space so what you
+do is you partition the design Vector
+
+ align:start position:0%
+do is you partition the design Vector
+ 
+
+ align:start position:0%
+do is you partition the design Vector
+into the flexible and inflexible
+
+ align:start position:0%
+into the flexible and inflexible
+ 
+
+ align:start position:0%
+into the flexible and inflexible
+part and when you do this in step two
+
+ align:start position:0%
+part and when you do this in step two
+ 
+
+ align:start position:0%
+part and when you do this in step two
+what's nice about this is you can then
+
+ align:start position:0%
+what's nice about this is you can then
+ 
+
+ align:start position:0%
+what's nice about this is you can then
+actually find families of designs right
+
+ align:start position:0%
+actually find families of designs right
+ 
+
+ align:start position:0%
+actually find families of designs right
+you can find families of designs where
+
+ align:start position:0%
+you can find families of designs where
+ 
+
+ align:start position:0%
+you can find families of designs where
+the we do have a little lag here the the
+
+ align:start position:0%
+the we do have a little lag here the the
+ 
+
+ align:start position:0%
+the we do have a little lag here the the
+you can find families of designs that
+
+ align:start position:0%
+you can find families of designs that
+ 
+
+ align:start position:0%
+you can find families of designs that
+share the constant part right that have
+
+ align:start position:0%
+share the constant part right that have
+ 
+
+ align:start position:0%
+share the constant part right that have
+the common so what I'm what's shown in
+
+ align:start position:0%
+the common so what I'm what's shown in
+ 
+
+ align:start position:0%
+the common so what I'm what's shown in
+this graph here this is again our design
+
+ align:start position:0%
+this graph here this is again our design
+ 
+
+ align:start position:0%
+this graph here this is again our design
+space kind of zoomed in a little bit
+
+ align:start position:0%
+space kind of zoomed in a little bit
+ 
+
+ align:start position:0%
+space kind of zoomed in a little bit
+more every one of these points that's
+
+ align:start position:0%
+more every one of these points that's
+ 
+
+ align:start position:0%
+more every one of these points that's
+connected with these lines uses the same
+
+ align:start position:0%
+connected with these lines uses the same
+ 
+
+ align:start position:0%
+connected with these lines uses the same
+type of
+
+ align:start position:0%
+type of
+ 
+
+ align:start position:0%
+type of
+satellite same transmitter power same
+
+ align:start position:0%
+satellite same transmitter power same
+ 
+
+ align:start position:0%
+satellite same transmitter power same
+antenna diameter and all of them have
+
+ align:start position:0%
+antenna diameter and all of them have
+ 
+
+ align:start position:0%
+antenna diameter and all of them have
+inner satellite links so so what
+
+ align:start position:0%
+inner satellite links so so what
+ 
+
+ align:start position:0%
+inner satellite links so so what
+effectively you're partitioning the
+
+ align:start position:0%
+effectively you're partitioning the
+ 
+
+ align:start position:0%
+effectively you're partitioning the
+design space into sub sets that share
+
+ align:start position:0%
+design space into sub sets that share
+ 
+
+ align:start position:0%
+design space into sub sets that share
+common features and then we call this a
+
+ align:start position:0%
+common features and then we call this a
+ 
+
+ align:start position:0%
+common features and then we call this a
+family of designs and the idea is you
+
+ align:start position:0%
+family of designs and the idea is you
+ 
+
+ align:start position:0%
+family of designs and the idea is you
+start small so on the left side and then
+
+ align:start position:0%
+start small so on the left side and then
+ 
+
+ align:start position:0%
+start small so on the left side and then
+you grow the system over time right but
+
+ align:start position:0%
+you grow the system over time right but
+ 
+
+ align:start position:0%
+you grow the system over time right but
+only if needed so when you do this your
+
+ align:start position:0%
+only if needed so when you do this your
+ 
+
+ align:start position:0%
+only if needed so when you do this your
+1440 um um strong design space turns out
+
+ align:start position:0%
+1440 um um strong design space turns out
+ 
+
+ align:start position:0%
+1440 um um strong design space turns out
+to be decomposable into 40 different
+
+ align:start position:0%
+to be decomposable into 40 different
+ 
+
+ align:start position:0%
+to be decomposable into 40 different
+paths now which path would you choose
+
+ align:start position:0%
+paths now which path would you choose
+ 
+
+ align:start position:0%
+paths now which path would you choose
+here well want to be as close to the
+
+ align:start position:0%
+here well want to be as close to the
+ 
+
+ align:start position:0%
+here well want to be as close to the
+Pito front as possible so this is an
+
+ align:start position:0%
+Pito front as possible so this is an
+ 
+
+ align:start position:0%
+Pito front as possible so this is an
+example of a of a path in this in this
+
+ align:start position:0%
+example of a of a path in this in this
+ 
+
+ align:start position:0%
+example of a of a path in this in this
+path if we started on the lower left we
+
+ align:start position:0%
+path if we started on the lower left we
+ 
+
+ align:start position:0%
+path if we started on the lower left we
+would start with 24 satellites and then
+
+ align:start position:0%
+would start with 24 satellites and then
+ 
+
+ align:start position:0%
+would start with 24 satellites and then
+uh we would actually move them uh to a
+
+ align:start position:0%
+uh we would actually move them uh to a
+ 
+
+ align:start position:0%
+uh we would actually move them uh to a
+lower altitude and add uh 30 more in
+
+ align:start position:0%
+lower altitude and add uh 30 more in
+ 
+
+ align:start position:0%
+lower altitude and add uh 30 more in
+step two and then you you would
+
+ align:start position:0%
+step two and then you you would
+ 
+
+ align:start position:0%
+step two and then you you would
+gradually grow the constellation over
+
+ align:start position:0%
+gradually grow the constellation over
+ 
+
+ align:start position:0%
+gradually grow the constellation over
+time you see that this is actually not
+
+ align:start position:0%
+time you see that this is actually not
+ 
+
+ align:start position:0%
+time you see that this is actually not
+too different from how GPS was done
+
+ align:start position:0%
+too different from how GPS was done
+ 
+
+ align:start position:0%
+too different from how GPS was done
+right the GPS
+
+ align:start position:0%
+right the GPS
+ 
+
+ align:start position:0%
+right the GPS
+constellation was was deployed in phases
+
+ align:start position:0%
+constellation was was deployed in phases
+ 
+
+ align:start position:0%
+constellation was was deployed in phases
+but it was not Market driven it was just
+
+ align:start position:0%
+but it was not Market driven it was just
+ 
+
+ align:start position:0%
+but it was not Market driven it was just
+sort of phasing the development for for
+
+ align:start position:0%
+sort of phasing the development for for
+ 
+
+ align:start position:0%
+sort of phasing the development for for
+risk reduction regions and spreading out
+
+ align:start position:0%
+risk reduction regions and spreading out
+ 
+
+ align:start position:0%
+risk reduction regions and spreading out
+the capital um the other thing that's
+
+ align:start position:0%
+the capital um the other thing that's
+ 
+
+ align:start position:0%
+the capital um the other thing that's
+interesting here is you see as you grow
+
+ align:start position:0%
+interesting here is you see as you grow
+ 
+
+ align:start position:0%
+interesting here is you see as you grow
+the constellation it moves further away
+
+ align:start position:0%
+the constellation it moves further away
+ 
+
+ align:start position:0%
+the constellation it moves further away
+see it moves further away from the front
+
+ align:start position:0%
+see it moves further away from the front
+ 
+
+ align:start position:0%
+see it moves further away from the front
+so when it's small this particular path
+
+ align:start position:0%
+so when it's small this particular path
+ 
+
+ align:start position:0%
+so when it's small this particular path
+it's close to being optimal and as you
+
+ align:start position:0%
+it's close to being optimal and as you
+ 
+
+ align:start position:0%
+it's close to being optimal and as you
+scale it up it becomes more suboptimal
+
+ align:start position:0%
+scale it up it becomes more suboptimal
+ 
+
+ align:start position:0%
+scale it up it becomes more suboptimal
+and there's other paths
+
+ align:start position:0%
+and there's other paths
+ 
+
+ align:start position:0%
+and there's other paths
+that have the opposite Behavior where
+
+ align:start position:0%
+that have the opposite Behavior where
+ 
+
+ align:start position:0%
+that have the opposite Behavior where
+when it's small it's kind of suboptimal
+
+ align:start position:0%
+when it's small it's kind of suboptimal
+ 
+
+ align:start position:0%
+when it's small it's kind of suboptimal
+and as you make it bigger it gets closer
+
+ align:start position:0%
+and as you make it bigger it gets closer
+ 
+
+ align:start position:0%
+and as you make it bigger it gets closer
+to optimality pretty interesting so
+
+ align:start position:0%
+to optimality pretty interesting so
+ 
+
+ align:start position:0%
+to optimality pretty interesting so
+that's step two find the
+
+ align:start position:0%
+that's step two find the
+ 
+
+ align:start position:0%
+that's step two find the
+paths step three you now have to model
+
+ align:start position:0%
+paths step three you now have to model
+ 
+
+ align:start position:0%
+paths step three you now have to model
+the actual uncertainty and in this case
+
+ align:start position:0%
+the actual uncertainty and in this case
+ 
+
+ align:start position:0%
+the actual uncertainty and in this case
+uh there are different ways to model
+
+ align:start position:0%
+uh there are different ways to model
+ 
+
+ align:start position:0%
+uh there are different ways to model
+uncertainties uh in this case what we
+
+ align:start position:0%
+uncertainties uh in this case what we
+ 
+
+ align:start position:0%
+uncertainties uh in this case what we
+used was a GBM model geometric brownan
+
+ align:start position:0%
+used was a GBM model geometric brownan
+ 
+
+ align:start position:0%
+used was a GBM model geometric brownan
+motion this is well known in physics uh
+
+ align:start position:0%
+motion this is well known in physics uh
+ 
+
+ align:start position:0%
+motion this is well known in physics uh
+it's been applied to statistics physics
+
+ align:start position:0%
+it's been applied to statistics physics
+ 
+
+ align:start position:0%
+it's been applied to statistics physics
+this has been applied to the stock
+
+ align:start position:0%
+this has been applied to the stock
+ 
+
+ align:start position:0%
+this has been applied to the stock
+market right and and the idea here is
+
+ align:start position:0%
+market right and and the idea here is
+ 
+
+ align:start position:0%
+market right and and the idea here is
+that uh in this case demand uh behaves
+
+ align:start position:0%
+that uh in this case demand uh behaves
+ 
+
+ align:start position:0%
+that uh in this case demand uh behaves
+like a particle in a fluid right that's
+
+ align:start position:0%
+like a particle in a fluid right that's
+ 
+
+ align:start position:0%
+like a particle in a fluid right that's
+that's kind of moving in an
+
+ align:start position:0%
+that's kind of moving in an
+ 
+
+ align:start position:0%
+that's kind of moving in an
+unpredictable fashion so this is the
+
+ align:start position:0%
+unpredictable fashion so this is the
+ 
+
+ align:start position:0%
+unpredictable fashion so this is the
+basic equation for this is the discrete
+
+ align:start position:0%
+basic equation for this is the discrete
+ 
+
+ align:start position:0%
+basic equation for this is the discrete
+version of of geometric Brown and motion
+
+ align:start position:0%
+version of of geometric Brown and motion
+ 
+
+ align:start position:0%
+version of of geometric Brown and motion
+you have um some Trend mu mu * delta T
+
+ align:start position:0%
+you have um some Trend mu mu * delta T
+ 
+
+ align:start position:0%
+you have um some Trend mu mu * delta T
+so the this is the delta in demand the
+
+ align:start position:0%
+so the this is the delta in demand the
+ 
+
+ align:start position:0%
+so the this is the delta in demand the
+change in demand divided by De demand so
+
+ align:start position:0%
+change in demand divided by De demand so
+ 
+
+ align:start position:0%
+change in demand divided by De demand so
+this is normalized change in demand is
+
+ align:start position:0%
+this is normalized change in demand is
+ 
+
+ align:start position:0%
+this is normalized change in demand is
+Mu * delta T so your your Trend time
+
+ align:start position:0%
+Mu * delta T so your your Trend time
+ 
+
+ align:start position:0%
+Mu * delta T so your your Trend time
+delta T plus uh Sigma * Epsilon * square
+
+ align:start position:0%
+delta T plus uh Sigma * Epsilon * square
+ 
+
+ align:start position:0%
+delta T plus uh Sigma * Epsilon * square
+root of delta T Epsilon is a standard
+
+ align:start position:0%
+root of delta T Epsilon is a standard
+ 
+
+ align:start position:0%
+root of delta T Epsilon is a standard
+normally distributed random variable
+
+ align:start position:0%
+normally distributed random variable
+ 
+
+ align:start position:0%
+normally distributed random variable
+between 0 and one and uh Epsilon uh and
+
+ align:start position:0%
+between 0 and one and uh Epsilon uh and
+ 
+
+ align:start position:0%
+between 0 and one and uh Epsilon uh and
+and sigma is your volatility essentially
+
+ align:start position:0%
+and sigma is your volatility essentially
+ 
+
+ align:start position:0%
+and sigma is your volatility essentially
+right so here's here's some examples if
+
+ align:start position:0%
+right so here's here's some examples if
+ 
+
+ align:start position:0%
+right so here's here's some examples if
+you start with with an initial demand of
+
+ align:start position:0%
+you start with with an initial demand of
+ 
+
+ align:start position:0%
+you start with with an initial demand of
+50, ,000 which is what they actually saw
+
+ align:start position:0%
+50, ,000 which is what they actually saw
+ 
+
+ align:start position:0%
+50, ,000 which is what they actually saw
+you know as a as an initial demand early
+
+ align:start position:0%
+you know as a as an initial demand early
+ 
+
+ align:start position:0%
+you know as a as an initial demand early
+on you have a growth of about 8% per
+
+ align:start position:0%
+on you have a growth of about 8% per
+ 
+
+ align:start position:0%
+on you have a growth of about 8% per
+year this is your
+
+ align:start position:0%
+year this is your
+ 
+
+ align:start position:0%
+year this is your
+Trend Plus in this case a volatility of
+
+ align:start position:0%
+Trend Plus in this case a volatility of
+ 
+
+ align:start position:0%
+Trend Plus in this case a volatility of
+40% per year which seems high but you
+
+ align:start position:0%
+40% per year which seems high but you
+ 
+
+ align:start position:0%
+40% per year which seems high but you
+know this kind of very new technology
+
+ align:start position:0%
+know this kind of very new technology
+ 
+
+ align:start position:0%
+know this kind of very new technology
+new systems is actually not that
+
+ align:start position:0%
+new systems is actually not that
+ 
+
+ align:start position:0%
+new systems is actually not that
+far-fetched you get three different
+
+ align:start position:0%
+far-fetched you get three different
+ 
+
+ align:start position:0%
+far-fetched you get three different
+these are there three examples of how
+
+ align:start position:0%
+these are there three examples of how
+ 
+
+ align:start position:0%
+these are there three examples of how
+demand might evolve these are just three
+
+ align:start position:0%
+demand might evolve these are just three
+ 
+
+ align:start position:0%
+demand might evolve these are just three
+scenarios so demand can go up it can go
+
+ align:start position:0%
+scenarios so demand can go up it can go
+ 
+
+ align:start position:0%
+scenarios so demand can go up it can go
+down and GBM is very nice but one of the
+
+ align:start position:0%
+down and GBM is very nice but one of the
+ 
+
+ align:start position:0%
+down and GBM is very nice but one of the
+downsides of GBM is you know there's
+
+ align:start position:0%
+downsides of GBM is you know there's
+ 
+
+ align:start position:0%
+downsides of GBM is you know there's
+infinitely many scenarios that you can
+
+ align:start position:0%
+infinitely many scenarios that you can
+ 
+
+ align:start position:0%
+infinitely many scenarios that you can
+generate because it's fundamentally even
+
+ align:start position:0%
+generate because it's fundamentally even
+ 
+
+ align:start position:0%
+generate because it's fundamentally even
+though it's discretized in time it's not
+
+ align:start position:0%
+though it's discretized in time it's not
+ 
+
+ align:start position:0%
+though it's discretized in time it's not
+discretized in in demand so a simpler
+
+ align:start position:0%
+discretized in in demand so a simpler
+ 
+
+ align:start position:0%
+discretized in in demand so a simpler
+version of this a more discret version
+
+ align:start position:0%
+version of this a more discret version
+ 
+
+ align:start position:0%
+version of this a more discret version
+is a so-called binomial lattice model so
+
+ align:start position:0%
+is a so-called binomial lattice model so
+ 
+
+ align:start position:0%
+is a so-called binomial lattice model so
+the way this works is again you start
+
+ align:start position:0%
+the way this works is again you start
+ 
+
+ align:start position:0%
+the way this works is again you start
+with some initial demand here on the
+
+ align:start position:0%
+with some initial demand here on the
+ 
+
+ align:start position:0%
+with some initial demand here on the
+left and then uh you've disc IED it such
+
+ align:start position:0%
+left and then uh you've disc IED it such
+ 
+
+ align:start position:0%
+left and then uh you've disc IED it such
+that um moving through time you can look
+
+ align:start position:0%
+that um moving through time you can look
+ 
+
+ align:start position:0%
+that um moving through time you can look
+at different scenarios right these scen
+
+ align:start position:0%
+at different scenarios right these scen
+ 
+
+ align:start position:0%
+at different scenarios right these scen
+scenarios could be you know the best
+
+ align:start position:0%
+scenarios could be you know the best
+ 
+
+ align:start position:0%
+scenarios could be you know the best
+scenario is things just keep growing
+
+ align:start position:0%
+scenario is things just keep growing
+ 
+
+ align:start position:0%
+scenario is things just keep growing
+right grow grow grow grow grow here uh
+
+ align:start position:0%
+right grow grow grow grow grow here uh
+ 
+
+ align:start position:0%
+right grow grow grow grow grow here uh
+time the 15 years have been subdivided
+
+ align:start position:0%
+time the 15 years have been subdivided
+ 
+
+ align:start position:0%
+time the 15 years have been subdivided
+into five three threeyear periods so
+
+ align:start position:0%
+into five three threeyear periods so
+ 
+
+ align:start position:0%
+into five three threeyear periods so
+here's a sample scenario demand goes up
+
+ align:start position:0%
+here's a sample scenario demand goes up
+ 
+
+ align:start position:0%
+here's a sample scenario demand goes up
+goes up and then it goes down twice and
+
+ align:start position:0%
+goes up and then it goes down twice and
+ 
+
+ align:start position:0%
+goes up and then it goes down twice and
+then it goes up again in the fifth
+
+ align:start position:0%
+then it goes up again in the fifth
+ 
+
+ align:start position:0%
+then it goes up again in the fifth
+period And so this is is a discretized
+
+ align:start position:0%
+period And so this is is a discretized
+ 
+
+ align:start position:0%
+period And so this is is a discretized
+random walk and you can choose the
+
+ align:start position:0%
+random walk and you can choose the
+ 
+
+ align:start position:0%
+random walk and you can choose the
+numbers so the the sigma the volatility
+
+ align:start position:0%
+numbers so the the sigma the volatility
+ 
+
+ align:start position:0%
+numbers so the the sigma the volatility
+the amount of the up and down movement
+
+ align:start position:0%
+the amount of the up and down movement
+ 
+
+ align:start position:0%
+the amount of the up and down movement
+and the probability P of going up and
+
+ align:start position:0%
+and the probability P of going up and
+ 
+
+ align:start position:0%
+and the probability P of going up and
+then the probability of one minus P of
+
+ align:start position:0%
+then the probability of one minus P of
+ 
+
+ align:start position:0%
+then the probability of one minus P of
+going down are chosen such that they're
+
+ align:start position:0%
+going down are chosen such that they're
+ 
+
+ align:start position:0%
+going down are chosen such that they're
+consistent with the GBM model so this
+
+ align:start position:0%
+consistent with the GBM model so this
+ 
+
+ align:start position:0%
+consistent with the GBM model so this
+model is statistically equivalent to the
+
+ align:start position:0%
+model is statistically equivalent to the
+ 
+
+ align:start position:0%
+model is statistically equivalent to the
+GBM model it's just discretized so the
+
+ align:start position:0%
+GBM model it's just discretized so the
+ 
+
+ align:start position:0%
+GBM model it's just discretized so the
+beauty of this is that you can now
+
+ align:start position:0%
+beauty of this is that you can now
+ 
+
+ align:start position:0%
+beauty of this is that you can now
+simplify this to 32 different scenarios
+
+ align:start position:0%
+simplify this to 32 different scenarios
+ 
+
+ align:start position:0%
+simplify this to 32 different scenarios
+instead of infinitely many and each of
+
+ align:start position:0%
+instead of infinitely many and each of
+ 
+
+ align:start position:0%
+instead of infinitely many and each of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+scenarios is not equally probable the
+
+ align:start position:0%
+scenarios is not equally probable the
+ 
+
+ align:start position:0%
+scenarios is not equally probable the
+pro there actually probability weighted
+
+ align:start position:0%
+pro there actually probability weighted
+ 
+
+ align:start position:0%
+pro there actually probability weighted
+scenarios depending on what mu and sigma
+
+ align:start position:0%
+scenarios depending on what mu and sigma
+ 
+
+ align:start position:0%
+scenarios depending on what mu and sigma
+are that are underlying right so now we
+
+ align:start position:0%
+are that are underlying right so now we
+ 
+
+ align:start position:0%
+are that are underlying right so now we
+have 40 paths right we have 40 Evolution
+
+ align:start position:0%
+have 40 paths right we have 40 Evolution
+ 
+
+ align:start position:0%
+have 40 paths right we have 40 Evolution
+Paths of the system and we have 32
+
+ align:start position:0%
+Paths of the system and we have 32
+ 
+
+ align:start position:0%
+Paths of the system and we have 32
+different future scenarios so what we do
+
+ align:start position:0%
+different future scenarios so what we do
+ 
+
+ align:start position:0%
+different future scenarios so what we do
+now in the next step four is to put the
+
+ align:start position:0%
+now in the next step four is to put the
+ 
+
+ align:start position:0%
+now in the next step four is to put the
+two together and calculate the cost of
+
+ align:start position:0%
+two together and calculate the cost of
+ 
+
+ align:start position:0%
+two together and calculate the cost of
+each path right calculate the cost of
+
+ align:start position:0%
+each path right calculate the cost of
+ 
+
+ align:start position:0%
+each path right calculate the cost of
+each path with respect to each of the
+
+ align:start position:0%
+each path with respect to each of the
+ 
+
+ align:start position:0%
+each path with respect to each of the
+demand scenarios look at the weighted
+
+ align:start position:0%
+demand scenarios look at the weighted
+ 
+
+ align:start position:0%
+demand scenarios look at the weighted
+average of all the possible paths and uh
+
+ align:start position:0%
+average of all the possible paths and uh
+ 
+
+ align:start position:0%
+average of all the possible paths and uh
+the one thing the trick the one tricky
+
+ align:start position:0%
+the one thing the trick the one tricky
+ 
+
+ align:start position:0%
+the one thing the trick the one tricky
+thing about this is you need to build in
+
+ align:start position:0%
+thing about this is you need to build in
+ 
+
+ align:start position:0%
+thing about this is you need to build in
+a decision rule such that if the system
+
+ align:start position:0%
+a decision rule such that if the system
+ 
+
+ align:start position:0%
+a decision rule such that if the system
+if demand exceeds capacity the system
+
+ align:start position:0%
+if demand exceeds capacity the system
+ 
+
+ align:start position:0%
+if demand exceeds capacity the system
+you're going to expand and move to the
+
+ align:start position:0%
+you're going to expand and move to the
+ 
+
+ align:start position:0%
+you're going to expand and move to the
+next stage you're going to Stage deploy
+
+ align:start position:0%
+next stage you're going to Stage deploy
+ 
+
+ align:start position:0%
+next stage you're going to Stage deploy
+the next phase uh and and there's many
+
+ align:start position:0%
+the next phase uh and and there's many
+ 
+
+ align:start position:0%
+the next phase uh and and there's many
+different ways of doing this decision
+
+ align:start position:0%
+different ways of doing this decision
+ 
+
+ align:start position:0%
+different ways of doing this decision
+rule so the the simplest one was chosen
+
+ align:start position:0%
+rule so the the simplest one was chosen
+ 
+
+ align:start position:0%
+rule so the the simplest one was chosen
+here and of course costs are discounted
+
+ align:start position:0%
+here and of course costs are discounted
+ 
+
+ align:start position:0%
+here and of course costs are discounted
+so let let me explain to you how this
+
+ align:start position:0%
+so let let me explain to you how this
+ 
+
+ align:start position:0%
+so let let me explain to you how this
+works so you know we we start um this
+
+ align:start position:0%
+works so you know we we start um this
+ 
+
+ align:start position:0%
+works so you know we we start um this
+simulation so the first uh initial
+
+ align:start position:0%
+simulation so the first uh initial
+ 
+
+ align:start position:0%
+simulation so the first uh initial
+deployment this is our initial stage one
+
+ align:start position:0%
+deployment this is our initial stage one
+ 
+
+ align:start position:0%
+deployment this is our initial stage one
+right for the constellation and then we
+
+ align:start position:0%
+right for the constellation and then we
+ 
+
+ align:start position:0%
+right for the constellation and then we
+start operating for uh two years demand
+
+ align:start position:0%
+start operating for uh two years demand
+ 
+
+ align:start position:0%
+start operating for uh two years demand
+in this period goes up you see the Ops
+
+ align:start position:0%
+in this period goes up you see the Ops
+ 
+
+ align:start position:0%
+in this period goes up you see the Ops
+cost in this case goes slightly down
+
+ align:start position:0%
+cost in this case goes slightly down
+ 
+
+ align:start position:0%
+cost in this case goes slightly down
+this is due to the discounting this is a
+
+ align:start position:0%
+this is due to the discounting this is a
+ 
+
+ align:start position:0%
+this is due to the discounting this is a
+discounting effect we arrive at the end
+
+ align:start position:0%
+discounting effect we arrive at the end
+ 
+
+ align:start position:0%
+discounting effect we arrive at the end
+of our first threeyear period and then
+
+ align:start position:0%
+of our first threeyear period and then
+ 
+
+ align:start position:0%
+of our first threeyear period and then
+the question is uh here's our capacity
+
+ align:start position:0%
+the question is uh here's our capacity
+ 
+
+ align:start position:0%
+the question is uh here's our capacity
+of the system what would you do in this
+
+ align:start position:0%
+of the system what would you do in this
+ 
+
+ align:start position:0%
+of the system what would you do in this
+situation let me ask somebody at MIT
+
+ align:start position:0%
+situation let me ask somebody at MIT
+ 
+
+ align:start position:0%
+situation let me ask somebody at MIT
+make sure you guys are still are still
+
+ align:start position:0%
+make sure you guys are still are still
+ 
+
+ align:start position:0%
+make sure you guys are still are still
+with me so what would you do in this
+
+ align:start position:0%
+with me so what would you do in this
+ 
+
+ align:start position:0%
+with me so what would you do in this
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+you you're now at the end of year
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody we lost you for a second halfway
+
+ align:start position:0%
+anybody we lost you for a second halfway
+ 
+
+ align:start position:0%
+anybody we lost you for a second halfway
+through your statement could you
+
+ align:start position:0%
+through your statement could you
+ 
+
+ align:start position:0%
+through your statement could you
+repeat yeah so you've you um you've done
+
+ align:start position:0%
+repeat yeah so you've you um you've done
+ 
+
+ align:start position:0%
+repeat yeah so you've you um you've done
+your initial 3 years you've deployed
+
+ align:start position:0%
+your initial 3 years you've deployed
+ 
+
+ align:start position:0%
+your initial 3 years you've deployed
+your initial constellation and you now
+
+ align:start position:0%
+your initial constellation and you now
+ 
+
+ align:start position:0%
+your initial constellation and you now
+have the situation shown on this chart
+
+ align:start position:0%
+have the situation shown on this chart
+ 
+
+ align:start position:0%
+have the situation shown on this chart
+what's the what's the right decision
+
+ align:start position:0%
+what's the what's the right decision
+ 
+
+ align:start position:0%
+what's the what's the right decision
+according to the decision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule what's the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decision okay I would keep it the same
+
+ align:start position:0%
+decision okay I would keep it the same
+ 
+
+ align:start position:0%
+decision okay I would keep it the same
+because Haven exceeded Demand
+
+ align:start position:0%
+because Haven exceeded Demand
+ 
+
+ align:start position:0%
+because Haven exceeded Demand
+yet but prepare to exactly you wait
+
+ align:start position:0%
+yet but prepare to exactly you wait
+ 
+
+ align:start position:0%
+yet but prepare to exactly you wait
+right because your is below Your
+
+ align:start position:0%
+right because your is below Your
+ 
+
+ align:start position:0%
+right because your is below Your
+Capacity so you keep it the same you
+
+ align:start position:0%
+Capacity so you keep it the same you
+ 
+
+ align:start position:0%
+Capacity so you keep it the same you
+don't do anything you just keep
+
+ align:start position:0%
+don't do anything you just keep
+ 
+
+ align:start position:0%
+don't do anything you just keep
+operating it's exactly right so um you
+
+ align:start position:0%
+operating it's exactly right so um you
+ 
+
+ align:start position:0%
+operating it's exactly right so um you
+have another three years right um during
+
+ align:start position:0%
+have another three years right um during
+ 
+
+ align:start position:0%
+have another three years right um during
+these three years uh demand keeps
+
+ align:start position:0%
+these three years uh demand keeps
+ 
+
+ align:start position:0%
+these three years uh demand keeps
+growing and you now at at year six
+
+ align:start position:0%
+growing and you now at at year six
+ 
+
+ align:start position:0%
+growing and you now at at year six
+arrive at this point here so what's the
+
+ align:start position:0%
+arrive at this point here so what's the
+ 
+
+ align:start position:0%
+arrive at this point here so what's the
+right decision now can I ask a question
+
+ align:start position:0%
+right decision now can I ask a question
+ 
+
+ align:start position:0%
+right decision now can I ask a question
+about the decision to stay the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same would you stay the
+
+ align:start position:0%
+same would you stay the
+ 
+
+ align:start position:0%
+same would you stay the
+same what what's happening to the demand
+
+ align:start position:0%
+same what what's happening to the demand
+ 
+
+ align:start position:0%
+same what what's happening to the demand
+line Veronica what's happening to the
+
+ align:start position:0%
+line Veronica what's happening to the
+ 
+
+ align:start position:0%
+line Veronica what's happening to the
+demand can I ask a qu a quick question
+
+ align:start position:0%
+demand can I ask a qu a quick question
+ 
+
+ align:start position:0%
+demand can I ask a qu a quick question
+first about the the decision to stay the
+
+ align:start position:0%
+first about the the decision to stay the
+ 
+
+ align:start position:0%
+first about the the decision to stay the
+same yes I feel like by waiting until
+
+ align:start position:0%
+same yes I feel like by waiting until
+ 
+
+ align:start position:0%
+same yes I feel like by waiting until
+we've exceeded demand to choose to
+
+ align:start position:0%
+we've exceeded demand to choose to
+ 
+
+ align:start position:0%
+we've exceeded demand to choose to
+expand the constellation we're
+
+ align:start position:0%
+expand the constellation we're
+ 
+
+ align:start position:0%
+expand the constellation we're
+introducing a lag between demand and
+
+ align:start position:0%
+introducing a lag between demand and
+ 
+
+ align:start position:0%
+introducing a lag between demand and
+capability that creates an inefficiency
+
+ align:start position:0%
+capability that creates an inefficiency
+ 
+
+ align:start position:0%
+capability that creates an inefficiency
+that may actually drive users away from
+
+ align:start position:0%
+that may actually drive users away from
+ 
+
+ align:start position:0%
+that may actually drive users away from
+the system and I see this kind of
+
+ align:start position:0%
+the system and I see this kind of
+ 
+
+ align:start position:0%
+the system and I see this kind of
+oscillatory effect where you would
+
+ align:start position:0%
+oscillatory effect where you would
+ 
+
+ align:start position:0%
+oscillatory effect where you would
+expand and then people would meet and
+
+ align:start position:0%
+expand and then people would meet and
+ 
+
+ align:start position:0%
+expand and then people would meet and
+then the system would be insufficient
+
+ align:start position:0%
+then the system would be insufficient
+ 
+
+ align:start position:0%
+then the system would be insufficient
+and then people would move to a
+
+ align:start position:0%
+and then people would move to a
+ 
+
+ align:start position:0%
+and then people would move to a
+different system and You' kind of have a
+
+ align:start position:0%
+different system and You' kind of have a
+ 
+
+ align:start position:0%
+different system and You' kind of have a
+yo-yo around the the maximum carrying
+
+ align:start position:0%
+yo-yo around the the maximum carrying
+ 
+
+ align:start position:0%
+yo-yo around the the maximum carrying
+capacity and that doesn't seem efficient
+
+ align:start position:0%
+capacity and that doesn't seem efficient
+ 
+
+ align:start position:0%
+capacity and that doesn't seem efficient
+to me so I'm wondering if you could
+
+ align:start position:0%
+to me so I'm wondering if you could
+ 
+
+ align:start position:0%
+to me so I'm wondering if you could
+speak to
+
+ align:start position:0%
+speak to
+ 
+
+ align:start position:0%
+speak to
+that yeah so what you're what you're ESS
+
+ align:start position:0%
+that yeah so what you're what you're ESS
+ 
+
+ align:start position:0%
+that yeah so what you're what you're ESS
+essentially you're arguing for is what I
+
+ align:start position:0%
+essentially you're arguing for is what I
+ 
+
+ align:start position:0%
+essentially you're arguing for is what I
+would call an anticipatory decision rule
+
+ align:start position:0%
+would call an anticipatory decision rule
+ 
+
+ align:start position:0%
+would call an anticipatory decision rule
+so you would actually so the decision
+
+ align:start position:0%
+so you would actually so the decision
+ 
+
+ align:start position:0%
+so you would actually so the decision
+here is to deploy right you got to
+
+ align:start position:0%
+here is to deploy right you got to
+ 
+
+ align:start position:0%
+here is to deploy right you got to
+deploy your second stage because you've
+
+ align:start position:0%
+deploy your second stage because you've
+ 
+
+ align:start position:0%
+deploy your second stage because you've
+saturated the system what you're arguing
+
+ align:start position:0%
+saturated the system what you're arguing
+ 
+
+ align:start position:0%
+saturated the system what you're arguing
+for um is to before this occurs you know
+
+ align:start position:0%
+for um is to before this occurs you know
+ 
+
+ align:start position:0%
+for um is to before this occurs you know
+like at 80% saturation that's when you
+
+ align:start position:0%
+like at 80% saturation that's when you
+ 
+
+ align:start position:0%
+like at 80% saturation that's when you
+trigger the next stage right in order to
+
+ align:start position:0%
+trigger the next stage right in order to
+ 
+
+ align:start position:0%
+trigger the next stage right in order to
+anticipate the um the saturation and so
+
+ align:start position:0%
+anticipate the um the saturation and so
+ 
+
+ align:start position:0%
+anticipate the um the saturation and so
+absolutely you could do this you know
+
+ align:start position:0%
+absolutely you could do this you know
+ 
+
+ align:start position:0%
+absolutely you could do this you know
+there there are many different decision
+
+ align:start position:0%
+there there are many different decision
+ 
+
+ align:start position:0%
+there there are many different decision
+rules that you can try when you design a
+
+ align:start position:0%
+rules that you can try when you design a
+ 
+
+ align:start position:0%
+rules that you can try when you design a
+flexible you know Deployable scalable
+
+ align:start position:0%
+flexible you know Deployable scalable
+ 
+
+ align:start position:0%
+flexible you know Deployable scalable
+system that's part of the decision space
+
+ align:start position:0%
+system that's part of the decision space
+ 
+
+ align:start position:0%
+system that's part of the decision space
+so in this in this particular example uh
+
+ align:start position:0%
+so in this in this particular example uh
+ 
+
+ align:start position:0%
+so in this in this particular example uh
+you know we just implemented the
+
+ align:start position:0%
+you know we just implemented the
+ 
+
+ align:start position:0%
+you know we just implemented the
+simplest possible decision rule which
+
+ align:start position:0%
+simplest possible decision rule which
+ 
+
+ align:start position:0%
+simplest possible decision rule which
+was at when saturation has occurred you
+
+ align:start position:0%
+was at when saturation has occurred you
+ 
+
+ align:start position:0%
+was at when saturation has occurred you
+do deploy the next stage but not before
+
+ align:start position:0%
+do deploy the next stage but not before
+ 
+
+ align:start position:0%
+do deploy the next stage but not before
+okay thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you is that is that
+
+ align:start position:0%
+you is that is that
+ 
+
+ align:start position:0%
+you is that is that
+clear yes thank
+
+ align:start position:0%
+clear yes thank
+ 
+
+ align:start position:0%
+clear yes thank
+you okay so we we deploy the second
+
+ align:start position:0%
+you okay so we we deploy the second
+ 
+
+ align:start position:0%
+you okay so we we deploy the second
+stage now and you can see there's
+
+ align:start position:0%
+stage now and you can see there's
+ 
+
+ align:start position:0%
+stage now and you can see there's
+another Spike here right of of capital
+
+ align:start position:0%
+another Spike here right of of capital
+ 
+
+ align:start position:0%
+another Spike here right of of capital
+that's needed
+
+ align:start position:0%
+that's needed
+ 
+
+ align:start position:0%
+that's needed
+it's not as high as the first initial
+
+ align:start position:0%
+it's not as high as the first initial
+ 
+
+ align:start position:0%
+it's not as high as the first initial
+stage but it is
+
+ align:start position:0%
+stage but it is
+ 
+
+ align:start position:0%
+stage but it is
+substantial um so now as as we watched
+
+ align:start position:0%
+substantial um so now as as we watched
+ 
+
+ align:start position:0%
+substantial um so now as as we watched
+the as we've deployed the next stage our
+
+ align:start position:0%
+the as we've deployed the next stage our
+ 
+
+ align:start position:0%
+the as we've deployed the next stage our
+capacity went uh to the higher limit so
+
+ align:start position:0%
+capacity went uh to the higher limit so
+ 
+
+ align:start position:0%
+capacity went uh to the higher limit so
+we're now at capacity level two uh we're
+
+ align:start position:0%
+we're now at capacity level two uh we're
+ 
+
+ align:start position:0%
+we're now at capacity level two uh we're
+now operating the system uh demand keeps
+
+ align:start position:0%
+now operating the system uh demand keeps
+ 
+
+ align:start position:0%
+now operating the system uh demand keeps
+growing that's good now we're at year
+
+ align:start position:0%
+growing that's good now we're at year
+ 
+
+ align:start position:0%
+growing that's good now we're at year
+nine uh you can see but we haven't yet
+
+ align:start position:0%
+nine uh you can see but we haven't yet
+ 
+
+ align:start position:0%
+nine uh you can see but we haven't yet
+saturated our new capacity so again the
+
+ align:start position:0%
+saturated our new capacity so again the
+ 
+
+ align:start position:0%
+saturated our new capacity so again the
+optimal decision is is to or I shouldn't
+
+ align:start position:0%
+optimal decision is is to or I shouldn't
+ 
+
+ align:start position:0%
+optimal decision is is to or I shouldn't
+say the optimal decision but the
+
+ align:start position:0%
+say the optimal decision but the
+ 
+
+ align:start position:0%
+say the optimal decision but the
+decision according to the rule is you
+
+ align:start position:0%
+decision according to the rule is you
+ 
+
+ align:start position:0%
+decision according to the rule is you
+just wait right you keep
+
+ align:start position:0%
+just wait right you keep
+ 
+
+ align:start position:0%
+just wait right you keep
+operating ah now from year 9 to year 12
+
+ align:start position:0%
+operating ah now from year 9 to year 12
+ 
+
+ align:start position:0%
+operating ah now from year 9 to year 12
+demand starts to go down right and this
+
+ align:start position:0%
+demand starts to go down right and this
+ 
+
+ align:start position:0%
+demand starts to go down right and this
+happens in some systems right you they
+
+ align:start position:0%
+happens in some systems right you they
+ 
+
+ align:start position:0%
+happens in some systems right you they
+growing and then they Peak and then
+
+ align:start position:0%
+growing and then they Peak and then
+ 
+
+ align:start position:0%
+growing and then they Peak and then
+things go down so in this case we wait
+
+ align:start position:0%
+things go down so in this case we wait
+ 
+
+ align:start position:0%
+things go down so in this case we wait
+and then in this scenario it goes down
+
+ align:start position:0%
+and then in this scenario it goes down
+ 
+
+ align:start position:0%
+and then in this scenario it goes down
+again you see how that works so what's
+
+ align:start position:0%
+again you see how that works so what's
+ 
+
+ align:start position:0%
+again you see how that works so what's
+nice about this is you can
+
+ align:start position:0%
+nice about this is you can
+ 
+
+ align:start position:0%
+nice about this is you can
+now in in this in this sense all the 32
+
+ align:start position:0%
+now in in this in this sense all the 32
+ 
+
+ align:start position:0%
+now in in this in this sense all the 32
+scenarios of possible Futures you can
+
+ align:start position:0%
+scenarios of possible Futures you can
+ 
+
+ align:start position:0%
+scenarios of possible Futures you can
+run them against the 40 different
+
+ align:start position:0%
+run them against the 40 different
+ 
+
+ align:start position:0%
+run them against the 40 different
+families of designs or Evolution paths
+
+ align:start position:0%
+families of designs or Evolution paths
+ 
+
+ align:start position:0%
+families of designs or Evolution paths
+and out of that you can find the best
+
+ align:start position:0%
+and out of that you can find the best
+ 
+
+ align:start position:0%
+and out of that you can find the best
+path right this is the path the path
+
+ align:start position:0%
+path right this is the path the path
+ 
+
+ align:start position:0%
+path right this is the path the path
+that on average I should point out on
+
+ align:start position:0%
+that on average I should point out on
+ 
+
+ align:start position:0%
+that on average I should point out on
+average will satisfy your demand at
+
+ align:start position:0%
+average will satisfy your demand at
+ 
+
+ align:start position:0%
+average will satisfy your demand at
+minimum life cycle cost given the
+
+ align:start position:0%
+minimum life cycle cost given the
+ 
+
+ align:start position:0%
+minimum life cycle cost given the
+uncertainty model that you've imposed
+
+ align:start position:0%
+uncertainty model that you've imposed
+ 
+
+ align:start position:0%
+uncertainty model that you've imposed
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why did it go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down this this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here no the capacity stays the same you
+
+ align:start position:0%
+here no the capacity stays the same you
+ 
+
+ align:start position:0%
+here no the capacity stays the same you
+don't go down in capacity the reason is
+
+ align:start position:0%
+don't go down in capacity the reason is
+ 
+
+ align:start position:0%
+don't go down in capacity the reason is
+this is a good question um this
+
+ align:start position:0%
+this is a good question um this
+ 
+
+ align:start position:0%
+this is a good question um this
+particular system a satellite
+
+ align:start position:0%
+particular system a satellite
+ 
+
+ align:start position:0%
+particular system a satellite
+constellation is dominated by fixed
+
+ align:start position:0%
+constellation is dominated by fixed
+ 
+
+ align:start position:0%
+constellation is dominated by fixed
+costs right so it you wouldn't retire
+
+ align:start position:0%
+costs right so it you wouldn't retire
+ 
+
+ align:start position:0%
+costs right so it you wouldn't retire
+half your satellites because then you
+
+ align:start position:0%
+half your satellites because then you
+ 
+
+ align:start position:0%
+half your satellites because then you
+would lose coverage also potentially
+
+ align:start position:0%
+would lose coverage also potentially
+ 
+
+ align:start position:0%
+would lose coverage also potentially
+right because you move you move move
+
+ align:start position:0%
+right because you move you move move
+ 
+
+ align:start position:0%
+right because you move you move move
+them to orbits that that give you the
+
+ align:start position:0%
+them to orbits that that give you the
+ 
+
+ align:start position:0%
+them to orbits that that give you the
+right coverage you just increase your
+
+ align:start position:0%
+right coverage you just increase your
+ 
+
+ align:start position:0%
+right coverage you just increase your
+capacity this is different from a system
+
+ align:start position:0%
+capacity this is different from a system
+ 
+
+ align:start position:0%
+capacity this is different from a system
+that is dominated by variable costs like
+
+ align:start position:0%
+that is dominated by variable costs like
+ 
+
+ align:start position:0%
+that is dominated by variable costs like
+for example if you operate a fleet of
+
+ align:start position:0%
+for example if you operate a fleet of
+ 
+
+ align:start position:0%
+for example if you operate a fleet of
+taxis you know and and for whatever
+
+ align:start position:0%
+taxis you know and and for whatever
+ 
+
+ align:start position:0%
+taxis you know and and for whatever
+reason demand goes way down you can go
+
+ align:start position:0%
+reason demand goes way down you can go
+ 
+
+ align:start position:0%
+reason demand goes way down you can go
+and park half your taxis and just not
+
+ align:start position:0%
+and park half your taxis and just not
+ 
+
+ align:start position:0%
+and park half your taxis and just not
+operate them you may still have to pay a
+
+ align:start position:0%
+operate them you may still have to pay a
+ 
+
+ align:start position:0%
+operate them you may still have to pay a
+lease on them but essentially you adap
+
+ align:start position:0%
+lease on them but essentially you adap
+ 
+
+ align:start position:0%
+lease on them but essentially you adap
+you can downward adapt the capacity of
+
+ align:start position:0%
+you can downward adapt the capacity of
+ 
+
+ align:start position:0%
+you can downward adapt the capacity of
+VI system you can't do that here it
+
+ align:start position:0%
+VI system you can't do that here it
+ 
+
+ align:start position:0%
+VI system you can't do that here it
+doesn't make sense right so that's the
+
+ align:start position:0%
+doesn't make sense right so that's the
+ 
+
+ align:start position:0%
+doesn't make sense right so that's the
+big difference between systems that are
+
+ align:start position:0%
+big difference between systems that are
+ 
+
+ align:start position:0%
+big difference between systems that are
+fundamentally um fixed costs dominated
+
+ align:start position:0%
+fundamentally um fixed costs dominated
+ 
+
+ align:start position:0%
+fundamentally um fixed costs dominated
+versus variable cost dominated so in
+
+ align:start position:0%
+versus variable cost dominated so in
+ 
+
+ align:start position:0%
+versus variable cost dominated so in
+this case we you know we just don't use
+
+ align:start position:0%
+this case we you know we just don't use
+ 
+
+ align:start position:0%
+this case we you know we just don't use
+it as efficiently in the last six
+
+ align:start position:0%
+it as efficiently in the last six
+ 
+
+ align:start position:0%
+it as efficiently in the last six
+years so the answer here is um the
+
+ align:start position:0%
+years so the answer here is um the
+ 
+
+ align:start position:0%
+years so the answer here is um the
+answer here is that there's an optimal
+
+ align:start position:0%
+answer here is that there's an optimal
+ 
+
+ align:start position:0%
+answer here is that there's an optimal
+path and that's shown here that will um
+
+ align:start position:0%
+path and that's shown here that will um
+ 
+
+ align:start position:0%
+path and that's shown here that will um
+for a given targeted capacity you you
+
+ align:start position:0%
+for a given targeted capacity you you
+ 
+
+ align:start position:0%
+for a given targeted capacity you you
+can then you know you can compare
+
+ align:start position:0%
+can then you know you can compare
+ 
+
+ align:start position:0%
+can then you know you can compare
+essentially this Loop path against the
+
+ align:start position:0%
+essentially this Loop path against the
+ 
+
+ align:start position:0%
+essentially this Loop path against the
+traditional fixed design and in this
+
+ align:start position:0%
+traditional fixed design and in this
+ 
+
+ align:start position:0%
+traditional fixed design and in this
+case you know the traditional
+
+ align:start position:0%
+case you know the traditional
+ 
+
+ align:start position:0%
+case you know the traditional
+architecture fixed architecture would
+
+ align:start position:0%
+architecture fixed architecture would
+ 
+
+ align:start position:0%
+architecture fixed architecture would
+cost about $2 billion to
+
+ align:start position:0%
+cost about $2 billion to
+ 
+
+ align:start position:0%
+cost about $2 billion to
+build and on average the red point is
+
+ align:start position:0%
+build and on average the red point is
+ 
+
+ align:start position:0%
+build and on average the red point is
+the average life cycle cost of the
+
+ align:start position:0%
+the average life cycle cost of the
+ 
+
+ align:start position:0%
+the average life cycle cost of the
+evolvable system is
+
+ align:start position:0%
+evolvable system is
+ 
+
+ align:start position:0%
+evolvable system is
+1.36 Right life cycle cost of the rid
+
+ align:start position:0%
+1.36 Right life cycle cost of the rid
+ 
+
+ align:start position:0%
+1.36 Right life cycle cost of the rid
+design versus the expected life cycle
+
+ align:start position:0%
+design versus the expected life cycle
+ 
+
+ align:start position:0%
+design versus the expected life cycle
+cost of the best best deployment
+
+ align:start position:0%
+cost of the best best deployment
+ 
+
+ align:start position:0%
+cost of the best best deployment
+strategy or stage deployment strategy
+
+ align:start position:0%
+strategy or stage deployment strategy
+ 
+
+ align:start position:0%
+strategy or stage deployment strategy
+which is um essentially the way that's
+
+ align:start position:0%
+which is um essentially the way that's
+ 
+
+ align:start position:0%
+which is um essentially the way that's
+calculated it's the probability weighted
+
+ align:start position:0%
+calculated it's the probability weighted
+ 
+
+ align:start position:0%
+calculated it's the probability weighted
+life cycle cost of each of the scenarios
+
+ align:start position:0%
+life cycle cost of each of the scenarios
+ 
+
+ align:start position:0%
+life cycle cost of each of the scenarios
+right against this path and the
+
+ align:start position:0%
+right against this path and the
+ 
+
+ align:start position:0%
+right against this path and the
+difference between those two numbers is
+
+ align:start position:0%
+difference between those two numbers is
+ 
+
+ align:start position:0%
+difference between those two numbers is
+about a third $650 million and that is
+
+ align:start position:0%
+about a third $650 million and that is
+ 
+
+ align:start position:0%
+about a third $650 million and that is
+the value of the real option that's the
+
+ align:start position:0%
+the value of the real option that's the
+ 
+
+ align:start position:0%
+the value of the real option that's the
+value of Designing the system with
+
+ align:start position:0%
+value of Designing the system with
+ 
+
+ align:start position:0%
+value of Designing the system with
+scalability with
+
+ align:start position:0%
+scalability with
+ 
+
+ align:start position:0%
+scalability with
+flexibility okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes uh that's true uh so the lifetime
+
+ align:start position:0%
+yes uh that's true uh so the lifetime
+ 
+
+ align:start position:0%
+yes uh that's true uh so the lifetime
+the question was is the life expectancy
+
+ align:start position:0%
+the question was is the life expectancy
+ 
+
+ align:start position:0%
+the question was is the life expectancy
+similar of course so the 15-year uh life
+
+ align:start position:0%
+similar of course so the 15-year uh life
+ 
+
+ align:start position:0%
+similar of course so the 15-year uh life
+of the whole system isn't is the same
+
+ align:start position:0%
+of the whole system isn't is the same
+ 
+
+ align:start position:0%
+of the whole system isn't is the same
+for both of course in the stage
+
+ align:start position:0%
+for both of course in the stage
+ 
+
+ align:start position:0%
+for both of course in the stage
+deployment strategy um some of the
+
+ align:start position:0%
+deployment strategy um some of the
+ 
+
+ align:start position:0%
+deployment strategy um some of the
+satellites are going to be younger right
+
+ align:start position:0%
+satellites are going to be younger right
+ 
+
+ align:start position:0%
+satellites are going to be younger right
+at the end of the 15 years and so they
+
+ align:start position:0%
+at the end of the 15 years and so they
+ 
+
+ align:start position:0%
+at the end of the 15 years and so they
+may have longer residual life left which
+
+ align:start position:0%
+may have longer residual life left which
+ 
+
+ align:start position:0%
+may have longer residual life left which
+is actually not included that's not even
+
+ align:start position:0%
+is actually not included that's not even
+ 
+
+ align:start position:0%
+is actually not included that's not even
+included in this uh real real option
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+y right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that's right so you could you could
+
+ align:start position:0%
+that that's right so you could you could
+ 
+
+ align:start position:0%
+that that's right so you could you could
+sort ofine this model to include a more
+
+ align:start position:0%
+sort ofine this model to include a more
+ 
+
+ align:start position:0%
+sort ofine this model to include a more
+a stage decommissioning right or stage
+
+ align:start position:0%
+a stage decommissioning right or stage
+ 
+
+ align:start position:0%
+a stage decommissioning right or stage
+transition to a Next Generation system
+
+ align:start position:0%
+transition to a Next Generation system
+ 
+
+ align:start position:0%
+transition to a Next Generation system
+so in this case you know in this model
+
+ align:start position:0%
+so in this case you know in this model
+ 
+
+ align:start position:0%
+so in this case you know in this model
+after 15 years boom you know everything
+
+ align:start position:0%
+after 15 years boom you know everything
+ 
+
+ align:start position:0%
+after 15 years boom you know everything
+you just finish uh no more revenues you
+
+ align:start position:0%
+you just finish uh no more revenues you
+ 
+
+ align:start position:0%
+you just finish uh no more revenues you
+just decommission a hard end a hard stop
+
+ align:start position:0%
+just decommission a hard end a hard stop
+ 
+
+ align:start position:0%
+just decommission a hard end a hard stop
+after 15 years but you could actually
+
+ align:start position:0%
+after 15 years but you could actually
+ 
+
+ align:start position:0%
+after 15 years but you could actually
+build you know transition and de
+
+ align:start position:0%
+build you know transition and de
+ 
+
+ align:start position:0%
+build you know transition and de
+commissioning models as well good point
+
+ align:start position:0%
+commissioning models as well good point
+ 
+
+ align:start position:0%
+commissioning models as well good point
+so so that's that's essentially the the
+
+ align:start position:0%
+so so that's that's essentially the the
+ 
+
+ align:start position:0%
+so so that's that's essentially the the
+case study I wanted to show you and you
+
+ align:start position:0%
+case study I wanted to show you and you
+ 
+
+ align:start position:0%
+case study I wanted to show you and you
+know you'd say oh well that that's a you
+
+ align:start position:0%
+know you'd say oh well that that's a you
+ 
+
+ align:start position:0%
+know you'd say oh well that that's a you
+know that's kind of like uh in in the US
+
+ align:start position:0%
+know that's kind of like uh in in the US
+ 
+
+ align:start position:0%
+know that's kind of like uh in in the US
+we we talk about Monday morning
+
+ align:start position:0%
+we we talk about Monday morning
+ 
+
+ align:start position:0%
+we we talk about Monday morning
+quarterbacking you know you you you
+
+ align:start position:0%
+quarterbacking you know you you you
+ 
+
+ align:start position:0%
+quarterbacking you know you you you
+comment on all the football games that
+
+ align:start position:0%
+comment on all the football games that
+ 
+
+ align:start position:0%
+comment on all the football games that
+happened and the M mistakes that the
+
+ align:start position:0%
+happened and the M mistakes that the
+ 
+
+ align:start position:0%
+happened and the M mistakes that the
+coach has made and I would have done
+
+ align:start position:0%
+coach has made and I would have done
+ 
+
+ align:start position:0%
+coach has made and I would have done
+this or I would have done that so yes
+
+ align:start position:0%
+this or I would have done that so yes
+ 
+
+ align:start position:0%
+this or I would have done that so yes
+you know this is sort of like looking at
+
+ align:start position:0%
+you know this is sort of like looking at
+ 
+
+ align:start position:0%
+you know this is sort of like looking at
+this problem in hindsight but the
+
+ align:start position:0%
+this problem in hindsight but the
+ 
+
+ align:start position:0%
+this problem in hindsight but the
+reality is that that um that uh this
+
+ align:start position:0%
+reality is that that um that uh this
+ 
+
+ align:start position:0%
+reality is that that um that uh this
+really has had a big impact and a big
+
+ align:start position:0%
+really has had a big impact and a big
+ 
+
+ align:start position:0%
+really has had a big impact and a big
+dampening effect and that the the new
+
+ align:start position:0%
+dampening effect and that the the new
+ 
+
+ align:start position:0%
+dampening effect and that the the new
+generation of systems I think are built
+
+ align:start position:0%
+generation of systems I think are built
+ 
+
+ align:start position:0%
+generation of systems I think are built
+much more intelligently you know with
+
+ align:start position:0%
+much more intelligently you know with
+ 
+
+ align:start position:0%
+much more intelligently you know with
+this kind of evolution in mind um I will
+
+ align:start position:0%
+this kind of evolution in mind um I will
+ 
+
+ align:start position:0%
+this kind of evolution in mind um I will
+also mention to you
+
+ align:start position:0%
+also mention to you
+ 
+
+ align:start position:0%
+also mention to you
+that idium is actually the system that
+
+ align:start position:0%
+that idium is actually the system that
+ 
+
+ align:start position:0%
+that idium is actually the system that
+went bankrupt first and the reason for
+
+ align:start position:0%
+went bankrupt first and the reason for
+ 
+
+ align:start position:0%
+went bankrupt first and the reason for
+the bankruptcy well one of the immediate
+
+ align:start position:0%
+the bankruptcy well one of the immediate
+ 
+
+ align:start position:0%
+the bankruptcy well one of the immediate
+reasons for the bankruptcy is because
+
+ align:start position:0%
+reasons for the bankruptcy is because
+ 
+
+ align:start position:0%
+reasons for the bankruptcy is because
+the way that the project was financed so
+
+ align:start position:0%
+the way that the project was financed so
+ 
+
+ align:start position:0%
+the way that the project was financed so
+about onethird of the funds those $5
+
+ align:start position:0%
+about onethird of the funds those $5
+ 
+
+ align:start position:0%
+about onethird of the funds those $5
+billion onethird of the funds for idium
+
+ align:start position:0%
+billion onethird of the funds for idium
+ 
+
+ align:start position:0%
+billion onethird of the funds for idium
+came from um Equity uh from mola so that
+
+ align:start position:0%
+came from um Equity uh from mola so that
+ 
+
+ align:start position:0%
+came from um Equity uh from mola so that
+was their own money that they lost about
+
+ align:start position:0%
+was their own money that they lost about
+ 
+
+ align:start position:0%
+was their own money that they lost about
+onethird was uh IPO initial public
+
+ align:start position:0%
+onethird was uh IPO initial public
+ 
+
+ align:start position:0%
+onethird was uh IPO initial public
+offering you know shares sold to the
+
+ align:start position:0%
+offering you know shares sold to the
+ 
+
+ align:start position:0%
+offering you know shares sold to the
+public and about onethird was bank loans
+
+ align:start position:0%
+public and about onethird was bank loans
+ 
+
+ align:start position:0%
+public and about onethird was bank loans
+and these bank loans were relatively
+
+ align:start position:0%
+and these bank loans were relatively
+ 
+
+ align:start position:0%
+and these bank loans were relatively
+expensive and the banks expect you know
+
+ align:start position:0%
+expensive and the banks expect you know
+ 
+
+ align:start position:0%
+expensive and the banks expect you know
+that they get paid back at a certain
+
+ align:start position:0%
+that they get paid back at a certain
+ 
+
+ align:start position:0%
+that they get paid back at a certain
+speed depending on you know the market
+
+ align:start position:0%
+speed depending on you know the market
+ 
+
+ align:start position:0%
+speed depending on you know the market
+Evolution and and it's essentially the
+
+ align:start position:0%
+Evolution and and it's essentially the
+ 
+
+ align:start position:0%
+Evolution and and it's essentially the
+inability to pay for and service their
+
+ align:start position:0%
+inability to pay for and service their
+ 
+
+ align:start position:0%
+inability to pay for and service their
+loans that caused the aradian bankruptcy
+
+ align:start position:0%
+loans that caused the aradian bankruptcy
+ 
+
+ align:start position:0%
+loans that caused the aradian bankruptcy
+and it turns out that the loans were
+
+ align:start position:0%
+and it turns out that the loans were
+ 
+
+ align:start position:0%
+and it turns out that the loans were
+about onethird of the total
+
+ align:start position:0%
+about onethird of the total
+ 
+
+ align:start position:0%
+about onethird of the total
+capitalization of the project so what I
+
+ align:start position:0%
+capitalization of the project so what I
+ 
+
+ align:start position:0%
+capitalization of the project so what I
+would argue I would argue that if they
+
+ align:start position:0%
+would argue I would argue that if they
+ 
+
+ align:start position:0%
+would argue I would argue that if they
+had done this more flexible staged
+
+ align:start position:0%
+had done this more flexible staged
+ 
+
+ align:start position:0%
+had done this more flexible staged
+approach they could have saved onethird
+
+ align:start position:0%
+approach they could have saved onethird
+ 
+
+ align:start position:0%
+approach they could have saved onethird
+which is about the value of the F option
+
+ align:start position:0%
+which is about the value of the F option
+ 
+
+ align:start position:0%
+which is about the value of the F option
+and capitalization and just built the
+
+ align:start position:0%
+and capitalization and just built the
+ 
+
+ align:start position:0%
+and capitalization and just built the
+system only with equity and with the
+
+ align:start position:0%
+system only with equity and with the
+ 
+
+ align:start position:0%
+system only with equity and with the
+money from the IPO and that would would
+
+ align:start position:0%
+money from the IPO and that would would
+ 
+
+ align:start position:0%
+money from the IPO and that would would
+have given them a lot more time you know
+
+ align:start position:0%
+have given them a lot more time you know
+ 
+
+ align:start position:0%
+have given them a lot more time you know
+they wouldn't have had to service those
+
+ align:start position:0%
+they wouldn't have had to service those
+ 
+
+ align:start position:0%
+they wouldn't have had to service those
+loans and it would have given a lot more
+
+ align:start position:0%
+loans and it would have given a lot more
+ 
+
+ align:start position:0%
+loans and it would have given a lot more
+time to wait for the market to develop
+
+ align:start position:0%
+time to wait for the market to develop
+ 
+
+ align:start position:0%
+time to wait for the market to develop
+which it eventually did um so there was
+
+ align:start position:0%
+which it eventually did um so there was
+ 
+
+ align:start position:0%
+which it eventually did um so there was
+there was the whole financial
+
+ align:start position:0%
+there was the whole financial
+ 
+
+ align:start position:0%
+there was the whole financial
+architecture was poorly done as well
+
+ align:start position:0%
+architecture was poorly done as well
+ 
+
+ align:start position:0%
+architecture was poorly done as well
+which is a whole another that's a whole
+
+ align:start position:0%
+which is a whole another that's a whole
+ 
+
+ align:start position:0%
+which is a whole another that's a whole
+another question uh Professor quick
+
+ align:start position:0%
+another question uh Professor quick
+ 
+
+ align:start position:0%
+another question uh Professor quick
+question there situations where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes uh so the question I'm just
+
+ align:start position:0%
+yes yes uh so the question I'm just
+ 
+
+ align:start position:0%
+yes yes uh so the question I'm just
+going to repeat it for you guys at MIT
+
+ align:start position:0%
+going to repeat it for you guys at MIT
+ 
+
+ align:start position:0%
+going to repeat it for you guys at MIT
+the question was are there are there
+
+ align:start position:0%
+the question was are there are there
+ 
+
+ align:start position:0%
+the question was are there are there
+cases where the flexible approach is not
+
+ align:start position:0%
+cases where the flexible approach is not
+ 
+
+ align:start position:0%
+cases where the flexible approach is not
+the best and the answer is yes so for
+
+ align:start position:0%
+the best and the answer is yes so for
+ 
+
+ align:start position:0%
+the best and the answer is yes so for
+example if you're in you know I know
+
+ align:start position:0%
+example if you're in you know I know
+ 
+
+ align:start position:0%
+example if you're in you know I know
+that you you're starting the energy
+
+ align:start position:0%
+that you you're starting the energy
+ 
+
+ align:start position:0%
+that you you're starting the energy
+energy markets if you're in a situation
+
+ align:start position:0%
+energy markets if you're in a situation
+ 
+
+ align:start position:0%
+energy markets if you're in a situation
+where you have guaranteed
+
+ align:start position:0%
+where you have guaranteed
+ 
+
+ align:start position:0%
+where you have guaranteed
+a guaranteed customer you know so the
+
+ align:start position:0%
+a guaranteed customer you know so the
+ 
+
+ align:start position:0%
+a guaranteed customer you know so the
+the government or one of the big
+
+ align:start position:0%
+the government or one of the big
+ 
+
+ align:start position:0%
+the government or one of the big
+utilities is entering into a long-term
+
+ align:start position:0%
+utilities is entering into a long-term
+ 
+
+ align:start position:0%
+utilities is entering into a long-term
+agreement with you that they will buy
+
+ align:start position:0%
+agreement with you that they will buy
+ 
+
+ align:start position:0%
+agreement with you that they will buy
+the power that you produce at a certain
+
+ align:start position:0%
+the power that you produce at a certain
+ 
+
+ align:start position:0%
+the power that you produce at a certain
+price for the next 20 years right um and
+
+ align:start position:0%
+price for the next 20 years right um and
+ 
+
+ align:start position:0%
+price for the next 20 years right um and
+so you're not subject to that market
+
+ align:start position:0%
+so you're not subject to that market
+ 
+
+ align:start position:0%
+so you're not subject to that market
+volatility but you have a long-term
+
+ align:start position:0%
+volatility but you have a long-term
+ 
+
+ align:start position:0%
+volatility but you have a long-term
+agreement including Clauses that say
+
+ align:start position:0%
+agreement including Clauses that say
+ 
+
+ align:start position:0%
+agreement including Clauses that say
+well if if the government doesn't do
+
+ align:start position:0%
+well if if the government doesn't do
+ 
+
+ align:start position:0%
+well if if the government doesn't do
+this then they'll they'll compensate you
+
+ align:start position:0%
+this then they'll they'll compensate you
+ 
+
+ align:start position:0%
+this then they'll they'll compensate you
+for any losses you know this is the
+
+ align:start position:0%
+for any losses you know this is the
+ 
+
+ align:start position:0%
+for any losses you know this is the
+financial AR contraction if you
+
+ align:start position:0%
+financial AR contraction if you
+ 
+
+ align:start position:0%
+financial AR contraction if you
+basically have eliminated demand
+
+ align:start position:0%
+basically have eliminated demand
+ 
+
+ align:start position:0%
+basically have eliminated demand
+uncertainty because of the particular
+
+ align:start position:0%
+uncertainty because of the particular
+ 
+
+ align:start position:0%
+uncertainty because of the particular
+contractual Arrangement then there's no
+
+ align:start position:0%
+contractual Arrangement then there's no
+ 
+
+ align:start position:0%
+contractual Arrangement then there's no
+reason you shouldn't build the system
+
+ align:start position:0%
+reason you shouldn't build the system
+ 
+
+ align:start position:0%
+reason you shouldn't build the system
+for a fixed capacity and
+
+ align:start position:0%
+for a fixed capacity and
+ 
+
+ align:start position:0%
+for a fixed capacity and
+um because you're then you can build
+
+ align:start position:0%
+um because you're then you can build
+ 
+
+ align:start position:0%
+um because you're then you can build
+something right on the Pito front
+
+ align:start position:0%
+something right on the Pito front
+ 
+
+ align:start position:0%
+something right on the Pito front
+because that particular uncertainty has
+
+ align:start position:0%
+because that particular uncertainty has
+ 
+
+ align:start position:0%
+because that particular uncertainty has
+been eliminated for for policy or
+
+ align:start position:0%
+been eliminated for for policy or
+ 
+
+ align:start position:0%
+been eliminated for for policy or
+contractual re reasons so good
+
+ align:start position:0%
+contractual re reasons so good
+ 
+
+ align:start position:0%
+contractual re reasons so good
+question okay um so we're almost almost
+
+ align:start position:0%
+question okay um so we're almost almost
+ 
+
+ align:start position:0%
+question okay um so we're almost almost
+there let me just try to uh summarize
+
+ align:start position:0%
+there let me just try to uh summarize
+ 
+
+ align:start position:0%
+there let me just try to uh summarize
+some of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the please go ahead um on the side
+
+ align:start position:0%
+the please go ahead um on the side
+ 
+
+ align:start position:0%
+the please go ahead um on the side
+before 37 um it seemed like um the
+
+ align:start position:0%
+before 37 um it seemed like um the
+ 
+
+ align:start position:0%
+before 37 um it seemed like um the
+probability waiting was for um kind of a
+
+ align:start position:0%
+probability waiting was for um kind of a
+ 
+
+ align:start position:0%
+probability waiting was for um kind of a
+a general capacity like uh something
+
+ align:start position:0%
+a general capacity like uh something
+ 
+
+ align:start position:0%
+a general capacity like uh something
+that could be adapted over the life
+
+ align:start position:0%
+that could be adapted over the life
+ 
+
+ align:start position:0%
+that could be adapted over the life
+cycle but here we're we're pinning down
+
+ align:start position:0%
+cycle but here we're we're pinning down
+ 
+
+ align:start position:0%
+cycle but here we're we're pinning down
+a a specific capacity so why is it the
+
+ align:start position:0%
+a a specific capacity so why is it the
+ 
+
+ align:start position:0%
+a a specific capacity so why is it the
+sum of probabilities then haven't kind
+
+ align:start position:0%
+sum of probabilities then haven't kind
+ 
+
+ align:start position:0%
+sum of probabilities then haven't kind
+of the probabilities been realized don't
+
+ align:start position:0%
+of the probabilities been realized don't
+ 
+
+ align:start position:0%
+of the probabilities been realized don't
+you know exactly what Your Capacity is
+
+ align:start position:0%
+you know exactly what Your Capacity is
+ 
+
+ align:start position:0%
+you know exactly what Your Capacity is
+that you're operating
+
+ align:start position:0%
+that you're operating
+ 
+
+ align:start position:0%
+that you're operating
+at yeah so so just to be clear on this
+
+ align:start position:0%
+at yeah so so just to be clear on this
+ 
+
+ align:start position:0%
+at yeah so so just to be clear on this
+so the probabilities those P subi
+
+ align:start position:0%
+so the probabilities those P subi
+ 
+
+ align:start position:0%
+so the probabilities those P subi
+they're they come from the lattice model
+
+ align:start position:0%
+they're they come from the lattice model
+ 
+
+ align:start position:0%
+they're they come from the lattice model
+they are determined by the lattice model
+
+ align:start position:0%
+they are determined by the lattice model
+ 
+
+ align:start position:0%
+they are determined by the lattice model
+so what you do is for those 32 scenarios
+
+ align:start position:0%
+so what you do is for those 32 scenarios
+ 
+
+ align:start position:0%
+so what you do is for those 32 scenarios
+of the future this is the pi right the I
+
+ align:start position:0%
+of the future this is the pi right the I
+ 
+
+ align:start position:0%
+of the future this is the pi right the I
+is the index is the is the uh for this
+
+ align:start position:0%
+is the index is the is the uh for this
+ 
+
+ align:start position:0%
+is the index is the is the uh for this
+particular future scenario for each
+
+ align:start position:0%
+particular future scenario for each
+ 
+
+ align:start position:0%
+particular future scenario for each
+future scenario you start with your you
+
+ align:start position:0%
+future scenario you start with your you
+ 
+
+ align:start position:0%
+future scenario you start with your you
+always start with A1 which is your
+
+ align:start position:0%
+always start with A1 which is your
+ 
+
+ align:start position:0%
+always start with A1 which is your
+initial configuration right of the
+
+ align:start position:0%
+initial configuration right of the
+ 
+
+ align:start position:0%
+initial configuration right of the
+constellation you always start with
+
+ align:start position:0%
+constellation you always start with
+ 
+
+ align:start position:0%
+constellation you always start with
+A1 and for each of those future
+
+ align:start position:0%
+A1 and for each of those future
+ 
+
+ align:start position:0%
+A1 and for each of those future
+scenarios you then simulate that future
+
+ align:start position:0%
+scenarios you then simulate that future
+ 
+
+ align:start position:0%
+scenarios you then simulate that future
+and you know if you know for those
+
+ align:start position:0%
+and you know if you know for those
+ 
+
+ align:start position:0%
+and you know if you know for those
+Futures where the demand does never
+
+ align:start position:0%
+Futures where the demand does never
+ 
+
+ align:start position:0%
+Futures where the demand does never
+really takes off and materializes you
+
+ align:start position:0%
+really takes off and materializes you
+ 
+
+ align:start position:0%
+really takes off and materializes you
+never actually trigger that next
+
+ align:start position:0%
+never actually trigger that next
+ 
+
+ align:start position:0%
+never actually trigger that next
+expansion stage and it's actually that
+
+ align:start position:0%
+expansion stage and it's actually that
+ 
+
+ align:start position:0%
+expansion stage and it's actually that
+asymmetry that gives you the advantage
+
+ align:start position:0%
+asymmetry that gives you the advantage
+ 
+
+ align:start position:0%
+asymmetry that gives you the advantage
+and um it's essentially not the
+
+ align:start position:0%
+and um it's essentially not the
+ 
+
+ align:start position:0%
+and um it's essentially not the
+deploying capacity when you really don't
+
+ align:start position:0%
+deploying capacity when you really don't
+ 
+
+ align:start position:0%
+deploying capacity when you really don't
+need it and um and so you do this for
+
+ align:start position:0%
+need it and um and so you do this for
+ 
+
+ align:start position:0%
+need it and um and so you do this for
+all of the end scenarios of the future
+
+ align:start position:0%
+all of the end scenarios of the future
+ 
+
+ align:start position:0%
+all of the end scenarios of the future
+and the pi is the probability waiting of
+
+ align:start position:0%
+and the pi is the probability waiting of
+ 
+
+ align:start position:0%
+and the pi is the probability waiting of
+each future scenario comes directly out
+
+ align:start position:0%
+each future scenario comes directly out
+ 
+
+ align:start position:0%
+each future scenario comes directly out
+of the lattice model that's not
+
+ align:start position:0%
+of the lattice model that's not
+ 
+
+ align:start position:0%
+of the lattice model that's not
+something that you have to manually
+
+ align:start position:0%
+something that you have to manually
+ 
+
+ align:start position:0%
+something that you have to manually
+determine right no I I understand that
+
+ align:start position:0%
+determine right no I I understand that
+ 
+
+ align:start position:0%
+determine right no I I understand that
+but here since we've kind of pinned down
+
+ align:start position:0%
+but here since we've kind of pinned down
+ 
+
+ align:start position:0%
+but here since we've kind of pinned down
+a capacity already we know what endpoint
+
+ align:start position:0%
+a capacity already we know what endpoint
+ 
+
+ align:start position:0%
+a capacity already we know what endpoint
+we're at I'm just wondering how the how
+
+ align:start position:0%
+we're at I'm just wondering how the how
+ 
+
+ align:start position:0%
+we're at I'm just wondering how the how
+the probabilities come into that or is
+
+ align:start position:0%
+the probabilities come into that or is
+ 
+
+ align:start position:0%
+the probabilities come into that or is
+it kind of working backwards now of all
+
+ align:start position:0%
+it kind of working backwards now of all
+ 
+
+ align:start position:0%
+it kind of working backwards now of all
+the out there on this specific
+
+ align:start position:0%
+the out there on this specific
+ 
+
+ align:start position:0%
+the out there on this specific
+plot I see what you're saying okay so
+
+ align:start position:0%
+plot I see what you're saying okay so
+ 
+
+ align:start position:0%
+plot I see what you're saying okay so
+the the left point the A1 point so the
+
+ align:start position:0%
+the the left point the A1 point so the
+ 
+
+ align:start position:0%
+the the left point the A1 point so the
+A1 point is driven by you need you need
+
+ align:start position:0%
+A1 point is driven by you need you need
+ 
+
+ align:start position:0%
+A1 point is driven by you need you need
+to make some assumptions about initial
+
+ align:start position:0%
+to make some assumptions about initial
+ 
+
+ align:start position:0%
+to make some assumptions about initial
+capacity and and then the end point the
+
+ align:start position:0%
+capacity and and then the end point the
+ 
+
+ align:start position:0%
+capacity and and then the end point the
+A4 is driven by how large you made the
+
+ align:start position:0%
+A4 is driven by how large you made the
+ 
+
+ align:start position:0%
+A4 is driven by how large you made the
+trade
+
+ align:start position:0%
+trade
+ 
+
+ align:start position:0%
+trade
+space so you if you could make the trade
+
+ align:start position:0%
+space so you if you could make the trade
+ 
+
+ align:start position:0%
+space so you if you could make the trade
+space you could make the design space
+
+ align:start position:0%
+space you could make the design space
+ 
+
+ align:start position:0%
+space you could make the design space
+even larger right this is a discretized
+
+ align:start position:0%
+even larger right this is a discretized
+ 
+
+ align:start position:0%
+even larger right this is a discretized
+uh full factorial design space you could
+
+ align:start position:0%
+uh full factorial design space you could
+ 
+
+ align:start position:0%
+uh full factorial design space you could
+make it even larger and then A4 would
+
+ align:start position:0%
+make it even larger and then A4 would
+ 
+
+ align:start position:0%
+make it even larger and then A4 would
+not be the end point this is just sort
+
+ align:start position:0%
+not be the end point this is just sort
+ 
+
+ align:start position:0%
+not be the end point this is just sort
+of a finite size effect due to the size
+
+ align:start position:0%
+of a finite size effect due to the size
+ 
+
+ align:start position:0%
+of a finite size effect due to the size
+of the trade
+
+ align:start position:0%
+of the trade
+ 
+
+ align:start position:0%
+of the trade
+space okay
+
+ align:start position:0%
+space okay
+ 
+
+ align:start position:0%
+space okay
+thanks
+
+ align:start position:0%
+thanks
+ 
+
+ align:start position:0%
+thanks
+okay all right so let me um let's go to
+
+ align:start position:0%
+okay all right so let me um let's go to
+ 
+
+ align:start position:0%
+okay all right so let me um let's go to
+the you know so the way I want to do the
+
+ align:start position:0%
+the you know so the way I want to do the
+ 
+
+ align:start position:0%
+the you know so the way I want to do the
+summary here is just go back to the
+
+ align:start position:0%
+summary here is just go back to the
+ 
+
+ align:start position:0%
+summary here is just go back to the
+learning objectives you know I always do
+
+ align:start position:0%
+learning objectives you know I always do
+ 
+
+ align:start position:0%
+learning objectives you know I always do
+this in every class you know let's close
+
+ align:start position:0%
+this in every class you know let's close
+ 
+
+ align:start position:0%
+this in every class you know let's close
+the loop what did I
+
+ align:start position:0%
+the loop what did I
+ 
+
+ align:start position:0%
+the loop what did I
+promise you in lecture one that you
+
+ align:start position:0%
+promise you in lecture one that you
+ 
+
+ align:start position:0%
+promise you in lecture one that you
+would learn in this class and you know
+
+ align:start position:0%
+would learn in this class and you know
+ 
+
+ align:start position:0%
+would learn in this class and you know
+each of you you're going to have to
+
+ align:start position:0%
+each of you you're going to have to
+ 
+
+ align:start position:0%
+each of you you're going to have to
+decide for yourself you know did I
+
+ align:start position:0%
+decide for yourself you know did I
+ 
+
+ align:start position:0%
+decide for yourself you know did I
+actually learn this did did we actually
+
+ align:start position:0%
+actually learn this did did we actually
+ 
+
+ align:start position:0%
+actually learn this did did we actually
+do this so this is sort of due diligence
+
+ align:start position:0%
+do this so this is sort of due diligence
+ 
+
+ align:start position:0%
+do this so this is sort of due diligence
+on the learning objectives and I have
+
+ align:start position:0%
+on the learning objectives and I have
+ 
+
+ align:start position:0%
+on the learning objectives and I have
+one slide on each of them so the first
+
+ align:start position:0%
+one slide on each of them so the first
+ 
+
+ align:start position:0%
+one slide on each of them so the first
+objective was to for you to really
+
+ align:start position:0%
+objective was to for you to really
+ 
+
+ align:start position:0%
+objective was to for you to really
+understand the system engineering
+
+ align:start position:0%
+understand the system engineering
+ 
+
+ align:start position:0%
+understand the system engineering
+standards and best practices as well as
+
+ align:start position:0%
+standards and best practices as well as
+ 
+
+ align:start position:0%
+standards and best practices as well as
+newer
+
+ align:start position:0%
+newer
+ 
+
+ align:start position:0%
+newer
+approaches number two is understand the
+
+ align:start position:0%
+approaches number two is understand the
+ 
+
+ align:start position:0%
+approaches number two is understand the
+key steps in the system Engineering
+
+ align:start position:0%
+key steps in the system Engineering
+ 
+
+ align:start position:0%
+key steps in the system Engineering
+Process number three was uh analyze and
+
+ align:start position:0%
+Process number three was uh analyze and
+ 
+
+ align:start position:0%
+Process number three was uh analyze and
+understand the role of humans in in the
+
+ align:start position:0%
+understand the role of humans in in the
+ 
+
+ align:start position:0%
+understand the role of humans in in the
+system as beneficiaries designers
+
+ align:start position:0%
+system as beneficiaries designers
+ 
+
+ align:start position:0%
+system as beneficiaries designers
+operators and so forth number four was
+
+ align:start position:0%
+operators and so forth number four was
+ 
+
+ align:start position:0%
+operators and so forth number four was
+um being honest and characterizing the
+
+ align:start position:0%
+um being honest and characterizing the
+ 
+
+ align:start position:0%
+um being honest and characterizing the
+limitations of system engineering as we
+
+ align:start position:0%
+limitations of system engineering as we
+ 
+
+ align:start position:0%
+limitations of system engineering as we
+as we practice it today and then uh
+
+ align:start position:0%
+as we practice it today and then uh
+ 
+
+ align:start position:0%
+as we practice it today and then uh
+objective five learning objective five
+
+ align:start position:0%
+objective five learning objective five
+ 
+
+ align:start position:0%
+objective five learning objective five
+was applying these methods and tools to
+
+ align:start position:0%
+was applying these methods and tools to
+ 
+
+ align:start position:0%
+was applying these methods and tools to
+a real even as not so complex cyber
+
+ align:start position:0%
+a real even as not so complex cyber
+ 
+
+ align:start position:0%
+a real even as not so complex cyber
+electromechanical system
+
+ align:start position:0%
+electromechanical system
+ 
+
+ align:start position:0%
+electromechanical system
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+se1 um essentially hopefully know we we
+
+ align:start position:0%
+se1 um essentially hopefully know we we
+ 
+
+ align:start position:0%
+se1 um essentially hopefully know we we
+didn't check the readings but I'm I'm
+
+ align:start position:0%
+didn't check the readings but I'm I'm
+ 
+
+ align:start position:0%
+didn't check the readings but I'm I'm
+hoping that you did your readings that
+
+ align:start position:0%
+hoping that you did your readings that
+ 
+
+ align:start position:0%
+hoping that you did your readings that
+you really feel like you understand the
+
+ align:start position:0%
+you really feel like you understand the
+ 
+
+ align:start position:0%
+you really feel like you understand the
+NASA system engineering handbook which
+
+ align:start position:0%
+NASA system engineering handbook which
+ 
+
+ align:start position:0%
+NASA system engineering handbook which
+is our our quasi textbook for this class
+
+ align:start position:0%
+is our our quasi textbook for this class
+ 
+
+ align:start position:0%
+is our our quasi textbook for this class
+but there's other uh other standards as
+
+ align:start position:0%
+but there's other uh other standards as
+ 
+
+ align:start position:0%
+but there's other uh other standards as
+well such as the enclos St the enclos
+
+ align:start position:0%
+well such as the enclos St the enclos
+ 
+
+ align:start position:0%
+well such as the enclos St the enclos
+handbook which is actually the basis for
+
+ align:start position:0%
+handbook which is actually the basis for
+ 
+
+ align:start position:0%
+handbook which is actually the basis for
+uh certification so several of you here
+
+ align:start position:0%
+uh certification so several of you here
+ 
+
+ align:start position:0%
+uh certification so several of you here
+at epfl mentioned to me that you're
+
+ align:start position:0%
+at epfl mentioned to me that you're
+ 
+
+ align:start position:0%
+at epfl mentioned to me that you're
+interested and certification so I I
+
+ align:start position:0%
+interested and certification so I I
+ 
+
+ align:start position:0%
+interested and certification so I I
+encourage that most of that is based on
+
+ align:start position:0%
+encourage that most of that is based on
+ 
+
+ align:start position:0%
+encourage that most of that is based on
+the on this uh number two uh I did
+
+ align:start position:0%
+the on this uh number two uh I did
+ 
+
+ align:start position:0%
+the on this uh number two uh I did
+mention the iso standard 15288 that's
+
+ align:start position:0%
+mention the iso standard 15288 that's
+ 
+
+ align:start position:0%
+mention the iso standard 15288 that's
+probably the best known standard you
+
+ align:start position:0%
+probably the best known standard you
+ 
+
+ align:start position:0%
+probably the best known standard you
+know ISO is a very located right here in
+
+ align:start position:0%
+know ISO is a very located right here in
+ 
+
+ align:start position:0%
+know ISO is a very located right here in
+Geneva ISO is a very important
+
+ align:start position:0%
+Geneva ISO is a very important
+ 
+
+ align:start position:0%
+Geneva ISO is a very important
+organization you know I know ISO
+
+ align:start position:0%
+organization you know I know ISO
+ 
+
+ align:start position:0%
+organization you know I know ISO
+standards are not the most exciting
+
+ align:start position:0%
+standards are not the most exciting
+ 
+
+ align:start position:0%
+standards are not the most exciting
+things to read but they have huge impact
+
+ align:start position:0%
+things to read but they have huge impact
+ 
+
+ align:start position:0%
+things to read but they have huge impact
+um and so 15288 is is is something
+
+ align:start position:0%
+um and so 15288 is is is something
+ 
+
+ align:start position:0%
+um and so 15288 is is is something
+that's well worldwide known and and
+
+ align:start position:0%
+that's well worldwide known and and
+ 
+
+ align:start position:0%
+that's well worldwide known and and
+across all all Industries really and
+
+ align:start position:0%
+across all all Industries really and
+ 
+
+ align:start position:0%
+across all all Industries really and
+then um I want to mention also the
+
+ align:start position:0%
+then um I want to mention also the
+ 
+
+ align:start position:0%
+then um I want to mention also the
+European systems engineering standard
+
+ align:start position:0%
+European systems engineering standard
+ 
+
+ align:start position:0%
+European systems engineering standard
+and fulker and I had a discussion about
+
+ align:start position:0%
+and fulker and I had a discussion about
+ 
+
+ align:start position:0%
+and fulker and I had a discussion about
+this earlier today uh this is uh issued
+
+ align:start position:0%
+this earlier today uh this is uh issued
+ 
+
+ align:start position:0%
+this earlier today uh this is uh issued
+by the U European space agency and it is
+
+ align:start position:0%
+by the U European space agency and it is
+ 
+
+ align:start position:0%
+by the U European space agency and it is
+a little there's some subtle differences
+
+ align:start position:0%
+a little there's some subtle differences
+ 
+
+ align:start position:0%
+a little there's some subtle differences
+between the ISA approach and the NASA
+
+ align:start position:0%
+between the ISA approach and the NASA
+ 
+
+ align:start position:0%
+between the ISA approach and the NASA
+approach and so for those of you on this
+
+ align:start position:0%
+approach and so for those of you on this
+ 
+
+ align:start position:0%
+approach and so for those of you on this
+side of the Atlantic uh I do encourage
+
+ align:start position:0%
+side of the Atlantic uh I do encourage
+ 
+
+ align:start position:0%
+side of the Atlantic uh I do encourage
+you to take a look at that ecss standard
+
+ align:start position:0%
+you to take a look at that ecss standard
+ 
+
+ align:start position:0%
+you to take a look at that ecss standard
+as well and then we we augmented this
+
+ align:start position:0%
+as well and then we we augmented this
+ 
+
+ align:start position:0%
+as well and then we we augmented this
+with you know different uh papers and
+
+ align:start position:0%
+with you know different uh papers and
+ 
+
+ align:start position:0%
+with you know different uh papers and
+readings and so forth so I want to do a
+
+ align:start position:0%
+readings and so forth so I want to do a
+ 
+
+ align:start position:0%
+readings and so forth so I want to do a
+very quick um this is our last concept
+
+ align:start position:0%
+very quick um this is our last concept
+ 
+
+ align:start position:0%
+very quick um this is our last concept
+question for the class so uh here's the
+
+ align:start position:0%
+question for the class so uh here's the
+ 
+
+ align:start position:0%
+question for the class so uh here's the
+link uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tiny.cc Capital SE standards and it's
+
+ align:start position:0%
+tiny.cc Capital SE standards and it's
+ 
+
+ align:start position:0%
+tiny.cc Capital SE standards and it's
+essentially uh I want to get some
+
+ align:start position:0%
+essentially uh I want to get some
+ 
+
+ align:start position:0%
+essentially uh I want to get some
+feedback uh what you think about these
+
+ align:start position:0%
+feedback uh what you think about these
+ 
+
+ align:start position:0%
+feedback uh what you think about these
+standards all outdated and surpassed by
+
+ align:start position:0%
+standards all outdated and surpassed by
+ 
+
+ align:start position:0%
+standards all outdated and surpassed by
+the digital Revolution one of you think
+
+ align:start position:0%
+the digital Revolution one of you think
+ 
+
+ align:start position:0%
+the digital Revolution one of you think
+that thinks that's true uh 90% of you
+
+ align:start position:0%
+that thinks that's true uh 90% of you
+ 
+
+ align:start position:0%
+that thinks that's true uh 90% of you
+think they're still they're useful
+
+ align:start position:0%
+think they're still they're useful
+ 
+
+ align:start position:0%
+think they're still they're useful
+codification of best
+
+ align:start position:0%
+codification of best
+ 
+
+ align:start position:0%
+codification of best
+practice um 15 14% think they can be
+
+ align:start position:0%
+practice um 15 14% think they can be
+ 
+
+ align:start position:0%
+practice um 15 14% think they can be
+dangerous if you adhere to them too
+
+ align:start position:0%
+dangerous if you adhere to them too
+ 
+
+ align:start position:0%
+dangerous if you adhere to them too
+closely um about 60% of you think
+
+ align:start position:0%
+closely um about 60% of you think
+ 
+
+ align:start position:0%
+closely um about 60% of you think
+they're essential reading for any
+
+ align:start position:0%
+they're essential reading for any
+ 
+
+ align:start position:0%
+they're essential reading for any
+serious system engineer and uh 3 10%
+
+ align:start position:0%
+serious system engineer and uh 3 10%
+ 
+
+ align:start position:0%
+serious system engineer and uh 3 10%
+said you would never use them as a daily
+
+ align:start position:0%
+said you would never use them as a daily
+ 
+
+ align:start position:0%
+said you would never use them as a daily
+reference book okay so that's that's
+
+ align:start position:0%
+reference book okay so that's that's
+ 
+
+ align:start position:0%
+reference book okay so that's that's
+good I think that's what do you think
+
+ align:start position:0%
+good I think that's what do you think
+ 
+
+ align:start position:0%
+good I think that's what do you think
+buker that's a pretty reasonable outcome
+
+ align:start position:0%
+buker that's a pretty reasonable outcome
+ 
+
+ align:start position:0%
+buker that's a pretty reasonable outcome
+you think okay but what is true is uh
+
+ align:start position:0%
+you think okay but what is true is uh
+ 
+
+ align:start position:0%
+you think okay but what is true is uh
+they're going to be referenced in
+
+ align:start position:0%
+they're going to be referenced in
+ 
+
+ align:start position:0%
+they're going to be referenced in
+contracts you know if you're if you're
+
+ align:start position:0%
+contracts you know if you're if you're
+ 
+
+ align:start position:0%
+contracts you know if you're if you're
+um if you're doing you know it depends
+
+ align:start position:0%
+um if you're doing you know it depends
+ 
+
+ align:start position:0%
+um if you're doing you know it depends
+again on on the industry that you're in
+
+ align:start position:0%
+again on on the industry that you're in
+ 
+
+ align:start position:0%
+again on on the industry that you're in
+but um you know you you're going to
+
+ align:start position:0%
+but um you know you you're going to
+ 
+
+ align:start position:0%
+but um you know you you're going to
+adhere to some of these things in
+
+ align:start position:0%
+adhere to some of these things in
+ 
+
+ align:start position:0%
+adhere to some of these things in
+contracts and if things don't go well
+
+ align:start position:0%
+contracts and if things don't go well
+ 
+
+ align:start position:0%
+contracts and if things don't go well
+people will actually check whether uh
+
+ align:start position:0%
+people will actually check whether uh
+ 
+
+ align:start position:0%
+people will actually check whether uh
+did you do this step did you do that
+
+ align:start position:0%
+did you do this step did you do that
+ 
+
+ align:start position:0%
+did you do this step did you do that
+step um so it does have you know real
+
+ align:start position:0%
+step um so it does have you know real
+ 
+
+ align:start position:0%
+step um so it does have you know real
+consequences okay great thank you very
+
+ align:start position:0%
+consequences okay great thank you very
+ 
+
+ align:start position:0%
+consequences okay great thank you very
+much that was that was good um step two
+
+ align:start position:0%
+much that was that was good um step two
+ 
+
+ align:start position:0%
+much that was that was good um step two
+you know the key steps the V model I
+
+ align:start position:0%
+you know the key steps the V model I
+ 
+
+ align:start position:0%
+you know the key steps the V model I
+think I'm not going to explain it again
+
+ align:start position:0%
+think I'm not going to explain it again
+ 
+
+ align:start position:0%
+think I'm not going to explain it again
+you know hopefully this is something
+
+ align:start position:0%
+you know hopefully this is something
+ 
+
+ align:start position:0%
+you know hopefully this is something
+that you will not forget and just one
+
+ align:start position:0%
+that you will not forget and just one
+ 
+
+ align:start position:0%
+that you will not forget and just one
+one point about the V model is you know
+
+ align:start position:0%
+one point about the V model is you know
+ 
+
+ align:start position:0%
+one point about the V model is you know
+it does not imply that that system
+
+ align:start position:0%
+it does not imply that that system
+ 
+
+ align:start position:0%
+it does not imply that that system
+engineering is always sequential you
+
+ align:start position:0%
+engineering is always sequential you
+ 
+
+ align:start position:0%
+engineering is always sequential you
+know there's it's possible to iterate
+
+ align:start position:0%
+know there's it's possible to iterate
+ 
+
+ align:start position:0%
+know there's it's possible to iterate
+between steps and across the whole v as
+
+ align:start position:0%
+between steps and across the whole v as
+ 
+
+ align:start position:0%
+between steps and across the whole v as
+well um se3 stakeholders and value
+
+ align:start position:0%
+well um se3 stakeholders and value
+ 
+
+ align:start position:0%
+well um se3 stakeholders and value
+Network so this is the uh the role of
+
+ align:start position:0%
+Network so this is the uh the role of
+ 
+
+ align:start position:0%
+Network so this is the uh the role of
+humans uh we talked about this very
+
+ align:start position:0%
+humans uh we talked about this very
+ 
+
+ align:start position:0%
+humans uh we talked about this very
+early on uh several of you talked about
+
+ align:start position:0%
+early on uh several of you talked about
+ 
+
+ align:start position:0%
+early on uh several of you talked about
+it during the oral exams here today you
+
+ align:start position:0%
+it during the oral exams here today you
+ 
+
+ align:start position:0%
+it during the oral exams here today you
+know the Hub and spoke versus the um the
+
+ align:start position:0%
+know the Hub and spoke versus the um the
+ 
+
+ align:start position:0%
+know the Hub and spoke versus the um the
+stakeholder value Network the method
+
+ align:start position:0%
+stakeholder value Network the method
+ 
+
+ align:start position:0%
+stakeholder value Network the method
+underlying this is critical but I do
+
+ align:start position:0%
+underlying this is critical but I do
+ 
+
+ align:start position:0%
+underlying this is critical but I do
+want to mention uh very quickly and this
+
+ align:start position:0%
+want to mention uh very quickly and this
+ 
+
+ align:start position:0%
+want to mention uh very quickly and this
+is something we didn't spend a lot of
+
+ align:start position:0%
+is something we didn't spend a lot of
+ 
+
+ align:start position:0%
+is something we didn't spend a lot of
+time on as human factors right how
+
+ align:start position:0%
+time on as human factors right how
+ 
+
+ align:start position:0%
+time on as human factors right how
+Design Systems so that humans can
+
+ align:start position:0%
+Design Systems so that humans can
+ 
+
+ align:start position:0%
+Design Systems so that humans can
+effectively and safely use them you know
+
+ align:start position:0%
+effectively and safely use them you know
+ 
+
+ align:start position:0%
+effectively and safely use them you know
+interfaces
+
+ align:start position:0%
+interfaces
+ 
+
+ align:start position:0%
+interfaces
+procedures um and and so this is a
+
+ align:start position:0%
+procedures um and and so this is a
+ 
+
+ align:start position:0%
+procedures um and and so this is a
+couple slides from one of my colleagues
+
+ align:start position:0%
+couple slides from one of my colleagues
+ 
+
+ align:start position:0%
+couple slides from one of my colleagues
+Missy Cummings this is actually some uh
+
+ align:start position:0%
+Missy Cummings this is actually some uh
+ 
+
+ align:start position:0%
+Missy Cummings this is actually some uh
+in a nuclear plant Kata you're going to
+
+ align:start position:0%
+in a nuclear plant Kata you're going to
+ 
+
+ align:start position:0%
+in a nuclear plant Kata you're going to
+like this uh lots of these dials and
+
+ align:start position:0%
+like this uh lots of these dials and
+ 
+
+ align:start position:0%
+like this uh lots of these dials and
+this is actually a Russian nuclear plant
+
+ align:start position:0%
+this is actually a Russian nuclear plant
+ 
+
+ align:start position:0%
+this is actually a Russian nuclear plant
+so it has it has a very uh specific
+
+ align:start position:0%
+so it has it has a very uh specific
+ 
+
+ align:start position:0%
+so it has it has a very uh specific
+layout and so the important questions in
+
+ align:start position:0%
+layout and so the important questions in
+ 
+
+ align:start position:0%
+layout and so the important questions in
+human factors are how do you best
+
+ align:start position:0%
+human factors are how do you best
+ 
+
+ align:start position:0%
+human factors are how do you best
+display status information what tasks do
+
+ align:start position:0%
+display status information what tasks do
+ 
+
+ align:start position:0%
+display status information what tasks do
+humans do what tasks what level of
+
+ align:start position:0%
+humans do what tasks what level of
+ 
+
+ align:start position:0%
+humans do what tasks what level of
+automation what are the training
+
+ align:start position:0%
+automation what are the training
+ 
+
+ align:start position:0%
+automation what are the training
+requirements and this is these are also
+
+ align:start position:0%
+requirements and this is these are also
+ 
+
+ align:start position:0%
+requirements and this is these are also
+very important questions and so you can
+
+ align:start position:0%
+very important questions and so you can
+ 
+
+ align:start position:0%
+very important questions and so you can
+apply you know the human systems
+
+ align:start position:0%
+apply you know the human systems
+ 
+
+ align:start position:0%
+apply you know the human systems
+Engineering Process very much uh anal
+
+ align:start position:0%
+Engineering Process very much uh anal
+ 
+
+ align:start position:0%
+Engineering Process very much uh anal
+analogous to what we covered in class so
+
+ align:start position:0%
+analogous to what we covered in class so
+ 
+
+ align:start position:0%
+analogous to what we covered in class so
+far so you do Mission and scenario
+
+ align:start position:0%
+far so you do Mission and scenario
+ 
+
+ align:start position:0%
+far so you do Mission and scenario
+analysis function function allocation
+
+ align:start position:0%
+analysis function function allocation
+ 
+
+ align:start position:0%
+analysis function function allocation
+and then in human factors you talk more
+
+ align:start position:0%
+and then in human factors you talk more
+ 
+
+ align:start position:0%
+and then in human factors you talk more
+about task analysis but essentially
+
+ align:start position:0%
+about task analysis but essentially
+ 
+
+ align:start position:0%
+about task analysis but essentially
+eventually leaves to leads to system
+
+ align:start position:0%
+eventually leaves to leads to system
+ 
+
+ align:start position:0%
+eventually leaves to leads to system
+design like what is the you know what
+
+ align:start position:0%
+design like what is the you know what
+ 
+
+ align:start position:0%
+design like what is the you know what
+are the buttons that you push what does
+
+ align:start position:0%
+are the buttons that you push what does
+ 
+
+ align:start position:0%
+are the buttons that you push what does
+the the layout uh look like or the user
+
+ align:start position:0%
+the the layout uh look like or the user
+ 
+
+ align:start position:0%
+the the layout uh look like or the user
+interface and so forth so you know I'm
+
+ align:start position:0%
+interface and so forth so you know I'm
+ 
+
+ align:start position:0%
+interface and so forth so you know I'm
+not I'm not presenting human factors as
+
+ align:start position:0%
+not I'm not presenting human factors as
+ 
+
+ align:start position:0%
+not I'm not presenting human factors as
+a separate topic but it the human
+
+ align:start position:0%
+a separate topic but it the human
+ 
+
+ align:start position:0%
+a separate topic but it the human
+factors requirements should be built in
+
+ align:start position:0%
+factors requirements should be built in
+ 
+
+ align:start position:0%
+factors requirements should be built in
+right from the
+
+ align:start position:0%
+right from the
+ 
+
+ align:start position:0%
+right from the
+start and uh essentially functional
+
+ align:start position:0%
+start and uh essentially functional
+ 
+
+ align:start position:0%
+start and uh essentially functional
+allocation is sort of the key question
+
+ align:start position:0%
+allocation is sort of the key question
+ 
+
+ align:start position:0%
+allocation is sort of the key question
+here how much is done by automation how
+
+ align:start position:0%
+here how much is done by automation how
+ 
+
+ align:start position:0%
+here how much is done by automation how
+much is done by humans and how do you
+
+ align:start position:0%
+much is done by humans and how do you
+ 
+
+ align:start position:0%
+much is done by humans and how do you
+split between the two and one of the
+
+ align:start position:0%
+split between the two and one of the
+ 
+
+ align:start position:0%
+split between the two and one of the
+most important things to consider here
+
+ align:start position:0%
+most important things to consider here
+ 
+
+ align:start position:0%
+most important things to consider here
+is this Human Performance curve and and
+
+ align:start position:0%
+is this Human Performance curve and and
+ 
+
+ align:start position:0%
+is this Human Performance curve and and
+we know this pretty well now that when
+
+ align:start position:0%
+we know this pretty well now that when
+ 
+
+ align:start position:0%
+we know this pretty well now that when
+humans are extremely highly loaded you
+
+ align:start position:0%
+humans are extremely highly loaded you
+ 
+
+ align:start position:0%
+humans are extremely highly loaded you
+know you have a huge uh workload you
+
+ align:start position:0%
+know you have a huge uh workload you
+ 
+
+ align:start position:0%
+know you have a huge uh workload you
+your performance goes down but
+
+ align:start position:0%
+your performance goes down but
+ 
+
+ align:start position:0%
+your performance goes down but
+interestingly if you're if you're under
+
+ align:start position:0%
+interestingly if you're if you're under
+ 
+
+ align:start position:0%
+interestingly if you're if you're under
+challenged your performance goes down as
+
+ align:start position:0%
+challenged your performance goes down as
+ 
+
+ align:start position:0%
+challenged your performance goes down as
+well and you know so for example people
+
+ align:start position:0%
+well and you know so for example people
+ 
+
+ align:start position:0%
+well and you know so for example people
+that are in power stations or you know
+
+ align:start position:0%
+that are in power stations or you know
+ 
+
+ align:start position:0%
+that are in power stations or you know
+mission control centers where nothing is
+
+ align:start position:0%
+mission control centers where nothing is
+ 
+
+ align:start position:0%
+mission control centers where nothing is
+happening for days and weeks you know
+
+ align:start position:0%
+happening for days and weeks you know
+ 
+
+ align:start position:0%
+happening for days and weeks you know
+they their attention goes down and they
+
+ align:start position:0%
+they their attention goes down and they
+ 
+
+ align:start position:0%
+they their attention goes down and they
+don't perform at their high level humans
+
+ align:start position:0%
+don't perform at their high level humans
+ 
+
+ align:start position:0%
+don't perform at their high level humans
+perform best at a moderate workload and
+
+ align:start position:0%
+perform best at a moderate workload and
+ 
+
+ align:start position:0%
+perform best at a moderate workload and
+and this is well known and it should
+
+ align:start position:0%
+and this is well known and it should
+ 
+
+ align:start position:0%
+and this is well known and it should
+influence how you design the human
+
+ align:start position:0%
+influence how you design the human
+ 
+
+ align:start position:0%
+influence how you design the human
+interface and the split among Automation
+
+ align:start position:0%
+interface and the split among Automation
+ 
+
+ align:start position:0%
+interface and the split among Automation
+and humans um se4 system complexity last
+
+ align:start position:0%
+and humans um se4 system complexity last
+ 
+
+ align:start position:0%
+and humans um se4 system complexity last
+time I will mention the magic number
+
+ align:start position:0%
+time I will mention the magic number
+ 
+
+ align:start position:0%
+time I will mention the magic number
+seven plus or minus two the the real
+
+ align:start position:0%
+seven plus or minus two the the real
+ 
+
+ align:start position:0%
+seven plus or minus two the the real
+limitations come in when we operate at
+
+ align:start position:0%
+limitations come in when we operate at
+ 
+
+ align:start position:0%
+limitations come in when we operate at
+levels you know three four five and six
+
+ align:start position:0%
+levels you know three four five and six
+ 
+
+ align:start position:0%
+levels you know three four five and six
+and the main reason for this is because
+
+ align:start position:0%
+and the main reason for this is because
+ 
+
+ align:start position:0%
+and the main reason for this is because
+now a single human cannot understand
+
+ align:start position:0%
+now a single human cannot understand
+ 
+
+ align:start position:0%
+now a single human cannot understand
+cannot remember cannot deal with all the
+
+ align:start position:0%
+cannot remember cannot deal with all the
+ 
+
+ align:start position:0%
+cannot remember cannot deal with all the
+detailed components and you need to
+
+ align:start position:0%
+detailed components and you need to
+ 
+
+ align:start position:0%
+detailed components and you need to
+split the work among teams among organiz
+
+ align:start position:0%
+split the work among teams among organiz
+ 
+
+ align:start position:0%
+split the work among teams among organiz
+ganizations and that creates extra
+
+ align:start position:0%
+ganizations and that creates extra
+ 
+
+ align:start position:0%
+ganizations and that creates extra
+interfaces and
+
+ align:start position:0%
+interfaces and
+ 
+
+ align:start position:0%
+interfaces and
+complexities okay and just to show you
+
+ align:start position:0%
+complexities okay and just to show you
+ 
+
+ align:start position:0%
+complexities okay and just to show you
+you know iridium we talked about iridium
+
+ align:start position:0%
+you know iridium we talked about iridium
+ 
+
+ align:start position:0%
+you know iridium we talked about iridium
+this is a very recent news story this is
+
+ align:start position:0%
+this is a very recent news story this is
+ 
+
+ align:start position:0%
+this is a very recent news story this is
+from October 29th the new iridium next
+
+ align:start position:0%
+from October 29th the new iridium next
+ 
+
+ align:start position:0%
+from October 29th the new iridium next
+has again been pushed back by four
+
+ align:start position:0%
+has again been pushed back by four
+ 
+
+ align:start position:0%
+has again been pushed back by four
+months uh this gentleman here is the uh
+
+ align:start position:0%
+months uh this gentleman here is the uh
+ 
+
+ align:start position:0%
+months uh this gentleman here is the uh
+CEO of the Iridium chief executive for
+
+ align:start position:0%
+CEO of the Iridium chief executive for
+ 
+
+ align:start position:0%
+CEO of the Iridium chief executive for
+iridium next Mr Dash and you know he's
+
+ align:start position:0%
+iridium next Mr Dash and you know he's
+ 
+
+ align:start position:0%
+iridium next Mr Dash and you know he's
+talking here about a particular
+
+ align:start position:0%
+talking here about a particular
+ 
+
+ align:start position:0%
+talking here about a particular
+particular Talis alenia and then ViaSat
+
+ align:start position:0%
+particular Talis alenia and then ViaSat
+ 
+
+ align:start position:0%
+particular Talis alenia and then ViaSat
+is one of the contractors there's a
+
+ align:start position:0%
+is one of the contractors there's a
+ 
+
+ align:start position:0%
+is one of the contractors there's a
+particular component that's been giving
+
+ align:start position:0%
+particular component that's been giving
+ 
+
+ align:start position:0%
+particular component that's been giving
+trouble uh and that's sort of in level
+
+ align:start position:0%
+trouble uh and that's sort of in level
+ 
+
+ align:start position:0%
+trouble uh and that's sort of in level
+three or four in the in the hierarchy
+
+ align:start position:0%
+three or four in the in the hierarchy
+ 
+
+ align:start position:0%
+three or four in the in the hierarchy
+and that's essentially delaying the
+
+ align:start position:0%
+and that's essentially delaying the
+ 
+
+ align:start position:0%
+and that's essentially delaying the
+whole system so there's there's an
+
+ align:start position:0%
+whole system so there's there's an
+ 
+
+ align:start position:0%
+whole system so there's there's an
+example of how you know the large
+
+ align:start position:0%
+example of how you know the large
+ 
+
+ align:start position:0%
+example of how you know the large
+complexity of the system is is uh is
+
+ align:start position:0%
+complexity of the system is is uh is
+ 
+
+ align:start position:0%
+complexity of the system is is uh is
+causing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issues but they are they are actually a
+
+ align:start position:0%
+issues but they are they are actually a
+ 
+
+ align:start position:0%
+issues but they are they are actually a
+plier to Talis alenia through the
+
+ align:start position:0%
+plier to Talis alenia through the
+ 
+
+ align:start position:0%
+plier to Talis alenia through the
+through the the whole chain right oh
+
+ align:start position:0%
+through the the whole chain right oh
+ 
+
+ align:start position:0%
+through the the whole chain right oh
+you're saying there's more going on than
+
+ align:start position:0%
+you're saying there's more going on than
+ 
+
+ align:start position:0%
+you're saying there's more going on than
+meets the eye yeah who knows who knows
+
+ align:start position:0%
+meets the eye yeah who knows who knows
+ 
+
+ align:start position:0%
+meets the eye yeah who knows who knows
+um okay and then finally here I want to
+
+ align:start position:0%
+um okay and then finally here I want to
+ 
+
+ align:start position:0%
+um okay and then finally here I want to
+mention uh application to a case study
+
+ align:start position:0%
+mention uh application to a case study
+ 
+
+ align:start position:0%
+mention uh application to a case study
+you know we used the canat 2016
+
+ align:start position:0%
+you know we used the canat 2016
+ 
+
+ align:start position:0%
+you know we used the canat 2016
+competition as a quote endquote safe
+
+ align:start position:0%
+competition as a quote endquote safe
+ 
+
+ align:start position:0%
+competition as a quote endquote safe
+case study uh and I have to say I'm
+
+ align:start position:0%
+case study uh and I have to say I'm
+ 
+
+ align:start position:0%
+case study uh and I have to say I'm
+really pleased with with uh how this
+
+ align:start position:0%
+really pleased with with uh how this
+ 
+
+ align:start position:0%
+really pleased with with uh how this
+worked out you had the 47 requirements
+
+ align:start position:0%
+worked out you had the 47 requirements
+ 
+
+ align:start position:0%
+worked out you had the 47 requirements
+as a starter uh you improved them you
+
+ align:start position:0%
+as a starter uh you improved them you
+ 
+
+ align:start position:0%
+as a starter uh you improved them you
+group them uh and my comments about the
+
+ align:start position:0%
+group them uh and my comments about the
+ 
+
+ align:start position:0%
+group them uh and my comments about the
+pdrs that we had a week ago are you know
+
+ align:start position:0%
+pdrs that we had a week ago are you know
+ 
+
+ align:start position:0%
+pdrs that we had a week ago are you know
+all P all teams passed successfully the
+
+ align:start position:0%
+all P all teams passed successfully the
+ 
+
+ align:start position:0%
+all P all teams passed successfully the
+PDR you know if this was a real PDR we
+
+ align:start position:0%
+PDR you know if this was a real PDR we
+ 
+
+ align:start position:0%
+PDR you know if this was a real PDR we
+would have issued a couple rids I think
+
+ align:start position:0%
+would have issued a couple rids I think
+ 
+
+ align:start position:0%
+would have issued a couple rids I think
+there were some couple of teams were
+
+ align:start position:0%
+there were some couple of teams were
+ 
+
+ align:start position:0%
+there were some couple of teams were
+over budget or needed to work out their
+
+ align:start position:0%
+over budget or needed to work out their
+ 
+
+ align:start position:0%
+over budget or needed to work out their
+aerodynamics in more detail but by and
+
+ align:start position:0%
+aerodynamics in more detail but by and
+ 
+
+ align:start position:0%
+aerodynamics in more detail but by and
+large I thought this was an excellent
+
+ align:start position:0%
+large I thought this was an excellent
+ 
+
+ align:start position:0%
+large I thought this was an excellent
+application of system engineering
+
+ align:start position:0%
+application of system engineering
+ 
+
+ align:start position:0%
+application of system engineering
+concept went beyond my expectations um
+
+ align:start position:0%
+concept went beyond my expectations um
+ 
+
+ align:start position:0%
+concept went beyond my expectations um
+several of you mentioned the importance
+
+ align:start position:0%
+several of you mentioned the importance
+ 
+
+ align:start position:0%
+several of you mentioned the importance
+of concept generation you know hybrid
+
+ align:start position:0%
+of concept generation you know hybrid
+ 
+
+ align:start position:0%
+of concept generation you know hybrid
+use of structured and unstructured
+
+ align:start position:0%
+use of structured and unstructured
+ 
+
+ align:start position:0%
+use of structured and unstructured
+creativity techniques uh I know at least
+
+ align:start position:0%
+creativity techniques uh I know at least
+ 
+
+ align:start position:0%
+creativity techniques uh I know at least
+one team applied to actually go to the
+
+ align:start position:0%
+one team applied to actually go to the
+ 
+
+ align:start position:0%
+one team applied to actually go to the
+competition and this shows you a couple
+
+ align:start position:0%
+competition and this shows you a couple
+ 
+
+ align:start position:0%
+competition and this shows you a couple
+examples so we had one team here at epfl
+
+ align:start position:0%
+examples so we had one team here at epfl
+ 
+
+ align:start position:0%
+examples so we had one team here at epfl
+using a bio inspirate design uh this is
+
+ align:start position:0%
+using a bio inspirate design uh this is
+ 
+
+ align:start position:0%
+using a bio inspirate design uh this is
+an actual seed uh air foil that actually
+
+ align:start position:0%
+an actual seed uh air foil that actually
+ 
+
+ align:start position:0%
+an actual seed uh air foil that actually
+occurs in nature and then uh here's an
+
+ align:start position:0%
+occurs in nature and then uh here's an
+ 
+
+ align:start position:0%
+occurs in nature and then uh here's an
+example from MIT the ralo wing team 7 so
+
+ align:start position:0%
+example from MIT the ralo wing team 7 so
+ 
+
+ align:start position:0%
+example from MIT the ralo wing team 7 so
+um I'm sorry I didn't mention all the
+
+ align:start position:0%
+um I'm sorry I didn't mention all the
+ 
+
+ align:start position:0%
+um I'm sorry I didn't mention all the
+teams here but it was really great to
+
+ align:start position:0%
+teams here but it was really great to
+ 
+
+ align:start position:0%
+teams here but it was really great to
+see um the application of this in the
+
+ align:start position:0%
+see um the application of this in the
+ 
+
+ align:start position:0%
+see um the application of this in the
+canet um competition case so uh the last
+
+ align:start position:0%
+canet um competition case so uh the last
+ 
+
+ align:start position:0%
+canet um competition case so uh the last
+thing I want to do and I only have one
+
+ align:start position:0%
+thing I want to do and I only have one
+ 
+
+ align:start position:0%
+thing I want to do and I only have one
+minute left actually I'm already
+
+ align:start position:0%
+minute left actually I'm already
+ 
+
+ align:start position:0%
+minute left actually I'm already
+slightly over time but I just want to
+
+ align:start position:0%
+slightly over time but I just want to
+ 
+
+ align:start position:0%
+slightly over time but I just want to
+give you some career and study
+
+ align:start position:0%
+give you some career and study
+ 
+
+ align:start position:0%
+give you some career and study
+recommendations so first of all you know
+
+ align:start position:0%
+recommendations so first of all you know
+ 
+
+ align:start position:0%
+recommendations so first of all you know
+uh I want to make sure that you knew and
+
+ align:start position:0%
+uh I want to make sure that you knew and
+ 
+
+ align:start position:0%
+uh I want to make sure that you knew and
+I said this in the first lecture this is
+
+ align:start position:0%
+I said this in the first lecture this is
+ 
+
+ align:start position:0%
+I said this in the first lecture this is
+there's a lot more to system engineering
+
+ align:start position:0%
+there's a lot more to system engineering
+ 
+
+ align:start position:0%
+there's a lot more to system engineering
+um and systems research than we were
+
+ align:start position:0%
+um and systems research than we were
+ 
+
+ align:start position:0%
+um and systems research than we were
+able to cover in this class so this
+
+ align:start position:0%
+able to cover in this class so this
+ 
+
+ align:start position:0%
+able to cover in this class so this
+class is really what I call a door
+
+ align:start position:0%
+class is really what I call a door
+ 
+
+ align:start position:0%
+class is really what I call a door
+opener to the world of system
+
+ align:start position:0%
+opener to the world of system
+ 
+
+ align:start position:0%
+opener to the world of system
+engineering if you want to go deeper
+
+ align:start position:0%
+engineering if you want to go deeper
+ 
+
+ align:start position:0%
+engineering if you want to go deeper
+there are deeper subjects um you know
+
+ align:start position:0%
+there are deeper subjects um you know
+ 
+
+ align:start position:0%
+there are deeper subjects um you know
+modelbased system engineering is a big
+
+ align:start position:0%
+modelbased system engineering is a big
+ 
+
+ align:start position:0%
+modelbased system engineering is a big
+Trend system safety and then in the
+
+ align:start position:0%
+Trend system safety and then in the
+ 
+
+ align:start position:0%
+Trend system safety and then in the
+spring I'm teaching a class uh called
+
+ align:start position:0%
+spring I'm teaching a class uh called
+ 
+
+ align:start position:0%
+spring I'm teaching a class uh called
+multi-disciplinary system optimization
+
+ align:start position:0%
+multi-disciplinary system optimization
+ 
+
+ align:start position:0%
+multi-disciplinary system optimization
+and it there is actually a WebEx uh
+
+ align:start position:0%
+and it there is actually a WebEx uh
+ 
+
+ align:start position:0%
+and it there is actually a WebEx uh
+access to it as well so it's not going
+
+ align:start position:0%
+access to it as well so it's not going
+ 
+
+ align:start position:0%
+access to it as well so it's not going
+to be officially offered as an epfl
+
+ align:start position:0%
+to be officially offered as an epfl
+ 
+
+ align:start position:0%
+to be officially offered as an epfl
+class but if individual students here
+
+ align:start position:0%
+class but if individual students here
+ 
+
+ align:start position:0%
+class but if individual students here
+are interested please contact me
+
+ align:start position:0%
+are interested please contact me
+ 
+
+ align:start position:0%
+are interested please contact me
+self-study you know there's system
+
+ align:start position:0%
+self-study you know there's system
+ 
+
+ align:start position:0%
+self-study you know there's system
+engineering Journal there's i e journals
+
+ align:start position:0%
+engineering Journal there's i e journals
+ 
+
+ align:start position:0%
+engineering Journal there's i e journals
+there's also you know for some of you
+
+ align:start position:0%
+there's also you know for some of you
+ 
+
+ align:start position:0%
+there's also you know for some of you
+this is maybe a little too soon but uh
+
+ align:start position:0%
+this is maybe a little too soon but uh
+ 
+
+ align:start position:0%
+this is maybe a little too soon but uh
+there's there's professional degrees in
+
+ align:start position:0%
+there's there's professional degrees in
+ 
+
+ align:start position:0%
+there's there's professional degrees in
+system engineering um for example at MIT
+
+ align:start position:0%
+system engineering um for example at MIT
+ 
+
+ align:start position:0%
+system engineering um for example at MIT
+we have the SDM program system design
+
+ align:start position:0%
+we have the SDM program system design
+ 
+
+ align:start position:0%
+we have the SDM program system design
+and management the average age of the
+
+ align:start position:0%
+and management the average age of the
+ 
+
+ align:start position:0%
+and management the average age of the
+students in that program is
+
+ align:start position:0%
+students in that program is
+ 
+
+ align:start position:0%
+students in that program is
+33 uh but it is um you know they're sort
+
+ align:start position:0%
+33 uh but it is um you know they're sort
+ 
+
+ align:start position:0%
+33 uh but it is um you know they're sort
+of coming back to get their masters in
+
+ align:start position:0%
+of coming back to get their masters in
+ 
+
+ align:start position:0%
+of coming back to get their masters in
+system design and management uh and
+
+ align:start position:0%
+system design and management uh and
+ 
+
+ align:start position:0%
+system design and management uh and
+there quite a bit of slown content as
+
+ align:start position:0%
+there quite a bit of slown content as
+ 
+
+ align:start position:0%
+there quite a bit of slown content as
+well so Finance you know understanding
+
+ align:start position:0%
+well so Finance you know understanding
+ 
+
+ align:start position:0%
+well so Finance you know understanding
+the financial how to build a business
+
+ align:start position:0%
+the financial how to build a business
+ 
+
+ align:start position:0%
+the financial how to build a business
+case around systems as well uh
+
+ align:start position:0%
+case around systems as well uh
+ 
+
+ align:start position:0%
+case around systems as well uh
+professional experience you know getting
+
+ align:start position:0%
+professional experience you know getting
+ 
+
+ align:start position:0%
+professional experience you know getting
+experience on actual projects like at
+
+ align:start position:0%
+experience on actual projects like at
+ 
+
+ align:start position:0%
+experience on actual projects like at
+MIT for example rexus you know you got
+
+ align:start position:0%
+MIT for example rexus you know you got
+ 
+
+ align:start position:0%
+MIT for example rexus you know you got
+the clean space one project we heard
+
+ align:start position:0%
+the clean space one project we heard
+ 
+
+ align:start position:0%
+the clean space one project we heard
+about octanus one solar impulse there
+
+ align:start position:0%
+about octanus one solar impulse there
+ 
+
+ align:start position:0%
+about octanus one solar impulse there
+are a lot of opportunities or and we
+
+ align:start position:0%
+are a lot of opportunities or and we
+ 
+
+ align:start position:0%
+are a lot of opportunities or and we
+also had a couple of uh people here
+
+ align:start position:0%
+also had a couple of uh people here
+ 
+
+ align:start position:0%
+also had a couple of uh people here
+mention that you're starting your own
+
+ align:start position:0%
+mention that you're starting your own
+ 
+
+ align:start position:0%
+mention that you're starting your own
+company your own Venture and you know
+
+ align:start position:0%
+company your own Venture and you know
+ 
+
+ align:start position:0%
+company your own Venture and you know
+when you're doing that you you have to
+
+ align:start position:0%
+when you're doing that you you have to
+ 
+
+ align:start position:0%
+when you're doing that you you have to
+be the system system engineer you have
+
+ align:start position:0%
+be the system system engineer you have
+ 
+
+ align:start position:0%
+be the system system engineer you have
+to understand all of these things
+
+ align:start position:0%
+to understand all of these things
+ 
+
+ align:start position:0%
+to understand all of these things
+interfaces suppliers requirements
+
+ align:start position:0%
+interfaces suppliers requirements
+ 
+
+ align:start position:0%
+interfaces suppliers requirements
+markets all that has to be integrated
+
+ align:start position:0%
+markets all that has to be integrated
+ 
+
+ align:start position:0%
+markets all that has to be integrated
+finally um you did hear about en cozy we
+
+ align:start position:0%
+finally um you did hear about en cozy we
+ 
+
+ align:start position:0%
+finally um you did hear about en cozy we
+had a quick dial in with them at an
+
+ align:start position:0%
+had a quick dial in with them at an
+ 
+
+ align:start position:0%
+had a quick dial in with them at an
+earlier session so if you're interested
+
+ align:start position:0%
+earlier session so if you're interested
+ 
+
+ align:start position:0%
+earlier session so if you're interested
+you can join either as a student or
+
+ align:start position:0%
+you can join either as a student or
+ 
+
+ align:start position:0%
+you can join either as a student or
+professional member and also
+
+ align:start position:0%
+professional member and also
+ 
+
+ align:start position:0%
+professional member and also
+certification this class was not
+
+ align:start position:0%
+certification this class was not
+ 
+
+ align:start position:0%
+certification this class was not
+spefically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a for that but if you're interested in
+
+ align:start position:0%
+a for that but if you're interested in
+ 
+
+ align:start position:0%
+a for that but if you're interested in
+this either have enough number of years
+
+ align:start position:0%
+this either have enough number of years
+ 
+
+ align:start position:0%
+this either have enough number of years
+of experience at the cep level and then
+
+ align:start position:0%
+of experience at the cep level and then
+ 
+
+ align:start position:0%
+of experience at the cep level and then
+finally please keep in touch and last
+
+ align:start position:0%
+finally please keep in touch and last
+ 
+
+ align:start position:0%
+finally please keep in touch and last
+but not least I want to thank all of you
+
+ align:start position:0%
+but not least I want to thank all of you
+ 
+
+ align:start position:0%
+but not least I want to thank all of you
+um the students at MIT at epfl our Tas
+
+ align:start position:0%
+um the students at MIT at epfl our Tas
+ 
+
+ align:start position:0%
+um the students at MIT at epfl our Tas
+uh le le Lou here at epfl Yana at MIT uh
+
+ align:start position:0%
+uh le le Lou here at epfl Yana at MIT uh
+ 
+
+ align:start position:0%
+uh le le Lou here at epfl Yana at MIT uh
+the technical staff who's been helping
+
+ align:start position:0%
+the technical staff who's been helping
+ 
+
+ align:start position:0%
+the technical staff who's been helping
+um you know run the technology uh vulker
+
+ align:start position:0%
+um you know run the technology uh vulker
+ 
+
+ align:start position:0%
+um you know run the technology uh vulker
+uh thank you and um and that's it so I
+
+ align:start position:0%
+uh thank you and um and that's it so I
+ 
+
+ align:start position:0%
+uh thank you and um and that's it so I
+want to thank all of you uh next week we
+
+ align:start position:0%
+want to thank all of you uh next week we
+ 
+
+ align:start position:0%
+want to thank all of you uh next week we
+do have a voluntary seminar on sort of
+
+ align:start position:0%
+do have a voluntary seminar on sort of
+ 
+
+ align:start position:0%
+do have a voluntary seminar on sort of
+future Trends and Manufacturing uh but
+
+ align:start position:0%
+future Trends and Manufacturing uh but
+ 
+
+ align:start position:0%
+future Trends and Manufacturing uh but
+again it's not mandatory uh it's going
+
+ align:start position:0%
+again it's not mandatory uh it's going
+ 
+
+ align:start position:0%
+again it's not mandatory uh it's going
+to be in the same place but it's like I
+
+ align:start position:0%
+to be in the same place but it's like I
+ 
+
+ align:start position:0%
+to be in the same place but it's like I
+said not part of the official class so
+
+ align:start position:0%
+said not part of the official class so
+ 
+
+ align:start position:0%
+said not part of the official class so
+with that sorry for running a little bit
+
+ align:start position:0%
+with that sorry for running a little bit
+ 
+
+ align:start position:0%
+with that sorry for running a little bit
+over time but um it's been really a joy
+
+ align:start position:0%
+over time but um it's been really a joy
+ 
+
+ align:start position:0%
+over time but um it's been really a joy
+to to teach this class in this kind of
+
+ align:start position:0%
+to to teach this class in this kind of
+ 
+
+ align:start position:0%
+to to teach this class in this kind of
+new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+format e
\ No newline at end of file
diff --git a/bf5IWKhSWRo.txt b/bf5IWKhSWRo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e57a99098e22e438924363a05f72bb9194ba96e9
--- /dev/null
+++ b/bf5IWKhSWRo.txt
@@ -0,0 +1,14059 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so like we're here but don't
+
+ align:start position:0%
+ocw.mit.edu so like we're here but don't
+ 
+
+ align:start position:0%
+ocw.mit.edu so like we're here but don't
+forget about you know this
+
+ align:start position:0%
+forget about you know this
+ 
+
+ align:start position:0%
+forget about you know this
+and so the quiz is next Thursday uh I'm
+
+ align:start position:0%
+and so the quiz is next Thursday uh I'm
+ 
+
+ align:start position:0%
+and so the quiz is next Thursday uh I'm
+going to I'm going to send an email out
+
+ align:start position:0%
+going to I'm going to send an email out
+ 
+
+ align:start position:0%
+going to I'm going to send an email out
+with office
+
+ align:start position:0%
+with office
+ 
+
+ align:start position:0%
+with office
+hours uh uh for for that for you know
+
+ align:start position:0%
+hours uh uh for for that for you know
+ 
+
+ align:start position:0%
+hours uh uh for for that for you know
+extra time but if anyone wants to meet
+
+ align:start position:0%
+extra time but if anyone wants to meet
+ 
+
+ align:start position:0%
+extra time but if anyone wants to meet
+anytime just send me an email please
+
+ align:start position:0%
+anytime just send me an email please
+ 
+
+ align:start position:0%
+anytime just send me an email please
+okay this pet 2 we decided is going to
+
+ align:start position:0%
+okay this pet 2 we decided is going to
+ 
+
+ align:start position:0%
+okay this pet 2 we decided is going to
+be due uh the day before on May 9th and
+
+ align:start position:0%
+be due uh the day before on May 9th and
+ 
+
+ align:start position:0%
+be due uh the day before on May 9th and
+that's when your pet 3 will be posted as
+
+ align:start position:0%
+that's when your pet 3 will be posted as
+ 
+
+ align:start position:0%
+that's when your pet 3 will be posted as
+well okay and P set 3 will have to do
+
+ align:start position:0%
+well okay and P set 3 will have to do
+ 
+
+ align:start position:0%
+well okay and P set 3 will have to do
+with the things we we've been talking
+
+ align:start position:0%
+with the things we we've been talking
+ 
+
+ align:start position:0%
+with the things we we've been talking
+about uh the last last you know two
+
+ align:start position:0%
+about uh the last last you know two
+ 
+
+ align:start position:0%
+about uh the last last you know two
+lectures and today which is you know
+
+ align:start position:0%
+lectures and today which is you know
+ 
+
+ align:start position:0%
+lectures and today which is you know
+what what you can do with solids okay um
+
+ align:start position:0%
+what what you can do with solids okay um
+ 
+
+ align:start position:0%
+what what you can do with solids okay um
+any questions about the plan the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+schedule
+
+ align:start position:0%
+schedule
+ 
+
+ align:start position:0%
+schedule
+okay right now
+
+ align:start position:0%
+okay right now
+ 
+
+ align:start position:0%
+okay right now
+um now there are other practice problems
+
+ align:start position:0%
+um now there are other practice problems
+ 
+
+ align:start position:0%
+um now there are other practice problems
+um I'll do I'll throw one out from last
+
+ align:start position:0%
+um I'll do I'll throw one out from last
+ 
+
+ align:start position:0%
+um I'll do I'll throw one out from last
+year's quiz so that that's a practice
+
+ align:start position:0%
+year's quiz so that that's a practice
+ 
+
+ align:start position:0%
+year's quiz so that that's a practice
+quiz from uh that I I gave out you know
+
+ align:start position:0%
+quiz from uh that I I gave out you know
+ 
+
+ align:start position:0%
+quiz from uh that I I gave out you know
+a couple maybe a year ago or two um and
+
+ align:start position:0%
+a couple maybe a year ago or two um and
+ 
+
+ align:start position:0%
+a couple maybe a year ago or two um and
+then there's last year's quiz and I'll
+
+ align:start position:0%
+then there's last year's quiz and I'll
+ 
+
+ align:start position:0%
+then there's last year's quiz and I'll
+pull a problem or two out from that and
+
+ align:start position:0%
+pull a problem or two out from that and
+ 
+
+ align:start position:0%
+pull a problem or two out from that and
+and we'll do one today and then maybe
+
+ align:start position:0%
+and we'll do one today and then maybe
+ 
+
+ align:start position:0%
+and we'll do one today and then maybe
+we'll look at another one on Tuesday
+
+ align:start position:0%
+we'll look at another one on Tuesday
+ 
+
+ align:start position:0%
+we'll look at another one on Tuesday
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh what I want to cover in terms of the
+
+ align:start position:0%
+uh what I want to cover in terms of the
+ 
+
+ align:start position:0%
+uh what I want to cover in terms of the
+lecture material today is I want to kind
+
+ align:start position:0%
+lecture material today is I want to kind
+ 
+
+ align:start position:0%
+lecture material today is I want to kind
+of briefly start with that band
+
+ align:start position:0%
+of briefly start with that band
+ 
+
+ align:start position:0%
+of briefly start with that band
+structure and kpace and make sure we're
+
+ align:start position:0%
+structure and kpace and make sure we're
+ 
+
+ align:start position:0%
+structure and kpace and make sure we're
+feeling good about it okay and then um
+
+ align:start position:0%
+feeling good about it okay and then um
+ 
+
+ align:start position:0%
+feeling good about it okay and then um
+tell you sort of a few other things you
+
+ align:start position:0%
+tell you sort of a few other things you
+ 
+
+ align:start position:0%
+tell you sort of a few other things you
+can do right we've talked about the band
+
+ align:start position:0%
+can do right we've talked about the band
+ 
+
+ align:start position:0%
+can do right we've talked about the band
+structure we've talked about how um it
+
+ align:start position:0%
+structure we've talked about how um it
+ 
+
+ align:start position:0%
+structure we've talked about how um it
+it has so much information well what
+
+ align:start position:0%
+it has so much information well what
+ 
+
+ align:start position:0%
+it has so much information well what
+other kinds of information is there what
+
+ align:start position:0%
+other kinds of information is there what
+ 
+
+ align:start position:0%
+other kinds of information is there what
+can you do with these sorts of
+
+ align:start position:0%
+can you do with these sorts of
+ 
+
+ align:start position:0%
+can you do with these sorts of
+properties um of solids um we're we're
+
+ align:start position:0%
+properties um of solids um we're we're
+ 
+
+ align:start position:0%
+properties um of solids um we're we're
+not going to you know this is I love
+
+ align:start position:0%
+not going to you know this is I love
+ 
+
+ align:start position:0%
+not going to you know this is I love
+this cartoon at some point his theory
+
+ align:start position:0%
+this cartoon at some point his theory
+ 
+
+ align:start position:0%
+this cartoon at some point his theory
+becomes so abstract it can only be
+
+ align:start position:0%
+becomes so abstract it can only be
+ 
+
+ align:start position:0%
+becomes so abstract it can only be
+conveyed using interpretive dance and
+
+ align:start position:0%
+conveyed using interpretive dance and
+ 
+
+ align:start position:0%
+conveyed using interpretive dance and
+mostly it's because of the visuals that
+
+ align:start position:0%
+mostly it's because of the visuals that
+ 
+
+ align:start position:0%
+mostly it's because of the visuals that
+I get on on my colleagues here at MIT
+
+ align:start position:0%
+I get on on my colleagues here at MIT
+ 
+
+ align:start position:0%
+I get on on my colleagues here at MIT
+kind of just dancing but um
+
+ align:start position:0%
+kind of just dancing but um
+ 
+
+ align:start position:0%
+kind of just dancing but um
+but I you know we're not going to get
+
+ align:start position:0%
+but I you know we're not going to get
+ 
+
+ align:start position:0%
+but I you know we're not going to get
+this complicated right so the point
+
+ align:start position:0%
+this complicated right so the point
+ 
+
+ align:start position:0%
+this complicated right so the point
+isn't for me to do a lecture on
+
+ align:start position:0%
+isn't for me to do a lecture on
+ 
+
+ align:start position:0%
+isn't for me to do a lecture on
+transport Theory and and tell you you
+
+ align:start position:0%
+transport Theory and and tell you you
+ 
+
+ align:start position:0%
+transport Theory and and tell you you
+know uh all about phonons and go into
+
+ align:start position:0%
+know uh all about phonons and go into
+ 
+
+ align:start position:0%
+know uh all about phonons and go into
+great detail about these different
+
+ align:start position:0%
+great detail about these different
+ 
+
+ align:start position:0%
+great detail about these different
+things that is again not been our Point
+
+ align:start position:0%
+things that is again not been our Point
+ 
+
+ align:start position:0%
+things that is again not been our Point
+here the point is uh to keep relevant
+
+ align:start position:0%
+here the point is uh to keep relevant
+ 
+
+ align:start position:0%
+here the point is uh to keep relevant
+and keep pretty applied in in this in
+
+ align:start position:0%
+and keep pretty applied in in this in
+ 
+
+ align:start position:0%
+and keep pretty applied in in this in
+this class so so I'm you know I'm going
+
+ align:start position:0%
+this class so so I'm you know I'm going
+ 
+
+ align:start position:0%
+this class so so I'm you know I'm going
+to give you sort of just a little hint
+
+ align:start position:0%
+to give you sort of just a little hint
+ 
+
+ align:start position:0%
+to give you sort of just a little hint
+as to what you can do uh with the Doss
+
+ align:start position:0%
+as to what you can do uh with the Doss
+ 
+
+ align:start position:0%
+as to what you can do uh with the Doss
+and the band structure um but we're not
+
+ align:start position:0%
+and the band structure um but we're not
+ 
+
+ align:start position:0%
+and the band structure um but we're not
+going to go into great detail but you
+
+ align:start position:0%
+going to go into great detail but you
+ 
+
+ align:start position:0%
+going to go into great detail but you
+can find those details in many places
+
+ align:start position:0%
+can find those details in many places
+ 
+
+ align:start position:0%
+can find those details in many places
+online and in books and if you come to
+
+ align:start position:0%
+online and in books and if you come to
+ 
+
+ align:start position:0%
+online and in books and if you come to
+me I'm happy to talk about these
+
+ align:start position:0%
+me I'm happy to talk about these
+ 
+
+ align:start position:0%
+me I'm happy to talk about these
+Concepts that we'll talk about So the
+
+ align:start position:0%
+Concepts that we'll talk about So the
+ 
+
+ align:start position:0%
+Concepts that we'll talk about So the
+plan So the plan is we're going to do a
+
+ align:start position:0%
+plan So the plan is we're going to do a
+ 
+
+ align:start position:0%
+plan So the plan is we're going to do a
+little bit of review Cas Bas feeling
+
+ align:start position:0%
+little bit of review Cas Bas feeling
+ 
+
+ align:start position:0%
+little bit of review Cas Bas feeling
+good about Oneness all that and then I
+
+ align:start position:0%
+good about Oneness all that and then I
+ 
+
+ align:start position:0%
+good about Oneness all that and then I
+want to um show you that um that problem
+
+ align:start position:0%
+want to um show you that um that problem
+ 
+
+ align:start position:0%
+want to um show you that um that problem
+we'll talk about just one band structure
+
+ align:start position:0%
+we'll talk about just one band structure
+ 
+
+ align:start position:0%
+we'll talk about just one band structure
+problem that I happened to give last
+
+ align:start position:0%
+problem that I happened to give last
+ 
+
+ align:start position:0%
+problem that I happened to give last
+year on the exam and then we'll do some
+
+ align:start position:0%
+year on the exam and then we'll do some
+ 
+
+ align:start position:0%
+year on the exam and then we'll do some
+we'll we'll talk a little bit about uh
+
+ align:start position:0%
+we'll we'll talk a little bit about uh
+ 
+
+ align:start position:0%
+we'll we'll talk a little bit about uh
+some properties electron transport
+
+ align:start position:0%
+some properties electron transport
+ 
+
+ align:start position:0%
+some properties electron transport
+couple minutes and then we'll talk about
+
+ align:start position:0%
+couple minutes and then we'll talk about
+ 
+
+ align:start position:0%
+couple minutes and then we'll talk about
+magnetization and then we'll do some
+
+ align:start position:0%
+magnetization and then we'll do some
+ 
+
+ align:start position:0%
+magnetization and then we'll do some
+calculations together again because I
+
+ align:start position:0%
+calculations together again because I
+ 
+
+ align:start position:0%
+calculations together again because I
+think that's been really enjoyable
+
+ align:start position:0%
+think that's been really enjoyable
+ 
+
+ align:start position:0%
+think that's been really enjoyable
+actually seriously I mean I always enjoy
+
+ align:start position:0%
+actually seriously I mean I always enjoy
+ 
+
+ align:start position:0%
+actually seriously I mean I always enjoy
+calculating together but do you feel
+
+ align:start position:0%
+calculating together but do you feel
+ 
+
+ align:start position:0%
+calculating together but do you feel
+like uh how many of you feel like that's
+
+ align:start position:0%
+like uh how many of you feel like that's
+ 
+
+ align:start position:0%
+like uh how many of you feel like that's
+useful to do some simulations here in
+
+ align:start position:0%
+useful to do some simulations here in
+ 
+
+ align:start position:0%
+useful to do some simulations here in
+class one two more okay okay cuz I think
+
+ align:start position:0%
+class one two more okay okay cuz I think
+ 
+
+ align:start position:0%
+class one two more okay okay cuz I think
+you know please ask questions you know
+
+ align:start position:0%
+you know please ask questions you know
+ 
+
+ align:start position:0%
+you know please ask questions you know
+that's like this is the time you know
+
+ align:start position:0%
+that's like this is the time you know
+ 
+
+ align:start position:0%
+that's like this is the time you know
+because um this is where we can if you
+
+ align:start position:0%
+because um this is where we can if you
+ 
+
+ align:start position:0%
+because um this is where we can if you
+have any questions please stop and say
+
+ align:start position:0%
+have any questions please stop and say
+ 
+
+ align:start position:0%
+have any questions please stop and say
+like I got no idea what you're talking
+
+ align:start position:0%
+like I got no idea what you're talking
+ 
+
+ align:start position:0%
+like I got no idea what you're talking
+about like that's okay I love those you
+
+ align:start position:0%
+about like that's okay I love those you
+ 
+
+ align:start position:0%
+about like that's okay I love those you
+know that's that's what I want to hear
+
+ align:start position:0%
+know that's that's what I want to hear
+ 
+
+ align:start position:0%
+know that's that's what I want to hear
+well that's actually not what I want to
+
+ align:start position:0%
+well that's actually not what I want to
+ 
+
+ align:start position:0%
+well that's actually not what I want to
+hear but if I hear it it's fine you know
+
+ align:start position:0%
+hear but if I hear it it's fine you know
+ 
+
+ align:start position:0%
+hear but if I hear it it's fine you know
+that helps me to to know sort of where
+
+ align:start position:0%
+that helps me to to know sort of where
+ 
+
+ align:start position:0%
+that helps me to to know sort of where
+where we need to have a little
+
+ align:start position:0%
+where we need to have a little
+ 
+
+ align:start position:0%
+where we need to have a little
+discussion okay now this is the concept
+
+ align:start position:0%
+discussion okay now this is the concept
+ 
+
+ align:start position:0%
+discussion okay now this is the concept
+that we have to be uh we have to be
+
+ align:start position:0%
+that we have to be uh we have to be
+ 
+
+ align:start position:0%
+that we have to be uh we have to be
+really good good in our understanding
+
+ align:start position:0%
+really good good in our understanding
+ 
+
+ align:start position:0%
+really good good in our understanding
+with this is really the key of this um
+
+ align:start position:0%
+with this is really the key of this um
+ 
+
+ align:start position:0%
+with this is really the key of this um
+sort of second part of the second part
+
+ align:start position:0%
+sort of second part of the second part
+ 
+
+ align:start position:0%
+sort of second part of the second part
+if you want of the class which is we did
+
+ align:start position:0%
+if you want of the class which is we did
+ 
+
+ align:start position:0%
+if you want of the class which is we did
+Quantum we did Quantum for atoms we did
+
+ align:start position:0%
+Quantum we did Quantum for atoms we did
+ 
+
+ align:start position:0%
+Quantum we did Quantum for atoms we did
+Quantum for molecules and now it's all
+
+ align:start position:0%
+Quantum for molecules and now it's all
+ 
+
+ align:start position:0%
+Quantum for molecules and now it's all
+about solids and the big difference is
+
+ align:start position:0%
+about solids and the big difference is
+ 
+
+ align:start position:0%
+about solids and the big difference is
+that you when you when you have a solid
+
+ align:start position:0%
+that you when you when you have a solid
+ 
+
+ align:start position:0%
+that you when you when you have a solid
+you have you know over and over and over
+
+ align:start position:0%
+you have you know over and over and over
+ 
+
+ align:start position:0%
+you have you know over and over and over
+again the same atom or same couple of
+
+ align:start position:0%
+again the same atom or same couple of
+ 
+
+ align:start position:0%
+again the same atom or same couple of
+atoms in your basis and therefore the
+
+ align:start position:0%
+atoms in your basis and therefore the
+ 
+
+ align:start position:0%
+atoms in your basis and therefore the
+same potential that the electron
+
+ align:start position:0%
+same potential that the electron
+ 
+
+ align:start position:0%
+same potential that the electron
+feels and over and over again how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times if I had to give a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number couple th well I'd say more like
+
+ align:start position:0%
+number couple th well I'd say more like
+ 
+
+ align:start position:0%
+number couple th well I'd say more like
+couple 10 to the 23rd
+
+ align:start position:0%
+couple 10 to the 23rd
+ 
+
+ align:start position:0%
+couple 10 to the 23rd
+thousands 10
+
+ align:start position:0%
+thousands 10
+ 
+
+ align:start position:0%
+thousands 10
+23 um that's how right I mean if I take
+
+ align:start position:0%
+23 um that's how right I mean if I take
+ 
+
+ align:start position:0%
+23 um that's how right I mean if I take
+a piece of material
+
+ align:start position:0%
+a piece of material
+ 
+
+ align:start position:0%
+a piece of material
+you know like this big you know this big
+
+ align:start position:0%
+you know like this big you know this big
+ 
+
+ align:start position:0%
+you know like this big you know this big
+um you know that's how well even this
+
+ align:start position:0%
+um you know that's how well even this
+ 
+
+ align:start position:0%
+um you know that's how well even this
+big even really tiny you got like you
+
+ align:start position:0%
+big even really tiny you got like you
+ 
+
+ align:start position:0%
+big even really tiny you got like you
+know 10 23rd repeats of this potential
+
+ align:start position:0%
+know 10 23rd repeats of this potential
+ 
+
+ align:start position:0%
+know 10 23rd repeats of this potential
+that's a lot so it's almost
+
+ align:start position:0%
+that's a lot so it's almost
+ 
+
+ align:start position:0%
+that's a lot so it's almost
+infinite um and when you have that kind
+
+ align:start position:0%
+infinite um and when you have that kind
+ 
+
+ align:start position:0%
+infinite um and when you have that kind
+of periodically repeating well that the
+
+ align:start position:0%
+of periodically repeating well that the
+ 
+
+ align:start position:0%
+of periodically repeating well that the
+electron feels something happens okay
+
+ align:start position:0%
+electron feels something happens okay
+ 
+
+ align:start position:0%
+electron feels something happens okay
+and and the something that happens was
+
+ align:start position:0%
+and and the something that happens was
+ 
+
+ align:start position:0%
+and and the something that happens was
+this mathematical thing that who can
+
+ align:start position:0%
+this mathematical thing that who can
+ 
+
+ align:start position:0%
+this mathematical thing that who can
+remember what it's called a it it was a
+
+ align:start position:0%
+remember what it's called a it it was a
+ 
+
+ align:start position:0%
+remember what it's called a it it was a
+theorem I
+
+ align:start position:0%
+theorem I
+ 
+
+ align:start position:0%
+theorem I
+believe blocks
+
+ align:start position:0%
+believe blocks
+ 
+
+ align:start position:0%
+believe blocks
+theorem and we don't know how we don't
+
+ align:start position:0%
+theorem and we don't know how we don't
+ 
+
+ align:start position:0%
+theorem and we don't know how we don't
+need to know much about blocks theorem
+
+ align:start position:0%
+need to know much about blocks theorem
+ 
+
+ align:start position:0%
+need to know much about blocks theorem
+except the end
+
+ align:start position:0%
+except the end
+ 
+
+ align:start position:0%
+except the end
+game right the key is what it means and
+
+ align:start position:0%
+game right the key is what it means and
+ 
+
+ align:start position:0%
+game right the key is what it means and
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+mathematical
+
+ align:start position:0%
+mathematical
+ 
+
+ align:start position:0%
+mathematical
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+consequence it's a consequence of having
+
+ align:start position:0%
+consequence it's a consequence of having
+ 
+
+ align:start position:0%
+consequence it's a consequence of having
+an electron and therefore its solution
+
+ align:start position:0%
+an electron and therefore its solution
+ 
+
+ align:start position:0%
+an electron and therefore its solution
+being a wave function that solves the
+
+ align:start position:0%
+being a wave function that solves the
+ 
+
+ align:start position:0%
+being a wave function that solves the
+shary equation it's a consequence of
+
+ align:start position:0%
+shary equation it's a consequence of
+ 
+
+ align:start position:0%
+shary equation it's a consequence of
+having that in the context of a periodic
+
+ align:start position:0%
+having that in the context of a periodic
+ 
+
+ align:start position:0%
+having that in the context of a periodic
+potential right you can't get around
+
+ align:start position:0%
+potential right you can't get around
+ 
+
+ align:start position:0%
+potential right you can't get around
+it it's a theorem so you you got to have
+
+ align:start position:0%
+it it's a theorem so you you got to have
+ 
+
+ align:start position:0%
+it it's a theorem so you you got to have
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this because of blocks theorem you got
+
+ align:start position:0%
+this because of blocks theorem you got
+ 
+
+ align:start position:0%
+this because of blocks theorem you got
+to have this sort of requirement if you
+
+ align:start position:0%
+to have this sort of requirement if you
+ 
+
+ align:start position:0%
+to have this sort of requirement if you
+want to think about as requirement that
+
+ align:start position:0%
+want to think about as requirement that
+ 
+
+ align:start position:0%
+want to think about as requirement that
+when the wave function
+
+ align:start position:0%
+when the wave function
+ 
+
+ align:start position:0%
+when the wave function
+repeats okay the properties just repeat
+
+ align:start position:0%
+repeats okay the properties just repeat
+ 
+
+ align:start position:0%
+repeats okay the properties just repeat
+the Den is the same here as it is here
+
+ align:start position:0%
+the Den is the same here as it is here
+ 
+
+ align:start position:0%
+the Den is the same here as it is here
+as it is here 10 the 23rd out but when
+
+ align:start position:0%
+as it is here 10 the 23rd out but when
+ 
+
+ align:start position:0%
+as it is here 10 the 23rd out but when
+the wave function repeats it picks up
+
+ align:start position:0%
+the wave function repeats it picks up
+ 
+
+ align:start position:0%
+the wave function repeats it picks up
+this phase
+
+ align:start position:0%
+this phase
+ 
+
+ align:start position:0%
+this phase
+okay and that phase is is a vector is a
+
+ align:start position:0%
+okay and that phase is is a vector is a
+ 
+
+ align:start position:0%
+okay and that phase is is a vector is a
+number that lives in k space that lives
+
+ align:start position:0%
+number that lives in k space that lives
+ 
+
+ align:start position:0%
+number that lives in k space that lives
+in the inverse space and that's why we
+
+ align:start position:0%
+in the inverse space and that's why we
+ 
+
+ align:start position:0%
+in the inverse space and that's why we
+spent all that time talking about what
+
+ align:start position:0%
+spent all that time talking about what
+ 
+
+ align:start position:0%
+spent all that time talking about what
+inverse space is what reciprocal space
+
+ align:start position:0%
+inverse space is what reciprocal space
+ 
+
+ align:start position:0%
+inverse space is what reciprocal space
+is right what k space is okay and that
+
+ align:start position:0%
+is right what k space is okay and that
+ 
+
+ align:start position:0%
+is right what k space is okay and that
+phase is
+
+ align:start position:0%
+phase is
+ 
+
+ align:start position:0%
+phase is
+um it it's you can think about it as a
+
+ align:start position:0%
+um it it's you can think about it as a
+ 
+
+ align:start position:0%
+um it it's you can think about it as a
+another quantum
+
+ align:start position:0%
+another quantum
+ 
+
+ align:start position:0%
+another quantum
+number so uh um the result of solving
+
+ align:start position:0%
+number so uh um the result of solving
+ 
+
+ align:start position:0%
+number so uh um the result of solving
+the shary equation and getting s in a
+
+ align:start position:0%
+the shary equation and getting s in a
+ 
+
+ align:start position:0%
+the shary equation and getting s in a
+periodic potential gives you a new
+
+ align:start position:0%
+periodic potential gives you a new
+ 
+
+ align:start position:0%
+periodic potential gives you a new
+number but it's very different than
+
+ align:start position:0%
+number but it's very different than
+ 
+
+ align:start position:0%
+number but it's very different than
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+numbers right how is it
+
+ align:start position:0%
+numbers right how is it
+ 
+
+ align:start position:0%
+numbers right how is it
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+yeah okay yeah right these are like one
+
+ align:start position:0%
+yeah okay yeah right these are like one
+ 
+
+ align:start position:0%
+yeah okay yeah right these are like one
+or two or 1 2 0 minus one um whereas
+
+ align:start position:0%
+or two or 1 2 0 minus one um whereas
+ 
+
+ align:start position:0%
+or two or 1 2 0 minus one um whereas
+this is like a a part of a place in
+
+ align:start position:0%
+this is like a a part of a place in
+ 
+
+ align:start position:0%
+this is like a a part of a place in
+space and what else is really
+
+ align:start position:0%
+space and what else is really
+ 
+
+ align:start position:0%
+space and what else is really
+interesting about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector it's in reciprocal
+
+ align:start position:0%
+Vector it's in reciprocal
+ 
+
+ align:start position:0%
+Vector it's in reciprocal
+space absolutely nice job I I'll you
+
+ align:start position:0%
+space absolutely nice job I I'll you
+ 
+
+ align:start position:0%
+space absolutely nice job I I'll you
+guys did that together totally team
+
+ align:start position:0%
+guys did that together totally team
+ 
+
+ align:start position:0%
+guys did that together totally team
+effort man I love it and what about what
+
+ align:start position:0%
+effort man I love it and what about what
+ 
+
+ align:start position:0%
+effort man I love it and what about what
+about uh what
+
+ align:start position:0%
+about uh what
+ 
+
+ align:start position:0%
+about uh what
+else it's a vector in reciprocal space
+
+ align:start position:0%
+else it's a vector in reciprocal space
+ 
+
+ align:start position:0%
+else it's a vector in reciprocal space
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+else okay well it it doesn't have to be
+
+ align:start position:0%
+else okay well it it doesn't have to be
+ 
+
+ align:start position:0%
+else okay well it it doesn't have to be
+but we said it doesn't really matter if
+
+ align:start position:0%
+but we said it doesn't really matter if
+ 
+
+ align:start position:0%
+but we said it doesn't really matter if
+you got out side of it because you just
+
+ align:start position:0%
+you got out side of it because you just
+ 
+
+ align:start position:0%
+you got out side of it because you just
+loop back but what about its variation
+
+ align:start position:0%
+loop back but what about its variation
+ 
+
+ align:start position:0%
+loop back but what about its variation
+in the bran Zone how can it
+
+ align:start position:0%
+in the bran Zone how can it
+ 
+
+ align:start position:0%
+in the bran Zone how can it
+vary yeah like this is a vector that can
+
+ align:start position:0%
+vary yeah like this is a vector that can
+ 
+
+ align:start position:0%
+vary yeah like this is a vector that can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+anything this thing can be anything
+
+ align:start position:0%
+anything this thing can be anything
+ 
+
+ align:start position:0%
+anything this thing can be anything
+these things can they be anything can L
+
+ align:start position:0%
+these things can they be anything can L
+ 
+
+ align:start position:0%
+these things can they be anything can L
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+Pi or Square < TK of two right so it's a
+
+ align:start position:0%
+Pi or Square < TK of two right so it's a
+ 
+
+ align:start position:0%
+Pi or Square < TK of two right so it's a
+different kind of quantum
+
+ align:start position:0%
+different kind of quantum
+ 
+
+ align:start position:0%
+different kind of quantum
+number but you see it has this same
+
+ align:start position:0%
+number but you see it has this same
+ 
+
+ align:start position:0%
+number but you see it has this same
+impact right because I mean what do
+
+ align:start position:0%
+impact right because I mean what do
+ 
+
+ align:start position:0%
+impact right because I mean what do
+these things do right like what is what
+
+ align:start position:0%
+these things do right like what is what
+ 
+
+ align:start position:0%
+these things do right like what is what
+does this do anyway what's one of the
+
+ align:start position:0%
+does this do anyway what's one of the
+ 
+
+ align:start position:0%
+does this do anyway what's one of the
+things that this does or this what does
+
+ align:start position:0%
+things that this does or this what does
+ 
+
+ align:start position:0%
+things that this does or this what does
+l do when I change L from you know zero
+
+ align:start position:0%
+l do when I change L from you know zero
+ 
+
+ align:start position:0%
+l do when I change L from you know zero
+to one what's one of the things that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens yeah yeah okay so let's let's
+
+ align:start position:0%
+happens yeah yeah okay so let's let's
+ 
+
+ align:start position:0%
+happens yeah yeah okay so let's let's
+write that down so we're moving from s
+
+ align:start position:0%
+write that down so we're moving from s
+ 
+
+ align:start position:0%
+write that down so we're moving from s
+well let's change n up to here to S 1 s
+
+ align:start position:0%
+well let's change n up to here to S 1 s
+ 
+
+ align:start position:0%
+well let's change n up to here to S 1 s
+2s and now you just said I'm moving to
+
+ align:start position:0%
+2s and now you just said I'm moving to
+ 
+
+ align:start position:0%
+2s and now you just said I'm moving to
+P now what what what is this that I'm
+
+ align:start position:0%
+P now what what what is this that I'm
+ 
+
+ align:start position:0%
+P now what what what is this that I'm
+always just assuming you know is what
+
+ align:start position:0%
+always just assuming you know is what
+ 
+
+ align:start position:0%
+always just assuming you know is what
+that vertical axis is what is
+
+ align:start position:0%
+that vertical axis is what is
+ 
+
+ align:start position:0%
+that vertical axis is what is
+it yeah so this is the energy going from
+
+ align:start position:0%
+it yeah so this is the energy going from
+ 
+
+ align:start position:0%
+it yeah so this is the energy going from
+lowest to highest exactly and so what
+
+ align:start position:0%
+lowest to highest exactly and so what
+ 
+
+ align:start position:0%
+lowest to highest exactly and so what
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+changing the quantum number L from zero
+
+ align:start position:0%
+changing the quantum number L from zero
+ 
+
+ align:start position:0%
+changing the quantum number L from zero
+to one
+
+ align:start position:0%
+to one
+ 
+
+ align:start position:0%
+to one
+do yeah moves it around
+
+ align:start position:0%
+do yeah moves it around
+ 
+
+ align:start position:0%
+do yeah moves it around
+right it moves it
+
+ align:start position:0%
+right it moves it
+ 
+
+ align:start position:0%
+right it moves it
+around okay so you can change the energy
+
+ align:start position:0%
+around okay so you can change the energy
+ 
+
+ align:start position:0%
+around okay so you can change the energy
+and actually you can also not change the
+
+ align:start position:0%
+and actually you can also not change the
+ 
+
+ align:start position:0%
+and actually you can also not change the
+energy M doesn't change the energy it
+
+ align:start position:0%
+energy M doesn't change the energy it
+ 
+
+ align:start position:0%
+energy M doesn't change the energy it
+gives
+
+ align:start position:0%
+gives
+ 
+
+ align:start position:0%
+gives
+degeneracy right but but certainly you
+
+ align:start position:0%
+degeneracy right but but certainly you
+ 
+
+ align:start position:0%
+degeneracy right but but certainly you
+can change the energy by changing these
+
+ align:start position:0%
+can change the energy by changing these
+ 
+
+ align:start position:0%
+can change the energy by changing these
+quantum
+
+ align:start position:0%
+quantum
+ 
+
+ align:start position:0%
+quantum
+numbers um that's what you can do with
+
+ align:start position:0%
+numbers um that's what you can do with
+ 
+
+ align:start position:0%
+numbers um that's what you can do with
+K right that's what K does K which is a
+
+ align:start position:0%
+K right that's what K does K which is a
+ 
+
+ align:start position:0%
+K right that's what K does K which is a
+result of living in a periodically
+
+ align:start position:0%
+result of living in a periodically
+ 
+
+ align:start position:0%
+result of living in a periodically
+repeating World K changes the levels it
+
+ align:start position:0%
+repeating World K changes the levels it
+ 
+
+ align:start position:0%
+repeating World K changes the levels it
+CH it's the same idea but it's very
+
+ align:start position:0%
+CH it's the same idea but it's very
+ 
+
+ align:start position:0%
+CH it's the same idea but it's very
+different but it has the same
+
+ align:start position:0%
+different but it has the same
+ 
+
+ align:start position:0%
+different but it has the same
+impact it changes these levels around
+
+ align:start position:0%
+impact it changes these levels around
+ 
+
+ align:start position:0%
+impact it changes these levels around
+and it's very different because it can
+
+ align:start position:0%
+and it's very different because it can
+ 
+
+ align:start position:0%
+and it's very different because it can
+do it continuously as opposed to these
+
+ align:start position:0%
+do it continuously as opposed to these
+ 
+
+ align:start position:0%
+do it continuously as opposed to these
+you know big
+
+ align:start position:0%
+you know big
+ 
+
+ align:start position:0%
+you know big
+leaps that um that we have in the atom
+
+ align:start position:0%
+leaps that um that we have in the atom
+ 
+
+ align:start position:0%
+leaps that um that we have in the atom
+okay or in the molecule right the
+
+ align:start position:0%
+okay or in the molecule right the
+ 
+
+ align:start position:0%
+okay or in the molecule right the
+molecule they're also um discret levels
+
+ align:start position:0%
+molecule they're also um discret levels
+ 
+
+ align:start position:0%
+molecule they're also um discret levels
+and so we got this picture that we came
+
+ align:start position:0%
+and so we got this picture that we came
+ 
+
+ align:start position:0%
+and so we got this picture that we came
+to last
+
+ align:start position:0%
+to last
+ 
+
+ align:start position:0%
+to last
+time where you see K can be a
+
+ align:start position:0%
+time where you see K can be a
+ 
+
+ align:start position:0%
+time where you see K can be a
+vector and it can live anywhere in this
+
+ align:start position:0%
+vector and it can live anywhere in this
+ 
+
+ align:start position:0%
+vector and it can live anywhere in this
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+okay and anytime you change it you may
+
+ align:start position:0%
+okay and anytime you change it you may
+ 
+
+ align:start position:0%
+okay and anytime you change it you may
+change the energy levels you may change
+
+ align:start position:0%
+change the energy levels you may change
+ 
+
+ align:start position:0%
+change the energy levels you may change
+them okay so it's a really important
+
+ align:start position:0%
+them okay so it's a really important
+ 
+
+ align:start position:0%
+them okay so it's a really important
+thing when you have a solid now
+
+ align:start position:0%
+thing when you have a solid now
+ 
+
+ align:start position:0%
+thing when you have a solid now
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+again how how would if if I had a solid
+
+ align:start position:0%
+again how how would if if I had a solid
+ 
+
+ align:start position:0%
+again how how would if if I had a solid
+but if if I have a peri periodically
+
+ align:start position:0%
+but if if I have a peri periodically
+ 
+
+ align:start position:0%
+but if if I have a peri periodically
+repeating atom but the distance between
+
+ align:start position:0%
+repeating atom but the distance between
+ 
+
+ align:start position:0%
+repeating atom but the distance between
+them is like 100
+
+ align:start position:0%
+them is like 100
+ 
+
+ align:start position:0%
+them is like 100
+angstroms what's the variation in these
+
+ align:start position:0%
+angstroms what's the variation in these
+ 
+
+ align:start position:0%
+angstroms what's the variation in these
+what's the impact of K going to be we
+
+ align:start position:0%
+what's the impact of K going to be we
+ 
+
+ align:start position:0%
+what's the impact of K going to be we
+did it in
+
+ align:start position:0%
+did it in
+ 
+
+ align:start position:0%
+did it in
+class relatively small like almost
+
+ align:start position:0%
+class relatively small like almost
+ 
+
+ align:start position:0%
+class relatively small like almost
+nothing because the whole effect comes
+
+ align:start position:0%
+nothing because the whole effect comes
+ 
+
+ align:start position:0%
+nothing because the whole effect comes
+comes from the fact that you have an
+
+ align:start position:0%
+comes from the fact that you have an
+ 
+
+ align:start position:0%
+comes from the fact that you have an
+electron in a lattice of periodic images
+
+ align:start position:0%
+electron in a lattice of periodic images
+ 
+
+ align:start position:0%
+electron in a lattice of periodic images
+where there a periodic potentials where
+
+ align:start position:0%
+where there a periodic potentials where
+ 
+
+ align:start position:0%
+where there a periodic potentials where
+they're sort of
+
+ align:start position:0%
+they're sort of
+ 
+
+ align:start position:0%
+they're sort of
+interacting right where they're close
+
+ align:start position:0%
+interacting right where they're close
+ 
+
+ align:start position:0%
+interacting right where they're close
+enough that there's some interaction if
+
+ align:start position:0%
+enough that there's some interaction if
+ 
+
+ align:start position:0%
+enough that there's some interaction if
+there's no interaction and your atoms
+
+ align:start position:0%
+there's no interaction and your atoms
+ 
+
+ align:start position:0%
+there's no interaction and your atoms
+are really really far
+
+ align:start position:0%
+are really really far
+ 
+
+ align:start position:0%
+are really really far
+apart okay then it's B basically like
+
+ align:start position:0%
+apart okay then it's B basically like
+ 
+
+ align:start position:0%
+apart okay then it's B basically like
+you just have isolated atoms sitting in
+
+ align:start position:0%
+you just have isolated atoms sitting in
+ 
+
+ align:start position:0%
+you just have isolated atoms sitting in
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+potentials and a whole lot empty space
+
+ align:start position:0%
+potentials and a whole lot empty space
+ 
+
+ align:start position:0%
+potentials and a whole lot empty space
+in between and then the levels will just
+
+ align:start position:0%
+in between and then the levels will just
+ 
+
+ align:start position:0%
+in between and then the levels will just
+look flat as a function of K space
+
+ align:start position:0%
+look flat as a function of K space
+ 
+
+ align:start position:0%
+look flat as a function of K space
+doesn't mean you can't vary K you could
+
+ align:start position:0%
+doesn't mean you can't vary K you could
+ 
+
+ align:start position:0%
+doesn't mean you can't vary K you could
+still vary K but the bands that you get
+
+ align:start position:0%
+still vary K but the bands that you get
+ 
+
+ align:start position:0%
+still vary K but the bands that you get
+will be completely flat they'll go back
+
+ align:start position:0%
+will be completely flat they'll go back
+ 
+
+ align:start position:0%
+will be completely flat they'll go back
+to your molecular level uh description
+
+ align:start position:0%
+to your molecular level uh description
+ 
+
+ align:start position:0%
+to your molecular level uh description
+so does everybody see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right and we talked about
+
+ align:start position:0%
+right and we talked about
+ 
+
+ align:start position:0%
+right and we talked about
+that and so then the question was well
+
+ align:start position:0%
+that and so then the question was well
+ 
+
+ align:start position:0%
+that and so then the question was well
+what playground of cave
+
+ align:start position:0%
+what playground of cave
+ 
+
+ align:start position:0%
+what playground of cave
+matters okay and this is um this is uh
+
+ align:start position:0%
+matters okay and this is um this is uh
+ 
+
+ align:start position:0%
+matters okay and this is um this is uh
+uh something we talked about but it's
+
+ align:start position:0%
+uh something we talked about but it's
+ 
+
+ align:start position:0%
+uh something we talked about but it's
+really important so I want to review it
+
+ align:start position:0%
+really important so I want to review it
+ 
+
+ align:start position:0%
+really important so I want to review it
+here okay so we just said that K is this
+
+ align:start position:0%
+here okay so we just said that K is this
+ 
+
+ align:start position:0%
+here okay so we just said that K is this
+new index that is a continuous variable
+
+ align:start position:0%
+new index that is a continuous variable
+ 
+
+ align:start position:0%
+new index that is a continuous variable
+that changes the energy levels it moves
+
+ align:start position:0%
+that changes the energy levels it moves
+ 
+
+ align:start position:0%
+that changes the energy levels it moves
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+around okay so what does that mean for a
+
+ align:start position:0%
+around okay so what does that mean for a
+ 
+
+ align:start position:0%
+around okay so what does that mean for a
+calculation right
+
+ align:start position:0%
+calculation right
+ 
+
+ align:start position:0%
+calculation right
+well one thing that it means is that
+
+ align:start position:0%
+well one thing that it means is that
+ 
+
+ align:start position:0%
+well one thing that it means is that
+when I do a calculation
+
+ align:start position:0%
+when I do a calculation
+ 
+
+ align:start position:0%
+when I do a calculation
+um I need a if if a if an energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level if an energy level can now do
+
+ align:start position:0%
+level if an energy level can now do
+ 
+
+ align:start position:0%
+level if an energy level can now do
+this right as a function of K then that
+
+ align:start position:0%
+this right as a function of K then that
+ 
+
+ align:start position:0%
+this right as a function of K then that
+means I need to actually do my
+
+ align:start position:0%
+means I need to actually do my
+ 
+
+ align:start position:0%
+means I need to actually do my
+calculation with a mesh of K points how
+
+ align:start position:0%
+calculation with a mesh of K points how
+ 
+
+ align:start position:0%
+calculation with a mesh of K points how
+fine a mesh do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need what's the answer to
+
+ align:start position:0%
+need what's the answer to
+ 
+
+ align:start position:0%
+need what's the answer to
+that thank you
+
+ align:start position:0%
+that thank you
+ 
+
+ align:start position:0%
+that thank you
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+CS yeah how curvy are my
+
+ align:start position:0%
+CS yeah how curvy are my
+ 
+
+ align:start position:0%
+CS yeah how curvy are my
+bands this is pretty curvy so maybe I
+
+ align:start position:0%
+bands this is pretty curvy so maybe I
+ 
+
+ align:start position:0%
+bands this is pretty curvy so maybe I
+need a lot of K points to capture this
+
+ align:start position:0%
+need a lot of K points to capture this
+ 
+
+ align:start position:0%
+need a lot of K points to capture this
+if I don't it's you know you got a grid
+
+ align:start position:0%
+if I don't it's you know you got a grid
+ 
+
+ align:start position:0%
+if I don't it's you know you got a grid
+I'm solving for this problem on a grid
+
+ align:start position:0%
+I'm solving for this problem on a grid
+ 
+
+ align:start position:0%
+I'm solving for this problem on a grid
+of K points basically and if I only have
+
+ align:start position:0%
+of K points basically and if I only have
+ 
+
+ align:start position:0%
+of K points basically and if I only have
+a k Point here and here well let's say I
+
+ align:start position:0%
+a k Point here and here well let's say I
+ 
+
+ align:start position:0%
+a k Point here and here well let's say I
+have it actually even worse I have it
+
+ align:start position:0%
+have it actually even worse I have it
+ 
+
+ align:start position:0%
+have it actually even worse I have it
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+here I'm not going to really um capture
+
+ align:start position:0%
+here I'm not going to really um capture
+ 
+
+ align:start position:0%
+here I'm not going to really um capture
+the right physics here okay so the
+
+ align:start position:0%
+the right physics here okay so the
+ 
+
+ align:start position:0%
+the right physics here okay so the
+density of K points has to be such that
+
+ align:start position:0%
+density of K points has to be such that
+ 
+
+ align:start position:0%
+density of K points has to be such that
+you capture the the features of in in
+
+ align:start position:0%
+you capture the the features of in in
+ 
+
+ align:start position:0%
+you capture the the features of in in
+terms of how much these energy levels
+
+ align:start position:0%
+terms of how much these energy levels
+ 
+
+ align:start position:0%
+terms of how much these energy levels
+vary so let's go back to these two atoms
+
+ align:start position:0%
+vary so let's go back to these two atoms
+ 
+
+ align:start position:0%
+vary so let's go back to these two atoms
+that are very far apart how many k
+
+ align:start position:0%
+that are very far apart how many k
+ 
+
+ align:start position:0%
+that are very far apart how many k
+points do I need for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those what if they're really far
+
+ align:start position:0%
+those what if they're really far
+ 
+
+ align:start position:0%
+those what if they're really far
+apart one oh well all the calculations
+
+ align:start position:0%
+apart one oh well all the calculations
+ 
+
+ align:start position:0%
+apart one oh well all the calculations
+you've been doing until we did the
+
+ align:start position:0%
+you've been doing until we did the
+ 
+
+ align:start position:0%
+you've been doing until we did the
+solids everything before that was
+
+ align:start position:0%
+solids everything before that was
+ 
+
+ align:start position:0%
+solids everything before that was
+actually one k point it was at 0000 0 we
+
+ align:start position:0%
+actually one k point it was at 0000 0 we
+ 
+
+ align:start position:0%
+actually one k point it was at 0000 0 we
+never varied it right we never worried
+
+ align:start position:0%
+never varied it right we never worried
+ 
+
+ align:start position:0%
+never varied it right we never worried
+about it it was never a problem it was
+
+ align:start position:0%
+about it it was never a problem it was
+ 
+
+ align:start position:0%
+about it it was never a problem it was
+never an index okay so now if if the
+
+ align:start position:0%
+never an index okay so now if if the
+ 
+
+ align:start position:0%
+never an index okay so now if if the
+bands are flat you could just have one k
+
+ align:start position:0%
+bands are flat you could just have one k
+ 
+
+ align:start position:0%
+bands are flat you could just have one k
+point and you've got the variation of
+
+ align:start position:0%
+point and you've got the variation of
+ 
+
+ align:start position:0%
+point and you've got the variation of
+the Bands nailed since they don't vary
+
+ align:start position:0%
+the Bands nailed since they don't vary
+ 
+
+ align:start position:0%
+the Bands nailed since they don't vary
+so you just need the one but if they
+
+ align:start position:0%
+so you just need the one but if they
+ 
+
+ align:start position:0%
+so you just need the one but if they
+vary a lot like if I bring atoms
+
+ align:start position:0%
+vary a lot like if I bring atoms
+ 
+
+ align:start position:0%
+vary a lot like if I bring atoms
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+and they vary a lot and there's a lot of
+
+ align:start position:0%
+and they vary a lot and there's a lot of
+ 
+
+ align:start position:0%
+and they vary a lot and there's a lot of
+interaction then I just need more and
+
+ align:start position:0%
+interaction then I just need more and
+ 
+
+ align:start position:0%
+interaction then I just need more and
+more K points to represent that
+
+ align:start position:0%
+more K points to represent that
+ 
+
+ align:start position:0%
+more K points to represent that
+correctly okay so so the K points is is
+
+ align:start position:0%
+correctly okay so so the K points is is
+ 
+
+ align:start position:0%
+correctly okay so so the K points is is
+a is something that's now an essential
+
+ align:start position:0%
+a is something that's now an essential
+ 
+
+ align:start position:0%
+a is something that's now an essential
+part of your
+
+ align:start position:0%
+part of your
+ 
+
+ align:start position:0%
+part of your
+calculation now that's that's talking
+
+ align:start position:0%
+calculation now that's that's talking
+ 
+
+ align:start position:0%
+calculation now that's that's talking
+about what you need to get the density
+
+ align:start position:0%
+about what you need to get the density
+ 
+
+ align:start position:0%
+about what you need to get the density
+right which is to get the wave function
+
+ align:start position:0%
+right which is to get the wave function
+ 
+
+ align:start position:0%
+right which is to get the wave function
+right which is to get the energy levels
+
+ align:start position:0%
+right which is to get the energy levels
+ 
+
+ align:start position:0%
+right which is to get the energy levels
+right okay that's a
+
+ align:start position:0%
+right okay that's a
+ 
+
+ align:start position:0%
+right okay that's a
+new you know component of a quantum
+
+ align:start position:0%
+new you know component of a quantum
+ 
+
+ align:start position:0%
+new you know component of a quantum
+mechanical simulation but then there was
+
+ align:start position:0%
+mechanical simulation but then there was
+ 
+
+ align:start position:0%
+mechanical simulation but then there was
+this other thing that's actually kind of
+
+ align:start position:0%
+this other thing that's actually kind of
+ 
+
+ align:start position:0%
+this other thing that's actually kind of
+a little bit separate in a way okay
+
+ align:start position:0%
+a little bit separate in a way okay
+ 
+
+ align:start position:0%
+a little bit separate in a way okay
+which is um to visualize that
+
+ align:start position:0%
+which is um to visualize that
+ 
+
+ align:start position:0%
+which is um to visualize that
+variation okay now visualizing this
+
+ align:start position:0%
+variation okay now visualizing this
+ 
+
+ align:start position:0%
+variation okay now visualizing this
+variation leads to these plots which are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called band structures this is the band
+
+ align:start position:0%
+called band structures this is the band
+ 
+
+ align:start position:0%
+called band structures this is the band
+structure of the
+
+ align:start position:0%
+structure of the
+ 
+
+ align:start position:0%
+structure of the
+material it's like uh oh it's like it's
+
+ align:start position:0%
+material it's like uh oh it's like it's
+ 
+
+ align:start position:0%
+material it's like uh oh it's like it's
+like a a you know it's another kind of
+
+ align:start position:0%
+like a a you know it's another kind of
+ 
+
+ align:start position:0%
+like a a you know it's another kind of
+phase map for for those of you who felt
+
+ align:start position:0%
+phase map for for those of you who felt
+ 
+
+ align:start position:0%
+phase map for for those of you who felt
+the excitement of phase diagrams in 3012
+
+ align:start position:0%
+the excitement of phase diagrams in 3012
+ 
+
+ align:start position:0%
+the excitement of phase diagrams in 3012
+this is like a phase map for that
+
+ align:start position:0%
+this is like a phase map for that
+ 
+
+ align:start position:0%
+this is like a phase map for that
+electron okay um it's it's it's a really
+
+ align:start position:0%
+electron okay um it's it's it's a really
+ 
+
+ align:start position:0%
+electron okay um it's it's it's a really
+important um uh uh description right of
+
+ align:start position:0%
+important um uh uh description right of
+ 
+
+ align:start position:0%
+important um uh uh description right of
+how electrons behave in
+
+ align:start position:0%
+how electrons behave in
+ 
+
+ align:start position:0%
+how electrons behave in
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+now this phase map is not everything
+
+ align:start position:0%
+now this phase map is not everything
+ 
+
+ align:start position:0%
+now this phase map is not everything
+going okay over there
+
+ align:start position:0%
+going okay over there
+ 
+
+ align:start position:0%
+going okay over there
+look look like you got hurt no you're
+
+ align:start position:0%
+look look like you got hurt no you're
+ 
+
+ align:start position:0%
+look look like you got hurt no you're
+good okay all right I got a little
+
+ align:start position:0%
+good okay all right I got a little
+ 
+
+ align:start position:0%
+good okay all right I got a little
+concerned but we're over it um the uh
+
+ align:start position:0%
+concerned but we're over it um the uh
+ 
+
+ align:start position:0%
+concerned but we're over it um the uh
+the the fa sorry the phase map okay
+
+ align:start position:0%
+the the fa sorry the phase map okay
+ 
+
+ align:start position:0%
+the the fa sorry the phase map okay
+is a walk through
+
+ align:start position:0%
+is a walk through
+ 
+
+ align:start position:0%
+is a walk through
+kpace now I just mentioned that you have
+
+ align:start position:0%
+kpace now I just mentioned that you have
+ 
+
+ align:start position:0%
+kpace now I just mentioned that you have
+a grid that you just have to put on here
+
+ align:start position:0%
+a grid that you just have to put on here
+ 
+
+ align:start position:0%
+a grid that you just have to put on here
+to do the
+
+ align:start position:0%
+to do the
+ 
+
+ align:start position:0%
+to do the
+calculation to get the Wiggles that may
+
+ align:start position:0%
+calculation to get the Wiggles that may
+ 
+
+ align:start position:0%
+calculation to get the Wiggles that may
+or may not be there well you should take
+
+ align:start position:0%
+or may not be there well you should take
+ 
+
+ align:start position:0%
+or may not be there well you should take
+a guess at whether you think they're
+
+ align:start position:0%
+a guess at whether you think they're
+ 
+
+ align:start position:0%
+a guess at whether you think they're
+there and then you should see and then
+
+ align:start position:0%
+there and then you should see and then
+ 
+
+ align:start position:0%
+there and then you should see and then
+you should converge it okay but now I'm
+
+ align:start position:0%
+you should converge it okay but now I'm
+ 
+
+ align:start position:0%
+you should converge it okay but now I'm
+taking a walk around in that
+
+ align:start position:0%
+taking a walk around in that
+ 
+
+ align:start position:0%
+taking a walk around in that
+zone and the question is where am I
+
+ align:start position:0%
+zone and the question is where am I
+ 
+
+ align:start position:0%
+zone and the question is where am I
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+go I
+
+ align:start position:0%
+go I
+ 
+
+ align:start position:0%
+go I
+mean should I just go to eat I mean well
+
+ align:start position:0%
+mean should I just go to eat I mean well
+ 
+
+ align:start position:0%
+mean should I just go to eat I mean well
+I I'm using 4x4x4 K points so I'm using
+
+ align:start position:0%
+I I'm using 4x4x4 K points so I'm using
+ 
+
+ align:start position:0%
+I I'm using 4x4x4 K points so I'm using
+a grid of 64 points and I'm plopping it
+
+ align:start position:0%
+a grid of 64 points and I'm plopping it
+ 
+
+ align:start position:0%
+a grid of 64 points and I'm plopping it
+down into this bran Zone should I just
+
+ align:start position:0%
+down into this bran Zone should I just
+ 
+
+ align:start position:0%
+down into this bran Zone should I just
+map should I just look at the energies
+
+ align:start position:0%
+map should I just look at the energies
+ 
+
+ align:start position:0%
+map should I just look at the energies
+at each of those points well you could
+
+ align:start position:0%
+at each of those points well you could
+ 
+
+ align:start position:0%
+at each of those points well you could
+do that right I mean ideally you'd like
+
+ align:start position:0%
+do that right I mean ideally you'd like
+ 
+
+ align:start position:0%
+do that right I mean ideally you'd like
+to be able to visualize this variation
+
+ align:start position:0%
+to be able to visualize this variation
+ 
+
+ align:start position:0%
+to be able to visualize this variation
+all over kpace at every single point
+
+ align:start position:0%
+all over kpace at every single point
+ 
+
+ align:start position:0%
+all over kpace at every single point
+okay but uh why don't we do that tell me
+
+ align:start position:0%
+okay but uh why don't we do that tell me
+ 
+
+ align:start position:0%
+okay but uh why don't we do that tell me
+why we don't usually do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interested is
+
+ align:start position:0%
+interested is
+ 
+
+ align:start position:0%
+interested is
+surfaces well that is true but that's
+
+ align:start position:0%
+surfaces well that is true but that's
+ 
+
+ align:start position:0%
+surfaces well that is true but that's
+more of a kind of density thing so
+
+ align:start position:0%
+more of a kind of density thing so
+ 
+
+ align:start position:0%
+more of a kind of density thing so
+that's where you want to know the
+
+ align:start position:0%
+that's where you want to know the
+ 
+
+ align:start position:0%
+that's where you want to know the
+density the iso surface of the charge
+
+ align:start position:0%
+density the iso surface of the charge
+ 
+
+ align:start position:0%
+density the iso surface of the charge
+density yeah me c
+
+ align:start position:0%
+density yeah me c
+ 
+
+ align:start position:0%
+density yeah me c
+am okay that's definitely that's
+
+ align:start position:0%
+am okay that's definitely that's
+ 
+
+ align:start position:0%
+am okay that's definitely that's
+definitely true but let's say you didn't
+
+ align:start position:0%
+definitely true but let's say you didn't
+ 
+
+ align:start position:0%
+definitely true but let's say you didn't
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that what if I you know I mean I'd like
+
+ align:start position:0%
+that what if I you know I mean I'd like
+ 
+
+ align:start position:0%
+that what if I you know I mean I'd like
+to do the most accurate calculation
+
+ align:start position:0%
+to do the most accurate calculation
+ 
+
+ align:start position:0%
+to do the most accurate calculation
+possible let's say I put a grid over
+
+ align:start position:0%
+possible let's say I put a grid over
+ 
+
+ align:start position:0%
+possible let's say I put a grid over
+this case base of like a million by a
+
+ align:start position:0%
+this case base of like a million by a
+ 
+
+ align:start position:0%
+this case base of like a million by a
+million by a million don't do that on
+
+ align:start position:0%
+million by a million don't do that on
+ 
+
+ align:start position:0%
+million by a million don't do that on
+the nanohub we'll get
+
+ align:start position:0%
+the nanohub we'll get
+ 
+
+ align:start position:0%
+the nanohub we'll get
+calls um but let's say I did that now
+
+ align:start position:0%
+calls um but let's say I did that now
+ 
+
+ align:start position:0%
+calls um but let's say I did that now
+I've got a million by a million by a
+
+ align:start position:0%
+I've got a million by a million by a
+ 
+
+ align:start position:0%
+I've got a million by a million by a
+million points in here where each point
+
+ align:start position:0%
+million points in here where each point
+ 
+
+ align:start position:0%
+million points in here where each point
+has a new set of energy you know igen
+
+ align:start position:0%
+has a new set of energy you know igen
+ 
+
+ align:start position:0%
+has a new set of energy you know igen
+values why can't I just visualize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah would it just take too long to
+
+ align:start position:0%
+that yeah would it just take too long to
+ 
+
+ align:start position:0%
+that yeah would it just take too long to
+well it would take a whole lot of time
+
+ align:start position:0%
+well it would take a whole lot of time
+ 
+
+ align:start position:0%
+well it would take a whole lot of time
+to simulate what about visualizing it
+
+ align:start position:0%
+to simulate what about visualizing it
+ 
+
+ align:start position:0%
+to simulate what about visualizing it
+though how would you visualize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but see it's not even really just
+
+ align:start position:0%
+that but see it's not even really just
+ 
+
+ align:start position:0%
+that but see it's not even really just
+3D right because at each one of these
+
+ align:start position:0%
+3D right because at each one of these
+ 
+
+ align:start position:0%
+3D right because at each one of these
+points I've got a spectrum of
+
+ align:start position:0%
+points I've got a spectrum of
+ 
+
+ align:start position:0%
+points I've got a spectrum of
+energies right so it's kind of like yeah
+
+ align:start position:0%
+energies right so it's kind of like yeah
+ 
+
+ align:start position:0%
+energies right so it's kind of like yeah
+it's making your it would be making your
+
+ align:start position:0%
+it's making your it would be making your
+ 
+
+ align:start position:0%
+it's making your it would be making your
+igen values each one into a 3D curve and
+
+ align:start position:0%
+igen values each one into a 3D curve and
+ 
+
+ align:start position:0%
+igen values each one into a 3D curve and
+I want to look at them
+
+ align:start position:0%
+I want to look at them
+ 
+
+ align:start position:0%
+I want to look at them
+all right uh you could do
+
+ align:start position:0%
+all right uh you could do
+ 
+
+ align:start position:0%
+all right uh you could do
+that you know but how you know you got
+
+ align:start position:0%
+that you know but how you know you got
+ 
+
+ align:start position:0%
+that you know but how you know you got
+to remember if I go down to here I'm not
+
+ align:start position:0%
+to remember if I go down to here I'm not
+ 
+
+ align:start position:0%
+to remember if I go down to here I'm not
+you can't just do it within this volume
+
+ align:start position:0%
+you can't just do it within this volume
+ 
+
+ align:start position:0%
+you can't just do it within this volume
+element right my igen values might shift
+
+ align:start position:0%
+element right my igen values might shift
+ 
+
+ align:start position:0%
+element right my igen values might shift
+up down sideways you know not sideways
+
+ align:start position:0%
+up down sideways you know not sideways
+ 
+
+ align:start position:0%
+up down sideways you know not sideways
+up down um in different ways depending
+
+ align:start position:0%
+up down um in different ways depending
+ 
+
+ align:start position:0%
+up down um in different ways depending
+on where I am how am I actually going to
+
+ align:start position:0%
+on where I am how am I actually going to
+ 
+
+ align:start position:0%
+on where I am how am I actually going to
+see that right so you know in a way what
+
+ align:start position:0%
+see that right so you know in a way what
+ 
+
+ align:start position:0%
+see that right so you know in a way what
+we have is actually a strong
+
+ align:start position:0%
+we have is actually a strong
+ 
+
+ align:start position:0%
+we have is actually a strong
+visualization challenge that um
+
+ align:start position:0%
+visualization challenge that um
+ 
+
+ align:start position:0%
+visualization challenge that um
+luckily there's sort of a good story
+
+ align:start position:0%
+luckily there's sort of a good story
+ 
+
+ align:start position:0%
+luckily there's sort of a good story
+here because
+
+ align:start position:0%
+here because
+ 
+
+ align:start position:0%
+here because
+luckily um we can just look at a 2d
+
+ align:start position:0%
+luckily um we can just look at a 2d
+ 
+
+ align:start position:0%
+luckily um we can just look at a 2d
+map of this variation and get all the
+
+ align:start position:0%
+map of this variation and get all the
+ 
+
+ align:start position:0%
+map of this variation and get all the
+information we need okay for almost all
+
+ align:start position:0%
+information we need okay for almost all
+ 
+
+ align:start position:0%
+information we need okay for almost all
+materials and so how do you get a 2d map
+
+ align:start position:0%
+materials and so how do you get a 2d map
+ 
+
+ align:start position:0%
+materials and so how do you get a 2d map
+well then instead of doing like the
+
+ align:start position:0%
+well then instead of doing like the
+ 
+
+ align:start position:0%
+well then instead of doing like the
+whole of volume you just walk through
+
+ align:start position:0%
+whole of volume you just walk through
+ 
+
+ align:start position:0%
+whole of volume you just walk through
+the volume along lines you literally
+
+ align:start position:0%
+the volume along lines you literally
+ 
+
+ align:start position:0%
+the volume along lines you literally
+just walk along this line and then this
+
+ align:start position:0%
+just walk along this line and then this
+ 
+
+ align:start position:0%
+just walk along this line and then this
+line and then down and then back and
+
+ align:start position:0%
+line and then down and then back and
+ 
+
+ align:start position:0%
+line and then down and then back and
+then up and as you're doing this walk
+
+ align:start position:0%
+then up and as you're doing this walk
+ 
+
+ align:start position:0%
+then up and as you're doing this walk
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+kpace you plot the energy bands and you
+
+ align:start position:0%
+kpace you plot the energy bands and you
+ 
+
+ align:start position:0%
+kpace you plot the energy bands and you
+connect them together and you draw lines
+
+ align:start position:0%
+connect them together and you draw lines
+ 
+
+ align:start position:0%
+connect them together and you draw lines
+between those you know those connections
+
+ align:start position:0%
+between those you know those connections
+ 
+
+ align:start position:0%
+between those you know those connections
+this is the same energy level just
+
+ align:start position:0%
+this is the same energy level just
+ 
+
+ align:start position:0%
+this is the same energy level just
+moving around along that
+
+ align:start position:0%
+moving around along that
+ 
+
+ align:start position:0%
+moving around along that
+walk okay
+
+ align:start position:0%
+walk okay
+ 
+
+ align:start position:0%
+walk okay
+so that seems like an
+
+ align:start position:0%
+so that seems like an
+ 
+
+ align:start position:0%
+so that seems like an
+oversimplification because I'm not going
+
+ align:start position:0%
+oversimplification because I'm not going
+ 
+
+ align:start position:0%
+oversimplification because I'm not going
+through the whole bran Zone by any means
+
+ align:start position:0%
+through the whole bran Zone by any means
+ 
+
+ align:start position:0%
+through the whole bran Zone by any means
+I'm just going through very particular
+
+ align:start position:0%
+I'm just going through very particular
+ 
+
+ align:start position:0%
+I'm just going through very particular
+lines in there and yet it's all we need
+
+ align:start position:0%
+lines in there and yet it's all we need
+ 
+
+ align:start position:0%
+lines in there and yet it's all we need
+and the reason is that um most of the
+
+ align:start position:0%
+and the reason is that um most of the
+ 
+
+ align:start position:0%
+and the reason is that um most of the
+things I want to know about a material
+
+ align:start position:0%
+things I want to know about a material
+ 
+
+ align:start position:0%
+things I want to know about a material
+most of the things I want to know are
+
+ align:start position:0%
+most of the things I want to know are
+ 
+
+ align:start position:0%
+most of the things I want to know are
+going to come from the the variation
+
+ align:start position:0%
+going to come from the the variation
+ 
+
+ align:start position:0%
+going to come from the the variation
+between in these bands between High
+
+ align:start position:0%
+between in these bands between High
+ 
+
+ align:start position:0%
+between in these bands between High
+symmetry points in kpace okay so I can
+
+ align:start position:0%
+symmetry points in kpace okay so I can
+ 
+
+ align:start position:0%
+symmetry points in kpace okay so I can
+go to other points in the bruan zone and
+
+ align:start position:0%
+go to other points in the bruan zone and
+ 
+
+ align:start position:0%
+go to other points in the bruan zone and
+I'll get other levels I'll get you know
+
+ align:start position:0%
+I'll get other levels I'll get you know
+ 
+
+ align:start position:0%
+I'll get other levels I'll get you know
+a different set of levels um but it's
+
+ align:start position:0%
+a different set of levels um but it's
+ 
+
+ align:start position:0%
+a different set of levels um but it's
+probably not going to add to my
+
+ align:start position:0%
+probably not going to add to my
+ 
+
+ align:start position:0%
+probably not going to add to my
+knowledge of the
+
+ align:start position:0%
+knowledge of the
+ 
+
+ align:start position:0%
+knowledge of the
+material and the properties that I can
+
+ align:start position:0%
+material and the properties that I can
+ 
+
+ align:start position:0%
+material and the properties that I can
+get so for example you know I'm very
+
+ align:start position:0%
+get so for example you know I'm very
+ 
+
+ align:start position:0%
+get so for example you know I'm very
+interested in this where this has a
+
+ align:start position:0%
+interested in this where this has a
+ 
+
+ align:start position:0%
+interested in this where this has a
+maximum the veilance band and where the
+
+ align:start position:0%
+maximum the veilance band and where the
+ 
+
+ align:start position:0%
+maximum the veilance band and where the
+cond ruction band has a minimum right
+
+ align:start position:0%
+cond ruction band has a minimum right
+ 
+
+ align:start position:0%
+cond ruction band has a minimum right
+and you'll notice the minimum for
+
+ align:start position:0%
+and you'll notice the minimum for
+ 
+
+ align:start position:0%
+and you'll notice the minimum for
+silicon is actually not at this High
+
+ align:start position:0%
+silicon is actually not at this High
+ 
+
+ align:start position:0%
+silicon is actually not at this High
+symmetry point x but it does come along
+
+ align:start position:0%
+symmetry point x but it does come along
+ 
+
+ align:start position:0%
+symmetry point x but it does come along
+the path to X from another high symmetry
+
+ align:start position:0%
+the path to X from another high symmetry
+ 
+
+ align:start position:0%
+the path to X from another high symmetry
+Point gamma it came along that path and
+
+ align:start position:0%
+Point gamma it came along that path and
+ 
+
+ align:start position:0%
+Point gamma it came along that path and
+there's no place in case base that gives
+
+ align:start position:0%
+there's no place in case base that gives
+ 
+
+ align:start position:0%
+there's no place in case base that gives
+me a lower point you see so I nailed the
+
+ align:start position:0%
+me a lower point you see so I nailed the
+ 
+
+ align:start position:0%
+me a lower point you see so I nailed the
+thing I needed I nailed it by going from
+
+ align:start position:0%
+thing I needed I nailed it by going from
+ 
+
+ align:start position:0%
+thing I needed I nailed it by going from
+one high symmetry point to another and
+
+ align:start position:0%
+one high symmetry point to another and
+ 
+
+ align:start position:0%
+one high symmetry point to another and
+that's what a band diagram is it's a
+
+ align:start position:0%
+that's what a band diagram is it's a
+ 
+
+ align:start position:0%
+that's what a band diagram is it's a
+it's a walk through Cas space along
+
+ align:start position:0%
+it's a walk through Cas space along
+ 
+
+ align:start position:0%
+it's a walk through Cas space along
+lines between High symmetry points and
+
+ align:start position:0%
+lines between High symmetry points and
+ 
+
+ align:start position:0%
+lines between High symmetry points and
+that gives you the map that you need and
+
+ align:start position:0%
+that gives you the map that you need and
+ 
+
+ align:start position:0%
+that gives you the map that you need and
+it's a really nice these sometimes look
+
+ align:start position:0%
+it's a really nice these sometimes look
+ 
+
+ align:start position:0%
+it's a really nice these sometimes look
+really complicated but just think it's
+
+ align:start position:0%
+really complicated but just think it's
+ 
+
+ align:start position:0%
+really complicated but just think it's
+saving you a whole lot of trouble and
+
+ align:start position:0%
+saving you a whole lot of trouble and
+ 
+
+ align:start position:0%
+saving you a whole lot of trouble and
+you know compared to all the data you
+
+ align:start position:0%
+you know compared to all the data you
+ 
+
+ align:start position:0%
+you know compared to all the data you
+actually could have but it's giving you
+
+ align:start position:0%
+actually could have but it's giving you
+ 
+
+ align:start position:0%
+actually could have but it's giving you
+what you need are there any
+
+ align:start position:0%
+what you need are there any
+ 
+
+ align:start position:0%
+what you need are there any
+uh questions about
+
+ align:start position:0%
+uh questions about
+ 
+
+ align:start position:0%
+uh questions about
+that it's kind of sort of the key Point
+
+ align:start position:0%
+that it's kind of sort of the key Point
+ 
+
+ align:start position:0%
+that it's kind of sort of the key Point
+here from this um band structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we talked about how
+
+ align:start position:0%
+and we talked about how
+ 
+
+ align:start position:0%
+and we talked about how
+um you uh you know we've talked about
+
+ align:start position:0%
+um you uh you know we've talked about
+ 
+
+ align:start position:0%
+um you uh you know we've talked about
+this how you you get your bands just
+
+ align:start position:0%
+this how you you get your bands just
+ 
+
+ align:start position:0%
+this how you you get your bands just
+like in an atom or a molecule you get
+
+ align:start position:0%
+like in an atom or a molecule you get
+ 
+
+ align:start position:0%
+like in an atom or a molecule you get
+your energy levels from solving the Sher
+
+ align:start position:0%
+your energy levels from solving the Sher
+ 
+
+ align:start position:0%
+your energy levels from solving the Sher
+equation and then you fill them
+
+ align:start position:0%
+equation and then you fill them
+ 
+
+ align:start position:0%
+equation and then you fill them
+up right using the poly exclusion rule
+
+ align:start position:0%
+up right using the poly exclusion rule
+ 
+
+ align:start position:0%
+up right using the poly exclusion rule
+right um add a little bit of Huns rule
+
+ align:start position:0%
+right um add a little bit of Huns rule
+ 
+
+ align:start position:0%
+right um add a little bit of Huns rule
+to it although that can be violated
+
+ align:start position:0%
+to it although that can be violated
+ 
+
+ align:start position:0%
+to it although that can be violated
+don't tell anyone um and uh and you fill
+
+ align:start position:0%
+don't tell anyone um and uh and you fill
+ 
+
+ align:start position:0%
+don't tell anyone um and uh and you fill
+them up and then you're done and when
+
+ align:start position:0%
+them up and then you're done and when
+ 
+
+ align:start position:0%
+them up and then you're done and when
+you're done you've got your firmy energy
+
+ align:start position:0%
+you're done you've got your firmy energy
+ 
+
+ align:start position:0%
+you're done you've got your firmy energy
+okay um that that's now it's the same
+
+ align:start position:0%
+okay um that that's now it's the same
+ 
+
+ align:start position:0%
+okay um that that's now it's the same
+exact thing here in the band structure
+
+ align:start position:0%
+exact thing here in the band structure
+ 
+
+ align:start position:0%
+exact thing here in the band structure
+okay you you fill your bands up until
+
+ align:start position:0%
+okay you you fill your bands up until
+ 
+
+ align:start position:0%
+okay you you fill your bands up until
+you've you filled them up with the
+
+ align:start position:0%
+you've you filled them up with the
+ 
+
+ align:start position:0%
+you've you filled them up with the
+number of electrons that you had in your
+
+ align:start position:0%
+number of electrons that you had in your
+ 
+
+ align:start position:0%
+number of electrons that you had in your
+simulation okay and uh then you've got
+
+ align:start position:0%
+simulation okay and uh then you've got
+ 
+
+ align:start position:0%
+simulation okay and uh then you've got
+your fir energy and then if there's a
+
+ align:start position:0%
+your fir energy and then if there's a
+ 
+
+ align:start position:0%
+your fir energy and then if there's a
+small Gap there and no bands cross it it
+
+ align:start position:0%
+small Gap there and no bands cross it it
+ 
+
+ align:start position:0%
+small Gap there and no bands cross it it
+cannot be a what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it cannot be
+
+ align:start position:0%
+it cannot be
+ 
+
+ align:start position:0%
+it cannot be
+a a metal it can be a
+
+ align:start position:0%
+a a metal it can be a
+ 
+
+ align:start position:0%
+a a metal it can be a
+conductor it can be a conductor a
+
+ align:start position:0%
+conductor it can be a conductor a
+ 
+
+ align:start position:0%
+conductor it can be a conductor a
+semiconductor or a really bad insulating
+
+ align:start position:0%
+semiconductor or a really bad insulating
+ 
+
+ align:start position:0%
+semiconductor or a really bad insulating
+conductor also known as an
+
+ align:start position:0%
+conductor also known as an
+ 
+
+ align:start position:0%
+conductor also known as an
+insulator but it can't be a
+
+ align:start position:0%
+insulator but it can't be a
+ 
+
+ align:start position:0%
+insulator but it can't be a
+metal right because if if no bands cross
+
+ align:start position:0%
+metal right because if if no bands cross
+ 
+
+ align:start position:0%
+metal right because if if no bands cross
+if there's a gap here between where you
+
+ align:start position:0%
+if there's a gap here between where you
+ 
+
+ align:start position:0%
+if there's a gap here between where you
+filled to and the next place then it's
+
+ align:start position:0%
+filled to and the next place then it's
+ 
+
+ align:start position:0%
+filled to and the next place then it's
+not a metal okay
+
+ align:start position:0%
+not a metal okay
+ 
+
+ align:start position:0%
+not a metal okay
+so we talked about that um and that's uh
+
+ align:start position:0%
+so we talked about that um and that's uh
+ 
+
+ align:start position:0%
+so we talked about that um and that's uh
+uh certainly if you have an odd number
+
+ align:start position:0%
+uh certainly if you have an odd number
+ 
+
+ align:start position:0%
+uh certainly if you have an odd number
+of electrons it has to be a metal
+
+ align:start position:0%
+of electrons it has to be a metal
+ 
+
+ align:start position:0%
+of electrons it has to be a metal
+okay um and there's a calculation I
+
+ align:start position:0%
+okay um and there's a calculation I
+ 
+
+ align:start position:0%
+okay um and there's a calculation I
+showed this last time uh of an insulator
+
+ align:start position:0%
+showed this last time uh of an insulator
+ 
+
+ align:start position:0%
+showed this last time uh of an insulator
+and we we also talked about how these
+
+ align:start position:0%
+and we we also talked about how these
+ 
+
+ align:start position:0%
+and we we also talked about how these
+um this density of
+
+ align:start position:0%
+um this density of
+ 
+
+ align:start position:0%
+um this density of
+States okay is another really important
+
+ align:start position:0%
+States okay is another really important
+ 
+
+ align:start position:0%
+States okay is another really important
+thing here and since this is in your
+
+ align:start position:0%
+thing here and since this is in your
+ 
+
+ align:start position:0%
+thing here and since this is in your
+homework as well in your current pet
+
+ align:start position:0%
+homework as well in your current pet
+ 
+
+ align:start position:0%
+homework as well in your current pet
+um now I'll get to transport in a sec um
+
+ align:start position:0%
+um now I'll get to transport in a sec um
+ 
+
+ align:start position:0%
+um now I'll get to transport in a sec um
+I want to make sure we know what density
+
+ align:start position:0%
+I want to make sure we know what density
+ 
+
+ align:start position:0%
+I want to make sure we know what density
+of states is okay
+
+ align:start position:0%
+of states is okay
+ 
+
+ align:start position:0%
+of states is okay
+um so what would the density of states
+
+ align:start position:0%
+um so what would the density of states
+ 
+
+ align:start position:0%
+um so what would the density of states
+of the um somebody tell me what the
+
+ align:start position:0%
+of the um somebody tell me what the
+ 
+
+ align:start position:0%
+of the um somebody tell me what the
+density of
+
+ align:start position:0%
+density of
+ 
+
+ align:start position:0%
+density of
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+of the carbon atom would look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like okay so let's let's draw so we had
+
+ align:start position:0%
+like okay so let's let's draw so we had
+ 
+
+ align:start position:0%
+like okay so let's let's draw so we had
+the carbon at would have 1 s and 2
+
+ align:start position:0%
+the carbon at would have 1 s and 2
+ 
+
+ align:start position:0%
+the carbon at would have 1 s and 2
+s and 2 p and how many would I put
+
+ align:start position:0%
+s and 2 p and how many would I put
+ 
+
+ align:start position:0%
+s and 2 p and how many would I put
+here okay and what about the next one
+
+ align:start position:0%
+here okay and what about the next one
+ 
+
+ align:start position:0%
+here okay and what about the next one
+okay I'm liking it and
+
+ align:start position:0%
+okay I'm liking it and
+ 
+
+ align:start position:0%
+okay I'm liking it and
+here two okay like that oh oh wait hold
+
+ align:start position:0%
+here two okay like that oh oh wait hold
+ 
+
+ align:start position:0%
+here two okay like that oh oh wait hold
+on okay thank you like this oh sorry all
+
+ align:start position:0%
+on okay thank you like this oh sorry all
+ 
+
+ align:start position:0%
+on okay thank you like this oh sorry all
+right that would be an open open shell
+
+ align:start position:0%
+right that would be an open open shell
+ 
+
+ align:start position:0%
+right that would be an open open shell
+signal it thank you very much okay now
+
+ align:start position:0%
+signal it thank you very much okay now
+ 
+
+ align:start position:0%
+signal it thank you very much okay now
+um okay so what's my what's my Den
+
+ align:start position:0%
+um okay so what's my what's my Den
+ 
+
+ align:start position:0%
+um okay so what's my what's my Den
+states of this how do I do
+
+ align:start position:0%
+states of this how do I do
+ 
+
+ align:start position:0%
+states of this how do I do
+it okay yeah so I'm seeing people go
+
+ align:start position:0%
+it okay yeah so I'm seeing people go
+ 
+
+ align:start position:0%
+it okay yeah so I'm seeing people go
+like this so this now so this was energy
+
+ align:start position:0%
+like this so this now so this was energy
+ 
+
+ align:start position:0%
+like this so this now so this was energy
+here and now this is going to be energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay what's my next
+
+ align:start position:0%
+here okay what's my next
+ 
+
+ align:start position:0%
+here okay what's my next
+step drawing a curve drawing a curve
+
+ align:start position:0%
+step drawing a curve drawing a curve
+ 
+
+ align:start position:0%
+step drawing a curve drawing a curve
+okay I'm going to draw a curve what is
+
+ align:start position:0%
+okay I'm going to draw a curve what is
+ 
+
+ align:start position:0%
+okay I'm going to draw a curve what is
+that that's 1 s why not I've just
+
+ align:start position:0%
+that that's 1 s why not I've just
+ 
+
+ align:start position:0%
+that that's 1 s why not I've just
+broadened it we'll make that 1 s
+
+ align:start position:0%
+broadened it we'll make that 1 s
+ 
+
+ align:start position:0%
+broadened it we'll make that 1 s
+and what's my next curve I want to draw
+
+ align:start position:0%
+and what's my next curve I want to draw
+ 
+
+ align:start position:0%
+and what's my next curve I want to draw
+okay sure and it should be spaced such
+
+ align:start position:0%
+okay sure and it should be spaced such
+ 
+
+ align:start position:0%
+okay sure and it should be spaced such
+that it is um it is about you know it
+
+ align:start position:0%
+that it is um it is about you know it
+ 
+
+ align:start position:0%
+that it is um it is about you know it
+should be the right energy spacing that
+
+ align:start position:0%
+should be the right energy spacing that
+ 
+
+ align:start position:0%
+should be the right energy spacing that
+I get from my quantum mechanical
+
+ align:start position:0%
+I get from my quantum mechanical
+ 
+
+ align:start position:0%
+I get from my quantum mechanical
+simulations okay and what's
+
+ align:start position:0%
+simulations okay and what's
+ 
+
+ align:start position:0%
+simulations okay and what's
+next to P let's make this go out
+
+ align:start position:0%
+next to P let's make this go out
+ 
+
+ align:start position:0%
+next to P let's make this go out
+further okay now 2p now how should I do
+
+ align:start position:0%
+further okay now 2p now how should I do
+ 
+
+ align:start position:0%
+further okay now 2p now how should I do
+this should I make it the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shift it
+
+ align:start position:0%
+shift it
+ 
+
+ align:start position:0%
+shift it
+down same is it different than to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us well let's see I mean I had two
+
+ align:start position:0%
+us well let's see I mean I had two
+ 
+
+ align:start position:0%
+us well let's see I mean I had two
+electrons in each of these how many
+
+ align:start position:0%
+electrons in each of these how many
+ 
+
+ align:start position:0%
+electrons in each of these how many
+electrons could go into
+
+ align:start position:0%
+electrons could go into
+ 
+
+ align:start position:0%
+electrons could go into
+2p six right so I actually have more
+
+ align:start position:0%
+2p six right so I actually have more
+ 
+
+ align:start position:0%
+2p six right so I actually have more
+states there I have three times as many
+
+ align:start position:0%
+states there I have three times as many
+ 
+
+ align:start position:0%
+states there I have three times as many
+as here so in a way if you're thinking
+
+ align:start position:0%
+as here so in a way if you're thinking
+ 
+
+ align:start position:0%
+as here so in a way if you're thinking
+about these as sort of a vertical line
+
+ align:start position:0%
+about these as sort of a vertical line
+ 
+
+ align:start position:0%
+about these as sort of a vertical line
+okay that is um that that is spread out
+
+ align:start position:0%
+okay that is um that that is spread out
+ 
+
+ align:start position:0%
+okay that is um that that is spread out
+by some smoothing function just to make
+
+ align:start position:0%
+by some smoothing function just to make
+ 
+
+ align:start position:0%
+by some smoothing function just to make
+it into a nice pretty
+
+ align:start position:0%
+it into a nice pretty
+ 
+
+ align:start position:0%
+it into a nice pretty
+curve I mean if it's an atom if it's
+
+ align:start position:0%
+curve I mean if it's an atom if it's
+ 
+
+ align:start position:0%
+curve I mean if it's an atom if it's
+really an atom then it's really just a
+
+ align:start position:0%
+really an atom then it's really just a
+ 
+
+ align:start position:0%
+really an atom then it's really just a
+line it's a Delta function okay
+
+ align:start position:0%
+line it's a Delta function okay
+ 
+
+ align:start position:0%
+line it's a Delta function okay
+um but then this should have three lines
+
+ align:start position:0%
+um but then this should have three lines
+ 
+
+ align:start position:0%
+um but then this should have three lines
+all on top of each other right and so if
+
+ align:start position:0%
+all on top of each other right and so if
+ 
+
+ align:start position:0%
+all on top of each other right and so if
+if I look at that it's going to lead to
+
+ align:start position:0%
+if I look at that it's going to lead to
+ 
+
+ align:start position:0%
+if I look at that it's going to lead to
+a a bigger
+
+ align:start position:0%
+a a bigger
+ 
+
+ align:start position:0%
+a a bigger
+Peak right that has you know more area
+
+ align:start position:0%
+Peak right that has you know more area
+ 
+
+ align:start position:0%
+Peak right that has you know more area
+under it right three times as much yeah
+
+ align:start position:0%
+under it right three times as much yeah
+ 
+
+ align:start position:0%
+under it right three times as much yeah
+okay so you can you can fit six
+
+ align:start position:0%
+okay so you can you can fit six
+ 
+
+ align:start position:0%
+okay so you can you can fit six
+electrons into this peak this is what
+
+ align:start position:0%
+electrons into this peak this is what
+ 
+
+ align:start position:0%
+electrons into this peak this is what
+the density of states is right it is
+
+ align:start position:0%
+the density of states is right it is
+ 
+
+ align:start position:0%
+the density of states is right it is
+uh the density of
+
+ align:start position:0%
+uh the density of
+ 
+
+ align:start position:0%
+uh the density of
+States um it is these levels it's these
+
+ align:start position:0%
+States um it is these levels it's these
+ 
+
+ align:start position:0%
+States um it is these levels it's these
+levels okay does everybody see that now
+
+ align:start position:0%
+levels okay does everybody see that now
+ 
+
+ align:start position:0%
+levels okay does everybody see that now
+where's my firmy energy
+
+ align:start position:0%
+where's my firmy energy
+ 
+
+ align:start position:0%
+where's my firmy energy
+for the carbon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atom is it over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it feels like it should be here
+
+ align:start position:0%
+here it feels like it should be here
+ 
+
+ align:start position:0%
+here it feels like it should be here
+right we like firmy energies between
+
+ align:start position:0%
+right we like firmy energies between
+ 
+
+ align:start position:0%
+right we like firmy energies between
+Peaks but that's just because we like
+
+ align:start position:0%
+Peaks but that's just because we like
+ 
+
+ align:start position:0%
+Peaks but that's just because we like
+semiconductors no we like Metals too and
+
+ align:start position:0%
+semiconductors no we like Metals too and
+ 
+
+ align:start position:0%
+semiconductors no we like Metals too and
+insulators they're all good so where
+
+ align:start position:0%
+insulators they're all good so where
+ 
+
+ align:start position:0%
+insulators they're all good so where
+should it be
+
+ align:start position:0%
+should it be
+ 
+
+ align:start position:0%
+should it be
+does this sound
+
+ align:start position:0%
+does this sound
+ 
+
+ align:start position:0%
+does this sound
+good over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here somebody tell me when to
+
+ align:start position:0%
+here somebody tell me when to
+ 
+
+ align:start position:0%
+here somebody tell me when to
+stop somebody say
+
+ align:start position:0%
+stop somebody say
+ 
+
+ align:start position:0%
+stop somebody say
+stop yeah okay now why am I stopping
+
+ align:start position:0%
+stop yeah okay now why am I stopping
+ 
+
+ align:start position:0%
+stop yeah okay now why am I stopping
+here so that's my firmy
+
+ align:start position:0%
+here so that's my firmy
+ 
+
+ align:start position:0%
+here so that's my firmy
+energy for the carbon atom why is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there well it's an atom so let's not
+
+ align:start position:0%
+there well it's an atom so let's not
+ 
+
+ align:start position:0%
+there well it's an atom so let's not
+think about it necessarily as conducting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the definition right I mean here
+
+ align:start position:0%
+that's the definition right I mean here
+ 
+
+ align:start position:0%
+that's the definition right I mean here
+I here I filled and I stopped well yeah
+
+ align:start position:0%
+I here I filled and I stopped well yeah
+ 
+
+ align:start position:0%
+I here I filled and I stopped well yeah
+so here I filled and I stopped and here
+
+ align:start position:0%
+so here I filled and I stopped and here
+ 
+
+ align:start position:0%
+so here I filled and I stopped and here
+I filled and I stopped and what uh the
+
+ align:start position:0%
+I filled and I stopped and what uh the
+ 
+
+ align:start position:0%
+I filled and I stopped and what uh the
+gentleman over there said is it's where
+
+ align:start position:0%
+gentleman over there said is it's where
+ 
+
+ align:start position:0%
+gentleman over there said is it's where
+you stop filling right and so here is
+
+ align:start position:0%
+you stop filling right and so here is
+ 
+
+ align:start position:0%
+you stop filling right and so here is
+where I stopped filling because I had
+
+ align:start position:0%
+where I stopped filling because I had
+ 
+
+ align:start position:0%
+where I stopped filling because I had
+this peak of
+
+ align:start position:0%
+this peak of
+ 
+
+ align:start position:0%
+this peak of
+states right it's a peak of states the
+
+ align:start position:0%
+states right it's a peak of states the
+ 
+
+ align:start position:0%
+states right it's a peak of states the
+density of
+
+ align:start position:0%
+density of
+ 
+
+ align:start position:0%
+density of
+states that is only filled by two
+
+ align:start position:0%
+states that is only filled by two
+ 
+
+ align:start position:0%
+states that is only filled by two
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+right does everybody see that right so
+
+ align:start position:0%
+right does everybody see that right so
+ 
+
+ align:start position:0%
+right does everybody see that right so
+you know so if I had
+
+ align:start position:0%
+you know so if I had
+ 
+
+ align:start position:0%
+you know so if I had
+um um something else like say neon would
+
+ align:start position:0%
+um um something else like say neon would
+ 
+
+ align:start position:0%
+um um something else like say neon would
+my firy energy be inside the
+
+ align:start position:0%
+my firy energy be inside the
+ 
+
+ align:start position:0%
+my firy energy be inside the
+peak no just outside of it because I
+
+ align:start position:0%
+peak no just outside of it because I
+ 
+
+ align:start position:0%
+peak no just outside of it because I
+would have filled it right yeah besides
+
+ align:start position:0%
+would have filled it right yeah besides
+ 
+
+ align:start position:0%
+would have filled it right yeah besides
+the change in the location of the FY
+
+ align:start position:0%
+the change in the location of the FY
+ 
+
+ align:start position:0%
+the change in the location of the FY
+energy would like the density States be
+
+ align:start position:0%
+energy would like the density States be
+ 
+
+ align:start position:0%
+energy would like the density States be
+like look the same for like nitrogen
+
+ align:start position:0%
+like look the same for like nitrogen
+ 
+
+ align:start position:0%
+like look the same for like nitrogen
+it's very good question it would
+
+ align:start position:0%
+it's very good question it would
+ 
+
+ align:start position:0%
+it's very good question it would
+actually in the sense that you know if
+
+ align:start position:0%
+actually in the sense that you know if
+ 
+
+ align:start position:0%
+actually in the sense that you know if
+you're looking at atoms all you're
+
+ align:start position:0%
+you're looking at atoms all you're
+ 
+
+ align:start position:0%
+you're looking at atoms all you're
+really doing you know a density of
+
+ align:start position:0%
+really doing you know a density of
+ 
+
+ align:start position:0%
+really doing you know a density of
+states is a little bit of an odd thing
+
+ align:start position:0%
+states is a little bit of an odd thing
+ 
+
+ align:start position:0%
+states is a little bit of an odd thing
+for an atom but I'm trying to explain it
+
+ align:start position:0%
+for an atom but I'm trying to explain it
+ 
+
+ align:start position:0%
+for an atom but I'm trying to explain it
+in the context of atoms because I really
+
+ align:start position:0%
+in the context of atoms because I really
+ 
+
+ align:start position:0%
+in the context of atoms because I really
+want you guys to see the connection okay
+
+ align:start position:0%
+want you guys to see the connection okay
+ 
+
+ align:start position:0%
+want you guys to see the connection okay
+and really what's what it is um but if
+
+ align:start position:0%
+and really what's what it is um but if
+ 
+
+ align:start position:0%
+and really what's what it is um but if
+you look at atoms they're just they're
+
+ align:start position:0%
+you look at atoms they're just they're
+ 
+
+ align:start position:0%
+you look at atoms they're just they're
+nothing more than levels and those
+
+ align:start position:0%
+nothing more than levels and those
+ 
+
+ align:start position:0%
+nothing more than levels and those
+discret
+
+ align:start position:0%
+discret
+ 
+
+ align:start position:0%
+discret
+levels okay become little shapes that
+
+ align:start position:0%
+levels okay become little shapes that
+ 
+
+ align:start position:0%
+levels okay become little shapes that
+you broaden a little so it would look
+
+ align:start position:0%
+you broaden a little so it would look
+ 
+
+ align:start position:0%
+you broaden a little so it would look
+the same as nitrogen because in nitrogen
+
+ align:start position:0%
+the same as nitrogen because in nitrogen
+ 
+
+ align:start position:0%
+the same as nitrogen because in nitrogen
+you would have that now what does that
+
+ align:start position:0%
+you would have that now what does that
+ 
+
+ align:start position:0%
+you would have that now what does that
+do well it'll change these energy level
+
+ align:start position:0%
+do well it'll change these energy level
+ 
+
+ align:start position:0%
+do well it'll change these energy level
+positions it'll shift them around right
+
+ align:start position:0%
+positions it'll shift them around right
+ 
+
+ align:start position:0%
+positions it'll shift them around right
+this may even change the 1s may go down
+
+ align:start position:0%
+this may even change the 1s may go down
+ 
+
+ align:start position:0%
+this may even change the 1s may go down
+or up this may change a little and then
+
+ align:start position:0%
+or up this may change a little and then
+ 
+
+ align:start position:0%
+or up this may change a little and then
+here you're going to change not the peak
+
+ align:start position:0%
+here you're going to change not the peak
+ 
+
+ align:start position:0%
+here you're going to change not the peak
+because you still got six states in you
+
+ align:start position:0%
+because you still got six states in you
+ 
+
+ align:start position:0%
+because you still got six states in you
+know you still got six electrons you can
+
+ align:start position:0%
+know you still got six electrons you can
+ 
+
+ align:start position:0%
+know you still got six electrons you can
+put in there but you will change the
+
+ align:start position:0%
+put in there but you will change the
+ 
+
+ align:start position:0%
+put in there but you will change the
+firmy energy within the peak because you
+
+ align:start position:0%
+firmy energy within the peak because you
+ 
+
+ align:start position:0%
+firmy energy within the peak because you
+can fill it by one
+
+ align:start position:0%
+can fill it by one
+ 
+
+ align:start position:0%
+can fill it by one
+more okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so and you know just like going all the
+
+ align:start position:0%
+so and you know just like going all the
+ 
+
+ align:start position:0%
+so and you know just like going all the
+way back to our first or second
+
+ align:start position:0%
+way back to our first or second
+ 
+
+ align:start position:0%
+way back to our first or second
+lecture where we had the orbitals of
+
+ align:start position:0%
+lecture where we had the orbitals of
+ 
+
+ align:start position:0%
+lecture where we had the orbitals of
+hydro of the hydrogen atom okay so we
+
+ align:start position:0%
+hydro of the hydrogen atom okay so we
+ 
+
+ align:start position:0%
+hydro of the hydrogen atom okay so we
+had the the nucleus and we had this
+
+ align:start position:0%
+had the the nucleus and we had this
+ 
+
+ align:start position:0%
+had the the nucleus and we had this
+electron that does not
+
+ align:start position:0%
+electron that does not
+ 
+
+ align:start position:0%
+electron that does not
+orbit but there it is orbiting and then
+
+ align:start position:0%
+orbit but there it is orbiting and then
+ 
+
+ align:start position:0%
+orbit but there it is orbiting and then
+we had like the 1s and then we had like
+
+ align:start position:0%
+we had like the 1s and then we had like
+ 
+
+ align:start position:0%
+we had like the 1s and then we had like
+the 2s
+
+ align:start position:0%
+the 2s
+ 
+
+ align:start position:0%
+the 2s
+and remember how we talked about it can
+
+ align:start position:0%
+and remember how we talked about it can
+ 
+
+ align:start position:0%
+and remember how we talked about it can
+actually make transitions between the
+
+ align:start position:0%
+actually make transitions between the
+ 
+
+ align:start position:0%
+actually make transitions between the
+two without actually existing between
+
+ align:start position:0%
+two without actually existing between
+ 
+
+ align:start position:0%
+two without actually existing between
+the two right there sometimes it has to
+
+ align:start position:0%
+the two right there sometimes it has to
+ 
+
+ align:start position:0%
+the two right there sometimes it has to
+cross paths which are totally forbidden
+
+ align:start position:0%
+cross paths which are totally forbidden
+ 
+
+ align:start position:0%
+cross paths which are totally forbidden
+it's sort of exciting it's like some
+
+ align:start position:0%
+it's sort of exciting it's like some
+ 
+
+ align:start position:0%
+it's sort of exciting it's like some
+sort of interesting fiction right that
+
+ align:start position:0%
+sort of interesting fiction right that
+ 
+
+ align:start position:0%
+sort of interesting fiction right that
+this electron is going on an adventure
+
+ align:start position:0%
+this electron is going on an adventure
+ 
+
+ align:start position:0%
+this electron is going on an adventure
+and well that's what this is right there
+
+ align:start position:0%
+and well that's what this is right there
+ 
+
+ align:start position:0%
+and well that's what this is right there
+is no state in here in this energy so
+
+ align:start position:0%
+is no state in here in this energy so
+ 
+
+ align:start position:0%
+is no state in here in this energy so
+the Doss tells you that too right that
+
+ align:start position:0%
+the Doss tells you that too right that
+ 
+
+ align:start position:0%
+the Doss tells you that too right that
+is is what's in the Dos that information
+
+ align:start position:0%
+is is what's in the Dos that information
+ 
+
+ align:start position:0%
+is is what's in the Dos that information
+is contained in the Doss there cannot
+
+ align:start position:0%
+is contained in the Doss there cannot
+ 
+
+ align:start position:0%
+is contained in the Doss there cannot
+be an
+
+ align:start position:0%
+be an
+ 
+
+ align:start position:0%
+be an
+electron with an energy that where
+
+ align:start position:0%
+electron with an energy that where
+ 
+
+ align:start position:0%
+electron with an energy that where
+there's no Doss there's no states to
+
+ align:start position:0%
+there's no Doss there's no states to
+ 
+
+ align:start position:0%
+there's no Doss there's no states to
+support it there okay so you know for an
+
+ align:start position:0%
+support it there okay so you know for an
+ 
+
+ align:start position:0%
+support it there okay so you know for an
+atom like the hydrogen atom or the
+
+ align:start position:0%
+atom like the hydrogen atom or the
+ 
+
+ align:start position:0%
+atom like the hydrogen atom or the
+carbon atom as well that's fairly
+
+ align:start position:0%
+carbon atom as well that's fairly
+ 
+
+ align:start position:0%
+carbon atom as well that's fairly
+obvious because you had your levels and
+
+ align:start position:0%
+obvious because you had your levels and
+ 
+
+ align:start position:0%
+obvious because you had your levels and
+you knew it couldn't be in between those
+
+ align:start position:0%
+you knew it couldn't be in between those
+ 
+
+ align:start position:0%
+you knew it couldn't be in between those
+levels that's the quantization stuff we
+
+ align:start position:0%
+levels that's the quantization stuff we
+ 
+
+ align:start position:0%
+levels that's the quantization stuff we
+talked about but now when you you get to
+
+ align:start position:0%
+talked about but now when you you get to
+ 
+
+ align:start position:0%
+talked about but now when you you get to
+solids and it's a more messy
+
+ align:start position:0%
+solids and it's a more messy
+ 
+
+ align:start position:0%
+solids and it's a more messy
+picture right but it's the same
+
+ align:start position:0%
+picture right but it's the same
+ 
+
+ align:start position:0%
+picture right but it's the same
+understanding that you get out of it
+
+ align:start position:0%
+understanding that you get out of it
+ 
+
+ align:start position:0%
+understanding that you get out of it
+it's the same exact understanding
+
+ align:start position:0%
+it's the same exact understanding
+ 
+
+ align:start position:0%
+it's the same exact understanding
+so what you do
+
+ align:start position:0%
+so what you do
+ 
+
+ align:start position:0%
+so what you do
+for you know atom molecule or solid is
+
+ align:start position:0%
+for you know atom molecule or solid is
+ 
+
+ align:start position:0%
+for you know atom molecule or solid is
+you take your levels you take your
+
+ align:start position:0%
+you take your levels you take your
+ 
+
+ align:start position:0%
+you take your levels you take your
+levels and you turn them
+
+ align:start position:0%
+levels and you turn them
+ 
+
+ align:start position:0%
+levels and you turn them
+over and you count up the number of
+
+ align:start position:0%
+over and you count up the number of
+ 
+
+ align:start position:0%
+over and you count up the number of
+states right and and that that has to be
+
+ align:start position:0%
+states right and and that that has to be
+ 
+
+ align:start position:0%
+states right and and that that has to be
+the same and you get shapes to the Doss
+
+ align:start position:0%
+the same and you get shapes to the Doss
+ 
+
+ align:start position:0%
+the same and you get shapes to the Doss
+if it was an atom I just had these
+
+ align:start position:0%
+if it was an atom I just had these
+ 
+
+ align:start position:0%
+if it was an atom I just had these
+little lines here from the levels and I
+
+ align:start position:0%
+little lines here from the levels and I
+ 
+
+ align:start position:0%
+little lines here from the levels and I
+broaden them now the levels are no
+
+ align:start position:0%
+broaden them now the levels are no
+ 
+
+ align:start position:0%
+broaden them now the levels are no
+longer
+
+ align:start position:0%
+longer
+ 
+
+ align:start position:0%
+longer
+flat if it's a solid they can vary and
+
+ align:start position:0%
+flat if it's a solid they can vary and
+ 
+
+ align:start position:0%
+flat if it's a solid they can vary and
+that when you turn that that on its side
+
+ align:start position:0%
+that when you turn that that on its side
+ 
+
+ align:start position:0%
+that when you turn that that on its side
+it can be like really kind of
+
+ align:start position:0%
+it can be like really kind of
+ 
+
+ align:start position:0%
+it can be like really kind of
+different right but it's telling you the
+
+ align:start position:0%
+different right but it's telling you the
+ 
+
+ align:start position:0%
+different right but it's telling you the
+same thing it's telling you exactly the
+
+ align:start position:0%
+same thing it's telling you exactly the
+ 
+
+ align:start position:0%
+same thing it's telling you exactly the
+same thing you're filling your electrons
+
+ align:start position:0%
+same thing you're filling your electrons
+ 
+
+ align:start position:0%
+same thing you're filling your electrons
+up through here and you're stopping well
+
+ align:start position:0%
+up through here and you're stopping well
+ 
+
+ align:start position:0%
+up through here and you're stopping well
+I don't know is that the firy energy I
+
+ align:start position:0%
+I don't know is that the firy energy I
+ 
+
+ align:start position:0%
+I don't know is that the firy energy I
+didn't tell you but if it is is then
+
+ align:start position:0%
+didn't tell you but if it is is then
+ 
+
+ align:start position:0%
+didn't tell you but if it is is then
+you're stopping there and those are your
+
+ align:start position:0%
+you're stopping there and those are your
+ 
+
+ align:start position:0%
+you're stopping there and those are your
+unoccupied bands and so forth okay does
+
+ align:start position:0%
+unoccupied bands and so forth okay does
+ 
+
+ align:start position:0%
+unoccupied bands and so forth okay does
+everybody see that it's the same
+
+ align:start position:0%
+everybody see that it's the same
+ 
+
+ align:start position:0%
+everybody see that it's the same
+uh same idea but it's more complicated
+
+ align:start position:0%
+uh same idea but it's more complicated
+ 
+
+ align:start position:0%
+uh same idea but it's more complicated
+when you have these curviness
+
+ align:start position:0%
+when you have these curviness
+ 
+
+ align:start position:0%
+when you have these curviness
+is yeah
+
+ align:start position:0%
+is yeah
+ 
+
+ align:start position:0%
+is yeah
+right we
+
+ align:start position:0%
+right we
+ 
+
+ align:start position:0%
+right we
+good sort of any
+
+ align:start position:0%
+good sort of any
+ 
+
+ align:start position:0%
+good sort of any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+thoughts yeah so you're looking at alop
+
+ align:start position:0%
+thoughts yeah so you're looking at alop
+ 
+
+ align:start position:0%
+thoughts yeah so you're looking at alop
+system so this Cas you have done I'm
+
+ align:start position:0%
+system so this Cas you have done I'm
+ 
+
+ align:start position:0%
+system so this Cas you have done I'm
+assuming that for gra this system be
+
+ align:start position:0%
+assuming that for gra this system be
+ 
+
+ align:start position:0%
+assuming that for gra this system be
+completely different completely
+
+ align:start position:0%
+completely different completely
+ 
+
+ align:start position:0%
+completely different completely
+different and so how and so how does
+
+ align:start position:0%
+different and so how and so how does
+ 
+
+ align:start position:0%
+different and so how and so how does
+that TI to solid density of States it's
+
+ align:start position:0%
+that TI to solid density of States it's
+ 
+
+ align:start position:0%
+that TI to solid density of States it's
+you can write the density of states for
+
+ align:start position:0%
+you can write the density of states for
+ 
+
+ align:start position:0%
+you can write the density of states for
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+material and and the same uh concept
+
+ align:start position:0%
+material and and the same uh concept
+ 
+
+ align:start position:0%
+material and and the same uh concept
+always holds right that you have these
+
+ align:start position:0%
+always holds right that you have these
+ 
+
+ align:start position:0%
+always holds right that you have these
+accessible places where the electron can
+
+ align:start position:0%
+accessible places where the electron can
+ 
+
+ align:start position:0%
+accessible places where the electron can
+be with
+
+ align:start position:0%
+be with
+ 
+
+ align:start position:0%
+be with
+some probability of them being there
+
+ align:start position:0%
+some probability of them being there
+ 
+
+ align:start position:0%
+some probability of them being there
+right um in other words it it it's all
+
+ align:start position:0%
+right um in other words it it it's all
+ 
+
+ align:start position:0%
+right um in other words it it it's all
+about how many possible energy levels
+
+ align:start position:0%
+about how many possible energy levels
+ 
+
+ align:start position:0%
+about how many possible energy levels
+you you have as a function of energy
+
+ align:start position:0%
+you you have as a function of energy
+ 
+
+ align:start position:0%
+you you have as a function of energy
+that's really what it is and so you know
+
+ align:start position:0%
+that's really what it is and so you know
+ 
+
+ align:start position:0%
+that's really what it is and so you know
+whatever material you have the density
+
+ align:start position:0%
+whatever material you have the density
+ 
+
+ align:start position:0%
+whatever material you have the density
+of states is is is simply has the same
+
+ align:start position:0%
+of states is is is simply has the same
+ 
+
+ align:start position:0%
+of states is is is simply has the same
+meaning but it will look very different
+
+ align:start position:0%
+meaning but it will look very different
+ 
+
+ align:start position:0%
+meaning but it will look very different
+and in Diamond you're going to get a big
+
+ align:start position:0%
+and in Diamond you're going to get a big
+ 
+
+ align:start position:0%
+and in Diamond you're going to get a big
+band Gap and in graphite well it's a
+
+ align:start position:0%
+band Gap and in graphite well it's a
+ 
+
+ align:start position:0%
+band Gap and in graphite well it's a
+metal right you have a Crossing in
+
+ align:start position:0%
+metal right you have a Crossing in
+ 
+
+ align:start position:0%
+metal right you have a Crossing in
+graphine you have a Crossing um at one
+
+ align:start position:0%
+graphine you have a Crossing um at one
+ 
+
+ align:start position:0%
+graphine you have a Crossing um at one
+part in the band structure goes right
+
+ align:start position:0%
+part in the band structure goes right
+ 
+
+ align:start position:0%
+part in the band structure goes right
+through the what would have been the
+
+ align:start position:0%
+through the what would have been the
+ 
+
+ align:start position:0%
+through the what would have been the
+Gap
+
+ align:start position:0%
+Gap
+ 
+
+ align:start position:0%
+Gap
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you know and that's why when you
+
+ align:start position:0%
+um and you know and that's why when you
+ 
+
+ align:start position:0%
+um and you know and that's why when you
+do your homework uh when you do p at
+
+ align:start position:0%
+do your homework uh when you do p at
+ 
+
+ align:start position:0%
+do your homework uh when you do p at
+five the the you know there are sort of
+
+ align:start position:0%
+five the the you know there are sort of
+ 
+
+ align:start position:0%
+five the the you know there are sort of
+two ways I want you to think about how
+
+ align:start position:0%
+two ways I want you to think about how
+ 
+
+ align:start position:0%
+two ways I want you to think about how
+these molecules absorb light one way is
+
+ align:start position:0%
+these molecules absorb light one way is
+ 
+
+ align:start position:0%
+these molecules absorb light one way is
+that they just have some cut
+
+ align:start position:0%
+that they just have some cut
+ 
+
+ align:start position:0%
+that they just have some cut
+off below which in energy or above which
+
+ align:start position:0%
+off below which in energy or above which
+ 
+
+ align:start position:0%
+off below which in energy or above which
+in wavelength they cannot absorb light
+
+ align:start position:0%
+in wavelength they cannot absorb light
+ 
+
+ align:start position:0%
+in wavelength they cannot absorb light
+so that's just a single cut off but the
+
+ align:start position:0%
+so that's just a single cut off but the
+ 
+
+ align:start position:0%
+so that's just a single cut off but the
+other way is to actually use the
+
+ align:start position:0%
+other way is to actually use the
+ 
+
+ align:start position:0%
+other way is to actually use the
+features in this in this uh plot of
+
+ align:start position:0%
+features in this in this uh plot of
+ 
+
+ align:start position:0%
+features in this in this uh plot of
+levels of accessible States for the
+
+ align:start position:0%
+levels of accessible States for the
+ 
+
+ align:start position:0%
+levels of accessible States for the
+electrons to use this
+
+ align:start position:0%
+electrons to use this
+ 
+
+ align:start position:0%
+electrons to use this
+information and and wait the absorption
+
+ align:start position:0%
+information and and wait the absorption
+ 
+
+ align:start position:0%
+information and and wait the absorption
+of the Sun by this because that's
+
+ align:start position:0%
+of the Sun by this because that's
+ 
+
+ align:start position:0%
+of the Sun by this because that's
+actually what's really going
+
+ align:start position:0%
+actually what's really going
+ 
+
+ align:start position:0%
+actually what's really going
+on okay is that the molecule cannot
+
+ align:start position:0%
+on okay is that the molecule cannot
+ 
+
+ align:start position:0%
+on okay is that the molecule cannot
+absorb the same at all the wavelengths
+
+ align:start position:0%
+absorb the same at all the wavelengths
+ 
+
+ align:start position:0%
+absorb the same at all the wavelengths
+of light because in some places it can't
+
+ align:start position:0%
+of light because in some places it can't
+ 
+
+ align:start position:0%
+of light because in some places it can't
+absorb any light right in some parts of
+
+ align:start position:0%
+absorb any light right in some parts of
+ 
+
+ align:start position:0%
+absorb any light right in some parts of
+the Doss there's no probability so
+
+ align:start position:0%
+the Doss there's no probability so
+ 
+
+ align:start position:0%
+the Doss there's no probability so
+that's um that turns out to have a
+
+ align:start position:0%
+that's um that turns out to have a
+ 
+
+ align:start position:0%
+that's um that turns out to have a
+really big
+
+ align:start position:0%
+really big
+ 
+
+ align:start position:0%
+really big
+impact
+
+ align:start position:0%
+impact
+ 
+
+ align:start position:0%
+impact
+right okay questions thoughts now let me
+
+ align:start position:0%
+right okay questions thoughts now let me
+ 
+
+ align:start position:0%
+right okay questions thoughts now let me
+um before I go
+
+ align:start position:0%
+um before I go
+ 
+
+ align:start position:0%
+um before I go
+on it's okay I I thought maybe we'd have
+
+ align:start position:0%
+on it's okay I I thought maybe we'd have
+ 
+
+ align:start position:0%
+on it's okay I I thought maybe we'd have
+time to do to look at uh intro to solar
+
+ align:start position:0%
+time to do to look at uh intro to solar
+ 
+
+ align:start position:0%
+time to do to look at uh intro to solar
+but that would have been ahead anyway oh
+
+ align:start position:0%
+but that would have been ahead anyway oh
+ 
+
+ align:start position:0%
+but that would have been ahead anyway oh
+wait no
+
+ align:start position:0%
+wait no
+ 
+
+ align:start position:0%
+wait no
+where is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+view
+
+ align:start position:0%
+view
+ 
+
+ align:start position:0%
+view
+huh that's not looking very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good I had a nice
+
+ align:start position:0%
+good I had a nice
+ 
+
+ align:start position:0%
+good I had a nice
+uh what I thought was a nice example of
+
+ align:start position:0%
+uh what I thought was a nice example of
+ 
+
+ align:start position:0%
+uh what I thought was a nice example of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+problem no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hang on one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+um oh boy never show anyone your desktop
+
+ align:start position:0%
+um oh boy never show anyone your desktop
+ 
+
+ align:start position:0%
+um oh boy never show anyone your desktop
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+presentation that's a bad
+
+ align:start position:0%
+presentation that's a bad
+ 
+
+ align:start position:0%
+presentation that's a bad
+idea um but anyway oh final
+
+ align:start position:0%
+idea um but anyway oh final
+ 
+
+ align:start position:0%
+idea um but anyway oh final
+quiz yeah that's from last year yeah
+
+ align:start position:0%
+quiz yeah that's from last year yeah
+ 
+
+ align:start position:0%
+quiz yeah that's from last year yeah
+don't worry it's not it's in a very safe
+
+ align:start position:0%
+don't worry it's not it's in a very safe
+ 
+
+ align:start position:0%
+don't worry it's not it's in a very safe
+location for this
+
+ align:start position:0%
+location for this
+ 
+
+ align:start position:0%
+location for this
+year actually it's very unsafe it's up
+
+ align:start position:0%
+year actually it's very unsafe it's up
+ 
+
+ align:start position:0%
+year actually it's very unsafe it's up
+here anyway uh wait where did it go
+
+ align:start position:0%
+here anyway uh wait where did it go
+ 
+
+ align:start position:0%
+here anyway uh wait where did it go
+ah why can't I see it here we
+
+ align:start position:0%
+ah why can't I see it here we
+ 
+
+ align:start position:0%
+ah why can't I see it here we
+go okay that's the problem I wanted to
+
+ align:start position:0%
+go okay that's the problem I wanted to
+ 
+
+ align:start position:0%
+go okay that's the problem I wanted to
+talk about okay so this was a problem
+
+ align:start position:0%
+talk about okay so this was a problem
+ 
+
+ align:start position:0%
+talk about okay so this was a problem
+from last year's
+
+ align:start position:0%
+from last year's
+ 
+
+ align:start position:0%
+from last year's
+quiz and
+
+ align:start position:0%
+quiz and
+ 
+
+ align:start position:0%
+quiz and
+um wa okay so your adviser has just
+
+ align:start position:0%
+um wa okay so your adviser has just
+ 
+
+ align:start position:0%
+um wa okay so your adviser has just
+spilled coffee on the culmination of
+
+ align:start position:0%
+spilled coffee on the culmination of
+ 
+
+ align:start position:0%
+spilled coffee on the culmination of
+your entire summer urra work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not a true story uh the
+
+ align:start position:0%
+this is not a true story uh the
+ 
+
+ align:start position:0%
+this is not a true story uh the
+prediction of the band structure of an
+
+ align:start position:0%
+prediction of the band structure of an
+ 
+
+ align:start position:0%
+prediction of the band structure of an
+amazing new material for solar cells
+
+ align:start position:0%
+amazing new material for solar cells
+ 
+
+ align:start position:0%
+amazing new material for solar cells
+unfortunately in your excitement to show
+
+ align:start position:0%
+unfortunately in your excitement to show
+ 
+
+ align:start position:0%
+unfortunately in your excitement to show
+your work you forgot to back up your
+
+ align:start position:0%
+your work you forgot to back up your
+ 
+
+ align:start position:0%
+your work you forgot to back up your
+data you dropped your computer in a hot
+
+ align:start position:0%
+data you dropped your computer in a hot
+ 
+
+ align:start position:0%
+data you dropped your computer in a hot
+tub and you forgot everything you
+
+ align:start position:0%
+tub and you forgot everything you
+ 
+
+ align:start position:0%
+tub and you forgot everything you
+did so you only have that one print out
+
+ align:start position:0%
+did so you only have that one print out
+ 
+
+ align:start position:0%
+did so you only have that one print out
+now stained with
+
+ align:start position:0%
+now stained with
+ 
+
+ align:start position:0%
+now stained with
+coffee can you believe it this is what
+
+ align:start position:0%
+coffee can you believe it this is what
+ 
+
+ align:start position:0%
+coffee can you believe it this is what
+you got nothing
+
+ align:start position:0%
+you got nothing
+ 
+
+ align:start position:0%
+you got nothing
+else okay
+
+ align:start position:0%
+else okay
+ 
+
+ align:start position:0%
+else okay
+was this material you want to put it
+
+ align:start position:0%
+was this material you want to put it
+ 
+
+ align:start position:0%
+was this material you want to put it
+back together because you know it was 4
+
+ align:start position:0%
+back together because you know it was 4
+ 
+
+ align:start position:0%
+back together because you know it was 4
+in the morning you would had a lot of
+
+ align:start position:0%
+in the morning you would had a lot of
+ 
+
+ align:start position:0%
+in the morning you would had a lot of
+noos but still you're pretty sure you
+
+ align:start position:0%
+noos but still you're pretty sure you
+ 
+
+ align:start position:0%
+noos but still you're pretty sure you
+remember it was going to change the
+
+ align:start position:0%
+remember it was going to change the
+ 
+
+ align:start position:0%
+remember it was going to change the
+whole field of solar okay now from this
+
+ align:start position:0%
+whole field of solar okay now from this
+ 
+
+ align:start position:0%
+whole field of solar okay now from this
+was this material a metal a
+
+ align:start position:0%
+was this material a metal a
+ 
+
+ align:start position:0%
+was this material a metal a
+semiconductor or an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insulator tell me
+
+ align:start position:0%
+insulator tell me
+ 
+
+ align:start position:0%
+insulator tell me
+why really
+
+ align:start position:0%
+why really
+ 
+
+ align:start position:0%
+why really
+seriously yeah doesn't the bands are
+
+ align:start position:0%
+seriously yeah doesn't the bands are
+ 
+
+ align:start position:0%
+seriously yeah doesn't the bands are
+crossing um looks like the tallest band
+
+ align:start position:0%
+crossing um looks like the tallest band
+ 
+
+ align:start position:0%
+crossing um looks like the tallest band
+Gap is just under the zero I could can't
+
+ align:start position:0%
+Gap is just under the zero I could can't
+ 
+
+ align:start position:0%
+Gap is just under the zero I could can't
+really tell and then it doesn't look
+
+ align:start position:0%
+really tell and then it doesn't look
+ 
+
+ align:start position:0%
+really tell and then it doesn't look
+like the for the
+
+ align:start position:0%
+like the for the
+ 
+
+ align:start position:0%
+like the for the
+crossing doesn't look like it can you
+
+ align:start position:0%
+crossing doesn't look like it can you
+ 
+
+ align:start position:0%
+crossing doesn't look like it can you
+can you be certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's also solar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell well you do need metal you know
+
+ align:start position:0%
+cell well you do need metal you know
+ 
+
+ align:start position:0%
+cell well you do need metal you know
+maybe it was a revolution in the contact
+
+ align:start position:0%
+maybe it was a revolution in the contact
+ 
+
+ align:start position:0%
+maybe it was a revolution in the contact
+in the metal
+
+ align:start position:0%
+in the metal
+ 
+
+ align:start position:0%
+in the metal
+contact that wouldn't Revol that
+
+ align:start position:0%
+contact that wouldn't Revol that
+ 
+
+ align:start position:0%
+contact that wouldn't Revol that
+wouldn't revolutionize solar PV but
+
+ align:start position:0%
+wouldn't revolutionize solar PV but
+ 
+
+ align:start position:0%
+wouldn't revolutionize solar PV but
+still um again see we're inclined to
+
+ align:start position:0%
+still um again see we're inclined to
+ 
+
+ align:start position:0%
+still um again see we're inclined to
+want to connect these things up right
+
+ align:start position:0%
+want to connect these things up right
+ 
+
+ align:start position:0%
+want to connect these things up right
+we're sort of used to staring at silicon
+
+ align:start position:0%
+we're sort of used to staring at silicon
+ 
+
+ align:start position:0%
+we're sort of used to staring at silicon
+and we think that's going to do that
+
+ align:start position:0%
+and we think that's going to do that
+ 
+
+ align:start position:0%
+and we think that's going to do that
+but I mean it's not I don't know that
+
+ align:start position:0%
+but I mean it's not I don't know that
+ 
+
+ align:start position:0%
+but I mean it's not I don't know that
+you have enough information
+
+ align:start position:0%
+you have enough information
+ 
+
+ align:start position:0%
+you have enough information
+here okay I'm not sure you know enough
+
+ align:start position:0%
+here okay I'm not sure you know enough
+ 
+
+ align:start position:0%
+here okay I'm not sure you know enough
+about this to know that this band didn't
+
+ align:start position:0%
+about this to know that this band didn't
+ 
+
+ align:start position:0%
+about this to know that this band didn't
+actually split and one of them crossed
+
+ align:start position:0%
+actually split and one of them crossed
+ 
+
+ align:start position:0%
+actually split and one of them crossed
+up and went this
+
+ align:start position:0%
+up and went this
+ 
+
+ align:start position:0%
+up and went this
+way right how do you know now there is
+
+ align:start position:0%
+way right how do you know now there is
+ 
+
+ align:start position:0%
+way right how do you know now there is
+one thing you know it's not there's one
+
+ align:start position:0%
+one thing you know it's not there's one
+ 
+
+ align:start position:0%
+one thing you know it's not there's one
+of those three you know it's
+
+ align:start position:0%
+of those three you know it's
+ 
+
+ align:start position:0%
+of those three you know it's
+not not an insulator why
+
+ align:start position:0%
+not not an insulator why
+ 
+
+ align:start position:0%
+not not an insulator why
+not because you can make out at least
+
+ align:start position:0%
+not because you can make out at least
+ 
+
+ align:start position:0%
+not because you can make out at least
+that much that these bands you know
+
+ align:start position:0%
+that much that these bands you know
+ 
+
+ align:start position:0%
+that much that these bands you know
+they're about an Eevee or two apart they
+
+ align:start position:0%
+they're about an Eevee or two apart they
+ 
+
+ align:start position:0%
+they're about an Eevee or two apart they
+may be closer they may overlap but this
+
+ align:start position:0%
+may be closer they may overlap but this
+ 
+
+ align:start position:0%
+may be closer they may overlap but this
+not going to be an insulator right but
+
+ align:start position:0%
+not going to be an insulator right but
+ 
+
+ align:start position:0%
+not going to be an insulator right but
+you can't tell right this it's a little
+
+ align:start position:0%
+you can't tell right this it's a little
+ 
+
+ align:start position:0%
+you can't tell right this it's a little
+bit of a tricky question um you seem to
+
+ align:start position:0%
+bit of a tricky question um you seem to
+ 
+
+ align:start position:0%
+bit of a tricky question um you seem to
+remember that the material would absorb
+
+ align:start position:0%
+remember that the material would absorb
+ 
+
+ align:start position:0%
+remember that the material would absorb
+light very efficiently reconstruct the
+
+ align:start position:0%
+light very efficiently reconstruct the
+ 
+
+ align:start position:0%
+light very efficiently reconstruct the
+band structure plot that would
+
+ align:start position:0%
+band structure plot that would
+ 
+
+ align:start position:0%
+band structure plot that would
+correspond to such a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material what are you supposed to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yeah structure that's asso with
+
+ align:start position:0%
+here yeah structure that's asso with
+ 
+
+ align:start position:0%
+here yeah structure that's asso with
+some W region wav of okay you could
+
+ align:start position:0%
+some W region wav of okay you could
+ 
+
+ align:start position:0%
+some W region wav of okay you could
+certainly do that and but
+
+ align:start position:0%
+certainly do that and but
+ 
+
+ align:start position:0%
+certainly do that and but
+now um and you know in a way any band
+
+ align:start position:0%
+now um and you know in a way any band
+ 
+
+ align:start position:0%
+now um and you know in a way any band
+structure you know above the band Gap is
+
+ align:start position:0%
+structure you know above the band Gap is
+ 
+
+ align:start position:0%
+structure you know above the band Gap is
+associated with the region of light
+
+ align:start position:0%
+associated with the region of light
+ 
+
+ align:start position:0%
+associated with the region of light
+because except for the band Gap below
+
+ align:start position:0%
+because except for the band Gap below
+ 
+
+ align:start position:0%
+because except for the band Gap below
+which you cannot absorb light right as
+
+ align:start position:0%
+which you cannot absorb light right as
+ 
+
+ align:start position:0%
+which you cannot absorb light right as
+soon as you start having States you can
+
+ align:start position:0%
+soon as you start having States you can
+ 
+
+ align:start position:0%
+soon as you start having States you can
+absorb light now but the key is here it
+
+ align:start position:0%
+absorb light now but the key is here it
+ 
+
+ align:start position:0%
+absorb light now but the key is here it
+absorbs light very efficiently so what
+
+ align:start position:0%
+absorbs light very efficiently so what
+ 
+
+ align:start position:0%
+absorbs light very efficiently so what
+do I need to do in
+
+ align:start position:0%
+do I need to do in
+ 
+
+ align:start position:0%
+do I need to do in
+here yeah you got to put a direct band
+
+ align:start position:0%
+here yeah you got to put a direct band
+ 
+
+ align:start position:0%
+here yeah you got to put a direct band
+Gap in there
+
+ align:start position:0%
+Gap in there
+ 
+
+ align:start position:0%
+Gap in there
+somehow that's the key so you got to
+
+ align:start position:0%
+somehow that's the key so you got to
+ 
+
+ align:start position:0%
+somehow that's the key so you got to
+reconstruct this and it didn't matter to
+
+ align:start position:0%
+reconstruct this and it didn't matter to
+ 
+
+ align:start position:0%
+reconstruct this and it didn't matter to
+me where and there were all kinds of
+
+ align:start position:0%
+me where and there were all kinds of
+ 
+
+ align:start position:0%
+me where and there were all kinds of
+really creative curves people drew right
+
+ align:start position:0%
+really creative curves people drew right
+ 
+
+ align:start position:0%
+really creative curves people drew right
+but somewhere in here maybe this is
+
+ align:start position:0%
+but somewhere in here maybe this is
+ 
+
+ align:start position:0%
+but somewhere in here maybe this is
+going to come down a little and then go
+
+ align:start position:0%
+going to come down a little and then go
+ 
+
+ align:start position:0%
+going to come down a little and then go
+down here right and then maybe come in
+
+ align:start position:0%
+down here right and then maybe come in
+ 
+
+ align:start position:0%
+down here right and then maybe come in
+like here where you can't
+
+ align:start position:0%
+like here where you can't
+ 
+
+ align:start position:0%
+like here where you can't
+see um you know but somehow you got to
+
+ align:start position:0%
+see um you know but somehow you got to
+ 
+
+ align:start position:0%
+see um you know but somehow you got to
+try to make this a direct bang at
+
+ align:start position:0%
+try to make this a direct bang at
+ 
+
+ align:start position:0%
+try to make this a direct bang at
+Material right it's actually pretty hard
+
+ align:start position:0%
+Material right it's actually pretty hard
+ 
+
+ align:start position:0%
+Material right it's actually pretty hard
+because the stain doesn't give you a lot
+
+ align:start position:0%
+because the stain doesn't give you a lot
+ 
+
+ align:start position:0%
+because the stain doesn't give you a lot
+of room but it's actually that mirrors
+
+ align:start position:0%
+of room but it's actually that mirrors
+ 
+
+ align:start position:0%
+of room but it's actually that mirrors
+how hard it is to do that for silicon in
+
+ align:start position:0%
+how hard it is to do that for silicon in
+ 
+
+ align:start position:0%
+how hard it is to do that for silicon in
+real life the stain and silicon are
+
+ align:start position:0%
+real life the stain and silicon are
+ 
+
+ align:start position:0%
+real life the stain and silicon are
+deeply
+
+ align:start position:0%
+deeply
+ 
+
+ align:start position:0%
+deeply
+connected one minute later you realize
+
+ align:start position:0%
+connected one minute later you realize
+ 
+
+ align:start position:0%
+connected one minute later you realize
+that actually it didn't absorb light
+
+ align:start position:0%
+that actually it didn't absorb light
+ 
+
+ align:start position:0%
+that actually it didn't absorb light
+efficiently at all but instead it was a
+
+ align:start position:0%
+efficiently at all but instead it was a
+ 
+
+ align:start position:0%
+efficiently at all but instead it was a
+revolutionary metal electrode now what
+
+ align:start position:0%
+revolutionary metal electrode now what
+ 
+
+ align:start position:0%
+revolutionary metal electrode now what
+would you
+
+ align:start position:0%
+would you
+ 
+
+ align:start position:0%
+would you
+draw right okay you you'd cross it up
+
+ align:start position:0%
+draw right okay you you'd cross it up
+ 
+
+ align:start position:0%
+draw right okay you you'd cross it up
+you'd draw maybe you'd try to get a lot
+
+ align:start position:0%
+you'd draw maybe you'd try to get a lot
+ 
+
+ align:start position:0%
+you'd draw maybe you'd try to get a lot
+of Wiggles in here if you could or just
+
+ align:start position:0%
+of Wiggles in here if you could or just
+ 
+
+ align:start position:0%
+of Wiggles in here if you could or just
+certainly several Crossings right so
+
+ align:start position:0%
+certainly several Crossings right so
+ 
+
+ align:start position:0%
+certainly several Crossings right so
+that the electrons can kind of you know
+
+ align:start position:0%
+that the electrons can kind of you know
+ 
+
+ align:start position:0%
+that the electrons can kind of you know
+don't really see any Gap you can't see a
+
+ align:start position:0%
+don't really see any Gap you can't see a
+ 
+
+ align:start position:0%
+don't really see any Gap you can't see a
+gap okay so that's kind of a a nice you
+
+ align:start position:0%
+gap okay so that's kind of a a nice you
+ 
+
+ align:start position:0%
+gap okay so that's kind of a a nice you
+know problem for um and you can see it's
+
+ align:start position:0%
+know problem for um and you can see it's
+ 
+
+ align:start position:0%
+know problem for um and you can see it's
+not you know there's not there not a
+
+ align:start position:0%
+not you know there's not there not a
+ 
+
+ align:start position:0%
+not you know there's not there not a
+very long problem but it does you got to
+
+ align:start position:0%
+very long problem but it does you got to
+ 
+
+ align:start position:0%
+very long problem but it does you got to
+know a few things to answer the question
+
+ align:start position:0%
+know a few things to answer the question
+ 
+
+ align:start position:0%
+know a few things to answer the question
+about these sorts of uh topics okay so
+
+ align:start position:0%
+about these sorts of uh topics okay so
+ 
+
+ align:start position:0%
+about these sorts of uh topics okay so
+we'll do another one of those uh next
+
+ align:start position:0%
+we'll do another one of those uh next
+ 
+
+ align:start position:0%
+we'll do another one of those uh next
+Tuesday or
+
+ align:start position:0%
+Tuesday or
+ 
+
+ align:start position:0%
+Tuesday or
+two um okay now let's talk about uh wait
+
+ align:start position:0%
+two um okay now let's talk about uh wait
+ 
+
+ align:start position:0%
+two um okay now let's talk about uh wait
+where am I here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about a few other properties
+
+ align:start position:0%
+let's talk about a few other properties
+ 
+
+ align:start position:0%
+let's talk about a few other properties
+that you can calculate um you know again
+
+ align:start position:0%
+that you can calculate um you know again
+ 
+
+ align:start position:0%
+that you can calculate um you know again
+I'm I'm not going to go into the details
+
+ align:start position:0%
+I'm I'm not going to go into the details
+ 
+
+ align:start position:0%
+I'm I'm not going to go into the details
+of Transport but this is sort of basic
+
+ align:start position:0%
+of Transport but this is sort of basic
+ 
+
+ align:start position:0%
+of Transport but this is sort of basic
+uh you know um uh double e or you know
+
+ align:start position:0%
+uh you know um uh double e or you know
+ 
+
+ align:start position:0%
+uh you know um uh double e or you know
+basic physics stuff if you put an
+
+ align:start position:0%
+basic physics stuff if you put an
+ 
+
+ align:start position:0%
+basic physics stuff if you put an
+electron in a field it's going to push
+
+ align:start position:0%
+electron in a field it's going to push
+ 
+
+ align:start position:0%
+electron in a field it's going to push
+it with a force and so the f equals ma
+
+ align:start position:0%
+it with a force and so the f equals ma
+ 
+
+ align:start position:0%
+it with a force and so the f equals ma
+of that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has energy greater than that Gap I don't
+
+ align:start position:0%
+has energy greater than that Gap I don't
+ 
+
+ align:start position:0%
+has energy greater than that Gap I don't
+you want a very small gap for electron
+
+ align:start position:0%
+you want a very small gap for electron
+ 
+
+ align:start position:0%
+you want a very small gap for electron
+or for a semiconductor uh for what
+
+ align:start position:0%
+or for a semiconductor uh for what
+ 
+
+ align:start position:0%
+or for a semiconductor uh for what
+application for solar cells uh yeah sure
+
+ align:start position:0%
+application for solar cells uh yeah sure
+ 
+
+ align:start position:0%
+application for solar cells uh yeah sure
+so that's a very good point and why who
+
+ align:start position:0%
+so that's a very good point and why who
+ 
+
+ align:start position:0%
+so that's a very good point and why who
+can tell me why you can't have a too low
+
+ align:start position:0%
+can tell me why you can't have a too low
+ 
+
+ align:start position:0%
+can tell me why you can't have a too low
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+gap and I'll talk about this as we move
+
+ align:start position:0%
+gap and I'll talk about this as we move
+ 
+
+ align:start position:0%
+gap and I'll talk about this as we move
+into solar PV
+
+ align:start position:0%
+into solar PV
+ 
+
+ align:start position:0%
+into solar PV
+but is not high enough and keep hopping
+
+ align:start position:0%
+but is not high enough and keep hopping
+ 
+
+ align:start position:0%
+but is not high enough and keep hopping
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+what that wouldn't necessarily be a
+
+ align:start position:0%
+what that wouldn't necessarily be a
+ 
+
+ align:start position:0%
+what that wouldn't necessarily be a
+problem yeah you probably get saturated
+
+ align:start position:0%
+problem yeah you probably get saturated
+ 
+
+ align:start position:0%
+problem yeah you probably get saturated
+with lower
+
+ align:start position:0%
+with lower
+ 
+
+ align:start position:0%
+with lower
+energy and what's wrong with that
+
+ align:start position:0%
+energy and what's wrong with that
+ 
+
+ align:start position:0%
+energy and what's wrong with that
+though you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notal well that's that's that's what it
+
+ align:start position:0%
+notal well that's that's that's what it
+ 
+
+ align:start position:0%
+notal well that's that's that's what it
+is is it it actually is what sets the
+
+ align:start position:0%
+is is it it actually is what sets the
+ 
+
+ align:start position:0%
+is is it it actually is what sets the
+potential of the cell so this goes back
+
+ align:start position:0%
+potential of the cell so this goes back
+ 
+
+ align:start position:0%
+potential of the cell so this goes back
+to and it's a very good question right
+
+ align:start position:0%
+to and it's a very good question right
+ 
+
+ align:start position:0%
+to and it's a very good question right
+why not just use the lowest Gap possible
+
+ align:start position:0%
+why not just use the lowest Gap possible
+ 
+
+ align:start position:0%
+why not just use the lowest Gap possible
+right and then you'll absorb all the
+
+ align:start position:0%
+right and then you'll absorb all the
+ 
+
+ align:start position:0%
+right and then you'll absorb all the
+light or most of the light well the
+
+ align:start position:0%
+light or most of the light well the
+ 
+
+ align:start position:0%
+light or most of the light well the
+reason is that it goes back to this
+
+ align:start position:0%
+reason is that it goes back to this
+ 
+
+ align:start position:0%
+reason is that it goes back to this
+picture that when you're when you're
+
+ align:start position:0%
+picture that when you're when you're
+ 
+
+ align:start position:0%
+picture that when you're when you're
+taking photons and making them into
+
+ align:start position:0%
+taking photons and making them into
+ 
+
+ align:start position:0%
+taking photons and making them into
+electrons what you're really doing is
+
+ align:start position:0%
+electrons what you're really doing is
+ 
+
+ align:start position:0%
+electrons what you're really doing is
+you're you know it's it's again it's
+
+ align:start position:0%
+you're you know it's it's again it's
+ 
+
+ align:start position:0%
+you're you know it's it's again it's
+that pumping water analogy you're you're
+
+ align:start position:0%
+that pumping water analogy you're you're
+ 
+
+ align:start position:0%
+that pumping water analogy you're you're
+giving the electrons energy and pushing
+
+ align:start position:0%
+giving the electrons energy and pushing
+ 
+
+ align:start position:0%
+giving the electrons energy and pushing
+them up a hill now um in the Solar fuels
+
+ align:start position:0%
+them up a hill now um in the Solar fuels
+ 
+
+ align:start position:0%
+them up a hill now um in the Solar fuels
+case we're using that push to change the
+
+ align:start position:0%
+case we're using that push to change the
+ 
+
+ align:start position:0%
+case we're using that push to change the
+molecule's configuration to store energy
+
+ align:start position:0%
+molecule's configuration to store energy
+ 
+
+ align:start position:0%
+molecule's configuration to store energy
+in the solar cell case we're using that
+
+ align:start position:0%
+in the solar cell case we're using that
+ 
+
+ align:start position:0%
+in the solar cell case we're using that
+push to to get Just Energy voltage out
+
+ align:start position:0%
+push to to get Just Energy voltage out
+ 
+
+ align:start position:0%
+push to to get Just Energy voltage out
+right and um if I you know so I'd like
+
+ align:start position:0%
+right and um if I you know so I'd like
+ 
+
+ align:start position:0%
+right and um if I you know so I'd like
+to not get just a teeny teeny bit of
+
+ align:start position:0%
+to not get just a teeny teeny bit of
+ 
+
+ align:start position:0%
+to not get just a teeny teeny bit of
+voltage right I'd like to get get it up
+
+ align:start position:0%
+voltage right I'd like to get get it up
+ 
+
+ align:start position:0%
+voltage right I'd like to get get it up
+a hill now if I try to you know push it
+
+ align:start position:0%
+a hill now if I try to you know push it
+ 
+
+ align:start position:0%
+a hill now if I try to you know push it
+if I if I make my gam b band Gap such
+
+ align:start position:0%
+if I if I make my gam b band Gap such
+ 
+
+ align:start position:0%
+if I if I make my gam b band Gap such
+that I push it can only push it really
+
+ align:start position:0%
+that I push it can only push it really
+ 
+
+ align:start position:0%
+that I push it can only push it really
+really high you might think you want
+
+ align:start position:0%
+really high you might think you want
+ 
+
+ align:start position:0%
+really high you might think you want
+that but then what happens doesn't
+
+ align:start position:0%
+that but then what happens doesn't
+ 
+
+ align:start position:0%
+that but then what happens doesn't
+absorb any light right so now you have
+
+ align:start position:0%
+absorb any light right so now you have
+ 
+
+ align:start position:0%
+absorb any light right so now you have
+these two competing effects small band
+
+ align:start position:0%
+these two competing effects small band
+ 
+
+ align:start position:0%
+these two competing effects small band
+Gap to absorb the light larger band Gap
+
+ align:start position:0%
+Gap to absorb the light larger band Gap
+ 
+
+ align:start position:0%
+Gap to absorb the light larger band Gap
+to give you more potential for your C
+
+ align:start position:0%
+to give you more potential for your C
+ 
+
+ align:start position:0%
+to give you more potential for your C
+large poal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small less but but more light and
+
+ align:start position:0%
+small less but but more light and
+ 
+
+ align:start position:0%
+small less but but more light and
+there's a sweet
+
+ align:start position:0%
+there's a sweet
+ 
+
+ align:start position:0%
+there's a sweet
+spot okay and I'll talk about that as I
+
+ align:start position:0%
+spot okay and I'll talk about that as I
+ 
+
+ align:start position:0%
+spot okay and I'll talk about that as I
+I'll talk about that a little bit on
+
+ align:start position:0%
+I'll talk about that a little bit on
+ 
+
+ align:start position:0%
+I'll talk about that a little bit on
+Tuesday okay that that is uh uh
+
+ align:start position:0%
+Tuesday okay that that is uh uh
+ 
+
+ align:start position:0%
+Tuesday okay that that is uh uh
+competing two competing attributes of
+
+ align:start position:0%
+competing two competing attributes of
+ 
+
+ align:start position:0%
+competing two competing attributes of
+solar PV that
+
+ align:start position:0%
+solar PV that
+ 
+
+ align:start position:0%
+solar PV that
+limit um you know how much energy you
+
+ align:start position:0%
+limit um you know how much energy you
+ 
+
+ align:start position:0%
+limit um you know how much energy you
+can you can get from the Sun um
+
+ align:start position:0%
+can you can get from the Sun um
+ 
+
+ align:start position:0%
+can you can get from the Sun um
+now the the so if you put an electron in
+
+ align:start position:0%
+now the the so if you put an electron in
+ 
+
+ align:start position:0%
+now the the so if you put an electron in
+a field it's going to move until it hits
+
+ align:start position:0%
+a field it's going to move until it hits
+ 
+
+ align:start position:0%
+a field it's going to move until it hits
+until you sort of hit this equilibrium
+
+ align:start position:0%
+until you sort of hit this equilibrium
+ 
+
+ align:start position:0%
+until you sort of hit this equilibrium
+point where the acceleration you know is
+
+ align:start position:0%
+point where the acceleration you know is
+ 
+
+ align:start position:0%
+point where the acceleration you know is
+is zero because it's um you know the
+
+ align:start position:0%
+is zero because it's um you know the
+ 
+
+ align:start position:0%
+is zero because it's um you know the
+force it feels is balanced by the
+
+ align:start position:0%
+force it feels is balanced by the
+ 
+
+ align:start position:0%
+force it feels is balanced by the
+scattering okay that's sort of basic um
+
+ align:start position:0%
+scattering okay that's sort of basic um
+ 
+
+ align:start position:0%
+scattering okay that's sort of basic um
+transport electron transport equations
+
+ align:start position:0%
+transport electron transport equations
+ 
+
+ align:start position:0%
+transport electron transport equations
+and so you can get an equation for the
+
+ align:start position:0%
+and so you can get an equation for the
+ 
+
+ align:start position:0%
+and so you can get an equation for the
+drift velocity of the electron or the
+
+ align:start position:0%
+drift velocity of the electron or the
+ 
+
+ align:start position:0%
+drift velocity of the electron or the
+thing that we care about a lot is this
+
+ align:start position:0%
+thing that we care about a lot is this
+ 
+
+ align:start position:0%
+thing that we care about a lot is this
+electrical conductivity right something
+
+ align:start position:0%
+electrical conductivity right something
+ 
+
+ align:start position:0%
+electrical conductivity right something
+that you can measure which is nothing
+
+ align:start position:0%
+that you can measure which is nothing
+ 
+
+ align:start position:0%
+that you can measure which is nothing
+more than the drift velocity times the
+
+ align:start position:0%
+more than the drift velocity times the
+ 
+
+ align:start position:0%
+more than the drift velocity times the
+number density that that's actually a
+
+ align:start position:0%
+number density that that's actually a
+ 
+
+ align:start position:0%
+number density that that's actually a
+hard thing to separate out but it can be
+
+ align:start position:0%
+hard thing to separate out but it can be
+ 
+
+ align:start position:0%
+hard thing to separate out but it can be
+done an experiment okay um and so the
+
+ align:start position:0%
+done an experiment okay um and so the
+ 
+
+ align:start position:0%
+done an experiment okay um and so the
+current is is that and and it's equal to
+
+ align:start position:0%
+current is is that and and it's equal to
+ 
+
+ align:start position:0%
+current is is that and and it's equal to
+the con Electro conductivity times the
+
+ align:start position:0%
+the con Electro conductivity times the
+ 
+
+ align:start position:0%
+the con Electro conductivity times the
+field now here's the thing that is
+
+ align:start position:0%
+field now here's the thing that is
+ 
+
+ align:start position:0%
+field now here's the thing that is
+actually um that equation then if you
+
+ align:start position:0%
+actually um that equation then if you
+ 
+
+ align:start position:0%
+actually um that equation then if you
+just look at these very simple sort of
+
+ align:start position:0%
+just look at these very simple sort of
+ 
+
+ align:start position:0%
+just look at these very simple sort of
+fals ma for an electron in a field that
+
+ align:start position:0%
+fals ma for an electron in a field that
+ 
+
+ align:start position:0%
+fals ma for an electron in a field that
+very simply comes down to this equation
+
+ align:start position:0%
+very simply comes down to this equation
+ 
+
+ align:start position:0%
+very simply comes down to this equation
+and here's the
+
+ align:start position:0%
+and here's the
+ 
+
+ align:start position:0%
+and here's the
+thing that
+
+ align:start position:0%
+thing that
+ 
+
+ align:start position:0%
+thing that
+mass okay what we want now is well
+
+ align:start position:0%
+mass okay what we want now is well
+ 
+
+ align:start position:0%
+mass okay what we want now is well
+what's the electron uh conductivity in
+
+ align:start position:0%
+what's the electron uh conductivity in
+ 
+
+ align:start position:0%
+what's the electron uh conductivity in
+the solid what's the electron
+
+ align:start position:0%
+the solid what's the electron
+ 
+
+ align:start position:0%
+the solid what's the electron
+conductivity in the solid and it turns
+
+ align:start position:0%
+conductivity in the solid and it turns
+ 
+
+ align:start position:0%
+conductivity in the solid and it turns
+out that that mass that's on the
+
+ align:start position:0%
+out that that mass that's on the
+ 
+
+ align:start position:0%
+out that that mass that's on the
+previous page that
+
+ align:start position:0%
+previous page that
+ 
+
+ align:start position:0%
+previous page that
+M it it becomes a kind of effective mass
+
+ align:start position:0%
+M it it becomes a kind of effective mass
+ 
+
+ align:start position:0%
+M it it becomes a kind of effective mass
+of the electron
+
+ align:start position:0%
+of the electron
+ 
+
+ align:start position:0%
+of the electron
+um that can be different
+
+ align:start position:0%
+um that can be different
+ 
+
+ align:start position:0%
+um that can be different
+than just the mass of the electron the
+
+ align:start position:0%
+than just the mass of the electron the
+ 
+
+ align:start position:0%
+than just the mass of the electron the
+standard mass of the electron the reason
+
+ align:start position:0%
+standard mass of the electron the reason
+ 
+
+ align:start position:0%
+standard mass of the electron the reason
+is that it's in this periodic Crystal
+
+ align:start position:0%
+is that it's in this periodic Crystal
+ 
+
+ align:start position:0%
+is that it's in this periodic Crystal
+remember you know the the electron is
+
+ align:start position:0%
+remember you know the the electron is
+ 
+
+ align:start position:0%
+remember you know the the electron is
+going to feel this very strange um
+
+ align:start position:0%
+going to feel this very strange um
+ 
+
+ align:start position:0%
+going to feel this very strange um
+environment when it's in a periodic
+
+ align:start position:0%
+environment when it's in a periodic
+ 
+
+ align:start position:0%
+environment when it's in a periodic
+Crystal and it's going to feel
+
+ align:start position:0%
+Crystal and it's going to feel
+ 
+
+ align:start position:0%
+Crystal and it's going to feel
+differences in its energy band and that
+
+ align:start position:0%
+differences in its energy band and that
+ 
+
+ align:start position:0%
+differences in its energy band and that
+changes what that does is it changes
+
+ align:start position:0%
+changes what that does is it changes
+ 
+
+ align:start position:0%
+changes what that does is it changes
+actually the effective mass of the
+
+ align:start position:0%
+actually the effective mass of the
+ 
+
+ align:start position:0%
+actually the effective mass of the
+electron as it's in different parts of
+
+ align:start position:0%
+electron as it's in different parts of
+ 
+
+ align:start position:0%
+electron as it's in different parts of
+kpace
+
+ align:start position:0%
+kpace
+ 
+
+ align:start position:0%
+kpace
+okay well it turns out that that effect
+
+ align:start position:0%
+okay well it turns out that that effect
+ 
+
+ align:start position:0%
+okay well it turns out that that effect
+mass is directly related to the this
+
+ align:start position:0%
+mass is directly related to the this
+ 
+
+ align:start position:0%
+mass is directly related to the this
+curvature this if you look at um I'm
+
+ align:start position:0%
+curvature this if you look at um I'm
+ 
+
+ align:start position:0%
+curvature this if you look at um I'm
+just rewriting the previous equation but
+
+ align:start position:0%
+just rewriting the previous equation but
+ 
+
+ align:start position:0%
+just rewriting the previous equation but
+now I'm putting in the band structure
+
+ align:start position:0%
+now I'm putting in the band structure
+ 
+
+ align:start position:0%
+now I'm putting in the band structure
+here these little V's are nothing more
+
+ align:start position:0%
+here these little V's are nothing more
+ 
+
+ align:start position:0%
+here these little V's are nothing more
+than the slope of e in the band
+
+ align:start position:0%
+than the slope of e in the band
+ 
+
+ align:start position:0%
+than the slope of e in the band
+structure the slope of the energy in the
+
+ align:start position:0%
+structure the slope of the energy in the
+ 
+
+ align:start position:0%
+structure the slope of the energy in the
+band structure versus K
+
+ align:start position:0%
+band structure versus K
+ 
+
+ align:start position:0%
+band structure versus K
+okay um and so so what so this is called
+
+ align:start position:0%
+okay um and so so what so this is called
+ 
+
+ align:start position:0%
+okay um and so so what so this is called
+effective Mass approximation it's an
+
+ align:start position:0%
+effective Mass approximation it's an
+ 
+
+ align:start position:0%
+effective Mass approximation it's an
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+but it's a pretty good one the electron
+
+ align:start position:0%
+but it's a pretty good one the electron
+ 
+
+ align:start position:0%
+but it's a pretty good one the electron
+feels a kind of different weight to it
+
+ align:start position:0%
+feels a kind of different weight to it
+ 
+
+ align:start position:0%
+feels a kind of different weight to it
+it's heavier light think about it that
+
+ align:start position:0%
+it's heavier light think about it that
+ 
+
+ align:start position:0%
+it's heavier light think about it that
+way depending on whether it's in a flat
+
+ align:start position:0%
+way depending on whether it's in a flat
+ 
+
+ align:start position:0%
+way depending on whether it's in a flat
+part of the band where it's really heavy
+
+ align:start position:0%
+part of the band where it's really heavy
+ 
+
+ align:start position:0%
+part of the band where it's really heavy
+or whether it's in a curvy part of the
+
+ align:start position:0%
+or whether it's in a curvy part of the
+ 
+
+ align:start position:0%
+or whether it's in a curvy part of the
+band where it's kind of feeling more
+
+ align:start position:0%
+band where it's kind of feeling more
+ 
+
+ align:start position:0%
+band where it's kind of feeling more
+light and bouncy okay and that changes
+
+ align:start position:0%
+light and bouncy okay and that changes
+ 
+
+ align:start position:0%
+light and bouncy okay and that changes
+the uh the
+
+ align:start position:0%
+the uh the
+ 
+
+ align:start position:0%
+the uh the
+connectivity right that can be measured
+
+ align:start position:0%
+connectivity right that can be measured
+ 
+
+ align:start position:0%
+connectivity right that can be measured
+and that so that's a really nice way
+
+ align:start position:0%
+and that so that's a really nice way
+ 
+
+ align:start position:0%
+and that so that's a really nice way
+just from the curvature of these bands
+
+ align:start position:0%
+just from the curvature of these bands
+ 
+
+ align:start position:0%
+just from the curvature of these bands
+it's a really nice way of getting a
+
+ align:start position:0%
+it's a really nice way of getting a
+ 
+
+ align:start position:0%
+it's a really nice way of getting a
+sense of how mobile an electron or ho is
+
+ align:start position:0%
+sense of how mobile an electron or ho is
+ 
+
+ align:start position:0%
+sense of how mobile an electron or ho is
+in a material all you have to do is you
+
+ align:start position:0%
+in a material all you have to do is you
+ 
+
+ align:start position:0%
+in a material all you have to do is you
+just take an integral over the second
+
+ align:start position:0%
+just take an integral over the second
+ 
+
+ align:start position:0%
+just take an integral over the second
+derivative of this uh or the derivative
+
+ align:start position:0%
+derivative of this uh or the derivative
+ 
+
+ align:start position:0%
+derivative of this uh or the derivative
+of that the slope basically as you go
+
+ align:start position:0%
+of that the slope basically as you go
+ 
+
+ align:start position:0%
+of that the slope basically as you go
+along case space there okay does any so
+
+ align:start position:0%
+along case space there okay does any so
+ 
+
+ align:start position:0%
+along case space there okay does any so
+does anybody know what a firmy function
+
+ align:start position:0%
+does anybody know what a firmy function
+ 
+
+ align:start position:0%
+does anybody know what a firmy function
+is it's just a weight but
+
+ align:start position:0%
+is it's just a weight but
+ 
+
+ align:start position:0%
+is it's just a weight but
+yeah how many of you know don't know
+
+ align:start position:0%
+yeah how many of you know don't know
+ 
+
+ align:start position:0%
+yeah how many of you know don't know
+what a firmy function is it's okay so
+
+ align:start position:0%
+what a firmy function is it's okay so
+ 
+
+ align:start position:0%
+what a firmy function is it's okay so
+it's basically you know this is this
+
+ align:start position:0%
+it's basically you know this is this
+ 
+
+ align:start position:0%
+it's basically you know this is this
+comes from fmy direct statistics it's
+
+ align:start position:0%
+comes from fmy direct statistics it's
+ 
+
+ align:start position:0%
+comes from fmy direct statistics it's
+not um in any way critical here but it's
+
+ align:start position:0%
+not um in any way critical here but it's
+ 
+
+ align:start position:0%
+not um in any way critical here but it's
+an occupation function it's saying that
+
+ align:start position:0%
+an occupation function it's saying that
+ 
+
+ align:start position:0%
+an occupation function it's saying that
+at a given
+
+ align:start position:0%
+at a given
+ 
+
+ align:start position:0%
+at a given
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+you're likely to have uh electrons or
+
+ align:start position:0%
+you're likely to have uh electrons or
+ 
+
+ align:start position:0%
+you're likely to have uh electrons or
+not um at at a certain energy and so the
+
+ align:start position:0%
+not um at at a certain energy and so the
+ 
+
+ align:start position:0%
+not um at at a certain energy and so the
+firmy function you know at zero
+
+ align:start position:0%
+firmy function you know at zero
+ 
+
+ align:start position:0%
+firmy function you know at zero
+temperature f is going to look like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where this would be one and this well
+
+ align:start position:0%
+where this would be one and this well
+ 
+
+ align:start position:0%
+where this would be one and this well
+this would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero but then as and the firmy function
+
+ align:start position:0%
+zero but then as and the firmy function
+ 
+
+ align:start position:0%
+zero but then as and the firmy function
+is uh one over e to the um e minus EF /
+
+ align:start position:0%
+is uh one over e to the um e minus EF /
+ 
+
+ align:start position:0%
+is uh one over e to the um e minus EF /
+KT uh plus
+
+ align:start position:0%
+KT uh plus
+ 
+
+ align:start position:0%
+KT uh plus
+one okay where e is where you are in the
+
+ align:start position:0%
+one okay where e is where you are in the
+ 
+
+ align:start position:0%
+one okay where e is where you are in the
+band structure e is where you are in the
+
+ align:start position:0%
+band structure e is where you are in the
+ 
+
+ align:start position:0%
+band structure e is where you are in the
+band structure and you're looking at
+
+ align:start position:0%
+band structure and you're looking at
+ 
+
+ align:start position:0%
+band structure and you're looking at
+this as you go above the firmy energy
+
+ align:start position:0%
+this as you go above the firmy energy
+ 
+
+ align:start position:0%
+this as you go above the firmy energy
+can electrons be there well at zero
+
+ align:start position:0%
+can electrons be there well at zero
+ 
+
+ align:start position:0%
+can electrons be there well at zero
+temperature no right but actually when
+
+ align:start position:0%
+temperature no right but actually when
+ 
+
+ align:start position:0%
+temperature no right but actually when
+you go to some finite temperature just
+
+ align:start position:0%
+you go to some finite temperature just
+ 
+
+ align:start position:0%
+you go to some finite temperature just
+temperature alone can kick electrons up
+
+ align:start position:0%
+temperature alone can kick electrons up
+ 
+
+ align:start position:0%
+temperature alone can kick electrons up
+can kick electrons up okay that's what
+
+ align:start position:0%
+can kick electrons up okay that's what
+ 
+
+ align:start position:0%
+can kick electrons up okay that's what
+the firmy function is is in that
+
+ align:start position:0%
+the firmy function is is in that
+ 
+
+ align:start position:0%
+the firmy function is is in that
+equation for um because at some
+
+ align:start position:0%
+equation for um because at some
+ 
+
+ align:start position:0%
+equation for um because at some
+temperature you can actually have a
+
+ align:start position:0%
+temperature you can actually have a
+ 
+
+ align:start position:0%
+temperature you can actually have a
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+that looks more like
+
+ align:start position:0%
+that looks more like
+ 
+
+ align:start position:0%
+that looks more like
+this tal
+
+ align:start position:0%
+this tal
+ 
+
+ align:start position:0%
+this tal
+z t equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something now what what's important here
+
+ align:start position:0%
+something now what what's important here
+ 
+
+ align:start position:0%
+something now what what's important here
+well what's important is that you know
+
+ align:start position:0%
+well what's important is that you know
+ 
+
+ align:start position:0%
+well what's important is that you know
+when you think about um
+
+ align:start position:0%
+when you think about um
+ 
+
+ align:start position:0%
+when you think about um
+conductivity you want to know you got
+
+ align:start position:0%
+conductivity you want to know you got
+ 
+
+ align:start position:0%
+conductivity you want to know you got
+you see the difference here between you
+
+ align:start position:0%
+you see the difference here between you
+ 
+
+ align:start position:0%
+you see the difference here between you
+know drift velocity and current or
+
+ align:start position:0%
+know drift velocity and current or
+ 
+
+ align:start position:0%
+know drift velocity and current or
+conductivity is that you got to know
+
+ align:start position:0%
+conductivity is that you got to know
+ 
+
+ align:start position:0%
+conductivity is that you got to know
+something about how many carriers you
+
+ align:start position:0%
+something about how many carriers you
+ 
+
+ align:start position:0%
+something about how many carriers you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+okay um and that's going to be
+
+ align:start position:0%
+okay um and that's going to be
+ 
+
+ align:start position:0%
+okay um and that's going to be
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+dependent does everybody see that that's
+
+ align:start position:0%
+dependent does everybody see that that's
+ 
+
+ align:start position:0%
+dependent does everybody see that that's
+why this is important now but what if my
+
+ align:start position:0%
+why this is important now but what if my
+ 
+
+ align:start position:0%
+why this is important now but what if my
+firmy function is like this and okay
+
+ align:start position:0%
+firmy function is like this and okay
+ 
+
+ align:start position:0%
+firmy function is like this and okay
+let's say I have silicon and I'm going
+
+ align:start position:0%
+let's say I have silicon and I'm going
+ 
+
+ align:start position:0%
+let's say I have silicon and I'm going
+to now plot on top of this um let me use
+
+ align:start position:0%
+to now plot on top of this um let me use
+ 
+
+ align:start position:0%
+to now plot on top of this um let me use
+a different color and plot on top of
+
+ align:start position:0%
+a different color and plot on top of
+ 
+
+ align:start position:0%
+a different color and plot on top of
+this the density of States okay and
+
+ align:start position:0%
+this the density of States okay and
+ 
+
+ align:start position:0%
+this the density of States okay and
+let's say my density of States was like
+
+ align:start position:0%
+let's say my density of States was like
+ 
+
+ align:start position:0%
+let's say my density of States was like
+this okay I don't know if it is or not
+
+ align:start position:0%
+this okay I don't know if it is or not
+ 
+
+ align:start position:0%
+this okay I don't know if it is or not
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+here's the band
+
+ align:start position:0%
+here's the band
+ 
+
+ align:start position:0%
+here's the band
+Gap this is my
+
+ align:start position:0%
+Gap this is my
+ 
+
+ align:start position:0%
+Gap this is my
+Doss that doesn't look like a different
+
+ align:start position:0%
+Doss that doesn't look like a different
+ 
+
+ align:start position:0%
+Doss that doesn't look like a different
+color at all it's not even close it's
+
+ align:start position:0%
+color at all it's not even close it's
+ 
+
+ align:start position:0%
+color at all it's not even close it's
+like they painted it yellow on the
+
+ align:start position:0%
+like they painted it yellow on the
+ 
+
+ align:start position:0%
+like they painted it yellow on the
+outside and seriously it's totally white
+
+ align:start position:0%
+outside and seriously it's totally white
+ 
+
+ align:start position:0%
+outside and seriously it's totally white
+all right anyway
+
+ align:start position:0%
+all right anyway
+ 
+
+ align:start position:0%
+all right anyway
+so um so here's my firmy function I'm at
+
+ align:start position:0%
+so um so here's my firmy function I'm at
+ 
+
+ align:start position:0%
+so um so here's my firmy function I'm at
+room temperature and this is my
+
+ align:start position:0%
+room temperature and this is my
+ 
+
+ align:start position:0%
+room temperature and this is my
+distribution of
+
+ align:start position:0%
+distribution of
+ 
+
+ align:start position:0%
+distribution of
+electrons okay here's the um you know
+
+ align:start position:0%
+electrons okay here's the um you know
+ 
+
+ align:start position:0%
+electrons okay here's the um you know
+here's the uh this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gap tell me what's going on
+
+ align:start position:0%
+gap tell me what's going on
+ 
+
+ align:start position:0%
+gap tell me what's going on
+here Somebody explain this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me yeah Sam even though there's
+
+ align:start position:0%
+me yeah Sam even though there's
+ 
+
+ align:start position:0%
+me yeah Sam even though there's
+probability that you can have electrons
+
+ align:start position:0%
+probability that you can have electrons
+ 
+
+ align:start position:0%
+probability that you can have electrons
+in those space because there's no space
+
+ align:start position:0%
+in those space because there's no space
+ 
+
+ align:start position:0%
+in those space because there's no space
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+I love it that's absolutely right you
+
+ align:start position:0%
+I love it that's absolutely right you
+ 
+
+ align:start position:0%
+I love it that's absolutely right you
+cannot have electrons there the firmy
+
+ align:start position:0%
+cannot have electrons there the firmy
+ 
+
+ align:start position:0%
+cannot have electrons there the firmy
+function says I
+
+ align:start position:0%
+function says I
+ 
+
+ align:start position:0%
+function says I
+can in your face fmy function says the
+
+ align:start position:0%
+can in your face fmy function says the
+ 
+
+ align:start position:0%
+can in your face fmy function says the
+Doss I didn't say that I would never say
+
+ align:start position:0%
+Doss I didn't say that I would never say
+ 
+
+ align:start position:0%
+Doss I didn't say that I would never say
+that to a fmy function but the Dos said
+
+ align:start position:0%
+that to a fmy function but the Dos said
+ 
+
+ align:start position:0%
+that to a fmy function but the Dos said
+it the do said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uhuh we got zero probability here man
+
+ align:start position:0%
+uhuh we got zero probability here man
+ 
+
+ align:start position:0%
+uhuh we got zero probability here man
+you can't be here so the Dos said no
+
+ align:start position:0%
+you can't be here so the Dos said no
+ 
+
+ align:start position:0%
+you can't be here so the Dos said no
+States No Deal go away so the firm
+
+ align:start position:0%
+States No Deal go away so the firm
+ 
+
+ align:start position:0%
+States No Deal go away so the firm
+function tried it said hey I got enough
+
+ align:start position:0%
+function tried it said hey I got enough
+ 
+
+ align:start position:0%
+function tried it said hey I got enough
+energy from temperature to give you a
+
+ align:start position:0%
+energy from temperature to give you a
+ 
+
+ align:start position:0%
+energy from temperature to give you a
+few electrons and the do says I don't
+
+ align:start position:0%
+few electrons and the do says I don't
+ 
+
+ align:start position:0%
+few electrons and the do says I don't
+want them because they're not at the
+
+ align:start position:0%
+want them because they're not at the
+ 
+
+ align:start position:0%
+want them because they're not at the
+energy where I've got any states right
+
+ align:start position:0%
+energy where I've got any states right
+ 
+
+ align:start position:0%
+energy where I've got any states right
+now what can I do then to
+
+ align:start position:0%
+now what can I do then to
+ 
+
+ align:start position:0%
+now what can I do then to
+populate the conduction band of
+
+ align:start position:0%
+populate the conduction band of
+ 
+
+ align:start position:0%
+populate the conduction band of
+silicon what can I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do more thermal energy I'm going to run
+
+ align:start position:0%
+do more thermal energy I'm going to run
+ 
+
+ align:start position:0%
+do more thermal energy I'm going to run
+my solar cell at 10,000 de well you
+
+ align:start position:0%
+my solar cell at 10,000 de well you
+ 
+
+ align:start position:0%
+my solar cell at 10,000 de well you
+could you'll get more and more and you
+
+ align:start position:0%
+could you'll get more and more and you
+ 
+
+ align:start position:0%
+could you'll get more and more and you
+will start to get electrons in there but
+
+ align:start position:0%
+will start to get electrons in there but
+ 
+
+ align:start position:0%
+will start to get electrons in there but
+actually that's not always
+
+ align:start position:0%
+actually that's not always
+ 
+
+ align:start position:0%
+actually that's not always
+practical so what is how do we get
+
+ align:start position:0%
+practical so what is how do we get
+ 
+
+ align:start position:0%
+practical so what is how do we get
+electrons into there then there are
+
+ align:start position:0%
+electrons into there then there are
+ 
+
+ align:start position:0%
+electrons into there then there are
+other reasons electrons come into those
+
+ align:start position:0%
+other reasons electrons come into those
+ 
+
+ align:start position:0%
+other reasons electrons come into those
+States you know but but what not just
+
+ align:start position:0%
+States you know but but what not just
+ 
+
+ align:start position:0%
+States you know but but what not just
+from thermal um but what's one way that
+
+ align:start position:0%
+from thermal um but what's one way that
+ 
+
+ align:start position:0%
+from thermal um but what's one way that
+we can get electrons in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there yeah what does doping do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it can change the fir energy
+
+ align:start position:0%
+well it can change the fir energy
+ 
+
+ align:start position:0%
+well it can change the fir energy
+but what might I dope silicon
+
+ align:start position:0%
+but what might I dope silicon
+ 
+
+ align:start position:0%
+but what might I dope silicon
+with phosphorus
+
+ align:start position:0%
+with phosphorus
+ 
+
+ align:start position:0%
+with phosphorus
+why excess electron compared to Silicon
+
+ align:start position:0%
+why excess electron compared to Silicon
+ 
+
+ align:start position:0%
+why excess electron compared to Silicon
+now if I have an excess
+
+ align:start position:0%
+now if I have an excess
+ 
+
+ align:start position:0%
+now if I have an excess
+electron sitting in my crystal then is
+
+ align:start position:0%
+electron sitting in my crystal then is
+ 
+
+ align:start position:0%
+electron sitting in my crystal then is
+it you know and and but really the
+
+ align:start position:0%
+it you know and and but really the
+ 
+
+ align:start position:0%
+it you know and and but really the
+crystal is still kind of
+
+ align:start position:0%
+crystal is still kind of
+ 
+
+ align:start position:0%
+crystal is still kind of
+silicon cuz I don't have many of these
+
+ align:start position:0%
+silicon cuz I don't have many of these
+ 
+
+ align:start position:0%
+silicon cuz I don't have many of these
+excess electrons I just have one
+
+ align:start position:0%
+excess electrons I just have one
+ 
+
+ align:start position:0%
+excess electrons I just have one
+phosphorus atom every thousand so it's
+
+ align:start position:0%
+phosphorus atom every thousand so it's
+ 
+
+ align:start position:0%
+phosphorus atom every thousand so it's
+really still silicon then but I filled
+
+ align:start position:0%
+really still silicon then but I filled
+ 
+
+ align:start position:0%
+really still silicon then but I filled
+all my electrons up to here and now I've
+
+ align:start position:0%
+all my electrons up to here and now I've
+ 
+
+ align:start position:0%
+all my electrons up to here and now I've
+got one extra where does it
+
+ align:start position:0%
+got one extra where does it
+ 
+
+ align:start position:0%
+got one extra where does it
+go goes in there and now I'm populating
+
+ align:start position:0%
+go goes in there and now I'm populating
+ 
+
+ align:start position:0%
+go goes in there and now I'm populating
+it without thermal energy right I don't
+
+ align:start position:0%
+it without thermal energy right I don't
+ 
+
+ align:start position:0%
+it without thermal energy right I don't
+need to work with my firy function I did
+
+ align:start position:0%
+need to work with my firy function I did
+ 
+
+ align:start position:0%
+need to work with my firy function I did
+it chemically I put in I put an atom in
+
+ align:start position:0%
+it chemically I put in I put an atom in
+ 
+
+ align:start position:0%
+it chemically I put in I put an atom in
+there that had a spare electron right
+
+ align:start position:0%
+there that had a spare electron right
+ 
+
+ align:start position:0%
+there that had a spare electron right
+and that is actually in fact exactly
+
+ align:start position:0%
+and that is actually in fact exactly
+ 
+
+ align:start position:0%
+and that is actually in fact exactly
+what happened
+
+ align:start position:0%
+what happened
+ 
+
+ align:start position:0%
+what happened
+in in you know in real materials who
+
+ align:start position:0%
+in in you know in real materials who
+ 
+
+ align:start position:0%
+in in you know in real materials who
+knows what it's called when you have an
+
+ align:start position:0%
+knows what it's called when you have an
+ 
+
+ align:start position:0%
+knows what it's called when you have an
+extra electron or an excess of
+
+ align:start position:0%
+extra electron or an excess of
+ 
+
+ align:start position:0%
+extra electron or an excess of
+electrons n
+
+ align:start position:0%
+electrons n
+ 
+
+ align:start position:0%
+electrons n
+type now what if I wanted holes what if
+
+ align:start position:0%
+type now what if I wanted holes what if
+ 
+
+ align:start position:0%
+type now what if I wanted holes what if
+I wanted extra
+
+ align:start position:0%
+I wanted extra
+ 
+
+ align:start position:0%
+I wanted extra
+holes B
+
+ align:start position:0%
+holes B
+ 
+
+ align:start position:0%
+holes B
+type and what would I put in
+
+ align:start position:0%
+type and what would I put in
+ 
+
+ align:start position:0%
+type and what would I put in
+there Boron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because less electron now you could you
+
+ align:start position:0%
+because less electron now you could you
+ 
+
+ align:start position:0%
+because less electron now you could you
+could dope it with many other things you
+
+ align:start position:0%
+could dope it with many other things you
+ 
+
+ align:start position:0%
+could dope it with many other things you
+don't have to dope silicon with just you
+
+ align:start position:0%
+don't have to dope silicon with just you
+ 
+
+ align:start position:0%
+don't have to dope silicon with just you
+know uh phosphorus or Boron it turns out
+
+ align:start position:0%
+know uh phosphorus or Boron it turns out
+ 
+
+ align:start position:0%
+know uh phosphorus or Boron it turns out
+that those are easy and and there some
+
+ align:start position:0%
+that those are easy and and there some
+ 
+
+ align:start position:0%
+that those are easy and and there some
+advantages in terms of the processing
+
+ align:start position:0%
+advantages in terms of the processing
+ 
+
+ align:start position:0%
+advantages in terms of the processing
+and you know chemically they can be
+
+ align:start position:0%
+and you know chemically they can be
+ 
+
+ align:start position:0%
+and you know chemically they can be
+happy but there are many ways of doping
+
+ align:start position:0%
+happy but there are many ways of doping
+ 
+
+ align:start position:0%
+happy but there are many ways of doping
+materials many many ways of doping
+
+ align:start position:0%
+materials many many ways of doping
+ 
+
+ align:start position:0%
+materials many many ways of doping
+materials and one of the things you do
+
+ align:start position:0%
+materials and one of the things you do
+ 
+
+ align:start position:0%
+materials and one of the things you do
+with doping there are many things you do
+
+ align:start position:0%
+with doping there are many things you do
+ 
+
+ align:start position:0%
+with doping there are many things you do
+with doping but one of the things you do
+
+ align:start position:0%
+with doping but one of the things you do
+ 
+
+ align:start position:0%
+with doping but one of the things you do
+is you get electrons or holes into these
+
+ align:start position:0%
+is you get electrons or holes into these
+ 
+
+ align:start position:0%
+is you get electrons or holes into these
+bands you populate them right but this
+
+ align:start position:0%
+bands you populate them right but this
+ 
+
+ align:start position:0%
+bands you populate them right but this
+expression is ignoring that this is just
+
+ align:start position:0%
+expression is ignoring that this is just
+ 
+
+ align:start position:0%
+expression is ignoring that this is just
+saying well we're going to use we're
+
+ align:start position:0%
+saying well we're going to use we're
+ 
+
+ align:start position:0%
+saying well we're going to use we're
+going to see if there's some thermal uh
+
+ align:start position:0%
+going to see if there's some thermal uh
+ 
+
+ align:start position:0%
+going to see if there's some thermal uh
+uh energy there and we'll use that
+
+ align:start position:0%
+uh energy there and we'll use that
+ 
+
+ align:start position:0%
+uh energy there and we'll use that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah any questions about that now um we
+
+ align:start position:0%
+yeah any questions about that now um we
+ 
+
+ align:start position:0%
+yeah any questions about that now um we
+talked about this a lot so I'm not going
+
+ align:start position:0%
+talked about this a lot so I'm not going
+ 
+
+ align:start position:0%
+talked about this a lot so I'm not going
+to go over this again that you know the
+
+ align:start position:0%
+to go over this again that you know the
+ 
+
+ align:start position:0%
+to go over this again that you know the
+direct transitions are easy for
+
+ align:start position:0%
+direct transitions are easy for
+ 
+
+ align:start position:0%
+direct transitions are easy for
+photons um the indirect ones where you
+
+ align:start position:0%
+photons um the indirect ones where you
+ 
+
+ align:start position:0%
+photons um the indirect ones where you
+shift the K where you are in kpace are
+
+ align:start position:0%
+shift the K where you are in kpace are
+ 
+
+ align:start position:0%
+shift the K where you are in kpace are
+hard okay um and that is why
+
+ align:start position:0%
+hard okay um and that is why
+ 
+
+ align:start position:0%
+hard okay um and that is why
+silicon is an expensive solar cell so
+
+ align:start position:0%
+silicon is an expensive solar cell so
+ 
+
+ align:start position:0%
+silicon is an expensive solar cell so
+we' we've talked about this I don't want
+
+ align:start position:0%
+we' we've talked about this I don't want
+ 
+
+ align:start position:0%
+we' we've talked about this I don't want
+to BL labor the point because I want to
+
+ align:start position:0%
+to BL labor the point because I want to
+ 
+
+ align:start position:0%
+to BL labor the point because I want to
+try to get to some
+
+ align:start position:0%
+try to get to some
+ 
+
+ align:start position:0%
+try to get to some
+simulations if possible any questions
+
+ align:start position:0%
+simulations if possible any questions
+ 
+
+ align:start position:0%
+simulations if possible any questions
+about that point though the optical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transitions right so the kinds of things
+
+ align:start position:0%
+transitions right so the kinds of things
+ 
+
+ align:start position:0%
+transitions right so the kinds of things
+you can get well you can get Optical
+
+ align:start position:0%
+you can get well you can get Optical
+ 
+
+ align:start position:0%
+you can get well you can get Optical
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um and you can also get magnetic
+
+ align:start position:0%
+um and you can also get magnetic
+ 
+
+ align:start position:0%
+um and you can also get magnetic
+properties from these densities of
+
+ align:start position:0%
+properties from these densities of
+ 
+
+ align:start position:0%
+properties from these densities of
+States so we talked about the optical
+
+ align:start position:0%
+States so we talked about the optical
+ 
+
+ align:start position:0%
+States so we talked about the optical
+properties and the optical properties is
+
+ align:start position:0%
+properties and the optical properties is
+ 
+
+ align:start position:0%
+properties and the optical properties is
+really the the the context of your um
+
+ align:start position:0%
+really the the the context of your um
+ 
+
+ align:start position:0%
+really the the the context of your um
+you know of your P set 5 but it's for a
+
+ align:start position:0%
+you know of your P set 5 but it's for a
+ 
+
+ align:start position:0%
+you know of your P set 5 but it's for a
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+um we haven't talked about magnetism and
+
+ align:start position:0%
+um we haven't talked about magnetism and
+ 
+
+ align:start position:0%
+um we haven't talked about magnetism and
+I want to come back to it because I did
+
+ align:start position:0%
+I want to come back to it because I did
+ 
+
+ align:start position:0%
+I want to come back to it because I did
+mention that electrons have Spin and
+
+ align:start position:0%
+mention that electrons have Spin and
+ 
+
+ align:start position:0%
+mention that electrons have Spin and
+therefore um they also have a magnetic
+
+ align:start position:0%
+therefore um they also have a magnetic
+ 
+
+ align:start position:0%
+therefore um they also have a magnetic
+moment and we call this just think of it
+
+ align:start position:0%
+moment and we call this just think of it
+ 
+
+ align:start position:0%
+moment and we call this just think of it
+as some constant that we call a bore
+
+ align:start position:0%
+as some constant that we call a bore
+ 
+
+ align:start position:0%
+as some constant that we call a bore
+Magneton it has a value
+
+ align:start position:0%
+Magneton it has a value
+ 
+
+ align:start position:0%
+Magneton it has a value
+okay um well and if you think about like
+
+ align:start position:0%
+okay um well and if you think about like
+ 
+
+ align:start position:0%
+okay um well and if you think about like
+an atom or a molecule you could just get
+
+ align:start position:0%
+an atom or a molecule you could just get
+ 
+
+ align:start position:0%
+an atom or a molecule you could just get
+that by knowing how many electrons are
+
+ align:start position:0%
+that by knowing how many electrons are
+ 
+
+ align:start position:0%
+that by knowing how many electrons are
+spinning in One Direction More than the
+
+ align:start position:0%
+spinning in One Direction More than the
+ 
+
+ align:start position:0%
+spinning in One Direction More than the
+other right so you can just count how
+
+ align:start position:0%
+other right so you can just count how
+ 
+
+ align:start position:0%
+other right so you can just count how
+many spin up electrons minus how many
+
+ align:start position:0%
+many spin up electrons minus how many
+ 
+
+ align:start position:0%
+many spin up electrons minus how many
+spin down electrons um you have and
+
+ align:start position:0%
+spin down electrons um you have and
+ 
+
+ align:start position:0%
+spin down electrons um you have and
+multiply that by the board Magneton and
+
+ align:start position:0%
+multiply that by the board Magneton and
+ 
+
+ align:start position:0%
+multiply that by the board Magneton and
+that'll give you the Magnetic Moment of
+
+ align:start position:0%
+that'll give you the Magnetic Moment of
+ 
+
+ align:start position:0%
+that'll give you the Magnetic Moment of
+the atom or molecule but what would I do
+
+ align:start position:0%
+the atom or molecule but what would I do
+ 
+
+ align:start position:0%
+the atom or molecule but what would I do
+for a solid
+
+ align:start position:0%
+for a solid
+ 
+
+ align:start position:0%
+for a solid
+so just like just like um do I still
+
+ align:start position:0%
+so just like just like um do I still
+ 
+
+ align:start position:0%
+so just like just like um do I still
+have it yeah see there's a there's the
+
+ align:start position:0%
+have it yeah see there's a there's the
+ 
+
+ align:start position:0%
+have it yeah see there's a there's the
+atomic picture where I could just count
+
+ align:start position:0%
+atomic picture where I could just count
+ 
+
+ align:start position:0%
+atomic picture where I could just count
+and in this case the difference is
+
+ align:start position:0%
+and in this case the difference is
+ 
+
+ align:start position:0%
+and in this case the difference is
+three right but now I've got a solid so
+
+ align:start position:0%
+three right but now I've got a solid so
+ 
+
+ align:start position:0%
+three right but now I've got a solid so
+what do I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I want to what what do I want to look
+
+ align:start position:0%
+do I want to what what do I want to look
+ 
+
+ align:start position:0%
+do I want to what what do I want to look
+at for a
+
+ align:start position:0%
+at for a
+ 
+
+ align:start position:0%
+at for a
+solid states density of states and it
+
+ align:start position:0%
+solid states density of states and it
+ 
+
+ align:start position:0%
+solid states density of states and it
+turns out that you can plot the density
+
+ align:start position:0%
+turns out that you can plot the density
+ 
+
+ align:start position:0%
+turns out that you can plot the density
+of states for spin up and spin down
+
+ align:start position:0%
+of states for spin up and spin down
+ 
+
+ align:start position:0%
+of states for spin up and spin down
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+separately and they can be different
+
+ align:start position:0%
+separately and they can be different
+ 
+
+ align:start position:0%
+separately and they can be different
+they can occupy those uh the two spins
+
+ align:start position:0%
+they can occupy those uh the two spins
+ 
+
+ align:start position:0%
+they can occupy those uh the two spins
+differently in a more complicated way
+
+ align:start position:0%
+differently in a more complicated way
+ 
+
+ align:start position:0%
+differently in a more complicated way
+but very much kind of same idea as what
+
+ align:start position:0%
+but very much kind of same idea as what
+ 
+
+ align:start position:0%
+but very much kind of same idea as what
+can happen in an atom but it's more
+
+ align:start position:0%
+can happen in an atom but it's more
+ 
+
+ align:start position:0%
+can happen in an atom but it's more
+complicated as you get these curvy bands
+
+ align:start position:0%
+complicated as you get these curvy bands
+ 
+
+ align:start position:0%
+complicated as you get these curvy bands
+and and all kinds of other things that
+
+ align:start position:0%
+and and all kinds of other things that
+ 
+
+ align:start position:0%
+and and all kinds of other things that
+can happen in a solid so now you look at
+
+ align:start position:0%
+can happen in a solid so now you look at
+ 
+
+ align:start position:0%
+can happen in a solid so now you look at
+the separate density of states for
+
+ align:start position:0%
+the separate density of states for
+ 
+
+ align:start position:0%
+the separate density of states for
+electrons with spin up versus spin down
+
+ align:start position:0%
+electrons with spin up versus spin down
+ 
+
+ align:start position:0%
+electrons with spin up versus spin down
+and that is something that I didn't talk
+
+ align:start position:0%
+and that is something that I didn't talk
+ 
+
+ align:start position:0%
+and that is something that I didn't talk
+about yet it's an input
+
+ align:start position:0%
+about yet it's an input
+ 
+
+ align:start position:0%
+about yet it's an input
+parameter in Siesta that is checked yes
+
+ align:start position:0%
+parameter in Siesta that is checked yes
+ 
+
+ align:start position:0%
+parameter in Siesta that is checked yes
+by default and it's called spin
+
+ align:start position:0%
+by default and it's called spin
+ 
+
+ align:start position:0%
+by default and it's called spin
+polarized question mark I think is what
+
+ align:start position:0%
+polarized question mark I think is what
+ 
+
+ align:start position:0%
+polarized question mark I think is what
+it's called spin polarized I should give
+
+ align:start position:0%
+it's called spin polarized I should give
+ 
+
+ align:start position:0%
+it's called spin polarized I should give
+the right intonation and you say yes or
+
+ align:start position:0%
+the right intonation and you say yes or
+ 
+
+ align:start position:0%
+the right intonation and you say yes or
+no and you say yes because that's the
+
+ align:start position:0%
+no and you say yes because that's the
+ 
+
+ align:start position:0%
+no and you say yes because that's the
+default but what are you doing when you
+
+ align:start position:0%
+default but what are you doing when you
+ 
+
+ align:start position:0%
+default but what are you doing when you
+say yes well what you're doing is you're
+
+ align:start position:0%
+say yes well what you're doing is you're
+ 
+
+ align:start position:0%
+say yes well what you're doing is you're
+telling the calculation to to allow the
+
+ align:start position:0%
+telling the calculation to to allow the
+ 
+
+ align:start position:0%
+telling the calculation to to allow the
+up and down electrons to have freedom
+
+ align:start position:0%
+up and down electrons to have freedom
+ 
+
+ align:start position:0%
+up and down electrons to have freedom
+from one another okay that's actually
+
+ align:start position:0%
+from one another okay that's actually
+ 
+
+ align:start position:0%
+from one another okay that's actually
+critical so if you didn't do that you
+
+ align:start position:0%
+critical so if you didn't do that you
+ 
+
+ align:start position:0%
+critical so if you didn't do that you
+would be simulating the material with
+
+ align:start position:0%
+would be simulating the material with
+ 
+
+ align:start position:0%
+would be simulating the material with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+constraint that the up and down
+
+ align:start position:0%
+constraint that the up and down
+ 
+
+ align:start position:0%
+constraint that the up and down
+electrons are exactly at the same
+
+ align:start position:0%
+electrons are exactly at the same
+ 
+
+ align:start position:0%
+electrons are exactly at the same
+energies okay so spin polarized it's
+
+ align:start position:0%
+energies okay so spin polarized it's
+ 
+
+ align:start position:0%
+energies okay so spin polarized it's
+it's a it's a the reason you do uh
+
+ align:start position:0%
+it's a it's a the reason you do uh
+ 
+
+ align:start position:0%
+it's a it's a the reason you do uh
+calculations that are not spin polarized
+
+ align:start position:0%
+calculations that are not spin polarized
+ 
+
+ align:start position:0%
+calculations that are not spin polarized
+is because many systems don't have a
+
+ align:start position:0%
+is because many systems don't have a
+ 
+
+ align:start position:0%
+is because many systems don't have a
+difference between up and down electrons
+
+ align:start position:0%
+difference between up and down electrons
+ 
+
+ align:start position:0%
+difference between up and down electrons
+right and and they are actually all the
+
+ align:start position:0%
+right and and they are actually all the
+ 
+
+ align:start position:0%
+right and and they are actually all the
+same right I mean you know if I looked
+
+ align:start position:0%
+same right I mean you know if I looked
+ 
+
+ align:start position:0%
+same right I mean you know if I looked
+at if I filled this up what do I have if
+
+ align:start position:0%
+at if I filled this up what do I have if
+ 
+
+ align:start position:0%
+at if I filled this up what do I have if
+I fill this up
+
+ align:start position:0%
+I fill this up
+ 
+
+ align:start position:0%
+I fill this up
+oh What atom is
+
+ align:start position:0%
+oh What atom is
+ 
+
+ align:start position:0%
+oh What atom is
+that it's
+
+ align:start position:0%
+that it's
+ 
+
+ align:start position:0%
+that it's
+neon and here every up electron is the
+
+ align:start position:0%
+neon and here every up electron is the
+ 
+
+ align:start position:0%
+neon and here every up electron is the
+same as every down electron for a given
+
+ align:start position:0%
+same as every down electron for a given
+ 
+
+ align:start position:0%
+same as every down electron for a given
+state right everything is the same here
+
+ align:start position:0%
+state right everything is the same here
+ 
+
+ align:start position:0%
+state right everything is the same here
+so it's not like this up
+
+ align:start position:0%
+so it's not like this up
+ 
+
+ align:start position:0%
+so it's not like this up
+electron of this p orbital wanted to be
+
+ align:start position:0%
+electron of this p orbital wanted to be
+ 
+
+ align:start position:0%
+electron of this p orbital wanted to be
+there and the down one wanted to be
+
+ align:start position:0%
+there and the down one wanted to be
+ 
+
+ align:start position:0%
+there and the down one wanted to be
+there that doesn't happen for neon and
+
+ align:start position:0%
+there that doesn't happen for neon and
+ 
+
+ align:start position:0%
+there that doesn't happen for neon and
+it doesn't happen for many systems and
+
+ align:start position:0%
+it doesn't happen for many systems and
+ 
+
+ align:start position:0%
+it doesn't happen for many systems and
+many materials but for certainly in some
+
+ align:start position:0%
+many materials but for certainly in some
+ 
+
+ align:start position:0%
+many materials but for certainly in some
+cases and certainly for magnetic
+
+ align:start position:0%
+cases and certainly for magnetic
+ 
+
+ align:start position:0%
+cases and certainly for magnetic
+materials that's what causes
+
+ align:start position:0%
+materials that's what causes
+ 
+
+ align:start position:0%
+materials that's what causes
+magnetism right it's that you have a
+
+ align:start position:0%
+magnetism right it's that you have a
+ 
+
+ align:start position:0%
+magnetism right it's that you have a
+difference between Spin up and spin down
+
+ align:start position:0%
+difference between Spin up and spin down
+ 
+
+ align:start position:0%
+difference between Spin up and spin down
+and that as you occupy the density of
+
+ align:start position:0%
+and that as you occupy the density of
+ 
+
+ align:start position:0%
+and that as you occupy the density of
+States you literally you get a
+
+ align:start position:0%
+States you literally you get a
+ 
+
+ align:start position:0%
+States you literally you get a
+difference in in the number right
+
+ align:start position:0%
+difference in in the number right
+ 
+
+ align:start position:0%
+difference in in the number right
+so that's what causes the
+
+ align:start position:0%
+so that's what causes the
+ 
+
+ align:start position:0%
+so that's what causes the
+magnetism so for for many materials you
+
+ align:start position:0%
+magnetism so for for many materials you
+ 
+
+ align:start position:0%
+magnetism so for for many materials you
+know there is no spin polarization or
+
+ align:start position:0%
+know there is no spin polarization or
+ 
+
+ align:start position:0%
+know there is no spin polarization or
+there or in other words there is no
+
+ align:start position:0%
+there or in other words there is no
+ 
+
+ align:start position:0%
+there or in other words there is no
+difference they they're just spin up and
+
+ align:start position:0%
+difference they they're just spin up and
+ 
+
+ align:start position:0%
+difference they they're just spin up and
+spin down is the same here same here
+
+ align:start position:0%
+spin down is the same here same here
+ 
+
+ align:start position:0%
+spin down is the same here same here
+same here right but if it's a magnetic
+
+ align:start position:0%
+same here right but if it's a magnetic
+ 
+
+ align:start position:0%
+same here right but if it's a magnetic
+material what you'll find is that if you
+
+ align:start position:0%
+material what you'll find is that if you
+ 
+
+ align:start position:0%
+material what you'll find is that if you
+plot the density of States separately
+
+ align:start position:0%
+plot the density of States separately
+ 
+
+ align:start position:0%
+plot the density of States separately
+for spin up and spin down electrons like
+
+ align:start position:0%
+for spin up and spin down electrons like
+ 
+
+ align:start position:0%
+for spin up and spin down electrons like
+in this case for for iron there's a
+
+ align:start position:0%
+in this case for for iron there's a
+ 
+
+ align:start position:0%
+in this case for for iron there's a
+difference and in fact the magnetic
+
+ align:start position:0%
+difference and in fact the magnetic
+ 
+
+ align:start position:0%
+difference and in fact the magnetic
+moment of that material is nothing more
+
+ align:start position:0%
+moment of that material is nothing more
+ 
+
+ align:start position:0%
+moment of that material is nothing more
+than the integral of that
+
+ align:start position:0%
+than the integral of that
+ 
+
+ align:start position:0%
+than the integral of that
+difference right again you're
+
+ align:start position:0%
+difference right again you're
+ 
+
+ align:start position:0%
+difference right again you're
+integrating the
+
+ align:start position:0%
+integrating the
+ 
+
+ align:start position:0%
+integrating the
+Doss and you're finding something really
+
+ align:start position:0%
+Doss and you're finding something really
+ 
+
+ align:start position:0%
+Doss and you're finding something really
+cool about the
+
+ align:start position:0%
+cool about the
+ 
+
+ align:start position:0%
+cool about the
+material okay so that's the same thing
+
+ align:start position:0%
+material okay so that's the same thing
+ 
+
+ align:start position:0%
+material okay so that's the same thing
+as just counting number of up and number
+
+ align:start position:0%
+as just counting number of up and number
+ 
+
+ align:start position:0%
+as just counting number of up and number
+of down but now you're counting it in in
+
+ align:start position:0%
+of down but now you're counting it in in
+ 
+
+ align:start position:0%
+of down but now you're counting it in in
+this very sort of complex filling of
+
+ align:start position:0%
+this very sort of complex filling of
+ 
+
+ align:start position:0%
+this very sort of complex filling of
+States you know that happens in a
+
+ align:start position:0%
+States you know that happens in a
+ 
+
+ align:start position:0%
+States you know that happens in a
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+okay any questions
+
+ align:start position:0%
+okay any questions
+ 
+
+ align:start position:0%
+okay any questions
+so if I if I did a calculation of iron
+
+ align:start position:0%
+so if I if I did a calculation of iron
+ 
+
+ align:start position:0%
+so if I if I did a calculation of iron
+with spin polarized checked no then um
+
+ align:start position:0%
+with spin polarized checked no then um
+ 
+
+ align:start position:0%
+with spin polarized checked no then um
+you see these would be identical and I'd
+
+ align:start position:0%
+you see these would be identical and I'd
+ 
+
+ align:start position:0%
+you see these would be identical and I'd
+get no
+
+ align:start position:0%
+get no
+ 
+
+ align:start position:0%
+get no
+magnetism okay and you can do that you
+
+ align:start position:0%
+magnetism okay and you can do that you
+ 
+
+ align:start position:0%
+magnetism okay and you can do that you
+can actually do the calculation of iron
+
+ align:start position:0%
+can actually do the calculation of iron
+ 
+
+ align:start position:0%
+can actually do the calculation of iron
+with spin polarized check no and it's
+
+ align:start position:0%
+with spin polarized check no and it's
+ 
+
+ align:start position:0%
+with spin polarized check no and it's
+completely wrong it's not the ground
+
+ align:start position:0%
+completely wrong it's not the ground
+ 
+
+ align:start position:0%
+completely wrong it's not the ground
+state of iron right um and but and if
+
+ align:start position:0%
+state of iron right um and but and if
+ 
+
+ align:start position:0%
+state of iron right um and but and if
+you do it with spin polarized on then it
+
+ align:start position:0%
+you do it with spin polarized on then it
+ 
+
+ align:start position:0%
+you do it with spin polarized on then it
+allows those up and down electrons to
+
+ align:start position:0%
+allows those up and down electrons to
+ 
+
+ align:start position:0%
+allows those up and down electrons to
+move relative to each other and you'll
+
+ align:start position:0%
+move relative to each other and you'll
+ 
+
+ align:start position:0%
+move relative to each other and you'll
+get uh the code will the outputs you'll
+
+ align:start position:0%
+get uh the code will the outputs you'll
+ 
+
+ align:start position:0%
+get uh the code will the outputs you'll
+see that there's a in the plots there's
+
+ align:start position:0%
+see that there's a in the plots there's
+ 
+
+ align:start position:0%
+see that there's a in the plots there's
+something called the projected density
+
+ align:start position:0%
+something called the projected density
+ 
+
+ align:start position:0%
+something called the projected density
+of States and it's projected for one
+
+ align:start position:0%
+of States and it's projected for one
+ 
+
+ align:start position:0%
+of States and it's projected for one
+Spin and another spin okay and that
+
+ align:start position:0%
+Spin and another spin okay and that
+ 
+
+ align:start position:0%
+Spin and another spin okay and that
+would allow you to um to calculate the
+
+ align:start position:0%
+would allow you to um to calculate the
+ 
+
+ align:start position:0%
+would allow you to um to calculate the
+magnetic properties and materials using
+
+ align:start position:0%
+magnetic properties and materials using
+ 
+
+ align:start position:0%
+magnetic properties and materials using
+the the nanohub tool and I think last
+
+ align:start position:0%
+the the nanohub tool and I think last
+ 
+
+ align:start position:0%
+the the nanohub tool and I think last
+year we did do uh we might have done a
+
+ align:start position:0%
+year we did do uh we might have done a
+ 
+
+ align:start position:0%
+year we did do uh we might have done a
+homework on that but this year we we
+
+ align:start position:0%
+homework on that but this year we we
+ 
+
+ align:start position:0%
+homework on that but this year we we
+won't but I want you to know about about
+
+ align:start position:0%
+won't but I want you to know about about
+ 
+
+ align:start position:0%
+won't but I want you to know about about
+it cuz it's it's kind of
+
+ align:start position:0%
+it cuz it's it's kind of
+ 
+
+ align:start position:0%
+it cuz it's it's kind of
+cool okay um any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions uh couple other things you can
+
+ align:start position:0%
+questions uh couple other things you can
+ 
+
+ align:start position:0%
+questions uh couple other things you can
+do and and I I you know these are just I
+
+ align:start position:0%
+do and and I I you know these are just I
+ 
+
+ align:start position:0%
+do and and I I you know these are just I
+just briefly one to First principles
+
+ align:start position:0%
+just briefly one to First principles
+ 
+
+ align:start position:0%
+just briefly one to First principles
+right Quantum molecular Dynamics you can
+
+ align:start position:0%
+right Quantum molecular Dynamics you can
+ 
+
+ align:start position:0%
+right Quantum molecular Dynamics you can
+do it you can do MD just like you did MD
+
+ align:start position:0%
+do it you can do MD just like you did MD
+ 
+
+ align:start position:0%
+do it you can do MD just like you did MD
+in the first part you're just getting F
+
+ align:start position:0%
+in the first part you're just getting F
+ 
+
+ align:start position:0%
+in the first part you're just getting F
+from uh Helman fan the Helman fan
+
+ align:start position:0%
+from uh Helman fan the Helman fan
+ 
+
+ align:start position:0%
+from uh Helman fan the Helman fan
+theorem which I sort of referred to a
+
+ align:start position:0%
+theorem which I sort of referred to a
+ 
+
+ align:start position:0%
+theorem which I sort of referred to a
+couple lectures ago um but it's
+
+ align:start position:0%
+couple lectures ago um but it's
+ 
+
+ align:start position:0%
+couple lectures ago um but it's
+basically just a way of getting the
+
+ align:start position:0%
+basically just a way of getting the
+ 
+
+ align:start position:0%
+basically just a way of getting the
+forces
+
+ align:start position:0%
+forces
+ 
+
+ align:start position:0%
+forces
+um using quantum mechanics and and I
+
+ align:start position:0%
+um using quantum mechanics and and I
+ 
+
+ align:start position:0%
+um using quantum mechanics and and I
+don't really want to go into it in
+
+ align:start position:0%
+don't really want to go into it in
+ 
+
+ align:start position:0%
+don't really want to go into it in
+detail but I just want to tell you you
+
+ align:start position:0%
+detail but I just want to tell you you
+ 
+
+ align:start position:0%
+detail but I just want to tell you you
+can get the force on these atoms from
+
+ align:start position:0%
+can get the force on these atoms from
+ 
+
+ align:start position:0%
+can get the force on these atoms from
+these quantum mechanical simulations and
+
+ align:start position:0%
+these quantum mechanical simulations and
+ 
+
+ align:start position:0%
+these quantum mechanical simulations and
+you can do Dynamics here's one I did a
+
+ align:start position:0%
+you can do Dynamics here's one I did a
+ 
+
+ align:start position:0%
+you can do Dynamics here's one I did a
+long time ago and here the problem was
+
+ align:start position:0%
+long time ago and here the problem was
+ 
+
+ align:start position:0%
+long time ago and here the problem was
+that how do nanot tubes grow was was a
+
+ align:start position:0%
+that how do nanot tubes grow was was a
+ 
+
+ align:start position:0%
+that how do nanot tubes grow was was a
+big question okay and so what we did is
+
+ align:start position:0%
+big question okay and so what we did is
+ 
+
+ align:start position:0%
+big question okay and so what we did is
+you know now what you have is you have a
+
+ align:start position:0%
+you know now what you have is you have a
+ 
+
+ align:start position:0%
+you know now what you have is you have a
+piece of iron
+
+ align:start position:0%
+piece of iron
+ 
+
+ align:start position:0%
+piece of iron
+here and this is what happens when you
+
+ align:start position:0%
+here and this is what happens when you
+ 
+
+ align:start position:0%
+here and this is what happens when you
+when you grow nanot tubes is you have
+
+ align:start position:0%
+when you grow nanot tubes is you have
+ 
+
+ align:start position:0%
+when you grow nanot tubes is you have
+these seed particles like iron right can
+
+ align:start position:0%
+these seed particles like iron right can
+ 
+
+ align:start position:0%
+these seed particles like iron right can
+be other things nickel other things will
+
+ align:start position:0%
+be other things nickel other things will
+ 
+
+ align:start position:0%
+be other things nickel other things will
+work um not gold uh and and then you
+
+ align:start position:0%
+work um not gold uh and and then you
+ 
+
+ align:start position:0%
+work um not gold uh and and then you
+flow some kind of gas over it that dumps
+
+ align:start position:0%
+flow some kind of gas over it that dumps
+ 
+
+ align:start position:0%
+flow some kind of gas over it that dumps
+carbon onto the Catalyst okay now the
+
+ align:start position:0%
+carbon onto the Catalyst okay now the
+ 
+
+ align:start position:0%
+carbon onto the Catalyst okay now the
+the the problem is that understanding
+
+ align:start position:0%
+the the problem is that understanding
+ 
+
+ align:start position:0%
+the the problem is that understanding
+how that then leads to the growth of a
+
+ align:start position:0%
+how that then leads to the growth of a
+ 
+
+ align:start position:0%
+how that then leads to the growth of a
+tube is is still an open question by the
+
+ align:start position:0%
+tube is is still an open question by the
+ 
+
+ align:start position:0%
+tube is is still an open question by the
+way still an open question nobody
+
+ align:start position:0%
+way still an open question nobody
+ 
+
+ align:start position:0%
+way still an open question nobody
+actually really knows the full answer to
+
+ align:start position:0%
+actually really knows the full answer to
+ 
+
+ align:start position:0%
+actually really knows the full answer to
+that but certainly people were just
+
+ align:start position:0%
+that but certainly people were just
+ 
+
+ align:start position:0%
+that but certainly people were just
+debating does the carbon go inside the
+
+ align:start position:0%
+debating does the carbon go inside the
+ 
+
+ align:start position:0%
+debating does the carbon go inside the
+the Catalyst or not does it stay on the
+
+ align:start position:0%
+the Catalyst or not does it stay on the
+ 
+
+ align:start position:0%
+the Catalyst or not does it stay on the
+surface does it saturate the Catalyst
+
+ align:start position:0%
+surface does it saturate the Catalyst
+ 
+
+ align:start position:0%
+surface does it saturate the Catalyst
+first and then come out you know from
+
+ align:start position:0%
+first and then come out you know from
+ 
+
+ align:start position:0%
+first and then come out you know from
+the the bulk from the particle and that
+
+ align:start position:0%
+the the bulk from the particle and that
+ 
+
+ align:start position:0%
+the the bulk from the particle and that
+that's a really that's a perfect problem
+
+ align:start position:0%
+that's a really that's a perfect problem
+ 
+
+ align:start position:0%
+that's a really that's a perfect problem
+for Quantum because there's so many
+
+ align:start position:0%
+for Quantum because there's so many
+ 
+
+ align:start position:0%
+for Quantum because there's so many
+different bonding environments and so
+
+ align:start position:0%
+different bonding environments and so
+ 
+
+ align:start position:0%
+different bonding environments and so
+many possibilities here that classical
+
+ align:start position:0%
+many possibilities here that classical
+ 
+
+ align:start position:0%
+many possibilities here that classical
+potentials will fail okay they're not
+
+ align:start position:0%
+potentials will fail okay they're not
+ 
+
+ align:start position:0%
+potentials will fail okay they're not
+going to capture all of the different
+
+ align:start position:0%
+going to capture all of the different
+ 
+
+ align:start position:0%
+going to capture all of the different
+you know complexities in how carbon
+
+ align:start position:0%
+you know complexities in how carbon
+ 
+
+ align:start position:0%
+you know complexities in how carbon
+needs to bond to iron inside and out and
+
+ align:start position:0%
+needs to bond to iron inside and out and
+ 
+
+ align:start position:0%
+needs to bond to iron inside and out and
+so it's a great problem for quantum
+
+ align:start position:0%
+so it's a great problem for quantum
+ 
+
+ align:start position:0%
+so it's a great problem for quantum
+mechanics and we studied this and showed
+
+ align:start position:0%
+mechanics and we studied this and showed
+ 
+
+ align:start position:0%
+mechanics and we studied this and showed
+you know we we fed the simulation carbon
+
+ align:start position:0%
+you know we we fed the simulation carbon
+ 
+
+ align:start position:0%
+you know we we fed the simulation carbon
+and we just watched sort of how the tube
+
+ align:start position:0%
+and we just watched sort of how the tube
+ 
+
+ align:start position:0%
+and we just watched sort of how the tube
+um winds up making its way uh out of the
+
+ align:start position:0%
+um winds up making its way uh out of the
+ 
+
+ align:start position:0%
+um winds up making its way uh out of the
+system and we show that it doesn't
+
+ align:start position:0%
+system and we show that it doesn't
+ 
+
+ align:start position:0%
+system and we show that it doesn't
+saturate actually inside the the iron
+
+ align:start position:0%
+saturate actually inside the the iron
+ 
+
+ align:start position:0%
+saturate actually inside the the iron
+but rather stays on the surface now one
+
+ align:start position:0%
+but rather stays on the surface now one
+ 
+
+ align:start position:0%
+but rather stays on the surface now one
+and it makes for cool movies
+
+ align:start position:0%
+and it makes for cool movies
+ 
+
+ align:start position:0%
+and it makes for cool movies
+um yeah I don't know how long it's so
+
+ align:start position:0%
+um yeah I don't know how long it's so
+ 
+
+ align:start position:0%
+um yeah I don't know how long it's so
+somebody tell me something you notice
+
+ align:start position:0%
+somebody tell me something you notice
+ 
+
+ align:start position:0%
+somebody tell me something you notice
+about this um besides just you know it's
+
+ align:start position:0%
+about this um besides just you know it's
+ 
+
+ align:start position:0%
+about this um besides just you know it's
+kind of a fun movie
+
+ align:start position:0%
+kind of a fun movie
+ 
+
+ align:start position:0%
+kind of a fun movie
+but do you notice anything like there's
+
+ align:start position:0%
+but do you notice anything like there's
+ 
+
+ align:start position:0%
+but do you notice anything like there's
+the initial nanot tube growth and that's
+
+ align:start position:0%
+the initial nanot tube growth and that's
+ 
+
+ align:start position:0%
+the initial nanot tube growth and that's
+where it
+
+ align:start position:0%
+where it
+ 
+
+ align:start position:0%
+where it
+ended so I noticed two things yeah Sun
+
+ align:start position:0%
+ended so I noticed two things yeah Sun
+ 
+
+ align:start position:0%
+ended so I noticed two things yeah Sun
+Rings are oh yeah yeah actually that's
+
+ align:start position:0%
+Rings are oh yeah yeah actually that's
+ 
+
+ align:start position:0%
+Rings are oh yeah yeah actually that's
+that's a really good point so so that
+
+ align:start position:0%
+that's a really good point so so that
+ 
+
+ align:start position:0%
+that's a really good point so so that
+was a you know very interesting part of
+
+ align:start position:0%
+was a you know very interesting part of
+ 
+
+ align:start position:0%
+was a you know very interesting part of
+the analysis is what kind what kind of
+
+ align:start position:0%
+the analysis is what kind what kind of
+ 
+
+ align:start position:0%
+the analysis is what kind what kind of
+carbon you get right when you catalyze
+
+ align:start position:0%
+carbon you get right when you catalyze
+ 
+
+ align:start position:0%
+carbon you get right when you catalyze
+Carbon on a Surface um what does it do
+
+ align:start position:0%
+Carbon on a Surface um what does it do
+ 
+
+ align:start position:0%
+Carbon on a Surface um what does it do
+right does it form nice graphing and
+
+ align:start position:0%
+right does it form nice graphing and
+ 
+
+ align:start position:0%
+right does it form nice graphing and
+then curve it or does it form the
+
+ align:start position:0%
+then curve it or does it form the
+ 
+
+ align:start position:0%
+then curve it or does it form the
+defects so that you can curve it where
+
+ align:start position:0%
+defects so that you can curve it where
+ 
+
+ align:start position:0%
+defects so that you can curve it where
+the penalties in energy coming from but
+
+ align:start position:0%
+the penalties in energy coming from but
+ 
+
+ align:start position:0%
+the penalties in energy coming from but
+actually I was going to say I was going
+
+ align:start position:0%
+actually I was going to say I was going
+ 
+
+ align:start position:0%
+actually I was going to say I was going
+to kind of say some negative things two
+
+ align:start position:0%
+to kind of say some negative things two
+ 
+
+ align:start position:0%
+to kind of say some negative things two
+negative things they're not negatives
+
+ align:start position:0%
+negative things they're not negatives
+ 
+
+ align:start position:0%
+negative things they're not negatives
+but they're
+
+ align:start position:0%
+but they're
+ 
+
+ align:start position:0%
+but they're
+limitations tell me something obvious
+
+ align:start position:0%
+limitations tell me something obvious
+ 
+
+ align:start position:0%
+limitations tell me something obvious
+about this compared to say the protein
+
+ align:start position:0%
+about this compared to say the protein
+ 
+
+ align:start position:0%
+about this compared to say the protein
+simulations you did in the first
+
+ align:start position:0%
+simulations you did in the first
+ 
+
+ align:start position:0%
+simulations you did in the first
+part yeah this is really tiny and how
+
+ align:start position:0%
+part yeah this is really tiny and how
+ 
+
+ align:start position:0%
+part yeah this is really tiny and how
+long do you think this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+went what is
+
+ align:start position:0%
+went what is
+ 
+
+ align:start position:0%
+went what is
+that uh I'm not going to tell you
+
+ align:start position:0%
+that uh I'm not going to tell you
+ 
+
+ align:start position:0%
+that uh I'm not going to tell you
+because that would make me feel old um a
+
+ align:start position:0%
+because that would make me feel old um a
+ 
+
+ align:start position:0%
+because that would make me feel old um a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+ago uh well so you know but anyway how
+
+ align:start position:0%
+ago uh well so you know but anyway how
+ 
+
+ align:start position:0%
+ago uh well so you know but anyway how
+long can you run a molecular Dynamic
+
+ align:start position:0%
+long can you run a molecular Dynamic
+ 
+
+ align:start position:0%
+long can you run a molecular Dynamic
+simulation having to do Quant mechanics
+
+ align:start position:0%
+simulation having to do Quant mechanics
+ 
+
+ align:start position:0%
+simulation having to do Quant mechanics
+at each
+
+ align:start position:0%
+at each
+ 
+
+ align:start position:0%
+at each
+step yeah
+
+ align:start position:0%
+step yeah
+ 
+
+ align:start position:0%
+step yeah
+like well how long could you do proteins
+
+ align:start position:0%
+like well how long could you do proteins
+ 
+
+ align:start position:0%
+like well how long could you do proteins
+with classical ND huge systems could you
+
+ align:start position:0%
+with classical ND huge systems could you
+ 
+
+ align:start position:0%
+with classical ND huge systems could you
+do them for seconds no but how
+
+ align:start position:0%
+do them for seconds no but how
+ 
+
+ align:start position:0%
+do them for seconds no but how
+long yeah actually even longer with
+
+ align:start position:0%
+long yeah actually even longer with
+ 
+
+ align:start position:0%
+long yeah actually even longer with
+classical MD you can get up to microsc
+
+ align:start position:0%
+classical MD you can get up to microsc
+ 
+
+ align:start position:0%
+classical MD you can get up to microsc
+now certainly nanoseconds is is just you
+
+ align:start position:0%
+now certainly nanoseconds is is just you
+ 
+
+ align:start position:0%
+now certainly nanoseconds is is just you
+know 10 100 NCS no problem here we're at
+
+ align:start position:0%
+know 10 100 NCS no problem here we're at
+ 
+
+ align:start position:0%
+know 10 100 NCS no problem here we're at
+we're at 10 picoseconds right even two
+
+ align:start position:0%
+we're at 10 picoseconds right even two
+ 
+
+ align:start position:0%
+we're at 10 picoseconds right even two
+Picos nowadays you can push
+
+ align:start position:0%
+Picos nowadays you can push
+ 
+
+ align:start position:0%
+Picos nowadays you can push
+50 100 pics but you wouldn't go further
+
+ align:start position:0%
+50 100 pics but you wouldn't go further
+ 
+
+ align:start position:0%
+50 100 pics but you wouldn't go further
+than that it's really hard right so the
+
+ align:start position:0%
+than that it's really hard right so the
+ 
+
+ align:start position:0%
+than that it's really hard right so the
+time and size are real really limited um
+
+ align:start position:0%
+time and size are real really limited um
+ 
+
+ align:start position:0%
+time and size are real really limited um
+and that's why we you know with with
+
+ align:start position:0%
+and that's why we you know with with
+ 
+
+ align:start position:0%
+and that's why we you know with with
+Quantum MD you study small systems for
+
+ align:start position:0%
+Quantum MD you study small systems for
+ 
+
+ align:start position:0%
+Quantum MD you study small systems for
+short time scales this was nanocluster
+
+ align:start position:0%
+short time scales this was nanocluster
+ 
+
+ align:start position:0%
+short time scales this was nanocluster
+growth um the other thing I I want to
+
+ align:start position:0%
+growth um the other thing I I want to
+ 
+
+ align:start position:0%
+growth um the other thing I I want to
+you know I I think Quantum these are
+
+ align:start position:0%
+you know I I think Quantum these are
+ 
+
+ align:start position:0%
+you know I I think Quantum these are
+just kind of other things you can do
+
+ align:start position:0%
+just kind of other things you can do
+ 
+
+ align:start position:0%
+just kind of other things you can do
+this is supposed to be you know just
+
+ align:start position:0%
+this is supposed to be you know just
+ 
+
+ align:start position:0%
+this is supposed to be you know just
+making sure you see that
+
+ align:start position:0%
+making sure you see that
+ 
+
+ align:start position:0%
+making sure you see that
+it's not just the band structure in DOS
+
+ align:start position:0%
+it's not just the band structure in DOS
+ 
+
+ align:start position:0%
+it's not just the band structure in DOS
+there are other things you can do a lot
+
+ align:start position:0%
+there are other things you can do a lot
+ 
+
+ align:start position:0%
+there are other things you can do a lot
+of things with Quantum simulations um
+
+ align:start position:0%
+of things with Quantum simulations um
+ 
+
+ align:start position:0%
+of things with Quantum simulations um
+water is is is a really cool problem and
+
+ align:start position:0%
+water is is is a really cool problem and
+ 
+
+ align:start position:0%
+water is is is a really cool problem and
+um I I love cendes I love reading about
+
+ align:start position:0%
+um I I love cendes I love reading about
+ 
+
+ align:start position:0%
+um I I love cendes I love reading about
+caves has anybody read about Cavendish
+
+ align:start position:0%
+caves has anybody read about Cavendish
+ 
+
+ align:start position:0%
+caves has anybody read about Cavendish
+he's such a fascinating guy um he's a
+
+ align:start position:0%
+he's such a fascinating guy um he's a
+ 
+
+ align:start position:0%
+he's such a fascinating guy um he's a
+university Dropout he compared the
+
+ align:start position:0%
+university Dropout he compared the
+ 
+
+ align:start position:0%
+university Dropout he compared the
+connectivities of electrolytes and
+
+ align:start position:0%
+connectivities of electrolytes and
+ 
+
+ align:start position:0%
+connectivities of electrolytes and
+express the version of oma way ahead of
+
+ align:start position:0%
+express the version of oma way ahead of
+ 
+
+ align:start position:0%
+express the version of oma way ahead of
+time um and uh he he measured uh the
+
+ align:start position:0%
+time um and uh he he measured uh the
+ 
+
+ align:start position:0%
+time um and uh he he measured uh the
+gravitational constant and um and he
+
+ align:start position:0%
+gravitational constant and um and he
+ 
+
+ align:start position:0%
+gravitational constant and um and he
+came up with really water which at that
+
+ align:start position:0%
+came up with really water which at that
+ 
+
+ align:start position:0%
+came up with really water which at that
+point was flist flist flist in and
+
+ align:start position:0%
+point was flist flist flist in and
+ 
+
+ align:start position:0%
+point was flist flist flist in and
+deistic air which I love those names um
+
+ align:start position:0%
+deistic air which I love those names um
+ 
+
+ align:start position:0%
+deistic air which I love those names um
+which is hydrogen oxygen but anyway um
+
+ align:start position:0%
+which is hydrogen oxygen but anyway um
+ 
+
+ align:start position:0%
+which is hydrogen oxygen but anyway um
+you know water has these really
+
+ align:start position:0%
+you know water has these really
+ 
+
+ align:start position:0%
+you know water has these really
+interesting properties this is a
+
+ align:start position:0%
+interesting properties this is a
+ 
+
+ align:start position:0%
+interesting properties this is a
+wonderful website to read about water
+
+ align:start position:0%
+wonderful website to read about water
+ 
+
+ align:start position:0%
+wonderful website to read about water
+I'll give you the answer it actually
+
+ align:start position:0%
+I'll give you the answer it actually
+ 
+
+ align:start position:0%
+I'll give you the answer it actually
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+right water sees water like this not
+
+ align:start position:0%
+right water sees water like this not
+ 
+
+ align:start position:0%
+right water sees water like this not
+like this right so um it really sees it
+
+ align:start position:0%
+like this right so um it really sees it
+ 
+
+ align:start position:0%
+like this right so um it really sees it
+you know much more spherical than we
+
+ align:start position:0%
+you know much more spherical than we
+ 
+
+ align:start position:0%
+you know much more spherical than we
+usually draw it um and yet it does have
+
+ align:start position:0%
+usually draw it um and yet it does have
+ 
+
+ align:start position:0%
+usually draw it um and yet it does have
+you know these very definite bondings
+
+ align:start position:0%
+you know these very definite bondings
+ 
+
+ align:start position:0%
+you know these very definite bondings
+that it likes to do and the point I want
+
+ align:start position:0%
+that it likes to do and the point I want
+ 
+
+ align:start position:0%
+that it likes to do and the point I want
+to make is when you go into an MD code
+
+ align:start position:0%
+to make is when you go into an MD code
+ 
+
+ align:start position:0%
+to make is when you go into an MD code
+and you put water in there did you use
+
+ align:start position:0%
+and you put water in there did you use
+ 
+
+ align:start position:0%
+and you put water in there did you use
+water in your protein simulations yeah
+
+ align:start position:0%
+water in your protein simulations yeah
+ 
+
+ align:start position:0%
+water in your protein simulations yeah
+what which water did you
+
+ align:start position:0%
+what which water did you
+ 
+
+ align:start position:0%
+what which water did you
+pick I mean you must have picked a
+
+ align:start position:0%
+pick I mean you must have picked a
+ 
+
+ align:start position:0%
+pick I mean you must have picked a
+potential or the code picked a
+
+ align:start position:0%
+potential or the code picked a
+ 
+
+ align:start position:0%
+potential or the code picked a
+potential right tip 3p tip 4p well
+
+ align:start position:0%
+potential right tip 3p tip 4p well
+ 
+
+ align:start position:0%
+potential right tip 3p tip 4p well
+there's hundreds of them there's hundred
+
+ align:start position:0%
+there's hundreds of them there's hundred
+ 
+
+ align:start position:0%
+there's hundreds of them there's hundred
+these are just a few water potentials
+
+ align:start position:0%
+these are just a few water potentials
+ 
+
+ align:start position:0%
+these are just a few water potentials
+why are there so many well because some
+
+ align:start position:0%
+why are there so many well because some
+ 
+
+ align:start position:0%
+why are there so many well because some
+of them reproduce some things better
+
+ align:start position:0%
+of them reproduce some things better
+ 
+
+ align:start position:0%
+of them reproduce some things better
+than others right and that gets to be a
+
+ align:start position:0%
+than others right and that gets to be a
+ 
+
+ align:start position:0%
+than others right and that gets to be a
+a really serious problem if you want to
+
+ align:start position:0%
+a really serious problem if you want to
+ 
+
+ align:start position:0%
+a really serious problem if you want to
+study some of the fundamental problems
+
+ align:start position:0%
+study some of the fundamental problems
+ 
+
+ align:start position:0%
+study some of the fundamental problems
+of water um and there's so many
+
+ align:start position:0%
+of water um and there's so many
+ 
+
+ align:start position:0%
+of water um and there's so many
+Mysteries that we still don't know um in
+
+ align:start position:0%
+Mysteries that we still don't know um in
+ 
+
+ align:start position:0%
+Mysteries that we still don't know um in
+terms of just what happens when water
+
+ align:start position:0%
+terms of just what happens when water
+ 
+
+ align:start position:0%
+terms of just what happens when water
+evaporates freezes um and so you know
+
+ align:start position:0%
+evaporates freezes um and so you know
+ 
+
+ align:start position:0%
+evaporates freezes um and so you know
+which one is best well this a perfect
+
+ align:start position:0%
+which one is best well this a perfect
+ 
+
+ align:start position:0%
+which one is best well this a perfect
+problem for quantum mechanics okay and
+
+ align:start position:0%
+problem for quantum mechanics okay and
+ 
+
+ align:start position:0%
+problem for quantum mechanics okay and
+and I won't uh go through the details
+
+ align:start position:0%
+and I won't uh go through the details
+ 
+
+ align:start position:0%
+and I won't uh go through the details
+but you know um you can you can do water
+
+ align:start position:0%
+but you know um you can you can do water
+ 
+
+ align:start position:0%
+but you know um you can you can do water
+with Quantum um and this is a good way
+
+ align:start position:0%
+with Quantum um and this is a good way
+ 
+
+ align:start position:0%
+with Quantum um and this is a good way
+to validate which potential you use in
+
+ align:start position:0%
+to validate which potential you use in
+ 
+
+ align:start position:0%
+to validate which potential you use in
+your classical simulations you can also
+
+ align:start position:0%
+your classical simulations you can also
+ 
+
+ align:start position:0%
+your classical simulations you can also
+calculate phonons you can just displace
+
+ align:start position:0%
+calculate phonons you can just displace
+ 
+
+ align:start position:0%
+calculate phonons you can just displace
+atoms and calculate energies uh energy
+
+ align:start position:0%
+atoms and calculate energies uh energy
+ 
+
+ align:start position:0%
+atoms and calculate energies uh energy
+differences and get frequencies right so
+
+ align:start position:0%
+differences and get frequencies right so
+ 
+
+ align:start position:0%
+differences and get frequencies right so
+you can calculate phonons and when you
+
+ align:start position:0%
+you can calculate phonons and when you
+ 
+
+ align:start position:0%
+you can calculate phonons and when you
+calculate phonons in a
+
+ align:start position:0%
+calculate phonons in a
+ 
+
+ align:start position:0%
+calculate phonons in a
+crystal that's different than in a
+
+ align:start position:0%
+crystal that's different than in a
+ 
+
+ align:start position:0%
+crystal that's different than in a
+molecule okay um when you calculate
+
+ align:start position:0%
+molecule okay um when you calculate
+ 
+
+ align:start position:0%
+molecule okay um when you calculate
+phonons in a crystal you're getting you
+
+ align:start position:0%
+phonons in a crystal you're getting you
+ 
+
+ align:start position:0%
+phonons in a crystal you're getting you
+know the waves the sound waves you're
+
+ align:start position:0%
+know the waves the sound waves you're
+ 
+
+ align:start position:0%
+know the waves the sound waves you're
+going to get the O the acoustic waves in
+
+ align:start position:0%
+going to get the O the acoustic waves in
+ 
+
+ align:start position:0%
+going to get the O the acoustic waves in
+the material right um so you know in in
+
+ align:start position:0%
+the material right um so you know in in
+ 
+
+ align:start position:0%
+the material right um so you know in in
+let's go just using water in a water
+
+ align:start position:0%
+let's go just using water in a water
+ 
+
+ align:start position:0%
+let's go just using water in a water
+molecule how many phonon modes do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have in a water
+
+ align:start position:0%
+have in a water
+ 
+
+ align:start position:0%
+have in a water
+molecule who can tell
+
+ align:start position:0%
+molecule who can tell
+ 
+
+ align:start position:0%
+molecule who can tell
+me take a guess it's a good guess let's
+
+ align:start position:0%
+me take a guess it's a good guess let's
+ 
+
+ align:start position:0%
+me take a guess it's a good guess let's
+get rid of translational and
+
+ align:start position:0%
+get rid of translational and
+ 
+
+ align:start position:0%
+get rid of translational and
+rotational how many ways can a a water
+
+ align:start position:0%
+rotational how many ways can a a water
+ 
+
+ align:start position:0%
+rotational how many ways can a a water
+molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretch yeah there's actually three
+
+ align:start position:0%
+stretch yeah there's actually three
+ 
+
+ align:start position:0%
+stretch yeah there's actually three
+right because you can have the O's can
+
+ align:start position:0%
+right because you can have the O's can
+ 
+
+ align:start position:0%
+right because you can have the O's can
+stretch and the bond can stretch but
+
+ align:start position:0%
+stretch and the bond can stretch but
+ 
+
+ align:start position:0%
+stretch and the bond can stretch but
+then there's sort of two different ways
+
+ align:start position:0%
+then there's sort of two different ways
+ 
+
+ align:start position:0%
+then there's sort of two different ways
+that it can go
+
+ align:start position:0%
+that it can go
+ 
+
+ align:start position:0%
+that it can go
+right and so
+
+ align:start position:0%
+right and so
+ 
+
+ align:start position:0%
+right and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh those are your phono modes for the
+
+ align:start position:0%
+uh those are your phono modes for the
+ 
+
+ align:start position:0%
+uh those are your phono modes for the
+molecule it's just stretch frequencies
+
+ align:start position:0%
+molecule it's just stretch frequencies
+ 
+
+ align:start position:0%
+molecule it's just stretch frequencies
+right and they can be measured in a
+
+ align:start position:0%
+right and they can be measured in a
+ 
+
+ align:start position:0%
+right and they can be measured in a
+solid you calculate your phono modes by
+
+ align:start position:0%
+solid you calculate your phono modes by
+ 
+
+ align:start position:0%
+solid you calculate your phono modes by
+moving atoms around in the latice right
+
+ align:start position:0%
+moving atoms around in the latice right
+ 
+
+ align:start position:0%
+moving atoms around in the latice right
+and that actually gives you um the
+
+ align:start position:0%
+and that actually gives you um the
+ 
+
+ align:start position:0%
+and that actually gives you um the
+behavior of of the wave of the sound
+
+ align:start position:0%
+behavior of of the wave of the sound
+ 
+
+ align:start position:0%
+behavior of of the wave of the sound
+waves in the material which tells you
+
+ align:start position:0%
+waves in the material which tells you
+ 
+
+ align:start position:0%
+waves in the material which tells you
+something about how sound travels in the
+
+ align:start position:0%
+something about how sound travels in the
+ 
+
+ align:start position:0%
+something about how sound travels in the
+solid you can calculate the sound
+
+ align:start position:0%
+solid you can calculate the sound
+ 
+
+ align:start position:0%
+solid you can calculate the sound
+velocity you can calculate thermal uh
+
+ align:start position:0%
+velocity you can calculate thermal uh
+ 
+
+ align:start position:0%
+velocity you can calculate thermal uh
+transport you can calculate the heat
+
+ align:start position:0%
+transport you can calculate the heat
+ 
+
+ align:start position:0%
+transport you can calculate the heat
+capacity of the material all of this uh
+
+ align:start position:0%
+capacity of the material all of this uh
+ 
+
+ align:start position:0%
+capacity of the material all of this uh
+are things that we do with quantum
+
+ align:start position:0%
+are things that we do with quantum
+ 
+
+ align:start position:0%
+are things that we do with quantum
+mechanics that we're not going to do you
+
+ align:start position:0%
+mechanics that we're not going to do you
+ 
+
+ align:start position:0%
+mechanics that we're not going to do you
+know in any of our problems or anymore
+
+ align:start position:0%
+know in any of our problems or anymore
+ 
+
+ align:start position:0%
+know in any of our problems or anymore
+but I just wanted you to be aware of
+
+ align:start position:0%
+but I just wanted you to be aware of
+ 
+
+ align:start position:0%
+but I just wanted you to be aware of
+some of the things that people do in in
+
+ align:start position:0%
+some of the things that people do in in
+ 
+
+ align:start position:0%
+some of the things that people do in in
+research and and that are you know uh uh
+
+ align:start position:0%
+research and and that are you know uh uh
+ 
+
+ align:start position:0%
+research and and that are you know uh uh
+really a big part of quantum mechanical
+
+ align:start position:0%
+really a big part of quantum mechanical
+ 
+
+ align:start position:0%
+really a big part of quantum mechanical
+simulations
+
+ align:start position:0%
+simulations
+ 
+
+ align:start position:0%
+simulations
+okay now um I so so those are some of
+
+ align:start position:0%
+okay now um I so so those are some of
+ 
+
+ align:start position:0%
+okay now um I so so those are some of
+the properties that was sort of the
+
+ align:start position:0%
+the properties that was sort of the
+ 
+
+ align:start position:0%
+the properties that was sort of the
+point here you can do a calculate a wide
+
+ align:start position:0%
+point here you can do a calculate a wide
+ 
+
+ align:start position:0%
+point here you can do a calculate a wide
+range of properties this has sort of
+
+ align:start position:0%
+range of properties this has sort of
+ 
+
+ align:start position:0%
+range of properties this has sort of
+been our Focus these
+
+ align:start position:0%
+been our Focus these
+ 
+
+ align:start position:0%
+been our Focus these
+two okay and we're going to stay with
+
+ align:start position:0%
+two okay and we're going to stay with
+ 
+
+ align:start position:0%
+two okay and we're going to stay with
+that Focus but there's a a very large
+
+ align:start position:0%
+that Focus but there's a a very large
+ 
+
+ align:start position:0%
+that Focus but there's a a very large
+range of things you can do um now I want
+
+ align:start position:0%
+range of things you can do um now I want
+ 
+
+ align:start position:0%
+range of things you can do um now I want
+to just end I got five minutes okay and
+
+ align:start position:0%
+to just end I got five minutes okay and
+ 
+
+ align:start position:0%
+to just end I got five minutes okay and
+I'm I'm going to start solar we'll start
+
+ align:start position:0%
+I'm I'm going to start solar we'll start
+ 
+
+ align:start position:0%
+I'm I'm going to start solar we'll start
+solar with this on uh Tuesday but for
+
+ align:start position:0%
+solar with this on uh Tuesday but for
+ 
+
+ align:start position:0%
+solar with this on uh Tuesday but for
+five minutes I want to do a simulation
+
+ align:start position:0%
+five minutes I want to do a simulation
+ 
+
+ align:start position:0%
+five minutes I want to do a simulation
+um so um so we'll start solar on two
+
+ align:start position:0%
+um so um so we'll start solar on two
+ 
+
+ align:start position:0%
+um so um so we'll start solar on two
+Tuesday but here we
+
+ align:start position:0%
+Tuesday but here we
+ 
+
+ align:start position:0%
+Tuesday but here we
+are you know which tool it is it's our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+favorite and we'll do another problem
+
+ align:start position:0%
+favorite and we'll do another problem
+ 
+
+ align:start position:0%
+favorite and we'll do another problem
+you know or two in class and I can I can
+
+ align:start position:0%
+you know or two in class and I can I can
+ 
+
+ align:start position:0%
+you know or two in class and I can I can
+do a little review I I sort of did that
+
+ align:start position:0%
+do a little review I I sort of did that
+ 
+
+ align:start position:0%
+do a little review I I sort of did that
+on Tuesday of this week does anybody
+
+ align:start position:0%
+on Tuesday of this week does anybody
+ 
+
+ align:start position:0%
+on Tuesday of this week does anybody
+want to do more review next week or what
+
+ align:start position:0%
+want to do more review next week or what
+ 
+
+ align:start position:0%
+want to do more review next week or what
+do you guys think a little bit yeah okay
+
+ align:start position:0%
+do you guys think a little bit yeah okay
+ 
+
+ align:start position:0%
+do you guys think a little bit yeah okay
+I can do some sort of like what I'll do
+
+ align:start position:0%
+I can do some sort of like what I'll do
+ 
+
+ align:start position:0%
+I can do some sort of like what I'll do
+next Tuesday is we'll do another
+
+ align:start position:0%
+next Tuesday is we'll do another
+ 
+
+ align:start position:0%
+next Tuesday is we'll do another
+homework problem from last
+
+ align:start position:0%
+homework problem from last
+ 
+
+ align:start position:0%
+homework problem from last
+um uh year another quiz problem from
+
+ align:start position:0%
+um uh year another quiz problem from
+ 
+
+ align:start position:0%
+um uh year another quiz problem from
+last year like we did today I'll ask if
+
+ align:start position:0%
+last year like we did today I'll ask if
+ 
+
+ align:start position:0%
+last year like we did today I'll ask if
+you have any questions about this
+
+ align:start position:0%
+you have any questions about this
+ 
+
+ align:start position:0%
+you have any questions about this
+practice uh quiz but I'll I'll also post
+
+ align:start position:0%
+practice uh quiz but I'll I'll also post
+ 
+
+ align:start position:0%
+practice uh quiz but I'll I'll also post
+the solutions and I'll I'll go over sort
+
+ align:start position:0%
+the solutions and I'll I'll go over sort
+ 
+
+ align:start position:0%
+the solutions and I'll I'll go over sort
+of some key things to keep in mind for
+
+ align:start position:0%
+of some key things to keep in mind for
+ 
+
+ align:start position:0%
+of some key things to keep in mind for
+the quiz okay so we'll spend the first
+
+ align:start position:0%
+the quiz okay so we'll spend the first
+ 
+
+ align:start position:0%
+the quiz okay so we'll spend the first
+half of class on that then but let me
+
+ align:start position:0%
+half of class on that then but let me
+ 
+
+ align:start position:0%
+half of class on that then but let me
+just spend the last few minutes here
+
+ align:start position:0%
+just spend the last few minutes here
+ 
+
+ align:start position:0%
+just spend the last few minutes here
+let's do a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulation okay
+
+ align:start position:0%
+simulation okay
+ 
+
+ align:start position:0%
+simulation okay
+it's open Notes open Notes
+
+ align:start position:0%
+it's open Notes open Notes
+ 
+
+ align:start position:0%
+it's open Notes open Notes
+yeah uh I think
+
+ align:start position:0%
+yeah uh I think
+ 
+
+ align:start position:0%
+yeah uh I think
+no cuz that's sort of like open every
+
+ align:start position:0%
+no cuz that's sort of like open every
+ 
+
+ align:start position:0%
+no cuz that's sort of like open every
+that's like everything right is it what
+
+ align:start position:0%
+that's like everything right is it what
+ 
+
+ align:start position:0%
+that's like everything right is it what
+did you guys do in the first part you
+
+ align:start position:0%
+did you guys do in the first part you
+ 
+
+ align:start position:0%
+did you guys do in the first part you
+had the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computers okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean um you know so okay let's put it
+
+ align:start position:0%
+I mean um you know so okay let's put it
+ 
+
+ align:start position:0%
+I mean um you know so okay let's put it
+this way if we do open computers then
+
+ align:start position:0%
+this way if we do open computers then
+ 
+
+ align:start position:0%
+this way if we do open computers then
+I'll make the problems
+
+ align:start position:0%
+I'll make the problems
+ 
+
+ align:start position:0%
+I'll make the problems
+harder okay all right because I think I
+
+ align:start position:0%
+harder okay all right because I think I
+ 
+
+ align:start position:0%
+harder okay all right because I think I
+mean I think because you know if you
+
+ align:start position:0%
+mean I think because you know if you
+ 
+
+ align:start position:0%
+mean I think because you know if you
+have the you know Wikipedia is pretty
+
+ align:start position:0%
+have the you know Wikipedia is pretty
+ 
+
+ align:start position:0%
+have the you know Wikipedia is pretty
+powerful right and and Google and so you
+
+ align:start position:0%
+powerful right and and Google and so you
+ 
+
+ align:start position:0%
+powerful right and and Google and so you
+know if you have that um you can find a
+
+ align:start position:0%
+know if you have that um you can find a
+ 
+
+ align:start position:0%
+know if you have that um you can find a
+lot of uh close answers um with the
+
+ align:start position:0%
+lot of uh close answers um with the
+ 
+
+ align:start position:0%
+lot of uh close answers um with the
+quick search so I I'd have to kind of be
+
+ align:start position:0%
+quick search so I I'd have to kind of be
+ 
+
+ align:start position:0%
+quick search so I I'd have to kind of be
+a little more creative but I you know
+
+ align:start position:0%
+a little more creative but I you know
+ 
+
+ align:start position:0%
+a little more creative but I you know
+you won't need your computers and it's
+
+ align:start position:0%
+you won't need your computers and it's
+ 
+
+ align:start position:0%
+you won't need your computers and it's
+full open Notes right so
+
+ align:start position:0%
+full open Notes right so
+ 
+
+ align:start position:0%
+full open Notes right so
+um okay now
+
+ align:start position:0%
+um okay now
+ 
+
+ align:start position:0%
+um okay now
+um here's what I wanted to do so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's go to our favorite thing here
+
+ align:start position:0%
+okay let's go to our favorite thing here
+ 
+
+ align:start position:0%
+okay let's go to our favorite thing here
+Siesta there it
+
+ align:start position:0%
+Siesta there it
+ 
+
+ align:start position:0%
+Siesta there it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um so I wanted to show you this uh first
+
+ align:start position:0%
+um so I wanted to show you this uh first
+ 
+
+ align:start position:0%
+um so I wanted to show you this uh first
+of all this feature here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is that spin polarized do you see
+
+ align:start position:0%
+which is that spin polarized do you see
+ 
+
+ align:start position:0%
+which is that spin polarized do you see
+yes no okay now when it's yes and I
+
+ align:start position:0%
+yes no okay now when it's yes and I
+ 
+
+ align:start position:0%
+yes no okay now when it's yes and I
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+silicon okay here's the um here's the
+
+ align:start position:0%
+silicon okay here's the um here's the
+ 
+
+ align:start position:0%
+silicon okay here's the um here's the
+calculation of the density of states of
+
+ align:start position:0%
+calculation of the density of states of
+ 
+
+ align:start position:0%
+calculation of the density of states of
+silicon is what I want to show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um what you are going to
+
+ align:start position:0%
+um what you are going to
+ 
+
+ align:start position:0%
+um what you are going to
+find oh I didn't plot the structure okay
+
+ align:start position:0%
+find oh I didn't plot the structure okay
+ 
+
+ align:start position:0%
+find oh I didn't plot the structure okay
+is that okay so this is kind of just
+
+ align:start position:0%
+is that okay so this is kind of just
+ 
+
+ align:start position:0%
+is that okay so this is kind of just
+rounding out our our Siesta uh you know
+
+ align:start position:0%
+rounding out our our Siesta uh you know
+ 
+
+ align:start position:0%
+rounding out our our Siesta uh you know
+understanding of what the tool does
+
+ align:start position:0%
+understanding of what the tool does
+ 
+
+ align:start position:0%
+understanding of what the tool does
+because there were just these few things
+
+ align:start position:0%
+because there were just these few things
+ 
+
+ align:start position:0%
+because there were just these few things
+that we hadn't talked about um this is
+
+ align:start position:0%
+that we hadn't talked about um this is
+ 
+
+ align:start position:0%
+that we hadn't talked about um this is
+the density of states and you now really
+
+ align:start position:0%
+the density of states and you now really
+ 
+
+ align:start position:0%
+the density of states and you now really
+feel your Oneness with this you know
+
+ align:start position:0%
+feel your Oneness with this you know
+ 
+
+ align:start position:0%
+feel your Oneness with this you know
+what these are you look at this and you
+
+ align:start position:0%
+what these are you look at this and you
+ 
+
+ align:start position:0%
+what these are you look at this and you
+you and you get emotional which is okay
+
+ align:start position:0%
+you and you get emotional which is okay
+ 
+
+ align:start position:0%
+you and you get emotional which is okay
+okay but look at this I also have
+
+ align:start position:0%
+okay but look at this I also have
+ 
+
+ align:start position:0%
+okay but look at this I also have
+here because I did um uh let's see if it
+
+ align:start position:0%
+here because I did um uh let's see if it
+ 
+
+ align:start position:0%
+here because I did um uh let's see if it
+does this
+
+ align:start position:0%
+does this
+ 
+
+ align:start position:0%
+does this
+right uh
+
+ align:start position:0%
+right uh
+ 
+
+ align:start position:0%
+right uh
+total and there look at that okay you
+
+ align:start position:0%
+total and there look at that okay you
+ 
+
+ align:start position:0%
+total and there look at that okay you
+see it's automatically doing what's
+
+ align:start position:0%
+see it's automatically doing what's
+ 
+
+ align:start position:0%
+see it's automatically doing what's
+called a projected density of States and
+
+ align:start position:0%
+called a projected density of States and
+ 
+
+ align:start position:0%
+called a projected density of States and
+what a projected density of states is is
+
+ align:start position:0%
+what a projected density of states is is
+ 
+
+ align:start position:0%
+what a projected density of states is is
+it's the density of States but only for
+
+ align:start position:0%
+it's the density of States but only for
+ 
+
+ align:start position:0%
+it's the density of States but only for
+certain part of the
+
+ align:start position:0%
+certain part of the
+ 
+
+ align:start position:0%
+certain part of the
+system which turns out to be really
+
+ align:start position:0%
+system which turns out to be really
+ 
+
+ align:start position:0%
+system which turns out to be really
+interesting like sometimes you just want
+
+ align:start position:0%
+interesting like sometimes you just want
+ 
+
+ align:start position:0%
+interesting like sometimes you just want
+to know the density of states for one
+
+ align:start position:0%
+to know the density of states for one
+ 
+
+ align:start position:0%
+to know the density of states for one
+type of atom where is that atom
+
+ align:start position:0%
+type of atom where is that atom
+ 
+
+ align:start position:0%
+type of atom where is that atom
+contributing to the states okay or in
+
+ align:start position:0%
+contributing to the states okay or in
+ 
+
+ align:start position:0%
+contributing to the states okay or in
+this case because I did spin polarized
+
+ align:start position:0%
+this case because I did spin polarized
+ 
+
+ align:start position:0%
+this case because I did spin polarized
+it's giving me the density of states for
+
+ align:start position:0%
+it's giving me the density of states for
+ 
+
+ align:start position:0%
+it's giving me the density of states for
+spin down and spin up separately and
+
+ align:start position:0%
+spin down and spin up separately and
+ 
+
+ align:start position:0%
+spin down and spin up separately and
+look at this they
+
+ align:start position:0%
+look at this they
+ 
+
+ align:start position:0%
+look at this they
+are um well spin down spin down it you
+
+ align:start position:0%
+are um well spin down spin down it you
+ 
+
+ align:start position:0%
+are um well spin down spin down it you
+can't see it um because there's some
+
+ align:start position:0%
+can't see it um because there's some
+ 
+
+ align:start position:0%
+can't see it um because there's some
+spin up in there they're exactly on top
+
+ align:start position:0%
+spin up in there they're exactly on top
+ 
+
+ align:start position:0%
+spin up in there they're exactly on top
+of each other what does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean there's all the spin up electrons
+
+ align:start position:0%
+mean there's all the spin up electrons
+ 
+
+ align:start position:0%
+mean there's all the spin up electrons
+when they're paired with spin down they
+
+ align:start position:0%
+when they're paired with spin down they
+ 
+
+ align:start position:0%
+when they're paired with spin down they
+all um have the same energy okay they
+
+ align:start position:0%
+all um have the same energy okay they
+ 
+
+ align:start position:0%
+all um have the same energy okay they
+have the exact same position on this and
+
+ align:start position:0%
+have the exact same position on this and
+ 
+
+ align:start position:0%
+have the exact same position on this and
+they lead to this total Doss here they
+
+ align:start position:0%
+they lead to this total Doss here they
+ 
+
+ align:start position:0%
+they lead to this total Doss here they
+just add up but now if and so if I did
+
+ align:start position:0%
+just add up but now if and so if I did
+ 
+
+ align:start position:0%
+just add up but now if and so if I did
+silicon with spin polarized off then um
+
+ align:start position:0%
+silicon with spin polarized off then um
+ 
+
+ align:start position:0%
+silicon with spin polarized off then um
+the answer would be exactly the same so
+
+ align:start position:0%
+the answer would be exactly the same so
+ 
+
+ align:start position:0%
+the answer would be exactly the same so
+there was really no need to do it with
+
+ align:start position:0%
+there was really no need to do it with
+ 
+
+ align:start position:0%
+there was really no need to do it with
+been polarized but it's the default and
+
+ align:start position:0%
+been polarized but it's the default and
+ 
+
+ align:start position:0%
+been polarized but it's the default and
+now if I do
+
+ align:start position:0%
+now if I do
+ 
+
+ align:start position:0%
+now if I do
+iron you see and I press
+
+ align:start position:0%
+iron you see and I press
+ 
+
+ align:start position:0%
+iron you see and I press
+simulate then um what you'll find is
+
+ align:start position:0%
+simulate then um what you'll find is
+ 
+
+ align:start position:0%
+simulate then um what you'll find is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um uh you should see a difference let's
+
+ align:start position:0%
+um uh you should see a difference let's
+ 
+
+ align:start position:0%
+um uh you should see a difference let's
+see if we
+
+ align:start position:0%
+see if we
+ 
+
+ align:start position:0%
+see if we
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+okay here is
+
+ align:start position:0%
+okay here is
+ 
+
+ align:start position:0%
+okay here is
+iron and now you have the total the
+
+ align:start position:0%
+iron and now you have the total the
+ 
+
+ align:start position:0%
+iron and now you have the total the
+total density of States oh what is this
+
+ align:start position:0%
+total density of States oh what is this
+ 
+
+ align:start position:0%
+total density of States oh what is this
+um I forget is this an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insulator how do I
+
+ align:start position:0%
+insulator how do I
+ 
+
+ align:start position:0%
+insulator how do I
+know because I got some Doss
+
+ align:start position:0%
+know because I got some Doss
+ 
+
+ align:start position:0%
+know because I got some Doss
+here right in at the firmy energy
+
+ align:start position:0%
+here right in at the firmy energy
+ 
+
+ align:start position:0%
+here right in at the firmy energy
+and if I do the the oh we got to do it
+
+ align:start position:0%
+and if I do the the oh we got to do it
+ 
+
+ align:start position:0%
+and if I do the the oh we got to do it
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+um Iron okay and now look at this this
+
+ align:start position:0%
+um Iron okay and now look at this this
+ 
+
+ align:start position:0%
+um Iron okay and now look at this this
+is beautiful there is um my spin okay so
+
+ align:start position:0%
+is beautiful there is um my spin okay so
+ 
+
+ align:start position:0%
+is beautiful there is um my spin okay so
+there is this is the total the green
+
+ align:start position:0%
+there is this is the total the green
+ 
+
+ align:start position:0%
+there is this is the total the green
+okay that's the total and look at this
+
+ align:start position:0%
+okay that's the total and look at this
+ 
+
+ align:start position:0%
+okay that's the total and look at this
+the red is the spin down and the blue is
+
+ align:start position:0%
+the red is the spin down and the blue is
+ 
+
+ align:start position:0%
+the red is the spin down and the blue is
+the spin up and look at those
+
+ align:start position:0%
+the spin up and look at those
+ 
+
+ align:start position:0%
+the spin up and look at those
+differences what does it mean
+
+ align:start position:0%
+differences what does it mean
+ 
+
+ align:start position:0%
+differences what does it mean
+I mean you got to integrate it to know
+
+ align:start position:0%
+I mean you got to integrate it to know
+ 
+
+ align:start position:0%
+I mean you got to integrate it to know
+but there's a difference there's a big
+
+ align:start position:0%
+but there's a difference there's a big
+ 
+
+ align:start position:0%
+but there's a difference there's a big
+difference in the spin up and spin down
+
+ align:start position:0%
+difference in the spin up and spin down
+ 
+
+ align:start position:0%
+difference in the spin up and spin down
+electrons and where they sit in energy
+
+ align:start position:0%
+electrons and where they sit in energy
+ 
+
+ align:start position:0%
+electrons and where they sit in energy
+space in the magnetic material there can
+
+ align:start position:0%
+space in the magnetic material there can
+ 
+
+ align:start position:0%
+space in the magnetic material there can
+be that's what makes it a magnet okay
+
+ align:start position:0%
+be that's what makes it a magnet okay
+ 
+
+ align:start position:0%
+be that's what makes it a magnet okay
+and so if you integrate that difference
+
+ align:start position:0%
+and so if you integrate that difference
+ 
+
+ align:start position:0%
+and so if you integrate that difference
+up to here well then you're going to get
+
+ align:start position:0%
+up to here well then you're going to get
+ 
+
+ align:start position:0%
+up to here well then you're going to get
+its magnetization right um if I
+
+ align:start position:0%
+its magnetization right um if I
+ 
+
+ align:start position:0%
+its magnetization right um if I
+simulated iron with spin polarized turn
+
+ align:start position:0%
+simulated iron with spin polarized turn
+ 
+
+ align:start position:0%
+simulated iron with spin polarized turn
+off it would force it would force those
+
+ align:start position:0%
+off it would force it would force those
+ 
+
+ align:start position:0%
+off it would force it would force those
+to be exactly the same and they would
+
+ align:start position:0%
+to be exactly the same and they would
+ 
+
+ align:start position:0%
+to be exactly the same and they would
+lie exact on top of each other just like
+
+ align:start position:0%
+lie exact on top of each other just like
+ 
+
+ align:start position:0%
+lie exact on top of each other just like
+they just did in Silicon okay but that
+
+ align:start position:0%
+they just did in Silicon okay but that
+ 
+
+ align:start position:0%
+they just did in Silicon okay but that
+would be not iron so you got to be aware
+
+ align:start position:0%
+would be not iron so you got to be aware
+ 
+
+ align:start position:0%
+would be not iron so you got to be aware
+of what this spin spin thing is and when
+
+ align:start position:0%
+of what this spin spin thing is and when
+ 
+
+ align:start position:0%
+of what this spin spin thing is and when
+you need it when it's important keeping
+
+ align:start position:0%
+you need it when it's important keeping
+ 
+
+ align:start position:0%
+you need it when it's important keeping
+it on is safe okay but I wanted you to
+
+ align:start position:0%
+it on is safe okay but I wanted you to
+ 
+
+ align:start position:0%
+it on is safe okay but I wanted you to
+know what it means so okay very good
+
+ align:start position:0%
+know what it means so okay very good
+ 
+
+ align:start position:0%
+know what it means so okay very good
+have a good weekend
\ No newline at end of file
diff --git a/cCmWW7Hu43A.txt b/cCmWW7Hu43A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a15257493b3fde4eaa7473976960603af65cc95
--- /dev/null
+++ b/cCmWW7Hu43A.txt
@@ -0,0 +1,635 @@
+align:start position:0%
+ 
+one particular series that shows up in
+
+ align:start position:0%
+one particular series that shows up in
+ 
+
+ align:start position:0%
+one particular series that shows up in
+many applications examples or problems
+
+ align:start position:0%
+many applications examples or problems
+ 
+
+ align:start position:0%
+many applications examples or problems
+is the geometric series the geometric
+
+ align:start position:0%
+is the geometric series the geometric
+ 
+
+ align:start position:0%
+is the geometric series the geometric
+series were given a certain number alpha
+
+ align:start position:0%
+series were given a certain number alpha
+ 
+
+ align:start position:0%
+series were given a certain number alpha
+and we want to sum all the powers of
+
+ align:start position:0%
+and we want to sum all the powers of
+ 
+
+ align:start position:0%
+and we want to sum all the powers of
+alpha starting from the zeroth power
+
+ align:start position:0%
+alpha starting from the zeroth power
+ 
+
+ align:start position:0%
+alpha starting from the zeroth power
+which is equal to 1 the first power and
+
+ align:start position:0%
+which is equal to 1 the first power and
+ 
+
+ align:start position:0%
+which is equal to 1 the first power and
+so on and this gives us an infinite
+
+ align:start position:0%
+so on and this gives us an infinite
+ 
+
+ align:start position:0%
+so on and this gives us an infinite
+series it's the sum of alpha to the I
+
+ align:start position:0%
+series it's the sum of alpha to the I
+ 
+
+ align:start position:0%
+series it's the sum of alpha to the I
+where I ranges from zero to infinity now
+
+ align:start position:0%
+where I ranges from zero to infinity now
+ 
+
+ align:start position:0%
+where I ranges from zero to infinity now
+for this series to converge we need
+
+ align:start position:0%
+for this series to converge we need
+ 
+
+ align:start position:0%
+for this series to converge we need
+subsequent terms the different terms in
+
+ align:start position:0%
+subsequent terms the different terms in
+ 
+
+ align:start position:0%
+subsequent terms the different terms in
+the series to become smaller and smaller
+
+ align:start position:0%
+the series to become smaller and smaller
+ 
+
+ align:start position:0%
+the series to become smaller and smaller
+and for this reason we're going to make
+
+ align:start position:0%
+and for this reason we're going to make
+ 
+
+ align:start position:0%
+and for this reason we're going to make
+the assumption that the number alpha is
+
+ align:start position:0%
+the assumption that the number alpha is
+ 
+
+ align:start position:0%
+the assumption that the number alpha is
+less than 1 in magnitude which implies
+
+ align:start position:0%
+less than 1 in magnitude which implies
+ 
+
+ align:start position:0%
+less than 1 in magnitude which implies
+that consecutive terms go to 0 let us
+
+ align:start position:0%
+that consecutive terms go to 0 let us
+ 
+
+ align:start position:0%
+that consecutive terms go to 0 let us
+introduce some notation let us denote
+
+ align:start position:0%
+introduce some notation let us denote
+ 
+
+ align:start position:0%
+introduce some notation let us denote
+the infinite sum by s and we're going to
+
+ align:start position:0%
+the infinite sum by s and we're going to
+ 
+
+ align:start position:0%
+the infinite sum by s and we're going to
+use that notation shortly one way of
+
+ align:start position:0%
+use that notation shortly one way of
+ 
+
+ align:start position:0%
+use that notation shortly one way of
+evaluating this series is to start from
+
+ align:start position:0%
+evaluating this series is to start from
+ 
+
+ align:start position:0%
+evaluating this series is to start from
+an algebraic identity namely the
+
+ align:start position:0%
+an algebraic identity namely the
+ 
+
+ align:start position:0%
+an algebraic identity namely the
+following let us take 1 minus alpha and
+
+ align:start position:0%
+following let us take 1 minus alpha and
+ 
+
+ align:start position:0%
+following let us take 1 minus alpha and
+multiply it by the terms in the series
+
+ align:start position:0%
+multiply it by the terms in the series
+ 
+
+ align:start position:0%
+multiply it by the terms in the series
+but going only up to the term alpha to
+
+ align:start position:0%
+but going only up to the term alpha to
+ 
+
+ align:start position:0%
+but going only up to the term alpha to
+the N so it's a finite series we do this
+
+ align:start position:0%
+the N so it's a finite series we do this
+ 
+
+ align:start position:0%
+the N so it's a finite series we do this
+multiplication we get a bunch of terms
+
+ align:start position:0%
+multiplication we get a bunch of terms
+ 
+
+ align:start position:0%
+multiplication we get a bunch of terms
+we do the cancellations and what is left
+
+ align:start position:0%
+we do the cancellations and what is left
+ 
+
+ align:start position:0%
+we do the cancellations and what is left
+at the end is 1 minus alpha to the power
+
+ align:start position:0%
+at the end is 1 minus alpha to the power
+ 
+
+ align:start position:0%
+at the end is 1 minus alpha to the power
+n plus 1 what we do next is we take the
+
+ align:start position:0%
+n plus 1 what we do next is we take the
+ 
+
+ align:start position:0%
+n plus 1 what we do next is we take the
+limit as n goes to infinity on the left
+
+ align:start position:0%
+limit as n goes to infinity on the left
+ 
+
+ align:start position:0%
+limit as n goes to infinity on the left
+hand side we have the term 1 minus alpha
+
+ align:start position:0%
+hand side we have the term 1 minus alpha
+ 
+
+ align:start position:0%
+hand side we have the term 1 minus alpha
+and then the limit of this finite series
+
+ align:start position:0%
+and then the limit of this finite series
+ 
+
+ align:start position:0%
+and then the limit of this finite series
+is by definition the infinite series
+
+ align:start position:0%
+is by definition the infinite series
+ 
+
+ align:start position:0%
+is by definition the infinite series
+which we are denoting by s on the right
+
+ align:start position:0%
+which we are denoting by s on the right
+ 
+
+ align:start position:0%
+which we are denoting by s on the right
+hand side we have the term 1 how about
+
+ align:start position:0%
+hand side we have the term 1 how about
+ 
+
+ align:start position:0%
+hand side we have the term 1 how about
+this term since alpha is less than 1 in
+
+ align:start position:0%
+this term since alpha is less than 1 in
+ 
+
+ align:start position:0%
+this term since alpha is less than 1 in
+magnitude this converges to 0 as alpha
+
+ align:start position:0%
+magnitude this converges to 0 as alpha
+ 
+
+ align:start position:0%
+magnitude this converges to 0 as alpha
+goes to infinity so that term disappears
+
+ align:start position:0%
+goes to infinity so that term disappears
+ 
+
+ align:start position:0%
+goes to infinity so that term disappears
+we can now solve this relation and we
+
+ align:start position:0%
+we can now solve this relation and we
+ 
+
+ align:start position:0%
+we can now solve this relation and we
+obtain that s is equal to 1 over 1 minus
+
+ align:start position:0%
+obtain that s is equal to 1 over 1 minus
+ 
+
+ align:start position:0%
+obtain that s is equal to 1 over 1 minus
+alpha and this is the formula for the
+
+ align:start position:0%
+alpha and this is the formula for the
+ 
+
+ align:start position:0%
+alpha and this is the formula for the
+infinite geometric series there's
+
+ align:start position:0%
+infinite geometric series there's
+ 
+
+ align:start position:0%
+infinite geometric series there's
+another way of deriving the same result
+
+ align:start position:0%
+another way of deriving the same result
+ 
+
+ align:start position:0%
+another way of deriving the same result
+which is interesting so let us go
+
+ align:start position:0%
+which is interesting so let us go
+ 
+
+ align:start position:0%
+which is interesting so let us go
+through it as well
+
+ align:start position:0%
+through it as well
+ 
+
+ align:start position:0%
+through it as well
+the infinite geometric series has one
+
+ align:start position:0%
+the infinite geometric series has one
+ 
+
+ align:start position:0%
+the infinite geometric series has one
+first term and then the remaining terms
+
+ align:start position:0%
+first term and then the remaining terms
+ 
+
+ align:start position:0%
+first term and then the remaining terms
+which is a sum for I going from 1 to
+
+ align:start position:0%
+which is a sum for I going from 1 to
+ 
+
+ align:start position:0%
+which is a sum for I going from 1 to
+infinity of alpha to the I now we can
+
+ align:start position:0%
+infinity of alpha to the I now we can
+ 
+
+ align:start position:0%
+infinity of alpha to the I now we can
+take a factor of alpha out of this
+
+ align:start position:0%
+take a factor of alpha out of this
+ 
+
+ align:start position:0%
+take a factor of alpha out of this
+infinite sum and write it as 1 plus
+
+ align:start position:0%
+infinite sum and write it as 1 plus
+ 
+
+ align:start position:0%
+infinite sum and write it as 1 plus
+alpha the sum of alpha to the I but
+
+ align:start position:0%
+alpha the sum of alpha to the I but
+ 
+
+ align:start position:0%
+alpha the sum of alpha to the I but
+because we took out one factor of alpha
+
+ align:start position:0%
+because we took out one factor of alpha
+ 
+
+ align:start position:0%
+because we took out one factor of alpha
+here we're going to have smaller powers
+
+ align:start position:0%
+here we're going to have smaller powers
+ 
+
+ align:start position:0%
+here we're going to have smaller powers
+so now the sum starts from 0 and goes up
+
+ align:start position:0%
+so now the sum starts from 0 and goes up
+ 
+
+ align:start position:0%
+so now the sum starts from 0 and goes up
+to infinity now this is just 1 plus
+
+ align:start position:0%
+to infinity now this is just 1 plus
+ 
+
+ align:start position:0%
+to infinity now this is just 1 plus
+alpha times s because here we have the
+
+ align:start position:0%
+alpha times s because here we have the
+ 
+
+ align:start position:0%
+alpha times s because here we have the
+infinite geometric series therefore if
+
+ align:start position:0%
+infinite geometric series therefore if
+ 
+
+ align:start position:0%
+infinite geometric series therefore if
+we subtract alpha s from both sides of
+
+ align:start position:0%
+we subtract alpha s from both sides of
+ 
+
+ align:start position:0%
+we subtract alpha s from both sides of
+this equality we get s times 1 minus
+
+ align:start position:0%
+this equality we get s times 1 minus
+ 
+
+ align:start position:0%
+this equality we get s times 1 minus
+alpha equal to 1 and now by moving one
+
+ align:start position:0%
+alpha equal to 1 and now by moving one
+ 
+
+ align:start position:0%
+alpha equal to 1 and now by moving one
+minus alpha to the denominator we get
+
+ align:start position:0%
+minus alpha to the denominator we get
+ 
+
+ align:start position:0%
+minus alpha to the denominator we get
+again the same expression so this is an
+
+ align:start position:0%
+again the same expression so this is an
+ 
+
+ align:start position:0%
+again the same expression so this is an
+alternative way of deriving the same
+
+ align:start position:0%
+alternative way of deriving the same
+ 
+
+ align:start position:0%
+alternative way of deriving the same
+result however there's one word of
+
+ align:start position:0%
+result however there's one word of
+ 
+
+ align:start position:0%
+result however there's one word of
+caution in this step we subtracted alpha
+
+ align:start position:0%
+caution in this step we subtracted alpha
+ 
+
+ align:start position:0%
+caution in this step we subtracted alpha
+s from both sides of the equation and in
+
+ align:start position:0%
+s from both sides of the equation and in
+ 
+
+ align:start position:0%
+s from both sides of the equation and in
+order to do that this is only possible
+
+ align:start position:0%
+order to do that this is only possible
+ 
+
+ align:start position:0%
+order to do that this is only possible
+if we take for granted that s is a
+
+ align:start position:0%
+if we take for granted that s is a
+ 
+
+ align:start position:0%
+if we take for granted that s is a
+finite number so this is taken for
+
+ align:start position:0%
+finite number so this is taken for
+ 
+
+ align:start position:0%
+finite number so this is taken for
+granted in order to carry out this
+
+ align:start position:0%
+granted in order to carry out this
+ 
+
+ align:start position:0%
+granted in order to carry out this
+derivation this is to be contrasted with
+
+ align:start position:0%
+derivation this is to be contrasted with
+ 
+
+ align:start position:0%
+derivation this is to be contrasted with
+the first derivation in which we didn't
+
+ align:start position:0%
+the first derivation in which we didn't
+ 
+
+ align:start position:0%
+the first derivation in which we didn't
+have to make any such assumption so
+
+ align:start position:0%
+have to make any such assumption so
+ 
+
+ align:start position:0%
+have to make any such assumption so
+strictly speaking for this derivation
+
+ align:start position:0%
+strictly speaking for this derivation
+ 
+
+ align:start position:0%
+strictly speaking for this derivation
+here to be correct we need to have some
+
+ align:start position:0%
+here to be correct we need to have some
+ 
+
+ align:start position:0%
+here to be correct we need to have some
+independent way of verifying that s is
+
+ align:start position:0%
+independent way of verifying that s is
+ 
+
+ align:start position:0%
+independent way of verifying that s is
+less than infinity but other than that
+
+ align:start position:0%
+less than infinity but other than that
+ 
+
+ align:start position:0%
+less than infinity but other than that
+it's an interesting algebraic trick
\ No newline at end of file
diff --git a/cN1mjMQyPBw.txt b/cN1mjMQyPBw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a0038131994fec6c4300ba25f8763777b1f51b2
--- /dev/null
+++ b/cN1mjMQyPBw.txt
@@ -0,0 +1,53 @@
+The biggest journey is made of
+individual steps
+
+the first one is a big one
+
+so is each step taking you further.
+
+Fifteen years ago OpenCourseWare took
+its first step
+
+revolutionary idea from MIT faculty to
+openly shared their teaching materials
+
+from the MIT classrooms with the world
+
+syllabi, notes, homework, assignments,
+videos, and more
+
+every year OpenCourseWare keeps growing
+
+adding hundreds of new learning
+resources to use at any time
+
+for free
+
+every year millions of people use
+OpenCourseWare to enhance their
+
+knowledge improve their lives and help
+their communities
+
+every year thousands of people tell us
+how OpenCourseWare
+
+has changed their lives for the better
+
+the most important step is the one you
+take today
+
+help us continue this free and open
+journey
+
+today help us celebrate 15 years of open sharing
+
+become one of 2001 supporters for this
+crowd funding campaign your donation
+
+will go farther because MathWorks will
+match donations up to $100,000
+
+we've come a long way and we're still moving step by step by step
+
+thank you
\ No newline at end of file
diff --git a/d5chZ4A54DI.txt b/d5chZ4A54DI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4fc5cb1a0c448d4c34b70520d30113c3ab2eece8
--- /dev/null
+++ b/d5chZ4A54DI.txt
@@ -0,0 +1,1051 @@
+align:start position:0%
+ 
+one of the reasons that high road
+
+ align:start position:0%
+one of the reasons that high road
+ 
+
+ align:start position:0%
+one of the reasons that high road
+companies like Saturn and others often
+
+ align:start position:0%
+companies like Saturn and others often
+ 
+
+ align:start position:0%
+companies like Saturn and others often
+don't get carried on is that once the
+
+ align:start position:0%
+don't get carried on is that once the
+ 
+
+ align:start position:0%
+don't get carried on is that once the
+founders leave the next generation of
+
+ align:start position:0%
+founders leave the next generation of
+ 
+
+ align:start position:0%
+founders leave the next generation of
+leaders don't carry on the same
+
+ align:start position:0%
+leaders don't carry on the same
+ 
+
+ align:start position:0%
+leaders don't carry on the same
+practices and so the culture goes back
+
+ align:start position:0%
+practices and so the culture goes back
+ 
+
+ align:start position:0%
+practices and so the culture goes back
+to more traditional organizations but
+
+ align:start position:0%
+to more traditional organizations but
+ 
+
+ align:start position:0%
+to more traditional organizations but
+there are ways to address this issue by
+
+ align:start position:0%
+there are ways to address this issue by
+ 
+
+ align:start position:0%
+there are ways to address this issue by
+building commitments to multiple
+
+ align:start position:0%
+building commitments to multiple
+ 
+
+ align:start position:0%
+building commitments to multiple
+stakeholders right into the bylaws of
+
+ align:start position:0%
+stakeholders right into the bylaws of
+ 
+
+ align:start position:0%
+stakeholders right into the bylaws of
+the corporation let's look at some
+
+ align:start position:0%
+the corporation let's look at some
+ 
+
+ align:start position:0%
+the corporation let's look at some
+examples we'll consider three different
+
+ align:start position:0%
+examples we'll consider three different
+ 
+
+ align:start position:0%
+examples we'll consider three different
+models first let's talk about what we
+
+ align:start position:0%
+models first let's talk about what we
+ 
+
+ align:start position:0%
+models first let's talk about what we
+call Benefit
+
+ align:start position:0%
+call Benefit
+ 
+
+ align:start position:0%
+call Benefit
+corporations benefit corporations build
+
+ align:start position:0%
+corporations benefit corporations build
+ 
+
+ align:start position:0%
+corporations benefit corporations build
+right into their charter three different
+
+ align:start position:0%
+right into their charter three different
+ 
+
+ align:start position:0%
+right into their charter three different
+objectives first they say they are going
+
+ align:start position:0%
+objectives first they say they are going
+ 
+
+ align:start position:0%
+objectives first they say they are going
+to commit to producing results that are
+
+ align:start position:0%
+to commit to producing results that are
+ 
+
+ align:start position:0%
+to commit to producing results that are
+good for their shareholders for their
+
+ align:start position:0%
+good for their shareholders for their
+ 
+
+ align:start position:0%
+good for their shareholders for their
+employees and for the economy secondly
+
+ align:start position:0%
+employees and for the economy secondly
+ 
+
+ align:start position:0%
+employees and for the economy secondly
+they are going to consider financial and
+
+ align:start position:0%
+they are going to consider financial and
+ 
+
+ align:start position:0%
+they are going to consider financial and
+non-financial considerations when making
+
+ align:start position:0%
+non-financial considerations when making
+ 
+
+ align:start position:0%
+non-financial considerations when making
+key decisions that allow them to keep
+
+ align:start position:0%
+key decisions that allow them to keep
+ 
+
+ align:start position:0%
+key decisions that allow them to keep
+the the benefits flowing to all of these
+
+ align:start position:0%
+the the benefits flowing to all of these
+ 
+
+ align:start position:0%
+the the benefits flowing to all of these
+stakeholders third they agree to be
+
+ align:start position:0%
+stakeholders third they agree to be
+ 
+
+ align:start position:0%
+stakeholders third they agree to be
+transparent they provide annual reports
+
+ align:start position:0%
+transparent they provide annual reports
+ 
+
+ align:start position:0%
+transparent they provide annual reports
+on their performance and their progress
+
+ align:start position:0%
+on their performance and their progress
+ 
+
+ align:start position:0%
+on their performance and their progress
+in addressing the interests of these
+
+ align:start position:0%
+in addressing the interests of these
+ 
+
+ align:start position:0%
+in addressing the interests of these
+multiple organizations one of the best
+
+ align:start position:0%
+multiple organizations one of the best
+ 
+
+ align:start position:0%
+multiple organizations one of the best
+known companies uh that is a benefit
+
+ align:start position:0%
+known companies uh that is a benefit
+ 
+
+ align:start position:0%
+known companies uh that is a benefit
+Corporation is Patagonia Patagonia is
+
+ align:start position:0%
+Corporation is Patagonia Patagonia is
+ 
+
+ align:start position:0%
+Corporation is Patagonia Patagonia is
+this very famous clothing maker and its
+
+ align:start position:0%
+this very famous clothing maker and its
+ 
+
+ align:start position:0%
+this very famous clothing maker and its
+CEO and founder Ivon shinard says
+
+ align:start position:0%
+CEO and founder Ivon shinard says
+ 
+
+ align:start position:0%
+CEO and founder Ivon shinard says
+Patagonia is trying to build a company
+
+ align:start position:0%
+Patagonia is trying to build a company
+ 
+
+ align:start position:0%
+Patagonia is trying to build a company
+that could last a 100 years benefit
+
+ align:start position:0%
+that could last a 100 years benefit
+ 
+
+ align:start position:0%
+that could last a 100 years benefit
+Corporation legislation creates the
+
+ align:start position:0%
+Corporation legislation creates the
+ 
+
+ align:start position:0%
+Corporation legislation creates the
+legal framework to enable mission-driven
+
+ align:start position:0%
+legal framework to enable mission-driven
+ 
+
+ align:start position:0%
+legal framework to enable mission-driven
+companies like Patagonia to stay
+
+ align:start position:0%
+companies like Patagonia to stay
+ 
+
+ align:start position:0%
+companies like Patagonia to stay
+mission-driven through succession
+
+ align:start position:0%
+mission-driven through succession
+ 
+
+ align:start position:0%
+mission-driven through succession
+through raising Capital through changes
+
+ align:start position:0%
+through raising Capital through changes
+ 
+
+ align:start position:0%
+through raising Capital through changes
+and ownership in doing so it
+
+ align:start position:0%
+and ownership in doing so it
+ 
+
+ align:start position:0%
+and ownership in doing so it
+institutionalizes the value the cultures
+
+ align:start position:0%
+institutionalizes the value the cultures
+ 
+
+ align:start position:0%
+institutionalizes the value the cultures
+the processes in the standards that are
+
+ align:start position:0%
+the processes in the standards that are
+ 
+
+ align:start position:0%
+the processes in the standards that are
+put in place by these Founders so by
+
+ align:start position:0%
+put in place by these Founders so by
+ 
+
+ align:start position:0%
+put in place by these Founders so by
+doing this we get some continuity in
+
+ align:start position:0%
+doing this we get some continuity in
+ 
+
+ align:start position:0%
+doing this we get some continuity in
+fact 22 States now allow companies to
+
+ align:start position:0%
+fact 22 States now allow companies to
+ 
+
+ align:start position:0%
+fact 22 States now allow companies to
+incorporate as benefit corporations
+
+ align:start position:0%
+incorporate as benefit corporations
+ 
+
+ align:start position:0%
+incorporate as benefit corporations
+within their boundaries and we have at
+
+ align:start position:0%
+within their boundaries and we have at
+ 
+
+ align:start position:0%
+within their boundaries and we have at
+this point about
+
+ align:start position:0%
+this point about
+ 
+
+ align:start position:0%
+this point about
+786 such companies another option is
+
+ align:start position:0%
+786 such companies another option is
+ 
+
+ align:start position:0%
+786 such companies another option is
+employee ownership you've probably heard
+
+ align:start position:0%
+employee ownership you've probably heard
+ 
+
+ align:start position:0%
+employee ownership you've probably heard
+the term ESOP Employee Stock ownership
+
+ align:start position:0%
+the term ESOP Employee Stock ownership
+ 
+
+ align:start position:0%
+the term ESOP Employee Stock ownership
+programs well employee ownership uh
+
+ align:start position:0%
+programs well employee ownership uh
+ 
+
+ align:start position:0%
+programs well employee ownership uh
+companies build a commitment to being
+
+ align:start position:0%
+companies build a commitment to being
+ 
+
+ align:start position:0%
+companies build a commitment to being
+successful financially both for
+
+ align:start position:0%
+successful financially both for
+ 
+
+ align:start position:0%
+successful financially both for
+traditional investors and for employee
+
+ align:start position:0%
+traditional investors and for employee
+ 
+
+ align:start position:0%
+traditional investors and for employee
+owners right into the structure and
+
+ align:start position:0%
+owners right into the structure and
+ 
+
+ align:start position:0%
+owners right into the structure and
+governance of the firm employees often
+
+ align:start position:0%
+governance of the firm employees often
+ 
+
+ align:start position:0%
+governance of the firm employees often
+have Representatives on the corporate
+
+ align:start position:0%
+have Representatives on the corporate
+ 
+
+ align:start position:0%
+have Representatives on the corporate
+Boards of directors but the key to
+
+ align:start position:0%
+Boards of directors but the key to
+ 
+
+ align:start position:0%
+Boards of directors but the key to
+success of these companies is to make
+
+ align:start position:0%
+success of these companies is to make
+ 
+
+ align:start position:0%
+success of these companies is to make
+employees feel like owners by building a
+
+ align:start position:0%
+employees feel like owners by building a
+ 
+
+ align:start position:0%
+employees feel like owners by building a
+culture of Engagement of ownership of
+
+ align:start position:0%
+culture of Engagement of ownership of
+ 
+
+ align:start position:0%
+culture of Engagement of ownership of
+encouraging employees to make
+
+ align:start position:0%
+encouraging employees to make
+ 
+
+ align:start position:0%
+encouraging employees to make
+suggestions for improving the operations
+
+ align:start position:0%
+suggestions for improving the operations
+ 
+
+ align:start position:0%
+suggestions for improving the operations
+and the performance of the organization
+
+ align:start position:0%
+and the performance of the organization
+ 
+
+ align:start position:0%
+and the performance of the organization
+and therefore aligning the incentives
+
+ align:start position:0%
+and therefore aligning the incentives
+ 
+
+ align:start position:0%
+and therefore aligning the incentives
+through compensation and through the
+
+ align:start position:0%
+through compensation and through the
+ 
+
+ align:start position:0%
+through compensation and through the
+culture of the organization so employee
+
+ align:start position:0%
+culture of the organization so employee
+ 
+
+ align:start position:0%
+culture of the organization so employee
+ownership companies have spread across
+
+ align:start position:0%
+ownership companies have spread across
+ 
+
+ align:start position:0%
+ownership companies have spread across
+their country there are about 10,000 of
+
+ align:start position:0%
+their country there are about 10,000 of
+ 
+
+ align:start position:0%
+their country there are about 10,000 of
+them and you can find them in almost any
+
+ align:start position:0%
+them and you can find them in almost any
+ 
+
+ align:start position:0%
+them and you can find them in almost any
+industry that you can think of the key
+
+ align:start position:0%
+industry that you can think of the key
+ 
+
+ align:start position:0%
+industry that you can think of the key
+to employee ownership though is to make
+
+ align:start position:0%
+to employee ownership though is to make
+ 
+
+ align:start position:0%
+to employee ownership though is to make
+sure employees are involved and to also
+
+ align:start position:0%
+sure employees are involved and to also
+ 
+
+ align:start position:0%
+sure employees are involved and to also
+worry a bit that they don't uh put all
+
+ align:start position:0%
+worry a bit that they don't uh put all
+ 
+
+ align:start position:0%
+worry a bit that they don't uh put all
+of their financial resources for
+
+ align:start position:0%
+of their financial resources for
+ 
+
+ align:start position:0%
+of their financial resources for
+retirement into the same company you
+
+ align:start position:0%
+retirement into the same company you
+ 
+
+ align:start position:0%
+retirement into the same company you
+also want to spread your investment a
+
+ align:start position:0%
+also want to spread your investment a
+ 
+
+ align:start position:0%
+also want to spread your investment a
+bit so that you don't come up short if
+
+ align:start position:0%
+bit so that you don't come up short if
+ 
+
+ align:start position:0%
+bit so that you don't come up short if
+the company uh happens not to be as
+
+ align:start position:0%
+the company uh happens not to be as
+ 
+
+ align:start position:0%
+the company uh happens not to be as
+successful as you would like there are
+
+ align:start position:0%
+successful as you would like there are
+ 
+
+ align:start position:0%
+successful as you would like there are
+other kinds of companies called
+
+ align:start position:0%
+other kinds of companies called
+ 
+
+ align:start position:0%
+other kinds of companies called
+cooperatives a Cooperative is a company
+
+ align:start position:0%
+cooperatives a Cooperative is a company
+ 
+
+ align:start position:0%
+cooperatives a Cooperative is a company
+that has lots of owners that pull their
+
+ align:start position:0%
+that has lots of owners that pull their
+ 
+
+ align:start position:0%
+that has lots of owners that pull their
+resources to get some job they all need
+
+ align:start position:0%
+resources to get some job they all need
+ 
+
+ align:start position:0%
+resources to get some job they all need
+done uh done together so if you happen
+
+ align:start position:0%
+done uh done together so if you happen
+ 
+
+ align:start position:0%
+done uh done together so if you happen
+to grow up on a farm you may have been
+
+ align:start position:0%
+to grow up on a farm you may have been
+ 
+
+ align:start position:0%
+to grow up on a farm you may have been
+part of a milk Cooperative where Farmers
+
+ align:start position:0%
+part of a milk Cooperative where Farmers
+ 
+
+ align:start position:0%
+part of a milk Cooperative where Farmers
+pool their resources and create
+
+ align:start position:0%
+pool their resources and create
+ 
+
+ align:start position:0%
+pool their resources and create
+a dairy to take the milk from their
+
+ align:start position:0%
+a dairy to take the milk from their
+ 
+
+ align:start position:0%
+a dairy to take the milk from their
+dairy cows there are Sawmills in Oregon
+
+ align:start position:0%
+dairy cows there are Sawmills in Oregon
+ 
+
+ align:start position:0%
+dairy cows there are Sawmills in Oregon
+here in Cambridge we have the MIT uh
+
+ align:start position:0%
+here in Cambridge we have the MIT uh
+ 
+
+ align:start position:0%
+here in Cambridge we have the MIT uh
+Co-op and the Harvard Cooperative
+
+ align:start position:0%
+Co-op and the Harvard Cooperative
+ 
+
+ align:start position:0%
+Co-op and the Harvard Cooperative
+Society bookstores that sell books and
+
+ align:start position:0%
+Society bookstores that sell books and
+ 
+
+ align:start position:0%
+Society bookstores that sell books and
+reference material and clothing uh to
+
+ align:start position:0%
+reference material and clothing uh to
+ 
+
+ align:start position:0%
+reference material and clothing uh to
+our students and to our faculty and then
+
+ align:start position:0%
+our students and to our faculty and then
+ 
+
+ align:start position:0%
+our students and to our faculty and then
+there's my favorite Cooperative as my ti
+
+ align:start position:0%
+there's my favorite Cooperative as my ti
+ 
+
+ align:start position:0%
+there's my favorite Cooperative as my ti
+suggests it's the Green Bay Packers
+
+ align:start position:0%
+suggests it's the Green Bay Packers
+ 
+
+ align:start position:0%
+suggests it's the Green Bay Packers
+Green Bay Packers are a community-owned
+
+ align:start position:0%
+Green Bay Packers are a community-owned
+ 
+
+ align:start position:0%
+Green Bay Packers are a community-owned
+football team started in the 1920s and
+
+ align:start position:0%
+football team started in the 1920s and
+ 
+
+ align:start position:0%
+football team started in the 1920s and
+how else could you have a city Green Bay
+
+ align:start position:0%
+how else could you have a city Green Bay
+ 
+
+ align:start position:0%
+how else could you have a city Green Bay
+Wisconsin with only about 100,000
+
+ align:start position:0%
+Wisconsin with only about 100,000
+ 
+
+ align:start position:0%
+Wisconsin with only about 100,000
+residents sustain a very successful
+
+ align:start position:0%
+residents sustain a very successful
+ 
+
+ align:start position:0%
+residents sustain a very successful
+highly competitive and often
+
+ align:start position:0%
+highly competitive and often
+ 
+
+ align:start position:0%
+highly competitive and often
+championship football team for all of
+
+ align:start position:0%
+championship football team for all of
+ 
+
+ align:start position:0%
+championship football team for all of
+these years it's because they are owned
+
+ align:start position:0%
+these years it's because they are owned
+ 
+
+ align:start position:0%
+these years it's because they are owned
+by the community and they can't be sold
+
+ align:start position:0%
+by the community and they can't be sold
+ 
+
+ align:start position:0%
+by the community and they can't be sold
+to some higher bidder who might make a
+
+ align:start position:0%
+to some higher bidder who might make a
+ 
+
+ align:start position:0%
+to some higher bidder who might make a
+profit off of it you also see some
+
+ align:start position:0%
+profit off of it you also see some
+ 
+
+ align:start position:0%
+profit off of it you also see some
+cooperatives in other countries probably
+
+ align:start position:0%
+cooperatives in other countries probably
+ 
+
+ align:start position:0%
+cooperatives in other countries probably
+the most famous one is the mandon
+
+ align:start position:0%
+the most famous one is the mandon
+ 
+
+ align:start position:0%
+the most famous one is the mandon
+set of Industries headquartered in The
+
+ align:start position:0%
+set of Industries headquartered in The
+ 
+
+ align:start position:0%
+set of Industries headquartered in The
+Basque region of Spain with companies
+
+ align:start position:0%
+Basque region of Spain with companies
+ 
+
+ align:start position:0%
+Basque region of Spain with companies
+that range from manufacturing to retail
+
+ align:start position:0%
+that range from manufacturing to retail
+ 
+
+ align:start position:0%
+that range from manufacturing to retail
+to high-tech to financial institutions
+
+ align:start position:0%
+to high-tech to financial institutions
+ 
+
+ align:start position:0%
+to high-tech to financial institutions
+they have uh over 81 different companies
+
+ align:start position:0%
+they have uh over 81 different companies
+ 
+
+ align:start position:0%
+they have uh over 81 different companies
+at the moment so we can build
+
+ align:start position:0%
+at the moment so we can build
+ 
+
+ align:start position:0%
+at the moment so we can build
+organizations in different kinds of ways
+
+ align:start position:0%
+organizations in different kinds of ways
+ 
+
+ align:start position:0%
+organizations in different kinds of ways
+and so the takeaway lesson that I hope
+
+ align:start position:0%
+and so the takeaway lesson that I hope
+ 
+
+ align:start position:0%
+and so the takeaway lesson that I hope
+you will have hear from this
+
+ align:start position:0%
+you will have hear from this
+ 
+
+ align:start position:0%
+you will have hear from this
+conversation is that it's possible if
+
+ align:start position:0%
+conversation is that it's possible if
+ 
+
+ align:start position:0%
+conversation is that it's possible if
+you are imaginative perhaps you can
+
+ align:start position:0%
+you are imaginative perhaps you can
+ 
+
+ align:start position:0%
+you are imaginative perhaps you can
+invent the new forms of organizations
+
+ align:start position:0%
+invent the new forms of organizations
+ 
+
+ align:start position:0%
+invent the new forms of organizations
+for the future that will meet the needs
+
+ align:start position:0%
+for the future that will meet the needs
+ 
+
+ align:start position:0%
+for the future that will meet the needs
+of all of their stakeholders and will be
+
+ align:start position:0%
+of all of their stakeholders and will be
+ 
+
+ align:start position:0%
+of all of their stakeholders and will be
+will be built to last for multiple
+
+ align:start position:0%
+will be built to last for multiple
+ 
+
+ align:start position:0%
+will be built to last for multiple
+generations and in doing so not only
+
+ align:start position:0%
+generations and in doing so not only
+ 
+
+ align:start position:0%
+generations and in doing so not only
+might you build organizations that work
+
+ align:start position:0%
+might you build organizations that work
+ 
+
+ align:start position:0%
+might you build organizations that work
+for investors customers and employees
+
+ align:start position:0%
+for investors customers and employees
+ 
+
+ align:start position:0%
+for investors customers and employees
+but maybe ones that help to sustain our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planet e
\ No newline at end of file
diff --git a/d_Mg_JnnevU.txt b/d_Mg_JnnevU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30989cad81ab65ccd0a8488c8aa8f9db8525454a
--- /dev/null
+++ b/d_Mg_JnnevU.txt
@@ -0,0 +1,3348 @@
+PROFESSOR: Good moRning.
+
+Again, we're left with
+a little stub of
+
+chapter six to finish.
+
+This was our first chapter on
+binary linear block codes.
+
+Very briefly, last time we
+developed the family of RM,
+
+Reed-Muller codes, parameterized
+by R and M.
+
+These are codes of length two
+to the M, and distance 2 to
+
+the M minus R for all reasonable
+combinations of M
+
+and R, integers.
+
+And the reason I do these first
+is because it gives us a
+
+nice big -- in fact,
+infinite --
+
+family of codes that kind
+of cover the waterfront.
+
+Let us see what we can
+reasonably get in terms of the
+
+parameters n k d in codes.
+
+And, of course, n k t d tell us
+most of what we know, want
+
+to know about the performance
+of moderate complexity codes
+
+in terms of coding gain.
+
+And it's easy to see that among
+these codes, we have
+
+sequences in which the coding
+gain goes -- the nominal
+
+coding gain goes to infinity.
+
+And we also know that there's
+at least one sequence, the
+
+bi-orthogonal sequence, for
+which the effective coding
+
+gain completely closes the
+gap to the Shannon limit.
+
+And in all likelihood, there
+are many such sequences,
+
+though I'm not aware of the
+actual result there.
+
+So it seems like we might be
+almost finished here, except I
+
+asked about what possible fly
+there could be in this
+
+ointment last time.
+
+And one of you alertly reported
+that we still really
+
+hadn't worried about decoding.
+
+And the implicit decoding
+algorithm here is minimum
+
+distance decoding.
+
+Exhaustive minimum distance
+decoding.
+
+We basically have to compute the
+minimum distance to each
+
+of the 2 to the k code words.
+
+And that's going to get a little
+tedious as soon as k
+
+gets up to 16 or 107
+or whatever.
+
+So it was recognized pretty
+early in the development of
+
+coding theory that this was
+the essential problem.
+
+The problem is not to construct
+codes whose
+
+performance under maximum
+likelihood decoding is near
+
+that of the Shannon limit
+-- you can use
+
+random codes for that.
+
+But in constructing these more
+algebraically structured
+
+codes, what we're really trying
+to do is to facilitate
+
+the decoding problem, which
+is the central problem.
+
+We need to find a
+decoding method
+
+that is actually feasible.
+
+And, of course, Shannon didn't
+address that at all.
+
+He just addressed the ultimate
+potential of these codes with
+
+the optimal decoding technique
+and didn't worry about its
+
+complexity.
+
+All right.
+
+So I'd say the fundamental
+problem here is decoding
+
+complexity.
+
+Now, one of the --
+
+an awful lot of the early work
+on coding was about binary
+
+codes, of course.
+
+But it also considered them in
+the context of binary decoding
+
+algorithms.
+
+In other words, what's assumed
+is what you send as a series
+
+of bits and what you receive
+as a series of bits.
+
+That's not the picture we have
+here in this course, where
+
+what we receive is a series
+of real numbers.
+
+Because we're going over a
+continuous additive white
+
+Gaussian noise channel.
+
+Of course, there are channels
+which are inherently digital,
+
+at least by the time the coding
+engineer can get his
+
+hands on them.
+
+What he's presented with
+is a string of bits.
+
+So it makes sense to consider
+codes for bit error
+
+correction.
+
+Classic codes of this type
+are, first of all, the
+
+repetition code.
+
+If I send this --
+
+if I use the 7 1 7 code, the
+repetition code of length 7,
+
+I'm going to be able to correct
+up to three errors.
+
+Three bit errors.
+
+Because four bits are still
+going to be correct.
+
+In a majority vote, we'll
+do the decoding.
+
+Most of you have probably
+seen Hamming codes.
+
+These are codes with minimum
+Hamming distance 3.
+
+That means if you make one
+error, you're still within the
+
+Hamming sphere of radius 1
+around the original code word.
+
+That's disjoined from all the
+other Hamming spheres, and so
+
+in principle you ought to be
+able to do single error
+
+correction with Hamming codes.
+
+And there are very simple
+algorithms for doing that.
+
+OK.
+
+But that may be what
+you have to do.
+
+The final point of chapter six
+is that in the additive white
+
+Gaussian noise context,
+that's not what you
+
+want to do at all.
+
+And I just want to say a few
+words about that because this
+
+is one of the Achille's heels
+of a lot of classical coding
+
+theory, which was addressed
+to the binary
+
+in, binary out situation.
+
+So let's talk about the penalty
+
+for making hard decisions.
+
+That is, by hard decision, we
+mean a binary decision.
+
+0, 1, plus or minus 1.
+
+And I'll do this fairly quickly,
+but in a way that I
+
+hope will stick.
+
+Let me draw our block diagram
+of our coding scheme.
+
+We've got a code.
+
+We've got an encoder,
+which basically
+
+puts out a code word.
+
+An n-tuple in the code.
+
+I'm going to consider
+the individual
+
+elements of this n-tuple.
+
+They're just elements of the
+binary field F2 And we go
+
+through our standard 2-PAM map,
+which maps them to s of
+
+xk, which is going
+to be in plus or
+
+minus alpha in general.
+
+Just plus or minus 1.
+
+Doesn't matter up to scaling.
+
+In order to send them, we're
+going to send this sequence of
+
+real numbers over the white
+Gaussian noise channel.
+
+And as a result, we're
+going to get out s --
+
+let's call it a received
+symbol --
+
+rk, which is the transmitted
+symbol plus some Gaussian
+
+noise symbol, nk.
+
+This is a real number.
+
+And then --
+
+then what we do?
+
+Now we're into the decoder.
+
+This is what we received, so
+it's free to us to choose what
+
+to do next.
+
+I'm going to say observe, first
+of all, that without
+
+loss of generality, we
+can decompose rk
+
+into a sign and magnitude.
+
+So this out here is going
+to be a sign of rk.
+
+And this is going to be
+the magnitude of rk.
+
+And let me just give
+this a name.
+
+Let me call this yk, and let
+me call this beta k.
+
+OK.
+
+So what is this?
+
+This is in plus or minus 1, and
+this is in the positive
+
+reals, so the non-negative
+reals.
+
+OK.
+
+And clearly, if I keep both of
+these, I haven't lost any
+
+information.
+
+This is just a way of
+representing rk in sign and
+
+magnitude form.
+
+Now, this is what's called
+the hard decision.
+
+Actually, let me do
+this differently.
+
+Let me pass this through the
+inverse to a 2-PAM map.
+
+So out of this, I get a yk,
+
+which is in F2 OK.
+
+Either of these --
+
+the real sign or the binary
+hard decision --
+
+could be considered to
+be the hard decision.
+
+Now, what am I doing here?
+
+I'm saying, well, if you force
+me to make a guess on whether
+
+this individual transmission was
+sending a 0 or 1, this is
+
+the most obvious guess.
+
+If I send --
+
+here's minus 1, here's our minus
+alpha, here's plus 1 --
+
+if I sent a plus 1, then my
+maximum likelihood per bit
+
+decision would be to decide
+the plus 1 was sent.
+
+If I get a positive sign in --
+
+what I'm really mapping here is
+rk, and minus 1 if I get a
+
+negative side.
+
+So that's what's called
+a hard decision.
+
+I'm going to decide right here
+what I think it was, what it
+
+most likely was.
+
+And this is the best
+way to do it.
+
+Just take the sign.
+
+This here is a real valued
+weight, often called the
+
+reliability, which is
+helpful to retain.
+
+That's the main point
+of what I'm going
+
+to talk to you about.
+
+If this is 0 --
+
+that means what we received
+was right on this boundary
+
+between the positive and
+negative side --
+
+then the reliability is 0.
+
+In likelihood terms, that means
+it's equally likely that
+
+what was sent was a plus
+1 or a minus 1.
+
+So in some sense, we get
+no information when the
+
+reliability is 0.
+
+Fails to discriminate between
+plus 1 and minus 1.
+
+The larger this is, the further
+we get out here.
+
+Or symmetrically, the further
+we get out here, the more
+
+certain we are that in that
+particular symbol, neither a
+
+plus or a minus was sent.
+
+OK And it actually tuRns out,
+if you work out the Gaussian
+
+numbers, that beta k is the
+log likelihood ratio up to
+
+scale of the more likely
+versus the log of the
+
+likelihood, or the more likely
+versus the less likely symbol.
+
+So it has a minimum of 0.
+
+The bigger it is, the
+more reliable.
+
+So it's natural to call
+it the reliability.
+
+OK.
+
+An awful lot of traditional
+algebraic decoding neglects
+
+this channel down here.
+
+It just says, OK, let's take
+these hard decisions and try
+
+to decode them.
+
+If you've previously had a
+coding class, then that's
+
+probably what they did.
+
+Or they assumed a context in
+which this was never available
+
+in the first place.
+
+And my only point here, my main
+point, is that that's a
+
+very bad thing to do.
+
+How can we evaluate that?
+
+Suppose we just take this top
+channel and don't look at the
+
+reliability.
+
+Then basically we have the
+channel model becomes a binary
+
+symmetric channel.
+
+We have bits in, bits out, and
+we have probably one minus p
+
+that if we send a
+0 we get a 0.
+
+And since it's symmetric,
+the same probability --
+
+if we send a 1, we get a 1 --
+
+and a probability p of
+making an error.
+
+So we get the traditional
+memoryless binary symmetric
+
+channel model.
+
+We can compute the capacity of
+this model and compare it to
+
+the capacity of the additive
+white Gaussian channel --
+
+this model.
+
+And depending on the signal to
+noise ratio, from a capacity
+
+calculation, we find that
+there is of the order
+
+of 2 or 3 dB loss.
+
+Well, as we go on in this
+course, we're going to find
+
+that 1 dB is a very worthwhile
+coding game.
+
+So to throw away 2 or 3 dB just
+by throwing away this
+
+information, is a
+bad thing to do.
+
+I can make this point in a
+different way by simply
+
+looking at what's the optimum
+decision rule.
+
+For say, let me take very simple
+code, just the 2-1-2
+
+repetition code.
+
+That's just 0,0,1,1.
+
+This is the code where you
+either send plus, plus, plus
+
+alpha, plus alpha, or minus
+alpha, minus alpha.
+
+And what's the decision
+region?
+
+It's obviously this
+45 degree line.
+
+And what is this squared
+distance to
+
+any decision region?
+
+It's 2 alpha squared, right?
+
+So basically, the probability
+of making an error is the
+
+probability that the noise
+variable has a magnitude in
+
+this dimension, and in this
+direction, greater than the
+
+square root of 2
+alpha squared.
+
+You've been through all those
+calculation several times now.
+
+All right.
+
+So this is -- if I keep
+reliability info -- in other
+
+words, if I keep the full
+received signal -- if I
+
+discard reliability, then
+basically what can I get out?
+
+Then my y, as I say, is in
+0, 0, 0, 1, 1, 0, 1, 1.
+
+There are only four possible
+things I can see in two
+
+transmissions through
+this channel.
+
+They're all binary two-tuples.
+
+And what does that mean?
+
+That means if my actual r is
+in this quadrant, then I'm
+
+going to make a hard decision
+of 0 and 0 both times.
+
+So I'm going to say I'm
+in this quadrant.
+
+And likewise, I'm basically
+going to decide which of these
+
+four quadrants I'm in, and
+that's all the information the
+
+decoder is going to have.
+
+So here I am at this
+point here.
+
+Now the decoder simply knows,
+via these two bits, which
+
+quadrant you're in.
+
+Now, it has to decide
+which of these two
+
+code words were sent.
+
+What's its maximum likelihood
+decision rule given just this
+
+information?
+
+AUDIENCE: 0, 0, [INAUDIBLE]
+
+0, 0, [INAUDIBLE]
+
+1, 1, 1, 1, 1.
+
+And in the other
+case, any one.
+
+PROFESSOR: OK.
+
+That's correct.
+
+So clearly, if you land
+in this quadrant,
+
+you decide 0, 0.
+
+Now, if you land down
+here, you decide
+
+1, 1 in this quadrant.
+
+And what am I going to
+do here or here?
+
+Actually, here the evidence
+is totally balanced.
+
+I have nothing that tells
+me whether to
+
+go one way or another.
+
+I could make an arbitrary
+decision in the hope of
+
+minimizing my error
+probability.
+
+Flip a coin.
+
+But whichever decision I make,
+what I'm going to find is that
+
+there's a probability of error
+that -- there's a certain
+
+noise, namely the noise that
+takes me from here to this
+
+decision boundary that is
+going to cause an error.
+
+Or if I decide the other way, it
+would be the one that goes
+
+from here to here.
+
+So I'm going to be stuck.
+
+There are going to be certain
+noise variables of length,
+
+now, merely alpha, or square
+distance alpha squared, that
+
+are going to cause me to make a
+decision error, ultimately.
+
+Regardless of how I set up
+this final block here.
+
+Decoder.
+
+Whatever rule I give to this
+decoder, it's only going to
+
+take, worst case, a noise of
+squared magnitude alpha
+
+squared to cause an error.
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE]
+
+PROFESSOR: That's right.
+
+I shouldn't have thrown
+this away.
+
+That's the elementary point
+I'm trying to make here.
+
+All right.
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE]
+
+the distance, d_min is
+different, essentially.
+
+I mean, we can put
+it that way.
+
+PROFESSOR: That's where I'm
+going, is that the effective
+
+minimum squared distance here
+is 2 alpha squared.
+
+And this is what shows up in
+our union-bound estimate in
+
+all of our --
+
+we do this kind of minimum
+distance decoding.
+
+But if I throw away this
+important information, then my
+
+effective minimum
+squared distance
+
+is only alpha squared.
+
+That is the bottom line here.
+
+In dB terms, how much
+of a cost is that?
+
+3 dB, right?
+
+So I've cost myself a factor
+of 2 in noise margin.
+
+So 3 dB loss.
+
+Because of lack of time, I won't
+go through the argument
+
+in the notes, which shows that,
+in fact, exactly the
+
+same thing occurs for any --
+
+whenever the minimum Hamming
+distance is even here in this
+
+code that I started from,
+you lose precisely 3 dB.
+
+It's not quite as clean an
+argument when the minimum
+
+Hamming distance is odd.
+
+Then you lose up to 3 dB, and
+it goes to 3 dB as the
+
+distance increases.
+
+But there's a very, pretty
+elementary geometric argument
+
+that hard decisions, again, cost
+you 3 dB loss, which is
+
+consistent with what
+the capacity
+
+calculation gives you.
+
+All right.
+
+Well, obviously the reason we
+did this is we were trying to
+
+simplify things.
+
+What would be the first step to
+unsimplify things and get
+
+some of this loss back?
+
+Let me suggest that what this
+amounts to is a two-level
+
+quantization of the received
+real number rk.
+
+What's the next number
+higher than 2?
+
+Integer.
+
+AUDIENCE: 3.
+
+PROFESSOR: 3.
+
+All right.
+
+How about a 3 level
+quantization here?
+
+OK.
+
+So what we're talking about is
+a highly quantized magnitude
+
+where instead of just making a
+decision boundary here, which
+
+is effectively what we did for
+2 level quantization, let's
+
+make some null zone here between
+some threshold plus t
+
+and some threshold minus t.
+
+And we'll say, in this region,
+the received symbol is
+
+unreliable.
+
+OK.
+
+That's called an erasure.
+
+So we make a quantized
+magnitude where rk --
+
+doesn't fit so neatly here.
+
+Let me just say this quantized
+magnitude is going to give me
+
+out something which is either
+going to be minus 1,
+
+a 0, or plus 1.
+
+It's going to be three levels,
+this is minus 1, 0, plus 1.
+
+Or I don't want the
+minus 1 there.
+
+The reliability is either a
+fixed reliability, or it's 0.
+
+OK.
+
+So now I've got a channel model
+that looks like this.
+
+If you work it out, it's called
+the binary erasure
+
+channel with errors.
+
+All transitions are possible.
+
+I can send a 0,1.
+
+I can receive, let's call it,
+a 0, a 1, or a question mark
+
+for -- this is called
+an erasure.
+
+And this is 1 minus p minus q,
+and this is p and this is q
+
+symmetrically, for some p and
+q, which you can evaluate.
+
+And let's choose this threshold
+t to optimize things
+
+and get the maximum capacity.
+
+Now if you do the capacity
+calculation, you'll find
+
+there's only 1 to 1.5 dB loss.
+
+Again, depending on the
+signal to noise ratio.
+
+So in effect, you've already
+bought back, just with this
+
+very simple method, half of the
+loss that you inflicted on
+
+yourself by making
+hard decisions.
+
+So making erasures is a good
+first step towards correcting
+
+this problem.
+
+And let's think about it again
+for this simple code.
+
+Suppose I establish these
+thresholds at
+
+plus t and minus t.
+
+Plus t and minus t.
+
+So now when I consider the
+problem that the decoder has,
+
+I have nine possible regions,
+all right, each with three
+
+possible decisions in
+two dimensions.
+
+And so what's my decision
+rule going to be now?
+
+For this 0, 0 decision, I'm
+going to include, of course,
+
+this region.
+
+But now if I land in this
+region, that means one of the
+
+received symbols was erased,
+but the other one gave me a
+
+definite indication.
+
+So the weight of evidence
+still goes up here.
+
+And similarly, like so.
+
+So my decision region for 0 --
+
+definitely for 0, 0
+is this region.
+
+And my decision region
+definitely for 1, 1 is the
+
+symmetric region.
+
+And, of course, I still have
+three regions where I really
+
+can't say anything.
+
+This is two erasures.
+
+This is 0, 1 --
+
+two conflicting pieces
+of evidence.
+
+This is 1, 0 -- two
+
+conflicting pieces of evidence.
+
+So I still have to flip
+a coin out in here.
+
+But how I improve things, that's
+measured by what's the
+
+minimum distance to --
+
+what's the minimum size of
+error it takes to make a
+
+decision error.
+
+And that's going to be either
+this length or this length.
+
+You see that?
+
+Just pretty clear,
+intuitively?
+
+So the game here is we first of
+all choose t so that these
+
+two lengths are the same.
+
+That's done by squeezing t.
+
+You see these go in opposite
+directions as t
+
+is raised or lowered.
+
+So we find the t such that
+these two are the same.
+
+Having equalized t, we find some
+value for the effective
+
+minimum squared distance, which
+is between alpha squared
+
+and 2 alpha squared.
+
+As I remember, this somehow
+gains about 1.5 dB.
+
+The moral is about the same.
+
+You can get about half of your
+loss back by using erasures.
+
+And again, this holds for any
+code which has an even minimum
+
+Hamming distance, if
+you can accept
+
+this method of analysis.
+
+All right.
+
+So a first step, even if you
+want to stay in the binary
+
+world, is to allow yourself
+to use erasures as well.
+
+That will claw back half of the
+loss that you might have
+
+incurred by using
+hard decisions.
+
+And, of course, even better
+would be to use a more highly
+
+quantized reliability and
+somehow have a decoding
+
+algorithm that can use
+soft decisions.
+
+Soft decisions are decisions
+that have reliability metrics
+
+attached to them.
+
+And in the early
+days of coding,
+
+people evaluated capacity.
+
+They evaluated this
+sort of thing.
+
+And it was pretty generally
+agreed that eight level
+
+quantization was going to be
+practically good enough.
+
+16 levels, certainly
+good enough.
+
+Nowadays you typically
+go up to 64 levels.
+
+You might go up to much higher
+numbers if you have little
+
+other things to worry
+about like timing
+
+recovery and so forth.
+
+But if you're purely in a
+synchronized, symbol by symbol
+
+transmission, then three or
+four bits of reliability
+
+information are going
+to be enough.
+
+So from an engineering
+point of view, that's
+
+a good way to go.
+
+Now, of course, you're going to
+need a decoding algorithm
+
+that can use soft decisions.
+
+So as we go along, I'm going to
+talk about error correcting
+
+decoding algorithms that are not
+much, because correcting
+
+errors only is a very bad
+thing to do here.
+
+Errors and erasure.
+
+Correcting decoding algorithms,
+which are fairly
+
+easy in algebraic
+code context.
+
+And then finally soft decision
+decoding algorithms, which is
+
+the kind we really want
+on this channel.
+
+We really want to use
+the soft decisions.
+
+We can't afford these
+huge losses.
+
+We can't even afford 1 to
+1 and a 1/2 dB loss.
+
+OK, so there's more set on
+this in the last part of
+
+chapter six, but that's
+all the time I want to
+
+spend on it in class.
+
+Does anyone have
+any questions?
+
+yes?
+
+AUDIENCE: [INAUDIBLE]
+
+transformation before we do
+the quantization, can we
+
+change the shape of the
+[UNINTELLIGIBLE]
+
+regions such that we can
+further improve the
+
+[INAUDIBLE PHRASE]
+
+improve the decoding?
+
+PROFESSOR: Well, that's
+an interesting idea.
+
+But think about it from
+an information
+
+theoretic point of view.
+
+Can you actually get more
+information by introducing a
+
+one-to-one transformation,
+whether it's linear or
+
+nonlinear, whatever?
+
+AUDIENCE: The point is, the
+original quantization is based
+
+on a straight line,
+[INAUDIBLE PHRASE].
+
+[UNINTELLIGIBLE PHRASE].
+
+PROFESSOR: You want to put a
+curved line on this plane?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK.
+
+That's going to imply decisions
+that are not symbol
+
+by symbol decisions.
+
+That's going to imply that you
+need to save r1 and r 2 in
+
+order even to just decide where
+you're in this and then
+
+go through some kind of
+quantization on the plane.
+
+And once you've got r1 and r2
+and you're trying to draw
+
+crazy boundaries, I suggest it's
+going to be simpler to
+
+just compute the Euclidean
+distance to each of these
+
+points, which results in
+this decision region.
+
+AUDIENCE: [INAUDIBLE PHRASE].
+
+PROFESSOR: OK.
+
+I don't see the rationale for
+it yet, but there's been a
+
+million innovations in this
+business, and you
+
+might have a good idea.
+
+Any other comments?
+
+I really appreciate comments
+that go anywhere.
+
+I like to address them now
+when they're ripe.
+
+OK.
+
+So let's go on to chapter
+seven and eight.
+
+[UNINTELLIGIBLE] here.
+
+Chapters seven and eight
+are closely related.
+
+This is really my bow to
+algebraic coding theory.
+
+I expect that if any of you
+have had a close course in
+
+coding before, that it
+was primarily on
+
+algebraic coding theory.
+
+How many of you have
+had a course in
+
+coding theory before?
+
+One, two, three.
+
+Not so many.
+
+Was it on algebraic
+coding theory?
+
+Yes?
+
+AUDIENCE: I [UNINTELLIGIBLE]
+two, one
+
+engineering and one algebraic.
+
+PROFESSOR: Excuse me?
+
+AUDIENCE: Two -- one for --
+actually, two algebraic and
+
+one out of kind of this stuff.
+
+PROFESSOR: OK.
+
+Well, you're a ringer then.
+
+What was the one
+on this stuff?
+
+AUDIENCE: It was out
+of Wicker's book.
+
+PROFESSOR: Out of?
+
+AUDIENCE: Wicker's book.
+
+PROFESSOR: Wicker's book
+on turbo codes.
+
+AUDIENCE: No, the data
+storage one.
+
+PROFESSOR: Data storage.
+
+OK.
+
+I don't know that book.
+
+But it talks about sophisticated
+soft decision
+
+type coding, and so forth.
+
+What was the course you took?
+
+AUDIENCE: Algebra.
+
+PROFESSOR: Algebraic.
+
+OK.
+
+All right.
+
+Well, let me just make a broad
+brush comment, which may or
+
+may not be supported
+by your previous
+
+exposure to coding theory.
+
+Which is that for many, many
+years, when people said coding
+
+theory, they meant algebraic
+coding theory, coding theory
+
+of block codes that are
+constructed by algebraic
+
+techniques like Reed-Muller
+codes, like Reed-Solomon
+
+codes, BCH codes,
+cyclic codes.
+
+And if you said, I want to
+leaRn some coding theory,
+
+asked your graduate student to
+go buy a textbook for you,
+
+it's probably going to
+be a textbook on
+
+algebraic coding theory.
+
+Meanwhile, there was a bunch
+of us who were off actually
+
+trying to construct codes
+for real channels.
+
+And conceRning with really how
+complex this is to implement,
+
+and what kind of performance
+can we really get.
+
+And we hardly ever used
+algebraic codes.
+
+Initially, we used convolutional
+codes with
+
+various kinds of decoding
+algorithms, threshold
+
+decoding, sequential decoding,
+the Viterbi algorithm.
+
+And these get more and more
+elaborate, and then finally
+
+the big step, well, the big
+step was to capacity
+
+approaching codes.
+
+Which now people are starting to
+call modeRn coding theory.
+
+Long, random-like codes
+that have an
+
+iterative decoding algorithm.
+
+And that's what we'll
+get to towards
+
+the end of this course.
+
+So from an engineers point of
+view, to some extent, of all
+
+this work on n k d and algebraic
+decoding algorithms
+
+and so forth was a massive
+distraction.
+
+It really missed the point.
+
+Sometimes because it assumed
+hard decisions.
+
+Or after assuming hard
+decisions, it assumed bounded
+
+distance decoding algorithms.
+
+But it was all --
+
+from Shannon's perspective, it
+was too deterministic, too
+
+constructed, too structured.
+
+You want more random elements
+in your coding scheme.
+
+However, two things: one, this
+theory is a beautiful theory,
+
+both the mathematical theory
+of finite fields and the
+
+coding theory, particularly of
+Reed-Solomon codes, which are
+
+uniquely the greatest
+accomplishment of algebraic
+
+coding theory, and which have
+proved to be very useful.
+
+And B, Reed-Solomon codes are
+something that as engineers,
+
+ought to be part of your tool
+kit, and you will find very
+
+useful a variety
+of situations.
+
+So the objective of this part of
+the course is, within some
+
+proportion within the overall
+scheme of the course, to give
+
+you exposure to this
+lovely theory.
+
+You can leaRn all about it just
+by reading a book or two.
+
+Probably less than one book.
+
+And to give you some exposure
+to Reed-Solomon codes, which
+
+have been used in practice.
+
+For more than 20 years, the
+deep space standard was a
+
+concatenated code.
+
+That means a sequence of two
+codes, of which the inner code
+
+was a convolutional code
+decoded by the Viterbi
+
+algorithm, which we'll talk
+about after this.
+
+And then the outer code, the
+code that cleans up errors
+
+made by the inner code, was a
+Reed-Solomon code of length
+
+255 over the finite field
+with 256 elements.
+
+And that's the dynamite
+combination that dominated the
+
+power-limited coding world
+for at least 20 years.
+
+So you ought to know,
+as a minimum, about
+
+Reed-Solomon codes.
+
+So that's my objective
+in going through
+
+these next two chapters.
+
+However, because these have
+not basically been on the
+
+winning path to get to the
+Shannon limit, I'm trying to
+
+limit it to three weeks max.
+
+And therefore, that means that
+the presentation is going to
+
+be a lot faster than what
+you're used to.
+
+I'll probably do as much in
+these three weeks as most
+
+people do in a term in
+an entire algebraic
+
+coding theory course.
+
+That's an exaggeration --
+
+people do a lot more -- but I
+try to at least hit all the
+
+main points that you
+need to know.
+
+So I apologize in advance if it
+seems that now we're on a
+
+very fast moving train.
+
+But you ought to know
+this stuff.
+
+You ought not to spend
+too much time on it.
+
+I'm trying to reconcile those
+two points of view.
+
+Any questions or comments?
+
+All right.
+
+Let's go.
+
+Chapter seven.
+
+We go through a series
+of algebraic objects.
+
+First, the integers,
+then groups.
+
+You certainly ought to know --
+you do know about integers.
+
+You ought to know about groups,
+at least a little bit.
+
+Let's see.
+
+What's next?
+
+Then fields, particularly
+finite.
+
+Then polynomials over fields,
+particularly finite.
+
+And then finally, from this we
+actually get to construct
+
+finite fields.
+
+And these are all things that
+you'll encounter again and
+
+again, have encountered.
+
+I think you've probably
+encountered everything except
+
+possibly for groups
+and finite fields.
+
+You certainly encountered
+polynomials over real and
+
+complex fields.
+
+And so in some sense, this is
+a broadening of what you
+
+already know.
+
+So I assume we start with the
+integers for two reasons.
+
+One is you already know about
+the factorization properties
+
+of the integers.
+
+We're going to --
+
+that leads to a little bit of
+number theory, which we're
+
+going to use when we talk about
+groups, finite groups,
+
+cyclic groups.
+
+So this is just to remind
+you, but it's
+
+also to put up a template.
+
+And we're going to find the
+algebraic properties of
+
+polynomials are very,
+very similar to
+
+those of the integers.
+
+This is because they're
+both rings.
+
+They're both in fact principal
+ideal domains.
+
+They're Euclidean domains.
+
+They both have a Euclidean
+division algorithm as their
+
+key mathematical property.
+
+And so pretty much any time you
+want to develop a result
+
+about the polynomials, you can
+start from the comparable
+
+results that you know about the
+integers and just change
+
+the notation.
+
+And you'll have a sketch of
+the proof for polynomials.
+
+So it's important to remind
+ourselves about
+
+the integers first.
+
+Now, when I say the
+factorization properties of
+
+the integers, I'm not talking
+about anything more
+
+complicated than what you
+leaRned in grade school.
+
+I just want to introduce
+a few terms.
+
+We have the notion
+of divisors.
+
+a divides b means that a times
+some quotient equals b.
+
+I could be talking about plus or
+minus, positive or negative
+
+integers here.
+
+Everything divides 0.
+
+OK.
+
+We have the idea of units,
+which are the invertible
+
+integers under multiplication.
+
+And what are those?
+
+Which integers have a
+multiplicative inverse?
+
+[UNINTELLIGIBLE]
+
+any of them?
+
+AUDIENCE: [INAUDIBLE PHRASE].
+
+PROFESSOR: [INAUDIBLE].
+
+All right.
+
+That's a little exercise that
+shows you that, in general,
+
+the invertible elements of any
+set that has an operation like
+
+multiplication form a group.
+
+[INAUDIBLE] group thing, these
+clearly form a group under
+
+multiplication that's
+isomorphic
+
+to the binary group.
+
+Well, in fact, we've already
+been using it --
+
+F2.
+
+OK.
+
+So we have units, and whenever
+we talk about the divisors,
+
+factorization, primes,
+so forth,
+
+the units are a nuisance.
+
+Because we can always multiply
+things by units and it doesn't
+
+affect factorization
+properties.
+
+This is [UNINTELLIGIBLE] a
+little bit more out there.
+
+What I eventually want
+to get to is --
+
+skipping a few things that
+are said in the notes --
+
+is unique factorization.
+
+Maybe before that I should
+define primes:
+
+are positive integers.
+
+The reason we stay positive
+is, again --
+
+of course, we could have a
+negative prime integer, but
+
+let's pick a unique
+representative of two units.
+
+Positive integers --
+
+I should've said in the notes
+greater than 1, we don't
+
+consider 1 to be a prime --
+
+that have no non-trivial
+divisors.
+
+And, of course, every integer
+has trivial divisors.
+
+Namely, plus or minus 1 and
+plus or minus itself.
+
+Let me give this a name.
+
+i.
+
+Not a very good name.
+
+How about n?
+
+So if we have any integer n,
+it's divisible by plus or
+
+minus one, plus or minus n --
+
+that doesn't count.
+
+So a prime is an integer that
+doesn't have any other
+
+divisors than these
+trivial ones.
+
+And then I want to get to unique
+factorization, which
+
+I'll just state, not prove.
+
+Which is that every integer
+is equal to a
+
+unique product of primes.
+
+And we always have to
+add up to units.
+
+We can add as many plus or minus
+1's to the product as we
+
+want, as long as we have
+an even number of them.
+
+And we'll have another
+factorization, so here, we
+
+want to exclude the units.
+
+And then we have unique
+factorization.
+
+OK.
+
+This is all grade school
+stuff, high
+
+school stuff maybe.
+
+Again, when I go through
+polynomials, you'll see there
+
+is a set of concept
+exactly like this.
+
+Now, where we want to get to
+is mod-n arithmetic, which
+
+again, you all know
+about, I assume.
+
+This is based on the fact --
+
+we can think of it as being
+based on Euclidean division
+
+algorithm, which basically
+proves that given any two
+
+integers m and n, we can write m
+as some qn plus r where 0 is
+
+less than or equal to r, less
+than or equal to n minus 1,
+
+and is called the remainder
+of m, modulo n.
+
+And how is this proved?
+
+Let's say these are both
+positive integers.
+
+Say m is a big integer,
+n is a small integer.
+
+We just keep subtracting integer
+multiples of n from m
+
+until we --
+
+you know, the remainder will
+start decreasing until we get
+
+the remainder in this range, and
+it's obvious that we can
+
+always get a remainder
+that's in that range.
+
+And further, that this
+decomposition is unique under
+
+this restriction on r.
+
+All right.
+
+So we write the m is congruent
+or equivalent to r mod n.
+
+That means it differs from r by
+a multiple of n where r is
+
+unique and r is in the set 0, 1,
+up through n minus 1, which
+
+we say are the residue
+classes mod n.
+
+It has to be one of
+those n things.
+
+OK?
+
+No one is having the slightest
+trouble with this, right?
+
+Boring.
+
+You've seen it all before.
+
+I hope.
+
+OK.
+
+So now you ask, suppose m equals
+r mod-n, and some other
+
+w equals s mod-n.
+
+What is m plus w mod-n, and you
+quickly prove that it's
+
+equal to r plus s mod-n.
+
+By transferring, by just
+checking the properties of
+
+ordinary arithmetic, you can use
+this kind of expression: m
+
+must equal something
+times n plus r.
+
+w must equal something
+times n plus s.
+
+So if we add m plus w, we're
+going to get something times n
+
+plus r plus s.
+
+And that is, by definition,
+going to be r plus s mod-n.
+
+So we get a well-defined
+addition rule for these
+
+residues, for the elements of
+this set of n residues Rn, or
+
+remainders.
+
+OK, so addition is
+well-defined.
+
+And similarly, multiplication
+is well-defined.
+
+mw mod-n, again, you can prove
+-- and this is done
+
+in the notes --
+
+that if mw mod-n can be
+found by taking rs and
+
+reducing it, mod-n.
+
+Maybe I should have congruent
+signs here, but I
+
+won't worry about it.
+
+So this is mod-n, addition
+and multiplication.
+
+So what this says is that Rn,
+combined with this mod-n
+
+addition operation, which in the
+notes I write in that way,
+
+and this mod-n multiplication
+operation --
+
+this is a well-defined set of n
+elements with a well-defined
+
+addition operation and
+a well-defined
+
+multiplication operation.
+
+And I don't prove any properties
+about it here, but
+
+I come back to prove that this
+has almost all of the
+
+properties that we
+want of a field.
+
+In fact, if n is a prime, it
+does have the properties that
+
+we want of a field.
+
+So we'll later prove that the
+finite field with p elements
+
+is simply rp with mod-p addition
+and multiplication.
+
+And, of course, for the
+particular case p equals 2, we
+
+already have a lot of experience
+with this.
+
+That's how we get the
+binary field.
+
+We just take the 0 and 1,
+considered as residues mod-2.
+
+And then the field addition and
+multiplication operations
+
+give us something that
+satisfies the
+
+axioms of the field.
+
+We'll find that works for every
+prime, and it doesn't
+
+work for non-primes.
+
+Can anyone quickly see why this
+isn't going to work for
+
+non-primes?
+
+Suppose n equals 6.
+
+Anyone quickly see why this set
+under these two operations
+
+isn't going to be a field?
+
+This, of course, assumes that
+you know what a field is,
+
+which we haven't actually
+said yet.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Excuse me?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: There's no inverse.
+
+In a field, every non-zero
+element has to have an
+
+inverse, just like in the
+real and complex field.
+
+But in the integers mod-6, 3
+times 2 is equal to 6, which
+
+is equal to 0.
+
+So there are two non-zero
+elements that multiplied
+
+together give 0.
+
+And that means that neither 3
+nor 2 can possibly have a
+
+multiplicative inverse.
+
+So that's why you have
+to have a prime.
+
+This doesn't happen, of course,
+if n were a prime.
+
+OK.
+
+So that's just a little warm
+up to remind you what mod-n
+
+arithmetic is like.
+
+And in particular, this is going
+to be the key element of
+
+a lot of proofs --
+
+the Euclidean division
+algorithm --
+
+both for integers and
+for polynomials.
+
+OK.
+
+So that, I hope, was review.
+
+Now we're going to talk
+about groups.
+
+So let's do it.
+
+How many of you feel you
+know what a group is?
+
+Less than half the class.
+
+OK.
+
+Well, we've been talking about
+groups so far here, but let's
+
+take a little bit more of
+an axiomatic approach.
+
+In the notes, I actually give
+two possible sets of axioms
+
+for a group.
+
+Let me start with
+a standard one.
+
+You've heard of something called
+the group property in
+
+this course.
+
+Well, first of all, what am I
+talking about when I'm talking
+
+about a group?
+
+I'm talking about a set, g,
+and I'm also talking about
+
+some operation on that set,
+which I'll use the mod
+
+addition circle-plus as
+the group property.
+
+Even if it's multiplication or
+matrix inversion or -- no, it
+
+couldn't be matrix inversion.
+
+What this means is that if we
+take any two elements of the
+
+group, then a plus b
+is well-defined.
+
+So you can think there's
+a table.
+
+Here are the elements
+of the group.
+
+a, b, c, d, e.
+
+a, b, c, d, e.
+
+And at this point, all we
+know is that we can
+
+fill out the table.
+
+We get something that
+goes in all here.
+
+All right?
+
+So that defines the group.
+
+AUDIENCE: [INAUDIBLE PHRASE].
+
+PROFESSOR: That means if I
+give a and b, then the
+
+quantity a plus b is --
+
+I can tell you what c is.
+
+There's a unique element in
+each of the cells of this
+
+addition table, or
+the group table.
+
+OK.
+
+Group property, also called
+closure, is the obvious one.
+
+What's an elementary condition
+of what all these sums have to
+
+be for this to be a group?
+
+Have to be all in the group.
+
+If I say I have a group that
+consists of 1,2,3,4,5,
+
+1,2,3,4,5 and my group
+operation is ordinary
+
+addition, then I can certainly
+fill out the table.
+
+And I get 2,3,4,5,6 --
+
+whoops.
+
+Yeah, that's the element that's
+not in the group.
+
+So in order to have a
+group, I want a --
+
+I mean, it's a plus b is in
+the group, all a and b.
+
+So the group is closed
+under addition.
+
+This was the property we used to
+define linearity for binary
+
+linear block codes.
+
+The sum of any two n-tuples
+had to be another
+
+n-tuple in the code.
+
+We have the associativity
+operation.
+
+This is a requirement on the
+binary operation, really.
+
+a plus b plus c has got to be
+equal to a plus b plus c.
+
+In other words, you can get
+rid of the parentheses.
+
+And this, an expression like
+that, is meaningful.
+
+It doesn't matter how you group,
+whether you add these
+
+two things first and then that,
+or add these two things
+
+first and then that.
+
+Maybe now is a good time to
+talk about the special
+
+property, which is
+not an axiom.
+
+So let me call it x abelian, or
+the commutative property.
+
+This is true if a plus
+b is equal to b
+
+plus a, all a, b group.
+
+Now this is, of course, true
+for ordinary addition and
+
+ordinary multiplication.
+
+It's not true for matrix
+multiplication.
+
+Say if I have a group of
+matrices, then in general, ab
+
+is not equal to ba.
+
+So for some groups this
+holds, for some
+
+groups it doesn't hold.
+
+In this course, almost without
+exception, every group we're
+
+going to talk about is
+an abelian group.
+
+That means that in adding
+things up, the
+
+order doesn't matter.
+
+So if that were true, then it in
+a plus b plus c, that means
+
+that's the same as c plus
+b plus a, or c plus
+
+a plus b, or whatever.
+
+All the properties that
+you're accustomed to
+
+from ordinary addition.
+
+But this is not one of the group
+axioms, and, of course,
+
+there are non-abelian groups.
+
+The smallest non-abelian group
+has size 6, and is the
+
+permutation group on
+three elements.
+
+So small groups are all --
+
+size 5 or less are
+all abelian.
+
+Because that's the only way
+we can do the group table.
+
+All right.
+
+So that's terminology
+at this point.
+
+It's not part of the axiom.
+
+But that's the reason that I use
+a symbol that looks like a
+
+plus, is I'm pretty much always
+thinking an abelian
+
+group, and I don't want to
+trouble you with thinking
+
+about non-abelian groups.
+
+OK.
+
+Then we have the identity
+property.
+
+There is an identity, which,
+in an abelian group, is
+
+always called --
+
+ordinarily called 0.
+
+In an additive group it's
+always called 0.
+
+So I'll call it 0.
+
+In more abstract treatments,
+it's called 1 or E for --
+
+what does E stand for?
+
+Eigen something.
+
+There's a 0 in g such that
+0 plus a equals --
+
+or a plus 0 --
+
+is always equal to a.
+
+The 0 is the null operator on
+any element of the group.
+
+If you add 0 to anything, you
+get what you started with.
+
+Clearly, we have such a thing
+in ordinary addition.
+
+Suppose I was talking in
+the real numbers under
+
+multiplication, is that
+a group, you guess?
+
+It's actually not.
+
+Suppose I talk about the
+non-zero real numbers under
+
+multiplication.
+
+Is that a group?
+
+Yes, and its identity is 1.
+
+1 as the thing that if you
+multiply it by anything, it
+
+leaves what you started with.
+
+There's the inverse, which we
+don't have in the reals under
+
+multiplication.
+
+For all a and g, there exists
+something called minus a --
+
+or a to the minus 1 in
+multiplicative notation --
+
+in g such that a plus
+minus a equals 0.
+
+That's an additive inverse.
+
+So in the real numbers, the
+inverse of a is minus a.
+
+In the integers, the
+inverse of a is
+
+minus a under addition.
+
+In the non-zero real numbers
+under multiplication, every
+
+non-zero real number does have
+a multiplicative inverse,
+
+which is called 1 over
+a, or a minus 1.
+
+That's why we have
+to exclude 0.
+
+0 does not an inverse.
+
+So a good example to think
+about is r-star, which is
+
+non-zero reals under ordinary
+multiplication, is a group.
+
+Is it an abelian group?
+
+Is ab equal to ba?
+
+Yeah.
+
+So this is an infinite
+abelian group.
+
+All right.
+
+OK.
+
+I want to show that
+the axioms lead to
+
+a permutation property.
+
+Because this is something
+that's going to come
+
+up again and again.
+
+One way of saying this is if I
+have, if a plus b equals c --
+
+suppose I write down that
+symbolic equation --
+
+then I can solve for any
+one of the three
+
+given the other two.
+
+How would I do that?
+
+If I'm given a and b, obviously,
+that tells me c
+
+from the table.
+
+If I'm given a and c, then a
+is equal to c minus b --
+
+I'm sorry -- b is equal
+to c minus a.
+
+I should say here, from this
+inverse, we're going to write
+
+b plus minus a in
+a simpler form.
+
+It's just b minus a.
+
+So the fact that we have an
+inverse sort of defines
+
+another operation, which
+we call subtraction,
+
+which is not abelian.
+
+Not commutative.
+
+a minus b is not equal
+to b minus a.
+
+But it's basically implicit
+in this that we
+
+subtract group elements.
+
+We can cancel group elements.
+
+If you have a plus c equal
+to b plus c, then a
+
+must be equal to b.
+
+Because you can subtract
+c from both sides.
+
+All right.
+
+OK.
+
+What does this mean that this
+gives us a constraint on the
+
+addition table of a group?
+
+Suppose I take a four element
+group, g, and one of the
+
+elements is going to be the zero
+element, and the other
+
+let's just call a, b, c.
+
+0, a, b, c.
+
+And I have a well-defined
+addition table, which
+
+includes, in here, only
+a 0, a, b, c.
+
+From the property of the
+identity, I can fill in some
+
+of these things.
+
+And now what freedom do I have
+to fill in the rest?
+
+How many group tables are
+there of size four?
+
+Well, the main point that I want
+to make with permutation
+
+property is that every row and
+every column has to be a
+
+permutation of the four
+elements 0, a, b, c.
+
+Why is that?
+
+Suppose I had another a
+in this column here.
+
+Then I would have a plus 0 is
+equal to a, and also a plus c
+
+is equal to a.
+
+But that would imply that c
+equals 0, which it isn't.
+
+All right.
+
+So in order to be able to solve
+this equation, this has
+
+to be something different
+from a, and likewise.
+
+Since I have, in this case, a
+finite group, I basically just
+
+have to write the group elements
+down here again in
+
+some order.
+
+It tuRns out that for four
+elements, there are exactly
+
+two ways of doing that,
+generically.
+
+One is sort of the
+cyclic group.
+
+I'm sorry --
+
+a, b, c, 0, a, c, 0, a, b.
+
+That's one way of filling out
+the table such that each row
+
+is a permutation
+of 0, a, b, c.
+
+Each column is a permutation
+of 0, a, b, c.
+
+So that's a legitimate
+group table.
+
+Let me just, for your interest,
+show you that that's
+
+not the only one.
+
+We could also do 0, a,
+b, c, 0, a, b, c.
+
+If I write 0 here, then
+I've got to write
+
+c there and b there.
+
+Got to write c here
+and b there.
+
+And then down here, the only
+choice I have is this.
+
+This is called the cyclic
+group of four elements.
+
+This is called the
+Klein four group.
+
+And this is all there is.
+
+Both of them tuRn out to be
+abelian if you check it out.
+
+And basically, this permutation
+property restricts
+
+these to be the possible groups
+of size four, abelian
+
+or non-abelian, just to
+satisfy the axiom.
+
+I actually prove in the notes
+that if you replace axioms a
+
+and b with the permutation
+property, you get another
+
+equivalent set of axioms
+for a group.
+
+So the permutation of properties
+is very basic.
+
+All you need is --
+
+for a set and a binary operation
+to form a group, all
+
+you need is identity,
+associativity, and the
+
+permutation property for
+the group table,
+
+the addition table.
+
+Simple proof of that
+in the notes.
+
+But this observation
+is going to be
+
+important as we go forward.
+
+It's a fundamental thing
+we're going to use.
+
+So you see a group can't
+just be anything.
+
+It already has very definite
+restrictions on it.
+
+All right.
+
+Anything else I want
+to say right here?
+
+OK, subtraction, cancellation.
+
+OK, I guess we can go into
+the next property,
+
+which is cyclic groups.
+
+And I'm only going to talk about
+finite cyclic groups, or
+
+finite groups in general.
+
+Now, a cyclic group
+is probably the
+
+simplest kind of group.
+
+Let me first put up the
+canonical cyclic group, which
+
+is the integers mod-n, which
+means the set of residues
+
+mod-n and the mod-n addition
+operation.
+
+Which is written just as Zn --
+
+there are various notations
+for it.
+
+But this, of course, we'll
+just write it as Zn.
+
+The integers mod-n.
+
+Does this form a group?
+
+Let's check the axioms.
+
+Certainly, let's take
+the original axioms.
+
+So the Rn is closed under
+addition mod-n.
+
+If we add two elements, we're
+going to get another element.
+
+The mod-n addition operation
+is associative.
+
+In fact, it's abelian.
+
+a plus b plus c is b plus c plus
+a -- it doesn't matter
+
+what order, from the
+same property
+
+for ordinary addition.
+
+Is there an identity in here?
+
+Yes.
+
+The 0 is one of the elements
+here and acts as the identity.
+
+0 plus anything mod-n is equal
+to the same thing mod-n.
+
+And is there an inverse?
+
+OK.
+
+Let's explicitly write out Rn
+as 0, 1 up to n minus 1.
+
+And then I claim that if I take
+any of these i, then n
+
+minus i is its inverse.
+
+n minus i is in the right
+range if not zero.
+
+The inverse of 0 is 0.
+
+The inverse of i between 1 and
+n minus 1 is going to be n
+
+minus i because if I add
+i to n minus i --
+
+is equal to n, take mod-n,
+that's equal to 0.
+
+So every element has the
+additive inverse.
+
+And so the group table has a
+very boring form, which does
+
+satisfy the permutation
+property.
+
+If I take Z5, for instance.
+
+0,1,2,3,4.
+
+0 plus anything looks
+like that.
+
+1 times anything is
+just 1,2,3,4 and 1
+
+plus 4 is 0 mod 5.
+
+2,3,4,0,1, and so forth.
+
+3, 4, 0, 1, 2, 4, 0, 1, 2, 3.
+
+Each row or column is just a
+cyclic shift to the previous
+
+row or column.
+
+Just fill it out.
+
+And does it satisfy the
+permutation property?
+
+Yes, it does.
+
+This one here, for instance, you
+can recognize as a cyclic
+
+group table.
+
+And so, apart from relabeling,
+this is the group table of Z4.
+
+Or we take a, b, c
+equal to 1, 2, 3.
+
+If two groups have the same
+group table up to relabelling,
+
+they're said to be isomorphic.
+
+OK?
+
+That's an important
+concept in math.
+
+And all it means is the two
+groups act the same, except
+
+that we've changed the names
+of the group elements.
+
+OK.
+
+So what I'm going to show
+is that all cyclic --
+
+this group is sort of cyclic
+because, as you see in the
+
+notes, we can think of adding
+1 as just being
+
+cycling around a circle.
+
+In this case, with
+5 points on it.
+
+And adding 2 is going two
+steps around the circle.
+
+And the elements on the
+circle are the group
+
+elements 0, 1, 2, 3, 4.
+
+And then we get to 5.
+
+We identify that with 0.
+
+So we close the loop.
+
+One we identify with 6.
+
+This with 7.
+
+This with 8.
+
+Up to as many as you like.
+
+So that's the intuition
+why these are
+
+called cyclic groups.
+
+The addition operation cycles
+rather than being on a line,
+
+as it would be with the ordinary
+integers, where we go
+
+infinitely in either
+direction.
+
+So the formal definition of a
+cyclic group is that g has a
+
+single generator.
+
+Call it a little g.
+
+And -- am I running over?
+
+Close to.
+
+Is that really right?
+
+I only have five minutes left.
+
+We're not going to go at
+the speed I had hoped.
+
+g is --
+
+what does that mean?
+
+If we know that g contains g,
+and this is never going to be
+
+equal to 0, then we know that
+g contains two elements at
+
+least: 0 and g.
+
+And by the group axioms, g
+contains g, g plus g, g
+
+plus g plus g --
+
+we can keep adding them.
+
+I'm going to call these the
+integer multiples of g.
+
+So this will be 1g, 2g, 3g.
+
+That's what I mean when
+I write an integer
+
+in front of g --
+
+I mean g plus itself, the
+integer number of times.
+
+And all those things, by the
+group properties, have to be
+
+in the group.
+
+All right?
+
+Again, restrict this
+to finite.
+
+It's a finite cyclic group.
+
+Then at some point,
+I have to --
+
+this is all the elements
+of the group.
+
+So at some point, I have
+to come along and
+
+say that ng is 0.
+
+If just by --
+
+when I say generator, the
+set generated by g is
+
+just 1g, 2g, 3g.
+
+And that's got to be all the
+elements of the group, so n
+
+times g has got to be 0.
+
+And that means, without putting
+too fine a point on
+
+it, that if n were 5, for
+instance, the group has to
+
+consist of 0g, 1g, 2g, 3g, 4g,
+and then 5g is equal to 0.
+
+So we call this 0g or 5g.
+
+And furthermore, the addition
+table of the group, we can,
+
+you know --
+
+however, if we add 2 g's to 3
+g's, we're going to 5 g's,
+
+which is 0.
+
+All right?
+
+So 2g plus 3g has got to
+be 5 g's, which is 0g.
+
+So this is what the addition
+table of the
+
+group has to look like.
+
+It's exactly the same, except
+we just make a one-to-one
+
+correspondence like that.
+
+So the conclusion is a
+finite cyclic group
+
+with n elements --
+
+I'll write the size of g by this
+absolute value thing --
+
+is isomorphic to the
+integers mod-n --
+
+this canonical cyclic group
+that we started with --
+
+must be isomorphic to Zn with
+the isomorphism being given by
+
+the one-to-one correspondence.
+
+i_g in the group corresponds
+to simply i in Zn, or 0 is
+
+less than or equal to
+i is less than or
+
+equal to n minus 1.
+
+The addition rule is
+exactly the same.
+
+OK, so this is a pretty
+sweeping conclusion.
+
+It says that really the only
+finite cyclic group up to
+
+relabeling is Zn.
+
+OK, so if you understand Zn,
+you understand all finite
+
+cyclic groups.
+
+Just in a general group, we're
+going to have some element
+
+which basically represents 1,
+called g, and its integer
+
+multiples, which represent
+2, 3, 4, and so forth.
+
+But we can operate with
+a group just as
+
+though it was Zn.
+
+So it's easy to understand
+finite cyclic groups.
+
+They all just look like this.
+
+Question?
+
+Yeah.
+
+AUDIENCE: Is the generator
+unique?
+
+PROFESSOR: No, it's not.
+
+No, it's not.
+
+Next time we'll start
+to talk about
+
+subgroups of Zn, for instance.
+
+In the set of Z5 --
+
+well, let me take this.
+
+All right.
+
+In Z5 --
+
+let me not even do that.
+
+In Z5, 1 is the generator, but
+because 5 is a prime, 2 is a
+
+generator, too.
+
+All right?
+
+Another way of writing.
+
+Let's take a generator
+equals 2 in Z5.
+
+Then g equals 2, 2g equals 4.
+
+3g equals 6, equals 1 mod-5.
+
+4g equals 3.
+
+And 5g, of course, equals
+5, which equals zero.
+
+So 2 is also a generator.
+
+And, in fact, 3 and 4
+are also generators.
+
+There are four generators.
+
+This is getting us right
+into the number theory.
+
+OK.
+
+So no, g does not
+have to be 1.
+
+g is just something that if
+you take all its integer
+
+multiples, you generate
+the group.
+
+OK, I guess we stop there, and
+we'll resume next time.
\ No newline at end of file
diff --git a/dz2vRqxf0HI.txt b/dz2vRqxf0HI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cb39be38a1decb234cdf2d8a48e609af85453e12
--- /dev/null
+++ b/dz2vRqxf0HI.txt
@@ -0,0 +1,315 @@
+align:start position:0%
+ 
+It turns out that much of what accounts
+
+ align:start position:0%
+It turns out that much of what accounts
+ 
+
+ align:start position:0%
+It turns out that much of what accounts
+for success in life is not skill or hard
+
+ align:start position:0%
+for success in life is not skill or hard
+ 
+
+ align:start position:0%
+for success in life is not skill or hard
+work but luck.
+
+ align:start position:0%
+work but luck.
+ 
+
+ align:start position:0%
+work but luck.
+And in that case,
+
+ align:start position:0%
+And in that case,
+ 
+
+ align:start position:0%
+And in that case,
+it's not true that rich people are rich
+
+ align:start position:0%
+it's not true that rich people are rich
+ 
+
+ align:start position:0%
+it's not true that rich people are rich
+because they deserve it or because they
+
+ align:start position:0%
+because they deserve it or because they
+ 
+
+ align:start position:0%
+because they deserve it or because they
+have skills or worked hard or they're
+
+ align:start position:0%
+have skills or worked hard or they're
+ 
+
+ align:start position:0%
+have skills or worked hard or they're
+just lucky. And why do we necessarily
+
+ align:start position:0%
+just lucky. And why do we necessarily
+ 
+
+ align:start position:0%
+just lucky. And why do we necessarily
+want to reward luck? Indeed, can't we
+
+ align:start position:0%
+want to reward luck? Indeed, can't we
+ 
+
+ align:start position:0%
+want to reward luck? Indeed, can't we
+think of redistribution as kind of luck
+
+ align:start position:0%
+think of redistribution as kind of luck
+ 
+
+ align:start position:0%
+think of redistribution as kind of luck
+insurance?
+
+ align:start position:0%
+insurance?
+ 
+
+ align:start position:0%
+insurance?
+Imagine a world where a random event's
+
+ align:start position:0%
+Imagine a world where a random event's
+ 
+
+ align:start position:0%
+Imagine a world where a random event's
+going to happen to you. You get hit by a
+
+ align:start position:0%
+going to happen to you. You get hit by a
+ 
+
+ align:start position:0%
+going to happen to you. You get hit by a
+car. We talked about why we want
+
+ align:start position:0%
+car. We talked about why we want
+ 
+
+ align:start position:0%
+car. We talked about why we want
+insurance, right? Want insurance to make
+
+ align:start position:0%
+insurance, right? Want insurance to make
+ 
+
+ align:start position:0%
+insurance, right? Want insurance to make
+sure if we get hit by the car, don't get
+
+ align:start position:0%
+sure if we get hit by the car, don't get
+ 
+
+ align:start position:0%
+sure if we get hit by the car, don't get
+hit by the car, we're in the same off.
+
+ align:start position:0%
+hit by the car, we're in the same off.
+ 
+
+ align:start position:0%
+hit by the car, we're in the same off.
+Well, same thing. Rolls talked about
+
+ align:start position:0%
+Well, same thing. Rolls talked about
+ 
+
+ align:start position:0%
+Well, same thing. Rolls talked about
+behind the veil of ignorance. Imagine
+
+ align:start position:0%
+behind the veil of ignorance. Imagine
+ 
+
+ align:start position:0%
+behind the veil of ignorance. Imagine
+before you're born, you don't know if
+
+ align:start position:0%
+before you're born, you don't know if
+ 
+
+ align:start position:0%
+before you're born, you don't know if
+you were rich or poor. You would choose
+
+ align:start position:0%
+you were rich or poor. You would choose
+ 
+
+ align:start position:0%
+you were rich or poor. You would choose
+a system which would ensure you against
+
+ align:start position:0%
+a system which would ensure you against
+ 
+
+ align:start position:0%
+a system which would ensure you against
+being poor.
+
+ align:start position:0%
+being poor.
+ 
+
+ align:start position:0%
+being poor.
+And that system which would involve
+
+ align:start position:0%
+And that system which would involve
+ 
+
+ align:start position:0%
+And that system which would involve
+transfers.
+
+ align:start position:0%
+transfers.
+ 
+
+ align:start position:0%
+transfers.
+So if much of success is due to luck,
+
+ align:start position:0%
+So if much of success is due to luck,
+ 
+
+ align:start position:0%
+So if much of success is due to luck,
+we're going to want a system that shoots
+
+ align:start position:0%
+we're going to want a system that shoots
+ 
+
+ align:start position:0%
+we're going to want a system that shoots
+the rich to the poor because the rich
+
+ align:start position:0%
+the rich to the poor because the rich
+ 
+
+ align:start position:0%
+the rich to the poor because the rich
+got lucky, the poor didn't. That's
+
+ align:start position:0%
+got lucky, the poor didn't. That's
+ 
+
+ align:start position:0%
+got lucky, the poor didn't. That's
+uncertainty we want to ensure against.
+
+ align:start position:0%
+uncertainty we want to ensure against.
+ 
+
+ align:start position:0%
+uncertainty we want to ensure against.
+Okay. Fascinating fact. If you if you
+
+ align:start position:0%
+Okay. Fascinating fact. If you if you
+ 
+
+ align:start position:0%
+Okay. Fascinating fact. If you if you
+interview people around the world and
+
+ align:start position:0%
+interview people around the world and
+ 
+
+ align:start position:0%
+interview people around the world and
+ask them
+
+ align:start position:0%
+ask them
+ 
+
+ align:start position:0%
+ask them
+is success mostly due to hard work or to
+
+ align:start position:0%
+is success mostly due to hard work or to
+ 
+
+ align:start position:0%
+is success mostly due to hard work or to
+luck. In the US people say hard work. In
+
+ align:start position:0%
+luck. In the US people say hard work. In
+ 
+
+ align:start position:0%
+luck. In the US people say hard work. In
+Europe people say luck. In Europe they
+
+ align:start position:0%
+Europe people say luck. In Europe they
+ 
+
+ align:start position:0%
+Europe people say luck. In Europe they
+have much higher redistribution than we
+
+ align:start position:0%
+have much higher redistribution than we
+ 
+
+ align:start position:0%
+have much higher redistribution than we
+do in the US.
+
+ align:start position:0%
+do in the US.
+ 
+
+ align:start position:0%
+do in the US.
+because they have a view that much more
+
+ align:start position:0%
+because they have a view that much more
+ 
+
+ align:start position:0%
+because they have a view that much more
+success comes from luck.
\ No newline at end of file
diff --git a/dzGar1Jnf90.txt b/dzGar1Jnf90.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6d27192b03f0799d5dab1fdc9a8c1afc887fc7d
--- /dev/null
+++ b/dzGar1Jnf90.txt
@@ -0,0 +1,10443 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as promised here's uh we're going into
+
+ align:start position:0%
+as promised here's uh we're going into
+ 
+
+ align:start position:0%
+as promised here's uh we're going into
+flux balance analysis
+
+ align:start position:0%
+flux balance analysis
+ 
+
+ align:start position:0%
+flux balance analysis
+the simplifications here are even
+
+ align:start position:0%
+the simplifications here are even
+ 
+
+ align:start position:0%
+the simplifications here are even
+greater than the ones that we
+
+ align:start position:0%
+greater than the ones that we
+ 
+
+ align:start position:0%
+greater than the ones that we
+have been making so far but hopefully
+
+ align:start position:0%
+have been making so far but hopefully
+ 
+
+ align:start position:0%
+have been making so far but hopefully
+you will see some benefit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're here uh
+
+ align:start position:0%
+we're here uh
+ 
+
+ align:start position:0%
+we're here uh
+assuming that time constant metabolic
+
+ align:start position:0%
+assuming that time constant metabolic
+ 
+
+ align:start position:0%
+assuming that time constant metabolic
+reactions are very fast compared to cell
+
+ align:start position:0%
+reactions are very fast compared to cell
+ 
+
+ align:start position:0%
+reactions are very fast compared to cell
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+cell growth you know we've seen the time
+
+ align:start position:0%
+cell growth you know we've seen the time
+ 
+
+ align:start position:0%
+cell growth you know we've seen the time
+constants are in the order of seconds or
+
+ align:start position:0%
+constants are in the order of seconds or
+ 
+
+ align:start position:0%
+constants are in the order of seconds or
+or sometimes less while growth might be
+
+ align:start position:0%
+or sometimes less while growth might be
+ 
+
+ align:start position:0%
+or sometimes less while growth might be
+on the order of hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even though we've seen interesting
+
+ align:start position:0%
+even though we've seen interesting
+ 
+
+ align:start position:0%
+even though we've seen interesting
+dynamics that can occur those phase
+
+ align:start position:0%
+dynamics that can occur those phase
+ 
+
+ align:start position:0%
+dynamics that can occur those phase
+diagrams that we had in the ordinary
+
+ align:start position:0%
+diagrams that we had in the ordinary
+ 
+
+ align:start position:0%
+diagrams that we had in the ordinary
+differential equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are also many
+
+ align:start position:0%
+there are also many
+ 
+
+ align:start position:0%
+there are also many
+it's very typical for a cell to be in
+
+ align:start position:0%
+it's very typical for a cell to be in
+ 
+
+ align:start position:0%
+it's very typical for a cell to be in
+fairly stable conditions you know
+
+ align:start position:0%
+fairly stable conditions you know
+ 
+
+ align:start position:0%
+fairly stable conditions you know
+there'll be a transition time and then
+
+ align:start position:0%
+there'll be a transition time and then
+ 
+
+ align:start position:0%
+there'll be a transition time and then
+they'll be stable again and that will be
+
+ align:start position:0%
+they'll be stable again and that will be
+ 
+
+ align:start position:0%
+they'll be stable again and that will be
+the steady-state assumption so we'll say
+
+ align:start position:0%
+the steady-state assumption so we'll say
+ 
+
+ align:start position:0%
+the steady-state assumption so we'll say
+there's no net accumulation of
+
+ align:start position:0%
+there's no net accumulation of
+ 
+
+ align:start position:0%
+there's no net accumulation of
+metabolites
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so even though there may be fluxes
+
+ align:start position:0%
+so even though there may be fluxes
+ 
+
+ align:start position:0%
+so even though there may be fluxes
+into and out of every metabolite the net
+
+ align:start position:0%
+into and out of every metabolite the net
+ 
+
+ align:start position:0%
+into and out of every metabolite the net
+change is zero and so that means this
+
+ align:start position:0%
+change is zero and so that means this
+ 
+
+ align:start position:0%
+change is zero and so that means this
+this equation we've seen a few times the
+
+ align:start position:0%
+this equation we've seen a few times the
+ 
+
+ align:start position:0%
+this equation we've seen a few times the
+change in x with respect to time
+
+ align:start position:0%
+change in x with respect to time
+ 
+
+ align:start position:0%
+change in x with respect to time
+is zero and that means the
+
+ align:start position:0%
+is zero and that means the
+ 
+
+ align:start position:0%
+is zero and that means the
+stoichiometric matrix times of times the
+
+ align:start position:0%
+stoichiometric matrix times of times the
+ 
+
+ align:start position:0%
+stoichiometric matrix times of times the
+flux rate for that
+
+ align:start position:0%
+flux rate for that
+ 
+
+ align:start position:0%
+flux rate for that
+for all relevant reactions you can think
+
+ align:start position:0%
+for all relevant reactions you can think
+ 
+
+ align:start position:0%
+for all relevant reactions you can think
+of as a matrix representation sum of all
+
+ align:start position:0%
+of as a matrix representation sum of all
+ 
+
+ align:start position:0%
+of as a matrix representation sum of all
+inputs and outputs that particular x
+
+ align:start position:0%
+inputs and outputs that particular x
+ 
+
+ align:start position:0%
+inputs and outputs that particular x
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+minus the transport vector which is kept
+
+ align:start position:0%
+minus the transport vector which is kept
+ 
+
+ align:start position:0%
+minus the transport vector which is kept
+separately
+
+ align:start position:0%
+separately
+ 
+
+ align:start position:0%
+separately
+is all zero
+
+ align:start position:0%
+is all zero
+ 
+
+ align:start position:0%
+is all zero
+so what does that mean that means the
+
+ align:start position:0%
+so what does that mean that means the
+ 
+
+ align:start position:0%
+so what does that mean that means the
+stoichiometric matrix times the internal
+
+ align:start position:0%
+stoichiometric matrix times the internal
+ 
+
+ align:start position:0%
+stoichiometric matrix times the internal
+fluxes is equal to transport across the
+
+ align:start position:0%
+fluxes is equal to transport across the
+ 
+
+ align:start position:0%
+fluxes is equal to transport across the
+membrane
+
+ align:start position:0%
+membrane
+ 
+
+ align:start position:0%
+membrane
+and this is something we'll i'll show
+
+ align:start position:0%
+and this is something we'll i'll show
+ 
+
+ align:start position:0%
+and this is something we'll i'll show
+you we're going to do this
+
+ align:start position:0%
+you we're going to do this
+ 
+
+ align:start position:0%
+you we're going to do this
+in two steps first we're going to solve
+
+ align:start position:0%
+in two steps first we're going to solve
+ 
+
+ align:start position:0%
+in two steps first we're going to solve
+for that as if there was an exact
+
+ align:start position:0%
+for that as if there was an exact
+ 
+
+ align:start position:0%
+for that as if there was an exact
+set of equations just the right number
+
+ align:start position:0%
+set of equations just the right number
+ 
+
+ align:start position:0%
+set of equations just the right number
+of equations just the right number of
+
+ align:start position:0%
+of equations just the right number of
+ 
+
+ align:start position:0%
+of equations just the right number of
+unknowns so you can actually get a
+
+ align:start position:0%
+unknowns so you can actually get a
+ 
+
+ align:start position:0%
+unknowns so you can actually get a
+solve for the unknown fluxes and then
+
+ align:start position:0%
+solve for the unknown fluxes and then
+ 
+
+ align:start position:0%
+solve for the unknown fluxes and then
+we'll work through it where it's
+
+ align:start position:0%
+we'll work through it where it's
+ 
+
+ align:start position:0%
+we'll work through it where it's
+actually under determined but there are
+
+ align:start position:0%
+actually under determined but there are
+ 
+
+ align:start position:0%
+actually under determined but there are
+inequality constraints first let's take
+
+ align:start position:0%
+inequality constraints first let's take
+ 
+
+ align:start position:0%
+inequality constraints first let's take
+the exact case
+
+ align:start position:0%
+the exact case
+ 
+
+ align:start position:0%
+the exact case
+because it so stoichiometry is known
+
+ align:start position:0%
+because it so stoichiometry is known
+ 
+
+ align:start position:0%
+because it so stoichiometry is known
+that's the s these are the zeros and
+
+ align:start position:0%
+that's the s these are the zeros and
+ 
+
+ align:start position:0%
+that's the s these are the zeros and
+ones minus ones twos and so on
+
+ align:start position:0%
+ones minus ones twos and so on
+ 
+
+ align:start position:0%
+ones minus ones twos and so on
+uh the uptake rates
+
+ align:start position:0%
+uh the uptake rates
+ 
+
+ align:start position:0%
+uh the uptake rates
+can be known in the sense that you can
+
+ align:start position:0%
+can be known in the sense that you can
+ 
+
+ align:start position:0%
+can be known in the sense that you can
+regulate the amount of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input and
+
+ align:start position:0%
+input and
+ 
+
+ align:start position:0%
+input and
+output by the the rate at which you
+
+ align:start position:0%
+output by the the rate at which you
+ 
+
+ align:start position:0%
+output by the the rate at which you
+remove
+
+ align:start position:0%
+remove
+ 
+
+ align:start position:0%
+remove
+substrates and add them
+
+ align:start position:0%
+substrates and add them
+ 
+
+ align:start position:0%
+substrates and add them
+and the metabolic fluxes are what you
+
+ align:start position:0%
+and the metabolic fluxes are what you
+ 
+
+ align:start position:0%
+and the metabolic fluxes are what you
+actually want this is in contrast to the
+
+ align:start position:0%
+actually want this is in contrast to the
+ 
+
+ align:start position:0%
+actually want this is in contrast to the
+red blood cell or other
+
+ align:start position:0%
+red blood cell or other
+ 
+
+ align:start position:0%
+red blood cell or other
+ordinary difference equation cases we
+
+ align:start position:0%
+ordinary difference equation cases we
+ 
+
+ align:start position:0%
+ordinary difference equation cases we
+were talking about where the rate
+
+ align:start position:0%
+were talking about where the rate
+ 
+
+ align:start position:0%
+were talking about where the rate
+equations were known but we were we're
+
+ align:start position:0%
+equations were known but we were we're
+ 
+
+ align:start position:0%
+equations were known but we were we're
+looking for concentrations here we're
+
+ align:start position:0%
+looking for concentrations here we're
+ 
+
+ align:start position:0%
+looking for concentrations here we're
+less concerned about concentrations and
+
+ align:start position:0%
+less concerned about concentrations and
+ 
+
+ align:start position:0%
+less concerned about concentrations and
+we want to learn what it might be the
+
+ align:start position:0%
+we want to learn what it might be the
+ 
+
+ align:start position:0%
+we want to learn what it might be the
+the fluxes and later what might be the
+
+ align:start position:0%
+the fluxes and later what might be the
+ 
+
+ align:start position:0%
+the fluxes and later what might be the
+optimal fluxes
+
+ align:start position:0%
+optimal fluxes
+ 
+
+ align:start position:0%
+optimal fluxes
+so slide 42
+
+ align:start position:0%
+so slide 42
+ 
+
+ align:start position:0%
+so slide 42
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a way nomenclature we focus on
+
+ align:start position:0%
+as a way nomenclature we focus on
+ 
+
+ align:start position:0%
+as a way nomenclature we focus on
+positive fluxes if we want to go the
+
+ align:start position:0%
+positive fluxes if we want to go the
+ 
+
+ align:start position:0%
+positive fluxes if we want to go the
+opposite direction we'll make that a
+
+ align:start position:0%
+opposite direction we'll make that a
+ 
+
+ align:start position:0%
+opposite direction we'll make that a
+another uh reverse flux
+
+ align:start position:0%
+another uh reverse flux
+ 
+
+ align:start position:0%
+another uh reverse flux
+separate flux so focusing on positive
+
+ align:start position:0%
+separate flux so focusing on positive
+ 
+
+ align:start position:0%
+separate flux so focusing on positive
+fluxes
+
+ align:start position:0%
+fluxes
+ 
+
+ align:start position:0%
+fluxes
+we know we might know the flux level in
+
+ align:start position:0%
+we know we might know the flux level in
+ 
+
+ align:start position:0%
+we know we might know the flux level in
+certain reactions that will help us have
+
+ align:start position:0%
+certain reactions that will help us have
+ 
+
+ align:start position:0%
+certain reactions that will help us have
+this the equations
+
+ align:start position:0%
+this the equations
+ 
+
+ align:start position:0%
+this the equations
+appropriately constrained
+
+ align:start position:0%
+appropriately constrained
+ 
+
+ align:start position:0%
+appropriately constrained
+we can control update rates
+
+ align:start position:0%
+we can control update rates
+ 
+
+ align:start position:0%
+we can control update rates
+we have we can have maximum values for
+
+ align:start position:0%
+we have we can have maximum values for
+ 
+
+ align:start position:0%
+we have we can have maximum values for
+uptake and internal fluxes
+
+ align:start position:0%
+uptake and internal fluxes
+ 
+
+ align:start position:0%
+uptake and internal fluxes
+so here's an example let's walk through
+
+ align:start position:0%
+so here's an example let's walk through
+ 
+
+ align:start position:0%
+so here's an example let's walk through
+it it's nice to have a couple of
+
+ align:start position:0%
+it it's nice to have a couple of
+ 
+
+ align:start position:0%
+it it's nice to have a couple of
+one or two examples where we walk
+
+ align:start position:0%
+one or two examples where we walk
+ 
+
+ align:start position:0%
+one or two examples where we walk
+through in a
+
+ align:start position:0%
+through in a
+ 
+
+ align:start position:0%
+through in a
+in a given class so here we're going to
+
+ align:start position:0%
+in a given class so here we're going to
+ 
+
+ align:start position:0%
+in a given class so here we're going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+an input
+
+ align:start position:0%
+an input
+ 
+
+ align:start position:0%
+an input
+molecule a it's transported across the
+
+ align:start position:0%
+molecule a it's transported across the
+ 
+
+ align:start position:0%
+molecule a it's transported across the
+membrane at a rate r sub a
+
+ align:start position:0%
+membrane at a rate r sub a
+ 
+
+ align:start position:0%
+membrane at a rate r sub a
+it then has essentially a decision fork
+
+ align:start position:0%
+it then has essentially a decision fork
+ 
+
+ align:start position:0%
+it then has essentially a decision fork
+here some fraction of the a is going to
+
+ align:start position:0%
+here some fraction of the a is going to
+ 
+
+ align:start position:0%
+here some fraction of the a is going to
+go through the x1 reaction and some
+
+ align:start position:0%
+go through the x1 reaction and some
+ 
+
+ align:start position:0%
+go through the x1 reaction and some
+fractions of the x2 the amount that goes
+
+ align:start position:0%
+fractions of the x2 the amount that goes
+ 
+
+ align:start position:0%
+fractions of the x2 the amount that goes
+through x1 and x2 is what we is what we
+
+ align:start position:0%
+through x1 and x2 is what we is what we
+ 
+
+ align:start position:0%
+through x1 and x2 is what we is what we
+want to know
+
+ align:start position:0%
+want to know
+ 
+
+ align:start position:0%
+want to know
+we are going to be given uh
+
+ align:start position:0%
+we are going to be given uh
+ 
+
+ align:start position:0%
+we are going to be given uh
+the we're going to essentially clamp
+
+ align:start position:0%
+the we're going to essentially clamp
+ 
+
+ align:start position:0%
+the we're going to essentially clamp
+control the rate it goes across the
+
+ align:start position:0%
+control the rate it goes across the
+ 
+
+ align:start position:0%
+control the rate it goes across the
+membrane r a so that's going to be a
+
+ align:start position:0%
+membrane r a so that's going to be a
+ 
+
+ align:start position:0%
+membrane r a so that's going to be a
+given you can see the constraint here r
+
+ align:start position:0%
+given you can see the constraint here r
+ 
+
+ align:start position:0%
+given you can see the constraint here r
+a is going to be 3
+
+ align:start position:0%
+a is going to be 3
+ 
+
+ align:start position:0%
+a is going to be 3
+and we're going to uh also know the rate
+
+ align:start position:0%
+and we're going to uh also know the rate
+ 
+
+ align:start position:0%
+and we're going to uh also know the rate
+at which b is removed and that's going
+
+ align:start position:0%
+at which b is removed and that's going
+ 
+
+ align:start position:0%
+at which b is removed and that's going
+to be kept constant at 1. so we're going
+
+ align:start position:0%
+to be kept constant at 1. so we're going
+ 
+
+ align:start position:0%
+to be kept constant at 1. so we're going
+to solve for the two internal fluxes x
+
+ align:start position:0%
+to solve for the two internal fluxes x
+ 
+
+ align:start position:0%
+to solve for the two internal fluxes x
+and maybe this external uh transport
+
+ align:start position:0%
+and maybe this external uh transport
+ 
+
+ align:start position:0%
+and maybe this external uh transport
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+are c
+
+ align:start position:0%
+are c
+ 
+
+ align:start position:0%
+are c
+now we know there's going to be
+
+ align:start position:0%
+now we know there's going to be
+ 
+
+ align:start position:0%
+now we know there's going to be
+conservation of mass so we can start
+
+ align:start position:0%
+conservation of mass so we can start
+ 
+
+ align:start position:0%
+conservation of mass so we can start
+setting up the flux balances in the
+
+ align:start position:0%
+setting up the flux balances in the
+ 
+
+ align:start position:0%
+setting up the flux balances in the
+upper
+
+ align:start position:0%
+upper
+ 
+
+ align:start position:0%
+upper
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+right-hand corner here of slide 43.
+
+ align:start position:0%
+right-hand corner here of slide 43.
+ 
+
+ align:start position:0%
+right-hand corner here of slide 43.
+take a look at a a is created
+
+ align:start position:0%
+take a look at a a is created
+ 
+
+ align:start position:0%
+take a look at a a is created
+essentially the intracellular
+
+ align:start position:0%
+essentially the intracellular
+ 
+
+ align:start position:0%
+essentially the intracellular
+concentration of a is dependent uh on r
+
+ align:start position:0%
+concentration of a is dependent uh on r
+ 
+
+ align:start position:0%
+concentration of a is dependent uh on r
+sub a and then it splits into x1 and x2
+
+ align:start position:0%
+sub a and then it splits into x1 and x2
+ 
+
+ align:start position:0%
+sub a and then it splits into x1 and x2
+so you know that r r sub a
+
+ align:start position:0%
+so you know that r r sub a
+ 
+
+ align:start position:0%
+so you know that r r sub a
+minus x1 minus x2 is going to be zero
+
+ align:start position:0%
+minus x1 minus x2 is going to be zero
+ 
+
+ align:start position:0%
+minus x1 minus x2 is going to be zero
+they're going to cancel out because a by
+
+ align:start position:0%
+they're going to cancel out because a by
+ 
+
+ align:start position:0%
+they're going to cancel out because a by
+steady state assumption is going to be
+
+ align:start position:0%
+steady state assumption is going to be
+ 
+
+ align:start position:0%
+steady state assumption is going to be
+constant even though the fluxes are not
+
+ align:start position:0%
+constant even though the fluxes are not
+ 
+
+ align:start position:0%
+constant even though the fluxes are not
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+uh their sum is and for b a similar
+
+ align:start position:0%
+uh their sum is and for b a similar
+ 
+
+ align:start position:0%
+uh their sum is and for b a similar
+argument we made x one
+
+ align:start position:0%
+argument we made x one
+ 
+
+ align:start position:0%
+argument we made x one
+which creates b has to uh sum with r sub
+
+ align:start position:0%
+which creates b has to uh sum with r sub
+ 
+
+ align:start position:0%
+which creates b has to uh sum with r sub
+b to zero and the same thing for c all
+
+ align:start position:0%
+b to zero and the same thing for c all
+ 
+
+ align:start position:0%
+b to zero and the same thing for c all
+the inputs have to equal the outputs
+
+ align:start position:0%
+the inputs have to equal the outputs
+ 
+
+ align:start position:0%
+the inputs have to equal the outputs
+we have these two constraints where
+
+ align:start position:0%
+we have these two constraints where
+ 
+
+ align:start position:0%
+we have these two constraints where
+we've just said we're going to
+
+ align:start position:0%
+we've just said we're going to
+ 
+
+ align:start position:0%
+we've just said we're going to
+clamp experimentally the amount of a
+
+ align:start position:0%
+clamp experimentally the amount of a
+ 
+
+ align:start position:0%
+clamp experimentally the amount of a
+going in and the amount of b coming out
+
+ align:start position:0%
+going in and the amount of b coming out
+ 
+
+ align:start position:0%
+going in and the amount of b coming out
+and we want to solve for the other three
+
+ align:start position:0%
+and we want to solve for the other three
+ 
+
+ align:start position:0%
+and we want to solve for the other three
+kinetic parameters so we have three
+
+ align:start position:0%
+kinetic parameters so we have three
+ 
+
+ align:start position:0%
+kinetic parameters so we have three
+equations and three unknowns
+
+ align:start position:0%
+equations and three unknowns
+ 
+
+ align:start position:0%
+equations and three unknowns
+the unknowns there's two internal fluxes
+
+ align:start position:0%
+the unknowns there's two internal fluxes
+ 
+
+ align:start position:0%
+the unknowns there's two internal fluxes
+and the r sub c
+
+ align:start position:0%
+and the r sub c
+ 
+
+ align:start position:0%
+and the r sub c
+and so another way of stating this
+
+ align:start position:0%
+and so another way of stating this
+ 
+
+ align:start position:0%
+and so another way of stating this
+equation x one plus x two is equal to
+
+ align:start position:0%
+equation x one plus x two is equal to
+ 
+
+ align:start position:0%
+equation x one plus x two is equal to
+three x because we know three going in
+
+ align:start position:0%
+three x because we know three going in
+ 
+
+ align:start position:0%
+three x because we know three going in
+has to equal x one x two by flux balance
+
+ align:start position:0%
+has to equal x one x two by flux balance
+ 
+
+ align:start position:0%
+has to equal x one x two by flux balance
+this is essentially the flux balance for
+
+ align:start position:0%
+this is essentially the flux balance for
+ 
+
+ align:start position:0%
+this is essentially the flux balance for
+a can be summarized as x1 plus x2 equals
+
+ align:start position:0%
+a can be summarized as x1 plus x2 equals
+ 
+
+ align:start position:0%
+a can be summarized as x1 plus x2 equals
+3 or in matrix formation it's the top
+
+ align:start position:0%
+3 or in matrix formation it's the top
+ 
+
+ align:start position:0%
+3 or in matrix formation it's the top
+uh row here 1 1 0
+
+ align:start position:0%
+uh row here 1 1 0
+ 
+
+ align:start position:0%
+uh row here 1 1 0
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it time
+
+ align:start position:0%
+it time
+ 
+
+ align:start position:0%
+it time
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+and the the 3 is in the
+
+ align:start position:0%
+and the the 3 is in the
+ 
+
+ align:start position:0%
+and the the 3 is in the
+transport
+
+ align:start position:0%
+transport
+ 
+
+ align:start position:0%
+transport
+column vector at the far right hand side
+
+ align:start position:0%
+column vector at the far right hand side
+ 
+
+ align:start position:0%
+column vector at the far right hand side
+and similarly you fill up the rest of
+
+ align:start position:0%
+and similarly you fill up the rest of
+ 
+
+ align:start position:0%
+and similarly you fill up the rest of
+the stoichiometric matrix with zeros and
+
+ align:start position:0%
+the stoichiometric matrix with zeros and
+ 
+
+ align:start position:0%
+the stoichiometric matrix with zeros and
+ones and twos and minus ones and the the
+
+ align:start position:0%
+ones and twos and minus ones and the the
+ 
+
+ align:start position:0%
+ones and twos and minus ones and the the
+transport the flux vectors are three one
+
+ align:start position:0%
+transport the flux vectors are three one
+ 
+
+ align:start position:0%
+transport the flux vectors are three one
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for the constraints that we have
+
+ align:start position:0%
+for the constraints that we have
+ 
+
+ align:start position:0%
+for the constraints that we have
+and they solve for this three equations
+
+ align:start position:0%
+and they solve for this three equations
+ 
+
+ align:start position:0%
+and they solve for this three equations
+three unknowns
+
+ align:start position:0%
+three unknowns
+ 
+
+ align:start position:0%
+three unknowns
+you can solve it uh by standard linear
+
+ align:start position:0%
+you can solve it uh by standard linear
+ 
+
+ align:start position:0%
+you can solve it uh by standard linear
+algebra tricks
+
+ align:start position:0%
+algebra tricks
+ 
+
+ align:start position:0%
+algebra tricks
+um just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s times v equals b so v is equal to
+
+ align:start position:0%
+s times v equals b so v is equal to
+ 
+
+ align:start position:0%
+s times v equals b so v is equal to
+inverse matrix s times b
+
+ align:start position:0%
+inverse matrix s times b
+ 
+
+ align:start position:0%
+inverse matrix s times b
+the matrix we had in the previous slide
+
+ align:start position:0%
+the matrix we had in the previous slide
+ 
+
+ align:start position:0%
+the matrix we had in the previous slide
+which was first row was 1 1 0. now
+
+ align:start position:0%
+which was first row was 1 1 0. now
+ 
+
+ align:start position:0%
+which was first row was 1 1 0. now
+when you do the inverse matrix you get
+
+ align:start position:0%
+when you do the inverse matrix you get
+ 
+
+ align:start position:0%
+when you do the inverse matrix you get
+this upper right hand portion and you
+
+ align:start position:0%
+this upper right hand portion and you
+ 
+
+ align:start position:0%
+this upper right hand portion and you
+multiply it out and you get the column
+
+ align:start position:0%
+multiply it out and you get the column
+ 
+
+ align:start position:0%
+multiply it out and you get the column
+vector solution which is 1 2 four for x1
+
+ align:start position:0%
+vector solution which is 1 2 four for x1
+ 
+
+ align:start position:0%
+vector solution which is 1 2 four for x1
+x2 and rc respectively now they're
+
+ align:start position:0%
+x2 and rc respectively now they're
+ 
+
+ align:start position:0%
+x2 and rc respectively now they're
+plugged into this diagram
+
+ align:start position:0%
+plugged into this diagram
+ 
+
+ align:start position:0%
+plugged into this diagram
+and you can see that the whole masses
+
+ align:start position:0%
+and you can see that the whole masses
+ 
+
+ align:start position:0%
+and you can see that the whole masses
+balance out
+
+ align:start position:0%
+balance out
+ 
+
+ align:start position:0%
+balance out
+three is equal to one plus two
+
+ align:start position:0%
+three is equal to one plus two
+ 
+
+ align:start position:0%
+three is equal to one plus two
+2 times c
+
+ align:start position:0%
+2 times c
+ 
+
+ align:start position:0%
+2 times c
+2 times 2 is equal to 4.
+
+ align:start position:0%
+2 times 2 is equal to 4.
+ 
+
+ align:start position:0%
+2 times 2 is equal to 4.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's an example where it's heavily
+
+ align:start position:0%
+so that's an example where it's heavily
+ 
+
+ align:start position:0%
+so that's an example where it's heavily
+constrained and so we can solve it
+
+ align:start position:0%
+constrained and so we can solve it
+ 
+
+ align:start position:0%
+constrained and so we can solve it
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+very often there are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+measurements that have been made we
+
+ align:start position:0%
+measurements that have been made we
+ 
+
+ align:start position:0%
+measurements that have been made we
+can't clamp all these fluxes and there
+
+ align:start position:0%
+can't clamp all these fluxes and there
+ 
+
+ align:start position:0%
+can't clamp all these fluxes and there
+are many more internal fluxes than
+
+ align:start position:0%
+are many more internal fluxes than
+ 
+
+ align:start position:0%
+are many more internal fluxes than
+external and so we have an
+
+ align:start position:0%
+external and so we have an
+ 
+
+ align:start position:0%
+external and so we have an
+underdetermined system
+
+ align:start position:0%
+underdetermined system
+ 
+
+ align:start position:0%
+underdetermined system
+what is a good system biologist to do at
+
+ align:start position:0%
+what is a good system biologist to do at
+ 
+
+ align:start position:0%
+what is a good system biologist to do at
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+well the formal solution is it's no
+
+ align:start position:0%
+well the formal solution is it's no
+ 
+
+ align:start position:0%
+well the formal solution is it's no
+longer a point a single point a nice
+
+ align:start position:0%
+longer a point a single point a nice
+ 
+
+ align:start position:0%
+longer a point a single point a nice
+column vector of of fluxes it's now an
+
+ align:start position:0%
+column vector of of fluxes it's now an
+ 
+
+ align:start position:0%
+column vector of of fluxes it's now an
+entire feasible space
+
+ align:start position:0%
+entire feasible space
+ 
+
+ align:start position:0%
+entire feasible space
+this is the kind of the cop-out answer
+
+ align:start position:0%
+this is the kind of the cop-out answer
+ 
+
+ align:start position:0%
+this is the kind of the cop-out answer
+is that okay we have fewer equations
+
+ align:start position:0%
+is that okay we have fewer equations
+ 
+
+ align:start position:0%
+is that okay we have fewer equations
+than we have unknowns that means the
+
+ align:start position:0%
+than we have unknowns that means the
+ 
+
+ align:start position:0%
+than we have unknowns that means the
+unknowns can occupy this entire
+
+ align:start position:0%
+unknowns can occupy this entire
+ 
+
+ align:start position:0%
+unknowns can occupy this entire
+multi-dimensional space where however
+
+ align:start position:0%
+multi-dimensional space where however
+ 
+
+ align:start position:0%
+multi-dimensional space where however
+many fluxes you have if you have
+
+ align:start position:0%
+many fluxes you have if you have
+ 
+
+ align:start position:0%
+many fluxes you have if you have
+hundreds of fluxes you'll have hundreds
+
+ align:start position:0%
+hundreds of fluxes you'll have hundreds
+ 
+
+ align:start position:0%
+hundreds of fluxes you'll have hundreds
+of dimensions so you have three fluxes a
+
+ align:start position:0%
+of dimensions so you have three fluxes a
+ 
+
+ align:start position:0%
+of dimensions so you have three fluxes a
+b and c
+
+ align:start position:0%
+b and c
+ 
+
+ align:start position:0%
+b and c
+then you'll get this kind of
+
+ align:start position:0%
+then you'll get this kind of
+ 
+
+ align:start position:0%
+then you'll get this kind of
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+multi-dimensional polyhedral region and
+
+ align:start position:0%
+multi-dimensional polyhedral region and
+ 
+
+ align:start position:0%
+multi-dimensional polyhedral region and
+anything inside that polyhedron is
+
+ align:start position:0%
+anything inside that polyhedron is
+ 
+
+ align:start position:0%
+anything inside that polyhedron is
+a is the acceptable solution to the
+
+ align:start position:0%
+a is the acceptable solution to the
+ 
+
+ align:start position:0%
+a is the acceptable solution to the
+under determined set well this is still
+
+ align:start position:0%
+under determined set well this is still
+ 
+
+ align:start position:0%
+under determined set well this is still
+progress in that you now know that
+
+ align:start position:0%
+progress in that you now know that
+ 
+
+ align:start position:0%
+progress in that you now know that
+that your solution is in there somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what if we wanted to find
+
+ align:start position:0%
+but what if we wanted to find
+ 
+
+ align:start position:0%
+but what if we wanted to find
+add some more constraints which are not
+
+ align:start position:0%
+add some more constraints which are not
+ 
+
+ align:start position:0%
+add some more constraints which are not
+now exact constraints anymore but
+
+ align:start position:0%
+now exact constraints anymore but
+ 
+
+ align:start position:0%
+now exact constraints anymore but
+they're more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an optimization process you might have
+
+ align:start position:0%
+an optimization process you might have
+ 
+
+ align:start position:0%
+an optimization process you might have
+this multi-dimensional polyhedron will
+
+ align:start position:0%
+this multi-dimensional polyhedron will
+ 
+
+ align:start position:0%
+this multi-dimensional polyhedron will
+be bounded by inequalities that it's
+
+ align:start position:0%
+be bounded by inequalities that it's
+ 
+
+ align:start position:0%
+be bounded by inequalities that it's
+less that's greater than zero right this
+
+ align:start position:0%
+less that's greater than zero right this
+ 
+
+ align:start position:0%
+less that's greater than zero right this
+positive or it's less of some maximum
+
+ align:start position:0%
+positive or it's less of some maximum
+ 
+
+ align:start position:0%
+positive or it's less of some maximum
+flux but then you want to find some
+
+ align:start position:0%
+flux but then you want to find some
+ 
+
+ align:start position:0%
+flux but then you want to find some
+optimal solution
+
+ align:start position:0%
+optimal solution
+ 
+
+ align:start position:0%
+optimal solution
+and the optimization
+
+ align:start position:0%
+and the optimization
+ 
+
+ align:start position:0%
+and the optimization
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+is the sort of thing that
+
+ align:start position:0%
+is the sort of thing that
+ 
+
+ align:start position:0%
+is the sort of thing that
+that math has uh been harnessed for in
+
+ align:start position:0%
+that math has uh been harnessed for in
+ 
+
+ align:start position:0%
+that math has uh been harnessed for in
+some other fields outside of ours such
+
+ align:start position:0%
+some other fields outside of ours such
+ 
+
+ align:start position:0%
+some other fields outside of ours such
+as economics when you're doing uh
+
+ align:start position:0%
+as economics when you're doing uh
+ 
+
+ align:start position:0%
+as economics when you're doing uh
+planning of
+
+ align:start position:0%
+planning of
+ 
+
+ align:start position:0%
+planning of
+you know transport or planning of
+
+ align:start position:0%
+you know transport or planning of
+ 
+
+ align:start position:0%
+you know transport or planning of
+economic investments and so forth you
+
+ align:start position:0%
+economic investments and so forth you
+ 
+
+ align:start position:0%
+economic investments and so forth you
+want to know how much of your resources
+
+ align:start position:0%
+want to know how much of your resources
+ 
+
+ align:start position:0%
+want to know how much of your resources
+do you want to send through the x1 root
+
+ align:start position:0%
+do you want to send through the x1 root
+ 
+
+ align:start position:0%
+do you want to send through the x1 root
+and how much do you want to send to the
+
+ align:start position:0%
+and how much do you want to send to the
+ 
+
+ align:start position:0%
+and how much do you want to send to the
+x2 root very analogous to the you know
+
+ align:start position:0%
+x2 root very analogous to the you know
+ 
+
+ align:start position:0%
+x2 root very analogous to the you know
+the situation we had in the previous
+
+ align:start position:0%
+the situation we had in the previous
+ 
+
+ align:start position:0%
+the situation we had in the previous
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and that that can be solved by linear
+
+ align:start position:0%
+and that that can be solved by linear
+ 
+
+ align:start position:0%
+and that that can be solved by linear
+programming when you're programming
+
+ align:start position:0%
+programming when you're programming
+ 
+
+ align:start position:0%
+programming when you're programming
+often finding economic applications
+
+ align:start position:0%
+often finding economic applications
+ 
+
+ align:start position:0%
+often finding economic applications
+so let's but we need to ask what is it
+
+ align:start position:0%
+so let's but we need to ask what is it
+ 
+
+ align:start position:0%
+so let's but we need to ask what is it
+we want to optimize in economics you
+
+ align:start position:0%
+we want to optimize in economics you
+ 
+
+ align:start position:0%
+we want to optimize in economics you
+want to optimize typically the bottom
+
+ align:start position:0%
+want to optimize typically the bottom
+ 
+
+ align:start position:0%
+want to optimize typically the bottom
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+you want to lower costs and increase
+
+ align:start position:0%
+you want to lower costs and increase
+ 
+
+ align:start position:0%
+you want to lower costs and increase
+profits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sort of what we have here is we have
+
+ align:start position:0%
+the sort of what we have here is we have
+ 
+
+ align:start position:0%
+the sort of what we have here is we have
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very commonly encountered many metabolic
+
+ align:start position:0%
+very commonly encountered many metabolic
+ 
+
+ align:start position:0%
+very commonly encountered many metabolic
+systems where you have this convex
+
+ align:start position:0%
+systems where you have this convex
+ 
+
+ align:start position:0%
+systems where you have this convex
+polyhedral cone convex just means that
+
+ align:start position:0%
+polyhedral cone convex just means that
+ 
+
+ align:start position:0%
+polyhedral cone convex just means that
+there's uh
+
+ align:start position:0%
+there's uh
+ 
+
+ align:start position:0%
+there's uh
+there are no little
+
+ align:start position:0%
+there are no little
+ 
+
+ align:start position:0%
+there are no little
+gaps in it no little carved out regions
+
+ align:start position:0%
+gaps in it no little carved out regions
+ 
+
+ align:start position:0%
+gaps in it no little carved out regions
+it's it's all um
+
+ align:start position:0%
+it's it's all um
+ 
+
+ align:start position:0%
+it's it's all um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh contain
+
+ align:start position:0%
+uh contain
+ 
+
+ align:start position:0%
+uh contain
+that convexity allows you to have now
+
+ align:start position:0%
+that convexity allows you to have now
+ 
+
+ align:start position:0%
+that convexity allows you to have now
+take a linear objective function say a
+
+ align:start position:0%
+take a linear objective function say a
+ 
+
+ align:start position:0%
+take a linear objective function say a
+multi-dimensional plane or a line
+
+ align:start position:0%
+multi-dimensional plane or a line
+ 
+
+ align:start position:0%
+multi-dimensional plane or a line
+that that you then move through this
+
+ align:start position:0%
+that that you then move through this
+ 
+
+ align:start position:0%
+that that you then move through this
+convex space and since there are no gaps
+
+ align:start position:0%
+convex space and since there are no gaps
+ 
+
+ align:start position:0%
+convex space and since there are no gaps
+in it you eventually move off
+
+ align:start position:0%
+in it you eventually move off
+ 
+
+ align:start position:0%
+in it you eventually move off
+as you move this objective function to
+
+ align:start position:0%
+as you move this objective function to
+ 
+
+ align:start position:0%
+as you move this objective function to
+the objective function gets better and
+
+ align:start position:0%
+the objective function gets better and
+ 
+
+ align:start position:0%
+the objective function gets better and
+better as it goes off through this
+
+ align:start position:0%
+better as it goes off through this
+ 
+
+ align:start position:0%
+better as it goes off through this
+feasible space it eventually gets to a
+
+ align:start position:0%
+feasible space it eventually gets to a
+ 
+
+ align:start position:0%
+feasible space it eventually gets to a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+where it leaves the feasible space and
+
+ align:start position:0%
+where it leaves the feasible space and
+ 
+
+ align:start position:0%
+where it leaves the feasible space and
+that is the maximum value the mo the
+
+ align:start position:0%
+that is the maximum value the mo the
+ 
+
+ align:start position:0%
+that is the maximum value the mo the
+optimal value for that objective
+
+ align:start position:0%
+optimal value for that objective
+ 
+
+ align:start position:0%
+optimal value for that objective
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+which so we can use this feasible space
+
+ align:start position:0%
+which so we can use this feasible space
+ 
+
+ align:start position:0%
+which so we can use this feasible space
+combined with this objective function to
+
+ align:start position:0%
+combined with this objective function to
+ 
+
+ align:start position:0%
+combined with this objective function to
+find some optimum
+
+ align:start position:0%
+find some optimum
+ 
+
+ align:start position:0%
+find some optimum
+now what is the objective function that
+
+ align:start position:0%
+now what is the objective function that
+ 
+
+ align:start position:0%
+now what is the objective function that
+we want to use
+
+ align:start position:0%
+we want to use
+ 
+
+ align:start position:0%
+we want to use
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we were doing red blood cell the
+
+ align:start position:0%
+if we were doing red blood cell the
+ 
+
+ align:start position:0%
+if we were doing red blood cell the
+objective function might be atp or redox
+
+ align:start position:0%
+objective function might be atp or redox
+ 
+
+ align:start position:0%
+objective function might be atp or redox
+or both or delivery oxygen
+
+ align:start position:0%
+or both or delivery oxygen
+ 
+
+ align:start position:0%
+or both or delivery oxygen
+and for a variety of other systems of
+
+ align:start position:0%
+and for a variety of other systems of
+ 
+
+ align:start position:0%
+and for a variety of other systems of
+importance to
+
+ align:start position:0%
+importance to
+ 
+
+ align:start position:0%
+importance to
+understanding
+
+ align:start position:0%
+understanding
+ 
+
+ align:start position:0%
+understanding
+health or biotechnology production
+
+ align:start position:0%
+health or biotechnology production
+ 
+
+ align:start position:0%
+health or biotechnology production
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+medical and engineering goals
+
+ align:start position:0%
+medical and engineering goals
+ 
+
+ align:start position:0%
+medical and engineering goals
+what we want to optimize is that is
+
+ align:start position:0%
+what we want to optimize is that is
+ 
+
+ align:start position:0%
+what we want to optimize is that is
+biomass the ability of the cells to grow
+
+ align:start position:0%
+biomass the ability of the cells to grow
+ 
+
+ align:start position:0%
+biomass the ability of the cells to grow
+and produce
+
+ align:start position:0%
+and produce
+ 
+
+ align:start position:0%
+and produce
+other cells or produce a particular
+
+ align:start position:0%
+other cells or produce a particular
+ 
+
+ align:start position:0%
+other cells or produce a particular
+subset of molecules in the cell let's
+
+ align:start position:0%
+subset of molecules in the cell let's
+ 
+
+ align:start position:0%
+subset of molecules in the cell let's
+deal mainly with the case of of cells
+
+ align:start position:0%
+deal mainly with the case of of cells
+ 
+
+ align:start position:0%
+deal mainly with the case of of cells
+producing cells and what this is is a
+
+ align:start position:0%
+producing cells and what this is is a
+ 
+
+ align:start position:0%
+producing cells and what this is is a
+sum over all the monomers all the
+
+ align:start position:0%
+sum over all the monomers all the
+ 
+
+ align:start position:0%
+sum over all the monomers all the
+components of the cell which represent
+
+ align:start position:0%
+components of the cell which represent
+ 
+
+ align:start position:0%
+components of the cell which represent
+the body of the cell
+
+ align:start position:0%
+the body of the cell
+ 
+
+ align:start position:0%
+the body of the cell
+so as you
+
+ align:start position:0%
+so as you
+ 
+
+ align:start position:0%
+so as you
+move as you transport small molecules in
+
+ align:start position:0%
+move as you transport small molecules in
+ 
+
+ align:start position:0%
+move as you transport small molecules in
+from the environment and incorporate it
+
+ align:start position:0%
+from the environment and incorporate it
+ 
+
+ align:start position:0%
+from the environment and incorporate it
+into the cell that's certainly you can
+
+ align:start position:0%
+into the cell that's certainly you can
+ 
+
+ align:start position:0%
+into the cell that's certainly you can
+think of as a sink it's removing those
+
+ align:start position:0%
+think of as a sink it's removing those
+ 
+
+ align:start position:0%
+think of as a sink it's removing those
+molecules from circulation from some
+
+ align:start position:0%
+molecules from circulation from some
+ 
+
+ align:start position:0%
+molecules from circulation from some
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and this uh
+
+ align:start position:0%
+and this uh
+ 
+
+ align:start position:0%
+and this uh
+the sum over all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components the ratios d of the monomers
+
+ align:start position:0%
+components the ratios d of the monomers
+ 
+
+ align:start position:0%
+components the ratios d of the monomers
+you can think of there's a ratio fixed
+
+ align:start position:0%
+you can think of there's a ratio fixed
+ 
+
+ align:start position:0%
+you can think of there's a ratio fixed
+ratio of alanine to glycine to leucine
+
+ align:start position:0%
+ratio of alanine to glycine to leucine
+ 
+
+ align:start position:0%
+ratio of alanine to glycine to leucine
+to all the other components of the cell
+
+ align:start position:0%
+to all the other components of the cell
+ 
+
+ align:start position:0%
+to all the other components of the cell
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+known you can you can know this without
+
+ align:start position:0%
+known you can you can know this without
+ 
+
+ align:start position:0%
+known you can you can know this without
+knowing lots of other parts of the
+
+ align:start position:0%
+knowing lots of other parts of the
+ 
+
+ align:start position:0%
+knowing lots of other parts of the
+system you want to know just by taking
+
+ align:start position:0%
+system you want to know just by taking
+ 
+
+ align:start position:0%
+system you want to know just by taking
+the cell and doing a chemical
+
+ align:start position:0%
+the cell and doing a chemical
+ 
+
+ align:start position:0%
+the cell and doing a chemical
+composition on it very simple experiment
+
+ align:start position:0%
+composition on it very simple experiment
+ 
+
+ align:start position:0%
+composition on it very simple experiment
+their tables of this known provide
+
+ align:start position:0%
+their tables of this known provide
+ 
+
+ align:start position:0%
+their tables of this known provide
+variety of cells and it hardly changes
+
+ align:start position:0%
+variety of cells and it hardly changes
+ 
+
+ align:start position:0%
+variety of cells and it hardly changes
+depending on much on the how the cell is
+
+ align:start position:0%
+depending on much on the how the cell is
+ 
+
+ align:start position:0%
+depending on much on the how the cell is
+growing but
+
+ align:start position:0%
+growing but
+ 
+
+ align:start position:0%
+growing but
+what sources of carbon and nitrogen do
+
+ align:start position:0%
+what sources of carbon and nitrogen do
+ 
+
+ align:start position:0%
+what sources of carbon and nitrogen do
+not greatly affect the ratio of alanine
+
+ align:start position:0%
+not greatly affect the ratio of alanine
+ 
+
+ align:start position:0%
+not greatly affect the ratio of alanine
+leucine and glycine because those are
+
+ align:start position:0%
+leucine and glycine because those are
+ 
+
+ align:start position:0%
+leucine and glycine because those are
+determined by what it takes to run the
+
+ align:start position:0%
+determined by what it takes to run the
+ 
+
+ align:start position:0%
+determined by what it takes to run the
+cell so this is important flux you can
+
+ align:start position:0%
+cell so this is important flux you can
+ 
+
+ align:start position:0%
+cell so this is important flux you can
+think of this as a kind of a lumped flux
+
+ align:start position:0%
+think of this as a kind of a lumped flux
+ 
+
+ align:start position:0%
+think of this as a kind of a lumped flux
+and this will be our objective function
+
+ align:start position:0%
+and this will be our objective function
+ 
+
+ align:start position:0%
+and this will be our objective function
+as well so the executive function is z
+
+ align:start position:0%
+as well so the executive function is z
+ 
+
+ align:start position:0%
+as well so the executive function is z
+sometimes called so z is going to be
+
+ align:start position:0%
+sometimes called so z is going to be
+ 
+
+ align:start position:0%
+sometimes called so z is going to be
+equal to the flux
+
+ align:start position:0%
+equal to the flux
+ 
+
+ align:start position:0%
+equal to the flux
+of growth
+
+ align:start position:0%
+of growth
+ 
+
+ align:start position:0%
+of growth
+so you can see that you have again the
+
+ align:start position:0%
+so you can see that you have again the
+ 
+
+ align:start position:0%
+so you can see that you have again the
+same equation again stoichiometric
+
+ align:start position:0%
+same equation again stoichiometric
+ 
+
+ align:start position:0%
+same equation again stoichiometric
+matrix times the internal flux is equal
+
+ align:start position:0%
+matrix times the internal flux is equal
+ 
+
+ align:start position:0%
+matrix times the internal flux is equal
+to the uptake fluxes
+
+ align:start position:0%
+to the uptake fluxes
+ 
+
+ align:start position:0%
+to the uptake fluxes
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and we've got this now this uh
+
+ align:start position:0%
+and we've got this now this uh
+ 
+
+ align:start position:0%
+and we've got this now this uh
+constraint this optimization function
+
+ align:start position:0%
+constraint this optimization function
+ 
+
+ align:start position:0%
+constraint this optimization function
+so let's take a just like you had a very
+
+ align:start position:0%
+so let's take a just like you had a very
+ 
+
+ align:start position:0%
+so let's take a just like you had a very
+simple uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exact solution before now let's take
+
+ align:start position:0%
+exact solution before now let's take
+ 
+
+ align:start position:0%
+exact solution before now let's take
+this very simple linear programming or
+
+ align:start position:0%
+this very simple linear programming or
+ 
+
+ align:start position:0%
+this very simple linear programming or
+lp solution where now
+
+ align:start position:0%
+lp solution where now
+ 
+
+ align:start position:0%
+lp solution where now
+it's underdetermined so we can't get the
+
+ align:start position:0%
+it's underdetermined so we can't get the
+ 
+
+ align:start position:0%
+it's underdetermined so we can't get the
+exact solution but we can ask what's the
+
+ align:start position:0%
+exact solution but we can ask what's the
+ 
+
+ align:start position:0%
+exact solution but we can ask what's the
+maximum for a particular objective
+
+ align:start position:0%
+maximum for a particular objective
+ 
+
+ align:start position:0%
+maximum for a particular objective
+function the objective function here is
+
+ align:start position:0%
+function the objective function here is
+ 
+
+ align:start position:0%
+function the objective function here is
+not going to be the biomass production
+
+ align:start position:0%
+not going to be the biomass production
+ 
+
+ align:start position:0%
+not going to be the biomass production
+of the entire cell it's going to be
+
+ align:start position:0%
+of the entire cell it's going to be
+ 
+
+ align:start position:0%
+of the entire cell it's going to be
+either maximizing the production of d
+
+ align:start position:0%
+either maximizing the production of d
+ 
+
+ align:start position:0%
+either maximizing the production of d
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+now this is a slightly different diagram
+
+ align:start position:0%
+now this is a slightly different diagram
+ 
+
+ align:start position:0%
+now this is a slightly different diagram
+than we had before we still have the
+
+ align:start position:0%
+than we had before we still have the
+ 
+
+ align:start position:0%
+than we had before we still have the
+rate of uptake of a on the left side of
+
+ align:start position:0%
+rate of uptake of a on the left side of
+ 
+
+ align:start position:0%
+rate of uptake of a on the left side of
+this kind of circular pseudo cell a goes
+
+ align:start position:0%
+this kind of circular pseudo cell a goes
+ 
+
+ align:start position:0%
+this kind of circular pseudo cell a goes
+in it makes the same binary decision of
+
+ align:start position:0%
+in it makes the same binary decision of
+ 
+
+ align:start position:0%
+in it makes the same binary decision of
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+two-way decision of uh
+
+ align:start position:0%
+two-way decision of uh
+ 
+
+ align:start position:0%
+two-way decision of uh
+x1 versus x2 it's not binary instances
+
+ align:start position:0%
+x1 versus x2 it's not binary instances
+ 
+
+ align:start position:0%
+x1 versus x2 it's not binary instances
+quantitative uh
+
+ align:start position:0%
+quantitative uh
+ 
+
+ align:start position:0%
+quantitative uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+real numbers determine how much x and
+
+ align:start position:0%
+real numbers determine how much x and
+ 
+
+ align:start position:0%
+real numbers determine how much x and
+how much x2
+
+ align:start position:0%
+how much x2
+ 
+
+ align:start position:0%
+how much x2
+and then if it takes the upper x1 root
+
+ align:start position:0%
+and then if it takes the upper x1 root
+ 
+
+ align:start position:0%
+and then if it takes the upper x1 root
+then it uh splits into b and c if it
+
+ align:start position:0%
+then it uh splits into b and c if it
+ 
+
+ align:start position:0%
+then it uh splits into b and c if it
+takes the x2 root it turns into b and d
+
+ align:start position:0%
+takes the x2 root it turns into b and d
+ 
+
+ align:start position:0%
+takes the x2 root it turns into b and d
+both cases it produces a b molecule
+
+ align:start position:0%
+both cases it produces a b molecule
+ 
+
+ align:start position:0%
+both cases it produces a b molecule
+because you can always already see a
+
+ align:start position:0%
+because you can always already see a
+ 
+
+ align:start position:0%
+because you can always already see a
+constraint coming up here which is the r
+
+ align:start position:0%
+constraint coming up here which is the r
+ 
+
+ align:start position:0%
+constraint coming up here which is the r
+a is going to be for rb
+
+ align:start position:0%
+a is going to be for rb
+ 
+
+ align:start position:0%
+a is going to be for rb
+however you go from a
+
+ align:start position:0%
+however you go from a
+ 
+
+ align:start position:0%
+however you go from a
+to to the outside again it's going to
+
+ align:start position:0%
+to to the outside again it's going to
+ 
+
+ align:start position:0%
+to to the outside again it's going to
+it's going to produce one molecule of b
+
+ align:start position:0%
+it's going to produce one molecule of b
+ 
+
+ align:start position:0%
+it's going to produce one molecule of b
+for every molecule a this is a perfect
+
+ align:start position:0%
+for every molecule a this is a perfect
+ 
+
+ align:start position:0%
+for every molecule a this is a perfect
+conservation reaction
+
+ align:start position:0%
+conservation reaction
+ 
+
+ align:start position:0%
+conservation reaction
+and we've we've uh we've said that we're
+
+ align:start position:0%
+and we've we've uh we've said that we're
+ 
+
+ align:start position:0%
+and we've we've uh we've said that we're
+only interested in positive fluxes so
+
+ align:start position:0%
+only interested in positive fluxes so
+ 
+
+ align:start position:0%
+only interested in positive fluxes so
+you get this little triangle here of
+
+ align:start position:0%
+you get this little triangle here of
+ 
+
+ align:start position:0%
+you get this little triangle here of
+x1 and x2 are greater than zero
+
+ align:start position:0%
+x1 and x2 are greater than zero
+ 
+
+ align:start position:0%
+x1 and x2 are greater than zero
+and they're constrained in that that
+
+ align:start position:0%
+and they're constrained in that that
+ 
+
+ align:start position:0%
+and they're constrained in that that
+we've said that
+
+ align:start position:0%
+we've said that
+ 
+
+ align:start position:0%
+we've said that
+r a we're going to clamp so that it
+
+ align:start position:0%
+r a we're going to clamp so that it
+ 
+
+ align:start position:0%
+r a we're going to clamp so that it
+can't have more than uh one on this
+
+ align:start position:0%
+can't have more than uh one on this
+ 
+
+ align:start position:0%
+can't have more than uh one on this
+arbitrary
+
+ align:start position:0%
+arbitrary
+ 
+
+ align:start position:0%
+arbitrary
+moles per liter per minute say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so x x1 plus x2 are constrained to
+
+ align:start position:0%
+and so x x1 plus x2 are constrained to
+ 
+
+ align:start position:0%
+and so x x1 plus x2 are constrained to
+be less than ra so they're less than one
+
+ align:start position:0%
+be less than ra so they're less than one
+ 
+
+ align:start position:0%
+be less than ra so they're less than one
+as well so you get this feasible space
+
+ align:start position:0%
+as well so you get this feasible space
+ 
+
+ align:start position:0%
+as well so you get this feasible space
+which is this diagonally cross-hatched
+
+ align:start position:0%
+which is this diagonally cross-hatched
+ 
+
+ align:start position:0%
+which is this diagonally cross-hatched
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+and that's that's the exact that's the
+
+ align:start position:0%
+and that's that's the exact that's the
+ 
+
+ align:start position:0%
+and that's that's the exact that's the
+exact solution that's the set of all
+
+ align:start position:0%
+exact solution that's the set of all
+ 
+
+ align:start position:0%
+exact solution that's the set of all
+exact solutions
+
+ align:start position:0%
+exact solutions
+ 
+
+ align:start position:0%
+exact solutions
+but now if you want to maximize a
+
+ align:start position:0%
+but now if you want to maximize a
+ 
+
+ align:start position:0%
+but now if you want to maximize a
+particular objective function z in this
+
+ align:start position:0%
+particular objective function z in this
+ 
+
+ align:start position:0%
+particular objective function z in this
+case let's maximize the production of d
+
+ align:start position:0%
+case let's maximize the production of d
+ 
+
+ align:start position:0%
+case let's maximize the production of d
+and we're not too concerned about
+
+ align:start position:0%
+and we're not too concerned about
+ 
+
+ align:start position:0%
+and we're not too concerned about
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+then then you get this line you can
+
+ align:start position:0%
+then then you get this line you can
+ 
+
+ align:start position:0%
+then then you get this line you can
+think of this as a hyperplane going you
+
+ align:start position:0%
+think of this as a hyperplane going you
+ 
+
+ align:start position:0%
+think of this as a hyperplane going you
+know a line basically going
+
+ align:start position:0%
+know a line basically going
+ 
+
+ align:start position:0%
+know a line basically going
+up through feasible space starting at
+
+ align:start position:0%
+up through feasible space starting at
+ 
+
+ align:start position:0%
+up through feasible space starting at
+the bottom of the slide going up and up
+
+ align:start position:0%
+the bottom of the slide going up and up
+ 
+
+ align:start position:0%
+the bottom of the slide going up and up
+and up until it just barely leaves the
+
+ align:start position:0%
+and up until it just barely leaves the
+ 
+
+ align:start position:0%
+and up until it just barely leaves the
+feasible space and when it does the last
+
+ align:start position:0%
+feasible space and when it does the last
+ 
+
+ align:start position:0%
+feasible space and when it does the last
+point it gets to is the maximum and the
+
+ align:start position:0%
+point it gets to is the maximum and the
+ 
+
+ align:start position:0%
+point it gets to is the maximum and the
+maximum happens here to be
+
+ align:start position:0%
+maximum happens here to be
+ 
+
+ align:start position:0%
+maximum happens here to be
+x1 equals 0 x2 equal to the max
+
+ align:start position:0%
+x1 equals 0 x2 equal to the max
+ 
+
+ align:start position:0%
+x1 equals 0 x2 equal to the max
+rd maximum rate of production of
+
+ align:start position:0%
+rd maximum rate of production of
+ 
+
+ align:start position:0%
+rd maximum rate of production of
+the molecule we're interested
+
+ align:start position:0%
+the molecule we're interested
+ 
+
+ align:start position:0%
+the molecule we're interested
+if we had an objective function that
+
+ align:start position:0%
+if we had an objective function that
+ 
+
+ align:start position:0%
+if we had an objective function that
+went off
+
+ align:start position:0%
+went off
+ 
+
+ align:start position:0%
+went off
+the other axis it would be x2 0 and x1
+
+ align:start position:0%
+the other axis it would be x2 0 and x1
+ 
+
+ align:start position:0%
+the other axis it would be x2 0 and x1
+equal to maximum rc
+
+ align:start position:0%
+equal to maximum rc
+ 
+
+ align:start position:0%
+equal to maximum rc
+so you can see how this works we create
+
+ align:start position:0%
+so you can see how this works we create
+ 
+
+ align:start position:0%
+so you can see how this works we create
+the feasible space we've
+
+ align:start position:0%
+the feasible space we've
+ 
+
+ align:start position:0%
+the feasible space we've
+designed an objective function z
+
+ align:start position:0%
+designed an objective function z
+ 
+
+ align:start position:0%
+designed an objective function z
+and we run the z off the edge of this
+
+ align:start position:0%
+and we run the z off the edge of this
+ 
+
+ align:start position:0%
+and we run the z off the edge of this
+convex space it's important to be convex
+
+ align:start position:0%
+convex space it's important to be convex
+ 
+
+ align:start position:0%
+convex space it's important to be convex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how applicable is linear programming
+
+ align:start position:0%
+so how applicable is linear programming
+ 
+
+ align:start position:0%
+so how applicable is linear programming
+and so-called flux balance analysis
+
+ align:start position:0%
+and so-called flux balance analysis
+ 
+
+ align:start position:0%
+and so-called flux balance analysis
+it works when the stoichiometry is well
+
+ align:start position:0%
+it works when the stoichiometry is well
+ 
+
+ align:start position:0%
+it works when the stoichiometry is well
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+for e coli it's well known for newly
+
+ align:start position:0%
+for e coli it's well known for newly
+ 
+
+ align:start position:0%
+for e coli it's well known for newly
+sequenced genomes we can make
+
+ align:start position:0%
+sequenced genomes we can make
+ 
+
+ align:start position:0%
+sequenced genomes we can make
+connections to previous
+
+ align:start position:0%
+connections to previous
+ 
+
+ align:start position:0%
+connections to previous
+enzymatic reactions and we can guess
+
+ align:start position:0%
+enzymatic reactions and we can guess
+ 
+
+ align:start position:0%
+enzymatic reactions and we can guess
+that what the stoichiometric matrix
+
+ align:start position:0%
+that what the stoichiometric matrix
+ 
+
+ align:start position:0%
+that what the stoichiometric matrix
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+but in that case the stoichiometry is
+
+ align:start position:0%
+but in that case the stoichiometry is
+ 
+
+ align:start position:0%
+but in that case the stoichiometry is
+less well-known and in which case you're
+
+ align:start position:0%
+less well-known and in which case you're
+ 
+
+ align:start position:0%
+less well-known and in which case you're
+going to have to really embrace your
+
+ align:start position:0%
+going to have to really embrace your
+ 
+
+ align:start position:0%
+going to have to really embrace your
+outliers when you get to the end you're
+
+ align:start position:0%
+outliers when you get to the end you're
+ 
+
+ align:start position:0%
+outliers when you get to the end you're
+going to see all the errors and go back
+
+ align:start position:0%
+going to see all the errors and go back
+ 
+
+ align:start position:0%
+going to see all the errors and go back
+and figure out what was wrong with our
+
+ align:start position:0%
+and figure out what was wrong with our
+ 
+
+ align:start position:0%
+and figure out what was wrong with our
+stoichiometric matrix derived from our
+
+ align:start position:0%
+stoichiometric matrix derived from our
+ 
+
+ align:start position:0%
+stoichiometric matrix derived from our
+genome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't need much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experimental information to run this
+
+ align:start position:0%
+experimental information to run this
+ 
+
+ align:start position:0%
+experimental information to run this
+but you you need some and we'll we'll
+
+ align:start position:0%
+but you you need some and we'll we'll
+ 
+
+ align:start position:0%
+but you you need some and we'll we'll
+explore two of them or at least to test
+
+ align:start position:0%
+explore two of them or at least to test
+ 
+
+ align:start position:0%
+explore two of them or at least to test
+how it how it's going to to do data
+
+ align:start position:0%
+how it how it's going to to do data
+ 
+
+ align:start position:0%
+how it how it's going to to do data
+so what are the
+
+ align:start position:0%
+so what are the
+ 
+
+ align:start position:0%
+so what are the
+precursors to cell growth
+
+ align:start position:0%
+precursors to cell growth
+ 
+
+ align:start position:0%
+precursors to cell growth
+that we are
+
+ align:start position:0%
+that we are
+ 
+
+ align:start position:0%
+that we are
+monitoring as a z function okay
+
+ align:start position:0%
+monitoring as a z function okay
+ 
+
+ align:start position:0%
+monitoring as a z function okay
+we want to come up with define this
+
+ align:start position:0%
+we want to come up with define this
+ 
+
+ align:start position:0%
+we want to come up with define this
+growth function
+
+ align:start position:0%
+growth function
+ 
+
+ align:start position:0%
+growth function
+in terms of biomass
+
+ align:start position:0%
+in terms of biomass
+ 
+
+ align:start position:0%
+in terms of biomass
+and there's like i say there's tables of
+
+ align:start position:0%
+and there's like i say there's tables of
+ 
+
+ align:start position:0%
+and there's like i say there's tables of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+composition we'll show one in a couple
+
+ align:start position:0%
+composition we'll show one in a couple
+ 
+
+ align:start position:0%
+composition we'll show one in a couple
+of slides
+
+ align:start position:0%
+of slides
+ 
+
+ align:start position:0%
+of slides
+but you can use this as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part of the complete metabolic network
+
+ align:start position:0%
+part of the complete metabolic network
+ 
+
+ align:start position:0%
+part of the complete metabolic network
+you can also use the observation
+
+ align:start position:0%
+you can also use the observation
+ 
+
+ align:start position:0%
+you can also use the observation
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+it can be described as some small number
+
+ align:start position:0%
+it can be described as some small number
+ 
+
+ align:start position:0%
+it can be described as some small number
+of biosynthetic precursors plus the
+
+ align:start position:0%
+of biosynthetic precursors plus the
+ 
+
+ align:start position:0%
+of biosynthetic precursors plus the
+energy and redox cofactors
+
+ align:start position:0%
+energy and redox cofactors
+ 
+
+ align:start position:0%
+energy and redox cofactors
+now there are many ways of doing in
+
+ align:start position:0%
+now there are many ways of doing in
+ 
+
+ align:start position:0%
+now there are many ways of doing in
+silico cells we show red blood cells
+
+ align:start position:0%
+silico cells we show red blood cells
+ 
+
+ align:start position:0%
+silico cells we show red blood cells
+ordinary addition equation
+
+ align:start position:0%
+ordinary addition equation
+ 
+
+ align:start position:0%
+ordinary addition equation
+the kind of in silica cells here with
+
+ align:start position:0%
+the kind of in silica cells here with
+ 
+
+ align:start position:0%
+the kind of in silica cells here with
+optimization is fairly limited the
+
+ align:start position:0%
+optimization is fairly limited the
+ 
+
+ align:start position:0%
+optimization is fairly limited the
+stoichiometric matrices have only been
+
+ align:start position:0%
+stoichiometric matrices have only been
+ 
+
+ align:start position:0%
+stoichiometric matrices have only been
+worked out for three maybe five cells
+
+ align:start position:0%
+worked out for three maybe five cells
+ 
+
+ align:start position:0%
+worked out for three maybe five cells
+three published
+
+ align:start position:0%
+three published
+ 
+
+ align:start position:0%
+three published
+yeast is on its way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is these are mostly hand
+
+ align:start position:0%
+and this is these are mostly hand
+ 
+
+ align:start position:0%
+and this is these are mostly hand
+curated there is definitely a need for
+
+ align:start position:0%
+curated there is definitely a need for
+ 
+
+ align:start position:0%
+curated there is definitely a need for
+getting a more automated input from
+
+ align:start position:0%
+getting a more automated input from
+ 
+
+ align:start position:0%
+getting a more automated input from
+genomic models to these
+
+ align:start position:0%
+genomic models to these
+ 
+
+ align:start position:0%
+genomic models to these
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+analyses
+
+ align:start position:0%
+analyses
+ 
+
+ align:start position:0%
+analyses
+here's some references here we'll be
+
+ align:start position:0%
+here's some references here we'll be
+ 
+
+ align:start position:0%
+here's some references here we'll be
+talking in a moment
+
+ align:start position:0%
+talking in a moment
+ 
+
+ align:start position:0%
+talking in a moment
+first we'll talk about the wild type
+
+ align:start position:0%
+first we'll talk about the wild type
+ 
+
+ align:start position:0%
+first we'll talk about the wild type
+case for each of these cells under a
+
+ align:start position:0%
+case for each of these cells under a
+ 
+
+ align:start position:0%
+case for each of these cells under a
+variety of different growth conditions
+
+ align:start position:0%
+variety of different growth conditions
+ 
+
+ align:start position:0%
+variety of different growth conditions
+then we'll move on to mutants and ask
+
+ align:start position:0%
+then we'll move on to mutants and ask
+ 
+
+ align:start position:0%
+then we'll move on to mutants and ask
+whether mutants or we expect to be
+
+ align:start position:0%
+whether mutants or we expect to be
+ 
+
+ align:start position:0%
+whether mutants or we expect to be
+optimal or not
+
+ align:start position:0%
+optimal or not
+ 
+
+ align:start position:0%
+optimal or not
+and that will be called minimization of
+
+ align:start position:0%
+and that will be called minimization of
+ 
+
+ align:start position:0%
+and that will be called minimization of
+metabolic adjustment
+
+ align:start position:0%
+metabolic adjustment
+ 
+
+ align:start position:0%
+metabolic adjustment
+now where do these stoichiometric
+
+ align:start position:0%
+now where do these stoichiometric
+ 
+
+ align:start position:0%
+now where do these stoichiometric
+matrices come from
+
+ align:start position:0%
+matrices come from
+ 
+
+ align:start position:0%
+matrices come from
+parenthetically the kinetic parameters
+
+ align:start position:0%
+parenthetically the kinetic parameters
+ 
+
+ align:start position:0%
+parenthetically the kinetic parameters
+that we're talking about
+
+ align:start position:0%
+that we're talking about
+ 
+
+ align:start position:0%
+that we're talking about
+are known for some of these complicated
+
+ align:start position:0%
+are known for some of these complicated
+ 
+
+ align:start position:0%
+are known for some of these complicated
+biochemical systems not just for red
+
+ align:start position:0%
+biochemical systems not just for red
+ 
+
+ align:start position:0%
+biochemical systems not just for red
+blood cell
+
+ align:start position:0%
+blood cell
+ 
+
+ align:start position:0%
+blood cell
+and where both the stoichiometric
+
+ align:start position:0%
+and where both the stoichiometric
+ 
+
+ align:start position:0%
+and where both the stoichiometric
+matrices and the kinetic parameters come
+
+ align:start position:0%
+matrices and the kinetic parameters come
+ 
+
+ align:start position:0%
+matrices and the kinetic parameters come
+from of course is a vast literature it's
+
+ align:start position:0%
+from of course is a vast literature it's
+ 
+
+ align:start position:0%
+from of course is a vast literature it's
+an unwieldy literature in the sense it
+
+ align:start position:0%
+an unwieldy literature in the sense it
+ 
+
+ align:start position:0%
+an unwieldy literature in the sense it
+was done at the time before anybody
+
+ align:start position:0%
+was done at the time before anybody
+ 
+
+ align:start position:0%
+was done at the time before anybody
+thought that we were going to be that
+
+ align:start position:0%
+thought that we were going to be that
+ 
+
+ align:start position:0%
+thought that we were going to be that
+they were going to be responsible for
+
+ align:start position:0%
+they were going to be responsible for
+ 
+
+ align:start position:0%
+they were going to be responsible for
+getting this into
+
+ align:start position:0%
+getting this into
+ 
+
+ align:start position:0%
+getting this into
+computer parcelable databases
+
+ align:start position:0%
+computer parcelable databases
+ 
+
+ align:start position:0%
+computer parcelable databases
+so it's mostly been re-entered
+
+ align:start position:0%
+so it's mostly been re-entered
+ 
+
+ align:start position:0%
+so it's mostly been re-entered
+by technicians into databases and you'll
+
+ align:start position:0%
+by technicians into databases and you'll
+ 
+
+ align:start position:0%
+by technicians into databases and you'll
+end up with these diagrams such as the
+
+ align:start position:0%
+end up with these diagrams such as the
+ 
+
+ align:start position:0%
+end up with these diagrams such as the
+central one where
+
+ align:start position:0%
+central one where
+ 
+
+ align:start position:0%
+central one where
+each of these boxes contains a is a node
+
+ align:start position:0%
+each of these boxes contains a is a node
+ 
+
+ align:start position:0%
+each of these boxes contains a is a node
+that contains a substrate and the lines
+
+ align:start position:0%
+that contains a substrate and the lines
+ 
+
+ align:start position:0%
+that contains a substrate and the lines
+are have enzyme commission numbers this
+
+ align:start position:0%
+are have enzyme commission numbers this
+ 
+
+ align:start position:0%
+are have enzyme commission numbers this
+you know this dotted you know this is a
+
+ align:start position:0%
+you know this dotted you know this is a
+ 
+
+ align:start position:0%
+you know this dotted you know this is a
+decimal
+
+ align:start position:0%
+decimal
+ 
+
+ align:start position:0%
+decimal
+multiple decimal point uh showing a
+
+ align:start position:0%
+multiple decimal point uh showing a
+ 
+
+ align:start position:0%
+multiple decimal point uh showing a
+hierarchical classification
+
+ align:start position:0%
+hierarchical classification
+ 
+
+ align:start position:0%
+hierarchical classification
+going from left to right getting more
+
+ align:start position:0%
+going from left to right getting more
+ 
+
+ align:start position:0%
+going from left to right getting more
+and more detailed in the enzymatic
+
+ align:start position:0%
+and more detailed in the enzymatic
+ 
+
+ align:start position:0%
+and more detailed in the enzymatic
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is built up in a database and from
+
+ align:start position:0%
+this is built up in a database and from
+ 
+
+ align:start position:0%
+this is built up in a database and from
+this you can
+
+ align:start position:0%
+this you can
+ 
+
+ align:start position:0%
+this you can
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+access such things as effects of kinetic
+
+ align:start position:0%
+access such things as effects of kinetic
+ 
+
+ align:start position:0%
+access such things as effects of kinetic
+constants effects of ph
+
+ align:start position:0%
+constants effects of ph
+ 
+
+ align:start position:0%
+constants effects of ph
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and other details
+
+ align:start position:0%
+and and other details
+ 
+
+ align:start position:0%
+and and other details
+and also from this you can get the
+
+ align:start position:0%
+and also from this you can get the
+ 
+
+ align:start position:0%
+and also from this you can get the
+stoichiometric uh matrices in principle
+
+ align:start position:0%
+stoichiometric uh matrices in principle
+ 
+
+ align:start position:0%
+stoichiometric uh matrices in principle
+because here you can see that you've got
+
+ align:start position:0%
+because here you can see that you've got
+ 
+
+ align:start position:0%
+because here you can see that you've got
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+input of adp plus glucose 6-phosphate
+
+ align:start position:0%
+input of adp plus glucose 6-phosphate
+ 
+
+ align:start position:0%
+input of adp plus glucose 6-phosphate
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+going into this reaction or coming out
+
+ align:start position:0%
+going into this reaction or coming out
+ 
+
+ align:start position:0%
+going into this reaction or coming out
+depending on which direction you're
+
+ align:start position:0%
+depending on which direction you're
+ 
+
+ align:start position:0%
+depending on which direction you're
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+and so those convert to zeros and ones
+
+ align:start position:0%
+and so those convert to zeros and ones
+ 
+
+ align:start position:0%
+and so those convert to zeros and ones
+in the matrix
+
+ align:start position:0%
+in the matrix
+ 
+
+ align:start position:0%
+in the matrix
+that's the source of the stoichiometric
+
+ align:start position:0%
+that's the source of the stoichiometric
+ 
+
+ align:start position:0%
+that's the source of the stoichiometric
+matrix which tells you what reactions
+
+ align:start position:0%
+matrix which tells you what reactions
+ 
+
+ align:start position:0%
+matrix which tells you what reactions
+are allowed what two
+
+ align:start position:0%
+are allowed what two
+ 
+
+ align:start position:0%
+are allowed what two
+things can come together or one
+
+ align:start position:0%
+things can come together or one
+ 
+
+ align:start position:0%
+things can come together or one
+thing can be converted by the various
+
+ align:start position:0%
+thing can be converted by the various
+ 
+
+ align:start position:0%
+thing can be converted by the various
+enzymes that actually exist in cells and
+
+ align:start position:0%
+enzymes that actually exist in cells and
+ 
+
+ align:start position:0%
+enzymes that actually exist in cells and
+you can toggle those on and off either
+
+ align:start position:0%
+you can toggle those on and off either
+ 
+
+ align:start position:0%
+you can toggle those on and off either
+by regulation or by evolutionary change
+
+ align:start position:0%
+by regulation or by evolutionary change
+ 
+
+ align:start position:0%
+by regulation or by evolutionary change
+or by genetic manipulation or
+
+ align:start position:0%
+or by genetic manipulation or
+ 
+
+ align:start position:0%
+or by genetic manipulation or
+mutagenesis you can basically have a
+
+ align:start position:0%
+mutagenesis you can basically have a
+ 
+
+ align:start position:0%
+mutagenesis you can basically have a
+universal matrix and you toggle on only
+
+ align:start position:0%
+universal matrix and you toggle on only
+ 
+
+ align:start position:0%
+universal matrix and you toggle on only
+the ones that you think happen in your
+
+ align:start position:0%
+the ones that you think happen in your
+ 
+
+ align:start position:0%
+the ones that you think happen in your
+organism
+
+ align:start position:0%
+organism
+ 
+
+ align:start position:0%
+organism
+that's how you get the stoichiometric
+
+ align:start position:0%
+that's how you get the stoichiometric
+ 
+
+ align:start position:0%
+that's how you get the stoichiometric
+matrix how you get the optimization
+
+ align:start position:0%
+matrix how you get the optimization
+ 
+
+ align:start position:0%
+matrix how you get the optimization
+function the z function to tell which is
+
+ align:start position:0%
+function the z function to tell which is
+ 
+
+ align:start position:0%
+function the z function to tell which is
+what how you want to make those
+
+ align:start position:0%
+what how you want to make those
+ 
+
+ align:start position:0%
+what how you want to make those
+decisions how much x1 and how much x2
+
+ align:start position:0%
+decisions how much x1 and how much x2
+ 
+
+ align:start position:0%
+decisions how much x1 and how much x2
+this is dependent on the biomass
+
+ align:start position:0%
+this is dependent on the biomass
+ 
+
+ align:start position:0%
+this is dependent on the biomass
+composition and the biomass composition
+
+ align:start position:0%
+composition and the biomass composition
+ 
+
+ align:start position:0%
+composition and the biomass composition
+as we you know said we have
+
+ align:start position:0%
+as we you know said we have
+ 
+
+ align:start position:0%
+as we you know said we have
+on the vertical axis here is the
+
+ align:start position:0%
+on the vertical axis here is the
+ 
+
+ align:start position:0%
+on the vertical axis here is the
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+in the growth reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which ranges here over almost eight logs
+
+ align:start position:0%
+which ranges here over almost eight logs
+ 
+
+ align:start position:0%
+which ranges here over almost eight logs
+from the from the lowest uh
+
+ align:start position:0%
+from the from the lowest uh
+ 
+
+ align:start position:0%
+from the from the lowest uh
+compositional
+
+ align:start position:0%
+compositional
+ 
+
+ align:start position:0%
+compositional
+fraction which are some of these
+
+ align:start position:0%
+fraction which are some of these
+ 
+
+ align:start position:0%
+fraction which are some of these
+coenzymes so just like enzymes they only
+
+ align:start position:0%
+coenzymes so just like enzymes they only
+ 
+
+ align:start position:0%
+coenzymes so just like enzymes they only
+need in
+
+ align:start position:0%
+need in
+ 
+
+ align:start position:0%
+need in
+small amounts
+
+ align:start position:0%
+small amounts
+ 
+
+ align:start position:0%
+small amounts
+to these that are needed both for
+
+ align:start position:0%
+to these that are needed both for
+ 
+
+ align:start position:0%
+to these that are needed both for
+major
+
+ align:start position:0%
+major
+ 
+
+ align:start position:0%
+major
+participants in hundreds of reactions
+
+ align:start position:0%
+participants in hundreds of reactions
+ 
+
+ align:start position:0%
+participants in hundreds of reactions
+like atp
+
+ align:start position:0%
+like atp
+ 
+
+ align:start position:0%
+like atp
+some of which contribute heavily to
+
+ align:start position:0%
+some of which contribute heavily to
+ 
+
+ align:start position:0%
+some of which contribute heavily to
+biomass so atp also contributes to
+
+ align:start position:0%
+biomass so atp also contributes to
+ 
+
+ align:start position:0%
+biomass so atp also contributes to
+you know large biomass like ribosomal
+
+ align:start position:0%
+you know large biomass like ribosomal
+ 
+
+ align:start position:0%
+you know large biomass like ribosomal
+rna
+
+ align:start position:0%
+rna
+ 
+
+ align:start position:0%
+rna
+and then the various amino acids which
+
+ align:start position:0%
+and then the various amino acids which
+ 
+
+ align:start position:0%
+and then the various amino acids which
+tend to be some of these
+
+ align:start position:0%
+tend to be some of these
+ 
+
+ align:start position:0%
+tend to be some of these
+many of these stars up at the higher
+
+ align:start position:0%
+many of these stars up at the higher
+ 
+
+ align:start position:0%
+many of these stars up at the higher
+levels like lysine leucine and the other
+
+ align:start position:0%
+levels like lysine leucine and the other
+ 
+
+ align:start position:0%
+levels like lysine leucine and the other
+18 amino acids
+
+ align:start position:0%
+18 amino acids
+ 
+
+ align:start position:0%
+18 amino acids
+okay so this these are
+
+ align:start position:0%
+okay so this these are
+ 
+
+ align:start position:0%
+okay so this these are
+examples of the numbers that would go
+
+ align:start position:0%
+examples of the numbers that would go
+ 
+
+ align:start position:0%
+examples of the numbers that would go
+into the
+
+ align:start position:0%
+into the
+ 
+
+ align:start position:0%
+into the
+optimization curve here these red
+
+ align:start position:0%
+optimization curve here these red
+ 
+
+ align:start position:0%
+optimization curve here these red
+hyperplanes
+
+ align:start position:0%
+hyperplanes
+ 
+
+ align:start position:0%
+hyperplanes
+would be that linear sum in the ratios
+
+ align:start position:0%
+would be that linear sum in the ratios
+ 
+
+ align:start position:0%
+would be that linear sum in the ratios
+in the previous slide
+
+ align:start position:0%
+in the previous slide
+ 
+
+ align:start position:0%
+in the previous slide
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've already seen we've already worked
+
+ align:start position:0%
+we've already seen we've already worked
+ 
+
+ align:start position:0%
+we've already seen we've already worked
+through an example where we slid one of
+
+ align:start position:0%
+through an example where we slid one of
+ 
+
+ align:start position:0%
+through an example where we slid one of
+these hyperplanes off the edge of in a
+
+ align:start position:0%
+these hyperplanes off the edge of in a
+ 
+
+ align:start position:0%
+these hyperplanes off the edge of in a
+two-dimensional model and got the
+
+ align:start position:0%
+two-dimensional model and got the
+ 
+
+ align:start position:0%
+two-dimensional model and got the
+optimum production of a particular
+
+ align:start position:0%
+optimum production of a particular
+ 
+
+ align:start position:0%
+optimum production of a particular
+substance d
+
+ align:start position:0%
+substance d
+ 
+
+ align:start position:0%
+substance d
+but now we're trying to optimize this
+
+ align:start position:0%
+but now we're trying to optimize this
+ 
+
+ align:start position:0%
+but now we're trying to optimize this
+linear sum of all the
+
+ align:start position:0%
+linear sum of all the
+ 
+
+ align:start position:0%
+linear sum of all the
+metabolites that go into the body of the
+
+ align:start position:0%
+metabolites that go into the body of the
+ 
+
+ align:start position:0%
+metabolites that go into the body of the
+organism
+
+ align:start position:0%
+organism
+ 
+
+ align:start position:0%
+organism
+and just focus on the green feasible
+
+ align:start position:0%
+and just focus on the green feasible
+ 
+
+ align:start position:0%
+and just focus on the green feasible
+space it's actually some of it's hidden
+
+ align:start position:0%
+space it's actually some of it's hidden
+ 
+
+ align:start position:0%
+space it's actually some of it's hidden
+behind the yellow but imagine this this
+
+ align:start position:0%
+behind the yellow but imagine this this
+ 
+
+ align:start position:0%
+behind the yellow but imagine this this
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+convex polyhedron
+
+ align:start position:0%
+convex polyhedron
+ 
+
+ align:start position:0%
+convex polyhedron
+of green which is feasible space fs for
+
+ align:start position:0%
+of green which is feasible space fs for
+ 
+
+ align:start position:0%
+of green which is feasible space fs for
+wild type wt
+
+ align:start position:0%
+wild type wt
+ 
+
+ align:start position:0%
+wild type wt
+and you can get an optimum you assume
+
+ align:start position:0%
+and you can get an optimum you assume
+ 
+
+ align:start position:0%
+and you can get an optimum you assume
+that this optim whatever the conditions
+
+ align:start position:0%
+that this optim whatever the conditions
+ 
+
+ align:start position:0%
+that this optim whatever the conditions
+that you're looking at
+
+ align:start position:0%
+that you're looking at
+ 
+
+ align:start position:0%
+that you're looking at
+has uh
+
+ align:start position:0%
+has uh
+ 
+
+ align:start position:0%
+has uh
+is likely to be achieved because for
+
+ align:start position:0%
+is likely to be achieved because for
+ 
+
+ align:start position:0%
+is likely to be achieved because for
+millions
+
+ align:start position:0%
+millions
+ 
+
+ align:start position:0%
+millions
+uh of years this organism has been
+
+ align:start position:0%
+uh of years this organism has been
+ 
+
+ align:start position:0%
+uh of years this organism has been
+living through all the different growth
+
+ align:start position:0%
+living through all the different growth
+ 
+
+ align:start position:0%
+living through all the different growth
+scenarios growth on glucose
+
+ align:start position:0%
+scenarios growth on glucose
+ 
+
+ align:start position:0%
+scenarios growth on glucose
+galactose various nitrogen sources and
+
+ align:start position:0%
+galactose various nitrogen sources and
+ 
+
+ align:start position:0%
+galactose various nitrogen sources and
+so forth so
+
+ align:start position:0%
+so forth so
+ 
+
+ align:start position:0%
+so forth so
+no matter what reasonable set of
+
+ align:start position:0%
+no matter what reasonable set of
+ 
+
+ align:start position:0%
+no matter what reasonable set of
+conditions you throw at it it's seen
+
+ align:start position:0%
+conditions you throw at it it's seen
+ 
+
+ align:start position:0%
+conditions you throw at it it's seen
+something like that before or some other
+
+ align:start position:0%
+something like that before or some other
+ 
+
+ align:start position:0%
+something like that before or some other
+combinations and so it's optimal for it
+
+ align:start position:0%
+combinations and so it's optimal for it
+ 
+
+ align:start position:0%
+combinations and so it's optimal for it
+and that's what that that that
+
+ align:start position:0%
+and that's what that that that
+ 
+
+ align:start position:0%
+and that's what that that that
+top
+
+ align:start position:0%
+top
+ 
+
+ align:start position:0%
+top
+right red dot means that's the option
+
+ align:start position:0%
+right red dot means that's the option
+ 
+
+ align:start position:0%
+right red dot means that's the option
+for the wild type moving this hyper
+
+ align:start position:0%
+for the wild type moving this hyper
+ 
+
+ align:start position:0%
+for the wild type moving this hyper
+plane which is the growth the sum of all
+
+ align:start position:0%
+plane which is the growth the sum of all
+ 
+
+ align:start position:0%
+plane which is the growth the sum of all
+the different growth components in the
+
+ align:start position:0%
+the different growth components in the
+ 
+
+ align:start position:0%
+the different growth components in the
+correct ratio so if you're going to
+
+ align:start position:0%
+correct ratio so if you're going to
+ 
+
+ align:start position:0%
+correct ratio so if you're going to
+optimize all those decisions x1s and x2s
+
+ align:start position:0%
+optimize all those decisions x1s and x2s
+ 
+
+ align:start position:0%
+optimize all those decisions x1s and x2s
+so that you get the right ratios so you
+
+ align:start position:0%
+so that you get the right ratios so you
+ 
+
+ align:start position:0%
+so that you get the right ratios so you
+don't get way too much say of some rare
+
+ align:start position:0%
+don't get way too much say of some rare
+ 
+
+ align:start position:0%
+don't get way too much say of some rare
+amino acid like tryptophan and not
+
+ align:start position:0%
+amino acid like tryptophan and not
+ 
+
+ align:start position:0%
+amino acid like tryptophan and not
+enough of the glycine say that's
+
+ align:start position:0%
+enough of the glycine say that's
+ 
+
+ align:start position:0%
+enough of the glycine say that's
+or alanine it's most common
+
+ align:start position:0%
+or alanine it's most common
+ 
+
+ align:start position:0%
+or alanine it's most common
+that's great for wild type under a
+
+ align:start position:0%
+that's great for wild type under a
+ 
+
+ align:start position:0%
+that's great for wild type under a
+variety of different growth conditions
+
+ align:start position:0%
+variety of different growth conditions
+ 
+
+ align:start position:0%
+variety of different growth conditions
+but what if you throw a real
+
+ align:start position:0%
+but what if you throw a real
+ 
+
+ align:start position:0%
+but what if you throw a real
+curveball and say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not give it a condition but but give it
+
+ align:start position:0%
+not give it a condition but but give it
+ 
+
+ align:start position:0%
+not give it a condition but but give it
+a perturbation it really doesn't see
+
+ align:start position:0%
+a perturbation it really doesn't see
+ 
+
+ align:start position:0%
+a perturbation it really doesn't see
+very often if at all which would be to
+
+ align:start position:0%
+very often if at all which would be to
+ 
+
+ align:start position:0%
+very often if at all which would be to
+knock out a gene completely by deletion
+
+ align:start position:0%
+knock out a gene completely by deletion
+ 
+
+ align:start position:0%
+knock out a gene completely by deletion
+or conceivably knock in a gene add a
+
+ align:start position:0%
+or conceivably knock in a gene add a
+ 
+
+ align:start position:0%
+or conceivably knock in a gene add a
+gene that it hasn't seen before very
+
+ align:start position:0%
+gene that it hasn't seen before very
+ 
+
+ align:start position:0%
+gene that it hasn't seen before very
+often
+
+ align:start position:0%
+often
+ 
+
+ align:start position:0%
+often
+well now you could say we're going to do
+
+ align:start position:0%
+well now you could say we're going to do
+ 
+
+ align:start position:0%
+well now you could say we're going to do
+the same optimization we'll run the same
+
+ align:start position:0%
+the same optimization we'll run the same
+ 
+
+ align:start position:0%
+the same optimization we'll run the same
+red hyper plane through the new phase so
+
+ align:start position:0%
+red hyper plane through the new phase so
+ 
+
+ align:start position:0%
+red hyper plane through the new phase so
+the new feasible space is
+
+ align:start position:0%
+the new feasible space is
+ 
+
+ align:start position:0%
+the new feasible space is
+reduced if it's a knockout could be
+
+ align:start position:0%
+reduced if it's a knockout could be
+ 
+
+ align:start position:0%
+reduced if it's a knockout could be
+increased if it's a knock in where
+
+ align:start position:0%
+increased if it's a knock in where
+ 
+
+ align:start position:0%
+increased if it's a knock in where
+you're adding a gene but if in this
+
+ align:start position:0%
+you're adding a gene but if in this
+ 
+
+ align:start position:0%
+you're adding a gene but if in this
+reduced space the the original optimum
+
+ align:start position:0%
+reduced space the the original optimum
+ 
+
+ align:start position:0%
+reduced space the the original optimum
+is no longer accessible and if you rerun
+
+ align:start position:0%
+is no longer accessible and if you rerun
+ 
+
+ align:start position:0%
+is no longer accessible and if you rerun
+the optimization running this plane off
+
+ align:start position:0%
+the optimization running this plane off
+ 
+
+ align:start position:0%
+the optimization running this plane off
+the edge you'll find a new red dot in
+
+ align:start position:0%
+the edge you'll find a new red dot in
+ 
+
+ align:start position:0%
+the edge you'll find a new red dot in
+the yellow space
+
+ align:start position:0%
+the yellow space
+ 
+
+ align:start position:0%
+the yellow space
+which is a knockout optimum
+
+ align:start position:0%
+which is a knockout optimum
+ 
+
+ align:start position:0%
+which is a knockout optimum
+but that could take after you do the
+
+ align:start position:0%
+but that could take after you do the
+ 
+
+ align:start position:0%
+but that could take after you do the
+knockout it could take evolutionary
+
+ align:start position:0%
+knockout it could take evolutionary
+ 
+
+ align:start position:0%
+knockout it could take evolutionary
+times or at least long lab times
+
+ align:start position:0%
+times or at least long lab times
+ 
+
+ align:start position:0%
+times or at least long lab times
+to allow all the other
+
+ align:start position:0%
+to allow all the other
+ 
+
+ align:start position:0%
+to allow all the other
+genes to mutate and be selected so they
+
+ align:start position:0%
+genes to mutate and be selected so they
+ 
+
+ align:start position:0%
+genes to mutate and be selected so they
+accommodate this new knockout
+
+ align:start position:0%
+accommodate this new knockout
+ 
+
+ align:start position:0%
+accommodate this new knockout
+that the wild type had plenty of time to
+
+ align:start position:0%
+that the wild type had plenty of time to
+ 
+
+ align:start position:0%
+that the wild type had plenty of time to
+do that had millions of years
+
+ align:start position:0%
+do that had millions of years
+ 
+
+ align:start position:0%
+do that had millions of years
+the yellow feasible space for the
+
+ align:start position:0%
+the yellow feasible space for the
+ 
+
+ align:start position:0%
+the yellow feasible space for the
+knockout may not have had that so you
+
+ align:start position:0%
+knockout may not have had that so you
+ 
+
+ align:start position:0%
+knockout may not have had that so you
+want to know what's this immediate
+
+ align:start position:0%
+want to know what's this immediate
+ 
+
+ align:start position:0%
+want to know what's this immediate
+response and for its immediate response
+
+ align:start position:0%
+response and for its immediate response
+ 
+
+ align:start position:0%
+response and for its immediate response
+you might imagine is you know showing
+
+ align:start position:0%
+you might imagine is you know showing
+ 
+
+ align:start position:0%
+you might imagine is you know showing
+here is an orthogonal
+
+ align:start position:0%
+here is an orthogonal
+ 
+
+ align:start position:0%
+here is an orthogonal
+you know a closest distance think of
+
+ align:start position:0%
+you know a closest distance think of
+ 
+
+ align:start position:0%
+you know a closest distance think of
+this as an euclidean distance
+
+ align:start position:0%
+this as an euclidean distance
+ 
+
+ align:start position:0%
+this as an euclidean distance
+in this multi-dimensional space between
+
+ align:start position:0%
+in this multi-dimensional space between
+ 
+
+ align:start position:0%
+in this multi-dimensional space between
+the wild type optimum and the projection
+
+ align:start position:0%
+the wild type optimum and the projection
+ 
+
+ align:start position:0%
+the wild type optimum and the projection
+onto the feasible space of the mutant
+
+ align:start position:0%
+onto the feasible space of the mutant
+ 
+
+ align:start position:0%
+onto the feasible space of the mutant
+now that distance
+
+ align:start position:0%
+now that distance
+ 
+
+ align:start position:0%
+now that distance
+the distance you should already start to
+
+ align:start position:0%
+the distance you should already start to
+ 
+
+ align:start position:0%
+the distance you should already start to
+be thinking that this is no longer
+
+ align:start position:0%
+be thinking that this is no longer
+ 
+
+ align:start position:0%
+be thinking that this is no longer
+linear programming this may be quadratic
+
+ align:start position:0%
+linear programming this may be quadratic
+ 
+
+ align:start position:0%
+linear programming this may be quadratic
+because the distance is a quadratic
+
+ align:start position:0%
+because the distance is a quadratic
+ 
+
+ align:start position:0%
+because the distance is a quadratic
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll see in particular since
+
+ align:start position:0%
+and we'll see in particular since
+ 
+
+ align:start position:0%
+and we'll see in particular since
+there's certain pathologies where you
+
+ align:start position:0%
+there's certain pathologies where you
+ 
+
+ align:start position:0%
+there's certain pathologies where you
+really are forced to take you can't just
+
+ align:start position:0%
+really are forced to take you can't just
+ 
+
+ align:start position:0%
+really are forced to take you can't just
+take a projection
+
+ align:start position:0%
+take a projection
+ 
+
+ align:start position:0%
+take a projection
+because sometimes those projections
+
+ align:start position:0%
+because sometimes those projections
+ 
+
+ align:start position:0%
+because sometimes those projections
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+can end up in a part of a space which is
+
+ align:start position:0%
+can end up in a part of a space which is
+ 
+
+ align:start position:0%
+can end up in a part of a space which is
+not feasible it's not this projection
+
+ align:start position:0%
+not feasible it's not this projection
+ 
+
+ align:start position:0%
+not feasible it's not this projection
+does not land on the yellow feasible
+
+ align:start position:0%
+does not land on the yellow feasible
+ 
+
+ align:start position:0%
+does not land on the yellow feasible
+space fs of the knockout so what you
+
+ align:start position:0%
+space fs of the knockout so what you
+ 
+
+ align:start position:0%
+space fs of the knockout so what you
+need to do is
+
+ align:start position:0%
+need to do is
+ 
+
+ align:start position:0%
+need to do is
+nudge this
+
+ align:start position:0%
+nudge this
+ 
+
+ align:start position:0%
+nudge this
+purple
+
+ align:start position:0%
+purple
+ 
+
+ align:start position:0%
+purple
+symbol up
+
+ align:start position:0%
+symbol up
+ 
+
+ align:start position:0%
+symbol up
+just to the nearest point of the
+
+ align:start position:0%
+just to the nearest point of the
+ 
+
+ align:start position:0%
+just to the nearest point of the
+feasible space which is minimizes the
+
+ align:start position:0%
+feasible space which is minimizes the
+ 
+
+ align:start position:0%
+feasible space which is minimizes the
+distance to the wild type optimum
+
+ align:start position:0%
+distance to the wild type optimum
+ 
+
+ align:start position:0%
+distance to the wild type optimum
+and still falls in feasible space now
+
+ align:start position:0%
+and still falls in feasible space now
+ 
+
+ align:start position:0%
+and still falls in feasible space now
+this is a quadratic programming
+
+ align:start position:0%
+this is a quadratic programming
+ 
+
+ align:start position:0%
+this is a quadratic programming
+algorithm it's it's really you know just
+
+ align:start position:0%
+algorithm it's it's really you know just
+ 
+
+ align:start position:0%
+algorithm it's it's really you know just
+the linear is very simple to think of is
+
+ align:start position:0%
+the linear is very simple to think of is
+ 
+
+ align:start position:0%
+the linear is very simple to think of is
+just moving this uh
+
+ align:start position:0%
+just moving this uh
+ 
+
+ align:start position:0%
+just moving this uh
+plane off the edge of the convex space
+
+ align:start position:0%
+plane off the edge of the convex space
+ 
+
+ align:start position:0%
+plane off the edge of the convex space
+quadratic programming is a bit more
+
+ align:start position:0%
+quadratic programming is a bit more
+ 
+
+ align:start position:0%
+quadratic programming is a bit more
+complicated but i think you get the idea
+
+ align:start position:0%
+complicated but i think you get the idea
+ 
+
+ align:start position:0%
+complicated but i think you get the idea
+you're minimizing that distance
+
+ align:start position:0%
+you're minimizing that distance
+ 
+
+ align:start position:0%
+you're minimizing that distance
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+with any good modeling exercise there
+
+ align:start position:0%
+with any good modeling exercise there
+ 
+
+ align:start position:0%
+with any good modeling exercise there
+should be some data lurking in the wings
+
+ align:start position:0%
+should be some data lurking in the wings
+ 
+
+ align:start position:0%
+should be some data lurking in the wings
+many of the network models that we will
+
+ align:start position:0%
+many of the network models that we will
+ 
+
+ align:start position:0%
+many of the network models that we will
+do are getting more ambitious than the
+
+ align:start position:0%
+do are getting more ambitious than the
+ 
+
+ align:start position:0%
+do are getting more ambitious than the
+even the massive amounts of data coming
+
+ align:start position:0%
+even the massive amounts of data coming
+ 
+
+ align:start position:0%
+even the massive amounts of data coming
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+there are two
+
+ align:start position:0%
+there are two
+ 
+
+ align:start position:0%
+there are two
+types of data that might lead to mind as
+
+ align:start position:0%
+types of data that might lead to mind as
+ 
+
+ align:start position:0%
+types of data that might lead to mind as
+being appropriate for this uh remember
+
+ align:start position:0%
+being appropriate for this uh remember
+ 
+
+ align:start position:0%
+being appropriate for this uh remember
+we said
+
+ align:start position:0%
+we said
+ 
+
+ align:start position:0%
+we said
+that what the organism has done is
+
+ align:start position:0%
+that what the organism has done is
+ 
+
+ align:start position:0%
+that what the organism has done is
+optimize the use of these networks
+
+ align:start position:0%
+optimize the use of these networks
+ 
+
+ align:start position:0%
+optimize the use of these networks
+so that you can maximize growth so the
+
+ align:start position:0%
+so that you can maximize growth so the
+ 
+
+ align:start position:0%
+so that you can maximize growth so the
+two sources of data that you'd want to
+
+ align:start position:0%
+two sources of data that you'd want to
+ 
+
+ align:start position:0%
+two sources of data that you'd want to
+test this
+
+ align:start position:0%
+test this
+ 
+
+ align:start position:0%
+test this
+with would be the flux state itself
+
+ align:start position:0%
+with would be the flux state itself
+ 
+
+ align:start position:0%
+with would be the flux state itself
+because you're saying you're predicting
+
+ align:start position:0%
+because you're saying you're predicting
+ 
+
+ align:start position:0%
+because you're saying you're predicting
+how much is going to be going in each
+
+ align:start position:0%
+how much is going to be going in each
+ 
+
+ align:start position:0%
+how much is going to be going in each
+flux direction
+
+ align:start position:0%
+flux direction
+ 
+
+ align:start position:0%
+flux direction
+and the growth data so it's you're
+
+ align:start position:0%
+and the growth data so it's you're
+ 
+
+ align:start position:0%
+and the growth data so it's you're
+making predictions
+
+ align:start position:0%
+making predictions
+ 
+
+ align:start position:0%
+making predictions
+that you will optimally use the fluxes
+
+ align:start position:0%
+that you will optimally use the fluxes
+ 
+
+ align:start position:0%
+that you will optimally use the fluxes
+in the network in order to maximize
+
+ align:start position:0%
+in the network in order to maximize
+ 
+
+ align:start position:0%
+in the network in order to maximize
+growth for various mutants
+
+ align:start position:0%
+growth for various mutants
+ 
+
+ align:start position:0%
+growth for various mutants
+and various different conditions of
+
+ align:start position:0%
+and various different conditions of
+ 
+
+ align:start position:0%
+and various different conditions of
+growth different carbon and nitrogen
+
+ align:start position:0%
+growth different carbon and nitrogen
+ 
+
+ align:start position:0%
+growth different carbon and nitrogen
+sources so
+
+ align:start position:0%
+sources so
+ 
+
+ align:start position:0%
+sources so
+here you have
+
+ align:start position:0%
+here you have
+ 
+
+ align:start position:0%
+here you have
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+group in zurich which is among the very
+
+ align:start position:0%
+group in zurich which is among the very
+ 
+
+ align:start position:0%
+group in zurich which is among the very
+few groups that can actually measure the
+
+ align:start position:0%
+few groups that can actually measure the
+ 
+
+ align:start position:0%
+few groups that can actually measure the
+measure the internal fluxes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for metabolic pathways that begin with
+
+ align:start position:0%
+for metabolic pathways that begin with
+ 
+
+ align:start position:0%
+for metabolic pathways that begin with
+say isotopically labeled glucose and end
+
+ align:start position:0%
+say isotopically labeled glucose and end
+ 
+
+ align:start position:0%
+say isotopically labeled glucose and end
+in the various amino acids you can
+
+ align:start position:0%
+in the various amino acids you can
+ 
+
+ align:start position:0%
+in the various amino acids you can
+measure these
+
+ align:start position:0%
+measure these
+ 
+
+ align:start position:0%
+measure these
+we prepared ourselves for this a little
+
+ align:start position:0%
+we prepared ourselves for this a little
+ 
+
+ align:start position:0%
+we prepared ourselves for this a little
+bit in the last class where we talked
+
+ align:start position:0%
+bit in the last class where we talked
+ 
+
+ align:start position:0%
+bit in the last class where we talked
+about isotopomers where you can have
+
+ align:start position:0%
+about isotopomers where you can have
+ 
+
+ align:start position:0%
+about isotopomers where you can have
+different chemical compounds that
+
+ align:start position:0%
+different chemical compounds that
+ 
+
+ align:start position:0%
+different chemical compounds that
+whose
+
+ align:start position:0%
+whose
+ 
+
+ align:start position:0%
+whose
+only difference
+
+ align:start position:0%
+only difference
+ 
+
+ align:start position:0%
+only difference
+they have basically identical
+
+ align:start position:0%
+they have basically identical
+ 
+
+ align:start position:0%
+they have basically identical
+identically
+
+ align:start position:0%
+identically
+ 
+
+ align:start position:0%
+identically
+chemically but in different carbon
+
+ align:start position:0%
+chemically but in different carbon
+ 
+
+ align:start position:0%
+chemically but in different carbon
+positions you have a carbon 13 in one
+
+ align:start position:0%
+positions you have a carbon 13 in one
+ 
+
+ align:start position:0%
+positions you have a carbon 13 in one
+place carbon 12
+
+ align:start position:0%
+place carbon 12
+ 
+
+ align:start position:0%
+place carbon 12
+another and the exact arrangement of
+
+ align:start position:0%
+another and the exact arrangement of
+ 
+
+ align:start position:0%
+another and the exact arrangement of
+carbon 12 and carbon 13s in this will
+
+ align:start position:0%
+carbon 12 and carbon 13s in this will
+ 
+
+ align:start position:0%
+carbon 12 and carbon 13s in this will
+determine the izotopia
+
+ align:start position:0%
+determine the izotopia
+ 
+
+ align:start position:0%
+determine the izotopia
+and if you have
+
+ align:start position:0%
+and if you have
+ 
+
+ align:start position:0%
+and if you have
+mixtures of carbon-12 and carbon-13
+
+ align:start position:0%
+mixtures of carbon-12 and carbon-13
+ 
+
+ align:start position:0%
+mixtures of carbon-12 and carbon-13
+glucose
+
+ align:start position:0%
+glucose
+ 
+
+ align:start position:0%
+glucose
+in the upper
+
+ align:start position:0%
+in the upper
+ 
+
+ align:start position:0%
+in the upper
+left-hand corner of this
+
+ align:start position:0%
+left-hand corner of this
+ 
+
+ align:start position:0%
+left-hand corner of this
+diagram includes glycolysis and pentose
+
+ align:start position:0%
+diagram includes glycolysis and pentose
+ 
+
+ align:start position:0%
+diagram includes glycolysis and pentose
+phosphate and tca cycle
+
+ align:start position:0%
+phosphate and tca cycle
+ 
+
+ align:start position:0%
+phosphate and tca cycle
+this this isotopically labeled glucose
+
+ align:start position:0%
+this this isotopically labeled glucose
+ 
+
+ align:start position:0%
+this this isotopically labeled glucose
+goes through here and then you need a
+
+ align:start position:0%
+goes through here and then you need a
+ 
+
+ align:start position:0%
+goes through here and then you need a
+little bit of modeling that you know
+
+ align:start position:0%
+little bit of modeling that you know
+ 
+
+ align:start position:0%
+little bit of modeling that you know
+that we won't go into
+
+ align:start position:0%
+that we won't go into
+ 
+
+ align:start position:0%
+that we won't go into
+uh that but that does require a
+
+ align:start position:0%
+uh that but that does require a
+ 
+
+ align:start position:0%
+uh that but that does require a
+stoichiometric matrix just like our
+
+ align:start position:0%
+stoichiometric matrix just like our
+ 
+
+ align:start position:0%
+stoichiometric matrix just like our
+optimization modeling does but now very
+
+ align:start position:0%
+optimization modeling does but now very
+ 
+
+ align:start position:0%
+optimization modeling does but now very
+independently of that you need to
+
+ align:start position:0%
+independently of that you need to
+ 
+
+ align:start position:0%
+independently of that you need to
+ask how the isotopes of glucose would
+
+ align:start position:0%
+ask how the isotopes of glucose would
+ 
+
+ align:start position:0%
+ask how the isotopes of glucose would
+make their way into the amino acids and
+
+ align:start position:0%
+make their way into the amino acids and
+ 
+
+ align:start position:0%
+make their way into the amino acids and
+then once you have that then given the
+
+ align:start position:0%
+then once you have that then given the
+ 
+
+ align:start position:0%
+then once you have that then given the
+amino acid ratios by mass spectrum nmr
+
+ align:start position:0%
+amino acid ratios by mass spectrum nmr
+ 
+
+ align:start position:0%
+amino acid ratios by mass spectrum nmr
+you can go back and calculate what the
+
+ align:start position:0%
+you can go back and calculate what the
+ 
+
+ align:start position:0%
+you can go back and calculate what the
+fluxes must have been in here once you
+
+ align:start position:0%
+fluxes must have been in here once you
+ 
+
+ align:start position:0%
+fluxes must have been in here once you
+have those fluxes then you're going to
+
+ align:start position:0%
+have those fluxes then you're going to
+ 
+
+ align:start position:0%
+have those fluxes then you're going to
+ask how close to optimal are they for
+
+ align:start position:0%
+ask how close to optimal are they for
+ 
+
+ align:start position:0%
+ask how close to optimal are they for
+the wild type
+
+ align:start position:0%
+the wild type
+ 
+
+ align:start position:0%
+the wild type
+under one condition for the mutant under
+
+ align:start position:0%
+under one condition for the mutant under
+ 
+
+ align:start position:0%
+under one condition for the mutant under
+the same condition for the wild have
+
+ align:start position:0%
+the same condition for the wild have
+ 
+
+ align:start position:0%
+the same condition for the wild have
+been mutant under different conditions
+
+ align:start position:0%
+been mutant under different conditions
+ 
+
+ align:start position:0%
+been mutant under different conditions
+okay so this is the first class of data
+
+ align:start position:0%
+okay so this is the first class of data
+ 
+
+ align:start position:0%
+okay so this is the first class of data
+that we'll use and it's the internal
+
+ align:start position:0%
+that we'll use and it's the internal
+ 
+
+ align:start position:0%
+that we'll use and it's the internal
+fluxes for wild type and mutants
+
+ align:start position:0%
+fluxes for wild type and mutants
+ 
+
+ align:start position:0%
+fluxes for wild type and mutants
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+look in the upper right hand corner
+
+ align:start position:0%
+look in the upper right hand corner
+ 
+
+ align:start position:0%
+look in the upper right hand corner
+where so you've got in the upper left
+
+ align:start position:0%
+where so you've got in the upper left
+ 
+
+ align:start position:0%
+where so you've got in the upper left
+hand corner is the icon color coded from
+
+ align:start position:0%
+hand corner is the icon color coded from
+ 
+
+ align:start position:0%
+hand corner is the icon color coded from
+the previous slide the upper right hand
+
+ align:start position:0%
+the previous slide the upper right hand
+ 
+
+ align:start position:0%
+the previous slide the upper right hand
+corner is the predictions for wild type
+
+ align:start position:0%
+corner is the predictions for wild type
+ 
+
+ align:start position:0%
+corner is the predictions for wild type
+using the linear programming or fba
+
+ align:start position:0%
+using the linear programming or fba
+ 
+
+ align:start position:0%
+using the linear programming or fba
+model you have predicted fluxes on the
+
+ align:start position:0%
+model you have predicted fluxes on the
+ 
+
+ align:start position:0%
+model you have predicted fluxes on the
+vertical axis
+
+ align:start position:0%
+vertical axis
+ 
+
+ align:start position:0%
+vertical axis
+and experimental fluxes on the
+
+ align:start position:0%
+and experimental fluxes on the
+ 
+
+ align:start position:0%
+and experimental fluxes on the
+horizontal axis
+
+ align:start position:0%
+horizontal axis
+ 
+
+ align:start position:0%
+horizontal axis
+you see here is
+
+ align:start position:0%
+you see here is
+ 
+
+ align:start position:0%
+you see here is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+good correlation coefficient of about 90
+
+ align:start position:0%
+good correlation coefficient of about 90
+ 
+
+ align:start position:0%
+good correlation coefficient of about 90
+plus percent
+
+ align:start position:0%
+plus percent
+ 
+
+ align:start position:0%
+plus percent
+and in and a probability that that this
+
+ align:start position:0%
+and in and a probability that that this
+ 
+
+ align:start position:0%
+and in and a probability that that this
+would you know not be random this is a a
+
+ align:start position:0%
+would you know not be random this is a a
+ 
+
+ align:start position:0%
+would you know not be random this is a a
+positive linear correlation
+
+ align:start position:0%
+positive linear correlation
+ 
+
+ align:start position:0%
+positive linear correlation
+is uh better than 10 to the minus
+
+ align:start position:0%
+is uh better than 10 to the minus
+ 
+
+ align:start position:0%
+is uh better than 10 to the minus
+seventh
+
+ align:start position:0%
+seventh
+ 
+
+ align:start position:0%
+seventh
+very unlikely that happened at random uh
+
+ align:start position:0%
+very unlikely that happened at random uh
+ 
+
+ align:start position:0%
+very unlikely that happened at random uh
+you know that you can focus in on the
+
+ align:start position:0%
+you know that you can focus in on the
+ 
+
+ align:start position:0%
+you know that you can focus in on the
+outliers like number 18 here but overall
+
+ align:start position:0%
+outliers like number 18 here but overall
+ 
+
+ align:start position:0%
+outliers like number 18 here but overall
+it's a good uh i mean and this can allow
+
+ align:start position:0%
+it's a good uh i mean and this can allow
+ 
+
+ align:start position:0%
+it's a good uh i mean and this can allow
+you to ask what experimental or model
+
+ align:start position:0%
+you to ask what experimental or model
+ 
+
+ align:start position:0%
+you to ask what experimental or model
+problems you might have
+
+ align:start position:0%
+problems you might have
+ 
+
+ align:start position:0%
+problems you might have
+but let's ask that's for wild type under
+
+ align:start position:0%
+but let's ask that's for wild type under
+ 
+
+ align:start position:0%
+but let's ask that's for wild type under
+uh you know common growth condition
+
+ align:start position:0%
+uh you know common growth condition
+ 
+
+ align:start position:0%
+uh you know common growth condition
+what about mutant under the same growth
+
+ align:start position:0%
+what about mutant under the same growth
+ 
+
+ align:start position:0%
+what about mutant under the same growth
+condition same
+
+ align:start position:0%
+condition same
+ 
+
+ align:start position:0%
+condition same
+stoichiometric modeling
+
+ align:start position:0%
+stoichiometric modeling
+ 
+
+ align:start position:0%
+stoichiometric modeling
+same measurements
+
+ align:start position:0%
+same measurements
+ 
+
+ align:start position:0%
+same measurements
+now the experimental fluxes versus
+
+ align:start position:0%
+now the experimental fluxes versus
+ 
+
+ align:start position:0%
+now the experimental fluxes versus
+predicted fluxes
+
+ align:start position:0%
+predicted fluxes
+ 
+
+ align:start position:0%
+predicted fluxes
+in the lower left-hand quadrant is
+
+ align:start position:0%
+in the lower left-hand quadrant is
+ 
+
+ align:start position:0%
+in the lower left-hand quadrant is
+almost completely random there's no
+
+ align:start position:0%
+almost completely random there's no
+ 
+
+ align:start position:0%
+almost completely random there's no
+positive or negative correlation that's
+
+ align:start position:0%
+positive or negative correlation that's
+ 
+
+ align:start position:0%
+positive or negative correlation that's
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+as we might have expected
+
+ align:start position:0%
+as we might have expected
+ 
+
+ align:start position:0%
+as we might have expected
+for the mutant remember it isn't
+
+ align:start position:0%
+for the mutant remember it isn't
+ 
+
+ align:start position:0%
+for the mutant remember it isn't
+optimal so you don't expect the inner
+
+ align:start position:0%
+optimal so you don't expect the inner
+ 
+
+ align:start position:0%
+optimal so you don't expect the inner
+linear programming method which produces
+
+ align:start position:0%
+linear programming method which produces
+ 
+
+ align:start position:0%
+linear programming method which produces
+the optimum to be appropriate unless we
+
+ align:start position:0%
+the optimum to be appropriate unless we
+ 
+
+ align:start position:0%
+the optimum to be appropriate unless we
+had allowed this to
+
+ align:start position:0%
+had allowed this to
+ 
+
+ align:start position:0%
+had allowed this to
+evolve in the laboratory for hundreds of
+
+ align:start position:0%
+evolve in the laboratory for hundreds of
+ 
+
+ align:start position:0%
+evolve in the laboratory for hundreds of
+generations or a sufficient number
+
+ align:start position:0%
+generations or a sufficient number
+ 
+
+ align:start position:0%
+generations or a sufficient number
+however many that is
+
+ align:start position:0%
+however many that is
+ 
+
+ align:start position:0%
+however many that is
+to get all the other genes or enough of
+
+ align:start position:0%
+to get all the other genes or enough of
+ 
+
+ align:start position:0%
+to get all the other genes or enough of
+the other genes to adapt
+
+ align:start position:0%
+the other genes to adapt
+ 
+
+ align:start position:0%
+the other genes to adapt
+so you get near an optimum in any case
+
+ align:start position:0%
+so you get near an optimum in any case
+ 
+
+ align:start position:0%
+so you get near an optimum in any case
+this one is random if you now use the
+
+ align:start position:0%
+this one is random if you now use the
+ 
+
+ align:start position:0%
+this one is random if you now use the
+quadratic programming approach the moma
+
+ align:start position:0%
+quadratic programming approach the moma
+ 
+
+ align:start position:0%
+quadratic programming approach the moma
+or minimization of metabolic adjustment
+
+ align:start position:0%
+or minimization of metabolic adjustment
+ 
+
+ align:start position:0%
+or minimization of metabolic adjustment
+now get the very exciting result that it
+
+ align:start position:0%
+now get the very exciting result that it
+ 
+
+ align:start position:0%
+now get the very exciting result that it
+now becomes statistically significant
+
+ align:start position:0%
+now becomes statistically significant
+ 
+
+ align:start position:0%
+now becomes statistically significant
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+still a few outliers uh 17 and 16 here
+
+ align:start position:0%
+still a few outliers uh 17 and 16 here
+ 
+
+ align:start position:0%
+still a few outliers uh 17 and 16 here
+in magenta and these are things where
+
+ align:start position:0%
+in magenta and these are things where
+ 
+
+ align:start position:0%
+in magenta and these are things where
+you can now make very specific tests
+
+ align:start position:0%
+you can now make very specific tests
+ 
+
+ align:start position:0%
+you can now make very specific tests
+because now you know
+
+ align:start position:0%
+because now you know
+ 
+
+ align:start position:0%
+because now you know
+which is which ones are most
+
+ align:start position:0%
+which is which ones are most
+ 
+
+ align:start position:0%
+which is which ones are most
+discrepant between the experimental and
+
+ align:start position:0%
+discrepant between the experimental and
+ 
+
+ align:start position:0%
+discrepant between the experimental and
+predicted fluxes and you can go in and
+
+ align:start position:0%
+predicted fluxes and you can go in and
+ 
+
+ align:start position:0%
+predicted fluxes and you can go in and
+ask what part of that model or what part
+
+ align:start position:0%
+ask what part of that model or what part
+ 
+
+ align:start position:0%
+ask what part of that model or what part
+of that data collection might be
+
+ align:start position:0%
+of that data collection might be
+ 
+
+ align:start position:0%
+of that data collection might be
+accounting for the
+
+ align:start position:0%
+accounting for the
+ 
+
+ align:start position:0%
+accounting for the
+poor fit
+
+ align:start position:0%
+poor fit
+ 
+
+ align:start position:0%
+poor fit
+but overall this starts to give one the
+
+ align:start position:0%
+but overall this starts to give one the
+ 
+
+ align:start position:0%
+but overall this starts to give one the
+impression that maybe
+
+ align:start position:0%
+impression that maybe
+ 
+
+ align:start position:0%
+impression that maybe
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the mutants will not be optimal and that
+
+ align:start position:0%
+the mutants will not be optimal and that
+ 
+
+ align:start position:0%
+the mutants will not be optimal and that
+they can be somewhat better served by
+
+ align:start position:0%
+they can be somewhat better served by
+ 
+
+ align:start position:0%
+they can be somewhat better served by
+this not this
+
+ align:start position:0%
+this not this
+ 
+
+ align:start position:0%
+this not this
+quasi-non-optimal solution
+
+ align:start position:0%
+quasi-non-optimal solution
+ 
+
+ align:start position:0%
+quasi-non-optimal solution
+and if you walk through various
+
+ align:start position:0%
+and if you walk through various
+ 
+
+ align:start position:0%
+and if you walk through various
+different conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with different knockouts you can see
+
+ align:start position:0%
+with different knockouts you can see
+ 
+
+ align:start position:0%
+with different knockouts you can see
+multiple examples of this so here in the
+
+ align:start position:0%
+multiple examples of this so here in the
+ 
+
+ align:start position:0%
+multiple examples of this so here in the
+upper left hand quadrant of slide 59
+
+ align:start position:0%
+upper left hand quadrant of slide 59
+ 
+
+ align:start position:0%
+upper left hand quadrant of slide 59
+where we have the carbon limitation
+
+ align:start position:0%
+where we have the carbon limitation
+ 
+
+ align:start position:0%
+where we have the carbon limitation
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+on the far left
+
+ align:start position:0%
+on the far left
+ 
+
+ align:start position:0%
+on the far left
+and then the comparison of the method
+
+ align:start position:0%
+and then the comparison of the method
+ 
+
+ align:start position:0%
+and then the comparison of the method
+for flux balance on wild type
+
+ align:start position:0%
+for flux balance on wild type
+ 
+
+ align:start position:0%
+for flux balance on wild type
+here's that
+
+ align:start position:0%
+here's that
+ 
+
+ align:start position:0%
+here's that
+0.9 correlation coefficient and good
+
+ align:start position:0%
+0.9 correlation coefficient and good
+ 
+
+ align:start position:0%
+0.9 correlation coefficient and good
+p-value
+
+ align:start position:0%
+p-value
+ 
+
+ align:start position:0%
+p-value
+and then comparing moma and fba and
+
+ align:start position:0%
+and then comparing moma and fba and
+ 
+
+ align:start position:0%
+and then comparing moma and fba and
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+the significance of switching from fba
+
+ align:start position:0%
+the significance of switching from fba
+ 
+
+ align:start position:0%
+the significance of switching from fba
+to moma is 3 times 10 to the minus 3
+
+ align:start position:0%
+to moma is 3 times 10 to the minus 3
+ 
+
+ align:start position:0%
+to moma is 3 times 10 to the minus 3
+indicating that the quadratic
+
+ align:start position:0%
+indicating that the quadratic
+ 
+
+ align:start position:0%
+indicating that the quadratic
+programming is the more appropriate
+
+ align:start position:0%
+programming is the more appropriate
+ 
+
+ align:start position:0%
+programming is the more appropriate
+application here and as you walk through
+
+ align:start position:0%
+application here and as you walk through
+ 
+
+ align:start position:0%
+application here and as you walk through
+this you'll see
+
+ align:start position:0%
+this you'll see
+ 
+
+ align:start position:0%
+this you'll see
+many good correlation coefficients and
+
+ align:start position:0%
+many good correlation coefficients and
+ 
+
+ align:start position:0%
+many good correlation coefficients and
+many improvements when you go to the
+
+ align:start position:0%
+many improvements when you go to the
+ 
+
+ align:start position:0%
+many improvements when you go to the
+quadratic or moma
+
+ align:start position:0%
+quadratic or moma
+ 
+
+ align:start position:0%
+quadratic or moma
+not every case but certainly many of
+
+ align:start position:0%
+not every case but certainly many of
+ 
+
+ align:start position:0%
+not every case but certainly many of
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that's one
+
+ align:start position:0%
+now that's one
+ 
+
+ align:start position:0%
+now that's one
+class of tests which is the internal
+
+ align:start position:0%
+class of tests which is the internal
+ 
+
+ align:start position:0%
+class of tests which is the internal
+fluxes which the the
+
+ align:start position:0%
+fluxes which the the
+ 
+
+ align:start position:0%
+fluxes which the the
+idea is that you adjust the internal
+
+ align:start position:0%
+idea is that you adjust the internal
+ 
+
+ align:start position:0%
+idea is that you adjust the internal
+fluxes
+
+ align:start position:0%
+fluxes
+ 
+
+ align:start position:0%
+fluxes
+until they're optimal to produce growth
+
+ align:start position:0%
+until they're optimal to produce growth
+ 
+
+ align:start position:0%
+until they're optimal to produce growth
+well how about measuring growth itself
+
+ align:start position:0%
+well how about measuring growth itself
+ 
+
+ align:start position:0%
+well how about measuring growth itself
+on a set of mutants
+
+ align:start position:0%
+on a set of mutants
+ 
+
+ align:start position:0%
+on a set of mutants
+again these mutants you expect uh
+
+ align:start position:0%
+again these mutants you expect uh
+ 
+
+ align:start position:0%
+again these mutants you expect uh
+will will follow the the moma
+
+ align:start position:0%
+will will follow the the moma
+ 
+
+ align:start position:0%
+will will follow the the moma
+prediction slightly better
+
+ align:start position:0%
+prediction slightly better
+ 
+
+ align:start position:0%
+prediction slightly better
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so slide 60
+
+ align:start position:0%
+so slide 60
+ 
+
+ align:start position:0%
+so slide 60
+is a particular way of measuring
+
+ align:start position:0%
+is a particular way of measuring
+ 
+
+ align:start position:0%
+is a particular way of measuring
+a large genome wide set of mutants this
+
+ align:start position:0%
+a large genome wide set of mutants this
+ 
+
+ align:start position:0%
+a large genome wide set of mutants this
+is not a trivial undertaking we know how
+
+ align:start position:0%
+is not a trivial undertaking we know how
+ 
+
+ align:start position:0%
+is not a trivial undertaking we know how
+to measure a transcriptome set of rnas
+
+ align:start position:0%
+to measure a transcriptome set of rnas
+ 
+
+ align:start position:0%
+to measure a transcriptome set of rnas
+well on microarrays maybe there's an
+
+ align:start position:0%
+well on microarrays maybe there's an
+ 
+
+ align:start position:0%
+well on microarrays maybe there's an
+analogous way to measure
+
+ align:start position:0%
+analogous way to measure
+ 
+
+ align:start position:0%
+analogous way to measure
+uh whole genomes worth of mutants
+
+ align:start position:0%
+uh whole genomes worth of mutants
+ 
+
+ align:start position:0%
+uh whole genomes worth of mutants
+ideally you would have a mutant not just
+
+ align:start position:0%
+ideally you would have a mutant not just
+ 
+
+ align:start position:0%
+ideally you would have a mutant not just
+one per gene one knockout where you per
+
+ align:start position:0%
+one per gene one knockout where you per
+ 
+
+ align:start position:0%
+one per gene one knockout where you per
+gene which is a maybe a
+
+ align:start position:0%
+gene which is a maybe a
+ 
+
+ align:start position:0%
+gene which is a maybe a
+very expensive hand-crafted deletion but
+
+ align:start position:0%
+very expensive hand-crafted deletion but
+ 
+
+ align:start position:0%
+very expensive hand-crafted deletion but
+you'd have a little targeted mutation in
+
+ align:start position:0%
+you'd have a little targeted mutation in
+ 
+
+ align:start position:0%
+you'd have a little targeted mutation in
+every domain that contributes to that
+
+ align:start position:0%
+every domain that contributes to that
+ 
+
+ align:start position:0%
+every domain that contributes to that
+gene function
+
+ align:start position:0%
+gene function
+ 
+
+ align:start position:0%
+gene function
+mutations in the
+
+ align:start position:0%
+mutations in the
+ 
+
+ align:start position:0%
+mutations in the
+dna regulatory elements
+
+ align:start position:0%
+dna regulatory elements
+ 
+
+ align:start position:0%
+dna regulatory elements
+various protein domains
+
+ align:start position:0%
+various protein domains
+ 
+
+ align:start position:0%
+various protein domains
+rna stability domain and so on
+
+ align:start position:0%
+rna stability domain and so on
+ 
+
+ align:start position:0%
+rna stability domain and so on
+not quite at that level of ideal but
+
+ align:start position:0%
+not quite at that level of ideal but
+ 
+
+ align:start position:0%
+not quite at that level of ideal but
+getting close to it it's transposon
+
+ align:start position:0%
+getting close to it it's transposon
+ 
+
+ align:start position:0%
+getting close to it it's transposon
+mutagenesis where you insert small
+
+ align:start position:0%
+mutagenesis where you insert small
+ 
+
+ align:start position:0%
+mutagenesis where you insert small
+bits of dna randomly throughout the
+
+ align:start position:0%
+bits of dna randomly throughout the
+ 
+
+ align:start position:0%
+bits of dna randomly throughout the
+genome
+
+ align:start position:0%
+genome
+ 
+
+ align:start position:0%
+genome
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+modern
+
+ align:start position:0%
+modern
+ 
+
+ align:start position:0%
+modern
+set of commonly used transposons are
+
+ align:start position:0%
+set of commonly used transposons are
+ 
+
+ align:start position:0%
+set of commonly used transposons are
+pretty random in their assertion site
+
+ align:start position:0%
+pretty random in their assertion site
+ 
+
+ align:start position:0%
+pretty random in their assertion site
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+and then you need a way of turning this
+
+ align:start position:0%
+and then you need a way of turning this
+ 
+
+ align:start position:0%
+and then you need a way of turning this
+collection of transposons into a readout
+
+ align:start position:0%
+collection of transposons into a readout
+ 
+
+ align:start position:0%
+collection of transposons into a readout
+of growth rates well one way to do this
+
+ align:start position:0%
+of growth rates well one way to do this
+ 
+
+ align:start position:0%
+of growth rates well one way to do this
+is have a population of
+
+ align:start position:0%
+is have a population of
+ 
+
+ align:start position:0%
+is have a population of
+cells each
+
+ align:start position:0%
+cells each
+ 
+
+ align:start position:0%
+cells each
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+their own distinctive transposon
+
+ align:start position:0%
+their own distinctive transposon
+ 
+
+ align:start position:0%
+their own distinctive transposon
+and growing them as a mixture
+
+ align:start position:0%
+and growing them as a mixture
+ 
+
+ align:start position:0%
+and growing them as a mixture
+and as growing and as they grow as a
+
+ align:start position:0%
+and as growing and as they grow as a
+ 
+
+ align:start position:0%
+and as growing and as they grow as a
+mixture
+
+ align:start position:0%
+mixture
+ 
+
+ align:start position:0%
+mixture
+the ones that that grow better
+
+ align:start position:0%
+the ones that that grow better
+ 
+
+ align:start position:0%
+the ones that that grow better
+will dominate the population
+
+ align:start position:0%
+will dominate the population
+ 
+
+ align:start position:0%
+will dominate the population
+and so their transposon hit the junction
+
+ align:start position:0%
+and so their transposon hit the junction
+ 
+
+ align:start position:0%
+and so their transposon hit the junction
+between the transpose the transposing is
+
+ align:start position:0%
+between the transpose the transposing is
+ 
+
+ align:start position:0%
+between the transpose the transposing is
+universal is present in every cell
+
+ align:start position:0%
+universal is present in every cell
+ 
+
+ align:start position:0%
+universal is present in every cell
+but where it
+
+ align:start position:0%
+but where it
+ 
+
+ align:start position:0%
+but where it
+sits is unique to that cell or nearly so
+
+ align:start position:0%
+sits is unique to that cell or nearly so
+ 
+
+ align:start position:0%
+sits is unique to that cell or nearly so
+so it sits in
+
+ align:start position:0%
+so it sits in
+ 
+
+ align:start position:0%
+so it sits in
+the junction between transposon and
+
+ align:start position:0%
+the junction between transposon and
+ 
+
+ align:start position:0%
+the junction between transposon and
+genome is unique and you want a way of
+
+ align:start position:0%
+genome is unique and you want a way of
+ 
+
+ align:start position:0%
+genome is unique and you want a way of
+assaying that what you actually that
+
+ align:start position:0%
+assaying that what you actually that
+ 
+
+ align:start position:0%
+assaying that what you actually that
+is you
+
+ align:start position:0%
+is you
+ 
+
+ align:start position:0%
+is you
+take the complete dna from the entire
+
+ align:start position:0%
+take the complete dna from the entire
+ 
+
+ align:start position:0%
+take the complete dna from the entire
+cell mixture
+
+ align:start position:0%
+cell mixture
+ 
+
+ align:start position:0%
+cell mixture
+and you want to say how much of each
+
+ align:start position:0%
+and you want to say how much of each
+ 
+
+ align:start position:0%
+and you want to say how much of each
+transposon exists so you cut the entire
+
+ align:start position:0%
+transposon exists so you cut the entire
+ 
+
+ align:start position:0%
+transposon exists so you cut the entire
+dna mixture with a restriction enzyme
+
+ align:start position:0%
+dna mixture with a restriction enzyme
+ 
+
+ align:start position:0%
+dna mixture with a restriction enzyme
+that cuts frequently so-called four
+
+ align:start position:0%
+that cuts frequently so-called four
+ 
+
+ align:start position:0%
+that cuts frequently so-called four
+cutter cuts with with about every 256
+
+ align:start position:0%
+cutter cuts with with about every 256
+ 
+
+ align:start position:0%
+cutter cuts with with about every 256
+base pairs on average and you like it on
+
+ align:start position:0%
+base pairs on average and you like it on
+ 
+
+ align:start position:0%
+base pairs on average and you like it on
+this very special kind of linker which
+
+ align:start position:0%
+this very special kind of linker which
+ 
+
+ align:start position:0%
+this very special kind of linker which
+is a linker which will not amplify with
+
+ align:start position:0%
+is a linker which will not amplify with
+ 
+
+ align:start position:0%
+is a linker which will not amplify with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+corresponding primer until some other
+
+ align:start position:0%
+corresponding primer until some other
+ 
+
+ align:start position:0%
+corresponding primer until some other
+dna synthesis has gone through because
+
+ align:start position:0%
+dna synthesis has gone through because
+ 
+
+ align:start position:0%
+dna synthesis has gone through because
+you see this little y
+
+ align:start position:0%
+you see this little y
+ 
+
+ align:start position:0%
+you see this little y
+linker is not perfectly waterproof base
+
+ align:start position:0%
+linker is not perfectly waterproof base
+ 
+
+ align:start position:0%
+linker is not perfectly waterproof base
+paired
+
+ align:start position:0%
+paired
+ 
+
+ align:start position:0%
+paired
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+requires
+
+ align:start position:0%
+requires
+ 
+
+ align:start position:0%
+requires
+dna polymerase to make a complement
+
+ align:start position:0%
+dna polymerase to make a complement
+ 
+
+ align:start position:0%
+dna polymerase to make a complement
+complement will bind the primer it's a
+
+ align:start position:0%
+complement will bind the primer it's a
+ 
+
+ align:start position:0%
+complement will bind the primer it's a
+long way of saying that only in cases
+
+ align:start position:0%
+long way of saying that only in cases
+ 
+
+ align:start position:0%
+long way of saying that only in cases
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+where you have a primer in the
+
+ align:start position:0%
+where you have a primer in the
+ 
+
+ align:start position:0%
+where you have a primer in the
+transposon near one of these y linkers
+
+ align:start position:0%
+transposon near one of these y linkers
+ 
+
+ align:start position:0%
+transposon near one of these y linkers
+will get amplification transposon alone
+
+ align:start position:0%
+will get amplification transposon alone
+ 
+
+ align:start position:0%
+will get amplification transposon alone
+you won't get it why link or alone you
+
+ align:start position:0%
+you won't get it why link or alone you
+ 
+
+ align:start position:0%
+you won't get it why link or alone you
+won't get it that's one step of
+
+ align:start position:0%
+won't get it that's one step of
+ 
+
+ align:start position:0%
+won't get it that's one step of
+enrichment and the reason you have to
+
+ align:start position:0%
+enrichment and the reason you have to
+ 
+
+ align:start position:0%
+enrichment and the reason you have to
+enrich is if you just through this whole
+
+ align:start position:0%
+enrich is if you just through this whole
+ 
+
+ align:start position:0%
+enrich is if you just through this whole
+thing on the microarray you get
+
+ align:start position:0%
+thing on the microarray you get
+ 
+
+ align:start position:0%
+thing on the microarray you get
+everything lighting up because every
+
+ align:start position:0%
+everything lighting up because every
+ 
+
+ align:start position:0%
+everything lighting up because every
+genome has every piece of the genome in
+
+ align:start position:0%
+genome has every piece of the genome in
+ 
+
+ align:start position:0%
+genome has every piece of the genome in
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the transposons are present in trace
+
+ align:start position:0%
+and the transposons are present in trace
+ 
+
+ align:start position:0%
+and the transposons are present in trace
+amounts
+
+ align:start position:0%
+amounts
+ 
+
+ align:start position:0%
+amounts
+so you need to amplify the junction
+
+ align:start position:0%
+so you need to amplify the junction
+ 
+
+ align:start position:0%
+so you need to amplify the junction
+fragment by first this trick followed by
+
+ align:start position:0%
+fragment by first this trick followed by
+ 
+
+ align:start position:0%
+fragment by first this trick followed by
+a t7 promoter this is a phage promoter
+
+ align:start position:0%
+a t7 promoter this is a phage promoter
+ 
+
+ align:start position:0%
+a t7 promoter this is a phage promoter
+very commonly used very clean
+
+ align:start position:0%
+very commonly used very clean
+ 
+
+ align:start position:0%
+very commonly used very clean
+rna polymerase background that's been
+
+ align:start position:0%
+rna polymerase background that's been
+ 
+
+ align:start position:0%
+rna polymerase background that's been
+incorporated into the any transpose on
+
+ align:start position:0%
+incorporated into the any transpose on
+ 
+
+ align:start position:0%
+incorporated into the any transpose on
+your favorite transposon so now you have
+
+ align:start position:0%
+your favorite transposon so now you have
+ 
+
+ align:start position:0%
+your favorite transposon so now you have
+two steps first this ligation mediated
+
+ align:start position:0%
+two steps first this ligation mediated
+ 
+
+ align:start position:0%
+two steps first this ligation mediated
+pcr and second the t7 in vitro
+
+ align:start position:0%
+pcr and second the t7 in vitro
+ 
+
+ align:start position:0%
+pcr and second the t7 in vitro
+transcription to make rna now you've
+
+ align:start position:0%
+transcription to make rna now you've
+ 
+
+ align:start position:0%
+transcription to make rna now you've
+basically reduced this to a problem
+
+ align:start position:0%
+basically reduced this to a problem
+ 
+
+ align:start position:0%
+basically reduced this to a problem
+similar to transcriptome
+
+ align:start position:0%
+similar to transcriptome
+ 
+
+ align:start position:0%
+similar to transcriptome
+uh microarrays we've done before now the
+
+ align:start position:0%
+uh microarrays we've done before now the
+ 
+
+ align:start position:0%
+uh microarrays we've done before now the
+rnas are surrogates for the amount of
+
+ align:start position:0%
+rnas are surrogates for the amount of
+ 
+
+ align:start position:0%
+rnas are surrogates for the amount of
+each strain
+
+ align:start position:0%
+each strain
+ 
+
+ align:start position:0%
+each strain
+we're not measuring rna we're made in
+
+ align:start position:0%
+we're not measuring rna we're made in
+ 
+
+ align:start position:0%
+we're not measuring rna we're made in
+rna that represents the transposon
+
+ align:start position:0%
+rna that represents the transposon
+ 
+
+ align:start position:0%
+rna that represents the transposon
+junction fragment and hence allows you
+
+ align:start position:0%
+junction fragment and hence allows you
+ 
+
+ align:start position:0%
+junction fragment and hence allows you
+to quantitate the amount of
+
+ align:start position:0%
+to quantitate the amount of
+ 
+
+ align:start position:0%
+to quantitate the amount of
+that particular mutant in a population
+
+ align:start position:0%
+that particular mutant in a population
+ 
+
+ align:start position:0%
+that particular mutant in a population
+as that mutant
+
+ align:start position:0%
+as that mutant
+ 
+
+ align:start position:0%
+as that mutant
+goes up or down in the population so
+
+ align:start position:0%
+goes up or down in the population so
+ 
+
+ align:start position:0%
+goes up or down in the population so
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+the rna from this assay
+
+ align:start position:0%
+the rna from this assay
+ 
+
+ align:start position:0%
+the rna from this assay
+so you might ask at this point
+
+ align:start position:0%
+so you might ask at this point
+ 
+
+ align:start position:0%
+so you might ask at this point
+well this is
+
+ align:start position:0%
+well this is
+ 
+
+ align:start position:0%
+well this is
+this is great but i don't trust it just
+
+ align:start position:0%
+this is great but i don't trust it just
+ 
+
+ align:start position:0%
+this is great but i don't trust it just
+like you some people might not have
+
+ align:start position:0%
+like you some people might not have
+ 
+
+ align:start position:0%
+like you some people might not have
+trusted mass spectrometry as being
+
+ align:start position:0%
+trusted mass spectrometry as being
+ 
+
+ align:start position:0%
+trusted mass spectrometry as being
+reproducible enough to be quantitative
+
+ align:start position:0%
+reproducible enough to be quantitative
+ 
+
+ align:start position:0%
+reproducible enough to be quantitative
+so the way that you determine whether
+
+ align:start position:0%
+so the way that you determine whether
+ 
+
+ align:start position:0%
+so the way that you determine whether
+something is sufficiently reproducible
+
+ align:start position:0%
+something is sufficiently reproducible
+ 
+
+ align:start position:0%
+something is sufficiently reproducible
+to be quantitative one way to do it is
+
+ align:start position:0%
+to be quantitative one way to do it is
+ 
+
+ align:start position:0%
+to be quantitative one way to do it is
+to do two independent selection
+
+ align:start position:0%
+to do two independent selection
+ 
+
+ align:start position:0%
+to do two independent selection
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+evolutionists might might say oh if we
+
+ align:start position:0%
+evolutionists might might say oh if we
+ 
+
+ align:start position:0%
+evolutionists might might say oh if we
+reran evolution all over again we would
+
+ align:start position:0%
+reran evolution all over again we would
+ 
+
+ align:start position:0%
+reran evolution all over again we would
+not get the same set of organisms we
+
+ align:start position:0%
+not get the same set of organisms we
+ 
+
+ align:start position:0%
+not get the same set of organisms we
+have on earth today that may be true but
+
+ align:start position:0%
+have on earth today that may be true but
+ 
+
+ align:start position:0%
+have on earth today that may be true but
+that's because there are all sorts of
+
+ align:start position:0%
+that's because there are all sorts of
+ 
+
+ align:start position:0%
+that's because there are all sorts of
+bottlenecks and historical events
+
+ align:start position:0%
+bottlenecks and historical events
+ 
+
+ align:start position:0%
+bottlenecks and historical events
+in this case
+
+ align:start position:0%
+in this case
+ 
+
+ align:start position:0%
+in this case
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've specifically tried to make it
+
+ align:start position:0%
+we've specifically tried to make it
+ 
+
+ align:start position:0%
+we've specifically tried to make it
+reproducible by avoiding bottlenecks by
+
+ align:start position:0%
+reproducible by avoiding bottlenecks by
+ 
+
+ align:start position:0%
+reproducible by avoiding bottlenecks by
+having every mutation every transposon
+
+ align:start position:0%
+having every mutation every transposon
+ 
+
+ align:start position:0%
+having every mutation every transposon
+type represented by a thousand different
+
+ align:start position:0%
+type represented by a thousand different
+ 
+
+ align:start position:0%
+type represented by a thousand different
+independent events
+
+ align:start position:0%
+independent events
+ 
+
+ align:start position:0%
+independent events
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+as well a thousand copies of every uh
+
+ align:start position:0%
+as well a thousand copies of every uh
+ 
+
+ align:start position:0%
+as well a thousand copies of every uh
+transposon hit so you keep the
+
+ align:start position:0%
+transposon hit so you keep the
+ 
+
+ align:start position:0%
+transposon hit so you keep the
+population size large and so it becomes
+
+ align:start position:0%
+population size large and so it becomes
+ 
+
+ align:start position:0%
+population size large and so it becomes
+more reproducible and this is and the
+
+ align:start position:0%
+more reproducible and this is and the
+ 
+
+ align:start position:0%
+more reproducible and this is and the
+way you measure the reproducibility you
+
+ align:start position:0%
+way you measure the reproducibility you
+ 
+
+ align:start position:0%
+way you measure the reproducibility you
+do the two selection experiments two uh
+
+ align:start position:0%
+do the two selection experiments two uh
+ 
+
+ align:start position:0%
+do the two selection experiments two uh
+independent um
+
+ align:start position:0%
+independent um
+ 
+
+ align:start position:0%
+independent um
+ideally independent sets of transposons
+
+ align:start position:0%
+ideally independent sets of transposons
+ 
+
+ align:start position:0%
+ideally independent sets of transposons
+subjected to exactly the same selection
+
+ align:start position:0%
+subjected to exactly the same selection
+ 
+
+ align:start position:0%
+subjected to exactly the same selection
+procedure and you see a very gratifying
+
+ align:start position:0%
+procedure and you see a very gratifying
+ 
+
+ align:start position:0%
+procedure and you see a very gratifying
+curve here with
+
+ align:start position:0%
+curve here with
+ 
+
+ align:start position:0%
+curve here with
+an r squared regression
+
+ align:start position:0%
+an r squared regression
+ 
+
+ align:start position:0%
+an r squared regression
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+in excess of 98 percent and the kind of
+
+ align:start position:0%
+in excess of 98 percent and the kind of
+ 
+
+ align:start position:0%
+in excess of 98 percent and the kind of
+scatter that you would be pleased to get
+
+ align:start position:0%
+scatter that you would be pleased to get
+ 
+
+ align:start position:0%
+scatter that you would be pleased to get
+in an rna microarray experiment so this
+
+ align:start position:0%
+in an rna microarray experiment so this
+ 
+
+ align:start position:0%
+in an rna microarray experiment so this
+is reproducible and therefore
+
+ align:start position:0%
+is reproducible and therefore
+ 
+
+ align:start position:0%
+is reproducible and therefore
+quant
+
+ align:start position:0%
+quant
+ 
+
+ align:start position:0%
+quant
+capable of producing quantitative data
+
+ align:start position:0%
+capable of producing quantitative data
+ 
+
+ align:start position:0%
+capable of producing quantitative data
+well now let's go back and compare it
+
+ align:start position:0%
+well now let's go back and compare it
+ 
+
+ align:start position:0%
+well now let's go back and compare it
+to the two different methods of modeling
+
+ align:start position:0%
+to the two different methods of modeling
+ 
+
+ align:start position:0%
+to the two different methods of modeling
+the flux optimization
+
+ align:start position:0%
+the flux optimization
+ 
+
+ align:start position:0%
+the flux optimization
+there's the fba or linear programming
+
+ align:start position:0%
+there's the fba or linear programming
+ 
+
+ align:start position:0%
+there's the fba or linear programming
+which assumes that the mutant is
+
+ align:start position:0%
+which assumes that the mutant is
+ 
+
+ align:start position:0%
+which assumes that the mutant is
+immediately optimal and then there's the
+
+ align:start position:0%
+immediately optimal and then there's the
+ 
+
+ align:start position:0%
+immediately optimal and then there's the
+moma or minimization of
+
+ align:start position:0%
+moma or minimization of
+ 
+
+ align:start position:0%
+moma or minimization of
+metabolic adjustment which doesn't
+
+ align:start position:0%
+metabolic adjustment which doesn't
+ 
+
+ align:start position:0%
+metabolic adjustment which doesn't
+assume off immediate optimality but
+
+ align:start position:0%
+assume off immediate optimality but
+ 
+
+ align:start position:0%
+assume off immediate optimality but
+assumes that it's close to
+
+ align:start position:0%
+assumes that it's close to
+ 
+
+ align:start position:0%
+assumes that it's close to
+the wild type optimum so starting at the
+
+ align:start position:0%
+the wild type optimum so starting at the
+ 
+
+ align:start position:0%
+the wild type optimum so starting at the
+top
+
+ align:start position:0%
+top
+ 
+
+ align:start position:0%
+top
+the linear flux balance you can classify
+
+ align:start position:0%
+the linear flux balance you can classify
+ 
+
+ align:start position:0%
+the linear flux balance you can classify
+the production predictions of the model
+
+ align:start position:0%
+the production predictions of the model
+ 
+
+ align:start position:0%
+the production predictions of the model
+you can for each gene then here we have
+
+ align:start position:0%
+you can for each gene then here we have
+ 
+
+ align:start position:0%
+you can for each gene then here we have
+uh over
+
+ align:start position:0%
+uh over
+ 
+
+ align:start position:0%
+uh over
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+almost 400 and almost 500 different
+
+ align:start position:0%
+almost 400 and almost 500 different
+ 
+
+ align:start position:0%
+almost 400 and almost 500 different
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+mutated
+
+ align:start position:0%
+mutated
+ 
+
+ align:start position:0%
+mutated
+and you first you run through these
+
+ align:start position:0%
+and you first you run through these
+ 
+
+ align:start position:0%
+and you first you run through these
+silicon predictions you can classify
+
+ align:start position:0%
+silicon predictions you can classify
+ 
+
+ align:start position:0%
+silicon predictions you can classify
+them as being essential
+
+ align:start position:0%
+them as being essential
+ 
+
+ align:start position:0%
+them as being essential
+for a particular growth condition they
+
+ align:start position:0%
+for a particular growth condition they
+ 
+
+ align:start position:0%
+for a particular growth condition they
+aren't necessarily essential for every
+
+ align:start position:0%
+aren't necessarily essential for every
+ 
+
+ align:start position:0%
+aren't necessarily essential for every
+growth condition but the
+
+ align:start position:0%
+growth condition but the
+ 
+
+ align:start position:0%
+growth condition but the
+growth conditions here it's essential or
+
+ align:start position:0%
+growth conditions here it's essential or
+ 
+
+ align:start position:0%
+growth conditions here it's essential or
+non-essential or something in between
+
+ align:start position:0%
+non-essential or something in between
+ 
+
+ align:start position:0%
+non-essential or something in between
+we'll just focus on the extremes of
+
+ align:start position:0%
+we'll just focus on the extremes of
+ 
+
+ align:start position:0%
+we'll just focus on the extremes of
+essential and non-essential and then
+
+ align:start position:0%
+essential and non-essential and then
+ 
+
+ align:start position:0%
+essential and non-essential and then
+then the experiment can be classified as
+
+ align:start position:0%
+then the experiment can be classified as
+ 
+
+ align:start position:0%
+then the experiment can be classified as
+to whether there's uh
+
+ align:start position:0%
+to whether there's uh
+ 
+
+ align:start position:0%
+to whether there's uh
+significant negative selection or no
+
+ align:start position:0%
+significant negative selection or no
+ 
+
+ align:start position:0%
+significant negative selection or no
+noticeable selection under particular
+
+ align:start position:0%
+noticeable selection under particular
+ 
+
+ align:start position:0%
+noticeable selection under particular
+growth conditions and so you expect the
+
+ align:start position:0%
+growth conditions and so you expect the
+ 
+
+ align:start position:0%
+growth conditions and so you expect the
+ones to be essential in these growth
+
+ align:start position:0%
+ones to be essential in these growth
+ 
+
+ align:start position:0%
+ones to be essential in these growth
+conditions to be heavily negative
+
+ align:start position:0%
+conditions to be heavily negative
+ 
+
+ align:start position:0%
+conditions to be heavily negative
+selectively and you have 80 examples of
+
+ align:start position:0%
+selectively and you have 80 examples of
+ 
+
+ align:start position:0%
+selectively and you have 80 examples of
+that out of 142 predicted
+
+ align:start position:0%
+that out of 142 predicted
+ 
+
+ align:start position:0%
+that out of 142 predicted
+however you wouldn't expect they need to
+
+ align:start position:0%
+however you wouldn't expect they need to
+ 
+
+ align:start position:0%
+however you wouldn't expect they need to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+missing in selection since they're
+
+ align:start position:0%
+missing in selection since they're
+ 
+
+ align:start position:0%
+missing in selection since they're
+essential so this 62 should be a 0 but a
+
+ align:start position:0%
+essential so this 62 should be a 0 but a
+ 
+
+ align:start position:0%
+essential so this 62 should be a 0 but a
+62. this is an example of what we're
+
+ align:start position:0%
+62. this is an example of what we're
+ 
+
+ align:start position:0%
+62. this is an example of what we're
+going to try to explain or use this as a
+
+ align:start position:0%
+going to try to explain or use this as a
+ 
+
+ align:start position:0%
+going to try to explain or use this as a
+way of generating interesting hypotheses
+
+ align:start position:0%
+way of generating interesting hypotheses
+ 
+
+ align:start position:0%
+way of generating interesting hypotheses
+about the exceptions or outliers
+
+ align:start position:0%
+about the exceptions or outliers
+ 
+
+ align:start position:0%
+about the exceptions or outliers
+similarly the non-essential genes should
+
+ align:start position:0%
+similarly the non-essential genes should
+ 
+
+ align:start position:0%
+similarly the non-essential genes should
+have no selection that's 180 in the
+
+ align:start position:0%
+have no selection that's 180 in the
+ 
+
+ align:start position:0%
+have no selection that's 180 in the
+lower right hand part of the upper
+
+ align:start position:0%
+lower right hand part of the upper
+ 
+
+ align:start position:0%
+lower right hand part of the upper
+fba
+
+ align:start position:0%
+fba
+ 
+
+ align:start position:0%
+fba
+but the 119 should be zero
+
+ align:start position:0%
+but the 119 should be zero
+ 
+
+ align:start position:0%
+but the 119 should be zero
+okay so one x the first pass explanation
+
+ align:start position:0%
+okay so one x the first pass explanation
+ 
+
+ align:start position:0%
+okay so one x the first pass explanation
+is okay we knew
+
+ align:start position:0%
+is okay we knew
+ 
+
+ align:start position:0%
+is okay we knew
+that these weren't going to be optimal
+
+ align:start position:0%
+that these weren't going to be optimal
+ 
+
+ align:start position:0%
+that these weren't going to be optimal
+right away so let's
+
+ align:start position:0%
+right away so let's
+ 
+
+ align:start position:0%
+right away so let's
+use the other model the the
+
+ align:start position:0%
+use the other model the the
+ 
+
+ align:start position:0%
+use the other model the the
+sub optimal nearly optimal model moma
+
+ align:start position:0%
+sub optimal nearly optimal model moma
+ 
+
+ align:start position:0%
+sub optimal nearly optimal model moma
+and see how well it does
+
+ align:start position:0%
+and see how well it does
+ 
+
+ align:start position:0%
+and see how well it does
+well on the far right hand side of slide
+
+ align:start position:0%
+well on the far right hand side of slide
+ 
+
+ align:start position:0%
+well on the far right hand side of slide
+62 you see the chi-square p-values how
+
+ align:start position:0%
+62 you see the chi-square p-values how
+ 
+
+ align:start position:0%
+62 you see the chi-square p-values how
+well the the
+
+ align:start position:0%
+well the the
+ 
+
+ align:start position:0%
+well the the
+predictions of agree with the uh
+
+ align:start position:0%
+predictions of agree with the uh
+ 
+
+ align:start position:0%
+predictions of agree with the uh
+observations and it is significant for
+
+ align:start position:0%
+observations and it is significant for
+ 
+
+ align:start position:0%
+observations and it is significant for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+linear programming it's 10 to the
+
+ align:start position:0%
+linear programming it's 10 to the
+ 
+
+ align:start position:0%
+linear programming it's 10 to the
+4 times 10 to the minus 3. fairly
+
+ align:start position:0%
+4 times 10 to the minus 3. fairly
+ 
+
+ align:start position:0%
+4 times 10 to the minus 3. fairly
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+and the moma is much more significant to
+
+ align:start position:0%
+and the moma is much more significant to
+ 
+
+ align:start position:0%
+and the moma is much more significant to
+the minus five it has improved some of
+
+ align:start position:0%
+the minus five it has improved some of
+ 
+
+ align:start position:0%
+the minus five it has improved some of
+those uh
+
+ align:start position:0%
+those uh
+ 
+
+ align:start position:0%
+those uh
+uh upper
+
+ align:start position:0%
+uh upper
+ 
+
+ align:start position:0%
+uh upper
+right 66 and lower left 108. those
+
+ align:start position:0%
+right 66 and lower left 108. those
+ 
+
+ align:start position:0%
+right 66 and lower left 108. those
+should still be those should still be
+
+ align:start position:0%
+should still be those should still be
+ 
+
+ align:start position:0%
+should still be those should still be
+zero and they're not and the extent that
+
+ align:start position:0%
+zero and they're not and the extent that
+ 
+
+ align:start position:0%
+zero and they're not and the extent that
+they're they dv
+
+ align:start position:0%
+they're they dv
+ 
+
+ align:start position:0%
+they're they dv
+deviate from
+
+ align:start position:0%
+deviate from
+ 
+
+ align:start position:0%
+deviate from
+the ideal expectation means that either
+
+ align:start position:0%
+the ideal expectation means that either
+ 
+
+ align:start position:0%
+the ideal expectation means that either
+the data
+
+ align:start position:0%
+the data
+ 
+
+ align:start position:0%
+the data
+are somehow the way we're collecting the
+
+ align:start position:0%
+are somehow the way we're collecting the
+ 
+
+ align:start position:0%
+are somehow the way we're collecting the
+data not the way we expected it or that
+
+ align:start position:0%
+data not the way we expected it or that
+ 
+
+ align:start position:0%
+data not the way we expected it or that
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model more likely the model has some
+
+ align:start position:0%
+model more likely the model has some
+ 
+
+ align:start position:0%
+model more likely the model has some
+problems in it and examples of problems
+
+ align:start position:0%
+problems in it and examples of problems
+ 
+
+ align:start position:0%
+problems in it and examples of problems
+for those two classes the
+
+ align:start position:0%
+for those two classes the
+ 
+
+ align:start position:0%
+for those two classes the
+predicted essential genes which show
+
+ align:start position:0%
+predicted essential genes which show
+ 
+
+ align:start position:0%
+predicted essential genes which show
+notes which uh
+
+ align:start position:0%
+notes which uh
+ 
+
+ align:start position:0%
+notes which uh
+show no selection might be examples of
+
+ align:start position:0%
+show no selection might be examples of
+ 
+
+ align:start position:0%
+show no selection might be examples of
+redundancies that we failed to model
+
+ align:start position:0%
+redundancies that we failed to model
+ 
+
+ align:start position:0%
+redundancies that we failed to model
+when we put together the stoichiometric
+
+ align:start position:0%
+when we put together the stoichiometric
+ 
+
+ align:start position:0%
+when we put together the stoichiometric
+matrix the stoichiometric matrix we take
+
+ align:start position:0%
+matrix the stoichiometric matrix we take
+ 
+
+ align:start position:0%
+matrix the stoichiometric matrix we take
+every known biochemical reaction
+
+ align:start position:0%
+every known biochemical reaction
+ 
+
+ align:start position:0%
+every known biochemical reaction
+we might take uh
+
+ align:start position:0%
+we might take uh
+ 
+
+ align:start position:0%
+we might take uh
+convincing homologs sequence homology
+
+ align:start position:0%
+convincing homologs sequence homology
+ 
+
+ align:start position:0%
+convincing homologs sequence homology
+level and say those might be examples of
+
+ align:start position:0%
+level and say those might be examples of
+ 
+
+ align:start position:0%
+level and say those might be examples of
+redundancy we might take analogous or
+
+ align:start position:0%
+redundancy we might take analogous or
+ 
+
+ align:start position:0%
+redundancy we might take analogous or
+parallel routes that are known
+
+ align:start position:0%
+parallel routes that are known
+ 
+
+ align:start position:0%
+parallel routes that are known
+documented biochemically where you can
+
+ align:start position:0%
+documented biochemically where you can
+ 
+
+ align:start position:0%
+documented biochemically where you can
+get to the same point by a series of
+
+ align:start position:0%
+get to the same point by a series of
+ 
+
+ align:start position:0%
+get to the same point by a series of
+possibly non-homo non-sequence
+
+ align:start position:0%
+possibly non-homo non-sequence
+ 
+
+ align:start position:0%
+possibly non-homo non-sequence
+homologous enzymatic steps so those are
+
+ align:start position:0%
+homologous enzymatic steps so those are
+ 
+
+ align:start position:0%
+homologous enzymatic steps so those are
+novel redundancies this is example of
+
+ align:start position:0%
+novel redundancies this is example of
+ 
+
+ align:start position:0%
+novel redundancies this is example of
+potential discovery
+
+ align:start position:0%
+potential discovery
+ 
+
+ align:start position:0%
+potential discovery
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and can be pursued in a very directed
+
+ align:start position:0%
+and can be pursued in a very directed
+ 
+
+ align:start position:0%
+and can be pursued in a very directed
+way because these are 66 very specific
+
+ align:start position:0%
+way because these are 66 very specific
+ 
+
+ align:start position:0%
+way because these are 66 very specific
+predictions
+
+ align:start position:0%
+predictions
+ 
+
+ align:start position:0%
+predictions
+108 non-essential
+
+ align:start position:0%
+108 non-essential
+ 
+
+ align:start position:0%
+108 non-essential
+gene knockouts which nevertheless showed
+
+ align:start position:0%
+gene knockouts which nevertheless showed
+ 
+
+ align:start position:0%
+gene knockouts which nevertheless showed
+negative selection could be examples of
+
+ align:start position:0%
+negative selection could be examples of
+ 
+
+ align:start position:0%
+negative selection could be examples of
+position effects where a mutation in one
+
+ align:start position:0%
+position effects where a mutation in one
+ 
+
+ align:start position:0%
+position effects where a mutation in one
+gene affects
+
+ align:start position:0%
+gene affects
+ 
+
+ align:start position:0%
+gene affects
+other genes that are close along the dna
+
+ align:start position:0%
+other genes that are close along the dna
+ 
+
+ align:start position:0%
+other genes that are close along the dna
+position meaning along the dna any an
+
+ align:start position:0%
+position meaning along the dna any an
+ 
+
+ align:start position:0%
+position meaning along the dna any an
+example of this is that that a um
+
+ align:start position:0%
+example of this is that that a um
+ 
+
+ align:start position:0%
+example of this is that that a um
+a variety of mutations in a gene which
+
+ align:start position:0%
+a variety of mutations in a gene which
+ 
+
+ align:start position:0%
+a variety of mutations in a gene which
+is upstream from another gene in an
+
+ align:start position:0%
+is upstream from another gene in an
+ 
+
+ align:start position:0%
+is upstream from another gene in an
+operon
+
+ align:start position:0%
+operon
+ 
+
+ align:start position:0%
+operon
+have polar effects on downstream genes
+
+ align:start position:0%
+have polar effects on downstream genes
+ 
+
+ align:start position:0%
+have polar effects on downstream genes
+due to the coupling of transcription and
+
+ align:start position:0%
+due to the coupling of transcription and
+ 
+
+ align:start position:0%
+due to the coupling of transcription and
+translation you can have all you can
+
+ align:start position:0%
+translation you can have all you can
+ 
+
+ align:start position:0%
+translation you can have all you can
+have other kinds of position effects as
+
+ align:start position:0%
+have other kinds of position effects as
+ 
+
+ align:start position:0%
+have other kinds of position effects as
+well these are two
+
+ align:start position:0%
+well these are two
+ 
+
+ align:start position:0%
+well these are two
+these are examples of
+
+ align:start position:0%
+these are examples of
+ 
+
+ align:start position:0%
+these are examples of
+possibly many explanations and
+
+ align:start position:0%
+possibly many explanations and
+ 
+
+ align:start position:0%
+possibly many explanations and
+discoveries that can contribute to
+
+ align:start position:0%
+discoveries that can contribute to
+ 
+
+ align:start position:0%
+discoveries that can contribute to
+the wonderful nature of you know it's a
+
+ align:start position:0%
+the wonderful nature of you know it's a
+ 
+
+ align:start position:0%
+the wonderful nature of you know it's a
+win-win situation either you get great
+
+ align:start position:0%
+win-win situation either you get great
+ 
+
+ align:start position:0%
+win-win situation either you get great
+correlation
+
+ align:start position:0%
+correlation
+ 
+
+ align:start position:0%
+correlation
+or you get great exceptions and
+
+ align:start position:0%
+or you get great exceptions and
+ 
+
+ align:start position:0%
+or you get great exceptions and
+discoveries or both
+
+ align:start position:0%
+discoveries or both
+ 
+
+ align:start position:0%
+discoveries or both
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+when we talked about redundancy as one
+
+ align:start position:0%
+when we talked about redundancy as one
+ 
+
+ align:start position:0%
+when we talked about redundancy as one
+of the possible explanations in the
+
+ align:start position:0%
+of the possible explanations in the
+ 
+
+ align:start position:0%
+of the possible explanations in the
+previous slide that brings up really
+
+ align:start position:0%
+previous slide that brings up really
+ 
+
+ align:start position:0%
+previous slide that brings up really
+important uh conceptual component of the
+
+ align:start position:0%
+important uh conceptual component of the
+ 
+
+ align:start position:0%
+important uh conceptual component of the
+post-genomic functional genomic world
+
+ align:start position:0%
+post-genomic functional genomic world
+ 
+
+ align:start position:0%
+post-genomic functional genomic world
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+what do we do about multiple homologous
+
+ align:start position:0%
+what do we do about multiple homologous
+ 
+
+ align:start position:0%
+what do we do about multiple homologous
+domains when you go through and you
+
+ align:start position:0%
+domains when you go through and you
+ 
+
+ align:start position:0%
+domains when you go through and you
+sequence genomes you find paralogs you
+
+ align:start position:0%
+sequence genomes you find paralogs you
+ 
+
+ align:start position:0%
+sequence genomes you find paralogs you
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+either whole genes or pieces of genes
+
+ align:start position:0%
+either whole genes or pieces of genes
+ 
+
+ align:start position:0%
+either whole genes or pieces of genes
+which have high sequence homology which
+
+ align:start position:0%
+which have high sequence homology which
+ 
+
+ align:start position:0%
+which have high sequence homology which
+we talked about at the beginning of the
+
+ align:start position:0%
+we talked about at the beginning of the
+ 
+
+ align:start position:0%
+we talked about at the beginning of the
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+and here's examples of three
+
+ align:start position:0%
+and here's examples of three
+ 
+
+ align:start position:0%
+and here's examples of three
+protein coding regions encode enzymes
+
+ align:start position:0%
+protein coding regions encode enzymes
+ 
+
+ align:start position:0%
+protein coding regions encode enzymes
+involved in the biosynthesis of amino of
+
+ align:start position:0%
+involved in the biosynthesis of amino of
+ 
+
+ align:start position:0%
+involved in the biosynthesis of amino of
+amino acids
+
+ align:start position:0%
+amino acids
+ 
+
+ align:start position:0%
+amino acids
+so you can imagine that when you grow
+
+ align:start position:0%
+so you can imagine that when you grow
+ 
+
+ align:start position:0%
+so you can imagine that when you grow
+the cells on minimal media
+
+ align:start position:0%
+the cells on minimal media
+ 
+
+ align:start position:0%
+the cells on minimal media
+that you're not so providing the amino
+
+ align:start position:0%
+that you're not so providing the amino
+ 
+
+ align:start position:0%
+that you're not so providing the amino
+acids so the cell has to make the amino
+
+ align:start position:0%
+acids so the cell has to make the amino
+ 
+
+ align:start position:0%
+acids so the cell has to make the amino
+acids if it's if it's got a mutation a
+
+ align:start position:0%
+acids if it's if it's got a mutation a
+ 
+
+ align:start position:0%
+acids if it's if it's got a mutation a
+transposon hit in one of these
+
+ align:start position:0%
+transposon hit in one of these
+ 
+
+ align:start position:0%
+transposon hit in one of these
+genes is key in the biosynthetic
+
+ align:start position:0%
+genes is key in the biosynthetic
+ 
+
+ align:start position:0%
+genes is key in the biosynthetic
+synthesis of lysine threonine or
+
+ align:start position:0%
+synthesis of lysine threonine or
+ 
+
+ align:start position:0%
+synthesis of lysine threonine or
+methionine then you might expect that it
+
+ align:start position:0%
+methionine then you might expect that it
+ 
+
+ align:start position:0%
+methionine then you might expect that it
+won't grow well it will be a selective
+
+ align:start position:0%
+won't grow well it will be a selective
+ 
+
+ align:start position:0%
+won't grow well it will be a selective
+disadvantage of minimal media unless one
+
+ align:start position:0%
+disadvantage of minimal media unless one
+ 
+
+ align:start position:0%
+disadvantage of minimal media unless one
+of the other genes covers for it uh it's
+
+ align:start position:0%
+of the other genes covers for it uh it's
+ 
+
+ align:start position:0%
+of the other genes covers for it uh it's
+possibly green so these have three to
+
+ align:start position:0%
+possibly green so these have three to
+ 
+
+ align:start position:0%
+possibly green so these have three to
+three two or three domains here color
+
+ align:start position:0%
+three two or three domains here color
+ 
+
+ align:start position:0%
+three two or three domains here color
+coded so the green domain
+
+ align:start position:0%
+coded so the green domain
+ 
+
+ align:start position:0%
+coded so the green domain
+is shared by these
+
+ align:start position:0%
+is shared by these
+ 
+
+ align:start position:0%
+is shared by these
+three biosynthetic proteins that are
+
+ align:start position:0%
+three biosynthetic proteins that are
+ 
+
+ align:start position:0%
+three biosynthetic proteins that are
+otherwise very different in their
+
+ align:start position:0%
+otherwise very different in their
+ 
+
+ align:start position:0%
+otherwise very different in their
+metabolic
+
+ align:start position:0%
+metabolic
+ 
+
+ align:start position:0%
+metabolic
+contributions
+
+ align:start position:0%
+contributions
+ 
+
+ align:start position:0%
+contributions
+and you might imagine that some of these
+
+ align:start position:0%
+and you might imagine that some of these
+ 
+
+ align:start position:0%
+and you might imagine that some of these
+green domains might cover for others
+
+ align:start position:0%
+green domains might cover for others
+ 
+
+ align:start position:0%
+green domains might cover for others
+when one of them is mutated
+
+ align:start position:0%
+when one of them is mutated
+ 
+
+ align:start position:0%
+when one of them is mutated
+one of them however the one in life c
+
+ align:start position:0%
+one of them however the one in life c
+ 
+
+ align:start position:0%
+one of them however the one in life c
+when it's got a transposon hit in that
+
+ align:start position:0%
+when it's got a transposon hit in that
+ 
+
+ align:start position:0%
+when it's got a transposon hit in that
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+the replication rate the selective
+
+ align:start position:0%
+the replication rate the selective
+ 
+
+ align:start position:0%
+the replication rate the selective
+disadvantage of mental media is severe
+
+ align:start position:0%
+disadvantage of mental media is severe
+ 
+
+ align:start position:0%
+disadvantage of mental media is severe
+it's a fact it's an order of magnitude
+
+ align:start position:0%
+it's a fact it's an order of magnitude
+ 
+
+ align:start position:0%
+it's a fact it's an order of magnitude
+while the others are more subtle it
+
+ align:start position:0%
+while the others are more subtle it
+ 
+
+ align:start position:0%
+while the others are more subtle it
+could be that the lycee covers for the
+
+ align:start position:0%
+could be that the lycee covers for the
+ 
+
+ align:start position:0%
+could be that the lycee covers for the
+other tube because it's made in large
+
+ align:start position:0%
+other tube because it's made in large
+ 
+
+ align:start position:0%
+other tube because it's made in large
+amounts is very active
+
+ align:start position:0%
+amounts is very active
+ 
+
+ align:start position:0%
+amounts is very active
+but the other two can't cover for the
+
+ align:start position:0%
+but the other two can't cover for the
+ 
+
+ align:start position:0%
+but the other two can't cover for the
+life c
+
+ align:start position:0%
+life c
+ 
+
+ align:start position:0%
+life c
+or there's a variety of other possible
+
+ align:start position:0%
+or there's a variety of other possible
+ 
+
+ align:start position:0%
+or there's a variety of other possible
+explanations for this observation
+
+ align:start position:0%
+explanations for this observation
+ 
+
+ align:start position:0%
+explanations for this observation
+the point is that this generates
+
+ align:start position:0%
+the point is that this generates
+ 
+
+ align:start position:0%
+the point is that this generates
+hypotheses that allow us to follow up on
+
+ align:start position:0%
+hypotheses that allow us to follow up on
+ 
+
+ align:start position:0%
+hypotheses that allow us to follow up on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the flux balance or moma
+
+ align:start position:0%
+the flux balance or moma
+ 
+
+ align:start position:0%
+the flux balance or moma
+type of modeling and i think it's what
+
+ align:start position:0%
+type of modeling and i think it's what
+ 
+
+ align:start position:0%
+type of modeling and i think it's what
+the reason i spent so much time on it is
+
+ align:start position:0%
+the reason i spent so much time on it is
+ 
+
+ align:start position:0%
+the reason i spent so much time on it is
+i think the concept of optimization is
+
+ align:start position:0%
+i think the concept of optimization is
+ 
+
+ align:start position:0%
+i think the concept of optimization is
+something that's important both in the
+
+ align:start position:0%
+something that's important both in the
+ 
+
+ align:start position:0%
+something that's important both in the
+sense that we're in engineering as
+
+ align:start position:0%
+sense that we're in engineering as
+ 
+
+ align:start position:0%
+sense that we're in engineering as
+engineers we're optimizing uh living
+
+ align:start position:0%
+engineers we're optimizing uh living
+ 
+
+ align:start position:0%
+engineers we're optimizing uh living
+systems and also as students of
+
+ align:start position:0%
+systems and also as students of
+ 
+
+ align:start position:0%
+systems and also as students of
+evolutionary systems where
+
+ align:start position:0%
+evolutionary systems where
+ 
+
+ align:start position:0%
+evolutionary systems where
+to understand what how those what those
+
+ align:start position:0%
+to understand what how those what those
+ 
+
+ align:start position:0%
+to understand what how those what those
+systems are optimized to do
+
+ align:start position:0%
+systems are optimized to do
+ 
+
+ align:start position:0%
+systems are optimized to do
+we need to
+
+ align:start position:0%
+we need to
+ 
+
+ align:start position:0%
+we need to
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+from this perspective
+
+ align:start position:0%
+from this perspective
+ 
+
+ align:start position:0%
+from this perspective
+so this is just where we what we've
+
+ align:start position:0%
+so this is just where we what we've
+ 
+
+ align:start position:0%
+so this is just where we what we've
+covered today we've covered both
+
+ align:start position:0%
+covered today we've covered both
+ 
+
+ align:start position:0%
+covered today we've covered both
+continuous and discrete
+
+ align:start position:0%
+continuous and discrete
+ 
+
+ align:start position:0%
+continuous and discrete
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ways of modeling molecular systems
+
+ align:start position:0%
+ways of modeling molecular systems
+ 
+
+ align:start position:0%
+ways of modeling molecular systems
+and in particular the red blood cell and
+
+ align:start position:0%
+and in particular the red blood cell and
+ 
+
+ align:start position:0%
+and in particular the red blood cell and
+the copy number control as a way of of
+
+ align:start position:0%
+the copy number control as a way of of
+ 
+
+ align:start position:0%
+the copy number control as a way of of
+dealing with metabolism and biopolymer
+
+ align:start position:0%
+dealing with metabolism and biopolymer
+ 
+
+ align:start position:0%
+dealing with metabolism and biopolymer
+synthesis separately and the flux
+
+ align:start position:0%
+synthesis separately and the flux
+ 
+
+ align:start position:0%
+synthesis separately and the flux
+balance has brought these together
+
+ align:start position:0%
+balance has brought these together
+ 
+
+ align:start position:0%
+balance has brought these together
+and brought in the notion of
+
+ align:start position:0%
+and brought in the notion of
+ 
+
+ align:start position:0%
+and brought in the notion of
+optimization okay so
+
+ align:start position:0%
+optimization okay so
+ 
+
+ align:start position:0%
+optimization okay so
+until next time
\ No newline at end of file
diff --git a/eCPASv7NaHk.txt b/eCPASv7NaHk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eaad4367fbf1158be350c734f2616bb3c59b7d2e
--- /dev/null
+++ b/eCPASv7NaHk.txt
@@ -0,0 +1,2724 @@
+The following content is
+provided by MIT OpenCourseWare
+
+under a Creative Commons
+license.
+
+Additional information about
+our license and MIT
+
+OpenCourseWare in general is
+available at ocw.MIT.edu.
+
+PROFESSOR: This, as you know, is
+the last lecture of thermal
+
+tensor properties of crystals
+for the semester.
+
+Come on, can't somebody
+go, aww, just to
+
+make me feel good?
+
+At least nobody said yay, so
+that makes me feel good, too.
+
+So I guess on balance I come
+out feeling pretty happy.
+
+What I'm going to do today is
+to talk a little bit more
+
+about forthright tensor
+properties, which we've not
+
+said much about.
+
+And I'm going to look at some
+scalar moduli and look at them
+
+for a couple of different
+symmetries and restrictions on
+
+the compliances.
+
+The surfaces that you might
+expect turn out to be really,
+
+really weird.
+
+Because these will be fourth
+order variation with the
+
+direction cosines.
+
+So when you take trigonometric
+functions and raise them to
+
+the fourth power, you get severe
+anisotropies for a
+
+great many of the
+scalar moduli.
+
+I'm sorry to say, years ago when
+I made the acquaintance
+
+of a computer programmer in
+course six who was looking for
+
+something challenging to do in
+connection with material
+
+science and engineering,
+I said, wow, have I got
+
+something for you.
+
+How about doing some
+computer graphics?
+
+And this was a few years
+ago when such
+
+products were fairly rare.
+
+And how about making a program
+that would let us see visually
+
+how some of these scalar
+moduli will vary with
+
+direction and provide the
+provision so you can turn them
+
+over in space, just as you would
+pick up a model in your
+
+hands and rotate it around
+till you finally came to
+
+appreciate it?
+
+And then for something like a
+triclinic crystal, where there
+
+are almost a couple of dozen
+different moduli, how about
+
+allowing people to scale up or
+scale down the value of one of
+
+the elastic constants
+and let them see
+
+how the shape changes?
+
+And oh, that was-- he went
+to work on it for a
+
+semester and came back.
+
+And it was a gorgeous thing.
+
+You could take a monoclinic
+representation of three
+
+dimensions of Young's modulus.
+
+Say you want to change S31.
+
+And it would change
+by a factor of 10.
+
+You'd see a big nose blow out
+on the surface and then
+
+contract down again.
+
+And you could turn around.
+
+Anyway, the program having told
+you how marvelous it is,
+
+it's no longer supported because
+of the operating
+
+system that it operated under
+having done defunct.
+
+But anyway, that was a fun
+thing to play with.
+
+AUDIENCE: What operating
+system?
+
+PROFESSOR: I don't even
+remember anymore.
+
+It was a fairly obscure one.
+
+Was not only the system, but it
+worked through a software
+
+package which operated
+on that system.
+
+All right.
+
+So we're going to talk today
+about fourth rank tensor
+
+properties.
+
+The most important--
+
+in fact, probably the only ones
+you've ever heard of, are
+
+the elastic, stiffnesses, and
+compliances, which are ways of
+
+representing strain in
+terms of stress or
+
+stress in terms of strain.
+
+I think I'll sort of see
+how the time plays out.
+
+If I finish just about
+everything that I'm hoping to
+
+say by on the hour, I think I'll
+just go an extra five or
+
+10 minutes.
+
+And then comes a great, grand,
+and traditional event at MIT.
+
+All semester long I've been
+grilling you with problem sets
+
+and quizzes, and you've had to
+dance through your steps just
+
+because I told you to.
+
+Now how's this for
+reciprocity--
+
+you get to evaluate me.
+
+You get to grade me.
+
+MIT, at the end of every
+semester, has a course
+
+evaluation.
+
+It's submitted anonymously by
+you, so you could really vent
+
+your spleen without ever having
+called to task for it.
+
+So when we finish, either for
+our break or at the end of a
+
+slightly extended first session,
+I will bow, to
+
+thunderous applause,
+I hope, and exit.
+
+And then you will be left alone
+to fill out the course
+
+evaluation.
+
+Corinne will collect them from
+you, and she will deliver them
+
+over to department
+headquarters.
+
+The results will be tabulated,
+and so will the comments.
+
+But they will not be in your
+hand, all of which I
+
+recognize, having spent
+hour after hour
+
+grading your quizzes.
+
+So they will be submitted
+to me in a
+
+completely sanitized fashion.
+
+I won't know who said what.
+
+A final question that I will
+answer before you ask it, what
+
+about the quizzes?
+
+How are you doing on them?
+
+Well, I have come
+to hate them.
+
+I think I will give one-question
+quizzes from now
+
+on the future.
+
+It takes me about five
+to seven minutes
+
+to grade each question.
+
+And there are about 25 of you.
+
+So it takes me, to grade one
+question, somewhere between
+
+two and 1/2 and three hours.
+
+And there are 10 questions
+on the two quizzes
+
+remaining to be graded.
+
+And so I let you do the
+arithmetic, and you can see
+
+what sort of torment I've been
+living in the last few days in
+
+return for the torment
+I put you through
+
+for two brief hours.
+
+So wow.
+
+I will leave it to you to decide
+who's getting the worst
+
+of this deal.
+
+OK, fourth rank tensors.
+
+Elasticity's probably the only
+one you can think of.
+
+Let me give you an example in
+this handout, an example of
+
+another forthright
+tensor property.
+
+And this is the piezoresistive
+effect, the way electrical
+
+resistance of the material
+changes in response to an
+
+applied stress.
+
+It's a pretty exotic property.
+
+I had never heard of it until
+I was at a meeting of the
+
+American Crystallographic
+Association and somebody,
+
+believe it or not, from
+Texas Instruments--
+
+so you better bet that this
+property is useful in
+
+technology--
+
+fellow named Ahmed Amin got
+up and gave a talk on the
+
+piezoresistive effect.
+
+And he had marvelous slides at
+the outset that defined the
+
+effect
+
+So what you have here on these
+few sheets is a few pages that
+
+define the piezoresistance
+effect.
+
+We're not going to do
+anything with it.
+
+It's a fourth rank tensor, so
+it will proceed to transform
+
+like other forthright tensors,
+such as elastic stiffness and
+
+compliance.
+
+I should warn you about these
+following pages, which were
+
+slides that he used
+at his talk.
+
+He seems to have done the
+lettering with a magic marker.
+
+Because all of the I's and J's
+are indistinguishable, which
+
+makes interpretation of what
+he's saying here a little bit
+
+challenging.
+
+And then the other thing that
+throws one off is that he uses
+
+x to represent stress.
+
+I don't know what field or in
+what discipline the elements
+
+of stress are called xij, but
+this is what he does.
+
+And once you figure that out,
+the interpretation of what he
+
+has said here is fairly
+apparent if
+
+you think about it.
+
+Anyway, he takes a state of
+zero stress and strain and
+
+expands it as a series, and
+then picks off different
+
+coefficients.
+
+And one of them is a set of
+moduli which he calls pi, pi
+
+subscript ijkl, which relate
+stress, xkl in his notation,
+
+to a change in the density,
+delta row ij.
+
+So here's a fourth rank tensor
+property that will indeed have
+
+to conform to all the
+restrictions for the moduli
+
+that we have defined
+for the elastic
+
+stiffnesses and moduli.
+
+All right.
+
+Let me then turn to
+stress and strain.
+
+We introduced the relation
+between stress and strain, but
+
+didn't really go into detail on
+the bizarre absorptions of
+
+factors of two or four that have
+to be done in order to
+
+make this come out in a nice,
+clean matrix form.
+
+So let me remind you of where
+these silly factors came in.
+
+We took our stress tensor, sigma
+1 1, sigma 1 2, sigma 1
+
+3, 2 1, 2 2, and 2 3, sigma 3
+1, sigma 3 2, and sigma 3 3.
+
+The tensor had to
+be symmetric.
+
+The off-diagonal term sigma
+ij had to be equal to
+
+the term sigma ij.
+
+And this was for the reason
+of mechanical equilibrium.
+
+These off-diagonal terms, sigma
+ij and sigma ij, we saw,
+
+exerted a torque on a body.
+
+And unless they were equal,
+the body would undergo an
+
+angular acceleration.
+
+And then we renumbered these
+according to the convention
+
+that as we would march down the
+diagonal of the tensor and
+
+take pairs of subscripts, 1 1,
+2 2, 3 3, represent them by a
+
+single 1, 2, and 3, then march
+up the side to define a sigma
+
+4, sigma 5, and a sigma 6.
+
+If you remember that little
+algorithm you can always keep
+
+straight what these reduced
+subscripts represent.
+
+So with that definition, then,
+the stress tensor reduced to
+
+sigma 1, sigma 6, sigma 5, sigma
+6, sigma 2, sigma 4,
+
+sigma 5, sigma 4, sigma 3.
+
+And that takes a tensor and
+degrades it to a matrix.
+
+Because there is no law of
+transformation for this
+
+representation of the
+elements of stress.
+
+OK, then we do something very
+similar with the strain
+
+tensor, epsilon 1 1, 1 2, 1 3,
+epsilon 2 1, epsilon 2 2,
+
+epsilon 2 3, epsilon 3 1,
+epsilon 3 2, epsilon 3 3.
+
+And we saw that for physical
+reasons this tensor also had
+
+to be symmetric.
+
+We had to have epsilon ij
+identical to epsilon ji, the
+
+reason being that if these
+off-diagonal shear strains
+
+were not equal, the state that
+we would be defining was one
+
+of actual deformation combined
+with rigid body rotation.
+
+So unless this was the case,
+the definition performed by
+
+the tensor epsilon iij
+would define rigid
+
+body notation as well.
+
+OK.
+
+We use the same process of
+renumbering to convert this
+
+from a tensor to a matrix.
+
+And we got this into a form,
+epsilon 1, epsilon 6, epsilon
+
+5, epsilon 6, epsilon 2, epsilon
+4, epsilon 5, epsilon
+
+4, epsilon 3.
+
+But in order to do that,
+we saw we had to
+
+consume a factor of two.
+
+So there is a factor of
+two built into the
+
+off-diagonal terms.
+
+And what we have put in here
+is we converted this to
+
+actually epsilon 1, 1/2, epsilon
+6, 1/2, epsilon 5.
+
+And I should have written that
+this way to begin with.
+
+So all these factors of two
+appear so that when we combine
+
+these epsilons we get a nice,
+clean matrix relation between
+
+stress and strain that doesn't
+involve factors of two.
+
+And that's a great convenience
+if we're going to be doing all
+
+of our deformation within
+the framework of
+
+one coordinate system.
+
+OK.
+
+So if we now use these
+definitions to write the
+
+stress in terms of strain, we
+will set up our fourth rank
+
+tensor property.
+
+If we do this first for the
+stress in terms of strain, you
+
+would have a tensor element of
+stress sigma 1 1, which would
+
+be equal to C1 1 1 1 times
+epsilon 1 1 plus C1 1 2 2,
+
+epsilon 2 2 plus C1 1
+3 3, epsilon 3 3.
+
+And then we would have, in
+addition, off-diagonal
+
+elements of strain.
+
+We'd have C1 1 2 3 times epsilon
+2 3 plus C1 1 3 2
+
+times epsilon 3 2 plus C1 1 2 1,
+epsilon 2 1 plus C1 1 1 2,
+
+epsilon 1 2 plus C1 1--
+
+and I should have made this 1
+3 so that the other integers
+
+come out right.
+
+And C1 1 1 2 times an epsilon 1
+1 1 2 plus a C 1 1 2 1 times
+
+an epsilon 2 1.
+
+So that is one line
+of the relation
+
+between stress and strain.
+
+And when we condense this to a
+matrix form, it is surprising,
+
+once we expand it once more,
+at how cumbersome this
+
+expression is.
+
+Now, why do I remind
+you of all this?
+
+Isn't it nice to work in the
+form of a fixed coordinate
+
+system where we can use a
+matrix for the Cijkl's?
+
+The answer is, fine, unless
+you want to change the
+
+coordinate system.
+
+And you might want to do that
+for practical reasons such as
+
+cutting out a specimen which
+makes it convenient to define
+
+the stiffnesses and compliances
+relative to a
+
+coordinate system taken
+along the logical
+
+directions in the specimen.
+
+And the other reason for doing
+it, and that is what I want to
+
+do a little bit of this
+afternoon, is to derive the
+
+symmetry restrictions on the
+stiffnesses and compliances.
+
+You cannot transform a matrix
+representation of the
+
+stiffness or the compliance.
+
+You can only do this for the
+full-blown tensor arrangement.
+
+So having collapsed down, which
+we'll do momentarily
+
+just to remind you of how it
+goes, we will have to expand
+
+again to derive symmetry
+restrictions.
+
+Do not exit at this point.
+
+We're not going to do any of
+these calculations in their
+
+full glory detail.
+
+We'll just set up the problem
+and then jump immediately to
+
+the outset.
+
+So how does this pay out if we
+try to make the condensation?
+
+I remind you again that the
+symbol C stands for stiffness,
+
+and the symbol S, which we'll
+see later, the Sijkl's are
+
+call compliances.
+
+And the perversity of that
+semantic description of these
+
+tensor elements is perverse for
+reasons that I have never
+
+really been able
+to understand.
+
+So if we go down to matrix form,
+we'll write instead of
+
+sigma 1 1, simply sigma 1 1.
+
+We'll call this C1 1 times
+epsilon 1 plus C1 2
+
+times epsilon 2.
+
+So far so good.
+
+C1 3 times epsilon 3.
+
+And now we have problems,
+because epsilon 2 3 was
+
+defined as 1/2 of epsilon 5.
+
+Now we'll have a C1
+5 here, and then a
+
+C1 3 2 is C1 5 again.
+
+And this also is 1/2
+of epsilon 5.
+
+And then similarly,
+this is C1--
+
+I'm sorry.
+
+This is C1 4.
+
+This is C1 5 times 1/2 of
+epsilon 5 plus C1 5 times 1/2
+
+of epsilon 5 plus C1 6 times
+1/2 of epsilon 6 plus C1 6
+
+times 1/2 of epsilon 6.
+
+So this, given the way in which
+we had defined matrix
+
+strain, initially in
+connection with
+
+piezoelectricity when we entered
+the realm of third
+
+rank tensors, this
+will play out OK.
+
+This says that sigma 1 is simply
+C1 epsilon 1 plus C1 2
+
+times epsilon 2 plus C1
+3 times epsilon 3.
+
+And now the 1/2 gets absorbed,
+and it's simply C1 4 times
+
+epsilon 4, and so on.
+
+If we look at another line, one
+that involves some of the
+
+off-diagonal terms and strain,
+if we, for example, look at
+
+sigma 2 3 and we write this down
+as sigma 2 3 times 1 1
+
+times epsilon 1 1 plus C2 3 2 2
+times epsilon 2 2 plus C2 3
+
+3 3 times epsilon 3 3 plus C--
+
+and I'll just write down a few
+of these additional terms.
+
+This would be C2 3 3 2 times
+epsilon 3 2 plus C2 3 2 3,
+
+epsilon 2 3, and then other
+terms for additional terms,
+
+and epsilon ij with i not equal
+to j, which are going to
+
+behave the same way.
+
+So if we convert this, we go
+to sigma, and we would call
+
+this sigma 4.
+
+This would be C4 1 in matrix
+notation times epsilon 1 plus
+
+C4 2 time epsilon 2 2 plus
+C4 3 times epsilon 3.
+
+And now this matrix element
+would be C4 4.
+
+And in place of the tensor
+element of strain epsilon 3 2,
+
+we would write 1/2
+of epsilon 4.
+
+And the next term is again a C4
+4 times a 1/2 epsilon 4 and
+
+the terms in epsilon 5
+and epsilon 6 would
+
+behave the same way.
+
+So you can see that the factor
+2 is absorbed, and this
+
+becomes simply C4 4
+times epsilon 4.
+
+So all the factors of
+2 have disappeared.
+
+And we can say, provided we
+remember the way we have
+
+condensed the elements of tensor
+strain, we can say with
+
+complete confidence that in our
+matrix notation, sigma i
+
+is Cij times epsilon j where i
+goes 1, 2, and 3, and j goes
+
+1, 2, 3 all the way up to six.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: No.
+
+No, no, these are the--
+
+yeah, I'm sorry.
+
+Yeah, inj.
+
+So it's a six by six
+matrix, right.
+
+Right you are.
+
+And this is a six by six.
+
+And in here are 36 businesses
+stiffnesses.
+
+OK, any comments other
+than, yuck?
+
+And again, if you stay
+in one coordinate
+
+system it's not so bad.
+
+In fact, instead of having nine
+by nine 81 terms you have
+
+36 stiffnesses.
+
+And that's a great
+convenience.
+
+Unfortunately, things are not
+quite so simple if we work
+
+with the compliances represented
+by the symbol S.
+
+And if we attempt to write
+strain in terms of stress,
+
+we'll have an S1 1 1
+1 times sigma 1.
+
+We'll have an S1 1 2 2 times
+sigma 2 2 plus an S1 1 3 3
+
+times a sigma 3 3 plus an S1 1
+2 3 times a sigma 2 3 plus an
+
+S1 1 3 2 times a sigma 3 2,
+and an S1 1 2 3 3 1 times
+
+sigma 3 1 plus an S1 1 3 times
+a sigma 1 3, and then other
+
+off-diagonal terms which I
+won't bother to mention.
+
+So if we convert this to matrix
+form, epsilon 1 1 would
+
+be replaced by the matrix
+term epsilon 1.
+
+S1 1 1 1 would become S1 1, and
+this would be sigma 1, and
+
+an S1 2 times a sigma 2, plus
+and S1 3 times sigma 3.
+
+And now we have a problem,
+Houston.
+
+Because we would have an S1 4
+times a sigma 4 plus an S1 4
+
+times sigma 4.
+
+And now in the sigmas there is
+no factor 1/2 in the matrix
+
+representation of stress as
+there was with strain.
+
+Because we ate the factor
+of 2 in defining strain.
+
+But now there is no factor
+of 2 and stress.
+
+So we're going to have to
+do something with that.
+
+So this would give us some
+additional terms, S1 5 times
+
+sigma 5, and then an S1 5
+times a sigma 5 again.
+
+So what are we going to do?
+
+Again, we're stuck.
+
+We can either say that epsilon
+i is equal to Sij times sigma
+
+j if j is not equal
+to 4, 5, or 6.
+
+Or we can absorb, again, a
+factor of 2 in the definition
+
+of the compliances.
+
+And that, again, since we will
+usually be working in one, and
+
+the same coordinate system, is
+the convenient thing to do.
+
+So what we will do is
+to define this as S1
+
+4 times sigma 4.
+
+And in so doing, we have to
+combine the factor of 2 into
+
+the definition of S1 4.
+
+So S1 4 would be equal to 1/2
+of S1 1 2 3 plus S1 1 3 2.
+
+So it's going to be 1/2 of one
+of these equal terms that
+
+involve one on-diagonal
+subscript and one
+
+off-diagonal subscript.
+
+So this is the only way we're
+going to be able to write a
+
+nice, clean matrix
+representation.
+
+Things get worse.
+
+AUDIENCE: Sir?
+
+PROFESSOR: Yes?
+
+AUDIENCE: You're sure
+of your [INAUDIBLE]?
+
+PROFESSOR: Yeah, this would
+be equal to 2S1 4.
+
+I'm sure it's 1/2.
+
+I'm not sure of what term
+would go in front.
+
+So I would have 2S1
+4 times sigma 4.
+
+And if I want to write this--
+
+I'm sorry.
+
+Let me go back to the full
+matrix expression.
+
+I would have S1 1 2 3 times
+sigma 2 3 plus S1 1 3 2
+
+times sigma 3 2.
+
+I know that sigma 2 3 is equal
+to sigma 3 2, so I could write
+
+this as S1 1 2 3 plus S1 1 3 2
+just simply times sigma 2 3,
+
+one of them.
+
+Now what I would really like to
+do is to write this as S1.
+
+Let's change this to sigma 4.
+
+I would like to write
+this as S1 4.
+
+So it follows then that
+S1 4 is equal to S1 2
+
+3 plus S1 1 3 2.
+
+And that is the other way
+around, isn't it?
+
+Thank you.
+
+I knew there was a factor of
+1/2, but it goes in here.
+
+AUDIENCE: And then there's
+no 2 at all.
+
+If you wanted to say that S1 1
+2 3 is equal to S, 1 1 3 2,
+
+then you would have S1
+4 equal to 2S1 1 3 2.
+
+PROFESSOR: OK, you're
+right, you're right.
+
+So it's this.
+
+Let's leave it at that.
+
+But if these are equal, we could
+say-- and we did show
+
+that the compliance tensor is
+symmetric, so we could say
+
+that this is equal to
+2S1 1 2 3 or 2S1 1 3
+
+2 as they're equal.
+
+I told you it was going to get
+bad, but I didn't think I
+
+would be contributing to it
+the extent that I am.
+
+I don't know if you really want
+to see this, but this
+
+gets even worse when we deal
+with something like epsilon 2
+
+3, where this is a term
+that would be
+
+replaced by epsilon 4.
+
+And then all of our absorbed
+factors come back to haunt us.
+
+Let me go through
+this quickly.
+
+This would be S2 3 1 1 times
+sigma 1 1 plus S2 3 2 2 times
+
+sigma 2 2 plus S2 3 3
+3 times sigma 3 3.
+
+And then we'll have these terms,
+off-diagonal terms S2 3
+
+3 1, sigma 3 1 plus S2 3 1 3
+times sigma 1 3, and so on,
+
+other terms.
+
+OK, and going from epsilon 2 3
+to epsilon 4, we have to put
+
+on a factor 1/2.
+
+And that says that that 1/2 is
+going to create problems in
+
+the first term in
+this expansion.
+
+We'd call this sigma 1 1.
+
+We'd like to call this S4 1.
+
+But what is S4 1 from what
+we have defined here?
+
+It's the sum of two
+tensor elements.
+
+So we will have to define, now,
+again, S4 1 equals the
+
+same as we did before.
+
+It's going to be equal to the
+term S2 3 1 1 plus S3 2 1 1 1.
+
+And therefore if I put a 1/2 in
+this definition, then that
+
+will cancel, so far.
+
+But then in the terms that
+come down in the lower
+
+quadrant of the matrix--
+
+and I will just right
+in two terms.
+
+We've got an S2 3 31 that
+we would write as S4
+
+4 times sigma 4.
+
+And then I would have another
+term, S4 4 times sigma 4.
+
+But the S4 4 really is a sum
+of two tensor elements.
+
+So my definition of an S4
+4 is that it should be--
+
+AUDIENCE: Isn't that sigma
+5 [INAUDIBLE]?
+
+PROFESSOR: You're right,
+you're right.
+
+Yeah, this is 5.
+
+So this was right, 3 1,
+and this is sigma 5.
+
+You're right.
+
+And I go to S4 5, yeah.
+
+No, sigma--
+
+OK, yeah.
+
+OK, let me cut to the chase.
+
+What we're going to have to do
+is to put in not the factor
+
+1/2 that we had here,
+but there's going to
+
+be a factor 4 that--
+
+something like S--
+
+which one are we dealing with?
+
+Things like S2 3 3 1,
+something like S4--
+
+and we're dealing with 5.
+
+S4 5 is going to be defined as
+S1, S2 3 1 3 plus S2 3 3 1
+
+plus S3 2 1 3 plus S3 2 3 1.
+
+So we're going to have to put in
+a factor of 1/4 in front of
+
+the S4 5 in order to accommodate
+for those terms.
+
+So our definition, then, in
+going from tensor compliances
+
+to matrix compliances is
+much more complicated.
+
+And the rule-- and just to
+summarize this, I gave you a
+
+handout last time.
+
+The necessary conventions to
+absorb these factors of 2 and
+
+4 is that--
+
+and I didn't bring it with me.
+
+OK, I just simply did not
+bring it with me.
+
+So I wouldn't attempt
+to summarize it.
+
+All right.
+
+So hopefully I've convinced you
+of nothing other than that
+
+these conversions are messy.
+
+But the summary is that for the
+compliances, the Sijkl,
+
+you take this equal to
+Slm if l and m are
+
+equal to 1, 2, or 3.
+
+Then you have to replace Sijkl
+by 1/2 of Slm if i, j, or kl
+
+is 4, 5, or 6.
+
+And then you have to write Sijkl
+as 1/4 of Slm if i, j,
+
+and kl are 4, 5, or 6.
+
+But once you're into the
+coordinate system, which will
+
+be fixed in matrix notation,
+things are simple, since you
+
+don't have to worry about
+these factors of 2 or 3.
+
+The reason I did this is I
+would like to now talk a
+
+little bit about how one can
+define important scalar moduli
+
+that describe a particular
+phenomenon.
+
+If you ask the question, how do
+mechanical properties vary
+
+with direction, we've got six
+unique elements of stress.
+
+And we've got six independent
+elements of
+
+strain that can work.
+
+And if you wanted to show how
+each one of those elements
+
+varied with the other
+one, you'd need 36--
+
+6 times 6, 36--
+
+representation surfaces
+and this is
+
+not going to be fruitful.
+
+So just as we did for
+piezoelectricity where we
+
+could define a scalar modulus
+which represented the
+
+component of polarization normal
+to a very thin plate--
+
+making it a thin plate means
+you're going to measure
+
+primarily the charge on the
+large surface, because
+
+polarization is charge
+per unit area.
+
+So if you looked at the surface
+of a plate with x1
+
+normal to the plate, you are
+going to have a specimen that
+
+primarily gives you a measure
+of P1, or the charge on a
+
+surface normal to x1.
+
+And then you could apply any
+of six different states of
+
+simple stress.
+
+And one thing that you could
+do is squeeze it with the
+
+tensile stress in the same
+direction as the
+
+normal to the surface.
+
+And that was the longitudinal
+piezoelectric modulus.
+
+Then on the quiz you looked at
+another modulus that related a
+
+component of polarization on
+another surface in response to
+
+a tensile stress that was
+not parallel to it.
+
+There are a number of such
+moduli and mechanical
+
+properties.
+
+Probably the most important
+one is something called
+
+Young's modulus, which I'm
+sure you've all heard of.
+
+And Young's modulus involves
+taking a very long rod of the
+
+material and hanging
+a weight on it.
+
+And that weight will
+induce a strain.
+
+And if we take this as the
+direction of x1, we will, with
+
+Young's modulus, relate the
+change of length to the
+
+initial length of the rod.
+
+And my question now is,
+rhetorically, do we want to do
+
+this in terms of stiffnesses
+or compliances?
+
+Does it make any difference?
+
+Yeah, makes a lot of difference
+in terms of the
+
+simplicity of the result
+that you get.
+
+Suppose we wanted to do this in
+terms of the compliances.
+
+What we'd be then applying
+would be a sigma 1.
+
+And this would be given
+by the compliance C1 1
+
+times the strain E1.
+
+That looks like exactly
+what we want.
+
+This delta l over l for this
+one-dimensional specimen with
+
+a one-dimensional directional
+applied stress, this would be
+
+simply epsilon 1.
+
+And that's force per
+unit area here.
+
+This would be sigma 1 1.
+
+And it looks as though what we
+want is a C1 1 1 that relates
+
+a sigma 1 1 to an epsilon 1 1.
+
+Is this going to be a definition
+that I would want
+
+to make for describing this?
+
+My colleague here shakes his
+head very seriously.
+
+No.
+
+Do you want to share
+your reservation?
+
+AUDIENCE: Because as I recall,
+Young's modulus, once strain
+
+is weaker output [INAUDIBLE]
+in terms of stress you're
+
+going to want a compliance.
+
+PROFESSOR: That's one answer.
+
+AUDIENCE: You could
+theoretically get either one
+
+[INAUDIBLE].
+
+PROFESSOR: If I could restate
+your objection, we can't
+
+impose a strain to
+get a stress.
+
+We really stresses the
+independent variable,
+
+practically speaking.
+
+We can stress it, but we can't
+instantly say, [INAUDIBLE]
+
+develop a epsilon 1.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You betcha.
+
+That's the reason.
+
+Added onto this is not only this
+term, but there will be a
+
+C1 2 times epsilon 2 plus
+a C1 3 times an
+
+epsilon 3, and so on.
+
+So we're not going to be able
+to get a nice, tidy relation
+
+between the tensile strain that
+we're measuring and the
+
+tensile uniaxial stress that
+is produced there.
+
+So the relation of stress in
+terms of strain that involves
+
+the stiffnesses is just
+not going to work.
+
+But if we would instead express
+epsilon1 in terms of a
+
+compliance, a matrix compliance
+S1 1 times sigma 1,
+
+that's all that she wrote.
+
+We're measuring this by design
+by selecting an elongated
+
+specimen for which we'll
+primarily be seeing epsilon 1.
+
+This is not to say these
+other strains exist.
+
+There will be lateral strains
+here that will be epsilon 2
+
+and epsilon 3.
+
+There will be shear strains.
+
+Sounds mind-boggling.
+
+You pull the sample in
+this direction, and
+
+what it does is shear.
+
+Well, if this were a single
+crystal, that would happen.
+
+And these would be other
+components of deformation.
+
+But if we measure a pi sigma 1
+and measure epsilon 1, then
+
+this is the way we have
+to define it.
+
+And the definition of Young's
+modulus is that 1 over S1 1 is
+
+sigma 1 over epsilon 1.
+
+And this is Young's modulus.
+
+I would hasten to observe that
+it is unfortunate that this
+
+very practical modulus involves
+the S's, which have
+
+all these complicated
+factors of 2 and 4.
+
+And therefore, if we try to go
+to a particular symmetry and
+
+ask the question, how does
+Young's modulus change as we
+
+cut this rod in different
+orientations
+
+from the single crystal.
+
+So I would like to illustrate
+for you how we would do this.
+
+I'm going to take a very,
+very simple example.
+
+If you look in the table of
+symmetry restrictions that I
+
+passed out a couple of times
+ago, prior to the quiz, for an
+
+isotropic the tensor has a
+different form than it does
+
+for a cubic crystal.
+
+Cubic crystals are elastically
+anisotropic.
+
+But the form of the stiffness
+tensor for an isotropic
+
+material was S1 1, S1 2,
+S1 2, 0, 0, 0, S1 2, S1
+
+1, S1 2, 0, 0, 0.
+
+Then the diagonal terms, if the
+material was isotropic,
+
+was 2s1 1 minus S1 2 for this
+term, 0, 0, 0, 0, 0, 0, and
+
+again, a 2S1 1 minus S1 2 plus
+a 0, and then 0, 0, 0, 0, 2S1
+
+1 minus S1 2.
+
+OK.
+
+Let me now derive Young's
+modulus as a function of
+
+direction and show that,
+in fact, this says that
+
+regardless how you orient the
+rod, the value of Young's
+
+modulus will stay the same.
+
+Let me also do something else
+first, though, which is
+
+something we should have
+scratched our head over when
+
+we first encountered it.
+
+Here's something curious.
+
+When we looked at symmetry
+constraints on single
+
+crystals, we found that for a
+cubic crystal, C6 6 had to be
+
+equal to 1/2 of C1 1 minus C1
+2 if the stiffnesses were to
+
+be independent for all symmetry
+transformations.
+
+For the compliances, however,
+we found that S6 6 had to be
+
+equal to 2 times S1
+1 minus S1 2.
+
+Two very different equalities
+between tensor elements to
+
+make the elastic behavior be
+invariant to the symmetry
+
+transformations of
+a cubic crystal.
+
+How come?
+
+How come these are
+so different?
+
+Well, they have to be, in terms
+of the tensor, the same
+
+sort of a quality.
+
+And the reason they don't look
+the same is because of our
+
+different absorption of the
+factors of 2 and 4 in defining
+
+the stiffnesses an in defining
+the compliances.
+
+Remember that for the Cijkl's
+there was no factor of 2 or 4
+
+introduced in defining
+the matrix elements.
+
+So this one is OK.
+
+This is a true equality between
+tensor elements, for
+
+any tensor whatsoever of fourth
+
+rank for a cubic crystal.
+
+For these terms, these
+are off-diagonal.
+
+This is an off-diagonal
+compliance.
+
+And our definition is that Sijkl
+is equal to Smn, for m
+
+and n not equal to 4, 5, or 6.
+
+Here's this crazy thing again.
+
+It's equal to 1/2 of Smn for
+m or n equal to 4, 5, or 6.
+
+And it's equal to 1/4
+of Smn for m and n
+
+equal to 4, 5, or 6.
+
+So S6 6 here is actually
+4S1 2 1 2.
+
+And that's supposedly equal to
+2S1 1, which is really S1 1 1,
+
+minus S1 1 2 2.
+
+And this says that 1/2 of S1
+2 1 2 is equal to S1 1 1 1
+
+minus S1 1 2 2.
+
+So this is exactly the same
+constraint on tensor elements,
+
+when we take out these
+factors of 2 and 4
+
+that have been absorbed.
+
+So this, in fact, although it
+looks very different with
+
+those factors absorbed, is
+exactly this same relation.
+
+So the symmetry constraint
+is the same.
+
+AUDIENCE: How'd you
+get 1/2 there?
+
+PROFESSOR: Hmm?
+
+How did I get 1/2 here?
+
+It's 4S1 2 2 had to be equal
+to 2S1 1 minus S1 2.
+
+And this was the equality.
+
+I'm working up this way.
+
+So this was the statement in
+the matrix forms of the
+
+compliances that I handed out.
+
+Looks different from the
+term on the left.
+
+So I wrote this now in terms
+of the matrix elements.
+
+And the factor of
+4 comes in here.
+
+The 2 was here in the equality
+that had to be held that the
+
+tensors stay invariant.
+
+And if I bring this 2 over on
+the left-hand side, it's
+
+exactly the same as when--
+
+AUDIENCE: Shouldn't
+it be 2 now?
+
+[INAUDIBLE].
+
+[INAUDIBLE] the right side.
+
+PROFESSOR: No, this is just
+replacement of the matrix
+
+terms with the definition
+of the tensor.
+
+AUDIENCE: Right, but
+[INAUDIBLE].
+
+AUDIENCE: You're just dividing
+4 by 2, right?
+
+PROFESSOR: Yeah, exactly.
+
+AUDIENCE: So wouldn't that
+make [INAUDIBLE]?
+
+PROFESSOR: Oh, ha, OK.
+
+AUDIENCE: You want to be able
+to [INAUDIBLE] by 4, so it'd
+
+be S12 1 2 equals 1/2
+the difference
+
+to be equal to that.
+
+PROFESSOR: OK, OK.
+
+Thank you.
+
+OK, let me then go back to
+what I started out to do.
+
+And I will write just one line
+of how we would go about
+
+expanding this just to indicate
+how intricate it is,
+
+and then I'll give a few
+examples for two point groups
+
+of how Young's modulus varies
+with direction.
+
+OK.
+
+What we're going to say, then,
+is that one of these
+
+compliances, S1 1 1 1 prime is
+going to be equal to l 1/4
+
+times S1 1 1 1 plus l 2/4 times
+S2 2 2 2 plus l 3/4
+
+times S3 3 3 3 .
+
+And just now doing what we know,
+that any Sijkl prime is
+
+going to be Cii, Cj capital J,
+Ck capital K, Cl capital L--
+
+these are direction cosines
+now, not stiffnesses--
+
+times Sijkl.
+
+So it's a quadrupole summation
+over all of the non-zero
+
+tensor elements.
+
+So what I'm doing now is
+taking these terms and
+
+expanding them to the
+full tensor form.
+
+So S1 1 1 1 prime, that's
+the first term in
+
+the transformed tensor.
+
+That's going to be these terms
+plus l1l2 squared times S1 1 2
+
+2 plus S2 2 1 1 plus l1 squared
+l3 squared times S1 1
+
+3 3 plus S3 3 1 1, and then
+still another term, l2 squared
+
+l3 squared times S2 2
+3 3 plus S3 3 2 2.
+
+And then there will be terms
+of the form l2 squared l3
+
+squared times, again, four
+terms, S3 2 3 2 plus S1 2 3 3
+
+plus S2 3 3 2 plus S2 3 2 3, and
+then similarly, terms in
+
+the squares of l1 and l2, and
+these would involve four terms
+
+of the form S1 2 1 2 plus
+permutation 0, and then l1
+
+squared l3 squared times, again,
+four terms, S1 3 1 3
+
+and permutation 0
+for four terms.
+
+OK.
+
+So what do we have now?
+
+We have an expression
+for S1 1 1 1 prime.
+
+And this is, in fact, 1 over
+Young's modulus E. And we've
+
+done this summation over the
+supposed non-zero tensor
+
+elements in the matrix for
+an isotropic material.
+
+And if I simplify this, and
+this will be just one more
+
+tedious and then we can see,
+that is for these equalities,
+
+we ought to, for l1, l2, l3,
+get the same value, S1 1.
+
+And that is indeed
+what happens.
+
+So the summation, if I simplify,
+is l 1/4 times S1 1
+
+plus l 2.4 times S2 2 plus
+l 3/4 times S3 3.
+
+And then a collection of terms
+plus l1 squared l2 squared, S1
+
+2 plus S2 1.
+
+And then similar terms in l1 and
+l3, l1 squared l3 squared,
+
+S1 3 plus S 3 1 plus l2 squared
+l3 squared times
+
+S2 3 plus S3 2.
+
+And then some terms that stand
+by themselves, l2 squared l3
+
+squared times S4 4 plus l1
+squared l2 squared S6 6 plus
+
+l1 squared plus l3 squared
+times S5 5.
+
+And consolidating this, this is
+going to be equal to l 1/4
+
+plus l 2/4 plus l
+3/4 times S1 1.
+
+And then combining terms in the
+second power of direction
+
+cosines, l1 squared l2 squared
+plus l1 squared l3 squared
+
+plus l2 squared l3 squared.
+
+And this is all times 2S1 2
+plus 2S1 1 minus 2S1 2.
+
+So S1 2 drops out.
+
+And all this will be simply l
+1/4 plus l 2/4 plus l 3/4.
+
+And then I'll add in the other
+terms here that involve
+
+products of squares of
+direction cosines.
+
+And all this is times S1 1.
+
+But this turns out to be equal
+to simply l1 squared plus l2
+
+squared plus l3 squared, the
+sum of the squares of the
+
+direction cosines of our rod,
+quantity squared times S1 1.
+
+And this term inside the
+parentheses is 1.
+
+So indeed, S1 1 prime
+is equal to S1 1.
+
+So the value of Young's modulus
+has not changed with
+
+direction if the form of the
+compliance tensor is like so.
+
+And I think you would probably
+have taken my word for that,
+
+but it was intended primarily as
+an example of how, when S1
+
+1 prime is the reciprocal of
+Young's modulus, how you would
+
+set up a transformation
+for S1 1 prime.
+
+And the form of this polynomial
+would be exactly
+
+the same, even for a triclinic
+crystal, if you included all
+
+the non-zero terms
+in this fashion.
+
+All right, so let me wrap things
+up in another couple
+
+minutes for some cases that
+are real symmetries, where
+
+Young's modulus is
+anisotropic.
+
+And working in exactly the same
+way for the tensor that
+
+is the appropriate one for a
+cubic crystal, we would lift
+
+out the form of the
+stiffness matrix.
+
+The reciprocal of Young's
+modulus is S1 1 prime, so what
+
+we're saying is we have
+a long, skinny rod.
+
+This is x1.
+
+And what we're doing, if this
+is a single crystal, is
+
+examining how Young's modulus
+changes as we change the
+
+direction of the rod to a new
+orientation, x1 prime, that's
+
+described by direction cosines
+l1, l2, L3, relative to x1.
+
+The expression that results by
+exactly the process that we
+
+muddled through a moment ago is
+that for a cubic crystal,
+
+the form of S1 1 prime as a
+function of direction does
+
+indeed give anisotropy.
+
+Isaiah It's S1 1 minus 2
+times S1 1 minus S1 2
+
+minus 1/2 of S4 4.
+
+Remember, for a cubic crystal, 1
+1, 2 2, and 1 4 are the only
+
+non-zero terms.
+
+And then this is times a
+polynomial l1 squared l2
+
+squared plus l2 squared
+l3 squared plus
+
+l3 squared l1 squared.
+
+So this is, again the reciprocal
+of Young's modulus.
+
+And it turns out to have a
+constant term, S1 1 , which is
+
+what we found for the
+isotropic material.
+
+But from that, as the direction
+cosines change, we
+
+subtract off a term that is a
+linear combination of 1 1, 1
+
+2, and 4 4.
+
+So the question is, is this
+positive or negative?
+
+The direction cosines are all
+squared, so this term here is
+
+always going to be positive.
+
+So are we going to take the
+thing that we found for an
+
+isotropic material, which was
+a constant, Young's modulus,
+
+which was 1 over S1 1 prime,
+and that's equal to the
+
+Young's modulus E.
+
+Are we going to add or subtract
+something to it?
+
+Well, it turns out that if you
+look at real materials, it can
+
+be either positive
+or negative.
+
+It's usually positive.
+
+So that says we are going to
+subtract off a term which goes
+
+as products of squares
+of direction cosines.
+
+And this is something that's
+going to be zero along the
+
+direction 1 0 0.
+
+So along the reference axes
+x1, x2, x3, which if you
+
+remember, where this form of
+the matrix came from was
+
+taking the axes along the edges
+of the cubic crystal.
+
+It turns out that this is going
+to be equal to 1/3 along
+
+the direction 1 1 1.
+
+So if this term is plus, nothing
+gets added onto the
+
+surface in the directions that
+correspond to the four-fold
+
+axes or the twofold axes
+of a cubic crystal.
+
+Nothing gets added
+on if it's plus.
+
+But along the body diagonals,
+this takes on a value of 1 3,
+
+so a positive thing
+gets added on.
+
+And the best way I can describe
+this surface-- it's
+
+not a simple surface--
+
+it looks like a cube
+with fuzzy edges.
+
+So we had a cube and started
+to dissolve it.
+
+So this is how the reciprocal
+of Young's
+
+modulus varies with direction.
+
+If, on the other hand, this
+term is negative--
+
+so this is what you get
+if it's positive.
+
+If it's negative, again, you
+start with the basic isotropic
+
+variation of 1 over S1 1 1.
+
+If it is negative, and there's
+one metal, that's molybdenum--
+
+molybdenum has a negative value
+of these compliances.
+
+It looks like a surface that has
+indentations along the 1 1
+
+1 direction.
+
+So it looks like something
+with a dimple in it.
+
+There is a final case, which
+is not realized for any
+
+material that I know
+of, if that term is
+
+0, then it's isotropic.
+
+Let me give you one other
+variation that comes straight
+
+out of [INAUDIBLE].
+
+And this is for a hexagonal
+crystal that might be a
+
+hexagonal close-packed
+crystal.
+
+For zinc specifically, which
+is a hexagonal close-packed
+
+metal, the form of the matrix is
+S1 1, S1 2, S1 3, 0, 0, 0,
+
+S1 1, S1 2, 0, 0, 0, S3 3,
+0, 0, 0, S4 4, 0, 0, S4
+
+4, 0, and S4 4.
+
+In the values of these specific
+compliances are 8.4
+
+for S1 1, for S1 2 1.1, for S1
+3, minus 7.8, for S3 3, 28.7,
+
+for S4 4, 26.4.
+
+And these are all in units of
+10 to the minus 12 meters
+
+squared per Newton.
+
+That's good old MKS units.
+
+It turns out that there are 10
+to the 2 meters squared per
+
+Newton per 1 centimeter
+squared per dyne, if
+
+you like CGS units.
+
+The form of the reciprocal of
+Young's modulus, it turns out
+
+to be a surface of revolution.
+
+This is x3, which is the
+direction of C. And that's the
+
+surface of revolution and the
+value of S1 1 prime as a
+
+function of the angle theta.
+
+That's the only parameter we
+need examine the variation
+
+with since it's a surface
+of revolution.
+
+S1 1 prime is equal to S1 1
+times the sine of theta to the
+
+fourth power plus S3 3 times
+the cosine of theta to the
+
+fourth power plus S4 4 plus
+2S1 3 times sine squared
+
+theta, cosine squared theta.
+
+So it's a fairly exotic surface,
+even as a surface of
+
+revolution.
+
+And what this looks like, it's
+something that peaks out at 3
+
+times 10 to the minus 12
+centimeters squared per dyne
+
+along the direction of C. It's
+something that comes down very
+
+sharply as you approach the
+normal to the C axis.
+
+And then there's a cute little
+wiggle just near the axis.
+
+So it looks something
+like that.
+
+Not a terribly isotropic
+surface, and a variation of
+
+Young's modulus of 3 to 1 in
+the direction parallel to C
+
+and perpendicular to C. So
+there are lots of exotic
+
+surfaces of this sort.
+
+All right.
+
+I did run a little bit over.
+
+And I will absent myself and
+let you express yourself
+
+candidly on the questionnaire.
+
+Except for these numbers that
+I just put up on the
+
+blackboard, I haven't really
+said anything about, much
+
+about, numbers.
+
+So let me pass around some
+examples, not for metals,
+
+which we just looked
+at, but for oxides.
+
+And this is interesting, because
+you'll remember there
+
+was an additional equality
+between the stiffnesses called
+
+the [? Kowshi ?]
+
+equality, which was supposed to
+hold for physical reasons,
+
+not for reasons of symmetry, if
+the forces were central, if
+
+the crystal was under a state
+of no stress, and if all of
+
+the atoms were situated at
+a center of symmetry.
+
+The first set of data that you
+have on the top sheet is for
+
+MGO, which is cubic.
+
+It's predominantly
+ionic compounds.
+
+And the atoms are all
+octahedrally coordinated.
+
+So all of the requirements
+for the [? Kowshi ?]
+
+equality should hold.
+
+And you can see they're
+not really exact.
+
+And that's probably due to
+the covalent character.
+
+The two different sets of data
+here are for measurements by
+
+two separate observers.
+
+The second page is for
+aluminum oxide.
+
+And again, you see the order of
+magnitudes of the numbers
+
+on the order of 10 to the 12
+dynes per centimeter squared
+
+in general, and variation from
+one to another for a lumen of
+
+a factor of about four.
+
+I meant to bring the book in,
+but I left it behind in my
+
+rush to come off.
+
+Where do you get
+these numbers?
+
+And it's hard to really find.
+
+And the book from which I took
+these data are by two workers,
+
+Simmons and Wang.
+
+And it's called Handbook
+of Elastic Constants,
+
+I think that is.
+
+And this is a book that was
+published by MIT Press.
+
+Valuable repository of data,
+but it's all numbers.
+
+And there are many, many
+materials in here.
+
+Simmons and Wang, interestingly,
+are
+
+geophysicists.
+
+Why should geophysicists
+care about stiffnesses?
+
+Why?
+
+Because these guys are going all
+over the face of the earth
+
+setting off little bits of
+explosive that send off
+
+seismic waves.
+
+And they probed the interior
+of the earth by the
+
+propagation of elastic waves.
+
+And the elastic waves depend
+on the square root of
+
+stiffnesses over the density
+of the material.
+
+So they're very, very interested
+in the elastic
+
+properties of particularly
+rock-forming minerals.
+
+Another interesting comment on
+this book is that there is no
+
+set of data for a single
+triclinic crystal.
+
+Too many stiffnesses that are
+independent, I guess, and too
+
+few materials that, fortunately,
+are anisotropic
+
+and triclinic.
+
+OK, I am going to quit.
+
+And thank you for
+your attention.
+
+You've been a good class.
+
+And we've covered all sorts of
+exotic aspects of the behavior
+
+of crystalline materials.
+
+And you might think with some
+justification that you know
+
+all there is to know about
+symmetry and tensor properties
+
+of materials.
+
+But nevertheless, I would
+caution you that you don't
+
+know everything.
+
+So I have a final handout fill
+in the chinks, the cracks that
+
+we've not been able to fill.
+
+And this is a set of data that
+is titled "Think You Know
+
+Everything?" And this will fill
+in some things that you
+
+really don't know.
+
+And it has a lot of very
+useful items on here.
+
+For example, there are
+293 different ways to
+
+make change for $1.
+
+You didn't know that.
+
+2/3 of the world's eggplant
+is grown in New Jersey.
+
+I'm a native of New Jersey, and
+even I didn't know that.
+
+The longest one-syllable word
+in the English language is
+
+"screeched." OK.
+
+And so it goes.
+
+In most advertisements--
+
+this is one I never checked
+out-- in most advertisements
+
+the time displayed on a watch
+is 10 minutes after 10:00.
+
+Don't know why.
+
+How many ridges are around
+the edge of a dime?
+
+118.
+
+And how many little dimples
+are there on a
+
+regulation golf ball?
+
+If you count them up, you'll
+find that there are 336.
+
+So I'll end with one for the
+benefit of some of our
+
+visiting students.
+
+In England, the Speaker of the
+House is not allowed to speak.
+
+There is my oxymoron
+of the day.
+
+And with that I shall
+leave you, and I
+
+hope you enjoy these.
+
+It's one of these things
+that circulates
+
+around on the internet.
+
+So as the sheet finishes, now
+you do know everything.
+
+So I'll leave you, and again I
+thank you for your faithful
+
+attendance.
+
+And you shall see me when you
+come to call for your quizzes.
+
+And I will, as most of you
+requested, send out an email
+
+to let you know when you can
+come and pick those up.
+
+So again, thank you.
+
+Enjoy the mid-term break.
+
+And take advantage of some of
+the really interesting things
+
+that go on extracurricularly
+around the institute.
+
+So that's it.
+
+Thank you, and au revoir.
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/feb9j65Iz4w.txt b/feb9j65Iz4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..10f82c210bbac28f33d6b0479de8d6b8674becaf
--- /dev/null
+++ b/feb9j65Iz4w.txt
@@ -0,0 +1,6491 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me just say our next topic
+
+ align:start position:0%
+okay let me just say our next topic
+ 
+
+ align:start position:0%
+okay let me just say our next topic
+moving really toward machine learning
+
+ align:start position:0%
+moving really toward machine learning
+ 
+
+ align:start position:0%
+moving really toward machine learning
+would be the last section of section of
+
+ align:start position:0%
+would be the last section of section of
+ 
+
+ align:start position:0%
+would be the last section of section of
+chapter six about stochastic gradient
+
+ align:start position:0%
+chapter six about stochastic gradient
+ 
+
+ align:start position:0%
+chapter six about stochastic gradient
+descent I think professor sois from
+
+ align:start position:0%
+descent I think professor sois from
+ 
+
+ align:start position:0%
+descent I think professor sois from
+computer science is if he's able he will
+
+ align:start position:0%
+computer science is if he's able he will
+ 
+
+ align:start position:0%
+computer science is if he's able he will
+take the class Friday and tell us about
+
+ align:start position:0%
+take the class Friday and tell us about
+ 
+
+ align:start position:0%
+take the class Friday and tell us about
+STDs stochastic gradient descent
+
+ align:start position:0%
+STDs stochastic gradient descent
+ 
+
+ align:start position:0%
+STDs stochastic gradient descent
+critical algorithm I mean that at a
+
+ align:start position:0%
+critical algorithm I mean that at a
+ 
+
+ align:start position:0%
+critical algorithm I mean that at a
+quick look
+
+ align:start position:0%
+quick look
+ 
+
+ align:start position:0%
+quick look
+stochastic gradient descent is does
+
+ align:start position:0%
+stochastic gradient descent is does
+ 
+
+ align:start position:0%
+stochastic gradient descent is does
+smaller batches at a time so it's
+
+ align:start position:0%
+smaller batches at a time so it's
+ 
+
+ align:start position:0%
+smaller batches at a time so it's
+computationally faster than pure
+
+ align:start position:0%
+computationally faster than pure
+ 
+
+ align:start position:0%
+computationally faster than pure
+gradient descent but also stochastic
+
+ align:start position:0%
+gradient descent but also stochastic
+ 
+
+ align:start position:0%
+gradient descent but also stochastic
+gradient descent is able to solve
+
+ align:start position:0%
+gradient descent is able to solve
+ 
+
+ align:start position:0%
+gradient descent is able to solve
+probabilistic problems where you're
+
+ align:start position:0%
+probabilistic problems where you're
+ 
+
+ align:start position:0%
+probabilistic problems where you're
+trying to minimize an expected value
+
+ align:start position:0%
+trying to minimize an expected value
+ 
+
+ align:start position:0%
+trying to minimize an expected value
+instead of a function anyway it's a
+
+ align:start position:0%
+instead of a function anyway it's a
+ 
+
+ align:start position:0%
+instead of a function anyway it's a
+important thing actually there's a
+
+ align:start position:0%
+important thing actually there's a
+ 
+
+ align:start position:0%
+important thing actually there's a
+lecture at two o'clock in brain in
+
+ align:start position:0%
+lecture at two o'clock in brain in
+ 
+
+ align:start position:0%
+lecture at two o'clock in brain in
+neuroscience about the gradient descent
+
+ align:start position:0%
+neuroscience about the gradient descent
+ 
+
+ align:start position:0%
+neuroscience about the gradient descent
+algorithms and then professor Boyd is
+
+ align:start position:0%
+algorithms and then professor Boyd is
+ 
+
+ align:start position:0%
+algorithms and then professor Boyd is
+speaking here at 4:30 this afternoon
+
+ align:start position:0%
+speaking here at 4:30 this afternoon
+ 
+
+ align:start position:0%
+speaking here at 4:30 this afternoon
+it's overwhelming so so I'm going to
+
+ align:start position:0%
+it's overwhelming so so I'm going to
+ 
+
+ align:start position:0%
+it's overwhelming so so I'm going to
+talk today about several topics that are
+
+ align:start position:0%
+talk today about several topics that are
+ 
+
+ align:start position:0%
+talk today about several topics that are
+specific parts of optimization linear
+
+ align:start position:0%
+specific parts of optimization linear
+ 
+
+ align:start position:0%
+specific parts of optimization linear
+programming is a very famous part of
+
+ align:start position:0%
+programming is a very famous part of
+ 
+
+ align:start position:0%
+programming is a very famous part of
+optimization I don't know if you've met
+
+ align:start position:0%
+optimization I don't know if you've met
+ 
+
+ align:start position:0%
+optimization I don't know if you've met
+it I think it's worth knowing that what
+
+ align:start position:0%
+it I think it's worth knowing that what
+ 
+
+ align:start position:0%
+it I think it's worth knowing that what
+the inputs are and what's the key fact
+
+ align:start position:0%
+the inputs are and what's the key fact
+ 
+
+ align:start position:0%
+the inputs are and what's the key fact
+about linear programming and of course
+
+ align:start position:0%
+about linear programming and of course
+ 
+
+ align:start position:0%
+about linear programming and of course
+also what are the algorithms that's
+
+ align:start position:0%
+also what are the algorithms that's
+ 
+
+ align:start position:0%
+also what are the algorithms that's
+usually what we want to know what's the
+
+ align:start position:0%
+usually what we want to know what's the
+ 
+
+ align:start position:0%
+usually what we want to know what's the
+problem what are the results the
+
+ align:start position:0%
+problem what are the results the
+ 
+
+ align:start position:0%
+problem what are the results the
+mathematical results and what are the
+
+ align:start position:0%
+mathematical results and what are the
+ 
+
+ align:start position:0%
+mathematical results and what are the
+computational tools yeah so that's a
+
+ align:start position:0%
+computational tools yeah so that's a
+ 
+
+ align:start position:0%
+computational tools yeah so that's a
+very established max-flow min-cut is
+
+ align:start position:0%
+very established max-flow min-cut is
+ 
+
+ align:start position:0%
+very established max-flow min-cut is
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+specifically linear programming that I
+
+ align:start position:0%
+specifically linear programming that I
+ 
+
+ align:start position:0%
+specifically linear programming that I
+think maybe would serve as the best
+
+ align:start position:0%
+think maybe would serve as the best
+ 
+
+ align:start position:0%
+think maybe would serve as the best
+example and then two-person games
+
+ align:start position:0%
+example and then two-person games
+ 
+
+ align:start position:0%
+example and then two-person games
+have you met those do so would you know
+
+ align:start position:0%
+have you met those do so would you know
+ 
+
+ align:start position:0%
+have you met those do so would you know
+what what the rules are at a two-person
+
+ align:start position:0%
+what what the rules are at a two-person
+ 
+
+ align:start position:0%
+what what the rules are at a two-person
+zero-sum game those are the in game
+
+ align:start position:0%
+zero-sum game those are the in game
+ 
+
+ align:start position:0%
+zero-sum game those are the in game
+theory those are the ones that are clear
+
+ align:start position:0%
+theory those are the ones that are clear
+ 
+
+ align:start position:0%
+theory those are the ones that are clear
+everything's well established there and
+
+ align:start position:0%
+everything's well established there and
+ 
+
+ align:start position:0%
+everything's well established there and
+in fact they're equivalent to or linear
+
+ align:start position:0%
+in fact they're equivalent to or linear
+ 
+
+ align:start position:0%
+in fact they're equivalent to or linear
+programs so that's why those two are
+
+ align:start position:0%
+programs so that's why those two are
+ 
+
+ align:start position:0%
+programs so that's why those two are
+coming in today and then the key fact
+
+ align:start position:0%
+coming in today and then the key fact
+ 
+
+ align:start position:0%
+coming in today and then the key fact
+about two-person games and about linear
+
+ align:start position:0%
+about two-person games and about linear
+ 
+
+ align:start position:0%
+about two-person games and about linear
+programming is duality so if there's any
+
+ align:start position:0%
+programming is duality so if there's any
+ 
+
+ align:start position:0%
+programming is duality so if there's any
+word on that board it's the one in
+
+ align:start position:0%
+word on that board it's the one in
+ 
+
+ align:start position:0%
+word on that board it's the one in
+capital letters that has mass content
+
+ align:start position:0%
+capital letters that has mass content
+ 
+
+ align:start position:0%
+capital letters that has mass content
+okay I'm just going to start with linear
+
+ align:start position:0%
+okay I'm just going to start with linear
+ 
+
+ align:start position:0%
+okay I'm just going to start with linear
+program and then move on okay so what's
+
+ align:start position:0%
+program and then move on okay so what's
+ 
+
+ align:start position:0%
+program and then move on okay so what's
+a linear programming linear program it's
+
+ align:start position:0%
+a linear programming linear program it's
+ 
+
+ align:start position:0%
+a linear programming linear program it's
+we're optimizing a linear cost function
+
+ align:start position:0%
+we're optimizing a linear cost function
+ 
+
+ align:start position:0%
+we're optimizing a linear cost function
+so we're a minute minimizing the cost C
+
+ align:start position:0%
+so we're a minute minimizing the cost C
+ 
+
+ align:start position:0%
+so we're a minute minimizing the cost C
+transpose X so that vector X is the
+
+ align:start position:0%
+transpose X so that vector X is the
+ 
+
+ align:start position:0%
+transpose X so that vector X is the
+unknown that we're looking for and this
+
+ align:start position:0%
+unknown that we're looking for and this
+ 
+
+ align:start position:0%
+unknown that we're looking for and this
+vector C is the cost vector so that is
+
+ align:start position:0%
+vector C is the cost vector so that is
+ 
+
+ align:start position:0%
+vector C is the cost vector so that is
+c1 x1 plus plus CN xn so you can see why
+
+ align:start position:0%
+c1 x1 plus plus CN xn so you can see why
+ 
+
+ align:start position:0%
+c1 x1 plus plus CN xn so you can see why
+it's called linear programming
+
+ align:start position:0%
+it's called linear programming
+ 
+
+ align:start position:0%
+it's called linear programming
+the cost is linear the constraints are
+
+ align:start position:0%
+the cost is linear the constraints are
+ 
+
+ align:start position:0%
+the cost is linear the constraints are
+also linear so the constraints on X are
+
+ align:start position:0%
+also linear so the constraints on X are
+ 
+
+ align:start position:0%
+also linear so the constraints on X are
+set of linear equations of course I'm
+
+ align:start position:0%
+set of linear equations of course I'm
+ 
+
+ align:start position:0%
+set of linear equations of course I'm
+not thinking of a as being a square
+
+ align:start position:0%
+not thinking of a as being a square
+ 
+
+ align:start position:0%
+not thinking of a as being a square
+invertible matrix no way if it were that
+
+ align:start position:0%
+invertible matrix no way if it were that
+ 
+
+ align:start position:0%
+invertible matrix no way if it were that
+would tell us what X had to be and we
+
+ align:start position:0%
+would tell us what X had to be and we
+ 
+
+ align:start position:0%
+would tell us what X had to be and we
+our problem would be over we we have we
+
+ align:start position:0%
+our problem would be over we we have we
+ 
+
+ align:start position:0%
+our problem would be over we we have we
+have n unknowns this is M by n of course
+
+ align:start position:0%
+have n unknowns this is M by n of course
+ 
+
+ align:start position:0%
+have n unknowns this is M by n of course
+X is n by 1 that's our unknown vector
+
+ align:start position:0%
+X is n by 1 that's our unknown vector
+ 
+
+ align:start position:0%
+X is n by 1 that's our unknown vector
+and I'm thinking that M will be smaller
+
+ align:start position:0%
+and I'm thinking that M will be smaller
+ 
+
+ align:start position:0%
+and I'm thinking that M will be smaller
+than n but we do have constraints and
+
+ align:start position:0%
+than n but we do have constraints and
+ 
+
+ align:start position:0%
+than n but we do have constraints and
+now comes the thing that makes linear
+
+ align:start position:0%
+now comes the thing that makes linear
+ 
+
+ align:start position:0%
+now comes the thing that makes linear
+programming not not actually linear and
+
+ align:start position:0%
+programming not not actually linear and
+ 
+
+ align:start position:0%
+programming not not actually linear and
+that's the constraint X greater equal
+
+ align:start position:0%
+that's the constraint X greater equal
+ 
+
+ align:start position:0%
+that's the constraint X greater equal
+zero and I've written that as a vector
+
+ align:start position:0%
+zero and I've written that as a vector
+ 
+
+ align:start position:0%
+zero and I've written that as a vector
+but that means that means x1 greater
+
+ align:start position:0%
+but that means that means x1 greater
+ 
+
+ align:start position:0%
+but that means that means x1 greater
+equals zero on to X so it's a vector
+
+ align:start position:0%
+equals zero on to X so it's a vector
+ 
+
+ align:start position:0%
+equals zero on to X so it's a vector
+inequality ok so we have a minimizing a
+
+ align:start position:0%
+inequality ok so we have a minimizing a
+ 
+
+ align:start position:0%
+inequality ok so we have a minimizing a
+very simple function with pretty
+
+ align:start position:0%
+very simple function with pretty
+ 
+
+ align:start position:0%
+very simple function with pretty
+straightforward constraints but in
+
+ align:start position:0%
+straightforward constraints but in
+ 
+
+ align:start position:0%
+straightforward constraints but in
+equality constraints so there the
+
+ align:start position:0%
+equality constraints so there the
+ 
+
+ align:start position:0%
+equality constraints so there the
+instead of these are these two together
+
+ align:start position:0%
+instead of these are these two together
+ 
+
+ align:start position:0%
+instead of these are these two together
+are the constraints that and it's in
+
+ align:start position:0%
+are the constraints that and it's in
+ 
+
+ align:start position:0%
+are the constraints that and it's in
+linear algebra in linear programming
+
+ align:start position:0%
+linear algebra in linear programming
+ 
+
+ align:start position:0%
+linear algebra in linear programming
+language this is called the feasible set
+
+ align:start position:0%
+language this is called the feasible set
+ 
+
+ align:start position:0%
+language this is called the feasible set
+X it's the constraint set capital okay
+
+ align:start position:0%
+X it's the constraint set capital okay
+ 
+
+ align:start position:0%
+X it's the constraint set capital okay
+and in the notes right ok so let me draw
+
+ align:start position:0%
+and in the notes right ok so let me draw
+ 
+
+ align:start position:0%
+and in the notes right ok so let me draw
+a picture to to show maybe here maybe
+
+ align:start position:0%
+a picture to to show maybe here maybe
+ 
+
+ align:start position:0%
+a picture to to show maybe here maybe
+I'll just ask how many of you are
+
+ align:start position:0%
+I'll just ask how many of you are
+ 
+
+ align:start position:0%
+I'll just ask how many of you are
+already familiar with linear programming
+
+ align:start position:0%
+already familiar with linear programming
+ 
+
+ align:start position:0%
+already familiar with linear programming
+oh Allah okay so I won't labor the point
+
+ align:start position:0%
+oh Allah okay so I won't labor the point
+ 
+
+ align:start position:0%
+oh Allah okay so I won't labor the point
+but let me just draw a picture so my
+
+ align:start position:0%
+but let me just draw a picture so my
+ 
+
+ align:start position:0%
+but let me just draw a picture so my
+picture will be just here so that's n
+
+ align:start position:0%
+picture will be just here so that's n
+ 
+
+ align:start position:0%
+picture will be just here so that's n
+equals 3 so this is the X 1 X 2 X 3
+
+ align:start position:0%
+equals 3 so this is the X 1 X 2 X 3
+ 
+
+ align:start position:0%
+equals 3 so this is the X 1 X 2 X 3
+space and X greater or equal 0 means
+
+ align:start position:0%
+space and X greater or equal 0 means
+ 
+
+ align:start position:0%
+space and X greater or equal 0 means
+what it means that I'm in this
+
+ align:start position:0%
+what it means that I'm in this
+ 
+
+ align:start position:0%
+what it means that I'm in this
+one-eighth of the space right if they're
+
+ align:start position:0%
+one-eighth of the space right if they're
+ 
+
+ align:start position:0%
+one-eighth of the space right if they're
+non-negative well I would say Quadrant
+
+ align:start position:0%
+non-negative well I would say Quadrant
+ 
+
+ align:start position:0%
+non-negative well I would say Quadrant
+but I really should say octant because
+
+ align:start position:0%
+but I really should say octant because
+ 
+
+ align:start position:0%
+but I really should say octant because
+it's in there's 1/8 of the full 3d space
+
+ align:start position:0%
+it's in there's 1/8 of the full 3d space
+ 
+
+ align:start position:0%
+it's in there's 1/8 of the full 3d space
+so I'm in here and then maybe I have M
+
+ align:start position:0%
+so I'm in here and then maybe I have M
+ 
+
+ align:start position:0%
+so I'm in here and then maybe I have M
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+maybe just one constraint like so so let
+
+ align:start position:0%
+maybe just one constraint like so so let
+ 
+
+ align:start position:0%
+maybe just one constraint like so so let
+me take the cost to be say X 1 plus 2 X
+
+ align:start position:0%
+me take the cost to be say X 1 plus 2 X
+ 
+
+ align:start position:0%
+me take the cost to be say X 1 plus 2 X
+2 plus 5 X 3 say and the constraint I'm
+
+ align:start position:0%
+2 plus 5 X 3 say and the constraint I'm
+ 
+
+ align:start position:0%
+2 plus 5 X 3 say and the constraint I'm
+just gonna have one equation X 1 plus X
+
+ align:start position:0%
+just gonna have one equation X 1 plus X
+ 
+
+ align:start position:0%
+just gonna have one equation X 1 plus X
+2 let me make it easy make that
+
+ align:start position:0%
+2 let me make it easy make that
+ 
+
+ align:start position:0%
+2 let me make it easy make that
+constraint an easy one too so this is
+
+ align:start position:0%
+constraint an easy one too so this is
+ 
+
+ align:start position:0%
+constraint an easy one too so this is
+the this is what we're going to minimize
+
+ align:start position:0%
+the this is what we're going to minimize
+ 
+
+ align:start position:0%
+the this is what we're going to minimize
+and that's what we have to satisfy as
+
+ align:start position:0%
+and that's what we have to satisfy as
+ 
+
+ align:start position:0%
+and that's what we have to satisfy as
+well as x equals 0 so that's a plain 1
+
+ align:start position:0%
+well as x equals 0 so that's a plain 1
+ 
+
+ align:start position:0%
+well as x equals 0 so that's a plain 1
+equation gives us a plane in r3 the
+
+ align:start position:0%
+equation gives us a plane in r3 the
+ 
+
+ align:start position:0%
+equation gives us a plane in r3 the
+plane would go through what hits the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axes at 3 0 0 and so the minimum the
+
+ align:start position:0%
+axes at 3 0 0 and so the minimum the
+ 
+
+ align:start position:0%
+axes at 3 0 0 and so the minimum the
+point has to lie on that plane and it
+
+ align:start position:0%
+point has to lie on that plane and it
+ 
+
+ align:start position:0%
+point has to lie on that plane and it
+has to lie in the octant so that plane
+
+ align:start position:0%
+has to lie in the octant so that plane
+ 
+
+ align:start position:0%
+has to lie in the octant so that plane
+is chopped off to be a triangle yeah
+
+ align:start position:0%
+is chopped off to be a triangle yeah
+ 
+
+ align:start position:0%
+is chopped off to be a triangle yeah
+this is a good visualization of linear
+
+ align:start position:0%
+this is a good visualization of linear
+ 
+
+ align:start position:0%
+this is a good visualization of linear
+programming and what's the conclusion
+
+ align:start position:0%
+programming and what's the conclusion
+ 
+
+ align:start position:0%
+programming and what's the conclusion
+well our cost is linear so the result is
+
+ align:start position:0%
+well our cost is linear so the result is
+ 
+
+ align:start position:0%
+well our cost is linear so the result is
+that one of these three corners is the
+
+ align:start position:0%
+that one of these three corners is the
+ 
+
+ align:start position:0%
+that one of these three corners is the
+winner it could happen it could happen
+
+ align:start position:0%
+winner it could happen it could happen
+ 
+
+ align:start position:0%
+winner it could happen it could happen
+that maybe I have equal values on those
+
+ align:start position:0%
+that maybe I have equal values on those
+ 
+
+ align:start position:0%
+that maybe I have equal values on those
+two corners and therefore all the way
+
+ align:start position:0%
+two corners and therefore all the way
+ 
+
+ align:start position:0%
+two corners and therefore all the way
+along would be also winners but when I
+
+ align:start position:0%
+along would be also winners but when I
+ 
+
+ align:start position:0%
+along would be also winners but when I
+have a linear function it's a maximum at
+
+ align:start position:0%
+have a linear function it's a maximum at
+ 
+
+ align:start position:0%
+have a linear function it's a maximum at
+the end and these are the ends those
+
+ align:start position:0%
+the end and these are the ends those
+ 
+
+ align:start position:0%
+the end and these are the ends those
+three corners so so three zero zero zero
+
+ align:start position:0%
+three corners so so three zero zero zero
+ 
+
+ align:start position:0%
+three corners so so three zero zero zero
+three zero or zero zero three are the
+
+ align:start position:0%
+three zero or zero zero three are the
+ 
+
+ align:start position:0%
+three zero or zero zero three are the
+three corners
+
+ align:start position:0%
+three corners
+ 
+
+ align:start position:0%
+three corners
+and one of those is the winner and the
+
+ align:start position:0%
+and one of those is the winner and the
+ 
+
+ align:start position:0%
+and one of those is the winner and the
+problem is solved and forth in fact for
+
+ align:start position:0%
+problem is solved and forth in fact for
+ 
+
+ align:start position:0%
+problem is solved and forth in fact for
+this case since I'm minimizing I guess
+
+ align:start position:0%
+this case since I'm minimizing I guess
+ 
+
+ align:start position:0%
+this case since I'm minimizing I guess
+it would be that corner that
+
+ align:start position:0%
+it would be that corner that
+ 
+
+ align:start position:0%
+it would be that corner that
+wind so let me give it a star not an x-y
+
+ align:start position:0%
+wind so let me give it a star not an x-y
+ 
+
+ align:start position:0%
+wind so let me give it a star not an x-y
+s-300 cuz that oh no that three so the
+
+ align:start position:0%
+s-300 cuz that oh no that three so the
+ 
+
+ align:start position:0%
+s-300 cuz that oh no that three so the
+value turned out to be three at the
+
+ align:start position:0%
+value turned out to be three at the
+ 
+
+ align:start position:0%
+value turned out to be three at the
+point 3 zeros it and that's a star okay
+
+ align:start position:0%
+point 3 zeros it and that's a star okay
+ 
+
+ align:start position:0%
+point 3 zeros it and that's a star okay
+good good good good okay what what more
+
+ align:start position:0%
+good good good good okay what what more
+ 
+
+ align:start position:0%
+good good good good okay what what more
+do I want to do I said yes should it be
+
+ align:start position:0%
+do I want to do I said yes should it be
+ 
+
+ align:start position:0%
+do I want to do I said yes should it be
+so no zero zero zero three
+
+ align:start position:0%
+so no zero zero zero three
+ 
+
+ align:start position:0%
+so no zero zero zero three
+where's the next three is three that's
+
+ align:start position:0%
+where's the next three is three that's
+ 
+
+ align:start position:0%
+where's the next three is three that's
+fine that gives us a chance I think that
+
+ align:start position:0%
+fine that gives us a chance I think that
+ 
+
+ align:start position:0%
+fine that gives us a chance I think that
+would give me cost of 15 this would give
+
+ align:start position:0%
+would give me cost of 15 this would give
+ 
+
+ align:start position:0%
+would give me cost of 15 this would give
+me a cost of 6 and that would give me
+
+ align:start position:0%
+me a cost of 6 and that would give me
+ 
+
+ align:start position:0%
+me a cost of 6 and that would give me
+across the street
+
+ align:start position:0%
+across the street
+ 
+
+ align:start position:0%
+across the street
+yeah it's obviously if we could
+
+ align:start position:0%
+yeah it's obviously if we could
+ 
+
+ align:start position:0%
+yeah it's obviously if we could
+enumerate all the corners we would have
+
+ align:start position:0%
+enumerate all the corners we would have
+ 
+
+ align:start position:0%
+enumerate all the corners we would have
+a super fast way to get the answer but
+
+ align:start position:0%
+a super fast way to get the answer but
+ 
+
+ align:start position:0%
+a super fast way to get the answer but
+the trouble is of course that for large
+
+ align:start position:0%
+the trouble is of course that for large
+ 
+
+ align:start position:0%
+the trouble is of course that for large
+values and an amount of M and n there
+
+ align:start position:0%
+values and an amount of M and n there
+ 
+
+ align:start position:0%
+values and an amount of M and n there
+are exponentially many corners and we
+
+ align:start position:0%
+are exponentially many corners and we
+ 
+
+ align:start position:0%
+are exponentially many corners and we
+don't want to see them all so that's
+
+ align:start position:0%
+don't want to see them all so that's
+ 
+
+ align:start position:0%
+don't want to see them all so that's
+what makes linear programming take time
+
+ align:start position:0%
+what makes linear programming take time
+ 
+
+ align:start position:0%
+what makes linear programming take time
+and need ideas so for algorithms there
+
+ align:start position:0%
+and need ideas so for algorithms there
+ 
+
+ align:start position:0%
+and need ideas so for algorithms there
+are two types of algorithms two types of
+
+ align:start position:0%
+are two types of algorithms two types of
+ 
+
+ align:start position:0%
+are two types of algorithms two types of
+codes it's all these the older as well
+
+ align:start position:0%
+codes it's all these the older as well
+ 
+
+ align:start position:0%
+codes it's all these the older as well
+established ones are so one way is the
+
+ align:start position:0%
+established ones are so one way is the
+ 
+
+ align:start position:0%
+established ones are so one way is the
+simplex method which finds a corner we
+
+ align:start position:0%
+simplex method which finds a corner we
+ 
+
+ align:start position:0%
+simplex method which finds a corner we
+know the optimum is some one of the
+
+ align:start position:0%
+know the optimum is some one of the
+ 
+
+ align:start position:0%
+know the optimum is some one of the
+corners so it can find it'll find one
+
+ align:start position:0%
+corners so it can find it'll find one
+ 
+
+ align:start position:0%
+corners so it can find it'll find one
+corner and we'll go to the next corner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if it starts if it starts at one of
+
+ align:start position:0%
+so if it starts if it starts at one of
+ 
+
+ align:start position:0%
+so if it starts if it starts at one of
+these corners it will travel along along
+
+ align:start position:0%
+these corners it will travel along along
+ 
+
+ align:start position:0%
+these corners it will travel along along
+an edge that lowers the cost and it has
+
+ align:start position:0%
+an edge that lowers the cost and it has
+ 
+
+ align:start position:0%
+an edge that lowers the cost and it has
+to stop at the end because it's linear
+
+ align:start position:0%
+to stop at the end because it's linear
+ 
+
+ align:start position:0%
+to stop at the end because it's linear
+the cost will keep going down and going
+
+ align:start position:0%
+the cost will keep going down and going
+ 
+
+ align:start position:0%
+the cost will keep going down and going
+down until it bumps up into bumps into
+
+ align:start position:0%
+down until it bumps up into bumps into
+ 
+
+ align:start position:0%
+down until it bumps up into bumps into
+the end point and then it can't go
+
+ align:start position:0%
+the end point and then it can't go
+ 
+
+ align:start position:0%
+the end point and then it can't go
+further and then we would from that next
+
+ align:start position:0%
+further and then we would from that next
+ 
+
+ align:start position:0%
+further and then we would from that next
+corner we would go to a next corner each
+
+ align:start position:0%
+corner we would go to a next corner each
+ 
+
+ align:start position:0%
+corner we would go to a next corner each
+time it's like steepest descent on the
+
+ align:start position:0%
+time it's like steepest descent on the
+ 
+
+ align:start position:0%
+time it's like steepest descent on the
+con the edges we from the first corner
+
+ align:start position:0%
+con the edges we from the first corner
+ 
+
+ align:start position:0%
+con the edges we from the first corner
+we go the steepest way till we can't go
+
+ align:start position:0%
+we go the steepest way till we can't go
+ 
+
+ align:start position:0%
+we go the steepest way till we can't go
+further we've hit another corner and we
+
+ align:start position:0%
+further we've hit another corner and we
+ 
+
+ align:start position:0%
+further we've hit another corner and we
+and we recompute a linear algebra find
+
+ align:start position:0%
+and we recompute a linear algebra find
+ 
+
+ align:start position:0%
+and we recompute a linear algebra find
+which direction is steepest from there
+
+ align:start position:0%
+which direction is steepest from there
+ 
+
+ align:start position:0%
+which direction is steepest from there
+and and so that's the idea of the
+
+ align:start position:0%
+and and so that's the idea of the
+ 
+
+ align:start position:0%
+and and so that's the idea of the
+simplex method which was invented by
+
+ align:start position:0%
+simplex method which was invented by
+ 
+
+ align:start position:0%
+simplex method which was invented by
+dancing and and the algebra is not going
+
+ align:start position:0%
+dancing and and the algebra is not going
+ 
+
+ align:start position:0%
+dancing and and the algebra is not going
+to be in today's lecture but it's
+
+ align:start position:0%
+to be in today's lecture but it's
+ 
+
+ align:start position:0%
+to be in today's lecture but it's
+straightforward well people have to
+
+ align:start position:0%
+straightforward well people have to
+ 
+
+ align:start position:0%
+straightforward well people have to
+optimize it because that's a highly
+
+ align:start position:0%
+optimize it because that's a highly
+ 
+
+ align:start position:0%
+optimize it because that's a highly
+frequently used method yeah okay but
+
+ align:start position:0%
+frequently used method yeah okay but
+ 
+
+ align:start position:0%
+frequently used method yeah okay but
+then about 20 years later maybe or 30 I
+
+ align:start position:0%
+then about 20 years later maybe or 30 I
+ 
+
+ align:start position:0%
+then about 20 years later maybe or 30 I
+remember going to a lecture in downtown
+
+ align:start position:0%
+remember going to a lecture in downtown
+ 
+
+ align:start position:0%
+remember going to a lecture in downtown
+Boston by karmarkar so I have to put his
+
+ align:start position:0%
+Boston by karmarkar so I have to put his
+ 
+
+ align:start position:0%
+Boston by karmarkar so I have to put his
+name down our marker and he was in the
+
+ align:start position:0%
+name down our marker and he was in the
+ 
+
+ align:start position:0%
+name down our marker and he was in the
+New York Times all the newspapers so it
+
+ align:start position:0%
+New York Times all the newspapers so it
+ 
+
+ align:start position:0%
+New York Times all the newspapers so it
+was a big deal he had an alternative
+
+ align:start position:0%
+was a big deal he had an alternative
+ 
+
+ align:start position:0%
+was a big deal he had an alternative
+algorithm and the exact algorithm he he
+
+ align:start position:0%
+algorithm and the exact algorithm he he
+ 
+
+ align:start position:0%
+algorithm and the exact algorithm he he
+proposed hasn't survived until today but
+
+ align:start position:0%
+proposed hasn't survived until today but
+ 
+
+ align:start position:0%
+proposed hasn't survived until today but
+the idea has and the idea was to go to
+
+ align:start position:0%
+the idea has and the idea was to go to
+ 
+
+ align:start position:0%
+the idea has and the idea was to go to
+travel inside the feasible set and not
+
+ align:start position:0%
+travel inside the feasible set and not
+ 
+
+ align:start position:0%
+travel inside the feasible set and not
+around the edges
+
+ align:start position:0%
+around the edges
+ 
+
+ align:start position:0%
+around the edges
+so his idea because in in in here we
+
+ align:start position:0%
+so his idea because in in in here we
+ 
+
+ align:start position:0%
+so his idea because in in in here we
+maybe travel down near that edge start
+
+ align:start position:0%
+maybe travel down near that edge start
+ 
+
+ align:start position:0%
+maybe travel down near that edge start
+again travel again so its steepest
+
+ align:start position:0%
+again travel again so its steepest
+ 
+
+ align:start position:0%
+again travel again so its steepest
+descent in the in the constraint set the
+
+ align:start position:0%
+descent in the in the constraint set the
+ 
+
+ align:start position:0%
+descent in the in the constraint set the
+feasible set and you can use calculus
+
+ align:start position:0%
+feasible set and you can use calculus
+ 
+
+ align:start position:0%
+feasible set and you can use calculus
+and and this idea so this is this is
+
+ align:start position:0%
+and and this idea so this is this is
+ 
+
+ align:start position:0%
+and and this idea so this is this is
+interior point methods so I'll just use
+
+ align:start position:0%
+interior point methods so I'll just use
+ 
+
+ align:start position:0%
+interior point methods so I'll just use
+the word interior that's telling us that
+
+ align:start position:0%
+the word interior that's telling us that
+ 
+
+ align:start position:0%
+the word interior that's telling us that
+we're we're inside the feasible set we
+
+ align:start position:0%
+we're we're inside the feasible set we
+ 
+
+ align:start position:0%
+we're we're inside the feasible set we
+don't hit come all the way to the
+
+ align:start position:0%
+don't hit come all the way to the
+ 
+
+ align:start position:0%
+don't hit come all the way to the
+boundary intentionally because we want
+
+ align:start position:0%
+boundary intentionally because we want
+ 
+
+ align:start position:0%
+boundary intentionally because we want
+room to move and to find derivatives
+
+ align:start position:0%
+room to move and to find derivatives
+ 
+
+ align:start position:0%
+room to move and to find derivatives
+empty whose Newton's message to minimize
+
+ align:start position:0%
+empty whose Newton's message to minimize
+ 
+
+ align:start position:0%
+empty whose Newton's message to minimize
+you see you choose a search Direction
+
+ align:start position:0%
+you see you choose a search Direction
+ 
+
+ align:start position:0%
+you see you choose a search Direction
+just as all of optimization does and in
+
+ align:start position:0%
+just as all of optimization does and in
+ 
+
+ align:start position:0%
+just as all of optimization does and in
+that search Direction you track it and
+
+ align:start position:0%
+that search Direction you track it and
+ 
+
+ align:start position:0%
+that search Direction you track it and
+you come you stop before you bump into
+
+ align:start position:0%
+you come you stop before you bump into
+ 
+
+ align:start position:0%
+you come you stop before you bump into
+the edge of the feasible set and then
+
+ align:start position:0%
+the edge of the feasible set and then
+ 
+
+ align:start position:0%
+the edge of the feasible set and then
+you compute derivatives again so you can
+
+ align:start position:0%
+you compute derivatives again so you can
+ 
+
+ align:start position:0%
+you compute derivatives again so you can
+use calculus and it it's a method that
+
+ align:start position:0%
+use calculus and it it's a method that
+ 
+
+ align:start position:0%
+use calculus and it it's a method that
+it's an idea that the interior idea came
+
+ align:start position:0%
+it's an idea that the interior idea came
+ 
+
+ align:start position:0%
+it's an idea that the interior idea came
+before car marker but he got super
+
+ align:start position:0%
+before car marker but he got super
+ 
+
+ align:start position:0%
+before car marker but he got super
+publicity so it really got attention got
+
+ align:start position:0%
+publicity so it really got attention got
+ 
+
+ align:start position:0%
+publicity so it really got attention got
+new thinking and new ideas came partly
+
+ align:start position:0%
+new thinking and new ideas came partly
+ 
+
+ align:start position:0%
+new thinking and new ideas came partly
+from people at MIT and and these two are
+
+ align:start position:0%
+from people at MIT and and these two are
+ 
+
+ align:start position:0%
+from people at MIT and and these two are
+now still locked in competition no one
+
+ align:start position:0%
+now still locked in competition no one
+ 
+
+ align:start position:0%
+now still locked in competition no one
+hasn't beaten the other in in all
+
+ align:start position:0%
+hasn't beaten the other in in all
+ 
+
+ align:start position:0%
+hasn't beaten the other in in all
+problems so so linear programming is
+
+ align:start position:0%
+problems so so linear programming is
+ 
+
+ align:start position:0%
+problems so so linear programming is
+here but then for nonlinear programming
+
+ align:start position:0%
+here but then for nonlinear programming
+ 
+
+ align:start position:0%
+here but then for nonlinear programming
+quadratic programming where the cost is
+
+ align:start position:0%
+quadratic programming where the cost is
+ 
+
+ align:start position:0%
+quadratic programming where the cost is
+quadratic nonlinear programming semi
+
+ align:start position:0%
+quadratic nonlinear programming semi
+ 
+
+ align:start position:0%
+quadratic nonlinear programming semi
+definite programming that's where you
+
+ align:start position:0%
+definite programming that's where you
+ 
+
+ align:start position:0%
+definite programming that's where you
+have a matrix unknown a matrix
+
+ align:start position:0%
+have a matrix unknown a matrix
+ 
+
+ align:start position:0%
+have a matrix unknown a matrix
+constraints those are all the more
+
+ align:start position:0%
+constraints those are all the more
+ 
+
+ align:start position:0%
+constraints those are all the more
+complicated you get the more it tends to
+
+ align:start position:0%
+complicated you get the more it tends to
+ 
+
+ align:start position:0%
+complicated you get the more it tends to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+interior point methods okay that's a
+
+ align:start position:0%
+interior point methods okay that's a
+ 
+
+ align:start position:0%
+interior point methods okay that's a
+summary of linear programming now I'd
+
+ align:start position:0%
+summary of linear programming now I'd
+ 
+
+ align:start position:0%
+summary of linear programming now I'd
+like to give an example and then I
+
+ align:start position:0%
+like to give an example and then I
+ 
+
+ align:start position:0%
+like to give an example and then I
+haven't told you the main well let me
+
+ align:start position:0%
+haven't told you the main well let me
+ 
+
+ align:start position:0%
+haven't told you the main well let me
+tell you the main fact about duality
+
+ align:start position:0%
+tell you the main fact about duality
+ 
+
+ align:start position:0%
+tell you the main fact about duality
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is really and I'll write that maybe
+
+ align:start position:0%
+this is really and I'll write that maybe
+ 
+
+ align:start position:0%
+this is really and I'll write that maybe
+here next to it so do a duality if
+
+ align:start position:0%
+here next to it so do a duality if
+ 
+
+ align:start position:0%
+here next to it so do a duality if
+there's a dual procure LP and that dual
+
+ align:start position:0%
+there's a dual procure LP and that dual
+ 
+
+ align:start position:0%
+there's a dual procure LP and that dual
+is going to do a maximum instead of a
+
+ align:start position:0%
+is going to do a maximum instead of a
+ 
+
+ align:start position:0%
+is going to do a maximum instead of a
+minimum and the cost is is going to
+
+ align:start position:0%
+minimum and the cost is is going to
+ 
+
+ align:start position:0%
+minimum and the cost is is going to
+involve the B from the primal problem so
+
+ align:start position:0%
+involve the B from the primal problem so
+ 
+
+ align:start position:0%
+involve the B from the primal problem so
+this is now called the primal problem
+
+ align:start position:0%
+this is now called the primal problem
+ 
+
+ align:start position:0%
+this is now called the primal problem
+and this is its dual so there are twin
+
+ align:start position:0%
+and this is its dual so there are twin
+ 
+
+ align:start position:0%
+and this is its dual so there are twin
+problems they use the same data but
+
+ align:start position:0%
+problems they use the same data but
+ 
+
+ align:start position:0%
+problems they use the same data but
+quite differently it's like transposing
+
+ align:start position:0%
+quite differently it's like transposing
+ 
+
+ align:start position:0%
+quite differently it's like transposing
+things so so let's call the unknown Y so
+
+ align:start position:0%
+things so so let's call the unknown Y so
+ 
+
+ align:start position:0%
+things so so let's call the unknown Y so
+for y to be the right hand side over
+
+ align:start position:0%
+for y to be the right hand side over
+ 
+
+ align:start position:0%
+for y to be the right hand side over
+here is M by 1 so that's maximize that
+
+ align:start position:0%
+here is M by 1 so that's maximize that
+ 
+
+ align:start position:0%
+here is M by 1 so that's maximize that
+we're subject to what are the
+
+ align:start position:0%
+we're subject to what are the
+ 
+
+ align:start position:0%
+we're subject to what are the
+constraints well the cost function over
+
+ align:start position:0%
+constraints well the cost function over
+ 
+
+ align:start position:0%
+constraints well the cost function over
+here see the cost vector goes into the
+
+ align:start position:0%
+here see the cost vector goes into the
+ 
+
+ align:start position:0%
+here see the cost vector goes into the
+constraints and I think the greater
+
+ align:start position:0%
+constraints and I think the greater
+ 
+
+ align:start position:0%
+constraints and I think the greater
+equal sign because obably becomes a less
+
+ align:start position:0%
+equal sign because obably becomes a less
+ 
+
+ align:start position:0%
+equal sign because obably becomes a less
+or equal to sign the a gets transposed I
+
+ align:start position:0%
+or equal to sign the a gets transposed I
+ 
+
+ align:start position:0%
+or equal to sign the a gets transposed I
+think that's probably probably the
+
+ align:start position:0%
+think that's probably probably the
+ 
+
+ align:start position:0%
+think that's probably probably the
+constraint in the dual and it happens it
+
+ align:start position:0%
+constraint in the dual and it happens it
+ 
+
+ align:start position:0%
+constraint in the dual and it happens it
+doesn't need Y we don't have y greater
+
+ align:start position:0%
+doesn't need Y we don't have y greater
+ 
+
+ align:start position:0%
+doesn't need Y we don't have y greater
+equal 0 over here ok so that's a dual
+
+ align:start position:0%
+equal 0 over here ok so that's a dual
+ 
+
+ align:start position:0%
+equal 0 over here ok so that's a dual
+problem it has a linear cost it has
+
+ align:start position:0%
+problem it has a linear cost it has
+ 
+
+ align:start position:0%
+problem it has a linear cost it has
+linear inequality constraints it can be
+
+ align:start position:0%
+linear inequality constraints it can be
+ 
+
+ align:start position:0%
+linear inequality constraints it can be
+solved by the simplex method you could
+
+ align:start position:0%
+solved by the simplex method you could
+ 
+
+ align:start position:0%
+solved by the simplex method you could
+choose whether you solve that one or
+
+ align:start position:0%
+choose whether you solve that one or
+ 
+
+ align:start position:0%
+choose whether you solve that one or
+this one because if you solve one you
+
+ align:start position:0%
+this one because if you solve one you
+ 
+
+ align:start position:0%
+this one because if you solve one you
+solve the other
+
+ align:start position:0%
+solve the other
+ 
+
+ align:start position:0%
+solve the other
+the two are closely connected and that's
+
+ align:start position:0%
+the two are closely connected and that's
+ 
+
+ align:start position:0%
+the two are closely connected and that's
+the key idea of duality so maybe I'll
+
+ align:start position:0%
+the key idea of duality so maybe I'll
+ 
+
+ align:start position:0%
+the key idea of duality so maybe I'll
+put the idea first of all of wheat
+
+ align:start position:0%
+put the idea first of all of wheat
+ 
+
+ align:start position:0%
+put the idea first of all of wheat
+duality which says that the this
+
+ align:start position:0%
+duality which says that the this
+ 
+
+ align:start position:0%
+duality which says that the this
+quantity that we're trying to maximize
+
+ align:start position:0%
+quantity that we're trying to maximize
+ 
+
+ align:start position:0%
+quantity that we're trying to maximize
+we're getting it as large as possible is
+
+ align:start position:0%
+we're getting it as large as possible is
+ 
+
+ align:start position:0%
+we're getting it as large as possible is
+always less lesser equal to any C
+
+ align:start position:0%
+always less lesser equal to any C
+ 
+
+ align:start position:0%
+always less lesser equal to any C
+transpose X this is for for any this is
+
+ align:start position:0%
+transpose X this is for for any this is
+ 
+
+ align:start position:0%
+transpose X this is for for any this is
+for any feasible allowed any can any any
+
+ align:start position:0%
+for any feasible allowed any can any any
+ 
+
+ align:start position:0%
+for any feasible allowed any can any any
+X&Y that are that satisfy the
+
+ align:start position:0%
+X&Y that are that satisfy the
+ 
+
+ align:start position:0%
+X&Y that are that satisfy the
+constraints remember feasible means
+
+ align:start position:0%
+constraints remember feasible means
+ 
+
+ align:start position:0%
+constraints remember feasible means
+satisfies the constraint so in other
+
+ align:start position:0%
+satisfies the constraint so in other
+ 
+
+ align:start position:0%
+satisfies the constraint so in other
+words this problem this maximization
+
+ align:start position:0%
+words this problem this maximization
+ 
+
+ align:start position:0%
+words this problem this maximization
+problem you're trying to push this up
+
+ align:start position:0%
+problem you're trying to push this up
+ 
+
+ align:start position:0%
+problem you're trying to push this up
+the minimization problem you're trying
+
+ align:start position:0%
+the minimization problem you're trying
+ 
+
+ align:start position:0%
+the minimization problem you're trying
+to pull this down and it's easy to show
+
+ align:start position:0%
+to pull this down and it's easy to show
+ 
+
+ align:start position:0%
+to pull this down and it's easy to show
+that the one that B transpose it's easy
+
+ align:start position:0%
+that the one that B transpose it's easy
+ 
+
+ align:start position:0%
+that the one that B transpose it's easy
+to show that inequality let's do that so
+
+ align:start position:0%
+to show that inequality let's do that so
+ 
+
+ align:start position:0%
+to show that inequality let's do that so
+B transpose Y true should be a one-line
+
+ align:start position:0%
+B transpose Y true should be a one-line
+ 
+
+ align:start position:0%
+B transpose Y true should be a one-line
+proof so B transpose Y ok what do I do
+
+ align:start position:0%
+proof so B transpose Y ok what do I do
+ 
+
+ align:start position:0%
+proof so B transpose Y ok what do I do
+so B transpose Y well I look over here
+
+ align:start position:0%
+so B transpose Y well I look over here
+ 
+
+ align:start position:0%
+so B transpose Y well I look over here
+that's where B shows up that's X
+
+ align:start position:0%
+that's where B shows up that's X
+ 
+
+ align:start position:0%
+that's where B shows up that's X
+transpose a transpose Y right because B
+
+ align:start position:0%
+transpose a transpose Y right because B
+ 
+
+ align:start position:0%
+transpose a transpose Y right because B
+is ax
+
+ align:start position:0%
+is ax
+ 
+
+ align:start position:0%
+is ax
+I'm feasible so my B is a X and for any
+
+ align:start position:0%
+I'm feasible so my B is a X and for any
+ 
+
+ align:start position:0%
+I'm feasible so my B is a X and for any
+X this is for this is for any X that B
+
+ align:start position:0%
+X this is for this is for any X that B
+ 
+
+ align:start position:0%
+X this is for this is for any X that B
+is going to be ax so am I good so far
+
+ align:start position:0%
+is going to be ax so am I good so far
+ 
+
+ align:start position:0%
+is going to be ax so am I good so far
+and now what do I do but now I look here
+
+ align:start position:0%
+and now what do I do but now I look here
+ 
+
+ align:start position:0%
+and now what do I do but now I look here
+I see a transpose Y sitting right in
+
+ align:start position:0%
+I see a transpose Y sitting right in
+ 
+
+ align:start position:0%
+I see a transpose Y sitting right in
+front of me so I say well ok unless or
+
+ align:start position:0%
+front of me so I say well ok unless or
+ 
+
+ align:start position:0%
+front of me so I say well ok unless or
+equal to and I guess I'm done a
+
+ align:start position:0%
+equal to and I guess I'm done a
+ 
+
+ align:start position:0%
+equal to and I guess I'm done a
+transpose wise less or equal to C so I
+
+ align:start position:0%
+transpose wise less or equal to C so I
+ 
+
+ align:start position:0%
+transpose wise less or equal to C so I
+have X transpose C C transpose X
+
+ align:start position:0%
+have X transpose C C transpose X
+ 
+
+ align:start position:0%
+have X transpose C C transpose X
+so so equal this equals this less or
+
+ align:start position:0%
+so so equal this equals this less or
+ 
+
+ align:start position:0%
+so so equal this equals this less or
+equal that I've got it weak duality is
+
+ align:start position:0%
+equal that I've got it weak duality is
+ 
+
+ align:start position:0%
+equal that I've got it weak duality is
+just put together the the requirements
+
+ align:start position:0%
+just put together the the requirements
+ 
+
+ align:start position:0%
+just put together the the requirements
+on x and y and you have it but word it
+
+ align:start position:0%
+on x and y and you have it but word it
+ 
+
+ align:start position:0%
+on x and y and you have it but word it
+was this important you know if the
+
+ align:start position:0%
+was this important you know if the
+ 
+
+ align:start position:0%
+was this important you know if the
+mathematics is right everything has to
+
+ align:start position:0%
+mathematics is right everything has to
+ 
+
+ align:start position:0%
+mathematics is right everything has to
+have it please play its role and so
+
+ align:start position:0%
+have it please play its role and so
+ 
+
+ align:start position:0%
+have it please play its role and so
+what's the role of X greater equal zero
+
+ align:start position:0%
+what's the role of X greater equal zero
+ 
+
+ align:start position:0%
+what's the role of X greater equal zero
+there why do we need X if we just even
+
+ align:start position:0%
+there why do we need X if we just even
+ 
+
+ align:start position:0%
+there why do we need X if we just even
+think of an equal one just a number Y
+
+ align:start position:0%
+think of an equal one just a number Y
+ 
+
+ align:start position:0%
+think of an equal one just a number Y
+where do we use the fact that X is
+
+ align:start position:0%
+where do we use the fact that X is
+ 
+
+ align:start position:0%
+where do we use the fact that X is
+greater or equal 0 do we do we use it
+
+ align:start position:0%
+greater or equal 0 do we do we use it
+ 
+
+ align:start position:0%
+greater or equal 0 do we do we use it
+this looks so so smooth because a
+
+ align:start position:0%
+this looks so so smooth because a
+ 
+
+ align:start position:0%
+this looks so so smooth because a
+transpose Y I'll write down as X
+
+ align:start position:0%
+transpose Y I'll write down as X
+ 
+
+ align:start position:0%
+transpose Y I'll write down as X
+transpose C for the moment just just so
+
+ align:start position:0%
+transpose C for the moment just just so
+ 
+
+ align:start position:0%
+transpose C for the moment just just so
+your eye says the same X transpose and
+
+ align:start position:0%
+your eye says the same X transpose and
+ 
+
+ align:start position:0%
+your eye says the same X transpose and
+the a transpose Y is lesser equals C
+
+ align:start position:0%
+the a transpose Y is lesser equals C
+ 
+
+ align:start position:0%
+the a transpose Y is lesser equals C
+where is X greater equal zero coming in
+
+ align:start position:0%
+where is X greater equal zero coming in
+ 
+
+ align:start position:0%
+where is X greater equal zero coming in
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah that's true but but I want to see
+
+ align:start position:0%
+yeah that's true but but I want to see
+ 
+
+ align:start position:0%
+yeah that's true but but I want to see
+yeah so here's my point that the fact
+
+ align:start position:0%
+yeah so here's my point that the fact
+ 
+
+ align:start position:0%
+yeah so here's my point that the fact
+that a transpose Y is lesser equals C
+
+ align:start position:0%
+that a transpose Y is lesser equals C
+ 
+
+ align:start position:0%
+that a transpose Y is lesser equals C
+that's fine highly important but if X
+
+ align:start position:0%
+that's fine highly important but if X
+ 
+
+ align:start position:0%
+that's fine highly important but if X
+was negative it would be the other way
+
+ align:start position:0%
+was negative it would be the other way
+ 
+
+ align:start position:0%
+was negative it would be the other way
+you would you would get the other way
+
+ align:start position:0%
+you would you would get the other way
+ 
+
+ align:start position:0%
+you would you would get the other way
+and you wouldn't have what you want so
+
+ align:start position:0%
+and you wouldn't have what you want so
+ 
+
+ align:start position:0%
+and you wouldn't have what you want so
+we really do use the fact that X is
+
+ align:start position:0%
+we really do use the fact that X is
+ 
+
+ align:start position:0%
+we really do use the fact that X is
+greater equals zero to say that I have
+
+ align:start position:0%
+greater equals zero to say that I have
+ 
+
+ align:start position:0%
+greater equals zero to say that I have
+national equal this and then I multiply
+
+ align:start position:0%
+national equal this and then I multiply
+ 
+
+ align:start position:0%
+national equal this and then I multiply
+by something positive and then I still
+
+ align:start position:0%
+by something positive and then I still
+ 
+
+ align:start position:0%
+by something positive and then I still
+have less we okay good so every it's the
+
+ align:start position:0%
+have less we okay good so every it's the
+ 
+
+ align:start position:0%
+have less we okay good so every it's the
+math is right everything does its part
+
+ align:start position:0%
+math is right everything does its part
+ 
+
+ align:start position:0%
+math is right everything does its part
+and then the of course the beautiful
+
+ align:start position:0%
+and then the of course the beautiful
+ 
+
+ align:start position:0%
+and then the of course the beautiful
+result the important result is that
+
+ align:start position:0%
+result the important result is that
+ 
+
+ align:start position:0%
+result the important result is that
+there's strong duality just called
+
+ align:start position:0%
+there's strong duality just called
+ 
+
+ align:start position:0%
+there's strong duality just called
+duality which is that at the maximum now
+
+ align:start position:0%
+duality which is that at the maximum now
+ 
+
+ align:start position:0%
+duality which is that at the maximum now
+this is not for any x and y but this is
+
+ align:start position:0%
+this is not for any x and y but this is
+ 
+
+ align:start position:0%
+this is not for any x and y but this is
+for this is going to be 4x
+
+ align:start position:0%
+for this is going to be 4x
+ 
+
+ align:start position:0%
+for this is going to be 4x
+why star the winner and X star the
+
+ align:start position:0%
+why star the winner and X star the
+ 
+
+ align:start position:0%
+why star the winner and X star the
+winner equality holds so that's to our
+
+ align:start position:0%
+winner equality holds so that's to our
+ 
+
+ align:start position:0%
+winner equality holds so that's to our
+the maximum in the dual problem is the
+
+ align:start position:0%
+the maximum in the dual problem is the
+ 
+
+ align:start position:0%
+the maximum in the dual problem is the
+same as the minimum in the primal
+
+ align:start position:0%
+same as the minimum in the primal
+ 
+
+ align:start position:0%
+same as the minimum in the primal
+problem the two have met there is no
+
+ align:start position:0%
+problem the two have met there is no
+ 
+
+ align:start position:0%
+problem the two have met there is no
+duality gap in some cooked up nonlinear
+
+ align:start position:0%
+duality gap in some cooked up nonlinear
+ 
+
+ align:start position:0%
+duality gap in some cooked up nonlinear
+problems there could be a gap between
+
+ align:start position:0%
+problems there could be a gap between
+ 
+
+ align:start position:0%
+problems there could be a gap between
+the maximum and the minimum but you hope
+
+ align:start position:0%
+the maximum and the minimum but you hope
+ 
+
+ align:start position:0%
+the maximum and the minimum but you hope
+not and here this the big theorem is not
+
+ align:start position:0%
+not and here this the big theorem is not
+ 
+
+ align:start position:0%
+not and here this the big theorem is not
+there equal a matter you push this out
+
+ align:start position:0%
+there equal a matter you push this out
+ 
+
+ align:start position:0%
+there equal a matter you push this out
+push that down so that's another way to
+
+ align:start position:0%
+push that down so that's another way to
+ 
+
+ align:start position:0%
+push that down so that's another way to
+say that duality is that this is I'm
+
+ align:start position:0%
+say that duality is that this is I'm
+ 
+
+ align:start position:0%
+say that duality is that this is I'm
+pushing that up at some map I could
+
+ align:start position:0%
+pushing that up at some map I could
+ 
+
+ align:start position:0%
+pushing that up at some map I could
+write that as a maximum of a minimum
+
+ align:start position:0%
+write that as a maximum of a minimum
+ 
+
+ align:start position:0%
+write that as a maximum of a minimum
+equaling a minimum of a maximum if I
+
+ align:start position:0%
+equaling a minimum of a maximum if I
+ 
+
+ align:start position:0%
+equaling a minimum of a maximum if I
+wanted so it's the duality in linear
+
+ align:start position:0%
+wanted so it's the duality in linear
+ 
+
+ align:start position:0%
+wanted so it's the duality in linear
+programming was the same as one woman's
+
+ align:start position:0%
+programming was the same as one woman's
+ 
+
+ align:start position:0%
+programming was the same as one woman's
+minimax theorem and his theorem applied
+
+ align:start position:0%
+minimax theorem and his theorem applied
+ 
+
+ align:start position:0%
+minimax theorem and his theorem applied
+to two-person games so the kief the key
+
+ align:start position:0%
+to two-person games so the kief the key
+ 
+
+ align:start position:0%
+to two-person games so the kief the key
+math result is that that is duality for
+
+ align:start position:0%
+math result is that that is duality for
+ 
+
+ align:start position:0%
+math result is that that is duality for
+linear programming and it's gonna be
+
+ align:start position:0%
+linear programming and it's gonna be
+ 
+
+ align:start position:0%
+linear programming and it's gonna be
+you'll see the same thing happening for
+
+ align:start position:0%
+you'll see the same thing happening for
+ 
+
+ align:start position:0%
+you'll see the same thing happening for
+two-person games and it's a minimax
+
+ align:start position:0%
+two-person games and it's a minimax
+ 
+
+ align:start position:0%
+two-person games and it's a minimax
+theorem or a saddle point or it's just
+
+ align:start position:0%
+theorem or a saddle point or it's just
+ 
+
+ align:start position:0%
+theorem or a saddle point or it's just
+things come out right yep yep so just to
+
+ align:start position:0%
+things come out right yep yep so just to
+ 
+
+ align:start position:0%
+things come out right yep yep so just to
+mention that mathematical programming of
+
+ align:start position:0%
+mention that mathematical programming of
+ 
+
+ align:start position:0%
+mention that mathematical programming of
+course includes much more difficult
+
+ align:start position:0%
+course includes much more difficult
+ 
+
+ align:start position:0%
+course includes much more difficult
+problems this is linear programming that
+
+ align:start position:0%
+problems this is linear programming that
+ 
+
+ align:start position:0%
+problems this is linear programming that
+problem as you see is as a beautiful
+
+ align:start position:0%
+problem as you see is as a beautiful
+ 
+
+ align:start position:0%
+problem as you see is as a beautiful
+simple theory and the paying attention
+
+ align:start position:0%
+simple theory and the paying attention
+ 
+
+ align:start position:0%
+simple theory and the paying attention
+is paying attention to the algorithm
+
+ align:start position:0%
+is paying attention to the algorithm
+ 
+
+ align:start position:0%
+is paying attention to the algorithm
+because you've got two important choices
+
+ align:start position:0%
+because you've got two important choices
+ 
+
+ align:start position:0%
+because you've got two important choices
+and they both get highly developed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now okay so for game now I'm gonna turn
+
+ align:start position:0%
+now okay so for game now I'm gonna turn
+ 
+
+ align:start position:0%
+now okay so for game now I'm gonna turn
+to well I'll do a example of max flow
+
+ align:start position:0%
+to well I'll do a example of max flow
+ 
+
+ align:start position:0%
+to well I'll do a example of max flow
+equal min cut to see what and then go to
+
+ align:start position:0%
+equal min cut to see what and then go to
+ 
+
+ align:start position:0%
+equal min cut to see what and then go to
+two two person game so here's a here's
+
+ align:start position:0%
+two two person game so here's a here's
+ 
+
+ align:start position:0%
+two two person game so here's a here's
+an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I start with a graph yeah let me
+
+ align:start position:0%
+okay so I start with a graph yeah let me
+ 
+
+ align:start position:0%
+okay so I start with a graph yeah let me
+just so this is the source this is the
+
+ align:start position:0%
+just so this is the source this is the
+ 
+
+ align:start position:0%
+just so this is the source this is the
+sink and I'm sending flow through the
+
+ align:start position:0%
+sink and I'm sending flow through the
+ 
+
+ align:start position:0%
+sink and I'm sending flow through the
+network so it's a network that I'm
+
+ align:start position:0%
+network so it's a network that I'm
+ 
+
+ align:start position:0%
+network so it's a network that I'm
+sending flow through so I'm so my job is
+
+ align:start position:0%
+sending flow through so I'm so my job is
+ 
+
+ align:start position:0%
+sending flow through so I'm so my job is
+to maximize yeah is to I'll set X at the
+
+ align:start position:0%
+to maximize yeah is to I'll set X at the
+ 
+
+ align:start position:0%
+to maximize yeah is to I'll set X at the
+source to be zero and then the flow the
+
+ align:start position:0%
+source to be zero and then the flow the
+ 
+
+ align:start position:0%
+source to be zero and then the flow the
+total flow will come into the sink so I
+
+ align:start position:0%
+total flow will come into the sink so I
+ 
+
+ align:start position:0%
+total flow will come into the sink so I
+want to maximize X at the sink so it's
+
+ align:start position:0%
+want to maximize X at the sink so it's
+ 
+
+ align:start position:0%
+want to maximize X at the sink so it's
+of linear programming and their
+
+ align:start position:0%
+of linear programming and their
+ 
+
+ align:start position:0%
+of linear programming and their
+constraint so what are the constraints
+
+ align:start position:0%
+constraint so what are the constraints
+ 
+
+ align:start position:0%
+constraint so what are the constraints
+every Edge has a capacity so let's see
+
+ align:start position:0%
+every Edge has a capacity so let's see
+ 
+
+ align:start position:0%
+every Edge has a capacity so let's see
+suppose that Edge has capacity 5 let me
+
+ align:start position:0%
+suppose that Edge has capacity 5 let me
+ 
+
+ align:start position:0%
+suppose that Edge has capacity 5 let me
+let me put capacities on all these edges
+
+ align:start position:0%
+let me put capacities on all these edges
+ 
+
+ align:start position:0%
+let me put capacities on all these edges
+2 1 3 4 I'm just stabbing around here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me say - ok I have no idea what's
+
+ align:start position:0%
+let me say - ok I have no idea what's
+ 
+
+ align:start position:0%
+let me say - ok I have no idea what's
+happening here
+
+ align:start position:0%
+happening here
+ 
+
+ align:start position:0%
+happening here
+but if we see the problem we'll probably
+
+ align:start position:0%
+but if we see the problem we'll probably
+ 
+
+ align:start position:0%
+but if we see the problem we'll probably
+be able to solve it so so these
+
+ align:start position:0%
+be able to solve it so so these
+ 
+
+ align:start position:0%
+be able to solve it so so these
+constraints are that the flow variable
+
+ align:start position:0%
+constraints are that the flow variable
+ 
+
+ align:start position:0%
+constraints are that the flow variable
+which would be would be the why that
+
+ align:start position:0%
+which would be would be the why that
+ 
+
+ align:start position:0%
+which would be would be the why that
+where I'm trying to maximize cannot to
+
+ align:start position:0%
+where I'm trying to maximize cannot to
+ 
+
+ align:start position:0%
+where I'm trying to maximize cannot to
+the amount of flow just in ordinary
+
+ align:start position:0%
+the amount of flow just in ordinary
+ 
+
+ align:start position:0%
+the amount of flow just in ordinary
+words the amount of flow on the edges
+
+ align:start position:0%
+words the amount of flow on the edges
+ 
+
+ align:start position:0%
+words the amount of flow on the edges
+can't go go higher than the capacity
+
+ align:start position:0%
+can't go go higher than the capacity
+ 
+
+ align:start position:0%
+can't go go higher than the capacity
+I could send eleven along this edge but
+
+ align:start position:0%
+I could send eleven along this edge but
+ 
+
+ align:start position:0%
+I could send eleven along this edge but
+then I've got nowhere to send it after
+
+ align:start position:0%
+then I've got nowhere to send it after
+ 
+
+ align:start position:0%
+then I've got nowhere to send it after
+that I could send well nine hundred on
+
+ align:start position:0%
+that I could send well nine hundred on
+ 
+
+ align:start position:0%
+that I could send well nine hundred on
+that edge but obviously it would get
+
+ align:start position:0%
+that edge but obviously it would get
+ 
+
+ align:start position:0%
+that edge but obviously it would get
+stuck there so the question is what's
+
+ align:start position:0%
+stuck there so the question is what's
+ 
+
+ align:start position:0%
+stuck there so the question is what's
+the maximum I can send through that
+
+ align:start position:0%
+the maximum I can send through that
+ 
+
+ align:start position:0%
+the maximum I can send through that
+network it's a classical problem and and
+
+ align:start position:0%
+network it's a classical problem and and
+ 
+
+ align:start position:0%
+network it's a classical problem and and
+in fact it's it's an integer programming
+
+ align:start position:0%
+in fact it's it's an integer programming
+ 
+
+ align:start position:0%
+in fact it's it's an integer programming
+problem I these are all integer
+
+ align:start position:0%
+problem I these are all integer
+ 
+
+ align:start position:0%
+problem I these are all integer
+capacities I could insist on integer
+
+ align:start position:0%
+capacities I could insist on integer
+ 
+
+ align:start position:0%
+capacities I could insist on integer
+flows but it's a very remarkable integer
+
+ align:start position:0%
+flows but it's a very remarkable integer
+ 
+
+ align:start position:0%
+flows but it's a very remarkable integer
+problem because I could allow fractions
+
+ align:start position:0%
+problem because I could allow fractions
+ 
+
+ align:start position:0%
+problem because I could allow fractions
+and the answer would not be it would not
+
+ align:start position:0%
+and the answer would not be it would not
+ 
+
+ align:start position:0%
+and the answer would not be it would not
+involve fractions in other words if I
+
+ align:start position:0%
+involve fractions in other words if I
+ 
+
+ align:start position:0%
+involve fractions in other words if I
+keep it as an integer problem then the
+
+ align:start position:0%
+keep it as an integer problem then the
+ 
+
+ align:start position:0%
+keep it as an integer problem then the
+mathematics is definitely harder for an
+
+ align:start position:0%
+mathematics is definitely harder for an
+ 
+
+ align:start position:0%
+mathematics is definitely harder for an
+integer problem what's different so so
+
+ align:start position:0%
+integer problem what's different so so
+ 
+
+ align:start position:0%
+integer problem what's different so so
+the x's could be integers or they could
+
+ align:start position:0%
+the x's could be integers or they could
+ 
+
+ align:start position:0%
+the x's could be integers or they could
+be real real numbers over here they were
+
+ align:start position:0%
+be real real numbers over here they were
+ 
+
+ align:start position:0%
+be real real numbers over here they were
+real numbers I happen to get an integer
+
+ align:start position:0%
+real numbers I happen to get an integer
+ 
+
+ align:start position:0%
+real numbers I happen to get an integer
+for this but if I put if I had 10
+
+ align:start position:0%
+for this but if I put if I had 10
+ 
+
+ align:start position:0%
+for this but if I put if I had 10
+crossing planes in 15 dimensions and the
+
+ align:start position:0%
+crossing planes in 15 dimensions and the
+ 
+
+ align:start position:0%
+crossing planes in 15 dimensions and the
+integers would be totally lost but the
+
+ align:start position:0%
+integers would be totally lost but the
+ 
+
+ align:start position:0%
+integers would be totally lost but the
+point is here that if I allow real
+
+ align:start position:0%
+point is here that if I allow real
+ 
+
+ align:start position:0%
+point is here that if I allow real
+numbers it doesn't get me any more flow
+
+ align:start position:0%
+numbers it doesn't get me any more flow
+ 
+
+ align:start position:0%
+numbers it doesn't get me any more flow
+that the winning flow is an integer
+
+ align:start position:0%
+that the winning flow is an integer
+ 
+
+ align:start position:0%
+that the winning flow is an integer
+anyway so it's an integer problem which
+
+ align:start position:0%
+anyway so it's an integer problem which
+ 
+
+ align:start position:0%
+anyway so it's an integer problem which
+can be safely relaxed and you can safely
+
+ align:start position:0%
+can be safely relaxed and you can safely
+ 
+
+ align:start position:0%
+can be safely relaxed and you can safely
+use simplex method or car markers method
+
+ align:start position:0%
+use simplex method or car markers method
+ 
+
+ align:start position:0%
+use simplex method or car markers method
+or in the interior point method
+
+ align:start position:0%
+or in the interior point method
+ 
+
+ align:start position:0%
+or in the interior point method
+with with non integers because in the
+
+ align:start position:0%
+with with non integers because in the
+ 
+
+ align:start position:0%
+with with non integers because in the
+interior here you're not ending it
+
+ align:start position:0%
+interior here you're not ending it
+ 
+
+ align:start position:0%
+interior here you're not ending it
+starting or ending at integers you can
+
+ align:start position:0%
+starting or ending at integers you can
+ 
+
+ align:start position:0%
+starting or ending at integers you can
+do it because the the integer answer
+
+ align:start position:0%
+do it because the the integer answer
+ 
+
+ align:start position:0%
+do it because the the integer answer
+will be in the end better okay and what
+
+ align:start position:0%
+will be in the end better okay and what
+ 
+
+ align:start position:0%
+will be in the end better okay and what
+is that answer
+
+ align:start position:0%
+is that answer
+ 
+
+ align:start position:0%
+is that answer
+III think I've made those capacities
+
+ align:start position:0%
+III think I've made those capacities
+ 
+
+ align:start position:0%
+III think I've made those capacities
+like too easy too
+
+ align:start position:0%
+like too easy too
+ 
+
+ align:start position:0%
+like too easy too
+oh I didn't do this one so so what shall
+
+ align:start position:0%
+oh I didn't do this one so so what shall
+ 
+
+ align:start position:0%
+oh I didn't do this one so so what shall
+I say so I make it large like nine I
+
+ align:start position:0%
+I say so I make it large like nine I
+ 
+
+ align:start position:0%
+I say so I make it large like nine I
+don't know okay what's the best we can
+
+ align:start position:0%
+don't know okay what's the best we can
+ 
+
+ align:start position:0%
+don't know okay what's the best we can
+do through that through that Network
+
+ align:start position:0%
+do through that through that Network
+ 
+
+ align:start position:0%
+do through that through that Network
+okay I can't see it from here yet what
+
+ align:start position:0%
+okay I can't see it from here yet what
+ 
+
+ align:start position:0%
+okay I can't see it from here yet what
+what should I do
+
+ align:start position:0%
+what should I do
+ 
+
+ align:start position:0%
+what should I do
+obviously in this simple problem I can
+
+ align:start position:0%
+obviously in this simple problem I can
+ 
+
+ align:start position:0%
+obviously in this simple problem I can
+get anything I want pretty much to this
+
+ align:start position:0%
+get anything I want pretty much to this
+ 
+
+ align:start position:0%
+get anything I want pretty much to this
+that far but then what can I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me let me even make that 19 okay so
+
+ align:start position:0%
+let me let me even make that 19 okay so
+ 
+
+ align:start position:0%
+let me let me even make that 19 okay so
+I'm I'm not imposing much of a limit on
+
+ align:start position:0%
+I'm I'm not imposing much of a limit on
+ 
+
+ align:start position:0%
+I'm I'm not imposing much of a limit on
+that edge either but these edges are
+
+ align:start position:0%
+that edge either but these edges are
+ 
+
+ align:start position:0%
+that edge either but these edges are
+quite tight limits and these are sort of
+
+ align:start position:0%
+quite tight limits and these are sort of
+ 
+
+ align:start position:0%
+quite tight limits and these are sort of
+intermediate limits well what do you
+
+ align:start position:0%
+intermediate limits well what do you
+ 
+
+ align:start position:0%
+intermediate limits well what do you
+think is the most I could send through
+
+ align:start position:0%
+think is the most I could send through
+ 
+
+ align:start position:0%
+think is the most I could send through
+and how would you show me that I
+
+ align:start position:0%
+and how would you show me that I
+ 
+
+ align:start position:0%
+and how would you show me that I
+couldn't send more that's the key
+
+ align:start position:0%
+couldn't send more that's the key
+ 
+
+ align:start position:0%
+couldn't send more that's the key
+question I want to get a bound on an
+
+ align:start position:0%
+question I want to get a bound on an
+ 
+
+ align:start position:0%
+question I want to get a bound on an
+upper bound on this maximum this maximum
+
+ align:start position:0%
+upper bound on this maximum this maximum
+ 
+
+ align:start position:0%
+upper bound on this maximum this maximum
+getting into the sink is less or equal
+
+ align:start position:0%
+getting into the sink is less or equal
+ 
+
+ align:start position:0%
+getting into the sink is less or equal
+to and what what number would you
+
+ align:start position:0%
+to and what what number would you
+ 
+
+ align:start position:0%
+to and what what number would you
+propose could I get a thousand through I
+
+ align:start position:0%
+propose could I get a thousand through I
+ 
+
+ align:start position:0%
+propose could I get a thousand through I
+could start but of course I I wouldn't
+
+ align:start position:0%
+could start but of course I I wouldn't
+ 
+
+ align:start position:0%
+could start but of course I I wouldn't
+tile up there I couldn't get further
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you what do you think the best I
+
+ align:start position:0%
+what do you what do you think the best I
+ 
+
+ align:start position:0%
+what do you what do you think the best I
+can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ten I can't do more than ten how how
+
+ align:start position:0%
+ten I can't do more than ten how how
+ 
+
+ align:start position:0%
+ten I can't do more than ten how how
+could I do ten twelve twelve this right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I I see him that way can this yeah
+
+ align:start position:0%
+so I I see him that way can this yeah
+ 
+
+ align:start position:0%
+so I I see him that way can this yeah
+absolutely you can split and then this
+
+ align:start position:0%
+absolutely you can split and then this
+ 
+
+ align:start position:0%
+absolutely you can split and then this
+can this go here and that would would be
+
+ align:start position:0%
+can this go here and that would would be
+ 
+
+ align:start position:0%
+can this go here and that would would be
+able to go there so I can get ten
+
+ align:start position:0%
+able to go there so I can get ten
+ 
+
+ align:start position:0%
+able to go there so I can get ten
+correct can I do anything better
+
+ align:start position:0%
+correct can I do anything better
+ 
+
+ align:start position:0%
+correct can I do anything better
+oh I could be sending some up this way
+
+ align:start position:0%
+oh I could be sending some up this way
+ 
+
+ align:start position:0%
+oh I could be sending some up this way
+at the same time so I could get three
+
+ align:start position:0%
+at the same time so I could get three
+ 
+
+ align:start position:0%
+at the same time so I could get three
+along the top
+
+ align:start position:0%
+along the top
+ 
+
+ align:start position:0%
+along the top
+I could so this is like an auction okay
+
+ align:start position:0%
+I could so this is like an auction okay
+ 
+
+ align:start position:0%
+I could so this is like an auction okay
+we can get up to 13 can we get so that
+
+ align:start position:0%
+we can get up to 13 can we get so that
+ 
+
+ align:start position:0%
+we can get up to 13 can we get so that
+that was three going this way and ten
+
+ align:start position:0%
+that was three going this way and ten
+ 
+
+ align:start position:0%
+that was three going this way and ten
+going this way is 13 and can I not
+
+ align:start position:0%
+going this way is 13 and can I not
+ 
+
+ align:start position:0%
+going this way is 13 and can I not
+exceed 13 do I hear 40 yeah oh I've got
+
+ align:start position:0%
+exceed 13 do I hear 40 yeah oh I've got
+ 
+
+ align:start position:0%
+exceed 13 do I hear 40 yeah oh I've got
+a lot of room for one more
+
+ align:start position:0%
+a lot of room for one more
+ 
+
+ align:start position:0%
+a lot of room for one more
+so okay so 14 many kids alright do I
+
+ align:start position:0%
+so okay so 14 many kids alright do I
+ 
+
+ align:start position:0%
+so okay so 14 many kids alright do I
+hear 15 if I did 12 then what would I do
+
+ align:start position:0%
+hear 15 if I did 12 then what would I do
+ 
+
+ align:start position:0%
+hear 15 if I did 12 then what would I do
+I send two up here okay what am I gonna
+
+ align:start position:0%
+I send two up here okay what am I gonna
+ 
+
+ align:start position:0%
+I send two up here okay what am I gonna
+do with them from here send them up
+
+ align:start position:0%
+do with them from here send them up
+ 
+
+ align:start position:0%
+do with them from here send them up
+again and along but then now you then
+
+ align:start position:0%
+again and along but then now you then
+ 
+
+ align:start position:0%
+again and along but then now you then
+the three that that I had right now what
+
+ align:start position:0%
+the three that that I had right now what
+ 
+
+ align:start position:0%
+the three that that I had right now what
+would be back of one problem and I'm
+
+ align:start position:0%
+would be back of one problem and I'm
+ 
+
+ align:start position:0%
+would be back of one problem and I'm
+looking for a bound to know when to quit
+
+ align:start position:0%
+looking for a bound to know when to quit
+ 
+
+ align:start position:0%
+looking for a bound to know when to quit
+to know when I've optimized that's the
+
+ align:start position:0%
+to know when I've optimized that's the
+ 
+
+ align:start position:0%
+to know when I've optimized that's the
+whole idea of duality is to find some
+
+ align:start position:0%
+whole idea of duality is to find some
+ 
+
+ align:start position:0%
+whole idea of duality is to find some
+upper thing that I'm trying to push down
+
+ align:start position:0%
+upper thing that I'm trying to push down
+ 
+
+ align:start position:0%
+upper thing that I'm trying to push down
+and but I can't go beyond it so so I
+
+ align:start position:0%
+and but I can't go beyond it so so I
+ 
+
+ align:start position:0%
+and but I can't go beyond it so so I
+don't think I could get more than to see
+
+ align:start position:0%
+don't think I could get more than to see
+ 
+
+ align:start position:0%
+don't think I could get more than to see
+everything has to cross this middle so
+
+ align:start position:0%
+everything has to cross this middle so
+ 
+
+ align:start position:0%
+everything has to cross this middle so
+three and four night I don't think I
+
+ align:start position:0%
+three and four night I don't think I
+ 
+
+ align:start position:0%
+three and four night I don't think I
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+b23 somebody said 24 more than 23 I
+
+ align:start position:0%
+b23 somebody said 24 more than 23 I
+ 
+
+ align:start position:0%
+b23 somebody said 24 more than 23 I
+would be very doubtful because I
+
+ align:start position:0%
+would be very doubtful because I
+ 
+
+ align:start position:0%
+would be very doubtful because I
+couldn't get it across the middle but
+
+ align:start position:0%
+couldn't get it across the middle but
+ 
+
+ align:start position:0%
+couldn't get it across the middle but
+then can I get 23 I doubt it
+
+ align:start position:0%
+then can I get 23 I doubt it
+ 
+
+ align:start position:0%
+then can I get 23 I doubt it
+maybe 14 as best possible so how would
+
+ align:start position:0%
+maybe 14 as best possible so how would
+ 
+
+ align:start position:0%
+maybe 14 as best possible so how would
+we show that 14 is best possible I think
+
+ align:start position:0%
+we show that 14 is best possible I think
+ 
+
+ align:start position:0%
+we show that 14 is best possible I think
+if I could find so this is called the
+
+ align:start position:0%
+if I could find so this is called the
+ 
+
+ align:start position:0%
+if I could find so this is called the
+cut a cut in this in this network so
+
+ align:start position:0%
+cut a cut in this in this network so
+ 
+
+ align:start position:0%
+cut a cut in this in this network so
+yeah I see a cut a cut like there you
+
+ align:start position:0%
+yeah I see a cut a cut like there you
+ 
+
+ align:start position:0%
+yeah I see a cut a cut like there you
+see that every bit of flow has got to
+
+ align:start position:0%
+see that every bit of flow has got to
+ 
+
+ align:start position:0%
+see that every bit of flow has got to
+cross that cut and the total capacity
+
+ align:start position:0%
+cross that cut and the total capacity
+ 
+
+ align:start position:0%
+cross that cut and the total capacity
+crossing is the 3 and the 1 and the 2
+
+ align:start position:0%
+crossing is the 3 and the 1 and the 2
+ 
+
+ align:start position:0%
+crossing is the 3 and the 1 and the 2
+and the 8 which is 14 so I can't get
+
+ align:start position:0%
+and the 8 which is 14 so I can't get
+ 
+
+ align:start position:0%
+and the 8 which is 14 so I can't get
+more than 14 through and somehow that
+
+ align:start position:0%
+more than 14 through and somehow that
+ 
+
+ align:start position:0%
+more than 14 through and somehow that
+cut is loaded to capacity probably those
+
+ align:start position:0%
+cut is loaded to capacity probably those
+ 
+
+ align:start position:0%
+cut is loaded to capacity probably those
+edges all all have to be fully up to
+
+ align:start position:0%
+edges all all have to be fully up to
+ 
+
+ align:start position:0%
+edges all all have to be fully up to
+capacity then that crossed the cut so so
+
+ align:start position:0%
+capacity then that crossed the cut so so
+ 
+
+ align:start position:0%
+capacity then that crossed the cut so so
+the cut is is a separation of edges that
+
+ align:start position:0%
+the cut is is a separation of edges that
+ 
+
+ align:start position:0%
+the cut is is a separation of edges that
+go with a source and sorry nodes that go
+
+ align:start position:0%
+go with a source and sorry nodes that go
+ 
+
+ align:start position:0%
+go with a source and sorry nodes that go
+with a source nodes that go with this
+
+ align:start position:0%
+with a source nodes that go with this
+ 
+
+ align:start position:0%
+with a source nodes that go with this
+thing yeah and and then it's the edges
+
+ align:start position:0%
+thing yeah and and then it's the edges
+ 
+
+ align:start position:0%
+thing yeah and and then it's the edges
+across the cut so I yeah is that okay
+
+ align:start position:0%
+across the cut so I yeah is that okay
+ 
+
+ align:start position:0%
+across the cut so I yeah is that okay
+for an example so that's the duality the
+
+ align:start position:0%
+for an example so that's the duality the
+ 
+
+ align:start position:0%
+for an example so that's the duality the
+maximum flow turned out to be 14 and the
+
+ align:start position:0%
+maximum flow turned out to be 14 and the
+ 
+
+ align:start position:0%
+maximum flow turned out to be 14 and the
+minimum cut turned out to be 14 and when
+
+ align:start position:0%
+minimum cut turned out to be 14 and when
+ 
+
+ align:start position:0%
+minimum cut turned out to be 14 and when
+those matched 14 equal 14 I know I'm
+
+ align:start position:0%
+those matched 14 equal 14 I know I'm
+ 
+
+ align:start position:0%
+those matched 14 equal 14 I know I'm
+through I know I'm through because I'm
+
+ align:start position:0%
+through I know I'm through because I'm
+ 
+
+ align:start position:0%
+through I know I'm through because I'm
+able to get 14 through and I could never
+
+ align:start position:0%
+able to get 14 through and I could never
+ 
+
+ align:start position:0%
+able to get 14 through and I could never
+get more yeah 3 & 4 & 6 & 8 yeah okay
+
+ align:start position:0%
+get more yeah 3 & 4 & 6 & 8 yeah okay
+ 
+
+ align:start position:0%
+get more yeah 3 & 4 & 6 & 8 yeah okay
+and of course the in a big network
+
+ align:start position:0%
+and of course the in a big network
+ 
+
+ align:start position:0%
+and of course the in a big network
+the cut is the maximum cut is not going
+
+ align:start position:0%
+the cut is the maximum cut is not going
+ 
+
+ align:start position:0%
+the cut is the maximum cut is not going
+to be visible well you couldn't you know
+
+ align:start position:0%
+to be visible well you couldn't you know
+ 
+
+ align:start position:0%
+to be visible well you couldn't you know
+they would have thousands of edges you
+
+ align:start position:0%
+they would have thousands of edges you
+ 
+
+ align:start position:0%
+they would have thousands of edges you
+couldn't see what you were doing but but
+
+ align:start position:0%
+couldn't see what you were doing but but
+ 
+
+ align:start position:0%
+couldn't see what you were doing but but
+you could solve this problem fast
+
+ align:start position:0%
+you could solve this problem fast
+ 
+
+ align:start position:0%
+you could solve this problem fast
+actually fast and and it's an important
+
+ align:start position:0%
+actually fast and and it's an important
+ 
+
+ align:start position:0%
+actually fast and and it's an important
+in practice it's an important example a
+
+ align:start position:0%
+in practice it's an important example a
+ 
+
+ align:start position:0%
+in practice it's an important example a
+lot of other things fit into the
+
+ align:start position:0%
+lot of other things fit into the
+ 
+
+ align:start position:0%
+lot of other things fit into the
+max-flow min-cut example and therefore
+
+ align:start position:0%
+max-flow min-cut example and therefore
+ 
+
+ align:start position:0%
+max-flow min-cut example and therefore
+solving it in faster than oh I didn't
+
+ align:start position:0%
+solving it in faster than oh I didn't
+ 
+
+ align:start position:0%
+solving it in faster than oh I didn't
+even say about speed
+
+ align:start position:0%
+even say about speed
+ 
+
+ align:start position:0%
+even say about speed
+so the simplex method almost always its
+
+ align:start position:0%
+so the simplex method almost always its
+ 
+
+ align:start position:0%
+so the simplex method almost always its
+average case den Spielman who was on the
+
+ align:start position:0%
+average case den Spielman who was on the
+ 
+
+ align:start position:0%
+average case den Spielman who was on the
+faculty here who's just terrific in this
+
+ align:start position:0%
+faculty here who's just terrific in this
+ 
+
+ align:start position:0%
+faculty here who's just terrific in this
+area was maybe among the first to study
+
+ align:start position:0%
+area was maybe among the first to study
+ 
+
+ align:start position:0%
+area was maybe among the first to study
+the average case so so for a for an
+
+ align:start position:0%
+the average case so so for a for an
+ 
+
+ align:start position:0%
+the average case so so for a for an
+average choice of a and B and C instead
+
+ align:start position:0%
+average choice of a and B and C instead
+ 
+
+ align:start position:0%
+average choice of a and B and C instead
+of making the worst choice for the worst
+
+ align:start position:0%
+of making the worst choice for the worst
+ 
+
+ align:start position:0%
+of making the worst choice for the worst
+choice you can create a feasible set
+
+ align:start position:0%
+choice you can create a feasible set
+ 
+
+ align:start position:0%
+choice you can create a feasible set
+that it has to go corner Corner corner
+
+ align:start position:0%
+that it has to go corner Corner corner
+ 
+
+ align:start position:0%
+that it has to go corner Corner corner
+corner until to get to the end so the
+
+ align:start position:0%
+corner until to get to the end so the
+ 
+
+ align:start position:0%
+corner until to get to the end so the
+simplex method would take exponentially
+
+ align:start position:0%
+simplex method would take exponentially
+ 
+
+ align:start position:0%
+simplex method would take exponentially
+long but that's extremely rare doesn't
+
+ align:start position:0%
+long but that's extremely rare doesn't
+ 
+
+ align:start position:0%
+long but that's extremely rare doesn't
+happen in practice I think and the
+
+ align:start position:0%
+happen in practice I think and the
+ 
+
+ align:start position:0%
+happen in practice I think and the
+average one is polynomial so it's a fast
+
+ align:start position:0%
+average one is polynomial so it's a fast
+ 
+
+ align:start position:0%
+average one is polynomial so it's a fast
+method on average this but and we can
+
+ align:start position:0%
+method on average this but and we can
+ 
+
+ align:start position:0%
+method on average this but and we can
+show actually that was a famous result
+
+ align:start position:0%
+show actually that was a famous result
+ 
+
+ align:start position:0%
+show actually that was a famous result
+it came from Russia that that linear
+
+ align:start position:0%
+it came from Russia that that linear
+ 
+
+ align:start position:0%
+it came from Russia that that linear
+programming is in the big P versus LP
+
+ align:start position:0%
+programming is in the big P versus LP
+ 
+
+ align:start position:0%
+programming is in the big P versus LP
+world linear programming goes with P
+
+ align:start position:0%
+world linear programming goes with P
+ 
+
+ align:start position:0%
+world linear programming goes with P
+linear programming is a problem that can
+
+ align:start position:0%
+linear programming is a problem that can
+ 
+
+ align:start position:0%
+linear programming is a problem that can
+be solved in polynomial time the simplex
+
+ align:start position:0%
+be solved in polynomial time the simplex
+ 
+
+ align:start position:0%
+be solved in polynomial time the simplex
+method won't always do it but it can be
+
+ align:start position:0%
+method won't always do it but it can be
+ 
+
+ align:start position:0%
+method won't always do it but it can be
+done yeah there came into the world
+
+ align:start position:0%
+done yeah there came into the world
+ 
+
+ align:start position:0%
+done yeah there came into the world
+ellipsoid methods and there was a
+
+ align:start position:0%
+ellipsoid methods and there was a
+ 
+
+ align:start position:0%
+ellipsoid methods and there was a
+exciting time to decide that linear
+
+ align:start position:0%
+exciting time to decide that linear
+ 
+
+ align:start position:0%
+exciting time to decide that linear
+programming was actually P and not LP
+
+ align:start position:0%
+programming was actually P and not LP
+ 
+
+ align:start position:0%
+programming was actually P and not LP
+yep okay so that's okay this is a case
+
+ align:start position:0%
+yep okay so that's okay this is a case
+ 
+
+ align:start position:0%
+yep okay so that's okay this is a case
+of duality where you can understand
+
+ align:start position:0%
+of duality where you can understand
+ 
+
+ align:start position:0%
+of duality where you can understand
+duality you can buy this by the state
+
+ align:start position:0%
+duality you can buy this by the state
+ 
+
+ align:start position:0%
+duality you can buy this by the state
+that the flow can't exceed the capacity
+
+ align:start position:0%
+that the flow can't exceed the capacity
+ 
+
+ align:start position:0%
+that the flow can't exceed the capacity
+of the cut so that's what duality is any
+
+ align:start position:0%
+of the cut so that's what duality is any
+ 
+
+ align:start position:0%
+of the cut so that's what duality is any
+flow it has to be less Rico the capacity
+
+ align:start position:0%
+flow it has to be less Rico the capacity
+ 
+
+ align:start position:0%
+flow it has to be less Rico the capacity
+of any cut their capacity being the sum
+
+ align:start position:0%
+of any cut their capacity being the sum
+ 
+
+ align:start position:0%
+of any cut their capacity being the sum
+of the one so of course there are other
+
+ align:start position:0%
+of the one so of course there are other
+ 
+
+ align:start position:0%
+of the one so of course there are other
+cuts that cut has to be crossed but
+
+ align:start position:0%
+cuts that cut has to be crossed but
+ 
+
+ align:start position:0%
+cuts that cut has to be crossed but
+that's got three seven fourteen twenty
+
+ align:start position:0%
+that's got three seven fourteen twenty
+ 
+
+ align:start position:0%
+that's got three seven fourteen twenty
+two capacity so it the fourteen capacity
+
+ align:start position:0%
+two capacity so it the fourteen capacity
+ 
+
+ align:start position:0%
+two capacity so it the fourteen capacity
+was the was the minimum and I gave the
+
+ align:start position:0%
+was the was the minimum and I gave the
+ 
+
+ align:start position:0%
+was the was the minimum and I gave the
+maximum nice isn't that nice
+
+ align:start position:0%
+maximum nice isn't that nice
+ 
+
+ align:start position:0%
+maximum nice isn't that nice
+yeah okay so there's another world here
+
+ align:start position:0%
+yeah okay so there's another world here
+ 
+
+ align:start position:0%
+yeah okay so there's another world here
+of two person games that also has
+
+ align:start position:0%
+of two person games that also has
+ 
+
+ align:start position:0%
+of two person games that also has
+duality and could be expressed so let me
+
+ align:start position:0%
+duality and could be expressed so let me
+ 
+
+ align:start position:0%
+duality and could be expressed so let me
+just talk finally today about two-person
+
+ align:start position:0%
+just talk finally today about two-person
+ 
+
+ align:start position:0%
+just talk finally today about two-person
+game so the two persons are X&Y of
+
+ align:start position:0%
+game so the two persons are X&Y of
+ 
+
+ align:start position:0%
+game so the two persons are X&Y of
+course what other names good they have
+
+ align:start position:0%
+course what other names good they have
+ 
+
+ align:start position:0%
+course what other names good they have
+and there's a there's a matrix involved
+
+ align:start position:0%
+and there's a there's a matrix involved
+ 
+
+ align:start position:0%
+and there's a there's a matrix involved
+this is the payoff matrix so let me take
+
+ align:start position:0%
+this is the payoff matrix so let me take
+ 
+
+ align:start position:0%
+this is the payoff matrix so let me take
+a very simple game first so X is going
+
+ align:start position:0%
+a very simple game first so X is going
+ 
+
+ align:start position:0%
+a very simple game first so X is going
+to choose one of these rows and Y is
+
+ align:start position:0%
+to choose one of these rows and Y is
+ 
+
+ align:start position:0%
+to choose one of these rows and Y is
+going to choose one of these columns and
+
+ align:start position:0%
+going to choose one of these columns and
+ 
+
+ align:start position:0%
+going to choose one of these columns and
+let's say payoff from x to y I like it
+
+ align:start position:0%
+let's say payoff from x to y I like it
+ 
+
+ align:start position:0%
+let's say payoff from x to y I like it
+that way because then X whose pain is is
+
+ align:start position:0%
+that way because then X whose pain is is
+ 
+
+ align:start position:0%
+that way because then X whose pain is is
+going to be minimizing as X was up here
+
+ align:start position:0%
+going to be minimizing as X was up here
+ 
+
+ align:start position:0%
+going to be minimizing as X was up here
+and y who's collecting is going to be
+
+ align:start position:0%
+and y who's collecting is going to be
+ 
+
+ align:start position:0%
+and y who's collecting is going to be
+maximizing as in the dual so so the
+
+ align:start position:0%
+maximizing as in the dual so so the
+ 
+
+ align:start position:0%
+maximizing as in the dual so so the
+payoff well let's see I think maybe one
+
+ align:start position:0%
+payoff well let's see I think maybe one
+ 
+
+ align:start position:0%
+payoff well let's see I think maybe one
+four to eight would be a probably a
+
+ align:start position:0%
+four to eight would be a probably a
+ 
+
+ align:start position:0%
+four to eight would be a probably a
+fairly easy game to play so that so it's
+
+ align:start position:0%
+fairly easy game to play so that so it's
+ 
+
+ align:start position:0%
+fairly easy game to play so that so it's
+a two-person game zero-sum games
+
+ align:start position:0%
+a two-person game zero-sum games
+ 
+
+ align:start position:0%
+a two-person game zero-sum games
+some means that means all all pay what
+
+ align:start position:0%
+some means that means all all pay what
+ 
+
+ align:start position:0%
+some means that means all all pay what
+ex pays goes to why why gets all that ex
+
+ align:start position:0%
+ex pays goes to why why gets all that ex
+ 
+
+ align:start position:0%
+ex pays goes to why why gets all that ex
+pace there's no third party here no
+
+ align:start position:0%
+pace there's no third party here no
+ 
+
+ align:start position:0%
+pace there's no third party here no
+lawyers involved okay so what would and
+
+ align:start position:0%
+lawyers involved okay so what would and
+ 
+
+ align:start position:0%
+lawyers involved okay so what would and
+why is going to choose a column and X is
+
+ align:start position:0%
+why is going to choose a column and X is
+ 
+
+ align:start position:0%
+why is going to choose a column and X is
+going to choose a row an X wants to make
+
+ align:start position:0%
+going to choose a row an X wants to make
+ 
+
+ align:start position:0%
+going to choose a row an X wants to make
+it small and Y wants to make it big okay
+
+ align:start position:0%
+it small and Y wants to make it big okay
+ 
+
+ align:start position:0%
+it small and Y wants to make it big okay
+so what happens in this game
+
+ align:start position:0%
+so what happens in this game
+ 
+
+ align:start position:0%
+so what happens in this game
+what does y choose to make it big the
+
+ align:start position:0%
+what does y choose to make it big the
+ 
+
+ align:start position:0%
+what does y choose to make it big the
+second column what does X choose to make
+
+ align:start position:0%
+second column what does X choose to make
+ 
+
+ align:start position:0%
+second column what does X choose to make
+it small the first row so it's gonna be
+
+ align:start position:0%
+it small the first row so it's gonna be
+ 
+
+ align:start position:0%
+it small the first row so it's gonna be
+focus in on that too because if Y keeps
+
+ align:start position:0%
+focus in on that too because if Y keeps
+ 
+
+ align:start position:0%
+focus in on that too because if Y keeps
+choosing that column two is the best the
+
+ align:start position:0%
+choosing that column two is the best the
+ 
+
+ align:start position:0%
+choosing that column two is the best the
+least that X is going to have to pay to
+
+ align:start position:0%
+least that X is going to have to pay to
+ 
+
+ align:start position:0%
+least that X is going to have to pay to
+and he achieves that by choosing the
+
+ align:start position:0%
+and he achieves that by choosing the
+ 
+
+ align:start position:0%
+and he achieves that by choosing the
+first row so it's a simple game that's a
+
+ align:start position:0%
+first row so it's a simple game that's a
+ 
+
+ align:start position:0%
+first row so it's a simple game that's a
+saddle point it's a it's a minimum for y
+
+ align:start position:0%
+saddle point it's a it's a minimum for y
+ 
+
+ align:start position:0%
+saddle point it's a it's a minimum for y
+in its column and it's a maximum for X
+
+ align:start position:0%
+in its column and it's a maximum for X
+ 
+
+ align:start position:0%
+in its column and it's a maximum for X
+in its row but of course a matrix and
+
+ align:start position:0%
+in its row but of course a matrix and
+ 
+
+ align:start position:0%
+in its row but of course a matrix and
+other matrix might not have such a
+
+ align:start position:0%
+other matrix might not have such a
+ 
+
+ align:start position:0%
+other matrix might not have such a
+saddle point so that may do you see okay
+
+ align:start position:0%
+saddle point so that may do you see okay
+ 
+
+ align:start position:0%
+saddle point so that may do you see okay
+with this game that would be a sort of
+
+ align:start position:0%
+with this game that would be a sort of
+ 
+
+ align:start position:0%
+with this game that would be a sort of
+straightforward game where simple
+
+ align:start position:0%
+straightforward game where simple
+ 
+
+ align:start position:0%
+straightforward game where simple
+strategy column two every time row one
+
+ align:start position:0%
+strategy column two every time row one
+ 
+
+ align:start position:0%
+strategy column two every time row one
+every time is the optimal but now let me
+
+ align:start position:0%
+every time is the optimal but now let me
+ 
+
+ align:start position:0%
+every time is the optimal but now let me
+just exchange that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again x1 and x2 y1 and y2 or their
+
+ align:start position:0%
+so again x1 and x2 y1 and y2 or their
+ 
+
+ align:start position:0%
+so again x1 and x2 y1 and y2 or their
+two column what happens now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well why kind of likes the big number
+
+ align:start position:0%
+well why kind of likes the big number
+ 
+
+ align:start position:0%
+well why kind of likes the big number
+eight there so goes for the second
+
+ align:start position:0%
+eight there so goes for the second
+ 
+
+ align:start position:0%
+eight there so goes for the second
+second column still has the bigger
+
+ align:start position:0%
+second column still has the bigger
+ 
+
+ align:start position:0%
+second column still has the bigger
+numbers so Y aims for column two
+
+ align:start position:0%
+numbers so Y aims for column two
+ 
+
+ align:start position:0%
+numbers so Y aims for column two
+but then what does X do what row does x
+
+ align:start position:0%
+but then what does X do what row does x
+ 
+
+ align:start position:0%
+but then what does X do what row does x
+choose if y is in there column to the
+
+ align:start position:0%
+choose if y is in there column to the
+ 
+
+ align:start position:0%
+choose if y is in there column to the
+second okay so so have I found a saddle
+
+ align:start position:0%
+second okay so so have I found a saddle
+ 
+
+ align:start position:0%
+second okay so so have I found a saddle
+point where Y chooses this column X
+
+ align:start position:0%
+point where Y chooses this column X
+ 
+
+ align:start position:0%
+point where Y chooses this column X
+chooses this row is that a saddle point
+
+ align:start position:0%
+chooses this row is that a saddle point
+ 
+
+ align:start position:0%
+chooses this row is that a saddle point
+no because what will Y do now he sees X
+
+ align:start position:0%
+no because what will Y do now he sees X
+ 
+
+ align:start position:0%
+no because what will Y do now he sees X
+choosing the second row all the time and
+
+ align:start position:0%
+choosing the second row all the time and
+ 
+
+ align:start position:0%
+choosing the second row all the time and
+why sees a four very tempting for in
+
+ align:start position:0%
+why sees a four very tempting for in
+ 
+
+ align:start position:0%
+why sees a four very tempting for in
+that row so Y is going to choose y one
+
+ align:start position:0%
+that row so Y is going to choose y one
+ 
+
+ align:start position:0%
+that row so Y is going to choose y one
+the first column pretty often not all
+
+ align:start position:0%
+the first column pretty often not all
+ 
+
+ align:start position:0%
+the first column pretty often not all
+the time because what happens if he just
+
+ align:start position:0%
+the time because what happens if he just
+ 
+
+ align:start position:0%
+the time because what happens if he just
+if Y chooses this column all the time
+
+ align:start position:0%
+if Y chooses this column all the time
+ 
+
+ align:start position:0%
+if Y chooses this column all the time
+then X will choose this row and only the
+
+ align:start position:0%
+then X will choose this row and only the
+ 
+
+ align:start position:0%
+then X will choose this row and only the
+payoff will only be one so that things
+
+ align:start position:0%
+payoff will only be one so that things
+ 
+
+ align:start position:0%
+payoff will only be one so that things
+went downhill for why they're so so this
+
+ align:start position:0%
+went downhill for why they're so so this
+ 
+
+ align:start position:0%
+went downhill for why they're so so this
+is not a saddle point and what do we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixed strategy which is why we'll choose
+
+ align:start position:0%
+mixed strategy which is why we'll choose
+ 
+
+ align:start position:0%
+mixed strategy which is why we'll choose
+the two columns with some probabilities
+
+ align:start position:0%
+the two columns with some probabilities
+ 
+
+ align:start position:0%
+the two columns with some probabilities
+that add to one
+
+ align:start position:0%
+that add to one
+ 
+
+ align:start position:0%
+that add to one
+so so the BIA so there be a third
+
+ align:start position:0%
+so so the BIA so there be a third
+ 
+
+ align:start position:0%
+so so the BIA so there be a third
+possibility that px 1 and one I'm sorry
+
+ align:start position:0%
+possibility that px 1 and one I'm sorry
+ 
+
+ align:start position:0%
+possibility that px 1 and one I'm sorry
+py 1 P times this column and 1 minus P
+
+ align:start position:0%
+py 1 P times this column and 1 minus P
+ 
+
+ align:start position:0%
+py 1 P times this column and 1 minus P
+times the second column so that'll be P
+
+ align:start position:0%
+times the second column so that'll be P
+ 
+
+ align:start position:0%
+times the second column so that'll be P
+plus 1 minus P times 8 and 4p plus
+
+ align:start position:0%
+plus 1 minus P times 8 and 4p plus
+ 
+
+ align:start position:0%
+plus 1 minus P times 8 and 4p plus
+one minus P times two that's that's this
+
+ align:start position:0%
+one minus P times two that's that's this
+ 
+
+ align:start position:0%
+one minus P times two that's that's this
+mixed column by by mixing his strategy
+
+ align:start position:0%
+mixed column by by mixing his strategy
+ 
+
+ align:start position:0%
+mixed column by by mixing his strategy
+why we have a strategy like a third
+
+ align:start position:0%
+why we have a strategy like a third
+ 
+
+ align:start position:0%
+why we have a strategy like a third
+person why three and of course the X is
+
+ align:start position:0%
+person why three and of course the X is
+ 
+
+ align:start position:0%
+person why three and of course the X is
+going to notice after a while what what
+
+ align:start position:0%
+going to notice after a while what what
+ 
+
+ align:start position:0%
+going to notice after a while what what
+what the strategy is this is an open
+
+ align:start position:0%
+what the strategy is this is an open
+ 
+
+ align:start position:0%
+what the strategy is this is an open
+competition you you're not hiding
+
+ align:start position:0%
+competition you you're not hiding
+ 
+
+ align:start position:0%
+competition you you're not hiding
+they're not able to hide anything you
+
+ align:start position:0%
+they're not able to hide anything you
+ 
+
+ align:start position:0%
+they're not able to hide anything you
+might take well maybe Y will jump around
+
+ align:start position:0%
+might take well maybe Y will jump around
+ 
+
+ align:start position:0%
+might take well maybe Y will jump around
+but that's foolishness Y is going to end
+
+ align:start position:0%
+but that's foolishness Y is going to end
+ 
+
+ align:start position:0%
+but that's foolishness Y is going to end
+up finding the best choice of P between
+
+ align:start position:0%
+up finding the best choice of P between
+ 
+
+ align:start position:0%
+up finding the best choice of P between
+0 & 1
+
+ align:start position:0%
+0 & 1
+ 
+
+ align:start position:0%
+0 & 1
+and it will actually be between 0 & 1
+
+ align:start position:0%
+and it will actually be between 0 & 1
+ 
+
+ align:start position:0%
+and it will actually be between 0 & 1
+because the extreme strategies of column
+
+ align:start position:0%
+because the extreme strategies of column
+ 
+
+ align:start position:0%
+because the extreme strategies of column
+1 and column 2 didn't or not winners but
+
+ align:start position:0%
+1 and column 2 didn't or not winners but
+ 
+
+ align:start position:0%
+1 and column 2 didn't or not winners but
+now X is going to do the same thing P X
+
+ align:start position:0%
+now X is going to do the same thing P X
+ 
+
+ align:start position:0%
+now X is going to do the same thing P X
+1 he's gonna he or she is going to
+
+ align:start position:0%
+1 he's gonna he or she is going to
+ 
+
+ align:start position:0%
+1 he's gonna he or she is going to
+combine those rows so so this would be P
+
+ align:start position:0%
+combine those rows so so this would be P
+ 
+
+ align:start position:0%
+combine those rows so so this would be P
+1 for the first row and 1 sorry P oh I
+
+ align:start position:0%
+1 for the first row and 1 sorry P oh I
+ 
+
+ align:start position:0%
+1 for the first row and 1 sorry P oh I
+better choose another number what's uh
+
+ align:start position:0%
+better choose another number what's uh
+ 
+
+ align:start position:0%
+better choose another number what's uh
+what's another letter than P Q okay Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this role was a combination of
+
+ align:start position:0%
+so so this role was a combination of
+ 
+
+ align:start position:0%
+so so this role was a combination of
+those rows so it's Q plus one minus Q
+
+ align:start position:0%
+those rows so it's Q plus one minus Q
+ 
+
+ align:start position:0%
+those rows so it's Q plus one minus Q
+times four in the first position and
+
+ align:start position:0%
+times four in the first position and
+ 
+
+ align:start position:0%
+times four in the first position and
+eight plus P times 8 and 1 minus the P
+
+ align:start position:0%
+eight plus P times 8 and 1 minus the P
+ 
+
+ align:start position:0%
+eight plus P times 8 and 1 minus the P
+and Q times 8 2 times 8 and 1 minus Q
+
+ align:start position:0%
+and Q times 8 2 times 8 and 1 minus Q
+ 
+
+ align:start position:0%
+and Q times 8 2 times 8 and 1 minus Q
+times 2
+
+ align:start position:0%
+times 2
+ 
+
+ align:start position:0%
+times 2
+I'm sorry that I've written this too
+
+ align:start position:0%
+I'm sorry that I've written this too
+ 
+
+ align:start position:0%
+I'm sorry that I've written this too
+small but but what's going to happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's going to determine P and Q and
+
+ align:start position:0%
+what's going to determine P and Q and
+ 
+
+ align:start position:0%
+what's going to determine P and Q and
+solve the game well if these are equal
+
+ align:start position:0%
+solve the game well if these are equal
+ 
+
+ align:start position:0%
+solve the game well if these are equal
+then what happens then X is okay with
+
+ align:start position:0%
+then what happens then X is okay with
+ 
+
+ align:start position:0%
+then what happens then X is okay with
+either one doesn't X has nothing to
+
+ align:start position:0%
+either one doesn't X has nothing to
+ 
+
+ align:start position:0%
+either one doesn't X has nothing to
+choose if those are equal and and Y is
+
+ align:start position:0%
+choose if those are equal and and Y is
+ 
+
+ align:start position:0%
+choose if those are equal and and Y is
+staying with this mixed strategy which
+
+ align:start position:0%
+staying with this mixed strategy which
+ 
+
+ align:start position:0%
+staying with this mixed strategy which
+gives him this third combination column
+
+ align:start position:0%
+gives him this third combination column
+ 
+
+ align:start position:0%
+gives him this third combination column
+then X is good now you might say well
+
+ align:start position:0%
+then X is good now you might say well
+ 
+
+ align:start position:0%
+then X is good now you might say well
+then X would do what it wanted but X
+
+ align:start position:0%
+then X would do what it wanted but X
+ 
+
+ align:start position:0%
+then X would do what it wanted but X
+couldn't do what it wanted if X doesn't
+
+ align:start position:0%
+couldn't do what it wanted if X doesn't
+ 
+
+ align:start position:0%
+couldn't do what it wanted if X doesn't
+stick with the optimal strategy Q for X
+
+ align:start position:0%
+stick with the optimal strategy Q for X
+ 
+
+ align:start position:0%
+stick with the optimal strategy Q for X
+then Y will take advantage so that you
+
+ align:start position:0%
+then Y will take advantage so that you
+ 
+
+ align:start position:0%
+then Y will take advantage so that you
+really the game settles down to once so
+
+ align:start position:0%
+really the game settles down to once so
+ 
+
+ align:start position:0%
+really the game settles down to once so
+so these should be equal so when the
+
+ align:start position:0%
+so these should be equal so when the
+ 
+
+ align:start position:0%
+so these should be equal so when the
+when those are equal what do I get IP it
+
+ align:start position:0%
+when those are equal what do I get IP it
+ 
+
+ align:start position:0%
+when those are equal what do I get IP it
+looks like I have 8 minus minus 7p there
+
+ align:start position:0%
+looks like I have 8 minus minus 7p there
+ 
+
+ align:start position:0%
+looks like I have 8 minus minus 7p there
+for the first one and here I have for P
+
+ align:start position:0%
+for the first one and here I have for P
+ 
+
+ align:start position:0%
+for the first one and here I have for P
+minus 2 P is 2 P plus 1 did I get that
+
+ align:start position:0%
+minus 2 P is 2 P plus 1 did I get that
+ 
+
+ align:start position:0%
+minus 2 P is 2 P plus 1 did I get that
+possibly right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+- for P - 2 P is the to peak and always
+
+ align:start position:0%
+- for P - 2 P is the to peak and always
+ 
+
+ align:start position:0%
+- for P - 2 P is the to peak and always
+- yeah okay so those are equal and that
+
+ align:start position:0%
+- yeah okay so those are equal and that
+ 
+
+ align:start position:0%
+- yeah okay so those are equal and that
+tells me that 9p is 6 and P is 2/3 so
+
+ align:start position:0%
+tells me that 9p is 6 and P is 2/3 so
+ 
+
+ align:start position:0%
+tells me that 9p is 6 and P is 2/3 so
+that turned out that the best strategy
+
+ align:start position:0%
+that turned out that the best strategy
+ 
+
+ align:start position:0%
+that turned out that the best strategy
+for y is 2/3 on the first column which
+
+ align:start position:0%
+for y is 2/3 on the first column which
+ 
+
+ align:start position:0%
+for y is 2/3 on the first column which
+didn't look so promising and 1/3 on the
+
+ align:start position:0%
+didn't look so promising and 1/3 on the
+ 
+
+ align:start position:0%
+didn't look so promising and 1/3 on the
+second and by that by creating that
+
+ align:start position:0%
+second and by that by creating that
+ 
+
+ align:start position:0%
+second and by that by creating that
+strategy what what do these numbers come
+
+ align:start position:0%
+strategy what what do these numbers come
+ 
+
+ align:start position:0%
+strategy what what do these numbers come
+out to be and they're supposed to come
+
+ align:start position:0%
+out to be and they're supposed to come
+ 
+
+ align:start position:0%
+out to be and they're supposed to come
+out equal so for P Plus so 4 times 2/3
+
+ align:start position:0%
+out equal so for P Plus so 4 times 2/3
+ 
+
+ align:start position:0%
+out equal so for P Plus so 4 times 2/3
+is 8/3 plus 1 minus P is 1/3 x plus 2/3
+
+ align:start position:0%
+is 8/3 plus 1 minus P is 1/3 x plus 2/3
+ 
+
+ align:start position:0%
+is 8/3 plus 1 minus P is 1/3 x plus 2/3
+is 10 thirds so I think that this is ten
+
+ align:start position:0%
+is 10 thirds so I think that this is ten
+ 
+
+ align:start position:0%
+is 10 thirds so I think that this is ten
+thirds and if that one isn't ten thirds
+
+ align:start position:0%
+thirds and if that one isn't ten thirds
+ 
+
+ align:start position:0%
+thirds and if that one isn't ten thirds
+I'm very surprised so it's 2/3
+
+ align:start position:0%
+I'm very surprised so it's 2/3
+ 
+
+ align:start position:0%
+I'm very surprised so it's 2/3
+well is it for P - P yeah tell me
+
+ align:start position:0%
+well is it for P - P yeah tell me
+ 
+
+ align:start position:0%
+well is it for P - P yeah tell me
+they're the same did I set them equal
+
+ align:start position:0%
+they're the same did I set them equal
+ 
+
+ align:start position:0%
+they're the same did I set them equal
+yeah I set them equal to find peace so
+
+ align:start position:0%
+yeah I set them equal to find peace so
+ 
+
+ align:start position:0%
+yeah I set them equal to find peace so
+they have to be the same except for
+
+ align:start position:0%
+they have to be the same except for
+ 
+
+ align:start position:0%
+they have to be the same except for
+instructor mistakes which never happened
+
+ align:start position:0%
+instructor mistakes which never happened
+ 
+
+ align:start position:0%
+instructor mistakes which never happened
+ok so those are those should be equal
+
+ align:start position:0%
+ok so those are those should be equal
+ 
+
+ align:start position:0%
+ok so those are those should be equal
+then X has no choice oh no way to do
+
+ align:start position:0%
+then X has no choice oh no way to do
+ 
+
+ align:start position:0%
+then X has no choice oh no way to do
+better choose these columns that he
+
+ align:start position:0%
+better choose these columns that he
+ 
+
+ align:start position:0%
+better choose these columns that he
+can't choose those columns free those
+
+ align:start position:0%
+can't choose those columns free those
+ 
+
+ align:start position:0%
+can't choose those columns free those
+roads freely because Y could take
+
+ align:start position:0%
+roads freely because Y could take
+ 
+
+ align:start position:0%
+roads freely because Y could take
+advantage unless so this would tell this
+
+ align:start position:0%
+advantage unless so this would tell this
+ 
+
+ align:start position:0%
+advantage unless so this would tell this
+would give the best strategy for q4 for
+
+ align:start position:0%
+would give the best strategy for q4 for
+ 
+
+ align:start position:0%
+would give the best strategy for q4 for
+the sorry the best q4 for X yep
+
+ align:start position:0%
+the sorry the best q4 for X yep
+ 
+
+ align:start position:0%
+the sorry the best q4 for X yep
+yes do you see that picture now there
+
+ align:start position:0%
+yes do you see that picture now there
+ 
+
+ align:start position:0%
+yes do you see that picture now there
+could be other it could be a much bigger
+
+ align:start position:0%
+could be other it could be a much bigger
+ 
+
+ align:start position:0%
+could be other it could be a much bigger
+matrix of course there could be other
+
+ align:start position:0%
+matrix of course there could be other
+ 
+
+ align:start position:0%
+matrix of course there could be other
+columns suppose there was a 0 0 column
+
+ align:start position:0%
+columns suppose there was a 0 0 column
+ 
+
+ align:start position:0%
+columns suppose there was a 0 0 column
+what difference what would be the effect
+
+ align:start position:0%
+what difference what would be the effect
+ 
+
+ align:start position:0%
+what difference what would be the effect
+on the optimal strategy of how
+
+ align:start position:0%
+on the optimal strategy of how
+ 
+
+ align:start position:0%
+on the optimal strategy of how
+additional column that additional option
+
+ align:start position:0%
+additional column that additional option
+ 
+
+ align:start position:0%
+additional column that additional option
+for y3 well he wouldn't take okay so
+
+ align:start position:0%
+for y3 well he wouldn't take okay so
+ 
+
+ align:start position:0%
+for y3 well he wouldn't take okay so
+let's make it more tempting 10 10 10
+
+ align:start position:0%
+let's make it more tempting 10 10 10
+ 
+
+ align:start position:0%
+let's make it more tempting 10 10 10
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+oh he wouldn't tell you that right yeah
+
+ align:start position:0%
+oh he wouldn't tell you that right yeah
+ 
+
+ align:start position:0%
+oh he wouldn't tell you that right yeah
+that was not so well I'm not sure what
+
+ align:start position:0%
+that was not so well I'm not sure what
+ 
+
+ align:start position:0%
+that was not so well I'm not sure what
+I'm trying to say here yeah
+
+ align:start position:0%
+I'm trying to say here yeah
+ 
+
+ align:start position:0%
+I'm trying to say here yeah
+there certainly could be there could be
+
+ align:start position:0%
+there certainly could be there could be
+ 
+
+ align:start position:0%
+there certainly could be there could be
+rows that are columns or rows for X that
+
+ align:start position:0%
+rows that are columns or rows for X that
+ 
+
+ align:start position:0%
+rows that are columns or rows for X that
+don't enter the mixed up for the optimal
+
+ align:start position:0%
+don't enter the mixed up for the optimal
+ 
+
+ align:start position:0%
+don't enter the mixed up for the optimal
+mix strategy and make strategy of some
+
+ align:start position:0%
+mix strategy and make strategy of some
+ 
+
+ align:start position:0%
+mix strategy and make strategy of some
+combination of strategies some
+
+ align:start position:0%
+combination of strategies some
+ 
+
+ align:start position:0%
+combination of strategies some
+combination of pure strategies like
+
+ align:start position:0%
+combination of pure strategies like
+ 
+
+ align:start position:0%
+combination of pure strategies like
+choose this column choose this row but
+
+ align:start position:0%
+choose this column choose this row but
+ 
+
+ align:start position:0%
+choose this column choose this row but
+some some columns may not or rows may
+
+ align:start position:0%
+some some columns may not or rows may
+ 
+
+ align:start position:0%
+some some columns may not or rows may
+not show up in the best mixture so I'll
+
+ align:start position:0%
+not show up in the best mixture so I'll
+ 
+
+ align:start position:0%
+not show up in the best mixture so I'll
+I won't complete that partial so like
+
+ align:start position:0%
+I won't complete that partial so like
+ 
+
+ align:start position:0%
+I won't complete that partial so like
+that okay so what do we do you see that
+
+ align:start position:0%
+that okay so what do we do you see that
+ 
+
+ align:start position:0%
+that okay so what do we do you see that
+we have a duality theorem we first of
+
+ align:start position:0%
+we have a duality theorem we first of
+ 
+
+ align:start position:0%
+we have a duality theorem we first of
+all you could write that as a linear
+
+ align:start position:0%
+all you could write that as a linear
+ 
+
+ align:start position:0%
+all you could write that as a linear
+program the unknown is P for X you know
+
+ align:start position:0%
+program the unknown is P for X you know
+ 
+
+ align:start position:0%
+program the unknown is P for X you know
+for y the unknown is Q for X so actually
+
+ align:start position:0%
+for y the unknown is Q for X so actually
+ 
+
+ align:start position:0%
+for y the unknown is Q for X so actually
+just have one unknown in this simple
+
+ align:start position:0%
+just have one unknown in this simple
+ 
+
+ align:start position:0%
+just have one unknown in this simple
+problem but for this small problem but
+
+ align:start position:0%
+problem but for this small problem but
+ 
+
+ align:start position:0%
+problem but for this small problem but
+you have a minimization and maximization
+
+ align:start position:0%
+you have a minimization and maximization
+ 
+
+ align:start position:0%
+you have a minimization and maximization
+they meet at the optimum and the duality
+
+ align:start position:0%
+they meet at the optimum and the duality
+ 
+
+ align:start position:0%
+they meet at the optimum and the duality
+theorem becomes the the theorem for for
+
+ align:start position:0%
+theorem becomes the the theorem for for
+ 
+
+ align:start position:0%
+theorem becomes the the theorem for for
+two person games linear programming
+
+ align:start position:0%
+two person games linear programming
+ 
+
+ align:start position:0%
+two person games linear programming
+matches two person games the point about
+
+ align:start position:0%
+matches two person games the point about
+ 
+
+ align:start position:0%
+matches two person games the point about
+two persons is very important three
+
+ align:start position:0%
+two persons is very important three
+ 
+
+ align:start position:0%
+two persons is very important three
+person games are incredibly complicated
+
+ align:start position:0%
+person games are incredibly complicated
+ 
+
+ align:start position:0%
+person games are incredibly complicated
+no no sería that this simple level would
+
+ align:start position:0%
+no no sería that this simple level would
+ 
+
+ align:start position:0%
+no no sería that this simple level would
+would solve three person games so that's
+
+ align:start position:0%
+would solve three person games so that's
+ 
+
+ align:start position:0%
+would solve three person games so that's
+where John Nash's Nobel Prize comes into
+
+ align:start position:0%
+where John Nash's Nobel Prize comes into
+ 
+
+ align:start position:0%
+where John Nash's Nobel Prize comes into
+the picture
+
+ align:start position:0%
+the picture
+ 
+
+ align:start position:0%
+the picture
+so his Nobel Prize was in economics
+
+ align:start position:0%
+so his Nobel Prize was in economics
+ 
+
+ align:start position:0%
+so his Nobel Prize was in economics
+because of the wide applications but he
+
+ align:start position:0%
+because of the wide applications but he
+ 
+
+ align:start position:0%
+because of the wide applications but he
+was able to analyze the problem of and
+
+ align:start position:0%
+was able to analyze the problem of and
+ 
+
+ align:start position:0%
+was able to analyze the problem of and
+for functions more than four matrices of
+
+ align:start position:0%
+for functions more than four matrices of
+ 
+
+ align:start position:0%
+for functions more than four matrices of
+three person or in person games so you
+
+ align:start position:0%
+three person or in person games so you
+ 
+
+ align:start position:0%
+three person or in person games so you
+know the story of John Nash the the book
+
+ align:start position:0%
+know the story of John Nash the the book
+ 
+
+ align:start position:0%
+know the story of John Nash the the book
+A Beautiful Mind and the movie A
+
+ align:start position:0%
+A Beautiful Mind and the movie A
+ 
+
+ align:start position:0%
+A Beautiful Mind and the movie A
+Beautiful Mind so it's one of those
+
+ align:start position:0%
+Beautiful Mind so it's one of those
+ 
+
+ align:start position:0%
+Beautiful Mind so it's one of those
+movies that involves MIT because he was
+
+ align:start position:0%
+movies that involves MIT because he was
+ 
+
+ align:start position:0%
+movies that involves MIT because he was
+here but you can't recognize anything
+
+ align:start position:0%
+here but you can't recognize anything
+ 
+
+ align:start position:0%
+here but you can't recognize anything
+about MIT the movie it's like Good Will
+
+ align:start position:0%
+about MIT the movie it's like Good Will
+ 
+
+ align:start position:0%
+about MIT the movie it's like Good Will
+Hunting you're you're maybe in some
+
+ align:start position:0%
+Hunting you're you're maybe in some
+ 
+
+ align:start position:0%
+Hunting you're you're maybe in some
+basement of some remote building but
+
+ align:start position:0%
+basement of some remote building but
+ 
+
+ align:start position:0%
+basement of some remote building but
+anyway it was of course a tragic tragic
+
+ align:start position:0%
+anyway it was of course a tragic tragic
+ 
+
+ align:start position:0%
+anyway it was of course a tragic tragic
+and then sure and wonderful and then
+
+ align:start position:0%
+and then sure and wonderful and then
+ 
+
+ align:start position:0%
+and then sure and wonderful and then
+tragic again for its he had so when I
+
+ align:start position:0%
+tragic again for its he had so when I
+ 
+
+ align:start position:0%
+tragic again for its he had so when I
+met him he was going to teach linear
+
+ align:start position:0%
+met him he was going to teach linear
+ 
+
+ align:start position:0%
+met him he was going to teach linear
+algebra one section but I never
+
+ align:start position:0%
+algebra one section but I never
+ 
+
+ align:start position:0%
+algebra one section but I never
+developed his that was when he was his
+
+ align:start position:0%
+developed his that was when he was his
+ 
+
+ align:start position:0%
+developed his that was when he was his
+mental state was going downhill and he
+
+ align:start position:0%
+mental state was going downhill and he
+ 
+
+ align:start position:0%
+mental state was going downhill and he
+moved to Princeton and and just stayed
+
+ align:start position:0%
+moved to Princeton and and just stayed
+ 
+
+ align:start position:0%
+moved to Princeton and and just stayed
+and then the wonderful thing was that he
+
+ align:start position:0%
+and then the wonderful thing was that he
+ 
+
+ align:start position:0%
+and then the wonderful thing was that he
+improved and then the very sad thing was
+
+ align:start position:0%
+improved and then the very sad thing was
+ 
+
+ align:start position:0%
+improved and then the very sad thing was
+its death in a car accident on the way
+
+ align:start position:0%
+its death in a car accident on the way
+ 
+
+ align:start position:0%
+its death in a car accident on the way
+home from from the Nobel Prize
+
+ align:start position:0%
+home from from the Nobel Prize
+ 
+
+ align:start position:0%
+home from from the Nobel Prize
+so quite a story on an amazing story
+
+ align:start position:0%
+so quite a story on an amazing story
+ 
+
+ align:start position:0%
+so quite a story on an amazing story
+yep okay so that's specific optimization
+
+ align:start position:0%
+yep okay so that's specific optimization
+ 
+
+ align:start position:0%
+yep okay so that's specific optimization
+problems linear programming and
+
+ align:start position:0%
+problems linear programming and
+ 
+
+ align:start position:0%
+problems linear programming and
+two-person games and I hope that Friday
+
+ align:start position:0%
+two-person games and I hope that Friday
+ 
+
+ align:start position:0%
+two-person games and I hope that Friday
+it will be professor swath anyway the
+
+ align:start position:0%
+it will be professor swath anyway the
+ 
+
+ align:start position:0%
+it will be professor swath anyway the
+lecture will certainly be about
+
+ align:start position:0%
+lecture will certainly be about
+ 
+
+ align:start position:0%
+lecture will certainly be about
+stochastic gradient descent good thanks
\ No newline at end of file
diff --git a/ffOGEN5WZu4.txt b/ffOGEN5WZu4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c829d26a3660bcfcbe5cc4a348fc2ce6e062f719
--- /dev/null
+++ b/ffOGEN5WZu4.txt
@@ -0,0 +1,227 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in this case study we're going to
+
+ align:start position:0%
+in this case study we're going to
+ 
+
+ align:start position:0%
+in this case study we're going to
+quickly look at how an image of your
+
+ align:start position:0%
+quickly look at how an image of your
+ 
+
+ align:start position:0%
+quickly look at how an image of your
+apparatus could become an interesting
+
+ align:start position:0%
+apparatus could become an interesting
+ 
+
+ align:start position:0%
+apparatus could become an interesting
+photograph to submit for a cover or used
+
+ align:start position:0%
+photograph to submit for a cover or used
+ 
+
+ align:start position:0%
+photograph to submit for a cover or used
+as a figure here we're suggesting a
+
+ align:start position:0%
+as a figure here we're suggesting a
+ 
+
+ align:start position:0%
+as a figure here we're suggesting a
+process now because I couldn't
+
+ align:start position:0%
+process now because I couldn't
+ 
+
+ align:start position:0%
+process now because I couldn't
+photograph the experiment as it was
+
+ align:start position:0%
+photograph the experiment as it was
+ 
+
+ align:start position:0%
+photograph the experiment as it was
+going on because it was a closed system
+
+ align:start position:0%
+going on because it was a closed system
+ 
+
+ align:start position:0%
+going on because it was a closed system
+I made an initial image of the apparatus
+
+ align:start position:0%
+I made an initial image of the apparatus
+ 
+
+ align:start position:0%
+I made an initial image of the apparatus
+used in the research the wires are
+
+ align:start position:0%
+used in the research the wires are
+ 
+
+ align:start position:0%
+used in the research the wires are
+heated to vaporized polymer material
+
+ align:start position:0%
+heated to vaporized polymer material
+ 
+
+ align:start position:0%
+heated to vaporized polymer material
+which is then deposited onto chips as
+
+ align:start position:0%
+which is then deposited onto chips as
+ 
+
+ align:start position:0%
+which is then deposited onto chips as
+you see here I first thought I would
+
+ align:start position:0%
+you see here I first thought I would
+ 
+
+ align:start position:0%
+you see here I first thought I would
+make a nice image for a cover leaving
+
+ align:start position:0%
+make a nice image for a cover leaving
+ 
+
+ align:start position:0%
+make a nice image for a cover leaving
+room for the journal's logo as it turned
+
+ align:start position:0%
+room for the journal's logo as it turned
+ 
+
+ align:start position:0%
+room for the journal's logo as it turned
+out that image was used for the MIT news
+
+ align:start position:0%
+out that image was used for the MIT news
+ 
+
+ align:start position:0%
+out that image was used for the MIT news
+page I then decided to add another piece
+
+ align:start position:0%
+page I then decided to add another piece
+ 
+
+ align:start position:0%
+page I then decided to add another piece
+of their apparatus to fill the whole
+
+ align:start position:0%
+of their apparatus to fill the whole
+ 
+
+ align:start position:0%
+of their apparatus to fill the whole
+image in the end we did submit this one
+
+ align:start position:0%
+image in the end we did submit this one
+ 
+
+ align:start position:0%
+image in the end we did submit this one
+for the cover but it didn't get it what
+
+ align:start position:0%
+for the cover but it didn't get it what
+ 
+
+ align:start position:0%
+for the cover but it didn't get it what
+we did get was something called the
+
+ align:start position:0%
+we did get was something called the
+ 
+
+ align:start position:0%
+we did get was something called the
+frest piece in the journal and
+
+ align:start position:0%
+frest piece in the journal and
+ 
+
+ align:start position:0%
+frest piece in the journal and
+surprisingly they preferred this
+
+ align:start position:0%
+surprisingly they preferred this
+ 
+
+ align:start position:0%
+surprisingly they preferred this
+inverted image which I made just for fun
+
+ align:start position:0%
+inverted image which I made just for fun
+ 
+
+ align:start position:0%
+inverted image which I made just for fun
+rather than the original frankly I
+
+ align:start position:0%
+rather than the original frankly I
+ 
+
+ align:start position:0%
+rather than the original frankly I
+personally preferred the first one but
+
+ align:start position:0%
+personally preferred the first one but
+ 
+
+ align:start position:0%
+personally preferred the first one but
+you know you just never know people's
+
+ align:start position:0%
+you know you just never know people's
+ 
+
+ align:start position:0%
+you know you just never know people's
+taste
\ No newline at end of file
diff --git a/g01r2YRH9ok.txt b/g01r2YRH9ok.txt
new file mode 100644
index 0000000000000000000000000000000000000000..98eb42b54de07a68d0d18af5a637dd0a860a1f9a
--- /dev/null
+++ b/g01r2YRH9ok.txt
@@ -0,0 +1,6251 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so we have a few
+
+ align:start position:0%
+ocw.mit.edu all right so we have a few
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so we have a few
+more uh PowerPoint things before I'm
+
+ align:start position:0%
+more uh PowerPoint things before I'm
+ 
+
+ align:start position:0%
+more uh PowerPoint things before I'm
+going to attempt using the board um so
+
+ align:start position:0%
+going to attempt using the board um so
+ 
+
+ align:start position:0%
+going to attempt using the board um so
+again we're in the transition metal unit
+
+ align:start position:0%
+again we're in the transition metal unit
+ 
+
+ align:start position:0%
+again we're in the transition metal unit
+and today we're going to introduce
+
+ align:start position:0%
+and today we're going to introduce
+ 
+
+ align:start position:0%
+and today we're going to introduce
+something called Crystal field Theory
+
+ align:start position:0%
+something called Crystal field Theory
+ 
+
+ align:start position:0%
+something called Crystal field Theory
+and this is in chapter 16 in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+book so let me just tell you about two
+
+ align:start position:0%
+book so let me just tell you about two
+ 
+
+ align:start position:0%
+book so let me just tell you about two
+different theories and again chemistry
+
+ align:start position:0%
+different theories and again chemistry
+ 
+
+ align:start position:0%
+different theories and again chemistry
+is an experimental science we collect
+
+ align:start position:0%
+is an experimental science we collect
+ 
+
+ align:start position:0%
+is an experimental science we collect
+data and then we try to come up with
+
+ align:start position:0%
+data and then we try to come up with
+ 
+
+ align:start position:0%
+data and then we try to come up with
+theories that explain the data so the
+
+ align:start position:0%
+theories that explain the data so the
+ 
+
+ align:start position:0%
+theories that explain the data so the
+theories aren't sort of 100% and some
+
+ align:start position:0%
+theories aren't sort of 100% and some
+ 
+
+ align:start position:0%
+theories aren't sort of 100% and some
+are more simple and some are more
+
+ align:start position:0%
+are more simple and some are more
+ 
+
+ align:start position:0%
+are more simple and some are more
+complicated to try to explain what we
+
+ align:start position:0%
+complicated to try to explain what we
+ 
+
+ align:start position:0%
+complicated to try to explain what we
+observe and some of these theories
+
+ align:start position:0%
+observe and some of these theories
+ 
+
+ align:start position:0%
+observe and some of these theories
+although they're pretty simple
+
+ align:start position:0%
+although they're pretty simple
+ 
+
+ align:start position:0%
+although they're pretty simple
+approximations of what's really going on
+
+ align:start position:0%
+approximations of what's really going on
+ 
+
+ align:start position:0%
+approximations of what's really going on
+do a pretty good job job of explaining
+
+ align:start position:0%
+do a pretty good job job of explaining
+ 
+
+ align:start position:0%
+do a pretty good job job of explaining
+the things that we are
+
+ align:start position:0%
+the things that we are
+ 
+
+ align:start position:0%
+the things that we are
+observing all right so there two there
+
+ align:start position:0%
+observing all right so there two there
+ 
+
+ align:start position:0%
+observing all right so there two there
+are two different kinds of theories that
+
+ align:start position:0%
+are two different kinds of theories that
+ 
+
+ align:start position:0%
+are two different kinds of theories that
+you'll hear about with transition metals
+
+ align:start position:0%
+you'll hear about with transition metals
+ 
+
+ align:start position:0%
+you'll hear about with transition metals
+you'll hear about Crystal field Theory
+
+ align:start position:0%
+you'll hear about Crystal field Theory
+ 
+
+ align:start position:0%
+you'll hear about Crystal field Theory
+and Lian field theories and so these
+
+ align:start position:0%
+and Lian field theories and so these
+ 
+
+ align:start position:0%
+and Lian field theories and so these
+were again developed to explain certain
+
+ align:start position:0%
+were again developed to explain certain
+ 
+
+ align:start position:0%
+were again developed to explain certain
+types of properties of coordination
+
+ align:start position:0%
+types of properties of coordination
+ 
+
+ align:start position:0%
+types of properties of coordination
+complexes of transition metals so there
+
+ align:start position:0%
+complexes of transition metals so there
+ 
+
+ align:start position:0%
+complexes of transition metals so there
+was Observe data and then people tried
+
+ align:start position:0%
+was Observe data and then people tried
+ 
+
+ align:start position:0%
+was Observe data and then people tried
+to think about how you could rationalize
+
+ align:start position:0%
+to think about how you could rationalize
+ 
+
+ align:start position:0%
+to think about how you could rationalize
+what was observed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the basic idea behind these theories
+
+ align:start position:0%
+so the basic idea behind these theories
+ 
+
+ align:start position:0%
+so the basic idea behind these theories
+is that um if you have your metal Ion
+
+ align:start position:0%
+is that um if you have your metal Ion
+ 
+
+ align:start position:0%
+is that um if you have your metal Ion
+with its given oxidation number and it's
+
+ align:start position:0%
+with its given oxidation number and it's
+ 
+
+ align:start position:0%
+with its given oxidation number and it's
+in the center of a coordination
+
+ align:start position:0%
+in the center of a coordination
+ 
+
+ align:start position:0%
+in the center of a coordination
+sphere the energy levels of the D
+
+ align:start position:0%
+sphere the energy levels of the D
+ 
+
+ align:start position:0%
+sphere the energy levels of the D
+orbitals for that particular metal are
+
+ align:start position:0%
+orbitals for that particular metal are
+ 
+
+ align:start position:0%
+orbitals for that particular metal are
+going to be altered when lians are bound
+
+ align:start position:0%
+going to be altered when lians are bound
+ 
+
+ align:start position:0%
+going to be altered when lians are bound
+compared to sort of a free a free system
+
+ align:start position:0%
+compared to sort of a free a free system
+ 
+
+ align:start position:0%
+compared to sort of a free a free system
+so The Binding of lians around that
+
+ align:start position:0%
+so The Binding of lians around that
+ 
+
+ align:start position:0%
+so The Binding of lians around that
+metal where there are those D orbitals
+
+ align:start position:0%
+metal where there are those D orbitals
+ 
+
+ align:start position:0%
+metal where there are those D orbitals
+associated with that metal is going to
+
+ align:start position:0%
+associated with that metal is going to
+ 
+
+ align:start position:0%
+associated with that metal is going to
+have an effect and create special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties so Crystal field Theory which
+
+ align:start position:0%
+properties so Crystal field Theory which
+ 
+
+ align:start position:0%
+properties so Crystal field Theory which
+is what we're going to be talking about
+
+ align:start position:0%
+is what we're going to be talking about
+ 
+
+ align:start position:0%
+is what we're going to be talking about
+is based on an ionic description
+
+ align:start position:0%
+is based on an ionic description
+ 
+
+ align:start position:0%
+is based on an ionic description
+basically you're going to be considering
+
+ align:start position:0%
+basically you're going to be considering
+ 
+
+ align:start position:0%
+basically you're going to be considering
+your lians as negative point charges a
+
+ align:start position:0%
+your lians as negative point charges a
+ 
+
+ align:start position:0%
+your lians as negative point charges a
+negative charge and you're going to ask
+
+ align:start position:0%
+negative charge and you're going to ask
+ 
+
+ align:start position:0%
+negative charge and you're going to ask
+the question is that negative charge
+
+ align:start position:0%
+the question is that negative charge
+ 
+
+ align:start position:0%
+the question is that negative charge
+pointed toward a d orbital if so that'll
+
+ align:start position:0%
+pointed toward a d orbital if so that'll
+ 
+
+ align:start position:0%
+pointed toward a d orbital if so that'll
+be repulsive and that's going to have an
+
+ align:start position:0%
+be repulsive and that's going to have an
+ 
+
+ align:start position:0%
+be repulsive and that's going to have an
+effect so
+
+ align:start position:0%
+effect so
+ 
+
+ align:start position:0%
+effect so
+uh ligan field Theory includes coent as
+
+ align:start position:0%
+uh ligan field Theory includes coent as
+ 
+
+ align:start position:0%
+uh ligan field Theory includes coent as
+well as ionic descriptions so um it is a
+
+ align:start position:0%
+well as ionic descriptions so um it is a
+ 
+
+ align:start position:0%
+well as ionic descriptions so um it is a
+more powerful uh Theory and it it can
+
+ align:start position:0%
+more powerful uh Theory and it it can
+ 
+
+ align:start position:0%
+more powerful uh Theory and it it can
+describe things a little bit better um
+
+ align:start position:0%
+describe things a little bit better um
+ 
+
+ align:start position:0%
+describe things a little bit better um
+but it's uh we don't have enough time to
+
+ align:start position:0%
+but it's uh we don't have enough time to
+ 
+
+ align:start position:0%
+but it's uh we don't have enough time to
+cover it here and if you're interested
+
+ align:start position:0%
+cover it here and if you're interested
+ 
+
+ align:start position:0%
+cover it here and if you're interested
+in transition metals you'll probably go
+
+ align:start position:0%
+in transition metals you'll probably go
+ 
+
+ align:start position:0%
+in transition metals you'll probably go
+on and take another chemistry course
+
+ align:start position:0%
+on and take another chemistry course
+ 
+
+ align:start position:0%
+on and take another chemistry course
+called 503 which is inorganic chemistry
+
+ align:start position:0%
+called 503 which is inorganic chemistry
+ 
+
+ align:start position:0%
+called 503 which is inorganic chemistry
+um so at this point we're just going to
+
+ align:start position:0%
+um so at this point we're just going to
+ 
+
+ align:start position:0%
+um so at this point we're just going to
+be doing the more Simple Theory which
+
+ align:start position:0%
+be doing the more Simple Theory which
+ 
+
+ align:start position:0%
+be doing the more Simple Theory which
+just considers the ionic descriptions
+
+ align:start position:0%
+just considers the ionic descriptions
+ 
+
+ align:start position:0%
+just considers the ionic descriptions
+but it does pretty well you can explain
+
+ align:start position:0%
+but it does pretty well you can explain
+ 
+
+ align:start position:0%
+but it does pretty well you can explain
+some some things with it but you should
+
+ align:start position:0%
+some some things with it but you should
+ 
+
+ align:start position:0%
+some some things with it but you should
+be aware that this is not uh sort of the
+
+ align:start position:0%
+be aware that this is not uh sort of the
+ 
+
+ align:start position:0%
+be aware that this is not uh sort of the
+uh the most that you can do a little bit
+
+ align:start position:0%
+uh the most that you can do a little bit
+ 
+
+ align:start position:0%
+uh the most that you can do a little bit
+better with another theory so you should
+
+ align:start position:0%
+better with another theory so you should
+ 
+
+ align:start position:0%
+better with another theory so you should
+just be aware of that that this is
+
+ align:start position:0%
+just be aware of that that this is
+ 
+
+ align:start position:0%
+just be aware of that that this is
+really the most simplistic kind of a
+
+ align:start position:0%
+really the most simplistic kind of a
+ 
+
+ align:start position:0%
+really the most simplistic kind of a
+representation or Theory to explain some
+
+ align:start position:0%
+representation or Theory to explain some
+ 
+
+ align:start position:0%
+representation or Theory to explain some
+of the properties of of uh coordination
+
+ align:start position:0%
+of the properties of of uh coordination
+ 
+
+ align:start position:0%
+of the properties of of uh coordination
+complexes all right so all of these
+
+ align:start position:0%
+complexes all right so all of these
+ 
+
+ align:start position:0%
+complexes all right so all of these
+theories uh require you to think in
+
+ align:start position:0%
+theories uh require you to think in
+ 
+
+ align:start position:0%
+theories uh require you to think in
+three diens mentions about de orbitals
+
+ align:start position:0%
+three diens mentions about de orbitals
+ 
+
+ align:start position:0%
+three diens mentions about de orbitals
+because they're all about the
+
+ align:start position:0%
+because they're all about the
+ 
+
+ align:start position:0%
+because they're all about the
+interactions with lians either calent or
+
+ align:start position:0%
+interactions with lians either calent or
+ 
+
+ align:start position:0%
+interactions with lians either calent or
+or um ionic interactions but they're all
+
+ align:start position:0%
+or um ionic interactions but they're all
+ 
+
+ align:start position:0%
+or um ionic interactions but they're all
+about the interactions of lians with
+
+ align:start position:0%
+about the interactions of lians with
+ 
+
+ align:start position:0%
+about the interactions of lians with
+those D orbitals so we I mentioned last
+
+ align:start position:0%
+those D orbitals so we I mentioned last
+ 
+
+ align:start position:0%
+those D orbitals so we I mentioned last
+time that you need to know the shapes of
+
+ align:start position:0%
+time that you need to know the shapes of
+ 
+
+ align:start position:0%
+time that you need to know the shapes of
+the D orbitals and you need to be able
+
+ align:start position:0%
+the D orbitals and you need to be able
+ 
+
+ align:start position:0%
+the D orbitals and you need to be able
+to draw them to some uh limited uh
+
+ align:start position:0%
+to draw them to some uh limited uh
+ 
+
+ align:start position:0%
+to draw them to some uh limited uh
+ability so we went through the names of
+
+ align:start position:0%
+ability so we went through the names of
+ 
+
+ align:start position:0%
+ability so we went through the names of
+the D orbitals last time let's just
+
+ align:start position:0%
+the D orbitals last time let's just
+ 
+
+ align:start position:0%
+the D orbitals last time let's just
+review it now because we're going to be
+
+ align:start position:0%
+review it now because we're going to be
+ 
+
+ align:start position:0%
+review it now because we're going to be
+talking about this more today so uh what
+
+ align:start position:0%
+talking about this more today so uh what
+ 
+
+ align:start position:0%
+talking about this more today so uh what
+is this guy up here
+
+ align:start position:0%
+is this guy up here
+ 
+
+ align:start position:0%
+is this guy up here
+that's DZ squ and here's our reference
+
+ align:start position:0%
+that's DZ squ and here's our reference
+ 
+
+ align:start position:0%
+that's DZ squ and here's our reference
+frame so Z is up here a y along here and
+
+ align:start position:0%
+frame so Z is up here a y along here and
+ 
+
+ align:start position:0%
+frame so Z is up here a y along here and
+X is coming out toward you so what about
+
+ align:start position:0%
+X is coming out toward you so what about
+ 
+
+ align:start position:0%
+X is coming out toward you so what about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one yeah dx^ 2us y sared uh down here
+
+ align:start position:0%
+one yeah dx^ 2us y sared uh down here
+ 
+
+ align:start position:0%
+one yeah dx^ 2us y sared uh down here
+what's that
+
+ align:start position:0%
+what's that
+ 
+
+ align:start position:0%
+what's that
+one yeah dxy so we're the the uh
+
+ align:start position:0%
+one yeah dxy so we're the the uh
+ 
+
+ align:start position:0%
+one yeah dxy so we're the the uh
+amplitudes are 45° off the axis in the
+
+ align:start position:0%
+amplitudes are 45° off the axis in the
+ 
+
+ align:start position:0%
+amplitudes are 45° off the axis in the
+XY plane
+
+ align:start position:0%
+XY plane
+ 
+
+ align:start position:0%
+XY plane
+over here we have dyz so now we're along
+
+ align:start position:0%
+over here we have dyz so now we're along
+ 
+
+ align:start position:0%
+over here we have dyz so now we're along
+Z and uh the last one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah XZ over
+
+ align:start position:0%
+is yeah XZ over
+ 
+
+ align:start position:0%
+is yeah XZ over
+here all right so those are the five D
+
+ align:start position:0%
+here all right so those are the five D
+ 
+
+ align:start position:0%
+here all right so those are the five D
+orbitals that we'll be talking about a
+
+ align:start position:0%
+orbitals that we'll be talking about a
+ 
+
+ align:start position:0%
+orbitals that we'll be talking about a
+lot uh in the next few lectures all
+
+ align:start position:0%
+lot uh in the next few lectures all
+ 
+
+ align:start position:0%
+lot uh in the next few lectures all
+right so let me just show you this is
+
+ align:start position:0%
+right so let me just show you this is
+ 
+
+ align:start position:0%
+right so let me just show you this is
+all it's really threedimensional so
+
+ align:start position:0%
+all it's really threedimensional so
+ 
+
+ align:start position:0%
+all it's really threedimensional so
+let's take a look at the
+
+ align:start position:0%
+let's take a look at the
+ 
+
+ align:start position:0%
+let's take a look at the
+three-dimensional image of these uh of
+
+ align:start position:0%
+three-dimensional image of these uh of
+ 
+
+ align:start position:0%
+three-dimensional image of these uh of
+these D orbitals
+
+ align:start position:0%
+these D orbitals
+ 
+
+ align:start position:0%
+these D orbitals
+so this is a uh DZ Square this isn't in
+
+ align:start position:0%
+so this is a uh DZ Square this isn't in
+ 
+
+ align:start position:0%
+so this is a uh DZ Square this isn't in
+your handout obviously it's a movie um
+
+ align:start position:0%
+your handout obviously it's a movie um
+ 
+
+ align:start position:0%
+your handout obviously it's a movie um
+but you can sort of get a little better
+
+ align:start position:0%
+but you can sort of get a little better
+ 
+
+ align:start position:0%
+but you can sort of get a little better
+sense of the three dimensions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right so the movie first
+
+ align:start position:0%
+here all right so the movie first
+ 
+
+ align:start position:0%
+here all right so the movie first
+rotates the axes I'm not sure why it
+
+ align:start position:0%
+rotates the axes I'm not sure why it
+ 
+
+ align:start position:0%
+rotates the axes I'm not sure why it
+does that um and then it's going to
+
+ align:start position:0%
+does that um and then it's going to
+ 
+
+ align:start position:0%
+does that um and then it's going to
+rotate the uh D orbitals so you can see
+
+ align:start position:0%
+rotate the uh D orbitals so you can see
+ 
+
+ align:start position:0%
+rotate the uh D orbitals so you can see
+the dut uh in the Middle with the hole
+
+ align:start position:0%
+the dut uh in the Middle with the hole
+ 
+
+ align:start position:0%
+the dut uh in the Middle with the hole
+and that the maximum amplitudes are
+
+ align:start position:0%
+and that the maximum amplitudes are
+ 
+
+ align:start position:0%
+and that the maximum amplitudes are
+along the Z axis here so this is DZ SAR
+
+ align:start position:0%
+along the Z axis here so this is DZ SAR
+ 
+
+ align:start position:0%
+along the Z axis here so this is DZ SAR
+and it's right along the orbitals are
+
+ align:start position:0%
+and it's right along the orbitals are
+ 
+
+ align:start position:0%
+and it's right along the orbitals are
+right along the Z axis which is
+
+ align:start position:0%
+right along the Z axis which is
+ 
+
+ align:start position:0%
+right along the Z axis which is
+important so now let's take a look at D
+
+ align:start position:0%
+important so now let's take a look at D
+ 
+
+ align:start position:0%
+important so now let's take a look at D
+x^2 minus
+
+ align:start position:0%
+x^2 minus
+ 
+
+ align:start position:0%
+x^2 minus
+y^2 and uh the important Point here is
+
+ align:start position:0%
+y^2 and uh the important Point here is
+ 
+
+ align:start position:0%
+y^2 and uh the important Point here is
+that the orbitals are directly on axis
+
+ align:start position:0%
+that the orbitals are directly on axis
+ 
+
+ align:start position:0%
+that the orbitals are directly on axis
+and the axes are the X and the Y so you
+
+ align:start position:0%
+and the axes are the X and the Y so you
+ 
+
+ align:start position:0%
+and the axes are the X and the Y so you
+can see how they're directly along those
+
+ align:start position:0%
+can see how they're directly along those
+ 
+
+ align:start position:0%
+can see how they're directly along those
+axes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so here's the next one so here we have
+
+ align:start position:0%
+so here's the next one so here we have
+ 
+
+ align:start position:0%
+so here's the next one so here we have
+dxy and now the orbitals are not along
+
+ align:start position:0%
+dxy and now the orbitals are not along
+ 
+
+ align:start position:0%
+dxy and now the orbitals are not along
+the axes they're 45 degre in between so
+
+ align:start position:0%
+the axes they're 45 degre in between so
+ 
+
+ align:start position:0%
+the axes they're 45 degre in between so
+they're not along they're in between
+
+ align:start position:0%
+they're not along they're in between
+ 
+
+ align:start position:0%
+they're not along they're in between
+which is the key Point uh for this D
+
+ align:start position:0%
+which is the key Point uh for this D
+ 
+
+ align:start position:0%
+which is the key Point uh for this D
+orbital in terms of what we're going to
+
+ align:start position:0%
+orbital in terms of what we're going to
+ 
+
+ align:start position:0%
+orbital in terms of what we're going to
+be talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we have some amplitude along the Z
+
+ align:start position:0%
+now we have some amplitude along the Z
+ 
+
+ align:start position:0%
+now we have some amplitude along the Z
+axis we have Z and x and again the
+
+ align:start position:0%
+axis we have Z and x and again the
+ 
+
+ align:start position:0%
+axis we have Z and x and again the
+orbitals are 45 Dees off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axes and we have one
+
+ align:start position:0%
+axes and we have one
+ 
+
+ align:start position:0%
+axes and we have one
+more so now we have Dy Z again 45°
+
+ align:start position:0%
+more so now we have Dy Z again 45°
+ 
+
+ align:start position:0%
+more so now we have Dy Z again 45°
+off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis all right so now you should have
+
+ align:start position:0%
+axis all right so now you should have
+ 
+
+ align:start position:0%
+axis all right so now you should have
+these sort of orbitals uh floating
+
+ align:start position:0%
+these sort of orbitals uh floating
+ 
+
+ align:start position:0%
+these sort of orbitals uh floating
+around inside your head and as we talk
+
+ align:start position:0%
+around inside your head and as we talk
+ 
+
+ align:start position:0%
+around inside your head and as we talk
+about bringing ligans in toward the
+
+ align:start position:0%
+about bringing ligans in toward the
+ 
+
+ align:start position:0%
+about bringing ligans in toward the
+orbitals you can think about how those
+
+ align:start position:0%
+orbitals you can think about how those
+ 
+
+ align:start position:0%
+orbitals you can think about how those
+ligans are coming in and what orbitals
+
+ align:start position:0%
+ligans are coming in and what orbitals
+ 
+
+ align:start position:0%
+ligans are coming in and what orbitals
+they going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+near so again Crystal field theory is
+
+ align:start position:0%
+near so again Crystal field theory is
+ 
+
+ align:start position:0%
+near so again Crystal field theory is
+just considering the ionic interactions
+
+ align:start position:0%
+just considering the ionic interactions
+ 
+
+ align:start position:0%
+just considering the ionic interactions
+and it's really considering the lians as
+
+ align:start position:0%
+and it's really considering the lians as
+ 
+
+ align:start position:0%
+and it's really considering the lians as
+negative point charges and so negative
+
+ align:start position:0%
+negative point charges and so negative
+ 
+
+ align:start position:0%
+negative point charges and so negative
+point charges are going to be repulsive
+
+ align:start position:0%
+point charges are going to be repulsive
+ 
+
+ align:start position:0%
+point charges are going to be repulsive
+with the D orbitals so D orbitals don't
+
+ align:start position:0%
+with the D orbitals so D orbitals don't
+ 
+
+ align:start position:0%
+with the D orbitals so D orbitals don't
+like it when you have this negatively
+
+ align:start position:0%
+like it when you have this negatively
+ 
+
+ align:start position:0%
+like it when you have this negatively
+charged ligan uh coming in and being
+
+ align:start position:0%
+charged ligan uh coming in and being
+ 
+
+ align:start position:0%
+charged ligan uh coming in and being
+near it will be repulsive uh near the D
+
+ align:start position:0%
+near it will be repulsive uh near the D
+ 
+
+ align:start position:0%
+near it will be repulsive uh near the D
+orbital so this is just another way to
+
+ align:start position:0%
+orbital so this is just another way to
+ 
+
+ align:start position:0%
+orbital so this is just another way to
+sort of draw that and we have our
+
+ align:start position:0%
+sort of draw that and we have our
+ 
+
+ align:start position:0%
+sort of draw that and we have our
+octahedral frame uh so here we're
+
+ align:start position:0%
+octahedral frame uh so here we're
+ 
+
+ align:start position:0%
+octahedral frame uh so here we're
+talking about an octahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometry and we can think about how
+
+ align:start position:0%
+geometry and we can think about how
+ 
+
+ align:start position:0%
+geometry and we can think about how
+lians are going to be affecting the D
+
+ align:start position:0%
+lians are going to be affecting the D
+ 
+
+ align:start position:0%
+lians are going to be affecting the D
+orbital in these various places if you
+
+ align:start position:0%
+orbital in these various places if you
+ 
+
+ align:start position:0%
+orbital in these various places if you
+had lians on all of these positions an
+
+ align:start position:0%
+had lians on all of these positions an
+ 
+
+ align:start position:0%
+had lians on all of these positions an
+octahedral arrangement around the metal
+
+ align:start position:0%
+octahedral arrangement around the metal
+ 
+
+ align:start position:0%
+octahedral arrangement around the metal
+and you can think of these lians as
+
+ align:start position:0%
+and you can think of these lians as
+ 
+
+ align:start position:0%
+and you can think of these lians as
+these negative point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charges and so this is just another uh
+
+ align:start position:0%
+charges and so this is just another uh
+ 
+
+ align:start position:0%
+charges and so this is just another uh
+depiction uh here are the de orbitals
+
+ align:start position:0%
+depiction uh here are the de orbitals
+ 
+
+ align:start position:0%
+depiction uh here are the de orbitals
+again it's a slightly different uh XYZ
+
+ align:start position:0%
+again it's a slightly different uh XYZ
+ 
+
+ align:start position:0%
+again it's a slightly different uh XYZ
+frame but not too much different and so
+
+ align:start position:0%
+frame but not too much different and so
+ 
+
+ align:start position:0%
+frame but not too much different and so
+here are our orbitals and these little
+
+ align:start position:0%
+here are our orbitals and these little
+ 
+
+ align:start position:0%
+here are our orbitals and these little
+uh Green Dots represent the point
+
+ align:start position:0%
+uh Green Dots represent the point
+ 
+
+ align:start position:0%
+uh Green Dots represent the point
+charges so what we'll be thinking about
+
+ align:start position:0%
+charges so what we'll be thinking about
+ 
+
+ align:start position:0%
+charges so what we'll be thinking about
+uh today is the effect of ligans being
+
+ align:start position:0%
+uh today is the effect of ligans being
+ 
+
+ align:start position:0%
+uh today is the effect of ligans being
+close to the de orbitals so you see here
+
+ align:start position:0%
+close to the de orbitals so you see here
+ 
+
+ align:start position:0%
+close to the de orbitals so you see here
+there's a ligan that's quite close up
+
+ align:start position:0%
+there's a ligan that's quite close up
+ 
+
+ align:start position:0%
+there's a ligan that's quite close up
+here and one down here in this picture
+
+ align:start position:0%
+here and one down here in this picture
+ 
+
+ align:start position:0%
+here and one down here in this picture
+these negative Point charged liens are
+
+ align:start position:0%
+these negative Point charged liens are
+ 
+
+ align:start position:0%
+these negative Point charged liens are
+also really close to the orbitals here
+
+ align:start position:0%
+also really close to the orbitals here
+ 
+
+ align:start position:0%
+also really close to the orbitals here
+they're not really as close they're sort
+
+ align:start position:0%
+they're not really as close they're sort
+ 
+
+ align:start position:0%
+they're not really as close they're sort
+of off axis
+
+ align:start position:0%
+of off axis
+ 
+
+ align:start position:0%
+of off axis
+and that becomes really
+
+ align:start position:0%
+and that becomes really
+ 
+
+ align:start position:0%
+and that becomes really
+important all right so let's now think
+
+ align:start position:0%
+important all right so let's now think
+ 
+
+ align:start position:0%
+important all right so let's now think
+about the different D orbitals and the
+
+ align:start position:0%
+about the different D orbitals and the
+ 
+
+ align:start position:0%
+about the different D orbitals and the
+lians when the lians are arranged in an
+
+ align:start position:0%
+lians when the lians are arranged in an
+ 
+
+ align:start position:0%
+lians when the lians are arranged in an
+octahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometry so in this case we have lians
+
+ align:start position:0%
+geometry so in this case we have lians
+ 
+
+ align:start position:0%
+geometry so in this case we have lians
+we have these ligans these negative
+
+ align:start position:0%
+we have these ligans these negative
+ 
+
+ align:start position:0%
+we have these ligans these negative
+point charges coming in on all the
+
+ align:start position:0%
+point charges coming in on all the
+ 
+
+ align:start position:0%
+point charges coming in on all the
+different axes and so if we think about
+
+ align:start position:0%
+different axes and so if we think about
+ 
+
+ align:start position:0%
+different axes and so if we think about
+it these are close and I mentioned that
+
+ align:start position:0%
+it these are close and I mentioned that
+ 
+
+ align:start position:0%
+it these are close and I mentioned that
+in in the last slide so a negative Point
+
+ align:start position:0%
+in in the last slide so a negative Point
+ 
+
+ align:start position:0%
+in in the last slide so a negative Point
+charge along Z is going to be very close
+
+ align:start position:0%
+charge along Z is going to be very close
+ 
+
+ align:start position:0%
+charge along Z is going to be very close
+to dz^2 and it will be repulsive uh for
+
+ align:start position:0%
+to dz^2 and it will be repulsive uh for
+ 
+
+ align:start position:0%
+to dz^2 and it will be repulsive uh for
+dx^ 2us y^2 the negative point charges
+
+ align:start position:0%
+dx^ 2us y^2 the negative point charges
+ 
+
+ align:start position:0%
+dx^ 2us y^2 the negative point charges
+along Y and along X are also going to be
+
+ align:start position:0%
+along Y and along X are also going to be
+ 
+
+ align:start position:0%
+along Y and along X are also going to be
+very close to these D orbitals and that
+
+ align:start position:0%
+very close to these D orbitals and that
+ 
+
+ align:start position:0%
+very close to these D orbitals and that
+will again be repulsive so we're going
+
+ align:start position:0%
+will again be repulsive so we're going
+ 
+
+ align:start position:0%
+will again be repulsive so we're going
+to have a large of repulsive interaction
+
+ align:start position:0%
+to have a large of repulsive interaction
+ 
+
+ align:start position:0%
+to have a large of repulsive interaction
+for these two orbitals with an
+
+ align:start position:0%
+for these two orbitals with an
+ 
+
+ align:start position:0%
+for these two orbitals with an
+octahedral uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometry so these two D orbitals are
+
+ align:start position:0%
+geometry so these two D orbitals are
+ 
+
+ align:start position:0%
+geometry so these two D orbitals are
+destabilized and they're destabilized by
+
+ align:start position:0%
+destabilized and they're destabilized by
+ 
+
+ align:start position:0%
+destabilized and they're destabilized by
+the same amount so when they're
+
+ align:start position:0%
+the same amount so when they're
+ 
+
+ align:start position:0%
+the same amount so when they're
+destabilized by the same amount what is
+
+ align:start position:0%
+destabilized by the same amount what is
+ 
+
+ align:start position:0%
+destabilized by the same amount what is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+called the energy of the orbitals are
+
+ align:start position:0%
+called the energy of the orbitals are
+ 
+
+ align:start position:0%
+called the energy of the orbitals are
+the same what's that
+
+ align:start position:0%
+the same what's that
+ 
+
+ align:start position:0%
+the same what's that
+called yeah so they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degenerate and so these two orbitals
+
+ align:start position:0%
+degenerate and so these two orbitals
+ 
+
+ align:start position:0%
+degenerate and so these two orbitals
+then will be more destabilized by those
+
+ align:start position:0%
+then will be more destabilized by those
+ 
+
+ align:start position:0%
+then will be more destabilized by those
+Lian negative point charges than the
+
+ align:start position:0%
+Lian negative point charges than the
+ 
+
+ align:start position:0%
+Lian negative point charges than the
+other sets of orbitals because they're
+
+ align:start position:0%
+other sets of orbitals because they're
+ 
+
+ align:start position:0%
+other sets of orbitals because they're
+off axis and the ligans are on axis so
+
+ align:start position:0%
+off axis and the ligans are on axis so
+ 
+
+ align:start position:0%
+off axis and the ligans are on axis so
+the negative point charges will be
+
+ align:start position:0%
+the negative point charges will be
+ 
+
+ align:start position:0%
+the negative point charges will be
+farther away from these guys and let's
+
+ align:start position:0%
+farther away from these guys and let's
+ 
+
+ align:start position:0%
+farther away from these guys and let's
+take uh a look at that as well so here
+
+ align:start position:0%
+take uh a look at that as well so here
+ 
+
+ align:start position:0%
+take uh a look at that as well so here
+we have uh our our three different our
+
+ align:start position:0%
+we have uh our our three different our
+ 
+
+ align:start position:0%
+we have uh our our three different our
+three other D orbitals and if lians are
+
+ align:start position:0%
+three other D orbitals and if lians are
+ 
+
+ align:start position:0%
+three other D orbitals and if lians are
+coming in as negative point charges on
+
+ align:start position:0%
+coming in as negative point charges on
+ 
+
+ align:start position:0%
+coming in as negative point charges on
+axis you're not going to be directly
+
+ align:start position:0%
+axis you're not going to be directly
+ 
+
+ align:start position:0%
+axis you're not going to be directly
+pointing at any of these orbitals
+
+ align:start position:0%
+pointing at any of these orbitals
+ 
+
+ align:start position:0%
+pointing at any of these orbitals
+because they're 45° off axis lians are
+
+ align:start position:0%
+because they're 45° off axis lians are
+ 
+
+ align:start position:0%
+because they're 45° off axis lians are
+on axis so it's not directly pointing
+
+ align:start position:0%
+on axis so it's not directly pointing
+ 
+
+ align:start position:0%
+on axis so it's not directly pointing
+toward any of
+
+ align:start position:0%
+toward any of
+ 
+
+ align:start position:0%
+toward any of
+them so these three orbitals then are
+
+ align:start position:0%
+them so these three orbitals then are
+ 
+
+ align:start position:0%
+them so these three orbitals then are
+stabilized relative to the other sets of
+
+ align:start position:0%
+stabilized relative to the other sets of
+ 
+
+ align:start position:0%
+stabilized relative to the other sets of
+orbitals we talked about and they're
+
+ align:start position:0%
+orbitals we talked about and they're
+ 
+
+ align:start position:0%
+orbitals we talked about and they're
+stabilized by the same amount so those
+
+ align:start position:0%
+stabilized by the same amount so those
+ 
+
+ align:start position:0%
+stabilized by the same amount so those
+three are also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degenerate all all right so to summarize
+
+ align:start position:0%
+degenerate all all right so to summarize
+ 
+
+ align:start position:0%
+degenerate all all right so to summarize
+then um you'll have a large repulsion
+
+ align:start position:0%
+then um you'll have a large repulsion
+ 
+
+ align:start position:0%
+then um you'll have a large repulsion
+for DX 2 minus y^2 and dz^2
+
+ align:start position:0%
+for DX 2 minus y^2 and dz^2
+ 
+
+ align:start position:0%
+for DX 2 minus y^2 and dz^2
+and it they will be more destabilized
+
+ align:start position:0%
+and it they will be more destabilized
+ 
+
+ align:start position:0%
+and it they will be more destabilized
+compared to the other orbitals there'll
+
+ align:start position:0%
+compared to the other orbitals there'll
+ 
+
+ align:start position:0%
+compared to the other orbitals there'll
+be a smaller repulsion for these three
+
+ align:start position:0%
+be a smaller repulsion for these three
+ 
+
+ align:start position:0%
+be a smaller repulsion for these three
+and they will be stabilized compared to
+
+ align:start position:0%
+and they will be stabilized compared to
+ 
+
+ align:start position:0%
+and they will be stabilized compared to
+these sets of
+
+ align:start position:0%
+these sets of
+ 
+
+ align:start position:0%
+these sets of
+orbitals and so here you're really
+
+ align:start position:0%
+orbitals and so here you're really
+ 
+
+ align:start position:0%
+orbitals and so here you're really
+thinking about comparing the D orbitals
+
+ align:start position:0%
+thinking about comparing the D orbitals
+ 
+
+ align:start position:0%
+thinking about comparing the D orbitals
+to a a case where the ligans are sort of
+
+ align:start position:0%
+to a a case where the ligans are sort of
+ 
+
+ align:start position:0%
+to a a case where the ligans are sort of
+all around we'll talk about that in a
+
+ align:start position:0%
+all around we'll talk about that in a
+ 
+
+ align:start position:0%
+all around we'll talk about that in a
+minute so if you localize your lians on
+
+ align:start position:0%
+minute so if you localize your lians on
+ 
+
+ align:start position:0%
+minute so if you localize your lians on
+axis how is this
+
+ align:start position:0%
+axis how is this
+ 
+
+ align:start position:0%
+axis how is this
+affected and this just reminds you and
+
+ align:start position:0%
+affected and this just reminds you and
+ 
+
+ align:start position:0%
+affected and this just reminds you and
+shows you the pictures again um so over
+
+ align:start position:0%
+shows you the pictures again um so over
+ 
+
+ align:start position:0%
+shows you the pictures again um so over
+here they're pointing much more directly
+
+ align:start position:0%
+here they're pointing much more directly
+ 
+
+ align:start position:0%
+here they're pointing much more directly
+toward and here they're away so if it
+
+ align:start position:0%
+toward and here they're away so if it
+ 
+
+ align:start position:0%
+toward and here they're away so if it
+helps you depending on how you like to
+
+ align:start position:0%
+helps you depending on how you like to
+ 
+
+ align:start position:0%
+helps you depending on how you like to
+think about it this is the same uh I had
+
+ align:start position:0%
+think about it this is the same uh I had
+ 
+
+ align:start position:0%
+think about it this is the same uh I had
+these orbitals uh in your hand out on
+
+ align:start position:0%
+these orbitals uh in your hand out on
+ 
+
+ align:start position:0%
+these orbitals uh in your hand out on
+the first page but just to show them
+
+ align:start position:0%
+the first page but just to show them
+ 
+
+ align:start position:0%
+the first page but just to show them
+again uh that you can think about how
+
+ align:start position:0%
+again uh that you can think about how
+ 
+
+ align:start position:0%
+again uh that you can think about how
+close they are see that lian's very
+
+ align:start position:0%
+close they are see that lian's very
+ 
+
+ align:start position:0%
+close they are see that lian's very
+close uh not nearly as close here so
+
+ align:start position:0%
+close uh not nearly as close here so
+ 
+
+ align:start position:0%
+close uh not nearly as close here so
+it's all about the geometry around the
+
+ align:start position:0%
+it's all about the geometry around the
+ 
+
+ align:start position:0%
+it's all about the geometry around the
+metal the geometry of the D orbitals the
+
+ align:start position:0%
+metal the geometry of the D orbitals the
+ 
+
+ align:start position:0%
+metal the geometry of the D orbitals the
+geometry of the
+
+ align:start position:0%
+geometry of the
+ 
+
+ align:start position:0%
+geometry of the
+lians okay so now I'm going to try
+
+ align:start position:0%
+lians okay so now I'm going to try
+ 
+
+ align:start position:0%
+lians okay so now I'm going to try
+rating on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board so here we're going to think about
+
+ align:start position:0%
+board so here we're going to think about
+ 
+
+ align:start position:0%
+board so here we're going to think about
+how you would draw a diag
+
+ align:start position:0%
+how you would draw a diag
+ 
+
+ align:start position:0%
+how you would draw a diag
+to represent the energy levels when you
+
+ align:start position:0%
+to represent the energy levels when you
+ 
+
+ align:start position:0%
+to represent the energy levels when you
+consider Crystal field
+
+ align:start position:0%
+consider Crystal field
+ 
+
+ align:start position:0%
+consider Crystal field
+Theory so you would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a what's called Crystal field splitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram so here energy would be going up
+
+ align:start position:0%
+diagram so here energy would be going up
+ 
+
+ align:start position:0%
+diagram so here energy would be going up
+and we have our case we
+
+ align:start position:0%
+and we have our case we
+ 
+
+ align:start position:0%
+and we have our case we
+have a hypothetical case where we have
+
+ align:start position:0%
+have a hypothetical case where we have
+ 
+
+ align:start position:0%
+have a hypothetical case where we have
+five D
+
+ align:start position:0%
+five D
+ 
+
+ align:start position:0%
+five D
+orbitals and so this is the average
+
+ align:start position:0%
+orbitals and so this is the average
+ 
+
+ align:start position:0%
+orbitals and so this is the average
+energy of the D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals average energy of D
+
+ align:start position:0%
+orbitals average energy of D
+ 
+
+ align:start position:0%
+orbitals average energy of D
+orbitals with um with the lians
+
+ align:start position:0%
+orbitals with um with the lians
+ 
+
+ align:start position:0%
+orbitals with um with the lians
+Bound in what's known as a spherical
+
+ align:start position:0%
+Bound in what's known as a spherical
+ 
+
+ align:start position:0%
+Bound in what's known as a spherical
+Crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field so this does not exist it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothetical so if the lians were
+
+ align:start position:0%
+hypothetical so if the lians were
+ 
+
+ align:start position:0%
+hypothetical so if the lians were
+everywhere in a sphere around your metal
+
+ align:start position:0%
+everywhere in a sphere around your metal
+ 
+
+ align:start position:0%
+everywhere in a sphere around your metal
+so this is our hypothetical spherical
+
+ align:start position:0%
+so this is our hypothetical spherical
+ 
+
+ align:start position:0%
+so this is our hypothetical spherical
+Crystal field and you imagine the metal
+
+ align:start position:0%
+Crystal field and you imagine the metal
+ 
+
+ align:start position:0%
+Crystal field and you imagine the metal
+is the inside and on the outside you
+
+ align:start position:0%
+is the inside and on the outside you
+ 
+
+ align:start position:0%
+is the inside and on the outside you
+have all the lians so lians are
+
+ align:start position:0%
+have all the lians so lians are
+ 
+
+ align:start position:0%
+have all the lians so lians are
+everywhere they're equally distributed
+
+ align:start position:0%
+everywhere they're equally distributed
+ 
+
+ align:start position:0%
+everywhere they're equally distributed
+everywhere and if they're equally
+
+ align:start position:0%
+everywhere and if they're equally
+ 
+
+ align:start position:0%
+everywhere and if they're equally
+distributed everywhere all the D
+
+ align:start position:0%
+distributed everywhere all the D
+ 
+
+ align:start position:0%
+distributed everywhere all the D
+orbitals would have the same energy so
+
+ align:start position:0%
+orbitals would have the same energy so
+ 
+
+ align:start position:0%
+orbitals would have the same energy so
+it's pointing toward everything equally
+
+ align:start position:0%
+it's pointing toward everything equally
+ 
+
+ align:start position:0%
+it's pointing toward everything equally
+so it's spherical it's completely
+
+ align:start position:0%
+so it's spherical it's completely
+ 
+
+ align:start position:0%
+so it's spherical it's completely
+surrounding the metal so this is a
+
+ align:start position:0%
+surrounding the metal so this is a
+ 
+
+ align:start position:0%
+surrounding the metal so this is a
+hypothetical case because that does not
+
+ align:start position:0%
+hypothetical case because that does not
+ 
+
+ align:start position:0%
+hypothetical case because that does not
+happen ligans are bound in discrete
+
+ align:start position:0%
+happen ligans are bound in discrete
+ 
+
+ align:start position:0%
+happen ligans are bound in discrete
+positions but if it did these would be
+
+ align:start position:0%
+positions but if it did these would be
+ 
+
+ align:start position:0%
+positions but if it did these would be
+of the same energy let me try to get
+
+ align:start position:0%
+of the same energy let me try to get
+ 
+
+ align:start position:0%
+of the same energy let me try to get
+this a little more flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so they're all the same energy
+
+ align:start position:0%
+all right so they're all the same energy
+ 
+
+ align:start position:0%
+all right so they're all the same energy
+well what happens then when you bring
+
+ align:start position:0%
+well what happens then when you bring
+ 
+
+ align:start position:0%
+well what happens then when you bring
+your lians in to their discrete
+
+ align:start position:0%
+your lians in to their discrete
+ 
+
+ align:start position:0%
+your lians in to their discrete
+positions so when you bring your ligans
+
+ align:start position:0%
+positions so when you bring your ligans
+ 
+
+ align:start position:0%
+positions so when you bring your ligans
+in in this case into octahedral geometry
+
+ align:start position:0%
+in in this case into octahedral geometry
+ 
+
+ align:start position:0%
+in in this case into octahedral geometry
+then things
+
+ align:start position:0%
+then things
+ 
+
+ align:start position:0%
+then things
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+then you have a destabilization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have a
+
+ align:start position:0%
+you have a
+ 
+
+ align:start position:0%
+you have a
+destabilization of your dx2 minus y^2
+
+ align:start position:0%
+destabilization of your dx2 minus y^2
+ 
+
+ align:start position:0%
+destabilization of your dx2 minus y^2
+and dz^2 orbitals so they're going to go
+
+ align:start position:0%
+and dz^2 orbitals so they're going to go
+ 
+
+ align:start position:0%
+and dz^2 orbitals so they're going to go
+up in energy and you'll have a
+
+ align:start position:0%
+up in energy and you'll have a
+ 
+
+ align:start position:0%
+up in energy and you'll have a
+stabilization of your
+
+ align:start position:0%
+stabilization of your
+ 
+
+ align:start position:0%
+stabilization of your
+dxy
+
+ align:start position:0%
+dxy
+ 
+
+ align:start position:0%
+dxy
+dyz and dxz orbitals they are going to
+
+ align:start position:0%
+dyz and dxz orbitals they are going to
+ 
+
+ align:start position:0%
+dyz and dxz orbitals they are going to
+go down in energy so in this
+
+ align:start position:0%
+go down in energy so in this
+ 
+
+ align:start position:0%
+go down in energy so in this
+hypothetical case the D orbitals have
+
+ align:start position:0%
+hypothetical case the D orbitals have
+ 
+
+ align:start position:0%
+hypothetical case the D orbitals have
+equal energy lians are everywhere
+
+ align:start position:0%
+equal energy lians are everywhere
+ 
+
+ align:start position:0%
+equal energy lians are everywhere
+they're pointing at all the D orbitals
+
+ align:start position:0%
+they're pointing at all the D orbitals
+ 
+
+ align:start position:0%
+they're pointing at all the D orbitals
+equally but in an octahedral
+
+ align:start position:0%
+equally but in an octahedral
+ 
+
+ align:start position:0%
+equally but in an octahedral
+case then two orbitals are destabilized
+
+ align:start position:0%
+case then two orbitals are destabilized
+ 
+
+ align:start position:0%
+case then two orbitals are destabilized
+go up in energy because those ligans now
+
+ align:start position:0%
+go up in energy because those ligans now
+ 
+
+ align:start position:0%
+go up in energy because those ligans now
+are pointing right at those orbitals
+
+ align:start position:0%
+are pointing right at those orbitals
+ 
+
+ align:start position:0%
+are pointing right at those orbitals
+they're not pointing equally everywhere
+
+ align:start position:0%
+they're not pointing equally everywhere
+ 
+
+ align:start position:0%
+they're not pointing equally everywhere
+so they're pointing at these orbitals so
+
+ align:start position:0%
+so they're pointing at these orbitals so
+ 
+
+ align:start position:0%
+so they're pointing at these orbitals so
+they go up in energy these orbitals are
+
+ align:start position:0%
+they go up in energy these orbitals are
+ 
+
+ align:start position:0%
+they go up in energy these orbitals are
+in between the axes so they're not
+
+ align:start position:0%
+in between the axes so they're not
+ 
+
+ align:start position:0%
+in between the axes so they're not
+affected as much and they get
+
+ align:start position:0%
+affected as much and they get
+ 
+
+ align:start position:0%
+affected as much and they get
+stabilized these orbitals have a name EG
+
+ align:start position:0%
+stabilized these orbitals have a name EG
+ 
+
+ align:start position:0%
+stabilized these orbitals have a name EG
+and and these orbitals have a name t2g
+
+ align:start position:0%
+and and these orbitals have a name t2g
+ 
+
+ align:start position:0%
+and and these orbitals have a name t2g
+for the octahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and the difference in energy
+
+ align:start position:0%
+case and the difference in energy
+ 
+
+ align:start position:0%
+case and the difference in energy
+between these sets of
+
+ align:start position:0%
+between these sets of
+ 
+
+ align:start position:0%
+between these sets of
+orbitals
+
+ align:start position:0%
+orbitals
+ 
+
+ align:start position:0%
+orbitals
+is is this um sign here sort of this
+
+ align:start position:0%
+is is this um sign here sort of this
+ 
+
+ align:start position:0%
+is is this um sign here sort of this
+Delta uh zero sign and actually o and
+
+ align:start position:0%
+Delta uh zero sign and actually o and
+ 
+
+ align:start position:0%
+Delta uh zero sign and actually o and
+that's for octahedral the O is for
+
+ align:start position:0%
+that's for octahedral the O is for
+ 
+
+ align:start position:0%
+that's for octahedral the O is for
+octahedral and it's the
+
+ align:start position:0%
+octahedral and it's the
+ 
+
+ align:start position:0%
+octahedral and it's the
+Crystal
+
+ align:start position:0%
+Crystal
+ 
+
+ align:start position:0%
+Crystal
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+splitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so it's how much the lians split
+
+ align:start position:0%
+energy so it's how much the lians split
+ 
+
+ align:start position:0%
+energy so it's how much the lians split
+the field so this theoretical case up
+
+ align:start position:0%
+the field so this theoretical case up
+ 
+
+ align:start position:0%
+the field so this theoretical case up
+here there's no splitting going on you
+
+ align:start position:0%
+here there's no splitting going on you
+ 
+
+ align:start position:0%
+here there's no splitting going on you
+bring in the lians and they cause a
+
+ align:start position:0%
+bring in the lians and they cause a
+ 
+
+ align:start position:0%
+bring in the lians and they cause a
+splitting they cause some orbitals to go
+
+ align:start position:0%
+splitting they cause some orbitals to go
+ 
+
+ align:start position:0%
+splitting they cause some orbitals to go
+up in energy and some to go down and the
+
+ align:start position:0%
+up in energy and some to go down and the
+ 
+
+ align:start position:0%
+up in energy and some to go down and the
+distance between them the degree of
+
+ align:start position:0%
+distance between them the degree of
+ 
+
+ align:start position:0%
+distance between them the degree of
+splitting is this octahedral Crystal
+
+ align:start position:0%
+splitting is this octahedral Crystal
+ 
+
+ align:start position:0%
+splitting is this octahedral Crystal
+field splitting
+
+ align:start position:0%
+field splitting
+ 
+
+ align:start position:0%
+field splitting
+energy now the overall energy of the
+
+ align:start position:0%
+energy now the overall energy of the
+ 
+
+ align:start position:0%
+energy now the overall energy of the
+system is
+
+ align:start position:0%
+system is
+ 
+
+ align:start position:0%
+system is
+maintained so if these go up and these
+
+ align:start position:0%
+maintained so if these go up and these
+ 
+
+ align:start position:0%
+maintained so if these go up and these
+go down to get everything to be
+
+ align:start position:0%
+go down to get everything to be
+ 
+
+ align:start position:0%
+go down to get everything to be
+equal let's see draw that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these parts some these should go up
+
+ align:start position:0%
+so these parts some these should go up
+ 
+
+ align:start position:0%
+so these parts some these should go up
+trying to draw this straight from this
+
+ align:start position:0%
+trying to draw this straight from this
+ 
+
+ align:start position:0%
+trying to draw this straight from this
+line uh these were going to go up in
+
+ align:start position:0%
+line uh these were going to go up in
+ 
+
+ align:start position:0%
+line uh these were going to go up in
+energy by plus 2 fths the octahedral
+
+ align:start position:0%
+energy by plus 2 fths the octahedral
+ 
+
+ align:start position:0%
+energy by plus 2 fths the octahedral
+crystal field splitting energy and these
+
+ align:start position:0%
+crystal field splitting energy and these
+ 
+
+ align:start position:0%
+crystal field splitting energy and these
+three orbitals are going to go down in
+
+ align:start position:0%
+three orbitals are going to go down in
+ 
+
+ align:start position:0%
+three orbitals are going to go down in
+energy will be stabilized by minus 2
+
+ align:start position:0%
+energy will be stabilized by minus 2
+ 
+
+ align:start position:0%
+energy will be stabilized by minus 2
+fths the octahedral crystal field
+
+ align:start position:0%
+fths the octahedral crystal field
+ 
+
+ align:start position:0%
+fths the octahedral crystal field
+splitting energy so two orbital are
+
+ align:start position:0%
+splitting energy so two orbital are
+ 
+
+ align:start position:0%
+splitting energy so two orbital are
+going up so it's by three fists three
+
+ align:start position:0%
+going up so it's by three fists three
+ 
+
+ align:start position:0%
+going up so it's by three fists three
+orbitals are going down so it's by two
+
+ align:start position:0%
+orbitals are going down so it's by two
+ 
+
+ align:start position:0%
+orbitals are going down so it's by two
+fists because it's going to have to
+
+ align:start position:0%
+fists because it's going to have to
+ 
+
+ align:start position:0%
+fists because it's going to have to
+equal out so you're not sort of creating
+
+ align:start position:0%
+equal out so you're not sort of creating
+ 
+
+ align:start position:0%
+equal out so you're not sort of creating
+a a different system here the energy is
+
+ align:start position:0%
+a a different system here the energy is
+ 
+
+ align:start position:0%
+a a different system here the energy is
+is going to be conserved the overall
+
+ align:start position:0%
+is going to be conserved the overall
+ 
+
+ align:start position:0%
+is going to be conserved the overall
+energy is maintained so two orbitals up
+
+ align:start position:0%
+energy is maintained so two orbitals up
+ 
+
+ align:start position:0%
+energy is maintained so two orbitals up
+2/3 three orbitals down uh two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fths
+
+ align:start position:0%
+fths
+ 
+
+ align:start position:0%
+fths
+okay so that's really it's a very simple
+
+ align:start position:0%
+okay so that's really it's a very simple
+ 
+
+ align:start position:0%
+okay so that's really it's a very simple
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+instead of the
+
+ align:start position:0%
+instead of the
+ 
+
+ align:start position:0%
+instead of the
+theoretical where all the lians are
+
+ align:start position:0%
+theoretical where all the lians are
+ 
+
+ align:start position:0%
+theoretical where all the lians are
+everywhere when you put them in
+
+ align:start position:0%
+everywhere when you put them in
+ 
+
+ align:start position:0%
+everywhere when you put them in
+octahedral Geometry it affects some of
+
+ align:start position:0%
+octahedral Geometry it affects some of
+ 
+
+ align:start position:0%
+octahedral Geometry it affects some of
+the D orbitals differently than others
+
+ align:start position:0%
+the D orbitals differently than others
+ 
+
+ align:start position:0%
+the D orbitals differently than others
+some orbitals go up in energy some go
+
+ align:start position:0%
+some orbitals go up in energy some go
+ 
+
+ align:start position:0%
+some orbitals go up in energy some go
+down the overall energy is
+
+ align:start position:0%
+down the overall energy is
+ 
+
+ align:start position:0%
+down the overall energy is
+maintained so let's look at an example
+
+ align:start position:0%
+maintained so let's look at an example
+ 
+
+ align:start position:0%
+maintained so let's look at an example
+now and figure out how to put electrons
+
+ align:start position:0%
+now and figure out how to put electrons
+ 
+
+ align:start position:0%
+now and figure out how to put electrons
+into this system so let's look at a case
+
+ align:start position:0%
+into this system so let's look at a case
+ 
+
+ align:start position:0%
+into this system so let's look at a case
+where we have
+
+ align:start position:0%
+where we have
+ 
+
+ align:start position:0%
+where we have
+chromium NH h33
+
+ align:start position:0%
+chromium NH h33
+ 
+
+ align:start position:0%
+chromium NH h33
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and BR
+
+ align:start position:0%
+and BR
+ 
+
+ align:start position:0%
+and BR
+are three so first we need to figure out
+
+ align:start position:0%
+are three so first we need to figure out
+ 
+
+ align:start position:0%
+are three so first we need to figure out
+the oxidation number of
+
+ align:start position:0%
+the oxidation number of
+ 
+
+ align:start position:0%
+the oxidation number of
+chromium having everything in the
+
+ align:start position:0%
+chromium having everything in the
+ 
+
+ align:start position:0%
+chromium having everything in the
+bracket here means that you have six
+
+ align:start position:0%
+bracket here means that you have six
+ 
+
+ align:start position:0%
+bracket here means that you have six
+lians total three NH3 lians three BR
+
+ align:start position:0%
+lians total three NH3 lians three BR
+ 
+
+ align:start position:0%
+lians total three NH3 lians three BR
+lians or bromide lians and those are all
+
+ align:start position:0%
+lians or bromide lians and those are all
+ 
+
+ align:start position:0%
+lians or bromide lians and those are all
+in one bracket there's no number in the
+
+ align:start position:0%
+in one bracket there's no number in the
+ 
+
+ align:start position:0%
+in one bracket there's no number in the
+corner of the bracket so that means the
+
+ align:start position:0%
+corner of the bracket so that means the
+ 
+
+ align:start position:0%
+corner of the bracket so that means the
+overall charge in this system has to be
+
+ align:start position:0%
+overall charge in this system has to be
+ 
+
+ align:start position:0%
+overall charge in this system has to be
+equal to zero so what will the oxidation
+
+ align:start position:0%
+equal to zero so what will the oxidation
+ 
+
+ align:start position:0%
+equal to zero so what will the oxidation
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+bromine it should be
+
+ align:start position:0%
+bromine it should be
+ 
+
+ align:start position:0%
+bromine it should be
+minus1 3 - 1's what about NH3 as a unit
+
+ align:start position:0%
+minus1 3 - 1's what about NH3 as a unit
+ 
+
+ align:start position:0%
+minus1 3 - 1's what about NH3 as a unit
+zero so 3 * 0 and what does that leave
+
+ align:start position:0%
+zero so 3 * 0 and what does that leave
+ 
+
+ align:start position:0%
+zero so 3 * 0 and what does that leave
+you with for the oxidation number of
+
+ align:start position:0%
+you with for the oxidation number of
+ 
+
+ align:start position:0%
+you with for the oxidation number of
+chromium plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three so we have plus three so now we
+
+ align:start position:0%
+three so we have plus three so now we
+ 
+
+ align:start position:0%
+three so we have plus three so now we
+can figure out the Del electron count
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to look up the group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the group number is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what can you see it up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there most people seem to be saying
+
+ align:start position:0%
+there most people seem to be saying
+ 
+
+ align:start position:0%
+there most people seem to be saying
+six okay so that's right so six - 3 is 3
+
+ align:start position:0%
+six okay so that's right so six - 3 is 3
+ 
+
+ align:start position:0%
+six okay so that's right so six - 3 is 3
+so this is a D3
+
+ align:start position:0%
+so this is a D3
+ 
+
+ align:start position:0%
+so this is a D3
+system so that means we're going to put
+
+ align:start position:0%
+system so that means we're going to put
+ 
+
+ align:start position:0%
+system so that means we're going to put
+in three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons so where would you guess I'm
+
+ align:start position:0%
+electrons so where would you guess I'm
+ 
+
+ align:start position:0%
+electrons so where would you guess I'm
+going to put those electrons down here
+
+ align:start position:0%
+going to put those electrons down here
+ 
+
+ align:start position:0%
+going to put those electrons down here
+or up here down am I what if I do
+
+ align:start position:0%
+or up here down am I what if I do
+ 
+
+ align:start position:0%
+or up here down am I what if I do
+this would that be good
+
+ align:start position:0%
+this would that be good
+ 
+
+ align:start position:0%
+this would that be good
+no so we we're coming back to some of
+
+ align:start position:0%
+no so we we're coming back to some of
+ 
+
+ align:start position:0%
+no so we we're coming back to some of
+the roles that you learned learned
+
+ align:start position:0%
+the roles that you learned learned
+ 
+
+ align:start position:0%
+the roles that you learned learned
+earlier in the semester so first you
+
+ align:start position:0%
+earlier in the semester so first you
+ 
+
+ align:start position:0%
+earlier in the semester so first you
+want to put them in the lowest energy
+
+ align:start position:0%
+want to put them in the lowest energy
+ 
+
+ align:start position:0%
+want to put them in the lowest energy
+orbital you don't want to ever have one
+
+ align:start position:0%
+orbital you don't want to ever have one
+ 
+
+ align:start position:0%
+orbital you don't want to ever have one
+with two parallel spins because that
+
+ align:start position:0%
+with two parallel spins because that
+ 
+
+ align:start position:0%
+with two parallel spins because that
+would give you the same four quantum
+
+ align:start position:0%
+would give you the same four quantum
+ 
+
+ align:start position:0%
+would give you the same four quantum
+numbers so that's not good and you also
+
+ align:start position:0%
+numbers so that's not good and you also
+ 
+
+ align:start position:0%
+numbers so that's not good and you also
+if a choice want to put them in if
+
+ align:start position:0%
+if a choice want to put them in if
+ 
+
+ align:start position:0%
+if a choice want to put them in if
+they're the same um energy put them in
+
+ align:start position:0%
+they're the same um energy put them in
+ 
+
+ align:start position:0%
+they're the same um energy put them in
+singly before you start to pair so those
+
+ align:start position:0%
+singly before you start to pair so those
+ 
+
+ align:start position:0%
+singly before you start to pair so those
+are all things that you talked about
+
+ align:start position:0%
+are all things that you talked about
+ 
+
+ align:start position:0%
+are all things that you talked about
+earlier in the system earlier in the
+
+ align:start position:0%
+earlier in the system earlier in the
+ 
+
+ align:start position:0%
+earlier in the system earlier in the
+semester so we put our three electrons
+
+ align:start position:0%
+semester so we put our three electrons
+ 
+
+ align:start position:0%
+semester so we put our three electrons
+in one to each orbital all the spins
+
+ align:start position:0%
+in one to each orbital all the spins
+ 
+
+ align:start position:0%
+in one to each orbital all the spins
+parallel so we have o offb principle
+
+ align:start position:0%
+parallel so we have o offb principle
+ 
+
+ align:start position:0%
+parallel so we have o offb principle
+poly exclusion and also Hun's rule all
+
+ align:start position:0%
+poly exclusion and also Hun's rule all
+ 
+
+ align:start position:0%
+poly exclusion and also Hun's rule all
+at play here with how we put in the
+
+ align:start position:0%
+at play here with how we put in the
+ 
+
+ align:start position:0%
+at play here with how we put in the
+electrons so now we can uh we
+
+ align:start position:0%
+electrons so now we can uh we
+ 
+
+ align:start position:0%
+electrons so now we can uh we
+can talk about the DN electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configuration and maybe I can write over
+
+ align:start position:0%
+configuration and maybe I can write over
+ 
+
+ align:start position:0%
+configuration and maybe I can write over
+here so that's just a way way of
+
+ align:start position:0%
+here so that's just a way way of
+ 
+
+ align:start position:0%
+here so that's just a way way of
+expressing how many electrons are down
+
+ align:start position:0%
+expressing how many electrons are down
+ 
+
+ align:start position:0%
+expressing how many electrons are down
+here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DN electron configuration so that would
+
+ align:start position:0%
+DN electron configuration so that would
+ 
+
+ align:start position:0%
+DN electron configuration so that would
+just be equal to
+
+ align:start position:0%
+just be equal to
+ 
+
+ align:start position:0%
+just be equal to
+t2g to the three so you list the name of
+
+ align:start position:0%
+t2g to the three so you list the name of
+ 
+
+ align:start position:0%
+t2g to the three so you list the name of
+these sets of orbitals and that's really
+
+ align:start position:0%
+these sets of orbitals and that's really
+ 
+
+ align:start position:0%
+these sets of orbitals and that's really
+why these have labels because it makes
+
+ align:start position:0%
+why these have labels because it makes
+ 
+
+ align:start position:0%
+why these have labels because it makes
+your life easier instead of listing all
+
+ align:start position:0%
+your life easier instead of listing all
+ 
+
+ align:start position:0%
+your life easier instead of listing all
+the orbitals each time so there are
+
+ align:start position:0%
+the orbitals each time so there are
+ 
+
+ align:start position:0%
+the orbitals each time so there are
+three in this lower energy
+
+ align:start position:0%
+three in this lower energy
+ 
+
+ align:start position:0%
+three in this lower energy
+level now we can also talk about um
+
+ align:start position:0%
+level now we can also talk about um
+ 
+
+ align:start position:0%
+level now we can also talk about um
+Crystal field stabilization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy Crystal field
+
+ align:start position:0%
+energy Crystal field
+ 
+
+ align:start position:0%
+energy Crystal field
+stabilization energy so don't get this
+
+ align:start position:0%
+stabilization energy so don't get this
+ 
+
+ align:start position:0%
+stabilization energy so don't get this
+confused with Crystal field splitting
+
+ align:start position:0%
+confused with Crystal field splitting
+ 
+
+ align:start position:0%
+confused with Crystal field splitting
+energy this is Crystal field
+
+ align:start position:0%
+energy this is Crystal field
+ 
+
+ align:start position:0%
+energy this is Crystal field
+stabilization energy and it's
+
+ align:start position:0%
+stabilization energy and it's
+ 
+
+ align:start position:0%
+stabilization energy and it's
+abbreviated CF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's really just thinking about
+
+ align:start position:0%
+and that's really just thinking about
+ 
+
+ align:start position:0%
+and that's really just thinking about
+how much you stabilize by this splitting
+
+ align:start position:0%
+how much you stabilize by this splitting
+ 
+
+ align:start position:0%
+how much you stabilize by this splitting
+so if you had this uh hypothetical
+
+ align:start position:0%
+so if you had this uh hypothetical
+ 
+
+ align:start position:0%
+so if you had this uh hypothetical
+spherical Crystal
+
+ align:start position:0%
+spherical Crystal
+ 
+
+ align:start position:0%
+spherical Crystal
+field your electrons would be in
+
+ align:start position:0%
+field your electrons would be in
+ 
+
+ align:start position:0%
+field your electrons would be in
+orbitals with this energy but they're
+
+ align:start position:0%
+orbitals with this energy but they're
+ 
+
+ align:start position:0%
+orbitals with this energy but they're
+not after the lians come in in the
+
+ align:start position:0%
+not after the lians come in in the
+ 
+
+ align:start position:0%
+not after the lians come in in the
+octahedral geometry the electrons are in
+
+ align:start position:0%
+octahedral geometry the electrons are in
+ 
+
+ align:start position:0%
+octahedral geometry the electrons are in
+the t2g orbitals so there's they're
+
+ align:start position:0%
+the t2g orbitals so there's they're
+ 
+
+ align:start position:0%
+the t2g orbitals so there's they're
+stabilized this is lower in energy than
+
+ align:start position:0%
+stabilized this is lower in energy than
+ 
+
+ align:start position:0%
+stabilized this is lower in energy than
+where they would have been before and so
+
+ align:start position:0%
+where they would have been before and so
+ 
+
+ align:start position:0%
+where they would have been before and so
+the crystal field stabilization energy
+
+ align:start position:0%
+the crystal field stabilization energy
+ 
+
+ align:start position:0%
+the crystal field stabilization energy
+is a way of indicating whether you've
+
+ align:start position:0%
+is a way of indicating whether you've
+ 
+
+ align:start position:0%
+is a way of indicating whether you've
+overall stabilized the system or not uh
+
+ align:start position:0%
+overall stabilized the system or not uh
+ 
+
+ align:start position:0%
+overall stabilized the system or not uh
+by this by this
+
+ align:start position:0%
+by this by this
+ 
+
+ align:start position:0%
+by this by this
+splitting so the way that you would do
+
+ align:start position:0%
+splitting so the way that you would do
+ 
+
+ align:start position:0%
+splitting so the way that you would do
+this is you would just look at where how
+
+ align:start position:0%
+this is you would just look at where how
+ 
+
+ align:start position:0%
+this is you would just look at where how
+you represent it look at where the
+
+ align:start position:0%
+you represent it look at where the
+ 
+
+ align:start position:0%
+you represent it look at where the
+electrons are and how much they're
+
+ align:start position:0%
+electrons are and how much they're
+ 
+
+ align:start position:0%
+electrons are and how much they're
+stabilized again three orbitals down
+
+ align:start position:0%
+stabilized again three orbitals down
+ 
+
+ align:start position:0%
+stabilized again three orbitals down
+minus 2 fths two orbitals up plus 3
+
+ align:start position:0%
+minus 2 fths two orbitals up plus 3
+ 
+
+ align:start position:0%
+minus 2 fths two orbitals up plus 3
+so in this case this would equal there
+
+ align:start position:0%
+so in this case this would equal there
+ 
+
+ align:start position:0%
+so in this case this would equal there
+are three electrons that are stabilized
+
+ align:start position:0%
+are three electrons that are stabilized
+ 
+
+ align:start position:0%
+are three electrons that are stabilized
+by minus 2 two fths of the octahedral
+
+ align:start position:0%
+by minus 2 two fths of the octahedral
+ 
+
+ align:start position:0%
+by minus 2 two fths of the octahedral
+crystal field splitting energy or you
+
+ align:start position:0%
+crystal field splitting energy or you
+ 
+
+ align:start position:0%
+crystal field splitting energy or you
+would have a stabilization of minus 6
+
+ align:start position:0%
+would have a stabilization of minus 6
+ 
+
+ align:start position:0%
+would have a stabilization of minus 6
+fths times the octahedral crystal field
+
+ align:start position:0%
+fths times the octahedral crystal field
+ 
+
+ align:start position:0%
+fths times the octahedral crystal field
+splitting
+
+ align:start position:0%
+splitting
+ 
+
+ align:start position:0%
+splitting
+energy so that would be the answer to
+
+ align:start position:0%
+energy so that would be the answer to
+ 
+
+ align:start position:0%
+energy so that would be the answer to
+that part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's look at um another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example and I'll write this in between
+
+ align:start position:0%
+example and I'll write this in between
+ 
+
+ align:start position:0%
+example and I'll write this in between
+here so here we have manganese with six
+
+ align:start position:0%
+here so here we have manganese with six
+ 
+
+ align:start position:0%
+here so here we have manganese with six
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+lians in
+
+ align:start position:0%
+lians in
+ 
+
+ align:start position:0%
+lians in
+Brackets and
+
+ align:start position:0%
+Brackets and
+ 
+
+ align:start position:0%
+Brackets and
+cl3 on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside so what is the
+
+ align:start position:0%
+outside so what is the
+ 
+
+ align:start position:0%
+outside so what is the
+overall what's the charge of just this
+
+ align:start position:0%
+overall what's the charge of just this
+ 
+
+ align:start position:0%
+overall what's the charge of just this
+this coordination complex so what's
+
+ align:start position:0%
+this coordination complex so what's
+ 
+
+ align:start position:0%
+this coordination complex so what's
+inside has uh six six lians to this
+
+ align:start position:0%
+inside has uh six six lians to this
+ 
+
+ align:start position:0%
+inside has uh six six lians to this
+inside the brackets so what's the charge
+
+ align:start position:0%
+inside the brackets so what's the charge
+ 
+
+ align:start position:0%
+inside the brackets so what's the charge
+of just that coordination complex
+
+ align:start position:0%
+of just that coordination complex
+ 
+
+ align:start position:0%
+of just that coordination complex
+overall it would be plus
+
+ align:start position:0%
+overall it would be plus
+ 
+
+ align:start position:0%
+overall it would be plus
+three and you know that because these
+
+ align:start position:0%
+three and you know that because these
+ 
+
+ align:start position:0%
+three and you know that because these
+are three negatively
+
+ align:start position:0%
+are three negatively
+ 
+
+ align:start position:0%
+are three negatively
+charged ions counter ions so when the
+
+ align:start position:0%
+charged ions counter ions so when the
+ 
+
+ align:start position:0%
+charged ions counter ions so when the
+whole thing is neutral with three CLS it
+
+ align:start position:0%
+whole thing is neutral with three CLS it
+ 
+
+ align:start position:0%
+whole thing is neutral with three CLS it
+means that had to have been plus three
+
+ align:start position:0%
+means that had to have been plus three
+ 
+
+ align:start position:0%
+means that had to have been plus three
+so what is the charge of
+
+ align:start position:0%
+so what is the charge of
+ 
+
+ align:start position:0%
+so what is the charge of
+water zero so what has to be the charge
+
+ align:start position:0%
+water zero so what has to be the charge
+ 
+
+ align:start position:0%
+water zero so what has to be the charge
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+metal plus
+
+ align:start position:0%
+metal plus
+ 
+
+ align:start position:0%
+metal plus
+three so now we can figure out the Del
+
+ align:start position:0%
+three so now we can figure out the Del
+ 
+
+ align:start position:0%
+three so now we can figure out the Del
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+count what group are we
+
+ align:start position:0%
+count what group are we
+ 
+
+ align:start position:0%
+count what group are we
+in 7 - 3 is 4 so we're a D4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system all right so now we're we have
+
+ align:start position:0%
+system all right so now we're we have
+ 
+
+ align:start position:0%
+system all right so now we're we have
+four electrons to put in and we're going
+
+ align:start position:0%
+four electrons to put in and we're going
+ 
+
+ align:start position:0%
+four electrons to put in and we're going
+to have a choice we're going to have a
+
+ align:start position:0%
+to have a choice we're going to have a
+ 
+
+ align:start position:0%
+to have a choice we're going to have a
+choice as to whether we put the fourth
+
+ align:start position:0%
+choice as to whether we put the fourth
+ 
+
+ align:start position:0%
+choice as to whether we put the fourth
+Lian up here I mean the fourth electron
+
+ align:start position:0%
+Lian up here I mean the fourth electron
+ 
+
+ align:start position:0%
+Lian up here I mean the fourth electron
+up here or keep the fourth electron down
+
+ align:start position:0%
+up here or keep the fourth electron down
+ 
+
+ align:start position:0%
+up here or keep the fourth electron down
+here and pair and so both of those are
+
+ align:start position:0%
+here and pair and so both of those are
+ 
+
+ align:start position:0%
+here and pair and so both of those are
+possibilities and it depends on the
+
+ align:start position:0%
+possibilities and it depends on the
+ 
+
+ align:start position:0%
+possibilities and it depends on the
+strength of the crystal field so let's
+
+ align:start position:0%
+strength of the crystal field so let's
+ 
+
+ align:start position:0%
+strength of the crystal field so let's
+let's look at uh those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams so there are two possibilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and we have again dx^ 2us y^2 dz^2
+
+ align:start position:0%
+and and we have again dx^ 2us y^2 dz^2
+ 
+
+ align:start position:0%
+and and we have again dx^ 2us y^2 dz^2
+up here we have our t2g system our EG so
+
+ align:start position:0%
+up here we have our t2g system our EG so
+ 
+
+ align:start position:0%
+up here we have our t2g system our EG so
+that's that's one drawing or we might
+
+ align:start position:0%
+that's that's one drawing or we might
+ 
+
+ align:start position:0%
+that's that's one drawing or we might
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case where we have something more like
+
+ align:start position:0%
+case where we have something more like
+ 
+
+ align:start position:0%
+case where we have something more like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+where there's a much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+larger a much larger separation between
+
+ align:start position:0%
+larger a much larger separation between
+ 
+
+ align:start position:0%
+larger a much larger separation between
+the sets of orbitals between the EG and
+
+ align:start position:0%
+the sets of orbitals between the EG and
+ 
+
+ align:start position:0%
+the sets of orbitals between the EG and
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t2g and so here's our Crystal field it's
+
+ align:start position:0%
+t2g and so here's our Crystal field it's
+ 
+
+ align:start position:0%
+t2g and so here's our Crystal field it's
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+here and here's another Crystal field
+
+ align:start position:0%
+here and here's another Crystal field
+ 
+
+ align:start position:0%
+here and here's another Crystal field
+splitting energy and this one is large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have a choice we have to put in
+
+ align:start position:0%
+so you have a choice we have to put in
+ 
+
+ align:start position:0%
+so you have a choice we have to put in
+four electrons and depending on whether
+
+ align:start position:0%
+four electrons and depending on whether
+ 
+
+ align:start position:0%
+four electrons and depending on whether
+it's a small splitting or a large
+
+ align:start position:0%
+it's a small splitting or a large
+ 
+
+ align:start position:0%
+it's a small splitting or a large
+splitting you're going to put them in
+
+ align:start position:0%
+splitting you're going to put them in
+ 
+
+ align:start position:0%
+splitting you're going to put them in
+differently so in this
+
+ align:start position:0%
+differently so in this
+ 
+
+ align:start position:0%
+differently so in this
+case we have a crystal field splitting
+
+ align:start position:0%
+case we have a crystal field splitting
+ 
+
+ align:start position:0%
+case we have a crystal field splitting
+energy that's less than what we call the
+
+ align:start position:0%
+energy that's less than what we call the
+ 
+
+ align:start position:0%
+energy that's less than what we call the
+pairing
+
+ align:start position:0%
+pairing
+ 
+
+ align:start position:0%
+pairing
+energy so the pairing energy is how much
+
+ align:start position:0%
+energy so the pairing energy is how much
+ 
+
+ align:start position:0%
+energy so the pairing energy is how much
+energy it takes to pair up the electrons
+
+ align:start position:0%
+energy it takes to pair up the electrons
+ 
+
+ align:start position:0%
+energy it takes to pair up the electrons
+they prefer to have their own orbital
+
+ align:start position:0%
+they prefer to have their own orbital
+ 
+
+ align:start position:0%
+they prefer to have their own orbital
+they would prefer not to be paired it
+
+ align:start position:0%
+they would prefer not to be paired it
+ 
+
+ align:start position:0%
+they would prefer not to be paired it
+takes a certain amount of energy to pair
+
+ align:start position:0%
+takes a certain amount of energy to pair
+ 
+
+ align:start position:0%
+takes a certain amount of energy to pair
+them so in this case
+
+ align:start position:0%
+them so in this case
+ 
+
+ align:start position:0%
+them so in this case
+because the the splitting is
+
+ align:start position:0%
+because the the splitting is
+ 
+
+ align:start position:0%
+because the the splitting is
+small this set of orbitals up here are
+
+ align:start position:0%
+small this set of orbitals up here are
+ 
+
+ align:start position:0%
+small this set of orbitals up here are
+really not that much higher in energy
+
+ align:start position:0%
+really not that much higher in energy
+ 
+
+ align:start position:0%
+really not that much higher in energy
+than these were so it's not that hard to
+
+ align:start position:0%
+than these were so it's not that hard to
+ 
+
+ align:start position:0%
+than these were so it's not that hard to
+put one up here and it takes more energy
+
+ align:start position:0%
+put one up here and it takes more energy
+ 
+
+ align:start position:0%
+put one up here and it takes more energy
+in this case to pair them up than it
+
+ align:start position:0%
+in this case to pair them up than it
+ 
+
+ align:start position:0%
+in this case to pair them up than it
+does to put one in the higher level so
+
+ align:start position:0%
+does to put one in the higher level so
+ 
+
+ align:start position:0%
+does to put one in the higher level so
+this one would have a drawing like this
+
+ align:start position:0%
+this one would have a drawing like this
+ 
+
+ align:start position:0%
+this one would have a drawing like this
+you have four electrons you put in one
+
+ align:start position:0%
+you have four electrons you put in one
+ 
+
+ align:start position:0%
+you have four electrons you put in one
+of them goes over
+
+ align:start position:0%
+of them goes over
+ 
+
+ align:start position:0%
+of them goes over
+there in this
+
+ align:start position:0%
+there in this
+ 
+
+ align:start position:0%
+there in this
+case we have a really big difference it
+
+ align:start position:0%
+case we have a really big difference it
+ 
+
+ align:start position:0%
+case we have a really big difference it
+would take a lot of energy to put an
+
+ align:start position:0%
+would take a lot of energy to put an
+ 
+
+ align:start position:0%
+would take a lot of energy to put an
+electron way up here so in this
+
+ align:start position:0%
+electron way up here so in this
+ 
+
+ align:start position:0%
+electron way up here so in this
+case the splitting energy is greater
+
+ align:start position:0%
+case the splitting energy is greater
+ 
+
+ align:start position:0%
+case the splitting energy is greater
+than the pairing energy this is really a
+
+ align:start position:0%
+than the pairing energy this is really a
+ 
+
+ align:start position:0%
+than the pairing energy this is really a
+lot higher up here it's small makes not
+
+ align:start position:0%
+lot higher up here it's small makes not
+ 
+
+ align:start position:0%
+lot higher up here it's small makes not
+much difference here the energy is large
+
+ align:start position:0%
+much difference here the energy is large
+ 
+
+ align:start position:0%
+much difference here the energy is large
+so in this case you would want to put
+
+ align:start position:0%
+so in this case you would want to put
+ 
+
+ align:start position:0%
+so in this case you would want to put
+your four electrons all down in the
+
+ align:start position:0%
+your four electrons all down in the
+ 
+
+ align:start position:0%
+your four electrons all down in the
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+level so let's just take a look at some
+
+ align:start position:0%
+level so let's just take a look at some
+ 
+
+ align:start position:0%
+level so let's just take a look at some
+of those rules and say them again so
+
+ align:start position:0%
+of those rules and say them again so
+ 
+
+ align:start position:0%
+of those rules and say them again so
+here when the splitting is small this is
+
+ align:start position:0%
+here when the splitting is small this is
+ 
+
+ align:start position:0%
+here when the splitting is small this is
+called a weak field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the ligans here they'll be weak field
+
+ align:start position:0%
+so the ligans here they'll be weak field
+ 
+
+ align:start position:0%
+so the ligans here they'll be weak field
+ligans and they'll be strong field
+
+ align:start position:0%
+ligans and they'll be strong field
+ 
+
+ align:start position:0%
+ligans and they'll be strong field
+ligans and we're going to talk about
+
+ align:start position:0%
+ligans and we're going to talk about
+ 
+
+ align:start position:0%
+ligans and we're going to talk about
+that uh next Monday how you will learn
+
+ align:start position:0%
+that uh next Monday how you will learn
+ 
+
+ align:start position:0%
+that uh next Monday how you will learn
+certain lians and whether they're weak
+
+ align:start position:0%
+certain lians and whether they're weak
+ 
+
+ align:start position:0%
+certain lians and whether they're weak
+field or strong field but if they're
+
+ align:start position:0%
+field or strong field but if they're
+ 
+
+ align:start position:0%
+field or strong field but if they're
+weak oh boy they cannot really split
+
+ align:start position:0%
+weak oh boy they cannot really split
+ 
+
+ align:start position:0%
+weak oh boy they cannot really split
+that energy very far they don't have a
+
+ align:start position:0%
+that energy very far they don't have a
+ 
+
+ align:start position:0%
+that energy very far they don't have a
+lot of strength they can't do a huge
+
+ align:start position:0%
+lot of strength they can't do a huge
+ 
+
+ align:start position:0%
+lot of strength they can't do a huge
+splitting they just you know they just
+
+ align:start position:0%
+splitting they just you know they just
+ 
+
+ align:start position:0%
+splitting they just you know they just
+do a little tiny amount of splitting
+
+ align:start position:0%
+do a little tiny amount of splitting
+ 
+
+ align:start position:0%
+do a little tiny amount of splitting
+they're pretty weak lians and in this
+
+ align:start position:0%
+they're pretty weak lians and in this
+ 
+
+ align:start position:0%
+they're pretty weak lians and in this
+case you would have have a
+
+ align:start position:0%
+case you would have have a
+ 
+
+ align:start position:0%
+case you would have have a
+strong a strong
+
+ align:start position:0%
+strong a strong
+ 
+
+ align:start position:0%
+strong a strong
+field where you'd have a large splitting
+
+ align:start position:0%
+field where you'd have a large splitting
+ 
+
+ align:start position:0%
+field where you'd have a large splitting
+so those lians come in and boy they take
+
+ align:start position:0%
+so those lians come in and boy they take
+ 
+
+ align:start position:0%
+so those lians come in and boy they take
+those de orbital energy levels and they
+
+ align:start position:0%
+those de orbital energy levels and they
+ 
+
+ align:start position:0%
+those de orbital energy levels and they
+split them really far apart so those are
+
+ align:start position:0%
+split them really far apart so those are
+ 
+
+ align:start position:0%
+split them really far apart so those are
+strong field lians they create a strong
+
+ align:start position:0%
+strong field lians they create a strong
+ 
+
+ align:start position:0%
+strong field lians they create a strong
+field and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large all right so if we look at some of
+
+ align:start position:0%
+large all right so if we look at some of
+ 
+
+ align:start position:0%
+large all right so if we look at some of
+these rules then so if our pairing
+
+ align:start position:0%
+these rules then so if our pairing
+ 
+
+ align:start position:0%
+these rules then so if our pairing
+energy is greater than that energy
+
+ align:start position:0%
+energy is greater than that energy
+ 
+
+ align:start position:0%
+energy is greater than that energy
+difference that means you have a weak
+
+ align:start position:0%
+difference that means you have a weak
+ 
+
+ align:start position:0%
+difference that means you have a weak
+field it's not much different so it's a
+
+ align:start position:0%
+field it's not much different so it's a
+ 
+
+ align:start position:0%
+field it's not much different so it's a
+weak field not much not much splittings
+
+ align:start position:0%
+weak field not much not much splittings
+ 
+
+ align:start position:0%
+weak field not much not much splittings
+the splitting is small and then what
+
+ align:start position:0%
+the splitting is small and then what
+ 
+
+ align:start position:0%
+the splitting is small and then what
+you're going to want to do is put all
+
+ align:start position:0%
+you're going to want to do is put all
+ 
+
+ align:start position:0%
+you're going to want to do is put all
+your electrons in singly to the fullest
+
+ align:start position:0%
+your electrons in singly to the fullest
+ 
+
+ align:start position:0%
+your electrons in singly to the fullest
+extent possible so you use both t2g and
+
+ align:start position:0%
+extent possible so you use both t2g and
+ 
+
+ align:start position:0%
+extent possible so you use both t2g and
+EG you put them all singly until you're
+
+ align:start position:0%
+EG you put them all singly until you're
+ 
+
+ align:start position:0%
+EG you put them all singly until you're
+done before you
+
+ align:start position:0%
+done before you
+ 
+
+ align:start position:0%
+done before you
+pair on the other hand if you have a
+
+ align:start position:0%
+pair on the other hand if you have a
+ 
+
+ align:start position:0%
+pair on the other hand if you have a
+strong field that's going to have a
+
+ align:start position:0%
+strong field that's going to have a
+ 
+
+ align:start position:0%
+strong field that's going to have a
+really large splitting big energy
+
+ align:start position:0%
+really large splitting big energy
+ 
+
+ align:start position:0%
+really large splitting big energy
+difference between t2g and EG sets of
+
+ align:start position:0%
+difference between t2g and EG sets of
+ 
+
+ align:start position:0%
+difference between t2g and EG sets of
+orbitals then that splitting energy is
+
+ align:start position:0%
+orbitals then that splitting energy is
+ 
+
+ align:start position:0%
+orbitals then that splitting energy is
+going to be greater than the pairing
+
+ align:start position:0%
+going to be greater than the pairing
+ 
+
+ align:start position:0%
+going to be greater than the pairing
+energy it's more favorable to pair than
+
+ align:start position:0%
+energy it's more favorable to pair than
+ 
+
+ align:start position:0%
+energy it's more favorable to pair than
+to make that big jump up to this higher
+
+ align:start position:0%
+to make that big jump up to this higher
+ 
+
+ align:start position:0%
+to make that big jump up to this higher
+energy level up here so in that case
+
+ align:start position:0%
+energy level up here so in that case
+ 
+
+ align:start position:0%
+energy level up here so in that case
+what you want to do is you want to pair
+
+ align:start position:0%
+what you want to do is you want to pair
+ 
+
+ align:start position:0%
+what you want to do is you want to pair
+them all up in
+
+ align:start position:0%
+them all up in
+ 
+
+ align:start position:0%
+them all up in
+t2g and only after this is completely
+
+ align:start position:0%
+t2g and only after this is completely
+ 
+
+ align:start position:0%
+t2g and only after this is completely
+full and you can't put any more
+
+ align:start position:0%
+full and you can't put any more
+ 
+
+ align:start position:0%
+full and you can't put any more
+electrons in there do you want to put an
+
+ align:start position:0%
+electrons in there do you want to put an
+ 
+
+ align:start position:0%
+electrons in there do you want to put an
+electron way up there in the EG sets of
+
+ align:start position:0%
+electron way up there in the EG sets of
+ 
+
+ align:start position:0%
+electron way up there in the EG sets of
+orbitals so uh what this what this uh
+
+ align:start position:0%
+orbitals so uh what this what this uh
+ 
+
+ align:start position:0%
+orbitals so uh what this what this uh
+means then is in this case you're going
+
+ align:start position:0%
+means then is in this case you're going
+ 
+
+ align:start position:0%
+means then is in this case you're going
+to have the maximum amount of unpaired
+
+ align:start position:0%
+to have the maximum amount of unpaired
+ 
+
+ align:start position:0%
+to have the maximum amount of unpaired
+electrons because you're going to try to
+
+ align:start position:0%
+electrons because you're going to try to
+ 
+
+ align:start position:0%
+electrons because you're going to try to
+keep them unpaired for as long as you
+
+ align:start position:0%
+keep them unpaired for as long as you
+ 
+
+ align:start position:0%
+keep them unpaired for as long as you
+possibly can and so this is referred to
+
+ align:start position:0%
+possibly can and so this is referred to
+ 
+
+ align:start position:0%
+possibly can and so this is referred to
+as a highs spin
+
+ align:start position:0%
+as a highs spin
+ 
+
+ align:start position:0%
+as a highs spin
+system in this case you're going to have
+
+ align:start position:0%
+system in this case you're going to have
+ 
+
+ align:start position:0%
+system in this case you're going to have
+the minimum number of unpaired you're
+
+ align:start position:0%
+the minimum number of unpaired you're
+ 
+
+ align:start position:0%
+the minimum number of unpaired you're
+trying to pair them up down here before
+
+ align:start position:0%
+trying to pair them up down here before
+ 
+
+ align:start position:0%
+trying to pair them up down here before
+you put one up here so this is a low
+
+ align:start position:0%
+you put one up here so this is a low
+ 
+
+ align:start position:0%
+you put one up here so this is a low
+spin system minimum number of unpaired
+
+ align:start position:0%
+spin system minimum number of unpaired
+ 
+
+ align:start position:0%
+spin system minimum number of unpaired
+electrons that are possible so these are
+
+ align:start position:0%
+electrons that are possible so these are
+ 
+
+ align:start position:0%
+electrons that are possible so these are
+our two um two diagrams that you'll see
+
+ align:start position:0%
+our two um two diagrams that you'll see
+ 
+
+ align:start position:0%
+our two um two diagrams that you'll see
+and uh one question on the on the
+
+ align:start position:0%
+and uh one question on the on the
+ 
+
+ align:start position:0%
+and uh one question on the on the
+problem set has you drawing these these
+
+ align:start position:0%
+problem set has you drawing these these
+ 
+
+ align:start position:0%
+problem set has you drawing these these
+diagrams for these different uh
+
+ align:start position:0%
+diagrams for these different uh
+ 
+
+ align:start position:0%
+diagrams for these different uh
+conditions now this particular one that
+
+ align:start position:0%
+conditions now this particular one that
+ 
+
+ align:start position:0%
+conditions now this particular one that
+we're talking about
+
+ align:start position:0%
+we're talking about
+ 
+
+ align:start position:0%
+we're talking about
+this particular complex is high Spin and
+
+ align:start position:0%
+this particular complex is high Spin and
+ 
+
+ align:start position:0%
+this particular complex is high Spin and
+so next week we're going to talk about
+
+ align:start position:0%
+so next week we're going to talk about
+ 
+
+ align:start position:0%
+so next week we're going to talk about
+why that's true and you'll learn about
+
+ align:start position:0%
+why that's true and you'll learn about
+ 
+
+ align:start position:0%
+why that's true and you'll learn about
+some of the ligans and be able to
+
+ align:start position:0%
+some of the ligans and be able to
+ 
+
+ align:start position:0%
+some of the ligans and be able to
+predict whether it's going to be a high
+
+ align:start position:0%
+predict whether it's going to be a high
+ 
+
+ align:start position:0%
+predict whether it's going to be a high
+spin or low spin
+
+ align:start position:0%
+spin or low spin
+ 
+
+ align:start position:0%
+spin or low spin
+system we can um also go through now and
+
+ align:start position:0%
+system we can um also go through now and
+ 
+
+ align:start position:0%
+system we can um also go through now and
+do uh electron uh configurations and
+
+ align:start position:0%
+do uh electron uh configurations and
+ 
+
+ align:start position:0%
+do uh electron uh configurations and
+also the crystal field um splitting
+
+ align:start position:0%
+also the crystal field um splitting
+ 
+
+ align:start position:0%
+also the crystal field um splitting
+energy so in this
+
+ align:start position:0%
+energy so in this
+ 
+
+ align:start position:0%
+energy so in this
+case our our DN
+
+ align:start position:0%
+case our our DN
+ 
+
+ align:start position:0%
+case our our DN
+configuration is going to be equal to
+
+ align:start position:0%
+configuration is going to be equal to
+ 
+
+ align:start position:0%
+configuration is going to be equal to
+there are three
+
+ align:start position:0%
+there are three
+ 
+
+ align:start position:0%
+there are three
+electrons in
+
+ align:start position:0%
+electrons in
+ 
+
+ align:start position:0%
+electrons in
+t2g and there's one electron in
+
+ align:start position:0%
+t2g and there's one electron in
+ 
+
+ align:start position:0%
+t2g and there's one electron in
+EG and over here we have DN equals in
+
+ align:start position:0%
+EG and over here we have DN equals in
+ 
+
+ align:start position:0%
+EG and over here we have DN equals in
+t2g we have four electrons so those are
+
+ align:start position:0%
+t2g we have four electrons so those are
+ 
+
+ align:start position:0%
+t2g we have four electrons so those are
+the differences in electron
+
+ align:start position:0%
+the differences in electron
+ 
+
+ align:start position:0%
+the differences in electron
+configuration and um
+
+ align:start position:0%
+configuration and um
+ 
+
+ align:start position:0%
+configuration and um
+in the crystal field stabilization
+
+ align:start position:0%
+in the crystal field stabilization
+ 
+
+ align:start position:0%
+in the crystal field stabilization
+energy we have we calculate that we have
+
+ align:start position:0%
+energy we have we calculate that we have
+ 
+
+ align:start position:0%
+energy we have we calculate that we have
+three electrons down
+
+ align:start position:0%
+three electrons down
+ 
+
+ align:start position:0%
+three electrons down
+here so we have three electrons in minus
+
+ align:start position:0%
+here so we have three electrons in minus
+ 
+
+ align:start position:0%
+here so we have three electrons in minus
+2 fths times the crystal field splitting
+
+ align:start position:0%
+2 fths times the crystal field splitting
+ 
+
+ align:start position:0%
+2 fths times the crystal field splitting
+energy and we have one
+
+ align:start position:0%
+energy and we have one
+ 
+
+ align:start position:0%
+energy and we have one
+electron up above so that's plus 3 fths
+
+ align:start position:0%
+electron up above so that's plus 3 fths
+ 
+
+ align:start position:0%
+electron up above so that's plus 3 fths
+there and so - 6 Plus + 3 is going to
+
+ align:start position:0%
+there and so - 6 Plus + 3 is going to
+ 
+
+ align:start position:0%
+there and so - 6 Plus + 3 is going to
+give us - 35ths time the octahedral
+
+ align:start position:0%
+give us - 35ths time the octahedral
+ 
+
+ align:start position:0%
+give us - 35ths time the octahedral
+crystal field splitting energy for this
+
+ align:start position:0%
+crystal field splitting energy for this
+ 
+
+ align:start position:0%
+crystal field splitting energy for this
+system here and you do need to put the
+
+ align:start position:0%
+system here and you do need to put the
+ 
+
+ align:start position:0%
+system here and you do need to put the
+symbol for the octahedral crystal field
+
+ align:start position:0%
+symbol for the octahedral crystal field
+ 
+
+ align:start position:0%
+symbol for the octahedral crystal field
+splitting energy in this not just the
+
+ align:start position:0%
+splitting energy in this not just the
+ 
+
+ align:start position:0%
+splitting energy in this not just the
+number so on the other
+
+ align:start position:0%
+number so on the other
+ 
+
+ align:start position:0%
+number so on the other
+side we only have uh electrons down
+
+ align:start position:0%
+side we only have uh electrons down
+ 
+
+ align:start position:0%
+side we only have uh electrons down
+here and so we're going to have
+
+ align:start position:0%
+here and so we're going to have
+ 
+
+ align:start position:0%
+here and so we're going to have
+four that are times - 2 fths and so our
+
+ align:start position:0%
+four that are times - 2 fths and so our
+ 
+
+ align:start position:0%
+four that are times - 2 fths and so our
+answer is going to be - 8 fths times the
+
+ align:start position:0%
+answer is going to be - 8 fths times the
+ 
+
+ align:start position:0%
+answer is going to be - 8 fths times the
+octahedral crystal field splitting
+
+ align:start position:0%
+octahedral crystal field splitting
+ 
+
+ align:start position:0%
+octahedral crystal field splitting
+energy and every once in a while some
+
+ align:start position:0%
+energy and every once in a while some
+ 
+
+ align:start position:0%
+energy and every once in a while some
+people like to indicate that there's
+
+ align:start position:0%
+people like to indicate that there's
+ 
+
+ align:start position:0%
+people like to indicate that there's
+also something paired so sometimes
+
+ align:start position:0%
+also something paired so sometimes
+ 
+
+ align:start position:0%
+also something paired so sometimes
+you'll see this plus PE which indicates
+
+ align:start position:0%
+you'll see this plus PE which indicates
+ 
+
+ align:start position:0%
+you'll see this plus PE which indicates
+one paired electron but that's sometimes
+
+ align:start position:0%
+one paired electron but that's sometimes
+ 
+
+ align:start position:0%
+one paired electron but that's sometimes
+you might be asked for that so um just
+
+ align:start position:0%
+you might be asked for that so um just
+ 
+
+ align:start position:0%
+you might be asked for that so um just
+to be aware I think your book doesn't
+
+ align:start position:0%
+to be aware I think your book doesn't
+ 
+
+ align:start position:0%
+to be aware I think your book doesn't
+use this but you will see that some
+
+ align:start position:0%
+use this but you will see that some
+ 
+
+ align:start position:0%
+use this but you will see that some
+places
+
+ align:start position:0%
+places
+ 
+
+ align:start position:0%
+places
+all right so that's how we would do uh
+
+ align:start position:0%
+all right so that's how we would do uh
+ 
+
+ align:start position:0%
+all right so that's how we would do uh
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+two all right so um let's uh quickly
+
+ align:start position:0%
+two all right so um let's uh quickly
+ 
+
+ align:start position:0%
+two all right so um let's uh quickly
+look at one more
+
+ align:start position:0%
+look at one more
+ 
+
+ align:start position:0%
+look at one more
+example and here it would be excellent
+
+ align:start position:0%
+example and here it would be excellent
+ 
+
+ align:start position:0%
+example and here it would be excellent
+to have another board but uh let's
+
+ align:start position:0%
+to have another board but uh let's
+ 
+
+ align:start position:0%
+to have another board but uh let's
+quickly do a little bit of erasing and
+
+ align:start position:0%
+quickly do a little bit of erasing and
+ 
+
+ align:start position:0%
+quickly do a little bit of erasing and
+leave our framework
+
+ align:start position:0%
+leave our framework
+ 
+
+ align:start position:0%
+leave our framework
+here all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do a little bit of erasing here get rid
+
+ align:start position:0%
+do a little bit of erasing here get rid
+ 
+
+ align:start position:0%
+do a little bit of erasing here get rid
+of this over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so in this case we're looking
+
+ align:start position:0%
+here okay so in this case we're looking
+ 
+
+ align:start position:0%
+here okay so in this case we're looking
+at Cobalt +
+
+ align:start position:0%
+at Cobalt +
+ 
+
+ align:start position:0%
+at Cobalt +
+2 and the first step is find the
+
+ align:start position:0%
+2 and the first step is find the
+ 
+
+ align:start position:0%
+2 and the first step is find the
+oxidation number but conveniently that
+
+ align:start position:0%
+oxidation number but conveniently that
+ 
+
+ align:start position:0%
+oxidation number but conveniently that
+was given to you it's plus two and then
+
+ align:start position:0%
+was given to you it's plus two and then
+ 
+
+ align:start position:0%
+was given to you it's plus two and then
+we need to do the electron
+
+ align:start position:0%
+we need to do the electron
+ 
+
+ align:start position:0%
+we need to do the electron
+count group number for
+
+ align:start position:0%
+count group number for
+ 
+
+ align:start position:0%
+count group number for
+Cobalt is N9 so we have 9 - 2 or seven
+
+ align:start position:0%
+Cobalt is N9 so we have 9 - 2 or seven
+ 
+
+ align:start position:0%
+Cobalt is N9 so we have 9 - 2 or seven
+so we have a D7
+
+ align:start position:0%
+so we have a D7
+ 
+
+ align:start position:0%
+so we have a D7
+system so for this we'll have a
+
+ align:start position:0%
+system so for this we'll have a
+ 
+
+ align:start position:0%
+system so for this we'll have a
+difference depending on whether you have
+
+ align:start position:0%
+difference depending on whether you have
+ 
+
+ align:start position:0%
+difference depending on whether you have
+a weak field or a strong field and how
+
+ align:start position:0%
+a weak field or a strong field and how
+ 
+
+ align:start position:0%
+a weak field or a strong field and how
+you put in your seven different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons so again if we look at the two
+
+ align:start position:0%
+electrons so again if we look at the two
+ 
+
+ align:start position:0%
+electrons so again if we look at the two
+different conditions
+
+ align:start position:0%
+different conditions
+ 
+
+ align:start position:0%
+different conditions
+if we first do this with a weak field
+
+ align:start position:0%
+if we first do this with a weak field
+ 
+
+ align:start position:0%
+if we first do this with a weak field
+then we're going to want to put in our
+
+ align:start position:0%
+then we're going to want to put in our
+ 
+
+ align:start position:0%
+then we're going to want to put in our
+electrons to the fullest extent possible
+
+ align:start position:0%
+electrons to the fullest extent possible
+ 
+
+ align:start position:0%
+electrons to the fullest extent possible
+before pairing so we would go in put one
+
+ align:start position:0%
+before pairing so we would go in put one
+ 
+
+ align:start position:0%
+before pairing so we would go in put one
+2 3 four five now we fill we put one in
+
+ align:start position:0%
+2 3 four five now we fill we put one in
+ 
+
+ align:start position:0%
+2 3 four five now we fill we put one in
+all of them so then we're going to come
+
+ align:start position:0%
+all of them so then we're going to come
+ 
+
+ align:start position:0%
+all of them so then we're going to come
+back and do six seven down
+
+ align:start position:0%
+back and do six seven down
+ 
+
+ align:start position:0%
+back and do six seven down
+here and so this will be the maximum
+
+ align:start position:0%
+here and so this will be the maximum
+ 
+
+ align:start position:0%
+here and so this will be the maximum
+number of unpair that you can possibly
+
+ align:start position:0%
+number of unpair that you can possibly
+ 
+
+ align:start position:0%
+number of unpair that you can possibly
+have or a high spin uh system in this
+
+ align:start position:0%
+have or a high spin uh system in this
+ 
+
+ align:start position:0%
+have or a high spin uh system in this
+case with a strong field takes a lot of
+
+ align:start position:0%
+case with a strong field takes a lot of
+ 
+
+ align:start position:0%
+case with a strong field takes a lot of
+energy to put the electrons up there so
+
+ align:start position:0%
+energy to put the electrons up there so
+ 
+
+ align:start position:0%
+energy to put the electrons up there so
+you're going to want to put them all in
+
+ align:start position:0%
+you're going to want to put them all in
+ 
+
+ align:start position:0%
+you're going to want to put them all in
+the bottom until you're done and you
+
+ align:start position:0%
+the bottom until you're done and you
+ 
+
+ align:start position:0%
+the bottom until you're done and you
+can't put anym down here when you have
+
+ align:start position:0%
+can't put anym down here when you have
+ 
+
+ align:start position:0%
+can't put anym down here when you have
+this strong field when you have this big
+
+ align:start position:0%
+this strong field when you have this big
+ 
+
+ align:start position:0%
+this strong field when you have this big
+big large splitting in energy the
+
+ align:start position:0%
+big large splitting in energy the
+ 
+
+ align:start position:0%
+big large splitting in energy the
+splitting in energy is much greater than
+
+ align:start position:0%
+splitting in energy is much greater than
+ 
+
+ align:start position:0%
+splitting in energy is much greater than
+the pairing energy better to pair than
+
+ align:start position:0%
+the pairing energy better to pair than
+ 
+
+ align:start position:0%
+the pairing energy better to pair than
+to put electrons up here so now would do
+
+ align:start position:0%
+to put electrons up here so now would do
+ 
+
+ align:start position:0%
+to put electrons up here so now would do
+one 2 3 four five six and unfortunately
+
+ align:start position:0%
+one 2 3 four five six and unfortunately
+ 
+
+ align:start position:0%
+one 2 3 four five six and unfortunately
+we have seven so one will have to go up
+
+ align:start position:0%
+we have seven so one will have to go up
+ 
+
+ align:start position:0%
+we have seven so one will have to go up
+there but only one so you see that the
+
+ align:start position:0%
+there but only one so you see that the
+ 
+
+ align:start position:0%
+there but only one so you see that the
+diagrams are different for seven with uh
+
+ align:start position:0%
+diagrams are different for seven with uh
+ 
+
+ align:start position:0%
+diagrams are different for seven with uh
+D7 system depending on whether you're a
+
+ align:start position:0%
+D7 system depending on whether you're a
+ 
+
+ align:start position:0%
+D7 system depending on whether you're a
+weak field or a strong field here you
+
+ align:start position:0%
+weak field or a strong field here you
+ 
+
+ align:start position:0%
+weak field or a strong field here you
+would have the minimum number one of
+
+ align:start position:0%
+would have the minimum number one of
+ 
+
+ align:start position:0%
+would have the minimum number one of
+unpaired electrons low spin here you
+
+ align:start position:0%
+unpaired electrons low spin here you
+ 
+
+ align:start position:0%
+unpaired electrons low spin here you
+have the maximum number uh which is
+
+ align:start position:0%
+have the maximum number uh which is
+ 
+
+ align:start position:0%
+have the maximum number uh which is
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+three and we can uh do our DN count here
+
+ align:start position:0%
+three and we can uh do our DN count here
+ 
+
+ align:start position:0%
+three and we can uh do our DN count here
+so now we have five
+
+ align:start position:0%
+so now we have five
+ 
+
+ align:start position:0%
+so now we have five
+electrons in
+
+ align:start position:0%
+electrons in
+ 
+
+ align:start position:0%
+electrons in
+t2g and we have two electrons in
+
+ align:start position:0%
+t2g and we have two electrons in
+ 
+
+ align:start position:0%
+t2g and we have two electrons in
+EG over here in t2g we have six and in
+
+ align:start position:0%
+EG over here in t2g we have six and in
+ 
+
+ align:start position:0%
+EG over here in t2g we have six and in
+EG we have only
+
+ align:start position:0%
+EG we have only
+ 
+
+ align:start position:0%
+EG we have only
+one and for the uh Crystal field uh
+
+ align:start position:0%
+one and for the uh Crystal field uh
+ 
+
+ align:start position:0%
+one and for the uh Crystal field uh
+splitting energy on this side we would
+
+ align:start position:0%
+splitting energy on this side we would
+ 
+
+ align:start position:0%
+splitting energy on this side we would
+have 5 * minus 2
+
+ align:start position:0%
+have 5 * minus 2
+ 
+
+ align:start position:0%
+have 5 * minus 2
+fths plus 2 * 3
+
+ align:start position:0%
+fths plus 2 * 3
+ 
+
+ align:start position:0%
+fths plus 2 * 3
+fths or a total of minus 4 FS
+
+ align:start position:0%
+fths or a total of minus 4 FS
+ 
+
+ align:start position:0%
+fths or a total of minus 4 FS
+times the splitting energy again we
+
+ align:start position:0%
+times the splitting energy again we
+ 
+
+ align:start position:0%
+times the splitting energy again we
+could add 2 PE for the pairing energy if
+
+ align:start position:0%
+could add 2 PE for the pairing energy if
+ 
+
+ align:start position:0%
+could add 2 PE for the pairing energy if
+that was asked for so optional plus 2
+
+ align:start position:0%
+that was asked for so optional plus 2
+ 
+
+ align:start position:0%
+that was asked for so optional plus 2
+PE and on this side we're going to have
+
+ align:start position:0%
+PE and on this side we're going to have
+ 
+
+ align:start position:0%
+PE and on this side we're going to have
+6 *
+
+ align:start position:0%
+6 *
+ 
+
+ align:start position:0%
+6 *
+-25 plus we have
+
+ align:start position:0%
+-25 plus we have
+ 
+
+ align:start position:0%
+-25 plus we have
+1 3 fths or an answer of - 9 FS times
+
+ align:start position:0%
+1 3 fths or an answer of - 9 FS times
+ 
+
+ align:start position:0%
+1 3 fths or an answer of - 9 FS times
+the octahedral crystal field splitting
+
+ align:start position:0%
+the octahedral crystal field splitting
+ 
+
+ align:start position:0%
+the octahedral crystal field splitting
+energy and again optional we could add
+
+ align:start position:0%
+energy and again optional we could add
+ 
+
+ align:start position:0%
+energy and again optional we could add
+three pairing energies for
+
+ align:start position:0%
+three pairing energies for
+ 
+
+ align:start position:0%
+three pairing energies for
+those okay wow we finished on time given
+
+ align:start position:0%
+those okay wow we finished on time given
+ 
+
+ align:start position:0%
+those okay wow we finished on time given
+all the technical uh issues that's great
+
+ align:start position:0%
+all the technical uh issues that's great
+ 
+
+ align:start position:0%
+all the technical uh issues that's great
+you should be able to finish your whole
+
+ align:start position:0%
+you should be able to finish your whole
+ 
+
+ align:start position:0%
+you should be able to finish your whole
+problem set and have uh experience doing
+
+ align:start position:0%
+problem set and have uh experience doing
+ 
+
+ align:start position:0%
+problem set and have uh experience doing
+these kinds of diagrams
\ No newline at end of file
diff --git a/g14939TMTCE.txt b/g14939TMTCE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a2b673b00257dfeafe0591a2fb5e080afbbccf63
--- /dev/null
+++ b/g14939TMTCE.txt
@@ -0,0 +1,2393 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional material from
+
+hundreds the MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR BAWENDI: Last time you
+talked about the first law
+
+of thermodynamics.
+
+And you talked about isothermal
+expansion, the
+
+Joule expansion.
+
+You saw a very important result.
+which is that for an
+
+ideal gas, the energy content
+is only dependent on the
+
+temperature, nothing else.
+
+Not the volume, not the
+pressure, it just cares about
+
+the temperature.
+
+So, if you have an isothermal
+process for an ideal gas, the
+
+energy doesn't change. q plus
+w is equal to zero for any
+
+isothermal process.
+
+And you also saw that du then
+could be written as Cv dT for
+
+an ideal gas always.
+
+This is not generally true.
+
+If you have a real gas and you
+write du is Cv dT, and your
+
+path is not a constant
+volume path, then you
+
+are making a mistake.
+
+But for an ideal gas, you
+can always write this.
+
+And this turns out to be very
+useful to remember.
+
+OK, now most processes that we
+deal with are not constant
+
+volume processes.
+
+So energy, which has this
+wonderful property here, du is
+
+Cv dt for constant volume
+process, which happens to be
+
+equal to d q, constant volume,
+because there's no change.
+
+there's no work if you've got
+a constant volume process.
+
+So du here is a very interesting
+quantity, because
+
+it's related to the heat that's
+going in or out of the
+
+system under constant
+volume process.
+
+But as I said, we're not
+operating usually in a
+
+constant volume environment.
+
+When I flail my arms around
+I generate work and heat.
+
+This is not a constant
+volume process.
+
+If I'm the system, what's
+constant when I do this?
+
+Anybody have an idea?
+
+What's the one function
+of state?
+
+I'm the system, the rest
+are the surrounding.
+
+What's the one function of state
+that's constant when I'm
+
+doing all my chemical
+reactions to
+
+move my arms around?
+
+Temperature?
+
+STUDENT: Pressure?
+
+PROFESSOR BAWENDI:
+Pressure, right.
+
+Pressure is constant.
+
+What is the pressure at?
+
+One atmosphere, one bar.
+
+So the most interesting
+processes are the processes
+
+where pressure is constant.
+
+When I had have a vial on bench
+top, and I do a chemical
+
+reaction in the vial, and it's
+open to the atmosphere, the
+
+pressure is constant
+at one atmosphere.
+
+When you've got your cells
+growing in your petri dish,
+
+the pressure is constant at
+one atmosphere, even if
+
+they're evolving gas, pressure
+is constant.
+
+So we'd really like to be able
+to find some sort of equation
+
+of state, or some sort of
+rather function of state
+
+that's going to relate the heat
+going in or out of the
+
+system with that function of
+state, because this isn't
+
+going to do it. du only relates
+to the heat under
+
+constant volume.
+
+And the heat is a really
+important thing to know.
+
+How much heat do you need to put
+into a system, or how much
+
+heat is going to come out of
+a system when something is
+
+happening in the system?
+
+All right, this is a really
+important quantity to know.
+
+Your boiling water or whatever,
+you want to know how
+
+much heat do you need to boil
+that amount of water under
+
+constant pressure?
+
+And this is where enthalpy
+comes in.
+
+You've all heard of enthalpy.
+
+H we're going to write it as
+the function of temperature
+
+and pressure.
+
+And the reason enthalpy was
+invented was exactly for that
+
+reason, because we need some
+way to figure out how to
+
+relate the heat coming in or
+out of a system under a
+
+constant pressure process.
+
+Because it's so important.
+
+And I should add and also under
+reversible work, where
+
+the external pressure is equal
+to the internal pressure.
+
+OK, so we're going to define
+enthalpy as u + pV, these are
+
+all functions of state here, So
+H is a function of state,
+
+and we're going to see now how
+this is, indeed, related to
+
+the heat flow in and
+out of the system.
+
+If you have a constant
+pressure,
+
+reversible work process.
+
+Let's take a system.
+
+Under constant pressure T1, V1,
+going to a second -- this
+
+is the system, so let me
+write the system here.
+
+And it's more dramatic if the
+system is a gas, p, T2, V2,
+
+And let's look at what happens
+to these functions of state,
+
+to H to u under this
+transformation.
+
+OK, so let's look at delta u.
+
+Delta u is q plus w.
+
+That's the first law.
+
+And this is a constant pressure
+path, so now I can
+
+write, this q is actually q
+under constant pressure.
+
+Little p means the path is
+a constant pressure path.
+
+And I'm doing reversible work.
+
+So that w is minus p, dV where
+p is the pressure inside the
+
+system, minus p delta V.
+Rearrange that, delta u is
+
+plus p delta V is
+equal to q p.
+
+All right, so this is the heat
+flowing in or out of the
+
+system, and these are all
+functions of state.
+
+This depends on the path.
+
+It tells you right here, the
+path is constant pressure.
+
+These don't depend on
+the path, right.
+
+V doesn't care how you
+get there. u doesn't
+
+care how you get there.
+
+In this case, p is a constant
+because the path is constant.
+
+So we can bring the p
+inside, delta u plus
+
+delta p V it's q p.
+
+Take this delta outside again,
+delta of u plus p V
+
+is equal to q p.
+
+And there you have it.
+
+There is the H right there.
+
+The u plus p V. Delta
+H is equal to q V.
+
+And this is the reason why
+enthalpy was invented, and why
+
+it's so important.
+
+Because we want to know this.
+
+So this for a finite change.
+
+If you want to have an
+infinitestimally small change,
+
+you end up writing
+dh is dq sub p.
+
+It's not always equal
+to the heat.
+
+It's only equal to the heat if
+your process is constant
+
+pressure reversible work.
+
+OK, so this is the kind of, this
+is the kind of concept
+
+that needs to be branded into
+your brain, so that if I come
+
+into your bedroom in the middle
+of the night and I
+
+whisper to you delta H, you
+know, you should wake up and
+
+say q p, right?
+
+Heat under constant pressure
+reversible work.
+
+This should become
+second nature.
+
+This is where the intuition
+comes from.
+
+This is why people
+right tables and
+
+tables of delta H's.
+
+Why you have delta H's from all
+these reactions, because
+
+this is basically the heat, and
+the heat is something we
+
+can measure, we can control.
+
+We can figure out how
+much heat is going
+
+in and out of something.
+
+This is what we're
+interested in.
+
+OK, so last time you
+looked at -- any
+
+questions on this first?
+
+Yes.
+
+STUDENT: [INAUDIBLE] from the T
+delta V to the delta p here?
+
+What was the reasoning
+behind that?
+
+PROFESSOR BAWENDI: p
+is constant here.
+
+It's constant pressure.
+
+OK, so now, last time you looked
+at the Joule expansion
+
+to teach you how to relate
+derivatives like du/dV.
+
+du/dV under constant
+temperature. du/dT under
+
+constant volume.
+
+You use the Joule expansion
+to find these quantities.
+
+Now these quantities were
+useful because you could
+
+relate them.
+
+The slope of changes, with
+respect to volume or
+
+temperature of the energy with
+respect to quantities that you
+
+understood, that you
+could measure.
+
+We're going to do the
+same thing here.
+
+So if we take as our natural
+variables for enthalpy to be
+
+temperature and pressure, and we
+have some sort of change in
+
+enthalpy, dH, and it's going
+to be related to changes in
+
+temperature and pressure through
+the derivatives dH
+
+through the slope of the
+enthalpy in the T direction,
+
+keeping pressure constant, dT
+plus the slope of enthalpy in
+
+the pressure direction, keeping
+the temperature
+
+constant, dp, and these are
+knobs that we can turn.
+
+We can change of temperature.
+
+We can change the pressure.
+
+These are physical knobs that
+are available to us as
+
+experimentalists.
+
+And so when we turn these knobs
+on our system, we want
+
+to know how the enthalpy is
+changing for that system.
+
+Because eventually they will
+tell us maybe things about how
+
+heat is changing further on.
+
+OK, but in order to relate
+turning these physical knob to
+
+this quantity here, which we
+don't have a very good feel
+
+for, we've got to have a
+feel for the slopes.
+
+If I keep the pressure
+constant.
+
+I change the temperature,
+what does that mean?
+
+What is dh/dT?
+
+If I keep the temperature
+constant, and just change the
+
+pressure, dH is going
+to change, but how
+
+is it going to change?
+
+What does this mean in terms of
+something I can physically
+
+understand?
+
+That's the program now for
+the next few minutes.
+
+What are these quantities?
+
+What is dH/dT as a function,
+keeping pressure constant,
+
+what is dH/dp, keeping
+temperature constant?
+
+All right, let's start with the
+first one, dH/dT, keeping
+
+the pressure constant.
+
+And we're going to look at a
+reversible process to help us
+
+out, but the result is going to
+be independent of whether
+
+or not we have a reversible
+process or
+
+irreversible process.
+
+Constant pressure, that means
+dp is equal to zero.
+
+So for reversible process,
+constant
+
+pressure, what do we know?
+
+This is already branded
+in your brain, right?
+
+Reversible process, constant
+pressure dH=dq.
+
+So we can write that down,
+dH=dq, constant pressure.
+
+That's by definition
+of enthalpy.
+
+That's why we created
+enthalpy.
+
+What else do we know?
+
+Well we can go look up here,
+looking at the differential,
+
+there are no approximations
+here.
+
+This is just an equality.
+
+I have a constant pressure
+process.
+
+This term here is
+equal to zero.
+
+That means that dH is also
+equal to dH/dT, constant
+
+pressure dT.
+
+All right, so now I've got
+more dH/dT under constant
+
+pressure. dH is equal to this,
+and it's also equal to this.
+
+All right, these two are
+equal to each other.
+
+Now, I know how to relate the
+heat flow to temperature
+
+change, through the heat
+capacity. dq constant pressure
+
+is that heat capacity, and I
+have to tell you the path for
+
+the heat capacity.
+
+So it's C sub p, the heat
+capacity under a constant
+
+pressure path, dT, all right?
+
+So these two are equal
+to each other.
+
+So, these two are equal to
+each other as well, which
+
+tells me that this derivative,
+dH/dT constant pressure is Cp.
+
+So now I have my first of my
+two slopes, in terms of
+
+something that's related to my
+system, the heat capacity of
+
+the system.
+
+Something I can measure and I
+can tabulate, and when I turn
+
+my dT knob here I know
+what's going to
+
+happen to the enthalpy.
+
+So this is the first,
+this is the one.
+
+So it's very similar to what we
+saw with the volume and the
+
+energy, where du/dV under
+constant temperature was equal
+
+to Cv in this case here, right.
+and you're going to
+
+find that there's a lot of these
+analogies between energy
+
+and enthalpy.
+
+You just change volume to
+pressure and basically you're
+
+looking at enthalpy under a
+constant -- anything that's
+
+done at a constant volume path
+with energy, there's the same
+
+thing happening under constant
+pressure path for enthalpy.
+
+So you can guess the answer
+usually that way.
+
+OK, so now we have the other
+one, dH/dp constant
+
+temperature.
+
+How do we relate this to
+something physical?
+
+Well, it's going to be an
+experiment, very much like the
+
+Joule experiment.
+
+The Joule experiment
+was a constant
+
+energy experiment, right.
+
+Here we're going to have to
+find a constant enthalpy
+
+experiment, and that is going
+to be the Joule-Thomson
+
+experiment.
+
+That's going to extract out
+a physical meaning to this
+
+derivative here.
+
+OK, the Joule-Thomson
+experiment.
+
+This is going to get us dH/dp
+constant temperature.
+
+What is this experiment?
+
+You take a throttle valve, which
+consists of some sort of
+
+porous plug between two
+cylinders that is insulated.
+
+There is insulation here.
+
+Insulation on the bottom.
+
+It's like a, think about a tube,
+a large tube, insulated
+
+tube, with a bunch of -- a
+frit inside here, which
+
+prevents flow of gas, which
+slows down the flow of gas
+
+from one side to the other.
+
+It's a blockage in
+this tube here.
+
+Then you put two pistons, one on
+that side here, and one on
+
+this side here, and the external
+pressure here, we're
+
+going to call that p1.
+
+The external pressure here,
+we're going to call that p2,
+
+and we're going to do it
+slowly enough that the
+
+pressure on this side of the
+cylinder is in equilibrium
+
+with the external pressure, and
+the pressure on this side
+
+of the cylinder is in
+
+equilibrium with this pressure.
+
+But not so slowly that these
+two are in equilibrium with
+
+each other.
+
+So this is restricting
+the flow, so there's
+
+some sweet spot here.
+
+When I'm pushing slowly enough
+here that the pressure here is
+
+equal to that one, but not so
+slowly that the air flow from
+
+here to here is fast, compared
+to how fast I'm pushing.
+
+You got the picture here?
+
+Any questions on that?
+
+All right, then as I push
+through, I'm going to start
+
+with all of my gas on this
+side, and at the end, I'm
+
+going to have all the gas
+on the other side.
+
+Let me first ask you this, is
+this a reversible or in
+
+irreversible process?
+
+Right, let me add one more piece
+of data here which I
+
+said in words, but which is
+actually important to write
+
+down before doing the problem.
+
+Is this a reverse
+-- any guesses?
+
+How many people vote for that
+this is a reversible process?
+
+I've got one vote back
+there, two votes,
+
+three votes, four votes.
+
+Anybody else?
+
+How many people think this
+is irreversible?
+
+It's about a tie, and everybody
+else doesn't now.
+
+All right, I'm going to give
+you ten seconds, fifteen
+
+seconds to make up your mind.
+
+You're not allowed to be
+on the fence here.
+
+You've got to decide,
+all right?
+
+This is, you can talk to your
+neighbors, you know, do a
+
+little bit of thinking.
+
+And I'm going to give you ten
+seconds to figure this out,
+
+what your vote is for that.
+
+All right, let's try again.
+
+How many people vote that
+this is reversible?
+
+That looks like a
+majority to me.
+
+Irreversible?
+
+Let's look at the
+show of hands?
+
+All right, so this is
+the majority here.
+
+Good thing physics doesn't
+work on the rule of the
+
+majority, otherwise we'd
+be in big trouble.
+
+Wow, let's walk through that.
+
+I'm sorry to say that this
+is the wrong answer.
+
+OK, why is that the
+wrong answer?
+
+Well, just think, you know,
+think about it.
+
+You're pushing through here.
+p1 is greater than p2.
+
+What does it mean for a process
+to be in equilibrium
+
+or reversible?
+
+It means at any point you can
+reverse the direction of time,
+
+and it will look fine, right.
+
+So now I'm pushing on this
+plug here, with p1
+
+greater than p2.
+
+I'm pushing, I'm pushing,
+I'm pushing. p1 is
+
+greater than p2.
+
+Then I want to reverse
+direction of time.
+
+I want the arrow of time to go
+so that the gas goes from p2
+
+to p1. p2 is less than p1.
+
+Is that going to work out?
+
+If p2, the pressure in p2, is
+less than the pressure in p1,
+
+is the gas going to want to go
+from p2 to p1 and the whole
+
+thing reverse back?
+
+You've got to put more pressure
+on one side than the
+
+other if you want to push
+that gas through
+
+the throttle, right?
+
+So this is where the time scale
+issue comes into play.
+
+I said let's do this slowly
+enough that this p1 is in
+
+equilibrium with this p1, but
+not so slowly that this
+
+pressure is equivalent
+to that pressure.
+
+If I do it really, really
+slowly, so that everything is
+
+reversible, well I won't be able
+to do it, because p1 and
+
+p2 are different.
+
+But suppose that I fix my
+pistons here, with p1 greater
+
+than p2, and I don't touch
+it, eventually p1
+
+will be equal to p2.
+
+I'll come to some sort
+of equilibrium.
+
+So this is a system which
+is out of equilibrium.
+
+If I stop, if I move slowly,
+if I move more slowly, then
+
+these two will want
+equilibrium.
+
+So this is an irreversible
+process.
+
+The Joule-Thomson experiment
+is irreversible.
+
+OK, important -- if you are part
+of this group here, think
+
+about it and make sure
+you understand that.
+
+All right, so this is
+the experiment.
+
+Now what are we doing
+with that?
+
+The initial state, let's look
+at what we are doing.
+
+So initially, we're going to
+have our piston, there's the
+
+plug sitting here.
+
+Our piston on the right side
+here fully out, and the piston
+
+on my right side, your left
+side, fully inside.
+
+There's no gas on
+that side here.
+
+So there's p2 sitting here.
+
+There is p1 sitting here, and
+all of the gas is sitting on
+
+that side of the plug.
+
+Then after we're done with the
+experiment, we'll have
+
+transferred all of the gas from
+one side to the other. p1
+
+here. p2 sitting here.
+
+And there's going to be some
+volume V2 and some volume V1,
+
+but are not necessarily
+the same.
+
+Especially since the pressures
+are different. we don't know
+
+yet about temperature so I don't
+know what to say about
+
+these volumes because I don't
+know what the temperatures'
+
+are going to do.
+
+OK, so let's go through this and
+see what we would do which
+
+is to calculate the
+heat and the work.
+
+This is well insulated.
+
+So, what is the -- let's
+do the first one here.
+
+What's q for this process here?
+
+Anybody?
+
+STUDENT Zero.
+
+PROFESSOR BAWENDI:
+Zero, right.
+
+This is an adiabatic process.
+
+It's well insulated.
+
+Heat is not going in or out,
+adiabatic. q is equal to zero.
+
+So all we need to find
+out is the work now.
+
+Let's divide it up into the two
+sides, the work going on
+
+on the left hand side, my left
+hand side or your left hand
+
+side, and the work going on
+on the right hand side.
+
+So let's first look at
+the left hand side.
+
+OK, so w, first of all, work is
+being done to the system on
+
+the left hand side here.
+
+I'm pressing on the gas.
+
+So I expect that to be
+a positive number.
+
+The pressure is constant, p.
+
+The V goes from V1 to zero.
+
+So we write down p1, V1.
+
+On the right hand side, the
+work, let's call this left
+
+hand side, let's call this
+right hand side.
+
+Here there's an expansion going
+on, so the system is
+
+doing work to the
+external world.
+
+This piston is being brought
+out, so we expect the work to
+
+be negative, negative.
+
+And we start out with
+zero volume.
+
+We end up with a volume of V2,
+and the external pressure is
+
+constant to p2.
+
+Minus p2, V2.
+
+Minus p delta V. So the total
+work is the work from the left
+
+hand side plus the work on the
+right hand side, which is p1
+
+V1 minus p2 V2.
+
+Which I can rewrite
+as minus delta pV.
+
+Delta pV is p2 V2 minus p1 V1.
+
+It's the pressure volume
+multiplied together at the
+
+final state, minus pressure
+volume from the initial state,
+
+with the minus sign
+here because it's
+
+the negative of that.
+
+All right, what is delta u?
+delta u is q plus w. q is
+
+zero. delta u is just w.
+
+So this is also just delta u.
+delta u is minus delta pV, for
+
+the process.
+
+OK, delta H is delta
+of u plus pV.
+
+By definition, that's how we
+define enthalpy up here.
+
+H is u plus pV.
+
+Delta H is delta of u plus pV,
+which is equal to delta u,
+
+plus delta pV.
+
+Now delta u is minus delta pV.
+
+So I have minus delta
+pV plus delta pV.
+
+This is equal to zero.
+
+So this irreversible process,
+this Joule-Thomson process, is
+
+a constant enthalpy process.
+
+Delta h for this process
+is equal to zero.
+
+Adiabatic q equal to zero.
+
+It's also delta H
+which is zero.
+
+The two didn't necessarily
+follow, because remember,
+
+delta H is dq so p is only true
+for a reversible constant
+
+pressure process.
+
+This is an irreversible
+process.
+
+So a priori, this was not
+necessarily true.
+
+It turns out after you do all
+the math, it turns out to be
+
+delta H equals zero.
+
+All right, so this is
+the experiment.
+
+How do we go from that
+experiment to the terms that
+
+we're trying to get,
+these slopes.
+
+Remember, we're trying to get
+delta H, we're trying to get
+
+dH/dT constant pressure and
+dH/dp constant temperature.
+
+OK, these are the two things
+were trying to get here.
+
+OK, so let's write down,
+what we know here.
+
+I'm missing something.
+
+Oh, we already know one thing.
+
+We already know this guy here.
+
+We already did that.
+
+OK, dH/dT constant
+pressure is Cp.
+
+That was easy one.
+
+So we already know that.
+
+So now we can write or
+differential dH as Cp dT plus
+
+dH/dp, constant temperature,
+dp.
+
+Now we want to find out
+what this guy is here.
+
+Now for this experiment, this
+is a constant enthalpy
+
+experiment for the Joule-Thomson
+experiment, this
+
+is equal to zero.
+
+So I can rearrange this to get
+this dH/dp in terms of things
+
+that I can either measure, like
+the heat capacity, or
+
+that I have control of,
+like dT and dp.
+
+So in this case, dH/dp constant
+temperature is minus
+
+Cp dT/dp, and this is under
+constant temperature, no, not
+
+constant temperature.
+
+Whatever the experi -- for
+that the experiment is.
+
+For that experiment, the
+constraint, so we need a
+
+constraint here, right, we
+need a constraint here.
+
+Right?
+
+We need a constraint here.
+
+The constraint isn't constant
+temperature because the
+
+temperature is going
+to be changing.
+
+It's not constant pressure,
+because we have a
+
+delta p going on.
+
+It's not constant
+volume either.
+
+The constraint is the constraint
+of the experiment,
+
+and the constraint of the
+experiment is that the
+
+enthalpy is constant.
+
+So the constraints
+we have here, is
+
+the constant enthalpy.
+
+It's the constant enthalpy
+process that we're looking at.
+
+This we can do experiments on.
+
+It's tabulated in books, and
+this we can measure in the
+
+experiment.
+
+Delta p here is the change in
+pressure from the left side to
+
+the right side, and we can put
+a thermometer, measure the
+
+temperature before the
+experiment, and measure the
+
+temperature after
+the experiment.
+
+So this is something
+we can measure.
+
+So now we have this derivative,
+in terms of
+
+physical quantities, things
+that we can measure.
+
+Things that we can relate
+to the properties of the
+
+substance that we're doing
+the experiment on.
+
+So this is basically delta
+T and delta p and the
+
+Joule-Thomson experiment.
+
+And so Joule and Thomson did
+these experiments, and they
+
+measured lots of gases, and they
+found that, in fact, this
+
+was something that they
+could measure.
+
+Sometimes it was positive,
+sometimes it was negative, and
+
+it was an interesting number.
+
+And so they defined them, after
+many experiments, the
+
+limit of this, delta T delta p
+and the limit of delta p goes
+
+to zero as the Joule-Thomson
+coefficient.
+
+So, basically dT/dp, constant
+enthalpy is equal to mu, by
+
+definition, Joule-Thomson, where
+mu Joule-Thomson is the
+
+Joule-Thomson coefficient, just
+like you saw last time
+
+eta sub j was the Joule
+coefficient for dT/dV under
+
+constant energy.
+
+So there's, again, total analogy
+here between what
+
+we're doing with enthalpy to
+what you did last time with
+
+energy, replace p with
+T and H with u.
+
+Flip those two and you
+get the same thing.
+
+OK, so now we have dH/dT is
+equal to Cp, and we can also
+
+write, then, dH/dp under
+constant temperature is equal
+
+to minus Cp mu Joule-Thomson.
+
+We have our two derivatives in
+terms of physical quantities,
+
+which is going to allow us,
+then, whenever we have a
+
+change to go back and, when we
+have a change where we adjust
+
+the temperature and the
+pressure, we'll be able to
+
+know what the enthalpy
+change is.
+
+OK, now let's take two cases.
+
+Let's first start talking
+about ideal gases.
+
+The last time you saw that for
+an ideal gas, the energy only
+
+cared about the temperature.
+
+It didn't care what the volume
+was doing. du/dV under
+
+constant temperature was equal
+to zero for an ideal gas.
+
+And by analogy, we expect the
+same thing to be true here,
+
+because enthalpy and energy
+have all this
+
+analogy going on here.
+
+So let's look at an ideal gas.
+
+So for an ideal gas, we saw that
+u was only a function of
+
+temperature.
+
+We also have the equation
+of state for an
+
+ideal gas, pV = nRT.
+
+We can write our definition of
+enthalpy, h is u plus pV.
+
+This only depends on the
+temperature. pV= nRT.
+
+So we have u only depends
+on temperature plus nRT.
+
+The only valuable now on this
+side is temperature.
+
+Pressure and volume
+have dropped out.
+
+So enthalpy, for an ideal gas,
+only cares about temperature.
+
+Pressure has dropped out of the
+picture completely here.
+
+So there is no p dependence
+here.
+
+H for an ideal gas is only a
+function of temperature.
+
+This is not true for a real
+gas, fortunately, but it's
+
+true for an ideal gas.
+
+So for an ideal gas then,
+dH/dp under constant
+
+temperature, that has
+to be equal to zero.
+
+Because temperature is constant
+H only cares about
+
+temperature. and that's
+equal to zero.
+
+And if that's equal to zero,
+that means that the
+
+Joule-Thomson coefficient
+for an ideal gas is
+
+also equal to zero.
+
+We're going to actually prove
+this later in the course.
+
+Right now, you're taking
+it for granted.
+
+Right now we told you Joule did
+all these experiments and
+
+he found out that for an ideal
+gas, that the limit in and
+
+ideal gas case was that the
+eta J was equal to zero.
+
+Therefore, from experiments,
+u is only a function of
+
+temperature for an ideal gas,
+and therefore from these
+
+experiments, we come
+out with delta H
+
+dH/dp is equal to zero.
+
+The Joule-Thomson coefficient
+is equal to zero.
+
+Later we are going to prove it
+exactly. but right now you're
+
+going to have to take
+it for granted.
+
+So, if the Joule-Thomson
+coefficient is equal to zero,
+
+just like we wrote, du = Cv dT
+for an ideal gas, we're going
+
+to have dH = Cp dT for
+an ideal gas as well.
+
+dH is Cp dT.
+
+This term goes away.
+dH = Cp dT.
+
+That's the only thing
+that's left behind.
+
+So if you know the heat
+capacity, you know the change
+
+in temperature, you know
+what enthalpy is doing
+
+for an ideal gas.
+
+This needs to be stressed that
+this is the ideal gas case.
+
+Now regular gases, real gases,
+fortunately as I
+
+said, don't obey this.
+
+This is important because we
+use this all the time for
+
+when, when we do technology.
+
+One example of Joule-Thomson
+coefficient being not equal to
+
+zero for a real gas that you've
+like experienced is if
+
+you take a bicycle pump, take
+a bicycle pump, and you're
+
+pumping up your tire, you're
+working pretty hard, so you're
+
+getting hot.
+
+But if you touch the valve going
+into your tire, which
+
+basically measures the
+temperature of the air going
+
+into your tire, that is
+getting hot, right.
+
+So if you've got to pump that
+tire really a lot, then you're
+
+going to you're going
+to really feel
+
+a lot of heat there.
+
+The compression of the,
+basically it's an adiabatic
+
+compression.
+
+You're taking the air inside
+of the pump and you're
+
+compressing it.
+
+You're doing it so fast that
+there's not enough time for
+
+heat to come out of the gas
+that's inside the pump towards
+
+the walls of the pump.
+
+So your time scale it just
+fast enough that this is
+
+basically an adiabatic
+compassion.
+
+Your compressing it really fast,
+all right, so you're
+
+changing the pressure.
+
+You're changing the pressure,
+and the temperature is going
+
+up. dT/dp is positive. dT/dp
+is positive. dT/dp is
+
+positive, well that's mu
+JT. dT/dp is mu JT.
+
+So for a real gas like air,
+this is a positive number.
+
+It's not zero.
+
+Air is not an ideal gas.
+
+It's one simple example of --
+
+The fact that mu JT is not zero
+for real gases is how we
+
+are able to liquify things like
+hydrogen and helium, by
+
+compressing them and pushing
+them through a nozzle, and the
+
+expansion through the nozzle
+cools the gas.
+
+Right, in this case here it
+wouldn't happen if it
+
+was an ideal gas.
+
+Or in many kinds of gas
+refrigerators where you push a
+
+gas through a nozzle close to
+room temperature, what you
+
+find is that the gas coming out
+on the other side under
+
+lower pressure is cooler than
+the gas that went through on
+
+the other side.
+
+Real refrigerators actually work
+with liquids that go into
+
+gases so use the latent heat of
+the liquid, so it doesn't
+
+really work like the
+Joule-Thomson expansion.
+
+So this is real.
+
+This is real, unlike the Joule
+coefficient which is very
+
+small so that most gases have
+tiny Joule coefficients.
+
+So if you do a Joule experiment,
+you hardly measure
+
+a temperature change.
+
+With real gases, here you
+do actually measure it.
+
+You can feel it with your finger
+on your bicycle tire.
+
+OK, so we're going to see this
+using a Van der Waal's gas.
+
+Let's look at a Van der Waal's
+gas and see what happens in
+
+the Van der Waal's gas.
+
+Any questions, first?
+
+What we've been talking about,
+the Joule-Thomson experiment,
+
+constant enthalpy process?
+
+OK, so let's take our
+Van der Waal's gas.
+
+Remember the equation of state
+for Van der Waal's gas is not
+
+pV is equal to nRT, but p plus
+the attraction term.
+
+And then V minus the excluded
+volume term is equal to RT.
+
+Two parameters, this is the
+attraction between two atoms
+
+or molecules in the gas phase.
+
+This is the repulsion,
+not the repulsion.
+
+This is the fact that we occupy
+a finite volume in
+
+space, because they're little
+hard spheres in this molecule.
+
+OK, in a few weeks, you're going
+to find out that we can
+
+calculate dH/dp from this
+equation of state, and you're
+
+going to find out that dH/dp
+from that equation of state is
+
+proportional to b
+minus a over RT.
+
+This is going to be probably
+a homework at
+
+some point to do this.
+
+For now, let's take
+it for granted.
+
+Let's take it for granted that
+we know how to calculate this
+
+derivative from an equation
+of state like this.
+
+But now we're going
+to use that.
+
+OK.
+
+So since dH/dp under constant
+temperature is proportional to
+
+minus mu JT, then we have that
+dT/dp under constant enthalpy
+
+than it is related to the
+negative of this, a over RT
+
+minus b
+
+All right, this is how the
+temperature changes when you
+
+change, when you have
+pressure changing.
+
+So when you do an expansion or
+compression, my adiabatic
+
+compression of my bicycle
+pump is dT/dp.
+
+All right.
+
+Or when I do an expansion of
+hydrogen or helium at low
+
+temperature, through a
+Joule-Thomson experiment, when
+
+I want to liquify hydrogen
+or helium.
+
+I want to cool a gas with a
+Joule-Thomson experiment, what
+
+temperature do I
+have to be at?
+
+So this tells you that you
+have to be careful what
+
+temperature you're at, because
+depending on how high, how big
+
+this temperature here is, you
+could either be, have a
+
+negative dT/dp, if this first
+term is small enough, meaning
+
+if temperature is very high,
+then you end up with a
+
+negative term.
+
+If the temperature is very
+small, then one over the
+
+temperature is large, and the
+first term wins and you have a
+
+positive number.
+
+So there's some special
+temperature which is going to
+
+depend on the gas where the
+first term is going to be
+
+equal to the second term, where
+Joule-Thomson is zero,
+
+or it's going to behave
+like an ideal gas.
+
+So when that is the case,
+we're going to call that
+
+temperature the inversion
+temperature or T inv.
+
+We call that inversion because
+on one side you end up cooling
+
+if you compress.
+
+And on the other side of that
+temperature you end up heating
+
+if you compress.
+
+OK, so there's some temperature,
+t inversion minus
+
+b where the gas behaves
+like an ideal gas.
+
+The Joule-Thomson coefficient
+is zero and that inversion
+
+temperature, you can
+solve for it.
+
+Conversion temperature is equal
+to a over R times b.
+
+OK, so when you are at that
+temperature, everything looks
+
+like an ideal gas,
+as far as the
+
+enthalpy changes are concerned.
+
+Now if you're at the temperature
+which is higher
+
+than the inversion temperature,
+in that case
+
+here, a over RT is small
+compared to b, and this is
+
+going to turn out
+to be negative.
+
+So if you had a high
+temperature, this a small
+
+compared to b.
+
+If you're negative, which means
+that dT/dp at constant H
+
+is less than zero.
+
+So that means that if you
+compress something
+
+it's going to cool.
+
+The temperature rises when the
+pressure drops, right?
+
+Or in this case here, if I do my
+Joule experiment delta p is
+
+negative, p2 is less than p1,
+that means that delta T is
+
+positive, right?
+
+So in this experiment here, this
+side is going to heat up.
+
+So for materials where T
+inversion is low, lower than
+
+room temperature, then you would
+end up heating up in
+
+this expansion.
+
+You're basically expanding the
+gas from one side to the other
+
+and the expansion causes the
+temperature to rise.
+
+If T is less than T inversion,
+you have the opposite case,
+
+and dT/dp is greater
+than zero.
+
+So in this experiment here,
+delta p is less than zero.
+
+You need to have this whole
+thing greater than zero.
+
+So delta T is less than
+zero as well.
+
+So if you're below the inversion
+temperature and you
+
+do the Joule-Thomson experiment,
+you're going to
+
+end up with something that's
+colder on this
+
+side than that side.
+
+Ideal gas would be the
+same temperature.
+
+But now, so this is where the
+refrigeration comes in.
+
+So if you take a gas, and you're
+below the inversion
+
+temperature and you make it go
+through this irreversible
+
+process, the gas comes
+out colder from that
+
+side than that side.
+
+So the work that you're doing to
+expand, to go through this
+
+experiment, ends up
+cooling the gas.
+
+OK, for most gases, T inversion
+is much greater than
+
+300 degrees Kelvin.
+
+Much greater than room
+temperature.
+
+For more most gases, if you
+do this experiment at room
+
+temperature, you end up cooling
+the gas, and you can
+
+cool it measurably, which is why
+also, your bicycle pump,
+
+you know, you push down,
+you compress, this is
+
+an expansion here.
+
+You're expanding from this
+side to that side.
+
+Bicycle pump you are compressing
+the gas, which is
+
+the opposite, you end up heating
+up the air in the
+
+bicycle pump in your
+compression.
+
+There are two exceptions to this
+rule that most gases have
+
+a T inversion which is greater
+than 300 degrees Kelvin, and
+
+that's hydrogen.
+
+The T inversion for hydrogen
+turns out to be 193 degrees
+
+Kelvin, and the T inversion for
+helium turns out to be 53
+
+degrees Kelvin.
+
+And so when, there's a lot of
+liquid helium that's being
+
+used on campus.
+
+We use a liquid helium.
+
+And so in order to make a liquid
+helium, you can't take
+
+helium at room temperature and
+do this, because if you did,
+
+you would just heat it up,
+because the room temperature
+
+is above the inversion
+temperature, so Joule-Thomson
+
+would heat up the helium.
+
+So you need first to take the
+liquid helium and cool it
+
+below 53 degrees Kelvin before
+you can do the Joule-Thomson
+
+to cool it even further
+to make liquid helium.
+
+So you have to do
+it in stages.
+
+You take your room temperature
+liquid helium, and you cool it
+
+with liquid nitrogen to 77
+degrees Kelvin, the new,
+
+you're not quite there yet,
+unfortunately right?
+
+Then you take hydrogen you cool
+it would liquid nitrogen
+
+to 77, then you can use
+your hydrogen gas.
+
+Do a Joule-Thomson hydrogen gas
+which you first cool with
+
+liquid nitrogen.
+
+Liquid nitrogen, 77, that's
+below 193, so you can do
+
+Joule-Thomson on hydrogen, cool
+the hydrogen to below 53,
+
+then use your cold hydrogen to
+cool the helium, and then you
+
+can do the Joule-Thomson on the
+helium to cool it further
+
+until it liquifies.
+
+So that's what you do when
+you make liquid helium.
+
+All right, any questions on
+this lecture or any of the
+
+concepts that we talked about?
+
+The last thing that we're going
+to do today then is to
+
+look at a relationship which
+is going to turn out to be
+
+very useful.
+
+It's a relationship for ideal
+gases which relates the heat
+
+capacities at constant pressure
+and constant volume.
+
+Cp = Cv + R. This is very useful
+because often you just
+
+have lots of tables of Cp's but
+sometimes you want to know
+
+what the energy change is going
+to be for the ideal gas,
+
+and you know that du
+is Cv dT not Cp dT.
+
+So, you need to know what Cv
+is, and if this is true
+
+always, then there's a
+very easy way to go
+
+from one to the other.
+
+We're going to do it two ways.
+
+Today we'll do the first way,
+and then next time we'll do
+
+the second way.
+
+The first way is just to turn
+the crank on the math, and the
+
+second way is to do
+a little bit more
+
+imaginative about the process.
+
+OK, let's just turn the
+crank on the maths.
+
+What do we know about
+the Cp and Cv?
+
+Well Cp, we already know how to
+relate it to dH/dT through
+
+the slope of the enthalpy, and
+we also related Cv to the
+
+slope of the energy with respect
+to temperature under
+
+constant volume.
+
+And we also know that
+H is u plus pV.
+
+Right, H is u plus pV.
+
+So we're going to take the
+derivatives of both sides of
+
+this equation here, by, with
+respect to temperature,
+
+keeping pressure constant.
+
+So we have dH/dT keeping
+pressure constant, is du/dT
+
+keeping pressure constant.
+
+Got to keep track of what's
+being constant, kept constant,
+
+plus dPV/dT, keeping pressure
+constant. dH/dT keeping
+
+pressure constant, that's just
+Cp, and then we have du/dT
+
+keeping pressure constant.
+
+The p is constant here, comes
+out of the equation, so we
+
+have p and then we have dV/dT
+well it's an ideal gas, an
+
+ideal gas for dV/dT for an ideal
+gas is equal to R over p
+
+because pV is equal
+to RT, right.
+
+So dV/dT is Rp.
+
+So dV/dT is times R over
+p, the p's are going
+
+to cancel out here.
+
+OK, so now it's very tempting
+at this state to say, oh
+
+there's the answer right
+here. du/dT is Cv.
+
+There I have it Cp is equal
+to Cv plus R, right?
+
+But even though it looks like
+that's the right way to do it,
+
+it's actually not right because
+it turns out to be
+
+right by sort of by accident.
+
+But here you've got pressure
+constant. du, this is du, not
+
+H here. du/dT is only equal
+to Cv when the volume is
+
+constant, not when the
+pressure is constant.
+
+So if you're going to turn the
+crank on the math correctly,
+
+you're going to have to change
+this p into a V somehow.
+
+Because this isn't Cv
+mathematically speaking.
+
+We don't know what it is yet.
+
+In order to change this from a
+p to a V, you have to use the
+
+chain rule.
+
+So let's use the chain rule.
+
+And then we'll be done.
+
+OK, so u is actually a function
+of temperature and
+
+volume, which in this case here
+could be a function of
+
+pressure and temperature.
+
+So if we want du/dT under
+constant pressure, you have to
+
+use the chain rule.
+
+There's the pressure
+sitting right here.
+
+It's going to be du/dT under
+constant volume, plus du/dV
+
+dV/dT under constant pressure.
+
+All right, chain rule. du/dT
+constant pressure is the
+
+direct derivative with respect
+to temperature here, which is
+
+sitting by itself under constant
+volume, keeping this
+
+constant but there
+is temperature
+
+sitting right here too.
+
+That's where that term comes
+from, du/dV dV/dT.
+
+Now, for an ideal gas, du/dV
+under constant temperature is
+
+equal to zero.
+
+It doesn't care what the
+volume is doing.
+
+It only cares what
+temperature is.
+
+If temperature is constant,
+there's no change in energy.
+
+For an ideal gas,
+this is zero.
+
+It's not zero for a real gas.
+
+Right, so this whole term
+disappears and for an ideal
+
+gas, it turns out that du/dT
+constant pressure is equal to
+
+du/dT constant volume, but
+this is equal to Cv
+
+for an ideal gas.
+
+It wouldn't be true for a real
+gas, and this is a common
+
+mistake that people make for
+real gases to equate this.
+
+This is only true for
+an ideal gas.
+
+Since it's true for an ideal
+gas, then we can go ahead and
+
+replace this with Cv, and then
+we have Cp with Cv plus R,
+
+which is what we were after.
+
+OK, next time we'll do the other
+way of getting to the
+
+same answer.
\ No newline at end of file
diff --git a/htYyCEdc8B4.txt b/htYyCEdc8B4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..13510f9a38c14de46a309cb2e64899c6cd6b013f
--- /dev/null
+++ b/htYyCEdc8B4.txt
@@ -0,0 +1,933 @@
+PROFESSOR: Recombinant DNA,
+often referred to also as
+
+genetic engineering.
+
+This is a series of techniques,
+series of methods
+
+that allow us to manipulate DNA
+for a variety of reasons.
+
+Now, we take it for granted.
+
+It's very much part of our
+everyday life in the
+
+laboratory.
+
+It's made a huge impact on
+the biotechnology and
+
+pharmaceutical industries
+as well.
+
+It wasn't always so
+uncontroversial.
+
+In fact, in the 1960s and '70s,
+when this technology was
+
+first being developed, it was
+great concern about scientists
+
+manipulating DNA, manipulating
+genetic material.
+
+In the city of Cambridge, in
+fact, had a moratorium for a
+
+while on the practice of
+genetic engineering or
+
+recombinant DNA technology,
+which fortunately, ultimately
+
+was overcome with good practices
+and I think good
+
+education about what the real
+limits of risk and benefit
+
+were so that now it's used very
+widely and, I would also
+
+say, very safely.
+
+The bottom line for what we're
+going to talk about today and
+
+for this section of the class is
+the ability to isolate and
+
+to amplify specific
+DNA sequences.
+
+They might be particular genes
+of interest to us.
+
+They might be whole genomes.
+
+They might be other regions of
+DNA, but we need to be able to
+
+isolate them from the cells of
+the organisms of interest,
+
+amplify them up into large
+quantities in order to be able
+
+to study them in detail, and to
+make modifications in them.
+
+This is done in a variety
+of organisms for
+
+a variety of purposes.
+
+One of them, and this is by no
+means the only one, but one
+
+that sort of strikes home
+is the ability to make
+
+therapeutic proteins, to be
+able to manufacture in the
+
+laboratory or in a company
+proteins they could have
+
+benefit for patients who are,
+for example, lacking the
+
+function of a particular protein
+or enzyme leading to a
+
+disease state.
+
+One can use these methods to
+produce that protein in the
+
+laboratory, and treat
+the individual.
+
+This can be done in bacteria
+such as E. coli.
+
+E. coli, which is the common
+gut bacterium that we all
+
+carry, a very useful organism.
+
+We use it in the lab.
+
+We're going to use in our
+demonstrations today.
+
+This is the standard vehicle
+in which we'd grow up,
+
+recombinant DNA, amplify
+recombinant DNA for further
+
+uses, but we can also make
+therapeutic proteins using the
+
+manufacturing capabilities
+of the bacterium.
+
+Plants, likewise,
+can be a source
+
+of therapeutic proteins.
+
+We can modify the genomes of
+plants so they will produce in
+
+large quantities therapeutic
+proteins of interest, which
+
+then can be ingested by the
+individual, which can reduce
+
+production costs significantly,
+
+and animals, likewise.
+
+We can manipulate the genes of
+animals so that they will
+
+express a protein of interest
+and secrete that protein, for
+
+example, into the milk.
+
+So there are so-called
+transgenic cows and transgenic
+
+goats that produce therapeutic
+proteins in the mammary gland
+
+and secrete those therapeutic
+proteins into the milk.
+
+So the individual just needs to
+drink the milk and receive
+
+the relevant dose.
+
+So there are lots of ways, that
+this technology can be
+
+helpful including in the
+context of medicine.
+
+We can also engineer
+organisms.
+
+I've already given you examples
+of that, but that was
+
+really for the purposes of using
+those organisms as a
+
+factory to make something
+of interest to us.
+
+But we can manipulate the genes
+of plants, for example,
+
+to make them resistant to
+various pests to make them
+
+more robust, to give them
+a longer shelf life.
+
+We can manipulate them for the
+better production of things
+
+that are valuable to us.
+
+Again, this is a bit of
+a controversial area,
+
+genetically modified foods, not
+always well-accepted by
+
+everyone because again, the
+thought is, this might be
+
+disrupting the food chain in
+important ways, and this might
+
+be ultimately not
+so beneficial.
+
+Personally don't agree with
+that, but lots of people do
+
+feel that way.
+
+We're going to teach you the
+methods that we use to allow
+
+us to do this.
+
+And again, in work that I've
+alluded to from my own lab, we
+
+use these methods to manipulate
+the genes of
+
+animals, in our case it's mice,
+but there are lots of
+
+animal species that one can use
+in order to create, for
+
+example, disease models.
+
+We talked to you about,
+Professor Brown talked to you
+
+about genetic diseases.
+
+They have specific alterations
+in genes.
+
+We can use these methods to make
+similar alterations in
+
+the genes of mice and other
+animal species and then study
+
+the disease process in those
+animals, develop new
+
+treatments in those animals
+in ways that are
+
+hard to do in people.
+
+So there's lots and lots, and
+these are just a few examples,
+
+lots and lots of important uses
+for genetic engineering
+
+and recombinant DNA
+technology.
+
+One that we'll emphasize in
+just a few lectures and is
+
+becoming extremely common and
+popular nowadays is DNA
+
+sequencing.
+
+You need to isolate the DNA from
+the organism of interest
+
+and then have it in such a
+fashion that you can sequence
+
+it's nucleotides.
+
+This is a very popular
+activity now.
+
+And specifically with respect
+to human health, DNA
+
+sequencing, But some of the
+other methods that we're going
+
+to talk about as well, allow
+us to characterize
+
+disease-causing mutations
+at molecular detail.
+
+So we know what causes x
+disease or y disease.
+
+We can understand the
+consequences for the
+
+individual-encoded proteins
+for the pathways that they
+
+regulate, and we can come up
+with better medicines.
+
+I think about this with respect
+to cancer, but it's
+
+really changing the treatment
+of all diseases as we
+
+understand more the molecular
+basis, the genetic basis of
+
+those diseases.
+
+And these techniques have
+been essential to
+
+allow us to do that.
+
+I want to cover a little bit
+of history so that you know
+
+from whence this came.
+
+Things really began
+to pick up in this
+
+field in the late 1960s.
+
+And the critical advance at this
+stage, was the discovery
+
+of a method to cleave DNA into
+defined fragments, to start
+
+with a genome or chromosome
+and to be able to cut it
+
+particular places reproducibly
+so that one could isolate
+
+fragments of DNA away from the
+mass of DNA, isolate a
+
+particular region of the DNA
+away from everything else
+
+using this method.
+
+It wasn't enough just
+to cut the DNA up.
+
+You had to amplify it up.
+
+In order to amplify it up, you
+needed a vessel in which to do
+
+the amplification, and the
+vessel of choice as I
+
+mentioned was bacteria.
+
+And this relied on a method that
+actually was known for
+
+decades before but actually was
+not used for this purpose
+
+until the early 1970s, and
+it's called bacterial
+
+transformation.
+
+You can transform bacteria by
+adding a new DNA sequence, and
+
+the bacteria will take up that
+new DNA sequence and begin to
+
+express the genes that are
+present on that DNA sequence
+
+as if it was one of their own.
+
+So the transfer of DNA a was
+critical, this process of
+
+bacterial transformation.
+
+And then the final thing which
+also occurred in the 1970s was
+
+the identification of methods to
+amplify DNA sequences once
+
+they got inside of bacteria.
+
+It wasn't enough to actually
+get them in there.
+
+You needed some special way
+to cause the bacterium to
+
+amplify, that is, to replicate
+the DNA that was present
+
+within them.
+
+And these three events, which
+all came together in about a
+
+five to ten year period, really
+initiated, launched
+
+what we now call the recombinant
+DNA revolution and
+
+initiated the biotechnology
+industry, which
+
+started in the mid 1970s.
+
+And an individual above all
+others who is credited with
+
+launching the biotechnology
+industry was Robert Swanson
+
+who in 1966 or so was
+sitting where you
+
+are as an MIT freshman.
+
+Bob Swanson was class
+of '69, actually.
+
+And at the age of 28, in 1976,
+founded the company Genentech
+
+with a scientist, Herb Boyer,
+who was very instrumental in
+
+some of those breakthroughs that
+I just mentioned to you.
+
+And I mention Bob to you now
+because of your connections
+
+through MIT.
+
+But he was a wonderful guy and
+sadly passed away from
+
+glioblastoma at the age of 52.
+
+So he didn't really get to fully
+realize the benefits of
+
+what he had started, but
+he did, in fact,
+
+start a great deal.
+
+And this is a famous statue at
+Genentech which shows Herb
+
+Boyer and Bob Swanson talking
+about the idea for the first
+
+time and you might notice over a
+beer, very important part of
+
+science, discussions
+over a beer.
+
+In addition to this connection
+to MIT and really in honor of
+
+Bob's connections to MIT, and
+a great pride that Bob had
+
+actually in MIT, credited MIT
+greatly with him learning
+
+about science, the importance of
+science, and also business.
+
+He got a degree in chemistry as
+well as a degree from the
+
+Sloan School.
+
+We decided when we launched the
+Koch Institute to name a
+
+very large space in the Koch
+Institute for Bob Swanson.
+
+It's called the Swanson
+Biotechnology Center.
+
+You can visit it.
+
+So it's a series of core
+facilities that support all of
+
+our researchers.
+
+And indeed, researchers across
+the MIT campus, and this is a
+
+nice quote from Bob's widow,
+Judy Swanson, who has been
+
+very supportive of
+this effort.
+
+So Bob Swanson and MIT, in many
+ways, actually, have a
+
+lot to do with the technology
+and the revolution that we're
+
+going to talk about now.
+
+All right.
+
+So as I mentioned, we are
+going to do a demo.
+
+We're going to teach you a
+real-life example now of how
+
+this work is done.
+
+And our goal is to
+clone a gene.
+
+You can actually wait
+right there, Anna.
+
+Thanks.
+
+We're going to clone a gene,
+and we're going to clone a
+
+particular gene.
+
+It's a toxin gene.
+
+It's a gene from a pathogenic
+bacterium.
+
+And you might ask the question,
+a reasonable
+
+question, why the heck
+would you do that?
+
+Why would you clone
+a toxin gene?
+
+So what do you think?
+
+What's the purpose in the
+laboratory of cloning out a
+
+toxin-encoding gene from
+a pathogenic bacterium?
+
+So several people have suggested
+the obvious was that
+
+you want to engage in global
+terror, which we actually
+
+don't support here at MIT, so
+we're going to take that down.
+
+But maybe somebody else
+is going to do that.
+
+So perhaps it would be good if
+we got one step ahead of the
+
+game, isolated the gene,
+manufactured the protein, and
+
+then made a vaccine against that
+toxin so that we could
+
+prevent the bad consequences
+of exposure to the toxin.
+
+Or maybe that thing is actually
+very interesting
+
+independent of its bad uses.
+
+We could learn stuff, which
+might be helpful ultimately in
+
+related activities.
+
+So for the general purpose of
+biomedical research, we often
+
+study how these organisms work
+because it can teach us
+
+things, sometimes surprising
+things that are
+
+useful down the road.
+
+The organism in question is
+Streptococcus pyogenes.
+
+Streptococcus pyogenes, which
+causes in certain cases, in
+
+certain individuals a disease
+called necrotizing fasciitis.
+
+Necrotizing fasciitis, which
+is otherwise more commonly
+
+called the flesh-eating
+disease.
+
+And you might think I'm
+joking, but I'm not.
+
+This is a true thing.
+
+This is a true thing, and some
+of you might be squeamish, and
+
+if you are, and I'm being
+serious here.
+
+If you're squeamish looking
+at ugly, nasty, disgusting
+
+pictures, close your
+eyes for a second.
+
+I'll tell you when you
+can open them.
+
+But this is an individual who
+was exposed to this bacterium
+
+and developed necrotizing
+fasciitis.
+
+That's a real-world case, so
+it is really pretty bad.
+
+You can open your eyes now
+if you closed them.
+
+I hesitate to show that slide
+because in the past, I've had
+
+a few boys throw up when
+I showed that slide.
+
+So what are we going to do?
+
+Well, we're going to
+isolate this gene.
+
+And in order to isolate this
+gene, we need to be able to
+
+separate it, this gene,
+from the chromosome
+
+in which it is contained.
+
+And the chromosome from which
+it is contained is the
+
+chromosome of S. pyogenes.
+
+So this is the S. pyogenes
+chromosome.
+
+It's about four million
+base pairs and it
+
+has about 1,000 genes.
+
+So spread throughout this
+circular chromosome, there are
+
+lots of genes.
+
+We're interested
+in one of them.
+
+Now, this chromosome also has
+another thing on it, which I
+
+hope you all know about from
+the material that Professor
+
+Sive just covered for you.
+
+What is the one piece of DNA
+material that all chromosomes
+
+need in order to replicate?
+
+AUDIENCE: Origin
+of replication.
+
+PROFESSOR: An origin of
+replication, very good.
+
+An origin of replication.
+
+It has an origin of replication,
+and then it has a
+
+bunch of genes.
+
+It has gene A. I'm just
+making this up.
+
+It has gene B, and it
+has a whole bunch of
+
+other genes as well.
+
+And then it has -- and imagine
+that this orange chalk was red
+
+because it's more effective
+if it's red.
+
+It has the T gene, and that's
+the toxin gene.
+
+So our goal is to transfer the
+T gene and not the rest of
+
+this stuff, because we don't
+actually care about the rest
+
+of the stuff.
+
+We just care about
+the T gene --
+
+into the E. coli cells for
+the reasons that I
+
+mentioned up there.
+
+And in order to do that, we have
+to grow large amounts of
+
+the organism that's going to
+in a sense donate the DNA.
+
+We then isolate the chromosomal
+DNA, and we'll
+
+show you how.
+
+We're then going to use this
+method to fragment the DNA not
+
+randomly, but in specific
+places.
+
+And then we're going to transfer
+the DNA of interest
+
+to E. coli using this method
+of transformation.
+
+We're going to take this
+fragment and move it through
+
+the membrane of the E. coli so
+that it becomes resident
+
+inside the E. coli cell.
+
+So now on to our demonstration
+and my lab assistant, Anna
+
+Deconinck, will help me here.
+
+So what we've done is to, in
+the laboratory, isolate S.
+
+pyogenes as well as E. coli,
+grow them up in large
+
+quantities.
+
+You've got your gloves, right?
+
+So I'll take the buffers.
+
+So we have various solutions and
+buffers that will allow us
+
+to sort of wash the stuff we
+don't want away from the
+
+bacterial cells, lice the
+bacterial membrane, isolate
+
+the nucleic acid away from all
+the other stuff that's inside
+
+the cells, and then we'll purify
+the chromosomal DNA.
+
+So Anna has grown up E. coli
+and S. pyogenes, taken that
+
+suspension of cells, and used
+a centrifuge to spin those
+
+cells down to the bottom of
+these tubes here-- you can
+
+show them, Anna-- these
+tubes here.
+
+And the first thing we need
+to do is get rid of the
+
+supernate, the broth that
+the cells grew in.
+
+So first, we're going
+to decant.
+
+Here, you can decant the
+pyogenes, but be
+
+careful with it.
+
+So we're going to decant this
+in order to grow up the
+
+amounts of bacteria
+that we need.
+
+Now we're doing this in a
+very small quantities.
+
+In fact, in industrial scale,
+you do it in huge--
+
+ANNA: Sorry.
+
+PROFESSOR: Ah, that's
+a problem.
+
+It's actually a bit
+more of a problem.
+
+ANNA: I just have a
+buffer to wash.
+
+PROFESSOR: I don't think that's
+going to do it, Anna.
+
+Dude, we may need to actually
+skip, we may need to cancel.
+
+This is a little more serious.
+
+Wait a minute.
+
+Well, I don't know.
+
+Maybe.
+
+Let's just see if it's
+safe or not.
+
+I think it'll be okay.
+
+All right.
+
+That was a joke.
+
+She did very well though,
+don't you think?
+
+She did very well.
+
+That was outstanding.
+
+Anybody want some apple juice?
+
+You're welcome to it.
+
+ANNA: It needs ice.
+
+PROFESSOR: Of course we would
+never bring pathogenic
+
+bacterium to class.
\ No newline at end of file
diff --git a/jgSn1mB8uSI.txt b/jgSn1mB8uSI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..005c43a4b1a9e1a98aa6f724ccbdf415080b29c3
--- /dev/null
+++ b/jgSn1mB8uSI.txt
@@ -0,0 +1,3391 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Good afternoon.
+
+So we are still in a
+discussion of atoms
+
+in external magnetic fields.
+
+And we are working our way
+up from simple static fields
+
+to time dependent fields.
+
+Last week and the
+week before, we
+
+covered external magnetic
+fields, Zeeman shifts,
+
+different coupling limits,
+strong field, and weak field.
+
+Last class on Friday,
+we talked about what
+
+happens when you put atoms
+into DC electric fields.
+
+So what we did was simple.
+
+Lowest order, which means
+in this case, second order
+
+perturbation theory.
+
+And we derived an
+explicit expression
+
+for the polarizability, alpha.
+
+And this polarizability
+tells us how energy levels
+
+are shifted quadratically
+with the electric field.
+
+I put some emphasis
+in talking about what
+
+is inside perturbation theory
+and identified with you that,
+
+yes, if you have
+an electric field,
+
+we have electrostatic energy.
+
+But in order to
+polarize the atoms,
+
+we have to create
+an internal energy.
+
+In a concrete example,
+if we have an s state,
+
+we have to mix a p state
+to create a dipole moment.
+
+And this costs energy.
+
+Exactly in the same way
+as when you have a spring
+
+and pull on the
+spring with gravity,
+
+you gain gravitational energy.
+
+But you have two pay
+exactly half of it
+
+to create internal
+energy in your spring.
+
+And this is actually the
+reason for this factor of 1/2
+
+as we discussed in great length.
+
+Question is do you have any
+questions about that part?
+
+Because we want to
+go to the next level.
+
+Perturbation theory?
+
+DC polorizability?
+
+So anyway, the menu
+for today is we
+
+have done perturbation theory
+here for weak electric fields.
+
+But the question came already
+up in class, is it really valid?
+
+Or for what regime
+is it invalid?
+
+So today I want to
+talk to you briefly
+
+what happens when we go
+beyond perturbation theory.
+
+When we go beyond the
+quadratic Stark effect.
+
+And that leads us
+to a discussion
+
+on stability of atoms in
+strong electric field and field
+
+ionization.
+
+I like to sort of feature
+it because it allows
+
+me to tell you something
+about the peculiar properties
+
+of Rydberg atoms.
+
+And also the
+ionization of Rydberg
+
+atoms through electric field.
+
+This is how people in our
+field create cold plasmas.
+
+And it's also a way to do a very
+sensitive detection of atoms.
+
+So what I'm telling you today
+is interesting for its own sake,
+
+but also because it's an
+important tool for manipulating
+
+atoms, creating plasmas,
+or sensitive detection.
+
+So this will probably only
+take 10 or 20 minutes.
+
+And then we want to go
+form DC electric fields
+
+to AC electric fields.
+
+So we then discuss
+the AC polarizability.
+
+And, well, that will take
+us from perturbation theory
+
+in a time independent way what
+we have done now for DC fields
+
+to time dependent
+perturbation theory.
+
+So all the topics are
+rather basic aspects
+
+of quantum physics.
+
+But as usual, I try to give
+you some special perspectives
+
+from the atomic physics side.
+
+So in perturbation theory, we
+have a mixture of other states.
+
+And this said mixture is
+done with the matrix element.
+
+And in perturbation
+theory, we always
+
+have an energy denominator.
+
+Intermediate state
+to ground state.
+
+And if the electric field
+is smaller than this value,
+
+then we have mixture of other
+states into the ground state.
+
+So usually when we estimate
+the validity of perturbation
+
+theory, we look
+for the state which
+
+is closest to the ground state.
+
+For which the energy
+denominator is smallest.
+
+So therefore, i here is the
+nearest state, but, and this
+
+is important, of
+opposite parity.
+
+Otherwise, because of the
+parity selection rule,
+
+the matrix element would
+be 0 and electric field
+
+does nothing.
+
+I made a comment on Friday,
+but let me do it again.
+
+That, of course, means that
+when we apply electric field
+
+to our favorite
+atoms, we don't have
+
+to worry about the
+other hyperfine states.
+
+The other hyperfine states have
+the same spatial wave function.
+
+Have the same parity.
+
+So we are really here talking
+about the first excited state.
+
+And a concrete example
+for those of you
+
+who work with alkalis
+with an s ground
+
+state, the relevant
+energy scale here
+
+is the excitation energy
+to the first p state.
+
+So let's just estimate it
+for a single electron atom.
+
+And well, this is a
+hydrogenic estimate.
+
+The excitation energy to
+the first excited state.
+
+1s to 2p is about 1 Rydberg.
+
+And the Rydberg is
+nothing, or Hartree,
+
+and that's nothing else
+than e square over a0.
+
+It's electric potential
+of two charges separated
+
+by Bohr radius.
+
+And if we estimate
+that the matrix element
+
+for strong transition is on
+the order of the Bohr radius,
+
+there are no other length
+scales in the problem,
+
+we find that the value for the
+electric field in atomic units
+
+is the charge divided by
+the Bohr radius squared.
+
+And this is really high.
+
+It is on the order of 5 times
+10 to the 9 volt per centimeter.
+
+And this is 1,000 times
+larger than laboratory
+
+electric fields.
+
+Those fields would just create
+sparking along the electrodes.
+
+You cannot apply such
+high electric fields
+
+in a laboratory.
+
+So, therefore, nothing
+to worry about.
+
+If you have ground state
+atoms, the Stark effect
+
+in perturbation theory
+is all you need.
+
+Actually, to be a little
+bit more precise when
+
+I used the Rydberg and a0, I
+made a little bit overestimate.
+
+So that the typically the
+critical electric field
+
+which would cause a breakdown
+of perturbation theory
+
+for the ground
+state is around 10
+
+to the 9 volt per centimeter.
+
+OK, so we are safe when we
+talk about ground states.
+
+But once we got to the excited
+state, we have degeneracy.
+
+p states have a
+three fold degeneracy
+
+and they are states
+with opposite parity.
+
+So we can't have mixing there.
+
+And actually as we will
+see for excited states,
+
+we have already a breakdown
+of perturbation theory
+
+at very, very small
+electric field.
+
+So let us discuss
+hydrogenic orbits
+
+with principal
+quantum number, n.
+
+And if you estimate what is
+the size of the matrix element?
+
+Well, it's not just a0.
+
+There is a scaling with
+n which is n square.
+
+The matrix element in higher
+and higher excited state scales
+
+with n square.
+
+Well, how does the
+energy separation scale?
+
+Well, let's not
+discuss hydrogen here.
+
+Because in hydrogen, energy
+levels are degenerate.
+
+And we would immediately
+get a breakdown
+
+of perturbation theory.
+
+Let's rather formulate
+it for general atoms.
+
+And we had this nice discussion
+about the quantum defect.
+
+So if we compare the energy of
+two l states, they scale as 1
+
+over n square.
+
+But for different l states, we
+have different quantum defects.
+
+Delta l plus 1.
+
+And here we have delta l.
+
+So, therefore, doing
+an expansion in m
+
+which we assume to be large, we
+find that the energy difference
+
+is proportional to the
+difference between the quantum
+
+defects for the
+two states we want
+
+to mix with the electric field.
+
+And then again, the scaling with
+the principal quantum number
+
+is n cube.
+
+So, therefore, we find
+for the critical field
+
+using the criterion
+I mentioned above.
+
+We take the energy splitting.
+
+The energy the denominator which
+appears in perturbation theory.
+
+We divide by the value
+of the matrix element.
+
+Well, we had the Rydberg
+constant or two times
+
+the Rydberg constant is nothing
+else than b squared over a0.
+
+The matrix element
+was 1 over a0.
+
+And then we have the difference
+between quantum defects.
+
+And now-- and this makes
+it really so dramatic.
+
+We had an n square scaling
+of the matrix element.
+
+And we have an into the minus 3
+scaling of energy differences.
+
+So that means the critical
+field scales by n to the 5.
+
+Go to an excited state
+with n equals 10.
+
+And the breakdown of
+perturbation theory
+
+happens 100,000 times earlier.
+
+So some of the scaling
+in atomic physics
+
+is very, very
+dramatic when you go
+
+to more highly excited state.
+
+If you threw in that quantum
+defects become very small,
+
+once you go beyond
+s and p states.
+
+The higher states just don't
+penetrate into the nucleus.
+
+So if l is larger than 2, if
+you have more complicated atoms,
+
+you may add the angular
+momentum of the core here.
+
+But so if you put n to the 5
+scaling and the small quantum
+
+defect together, you find
+that critical electric fields
+
+are smaller than one
+volt per centimeter
+
+already for principal
+quantum numbers as low as 7.
+
+So that means bring a 1.5 volt
+battery close to your atom
+
+and you drive it crazy.
+
+You drive it out of
+perturbation theory.
+
+So what we have
+is the following.
+
+We have, of course,
+the structure
+
+of atoms in excited field.
+
+Here is the electric field.
+
+And let me just
+pick three n values.
+
+18, 19, 20.
+
+And now the
+structure, of course,
+
+is that by the
+criterion I actually
+
+gave you was the criterion for
+the application of perturbation
+
+theory.
+
+If the energy levels are
+smaller than the matrix element,
+
+you have to rediagonalize
+between those levels.
+
+And that gives you then not a
+quadratic, but a linear effect.
+
+So, therefore, the
+structure is here
+
+that you have a region where
+you have strong l mixing.
+
+So you have to use
+degenerate perturbation
+
+theory for the
+different l states.
+
+But the many folds in n, the
+principle quantum number,
+
+are still well separated.
+
+But then, eventually,
+when you go further,
+
+you have a region which
+is called n mixing.
+
+So now the electric
+field is really
+
+completely rediagonalizing your
+states with different quantum
+
+numbers, n.
+
+So the result of
+this discussion is
+
+that highly excited
+states of atoms
+
+behave very differently
+from ground state atoms.
+
+And n to the 5 scaling
+is sensitivity to volt
+
+per centimeter.
+
+Level mixing all over the place.
+
+And that's why for those
+highly excited states,
+
+people have coined the word
+Rydberg atoms or Rydberg
+
+matter.
+
+That means atoms with higher
+principal quantum numbers.
+
+And the study of Rydberg
+atoms was pioneered, well,
+
+the early pioneering work
+by our own, Dan Kleppner.
+
+And then Herbert
+Walther in Munich
+
+who happened to be
+my Ph.D. Advisor.
+
+And finally, Serge
+Haroche, who was recognized
+
+with the last Nobel Prize
+together with Dave Wineland.
+
+So this is not just theory.
+
+What I am showing to
+you here is spectroscopy
+
+done at MIT by Dan Kleppner.
+
+So what is done here is
+from the ground state,
+
+they excite to an excited state.
+
+And whenever you hit an excited
+state, you see a signal.
+
+Let's focus on the upper part.
+
+So if at a given electric
+field, you scan the laser,
+
+you get one of those traces.
+
+You find peaks, peaks, peaks.
+
+And those peaks correspond to
+the different and many folds
+
+with strong Stark mixing.
+
+And eventually when you go
+to somewhat higher field,
+
+you have states
+all over the place.
+
+And this is the regime where
+you have done n mixing.
+
+So in the '70s and
+'80s, there was really,
+
+those experiments obtained
+a clear understanding
+
+and description
+of atoms in, well,
+
+I would say high
+electric fields.
+
+But the fields were not so high.
+
+It was just the atoms were
+very sensitive that already
+
+is at lower electric
+fields, they
+
+reached what is regarded
+as the high-field limit.
+
+Now the question is
+when we recorded signal,
+
+suddenly the traces stop.
+
+And that means the electric
+field is now so high
+
+that the atom no longer
+has a stable state.
+
+The electric field is so
+high that it literally rips
+
+the electron away from the atom.
+
+And if you go to higher
+states, the electric field
+
+where this happens is lower.
+
+This is the process
+of field ionization
+
+and that's what we
+want to discuss next.
+
+Question?
+
+AUDIENCE: Um, for what atoms?
+
+PROFESSOR: Those studies were
+actually done for lithium.
+
+It's actually peculiar.
+
+Dan Kleppner really
+liked hydrogen.
+
+Dan Kleppner is the
+person who tried
+
+to do almost all
+experiments with hydrogen.
+
+The famous BEC experiment.
+
+He also had the
+Rydberg experiment
+
+which was just in building 26
+where Vladan Vuletic teaches
+
+now, his labs.
+
+This is where
+spectroscopy of hydrogen
+
+were done with the
+goal of a precision
+
+measurement of the
+Rydberg constant.
+
+So we excited hydrogen to
+some of those high levels.
+
+But as probably
+the experts know,
+
+the hydrogen atom is the
+hardest atom to work with.
+
+Because you need
+[INAUDIBLE] and alpha.
+
+You have this huge gap to
+the first excited state.
+
+And that's why if
+you can get away,
+
+you try to work
+with other atoms.
+
+And in those
+experiments, those people
+
+worked with the lithium atom.
+
+So the lithium atom
+has a quantum defect
+
+which will actually contrast
+to hydrogen where the quantum
+
+defect is 0.
+
+And this will actually
+be very, very important
+
+for field ionization as
+I want to discuss now.
+
+Other questions?
+
+OK, so at a given electric
+field, states, so to speak,
+
+just disappear.
+
+They're no longer stable.
+
+And this is the process which
+is called field ionization.
+
+So the phenomenon is
+that sufficiently strong
+
+electric fields ionize the atom.
+
+And whenever there
+is a simple model
+
+and I can give you an analytic
+answer, I try to do that.
+
+Because I feel a
+lot of our intuition
+
+is shaped by understanding
+simple models.
+
+And the simplest model
+for field ionization
+
+is just the classical
+model by calculating
+
+what is the settle point
+in the combined potential.
+
+The combined potential
+of the nucleus
+
+which is a Coulomb potential
+and the external magnetic field.
+
+So many features
+of the experiment
+
+can be understood by this
+simple three line derivation.
+
+So we have a potential.
+
+One part of it is the
+Coulomb potential.
+
+And focusing on one
+spatial direction here.
+
+And then, in addition, we
+apply an electric field.
+
+And the electric field
+creates a linear potential.
+
+And if I take the sum of the
+two, well, at large distances,
+
+see, it's the electric
+field which dominates.
+
+Then the Coulomb
+potential takes over.
+
+So that's how it looks like.
+
+So now we have the situation
+if we would put in atoms
+
+and we would look at
+the energy eigenvalues.
+
+At this point, this is
+the maximum excited state
+
+in the atom which
+is still stable.
+
+So what I want to derive
+for you is what determines
+
+the stability is simply
+the settle point.
+
+When the binding energy of
+the excited state for which we
+
+use the Rydberg
+formula is not stronger
+
+than the position
+of the settle point,
+
+the atom becomes unstable it
+and becomes field ionized.
+
+And we'll discuss
+a little bit later
+
+if this really
+applies to real atoms.
+
+The quick answer is for lithium
+and all the other atoms,
+
+it applies.
+
+For hydrogen, it doesn't.
+
+Because hydrogen has
+too many symmetries.
+
+Too many exact degeneracies.
+
+OK, so the total potential
+is the Coulomb potential
+
+plus the electric potential.
+
+What we need is the position
+of the settle point.
+
+Where we have a
+maximum in this one.
+
+This is a one dimensional cut.
+
+And this one dimensional cut
+has a maximum at this position.
+
+And by taking the derivative
+of the total potential,
+
+you immediately find
+this to be of that value.
+
+And now what we are
+calculating next
+
+is what is the potential
+energy at this point.
+
+And, well, this is just copy
+from the notes, e to the 3/2.
+
+And now what we want
+to do is we want
+
+to postulate that
+for field ionization,
+
+this should be able to the
+binding energy of the electron.
+
+Which is nothing
+else than the Rydberg
+
+constant divided by n square.
+
+OK, now here, we
+have the square root
+
+of the electric field
+from this calculation.
+
+So that means the critical
+electric field will scale as 1
+
+over n to the 4.
+
+And this is a
+famous scaling which
+
+can be found in many textbooks.
+
+That the critical electric
+field for ionization equals,
+
+and now, that's the
+beauty of atomic units,
+
+it is 1/16, n to the 4.
+
+Beautiful formula derived from
+the settle point criteria.
+
+Of course, what I mean here is,
+and if you do the derivation,
+
+it's in atomic units.
+
+Which means in units
+of the atomic unit
+
+of the electric field which is
+e over the Bohr radius squared.
+
+So it's a simple model.
+
+It's an analytic result.
+
+The question is is it valid?
+
+Does it make any sense?
+
+And the answer is yes, but in
+a quantum mechanical problem,
+
+you would actually solve
+Schroedinger's equation,
+
+such a potential.
+
+But then, the onset
+of field ionization
+
+comes when tunnelling becomes
+possible for this barrier.
+
+But it is the
+nature of tunnelling
+
+that if you're a little bit too
+low, tunneling is negligible.
+
+You may have ionization rates
+of 1 per millisecond or so.
+
+And if you just go
+a little bit closer,
+
+it becomes exponentially larger.
+
+So, therefore, this scaling
+is very, very accurate.
+
+Because the transition where
+you go from weak tunneling,
+
+to strong tunneling, to
+spilling over the barrier,
+
+it's a very narrow range
+of electric fields.
+
+But, yes, people have looked
+at it in great details
+
+and have calculated
+corrections due to tunneling.
+
+So these are quantum corrections
+to the classical threshold
+
+which I just calculated.
+
+But now in hydrogen, a lot of
+n, l mixing matrix elements,
+
+matrix elements due
+to the electric field
+
+between an l states vanish.
+
+Hydrogen is just too
+pure, too precise.
+
+There is actually
+parabolic quantum numbers
+
+where you can
+exactly diagonalize
+
+hydrogen electric fields.
+
+And you find some stable
+states which do not decay.
+
+And they are above the
+classical threshold
+
+we have just calculated.
+
+So as Dan Kleppner would have
+said, the simplest of all atoms
+
+is the most complicated when
+it comes to field ionization.
+
+Because it has a
+lot of stable states
+
+above the classical barrier.
+
+So you can sort of
+envision that there
+
+will be orbits which are
+just confined to this region.
+
+And the electron never
+samples the settle point.
+
+And if you look at it
+this diagram on the wiki,
+
+these are actually
+calculations for hydrogen
+
+which include ionization rates.
+
+You will find that
+the states which
+
+are the ones which
+go down, which
+
+are on the downhill side
+of the electric field,
+
+you see always here marked
+an onset for ionization.
+
+And then you see
+a rapid increase
+
+in the ionization rate.
+
+But you also see
+those hydrogenic state
+
+which go upward in energy
+and they refuse to ionize.
+
+Because of the symmetry
+of parabolic coordinates
+
+and the things I've mentioned.
+
+Anyway, it's too especially
+to spend more time here
+
+in class on it, but I just
+think you should at least know
+
+qualitatively what is
+different for hydrogen.
+
+OK, so that's what
+I wanted to tell you
+
+about high electric fields and
+field ionization in principle.
+
+Let me now briefly mention
+important applications
+
+of field ionization.
+
+One is close to 100% detection
+efficiency for atoms.
+
+If you want to
+detect single atoms,
+
+for instance, you'll
+have a krypton sample
+
+and you want to find a
+rare isotope of krypton
+
+for dating the material.
+
+You need an extremely
+high sensitivity
+
+and you may just have a few
+single atoms in the sample.
+
+One way to do it would be
+that you excite the atom maybe
+
+through an intermediate
+state, to Rydberg state.
+
+And then by just applying
+a few volt per centimeter,
+
+you get an ion.
+
+And ions can be counted
+by particle detectors.
+
+You can accelerate the ion,
+smash it into a surface
+
+and count the particles with
+close to 100% efficiency.
+
+And this is one of the most
+sensitive detection schemes.
+
+I remember in the
+aftermath of Chernobyl,
+
+there was an interest
+in detection schemes
+
+for radioactive strontium.
+
+And on the wiki, I
+give you a reference
+
+where some people developed
+this resonance ionization
+
+spectroscopy for
+some atomic isotopes.
+
+Which unfortunately
+appeared more frequently
+
+after the Chernobyl disaster.
+
+And they developed
+a method based
+
+on excitation to Rydberg states.
+
+Which was more sensitive
+than other methods.
+
+You may ask why don't you
+ionize it with a laser?
+
+Well, the fact is, you can
+photoionize it with a laser.
+
+It's another alternative, but
+it takes much more laser power.
+
+Because if you excite
+into the continuum,
+
+the matrix element
+is much smaller.
+
+And often, if you want to have
+100% ionization probability
+
+to go into the continuum, you
+need such high laser power
+
+that you may get some background
+of resonant ionization
+
+of other elements and such.
+
+So Rydberg atoms is really
+the smart way to go.
+
+You go to an almost bound to
+an almost unbound electron.
+
+And then it's just
+the electric field
+
+which causes the final
+act of ionization.
+
+I also want to briefly mention
+that the famous experiments
+
+on Rydberg atoms by
+Herbert Walther and Serge
+
+Haroche and collaborators
+would not have been possible
+
+without field ionization.
+
+I give you this one
+reference, but I'm
+
+sure you'll find more
+in the actually very,
+
+very nicely written Nobel
+lecture of Serge Haroche.
+
+I just read it a few
+weeks ago and it's
+
+a delight to read how
+he exposes the field.
+
+So they did QED experiments by
+having microwave transitions
+
+between atoms in two
+highly excited states.
+
+Let's say with principal
+quantum number 50 and 51.
+
+So that's now conveniently
+in the microwave regime.
+
+Then those atoms are
+passed through a cavity.
+
+And in this cavity, single atoms
+interact with single photons.
+
+And they have done beautiful
+quantum non-demolition
+
+experiments of single photons.
+
+I mean that's really wonderful,
+state of the art experiments.
+
+Back to Rydberg atoms
+and field ionization.
+
+Eventually, the read
+out of those experiments
+
+was you prepare atoms
+in the state 50 or 51.
+
+And afterwards, if they have
+absorbed or emitted a photon,
+
+they should be in
+a different state.
+
+So you were interested in a very
+high detection efficiency which
+
+could distinguish
+between 50 and 51.
+
+And of course there is a
+way to distinguish that.
+
+And this is because
+of n to the 4.
+
+You first apply
+an electric field
+
+which can only field ionized 51.
+
+And then you allow
+the atoms to propagate
+
+into a slightly
+higher electric field.
+
+And then the 50s are ionized.
+
+So the standard
+experiment is that you
+
+pass those atoms between
+two field plates.
+
+And by putting an angle
+between them that indicates
+
+the voltage is increasing.
+
+And then you have
+two little holes.
+
+You have some channel-drawn
+particle detectors.
+
+And the first detector
+will detect the 51s
+
+and the second detector will
+detect the lower lying states.
+
+So you can detect every
+atom with high probability,
+
+but also in a state
+selective way.
+
+So this way of doing state
+selective field ionization
+
+based on the discussion
+we had earlier, this
+
+is sort of the method of
+choice for experiments
+
+involving Rydberg atoms.
+
+Any questions about atoms
+in the electric fields?
+
+Well, then.
+
+Frequently we add
+time dependence.
+
+So what we should
+do next is atoms
+
+in oscillating electric fields.
+
+It's also a good way to
+review what we have done.
+
+Because the first
+thing to do now
+
+is we calculate the
+polarizability for AC fields.
+
+We calculate the
+AC Stark effect.
+
+And, of course, if in the AC
+Stark effect we said omega 2, 0
+
+will retrieve the
+DC Stark effect.
+
+So in a way, what I'm
+doing for you now is
+
+I'm using time dependent
+perturbation theory
+
+to obtain a new result.
+
+But it will reproduce
+the result of time
+
+independent perturbation theory
+which we have just discussed.
+
+All right, so atoms in
+oscillating electric fields.
+
+Of course the next
+step is, and this
+
+is where we are
+working towards, we
+
+will in the next few lectures
+starting on Wednesday.
+
+Well, then there is Spring
+Break, but in the next lectures
+
+develop a deep
+understanding what
+
+happens when atoms
+interact with light.
+
+And oscillating electric
+fields is already
+
+pretty close to light.
+
+And I want to
+actually also show you
+
+that we capture already a
+lot of the phenomena which
+
+happen with light except
+for a full understanding
+
+of spontaneous emission.
+
+So we pretty much when we use
+an oscillating electric field,
+
+we allow the atom to
+interact with just one
+
+mode of the
+electromagnetic field.
+
+Which is filled with
+a coherent state.
+
+And this is so classical
+that we don't even
+
+need field quantization.
+
+We just use a classical
+electric field.
+
+And this already gives us the
+interaction of atoms with light
+
+except for spontaneous
+emission which
+
+involves all the other modes.
+
+So that's what we do later.
+
+But today, we just do the
+same classical description
+
+of an atom in an
+oscillating electric field.
+
+And this is the theory
+of the AC Stark effect.
+
+So all we do is application
+of time dependent perturbation
+
+theory.
+
+So our electric field
+is now time dependent.
+
+It has a value epsilon,
+polarization e hat,
+
+and it oscillates.
+
+Our perturbation
+Hamiltonian is exactly
+
+the same dipole Hamiltonian
+we had before for the DC Stark
+
+effect.
+
+But now it's a
+time dependent one.
+
+And it will be useful to break
+up the oscillating term in e
+
+to the i omega, t and e
+to the minus i omega t.
+
+I don't want to bore you with
+perturbation theory in quantum
+
+mechanics because you've
+all seen it in 805 or 806.
+
+I just want to
+jump to the result.
+
+You find more details
+about it on the wiki.
+
+But all you do is you
+parametrize your wave function,
+
+you expand it into
+eigenstates with amplitude an.
+
+And then you put it into
+the Schroedinger equation
+
+and assume that for
+short times the atom
+
+is in the ground state.
+
+The amplitude of the
+ground state is 1.
+
+And the amplitude
+of the excited state
+
+is infinitesimal that you
+can use the lowest order
+
+perturbation.
+
+This immediately gives
+you the first order result
+
+for the amplitude in
+an excited state, k.
+
+It only comes about because
+your initial state, the ground
+
+state, is coupled by the matrix
+element to the excited state.
+
+It's linear in the
+applied electric field.
+
+So what you do is you have
+the Schroedinger equation
+
+and you integrate it
+from times 0 to time 1.
+
+And since you have e
+to the i omega, t and e
+
+to the minus i omega t, you
+get two time dependent terms.
+
+e to the i.
+
+So what appears now is we
+have the frequencies omega
+
+n of the excited state.
+
+And now when we couple
+the excited state, k,
+
+to the ground
+state, what appears
+
+is the frequency
+difference between the two.
+
+That's pretty much
+the excitation gap.
+
+And we have a time dependent
+oscillation at omega.
+
+And then we have, of
+course, the same term
+
+where we flip the
+sign from omega--
+
+let me write that more clearly.
+
+Where we flip the sign
+from omega to minus omega.
+
+So that's the second term.
+
+By integrating an exponential
+function with respect to time,
+
+we get an energy and a frequency
+denominator which is this one.
+
+So this is really
+just straight forward,
+
+most basic plain
+vanilla application
+
+of perturbation theory.
+
+The only thing I want to
+discuss because it sometimes
+
+confuses people is
+that we integrate
+
+from times 0 to the finite time.
+
+And then you integrate,
+you get contributions
+
+from the upper
+integration limit.
+
+And from the lower
+integration limit.
+
+And this contribution at
+the lower integration limit
+
+is actually a transient.
+
+It is at the frequency.
+
+It doesn't depend on omega.
+
+So it's a beat node between
+the ground and excited state.
+
+I could say at
+frequency omega k,
+
+but then it's together with the
+ground state, it's omega kg.
+
+And this is due to if you
+switch on a perturbation,
+
+it's like you suddenly
+switch on the drive
+
+of an harmonic oscillator.
+
+And you have some ringing.
+
+You have a transient at
+the natural frequency
+
+of the harmonic oscillator.
+
+It has nothing to
+do with the drive.
+
+It's just a sudden onset.
+
+It's transient and frequent
+due to the sudden switch on.
+
+So like any
+transient, we haven't
+
+included damping in here.
+
+We don't have
+spontaneous emission.
+
+Everything is undamped.
+
+But eventually, all
+those transients
+
+will damp out with time.
+
+And as we should have known
+also from the beginning,
+
+when we drive a system, when
+we switch on a perturbation,
+
+just think about an
+harmonic oscillator.
+
+You have a response at the
+harmonic oscillator frequency
+
+which is always
+transient in nature.
+
+And then you have a response
+at the dry frequency.
+
+And we are
+interested, of course,
+
+only in the driven response
+The driven response
+
+is at frequency
+plus minus omega.
+
+That's how we drive it.
+
+But now I have to
+be careful since I'm
+
+looking at the amplitude and I
+factor out the time dependence
+
+of the time dependence of
+the wave function, the time
+
+dependence of the eigenstates.
+
+I'm now looking for drive
+terms in this expression
+
+for the amplitude which
+are at frequency omega,
+
+but modified by the ground.
+
+Or the frequency of
+the ground state.
+
+But anyway, what I mean
+is the relevant term
+
+is the one which
+depends on omega.
+
+And in the following discussion,
+I simply drop the minus 1
+
+because it's a transient.
+
+If you would switch on your
+time dependent electric field
+
+in a smoother way, this
+term would disappear.
+
+OK, let's now be specific.
+
+Let's assume the electric field
+points in the z direction.
+
+For an isotropic medium,
+the dipole moment,
+
+the time dependent dipole
+moment which we induce
+
+is also pointing
+in the z direction.
+
+And so we want to calculate now
+what is the dipole moment which
+
+is created by the drive term?
+
+By the driven electric Field
+
+And for that, we simply
+use the perturbation theory
+
+we have just applied.
+
+We take the ground state and
+its first order correction.
+
+And calculate the expectation
+value of the dipole moment.
+
+In the line at the top, we
+have the first order correction
+
+to the ground state
+wave function.
+
+And so we just plug it in.
+
+And what we obtain
+is result where
+
+we have the matrix
+elements squared.
+
+Remember, we do first
+order perturbation theory
+
+which is one occurrence
+of the matrix element,
+
+but now we take a
+second matrix element
+
+because we're interested
+in the dipole operator.
+
+So this gives us now a sum
+over matrix element squared.
+
+We have e to the plus i omega
+t and e to the minus i omega t.
+
+This means we get 2 times the
+real part of this expression.
+
+And the time dependent
+term is e to the i omega t.
+
+And then we have the term
+with plus and minus omega.
+
+Yes.
+
+And so, most
+importantly, everything
+
+is driven by the electric field.
+
+We can now just to write
+the result in an easier way,
+
+we can use this result
+with omega minus omega.
+
+And the real part
+and write that.
+
+We can write that as
+2 times omega k, g.
+
+Omega k, g squared minus omega
+squared, times cosine omega t,
+
+times the electric field.
+
+And now finally, we
+have the matrix element.
+
+We have integrated the e to the
+i omega t function and such.
+
+So what we have here now is the
+time dependent electric field.
+
+And what we have
+here is the factor
+
+by which we multiply
+the electric field
+
+to obtain the bipole moment.
+
+And this is the
+definition of the now
+
+time dependent or frequency
+dependent polarizability.
+
+AUDIENCE: Excuse me.
+
+PROFESSOR: Yes?
+
+AUDIENCE: Why are we only
+getting the cosine and not
+
+[INAUDIBLE]?
+
+You only multiply by the other
+terms to get the [INAUDIBLE]?
+
+In terms of the cosine.
+
+PROFESSOR: I haven't
+done the math yesterday
+
+when I prepared for the class.
+
+I did it a while ago
+when I wrote those notes,
+
+but you know, one comment, I
+know you don't want to hear it,
+
+but it's a following.
+
+This system has no
+dissipation at all.
+
+And when I drive
+it, I will always
+
+get a response which is
+in phase with the drive.
+
+It can be cosine omega t,
+or minus cosine omega t.
+
+You cannot get a
+quadrature at this point.
+
+So if you find I've made a
+mistake, and you would say,
+
+there is a sine, omega
+term, I've made a mistake.
+
+I know for physical reasons,
+I cannot get a phase shift.
+
+You only get a phase shift
+in the response of a system
+
+to drive when you
+have dissipation.
+
+AUDIENCE: OK.
+
+I'll have to talk with you.
+
+PROFESSOR: But why
+don't-- I mean,
+
+I know the result is correct.
+
+And this is just, I
+hate to spend class time
+
+in trying to figure out
+if I've omitted one term.
+
+AUDIENCE: The real part.
+
+PROFESSOR: But the real part
+what I've probably done is--
+
+AUDIENCE: I think that's
+probably what you did.
+
+Yeah.
+
+Thank you.
+
+PROFESSOR: I think
+that's what I did.
+
+So let me, therefore,
+also say we have now
+
+included the real part of it.
+
+Yes.
+
+OK, thank you.
+
+OK, this part here
+can actually--
+
+that's how we often report.
+
+And that's how you often
+find in textbook the result,
+
+the frequency dependence
+of the AC polarizability.
+
+But I like to rewrite it
+now in a different way which
+
+is identical.
+
+And it shows now that there
+are two contributions.
+
+And I will discuss
+them in a moment.
+
+But those two contributions,
+one has in the denominator,
+
+let's assume we excite the
+system close to resonance.
+
+Omega is close to omega kg.
+
+Then one term is
+much, much closer.
+
+It's to a near
+resonant excitation.
+
+And from our discussion
+about rotating frames,
+
+we have all of this near
+resonant excitation corresponds
+
+to a corotating term.
+
+And the other one corresponds
+to a counter rotating term.
+
+We've not assumed any
+rotating fields here,
+
+but we find those terms with
+the same mathematical signature.
+
+And I will discuss
+that little bit later.
+
+But the physics is between the
+corotating and counterrotating
+
+term.
+
+And it's the
+corotating term which
+
+is the term which [INAUDIBLE]
+the so-called rotating
+
+wave approximation.
+
+I just want to identify
+those two terms
+
+and let's hold the thought for
+until we have the discussion.
+
+What I first want to say
+is the limiting case.
+
+We have not made any
+assumptions about frequency.
+
+When we let omega go to 0,
+we obtain the DC result.
+
+It is important to point
+out that when we have the DC
+
+result, we can only get to
+correct results because we have
+
+equal contributions from co
+and counterrotating terms.
+
+So that's sort of a
+question one could ask.
+
+You know, which mistake do you
+do for the DC polarizability
+
+when you do the rotating
+wave approximation?
+
+Well, you miss out
+on exactly 50% of it.
+
+Because both terms
+become equally important.
+
+I have deliberately focused
+here on the calculation
+
+of the dipole moment.
+
+Because the dipole, I simply
+calculated the dipole moment
+
+as being proportion
+to the electric field.
+
+And the coefficient in front of
+it is alpha the polarizability.
+
+You may remember that
+when we calculated
+
+the effect of a
+static electric field,
+
+we looked for the DC Stark shift
+for the shift of energy levels.
+
+We can now discuss also
+the AC Stark shift.
+
+Which is a shift of the
+energy levels due to the time
+
+dependent field.
+
+But I have to say you have
+to be a little bit careful.
+
+And sometimes when I looked
+at equations like this,
+
+there is a moment of confusion
+what you want to actually,
+
+what the question is.
+
+Because the wave function is now
+a time dependent wave function.
+
+It's a driven system.
+
+It's no longer your time
+independent Schroedinger
+
+equation and you
+are asked, what is
+
+the shift in the
+value of eigenvalues?
+
+So the AC Stark
+shift here is now
+
+given by the frequency
+dependent polarizability.
+
+And then, and I know some
+textbooks do it right away.
+
+And at the end of the
+day, it may confuse you.
+
+It uses an average of e square.
+
+So in other words, if you
+have an electric field which
+
+is cosine omega t, and you
+calculate what is the AC Stark
+
+shift, you get
+another factor of 1/2.
+
+Because cosine square omega
+t time average is 1/2.
+
+So anyway, just
+think about that.
+
+It's one of those factors
+of 1/2 which is confusing.
+
+Will, you have a question?
+
+AUDIENCE: So when
+we take omega goes
+
+to 0 from our previous
+results, are we still justified
+
+in neglecting the
+transient term?
+
+PROFESSOR: Yes.
+
+But why?
+
+What will happen is
+the transient term
+
+is really a term which
+has time dependence.
+
+And even if omega is 0,
+just the step function
+
+of switching it on
+creates an oscillation
+
+in the atom at a frequency
+which is omega excited
+
+state minus omega ground state.
+
+You may think
+about it like this.
+
+I give you more the
+intuitive answer.
+
+Take an atoms and put
+it in electric field.
+
+If you gradually switch
+on the electric field,
+
+you create a dipole moment
+by mixing at 0 frequency
+
+a p state into the s state.
+
+And that displaces the
+electron from the origin.
+
+But if you suddenly switch
+on the electric field,
+
+you actually create a
+response of the atoms which
+
+has a beat node between the
+excitation frequency of the p
+
+state and the excitation
+frequency of the s state.
+
+And what you regard is the
+DC response of the atom
+
+is everything except
+for this transient term.
+
+However, and this tells
+you maybe something
+
+about the different formulas
+in quantum mechanics
+
+when we talked about the
+time independent perturbation
+
+theory.
+
+We never worried
+about the switch
+
+on because we just did time
+independent perturbation theory
+
+and we sort of assumed that the
+perturbation term had already
+
+existed from the
+beginning of the universe.
+
+So it's not that we
+excluded the term.
+
+We formulated the
+theory in such a way
+
+that the term just
+didn't appear.
+
+But if you switch on a DC
+field, you should actually
+
+if you want an
+accurate description,
+
+do time dependent
+perturbation theory,
+
+you get the transient
+term even for DC field.
+
+And then you discuss
+it away the way I did.
+
+OK, so if you want, these
+are the textbook results.
+
+We could stop here.
+
+But I want to add three
+points to the discussion.
+
+You can also see at
+this point, we really
+
+understand that AC
+Stark shift theory
+
+as you find it in generic
+quantum mechanics textbooks.
+
+And now I want to give
+you a little bit of sort
+
+of extra insight based on my
+knowledge of atomic physics.
+
+So there are three points I
+would like to discuss here.
+
+The first one is the relation
+to the dressed-atom picture.
+
+The second one is I want
+to parametrize the results
+
+for the polarizability using
+the concept of oscillator
+
+strengths.
+
+And thirdly, I want
+to tell you how
+
+you can, already at this point,
+take our result for the AC
+
+polarizability and calculate
+how do atoms absorb light
+
+and what is the dispersive
+phase shift which atoms generate
+
+when they're exposed to light.
+
+Or in other words,
+I want to show you
+
+that based on this
+simple result,
+
+we have pretty much already
+all the information we need
+
+to understand how absorption
+imaging and dispersive
+
+imaging is done
+in the laboratory.
+
+So these are the
+three directions
+
+I would like to take it.
+
+So let's start with number one.
+
+The relation to
+the dressed-atom.
+
+So what I want to show you now
+is that a result we obtained
+
+in time dependent
+perturbation theory,
+
+we could've actually obtained
+in time independent perturbation
+
+theory by not using a
+coherent electric field which
+
+oscillates.
+
+But just assuming that
+they're stationary Fock states
+
+of photons.
+
+And this is actually the
+dressed-atom picture.
+
+I know I'm throwing now a
+lot of sort of lingo at you.
+
+It's actually
+very, very trivial.
+
+But I want to show you that you
+have a result where if you just
+
+open your eyes, you see actually
+the dressed-atom shining
+
+through.
+
+So what we had is we had
+an energy shift here.
+
+Which was let me just
+summarize what we have derived.
+
+Was this result with
+a polarizability
+
+which we derived.
+
+And let me rewrite the
+results from above.
+
+So this is why I made the
+remark about the averaging
+
+of the electric field.
+
+If you combine it
+with, as you will see,
+
+Rabi frequencies and
+dressed-atom picture,
+
+you'll need the amplitude
+of the electric field.
+
+And formulated in the amplitude
+of the electric field,
+
+you have a one quarter.
+
+And this is not a mistake.
+
+And you can really trace
+it down to the time
+
+average of the cosine term.
+
+OK, so this is now-- I'm really
+copying from the previous page.
+
+We had the difference frequency
+between state 1 and state 2.
+
+So I'm simply assuming
+that we couple two states.
+
+Now an s and p
+state, If you want.
+
+We have a matrix
+element which is
+
+the matrix element of
+the position operator,
+
+z, between state 1
+and state 2 squared.
+
+We have an energy denominator
+which was this one.
+
+And we have-- so I'm just
+rewriting the previous result.
+
+But now I usually
+hate matrix elements
+
+when they appear in an equation.
+
+I mean, who knows
+matrix elements.
+
+What is the relevant
+thing when we
+
+couple two different states
+is the Rabi frequency.
+
+Frequency units is what we want.
+
+So, therefore, I have
+prepared the formula
+
+that I can take
+the matrix element
+
+with the electric field.
+
+And this is nothing else than
+the Rabi frequency squared.
+
+Or actually, one is
+measured as energy units.
+
+The other is frequency units.
+
+So there is an h bar square.
+
+So, therefore, I have
+now written this result
+
+in what I think is a more
+physically insightful way
+
+by explicitly identifying
+the Rabi frequency which
+
+couples ground and
+excited states.
+
+And I also want
+to separate, want
+
+to introduce the
+detuning of the time
+
+dependent oscillating
+electric field from resonance.
+
+And then I obtain this result.
+
+Doesn't it look so much simpler
+than what we had before?
+
+And it has a lot of
+physics we can discuss now.
+
+One over delta is sort
+of like an AC Stark
+
+effect in one limit.
+
+It's a far-off resonant case of
+an optical trapping potential.
+
+So this formula has
+a lot of insight
+
+which I want to provide now.
+
+The second part I give you the
+name and the interpretation
+
+will become obvious in a moment.
+
+Is the important
+Bloch-Siegert shift.
+
+It is the AC Stark shift due
+to the counterrotating term.
+
+So what I'm motivating here
+is just don't get confused.
+
+What I write down
+is very simple.
+
+And I sometimes use advanced
+language for those of you
+
+who have heard those buzz words.
+
+But what I really mean
+is what I want to discuss
+
+and you to follow are the
+simple steps we do here.
+
+So anyway, what
+I've just done is
+
+I've rewritten the result
+from the previous page
+
+by just introducing
+what I suggest
+
+as more physically
+appealing symbols.
+
+And now I want to remind you
+that this result for the AC
+
+Stark effect doesn't it look
+very similar not to a result,
+
+to the standard result of
+time independent perturbation
+
+theory?
+
+And, of course, you
+remember that in time
+
+independent
+perturbation theory, you
+
+get an energy shift which is
+the square of a matrix element
+
+divided by detuning.
+
+So it seems when we inspect
+our result for the AC Stark
+
+effect which came from time
+dependent perturbation theory,
+
+that this result here has
+actually-- if we map it
+
+on time independent perturbation
+theory, it has two terms.
+
+Both coupled by
+the Rabi frequency.
+
+But one has a detuning of delta.
+
+And the other has a detuning
+of minus 2 omega, minus delta.
+
+So it seems that the result
+for the AC Stark shift
+
+can be completely understood
+by a mixture of not one,
+
+but two different states
+with different detunings.
+
+And this is exactly
+what we will do
+
+in 8.422 in the
+dressed-atom picture
+
+when we have quantized
+the electromagnetic field.
+
+In other words, we have photons.
+
+Because then what we
+have is the following.
+
+We have the ground state
+with n photons, n gamma.
+
+Well, there are sort of
+n quanta in the system.
+
+n photons.
+
+But what we can do is we can now
+have one quantum of excitation
+
+with the atom.
+
+And n minus 1 photon.
+
+So it's almost like
+absorbing a photon.
+
+And this state has
+a detuning of delta.
+
+But then we can also
+consider an excited state.
+
+In other words, here, we
+connect to the excited state
+
+by absorbing a photon.
+
+But we can also, we talk
+about it more later,
+
+we can also connect
+to the excited state
+
+by emitting a photon.
+
+So this state has now not
+one quantum of excitation,
+
+there's three quanta
+of excitation.
+
+One in the atom and
+two in the photon.
+
+So, therefore, its detuning
+is now much, much larger.
+
+Actually, if we're on
+resonant, the detuning
+
+would be just 2 omega.
+
+But if you are detuned,
+there is the delta.
+
+So in other words,
+we can just say
+
+if it would do
+time independent--
+
+I'm not doing it here.
+
+And I leave kind
+of all the beauty
+
+to when we discuss the
+dressed-atom picture
+
+in its full-fledged version.
+
+But all I'm telling you is that
+the result for the AC Stark
+
+shift looks like type
+independent perturbation theory
+
+with those two detunings.
+
+And I'm now offering you the
+physical picture behind it
+
+by saying, look, when we
+have the ground state with n
+
+photons, and we have
+those two other states,
+
+they have exactly the detuning
+which our results suggests.
+
+And yes, indeed, if you look at
+the many folds for those three
+
+states and we would simply do
+time independent perturbation
+
+theory, we would find exactly
+the same frequency shifts,
+
+the AC Stark shift
+as we just obtained
+
+in a time dependent picture.
+
+So in other words, what
+I'm telling you is there
+
+are two ways to obtain
+the AC Stark shift.
+
+One is you do time dependent
+perturbation theory assuming
+
+oscillating electric field.
+
+And that would mean in
+the quantized language
+
+you assume the electromagnetic
+field is in a coherent state.
+
+Alternatively, you can
+quantize the electric field
+
+and introduce Fock states.
+
+And then because Fock
+states are type independent,
+
+then these are the eigenstates
+of the electromagnetic field
+
+in a cavity.
+
+And now you obtain the
+same atomic level shift
+
+in time independent
+perturbation theory.
+
+So in other words, we can
+have photon number states.
+
+And do time independent
+perturbation theory.
+
+Or alternatively, we can use a
+semi-classical electric field.
+
+Which means we have a
+classical electric field.
+
+And then we can treat
+it in time dependent.
+
+All the textbooks generally
+use the latter approach.
+
+Because it uses a same
+classical electric field.
+
+But I can tell you, I strongly
+prefer the first approach.
+
+Because in the
+first approach, you
+
+have no problems whatsoever.
+
+What is the time
+dependent wave function?
+
+What is an energy level shift
+when you have a driven system?
+
+In a time independent
+way, everything just
+
+is simple and right
+there in a simple way.
+
+But it's two different
+physical regimes.
+
+Questions?
+
+OK, second point of
+discussion is the concept
+
+of the oscillator strengths.
+
+So what I'm teaching in
+the next five minutes
+
+is so old-fashioned
+that I sometimes
+
+wonder should I still
+teach it or not.
+
+On the other hand, you find
+it in all the textbooks.
+
+You also want to understand
+a little bit the tradition.
+
+And at least I'm giving
+you some motivation
+
+to learn about it that if
+I parametrize the matrix
+
+element with an
+oscillators strength.
+
+And most of your atoms,
+most of the alkali atoms
+
+have an oscillator
+strength for the s
+
+to p transition for the D-lines.
+
+Which is unity.
+
+You can actually write down
+what is the matrix element.
+
+What is the spontaneous lifetime
+of your atom without knowing
+
+anything about atomic structure.
+
+Just memorizing that f equals
+1, the oscillator strength
+
+is 1 is pretty much all you
+have to know about your atom.
+
+And the rest, the only
+other thing you have to know
+
+is what is the resonant
+frequency of your laser?
+
+780 nanometer?
+
+589 nanometer?
+
+671 nanometer?
+
+So the modern motivation for
+this old-fashioned concept
+
+is for simple atoms where
+the oscillator strength
+
+is close to 1, this is
+probably the parametrization
+
+you want to use
+because you can forget
+
+about the atomic structure.
+
+So but the derivation
+would go as follows.
+
+I want to compare our result.
+
+How an atom responds
+to an electric field.
+
+I want to compare this
+result to the result
+
+of a classical oscillator.
+
+So compare our result
+for the AC polarizability
+
+to a classical
+harmonic oscillator.
+
+So I assume this classical
+harmonic oscillator
+
+has a charge, a mass
+term, and a frequency.
+
+And both the atom and the
+classical harmonic oscillator
+
+are driven by the time
+dependent electric field.
+
+Which we have already
+parametrized by cosine omega t.
+
+OK.
+
+If you look at the classical
+harmonic oscillator,
+
+you find that the--
+you drive it at omega
+
+and ask what is it time
+dependent dipole moment?
+
+It's driven by the cosine term.
+
+And what I mean, of
+course, is dipole moment
+
+of a classical
+harmonic oscillator
+
+is nothing else than
+charge times displacement.
+
+And, well, if you
+spend one minute
+
+and solve the equation for the
+driven harmonic oscillator,
+
+you find that the response,
+the amplitude, the steady state
+
+amplitude, [? zk ?] of
+the harmonic oscillator
+
+is cosine omega t.
+
+Times a prefactor which
+I'm writing down now.
+
+There is this resonant behavior.
+
+So that's the response of the
+classical harmonic oscillator.
+
+And yeah.
+
+So this is just classical
+harmonic oscillator physics.
+
+And I now want to
+define a quantity which
+
+I call the oscillator
+strength of the atom.
+
+So I'm just jumping now from the
+harmonic oscillator to the atom
+
+and then I combine a the two.
+
+And the oscillator
+strength is nothing else
+
+than a parametrization
+of the matrix element
+
+with between different states.
+
+But it's dimensionless.
+
+And it's made dimensionless
+by using the mass.
+
+By using h-bar.
+
+And by using the
+transition frequency.
+
+So the atomic-- let me just
+make sure we take care of it.
+
+This is the result for the
+classical harmonic oscillator.
+
+And this is now the
+result for the atom
+
+that we have found already they
+the result for the atom before.
+
+And now I'm rewriting
+it simply by expressing
+
+the matrix element square
+by the oscillator strength.
+
+And this here is just
+another expression
+
+for the polarizability alpha.
+
+Well, let's now
+compare the result
+
+of a quantum mechanical
+atom exactly described
+
+by time dependent
+perturbation theory
+
+to the result of a classical
+harmonic oscillator.
+
+The frequency
+structure is the same.
+
+So if I would know say
+we have an ensemble
+
+of harmonic oscillators,
+and the harmonic oscillators
+
+may have different frequencies
+and different charges.
+
+Then I have made those
+formulas exactly equal.
+
+And I can now formulate
+that the atom reacts
+
+to an electric field to time
+dependent electric field.
+
+Exactly as an ensemble
+of classical oscillators
+
+with effective charge.
+
+If I would say I have an
+ensemble of oscillators
+
+with effective charge,
+then the response
+
+of the atom and the
+response of the ensemble
+
+of classical oscillators
+is absolutely identical.
+
+So the atom response is a
+set classical oscillators
+
+with an effective charge
+which is given here.
+
+So, therefore, you
+don't have to go further
+
+if you want to have any
+intuition how an atom reacts
+
+to light.
+
+The classical
+harmonic oscillator
+
+is not an approximation.
+
+It is exact.
+
+So that result is
+relevant because it
+
+allows us to clearly formulate
+the classical correspondence.
+
+The second thing is
+as you can easily
+
+show with basic
+commutator algebra,
+
+there is the Thomas
+Kuhn sum rule
+
+which is discussed in all
+texts in quantum physics
+
+which says that the sum over
+all oscillator strengths is 1.
+
+So, therefore, we know
+if we have transitions
+
+from the ground state
+to different states,
+
+the sum of all the oscillator
+strengths to all the states
+
+can only be 1.
+
+And another advantage of the
+formulation with oscillator
+
+strength is that it is
+a dimensionless unit.
+
+It's a dimensionless
+parameter which tells us
+
+how the atom corresponds to an
+external electromagnetic field.
+
+I just need two or
+three more minutes
+
+to show you what that means.
+
+If you have hydrogen,
+the 1s to 2p transition
+
+is the strongest transition.
+
+And it has a matrix
+element which
+
+corresponds to an oscillator
+strength of about 0.4.
+
+So the rest comes from
+more highly excited states.
+
+However, for alkali atoms, the
+D-line, the s to p transition
+
+has an oscillator strength.
+
+I didn't write down
+the second digit,
+
+but it's with excellent
+approximation, 1.98
+
+or something.
+
+So not just qualitatively,
+almost quantitatively,
+
+you capture the response from
+the atom by saying f equals 1.
+
+So if you use for the
+alkali atoms f equals 1,
+
+then simply the transition
+frequency of the D-line
+
+gives you the
+polarizability alpha.
+
+And as we will see later,
+because we haven't introduced
+
+it is, but it will also give you
+gamma the natural line beats.
+
+Because all the coupling to
+the electromagnetic field
+
+to an external field is
+really captured by saying what
+
+the matrix element is.
+
+And f equals 1 is
+nothing else than saying
+
+the matrix element
+is such and such.
+
+And, indeed, if I now use the
+definition of the oscillator
+
+strength in reverse,
+the matrix element
+
+between two transitions,
+between two states
+
+is the matrix element squared
+is the oscillator length
+
+times one half.
+
+And if you just go back
+and look at the formula,
+
+you find that this
+is now dimensionless.
+
+So we need now because the left
+hand side is the length square,
+
+we need two lengths.
+
+One is the Compton wave length
+which is h-bar over 2 times
+
+the mass of the electron.
+
+And lambda bar is the
+transition wave lengths,
+
+lambda divided by 2 pi.
+
+So, therefore, I haven't found
+it anywhere in textbooks,
+
+but this is my sort
+of summary of this.
+
+If you have a strong
+transition, and strong
+
+means that the oscillator
+length is close to 1,
+
+then the matrix element
+for the transition
+
+is approximately
+the geometric mean
+
+of the Compton wave
+length of the electron.
+
+And the reduced wave lengths
+of the resonant transition.
+
+So now if you want
+to know what is
+
+the matrix element for
+the d-line of rubidium,
+
+take the wave length
+of 780 nanometer.
+
+Take the Compton wave
+lengths of the electron
+
+and you get an
+accurate expression.
+
+I know time is over.
+
+Any questions?
+
+All right.
\ No newline at end of file
diff --git a/jwh7LqjT4w0.txt b/jwh7LqjT4w0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4768072dd1e2877e257ed99da16b2be5af730371
--- /dev/null
+++ b/jwh7LqjT4w0.txt
@@ -0,0 +1,10523 @@
+align:start position:0%
+ 
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+a Creative Commons license your support
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+will help MIT OpenCourseWare continue to
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+materials from hundreds of MIT courses
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+ align:start position:0%
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+ 
+
+ align:start position:0%
+ 
+so welcome back everybody
+
+ align:start position:0%
+so welcome back everybody
+ 
+
+ align:start position:0%
+so welcome back everybody
+so this is the final exam a checklist so
+
+ align:start position:0%
+so this is the final exam a checklist so
+ 
+
+ align:start position:0%
+so this is the final exam a checklist so
+with a single oscillator we need to make
+
+ align:start position:0%
+with a single oscillator we need to make
+ 
+
+ align:start position:0%
+with a single oscillator we need to make
+sure that you know how to write down the
+
+ align:start position:0%
+sure that you know how to write down the
+ 
+
+ align:start position:0%
+sure that you know how to write down the
+equation of motion we have discussed
+
+ align:start position:0%
+equation of motion we have discussed
+ 
+
+ align:start position:0%
+equation of motion we have discussed
+about damped under damped critically
+
+ align:start position:0%
+about damped under damped critically
+ 
+
+ align:start position:0%
+about damped under damped critically
+damped and oba tempered attached
+
+ align:start position:0%
+damped and oba tempered attached
+ 
+
+ align:start position:0%
+damped and oba tempered attached
+oscillators and we have tried to drive
+
+ align:start position:0%
+oscillators and we have tried to drive
+ 
+
+ align:start position:0%
+oscillators and we have tried to drive
+oscillators and we observe transient
+
+ align:start position:0%
+oscillators and we observe transient
+ 
+
+ align:start position:0%
+oscillators and we observe transient
+behavior and steady state solution
+
+ align:start position:0%
+behavior and steady state solution
+ 
+
+ align:start position:0%
+behavior and steady state solution
+resonance right so which we actually
+
+ align:start position:0%
+resonance right so which we actually
+ 
+
+ align:start position:0%
+resonance right so which we actually
+demonstrated lab by breaking glass and
+
+ align:start position:0%
+demonstrated lab by breaking glass and
+ 
+
+ align:start position:0%
+demonstrated lab by breaking glass and
+then we move on and try to cup or
+
+ align:start position:0%
+then we move on and try to cup or
+ 
+
+ align:start position:0%
+then we move on and try to cup or
+multiple object together and that brings
+
+ align:start position:0%
+multiple object together and that brings
+ 
+
+ align:start position:0%
+multiple object together and that brings
+us to the capital system what are the
+
+ align:start position:0%
+us to the capital system what are the
+ 
+
+ align:start position:0%
+us to the capital system what are the
+normal modes and how to issues of and
+
+ align:start position:0%
+normal modes and how to issues of and
+ 
+
+ align:start position:0%
+normal modes and how to issues of and
+minus 1 k matrix eigenvalue problem
+
+ align:start position:0%
+minus 1 k matrix eigenvalue problem
+ 
+
+ align:start position:0%
+minus 1 k matrix eigenvalue problem
+right and what is actually for solution
+
+ align:start position:0%
+right and what is actually for solution
+ 
+
+ align:start position:0%
+right and what is actually for solution
+for the description cup of the system
+
+ align:start position:0%
+for the description cup of the system
+ 
+
+ align:start position:0%
+for the description cup of the system
+and can we actually drive the Chabad
+
+ align:start position:0%
+and can we actually drive the Chabad
+ 
+
+ align:start position:0%
+and can we actually drive the Chabad
+system and we found out we can and also
+
+ align:start position:0%
+system and we found out we can and also
+ 
+
+ align:start position:0%
+system and we found out we can and also
+the system will respond as well similar
+
+ align:start position:0%
+the system will respond as well similar
+ 
+
+ align:start position:0%
+the system will respond as well similar
+to what we have see in the single
+
+ align:start position:0%
+to what we have see in the single
+ 
+
+ align:start position:0%
+to what we have see in the single
+oscillator case we see resonance as well
+
+ align:start position:0%
+oscillator case we see resonance as well
+ 
+
+ align:start position:0%
+oscillator case we see resonance as well
+we can excite one of the normal mode by
+
+ align:start position:0%
+we can excite one of the normal mode by
+ 
+
+ align:start position:0%
+we can excite one of the normal mode by
+driving the cup of the system and then
+
+ align:start position:0%
+driving the cup of the system and then
+ 
+
+ align:start position:0%
+driving the cup of the system and then
+we put more and more objects and until
+
+ align:start position:0%
+we put more and more objects and until
+ 
+
+ align:start position:0%
+we put more and more objects and until
+at some point we have infinite number of
+
+ align:start position:0%
+at some point we have infinite number of
+ 
+
+ align:start position:0%
+at some point we have infinite number of
+capital of object what is issued a
+
+ align:start position:0%
+capital of object what is issued a
+ 
+
+ align:start position:0%
+capital of object what is issued a
+solution of refraction and the
+
+ align:start position:0%
+solution of refraction and the
+ 
+
+ align:start position:0%
+solution of refraction and the
+transmission refraction and the
+
+ align:start position:0%
+transmission refraction and the
+ 
+
+ align:start position:0%
+transmission refraction and the
+translation symmetric system I so that
+
+ align:start position:0%
+translation symmetric system I so that
+ 
+
+ align:start position:0%
+translation symmetric system I so that
+is actually a discussion of symmetry we
+
+ align:start position:0%
+is actually a discussion of symmetry we
+ 
+
+ align:start position:0%
+is actually a discussion of symmetry we
+go to the continue limit we actually
+
+ align:start position:0%
+go to the continue limit we actually
+ 
+
+ align:start position:0%
+go to the continue limit we actually
+found wave and wave equations right so
+
+ align:start position:0%
+found wave and wave equations right so
+ 
+
+ align:start position:0%
+found wave and wave equations right so
+we found that partly we make the phase
+
+ align:start position:0%
+we found that partly we make the phase
+ 
+
+ align:start position:0%
+we found that partly we make the phase
+transition from single object vibration
+
+ align:start position:0%
+transition from single object vibration
+ 
+
+ align:start position:0%
+transition from single object vibration
+to waves and that is issue achievement
+
+ align:start position:0%
+to waves and that is issue achievement
+ 
+
+ align:start position:0%
+to waves and that is issue achievement
+we have done in 3 and we have discussed
+
+ align:start position:0%
+we have done in 3 and we have discussed
+ 
+
+ align:start position:0%
+we have done in 3 and we have discussed
+about different systems massive string
+
+ align:start position:0%
+about different systems massive string
+ 
+
+ align:start position:0%
+about different systems massive string
+massive spring song wave electromagnetic
+
+ align:start position:0%
+massive spring song wave electromagnetic
+ 
+
+ align:start position:0%
+massive spring song wave electromagnetic
+waves and we have discussed the progress
+
+ align:start position:0%
+waves and we have discussed the progress
+ 
+
+ align:start position:0%
+waves and we have discussed the progress
+a progressive wave and standing waves
+
+ align:start position:0%
+a progressive wave and standing waves
+ 
+
+ align:start position:0%
+a progressive wave and standing waves
+for the bound system we have also normal
+
+ align:start position:0%
+for the bound system we have also normal
+ 
+
+ align:start position:0%
+for the bound system we have also normal
+modes and we discuss about how to
+
+ align:start position:0%
+modes and we discuss about how to
+ 
+
+ align:start position:0%
+modes and we discuss about how to
+actually do food year decomposition and
+
+ align:start position:0%
+actually do food year decomposition and
+ 
+
+ align:start position:0%
+actually do food year decomposition and
+what is actually the physical meaning of
+
+ align:start position:0%
+what is actually the physical meaning of
+ 
+
+ align:start position:0%
+what is actually the physical meaning of
+food area basi decomposition in L 3 and
+
+ align:start position:0%
+food area basi decomposition in L 3 and
+ 
+
+ align:start position:0%
+food area basi decomposition in L 3 and
+4 the infinite system we also learned
+
+ align:start position:0%
+4 the infinite system we also learned
+ 
+
+ align:start position:0%
+4 the infinite system we also learned
+about food year transform and
+
+ align:start position:0%
+about food year transform and
+ 
+
+ align:start position:0%
+about food year transform and
+uncertainty principles and we actually
+
+ align:start position:0%
+uncertainty principles and we actually
+ 
+
+ align:start position:0%
+uncertainty principles and we actually
+learn to your pride boundary conditions
+
+ align:start position:0%
+learn to your pride boundary conditions
+ 
+
+ align:start position:0%
+learn to your pride boundary conditions
+so that actually we constrained the
+
+ align:start position:0%
+so that actually we constrained the
+ 
+
+ align:start position:0%
+so that actually we constrained the
+possible wavelengths of the normal modes
+
+ align:start position:0%
+possible wavelengths of the normal modes
+ 
+
+ align:start position:0%
+possible wavelengths of the normal modes
+and therefore we also learned about how
+
+ align:start position:0%
+and therefore we also learned about how
+ 
+
+ align:start position:0%
+and therefore we also learned about how
+to as we put a system or together and
+
+ align:start position:0%
+to as we put a system or together and
+ 
+
+ align:start position:0%
+to as we put a system or together and
+finally how to actually determine the
+
+ align:start position:0%
+finally how to actually determine the
+ 
+
+ align:start position:0%
+finally how to actually determine the
+dispersion relation which is Omega as a
+
+ align:start position:0%
+dispersion relation which is Omega as a
+ 
+
+ align:start position:0%
+dispersion relation which is Omega as a
+function of K the web number so until
+
+ align:start position:0%
+function of K the web number so until
+ 
+
+ align:start position:0%
+function of K the web number so until
+now we actually discuss idealize the
+
+ align:start position:0%
+now we actually discuss idealize the
+ 
+
+ align:start position:0%
+now we actually discuss idealize the
+system and we also move on to discuss
+
+ align:start position:0%
+system and we also move on to discuss
+ 
+
+ align:start position:0%
+system and we also move on to discuss
+dispersive medium so we have learned
+
+ align:start position:0%
+dispersive medium so we have learned
+ 
+
+ align:start position:0%
+dispersive medium so we have learned
+some more even more about dispersion
+
+ align:start position:0%
+some more even more about dispersion
+ 
+
+ align:start position:0%
+some more even more about dispersion
+relation for a dispersive medium and the
+
+ align:start position:0%
+relation for a dispersive medium and the
+ 
+
+ align:start position:0%
+relation for a dispersive medium and the
+signal transmission how to issue the
+
+ align:start position:0%
+signal transmission how to issue the
+ 
+
+ align:start position:0%
+signal transmission how to issue the
+send signal right through highly
+
+ align:start position:0%
+send signal right through highly
+ 
+
+ align:start position:0%
+send signal right through highly
+dispersive medium right that the
+
+ align:start position:0%
+dispersive medium right that the
+ 
+
+ align:start position:0%
+dispersive medium right that the
+solution we were proposing is to use a
+
+ align:start position:0%
+solution we were proposing is to use a
+ 
+
+ align:start position:0%
+solution we were proposing is to use a
+amplitude modulation
+
+ align:start position:0%
+amplitude modulation
+ 
+
+ align:start position:0%
+amplitude modulation
+modulation radio and as of the problem
+
+ align:start position:0%
+modulation radio and as of the problem
+ 
+
+ align:start position:0%
+modulation radio and as of the problem
+of dispersion and group velocity and
+
+ align:start position:0%
+of dispersion and group velocity and
+ 
+
+ align:start position:0%
+of dispersion and group velocity and
+phase velocity we covered that and also
+
+ align:start position:0%
+phase velocity we covered that and also
+ 
+
+ align:start position:0%
+phase velocity we covered that and also
+as I mentioned before the uncertainty
+
+ align:start position:0%
+as I mentioned before the uncertainty
+ 
+
+ align:start position:0%
+as I mentioned before the uncertainty
+principle a 2 3 as the assistance so we
+
+ align:start position:0%
+principle a 2 3 as the assistance so we
+ 
+
+ align:start position:0%
+principle a 2 3 as the assistance so we
+have bound system which we have no more
+
+ align:start position:0%
+have bound system which we have no more
+ 
+
+ align:start position:0%
+have bound system which we have no more
+modes for 2 dimensional and 3
+
+ align:start position:0%
+modes for 2 dimensional and 3
+ 
+
+ align:start position:0%
+modes for 2 dimensional and 3
+dimensional systems as well you can see
+
+ align:start position:0%
+dimensional systems as well you can see
+ 
+
+ align:start position:0%
+dimensional systems as well you can see
+no more will appraise so to just make
+
+ align:start position:0%
+no more will appraise so to just make
+ 
+
+ align:start position:0%
+no more will appraise so to just make
+sure that you know how to actually
+
+ align:start position:0%
+sure that you know how to actually
+ 
+
+ align:start position:0%
+sure that you know how to actually
+derive all those standing waves for a
+
+ align:start position:0%
+derive all those standing waves for a
+ 
+
+ align:start position:0%
+derive all those standing waves for a
+different dimension of system
+
+ align:start position:0%
+different dimension of system
+ 
+
+ align:start position:0%
+different dimension of system
+and we actually showed and approved
+
+ align:start position:0%
+and we actually showed and approved
+ 
+
+ align:start position:0%
+and we actually showed and approved
+geometrical optics which is actually a
+
+ align:start position:0%
+geometrical optics which is actually a
+ 
+
+ align:start position:0%
+geometrical optics which is actually a
+direct consequence of waves wavefunction
+
+ align:start position:0%
+direct consequence of waves wavefunction
+ 
+
+ align:start position:0%
+direct consequence of waves wavefunction
+continuation of the wave function the
+
+ align:start position:0%
+continuation of the wave function the
+ 
+
+ align:start position:0%
+continuation of the wave function the
+boundary condition and we learned about
+
+ align:start position:0%
+boundary condition and we learned about
+ 
+
+ align:start position:0%
+boundary condition and we learned about
+the refraction duel and those of Snell's
+
+ align:start position:0%
+the refraction duel and those of Snell's
+ 
+
+ align:start position:0%
+the refraction duel and those of Snell's
+law we talked about polarize the waves
+
+ align:start position:0%
+law we talked about polarize the waves
+ 
+
+ align:start position:0%
+law we talked about polarize the waves
+linear the circularly polarized
+
+ align:start position:0%
+linear the circularly polarized
+ 
+
+ align:start position:0%
+linear the circularly polarized
+elliptically polarized and the polarizer
+
+ align:start position:0%
+elliptically polarized and the polarizer
+ 
+
+ align:start position:0%
+elliptically polarized and the polarizer
+and quarter wave plate and at the end of
+
+ align:start position:0%
+and quarter wave plate and at the end of
+ 
+
+ align:start position:0%
+and quarter wave plate and at the end of
+the discussion of two shitty system we
+
+ align:start position:0%
+the discussion of two shitty system we
+ 
+
+ align:start position:0%
+the discussion of two shitty system we
+actually discussed about how to actually
+
+ align:start position:0%
+actually discussed about how to actually
+ 
+
+ align:start position:0%
+actually discussed about how to actually
+generate electromagnetic wave by
+
+ align:start position:0%
+generate electromagnetic wave by
+ 
+
+ align:start position:0%
+generate electromagnetic wave by
+accelerated charge okay finally we went
+
+ align:start position:0%
+accelerated charge okay finally we went
+ 
+
+ align:start position:0%
+accelerated charge okay finally we went
+on and talked about how those young
+
+ align:start position:0%
+on and talked about how those young
+ 
+
+ align:start position:0%
+on and talked about how those young
+waves propagate in Thai electrics and
+
+ align:start position:0%
+waves propagate in Thai electrics and
+ 
+
+ align:start position:0%
+waves propagate in Thai electrics and
+again boundary condition which these two
+
+ align:start position:0%
+again boundary condition which these two
+ 
+
+ align:start position:0%
+again boundary condition which these two
+interesting phenomena which belongs only
+
+ align:start position:0%
+interesting phenomena which belongs only
+ 
+
+ align:start position:0%
+interesting phenomena which belongs only
+to electromagnetic waves for example
+
+ align:start position:0%
+to electromagnetic waves for example
+ 
+
+ align:start position:0%
+to electromagnetic waves for example
+Brewster's angle right and also the
+
+ align:start position:0%
+Brewster's angle right and also the
+ 
+
+ align:start position:0%
+Brewster's angle right and also the
+refraction mp2 refracted wave amplitude
+
+ align:start position:0%
+refraction mp2 refracted wave amplitude
+ 
+
+ align:start position:0%
+refraction mp2 refracted wave amplitude
+is actually carbon by the property of
+
+ align:start position:0%
+is actually carbon by the property of
+ 
+
+ align:start position:0%
+is actually carbon by the property of
+the electromagnetic waves which is
+
+ align:start position:0%
+the electromagnetic waves which is
+ 
+
+ align:start position:0%
+the electromagnetic waves which is
+actually coming from the laws which
+
+ align:start position:0%
+actually coming from the laws which
+ 
+
+ align:start position:0%
+actually coming from the laws which
+governs it also meant a wave which is
+
+ align:start position:0%
+governs it also meant a wave which is
+ 
+
+ align:start position:0%
+governs it also meant a wave which is
+Maxwell's equations in matter and we
+
+ align:start position:0%
+Maxwell's equations in matter and we
+ 
+
+ align:start position:0%
+Maxwell's equations in matter and we
+were trying to also manipulate lost
+
+ align:start position:0%
+were trying to also manipulate lost
+ 
+
+ align:start position:0%
+were trying to also manipulate lost
+weight by adding them together and we
+
+ align:start position:0%
+weight by adding them together and we
+ 
+
+ align:start position:0%
+weight by adding them together and we
+see constructive and destructive
+
+ align:start position:0%
+see constructive and destructive
+ 
+
+ align:start position:0%
+see constructive and destructive
+interference and diffraction phenomena
+
+ align:start position:0%
+interference and diffraction phenomena
+ 
+
+ align:start position:0%
+interference and diffraction phenomena
+and then we connect that to quantum
+
+ align:start position:0%
+and then we connect that to quantum
+ 
+
+ align:start position:0%
+and then we connect that to quantum
+mechanics by showing you a single
+
+ align:start position:0%
+mechanics by showing you a single
+ 
+
+ align:start position:0%
+mechanics by showing you a single
+electron interference experiment and
+
+ align:start position:0%
+electron interference experiment and
+ 
+
+ align:start position:0%
+electron interference experiment and
+that connects us to the beginning of the
+
+ align:start position:0%
+that connects us to the beginning of the
+ 
+
+ align:start position:0%
+that connects us to the beginning of the
+quantum mechanics which is actually
+
+ align:start position:0%
+quantum mechanics which is actually
+ 
+
+ align:start position:0%
+quantum mechanics which is actually
+public a probability waves which you
+
+ align:start position:0%
+public a probability waves which you
+ 
+
+ align:start position:0%
+public a probability waves which you
+have to be different from all the waves
+
+ align:start position:0%
+have to be different from all the waves
+ 
+
+ align:start position:0%
+have to be different from all the waves
+we have been discussing but you are
+
+ align:start position:0%
+we have been discussing but you are
+ 
+
+ align:start position:0%
+we have been discussing but you are
+going to learn a lot more in Airport
+
+ align:start position:0%
+going to learn a lot more in Airport
+ 
+
+ align:start position:0%
+going to learn a lot more in Airport
+okay so Tom don't worry
+
+ align:start position:0%
+okay so Tom don't worry
+ 
+
+ align:start position:0%
+okay so Tom don't worry
+alright so that decision to check this
+
+ align:start position:0%
+alright so that decision to check this
+ 
+
+ align:start position:0%
+alright so that decision to check this
+you can see that I can write it in two
+
+ align:start position:0%
+you can see that I can write it in two
+ 
+
+ align:start position:0%
+you can see that I can write it in two
+patches so it's not a bad already
+
+ align:start position:0%
+patches so it's not a bad already
+ 
+
+ align:start position:0%
+patches so it's not a bad already
+and I hope that there were nothing
+
+ align:start position:0%
+and I hope that there were nothing
+ 
+
+ align:start position:0%
+and I hope that there were nothing
+really sounds like new to you by now
+
+ align:start position:0%
+really sounds like new to you by now
+ 
+
+ align:start position:0%
+really sounds like new to you by now
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+if you find anything is new you have to
+
+ align:start position:0%
+if you find anything is new you have to
+ 
+
+ align:start position:0%
+if you find anything is new you have to
+review that part that means you're mr.
+
+ align:start position:0%
+review that part that means you're mr.
+ 
+
+ align:start position:0%
+review that part that means you're mr.
+Cass all right so what I'm going to do
+
+ align:start position:0%
+Cass all right so what I'm going to do
+ 
+
+ align:start position:0%
+Cass all right so what I'm going to do
+now is to go through all the material
+
+ align:start position:0%
+now is to go through all the material
+ 
+
+ align:start position:0%
+now is to go through all the material
+faster than the speed of light all right
+
+ align:start position:0%
+faster than the speed of light all right
+ 
+
+ align:start position:0%
+faster than the speed of light all right
+so that you will get nothing no you are
+
+ align:start position:0%
+so that you will get nothing no you are
+ 
+
+ align:start position:0%
+so that you will get nothing no you are
+going to get a list of the topic and you
+
+ align:start position:0%
+going to get a list of the topic and you
+ 
+
+ align:start position:0%
+going to get a list of the topic and you
+just have to feel it if you feel good
+
+ align:start position:0%
+just have to feel it if you feel good
+ 
+
+ align:start position:0%
+just have to feel it if you feel good
+like when you are having a cupcake right
+
+ align:start position:0%
+like when you are having a cupcake right
+ 
+
+ align:start position:0%
+like when you are having a cupcake right
+then you are good for the pie now if you
+
+ align:start position:0%
+then you are good for the pie now if you
+ 
+
+ align:start position:0%
+then you are good for the pie now if you
+don't feel good
+
+ align:start position:0%
+don't feel good
+ 
+
+ align:start position:0%
+don't feel good
+what is Professor D talking about he's
+
+ align:start position:0%
+what is Professor D talking about he's
+ 
+
+ align:start position:0%
+what is Professor D talking about he's
+talking about nonsense now then you are
+
+ align:start position:0%
+talking about nonsense now then you are
+ 
+
+ align:start position:0%
+talking about nonsense now then you are
+in trouble and you have to review that
+
+ align:start position:0%
+in trouble and you have to review that
+ 
+
+ align:start position:0%
+in trouble and you have to review that
+part all right
+
+ align:start position:0%
+part all right
+ 
+
+ align:start position:0%
+part all right
+okay so that's it ladoo up so that start
+
+ align:start position:0%
+okay so that's it ladoo up so that start
+ 
+
+ align:start position:0%
+okay so that's it ladoo up so that start
+all right so why a or three so we
+
+ align:start position:0%
+all right so why a or three so we
+ 
+
+ align:start position:0%
+all right so why a or three so we
+started a discussion welcome we started
+
+ align:start position:0%
+started a discussion welcome we started
+ 
+
+ align:start position:0%
+started a discussion welcome we started
+a discussion of a Austrey and it's way
+
+ align:start position:0%
+a discussion of a Austrey and it's way
+ 
+
+ align:start position:0%
+a discussion of a Austrey and it's way
+vibrational wave so it's an end of this
+
+ align:start position:0%
+vibrational wave so it's an end of this
+ 
+
+ align:start position:0%
+vibrational wave so it's an end of this
+ao3
+
+ align:start position:0%
+ao3
+ 
+
+ align:start position:0%
+ao3
+and the that the motivation is really
+
+ align:start position:0%
+and the that the motivation is really
+ 
+
+ align:start position:0%
+and the that the motivation is really
+simple because we cannot even recognize
+
+ align:start position:0%
+simple because we cannot even recognize
+ 
+
+ align:start position:0%
+simple because we cannot even recognize
+the universe without using waves and
+
+ align:start position:0%
+the universe without using waves and
+ 
+
+ align:start position:0%
+the universe without using waves and
+vibration right then you cannot see me
+
+ align:start position:0%
+vibration right then you cannot see me
+ 
+
+ align:start position:0%
+vibration right then you cannot see me
+and you cannot hear anything and you
+
+ align:start position:0%
+and you cannot hear anything and you
+ 
+
+ align:start position:0%
+and you cannot hear anything and you
+cannot feel the vibration so the
+
+ align:start position:0%
+cannot feel the vibration so the
+ 
+
+ align:start position:0%
+cannot feel the vibration so the
+rotation of a black hole by your body
+
+ align:start position:0%
+rotation of a black hole by your body
+ 
+
+ align:start position:0%
+rotation of a black hole by your body
+anymore then it's not very cool right so
+
+ align:start position:0%
+anymore then it's not very cool right so
+ 
+
+ align:start position:0%
+anymore then it's not very cool right so
+therefore we as you study a o32
+
+ align:start position:0%
+therefore we as you study a o32
+ 
+
+ align:start position:0%
+therefore we as you study a o32
+understand the basic ideas about waves
+
+ align:start position:0%
+understand the basic ideas about waves
+ 
+
+ align:start position:0%
+understand the basic ideas about waves
+and vibrations and we found that wave
+
+ align:start position:0%
+and vibrations and we found that wave
+ 
+
+ align:start position:0%
+and vibrations and we found that wave
+and vibrations are actually interesting
+
+ align:start position:0%
+and vibrations are actually interesting
+ 
+
+ align:start position:0%
+and vibrations are actually interesting
+phenomena waves are actually connected
+
+ align:start position:0%
+phenomena waves are actually connected
+ 
+
+ align:start position:0%
+phenomena waves are actually connected
+to vibration because if you look at only
+
+ align:start position:0%
+to vibration because if you look at only
+ 
+
+ align:start position:0%
+to vibration because if you look at only
+as for example a single object on these
+
+ align:start position:0%
+as for example a single object on these
+ 
+
+ align:start position:0%
+as for example a single object on these
+waves you will see you actually see that
+
+ align:start position:0%
+waves you will see you actually see that
+ 
+
+ align:start position:0%
+waves you will see you actually see that
+is actually a single object which is a
+
+ align:start position:0%
+is actually a single object which is a
+ 
+
+ align:start position:0%
+is actually a single object which is a
+sturdy up up and down oscillating up and
+
+ align:start position:0%
+sturdy up up and down oscillating up and
+ 
+
+ align:start position:0%
+sturdy up up and down oscillating up and
+down and this is your vibration so there
+
+ align:start position:0%
+down and this is your vibration so there
+ 
+
+ align:start position:0%
+down and this is your vibration so there
+is a close connection between single
+
+ align:start position:0%
+is a close connection between single
+ 
+
+ align:start position:0%
+is a close connection between single
+particle vibration and the waves and
+
+ align:start position:0%
+particle vibration and the waves and
+ 
+
+ align:start position:0%
+particle vibration and the waves and
+that is actually the first thing we as
+
+ align:start position:0%
+that is actually the first thing we as
+ 
+
+ align:start position:0%
+that is actually the first thing we as
+you learn therefore we need to first
+
+ align:start position:0%
+you learn therefore we need to first
+ 
+
+ align:start position:0%
+you learn therefore we need to first
+understand that you do
+
+ align:start position:0%
+understand that you do
+ 
+
+ align:start position:0%
+understand that you do
+of a single particle system and we use
+
+ align:start position:0%
+of a single particle system and we use
+ 
+
+ align:start position:0%
+of a single particle system and we use
+make use of this opportunity to actually
+
+ align:start position:0%
+make use of this opportunity to actually
+ 
+
+ align:start position:0%
+make use of this opportunity to actually
+start the discussion of scientific
+
+ align:start position:0%
+start the discussion of scientific
+ 
+
+ align:start position:0%
+start the discussion of scientific
+master right so using this opportunity
+
+ align:start position:0%
+master right so using this opportunity
+ 
+
+ align:start position:0%
+master right so using this opportunity
+basically what we have been doing for
+
+ align:start position:0%
+basically what we have been doing for
+ 
+
+ align:start position:0%
+basically what we have been doing for
+the whole class is the following so the
+
+ align:start position:0%
+the whole class is the following so the
+ 
+
+ align:start position:0%
+the whole class is the following so the
+first step is always to translate a
+
+ align:start position:0%
+first step is always to translate a
+ 
+
+ align:start position:0%
+first step is always to translate a
+physical situation which we are
+
+ align:start position:0%
+physical situation which we are
+ 
+
+ align:start position:0%
+physical situation which we are
+interested in to mathematics right
+
+ align:start position:0%
+interested in to mathematics right
+ 
+
+ align:start position:0%
+interested in to mathematics right
+because mathematics is the only language
+
+ align:start position:0%
+because mathematics is the only language
+ 
+
+ align:start position:0%
+because mathematics is the only language
+which we know which describe the nature
+
+ align:start position:0%
+which we know which describe the nature
+ 
+
+ align:start position:0%
+which we know which describe the nature
+if you come out with a new language and
+
+ align:start position:0%
+if you come out with a new language and
+ 
+
+ align:start position:0%
+if you come out with a new language and
+that is going to be super duper
+
+ align:start position:0%
+that is going to be super duper
+ 
+
+ align:start position:0%
+that is going to be super duper
+breakthrough
+
+ align:start position:0%
+breakthrough
+ 
+
+ align:start position:0%
+breakthrough
+it cannot be estimated by Nobel Prize
+
+ align:start position:0%
+it cannot be estimated by Nobel Prize
+ 
+
+ align:start position:0%
+it cannot be estimated by Nobel Prize
+but there the problem we are facing now
+
+ align:start position:0%
+but there the problem we are facing now
+ 
+
+ align:start position:0%
+but there the problem we are facing now
+is that this is the only language we
+
+ align:start position:0%
+is that this is the only language we
+ 
+
+ align:start position:0%
+is that this is the only language we
+know which works
+
+ align:start position:0%
+know which works
+ 
+
+ align:start position:0%
+know which works
+therefore we actually really follow this
+
+ align:start position:0%
+therefore we actually really follow this
+ 
+
+ align:start position:0%
+therefore we actually really follow this
+recipe for which is actually similar to
+
+ align:start position:0%
+recipe for which is actually similar to
+ 
+
+ align:start position:0%
+recipe for which is actually similar to
+many many other physics class and we
+
+ align:start position:0%
+many many other physics class and we
+ 
+
+ align:start position:0%
+many many other physics class and we
+have a physical situation we use laws of
+
+ align:start position:0%
+have a physical situation we use laws of
+ 
+
+ align:start position:0%
+have a physical situation we use laws of
+nature or models and we have a
+
+ align:start position:0%
+nature or models and we have a
+ 
+
+ align:start position:0%
+nature or models and we have a
+mathematical description which is the
+
+ align:start position:0%
+mathematical description which is the
+ 
+
+ align:start position:0%
+mathematical description which is the
+equation of motion and this is actually
+
+ align:start position:0%
+equation of motion and this is actually
+ 
+
+ align:start position:0%
+equation of motion and this is actually
+the hardest part because you need to
+
+ align:start position:0%
+the hardest part because you need to
+ 
+
+ align:start position:0%
+the hardest part because you need to
+first define a coordinate system so that
+
+ align:start position:0%
+first define a coordinate system so that
+ 
+
+ align:start position:0%
+first define a coordinate system so that
+we can express everything in a system in
+
+ align:start position:0%
+we can express everything in a system in
+ 
+
+ align:start position:0%
+we can express everything in a system in
+that system then you can actually make
+
+ align:start position:0%
+that system then you can actually make
+ 
+
+ align:start position:0%
+that system then you can actually make
+use of the physical law you have learned
+
+ align:start position:0%
+use of the physical law you have learned
+ 
+
+ align:start position:0%
+use of the physical law you have learned
+from the previous l1 and l2 to write
+
+ align:start position:0%
+from the previous l1 and l2 to write
+ 
+
+ align:start position:0%
+from the previous l1 and l2 to write
+down the equation of motion and most of
+
+ align:start position:0%
+down the equation of motion and most of
+ 
+
+ align:start position:0%
+down the equation of motion and most of
+the mistake and also most of the
+
+ align:start position:0%
+the mistake and also most of the
+ 
+
+ align:start position:0%
+the mistake and also most of the
+department or difficulty you are facing
+
+ align:start position:0%
+department or difficulty you are facing
+ 
+
+ align:start position:0%
+department or difficulty you are facing
+is always in this step actually then we
+
+ align:start position:0%
+is always in this step actually then we
+ 
+
+ align:start position:0%
+is always in this step actually then we
+can actually solve the equation of
+
+ align:start position:0%
+can actually solve the equation of
+ 
+
+ align:start position:0%
+can actually solve the equation of
+motion which is actually strictly
+
+ align:start position:0%
+motion which is actually strictly
+ 
+
+ align:start position:0%
+motion which is actually strictly
+speaking on my problem is the math
+
+ align:start position:0%
+speaking on my problem is the math
+ 
+
+ align:start position:0%
+speaking on my problem is the math
+department problem ok and yeah that's
+
+ align:start position:0%
+department problem ok and yeah that's
+ 
+
+ align:start position:0%
+department problem ok and yeah that's
+their problem anyway then we solve the
+
+ align:start position:0%
+their problem anyway then we solve the
+ 
+
+ align:start position:0%
+their problem anyway then we solve the
+equation of motion and you will keep it
+
+ align:start position:0%
+equation of motion and you will keep it
+ 
+
+ align:start position:0%
+equation of motion and you will keep it
+even the formula then we use initial
+
+ align:start position:0%
+even the formula then we use initial
+ 
+
+ align:start position:0%
+even the formula then we use initial
+conditions and the main protection and
+
+ align:start position:0%
+conditions and the main protection and
+ 
+
+ align:start position:0%
+conditions and the main protection and
+we would like to compare that to
+
+ align:start position:0%
+we would like to compare that to
+ 
+
+ align:start position:0%
+we would like to compare that to
+experimental result and that is actually
+
+ align:start position:0%
+experimental result and that is actually
+ 
+
+ align:start position:0%
+experimental result and that is actually
+the general thing which we have been
+
+ align:start position:0%
+the general thing which we have been
+ 
+
+ align:start position:0%
+the general thing which we have been
+doing for physics so that's I should
+
+ align:start position:0%
+doing for physics so that's I should
+ 
+
+ align:start position:0%
+doing for physics so that's I should
+take a look at
+
+ align:start position:0%
+take a look at
+ 
+
+ align:start position:0%
+take a look at
+those examples those are examples of
+
+ align:start position:0%
+those examples those are examples of
+ 
+
+ align:start position:0%
+those examples those are examples of
+simple harmonic motions and you can see
+
+ align:start position:0%
+simple harmonic motions and you can see
+ 
+
+ align:start position:0%
+simple harmonic motions and you can see
+that this older system have one object
+
+ align:start position:0%
+that this older system have one object
+ 
+
+ align:start position:0%
+that this older system have one object
+which is actually oscillating and you
+
+ align:start position:0%
+which is actually oscillating and you
+ 
+
+ align:start position:0%
+which is actually oscillating and you
+can see that actually their equation of
+
+ align:start position:0%
+can see that actually their equation of
+ 
+
+ align:start position:0%
+can see that actually their equation of
+motion really similar to each other is
+
+ align:start position:0%
+motion really similar to each other is
+ 
+
+ align:start position:0%
+motion really similar to each other is
+Theta double dot plus Omega zero squared
+
+ align:start position:0%
+Theta double dot plus Omega zero squared
+ 
+
+ align:start position:0%
+Theta double dot plus Omega zero squared
+theta equal to zero for those idealized
+
+ align:start position:0%
+theta equal to zero for those idealized
+ 
+
+ align:start position:0%
+theta equal to zero for those idealized
+simple harmonic motion and we actually
+
+ align:start position:0%
+simple harmonic motion and we actually
+ 
+
+ align:start position:0%
+simple harmonic motion and we actually
+learned that the solution of those
+
+ align:start position:0%
+learned that the solution of those
+ 
+
+ align:start position:0%
+learned that the solution of those
+equations actually the same which is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cosine function then we actually went
+
+ align:start position:0%
+cosine function then we actually went
+ 
+
+ align:start position:0%
+cosine function then we actually went
+ahead and add more craziness to the to
+
+ align:start position:0%
+ahead and add more craziness to the to
+ 
+
+ align:start position:0%
+ahead and add more craziness to the to
+the system so basically what we actually
+
+ align:start position:0%
+the system so basically what we actually
+ 
+
+ align:start position:0%
+the system so basically what we actually
+tried to do is to add a drag force I
+
+ align:start position:0%
+tried to do is to add a drag force I
+ 
+
+ align:start position:0%
+tried to do is to add a drag force I
+into the again and we were wondering if
+
+ align:start position:0%
+into the again and we were wondering if
+ 
+
+ align:start position:0%
+into the again and we were wondering if
+this more realistic description can
+
+ align:start position:0%
+this more realistic description can
+ 
+
+ align:start position:0%
+this more realistic description can
+actually match with experimental data
+
+ align:start position:0%
+actually match with experimental data
+ 
+
+ align:start position:0%
+actually match with experimental data
+all right so this is actually the
+
+ align:start position:0%
+all right so this is actually the
+ 
+
+ align:start position:0%
+all right so this is actually the
+equation of motion and the additional
+
+ align:start position:0%
+equation of motion and the additional
+ 
+
+ align:start position:0%
+equation of motion and the additional
+turn this edge with the one in the
+
+ align:start position:0%
+turn this edge with the one in the
+ 
+
+ align:start position:0%
+turn this edge with the one in the
+middle gamma C dot dot turn and after
+
+ align:start position:0%
+middle gamma C dot dot turn and after
+ 
+
+ align:start position:0%
+middle gamma C dot dot turn and after
+adding this turn not only it is real
+
+ align:start position:0%
+adding this turn not only it is real
+ 
+
+ align:start position:0%
+adding this turn not only it is real
+interesting model to describe the the
+
+ align:start position:0%
+interesting model to describe the the
+ 
+
+ align:start position:0%
+interesting model to describe the the
+physical system we are talking about but
+
+ align:start position:0%
+physical system we are talking about but
+ 
+
+ align:start position:0%
+physical system we are talking about but
+the mathematical solution is far much
+
+ align:start position:0%
+the mathematical solution is far much
+ 
+
+ align:start position:0%
+the mathematical solution is far much
+more richer than what we should talk
+
+ align:start position:0%
+more richer than what we should talk
+ 
+
+ align:start position:0%
+more richer than what we should talk
+about in the single harmonic oscillator
+
+ align:start position:0%
+about in the single harmonic oscillator
+ 
+
+ align:start position:0%
+about in the single harmonic oscillator
+case basically you will see that the
+
+ align:start position:0%
+case basically you will see that the
+ 
+
+ align:start position:0%
+case basically you will see that the
+general solution depends on the size of
+
+ align:start position:0%
+general solution depends on the size of
+ 
+
+ align:start position:0%
+general solution depends on the size of
+the gamma
+
+ align:start position:0%
+the gamma
+ 
+
+ align:start position:0%
+the gamma
+compared to Omega 0 which is the
+
+ align:start position:0%
+compared to Omega 0 which is the
+ 
+
+ align:start position:0%
+compared to Omega 0 which is the
+oscillation the natural frequency of the
+
+ align:start position:0%
+oscillation the natural frequency of the
+ 
+
+ align:start position:0%
+oscillation the natural frequency of the
+system ok and you can see there are
+
+ align:start position:0%
+system ok and you can see there are
+ 
+
+ align:start position:0%
+system ok and you can see there are
+three distinct different kinds of
+
+ align:start position:0%
+three distinct different kinds of
+ 
+
+ align:start position:0%
+three distinct different kinds of
+solution they have different
+
+ align:start position:0%
+solution they have different
+ 
+
+ align:start position:0%
+solution they have different
+mathematical form and we call them under
+
+ align:start position:0%
+mathematical form and we call them under
+ 
+
+ align:start position:0%
+mathematical form and we call them under
+temperature solution critically damped
+
+ align:start position:0%
+temperature solution critically damped
+ 
+
+ align:start position:0%
+temperature solution critically damped
+as a solution and over time the solution
+
+ align:start position:0%
+as a solution and over time the solution
+ 
+
+ align:start position:0%
+as a solution and over time the solution
+okay so those equation will be given to
+
+ align:start position:0%
+okay so those equation will be given to
+ 
+
+ align:start position:0%
+okay so those equation will be given to
+you and the excitement is the following
+
+ align:start position:0%
+you and the excitement is the following
+ 
+
+ align:start position:0%
+you and the excitement is the following
+so you can see that those solution if
+
+ align:start position:0%
+so you can see that those solution if
+ 
+
+ align:start position:0%
+so you can see that those solution if
+you plot the solution
+
+ align:start position:0%
+you plot the solution
+ 
+
+ align:start position:0%
+you plot the solution
+on time they looks completely different
+
+ align:start position:0%
+on time they looks completely different
+ 
+
+ align:start position:0%
+on time they looks completely different
+as a punctual time right so so in the
+
+ align:start position:0%
+as a punctual time right so so in the
+ 
+
+ align:start position:0%
+as a punctual time right so so in the
+case of no tempting the amplitudes issue
+
+ align:start position:0%
+case of no tempting the amplitudes issue
+ 
+
+ align:start position:0%
+case of no tempting the amplitudes issue
+the constant is not actually reducing as
+
+ align:start position:0%
+the constant is not actually reducing as
+ 
+
+ align:start position:0%
+the constant is not actually reducing as
+a function of time and but when the
+
+ align:start position:0%
+a function of time and but when the
+ 
+
+ align:start position:0%
+a function of time and but when the
+tempter system is should the temp is a
+
+ align:start position:0%
+tempter system is should the temp is a
+ 
+
+ align:start position:0%
+tempter system is should the temp is a
+turned on then in the under Templar
+
+ align:start position:0%
+turned on then in the under Templar
+ 
+
+ align:start position:0%
+turned on then in the under Templar
+situation you can see that the amplitude
+
+ align:start position:0%
+situation you can see that the amplitude
+ 
+
+ align:start position:0%
+situation you can see that the amplitude
+is reducing as a punctual time and if
+
+ align:start position:0%
+is reducing as a punctual time and if
+ 
+
+ align:start position:0%
+is reducing as a punctual time and if
+you have too much damping you put how
+
+ align:start position:0%
+you have too much damping you put how
+ 
+
+ align:start position:0%
+you have too much damping you put how
+oscillator into something qui for
+
+ align:start position:0%
+oscillator into something qui for
+ 
+
+ align:start position:0%
+oscillator into something qui for
+example and you see that the oscillation
+
+ align:start position:0%
+example and you see that the oscillation
+ 
+
+ align:start position:0%
+example and you see that the oscillation
+actually disappear right the cool thing
+
+ align:start position:0%
+actually disappear right the cool thing
+ 
+
+ align:start position:0%
+actually disappear right the cool thing
+is the following the excitement from as
+
+ align:start position:0%
+is the following the excitement from as
+ 
+
+ align:start position:0%
+is the following the excitement from as
+a physicist at all those crazy
+
+ align:start position:0%
+a physicist at all those crazy
+ 
+
+ align:start position:0%
+a physicist at all those crazy
+mathematical solution as to the match
+
+ align:start position:0%
+mathematical solution as to the match
+ 
+
+ align:start position:0%
+mathematical solution as to the match
+with experimental result wow that is
+
+ align:start position:0%
+with experimental result wow that is
+ 
+
+ align:start position:0%
+with experimental result wow that is
+really cool night because there is no
+
+ align:start position:0%
+really cool night because there is no
+ 
+
+ align:start position:0%
+really cool night because there is no
+nobody say that this should match and
+
+ align:start position:0%
+nobody say that this should match and
+ 
+
+ align:start position:0%
+nobody say that this should match and
+and how naturally should learn that okay
+
+ align:start position:0%
+and how naturally should learn that okay
+ 
+
+ align:start position:0%
+and how naturally should learn that okay
+when should I should change the behavior
+
+ align:start position:0%
+when should I should change the behavior
+ 
+
+ align:start position:0%
+when should I should change the behavior
+of the system right so this is actually
+
+ align:start position:0%
+of the system right so this is actually
+ 
+
+ align:start position:0%
+of the system right so this is actually
+really a miracle that the this
+
+ align:start position:0%
+really a miracle that the this
+ 
+
+ align:start position:0%
+really a miracle that the this
+complicated mathematical description
+
+ align:start position:0%
+complicated mathematical description
+ 
+
+ align:start position:0%
+complicated mathematical description
+actually is useful and is assessory
+
+ align:start position:0%
+actually is useful and is assessory
+ 
+
+ align:start position:0%
+actually is useful and is assessory
+super useful to describe the natural
+
+ align:start position:0%
+super useful to describe the natural
+ 
+
+ align:start position:0%
+super useful to describe the natural
+okay so once we actually have learned
+
+ align:start position:0%
+okay so once we actually have learned
+ 
+
+ align:start position:0%
+okay so once we actually have learned
+that we can now add a driving force in
+
+ align:start position:0%
+that we can now add a driving force in
+ 
+
+ align:start position:0%
+that we can now add a driving force in
+tool again okay so from the equation
+
+ align:start position:0%
+tool again okay so from the equation
+ 
+
+ align:start position:0%
+tool again okay so from the equation
+here we can see that there's a natural
+
+ align:start position:0%
+here we can see that there's a natural
+ 
+
+ align:start position:0%
+here we can see that there's a natural
+frequency Omega zero of this system and
+
+ align:start position:0%
+frequency Omega zero of this system and
+ 
+
+ align:start position:0%
+frequency Omega zero of this system and
+there is a track for strand which is
+
+ align:start position:0%
+there is a track for strand which is
+ 
+
+ align:start position:0%
+there is a track for strand which is
+actually to quantify how much track we
+
+ align:start position:0%
+actually to quantify how much track we
+ 
+
+ align:start position:0%
+actually to quantify how much track we
+have we have a comma there okay and we
+
+ align:start position:0%
+have we have a comma there okay and we
+ 
+
+ align:start position:0%
+have we have a comma there okay and we
+are driving it at a driving frequency
+
+ align:start position:0%
+are driving it at a driving frequency
+ 
+
+ align:start position:0%
+are driving it at a driving frequency
+Omega T so what we have learned from
+
+ align:start position:0%
+Omega T so what we have learned from
+ 
+
+ align:start position:0%
+Omega T so what we have learned from
+here is that if you are driving this
+
+ align:start position:0%
+here is that if you are driving this
+ 
+
+ align:start position:0%
+here is that if you are driving this
+cistern for example and shaking the
+
+ align:start position:0%
+cistern for example and shaking the
+ 
+
+ align:start position:0%
+cistern for example and shaking the
+student shaking you okay in the
+
+ align:start position:0%
+student shaking you okay in the
+ 
+
+ align:start position:0%
+student shaking you okay in the
+beginning this student is going to
+
+ align:start position:0%
+beginning this student is going to
+ 
+
+ align:start position:0%
+beginning this student is going to
+resist no don't shake me come on right
+
+ align:start position:0%
+resist no don't shake me come on right
+ 
+
+ align:start position:0%
+resist no don't shake me come on right
+but at some point he knows that
+
+ align:start position:0%
+but at some point he knows that
+ 
+
+ align:start position:0%
+but at some point he knows that
+Professor D is ready to eat
+
+ align:start position:0%
+Professor D is ready to eat
+ 
+
+ align:start position:0%
+Professor D is ready to eat
+therefore he is going to be shaked at
+
+ align:start position:0%
+therefore he is going to be shaked at
+ 
+
+ align:start position:0%
+therefore he is going to be shaked at
+the frequency I like okay so that is
+
+ align:start position:0%
+the frequency I like okay so that is
+ 
+
+ align:start position:0%
+the frequency I like okay so that is
+actually what is happening here
+
+ align:start position:0%
+actually what is happening here
+ 
+
+ align:start position:0%
+actually what is happening here
+so we this is so called the transient
+
+ align:start position:0%
+so we this is so called the transient
+ 
+
+ align:start position:0%
+so we this is so called the transient
+behavior right so adding the peak in in
+
+ align:start position:0%
+behavior right so adding the peak in in
+ 
+
+ align:start position:0%
+behavior right so adding the peak in in
+the system doesn't like it right so this
+
+ align:start position:0%
+the system doesn't like it right so this
+ 
+
+ align:start position:0%
+the system doesn't like it right so this
+is I should be making use of the
+
+ align:start position:0%
+is I should be making use of the
+ 
+
+ align:start position:0%
+is I should be making use of the
+superposition principle right so you can
+
+ align:start position:0%
+superposition principle right so you can
+ 
+
+ align:start position:0%
+superposition principle right so you can
+solve that that homogeneous solution
+
+ align:start position:0%
+solve that that homogeneous solution
+ 
+
+ align:start position:0%
+solve that that homogeneous solution
+which is I should be in the right hand
+
+ align:start position:0%
+which is I should be in the right hand
+ 
+
+ align:start position:0%
+which is I should be in the right hand
+side it depends on the physical
+
+ align:start position:0%
+side it depends on the physical
+ 
+
+ align:start position:0%
+side it depends on the physical
+situation you are talking about you
+
+ align:start position:0%
+situation you are talking about you
+ 
+
+ align:start position:0%
+situation you are talking about you
+choose the corresponding homogeneous
+
+ align:start position:0%
+choose the corresponding homogeneous
+ 
+
+ align:start position:0%
+choose the corresponding homogeneous
+solution and lapland psy is actually the
+
+ align:start position:0%
+solution and lapland psy is actually the
+ 
+
+ align:start position:0%
+solution and lapland psy is actually the
+driving force from G&G right and that is
+
+ align:start position:0%
+driving force from G&G right and that is
+ 
+
+ align:start position:0%
+driving force from G&G right and that is
+actually going to win at the end of the
+
+ align:start position:0%
+actually going to win at the end of the
+ 
+
+ align:start position:0%
+actually going to win at the end of the
+experiment right because I'm going to
+
+ align:start position:0%
+experiment right because I'm going to
+ 
+
+ align:start position:0%
+experiment right because I'm going to
+shake it forever until the end of the
+
+ align:start position:0%
+shake it forever until the end of the
+ 
+
+ align:start position:0%
+shake it forever until the end of the
+universe right so so you can see that at
+
+ align:start position:0%
+universe right so so you can see that at
+ 
+
+ align:start position:0%
+universe right so so you can see that at
+the end you what is actually lap over is
+
+ align:start position:0%
+the end you what is actually lap over is
+ 
+
+ align:start position:0%
+the end you what is actually lap over is
+really the steady-state solution and he
+
+ align:start position:0%
+really the steady-state solution and he
+ 
+
+ align:start position:0%
+really the steady-state solution and he
+has this structure a Omega D depends on
+
+ align:start position:0%
+has this structure a Omega D depends on
+ 
+
+ align:start position:0%
+has this structure a Omega D depends on
+Omega and you get restless behavior
+
+ align:start position:0%
+Omega and you get restless behavior
+ 
+
+ align:start position:0%
+Omega and you get restless behavior
+don't forget to review that and also you
+
+ align:start position:0%
+don't forget to review that and also you
+ 
+
+ align:start position:0%
+don't forget to review that and also you
+have delayed in face because when I
+
+ align:start position:0%
+have delayed in face because when I
+ 
+
+ align:start position:0%
+have delayed in face because when I
+shake the student the student needs some
+
+ align:start position:0%
+shake the student the student needs some
+ 
+
+ align:start position:0%
+shake the student the student needs some
+time to respond right therefore the
+
+ align:start position:0%
+time to respond right therefore the
+ 
+
+ align:start position:0%
+time to respond right therefore the
+theta is actually nonzero if the student
+
+ align:start position:0%
+theta is actually nonzero if the student
+ 
+
+ align:start position:0%
+theta is actually nonzero if the student
+is damped okay all right so now we have
+
+ align:start position:0%
+is damped okay all right so now we have
+ 
+
+ align:start position:0%
+is damped okay all right so now we have
+learned all the secrets about a single
+
+ align:start position:0%
+learned all the secrets about a single
+ 
+
+ align:start position:0%
+learned all the secrets about a single
+object system then we can now go ahead
+
+ align:start position:0%
+object system then we can now go ahead
+ 
+
+ align:start position:0%
+object system then we can now go ahead
+and study coupled oscillators there are
+
+ align:start position:0%
+and study coupled oscillators there are
+ 
+
+ align:start position:0%
+and study coupled oscillators there are
+a few examples here which is coupled
+
+ align:start position:0%
+a few examples here which is coupled
+ 
+
+ align:start position:0%
+a few examples here which is coupled
+upon to dance or Cobo the stream
+
+ align:start position:0%
+upon to dance or Cobo the stream
+ 
+
+ align:start position:0%
+upon to dance or Cobo the stream
+assistance and we found that a very
+
+ align:start position:0%
+assistance and we found that a very
+ 
+
+ align:start position:0%
+assistance and we found that a very
+useful description of this kind of
+
+ align:start position:0%
+useful description of this kind of
+ 
+
+ align:start position:0%
+useful description of this kind of
+system is to make use of the magic
+
+ align:start position:0%
+system is to make use of the magic
+ 
+
+ align:start position:0%
+system is to make use of the magic
+language okay so originally if you have
+
+ align:start position:0%
+language okay so originally if you have
+ 
+
+ align:start position:0%
+language okay so originally if you have
+n objects in the system you have n
+
+ align:start position:0%
+n objects in the system you have n
+ 
+
+ align:start position:0%
+n objects in the system you have n
+equations of motions and that looks
+
+ align:start position:0%
+equations of motions and that looks
+ 
+
+ align:start position:0%
+equations of motions and that looks
+horrible right but what is actually done
+
+ align:start position:0%
+horrible right but what is actually done
+ 
+
+ align:start position:0%
+horrible right but what is actually done
+in our series that we actually
+
+ align:start position:0%
+in our series that we actually
+ 
+
+ align:start position:0%
+in our series that we actually
+introduced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the notation with metrics basically if
+
+ align:start position:0%
+the notation with metrics basically if
+ 
+
+ align:start position:0%
+the notation with metrics basically if
+you write everything in terms of metrics
+
+ align:start position:0%
+you write everything in terms of metrics
+ 
+
+ align:start position:0%
+you write everything in terms of metrics
+then it looks really friendly right and
+
+ align:start position:0%
+then it looks really friendly right and
+ 
+
+ align:start position:0%
+then it looks really friendly right and
+it looks really like a single oscillator
+
+ align:start position:0%
+it looks really like a single oscillator
+ 
+
+ align:start position:0%
+it looks really like a single oscillator
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+although solving this this equation is
+
+ align:start position:0%
+although solving this this equation is
+ 
+
+ align:start position:0%
+although solving this this equation is
+still a little bit more work okay and
+
+ align:start position:0%
+still a little bit more work okay and
+ 
+
+ align:start position:0%
+still a little bit more work okay and
+basically you can see that from this
+
+ align:start position:0%
+basically you can see that from this
+ 
+
+ align:start position:0%
+basically you can see that from this
+example we can actually write M minus 1
+
+ align:start position:0%
+example we can actually write M minus 1
+ 
+
+ align:start position:0%
+example we can actually write M minus 1
+K matrix and the whole equation movie
+
+ align:start position:0%
+K matrix and the whole equation movie
+ 
+
+ align:start position:0%
+K matrix and the whole equation movie
+which equation of motion problem solving
+
+ align:start position:0%
+which equation of motion problem solving
+ 
+
+ align:start position:0%
+which equation of motion problem solving
+problem become M as 1 K matrix
+
+ align:start position:0%
+problem become M as 1 K matrix
+ 
+
+ align:start position:0%
+problem become M as 1 K matrix
+eigenvalue problem what is actually M is
+
+ align:start position:0%
+eigenvalue problem what is actually M is
+ 
+
+ align:start position:0%
+eigenvalue problem what is actually M is
+1 make K matrix ok this is as with
+
+ align:start position:0%
+1 make K matrix ok this is as with
+ 
+
+ align:start position:0%
+1 make K matrix ok this is as with
+describing how each component in the
+
+ align:start position:0%
+describing how each component in the
+ 
+
+ align:start position:0%
+describing how each component in the
+system should interact with each other
+
+ align:start position:0%
+system should interact with each other
+ 
+
+ align:start position:0%
+system should interact with each other
+right so once we have this we can
+
+ align:start position:0%
+right so once we have this we can
+ 
+
+ align:start position:0%
+right so once we have this we can
+actually solve the eigenvalue problem
+
+ align:start position:0%
+actually solve the eigenvalue problem
+ 
+
+ align:start position:0%
+actually solve the eigenvalue problem
+and we are going to be able to figure
+
+ align:start position:0%
+and we are going to be able to figure
+ 
+
+ align:start position:0%
+and we are going to be able to figure
+out the normal modes of those system so
+
+ align:start position:0%
+out the normal modes of those system so
+ 
+
+ align:start position:0%
+out the normal modes of those system so
+what is actually normal mode normal mode
+
+ align:start position:0%
+what is actually normal mode normal mode
+ 
+
+ align:start position:0%
+what is actually normal mode normal mode
+is a situation where all the components
+
+ align:start position:0%
+is a situation where all the components
+ 
+
+ align:start position:0%
+is a situation where all the components
+in the system are oscillating at the
+
+ align:start position:0%
+in the system are oscillating at the
+ 
+
+ align:start position:0%
+in the system are oscillating at the
+same frequency and the also at the same
+
+ align:start position:0%
+same frequency and the also at the same
+ 
+
+ align:start position:0%
+same frequency and the also at the same
+phase okay so that is actually the
+
+ align:start position:0%
+phase okay so that is actually the
+ 
+
+ align:start position:0%
+phase okay so that is actually the
+definition of normal mode and also
+
+ align:start position:0%
+definition of normal mode and also
+ 
+
+ align:start position:0%
+definition of normal mode and also
+actually what is actually used in debris
+
+ align:start position:0%
+actually what is actually used in debris
+ 
+
+ align:start position:0%
+actually what is actually used in debris
+ation also which leads us to the
+
+ align:start position:0%
+ation also which leads us to the
+ 
+
+ align:start position:0%
+ation also which leads us to the
+eigenvalue problem we define Z equal to
+
+ align:start position:0%
+eigenvalue problem we define Z equal to
+ 
+
+ align:start position:0%
+eigenvalue problem we define Z equal to
+exponential I Omega T plus Phi everybody
+
+ align:start position:0%
+exponential I Omega T plus Phi everybody
+ 
+
+ align:start position:0%
+exponential I Omega T plus Phi everybody
+is resonating at Omega and also a phase
+
+ align:start position:0%
+is resonating at Omega and also a phase
+ 
+
+ align:start position:0%
+is resonating at Omega and also a phase
+Phi right so that is actually what we
+
+ align:start position:0%
+Phi right so that is actually what we
+ 
+
+ align:start position:0%
+Phi right so that is actually what we
+actually learned and what is actually
+
+ align:start position:0%
+actually learned and what is actually
+ 
+
+ align:start position:0%
+actually learned and what is actually
+the physical meaning of the those normal
+
+ align:start position:0%
+the physical meaning of the those normal
+ 
+
+ align:start position:0%
+the physical meaning of the those normal
+modes so if we plot the locus of the two
+
+ align:start position:0%
+modes so if we plot the locus of the two
+ 
+
+ align:start position:0%
+modes so if we plot the locus of the two
+coupled pendulum partment what we
+
+ align:start position:0%
+coupled pendulum partment what we
+ 
+
+ align:start position:0%
+coupled pendulum partment what we
+actually see is the following so
+
+ align:start position:0%
+actually see is the following so
+ 
+
+ align:start position:0%
+actually see is the following so
+basically you will see that the locust
+
+ align:start position:0%
+basically you will see that the locust
+ 
+
+ align:start position:0%
+basically you will see that the locust
+looks like do the complicated as a
+
+ align:start position:0%
+looks like do the complicated as a
+ 
+
+ align:start position:0%
+looks like do the complicated as a
+function of time if you plot XY x 2
+
+ align:start position:0%
+function of time if you plot XY x 2
+ 
+
+ align:start position:0%
+function of time if you plot XY x 2
+versus time but if we rotate this system
+
+ align:start position:0%
+versus time but if we rotate this system
+ 
+
+ align:start position:0%
+versus time but if we rotate this system
+a bit then we find that this is a really
+
+ align:start position:0%
+a bit then we find that this is a really
+ 
+
+ align:start position:0%
+a bit then we find that this is a really
+interesting projection which is the
+
+ align:start position:0%
+interesting projection which is the
+ 
+
+ align:start position:0%
+interesting projection which is the
+principal cordon
+
+ align:start position:0%
+principal cordon
+ 
+
+ align:start position:0%
+principal cordon
+we see that actually all those crazy
+
+ align:start position:0%
+we see that actually all those crazy
+ 
+
+ align:start position:0%
+we see that actually all those crazy
+strange phenomena we see with carpet
+
+ align:start position:0%
+strange phenomena we see with carpet
+ 
+
+ align:start position:0%
+strange phenomena we see with carpet
+assistants are just illusions actually
+
+ align:start position:0%
+assistants are just illusions actually
+ 
+
+ align:start position:0%
+assistants are just illusions actually
+you can understand them by really using
+
+ align:start position:0%
+you can understand them by really using
+ 
+
+ align:start position:0%
+you can understand them by really using
+the right projection okay - one well -
+
+ align:start position:0%
+the right projection okay - one well -
+ 
+
+ align:start position:0%
+the right projection okay - one well -
+to the right coordinate system then you
+
+ align:start position:0%
+to the right coordinate system then you
+ 
+
+ align:start position:0%
+to the right coordinate system then you
+will see that HD decision is - in still
+
+ align:start position:0%
+will see that HD decision is - in still
+ 
+
+ align:start position:0%
+will see that HD decision is - in still
+simple harmonic motion okay so that is
+
+ align:start position:0%
+simple harmonic motion okay so that is
+ 
+
+ align:start position:0%
+simple harmonic motion okay so that is
+actually the cool thing which we learn
+
+ align:start position:0%
+actually the cool thing which we learn
+ 
+
+ align:start position:0%
+actually the cool thing which we learn
+from a coupled system so we learned
+
+ align:start position:0%
+from a coupled system so we learned
+ 
+
+ align:start position:0%
+from a coupled system so we learned
+about how to resolve the cop of the
+
+ align:start position:0%
+about how to resolve the cop of the
+ 
+
+ align:start position:0%
+about how to resolve the cop of the
+system and we also learned about going
+
+ align:start position:0%
+system and we also learned about going
+ 
+
+ align:start position:0%
+system and we also learned about going
+to infinite number of coupled system ok
+
+ align:start position:0%
+to infinite number of coupled system ok
+ 
+
+ align:start position:0%
+to infinite number of coupled system ok
+so then this is an example here so for
+
+ align:start position:0%
+so then this is an example here so for
+ 
+
+ align:start position:0%
+so then this is an example here so for
+example I can hear Pentagon and Springs
+
+ align:start position:0%
+example I can hear Pentagon and Springs
+ 
+
+ align:start position:0%
+example I can hear Pentagon and Springs
+and we connect them all together and and
+
+ align:start position:0%
+and we connect them all together and and
+ 
+
+ align:start position:0%
+and we connect them all together and and
+I need to hire many many students so
+
+ align:start position:0%
+I need to hire many many students so
+ 
+
+ align:start position:0%
+I need to hire many many students so
+that they praise it or the prayers until
+
+ align:start position:0%
+that they praise it or the prayers until
+ 
+
+ align:start position:0%
+that they praise it or the prayers until
+you know few up the whole universe right
+
+ align:start position:0%
+you know few up the whole universe right
+ 
+
+ align:start position:0%
+you know few up the whole universe right
+so this is actually the idea of infini
+
+ align:start position:0%
+so this is actually the idea of infini
+ 
+
+ align:start position:0%
+so this is actually the idea of infini
+system okay and you can see that that
+
+ align:start position:0%
+system okay and you can see that that
+ 
+
+ align:start position:0%
+system okay and you can see that that
+means my n minus 1 K matrix going to be
+
+ align:start position:0%
+means my n minus 1 K matrix going to be
+ 
+
+ align:start position:0%
+means my n minus 1 K matrix going to be
+infinite as infinitely long matrix okay
+
+ align:start position:0%
+infinite as infinitely long matrix okay
+ 
+
+ align:start position:0%
+infinite as infinitely long matrix okay
+it's two dimensional and the a is
+
+ align:start position:0%
+it's two dimensional and the a is
+ 
+
+ align:start position:0%
+it's two dimensional and the a is
+infinitely long and that sounds really
+
+ align:start position:0%
+infinitely long and that sounds really
+ 
+
+ align:start position:0%
+infinitely long and that sounds really
+scary and in general we don't know how
+
+ align:start position:0%
+scary and in general we don't know how
+ 
+
+ align:start position:0%
+scary and in general we don't know how
+to deal with this okay and it can be
+
+ align:start position:0%
+to deal with this okay and it can be
+ 
+
+ align:start position:0%
+to deal with this okay and it can be
+arbitrarily crazy as you can imagine
+
+ align:start position:0%
+arbitrarily crazy as you can imagine
+ 
+
+ align:start position:0%
+arbitrarily crazy as you can imagine
+okay so what we should discuss in a or
+
+ align:start position:0%
+okay so what we should discuss in a or
+ 
+
+ align:start position:0%
+okay so what we should discuss in a or
+three is a special case basically we are
+
+ align:start position:0%
+three is a special case basically we are
+ 
+
+ align:start position:0%
+three is a special case basically we are
+discussing about systems which are
+
+ align:start position:0%
+discussing about systems which are
+ 
+
+ align:start position:0%
+discussing about systems which are
+having a special kind of symmetry which
+
+ align:start position:0%
+having a special kind of symmetry which
+ 
+
+ align:start position:0%
+having a special kind of symmetry which
+is translation symmetry as you can see
+
+ align:start position:0%
+is translation symmetry as you can see
+ 
+
+ align:start position:0%
+is translation symmetry as you can see
+from all those figures and you can see
+
+ align:start position:0%
+from all those figures and you can see
+ 
+
+ align:start position:0%
+from all those figures and you can see
+that all those figures will have to all
+
+ align:start position:0%
+that all those figures will have to all
+ 
+
+ align:start position:0%
+that all those figures will have to all
+have the same normal modes right because
+
+ align:start position:0%
+have the same normal modes right because
+ 
+
+ align:start position:0%
+have the same normal modes right because
+of the space translation symmetry what
+
+ align:start position:0%
+of the space translation symmetry what
+ 
+
+ align:start position:0%
+of the space translation symmetry what
+we actually discussed above is that we
+
+ align:start position:0%
+we actually discussed above is that we
+ 
+
+ align:start position:0%
+we actually discussed above is that we
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+as matrix which essentially used to
+
+ align:start position:0%
+as matrix which essentially used to
+ 
+
+ align:start position:0%
+as matrix which essentially used to
+describe the kind of symmetry that this
+
+ align:start position:0%
+describe the kind of symmetry that this
+ 
+
+ align:start position:0%
+describe the kind of symmetry that this
+system is should satisfy right and we if
+
+ align:start position:0%
+system is should satisfy right and we if
+ 
+
+ align:start position:0%
+system is should satisfy right and we if
+we if we calculate a communicator
+
+ align:start position:0%
+we if we calculate a communicator
+ 
+
+ align:start position:0%
+we if we calculate a communicator
+s and M is quite a matrix if their
+
+ align:start position:0%
+s and M is quite a matrix if their
+ 
+
+ align:start position:0%
+s and M is quite a matrix if their
+company this communicator shows that if
+
+ align:start position:0%
+company this communicator shows that if
+ 
+
+ align:start position:0%
+company this communicator shows that if
+you evaluate this communicator and you
+
+ align:start position:0%
+you evaluate this communicator and you
+ 
+
+ align:start position:0%
+you evaluate this communicator and you
+get 0 that means they commute and that
+
+ align:start position:0%
+get 0 that means they commute and that
+ 
+
+ align:start position:0%
+get 0 that means they commute and that
+the consequence is that the S matrix and
+
+ align:start position:0%
+the consequence is that the S matrix and
+ 
+
+ align:start position:0%
+the consequence is that the S matrix and
+SMI 1 K matrix will share the same
+
+ align:start position:0%
+SMI 1 K matrix will share the same
+ 
+
+ align:start position:0%
+SMI 1 K matrix will share the same
+eigenvectors
+
+ align:start position:0%
+eigenvectors
+ 
+
+ align:start position:0%
+eigenvectors
+ok so you don't really need to know how
+
+ align:start position:0%
+ok so you don't really need to know how
+ 
+
+ align:start position:0%
+ok so you don't really need to know how
+to derive this conclusion to a ripe this
+
+ align:start position:0%
+to derive this conclusion to a ripe this
+ 
+
+ align:start position:0%
+to derive this conclusion to a ripe this
+conclusion but it is actually very
+
+ align:start position:0%
+conclusion but it is actually very
+ 
+
+ align:start position:0%
+conclusion but it is actually very
+useful conclusion so that means instead
+
+ align:start position:0%
+useful conclusion so that means instead
+ 
+
+ align:start position:0%
+useful conclusion so that means instead
+of solving and minus 1 K matrix eigen
+
+ align:start position:0%
+of solving and minus 1 K matrix eigen
+ 
+
+ align:start position:0%
+of solving and minus 1 K matrix eigen
+value problem I can now go ahead to
+
+ align:start position:0%
+value problem I can now go ahead to
+ 
+
+ align:start position:0%
+value problem I can now go ahead to
+solve the S matrix eigen value problem
+
+ align:start position:0%
+solve the S matrix eigen value problem
+ 
+
+ align:start position:0%
+solve the S matrix eigen value problem
+and you ready that's much easier okay so
+
+ align:start position:0%
+and you ready that's much easier okay so
+ 
+
+ align:start position:0%
+and you ready that's much easier okay so
+for the exam you need to know how to
+
+ align:start position:0%
+for the exam you need to know how to
+ 
+
+ align:start position:0%
+for the exam you need to know how to
+write down as matrix you need to know
+
+ align:start position:0%
+write down as matrix you need to know
+ 
+
+ align:start position:0%
+write down as matrix you need to know
+how to solve icon value problems
+
+ align:start position:0%
+how to solve icon value problems
+ 
+
+ align:start position:0%
+how to solve icon value problems
+including image why make a matrix and
+
+ align:start position:0%
+including image why make a matrix and
+ 
+
+ align:start position:0%
+including image why make a matrix and
+the S matrix and then we can actually
+
+ align:start position:0%
+the S matrix and then we can actually
+ 
+
+ align:start position:0%
+the S matrix and then we can actually
+get to normal mode frequency Omega
+
+ align:start position:0%
+get to normal mode frequency Omega
+ 
+
+ align:start position:0%
+get to normal mode frequency Omega
+Square and we can also solve the
+
+ align:start position:0%
+Square and we can also solve the
+ 
+
+ align:start position:0%
+Square and we can also solve the
+corresponding normal mode and here is
+
+ align:start position:0%
+corresponding normal mode and here is
+ 
+
+ align:start position:0%
+corresponding normal mode and here is
+actually telling you what will be the
+
+ align:start position:0%
+actually telling you what will be the
+ 
+
+ align:start position:0%
+actually telling you what will be the
+solution for the space translation
+
+ align:start position:0%
+solution for the space translation
+ 
+
+ align:start position:0%
+solution for the space translation
+symmetric system and basically what you
+
+ align:start position:0%
+symmetric system and basically what you
+ 
+
+ align:start position:0%
+symmetric system and basically what you
+see is that making use of s matrix
+
+ align:start position:0%
+see is that making use of s matrix
+ 
+
+ align:start position:0%
+see is that making use of s matrix
+actually prints you look to a conclusion
+
+ align:start position:0%
+actually prints you look to a conclusion
+ 
+
+ align:start position:0%
+actually prints you look to a conclusion
+AJ must be a proportional to exponential
+
+ align:start position:0%
+AJ must be a proportional to exponential
+ 
+
+ align:start position:0%
+AJ must be a proportional to exponential
+IJ K a where this a is actually the
+
+ align:start position:0%
+IJ K a where this a is actually the
+ 
+
+ align:start position:0%
+IJ K a where this a is actually the
+length scale of this system the this
+
+ align:start position:0%
+length scale of this system the this
+ 
+
+ align:start position:0%
+length scale of this system the this
+distance between all those little mass
+
+ align:start position:0%
+distance between all those little mass
+ 
+
+ align:start position:0%
+distance between all those little mass
+and J is actually a label which tells
+
+ align:start position:0%
+and J is actually a label which tells
+ 
+
+ align:start position:0%
+and J is actually a label which tells
+you which little mess I'm talking about
+
+ align:start position:0%
+you which little mess I'm talking about
+ 
+
+ align:start position:0%
+you which little mess I'm talking about
+and K is actually some arbitrary
+
+ align:start position:0%
+and K is actually some arbitrary
+ 
+
+ align:start position:0%
+and K is actually some arbitrary
+constant when by now you should have the
+
+ align:start position:0%
+constant when by now you should have the
+ 
+
+ align:start position:0%
+constant when by now you should have the
+idea basically that's that's what the
+
+ align:start position:0%
+idea basically that's that's what the
+ 
+
+ align:start position:0%
+idea basically that's that's what the
+hardest is the wave number
+
+ align:start position:0%
+hardest is the wave number
+ 
+
+ align:start position:0%
+hardest is the wave number
+so that is really cool so that's also oh
+
+ align:start position:0%
+so that is really cool so that's also oh
+ 
+
+ align:start position:0%
+so that is really cool so that's also oh
+I shoulda print you know the bands and
+
+ align:start position:0%
+I shoulda print you know the bands and
+ 
+
+ align:start position:0%
+I shoulda print you know the bands and
+basically you can see that we can also
+
+ align:start position:0%
+basically you can see that we can also
+ 
+
+ align:start position:0%
+basically you can see that we can also
+write down the a K because we know that
+
+ align:start position:0%
+write down the a K because we know that
+ 
+
+ align:start position:0%
+write down the a K because we know that
+H a would be proportional to exponential
+
+ align:start position:0%
+H a would be proportional to exponential
+ 
+
+ align:start position:0%
+H a would be proportional to exponential
+I Chi ka after solving the eigenvalue
+
+ align:start position:0%
+I Chi ka after solving the eigenvalue
+ 
+
+ align:start position:0%
+I Chi ka after solving the eigenvalue
+problem for as matrix then we actually
+
+ align:start position:0%
+problem for as matrix then we actually
+ 
+
+ align:start position:0%
+problem for as matrix then we actually
+went one step forward to make it
+
+ align:start position:0%
+went one step forward to make it
+ 
+
+ align:start position:0%
+went one step forward to make it
+continuous right so basically we we make
+
+ align:start position:0%
+continuous right so basically we we make
+ 
+
+ align:start position:0%
+continuous right so basically we we make
+the space between particles very very
+
+ align:start position:0%
+the space between particles very very
+ 
+
+ align:start position:0%
+the space between particles very very
+small and also at the same time we make
+
+ align:start position:0%
+small and also at the same time we make
+ 
+
+ align:start position:0%
+small and also at the same time we make
+sure that the string doesn't become
+
+ align:start position:0%
+sure that the string doesn't become
+ 
+
+ align:start position:0%
+sure that the string doesn't become
+super massive right
+
+ align:start position:0%
+super massive right
+ 
+
+ align:start position:0%
+super massive right
+and we actually concluded that we get
+
+ align:start position:0%
+and we actually concluded that we get
+ 
+
+ align:start position:0%
+and we actually concluded that we get
+some kind of equation popping out from
+
+ align:start position:0%
+some kind of equation popping out from
+ 
+
+ align:start position:0%
+some kind of equation popping out from
+this exercise and minus 1 k matrix
+
+ align:start position:0%
+this exercise and minus 1 k matrix
+ 
+
+ align:start position:0%
+this exercise and minus 1 k matrix
+become minus T over Rho L partial square
+
+ align:start position:0%
+become minus T over Rho L partial square
+ 
+
+ align:start position:0%
+become minus T over Rho L partial square
+partial k x squared you don't have to
+
+ align:start position:0%
+partial k x squared you don't have to
+ 
+
+ align:start position:0%
+partial k x squared you don't have to
+really derive this for the exam but you
+
+ align:start position:0%
+really derive this for the exam but you
+ 
+
+ align:start position:0%
+really derive this for the exam but you
+need to know the conclusion and the five
+
+ align:start position:0%
+need to know the conclusion and the five
+ 
+
+ align:start position:0%
+need to know the conclusion and the five
+sides they become sigh so punctual x and
+
+ align:start position:0%
+sides they become sigh so punctual x and
+ 
+
+ align:start position:0%
+sides they become sigh so punctual x and
+t and the magical function is you
+
+ align:start position:0%
+t and the magical function is you
+ 
+
+ align:start position:0%
+t and the magical function is you
+appeared which is the wave equation oh
+
+ align:start position:0%
+appeared which is the wave equation oh
+ 
+
+ align:start position:0%
+appeared which is the wave equation oh
+my god this is the whole craziness we
+
+ align:start position:0%
+my god this is the whole craziness we
+ 
+
+ align:start position:0%
+my god this is the whole craziness we
+have been dealing with hole a or three
+
+ align:start position:0%
+have been dealing with hole a or three
+ 
+
+ align:start position:0%
+have been dealing with hole a or three
+right then this is actually really
+
+ align:start position:0%
+right then this is actually really
+ 
+
+ align:start position:0%
+right then this is actually really
+remarkable that we actually can come
+
+ align:start position:0%
+remarkable that we actually can come
+ 
+
+ align:start position:0%
+remarkable that we actually can come
+from single up to a solution putting it
+
+ align:start position:0%
+from single up to a solution putting it
+ 
+
+ align:start position:0%
+from single up to a solution putting it
+all together make it continues the
+
+ align:start position:0%
+all together make it continues the
+ 
+
+ align:start position:0%
+all together make it continues the
+endless equation really pop out and this
+
+ align:start position:0%
+endless equation really pop out and this
+ 
+
+ align:start position:0%
+endless equation really pop out and this
+equation should really describe multiple
+
+ align:start position:0%
+equation should really describe multiple
+ 
+
+ align:start position:0%
+equation should really describe multiple
+systems then we went ahead to actually
+
+ align:start position:0%
+systems then we went ahead to actually
+ 
+
+ align:start position:0%
+systems then we went ahead to actually
+discuss the property of the wave
+
+ align:start position:0%
+discuss the property of the wave
+ 
+
+ align:start position:0%
+discuss the property of the wave
+equation it looks like this they say the
+
+ align:start position:0%
+equation it looks like this they say the
+ 
+
+ align:start position:0%
+equation it looks like this they say the
+I replace the P over Rho L by V P Square
+
+ align:start position:0%
+I replace the P over Rho L by V P Square
+ 
+
+ align:start position:0%
+I replace the P over Rho L by V P Square
+by now you know the meaning will be P is
+
+ align:start position:0%
+by now you know the meaning will be P is
+ 
+
+ align:start position:0%
+by now you know the meaning will be P is
+actually the phase velocity and we
+
+ align:start position:0%
+actually the phase velocity and we
+ 
+
+ align:start position:0%
+actually the phase velocity and we
+discussed two kinds of solutions a
+
+ align:start position:0%
+discussed two kinds of solutions a
+ 
+
+ align:start position:0%
+discussed two kinds of solutions a
+special kind of solution the first kind
+
+ align:start position:0%
+special kind of solution the first kind
+ 
+
+ align:start position:0%
+special kind of solution the first kind
+is normal mode the second one is
+
+ align:start position:0%
+is normal mode the second one is
+ 
+
+ align:start position:0%
+is normal mode the second one is
+progressive wave solution or traveling
+
+ align:start position:0%
+progressive wave solution or traveling
+ 
+
+ align:start position:0%
+progressive wave solution or traveling
+wave solution whatever name you want
+
+ align:start position:0%
+wave solution whatever name you want
+ 
+
+ align:start position:0%
+wave solution whatever name you want
+coin the state should take a look at the
+
+ align:start position:0%
+coin the state should take a look at the
+ 
+
+ align:start position:0%
+coin the state should take a look at the
+normal modes what we have have we
+
+ align:start position:0%
+normal modes what we have have we
+ 
+
+ align:start position:0%
+normal modes what we have have we
+learned so if you have a bond system in
+
+ align:start position:0%
+learned so if you have a bond system in
+ 
+
+ align:start position:0%
+learned so if you have a bond system in
+pound continuous system the normal mode
+
+ align:start position:0%
+pound continuous system the normal mode
+ 
+
+ align:start position:0%
+pound continuous system the normal mode
+is actually standing waves for the wave
+
+ align:start position:0%
+is actually standing waves for the wave
+ 
+
+ align:start position:0%
+is actually standing waves for the wave
+equation we discussed and basically the
+
+ align:start position:0%
+equation we discussed and basically the
+ 
+
+ align:start position:0%
+equation we discussed and basically the
+functional form is a and saying okay and
+
+ align:start position:0%
+functional form is a and saying okay and
+ 
+
+ align:start position:0%
+functional form is a and saying okay and
+X plus alpha m and sine Omega M T plus
+
+ align:start position:0%
+X plus alpha m and sine Omega M T plus
+ 
+
+ align:start position:0%
+X plus alpha m and sine Omega M T plus
+beta m okay so what we actually learned
+
+ align:start position:0%
+beta m okay so what we actually learned
+ 
+
+ align:start position:0%
+beta m okay so what we actually learned
+from from the previous lecture is the
+
+ align:start position:0%
+from from the previous lecture is the
+ 
+
+ align:start position:0%
+from from the previous lecture is the
+following so basically you can actually
+
+ align:start position:0%
+following so basically you can actually
+ 
+
+ align:start position:0%
+following so basically you can actually
+decide the km and Appa and by boundary
+
+ align:start position:0%
+decide the km and Appa and by boundary
+ 
+
+ align:start position:0%
+decide the km and Appa and by boundary
+conditions right so before you introduce
+
+ align:start position:0%
+conditions right so before you introduce
+ 
+
+ align:start position:0%
+conditions right so before you introduce
+boundary conditions which are the
+
+ align:start position:0%
+boundary conditions which are the
+ 
+
+ align:start position:0%
+boundary conditions which are the
+conditions allow you to describe
+
+ align:start position:0%
+conditions allow you to describe
+ 
+
+ align:start position:0%
+conditions allow you to describe
+multiple nearby system consistently okay
+
+ align:start position:0%
+multiple nearby system consistently okay
+ 
+
+ align:start position:0%
+multiple nearby system consistently okay
+so that is actually the meaning of
+
+ align:start position:0%
+so that is actually the meaning of
+ 
+
+ align:start position:0%
+so that is actually the meaning of
+boundary condition before you introduce
+
+ align:start position:0%
+boundary condition before you introduce
+ 
+
+ align:start position:0%
+boundary condition before you introduce
+that KN and alpha n a Puteri number
+
+ align:start position:0%
+that KN and alpha n a Puteri number
+ 
+
+ align:start position:0%
+that KN and alpha n a Puteri number
+whatever number you can you choose
+
+ align:start position:0%
+whatever number you can you choose
+ 
+
+ align:start position:0%
+whatever number you can you choose
+easily can satisfy the wave equation but
+
+ align:start position:0%
+easily can satisfy the wave equation but
+ 
+
+ align:start position:0%
+easily can satisfy the wave equation but
+after you actually introduce the
+
+ align:start position:0%
+after you actually introduce the
+ 
+
+ align:start position:0%
+after you actually introduce the
+boundary condition you figure that out
+
+ align:start position:0%
+boundary condition you figure that out
+ 
+
+ align:start position:0%
+boundary condition you figure that out
+from the front from a problem you are
+
+ align:start position:0%
+from the front from a problem you are
+ 
+
+ align:start position:0%
+from the front from a problem you are
+given then K N and alpha n cannot be
+
+ align:start position:0%
+given then K N and alpha n cannot be
+ 
+
+ align:start position:0%
+given then K N and alpha n cannot be
+arbitrary anymore and they usually pick
+
+ align:start position:0%
+arbitrary anymore and they usually pick
+ 
+
+ align:start position:0%
+arbitrary anymore and they usually pick
+on discrete numbers okay so that is
+
+ align:start position:0%
+on discrete numbers okay so that is
+ 
+
+ align:start position:0%
+on discrete numbers okay so that is
+actually what we actually learned from
+
+ align:start position:0%
+actually what we actually learned from
+ 
+
+ align:start position:0%
+actually what we actually learned from
+the previous lectures and the finally we
+
+ align:start position:0%
+the previous lectures and the finally we
+ 
+
+ align:start position:0%
+the previous lectures and the finally we
+will also see that on Omega n is
+
+ align:start position:0%
+will also see that on Omega n is
+ 
+
+ align:start position:0%
+will also see that on Omega n is
+actually determined by the property of
+
+ align:start position:0%
+actually determined by the property of
+ 
+
+ align:start position:0%
+actually determined by the property of
+the system by so called dispersion
+
+ align:start position:0%
+the system by so called dispersion
+ 
+
+ align:start position:0%
+the system by so called dispersion
+relation in this case is linear is
+
+ align:start position:0%
+relation in this case is linear is
+ 
+
+ align:start position:0%
+relation in this case is linear is
+proportional to K n because we are
+
+ align:start position:0%
+proportional to K n because we are
+ 
+
+ align:start position:0%
+proportional to K n because we are
+talking about assets per step median for
+
+ align:start position:0%
+talking about assets per step median for
+ 
+
+ align:start position:0%
+talking about assets per step median for
+the moment and we have this beta n which
+
+ align:start position:0%
+the moment and we have this beta n which
+ 
+
+ align:start position:0%
+the moment and we have this beta n which
+is actually related to the initial
+
+ align:start position:0%
+is actually related to the initial
+ 
+
+ align:start position:0%
+is actually related to the initial
+condition and a.m. which can actually be
+
+ align:start position:0%
+condition and a.m. which can actually be
+ 
+
+ align:start position:0%
+condition and a.m. which can actually be
+determined by food year decomposition
+
+ align:start position:0%
+determined by food year decomposition
+ 
+
+ align:start position:0%
+determined by food year decomposition
+right so if you are not familiar with
+
+ align:start position:0%
+right so if you are not familiar with
+ 
+
+ align:start position:0%
+right so if you are not familiar with
+this you have to really review how to do
+
+ align:start position:0%
+this you have to really review how to do
+ 
+
+ align:start position:0%
+this you have to really review how to do
+food their decomposition okay I know
+
+ align:start position:0%
+food their decomposition okay I know
+ 
+
+ align:start position:0%
+food their decomposition okay I know
+most of you
+
+ align:start position:0%
+most of you
+ 
+
+ align:start position:0%
+most of you
+we did very well in the meter but maybe
+
+ align:start position:0%
+we did very well in the meter but maybe
+ 
+
+ align:start position:0%
+we did very well in the meter but maybe
+some of you actually forgot how to
+
+ align:start position:0%
+some of you actually forgot how to
+ 
+
+ align:start position:0%
+some of you actually forgot how to
+actually determine a.m. and it would be
+
+ align:start position:0%
+actually determine a.m. and it would be
+ 
+
+ align:start position:0%
+actually determine a.m. and it would be
+very very important to rebuild that for
+
+ align:start position:0%
+very very important to rebuild that for
+ 
+
+ align:start position:0%
+very very important to rebuild that for
+the preparation for the final now the
+
+ align:start position:0%
+the preparation for the final now the
+ 
+
+ align:start position:0%
+the preparation for the final now the
+second set of solution in Safari so you
+
+ align:start position:0%
+second set of solution in Safari so you
+ 
+
+ align:start position:0%
+second set of solution in Safari so you
+have progress progressing waves and the
+
+ align:start position:0%
+have progress progressing waves and the
+ 
+
+ align:start position:0%
+have progress progressing waves and the
+functional form is really interesting so
+
+ align:start position:0%
+functional form is really interesting so
+ 
+
+ align:start position:0%
+functional form is really interesting so
+you can see it's actually can be written
+
+ align:start position:0%
+you can see it's actually can be written
+ 
+
+ align:start position:0%
+you can see it's actually can be written
+as f f is an arbitrary function x + - v
+
+ align:start position:0%
+as f f is an arbitrary function x + - v
+ 
+
+ align:start position:0%
+as f f is an arbitrary function x + - v
+PT type a CD that is as you described in
+
+ align:start position:0%
+PT type a CD that is as you described in
+ 
+
+ align:start position:0%
+PT type a CD that is as you described in
+a wave which is traveling to the
+
+ align:start position:0%
+a wave which is traveling to the
+ 
+
+ align:start position:0%
+a wave which is traveling to the
+positive to a negative or positive
+
+ align:start position:0%
+positive to a negative or positive
+ 
+
+ align:start position:0%
+positive to a negative or positive
+direction in the X direction and or you
+
+ align:start position:0%
+direction in the X direction and or you
+ 
+
+ align:start position:0%
+direction in the X direction and or you
+can easily write it down as G function
+
+ align:start position:0%
+can easily write it down as G function
+ 
+
+ align:start position:0%
+can easily write it down as G function
+KX plus minus Omega T actually they
+
+ align:start position:0%
+KX plus minus Omega T actually they
+ 
+
+ align:start position:0%
+KX plus minus Omega T actually they
+actually all works for wave equations
+
+ align:start position:0%
+actually all works for wave equations
+ 
+
+ align:start position:0%
+actually all works for wave equations
+now we actually went ahead and and apply
+
+ align:start position:0%
+now we actually went ahead and and apply
+ 
+
+ align:start position:0%
+now we actually went ahead and and apply
+the approach which we learn from the the
+
+ align:start position:0%
+the approach which we learn from the the
+ 
+
+ align:start position:0%
+the approach which we learn from the the
+general solution of web equation two
+
+ align:start position:0%
+general solution of web equation two
+ 
+
+ align:start position:0%
+general solution of web equation two
+massive strings and we discussed about
+
+ align:start position:0%
+massive strings and we discussed about
+ 
+
+ align:start position:0%
+massive strings and we discussed about
+some waves right for the Sun waves it
+
+ align:start position:0%
+some waves right for the Sun waves it
+ 
+
+ align:start position:0%
+some waves right for the Sun waves it
+will be important to actually review
+
+ align:start position:0%
+will be important to actually review
+ 
+
+ align:start position:0%
+will be important to actually review
+what are the boundary conditions for the
+
+ align:start position:0%
+what are the boundary conditions for the
+ 
+
+ align:start position:0%
+what are the boundary conditions for the
+displacement of the of the molecule in
+
+ align:start position:0%
+displacement of the of the molecule in
+ 
+
+ align:start position:0%
+displacement of the of the molecule in
+the in the Sun wave compared to the
+
+ align:start position:0%
+the in the Sun wave compared to the
+ 
+
+ align:start position:0%
+the in the Sun wave compared to the
+pressure deviation from the run pressure
+
+ align:start position:0%
+pressure deviation from the run pressure
+ 
+
+ align:start position:0%
+pressure deviation from the run pressure
+okay so I think it's important to make
+
+ align:start position:0%
+okay so I think it's important to make
+ 
+
+ align:start position:0%
+okay so I think it's important to make
+sure that you understand the difference
+
+ align:start position:0%
+sure that you understand the difference
+ 
+
+ align:start position:0%
+sure that you understand the difference
+between these two what are the boundary
+
+ align:start position:0%
+between these two what are the boundary
+ 
+
+ align:start position:0%
+between these two what are the boundary
+conditions and and basically issue
+
+ align:start position:0%
+conditions and and basically issue
+ 
+
+ align:start position:0%
+conditions and and basically issue
+actually be very similar to the solution
+
+ align:start position:0%
+actually be very similar to the solution
+ 
+
+ align:start position:0%
+actually be very similar to the solution
+the boundary condition for the massive
+
+ align:start position:0%
+the boundary condition for the massive
+ 
+
+ align:start position:0%
+the boundary condition for the massive
+high strings and we also talked about
+
+ align:start position:0%
+high strings and we also talked about
+ 
+
+ align:start position:0%
+high strings and we also talked about
+electromagnetic waves right and that is
+
+ align:start position:0%
+electromagnetic waves right and that is
+ 
+
+ align:start position:0%
+electromagnetic waves right and that is
+actually another topic which you really
+
+ align:start position:0%
+actually another topic which you really
+ 
+
+ align:start position:0%
+actually another topic which you really
+have to review and several things which
+
+ align:start position:0%
+have to review and several things which
+ 
+
+ align:start position:0%
+have to review and several things which
+is actually interesting is that electric
+
+ align:start position:0%
+is actually interesting is that electric
+ 
+
+ align:start position:0%
+is actually interesting is that electric
+field cannot dip with our magnetic field
+
+ align:start position:0%
+field cannot dip with our magnetic field
+ 
+
+ align:start position:0%
+field cannot dip with our magnetic field
+right they are always together no matter
+
+ align:start position:0%
+right they are always together no matter
+ 
+
+ align:start position:0%
+right they are always together no matter
+what right so if you have a traveling
+
+ align:start position:0%
+what right so if you have a traveling
+ 
+
+ align:start position:0%
+what right so if you have a traveling
+electric field the
+
+ align:start position:0%
+electric field the
+ 
+
+ align:start position:0%
+electric field the
+there must be a chair boarding magnetic
+
+ align:start position:0%
+there must be a chair boarding magnetic
+ 
+
+ align:start position:0%
+there must be a chair boarding magnetic
+field and that is actually governed by
+
+ align:start position:0%
+field and that is actually governed by
+ 
+
+ align:start position:0%
+field and that is actually governed by
+the Maxwell's equation because before we
+
+ align:start position:0%
+the Maxwell's equation because before we
+ 
+
+ align:start position:0%
+the Maxwell's equation because before we
+actually go into the detail of those we
+
+ align:start position:0%
+actually go into the detail of those we
+ 
+
+ align:start position:0%
+actually go into the detail of those we
+also discussed about dispersive medium
+
+ align:start position:0%
+also discussed about dispersive medium
+ 
+
+ align:start position:0%
+also discussed about dispersive medium
+right so in the case of dispersive
+
+ align:start position:0%
+right so in the case of dispersive
+ 
+
+ align:start position:0%
+right so in the case of dispersive
+medium we actually use the special kind
+
+ align:start position:0%
+medium we actually use the special kind
+ 
+
+ align:start position:0%
+medium we actually use the special kind
+of example which is strings with
+
+ align:start position:0%
+of example which is strings with
+ 
+
+ align:start position:0%
+of example which is strings with
+stiffness right so basically what we
+
+ align:start position:0%
+stiffness right so basically what we
+ 
+
+ align:start position:0%
+stiffness right so basically what we
+actually found is that if you have a
+
+ align:start position:0%
+actually found is that if you have a
+ 
+
+ align:start position:0%
+actually found is that if you have a
+certain kinds of wave equation like like
+
+ align:start position:0%
+certain kinds of wave equation like like
+ 
+
+ align:start position:0%
+certain kinds of wave equation like like
+this one yeah I know I should writing
+
+ align:start position:0%
+this one yeah I know I should writing
+ 
+
+ align:start position:0%
+this one yeah I know I should writing
+this one here basically if I add
+
+ align:start position:0%
+this one here basically if I add
+ 
+
+ align:start position:0%
+this one here basically if I add
+additional tend to describe the
+
+ align:start position:0%
+additional tend to describe the
+ 
+
+ align:start position:0%
+additional tend to describe the
+stiffness right then what is actually
+
+ align:start position:0%
+stiffness right then what is actually
+ 
+
+ align:start position:0%
+stiffness right then what is actually
+going to happen is that the dispersion
+
+ align:start position:0%
+going to happen is that the dispersion
+ 
+
+ align:start position:0%
+going to happen is that the dispersion
+relation when I ask you to approach the
+
+ align:start position:0%
+relation when I ask you to approach the
+ 
+
+ align:start position:0%
+relation when I ask you to approach the
+dispersion relation usually and
+
+ align:start position:0%
+dispersion relation usually and
+ 
+
+ align:start position:0%
+dispersion relation usually and
+requesting you to find the relation
+
+ align:start position:0%
+requesting you to find the relation
+ 
+
+ align:start position:0%
+requesting you to find the relation
+between Omega and the K and I'm going
+
+ align:start position:0%
+between Omega and the K and I'm going
+ 
+
+ align:start position:0%
+between Omega and the K and I'm going
+over this in more detail because I see
+
+ align:start position:0%
+over this in more detail because I see
+ 
+
+ align:start position:0%
+over this in more detail because I see
+so many similar mistakes in the mid ton
+
+ align:start position:0%
+so many similar mistakes in the mid ton
+ 
+
+ align:start position:0%
+so many similar mistakes in the mid ton
+so basically what I am asking is Omega
+
+ align:start position:0%
+so basically what I am asking is Omega
+ 
+
+ align:start position:0%
+so basically what I am asking is Omega
+versus K and in the if we don't have
+
+ align:start position:0%
+versus K and in the if we don't have
+ 
+
+ align:start position:0%
+versus K and in the if we don't have
+this turn then basically you have a
+
+ align:start position:0%
+this turn then basically you have a
+ 
+
+ align:start position:0%
+this turn then basically you have a
+straight line straight line means you
+
+ align:start position:0%
+straight line straight line means you
+ 
+
+ align:start position:0%
+straight line straight line means you
+have a non dispersive medium right and
+
+ align:start position:0%
+have a non dispersive medium right and
+ 
+
+ align:start position:0%
+have a non dispersive medium right and
+if you add this turn you need to know
+
+ align:start position:0%
+if you add this turn you need to know
+ 
+
+ align:start position:0%
+if you add this turn you need to know
+how to evaluate the dispersion relation
+
+ align:start position:0%
+how to evaluate the dispersion relation
+ 
+
+ align:start position:0%
+how to evaluate the dispersion relation
+the quickest way to evaluate the
+
+ align:start position:0%
+the quickest way to evaluate the
+ 
+
+ align:start position:0%
+the quickest way to evaluate the
+dispersion relation is to just simply
+
+ align:start position:0%
+dispersion relation is to just simply
+ 
+
+ align:start position:0%
+dispersion relation is to just simply
+plug in the progressing wave solution
+
+ align:start position:0%
+plug in the progressing wave solution
+ 
+
+ align:start position:0%
+plug in the progressing wave solution
+for them for the G function or harmonic
+
+ align:start position:0%
+for them for the G function or harmonic
+ 
+
+ align:start position:0%
+for them for the G function or harmonic
+focusing wave resolution sine Omega KX
+
+ align:start position:0%
+focusing wave resolution sine Omega KX
+ 
+
+ align:start position:0%
+focusing wave resolution sine Omega KX
+plus minus Omega T into this equation
+
+ align:start position:0%
+plus minus Omega T into this equation
+ 
+
+ align:start position:0%
+plus minus Omega T into this equation
+then you will be able to figure out the
+
+ align:start position:0%
+then you will be able to figure out the
+ 
+
+ align:start position:0%
+then you will be able to figure out the
+dispersion relation and what we actually
+
+ align:start position:0%
+dispersion relation and what we actually
+ 
+
+ align:start position:0%
+dispersion relation and what we actually
+figure out is the following if we
+
+ align:start position:0%
+figure out is the following if we
+ 
+
+ align:start position:0%
+figure out is the following if we
+actually include stiffness then you can
+
+ align:start position:0%
+actually include stiffness then you can
+ 
+
+ align:start position:0%
+actually include stiffness then you can
+see that the dispersion relation is not
+
+ align:start position:0%
+see that the dispersion relation is not
+ 
+
+ align:start position:0%
+see that the dispersion relation is not
+a lie
+
+ align:start position:0%
+a lie
+ 
+
+ align:start position:0%
+a lie
+anymore and the accession essentially
+
+ align:start position:0%
+anymore and the accession essentially
+ 
+
+ align:start position:0%
+anymore and the accession essentially
+some kind of curve and the slope is
+
+ align:start position:0%
+some kind of curve and the slope is
+ 
+
+ align:start position:0%
+some kind of curve and the slope is
+actually changing okay
+
+ align:start position:0%
+actually changing okay
+ 
+
+ align:start position:0%
+actually changing okay
+and there are dramatic or consequence
+
+ align:start position:0%
+and there are dramatic or consequence
+ 
+
+ align:start position:0%
+and there are dramatic or consequence
+from this thing right that means if I
+
+ align:start position:0%
+from this thing right that means if I
+ 
+
+ align:start position:0%
+from this thing right that means if I
+have a troubling wave okay with
+
+ align:start position:0%
+have a troubling wave okay with
+ 
+
+ align:start position:0%
+have a troubling wave okay with
+different wavelengths that means the
+
+ align:start position:0%
+different wavelengths that means the
+ 
+
+ align:start position:0%
+different wavelengths that means the
+phase velocity VP equal to Omega over K
+
+ align:start position:0%
+phase velocity VP equal to Omega over K
+ 
+
+ align:start position:0%
+phase velocity VP equal to Omega over K
+is going to be different for different
+
+ align:start position:0%
+is going to be different for different
+ 
+
+ align:start position:0%
+is going to be different for different
+for waves with different frequency or
+
+ align:start position:0%
+for waves with different frequency or
+ 
+
+ align:start position:0%
+for waves with different frequency or
+different wavelengths okay so that is
+
+ align:start position:0%
+different wavelengths okay so that is
+ 
+
+ align:start position:0%
+different wavelengths okay so that is
+actually clearly a problem because if I
+
+ align:start position:0%
+actually clearly a problem because if I
+ 
+
+ align:start position:0%
+actually clearly a problem because if I
+have initially produce a signal which is
+
+ align:start position:0%
+have initially produce a signal which is
+ 
+
+ align:start position:0%
+have initially produce a signal which is
+triangle and I'd like the proper gay
+
+ align:start position:0%
+triangle and I'd like the proper gay
+ 
+
+ align:start position:0%
+triangle and I'd like the proper gay
+what is going to happen is that the slow
+
+ align:start position:0%
+what is going to happen is that the slow
+ 
+
+ align:start position:0%
+what is going to happen is that the slow
+component will be lagged behind those
+
+ align:start position:0%
+component will be lagged behind those
+ 
+
+ align:start position:0%
+component will be lagged behind those
+are the slow component and the first
+
+ align:start position:0%
+are the slow component and the first
+ 
+
+ align:start position:0%
+are the slow component and the first
+component will go ahead of the nominal
+
+ align:start position:0%
+component will go ahead of the nominal
+ 
+
+ align:start position:0%
+component will go ahead of the nominal
+speed right so there will be a spread of
+
+ align:start position:0%
+speed right so there will be a spread of
+ 
+
+ align:start position:0%
+speed right so there will be a spread of
+the signal or judge originally maybe you
+
+ align:start position:0%
+the signal or judge originally maybe you
+ 
+
+ align:start position:0%
+the signal or judge originally maybe you
+have some kind of a square wave and this
+
+ align:start position:0%
+have some kind of a square wave and this
+ 
+
+ align:start position:0%
+have some kind of a square wave and this
+thing will become something which is
+
+ align:start position:0%
+thing will become something which is
+ 
+
+ align:start position:0%
+thing will become something which is
+actually along which it is smeared out
+
+ align:start position:0%
+actually along which it is smeared out
+ 
+
+ align:start position:0%
+actually along which it is smeared out
+in space and you deuce the the
+
+ align:start position:0%
+in space and you deuce the the
+ 
+
+ align:start position:0%
+in space and you deuce the the
+information and that we are going to
+
+ align:start position:0%
+information and that we are going to
+ 
+
+ align:start position:0%
+information and that we are going to
+talk about that later and we also
+
+ align:start position:0%
+talk about that later and we also
+ 
+
+ align:start position:0%
+talk about that later and we also
+learned about group velocity so what is
+
+ align:start position:0%
+learned about group velocity so what is
+ 
+
+ align:start position:0%
+learned about group velocity so what is
+a group velocity group velocity VP vbg
+
+ align:start position:0%
+a group velocity group velocity VP vbg
+ 
+
+ align:start position:0%
+a group velocity group velocity VP vbg
+essentially partial Omega hydrocal right
+
+ align:start position:0%
+essentially partial Omega hydrocal right
+ 
+
+ align:start position:0%
+essentially partial Omega hydrocal right
+which is actually the slope of
+
+ align:start position:0%
+which is actually the slope of
+ 
+
+ align:start position:0%
+which is actually the slope of
+tangential line here and well the phase
+
+ align:start position:0%
+tangential line here and well the phase
+ 
+
+ align:start position:0%
+tangential line here and well the phase
+velocity is actually connecting this
+
+ align:start position:0%
+velocity is actually connecting this
+ 
+
+ align:start position:0%
+velocity is actually connecting this
+point to that point and the slope of
+
+ align:start position:0%
+point to that point and the slope of
+ 
+
+ align:start position:0%
+point to that point and the slope of
+this this line is actually the phase
+
+ align:start position:0%
+this this line is actually the phase
+ 
+
+ align:start position:0%
+this this line is actually the phase
+phase velocity and the slope of the line
+
+ align:start position:0%
+phase velocity and the slope of the line
+ 
+
+ align:start position:0%
+phase velocity and the slope of the line
+cutting through this point which is
+
+ align:start position:0%
+cutting through this point which is
+ 
+
+ align:start position:0%
+cutting through this point which is
+actually giving you the group velocity
+
+ align:start position:0%
+actually giving you the group velocity
+ 
+
+ align:start position:0%
+actually giving you the group velocity
+and we actually learn the definition of
+
+ align:start position:0%
+and we actually learn the definition of
+ 
+
+ align:start position:0%
+and we actually learn the definition of
+the consequence
+
+ align:start position:0%
+the consequence
+ 
+
+ align:start position:0%
+the consequence
+of group velocity and phase velocity by
+
+ align:start position:0%
+of group velocity and phase velocity by
+ 
+
+ align:start position:0%
+of group velocity and phase velocity by
+introducing you a bit phenomena
+
+ align:start position:0%
+introducing you a bit phenomena
+ 
+
+ align:start position:0%
+introducing you a bit phenomena
+basically we add two waves with similar
+
+ align:start position:0%
+basically we add two waves with similar
+ 
+
+ align:start position:0%
+basically we add two waves with similar
+with wavelength or wave number basically
+
+ align:start position:0%
+with wavelength or wave number basically
+ 
+
+ align:start position:0%
+with wavelength or wave number basically
+what we see is the power in so basically
+
+ align:start position:0%
+what we see is the power in so basically
+ 
+
+ align:start position:0%
+what we see is the power in so basically
+you see some behavior like this we see
+
+ align:start position:0%
+you see some behavior like this we see
+ 
+
+ align:start position:0%
+you see some behavior like this we see
+this this superposition of these two
+
+ align:start position:0%
+this this superposition of these two
+ 
+
+ align:start position:0%
+this this superposition of these two
+waves which produce a bit phenomena can
+
+ align:start position:0%
+waves which produce a bit phenomena can
+ 
+
+ align:start position:0%
+waves which produce a bit phenomena can
+be understood by some synchronization
+
+ align:start position:0%
+be understood by some synchronization
+ 
+
+ align:start position:0%
+be understood by some synchronization
+oscillating really fast modulated by
+
+ align:start position:0%
+oscillating really fast modulated by
+ 
+
+ align:start position:0%
+oscillating really fast modulated by
+much slowed or mareting envelope
+
+ align:start position:0%
+much slowed or mareting envelope
+ 
+
+ align:start position:0%
+much slowed or mareting envelope
+basically you can actually understand
+
+ align:start position:0%
+basically you can actually understand
+ 
+
+ align:start position:0%
+basically you can actually understand
+the pit phenomena by decomposing to by
+
+ align:start position:0%
+the pit phenomena by decomposing to by
+ 
+
+ align:start position:0%
+the pit phenomena by decomposing to by
+actually identifying these two
+
+ align:start position:0%
+actually identifying these two
+ 
+
+ align:start position:0%
+actually identifying these two
+interesting structure and the speed of
+
+ align:start position:0%
+interesting structure and the speed of
+ 
+
+ align:start position:0%
+interesting structure and the speed of
+odd all those little Peaks is actually
+
+ align:start position:0%
+odd all those little Peaks is actually
+ 
+
+ align:start position:0%
+odd all those little Peaks is actually
+traveling at phase velocity and the
+
+ align:start position:0%
+traveling at phase velocity and the
+ 
+
+ align:start position:0%
+traveling at phase velocity and the
+speed of the envelope is actually found
+
+ align:start position:0%
+speed of the envelope is actually found
+ 
+
+ align:start position:0%
+speed of the envelope is actually found
+to be traveling at group velocity okay
+
+ align:start position:0%
+to be traveling at group velocity okay
+ 
+
+ align:start position:0%
+to be traveling at group velocity okay
+so that is actually what we have learned
+
+ align:start position:0%
+so that is actually what we have learned
+ 
+
+ align:start position:0%
+so that is actually what we have learned
+and we can have group velocity and the
+
+ align:start position:0%
+and we can have group velocity and the
+ 
+
+ align:start position:0%
+and we can have group velocity and the
+phase velocity troubling at the same
+
+ align:start position:0%
+phase velocity troubling at the same
+ 
+
+ align:start position:0%
+phase velocity troubling at the same
+direction and we can also have negative
+
+ align:start position:0%
+direction and we can also have negative
+ 
+
+ align:start position:0%
+direction and we can also have negative
+group velocity right so that is a
+
+ align:start position:0%
+group velocity right so that is a
+ 
+
+ align:start position:0%
+group velocity right so that is a
+technique which is really really very
+
+ align:start position:0%
+technique which is really really very
+ 
+
+ align:start position:0%
+technique which is really really very
+difficult and then still trying to
+
+ align:start position:0%
+difficult and then still trying to
+ 
+
+ align:start position:0%
+difficult and then still trying to
+practice and make sure that I can't a
+
+ align:start position:0%
+practice and make sure that I can't a
+ 
+
+ align:start position:0%
+practice and make sure that I can't a
+model in three basically is like the
+
+ align:start position:0%
+model in three basically is like the
+ 
+
+ align:start position:0%
+model in three basically is like the
+whole system the whole edita structure I
+
+ align:start position:0%
+whole system the whole edita structure I
+ 
+
+ align:start position:0%
+whole system the whole edita structure I
+should be moving in a positive direction
+
+ align:start position:0%
+should be moving in a positive direction
+ 
+
+ align:start position:0%
+should be moving in a positive direction
+but the body or say the envelope is
+
+ align:start position:0%
+but the body or say the envelope is
+ 
+
+ align:start position:0%
+but the body or say the envelope is
+actually moving in the negative x
+
+ align:start position:0%
+actually moving in the negative x
+ 
+
+ align:start position:0%
+actually moving in the negative x
+direction so that is actually also
+
+ align:start position:0%
+direction so that is actually also
+ 
+
+ align:start position:0%
+direction so that is actually also
+possible and you can actually construct
+
+ align:start position:0%
+possible and you can actually construct
+ 
+
+ align:start position:0%
+possible and you can actually construct
+a system which you have negative group
+
+ align:start position:0%
+a system which you have negative group
+ 
+
+ align:start position:0%
+a system which you have negative group
+asset so once we have done that we
+
+ align:start position:0%
+asset so once we have done that we
+ 
+
+ align:start position:0%
+asset so once we have done that we
+actually also try to understand further
+
+ align:start position:0%
+actually also try to understand further
+ 
+
+ align:start position:0%
+actually also try to understand further
+the description of the solution for the
+
+ align:start position:0%
+the description of the solution for the
+ 
+
+ align:start position:0%
+the description of the solution for the
+discrete dispersive
+
+ align:start position:0%
+discrete dispersive
+ 
+
+ align:start position:0%
+discrete dispersive
+right so basically what we actually went
+
+ align:start position:0%
+right so basically what we actually went
+ 
+
+ align:start position:0%
+right so basically what we actually went
+over during the class is that okay now
+
+ align:start position:0%
+over during the class is that okay now
+ 
+
+ align:start position:0%
+over during the class is that okay now
+if the F function f of T is describing
+
+ align:start position:0%
+if the F function f of T is describing
+ 
+
+ align:start position:0%
+if the F function f of T is describing
+Eunji's hand and I'm holding infinitely
+
+ align:start position:0%
+Eunji's hand and I'm holding infinitely
+ 
+
+ align:start position:0%
+Eunji's hand and I'm holding infinitely
+long string and I shake it as a function
+
+ align:start position:0%
+long string and I shake it as a function
+ 
+
+ align:start position:0%
+long string and I shake it as a function
+of time and that is actually this motion
+
+ align:start position:0%
+of time and that is actually this motion
+ 
+
+ align:start position:0%
+of time and that is actually this motion
+is actually described by this F function
+
+ align:start position:0%
+is actually described by this F function
+ 
+
+ align:start position:0%
+is actually described by this F function
+okay what we actually know is that this
+
+ align:start position:0%
+okay what we actually know is that this
+ 
+
+ align:start position:0%
+okay what we actually know is that this
+this oscillation okay I can I can do
+
+ align:start position:0%
+this oscillation okay I can I can do
+ 
+
+ align:start position:0%
+this oscillation okay I can I can do
+whatever I want but the all kind of F
+
+ align:start position:0%
+whatever I want but the all kind of F
+ 
+
+ align:start position:0%
+whatever I want but the all kind of F
+function can be described a
+
+ align:start position:0%
+function can be described a
+ 
+
+ align:start position:0%
+function can be described a
+superposition of many many many waves
+
+ align:start position:0%
+superposition of many many many waves
+ 
+
+ align:start position:0%
+superposition of many many many waves
+with different angular frequency okay so
+
+ align:start position:0%
+with different angular frequency okay so
+ 
+
+ align:start position:0%
+with different angular frequency okay so
+that's a miracle which we pal row from
+
+ align:start position:0%
+that's a miracle which we pal row from
+ 
+
+ align:start position:0%
+that's a miracle which we pal row from
+the maths Department again and you can
+
+ align:start position:0%
+the maths Department again and you can
+ 
+
+ align:start position:0%
+the maths Department again and you can
+see that F function can be written as a
+
+ align:start position:0%
+see that F function can be written as a
+ 
+
+ align:start position:0%
+see that F function can be written as a
+sum of all kinds of different waves with
+
+ align:start position:0%
+sum of all kinds of different waves with
+ 
+
+ align:start position:0%
+sum of all kinds of different waves with
+different angular frequency with
+
+ align:start position:0%
+different angular frequency with
+ 
+
+ align:start position:0%
+different angular frequency with
+population see you make Omega this this
+
+ align:start position:0%
+population see you make Omega this this
+ 
+
+ align:start position:0%
+population see you make Omega this this
+is actually the weight which we make
+
+ align:start position:0%
+is actually the weight which we make
+ 
+
+ align:start position:0%
+is actually the weight which we make
+them become the F function okay and we
+
+ align:start position:0%
+them become the F function okay and we
+ 
+
+ align:start position:0%
+them become the F function okay and we
+can actually figure out the C Omega by
+
+ align:start position:0%
+can actually figure out the C Omega by
+ 
+
+ align:start position:0%
+can actually figure out the C Omega by
+doing a Fourier transform and finally
+
+ align:start position:0%
+doing a Fourier transform and finally
+ 
+
+ align:start position:0%
+doing a Fourier transform and finally
+what will be the resulting wave function
+
+ align:start position:0%
+what will be the resulting wave function
+ 
+
+ align:start position:0%
+what will be the resulting wave function
+sigh XT which is actually the wave
+
+ align:start position:0%
+sigh XT which is actually the wave
+ 
+
+ align:start position:0%
+sigh XT which is actually the wave
+function generated by the oscillation of
+
+ align:start position:0%
+function generated by the oscillation of
+ 
+
+ align:start position:0%
+function generated by the oscillation of
+my hand and also carbon by the wave
+
+ align:start position:0%
+my hand and also carbon by the wave
+ 
+
+ align:start position:0%
+my hand and also carbon by the wave
+equation which give you the relation
+
+ align:start position:0%
+equation which give you the relation
+ 
+
+ align:start position:0%
+equation which give you the relation
+between Omega and the K can be written
+
+ align:start position:0%
+between Omega and the K can be written
+ 
+
+ align:start position:0%
+between Omega and the K can be written
+in in that functional form okay so so
+
+ align:start position:0%
+in in that functional form okay so so
+ 
+
+ align:start position:0%
+in in that functional form okay so so
+the good news is that with the help of
+
+ align:start position:0%
+the good news is that with the help of
+ 
+
+ align:start position:0%
+the good news is that with the help of
+buddhir transform we can issue the also
+
+ align:start position:0%
+buddhir transform we can issue the also
+ 
+
+ align:start position:0%
+buddhir transform we can issue the also
+describe and predict what is going to
+
+ align:start position:0%
+describe and predict what is going to
+ 
+
+ align:start position:0%
+describe and predict what is going to
+happen no matter if this system is
+
+ align:start position:0%
+happen no matter if this system is
+ 
+
+ align:start position:0%
+happen no matter if this system is
+dispersive or not dispersive using this
+
+ align:start position:0%
+dispersive or not dispersive using this
+ 
+
+ align:start position:0%
+dispersive or not dispersive using this
+approach okay so that is actually really
+
+ align:start position:0%
+approach okay so that is actually really
+ 
+
+ align:start position:0%
+approach okay so that is actually really
+cool and you can of course you can do a
+
+ align:start position:0%
+cool and you can of course you can do a
+ 
+
+ align:start position:0%
+cool and you can of course you can do a
+cross-check just to assume that this
+
+ align:start position:0%
+cross-check just to assume that this
+ 
+
+ align:start position:0%
+cross-check just to assume that this
+sort is this is a non dispersive media
+
+ align:start position:0%
+sort is this is a non dispersive media
+ 
+
+ align:start position:0%
+sort is this is a non dispersive media
+and you are also going to get back to
+
+ align:start position:0%
+and you are also going to get back to
+ 
+
+ align:start position:0%
+and you are also going to get back to
+what you should expect the solution to
+
+ align:start position:0%
+what you should expect the solution to
+ 
+
+ align:start position:0%
+what you should expect the solution to
+non dispersive medium for the sigh XT so
+
+ align:start position:0%
+non dispersive medium for the sigh XT so
+ 
+
+ align:start position:0%
+non dispersive medium for the sigh XT so
+that is actually one thing which is
+
+ align:start position:0%
+that is actually one thing which is
+ 
+
+ align:start position:0%
+that is actually one thing which is
+really remarkable and you know I think
+
+ align:start position:0%
+really remarkable and you know I think
+ 
+
+ align:start position:0%
+really remarkable and you know I think
+what is actually needed to to know is
+
+ align:start position:0%
+what is actually needed to to know is
+ 
+
+ align:start position:0%
+what is actually needed to to know is
+not a deviation of Otto's formula but
+
+ align:start position:0%
+not a deviation of Otto's formula but
+ 
+
+ align:start position:0%
+not a deviation of Otto's formula but
+how to issue the practing and the
+
+ align:start position:0%
+how to issue the practing and the
+ 
+
+ align:start position:0%
+how to issue the practing and the
+derived C Omega right by using the
+
+ align:start position:0%
+derived C Omega right by using the
+ 
+
+ align:start position:0%
+derived C Omega right by using the
+formula you are given and how to
+
+ align:start position:0%
+formula you are given and how to
+ 
+
+ align:start position:0%
+formula you are given and how to
+actually then put together or the
+
+ align:start position:0%
+actually then put together or the
+ 
+
+ align:start position:0%
+actually then put together or the
+solution and the camp and the picker the
+
+ align:start position:0%
+solution and the camp and the picker the
+ 
+
+ align:start position:0%
+solution and the camp and the picker the
+resulting solution for the site XT which
+
+ align:start position:0%
+resulting solution for the site XT which
+ 
+
+ align:start position:0%
+resulting solution for the site XT which
+is actually really the solution we
+
+ align:start position:0%
+is actually really the solution we
+ 
+
+ align:start position:0%
+is actually really the solution we
+really care okay so for that you need to
+
+ align:start position:0%
+really care okay so for that you need to
+ 
+
+ align:start position:0%
+really care okay so for that you need to
+know how to do the integration you need
+
+ align:start position:0%
+know how to do the integration you need
+ 
+
+ align:start position:0%
+know how to do the integration you need
+to know how to derive the dispersion
+
+ align:start position:0%
+to know how to derive the dispersion
+ 
+
+ align:start position:0%
+to know how to derive the dispersion
+relation then what is HP lap over is to
+
+ align:start position:0%
+relation then what is HP lap over is to
+ 
+
+ align:start position:0%
+relation then what is HP lap over is to
+put them pregnant in into that equation
+
+ align:start position:0%
+put them pregnant in into that equation
+ 
+
+ align:start position:0%
+put them pregnant in into that equation
+which is actually also given to you in a
+
+ align:start position:0%
+which is actually also given to you in a
+ 
+
+ align:start position:0%
+which is actually also given to you in a
+formula and and we will not ask you to
+
+ align:start position:0%
+formula and and we will not ask you to
+ 
+
+ align:start position:0%
+formula and and we will not ask you to
+do very very complicated integration for
+
+ align:start position:0%
+do very very complicated integration for
+ 
+
+ align:start position:0%
+do very very complicated integration for
+sure in a panel so what is actually the
+
+ align:start position:0%
+sure in a panel so what is actually the
+ 
+
+ align:start position:0%
+sure in a panel so what is actually the
+consequence so basically one thing which
+
+ align:start position:0%
+consequence so basically one thing which
+ 
+
+ align:start position:0%
+consequence so basically one thing which
+is interesting to know is that if you
+
+ align:start position:0%
+is interesting to know is that if you
+ 
+
+ align:start position:0%
+is interesting to know is that if you
+have waves in a coordinate space which
+
+ align:start position:0%
+have waves in a coordinate space which
+ 
+
+ align:start position:0%
+have waves in a coordinate space which
+is really widely spread out and you can
+
+ align:start position:0%
+is really widely spread out and you can
+ 
+
+ align:start position:0%
+is really widely spread out and you can
+do Fourier transform to get the weight
+
+ align:start position:0%
+do Fourier transform to get the weight
+ 
+
+ align:start position:0%
+do Fourier transform to get the weight
+population in the frequency space when
+
+ align:start position:0%
+population in the frequency space when
+ 
+
+ align:start position:0%
+population in the frequency space when
+we find is that when when this wave is
+
+ align:start position:0%
+we find is that when when this wave is
+ 
+
+ align:start position:0%
+we find is that when when this wave is
+really really wide in the space then
+
+ align:start position:0%
+really really wide in the space then
+ 
+
+ align:start position:0%
+really really wide in the space then
+what we find is that actually the web
+
+ align:start position:0%
+what we find is that actually the web
+ 
+
+ align:start position:0%
+what we find is that actually the web
+population in the frequency space is
+
+ align:start position:0%
+population in the frequency space is
+ 
+
+ align:start position:0%
+population in the frequency space is
+very narrow okay by using Fourier
+
+ align:start position:0%
+very narrow okay by using Fourier
+ 
+
+ align:start position:0%
+very narrow okay by using Fourier
+transform the notice issue the result
+
+ align:start position:0%
+transform the notice issue the result
+ 
+
+ align:start position:0%
+transform the notice issue the result
+and on the other hand if you have a
+
+ align:start position:0%
+and on the other hand if you have a
+ 
+
+ align:start position:0%
+and on the other hand if you have a
+pretty very narrow pulse in the
+
+ align:start position:0%
+pretty very narrow pulse in the
+ 
+
+ align:start position:0%
+pretty very narrow pulse in the
+coordinate space for example I to this
+
+ align:start position:0%
+coordinate space for example I to this
+ 
+
+ align:start position:0%
+coordinate space for example I to this
+very very really quickly alright I
+
+ align:start position:0%
+very very really quickly alright I
+ 
+
+ align:start position:0%
+very very really quickly alright I
+create a very narrow pulse and what is
+
+ align:start position:0%
+create a very narrow pulse and what is
+ 
+
+ align:start position:0%
+create a very narrow pulse and what is
+actually happening is that I will have
+
+ align:start position:0%
+actually happening is that I will have
+ 
+
+ align:start position:0%
+actually happening is that I will have
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+a very wide range of frequency space to
+
+ align:start position:0%
+a very wide range of frequency space to
+ 
+
+ align:start position:0%
+a very wide range of frequency space to
+describe this very narrow pulse okay so
+
+ align:start position:0%
+describe this very narrow pulse okay so
+ 
+
+ align:start position:0%
+describe this very narrow pulse okay so
+that these two direct consequences of
+
+ align:start position:0%
+that these two direct consequences of
+ 
+
+ align:start position:0%
+that these two direct consequences of
+that is uncertainty principle and this
+
+ align:start position:0%
+that is uncertainty principle and this
+ 
+
+ align:start position:0%
+that is uncertainty principle and this
+actually closely connected to the
+
+ align:start position:0%
+actually closely connected to the
+ 
+
+ align:start position:0%
+actually closely connected to the
+uncertainty principle we talked about in
+
+ align:start position:0%
+uncertainty principle we talked about in
+ 
+
+ align:start position:0%
+uncertainty principle we talked about in
+a quantum mechanics Delta P times Delta
+
+ align:start position:0%
+a quantum mechanics Delta P times Delta
+ 
+
+ align:start position:0%
+a quantum mechanics Delta P times Delta
+X greater or equal to H bar over 2 all
+
+ align:start position:0%
+X greater or equal to H bar over 2 all
+ 
+
+ align:start position:0%
+X greater or equal to H bar over 2 all
+right so we have done with the
+
+ align:start position:0%
+right so we have done with the
+ 
+
+ align:start position:0%
+right so we have done with the
+one-dimensional case and we also talked
+
+ align:start position:0%
+one-dimensional case and we also talked
+ 
+
+ align:start position:0%
+one-dimensional case and we also talked
+about a two dimensional and the three
+
+ align:start position:0%
+about a two dimensional and the three
+ 
+
+ align:start position:0%
+about a two dimensional and the three
+dimensional case and this is an example
+
+ align:start position:0%
+dimensional case and this is an example
+ 
+
+ align:start position:0%
+dimensional case and this is an example
+of two dimensional membranes and
+
+ align:start position:0%
+of two dimensional membranes and
+ 
+
+ align:start position:0%
+of two dimensional membranes and
+actually a constraint so that the
+
+ align:start position:0%
+actually a constraint so that the
+ 
+
+ align:start position:0%
+actually a constraint so that the
+boundary condition at the boundary is
+
+ align:start position:0%
+boundary condition at the boundary is
+ 
+
+ align:start position:0%
+boundary condition at the boundary is
+equal the wave function is equal to zero
+
+ align:start position:0%
+equal the wave function is equal to zero
+ 
+
+ align:start position:0%
+equal the wave function is equal to zero
+and you can easily identify all those
+
+ align:start position:0%
+and you can easily identify all those
+ 
+
+ align:start position:0%
+and you can easily identify all those
+normal modes and we went ahead also to
+
+ align:start position:0%
+normal modes and we went ahead also to
+ 
+
+ align:start position:0%
+normal modes and we went ahead also to
+talk about geometric optics lots
+
+ align:start position:0%
+talk about geometric optics lots
+ 
+
+ align:start position:0%
+talk about geometric optics lots
+basically how how do we actually write
+
+ align:start position:0%
+basically how how do we actually write
+ 
+
+ align:start position:0%
+basically how how do we actually write
+that is to have a plane wave first you
+
+ align:start position:0%
+that is to have a plane wave first you
+ 
+
+ align:start position:0%
+that is to have a plane wave first you
+have a plane wave propagating toward the
+
+ align:start position:0%
+have a plane wave propagating toward the
+ 
+
+ align:start position:0%
+have a plane wave propagating toward the
+boundary of two different median and we
+
+ align:start position:0%
+boundary of two different median and we
+ 
+
+ align:start position:0%
+boundary of two different median and we
+were wondering what is actually the
+
+ align:start position:0%
+were wondering what is actually the
+ 
+
+ align:start position:0%
+were wondering what is actually the
+refracted wave and the transmitted wave
+
+ align:start position:0%
+refracted wave and the transmitted wave
+ 
+
+ align:start position:0%
+refracted wave and the transmitted wave
+by using like two by making sure just
+
+ align:start position:0%
+by using like two by making sure just
+ 
+
+ align:start position:0%
+by using like two by making sure just
+one point which is that the membranes
+
+ align:start position:0%
+one point which is that the membranes
+ 
+
+ align:start position:0%
+one point which is that the membranes
+doesn't break okay the wave function is
+
+ align:start position:0%
+doesn't break okay the wave function is
+ 
+
+ align:start position:0%
+doesn't break okay the wave function is
+continuous at this boundary that's the
+
+ align:start position:0%
+continuous at this boundary that's the
+ 
+
+ align:start position:0%
+continuous at this boundary that's the
+only assumption which we use we went
+
+ align:start position:0%
+only assumption which we use we went
+ 
+
+ align:start position:0%
+only assumption which we use we went
+through the mathematics which we don't
+
+ align:start position:0%
+through the mathematics which we don't
+ 
+
+ align:start position:0%
+through the mathematics which we don't
+really need to to remember all of them
+
+ align:start position:0%
+really need to to remember all of them
+ 
+
+ align:start position:0%
+really need to to remember all of them
+but you really need to remember the
+
+ align:start position:0%
+but you really need to remember the
+ 
+
+ align:start position:0%
+but you really need to remember the
+consequence the consequence is the
+
+ align:start position:0%
+consequence the consequence is the
+ 
+
+ align:start position:0%
+consequence the consequence is the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+so basically what we see is that if you
+
+ align:start position:0%
+so basically what we see is that if you
+ 
+
+ align:start position:0%
+so basically what we see is that if you
+have in certain frame wave which in
+
+ align:start position:0%
+have in certain frame wave which in
+ 
+
+ align:start position:0%
+have in certain frame wave which in
+certain angle theta-1 the refractive
+
+ align:start position:0%
+certain angle theta-1 the refractive
+ 
+
+ align:start position:0%
+certain angle theta-1 the refractive
+wave will be having an angle of theta
+
+ align:start position:0%
+wave will be having an angle of theta
+ 
+
+ align:start position:0%
+wave will be having an angle of theta
+one as well so that's actually the first
+
+ align:start position:0%
+one as well so that's actually the first
+ 
+
+ align:start position:0%
+one as well so that's actually the first
+law of refraction refraction law and the
+
+ align:start position:0%
+law of refraction refraction law and the
+ 
+
+ align:start position:0%
+law of refraction refraction law and the
+second one which we learn is that the
+
+ align:start position:0%
+second one which we learn is that the
+ 
+
+ align:start position:0%
+second one which we learn is that the
+transmitted wave where satisfies Snell's
+
+ align:start position:0%
+transmitted wave where satisfies Snell's
+ 
+
+ align:start position:0%
+transmitted wave where satisfies Snell's
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+and one sign theta 1 equal to n 2 sine
+
+ align:start position:0%
+and one sign theta 1 equal to n 2 sine
+ 
+
+ align:start position:0%
+and one sign theta 1 equal to n 2 sine
+theta 2 and that is that should be very
+
+ align:start position:0%
+theta 2 and that is that should be very
+ 
+
+ align:start position:0%
+theta 2 and that is that should be very
+interesting because this Snell's law ok
+
+ align:start position:0%
+interesting because this Snell's law ok
+ 
+
+ align:start position:0%
+interesting because this Snell's law ok
+have also nothing to do with Maxwell's
+
+ align:start position:0%
+have also nothing to do with Maxwell's
+ 
+
+ align:start position:0%
+have also nothing to do with Maxwell's
+equation you see right that's actually
+
+ align:start position:0%
+equation you see right that's actually
+ 
+
+ align:start position:0%
+equation you see right that's actually
+what you actually can learn from here it
+
+ align:start position:0%
+what you actually can learn from here it
+ 
+
+ align:start position:0%
+what you actually can learn from here it
+will usually use electromagnetic waves
+
+ align:start position:0%
+will usually use electromagnetic waves
+ 
+
+ align:start position:0%
+will usually use electromagnetic waves
+to demonstrate Snell's law right but
+
+ align:start position:0%
+to demonstrate Snell's law right but
+ 
+
+ align:start position:0%
+to demonstrate Snell's law right but
+from else we learned that it has nothing
+
+ align:start position:0%
+from else we learned that it has nothing
+ 
+
+ align:start position:0%
+from else we learned that it has nothing
+to do with in M Maxwell's equation
+
+ align:start position:0%
+to do with in M Maxwell's equation
+ 
+
+ align:start position:0%
+to do with in M Maxwell's equation
+applies to all kinds of different
+
+ align:start position:0%
+applies to all kinds of different
+ 
+
+ align:start position:0%
+applies to all kinds of different
+systems which you can which can be
+
+ align:start position:0%
+systems which you can which can be
+ 
+
+ align:start position:0%
+systems which you can which can be
+described by wave functions so that is
+
+ align:start position:0%
+described by wave functions so that is
+ 
+
+ align:start position:0%
+described by wave functions so that is
+actually the very important consequence
+
+ align:start position:0%
+actually the very important consequence
+ 
+
+ align:start position:0%
+actually the very important consequence
+but on the other hand as we already
+
+ align:start position:0%
+but on the other hand as we already
+ 
+
+ align:start position:0%
+but on the other hand as we already
+discussed later the relative amplitude
+
+ align:start position:0%
+discussed later the relative amplitude
+ 
+
+ align:start position:0%
+discussed later the relative amplitude
+of the in certain wave refractive wave
+
+ align:start position:0%
+of the in certain wave refractive wave
+ 
+
+ align:start position:0%
+of the in certain wave refractive wave
+and transmitted wave the relative
+
+ align:start position:0%
+and transmitted wave the relative
+ 
+
+ align:start position:0%
+and transmitted wave the relative
+amplitude is governed by Maxwell's
+
+ align:start position:0%
+amplitude is governed by Maxwell's
+ 
+
+ align:start position:0%
+amplitude is governed by Maxwell's
+equations so I would like to make a
+
+ align:start position:0%
+equations so I would like to make a
+ 
+
+ align:start position:0%
+equations so I would like to make a
+really crystal clear so the relative
+
+ align:start position:0%
+really crystal clear so the relative
+ 
+
+ align:start position:0%
+really crystal clear so the relative
+amplitude is governed by really the
+
+ align:start position:0%
+amplitude is governed by really the
+ 
+
+ align:start position:0%
+amplitude is governed by really the
+physical laws which actually governs the
+
+ align:start position:0%
+physical laws which actually governs the
+ 
+
+ align:start position:0%
+physical laws which actually governs the
+publication of those prime waves ok so I
+
+ align:start position:0%
+publication of those prime waves ok so I
+ 
+
+ align:start position:0%
+publication of those prime waves ok so I
+think we can actually take a five-minute
+
+ align:start position:0%
+think we can actually take a five-minute
+ 
+
+ align:start position:0%
+think we can actually take a five-minute
+break to help some some here and of
+
+ align:start position:0%
+break to help some some here and of
+ 
+
+ align:start position:0%
+break to help some some here and of
+course you can we are welcome to
+
+ align:start position:0%
+course you can we are welcome to
+ 
+
+ align:start position:0%
+course you can we are welcome to
+continue to use all those tools and the
+
+ align:start position:0%
+continue to use all those tools and the
+ 
+
+ align:start position:0%
+continue to use all those tools and the
+coffee when coming back at 38
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so welcome back everybody from the
+
+ align:start position:0%
+okay so welcome back everybody from the
+ 
+
+ align:start position:0%
+okay so welcome back everybody from the
+break so yeah so we are going to
+
+ align:start position:0%
+break so yeah so we are going to
+ 
+
+ align:start position:0%
+break so yeah so we are going to
+continue the discussion so we have
+
+ align:start position:0%
+continue the discussion so we have
+ 
+
+ align:start position:0%
+continue the discussion so we have
+actually learned about the two important
+
+ align:start position:0%
+actually learned about the two important
+ 
+
+ align:start position:0%
+actually learned about the two important
+laws for the geometrical optics and we
+
+ align:start position:0%
+laws for the geometrical optics and we
+ 
+
+ align:start position:0%
+laws for the geometrical optics and we
+actually also went ahead to discuss the
+
+ align:start position:0%
+actually also went ahead to discuss the
+ 
+
+ align:start position:0%
+actually also went ahead to discuss the
+polarization itself in greater detail so
+
+ align:start position:0%
+polarization itself in greater detail so
+ 
+
+ align:start position:0%
+polarization itself in greater detail so
+for example we can have the nearly
+
+ align:start position:0%
+for example we can have the nearly
+ 
+
+ align:start position:0%
+for example we can have the nearly
+polarized wave so basically the wave
+
+ align:start position:0%
+polarized wave so basically the wave
+ 
+
+ align:start position:0%
+polarized wave so basically the wave
+sees a ship moving up and down up and
+
+ align:start position:0%
+sees a ship moving up and down up and
+ 
+
+ align:start position:0%
+sees a ship moving up and down up and
+down but the direction of the of the
+
+ align:start position:0%
+down but the direction of the of the
+ 
+
+ align:start position:0%
+down but the direction of the of the
+vector field doesn't doesn't change okay
+
+ align:start position:0%
+vector field doesn't doesn't change okay
+ 
+
+ align:start position:0%
+vector field doesn't doesn't change okay
+it's always for example initially if
+
+ align:start position:0%
+it's always for example initially if
+ 
+
+ align:start position:0%
+it's always for example initially if
+it's in X direction and he's actually at
+
+ align:start position:0%
+it's in X direction and he's actually at
+ 
+
+ align:start position:0%
+it's in X direction and he's actually at
+the X direction forever and in that case
+
+ align:start position:0%
+the X direction forever and in that case
+ 
+
+ align:start position:0%
+the X direction forever and in that case
+I call it linearly polarized okay of
+
+ align:start position:0%
+I call it linearly polarized okay of
+ 
+
+ align:start position:0%
+I call it linearly polarized okay of
+course I can also have the case that I
+
+ align:start position:0%
+course I can also have the case that I
+ 
+
+ align:start position:0%
+course I can also have the case that I
+can actually have a superposition of two
+
+ align:start position:0%
+can actually have a superposition of two
+ 
+
+ align:start position:0%
+can actually have a superposition of two
+waves one is actually having the
+
+ align:start position:0%
+waves one is actually having the
+ 
+
+ align:start position:0%
+waves one is actually having the
+electric field in the X direction and
+
+ align:start position:0%
+electric field in the X direction and
+ 
+
+ align:start position:0%
+electric field in the X direction and
+the other one is Asia in the Y direction
+
+ align:start position:0%
+the other one is Asia in the Y direction
+ 
+
+ align:start position:0%
+the other one is Asia in the Y direction
+and they are off by a face of PI over 2
+
+ align:start position:0%
+and they are off by a face of PI over 2
+ 
+
+ align:start position:0%
+and they are off by a face of PI over 2
+if that happens then basically you will
+
+ align:start position:0%
+if that happens then basically you will
+ 
+
+ align:start position:0%
+if that happens then basically you will
+see that you produce something really
+
+ align:start position:0%
+see that you produce something really
+ 
+
+ align:start position:0%
+see that you produce something really
+interesting the direction of the
+
+ align:start position:0%
+interesting the direction of the
+ 
+
+ align:start position:0%
+interesting the direction of the
+electric field is going to be rotating
+
+ align:start position:0%
+electric field is going to be rotating
+ 
+
+ align:start position:0%
+electric field is going to be rotating
+as a function of time as a function of
+
+ align:start position:0%
+as a function of time as a function of
+ 
+
+ align:start position:0%
+as a function of time as a function of
+the space this wave phase in trouble and
+
+ align:start position:0%
+the space this wave phase in trouble and
+ 
+
+ align:start position:0%
+the space this wave phase in trouble and
+that we actually call it circularly
+
+ align:start position:0%
+that we actually call it circularly
+ 
+
+ align:start position:0%
+that we actually call it circularly
+polarized waves and and we can also have
+
+ align:start position:0%
+polarized waves and and we can also have
+ 
+
+ align:start position:0%
+polarized waves and and we can also have
+a difficulty polarized wave then we
+
+ align:start position:0%
+a difficulty polarized wave then we
+ 
+
+ align:start position:0%
+a difficulty polarized wave then we
+learned about how to issue the two
+
+ align:start position:0%
+learned about how to issue the two
+ 
+
+ align:start position:0%
+learned about how to issue the two
+filtering which is actually the
+
+ align:start position:0%
+filtering which is actually the
+ 
+
+ align:start position:0%
+filtering which is actually the
+polarizer so suppose I have a perfect
+
+ align:start position:0%
+polarizer so suppose I have a perfect
+ 
+
+ align:start position:0%
+polarizer so suppose I have a perfect
+conductor here where I have the easy
+
+ align:start position:0%
+conductor here where I have the easy
+ 
+
+ align:start position:0%
+conductor here where I have the easy
+axis which is actually described by the
+
+ align:start position:0%
+axis which is actually described by the
+ 
+
+ align:start position:0%
+axis which is actually described by the
+green arrow there and you can see that
+
+ align:start position:0%
+green arrow there and you can see that
+ 
+
+ align:start position:0%
+green arrow there and you can see that
+easy access means that if you have
+
+ align:start position:0%
+easy access means that if you have
+ 
+
+ align:start position:0%
+easy access means that if you have
+electric field parallel to the
+
+ align:start position:0%
+electric field parallel to the
+ 
+
+ align:start position:0%
+electric field parallel to the
+axis okay and then since that's an easy
+
+ align:start position:0%
+axis okay and then since that's an easy
+ 
+
+ align:start position:0%
+axis okay and then since that's an easy
+axis so it's supposed to be easy
+
+ align:start position:0%
+axis so it's supposed to be easy
+ 
+
+ align:start position:0%
+axis so it's supposed to be easy
+therefore this electric field is going
+
+ align:start position:0%
+therefore this electric field is going
+ 
+
+ align:start position:0%
+therefore this electric field is going
+to be passing through the polarizer and
+
+ align:start position:0%
+to be passing through the polarizer and
+ 
+
+ align:start position:0%
+to be passing through the polarizer and
+the other hand if the electric field is
+
+ align:start position:0%
+the other hand if the electric field is
+ 
+
+ align:start position:0%
+the other hand if the electric field is
+perpendicular to the direction of the
+
+ align:start position:0%
+perpendicular to the direction of the
+ 
+
+ align:start position:0%
+perpendicular to the direction of the
+easy axis that means is taking the
+
+ align:start position:0%
+easy axis that means is taking the
+ 
+
+ align:start position:0%
+easy axis that means is taking the
+perfect conductor in a hard way
+
+ align:start position:0%
+perfect conductor in a hard way
+ 
+
+ align:start position:0%
+perfect conductor in a hard way
+therefore when I pass through when he is
+
+ align:start position:0%
+therefore when I pass through when he is
+ 
+
+ align:start position:0%
+therefore when I pass through when he is
+trying to pass through the appropriate
+
+ align:start position:0%
+trying to pass through the appropriate
+ 
+
+ align:start position:0%
+trying to pass through the appropriate
+conductor the electrons in those punkin
+
+ align:start position:0%
+conductor the electrons in those punkin
+ 
+
+ align:start position:0%
+conductor the electrons in those punkin
+data is going to be working like crazy
+
+ align:start position:0%
+data is going to be working like crazy
+ 
+
+ align:start position:0%
+data is going to be working like crazy
+to the fret this wave when the direction
+
+ align:start position:0%
+to the fret this wave when the direction
+ 
+
+ align:start position:0%
+to the fret this wave when the direction
+of the electric field is perpendicular
+
+ align:start position:0%
+of the electric field is perpendicular
+ 
+
+ align:start position:0%
+of the electric field is perpendicular
+to the direction of the easy axis okay
+
+ align:start position:0%
+to the direction of the easy axis okay
+ 
+
+ align:start position:0%
+to the direction of the easy axis okay
+so that is essentially how things as she
+
+ align:start position:0%
+so that is essentially how things as she
+ 
+
+ align:start position:0%
+so that is essentially how things as she
+works for example so in the you know
+
+ align:start position:0%
+works for example so in the you know
+ 
+
+ align:start position:0%
+works for example so in the you know
+first example you can see that in this
+
+ align:start position:0%
+first example you can see that in this
+ 
+
+ align:start position:0%
+first example you can see that in this
+case you have easy axis which is
+
+ align:start position:0%
+case you have easy axis which is
+ 
+
+ align:start position:0%
+case you have easy axis which is
+actually perpendicular to a direction of
+
+ align:start position:0%
+actually perpendicular to a direction of
+ 
+
+ align:start position:0%
+actually perpendicular to a direction of
+the electric field which is a red field
+
+ align:start position:0%
+the electric field which is a red field
+ 
+
+ align:start position:0%
+the electric field which is a red field
+then this wave says we got refracted
+
+ align:start position:0%
+then this wave says we got refracted
+ 
+
+ align:start position:0%
+then this wave says we got refracted
+there will be no transmission sorry no
+
+ align:start position:0%
+there will be no transmission sorry no
+ 
+
+ align:start position:0%
+there will be no transmission sorry no
+no are no electromagnetic field passing
+
+ align:start position:0%
+no are no electromagnetic field passing
+ 
+
+ align:start position:0%
+no are no electromagnetic field passing
+the perfect data and on the other hand
+
+ align:start position:0%
+the perfect data and on the other hand
+ 
+
+ align:start position:0%
+the perfect data and on the other hand
+if you have another perfect conductor
+
+ align:start position:0%
+if you have another perfect conductor
+ 
+
+ align:start position:0%
+if you have another perfect conductor
+which you have easy access which uses
+
+ align:start position:0%
+which you have easy access which uses
+ 
+
+ align:start position:0%
+which you have easy access which uses
+should be parallel to the electric field
+
+ align:start position:0%
+should be parallel to the electric field
+ 
+
+ align:start position:0%
+should be parallel to the electric field
+then you can actually you will see that
+
+ align:start position:0%
+then you can actually you will see that
+ 
+
+ align:start position:0%
+then you can actually you will see that
+actually you will pass through the the
+
+ align:start position:0%
+actually you will pass through the the
+ 
+
+ align:start position:0%
+actually you will pass through the the
+perfect conductor okay so that is
+
+ align:start position:0%
+perfect conductor okay so that is
+ 
+
+ align:start position:0%
+perfect conductor okay so that is
+actually the polarizer and also we
+
+ align:start position:0%
+actually the polarizer and also we
+ 
+
+ align:start position:0%
+actually the polarizer and also we
+discuss about a quarter wave plate which
+
+ align:start position:0%
+discuss about a quarter wave plate which
+ 
+
+ align:start position:0%
+discuss about a quarter wave plate which
+I always suggest you to have a review
+
+ align:start position:0%
+I always suggest you to have a review
+ 
+
+ align:start position:0%
+I always suggest you to have a review
+about the concept which we have learn
+
+ align:start position:0%
+about the concept which we have learn
+ 
+
+ align:start position:0%
+about the concept which we have learn
+about polarizer and quarter wave plate
+
+ align:start position:0%
+about polarizer and quarter wave plate
+ 
+
+ align:start position:0%
+about polarizer and quarter wave plate
+so that you make sure that you
+
+ align:start position:0%
+so that you make sure that you
+ 
+
+ align:start position:0%
+so that you make sure that you
+understand how to issue the calculate
+
+ align:start position:0%
+understand how to issue the calculate
+ 
+
+ align:start position:0%
+understand how to issue the calculate
+the electric field the electric field
+
+ align:start position:0%
+the electric field the electric field
+ 
+
+ align:start position:0%
+the electric field the electric field
+after passing through polarizer and
+
+ align:start position:0%
+after passing through polarizer and
+ 
+
+ align:start position:0%
+after passing through polarizer and
+quarter wave plate and how the security
+
+ align:start position:0%
+quarter wave plate and how the security
+ 
+
+ align:start position:0%
+quarter wave plate and how the security
+or elliptically polarized wave are
+
+ align:start position:0%
+or elliptically polarized wave are
+ 
+
+ align:start position:0%
+or elliptically polarized wave are
+created using this load all those
+
+ align:start position:0%
+created using this load all those
+ 
+
+ align:start position:0%
+created using this load all those
+WordPress etc
+
+ align:start position:0%
+WordPress etc
+ 
+
+ align:start position:0%
+WordPress etc
+okay all right so the next thing which
+
+ align:start position:0%
+okay all right so the next thing which
+ 
+
+ align:start position:0%
+okay all right so the next thing which
+we actually discussed during the class
+
+ align:start position:0%
+we actually discussed during the class
+ 
+
+ align:start position:0%
+we actually discussed during the class
+is how do we actually produce
+
+ align:start position:0%
+is how do we actually produce
+ 
+
+ align:start position:0%
+is how do we actually produce
+electromagnetic waves I think by now
+
+ align:start position:0%
+electromagnetic waves I think by now
+ 
+
+ align:start position:0%
+electromagnetic waves I think by now
+usually actually know that a stationary
+
+ align:start position:0%
+usually actually know that a stationary
+ 
+
+ align:start position:0%
+usually actually know that a stationary
+charge doesn't produce electromagnetic
+
+ align:start position:0%
+charge doesn't produce electromagnetic
+ 
+
+ align:start position:0%
+charge doesn't produce electromagnetic
+wave even a moving charge at constant
+
+ align:start position:0%
+wave even a moving charge at constant
+ 
+
+ align:start position:0%
+wave even a moving charge at constant
+speed doesn't create electromagnetic
+
+ align:start position:0%
+speed doesn't create electromagnetic
+ 
+
+ align:start position:0%
+speed doesn't create electromagnetic
+wave so how do we actually create
+
+ align:start position:0%
+wave so how do we actually create
+ 
+
+ align:start position:0%
+wave so how do we actually create
+electromagnetic wave which propagate to
+
+ align:start position:0%
+electromagnetic wave which propagate to
+ 
+
+ align:start position:0%
+electromagnetic wave which propagate to
+the edge of the universe that is
+
+ align:start position:0%
+the edge of the universe that is
+ 
+
+ align:start position:0%
+the edge of the universe that is
+actually the trick is to create a kink
+
+ align:start position:0%
+actually the trick is to create a kink
+ 
+
+ align:start position:0%
+actually the trick is to create a kink
+in the fuel line right so you have to
+
+ align:start position:0%
+in the fuel line right so you have to
+ 
+
+ align:start position:0%
+in the fuel line right so you have to
+accelerate and stop it okay accelerate
+
+ align:start position:0%
+accelerate and stop it okay accelerate
+ 
+
+ align:start position:0%
+accelerate and stop it okay accelerate
+and the end I'll try to h2 the stop the
+
+ align:start position:0%
+and the end I'll try to h2 the stop the
+ 
+
+ align:start position:0%
+and the end I'll try to h2 the stop the
+acceleration okay
+
+ align:start position:0%
+acceleration okay
+ 
+
+ align:start position:0%
+acceleration okay
+so then you can create a kink okay and
+
+ align:start position:0%
+so then you can create a kink okay and
+ 
+
+ align:start position:0%
+so then you can create a kink okay and
+this kink is going to be public ating
+
+ align:start position:0%
+this kink is going to be public ating
+ 
+
+ align:start position:0%
+this kink is going to be public ating
+out of the function of time and this
+
+ align:start position:0%
+out of the function of time and this
+ 
+
+ align:start position:0%
+out of the function of time and this
+kink is actually creating the so-called
+
+ align:start position:0%
+kink is actually creating the so-called
+ 
+
+ align:start position:0%
+kink is actually creating the so-called
+radiation from this accelerated charge
+
+ align:start position:0%
+radiation from this accelerated charge
+ 
+
+ align:start position:0%
+radiation from this accelerated charge
+so you don't really need to remember all
+
+ align:start position:0%
+so you don't really need to remember all
+ 
+
+ align:start position:0%
+so you don't really need to remember all
+the debris ation but you really need to
+
+ align:start position:0%
+the debris ation but you really need to
+ 
+
+ align:start position:0%
+the debris ation but you really need to
+know the conclusion so what is the
+
+ align:start position:0%
+know the conclusion so what is the
+ 
+
+ align:start position:0%
+know the conclusion so what is the
+conclusion is allowing the the radiated
+
+ align:start position:0%
+conclusion is allowing the the radiated
+ 
+
+ align:start position:0%
+conclusion is allowing the the radiated
+electric field is actually equal to
+
+ align:start position:0%
+electric field is actually equal to
+ 
+
+ align:start position:0%
+electric field is actually equal to
+minus very important is a minus sign in
+
+ align:start position:0%
+minus very important is a minus sign in
+ 
+
+ align:start position:0%
+minus very important is a minus sign in
+front of it which is a common mistake -
+
+ align:start position:0%
+front of it which is a common mistake -
+ 
+
+ align:start position:0%
+front of it which is a common mistake -
+to drop it and the Q is actually the
+
+ align:start position:0%
+to drop it and the Q is actually the
+ 
+
+ align:start position:0%
+to drop it and the Q is actually the
+charge of the oscillating the
+
+ align:start position:0%
+charge of the oscillating the
+ 
+
+ align:start position:0%
+charge of the oscillating the
+accelerated charge right proportional to
+
+ align:start position:0%
+accelerated charge right proportional to
+ 
+
+ align:start position:0%
+accelerated charge right proportional to
+the charge right if the particle is more
+
+ align:start position:0%
+the charge right if the particle is more
+ 
+
+ align:start position:0%
+the charge right if the particle is more
+charged then you have more radiation a
+
+ align:start position:0%
+charged then you have more radiation a
+ 
+
+ align:start position:0%
+charged then you have more radiation a
+perp is actually the the acceleration
+
+ align:start position:0%
+perp is actually the the acceleration
+ 
+
+ align:start position:0%
+perp is actually the the acceleration
+projected to which is the perpendicular
+
+ align:start position:0%
+projected to which is the perpendicular
+ 
+
+ align:start position:0%
+projected to which is the perpendicular
+projection of the acceleration of the
+
+ align:start position:0%
+projection of the acceleration of the
+ 
+
+ align:start position:0%
+projection of the acceleration of the
+particle with respect to the direction
+
+ align:start position:0%
+particle with respect to the direction
+ 
+
+ align:start position:0%
+particle with respect to the direction
+of propagation is actually so-called a
+
+ align:start position:0%
+of propagation is actually so-called a
+ 
+
+ align:start position:0%
+of propagation is actually so-called a
+perp and only the perpendicular
+
+ align:start position:0%
+perp and only the perpendicular
+ 
+
+ align:start position:0%
+perp and only the perpendicular
+Direction acceleration as she counts
+
+ align:start position:0%
+Direction acceleration as she counts
+ 
+
+ align:start position:0%
+Direction acceleration as she counts
+okay the one which is usually parallel
+
+ align:start position:0%
+okay the one which is usually parallel
+ 
+
+ align:start position:0%
+okay the one which is usually parallel
+to the Dirac
+
+ align:start position:0%
+to the Dirac
+ 
+
+ align:start position:0%
+to the Dirac
+no obligation doesn't really count as
+
+ align:start position:0%
+no obligation doesn't really count as
+ 
+
+ align:start position:0%
+no obligation doesn't really count as
+you can see from this equation and the T
+
+ align:start position:0%
+you can see from this equation and the T
+ 
+
+ align:start position:0%
+you can see from this equation and the T
+Prime what is T prime T prime is
+
+ align:start position:0%
+Prime what is T prime T prime is
+ 
+
+ align:start position:0%
+Prime what is T prime T prime is
+actually P minus RT by L divided by C so
+
+ align:start position:0%
+actually P minus RT by L divided by C so
+ 
+
+ align:start position:0%
+actually P minus RT by L divided by C so
+T prime is the time so that is
+
+ align:start position:0%
+T prime is the time so that is
+ 
+
+ align:start position:0%
+T prime is the time so that is
+actually tells you is telling you that
+
+ align:start position:0%
+actually tells you is telling you that
+ 
+
+ align:start position:0%
+actually tells you is telling you that
+it takes some time for the information
+
+ align:start position:0%
+it takes some time for the information
+ 
+
+ align:start position:0%
+it takes some time for the information
+to propagate from the origin which is
+
+ align:start position:0%
+to propagate from the origin which is
+ 
+
+ align:start position:0%
+to propagate from the origin which is
+the post position of the of the moving
+
+ align:start position:0%
+the post position of the of the moving
+ 
+
+ align:start position:0%
+the post position of the of the moving
+charge to the observer which is HD are
+
+ align:start position:0%
+charge to the observer which is HD are
+ 
+
+ align:start position:0%
+charge to the observer which is HD are
+this distance away from the moving
+
+ align:start position:0%
+this distance away from the moving
+ 
+
+ align:start position:0%
+this distance away from the moving
+charge okay so so the information takes
+
+ align:start position:0%
+charge okay so so the information takes
+ 
+
+ align:start position:0%
+charge okay so so the information takes
+some time to propagate and you cannot
+
+ align:start position:0%
+some time to propagate and you cannot
+ 
+
+ align:start position:0%
+some time to propagate and you cannot
+know what is actually really happening
+
+ align:start position:0%
+know what is actually really happening
+ 
+
+ align:start position:0%
+know what is actually really happening
+for example 100 light years away from
+
+ align:start position:0%
+for example 100 light years away from
+ 
+
+ align:start position:0%
+for example 100 light years away from
+Earth as you have no idea about what is
+
+ align:start position:0%
+Earth as you have no idea about what is
+ 
+
+ align:start position:0%
+Earth as you have no idea about what is
+happening maybe a black hole is created
+
+ align:start position:0%
+happening maybe a black hole is created
+ 
+
+ align:start position:0%
+happening maybe a black hole is created
+there and it's going to do so suckers
+
+ align:start position:0%
+there and it's going to do so suckers
+ 
+
+ align:start position:0%
+there and it's going to do so suckers
+everybody up in a few years but nobody
+
+ align:start position:0%
+everybody up in a few years but nobody
+ 
+
+ align:start position:0%
+everybody up in a few years but nobody
+know and though we don't care because we
+
+ align:start position:0%
+know and though we don't care because we
+ 
+
+ align:start position:0%
+know and though we don't care because we
+cannot control all right all right so
+
+ align:start position:0%
+cannot control all right all right so
+ 
+
+ align:start position:0%
+cannot control all right all right so
+that is actually very important also
+
+ align:start position:0%
+that is actually very important also
+ 
+
+ align:start position:0%
+that is actually very important also
+very important to know the magnetic
+
+ align:start position:0%
+very important to know the magnetic
+ 
+
+ align:start position:0%
+very important to know the magnetic
+field map it must be there you can see
+
+ align:start position:0%
+field map it must be there you can see
+ 
+
+ align:start position:0%
+field map it must be there you can see
+the relation between magnetic field and
+
+ align:start position:0%
+the relation between magnetic field and
+ 
+
+ align:start position:0%
+the relation between magnetic field and
+the electric field and the pointing
+
+ align:start position:0%
+the electric field and the pointing
+ 
+
+ align:start position:0%
+the electric field and the pointing
+vector is actually also a short field
+
+ align:start position:0%
+vector is actually also a short field
+ 
+
+ align:start position:0%
+vector is actually also a short field
+and when we actually went ahead are
+
+ align:start position:0%
+and when we actually went ahead are
+ 
+
+ align:start position:0%
+and when we actually went ahead are
+given all the knowledge we have learned
+
+ align:start position:0%
+given all the knowledge we have learned
+ 
+
+ align:start position:0%
+given all the knowledge we have learned
+we discuss about how to take very
+
+ align:start position:0%
+we discuss about how to take very
+ 
+
+ align:start position:0%
+we discuss about how to take very
+beautiful photo using polarizer filter
+
+ align:start position:0%
+beautiful photo using polarizer filter
+ 
+
+ align:start position:0%
+beautiful photo using polarizer filter
+and we discuss about how to filter out
+
+ align:start position:0%
+and we discuss about how to filter out
+ 
+
+ align:start position:0%
+and we discuss about how to filter out
+the scattered light from the Sun and
+
+ align:start position:0%
+the scattered light from the Sun and
+ 
+
+ align:start position:0%
+the scattered light from the Sun and
+you'll be in - it would be nice to
+
+ align:start position:0%
+you'll be in - it would be nice to
+ 
+
+ align:start position:0%
+you'll be in - it would be nice to
+figure out why this is the case how this
+
+ align:start position:0%
+figure out why this is the case how this
+ 
+
+ align:start position:0%
+figure out why this is the case how this
+apologizer light scatter iliza created
+
+ align:start position:0%
+apologizer light scatter iliza created
+ 
+
+ align:start position:0%
+apologizer light scatter iliza created
+okay is purely geometric oh and also we
+
+ align:start position:0%
+okay is purely geometric oh and also we
+ 
+
+ align:start position:0%
+okay is purely geometric oh and also we
+discuss about Brewster's angle and also
+
+ align:start position:0%
+discuss about Brewster's angle and also
+ 
+
+ align:start position:0%
+discuss about Brewster's angle and also
+how HD la as UD to the explanation of
+
+ align:start position:0%
+how HD la as UD to the explanation of
+ 
+
+ align:start position:0%
+how HD la as UD to the explanation of
+the filtering of the light the refracted
+
+ align:start position:0%
+the filtering of the light the refracted
+ 
+
+ align:start position:0%
+the filtering of the light the refracted
+light from fondo with ample window of a
+
+ align:start position:0%
+light from fondo with ample window of a
+ 
+
+ align:start position:0%
+light from fondo with ample window of a
+car or from from the water and this is
+
+ align:start position:0%
+car or from from the water and this is
+ 
+
+ align:start position:0%
+car or from from the water and this is
+actually a demonstration of the summary
+
+ align:start position:0%
+actually a demonstration of the summary
+ 
+
+ align:start position:0%
+actually a demonstration of the summary
+of two
+
+ align:start position:0%
+of two
+ 
+
+ align:start position:0%
+of two
+Stangl so HD so somebody reminded me
+
+ align:start position:0%
+Stangl so HD so somebody reminded me
+ 
+
+ align:start position:0%
+Stangl so HD so somebody reminded me
+that the amplitude should be given as I
+
+ align:start position:0%
+that the amplitude should be given as I
+ 
+
+ align:start position:0%
+that the amplitude should be given as I
+think if this is actually the amplitude
+
+ align:start position:0%
+think if this is actually the amplitude
+ 
+
+ align:start position:0%
+think if this is actually the amplitude
+formula for Brewster's angle will be
+
+ align:start position:0%
+formula for Brewster's angle will be
+ 
+
+ align:start position:0%
+formula for Brewster's angle will be
+given to you if that is actually asked
+
+ align:start position:0%
+given to you if that is actually asked
+ 
+
+ align:start position:0%
+given to you if that is actually asked
+in the in the final exam so don't be
+
+ align:start position:0%
+in the in the final exam so don't be
+ 
+
+ align:start position:0%
+in the in the final exam so don't be
+worried about it and you don't have to
+
+ align:start position:0%
+worried about it and you don't have to
+ 
+
+ align:start position:0%
+worried about it and you don't have to
+remember this formula and I'm not going
+
+ align:start position:0%
+remember this formula and I'm not going
+ 
+
+ align:start position:0%
+remember this formula and I'm not going
+to ask you to derive de to sing such a
+
+ align:start position:0%
+to ask you to derive de to sing such a
+ 
+
+ align:start position:0%
+to ask you to derive de to sing such a
+short time that three hours in the final
+
+ align:start position:0%
+short time that three hours in the final
+ 
+
+ align:start position:0%
+short time that three hours in the final
+exam but the what is actually very
+
+ align:start position:0%
+exam but the what is actually very
+ 
+
+ align:start position:0%
+exam but the what is actually very
+important is to know how this Brewster's
+
+ align:start position:0%
+important is to know how this Brewster's
+ 
+
+ align:start position:0%
+important is to know how this Brewster's
+angle why there's no refracted light
+
+ align:start position:0%
+angle why there's no refracted light
+ 
+
+ align:start position:0%
+angle why there's no refracted light
+polarized in the in a way that you know
+
+ align:start position:0%
+polarized in the in a way that you know
+ 
+
+ align:start position:0%
+polarized in the in a way that you know
+the the polarization should be why the
+
+ align:start position:0%
+the the polarization should be why the
+ 
+
+ align:start position:0%
+the the polarization should be why the
+refracted light is actually polarized
+
+ align:start position:0%
+refracted light is actually polarized
+ 
+
+ align:start position:0%
+refracted light is actually polarized
+for example and also why the the
+
+ align:start position:0%
+for example and also why the the
+ 
+
+ align:start position:0%
+for example and also why the the
+transmission transmitted wave is a
+
+ align:start position:0%
+transmission transmitted wave is a
+ 
+
+ align:start position:0%
+transmission transmitted wave is a
+suicide be polarized and I think the
+
+ align:start position:0%
+suicide be polarized and I think the
+ 
+
+ align:start position:0%
+suicide be polarized and I think the
+conclusions you need to remember and and
+
+ align:start position:0%
+conclusions you need to remember and and
+ 
+
+ align:start position:0%
+conclusions you need to remember and and
+the you need to know how to calculate
+
+ align:start position:0%
+the you need to know how to calculate
+ 
+
+ align:start position:0%
+the you need to know how to calculate
+the angle at least right because for
+
+ align:start position:0%
+the angle at least right because for
+ 
+
+ align:start position:0%
+the angle at least right because for
+this poor depolarized lied to be
+
+ align:start position:0%
+this poor depolarized lied to be
+ 
+
+ align:start position:0%
+this poor depolarized lied to be
+produced in the refracted light you need
+
+ align:start position:0%
+produced in the refracted light you need
+ 
+
+ align:start position:0%
+produced in the refracted light you need
+to have normal angle between the
+
+ align:start position:0%
+to have normal angle between the
+ 
+
+ align:start position:0%
+to have normal angle between the
+direction of the refracted light in the
+
+ align:start position:0%
+direction of the refracted light in the
+ 
+
+ align:start position:0%
+direction of the refracted light in the
+direction of the transmitted light and
+
+ align:start position:0%
+direction of the transmitted light and
+ 
+
+ align:start position:0%
+direction of the transmitted light and
+that you should be able to remember
+
+ align:start position:0%
+that you should be able to remember
+ 
+
+ align:start position:0%
+that you should be able to remember
+right and you should be able to derive
+
+ align:start position:0%
+right and you should be able to derive
+ 
+
+ align:start position:0%
+right and you should be able to derive
+down so from your mind as well because
+
+ align:start position:0%
+down so from your mind as well because
+ 
+
+ align:start position:0%
+down so from your mind as well because
+that means the direction of the
+
+ align:start position:0%
+that means the direction of the
+ 
+
+ align:start position:0%
+that means the direction of the
+oscillation of the molecule at the
+
+ align:start position:0%
+oscillation of the molecule at the
+ 
+
+ align:start position:0%
+oscillation of the molecule at the
+boundary will be actually in the
+
+ align:start position:0%
+boundary will be actually in the
+ 
+
+ align:start position:0%
+boundary will be actually in the
+direction of publication of the
+
+ align:start position:0%
+direction of publication of the
+ 
+
+ align:start position:0%
+direction of publication of the
+refracted ray therefore that cannot be a
+
+ align:start position:0%
+refracted ray therefore that cannot be a
+ 
+
+ align:start position:0%
+refracted ray therefore that cannot be a
+solution to the proper Singh in a two
+
+ align:start position:0%
+solution to the proper Singh in a two
+ 
+
+ align:start position:0%
+solution to the proper Singh in a two
+magnetic wave therefore the refractive
+
+ align:start position:0%
+magnetic wave therefore the refractive
+ 
+
+ align:start position:0%
+magnetic wave therefore the refractive
+waves are polarized right so if you
+
+ align:start position:0%
+waves are polarized right so if you
+ 
+
+ align:start position:0%
+waves are polarized right so if you
+follow this logic then you don't really
+
+ align:start position:0%
+follow this logic then you don't really
+ 
+
+ align:start position:0%
+follow this logic then you don't really
+need to to memorize all those formulas
+
+ align:start position:0%
+need to to memorize all those formulas
+ 
+
+ align:start position:0%
+need to to memorize all those formulas
+all right so finally in the last part of
+
+ align:start position:0%
+all right so finally in the last part of
+ 
+
+ align:start position:0%
+all right so finally in the last part of
+the course we focus on the superpussy
+
+ align:start position:0%
+the course we focus on the superpussy
+ 
+
+ align:start position:0%
+the course we focus on the superpussy
+of many many electromagnetic wave so it
+
+ align:start position:0%
+of many many electromagnetic wave so it
+ 
+
+ align:start position:0%
+of many many electromagnetic wave so it
+can produce constructive interference or
+
+ align:start position:0%
+can produce constructive interference or
+ 
+
+ align:start position:0%
+can produce constructive interference or
+that means all those waves are in phase
+
+ align:start position:0%
+that means all those waves are in phase
+ 
+
+ align:start position:0%
+that means all those waves are in phase
+right and you can have destructive
+
+ align:start position:0%
+right and you can have destructive
+ 
+
+ align:start position:0%
+right and you can have destructive
+interference when they are out of phase
+
+ align:start position:0%
+interference when they are out of phase
+ 
+
+ align:start position:0%
+interference when they are out of phase
+okay and that is actually very important
+
+ align:start position:0%
+okay and that is actually very important
+ 
+
+ align:start position:0%
+okay and that is actually very important
+topic as you should review that for the
+
+ align:start position:0%
+topic as you should review that for the
+ 
+
+ align:start position:0%
+topic as you should review that for the
+preparation of the final and you can see
+
+ align:start position:0%
+preparation of the final and you can see
+ 
+
+ align:start position:0%
+preparation of the final and you can see
+that the distri concrete example which
+
+ align:start position:0%
+that the distri concrete example which
+ 
+
+ align:start position:0%
+that the distri concrete example which
+we use during the class a laser beam we
+
+ align:start position:0%
+we use during the class a laser beam we
+ 
+
+ align:start position:0%
+we use during the class a laser beam we
+talked about water ripple you know demo
+
+ align:start position:0%
+talked about water ripple you know demo
+ 
+
+ align:start position:0%
+talked about water ripple you know demo
+and we also studied how to issue the
+
+ align:start position:0%
+and we also studied how to issue the
+ 
+
+ align:start position:0%
+and we also studied how to issue the
+make use of this phenomena to design a
+
+ align:start position:0%
+make use of this phenomena to design a
+ 
+
+ align:start position:0%
+make use of this phenomena to design a
+phased radar so to detect this unknown
+
+ align:start position:0%
+phased radar so to detect this unknown
+ 
+
+ align:start position:0%
+phased radar so to detect this unknown
+object and Skype what we actually really
+
+ align:start position:0%
+object and Skype what we actually really
+ 
+
+ align:start position:0%
+object and Skype what we actually really
+need to have electromagnetic wave
+
+ align:start position:0%
+need to have electromagnetic wave
+ 
+
+ align:start position:0%
+need to have electromagnetic wave
+pointing to a specific direction and
+
+ align:start position:0%
+pointing to a specific direction and
+ 
+
+ align:start position:0%
+pointing to a specific direction and
+that can be achieved by using motifs
+
+ align:start position:0%
+that can be achieved by using motifs
+ 
+
+ align:start position:0%
+that can be achieved by using motifs
+lead trans motifs lead interference and
+
+ align:start position:0%
+lead trans motifs lead interference and
+ 
+
+ align:start position:0%
+lead trans motifs lead interference and
+this is actually that the property of
+
+ align:start position:0%
+this is actually that the property of
+ 
+
+ align:start position:0%
+this is actually that the property of
+the two slit interference pattern and
+
+ align:start position:0%
+the two slit interference pattern and
+ 
+
+ align:start position:0%
+the two slit interference pattern and
+you are going to have many many Peaks
+
+ align:start position:0%
+you are going to have many many Peaks
+ 
+
+ align:start position:0%
+you are going to have many many Peaks
+they have equal height I for two slit
+
+ align:start position:0%
+they have equal height I for two slit
+ 
+
+ align:start position:0%
+they have equal height I for two slit
+interference if you ignore any if that
+
+ align:start position:0%
+interference if you ignore any if that
+ 
+
+ align:start position:0%
+interference if you ignore any if that
+coming from diffraction okay so if we
+
+ align:start position:0%
+coming from diffraction okay so if we
+ 
+
+ align:start position:0%
+coming from diffraction okay so if we
+assume that the speed is I should
+
+ align:start position:0%
+assume that the speed is I should
+ 
+
+ align:start position:0%
+assume that the speed is I should
+infinite this small right the slit is
+
+ align:start position:0%
+infinite this small right the slit is
+ 
+
+ align:start position:0%
+infinite this small right the slit is
+super duper narrow and then we can
+
+ align:start position:0%
+super duper narrow and then we can
+ 
+
+ align:start position:0%
+super duper narrow and then we can
+actually ignore the diffraction a single
+
+ align:start position:0%
+actually ignore the diffraction a single
+ 
+
+ align:start position:0%
+actually ignore the diffraction a single
+slit diffraction if that then all the
+
+ align:start position:0%
+slit diffraction if that then all the
+ 
+
+ align:start position:0%
+slit diffraction if that then all the
+peaks due to these two slit interference
+
+ align:start position:0%
+peaks due to these two slit interference
+ 
+
+ align:start position:0%
+peaks due to these two slit interference
+we have the same height on the other
+
+ align:start position:0%
+we have the same height on the other
+ 
+
+ align:start position:0%
+we have the same height on the other
+hand when we actually start to increase
+
+ align:start position:0%
+hand when we actually start to increase
+ 
+
+ align:start position:0%
+hand when we actually start to increase
+the number of sleet for example n equal
+
+ align:start position:0%
+the number of sleet for example n equal
+ 
+
+ align:start position:0%
+the number of sleet for example n equal
+to 3 n equal to 4 and equal to 5 and
+
+ align:start position:0%
+to 3 n equal to 4 and equal to 5 and
+ 
+
+ align:start position:0%
+to 3 n equal to 4 and equal to 5 and
+equal to 6 because you can see that the
+
+ align:start position:0%
+equal to 6 because you can see that the
+ 
+
+ align:start position:0%
+equal to 6 because you can see that the
+structure of the intensity as a function
+
+ align:start position:0%
+structure of the intensity as a function
+ 
+
+ align:start position:0%
+structure of the intensity as a function
+of delta which stuff which is the phase
+
+ align:start position:0%
+of delta which stuff which is the phase
+ 
+
+ align:start position:0%
+of delta which stuff which is the phase
+difference is actually changing and you
+
+ align:start position:0%
+difference is actually changing and you
+ 
+
+ align:start position:0%
+difference is actually changing and you
+can see that the general
+
+ align:start position:0%
+can see that the general
+ 
+
+ align:start position:0%
+can see that the general
+structure is the powering so if you have
+
+ align:start position:0%
+structure is the powering so if you have
+ 
+
+ align:start position:0%
+structure is the powering so if you have
+an equal to 3 then basically you have to
+
+ align:start position:0%
+an equal to 3 then basically you have to
+ 
+
+ align:start position:0%
+an equal to 3 then basically you have to
+add ow and and between then you have one
+
+ align:start position:0%
+add ow and and between then you have one
+ 
+
+ align:start position:0%
+add ow and and between then you have one
+child and if you have unequal to 6 then
+
+ align:start position:0%
+child and if you have unequal to 6 then
+ 
+
+ align:start position:0%
+child and if you have unequal to 6 then
+basically you have to word out and
+
+ align:start position:0%
+basically you have to word out and
+ 
+
+ align:start position:0%
+basically you have to word out and
+somehow there are four children in in
+
+ align:start position:0%
+somehow there are four children in in
+ 
+
+ align:start position:0%
+somehow there are four children in in
+this collection right so basically a lot
+
+ align:start position:0%
+this collection right so basically a lot
+ 
+
+ align:start position:0%
+this collection right so basically a lot
+is actually what is we actually learn
+
+ align:start position:0%
+is actually what is we actually learn
+ 
+
+ align:start position:0%
+is actually what is we actually learn
+from the solution of the motifs lead
+
+ align:start position:0%
+from the solution of the motifs lead
+ 
+
+ align:start position:0%
+from the solution of the motifs lead
+interference and though in this way we
+
+ align:start position:0%
+interference and though in this way we
+ 
+
+ align:start position:0%
+interference and though in this way we
+can actually make the wheels of the
+
+ align:start position:0%
+can actually make the wheels of the
+ 
+
+ align:start position:0%
+can actually make the wheels of the
+principal Maxima as narrow as you you
+
+ align:start position:0%
+principal Maxima as narrow as you you
+ 
+
+ align:start position:0%
+principal Maxima as narrow as you you
+want okay so that is actually why first
+
+ align:start position:0%
+want okay so that is actually why first
+ 
+
+ align:start position:0%
+want okay so that is actually why first
+phase the radii works and then we
+
+ align:start position:0%
+phase the radii works and then we
+ 
+
+ align:start position:0%
+phase the radii works and then we
+discuss about the fraction so so that is
+
+ align:start position:0%
+discuss about the fraction so so that is
+ 
+
+ align:start position:0%
+discuss about the fraction so so that is
+AG related again to the the explanation
+
+ align:start position:0%
+AG related again to the the explanation
+ 
+
+ align:start position:0%
+AG related again to the the explanation
+of laser ping and we discuss about the
+
+ align:start position:0%
+of laser ping and we discuss about the
+ 
+
+ align:start position:0%
+of laser ping and we discuss about the
+design of a Star Trek ship the gun front
+
+ align:start position:0%
+design of a Star Trek ship the gun front
+ 
+
+ align:start position:0%
+design of a Star Trek ship the gun front
+for the ship and we also talk about
+
+ align:start position:0%
+for the ship and we also talk about
+ 
+
+ align:start position:0%
+for the ship and we also talk about
+resolution and what is actually
+
+ align:start position:0%
+resolution and what is actually
+ 
+
+ align:start position:0%
+resolution and what is actually
+happening here is the following singles
+
+ align:start position:0%
+happening here is the following singles
+ 
+
+ align:start position:0%
+happening here is the following singles
+the diffraction is actually can be
+
+ align:start position:0%
+the diffraction is actually can be
+ 
+
+ align:start position:0%
+the diffraction is actually can be
+viewed as infinite number of source
+
+ align:start position:0%
+viewed as infinite number of source
+ 
+
+ align:start position:0%
+viewed as infinite number of source
+interference right and you just need to
+
+ align:start position:0%
+interference right and you just need to
+ 
+
+ align:start position:0%
+interference right and you just need to
+integrate over order or the point like
+
+ align:start position:0%
+integrate over order or the point like
+ 
+
+ align:start position:0%
+integrate over order or the point like
+source between between the two wars and
+
+ align:start position:0%
+source between between the two wars and
+ 
+
+ align:start position:0%
+source between between the two wars and
+all of them are acting like severe cold
+
+ align:start position:0%
+all of them are acting like severe cold
+ 
+
+ align:start position:0%
+all of them are acting like severe cold
+wave source right so basically for every
+
+ align:start position:0%
+wave source right so basically for every
+ 
+
+ align:start position:0%
+wave source right so basically for every
+point continuously every points between
+
+ align:start position:0%
+point continuously every points between
+ 
+
+ align:start position:0%
+point continuously every points between
+these two was a point source of vertical
+
+ align:start position:0%
+these two was a point source of vertical
+ 
+
+ align:start position:0%
+these two was a point source of vertical
+wave and that is actually a Huygens
+
+ align:start position:0%
+wave and that is actually a Huygens
+ 
+
+ align:start position:0%
+wave and that is actually a Huygens
+principle and we can see that the
+
+ align:start position:0%
+principle and we can see that the
+ 
+
+ align:start position:0%
+principle and we can see that the
+structures of the intensity as a
+
+ align:start position:0%
+structures of the intensity as a
+ 
+
+ align:start position:0%
+structures of the intensity as a
+function of position is the following so
+
+ align:start position:0%
+function of position is the following so
+ 
+
+ align:start position:0%
+function of position is the following so
+basically you have a principal Maxima
+
+ align:start position:0%
+basically you have a principal Maxima
+ 
+
+ align:start position:0%
+basically you have a principal Maxima
+which is actually a peak at in the
+
+ align:start position:0%
+which is actually a peak at in the
+ 
+
+ align:start position:0%
+which is actually a peak at in the
+middle and at some angle basically you
+
+ align:start position:0%
+middle and at some angle basically you
+ 
+
+ align:start position:0%
+middle and at some angle basically you
+have destructive interference such that
+
+ align:start position:0%
+have destructive interference such that
+ 
+
+ align:start position:0%
+have destructive interference such that
+if you integrate over all the
+
+ align:start position:0%
+if you integrate over all the
+ 
+
+ align:start position:0%
+if you integrate over all the
+contribution of infinite number source
+
+ align:start position:0%
+contribution of infinite number source
+ 
+
+ align:start position:0%
+contribution of infinite number source
+in this window basically you see that
+
+ align:start position:0%
+in this window basically you see that
+ 
+
+ align:start position:0%
+in this window basically you see that
+they completely cancel each other so
+
+ align:start position:0%
+they completely cancel each other so
+ 
+
+ align:start position:0%
+they completely cancel each other so
+that is actually the origin of all those
+
+ align:start position:0%
+that is actually the origin of all those
+ 
+
+ align:start position:0%
+that is actually the origin of all those
+this the tip structure minima and then
+
+ align:start position:0%
+this the tip structure minima and then
+ 
+
+ align:start position:0%
+this the tip structure minima and then
+after the minima issue did you see
+
+ align:start position:0%
+after the minima issue did you see
+ 
+
+ align:start position:0%
+after the minima issue did you see
+another peak but the height of the peak
+
+ align:start position:0%
+another peak but the height of the peak
+ 
+
+ align:start position:0%
+another peak but the height of the peak
+is a is suppressed by 1 over beta square
+
+ align:start position:0%
+is a is suppressed by 1 over beta square
+ 
+
+ align:start position:0%
+is a is suppressed by 1 over beta square
+and it would be good to review that and
+
+ align:start position:0%
+and it would be good to review that and
+ 
+
+ align:start position:0%
+and it would be good to review that and
+what is actually the consequence so if
+
+ align:start position:0%
+what is actually the consequence so if
+ 
+
+ align:start position:0%
+what is actually the consequence so if
+you shoot a laser beam to the to the
+
+ align:start position:0%
+you shoot a laser beam to the to the
+ 
+
+ align:start position:0%
+you shoot a laser beam to the to the
+moon basically the size of the laser
+
+ align:start position:0%
+moon basically the size of the laser
+ 
+
+ align:start position:0%
+moon basically the size of the laser
+beam will be very large
+
+ align:start position:0%
+beam will be very large
+ 
+
+ align:start position:0%
+beam will be very large
+after you learn it was three you know
+
+ align:start position:0%
+after you learn it was three you know
+ 
+
+ align:start position:0%
+after you learn it was three you know
+that the size of the laser beam is going
+
+ align:start position:0%
+that the size of the laser beam is going
+ 
+
+ align:start position:0%
+that the size of the laser beam is going
+to be very very large due to
+
+ align:start position:0%
+to be very very large due to
+ 
+
+ align:start position:0%
+to be very very large due to
+interference between all the point x
+
+ align:start position:0%
+interference between all the point x
+ 
+
+ align:start position:0%
+interference between all the point x
+source from the funded isoprene okay and
+
+ align:start position:0%
+source from the funded isoprene okay and
+ 
+
+ align:start position:0%
+source from the funded isoprene okay and
+finally we can put them all together so
+
+ align:start position:0%
+finally we can put them all together so
+ 
+
+ align:start position:0%
+finally we can put them all together so
+the single slit diffraction and the
+
+ align:start position:0%
+the single slit diffraction and the
+ 
+
+ align:start position:0%
+the single slit diffraction and the
+mattias lead interference you can put
+
+ align:start position:0%
+mattias lead interference you can put
+ 
+
+ align:start position:0%
+mattias lead interference you can put
+them all together and basically what you
+
+ align:start position:0%
+them all together and basically what you
+ 
+
+ align:start position:0%
+them all together and basically what you
+you get is the power so basically you
+
+ align:start position:0%
+you get is the power so basically you
+ 
+
+ align:start position:0%
+you get is the power so basically you
+have what is the interference pattern
+
+ align:start position:0%
+have what is the interference pattern
+ 
+
+ align:start position:0%
+have what is the interference pattern
+which is shown there but the now the
+
+ align:start position:0%
+which is shown there but the now the
+ 
+
+ align:start position:0%
+which is shown there but the now the
+intensity of the motifs the pattern is
+
+ align:start position:0%
+intensity of the motifs the pattern is
+ 
+
+ align:start position:0%
+intensity of the motifs the pattern is
+modulated by the single slit diffraction
+
+ align:start position:0%
+modulated by the single slit diffraction
+ 
+
+ align:start position:0%
+modulated by the single slit diffraction
+pattern and of course the the for
+
+ align:start position:0%
+pattern and of course the the for
+ 
+
+ align:start position:0%
+pattern and of course the the for
+formula will be given to you but on the
+
+ align:start position:0%
+formula will be given to you but on the
+ 
+
+ align:start position:0%
+formula will be given to you but on the
+other hand you are also requested to to
+
+ align:start position:0%
+other hand you are also requested to to
+ 
+
+ align:start position:0%
+other hand you are also requested to to
+know how to actually calculate just to
+
+ align:start position:0%
+know how to actually calculate just to
+ 
+
+ align:start position:0%
+know how to actually calculate just to
+add the contribution from you know
+
+ align:start position:0%
+add the contribution from you know
+ 
+
+ align:start position:0%
+add the contribution from you know
+motifs sleep together in case if we
+
+ align:start position:0%
+motifs sleep together in case if we
+ 
+
+ align:start position:0%
+motifs sleep together in case if we
+actually change the amplitude of the
+
+ align:start position:0%
+actually change the amplitude of the
+ 
+
+ align:start position:0%
+actually change the amplitude of the
+incident light or we change the face
+
+ align:start position:0%
+incident light or we change the face
+ 
+
+ align:start position:0%
+incident light or we change the face
+like what we should in the homework okay
+
+ align:start position:0%
+like what we should in the homework okay
+ 
+
+ align:start position:0%
+like what we should in the homework okay
+and I think that is should be one
+
+ align:start position:0%
+and I think that is should be one
+ 
+
+ align:start position:0%
+and I think that is should be one
+important point and you should actually
+
+ align:start position:0%
+important point and you should actually
+ 
+
+ align:start position:0%
+important point and you should actually
+review that and if you are not if you
+
+ align:start position:0%
+review that and if you are not if you
+ 
+
+ align:start position:0%
+review that and if you are not if you
+are not sure about how to proceed with
+
+ align:start position:0%
+are not sure about how to proceed with
+ 
+
+ align:start position:0%
+are not sure about how to proceed with
+that you would be good to review lecture
+
+ align:start position:0%
+that you would be good to review lecture
+ 
+
+ align:start position:0%
+that you would be good to review lecture
+22 nature 23 so finally we talked about
+
+ align:start position:0%
+22 nature 23 so finally we talked about
+ 
+
+ align:start position:0%
+22 nature 23 so finally we talked about
+the connection to quantum mechanics so
+
+ align:start position:0%
+the connection to quantum mechanics so
+ 
+
+ align:start position:0%
+the connection to quantum mechanics so
+Einstein already told us that I have
+
+ align:start position:0%
+Einstein already told us that I have
+ 
+
+ align:start position:0%
+Einstein already told us that I have
+said so many times
+
+ align:start position:0%
+said so many times
+ 
+
+ align:start position:0%
+said so many times
+God doesn't pray
+
+ align:start position:0%
+God doesn't pray
+ 
+
+ align:start position:0%
+God doesn't pray
+ties with the world but what we actually
+
+ align:start position:0%
+ties with the world but what we actually
+ 
+
+ align:start position:0%
+ties with the world but what we actually
+find is that there are two very
+
+ align:start position:0%
+find is that there are two very
+ 
+
+ align:start position:0%
+find is that there are two very
+interesting scene which we found the
+
+ align:start position:0%
+interesting scene which we found the
+ 
+
+ align:start position:0%
+interesting scene which we found the
+first thing is that if we have a single
+
+ align:start position:0%
+first thing is that if we have a single
+ 
+
+ align:start position:0%
+first thing is that if we have a single
+photon source and basically if we don't
+
+ align:start position:0%
+photon source and basically if we don't
+ 
+
+ align:start position:0%
+photon source and basically if we don't
+if we don't play dice we cannot HD
+
+ align:start position:0%
+if we don't play dice we cannot HD
+ 
+
+ align:start position:0%
+if we don't play dice we cannot HD
+explain the intensity of the okay after
+
+ align:start position:0%
+explain the intensity of the okay after
+ 
+
+ align:start position:0%
+explain the intensity of the okay after
+this single photon source passed through
+
+ align:start position:0%
+this single photon source passed through
+ 
+
+ align:start position:0%
+this single photon source passed through
+two polarizers and what happens is the
+
+ align:start position:0%
+two polarizers and what happens is the
+ 
+
+ align:start position:0%
+two polarizers and what happens is the
+power in so basically the result of a
+
+ align:start position:0%
+power in so basically the result of a
+ 
+
+ align:start position:0%
+power in so basically the result of a
+single photon source tells you that you
+
+ align:start position:0%
+single photon source tells you that you
+ 
+
+ align:start position:0%
+single photon source tells you that you
+would really need to pray ties so that
+
+ align:start position:0%
+would really need to pray ties so that
+ 
+
+ align:start position:0%
+would really need to pray ties so that
+you can actually get the result without
+
+ align:start position:0%
+you can actually get the result without
+ 
+
+ align:start position:0%
+you can actually get the result without
+it without in polarized light intensity
+
+ align:start position:0%
+it without in polarized light intensity
+ 
+
+ align:start position:0%
+it without in polarized light intensity
+and also the second as pseudo experiment
+
+ align:start position:0%
+and also the second as pseudo experiment
+ 
+
+ align:start position:0%
+and also the second as pseudo experiment
+we actually discuss is that if you have
+
+ align:start position:0%
+we actually discuss is that if you have
+ 
+
+ align:start position:0%
+we actually discuss is that if you have
+video board basically you have have been
+
+ align:start position:0%
+video board basically you have have been
+ 
+
+ align:start position:0%
+video board basically you have have been
+pass through the two slit experiment
+
+ align:start position:0%
+pass through the two slit experiment
+ 
+
+ align:start position:0%
+pass through the two slit experiment
+basically you are going to get is too
+
+ align:start position:0%
+basically you are going to get is too
+ 
+
+ align:start position:0%
+basically you are going to get is too
+pious Gaussian light distribution and if
+
+ align:start position:0%
+pious Gaussian light distribution and if
+ 
+
+ align:start position:0%
+pious Gaussian light distribution and if
+you have a single electron source what
+
+ align:start position:0%
+you have a single electron source what
+ 
+
+ align:start position:0%
+you have a single electron source what
+it does is that you actually interfere
+
+ align:start position:0%
+it does is that you actually interfere
+ 
+
+ align:start position:0%
+it does is that you actually interfere
+with itself as an electron single
+
+ align:start position:0%
+with itself as an electron single
+ 
+
+ align:start position:0%
+with itself as an electron single
+electron can interfere with itself and
+
+ align:start position:0%
+electron can interfere with itself and
+ 
+
+ align:start position:0%
+electron can interfere with itself and
+produce a pattern which is actually very
+
+ align:start position:0%
+produce a pattern which is actually very
+ 
+
+ align:start position:0%
+produce a pattern which is actually very
+similar to what we see in the top was
+
+ align:start position:0%
+similar to what we see in the top was
+ 
+
+ align:start position:0%
+similar to what we see in the top was
+lead interference pattern so that is
+
+ align:start position:0%
+lead interference pattern so that is
+ 
+
+ align:start position:0%
+lead interference pattern so that is
+actually really remarkable and also we
+
+ align:start position:0%
+actually really remarkable and also we
+ 
+
+ align:start position:0%
+actually really remarkable and also we
+talk about a single slit single electron
+
+ align:start position:0%
+talk about a single slit single electron
+ 
+
+ align:start position:0%
+talk about a single slit single electron
+experiment basically that give you also
+
+ align:start position:0%
+experiment basically that give you also
+ 
+
+ align:start position:0%
+experiment basically that give you also
+diffraction pattern we have to use the
+
+ align:start position:0%
+diffraction pattern we have to use the
+ 
+
+ align:start position:0%
+diffraction pattern we have to use the
+wave function to describe the position
+
+ align:start position:0%
+wave function to describe the position
+ 
+
+ align:start position:0%
+wave function to describe the position
+the probability density of the position
+
+ align:start position:0%
+the probability density of the position
+ 
+
+ align:start position:0%
+the probability density of the position
+of the electron on the screen and that
+
+ align:start position:0%
+of the electron on the screen and that
+ 
+
+ align:start position:0%
+of the electron on the screen and that
+is actually closely connected to the
+
+ align:start position:0%
+is actually closely connected to the
+ 
+
+ align:start position:0%
+is actually closely connected to the
+uncertainty principle which we as we
+
+ align:start position:0%
+uncertainty principle which we as we
+ 
+
+ align:start position:0%
+uncertainty principle which we as we
+discussed earlier Delta P Delta X
+
+ align:start position:0%
+discussed earlier Delta P Delta X
+ 
+
+ align:start position:0%
+discussed earlier Delta P Delta X
+greater or equal to H bar over 2 so if
+
+ align:start position:0%
+greater or equal to H bar over 2 so if
+ 
+
+ align:start position:0%
+greater or equal to H bar over 2 so if
+you have a very narrow window that means
+
+ align:start position:0%
+you have a very narrow window that means
+ 
+
+ align:start position:0%
+you have a very narrow window that means
+you have very small Delta
+
+ align:start position:0%
+you have very small Delta
+ 
+
+ align:start position:0%
+you have very small Delta
+so you have you have very very good
+
+ align:start position:0%
+so you have you have very very good
+ 
+
+ align:start position:0%
+so you have you have very very good
+confidence about the location of the
+
+ align:start position:0%
+confidence about the location of the
+ 
+
+ align:start position:0%
+confidence about the location of the
+electron and then the momentum he says
+
+ align:start position:0%
+electron and then the momentum he says
+ 
+
+ align:start position:0%
+electron and then the momentum he says
+in the next project the momentum in the
+
+ align:start position:0%
+in the next project the momentum in the
+ 
+
+ align:start position:0%
+in the next project the momentum in the
+X direction you have large uncertainty
+
+ align:start position:0%
+X direction you have large uncertainty
+ 
+
+ align:start position:0%
+X direction you have large uncertainty
+according to this equation and that
+
+ align:start position:0%
+according to this equation and that
+ 
+
+ align:start position:0%
+according to this equation and that
+essentially can be seen from this single
+
+ align:start position:0%
+essentially can be seen from this single
+ 
+
+ align:start position:0%
+essentially can be seen from this single
+slit diffraction diffraction pattern and
+
+ align:start position:0%
+slit diffraction diffraction pattern and
+ 
+
+ align:start position:0%
+slit diffraction diffraction pattern and
+in this course we connected to what we
+
+ align:start position:0%
+in this course we connected to what we
+ 
+
+ align:start position:0%
+in this course we connected to what we
+have learned before so where's this how
+
+ align:start position:0%
+have learned before so where's this how
+ 
+
+ align:start position:0%
+have learned before so where's this how
+to actually describe the what this issue
+
+ align:start position:0%
+to actually describe the what this issue
+ 
+
+ align:start position:0%
+to actually describe the what this issue
+is really the dispersion relation okay
+
+ align:start position:0%
+is really the dispersion relation okay
+ 
+
+ align:start position:0%
+is really the dispersion relation okay
+of the probability density wave is
+
+ align:start position:0%
+of the probability density wave is
+ 
+
+ align:start position:0%
+of the probability density wave is
+actually coming from showing the strong
+
+ align:start position:0%
+actually coming from showing the strong
+ 
+
+ align:start position:0%
+actually coming from showing the strong
+vigorous equation and this is actually
+
+ align:start position:0%
+vigorous equation and this is actually
+ 
+
+ align:start position:0%
+vigorous equation and this is actually
+given here we actually previously talked
+
+ align:start position:0%
+given here we actually previously talked
+ 
+
+ align:start position:0%
+given here we actually previously talked
+about that and and the consequence is
+
+ align:start position:0%
+about that and and the consequence is
+ 
+
+ align:start position:0%
+about that and and the consequence is
+appalling so basically you can actually
+
+ align:start position:0%
+appalling so basically you can actually
+ 
+
+ align:start position:0%
+appalling so basically you can actually
+describe the evolution of the wave
+
+ align:start position:0%
+describe the evolution of the wave
+ 
+
+ align:start position:0%
+describe the evolution of the wave
+function as a function of time by using
+
+ align:start position:0%
+function as a function of time by using
+ 
+
+ align:start position:0%
+function as a function of time by using
+this wave equation and this wave
+
+ align:start position:0%
+this wave equation and this wave
+ 
+
+ align:start position:0%
+this wave equation and this wave
+equation says she decided different from
+
+ align:start position:0%
+equation says she decided different from
+ 
+
+ align:start position:0%
+equation says she decided different from
+what we actually have learned before and
+
+ align:start position:0%
+what we actually have learned before and
+ 
+
+ align:start position:0%
+what we actually have learned before and
+we also can use what we have learned
+
+ align:start position:0%
+we also can use what we have learned
+ 
+
+ align:start position:0%
+we also can use what we have learned
+from l3 to solve
+
+ align:start position:0%
+from l3 to solve
+ 
+
+ align:start position:0%
+from l3 to solve
+particle in a box problem which is
+
+ align:start position:0%
+particle in a box problem which is
+ 
+
+ align:start position:0%
+particle in a box problem which is
+actually covered in lecture number 23
+
+ align:start position:0%
+actually covered in lecture number 23
+ 
+
+ align:start position:0%
+actually covered in lecture number 23
+and I just want to say that you need to
+
+ align:start position:0%
+and I just want to say that you need to
+ 
+
+ align:start position:0%
+and I just want to say that you need to
+know the general principle but I'm not
+
+ align:start position:0%
+know the general principle but I'm not
+ 
+
+ align:start position:0%
+know the general principle but I'm not
+teaching ao4 so I'm not expecting you to
+
+ align:start position:0%
+teaching ao4 so I'm not expecting you to
+ 
+
+ align:start position:0%
+teaching ao4 so I'm not expecting you to
+solve quantum mechanics
+
+ align:start position:0%
+solve quantum mechanics
+ 
+
+ align:start position:0%
+solve quantum mechanics
+pappan but i would like to say that okay
+
+ align:start position:0%
+pappan but i would like to say that okay
+ 
+
+ align:start position:0%
+pappan but i would like to say that okay
+from this point he says should be
+
+ align:start position:0%
+from this point he says should be
+ 
+
+ align:start position:0%
+from this point he says should be
+motivating you to take a oh for right
+
+ align:start position:0%
+motivating you to take a oh for right
+ 
+
+ align:start position:0%
+motivating you to take a oh for right
+because there can be a lot of fun there
+
+ align:start position:0%
+because there can be a lot of fun there
+ 
+
+ align:start position:0%
+because there can be a lot of fun there
+as well and is actually closely related
+
+ align:start position:0%
+as well and is actually closely related
+ 
+
+ align:start position:0%
+as well and is actually closely related
+to what we have learned from elf ao3
+
+ align:start position:0%
+to what we have learned from elf ao3
+ 
+
+ align:start position:0%
+to what we have learned from elf ao3
+so I just want to say in the last point
+
+ align:start position:0%
+so I just want to say in the last point
+ 
+
+ align:start position:0%
+so I just want to say in the last point
+is that this is actually really not the
+
+ align:start position:0%
+is that this is actually really not the
+ 
+
+ align:start position:0%
+is that this is actually really not the
+end of the vibrational waves it's just
+
+ align:start position:0%
+end of the vibrational waves it's just
+ 
+
+ align:start position:0%
+end of the vibrational waves it's just
+the beginning and there's a path toward
+
+ align:start position:0%
+the beginning and there's a path toward
+ 
+
+ align:start position:0%
+the beginning and there's a path toward
+a peak and you may take a long time to
+
+ align:start position:0%
+a peak and you may take a long time to
+ 
+
+ align:start position:0%
+a peak and you may take a long time to
+reach the peak
+
+ align:start position:0%
+reach the peak
+ 
+
+ align:start position:0%
+reach the peak
+all right and I would like to let you
+
+ align:start position:0%
+all right and I would like to let you
+ 
+
+ align:start position:0%
+all right and I would like to let you
+know that I'm really really very happy
+
+ align:start position:0%
+know that I'm really really very happy
+ 
+
+ align:start position:0%
+know that I'm really really very happy
+to be your lecturer this semester and I
+
+ align:start position:0%
+to be your lecturer this semester and I
+ 
+
+ align:start position:0%
+to be your lecturer this semester and I
+really enjoy teaching this class and
+
+ align:start position:0%
+really enjoy teaching this class and
+ 
+
+ align:start position:0%
+really enjoy teaching this class and
+getting your response when I ask
+
+ align:start position:0%
+getting your response when I ask
+ 
+
+ align:start position:0%
+getting your response when I ask
+questions thank you for the support and
+
+ align:start position:0%
+questions thank you for the support and
+ 
+
+ align:start position:0%
+questions thank you for the support and
+I would like to say good luck with the
+
+ align:start position:0%
+I would like to say good luck with the
+ 
+
+ align:start position:0%
+I would like to say good luck with the
+final exam and we have a hundred
+
+ align:start position:0%
+final exam and we have a hundred
+ 
+
+ align:start position:0%
+final exam and we have a hundred
+contribution on Piazza many thanks to
+
+ align:start position:0%
+contribution on Piazza many thanks to
+ 
+
+ align:start position:0%
+contribution on Piazza many thanks to
+Union who is actually doing all the hard
+
+ align:start position:0%
+Union who is actually doing all the hard
+ 
+
+ align:start position:0%
+Union who is actually doing all the hard
+work day and night and thank you very
+
+ align:start position:0%
+work day and night and thank you very
+ 
+
+ align:start position:0%
+work day and night and thank you very
+much and see you around and ID in the
+
+ align:start position:0%
+much and see you around and ID in the
+ 
+
+ align:start position:0%
+much and see you around and ID in the
+future thank you
+
+ align:start position:0%
+future thank you
+ 
+
+ align:start position:0%
+future thank you
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/k2inA31Gups.txt b/k2inA31Gups.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ae06a7a5f194c61f3ebfc187a677dea2b1d2a4b
--- /dev/null
+++ b/k2inA31Gups.txt
@@ -0,0 +1,10171 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inference again this was just an
+
+ align:start position:0%
+inference again this was just an
+ 
+
+ align:start position:0%
+inference again this was just an
+overview of what you can do in Bayesian
+
+ align:start position:0%
+overview of what you can do in Bayesian
+ 
+
+ align:start position:0%
+overview of what you can do in Bayesian
+inference and last time we started
+
+ align:start position:0%
+inference and last time we started
+ 
+
+ align:start position:0%
+inference and last time we started
+defining what's called Jeffrey's priors
+
+ align:start position:0%
+defining what's called Jeffrey's priors
+ 
+
+ align:start position:0%
+defining what's called Jeffrey's priors
+right so when you do Bayesian inference
+
+ align:start position:0%
+right so when you do Bayesian inference
+ 
+
+ align:start position:0%
+right so when you do Bayesian inference
+you have to introduce a prior on your
+
+ align:start position:0%
+you have to introduce a prior on your
+ 
+
+ align:start position:0%
+you have to introduce a prior on your
+parameter and we said that usually it's
+
+ align:start position:0%
+parameter and we said that usually it's
+ 
+
+ align:start position:0%
+parameter and we said that usually it's
+something that encodes your domain
+
+ align:start position:0%
+something that encodes your domain
+ 
+
+ align:start position:0%
+something that encodes your domain
+knowledge about where the parameter
+
+ align:start position:0%
+knowledge about where the parameter
+ 
+
+ align:start position:0%
+knowledge about where the parameter
+could be but there's also some
+
+ align:start position:0%
+could be but there's also some
+ 
+
+ align:start position:0%
+could be but there's also some
+principled way to do it if you want to
+
+ align:start position:0%
+principled way to do it if you want to
+ 
+
+ align:start position:0%
+principled way to do it if you want to
+do Bayesian inference without really
+
+ align:start position:0%
+do Bayesian inference without really
+ 
+
+ align:start position:0%
+do Bayesian inference without really
+having to think about it and for example
+
+ align:start position:0%
+having to think about it and for example
+ 
+
+ align:start position:0%
+having to think about it and for example
+one of the natural priors were those non
+
+ align:start position:0%
+one of the natural priors were those non
+ 
+
+ align:start position:0%
+one of the natural priors were those non
+informative priors right if you're on a
+
+ align:start position:0%
+informative priors right if you're on a
+ 
+
+ align:start position:0%
+informative priors right if you're on a
+compact set it's a uniform prior over
+
+ align:start position:0%
+compact set it's a uniform prior over
+ 
+
+ align:start position:0%
+compact set it's a uniform prior over
+this set if you're on an infinite set
+
+ align:start position:0%
+this set if you're on an infinite set
+ 
+
+ align:start position:0%
+this set if you're on an infinite set
+you can still think of taking the old
+
+ align:start position:0%
+you can still think of taking the old
+ 
+
+ align:start position:0%
+you can still think of taking the old
+ones prior and that's called and
+
+ align:start position:0%
+ones prior and that's called and
+ 
+
+ align:start position:0%
+ones prior and that's called and
+something probably that's always equal
+
+ align:start position:0%
+something probably that's always equal
+ 
+
+ align:start position:0%
+something probably that's always equal
+to one and that's an improper prior if
+
+ align:start position:0%
+to one and that's an improper prior if
+ 
+
+ align:start position:0%
+to one and that's an improper prior if
+you're an infinite set and/or
+
+ align:start position:0%
+you're an infinite set and/or
+ 
+
+ align:start position:0%
+you're an infinite set and/or
+proportional to one and so another
+
+ align:start position:0%
+proportional to one and so another
+ 
+
+ align:start position:0%
+proportional to one and so another
+project you can think of in the case
+
+ align:start position:0%
+project you can think of in the case
+ 
+
+ align:start position:0%
+project you can think of in the case
+where you have a Fisher information
+
+ align:start position:0%
+where you have a Fisher information
+ 
+
+ align:start position:0%
+where you have a Fisher information
+which is well defined is something
+
+ align:start position:0%
+which is well defined is something
+ 
+
+ align:start position:0%
+which is well defined is something
+called Jeffrey's prior and this prior is
+
+ align:start position:0%
+called Jeffrey's prior and this prior is
+ 
+
+ align:start position:0%
+called Jeffrey's prior and this prior is
+a prior which is proportional to square
+
+ align:start position:0%
+a prior which is proportional to square
+ 
+
+ align:start position:0%
+a prior which is proportional to square
+root of the determinant of the Fisher
+
+ align:start position:0%
+root of the determinant of the Fisher
+ 
+
+ align:start position:0%
+root of the determinant of the Fisher
+information matrix and if you just have
+
+ align:start position:0%
+information matrix and if you just have
+ 
+
+ align:start position:0%
+information matrix and if you just have
+if you're in one dimension it's
+
+ align:start position:0%
+if you're in one dimension it's
+ 
+
+ align:start position:0%
+if you're in one dimension it's
+basically proportional to square root of
+
+ align:start position:0%
+basically proportional to square root of
+ 
+
+ align:start position:0%
+basically proportional to square root of
+the Fisher information coefficient which
+
+ align:start position:0%
+the Fisher information coefficient which
+ 
+
+ align:start position:0%
+the Fisher information coefficient which
+we know for example as the synthetic
+
+ align:start position:0%
+we know for example as the synthetic
+ 
+
+ align:start position:0%
+we know for example as the synthetic
+variance at this of the maximum
+
+ align:start position:0%
+variance at this of the maximum
+ 
+
+ align:start position:0%
+variance at this of the maximum
+likelihood estimator and and it turns
+
+ align:start position:0%
+likelihood estimator and and it turns
+ 
+
+ align:start position:0%
+likelihood estimator and and it turns
+out that it's basically so square root
+
+ align:start position:0%
+out that it's basically so square root
+ 
+
+ align:start position:0%
+out that it's basically so square root
+of this thing is basically 1 over the
+
+ align:start position:0%
+of this thing is basically 1 over the
+ 
+
+ align:start position:0%
+of this thing is basically 1 over the
+standard deviation of the maximum
+
+ align:start position:0%
+standard deviation of the maximum
+ 
+
+ align:start position:0%
+standard deviation of the maximum
+likelihood estimator and so you can
+
+ align:start position:0%
+likelihood estimator and so you can
+ 
+
+ align:start position:0%
+likelihood estimator and so you can
+compute this right so you can compute
+
+ align:start position:0%
+compute this right so you can compute
+ 
+
+ align:start position:0%
+compute this right so you can compute
+for the maximum likelihood estimator we
+
+ align:start position:0%
+for the maximum likelihood estimator we
+ 
+
+ align:start position:0%
+for the maximum likelihood estimator we
+know that the variance is going to be P
+
+ align:start position:0%
+know that the variance is going to be P
+ 
+
+ align:start position:0%
+know that the variance is going to be P
+1 minus P in the in the Bernoulli
+
+ align:start position:0%
+1 minus P in the in the Bernoulli
+ 
+
+ align:start position:0%
+1 minus P in the in the Bernoulli
+statistical experiment so you get this 1
+
+ align:start position:0%
+statistical experiment so you get this 1
+ 
+
+ align:start position:0%
+statistical experiment so you get this 1
+over square root of this thing
+
+ align:start position:0%
+over square root of this thing
+ 
+
+ align:start position:0%
+over square root of this thing
+and for example in the Gaussian setting
+
+ align:start position:0%
+and for example in the Gaussian setting
+ 
+
+ align:start position:0%
+and for example in the Gaussian setting
+you actually have the Fisher information
+
+ align:start position:0%
+you actually have the Fisher information
+ 
+
+ align:start position:0%
+you actually have the Fisher information
+even in the multivariate one is actually
+
+ align:start position:0%
+even in the multivariate one is actually
+ 
+
+ align:start position:0%
+even in the multivariate one is actually
+going to be something like the identity
+
+ align:start position:0%
+going to be something like the identity
+ 
+
+ align:start position:0%
+going to be something like the identity
+matrix so this is proportional to one
+
+ align:start position:0%
+matrix so this is proportional to one
+ 
+
+ align:start position:0%
+matrix so this is proportional to one
+it's the improper prior that you get in
+
+ align:start position:0%
+it's the improper prior that you get in
+ 
+
+ align:start position:0%
+it's the improper prior that you get in
+this case okay meaning that for the
+
+ align:start position:0%
+this case okay meaning that for the
+ 
+
+ align:start position:0%
+this case okay meaning that for the
+Gaussian setting no no place where you
+
+ align:start position:0%
+Gaussian setting no no place where you
+ 
+
+ align:start position:0%
+Gaussian setting no no place where you
+Center your Gaussian is actually better
+
+ align:start position:0%
+Center your Gaussian is actually better
+ 
+
+ align:start position:0%
+Center your Gaussian is actually better
+than any other alright so we basically
+
+ align:start position:0%
+than any other alright so we basically
+ 
+
+ align:start position:0%
+than any other alright so we basically
+left on this slide where we saw that
+
+ align:start position:0%
+left on this slide where we saw that
+ 
+
+ align:start position:0%
+left on this slide where we saw that
+Jeffrey's priors satisfy a repair
+
+ align:start position:0%
+Jeffrey's priors satisfy a repair
+ 
+
+ align:start position:0%
+Jeffrey's priors satisfy a repair
+motorization they're invariant by from
+
+ align:start position:0%
+motorization they're invariant by from
+ 
+
+ align:start position:0%
+motorization they're invariant by from
+transformation of your parameter which
+
+ align:start position:0%
+transformation of your parameter which
+ 
+
+ align:start position:0%
+transformation of your parameter which
+is a desirable property and and they say
+
+ align:start position:0%
+is a desirable property and and they say
+ 
+
+ align:start position:0%
+is a desirable property and and they say
+in a way it says that well if I have my
+
+ align:start position:0%
+in a way it says that well if I have my
+ 
+
+ align:start position:0%
+in a way it says that well if I have my
+prior on theta and then I certainly
+
+ align:start position:0%
+prior on theta and then I certainly
+ 
+
+ align:start position:0%
+prior on theta and then I certainly
+decide that theta is not the parameter I
+
+ align:start position:0%
+decide that theta is not the parameter I
+ 
+
+ align:start position:0%
+decide that theta is not the parameter I
+want to use to parameterize my problem
+
+ align:start position:0%
+want to use to parameterize my problem
+ 
+
+ align:start position:0%
+want to use to parameterize my problem
+actually what I want is five theta for
+
+ align:start position:0%
+actually what I want is five theta for
+ 
+
+ align:start position:0%
+actually what I want is five theta for
+thing for example as theta being the
+
+ align:start position:0%
+thing for example as theta being the
+ 
+
+ align:start position:0%
+thing for example as theta being the
+mean of a Gaussian and Phi of theta as
+
+ align:start position:0%
+mean of a Gaussian and Phi of theta as
+ 
+
+ align:start position:0%
+mean of a Gaussian and Phi of theta as
+being this mean to the cube okay this is
+
+ align:start position:0%
+being this mean to the cube okay this is
+ 
+
+ align:start position:0%
+being this mean to the cube okay this is
+a one-to-one map Phi right so for
+
+ align:start position:0%
+a one-to-one map Phi right so for
+ 
+
+ align:start position:0%
+a one-to-one map Phi right so for
+example if I want to go from theta
+
+ align:start position:0%
+example if I want to go from theta
+ 
+
+ align:start position:0%
+example if I want to go from theta
+choose theta cube and now I decide that
+
+ align:start position:0%
+choose theta cube and now I decide that
+ 
+
+ align:start position:0%
+choose theta cube and now I decide that
+this is the actual parameter that I want
+
+ align:start position:0%
+this is the actual parameter that I want
+ 
+
+ align:start position:0%
+this is the actual parameter that I want
+well then it means that on this
+
+ align:start position:0%
+well then it means that on this
+ 
+
+ align:start position:0%
+well then it means that on this
+parameter my original prior is going to
+
+ align:start position:0%
+parameter my original prior is going to
+ 
+
+ align:start position:0%
+parameter my original prior is going to
+induce another prior and here it says
+
+ align:start position:0%
+induce another prior and here it says
+ 
+
+ align:start position:0%
+induce another prior and here it says
+well this prior is actually also
+
+ align:start position:0%
+well this prior is actually also
+ 
+
+ align:start position:0%
+well this prior is actually also
+Jeffrey's prior okay so it's essentially
+
+ align:start position:0%
+Jeffrey's prior okay so it's essentially
+ 
+
+ align:start position:0%
+Jeffrey's prior okay so it's essentially
+telling you that for this new
+
+ align:start position:0%
+telling you that for this new
+ 
+
+ align:start position:0%
+telling you that for this new
+parameterization if you take Jeffrey's
+
+ align:start position:0%
+parameterization if you take Jeffrey's
+ 
+
+ align:start position:0%
+parameterization if you take Jeffrey's
+prior then you actually go back to
+
+ align:start position:0%
+prior then you actually go back to
+ 
+
+ align:start position:0%
+prior then you actually go back to
+having exactly something that's of the
+
+ align:start position:0%
+having exactly something that's of the
+ 
+
+ align:start position:0%
+having exactly something that's of the
+form skirt of determinate of the Fisher
+
+ align:start position:0%
+form skirt of determinate of the Fisher
+ 
+
+ align:start position:0%
+form skirt of determinate of the Fisher
+information but this thing with respect
+
+ align:start position:0%
+information but this thing with respect
+ 
+
+ align:start position:0%
+information but this thing with respect
+to your new parameter ization all right
+
+ align:start position:0%
+to your new parameter ization all right
+ 
+
+ align:start position:0%
+to your new parameter ization all right
+and so why is this true well it's just
+
+ align:start position:0%
+and so why is this true well it's just
+ 
+
+ align:start position:0%
+and so why is this true well it's just
+this change of variable theorem right so
+
+ align:start position:0%
+this change of variable theorem right so
+ 
+
+ align:start position:0%
+this change of variable theorem right so
+it's essentially telling you that if you
+
+ align:start position:0%
+it's essentially telling you that if you
+ 
+
+ align:start position:0%
+it's essentially telling you that if you
+call let's call P well let's call P
+
+ align:start position:0%
+call let's call P well let's call P
+ 
+
+ align:start position:0%
+call let's call P well let's call P
+tilde of Geeta prior over ETA and you
+
+ align:start position:0%
+tilde of Geeta prior over ETA and you
+ 
+
+ align:start position:0%
+tilde of Geeta prior over ETA and you
+have PI's of theta as the prior of theta
+
+ align:start position:0%
+have PI's of theta as the prior of theta
+ 
+
+ align:start position:0%
+have PI's of theta as the prior of theta
+then just by since ETA is of the form
+
+ align:start position:0%
+then just by since ETA is of the form
+ 
+
+ align:start position:0%
+then just by since ETA is of the form
+Phi of theta just by change of variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's essentially a
+
+ align:start position:0%
+right so that's essentially a
+ 
+
+ align:start position:0%
+right so that's essentially a
+probability result it says that PI tilde
+
+ align:start position:0%
+probability result it says that PI tilde
+ 
+
+ align:start position:0%
+probability result it says that PI tilde
+of eta is equal to PI of ETA times D PI
+
+ align:start position:0%
+of eta is equal to PI of ETA times D PI
+ 
+
+ align:start position:0%
+of eta is equal to PI of ETA times D PI
+of theta times D theta over D ETA and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry is that the one should I'm gonna
+
+ align:start position:0%
+sorry is that the one should I'm gonna
+ 
+
+ align:start position:0%
+sorry is that the one should I'm gonna
+have to write it because I always forget
+
+ align:start position:0%
+have to write it because I always forget
+ 
+
+ align:start position:0%
+have to write it because I always forget
+this so if I take a function okay so
+
+ align:start position:0%
+this so if I take a function okay so
+ 
+
+ align:start position:0%
+this so if I take a function okay so
+what I want is to check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so I want a function of ETA
+
+ align:start position:0%
+okay okay so I want a function of ETA
+ 
+
+ align:start position:0%
+okay okay so I want a function of ETA
+that I can put here and what I know is
+
+ align:start position:0%
+that I can put here and what I know is
+ 
+
+ align:start position:0%
+that I can put here and what I know is
+that this is H of Phi of theta
+
+ align:start position:0%
+that this is H of Phi of theta
+ 
+
+ align:start position:0%
+that this is H of Phi of theta
+all right so sorry eta is five data
+
+ align:start position:0%
+all right so sorry eta is five data
+ 
+
+ align:start position:0%
+all right so sorry eta is five data
+right yeah so what I'm gonna do is I'm
+
+ align:start position:0%
+right yeah so what I'm gonna do is I'm
+ 
+
+ align:start position:0%
+right yeah so what I'm gonna do is I'm
+gonna do the change of variable theta is
+
+ align:start position:0%
+gonna do the change of variable theta is
+ 
+
+ align:start position:0%
+gonna do the change of variable theta is
+Phi inverse so eta is Phi of theta which
+
+ align:start position:0%
+Phi inverse so eta is Phi of theta which
+ 
+
+ align:start position:0%
+Phi inverse so eta is Phi of theta which
+means that D eta is equal to D twelve to
+
+ align:start position:0%
+means that D eta is equal to D twelve to
+ 
+
+ align:start position:0%
+means that D eta is equal to D twelve to
+Phi prime of theta D theta so what I'm
+
+ align:start position:0%
+Phi prime of theta D theta so what I'm
+ 
+
+ align:start position:0%
+Phi prime of theta D theta so what I'm
+gonna write this I'm gonna get integral
+
+ align:start position:0%
+gonna write this I'm gonna get integral
+ 
+
+ align:start position:0%
+gonna write this I'm gonna get integral
+of H actually me write this as a
+
+ align:start position:0%
+of H actually me write this as a
+ 
+
+ align:start position:0%
+of H actually me write this as a
+comfortable writing this as e with
+
+ align:start position:0%
+comfortable writing this as e with
+ 
+
+ align:start position:0%
+comfortable writing this as e with
+respect to a tie of HIV time okay so
+
+ align:start position:0%
+respect to a tie of HIV time okay so
+ 
+
+ align:start position:0%
+respect to a tie of HIV time okay so
+that's just it according to being drawn
+
+ align:start position:0%
+that's just it according to being drawn
+ 
+
+ align:start position:0%
+that's just it according to being drawn
+from the prior and I want to write this
+
+ align:start position:0%
+from the prior and I want to write this
+ 
+
+ align:start position:0%
+from the prior and I want to write this
+as the integral of H of ETA times some
+
+ align:start position:0%
+as the integral of H of ETA times some
+ 
+
+ align:start position:0%
+as the integral of H of ETA times some
+function right so this is the integral
+
+ align:start position:0%
+function right so this is the integral
+ 
+
+ align:start position:0%
+function right so this is the integral
+of H of Phi of theta phi of theta now
+
+ align:start position:0%
+of H of Phi of theta phi of theta now
+ 
+
+ align:start position:0%
+of H of Phi of theta phi of theta now
+I'm gonna do my change of variable so
+
+ align:start position:0%
+I'm gonna do my change of variable so
+ 
+
+ align:start position:0%
+I'm gonna do my change of variable so
+this is gonna be the integral of H of
+
+ align:start position:0%
+this is gonna be the integral of H of
+ 
+
+ align:start position:0%
+this is gonna be the integral of H of
+theta and then Phi of Phi Theta is and
+
+ align:start position:0%
+theta and then Phi of Phi Theta is and
+ 
+
+ align:start position:0%
+theta and then Phi of Phi Theta is and
+then prime of theta okay and so what is
+
+ align:start position:0%
+then prime of theta okay and so what is
+ 
+
+ align:start position:0%
+then prime of theta okay and so what is
+pi of Phi Theta so this thing is
+
+ align:start position:0%
+pi of Phi Theta so this thing is
+ 
+
+ align:start position:0%
+pi of Phi Theta so this thing is
+proportional so we're in say dimension
+
+ align:start position:0%
+proportional so we're in say dimension
+ 
+
+ align:start position:0%
+proportional so we're in say dimension
+one so it's proportional of square root
+
+ align:start position:0%
+one so it's proportional of square root
+ 
+
+ align:start position:0%
+one so it's proportional of square root
+of the Fisher information and the Fisher
+
+ align:start position:0%
+of the Fisher information and the Fisher
+ 
+
+ align:start position:0%
+of the Fisher information and the Fisher
+information we know is the expectation
+
+ align:start position:0%
+information we know is the expectation
+ 
+
+ align:start position:0%
+information we know is the expectation
+of the square of the derivative of the
+
+ align:start position:0%
+of the square of the derivative of the
+ 
+
+ align:start position:0%
+of the square of the derivative of the
+log likelihood right so this is square
+
+ align:start position:0%
+log likelihood right so this is square
+ 
+
+ align:start position:0%
+log likelihood right so this is square
+root of the expectation
+
+ align:start position:0%
+root of the expectation
+ 
+
+ align:start position:0%
+root of the expectation
+d over the theta of log of well now I
+
+ align:start position:0%
+d over the theta of log of well now I
+ 
+
+ align:start position:0%
+d over the theta of log of well now I
+need the density well let's just call it
+
+ align:start position:0%
+need the density well let's just call it
+ 
+
+ align:start position:0%
+need the density well let's just call it
+log let's call it L of theta and I want
+
+ align:start position:0%
+log let's call it L of theta and I want
+ 
+
+ align:start position:0%
+log let's call it L of theta and I want
+this to be taken at Phi inverse beta
+
+ align:start position:0%
+this to be taken at Phi inverse beta
+ 
+
+ align:start position:0%
+this to be taken at Phi inverse beta
+squared and then what I pick up is the
+
+ align:start position:0%
+squared and then what I pick up is the
+ 
+
+ align:start position:0%
+squared and then what I pick up is the
+so I'm going to put everything under the
+
+ align:start position:0%
+so I'm going to put everything under the
+ 
+
+ align:start position:0%
+so I'm going to put everything under the
+square so I get Phi prime of theta
+
+ align:start position:0%
+square so I get Phi prime of theta
+ 
+
+ align:start position:0%
+square so I get Phi prime of theta
+squared D theta ok so now I have the
+
+ align:start position:0%
+squared D theta ok so now I have the
+ 
+
+ align:start position:0%
+squared D theta ok so now I have the
+expectation of a squared this does not
+
+ align:start position:0%
+expectation of a squared this does not
+ 
+
+ align:start position:0%
+expectation of a squared this does not
+depend so this is sorry this is L of
+
+ align:start position:0%
+depend so this is sorry this is L of
+ 
+
+ align:start position:0%
+depend so this is sorry this is L of
+theta this is the expectation of L of
+
+ align:start position:0%
+theta this is the expectation of L of
+ 
+
+ align:start position:0%
+theta this is the expectation of L of
+theta and X right that's for some
+
+ align:start position:0%
+theta and X right that's for some
+ 
+
+ align:start position:0%
+theta and X right that's for some
+variable and the expectation here is
+
+ align:start position:0%
+variable and the expectation here is
+ 
+
+ align:start position:0%
+variable and the expectation here is
+with respect to X that's just the
+
+ align:start position:0%
+with respect to X that's just the
+ 
+
+ align:start position:0%
+with respect to X that's just the
+definition of the feature information so
+
+ align:start position:0%
+definition of the feature information so
+ 
+
+ align:start position:0%
+definition of the feature information so
+now I'm going to squeeze this guy into
+
+ align:start position:0%
+now I'm going to squeeze this guy into
+ 
+
+ align:start position:0%
+now I'm going to squeeze this guy into
+the expectation it does not depend on X
+
+ align:start position:0%
+the expectation it does not depend on X
+ 
+
+ align:start position:0%
+the expectation it does not depend on X
+it just acts as a constant and so what I
+
+ align:start position:0%
+it just acts as a constant and so what I
+ 
+
+ align:start position:0%
+it just acts as a constant and so what I
+have now is that this is actually
+
+ align:start position:0%
+have now is that this is actually
+ 
+
+ align:start position:0%
+have now is that this is actually
+proportional to the integral of H ETA
+
+ align:start position:0%
+proportional to the integral of H ETA
+ 
+
+ align:start position:0%
+proportional to the integral of H ETA
+times the square root of the expectation
+
+ align:start position:0%
+times the square root of the expectation
+ 
+
+ align:start position:0%
+times the square root of the expectation
+with respect to X of what well here I
+
+ align:start position:0%
+with respect to X of what well here I
+ 
+
+ align:start position:0%
+with respect to X of what well here I
+have D over D theta of log of theta and
+
+ align:start position:0%
+have D over D theta of log of theta and
+ 
+
+ align:start position:0%
+have D over D theta of log of theta and
+here this guy is really D ETA over D
+
+ align:start position:0%
+here this guy is really D ETA over D
+ 
+
+ align:start position:0%
+here this guy is really D ETA over D
+theta right ok so now what I'm really
+
+ align:start position:0%
+theta right ok so now what I'm really
+ 
+
+ align:start position:0%
+theta right ok so now what I'm really
+left by so I get D over D theta times
+
+ align:start position:0%
+left by so I get D over D theta times
+ 
+
+ align:start position:0%
+left by so I get D over D theta times
+this sorry times D theta over D ETA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's just D over D ETA of log of
+
+ align:start position:0%
+so that's just D over D ETA of log of
+ 
+
+ align:start position:0%
+so that's just D over D ETA of log of
+ETA
+
+ align:start position:0%
+ETA
+ 
+
+ align:start position:0%
+ETA
+X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this guy is now becoming DITA
+
+ align:start position:0%
+and then this guy is now becoming DITA
+ 
+
+ align:start position:0%
+and then this guy is now becoming DITA
+right okay so this was a mess this is a
+
+ align:start position:0%
+right okay so this was a mess this is a
+ 
+
+ align:start position:0%
+right okay so this was a mess this is a
+complete mess because they actually want
+
+ align:start position:0%
+complete mess because they actually want
+ 
+
+ align:start position:0%
+complete mess because they actually want
+to use fire should not actually
+
+ align:start position:0%
+to use fire should not actually
+ 
+
+ align:start position:0%
+to use fire should not actually
+introduce fire at all I should just talk
+
+ align:start position:0%
+introduce fire at all I should just talk
+ 
+
+ align:start position:0%
+introduce fire at all I should just talk
+about overdue data type of things and
+
+ align:start position:0%
+about overdue data type of things and
+ 
+
+ align:start position:0%
+about overdue data type of things and
+then that would actually make my life so
+
+ align:start position:0%
+then that would actually make my life so
+ 
+
+ align:start position:0%
+then that would actually make my life so
+much easier
+
+ align:start position:0%
+much easier
+ 
+
+ align:start position:0%
+much easier
+okay I'm not going to spend more time on
+
+ align:start position:0%
+okay I'm not going to spend more time on
+ 
+
+ align:start position:0%
+okay I'm not going to spend more time on
+this this is really just the idea right
+
+ align:start position:0%
+this this is really just the idea right
+ 
+
+ align:start position:0%
+this this is really just the idea right
+you have square root of a square in
+
+ align:start position:0%
+you have square root of a square in
+ 
+
+ align:start position:0%
+you have square root of a square in
+there and then when you do your change
+
+ align:start position:0%
+there and then when you do your change
+ 
+
+ align:start position:0%
+there and then when you do your change
+your variable you just pick up a square
+
+ align:start position:0%
+your variable you just pick up a square
+ 
+
+ align:start position:0%
+your variable you just pick up a square
+you just pick up something and here and
+
+ align:start position:0%
+you just pick up something and here and
+ 
+
+ align:start position:0%
+you just pick up something and here and
+so you just move this thing in there you
+
+ align:start position:0%
+so you just move this thing in there you
+ 
+
+ align:start position:0%
+so you just move this thing in there you
+get a square it goes inside the square
+
+ align:start position:0%
+get a square it goes inside the square
+ 
+
+ align:start position:0%
+get a square it goes inside the square
+and so your derivative of the log
+
+ align:start position:0%
+and so your derivative of the log
+ 
+
+ align:start position:0%
+and so your derivative of the log
+likelihood with the respective theta
+
+ align:start position:0%
+likelihood with the respective theta
+ 
+
+ align:start position:0%
+likelihood with the respective theta
+becomes a derivative of the likelihood
+
+ align:start position:0%
+becomes a derivative of the likelihood
+ 
+
+ align:start position:0%
+becomes a derivative of the likelihood
+respect to theta and that's just that's
+
+ align:start position:0%
+respect to theta and that's just that's
+ 
+
+ align:start position:0%
+respect to theta and that's just that's
+the only thing that's happening here
+
+ align:start position:0%
+the only thing that's happening here
+ 
+
+ align:start position:0%
+the only thing that's happening here
+I'm just being super sloppy for some
+
+ align:start position:0%
+I'm just being super sloppy for some
+ 
+
+ align:start position:0%
+I'm just being super sloppy for some
+reason okay and then of course now what
+
+ align:start position:0%
+reason okay and then of course now what
+ 
+
+ align:start position:0%
+reason okay and then of course now what
+you're left with is that this is really
+
+ align:start position:0%
+you're left with is that this is really
+ 
+
+ align:start position:0%
+you're left with is that this is really
+just proportional well this is actually
+
+ align:start position:0%
+just proportional well this is actually
+ 
+
+ align:start position:0%
+just proportional well this is actually
+equal everything is proportional but
+
+ align:start position:0%
+equal everything is proportional but
+ 
+
+ align:start position:0%
+equal everything is proportional but
+this is equal to the Fisher information
+
+ align:start position:0%
+this is equal to the Fisher information
+ 
+
+ align:start position:0%
+this is equal to the Fisher information
+tilde with respect to Chiquita now right
+
+ align:start position:0%
+tilde with respect to Chiquita now right
+ 
+
+ align:start position:0%
+tilde with respect to Chiquita now right
+you're doing this with respect to ETA
+
+ align:start position:0%
+you're doing this with respect to ETA
+ 
+
+ align:start position:0%
+you're doing this with respect to ETA
+and so that's a new that's your new
+
+ align:start position:0%
+and so that's a new that's your new
+ 
+
+ align:start position:0%
+and so that's a new that's your new
+prior with respect to theta okay so one
+
+ align:start position:0%
+prior with respect to theta okay so one
+ 
+
+ align:start position:0%
+prior with respect to theta okay so one
+thing that you want to do once you have
+
+ align:start position:0%
+thing that you want to do once you have
+ 
+
+ align:start position:0%
+thing that you want to do once you have
+so remember when you actually compute
+
+ align:start position:0%
+so remember when you actually compute
+ 
+
+ align:start position:0%
+so remember when you actually compute
+your your posterior right rather than
+
+ align:start position:0%
+your your posterior right rather than
+ 
+
+ align:start position:0%
+your your posterior right rather than
+having so you start with a prior and you
+
+ align:start position:0%
+having so you start with a prior and you
+ 
+
+ align:start position:0%
+having so you start with a prior and you
+have some observations let's say x1 to
+
+ align:start position:0%
+have some observations let's say x1 to
+ 
+
+ align:start position:0%
+have some observations let's say x1 to
+xn when you do Bayesian inference rather
+
+ align:start position:0%
+xn when you do Bayesian inference rather
+ 
+
+ align:start position:0%
+xn when you do Bayesian inference rather
+than spitting out just some theta hat
+
+ align:start position:0%
+than spitting out just some theta hat
+ 
+
+ align:start position:0%
+than spitting out just some theta hat
+which is an estimator for theta you
+
+ align:start position:0%
+which is an estimator for theta you
+ 
+
+ align:start position:0%
+which is an estimator for theta you
+actually spit out an entire posterior
+
+ align:start position:0%
+actually spit out an entire posterior
+ 
+
+ align:start position:0%
+actually spit out an entire posterior
+distribution PI of theta given X 1 xn ok
+
+ align:start position:0%
+distribution PI of theta given X 1 xn ok
+ 
+
+ align:start position:0%
+distribution PI of theta given X 1 xn ok
+so there's an entire distribution on the
+
+ align:start position:0%
+so there's an entire distribution on the
+ 
+
+ align:start position:0%
+so there's an entire distribution on the
+candidates theta and you can actually
+
+ align:start position:0%
+candidates theta and you can actually
+ 
+
+ align:start position:0%
+candidates theta and you can actually
+use this to perform inference rather
+
+ align:start position:0%
+use this to perform inference rather
+ 
+
+ align:start position:0%
+use this to perform inference rather
+than just having one number okay and so
+
+ align:start position:0%
+than just having one number okay and so
+ 
+
+ align:start position:0%
+than just having one number okay and so
+you could actually build confidence
+
+ align:start position:0%
+you could actually build confidence
+ 
+
+ align:start position:0%
+you could actually build confidence
+regions from this thing okay and so a a
+
+ align:start position:0%
+regions from this thing okay and so a a
+ 
+
+ align:start position:0%
+regions from this thing okay and so a a
+Bayesian
+
+ align:start position:0%
+Bayesian
+ 
+
+ align:start position:0%
+Bayesian
+confidence interval so if your set of
+
+ align:start position:0%
+confidence interval so if your set of
+ 
+
+ align:start position:0%
+confidence interval so if your set of
+parameters is included in the real line
+
+ align:start position:0%
+parameters is included in the real line
+ 
+
+ align:start position:0%
+parameters is included in the real line
+then you can actually it's not even it's
+
+ align:start position:0%
+then you can actually it's not even it's
+ 
+
+ align:start position:0%
+then you can actually it's not even it's
+not even guaranteed to be to be an
+
+ align:start position:0%
+not even guaranteed to be to be an
+ 
+
+ align:start position:0%
+not even guaranteed to be to be an
+interval so let me call it a confidence
+
+ align:start position:0%
+interval so let me call it a confidence
+ 
+
+ align:start position:0%
+interval so let me call it a confidence
+region so a bayesian confidence region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's just a random subspace so
+
+ align:start position:0%
+okay so it's just a random subspace so
+ 
+
+ align:start position:0%
+okay so it's just a random subspace so
+let's call it R is included in theta and
+
+ align:start position:0%
+let's call it R is included in theta and
+ 
+
+ align:start position:0%
+let's call it R is included in theta and
+when you had the deterministic one we
+
+ align:start position:0%
+when you had the deterministic one we
+ 
+
+ align:start position:0%
+when you had the deterministic one we
+had a definition which was with respect
+
+ align:start position:0%
+had a definition which was with respect
+ 
+
+ align:start position:0%
+had a definition which was with respect
+to the randomness of the data right
+
+ align:start position:0%
+to the randomness of the data right
+ 
+
+ align:start position:0%
+to the randomness of the data right
+that's how you actually had a random
+
+ align:start position:0%
+that's how you actually had a random
+ 
+
+ align:start position:0%
+that's how you actually had a random
+subset you had a random confidence
+
+ align:start position:0%
+subset you had a random confidence
+ 
+
+ align:start position:0%
+subset you had a random confidence
+interval here it's actually conditioned
+
+ align:start position:0%
+interval here it's actually conditioned
+ 
+
+ align:start position:0%
+interval here it's actually conditioned
+on the data but with respect to the
+
+ align:start position:0%
+on the data but with respect to the
+ 
+
+ align:start position:0%
+on the data but with respect to the
+randomness that you actually get from
+
+ align:start position:0%
+randomness that you actually get from
+ 
+
+ align:start position:0%
+randomness that you actually get from
+your posterior distribution
+
+ align:start position:0%
+your posterior distribution
+ 
+
+ align:start position:0%
+your posterior distribution
+okay so such that the probability that
+
+ align:start position:0%
+okay so such that the probability that
+ 
+
+ align:start position:0%
+okay so such that the probability that
+your theta belongs to this confidence
+
+ align:start position:0%
+your theta belongs to this confidence
+ 
+
+ align:start position:0%
+your theta belongs to this confidence
+region given X 1 xn and say at least 1
+
+ align:start position:0%
+region given X 1 xn and say at least 1
+ 
+
+ align:start position:0%
+region given X 1 xn and say at least 1
+minus alpha let's just take it equal to
+
+ align:start position:0%
+minus alpha let's just take it equal to
+ 
+
+ align:start position:0%
+minus alpha let's just take it equal to
+1 minus alpha okay so that's a
+
+ align:start position:0%
+1 minus alpha okay so that's a
+ 
+
+ align:start position:0%
+1 minus alpha okay so that's a
+confidence region at lab at level 1
+
+ align:start position:0%
+confidence region at lab at level 1
+ 
+
+ align:start position:0%
+confidence region at lab at level 1
+minus alpha okay so that's one way so
+
+ align:start position:0%
+minus alpha okay so that's one way so
+ 
+
+ align:start position:0%
+minus alpha okay so that's one way so
+why would you actually I when I actually
+
+ align:start position:0%
+why would you actually I when I actually
+ 
+
+ align:start position:0%
+why would you actually I when I actually
+implement Bayesian inference I'm
+
+ align:start position:0%
+implement Bayesian inference I'm
+ 
+
+ align:start position:0%
+implement Bayesian inference I'm
+actually spinning out an entire
+
+ align:start position:0%
+actually spinning out an entire
+ 
+
+ align:start position:0%
+actually spinning out an entire
+distribution I need to summarize this
+
+ align:start position:0%
+distribution I need to summarize this
+ 
+
+ align:start position:0%
+distribution I need to summarize this
+this thing to communicate it right I
+
+ align:start position:0%
+this thing to communicate it right I
+ 
+
+ align:start position:0%
+this thing to communicate it right I
+cannot just say this is this entire
+
+ align:start position:0%
+cannot just say this is this entire
+ 
+
+ align:start position:0%
+cannot just say this is this entire
+function I want to know where are the
+
+ align:start position:0%
+function I want to know where are the
+ 
+
+ align:start position:0%
+function I want to know where are the
+regions of high probability where my
+
+ align:start position:0%
+regions of high probability where my
+ 
+
+ align:start position:0%
+regions of high probability where my
+parameter is supposed to be and so here
+
+ align:start position:0%
+parameter is supposed to be and so here
+ 
+
+ align:start position:0%
+parameter is supposed to be and so here
+when I have this thing what I actually
+
+ align:start position:0%
+when I have this thing what I actually
+ 
+
+ align:start position:0%
+when I have this thing what I actually
+want to have is something that says well
+
+ align:start position:0%
+want to have is something that says well
+ 
+
+ align:start position:0%
+want to have is something that says well
+I want to summarize this thing into some
+
+ align:start position:0%
+I want to summarize this thing into some
+ 
+
+ align:start position:0%
+I want to summarize this thing into some
+subset of the real line in which I'm
+
+ align:start position:0%
+subset of the real line in which I'm
+ 
+
+ align:start position:0%
+subset of the real line in which I'm
+sure that the area under the curve here
+
+ align:start position:0%
+sure that the area under the curve here
+ 
+
+ align:start position:0%
+sure that the area under the curve here
+of my posterior is actually 1 minus
+
+ align:start position:0%
+of my posterior is actually 1 minus
+ 
+
+ align:start position:0%
+of my posterior is actually 1 minus
+alpha and there's many ways to do this
+
+ align:start position:0%
+alpha and there's many ways to do this
+ 
+
+ align:start position:0%
+alpha and there's many ways to do this
+right so one way to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to look at level sets and so rather
+
+ align:start position:0%
+is to look at level sets and so rather
+ 
+
+ align:start position:0%
+is to look at level sets and so rather
+than actually so let's say my my
+
+ align:start position:0%
+than actually so let's say my my
+ 
+
+ align:start position:0%
+than actually so let's say my my
+posterior looks like this I know for
+
+ align:start position:0%
+posterior looks like this I know for
+ 
+
+ align:start position:0%
+posterior looks like this I know for
+example if I have a Gaussian
+
+ align:start position:0%
+example if I have a Gaussian
+ 
+
+ align:start position:0%
+example if I have a Gaussian
+distribution I can actually take my
+
+ align:start position:0%
+distribution I can actually take my
+ 
+
+ align:start position:0%
+distribution I can actually take my
+posterior to be my posterior is actually
+
+ align:start position:0%
+posterior to be my posterior is actually
+ 
+
+ align:start position:0%
+posterior to be my posterior is actually
+going to be Gaussian and what I can do
+
+ align:start position:0%
+going to be Gaussian and what I can do
+ 
+
+ align:start position:0%
+going to be Gaussian and what I can do
+is to try to cut it here on the y axis
+
+ align:start position:0%
+is to try to cut it here on the y axis
+ 
+
+ align:start position:0%
+is to try to cut it here on the y axis
+so that now the area under the curve
+
+ align:start position:0%
+so that now the area under the curve
+ 
+
+ align:start position:0%
+so that now the area under the curve
+when I cut here is actually 1 minus
+
+ align:start position:0%
+when I cut here is actually 1 minus
+ 
+
+ align:start position:0%
+when I cut here is actually 1 minus
+alpha okay so I have some threshold tau
+
+ align:start position:0%
+alpha okay so I have some threshold tau
+ 
+
+ align:start position:0%
+alpha okay so I have some threshold tau
+if tau goes to plus infinity then I'm
+
+ align:start position:0%
+if tau goes to plus infinity then I'm
+ 
+
+ align:start position:0%
+if tau goes to plus infinity then I'm
+gonna have that this area under the
+
+ align:start position:0%
+gonna have that this area under the
+ 
+
+ align:start position:0%
+gonna have that this area under the
+curve here is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well no no so the air end of the curve
+
+ align:start position:0%
+well no no so the air end of the curve
+ 
+
+ align:start position:0%
+well no no so the air end of the curve
+when Tao is going to plus infinity think
+
+ align:start position:0%
+when Tao is going to plus infinity think
+ 
+
+ align:start position:0%
+when Tao is going to plus infinity think
+of the small the when Tao is just like
+
+ align:start position:0%
+of the small the when Tao is just like
+ 
+
+ align:start position:0%
+of the small the when Tao is just like
+right here so this is actually going to
+
+ align:start position:0%
+right here so this is actually going to
+ 
+
+ align:start position:0%
+right here so this is actually going to
+zero right and so I start here and then
+
+ align:start position:0%
+zero right and so I start here and then
+ 
+
+ align:start position:0%
+zero right and so I start here and then
+I start going down and down and down and
+
+ align:start position:0%
+I start going down and down and down and
+ 
+
+ align:start position:0%
+I start going down and down and down and
+down until I actually get something
+
+ align:start position:0%
+down until I actually get something
+ 
+
+ align:start position:0%
+down until I actually get something
+which is going down to one plus alpha
+
+ align:start position:0%
+which is going down to one plus alpha
+ 
+
+ align:start position:0%
+which is going down to one plus alpha
+but if tau is going down to zero then my
+
+ align:start position:0%
+but if tau is going down to zero then my
+ 
+
+ align:start position:0%
+but if tau is going down to zero then my
+area under the curve is going to if tau
+
+ align:start position:0%
+area under the curve is going to if tau
+ 
+
+ align:start position:0%
+area under the curve is going to if tau
+is here I'm cutting nowhere and so I'm
+
+ align:start position:0%
+is here I'm cutting nowhere and so I'm
+ 
+
+ align:start position:0%
+is here I'm cutting nowhere and so I'm
+getting one right agree
+
+ align:start position:0%
+getting one right agree
+ 
+
+ align:start position:0%
+getting one right agree
+think of when tau is very close to zero
+
+ align:start position:0%
+think of when tau is very close to zero
+ 
+
+ align:start position:0%
+think of when tau is very close to zero
+I'm cutting as very far here and so I'm
+
+ align:start position:0%
+I'm cutting as very far here and so I'm
+ 
+
+ align:start position:0%
+I'm cutting as very far here and so I'm
+getting some area under the curve which
+
+ align:start position:0%
+getting some area under the curve which
+ 
+
+ align:start position:0%
+getting some area under the curve which
+is almost everything and so it's going
+
+ align:start position:0%
+is almost everything and so it's going
+ 
+
+ align:start position:0%
+is almost everything and so it's going
+to one iced out going down to zero yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it does not I mean so this is a
+
+ align:start position:0%
+no it does not I mean so this is a
+ 
+
+ align:start position:0%
+no it does not I mean so this is a
+picture this picture so those two things
+
+ align:start position:0%
+picture this picture so those two things
+ 
+
+ align:start position:0%
+picture this picture so those two things
+work for all of them right but when you
+
+ align:start position:0%
+work for all of them right but when you
+ 
+
+ align:start position:0%
+work for all of them right but when you
+have a bino model actually this is
+
+ align:start position:0%
+have a bino model actually this is
+ 
+
+ align:start position:0%
+have a bino model actually this is
+actually when things start to become
+
+ align:start position:0%
+actually when things start to become
+ 
+
+ align:start position:0%
+actually when things start to become
+interesting right so when we had when we
+
+ align:start position:0%
+interesting right so when we had when we
+ 
+
+ align:start position:0%
+interesting right so when we had when we
+built a frequentist confidence interval
+
+ align:start position:0%
+built a frequentist confidence interval
+ 
+
+ align:start position:0%
+built a frequentist confidence interval
+it was always of the form x-bar plus or
+
+ align:start position:0%
+it was always of the form x-bar plus or
+ 
+
+ align:start position:0%
+it was always of the form x-bar plus or
+minus something but now if I start to
+
+ align:start position:0%
+minus something but now if I start to
+ 
+
+ align:start position:0%
+minus something but now if I start to
+have a posterior that looks like this
+
+ align:start position:0%
+have a posterior that looks like this
+ 
+
+ align:start position:0%
+have a posterior that looks like this
+I'm gonna start cutting off I'm gonna
+
+ align:start position:0%
+I'm gonna start cutting off I'm gonna
+ 
+
+ align:start position:0%
+I'm gonna start cutting off I'm gonna
+have to I mean my confidence region is
+
+ align:start position:0%
+have to I mean my confidence region is
+ 
+
+ align:start position:0%
+have to I mean my confidence region is
+going to be the union of those two
+
+ align:start position:0%
+going to be the union of those two
+ 
+
+ align:start position:0%
+going to be the union of those two
+things right and it really reflects the
+
+ align:start position:0%
+things right and it really reflects the
+ 
+
+ align:start position:0%
+things right and it really reflects the
+fact that there's this bimodal thing
+
+ align:start position:0%
+fact that there's this bimodal thing
+ 
+
+ align:start position:0%
+fact that there's this bimodal thing
+it's gonna say well with higher
+
+ align:start position:0%
+it's gonna say well with higher
+ 
+
+ align:start position:0%
+it's gonna say well with higher
+probability I'm actually going to be
+
+ align:start position:0%
+probability I'm actually going to be
+ 
+
+ align:start position:0%
+probability I'm actually going to be
+either here or here now the meaning here
+
+ align:start position:0%
+either here or here now the meaning here
+ 
+
+ align:start position:0%
+either here or here now the meaning here
+of a bayesian Conference region and a
+
+ align:start position:0%
+of a bayesian Conference region and a
+ 
+
+ align:start position:0%
+of a bayesian Conference region and a
+confidence interval or completely
+
+ align:start position:0%
+confidence interval or completely
+ 
+
+ align:start position:0%
+confidence interval or completely
+distinct notions right
+
+ align:start position:0%
+distinct notions right
+ 
+
+ align:start position:0%
+distinct notions right
+and it's actually I'm gonna work out an
+
+ align:start position:0%
+and it's actually I'm gonna work out an
+ 
+
+ align:start position:0%
+and it's actually I'm gonna work out an
+example with you so that we can actually
+
+ align:start position:0%
+example with you so that we can actually
+ 
+
+ align:start position:0%
+example with you so that we can actually
+see that sometimes I mean both of them
+
+ align:start position:0%
+see that sometimes I mean both of them
+ 
+
+ align:start position:0%
+see that sometimes I mean both of them
+actually you can come up with some crazy
+
+ align:start position:0%
+actually you can come up with some crazy
+ 
+
+ align:start position:0%
+actually you can come up with some crazy
+paradoxes so since we don't have that
+
+ align:start position:0%
+paradoxes so since we don't have that
+ 
+
+ align:start position:0%
+paradoxes so since we don't have that
+much time I will actually talk to you
+
+ align:start position:0%
+much time I will actually talk to you
+ 
+
+ align:start position:0%
+much time I will actually talk to you
+about why in some instances it's
+
+ align:start position:0%
+about why in some instances it's
+ 
+
+ align:start position:0%
+about why in some instances it's
+actually a good idea to think of
+
+ align:start position:0%
+actually a good idea to think of
+ 
+
+ align:start position:0%
+actually a good idea to think of
+Bayesian confidence intervals rather
+
+ align:start position:0%
+Bayesian confidence intervals rather
+ 
+
+ align:start position:0%
+Bayesian confidence intervals rather
+than frequentist ones so before I go
+
+ align:start position:0%
+than frequentist ones so before I go
+ 
+
+ align:start position:0%
+than frequentist ones so before I go
+into more details about what those
+
+ align:start position:0%
+into more details about what those
+ 
+
+ align:start position:0%
+into more details about what those
+Bayesian confidence intervals are let's
+
+ align:start position:0%
+Bayesian confidence intervals are let's
+ 
+
+ align:start position:0%
+Bayesian confidence intervals are let's
+remind ourselves what is it
+
+ align:start position:0%
+remind ourselves what is it
+ 
+
+ align:start position:0%
+remind ourselves what is it
+mean do you have a frequentist
+
+ align:start position:0%
+mean do you have a frequentist
+ 
+
+ align:start position:0%
+mean do you have a frequentist
+confidence interval right so okay so
+
+ align:start position:0%
+confidence interval right so okay so
+ 
+
+ align:start position:0%
+confidence interval right so okay so
+when I have a frequentist point
+
+ align:start position:0%
+when I have a frequentist point
+ 
+
+ align:start position:0%
+when I have a frequentist point
+confidence interval let's say something
+
+ align:start position:0%
+confidence interval let's say something
+ 
+
+ align:start position:0%
+confidence interval let's say something
+like X bar and it's minus 1.96 the Sigma
+
+ align:start position:0%
+like X bar and it's minus 1.96 the Sigma
+ 
+
+ align:start position:0%
+like X bar and it's minus 1.96 the Sigma
+over root N and X Bar n plus 1 point 9 6
+
+ align:start position:0%
+over root N and X Bar n plus 1 point 9 6
+ 
+
+ align:start position:0%
+over root N and X Bar n plus 1 point 9 6
+Sigma over ribbon right so that's the
+
+ align:start position:0%
+Sigma over ribbon right so that's the
+ 
+
+ align:start position:0%
+Sigma over ribbon right so that's the
+confidence interval that you get for the
+
+ align:start position:0%
+confidence interval that you get for the
+ 
+
+ align:start position:0%
+confidence interval that you get for the
+mean of some Gaussian with known
+
+ align:start position:0%
+mean of some Gaussian with known
+ 
+
+ align:start position:0%
+mean of some Gaussian with known
+variants to be equal to Sigma square ok
+
+ align:start position:0%
+variants to be equal to Sigma square ok
+ 
+
+ align:start position:0%
+variants to be equal to Sigma square ok
+so what we know is that the meaning of
+
+ align:start position:0%
+so what we know is that the meaning of
+ 
+
+ align:start position:0%
+so what we know is that the meaning of
+this is the probability that theta
+
+ align:start position:0%
+this is the probability that theta
+ 
+
+ align:start position:0%
+this is the probability that theta
+belongs to this is equal to 95 percent
+
+ align:start position:0%
+belongs to this is equal to 95 percent
+ 
+
+ align:start position:0%
+belongs to this is equal to 95 percent
+right and this more general you can
+
+ align:start position:0%
+right and this more general you can
+ 
+
+ align:start position:0%
+right and this more general you can
+think of being Q alpha over 2 and when
+
+ align:start position:0%
+think of being Q alpha over 2 and when
+ 
+
+ align:start position:0%
+think of being Q alpha over 2 and when
+you're gonna get is 1 minus alpha here
+
+ align:start position:0%
+you're gonna get is 1 minus alpha here
+ 
+
+ align:start position:0%
+you're gonna get is 1 minus alpha here
+okay so what does it mean here well it
+
+ align:start position:0%
+okay so what does it mean here well it
+ 
+
+ align:start position:0%
+okay so what does it mean here well it
+means it looks very much like what we
+
+ align:start position:0%
+means it looks very much like what we
+ 
+
+ align:start position:0%
+means it looks very much like what we
+have here except that we're not
+
+ align:start position:0%
+have here except that we're not
+ 
+
+ align:start position:0%
+have here except that we're not
+conditioning on X 1 xn and we should not
+
+ align:start position:0%
+conditioning on X 1 xn and we should not
+ 
+
+ align:start position:0%
+conditioning on X 1 xn and we should not
+because there was a question like that
+
+ align:start position:0%
+because there was a question like that
+ 
+
+ align:start position:0%
+because there was a question like that
+in the midterm if I condition on X 1 X
+
+ align:start position:0%
+in the midterm if I condition on X 1 X
+ 
+
+ align:start position:0%
+in the midterm if I condition on X 1 X
+and this probability is either 0 or 1
+
+ align:start position:0%
+and this probability is either 0 or 1
+ 
+
+ align:start position:0%
+and this probability is either 0 or 1
+okay because once I condition so here
+
+ align:start position:0%
+okay because once I condition so here
+ 
+
+ align:start position:0%
+okay because once I condition so here
+this probability actually here is with
+
+ align:start position:0%
+this probability actually here is with
+ 
+
+ align:start position:0%
+this probability actually here is with
+respect to the randomness in X 1 xn so
+
+ align:start position:0%
+respect to the randomness in X 1 xn so
+ 
+
+ align:start position:0%
+respect to the randomness in X 1 xn so
+if I condition let's call this thing our
+
+ align:start position:0%
+if I condition let's call this thing our
+ 
+
+ align:start position:0%
+if I condition let's call this thing our
+frack for frequent test well given X 1
+
+ align:start position:0%
+frack for frequent test well given X 1
+ 
+
+ align:start position:0%
+frack for frequent test well given X 1
+xn and actually at only 2 nu X 1 xn
+
+ align:start position:0%
+xn and actually at only 2 nu X 1 xn
+ 
+
+ align:start position:0%
+xn and actually at only 2 nu X 1 xn
+really what I need to know is what xn
+
+ align:start position:0%
+really what I need to know is what xn
+ 
+
+ align:start position:0%
+really what I need to know is what xn
+bar is well this thing now is what it's
+
+ align:start position:0%
+bar is well this thing now is what it's
+ 
+
+ align:start position:0%
+bar is well this thing now is what it's
+1 if theta is in R and it's 0 if theta
+
+ align:start position:0%
+1 if theta is in R and it's 0 if theta
+ 
+
+ align:start position:0%
+1 if theta is in R and it's 0 if theta
+is not in our right that's all there is
+
+ align:start position:0%
+is not in our right that's all there is
+ 
+
+ align:start position:0%
+is not in our right that's all there is
+this is a deterministic confidence
+
+ align:start position:0%
+this is a deterministic confidence
+ 
+
+ align:start position:0%
+this is a deterministic confidence
+interval once I condition on X M 1 X n
+
+ align:start position:0%
+interval once I condition on X M 1 X n
+ 
+
+ align:start position:0%
+interval once I condition on X M 1 X n
+so I have a number the average is maybe
+
+ align:start position:0%
+so I have a number the average is maybe
+ 
+
+ align:start position:0%
+so I have a number the average is maybe
+3 and so I get 3 either theta is between
+
+ align:start position:0%
+3 and so I get 3 either theta is between
+ 
+
+ align:start position:0%
+3 and so I get 3 either theta is between
+3 minus 0.5 or in 3 point plus 0.5 or
+
+ align:start position:0%
+3 minus 0.5 or in 3 point plus 0.5 or
+ 
+
+ align:start position:0%
+3 minus 0.5 or in 3 point plus 0.5 or
+it's not and
+
+ align:start position:0%
+it's not and
+ 
+
+ align:start position:0%
+it's not and
+there's basically I mean I read it as
+
+ align:start position:0%
+there's basically I mean I read it as
+ 
+
+ align:start position:0%
+there's basically I mean I read it as
+probability but it's really not a
+
+ align:start position:0%
+probability but it's really not a
+ 
+
+ align:start position:0%
+probability but it's really not a
+probabilistic thing minutes either is
+
+ align:start position:0%
+probabilistic thing minutes either is
+ 
+
+ align:start position:0%
+probabilistic thing minutes either is
+sure or not agreed so what does it mean
+
+ align:start position:0%
+sure or not agreed so what does it mean
+ 
+
+ align:start position:0%
+sure or not agreed so what does it mean
+to have a frequentist confidence
+
+ align:start position:0%
+to have a frequentist confidence
+ 
+
+ align:start position:0%
+to have a frequentist confidence
+interval and means that if I were so and
+
+ align:start position:0%
+interval and means that if I were so and
+ 
+
+ align:start position:0%
+interval and means that if I were so and
+here it was where the word frequentist
+
+ align:start position:0%
+here it was where the word frequentist
+ 
+
+ align:start position:0%
+here it was where the word frequentist
+comes from it says that if I repeat this
+
+ align:start position:0%
+comes from it says that if I repeat this
+ 
+
+ align:start position:0%
+comes from it says that if I repeat this
+experiment over and over meaning that on
+
+ align:start position:0%
+experiment over and over meaning that on
+ 
+
+ align:start position:0%
+experiment over and over meaning that on
+Monday I could like the sample of size N
+
+ align:start position:0%
+Monday I could like the sample of size N
+ 
+
+ align:start position:0%
+Monday I could like the sample of size N
+and I build a confidence interval and
+
+ align:start position:0%
+and I build a confidence interval and
+ 
+
+ align:start position:0%
+and I build a confidence interval and
+then on Tuesday I collect another sample
+
+ align:start position:0%
+then on Tuesday I collect another sample
+ 
+
+ align:start position:0%
+then on Tuesday I collect another sample
+of size N and I build a confidence
+
+ align:start position:0%
+of size N and I build a confidence
+ 
+
+ align:start position:0%
+of size N and I build a confidence
+interval and on Wednesday I do this
+
+ align:start position:0%
+interval and on Wednesday I do this
+ 
+
+ align:start position:0%
+interval and on Wednesday I do this
+again and again what's gonna happen is
+
+ align:start position:0%
+again and again what's gonna happen is
+ 
+
+ align:start position:0%
+again and again what's gonna happen is
+the following I'm gonna have my truth
+
+ align:start position:0%
+the following I'm gonna have my truth
+ 
+
+ align:start position:0%
+the following I'm gonna have my truth
+theta that lives here and then on Monday
+
+ align:start position:0%
+theta that lives here and then on Monday
+ 
+
+ align:start position:0%
+theta that lives here and then on Monday
+this is the confidence interval that I
+
+ align:start position:0%
+this is the confidence interval that I
+ 
+
+ align:start position:0%
+this is the confidence interval that I
+build okay so this is the real line the
+
+ align:start position:0%
+build okay so this is the real line the
+ 
+
+ align:start position:0%
+build okay so this is the real line the
+truth theta is here and this is the
+
+ align:start position:0%
+truth theta is here and this is the
+ 
+
+ align:start position:0%
+truth theta is here and this is the
+comfortable I build on Monday
+
+ align:start position:0%
+comfortable I build on Monday
+ 
+
+ align:start position:0%
+comfortable I build on Monday
+all right so X bar was here and this is
+
+ align:start position:0%
+all right so X bar was here and this is
+ 
+
+ align:start position:0%
+all right so X bar was here and this is
+my confidence interval on Tuesday I
+
+ align:start position:0%
+my confidence interval on Tuesday I
+ 
+
+ align:start position:0%
+my confidence interval on Tuesday I
+built this confidence interval maybe
+
+ align:start position:0%
+built this confidence interval maybe
+ 
+
+ align:start position:0%
+built this confidence interval maybe
+thanks bar was closer to theta a bit
+
+ align:start position:0%
+thanks bar was closer to theta a bit
+ 
+
+ align:start position:0%
+thanks bar was closer to theta a bit
+smaller but then on Wednesday I built
+
+ align:start position:0%
+smaller but then on Wednesday I built
+ 
+
+ align:start position:0%
+smaller but then on Wednesday I built
+this confidence interval I'm not here
+
+ align:start position:0%
+this confidence interval I'm not here
+ 
+
+ align:start position:0%
+this confidence interval I'm not here
+it's not in there and that's this case
+
+ align:start position:0%
+it's not in there and that's this case
+ 
+
+ align:start position:0%
+it's not in there and that's this case
+right it happens that it's just not in
+
+ align:start position:0%
+right it happens that it's just not in
+ 
+
+ align:start position:0%
+right it happens that it's just not in
+there and then on Thursday I build
+
+ align:start position:0%
+there and then on Thursday I build
+ 
+
+ align:start position:0%
+there and then on Thursday I build
+another one I almost miss it but I'm in
+
+ align:start position:0%
+another one I almost miss it but I'm in
+ 
+
+ align:start position:0%
+another one I almost miss it but I'm in
+there etc maybe here I miss again and so
+
+ align:start position:0%
+there etc maybe here I miss again and so
+ 
+
+ align:start position:0%
+there etc maybe here I miss again and so
+what it means to have a confidence
+
+ align:start position:0%
+what it means to have a confidence
+ 
+
+ align:start position:0%
+what it means to have a confidence
+interval so what does it mean to have a
+
+ align:start position:0%
+interval so what does it mean to have a
+ 
+
+ align:start position:0%
+interval so what does it mean to have a
+confidence interval at 95% yeah so it
+
+ align:start position:0%
+confidence interval at 95% yeah so it
+ 
+
+ align:start position:0%
+confidence interval at 95% yeah so it
+means that if I repeat this the
+
+ align:start position:0%
+means that if I repeat this the
+ 
+
+ align:start position:0%
+means that if I repeat this the
+frequency of times hence the word
+
+ align:start position:0%
+frequency of times hence the word
+ 
+
+ align:start position:0%
+frequency of times hence the word
+frequentist at which I'm actually going
+
+ align:start position:0%
+frequentist at which I'm actually going
+ 
+
+ align:start position:0%
+frequentist at which I'm actually going
+to overlap that I'm actually going to
+
+ align:start position:0%
+to overlap that I'm actually going to
+ 
+
+ align:start position:0%
+to overlap that I'm actually going to
+contain theta should be 95% that's what
+
+ align:start position:0%
+contain theta should be 95% that's what
+ 
+
+ align:start position:0%
+contain theta should be 95% that's what
+frequencies means so it's just a matter
+
+ align:start position:0%
+frequencies means so it's just a matter
+ 
+
+ align:start position:0%
+frequencies means so it's just a matter
+of life trusting that so on one given
+
+ align:start position:0%
+of life trusting that so on one given
+ 
+
+ align:start position:0%
+of life trusting that so on one given
+thing one given realization of your data
+
+ align:start position:0%
+thing one given realization of your data
+ 
+
+ align:start position:0%
+thing one given realization of your data
+it's not telling you anything right
+
+ align:start position:0%
+it's not telling you anything right
+ 
+
+ align:start position:0%
+it's not telling you anything right
+there is there or not so it's not really
+
+ align:start position:0%
+there is there or not so it's not really
+ 
+
+ align:start position:0%
+there is there or not so it's not really
+something that's actually something that
+
+ align:start position:0%
+something that's actually something that
+ 
+
+ align:start position:0%
+something that's actually something that
+assesses the confidence of your decision
+
+ align:start position:0%
+assesses the confidence of your decision
+ 
+
+ align:start position:0%
+assesses the confidence of your decision
+such as theta is in there or not it's
+
+ align:start position:0%
+such as theta is in there or not it's
+ 
+
+ align:start position:0%
+such as theta is in there or not it's
+something that assesses the confidence
+
+ align:start position:0%
+something that assesses the confidence
+ 
+
+ align:start position:0%
+something that assesses the confidence
+you have in the method that you're using
+
+ align:start position:0%
+you have in the method that you're using
+ 
+
+ align:start position:0%
+you have in the method that you're using
+if you were to repeat it over and again
+
+ align:start position:0%
+if you were to repeat it over and again
+ 
+
+ align:start position:0%
+if you were to repeat it over and again
+would be the same thing
+
+ align:start position:0%
+would be the same thing
+ 
+
+ align:start position:0%
+would be the same thing
+would be 95% of the time correct right
+
+ align:start position:0%
+would be 95% of the time correct right
+ 
+
+ align:start position:0%
+would be 95% of the time correct right
+so for example we know that we could
+
+ align:start position:0%
+so for example we know that we could
+ 
+
+ align:start position:0%
+so for example we know that we could
+build a test right so it's pretty clear
+
+ align:start position:0%
+build a test right so it's pretty clear
+ 
+
+ align:start position:0%
+build a test right so it's pretty clear
+that you can actually build a test for
+
+ align:start position:0%
+that you can actually build a test for
+ 
+
+ align:start position:0%
+that you can actually build a test for
+whether theta is equal to theta naught
+
+ align:start position:0%
+whether theta is equal to theta naught
+ 
+
+ align:start position:0%
+whether theta is equal to theta naught
+or not equal to theta or not by just
+
+ align:start position:0%
+or not equal to theta or not by just
+ 
+
+ align:start position:0%
+or not equal to theta or not by just
+checking whether theta naught is in a
+
+ align:start position:0%
+checking whether theta naught is in a
+ 
+
+ align:start position:0%
+checking whether theta naught is in a
+confidence interval or not and what it
+
+ align:start position:0%
+confidence interval or not and what it
+ 
+
+ align:start position:0%
+confidence interval or not and what it
+means is that if you actually are doing
+
+ align:start position:0%
+means is that if you actually are doing
+ 
+
+ align:start position:0%
+means is that if you actually are doing
+those tests at 90 at 5% then it means
+
+ align:start position:0%
+those tests at 90 at 5% then it means
+ 
+
+ align:start position:0%
+those tests at 90 at 5% then it means
+that 5% of the time you should do this
+
+ align:start position:0%
+that 5% of the time you should do this
+ 
+
+ align:start position:0%
+that 5% of the time you should do this
+over and again 5% of the time you're
+
+ align:start position:0%
+over and again 5% of the time you're
+ 
+
+ align:start position:0%
+over and again 5% of the time you're
+gonna be wrong
+
+ align:start position:0%
+gonna be wrong
+ 
+
+ align:start position:0%
+gonna be wrong
+I mentioned my wife does come does
+
+ align:start position:0%
+I mentioned my wife does come does
+ 
+
+ align:start position:0%
+I mentioned my wife does come does
+market research and she does maybe I
+
+ align:start position:0%
+market research and she does maybe I
+ 
+
+ align:start position:0%
+market research and she does maybe I
+don't know a hundred thousand tests a
+
+ align:start position:0%
+don't know a hundred thousand tests a
+ 
+
+ align:start position:0%
+don't know a hundred thousand tests a
+year and if they do all of them at 1%
+
+ align:start position:0%
+year and if they do all of them at 1%
+ 
+
+ align:start position:0%
+year and if they do all of them at 1%
+then it means that 1% of the time which
+
+ align:start position:0%
+then it means that 1% of the time which
+ 
+
+ align:start position:0%
+then it means that 1% of the time which
+is a lot of time right when you do a
+
+ align:start position:0%
+is a lot of time right when you do a
+ 
+
+ align:start position:0%
+is a lot of time right when you do a
+hundred thousand a year it's 1,000 of
+
+ align:start position:0%
+hundred thousand a year it's 1,000 of
+ 
+
+ align:start position:0%
+hundred thousand a year it's 1,000 of
+them are actually wrong I mean they're
+
+ align:start position:0%
+them are actually wrong I mean they're
+ 
+
+ align:start position:0%
+them are actually wrong I mean they're
+she's actually you know hedging against
+
+ align:start position:0%
+she's actually you know hedging against
+ 
+
+ align:start position:0%
+she's actually you know hedging against
+the fact that 1% of them are going to be
+
+ align:start position:0%
+the fact that 1% of them are going to be
+ 
+
+ align:start position:0%
+the fact that 1% of them are going to be
+wrong that's the thousand of them that
+
+ align:start position:0%
+wrong that's the thousand of them that
+ 
+
+ align:start position:0%
+wrong that's the thousand of them that
+are gonna be wrong just like if you do
+
+ align:start position:0%
+are gonna be wrong just like if you do
+ 
+
+ align:start position:0%
+are gonna be wrong just like if you do
+this a hundred thousand times at 95%
+
+ align:start position:0%
+this a hundred thousand times at 95%
+ 
+
+ align:start position:0%
+this a hundred thousand times at 95%
+five thousand of those guys are actually
+
+ align:start position:0%
+five thousand of those guys are actually
+ 
+
+ align:start position:0%
+five thousand of those guys are actually
+not gonna be the correct ones okay so I
+
+ align:start position:0%
+not gonna be the correct ones okay so I
+ 
+
+ align:start position:0%
+not gonna be the correct ones okay so I
+mean it's kind of scary but that's the
+
+ align:start position:0%
+mean it's kind of scary but that's the
+ 
+
+ align:start position:0%
+mean it's kind of scary but that's the
+way it is so that's what the frequentist
+
+ align:start position:0%
+way it is so that's what the frequentist
+ 
+
+ align:start position:0%
+way it is so that's what the frequentist
+interpretation of this is now as I
+
+ align:start position:0%
+interpretation of this is now as I
+ 
+
+ align:start position:0%
+interpretation of this is now as I
+mentioned when we started this Bayesian
+
+ align:start position:0%
+mentioned when we started this Bayesian
+ 
+
+ align:start position:0%
+mentioned when we started this Bayesian
+chapter I said Bayesian statistics sort
+
+ align:start position:0%
+chapter I said Bayesian statistics sort
+ 
+
+ align:start position:0%
+chapter I said Bayesian statistics sort
+of converge to I mean Bayesian decisions
+
+ align:start position:0%
+of converge to I mean Bayesian decisions
+ 
+
+ align:start position:0%
+of converge to I mean Bayesian decisions
+and Bayesian methods sort of converged
+
+ align:start position:0%
+and Bayesian methods sort of converged
+ 
+
+ align:start position:0%
+and Bayesian methods sort of converged
+to frequentist methods they sort of when
+
+ align:start position:0%
+to frequentist methods they sort of when
+ 
+
+ align:start position:0%
+to frequentist methods they sort of when
+the sample size is large enough they
+
+ align:start position:0%
+the sample size is large enough they
+ 
+
+ align:start position:0%
+the sample size is large enough they
+sort of lead to the same decisions and
+
+ align:start position:0%
+sort of lead to the same decisions and
+ 
+
+ align:start position:0%
+sort of lead to the same decisions and
+in general there need not be the same
+
+ align:start position:0%
+in general there need not be the same
+ 
+
+ align:start position:0%
+in general there need not be the same
+but they tend to actually when the
+
+ align:start position:0%
+but they tend to actually when the
+ 
+
+ align:start position:0%
+but they tend to actually when the
+sample size is large enough to have the
+
+ align:start position:0%
+sample size is large enough to have the
+ 
+
+ align:start position:0%
+sample size is large enough to have the
+same behavior think about for example
+
+ align:start position:0%
+same behavior think about for example
+ 
+
+ align:start position:0%
+same behavior think about for example
+the posterior that you have when you
+
+ align:start position:0%
+the posterior that you have when you
+ 
+
+ align:start position:0%
+the posterior that you have when you
+have in the gaussian case right we said
+
+ align:start position:0%
+have in the gaussian case right we said
+ 
+
+ align:start position:0%
+have in the gaussian case right we said
+that in the gaussian case what you're
+
+ align:start position:0%
+that in the gaussian case what you're
+ 
+
+ align:start position:0%
+that in the gaussian case what you're
+gonna see is that it's as if you had an
+
+ align:start position:0%
+gonna see is that it's as if you had an
+ 
+
+ align:start position:0%
+gonna see is that it's as if you had an
+extra observation which was essentially
+
+ align:start position:0%
+extra observation which was essentially
+ 
+
+ align:start position:0%
+extra observation which was essentially
+given by your prior okay and and now
+
+ align:start position:0%
+given by your prior okay and and now
+ 
+
+ align:start position:0%
+given by your prior okay and and now
+it's the the what's gonna happen is that
+
+ align:start position:0%
+it's the the what's gonna happen is that
+ 
+
+ align:start position:0%
+it's the the what's gonna happen is that
+when the this just one observation among
+
+ align:start position:0%
+when the this just one observation among
+ 
+
+ align:start position:0%
+when the this just one observation among
+n plus one it's really going to be truly
+
+ align:start position:0%
+n plus one it's really going to be truly
+ 
+
+ align:start position:0%
+n plus one it's really going to be truly
+you know drawn and you won't see it when
+
+ align:start position:0%
+you know drawn and you won't see it when
+ 
+
+ align:start position:0%
+you know drawn and you won't see it when
+the sample size grows large
+
+ align:start position:0%
+the sample size grows large
+ 
+
+ align:start position:0%
+the sample size grows large
+so Bayesian methods are particularly
+
+ align:start position:0%
+so Bayesian methods are particularly
+ 
+
+ align:start position:0%
+so Bayesian methods are particularly
+useful when you have a small sample size
+
+ align:start position:0%
+useful when you have a small sample size
+ 
+
+ align:start position:0%
+useful when you have a small sample size
+and when you have a small sample size
+
+ align:start position:0%
+and when you have a small sample size
+ 
+
+ align:start position:0%
+and when you have a small sample size
+you can actually the effect of the prior
+
+ align:start position:0%
+you can actually the effect of the prior
+ 
+
+ align:start position:0%
+you can actually the effect of the prior
+is going to be bigger but most
+
+ align:start position:0%
+is going to be bigger but most
+ 
+
+ align:start position:0%
+is going to be bigger but most
+importantly you're not going to have to
+
+ align:start position:0%
+importantly you're not going to have to
+ 
+
+ align:start position:0%
+importantly you're not going to have to
+repeat this thing
+
+ align:start position:0%
+repeat this thing
+ 
+
+ align:start position:0%
+repeat this thing
+and again and you're gonna have a
+
+ align:start position:0%
+and again and you're gonna have a
+ 
+
+ align:start position:0%
+and again and you're gonna have a
+meaning you're gonna have to have
+
+ align:start position:0%
+meaning you're gonna have to have
+ 
+
+ align:start position:0%
+meaning you're gonna have to have
+something that has a meaning for this
+
+ align:start position:0%
+something that has a meaning for this
+ 
+
+ align:start position:0%
+something that has a meaning for this
+particular data set that you have right
+
+ align:start position:0%
+particular data set that you have right
+ 
+
+ align:start position:0%
+particular data set that you have right
+when I said that the probability that
+
+ align:start position:0%
+when I said that the probability that
+ 
+
+ align:start position:0%
+when I said that the probability that
+theta belongs to R and here I'm going to
+
+ align:start position:0%
+theta belongs to R and here I'm going to
+ 
+
+ align:start position:0%
+theta belongs to R and here I'm going to
+specify the fact that it's a Bayesian
+
+ align:start position:0%
+specify the fact that it's a Bayesian
+ 
+
+ align:start position:0%
+specify the fact that it's a Bayesian
+confidence region like this one this is
+
+ align:start position:0%
+confidence region like this one this is
+ 
+
+ align:start position:0%
+confidence region like this one this is
+actually conditionally on the data that
+
+ align:start position:0%
+actually conditionally on the data that
+ 
+
+ align:start position:0%
+actually conditionally on the data that
+you've collected it says given this data
+
+ align:start position:0%
+you've collected it says given this data
+ 
+
+ align:start position:0%
+you've collected it says given this data
+given the points that you have just put
+
+ align:start position:0%
+given the points that you have just put
+ 
+
+ align:start position:0%
+given the points that you have just put
+in some numbers if you want in there
+
+ align:start position:0%
+in some numbers if you want in there
+ 
+
+ align:start position:0%
+in some numbers if you want in there
+it's actually telling you the
+
+ align:start position:0%
+it's actually telling you the
+ 
+
+ align:start position:0%
+it's actually telling you the
+probability that theta belongs to this
+
+ align:start position:0%
+probability that theta belongs to this
+ 
+
+ align:start position:0%
+probability that theta belongs to this
+Bayesian thing to this Bayesian
+
+ align:start position:0%
+Bayesian thing to this Bayesian
+ 
+
+ align:start position:0%
+Bayesian thing to this Bayesian
+confidence region here since I've
+
+ align:start position:0%
+confidence region here since I've
+ 
+
+ align:start position:0%
+confidence region here since I've
+conditioned on X 1 X n this probability
+
+ align:start position:0%
+conditioned on X 1 X n this probability
+ 
+
+ align:start position:0%
+conditioned on X 1 X n this probability
+is really just with respect to theta
+
+ align:start position:0%
+is really just with respect to theta
+ 
+
+ align:start position:0%
+is really just with respect to theta
+drawn from the prior right and so now it
+
+ align:start position:0%
+drawn from the prior right and so now it
+ 
+
+ align:start position:0%
+drawn from the prior right and so now it
+has a slightly different meaning is just
+
+ align:start position:0%
+has a slightly different meaning is just
+ 
+
+ align:start position:0%
+has a slightly different meaning is just
+telling you that when I it's really
+
+ align:start position:0%
+telling you that when I it's really
+ 
+
+ align:start position:0%
+telling you that when I it's really
+making a statement about where the
+
+ align:start position:0%
+making a statement about where the
+ 
+
+ align:start position:0%
+making a statement about where the
+regions of high probability of your
+
+ align:start position:0%
+regions of high probability of your
+ 
+
+ align:start position:0%
+regions of high probability of your
+posterior are now why is that useful
+
+ align:start position:0%
+posterior are now why is that useful
+ 
+
+ align:start position:0%
+posterior are now why is that useful
+well there was actually there's actually
+
+ align:start position:0%
+well there was actually there's actually
+ 
+
+ align:start position:0%
+well there was actually there's actually
+an interesting story that goes behind
+
+ align:start position:0%
+an interesting story that goes behind
+ 
+
+ align:start position:0%
+an interesting story that goes behind
+Bayesian methods the anybody knows the
+
+ align:start position:0%
+Bayesian methods the anybody knows the
+ 
+
+ align:start position:0%
+Bayesian methods the anybody knows the
+the story of the USS scorpion do you
+
+ align:start position:0%
+the story of the USS scorpion do you
+ 
+
+ align:start position:0%
+the story of the USS scorpion do you
+know this the story so that was a
+
+ align:start position:0%
+know this the story so that was a
+ 
+
+ align:start position:0%
+know this the story so that was a
+American vessel that disappeared I think
+
+ align:start position:0%
+American vessel that disappeared I think
+ 
+
+ align:start position:0%
+American vessel that disappeared I think
+he was like close to Bermuda or
+
+ align:start position:0%
+he was like close to Bermuda or
+ 
+
+ align:start position:0%
+he was like close to Bermuda or
+something but you know you can tell the
+
+ align:start position:0%
+something but you know you can tell the
+ 
+
+ align:start position:0%
+something but you know you can tell the
+story the malaysian airlines'
+
+ align:start position:0%
+story the malaysian airlines'
+ 
+
+ align:start position:0%
+story the malaysian airlines'
+except that i don't think it's such a
+
+ align:start position:0%
+except that i don't think it's such a
+ 
+
+ align:start position:0%
+except that i don't think it's such a
+successful story but the idea was
+
+ align:start position:0%
+successful story but the idea was
+ 
+
+ align:start position:0%
+successful story but the idea was
+essentially we're trying to find where
+
+ align:start position:0%
+essentially we're trying to find where
+ 
+
+ align:start position:0%
+essentially we're trying to find where
+this thing happened and of course you
+
+ align:start position:0%
+this thing happened and of course you
+ 
+
+ align:start position:0%
+this thing happened and of course you
+don't have this is a one-time thing you
+
+ align:start position:0%
+don't have this is a one-time thing you
+ 
+
+ align:start position:0%
+don't have this is a one-time thing you
+actually have you need something that
+
+ align:start position:0%
+actually have you need something that
+ 
+
+ align:start position:0%
+actually have you need something that
+works once it's something that works for
+
+ align:start position:0%
+works once it's something that works for
+ 
+
+ align:start position:0%
+works once it's something that works for
+this particular vessel and you don't
+
+ align:start position:0%
+this particular vessel and you don't
+ 
+
+ align:start position:0%
+this particular vessel and you don't
+care if you go to the navy and you tell
+
+ align:start position:0%
+care if you go to the navy and you tell
+ 
+
+ align:start position:0%
+care if you go to the navy and you tell
+them well you know here's the method and
+
+ align:start position:0%
+them well you know here's the method and
+ 
+
+ align:start position:0%
+them well you know here's the method and
+for ninety five out of a hundred vessels
+
+ align:start position:0%
+for ninety five out of a hundred vessels
+ 
+
+ align:start position:0%
+for ninety five out of a hundred vessels
+that you're gonna lose we're gonna be
+
+ align:start position:0%
+that you're gonna lose we're gonna be
+ 
+
+ align:start position:0%
+that you're gonna lose we're gonna be
+able to find it and and they want this
+
+ align:start position:0%
+able to find it and and they want this
+ 
+
+ align:start position:0%
+able to find it and and they want this
+to work for this particular one and so
+
+ align:start position:0%
+to work for this particular one and so
+ 
+
+ align:start position:0%
+to work for this particular one and so
+they were looking and they were you know
+
+ align:start position:0%
+they were looking and they were you know
+ 
+
+ align:start position:0%
+they were looking and they were you know
+they were diving in different places and
+
+ align:start position:0%
+they were diving in different places and
+ 
+
+ align:start position:0%
+they were diving in different places and
+and suddenly they brought in this guy I
+
+ align:start position:0%
+and suddenly they brought in this guy I
+ 
+
+ align:start position:0%
+and suddenly they brought in this guy I
+forget his name I mean there's a whole
+
+ align:start position:0%
+forget his name I mean there's a whole
+ 
+
+ align:start position:0%
+forget his name I mean there's a whole
+story about this on Wikipedia and he
+
+ align:start position:0%
+story about this on Wikipedia and he
+ 
+
+ align:start position:0%
+story about this on Wikipedia and he
+started collecting the data that they
+
+ align:start position:0%
+started collecting the data that they
+ 
+
+ align:start position:0%
+started collecting the data that they
+had from different dives and maybe from
+
+ align:start position:0%
+had from different dives and maybe from
+ 
+
+ align:start position:0%
+had from different dives and maybe from
+currents and it started to put
+
+ align:start position:0%
+currents and it started to put
+ 
+
+ align:start position:0%
+currents and it started to put
+everything and he said okay what is the
+
+ align:start position:0%
+everything and he said okay what is the
+ 
+
+ align:start position:0%
+everything and he said okay what is the
+posterior distribution of the location
+
+ align:start position:0%
+posterior distribution of the location
+ 
+
+ align:start position:0%
+posterior distribution of the location
+of the vessel given all the things that
+
+ align:start position:0%
+of the vessel given all the things that
+ 
+
+ align:start position:0%
+of the vessel given all the things that
+I've seen and what are you have you seen
+
+ align:start position:0%
+I've seen and what are you have you seen
+ 
+
+ align:start position:0%
+I've seen and what are you have you seen
+well you've seen that
+
+ align:start position:0%
+well you've seen that
+ 
+
+ align:start position:0%
+well you've seen that
+it's not here it's not there and it's
+
+ align:start position:0%
+it's not here it's not there and it's
+ 
+
+ align:start position:0%
+it's not here it's not there and it's
+not there and you've also seen that the
+
+ align:start position:0%
+not there and you've also seen that the
+ 
+
+ align:start position:0%
+not there and you've also seen that the
+currents are going that way and the wind
+
+ align:start position:0%
+currents are going that way and the wind
+ 
+
+ align:start position:0%
+currents are going that way and the wind
+we're going that way and you can
+
+ align:start position:0%
+we're going that way and you can
+ 
+
+ align:start position:0%
+we're going that way and you can
+actually put some model and try to
+
+ align:start position:0%
+actually put some model and try to
+ 
+
+ align:start position:0%
+actually put some model and try to
+understand this now given this for this
+
+ align:start position:0%
+understand this now given this for this
+ 
+
+ align:start position:0%
+understand this now given this for this
+particular data that you have you can
+
+ align:start position:0%
+particular data that you have you can
+ 
+
+ align:start position:0%
+particular data that you have you can
+actually think of having a
+
+ align:start position:0%
+actually think of having a
+ 
+
+ align:start position:0%
+actually think of having a
+two-dimensional density that tells you
+
+ align:start position:0%
+two-dimensional density that tells you
+ 
+
+ align:start position:0%
+two-dimensional density that tells you
+where it's more likely then that the
+
+ align:start position:0%
+where it's more likely then that the
+ 
+
+ align:start position:0%
+where it's more likely then that the
+vessel is and where are you going to be
+
+ align:start position:0%
+vessel is and where are you going to be
+ 
+
+ align:start position:0%
+vessel is and where are you going to be
+looking for well if it's a multi-modal
+
+ align:start position:0%
+looking for well if it's a multi-modal
+ 
+
+ align:start position:0%
+looking for well if it's a multi-modal
+distribution you're just gonna go to the
+
+ align:start position:0%
+distribution you're just gonna go to the
+ 
+
+ align:start position:0%
+distribution you're just gonna go to the
+highest mode first because that's where
+
+ align:start position:0%
+highest mode first because that's where
+ 
+
+ align:start position:0%
+highest mode first because that's where
+it's the most likely to be and maybe
+
+ align:start position:0%
+it's the most likely to be and maybe
+ 
+
+ align:start position:0%
+it's the most likely to be and maybe
+it's not there so you're just gonna
+
+ align:start position:0%
+it's not there so you're just gonna
+ 
+
+ align:start position:0%
+it's not there so you're just gonna
+update your posterior based on the fact
+
+ align:start position:0%
+update your posterior based on the fact
+ 
+
+ align:start position:0%
+update your posterior based on the fact
+that it's not there and do it again
+
+ align:start position:0%
+that it's not there and do it again
+ 
+
+ align:start position:0%
+that it's not there and do it again
+and actually after - two dives I think
+
+ align:start position:0%
+and actually after - two dives I think
+ 
+
+ align:start position:0%
+and actually after - two dives I think
+he actually found the thing and that's
+
+ align:start position:0%
+he actually found the thing and that's
+ 
+
+ align:start position:0%
+he actually found the thing and that's
+exactly where Bayesian statistics start
+
+ align:start position:0%
+exactly where Bayesian statistics start
+ 
+
+ align:start position:0%
+exactly where Bayesian statistics start
+to kick in because you put a lot of
+
+ align:start position:0%
+to kick in because you put a lot of
+ 
+
+ align:start position:0%
+to kick in because you put a lot of
+knowledge into your into your model but
+
+ align:start position:0%
+knowledge into your into your model but
+ 
+
+ align:start position:0%
+knowledge into your into your model but
+you also can actually factor in a bunch
+
+ align:start position:0%
+you also can actually factor in a bunch
+ 
+
+ align:start position:0%
+you also can actually factor in a bunch
+of information right the model you had
+
+ align:start position:0%
+of information right the model you had
+ 
+
+ align:start position:0%
+of information right the model you had
+to build a model that was actually
+
+ align:start position:0%
+to build a model that was actually
+ 
+
+ align:start position:0%
+to build a model that was actually
+taking into account currents and and and
+
+ align:start position:0%
+taking into account currents and and and
+ 
+
+ align:start position:0%
+taking into account currents and and and
+when and what you can't have as a
+
+ align:start position:0%
+when and what you can't have as a
+ 
+
+ align:start position:0%
+when and what you can't have as a
+guarantee is that when you talk about
+
+ align:start position:0%
+guarantee is that when you talk about
+ 
+
+ align:start position:0%
+guarantee is that when you talk about
+the probability that this vessel is you
+
+ align:start position:0%
+the probability that this vessel is you
+ 
+
+ align:start position:0%
+the probability that this vessel is you
+know in this location given what you've
+
+ align:start position:0%
+know in this location given what you've
+ 
+
+ align:start position:0%
+know in this location given what you've
+observed in the past it actually has
+
+ align:start position:0%
+observed in the past it actually has
+ 
+
+ align:start position:0%
+observed in the past it actually has
+some sense whereas if you were to use a
+
+ align:start position:0%
+some sense whereas if you were to use a
+ 
+
+ align:start position:0%
+some sense whereas if you were to use a
+a frequentist approach then there's no
+
+ align:start position:0%
+a frequentist approach then there's no
+ 
+
+ align:start position:0%
+a frequentist approach then there's no
+probability either it's underneath this
+
+ align:start position:0%
+probability either it's underneath this
+ 
+
+ align:start position:0%
+probability either it's underneath this
+position or it's not right so that's
+
+ align:start position:0%
+position or it's not right so that's
+ 
+
+ align:start position:0%
+position or it's not right so that's
+actually where it it start to make sense
+
+ align:start position:0%
+actually where it it start to make sense
+ 
+
+ align:start position:0%
+actually where it it start to make sense
+and so you can actually build this and
+
+ align:start position:0%
+and so you can actually build this and
+ 
+
+ align:start position:0%
+and so you can actually build this and
+there's actually a lot of methods that
+
+ align:start position:0%
+there's actually a lot of methods that
+ 
+
+ align:start position:0%
+there's actually a lot of methods that
+are based on you know for search that
+
+ align:start position:0%
+are based on you know for search that
+ 
+
+ align:start position:0%
+are based on you know for search that
+are based on Bayesian methods I think
+
+ align:start position:0%
+are based on Bayesian methods I think
+ 
+
+ align:start position:0%
+are based on Bayesian methods I think
+for example the Higgs boson which based
+
+ align:start position:0%
+for example the Higgs boson which based
+ 
+
+ align:start position:0%
+for example the Higgs boson which based
+on a lot of Bayesian methods because
+
+ align:start position:0%
+on a lot of Bayesian methods because
+ 
+
+ align:start position:0%
+on a lot of Bayesian methods because
+this is something you need to find once
+
+ align:start position:0%
+this is something you need to find once
+ 
+
+ align:start position:0%
+this is something you need to find once
+right I mean there was a lot of prior
+
+ align:start position:0%
+right I mean there was a lot of prior
+ 
+
+ align:start position:0%
+right I mean there was a lot of prior
+that has to be built in okay so now you
+
+ align:start position:0%
+that has to be built in okay so now you
+ 
+
+ align:start position:0%
+that has to be built in okay so now you
+build this confidence interval and the
+
+ align:start position:0%
+build this confidence interval and the
+ 
+
+ align:start position:0%
+build this confidence interval and the
+nicest way to do it is to use level sets
+
+ align:start position:0%
+nicest way to do it is to use level sets
+ 
+
+ align:start position:0%
+nicest way to do it is to use level sets
+but again just like for gaussians right
+
+ align:start position:0%
+but again just like for gaussians right
+ 
+
+ align:start position:0%
+but again just like for gaussians right
+I mean if I had even in the in the even
+
+ align:start position:0%
+I mean if I had even in the in the even
+ 
+
+ align:start position:0%
+I mean if I had even in the in the even
+in the Gaussian case I decided to go at
+
+ align:start position:0%
+in the Gaussian case I decided to go at
+ 
+
+ align:start position:0%
+in the Gaussian case I decided to go at
+X bar plus or minus something but I
+
+ align:start position:0%
+X bar plus or minus something but I
+ 
+
+ align:start position:0%
+X bar plus or minus something but I
+could go at like something that's
+
+ align:start position:0%
+could go at like something that's
+ 
+
+ align:start position:0%
+could go at like something that's
+completely asymmetric so what's
+
+ align:start position:0%
+completely asymmetric so what's
+ 
+
+ align:start position:0%
+completely asymmetric so what's
+happening is that tier this method
+
+ align:start position:0%
+happening is that tier this method
+ 
+
+ align:start position:0%
+happening is that tier this method
+guarantees that you're gonna have the
+
+ align:start position:0%
+guarantees that you're gonna have the
+ 
+
+ align:start position:0%
+guarantees that you're gonna have the
+narrow as possible confidence intervals
+
+ align:start position:0%
+narrow as possible confidence intervals
+ 
+
+ align:start position:0%
+narrow as possible confidence intervals
+that's essentially what it's telling you
+
+ align:start position:0%
+that's essentially what it's telling you
+ 
+
+ align:start position:0%
+that's essentially what it's telling you
+okay because every time I'm choosing a
+
+ align:start position:0%
+okay because every time I'm choosing a
+ 
+
+ align:start position:0%
+okay because every time I'm choosing a
+point starting from here I'm actually
+
+ align:start position:0%
+point starting from here I'm actually
+ 
+
+ align:start position:0%
+point starting from here I'm actually
+putting as much area under the curve as
+
+ align:start position:0%
+putting as much area under the curve as
+ 
+
+ align:start position:0%
+putting as much area under the curve as
+I can all right
+
+ align:start position:0%
+I can all right
+ 
+
+ align:start position:0%
+I can all right
+so so those are called Bayesian
+
+ align:start position:0%
+so so those are called Bayesian
+ 
+
+ align:start position:0%
+so so those are called Bayesian
+confessional oh yeah and I promise you
+
+ align:start position:0%
+confessional oh yeah and I promise you
+ 
+
+ align:start position:0%
+confessional oh yeah and I promise you
+that we're gonna work on some example
+
+ align:start position:0%
+that we're gonna work on some example
+ 
+
+ align:start position:0%
+that we're gonna work on some example
+that actually sort of sort of give the
+
+ align:start position:0%
+that actually sort of sort of give the
+ 
+
+ align:start position:0%
+that actually sort of sort of give the
+meeting to what I just told you
+
+ align:start position:0%
+meeting to what I just told you
+ 
+
+ align:start position:0%
+meeting to what I just told you
+with like actual numbers so this is
+
+ align:start position:0%
+with like actual numbers so this is
+ 
+
+ align:start position:0%
+with like actual numbers so this is
+something that's taken from Worcester
+
+ align:start position:0%
+something that's taken from Worcester
+ 
+
+ align:start position:0%
+something that's taken from Worcester
+mins book and that's also it's all it's
+
+ align:start position:0%
+mins book and that's also it's all it's
+ 
+
+ align:start position:0%
+mins book and that's also it's all it's
+coming from a paper from stats paper
+
+ align:start position:0%
+coming from a paper from stats paper
+ 
+
+ align:start position:0%
+coming from a paper from stats paper
+from walpert and I don't know who from
+
+ align:start position:0%
+from walpert and I don't know who from
+ 
+
+ align:start position:0%
+from walpert and I don't know who from
+the 80s and essentially this is how it
+
+ align:start position:0%
+the 80s and essentially this is how it
+ 
+
+ align:start position:0%
+the 80s and essentially this is how it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+so observe assume that you have N equals
+
+ align:start position:0%
+so observe assume that you have N equals
+ 
+
+ align:start position:0%
+so observe assume that you have N equals
+two observations and you have y1 so
+
+ align:start position:0%
+two observations and you have y1 so
+ 
+
+ align:start position:0%
+two observations and you have y1 so
+those observations are y1 let no sorry
+
+ align:start position:0%
+those observations are y1 let no sorry
+ 
+
+ align:start position:0%
+those observations are y1 let no sorry
+let's call them x1 which is theta plus
+
+ align:start position:0%
+let's call them x1 which is theta plus
+ 
+
+ align:start position:0%
+let's call them x1 which is theta plus
+epsilon 1 and X 2 which is theta plus
+
+ align:start position:0%
+epsilon 1 and X 2 which is theta plus
+ 
+
+ align:start position:0%
+epsilon 1 and X 2 which is theta plus
+epsilon 2 or epsilon 1 and epsilon 2 are
+
+ align:start position:0%
+epsilon 2 or epsilon 1 and epsilon 2 are
+ 
+
+ align:start position:0%
+epsilon 2 or epsilon 1 and epsilon 2 are
+iid and the probability that epsilon I
+
+ align:start position:0%
+iid and the probability that epsilon I
+ 
+
+ align:start position:0%
+iid and the probability that epsilon I
+is equal to plus 1 is equal to the
+
+ align:start position:0%
+is equal to plus 1 is equal to the
+ 
+
+ align:start position:0%
+is equal to plus 1 is equal to the
+probability that X 1 I is equal to minus
+
+ align:start position:0%
+probability that X 1 I is equal to minus
+ 
+
+ align:start position:0%
+probability that X 1 I is equal to minus
+1 is equal to 1/2 okay so it's just the
+
+ align:start position:0%
+1 is equal to 1/2 okay so it's just the
+ 
+
+ align:start position:0%
+1 is equal to 1/2 okay so it's just the
+uniform sign plus minus 1 okay now let's
+
+ align:start position:0%
+uniform sign plus minus 1 okay now let's
+ 
+
+ align:start position:0%
+uniform sign plus minus 1 okay now let's
+think about so you're trying to do some
+
+ align:start position:0%
+think about so you're trying to do some
+ 
+
+ align:start position:0%
+think about so you're trying to do some
+inference on theta maybe you actually
+
+ align:start position:0%
+inference on theta maybe you actually
+ 
+
+ align:start position:0%
+inference on theta maybe you actually
+want to find some inference on theta
+
+ align:start position:0%
+want to find some inference on theta
+ 
+
+ align:start position:0%
+want to find some inference on theta
+that's actually based on and that's
+
+ align:start position:0%
+that's actually based on and that's
+ 
+
+ align:start position:0%
+that's actually based on and that's
+based only on the epsilon x1 and x2 okay
+
+ align:start position:0%
+based only on the epsilon x1 and x2 okay
+ 
+
+ align:start position:0%
+based only on the epsilon x1 and x2 okay
+so I'm gonna actually build a confidence
+
+ align:start position:0%
+so I'm gonna actually build a confidence
+ 
+
+ align:start position:0%
+so I'm gonna actually build a confidence
+interval but what I really want to build
+
+ align:start position:0%
+interval but what I really want to build
+ 
+
+ align:start position:0%
+interval but what I really want to build
+is a is but let's start thinking about
+
+ align:start position:0%
+is a is but let's start thinking about
+ 
+
+ align:start position:0%
+is a is but let's start thinking about
+how I would find an estimator for those
+
+ align:start position:0%
+how I would find an estimator for those
+ 
+
+ align:start position:0%
+how I would find an estimator for those
+two things well what values am I going
+
+ align:start position:0%
+two things well what values am I going
+ 
+
+ align:start position:0%
+two things well what values am I going
+to be getting right so I'm gonna get
+
+ align:start position:0%
+to be getting right so I'm gonna get
+ 
+
+ align:start position:0%
+to be getting right so I'm gonna get
+either theta plus 1 or theta minus 1 and
+
+ align:start position:0%
+either theta plus 1 or theta minus 1 and
+ 
+
+ align:start position:0%
+either theta plus 1 or theta minus 1 and
+actually I can get basically four
+
+ align:start position:0%
+actually I can get basically four
+ 
+
+ align:start position:0%
+actually I can get basically four
+different observations right sorry four
+
+ align:start position:0%
+different observations right sorry four
+ 
+
+ align:start position:0%
+different observations right sorry four
+different pairs of observations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus plus theta minus Oh agreed
+
+ align:start position:0%
+plus plus theta minus Oh agreed
+ 
+
+ align:start position:0%
+plus plus theta minus Oh agreed
+those are the four possible observations
+
+ align:start position:0%
+those are the four possible observations
+ 
+
+ align:start position:0%
+those are the four possible observations
+that I can get agree either they're both
+
+ align:start position:0%
+that I can get agree either they're both
+ 
+
+ align:start position:0%
+that I can get agree either they're both
+equal to plus one
+
+ align:start position:0%
+equal to plus one
+ 
+
+ align:start position:0%
+equal to plus one
+the both equal to minus one or one of
+
+ align:start position:0%
+the both equal to minus one or one of
+ 
+
+ align:start position:0%
+the both equal to minus one or one of
+the two is equal to plus one the other
+
+ align:start position:0%
+the two is equal to plus one the other
+ 
+
+ align:start position:0%
+the two is equal to plus one the other
+one to minus one for the Epsilon's okay
+
+ align:start position:0%
+one to minus one for the Epsilon's okay
+ 
+
+ align:start position:0%
+one to minus one for the Epsilon's okay
+so the four observations I can get so in
+
+ align:start position:0%
+so the four observations I can get so in
+ 
+
+ align:start position:0%
+so the four observations I can get so in
+particular if they take the same value
+
+ align:start position:0%
+particular if they take the same value
+ 
+
+ align:start position:0%
+particular if they take the same value
+you know it's it's either theta plus 1
+
+ align:start position:0%
+you know it's it's either theta plus 1
+ 
+
+ align:start position:0%
+you know it's it's either theta plus 1
+or theta minus 1 and if they take a
+
+ align:start position:0%
+or theta minus 1 and if they take a
+ 
+
+ align:start position:0%
+or theta minus 1 and if they take a
+different value I know one of them is
+
+ align:start position:0%
+different value I know one of them is
+ 
+
+ align:start position:0%
+different value I know one of them is
+theta plus one and one is actually theta
+
+ align:start position:0%
+theta plus one and one is actually theta
+ 
+
+ align:start position:0%
+theta plus one and one is actually theta
+minus one so in particular if I take the
+
+ align:start position:0%
+minus one so in particular if I take the
+ 
+
+ align:start position:0%
+minus one so in particular if I take the
+average of those two guys when they take
+
+ align:start position:0%
+average of those two guys when they take
+ 
+
+ align:start position:0%
+average of those two guys when they take
+different values I know I'm actually
+
+ align:start position:0%
+different values I know I'm actually
+ 
+
+ align:start position:0%
+different values I know I'm actually
+getting clear too right so let's build a
+
+ align:start position:0%
+getting clear too right so let's build a
+ 
+
+ align:start position:0%
+getting clear too right so let's build a
+confidence region okay so I'm actually
+
+ align:start position:0%
+confidence region okay so I'm actually
+ 
+
+ align:start position:0%
+confidence region okay so I'm actually
+going to take a conference region which
+
+ align:start position:0%
+going to take a conference region which
+ 
+
+ align:start position:0%
+going to take a conference region which
+is just a singleton and I'm gonna say
+
+ align:start position:0%
+is just a singleton and I'm gonna say
+ 
+
+ align:start position:0%
+is just a singleton and I'm gonna say
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+well if x1 is equal to x2 I'm just gonna
+
+ align:start position:0%
+well if x1 is equal to x2 I'm just gonna
+ 
+
+ align:start position:0%
+well if x1 is equal to x2 I'm just gonna
+take x1 minus 1 okay so I'm just saying
+
+ align:start position:0%
+take x1 minus 1 okay so I'm just saying
+ 
+
+ align:start position:0%
+take x1 minus 1 okay so I'm just saying
+well I'm never gonna be able to resolve
+
+ align:start position:0%
+well I'm never gonna be able to resolve
+ 
+
+ align:start position:0%
+well I'm never gonna be able to resolve
+whether it's plus 1 or minus 1 that
+
+ align:start position:0%
+whether it's plus 1 or minus 1 that
+ 
+
+ align:start position:0%
+whether it's plus 1 or minus 1 that
+actually gives me the best one so I'm
+
+ align:start position:0%
+actually gives me the best one so I'm
+ 
+
+ align:start position:0%
+actually gives me the best one so I'm
+just gonna take a dive and say well it's
+
+ align:start position:0%
+just gonna take a dive and say well it's
+ 
+
+ align:start position:0%
+just gonna take a dive and say well it's
+just plus 1 okay and then if they're
+
+ align:start position:0%
+just plus 1 okay and then if they're
+ 
+
+ align:start position:0%
+just plus 1 okay and then if they're
+different then here I can do much better
+
+ align:start position:0%
+different then here I can do much better
+ 
+
+ align:start position:0%
+different then here I can do much better
+I'm gonna actually just take the average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what I claim is that this is a
+
+ align:start position:0%
+okay now what I claim is that this is a
+ 
+
+ align:start position:0%
+okay now what I claim is that this is a
+confidence region and by default when I
+
+ align:start position:0%
+confidence region and by default when I
+ 
+
+ align:start position:0%
+confidence region and by default when I
+don't mention it this is a frequentist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+confidence region at level 75 percent
+
+ align:start position:0%
+confidence region at level 75 percent
+ 
+
+ align:start position:0%
+confidence region at level 75 percent
+okay so let's just check that to check
+
+ align:start position:0%
+okay so let's just check that to check
+ 
+
+ align:start position:0%
+okay so let's just check that to check
+that this is correct I need to check
+
+ align:start position:0%
+that this is correct I need to check
+ 
+
+ align:start position:0%
+that this is correct I need to check
+that the probability under the
+
+ align:start position:0%
+that the probability under the
+ 
+
+ align:start position:0%
+that the probability under the
+realization of x1 and x2 that theta
+
+ align:start position:0%
+realization of x1 and x2 that theta
+ 
+
+ align:start position:0%
+realization of x1 and x2 that theta
+belongs is one of those two guys is
+
+ align:start position:0%
+belongs is one of those two guys is
+ 
+
+ align:start position:0%
+belongs is one of those two guys is
+actually equal to point 75
+
+ align:start position:0%
+actually equal to point 75
+ 
+
+ align:start position:0%
+actually equal to point 75
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just a frequencies confidence
+
+ align:start position:0%
+it's just a frequencies confidence
+ 
+
+ align:start position:0%
+it's just a frequencies confidence
+interval that need not it does not need
+
+ align:start position:0%
+interval that need not it does not need
+ 
+
+ align:start position:0%
+interval that need not it does not need
+to be an interval actually in this case
+
+ align:start position:0%
+to be an interval actually in this case
+ 
+
+ align:start position:0%
+to be an interval actually in this case
+it's gonna be an interval but that's
+
+ align:start position:0%
+it's gonna be an interval but that's
+ 
+
+ align:start position:0%
+it's gonna be an interval but that's
+just what it means
+
+ align:start position:0%
+just what it means
+ 
+
+ align:start position:0%
+just what it means
+yeah Region four Bayesian was just
+
+ align:start position:0%
+yeah Region four Bayesian was just
+ 
+
+ align:start position:0%
+yeah Region four Bayesian was just
+because I mean the confidence intervals
+
+ align:start position:0%
+because I mean the confidence intervals
+ 
+
+ align:start position:0%
+because I mean the confidence intervals
+when we're frequentist we tend to make
+
+ align:start position:0%
+when we're frequentist we tend to make
+ 
+
+ align:start position:0%
+when we're frequentist we tend to make
+them intervals by because we want but
+
+ align:start position:0%
+them intervals by because we want but
+ 
+
+ align:start position:0%
+them intervals by because we want but
+when your vision you're doing this
+
+ align:start position:0%
+when your vision you're doing this
+ 
+
+ align:start position:0%
+when your vision you're doing this
+levels that thing you cannot really
+
+ align:start position:0%
+levels that thing you cannot really
+ 
+
+ align:start position:0%
+levels that thing you cannot really
+guarantee unless it's unimodal it's
+
+ align:start position:0%
+guarantee unless it's unimodal it's
+ 
+
+ align:start position:0%
+guarantee unless it's unimodal it's
+gonna be an integral so region is just a
+
+ align:start position:0%
+gonna be an integral so region is just a
+ 
+
+ align:start position:0%
+gonna be an integral so region is just a
+way to not have to say interval in case
+
+ align:start position:0%
+way to not have to say interval in case
+ 
+
+ align:start position:0%
+way to not have to say interval in case
+it's not okay so I have this distinct so
+
+ align:start position:0%
+it's not okay so I have this distinct so
+ 
+
+ align:start position:0%
+it's not okay so I have this distinct so
+what I need to check is the probability
+
+ align:start position:0%
+what I need to check is the probability
+ 
+
+ align:start position:0%
+what I need to check is the probability
+that theta is in one of those two things
+
+ align:start position:0%
+that theta is in one of those two things
+ 
+
+ align:start position:0%
+that theta is in one of those two things
+right so what I need to find is the
+
+ align:start position:0%
+right so what I need to find is the
+ 
+
+ align:start position:0%
+right so what I need to find is the
+probability of theta is in in well X 1
+
+ align:start position:0%
+probability of theta is in in well X 1
+ 
+
+ align:start position:0%
+probability of theta is in in well X 1
+minus 1 and X 1 is not equal to X 2 and
+
+ align:start position:0%
+minus 1 and X 1 is not equal to X 2 and
+ 
+
+ align:start position:0%
+minus 1 and X 1 is not equal to X 2 and
+those are disjoint events is the plus
+
+ align:start position:0%
+those are disjoint events is the plus
+ 
+
+ align:start position:0%
+those are disjoint events is the plus
+the probability of theta is in X 1 plus
+
+ align:start position:0%
+the probability of theta is in X 1 plus
+ 
+
+ align:start position:0%
+the probability of theta is in X 1 plus
+X 2 over 2 and X 1 sorry that's equal
+
+ align:start position:0%
+X 2 over 2 and X 1 sorry that's equal
+ 
+
+ align:start position:0%
+X 2 over 2 and X 1 sorry that's equal
+that's different okay and okay just
+
+ align:start position:0%
+that's different okay and okay just
+ 
+
+ align:start position:0%
+that's different okay and okay just
+before we actually finish the
+
+ align:start position:0%
+before we actually finish the
+ 
+
+ align:start position:0%
+before we actually finish the
+computation why do I have 75% so
+
+ align:start position:0%
+computation why do I have 75% so
+ 
+
+ align:start position:0%
+computation why do I have 75% so
+refreshed percent is 3/4 so it means
+
+ align:start position:0%
+refreshed percent is 3/4 so it means
+ 
+
+ align:start position:0%
+refreshed percent is 3/4 so it means
+that we have four cases and essentially
+
+ align:start position:0%
+that we have four cases and essentially
+ 
+
+ align:start position:0%
+that we have four cases and essentially
+I did not account for one case and it's
+
+ align:start position:0%
+I did not account for one case and it's
+ 
+
+ align:start position:0%
+I did not account for one case and it's
+true I did not account for this case
+
+ align:start position:0%
+true I did not account for this case
+ 
+
+ align:start position:0%
+true I did not account for this case
+when the both of the epsilon i's are
+
+ align:start position:0%
+when the both of the epsilon i's are
+ 
+
+ align:start position:0%
+when the both of the epsilon i's are
+equal to minus 1 right so this is
+
+ align:start position:0%
+equal to minus 1 right so this is
+ 
+
+ align:start position:0%
+equal to minus 1 right so this is
+essentially the one I'm not gonna be
+
+ align:start position:0%
+essentially the one I'm not gonna be
+ 
+
+ align:start position:0%
+essentially the one I'm not gonna be
+able to account for and so we'll see
+
+ align:start position:0%
+able to account for and so we'll see
+ 
+
+ align:start position:0%
+able to account for and so we'll see
+that in a second so in this case we know
+
+ align:start position:0%
+that in a second so in this case we know
+ 
+
+ align:start position:0%
+that in a second so in this case we know
+that everything goes great right so in
+
+ align:start position:0%
+that everything goes great right so in
+ 
+
+ align:start position:0%
+that everything goes great right so in
+this case this is okay well that's just
+
+ align:start position:0%
+this case this is okay well that's just
+ 
+
+ align:start position:0%
+this case this is okay well that's just
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+let's start from the first line so the
+
+ align:start position:0%
+let's start from the first line so the
+ 
+
+ align:start position:0%
+let's start from the first line so the
+first line is the probability that theta
+
+ align:start position:0%
+first line is the probability that theta
+ 
+
+ align:start position:0%
+first line is the probability that theta
+is equal to X 1 minus 1 and those two
+
+ align:start position:0%
+is equal to X 1 minus 1 and those two
+ 
+
+ align:start position:0%
+is equal to X 1 minus 1 and those two
+are equal so this is the probability
+
+ align:start position:0%
+are equal so this is the probability
+ 
+
+ align:start position:0%
+are equal so this is the probability
+that theta is equal to well this is what
+
+ align:start position:0%
+that theta is equal to well this is what
+ 
+
+ align:start position:0%
+that theta is equal to well this is what
+this is theta plus epsilon 1 minus 1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon 1 is equal to epsilon 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because I can remove the theta
+
+ align:start position:0%
+right because I can remove the theta
+ 
+
+ align:start position:0%
+right because I can remove the theta
+from here and I can actually remove the
+
+ align:start position:0%
+from here and I can actually remove the
+ 
+
+ align:start position:0%
+from here and I can actually remove the
+theta from here so that this guy here is
+
+ align:start position:0%
+theta from here so that this guy here is
+ 
+
+ align:start position:0%
+theta from here so that this guy here is
+just epsilon one is equal to one so when
+
+ align:start position:0%
+just epsilon one is equal to one so when
+ 
+
+ align:start position:0%
+just epsilon one is equal to one so when
+I intersect with this guy it's actually
+
+ align:start position:0%
+I intersect with this guy it's actually
+ 
+
+ align:start position:0%
+I intersect with this guy it's actually
+the same thing as epsilon 1 is equal to
+
+ align:start position:0%
+the same thing as epsilon 1 is equal to
+ 
+
+ align:start position:0%
+the same thing as epsilon 1 is equal to
+one as well epsilon 2 is equal to 1 is 1
+
+ align:start position:0%
+one as well epsilon 2 is equal to 1 is 1
+ 
+
+ align:start position:0%
+one as well epsilon 2 is equal to 1 is 1
+okay so this first thing is actually
+
+ align:start position:0%
+okay so this first thing is actually
+ 
+
+ align:start position:0%
+okay so this first thing is actually
+equal to the probability that epsilon 1
+
+ align:start position:0%
+equal to the probability that epsilon 1
+ 
+
+ align:start position:0%
+equal to the probability that epsilon 1
+is equal to 1 and epsilon 2 is equal to
+
+ align:start position:0%
+is equal to 1 and epsilon 2 is equal to
+ 
+
+ align:start position:0%
+is equal to 1 and epsilon 2 is equal to
+1 which is equal to what we have 1/4
+
+ align:start position:0%
+1 which is equal to what we have 1/4
+ 
+
+ align:start position:0%
+1 which is equal to what we have 1/4
+right so that's just the first case over
+
+ align:start position:0%
+right so that's just the first case over
+ 
+
+ align:start position:0%
+right so that's just the first case over
+there they're independent now I still
+
+ align:start position:0%
+there they're independent now I still
+ 
+
+ align:start position:0%
+there they're independent now I still
+need to do the second one so this case
+
+ align:start position:0%
+need to do the second one so this case
+ 
+
+ align:start position:0%
+need to do the second one so this case
+is what well when those things are equal
+
+ align:start position:0%
+is what well when those things are equal
+ 
+
+ align:start position:0%
+is what well when those things are equal
+X 1 plus X 2 over 2 is what well I get
+
+ align:start position:0%
+X 1 plus X 2 over 2 is what well I get
+ 
+
+ align:start position:0%
+X 1 plus X 2 over 2 is what well I get
+theta plus theta over 2 so that's just
+
+ align:start position:0%
+theta plus theta over 2 so that's just
+ 
+
+ align:start position:0%
+theta plus theta over 2 so that's just
+equal to the probability that epsilon 1
+
+ align:start position:0%
+equal to the probability that epsilon 1
+ 
+
+ align:start position:0%
+equal to the probability that epsilon 1
+plus epsilon 2 over 2 is equal to 0 and
+
+ align:start position:0%
+plus epsilon 2 over 2 is equal to 0 and
+ 
+
+ align:start position:0%
+plus epsilon 2 over 2 is equal to 0 and
+epsilon 1 is different from epsilon 2
+
+ align:start position:0%
+epsilon 1 is different from epsilon 2
+ 
+
+ align:start position:0%
+epsilon 1 is different from epsilon 2
+agreed I just removed the Thetas from
+
+ align:start position:0%
+agreed I just removed the Thetas from
+ 
+
+ align:start position:0%
+agreed I just removed the Thetas from
+these equations because I can't they're
+
+ align:start position:0%
+these equations because I can't they're
+ 
+
+ align:start position:0%
+these equations because I can't they're
+just on both sides every time ok and so
+
+ align:start position:0%
+just on both sides every time ok and so
+ 
+
+ align:start position:0%
+just on both sides every time ok and so
+that means what that means that the
+
+ align:start position:0%
+that means what that means that the
+ 
+
+ align:start position:0%
+that means what that means that the
+second part so this thing is actually
+
+ align:start position:0%
+second part so this thing is actually
+ 
+
+ align:start position:0%
+second part so this thing is actually
+equal to 1/4 plus the probability at
+
+ align:start position:0%
+equal to 1/4 plus the probability at
+ 
+
+ align:start position:0%
+equal to 1/4 plus the probability at
+epsilon 1 and epsilon 2 over 2 is equal
+
+ align:start position:0%
+epsilon 1 and epsilon 2 over 2 is equal
+ 
+
+ align:start position:0%
+epsilon 1 and epsilon 2 over 2 is equal
+to 0 I can remove the 2 so this is just
+
+ align:start position:0%
+to 0 I can remove the 2 so this is just
+ 
+
+ align:start position:0%
+to 0 I can remove the 2 so this is just
+the probably at 1 is 1 and the other one
+
+ align:start position:0%
+the probably at 1 is 1 and the other one
+ 
+
+ align:start position:0%
+the probably at 1 is 1 and the other one
+is minus 1 right
+
+ align:start position:0%
+is minus 1 right
+ 
+
+ align:start position:0%
+is minus 1 right
+so that's equal to the probability that
+
+ align:start position:0%
+so that's equal to the probability that
+ 
+
+ align:start position:0%
+so that's equal to the probability that
+epsilon 1 is equal to 1 and epsilon 2 is
+
+ align:start position:0%
+epsilon 1 is equal to 1 and epsilon 2 is
+ 
+
+ align:start position:0%
+epsilon 1 is equal to 1 and epsilon 2 is
+equal to minus 1 plus the probability
+
+ align:start position:0%
+equal to minus 1 plus the probability
+ 
+
+ align:start position:0%
+equal to minus 1 plus the probability
+that epsilon 1 is equal to minus 1 and
+
+ align:start position:0%
+that epsilon 1 is equal to minus 1 and
+ 
+
+ align:start position:0%
+that epsilon 1 is equal to minus 1 and
+epsilon 2 is equal to plus 1 ok because
+
+ align:start position:0%
+epsilon 2 is equal to plus 1 ok because
+ 
+
+ align:start position:0%
+epsilon 2 is equal to plus 1 ok because
+they're disjoint events so I can break
+
+ align:start position:0%
+they're disjoint events so I can break
+ 
+
+ align:start position:0%
+they're disjoint events so I can break
+them into the sum of the two and each of
+
+ align:start position:0%
+them into the sum of the two and each of
+ 
+
+ align:start position:0%
+them into the sum of the two and each of
+those guy is also one of the you know
+
+ align:start position:0%
+those guy is also one of the you know
+ 
+
+ align:start position:0%
+those guy is also one of the you know
+atomic part of it right one of the basic
+
+ align:start position:0%
+atomic part of it right one of the basic
+ 
+
+ align:start position:0%
+atomic part of it right one of the basic
+things and so each of those guys has
+
+ align:start position:0%
+things and so each of those guys has
+ 
+
+ align:start position:0%
+things and so each of those guys has
+probability 1/4 and so here we can
+
+ align:start position:0%
+probability 1/4 and so here we can
+ 
+
+ align:start position:0%
+probability 1/4 and so here we can
+really see that we accounted for
+
+ align:start position:0%
+really see that we accounted for
+ 
+
+ align:start position:0%
+really see that we accounted for
+everything except for the case when
+
+ align:start position:0%
+everything except for the case when
+ 
+
+ align:start position:0%
+everything except for the case when
+epsilon 1 was equal to minus 1 and
+
+ align:start position:0%
+epsilon 1 was equal to minus 1 and
+ 
+
+ align:start position:0%
+epsilon 1 was equal to minus 1 and
+epsilon 2 is equal to minus 1 so this is
+
+ align:start position:0%
+epsilon 2 is equal to minus 1 so this is
+ 
+
+ align:start position:0%
+epsilon 2 is equal to minus 1 so this is
+1/4 this is 1/4 so the whole thing is
+
+ align:start position:0%
+1/4 this is 1/4 so the whole thing is
+ 
+
+ align:start position:0%
+1/4 this is 1/4 so the whole thing is
+equal to 3/4 so now what we have is that
+
+ align:start position:0%
+equal to 3/4 so now what we have is that
+ 
+
+ align:start position:0%
+equal to 3/4 so now what we have is that
+the probability that epsilon 1
+
+ align:start position:0%
+the probability that epsilon 1
+ 
+
+ align:start position:0%
+the probability that epsilon 1
+is in so the probability that theta
+
+ align:start position:0%
+is in so the probability that theta
+ 
+
+ align:start position:0%
+is in so the probability that theta
+belongs to this conference region is
+
+ align:start position:0%
+belongs to this conference region is
+ 
+
+ align:start position:0%
+belongs to this conference region is
+equal to 3/4 and that's very nice and
+
+ align:start position:0%
+equal to 3/4 and that's very nice and
+ 
+
+ align:start position:0%
+equal to 3/4 and that's very nice and
+you know but the thing is some people
+
+ align:start position:0%
+you know but the thing is some people
+ 
+
+ align:start position:0%
+you know but the thing is some people
+are sort of I mean it's not super nice
+
+ align:start position:0%
+are sort of I mean it's not super nice
+ 
+
+ align:start position:0%
+are sort of I mean it's not super nice
+to be able to say this because in a way
+
+ align:start position:0%
+to be able to say this because in a way
+ 
+
+ align:start position:0%
+to be able to say this because in a way
+I know that if I observe X 1 and X 2
+
+ align:start position:0%
+I know that if I observe X 1 and X 2
+ 
+
+ align:start position:0%
+I know that if I observe X 1 and X 2
+that are different I know for sure that
+
+ align:start position:0%
+that are different I know for sure that
+ 
+
+ align:start position:0%
+that are different I know for sure that
+X is that theta that I actually got the
+
+ align:start position:0%
+X is that theta that I actually got the
+ 
+
+ align:start position:0%
+X is that theta that I actually got the
+right data right that this confidence
+
+ align:start position:0%
+right data right that this confidence
+ 
+
+ align:start position:0%
+right data right that this confidence
+interval is actually happening at a with
+
+ align:start position:0%
+interval is actually happening at a with
+ 
+
+ align:start position:0%
+interval is actually happening at a with
+probability 1 and the problem is that I
+
+ align:start position:0%
+probability 1 and the problem is that I
+ 
+
+ align:start position:0%
+probability 1 and the problem is that I
+do not know I cannot make this precise
+
+ align:start position:0%
+do not know I cannot make this precise
+ 
+
+ align:start position:0%
+do not know I cannot make this precise
+with the notion of frequentist
+
+ align:start position:0%
+with the notion of frequentist
+ 
+
+ align:start position:0%
+with the notion of frequentist
+confidence intervals okay because
+
+ align:start position:0%
+confidence intervals okay because
+ 
+
+ align:start position:0%
+confidence intervals okay because
+frequencies conference intervals have to
+
+ align:start position:0%
+frequencies conference intervals have to
+ 
+
+ align:start position:0%
+frequencies conference intervals have to
+account for the fact that in the future
+
+ align:start position:0%
+account for the fact that in the future
+ 
+
+ align:start position:0%
+account for the fact that in the future
+it might not be the case that x1 and x2
+
+ align:start position:0%
+it might not be the case that x1 and x2
+ 
+
+ align:start position:0%
+it might not be the case that x1 and x2
+are different so Bayesian confidence
+
+ align:start position:0%
+are different so Bayesian confidence
+ 
+
+ align:start position:0%
+are different so Bayesian confidence
+regions by definition well they're all
+
+ align:start position:0%
+regions by definition well they're all
+ 
+
+ align:start position:0%
+regions by definition well they're all
+gone but they're conditioned on the data
+
+ align:start position:0%
+gone but they're conditioned on the data
+ 
+
+ align:start position:0%
+gone but they're conditioned on the data
+that I have and so that's what I want I
+
+ align:start position:0%
+that I have and so that's what I want I
+ 
+
+ align:start position:0%
+that I have and so that's what I want I
+want to be able to make a statement
+
+ align:start position:0%
+want to be able to make a statement
+ 
+
+ align:start position:0%
+want to be able to make a statement
+conditionally on the on the data that I
+
+ align:start position:0%
+conditionally on the on the data that I
+ 
+
+ align:start position:0%
+conditionally on the on the data that I
+have okay so if I want to be able to
+
+ align:start position:0%
+have okay so if I want to be able to
+ 
+
+ align:start position:0%
+have okay so if I want to be able to
+make this statement I'm gonna have to
+
+ align:start position:0%
+make this statement I'm gonna have to
+ 
+
+ align:start position:0%
+make this statement I'm gonna have to
+put if I want to build a Bayesian
+
+ align:start position:0%
+put if I want to build a Bayesian
+ 
+
+ align:start position:0%
+put if I want to build a Bayesian
+confidence region I'm gonna have to put
+
+ align:start position:0%
+confidence region I'm gonna have to put
+ 
+
+ align:start position:0%
+confidence region I'm gonna have to put
+a prior on theta so without loss of
+
+ align:start position:0%
+a prior on theta so without loss of
+ 
+
+ align:start position:0%
+a prior on theta so without loss of
+generality I mean maybe with but let's
+
+ align:start position:0%
+generality I mean maybe with but let's
+ 
+
+ align:start position:0%
+generality I mean maybe with but let's
+say assume that pi is a prior on theta
+
+ align:start position:0%
+say assume that pi is a prior on theta
+ 
+
+ align:start position:0%
+say assume that pi is a prior on theta
+and let's assume that pi of j is
+
+ align:start position:0%
+and let's assume that pi of j is
+ 
+
+ align:start position:0%
+and let's assume that pi of j is
+strictly positive for all integers J
+
+ align:start position:0%
+strictly positive for all integers J
+ 
+
+ align:start position:0%
+strictly positive for all integers J
+equals say 0 well actually for all J in
+
+ align:start position:0%
+equals say 0 well actually for all J in
+ 
+
+ align:start position:0%
+equals say 0 well actually for all J in
+the integers ok positive or negative ok
+
+ align:start position:0%
+the integers ok positive or negative ok
+ 
+
+ align:start position:0%
+the integers ok positive or negative ok
+so that's a pretty weak assumption on my
+
+ align:start position:0%
+so that's a pretty weak assumption on my
+ 
+
+ align:start position:0%
+so that's a pretty weak assumption on my
+prior I'm just saying I'm just assuming
+
+ align:start position:0%
+prior I'm just saying I'm just assuming
+ 
+
+ align:start position:0%
+prior I'm just saying I'm just assuming
+that theta is some integer and now let's
+
+ align:start position:0%
+that theta is some integer and now let's
+ 
+
+ align:start position:0%
+that theta is some integer and now let's
+build our confidence or a Bayesian
+
+ align:start position:0%
+build our confidence or a Bayesian
+ 
+
+ align:start position:0%
+build our confidence or a Bayesian
+confidence region well if I want to
+
+ align:start position:0%
+confidence region well if I want to
+ 
+
+ align:start position:0%
+confidence region well if I want to
+build a Bayesian confidence region I
+
+ align:start position:0%
+build a Bayesian confidence region I
+ 
+
+ align:start position:0%
+build a Bayesian confidence region I
+need to understand what my posterior is
+
+ align:start position:0%
+need to understand what my posterior is
+ 
+
+ align:start position:0%
+need to understand what my posterior is
+gonna be okay and if I want to
+
+ align:start position:0%
+gonna be okay and if I want to
+ 
+
+ align:start position:0%
+gonna be okay and if I want to
+understand what my posterior is gonna be
+
+ align:start position:0%
+understand what my posterior is gonna be
+ 
+
+ align:start position:0%
+understand what my posterior is gonna be
+I actually need to build
+
+ align:start position:0%
+I actually need to build
+ 
+
+ align:start position:0%
+I actually need to build
+a likelihood right so we know that it's
+
+ align:start position:0%
+a likelihood right so we know that it's
+ 
+
+ align:start position:0%
+a likelihood right so we know that it's
+the product of the likelihood and of the
+
+ align:start position:0%
+the product of the likelihood and of the
+ 
+
+ align:start position:0%
+the product of the likelihood and of the
+prior / okay so so what is my likelihood
+
+ align:start position:0%
+prior / okay so so what is my likelihood
+ 
+
+ align:start position:0%
+prior / okay so so what is my likelihood
+right so my likelihood is the
+
+ align:start position:0%
+right so my likelihood is the
+ 
+
+ align:start position:0%
+right so my likelihood is the
+probability of x1 x2 given theta right
+
+ align:start position:0%
+probability of x1 x2 given theta right
+ 
+
+ align:start position:0%
+probability of x1 x2 given theta right
+that's what the likelihood should be and
+
+ align:start position:0%
+that's what the likelihood should be and
+ 
+
+ align:start position:0%
+that's what the likelihood should be and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+now let's say that actually just to make
+
+ align:start position:0%
+now let's say that actually just to make
+ 
+
+ align:start position:0%
+now let's say that actually just to make
+things a little simpler let us assume
+
+ align:start position:0%
+things a little simpler let us assume
+ 
+
+ align:start position:0%
+things a little simpler let us assume
+that X 1 is equal to I don't know 5 and
+
+ align:start position:0%
+that X 1 is equal to I don't know 5 and
+ 
+
+ align:start position:0%
+that X 1 is equal to I don't know 5 and
+X 2 is equal to 7
+
+ align:start position:0%
+X 2 is equal to 7
+ 
+
+ align:start position:0%
+X 2 is equal to 7
+okay so this is exactly I'm not going to
+
+ align:start position:0%
+okay so this is exactly I'm not going to
+ 
+
+ align:start position:0%
+okay so this is exactly I'm not going to
+take the case where they're actually
+
+ align:start position:0%
+take the case where they're actually
+ 
+
+ align:start position:0%
+take the case where they're actually
+equal to each other because they know
+
+ align:start position:0%
+equal to each other because they know
+ 
+
+ align:start position:0%
+equal to each other because they know
+that in this case x1 and x2 are
+
+ align:start position:0%
+that in this case x1 and x2 are
+ 
+
+ align:start position:0%
+that in this case x1 and x2 are
+different I know I'm gonna actually nail
+
+ align:start position:0%
+different I know I'm gonna actually nail
+ 
+
+ align:start position:0%
+different I know I'm gonna actually nail
+exactly what data is by looking at the
+
+ align:start position:0%
+exactly what data is by looking at the
+ 
+
+ align:start position:0%
+exactly what data is by looking at the
+average of those guys right here it must
+
+ align:start position:0%
+average of those guys right here it must
+ 
+
+ align:start position:0%
+average of those guys right here it must
+be that theta is equal to 0 to 6 so what
+
+ align:start position:0%
+be that theta is equal to 0 to 6 so what
+ 
+
+ align:start position:0%
+be that theta is equal to 0 to 6 so what
+I want is to compute the likelihood at 5
+
+ align:start position:0%
+I want is to compute the likelihood at 5
+ 
+
+ align:start position:0%
+I want is to compute the likelihood at 5
+& 7
+
+ align:start position:0%
+& 7
+ 
+
+ align:start position:0%
+& 7
+okay what is this likelihood well if
+
+ align:start position:0%
+okay what is this likelihood well if
+ 
+
+ align:start position:0%
+okay what is this likelihood well if
+theta is equal to 6 that's just the
+
+ align:start position:0%
+theta is equal to 6 that's just the
+ 
+
+ align:start position:0%
+theta is equal to 6 that's just the
+probability that I observe 5 & 7 right
+
+ align:start position:0%
+probability that I observe 5 & 7 right
+ 
+
+ align:start position:0%
+probability that I observe 5 & 7 right
+so what is the probability observe 5 & 7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah one that's 1/4 right is the
+
+ align:start position:0%
+yeah one that's 1/4 right is the
+ 
+
+ align:start position:0%
+yeah one that's 1/4 right is the
+probability I have minus 1 on the first
+
+ align:start position:0%
+probability I have minus 1 on the first
+ 
+
+ align:start position:0%
+probability I have minus 1 on the first
+on the for the first epsilon 1 right so
+
+ align:start position:0%
+on the for the first epsilon 1 right so
+ 
+
+ align:start position:0%
+on the for the first epsilon 1 right so
+this is an if then a 6 this is the
+
+ align:start position:0%
+this is an if then a 6 this is the
+ 
+
+ align:start position:0%
+this is an if then a 6 this is the
+probability that epsilon 1 is equal to
+
+ align:start position:0%
+probability that epsilon 1 is equal to
+ 
+
+ align:start position:0%
+probability that epsilon 1 is equal to
+plus one a to minus 1 and epsilon 2 is
+
+ align:start position:0%
+plus one a to minus 1 and epsilon 2 is
+ 
+
+ align:start position:0%
+plus one a to minus 1 and epsilon 2 is
+equal to plus 1 which is equal to 1/4 so
+
+ align:start position:0%
+equal to plus 1 which is equal to 1/4 so
+ 
+
+ align:start position:0%
+equal to plus 1 which is equal to 1/4 so
+this probability is 1/4 if theta is
+
+ align:start position:0%
+this probability is 1/4 if theta is
+ 
+
+ align:start position:0%
+this probability is 1/4 if theta is
+different from 6 what is this
+
+ align:start position:0%
+different from 6 what is this
+ 
+
+ align:start position:0%
+different from 6 what is this
+probability so if theta is different
+
+ align:start position:0%
+probability so if theta is different
+ 
+
+ align:start position:0%
+probability so if theta is different
+from 6 since we know that we've only
+
+ align:start position:0%
+from 6 since we know that we've only
+ 
+
+ align:start position:0%
+from 6 since we know that we've only
+loaded the integers right so theta has
+
+ align:start position:0%
+loaded the integers right so theta has
+ 
+
+ align:start position:0%
+loaded the integers right so theta has
+to be another integer what is the
+
+ align:start position:0%
+to be another integer what is the
+ 
+
+ align:start position:0%
+to be another integer what is the
+probability that I see 5 and 7 0 so
+
+ align:start position:0%
+probability that I see 5 and 7 0 so
+ 
+
+ align:start position:0%
+probability that I see 5 and 7 0 so
+that's my likelihood and if I want to
+
+ align:start position:0%
+that's my likelihood and if I want to
+ 
+
+ align:start position:0%
+that's my likelihood and if I want to
+know what my posterior is well it's just
+
+ align:start position:0%
+know what my posterior is well it's just
+ 
+
+ align:start position:0%
+know what my posterior is well it's just
+pi of theta times P of 5 6 given theta
+
+ align:start position:0%
+pi of theta times P of 5 6 given theta
+ 
+
+ align:start position:0%
+pi of theta times P of 5 6 given theta
+divided by the sum over all cheese say
+
+ align:start position:0%
+divided by the sum over all cheese say
+ 
+
+ align:start position:0%
+divided by the sum over all cheese say
+in Z all right so now I just need to
+
+ align:start position:0%
+in Z all right so now I just need to
+ 
+
+ align:start position:0%
+in Z all right so now I just need to
+normalize this thing so of PI of T P of
+
+ align:start position:0%
+normalize this thing so of PI of T P of
+ 
+
+ align:start position:0%
+normalize this thing so of PI of T P of
+5 6 given T agree that's just the
+
+ align:start position:0%
+5 6 given T agree that's just the
+ 
+
+ align:start position:0%
+5 6 given T agree that's just the
+definition of the posterior but when I
+
+ align:start position:0%
+definition of the posterior but when I
+ 
+
+ align:start position:0%
+definition of the posterior but when I
+sum these guys there's only one that
+
+ align:start position:0%
+sum these guys there's only one that
+ 
+
+ align:start position:0%
+sum these guys there's only one that
+counts because for those things we know
+
+ align:start position:0%
+counts because for those things we know
+ 
+
+ align:start position:0%
+counts because for those things we know
+that this is actually equal to 0 for
+
+ align:start position:0%
+that this is actually equal to 0 for
+ 
+
+ align:start position:0%
+that this is actually equal to 0 for
+every T except for when T is equal to 6
+
+ align:start position:0%
+every T except for when T is equal to 6
+ 
+
+ align:start position:0%
+every T except for when T is equal to 6
+so this entire sum here is actually
+
+ align:start position:0%
+so this entire sum here is actually
+ 
+
+ align:start position:0%
+so this entire sum here is actually
+equal to PI of 6 times P of 5 6
+
+ align:start position:0%
+equal to PI of 6 times P of 5 6
+ 
+
+ align:start position:0%
+equal to PI of 6 times P of 5 6
+sorry 5 7 of 5 7
+
+ align:start position:0%
+sorry 5 7 of 5 7
+ 
+
+ align:start position:0%
+sorry 5 7 of 5 7
+given that I see given that theta is
+
+ align:start position:0%
+given that I see given that theta is
+ 
+
+ align:start position:0%
+given that I see given that theta is
+equal to 6 which we know is equal to 1/4
+
+ align:start position:0%
+equal to 6 which we know is equal to 1/4
+ 
+
+ align:start position:0%
+equal to 6 which we know is equal to 1/4
+and I did not tell you what PI of 6 was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but it's the same thing here the
+
+ align:start position:0%
+but it's the same thing here the
+ 
+
+ align:start position:0%
+but it's the same thing here the
+posterior foresee any theater that's not
+
+ align:start position:0%
+posterior foresee any theater that's not
+ 
+
+ align:start position:0%
+posterior foresee any theater that's not
+six is actually gonna be this guy is
+
+ align:start position:0%
+six is actually gonna be this guy is
+ 
+
+ align:start position:0%
+six is actually gonna be this guy is
+going to be equal to zero so I really
+
+ align:start position:0%
+going to be equal to zero so I really
+ 
+
+ align:start position:0%
+going to be equal to zero so I really
+don't care what this guy is so what it
+
+ align:start position:0%
+don't care what this guy is so what it
+ 
+
+ align:start position:0%
+don't care what this guy is so what it
+means is that my posterior becomes what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it becomes so posterior PI of theta
+
+ align:start position:0%
+it becomes so posterior PI of theta
+ 
+
+ align:start position:0%
+it becomes so posterior PI of theta
+given five and seven is equal to well
+
+ align:start position:0%
+given five and seven is equal to well
+ 
+
+ align:start position:0%
+given five and seven is equal to well
+when theta is equal to is not equal to 6
+
+ align:start position:0%
+when theta is equal to is not equal to 6
+ 
+
+ align:start position:0%
+when theta is equal to is not equal to 6
+this is actually 0 so we regardless of
+
+ align:start position:0%
+this is actually 0 so we regardless of
+ 
+
+ align:start position:0%
+this is actually 0 so we regardless of
+what I do here I get something which is
+
+ align:start position:0%
+what I do here I get something which is
+ 
+
+ align:start position:0%
+what I do here I get something which is
+0 and if theta is equal to 6 what I get
+
+ align:start position:0%
+0 and if theta is equal to 6 what I get
+ 
+
+ align:start position:0%
+0 and if theta is equal to 6 what I get
+is PI of 6 times P of 5 7 given 6 which
+
+ align:start position:0%
+is PI of 6 times P of 5 7 given 6 which
+ 
+
+ align:start position:0%
+is PI of 6 times P of 5 7 given 6 which
+have just computed here which is 1/4
+
+ align:start position:0%
+have just computed here which is 1/4
+ 
+
+ align:start position:0%
+have just computed here which is 1/4
+divided by PI of 6 the times 1/4 so it's
+
+ align:start position:0%
+divided by PI of 6 the times 1/4 so it's
+ 
+
+ align:start position:0%
+divided by PI of 6 the times 1/4 so it's
+the ratio of two things that are
+
+ align:start position:0%
+the ratio of two things that are
+ 
+
+ align:start position:0%
+the ratio of two things that are
+identical so I get 1 so now my posterior
+
+ align:start position:0%
+identical so I get 1 so now my posterior
+ 
+
+ align:start position:0%
+identical so I get 1 so now my posterior
+tells me that given that I observe 5 and
+
+ align:start position:0%
+tells me that given that I observe 5 and
+ 
+
+ align:start position:0%
+tells me that given that I observe 5 and
+7 the theta is giving me it has to be 1
+
+ align:start position:0%
+7 the theta is giving me it has to be 1
+ 
+
+ align:start position:0%
+7 the theta is giving me it has to be 1
+with probability 6 with probability 1 so
+
+ align:start position:0%
+with probability 6 with probability 1 so
+ 
+
+ align:start position:0%
+with probability 6 with probability 1 so
+now I sort of say that this thing here
+
+ align:start position:0%
+now I sort of say that this thing here
+ 
+
+ align:start position:0%
+now I sort of say that this thing here
+so now I can act this is not something
+
+ align:start position:0%
+so now I can act this is not something
+ 
+
+ align:start position:0%
+so now I can act this is not something
+that actually makes sense
+
+ align:start position:0%
+that actually makes sense
+ 
+
+ align:start position:0%
+that actually makes sense
+when I talk about frequentist confidence
+
+ align:start position:0%
+when I talk about frequentist confidence
+ 
+
+ align:start position:0%
+when I talk about frequentist confidence
+intervals I cannot really they don't
+
+ align:start position:0%
+intervals I cannot really they don't
+ 
+
+ align:start position:0%
+intervals I cannot really they don't
+really make sense to talk about
+
+ align:start position:0%
+really make sense to talk about
+ 
+
+ align:start position:0%
+really make sense to talk about
+confidence intervals given something and
+
+ align:start position:0%
+confidence intervals given something and
+ 
+
+ align:start position:0%
+confidence intervals given something and
+so now given that I observed 5 and 7 I
+
+ align:start position:0%
+so now given that I observed 5 and 7 I
+ 
+
+ align:start position:0%
+so now given that I observed 5 and 7 I
+know that the probability of data is
+
+ align:start position:0%
+know that the probability of data is
+ 
+
+ align:start position:0%
+know that the probability of data is
+equal to 1 and in this sense the
+
+ align:start position:0%
+equal to 1 and in this sense the
+ 
+
+ align:start position:0%
+equal to 1 and in this sense the
+Bayesian confidence interval is actually
+
+ align:start position:0%
+Bayesian confidence interval is actually
+ 
+
+ align:start position:0%
+Bayesian confidence interval is actually
+more meaningful so one thing I want to
+
+ align:start position:0%
+more meaningful so one thing I want to
+ 
+
+ align:start position:0%
+more meaningful so one thing I want to
+actually say about this Bayesian
+
+ align:start position:0%
+actually say about this Bayesian
+ 
+
+ align:start position:0%
+actually say about this Bayesian
+confidence interval is that it's it's I
+
+ align:start position:0%
+confidence interval is that it's it's I
+ 
+
+ align:start position:0%
+confidence interval is that it's it's I
+mean here it's equal to the value 1
+
+ align:start position:0%
+mean here it's equal to the value 1
+ 
+
+ align:start position:0%
+mean here it's equal to the value 1
+right so it really encompasses the thing
+
+ align:start position:0%
+right so it really encompasses the thing
+ 
+
+ align:start position:0%
+right so it really encompasses the thing
+that we want but the fact that we
+
+ align:start position:0%
+that we want but the fact that we
+ 
+
+ align:start position:0%
+that we want but the fact that we
+actually computed it using the Bayesian
+
+ align:start position:0%
+actually computed it using the Bayesian
+ 
+
+ align:start position:0%
+actually computed it using the Bayesian
+posterior and the Bayesian rule did not
+
+ align:start position:0%
+posterior and the Bayesian rule did not
+ 
+
+ align:start position:0%
+posterior and the Bayesian rule did not
+really matter for this argument all I
+
+ align:start position:0%
+really matter for this argument all I
+ 
+
+ align:start position:0%
+really matter for this argument all I
+just said it with it had a prior but
+
+ align:start position:0%
+just said it with it had a prior but
+ 
+
+ align:start position:0%
+just said it with it had a prior but
+just what I want to illustrate is the
+
+ align:start position:0%
+just what I want to illustrate is the
+ 
+
+ align:start position:0%
+just what I want to illustrate is the
+fact that we can actually give a meaning
+
+ align:start position:0%
+fact that we can actually give a meaning
+ 
+
+ align:start position:0%
+fact that we can actually give a meaning
+to the probability of that theta is
+
+ align:start position:0%
+to the probability of that theta is
+ 
+
+ align:start position:0%
+to the probability of that theta is
+equal to 6 given that I see 5 & 7
+
+ align:start position:0%
+equal to 6 given that I see 5 & 7
+ 
+
+ align:start position:0%
+equal to 6 given that I see 5 & 7
+whereas we do not really in the other
+
+ align:start position:0%
+whereas we do not really in the other
+ 
+
+ align:start position:0%
+whereas we do not really in the other
+cases and we don't have to be
+
+ align:start position:0%
+cases and we don't have to be
+ 
+
+ align:start position:0%
+cases and we don't have to be
+particularly precise in the prior on
+
+ align:start position:0%
+particularly precise in the prior on
+ 
+
+ align:start position:0%
+particularly precise in the prior on
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+to be able to give data this to give
+
+ align:start position:0%
+to be able to give data this to give
+ 
+
+ align:start position:0%
+to be able to give data this to give
+this meeting okay all right so now as I
+
+ align:start position:0%
+this meeting okay all right so now as I
+ 
+
+ align:start position:0%
+this meeting okay all right so now as I
+said I think the main power of Bayesian
+
+ align:start position:0%
+said I think the main power of Bayesian
+ 
+
+ align:start position:0%
+said I think the main power of Bayesian
+inference is that it spits out the
+
+ align:start position:0%
+inference is that it spits out the
+ 
+
+ align:start position:0%
+inference is that it spits out the
+posterior distribution and not just a
+
+ align:start position:0%
+posterior distribution and not just a
+ 
+
+ align:start position:0%
+posterior distribution and not just a
+single number like frequentist would
+
+ align:start position:0%
+single number like frequentist would
+ 
+
+ align:start position:0%
+single number like frequentist would
+give you then you know we can say
+
+ align:start position:0%
+give you then you know we can say
+ 
+
+ align:start position:0%
+give you then you know we can say
+decorate our theta hat or point estimate
+
+ align:start position:0%
+decorate our theta hat or point estimate
+ 
+
+ align:start position:0%
+decorate our theta hat or point estimate
+with maybe some confidence interval
+
+ align:start position:0%
+with maybe some confidence interval
+ 
+
+ align:start position:0%
+with maybe some confidence interval
+maybe we can do a bunch of tests but at
+
+ align:start position:0%
+maybe we can do a bunch of tests but at
+ 
+
+ align:start position:0%
+maybe we can do a bunch of tests but at
+the end of the day we just have
+
+ align:start position:0%
+the end of the day we just have
+ 
+
+ align:start position:0%
+the end of the day we just have
+essentially one number all right and
+
+ align:start position:0%
+essentially one number all right and
+ 
+
+ align:start position:0%
+essentially one number all right and
+maybe we can sort of understand what the
+
+ align:start position:0%
+maybe we can sort of understand what the
+ 
+
+ align:start position:0%
+maybe we can sort of understand what the
+fluctuations of this number are in a
+
+ align:start position:0%
+fluctuations of this number are in a
+ 
+
+ align:start position:0%
+fluctuations of this number are in a
+frequentist set up but but the Bayesian
+
+ align:start position:0%
+frequentist set up but but the Bayesian
+ 
+
+ align:start position:0%
+frequentist set up but but the Bayesian
+framework is essentially giving you a
+
+ align:start position:0%
+framework is essentially giving you a
+ 
+
+ align:start position:0%
+framework is essentially giving you a
+natural method and you can interpret it
+
+ align:start position:0%
+natural method and you can interpret it
+ 
+
+ align:start position:0%
+natural method and you can interpret it
+in terms of the probabilities that are
+
+ align:start position:0%
+in terms of the probabilities that are
+ 
+
+ align:start position:0%
+in terms of the probabilities that are
+associated to the prior but you can
+
+ align:start position:0%
+associated to the prior but you can
+ 
+
+ align:start position:0%
+associated to the prior but you can
+actually also try to make some right so
+
+ align:start position:0%
+actually also try to make some right so
+ 
+
+ align:start position:0%
+actually also try to make some right so
+a vision if you give me any prior you're
+
+ align:start position:0%
+a vision if you give me any prior you're
+ 
+
+ align:start position:0%
+a vision if you give me any prior you're
+gonna actually build an estimator from
+
+ align:start position:0%
+gonna actually build an estimator from
+ 
+
+ align:start position:0%
+gonna actually build an estimator from
+this fryer maybe from the posterior and
+
+ align:start position:0%
+this fryer maybe from the posterior and
+ 
+
+ align:start position:0%
+this fryer maybe from the posterior and
+maybe it's gonna have some frequencies
+
+ align:start position:0%
+maybe it's gonna have some frequencies
+ 
+
+ align:start position:0%
+maybe it's gonna have some frequencies
+properties and that's what's really nice
+
+ align:start position:0%
+properties and that's what's really nice
+ 
+
+ align:start position:0%
+properties and that's what's really nice
+about visions is that you can actually
+
+ align:start position:0%
+about visions is that you can actually
+ 
+
+ align:start position:0%
+about visions is that you can actually
+try to give some frequencies properties
+
+ align:start position:0%
+try to give some frequencies properties
+ 
+
+ align:start position:0%
+try to give some frequencies properties
+of Bayesian with methods that are built
+
+ align:start position:0%
+of Bayesian with methods that are built
+ 
+
+ align:start position:0%
+of Bayesian with methods that are built
+using Bayesian methodology but you
+
+ align:start position:0%
+using Bayesian methodology but you
+ 
+
+ align:start position:0%
+using Bayesian methodology but you
+cannot really go the other way around if
+
+ align:start position:0%
+cannot really go the other way around if
+ 
+
+ align:start position:0%
+cannot really go the other way around if
+I give you a frequencies methodology how
+
+ align:start position:0%
+I give you a frequencies methodology how
+ 
+
+ align:start position:0%
+I give you a frequencies methodology how
+are you gonna say something about the
+
+ align:start position:0%
+are you gonna say something about the
+ 
+
+ align:start position:0%
+are you gonna say something about the
+fact that you know the Prai there's a
+
+ align:start position:0%
+fact that you know the Prai there's a
+ 
+
+ align:start position:0%
+fact that you know the Prai there's a
+prior going on etc and so this is
+
+ align:start position:0%
+prior going on etc and so this is
+ 
+
+ align:start position:0%
+prior going on etc and so this is
+actually one of the things there's
+
+ align:start position:0%
+actually one of the things there's
+ 
+
+ align:start position:0%
+actually one of the things there's
+actually some research that's going on
+
+ align:start position:0%
+actually some research that's going on
+ 
+
+ align:start position:0%
+actually some research that's going on
+for this they call it a Bayesian a
+
+ align:start position:0%
+for this they call it a Bayesian a
+ 
+
+ align:start position:0%
+for this they call it a Bayesian a
+posterior concentration and one of the
+
+ align:start position:0%
+posterior concentration and one of the
+ 
+
+ align:start position:0%
+posterior concentration and one of the
+things so there's something called the
+
+ align:start position:0%
+things so there's something called the
+ 
+
+ align:start position:0%
+things so there's something called the
+Bernstein von Mises theorem and those
+
+ align:start position:0%
+Bernstein von Mises theorem and those
+ 
+
+ align:start position:0%
+Bernstein von Mises theorem and those
+are class of theorems and those are
+
+ align:start position:0%
+are class of theorems and those are
+ 
+
+ align:start position:0%
+are class of theorems and those are
+essentially methods that tell you well
+
+ align:start position:0%
+essentially methods that tell you well
+ 
+
+ align:start position:0%
+essentially methods that tell you well
+if I actually run a Bayesian method and
+
+ align:start position:0%
+if I actually run a Bayesian method and
+ 
+
+ align:start position:0%
+if I actually run a Bayesian method and
+I look at the posterior that I get right
+
+ align:start position:0%
+I look at the posterior that I get right
+ 
+
+ align:start position:0%
+I look at the posterior that I get right
+it's gonna be something like this but
+
+ align:start position:0%
+it's gonna be something like this but
+ 
+
+ align:start position:0%
+it's gonna be something like this but
+now I try to study this in a frequentist
+
+ align:start position:0%
+now I try to study this in a frequentist
+ 
+
+ align:start position:0%
+now I try to study this in a frequentist
+point of view there's actually a true
+
+ align:start position:0%
+point of view there's actually a true
+ 
+
+ align:start position:0%
+point of view there's actually a true
+parameter theta somewhere the true one
+
+ align:start position:0%
+parameter theta somewhere the true one
+ 
+
+ align:start position:0%
+parameter theta somewhere the true one
+there's no prior for this guy this is
+
+ align:start position:0%
+there's no prior for this guy this is
+ 
+
+ align:start position:0%
+there's no prior for this guy this is
+just one fixed number is it true that as
+
+ align:start position:0%
+just one fixed number is it true that as
+ 
+
+ align:start position:0%
+just one fixed number is it true that as
+my sample size is going to go to
+
+ align:start position:0%
+my sample size is going to go to
+ 
+
+ align:start position:0%
+my sample size is going to go to
+infinity then this thing is going to
+
+ align:start position:0%
+infinity then this thing is going to
+ 
+
+ align:start position:0%
+infinity then this thing is going to
+concentrate around theta and the rate of
+
+ align:start position:0%
+concentrate around theta and the rate of
+ 
+
+ align:start position:0%
+concentrate around theta and the rate of
+concentration of this thing the size of
+
+ align:start position:0%
+concentration of this thing the size of
+ 
+
+ align:start position:0%
+concentration of this thing the size of
+this with the standard deviation of this
+
+ align:start position:0%
+this with the standard deviation of this
+ 
+
+ align:start position:0%
+this with the standard deviation of this
+thing is something that should decay
+
+ align:start position:0%
+thing is something that should decay
+ 
+
+ align:start position:0%
+thing is something that should decay
+maybe like 1 over square root of N or
+
+ align:start position:0%
+maybe like 1 over square root of N or
+ 
+
+ align:start position:0%
+maybe like 1 over square root of N or
+something like this and the rate of
+
+ align:start position:0%
+something like this and the rate of
+ 
+
+ align:start position:0%
+something like this and the rate of
+posterior concentration
+
+ align:start position:0%
+posterior concentration
+ 
+
+ align:start position:0%
+posterior concentration
+when you characterize it is called the
+
+ align:start position:0%
+when you characterize it is called the
+ 
+
+ align:start position:0%
+when you characterize it is called the
+Bernstein when mesosphere and so people
+
+ align:start position:0%
+Bernstein when mesosphere and so people
+ 
+
+ align:start position:0%
+Bernstein when mesosphere and so people
+are looking at this in some
+
+ align:start position:0%
+are looking at this in some
+ 
+
+ align:start position:0%
+are looking at this in some
+nonparametric cases you can do it in
+
+ align:start position:0%
+nonparametric cases you can do it in
+ 
+
+ align:start position:0%
+nonparametric cases you can do it in
+pretty much everything we've been doing
+
+ align:start position:0%
+pretty much everything we've been doing
+ 
+
+ align:start position:0%
+pretty much everything we've been doing
+before right you can do it for you know
+
+ align:start position:0%
+before right you can do it for you know
+ 
+
+ align:start position:0%
+before right you can do it for you know
+nonparametric regression estimation or
+
+ align:start position:0%
+nonparametric regression estimation or
+ 
+
+ align:start position:0%
+nonparametric regression estimation or
+density estimation you can do it for of
+
+ align:start position:0%
+density estimation you can do it for of
+ 
+
+ align:start position:0%
+density estimation you can do it for of
+course you can do it for sparse
+
+ align:start position:0%
+course you can do it for sparse
+ 
+
+ align:start position:0%
+course you can do it for sparse
+estimation if you want okay so you can
+
+ align:start position:0%
+estimation if you want okay so you can
+ 
+
+ align:start position:0%
+estimation if you want okay so you can
+actually compute the posterior and and
+
+ align:start position:0%
+actually compute the posterior and and
+ 
+
+ align:start position:0%
+actually compute the posterior and and
+and and and and and yeah and so you can
+
+ align:start position:0%
+and and and and and yeah and so you can
+ 
+
+ align:start position:0%
+and and and and and yeah and so you can
+think of it as being just a method
+
+ align:start position:0%
+think of it as being just a method
+ 
+
+ align:start position:0%
+think of it as being just a method
+somehow now the estimator I'm talking
+
+ align:start position:0%
+somehow now the estimator I'm talking
+ 
+
+ align:start position:0%
+somehow now the estimator I'm talking
+about so that's just the general
+
+ align:start position:0%
+about so that's just the general
+ 
+
+ align:start position:0%
+about so that's just the general
+Bayesian posterior concentration but you
+
+ align:start position:0%
+Bayesian posterior concentration but you
+ 
+
+ align:start position:0%
+Bayesian posterior concentration but you
+can also try to understand what is the
+
+ align:start position:0%
+can also try to understand what is the
+ 
+
+ align:start position:0%
+can also try to understand what is the
+property of something that's extracted
+
+ align:start position:0%
+property of something that's extracted
+ 
+
+ align:start position:0%
+property of something that's extracted
+from this posterior and one thing that
+
+ align:start position:0%
+from this posterior and one thing that
+ 
+
+ align:start position:0%
+from this posterior and one thing that
+we actually described was for example
+
+ align:start position:0%
+we actually described was for example
+ 
+
+ align:start position:0%
+we actually described was for example
+well given this guy maybe it's a good
+
+ align:start position:0%
+well given this guy maybe it's a good
+ 
+
+ align:start position:0%
+well given this guy maybe it's a good
+idea to think about what the mean of
+
+ align:start position:0%
+idea to think about what the mean of
+ 
+
+ align:start position:0%
+idea to think about what the mean of
+this thing is right so there's gonna be
+
+ align:start position:0%
+this thing is right so there's gonna be
+ 
+
+ align:start position:0%
+this thing is right so there's gonna be
+some theta hat which is just the
+
+ align:start position:0%
+some theta hat which is just the
+ 
+
+ align:start position:0%
+some theta hat which is just the
+integral of theta pi theta given X 1 xn
+
+ align:start position:0%
+integral of theta pi theta given X 1 xn
+ 
+
+ align:start position:0%
+integral of theta pi theta given X 1 xn
+so that's my posterior D theta right so
+
+ align:start position:0%
+so that's my posterior D theta right so
+ 
+
+ align:start position:0%
+so that's my posterior D theta right so
+that's the posterior mean that's the
+
+ align:start position:0%
+that's the posterior mean that's the
+ 
+
+ align:start position:0%
+that's the posterior mean that's the
+expected value with respect to the
+
+ align:start position:0%
+expected value with respect to the
+ 
+
+ align:start position:0%
+expected value with respect to the
+posterior distribution and I want to
+
+ align:start position:0%
+posterior distribution and I want to
+ 
+
+ align:start position:0%
+posterior distribution and I want to
+know how does this thing behave how
+
+ align:start position:0%
+know how does this thing behave how
+ 
+
+ align:start position:0%
+know how does this thing behave how
+close it is to a true theta if I
+
+ align:start position:0%
+close it is to a true theta if I
+ 
+
+ align:start position:0%
+close it is to a true theta if I
+actually arm if I'm in a frequency setup
+
+ align:start position:0%
+actually arm if I'm in a frequency setup
+ 
+
+ align:start position:0%
+actually arm if I'm in a frequency setup
+so that's the posterior mean but this is
+
+ align:start position:0%
+so that's the posterior mean but this is
+ 
+
+ align:start position:0%
+so that's the posterior mean but this is
+not the only thing I can actually spit
+
+ align:start position:0%
+not the only thing I can actually spit
+ 
+
+ align:start position:0%
+not the only thing I can actually spit
+out right this is definitely uniquely
+
+ align:start position:0%
+out right this is definitely uniquely
+ 
+
+ align:start position:0%
+out right this is definitely uniquely
+defined if you give me a distribution I
+
+ align:start position:0%
+defined if you give me a distribution I
+ 
+
+ align:start position:0%
+defined if you give me a distribution I
+can actually spit out its posterior mean
+
+ align:start position:0%
+can actually spit out its posterior mean
+ 
+
+ align:start position:0%
+can actually spit out its posterior mean
+but I can also think of the posterior
+
+ align:start position:0%
+but I can also think of the posterior
+ 
+
+ align:start position:0%
+but I can also think of the posterior
+median but now if this is not continuous
+
+ align:start position:0%
+median but now if this is not continuous
+ 
+
+ align:start position:0%
+median but now if this is not continuous
+you might have some uncertainty maybe
+
+ align:start position:0%
+you might have some uncertainty maybe
+ 
+
+ align:start position:0%
+you might have some uncertainty maybe
+the median is not uniquely defined and
+
+ align:start position:0%
+the median is not uniquely defined and
+ 
+
+ align:start position:0%
+the median is not uniquely defined and
+so maybe that's not something you use as
+
+ align:start position:0%
+so maybe that's not something you use as
+ 
+
+ align:start position:0%
+so maybe that's not something you use as
+much maybe you can actually talk about
+
+ align:start position:0%
+much maybe you can actually talk about
+ 
+
+ align:start position:0%
+much maybe you can actually talk about
+the posterior mode alright so for
+
+ align:start position:0%
+the posterior mode alright so for
+ 
+
+ align:start position:0%
+the posterior mode alright so for
+example if your posterior density looks
+
+ align:start position:0%
+example if your posterior density looks
+ 
+
+ align:start position:0%
+example if your posterior density looks
+like this then maybe you just want to
+
+ align:start position:0%
+like this then maybe you just want to
+ 
+
+ align:start position:0%
+like this then maybe you just want to
+summarize your posterior with this
+
+ align:start position:0%
+summarize your posterior with this
+ 
+
+ align:start position:0%
+summarize your posterior with this
+number so clearly in this case it's not
+
+ align:start position:0%
+number so clearly in this case it's not
+ 
+
+ align:start position:0%
+number so clearly in this case it's not
+such a good idea because you completely
+
+ align:start position:0%
+such a good idea because you completely
+ 
+
+ align:start position:0%
+such a good idea because you completely
+forget about this mode but maybe that's
+
+ align:start position:0%
+forget about this mode but maybe that's
+ 
+
+ align:start position:0%
+forget about this mode but maybe that's
+what you want to do maybe you want to
+
+ align:start position:0%
+what you want to do maybe you want to
+ 
+
+ align:start position:0%
+what you want to do maybe you want to
+focus on the most peak mode and this is
+
+ align:start position:0%
+focus on the most peak mode and this is
+ 
+
+ align:start position:0%
+focus on the most peak mode and this is
+actually called max maximum is a
+
+ align:start position:0%
+actually called max maximum is a
+ 
+
+ align:start position:0%
+actually called max maximum is a
+posterior
+
+ align:start position:0%
+posterior
+ 
+
+ align:start position:0%
+posterior
+as I said you maybe you want to sample
+
+ align:start position:0%
+as I said you maybe you want to sample
+ 
+
+ align:start position:0%
+as I said you maybe you want to sample
+from this posterior distribution okay
+
+ align:start position:0%
+from this posterior distribution okay
+ 
+
+ align:start position:0%
+from this posterior distribution okay
+and so in all these cases this Bayesian
+
+ align:start position:0%
+and so in all these cases this Bayesian
+ 
+
+ align:start position:0%
+and so in all these cases this Bayesian
+estimators will depend on the prior
+
+ align:start position:0%
+estimators will depend on the prior
+ 
+
+ align:start position:0%
+estimators will depend on the prior
+distribution and the hope is that as the
+
+ align:start position:0%
+distribution and the hope is that as the
+ 
+
+ align:start position:0%
+distribution and the hope is that as the
+sample size grows you won't see that
+
+ align:start position:0%
+sample size grows you won't see that
+ 
+
+ align:start position:0%
+sample size grows you won't see that
+again okay so to conclude let's just do
+
+ align:start position:0%
+again okay so to conclude let's just do
+ 
+
+ align:start position:0%
+again okay so to conclude let's just do
+a couple of experiments right so if I
+
+ align:start position:0%
+a couple of experiments right so if I
+ 
+
+ align:start position:0%
+a couple of experiments right so if I
+look at did we do this yeah so for
+
+ align:start position:0%
+look at did we do this yeah so for
+ 
+
+ align:start position:0%
+look at did we do this yeah so for
+example so let's focus on the posterior
+
+ align:start position:0%
+example so let's focus on the posterior
+ 
+
+ align:start position:0%
+example so let's focus on the posterior
+mean and we know so remember in an
+
+ align:start position:0%
+mean and we know so remember in an
+ 
+
+ align:start position:0%
+mean and we know so remember in an
+experiment one answering the example one
+
+ align:start position:0%
+experiment one answering the example one
+ 
+
+ align:start position:0%
+experiment one answering the example one
+what we had was X 1 X n that were iid
+
+ align:start position:0%
+what we had was X 1 X n that were iid
+ 
+
+ align:start position:0%
+what we had was X 1 X n that were iid
+bernal EP and the prior I put on PI on P
+
+ align:start position:0%
+bernal EP and the prior I put on PI on P
+ 
+
+ align:start position:0%
+bernal EP and the prior I put on PI on P
+was a beta with parameter AAA okay and
+
+ align:start position:0%
+was a beta with parameter AAA okay and
+ 
+
+ align:start position:0%
+was a beta with parameter AAA okay and
+if I go back to what we computed you can
+
+ align:start position:0%
+if I go back to what we computed you can
+ 
+
+ align:start position:0%
+if I go back to what we computed you can
+actually compute the posterior of this
+
+ align:start position:0%
+actually compute the posterior of this
+ 
+
+ align:start position:0%
+actually compute the posterior of this
+thing and we know that it's actually
+
+ align:start position:0%
+thing and we know that it's actually
+ 
+
+ align:start position:0%
+thing and we know that it's actually
+gonna be sorry that was uniform worse
+
+ align:start position:0%
+gonna be sorry that was uniform worse
+ 
+
+ align:start position:0%
+gonna be sorry that was uniform worse
+yeah so what we get is that the
+
+ align:start position:0%
+yeah so what we get is that the
+ 
+
+ align:start position:0%
+yeah so what we get is that the
+posterior this thing is actually going
+
+ align:start position:0%
+posterior this thing is actually going
+ 
+
+ align:start position:0%
+posterior this thing is actually going
+to be a beta with parameter a plus the
+
+ align:start position:0%
+to be a beta with parameter a plus the
+ 
+
+ align:start position:0%
+to be a beta with parameter a plus the
+sum so a plus the number of ones and a
+
+ align:start position:0%
+sum so a plus the number of ones and a
+ 
+
+ align:start position:0%
+sum so a plus the number of ones and a
+plus the number of zeros okay and the
+
+ align:start position:0%
+plus the number of zeros okay and the
+ 
+
+ align:start position:0%
+plus the number of zeros okay and the
+posterior the beta was just something
+
+ align:start position:0%
+posterior the beta was just something
+ 
+
+ align:start position:0%
+posterior the beta was just something
+that looked like the density was P to
+
+ align:start position:0%
+that looked like the density was P to
+ 
+
+ align:start position:0%
+that looked like the density was P to
+the a minus 1 1 minus P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I want to understand the
+
+ align:start position:0%
+okay so if I want to understand the
+ 
+
+ align:start position:0%
+okay so if I want to understand the
+posterior mean I need to be able to
+
+ align:start position:0%
+posterior mean I need to be able to
+ 
+
+ align:start position:0%
+posterior mean I need to be able to
+compute the expectation of a beta and
+
+ align:start position:0%
+compute the expectation of a beta and
+ 
+
+ align:start position:0%
+compute the expectation of a beta and
+then maybe plug in a for a plus this guy
+
+ align:start position:0%
+then maybe plug in a for a plus this guy
+ 
+
+ align:start position:0%
+then maybe plug in a for a plus this guy
+a minus this guy okay so actually let me
+
+ align:start position:0%
+a minus this guy okay so actually let me
+ 
+
+ align:start position:0%
+a minus this guy okay so actually let me
+do this okay so what is the expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I want is something that looks
+
+ align:start position:0%
+so what I want is something that looks
+ 
+
+ align:start position:0%
+so what I want is something that looks
+like the integral between 0 and 1 of P
+
+ align:start position:0%
+like the integral between 0 and 1 of P
+ 
+
+ align:start position:0%
+like the integral between 0 and 1 of P
+times a minus 1 sorry P times P a minus
+
+ align:start position:0%
+times a minus 1 sorry P times P a minus
+ 
+
+ align:start position:0%
+times a minus 1 sorry P times P a minus
+1 1 minus P B minus 1 do we agree that
+
+ align:start position:0%
+1 1 minus P B minus 1 do we agree that
+ 
+
+ align:start position:0%
+1 1 minus P B minus 1 do we agree that
+this and then there's a normalizing
+
+ align:start position:0%
+this and then there's a normalizing
+ 
+
+ align:start position:0%
+this and then there's a normalizing
+constant let's call it C okay so this is
+
+ align:start position:0%
+constant let's call it C okay so this is
+ 
+
+ align:start position:0%
+constant let's call it C okay so this is
+what I need to compute so that's C of a
+
+ align:start position:0%
+what I need to compute so that's C of a
+ 
+
+ align:start position:0%
+what I need to compute so that's C of a
+and B do we agree that this is the
+
+ align:start position:0%
+and B do we agree that this is the
+ 
+
+ align:start position:0%
+and B do we agree that this is the
+posterior mean with respect to a beta
+
+ align:start position:0%
+posterior mean with respect to a beta
+ 
+
+ align:start position:0%
+posterior mean with respect to a beta
+with parameters a and B right I just
+
+ align:start position:0%
+with parameters a and B right I just
+ 
+
+ align:start position:0%
+with parameters a and B right I just
+integrate P against the density so what
+
+ align:start position:0%
+integrate P against the density so what
+ 
+
+ align:start position:0%
+integrate P against the density so what
+does this thing look like well I can
+
+ align:start position:0%
+does this thing look like well I can
+ 
+
+ align:start position:0%
+does this thing look like well I can
+actually move this guy in here and here
+
+ align:start position:0%
+actually move this guy in here and here
+ 
+
+ align:start position:0%
+actually move this guy in here and here
+I'm going to have a plus 1 minus 1 okay
+
+ align:start position:0%
+I'm going to have a plus 1 minus 1 okay
+ 
+
+ align:start position:0%
+I'm going to have a plus 1 minus 1 okay
+so the problem is that this thing is
+
+ align:start position:0%
+so the problem is that this thing is
+ 
+
+ align:start position:0%
+so the problem is that this thing is
+actually the constant is going to play a
+
+ align:start position:0%
+actually the constant is going to play a
+ 
+
+ align:start position:0%
+actually the constant is going to play a
+big role right because this is
+
+ align:start position:0%
+big role right because this is
+ 
+
+ align:start position:0%
+big role right because this is
+essentially equal to C A plus 1 B
+
+ align:start position:0%
+essentially equal to C A plus 1 B
+ 
+
+ align:start position:0%
+essentially equal to C A plus 1 B
+divided by C a B where C a plus 1 B is
+
+ align:start position:0%
+divided by C a B where C a plus 1 B is
+ 
+
+ align:start position:0%
+divided by C a B where C a plus 1 B is
+just the normalizing constant of a beta
+
+ align:start position:0%
+just the normalizing constant of a beta
+ 
+
+ align:start position:0%
+just the normalizing constant of a beta
+ei plus 1 B so I need to know the ratio
+
+ align:start position:0%
+ei plus 1 B so I need to know the ratio
+ 
+
+ align:start position:0%
+ei plus 1 B so I need to know the ratio
+of those two constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is not something I mean this is
+
+ align:start position:0%
+and this is not something I mean this is
+ 
+
+ align:start position:0%
+and this is not something I mean this is
+just a calculus exercise so in this case
+
+ align:start position:0%
+just a calculus exercise so in this case
+ 
+
+ align:start position:0%
+just a calculus exercise so in this case
+what you get is sorry in this case you
+
+ align:start position:0%
+what you get is sorry in this case you
+ 
+
+ align:start position:0%
+what you get is sorry in this case you
+get well okay so we get essentially a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by I think it's a plus B yeah
+
+ align:start position:0%
+divided by I think it's a plus B yeah
+ 
+
+ align:start position:0%
+divided by I think it's a plus B yeah
+it's a plus B so that's this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and when I plug in a to be this guy and
+
+ align:start position:0%
+and when I plug in a to be this guy and
+ 
+
+ align:start position:0%
+and when I plug in a to be this guy and
+B to be this guy but I get is a plus
+
+ align:start position:0%
+B to be this guy but I get is a plus
+ 
+
+ align:start position:0%
+B to be this guy but I get is a plus
+some of the X I and then I get a plus
+
+ align:start position:0%
+some of the X I and then I get a plus
+ 
+
+ align:start position:0%
+some of the X I and then I get a plus
+this guy a plus n minus this guy so
+
+ align:start position:0%
+this guy a plus n minus this guy so
+ 
+
+ align:start position:0%
+this guy a plus n minus this guy so
+those two guys go away and I'm left with
+
+ align:start position:0%
+those two guys go away and I'm left with
+ 
+
+ align:start position:0%
+those two guys go away and I'm left with
+qu a plus n which does not work so ya
+
+ align:start position:0%
+qu a plus n which does not work so ya
+ 
+
+ align:start position:0%
+qu a plus n which does not work so ya
+know that actually works and so now what
+
+ align:start position:0%
+know that actually works and so now what
+ 
+
+ align:start position:0%
+know that actually works and so now what
+I do I can actually divide and get this
+
+ align:start position:0%
+I do I can actually divide and get this
+ 
+
+ align:start position:0%
+I do I can actually divide and get this
+thing over there okay so what you can
+
+ align:start position:0%
+thing over there okay so what you can
+ 
+
+ align:start position:0%
+thing over there okay so what you can
+see the the reason why this thing has
+
+ align:start position:0%
+see the the reason why this thing has
+ 
+
+ align:start position:0%
+see the the reason why this thing has
+been divided is that you can really see
+
+ align:start position:0%
+been divided is that you can really see
+ 
+
+ align:start position:0%
+been divided is that you can really see
+that as n goes to infinity then this
+
+ align:start position:0%
+that as n goes to infinity then this
+ 
+
+ align:start position:0%
+that as n goes to infinity then this
+thing behaves like xn bar which is our
+
+ align:start position:0%
+thing behaves like xn bar which is our
+ 
+
+ align:start position:0%
+thing behaves like xn bar which is our
+frequentist estimator the effect of a is
+
+ align:start position:0%
+frequentist estimator the effect of a is
+ 
+
+ align:start position:0%
+frequentist estimator the effect of a is
+actually going away the effect of the
+
+ align:start position:0%
+actually going away the effect of the
+ 
+
+ align:start position:0%
+actually going away the effect of the
+prior which is completely captured by a
+
+ align:start position:0%
+prior which is completely captured by a
+ 
+
+ align:start position:0%
+prior which is completely captured by a
+is going away as n goes to infinity is
+
+ align:start position:0%
+is going away as n goes to infinity is
+ 
+
+ align:start position:0%
+is going away as n goes to infinity is
+there any question you guys have a
+
+ align:start position:0%
+there any question you guys have a
+ 
+
+ align:start position:0%
+there any question you guys have a
+question what is it
+
+ align:start position:0%
+question what is it
+ 
+
+ align:start position:0%
+question what is it
+give a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it / what oh yeah yeah then I said
+
+ align:start position:0%
+is it / what oh yeah yeah then I said
+ 
+
+ align:start position:0%
+is it / what oh yeah yeah then I said
+that this is equal to this right when so
+
+ align:start position:0%
+that this is equal to this right when so
+ 
+
+ align:start position:0%
+that this is equal to this right when so
+that's four that's four a becomes a plus
+
+ align:start position:0%
+that's four that's four a becomes a plus
+ 
+
+ align:start position:0%
+that's four that's four a becomes a plus
+some of the excise and B becomes a plus
+
+ align:start position:0%
+some of the excise and B becomes a plus
+ 
+
+ align:start position:0%
+some of the excise and B becomes a plus
+n minus some of the excise okay so
+
+ align:start position:0%
+n minus some of the excise okay so
+ 
+
+ align:start position:0%
+n minus some of the excise okay so
+that's just for the posterior one this
+
+ align:start position:0%
+that's just for the posterior one this
+ 
+
+ align:start position:0%
+that's just for the posterior one this
+guy to a right so I get a plus a plus n
+
+ align:start position:0%
+guy to a right so I get a plus a plus n
+ 
+
+ align:start position:0%
+guy to a right so I get a plus a plus n
+and then those two guys cancel okay and
+
+ align:start position:0%
+and then those two guys cancel okay and
+ 
+
+ align:start position:0%
+and then those two guys cancel okay and
+that's what you have here so for a is
+
+ align:start position:0%
+that's what you have here so for a is
+ 
+
+ align:start position:0%
+that's what you have here so for a is
+equal to one-half and I claim that this
+
+ align:start position:0%
+equal to one-half and I claim that this
+ 
+
+ align:start position:0%
+equal to one-half and I claim that this
+is Jeffrey's prior because remember
+
+ align:start position:0%
+is Jeffrey's prior because remember
+ 
+
+ align:start position:0%
+is Jeffrey's prior because remember
+Jeffrey's was what well it was square
+
+ align:start position:0%
+Jeffrey's was what well it was square
+ 
+
+ align:start position:0%
+Jeffrey's was what well it was square
+roots it was proportional to square root
+
+ align:start position:0%
+roots it was proportional to square root
+ 
+
+ align:start position:0%
+roots it was proportional to square root
+of P one minus P which I can write as P
+
+ align:start position:0%
+of P one minus P which I can write as P
+ 
+
+ align:start position:0%
+of P one minus P which I can write as P
+to the one-half 1 minus P to the
+
+ align:start position:0%
+to the one-half 1 minus P to the
+ 
+
+ align:start position:0%
+to the one-half 1 minus P to the
+one-half so it's just the case a is
+
+ align:start position:0%
+one-half so it's just the case a is
+ 
+
+ align:start position:0%
+one-half so it's just the case a is
+equal to one-half
+
+ align:start position:0%
+equal to one-half
+ 
+
+ align:start position:0%
+equal to one-half
+okay so if I use Jeffrey's prior I just
+
+ align:start position:0%
+okay so if I use Jeffrey's prior I just
+ 
+
+ align:start position:0%
+okay so if I use Jeffrey's prior I just
+plug in a equals to 1/2 and this is what
+
+ align:start position:0%
+plug in a equals to 1/2 and this is what
+ 
+
+ align:start position:0%
+plug in a equals to 1/2 and this is what
+I get
+
+ align:start position:0%
+I get
+ 
+
+ align:start position:0%
+I get
+ok so those things are gonna have an
+
+ align:start position:0%
+ok so those things are gonna have an
+ 
+
+ align:start position:0%
+ok so those things are gonna have an
+impact again when n is moderately large
+
+ align:start position:0%
+impact again when n is moderately large
+ 
+
+ align:start position:0%
+impact again when n is moderately large
+for large n those things whether you
+
+ align:start position:0%
+for large n those things whether you
+ 
+
+ align:start position:0%
+for large n those things whether you
+take Jeffrey's prior or you take
+
+ align:start position:0%
+take Jeffrey's prior or you take
+ 
+
+ align:start position:0%
+take Jeffrey's prior or you take
+whatever age you prefer it's gonna have
+
+ align:start position:0%
+whatever age you prefer it's gonna have
+ 
+
+ align:start position:0%
+whatever age you prefer it's gonna have
+no impact whatsoever but if n if a if n
+
+ align:start position:0%
+no impact whatsoever but if n if a if n
+ 
+
+ align:start position:0%
+no impact whatsoever but if n if a if n
+is like of the order of 10 maybe then
+
+ align:start position:0%
+is like of the order of 10 maybe then
+ 
+
+ align:start position:0%
+is like of the order of 10 maybe then
+you're gonna start to see some impact
+
+ align:start position:0%
+you're gonna start to see some impact
+ 
+
+ align:start position:0%
+you're gonna start to see some impact
+depending on what a you want to pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and in the in the second example
+
+ align:start position:0%
+okay and in the in the second example
+ 
+
+ align:start position:0%
+okay and in the in the second example
+well here we actually computed the
+
+ align:start position:0%
+well here we actually computed the
+ 
+
+ align:start position:0%
+well here we actually computed the
+posterior to be this guy well here I can
+
+ align:start position:0%
+posterior to be this guy well here I can
+ 
+
+ align:start position:0%
+posterior to be this guy well here I can
+just read off what the expectation is
+
+ align:start position:0%
+just read off what the expectation is
+ 
+
+ align:start position:0%
+just read off what the expectation is
+right I mean I don't have to actually
+
+ align:start position:0%
+right I mean I don't have to actually
+ 
+
+ align:start position:0%
+right I mean I don't have to actually
+compute the expectation of a Gaussian
+
+ align:start position:0%
+compute the expectation of a Gaussian
+ 
+
+ align:start position:0%
+compute the expectation of a Gaussian
+it's just X n bar and so in this case
+
+ align:start position:0%
+it's just X n bar and so in this case
+ 
+
+ align:start position:0%
+it's just X n bar and so in this case
+there's actually no I mean when I have
+
+ align:start position:0%
+there's actually no I mean when I have
+ 
+
+ align:start position:0%
+there's actually no I mean when I have
+non informative fryer for a Gaussian
+
+ align:start position:0%
+non informative fryer for a Gaussian
+ 
+
+ align:start position:0%
+non informative fryer for a Gaussian
+then I have basically xn bar and so as
+
+ align:start position:0%
+then I have basically xn bar and so as
+ 
+
+ align:start position:0%
+then I have basically xn bar and so as
+you can see actually this is an
+
+ align:start position:0%
+you can see actually this is an
+ 
+
+ align:start position:0%
+you can see actually this is an
+interesting example when I actually look
+
+ align:start position:0%
+interesting example when I actually look
+ 
+
+ align:start position:0%
+interesting example when I actually look
+at the posterior
+
+ align:start position:0%
+at the posterior
+ 
+
+ align:start position:0%
+at the posterior
+it's not something that costs me a lot
+
+ align:start position:0%
+it's not something that costs me a lot
+ 
+
+ align:start position:0%
+it's not something that costs me a lot
+to communicate to you right there's one
+
+ align:start position:0%
+to communicate to you right there's one
+ 
+
+ align:start position:0%
+to communicate to you right there's one
+symbol here one symbol here and one
+
+ align:start position:0%
+symbol here one symbol here and one
+ 
+
+ align:start position:0%
+symbol here one symbol here and one
+symbol here right I tell you the
+
+ align:start position:0%
+symbol here right I tell you the
+ 
+
+ align:start position:0%
+symbol here right I tell you the
+posterior is a Gaussian with mean xn bar
+
+ align:start position:0%
+posterior is a Gaussian with mean xn bar
+ 
+
+ align:start position:0%
+posterior is a Gaussian with mean xn bar
+and variance 1 over n when I actually
+
+ align:start position:0%
+and variance 1 over n when I actually
+ 
+
+ align:start position:0%
+and variance 1 over n when I actually
+turned that into a posterior mean I'm
+
+ align:start position:0%
+turned that into a posterior mean I'm
+ 
+
+ align:start position:0%
+turned that into a posterior mean I'm
+dropping all this information I'm just
+
+ align:start position:0%
+dropping all this information I'm just
+ 
+
+ align:start position:0%
+dropping all this information I'm just
+giving you the first parameter so you
+
+ align:start position:0%
+giving you the first parameter so you
+ 
+
+ align:start position:0%
+giving you the first parameter so you
+can see there's actually much more
+
+ align:start position:0%
+can see there's actually much more
+ 
+
+ align:start position:0%
+can see there's actually much more
+information in the posterior then there
+
+ align:start position:0%
+information in the posterior then there
+ 
+
+ align:start position:0%
+information in the posterior then there
+is in the than there is in the posterior
+
+ align:start position:0%
+is in the than there is in the posterior
+ 
+
+ align:start position:0%
+is in the than there is in the posterior
+mean the posterior mean is just a point
+
+ align:start position:0%
+mean the posterior mean is just a point
+ 
+
+ align:start position:0%
+mean the posterior mean is just a point
+it's not telling me how confident I am
+
+ align:start position:0%
+it's not telling me how confident I am
+ 
+
+ align:start position:0%
+it's not telling me how confident I am
+in this point and this thing is actually
+
+ align:start position:0%
+in this point and this thing is actually
+ 
+
+ align:start position:0%
+in this point and this thing is actually
+very interesting okay so you can talk
+
+ align:start position:0%
+very interesting okay so you can talk
+ 
+
+ align:start position:0%
+very interesting okay so you can talk
+about the posterior variance that's
+
+ align:start position:0%
+about the posterior variance that's
+ 
+
+ align:start position:0%
+about the posterior variance that's
+associated to it right you can talk
+
+ align:start position:0%
+associated to it right you can talk
+ 
+
+ align:start position:0%
+associated to it right you can talk
+about as an output you could give the
+
+ align:start position:0%
+about as an output you could give the
+ 
+
+ align:start position:0%
+about as an output you could give the
+posterior mean in the posterior variance
+
+ align:start position:0%
+posterior mean in the posterior variance
+ 
+
+ align:start position:0%
+posterior mean in the posterior variance
+and those things are actually
+
+ align:start position:0%
+and those things are actually
+ 
+
+ align:start position:0%
+and those things are actually
+interesting all right so I think this is
+
+ align:start position:0%
+interesting all right so I think this is
+ 
+
+ align:start position:0%
+interesting all right so I think this is
+it so as I said in general just like in
+
+ align:start position:0%
+it so as I said in general just like in
+ 
+
+ align:start position:0%
+it so as I said in general just like in
+this case you do not the choice of the
+
+ align:start position:0%
+this case you do not the choice of the
+ 
+
+ align:start position:0%
+this case you do not the choice of the
+priors being the the impact of the prior
+
+ align:start position:0%
+priors being the the impact of the prior
+ 
+
+ align:start position:0%
+priors being the the impact of the prior
+is being washed away as the sample size
+
+ align:start position:0%
+is being washed away as the sample size
+ 
+
+ align:start position:0%
+is being washed away as the sample size
+goes to infinity just while I here
+
+ align:start position:0%
+goes to infinity just while I here
+ 
+
+ align:start position:0%
+goes to infinity just while I here
+there's no impact of the priority with a
+
+ align:start position:0%
+there's no impact of the priority with a
+ 
+
+ align:start position:0%
+there's no impact of the priority with a
+non informative one but if you actually
+
+ align:start position:0%
+non informative one but if you actually
+ 
+
+ align:start position:0%
+non informative one but if you actually
+had an informative one you know CF
+
+ align:start position:0%
+had an informative one you know CF
+ 
+
+ align:start position:0%
+had an informative one you know CF
+homework yeah yeah so CF homework you
+
+ align:start position:0%
+homework yeah yeah so CF homework you
+ 
+
+ align:start position:0%
+homework yeah yeah so CF homework you
+would actually see an impact of the
+
+ align:start position:0%
+would actually see an impact of the
+ 
+
+ align:start position:0%
+would actually see an impact of the
+prior which again would be washed away
+
+ align:start position:0%
+prior which again would be washed away
+ 
+
+ align:start position:0%
+prior which again would be washed away
+as your sample size increases here it
+
+ align:start position:0%
+as your sample size increases here it
+ 
+
+ align:start position:0%
+as your sample size increases here it
+goes away you just get xn bar over one
+
+ align:start position:0%
+goes away you just get xn bar over one
+ 
+
+ align:start position:0%
+goes away you just get xn bar over one
+and and actually in this cases you see
+
+ align:start position:0%
+and and actually in this cases you see
+ 
+
+ align:start position:0%
+and and actually in this cases you see
+that the posterior distribution
+
+ align:start position:0%
+that the posterior distribution
+ 
+
+ align:start position:0%
+that the posterior distribution
+converges to sorry the Bayesian
+
+ align:start position:0%
+converges to sorry the Bayesian
+ 
+
+ align:start position:0%
+converges to sorry the Bayesian
+estimator is asymptotically normal this
+
+ align:start position:0%
+estimator is asymptotically normal this
+ 
+
+ align:start position:0%
+estimator is asymptotically normal this
+is different from the distribution of
+
+ align:start position:0%
+is different from the distribution of
+ 
+
+ align:start position:0%
+is different from the distribution of
+the posterior right this is just the
+
+ align:start position:0%
+the posterior right this is just the
+ 
+
+ align:start position:0%
+the posterior right this is just the
+posterior mean which happens to be
+
+ align:start position:0%
+posterior mean which happens to be
+ 
+
+ align:start position:0%
+posterior mean which happens to be
+asymptotically normal but the posterior
+
+ align:start position:0%
+asymptotically normal but the posterior
+ 
+
+ align:start position:0%
+asymptotically normal but the posterior
+may not have a I mean here the posterior
+
+ align:start position:0%
+may not have a I mean here the posterior
+ 
+
+ align:start position:0%
+may not have a I mean here the posterior
+is is a beta right I mean it's not
+
+ align:start position:0%
+is is a beta right I mean it's not
+ 
+
+ align:start position:0%
+is is a beta right I mean it's not
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+okay so there's different those things
+
+ align:start position:0%
+okay so there's different those things
+ 
+
+ align:start position:0%
+okay so there's different those things
+are two different things
+
+ align:start position:0%
+are two different things
+ 
+
+ align:start position:0%
+are two different things
+your question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a unit on one right that was the
+
+ align:start position:0%
+a unit on one right that was the
+ 
+
+ align:start position:0%
+a unit on one right that was the
+improper prior yeah well I mean yeah so
+
+ align:start position:0%
+improper prior yeah well I mean yeah so
+ 
+
+ align:start position:0%
+improper prior yeah well I mean yeah so
+it's essentially telling you that right
+
+ align:start position:0%
+it's essentially telling you that right
+ 
+
+ align:start position:0%
+it's essentially telling you that right
+so we said that when you have an
+
+ align:start position:0%
+so we said that when you have an
+ 
+
+ align:start position:0%
+so we said that when you have an
+improper when you have a non informative
+
+ align:start position:0%
+improper when you have a non informative
+ 
+
+ align:start position:0%
+improper when you have a non informative
+fryer essentially the maximum likelihood
+
+ align:start position:0%
+fryer essentially the maximum likelihood
+ 
+
+ align:start position:0%
+fryer essentially the maximum likelihood
+is the maximum a-posteriori right but in
+
+ align:start position:0%
+is the maximum a-posteriori right but in
+ 
+
+ align:start position:0%
+is the maximum a-posteriori right but in
+this case there's so much symmetry that
+
+ align:start position:0%
+this case there's so much symmetry that
+ 
+
+ align:start position:0%
+this case there's so much symmetry that
+it just so happens to the maximum I mean
+
+ align:start position:0%
+it just so happens to the maximum I mean
+ 
+
+ align:start position:0%
+it just so happens to the maximum I mean
+this thing is completely symmetric
+
+ align:start position:0%
+this thing is completely symmetric
+ 
+
+ align:start position:0%
+this thing is completely symmetric
+around its maximum so it means that the
+
+ align:start position:0%
+around its maximum so it means that the
+ 
+
+ align:start position:0%
+around its maximum so it means that the
+expectation is equal to maximum 2d art
+
+ align:start position:0%
+expectation is equal to maximum 2d art
+ 
+
+ align:start position:0%
+expectation is equal to maximum 2d art
+max yeah but hence do not pick the wrong
+
+ align:start position:0%
+max yeah but hence do not pick the wrong
+ 
+
+ align:start position:0%
+max yeah but hence do not pick the wrong
+prior I mean of course it would I mean
+
+ align:start position:0%
+prior I mean of course it would I mean
+ 
+
+ align:start position:0%
+prior I mean of course it would I mean
+it would mess up to of course I mean
+
+ align:start position:0%
+it would mess up to of course I mean
+ 
+
+ align:start position:0%
+it would mess up to of course I mean
+you're putting extra information but you
+
+ align:start position:0%
+you're putting extra information but you
+ 
+
+ align:start position:0%
+you're putting extra information but you
+could say the same thing by saying well
+
+ align:start position:0%
+could say the same thing by saying well
+ 
+
+ align:start position:0%
+could say the same thing by saying well
+the issue with frequencies methods is
+
+ align:start position:0%
+the issue with frequencies methods is
+ 
+
+ align:start position:0%
+the issue with frequencies methods is
+that if you mess up the choice of your
+
+ align:start position:0%
+that if you mess up the choice of your
+ 
+
+ align:start position:0%
+that if you mess up the choice of your
+likelihood then it's gonna mess up your
+
+ align:start position:0%
+likelihood then it's gonna mess up your
+ 
+
+ align:start position:0%
+likelihood then it's gonna mess up your
+output so here you just have two chances
+
+ align:start position:0%
+output so here you just have two chances
+ 
+
+ align:start position:0%
+output so here you just have two chances
+of messing it up right you have the well
+
+ align:start position:0%
+of messing it up right you have the well
+ 
+
+ align:start position:0%
+of messing it up right you have the well
+it's going so you have the product of
+
+ align:start position:0%
+it's going so you have the product of
+ 
+
+ align:start position:0%
+it's going so you have the product of
+the likelihood and the end the prior and
+
+ align:start position:0%
+the likelihood and the end the prior and
+ 
+
+ align:start position:0%
+the likelihood and the end the prior and
+you have one more chance to to but it's
+
+ align:start position:0%
+you have one more chance to to but it's
+ 
+
+ align:start position:0%
+you have one more chance to to but it's
+true if you assume that the model is
+
+ align:start position:0%
+true if you assume that the model is
+ 
+
+ align:start position:0%
+true if you assume that the model is
+right and of course finding the wrong
+
+ align:start position:0%
+right and of course finding the wrong
+ 
+
+ align:start position:0%
+right and of course finding the wrong
+prior could completely mess up thing if
+
+ align:start position:0%
+prior could completely mess up thing if
+ 
+
+ align:start position:0%
+prior could completely mess up thing if
+your prior for example has no support on
+
+ align:start position:0%
+your prior for example has no support on
+ 
+
+ align:start position:0%
+your prior for example has no support on
+the true parameter but if your prior has
+
+ align:start position:0%
+the true parameter but if your prior has
+ 
+
+ align:start position:0%
+the true parameter but if your prior has
+a positive weight on the true parameter
+
+ align:start position:0%
+a positive weight on the true parameter
+ 
+
+ align:start position:0%
+a positive weight on the true parameter
+as n goes to infinity you know I mean
+
+ align:start position:0%
+as n goes to infinity you know I mean
+ 
+
+ align:start position:0%
+as n goes to infinity you know I mean
+okay I cannot speak for all counter
+
+ align:start position:0%
+okay I cannot speak for all counter
+ 
+
+ align:start position:0%
+okay I cannot speak for all counter
+examples in the world but I'm sure under
+
+ align:start position:0%
+examples in the world but I'm sure under
+ 
+
+ align:start position:0%
+examples in the world but I'm sure under
+minor technical conditions you can
+
+ align:start position:0%
+minor technical conditions you can
+ 
+
+ align:start position:0%
+minor technical conditions you can
+guarantee that your posterior mean is
+
+ align:start position:0%
+guarantee that your posterior mean is
+ 
+
+ align:start position:0%
+guarantee that your posterior mean is
+gonna converge to what you needed to
+
+ align:start position:0%
+gonna converge to what you needed to
+ 
+
+ align:start position:0%
+gonna converge to what you needed to
+convert to any other question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I think this sort of closes
+
+ align:start position:0%
+all right so I think this sort of closes
+ 
+
+ align:start position:0%
+all right so I think this sort of closes
+the more traditional mathematical not
+
+ align:start position:0%
+the more traditional mathematical not
+ 
+
+ align:start position:0%
+the more traditional mathematical not
+mathematical but you know traditional
+
+ align:start position:0%
+mathematical but you know traditional
+ 
+
+ align:start position:0%
+mathematical but you know traditional
+statistics part of this class and from
+
+ align:start position:0%
+statistics part of this class and from
+ 
+
+ align:start position:0%
+statistics part of this class and from
+here on we'll talk about more
+
+ align:start position:0%
+here on we'll talk about more
+ 
+
+ align:start position:0%
+here on we'll talk about more
+multivariate statistics starting with
+
+ align:start position:0%
+multivariate statistics starting with
+ 
+
+ align:start position:0%
+multivariate statistics starting with
+principal component analysis so that's
+
+ align:start position:0%
+principal component analysis so that's
+ 
+
+ align:start position:0%
+principal component analysis so that's
+more like when you have multiple data we
+
+ align:start position:0%
+more like when you have multiple data we
+ 
+
+ align:start position:0%
+more like when you have multiple data we
+started in a way to talk about
+
+ align:start position:0%
+started in a way to talk about
+ 
+
+ align:start position:0%
+started in a way to talk about
+multivariate statistics when we talked
+
+ align:start position:0%
+multivariate statistics when we talked
+ 
+
+ align:start position:0%
+multivariate statistics when we talked
+about multivariate regression but we'll
+
+ align:start position:0%
+about multivariate regression but we'll
+ 
+
+ align:start position:0%
+about multivariate regression but we'll
+move on to you know principal component
+
+ align:start position:0%
+move on to you know principal component
+ 
+
+ align:start position:0%
+move on to you know principal component
+analysis I'll talk a bit about multiple
+
+ align:start position:0%
+analysis I'll talk a bit about multiple
+ 
+
+ align:start position:0%
+analysis I'll talk a bit about multiple
+testing I haven't made my mind yet about
+
+ align:start position:0%
+testing I haven't made my mind yet about
+ 
+
+ align:start position:0%
+testing I haven't made my mind yet about
+what we'll talk really in December but I
+
+ align:start position:0%
+what we'll talk really in December but I
+ 
+
+ align:start position:0%
+what we'll talk really in December but I
+want to make sure that you have a taste
+
+ align:start position:0%
+want to make sure that you have a taste
+ 
+
+ align:start position:0%
+want to make sure that you have a taste
+and the flavor of what you know is being
+
+ align:start position:0%
+and the flavor of what you know is being
+ 
+
+ align:start position:0%
+and the flavor of what you know is being
+interesting in statistics these days
+
+ align:start position:0%
+interesting in statistics these days
+ 
+
+ align:start position:0%
+interesting in statistics these days
+especially as you go towards more
+
+ align:start position:0%
+especially as you go towards more
+ 
+
+ align:start position:0%
+especially as you go towards more
+machine learning type of questions where
+
+ align:start position:0%
+machine learning type of questions where
+ 
+
+ align:start position:0%
+machine learning type of questions where
+really the focus is on prediction rather
+
+ align:start position:0%
+really the focus is on prediction rather
+ 
+
+ align:start position:0%
+really the focus is on prediction rather
+than the modeling itself I will talk
+
+ align:start position:0%
+than the modeling itself I will talk
+ 
+
+ align:start position:0%
+than the modeling itself I will talk
+about logistic regression as well for
+
+ align:start position:0%
+about logistic regression as well for
+ 
+
+ align:start position:0%
+about logistic regression as well for
+example which is and generalized linear
+
+ align:start position:0%
+example which is and generalized linear
+ 
+
+ align:start position:0%
+example which is and generalized linear
+models which is just the generalization
+
+ align:start position:0%
+models which is just the generalization
+ 
+
+ align:start position:0%
+models which is just the generalization
+in the case that Y does not take value
+
+ align:start position:0%
+in the case that Y does not take value
+ 
+
+ align:start position:0%
+in the case that Y does not take value
+in the whole real line may be 0 1 for
+
+ align:start position:0%
+in the whole real line may be 0 1 for
+ 
+
+ align:start position:0%
+in the whole real line may be 0 1 for
+example for regression all right thanks
\ No newline at end of file
diff --git a/k2jN_26m8LM.txt b/k2jN_26m8LM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9fc630d8693d3283309d1249f42c38998bd080ef
--- /dev/null
+++ b/k2jN_26m8LM.txt
@@ -0,0 +1,4377 @@
+OK.
+
+Good morning everyone.
+
+As I mentioned at the last lecture, we're
+now moving into the nitty-gritty of the subsystems.
+
+And we have quite an extraordinary list of
+speakers who actually worked on the original
+
+design of these systems.
+
+And, as Professor Cohen mentioned, not only
+did they design these systems for the shuttle
+
+but, in most cases, they came from having
+designed essentially the same systems on the
+
+Apollo program.
+
+So, in the question and answer period, if
+there are some things that you'd like to know
+
+about the comparison of Apollo and Shuttle,
+and also any questions about the future since
+
+some of you will be writing up possibilities
+for future development of some of these systems,
+
+please ask the questions.
+
+And I spoke with Tom Moser, and he's fully
+prepared to handle questions during the talk.
+
+Because there will be a lot of fairly detailed
+technical stuff, so if there's something that
+
+you're not familiar with, you don't understand
+or just have questions about, please ask while
+
+the lecture is going on.
+
+I want to remind you, we have fairly extensive
+bios for all the speakers.
+
+Rather than take the time in class to read
+through this, I've posted them all on the
+
+class website.
+
+So my suggestion is go to the class website
+before each class and just see the background
+
+of the lecture.
+
+Professor Cohen is going to make some personal
+remarks about, well, whatever it is that you
+
+want to say about our speaker.
+
+Before we go into that, two things.
+
+Tom Moser asked me if we had this book.
+
+This actually is my personal copy.
+
+I'm going to put it on reserve.
+
+We may actually have it in the library as
+well.
+
+I'll check, and I'll make sure that this gets
+on reserve.
+
+This really is a rather complete book.
+
+A lot the material that you've seen, the early
+design of the shuttle is in here, discussions
+
+of subsystems, and then detailed discussions
+of the individual flights all the way up through
+
+the first hundred shuttle flights.
+
+It's a very nice resource, and we'll have
+it on reserve in the library.
+
+The next thing.
+
+I believe I have now indications from everybody
+about what you want to do your paper on.
+
+We have two groups doing GN&C.
+
+One group doing displays and controls.
+
+We had two small groups interested in the
+propulsion system.
+
+And I've asked Brian and other people, you've
+gotten together?
+
+OK.
+
+Only one person, Dan, I think, indicated an
+interest in the thermal protection system.
+
+I know we've got a lot people on GN&C.
+
+One of you, I think, had actually indicated
+an interest in thermal protection.
+
+I will leave that up to you.
+
+If somebody would like to work on thermal
+protection with Dan, he's back there and is
+
+available, I guess.
+
+We have one group which is going to do a little
+bit of a different sort of project on modularity
+
+and some of the design methods that went into
+the shuttle compared to modern techniques
+
+that are available now, so we'll be interested
+in seeing what you'll come up with.
+
+And then we had a group that wants to look
+at the propulsion system, but from the point
+
+of view of fuel storage and what the system
+would have looked like if we had possibly
+
+used alternate fuels.
+
+We've got a nice spectrum of things that people
+will look at.
+
+Any time you'd like to come and talk with
+me, with Professor Cohen or take advantage
+
+of one of the speakers who happens to be talking
+about the area that you're interested in,
+
+please do that.
+
+We do have time usually after class, if you're
+free.
+
+The speakers will generally be available so
+take advantage of it.
+
+OK.
+
+That's enough talking from me.
+
+Aaron, I'll give this to you..
+
+I just have a few personal comments about
+Mr. Moser.
+
+He is going to talk to you today, lecture
+you today about the structures on the space
+
+shuttle.
+
+But Tom, as Jeff mentioned, did the same work
+on the Apollo program.
+
+I was the manager of the Command and Service
+Module on Apollo and on the Space Shuttle
+
+Orbiter, so Tom and I have been working tighter
+for many years.
+
+And I relied very, very heavily on Tom throughout
+the years.
+
+I told a little anecdote the other day, and
+just let me say it again because the person
+
+that helped me with it is Tom Moser.
+
+During one of the shuttle missions, we were
+getting ready to come back, about 11:00 at
+
+night, I was getting ready to leave my house
+to go to the Control Center, which I live
+
+about ten minutes away, and we were getting
+ready to make the de-orbit burn, I got a call
+
+from Rockwell International, their head of
+the program there.
+
+And he said, Aaron, we just did this test.
+
+We took the panel of tiles and dumped it into
+a bucket of waterproofing agent and all the
+
+tiles came off.
+
+I said what do you want me to do with that
+information?
+
+I said they're getting ready to come back
+and there's not much I can do about that.
+
+You're telling me all the tiles are going
+to come off?
+
+He said no, they're not because that's not
+really what we did on the shuttle.
+
+I said well, why did you do that test?
+
+That's sort of a dumb test.
+
+I had a decision to make, whether I'd call
+the people in the Control Center like Chris
+
+Kraft and tell him we did this test and all
+the tiles are going to come off.
+
+But we've got to come back.
+
+I decided what I would do is call my good
+colleague Tom Moser.
+
+I said Tom, what should we do?
+
+We talked for a while and talked for a while,
+and we decided to keep this information to
+
+ourselves until after the landing.
+
+It turns out it all worked out fine.
+
+There were no problems.
+
+But my point to you is that how much I relied
+on Tom.
+
+The other point is you may find yourself in
+that type of situation some day on a project
+
+maybe not associated with that.
+
+Tom turned out to be afterward my Deputy Manager
+in the Orbiter Project Office.
+
+Then he went on to become Head of Engineering
+at the Johnson Space Center and then went
+
+on to be Director of the Space Station in
+Washington, DC and now is a consultant.
+
+So, with no further ado, let me turn it over
+to Tom.
+
+One thing I learned to do is have my own mic
+because Aaron will keep it.
+
+One of the advantages to having a gray beard,
+besides some of the folks in the back, is
+
+I'm not going to refer to him as Professor
+Cohen or as Professor Hoffman.
+
+It's Jeff and Aaron.
+
+It's not out of disrespect.
+
+It's just the way I grew up so that's OK to
+do.
+
+When Aaron asked me to do this, and Jeff,
+I thought that's easy, I'll just pull out
+
+some of my old notes and stuff like that and
+I will be up the next day.
+
+Until Jeff sent me the syllabus and what it
+was to do, it made me start thinking about
+
+what I'd spent a good part of my life doing.
+
+And that was designing and development of
+the shuttle with Aaron and some of the others,
+
+but from a systems engineering perspective
+which you guys are doing.
+
+So, what I did is I went back and looked at
+everything from a systems engineering point
+
+of view from 1968 all the way until '81 when
+the shuttle flew.
+
+But I looked at it through the knothole of
+a structure and thermal person.
+
+So, that's what I'm going to present to you
+today.
+
+And, as you go through each phase of the program
+it changes.
+
+And sometimes it's down to the minute detail
+and other times it is the macro.
+
+That's my objective, and I hope we accomplish
+that.
+
+Ask me any questions any time that you want
+to.
+
+Just a little bit of credit and recognition
+of some of the people that made this thing
+
+happen.
+
+You're going to hear from a lot of these people.
+
+You won't hear from John Yardley or Max Faget
+because they are deceased now, but these people
+
+up here made this program go.
+
+And then you will have also some references
+that give you a lot more detail than I'm going
+
+to give you today, even though I'm going to
+cover a lot of it.
+
+There is one unique thing about a program
+like this that is complex.
+
+And that is the technical team and the management
+team have to work together and get together.
+
+Everybody that is listed up there stayed on
+this program from day one, and that is key.
+
+I don't think there has been a program since
+then that that has happened.
+
+And I think that if people judge the Shuttle
+Program as being successful, I think that
+
+that's a major contribution to that success.
+
+Beginning in '68 when the concept studies
+began, all the way down to operations from
+
+a structural perspective, what is important
+at each one of those phases in its weight
+
+and cost and produceability from day one.
+
+But then it gets into the certification phase,
+the last part of the program, how are you
+
+going to certify this thing?
+
+How are you going to prove that it's good
+for flight?
+
+How are you going to prove that the crew is
+safe?
+
+And you have to do it on the ground.
+
+So, it's a completely different knothole you're
+looking through and a completely different
+
+set of parameters.
+
+I didn't start on Apollo at the beginning
+like Aaron did.
+
+I came out a little bit later.
+
+But, in this program, I had the good fortune
+of working on it from sketchpad to launch
+
+pad.
+
+And that's the way I characterized it.
+
+And Aaron didn't know this, but at the end
+I would have worked for free to complete the
+
+program because I was going to see something
+from beginning to end.
+
+And so if you ever had that opportunity to
+get on the program at the very beginning,
+
+I don't care what knothole you're looking
+at it through, stay on that program if you
+
+can because it's a completely different life
+at every step along the way.
+
+So, from the knothole of Orbiter structure,
+I'm going to break this thing into two pieces,
+
+Orbiter structure and the thermal protection
+system..
+
+On the concept studies that began in '68,
+what was the objective of those concept studies?
+
+Conceiving, characterizing and characterizing
+by qualitative and quantitative concepts that
+
+would appear to work.
+
+So, it was determining really the feasibility
+of the concepts.
+
+When that began, the only requirement in the
+Shuttle Program was to have a reusable space
+
+transportation system.
+
+Get something that goes from earth to low
+earth orbit and back reliably and reusable.
+
+There wasn't a requirement on payload size,
+there wasn't a requirement on number of missions,
+
+there wasn't a requirement on any of those
+things.
+
+That's what it was.
+
+The variables that we all looked at, though,
+were budgets, yearly budgets, developments
+
+costs, operations cost.
+
+And you'll see, as you go through some of
+this stuff, and probably some of the stuff
+
+that Dale Myers showed you, is development
+cost, you can spend a lot of money on development
+
+and reduce the operations cost or you can
+spend a little bit of money on development
+
+and have very high operational cost.
+
+So, there's a trade there.
+
+And when you're dealing with budgets that
+you really don't understand exactly what they
+
+are, that's a very important variable.
+
+Payload mass and size is important from a
+structural and thermal standpoint because
+
+it has to do with mass and it has to do with
+energy that has to be dissipated during reentry.
+
+The operational orbit is important.
+
+Fully reusable flight systems or partially
+reusable, and that's a trade on cost and weight.
+
+Turnaround time and cross-range.
+
+Cross-range was critical to us at this point
+because NASA didn't have a requirement for
+
+cross-range.
+
+And that's cross-range after you come back
+into the atmosphere to be able to deviate
+
+your normal ballistic trajectory coming back
+in.
+
+But the Air Force thought that they had a
+requirement so we had to include that.
+
+And then, as we got into the next phase of
+it, looking at what was important from a structural
+
+standpoint is the efficiency of the load path,
+the weight, the payload size, the aerodynamic
+
+surface loading, now we're beginning to get
+in and look at what are the wing loads, et
+
+cetera, and how does that manifest itself
+in weight and produceability?
+
+We did that under two years of contracted
+effort.
+
+Then within JSC, the Johnson Space Center,
+which was formally the Manned Space Craft
+
+Center, we conceptionally looked at designs
+in-house.
+
+And we looked at 53 different designs.
+
+You talk about a systems engineering thing,
+what we did was got a group of people about
+
+the size of this room and went away and locked
+ourselves up.
+
+But we had expertise in every area, propulsion,
+guidance and control, aerodynamics, aero heating,
+
+that kind of stuff.
+
+And we were almost doing a configuration a
+week when we did that.
+
+So, when you look at 53 different configurations
+over basically a two-year period, we were
+
+not only just looking at it but we were quantifying
+then, what it meant in terms of all the parameters
+
+that I showed you a while ago.
+
+How much did it cost?
+
+What was the development cost?
+
+What was the operations cost?
+
+What was the weight?
+
+What was the maximum temperature as we saw
+on the vehicle?
+
+Was there a thermal protection system that
+could accommodate those types of temperatures?
+
+That was the characterization in the systems
+engineering parameters that we used.
+
+Tom, where these designs kind of refined?
+
+Were you refining with each iteration or was
+it like we'll try this for a couple iterations
+
+and then maybe try something completely different?
+
+Were you working towards a final [OVERLAPPING
+VOICES]?
+
+Well, what we were doing was looking at the
+variables.
+
+In other words, like here, when we looked
+at 53 different things, we looked at payloads
+
+ranging anywhere from 15,000 to 40,000 pounds.
+
+We didn't know what the answer was going to
+be.
+
+The driving thing there was reusability and
+cost profile.
+
+We thought we knew what we could afford to
+do.
+
+We looked at payloads from 8 feet in diameter
+to 15 feet in diameter, 30 feet long to 75
+
+feet long.
+
+We were looking at all of those things.
+
+And, as we did that, we changed configuration
+from a straight wing, which is not good for
+
+cross-range, to a delta wing which is better
+for a cross-range, to a double delta wing
+
+which is even more structurally efficient.
+
+Landing weights then was important.
+
+Just like everybody saw the plane landing
+last night, it had to get that landing weight
+
+down to where it could control it.
+
+Well, that was the same thing we were doing.
+
+We were looking at landing weights, not only
+from a controllability but also from a produceability.
+
+We looked at weights from 70,000 to 215,000
+pounds, boosters from fully reusable to partially
+
+reusable, propulsion systems and various types
+of things.
+
+We even looked at air breathers so that they
+didn't have to come back a dead stick like
+
+they do now when Jeff was in the vehicle.
+
+And pressure fed and pump fed systems.
+
+There was simplicity and complications in
+all of them.
+
+Tankage, internal or external to the Orbiter.
+
+Could you maybe say, for people's benefit
+here who have grown up in the computer age,
+
+something about the tools that you had?
+
+I am going to do that in a minute.
+
+You are, OK.
+
+I'm going to give you a challenge, too.
+
+So, we looked at all of those.
+
+And, we not only looked at it, we quantified
+it to the extent that we could get the first
+
+order estimates on what the cost in all those
+things where.
+
+Now then, I chose a couple of them here.
+
+This was one of the early designs of the Orbiter.
+
+Look where the locks and hydrogen are.
+
+It's inside the Orbiter.
+
+It has a straight wing so it was fairly lightweight,
+except for having to carry all that tankage.
+
+The engines were on the Orbiter itself, but
+the payload was really small.
+
+Very low cross-range, very low payload.
+
+So that was probably the 8 foot diameter 40,000
+pound payload.
+
+We evolved that over a series of studies until
+we finally got down to about February of '72
+
+where we said we're going to have to have
+a larger payload than this.
+
+And the cost profile didn't fit.
+
+What we did is we came up with a configuration
+that's almost like the shuttle that you see
+
+today.
+
+Large payload, all the propulsion systems,
+the main propulsion systems are outside the
+
+Orbiter.
+
+And it's a fly back, and part of it was throwaway.
+
+In this case, we had a booster in line with
+the external tank rather than in parallel
+
+with it like the SRBs are today.
+
+Basically that's what we started the detailed
+design and development with, but not exactly.
+
+And I'll show you that.
+
+Now then, some of us who like to worry about
+load pass and simplicity and low weight of
+
+the structure, we said ah-ha.
+
+What we will do is put the engines on the
+external tank.
+
+All the mass is down here.
+
+Very little mass up here.
+
+And for boost reduce the weight of the Orbiter,
+which is going to reduce development and operations
+
+costs a whole bunch and thermal protection
+system, but we have to swing these engines
+
+for reusability from the external tank back
+up the Orbiter and stow them for entry.
+
+Well, our brother in mechanical engineers,
+they beat us pretty hard.
+
+They beat us black and blue.
+
+Anyway, that was a concept that we looked
+at very late in the program.
+
+And that didn't go anywhere, even though Max
+Faget and I wanted to do it pretty badly.
+
+As we continue now.
+
+Now we're four years into the thing, we've
+done all these systems engineering analysis,
+
+so we end up with a final concept.
+
+Here's what we want.
+
+We want a 2.5 stage launch vehicle because
+it costs too much basically to fly back the
+
+booster.
+
+We just didn't have the money so we said we
+want to have the most important part be fully
+
+reusable, so that was the Orbiter.
+
+It was going to be a delta wing.
+
+We figured that the mission life, we had a
+mission model of 500 total missions, 100 missions
+
+per vehicle, and there were five vehicles.
+
+We had an ascent acceleration of 3 g's.
+
+Why was that?
+
+Really, the requirement was to keep down the
+inertia loads, but it was also to let people
+
+off the street flying the thing.
+
+Go ahead.
+
+What constitutes half a stage?
+
+Half a stage means that the external tank
+is like a half a stage.
+
+The SRB is a stage, the engine, the Orbiter
+is a stage, but the tank is a half a stage.
+
+We kept the max dynamic pressure down because
+that was a major driver for control systems
+
+and for aerodynamic services.
+
+You would love not to have the wings on the
+Orbiter going uphill.
+
+That's a penalty that you pay.
+
+So, one of the things to help reduce that
+is to keep that aerodynamic load down on the
+
+wings.
+
+Then for atmospheric flights, and I'm going
+to talk a little bit more about that, we said
+
+this thing is going to come back like an airplane.
+
+Let's fly it.
+
+Let's design it like an airplane 2.5 g normal
+maneuver load factor and a negative 1 g.
+
+A crew of four for one week.
+
+That becomes kind of important because that
+sized the crew module, that sized a lot of
+
+the environmental control systems you'll hear
+about later and other things in the life support
+
+systems.
+
+So, without a lot of changes, to show you
+what the flexibility and capability of this
+
+vehicle is, the Orbiter is now flying seven
+people for two weeks.
+
+So, it went from 28 man days to 63 man days
+basically.
+
+And I don't think a lot of people understand
+what that has done.
+
+And there is a lot more robustness in the
+Orbiter, in the shuttle system that was not
+
+designed into it but had some inherent capability.
+
+And also some of it was a little bit of forethought
+in the thing.
+
+Here comes the Air Force stuff.
+
+65,000 pounds up.
+
+40,000 pounds return.
+
+That was the requirements.
+
+15 x 60.
+
+Another important thing is we didn't know
+what they'd be but maybe up to five payloads
+
+at a time.
+
+And that's going to become a problem, I'll
+show you about in a minute, as we start peeling
+
+this systems engineering onion of getting
+down into the details.
+
+And deployable payloads.
+
+Cross-range.
+
+A little less than 1300 nautical miles cross-range.
+
+TPS material.
+
+We didn't know what the hell it was going
+to be, but that's what we started with.
+
+So, we began the contract for design, development,
+test and evaluation.
+
+NASA does pretty good stuff in-house.
+
+And I think with Dr.
+
+Mike Griffin at the helm now you're going
+to see a lot more of that coming into NASA
+
+where they're doing a lot of stuff in-house.
+
+But when it gets down to doing the detail,
+design and manufacturing and cost-control,
+
+down to the detailed parts and manifesting
+everything around, that's where the contract
+
+is.
+
+NASA doesn't have that capability in a large
+program.
+
+So, this is where we gave a contract to Rockwell
+International.
+
+They had the integration contract.
+
+And another company, Martin, had the external
+tank.
+
+[Backhaul?] had the SRBs.
+
+And who else am I missing?
+
+And Rockwell had the integration and Orbiter
+contract, both.
+
+This is what they started with.
+
+That was their authority to proceed configuration,
+even though this is shown as in 1972.
+
+But you see there is very little difference
+in the configuration then and what the configuration
+
+is today.
+
+There was some minor mods which are not worthy
+of even talking about right now.
+
+But let me give Aaron a lot of credit.
+
+His favorite word, the whole time he was the
+project manager, was no.
+
+And he had above his blackboard better is
+the enemy of good.
+
+We've got something.
+
+We know it will work.
+
+We knew that damn configuration would work.
+
+And Aaron got inundated with people coming
+back after we started the program.
+
+Aaron, if you put reaction control jets out
+on the wing tips and here and up on the vertical
+
+stabilizer you get a lot more control authority.
+
+And when you guys start looking at this guidance
+and control stuff in propulsion you're going
+
+to come up with that.
+
+But it complicated the entry in the thermal
+protection system.
+
+It complicated getting the fuel to those things,
+so Aaron said no, no, no.
+
+And the astronauts would come in.
+
+They'll always meet with Aaron at 7:00 in
+the morning because that's when they would
+
+get their word in.
+
+And so they would have to go do flight training
+or something like that.
+
+And, as they walked out the door, Aaron would
+say no.
+
+They didn't hear him, but it was always no.
+
+And that was critical in this thing.
+
+And so the program came in at $5.1 billion.
+
+It started $5.1 billion.
+
+It came in at $5.1 billion.
+
+It was only because of being able to say no.
+
+But to say no you better do a good systems
+engineering job at the beginning.
+
+And were there some faults and errors?
+
+Yeah.
+
+I'll confess and open my kimono here on the
+few of the things, but all in all it wasn't
+
+too bad.
+
+And I will say one other thing about systems
+engineering.
+
+It was interesting to watch four or five different
+large companies look at the various concepts.
+
+I can say this now because none of these companies
+even exist in the form that they were then.
+
+Grumman had a very large systems engineering
+organization.
+
+Rockwell had a very small systems engineering
+organization, almost down to one or two people,
+
+but they were extremely good.
+
+They were extremely good systems engineers.
+
+NASA went with Rockwell for a number of reasons,
+but one of the things that probably benefited
+
+the program was having a very concentrated
+set of engineering requirements coming out
+
+of a systems engineer which almost turned
+out to be one guy, Ed Smith.
+
+And he was very, very good at that.
+
+The reason I bring that up to you, the thing
+that's most defficient, from my perspective
+
+now in the United States today, are good systems
+engineers.
+
+Very good thermal engineers, good structural
+engineers, good propulsion engineers.
+
+There are very few systems engineers that
+are good.
+
+If you make a note of that and become one
+of those, you'd be highly sought after.
+
+So, a little bit of this is a repeat.
+
+As we went into these requirements, and from
+a government system's perspective, now the
+
+challenge was to give the contractor the requirements
+that they need but don't over-specify the
+
+requirements.
+
+We were very careful to say here are the top
+level requirements, don't ask us what the
+
+internal loads on the wing are because we're
+not going to tell you what that is.
+
+That is for you to decide.
+
+And, if you want to change something within
+these constraints, you can change it.
+
+But the burden is on you to make everything
+else right.
+
+That is something that I think the Orbiter
+did probably better than the external tank.
+
+I'll just say it like it is.
+
+Go ahead.
+
+I'm just wondering, sir, what happened to
+the canard configuration with the delta wing?
+
+What happened to it?
+
+Yeah.
+
+It was not selected.
+
+And I don't remember why it was not selected.
+
+What was driving it, I don't know.
+
+I don't have those notes anymore.
+
+It could have been cross-range.
+
+I don't remember that particular configuration,
+if it had the required cross-range for the
+
+payload mass.
+
+I just don't remember.
+
+I don't think it would have been cost.
+
+I think it was a lot of complexity.
+
+Well, it did have complexity so it had to
+add some cost.
+
+Weight-wise, it probably was not too different
+just because of the control authority of having
+
+the canards there.
+
+But that's a good question.
+
+Tom, you might mention [UNINTELLIGIBLE PHRASE].
+
+I'm going to touch on that, again, a little
+bit in a minute about what we did in surveying
+
+and determining the loads.
+
+And let me hold that if I can.
+
+Now we have begun with the design..
+
+When you use the term top level requirements,
+what does the top level refer to as opposed
+
+to just requirements or performance requirements?
+
+Well, the top level requirement changes as
+the phase changes.
+
+The very beginning, in '68, the top level
+requirement was a transportation system.
+
+We don't know what it's going to be, reusable,
+and we don't know how much payload it is going
+
+to have to carry.
+
+So, that was the top level requirement.
+
+Then it was to look at all of the combinations
+of things that you could create.
+
+The solution was it is feasible and we think
+that this is about what it's going to cost.
+
+Now, as we get into this point, these are
+the top level requirements.
+
+So, the granularity of the requirements increases
+as the program advances.
+
+Good question..
+
+For the challenges, now I'm going to call
+it the challenges of beginning this thing,
+
+we know what the configuration is, you know
+what the design life is, et cetera, all that
+
+kind of stuff, but we still haven't decided
+on what the material of the airframe is going
+
+to be.
+
+We estimated some stuff because it could be
+aluminum or it could be titanium and this
+
+is what it would be.
+
+And it all fits within the right cost and
+performance envelopes, but let's optimize
+
+that from a systems standpoint a little bit
+and see what that is.
+
+Some of the challenges in structural design,
+and I'm going to talk about each one of these
+
+things that's listed on here separately, should
+the cabin be an integral part of the fuselage
+
+or should it be a pressure vessel floating
+within the fuselage?
+
+Trade to be made.
+
+How are we going to account for thermal stress
+in this?
+
+Well, what the hell is thermal stress?
+
+Apollo, we didn't care a whole lot about thermal
+stress.
+
+It really wasn't an issue, not to the extent
+that a vehicle like this is.
+
+It was very sensitive for thermal stress.
+
+Compartment venting.
+
+We'll talk more about that.
+
+Major structure concept trades to reduce weight
+basically.
+
+And then how in the hell do we get the design
+loads on this thing?
+
+From a structural design criteria we said,
+well, let's start with 1.5.
+
+That's what all airplanes are designed for
+so we'll do that.
+
+Even though some of the boosters were designed
+for 1.25.
+
+Does everybody know what an ultimate factor
+safety is?
+
+That's the allowable of the material that
+you've decided to use compared to the maximum
+
+expected load that you will ever want to see,
+three sigma kind of loads.
+
+And then whatever the factor is about that,
+that's the factor of safety.
+
+So, you simply take the maximum loads you
+can expect to find, multiply it by 1.4 and
+
+it better meet what the allowable is.
+
+If there's margin in that allowable then that's
+called a design margin.
+
+Ideally, you would like to have zero margin.
+
+That still gives you a 40% factor of safety.
+
+Everybody with me?
+
+Yield is classically something that you decided
+on material.
+
+Well, I want to also have a factor safety
+on yield.
+
+And we sat around and asked ourselves why
+the hell do we care about that?
+
+The only thing you don't want it to do is
+you don't want it to deform such that it won't
+
+operate so doors won't open, hinges won't
+work, et cetera.
+
+We did not impose that on the program of the
+yield factor safety.
+
+We didn't on the Orbiter.
+
+The external tank did.
+
+And they paid a weight for that because if
+you put a 1.2 factor safety on yield for some
+
+materials, that gives you a lower allowable
+than an ultimate factor safety when you're
+
+really only interested in ultimate strength.
+
+And then we had said thermal stress is going
+to be important, but we don't want to be so
+
+conservative that we let the thermal stress
+add in such a way that it adds conservatism.
+
+But, at the same time, we don't want it to
+count on it if it's relieving when we cannot
+
+really rely on it to be there.
+
+So, it is decreasing from the stress point
+of view.
+
+A scatter factor of four on life for a hundred
+missions.
+
+What is scatter factor?
+
+Scatter factor just means a factor of four.
+
+If you have 10,000 cycles at 20,000 psi stress
+then you have to certify it for 40,000 cycles.
+
+Typically, most airplanes you fly around on,
+they have a design life of about 20,000 flight
+
+hours.
+
+I think that's about right.
+
+They are fatigue tested to 80,000 flight hours
+to make sure that they have that kind of factor
+
+on life.
+
+And then we said well, this thing is going
+to be used a lot, we've never looked at that
+
+before so we will arbitrarily say we'll use
+a 1.2 factor at the end of life or ultimate.
+
+And then these are just classical engineering
+material allowables that everybody uses today.
+
+A lot of people have mentioned lately, as
+we were thinking of the end of the life of
+
+the shuttle, that although it was designed
+for a hundred missions, I guess it was always
+
+assumed that those hundred missions would
+be flown over the course of just a few years.
+
+And so, I think it's true, you more concerned
+with the long-term effects of stress than
+
+things like weathering or being exposed to
+salt, air over 20 years.
+
+Is that correct?
+
+Well, you hit a very key point.
+
+And you're exactly right.
+
+It turns out a hundred missions wasn't really
+designing anything.
+
+I mean it could have.
+
+Well, as a matter of fact, it didn't.
+
+I don't know of anything.
+
+A hundred missions design is for a cyclic
+stress, high cycle, low stress fatigue or
+
+low cycle high stress.
+
+It didn't.
+
+But the environment sitting around or the
+life of the material exposed has.
+
+The leading edge turned out to be there is
+a degradation in the strength of the leading
+
+edge material, the carbon-carbon material
+because of being exposed to the conditions.
+
+There was some corrosion found in the wings
+during an inspection.
+
+Nothing was wrong with the low carrying capability,
+except it was beginning to corrode.
+
+[UNINTELLIGIBLE PHRASE] You've got me mixed
+up with somebody else.
+
+I'm not talking about avionics.
+
+[LAUGHTER] No, but it's true.
+
+There, I think, just to bring that up, the
+idea was they would not be good for that length
+
+of time so change them out, we're going to
+have to upgrade them anyway.
+
+Aaron, I think, just left being program manager
+when they decided to change,no you still were
+
+there, they decided to change the general-purpose
+computers.
+
+It took ten years to change the general-purpose
+computers because of all the certification.
+
+Did the use and safety factors, like what
+numbers you were using, how much did the Apollo
+
+program [UNINTELLIGIBLE PHRASE] aircraft safety
+factors?
+
+The Apollo program was like 1.2 factor of
+safety, as I recall, because it was a single
+
+use item.
+
+And I'm going to take the opportunity to go
+back and verify that, but I think that's was
+
+right for some conditions.
+
+And it could have been 1.5 on others.
+
+I know on pressure alone it was 1.5 psi.
+
+You say, well, why was it different for pressure
+than it was for others?
+
+Because there was some historical data there
+that NASA had that said that was the right
+
+thing to use.
+
+But that's a good question.
+
+Now you've caught me.
+
+I can remember on the boosters it was 1.25,
+but on the command module itself, let me retract
+
+that, it was probably 1.5.
+
+It was 1.25 on the boosters and 1.5 on the
+crude part of the vehicle.
+
+One of the challenges that we had here was
+to establish a criteria.
+
+These were our objectives.
+
+To assure that there was a realistic stress
+that we're putting in the vehicle and we weren't
+
+being overly conservative with it.
+
+We were not reducing the stress because of
+thermal gradients.
+
+And then we were incorporating the classical
+pressure induced stress.
+
+And now what were the details of that?
+
+Here were the details.
+
+We came up with this algorithm that says we
+will use a factor of 1.4 on all external loads
+
+because that's aerodynamic loads, inertia
+loads and so forth.
+
+We will use a factor of 1.4 on the thermally
+induced loads, if you will.
+
+They are really thermally induced strains
+and stress.
+
+We'll use a 1.4 factor on that if it's additive
+to the mechanical, but if it's subtractive
+
+we'll only use one because we probably won't
+reach the maximum thermal conditions so you
+
+cannot rely on that.
+
+On pressure, we used 1.4.
+
+Unless it was pressure alone, we used 1.5.
+
+But the whole thing is we would never have
+less than 1.4 of the total combined load.
+
+So, that's what we did.
+
+And so you say why in the hell did you do
+that?
+
+Why did you have to go to that kind of detail?
+
+The reason being is because you probably had
+about 30,000 stress engineers working on the
+
+program, and they needed to know how to combine
+this stuff.
+
+If you didn't, this guy is going to do one
+thing and this guy is going to do something
+
+different.
+
+We got it down to that level to save weight
+in the vehicle and save complexity in the
+
+vehicle.
+
+Well, we have our criteria set now.
+
+Let me give one more story on marginal safety.
+
+One of the people that I showed you at the
+top of the credits list was John Yardley.
+
+And probably Aaron and Larry Young and other
+people would probably agree with this, John
+
+Yardley is probably the best engineer that
+I ever knew in my entire life.
+
+He's probably one of the best managers I ever
+knew.
+
+John Yardley had the job of being the Program
+Manager on McDonnell Douglas F4 aircraft.
+
+And he was an old stress guy.
+
+He knew that weight was going to be a critical
+parameter in the success of that program and
+
+he had to keep the weight out.
+
+What he did, on that previous slide where
+I showed you the stress criteria and make
+
+sure that you have a zero margin of safety
+with a factor of 1.4, is he told all the stress
+
+engineers, because they all worked for him,
+design to a negative 10%.
+
+Which means if you really do your job right
+this thing is not going to be able to reach
+
+ultimate load.
+
+It's going to break.
+
+But he also knew that they were probably conservative
+because he was one of those guys.
+
+And he also had in his hip pocket, if he's
+wrong he would find out because he had the
+
+opportunity to do an ultimate load test on
+the airframe.
+
+It turns out he did the ultimate load test,
+it passed the ultimate load capability and
+
+he saved a bunch of weight in airplane which
+made it a very successful airplane.
+
+Sometimes from a systems perspective, it's
+what you learn in the details or in the trenches
+
+as you're coming up and being able to apply
+it the same way that Aaron did a lot of stuff
+
+as he was managing the program.
+
+On the airframe we looked at a lot of different
+structural materials, we looked at a lot of
+
+different TPS materials, and some of the parameters
+that were coming out in there was not only
+
+strength of the material but how much heat
+sink there was because you were having to
+
+rely on that to keep the weights down.
+
+And let me go up one slide and show you something
+here.
+
+I don't know if you can read that, but on
+the left side what it was is it was all aluminum
+
+airframe.
+
+It had an ablator thermal protection system
+on it.
+
+And you said, well, I thought you said it
+was going to be fully reusable.
+
+Well, we also had a cost constraint.
+
+So we put that in there as a reference point.
+
+And that was the lowest cost.
+
+And here's weight up here.
+
+It wasn't quite the lowest weight, it was
+pretty low, but it still was violating the
+
+objectives and requirements that we had.
+
+And we said that will be our reference point.
+
+Then we looked at different types of aluminum.
+
+We looked a beryllium.
+
+We looked at titanium.
+
+We looked at the thermal protection system
+on a beryllium substrate.
+
+Every kind of combination you could think
+of.
+
+The interesting thing was, look where the
+whites were staying.
+
+They were all staying within the 60,000 to
+80,000 pound total weight envelope.
+
+What was happening is we were decreasing the
+thermal protection system thickness.
+
+If we were using titanium, which we could
+operate to 600 degrees, the TPS weight was
+
+going down.
+
+Titanium was not as good a heat sink as aluminum,
+even though we're working it to a higher temperature.
+
+And it turned out that the combination of
+TPS plus structure was pretty much a constant.
+
+I'm oversimplifying it, but that's basically
+what it was.
+
+And you can see where the cost was.
+
+This is beryllium titanium.
+
+The cost was way out of whack compared to
+everything else, so we said we're not going
+
+to do that.
+
+And there were some other exotic materials
+over here for hot structures.
+
+We said let's now decide what this airframe
+material is going to be.
+
+It's going to either be aluminum or titanium.
+
+And total weight, total cost doesn't make
+any difference, they're about the same.
+
+We weren't' smart enough to decide so we went
+out to the skunk works.
+
+Kelly Johnson skunk works, I don't know if
+you know what that means.
+
+Kelly Johnson designed and built more airplanes
+in a short period of time.
+
+And they were the ones, Larry, was it in the
+`50s, the SR-71 was designed, the Black Bird?
+
+I think it was in the 1950s.
+
+It was somewhere in there.
+
+They had to develop titanium for that airplane.
+
+It was a hot structure design.
+
+We went out and spent some time with Kelly
+Johnson.
+
+We went through all this stuff with him.
+
+All right, Mr.
+
+Johnson, at the end of the day it's a mix
+for us.
+
+Would you build it out of aluminum or titanium?
+
+He said aluminum.
+
+And the reason being is because titanium was
+so difficult to work to produce.
+
+The manufacturing was difficult.
+
+Today it's a lot less difficult than it was
+then.
+
+We made the decision and went with aluminum,
+so we had to protect that structure to 350
+
+degrees.
+
+That was a lot of work and a lot of analysis
+to make that decision.
+
+And we talked to Aaron and said that's what
+we want to do, and he said go for it.
+
+The next thing we looked at, we got the airframe
+design, now we're starting to put together
+
+the fuselage.
+
+We said we can put this crew cabin as part
+of an integral part of the fuselage or we
+
+can make it a separate pressure vessel inside.
+
+Went through the trades on this.
+
+And we came up with some of the discrete advantages.
+
+It's a purely simple pressure vessel when
+you don't have any inertia loads, except the
+
+mass that is inside the crew module itself.
+
+There is a discrete attachment between the
+crew module and the forward fuselage which
+
+means you could start the design and construction
+of these two things in parallel.
+
+And simple interfaces are important.
+
+Somebody mentioned modularity, and it's probably
+modularity in some analytical tools.
+
+But simple interfaces where you're putting
+things together are extremely important.
+
+So, this created a very simple interface for
+us.
+
+Also, we didn't have a lot of heat transfer
+to the crew module.
+
+It was easy to control the environment within
+the crew module.
+
+And we designed it out of a material, a 2219
+aluminum, which had an inherent advantage
+
+of if it gets a crack, the crack doesn't grow
+catastrophically under the operating stress
+
+before it starts leaking a lot.
+
+Well, that's good because, from a crew safety
+standpoint, you know that if the seals are
+
+working and it's still leaking you've got
+a crack in that pressure vessel but it's not
+
+going to be a crack that is going to propagate
+to be a catastrophic failure.
+
+We chose the floating design.
+
+When I talked a while ago about the crew of
+seven in two weeks now compared to four for
+
+seven days, back in '72 we said we don't know
+what the requirements are going to be, but
+
+let's make this thing as robust as we can
+without penalizing ourselves weight-wise.
+
+So, we went back to Apollo and said what were
+all the densities in the Command Module for
+
+the Crew Module?
+
+We figured out a density and a volume.
+
+We said that will be our baseline.
+
+That's what we came up with.
+
+Well, for another 50 pounds of weight, we
+could increase the carrying capability of
+
+the crew module by about 500 pounds.
+
+That was a good trade at that time so we did
+it.
+
+We just said we're going to design this thing.
+
+Instead of for 25,000 pounds we'll design
+it for 30,000 pounds of payload carrying capability
+
+within the crew module.
+
+It turned out to be a good decision.
+
+We weren't smart enough to know operationally
+we'll need larger crews for a longer period
+
+of time, but that helped us out a lot.
+
+You probably also want to mention, when you
+look at the structure of the crew cabin, in
+
+both of the shuttle disasters, the Challenger
+and Columbia, we have every indication that
+
+the crew cabin actually survived the breakup
+of the Orbiter.
+
+So, it really was an excellent structure.
+
+I'm glad you brought that up.
+
+As a matter of fact, I have a note here to
+bring it up myself.
+
+Jeff is exactly right that that's what it
+did, but it was never designed to be a crew
+
+escape module.
+
+It had some inherent capabilities, probably
+could survive some things that it couldn't
+
+had it been part of the fuselage, different
+flight regime, so it had that inherent capability.
+
+But it was never designed -- And I know there
+was a lot of talk after Challenger that it
+
+looked like it would have survived all the
+way, but it would have never made it all the
+
+way.
+
+But it would have under a lot of conditions.
+
+We said Apollo didn't have a lot of thermal
+stress issues, but we know this vehicle now
+
+we've skinnied down weight-wise as much as
+we can to the extent that the thermal gradients
+
+between any two different pieces of structure,
+where they were different materials or different
+
+masses is going to cause a thermal gradient.
+
+And thermal gradient cause thermal stresses.
+
+And you will see in a minute that was not
+only important to stress but is important
+
+to all these tiles we were sticking on the
+outside of this thing.
+
+So we said we have to look at every one of
+these thermal gradients and we have to understand
+
+what that induced stress is because we had
+an indication it was going to probably contribute
+
+about 30% of the total stress in the vehicle.
+
+It was going to be from thermal stressors
+at different flight regimes.
+
+Kelly Johnson helped us out pretty well deciding
+on aluminum and titanium.
+
+We said why don't we just fix this thing?
+
+We'll design around all the thermal stress.
+
+We'll put stress relief in it, like expansion
+joints along the sidewalk.
+
+We'll do all these kinds of cute things and
+we'll simplify the heck out of this.
+
+As a matter of fact, the SR-71, the Black
+Bird, it had huge thermal stress problems.
+
+So the wing on an SR-71, normally the skin
+carries a lot of the wing bending.
+
+Not true on an SR-71.
+
+It's corrugated skin so it can expand and
+contract.
+
+All the wing bending is carried in the spar
+caps, the frames that go out the entire wing,
+
+and the caps themselves.
+
+They paid a penalty but avoided the thermal
+stress issue.
+
+We said we'll be smart with that.
+
+We'll go talk to the SR-71 guys.
+
+And we'll go talk to the Concorde.
+
+The Concorde was an airplane that had high
+thermal stress, even though it wasn't that
+
+high a temperature.
+
+I think it was reaching 500 or 600 degrees
+outside, but it was moving fuel around all
+
+over the vehicle.
+
+So when it moved this high mass of fuel from
+one part of the vehicle to the other, it was
+
+creating big thermal stresses.
+
+They knew what to do.
+
+They designed in stress relief at these high
+points.
+
+It bit them.
+
+Every time they did it they had fatigue failures.
+
+Every time they did that.
+
+They finally gave up and said just accommodate.
+
+We said we'll do that.
+
+Now then, we decided on that criteria.
+
+We're going to account for thermal stress,
+but how can we do it?
+
+We don't have a 3D model that we can apply
+mechanical loads to, I'll call aero loads
+
+mechanical loads, and temperature distribution.
+
+The finite element model didn't exist.
+
+We had a finite element model that had 50,000
+degrees of freedom, but we didn't have a computing
+
+capability to combine thermal and mechanical
+loads on there at the same time to be able
+
+to decide how to size the structure.
+
+We said now we've got a problem.
+
+What the hell are we going to do about that?
+
+What we did is looked at what were the conditions
+causing the thermal stress?
+
+Going uphill thermal stress is not an issue.
+
+It's all coming back in, in the entry phase.
+
+We knew we had initial conditions that were
+going to primarily be the cause of it.
+
+Coming back where the vehicle had been sitting
+in top sun for a long time, bottom sun for
+
+a long time, side sun for a long time, so
+we looked at those initial conditions as being
+
+the worse.
+
+And we proved to ourselves that it was the
+worst.
+
+Then what we cleverly did is we went around
+the vehicle where we had a detailed structural
+
+model of a lot of stuff.
+
+And we created a hundred different thermal
+models of different types of structure.
+
+This is one that was in the wing truss.
+
+We had a wing skin panel, we had a truss member
+and a lower wing skin panel.
+
+And we did a detailed thermal analysis of
+these hundred models.
+
+We then applied that to a structural model
+simplified, which was giving us the internal
+
+loads and stresses that we needed, and then
+we hand extrapolated that over the entire
+
+vehicle.
+
+There was no other way to do it.
+
+So, as you look at your analytical capability
+probably on your damn laptop now, computing
+
+capability, you couldn't really do it on that,
+but think about that.
+
+And I noticed nobody wants to talk about structures
+as one of these groups.
+
+If one of you changes then I'm going to feel
+really good when I go back and fight the hurricane
+
+in Texas.
+
+But that's the way we did that.
+
+It was a necessity that we had, but we didn't
+have the capability so we invented a way to
+
+do it.
+
+And, I'll show you in a minute, it worked.
+
+Another issue that we had.
+
+Normally you'd like to just vent everything
+through one area in the vehicle, but we couldn't
+
+do that because the payload bay had to be
+very clean.
+
+It had to be contamination free.
+
+And there was hydrogen in the backend of the
+vehicle.
+
+There was a pressure vessel in the front-end
+and a bulkhead up there.
+
+We said what we've got to do is we have dictated
+to ourselves that we have to design a venting
+
+system.
+
+This turned out to be a major part of a lot
+of internal loads in the vehicle because of
+
+venting from one compartment to the other.
+
+And, stop and think about it, we had vents
+all along the fuselage.
+
+We had a different pressure coefficient at
+each one of these vents for our various attitudes
+
+during ascent, for our various attitudes during
+entry, so we now had a whole myriad of complicated
+
+internal pressures that we had to accommodate.
+
+But that was pretty straightforward.
+
+We just complicated our design with the venting
+system that we had, but we had to do it to
+
+meet the requirement.
+
+I don't know that people are actually aware
+that there are all these vent doors because
+
+it's not something that you would normally
+pay attention to in the pictures.
+
+That's right, you don't.
+
+As a matter of fact, in this book that Jeff
+referenced, it shows where all the vent doors
+
+are.
+
+I didn't show that detail to you today.
+
+And they do open and close at different times
+during ascent and entry.
+
+Venting just for carbon dioxide gases?
+
+No.
+
+When you start off you're at one atmosphere,
+right?
+
+As you rapidly go uphill there's a delta p
+across internal bulkheads and internal compartments,
+
+internal and outside the vehicle.
+
+And, depending on what the flight regime is
+and where the shockwave is and where the vent
+
+door is, it's changing the whole venting thing.
+
+That's a whole lecture in itself on what we
+did.
+
+The crew compartment is designed to have a
+delta pressure of one atmosphere, but inside
+
+the payload bay, that's not designed to be
+a pressurized environment.
+
+And so you need to be sure that the air can
+get out of the payload bay fast enough that
+
+you don't over-pressurize, for instance, the
+payload bay doors or other parts of the structure.
+
+There were some other trades that we had to
+make.
+
+Let me skip forward so you can better understand
+this.
+
+For reference purposes, the main engines are
+here, 1.5 million pounds of thrust coming
+
+into this part of the vehicle.
+
+There is a Longeron that goes all the way
+along here.
+
+A big mass up here with a crew module.
+
+And the crew module, I showed you, had just
+discrete attachment points.
+
+All of the ascent inertia loads are reacted
+right here, so all these loads go along this
+
+Longeron.
+
+Now, all of a sudden we have a very good and
+efficient load path.
+
+The wing right here, this is a primary load
+carrying member of the wing.
+
+That's a spar.
+
+And it ties into this big bulkhead which is
+right here.
+
+When Jeff talks about the pressure differential,
+don't forget this thing is 15 feet in diameter
+
+here so you can imagine the total loads you
+have on that with a couple of psi delta p.
+
+It's big.
+
+That was a significant part of the driving
+stresses in that.
+
+Another point I want to make about this is
+-- Well, I talked about simple interfaces
+
+between the crew module and the forward fuselage
+with bolted attachments.
+
+We had a simple interface between the wing
+and the mid fuselage.
+
+A simple interface between the mid fuselage
+and the aft fuselage.
+
+The same thing with the vertical stabilizer
+and aft fuselage and these orbital maneuvering
+
+propulsion system.
+
+That was important, from a structural point
+of view, to be able to modularize and analyze
+
+these things.
+
+But it was also important because four different
+contractors built all these parts so they
+
+had to have an interface that they could not
+only design and analyze to but that they could
+
+physically attach to.
+
+Sometimes, when you have just a sketch on
+a piece of paper, you don't think about that.
+
+And it does cause a little bit of complexity
+sometimes in a program.
+
+The main thrust structure is carrying 1.5
+million pounds of load from the engines.
+
+How do we design that?
+
+Well, we could have done a space frame or
+we could have done a truss configuration.
+
+We decided to go with the space frame or the
+truss rather than a plate girder, the term
+
+I didn't use correctly.
+
+And with that we saved 1700 pounds of weight
+in the vehicle.
+
+We used titanium.
+
+And this is a compression design.
+
+We thought we needed to get a little bit more
+weight out of this thing.
+
+What can we do to increase the compression
+modulus of titanium?
+
+We put boron/epoxy, scabbed it on the axial
+load members of the thrust structure, and
+
+that's the way we got a lot of that weight
+out.
+
+That was a manufacturing problem, I won't
+go into now, of how you build this thrust
+
+structure, but it works fine.
+
+The aft wing carried through -- Excuse me.
+
+Go ahead.
+
+I just had a quick question.
+
+Sure.
+
+We heard earlier that there was a CG problem
+in that the CG was too far forward in the
+
+aft [but bled in the back?] for a number a
+number of missions.
+
+I was wondering how that weight that they
+had to add to the CG compared to the weight
+
+that you guys saved.
+
+The weight of the payloads themselves, you're
+saying that there was a problem if heavy weights
+
+were too far aft or too far forward?
+
+The Orbiter.
+
+I guess the CG location was too far forward
+and they had to adjust it on certain missions
+
+by adding weight near the back.
+
+Well, what that is, that is true and that's
+a problem.
+
+It's not a problem.
+
+It's something that has to be addressed on
+every mission, depending on what the payload
+
+is that you're carrying.
+
+If you have a real heavy forward payload,
+yeah, you have to add some ballast to the
+
+aft end of the thing.
+
+Now, normally the way they do it is they'll
+find some payload that can fit in the aft
+
+end to help ballast that.
+
+But I think, in some of the early flights,
+we put some ballast in the back for CG control.
+
+We've carried many tons of lead into orbit,
+so it was ballasting the thing for control
+
+purposes.
+
+The same way yesterday in Jet Blue, a lot
+of people had to move to the back end of the
+
+airplane because they wanted that CG for a
+little bit different landing performance.
+
+1307 bulkhead, we saved about 500 pounds there.
+
+Now, see what we're doing?
+
+We started out with the initial trades in
+the early concept phases.
+
+What's the wing loading?
+
+We didn't care about what the internal structure
+trades were.
+
+Now we're getting down to trading all the
+stuff at a semi-macro level.
+
+And I'll show you in a minute a micro-level
+that we had to get into, which was pretty
+
+interesting.
+
+How are we doing time-wise?
+
+We're OK.
+
+So, we saved some weight there.
+
+An interesting thing about the payload bay
+doors.
+
+We decided that for this vehicle to be safe
+and to re-enter those doors had to close.
+
+We had a lot of trouble in Gemini with things
+on orbit not working.
+
+Mechanical systems quite often are problems.
+
+Docking systems are problems.
+
+There have been a lot of door problems on
+orbit in spacecraft.
+
+And you design them and you put them in thermal
+vacuum chambers and they all work, but you
+
+get on orbit and sometimes they don't work.
+
+Maybe it's thermal distortion that we're not
+accounting for.
+
+So, we said that is critical.
+
+We've got to close these payload bay doors.
+
+What we did was say the way we're going to
+do that is the payload doors will carry only
+
+two types of load.
+
+They will carry pressure loads, like Jeff
+talked about, and they'll carry torsion loads.
+
+Because, if they are closed, we know that
+it is good for torsion in the vehicle, reacting
+
+torsional loads.
+
+But we will not let them carry body bending
+loads or else we cannot make them flexible
+
+enough.
+
+What we did is all of the body bending in
+this vehicle is carried along this Longeron
+
+through this section in the lower skin of
+the vehicle.
+
+This is the modulus of the vehicle, if you
+will, at a cross-section here between this
+
+Longeron and the lower skin.
+
+Payload bay doors don't come into being.
+
+And the way the doors close on orbit is they
+start zipping along from here up to the top
+
+because they are flexible.
+
+And the same way back here, they zip closed,
+zipping just a latch at a time.
+
+They were sort of ratcheting themselves closed.
+
+And then they close along the center line.
+
+There has never been a problem with payload
+bay door closures on orbit.
+
+It was something we decided to add to the
+design.
+
+We could have made the vehicle lighter had
+we not done that, but we would have also complicated
+
+the safety of the vehicle if we had done it.
+
+Sort of in line, but it's not the CG thing,
+we had a payload attachment issue.
+
+And, when we were laying out all this stuff
+in the early `70s, we didn't know what the
+
+payloads were.
+
+We knew what the total mass was.
+
+We knew there may be five at a time.
+
+We didn't know what they were.
+
+Now, you can just go in and bolt a payload
+into the fuselage of the Orbiter.
+
+And if you just do that randomly or without
+thinking about it, now all of a sudden you
+
+start analyzing the Orbiter and you start
+twisting it, what happens?
+
+The payload becomes part of the load path.
+
+Now, all of a sudden, you have impacted the
+design of the payload or maybe you have impacted
+
+the design of the Orbiter depending on what
+is happening in the payload.
+
+We said ah-ha, what we'll do is make it so
+it's statically determinant.
+
+If two things are attached statically determinately
+they cannot interact with one another as far
+
+as their stiffnesses are concerned.
+
+We said that's what we're going to do.
+
+We'll put attachments along the Longerons
+to carry the axial loads, some along the keel
+
+to carry some of the lateral loads.
+
+Viola, we've got it.
+
+So, the requirement became that we would design
+it that way.
+
+Our next step was, and you can ask Al Louviere
+when he comes up about that because Al Louviere
+
+and Max Faget told me they would never fly
+with those Longerons that way.
+
+We did it anyway.
+
+What we had to do then was say now we understand
+what the attachment is.
+
+How do we determine within the CG constraints
+for these different masses -- And we had to
+
+assume what they were not knowing exactly
+the definition of the payloads.
+
+We did a Monte Carlo analysis.
+
+Ten million cases of combined payloads.
+
+CG locations, numbers of payloads, forward,
+aft, all that.
+
+And we did that with a Monte Carlo analysis.
+
+We said voila, that's where we're going to
+design the mid fuselage.
+
+That's the way we did it.
+
+Now getting into the detail design loads.
+
+How do we determine all these things now?
+
+Because now it's coming down to sizing the
+vehicle.
+
+This part of the flight regime from liftoff
+through max Q, that's a critical loading condition,
+
+a critical design for the Orbiter.
+
+When it gets into orbit pretty benign.
+
+Nothing is really happening up there except
+some temperatures which are going to be important
+
+at this point over here, because now all of
+a sudden you start adding more heat into it.
+
+Now you get into the regime where you're maneuvering
+in the atmosphere.
+
+Now you're in a different loading regime which
+becomes critical.
+
+So, critical as far as the airframe is concerned,
+is here and over here only.
+
+Let me break that down into the constituent
+portions there.
+
+Liftoff loads.
+
+We had another statistical challenge here
+because what we had to do was needed to look
+
+at all the variables associated with the rocket
+engines.
+
+They have start sequences.
+
+We've got three main engines that are not
+going to start exactly the same time.
+
+They're not going to come up with the same
+thrust profile as they start up.
+
+The thrust vector misalignment is going to
+be different.
+
+And we also had to look at ignition over pressure.
+
+And I'll show you that was a surprise to us.
+
+Also part of liftoff we had to look at winds
+and gusts, vortex shedding, proximity of aerodynamics
+
+to the other structures is on the gantry in
+the pad.
+
+And then we had to do the pressurization and
+also look at shrinkage of these vehicles that
+
+components or elements at cryo-temperatures.
+
+Here was a cross-section, in a generic sense,
+of what's happening during liftoff.
+
+There is some combination of winds that you
+have to account for.
+
+And I will show you what we did there.
+
+The thrust profile from the SSMEs.
+
+The SRBs come up to thrust after you get confirmation
+that the engines are operating at full performance.
+
+And there is a lot of vibration acceleration
+going on.
+
+Here is something that becomes pretty obvious
+after a while.
+
+When you have a vehicle that is tied down
+here with a base moment and you put 1.5 million
+
+pounds of thrust on it, this vehicle is going
+to bend over this way.
+
+There is a lot of strained energy in the solid
+rocket motors when that happens.
+
+If you were to ignite the SRBs, when that
+vehicle is over here, the party is over because
+
+it releases all that strained energy and the
+SRBs couldn't take it.
+
+When you see the Orbiter prior to liftoff,
+the SSMEs will come up, you will see the vehicle
+
+do like this.
+
+And then, when it comes back over zero, viola,
+you kick off the SRBs.
+
+But you have to wait until it gets back to
+that neutral point.
+
+A little detail that is pretty important.
+
+Ascent.
+
+A really complicated part of the design of
+the vehicle, especially with the aerodynamic
+
+surfaces.
+
+As I said before, you would like for these
+things not to be there during ascent.
+
+They don't buy you anything.
+
+You just need them coming back.
+
+Some other complications here are the acoustic
+effects will become important, as I'll show
+
+you, in acoustic fatigue for the vehicle.
+
+I showed you life.
+
+Well, that's going to be a critical thing.
+
+Another thing is the plumes of the vehicle
+are changing the pressure distribution as
+
+you're going up.
+
+The pressure distribution along the Orbiter,
+especially the wing, is changing the whole
+
+times you're accelerating, not only through
+the various mach regimes but also because
+
+of the blockage from the plume expansion.
+
+We said how in the world are going to do that?
+
+We cannot analyze all those things.
+
+If we do it deterministically, you won't get
+a capability that you need, we thought, operational.
+
+We said what we'll do is one piece of data
+that we had, we had synthetic wind profiles
+
+for everything that existed at the Cape.
+
+We said that's a given.
+
+We'll use these synthetic wind profiles as
+a guideline to all of our winds aloft.
+
+What we need to do is decide what the angle
+of attack and the side slip is going to be
+
+through this vehicle flying through these
+winds and a control system that's changing
+
+the attitude of the vehicle.
+
+That's a factor that we have to consider and
+that's going to be important for the design
+
+of the elevon surfaces and all because they're
+getting loaded up pretty heavily at that time.
+
+There are dispersions in the propulsion system
+that have to be added.
+
+And then what we decided to do, after we looked
+at all that, we said what we're going to do
+
+is we're going to take all these parameters,
+and you won't find this in any textbook, but
+
+we created something called a squatcheloid.
+
+And I forgot to look up what squatcheloid
+means.
+
+It must be a Greek term that was really good.
+
+But what we did was flew the vehicle through
+different mach numbers.
+
+And we looked at the various conditions we
+could get at for combinations of dynamic pressure
+
+and angle of attack and dynamic pressure and
+side slip for all the mach numbers, and then
+
+we said is that realistic to do, not only
+from a control systems standpoint but from
+
+a standpoint of the propulsion system capability?
+
+And we said it is feasible to do so we ought
+to design within those envelopes.
+
+What we did was walked our way around all
+of these external points with pressure and
+
+inertial loads and everything else and we
+looked at the structural model that we had
+
+simplified.
+
+And we said we found the points that were
+critical for the vertical stabilizer, for
+
+the outboard elevon, et cetera, and that's
+the way we designed the vehicle for ascent
+
+loads.
+
+The thing that that enabled us to do, too,
+is it enabled us to do a rational combination
+
+that Aaron brought up a while ago.
+
+What did you do with the SSMEs for engine
+out and that kind of stuff?
+
+It let us do a rational combination of engine
+out and also engine vector control.
+
+You could design the thrust structure so that
+the engines went out to the extremes, but
+
+it didn't make sense as far as the control
+system was concerned.
+
+What we did is we saved a lot of weight in
+the vehicle by using a deterministic or realistic,
+
+I should say, SSME thrust profile and vector
+characteristics.
+
+Well, I just mention that.
+
+That's what the squatcheloid did for it.
+
+Also what it did was then gave the guys who
+were designing ascent trajectories, now they
+
+had an envelope to design to, which was key
+for their operations.
+
+Next problem.
+
+Now we come back to descent loads.
+
+When you said that you designed it for realistic
+cases instead of worst cases, does that mean
+
+the engines were never able to vector all
+the way out to maximum?
+
+Right.
+
+It just could not happen?
+
+It could not happen.
+
+That was a failure mode that it had enough
+redundancy and it couldn't happen, and there
+
+wasn't any need of creating a load condition
+like that.
+
+It couldn't happen.
+
+OK, so you looked for it.
+
+We looked for the cases where you could be
+in the worst case winds, the worst case misalignment
+
+with the SRB, with the different throttling
+of the engines.
+
+And we did all that and said to control this
+vehicle, because if you cannot control the
+
+vehicle there's no need to look at that load
+case.
+
+We said to control it within those environments,
+what's the extreme of the engines?
+
+We said that's a design case for the thrust
+structure.
+
+Good question.
+
+Descent loads.
+
+This was pretty easy.
+
+The structure guys said this is a piece of
+cake because this vehicle is coming back in,
+
+in a ballistic trajectory.
+
+And, viola, there are not even loads on this
+vehicle.
+
+Well, that didn't make a whole lot of sense
+because we knew that there would have to be
+
+more maneuvering capability than anybody was
+fessing up to.
+
+Not that they weren't trying to hide it, but
+we weren't smart enough.
+
+The Aaron Cohen guys weren't smart enough
+to know all the conditions we would have to
+
+fly it to.
+
+What we did was we went through the classical
+Venn diagram where you're plotting for different
+
+mach numbers.
+
+The normal load factor versus the velocity
+of the vehicle that it can fly in that flight
+
+regime.
+
+We said if this thing is going to behave like
+an airplane and have to perform like an airplane,
+
+we are going to design it like an airplane.
+
+We caught a lot of guff.
+
+When Bass Redd comes in and talks in the future
+ask him about this because he fought us on
+
+this hand and foot.
+
+He said you guys don't have to design it that
+way.
+
+We said well, we're going to, but let him
+have capability in his aerodynamics and talk
+
+to the control system guys about that, too.
+
+And I see the Draper guys left on that.
+
+[LAUGHTER] We said we're going to build in
+that capability for this thing to maneuver
+
+like an airplane.
+
+2.5 g's normal load factor.
+
+Follow-up classical Venn diagram where we
+have equivalent airspeed of 375 psf.
+
+We were determining what the equivalent air
+speed for those conditions was.
+
+And then we did it.
+
+Now we've gotten up to a point I'll call CDR,
+and a point I should have mentioned a while
+
+ago.
+
+When I showed the authority to proceed, there
+aren't any drawings which exist, except some
+
+sketches.
+
+I mean there are mol line drawings and that's
+about it.
+
+And the mol line of the vehicle was what came
+out of all the other studies.
+
+It said that's it, we've got to put everything
+within this mol line for this vehicle to perform
+
+like it is.
+
+But there are no detailed drawings.
+
+When you get to a preliminary design review
+in a classical design and development program,
+
+typically that's about where you reach 10%
+of your drawings that are released.
+
+And what does it mean to release a drawing?
+
+That means you sign it off, whatever your
+discipline is, and it say we can make this
+
+airplane to these drawings and it's given
+to the people to go make it.
+
+So, once you release a drawing you don't ever
+want to bring it back and change it because
+
+it costs you a lot of money.
+
+The PDR, which was somewhere like about '73,
+'74, somewhere like that, that was the state
+
+which we existed.
+
+We hadn't defined everything on the structural
+low pass like I told you about a while ago,
+
+nor the materials.
+
+Now we're at the detail design.
+
+Now we're into CDR, that's the critical design
+review, and 90% of all your drawings are released.
+
+And now it gets very expensive to go back
+and change.
+
+You can just see how it would ripple through
+the entire operation if you change a drawing
+
+at that time.
+
+You have to, to make it work sometimes, but
+you like not to change it.
+
+What we have to do here, our challenge from
+a structural point of view is to complete
+
+the design, do some of the details which means
+get weight out of the vehicle where you can
+
+scrape it without really changing a lot of
+stuff.
+
+And then also decide how you're going to certify
+the vehicle.
+
+It means what you're going to do on the ground
+to say it's really safe for the crew to get
+
+in.
+
+That's what that was.
+
+Weight reduction is a major part of the program.
+
+Here are some of the things that we took out
+about this timeframe.
+
+We took out 900 pounds of weight in the payload
+bay doors.
+
+We didn't change the configuration, they were
+still flexible, but they were aluminum honeycomb.
+
+We said we can save 900 pounds if we go to
+graphite/epoxy.
+
+Graphite/epoxy characterization of the material
+didn't even exist then.
+
+Literally Aaron, myself and three or four
+other guys sat around.
+
+We said OK, Aaron, this is what we have, this
+is what we know about it, here are the risks
+
+associated and here is the weight savings.
+
+Go for it.
+
+So, we went for it and it worked.
+
+That was the largest graphite/epoxy structure
+ever flown.
+
+We characterized it, passed that on to the
+industry and that helped a bunch.
+
+Another little interesting thing -- I have
+to watch my time here.
+
+I mentioned the spending profile.
+
+Well, we got into the program about the time
+we were starting to make the payload bay doors,
+
+which is probably '75, '76.
+
+And Aaron didn't get all the money that he
+needed.
+
+We built the first set of payload bay doors,
+which is people process dependant.
+
+It's like laying up fiberglass.
+
+It was all hand layup with epoxy and bake
+it and all that kind of stuff.
+
+We got the first set built and we fired everybody
+because we didn't have enough money to keep
+
+them on the payroll for the rest of that year.
+
+We literally laid everybody off at Rockwell
+in Tulsa.
+
+And they came back a year later, not all of
+them, but we had to start over again.
+
+So, there is a risk associated with that.
+
+Thrust structure.
+
+We saved 1200 pounds by stiffening, like I
+told you about a while ago.
+
+And then we used a bunch of other composites.
+
+A lot of people said, especially after Challenger,
+let's get rid of this vehicle because it's
+
+antiquated and was designed too long ago.
+
+That probably is still one of the most advanced
+composite structure vehicles flying today.
+
+Except, where there is a lot of aluminum honeycomb,
+you probably could go with graphite/epoxy.
+
+And I will give you a challenge with that
+later on.
+
+But there are beryllium aluminum struts in
+here.
+
+There are boron/epoxy scab on devices.
+
+There is graphite/epoxy all over the vehicle.
+
+Not all over the vehicle.
+
+In a lot of places in the vehicle.
+
+The vehicle has got a lot of composites.
+
+And we stretched to be able to do that.
+
+Certification.
+
+Now we've got the thing pretty well designed.
+
+What are we going to do to certify this thing?
+
+This is where we deviated from the norm and
+were pretty innovative.
+
+Classically, in the way this program started
+off, there was a dedicated structural test
+
+article and there was a dedicated fatigue
+test article.
+
+There were a couple of problems with that.
+
+If you don't need it, you might as well not
+build it, even though that was in the program.
+
+The situation was, as I showed you a while
+ago, thermal stress was a major part of that.
+
+You couldn't apply a mechanical and thermal
+load to this vehicle and still be practical.
+
+Concorde did it.
+
+The way that Concorde was designed and certified,
+they applied mechanical loads in an environment
+
+in which they could induce the temperature
+by convective heating on that vehicle.
+
+And it took them like three years to test
+the vehicle.
+
+And it was extremely expensive.
+
+It was a big jobs program for Greg Britton
+and France and some of the others, but we
+
+decided we couldn't afford to do that so we
+are going to have to figure out how else to
+
+do it.
+
+Besides that, Aaron had $100 million problem
+that year.
+
+What can you guy help us do?
+
+What we'll do, we think we can do this, is
+take an airframe and we will apply 110% of
+
+the limit mechanical loads only to it.
+
+And that doesn't certify anything.
+
+And then we will put strain gauges all over
+this vehicle.
+
+And we will pre-predict what the strain response
+is going to be for 3,000 points on the vehicle.
+
+If we can pre-predict what the strain response
+is for applying a bunch of different loads
+
+then we know how to analyze the vehicle.
+
+That proves we know how to analyze it.
+
+We can extrapolate to 140% to our ultimate
+load capability from mechanical, and we will
+
+add the thermal stress to it analytically.
+
+So, we did that.
+
+And then we refurbished the vehicle and that
+became Challenger.
+
+The test article is going to cost $100 million.
+
+We said we don't need it.
+
+We'll use it for a flight airframe.
+
+And Aaron gave us a little ceramic eagle for
+doing it.
+
+Don't anybody expect As out of this deal,
+if Aaron has anything to do with it.
+
+There it was.
+
+We applied the million and a half pounds of
+load at the backend.
+
+We concentrated through loading fixtures,
+loads on the wings of the fuselage, put pressure
+
+differential at various points on the vehicle,
+and we did exactly what I said.
+
+Fatigue life.
+
+Mechanical fatigue was not a problem.
+
+Acoustic fatigue was an issue because we had
+some really lightweight structures and really
+
+high acoustic levels.
+
+You cannot see it here.
+
+It was like 165 DB around the base-end of
+the thing, lower levels on other portions,
+
+so we said how are we going to do that?
+
+We came up with a different way to do it.
+
+What we will do is we'll go around the vehicle
+and we will identify a characteristic structure,
+
+graphite/epoxy, aluminum, 7075-T6 aluminum
+fuselage up here, wing elevon, aluminum honeycomb,
+
+et cetera.
+
+We identified 44 test articles.
+
+We said that's what we'll do.
+
+We went to Aaron and said it's going to take
+us 44 test articles.
+
+We went through all the rationale with each
+one of them, and he said you can have 14.
+
+And so we said but that won't work.
+
+He said go figure it out.
+
+We went back and scratched out heads.
+
+Sure enough, we figured out how to do more
+extrapolation.
+
+So, we had 14 test articles that you see.
+
+And then what we did was say now we've got
+our test articles.
+
+Our approach to this thing was we would test
+them to failure acoustically.
+
+Now we have an acoustic allowable for that
+type of structure because it's a function
+
+of the details.
+
+I mean it had to be the detail.
+
+And, in addition to making sure we have a
+good test, if this was our acoustic fatigue
+
+test article, only the center third was a
+viable part of the test because the rest of
+
+it is boundary conditions that weren't right
+because they were clamped along the edges
+
+or whatever.
+
+We said only the middle third of the test
+article is viable.
+
+We tested that, we got a fatigue allowable
+from acoustics and then we degraded it analytically
+
+for combined mechanical and combined thermal.
+
+We did that and said also we know that it's
+probably not going to fail on the first flight
+
+so we'll do some inspections.
+
+Tom, let me just make a comment.
+
+He made it sound a lot simpler than it was.
+
+One thing that's important, whenever you do
+a project or you're in charge of something,
+
+you don't want to have yes people around you.
+
+You want to have people that say you're not
+doing it right.
+
+And it didn't go down that simple.
+
+They were not yes people, believe me.
+
+They were certainly not yes, sir, we're going
+to go do this.
+
+That's very important.
+
+It's a wonder we still speak to one another.
+
+[LAUGHTER] I'm sorry.
+
+I don't know what a test article is.
+
+It's a test specimen.
+
+If you wanted to put so much mass in here
+and you weren't sure whether this seam was
+
+going to work.
+
+You just put that much mass in here.
+
+You add a little bit more to it and you see
+if that seam breaks.
+
+That's your test article.
+
+That's what it is, just a test specimen, test
+article.
+
+But that's a good point because, don't forget,
+we start off with two entire $100 million
+
+test articles for static test and for fatigue
+test.
+
+Not counting acoustic fatigue.
+
+That was just mechanical fatigue.
+
+As we got into it we said we don't need that.
+
+Did the Challenger's mission life drop because
+of the test?
+
+No.
+
+As a matter of fact, that's a very good question.
+
+That was one of the questions that was asked
+by the investigation is what's different about
+
+this vehicle than any other vehicles?
+
+Well, it was a static test article.
+
+And we showed ad nauseam that had nothing
+to do with the failure of Challenger.
+
+The leading edge was not -- Oh, no, excuse
+me.
+
+I'm off on Columbia now.
+
+No, it didn't have anything to do with it.
+
+As a matter of fact, this is getting into
+detailed details now, when you apply above
+
+a limit load on a vehicle like we did on Challenger
+it puts a lot of the joints in residual compression.
+
+There is compression at the joint just as
+you load it and you unload it.
+
+And residual compression increases the fatigue
+life of the vehicle.
+
+And the reason it does is because fatigue
+is the function of tensile cycles, not compressive
+
+cycles normally.
+
+When McDonnell Douglas tested a DC-10 and
+they proof load a vehicle, it carries a premium
+
+on the selling price for that because it theoretically
+has a longer life than one that hasn't been
+
+loaded.
+
+Good question.
+
+Tom, one more question.
+
+Yeah.
+
+How much did an increase in computer processing
+speed and availability allow you to do these
+
+extrapolations and like do the thermal testing
+just analytically?
+
+Was that a key factor?
+
+You mean how much as it increased?
+
+Well, how much did it increase between like,
+say, Apollo and designing the Shuttle.
+
+Not a whole lot.
+
+As far as the analytical capabilities of the
+finite element models and all, you could get
+
+more detail through simplification.
+
+There are more elements available, let me
+put it that way.
+
+But as far as the crunching capability, it
+increased somewhat but we were still, you
+
+know, if you have to go from here to here,
+we were about here.
+
+That isn't a quantitative answer for you,
+but we're still a long way.
+
+We basically used mainframes, and we did have
+the NASTRAN model.
+
+Yeah, we had NASTRAN.
+
+But NASTRAN didn't have, on a large model
+like that, the large capability for structural
+
+loads and thermal loads.
+
+But you used to put your cards in one day
+and it would take a couple days before you
+
+got your answer.
+
+To do a complete load cycle on this vehicle
+for internal loads it was something like three
+
+months it would take us to do that.
+
+And so it was quite [OVERLAPPING VOICES].
+
+That's another story.
+
+Thermal protection system.
+
+Change gears now.
+
+Let's talk about the thing that protects the
+vehicle.
+
+Now I'm going to switch back and go back to
+get ready to proceed toward preliminary design.
+
+What were the requirements on the thermal
+protection system?
+
+It had to protect the vehicle from max temperatures
+like about 2800 degrees on the surface, reusable
+
+100 times, it had to be lightweight and had
+to be cost-effective.
+
+Pretty simple high-level requirements.
+
+And Dr.
+
+Bob Ried will talk to you about the things
+that they derived as far as the aerothermal
+
+in this and how it became that, but it was
+a given to us.
+
+What did we know about this thing?
+
+Well, we had some ablative TPS experience
+from Apollo.
+
+Gemini had some metallic TPS on it primarily
+Rene 41 and some other exotic materials.
+
+Mercury had an ablative TPS, but they weren't
+reusable.
+
+They were hot structure designs which existed
+but that we didn't have materials that could
+
+carry the load at temperature such that it
+could be a fully hot structural design, and
+
+that was extremely complex.
+
+Metallic TPS, we could get there theoretically
+with some fairly exotic materials called columbium
+
+and Rene 41 and some other things, but the
+devil is in the detail in that.
+
+Let me tell you a story about that.
+
+We were looking at some Haynes 188 panels.
+
+And so we had a test article, a big panel
+about the size of the desk that you're sitting
+
+at, any one of you there, and it was corrugated
+so that it could expand and contract.
+
+And it was good for 1800 degrees, so we tested
+it to 1800 degrees in the center of the panel
+
+multiple times.
+
+And it had a frame around it where the panel
+could move around because it needed to, to
+
+be able to thermally expand.
+
+And the center of the panel was 1800 degrees,
+the edge of the panel where the heat sink
+
+was, was 40 degrees lower temperature than
+the center.
+
+And the panel floated within a gap maybe about
+like that, so it could move around pretty
+
+good.
+
+But what it also did, with that temperature
+differential of 40 degrees, we got something
+
+called creep buckling.
+
+The structure expanded and crept and deformed
+permanently.
+
+Had we flown that vehicle, had we designed
+a vehicle like that, what that would have
+
+done is would have allowed plasma to flow
+through the shingles, if you will, and into
+
+the structure.
+
+And that's exactly what happened in Columbia.
+
+Letting the hot plasma gas get in the vehicle,
+you cannot stand it.
+
+It's the details about that.
+
+We said we're not going to go with a metallic
+design.
+
+Plus, if you scratch it, it oxidizes.
+
+And, if it oxidizes, then it can fail.
+
+So we went with something that was just coming
+online, and that was a fused silica material.
+
+And fused silica is pure sand, pure silica
+material.
+
+That's all in the world it is.
+
+The process is you make it into a fibrous
+structure, if you will.
+
+Fibrous material is a better term.
+
+A fibrous material that is mostly air.
+
+It is about the same density as balsa wood.
+
+It has an ultimate strength of about 12 psi,
+tensile load is about all that it can take,
+
+but it has a thermal performance that is fantastic.
+
+As you will recall this chart here, when you
+look at LI-1500, is what that was with aluminum,
+
+and that's what we went with, we used this
+same characterization to decide what the material
+
+we were going to use was on the vehicle from
+a weight standpoint and a cost standpoint.
+
+The way the tiles work thermally like this
+is the low strength brittle, almost like glassy
+
+material, it's a ceramic, is coated with literally
+a glass coating on the outside about 60-thousandths
+
+of an inch thick and it's black.
+
+As the vehicle comes back in and dissipates
+its energy through drag and heating, 90% of
+
+the heat is radiated away from the vehicle,
+10% of it goes into the vehicle.
+
+But this is such a good thermal isolator,
+a poor thermal conductor, by the time the
+
+heat gets to the vehicle, the vehicle is back
+into an atmosphere where it's not heating
+
+anymore.
+
+That dictated the thickness of these tiles,
+of this silica material.
+
+The vehicle has got almost 21,000 tiles on
+it, and they vary anywhere from a half inch
+
+thick up to about three inches thick.
+
+It's sculptured to stay within the mol line
+because the aerodynamicist told us what it
+
+has to be.
+
+And so what we did was sculptured the TPS
+so that we didn't have any more than we needed.
+
+Great job by all the thermal analysts.
+
+I mean they did this fantastic.
+
+I want to mention, when that says 9 pound
+or 22 pound tiles, that's not the weight of
+
+each individual tile, that's the density per
+cubic foot.
+
+Per cubic foot, correct.
+
+Thank you, Jeff.
+
+What was the footnote about Columbia on that?
+
+On the last chart, Tom, there is a footnote
+about the difference in the Columbia.
+
+Let me come back to that in just one second.
+
+What I want to talk to you about right now,
+this is something I had from some old material.
+
+I was just trying to get a characterization.
+
+What that said is on Columbia there was an
+infrared sensor as an experiment.
+
+So, the number of tiles varied on that vehicle
+compared to all the other vehicles because
+
+of this infrared thing at the top of the vertical
+stabilizer.
+
+I should have cut that off.
+
+You're reading too close.
+
+[LAUGHTER] We thought let's figure out how
+to take this fragile material and put it on
+
+this aluminum structure which has a high thermal
+coefficient of expansion.
+
+The tiles have almost a zero thermal coefficient
+expansion.
+
+We said we've got to isolate that.
+
+We put a strain isolation pad [UNINTELLIGIBLE
+PHRASE].
+
+Why do they vary in density?
+
+Yeah.
+
+Because primarily for strength, for one of
+the things.
+
+And the LI-2200 was a little bit higher temperature
+capability.
+
+And I don't remember [OVERLAPPING VOICES].
+
+But it had a little higher peak temperature
+capability.
+
+And that was dictated by what one of the failure
+modes of a tile was if you exceed the temperature
+
+too much it starts slumping.
+
+I don't want to say melting but it begins
+to distort.
+
+And a LI-2200 didn't distort to the same extent
+that a LI-900 tile did.
+
+We said let's isolate the structure here from
+this material up here which is required to
+
+keep from failing all these tiles, so we put
+something between them.
+
+It was just a very loosely woven felt material.
+
+Now we proved that the aluminum can expand
+all it wants to, or within limits, we looked
+
+at it realistically, and that the tile was
+OK, except the tile couldn't be too large
+
+because of this relative expansion and contraction.
+
+So, that dictated the size of the tile.
+
+We literally pre-cracked them, if you will.
+
+We put expansion joints is another way of
+looking at it.
+
+A typical tile is 6 inches by 6 inches when
+it gets into the highly heated area.
+
+Now all of a sudden we've got some room for
+the title to move relative to one another,
+
+structure to move underneath it because of
+the strain isolation pad.
+
+And we said, viola, we've got this problem
+fixed.
+
+We're good to go..
+
+We said we've got 25,000 of these tiles that
+we now have to certify that they're good to
+
+go for the vehicle.
+
+There were gaps between the tiles?
+
+Correct.
+
+But, when you re-enter, do the tiles expand
+so that there are no gaps?
+
+No.
+
+What we do is make sure that the gap can just
+close but not close such that you're loading
+
+one tile relative to the other.
+
+That set the gap.
+
+And, if during manufacturing which is not
+that precise, if the gap was too large we
+
+just stuck a gap filler in.
+
+Not the one that was on the last vehicle.
+
+It's a different kind of gap fill.
+
+Just a piece of Nomex or SIP material strain
+isolation pad coated with rubber or with RTV,
+
+and we stuck it in between the tile just to
+reduce the flow if the gap was too large.
+
+So there is no chance that you would have
+hot plasma coming in between them?
+
+Yes, there is a chance you can have plasma
+going through there if the gap is too large.
+
+We had a very specific requirement.
+
+I think it was like 90-thousandths of an inch
+between tiles.
+
+And if it were, say, 130-thousandths of an
+inch, as installed because of tolerance buildup
+
+and all that kind of stuff, then what we did
+was stuck a plasma flow preclude, if you will,
+
+a gap filler between those to stop the plasma
+flow from getting between the tiles.
+
+And we had some experience where we lost some
+gap fillers, plasma flowed between the tiles,
+
+caused excessive heating on the tiles and
+started causing them to slump and melt a little
+
+bit, did a little bit of structural deformation
+but nothing significant.
+
+Losing gap filler was a turnaround issue,
+not a safety of flight issue.
+
+We made sure of that.
+
+Excellent question.
+
+This is more of a general question, but I'm
+wondering if since then anybody has done any
+
+work to find a material that could accomplish
+both tasks, the structure and the thermal
+
+protection rather than having to deal with
+these types of issues.
+
+That was back to one of my trades were we
+said let's take that approach and see if we
+
+cannot design a vehicle that can take the
+temperature and the loads, too, both.
+
+There was no material that existed.
+
+I don't think a material exists today that
+I know of to be worked to a high enough stress
+
+that you can keep the weight down to have
+those kinds of temperatures and to be worked
+
+at a high temperature.
+
+I think on the X-33 design they were talking
+once again of trying to make it out of a metallic
+
+structure.
+
+Part of it was structure and part of it was
+tons.
+
+But we never got to the point of being able
+to fly and test it.
+
+But they also were using a thermal isolation
+system like tiles over part of the vehicle
+
+on the X-33.
+
+The Buran, which was the Soviet copy of the
+Shuttle, they were very anxious to get away
+
+from the expense of the tiles.
+
+And they ended up with a thermal protection
+system not very different than what you said.
+
+You mean they had tiles?
+
+Yeah.
+
+As a matter of fact, I remember they were
+more like bigger blankets.
+
+That's a good point, Larry.
+
+I was about to skip over it.
+
+I said they were typically 6 inches where
+they were really thick, but in other areas
+
+we made like 12 or 15 inch tiles that were
+very thin.
+
+And the reason we could do that is we decided
+if they crack it doesn't matter because the
+
+gap wouldn't be large enough for the plasma
+flow to go through there and it would simply
+
+be a self-relieving.
+
+So, we tried to reduce the cost of manufacturing
+by making some of these tiles larger.
+
+And I will show you that in just a second.
+
+I'm going to skip forward here and show you
+one thing..
+
+That's 50-thousandths of an inch.
+
+The allowable for the tile was 12 psi.
+
+The ultimate stress was 12 psi.
+
+The allowable stress was about 8 psi.
+
+And that's with the total loads combined on
+the tile.
+
+What do you have to consider in one of these
+25,000 tiles that you have to assure is not
+
+going to come off the vehicle?
+
+Remember I said when we looked in the early
+phase studies of the vehicle we were looking
+
+at wing loads and stuff like that?
+
+Then we got into how is the wing going to
+carry the load into the fuselage to the spar
+
+and what was our design trade on that?
+
+Those were sort of macro and semi-macro systems
+engineering studies.
+
+Now we're into a micro.
+
+Now we've got this little critical part, 6
+inches by 6 inches.
+
+Lose any one of about 10,000 and you lose
+the vehicle.
+
+It's got an 8 psi allowable strength.
+
+We said well, that's no big deal.
+
+What are all the environments on this thing?
+
+We started looking at pre-liftoff, liftoff,
+ascent, et cetera.
+
+There is always something called mismatch.
+
+When you take something that is not perfectly
+smooth and you bond something to it and they
+
+are not to the same flatness, if you will,
+there is going to be a stress induced into
+
+both parts of those.
+
+Well, the structure doesn't care about that
+stress but this little 8 psi allowable tile
+
+does.
+
+It says we cannot exceed about 19-thousandths
+of an inch under one of these tiles for this
+
+to happen.
+
+There is ignition over pressure during ascent.
+
+There is acoustic and vibration and that kind
+of stuff that has to be considered.
+
+On ascent there are gradients because of shock
+moving across the tile.
+
+There is internal pressure.
+
+There is skin friction and drag on the tile,
+so you've got to consider that.
+
+You have to consider the dynamics, the inertial
+loads induced in it.
+
+And the out of plane deflection is now the
+vehicle flying.
+
+The structure is deforming.
+
+So, you've got to consider that.
+
+Now you can see you've got 25,000 tiles with
+all these combinations of load conditions
+
+so how in the hell do you design that?
+
+This is the characterization of it.
+
+This is what happens with a structural deformation
+of like 10-thousandths of an inch deflection
+
+underneath a tile.
+
+With that kind of formation it causes 1 psi.
+
+And it linear almost.
+
+So, 20-thousandths of an inch deflection is
+going to cause 2 psi.
+
+Well, 2 psi is not a lot but it's a quarter
+of your allowable.
+
+We said we've got to consider that.
+
+We have to understand what is happening to
+this structure as you fly it, a condition.
+
+This is a free body, if you will, of the pressure
+distribution on a tile.
+
+It has internal pressure within the tile.
+
+It has a pressure differential on the outside
+of the tile because of a shockwave moving
+
+across it because of the pressure as it varies
+around the vehicle.
+
+So, you have to consider all of that.
+
+We did all that and said we've got a problem,
+because what happened was all of a sudden
+
+our allowable on our tile was decreased by
+half.
+
+And this was not good.
+
+We screwed up, in the systems engineering
+point of view, when we did this.
+
+Remember we put the strain isolation pad underneath
+the tile and we did all these other loads
+
+on it?
+
+What we forgot, or what we didn't realize
+was this strain isolation pad had little stiff
+
+spots in it because of the way it was stitched
+to keep the strain isolation pad together.
+
+And every stiff spot acted like a hard point.
+
+Now, when you take a tile and you put external
+loads on it and there is a stress concentration
+
+on each one of those things, that stress concentration
+had an amplification of two.
+
+All of a sudden our allowable were decreased
+by a factor of two.
+
+And we thought we have a major problem.
+
+This is when Aaron and I got to know one another
+better than we ever wanted to.
+
+We met every day on this thing.
+
+We had tiles bonded all over the vehicle.
+
+Necessity was the mother of invention.
+
+What we had to do was dissipate this stress
+concentration.
+
+We said we'll put a plate underneath it, a
+graphite/epoxy plate or something like that.
+
+That would have added a lot of weight to the
+vehicle.
+
+Glen Ecord, a materials guy came up with the
+idea in the lab one weekend, he took silica
+
+powder in water and just painted it on the
+bottom of the tile.
+
+What it did was fill all the pours in the
+tile for about three-sixteenths of an inch.
+
+And just compacted themselves in there.
+
+And that was an inherent capability of a tile
+with that powder packed in it, if you will,
+
+that doubled the strength of the tile.
+
+What it did is it dissipated the load from
+being concentrated into the tile.
+
+So, without any weight, some cost, we had
+to pull some tiles off the vehicle and densify
+
+them.
+
+Now all tiles are densified.
+
+I meant to bring one to show you today but
+I didn't.
+
+Analytically, we went through 25,000 tiles.
+
+Here was our factor of safety distribution
+over the entire vehicle.
+
+We said we're good for that, but the thing
+we don't know is if the tile is really bonded
+
+on the vehicle like it should be.
+
+We said we can fix that problem.
+
+We will verify it.
+
+We will pull on every tile and make sure that
+it has a capability of the maximum expected
+
+mechanical load that it is going to see.
+
+And so we pulled on every tile.
+
+And John Yardley, being an old stress guy,
+says let me ask you a question.
+
+When you pull on every tile, how do you know
+you haven't induced more damage and decreased
+
+the allowable of the title because of your
+proof test?
+
+Good question.
+
+Easy answer.
+
+We'll put a microphone on every tile and we
+will characterize the sound of the tile as
+
+we pull up on it, and we will get a sound
+allowable, if you will, for proof-testing
+
+the tile.
+
+We did that on every tile that had to be proof-tested.
+
+We had an acoustic emission device, we had
+a microphone on there, we characterized all
+
+these tiles and we did it.
+
+Another little mother's necessity of invention.
+
+And I'm not going to go through this.
+
+You'll get a handout of this.
+
+What this did is said you cannot proof load
+every tile, every tile is not densified, some
+
+tiles are thick, some tiles are thin, but
+prove under no uncertain conditions that you're
+
+safe to fly.
+
+We went through this logic on everything.
+
+Some of these things had gates that said go
+directly to fly.
+
+Others we had to go through.
+
+Others we had to pull off the vehicle and
+densify and proof load and do a bunch of other
+
+things to prove that they were OK.
+
+We got there.
+
+Now we're into operations.
+
+We're just about out of time.
+
+I know.
+
+I've got three minutes left.
+
+Can I have all three?
+
+OK.
+
+Here is what we did.
+
+We did some pretty innovative things on this
+thing, and I think I've shown you some of
+
+that stuff.
+
+But what were the surprises we had on the
+first flight?
+
+Not very many.
+
+As we were going uphill, I told you about
+the plume effect from the engines blocking
+
+the flow, that causes the pressure distribution
+on the wing to be different than we designed
+
+for.
+
+The center pressure was further aft and outboard.
+
+That loaded up the wing more.
+
+It could not fly to the design conditions
+that we needed to under worse case.
+
+And I'll tell you what we did on that.
+
+Well, let me just tell you right now.
+
+What we did was almost day-of-launch wind
+analysis, loads analysis for the wings with
+
+load indicators in the wing to understand
+what a specific flight regime was going to
+
+do for that vehicle.
+
+And we literally designed the trajectories
+for the first six or eight or ten shuttle
+
+flights so it stayed within a reduced capability
+of the vehicle.
+
+Because we characterized it so well, we could
+do that.
+
+The other thing was the overpressure of the
+vehicle, when the main engines let off there
+
+was an accumulation of hydrogen gas underneath
+the vehicle.
+
+And as soon as the engines fired it ignited
+that hydrogen and sent a big shockwave up
+
+the vehicle.
+
+It could have been pretty bad but it wasn't,
+so we fixed that by isolating the isolation
+
+and also burning it off prior to engine ignition.
+
+And then we got some tile damage from external
+tank.
+
+We fixed that.
+
+After about the second or third flight on
+the external tank, we changed the foam process
+
+and controlled that.
+
+And so those were our only surprises.
+
+You remember the chart that I showed you of
+all the combined environments on a tile?
+
+This is not politically correct what I'm going
+to say, but I'm going to say it anyway.
+
+The shockwaves, the pressure, the out of plane
+deformation, all that, you didn't see debris
+
+anyplace on that chart.
+
+Those tiles are not designed for debris, period.
+
+You can rationalize it.
+
+You can arm wave it.
+
+You can statistically analyze it.
+
+The vehicle is not designed to fly in debris.
+
+It can take every other thing it's designed
+for, but it cannot take what it's not designed
+
+for.
+
+The engineers today have two choices.
+
+They can either eliminate the debris from
+the external tank or, in my judgment, they
+
+can go back and recertify the tiles for the
+expected debris.
+
+And that's probably not too big a deal, but
+they cannot say we're ready to fly, going
+
+through a logic matrix like I did, until they
+do that.
+
+OK, guys and gals.
+
+Here are some challenges for you.
+
+As you go through from the beginning of a
+program, I would like you to be looking at
+
+this crew exploration vehicle, what other
+parameters would you look at other than what
+
+I've shown you here and what tools would you
+use?
+
+On the combined thermal mechanical, I think
+a lot can be done on that.
+
+I don't know what all the computing capability
+is today, but I think that you could really
+
+simplify and probably decrease the weight
+of the vehicle by doing that.
+
+Could they be made more rugged?
+
+Yeah, they probably could.
+
+But be careful.
+
+This is a big systems engineering issue and
+it's a political issue.
+
+And I'm going to get off the stage here in
+one second.
+
+Should there be a dedicated crew escape system
+or should the reliability be built in the
+
+vehicle?
+
+And I'll promise you that answer is not known.
+
+It may be known from a political standpoint
+that you have to have a crew escape system,
+
+and that's OK.
+
+If that's a requirement, that's a requirement,
+but in a total system crew safety reliability
+
+that's not obvious.
+
+It depends on what the design is and what
+the reliability of the constituent elements
+
+are.
+
+How would you fix the ET?
+
+Put shrink wrap all over it.
+
+Another thing that's not part of the curriculum
+here is political systems engineering.
+
+You can have the best engineering design in
+the world, but if you don't have the political
+
+support in a program like this it doesn't
+matter.
+
+How does political influence come into a systems
+engineering thing, kind of like the crew escape
+
+system?
+
+Thank you.
+
+[APPLAUSE] Well, that was just super.
+
+This is hopefully the first of many lectures
+which will take us to a much greater depth
+
+[then when we did the shuttle system?].
\ No newline at end of file
diff --git a/kDhR4Zm53zc.txt b/kDhR4Zm53zc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..15a1150facff030597b8d42fe53d476029768990
--- /dev/null
+++ b/kDhR4Zm53zc.txt
@@ -0,0 +1,9272 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu last time we were talking
+
+ align:start position:0%
+ocw.mit.edu last time we were talking
+ 
+
+ align:start position:0%
+ocw.mit.edu last time we were talking
+about binary search and I sort of left a
+
+ align:start position:0%
+about binary search and I sort of left a
+ 
+
+ align:start position:0%
+about binary search and I sort of left a
+promise to you which I need to pick up I
+
+ align:start position:0%
+promise to you which I need to pick up I
+ 
+
+ align:start position:0%
+promise to you which I need to pick up I
+want to remind mind you we're talking
+
+ align:start position:0%
+want to remind mind you we're talking
+ 
+
+ align:start position:0%
+want to remind mind you we're talking
+about search which is a very fundamental
+
+ align:start position:0%
+about search which is a very fundamental
+ 
+
+ align:start position:0%
+about search which is a very fundamental
+thing that we do in a whole lot of
+
+ align:start position:0%
+thing that we do in a whole lot of
+ 
+
+ align:start position:0%
+thing that we do in a whole lot of
+applications we want to go find things
+
+ align:start position:0%
+applications we want to go find things
+ 
+
+ align:start position:0%
+applications we want to go find things
+in some data set and I'll remind you
+
+ align:start position:0%
+in some data set and I'll remind you
+ 
+
+ align:start position:0%
+in some data set and I'll remind you
+that we sort of separated out two cases
+
+ align:start position:0%
+that we sort of separated out two cases
+ 
+
+ align:start position:0%
+that we sort of separated out two cases
+we said if we
+
+ align:start position:0%
+we said if we
+ 
+
+ align:start position:0%
+we said if we
+had an ordered
+
+ align:start position:0%
+had an ordered
+ 
+
+ align:start position:0%
+had an ordered
+list we could use binary search and we
+
+ align:start position:0%
+list we could use binary search and we
+ 
+
+ align:start position:0%
+list we could use binary search and we
+said that was logarithmic took log end
+
+ align:start position:0%
+said that was logarithmic took log end
+ 
+
+ align:start position:0%
+said that was logarithmic took log end
+time where ends the size of the of the
+
+ align:start position:0%
+time where ends the size of the of the
+ 
+
+ align:start position:0%
+time where ends the size of the of the
+list if it was an unordered list
+
+ align:start position:0%
+list if it was an unordered list
+ 
+
+ align:start position:0%
+list if it was an unordered list
+we were basically stuck with linear
+
+ align:start position:0%
+we were basically stuck with linear
+ 
+
+ align:start position:0%
+we were basically stuck with linear
+search got to walk through the whole
+
+ align:start position:0%
+search got to walk through the whole
+ 
+
+ align:start position:0%
+search got to walk through the whole
+list to see if the thing's there so that
+
+ align:start position:0%
+list to see if the thing's there so that
+ 
+
+ align:start position:0%
+list to see if the thing's there so that
+was of order
+
+ align:start position:0%
+was of order
+ 
+
+ align:start position:0%
+was of order
+in and then one of the things that I
+
+ align:start position:0%
+in and then one of the things that I
+ 
+
+ align:start position:0%
+in and then one of the things that I
+suggested was that if we could figure
+
+ align:start position:0%
+suggested was that if we could figure
+ 
+
+ align:start position:0%
+suggested was that if we could figure
+out some way to order it and in
+
+ align:start position:0%
+out some way to order it and in
+ 
+
+ align:start position:0%
+out some way to order it and in
+particular if we could order it in N log
+
+ align:start position:0%
+particular if we could order it in N log
+ 
+
+ align:start position:0%
+particular if we could order it in N log
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and we still haven't done that but
+
+ align:start position:0%
+time and we still haven't done that but
+ 
+
+ align:start position:0%
+time and we still haven't done that but
+if we could do that then we said the
+
+ align:start position:0%
+if we could do that then we said the
+ 
+
+ align:start position:0%
+if we could do that then we said the
+complexity changed a little bit but
+
+ align:start position:0%
+complexity changed a little bit but
+ 
+
+ align:start position:0%
+complexity changed a little bit but
+changed in a way that I want to remind
+
+ align:start position:0%
+changed in a way that I want to remind
+ 
+
+ align:start position:0%
+changed in a way that I want to remind
+you and the change was that in this case
+
+ align:start position:0%
+you and the change was that in this case
+ 
+
+ align:start position:0%
+you and the change was that in this case
+if I'm doing a single search I've got a
+
+ align:start position:0%
+if I'm doing a single search I've got a
+ 
+
+ align:start position:0%
+if I'm doing a single search I've got a
+choice I could still do the linear case
+
+ align:start position:0%
+choice I could still do the linear case
+ 
+
+ align:start position:0%
+choice I could still do the linear case
+which is order
+
+ align:start position:0%
+which is order
+ 
+
+ align:start position:0%
+which is order
+n or I could say look take the list
+
+ align:start position:0%
+n or I could say look take the list
+ 
+
+ align:start position:0%
+n or I could say look take the list
+let's sort it and then search it but in
+
+ align:start position:0%
+let's sort it and then search it but in
+ 
+
+ align:start position:0%
+let's sort it and then search it but in
+that case we said well to sort
+
+ align:start position:0%
+that case we said well to sort
+ 
+
+ align:start position:0%
+that case we said well to sort
+it was going to take n log n time
+
+ align:start position:0%
+it was going to take n log n time
+ 
+
+ align:start position:0%
+it was going to take n log n time
+assuming I can do that once I have it
+
+ align:start position:0%
+assuming I can do that once I have it
+ 
+
+ align:start position:0%
+assuming I can do that once I have it
+sort it I can search
+
+ align:start position:0%
+sort it I can search
+ 
+
+ align:start position:0%
+sort it I can search
+it in log end
+
+ align:start position:0%
+it in log end
+ 
+
+ align:start position:0%
+it in log end
+time but that still isn't as good as
+
+ align:start position:0%
+time but that still isn't as good as
+ 
+
+ align:start position:0%
+time but that still isn't as good as
+just doing n and this led to this idea
+
+ align:start position:0%
+just doing n and this led to this idea
+ 
+
+ align:start position:0%
+just doing n and this led to this idea
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amortization which is I need to not only
+
+ align:start position:0%
+amortization which is I need to not only
+ 
+
+ align:start position:0%
+amortization which is I need to not only
+factor in the cost but how am I going to
+
+ align:start position:0%
+factor in the cost but how am I going to
+ 
+
+ align:start position:0%
+factor in the cost but how am I going to
+use it and typically I'm not going to
+
+ align:start position:0%
+use it and typically I'm not going to
+ 
+
+ align:start position:0%
+use it and typically I'm not going to
+just search Once in a list I'm going to
+
+ align:start position:0%
+just search Once in a list I'm going to
+ 
+
+ align:start position:0%
+just search Once in a list I'm going to
+search multiple times so if I have to do
+
+ align:start position:0%
+search multiple times so if I have to do
+ 
+
+ align:start position:0%
+search multiple times so if I have to do
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+searches then in the linear case I got
+
+ align:start position:0%
+searches then in the linear case I got
+ 
+
+ align:start position:0%
+searches then in the linear case I got
+to do order N Things K times it's order
+
+ align:start position:0%
+to do order N Things K times it's order
+ 
+
+ align:start position:0%
+to do order N Things K times it's order
+K in whereas in the ordered
+
+ align:start position:0%
+K in whereas in the ordered
+ 
+
+ align:start position:0%
+K in whereas in the ordered
+case I need to get sorted which is still
+
+ align:start position:0%
+case I need to get sorted which is still
+ 
+
+ align:start position:0%
+case I need to get sorted which is still
+n log n but then the search is only log
+
+ align:start position:0%
+n log n but then the search is only log
+ 
+
+ align:start position:0%
+n log n but then the search is only log
+n and I need to do K of
+
+ align:start position:0%
+n and I need to do K of
+ 
+
+ align:start position:0%
+n and I need to do K of
+those and we suggested while this is
+
+ align:start position:0%
+those and we suggested while this is
+ 
+
+ align:start position:0%
+those and we suggested while this is
+better than
+
+ align:start position:0%
+better than
+ 
+
+ align:start position:0%
+better than
+that this is certainly better than
+
+ align:start position:0%
+that this is certainly better than
+ 
+
+ align:start position:0%
+that this is certainly better than
+that n plus K All Times log n is in
+
+ align:start position:0%
+that n plus K All Times log n is in
+ 
+
+ align:start position:0%
+that n plus K All Times log n is in
+general going to be much better than K *
+
+ align:start position:0%
+general going to be much better than K *
+ 
+
+ align:start position:0%
+general going to be much better than K *
+n depends on n and K but obviously Zen
+
+ align:start position:0%
+n depends on n and K but obviously Zen
+ 
+
+ align:start position:0%
+n depends on n and K but obviously Zen
+gets big that one's going to be
+
+ align:start position:0%
+gets big that one's going to be
+ 
+
+ align:start position:0%
+gets big that one's going to be
+better and that's just a way of
+
+ align:start position:0%
+better and that's just a way of
+ 
+
+ align:start position:0%
+better and that's just a way of
+reminding you that um we want to think
+
+ align:start position:0%
+reminding you that um we want to think
+ 
+
+ align:start position:0%
+reminding you that um we want to think
+carefully about what are the things
+
+ align:start position:0%
+carefully about what are the things
+ 
+
+ align:start position:0%
+carefully about what are the things
+we're trying to measure when we talk
+
+ align:start position:0%
+we're trying to measure when we talk
+ 
+
+ align:start position:0%
+we're trying to measure when we talk
+about complexity here it's both the size
+
+ align:start position:0%
+about complexity here it's both the size
+ 
+
+ align:start position:0%
+about complexity here it's both the size
+of the thing and how often am I going to
+
+ align:start position:0%
+of the thing and how often am I going to
+ 
+
+ align:start position:0%
+of the thing and how often am I going to
+use it and there's some
+
+ align:start position:0%
+use it and there's some
+ 
+
+ align:start position:0%
+use it and there's some
+trade-offs but I still haven't said how
+
+ align:start position:0%
+trade-offs but I still haven't said how
+ 
+
+ align:start position:0%
+trade-offs but I still haven't said how
+am I going to get an N log n sorting
+
+ align:start position:0%
+am I going to get an N log n sorting
+ 
+
+ align:start position:0%
+am I going to get an N log n sorting
+algorithm and that's what I want to do
+
+ align:start position:0%
+algorithm and that's what I want to do
+ 
+
+ align:start position:0%
+algorithm and that's what I want to do
+today one of the two things I want to do
+
+ align:start position:0%
+today one of the two things I want to do
+ 
+
+ align:start position:0%
+today one of the two things I want to do
+today right to set the stage for this
+
+ align:start position:0%
+today right to set the stage for this
+ 
+
+ align:start position:0%
+today right to set the stage for this
+let's go back just for a second to
+
+ align:start position:0%
+let's go back just for a second to
+ 
+
+ align:start position:0%
+let's go back just for a second to
+binary
+
+ align:start position:0%
+binary
+ 
+
+ align:start position:0%
+binary
+search the end of the lecture I said
+
+ align:start position:0%
+search the end of the lecture I said
+ 
+
+ align:start position:0%
+search the end of the lecture I said
+binary search was an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a divide and conquer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm sort of an a till of the Hun
+
+ align:start position:0%
+algorithm sort of an a till of the Hun
+ 
+
+ align:start position:0%
+algorithm sort of an a till of the Hun
+kind of approach to doing things if you
+
+ align:start position:0%
+kind of approach to doing things if you
+ 
+
+ align:start position:0%
+kind of approach to doing things if you
+like so let me say this boy I could have
+
+ align:start position:0%
+like so let me say this boy I could have
+ 
+
+ align:start position:0%
+like so let me say this boy I could have
+made a really bad political joke there
+
+ align:start position:0%
+made a really bad political joke there
+ 
+
+ align:start position:0%
+made a really bad political joke there
+which I will forego right so let's say
+
+ align:start position:0%
+which I will forego right so let's say
+ 
+
+ align:start position:0%
+which I will forego right so let's say
+what this actually means divide and
+
+ align:start position:0%
+what this actually means divide and
+ 
+
+ align:start position:0%
+what this actually means divide and
+conquer divide and conquer says
+
+ align:start position:0%
+conquer divide and conquer says
+ 
+
+ align:start position:0%
+conquer divide and conquer says
+basically do the following split the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem into several
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems of the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type okay I'll come back in a second to
+
+ align:start position:0%
+type okay I'll come back in a second to
+ 
+
+ align:start position:0%
+type okay I'll come back in a second to
+how binary search matches in that but
+
+ align:start position:0%
+how binary search matches in that but
+ 
+
+ align:start position:0%
+how binary search matches in that but
+that's what we're going to do for each
+
+ align:start position:0%
+that's what we're going to do for each
+ 
+
+ align:start position:0%
+that's what we're going to do for each
+of those sub
+
+ align:start position:0%
+of those sub
+ 
+
+ align:start position:0%
+of those sub
+problems going to solve them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independently and then we're going to
+
+ align:start position:0%
+independently and then we're going to
+ 
+
+ align:start position:0%
+independently and then we're going to
+combine those Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's called divide and conquer for
+
+ align:start position:0%
+and it's called divide and conquer for
+ 
+
+ align:start position:0%
+and it's called divide and conquer for
+the obvious reason I'm going to divide
+
+ align:start position:0%
+the obvious reason I'm going to divide
+ 
+
+ align:start position:0%
+the obvious reason I'm going to divide
+it up into sub problems with the hope
+
+ align:start position:0%
+it up into sub problems with the hope
+ 
+
+ align:start position:0%
+it up into sub problems with the hope
+that those sub problems get easier going
+
+ align:start position:0%
+that those sub problems get easier going
+ 
+
+ align:start position:0%
+that those sub problems get easier going
+to be easier to conquer if you like and
+
+ align:start position:0%
+to be easier to conquer if you like and
+ 
+
+ align:start position:0%
+to be easier to conquer if you like and
+then I'm going to merge them back now in
+
+ align:start position:0%
+then I'm going to merge them back now in
+ 
+
+ align:start position:0%
+then I'm going to merge them back now in
+the binary search case in some sense
+
+ align:start position:0%
+the binary search case in some sense
+ 
+
+ align:start position:0%
+the binary search case in some sense
+this was a little bit trivial what what
+
+ align:start position:0%
+this was a little bit trivial what what
+ 
+
+ align:start position:0%
+this was a little bit trivial what what
+trival right trivial blah what was the
+
+ align:start position:0%
+trival right trivial blah what was the
+ 
+
+ align:start position:0%
+trival right trivial blah what was the
+divide the Divide was breaking a big
+
+ align:start position:0%
+divide the Divide was breaking a big
+ 
+
+ align:start position:0%
+divide the Divide was breaking a big
+search up into a half a search we
+
+ align:start position:0%
+search up into a half a search we
+ 
+
+ align:start position:0%
+search up into a half a search we
+actually threw half of the list away and
+
+ align:start position:0%
+actually threw half of the list away and
+ 
+
+ align:start position:0%
+actually threw half of the list away and
+we kept dividing it down
+
+ align:start position:0%
+we kept dividing it down
+ 
+
+ align:start position:0%
+we kept dividing it down
+until ultimately we got something of
+
+ align:start position:0%
+until ultimately we got something of
+ 
+
+ align:start position:0%
+until ultimately we got something of
+size one to search that's really easy
+
+ align:start position:0%
+size one to search that's really easy
+ 
+
+ align:start position:0%
+size one to search that's really easy
+the combination was also sort of trivial
+
+ align:start position:0%
+the combination was also sort of trivial
+ 
+
+ align:start position:0%
+the combination was also sort of trivial
+in this case because the solution to the
+
+ align:start position:0%
+in this case because the solution to the
+ 
+
+ align:start position:0%
+in this case because the solution to the
+sub problem was in fact the solution to
+
+ align:start position:0%
+sub problem was in fact the solution to
+ 
+
+ align:start position:0%
+sub problem was in fact the solution to
+the larger problem okay but there's the
+
+ align:start position:0%
+the larger problem okay but there's the
+ 
+
+ align:start position:0%
+the larger problem okay but there's the
+idea of divide and conquer I'm going to
+
+ align:start position:0%
+idea of divide and conquer I'm going to
+ 
+
+ align:start position:0%
+idea of divide and conquer I'm going to
+use exactly that same idea to tackle
+
+ align:start position:0%
+use exactly that same idea to tackle
+ 
+
+ align:start position:0%
+use exactly that same idea to tackle
+sort again I got an unordered list of n
+
+ align:start position:0%
+sort again I got an unordered list of n
+ 
+
+ align:start position:0%
+sort again I got an unordered list of n
+elements I want to sort it into a
+
+ align:start position:0%
+elements I want to sort it into a
+ 
+
+ align:start position:0%
+elements I want to sort it into a
+obviously into a sorted list in that
+
+ align:start position:0%
+obviously into a sorted list in that
+ 
+
+ align:start position:0%
+obviously into a sorted list in that
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+algorithm is actually a really nice
+
+ align:start position:0%
+algorithm is actually a really nice
+ 
+
+ align:start position:0%
+algorithm is actually a really nice
+algorithm called merge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort and it's actually a fairly old
+
+ align:start position:0%
+sort and it's actually a fairly old
+ 
+
+ align:start position:0%
+sort and it's actually a fairly old
+algorithm it was invented in 1945 by
+
+ align:start position:0%
+algorithm it was invented in 1945 by
+ 
+
+ align:start position:0%
+algorithm it was invented in 1945 by
+John Von noyman one of the
+
+ align:start position:0%
+John Von noyman one of the
+ 
+
+ align:start position:0%
+John Von noyman one of the
+pioneers of computer
+
+ align:start position:0%
+pioneers of computer
+ 
+
+ align:start position:0%
+pioneers of computer
+science and here's the idea behind merge
+
+ align:start position:0%
+science and here's the idea behind merge
+ 
+
+ align:start position:0%
+science and here's the idea behind merge
+sort actually I'm going to come into it
+
+ align:start position:0%
+sort actually I'm going to come into it
+ 
+
+ align:start position:0%
+sort actually I'm going to come into it
+I'm going to back into it in a funny way
+
+ align:start position:0%
+I'm going to back into it in a funny way
+ 
+
+ align:start position:0%
+I'm going to back into it in a funny way
+let's assume that I could somehow get to
+
+ align:start position:0%
+let's assume that I could somehow get to
+ 
+
+ align:start position:0%
+let's assume that I could somehow get to
+the stage where I've got two sorted
+
+ align:start position:0%
+the stage where I've got two sorted
+ 
+
+ align:start position:0%
+the stage where I've got two sorted
+lists how hard does it work or how much
+
+ align:start position:0%
+lists how hard does it work or how much
+ 
+
+ align:start position:0%
+lists how hard does it work or how much
+work do I have to do to actually merge
+
+ align:start position:0%
+work do I have to do to actually merge
+ 
+
+ align:start position:0%
+work do I have to do to actually merge
+them together all right so let me give
+
+ align:start position:0%
+them together all right so let me give
+ 
+
+ align:start position:0%
+them together all right so let me give
+you an example suppose I want to merge
+
+ align:start position:0%
+you an example suppose I want to merge
+ 
+
+ align:start position:0%
+you an example suppose I want to merge
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+lists and they're
+
+ align:start position:0%
+lists and they're
+ 
+
+ align:start position:0%
+lists and they're
+sorted just to give you an example
+
+ align:start position:0%
+sorted just to give you an example
+ 
+
+ align:start position:0%
+sorted just to give you an example
+here's one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+list right 312 17
+
+ align:start position:0%
+list right 312 17
+ 
+
+ align:start position:0%
+list right 312 17
+24 God bless you here's another list 1 2
+
+ align:start position:0%
+24 God bless you here's another list 1 2
+ 
+
+ align:start position:0%
+24 God bless you here's another list 1 2
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+30 I haven't said how I'm going to get
+
+ align:start position:0%
+30 I haven't said how I'm going to get
+ 
+
+ align:start position:0%
+30 I haven't said how I'm going to get
+those sorted lists but imagine I had two
+
+ align:start position:0%
+those sorted lists but imagine I had two
+ 
+
+ align:start position:0%
+those sorted lists but imagine I had two
+sorted lists like that how hard is it to
+
+ align:start position:0%
+sorted lists like that how hard is it to
+ 
+
+ align:start position:0%
+sorted lists like that how hard is it to
+merge them well it's pretty easy right I
+
+ align:start position:0%
+merge them well it's pretty easy right I
+ 
+
+ align:start position:0%
+merge them well it's pretty easy right I
+start at the beginning of each list and
+
+ align:start position:0%
+start at the beginning of each list and
+ 
+
+ align:start position:0%
+start at the beginning of each list and
+I say is one less than three sure so
+
+ align:start position:0%
+I say is one less than three sure so
+ 
+
+ align:start position:0%
+I say is one less than three sure so
+that says one should be the first
+
+ align:start position:0%
+that says one should be the first
+ 
+
+ align:start position:0%
+that says one should be the first
+element in my merge
+
+ align:start position:0%
+element in my merge
+ 
+
+ align:start position:0%
+element in my merge
+list now compare the first element in
+
+ align:start position:0%
+list now compare the first element in
+ 
+
+ align:start position:0%
+list now compare the first element in
+each of these lists two is less than
+
+ align:start position:0%
+each of these lists two is less than
+ 
+
+ align:start position:0%
+each of these lists two is less than
+three so two ought to be the next
+
+ align:start position:0%
+three so two ought to be the next
+ 
+
+ align:start position:0%
+three so two ought to be the next
+element of the list and you get the idea
+
+ align:start position:0%
+element of the list and you get the idea
+ 
+
+ align:start position:0%
+element of the list and you get the idea
+what do I do next I'm going to compare
+
+ align:start position:0%
+what do I do next I'm going to compare
+ 
+
+ align:start position:0%
+what do I do next I'm going to compare
+three against four
+
+ align:start position:0%
+three against four
+ 
+
+ align:start position:0%
+three against four
+three is the smallest one then I'm going
+
+ align:start position:0%
+three is the smallest one then I'm going
+ 
+
+ align:start position:0%
+three is the smallest one then I'm going
+to compare four against 12 which is
+
+ align:start position:0%
+to compare four against 12 which is
+ 
+
+ align:start position:0%
+to compare four against 12 which is
+going to give me four and then what do I
+
+ align:start position:0%
+going to give me four and then what do I
+ 
+
+ align:start position:0%
+going to give me four and then what do I
+have to do 12 against 30 12 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller take that out 17 against
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+30 24 against
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+30 and by this stage I got nothing left
+
+ align:start position:0%
+30 and by this stage I got nothing left
+ 
+
+ align:start position:0%
+30 and by this stage I got nothing left
+in this one so I just add the rest of
+
+ align:start position:0%
+in this one so I just add the rest of
+ 
+
+ align:start position:0%
+in this one so I just add the rest of
+that l in
+
+ align:start position:0%
+that l in
+ 
+
+ align:start position:0%
+that l in
+wow I can sort two lists or I can merge
+
+ align:start position:0%
+wow I can sort two lists or I can merge
+ 
+
+ align:start position:0%
+wow I can sort two lists or I can merge
+two lists I said it poorly what's the
+
+ align:start position:0%
+two lists I said it poorly what's the
+ 
+
+ align:start position:0%
+two lists I said it poorly what's the
+point how many operations did it take me
+
+ align:start position:0%
+point how many operations did it take me
+ 
+
+ align:start position:0%
+point how many operations did it take me
+to do this seven comparisons right I got
+
+ align:start position:0%
+to do this seven comparisons right I got
+ 
+
+ align:start position:0%
+to do this seven comparisons right I got
+eight elements it took me seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comparisons because I can take advantage
+
+ align:start position:0%
+comparisons because I can take advantage
+ 
+
+ align:start position:0%
+comparisons because I can take advantage
+of the fact I know I only ever have to
+
+ align:start position:0%
+of the fact I know I only ever have to
+ 
+
+ align:start position:0%
+of the fact I know I only ever have to
+look at the first element of each
+
+ align:start position:0%
+look at the first element of each
+ 
+
+ align:start position:0%
+look at the first element of each
+sublist those are the only things I need
+
+ align:start position:0%
+sublist those are the only things I need
+ 
+
+ align:start position:0%
+sublist those are the only things I need
+to compare and when I run out of one
+
+ align:start position:0%
+to compare and when I run out of one
+ 
+
+ align:start position:0%
+to compare and when I run out of one
+list I just add the rest of the list in
+
+ align:start position:0%
+list I just add the rest of the list in
+ 
+
+ align:start position:0%
+list I just add the rest of the list in
+okay what's the order of complexity
+
+ align:start position:0%
+okay what's the order of complexity
+ 
+
+ align:start position:0%
+okay what's the order of complexity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+merging I heard it somewhere very
+
+ align:start position:0%
+merging I heard it somewhere very
+ 
+
+ align:start position:0%
+merging I heard it somewhere very
+quietly sorry n thank you linear
+
+ align:start position:0%
+quietly sorry n thank you linear
+ 
+
+ align:start position:0%
+quietly sorry n thank you linear
+absolutely right and what's n by the way
+
+ align:start position:0%
+absolutely right and what's n by the way
+ 
+
+ align:start position:0%
+absolutely right and what's n by the way
+here what's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measuring in both lists right so this is
+
+ align:start position:0%
+measuring in both lists right so this is
+ 
+
+ align:start position:0%
+measuring in both lists right so this is
+linear order n and n is the sum of the
+
+ align:start position:0%
+linear order n and n is the sum of the
+ 
+
+ align:start position:0%
+linear order n and n is the sum of the
+element or sorry of the number of
+
+ align:start position:0%
+element or sorry of the number of
+ 
+
+ align:start position:0%
+element or sorry of the number of
+elements in each list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I thought I was going to back my
+
+ align:start position:0%
+okay so I thought I was going to back my
+ 
+
+ align:start position:0%
+okay so I thought I was going to back my
+way into this that gives
+
+ align:start position:0%
+way into this that gives
+ 
+
+ align:start position:0%
+way into this that gives
+me a way to merge things so here's what
+
+ align:start position:0%
+me a way to merge things so here's what
+ 
+
+ align:start position:0%
+me a way to merge things so here's what
+merge sort would do right merge
+
+ align:start position:0%
+merge sort would do right merge
+ 
+
+ align:start position:0%
+merge sort would do right merge
+sort takes this
+
+ align:start position:0%
+sort takes this
+ 
+
+ align:start position:0%
+sort takes this
+idea of divide and
+
+ align:start position:0%
+idea of divide and
+ 
+
+ align:start position:0%
+idea of divide and
+conquer and it does the following it
+
+ align:start position:0%
+conquer and it does the following it
+ 
+
+ align:start position:0%
+conquer and it does the following it
+says let's divide the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+list in
+
+ align:start position:0%
+list in
+ 
+
+ align:start position:0%
+list in
+half there's the the div divide and
+
+ align:start position:0%
+half there's the the div divide and
+ 
+
+ align:start position:0%
+half there's the the div divide and
+conquer and let's keep dividing each of
+
+ align:start position:0%
+conquer and let's keep dividing each of
+ 
+
+ align:start position:0%
+conquer and let's keep dividing each of
+those lists in half until we get down to
+
+ align:start position:0%
+those lists in half until we get down to
+ 
+
+ align:start position:0%
+those lists in half until we get down to
+something that's really easy to sort
+
+ align:start position:0%
+something that's really easy to sort
+ 
+
+ align:start position:0%
+something that's really easy to sort
+what's the simplest thing to
+
+ align:start position:0%
+what's the simplest thing to
+ 
+
+ align:start position:0%
+what's the simplest thing to
+sort list to size one right right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continue
+
+ align:start position:0%
+continue
+ 
+
+ align:start position:0%
+continue
+until we have Singleton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lists once I got list of size one
+
+ align:start position:0%
+lists once I got list of size one
+ 
+
+ align:start position:0%
+lists once I got list of size one
+they're sorted
+
+ align:start position:0%
+they're sorted
+ 
+
+ align:start position:0%
+they're sorted
+and then combine them and combine them
+
+ align:start position:0%
+and then combine them and combine them
+ 
+
+ align:start position:0%
+and then combine them and combine them
+by doing a
+
+ align:start position:0%
+by doing a
+ 
+
+ align:start position:0%
+by doing a
+merge the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sublists and again you see that flavor
+
+ align:start position:0%
+sublists and again you see that flavor
+ 
+
+ align:start position:0%
+sublists and again you see that flavor
+I'm going to just keep dividing it up
+
+ align:start position:0%
+I'm going to just keep dividing it up
+ 
+
+ align:start position:0%
+I'm going to just keep dividing it up
+until I get something really easy and
+
+ align:start position:0%
+until I get something really easy and
+ 
+
+ align:start position:0%
+until I get something really easy and
+then I'm going to combine and this is
+
+ align:start position:0%
+then I'm going to combine and this is
+ 
+
+ align:start position:0%
+then I'm going to combine and this is
+different than binary search now the
+
+ align:start position:0%
+different than binary search now the
+ 
+
+ align:start position:0%
+different than binary search now the
+combine is going to have to do some work
+
+ align:start position:0%
+combine is going to have to do some work
+ 
+
+ align:start position:0%
+combine is going to have to do some work
+so I've given you a piece of code that
+
+ align:start position:0%
+so I've given you a piece of code that
+ 
+
+ align:start position:0%
+so I've given you a piece of code that
+does this I'm going to come back to it
+
+ align:start position:0%
+does this I'm going to come back to it
+ 
+
+ align:start position:0%
+does this I'm going to come back to it
+in a second but it's up there but what
+
+ align:start position:0%
+in a second but it's up there but what
+ 
+
+ align:start position:0%
+in a second but it's up there but what
+I'd like to do is to try and give you a
+
+ align:start position:0%
+I'd like to do is to try and give you a
+ 
+
+ align:start position:0%
+I'd like to do is to try and give you a
+sort of a little simulation of how this
+
+ align:start position:0%
+sort of a little simulation of how this
+ 
+
+ align:start position:0%
+sort of a little simulation of how this
+would work and I was going to originally
+
+ align:start position:0%
+would work and I was going to originally
+ 
+
+ align:start position:0%
+would work and I was going to originally
+make the Tas come up here and do it but
+
+ align:start position:0%
+make the Tas come up here and do it but
+ 
+
+ align:start position:0%
+make the Tas come up here and do it but
+I don't have enough Tas to do a full
+
+ align:start position:0%
+I don't have enough Tas to do a full
+ 
+
+ align:start position:0%
+I don't have enough Tas to do a full
+merge sort so I'm hoping and I also I
+
+ align:start position:0%
+merge sort so I'm hoping and I also I
+ 
+
+ align:start position:0%
+merge sort so I'm hoping and I also I
+have these really Hightech props I spent
+
+ align:start position:0%
+have these really Hightech props I spent
+ 
+
+ align:start position:0%
+have these really Hightech props I spent
+tons and tons of Department money on
+
+ align:start position:0%
+tons and tons of Department money on
+ 
+
+ align:start position:0%
+tons and tons of Department money on
+them as you can see I hope you can see
+
+ align:start position:0%
+them as you can see I hope you can see
+ 
+
+ align:start position:0%
+them as you can see I hope you can see
+this because I'm going to try and
+
+ align:start position:0%
+this because I'm going to try and
+ 
+
+ align:start position:0%
+this because I'm going to try and
+simulate what a merge sort does I've got
+
+ align:start position:0%
+simulate what a merge sort does I've got
+ 
+
+ align:start position:0%
+simulate what a merge sort does I've got
+eight things I want to sort here and
+
+ align:start position:0%
+eight things I want to sort here and
+ 
+
+ align:start position:0%
+eight things I want to sort here and
+those initially start out here at top
+
+ align:start position:0%
+those initially start out here at top
+ 
+
+ align:start position:0%
+those initially start out here at top
+level first step is divide them in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half right and I should have had them
+
+ align:start position:0%
+half right and I should have had them
+ 
+
+ align:start position:0%
+half right and I should have had them
+marker here remember I need to come back
+
+ align:start position:0%
+marker here remember I need to come back
+ 
+
+ align:start position:0%
+marker here remember I need to come back
+there not yet done what do I do divide
+
+ align:start position:0%
+there not yet done what do I do divide
+ 
+
+ align:start position:0%
+there not yet done what do I do divide
+them in half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+okay you know if I had like shells and
+
+ align:start position:0%
+okay you know if I had like shells and
+ 
+
+ align:start position:0%
+okay you know if I had like shells and
+peas here I could make some more money
+
+ align:start position:0%
+peas here I could make some more money
+ 
+
+ align:start position:0%
+peas here I could make some more money
+right all right what do I do I divide
+
+ align:start position:0%
+right all right what do I do I divide
+ 
+
+ align:start position:0%
+right all right what do I do I divide
+them in half one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time let me cluster them because really
+
+ align:start position:0%
+time let me cluster them because really
+ 
+
+ align:start position:0%
+time let me cluster them because really
+what I have sorry separate them out I've
+
+ align:start position:0%
+what I have sorry separate them out I've
+ 
+
+ align:start position:0%
+what I have sorry separate them out I've
+gone from one problem size eight down to
+
+ align:start position:0%
+gone from one problem size eight down to
+ 
+
+ align:start position:0%
+gone from one problem size eight down to
+eight problems of size one at this stage
+
+ align:start position:0%
+eight problems of size one at this stage
+ 
+
+ align:start position:0%
+eight problems of size one at this stage
+I'm at my Singleton case so this is easy
+
+ align:start position:0%
+I'm at my Singleton case so this is easy
+ 
+
+ align:start position:0%
+I'm at my Singleton case so this is easy
+what do I do I merge and the merge is
+
+ align:start position:0%
+what do I do I merge and the merge is
+ 
+
+ align:start position:0%
+what do I do I merge and the merge is
+put them in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order okay what do I do next obvious
+
+ align:start position:0%
+order okay what do I do next obvious
+ 
+
+ align:start position:0%
+order okay what do I do next obvious
+thing I merg these and that as we saw
+
+ align:start position:0%
+thing I merg these and that as we saw
+ 
+
+ align:start position:0%
+thing I merg these and that as we saw
+was a nice linear operation it's fun to
+
+ align:start position:0%
+was a nice linear operation it's fun to
+ 
+
+ align:start position:0%
+was a nice linear operation it's fun to
+do it upside down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then one more merch which is I take
+
+ align:start position:0%
+and then one more merch which is I take
+ 
+
+ align:start position:0%
+and then one more merch which is I take
+the smallest elements of each one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+until get to where I
+
+ align:start position:0%
+until get to where I
+ 
+
+ align:start position:0%
+until get to where I
+want wow aren't you
+
+ align:start position:0%
+want wow aren't you
+ 
+
+ align:start position:0%
+want wow aren't you
+impressed okay no please don't clap not
+
+ align:start position:0%
+impressed okay no please don't clap not
+ 
+
+ align:start position:0%
+impressed okay no please don't clap not
+for that one now let me do it a second
+
+ align:start position:0%
+for that one now let me do it a second
+ 
+
+ align:start position:0%
+for that one now let me do it a second
+time to show you that that's sorry I'm
+
+ align:start position:0%
+time to show you that that's sorry I'm
+ 
+
+ align:start position:0%
+time to show you that that's sorry I'm
+saying this poorly let me say it again
+
+ align:start position:0%
+saying this poorly let me say it again
+ 
+
+ align:start position:0%
+saying this poorly let me say it again
+that's the general idea what was what
+
+ align:start position:0%
+that's the general idea what was what
+ 
+
+ align:start position:0%
+that's the general idea what was what
+should you see out of that I just kept
+
+ align:start position:0%
+should you see out of that I just kept
+ 
+
+ align:start position:0%
+should you see out of that I just kept
+subdividing down till I got really easy
+
+ align:start position:0%
+subdividing down till I got really easy
+ 
+
+ align:start position:0%
+subdividing down till I got really easy
+problems and then I combined them back I
+
+ align:start position:0%
+problems and then I combined them back I
+ 
+
+ align:start position:0%
+problems and then I combined them back I
+actually misled you slightly there or
+
+ align:start position:0%
+actually misled you slightly there or
+ 
+
+ align:start position:0%
+actually misled you slightly there or
+maybe a lot because I did it in parallel
+
+ align:start position:0%
+maybe a lot because I did it in parallel
+ 
+
+ align:start position:0%
+maybe a lot because I did it in parallel
+and in fact let me just Shuffle these up
+
+ align:start position:0%
+and in fact let me just Shuffle these up
+ 
+
+ align:start position:0%
+and in fact let me just Shuffle these up
+a little bit really what's going to
+
+ align:start position:0%
+a little bit really what's going to
+ 
+
+ align:start position:0%
+a little bit really what's going to
+happen here because this is a sequential
+
+ align:start position:0%
+happen here because this is a sequential
+ 
+
+ align:start position:0%
+happen here because this is a sequential
+computer is that we're going to start
+
+ align:start position:0%
+computer is that we're going to start
+ 
+
+ align:start position:0%
+computer is that we're going to start
+off up
+
+ align:start position:0%
+off up
+ 
+
+ align:start position:0%
+off up
+here at top level we're going to divide
+
+ align:start position:0%
+here at top level we're going to divide
+ 
+
+ align:start position:0%
+here at top level we're going to divide
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half and then we're going to do the
+
+ align:start position:0%
+half and then we're going to do the
+ 
+
+ align:start position:0%
+half and then we're going to do the
+complete subdivision and merge here
+
+ align:start position:0%
+complete subdivision and merge here
+ 
+
+ align:start position:0%
+complete subdivision and merge here
+before we ever come back and do this one
+
+ align:start position:0%
+before we ever come back and do this one
+ 
+
+ align:start position:0%
+before we ever come back and do this one
+right we're going to do a
+
+ align:start position:0%
+right we're going to do a
+ 
+
+ align:start position:0%
+right we're going to do a
+division here and then a division there
+
+ align:start position:0%
+division here and then a division there
+ 
+
+ align:start position:0%
+division here and then a division there
+at that stage we can merge these and
+
+ align:start position:0%
+at that stage we can merge these and
+ 
+
+ align:start position:0%
+at that stage we can merge these and
+then take this down do the division
+
+ align:start position:0%
+then take this down do the division
+ 
+
+ align:start position:0%
+then take this down do the division
+merge and bring them back whoops sorry
+
+ align:start position:0%
+merge and bring them back whoops sorry
+ 
+
+ align:start position:0%
+merge and bring them back whoops sorry
+about that and bring them back
+
+ align:start position:0%
+about that and bring them back
+ 
+
+ align:start position:0%
+about that and bring them back
+up okay let me show you an example by
+
+ align:start position:0%
+up okay let me show you an example by
+ 
+
+ align:start position:0%
+up okay let me show you an example by
+running that I've got a little list I've
+
+ align:start position:0%
+running that I've got a little list I've
+ 
+
+ align:start position:0%
+running that I've got a little list I've
+made here called
+
+ align:start position:0%
+made here called
+ 
+
+ align:start position:0%
+made here called
+test let's run merge sword on
+
+ align:start position:0%
+test let's run merge sword on
+ 
+
+ align:start position:0%
+test let's run merge sword on
+it then we'll look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code okay what I would like you to see
+
+ align:start position:0%
+code okay what I would like you to see
+ 
+
+ align:start position:0%
+code okay what I would like you to see
+is I've been printing out as I went
+
+ align:start position:0%
+is I've been printing out as I went
+ 
+
+ align:start position:0%
+is I've been printing out as I went
+along actually that's backup slightly
+
+ align:start position:0%
+along actually that's backup slightly
+ 
+
+ align:start position:0%
+along actually that's backup slightly
+and look at the code there's merge
+
+ align:start position:0%
+and look at the code there's merge
+ 
+
+ align:start position:0%
+and look at the code there's merge
+sort takes in a list what does it say to
+
+ align:start position:0%
+sort takes in a list what does it say to
+ 
+
+ align:start position:0%
+sort takes in a list what does it say to
+do it says check to see if I'm in that
+
+ align:start position:0%
+do it says check to see if I'm in that
+ 
+
+ align:start position:0%
+do it says check to see if I'm in that
+base case it's the list of less of
+
+ align:start position:0%
+base case it's the list of less of
+ 
+
+ align:start position:0%
+base case it's the list of less of
+length less than two is it one basically
+
+ align:start position:0%
+length less than two is it one basically
+ 
+
+ align:start position:0%
+length less than two is it one basically
+in which case just return a copy of the
+
+ align:start position:0%
+in which case just return a copy of the
+ 
+
+ align:start position:0%
+in which case just return a copy of the
+list okay that's the simple case
+
+ align:start position:0%
+list okay that's the simple case
+ 
+
+ align:start position:0%
+list okay that's the simple case
+otherwise notice what it says to do it
+
+ align:start position:0%
+otherwise notice what it says to do it
+ 
+
+ align:start position:0%
+otherwise notice what it says to do it
+says find the midpoint and split the
+
+ align:start position:0%
+says find the midpoint and split the
+ 
+
+ align:start position:0%
+says find the midpoint and split the
+list in half right copy of the back end
+
+ align:start position:0%
+list in half right copy of the back end
+ 
+
+ align:start position:0%
+list in half right copy of the back end
+sorry copy of the left side copy of the
+
+ align:start position:0%
+sorry copy of the left side copy of the
+ 
+
+ align:start position:0%
+sorry copy of the left side copy of the
+right side run merge sour on those by
+
+ align:start position:0%
+right side run merge sour on those by
+ 
+
+ align:start position:0%
+right side run merge sour on those by
+induction if it does the right thing I'm
+
+ align:start position:0%
+induction if it does the right thing I'm
+ 
+
+ align:start position:0%
+induction if it does the right thing I'm
+going to get back two lists and I'm
+
+ align:start position:0%
+going to get back two lists and I'm
+ 
+
+ align:start position:0%
+going to get back two lists and I'm
+going to then merge them together and
+
+ align:start position:0%
+going to then merge them together and
+ 
+
+ align:start position:0%
+going to then merge them together and
+notice what I'm going to do I'm going to
+
+ align:start position:0%
+notice what I'm going to do I'm going to
+ 
+
+ align:start position:0%
+notice what I'm going to do I'm going to
+print here the list as we go into it and
+
+ align:start position:0%
+print here the list as we go into it and
+ 
+
+ align:start position:0%
+print here the list as we go into it and
+a print of the merge when we're done and
+
+ align:start position:0%
+a print of the merge when we're done and
+ 
+
+ align:start position:0%
+a print of the merge when we're done and
+then just return that merge up here
+
+ align:start position:0%
+then just return that merge up here
+ 
+
+ align:start position:0%
+then just return that merge up here
+there's a little more code there I'll
+
+ align:start position:0%
+there's a little more code there I'll
+ 
+
+ align:start position:0%
+there's a little more code there I'll
+let you dis grock it but you can see
+
+ align:start position:0%
+let you dis grock it but you can see
+ 
+
+ align:start position:0%
+let you dis grock it but you can see
+it's basically doing what I did over
+
+ align:start position:0%
+it's basically doing what I did over
+ 
+
+ align:start position:0%
+it's basically doing what I did over
+there setting up two indices for the two
+
+ align:start position:0%
+there setting up two indices for the two
+ 
+
+ align:start position:0%
+there setting up two indices for the two
+sublist is just walking down finding the
+
+ align:start position:0%
+sublist is just walking down finding the
+ 
+
+ align:start position:0%
+sublist is just walking down finding the
+smallest element putting it into a new
+
+ align:start position:0%
+smallest element putting it into a new
+ 
+
+ align:start position:0%
+smallest element putting it into a new
+list when it gets to the end one of the
+
+ align:start position:0%
+list when it gets to the end one of the
+ 
+
+ align:start position:0%
+list when it gets to the end one of the
+lists it skips to the next part and only
+
+ align:start position:0%
+lists it skips to the next part and only
+ 
+
+ align:start position:0%
+lists it skips to the next part and only
+one of these two pieces will get called
+
+ align:start position:0%
+one of these two pieces will get called
+ 
+
+ align:start position:0%
+one of these two pieces will get called
+because only one of them is going to
+
+ align:start position:0%
+because only one of them is going to
+ 
+
+ align:start position:0%
+because only one of them is going to
+have things left over it's going to add
+
+ align:start position:0%
+have things left over it's going to add
+ 
+
+ align:start position:0%
+have things left over it's going to add
+the other pieces
+
+ align:start position:0%
+the other pieces
+ 
+
+ align:start position:0%
+the other pieces
+in okay if you look at that then let's
+
+ align:start position:0%
+in okay if you look at that then let's
+ 
+
+ align:start position:0%
+in okay if you look at that then let's
+look at what happened when we ran this
+
+ align:start position:0%
+look at what happened when we ran this
+ 
+
+ align:start position:0%
+look at what happened when we ran this
+right we started off with a call with
+
+ align:start position:0%
+right we started off with a call with
+ 
+
+ align:start position:0%
+right we started off with a call with
+that list aha split it in half it's
+
+ align:start position:0%
+that list aha split it in half it's
+ 
+
+ align:start position:0%
+that list aha split it in half it's
+going down the left side of this that
+
+ align:start position:0%
+going down the left side of this that
+ 
+
+ align:start position:0%
+going down the left side of this that
+got split in half and that got split in
+
+ align:start position:0%
+got split in half and that got split in
+ 
+
+ align:start position:0%
+got split in half and that got split in
+half until I got to a list of size one
+
+ align:start position:0%
+half until I got to a list of size one
+ 
+
+ align:start position:0%
+half until I got to a list of size one
+there's the first list of size one
+
+ align:start position:0%
+there's the first list of size one
+ 
+
+ align:start position:0%
+there's the first list of size one
+there's the second list to size one so I
+
+ align:start position:0%
+there's the second list to size one so I
+ 
+
+ align:start position:0%
+there's the second list to size one so I
+merg them it's now in the right order
+
+ align:start position:0%
+merg them it's now in the right order
+ 
+
+ align:start position:0%
+merg them it's now in the right order
+and that's coming from right there
+
+ align:start position:0%
+and that's coming from right there
+ 
+
+ align:start position:0%
+and that's coming from right there
+having done that it goes back up and
+
+ align:start position:0%
+having done that it goes back up and
+ 
+
+ align:start position:0%
+having done that it goes back up and
+picks the second subl list which came
+
+ align:start position:0%
+picks the second subl list which came
+ 
+
+ align:start position:0%
+picks the second subl list which came
+actually I should have said came from
+
+ align:start position:0%
+actually I should have said came from
+ 
+
+ align:start position:0%
+actually I should have said came from
+there right gets it down to base case
+
+ align:start position:0%
+there right gets it down to base case
+ 
+
+ align:start position:0%
+there right gets it down to base case
+merges it when these two merges are done
+
+ align:start position:0%
+merges it when these two merges are done
+ 
+
+ align:start position:0%
+merges it when these two merges are done
+we're basically at a stage in that
+
+ align:start position:0%
+we're basically at a stage in that
+ 
+
+ align:start position:0%
+we're basically at a stage in that
+Branch where we can now merge those two
+
+ align:start position:0%
+Branch where we can now merge those two
+ 
+
+ align:start position:0%
+Branch where we can now merge those two
+together which gives us that and it goes
+
+ align:start position:0%
+together which gives us that and it goes
+ 
+
+ align:start position:0%
+together which gives us that and it goes
+through the rest of
+
+ align:start position:0%
+through the rest of
+ 
+
+ align:start position:0%
+through the rest of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay a really nice
+
+ align:start position:0%
+okay a really nice
+ 
+
+ align:start position:0%
+okay a really nice
+algorithm as I said an example of divide
+
+ align:start position:0%
+algorithm as I said an example of divide
+ 
+
+ align:start position:0%
+algorithm as I said an example of divide
+and conquer notice here that it's
+
+ align:start position:0%
+and conquer notice here that it's
+ 
+
+ align:start position:0%
+and conquer notice here that it's
+different than the binary search case
+
+ align:start position:0%
+different than the binary search case
+ 
+
+ align:start position:0%
+different than the binary search case
+we're certainly dividing down but the
+
+ align:start position:0%
+we're certainly dividing down but the
+ 
+
+ align:start position:0%
+we're certainly dividing down but the
+combination now actually takes some work
+
+ align:start position:0%
+combination now actually takes some work
+ 
+
+ align:start position:0%
+combination now actually takes some work
+right I have to actually figure out how
+
+ align:start position:0%
+right I have to actually figure out how
+ 
+
+ align:start position:0%
+right I have to actually figure out how
+to put them back together and that's a
+
+ align:start position:0%
+to put them back together and that's a
+ 
+
+ align:start position:0%
+to put them back together and that's a
+general thing you want to keep in mind
+
+ align:start position:0%
+general thing you want to keep in mind
+ 
+
+ align:start position:0%
+general thing you want to keep in mind
+when you're thinking about designing a
+
+ align:start position:0%
+when you're thinking about designing a
+ 
+
+ align:start position:0%
+when you're thinking about designing a
+divide and conquer kind of algorithm you
+
+ align:start position:0%
+divide and conquer kind of algorithm you
+ 
+
+ align:start position:0%
+divide and conquer kind of algorithm you
+really want to get the power of dividing
+
+ align:start position:0%
+really want to get the power of dividing
+ 
+
+ align:start position:0%
+really want to get the power of dividing
+things up but if you end up doing a ton
+
+ align:start position:0%
+things up but if you end up doing a ton
+ 
+
+ align:start position:0%
+things up but if you end up doing a ton
+of work at the combination stage you may
+
+ align:start position:0%
+of work at the combination stage you may
+ 
+
+ align:start position:0%
+of work at the combination stage you may
+not have gained anything so you really
+
+ align:start position:0%
+not have gained anything so you really
+ 
+
+ align:start position:0%
+not have gained anything so you really
+want to think that
+
+ align:start position:0%
+want to think that
+ 
+
+ align:start position:0%
+want to think that
+tradeoff all right having said that
+
+ align:start position:0%
+tradeoff all right having said that
+ 
+
+ align:start position:0%
+tradeoff all right having said that
+what's the complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here well there's a dumb question
+
+ align:start position:0%
+here well there's a dumb question
+ 
+
+ align:start position:0%
+here well there's a dumb question
+because I've been telling you for the
+
+ align:start position:0%
+because I've been telling you for the
+ 
+
+ align:start position:0%
+because I've been telling you for the
+last two lectures the complexity is n
+
+ align:start position:0%
+last two lectures the complexity is n
+ 
+
+ align:start position:0%
+last two lectures the complexity is n
+log n but let's see if it really is
+
+ align:start position:0%
+log n but let's see if it really is
+ 
+
+ align:start position:0%
+log n but let's see if it really is
+what's the complexity
+
+ align:start position:0%
+what's the complexity
+ 
+
+ align:start position:0%
+what's the complexity
+here if we think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it we start off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah with a problem of sizing
+
+ align:start position:0%
+yeah with a problem of sizing
+ 
+
+ align:start position:0%
+yeah with a problem of sizing
+n what do we do we split it into two
+
+ align:start position:0%
+n what do we do we split it into two
+ 
+
+ align:start position:0%
+n what do we do we split it into two
+problems of size
+
+ align:start position:0%
+problems of size
+ 
+
+ align:start position:0%
+problems of size
+n/2 those get split each into two
+
+ align:start position:0%
+n/2 those get split each into two
+ 
+
+ align:start position:0%
+n/2 those get split each into two
+problems of size n over4 and we keep
+
+ align:start position:0%
+problems of size n over4 and we keep
+ 
+
+ align:start position:0%
+problems of size n over4 and we keep
+doing that until we get down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to a level in this tree where we have
+
+ align:start position:0%
+to a level in this tree where we have
+ 
+
+ align:start position:0%
+to a level in this tree where we have
+only Singleton left
+
+ align:start position:0%
+only Singleton left
+ 
+
+ align:start position:0%
+only Singleton left
+over okay once we're there we have to do
+
+ align:start position:0%
+over okay once we're there we have to do
+ 
+
+ align:start position:0%
+over okay once we're there we have to do
+the merge and notice what happens here
+
+ align:start position:0%
+the merge and notice what happens here
+ 
+
+ align:start position:0%
+the merge and notice what happens here
+we said each of the merge operations was
+
+ align:start position:0%
+we said each of the merge operations was
+ 
+
+ align:start position:0%
+we said each of the merge operations was
+of of of of order n but n is different
+
+ align:start position:0%
+of of of of order n but n is different
+ 
+
+ align:start position:0%
+of of of of order n but n is different
+right down here I've just got two things
+
+ align:start position:0%
+right down here I've just got two things
+ 
+
+ align:start position:0%
+right down here I've just got two things
+to merge and then I've got things of
+
+ align:start position:0%
+to merge and then I've got things of
+ 
+
+ align:start position:0%
+to merge and then I've got things of
+size two to merge and then things of
+
+ align:start position:0%
+size two to merge and then things of
+ 
+
+ align:start position:0%
+size two to merge and then things of
+size four to merge but notice the
+
+ align:start position:0%
+size four to merge but notice the
+ 
+
+ align:start position:0%
+size four to merge but notice the
+trade-off I have
+
+ align:start position:0%
+trade-off I have
+ 
+
+ align:start position:0%
+trade-off I have
+n operations if you like down there of
+
+ align:start position:0%
+n operations if you like down there of
+ 
+
+ align:start position:0%
+n operations if you like down there of
+size one up here I have n over two
+
+ align:start position:0%
+size one up here I have n over two
+ 
+
+ align:start position:0%
+size one up here I have n over two
+operations of size two up here I've got
+
+ align:start position:0%
+operations of size two up here I've got
+ 
+
+ align:start position:0%
+operations of size two up here I've got
+n over4 operations of size four so I
+
+ align:start position:0%
+n over4 operations of size four so I
+ 
+
+ align:start position:0%
+n over4 operations of size four so I
+always have to do a merge of n
+
+ align:start position:0%
+always have to do a merge of n
+ 
+
+ align:start position:0%
+always have to do a merge of n
+elements how much time does that
+
+ align:start position:0%
+elements how much time does that
+ 
+
+ align:start position:0%
+elements how much time does that
+take well we said it right
+
+ align:start position:0%
+take well we said it right
+ 
+
+ align:start position:0%
+take well we said it right
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+oops where did I put it right there
+
+ align:start position:0%
+oops where did I put it right there
+ 
+
+ align:start position:0%
+oops where did I put it right there
+order n so I have order
+
+ align:start position:0%
+order n so I have order
+ 
+
+ align:start position:0%
+order n so I have order
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operations at each level in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree and then how many levels deep am I
+
+ align:start position:0%
+tree and then how many levels deep am I
+ 
+
+ align:start position:0%
+tree and then how many levels deep am I
+well that's the Divide right so how many
+
+ align:start position:0%
+well that's the Divide right so how many
+ 
+
+ align:start position:0%
+well that's the Divide right so how many
+levels do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have log M because at each stage I'm
+
+ align:start position:0%
+have log M because at each stage I'm
+ 
+
+ align:start position:0%
+have log M because at each stage I'm
+cutting the problem in half so I start
+
+ align:start position:0%
+cutting the problem in half so I start
+ 
+
+ align:start position:0%
+cutting the problem in half so I start
+off with n then it's n/2 n 4 n/8 so I
+
+ align:start position:0%
+off with n then it's n/2 n 4 n/8 so I
+ 
+
+ align:start position:0%
+off with n then it's n/2 n 4 n/8 so I
+got n so I have n operations log n times
+
+ align:start position:0%
+got n so I have n operations log n times
+ 
+
+ align:start position:0%
+got n so I have n operations log n times
+there we
+
+ align:start position:0%
+there we
+ 
+
+ align:start position:0%
+there we
+go and log
+
+ align:start position:0%
+go and log
+ 
+
+ align:start position:0%
+go and log
+in took us a long time to get there but
+
+ align:start position:0%
+in took us a long time to get there but
+ 
+
+ align:start position:0%
+in took us a long time to get there but
+it's a nice algorithm to
+
+ align:start position:0%
+it's a nice algorithm to
+ 
+
+ align:start position:0%
+it's a nice algorithm to
+have all right let me generalize this
+
+ align:start position:0%
+have all right let me generalize this
+ 
+
+ align:start position:0%
+have all right let me generalize this
+slightly
+
+ align:start position:0%
+slightly
+ 
+
+ align:start position:0%
+slightly
+okay when we get a problem a standard
+
+ align:start position:0%
+okay when we get a problem a standard
+ 
+
+ align:start position:0%
+okay when we get a problem a standard
+tool to try and attack it with is to say
+
+ align:start position:0%
+tool to try and attack it with is to say
+ 
+
+ align:start position:0%
+tool to try and attack it with is to say
+is there some way to break this problem
+
+ align:start position:0%
+is there some way to break this problem
+ 
+
+ align:start position:0%
+is there some way to break this problem
+problem down into simpler or shouldn't
+
+ align:start position:0%
+problem down into simpler or shouldn't
+ 
+
+ align:start position:0%
+problem down into simpler or shouldn't
+say simpler smaller versions of the same
+
+ align:start position:0%
+say simpler smaller versions of the same
+ 
+
+ align:start position:0%
+say simpler smaller versions of the same
+problem okay if I can do that it's a
+
+ align:start position:0%
+problem okay if I can do that it's a
+ 
+
+ align:start position:0%
+problem okay if I can do that it's a
+good candidate for divide and conquer
+
+ align:start position:0%
+good candidate for divide and conquer
+ 
+
+ align:start position:0%
+good candidate for divide and conquer
+and then the things I have to ask is how
+
+ align:start position:0%
+and then the things I have to ask is how
+ 
+
+ align:start position:0%
+and then the things I have to ask is how
+much of a division do I want to do the
+
+ align:start position:0%
+much of a division do I want to do the
+ 
+
+ align:start position:0%
+much of a division do I want to do the
+obvious ones to divide it in half but
+
+ align:start position:0%
+obvious ones to divide it in half but
+ 
+
+ align:start position:0%
+obvious ones to divide it in half but
+there may be cases where there are
+
+ align:start position:0%
+there may be cases where there are
+ 
+
+ align:start position:0%
+there may be cases where there are
+different divisions you want to have
+
+ align:start position:0%
+different divisions you want to have
+ 
+
+ align:start position:0%
+different divisions you want to have
+take place the second question I want to
+
+ align:start position:0%
+take place the second question I want to
+ 
+
+ align:start position:0%
+take place the second question I want to
+ask is what's the base case when do I
+
+ align:start position:0%
+ask is what's the base case when do I
+ 
+
+ align:start position:0%
+ask is what's the base case when do I
+get down to a problem small enough that
+
+ align:start position:0%
+get down to a problem small enough that
+ 
+
+ align:start position:0%
+get down to a problem small enough that
+it's basically trivial to solve here it
+
+ align:start position:0%
+it's basically trivial to solve here it
+ 
+
+ align:start position:0%
+it's basically trivial to solve here it
+was list of size one I put have stopped
+
+ align:start position:0%
+was list of size one I put have stopped
+ 
+
+ align:start position:0%
+was list of size one I put have stopped
+at list a size two right that's an easy
+
+ align:start position:0%
+at list a size two right that's an easy
+ 
+
+ align:start position:0%
+at list a size two right that's an easy
+comparison do one comparison and return
+
+ align:start position:0%
+comparison do one comparison and return
+ 
+
+ align:start position:0%
+comparison do one comparison and return
+one of two possible orders on it but I
+
+ align:start position:0%
+one of two possible orders on it but I
+ 
+
+ align:start position:0%
+one of two possible orders on it but I
+need you to decide that the third thing
+
+ align:start position:0%
+need you to decide that the third thing
+ 
+
+ align:start position:0%
+need you to decide that the third thing
+I need to decide is how do I combine
+
+ align:start position:0%
+I need to decide is how do I combine
+ 
+
+ align:start position:0%
+I need to decide is how do I combine
+okay and I'll point out to you in the
+
+ align:start position:0%
+okay and I'll point out to you in the
+ 
+
+ align:start position:0%
+okay and I'll point out to you in the
+binary search case combination was
+
+ align:start position:0%
+binary search case combination was
+ 
+
+ align:start position:0%
+binary search case combination was
+trivial right answer to the final search
+
+ align:start position:0%
+trivial right answer to the final search
+ 
+
+ align:start position:0%
+trivial right answer to the final search
+was just the answer all the way up here
+
+ align:start position:0%
+was just the answer all the way up here
+ 
+
+ align:start position:0%
+was just the answer all the way up here
+little more work and that's why I'll
+
+ align:start position:0%
+little more work and that's why I'll
+ 
+
+ align:start position:0%
+little more work and that's why I'll
+come back to that idea if it if I'm
+
+ align:start position:0%
+come back to that idea if it if I'm
+ 
+
+ align:start position:0%
+come back to that idea if it if I'm
+basically just squeezing Jello that is
+
+ align:start position:0%
+basically just squeezing Jello that is
+ 
+
+ align:start position:0%
+basically just squeezing Jello that is
+I'm trying to make the problem simpler
+
+ align:start position:0%
+I'm trying to make the problem simpler
+ 
+
+ align:start position:0%
+I'm trying to make the problem simpler
+but the combination turns out to be
+
+ align:start position:0%
+but the combination turns out to be
+ 
+
+ align:start position:0%
+but the combination turns out to be
+really complex I've not gained anything
+
+ align:start position:0%
+really complex I've not gained anything
+ 
+
+ align:start position:0%
+really complex I've not gained anything
+so things that are good candidates for
+
+ align:start position:0%
+so things that are good candidates for
+ 
+
+ align:start position:0%
+so things that are good candidates for
+divide and conquer are problems where
+
+ align:start position:0%
+divide and conquer are problems where
+ 
+
+ align:start position:0%
+divide and conquer are problems where
+it's easy to figure out how to divide
+
+ align:start position:0%
+it's easy to figure out how to divide
+ 
+
+ align:start position:0%
+it's easy to figure out how to divide
+down and the combination is of low
+
+ align:start position:0%
+down and the combination is of low
+ 
+
+ align:start position:0%
+down and the combination is of low
+complexity be nice if it was less than
+
+ align:start position:0%
+complexity be nice if it was less than
+ 
+
+ align:start position:0%
+complexity be nice if it was less than
+linear but linear is nice because then
+
+ align:start position:0%
+linear but linear is nice because then
+ 
+
+ align:start position:0%
+linear but linear is nice because then
+I'm going to get that n log in kind of
+
+ align:start position:0%
+I'm going to get that n log in kind of
+ 
+
+ align:start position:0%
+I'm going to get that n log in kind of
+behavior and if you ask the Tas in
+
+ align:start position:0%
+behavior and if you ask the Tas in
+ 
+
+ align:start position:0%
+behavior and if you ask the Tas in
+recitation tomorrow they'll tell you
+
+ align:start position:0%
+recitation tomorrow they'll tell you
+ 
+
+ align:start position:0%
+recitation tomorrow they'll tell you
+that you see a lot of nlog and
+
+ align:start position:0%
+that you see a lot of nlog and
+ 
+
+ align:start position:0%
+that you see a lot of nlog and
+algorithms in computer science it's a
+
+ align:start position:0%
+algorithms in computer science it's a
+ 
+
+ align:start position:0%
+algorithms in computer science it's a
+very common class of algorithm and it's
+
+ align:start position:0%
+very common class of algorithm and it's
+ 
+
+ align:start position:0%
+very common class of algorithm and it's
+a very useful one to
+
+ align:start position:0%
+a very useful one to
+ 
+
+ align:start position:0%
+a very useful one to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+one of the questions we could still ask
+
+ align:start position:0%
+one of the questions we could still ask
+ 
+
+ align:start position:0%
+one of the questions we could still ask
+is right we got binary search which has
+
+ align:start position:0%
+is right we got binary search which has
+ 
+
+ align:start position:0%
+is right we got binary search which has
+got this nice log
+
+ align:start position:0%
+got this nice log
+ 
+
+ align:start position:0%
+got this nice log
+Behavior if we can sort things um you
+
+ align:start position:0%
+Behavior if we can sort things um you
+ 
+
+ align:start position:0%
+Behavior if we can sort things um you
+know we get this this n log n behavior
+
+ align:start position:0%
+know we get this this n log n behavior
+ 
+
+ align:start position:0%
+know we get this this n log n behavior
+and we got an N log n Behavior overall
+
+ align:start position:0%
+and we got an N log n Behavior overall
+ 
+
+ align:start position:0%
+and we got an N log n Behavior overall
+but can we actually do better in terms
+
+ align:start position:0%
+but can we actually do better in terms
+ 
+
+ align:start position:0%
+but can we actually do better in terms
+of searching and I'm going to show you
+
+ align:start position:0%
+of searching and I'm going to show you
+ 
+
+ align:start position:0%
+of searching and I'm going to show you
+one last technique that in fact I'm
+
+ align:start position:0%
+one last technique that in fact I'm
+ 
+
+ align:start position:0%
+one last technique that in fact I'm
+going a weir put quotes around the word
+
+ align:start position:0%
+going a weir put quotes around the word
+ 
+
+ align:start position:0%
+going a weir put quotes around the word
+better but it does better than uh even
+
+ align:start position:0%
+better but it does better than uh even
+ 
+
+ align:start position:0%
+better but it does better than uh even
+this kind of binary search
+
+ align:start position:0%
+this kind of binary search
+ 
+
+ align:start position:0%
+this kind of binary search
+that's a method called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hashing
+
+ align:start position:0%
+hashing
+ 
+
+ align:start position:0%
+hashing
+okay you've actually seen hashing you
+
+ align:start position:0%
+okay you've actually seen hashing you
+ 
+
+ align:start position:0%
+okay you've actually seen hashing you
+just don't know it hashing is the
+
+ align:start position:0%
+just don't know it hashing is the
+ 
+
+ align:start position:0%
+just don't know it hashing is the
+technique that's used in Python to
+
+ align:start position:0%
+technique that's used in Python to
+ 
+
+ align:start position:0%
+technique that's used in Python to
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+dictionaries hashing is used when you
+
+ align:start position:0%
+dictionaries hashing is used when you
+ 
+
+ align:start position:0%
+dictionaries hashing is used when you
+actually come into Logan airport and
+
+ align:start position:0%
+actually come into Logan airport and
+ 
+
+ align:start position:0%
+actually come into Logan airport and
+immigration or Homeland Security checks
+
+ align:start position:0%
+immigration or Homeland Security checks
+ 
+
+ align:start position:0%
+immigration or Homeland Security checks
+your picture against a database um
+
+ align:start position:0%
+your picture against a database um
+ 
+
+ align:start position:0%
+your picture against a database um
+hashing is used every time you enter a
+
+ align:start position:0%
+hashing is used every time you enter a
+ 
+
+ align:start position:0%
+hashing is used every time you enter a
+password into a system so what in the
+
+ align:start position:0%
+password into a system so what in the
+ 
+
+ align:start position:0%
+password into a system so what in the
+world is hashing well let me start with
+
+ align:start position:0%
+world is hashing well let me start with
+ 
+
+ align:start position:0%
+world is hashing well let me start with
+a simple little example
+
+ align:start position:0%
+a simple little example
+ 
+
+ align:start position:0%
+a simple little example
+suppose I want to
+
+ align:start position:0%
+suppose I want to
+ 
+
+ align:start position:0%
+suppose I want to
+represent a
+
+ align:start position:0%
+represent a
+ 
+
+ align:start position:0%
+represent a
+collection of integers this is a really
+
+ align:start position:0%
+collection of integers this is a really
+ 
+
+ align:start position:0%
+collection of integers this is a really
+easy little
+
+ align:start position:0%
+easy little
+ 
+
+ align:start position:0%
+easy little
+example and I promise you that the
+
+ align:start position:0%
+example and I promise you that the
+ 
+
+ align:start position:0%
+example and I promise you that the
+integers are never going to be anything
+
+ align:start position:0%
+integers are never going to be anything
+ 
+
+ align:start position:0%
+integers are never going to be anything
+other than between the range of 0 to
+
+ align:start position:0%
+other than between the range of 0 to
+ 
+
+ align:start position:0%
+other than between the range of 0 to
+nine okay so it might be the collection
+
+ align:start position:0%
+nine okay so it might be the collection
+ 
+
+ align:start position:0%
+nine okay so it might be the collection
+one and five it might be 2 3 48 I mean
+
+ align:start position:0%
+one and five it might be 2 3 48 I mean
+ 
+
+ align:start position:0%
+one and five it might be 2 3 48 I mean
+some collection of integers but I
+
+ align:start position:0%
+some collection of integers but I
+ 
+
+ align:start position:0%
+some collection of integers but I
+guarantee you it's between zero and nine
+
+ align:start position:0%
+guarantee you it's between zero and nine
+ 
+
+ align:start position:0%
+guarantee you it's between zero and nine
+here's the trick I can
+
+ align:start position:0%
+here's the trick I can
+ 
+
+ align:start position:0%
+here's the trick I can
+play I can build
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+count I could build a
+
+ align:start position:0%
+count I could build a
+ 
+
+ align:start position:0%
+count I could build a
+list with spots for all of those
+
+ align:start position:0%
+list with spots for all of those
+ 
+
+ align:start position:0%
+list with spots for all of those
+elements 0 1 2 3 4 5 6 78 n and then
+
+ align:start position:0%
+elements 0 1 2 3 4 5 6 78 n and then
+ 
+
+ align:start position:0%
+elements 0 1 2 3 4 5 6 78 n and then
+when I want to create my set I could
+
+ align:start position:0%
+when I want to create my set I could
+ 
+
+ align:start position:0%
+when I want to create my set I could
+simply put a
+
+ align:start position:0%
+simply put a
+ 
+
+ align:start position:0%
+simply put a
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+everywhere that that integer Falls so if
+
+ align:start position:0%
+everywhere that that integer Falls so if
+ 
+
+ align:start position:0%
+everywhere that that integer Falls so if
+I wanted to represent that for example
+
+ align:start position:0%
+I wanted to represent that for example
+ 
+
+ align:start position:0%
+I wanted to represent that for example
+this is the set
+
+ align:start position:0%
+this is the set
+ 
+
+ align:start position:0%
+this is the set
+two six and eight I put a one in those
+
+ align:start position:0%
+two six and eight I put a one in those
+ 
+
+ align:start position:0%
+two six and eight I put a one in those
+slots right this seems a little weird
+
+ align:start position:0%
+slots right this seems a little weird
+ 
+
+ align:start position:0%
+slots right this seems a little weird
+but the bear with me for a second in
+
+ align:start position:0%
+but the bear with me for a second in
+ 
+
+ align:start position:0%
+but the bear with me for a second in
+fact I've given you a little piece of
+
+ align:start position:0%
+fact I've given you a little piece of
+ 
+
+ align:start position:0%
+fact I've given you a little piece of
+code to do
+
+ align:start position:0%
+code to do
+ 
+
+ align:start position:0%
+code to do
+it which is the next piece of code on
+
+ align:start position:0%
+it which is the next piece of code on
+ 
+
+ align:start position:0%
+it which is the next piece of code on
+the on the
+
+ align:start position:0%
+the on the
+ 
+
+ align:start position:0%
+the on the
+handout so let's take a look at it for a
+
+ align:start position:0%
+handout so let's take a look at it for a
+ 
+
+ align:start position:0%
+handout so let's take a look at it for a
+second right this little set of code
+
+ align:start position:0%
+second right this little set of code
+ 
+
+ align:start position:0%
+second right this little set of code
+here from create insert and member
+
+ align:start position:0%
+here from create insert and member
+ 
+
+ align:start position:0%
+here from create insert and member
+what's create do it says given a low and
+
+ align:start position:0%
+what's create do it says given a low and
+ 
+
+ align:start position:0%
+what's create do it says given a low and
+a high range in this case it' be zero to
+
+ align:start position:0%
+a high range in this case it' be zero to
+ 
+
+ align:start position:0%
+a high range in this case it' be zero to
+n9ine I'm going to build
+
+ align:start position:0%
+n9ine I'm going to build
+ 
+
+ align:start position:0%
+n9ine I'm going to build
+ah a list right you can see that little
+
+ align:start position:0%
+ah a list right you can see that little
+ 
+
+ align:start position:0%
+ah a list right you can see that little
+Loop through going through there what am
+
+ align:start position:0%
+Loop through going through there what am
+ 
+
+ align:start position:0%
+Loop through going through there what am
+I doing I'm creating a list with just
+
+ align:start position:0%
+I doing I'm creating a list with just
+ 
+
+ align:start position:0%
+I doing I'm creating a list with just
+that special symbol none in it so I'm
+
+ align:start position:0%
+that special symbol none in it so I'm
+ 
+
+ align:start position:0%
+that special symbol none in it so I'm
+building the list I'm returning that as
+
+ align:start position:0%
+building the list I'm returning that as
+ 
+
+ align:start position:0%
+building the list I'm returning that as
+my set and then to create the object
+
+ align:start position:0%
+my set and then to create the object
+ 
+
+ align:start position:0%
+my set and then to create the object
+I'll simply do a set of inserts if I
+
+ align:start position:0%
+I'll simply do a set of inserts if I
+ 
+
+ align:start position:0%
+I'll simply do a set of inserts if I
+want the values 2 six and eight in there
+
+ align:start position:0%
+want the values 2 six and eight in there
+ 
+
+ align:start position:0%
+want the values 2 six and eight in there
+I would do an insert of two into that
+
+ align:start position:0%
+I would do an insert of two into that
+ 
+
+ align:start position:0%
+I would do an insert of two into that
+set an insert of six into that set and
+
+ align:start position:0%
+set an insert of six into that set and
+ 
+
+ align:start position:0%
+set an insert of six into that set and
+an insert of eight into that set and
+
+ align:start position:0%
+an insert of eight into that set and
+ 
+
+ align:start position:0%
+an insert of eight into that set and
+what does it do it marks a one in each
+
+ align:start position:0%
+what does it do it marks a one in each
+ 
+
+ align:start position:0%
+what does it do it marks a one in each
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+spots now what did I want to do I wanted
+
+ align:start position:0%
+spots now what did I want to do I wanted
+ 
+
+ align:start position:0%
+spots now what did I want to do I wanted
+to check membership I want to do search
+
+ align:start position:0%
+to check membership I want to do search
+ 
+
+ align:start position:0%
+to check membership I want to do search
+well that's simple given that
+
+ align:start position:0%
+well that's simple given that
+ 
+
+ align:start position:0%
+well that's simple given that
+representation and some value I just say
+
+ align:start position:0%
+representation and some value I just say
+ 
+
+ align:start position:0%
+representation and some value I just say
+G is it
+
+ align:start position:0%
+G is it
+ 
+
+ align:start position:0%
+G is it
+there what's the order of complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I know I drive you not asking
+
+ align:start position:0%
+here I know I drive you not asking
+ 
+
+ align:start position:0%
+here I know I drive you not asking
+questions what's the order of complexity
+
+ align:start position:0%
+questions what's the order of complexity
+ 
+
+ align:start position:0%
+questions what's the order of complexity
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+quadratic
+
+ align:start position:0%
+quadratic
+ 
+
+ align:start position:0%
+quadratic
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant any taker I know I have the
+
+ align:start position:0%
+constant any taker I know I have the
+ 
+
+ align:start position:0%
+constant any taker I know I have the
+wrong glasses on to see hands up too but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh who said it constant
+
+ align:start position:0%
+uh who said it constant
+ 
+
+ align:start position:0%
+uh who said it constant
+why yeah thank you all right it is
+
+ align:start position:0%
+why yeah thank you all right it is
+ 
+
+ align:start position:0%
+why yeah thank you all right it is
+constant you keep sitting back there
+
+ align:start position:0%
+constant you keep sitting back there
+ 
+
+ align:start position:0%
+constant you keep sitting back there
+where I can't get to you thank you very
+
+ align:start position:0%
+where I can't get to you thank you very
+ 
+
+ align:start position:0%
+where I can't get to you thank you very
+much why is it constant remember we said
+
+ align:start position:0%
+much why is it constant remember we said
+ 
+
+ align:start position:0%
+much why is it constant remember we said
+we designed lists so that the access no
+
+ align:start position:0%
+we designed lists so that the access no
+ 
+
+ align:start position:0%
+we designed lists so that the access no
+matter where it was in the list was of
+
+ align:start position:0%
+matter where it was in the list was of
+ 
+
+ align:start position:0%
+matter where it was in the list was of
+constant time that is another way of
+
+ align:start position:0%
+constant time that is another way of
+ 
+
+ align:start position:0%
+constant time that is another way of
+saying that looking up this thing here
+
+ align:start position:0%
+saying that looking up this thing here
+ 
+
+ align:start position:0%
+saying that looking up this thing here
+is constant so this is constant time
+
+ align:start position:0%
+is constant so this is constant time
+ 
+
+ align:start position:0%
+is constant so this is constant time
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay come on you know representing
+
+ align:start position:0%
+one okay come on you know representing
+ 
+
+ align:start position:0%
+one okay come on you know representing
+sets of integers this is pretty dumb
+
+ align:start position:0%
+sets of integers this is pretty dumb
+ 
+
+ align:start position:0%
+sets of integers this is pretty dumb
+suppose I want to have a set of
+
+ align:start position:0%
+suppose I want to have a set of
+ 
+
+ align:start position:0%
+suppose I want to have a set of
+characters how could I do that well the
+
+ align:start position:0%
+characters how could I do that well the
+ 
+
+ align:start position:0%
+characters how could I do that well the
+idea of a hash what's called a hash
+
+ align:start position:0%
+idea of a hash what's called a hash
+ 
+
+ align:start position:0%
+idea of a hash what's called a hash
+function is to have some way of mapping
+
+ align:start position:0%
+function is to have some way of mapping
+ 
+
+ align:start position:0%
+function is to have some way of mapping
+any kind of data into integers so let's
+
+ align:start position:0%
+any kind of data into integers so let's
+ 
+
+ align:start position:0%
+any kind of data into integers so let's
+look at the second
+
+ align:start position:0%
+look at the second
+ 
+
+ align:start position:0%
+look at the second
+example all right ah I keep doing
+
+ align:start position:0%
+example all right ah I keep doing
+ 
+
+ align:start position:0%
+example all right ah I keep doing
+that this piece of code
+
+ align:start position:0%
+that this piece of code
+ 
+
+ align:start position:0%
+that this piece of code
+from here to here gives me a way of now
+
+ align:start position:0%
+from here to here gives me a way of now
+ 
+
+ align:start position:0%
+from here to here gives me a way of now
+creating a hash table of size
+
+ align:start position:0%
+creating a hash table of size
+ 
+
+ align:start position:0%
+creating a hash table of size
+256 O is a built-in python
+
+ align:start position:0%
+256 O is a built-in python
+ 
+
+ align:start position:0%
+256 O is a built-in python
+representation there's lots of them
+
+ align:start position:0%
+representation there's lots of them
+ 
+
+ align:start position:0%
+representation there's lots of them
+around that takes any character and
+
+ align:start position:0%
+around that takes any character and
+ 
+
+ align:start position:0%
+around that takes any character and
+gives you back an integer in fact just
+
+ align:start position:0%
+gives you back an integer in fact just
+ 
+
+ align:start position:0%
+gives you back an integer in fact just
+to show that to you if I go down here
+
+ align:start position:0%
+to show that to you if I go down here
+ 
+
+ align:start position:0%
+to show that to you if I go down here
+and I type
+
+ align:start position:0%
+and I type
+ 
+
+ align:start position:0%
+and I type
+O ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry I did that wrong let me try again
+
+ align:start position:0%
+sorry I did that wrong let me try again
+ 
+
+ align:start position:0%
+sorry I did that wrong let me try again
+we'll get to exceptions in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second I give it some character it gives
+
+ align:start position:0%
+second I give it some character it gives
+ 
+
+ align:start position:0%
+second I give it some character it gives
+me back an integer representing and it
+
+ align:start position:0%
+me back an integer representing and it
+ 
+
+ align:start position:0%
+me back an integer representing and it
+looks weird why is three come back to
+
+ align:start position:0%
+looks weird why is three come back to
+ 
+
+ align:start position:0%
+looks weird why is three come back to
+some other thing that's the internal
+
+ align:start position:0%
+some other thing that's the internal
+ 
+
+ align:start position:0%
+some other thing that's the internal
+representation that python uses for this
+
+ align:start position:0%
+representation that python uses for this
+ 
+
+ align:start position:0%
+representation that python uses for this
+if I give it some other
+
+ align:start position:0%
+if I give it some other
+ 
+
+ align:start position:0%
+if I give it some other
+character now it would help if I could
+
+ align:start position:0%
+character now it would help if I could
+ 
+
+ align:start position:0%
+character now it would help if I could
+type and give it some other character
+
+ align:start position:0%
+type and give it some other character
+ 
+
+ align:start position:0%
+type and give it some other character
+gives me back a
+
+ align:start position:0%
+gives me back a
+ 
+
+ align:start position:0%
+gives me back a
+representation so now here's the idea I
+
+ align:start position:0%
+representation so now here's the idea I
+ 
+
+ align:start position:0%
+representation so now here's the idea I
+build a list 256 elements long right and
+
+ align:start position:0%
+build a list 256 elements long right and
+ 
+
+ align:start position:0%
+build a list 256 elements long right and
+I fill it up with those special
+
+ align:start position:0%
+I fill it up with those special
+ 
+
+ align:start position:0%
+I fill it up with those special
+characters none that's what create is
+
+ align:start position:0%
+characters none that's what create is
+ 
+
+ align:start position:0%
+characters none that's what create is
+going to do right here and then hash
+
+ align:start position:0%
+going to do right here and then hash
+ 
+
+ align:start position:0%
+going to do right here and then hash
+character takes in any string or
+
+ align:start position:0%
+character takes in any string or
+ 
+
+ align:start position:0%
+character takes in any string or
+character Single Character gives me back
+
+ align:start position:0%
+character Single Character gives me back
+ 
+
+ align:start position:0%
+character Single Character gives me back
+a number and notice what I do if I want
+
+ align:start position:0%
+a number and notice what I do if I want
+ 
+
+ align:start position:0%
+a number and notice what I do if I want
+to create a set or a sequence
+
+ align:start position:0%
+to create a set or a sequence
+ 
+
+ align:start position:0%
+to create a set or a sequence
+representing these things I simply
+
+ align:start position:0%
+representing these things I simply
+ 
+
+ align:start position:0%
+representing these things I simply
+insert into that list that goes through
+
+ align:start position:0%
+insert into that list that goes through
+ 
+
+ align:start position:0%
+insert into that list that goes through
+and puts ones in the right place and
+
+ align:start position:0%
+and puts ones in the right place and
+ 
+
+ align:start position:0%
+and puts ones in the right place and
+then if I want to find out if a
+
+ align:start position:0%
+then if I want to find out if a
+ 
+
+ align:start position:0%
+then if I want to find out if a
+something's there I do the same thing
+
+ align:start position:0%
+something's there I do the same thing
+ 
+
+ align:start position:0%
+something's there I do the same thing
+but notice now hash is converting the
+
+ align:start position:0%
+but notice now hash is converting the
+ 
+
+ align:start position:0%
+but notice now hash is converting the
+input into an
+
+ align:start position:0%
+input into an
+ 
+
+ align:start position:0%
+input into an
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+okay so what's the idea if I know what
+
+ align:start position:0%
+okay so what's the idea if I know what
+ 
+
+ align:start position:0%
+okay so what's the idea if I know what
+my hash function does it maps in this
+
+ align:start position:0%
+my hash function does it maps in this
+ 
+
+ align:start position:0%
+my hash function does it maps in this
+case characters into a range 0 to 256 0
+
+ align:start position:0%
+case characters into a range 0 to 256 0
+ 
+
+ align:start position:0%
+case characters into a range 0 to 256 0
+to 255 I create a list that long and I
+
+ align:start position:0%
+to 255 I create a list that long and I
+ 
+
+ align:start position:0%
+to 255 I create a list that long and I
+simply Mark things and my lookup is
+
+ align:start position:0%
+simply Mark things and my lookup is
+ 
+
+ align:start position:0%
+simply Mark things and my lookup is
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+constant all right characters are simple
+
+ align:start position:0%
+constant all right characters are simple
+ 
+
+ align:start position:0%
+constant all right characters are simple
+suppose you want to represent sets of
+
+ align:start position:0%
+suppose you want to represent sets of
+ 
+
+ align:start position:0%
+suppose you want to represent sets of
+strings
+
+ align:start position:0%
+strings
+ 
+
+ align:start position:0%
+strings
+well you basically just generalize the
+
+ align:start position:0%
+well you basically just generalize the
+ 
+
+ align:start position:0%
+well you basically just generalize the
+hash function I think one of the classic
+
+ align:start position:0%
+hash function I think one of the classic
+ 
+
+ align:start position:0%
+hash function I think one of the classic
+ones for Strings is called The Raven
+
+ align:start position:0%
+ones for Strings is called The Raven
+ 
+
+ align:start position:0%
+ones for Strings is called The Raven
+carp algorithm and it's simply the same
+
+ align:start position:0%
+carp algorithm and it's simply the same
+ 
+
+ align:start position:0%
+carp algorithm and it's simply the same
+idea that you have a mapping from your
+
+ align:start position:0%
+idea that you have a mapping from your
+ 
+
+ align:start position:0%
+idea that you have a mapping from your
+input into a set of
+
+ align:start position:0%
+input into a set of
+ 
+
+ align:start position:0%
+input into a set of
+integers wow okay maybe not so well but
+
+ align:start position:0%
+integers wow okay maybe not so well but
+ 
+
+ align:start position:0%
+integers wow okay maybe not so well but
+this is now constant right this is
+
+ align:start position:0%
+this is now constant right this is
+ 
+
+ align:start position:0%
+this is now constant right this is
+constant time access so I can do
+
+ align:start position:0%
+constant time access so I can do
+ 
+
+ align:start position:0%
+constant time access so I can do
+searching in constant time which is
+
+ align:start position:0%
+searching in constant time which is
+ 
+
+ align:start position:0%
+searching in constant time which is
+great where's the
+
+ align:start position:0%
+great where's the
+ 
+
+ align:start position:0%
+great where's the
+penalty what did I trade off here
+
+ align:start position:0%
+penalty what did I trade off here
+ 
+
+ align:start position:0%
+penalty what did I trade off here
+well I'm going to suggest that what I
+
+ align:start position:0%
+well I'm going to suggest that what I
+ 
+
+ align:start position:0%
+well I'm going to suggest that what I
+did was I really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time makes me sound like an
+
+ align:start position:0%
+time makes me sound like an
+ 
+
+ align:start position:0%
+time makes me sound like an
+astrophysicist somehow right what do I
+
+ align:start position:0%
+astrophysicist somehow right what do I
+ 
+
+ align:start position:0%
+astrophysicist somehow right what do I
+mean by that I have constant time access
+
+ align:start position:0%
+mean by that I have constant time access
+ 
+
+ align:start position:0%
+mean by that I have constant time access
+which is great but I paid a price which
+
+ align:start position:0%
+which is great but I paid a price which
+ 
+
+ align:start position:0%
+which is great but I paid a price which
+is I had to use up some space in the
+
+ align:start position:0%
+is I had to use up some space in the
+ 
+
+ align:start position:0%
+is I had to use up some space in the
+case of integers it was easy in the case
+
+ align:start position:0%
+case of integers it was easy in the case
+ 
+
+ align:start position:0%
+case of integers it was easy in the case
+of characters so I have to give up a
+
+ align:start position:0%
+of characters so I have to give up a
+ 
+
+ align:start position:0%
+of characters so I have to give up a
+list of 256 no no big deal imagine now
+
+ align:start position:0%
+list of 256 no no big deal imagine now
+ 
+
+ align:start position:0%
+list of 256 no no big deal imagine now
+you want to do faces right you got a
+
+ align:start position:0%
+you want to do faces right you got a
+ 
+
+ align:start position:0%
+you want to do faces right you got a
+picture of somebody's face it's a
+
+ align:start position:0%
+picture of somebody's face it's a
+ 
+
+ align:start position:0%
+picture of somebody's face it's a
+million pixels each pixel has a range of
+
+ align:start position:0%
+million pixels each pixel has a range of
+ 
+
+ align:start position:0%
+million pixels each pixel has a range of
+values from zero to 256 I want to Hash a
+
+ align:start position:0%
+values from zero to 256 I want to Hash a
+ 
+
+ align:start position:0%
+values from zero to 256 I want to Hash a
+face with some function into an integer
+
+ align:start position:0%
+face with some function into an integer
+ 
+
+ align:start position:0%
+face with some function into an integer
+okay I may not want to do the full range
+
+ align:start position:0%
+okay I may not want to do the full range
+ 
+
+ align:start position:0%
+okay I may not want to do the full range
+of this but I may decide I have to use a
+
+ align:start position:0%
+of this but I may decide I have to use a
+ 
+
+ align:start position:0%
+of this but I may decide I have to use a
+lot of gigabytes of space in order to do
+
+ align:start position:0%
+lot of gigabytes of space in order to do
+ 
+
+ align:start position:0%
+lot of gigabytes of space in order to do
+the trade-off the reason I'm showing you
+
+ align:start position:0%
+the trade-off the reason I'm showing you
+ 
+
+ align:start position:0%
+the trade-off the reason I'm showing you
+this is that this is again a common
+
+ align:start position:0%
+this is that this is again a common
+ 
+
+ align:start position:0%
+this is that this is again a common
+trade-off in computer science that in
+
+ align:start position:0%
+trade-off in computer science that in
+ 
+
+ align:start position:0%
+trade-off in computer science that in
+many cases I can gain efficiency if I'm
+
+ align:start position:0%
+many cases I can gain efficiency if I'm
+ 
+
+ align:start position:0%
+many cases I can gain efficiency if I'm
+willing to give up space
+
+ align:start position:0%
+willing to give up space
+ 
+
+ align:start position:0%
+willing to give up space
+having said that though there may still
+
+ align:start position:0%
+having said that though there may still
+ 
+
+ align:start position:0%
+having said that though there may still
+be a problem or there ought to be a
+
+ align:start position:0%
+be a problem or there ought to be a
+ 
+
+ align:start position:0%
+be a problem or there ought to be a
+problem that may be bugging you slightly
+
+ align:start position:0%
+problem that may be bugging you slightly
+ 
+
+ align:start position:0%
+problem that may be bugging you slightly
+which is how do I
+
+ align:start position:0%
+which is how do I
+ 
+
+ align:start position:0%
+which is how do I
+guarantee that my hash function takes
+
+ align:start position:0%
+guarantee that my hash function takes
+ 
+
+ align:start position:0%
+guarantee that my hash function takes
+any input into exactly one spot in the
+
+ align:start position:0%
+any input into exactly one spot in the
+ 
+
+ align:start position:0%
+any input into exactly one spot in the
+storage
+
+ align:start position:0%
+storage
+ 
+
+ align:start position:0%
+storage
+space the answer is I can't okay in the
+
+ align:start position:0%
+space the answer is I can't okay in the
+ 
+
+ align:start position:0%
+space the answer is I can't okay in the
+simple case of integers I can't but in
+
+ align:start position:0%
+simple case of integers I can't but in
+ 
+
+ align:start position:0%
+simple case of integers I can't but in
+the case of something more complex like
+
+ align:start position:0%
+the case of something more complex like
+ 
+
+ align:start position:0%
+the case of something more complex like
+faces or fingerprints or passwords for
+
+ align:start position:0%
+faces or fingerprints or passwords for
+ 
+
+ align:start position:0%
+faces or fingerprints or passwords for
+that matter it's hard to design a hash
+
+ align:start position:0%
+that matter it's hard to design a hash
+ 
+
+ align:start position:0%
+that matter it's hard to design a hash
+function that has completely even
+
+ align:start position:0%
+function that has completely even
+ 
+
+ align:start position:0%
+function that has completely even
+distribution meaning that it takes any
+
+ align:start position:0%
+distribution meaning that it takes any
+ 
+
+ align:start position:0%
+distribution meaning that it takes any
+input into exactly one output spot so
+
+ align:start position:0%
+input into exactly one output spot so
+ 
+
+ align:start position:0%
+input into exactly one output spot so
+what you typically do in a hash case is
+
+ align:start position:0%
+what you typically do in a hash case is
+ 
+
+ align:start position:0%
+what you typically do in a hash case is
+you design your code to deal with that
+
+ align:start position:0%
+you design your code to deal with that
+ 
+
+ align:start position:0%
+you design your code to deal with that
+you try and design actually I'm going to
+
+ align:start position:0%
+you try and design actually I'm going to
+ 
+
+ align:start position:0%
+you try and design actually I'm going to
+come back to that in a second you try
+
+ align:start position:0%
+come back to that in a second you try
+ 
+
+ align:start position:0%
+come back to that in a second you try
+and use a hash function that spreads
+
+ align:start position:0%
+and use a hash function that spreads
+ 
+
+ align:start position:0%
+and use a hash function that spreads
+things out pretty evenly but the places
+
+ align:start position:0%
+things out pretty evenly but the places
+ 
+
+ align:start position:0%
+things out pretty evenly but the places
+you store into and those lists may have
+
+ align:start position:0%
+you store into and those lists may have
+ 
+
+ align:start position:0%
+you store into and those lists may have
+to themselves have a small list in there
+
+ align:start position:0%
+to themselves have a small list in there
+ 
+
+ align:start position:0%
+to themselves have a small list in there
+and when you go to check something you
+
+ align:start position:0%
+and when you go to check something you
+ 
+
+ align:start position:0%
+and when you go to check something you
+may have to do a linear search through
+
+ align:start position:0%
+may have to do a linear search through
+ 
+
+ align:start position:0%
+may have to do a linear search through
+the elements in that list the good news
+
+ align:start position:0%
+the elements in that list the good news
+ 
+
+ align:start position:0%
+the elements in that list the good news
+is the elements in any one spot in the
+
+ align:start position:0%
+is the elements in any one spot in the
+ 
+
+ align:start position:0%
+is the elements in any one spot in the
+hash table are likely to be a small
+
+ align:start position:0%
+hash table are likely to be a small
+ 
+
+ align:start position:0%
+hash table are likely to be a small
+number 3 four five so the search is
+
+ align:start position:0%
+number 3 four five so the search is
+ 
+
+ align:start position:0%
+number 3 four five so the search is
+really easy you're not Sear searching a
+
+ align:start position:0%
+really easy you're not Sear searching a
+ 
+
+ align:start position:0%
+really easy you're not Sear searching a
+million things you're searching three or
+
+ align:start position:0%
+million things you're searching three or
+ 
+
+ align:start position:0%
+million things you're searching three or
+four things but nonetheless you have to
+
+ align:start position:0%
+four things but nonetheless you have to
+ 
+
+ align:start position:0%
+four things but nonetheless you have to
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+tradeoff the last thing I want to say
+
+ align:start position:0%
+tradeoff the last thing I want to say
+ 
+
+ align:start position:0%
+tradeoff the last thing I want to say
+about hashes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are that they're actually really hard to
+
+ align:start position:0%
+are that they're actually really hard to
+ 
+
+ align:start position:0%
+are that they're actually really hard to
+create there's been a lot of work done
+
+ align:start position:0%
+create there's been a lot of work done
+ 
+
+ align:start position:0%
+create there's been a lot of work done
+in these over the years but in fact it's
+
+ align:start position:0%
+in these over the years but in fact it's
+ 
+
+ align:start position:0%
+in these over the years but in fact it's
+pretty hard to invent a good hash
+
+ align:start position:0%
+pretty hard to invent a good hash
+ 
+
+ align:start position:0%
+pretty hard to invent a good hash
+function so my advice to you is if you
+
+ align:start position:0%
+function so my advice to you is if you
+ 
+
+ align:start position:0%
+function so my advice to you is if you
+want to use something with a hash go to
+
+ align:start position:0%
+want to use something with a hash go to
+ 
+
+ align:start position:0%
+want to use something with a hash go to
+a library look up a good hash function
+
+ align:start position:0%
+a library look up a good hash function
+ 
+
+ align:start position:0%
+a library look up a good hash function
+okay for Strings there's a classic set
+
+ align:start position:0%
+okay for Strings there's a classic set
+ 
+
+ align:start position:0%
+okay for Strings there's a classic set
+of them that work pretty well for
+
+ align:start position:0%
+of them that work pretty well for
+ 
+
+ align:start position:0%
+of them that work pretty well for
+integers there's some real simple ones
+
+ align:start position:0%
+integers there's some real simple ones
+ 
+
+ align:start position:0%
+integers there's some real simple ones
+if there's something more complex find a
+
+ align:start position:0%
+if there's something more complex find a
+ 
+
+ align:start position:0%
+if there's something more complex find a
+good hash function but designing a
+
+ align:start position:0%
+good hash function but designing a
+ 
+
+ align:start position:0%
+good hash function but designing a
+really good hash function takes a lot of
+
+ align:start position:0%
+really good hash function takes a lot of
+ 
+
+ align:start position:0%
+really good hash function takes a lot of
+effort because you want it to have that
+
+ align:start position:0%
+effort because you want it to have that
+ 
+
+ align:start position:0%
+effort because you want it to have that
+even distribution you'd like it to have
+
+ align:start position:0%
+even distribution you'd like it to have
+ 
+
+ align:start position:0%
+even distribution you'd like it to have
+as few duplicates if you like in each
+
+ align:start position:0%
+as few duplicates if you like in each
+ 
+
+ align:start position:0%
+as few duplicates if you like in each
+spot in the hash table for each one of
+
+ align:start position:0%
+spot in the hash table for each one of
+ 
+
+ align:start position:0%
+spot in the hash table for each one of
+the things that you
+
+ align:start position:0%
+the things that you
+ 
+
+ align:start position:0%
+the things that you
+use okay let me pull back for a second
+
+ align:start position:0%
+use okay let me pull back for a second
+ 
+
+ align:start position:0%
+use okay let me pull back for a second
+then what have we done over the last
+
+ align:start position:0%
+then what have we done over the last
+ 
+
+ align:start position:0%
+then what have we done over the last
+three or four lectures
+
+ align:start position:0%
+three or four lectures
+ 
+
+ align:start position:0%
+three or four lectures
+we've started introducing you to classes
+
+ align:start position:0%
+we've started introducing you to classes
+ 
+
+ align:start position:0%
+we've started introducing you to classes
+of algorithms things that I'd like you
+
+ align:start position:0%
+of algorithms things that I'd like you
+ 
+
+ align:start position:0%
+of algorithms things that I'd like you
+to be able to see are how to do some
+
+ align:start position:0%
+to be able to see are how to do some
+ 
+
+ align:start position:0%
+to be able to see are how to do some
+simple complexity analysis perhaps more
+
+ align:start position:0%
+simple complexity analysis perhaps more
+ 
+
+ align:start position:0%
+simple complexity analysis perhaps more
+importantly how to recognize a kind of
+
+ align:start position:0%
+importantly how to recognize a kind of
+ 
+
+ align:start position:0%
+importantly how to recognize a kind of
+algorithm based on its properties and
+
+ align:start position:0%
+algorithm based on its properties and
+ 
+
+ align:start position:0%
+algorithm based on its properties and
+know what class it belongs to this is a
+
+ align:start position:0%
+know what class it belongs to this is a
+ 
+
+ align:start position:0%
+know what class it belongs to this is a
+hint if you like leading towards the
+
+ align:start position:0%
+hint if you like leading towards the
+ 
+
+ align:start position:0%
+hint if you like leading towards the
+next Quiz that you ought to be able to
+
+ align:start position:0%
+next Quiz that you ought to be able to
+ 
+
+ align:start position:0%
+next Quiz that you ought to be able to
+say that looks like a logarithmic
+
+ align:start position:0%
+say that looks like a logarithmic
+ 
+
+ align:start position:0%
+say that looks like a logarithmic
+algorithm because it's got a particular
+
+ align:start position:0%
+algorithm because it's got a particular
+ 
+
+ align:start position:0%
+algorithm because it's got a particular
+property that looks like an N log n
+
+ align:start position:0%
+property that looks like an N log n
+ 
+
+ align:start position:0%
+property that looks like an N log n
+algorithm because it has a particular
+
+ align:start position:0%
+algorithm because it has a particular
+ 
+
+ align:start position:0%
+algorithm because it has a particular
+property and the third thing we've done
+
+ align:start position:0%
+property and the third thing we've done
+ 
+
+ align:start position:0%
+property and the third thing we've done
+is we've given you now a set set of sort
+
+ align:start position:0%
+is we've given you now a set set of sort
+ 
+
+ align:start position:0%
+is we've given you now a set set of sort
+of standard algorithms if you like Brute
+
+ align:start position:0%
+of standard algorithms if you like Brute
+ 
+
+ align:start position:0%
+of standard algorithms if you like Brute
+Force just walk through every possible
+
+ align:start position:0%
+Force just walk through every possible
+ 
+
+ align:start position:0%
+Force just walk through every possible
+case right works well if problem sizes
+
+ align:start position:0%
+case right works well if problem sizes
+ 
+
+ align:start position:0%
+case right works well if problem sizes
+are small we've had a number of variants
+
+ align:start position:0%
+are small we've had a number of variants
+ 
+
+ align:start position:0%
+are small we've had a number of variants
+of guess and check or hypothesize and
+
+ align:start position:0%
+of guess and check or hypothesize and
+ 
+
+ align:start position:0%
+of guess and check or hypothesize and
+test where you try and guess the
+
+ align:start position:0%
+test where you try and guess the
+ 
+
+ align:start position:0%
+test where you try and guess the
+solution and then check it and use that
+
+ align:start position:0%
+solution and then check it and use that
+ 
+
+ align:start position:0%
+solution and then check it and use that
+to refine your search success of
+
+ align:start position:0%
+to refine your search success of
+ 
+
+ align:start position:0%
+to refine your search success of
+approximation Newton rafson was one nice
+
+ align:start position:0%
+approximation Newton rafson was one nice
+ 
+
+ align:start position:0%
+approximation Newton rafson was one nice
+example but there's a whole class of
+
+ align:start position:0%
+example but there's a whole class of
+ 
+
+ align:start position:0%
+example but there's a whole class of
+things that get closer and closer
+
+ align:start position:0%
+things that get closer and closer
+ 
+
+ align:start position:0%
+things that get closer and closer
+reducing your error as you go along uh
+
+ align:start position:0%
+reducing your error as you go along uh
+ 
+
+ align:start position:0%
+reducing your error as you go along uh
+divide and conquer
+
+ align:start position:0%
+divide and conquer
+ 
+
+ align:start position:0%
+divide and conquer
+right and actually I guess in between
+
+ align:start position:0%
+right and actually I guess in between
+ 
+
+ align:start position:0%
+right and actually I guess in between
+their bsection which is really just a
+
+ align:start position:0%
+their bsection which is really just a
+ 
+
+ align:start position:0%
+their bsection which is really just a
+variant of of of successive
+
+ align:start position:0%
+variant of of of successive
+ 
+
+ align:start position:0%
+variant of of of successive
+approximation but divide and conquer as
+
+ align:start position:0%
+approximation but divide and conquer as
+ 
+
+ align:start position:0%
+approximation but divide and conquer as
+a class of algorithm these are tools you
+
+ align:start position:0%
+a class of algorithm these are tools you
+ 
+
+ align:start position:0%
+a class of algorithm these are tools you
+want in your toolbox these are the kinds
+
+ align:start position:0%
+want in your toolbox these are the kinds
+ 
+
+ align:start position:0%
+want in your toolbox these are the kinds
+of algorithms that you should be able to
+
+ align:start position:0%
+of algorithms that you should be able to
+ 
+
+ align:start position:0%
+of algorithms that you should be able to
+recognize and what I'd like you to begin
+
+ align:start position:0%
+recognize and what I'd like you to begin
+ 
+
+ align:start position:0%
+recognize and what I'd like you to begin
+to do is to look at a problem and say
+
+ align:start position:0%
+to do is to look at a problem and say
+ 
+
+ align:start position:0%
+to do is to look at a problem and say
+gee which kind of algorithm is most
+
+ align:start position:0%
+gee which kind of algorithm is most
+ 
+
+ align:start position:0%
+gee which kind of algorithm is most
+likely to be successful on this problem
+
+ align:start position:0%
+likely to be successful on this problem
+ 
+
+ align:start position:0%
+likely to be successful on this problem
+and map it into that
+
+ align:start position:0%
+and map it into that
+ 
+
+ align:start position:0%
+and map it into that
+case Okay starting next don't worry I'm
+
+ align:start position:0%
+case Okay starting next don't worry I'm
+ 
+
+ align:start position:0%
+case Okay starting next don't worry I'm
+not going to quit 36 minutes after I got
+
+ align:start position:0%
+not going to quit 36 minutes after I got
+ 
+
+ align:start position:0%
+not going to quit 36 minutes after I got
+one more topic for today but jumping
+
+ align:start position:0%
+one more topic for today but jumping
+ 
+
+ align:start position:0%
+one more topic for today but jumping
+ahead I'm going to skip in a second now
+
+ align:start position:0%
+ahead I'm going to skip in a second now
+ 
+
+ align:start position:0%
+ahead I'm going to skip in a second now
+to talk about one last linguistic thing
+
+ align:start position:0%
+to talk about one last linguistic thing
+ 
+
+ align:start position:0%
+to talk about one last linguistic thing
+from from python but I want to preface
+
+ align:start position:0%
+from from python but I want to preface
+ 
+
+ align:start position:0%
+from from python but I want to preface
+Professor good tag is going to pick up
+
+ align:start position:0%
+Professor good tag is going to pick up
+ 
+
+ align:start position:0%
+Professor good tag is going to pick up
+next week and what we're going to start
+
+ align:start position:0%
+next week and what we're going to start
+ 
+
+ align:start position:0%
+next week and what we're going to start
+doing then is taking these classes of
+
+ align:start position:0%
+doing then is taking these classes of
+ 
+
+ align:start position:0%
+doing then is taking these classes of
+algorithms and start start looking at
+
+ align:start position:0%
+algorithms and start start looking at
+ 
+
+ align:start position:0%
+algorithms and start start looking at
+much more complex algorithms things
+
+ align:start position:0%
+much more complex algorithms things
+ 
+
+ align:start position:0%
+much more complex algorithms things
+you're more likely to use in problems
+
+ align:start position:0%
+you're more likely to use in problems
+ 
+
+ align:start position:0%
+you're more likely to use in problems
+things like napsack Pro napsack problems
+
+ align:start position:0%
+things like napsack Pro napsack problems
+ 
+
+ align:start position:0%
+things like napsack Pro napsack problems
+as we move ahead but the tools you've
+
+ align:start position:0%
+as we move ahead but the tools you've
+ 
+
+ align:start position:0%
+as we move ahead but the tools you've
+seen so far are really the things that
+
+ align:start position:0%
+seen so far are really the things that
+ 
+
+ align:start position:0%
+seen so far are really the things that
+we're going to see as we build those
+
+ align:start position:0%
+we're going to see as we build those
+ 
+
+ align:start position:0%
+we're going to see as we build those
+algorithms okay I want to spend the last
+
+ align:start position:0%
+algorithms okay I want to spend the last
+ 
+
+ align:start position:0%
+algorithms okay I want to spend the last
+portion of this lecture doing one last
+
+ align:start position:0%
+portion of this lecture doing one last
+ 
+
+ align:start position:0%
+portion of this lecture doing one last
+piece of linguistic stuff one last
+
+ align:start position:0%
+piece of linguistic stuff one last
+ 
+
+ align:start position:0%
+piece of linguistic stuff one last
+little uh thing from Python and that's
+
+ align:start position:0%
+little uh thing from Python and that's
+ 
+
+ align:start position:0%
+little uh thing from Python and that's
+to talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exceptions
+
+ align:start position:0%
+exceptions
+ 
+
+ align:start position:0%
+exceptions
+okay you've actually seen exceptions a
+
+ align:start position:0%
+okay you've actually seen exceptions a
+ 
+
+ align:start position:0%
+okay you've actually seen exceptions a
+lot you just didn't know that's what
+
+ align:start position:0%
+lot you just didn't know that's what
+ 
+
+ align:start position:0%
+lot you just didn't know that's what
+they were because exceptions show up
+
+ align:start position:0%
+they were because exceptions show up
+ 
+
+ align:start position:0%
+they were because exceptions show up
+everywhere in Python and let me give you
+
+ align:start position:0%
+everywhere in Python and let me give you
+ 
+
+ align:start position:0%
+everywhere in Python and let me give you
+a couple of
+
+ align:start position:0%
+a couple of
+ 
+
+ align:start position:0%
+a couple of
+examples clear some space here
+
+ align:start position:0%
+examples clear some space here
+ 
+
+ align:start position:0%
+examples clear some space here
+if I type in that
+
+ align:start position:0%
+if I type in that
+ 
+
+ align:start position:0%
+if I type in that
+expression I get an error right because
+
+ align:start position:0%
+expression I get an error right because
+ 
+
+ align:start position:0%
+expression I get an error right because
+it's not defined but in fact what this
+
+ align:start position:0%
+it's not defined but in fact what this
+ 
+
+ align:start position:0%
+it's not defined but in fact what this
+did was it threw an exception and the
+
+ align:start position:0%
+did was it threw an exception and the
+ 
+
+ align:start position:0%
+did was it threw an exception and the
+exceptions an a called a name error
+
+ align:start position:0%
+exceptions an a called a name error
+ 
+
+ align:start position:0%
+exceptions an a called a name error
+exception it says you gave me something
+
+ align:start position:0%
+exception it says you gave me something
+ 
+
+ align:start position:0%
+exception it says you gave me something
+I didn't know how to deal with I'm going
+
+ align:start position:0%
+I didn't know how to deal with I'm going
+ 
+
+ align:start position:0%
+I didn't know how to deal with I'm going
+to throw it or raise it to use the right
+
+ align:start position:0%
+to throw it or raise it to use the right
+ 
+
+ align:start position:0%
+to throw it or raise it to use the right
+term to somebody in case they can handle
+
+ align:start position:0%
+term to somebody in case they can handle
+ 
+
+ align:start position:0%
+term to somebody in case they can handle
+it but it's a particular kind of of of
+
+ align:start position:0%
+it but it's a particular kind of of of
+ 
+
+ align:start position:0%
+it but it's a particular kind of of of
+exception I might do something like I
+
+ align:start position:0%
+exception I might do something like I
+ 
+
+ align:start position:0%
+exception I might do something like I
+remind you I had test if I do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try and get the 10th element of a list
+
+ align:start position:0%
+try and get the 10th element of a list
+ 
+
+ align:start position:0%
+try and get the 10th element of a list
+that's only eight long I get what looks
+
+ align:start position:0%
+that's only eight long I get what looks
+ 
+
+ align:start position:0%
+that's only eight long I get what looks
+like an error but it's actually throwing
+
+ align:start position:0%
+like an error but it's actually throwing
+ 
+
+ align:start position:0%
+like an error but it's actually throwing
+an exception and the exception is right
+
+ align:start position:0%
+an exception and the exception is right
+ 
+
+ align:start position:0%
+an exception and the exception is right
+there it says it's an index error that
+
+ align:start position:0%
+there it says it's an index error that
+ 
+
+ align:start position:0%
+there it says it's an index error that
+is it's trying to do something going
+
+ align:start position:0%
+is it's trying to do something going
+ 
+
+ align:start position:0%
+is it's trying to do something going
+beyond the range of what this thing
+
+ align:start position:0%
+beyond the range of what this thing
+ 
+
+ align:start position:0%
+beyond the range of what this thing
+could deal
+
+ align:start position:0%
+could deal
+ 
+
+ align:start position:0%
+could deal
+with okay you say come on I've seen
+
+ align:start position:0%
+with okay you say come on I've seen
+ 
+
+ align:start position:0%
+with okay you say come on I've seen
+these all the time every time I type
+
+ align:start position:0%
+these all the time every time I type
+ 
+
+ align:start position:0%
+these all the time every time I type
+something into my program it does one of
+
+ align:start position:0%
+something into my program it does one of
+ 
+
+ align:start position:0%
+something into my program it does one of
+these things right when we're just
+
+ align:start position:0%
+these things right when we're just
+ 
+
+ align:start position:0%
+these things right when we're just
+interacting with Idol with the
+
+ align:start position:0%
+interacting with Idol with the
+ 
+
+ align:start position:0%
+interacting with Idol with the
+interactive editor or sorry the
+
+ align:start position:0%
+interactive editor or sorry the
+ 
+
+ align:start position:0%
+interactive editor or sorry the
+interactive environment if you like
+
+ align:start position:0%
+interactive environment if you like
+ 
+
+ align:start position:0%
+interactive environment if you like
+that's what you expect what's happening
+
+ align:start position:0%
+that's what you expect what's happening
+ 
+
+ align:start position:0%
+that's what you expect what's happening
+is that we're typing in something an
+
+ align:start position:0%
+is that we're typing in something an
+ 
+
+ align:start position:0%
+is that we're typing in something an
+expression it doesn't know how to deal
+
+ align:start position:0%
+expression it doesn't know how to deal
+ 
+
+ align:start position:0%
+expression it doesn't know how to deal
+with it's raising the exception but it's
+
+ align:start position:0%
+with it's raising the exception but it's
+ 
+
+ align:start position:0%
+with it's raising the exception but it's
+this simply bubbling up to the top level
+
+ align:start position:0%
+this simply bubbling up to the top level
+ 
+
+ align:start position:0%
+this simply bubbling up to the top level
+saying you've got a
+
+ align:start position:0%
+saying you've got a
+ 
+
+ align:start position:0%
+saying you've got a
+problemos it's been a long day suppose
+
+ align:start position:0%
+problemos it's been a long day suppose
+ 
+
+ align:start position:0%
+problemos it's been a long day suppose
+instead you're in the middle of some
+
+ align:start position:0%
+instead you're in the middle of some
+ 
+
+ align:start position:0%
+instead you're in the middle of some
+deep piece of coat and you get one of
+
+ align:start position:0%
+deep piece of coat and you get one of
+ 
+
+ align:start position:0%
+deep piece of coat and you get one of
+these cases it's kind of annoying if it
+
+ align:start position:0%
+these cases it's kind of annoying if it
+ 
+
+ align:start position:0%
+these cases it's kind of annoying if it
+throws it all the way back up to top
+
+ align:start position:0%
+throws it all the way back up to top
+ 
+
+ align:start position:0%
+throws it all the way back up to top
+level for you to fix if it's truly a bug
+
+ align:start position:0%
+level for you to fix if it's truly a bug
+ 
+
+ align:start position:0%
+level for you to fix if it's truly a bug
+that's the right thing to do you want to
+
+ align:start position:0%
+that's the right thing to do you want to
+ 
+
+ align:start position:0%
+that's the right thing to do you want to
+catch it but in many cases exceptions
+
+ align:start position:0%
+catch it but in many cases exceptions
+ 
+
+ align:start position:0%
+catch it but in many cases exceptions
+are things that in fact you as a program
+
+ align:start position:0%
+are things that in fact you as a program
+ 
+
+ align:start position:0%
+are things that in fact you as a program
+designer could have handled so I'm going
+
+ align:start position:0%
+designer could have handled so I'm going
+ 
+
+ align:start position:0%
+designer could have handled so I'm going
+to distinguish in fact between unhandled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exceptions which are the things that we
+
+ align:start position:0%
+exceptions which are the things that we
+ 
+
+ align:start position:0%
+exceptions which are the things that we
+saw
+
+ align:start position:0%
+saw
+ 
+
+ align:start position:0%
+saw
+there and handled exceptions I'm going
+
+ align:start position:0%
+there and handled exceptions I'm going
+ 
+
+ align:start position:0%
+there and handled exceptions I'm going
+to show you in a second how to handle
+
+ align:start position:0%
+to show you in a second how to handle
+ 
+
+ align:start position:0%
+to show you in a second how to handle
+them but let's look at an example what
+
+ align:start position:0%
+them but let's look at an example what
+ 
+
+ align:start position:0%
+them but let's look at an example what
+do I mean by a handled
+
+ align:start position:0%
+do I mean by a handled
+ 
+
+ align:start position:0%
+do I mean by a handled
+exception well let's look at the next
+
+ align:start position:0%
+exception well let's look at the next
+ 
+
+ align:start position:0%
+exception well let's look at the next
+piece of
+
+ align:start position:0%
+piece of
+ 
+
+ align:start position:0%
+piece of
+code okay it's right here it's called
+
+ align:start position:0%
+code okay it's right here it's called
+ 
+
+ align:start position:0%
+code okay it's right here it's called
+read float look at it in a second
+
+ align:start position:0%
+read float look at it in a second
+ 
+
+ align:start position:0%
+read float look at it in a second
+well let me set set the stage up for
+
+ align:start position:0%
+well let me set set the stage up for
+ 
+
+ align:start position:0%
+well let me set set the stage up for
+this suppose I want to input or sorry I
+
+ align:start position:0%
+this suppose I want to input or sorry I
+ 
+
+ align:start position:0%
+this suppose I want to input or sorry I
+want you as a user to input a floating
+
+ align:start position:0%
+want you as a user to input a floating
+ 
+
+ align:start position:0%
+want you as a user to input a floating
+Point number right we talked about
+
+ align:start position:0%
+Point number right we talked about
+ 
+
+ align:start position:0%
+Point number right we talked about
+things you could do to try and make sure
+
+ align:start position:0%
+things you could do to try and make sure
+ 
+
+ align:start position:0%
+things you could do to try and make sure
+that happens you could run through a
+
+ align:start position:0%
+that happens you could run through a
+ 
+
+ align:start position:0%
+that happens you could run through a
+little Loop to say keep trying until you
+
+ align:start position:0%
+little Loop to say keep trying until you
+ 
+
+ align:start position:0%
+little Loop to say keep trying until you
+get one but one of the ways I could deal
+
+ align:start position:0%
+get one but one of the ways I could deal
+ 
+
+ align:start position:0%
+get one but one of the ways I could deal
+with it is what's shown here what's this
+
+ align:start position:0%
+with it is what's shown here what's this
+ 
+
+ align:start position:0%
+with it is what's shown here what's this
+little Loop say to do this little Loop
+
+ align:start position:0%
+little Loop say to do this little Loop
+ 
+
+ align:start position:0%
+little Loop say to do this little Loop
+says oops wrong one this little Loop
+
+ align:start position:0%
+says oops wrong one this little Loop
+ 
+
+ align:start position:0%
+says oops wrong one this little Loop
+says I'm going to write a function or
+
+ align:start position:0%
+says I'm going to write a function or
+ 
+
+ align:start position:0%
+says I'm going to write a function or
+procedure that takes in two messages I'm
+
+ align:start position:0%
+procedure that takes in two messages I'm
+ 
+
+ align:start position:0%
+procedure that takes in two messages I'm
+going to run through a loop and I'm
+
+ align:start position:0%
+going to run through a loop and I'm
+ 
+
+ align:start position:0%
+going to run through a loop and I'm
+going to request some input which I'm
+
+ align:start position:0%
+going to request some input which I'm
+ 
+
+ align:start position:0%
+going to request some input which I'm
+going to read in with with raw input I'm
+
+ align:start position:0%
+going to read in with with raw input I'm
+ 
+
+ align:start position:0%
+going to read in with with raw input I'm
+going to store that into Val and this as
+
+ align:start position:0%
+going to store that into Val and this as
+ 
+
+ align:start position:0%
+going to store that into Val and this as
+you might expect I'm going to then try
+
+ align:start position:0%
+you might expect I'm going to then try
+ 
+
+ align:start position:0%
+you might expect I'm going to then try
+and see if I can convert that into a
+
+ align:start position:0%
+and see if I can convert that into a
+ 
+
+ align:start position:0%
+and see if I can convert that into a
+float oh wait a minute that's a little
+
+ align:start position:0%
+float oh wait a minute that's a little
+ 
+
+ align:start position:0%
+float oh wait a minute that's a little
+different than what we did last time
+
+ align:start position:0%
+different than what we did last time
+ 
+
+ align:start position:0%
+different than what we did last time
+right last time we checked the type and
+
+ align:start position:0%
+right last time we checked the type and
+ 
+
+ align:start position:0%
+right last time we checked the type and
+said if it is a float you're okay if not
+
+ align:start position:0%
+said if it is a float you're okay if not
+ 
+
+ align:start position:0%
+said if it is a float you're okay if not
+carry on this case what would happen
+
+ align:start position:0%
+carry on this case what would happen
+ 
+
+ align:start position:0%
+carry on this case what would happen
+well float is going to try and do the
+
+ align:start position:0%
+well float is going to try and do the
+ 
+
+ align:start position:0%
+well float is going to try and do the
+the coion it's going to try and turn it
+
+ align:start position:0%
+the coion it's going to try and turn it
+ 
+
+ align:start position:0%
+the coion it's going to try and turn it
+into a floating Point number if it does
+
+ align:start position:0%
+into a floating Point number if it does
+ 
+
+ align:start position:0%
+into a floating Point number if it does
+I'm great right and i' like this to
+
+ align:start position:0%
+I'm great right and i' like this to
+ 
+
+ align:start position:0%
+I'm great right and i' like this to
+return Val if it doesn't float's going
+
+ align:start position:0%
+return Val if it doesn't float's going
+ 
+
+ align:start position:0%
+return Val if it doesn't float's going
+to throw or raise to use the right term
+
+ align:start position:0%
+to throw or raise to use the right term
+ 
+
+ align:start position:0%
+to throw or raise to use the right term
+an exception it's going to say something
+
+ align:start position:0%
+an exception it's going to say something
+ 
+
+ align:start position:0%
+an exception it's going to say something
+like a type error in fact let's try it
+
+ align:start position:0%
+like a type error in fact let's try it
+ 
+
+ align:start position:0%
+like a type error in fact let's try it
+over here right if I go over here and I
+
+ align:start position:0%
+over here right if I go over here and I
+ 
+
+ align:start position:0%
+over here right if I go over here and I
+say float of three it's going to do the
+
+ align:start position:0%
+say float of three it's going to do the
+ 
+
+ align:start position:0%
+say float of three it's going to do the
+conversion but if I say turn this into a
+
+ align:start position:0%
+conversion but if I say turn this into a
+ 
+
+ align:start position:0%
+conversion but if I say turn this into a
+float ah it throws a value error
+
+ align:start position:0%
+float ah it throws a value error
+ 
+
+ align:start position:0%
+float ah it throws a value error
+exception it says it's wrong kind of
+
+ align:start position:0%
+exception it says it's wrong kind of
+ 
+
+ align:start position:0%
+exception it says it's wrong kind of
+value that I've got so I'm going to
+
+ align:start position:0%
+value that I've got so I'm going to
+ 
+
+ align:start position:0%
+value that I've got so I'm going to
+write a little piece of code that says
+
+ align:start position:0%
+write a little piece of code that says
+ 
+
+ align:start position:0%
+write a little piece of code that says
+if it gives me a float I'm set but if
+
+ align:start position:0%
+if it gives me a float I'm set but if
+ 
+
+ align:start position:0%
+if it gives me a float I'm set but if
+not I'd like to have the code handled
+
+ align:start position:0%
+not I'd like to have the code handled
+ 
+
+ align:start position:0%
+not I'd like to have the code handled
+the exception and that's what this funky
+
+ align:start position:0%
+the exception and that's what this funky
+ 
+
+ align:start position:0%
+the exception and that's what this funky
+Tri accept thing does okay this is a tri
+
+ align:start position:0%
+Tri accept thing does okay this is a tri
+ 
+
+ align:start position:0%
+Tri accept thing does okay this is a tri
+accept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+block and here's the flow of control
+
+ align:start position:0%
+block and here's the flow of control
+ 
+
+ align:start position:0%
+block and here's the flow of control
+that takes place in there when I hit a
+
+ align:start position:0%
+that takes place in there when I hit a
+ 
+
+ align:start position:0%
+that takes place in there when I hit a
+try Block it's going to literally do
+
+ align:start position:0%
+try Block it's going to literally do
+ 
+
+ align:start position:0%
+try Block it's going to literally do
+that it's going to try and execute the
+
+ align:start position:0%
+that it's going to try and execute the
+ 
+
+ align:start position:0%
+that it's going to try and execute the
+instructions if it can successfully
+
+ align:start position:0%
+instructions if it can successfully
+ 
+
+ align:start position:0%
+instructions if it can successfully
+execute the instructions it is going to
+
+ align:start position:0%
+execute the instructions it is going to
+ 
+
+ align:start position:0%
+execute the instructions it is going to
+skip past the accept block and just
+
+ align:start position:0%
+skip past the accept block and just
+ 
+
+ align:start position:0%
+skip past the accept block and just
+carry on with the rest of the code if
+
+ align:start position:0%
+carry on with the rest of the code if
+ 
+
+ align:start position:0%
+carry on with the rest of the code if
+however it raises an
+
+ align:start position:0%
+however it raises an
+ 
+
+ align:start position:0%
+however it raises an
+exception that exception at least in
+
+ align:start position:0%
+exception that exception at least in
+ 
+
+ align:start position:0%
+exception that exception at least in
+this case where it's a pure accept with
+
+ align:start position:0%
+this case where it's a pure accept with
+ 
+
+ align:start position:0%
+this case where it's a pure accept with
+no tags on it is going to get if you
+
+ align:start position:0%
+no tags on it is going to get if you
+ 
+
+ align:start position:0%
+no tags on it is going to get if you
+like thrown directly to the accept block
+
+ align:start position:0%
+like thrown directly to the accept block
+ 
+
+ align:start position:0%
+like thrown directly to the accept block
+and it's going to try and execute that
+
+ align:start position:0%
+and it's going to try and execute that
+ 
+
+ align:start position:0%
+and it's going to try and execute that
+so notice what's going to happen here
+
+ align:start position:0%
+so notice what's going to happen here
+ 
+
+ align:start position:0%
+so notice what's going to happen here
+then if I give it something that can be
+
+ align:start position:0%
+then if I give it something that can be
+ 
+
+ align:start position:0%
+then if I give it something that can be
+turned into a float I come in here I
+
+ align:start position:0%
+turned into a float I come in here I
+ 
+
+ align:start position:0%
+turned into a float I come in here I
+read the input I'm if it can be turned
+
+ align:start position:0%
+read the input I'm if it can be turned
+ 
+
+ align:start position:0%
+read the input I'm if it can be turned
+into a float I'm going to just return
+
+ align:start position:0%
+into a float I'm going to just return
+ 
+
+ align:start position:0%
+into a float I'm going to just return
+the value and I'm set if not it's
+
+ align:start position:0%
+the value and I'm set if not it's
+ 
+
+ align:start position:0%
+the value and I'm set if not it's
+basically going to throw it to this
+
+ align:start position:0%
+basically going to throw it to this
+ 
+
+ align:start position:0%
+basically going to throw it to this
+point in which case I'm going to print
+
+ align:start position:0%
+point in which case I'm going to print
+ 
+
+ align:start position:0%
+point in which case I'm going to print
+out an error message and oh yeah I'm
+
+ align:start position:0%
+out an error message and oh yeah I'm
+ 
+
+ align:start position:0%
+out an error message and oh yeah I'm
+still in that while loop so it's going
+
+ align:start position:0%
+still in that while loop so it's going
+ 
+
+ align:start position:0%
+still in that while loop so it's going
+to go around so in fact if I go here and
+
+ align:start position:0%
+to go around so in fact if I go here and
+ 
+
+ align:start position:0%
+to go around so in fact if I go here and
+let me uncomment
+
+ align:start position:0%
+let me uncomment
+ 
+
+ align:start position:0%
+let me uncomment
+this and run the
+
+ align:start position:0%
+this and run the
+ 
+
+ align:start position:0%
+this and run the
+code says enter a float and if I give it
+
+ align:start position:0%
+code says enter a float and if I give it
+ 
+
+ align:start position:0%
+code says enter a float and if I give it
+something that can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be uh sorry I've got yes never mind the
+
+ align:start position:0%
+be uh sorry I've got yes never mind the
+ 
+
+ align:start position:0%
+be uh sorry I've got yes never mind the
+grades crap uh where did I have
+
+ align:start position:0%
+grades crap uh where did I have
+ 
+
+ align:start position:0%
+grades crap uh where did I have
+that let me comment that out
+
+ align:start position:0%
+that let me comment that out
+ 
+
+ align:start position:0%
+that let me comment that out
+somehow it's appropriate in the middle
+
+ align:start position:0%
+somehow it's appropriate in the middle
+ 
+
+ align:start position:0%
+somehow it's appropriate in the middle
+of my lecture for it to say whoops at me
+
+ align:start position:0%
+of my lecture for it to say whoops at me
+ 
+
+ align:start position:0%
+of my lecture for it to say whoops at me
+but uh wasn't what I
+
+ align:start position:0%
+but uh wasn't what I
+ 
+
+ align:start position:0%
+but uh wasn't what I
+intended and we will try this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again okay says enter a float I give it
+
+ align:start position:0%
+again okay says enter a float I give it
+ 
+
+ align:start position:0%
+again okay says enter a float I give it
+something that can be converted into a
+
+ align:start position:0%
+something that can be converted into a
+ 
+
+ align:start position:0%
+something that can be converted into a
+float it says fine let me go back and
+
+ align:start position:0%
+float it says fine let me go back and
+ 
+
+ align:start position:0%
+float it says fine let me go back and
+run it again though if I run it again it
+
+ align:start position:0%
+run it again though if I run it again it
+ 
+
+ align:start position:0%
+run it again though if I run it again it
+says enter a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+float aha it goes into that except
+
+ align:start position:0%
+float aha it goes into that except
+ 
+
+ align:start position:0%
+float aha it goes into that except
+portion prints out a message and goes
+
+ align:start position:0%
+portion prints out a message and goes
+ 
+
+ align:start position:0%
+portion prints out a message and goes
+back around the H Loop to say try again
+
+ align:start position:0%
+back around the H Loop to say try again
+ 
+
+ align:start position:0%
+back around the H Loop to say try again
+and it's going to keep keep doing this
+
+ align:start position:0%
+and it's going to keep keep doing this
+ 
+
+ align:start position:0%
+and it's going to keep keep doing this
+until I give it something that does
+
+ align:start position:0%
+until I give it something that does
+ 
+
+ align:start position:0%
+until I give it something that does
+serve as a
+
+ align:start position:0%
+serve as a
+ 
+
+ align:start position:0%
+serve as a
+float all right so an exception then has
+
+ align:start position:0%
+float all right so an exception then has
+ 
+
+ align:start position:0%
+float all right so an exception then has
+this format that I can control as a
+
+ align:start position:0%
+this format that I can control as a
+ 
+
+ align:start position:0%
+this format that I can control as a
+programmer why would I want to use this
+
+ align:start position:0%
+programmer why would I want to use this
+ 
+
+ align:start position:0%
+programmer why would I want to use this
+well some things I can actually expect
+
+ align:start position:0%
+well some things I can actually expect
+ 
+
+ align:start position:0%
+well some things I can actually expect
+may happen and I want to handle them the
+
+ align:start position:0%
+may happen and I want to handle them the
+ 
+
+ align:start position:0%
+may happen and I want to handle them the
+float example is a simple one I'm going
+
+ align:start position:0%
+float example is a simple one I'm going
+ 
+
+ align:start position:0%
+float example is a simple one I'm going
+to generalize in a second here's a
+
+ align:start position:0%
+to generalize in a second here's a
+ 
+
+ align:start position:0%
+to generalize in a second here's a
+better example I'm writing a piece of
+
+ align:start position:0%
+better example I'm writing a piece of
+ 
+
+ align:start position:0%
+better example I'm writing a piece of
+code that wants to input a file and I
+
+ align:start position:0%
+code that wants to input a file and I
+ 
+
+ align:start position:0%
+code that wants to input a file and I
+can certainly imagine something that
+
+ align:start position:0%
+can certainly imagine something that
+ 
+
+ align:start position:0%
+can certainly imagine something that
+says give me the file name I'm going to
+
+ align:start position:0%
+says give me the file name I'm going to
+ 
+
+ align:start position:0%
+says give me the file name I'm going to
+do something with it I can't guarantee
+
+ align:start position:0%
+do something with it I can't guarantee
+ 
+
+ align:start position:0%
+do something with it I can't guarantee
+that the file may exist under that name
+
+ align:start position:0%
+that the file may exist under that name
+ 
+
+ align:start position:0%
+that the file may exist under that name
+but I know that's something that might
+
+ align:start position:0%
+but I know that's something that might
+ 
+
+ align:start position:0%
+but I know that's something that might
+occur so a nice way to handle it is to
+
+ align:start position:0%
+occur so a nice way to handle it is to
+ 
+
+ align:start position:0%
+occur so a nice way to handle it is to
+write it as an exception that says
+
+ align:start position:0%
+write it as an exception that says
+ 
+
+ align:start position:0%
+write it as an exception that says
+here's what I want to do if I get the
+
+ align:start position:0%
+here's what I want to do if I get the
+ 
+
+ align:start position:0%
+here's what I want to do if I get the
+file but just in case the file name's
+
+ align:start position:0%
+file but just in case the file name's
+ 
+
+ align:start position:0%
+file but just in case the file name's
+not there here's what I want to do in
+
+ align:start position:0%
+not there here's what I want to do in
+ 
+
+ align:start position:0%
+not there here's what I want to do in
+that case to handle it let me specify
+
+ align:start position:0%
+that case to handle it let me specify
+ 
+
+ align:start position:0%
+that case to handle it let me specify
+what the exception should
+
+ align:start position:0%
+what the exception should
+ 
+
+ align:start position:0%
+what the exception should
+do all right in the example I just wrote
+
+ align:start position:0%
+do all right in the example I just wrote
+ 
+
+ align:start position:0%
+do all right in the example I just wrote
+here this is pretty trivial right okay
+
+ align:start position:0%
+here this is pretty trivial right okay
+ 
+
+ align:start position:0%
+here this is pretty trivial right okay
+I'm trying to input floats I could
+
+ align:start position:0%
+I'm trying to input floats I could
+ 
+
+ align:start position:0%
+I'm trying to input floats I could
+generalize this pretty nicely imagine
+
+ align:start position:0%
+generalize this pretty nicely imagine
+ 
+
+ align:start position:0%
+generalize this pretty nicely imagine
+the same kind of idea where I want to
+
+ align:start position:0%
+the same kind of idea where I want to
+ 
+
+ align:start position:0%
+the same kind of idea where I want to
+Simply say I want to take input of
+
+ align:start position:0%
+Simply say I want to take input of
+ 
+
+ align:start position:0%
+Simply say I want to take input of
+anything and try and see how to make
+
+ align:start position:0%
+anything and try and see how to make
+ 
+
+ align:start position:0%
+anything and try and see how to make
+sure I get the right kind of thing I
+
+ align:start position:0%
+sure I get the right kind of thing I
+ 
+
+ align:start position:0%
+sure I get the right kind of thing I
+want to make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polymorphic well that's pretty easy to
+
+ align:start position:0%
+polymorphic well that's pretty easy to
+ 
+
+ align:start position:0%
+polymorphic well that's pretty easy to
+do that is basically the next example
+
+ align:start position:0%
+do that is basically the next example
+ 
+
+ align:start position:0%
+do that is basically the next example
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+here okay in fact let me comment this
+
+ align:start position:0%
+here okay in fact let me comment this
+ 
+
+ align:start position:0%
+here okay in fact let me comment this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+out I can do exactly the same kind of
+
+ align:start position:0%
+out I can do exactly the same kind of
+ 
+
+ align:start position:0%
+out I can do exactly the same kind of
+thing right but now what I'm going to
+
+ align:start position:0%
+thing right but now what I'm going to
+ 
+
+ align:start position:0%
+thing right but now what I'm going to
+try and do is read in a set of values
+
+ align:start position:0%
+try and do is read in a set of values
+ 
+
+ align:start position:0%
+try and do is read in a set of values
+where I'm going to give it a type of
+
+ align:start position:0%
+where I'm going to give it a type of
+ 
+
+ align:start position:0%
+where I'm going to give it a type of
+value as well as the messages formats
+
+ align:start position:0%
+value as well as the messages formats
+ 
+
+ align:start position:0%
+value as well as the messages formats
+the same I'm going to ask for some input
+
+ align:start position:0%
+the same I'm going to ask for some input
+ 
+
+ align:start position:0%
+the same I'm going to ask for some input
+and then I'm going to use that procedure
+
+ align:start position:0%
+and then I'm going to use that procedure
+ 
+
+ align:start position:0%
+and then I'm going to use that procedure
+to check is this the right type of value
+
+ align:start position:0%
+to check is this the right type of value
+ 
+
+ align:start position:0%
+to check is this the right type of value
+and I'm going to try and use that to do
+
+ align:start position:0%
+and I'm going to try and use that to do
+ 
+
+ align:start position:0%
+and I'm going to try and use that to do
+the coercion if you like same thing if
+
+ align:start position:0%
+the coercion if you like same thing if
+ 
+
+ align:start position:0%
+the coercion if you like same thing if
+it works I'm going to skip that if it
+
+ align:start position:0%
+it works I'm going to skip that if it
+ 
+
+ align:start position:0%
+it works I'm going to skip that if it
+not it's going to throw the
+
+ align:start position:0%
+not it's going to throw the
+ 
+
+ align:start position:0%
+not it's going to throw the
+exception why is this nice well that's a
+
+ align:start position:0%
+exception why is this nice well that's a
+ 
+
+ align:start position:0%
+exception why is this nice well that's a
+handy piece of code right because
+
+ align:start position:0%
+handy piece of code right because
+ 
+
+ align:start position:0%
+handy piece of code right because
+imagine I've got that now I can now
+
+ align:start position:0%
+imagine I've got that now I can now
+ 
+
+ align:start position:0%
+imagine I've got that now I can now
+store that away in some file name input
+
+ align:start position:0%
+store that away in some file name input
+ 
+
+ align:start position:0%
+store that away in some file name input
+top py and import it into every one of
+
+ align:start position:0%
+top py and import it into every one of
+ 
+
+ align:start position:0%
+top py and import it into every one of
+my procedure functions sorry my files of
+
+ align:start position:0%
+my procedure functions sorry my files of
+ 
+
+ align:start position:0%
+my procedure functions sorry my files of
+procedures because it's a standard way
+
+ align:start position:0%
+procedures because it's a standard way
+ 
+
+ align:start position:0%
+procedures because it's a standard way
+of now giving me the
+
+ align:start position:0%
+of now giving me the
+ 
+
+ align:start position:0%
+of now giving me the
+input okay so far though I've just shown
+
+ align:start position:0%
+input okay so far though I've just shown
+ 
+
+ align:start position:0%
+input okay so far though I've just shown
+you what happens inside a piece of code
+
+ align:start position:0%
+you what happens inside a piece of code
+ 
+
+ align:start position:0%
+you what happens inside a piece of code
+it raises an exception it goes to that
+
+ align:start position:0%
+it raises an exception it goes to that
+ 
+
+ align:start position:0%
+it raises an exception it goes to that
+except Clause we don't have to use it
+
+ align:start position:0%
+except Clause we don't have to use it
+ 
+
+ align:start position:0%
+except Clause we don't have to use it
+just inside of one place we can actually
+
+ align:start position:0%
+just inside of one place we can actually
+ 
+
+ align:start position:0%
+just inside of one place we can actually
+use it more generally and that gets me
+
+ align:start position:0%
+use it more generally and that gets me
+ 
+
+ align:start position:0%
+use it more generally and that gets me
+to the last example I wanted to show you
+
+ align:start position:0%
+to the last example I wanted to show you
+ 
+
+ align:start position:0%
+to the last example I wanted to show you
+and let me uncomment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this let's take a look at this code
+
+ align:start position:0%
+this let's take a look at this code
+ 
+
+ align:start position:0%
+this let's take a look at this code
+this looks like a handy piece of code to
+
+ align:start position:0%
+this looks like a handy piece of code to
+ 
+
+ align:start position:0%
+this looks like a handy piece of code to
+have given what we just recently did to
+
+ align:start position:0%
+have given what we just recently did to
+ 
+
+ align:start position:0%
+have given what we just recently did to
+you right get grades it's a little
+
+ align:start position:0%
+you right get grades it's a little
+ 
+
+ align:start position:0%
+you right get grades it's a little
+function that's going to say give me a
+
+ align:start position:0%
+function that's going to say give me a
+ 
+
+ align:start position:0%
+function that's going to say give me a
+file name and I'm going to go off and
+
+ align:start position:0%
+file name and I'm going to go off and
+ 
+
+ align:start position:0%
+file name and I'm going to go off and
+open that up okay and bind it to a local
+
+ align:start position:0%
+open that up okay and bind it to a local
+ 
+
+ align:start position:0%
+open that up okay and bind it to a local
+variable and if it's successful then I
+
+ align:start position:0%
+variable and if it's successful then I
+ 
+
+ align:start position:0%
+variable and if it's successful then I
+just like to go off and do some things
+
+ align:start position:0%
+just like to go off and do some things
+ 
+
+ align:start position:0%
+just like to go off and do some things
+like turn it into a list so I can
+
+ align:start position:0%
+like turn it into a list so I can
+ 
+
+ align:start position:0%
+like turn it into a list so I can
+compute average score or distributions
+
+ align:start position:0%
+compute average score or distributions
+ 
+
+ align:start position:0%
+compute average score or distributions
+or something else I don't really care
+
+ align:start position:0%
+or something else I don't really care
+ 
+
+ align:start position:0%
+or something else I don't really care
+what's going on in here notice though
+
+ align:start position:0%
+what's going on in here notice though
+ 
+
+ align:start position:0%
+what's going on in here notice though
+what I've done
+
+ align:start position:0%
+what I've done
+ 
+
+ align:start position:0%
+what I've done
+open if it doesn't succeed is going to
+
+ align:start position:0%
+open if it doesn't succeed is going to
+ 
+
+ align:start position:0%
+open if it doesn't succeed is going to
+to raise a particular kind of exception
+
+ align:start position:0%
+to raise a particular kind of exception
+ 
+
+ align:start position:0%
+to raise a particular kind of exception
+called IO a and so I've done a little
+
+ align:start position:0%
+called IO a and so I've done a little
+ 
+
+ align:start position:0%
+called IO a and so I've done a little
+bit different thing here which is I've
+
+ align:start position:0%
+bit different thing here which is I've
+ 
+
+ align:start position:0%
+bit different thing here which is I've
+put the except part of the block with IO
+
+ align:start position:0%
+put the except part of the block with IO
+ 
+
+ align:start position:0%
+put the except part of the block with IO
+a what does that say it says if in the
+
+ align:start position:0%
+a what does that say it says if in the
+ 
+
+ align:start position:0%
+a what does that say it says if in the
+code up here I get a an exception of
+
+ align:start position:0%
+code up here I get a an exception of
+ 
+
+ align:start position:0%
+code up here I get a an exception of
+that sort I'm going to go to this place
+
+ align:start position:0%
+that sort I'm going to go to this place
+ 
+
+ align:start position:0%
+that sort I'm going to go to this place
+to handle it on the other hand if I'm
+
+ align:start position:0%
+to handle it on the other hand if I'm
+ 
+
+ align:start position:0%
+to handle it on the other hand if I'm
+inside this procedure and some other
+
+ align:start position:0%
+inside this procedure and some other
+ 
+
+ align:start position:0%
+inside this procedure and some other
+exception is raised that's not tagged by
+
+ align:start position:0%
+exception is raised that's not tagged by
+ 
+
+ align:start position:0%
+exception is raised that's not tagged by
+that one it's going to raise it up the
+
+ align:start position:0%
+that one it's going to raise it up the
+ 
+
+ align:start position:0%
+that one it's going to raise it up the
+chain if that procedure was called by
+
+ align:start position:0%
+chain if that procedure was called by
+ 
+
+ align:start position:0%
+chain if that procedure was called by
+some other procedure is going to say is
+
+ align:start position:0%
+some other procedure is going to say is
+ 
+
+ align:start position:0%
+some other procedure is going to say is
+there an exception Block in there that
+
+ align:start position:0%
+there an exception Block in there that
+ 
+
+ align:start position:0%
+there an exception Block in there that
+can handle that if not I'm going to keep
+
+ align:start position:0%
+can handle that if not I'm going to keep
+ 
+
+ align:start position:0%
+can handle that if not I'm going to keep
+going up the chain until eventually I
+
+ align:start position:0%
+going up the chain until eventually I
+ 
+
+ align:start position:0%
+going up the chain until eventually I
+get to the top level and you can see
+
+ align:start position:0%
+get to the top level and you can see
+ 
+
+ align:start position:0%
+get to the top level and you can see
+that down here I'm going to run this in
+
+ align:start position:0%
+that down here I'm going to run this in
+ 
+
+ align:start position:0%
+that down here I'm going to run this in
+a second but this is just a piece of
+
+ align:start position:0%
+a second but this is just a piece of
+ 
+
+ align:start position:0%
+a second but this is just a piece of
+code where I'm going to say gee if I can
+
+ align:start position:0%
+code where I'm going to say gee if I can
+ 
+
+ align:start position:0%
+code where I'm going to say gee if I can
+get the grades do something if
+
+ align:start position:0%
+get the grades do something if
+ 
+
+ align:start position:0%
+get the grades do something if
+not carry on right and if I go ahead and
+
+ align:start position:0%
+not carry on right and if I go ahead and
+ 
+
+ align:start position:0%
+not carry on right and if I go ahead and
+run
+
+ align:start position:0%
+run
+ 
+
+ align:start position:0%
+run
+this and now it's going to say whoops at
+
+ align:start position:0%
+this and now it's going to say whoops at
+ 
+
+ align:start position:0%
+this and now it's going to say whoops at
+me okay what
+
+ align:start position:0%
+me okay what
+ 
+
+ align:start position:0%
+me okay what
+happened I'm down here and try I'm
+
+ align:start position:0%
+happened I'm down here and try I'm
+ 
+
+ align:start position:0%
+happened I'm down here and try I'm
+trying to do get grades which is a call
+
+ align:start position:0%
+trying to do get grades which is a call
+ 
+
+ align:start position:0%
+trying to do get grades which is a call
+to that function which is not bound in
+
+ align:start position:0%
+to that function which is not bound in
+ 
+
+ align:start position:0%
+to that function which is not bound in
+my in my in my there in my computer that
+
+ align:start position:0%
+my in my in my there in my computer that
+ 
+
+ align:start position:0%
+my in my in my there in my computer that
+says it's in here it's in this Tri block
+
+ align:start position:0%
+says it's in here it's in this Tri block
+ 
+
+ align:start position:0%
+says it's in here it's in this Tri block
+it raised an exception but it wasn't an
+
+ align:start position:0%
+it raised an exception but it wasn't an
+ 
+
+ align:start position:0%
+it raised an exception but it wasn't an
+IO error so it passes it back past this
+
+ align:start position:0%
+IO error so it passes it back past this
+ 
+
+ align:start position:0%
+IO error so it passes it back past this
+exception up to this level which gets to
+
+ align:start position:0%
+exception up to this level which gets to
+ 
+
+ align:start position:0%
+exception up to this level which gets to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+exception so let me say this a little
+
+ align:start position:0%
+exception so let me say this a little
+ 
+
+ align:start position:0%
+exception so let me say this a little
+bit better then I can write exceptions
+
+ align:start position:0%
+bit better then I can write exceptions
+ 
+
+ align:start position:0%
+bit better then I can write exceptions
+inside a piece of code try this if it
+
+ align:start position:0%
+inside a piece of code try this if it
+ 
+
+ align:start position:0%
+inside a piece of code try this if it
+doesn't work I can have an exception
+
+ align:start position:0%
+doesn't work I can have an exception
+ 
+
+ align:start position:0%
+doesn't work I can have an exception
+that catches any error at that level or
+
+ align:start position:0%
+that catches any error at that level or
+ 
+
+ align:start position:0%
+that catches any error at that level or
+I can say catch only these kinds of
+
+ align:start position:0%
+I can say catch only these kinds of
+ 
+
+ align:start position:0%
+I can say catch only these kinds of
+Errors at that level otherwise pass them
+
+ align:start position:0%
+Errors at that level otherwise pass them
+ 
+
+ align:start position:0%
+Errors at that level otherwise pass them
+up the chain and that exception will
+
+ align:start position:0%
+up the chain and that exception will
+ 
+
+ align:start position:0%
+up the chain and that exception will
+keep getting passed up the chain of
+
+ align:start position:0%
+keep getting passed up the chain of
+ 
+
+ align:start position:0%
+keep getting passed up the chain of
+calls until it either gets to top level
+
+ align:start position:0%
+calls until it either gets to top level
+ 
+
+ align:start position:0%
+calls until it either gets to top level
+in which case it looks like what you see
+
+ align:start position:0%
+in which case it looks like what you see
+ 
+
+ align:start position:0%
+in which case it looks like what you see
+all the time looks like an error but it
+
+ align:start position:0%
+all the time looks like an error but it
+ 
+
+ align:start position:0%
+all the time looks like an error but it
+tells you what the error came from or it
+
+ align:start position:0%
+tells you what the error came from or it
+ 
+
+ align:start position:0%
+tells you what the error came from or it
+gets an exception Handler that can deal
+
+ align:start position:0%
+gets an exception Handler that can deal
+ 
+
+ align:start position:0%
+gets an exception Handler that can deal
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+it okay so the last thing to say about
+
+ align:start position:0%
+it okay so the last thing to say about
+ 
+
+ align:start position:0%
+it okay so the last thing to say about
+this is what's the difference between an
+
+ align:start position:0%
+this is what's the difference between an
+ 
+
+ align:start position:0%
+this is what's the difference between an
+exception and an assert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we introduced asserts earlier on
+
+ align:start position:0%
+right we introduced asserts earlier on
+ 
+
+ align:start position:0%
+right we introduced asserts earlier on
+you've actually seen them in some pieces
+
+ align:start position:0%
+you've actually seen them in some pieces
+ 
+
+ align:start position:0%
+you've actually seen them in some pieces
+of code so um you know what's the
+
+ align:start position:0%
+of code so um you know what's the
+ 
+
+ align:start position:0%
+of code so um you know what's the
+difference between the two of
+
+ align:start position:0%
+difference between the two of
+ 
+
+ align:start position:0%
+difference between the two of
+them well here's my way of describing
+
+ align:start position:0%
+them well here's my way of describing
+ 
+
+ align:start position:0%
+them well here's my way of describing
+it the goal of an assert or an assert
+
+ align:start position:0%
+it the goal of an assert or an assert
+ 
+
+ align:start position:0%
+it the goal of an assert or an assert
+statement is basically to say look you
+
+ align:start position:0%
+statement is basically to say look you
+ 
+
+ align:start position:0%
+statement is basically to say look you
+can be sure that my function is going to
+
+ align:start position:0%
+can be sure that my function is going to
+ 
+
+ align:start position:0%
+can be sure that my function is going to
+give this kind of result if you give me
+
+ align:start position:0%
+give this kind of result if you give me
+ 
+
+ align:start position:0%
+give this kind of result if you give me
+inputs of a particular type sorry wrong
+
+ align:start position:0%
+inputs of a particular type sorry wrong
+ 
+
+ align:start position:0%
+inputs of a particular type sorry wrong
+way saying it if you give me inputs that
+
+ align:start position:0%
+way saying it if you give me inputs that
+ 
+
+ align:start position:0%
+way saying it if you give me inputs that
+satisfy some particular
+
+ align:start position:0%
+satisfy some particular
+ 
+
+ align:start position:0%
+satisfy some particular
+constraints right that was the kind of
+
+ align:start position:0%
+constraints right that was the kind of
+ 
+
+ align:start position:0%
+constraints right that was the kind of
+thing you saw aert said here are some
+
+ align:start position:0%
+thing you saw aert said here are some
+ 
+
+ align:start position:0%
+thing you saw aert said here are some
+conditions to test if they're true I'm
+
+ align:start position:0%
+conditions to test if they're true I'm
+ 
+
+ align:start position:0%
+conditions to test if they're true I'm
+going to let the rest of the code run if
+
+ align:start position:0%
+going to let the rest of the code run if
+ 
+
+ align:start position:0%
+going to let the rest of the code run if
+not I'm going to throw an error right so
+
+ align:start position:0%
+not I'm going to throw an error right so
+ 
+
+ align:start position:0%
+not I'm going to throw an error right so
+the assertion is basically saying we got
+
+ align:start position:0%
+the assertion is basically saying we got
+ 
+
+ align:start position:0%
+the assertion is basically saying we got
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preconditions those are the Clauses
+
+ align:start position:0%
+preconditions those are the Clauses
+ 
+
+ align:start position:0%
+preconditions those are the Clauses
+inside the assert that have to be true
+
+ align:start position:0%
+inside the assert that have to be true
+ 
+
+ align:start position:0%
+inside the assert that have to be true
+and there's a post
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition and in essence what the assert
+
+ align:start position:0%
+condition and in essence what the assert
+ 
+
+ align:start position:0%
+condition and in essence what the assert
+is saying is or rather the programmer
+
+ align:start position:0%
+is saying is or rather the programmer
+ 
+
+ align:start position:0%
+is saying is or rather the programmer
+saying using the assert is if you give
+
+ align:start position:0%
+saying using the assert is if you give
+ 
+
+ align:start position:0%
+saying using the assert is if you give
+me input that satisfies the
+
+ align:start position:0%
+me input that satisfies the
+ 
+
+ align:start position:0%
+me input that satisfies the
+preconditions I'm guaranteeing to you
+
+ align:start position:0%
+preconditions I'm guaranteeing to you
+ 
+
+ align:start position:0%
+preconditions I'm guaranteeing to you
+that my code is going to give you
+
+ align:start position:0%
+that my code is going to give you
+ 
+
+ align:start position:0%
+that my code is going to give you
+something that that meets the postc
+
+ align:start position:0%
+something that that meets the postc
+ 
+
+ align:start position:0%
+something that that meets the postc
+condition it's going to do the right
+
+ align:start position:0%
+condition it's going to do the right
+ 
+
+ align:start position:0%
+condition it's going to do the right
+thing and as a consequence as you saw
+
+ align:start position:0%
+thing and as a consequence as you saw
+ 
+
+ align:start position:0%
+thing and as a consequence as you saw
+with the asserts if the preconditions
+
+ align:start position:0%
+with the asserts if the preconditions
+ 
+
+ align:start position:0%
+with the asserts if the preconditions
+aren't true it throws an error okay it
+
+ align:start position:0%
+aren't true it throws an error okay it
+ 
+
+ align:start position:0%
+aren't true it throws an error okay it
+goes back up the top level saying stops
+
+ align:start position:0%
+goes back up the top level saying stops
+ 
+
+ align:start position:0%
+goes back up the top level saying stops
+operation immediately and goes back up
+
+ align:start position:0%
+operation immediately and goes back up
+ 
+
+ align:start position:0%
+operation immediately and goes back up
+the top level
+
+ align:start position:0%
+the top level
+ 
+
+ align:start position:0%
+the top level
+okay asserts in fact are nice in the
+
+ align:start position:0%
+okay asserts in fact are nice in the
+ 
+
+ align:start position:0%
+okay asserts in fact are nice in the
+sense that they let you check conditions
+
+ align:start position:0%
+sense that they let you check conditions
+ 
+
+ align:start position:0%
+sense that they let you check conditions
+at debugging time or testing time so you
+
+ align:start position:0%
+at debugging time or testing time so you
+ 
+
+ align:start position:0%
+at debugging time or testing time so you
+can actually use them to see where your
+
+ align:start position:0%
+can actually use them to see where your
+ 
+
+ align:start position:0%
+can actually use them to see where your
+code is
+
+ align:start position:0%
+code is
+ 
+
+ align:start position:0%
+code is
+going an exception when you use an
+
+ align:start position:0%
+going an exception when you use an
+ 
+
+ align:start position:0%
+going an exception when you use an
+exception basically what you're saying
+
+ align:start position:0%
+exception basically what you're saying
+ 
+
+ align:start position:0%
+exception basically what you're saying
+is look you can do anything you want
+
+ align:start position:0%
+is look you can do anything you want
+ 
+
+ align:start position:0%
+is look you can do anything you want
+with my function and you can be sure
+
+ align:start position:0%
+with my function and you can be sure
+ 
+
+ align:start position:0%
+with my function and you can be sure
+that I'm going to tell you if something
+
+ align:start position:0%
+that I'm going to tell you if something
+ 
+
+ align:start position:0%
+that I'm going to tell you if something
+is going wrong and in many cases I'm
+
+ align:start position:0%
+is going wrong and in many cases I'm
+ 
+
+ align:start position:0%
+is going wrong and in many cases I'm
+going to handle it
+
+ align:start position:0%
+going to handle it
+ 
+
+ align:start position:0%
+going to handle it
+myself so as as much as possible the
+
+ align:start position:0%
+myself so as as much as possible the
+ 
+
+ align:start position:0%
+myself so as as much as possible the
+exceptions are going to try and handle
+
+ align:start position:0%
+exceptions are going to try and handle
+ 
+
+ align:start position:0%
+exceptions are going to try and handle
+unexpected things actually wrong term
+
+ align:start position:0%
+unexpected things actually wrong term
+ 
+
+ align:start position:0%
+unexpected things actually wrong term
+you expected them but not what the the
+
+ align:start position:0%
+you expected them but not what the the
+ 
+
+ align:start position:0%
+you expected them but not what the the
+user did it's going to try and handle
+
+ align:start position:0%
+user did it's going to try and handle
+ 
+
+ align:start position:0%
+user did it's going to try and handle
+conditions other than the normal ones
+
+ align:start position:0%
+conditions other than the normal ones
+ 
+
+ align:start position:0%
+conditions other than the normal ones
+itself so you can use the thing in any
+
+ align:start position:0%
+itself so you can use the thing in any
+ 
+
+ align:start position:0%
+itself so you can use the thing in any
+way if it can't it's going to try and
+
+ align:start position:0%
+way if it can't it's going to try and
+ 
+
+ align:start position:0%
+way if it can't it's going to try and
+throw it to somebody else to handle and
+
+ align:start position:0%
+throw it to somebody else to handle and
+ 
+
+ align:start position:0%
+throw it to somebody else to handle and
+only if there is no Handler for that
+
+ align:start position:0%
+only if there is no Handler for that
+ 
+
+ align:start position:0%
+only if there is no Handler for that
+unexpected condition will it come up to
+
+ align:start position:0%
+unexpected condition will it come up to
+ 
+
+ align:start position:0%
+unexpected condition will it come up to
+top level so summarizing better assert
+
+ align:start position:0%
+top level so summarizing better assert
+ 
+
+ align:start position:0%
+top level so summarizing better assert
+is something you put in to say to the
+
+ align:start position:0%
+is something you put in to say to the
+ 
+
+ align:start position:0%
+is something you put in to say to the
+user make sure you're giving me input of
+
+ align:start position:0%
+user make sure you're giving me input of
+ 
+
+ align:start position:0%
+user make sure you're giving me input of
+this type but I'm going to guarantee you
+
+ align:start position:0%
+this type but I'm going to guarantee you
+ 
+
+ align:start position:0%
+this type but I'm going to guarantee you
+the rest of the code works correctly
+
+ align:start position:0%
+the rest of the code works correctly
+ 
+
+ align:start position:0%
+the rest of the code works correctly
+exceptions and exception handlers are
+
+ align:start position:0%
+exceptions and exception handlers are
+ 
+
+ align:start position:0%
+exceptions and exception handlers are
+saying here here are the odd cases that
+
+ align:start position:0%
+saying here here are the odd cases that
+ 
+
+ align:start position:0%
+saying here here are the odd cases that
+I might see and here's what I'd like to
+
+ align:start position:0%
+I might see and here's what I'd like to
+ 
+
+ align:start position:0%
+I might see and here's what I'd like to
+do in those cases in order to try and be
+
+ align:start position:0%
+do in those cases in order to try and be
+ 
+
+ align:start position:0%
+do in those cases in order to try and be
+able to deal with
+
+ align:start position:0%
+able to deal with
+ 
+
+ align:start position:0%
+able to deal with
+them last thing to say is why would you
+
+ align:start position:0%
+them last thing to say is why would you
+ 
+
+ align:start position:0%
+them last thing to say is why would you
+want to have
+
+ align:start position:0%
+want to have
+ 
+
+ align:start position:0%
+want to have
+exceptions well let's go back to that
+
+ align:start position:0%
+exceptions well let's go back to that
+ 
+
+ align:start position:0%
+exceptions well let's go back to that
+case of inputting a simple little
+
+ align:start position:0%
+case of inputting a simple little
+ 
+
+ align:start position:0%
+case of inputting a simple little
+floating
+
+ align:start position:0%
+floating
+ 
+
+ align:start position:0%
+floating
+point if I'm expecting mostly numbers in
+
+ align:start position:0%
+point if I'm expecting mostly numbers in
+ 
+
+ align:start position:0%
+point if I'm expecting mostly numbers in
+I can certainly try and do the coercion
+
+ align:start position:0%
+I can certainly try and do the coercion
+ 
+
+ align:start position:0%
+I can certainly try and do the coercion
+I could have done that just doing the
+
+ align:start position:0%
+I could have done that just doing the
+ 
+
+ align:start position:0%
+I could have done that just doing the
+coercion right the problem is I want to
+
+ align:start position:0%
+coercion right the problem is I want to
+ 
+
+ align:start position:0%
+coercion right the problem is I want to
+know if in fact I've got something
+
+ align:start position:0%
+know if in fact I've got something
+ 
+
+ align:start position:0%
+know if in fact I've got something
+that's not of the form I expect I'm much
+
+ align:start position:0%
+that's not of the form I expect I'm much
+ 
+
+ align:start position:0%
+that's not of the form I expect I'm much
+better having an exception get handled
+
+ align:start position:0%
+better having an exception get handled
+ 
+
+ align:start position:0%
+better having an exception get handled
+at the time of input than to let that
+
+ align:start position:0%
+at the time of input than to let that
+ 
+
+ align:start position:0%
+at the time of input than to let that
+prop that value rather propagate through
+
+ align:start position:0%
+prop that value rather propagate through
+ 
+
+ align:start position:0%
+prop that value rather propagate through
+a whole bunch of code until eventually
+
+ align:start position:0%
+a whole bunch of code until eventually
+ 
+
+ align:start position:0%
+a whole bunch of code until eventually
+it hits an error 17 calls later and you
+
+ align:start position:0%
+it hits an error 17 calls later and you
+ 
+
+ align:start position:0%
+it hits an error 17 calls later and you
+have no clue where it came from so the
+
+ align:start position:0%
+have no clue where it came from so the
+ 
+
+ align:start position:0%
+have no clue where it came from so the
+exceptions are useful when you want to
+
+ align:start position:0%
+exceptions are useful when you want to
+ 
+
+ align:start position:0%
+exceptions are useful when you want to
+have the ability to say I expect in
+
+ align:start position:0%
+have the ability to say I expect in
+ 
+
+ align:start position:0%
+have the ability to say I expect in
+general this kind of behavior but I do
+
+ align:start position:0%
+general this kind of behavior but I do
+ 
+
+ align:start position:0%
+general this kind of behavior but I do
+know there are some other things that
+
+ align:start position:0%
+know there are some other things that
+ 
+
+ align:start position:0%
+know there are some other things that
+might happen and here's what I'd like to
+
+ align:start position:0%
+might happen and here's what I'd like to
+ 
+
+ align:start position:0%
+might happen and here's what I'd like to
+do in each one of those cases but I do
+
+ align:start position:0%
+do in each one of those cases but I do
+ 
+
+ align:start position:0%
+do in each one of those cases but I do
+want to make sure that I don't let a
+
+ align:start position:0%
+want to make sure that I don't let a
+ 
+
+ align:start position:0%
+want to make sure that I don't let a
+value that I'm not expecting pass
+
+ align:start position:0%
+value that I'm not expecting pass
+ 
+
+ align:start position:0%
+value that I'm not expecting pass
+through that goes back to that idea of
+
+ align:start position:0%
+through that goes back to that idea of
+ 
+
+ align:start position:0%
+through that goes back to that idea of
+sort of discipline coding it's easy to
+
+ align:start position:0%
+sort of discipline coding it's easy to
+ 
+
+ align:start position:0%
+sort of discipline coding it's easy to
+have assumptions about what you think
+
+ align:start position:0%
+have assumptions about what you think
+ 
+
+ align:start position:0%
+have assumptions about what you think
+are going to come into the program when
+
+ align:start position:0%
+are going to come into the program when
+ 
+
+ align:start position:0%
+are going to come into the program when
+you write it if you really know what
+
+ align:start position:0%
+you write it if you really know what
+ 
+
+ align:start position:0%
+you write it if you really know what
+they are use an assert but if you think
+
+ align:start position:0%
+they are use an assert but if you think
+ 
+
+ align:start position:0%
+they are use an assert but if you think
+there's going to be some flexibility you
+
+ align:start position:0%
+there's going to be some flexibility you
+ 
+
+ align:start position:0%
+there's going to be some flexibility you
+want to prevent the user getting trapped
+
+ align:start position:0%
+want to prevent the user getting trapped
+ 
+
+ align:start position:0%
+want to prevent the user getting trapped
+in a bad spot and exceptions as a
+
+ align:start position:0%
+in a bad spot and exceptions as a
+ 
+
+ align:start position:0%
+in a bad spot and exceptions as a
+consequence are a good thing to use
\ No newline at end of file
diff --git a/kiCNa95DnnE.txt b/kiCNa95DnnE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..405a2d590e4bfd5f17e299da4d0787bc8c0a470e
--- /dev/null
+++ b/kiCNa95DnnE.txt
@@ -0,0 +1,3875 @@
+align:start position:0%
+ 
+so remember as VFR pilot
+
+ align:start position:0%
+so remember as VFR pilot
+ 
+
+ align:start position:0%
+so remember as VFR pilot
+she's gonna be doing stuff that is in
+
+ align:start position:0%
+she's gonna be doing stuff that is in
+ 
+
+ align:start position:0%
+she's gonna be doing stuff that is in
+some ways more challenging than what
+
+ align:start position:0%
+some ways more challenging than what
+ 
+
+ align:start position:0%
+some ways more challenging than what
+airline pilots do because you're always
+
+ align:start position:0%
+airline pilots do because you're always
+ 
+
+ align:start position:0%
+airline pilots do because you're always
+trying to keep clearances from clouds
+
+ align:start position:0%
+trying to keep clearances from clouds
+ 
+
+ align:start position:0%
+trying to keep clearances from clouds
+that the IFR pilots don't care about and
+
+ align:start position:0%
+that the IFR pilots don't care about and
+ 
+
+ align:start position:0%
+that the IFR pilots don't care about and
+if you're flying a low performance
+
+ align:start position:0%
+if you're flying a low performance
+ 
+
+ align:start position:0%
+if you're flying a low performance
+airplane you're also dealing with you
+
+ align:start position:0%
+airplane you're also dealing with you
+ 
+
+ align:start position:0%
+airplane you're also dealing with you
+know flying through the leather instead
+
+ align:start position:0%
+know flying through the leather instead
+ 
+
+ align:start position:0%
+know flying through the leather instead
+of it's going on top of it so while
+
+ align:start position:0%
+of it's going on top of it so while
+ 
+
+ align:start position:0%
+of it's going on top of it so while
+you're the VFR only pilot these
+
+ align:start position:0%
+you're the VFR only pilot these
+ 
+
+ align:start position:0%
+you're the VFR only pilot these
+non-local flights really pay attention
+
+ align:start position:0%
+non-local flights really pay attention
+ 
+
+ align:start position:0%
+non-local flights really pay attention
+to whether airspace go and study this a
+
+ align:start position:0%
+to whether airspace go and study this a
+ 
+
+ align:start position:0%
+to whether airspace go and study this a
+little bit before the exam here are the
+
+ align:start position:0%
+little bit before the exam here are the
+ 
+
+ align:start position:0%
+little bit before the exam here are the
+different kinds remember Class A is up
+
+ align:start position:0%
+different kinds remember Class A is up
+ 
+
+ align:start position:0%
+different kinds remember Class A is up
+high in an instrument clearance Class B
+
+ align:start position:0%
+high in an instrument clearance Class B
+ 
+
+ align:start position:0%
+high in an instrument clearance Class B
+is around the biggest airports class
+
+ align:start position:0%
+is around the biggest airports class
+ 
+
+ align:start position:0%
+is around the biggest airports class
+Charlie's around Manchester New
+
+ align:start position:0%
+Charlie's around Manchester New
+ 
+
+ align:start position:0%
+Charlie's around Manchester New
+Hampshire and D is for Hanscom and E is
+
+ align:start position:0%
+Hampshire and D is for Hanscom and E is
+ 
+
+ align:start position:0%
+Hampshire and D is for Hanscom and E is
+kind of everywhere else okay
+
+ align:start position:0%
+kind of everywhere else okay
+ 
+
+ align:start position:0%
+kind of everywhere else okay
+the goal for the basic VFR weather
+
+ align:start position:0%
+the goal for the basic VFR weather
+ 
+
+ align:start position:0%
+the goal for the basic VFR weather
+minimums is to make sure that an IFR
+
+ align:start position:0%
+minimums is to make sure that an IFR
+ 
+
+ align:start position:0%
+minimums is to make sure that an IFR
+plane coming out of the cloud has time
+
+ align:start position:0%
+plane coming out of the cloud has time
+ 
+
+ align:start position:0%
+plane coming out of the cloud has time
+to see and avoid you because the air
+
+ align:start position:0%
+to see and avoid you because the air
+ 
+
+ align:start position:0%
+to see and avoid you because the air
+traffic controllers job is to separate
+
+ align:start position:0%
+traffic controllers job is to separate
+ 
+
+ align:start position:0%
+traffic controllers job is to separate
+IFR airplanes from each other not to
+
+ align:start position:0%
+IFR airplanes from each other not to
+ 
+
+ align:start position:0%
+IFR airplanes from each other not to
+separate IFR and VFR traffic they will
+
+ align:start position:0%
+separate IFR and VFR traffic they will
+ 
+
+ align:start position:0%
+separate IFR and VFR traffic they will
+tell you about them but you're
+
+ align:start position:0%
+tell you about them but you're
+ 
+
+ align:start position:0%
+tell you about them but you're
+responsible as the VFR pilot for staying
+
+ align:start position:0%
+responsible as the VFR pilot for staying
+ 
+
+ align:start position:0%
+responsible as the VFR pilot for staying
+reasonably clear of clouds so just
+
+ align:start position:0%
+reasonably clear of clouds so just
+ 
+
+ align:start position:0%
+reasonably clear of clouds so just
+review these cloud clearances Class E
+
+ align:start position:0%
+review these cloud clearances Class E
+ 
+
+ align:start position:0%
+review these cloud clearances Class E
+you can see that this is a pretty good
+
+ align:start position:0%
+you can see that this is a pretty good
+ 
+
+ align:start position:0%
+you can see that this is a pretty good
+one to remember for the test 500 below a
+
+ align:start position:0%
+one to remember for the test 500 below a
+ 
+
+ align:start position:0%
+one to remember for the test 500 below a
+thousand above two thousand horizontally
+
+ align:start position:0%
+thousand above two thousand horizontally
+ 
+
+ align:start position:0%
+thousand above two thousand horizontally
+if you're really low in Class G airspace
+
+ align:start position:0%
+if you're really low in Class G airspace
+ 
+
+ align:start position:0%
+if you're really low in Class G airspace
+you can do some crazy stuff again I
+
+ align:start position:0%
+you can do some crazy stuff again I
+ 
+
+ align:start position:0%
+you can do some crazy stuff again I
+don't think this is really there to let
+
+ align:start position:0%
+don't think this is really there to let
+ 
+
+ align:start position:0%
+don't think this is really there to let
+you you know go from Boston to Chicago
+
+ align:start position:0%
+you you know go from Boston to Chicago
+ 
+
+ align:start position:0%
+you you know go from Boston to Chicago
+Scott running with you know one mile of
+
+ align:start position:0%
+Scott running with you know one mile of
+ 
+
+ align:start position:0%
+Scott running with you know one mile of
+visibility and just clear of the clouds
+
+ align:start position:0%
+visibility and just clear of the clouds
+ 
+
+ align:start position:0%
+visibility and just clear of the clouds
+I think it's more to enable people to
+
+ align:start position:0%
+I think it's more to enable people to
+ 
+
+ align:start position:0%
+I think it's more to enable people to
+say take off and do pattern work at
+
+ align:start position:0%
+say take off and do pattern work at
+ 
+
+ align:start position:0%
+say take off and do pattern work at
+their home Airport in some kind of
+
+ align:start position:0%
+their home Airport in some kind of
+ 
+
+ align:start position:0%
+their home Airport in some kind of
+little tiny very slow airplane pattern
+
+ align:start position:0%
+little tiny very slow airplane pattern
+ 
+
+ align:start position:0%
+little tiny very slow airplane pattern
+work is just what we were drying on the
+
+ align:start position:0%
+work is just what we were drying on the
+ 
+
+ align:start position:0%
+work is just what we were drying on the
+chalk board flying the traffic pattern
+
+ align:start position:0%
+chalk board flying the traffic pattern
+ 
+
+ align:start position:0%
+chalk board flying the traffic pattern
+at an airport
+
+ align:start position:0%
+at an airport
+ 
+
+ align:start position:0%
+at an airport
+so again yeah just review the
+
+ align:start position:0%
+so again yeah just review the
+ 
+
+ align:start position:0%
+so again yeah just review the
+presentation or the fa book so you know
+
+ align:start position:0%
+presentation or the fa book so you know
+ 
+
+ align:start position:0%
+presentation or the fa book so you know
+your weather minimums
+
+ align:start position:0%
+your weather minimums
+ 
+
+ align:start position:0%
+your weather minimums
+yeah incredibly at night for class G
+
+ align:start position:0%
+yeah incredibly at night for class G
+ 
+
+ align:start position:0%
+yeah incredibly at night for class G
+getting back to that pattern work thing
+
+ align:start position:0%
+getting back to that pattern work thing
+ 
+
+ align:start position:0%
+getting back to that pattern work thing
+if you want to go out and practice
+
+ align:start position:0%
+if you want to go out and practice
+ 
+
+ align:start position:0%
+if you want to go out and practice
+takeoffs and landings at night if you
+
+ align:start position:0%
+takeoffs and landings at night if you
+ 
+
+ align:start position:0%
+takeoffs and landings at night if you
+stay within half a mile of the runway
+
+ align:start position:0%
+stay within half a mile of the runway
+ 
+
+ align:start position:0%
+stay within half a mile of the runway
+you can go right down to one mile of
+
+ align:start position:0%
+you can go right down to one mile of
+ 
+
+ align:start position:0%
+you can go right down to one mile of
+visibility and right off right up to the
+
+ align:start position:0%
+visibility and right off right up to the
+ 
+
+ align:start position:0%
+visibility and right off right up to the
+clouds
+
+ align:start position:0%
+clouds
+ 
+
+ align:start position:0%
+clouds
+okay here's that chart again learn it
+
+ align:start position:0%
+okay here's that chart again learn it
+ 
+
+ align:start position:0%
+okay here's that chart again learn it
+know it special VFR actually if you're
+
+ align:start position:0%
+know it special VFR actually if you're
+ 
+
+ align:start position:0%
+know it special VFR actually if you're
+at Hanscom and the weather is below the
+
+ align:start position:0%
+at Hanscom and the weather is below the
+ 
+
+ align:start position:0%
+at Hanscom and the weather is below the
+basic minimums and you say you want to
+
+ align:start position:0%
+basic minimums and you say you want to
+ 
+
+ align:start position:0%
+basic minimums and you say you want to
+do some pattern work anyway either in a
+
+ align:start position:0%
+do some pattern work anyway either in a
+ 
+
+ align:start position:0%
+do some pattern work anyway either in a
+helicopter or an airplane you can
+
+ align:start position:0%
+helicopter or an airplane you can
+ 
+
+ align:start position:0%
+helicopter or an airplane you can
+request they can't offer it but you can
+
+ align:start position:0%
+request they can't offer it but you can
+ 
+
+ align:start position:0%
+request they can't offer it but you can
+request a special VFR clearance and
+
+ align:start position:0%
+request a special VFR clearance and
+ 
+
+ align:start position:0%
+request a special VFR clearance and
+they'll say okay there's not too much
+
+ align:start position:0%
+they'll say okay there's not too much
+ 
+
+ align:start position:0%
+they'll say okay there's not too much
+higher traffic right now so you you know
+
+ align:start position:0%
+higher traffic right now so you you know
+ 
+
+ align:start position:0%
+higher traffic right now so you you know
+take off and land and do your do your
+
+ align:start position:0%
+take off and land and do your do your
+ 
+
+ align:start position:0%
+take off and land and do your do your
+stuff if it's a night you'll have to be
+
+ align:start position:0%
+stuff if it's a night you'll have to be
+ 
+
+ align:start position:0%
+stuff if it's a night you'll have to be
+an IFR pilot basically cirrus publishes
+
+ align:start position:0%
+an IFR pilot basically cirrus publishes
+ 
+
+ align:start position:0%
+an IFR pilot basically cirrus publishes
+this good personal minimum matrix I
+
+ align:start position:0%
+this good personal minimum matrix I
+ 
+
+ align:start position:0%
+this good personal minimum matrix I
+wouldn't say that you have to adopt
+
+ align:start position:0%
+wouldn't say that you have to adopt
+ 
+
+ align:start position:0%
+wouldn't say that you have to adopt
+their specific numbers but I think their
+
+ align:start position:0%
+their specific numbers but I think their
+ 
+
+ align:start position:0%
+their specific numbers but I think their
+way of thinking isn't bad so notice
+
+ align:start position:0%
+way of thinking isn't bad so notice
+ 
+
+ align:start position:0%
+way of thinking isn't bad so notice
+they're saying you know if you are let's
+
+ align:start position:0%
+they're saying you know if you are let's
+ 
+
+ align:start position:0%
+they're saying you know if you are let's
+see an average pilot so you've got you
+
+ align:start position:0%
+see an average pilot so you've got you
+ 
+
+ align:start position:0%
+see an average pilot so you've got you
+know ten IFR hours within the last 90
+
+ align:start position:0%
+know ten IFR hours within the last 90
+ 
+
+ align:start position:0%
+know ten IFR hours within the last 90
+days you've done you know one not on out
+
+ align:start position:0%
+days you've done you know one not on out
+ 
+
+ align:start position:0%
+days you've done you know one not on out
+of it approach within the last 90 days
+
+ align:start position:0%
+of it approach within the last 90 days
+ 
+
+ align:start position:0%
+of it approach within the last 90 days
+I'll go over here and go down to a 500
+
+ align:start position:0%
+I'll go over here and go down to a 500
+ 
+
+ align:start position:0%
+I'll go over here and go down to a 500
+foot ceiling in two miles of visibility
+
+ align:start position:0%
+foot ceiling in two miles of visibility
+ 
+
+ align:start position:0%
+foot ceiling in two miles of visibility
+don't go down to the published approach
+
+ align:start position:0%
+don't go down to the published approach
+ 
+
+ align:start position:0%
+don't go down to the published approach
+minimums which are designed for a two
+
+ align:start position:0%
+minimums which are designed for a two
+ 
+
+ align:start position:0%
+minimums which are designed for a two
+pilot professional crew unless you know
+
+ align:start position:0%
+pilot professional crew unless you know
+ 
+
+ align:start position:0%
+pilot professional crew unless you know
+you're very current you've done a whole
+
+ align:start position:0%
+you're very current you've done a whole
+ 
+
+ align:start position:0%
+you're very current you've done a whole
+bunch of flying in the last 90 days
+
+ align:start position:0%
+bunch of flying in the last 90 days
+ 
+
+ align:start position:0%
+bunch of flying in the last 90 days
+anyway so they just try to fit they try
+
+ align:start position:0%
+anyway so they just try to fit they try
+ 
+
+ align:start position:0%
+anyway so they just try to fit they try
+to say how challenging is this like how
+
+ align:start position:0%
+to say how challenging is this like how
+ 
+
+ align:start position:0%
+to say how challenging is this like how
+experienced are you in general how
+
+ align:start position:0%
+experienced are you in general how
+ 
+
+ align:start position:0%
+experienced are you in general how
+experienced are you recently and come up
+
+ align:start position:0%
+experienced are you recently and come up
+ 
+
+ align:start position:0%
+experienced are you recently and come up
+with some numbers so again you can pull
+
+ align:start position:0%
+with some numbers so again you can pull
+ 
+
+ align:start position:0%
+with some numbers so again you can pull
+this out of the slide and just to
+
+ align:start position:0%
+this out of the slide and just to
+ 
+
+ align:start position:0%
+this out of the slide and just to
+clarify what we're talking about when we
+
+ align:start position:0%
+clarify what we're talking about when we
+ 
+
+ align:start position:0%
+clarify what we're talking about when we
+talk about personal minimums so there
+
+ align:start position:0%
+talk about personal minimums so there
+ 
+
+ align:start position:0%
+talk about personal minimums so there
+there are minimums that you have to know
+
+ align:start position:0%
+there are minimums that you have to know
+ 
+
+ align:start position:0%
+there are minimums that you have to know
+for the FAA exam like we were just
+
+ align:start position:0%
+for the FAA exam like we were just
+ 
+
+ align:start position:0%
+for the FAA exam like we were just
+talking about in terms of the minimum
+
+ align:start position:0%
+talking about in terms of the minimum
+ 
+
+ align:start position:0%
+talking about in terms of the minimum
+visibility that must be
+
+ align:start position:0%
+visibility that must be
+ 
+
+ align:start position:0%
+visibility that must be
+there in order to for you to fly in
+
+ align:start position:0%
+there in order to for you to fly in
+ 
+
+ align:start position:0%
+there in order to for you to fly in
+certain classes of airspace but then
+
+ align:start position:0%
+certain classes of airspace but then
+ 
+
+ align:start position:0%
+certain classes of airspace but then
+there are also minimums that you set on
+
+ align:start position:0%
+there are also minimums that you set on
+ 
+
+ align:start position:0%
+there are also minimums that you set on
+yourself to be a safe pilot and to be
+
+ align:start position:0%
+yourself to be a safe pilot and to be
+ 
+
+ align:start position:0%
+yourself to be a safe pilot and to be
+kind of knowledgeable about what your
+
+ align:start position:0%
+kind of knowledgeable about what your
+ 
+
+ align:start position:0%
+kind of knowledgeable about what your
+restrictions and what your experience
+
+ align:start position:0%
+restrictions and what your experience
+ 
+
+ align:start position:0%
+restrictions and what your experience
+and what your currency is so for example
+
+ align:start position:0%
+and what your currency is so for example
+ 
+
+ align:start position:0%
+and what your currency is so for example
+we talked about crosswind so there isn't
+
+ align:start position:0%
+we talked about crosswind so there isn't
+ 
+
+ align:start position:0%
+we talked about crosswind so there isn't
+an FA reg necessarily you know as long
+
+ align:start position:0%
+an FA reg necessarily you know as long
+ 
+
+ align:start position:0%
+an FA reg necessarily you know as long
+as it's within your aircraft's operating
+
+ align:start position:0%
+as it's within your aircraft's operating
+ 
+
+ align:start position:0%
+as it's within your aircraft's operating
+conditions there's no specific reason
+
+ align:start position:0%
+conditions there's no specific reason
+ 
+
+ align:start position:0%
+conditions there's no specific reason
+why you know a 15 or 20 knot crosswind
+
+ align:start position:0%
+why you know a 15 or 20 knot crosswind
+ 
+
+ align:start position:0%
+why you know a 15 or 20 knot crosswind
+is a problem but maybe you're not very
+
+ align:start position:0%
+is a problem but maybe you're not very
+ 
+
+ align:start position:0%
+is a problem but maybe you're not very
+comfortable with it you haven't done a
+
+ align:start position:0%
+comfortable with it you haven't done a
+ 
+
+ align:start position:0%
+comfortable with it you haven't done a
+lot of slips recently you're still
+
+ align:start position:0%
+lot of slips recently you're still
+ 
+
+ align:start position:0%
+lot of slips recently you're still
+getting used to your aircraft so you
+
+ align:start position:0%
+getting used to your aircraft so you
+ 
+
+ align:start position:0%
+getting used to your aircraft so you
+might say you know a smaller crosswind
+
+ align:start position:0%
+might say you know a smaller crosswind
+ 
+
+ align:start position:0%
+might say you know a smaller crosswind
+or gusting winds would be appropriate
+
+ align:start position:0%
+or gusting winds would be appropriate
+ 
+
+ align:start position:0%
+or gusting winds would be appropriate
+for you to land it so that's setting a
+
+ align:start position:0%
+for you to land it so that's setting a
+ 
+
+ align:start position:0%
+for you to land it so that's setting a
+personal minimum on yourself and this
+
+ align:start position:0%
+personal minimum on yourself and this
+ 
+
+ align:start position:0%
+personal minimum on yourself and this
+this is an example of personal minimums
+
+ align:start position:0%
+this is an example of personal minimums
+ 
+
+ align:start position:0%
+this is an example of personal minimums
+based on your experience and your
+
+ align:start position:0%
+based on your experience and your
+ 
+
+ align:start position:0%
+based on your experience and your
+currency and the FAA will never suggest
+
+ align:start position:0%
+currency and the FAA will never suggest
+ 
+
+ align:start position:0%
+currency and the FAA will never suggest
+this but the appropriate escape from you
+
+ align:start position:0%
+this but the appropriate escape from you
+ 
+
+ align:start position:0%
+this but the appropriate escape from you
+know a challenging situation that you
+
+ align:start position:0%
+know a challenging situation that you
+ 
+
+ align:start position:0%
+know a challenging situation that you
+think might be on the edge of safety is
+
+ align:start position:0%
+think might be on the edge of safety is
+ 
+
+ align:start position:0%
+think might be on the edge of safety is
+to rent the five-seat sr22 instead of
+
+ align:start position:0%
+to rent the five-seat sr22 instead of
+ 
+
+ align:start position:0%
+to rent the five-seat sr22 instead of
+the forc'd sr20 and go with an
+
+ align:start position:0%
+the forc'd sr20 and go with an
+ 
+
+ align:start position:0%
+the forc'd sr20 and go with an
+instructor so it's as easy as that
+
+ align:start position:0%
+instructor so it's as easy as that
+ 
+
+ align:start position:0%
+instructor so it's as easy as that
+ok remember this was confusing they use
+
+ align:start position:0%
+ok remember this was confusing they use
+ 
+
+ align:start position:0%
+ok remember this was confusing they use
+category in class to mean totally two
+
+ align:start position:0%
+category in class to mean totally two
+ 
+
+ align:start position:0%
+category in class to mean totally two
+totally different things for getting
+
+ align:start position:0%
+totally different things for getting
+ 
+
+ align:start position:0%
+totally different things for getting
+your pilot's certificate the category is
+
+ align:start position:0%
+your pilot's certificate the category is
+ 
+
+ align:start position:0%
+your pilot's certificate the category is
+there on the left something like an
+
+ align:start position:0%
+there on the left something like an
+ 
+
+ align:start position:0%
+there on the left something like an
+airplane versus a rotorcraft
+
+ align:start position:0%
+airplane versus a rotorcraft
+ 
+
+ align:start position:0%
+airplane versus a rotorcraft
+and the class would be you know multi
+
+ align:start position:0%
+and the class would be you know multi
+ 
+
+ align:start position:0%
+and the class would be you know multi
+engine land versus helicopter category
+
+ align:start position:0%
+engine land versus helicopter category
+ 
+
+ align:start position:0%
+engine land versus helicopter category
+class but then for aircraft they do
+
+ align:start position:0%
+class but then for aircraft they do
+ 
+
+ align:start position:0%
+class but then for aircraft they do
+something totally different and they say
+
+ align:start position:0%
+something totally different and they say
+ 
+
+ align:start position:0%
+something totally different and they say
+category would be you know normal
+
+ align:start position:0%
+category would be you know normal
+ 
+
+ align:start position:0%
+category would be you know normal
+category or acrobatic and class would be
+
+ align:start position:0%
+category or acrobatic and class would be
+ 
+
+ align:start position:0%
+category or acrobatic and class would be
+airplane so they may ask you about this
+
+ align:start position:0%
+airplane so they may ask you about this
+ 
+
+ align:start position:0%
+airplane so they may ask you about this
+just because they like the torque for
+
+ align:start position:0%
+just because they like the torque for
+ 
+
+ align:start position:0%
+just because they like the torque for
+you the four forces of flight remember
+
+ align:start position:0%
+you the four forces of flight remember
+ 
+
+ align:start position:0%
+you the four forces of flight remember
+these Tina talked about them if you're
+
+ align:start position:0%
+these Tina talked about them if you're
+ 
+
+ align:start position:0%
+these Tina talked about them if you're
+just bombing along straight and level
+
+ align:start position:0%
+just bombing along straight and level
+ 
+
+ align:start position:0%
+just bombing along straight and level
+not accelerating then they're gonna all
+
+ align:start position:0%
+not accelerating then they're gonna all
+ 
+
+ align:start position:0%
+not accelerating then they're gonna all
+be in balance because F equals MA
+
+ align:start position:0%
+be in balance because F equals MA
+ 
+
+ align:start position:0%
+be in balance because F equals MA
+equals whatever get remembers math
+
+ align:start position:0%
+equals whatever get remembers math
+ 
+
+ align:start position:0%
+equals whatever get remembers math
+anyway F equals MA I know that much
+
+ align:start position:0%
+anyway F equals MA I know that much
+ 
+
+ align:start position:0%
+anyway F equals MA I know that much
+remember the three axes they'll ask you
+
+ align:start position:0%
+remember the three axes they'll ask you
+ 
+
+ align:start position:0%
+remember the three axes they'll ask you
+about this on the test usually in
+
+ align:start position:0%
+about this on the test usually in
+ 
+
+ align:start position:0%
+about this on the test usually in
+combination with some other stuff so
+
+ align:start position:0%
+combination with some other stuff so
+ 
+
+ align:start position:0%
+combination with some other stuff so
+rotation about the vertical axis is
+
+ align:start position:0%
+rotation about the vertical axis is
+ 
+
+ align:start position:0%
+rotation about the vertical axis is
+going to be yaw rotation about the this
+
+ align:start position:0%
+going to be yaw rotation about the this
+ 
+
+ align:start position:0%
+going to be yaw rotation about the this
+is complicated let's see rotation about
+
+ align:start position:0%
+is complicated let's see rotation about
+ 
+
+ align:start position:0%
+is complicated let's see rotation about
+the lateral axis is going to be pitch
+
+ align:start position:0%
+the lateral axis is going to be pitch
+ 
+
+ align:start position:0%
+the lateral axis is going to be pitch
+rotation around the longitudinal axis I
+
+ align:start position:0%
+rotation around the longitudinal axis I
+ 
+
+ align:start position:0%
+rotation around the longitudinal axis I
+believe will be roll so that's a little
+
+ align:start position:0%
+believe will be roll so that's a little
+ 
+
+ align:start position:0%
+believe will be roll so that's a little
+bit confusing since yeah here we have it
+
+ align:start position:0%
+bit confusing since yeah here we have it
+ 
+
+ align:start position:0%
+bit confusing since yeah here we have it
+pitch roll yaw right so think about it
+
+ align:start position:0%
+pitch roll yaw right so think about it
+ 
+
+ align:start position:0%
+pitch roll yaw right so think about it
+roll is really the lateral motion but
+
+ align:start position:0%
+roll is really the lateral motion but
+ 
+
+ align:start position:0%
+roll is really the lateral motion but
+it's around the longitudinal axis so
+
+ align:start position:0%
+it's around the longitudinal axis so
+ 
+
+ align:start position:0%
+it's around the longitudinal axis so
+don't get confused there remember why
+
+ align:start position:0%
+don't get confused there remember why
+ 
+
+ align:start position:0%
+don't get confused there remember why
+Johnny Cessna can't hover is also a
+
+ align:start position:0%
+Johnny Cessna can't hover is also a
+ 
+
+ align:start position:0%
+Johnny Cessna can't hover is also a
+limit for this is this limits everything
+
+ align:start position:0%
+limit for this is this limits everything
+ 
+
+ align:start position:0%
+limit for this is this limits everything
+basically the stalling angle of attack
+
+ align:start position:0%
+basically the stalling angle of attack
+ 
+
+ align:start position:0%
+basically the stalling angle of attack
+is why you need a helicopter if you want
+
+ align:start position:0%
+is why you need a helicopter if you want
+ 
+
+ align:start position:0%
+is why you need a helicopter if you want
+to hover and it is why you need to
+
+ align:start position:0%
+to hover and it is why you need to
+ 
+
+ align:start position:0%
+to hover and it is why you need to
+maintain a reasonable airspeed when
+
+ align:start position:0%
+maintain a reasonable airspeed when
+ 
+
+ align:start position:0%
+maintain a reasonable airspeed when
+you're a landing and it's also it limits
+
+ align:start position:0%
+you're a landing and it's also it limits
+ 
+
+ align:start position:0%
+you're a landing and it's also it limits
+your runway right if you had an airplane
+
+ align:start position:0%
+your runway right if you had an airplane
+ 
+
+ align:start position:0%
+your runway right if you had an airplane
+that didn't stall till it reached some
+
+ align:start position:0%
+that didn't stall till it reached some
+ 
+
+ align:start position:0%
+that didn't stall till it reached some
+crazy angle attack you could probably
+
+ align:start position:0%
+crazy angle attack you could probably
+ 
+
+ align:start position:0%
+crazy angle attack you could probably
+take off and land in 50 feet right and
+
+ align:start position:0%
+take off and land in 50 feet right and
+ 
+
+ align:start position:0%
+take off and land in 50 feet right and
+remember that we talked about even a
+
+ align:start position:0%
+remember that we talked about even a
+ 
+
+ align:start position:0%
+remember that we talked about even a
+paper airplane can generate lift so it's
+
+ align:start position:0%
+paper airplane can generate lift so it's
+ 
+
+ align:start position:0%
+paper airplane can generate lift so it's
+not about the shape of the cross section
+
+ align:start position:0%
+not about the shape of the cross section
+ 
+
+ align:start position:0%
+not about the shape of the cross section
+of the wing that is making you be able
+
+ align:start position:0%
+of the wing that is making you be able
+ 
+
+ align:start position:0%
+of the wing that is making you be able
+to generate lift it's the angle of
+
+ align:start position:0%
+to generate lift it's the angle of
+ 
+
+ align:start position:0%
+to generate lift it's the angle of
+attack and your ability to deflect air
+
+ align:start position:0%
+attack and your ability to deflect air
+ 
+
+ align:start position:0%
+attack and your ability to deflect air
+molecules down that's what generates
+
+ align:start position:0%
+molecules down that's what generates
+ 
+
+ align:start position:0%
+molecules down that's what generates
+lift that shape of the airfoil is just
+
+ align:start position:0%
+lift that shape of the airfoil is just
+ 
+
+ align:start position:0%
+lift that shape of the airfoil is just
+what Philip was saying that allows you
+
+ align:start position:0%
+what Philip was saying that allows you
+ 
+
+ align:start position:0%
+what Philip was saying that allows you
+to have the stall speed be lowered all
+
+ align:start position:0%
+to have the stall speed be lowered all
+ 
+
+ align:start position:0%
+to have the stall speed be lowered all
+right so remember your left-turning
+
+ align:start position:0%
+right so remember your left-turning
+ 
+
+ align:start position:0%
+right so remember your left-turning
+tendencies mostly you just remember that
+
+ align:start position:0%
+tendencies mostly you just remember that
+ 
+
+ align:start position:0%
+tendencies mostly you just remember that
+you need right rudder and a couple
+
+ align:start position:0%
+you need right rudder and a couple
+ 
+
+ align:start position:0%
+you need right rudder and a couple
+questions had come up on gyroscopic
+
+ align:start position:0%
+questions had come up on gyroscopic
+ 
+
+ align:start position:0%
+questions had come up on gyroscopic
+precession so I added two videos about
+
+ align:start position:0%
+precession so I added two videos about
+ 
+
+ align:start position:0%
+precession so I added two videos about
+gyroscopes to help you understand
+
+ align:start position:0%
+gyroscopes to help you understand
+ 
+
+ align:start position:0%
+gyroscopes to help you understand
+gyroscopic precession and why that force
+
+ align:start position:0%
+gyroscopic precession and why that force
+ 
+
+ align:start position:0%
+gyroscopic precession and why that force
+is applied 90 degrees later and
+
+ align:start position:0%
+is applied 90 degrees later and
+ 
+
+ align:start position:0%
+is applied 90 degrees later and
+those are really fun videos you can look
+
+ align:start position:0%
+those are really fun videos you can look
+ 
+
+ align:start position:0%
+those are really fun videos you can look
+at their in the slide deck called QA and
+
+ align:start position:0%
+at their in the slide deck called QA and
+ 
+
+ align:start position:0%
+at their in the slide deck called QA and
+review ok so let's go back to the
+
+ align:start position:0%
+review ok so let's go back to the
+ 
+
+ align:start position:0%
+review ok so let's go back to the
+altitudes so true altitude is your
+
+ align:start position:0%
+altitudes so true altitude is your
+ 
+
+ align:start position:0%
+altitudes so true altitude is your
+actual height above sea level this is
+
+ align:start position:0%
+actual height above sea level this is
+ 
+
+ align:start position:0%
+actual height above sea level this is
+what's important if you want to get over
+
+ align:start position:0%
+what's important if you want to get over
+ 
+
+ align:start position:0%
+what's important if you want to get over
+on mountain because the altitude on the
+
+ align:start position:0%
+on mountain because the altitude on the
+ 
+
+ align:start position:0%
+on mountain because the altitude on the
+chart for the mountain is also the
+
+ align:start position:0%
+chart for the mountain is also the
+ 
+
+ align:start position:0%
+chart for the mountain is also the
+actual height above sea level indicated
+
+ align:start position:0%
+actual height above sea level indicated
+ 
+
+ align:start position:0%
+actual height above sea level indicated
+it's what your L Timoner shows if you're
+
+ align:start position:0%
+it's what your L Timoner shows if you're
+ 
+
+ align:start position:0%
+it's what your L Timoner shows if you're
+below 18,000 feet and it's not some
+
+ align:start position:0%
+below 18,000 feet and it's not some
+ 
+
+ align:start position:0%
+below 18,000 feet and it's not some
+insane temperature and you've got a
+
+ align:start position:0%
+insane temperature and you've got a
+ 
+
+ align:start position:0%
+insane temperature and you've got a
+current altimeter setting from air
+
+ align:start position:0%
+current altimeter setting from air
+ 
+
+ align:start position:0%
+current altimeter setting from air
+traffic control as you fly along with
+
+ align:start position:0%
+traffic control as you fly along with
+ 
+
+ align:start position:0%
+traffic control as you fly along with
+VFR advisories they'll keep updating you
+
+ align:start position:0%
+VFR advisories they'll keep updating you
+ 
+
+ align:start position:0%
+VFR advisories they'll keep updating you
+with altitudes if you're not talking to
+
+ align:start position:0%
+with altitudes if you're not talking to
+ 
+
+ align:start position:0%
+with altitudes if you're not talking to
+ATC you know you may to nin to the
+
+ align:start position:0%
+ATC you know you may to nin to the
+ 
+
+ align:start position:0%
+ATC you know you may to nin to the
+airports that you're flying over to get
+
+ align:start position:0%
+airports that you're flying over to get
+ 
+
+ align:start position:0%
+airports that you're flying over to get
+the altimeter there if you have your
+
+ align:start position:0%
+the altimeter there if you have your
+ 
+
+ align:start position:0%
+the altimeter there if you have your
+correctly set altimeter it should be
+
+ align:start position:0%
+correctly set altimeter it should be
+ 
+
+ align:start position:0%
+correctly set altimeter it should be
+pretty close to your true altitude but
+
+ align:start position:0%
+pretty close to your true altitude but
+ 
+
+ align:start position:0%
+pretty close to your true altitude but
+and the GPS will give it to you as well
+
+ align:start position:0%
+and the GPS will give it to you as well
+ 
+
+ align:start position:0%
+and the GPS will give it to you as well
+all right absolute height above the
+
+ align:start position:0%
+all right absolute height above the
+ 
+
+ align:start position:0%
+all right absolute height above the
+ground I don't think that's ever really
+
+ align:start position:0%
+ground I don't think that's ever really
+ 
+
+ align:start position:0%
+ground I don't think that's ever really
+relevant pressure altitude is what you
+
+ align:start position:0%
+relevant pressure altitude is what you
+ 
+
+ align:start position:0%
+relevant pressure altitude is what you
+see if you tune your altimeter to to
+
+ align:start position:0%
+see if you tune your altimeter to to
+ 
+
+ align:start position:0%
+see if you tune your altimeter to to
+nine or nine or two density is critical
+
+ align:start position:0%
+nine or nine or two density is critical
+ 
+
+ align:start position:0%
+nine or nine or two density is critical
+for determining performance of both the
+
+ align:start position:0%
+for determining performance of both the
+ 
+
+ align:start position:0%
+for determining performance of both the
+aircraft in the engine so that's a
+
+ align:start position:0%
+aircraft in the engine so that's a
+ 
+
+ align:start position:0%
+aircraft in the engine so that's a
+measure of you know how many actual
+
+ align:start position:0%
+measure of you know how many actual
+ 
+
+ align:start position:0%
+measure of you know how many actual
+molecules of air are there gonna be in a
+
+ align:start position:0%
+molecules of air are there gonna be in a
+ 
+
+ align:start position:0%
+molecules of air are there gonna be in a
+one liter cylinder for example know your
+
+ align:start position:0%
+one liter cylinder for example know your
+ 
+
+ align:start position:0%
+one liter cylinder for example know your
+taxiway and runway markings this has
+
+ align:start position:0%
+taxiway and runway markings this has
+ 
+
+ align:start position:0%
+taxiway and runway markings this has
+practical value and also test value one
+
+ align:start position:0%
+practical value and also test value one
+ 
+
+ align:start position:0%
+practical value and also test value one
+easy thing to remember is if you're
+
+ align:start position:0%
+easy thing to remember is if you're
+ 
+
+ align:start position:0%
+easy thing to remember is if you're
+driving along a taxiway in your aircraft
+
+ align:start position:0%
+driving along a taxiway in your aircraft
+ 
+
+ align:start position:0%
+driving along a taxiway in your aircraft
+you will see yellow paint on a black pay
+
+ align:start position:0%
+you will see yellow paint on a black pay
+ 
+
+ align:start position:0%
+you will see yellow paint on a black pay
+of surface so that sign tells you what
+
+ align:start position:0%
+of surface so that sign tells you what
+ 
+
+ align:start position:0%
+of surface so that sign tells you what
+taxiway that you're actually on just
+
+ align:start position:0%
+taxiway that you're actually on just
+ 
+
+ align:start position:0%
+taxiway that you're actually on just
+like the real-world experience of yellow
+
+ align:start position:0%
+like the real-world experience of yellow
+ 
+
+ align:start position:0%
+like the real-world experience of yellow
+paint on black everything else is kind
+
+ align:start position:0%
+paint on black everything else is kind
+ 
+
+ align:start position:0%
+paint on black everything else is kind
+of reasonably self-explanatory they
+
+ align:start position:0%
+of reasonably self-explanatory they
+ 
+
+ align:start position:0%
+of reasonably self-explanatory they
+probably even though if you're not an
+
+ align:start position:0%
+probably even though if you're not an
+ 
+
+ align:start position:0%
+probably even though if you're not an
+instrument pilot they want you to know
+
+ align:start position:0%
+instrument pilot they want you to know
+ 
+
+ align:start position:0%
+instrument pilot they want you to know
+about this ILS hold short line so if
+
+ align:start position:0%
+about this ILS hold short line so if
+ 
+
+ align:start position:0%
+about this ILS hold short line so if
+it's kind of bad weather conditions and
+
+ align:start position:0%
+it's kind of bad weather conditions and
+ 
+
+ align:start position:0%
+it's kind of bad weather conditions and
+they're using the ILS they don't want
+
+ align:start position:0%
+they're using the ILS they don't want
+ 
+
+ align:start position:0%
+they're using the ILS they don't want
+you going beyond there because your
+
+ align:start position:0%
+you going beyond there because your
+ 
+
+ align:start position:0%
+you going beyond there because your
+metal airplane might interfere with the
+
+ align:start position:0%
+metal airplane might interfere with the
+ 
+
+ align:start position:0%
+metal airplane might interfere with the
+radio beams that are being sent up
+
+ align:start position:0%
+radio beams that are being sent up
+ 
+
+ align:start position:0%
+radio beams that are being sent up
+- landing IFR airplanes remember L over
+
+ align:start position:0%
+- landing IFR airplanes remember L over
+ 
+
+ align:start position:0%
+- landing IFR airplanes remember L over
+D max for a best glide speed so all
+
+ align:start position:0%
+D max for a best glide speed so all
+ 
+
+ align:start position:0%
+D max for a best glide speed so all
+these climb speeds guides beads etc are
+
+ align:start position:0%
+these climb speeds guides beads etc are
+ 
+
+ align:start position:0%
+these climb speeds guides beads etc are
+driven off of the points at which the
+
+ align:start position:0%
+driven off of the points at which the
+ 
+
+ align:start position:0%
+driven off of the points at which the
+various drags reach a minimum or a
+
+ align:start position:0%
+various drags reach a minimum or a
+ 
+
+ align:start position:0%
+various drags reach a minimum or a
+minimum per per mile traveled
+
+ align:start position:0%
+minimum per per mile traveled
+ 
+
+ align:start position:0%
+minimum per per mile traveled
+thunderstorms
+
+ align:start position:0%
+thunderstorms
+ 
+
+ align:start position:0%
+thunderstorms
+the one thing you I hope you do remember
+
+ align:start position:0%
+the one thing you I hope you do remember
+ 
+
+ align:start position:0%
+the one thing you I hope you do remember
+is that everything is bad about
+
+ align:start position:0%
+is that everything is bad about
+ 
+
+ align:start position:0%
+is that everything is bad about
+convective clouds unstable air leads to
+
+ align:start position:0%
+convective clouds unstable air leads to
+ 
+
+ align:start position:0%
+convective clouds unstable air leads to
+cumulus clouds they can become
+
+ align:start position:0%
+cumulus clouds they can become
+ 
+
+ align:start position:0%
+cumulus clouds they can become
+cumulonimbus clouds and now you have a
+
+ align:start position:0%
+cumulonimbus clouds and now you have a
+ 
+
+ align:start position:0%
+cumulonimbus clouds and now you have a
+really bad hazard aviation with terrible
+
+ align:start position:0%
+really bad hazard aviation with terrible
+ 
+
+ align:start position:0%
+really bad hazard aviation with terrible
+icing terrible turbulence may be hail so
+
+ align:start position:0%
+icing terrible turbulence may be hail so
+ 
+
+ align:start position:0%
+icing terrible turbulence may be hail so
+the squall line I think they sometimes
+
+ align:start position:0%
+the squall line I think they sometimes
+ 
+
+ align:start position:0%
+the squall line I think they sometimes
+ask about this on the test the frontal
+
+ align:start position:0%
+ask about this on the test the frontal
+ 
+
+ align:start position:0%
+ask about this on the test the frontal
+band of thunderstorms so just you know
+
+ align:start position:0%
+band of thunderstorms so just you know
+ 
+
+ align:start position:0%
+band of thunderstorms so just you know
+it's hard to get around them and you
+
+ align:start position:0%
+it's hard to get around them and you
+ 
+
+ align:start position:0%
+it's hard to get around them and you
+know you may have to go 500 miles out of
+
+ align:start position:0%
+know you may have to go 500 miles out of
+ 
+
+ align:start position:0%
+know you may have to go 500 miles out of
+your way to get around the cold front or
+
+ align:start position:0%
+your way to get around the cold front or
+ 
+
+ align:start position:0%
+your way to get around the cold front or
+hang out on the ground for a few hours
+
+ align:start position:0%
+hang out on the ground for a few hours
+ 
+
+ align:start position:0%
+hang out on the ground for a few hours
+and wait for it to pass
+
+ align:start position:0%
+and wait for it to pass
+ 
+
+ align:start position:0%
+and wait for it to pass
+also just big changes in weather usually
+
+ align:start position:0%
+also just big changes in weather usually
+ 
+
+ align:start position:0%
+also just big changes in weather usually
+are not a good thing so whether it's a
+
+ align:start position:0%
+are not a good thing so whether it's a
+ 
+
+ align:start position:0%
+are not a good thing so whether it's a
+big change in the barometric pressure or
+
+ align:start position:0%
+big change in the barometric pressure or
+ 
+
+ align:start position:0%
+big change in the barometric pressure or
+as we saw from yesterday today to today
+
+ align:start position:0%
+as we saw from yesterday today to today
+ 
+
+ align:start position:0%
+as we saw from yesterday today to today
+like a 4050 degree increase in the
+
+ align:start position:0%
+like a 4050 degree increase in the
+ 
+
+ align:start position:0%
+like a 4050 degree increase in the
+temperature it's going to be accompanied
+
+ align:start position:0%
+temperature it's going to be accompanied
+ 
+
+ align:start position:0%
+temperature it's going to be accompanied
+by massive gusting winds today is not a
+
+ align:start position:0%
+by massive gusting winds today is not a
+ 
+
+ align:start position:0%
+by massive gusting winds today is not a
+good day to go flying yeah although
+
+ align:start position:0%
+good day to go flying yeah although
+ 
+
+ align:start position:0%
+good day to go flying yeah although
+actually it might not just be the day it
+
+ align:start position:0%
+actually it might not just be the day it
+ 
+
+ align:start position:0%
+actually it might not just be the day it
+might be you know now referring the
+
+ align:start position:0%
+might be you know now referring the
+ 
+
+ align:start position:0%
+might be you know now referring the
+helicopter from Los Angeles back to
+
+ align:start position:0%
+helicopter from Los Angeles back to
+ 
+
+ align:start position:0%
+helicopter from Los Angeles back to
+Boston and you know there was a
+
+ align:start position:0%
+Boston and you know there was a
+ 
+
+ align:start position:0%
+Boston and you know there was a
+thunderstorm coming in so we just landed
+
+ align:start position:0%
+thunderstorm coming in so we just landed
+ 
+
+ align:start position:0%
+thunderstorm coming in so we just landed
+in an airport it was probably gusting
+
+ align:start position:0%
+in an airport it was probably gusting
+ 
+
+ align:start position:0%
+in an airport it was probably gusting
+about 30 knots at the time which isn't
+
+ align:start position:0%
+about 30 knots at the time which isn't
+ 
+
+ align:start position:0%
+about 30 knots at the time which isn't
+that bad for Robinson the four-seat
+
+ align:start position:0%
+that bad for Robinson the four-seat
+ 
+
+ align:start position:0%
+that bad for Robinson the four-seat
+Robinson but the helicopter and a hangar
+
+ align:start position:0%
+Robinson but the helicopter and a hangar
+ 
+
+ align:start position:0%
+Robinson but the helicopter and a hangar
+you know there's a huge storm and the
+
+ align:start position:0%
+you know there's a huge storm and the
+ 
+
+ align:start position:0%
+you know there's a huge storm and the
+two hours later later we took off in
+
+ align:start position:0%
+two hours later later we took off in
+ 
+
+ align:start position:0%
+two hours later later we took off in
+beautiful weather and continued our
+
+ align:start position:0%
+beautiful weather and continued our
+ 
+
+ align:start position:0%
+beautiful weather and continued our
+flight so don't you know there is an
+
+ align:start position:0%
+flight so don't you know there is an
+ 
+
+ align:start position:0%
+flight so don't you know there is an
+airport usually every 10 or 15 minutes
+
+ align:start position:0%
+airport usually every 10 or 15 minutes
+ 
+
+ align:start position:0%
+airport usually every 10 or 15 minutes
+of flight time so take advantage of that
+
+ align:start position:0%
+of flight time so take advantage of that
+ 
+
+ align:start position:0%
+of flight time so take advantage of that
+if things are getting beyond your
+
+ align:start position:0%
+if things are getting beyond your
+ 
+
+ align:start position:0%
+if things are getting beyond your
+comfort zone don't just blindly continue
+
+ align:start position:0%
+comfort zone don't just blindly continue
+ 
+
+ align:start position:0%
+comfort zone don't just blindly continue
+to your destination so remember the lee
+
+ align:start position:0%
+to your destination so remember the lee
+ 
+
+ align:start position:0%
+to your destination so remember the lee
+side of mountains is where you can get a
+
+ align:start position:0%
+side of mountains is where you can get a
+ 
+
+ align:start position:0%
+side of mountains is where you can get a
+lot of turbulence and downdrafts a
+
+ align:start position:0%
+lot of turbulence and downdrafts a
+ 
+
+ align:start position:0%
+lot of turbulence and downdrafts a
+little airplane doesn't have a whole lot
+
+ align:start position:0%
+little airplane doesn't have a whole lot
+ 
+
+ align:start position:0%
+little airplane doesn't have a whole lot
+of kind performance usually especially
+
+ align:start position:0%
+of kind performance usually especially
+ 
+
+ align:start position:0%
+of kind performance usually especially
+up in higher altitudes
+
+ align:start position:0%
+up in higher altitudes
+ 
+
+ align:start position:0%
+up in higher altitudes
+so be cautious about crossing big
+
+ align:start position:0%
+so be cautious about crossing big
+ 
+
+ align:start position:0%
+so be cautious about crossing big
+mountain ranges unless the winds law
+
+ align:start position:0%
+mountain ranges unless the winds law
+ 
+
+ align:start position:0%
+mountain ranges unless the winds law
+forecast is for very light winds indeed
+
+ align:start position:0%
+forecast is for very light winds indeed
+ 
+
+ align:start position:0%
+forecast is for very light winds indeed
+icing also super bad again as the VFR
+
+ align:start position:0%
+icing also super bad again as the VFR
+ 
+
+ align:start position:0%
+icing also super bad again as the VFR
+pilots you shouldn't have to worry about
+
+ align:start position:0%
+pilots you shouldn't have to worry about
+ 
+
+ align:start position:0%
+pilots you shouldn't have to worry about
+this once you get into instrument flying
+
+ align:start position:0%
+this once you get into instrument flying
+ 
+
+ align:start position:0%
+this once you get into instrument flying
+that's a help a lot of you will this is
+
+ align:start position:0%
+that's a help a lot of you will this is
+ 
+
+ align:start position:0%
+that's a help a lot of you will this is
+really what limits your ability to
+
+ align:start position:0%
+really what limits your ability to
+ 
+
+ align:start position:0%
+really what limits your ability to
+travel around in a piper Cessna or
+
+ align:start position:0%
+travel around in a piper Cessna or
+ 
+
+ align:start position:0%
+travel around in a piper Cessna or
+Cirrus during the winter and shoulder
+
+ align:start position:0%
+Cirrus during the winter and shoulder
+ 
+
+ align:start position:0%
+Cirrus during the winter and shoulder
+seasons remember how to read the meats
+
+ align:start position:0%
+seasons remember how to read the meats
+ 
+
+ align:start position:0%
+seasons remember how to read the meats
+are so this is back to Peachtree DeKalb
+
+ align:start position:0%
+are so this is back to Peachtree DeKalb
+ 
+
+ align:start position:0%
+are so this is back to Peachtree DeKalb
+Airport in Atlanta so there's it's the
+
+ align:start position:0%
+Airport in Atlanta so there's it's the
+ 
+
+ align:start position:0%
+Airport in Atlanta so there's it's the
+16th at 16 53 so about almost 5 p.m. in
+
+ align:start position:0%
+16th at 16 53 so about almost 5 p.m. in
+ 
+
+ align:start position:0%
+16th at 16 53 so about almost 5 p.m. in
+London Zulu time winds are variable at
+
+ align:start position:0%
+London Zulu time winds are variable at
+ 
+
+ align:start position:0%
+London Zulu time winds are variable at
+410 statute miles of visibility overcast
+
+ align:start position:0%
+410 statute miles of visibility overcast
+ 
+
+ align:start position:0%
+410 statute miles of visibility overcast
+6000 feet that's 6,000 feet above the
+
+ align:start position:0%
+6000 feet that's 6,000 feet above the
+ 
+
+ align:start position:0%
+6000 feet that's 6,000 feet above the
+airport not above sea level
+
+ align:start position:0%
+airport not above sea level
+ 
+
+ align:start position:0%
+airport not above sea level
+temps 14 dew points -7 altimeter three
+
+ align:start position:0%
+temps 14 dew points -7 altimeter three
+ 
+
+ align:start position:0%
+temps 14 dew points -7 altimeter three
+zero one five oh and in the remarks it
+
+ align:start position:0%
+zero one five oh and in the remarks it
+ 
+
+ align:start position:0%
+zero one five oh and in the remarks it
+says the rain ended 46 minutes after the
+
+ align:start position:0%
+says the rain ended 46 minutes after the
+ 
+
+ align:start position:0%
+says the rain ended 46 minutes after the
+hour there you have it
+
+ align:start position:0%
+hour there you have it
+ 
+
+ align:start position:0%
+hour there you have it
+alright human factor summary so you are
+
+ align:start position:0%
+alright human factor summary so you are
+ 
+
+ align:start position:0%
+alright human factor summary so you are
+the weakest link and if you develop some
+
+ align:start position:0%
+the weakest link and if you develop some
+ 
+
+ align:start position:0%
+the weakest link and if you develop some
+personal minimums you'll be way ahead of
+
+ align:start position:0%
+personal minimums you'll be way ahead of
+ 
+
+ align:start position:0%
+personal minimums you'll be way ahead of
+the game
+
+ align:start position:0%
+the game
+ 
+
+ align:start position:0%
+the game
+they should also factor in your recent
+
+ align:start position:0%
+they should also factor in your recent
+ 
+
+ align:start position:0%
+they should also factor in your recent
+experience not just your overall level
+
+ align:start position:0%
+experience not just your overall level
+ 
+
+ align:start position:0%
+experience not just your overall level
+of flying and always remember that it's
+
+ align:start position:0%
+of flying and always remember that it's
+ 
+
+ align:start position:0%
+of flying and always remember that it's
+a big aviation community there's a lot
+
+ align:start position:0%
+a big aviation community there's a lot
+ 
+
+ align:start position:0%
+a big aviation community there's a lot
+of people are happy to go flying
+
+ align:start position:0%
+of people are happy to go flying
+ 
+
+ align:start position:0%
+of people are happy to go flying
+you can send mail to the members of the
+
+ align:start position:0%
+you can send mail to the members of the
+ 
+
+ align:start position:0%
+you can send mail to the members of the
+MIT Flying Club and just take a copilot
+
+ align:start position:0%
+MIT Flying Club and just take a copilot
+ 
+
+ align:start position:0%
+MIT Flying Club and just take a copilot
+that's how the airlines have cut risk
+
+ align:start position:0%
+that's how the airlines have cut risk
+ 
+
+ align:start position:0%
+that's how the airlines have cut risk
+almost to zero magnetic variation this
+
+ align:start position:0%
+almost to zero magnetic variation this
+ 
+
+ align:start position:0%
+almost to zero magnetic variation this
+is kind of a topic that tends to snag
+
+ align:start position:0%
+is kind of a topic that tends to snag
+ 
+
+ align:start position:0%
+is kind of a topic that tends to snag
+people on the knowledge test so just
+
+ align:start position:0%
+people on the knowledge test so just
+ 
+
+ align:start position:0%
+people on the knowledge test so just
+remember you can read arrived it from
+
+ align:start position:0%
+remember you can read arrived it from
+ 
+
+ align:start position:0%
+remember you can read arrived it from
+the vor if you ever get stuck and East
+
+ align:start position:0%
+the vor if you ever get stuck and East
+ 
+
+ align:start position:0%
+the vor if you ever get stuck and East
+is leased West is best deviation then
+
+ align:start position:0%
+is leased West is best deviation then
+ 
+
+ align:start position:0%
+is leased West is best deviation then
+don't don't get deviation and variation
+
+ align:start position:0%
+don't don't get deviation and variation
+ 
+
+ align:start position:0%
+don't don't get deviation and variation
+confused so deviation remember
+
+ align:start position:0%
+confused so deviation remember
+ 
+
+ align:start position:0%
+confused so deviation remember
+is that tiny little correction that's
+
+ align:start position:0%
+is that tiny little correction that's
+ 
+
+ align:start position:0%
+is that tiny little correction that's
+printed right underneath the compass
+
+ align:start position:0%
+printed right underneath the compass
+ 
+
+ align:start position:0%
+printed right underneath the compass
+flight planning tip you saw this slide
+
+ align:start position:0%
+flight planning tip you saw this slide
+ 
+
+ align:start position:0%
+flight planning tip you saw this slide
+earlier even the far 61 and far 91 allow
+
+ align:start position:0%
+earlier even the far 61 and far 91 allow
+ 
+
+ align:start position:0%
+earlier even the far 61 and far 91 allow
+it and doesn't mean it's wise so if you
+
+ align:start position:0%
+it and doesn't mean it's wise so if you
+ 
+
+ align:start position:0%
+it and doesn't mean it's wise so if you
+look at far 121 and far 135 for charter
+
+ align:start position:0%
+look at far 121 and far 135 for charter
+ 
+
+ align:start position:0%
+look at far 121 and far 135 for charter
+and scheduled airline service they show
+
+ align:start position:0%
+and scheduled airline service they show
+ 
+
+ align:start position:0%
+and scheduled airline service they show
+you that there's some extra safety
+
+ align:start position:0%
+you that there's some extra safety
+ 
+
+ align:start position:0%
+you that there's some extra safety
+margins that can be built in night
+
+ align:start position:0%
+margins that can be built in night
+ 
+
+ align:start position:0%
+margins that can be built in night
+flying advice you just heard remember is
+
+ align:start position:0%
+flying advice you just heard remember is
+ 
+
+ align:start position:0%
+flying advice you just heard remember is
+the owner/operator you're responsible
+
+ align:start position:0%
+the owner/operator you're responsible
+ 
+
+ align:start position:0%
+the owner/operator you're responsible
+for keeping the airplane air worthy if
+
+ align:start position:0%
+for keeping the airplane air worthy if
+ 
+
+ align:start position:0%
+for keeping the airplane air worthy if
+you do choose to go out and buy an
+
+ align:start position:0%
+you do choose to go out and buy an
+ 
+
+ align:start position:0%
+you do choose to go out and buy an
+aircraft so these responsibilities are
+
+ align:start position:0%
+aircraft so these responsibilities are
+ 
+
+ align:start position:0%
+aircraft so these responsibilities are
+you know for most of you going to be on
+
+ align:start position:0%
+you know for most of you going to be on
+ 
+
+ align:start position:0%
+you know for most of you going to be on
+the flight school however you're still
+
+ align:start position:0%
+the flight school however you're still
+ 
+
+ align:start position:0%
+the flight school however you're still
+the final authority as the pilot and you
+
+ align:start position:0%
+the final authority as the pilot and you
+ 
+
+ align:start position:0%
+the final authority as the pilot and you
+can deviate from the rules in an
+
+ align:start position:0%
+can deviate from the rules in an
+ 
+
+ align:start position:0%
+can deviate from the rules in an
+emergency and you only have to report
+
+ align:start position:0%
+emergency and you only have to report
+ 
+
+ align:start position:0%
+emergency and you only have to report
+the deviation if requested I think that
+
+ align:start position:0%
+the deviation if requested I think that
+ 
+
+ align:start position:0%
+the deviation if requested I think that
+the feds like to ask this on the
+
+ align:start position:0%
+the feds like to ask this on the
+ 
+
+ align:start position:0%
+the feds like to ask this on the
+knowledge test because the natural
+
+ align:start position:0%
+knowledge test because the natural
+ 
+
+ align:start position:0%
+knowledge test because the natural
+answer is of course you have to report
+
+ align:start position:0%
+answer is of course you have to report
+ 
+
+ align:start position:0%
+answer is of course you have to report
+the deviation and I declared it an
+
+ align:start position:0%
+the deviation and I declared it an
+ 
+
+ align:start position:0%
+the deviation and I declared it an
+emergency and I broke the rules but you
+
+ align:start position:0%
+emergency and I broke the rules but you
+ 
+
+ align:start position:0%
+emergency and I broke the rules but you
+don't actually have to report that
+
+ align:start position:0%
+don't actually have to report that
+ 
+
+ align:start position:0%
+don't actually have to report that
+unless they ask you to but even aside
+
+ align:start position:0%
+unless they ask you to but even aside
+ 
+
+ align:start position:0%
+unless they ask you to but even aside
+from an emergency you're the pilot and
+
+ align:start position:0%
+from an emergency you're the pilot and
+ 
+
+ align:start position:0%
+from an emergency you're the pilot and
+command even if someone very assertively
+
+ align:start position:0%
+command even if someone very assertively
+ 
+
+ align:start position:0%
+command even if someone very assertively
+tells you to land and hold short or to
+
+ align:start position:0%
+tells you to land and hold short or to
+ 
+
+ align:start position:0%
+tells you to land and hold short or to
+fly straight to the numbers which means
+
+ align:start position:0%
+fly straight to the numbers which means
+ 
+
+ align:start position:0%
+fly straight to the numbers which means
+don't fly the profit proper traffic
+
+ align:start position:0%
+don't fly the profit proper traffic
+ 
+
+ align:start position:0%
+don't fly the profit proper traffic
+pattern but but land very quickly or
+
+ align:start position:0%
+pattern but but land very quickly or
+ 
+
+ align:start position:0%
+pattern but but land very quickly or
+tells you you know no delay on the go
+
+ align:start position:0%
+tells you you know no delay on the go
+ 
+
+ align:start position:0%
+tells you you know no delay on the go
+because they want you to get out quickly
+
+ align:start position:0%
+because they want you to get out quickly
+ 
+
+ align:start position:0%
+because they want you to get out quickly
+they have other jets
+
+ align:start position:0%
+they have other jets
+ 
+
+ align:start position:0%
+they have other jets
+you can just say unable and they have to
+
+ align:start position:0%
+you can just say unable and they have to
+ 
+
+ align:start position:0%
+you can just say unable and they have to
+deal with it and make sure you're flying
+
+ align:start position:0%
+deal with it and make sure you're flying
+ 
+
+ align:start position:0%
+deal with it and make sure you're flying
+safely and if you especially as a
+
+ align:start position:0%
+safely and if you especially as a
+ 
+
+ align:start position:0%
+safely and if you especially as a
+student pilot need extra time or extra
+
+ align:start position:0%
+student pilot need extra time or extra
+ 
+
+ align:start position:0%
+student pilot need extra time or extra
+consideration just add student pilot to
+
+ align:start position:0%
+consideration just add student pilot to
+ 
+
+ align:start position:0%
+consideration just add student pilot to
+the end of all your radio calls and
+
+ align:start position:0%
+the end of all your radio calls and
+ 
+
+ align:start position:0%
+the end of all your radio calls and
+they'll give you plenty of room to make
+
+ align:start position:0%
+they'll give you plenty of room to make
+ 
+
+ align:start position:0%
+they'll give you plenty of room to make
+mistakes but they might also make you
+
+ align:start position:0%
+mistakes but they might also make you
+ 
+
+ align:start position:0%
+mistakes but they might also make you
+sit there and fly a bunch of 360s while
+
+ align:start position:0%
+sit there and fly a bunch of 360s while
+ 
+
+ align:start position:0%
+sit there and fly a bunch of 360s while
+they land everybody else and then give
+
+ align:start position:0%
+they land everybody else and then give
+ 
+
+ align:start position:0%
+they land everybody else and then give
+you time and yeah so safety is not high
+
+ align:start position:0%
+you time and yeah so safety is not high
+ 
+
+ align:start position:0%
+you time and yeah so safety is not high
+tech it should be probably you know we
+
+ align:start position:0%
+tech it should be probably you know we
+ 
+
+ align:start position:0%
+tech it should be probably you know we
+should actually all the stuff that
+
+ align:start position:0%
+should actually all the stuff that
+ 
+
+ align:start position:0%
+should actually all the stuff that
+Michael showed you that's embedded in
+
+ align:start position:0%
+Michael showed you that's embedded in
+ 
+
+ align:start position:0%
+Michael showed you that's embedded in
+that DJI drone should probably be in
+
+ align:start position:0%
+that DJI drone should probably be in
+ 
+
+ align:start position:0%
+that DJI drone should probably be in
+these multi-million dollar aircraft but
+
+ align:start position:0%
+these multi-million dollar aircraft but
+ 
+
+ align:start position:0%
+these multi-million dollar aircraft but
+it's not so in the meantime
+
+ align:start position:0%
+it's not so in the meantime
+ 
+
+ align:start position:0%
+it's not so in the meantime
+you know since an airliner isn't
+
+ align:start position:0%
+you know since an airliner isn't
+ 
+
+ align:start position:0%
+you know since an airliner isn't
+actually that much smarter than a little
+
+ align:start position:0%
+actually that much smarter than a little
+ 
+
+ align:start position:0%
+actually that much smarter than a little
+Cessna you know why is it safer and if
+
+ align:start position:0%
+Cessna you know why is it safer and if
+ 
+
+ align:start position:0%
+Cessna you know why is it safer and if
+you take that perspective and just adapt
+
+ align:start position:0%
+you take that perspective and just adapt
+ 
+
+ align:start position:0%
+you take that perspective and just adapt
+all the things the airlines have done
+
+ align:start position:0%
+all the things the airlines have done
+ 
+
+ align:start position:0%
+all the things the airlines have done
+you can make flying that little Cessna
+
+ align:start position:0%
+you can make flying that little Cessna
+ 
+
+ align:start position:0%
+you can make flying that little Cessna
+dramatically safer
+
+ align:start position:0%
+dramatically safer
+ 
+
+ align:start position:0%
+dramatically safer
+so that means recurrent training you
+
+ align:start position:0%
+so that means recurrent training you
+ 
+
+ align:start position:0%
+so that means recurrent training you
+know maybe go up with an instructor
+
+ align:start position:0%
+know maybe go up with an instructor
+ 
+
+ align:start position:0%
+know maybe go up with an instructor
+every three months instead of the every
+
+ align:start position:0%
+every three months instead of the every
+ 
+
+ align:start position:0%
+every three months instead of the every
+two years that the FAA requires the
+
+ align:start position:0%
+two years that the FAA requires the
+ 
+
+ align:start position:0%
+two years that the FAA requires the
+instrument flying skills are really
+
+ align:start position:0%
+instrument flying skills are really
+ 
+
+ align:start position:0%
+instrument flying skills are really
+important for VFR safety they make you a
+
+ align:start position:0%
+important for VFR safety they make you a
+ 
+
+ align:start position:0%
+important for VFR safety they make you a
+much better pilot you know at night as
+
+ align:start position:0%
+much better pilot you know at night as
+ 
+
+ align:start position:0%
+much better pilot you know at night as
+we've just discussed and even bombing
+
+ align:start position:0%
+we've just discussed and even bombing
+ 
+
+ align:start position:0%
+we've just discussed and even bombing
+around during the day you'll be able to
+
+ align:start position:0%
+around during the day you'll be able to
+ 
+
+ align:start position:0%
+around during the day you'll be able to
+fly with about five percent of your
+
+ align:start position:0%
+fly with about five percent of your
+ 
+
+ align:start position:0%
+fly with about five percent of your
+mental energy instead of 50% if you are
+
+ align:start position:0%
+mental energy instead of 50% if you are
+ 
+
+ align:start position:0%
+mental energy instead of 50% if you are
+an instrument-rated pilot on a nice VFR
+
+ align:start position:0%
+an instrument-rated pilot on a nice VFR
+ 
+
+ align:start position:0%
+an instrument-rated pilot on a nice VFR
+day the two pilot crew and checklist is
+
+ align:start position:0%
+day the two pilot crew and checklist is
+ 
+
+ align:start position:0%
+day the two pilot crew and checklist is
+really the cornerstone of the airline
+
+ align:start position:0%
+really the cornerstone of the airline
+ 
+
+ align:start position:0%
+really the cornerstone of the airline
+safety system so and you can take
+
+ align:start position:0%
+safety system so and you can take
+ 
+
+ align:start position:0%
+safety system so and you can take
+advantage of that as a ga pilot even
+
+ align:start position:0%
+advantage of that as a ga pilot even
+ 
+
+ align:start position:0%
+advantage of that as a ga pilot even
+though the FA you know really about 5%
+
+ align:start position:0%
+though the FA you know really about 5%
+ 
+
+ align:start position:0%
+though the FA you know really about 5%
+of the FAA which is the one you've seen
+
+ align:start position:0%
+of the FAA which is the one you've seen
+ 
+
+ align:start position:0%
+of the FAA which is the one you've seen
+and interacted with it's all about
+
+ align:start position:0%
+and interacted with it's all about
+ 
+
+ align:start position:0%
+and interacted with it's all about
+encouraging people to be single pilots
+
+ align:start position:0%
+encouraging people to be single pilots
+ 
+
+ align:start position:0%
+encouraging people to be single pilots
+and 95% of the FAA is about forbidding
+
+ align:start position:0%
+and 95% of the FAA is about forbidding
+ 
+
+ align:start position:0%
+and 95% of the FAA is about forbidding
+people to operate single pilot every
+
+ align:start position:0%
+people to operate single pilot every
+ 
+
+ align:start position:0%
+people to operate single pilot every
+part of the FAA that regulates you know
+
+ align:start position:0%
+part of the FAA that regulates you know
+ 
+
+ align:start position:0%
+part of the FAA that regulates you know
+the airlines and charters of sizeable
+
+ align:start position:0%
+the airlines and charters of sizeable
+ 
+
+ align:start position:0%
+the airlines and charters of sizeable
+airplanes they say no of course you
+
+ align:start position:0%
+airplanes they say no of course you
+ 
+
+ align:start position:0%
+airplanes they say no of course you
+can't operate a single pilot that would
+
+ align:start position:0%
+can't operate a single pilot that would
+ 
+
+ align:start position:0%
+can't operate a single pilot that would
+be incredibly dangerous alright so just
+
+ align:start position:0%
+be incredibly dangerous alright so just
+ 
+
+ align:start position:0%
+be incredibly dangerous alright so just
+remember study a little bit about the
+
+ align:start position:0%
+remember study a little bit about the
+ 
+
+ align:start position:0%
+remember study a little bit about the
+part 61 and part 91 for learning - we
+
+ align:start position:0%
+part 61 and part 91 for learning - we
+ 
+
+ align:start position:0%
+part 61 and part 91 for learning - we
+know what does it take to be and
+
+ align:start position:0%
+know what does it take to be and
+ 
+
+ align:start position:0%
+know what does it take to be and
+maintain your status as a pilot or being
+
+ align:start position:0%
+maintain your status as a pilot or being
+ 
+
+ align:start position:0%
+maintain your status as a pilot or being
+able to exercise your privileges as a
+
+ align:start position:0%
+able to exercise your privileges as a
+ 
+
+ align:start position:0%
+able to exercise your privileges as a
+pilot that certificate never expires
+
+ align:start position:0%
+pilot that certificate never expires
+ 
+
+ align:start position:0%
+pilot that certificate never expires
+part 91 is about what you can do with an
+
+ align:start position:0%
+part 91 is about what you can do with an
+ 
+
+ align:start position:0%
+part 91 is about what you can do with an
+airplane operated privately and then
+
+ align:start position:0%
+airplane operated privately and then
+ 
+
+ align:start position:0%
+airplane operated privately and then
+there's this little corner over there
+
+ align:start position:0%
+there's this little corner over there
+ 
+
+ align:start position:0%
+there's this little corner over there
+under title 49 part 830 having to do
+
+ align:start position:0%
+under title 49 part 830 having to do
+ 
+
+ align:start position:0%
+under title 49 part 830 having to do
+with accident reporting and
+
+ align:start position:0%
+with accident reporting and
+ 
+
+ align:start position:0%
+with accident reporting and
+investigation if you want to get a
+
+ align:start position:0%
+investigation if you want to get a
+ 
+
+ align:start position:0%
+investigation if you want to get a
+hundred on the fa knowledge test a lot
+
+ align:start position:0%
+hundred on the fa knowledge test a lot
+ 
+
+ align:start position:0%
+hundred on the fa knowledge test a lot
+of East Coast Aero Club customers seem
+
+ align:start position:0%
+of East Coast Aero Club customers seem
+ 
+
+ align:start position:0%
+of East Coast Aero Club customers seem
+to over study I see a lot of 95 97 98
+
+ align:start position:0%
+to over study I see a lot of 95 97 98
+ 
+
+ align:start position:0%
+to over study I see a lot of 95 97 98
+and 100's actual 100's just reread the
+
+ align:start position:0%
+and 100's actual 100's just reread the
+ 
+
+ align:start position:0%
+and 100's actual 100's just reread the
+FAA text
+
+ align:start position:0%
+FAA text
+ 
+
+ align:start position:0%
+FAA text
+I mean they can't ask you anything
+
+ align:start position:0%
+I mean they can't ask you anything
+ 
+
+ align:start position:0%
+I mean they can't ask you anything
+that's not in one of their own PDFs that
+
+ align:start position:0%
+that's not in one of their own PDFs that
+ 
+
+ align:start position:0%
+that's not in one of their own PDFs that
+includes the far aim though the the
+
+ align:start position:0%
+includes the far aim though the the
+ 
+
+ align:start position:0%
+includes the far aim though the the
+regulations and the aeronautical
+
+ align:start position:0%
+regulations and the aeronautical
+ 
+
+ align:start position:0%
+regulations and the aeronautical
+information manual there are test prep
+
+ align:start position:0%
+information manual there are test prep
+ 
+
+ align:start position:0%
+information manual there are test prep
+books and all nine equivalents that are
+
+ align:start position:0%
+books and all nine equivalents that are
+ 
+
+ align:start position:0%
+books and all nine equivalents that are
+worth it to finish this course actually
+
+ align:start position:0%
+worth it to finish this course actually
+ 
+
+ align:start position:0%
+worth it to finish this course actually
+you can get this you'll be able to get
+
+ align:start position:0%
+you can get this you'll be able to get
+ 
+
+ align:start position:0%
+you can get this you'll be able to get
+actually we don't even need to email you
+
+ align:start position:0%
+actually we don't even need to email you
+ 
+
+ align:start position:0%
+actually we don't even need to email you
+because if you have the course homepage
+
+ align:start position:0%
+because if you have the course homepage
+ 
+
+ align:start position:0%
+because if you have the course homepage
+you can see it here you go to this king
+
+ align:start position:0%
+you can see it here you go to this king
+ 
+
+ align:start position:0%
+you can see it here you go to this king
+school thing and you say you want to do
+
+ align:start position:0%
+school thing and you say you want to do
+ 
+
+ align:start position:0%
+school thing and you say you want to do
+60 questions 60 is a number of questions
+
+ align:start position:0%
+60 questions 60 is a number of questions
+ 
+
+ align:start position:0%
+60 questions 60 is a number of questions
+on the actual exam so we're making our
+
+ align:start position:0%
+on the actual exam so we're making our
+ 
+
+ align:start position:0%
+on the actual exam so we're making our
+final exam being the same and then you
+
+ align:start position:0%
+final exam being the same and then you
+ 
+
+ align:start position:0%
+final exam being the same and then you
+start test and you send us the results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll be happy
+
+ align:start position:0%
+and we'll be happy
+ 
+
+ align:start position:0%
+and we'll be happy
+all right next steps if you want to
+
+ align:start position:0%
+all right next steps if you want to
+ 
+
+ align:start position:0%
+all right next steps if you want to
+continue your journey beyond this class
+
+ align:start position:0%
+continue your journey beyond this class
+ 
+
+ align:start position:0%
+continue your journey beyond this class
+maybe that's for the one or two people
+
+ align:start position:0%
+maybe that's for the one or two people
+ 
+
+ align:start position:0%
+maybe that's for the one or two people
+that applies that actually want to
+
+ align:start position:0%
+that applies that actually want to
+ 
+
+ align:start position:0%
+that applies that actually want to
+continue their journey can I borrow the
+
+ align:start position:0%
+continue their journey can I borrow the
+ 
+
+ align:start position:0%
+continue their journey can I borrow the
+pointer for just a second this for the
+
+ align:start position:0%
+pointer for just a second this for the
+ 
+
+ align:start position:0%
+pointer for just a second this for the
+guys that we're getting tripped up
+
+ align:start position:0%
+guys that we're getting tripped up
+ 
+
+ align:start position:0%
+guys that we're getting tripped up
+thinking it was a river that's exactly
+
+ align:start position:0%
+thinking it was a river that's exactly
+ 
+
+ align:start position:0%
+thinking it was a river that's exactly
+what we're talking about this is a
+
+ align:start position:0%
+what we're talking about this is a
+ 
+
+ align:start position:0%
+what we're talking about this is a
+Boston Logan these blue lines circles
+
+ align:start position:0%
+Boston Logan these blue lines circles
+ 
+
+ align:start position:0%
+Boston Logan these blue lines circles
+that are rounded are not rivers it's
+
+ align:start position:0%
+that are rounded are not rivers it's
+ 
+
+ align:start position:0%
+that are rounded are not rivers it's
+indicating that class Bravo airspace and
+
+ align:start position:0%
+indicating that class Bravo airspace and
+ 
+
+ align:start position:0%
+indicating that class Bravo airspace and
+I have it open over here if you want to
+
+ align:start position:0%
+I have it open over here if you want to
+ 
+
+ align:start position:0%
+I have it open over here if you want to
+take a look okay so yeah join the flying
+
+ align:start position:0%
+take a look okay so yeah join the flying
+ 
+
+ align:start position:0%
+take a look okay so yeah join the flying
+club go visit a flight school most of
+
+ align:start position:0%
+club go visit a flight school most of
+ 
+
+ align:start position:0%
+club go visit a flight school most of
+the busier US airports have some kind of
+
+ align:start position:0%
+the busier US airports have some kind of
+ 
+
+ align:start position:0%
+the busier US airports have some kind of
+flight school that you can do and yeah
+
+ align:start position:0%
+flight school that you can do and yeah
+ 
+
+ align:start position:0%
+flight school that you can do and yeah
+in the two hours that are remaining to
+
+ align:start position:0%
+in the two hours that are remaining to
+ 
+
+ align:start position:0%
+in the two hours that are remaining to
+me for this presentation I would just
+
+ align:start position:0%
+me for this presentation I would just
+ 
+
+ align:start position:0%
+me for this presentation I would just
+like to say thank you now we're saying
+
+ align:start position:0%
+like to say thank you now we're saying
+ 
+
+ align:start position:0%
+like to say thank you now we're saying
+thank you but just to clarify there's
+
+ align:start position:0%
+thank you but just to clarify there's
+ 
+
+ align:start position:0%
+thank you but just to clarify there's
+there's a really cool guest speaker
+
+ align:start position:0%
+there's a really cool guest speaker
+ 
+
+ align:start position:0%
+there's a really cool guest speaker
+coming next but for the purposes of our
+
+ align:start position:0%
+coming next but for the purposes of our
+ 
+
+ align:start position:0%
+coming next but for the purposes of our
+teaching thank you very much and we'll
+
+ align:start position:0%
+teaching thank you very much and we'll
+ 
+
+ align:start position:0%
+teaching thank you very much and we'll
+take any questions
+
+ align:start position:0%
+take any questions
+ 
+
+ align:start position:0%
+take any questions
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/kpUg96uZk2M.txt b/kpUg96uZk2M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9861eb90ebf259df6c8d8fa1993e0ec877ad7450
--- /dev/null
+++ b/kpUg96uZk2M.txt
@@ -0,0 +1,7787 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so let's get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh it's interesting that some of your
+
+ align:start position:0%
+oh it's interesting that some of your
+ 
+
+ align:start position:0%
+oh it's interesting that some of your
+questions had to do with things that I
+
+ align:start position:0%
+questions had to do with things that I
+ 
+
+ align:start position:0%
+questions had to do with things that I
+didn't quite cover in lecture but that's
+
+ align:start position:0%
+didn't quite cover in lecture but that's
+ 
+
+ align:start position:0%
+didn't quite cover in lecture but that's
+fine I'm going to cover them at the
+
+ align:start position:0%
+fine I'm going to cover them at the
+ 
+
+ align:start position:0%
+fine I'm going to cover them at the
+beginning of today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture this is a really important
+
+ align:start position:0%
+lecture this is a really important
+ 
+
+ align:start position:0%
+lecture this is a really important
+question how do you know what channel an
+
+ align:start position:0%
+question how do you know what channel an
+ 
+
+ align:start position:0%
+question how do you know what channel an
+is how do you know what I in a
+
+ align:start position:0%
+is how do you know what I in a
+ 
+
+ align:start position:0%
+is how do you know what I in a
+particular channel is
+
+ align:start position:0%
+particular channel is
+ 
+
+ align:start position:0%
+particular channel is
+conducting it's actually hard to
+
+ align:start position:0%
+conducting it's actually hard to
+ 
+
+ align:start position:0%
+conducting it's actually hard to
+determine they're very ious ways to do
+
+ align:start position:0%
+determine they're very ious ways to do
+ 
+
+ align:start position:0%
+determine they're very ious ways to do
+it where you can
+
+ align:start position:0%
+it where you can
+ 
+
+ align:start position:0%
+it where you can
+specifically um label the iron or follow
+
+ align:start position:0%
+specifically um label the iron or follow
+ 
+
+ align:start position:0%
+specifically um label the iron or follow
+a particular ion and address whether or
+
+ align:start position:0%
+a particular ion and address whether or
+ 
+
+ align:start position:0%
+a particular ion and address whether or
+not it's getting into a cell or across a
+
+ align:start position:0%
+not it's getting into a cell or across a
+ 
+
+ align:start position:0%
+not it's getting into a cell or across a
+membrane when there's a particular ION
+
+ align:start position:0%
+membrane when there's a particular ION
+ 
+
+ align:start position:0%
+membrane when there's a particular ION
+channel present but it's not completely
+
+ align:start position:0%
+channel present but it's not completely
+ 
+
+ align:start position:0%
+channel present but it's not completely
+trivial one of the things I didn't have
+
+ align:start position:0%
+trivial one of the things I didn't have
+ 
+
+ align:start position:0%
+trivial one of the things I didn't have
+time to go through with you but which is
+
+ align:start position:0%
+time to go through with you but which is
+ 
+
+ align:start position:0%
+time to go through with you but which is
+on one of the Powerpoints though is the
+
+ align:start position:0%
+on one of the Powerpoints though is the
+ 
+
+ align:start position:0%
+on one of the Powerpoints though is the
+fact that ion channels are really
+
+ align:start position:0%
+fact that ion channels are really
+ 
+
+ align:start position:0%
+fact that ion channels are really
+selective and they don't conduct ions on
+
+ align:start position:0%
+selective and they don't conduct ions on
+ 
+
+ align:start position:0%
+selective and they don't conduct ions on
+the base of size okay so you're not
+
+ align:start position:0%
+the base of size okay so you're not
+ 
+
+ align:start position:0%
+the base of size okay so you're not
+going to get a large ion CH channel that
+
+ align:start position:0%
+going to get a large ion CH channel that
+ 
+
+ align:start position:0%
+going to get a large ion CH channel that
+can accommodate a large ion also
+
+ align:start position:0%
+can accommodate a large ion also
+ 
+
+ align:start position:0%
+can accommodate a large ion also
+accommodating a small ion it's not a
+
+ align:start position:0%
+accommodating a small ion it's not a
+ 
+
+ align:start position:0%
+accommodating a small ion it's not a
+matter about of just opening up a space
+
+ align:start position:0%
+matter about of just opening up a space
+ 
+
+ align:start position:0%
+matter about of just opening up a space
+there are also charge considerations
+
+ align:start position:0%
+there are also charge considerations
+ 
+
+ align:start position:0%
+there are also charge considerations
+where the ions actually interact with
+
+ align:start position:0%
+where the ions actually interact with
+ 
+
+ align:start position:0%
+where the ions actually interact with
+the molecules in the channel in the
+
+ align:start position:0%
+the molecules in the channel in the
+ 
+
+ align:start position:0%
+the molecules in the channel in the
+actual pour through the membrane and
+
+ align:start position:0%
+actual pour through the membrane and
+ 
+
+ align:start position:0%
+actual pour through the membrane and
+it's that interaction which it selects
+
+ align:start position:0%
+it's that interaction which it selects
+ 
+
+ align:start position:0%
+it's that interaction which it selects
+for a particular ion but this notion of
+
+ align:start position:0%
+for a particular ion but this notion of
+ 
+
+ align:start position:0%
+for a particular ion but this notion of
+exactly what ions channels are
+
+ align:start position:0%
+exactly what ions channels are
+ 
+
+ align:start position:0%
+exactly what ions channels are
+conducting has been many many decades of
+
+ align:start position:0%
+conducting has been many many decades of
+ 
+
+ align:start position:0%
+conducting has been many many decades of
+work and what I've written up here is
+
+ align:start position:0%
+work and what I've written up here is
+ 
+
+ align:start position:0%
+work and what I've written up here is
+correct but if you want to explore it
+
+ align:start position:0%
+correct but if you want to explore it
+ 
+
+ align:start position:0%
+correct but if you want to explore it
+more with me come and talk during office
+
+ align:start position:0%
+more with me come and talk during office
+ 
+
+ align:start position:0%
+more with me come and talk during office
+hours and then a number of you started
+
+ align:start position:0%
+hours and then a number of you started
+ 
+
+ align:start position:0%
+hours and then a number of you started
+asking me about modulation of
+
+ align:start position:0%
+asking me about modulation of
+ 
+
+ align:start position:0%
+asking me about modulation of
+neurotransmitters which I'll talk about
+
+ align:start position:0%
+neurotransmitters which I'll talk about
+ 
+
+ align:start position:0%
+neurotransmitters which I'll talk about
+in today's lecture and these are clearly
+
+ align:start position:0%
+in today's lecture and these are clearly
+ 
+
+ align:start position:0%
+in today's lecture and these are clearly
+of interest because many recreational
+
+ align:start position:0%
+of interest because many recreational
+ 
+
+ align:start position:0%
+of interest because many recreational
+drugs and medications mod modulate
+
+ align:start position:0%
+drugs and medications mod modulate
+ 
+
+ align:start position:0%
+drugs and medications mod modulate
+neurotransmitter amounts and that is how
+
+ align:start position:0%
+neurotransmitter amounts and that is how
+ 
+
+ align:start position:0%
+neurotransmitter amounts and that is how
+they work so for example some of you
+
+ align:start position:0%
+they work so for example some of you
+ 
+
+ align:start position:0%
+they work so for example some of you
+might be taking things called SSRI
+
+ align:start position:0%
+might be taking things called SSRI
+ 
+
+ align:start position:0%
+might be taking things called SSRI
+specific serotonin reuptake Inhibitors
+
+ align:start position:0%
+specific serotonin reuptake Inhibitors
+ 
+
+ align:start position:0%
+specific serotonin reuptake Inhibitors
+like Prozac which make you feel less
+
+ align:start position:0%
+like Prozac which make you feel less
+ 
+
+ align:start position:0%
+like Prozac which make you feel less
+anxious and better about things and
+
+ align:start position:0%
+anxious and better about things and
+ 
+
+ align:start position:0%
+anxious and better about things and
+these act by prolonging serotonin
+
+ align:start position:0%
+these act by prolonging serotonin
+ 
+
+ align:start position:0%
+these act by prolonging serotonin
+activity by preventing it from being
+
+ align:start position:0%
+activity by preventing it from being
+ 
+
+ align:start position:0%
+activity by preventing it from being
+retaken up into cells and I'll touch on
+
+ align:start position:0%
+retaken up into cells and I'll touch on
+ 
+
+ align:start position:0%
+retaken up into cells and I'll touch on
+this at the beginning of the lecture and
+
+ align:start position:0%
+this at the beginning of the lecture and
+ 
+
+ align:start position:0%
+this at the beginning of the lecture and
+it takes a while is what I've written
+
+ align:start position:0%
+it takes a while is what I've written
+ 
+
+ align:start position:0%
+it takes a while is what I've written
+here for these medications to start
+
+ align:start position:0%
+here for these medications to start
+ 
+
+ align:start position:0%
+here for these medications to start
+working because you're really asking for
+
+ align:start position:0%
+working because you're really asking for
+ 
+
+ align:start position:0%
+working because you're really asking for
+a rearrangement of the whole synaptic
+
+ align:start position:0%
+a rearrangement of the whole synaptic
+ 
+
+ align:start position:0%
+a rearrangement of the whole synaptic
+process and the synaptic structure in
+
+ align:start position:0%
+process and the synaptic structure in
+ 
+
+ align:start position:0%
+process and the synaptic structure in
+order that they can work and here's
+
+ align:start position:0%
+order that they can work and here's
+ 
+
+ align:start position:0%
+order that they can work and here's
+another one what about amphetamines are
+
+ align:start position:0%
+another one what about amphetamines are
+ 
+
+ align:start position:0%
+another one what about amphetamines are
+they neurotransmitters no they they
+
+ align:start position:0%
+they neurotransmitters no they they
+ 
+
+ align:start position:0%
+they neurotransmitters no they they
+increase the release of dopamine which
+
+ align:start position:0%
+increase the release of dopamine which
+ 
+
+ align:start position:0%
+increase the release of dopamine which
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+neurotransmitter um and they also seem
+
+ align:start position:0%
+neurotransmitter um and they also seem
+ 
+
+ align:start position:0%
+neurotransmitter um and they also seem
+to inhibit re-uptake of dopamine and
+
+ align:start position:0%
+to inhibit re-uptake of dopamine and
+ 
+
+ align:start position:0%
+to inhibit re-uptake of dopamine and
+serotonin as I'll I'll talk about
+
+ align:start position:0%
+serotonin as I'll I'll talk about
+ 
+
+ align:start position:0%
+serotonin as I'll I'll talk about
+reuptake very briefly in a
+
+ align:start position:0%
+reuptake very briefly in a
+ 
+
+ align:start position:0%
+reuptake very briefly in a
+moment for many medications both
+
+ align:start position:0%
+moment for many medications both
+ 
+
+ align:start position:0%
+moment for many medications both
+actually for many medications no matter
+
+ align:start position:0%
+actually for many medications no matter
+ 
+
+ align:start position:0%
+actually for many medications no matter
+whether or not they affect your brain or
+
+ align:start position:0%
+whether or not they affect your brain or
+ 
+
+ align:start position:0%
+whether or not they affect your brain or
+other parts of your body the precise
+
+ align:start position:0%
+other parts of your body the precise
+ 
+
+ align:start position:0%
+other parts of your body the precise
+mechanism of action is not is really not
+
+ align:start position:0%
+mechanism of action is not is really not
+ 
+
+ align:start position:0%
+mechanism of action is not is really not
+known there are guesses there's data but
+
+ align:start position:0%
+known there are guesses there's data but
+ 
+
+ align:start position:0%
+known there are guesses there's data but
+the precise mechanism is often not known
+
+ align:start position:0%
+the precise mechanism is often not known
+ 
+
+ align:start position:0%
+the precise mechanism is often not known
+so let's use that as a
+
+ align:start position:0%
+so let's use that as a
+ 
+
+ align:start position:0%
+so let's use that as a
+segue into our lecture I won't have
+
+ align:start position:0%
+segue into our lecture I won't have
+ 
+
+ align:start position:0%
+segue into our lecture I won't have
+office hours today due to my schedule I
+
+ align:start position:0%
+office hours today due to my schedule I
+ 
+
+ align:start position:0%
+office hours today due to my schedule I
+will have them next Wednesday due to the
+
+ align:start position:0%
+will have them next Wednesday due to the
+ 
+
+ align:start position:0%
+will have them next Wednesday due to the
+vacation schedule and you're welcome to
+
+ align:start position:0%
+vacation schedule and you're welcome to
+ 
+
+ align:start position:0%
+vacation schedule and you're welcome to
+email me in the meantime all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've been walking through the cells
+
+ align:start position:0%
+we've been walking through the cells
+ 
+
+ align:start position:0%
+we've been walking through the cells
+involved in nervous system formation the
+
+ align:start position:0%
+involved in nervous system formation the
+ 
+
+ align:start position:0%
+involved in nervous system formation the
+connections between the cells and now
+
+ align:start position:0%
+connections between the cells and now
+ 
+
+ align:start position:0%
+connections between the cells and now
+today we're going to finish talking
+
+ align:start position:0%
+today we're going to finish talking
+ 
+
+ align:start position:0%
+today we're going to finish talking
+about the connections between the cells
+
+ align:start position:0%
+about the connections between the cells
+ 
+
+ align:start position:0%
+about the connections between the cells
+and segue into the incredibly complex
+
+ align:start position:0%
+and segue into the incredibly complex
+ 
+
+ align:start position:0%
+and segue into the incredibly complex
+topic of circuits in the nervous
+
+ align:start position:0%
+topic of circuits in the nervous
+ 
+
+ align:start position:0%
+topic of circuits in the nervous
+system so today the first thing I want
+
+ align:start position:0%
+system so today the first thing I want
+ 
+
+ align:start position:0%
+system so today the first thing I want
+to talk about is
+
+ align:start position:0%
+to talk about is
+ 
+
+ align:start position:0%
+to talk about is
+regulating
+
+ align:start position:0%
+regulating
+ 
+
+ align:start position:0%
+regulating
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+synapses and you
+
+ align:start position:0%
+synapses and you
+ 
+
+ align:start position:0%
+synapses and you
+remember that we're talking about
+
+ align:start position:0%
+remember that we're talking about
+ 
+
+ align:start position:0%
+remember that we're talking about
+chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synapses and the second thing I want to
+
+ align:start position:0%
+synapses and the second thing I want to
+ 
+
+ align:start position:0%
+synapses and the second thing I want to
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+about are circuits is there a problem
+
+ align:start position:0%
+about are circuits is there a problem
+ 
+
+ align:start position:0%
+about are circuits is there a problem
+can you hear me okay at the back thumbs
+
+ align:start position:0%
+can you hear me okay at the back thumbs
+ 
+
+ align:start position:0%
+can you hear me okay at the back thumbs
+up great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good when I introduced circuits when I
+
+ align:start position:0%
+good when I introduced circuits when I
+ 
+
+ align:start position:0%
+good when I introduced circuits when I
+introduced synapses to you
+
+ align:start position:0%
+introduced synapses to you
+ 
+
+ align:start position:0%
+introduced synapses to you
+I told you that one of the reasons that
+
+ align:start position:0%
+I told you that one of the reasons that
+ 
+
+ align:start position:0%
+I told you that one of the reasons that
+there was this chemical synapse in the
+
+ align:start position:0%
+there was this chemical synapse in the
+ 
+
+ align:start position:0%
+there was this chemical synapse in the
+midst with it slow chemical synapse in
+
+ align:start position:0%
+midst with it slow chemical synapse in
+ 
+
+ align:start position:0%
+midst with it slow chemical synapse in
+the midst of this rapid electrical
+
+ align:start position:0%
+the midst of this rapid electrical
+ 
+
+ align:start position:0%
+the midst of this rapid electrical
+transmission was because you could
+
+ align:start position:0%
+transmission was because you could
+ 
+
+ align:start position:0%
+transmission was because you could
+regulate synapses and that is really
+
+ align:start position:0%
+regulate synapses and that is really
+ 
+
+ align:start position:0%
+regulate synapses and that is really
+what fine-tunes US it allows us to
+
+ align:start position:0%
+what fine-tunes US it allows us to
+ 
+
+ align:start position:0%
+what fine-tunes US it allows us to
+respond in a graded way to stimuli both
+
+ align:start position:0%
+respond in a graded way to stimuli both
+ 
+
+ align:start position:0%
+respond in a graded way to stimuli both
+from within the body and outside it
+
+ align:start position:0%
+from within the body and outside it
+ 
+
+ align:start position:0%
+from within the body and outside it
+allows the body to adapt in ways that
+
+ align:start position:0%
+allows the body to adapt in ways that
+ 
+
+ align:start position:0%
+allows the body to adapt in ways that
+are not all or none where action
+
+ align:start position:0%
+are not all or none where action
+ 
+
+ align:start position:0%
+are not all or none where action
+potentials are all or none the overall
+
+ align:start position:0%
+potentials are all or none the overall
+ 
+
+ align:start position:0%
+potentials are all or none the overall
+response of the body clearly isn't it's
+
+ align:start position:0%
+response of the body clearly isn't it's
+ 
+
+ align:start position:0%
+response of the body clearly isn't it's
+very nuanced and all of this has to do
+
+ align:start position:0%
+very nuanced and all of this has to do
+ 
+
+ align:start position:0%
+very nuanced and all of this has to do
+with regulating chemical synapses and
+
+ align:start position:0%
+with regulating chemical synapses and
+ 
+
+ align:start position:0%
+with regulating chemical synapses and
+that's what we'll talk about for a few
+
+ align:start position:0%
+that's what we'll talk about for a few
+ 
+
+ align:start position:0%
+that's what we'll talk about for a few
+moments you can regulate chemical
+
+ align:start position:0%
+moments you can regulate chemical
+ 
+
+ align:start position:0%
+moments you can regulate chemical
+synapses by changing the amount of
+
+ align:start position:0%
+synapses by changing the amount of
+ 
+
+ align:start position:0%
+synapses by changing the amount of
+neurotransmitter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you think about this for a moment
+
+ align:start position:0%
+and if you think about this for a moment
+ 
+
+ align:start position:0%
+and if you think about this for a moment
+if you think about the synapse there's
+
+ align:start position:0%
+if you think about the synapse there's
+ 
+
+ align:start position:0%
+if you think about the synapse there's
+the neurotransmitter released into the
+
+ align:start position:0%
+the neurotransmitter released into the
+ 
+
+ align:start position:0%
+the neurotransmitter released into the
+space between the two cells diffuses
+
+ align:start position:0%
+space between the two cells diffuses
+ 
+
+ align:start position:0%
+space between the two cells diffuses
+across the synaptic Clift and then does
+
+ align:start position:0%
+across the synaptic Clift and then does
+ 
+
+ align:start position:0%
+across the synaptic Clift and then does
+something to the post synaptic cell
+
+ align:start position:0%
+something to the post synaptic cell
+ 
+
+ align:start position:0%
+something to the post synaptic cell
+potentially to lead to an action
+
+ align:start position:0%
+potentially to lead to an action
+ 
+
+ align:start position:0%
+potentially to lead to an action
+potential now if that neurotransmitter
+
+ align:start position:0%
+potential now if that neurotransmitter
+ 
+
+ align:start position:0%
+potential now if that neurotransmitter
+stuck around in the space between the
+
+ align:start position:0%
+stuck around in the space between the
+ 
+
+ align:start position:0%
+stuck around in the space between the
+cells it would keep stimulating the post
+
+ align:start position:0%
+cells it would keep stimulating the post
+ 
+
+ align:start position:0%
+cells it would keep stimulating the post
+synaptic cell over and over and as more
+
+ align:start position:0%
+synaptic cell over and over and as more
+ 
+
+ align:start position:0%
+synaptic cell over and over and as more
+neurotransmitter was released so the
+
+ align:start position:0%
+neurotransmitter was released so the
+ 
+
+ align:start position:0%
+neurotransmitter was released so the
+post synaptic cell would be further
+
+ align:start position:0%
+post synaptic cell would be further
+ 
+
+ align:start position:0%
+post synaptic cell would be further
+stimulated and you'd get to a point
+
+ align:start position:0%
+stimulated and you'd get to a point
+ 
+
+ align:start position:0%
+stimulated and you'd get to a point
+where the post synaptic neuron was
+
+ align:start position:0%
+where the post synaptic neuron was
+ 
+
+ align:start position:0%
+where the post synaptic neuron was
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+overstimulated and that's clearly not a
+
+ align:start position:0%
+overstimulated and that's clearly not a
+ 
+
+ align:start position:0%
+overstimulated and that's clearly not a
+way to regulate responsiveness to any
+
+ align:start position:0%
+way to regulate responsiveness to any
+ 
+
+ align:start position:0%
+way to regulate responsiveness to any
+stimuli so
+
+ align:start position:0%
+stimuli so
+ 
+
+ align:start position:0%
+stimuli so
+neurotransmitter does not stay in the
+
+ align:start position:0%
+neurotransmitter does not stay in the
+ 
+
+ align:start position:0%
+neurotransmitter does not stay in the
+synaptic Clift for very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long so it's changing the amount of
+
+ align:start position:0%
+long so it's changing the amount of
+ 
+
+ align:start position:0%
+long so it's changing the amount of
+neurot
+
+ align:start position:0%
+neurot
+ 
+
+ align:start position:0%
+neurot
+transmitter
+
+ align:start position:0%
+transmitter
+ 
+
+ align:start position:0%
+transmitter
+via
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degradation once neurotransmitter is
+
+ align:start position:0%
+degradation once neurotransmitter is
+ 
+
+ align:start position:0%
+degradation once neurotransmitter is
+released in some cases it's degraded by
+
+ align:start position:0%
+released in some cases it's degraded by
+ 
+
+ align:start position:0%
+released in some cases it's degraded by
+specific enzymes for example in the case
+
+ align:start position:0%
+specific enzymes for example in the case
+ 
+
+ align:start position:0%
+specific enzymes for example in the case
+of acetyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choline there's a particular enzyme that
+
+ align:start position:0%
+choline there's a particular enzyme that
+ 
+
+ align:start position:0%
+choline there's a particular enzyme that
+breaks down acetyl choline and if that
+
+ align:start position:0%
+breaks down acetyl choline and if that
+ 
+
+ align:start position:0%
+breaks down acetyl choline and if that
+enzyme is inhibited you go into
+
+ align:start position:0%
+enzyme is inhibited you go into
+ 
+
+ align:start position:0%
+enzyme is inhibited you go into
+respiratory shock you cannot breathe
+
+ align:start position:0%
+respiratory shock you cannot breathe
+ 
+
+ align:start position:0%
+respiratory shock you cannot breathe
+anymore because you you have to activate
+
+ align:start position:0%
+anymore because you you have to activate
+ 
+
+ align:start position:0%
+anymore because you you have to activate
+and inactivate the muscles via the
+
+ align:start position:0%
+and inactivate the muscles via the
+ 
+
+ align:start position:0%
+and inactivate the muscles via the
+nerves as you
+
+ align:start position:0%
+nerves as you
+ 
+
+ align:start position:0%
+nerves as you
+breathe you can also regulate the amount
+
+ align:start position:0%
+breathe you can also regulate the amount
+ 
+
+ align:start position:0%
+breathe you can also regulate the amount
+of neurotransmitter by something called
+
+ align:start position:0%
+of neurotransmitter by something called
+ 
+
+ align:start position:0%
+of neurotransmitter by something called
+reuptake sometimes called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reabsorption where the
+
+ align:start position:0%
+reabsorption where the
+ 
+
+ align:start position:0%
+reabsorption where the
+neurotransmitter
+
+ align:start position:0%
+neurotransmitter
+ 
+
+ align:start position:0%
+neurotransmitter
+so where the neurotransmitter is
+
+ align:start position:0%
+so where the neurotransmitter is
+ 
+
+ align:start position:0%
+so where the neurotransmitter is
+released and then it's taken up by the
+
+ align:start position:0%
+released and then it's taken up by the
+ 
+
+ align:start position:0%
+released and then it's taken up by the
+pratic cell which is kind of a a Frugal
+
+ align:start position:0%
+pratic cell which is kind of a a Frugal
+ 
+
+ align:start position:0%
+pratic cell which is kind of a a Frugal
+way of doing things it doesn't have to
+
+ align:start position:0%
+way of doing things it doesn't have to
+ 
+
+ align:start position:0%
+way of doing things it doesn't have to
+keep synthesizing the neurotransmitter
+
+ align:start position:0%
+keep synthesizing the neurotransmitter
+ 
+
+ align:start position:0%
+keep synthesizing the neurotransmitter
+and that so reabsorb reuptake by the
+
+ align:start position:0%
+and that so reabsorb reuptake by the
+ 
+
+ align:start position:0%
+and that so reabsorb reuptake by the
+pratic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell and that is the case for
+
+ align:start position:0%
+cell and that is the case for
+ 
+
+ align:start position:0%
+cell and that is the case for
+serotonin and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dopamine and then in some cases you can
+
+ align:start position:0%
+dopamine and then in some cases you can
+ 
+
+ align:start position:0%
+dopamine and then in some cases you can
+regulate the in synth is the amount of
+
+ align:start position:0%
+regulate the in synth is the amount of
+ 
+
+ align:start position:0%
+regulate the in synth is the amount of
+neurotransmitter that's being made and
+
+ align:start position:0%
+neurotransmitter that's being made and
+ 
+
+ align:start position:0%
+neurotransmitter that's being made and
+the big class of neurotransmitters
+
+ align:start position:0%
+the big class of neurotransmitters
+ 
+
+ align:start position:0%
+the big class of neurotransmitters
+regulated in this way are the
+
+ align:start position:0%
+regulated in this way are the
+ 
+
+ align:start position:0%
+regulated in this way are the
+endorphins which are a group of peptide
+
+ align:start position:0%
+endorphins which are a group of peptide
+ 
+
+ align:start position:0%
+endorphins which are a group of peptide
+neurotransmitters that are the natural
+
+ align:start position:0%
+neurotransmitters that are the natural
+ 
+
+ align:start position:0%
+neurotransmitters that are the natural
+opiates of the body the natural pain um
+
+ align:start position:0%
+opiates of the body the natural pain um
+ 
+
+ align:start position:0%
+opiates of the body the natural pain um
+Regulators of the body and all of these
+
+ align:start position:0%
+Regulators of the body and all of these
+ 
+
+ align:start position:0%
+Regulators of the body and all of these
+processes are regulatable both for
+
+ align:start position:0%
+processes are regulatable both for
+ 
+
+ align:start position:0%
+processes are regulatable both for
+modulating normal
+
+ align:start position:0%
+modulating normal
+ 
+
+ align:start position:0%
+modulating normal
+synapses and also in all cases for for
+
+ align:start position:0%
+synapses and also in all cases for for
+ 
+
+ align:start position:0%
+synapses and also in all cases for for
+medication um for medication targets for
+
+ align:start position:0%
+medication um for medication targets for
+ 
+
+ align:start position:0%
+medication um for medication targets for
+drug targets so normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modulation and Drug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+targets let's look at a couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slides acety choline is is a
+
+ align:start position:0%
+slides acety choline is is a
+ 
+
+ align:start position:0%
+slides acety choline is is a
+neurotransmitter that binds its receptor
+
+ align:start position:0%
+neurotransmitter that binds its receptor
+ 
+
+ align:start position:0%
+neurotransmitter that binds its receptor
+on the post synaptic membrane and after
+
+ align:start position:0%
+on the post synaptic membrane and after
+ 
+
+ align:start position:0%
+on the post synaptic membrane and after
+it's done so actil colonas the E here
+
+ align:start position:0%
+it's done so actil colonas the E here
+ 
+
+ align:start position:0%
+it's done so actil colonas the E here
+comes and breaks it down and stops IT
+
+ align:start position:0%
+comes and breaks it down and stops IT
+ 
+
+ align:start position:0%
+comes and breaks it down and stops IT
+restimulating the post synaptic
+
+ align:start position:0%
+restimulating the post synaptic
+ 
+
+ align:start position:0%
+restimulating the post synaptic
+cell many nerve
+
+ align:start position:0%
+cell many nerve
+ 
+
+ align:start position:0%
+cell many nerve
+gases sarin was one of the famous ones
+
+ align:start position:0%
+gases sarin was one of the famous ones
+ 
+
+ align:start position:0%
+gases sarin was one of the famous ones
+that was used in the Japanese
+
+ align:start position:0%
+that was used in the Japanese
+ 
+
+ align:start position:0%
+that was used in the Japanese
+underground some years ago inhibit atil
+
+ align:start position:0%
+underground some years ago inhibit atil
+ 
+
+ align:start position:0%
+underground some years ago inhibit atil
+colonas and in that case you get a
+
+ align:start position:0%
+colonas and in that case you get a
+ 
+
+ align:start position:0%
+colonas and in that case you get a
+buildup of acetel choline in the post in
+
+ align:start position:0%
+buildup of acetel choline in the post in
+ 
+
+ align:start position:0%
+buildup of acetel choline in the post in
+the synaptic cleft you get repeated
+
+ align:start position:0%
+the synaptic cleft you get repeated
+ 
+
+ align:start position:0%
+the synaptic cleft you get repeated
+stimulation of the post synaptic cell
+
+ align:start position:0%
+stimulation of the post synaptic cell
+ 
+
+ align:start position:0%
+stimulation of the post synaptic cell
+and that leads to as I said respiratory
+
+ align:start position:0%
+and that leads to as I said respiratory
+ 
+
+ align:start position:0%
+and that leads to as I said respiratory
+um paralysis and
+
+ align:start position:0%
+um paralysis and
+ 
+
+ align:start position:0%
+um paralysis and
+death our troops overseas have with them
+
+ align:start position:0%
+death our troops overseas have with them
+ 
+
+ align:start position:0%
+death our troops overseas have with them
+vials of
+
+ align:start position:0%
+vials of
+ 
+
+ align:start position:0%
+vials of
+atropine atropine is a competitive
+
+ align:start position:0%
+atropine atropine is a competitive
+ 
+
+ align:start position:0%
+atropine atropine is a competitive
+inhibitor of acetyl choline binds to the
+
+ align:start position:0%
+inhibitor of acetyl choline binds to the
+ 
+
+ align:start position:0%
+inhibitor of acetyl choline binds to the
+receptor and prevents acety choline from
+
+ align:start position:0%
+receptor and prevents acety choline from
+ 
+
+ align:start position:0%
+receptor and prevents acety choline from
+binding and in the case of a nerve gas
+
+ align:start position:0%
+binding and in the case of a nerve gas
+ 
+
+ align:start position:0%
+binding and in the case of a nerve gas
+attack if you inject yourself with
+
+ align:start position:0%
+attack if you inject yourself with
+ 
+
+ align:start position:0%
+attack if you inject yourself with
+atropine you'll stop the acetyl choline
+
+ align:start position:0%
+atropine you'll stop the acetyl choline
+ 
+
+ align:start position:0%
+atropine you'll stop the acetyl choline
+from working and you'll be okay you get
+
+ align:start position:0%
+from working and you'll be okay you get
+ 
+
+ align:start position:0%
+from working and you'll be okay you get
+a little kind of floppy but you can
+
+ align:start position:0%
+a little kind of floppy but you can
+ 
+
+ align:start position:0%
+a little kind of floppy but you can
+survive because they're alternate
+
+ align:start position:0%
+survive because they're alternate
+ 
+
+ align:start position:0%
+survive because they're alternate
+mechanisms of um stimulating those
+
+ align:start position:0%
+mechanisms of um stimulating those
+ 
+
+ align:start position:0%
+mechanisms of um stimulating those
+nerves
+
+ align:start position:0%
+nerves
+ 
+
+ align:start position:0%
+nerves
+okay here's serotonin the reuptake
+
+ align:start position:0%
+okay here's serotonin the reuptake
+ 
+
+ align:start position:0%
+okay here's serotonin the reuptake
+pathway serotonin is released as all
+
+ align:start position:0%
+pathway serotonin is released as all
+ 
+
+ align:start position:0%
+pathway serotonin is released as all
+neurotransmitters and then it's
+
+ align:start position:0%
+neurotransmitters and then it's
+ 
+
+ align:start position:0%
+neurotransmitters and then it's
+reabsorbed by the pratic cell and ssris
+
+ align:start position:0%
+reabsorbed by the pratic cell and ssris
+ 
+
+ align:start position:0%
+reabsorbed by the pratic cell and ssris
+whose mechanism of action is really not
+
+ align:start position:0%
+whose mechanism of action is really not
+ 
+
+ align:start position:0%
+whose mechanism of action is really not
+understood do something to block the
+
+ align:start position:0%
+understood do something to block the
+ 
+
+ align:start position:0%
+understood do something to block the
+re-uptake of
+
+ align:start position:0%
+re-uptake of
+ 
+
+ align:start position:0%
+re-uptake of
+Serotonin all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the other way clearly that one
+
+ align:start position:0%
+right the other way clearly that one
+ 
+
+ align:start position:0%
+right the other way clearly that one
+could modulate how often synapses are
+
+ align:start position:0%
+could modulate how often synapses are
+ 
+
+ align:start position:0%
+could modulate how often synapses are
+active or how often the post synaptic
+
+ align:start position:0%
+active or how often the post synaptic
+ 
+
+ align:start position:0%
+active or how often the post synaptic
+cell is stimulated is by modulating The
+
+ align:start position:0%
+cell is stimulated is by modulating The
+ 
+
+ align:start position:0%
+cell is stimulated is by modulating The
+receptors intuitively if you have more
+
+ align:start position:0%
+receptors intuitively if you have more
+ 
+
+ align:start position:0%
+receptors intuitively if you have more
+receptors the neurotransmitter has more
+
+ align:start position:0%
+receptors the neurotransmitter has more
+ 
+
+ align:start position:0%
+receptors the neurotransmitter has more
+place to bind it can send a greater
+
+ align:start position:0%
+place to bind it can send a greater
+ 
+
+ align:start position:0%
+place to bind it can send a greater
+signal by changing membrane potential if
+
+ align:start position:0%
+signal by changing membrane potential if
+ 
+
+ align:start position:0%
+signal by changing membrane potential if
+you decrease the number of receptors and
+
+ align:start position:0%
+you decrease the number of receptors and
+ 
+
+ align:start position:0%
+you decrease the number of receptors and
+so on and it turns out if you modify The
+
+ align:start position:0%
+so on and it turns out if you modify The
+ 
+
+ align:start position:0%
+so on and it turns out if you modify The
+receptors if you put phosphate groups on
+
+ align:start position:0%
+receptors if you put phosphate groups on
+ 
+
+ align:start position:0%
+receptors if you put phosphate groups on
+them sometimes you can also change how
+
+ align:start position:0%
+them sometimes you can also change how
+ 
+
+ align:start position:0%
+them sometimes you can also change how
+well they act so the other thing to
+
+ align:start position:0%
+well they act so the other thing to
+ 
+
+ align:start position:0%
+well they act so the other thing to
+do to modulate synaptic activity is by
+
+ align:start position:0%
+do to modulate synaptic activity is by
+ 
+
+ align:start position:0%
+do to modulate synaptic activity is by
+changing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receptors and there are really three
+
+ align:start position:0%
+receptors and there are really three
+ 
+
+ align:start position:0%
+receptors and there are really three
+ways to do
+
+ align:start position:0%
+ways to do
+ 
+
+ align:start position:0%
+ways to do
+this change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number or change in the type the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtype of a receptor where there might
+
+ align:start position:0%
+subtype of a receptor where there might
+ 
+
+ align:start position:0%
+subtype of a receptor where there might
+be a subtle change in amino acid because
+
+ align:start position:0%
+be a subtle change in amino acid because
+ 
+
+ align:start position:0%
+be a subtle change in amino acid because
+you're using now a different Gene to
+
+ align:start position:0%
+you're using now a different Gene to
+ 
+
+ align:start position:0%
+you're using now a different Gene to
+make the receptor you can increase or
+
+ align:start position:0%
+make the receptor you can increase or
+ 
+
+ align:start position:0%
+make the receptor you can increase or
+change the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+affinity for
+
+ align:start position:0%
+affinity for
+ 
+
+ align:start position:0%
+affinity for
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neurotransmitter and you can change
+
+ align:start position:0%
+neurotransmitter and you can change
+ 
+
+ align:start position:0%
+neurotransmitter and you can change
+receptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+responsiveness all of these three things
+
+ align:start position:0%
+responsiveness all of these three things
+ 
+
+ align:start position:0%
+responsiveness all of these three things
+have got something to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+learning and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+memory they have to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+addiction and all of these changes are
+
+ align:start position:0%
+addiction and all of these changes are
+ 
+
+ align:start position:0%
+addiction and all of these changes are
+slow they occur over
+
+ align:start position:0%
+slow they occur over
+ 
+
+ align:start position:0%
+slow they occur over
+minutes
+
+ align:start position:0%
+minutes
+ 
+
+ align:start position:0%
+minutes
+days weeks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even and for some we understand how
+
+ align:start position:0%
+even and for some we understand how
+ 
+
+ align:start position:0%
+even and for some we understand how
+these changes occur but for many we
+
+ align:start position:0%
+these changes occur but for many we
+ 
+
+ align:start position:0%
+these changes occur but for many we
+don't the outcome of changing the
+
+ align:start position:0%
+don't the outcome of changing the
+ 
+
+ align:start position:0%
+don't the outcome of changing the
+receptors and I see we have a board
+
+ align:start position:0%
+receptors and I see we have a board
+ 
+
+ align:start position:0%
+receptors and I see we have a board
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+here um so I'm going to put this on
+
+ align:start position:0%
+here um so I'm going to put this on
+ 
+
+ align:start position:0%
+here um so I'm going to put this on
+actually let me put this board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down and this board
+
+ align:start position:0%
+down and this board
+ 
+
+ align:start position:0%
+down and this board
+up one of the outcomes of changing all
+
+ align:start position:0%
+up one of the outcomes of changing all
+ 
+
+ align:start position:0%
+up one of the outcomes of changing all
+of these parameters about The receptors
+
+ align:start position:0%
+of these parameters about The receptors
+ 
+
+ align:start position:0%
+of these parameters about The receptors
+is that over a long period of time you
+
+ align:start position:0%
+is that over a long period of time you
+ 
+
+ align:start position:0%
+is that over a long period of time you
+really change how a synapse works and
+
+ align:start position:0%
+really change how a synapse works and
+ 
+
+ align:start position:0%
+really change how a synapse works and
+you can change how a synapse Works
+
+ align:start position:0%
+you can change how a synapse Works
+ 
+
+ align:start position:0%
+you can change how a synapse Works
+through these parameters by repeatedly
+
+ align:start position:0%
+through these parameters by repeatedly
+ 
+
+ align:start position:0%
+through these parameters by repeatedly
+stimulating that synapse okay this is
+
+ align:start position:0%
+stimulating that synapse okay this is
+ 
+
+ align:start position:0%
+stimulating that synapse okay this is
+what practice does when you practice
+
+ align:start position:0%
+what practice does when you practice
+ 
+
+ align:start position:0%
+what practice does when you practice
+your musical instrument or you practice
+
+ align:start position:0%
+your musical instrument or you practice
+ 
+
+ align:start position:0%
+your musical instrument or you practice
+your biochemistry problems and you do it
+
+ align:start position:0%
+your biochemistry problems and you do it
+ 
+
+ align:start position:0%
+your biochemistry problems and you do it
+over and over you're changing the
+
+ align:start position:0%
+over and over you're changing the
+ 
+
+ align:start position:0%
+over and over you're changing the
+synapses that allow you to engage these
+
+ align:start position:0%
+synapses that allow you to engage these
+ 
+
+ align:start position:0%
+synapses that allow you to engage these
+problems and these
+
+ align:start position:0%
+problems and these
+ 
+
+ align:start position:0%
+problems and these
+processes have got names so let me just
+
+ align:start position:0%
+processes have got names so let me just
+ 
+
+ align:start position:0%
+processes have got names so let me just
+complete this so by changing receptors
+
+ align:start position:0%
+complete this so by changing receptors
+ 
+
+ align:start position:0%
+complete this so by changing receptors
+so that repeated synaptic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stimulation changes the responsiveness
+
+ align:start position:0%
+stimulation changes the responsiveness
+ 
+
+ align:start position:0%
+stimulation changes the responsiveness
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synapse generally
+
+ align:start position:0%
+synapse generally
+ 
+
+ align:start position:0%
+synapse generally
+as I say Through The receptors in this
+
+ align:start position:0%
+as I say Through The receptors in this
+ 
+
+ align:start position:0%
+as I say Through The receptors in this
+case okay and they there there two
+
+ align:start position:0%
+case okay and they there there two
+ 
+
+ align:start position:0%
+case okay and they there there two
+outputs one you can
+
+ align:start position:0%
+outputs one you can
+ 
+
+ align:start position:0%
+outputs one you can
+increase the synaptic response you can
+
+ align:start position:0%
+increase the synaptic response you can
+ 
+
+ align:start position:0%
+increase the synaptic response you can
+make it more likely that there'll be an
+
+ align:start position:0%
+make it more likely that there'll be an
+ 
+
+ align:start position:0%
+make it more likely that there'll be an
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+potential and that would take place at
+
+ align:start position:0%
+potential and that would take place at
+ 
+
+ align:start position:0%
+potential and that would take place at
+excitatory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synapsis and this process is known as
+
+ align:start position:0%
+synapsis and this process is known as
+ 
+
+ align:start position:0%
+synapsis and this process is known as
+long long term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentiation it's the stuff you want
+
+ align:start position:0%
+potentiation it's the stuff you want
+ 
+
+ align:start position:0%
+potentiation it's the stuff you want
+when you're trying to learn something
+
+ align:start position:0%
+when you're trying to learn something
+ 
+
+ align:start position:0%
+when you're trying to learn something
+it's believed to be the way memory works
+
+ align:start position:0%
+it's believed to be the way memory works
+ 
+
+ align:start position:0%
+it's believed to be the way memory works
+you can also decrease the response of a
+
+ align:start position:0%
+you can also decrease the response of a
+ 
+
+ align:start position:0%
+you can also decrease the response of a
+particular synapse and that would work
+
+ align:start position:0%
+particular synapse and that would work
+ 
+
+ align:start position:0%
+particular synapse and that would work
+if it was an inhibitory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synapse and in that case the process is
+
+ align:start position:0%
+synapse and in that case the process is
+ 
+
+ align:start position:0%
+synapse and in that case the process is
+called long-term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's just write it out
+
+ align:start position:0%
+let's just write it out
+ 
+
+ align:start position:0%
+let's just write it out
+long-term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depression both of these processes have
+
+ align:start position:0%
+depression both of these processes have
+ 
+
+ align:start position:0%
+depression both of these processes have
+been shown to work in the lab in culture
+
+ align:start position:0%
+been shown to work in the lab in culture
+ 
+
+ align:start position:0%
+been shown to work in the lab in culture
+hard to do those experiments in real
+
+ align:start position:0%
+hard to do those experiments in real
+ 
+
+ align:start position:0%
+hard to do those experiments in real
+animals but it's believed that that's
+
+ align:start position:0%
+animals but it's believed that that's
+ 
+
+ align:start position:0%
+animals but it's believed that that's
+how memory works so on your first
+
+ align:start position:0%
+how memory works so on your first
+ 
+
+ align:start position:0%
+how memory works so on your first
+handout I've drawn out for you the idea
+
+ align:start position:0%
+handout I've drawn out for you the idea
+ 
+
+ align:start position:0%
+handout I've drawn out for you the idea
+here's a normal axon the pr synaptic and
+
+ align:start position:0%
+here's a normal axon the pr synaptic and
+ 
+
+ align:start position:0%
+here's a normal axon the pr synaptic and
+the post synaptic cell neurotrans
+
+ align:start position:0%
+the post synaptic cell neurotrans
+ 
+
+ align:start position:0%
+the post synaptic cell neurotrans
+Transit is released it engages receptors
+
+ align:start position:0%
+Transit is released it engages receptors
+ 
+
+ align:start position:0%
+Transit is released it engages receptors
+and at some frequency there's an action
+
+ align:start position:0%
+and at some frequency there's an action
+ 
+
+ align:start position:0%
+and at some frequency there's an action
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+elicited if you change if you repeatedly
+
+ align:start position:0%
+elicited if you change if you repeatedly
+ 
+
+ align:start position:0%
+elicited if you change if you repeatedly
+stimulate that axon over time days
+
+ align:start position:0%
+stimulate that axon over time days
+ 
+
+ align:start position:0%
+stimulate that axon over time days
+minutes you change the receptor Spectrum
+
+ align:start position:0%
+minutes you change the receptor Spectrum
+ 
+
+ align:start position:0%
+minutes you change the receptor Spectrum
+on the post synaptic cell and in
+
+ align:start position:0%
+on the post synaptic cell and in
+ 
+
+ align:start position:0%
+on the post synaptic cell and in
+long-term potentiation responsiveness
+
+ align:start position:0%
+long-term potentiation responsiveness
+ 
+
+ align:start position:0%
+long-term potentiation responsiveness
+increases whereas in long-term
+
+ align:start position:0%
+increases whereas in long-term
+ 
+
+ align:start position:0%
+increases whereas in long-term
+depression you decrease receptor number
+
+ align:start position:0%
+depression you decrease receptor number
+ 
+
+ align:start position:0%
+depression you decrease receptor number
+or some other parameter and you lead to
+
+ align:start position:0%
+or some other parameter and you lead to
+ 
+
+ align:start position:0%
+or some other parameter and you lead to
+decreased responsiveness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let us move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to our second topic which is that of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circuits which refers to multiple
+
+ align:start position:0%
+circuits which refers to multiple
+ 
+
+ align:start position:0%
+circuits which refers to multiple
+connectivities multiple synapses forming
+
+ align:start position:0%
+connectivities multiple synapses forming
+ 
+
+ align:start position:0%
+connectivities multiple synapses forming
+in a way that is stable and that can
+
+ align:start position:0%
+in a way that is stable and that can
+ 
+
+ align:start position:0%
+in a way that is stable and that can
+lead to particular outcomes of
+
+ align:start position:0%
+lead to particular outcomes of
+ 
+
+ align:start position:0%
+lead to particular outcomes of
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stimuli let's look at your next handout
+
+ align:start position:0%
+stimuli let's look at your next handout
+ 
+
+ align:start position:0%
+stimuli let's look at your next handout
+to try to get a sense of where we
+
+ align:start position:0%
+to try to get a sense of where we
+ 
+
+ align:start position:0%
+to try to get a sense of where we
+are so I've diagrammed this out for you
+
+ align:start position:0%
+are so I've diagrammed this out for you
+ 
+
+ align:start position:0%
+are so I've diagrammed this out for you
+and I've started here with some kind of
+
+ align:start position:0%
+and I've started here with some kind of
+ 
+
+ align:start position:0%
+and I've started here with some kind of
+sensory neuron an interneuron and a
+
+ align:start position:0%
+sensory neuron an interneuron and a
+ 
+
+ align:start position:0%
+sensory neuron an interneuron and a
+motor neuron three connected
+
+ align:start position:0%
+motor neuron three connected
+ 
+
+ align:start position:0%
+motor neuron three connected
+neurons you could put a lot of these
+
+ align:start position:0%
+neurons you could put a lot of these
+ 
+
+ align:start position:0%
+neurons you could put a lot of these
+other things called called interneurons
+
+ align:start position:0%
+other things called called interneurons
+ 
+
+ align:start position:0%
+other things called called interneurons
+in the way Sensory neurons receive
+
+ align:start position:0%
+in the way Sensory neurons receive
+ 
+
+ align:start position:0%
+in the way Sensory neurons receive
+signals motor neurons tell things to
+
+ align:start position:0%
+signals motor neurons tell things to
+ 
+
+ align:start position:0%
+signals motor neurons tell things to
+happen like muscles to work and Inter
+
+ align:start position:0%
+happen like muscles to work and Inter
+ 
+
+ align:start position:0%
+happen like muscles to work and Inter
+neurons of which there can be many are
+
+ align:start position:0%
+neurons of which there can be many are
+ 
+
+ align:start position:0%
+neurons of which there can be many are
+the connectors between sensory and motor
+
+ align:start position:0%
+the connectors between sensory and motor
+ 
+
+ align:start position:0%
+the connectors between sensory and motor
+neurons there's an input and there's an
+
+ align:start position:0%
+neurons there's an input and there's an
+ 
+
+ align:start position:0%
+neurons there's an input and there's an
+output and what happens in
+
+ align:start position:0%
+output and what happens in
+ 
+
+ align:start position:0%
+output and what happens in
+between this is a synthesis of what
+
+ align:start position:0%
+between this is a synthesis of what
+ 
+
+ align:start position:0%
+between this is a synthesis of what
+we've talked about over the last couple
+
+ align:start position:0%
+we've talked about over the last couple
+ 
+
+ align:start position:0%
+we've talked about over the last couple
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+lectures the sensory neuron makes
+
+ align:start position:0%
+lectures the sensory neuron makes
+ 
+
+ align:start position:0%
+lectures the sensory neuron makes
+multiple synapses onto the interneuron
+
+ align:start position:0%
+multiple synapses onto the interneuron
+ 
+
+ align:start position:0%
+multiple synapses onto the interneuron
+they can be excitatory or inhibitory
+
+ align:start position:0%
+they can be excitatory or inhibitory
+ 
+
+ align:start position:0%
+they can be excitatory or inhibitory
+they're summated the interneuron then
+
+ align:start position:0%
+they're summated the interneuron then
+ 
+
+ align:start position:0%
+they're summated the interneuron then
+decides whether to make an action
+
+ align:start position:0%
+decides whether to make an action
+ 
+
+ align:start position:0%
+decides whether to make an action
+potential or not action potential yes or
+
+ align:start position:0%
+potential or not action potential yes or
+ 
+
+ align:start position:0%
+potential or not action potential yes or
+no in each case if it makes an action
+
+ align:start position:0%
+no in each case if it makes an action
+ 
+
+ align:start position:0%
+no in each case if it makes an action
+potential it sends its signal to the
+
+ align:start position:0%
+potential it sends its signal to the
+ 
+
+ align:start position:0%
+potential it sends its signal to the
+next neuron the motor neuron that motor
+
+ align:start position:0%
+next neuron the motor neuron that motor
+ 
+
+ align:start position:0%
+next neuron the motor neuron that motor
+neuron is getting a bunch of inputs
+
+ align:start position:0%
+neuron is getting a bunch of inputs
+ 
+
+ align:start position:0%
+neuron is getting a bunch of inputs
+excitatory or inhibitory and it again
+
+ align:start position:0%
+excitatory or inhibitory and it again
+ 
+
+ align:start position:0%
+excitatory or inhibitory and it again
+has to decide whether or not there's an
+
+ align:start position:0%
+has to decide whether or not there's an
+ 
+
+ align:start position:0%
+has to decide whether or not there's an
+action potential okay so that's the
+
+ align:start position:0%
+action potential okay so that's the
+ 
+
+ align:start position:0%
+action potential okay so that's the
+context that puts circuits where we have
+
+ align:start position:0%
+context that puts circuits where we have
+ 
+
+ align:start position:0%
+context that puts circuits where we have
+been discussing the process of setting
+
+ align:start position:0%
+been discussing the process of setting
+ 
+
+ align:start position:0%
+been discussing the process of setting
+up the connections in the nervous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system the thing about circuits and
+
+ align:start position:0%
+system the thing about circuits and
+ 
+
+ align:start position:0%
+system the thing about circuits and
+here's a term you should know is that
+
+ align:start position:0%
+here's a term you should know is that
+ 
+
+ align:start position:0%
+here's a term you should know is that
+they have to do with
+
+ align:start position:0%
+they have to do with
+ 
+
+ align:start position:0%
+they have to do with
+axon path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finding and so let's for a moment forget
+
+ align:start position:0%
+finding and so let's for a moment forget
+ 
+
+ align:start position:0%
+finding and so let's for a moment forget
+this diag
+
+ align:start position:0%
+this diag
+ 
+
+ align:start position:0%
+this diag
+which is a diagram of what there is in
+
+ align:start position:0%
+which is a diagram of what there is in
+ 
+
+ align:start position:0%
+which is a diagram of what there is in
+the adult and let's think about how
+
+ align:start position:0%
+the adult and let's think about how
+ 
+
+ align:start position:0%
+the adult and let's think about how
+these circuits are set up the circuits
+
+ align:start position:0%
+these circuits are set up the circuits
+ 
+
+ align:start position:0%
+these circuits are set up the circuits
+that we have in our brains and in our
+
+ align:start position:0%
+that we have in our brains and in our
+ 
+
+ align:start position:0%
+that we have in our brains and in our
+bodies are of the close to uncountable
+
+ align:start position:0%
+bodies are of the close to uncountable
+ 
+
+ align:start position:0%
+bodies are of the close to uncountable
+I'm not sure we ever will count them in
+
+ align:start position:0%
+I'm not sure we ever will count them in
+ 
+
+ align:start position:0%
+I'm not sure we ever will count them in
+an animal as complex as ourselves it's
+
+ align:start position:0%
+an animal as complex as ourselves it's
+ 
+
+ align:start position:0%
+an animal as complex as ourselves it's
+been done in
+
+ align:start position:0%
+been done in
+ 
+
+ align:start position:0%
+been done in
+cbtis which has got a thousand cells the
+
+ align:start position:0%
+cbtis which has got a thousand cells the
+ 
+
+ align:start position:0%
+cbtis which has got a thousand cells the
+little worm we talked about it's got a
+
+ align:start position:0%
+little worm we talked about it's got a
+ 
+
+ align:start position:0%
+little worm we talked about it's got a
+thousand cells and all of the connect
+
+ align:start position:0%
+thousand cells and all of the connect
+ 
+
+ align:start position:0%
+thousand cells and all of the connect
+in cbdas have been mapped and they are
+
+ align:start position:0%
+in cbdas have been mapped and they are
+ 
+
+ align:start position:0%
+in cbdas have been mapped and they are
+extremely complex but that's just a
+
+ align:start position:0%
+extremely complex but that's just a
+ 
+
+ align:start position:0%
+extremely complex but that's just a
+handful of neurons when you're talking
+
+ align:start position:0%
+handful of neurons when you're talking
+ 
+
+ align:start position:0%
+handful of neurons when you're talking
+about 10 to the 10th 10 to the 11th
+
+ align:start position:0%
+about 10 to the 10th 10 to the 11th
+ 
+
+ align:start position:0%
+about 10 to the 10th 10 to the 11th
+neurons those connections are
+
+ align:start position:0%
+neurons those connections are
+ 
+
+ align:start position:0%
+neurons those connections are
+enormous but we can ask some basic
+
+ align:start position:0%
+enormous but we can ask some basic
+ 
+
+ align:start position:0%
+enormous but we can ask some basic
+questions okay and let's just state it
+
+ align:start position:0%
+questions okay and let's just state it
+ 
+
+ align:start position:0%
+questions okay and let's just state it
+neurons are
+
+ align:start position:0%
+neurons are
+ 
+
+ align:start position:0%
+neurons are
+connected to form circuits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can say that they're functional
+
+ align:start position:0%
+we can say that they're functional
+ 
+
+ align:start position:0%
+we can say that they're functional
+circuits if you
+
+ align:start position:0%
+circuits if you
+ 
+
+ align:start position:0%
+circuits if you
+like that is implicit and the big
+
+ align:start position:0%
+like that is implicit and the big
+ 
+
+ align:start position:0%
+like that is implicit and the big
+question is how do these circuits know
+
+ align:start position:0%
+question is how do these circuits know
+ 
+
+ align:start position:0%
+question is how do these circuits know
+where to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form or if you like the
+
+ align:start position:0%
+form or if you like the
+ 
+
+ align:start position:0%
+form or if you like the
+restatement how do the neurons know
+
+ align:start position:0%
+restatement how do the neurons know
+ 
+
+ align:start position:0%
+restatement how do the neurons know
+where to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know where to go and where to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connect and there are two kind of
+
+ align:start position:0%
+connect and there are two kind of
+ 
+
+ align:start position:0%
+connect and there are two kind of
+intuitive answers both of which turn out
+
+ align:start position:0%
+intuitive answers both of which turn out
+ 
+
+ align:start position:0%
+intuitive answers both of which turn out
+to be correct either the neurons just go
+
+ align:start position:0%
+to be correct either the neurons just go
+ 
+
+ align:start position:0%
+to be correct either the neurons just go
+every which way and if it works that's
+
+ align:start position:0%
+every which way and if it works that's
+ 
+
+ align:start position:0%
+every which way and if it works that's
+retained and the rest of the connections
+
+ align:start position:0%
+retained and the rest of the connections
+ 
+
+ align:start position:0%
+retained and the rest of the connections
+just are dissolved and go way and that's
+
+ align:start position:0%
+just are dissolved and go way and that's
+ 
+
+ align:start position:0%
+just are dissolved and go way and that's
+true but the bigger truth is that the
+
+ align:start position:0%
+true but the bigger truth is that the
+ 
+
+ align:start position:0%
+true but the bigger truth is that the
+neurons are told where to
+
+ align:start position:0%
+neurons are told where to
+ 
+
+ align:start position:0%
+neurons are told where to
+go so you can phrase these that the
+
+ align:start position:0%
+go so you can phrase these that the
+ 
+
+ align:start position:0%
+go so you can phrase these that the
+neurons undergo some kind of random
+
+ align:start position:0%
+neurons undergo some kind of random
+ 
+
+ align:start position:0%
+neurons undergo some kind of random
+process where neurons
+
+ align:start position:0%
+process where neurons
+ 
+
+ align:start position:0%
+process where neurons
+survive if connections M are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+made or there's some kind of guided
+
+ align:start position:0%
+made or there's some kind of guided
+ 
+
+ align:start position:0%
+made or there's some kind of guided
+process where the neurons are told where
+
+ align:start position:0%
+process where the neurons are told where
+ 
+
+ align:start position:0%
+process where the neurons are told where
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go and both of these turn out after many
+
+ align:start position:0%
+go and both of these turn out after many
+ 
+
+ align:start position:0%
+go and both of these turn out after many
+many years of work to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct let's look at some slides here
+
+ align:start position:0%
+correct let's look at some slides here
+ 
+
+ align:start position:0%
+correct let's look at some slides here
+this is work from Professor fee over in
+
+ align:start position:0%
+this is work from Professor fee over in
+ 
+
+ align:start position:0%
+this is work from Professor fee over in
+brain and cognitive science he studies
+
+ align:start position:0%
+brain and cognitive science he studies
+ 
+
+ align:start position:0%
+brain and cognitive science he studies
+these little books birds and their s
+
+ align:start position:0%
+these little books birds and their s
+ 
+
+ align:start position:0%
+these little books birds and their s
+circuit which forms and reforms during
+
+ align:start position:0%
+circuit which forms and reforms during
+ 
+
+ align:start position:0%
+circuit which forms and reforms during
+the life of the bird the circuit is
+
+ align:start position:0%
+the life of the bird the circuit is
+ 
+
+ align:start position:0%
+the life of the bird the circuit is
+complicated these are not single neurons
+
+ align:start position:0%
+complicated these are not single neurons
+ 
+
+ align:start position:0%
+complicated these are not single neurons
+there are bundles of neurons but it's
+
+ align:start position:0%
+there are bundles of neurons but it's
+ 
+
+ align:start position:0%
+there are bundles of neurons but it's
+kind of mappable and this is one of the
+
+ align:start position:0%
+kind of mappable and this is one of the
+ 
+
+ align:start position:0%
+kind of mappable and this is one of the
+circuits it's got something to do with
+
+ align:start position:0%
+circuits it's got something to do with
+ 
+
+ align:start position:0%
+circuits it's got something to do with
+song within the bird brain it's not the
+
+ align:start position:0%
+song within the bird brain it's not the
+ 
+
+ align:start position:0%
+song within the bird brain it's not the
+entire circuit that's one of the things
+
+ align:start position:0%
+entire circuit that's one of the things
+ 
+
+ align:start position:0%
+entire circuit that's one of the things
+that's going on here on
+
+ align:start position:0%
+that's going on here on
+ 
+
+ align:start position:0%
+that's going on here on
+campus but when you start thinking about
+
+ align:start position:0%
+campus but when you start thinking about
+ 
+
+ align:start position:0%
+campus but when you start thinking about
+things like language I really like the
+
+ align:start position:0%
+things like language I really like the
+ 
+
+ align:start position:0%
+things like language I really like the
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+because these are activity plots of the
+
+ align:start position:0%
+because these are activity plots of the
+ 
+
+ align:start position:0%
+because these are activity plots of the
+brain that can be done in a number of
+
+ align:start position:0%
+brain that can be done in a number of
+ 
+
+ align:start position:0%
+brain that can be done in a number of
+ways by monitoring oxygen uptake or
+
+ align:start position:0%
+ways by monitoring oxygen uptake or
+ 
+
+ align:start position:0%
+ways by monitoring oxygen uptake or
+glucose use but you can look and see
+
+ align:start position:0%
+glucose use but you can look and see
+ 
+
+ align:start position:0%
+glucose use but you can look and see
+different parts of the brain active and
+
+ align:start position:0%
+different parts of the brain active and
+ 
+
+ align:start position:0%
+different parts of the brain active and
+when you think about language here are
+
+ align:start position:0%
+when you think about language here are
+ 
+
+ align:start position:0%
+when you think about language here are
+these four parts of the brain actually
+
+ align:start position:0%
+these four parts of the brain actually
+ 
+
+ align:start position:0%
+these four parts of the brain actually
+here's a huge part of the brain used to
+
+ align:start position:0%
+here's a huge part of the brain used to
+ 
+
+ align:start position:0%
+here's a huge part of the brain used to
+generate words each of these parts of
+
+ align:start position:0%
+generate words each of these parts of
+ 
+
+ align:start position:0%
+generate words each of these parts of
+the brain are millions and millions of
+
+ align:start position:0%
+the brain are millions and millions of
+ 
+
+ align:start position:0%
+the brain are millions and millions of
+neurons which are connected to one
+
+ align:start position:0%
+neurons which are connected to one
+ 
+
+ align:start position:0%
+neurons which are connected to one
+another within these regions
+
+ align:start position:0%
+another within these regions
+ 
+
+ align:start position:0%
+another within these regions
+and then each of these regions is
+
+ align:start position:0%
+and then each of these regions is
+ 
+
+ align:start position:0%
+and then each of these regions is
+connected to one another and each of
+
+ align:start position:0%
+connected to one another and each of
+ 
+
+ align:start position:0%
+connected to one another and each of
+those regions is connected to the output
+
+ align:start position:0%
+those regions is connected to the output
+ 
+
+ align:start position:0%
+those regions is connected to the output
+which would be all of your vocal
+
+ align:start position:0%
+which would be all of your vocal
+ 
+
+ align:start position:0%
+which would be all of your vocal
+apparatus and all of this is connected
+
+ align:start position:0%
+apparatus and all of this is connected
+ 
+
+ align:start position:0%
+apparatus and all of this is connected
+to your auditory apparatus to your
+
+ align:start position:0%
+to your auditory apparatus to your
+ 
+
+ align:start position:0%
+to your auditory apparatus to your
+visual system so that you can read words
+
+ align:start position:0%
+visual system so that you can read words
+ 
+
+ align:start position:0%
+visual system so that you can read words
+they can be processed and so on the
+
+ align:start position:0%
+they can be processed and so on the
+ 
+
+ align:start position:0%
+they can be processed and so on the
+connections that give language probably
+
+ align:start position:0%
+connections that give language probably
+ 
+
+ align:start position:0%
+connections that give language probably
+take a very large part of your brain I
+
+ align:start position:0%
+take a very large part of your brain I
+ 
+
+ align:start position:0%
+take a very large part of your brain I
+would throw out 15 to 20% of your brain
+
+ align:start position:0%
+would throw out 15 to 20% of your brain
+ 
+
+ align:start position:0%
+would throw out 15 to 20% of your brain
+is involved in some aspect of language
+
+ align:start position:0%
+is involved in some aspect of language
+ 
+
+ align:start position:0%
+is involved in some aspect of language
+receiving generating or output and the
+
+ align:start position:0%
+receiving generating or output and the
+ 
+
+ align:start position:0%
+receiving generating or output and the
+circuits there as I said are enormous
+
+ align:start position:0%
+circuits there as I said are enormous
+ 
+
+ align:start position:0%
+circuits there as I said are enormous
+okay so do neurons know where to go let
+
+ align:start position:0%
+okay so do neurons know where to go let
+ 
+
+ align:start position:0%
+okay so do neurons know where to go let
+me go with you this isn't on your
+
+ align:start position:0%
+me go with you this isn't on your
+ 
+
+ align:start position:0%
+me go with you this isn't on your
+handout this is to look on the screen do
+
+ align:start position:0%
+handout this is to look on the screen do
+ 
+
+ align:start position:0%
+handout this is to look on the screen do
+neurons know where to connect there was
+
+ align:start position:0%
+neurons know where to connect there was
+ 
+
+ align:start position:0%
+neurons know where to connect there was
+a very famous experiment done by sper
+
+ align:start position:0%
+a very famous experiment done by sper
+ 
+
+ align:start position:0%
+a very famous experiment done by sper
+some many years ago Roger Sperry who got
+
+ align:start position:0%
+some many years ago Roger Sperry who got
+ 
+
+ align:start position:0%
+some many years ago Roger Sperry who got
+a Nobel Prize for his work that involved
+
+ align:start position:0%
+a Nobel Prize for his work that involved
+ 
+
+ align:start position:0%
+a Nobel Prize for his work that involved
+a frog and it involved figuring out
+
+ align:start position:0%
+a frog and it involved figuring out
+ 
+
+ align:start position:0%
+a frog and it involved figuring out
+where the neurons in the retina went so
+
+ align:start position:0%
+where the neurons in the retina went so
+ 
+
+ align:start position:0%
+where the neurons in the retina went so
+it turns out if you look at your eyes
+
+ align:start position:0%
+it turns out if you look at your eyes
+ 
+
+ align:start position:0%
+it turns out if you look at your eyes
+okay there are neurons that go from your
+
+ align:start position:0%
+okay there are neurons that go from your
+ 
+
+ align:start position:0%
+okay there are neurons that go from your
+eye back into your
+
+ align:start position:0%
+eye back into your
+ 
+
+ align:start position:0%
+eye back into your
+brain the neurons on the side of your
+
+ align:start position:0%
+brain the neurons on the side of your
+ 
+
+ align:start position:0%
+brain the neurons on the side of your
+nose are called the nasal neurons and
+
+ align:start position:0%
+nose are called the nasal neurons and
+ 
+
+ align:start position:0%
+nose are called the nasal neurons and
+the neurons on the side of your the
+
+ align:start position:0%
+the neurons on the side of your the
+ 
+
+ align:start position:0%
+the neurons on the side of your the
+outside of your face are called temporal
+
+ align:start position:0%
+outside of your face are called temporal
+ 
+
+ align:start position:0%
+outside of your face are called temporal
+neurons and what sper did was to take an
+
+ align:start position:0%
+neurons and what sper did was to take an
+ 
+
+ align:start position:0%
+neurons and what sper did was to take an
+adult frog and rotate the eye
+
+ align:start position:0%
+adult frog and rotate the eye
+ 
+
+ align:start position:0%
+adult frog and rotate the eye
+180° so that the nasal neurons would now
+
+ align:start position:0%
+180° so that the nasal neurons would now
+ 
+
+ align:start position:0%
+180° so that the nasal neurons would now
+be on the outside of the head the
+
+ align:start position:0%
+be on the outside of the head the
+ 
+
+ align:start position:0%
+be on the outside of the head the
+temporal neurons would be on the inside
+
+ align:start position:0%
+temporal neurons would be on the inside
+ 
+
+ align:start position:0%
+temporal neurons would be on the inside
+of the head okay and you know for a
+
+ align:start position:0%
+of the head okay and you know for a
+ 
+
+ align:start position:0%
+of the head okay and you know for a
+while after the operation the Frog was
+
+ align:start position:0%
+while after the operation the Frog was
+ 
+
+ align:start position:0%
+while after the operation the Frog was
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+confused but after a while it actually
+
+ align:start position:0%
+confused but after a while it actually
+ 
+
+ align:start position:0%
+confused but after a while it actually
+recovered so let's lay out this and the
+
+ align:start position:0%
+recovered so let's lay out this and the
+ 
+
+ align:start position:0%
+recovered so let's lay out this and the
+recovery as I'm going to tell you told
+
+ align:start position:0%
+recovery as I'm going to tell you told
+ 
+
+ align:start position:0%
+recovery as I'm going to tell you told
+Sperry and the world that neurons were
+
+ align:start position:0%
+Sperry and the world that neurons were
+ 
+
+ align:start position:0%
+Sperry and the world that neurons were
+told where to go so here is the retina
+
+ align:start position:0%
+told where to go so here is the retina
+ 
+
+ align:start position:0%
+told where to go so here is the retina
+depicted as a circle and here's a part
+
+ align:start position:0%
+depicted as a circle and here's a part
+ 
+
+ align:start position:0%
+depicted as a circle and here's a part
+of the brain called the optic tectum
+
+ align:start position:0%
+of the brain called the optic tectum
+ 
+
+ align:start position:0%
+of the brain called the optic tectum
+that the neurons connect to it's the
+
+ align:start position:0%
+that the neurons connect to it's the
+ 
+
+ align:start position:0%
+that the neurons connect to it's the
+first part of their circuit here are the
+
+ align:start position:0%
+first part of their circuit here are the
+ 
+
+ align:start position:0%
+first part of their circuit here are the
+temporal neurons connecting to the C
+
+ align:start position:0%
+temporal neurons connecting to the C
+ 
+
+ align:start position:0%
+temporal neurons connecting to the C
+region of the brain and the nasal
+
+ align:start position:0%
+region of the brain and the nasal
+ 
+
+ align:start position:0%
+region of the brain and the nasal
+neurons connecting to the r
+
+ align:start position:0%
+neurons connecting to the r
+ 
+
+ align:start position:0%
+neurons connecting to the r
+region so after to this rotation there
+
+ align:start position:0%
+region so after to this rotation there
+ 
+
+ align:start position:0%
+region so after to this rotation there
+were two possibilities one was that the
+
+ align:start position:0%
+were two possibilities one was that the
+ 
+
+ align:start position:0%
+were two possibilities one was that the
+axons growing out so so let's let's just
+
+ align:start position:0%
+axons growing out so so let's let's just
+ 
+
+ align:start position:0%
+axons growing out so so let's let's just
+be clear in this rotation these axons
+
+ align:start position:0%
+be clear in this rotation these axons
+ 
+
+ align:start position:0%
+be clear in this rotation these axons
+were severed they were cut they had to
+
+ align:start position:0%
+were severed they were cut they had to
+ 
+
+ align:start position:0%
+were severed they were cut they had to
+regrow and find their targets if they
+
+ align:start position:0%
+regrow and find their targets if they
+ 
+
+ align:start position:0%
+regrow and find their targets if they
+could so one possibility would be that
+
+ align:start position:0%
+could so one possibility would be that
+ 
+
+ align:start position:0%
+could so one possibility would be that
+the axons would grow out of this retina
+
+ align:start position:0%
+the axons would grow out of this retina
+ 
+
+ align:start position:0%
+the axons would grow out of this retina
+and they'd grow everywhere and they
+
+ align:start position:0%
+and they'd grow everywhere and they
+ 
+
+ align:start position:0%
+and they'd grow everywhere and they
+would make really wrong connections and
+
+ align:start position:0%
+would make really wrong connections and
+ 
+
+ align:start position:0%
+would make really wrong connections and
+things would be a mess in actual fact
+
+ align:start position:0%
+things would be a mess in actual fact
+ 
+
+ align:start position:0%
+things would be a mess in actual fact
+what really happened was that the nasal
+
+ align:start position:0%
+what really happened was that the nasal
+ 
+
+ align:start position:0%
+what really happened was that the nasal
+neurons even though they were on the
+
+ align:start position:0%
+neurons even though they were on the
+ 
+
+ align:start position:0%
+neurons even though they were on the
+wrong side of the face found their way
+
+ align:start position:0%
+wrong side of the face found their way
+ 
+
+ align:start position:0%
+wrong side of the face found their way
+to the r region and the texal neurons
+
+ align:start position:0%
+to the r region and the texal neurons
+ 
+
+ align:start position:0%
+to the r region and the texal neurons
+found their way to the Sea region just
+
+ align:start position:0%
+found their way to the Sea region just
+ 
+
+ align:start position:0%
+found their way to the Sea region just
+like they had connected to before and
+
+ align:start position:0%
+like they had connected to before and
+ 
+
+ align:start position:0%
+like they had connected to before and
+this was a really profound experiment
+
+ align:start position:0%
+this was a really profound experiment
+ 
+
+ align:start position:0%
+this was a really profound experiment
+that told investigators that axons knew
+
+ align:start position:0%
+that told investigators that axons knew
+ 
+
+ align:start position:0%
+that told investigators that axons knew
+where to go and we know the molecular
+
+ align:start position:0%
+where to go and we know the molecular
+ 
+
+ align:start position:0%
+where to go and we know the molecular
+basis of this now but I'm not going to
+
+ align:start position:0%
+basis of this now but I'm not going to
+ 
+
+ align:start position:0%
+basis of this now but I'm not going to
+tell you about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it in order to understand more about
+
+ align:start position:0%
+it in order to understand more about
+ 
+
+ align:start position:0%
+it in order to understand more about
+this guidance process you need to
+
+ align:start position:0%
+this guidance process you need to
+ 
+
+ align:start position:0%
+this guidance process you need to
+understand a part of the axon that we
+
+ align:start position:0%
+understand a part of the axon that we
+ 
+
+ align:start position:0%
+understand a part of the axon that we
+haven't discussed and a time in the
+
+ align:start position:0%
+haven't discussed and a time in the
+ 
+
+ align:start position:0%
+haven't discussed and a time in the
+neurons life that we haven't discussed
+
+ align:start position:0%
+neurons life that we haven't discussed
+ 
+
+ align:start position:0%
+neurons life that we haven't discussed
+either and that is a time when neurons
+
+ align:start position:0%
+either and that is a time when neurons
+ 
+
+ align:start position:0%
+either and that is a time when neurons
+are growing most neuronal growth takes
+
+ align:start position:0%
+are growing most neuronal growth takes
+ 
+
+ align:start position:0%
+are growing most neuronal growth takes
+place during embryonic development but
+
+ align:start position:0%
+place during embryonic development but
+ 
+
+ align:start position:0%
+place during embryonic development but
+it continues throughout life and so this
+
+ align:start position:0%
+it continues throughout life and so this
+ 
+
+ align:start position:0%
+it continues throughout life and so this
+is a developmental process but also in
+
+ align:start position:0%
+is a developmental process but also in
+ 
+
+ align:start position:0%
+is a developmental process but also in
+that experiment that was an adult frog
+
+ align:start position:0%
+that experiment that was an adult frog
+ 
+
+ align:start position:0%
+that experiment that was an adult frog
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guidance of neurons and as we'll
+
+ align:start position:0%
+guidance of neurons and as we'll
+ 
+
+ align:start position:0%
+guidance of neurons and as we'll
+discuss particularly
+
+ align:start position:0%
+discuss particularly
+ 
+
+ align:start position:0%
+discuss particularly
+axons occurs
+
+ align:start position:0%
+axons occurs
+ 
+
+ align:start position:0%
+axons occurs
+during
+
+ align:start position:0%
+during
+ 
+
+ align:start position:0%
+during
+development and
+
+ align:start position:0%
+development and
+ 
+
+ align:start position:0%
+development and
+repair and learning as well we can put
+
+ align:start position:0%
+repair and learning as well we can put
+ 
+
+ align:start position:0%
+repair and learning as well we can put
+that up as well during development
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repair and
+
+ align:start position:0%
+repair and
+ 
+
+ align:start position:0%
+repair and
+learning although I'd say for learning
+
+ align:start position:0%
+learning although I'd say for learning
+ 
+
+ align:start position:0%
+learning although I'd say for learning
+there's a bit of a question mark whether
+
+ align:start position:0%
+there's a bit of a question mark whether
+ 
+
+ align:start position:0%
+there's a bit of a question mark whether
+that's true but I think it's probably
+
+ align:start position:0%
+that's true but I think it's probably
+ 
+
+ align:start position:0%
+that's true but I think it's probably
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+okay and the cell that we need to
+
+ align:start position:0%
+okay and the cell that we need to
+ 
+
+ align:start position:0%
+okay and the cell that we need to
+consider is a committed neuron which is
+
+ align:start position:0%
+consider is a committed neuron which is
+ 
+
+ align:start position:0%
+consider is a committed neuron which is
+called a neuroblast doesn't matter but
+
+ align:start position:0%
+called a neuroblast doesn't matter but
+ 
+
+ align:start position:0%
+called a neuroblast doesn't matter but
+here's your committed
+
+ align:start position:0%
+here's your committed
+ 
+
+ align:start position:0%
+here's your committed
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+neuron have to think back to past
+
+ align:start position:0%
+neuron have to think back to past
+ 
+
+ align:start position:0%
+neuron have to think back to past
+lectures a neuron that knows that it's
+
+ align:start position:0%
+lectures a neuron that knows that it's
+ 
+
+ align:start position:0%
+lectures a neuron that knows that it's
+going to be a neuron but hasn't decided
+
+ align:start position:0%
+going to be a neuron but hasn't decided
+ 
+
+ align:start position:0%
+going to be a neuron but hasn't decided
+to hasn't become one yet hasn't
+
+ align:start position:0%
+to hasn't become one yet hasn't
+ 
+
+ align:start position:0%
+to hasn't become one yet hasn't
+differentiated it's called a
+
+ align:start position:0%
+differentiated it's called a
+ 
+
+ align:start position:0%
+differentiated it's called a
+neuroblast and here it is it's just a
+
+ align:start position:0%
+neuroblast and here it is it's just a
+ 
+
+ align:start position:0%
+neuroblast and here it is it's just a
+cell body with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleus and over time this neuroblast
+
+ align:start position:0%
+nucleus and over time this neuroblast
+ 
+
+ align:start position:0%
+nucleus and over time this neuroblast
+sends out processes that are called
+
+ align:start position:0%
+sends out processes that are called
+ 
+
+ align:start position:0%
+sends out processes that are called
+neurites they initially look the same
+
+ align:start position:0%
+neurites they initially look the same
+ 
+
+ align:start position:0%
+neurites they initially look the same
+soon some of them become dendrites and
+
+ align:start position:0%
+soon some of them become dendrites and
+ 
+
+ align:start position:0%
+soon some of them become dendrites and
+one of them becomes an
+
+ align:start position:0%
+one of them becomes an
+ 
+
+ align:start position:0%
+one of them becomes an
+axon so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neurite axon plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dendrite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outgrowth so you have a cell now
+
+ align:start position:0%
+outgrowth so you have a cell now
+ 
+
+ align:start position:0%
+outgrowth so you have a cell now
+with some
+
+ align:start position:0%
+with some
+ 
+
+ align:start position:0%
+with some
+processes and one of these is going to
+
+ align:start position:0%
+processes and one of these is going to
+ 
+
+ align:start position:0%
+processes and one of these is going to
+be the axon and that axon grows and it's
+
+ align:start position:0%
+be the axon and that axon grows and it's
+ 
+
+ align:start position:0%
+be the axon and that axon grows and it's
+during that growth process that it
+
+ align:start position:0%
+during that growth process that it
+ 
+
+ align:start position:0%
+during that growth process that it
+figures out where to go the cell body
+
+ align:start position:0%
+figures out where to go the cell body
+ 
+
+ align:start position:0%
+figures out where to go the cell body
+doesn't move the dendrites don't move
+
+ align:start position:0%
+doesn't move the dendrites don't move
+ 
+
+ align:start position:0%
+doesn't move the dendrites don't move
+it's the axon that is doing the path
+
+ align:start position:0%
+it's the axon that is doing the path
+ 
+
+ align:start position:0%
+it's the axon that is doing the path
+finding so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axon extends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+eventually Finds Its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Target and this
+
+ align:start position:0%
+Target and this
+ 
+
+ align:start position:0%
+Target and this
+extension is a growth process that we'll
+
+ align:start position:0%
+extension is a growth process that we'll
+ 
+
+ align:start position:0%
+extension is a growth process that we'll
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+about okay for every a nerve when we
+
+ align:start position:0%
+about okay for every a nerve when we
+ 
+
+ align:start position:0%
+about okay for every a nerve when we
+talk about nerves there are actually
+
+ align:start position:0%
+talk about nerves there are actually
+ 
+
+ align:start position:0%
+talk about nerves there are actually
+many many ax many neurons many axons
+
+ align:start position:0%
+many many ax many neurons many axons
+ 
+
+ align:start position:0%
+many many ax many neurons many axons
+they're bundles of axons and there's
+
+ align:start position:0%
+they're bundles of axons and there's
+ 
+
+ align:start position:0%
+they're bundles of axons and there's
+something about the first axon to find a
+
+ align:start position:0%
+something about the first axon to find a
+ 
+
+ align:start position:0%
+something about the first axon to find a
+Target that's very important the Pioneer
+
+ align:start position:0%
+Target that's very important the Pioneer
+ 
+
+ align:start position:0%
+Target that's very important the Pioneer
+axon the first one finds the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Target and then others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follow the same path it kind of lays
+
+ align:start position:0%
+follow the same path it kind of lays
+ 
+
+ align:start position:0%
+follow the same path it kind of lays
+down a path
+
+ align:start position:0%
+down a path
+ 
+
+ align:start position:0%
+down a path
+and they form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bundles also called
+
+ align:start position:0%
+bundles also called
+ 
+
+ align:start position:0%
+bundles also called
+facies and these
+
+ align:start position:0%
+facies and these
+ 
+
+ align:start position:0%
+facies and these
+fices
+
+ align:start position:0%
+fices
+ 
+
+ align:start position:0%
+fices
+together make the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nerve the part of the axon that's really
+
+ align:start position:0%
+nerve the part of the axon that's really
+ 
+
+ align:start position:0%
+nerve the part of the axon that's really
+important for this process is the very
+
+ align:start position:0%
+important for this process is the very
+ 
+
+ align:start position:0%
+important for this process is the very
+tip of the axon and it has a special
+
+ align:start position:0%
+tip of the axon and it has a special
+ 
+
+ align:start position:0%
+tip of the axon and it has a special
+name called the growth cone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the ax on tip or the growth
+
+ align:start position:0%
+so the ax on tip or the growth
+ 
+
+ align:start position:0%
+so the ax on tip or the growth
+cone is
+
+ align:start position:0%
+cone is
+ 
+
+ align:start position:0%
+cone is
+crucial and we can draw it on the
+
+ align:start position:0%
+crucial and we can draw it on the
+ 
+
+ align:start position:0%
+crucial and we can draw it on the
+board if we now
+
+ align:start position:0%
+board if we now
+ 
+
+ align:start position:0%
+board if we now
+draw an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axon and we've blown it up now so
+
+ align:start position:0%
+axon and we've blown it up now so
+ 
+
+ align:start position:0%
+axon and we've blown it up now so
+usually you know we blow up and we lose
+
+ align:start position:0%
+usually you know we blow up and we lose
+ 
+
+ align:start position:0%
+usually you know we blow up and we lose
+bits but now we're not going to lose any
+
+ align:start position:0%
+bits but now we're not going to lose any
+ 
+
+ align:start position:0%
+bits but now we're not going to lose any
+bit of it here's the axon and down the
+
+ align:start position:0%
+bit of it here's the axon and down the
+ 
+
+ align:start position:0%
+bit of it here's the axon and down the
+length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the axon are parallel
+
+ align:start position:0%
+of the axon are parallel
+ 
+
+ align:start position:0%
+of the axon are parallel
+microtubules many of them and these
+
+ align:start position:0%
+microtubules many of them and these
+ 
+
+ align:start position:0%
+microtubules many of them and these
+microtubules both stabilize the
+
+ align:start position:0%
+microtubules both stabilize the
+ 
+
+ align:start position:0%
+microtubules both stabilize the
+axon and also transport substances to
+
+ align:start position:0%
+axon and also transport substances to
+ 
+
+ align:start position:0%
+axon and also transport substances to
+and from the cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body so they
+
+ align:start position:0%
+body so they
+ 
+
+ align:start position:0%
+body so they
+stabilize the
+
+ align:start position:0%
+stabilize the
+ 
+
+ align:start position:0%
+stabilize the
+shape of very long axons and they also
+
+ align:start position:0%
+shape of very long axons and they also
+ 
+
+ align:start position:0%
+shape of very long axons and they also
+transport like little railway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tracks substances to and from the cell
+
+ align:start position:0%
+tracks substances to and from the cell
+ 
+
+ align:start position:0%
+tracks substances to and from the cell
+body that's not the tip of the
+
+ align:start position:0%
+body that's not the tip of the
+ 
+
+ align:start position:0%
+body that's not the tip of the
+axon at the very tip the microtubules
+
+ align:start position:0%
+axon at the very tip the microtubules
+ 
+
+ align:start position:0%
+axon at the very tip the microtubules
+end and they
+
+ align:start position:0%
+end and they
+ 
+
+ align:start position:0%
+end and they
+interdigitate with these finger-like
+
+ align:start position:0%
+interdigitate with these finger-like
+ 
+
+ align:start position:0%
+interdigitate with these finger-like
+protrusions which are very Dynamic that
+
+ align:start position:0%
+protrusions which are very Dynamic that
+ 
+
+ align:start position:0%
+protrusions which are very Dynamic that
+means they change all the time and these
+
+ align:start position:0%
+means they change all the time and these
+ 
+
+ align:start position:0%
+means they change all the time and these
+protrusions
+
+ align:start position:0%
+protrusions
+ 
+
+ align:start position:0%
+protrusions
+protrude because of polymerized actin
+
+ align:start position:0%
+protrude because of polymerized actin
+ 
+
+ align:start position:0%
+protrude because of polymerized actin
+and you might be saying we heard about
+
+ align:start position:0%
+and you might be saying we heard about
+ 
+
+ align:start position:0%
+and you might be saying we heard about
+that already Yes you heard about that in
+
+ align:start position:0%
+that already Yes you heard about that in
+ 
+
+ align:start position:0%
+that already Yes you heard about that in
+morphogenesis we've talked about this
+
+ align:start position:0%
+morphogenesis we've talked about this
+ 
+
+ align:start position:0%
+morphogenesis we've talked about this
+cell biology is cell biology whether
+
+ align:start position:0%
+cell biology is cell biology whether
+ 
+
+ align:start position:0%
+cell biology is cell biology whether
+it's about neurons or cells in your
+
+ align:start position:0%
+it's about neurons or cells in your
+ 
+
+ align:start position:0%
+it's about neurons or cells in your
+stomach or cells in your that give rise
+
+ align:start position:0%
+stomach or cells in your that give rise
+ 
+
+ align:start position:0%
+stomach or cells in your that give rise
+to the hairs on your head all of these
+
+ align:start position:0%
+to the hairs on your head all of these
+ 
+
+ align:start position:0%
+to the hairs on your head all of these
+cells are just cells so there are these
+
+ align:start position:0%
+cells are just cells so there are these
+ 
+
+ align:start position:0%
+cells are just cells so there are these
+protrusions at the
+
+ align:start position:0%
+protrusions at the
+ 
+
+ align:start position:0%
+protrusions at the
+end so this whole thing is the axon but
+
+ align:start position:0%
+end so this whole thing is the axon but
+ 
+
+ align:start position:0%
+end so this whole thing is the axon but
+the very end is the growth
+
+ align:start position:0%
+the very end is the growth
+ 
+
+ align:start position:0%
+the very end is the growth
+cone this very end is the growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cone and these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protrusions go by the name of
+
+ align:start position:0%
+protrusions go by the name of
+ 
+
+ align:start position:0%
+protrusions go by the name of
+filopodia
+
+ align:start position:0%
+filopodia
+ 
+
+ align:start position:0%
+filopodia
+fenus and lamellopodia more flattened
+
+ align:start position:0%
+fenus and lamellopodia more flattened
+ 
+
+ align:start position:0%
+fenus and lamellopodia more flattened
+feet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they protrude because of the
+
+ align:start position:0%
+and they protrude because of the
+ 
+
+ align:start position:0%
+and they protrude because of the
+polymerization of actin within them so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's F
+
+ align:start position:0%
+there's F
+ 
+
+ align:start position:0%
+there's F
+actin leads
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protrusions well that's one important
+
+ align:start position:0%
+protrusions well that's one important
+ 
+
+ align:start position:0%
+protrusions well that's one important
+thing and I'll show you a movie in a
+
+ align:start position:0%
+thing and I'll show you a movie in a
+ 
+
+ align:start position:0%
+thing and I'll show you a movie in a
+moment to show you that as an axon grows
+
+ align:start position:0%
+moment to show you that as an axon grows
+ 
+
+ align:start position:0%
+moment to show you that as an axon grows
+it's sending out zillions of these
+
+ align:start position:0%
+it's sending out zillions of these
+ 
+
+ align:start position:0%
+it's sending out zillions of these
+things all the time that are kind of
+
+ align:start position:0%
+things all the time that are kind of
+ 
+
+ align:start position:0%
+things all the time that are kind of
+feeling their way around the place
+
+ align:start position:0%
+feeling their way around the place
+ 
+
+ align:start position:0%
+feeling their way around the place
+actually I'll no I won't show you now
+
+ align:start position:0%
+actually I'll no I won't show you now
+ 
+
+ align:start position:0%
+actually I'll no I won't show you now
+because there's an intervening slide but
+
+ align:start position:0%
+because there's an intervening slide but
+ 
+
+ align:start position:0%
+because there's an intervening slide but
+the other thing you should know is that
+
+ align:start position:0%
+the other thing you should know is that
+ 
+
+ align:start position:0%
+the other thing you should know is that
+like all cells there are receptors on
+
+ align:start position:0%
+like all cells there are receptors on
+ 
+
+ align:start position:0%
+like all cells there are receptors on
+the surface of the growth cone that are
+
+ align:start position:0%
+the surface of the growth cone that are
+ 
+
+ align:start position:0%
+the surface of the growth cone that are
+also sampling what lians are in the
+
+ align:start position:0%
+also sampling what lians are in the
+ 
+
+ align:start position:0%
+also sampling what lians are in the
+environment and if the lians are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+favorable they will either stabilize
+
+ align:start position:0%
+favorable they will either stabilize
+ 
+
+ align:start position:0%
+favorable they will either stabilize
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+protrusions and make more of them take
+
+ align:start position:0%
+protrusions and make more of them take
+ 
+
+ align:start position:0%
+protrusions and make more of them take
+place so here are receptors all over the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receptor and if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receptors contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lians then again you will get fa actin
+
+ align:start position:0%
+lians then again you will get fa actin
+ 
+
+ align:start position:0%
+lians then again you will get fa actin
+formed and protrusions will be formed
+
+ align:start position:0%
+formed and protrusions will be formed
+ 
+
+ align:start position:0%
+formed and protrusions will be formed
+and they will be
+
+ align:start position:0%
+and they will be
+ 
+
+ align:start position:0%
+and they will be
+stabilized okay the growth cone is
+
+ align:start position:0%
+stabilized okay the growth cone is
+ 
+
+ align:start position:0%
+stabilized okay the growth cone is
+Paramount to axon outgrowth there are
+
+ align:start position:0%
+Paramount to axon outgrowth there are
+ 
+
+ align:start position:0%
+Paramount to axon outgrowth there are
+signals which both attract axons towards
+
+ align:start position:0%
+signals which both attract axons towards
+ 
+
+ align:start position:0%
+signals which both attract axons towards
+them and signals which repel
+
+ align:start position:0%
+them and signals which repel
+ 
+
+ align:start position:0%
+them and signals which repel
+axons we can call those not surprisingly
+
+ align:start position:0%
+axons we can call those not surprisingly
+ 
+
+ align:start position:0%
+axons we can call those not surprisingly
+attractive
+
+ align:start position:0%
+attractive
+ 
+
+ align:start position:0%
+attractive
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+signals we'll talk about someon
+
+ align:start position:0%
+signals we'll talk about someon
+ 
+
+ align:start position:0%
+signals we'll talk about someon
+moment and in that case the growth cone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extends and it
+
+ align:start position:0%
+extends and it
+ 
+
+ align:start position:0%
+extends and it
+extends not to be the dead horse here
+
+ align:start position:0%
+extends not to be the dead horse here
+ 
+
+ align:start position:0%
+extends not to be the dead horse here
+but because F actin increases or is
+
+ align:start position:0%
+but because F actin increases or is
+ 
+
+ align:start position:0%
+but because F actin increases or is
+stabilized and the flip is that the
+
+ align:start position:0%
+stabilized and the flip is that the
+ 
+
+ align:start position:0%
+stabilized and the flip is that the
+growth cone can be destabilized and
+
+ align:start position:0%
+growth cone can be destabilized and
+ 
+
+ align:start position:0%
+growth cone can be destabilized and
+literally
+
+ align:start position:0%
+literally
+ 
+
+ align:start position:0%
+literally
+collapse under repulsive signals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cone
+
+ align:start position:0%
+cone
+ 
+
+ align:start position:0%
+cone
+collapses and it collapses because fa
+
+ align:start position:0%
+collapses and it collapses because fa
+ 
+
+ align:start position:0%
+collapses and it collapses because fa
+actin now becomes G globular or
+
+ align:start position:0%
+actin now becomes G globular or
+ 
+
+ align:start position:0%
+actin now becomes G globular or
+unpolymerized Acton using exactly the
+
+ align:start position:0%
+unpolymerized Acton using exactly the
+ 
+
+ align:start position:0%
+unpolymerized Acton using exactly the
+same processes that we talked about
+
+ align:start position:0%
+same processes that we talked about
+ 
+
+ align:start position:0%
+same processes that we talked about
+during the morphogenesis lecture let's
+
+ align:start position:0%
+during the morphogenesis lecture let's
+ 
+
+ align:start position:0%
+during the morphogenesis lecture let's
+look at a couple of slides you don't
+
+ align:start position:0%
+look at a couple of slides you don't
+ 
+
+ align:start position:0%
+look at a couple of slides you don't
+have these so just look on the screen
+
+ align:start position:0%
+have these so just look on the screen
+ 
+
+ align:start position:0%
+have these so just look on the screen
+this is a cell drawn in professor
+
+ align:start position:0%
+this is a cell drawn in professor
+ 
+
+ align:start position:0%
+this is a cell drawn in professor
+loish's book here's the Leading Edge of
+
+ align:start position:0%
+loish's book here's the Leading Edge of
+ 
+
+ align:start position:0%
+loish's book here's the Leading Edge of
+the cell the direction of the cell is
+
+ align:start position:0%
+the cell the direction of the cell is
+ 
+
+ align:start position:0%
+the cell the direction of the cell is
+where there is lots of polymerized
+
+ align:start position:0%
+where there is lots of polymerized
+ 
+
+ align:start position:0%
+where there is lots of polymerized
+actin this I've just drawn on the board
+
+ align:start position:0%
+actin this I've just drawn on the board
+ 
+
+ align:start position:0%
+actin this I've just drawn on the board
+and here is an axonal growth cone and I
+
+ align:start position:0%
+and here is an axonal growth cone and I
+ 
+
+ align:start position:0%
+and here is an axonal growth cone and I
+really like this movie it's a timelaps
+
+ align:start position:0%
+really like this movie it's a timelaps
+ 
+
+ align:start position:0%
+really like this movie it's a timelaps
+taken over 10 minutes and you can see
+
+ align:start position:0%
+taken over 10 minutes and you can see
+ 
+
+ align:start position:0%
+taken over 10 minutes and you can see
+all these things at the end and on the
+
+ align:start position:0%
+all these things at the end and on the
+ 
+
+ align:start position:0%
+all these things at the end and on the
+sides
+
+ align:start position:0%
+sides
+ 
+
+ align:start position:0%
+sides
+these protrusions from the cell very
+
+ align:start position:0%
+these protrusions from the cell very
+ 
+
+ align:start position:0%
+these protrusions from the cell very
+active they're forming they're
+
+ align:start position:0%
+active they're forming they're
+ 
+
+ align:start position:0%
+active they're forming they're
+disaggregating forming again
+
+ align:start position:0%
+disaggregating forming again
+ 
+
+ align:start position:0%
+disaggregating forming again
+disaggregating as the cell those are the
+
+ align:start position:0%
+disaggregating as the cell those are the
+ 
+
+ align:start position:0%
+disaggregating as the cell those are the
+lamellopodia and the filopodia as the
+
+ align:start position:0%
+lamellopodia and the filopodia as the
+ 
+
+ align:start position:0%
+lamellopodia and the filopodia as the
+cell is kind of feeling its way through
+
+ align:start position:0%
+cell is kind of feeling its way through
+ 
+
+ align:start position:0%
+cell is kind of feeling its way through
+the environment trying to find somewhere
+
+ align:start position:0%
+the environment trying to find somewhere
+ 
+
+ align:start position:0%
+the environment trying to find somewhere
+to go okay so this is a real exploratory
+
+ align:start position:0%
+to go okay so this is a real exploratory
+ 
+
+ align:start position:0%
+to go okay so this is a real exploratory
+process by this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good what are these guidance signals
+
+ align:start position:0%
+good what are these guidance signals
+ 
+
+ align:start position:0%
+good what are these guidance signals
+well this is not a mystery either lians
+
+ align:start position:0%
+well this is not a mystery either lians
+ 
+
+ align:start position:0%
+well this is not a mystery either lians
+we know about receptors you know about
+
+ align:start position:0%
+we know about receptors you know about
+ 
+
+ align:start position:0%
+we know about receptors you know about
+the guidance signals are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lians and these
+
+ align:start position:0%
+lians and these
+ 
+
+ align:start position:0%
+lians and these
+lians when they're found to a
+
+ align:start position:0%
+lians when they're found to a
+ 
+
+ align:start position:0%
+lians when they're found to a
+receptor lead to signal transduction and
+
+ align:start position:0%
+receptor lead to signal transduction and
+ 
+
+ align:start position:0%
+receptor lead to signal transduction and
+acts on outgrowth so
+
+ align:start position:0%
+acts on outgrowth so
+ 
+
+ align:start position:0%
+acts on outgrowth so
+lians and we'll put in parentheses plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receptors to signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transduction and a change in the growth
+
+ align:start position:0%
+transduction and a change in the growth
+ 
+
+ align:start position:0%
+transduction and a change in the growth
+code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are two kinds of guidance signals
+
+ align:start position:0%
+there are two kinds of guidance signals
+ 
+
+ align:start position:0%
+there are two kinds of guidance signals
+that are reasonably separate from one
+
+ align:start position:0%
+that are reasonably separate from one
+ 
+
+ align:start position:0%
+that are reasonably separate from one
+another they're called short range and
+
+ align:start position:0%
+another they're called short range and
+ 
+
+ align:start position:0%
+another they're called short range and
+long range guidance
+
+ align:start position:0%
+long range guidance
+ 
+
+ align:start position:0%
+long range guidance
+signals short range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signals require contact between the axon
+
+ align:start position:0%
+signals require contact between the axon
+ 
+
+ align:start position:0%
+signals require contact between the axon
+and the extracellular Matrix or the axon
+
+ align:start position:0%
+and the extracellular Matrix or the axon
+ 
+
+ align:start position:0%
+and the extracellular Matrix or the axon
+and another cell so there's some
+
+ align:start position:0%
+and another cell so there's some
+ 
+
+ align:start position:0%
+and another cell so there's some
+localized accumulation of a signal
+
+ align:start position:0%
+localized accumulation of a signal
+ 
+
+ align:start position:0%
+localized accumulation of a signal
+signal and that has to be um directly
+
+ align:start position:0%
+signal and that has to be um directly
+ 
+
+ align:start position:0%
+signal and that has to be um directly
+contacted between by the growth cones so
+
+ align:start position:0%
+contacted between by the growth cones so
+ 
+
+ align:start position:0%
+contacted between by the growth cones so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+require
+
+ align:start position:0%
+require
+ 
+
+ align:start position:0%
+require
+axon
+
+ align:start position:0%
+axon
+ 
+
+ align:start position:0%
+axon
+ECM or cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contact these
+
+ align:start position:0%
+contact these
+ 
+
+ align:start position:0%
+contact these
+signals are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffusible
+
+ align:start position:0%
+diffusible
+ 
+
+ align:start position:0%
+diffusible
+therefore and they include things like
+
+ align:start position:0%
+therefore and they include things like
+ 
+
+ align:start position:0%
+therefore and they include things like
+aminon which is a part of the
+
+ align:start position:0%
+aminon which is a part of the
+ 
+
+ align:start position:0%
+aminon which is a part of the
+extracellular Matrix but also an axon
+
+ align:start position:0%
+extracellular Matrix but also an axon
+ 
+
+ align:start position:0%
+extracellular Matrix but also an axon
+guidance signal and then there are long
+
+ align:start position:0%
+guidance signal and then there are long
+ 
+
+ align:start position:0%
+guidance signal and then there are long
+range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signals which would be the flip of the
+
+ align:start position:0%
+signals which would be the flip of the
+ 
+
+ align:start position:0%
+signals which would be the flip of the
+short range these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffusible and they can be concentration
+
+ align:start position:0%
+diffusible and they can be concentration
+ 
+
+ align:start position:0%
+diffusible and they can be concentration
+dependent in their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effect and we talked about things like
+
+ align:start position:0%
+effect and we talked about things like
+ 
+
+ align:start position:0%
+effect and we talked about things like
+this previously when we talked about
+
+ align:start position:0%
+this previously when we talked about
+ 
+
+ align:start position:0%
+this previously when we talked about
+morphogens other lians that can act at
+
+ align:start position:0%
+morphogens other lians that can act at
+ 
+
+ align:start position:0%
+morphogens other lians that can act at
+different concentrations in different
+
+ align:start position:0%
+different concentrations in different
+ 
+
+ align:start position:0%
+different concentrations in different
+ways okay and an example that I'll
+
+ align:start position:0%
+ways okay and an example that I'll
+ 
+
+ align:start position:0%
+ways okay and an example that I'll
+Explore More with you is the netron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protein all right let me see what I have
+
+ align:start position:0%
+protein all right let me see what I have
+ 
+
+ align:start position:0%
+protein all right let me see what I have
+here okay this is nice this is on your
+
+ align:start position:0%
+here okay this is nice this is on your
+ 
+
+ align:start position:0%
+here okay this is nice this is on your
+this is your next handout and this is an
+
+ align:start position:0%
+this is your next handout and this is an
+ 
+
+ align:start position:0%
+this is your next handout and this is an
+assay for short range guidance signals
+
+ align:start position:0%
+assay for short range guidance signals
+ 
+
+ align:start position:0%
+assay for short range guidance signals
+it's called a stripe assay and this was
+
+ align:start position:0%
+it's called a stripe assay and this was
+ 
+
+ align:start position:0%
+it's called a stripe assay and this was
+how it was found what those nasal and re
+
+ align:start position:0%
+how it was found what those nasal and re
+ 
+
+ align:start position:0%
+how it was found what those nasal and re
+those nasal and temporal retinal neurons
+
+ align:start position:0%
+those nasal and temporal retinal neurons
+ 
+
+ align:start position:0%
+those nasal and temporal retinal neurons
+grew on the idea is you take a plastic
+
+ align:start position:0%
+grew on the idea is you take a plastic
+ 
+
+ align:start position:0%
+grew on the idea is you take a plastic
+dish and you put stripes of different
+
+ align:start position:0%
+dish and you put stripes of different
+ 
+
+ align:start position:0%
+dish and you put stripes of different
+molecules on the dish and then you put
+
+ align:start position:0%
+molecules on the dish and then you put
+ 
+
+ align:start position:0%
+molecules on the dish and then you put
+neurons all the way along one side of
+
+ align:start position:0%
+neurons all the way along one side of
+ 
+
+ align:start position:0%
+neurons all the way along one side of
+the dish and you look at them you ask
+
+ align:start position:0%
+the dish and you look at them you ask
+ 
+
+ align:start position:0%
+the dish and you look at them you ask
+where they grow and they'll choose where
+
+ align:start position:0%
+where they grow and they'll choose where
+ 
+
+ align:start position:0%
+where they grow and they'll choose where
+to grow and if they like one of the
+
+ align:start position:0%
+to grow and if they like one of the
+ 
+
+ align:start position:0%
+to grow and if they like one of the
+molecules if they can interact with one
+
+ align:start position:0%
+molecules if they can interact with one
+ 
+
+ align:start position:0%
+molecules if they can interact with one
+of the molecules on the dish they will
+
+ align:start position:0%
+of the molecules on the dish they will
+ 
+
+ align:start position:0%
+of the molecules on the dish they will
+grow in particular stripes and not in
+
+ align:start position:0%
+grow in particular stripes and not in
+ 
+
+ align:start position:0%
+grow in particular stripes and not in
+other stripes and that gives you your
+
+ align:start position:0%
+other stripes and that gives you your
+ 
+
+ align:start position:0%
+other stripes and that gives you your
+experiment and control in one dish this
+
+ align:start position:0%
+experiment and control in one dish this
+ 
+
+ align:start position:0%
+experiment and control in one dish this
+is what it looks like so here are the
+
+ align:start position:0%
+is what it looks like so here are the
+ 
+
+ align:start position:0%
+is what it looks like so here are the
+neurons from the nasal side of the
+
+ align:start position:0%
+neurons from the nasal side of the
+ 
+
+ align:start position:0%
+neurons from the nasal side of the
+retina and those nasal neurons which
+
+ align:start position:0%
+retina and those nasal neurons which
+ 
+
+ align:start position:0%
+retina and those nasal neurons which
+project to the r side of the tectum grow
+
+ align:start position:0%
+project to the r side of the tectum grow
+ 
+
+ align:start position:0%
+project to the r side of the tectum grow
+on R membranes but not on C membranes
+
+ align:start position:0%
+on R membranes but not on C membranes
+ 
+
+ align:start position:0%
+on R membranes but not on C membranes
+which is where they don't go you may not
+
+ align:start position:0%
+which is where they don't go you may not
+ 
+
+ align:start position:0%
+which is where they don't go you may not
+have this but you can go back and look
+
+ align:start position:0%
+have this but you can go back and look
+ 
+
+ align:start position:0%
+have this but you can go back and look
+at this later on all
+
+ align:start position:0%
+at this later on all
+ 
+
+ align:start position:0%
+at this later on all
+right but let's move on now to an
+
+ align:start position:0%
+right but let's move on now to an
+ 
+
+ align:start position:0%
+right but let's move on now to an
+example that I want to spend a bit of
+
+ align:start position:0%
+example that I want to spend a bit of
+ 
+
+ align:start position:0%
+example that I want to spend a bit of
+time on and the
+
+ align:start position:0%
+time on and the
+ 
+
+ align:start position:0%
+time on and the
+example of a long range signal is
+
+ align:start position:0%
+example of a long range signal is
+ 
+
+ align:start position:0%
+example of a long range signal is
+netron in the spinal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cord and what we're going to talk about
+
+ align:start position:0%
+cord and what we're going to talk about
+ 
+
+ align:start position:0%
+cord and what we're going to talk about
+are two types of neurons one of which
+
+ align:start position:0%
+are two types of neurons one of which
+ 
+
+ align:start position:0%
+are two types of neurons one of which
+are growing down the spine spinal cord
+
+ align:start position:0%
+are growing down the spine spinal cord
+ 
+
+ align:start position:0%
+are growing down the spine spinal cord
+from the back more towards the belly and
+
+ align:start position:0%
+from the back more towards the belly and
+ 
+
+ align:start position:0%
+from the back more towards the belly and
+another type of neuron that's growing
+
+ align:start position:0%
+another type of neuron that's growing
+ 
+
+ align:start position:0%
+another type of neuron that's growing
+more from the belly side of the spinal
+
+ align:start position:0%
+more from the belly side of the spinal
+ 
+
+ align:start position:0%
+more from the belly side of the spinal
+cord back towards the back okay and
+
+ align:start position:0%
+cord back towards the back okay and
+ 
+
+ align:start position:0%
+cord back towards the back okay and
+those neurons always know where to go
+
+ align:start position:0%
+those neurons always know where to go
+ 
+
+ align:start position:0%
+those neurons always know where to go
+and it turns out they are told where to
+
+ align:start position:0%
+and it turns out they are told where to
+ 
+
+ align:start position:0%
+and it turns out they are told where to
+go by the same signal so there are two
+
+ align:start position:0%
+go by the same signal so there are two
+ 
+
+ align:start position:0%
+go by the same signal so there are two
+types of neurons there are
+
+ align:start position:0%
+types of neurons there are
+ 
+
+ align:start position:0%
+types of neurons there are
+um these things called
+
+ align:start position:0%
+um these things called
+ 
+
+ align:start position:0%
+um these things called
+cheral neurons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+grow
+
+ align:start position:0%
+grow
+ 
+
+ align:start position:0%
+grow
+ventrally or
+
+ align:start position:0%
+ventrally or
+ 
+
+ align:start position:0%
+ventrally or
+down towards something called the floor
+
+ align:start position:0%
+down towards something called the floor
+ 
+
+ align:start position:0%
+down towards something called the floor
+plate I'll show you in the
+
+ align:start position:0%
+plate I'll show you in the
+ 
+
+ align:start position:0%
+plate I'll show you in the
+diagram and then there these other ones
+
+ align:start position:0%
+diagram and then there these other ones
+ 
+
+ align:start position:0%
+diagram and then there these other ones
+called trar
+
+ align:start position:0%
+called trar
+ 
+
+ align:start position:0%
+called trar
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+neurons that grow
+
+ align:start position:0%
+neurons that grow
+ 
+
+ align:start position:0%
+neurons that grow
+dorsally or
+
+ align:start position:0%
+dorsally or
+ 
+
+ align:start position:0%
+dorsally or
+up and they grow away from this thing
+
+ align:start position:0%
+up and they grow away from this thing
+ 
+
+ align:start position:0%
+up and they grow away from this thing
+called the floor plate and it turns out
+
+ align:start position:0%
+called the floor plate and it turns out
+ 
+
+ align:start position:0%
+called the floor plate and it turns out
+using an xplant assay that I'll go
+
+ align:start position:0%
+using an xplant assay that I'll go
+ 
+
+ align:start position:0%
+using an xplant assay that I'll go
+through with you in your slides but you
+
+ align:start position:0%
+through with you in your slides but you
+ 
+
+ align:start position:0%
+through with you in your slides but you
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+understand it was found that a single
+
+ align:start position:0%
+understand it was found that a single
+ 
+
+ align:start position:0%
+understand it was found that a single
+molecule called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+netron which is a secreted liand a
+
+ align:start position:0%
+netron which is a secreted liand a
+ 
+
+ align:start position:0%
+netron which is a secreted liand a
+secreted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Protein that's expressed in the floor
+
+ align:start position:0%
+Protein that's expressed in the floor
+ 
+
+ align:start position:0%
+Protein that's expressed in the floor
+plate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we'll talk about in a
+
+ align:start position:0%
+which we'll talk about in a
+ 
+
+ align:start position:0%
+which we'll talk about in a
+moment is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attractive for the cheral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neurons and
+
+ align:start position:0%
+neurons and
+ 
+
+ align:start position:0%
+neurons and
+repulsive for the trar neurons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it also turns out as we'll go
+
+ align:start position:0%
+and it also turns out as we'll go
+ 
+
+ align:start position:0%
+and it also turns out as we'll go
+through in a moment that this has to do
+
+ align:start position:0%
+through in a moment that this has to do
+ 
+
+ align:start position:0%
+through in a moment that this has to do
+with different receptors and different
+
+ align:start position:0%
+with different receptors and different
+ 
+
+ align:start position:0%
+with different receptors and different
+receptor diers which bind the same liand
+
+ align:start position:0%
+receptor diers which bind the same liand
+ 
+
+ align:start position:0%
+receptor diers which bind the same liand
+and so here there is something called
+
+ align:start position:0%
+and so here there is something called
+ 
+
+ align:start position:0%
+and so here there is something called
+for the cissal neurons there's something
+
+ align:start position:0%
+for the cissal neurons there's something
+ 
+
+ align:start position:0%
+for the cissal neurons there's something
+called a
+
+ align:start position:0%
+called a
+ 
+
+ align:start position:0%
+called a
+DCC
+
+ align:start position:0%
+DCC
+ 
+
+ align:start position:0%
+DCC
+DCC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recepto and for the tro neurons there is
+
+ align:start position:0%
+recepto and for the tro neurons there is
+ 
+
+ align:start position:0%
+recepto and for the tro neurons there is
+a DC
+
+ align:start position:0%
+a DC
+ 
+
+ align:start position:0%
+a DC
+C Unk
+
+ align:start position:0%
+C Unk
+ 
+
+ align:start position:0%
+C Unk
+five receptor pair and this will not
+
+ align:start position:0%
+five receptor pair and this will not
+ 
+
+ align:start position:0%
+five receptor pair and this will not
+mean much to you but now you can write
+
+ align:start position:0%
+mean much to you but now you can write
+ 
+
+ align:start position:0%
+mean much to you but now you can write
+it down and then you can go through your
+
+ align:start position:0%
+it down and then you can go through your
+ 
+
+ align:start position:0%
+it down and then you can go through your
+slides and you'll have a reference point
+
+ align:start position:0%
+slides and you'll have a reference point
+ 
+
+ align:start position:0%
+slides and you'll have a reference point
+on right with you okay so here is the
+
+ align:start position:0%
+on right with you okay so here is the
+ 
+
+ align:start position:0%
+on right with you okay so here is the
+diagram the cell bodies of the cheral
+
+ align:start position:0%
+diagram the cell bodies of the cheral
+ 
+
+ align:start position:0%
+diagram the cell bodies of the cheral
+neurons are up in near this region of
+
+ align:start position:0%
+neurons are up in near this region of
+ 
+
+ align:start position:0%
+neurons are up in near this region of
+the spinal cord called the roof plate
+
+ align:start position:0%
+the spinal cord called the roof plate
+ 
+
+ align:start position:0%
+the spinal cord called the roof plate
+it's the top of the spinal cord
+
+ align:start position:0%
+it's the top of the spinal cord
+ 
+
+ align:start position:0%
+it's the top of the spinal cord
+and on the bottom of the spinal cord
+
+ align:start position:0%
+and on the bottom of the spinal cord
+ 
+
+ align:start position:0%
+and on the bottom of the spinal cord
+near your belly there's a kind of a
+
+ align:start position:0%
+near your belly there's a kind of a
+ 
+
+ align:start position:0%
+near your belly there's a kind of a
+cone-shaped group of cells that forms
+
+ align:start position:0%
+cone-shaped group of cells that forms
+ 
+
+ align:start position:0%
+cone-shaped group of cells that forms
+this thing called the floor plate the
+
+ align:start position:0%
+this thing called the floor plate the
+ 
+
+ align:start position:0%
+this thing called the floor plate the
+floor plate doesn't actually make
+
+ align:start position:0%
+floor plate doesn't actually make
+ 
+
+ align:start position:0%
+floor plate doesn't actually make
+neurons it turns out to be a really
+
+ align:start position:0%
+neurons it turns out to be a really
+ 
+
+ align:start position:0%
+neurons it turns out to be a really
+important source of signals it's an
+
+ align:start position:0%
+important source of signals it's an
+ 
+
+ align:start position:0%
+important source of signals it's an
+organizer if you like and it not only
+
+ align:start position:0%
+organizer if you like and it not only
+ 
+
+ align:start position:0%
+organizer if you like and it not only
+organizes these axons in the spinal cord
+
+ align:start position:0%
+organizes these axons in the spinal cord
+ 
+
+ align:start position:0%
+organizes these axons in the spinal cord
+it actually also organizes your midline
+
+ align:start position:0%
+it actually also organizes your midline
+ 
+
+ align:start position:0%
+it actually also organizes your midline
+and it's one of the reasons if you're
+
+ align:start position:0%
+and it's one of the reasons if you're
+ 
+
+ align:start position:0%
+and it's one of the reasons if you're
+missing the midline of the body things
+
+ align:start position:0%
+missing the midline of the body things
+ 
+
+ align:start position:0%
+missing the midline of the body things
+go wrong it's because the floor plates
+
+ align:start position:0%
+go wrong it's because the floor plates
+ 
+
+ align:start position:0%
+go wrong it's because the floor plates
+not there so the floor Plate's an
+
+ align:start position:0%
+not there so the floor Plate's an
+ 
+
+ align:start position:0%
+not there so the floor Plate's an
+organizer there the cheral neurons
+
+ align:start position:0%
+organizer there the cheral neurons
+ 
+
+ align:start position:0%
+organizer there the cheral neurons
+growing towards it and here are the tro
+
+ align:start position:0%
+growing towards it and here are the tro
+ 
+
+ align:start position:0%
+growing towards it and here are the tro
+neurons growing away from the floor
+
+ align:start position:0%
+neurons growing away from the floor
+ 
+
+ align:start position:0%
+neurons growing away from the floor
+plate this is what it looks like if you
+
+ align:start position:0%
+plate this is what it looks like if you
+ 
+
+ align:start position:0%
+plate this is what it looks like if you
+do an imuno stain the cell bodies are in
+
+ align:start position:0%
+do an imuno stain the cell bodies are in
+ 
+
+ align:start position:0%
+do an imuno stain the cell bodies are in
+red and here are the cheral neurons
+
+ align:start position:0%
+red and here are the cheral neurons
+ 
+
+ align:start position:0%
+red and here are the cheral neurons
+coming down in the spinal cord and this
+
+ align:start position:0%
+coming down in the spinal cord and this
+ 
+
+ align:start position:0%
+coming down in the spinal cord and this
+is a section through the spinal cord
+
+ align:start position:0%
+is a section through the spinal cord
+ 
+
+ align:start position:0%
+is a section through the spinal cord
+okay you've cut through cut through at
+
+ align:start position:0%
+okay you've cut through cut through at
+ 
+
+ align:start position:0%
+okay you've cut through cut through at
+the waist and then turned the section on
+
+ align:start position:0%
+the waist and then turned the section on
+ 
+
+ align:start position:0%
+the waist and then turned the section on
+its side so you're looking into the
+
+ align:start position:0%
+its side so you're looking into the
+ 
+
+ align:start position:0%
+its side so you're looking into the
+spinal cord which would be coming out in
+
+ align:start position:0%
+spinal cord which would be coming out in
+ 
+
+ align:start position:0%
+spinal cord which would be coming out in
+its length from the board from the
+
+ align:start position:0%
+its length from the board from the
+ 
+
+ align:start position:0%
+its length from the board from the
+screen all right here's an explant assay
+
+ align:start position:0%
+screen all right here's an explant assay
+ 
+
+ align:start position:0%
+screen all right here's an explant assay
+to figure out whether or not that floor
+
+ align:start position:0%
+to figure out whether or not that floor
+ 
+
+ align:start position:0%
+to figure out whether or not that floor
+plate has got something to do with the
+
+ align:start position:0%
+plate has got something to do with the
+ 
+
+ align:start position:0%
+plate has got something to do with the
+direction that those cissal neurons grow
+
+ align:start position:0%
+direction that those cissal neurons grow
+ 
+
+ align:start position:0%
+direction that those cissal neurons grow
+it's on your
+
+ align:start position:0%
+it's on your
+ 
+
+ align:start position:0%
+it's on your
+handout the idea was to take a piece of
+
+ align:start position:0%
+handout the idea was to take a piece of
+ 
+
+ align:start position:0%
+handout the idea was to take a piece of
+dorsal spinal cord that hadn't started
+
+ align:start position:0%
+dorsal spinal cord that hadn't started
+ 
+
+ align:start position:0%
+dorsal spinal cord that hadn't started
+to send neurons out yet and to culture
+
+ align:start position:0%
+to send neurons out yet and to culture
+ 
+
+ align:start position:0%
+to send neurons out yet and to culture
+it together in the laboratory in a
+
+ align:start position:0%
+it together in the laboratory in a
+ 
+
+ align:start position:0%
+it together in the laboratory in a
+plastic dish with some with some fluid
+
+ align:start position:0%
+plastic dish with some with some fluid
+ 
+
+ align:start position:0%
+plastic dish with some with some fluid
+and nutrients and so on and ask what
+
+ align:start position:0%
+and nutrients and so on and ask what
+ 
+
+ align:start position:0%
+and nutrients and so on and ask what
+happened and if you did that that dorsal
+
+ align:start position:0%
+happened and if you did that that dorsal
+ 
+
+ align:start position:0%
+happened and if you did that that dorsal
+spinal cord sent out neurons towards the
+
+ align:start position:0%
+spinal cord sent out neurons towards the
+ 
+
+ align:start position:0%
+spinal cord sent out neurons towards the
+floor
+
+ align:start position:0%
+floor
+ 
+
+ align:start position:0%
+floor
+plate on the other hand you could see
+
+ align:start position:0%
+plate on the other hand you could see
+ 
+
+ align:start position:0%
+plate on the other hand you could see
+that that experiment was specific
+
+ align:start position:0%
+that that experiment was specific
+ 
+
+ align:start position:0%
+that that experiment was specific
+because if you put the dorsal spinal
+
+ align:start position:0%
+because if you put the dorsal spinal
+ 
+
+ align:start position:0%
+because if you put the dorsal spinal
+cord together with some roof plate
+
+ align:start position:0%
+cord together with some roof plate
+ 
+
+ align:start position:0%
+cord together with some roof plate
+nothing happened there was no outgrowth
+
+ align:start position:0%
+nothing happened there was no outgrowth
+ 
+
+ align:start position:0%
+nothing happened there was no outgrowth
+so there was something special about
+
+ align:start position:0%
+so there was something special about
+ 
+
+ align:start position:0%
+so there was something special about
+this floor plate that elicited that
+
+ align:start position:0%
+this floor plate that elicited that
+ 
+
+ align:start position:0%
+this floor plate that elicited that
+cheral axon outgrowth and the idea idea
+
+ align:start position:0%
+cheral axon outgrowth and the idea idea
+ 
+
+ align:start position:0%
+cheral axon outgrowth and the idea idea
+is that the floor plate was attracting
+
+ align:start position:0%
+is that the floor plate was attracting
+ 
+
+ align:start position:0%
+is that the floor plate was attracting
+the cheral
+
+ align:start position:0%
+the cheral
+ 
+
+ align:start position:0%
+the cheral
+axons this is what it really looks like
+
+ align:start position:0%
+axons this is what it really looks like
+ 
+
+ align:start position:0%
+axons this is what it really looks like
+here's a chunk of dorsal spinal cord and
+
+ align:start position:0%
+here's a chunk of dorsal spinal cord and
+ 
+
+ align:start position:0%
+here's a chunk of dorsal spinal cord and
+floor plate and here are the growing
+
+ align:start position:0%
+floor plate and here are the growing
+ 
+
+ align:start position:0%
+floor plate and here are the growing
+axons and here's the control
+
+ align:start position:0%
+axons and here's the control
+ 
+
+ align:start position:0%
+axons and here's the control
+experiment all right so what is the
+
+ align:start position:0%
+experiment all right so what is the
+ 
+
+ align:start position:0%
+experiment all right so what is the
+protein involved well the idea was that
+
+ align:start position:0%
+protein involved well the idea was that
+ 
+
+ align:start position:0%
+protein involved well the idea was that
+it was something in the floor plate and
+
+ align:start position:0%
+it was something in the floor plate and
+ 
+
+ align:start position:0%
+it was something in the floor plate and
+it was really hard to find this because
+
+ align:start position:0%
+it was really hard to find this because
+ 
+
+ align:start position:0%
+it was really hard to find this because
+there's not much of it Professor Tessier
+
+ align:start position:0%
+there's not much of it Professor Tessier
+ 
+
+ align:start position:0%
+there's not much of it Professor Tessier
+LaVine who is now president of
+
+ align:start position:0%
+LaVine who is now president of
+ 
+
+ align:start position:0%
+LaVine who is now president of
+Rockefeller University but at the time
+
+ align:start position:0%
+Rockefeller University but at the time
+ 
+
+ align:start position:0%
+Rockefeller University but at the time
+time was running a research laboratory
+
+ align:start position:0%
+time was running a research laboratory
+ 
+
+ align:start position:0%
+time was running a research laboratory
+and he and many undergraduates and
+
+ align:start position:0%
+and he and many undergraduates and
+ 
+
+ align:start position:0%
+and he and many undergraduates and
+graduate students and postdocs and so on
+
+ align:start position:0%
+graduate students and postdocs and so on
+ 
+
+ align:start position:0%
+graduate students and postdocs and so on
+went ahead and dissected many many
+
+ align:start position:0%
+went ahead and dissected many many
+ 
+
+ align:start position:0%
+went ahead and dissected many many
+little floor plates and they also found
+
+ align:start position:0%
+little floor plates and they also found
+ 
+
+ align:start position:0%
+little floor plates and they also found
+that the brain of the chicken contained
+
+ align:start position:0%
+that the brain of the chicken contained
+ 
+
+ align:start position:0%
+that the brain of the chicken contained
+the same kind of activity so they
+
+ align:start position:0%
+the same kind of activity so they
+ 
+
+ align:start position:0%
+the same kind of activity so they
+dissected out many thousands I believe
+
+ align:start position:0%
+dissected out many thousands I believe
+ 
+
+ align:start position:0%
+dissected out many thousands I believe
+it was
+
+ align:start position:0%
+it was
+ 
+
+ align:start position:0%
+it was
+35,000 chick brains and spinal cords and
+
+ align:start position:0%
+35,000 chick brains and spinal cords and
+ 
+
+ align:start position:0%
+35,000 chick brains and spinal cords and
+they did biochemistry on this material
+
+ align:start position:0%
+they did biochemistry on this material
+ 
+
+ align:start position:0%
+they did biochemistry on this material
+and they used the xplant essay that I
+
+ align:start position:0%
+and they used the xplant essay that I
+ 
+
+ align:start position:0%
+and they used the xplant essay that I
+just showed you you where instead of the
+
+ align:start position:0%
+just showed you you where instead of the
+ 
+
+ align:start position:0%
+just showed you you where instead of the
+floor plate you'd have a little pallet
+
+ align:start position:0%
+floor plate you'd have a little pallet
+ 
+
+ align:start position:0%
+floor plate you'd have a little pallet
+of material in which you'd soaked the
+
+ align:start position:0%
+of material in which you'd soaked the
+ 
+
+ align:start position:0%
+of material in which you'd soaked the
+material that you purified by
+
+ align:start position:0%
+material that you purified by
+ 
+
+ align:start position:0%
+material that you purified by
+biochemistry from your shushed up
+
+ align:start position:0%
+biochemistry from your shushed up
+ 
+
+ align:start position:0%
+biochemistry from your shushed up
+dissected brains and from this it was
+
+ align:start position:0%
+dissected brains and from this it was
+ 
+
+ align:start position:0%
+dissected brains and from this it was
+really successful from this they got a
+
+ align:start position:0%
+really successful from this they got a
+ 
+
+ align:start position:0%
+really successful from this they got a
+single protein here's the RNA for the
+
+ align:start position:0%
+single protein here's the RNA for the
+ 
+
+ align:start position:0%
+single protein here's the RNA for the
+Protein that's right expressed in the
+
+ align:start position:0%
+Protein that's right expressed in the
+ 
+
+ align:start position:0%
+Protein that's right expressed in the
+floor plate that's what the white is
+
+ align:start position:0%
+floor plate that's what the white is
+ 
+
+ align:start position:0%
+floor plate that's what the white is
+that's the RNA this is an incu
+
+ align:start position:0%
+that's the RNA this is an incu
+ 
+
+ align:start position:0%
+that's the RNA this is an incu
+hybridization and they called it netrin
+
+ align:start position:0%
+hybridization and they called it netrin
+ 
+
+ align:start position:0%
+hybridization and they called it netrin
+netrin protein diffuses away from the
+
+ align:start position:0%
+netrin protein diffuses away from the
+ 
+
+ align:start position:0%
+netrin protein diffuses away from the
+the floor plate but it's still mostly on
+
+ align:start position:0%
+the floor plate but it's still mostly on
+ 
+
+ align:start position:0%
+the floor plate but it's still mostly on
+this ventral side of the spinal cord and
+
+ align:start position:0%
+this ventral side of the spinal cord and
+ 
+
+ align:start position:0%
+this ventral side of the spinal cord and
+you could show that netron was important
+
+ align:start position:0%
+you could show that netron was important
+ 
+
+ align:start position:0%
+you could show that netron was important
+because if you made a mouse that lacked
+
+ align:start position:0%
+because if you made a mouse that lacked
+ 
+
+ align:start position:0%
+because if you made a mouse that lacked
+netron here's the mouse that lacks
+
+ align:start position:0%
+netron here's the mouse that lacks
+ 
+
+ align:start position:0%
+netron here's the mouse that lacks
+netron the cheral neurons go all over
+
+ align:start position:0%
+netron the cheral neurons go all over
+ 
+
+ align:start position:0%
+netron the cheral neurons go all over
+the place they really don't know where
+
+ align:start position:0%
+the place they really don't know where
+ 
+
+ align:start position:0%
+the place they really don't know where
+to go all right The netron
+
+ align:start position:0%
+to go all right The netron
+ 
+
+ align:start position:0%
+to go all right The netron
+receptors as I drew on the board you can
+
+ align:start position:0%
+receptors as I drew on the board you can
+ 
+
+ align:start position:0%
+receptors as I drew on the board you can
+look on your last handout are twofold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of them are called DCC they're
+
+ align:start position:0%
+one of them are called DCC they're
+ 
+
+ align:start position:0%
+one of them are called DCC they're
+tyrosine
+
+ align:start position:0%
+tyrosine
+ 
+
+ align:start position:0%
+tyrosine
+kinases they also activate gtpases and
+
+ align:start position:0%
+kinases they also activate gtpases and
+ 
+
+ align:start position:0%
+kinases they also activate gtpases and
+do some other signal transduction and
+
+ align:start position:0%
+do some other signal transduction and
+ 
+
+ align:start position:0%
+do some other signal transduction and
+when netron binds to a dimer of
+
+ align:start position:0%
+when netron binds to a dimer of
+ 
+
+ align:start position:0%
+when netron binds to a dimer of
+DCC you get fum that's made micr tubules
+
+ align:start position:0%
+DCC you get fum that's made micr tubules
+ 
+
+ align:start position:0%
+DCC you get fum that's made micr tubules
+grow and the growth cone extends on the
+
+ align:start position:0%
+grow and the growth cone extends on the
+ 
+
+ align:start position:0%
+grow and the growth cone extends on the
+other hand when you get this
+
+ align:start position:0%
+other hand when you get this
+ 
+
+ align:start position:0%
+other hand when you get this
+heterodimer DCC and an5 or a different
+
+ align:start position:0%
+heterodimer DCC and an5 or a different
+ 
+
+ align:start position:0%
+heterodimer DCC and an5 or a different
+homodimer you you get cytoskeletal
+
+ align:start position:0%
+homodimer you you get cytoskeletal
+ 
+
+ align:start position:0%
+homodimer you you get cytoskeletal
+remodeling gacon made and the growth
+
+ align:start position:0%
+remodeling gacon made and the growth
+ 
+
+ align:start position:0%
+remodeling gacon made and the growth
+cone
+
+ align:start position:0%
+cone
+ 
+
+ align:start position:0%
+cone
+collapses okay close enough we'll stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there for
\ No newline at end of file
diff --git a/l1t2_5UZhPA.txt b/l1t2_5UZhPA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..12adbf073379daa128f3f935962cb9c0236d9fd1
--- /dev/null
+++ b/l1t2_5UZhPA.txt
@@ -0,0 +1,10771 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+I'm gonna be talking today about how
+
+ align:start position:0%
+I'm gonna be talking today about how
+ 
+
+ align:start position:0%
+I'm gonna be talking today about how
+infants and kids start to develop an
+
+ align:start position:0%
+infants and kids start to develop an
+ 
+
+ align:start position:0%
+infants and kids start to develop an
+understanding of communication and why
+
+ align:start position:0%
+understanding of communication and why
+ 
+
+ align:start position:0%
+understanding of communication and why
+this is an important topic for
+
+ align:start position:0%
+this is an important topic for
+ 
+
+ align:start position:0%
+this is an important topic for
+understanding human intelligence so what
+
+ align:start position:0%
+understanding human intelligence so what
+ 
+
+ align:start position:0%
+understanding human intelligence so what
+is communication so really basically
+
+ align:start position:0%
+is communication so really basically
+ 
+
+ align:start position:0%
+is communication so really basically
+communication is the transfer is a
+
+ align:start position:0%
+communication is the transfer is a
+ 
+
+ align:start position:0%
+communication is the transfer is a
+transfer or exchange of information and
+
+ align:start position:0%
+transfer or exchange of information and
+ 
+
+ align:start position:0%
+transfer or exchange of information and
+importantly in human communication this
+
+ align:start position:0%
+importantly in human communication this
+ 
+
+ align:start position:0%
+importantly in human communication this
+isn't just any kind of information but
+
+ align:start position:0%
+isn't just any kind of information but
+ 
+
+ align:start position:0%
+isn't just any kind of information but
+it's specifically the kind of
+
+ align:start position:0%
+it's specifically the kind of
+ 
+
+ align:start position:0%
+it's specifically the kind of
+information that's in our heads and in
+
+ align:start position:0%
+information that's in our heads and in
+ 
+
+ align:start position:0%
+information that's in our heads and in
+our minds so for example this
+
+ align:start position:0%
+our minds so for example this
+ 
+
+ align:start position:0%
+our minds so for example this
+information in my head right now that
+
+ align:start position:0%
+information in my head right now that
+ 
+
+ align:start position:0%
+information in my head right now that
+I'm going to be transferring to you over
+
+ align:start position:0%
+I'm going to be transferring to you over
+ 
+
+ align:start position:0%
+I'm going to be transferring to you over
+the course of this talk and the reason
+
+ align:start position:0%
+the course of this talk and the reason
+ 
+
+ align:start position:0%
+the course of this talk and the reason
+we need communication to do this and
+
+ align:start position:0%
+we need communication to do this and
+ 
+
+ align:start position:0%
+we need communication to do this and
+that we use it all the time
+
+ align:start position:0%
+that we use it all the time
+ 
+
+ align:start position:0%
+that we use it all the time
+is obviously that everyone has minds of
+
+ align:start position:0%
+is obviously that everyone has minds of
+ 
+
+ align:start position:0%
+is obviously that everyone has minds of
+their own and that we don't have access
+
+ align:start position:0%
+their own and that we don't have access
+ 
+
+ align:start position:0%
+their own and that we don't have access
+to the mental states of others and we
+
+ align:start position:0%
+to the mental states of others and we
+ 
+
+ align:start position:0%
+to the mental states of others and we
+can't automatically transfer our own
+
+ align:start position:0%
+can't automatically transfer our own
+ 
+
+ align:start position:0%
+can't automatically transfer our own
+mental states so there's without some
+
+ align:start position:0%
+mental states so there's without some
+ 
+
+ align:start position:0%
+mental states so there's without some
+means of making those mental states
+
+ align:start position:0%
+means of making those mental states
+ 
+
+ align:start position:0%
+means of making those mental states
+observable in the form of communicating
+
+ align:start position:0%
+observable in the form of communicating
+ 
+
+ align:start position:0%
+observable in the form of communicating
+with them so people are both cognitive
+
+ align:start position:0%
+with them so people are both cognitive
+ 
+
+ align:start position:0%
+with them so people are both cognitive
+beings we have to sort of navigate the
+
+ align:start position:0%
+beings we have to sort of navigate the
+ 
+
+ align:start position:0%
+beings we have to sort of navigate the
+thoughts in our heads and try to figure
+
+ align:start position:0%
+thoughts in our heads and try to figure
+ 
+
+ align:start position:0%
+thoughts in our heads and try to figure
+out the thoughts that our other's heads
+
+ align:start position:0%
+out the thoughts that our other's heads
+ 
+
+ align:start position:0%
+out the thoughts that our other's heads
+but we're also social beings we really
+
+ align:start position:0%
+but we're also social beings we really
+ 
+
+ align:start position:0%
+but we're also social beings we really
+benefit from gaining access to the
+
+ align:start position:0%
+benefit from gaining access to the
+ 
+
+ align:start position:0%
+benefit from gaining access to the
+thoughts and the minds of others and
+
+ align:start position:0%
+thoughts and the minds of others and
+ 
+
+ align:start position:0%
+thoughts and the minds of others and
+giving them access to our own thoughts
+
+ align:start position:0%
+giving them access to our own thoughts
+ 
+
+ align:start position:0%
+giving them access to our own thoughts
+so for example for cooperation
+
+ align:start position:0%
+so for example for cooperation
+ 
+
+ align:start position:0%
+so for example for cooperation
+competition learning and teaching and
+
+ align:start position:0%
+competition learning and teaching and
+ 
+
+ align:start position:0%
+competition learning and teaching and
+all the kinds of social interactions we
+
+ align:start position:0%
+all the kinds of social interactions we
+ 
+
+ align:start position:0%
+all the kinds of social interactions we
+do with each other we have to be able to
+
+ align:start position:0%
+do with each other we have to be able to
+ 
+
+ align:start position:0%
+do with each other we have to be able to
+share the contents of our mental states
+
+ align:start position:0%
+share the contents of our mental states
+ 
+
+ align:start position:0%
+share the contents of our mental states
+and it's this sort of joint both
+
+ align:start position:0%
+and it's this sort of joint both
+ 
+
+ align:start position:0%
+and it's this sort of joint both
+cognitive and social nature of
+
+ align:start position:0%
+cognitive and social nature of
+ 
+
+ align:start position:0%
+cognitive and social nature of
+communication that I think makes it
+
+ align:start position:0%
+communication that I think makes it
+ 
+
+ align:start position:0%
+communication that I think makes it
+especially important for understanding
+
+ align:start position:0%
+especially important for understanding
+ 
+
+ align:start position:0%
+especially important for understanding
+the development of human intelligence
+
+ align:start position:0%
+the development of human intelligence
+ 
+
+ align:start position:0%
+the development of human intelligence
+it sort of Crosscut's a lot of these
+
+ align:start position:0%
+it sort of Crosscut's a lot of these
+ 
+
+ align:start position:0%
+it sort of Crosscut's a lot of these
+core knowledge domains that Liz talked
+
+ align:start position:0%
+core knowledge domains that Liz talked
+ 
+
+ align:start position:0%
+core knowledge domains that Liz talked
+about in her talk
+
+ align:start position:0%
+about in her talk
+ 
+
+ align:start position:0%
+about in her talk
+so human communication requires
+
+ align:start position:0%
+so human communication requires
+ 
+
+ align:start position:0%
+so human communication requires
+reasoning about others cognitive states
+
+ align:start position:0%
+reasoning about others cognitive states
+ 
+
+ align:start position:0%
+reasoning about others cognitive states
+so understanding what other's beliefs
+
+ align:start position:0%
+so understanding what other's beliefs
+ 
+
+ align:start position:0%
+so understanding what other's beliefs
+and desires and intentions are
+
+ align:start position:0%
+and desires and intentions are
+ 
+
+ align:start position:0%
+and desires and intentions are
+it also requires reasoning about social
+
+ align:start position:0%
+it also requires reasoning about social
+ 
+
+ align:start position:0%
+it also requires reasoning about social
+interaction so understanding that
+
+ align:start position:0%
+interaction so understanding that
+ 
+
+ align:start position:0%
+interaction so understanding that
+typically these kinds of thoughts and
+
+ align:start position:0%
+typically these kinds of thoughts and
+ 
+
+ align:start position:0%
+typically these kinds of thoughts and
+beliefs and intentions are not shared
+
+ align:start position:0%
+beliefs and intentions are not shared
+ 
+
+ align:start position:0%
+beliefs and intentions are not shared
+among different people everyone has
+
+ align:start position:0%
+among different people everyone has
+ 
+
+ align:start position:0%
+among different people everyone has
+their own that are unobservable and
+
+ align:start position:0%
+their own that are unobservable and
+ 
+
+ align:start position:0%
+their own that are unobservable and
+housed in their own heads but that in
+
+ align:start position:0%
+housed in their own heads but that in
+ 
+
+ align:start position:0%
+housed in their own heads but that in
+the context of a particular kind of
+
+ align:start position:0%
+the context of a particular kind of
+ 
+
+ align:start position:0%
+the context of a particular kind of
+social interaction these people can
+
+ align:start position:0%
+social interaction these people can
+ 
+
+ align:start position:0%
+social interaction these people can
+intentionally share their thoughts with
+
+ align:start position:0%
+intentionally share their thoughts with
+ 
+
+ align:start position:0%
+intentionally share their thoughts with
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+and communication often involves
+
+ align:start position:0%
+and communication often involves
+ 
+
+ align:start position:0%
+and communication often involves
+reasoning about a third thing which is
+
+ align:start position:0%
+reasoning about a third thing which is
+ 
+
+ align:start position:0%
+reasoning about a third thing which is
+language or communicative signals
+
+ align:start position:0%
+language or communicative signals
+ 
+
+ align:start position:0%
+language or communicative signals
+outside of language as well and so I'm
+
+ align:start position:0%
+outside of language as well and so I'm
+ 
+
+ align:start position:0%
+outside of language as well and so I'm
+going to come back to this point at the
+
+ align:start position:0%
+going to come back to this point at the
+ 
+
+ align:start position:0%
+going to come back to this point at the
+end but all these types of reasoning are
+
+ align:start position:0%
+end but all these types of reasoning are
+ 
+
+ align:start position:0%
+end but all these types of reasoning are
+going to come up in the studies about
+
+ align:start position:0%
+going to come up in the studies about
+ 
+
+ align:start position:0%
+going to come up in the studies about
+infant communication that I described in
+
+ align:start position:0%
+infant communication that I described in
+ 
+
+ align:start position:0%
+infant communication that I described in
+the talk and so Liz talked about how
+
+ align:start position:0%
+the talk and so Liz talked about how
+ 
+
+ align:start position:0%
+the talk and so Liz talked about how
+infants start out with these coherent
+
+ align:start position:0%
+infants start out with these coherent
+ 
+
+ align:start position:0%
+infants start out with these coherent
+separate principle core knowledge
+
+ align:start position:0%
+separate principle core knowledge
+ 
+
+ align:start position:0%
+separate principle core knowledge
+systems that contain some limited
+
+ align:start position:0%
+systems that contain some limited
+ 
+
+ align:start position:0%
+systems that contain some limited
+representations for reasoning about the
+
+ align:start position:0%
+representations for reasoning about the
+ 
+
+ align:start position:0%
+representations for reasoning about the
+world and which kind of come together
+
+ align:start position:0%
+world and which kind of come together
+ 
+
+ align:start position:0%
+world and which kind of come together
+around the end of the first year so if
+
+ align:start position:0%
+around the end of the first year so if
+ 
+
+ align:start position:0%
+around the end of the first year so if
+we want to figure out how to build a
+
+ align:start position:0%
+we want to figure out how to build a
+ 
+
+ align:start position:0%
+we want to figure out how to build a
+model of how social cognitive
+
+ align:start position:0%
+model of how social cognitive
+ 
+
+ align:start position:0%
+model of how social cognitive
+development works we're going to need to
+
+ align:start position:0%
+development works we're going to need to
+ 
+
+ align:start position:0%
+development works we're going to need to
+understand how an infant starts to
+
+ align:start position:0%
+understand how an infant starts to
+ 
+
+ align:start position:0%
+understand how an infant starts to
+figure out using these the core
+
+ align:start position:0%
+figure out using these the core
+ 
+
+ align:start position:0%
+figure out using these the core
+knowledge that they have early in life
+
+ align:start position:0%
+knowledge that they have early in life
+ 
+
+ align:start position:0%
+knowledge that they have early in life
+the components of communication and also
+
+ align:start position:0%
+the components of communication and also
+ 
+
+ align:start position:0%
+the components of communication and also
+how these components come together so
+
+ align:start position:0%
+how these components come together so
+ 
+
+ align:start position:0%
+how these components come together so
+that infants can build a more complex
+
+ align:start position:0%
+that infants can build a more complex
+ 
+
+ align:start position:0%
+that infants can build a more complex
+causal model of communication like
+
+ align:start position:0%
+causal model of communication like
+ 
+
+ align:start position:0%
+causal model of communication like
+adults have so in it this is just to
+
+ align:start position:0%
+adults have so in it this is just to
+ 
+
+ align:start position:0%
+adults have so in it this is just to
+illustrate the points I'm making about
+
+ align:start position:0%
+illustrate the points I'm making about
+ 
+
+ align:start position:0%
+illustrate the points I'm making about
+the communicative situation so in any
+
+ align:start position:0%
+the communicative situation so in any
+ 
+
+ align:start position:0%
+the communicative situation so in any
+given communicative situation we can't
+
+ align:start position:0%
+given communicative situation we can't
+ 
+
+ align:start position:0%
+given communicative situation we can't
+just think about the words that are
+
+ align:start position:0%
+just think about the words that are
+ 
+
+ align:start position:0%
+just think about the words that are
+being said or what we're hearing we need
+
+ align:start position:0%
+being said or what we're hearing we need
+ 
+
+ align:start position:0%
+being said or what we're hearing we need
+to think about it in this broader
+
+ align:start position:0%
+to think about it in this broader
+ 
+
+ align:start position:0%
+to think about it in this broader
+context of having a communicator or
+
+ align:start position:0%
+context of having a communicator or
+ 
+
+ align:start position:0%
+context of having a communicator or
+maybe multiple communicators an
+
+ align:start position:0%
+maybe multiple communicators an
+ 
+
+ align:start position:0%
+maybe multiple communicators an
+addressee or an audience and also the
+
+ align:start position:0%
+addressee or an audience and also the
+ 
+
+ align:start position:0%
+addressee or an audience and also the
+things that the communicator saying and
+
+ align:start position:0%
+things that the communicator saying and
+ 
+
+ align:start position:0%
+things that the communicator saying and
+the broader context that allow us to
+
+ align:start position:0%
+the broader context that allow us to
+ 
+
+ align:start position:0%
+the broader context that allow us to
+figure out what's going on in this
+
+ align:start position:0%
+figure out what's going on in this
+ 
+
+ align:start position:0%
+figure out what's going on in this
+social interaction so it really requires
+
+ align:start position:0%
+social interaction so it really requires
+ 
+
+ align:start position:0%
+social interaction so it really requires
+understanding that the communicators
+
+ align:start position:0%
+understanding that the communicators
+ 
+
+ align:start position:0%
+understanding that the communicators
+mental states are being transferred in
+
+ align:start position:0%
+mental states are being transferred in
+ 
+
+ align:start position:0%
+mental states are being transferred in
+this causal way to the mind of the
+
+ align:start position:0%
+this causal way to the mind of the
+ 
+
+ align:start position:0%
+this causal way to the mind of the
+addressee so I'm going to structure the
+
+ align:start position:0%
+addressee so I'm going to structure the
+ 
+
+ align:start position:0%
+addressee so I'm going to structure the
+talk in terms of some important insights
+
+ align:start position:0%
+talk in terms of some important insights
+ 
+
+ align:start position:0%
+talk in terms of some important insights
+from the philosophy of human language
+
+ align:start position:0%
+from the philosophy of human language
+ 
+
+ align:start position:0%
+from the philosophy of human language
+and communication that I think have
+
+ align:start position:0%
+and communication that I think have
+ 
+
+ align:start position:0%
+and communication that I think have
+really guided the way we have the way
+
+ align:start position:0%
+really guided the way we have the way
+ 
+
+ align:start position:0%
+really guided the way we have the way
+researchers in the last say 50 years
+
+ align:start position:0%
+researchers in the last say 50 years
+ 
+
+ align:start position:0%
+researchers in the last say 50 years
+have been thinking about the development
+
+ align:start position:0%
+have been thinking about the development
+ 
+
+ align:start position:0%
+have been thinking about the development
+of human communication as well so I'm
+
+ align:start position:0%
+of human communication as well so I'm
+ 
+
+ align:start position:0%
+of human communication as well so I'm
+gonna broadly illustrate the three
+
+ align:start position:0%
+gonna broadly illustrate the three
+ 
+
+ align:start position:0%
+gonna broadly illustrate the three
+points that I'm taking from each and
+
+ align:start position:0%
+points that I'm taking from each and
+ 
+
+ align:start position:0%
+points that I'm taking from each and
+then I'll expand on them in each section
+
+ align:start position:0%
+then I'll expand on them in each section
+ 
+
+ align:start position:0%
+then I'll expand on them in each section
+so the first insight that I think is
+
+ align:start position:0%
+so the first insight that I think is
+ 
+
+ align:start position:0%
+so the first insight that I think is
+really important for understanding how
+
+ align:start position:0%
+really important for understanding how
+ 
+
+ align:start position:0%
+really important for understanding how
+we think about communication comes from
+
+ align:start position:0%
+we think about communication comes from
+ 
+
+ align:start position:0%
+we think about communication comes from
+John Austin who brought up the important
+
+ align:start position:0%
+John Austin who brought up the important
+ 
+
+ align:start position:0%
+John Austin who brought up the important
+point so before Austin people tended to
+
+ align:start position:0%
+point so before Austin people tended to
+ 
+
+ align:start position:0%
+point so before Austin people tended to
+think about language or study language a
+
+ align:start position:0%
+think about language or study language a
+ 
+
+ align:start position:0%
+think about language or study language a
+lot in terms of language itself in this
+
+ align:start position:0%
+lot in terms of language itself in this
+ 
+
+ align:start position:0%
+lot in terms of language itself in this
+semantics and syntax and just the
+
+ align:start position:0%
+semantics and syntax and just the
+ 
+
+ align:start position:0%
+semantics and syntax and just the
+language signal but Austin pointed out
+
+ align:start position:0%
+language signal but Austin pointed out
+ 
+
+ align:start position:0%
+language signal but Austin pointed out
+that language is actually not just
+
+ align:start position:0%
+that language is actually not just
+ 
+
+ align:start position:0%
+that language is actually not just
+about the content but it's also in
+
+ align:start position:0%
+about the content but it's also in
+ 
+
+ align:start position:0%
+about the content but it's also in
+action it's actually something that we
+
+ align:start position:0%
+action it's actually something that we
+ 
+
+ align:start position:0%
+action it's actually something that we
+use and that we we do things with it in
+
+ align:start position:0%
+use and that we we do things with it in
+ 
+
+ align:start position:0%
+use and that we we do things with it in
+the same way that we do things and
+
+ align:start position:0%
+the same way that we do things and
+ 
+
+ align:start position:0%
+the same way that we do things and
+accomplish things in the world using
+
+ align:start position:0%
+accomplish things in the world using
+ 
+
+ align:start position:0%
+accomplish things in the world using
+other kinds of actions that we engage in
+
+ align:start position:0%
+other kinds of actions that we engage in
+ 
+
+ align:start position:0%
+other kinds of actions that we engage in
+so Austin's sort of brought up this
+
+ align:start position:0%
+so Austin's sort of brought up this
+ 
+
+ align:start position:0%
+so Austin's sort of brought up this
+important distinction that language is
+
+ align:start position:0%
+important distinction that language is
+ 
+
+ align:start position:0%
+important distinction that language is
+not just about the content so to
+
+ align:start position:0%
+not just about the content so to
+ 
+
+ align:start position:0%
+not just about the content so to
+illustrate with an example in this
+
+ align:start position:0%
+illustrate with an example in this
+ 
+
+ align:start position:0%
+illustrate with an example in this
+communicative interaction there's
+
+ align:start position:0%
+communicative interaction there's
+ 
+
+ align:start position:0%
+communicative interaction there's
+language here this person is saying is
+
+ align:start position:0%
+language here this person is saying is
+ 
+
+ align:start position:0%
+language here this person is saying is
+there any salt and Austin analyze this
+
+ align:start position:0%
+there any salt and Austin analyze this
+ 
+
+ align:start position:0%
+there any salt and Austin analyze this
+in terms of not only what the words
+
+ align:start position:0%
+in terms of not only what the words
+ 
+
+ align:start position:0%
+in terms of not only what the words
+meant but in terms of three layers of
+
+ align:start position:0%
+meant but in terms of three layers of
+ 
+
+ align:start position:0%
+meant but in terms of three layers of
+intentionality so in this simple
+
+ align:start position:0%
+intentionality so in this simple
+ 
+
+ align:start position:0%
+intentionality so in this simple
+interaction he pointed out that there's
+
+ align:start position:0%
+interaction he pointed out that there's
+ 
+
+ align:start position:0%
+interaction he pointed out that there's
+a locution airy Act or the meaning of
+
+ align:start position:0%
+a locution airy Act or the meaning of
+ 
+
+ align:start position:0%
+a locution airy Act or the meaning of
+the sentence which is that there's a
+
+ align:start position:0%
+the sentence which is that there's a
+ 
+
+ align:start position:0%
+the sentence which is that there's a
+question being asked about the presence
+
+ align:start position:0%
+question being asked about the presence
+ 
+
+ align:start position:0%
+question being asked about the presence
+of salt but that there's actually
+
+ align:start position:0%
+of salt but that there's actually
+ 
+
+ align:start position:0%
+of salt but that there's actually
+something else going on here as well
+
+ align:start position:0%
+something else going on here as well
+ 
+
+ align:start position:0%
+something else going on here as well
+which is that there's an illocutionary
+
+ align:start position:0%
+which is that there's an illocutionary
+ 
+
+ align:start position:0%
+which is that there's an illocutionary
+action which is what he considers to be
+
+ align:start position:0%
+action which is what he considers to be
+ 
+
+ align:start position:0%
+action which is what he considers to be
+sort of the intention underlying the
+
+ align:start position:0%
+sort of the intention underlying the
+ 
+
+ align:start position:0%
+sort of the intention underlying the
+action which is to request the salt so
+
+ align:start position:0%
+action which is to request the salt so
+ 
+
+ align:start position:0%
+action which is to request the salt so
+if you actually just read this sentence
+
+ align:start position:0%
+if you actually just read this sentence
+ 
+
+ align:start position:0%
+if you actually just read this sentence
+it it's kind of under determined it's
+
+ align:start position:0%
+it it's kind of under determined it's
+ 
+
+ align:start position:0%
+it it's kind of under determined it's
+not necessarily obvious that this
+
+ align:start position:0%
+not necessarily obvious that this
+ 
+
+ align:start position:0%
+not necessarily obvious that this
+person's asking the other person at this
+
+ align:start position:0%
+person's asking the other person at this
+ 
+
+ align:start position:0%
+person's asking the other person at this
+table to pass the salt but if you take
+
+ align:start position:0%
+table to pass the salt but if you take
+ 
+
+ align:start position:0%
+table to pass the salt but if you take
+it within the broader context of the
+
+ align:start position:0%
+it within the broader context of the
+ 
+
+ align:start position:0%
+it within the broader context of the
+interaction you can understand that
+
+ align:start position:0%
+interaction you can understand that
+ 
+
+ align:start position:0%
+interaction you can understand that
+what's really going on here is not just
+
+ align:start position:0%
+what's really going on here is not just
+ 
+
+ align:start position:0%
+what's really going on here is not just
+a sentence being produced but rather one
+
+ align:start position:0%
+a sentence being produced but rather one
+ 
+
+ align:start position:0%
+a sentence being produced but rather one
+individual requesting something from
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+ align:start position:0%
+individual requesting something from
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+
+ align:start position:0%
+individual requesting something from
+another who's then supposed to
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+ align:start position:0%
+another who's then supposed to
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+
+ align:start position:0%
+another who's then supposed to
+understand the request and in the third
+
+ align:start position:0%
+understand the request and in the third
+ 
+
+ align:start position:0%
+understand the request and in the third
+layer of analysis cause the addressee to
+
+ align:start position:0%
+layer of analysis cause the addressee to
+ 
+
+ align:start position:0%
+layer of analysis cause the addressee to
+provide the salt so the idea is that
+
+ align:start position:0%
+provide the salt so the idea is that
+ 
+
+ align:start position:0%
+provide the salt so the idea is that
+there are these multiple things going on
+
+ align:start position:0%
+there are these multiple things going on
+ 
+
+ align:start position:0%
+there are these multiple things going on
+in the context of a communicative
+
+ align:start position:0%
+in the context of a communicative
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+
+ align:start position:0%
+in the context of a communicative
+interaction involving language the that
+
+ align:start position:0%
+interaction involving language the that
+ 
+
+ align:start position:0%
+interaction involving language the that
+sort of go beyond the words that are
+
+ align:start position:0%
+sort of go beyond the words that are
+ 
+
+ align:start position:0%
+sort of go beyond the words that are
+actually being spoken here and so if
+
+ align:start position:0%
+actually being spoken here and so if
+ 
+
+ align:start position:0%
+actually being spoken here and so if
+you're an infant
+
+ align:start position:0%
+you're an infant
+ 
+
+ align:start position:0%
+you're an infant
+just like in philosophy of language the
+
+ align:start position:0%
+just like in philosophy of language the
+ 
+
+ align:start position:0%
+just like in philosophy of language the
+focus in infant infant cognitive
+
+ align:start position:0%
+focus in infant infant cognitive
+ 
+
+ align:start position:0%
+focus in infant infant cognitive
+development also for a long time and
+
+ align:start position:0%
+development also for a long time and
+ 
+
+ align:start position:0%
+development also for a long time and
+still is we still need to understand
+
+ align:start position:0%
+still is we still need to understand
+ 
+
+ align:start position:0%
+still is we still need to understand
+these things is on was on understanding
+
+ align:start position:0%
+these things is on was on understanding
+ 
+
+ align:start position:0%
+these things is on was on understanding
+how infants learn words or how infants
+
+ align:start position:0%
+how infants learn words or how infants
+ 
+
+ align:start position:0%
+how infants learn words or how infants
+figure out the meaning of language and
+
+ align:start position:0%
+figure out the meaning of language and
+ 
+
+ align:start position:0%
+figure out the meaning of language and
+how it relates to objects in the
+
+ align:start position:0%
+how it relates to objects in the
+ 
+
+ align:start position:0%
+how it relates to objects in the
+environment and later to add the
+
+ align:start position:0%
+environment and later to add the
+ 
+
+ align:start position:0%
+environment and later to add the
+abstract concepts that language
+
+ align:start position:0%
+abstract concepts that language
+ 
+
+ align:start position:0%
+abstract concepts that language
+indicates but importantly understanding
+
+ align:start position:0%
+indicates but importantly understanding
+ 
+
+ align:start position:0%
+indicates but importantly understanding
+communication for an infant is going to
+
+ align:start position:0%
+communication for an infant is going to
+ 
+
+ align:start position:0%
+communication for an infant is going to
+be more than about just figuring out the
+
+ align:start position:0%
+be more than about just figuring out the
+ 
+
+ align:start position:0%
+be more than about just figuring out the
+meaning of these words and so following
+
+ align:start position:0%
+meaning of these words and so following
+ 
+
+ align:start position:0%
+meaning of these words and so following
+them the philosophical tradition of
+
+ align:start position:0%
+them the philosophical tradition of
+ 
+
+ align:start position:0%
+them the philosophical tradition of
+people like Austin who introduced the
+
+ align:start position:0%
+people like Austin who introduced the
+ 
+
+ align:start position:0%
+people like Austin who introduced the
+study of
+
+ align:start position:0%
+study of
+ 
+
+ align:start position:0%
+study of
+Mattox to language developmental
+
+ align:start position:0%
+Mattox to language developmental
+ 
+
+ align:start position:0%
+Mattox to language developmental
+psychologists as well started thinking
+
+ align:start position:0%
+psychologists as well started thinking
+ 
+
+ align:start position:0%
+psychologists as well started thinking
+about the importance of recognizing
+
+ align:start position:0%
+about the importance of recognizing
+ 
+
+ align:start position:0%
+about the importance of recognizing
+communication as this broader action in
+
+ align:start position:0%
+communication as this broader action in
+ 
+
+ align:start position:0%
+communication as this broader action in
+its context for understanding how
+
+ align:start position:0%
+its context for understanding how
+ 
+
+ align:start position:0%
+its context for understanding how
+infants come to be good communicators
+
+ align:start position:0%
+infants come to be good communicators
+ 
+
+ align:start position:0%
+infants come to be good communicators
+themselves so if communication involves
+
+ align:start position:0%
+themselves so if communication involves
+ 
+
+ align:start position:0%
+themselves so if communication involves
+this whole context of action and
+
+ align:start position:0%
+this whole context of action and
+ 
+
+ align:start position:0%
+this whole context of action and
+interaction between people if you're a
+
+ align:start position:0%
+interaction between people if you're a
+ 
+
+ align:start position:0%
+interaction between people if you're a
+baby who's in the business of
+
+ align:start position:0%
+baby who's in the business of
+ 
+
+ align:start position:0%
+baby who's in the business of
+understanding the social world the agent
+
+ align:start position:0%
+understanding the social world the agent
+ 
+
+ align:start position:0%
+understanding the social world the agent
+world in the world of language you're
+
+ align:start position:0%
+world in the world of language you're
+ 
+
+ align:start position:0%
+world in the world of language you're
+going to be well served by developing an
+
+ align:start position:0%
+going to be well served by developing an
+ 
+
+ align:start position:0%
+going to be well served by developing an
+ability to identify these kinds of
+
+ align:start position:0%
+ability to identify these kinds of
+ 
+
+ align:start position:0%
+ability to identify these kinds of
+communicative actions or situations and
+
+ align:start position:0%
+communicative actions or situations and
+ 
+
+ align:start position:0%
+communicative actions or situations and
+their components and to begin to
+
+ align:start position:0%
+their components and to begin to
+ 
+
+ align:start position:0%
+their components and to begin to
+understand how they work so how do
+
+ align:start position:0%
+understand how they work so how do
+ 
+
+ align:start position:0%
+understand how they work so how do
+infants start to figure out when
+
+ align:start position:0%
+infants start to figure out when
+ 
+
+ align:start position:0%
+infants start to figure out when
+communication is going on in the world
+
+ align:start position:0%
+communication is going on in the world
+ 
+
+ align:start position:0%
+communication is going on in the world
+around them rather than just identifying
+
+ align:start position:0%
+around them rather than just identifying
+ 
+
+ align:start position:0%
+around them rather than just identifying
+words and associating them with objects
+
+ align:start position:0%
+words and associating them with objects
+ 
+
+ align:start position:0%
+words and associating them with objects
+so actually there's a lot of evidence
+
+ align:start position:0%
+so actually there's a lot of evidence
+ 
+
+ align:start position:0%
+so actually there's a lot of evidence
+that infants are identifying key
+
+ align:start position:0%
+that infants are identifying key
+ 
+
+ align:start position:0%
+that infants are identifying key
+features of communicative situations
+
+ align:start position:0%
+features of communicative situations
+ 
+
+ align:start position:0%
+features of communicative situations
+really early in life so from the time
+
+ align:start position:0%
+really early in life so from the time
+ 
+
+ align:start position:0%
+really early in life so from the time
+they're born newborn human infants
+
+ align:start position:0%
+they're born newborn human infants
+ 
+
+ align:start position:0%
+they're born newborn human infants
+prefer listening to speech over other
+
+ align:start position:0%
+prefer listening to speech over other
+ 
+
+ align:start position:0%
+prefer listening to speech over other
+sounds so the typical method that's used
+
+ align:start position:0%
+sounds so the typical method that's used
+ 
+
+ align:start position:0%
+sounds so the typical method that's used
+to measure the preference of an infant
+
+ align:start position:0%
+to measure the preference of an infant
+ 
+
+ align:start position:0%
+to measure the preference of an infant
+who's only one to four days old is to
+
+ align:start position:0%
+who's only one to four days old is to
+ 
+
+ align:start position:0%
+who's only one to four days old is to
+have them suck on a pacifier that's
+
+ align:start position:0%
+have them suck on a pacifier that's
+ 
+
+ align:start position:0%
+have them suck on a pacifier that's
+connected to a machine that detects how
+
+ align:start position:0%
+connected to a machine that detects how
+ 
+
+ align:start position:0%
+connected to a machine that detects how
+strongly infants are sucking and then
+
+ align:start position:0%
+strongly infants are sucking and then
+ 
+
+ align:start position:0%
+strongly infants are sucking and then
+the sucking is used as a measure of
+
+ align:start position:0%
+the sucking is used as a measure of
+ 
+
+ align:start position:0%
+the sucking is used as a measure of
+infant's arousal upon hearing a
+
+ align:start position:0%
+infant's arousal upon hearing a
+ 
+
+ align:start position:0%
+infant's arousal upon hearing a
+particular sound or being exposed to a
+
+ align:start position:0%
+particular sound or being exposed to a
+ 
+
+ align:start position:0%
+particular sound or being exposed to a
+particular stimulus and so what
+
+ align:start position:0%
+particular stimulus and so what
+ 
+
+ align:start position:0%
+particular stimulus and so what
+researchers found is that if you have
+
+ align:start position:0%
+researchers found is that if you have
+ 
+
+ align:start position:0%
+researchers found is that if you have
+infants suck on this pacifier while
+
+ align:start position:0%
+infants suck on this pacifier while
+ 
+
+ align:start position:0%
+infants suck on this pacifier while
+listening to speech sound and norm
+
+ align:start position:0%
+listening to speech sound and norm
+ 
+
+ align:start position:0%
+listening to speech sound and norm
+speech sounds and alternation non-speech
+
+ align:start position:0%
+speech sounds and alternation non-speech
+ 
+
+ align:start position:0%
+speech sounds and alternation non-speech
+sounds being a sine wave produce sounds
+
+ align:start position:0%
+sounds being a sine wave produce sounds
+ 
+
+ align:start position:0%
+sounds being a sine wave produce sounds
+that are very similar to speech in their
+
+ align:start position:0%
+that are very similar to speech in their
+ 
+
+ align:start position:0%
+that are very similar to speech in their
+features if you listen to it has the
+
+ align:start position:0%
+features if you listen to it has the
+ 
+
+ align:start position:0%
+features if you listen to it has the
+prasada contours of speech and sounds a
+
+ align:start position:0%
+prasada contours of speech and sounds a
+ 
+
+ align:start position:0%
+prasada contours of speech and sounds a
+lot like it but it's not actually speech
+
+ align:start position:0%
+lot like it but it's not actually speech
+ 
+
+ align:start position:0%
+lot like it but it's not actually speech
+you can't understand you can't actually
+
+ align:start position:0%
+you can't understand you can't actually
+ 
+
+ align:start position:0%
+you can't understand you can't actually
+parse any words from it infants showed a
+
+ align:start position:0%
+parse any words from it infants showed a
+ 
+
+ align:start position:0%
+parse any words from it infants showed a
+preference for listening to speech over
+
+ align:start position:0%
+preference for listening to speech over
+ 
+
+ align:start position:0%
+preference for listening to speech over
+non speech or more arousal than they
+
+ align:start position:0%
+non speech or more arousal than they
+ 
+
+ align:start position:0%
+non speech or more arousal than they
+listen to speech they maintained their
+
+ align:start position:0%
+listen to speech they maintained their
+ 
+
+ align:start position:0%
+listen to speech they maintained their
+arousal for speech over the course of
+
+ align:start position:0%
+arousal for speech over the course of
+ 
+
+ align:start position:0%
+arousal for speech over the course of
+the experiment but for non speech it
+
+ align:start position:0%
+the experiment but for non speech it
+ 
+
+ align:start position:0%
+the experiment but for non speech it
+decline and so extremely early in life
+
+ align:start position:0%
+decline and so extremely early in life
+ 
+
+ align:start position:0%
+decline and so extremely early in life
+infants seem to have this bias for
+
+ align:start position:0%
+infants seem to have this bias for
+ 
+
+ align:start position:0%
+infants seem to have this bias for
+paying attention to the primary
+
+ align:start position:0%
+paying attention to the primary
+ 
+
+ align:start position:0%
+paying attention to the primary
+communicative signal of our species that
+
+ align:start position:0%
+communicative signal of our species that
+ 
+
+ align:start position:0%
+communicative signal of our species that
+is humans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quite early in life as well infants
+
+ align:start position:0%
+quite early in life as well infants
+ 
+
+ align:start position:0%
+quite early in life as well infants
+recognize that speech recognize some of
+
+ align:start position:0%
+recognize that speech recognize some of
+ 
+
+ align:start position:0%
+recognize that speech recognize some of
+the important features of the social
+
+ align:start position:0%
+the important features of the social
+ 
+
+ align:start position:0%
+the important features of the social
+context surrounding speech so getting
+
+ align:start position:0%
+context surrounding speech so getting
+ 
+
+ align:start position:0%
+context surrounding speech so getting
+more into the domain of the important
+
+ align:start position:0%
+more into the domain of the important
+ 
+
+ align:start position:0%
+more into the domain of the important
+features for communication so by six
+
+ align:start position:0%
+features for communication so by six
+ 
+
+ align:start position:0%
+features for communication so by six
+months infants seem to recognize that
+
+ align:start position:0%
+months infants seem to recognize that
+ 
+
+ align:start position:0%
+months infants seem to recognize that
+speech is human produced or at least
+
+ align:start position:0%
+speech is human produced or at least
+ 
+
+ align:start position:0%
+speech is human produced or at least
+associate speech with other humans and
+
+ align:start position:0%
+associate speech with other humans and
+ 
+
+ align:start position:0%
+associate speech with other humans and
+also human directed so in one study
+
+ align:start position:0%
+also human directed so in one study
+ 
+
+ align:start position:0%
+also human directed so in one study
+infants saw pictures of human faces or
+
+ align:start position:0%
+infants saw pictures of human faces or
+ 
+
+ align:start position:0%
+infants saw pictures of human faces or
+faces of monkeys and they heard
+
+ align:start position:0%
+faces of monkeys and they heard
+ 
+
+ align:start position:0%
+faces of monkeys and they heard
+different sounds so they either heard it
+
+ align:start position:0%
+different sounds so they either heard it
+ 
+
+ align:start position:0%
+different sounds so they either heard it
+seems like that sound isn't on but
+
+ align:start position:0%
+seems like that sound isn't on but
+ 
+
+ align:start position:0%
+seems like that sound isn't on but
+that's okay
+
+ align:start position:0%
+that's okay
+ 
+
+ align:start position:0%
+that's okay
+so they either so they either heard a
+
+ align:start position:0%
+so they either so they either heard a
+ 
+
+ align:start position:0%
+so they either so they either heard a
+speech sound in a language they'd never
+
+ align:start position:0%
+speech sound in a language they'd never
+ 
+
+ align:start position:0%
+speech sound in a language they'd never
+heard before repeating itself or they
+
+ align:start position:0%
+heard before repeating itself or they
+ 
+
+ align:start position:0%
+heard before repeating itself or they
+heard a monkey call an infants in one
+
+ align:start position:0%
+heard a monkey call an infants in one
+ 
+
+ align:start position:0%
+heard a monkey call an infants in one
+trial either saw so in the first trial
+
+ align:start position:0%
+trial either saw so in the first trial
+ 
+
+ align:start position:0%
+trial either saw so in the first trial
+said they'd see the human face and then
+
+ align:start position:0%
+said they'd see the human face and then
+ 
+
+ align:start position:0%
+said they'd see the human face and then
+they could listen repeatedly to a speech
+
+ align:start position:0%
+they could listen repeatedly to a speech
+ 
+
+ align:start position:0%
+they could listen repeatedly to a speech
+sound until they looked away for two
+
+ align:start position:0%
+sound until they looked away for two
+ 
+
+ align:start position:0%
+sound until they looked away for two
+seconds and then they would see a monkey
+
+ align:start position:0%
+seconds and then they would see a monkey
+ 
+
+ align:start position:0%
+seconds and then they would see a monkey
+face and then they would hear either a
+
+ align:start position:0%
+face and then they would hear either a
+ 
+
+ align:start position:0%
+face and then they would hear either a
+speech under a monkey sound and be able
+
+ align:start position:0%
+speech under a monkey sound and be able
+ 
+
+ align:start position:0%
+speech under a monkey sound and be able
+to look at this image while listening to
+
+ align:start position:0%
+to look at this image while listening to
+ 
+
+ align:start position:0%
+to look at this image while listening to
+that sound until they looked away for
+
+ align:start position:0%
+that sound until they looked away for
+ 
+
+ align:start position:0%
+that sound until they looked away for
+two seconds and so they got all possible
+
+ align:start position:0%
+two seconds and so they got all possible
+ 
+
+ align:start position:0%
+two seconds and so they got all possible
+combinations sometimes they saw a human
+
+ align:start position:0%
+combinations sometimes they saw a human
+ 
+
+ align:start position:0%
+combinations sometimes they saw a human
+face and listen to speech sometimes they
+
+ align:start position:0%
+face and listen to speech sometimes they
+ 
+
+ align:start position:0%
+face and listen to speech sometimes they
+saw a human face and listen that the
+
+ align:start position:0%
+saw a human face and listen that the
+ 
+
+ align:start position:0%
+saw a human face and listen that the
+monkey sounds and sometimes they said
+
+ align:start position:0%
+monkey sounds and sometimes they said
+ 
+
+ align:start position:0%
+monkey sounds and sometimes they said
+the monkey face and listen to either
+
+ align:start position:0%
+the monkey face and listen to either
+ 
+
+ align:start position:0%
+the monkey face and listen to either
+human speech or the monkey sound and the
+
+ align:start position:0%
+human speech or the monkey sound and the
+ 
+
+ align:start position:0%
+human speech or the monkey sound and the
+idea and the question was whether
+
+ align:start position:0%
+idea and the question was whether
+ 
+
+ align:start position:0%
+idea and the question was whether
+infants could actually could match the
+
+ align:start position:0%
+infants could actually could match the
+ 
+
+ align:start position:0%
+infants could actually could match the
+speech sounds to humans and recognize
+
+ align:start position:0%
+speech sounds to humans and recognize
+ 
+
+ align:start position:0%
+speech sounds to humans and recognize
+that they should be produced by the
+
+ align:start position:0%
+that they should be produced by the
+ 
+
+ align:start position:0%
+that they should be produced by the
+human rather than the monkey and that's
+
+ align:start position:0%
+human rather than the monkey and that's
+ 
+
+ align:start position:0%
+human rather than the monkey and that's
+what they found so you can see that when
+
+ align:start position:0%
+what they found so you can see that when
+ 
+
+ align:start position:0%
+what they found so you can see that when
+infants heard speech they were much more
+
+ align:start position:0%
+infants heard speech they were much more
+ 
+
+ align:start position:0%
+infants heard speech they were much more
+likely to look at the yet they were
+
+ align:start position:0%
+likely to look at the yet they were
+ 
+
+ align:start position:0%
+likely to look at the yet they were
+looking at the human when they heard
+
+ align:start position:0%
+looking at the human when they heard
+ 
+
+ align:start position:0%
+looking at the human when they heard
+speech and then they were looking at the
+
+ align:start position:0%
+speech and then they were looking at the
+ 
+
+ align:start position:0%
+speech and then they were looking at the
+monkey when they heard the monkey calls
+
+ align:start position:0%
+monkey when they heard the monkey calls
+ 
+
+ align:start position:0%
+monkey when they heard the monkey calls
+I'm similarly infants seem to understand
+
+ align:start position:0%
+I'm similarly infants seem to understand
+ 
+
+ align:start position:0%
+I'm similarly infants seem to understand
+by six months that speech is directed at
+
+ align:start position:0%
+by six months that speech is directed at
+ 
+
+ align:start position:0%
+by six months that speech is directed at
+other humans so when they saw a person
+
+ align:start position:0%
+other humans so when they saw a person
+ 
+
+ align:start position:0%
+other humans so when they saw a person
+talking talking behind a barrier versus
+
+ align:start position:0%
+talking talking behind a barrier versus
+ 
+
+ align:start position:0%
+talking talking behind a barrier versus
+acting so sort of swiping with her hand
+
+ align:start position:0%
+acting so sort of swiping with her hand
+ 
+
+ align:start position:0%
+acting so sort of swiping with her hand
+behind a barrier and then the barrier
+
+ align:start position:0%
+behind a barrier and then the barrier
+ 
+
+ align:start position:0%
+behind a barrier and then the barrier
+was revealed to reveal either a person
+
+ align:start position:0%
+was revealed to reveal either a person
+ 
+
+ align:start position:0%
+was revealed to reveal either a person
+or an object infants look longer for the
+
+ align:start position:0%
+or an object infants look longer for the
+ 
+
+ align:start position:0%
+or an object infants look longer for the
+speaking familiarization when they saw
+
+ align:start position:0%
+speaking familiarization when they saw
+ 
+
+ align:start position:0%
+speaking familiarization when they saw
+that there had been an object behind the
+
+ align:start position:0%
+that there had been an object behind the
+ 
+
+ align:start position:0%
+that there had been an object behind the
+barrier than a person suggesting that
+
+ align:start position:0%
+barrier than a person suggesting that
+ 
+
+ align:start position:0%
+barrier than a person suggesting that
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+did speech to be directed towards
+
+ align:start position:0%
+did speech to be directed towards
+ 
+
+ align:start position:0%
+did speech to be directed towards
+another person and in contrast when they
+
+ align:start position:0%
+another person and in contrast when they
+ 
+
+ align:start position:0%
+another person and in contrast when they
+saw the person swiping they look much
+
+ align:start position:0%
+saw the person swiping they look much
+ 
+
+ align:start position:0%
+saw the person swiping they look much
+longer when they saw a person behind the
+
+ align:start position:0%
+longer when they saw a person behind the
+ 
+
+ align:start position:0%
+longer when they saw a person behind the
+barrier because typically we don't swipe
+
+ align:start position:0%
+barrier because typically we don't swipe
+ 
+
+ align:start position:0%
+barrier because typically we don't swipe
+it people we tend to speak to them so so
+
+ align:start position:0%
+it people we tend to speak to them so so
+ 
+
+ align:start position:0%
+it people we tend to speak to them so so
+this suggests that infants understand
+
+ align:start position:0%
+this suggests that infants understand
+ 
+
+ align:start position:0%
+this suggests that infants understand
+some of the features of the context in
+
+ align:start position:0%
+some of the features of the context in
+ 
+
+ align:start position:0%
+some of the features of the context in
+which communication in which human
+
+ align:start position:0%
+which communication in which human
+ 
+
+ align:start position:0%
+which communication in which human
+communication is produced importantly it
+
+ align:start position:0%
+communication is produced importantly it
+ 
+
+ align:start position:0%
+communication is produced importantly it
+infants do still seem to be developing
+
+ align:start position:0%
+infants do still seem to be developing
+ 
+
+ align:start position:0%
+infants do still seem to be developing
+this ability over the first year of life
+
+ align:start position:0%
+this ability over the first year of life
+ 
+
+ align:start position:0%
+this ability over the first year of life
+because it's not until ten months that
+
+ align:start position:0%
+because it's not until ten months that
+ 
+
+ align:start position:0%
+because it's not until ten months that
+they expect mutual gaze between speakers
+
+ align:start position:0%
+they expect mutual gaze between speakers
+ 
+
+ align:start position:0%
+they expect mutual gaze between speakers
+which tends to be important part of
+
+ align:start position:0%
+which tends to be important part of
+ 
+
+ align:start position:0%
+which tends to be important part of
+understanding the social context of
+
+ align:start position:0%
+understanding the social context of
+ 
+
+ align:start position:0%
+understanding the social context of
+communication so in this study infants
+
+ align:start position:0%
+communication so in this study infants
+ 
+
+ align:start position:0%
+communication so in this study infants
+saw two people facing each other this is
+
+ align:start position:0%
+saw two people facing each other this is
+ 
+
+ align:start position:0%
+saw two people facing each other this is
+just one of the experiments from the
+
+ align:start position:0%
+just one of the experiments from the
+ 
+
+ align:start position:0%
+just one of the experiments from the
+study but you can see that they saw the
+
+ align:start position:0%
+study but you can see that they saw the
+ 
+
+ align:start position:0%
+study but you can see that they saw the
+two people looking at each other and
+
+ align:start position:0%
+two people looking at each other and
+ 
+
+ align:start position:0%
+two people looking at each other and
+speaking to each other or the two people
+
+ align:start position:0%
+speaking to each other or the two people
+ 
+
+ align:start position:0%
+speaking to each other or the two people
+looking apart and speaking to each other
+
+ align:start position:0%
+looking apart and speaking to each other
+ 
+
+ align:start position:0%
+looking apart and speaking to each other
+and infants expected that infants at
+
+ align:start position:0%
+and infants expected that infants at
+ 
+
+ align:start position:0%
+and infants expected that infants at
+nine months didn't differentiate between
+
+ align:start position:0%
+nine months didn't differentiate between
+ 
+
+ align:start position:0%
+nine months didn't differentiate between
+these at all so at nine months they
+
+ align:start position:0%
+these at all so at nine months they
+ 
+
+ align:start position:0%
+these at all so at nine months they
+didn't necessarily think that the people
+
+ align:start position:0%
+didn't necessarily think that the people
+ 
+
+ align:start position:0%
+didn't necessarily think that the people
+were going to look at each other when
+
+ align:start position:0%
+were going to look at each other when
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+
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+gaze
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+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
+so the question I've explored in my
+ 
+
+ align:start position:0%
+so the question I've explored in my
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+that that speech using speech because
+ 
+
+ align:start position:0%
+that that speech using speech because
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+
+ align:start position:0%
+this is something that infants seem to
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+
+ align:start position:0%
+this is something that infants seem to
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+
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+recognize as a signal that's important
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+
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+
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+
+ align:start position:0%
+in communicative contexts can transfer
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+
+ align:start position:0%
+information between individuals so we
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+
+ align:start position:0%
+information between individuals so we
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+
+ align:start position:0%
+can use speech to communicate with each
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+ align:start position:0%
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+
+ align:start position:0%
+other about what we're interested in so
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+
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+other about what we're interested in so
+if I'm observing this interaction
+
+ align:start position:0%
+if I'm observing this interaction
+ 
+
+ align:start position:0%
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+between a communicator and addressee I
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+
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+can infer that the if the communicator
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+can infer that the if the communicator
+says the cup and there's only one cup
+
+ align:start position:0%
+says the cup and there's only one cup
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+
+ align:start position:0%
+says the cup and there's only one cup
+present the addressee is probably going
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+present the addressee is probably going
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+
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+
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+to be able to figure out what it is that
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+
+ align:start position:0%
+to be able to figure out what it is that
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+
+ align:start position:0%
+the communicator wants and I can figure
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+
+ align:start position:0%
+the communicator wants and I can figure
+this out even from a third party
+
+ align:start position:0%
+this out even from a third party
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+this out even from a third party
+perspective and I can also understand
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+perspective and I can also understand
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+
+ align:start position:0%
+perspective and I can also understand
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+ align:start position:0%
+that other kinds of sounds like perhaps
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+
+ align:start position:0%
+that other kinds of sounds like perhaps
+a positive emotional vocalization are
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+communicating to the addressee what the
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+communicating to the addressee what the
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+communicator is interested in so speech
+ 
+
+ align:start position:0%
+communicator is interested in so speech
+and also other communicative signals as
+
+ align:start position:0%
+and also other communicative signals as
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+
+ align:start position:0%
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+
+ align:start position:0%
+well that can specify this sort of
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+ align:start position:0%
+well that can specify this sort of
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+ align:start position:0%
+information perhaps like pointing or
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+ align:start position:0%
+information perhaps like pointing or
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+ align:start position:0%
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+particular kinds of gestures can
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+ align:start position:0%
+transfer information from one individual
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+ align:start position:0%
+transfer information from one individual
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+
+ align:start position:0%
+to another
+ 
+
+ align:start position:0%
+to another
+so speech is going to be more effective
+
+ align:start position:0%
+so speech is going to be more effective
+ 
+
+ align:start position:0%
+so speech is going to be more effective
+for communicating than other kinds of
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+ align:start position:0%
+for communicating than other kinds of
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+
+ align:start position:0%
+for communicating than other kinds of
+non-communicative actions and
+
+ align:start position:0%
+non-communicative actions and
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+
+ align:start position:0%
+non-communicative actions and
+importantly for the purposes of this
+
+ align:start position:0%
+importantly for the purposes of this
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+
+ align:start position:0%
+importantly for the purposes of this
+study you're not just going to know that
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+ align:start position:0%
+study you're not just going to know that
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+
+ align:start position:0%
+study you're not just going to know that
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+ align:start position:0%
+communicate communicative information
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+
+ align:start position:0%
+communicate communicative information
+transfer is going on because you know
+
+ align:start position:0%
+transfer is going on because you know
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+
+ align:start position:0%
+transfer is going on because you know
+what the word cup means even in a
+
+ align:start position:0%
+what the word cup means even in a
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+
+ align:start position:0%
+what the word cup means even in a
+situation where other kinds of words
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+ align:start position:0%
+situation where other kinds of words
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+
+ align:start position:0%
+situation where other kinds of words
+where you're listening to a foreign
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+ align:start position:0%
+where you're listening to a foreign
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+
+ align:start position:0%
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+language and you have no idea what the
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+communicate information transfer can
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+communicate information transfer can
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+happen so we've all had the experience
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+of being in a foreign country presumably
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+where you're listening to people speak
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+to each other you can't necessarily
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+understand what they're saying but you
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+know that information transfer is
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+know that information transfer is
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+ align:start position:0%
+happening so the interesting thing about
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+
+ align:start position:0%
+happening so the interesting thing about
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+communicative actions like speech is
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+information even when we don't know what
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+ourselves and this insight suggests that
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+ourselves and this insight suggests that
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+ align:start position:0%
+maybe if you're an infant one really
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+
+ align:start position:0%
+maybe if you're an infant one really
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+
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+
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+communications going on like this might
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+communications going on like this might
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+ align:start position:0%
+provide infants with this really
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+
+ align:start position:0%
+provide infants with this really
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+powerful way of being able to track the
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+powerful way of being able to track the
+information flow between two other
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+information flow between two other
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+
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+information flow between two other
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+
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+people's minds and also to figure out
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+based on their responses to each other
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+
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+what the actual content of the words
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+what the actual content of the words
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+
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+what the actual content of the words
+might mean so we asked whether infants
+
+ align:start position:0%
+might mean so we asked whether infants
+ 
+
+ align:start position:0%
+might mean so we asked whether infants
+recognize that speech is communicative
+
+ align:start position:0%
+recognize that speech is communicative
+ 
+
+ align:start position:0%
+recognize that speech is communicative
+at 12 months of age and so in the
+
+ align:start position:0%
+at 12 months of age and so in the
+ 
+
+ align:start position:0%
+at 12 months of age and so in the
+procedure of the study infants were
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+ align:start position:0%
+procedure of the study infants were
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+
+ align:start position:0%
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+
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+privy to add a third party interaction
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+
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+between a communicator and addressee and
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+
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+between a communicator and addressee and
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+the infant is always just observing the
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+
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+the infant is always just observing the
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+interaction this is so that we can
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+
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+interaction this is so that we can
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+ align:start position:0%
+isolate whether infants think that
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+ align:start position:0%
+isolate whether infants think that
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+
+ align:start position:0%
+communicate that certain communicative
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+
+ align:start position:0%
+communicate that certain communicative
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+
+ align:start position:0%
+vocalizations can transfer information
+ 
+
+ align:start position:0%
+vocalizations can transfer information
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+
+ align:start position:0%
+from the communicator to an addressee
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+
+ align:start position:0%
+from the communicator to an addressee
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+
+ align:start position:0%
+even when the infant themselves has all
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+
+ align:start position:0%
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+the information so the third party
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+ align:start position:0%
+the information so the third party
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+
+ align:start position:0%
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+nature this procedure is important here
+
+ align:start position:0%
+nature this procedure is important here
+ 
+
+ align:start position:0%
+nature this procedure is important here
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+ align:start position:0%
+for seeing whether infants really are
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+
+ align:start position:0%
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+thinking about the fact that thoughts
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+
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+are typically isolated in particular
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+
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+
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+communication they can be shared so in
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+
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+violation of expectation paradigm so in
+ 
+
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+this kind of experiment as many of you
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+ align:start position:0%
+this kind of experiment as many of you
+ 
+
+ align:start position:0%
+this kind of experiment as many of you
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+ align:start position:0%
+probably know infants are sort of shown
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+
+ align:start position:0%
+probably know infants are sort of shown
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+
+ align:start position:0%
+a story through a series of scenes and
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+
+ align:start position:0%
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+
+ align:start position:0%
+then in the last scene or series of
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+
+ align:start position:0%
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+
+ align:start position:0%
+scenes they're shown different kinds of
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+
+ align:start position:0%
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+endings and we're interested in whether
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+
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+endings and we're interested in whether
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+infants are surprised or look longer at
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+
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+infants are surprised or look longer at
+some
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+ align:start position:0%
+some
+ 
+
+ align:start position:0%
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+and names more than they do with others
+
+ align:start position:0%
+and names more than they do with others
+ 
+
+ align:start position:0%
+and names more than they do with others
+so infants in these studies were shown a
+
+ align:start position:0%
+so infants in these studies were shown a
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+
+ align:start position:0%
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+ align:start position:0%
+live display where they had an actor in
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+
+ align:start position:0%
+live display where they had an actor in
+front of them in a stage first they were
+
+ align:start position:0%
+front of them in a stage first they were
+ 
+
+ align:start position:0%
+front of them in a stage first they were
+familiarized with this actor showing a
+
+ align:start position:0%
+familiarized with this actor showing a
+ 
+
+ align:start position:0%
+familiarized with this actor showing a
+preference for an object by picking it
+
+ align:start position:0%
+preference for an object by picking it
+ 
+
+ align:start position:0%
+preference for an object by picking it
+up and playing with it repeatedly in
+
+ align:start position:0%
+up and playing with it repeatedly in
+ 
+
+ align:start position:0%
+up and playing with it repeatedly in
+three separate scenes and so as in the
+
+ align:start position:0%
+three separate scenes and so as in the
+ 
+
+ align:start position:0%
+three separate scenes and so as in the
+studies by Amanda Woodward that Liz
+
+ align:start position:0%
+studies by Amanda Woodward that Liz
+ 
+
+ align:start position:0%
+studies by Amanda Woodward that Liz
+already mentioned infants tend to
+
+ align:start position:0%
+already mentioned infants tend to
+ 
+
+ align:start position:0%
+already mentioned infants tend to
+infants by 12 months and as early as
+
+ align:start position:0%
+infants by 12 months and as early as
+ 
+
+ align:start position:0%
+infants by 12 months and as early as
+three months will attribute a goal to
+
+ align:start position:0%
+three months will attribute a goal to
+ 
+
+ align:start position:0%
+three months will attribute a goal to
+this person for reaching for that
+
+ align:start position:0%
+this person for reaching for that
+ 
+
+ align:start position:0%
+this person for reaching for that
+particular target object so after being
+
+ align:start position:0%
+particular target object so after being
+ 
+
+ align:start position:0%
+particular target object so after being
+familiarized to this infant saw an
+
+ align:start position:0%
+familiarized to this infant saw an
+ 
+
+ align:start position:0%
+familiarized to this infant saw an
+address see who is a new person present
+
+ align:start position:0%
+address see who is a new person present
+ 
+
+ align:start position:0%
+address see who is a new person present
+in a totally different part of the stage
+
+ align:start position:0%
+in a totally different part of the stage
+ 
+
+ align:start position:0%
+in a totally different part of the stage
+they had never seen this person before
+
+ align:start position:0%
+they had never seen this person before
+ 
+
+ align:start position:0%
+they had never seen this person before
+and they'd never seen the two people
+
+ align:start position:0%
+and they'd never seen the two people
+ 
+
+ align:start position:0%
+and they'd never seen the two people
+together before this person reached for
+
+ align:start position:0%
+together before this person reached for
+ 
+
+ align:start position:0%
+together before this person reached for
+both objects in turn so first she
+
+ align:start position:0%
+both objects in turn so first she
+ 
+
+ align:start position:0%
+both objects in turn so first she
+grabbed this one then this one and then
+
+ align:start position:0%
+grabbed this one then this one and then
+ 
+
+ align:start position:0%
+grabbed this one then this one and then
+this one and then this one again to show
+
+ align:start position:0%
+this one and then this one again to show
+ 
+
+ align:start position:0%
+this one and then this one again to show
+that she didn't have a preference
+
+ align:start position:0%
+that she didn't have a preference
+ 
+
+ align:start position:0%
+that she didn't have a preference
+between the objects and could reach both
+
+ align:start position:0%
+between the objects and could reach both
+ 
+
+ align:start position:0%
+between the objects and could reach both
+of them then in the test scene so this
+
+ align:start position:0%
+of them then in the test scene so this
+ 
+
+ align:start position:0%
+of them then in the test scene so this
+is the ending that we showed infants
+
+ align:start position:0%
+is the ending that we showed infants
+ 
+
+ align:start position:0%
+is the ending that we showed infants
+they saw the two people together for the
+
+ align:start position:0%
+they saw the two people together for the
+ 
+
+ align:start position:0%
+they saw the two people together for the
+first time but now the communicator
+
+ align:start position:0%
+first time but now the communicator
+ 
+
+ align:start position:0%
+first time but now the communicator
+couldn't reach the objects because only
+
+ align:start position:0%
+couldn't reach the objects because only
+ 
+
+ align:start position:0%
+couldn't reach the objects because only
+her face would had access to the stage
+
+ align:start position:0%
+her face would had access to the stage
+ 
+
+ align:start position:0%
+her face would had access to the stage
+but the addressee could still reach them
+
+ align:start position:0%
+but the addressee could still reach them
+ 
+
+ align:start position:0%
+but the addressee could still reach them
+just fine at this point the the crucial
+
+ align:start position:0%
+just fine at this point the the crucial
+ 
+
+ align:start position:0%
+just fine at this point the the crucial
+manipulation was the vocalization
+
+ align:start position:0%
+manipulation was the vocalization
+ 
+
+ align:start position:0%
+manipulation was the vocalization
+uttered by the communicator so she
+
+ align:start position:0%
+uttered by the communicator so she
+ 
+
+ align:start position:0%
+uttered by the communicator so she
+either produced a speech sound the
+
+ align:start position:0%
+either produced a speech sound the
+ 
+
+ align:start position:0%
+either produced a speech sound the
+nonsense word koba which infants had not
+
+ align:start position:0%
+nonsense word koba which infants had not
+ 
+
+ align:start position:0%
+nonsense word koba which infants had not
+heard before she produced a coughing
+
+ align:start position:0%
+heard before she produced a coughing
+ 
+
+ align:start position:0%
+heard before she produced a coughing
+sound so something that would typically
+
+ align:start position:0%
+sound so something that would typically
+ 
+
+ align:start position:0%
+sound so something that would typically
+be physiological and not intentional or
+
+ align:start position:0%
+be physiological and not intentional or
+ 
+
+ align:start position:0%
+be physiological and not intentional or
+communicative in any way or an emotional
+
+ align:start position:0%
+communicative in any way or an emotional
+ 
+
+ align:start position:0%
+communicative in any way or an emotional
+vocalization so a sound that perhaps
+
+ align:start position:0%
+vocalization so a sound that perhaps
+ 
+
+ align:start position:0%
+vocalization so a sound that perhaps
+could convey information if I say ooh
+
+ align:start position:0%
+could convey information if I say ooh
+ 
+
+ align:start position:0%
+could convey information if I say ooh
+you might think I'm interested in
+
+ align:start position:0%
+you might think I'm interested in
+ 
+
+ align:start position:0%
+you might think I'm interested in
+something I'm feeling positive but you
+
+ align:start position:0%
+something I'm feeling positive but you
+ 
+
+ align:start position:0%
+something I'm feeling positive but you
+won't necessarily know what it is so
+
+ align:start position:0%
+won't necessarily know what it is so
+ 
+
+ align:start position:0%
+won't necessarily know what it is so
+this one's sort of in the middle of the
+
+ align:start position:0%
+this one's sort of in the middle of the
+ 
+
+ align:start position:0%
+this one's sort of in the middle of the
+other two and then infants saw the
+
+ align:start position:0%
+other two and then infants saw the
+ 
+
+ align:start position:0%
+other two and then infants saw the
+addressee either provide the target
+
+ align:start position:0%
+addressee either provide the target
+ 
+
+ align:start position:0%
+addressee either provide the target
+object that the communicator had reached
+
+ align:start position:0%
+object that the communicator had reached
+ 
+
+ align:start position:0%
+object that the communicator had reached
+for before or the non target object and
+
+ align:start position:0%
+for before or the non target object and
+ 
+
+ align:start position:0%
+for before or the non target object and
+the question is do infants understand
+
+ align:start position:0%
+the question is do infants understand
+ 
+
+ align:start position:0%
+the question is do infants understand
+that speech as a communicative signal do
+
+ align:start position:0%
+that speech as a communicative signal do
+ 
+
+ align:start position:0%
+that speech as a communicative signal do
+they have some expectation that even
+
+ align:start position:0%
+they have some expectation that even
+ 
+
+ align:start position:0%
+they have some expectation that even
+though they've never heard this
+
+ align:start position:0%
+though they've never heard this
+ 
+
+ align:start position:0%
+though they've never heard this
+particular speech sound used before that
+
+ align:start position:0%
+particular speech sound used before that
+ 
+
+ align:start position:0%
+particular speech sound used before that
+speech can transfer information such
+
+ align:start position:0%
+speech can transfer information such
+ 
+
+ align:start position:0%
+speech can transfer information such
+that the addressee will now be able to
+
+ align:start position:0%
+that the addressee will now be able to
+ 
+
+ align:start position:0%
+that the addressee will now be able to
+select the correct object whereas
+
+ align:start position:0%
+select the correct object whereas
+ 
+
+ align:start position:0%
+select the correct object whereas
+non-speech vocalizations like coughing
+
+ align:start position:0%
+non-speech vocalizations like coughing
+ 
+
+ align:start position:0%
+non-speech vocalizations like coughing
+and emotional vocalizations can't so if
+
+ align:start position:0%
+and emotional vocalizations can't so if
+ 
+
+ align:start position:0%
+and emotional vocalizations can't so if
+so infants in the speech condition
+
+ align:start position:0%
+so infants in the speech condition
+ 
+
+ align:start position:0%
+so infants in the speech condition
+should look longer tune on target than
+
+ align:start position:0%
+should look longer tune on target than
+ 
+
+ align:start position:0%
+should look longer tune on target than
+target actions finding these responses
+
+ align:start position:0%
+target actions finding these responses
+ 
+
+ align:start position:0%
+target actions finding these responses
+finding these unexpected and infants in
+
+ align:start position:0%
+finding these unexpected and infants in
+ 
+
+ align:start position:0%
+finding these unexpected and infants in
+the other two conditions
+
+ align:start position:0%
+the other two conditions
+ 
+
+ align:start position:0%
+the other two conditions
+differentiate between the two and this
+
+ align:start position:0%
+differentiate between the two and this
+ 
+
+ align:start position:0%
+differentiate between the two and this
+is what we found sofa then the speech
+
+ align:start position:0%
+is what we found sofa then the speech
+ 
+
+ align:start position:0%
+is what we found sofa then the speech
+condition infants are looking longer to
+
+ align:start position:0%
+condition infants are looking longer to
+ 
+
+ align:start position:0%
+condition infants are looking longer to
+non-target than targets suggesting that
+
+ align:start position:0%
+non-target than targets suggesting that
+ 
+
+ align:start position:0%
+non-target than targets suggesting that
+they understand that speech can transfer
+
+ align:start position:0%
+they understand that speech can transfer
+ 
+
+ align:start position:0%
+they understand that speech can transfer
+information about the communicators goal
+
+ align:start position:0%
+information about the communicators goal
+ 
+
+ align:start position:0%
+information about the communicators goal
+but when the communicator costs are
+
+ align:start position:0%
+but when the communicator costs are
+ 
+
+ align:start position:0%
+but when the communicator costs are
+produced as an emotional vocalization
+
+ align:start position:0%
+produced as an emotional vocalization
+ 
+
+ align:start position:0%
+produced as an emotional vocalization
+infants don't show these same
+
+ align:start position:0%
+infants don't show these same
+ 
+
+ align:start position:0%
+infants don't show these same
+expectations so this is some initial
+
+ align:start position:0%
+expectations so this is some initial
+ 
+
+ align:start position:0%
+expectations so this is some initial
+evidence that by 12 months infants not
+
+ align:start position:0%
+evidence that by 12 months infants not
+ 
+
+ align:start position:0%
+evidence that by 12 months infants not
+only recognize the context in which
+
+ align:start position:0%
+only recognize the context in which
+ 
+
+ align:start position:0%
+only recognize the context in which
+communication occurs and attend to
+
+ align:start position:0%
+communication occurs and attend to
+ 
+
+ align:start position:0%
+communication occurs and attend to
+speech is a special signal for
+
+ align:start position:0%
+speech is a special signal for
+ 
+
+ align:start position:0%
+speech is a special signal for
+communication but they also understand
+
+ align:start position:0%
+communication but they also understand
+ 
+
+ align:start position:0%
+communication but they also understand
+that that speech is something that's
+
+ align:start position:0%
+that that speech is something that's
+ 
+
+ align:start position:0%
+that that speech is something that's
+able to transfer information between two
+
+ align:start position:0%
+able to transfer information between two
+ 
+
+ align:start position:0%
+able to transfer information between two
+people so we also ran a few control
+
+ align:start position:0%
+people so we also ran a few control
+ 
+
+ align:start position:0%
+people so we also ran a few control
+conditions to rule out alternative
+
+ align:start position:0%
+conditions to rule out alternative
+ 
+
+ align:start position:0%
+conditions to rule out alternative
+explanations for this so one important
+
+ align:start position:0%
+explanations for this so one important
+ 
+
+ align:start position:0%
+explanations for this so one important
+question is our infants really reasoning
+
+ align:start position:0%
+question is our infants really reasoning
+ 
+
+ align:start position:0%
+question is our infants really reasoning
+about the the addresses access to
+
+ align:start position:0%
+about the the addresses access to
+ 
+
+ align:start position:0%
+about the the addresses access to
+information in this situation so for
+
+ align:start position:0%
+information in this situation so for
+ 
+
+ align:start position:0%
+information in this situation so for
+example in the case where the if infants
+
+ align:start position:0%
+example in the case where the if infants
+ 
+
+ align:start position:0%
+example in the case where the if infants
+are really reasoning with the addresses
+
+ align:start position:0%
+are really reasoning with the addresses
+ 
+
+ align:start position:0%
+are really reasoning with the addresses
+access to information then in a case
+
+ align:start position:0%
+access to information then in a case
+ 
+
+ align:start position:0%
+access to information then in a case
+where the communicator it makes a
+
+ align:start position:0%
+where the communicator it makes a
+ 
+
+ align:start position:0%
+where the communicator it makes a
+positive emotional vocalization and the
+
+ align:start position:0%
+positive emotional vocalization and the
+ 
+
+ align:start position:0%
+positive emotional vocalization and the
+addressee has previous information about
+
+ align:start position:0%
+addressee has previous information about
+ 
+
+ align:start position:0%
+addressee has previous information about
+what she's interested in so for example
+
+ align:start position:0%
+what she's interested in so for example
+ 
+
+ align:start position:0%
+what she's interested in so for example
+if she just saw that the communicator
+
+ align:start position:0%
+if she just saw that the communicator
+ 
+
+ align:start position:0%
+if she just saw that the communicator
+was trying to feed her child or wanted a
+
+ align:start position:0%
+was trying to feed her child or wanted a
+ 
+
+ align:start position:0%
+was trying to feed her child or wanted a
+drink of water she might know now that a
+
+ align:start position:0%
+drink of water she might know now that a
+ 
+
+ align:start position:0%
+drink of water she might know now that a
+positive emotional vocalization is
+
+ align:start position:0%
+positive emotional vocalization is
+ 
+
+ align:start position:0%
+positive emotional vocalization is
+indicating something like the cup so we
+
+ align:start position:0%
+indicating something like the cup so we
+ 
+
+ align:start position:0%
+indicating something like the cup so we
+set up a scenario like this as well in
+
+ align:start position:0%
+set up a scenario like this as well in
+ 
+
+ align:start position:0%
+set up a scenario like this as well in
+this case it's exactly the same as the
+
+ align:start position:0%
+this case it's exactly the same as the
+ 
+
+ align:start position:0%
+this case it's exactly the same as the
+previous study except that the addressee
+
+ align:start position:0%
+previous study except that the addressee
+ 
+
+ align:start position:0%
+previous study except that the addressee
+had visual access to the communicators
+
+ align:start position:0%
+had visual access to the communicators
+ 
+
+ align:start position:0%
+had visual access to the communicators
+preference during the familiarization
+
+ align:start position:0%
+preference during the familiarization
+ 
+
+ align:start position:0%
+preference during the familiarization
+phase so now she knows what it is that
+
+ align:start position:0%
+phase so now she knows what it is that
+ 
+
+ align:start position:0%
+phase so now she knows what it is that
+the communicator likes and this is
+
+ align:start position:0%
+the communicator likes and this is
+ 
+
+ align:start position:0%
+the communicator likes and this is
+important for making sure that infants
+
+ align:start position:0%
+important for making sure that infants
+ 
+
+ align:start position:0%
+important for making sure that infants
+recognize that something like visual
+
+ align:start position:0%
+recognize that something like visual
+ 
+
+ align:start position:0%
+recognize that something like visual
+access can provide the addressee with
+
+ align:start position:0%
+access can provide the addressee with
+ 
+
+ align:start position:0%
+access can provide the addressee with
+information about the communicators
+
+ align:start position:0%
+information about the communicators
+ 
+
+ align:start position:0%
+information about the communicators
+interest so now infants all the same
+
+ align:start position:0%
+interest so now infants all the same
+ 
+
+ align:start position:0%
+interest so now infants all the same
+address see familiarization and then in
+
+ align:start position:0%
+address see familiarization and then in
+ 
+
+ align:start position:0%
+address see familiarization and then in
+the test they saw the communicator
+
+ align:start position:0%
+the test they saw the communicator
+ 
+
+ align:start position:0%
+the test they saw the communicator
+produce the vocalization once again so
+
+ align:start position:0%
+produce the vocalization once again so
+ 
+
+ align:start position:0%
+produce the vocalization once again so
+now even though o is a not was not
+
+ align:start position:0%
+now even though o is a not was not
+ 
+
+ align:start position:0%
+now even though o is a not was not
+treated as a communicative vocalization
+
+ align:start position:0%
+treated as a communicative vocalization
+ 
+
+ align:start position:0%
+treated as a communicative vocalization
+in the previous studies if infants are
+
+ align:start position:0%
+in the previous studies if infants are
+ 
+
+ align:start position:0%
+in the previous studies if infants are
+reasoning about the kinds of information
+
+ align:start position:0%
+reasoning about the kinds of information
+ 
+
+ align:start position:0%
+reasoning about the kinds of information
+that the addressee has access to they
+
+ align:start position:0%
+that the addressee has access to they
+ 
+
+ align:start position:0%
+that the addressee has access to they
+should now expect that the addressee
+
+ align:start position:0%
+should now expect that the addressee
+ 
+
+ align:start position:0%
+should now expect that the addressee
+will provide the target object because
+
+ align:start position:0%
+will provide the target object because
+ 
+
+ align:start position:0%
+will provide the target object because
+she knows from a previous C and what the
+
+ align:start position:0%
+she knows from a previous C and what the
+ 
+
+ align:start position:0%
+she knows from a previous C and what the
+communicator was in
+
+ align:start position:0%
+communicator was in
+ 
+
+ align:start position:0%
+communicator was in
+student so this is important also for
+
+ align:start position:0%
+student so this is important also for
+ 
+
+ align:start position:0%
+student so this is important also for
+ruling out the possibility that maybe
+
+ align:start position:0%
+ruling out the possibility that maybe
+ 
+
+ align:start position:0%
+ruling out the possibility that maybe
+just hearing these non-communicative
+
+ align:start position:0%
+just hearing these non-communicative
+ 
+
+ align:start position:0%
+just hearing these non-communicative
+vocalizations surprises or confuses
+
+ align:start position:0%
+vocalizations surprises or confuses
+ 
+
+ align:start position:0%
+vocalizations surprises or confuses
+infants or makes them unable to reason
+
+ align:start position:0%
+infants or makes them unable to reason
+ 
+
+ align:start position:0%
+infants or makes them unable to reason
+about the scenario anymore here they're
+
+ align:start position:0%
+about the scenario anymore here they're
+ 
+
+ align:start position:0%
+about the scenario anymore here they're
+getting a non communicative vocalization
+
+ align:start position:0%
+getting a non communicative vocalization
+ 
+
+ align:start position:0%
+getting a non communicative vocalization
+but the addressee has access to
+
+ align:start position:0%
+but the addressee has access to
+ 
+
+ align:start position:0%
+but the addressee has access to
+information and here as in the speech
+
+ align:start position:0%
+information and here as in the speech
+ 
+
+ align:start position:0%
+information and here as in the speech
+condition infants look longer at the non
+
+ align:start position:0%
+condition infants look longer at the non
+ 
+
+ align:start position:0%
+condition infants look longer at the non
+target outcome so this is just sort of a
+
+ align:start position:0%
+target outcome so this is just sort of a
+ 
+
+ align:start position:0%
+target outcome so this is just sort of a
+some evidence that infants are really
+
+ align:start position:0%
+some evidence that infants are really
+ 
+
+ align:start position:0%
+some evidence that infants are really
+thinking about the idea that relevant
+
+ align:start position:0%
+thinking about the idea that relevant
+ 
+
+ align:start position:0%
+thinking about the idea that relevant
+sources of information such as a
+
+ align:start position:0%
+sources of information such as a
+ 
+
+ align:start position:0%
+sources of information such as a
+communicative vocalization but also
+
+ align:start position:0%
+communicative vocalization but also
+ 
+
+ align:start position:0%
+communicative vocalization but also
+prior visual access can give the address
+
+ align:start position:0%
+prior visual access can give the address
+ 
+
+ align:start position:0%
+prior visual access can give the address
+the information about the communicators
+
+ align:start position:0%
+the information about the communicators
+ 
+
+ align:start position:0%
+the information about the communicators
+goal so they are reasoning about
+
+ align:start position:0%
+goal so they are reasoning about
+ 
+
+ align:start position:0%
+goal so they are reasoning about
+information access another important
+
+ align:start position:0%
+information access another important
+ 
+
+ align:start position:0%
+information access another important
+question is are they really thinking
+
+ align:start position:0%
+question is are they really thinking
+ 
+
+ align:start position:0%
+question is are they really thinking
+about the source of information or do
+
+ align:start position:0%
+about the source of information or do
+ 
+
+ align:start position:0%
+about the source of information or do
+they have so what's what's really the
+
+ align:start position:0%
+they have so what's what's really the
+ 
+
+ align:start position:0%
+they have so what's what's really the
+mechanism behind what infants are doing
+
+ align:start position:0%
+mechanism behind what infants are doing
+ 
+
+ align:start position:0%
+mechanism behind what infants are doing
+here are they thinking something like
+
+ align:start position:0%
+here are they thinking something like
+ 
+
+ align:start position:0%
+here are they thinking something like
+when I hear speech everything will go
+
+ align:start position:0%
+when I hear speech everything will go
+ 
+
+ align:start position:0%
+when I hear speech everything will go
+well or the speaker is gonna get what
+
+ align:start position:0%
+well or the speaker is gonna get what
+ 
+
+ align:start position:0%
+well or the speaker is gonna get what
+she wants are they really thinking about
+
+ align:start position:0%
+she wants are they really thinking about
+ 
+
+ align:start position:0%
+she wants are they really thinking about
+communication in this causal way where
+
+ align:start position:0%
+communication in this causal way where
+ 
+
+ align:start position:0%
+communication in this causal way where
+the information has to come from the
+
+ align:start position:0%
+the information has to come from the
+ 
+
+ align:start position:0%
+the information has to come from the
+speaker and be delivered to the listener
+
+ align:start position:0%
+speaker and be delivered to the listener
+ 
+
+ align:start position:0%
+speaker and be delivered to the listener
+in order for it to work so to test for
+
+ align:start position:0%
+in order for it to work so to test for
+ 
+
+ align:start position:0%
+in order for it to work so to test for
+this infants another communicator
+
+ align:start position:0%
+this infants another communicator
+ 
+
+ align:start position:0%
+this infants another communicator
+familiarisation here the communicators
+
+ align:start position:0%
+familiarisation here the communicators
+ 
+
+ align:start position:0%
+familiarisation here the communicators
+alone so they've never seen the two
+
+ align:start position:0%
+alone so they've never seen the two
+ 
+
+ align:start position:0%
+alone so they've never seen the two
+people together before she reaches for
+
+ align:start position:0%
+people together before she reaches for
+ 
+
+ align:start position:0%
+people together before she reaches for
+the target object then they see the
+
+ align:start position:0%
+the target object then they see the
+ 
+
+ align:start position:0%
+the target object then they see the
+addressee again and then in the test
+
+ align:start position:0%
+addressee again and then in the test
+ 
+
+ align:start position:0%
+addressee again and then in the test
+scene in this case the addressee is the
+
+ align:start position:0%
+scene in this case the addressee is the
+ 
+
+ align:start position:0%
+scene in this case the addressee is the
+one who produces a speech so speech is
+
+ align:start position:0%
+one who produces a speech so speech is
+ 
+
+ align:start position:0%
+one who produces a speech so speech is
+present in the scene as it was before
+
+ align:start position:0%
+present in the scene as it was before
+ 
+
+ align:start position:0%
+present in the scene as it was before
+but it's not being produced by the
+
+ align:start position:0%
+but it's not being produced by the
+ 
+
+ align:start position:0%
+but it's not being produced by the
+communicator or the person who showed a
+
+ align:start position:0%
+communicator or the person who showed a
+ 
+
+ align:start position:0%
+communicator or the person who showed a
+preference
+
+ align:start position:0%
+preference
+ 
+
+ align:start position:0%
+preference
+so if infants just think that speech
+
+ align:start position:0%
+so if infants just think that speech
+ 
+
+ align:start position:0%
+so if infants just think that speech
+leads to people obtaining their goals or
+
+ align:start position:0%
+leads to people obtaining their goals or
+ 
+
+ align:start position:0%
+leads to people obtaining their goals or
+magical outcomes happening then they
+
+ align:start position:0%
+magical outcomes happening then they
+ 
+
+ align:start position:0%
+magical outcomes happening then they
+should expect the addressee to provide
+
+ align:start position:0%
+should expect the addressee to provide
+ 
+
+ align:start position:0%
+should expect the addressee to provide
+the target here as well but if they
+
+ align:start position:0%
+the target here as well but if they
+ 
+
+ align:start position:0%
+the target here as well but if they
+understand that they don't know anything
+
+ align:start position:0%
+understand that they don't know anything
+ 
+
+ align:start position:0%
+understand that they don't know anything
+about the addressee in which case this
+
+ align:start position:0%
+about the addressee in which case this
+ 
+
+ align:start position:0%
+about the addressee in which case this
+is not really informative about either
+
+ align:start position:0%
+is not really informative about either
+ 
+
+ align:start position:0%
+is not really informative about either
+object then they should look equally to
+
+ align:start position:0%
+object then they should look equally to
+ 
+
+ align:start position:0%
+object then they should look equally to
+both outcomes and in fact this is what
+
+ align:start position:0%
+both outcomes and in fact this is what
+ 
+
+ align:start position:0%
+both outcomes and in fact this is what
+they do at 12 months so infants here
+
+ align:start position:0%
+they do at 12 months so infants here
+ 
+
+ align:start position:0%
+they do at 12 months so infants here
+don't expect information to be
+
+ align:start position:0%
+don't expect information to be
+ 
+
+ align:start position:0%
+don't expect information to be
+transferred from one person to another
+
+ align:start position:0%
+transferred from one person to another
+ 
+
+ align:start position:0%
+transferred from one person to another
+unless the first person who communicated
+
+ align:start position:0%
+unless the first person who communicated
+ 
+
+ align:start position:0%
+unless the first person who communicated
+is the one who actually had the
+
+ align:start position:0%
+is the one who actually had the
+ 
+
+ align:start position:0%
+is the one who actually had the
+information to provide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in by 12 months infants seem to
+
+ align:start position:0%
+so in by 12 months infants seem to
+ 
+
+ align:start position:0%
+so in by 12 months infants seem to
+recognize that speech is communicative
+
+ align:start position:0%
+recognize that speech is communicative
+ 
+
+ align:start position:0%
+recognize that speech is communicative
+and they seem to have some of the parts
+
+ align:start position:0%
+and they seem to have some of the parts
+ 
+
+ align:start position:0%
+and they seem to have some of the parts
+of a causal model of communication
+
+ align:start position:0%
+of a causal model of communication
+ 
+
+ align:start position:0%
+of a causal model of communication
+they're not just thinking about speech
+
+ align:start position:0%
+they're not just thinking about speech
+ 
+
+ align:start position:0%
+they're not just thinking about speech
+as something that can produce successful
+
+ align:start position:0%
+as something that can produce successful
+ 
+
+ align:start position:0%
+as something that can produce successful
+outcomes but as something that can be
+
+ align:start position:0%
+outcomes but as something that can be
+ 
+
+ align:start position:0%
+outcomes but as something that can be
+used to have information move from the
+
+ align:start position:0%
+used to have information move from the
+ 
+
+ align:start position:0%
+used to have information move from the
+mind of one individual to another so a
+
+ align:start position:0%
+mind of one individual to another so a
+ 
+
+ align:start position:0%
+mind of one individual to another so a
+12 month olds seem to recognize that
+
+ align:start position:0%
+12 month olds seem to recognize that
+ 
+
+ align:start position:0%
+12 month olds seem to recognize that
+speech is communicative but we really
+
+ align:start position:0%
+speech is communicative but we really
+ 
+
+ align:start position:0%
+speech is communicative but we really
+wanted to get it the idea that
+
+ align:start position:0%
+wanted to get it the idea that
+ 
+
+ align:start position:0%
+wanted to get it the idea that
+understanding that speech is
+
+ align:start position:0%
+understanding that speech is
+ 
+
+ align:start position:0%
+understanding that speech is
+communicative might be something that
+
+ align:start position:0%
+communicative might be something that
+ 
+
+ align:start position:0%
+communicative might be something that
+drives and guides were learning and
+
+ align:start position:0%
+drives and guides were learning and
+ 
+
+ align:start position:0%
+drives and guides were learning and
+language acquisition rather than
+
+ align:start position:0%
+language acquisition rather than
+ 
+
+ align:start position:0%
+language acquisition rather than
+something that is as a result so what a
+
+ align:start position:0%
+something that is as a result so what a
+ 
+
+ align:start position:0%
+something that is as a result so what a
+12 month old could be doing in this
+
+ align:start position:0%
+12 month old could be doing in this
+ 
+
+ align:start position:0%
+12 month old could be doing in this
+study is hearing the word Koba
+
+ align:start position:0%
+study is hearing the word Koba
+ 
+
+ align:start position:0%
+study is hearing the word Koba
+associating it with the object that the
+
+ align:start position:0%
+associating it with the object that the
+ 
+
+ align:start position:0%
+associating it with the object that the
+communicator had reached for and then
+
+ align:start position:0%
+communicator had reached for and then
+ 
+
+ align:start position:0%
+communicator had reached for and then
+thinking okay that one's the Koba so
+
+ align:start position:0%
+thinking okay that one's the Koba so
+ 
+
+ align:start position:0%
+thinking okay that one's the Koba so
+that's what the address he should reach
+
+ align:start position:0%
+that's what the address he should reach
+ 
+
+ align:start position:0%
+that's what the address he should reach
+for but in these studies we were
+
+ align:start position:0%
+for but in these studies we were
+ 
+
+ align:start position:0%
+for but in these studies we were
+interested in whether infants at an even
+
+ align:start position:0%
+interested in whether infants at an even
+ 
+
+ align:start position:0%
+interested in whether infants at an even
+younger age who would very very very
+
+ align:start position:0%
+younger age who would very very very
+ 
+
+ align:start position:0%
+younger age who would very very very
+unlikely to be associating the word with
+
+ align:start position:0%
+unlikely to be associating the word with
+ 
+
+ align:start position:0%
+unlikely to be associating the word with
+the object are learning a label for the
+
+ align:start position:0%
+the object are learning a label for the
+ 
+
+ align:start position:0%
+the object are learning a label for the
+object over the course of the study
+
+ align:start position:0%
+object over the course of the study
+ 
+
+ align:start position:0%
+object over the course of the study
+would also recognize that speech can
+
+ align:start position:0%
+would also recognize that speech can
+ 
+
+ align:start position:0%
+would also recognize that speech can
+transfer information about one person to
+
+ align:start position:0%
+transfer information about one person to
+ 
+
+ align:start position:0%
+transfer information about one person to
+another person and so for this reason we
+
+ align:start position:0%
+another person and so for this reason we
+ 
+
+ align:start position:0%
+another person and so for this reason we
+tested six month olds because six month
+
+ align:start position:0%
+tested six month olds because six month
+ 
+
+ align:start position:0%
+tested six month olds because six month
+olds understand only some very very
+
+ align:start position:0%
+olds understand only some very very
+ 
+
+ align:start position:0%
+olds understand only some very very
+common words in their environment and
+
+ align:start position:0%
+common words in their environment and
+ 
+
+ align:start position:0%
+common words in their environment and
+will look to the right object when they
+
+ align:start position:0%
+will look to the right object when they
+ 
+
+ align:start position:0%
+will look to the right object when they
+hear the label for it but there's these
+
+ align:start position:0%
+hear the label for it but there's these
+ 
+
+ align:start position:0%
+hear the label for it but there's these
+are very very limited words and there's
+
+ align:start position:0%
+are very very limited words and there's
+ 
+
+ align:start position:0%
+are very very limited words and there's
+no evidence for learning a word in a
+
+ align:start position:0%
+no evidence for learning a word in a
+ 
+
+ align:start position:0%
+no evidence for learning a word in a
+single trial which is what they would
+
+ align:start position:0%
+single trial which is what they would
+ 
+
+ align:start position:0%
+single trial which is what they would
+have to do in this study they would have
+
+ align:start position:0%
+have to do in this study they would have
+ 
+
+ align:start position:0%
+have to do in this study they would have
+to hear Koba and then think back to what
+
+ align:start position:0%
+to hear Koba and then think back to what
+ 
+
+ align:start position:0%
+to hear Koba and then think back to what
+the ad communicator had reached for and
+
+ align:start position:0%
+the ad communicator had reached for and
+ 
+
+ align:start position:0%
+the ad communicator had reached for and
+really learn learn that word over the
+
+ align:start position:0%
+really learn learn that word over the
+ 
+
+ align:start position:0%
+really learn learn that word over the
+course of study which we have no
+
+ align:start position:0%
+course of study which we have no
+ 
+
+ align:start position:0%
+course of study which we have no
+evidence that a six-month-old can do so
+
+ align:start position:0%
+evidence that a six-month-old can do so
+ 
+
+ align:start position:0%
+evidence that a six-month-old can do so
+the goal of looking at this age group
+
+ align:start position:0%
+the goal of looking at this age group
+ 
+
+ align:start position:0%
+the goal of looking at this age group
+was to see whether infants might have a
+
+ align:start position:0%
+was to see whether infants might have a
+ 
+
+ align:start position:0%
+was to see whether infants might have a
+more abstract understanding of the idea
+
+ align:start position:0%
+more abstract understanding of the idea
+ 
+
+ align:start position:0%
+more abstract understanding of the idea
+that when speech is produced information
+
+ align:start position:0%
+that when speech is produced information
+ 
+
+ align:start position:0%
+that when speech is produced information
+can be transferred from one person to
+
+ align:start position:0%
+can be transferred from one person to
+ 
+
+ align:start position:0%
+can be transferred from one person to
+another even when they can when they
+
+ align:start position:0%
+another even when they can when they
+ 
+
+ align:start position:0%
+another even when they can when they
+themselves don't know what that
+
+ align:start position:0%
+themselves don't know what that
+ 
+
+ align:start position:0%
+themselves don't know what that
+information or what the the link between
+
+ align:start position:0%
+information or what the the link between
+ 
+
+ align:start position:0%
+information or what the the link between
+the word and the object so six-month-old
+
+ align:start position:0%
+the word and the object so six-month-old
+ 
+
+ align:start position:0%
+the word and the object so six-month-old
+saw the same scenes we give them the
+
+ align:start position:0%
+saw the same scenes we give them the
+ 
+
+ align:start position:0%
+saw the same scenes we give them the
+speech versus cough contrast and they
+
+ align:start position:0%
+speech versus cough contrast and they
+ 
+
+ align:start position:0%
+speech versus cough contrast and they
+look the same as the 12 month olds here
+
+ align:start position:0%
+look the same as the 12 month olds here
+ 
+
+ align:start position:0%
+look the same as the 12 month olds here
+so you can see that in the speech case
+
+ align:start position:0%
+so you can see that in the speech case
+ 
+
+ align:start position:0%
+so you can see that in the speech case
+they're looking longer for the
+
+ align:start position:0%
+they're looking longer for the
+ 
+
+ align:start position:0%
+they're looking longer for the
+non-target outcome in the COFF case
+
+ align:start position:0%
+non-target outcome in the COFF case
+ 
+
+ align:start position:0%
+non-target outcome in the COFF case
+they're looking longer for the target
+
+ align:start position:0%
+they're looking longer for the target
+ 
+
+ align:start position:0%
+they're looking longer for the target
+outcome and so we haven't done all the
+
+ align:start position:0%
+outcome and so we haven't done all the
+ 
+
+ align:start position:0%
+outcome and so we haven't done all the
+same control conditions as with the 12
+
+ align:start position:0%
+same control conditions as with the 12
+ 
+
+ align:start position:0%
+same control conditions as with the 12
+month olds here so I think there's a lot
+
+ align:start position:0%
+month olds here so I think there's a lot
+ 
+
+ align:start position:0%
+month olds here so I think there's a lot
+of room for questions about how is six
+
+ align:start position:0%
+of room for questions about how is six
+ 
+
+ align:start position:0%
+of room for questions about how is six
+month olds understanding of
+
+ align:start position:0%
+month olds understanding of
+ 
+
+ align:start position:0%
+month olds understanding of
+munication in this causal way more
+
+ align:start position:0%
+munication in this causal way more
+ 
+
+ align:start position:0%
+munication in this causal way more
+limited than the understanding of 12
+
+ align:start position:0%
+limited than the understanding of 12
+ 
+
+ align:start position:0%
+limited than the understanding of 12
+month olds would a six month old think
+
+ align:start position:0%
+month olds would a six month old think
+ 
+
+ align:start position:0%
+month olds would a six month old think
+that if speech was produced by a loud
+
+ align:start position:0%
+that if speech was produced by a loud
+ 
+
+ align:start position:0%
+that if speech was produced by a loud
+speaker or by the addressee that the
+
+ align:start position:0%
+speaker or by the addressee that the
+ 
+
+ align:start position:0%
+speaker or by the addressee that the
+communicator would still get the right
+
+ align:start position:0%
+communicator would still get the right
+ 
+
+ align:start position:0%
+communicator would still get the right
+object so there are a lot of open
+
+ align:start position:0%
+object so there are a lot of open
+ 
+
+ align:start position:0%
+object so there are a lot of open
+questions about the sort of basic these
+
+ align:start position:0%
+questions about the sort of basic these
+ 
+
+ align:start position:0%
+questions about the sort of basic these
+basic questions about how infants
+
+ align:start position:0%
+basic questions about how infants
+ 
+
+ align:start position:0%
+basic questions about how infants
+understanding of communicative
+
+ align:start position:0%
+understanding of communicative
+ 
+
+ align:start position:0%
+understanding of communicative
+information transfer starts out so these
+
+ align:start position:0%
+information transfer starts out so these
+ 
+
+ align:start position:0%
+information transfer starts out so these
+experiments suggest that by six months
+
+ align:start position:0%
+experiments suggest that by six months
+ 
+
+ align:start position:0%
+experiments suggest that by six months
+infants seem to understand that speech
+
+ align:start position:0%
+infants seem to understand that speech
+ 
+
+ align:start position:0%
+infants seem to understand that speech
+is communicative and they in addition to
+
+ align:start position:0%
+is communicative and they in addition to
+ 
+
+ align:start position:0%
+is communicative and they in addition to
+the other studies suggest they
+
+ align:start position:0%
+the other studies suggest they
+ 
+
+ align:start position:0%
+the other studies suggest they
+understand some of the features of
+
+ align:start position:0%
+understand some of the features of
+ 
+
+ align:start position:0%
+understand some of the features of
+communicative interactions and they
+
+ align:start position:0%
+communicative interactions and they
+ 
+
+ align:start position:0%
+communicative interactions and they
+recognize that it transfers information
+
+ align:start position:0%
+recognize that it transfers information
+ 
+
+ align:start position:0%
+recognize that it transfers information
+from one person to another and I'd like
+
+ align:start position:0%
+from one person to another and I'd like
+ 
+
+ align:start position:0%
+from one person to another and I'd like
+to argue that this might be something
+
+ align:start position:0%
+to argue that this might be something
+ 
+
+ align:start position:0%
+to argue that this might be something
+that provides a mechanism for language
+
+ align:start position:0%
+that provides a mechanism for language
+ 
+
+ align:start position:0%
+that provides a mechanism for language
+and knowledge acquisition so sort of
+
+ align:start position:0%
+and knowledge acquisition so sort of
+ 
+
+ align:start position:0%
+and knowledge acquisition so sort of
+guides infants to the kinds of relevant
+
+ align:start position:0%
+guides infants to the kinds of relevant
+ 
+
+ align:start position:0%
+guides infants to the kinds of relevant
+interactions where they might want to
+
+ align:start position:0%
+interactions where they might want to
+ 
+
+ align:start position:0%
+interactions where they might want to
+learn things about people and their
+
+ align:start position:0%
+learn things about people and their
+ 
+
+ align:start position:0%
+learn things about people and their
+mental states and the words that they're
+
+ align:start position:0%
+mental states and the words that they're
+ 
+
+ align:start position:0%
+mental states and the words that they're
+using rather than first learning those
+
+ align:start position:0%
+using rather than first learning those
+ 
+
+ align:start position:0%
+using rather than first learning those
+words through association and then later
+
+ align:start position:0%
+words through association and then later
+ 
+
+ align:start position:0%
+words through association and then later
+coming to this more abstract
+
+ align:start position:0%
+coming to this more abstract
+ 
+
+ align:start position:0%
+coming to this more abstract
+understanding so the idea of the
+
+ align:start position:0%
+understanding so the idea of the
+ 
+
+ align:start position:0%
+understanding so the idea of the
+infant's might start out with this
+
+ align:start position:0%
+infant's might start out with this
+ 
+
+ align:start position:0%
+infant's might start out with this
+understanding of what communication is
+
+ align:start position:0%
+understanding of what communication is
+ 
+
+ align:start position:0%
+understanding of what communication is
+and when it's happening and then can
+
+ align:start position:0%
+and when it's happening and then can
+ 
+
+ align:start position:0%
+and when it's happening and then can
+sort of fill in the rest from there and
+
+ align:start position:0%
+sort of fill in the rest from there and
+ 
+
+ align:start position:0%
+sort of fill in the rest from there and
+that this might be one of the earlier
+
+ align:start position:0%
+that this might be one of the earlier
+ 
+
+ align:start position:0%
+that this might be one of the earlier
+blocks of that so I'll try to go fairly
+
+ align:start position:0%
+blocks of that so I'll try to go fairly
+ 
+
+ align:start position:0%
+blocks of that so I'll try to go fairly
+quickly through the rest so the second
+
+ align:start position:0%
+quickly through the rest so the second
+ 
+
+ align:start position:0%
+quickly through the rest so the second
+insight I wanted to bring out that I
+
+ align:start position:0%
+insight I wanted to bring out that I
+ 
+
+ align:start position:0%
+insight I wanted to bring out that I
+think is especially important is that
+
+ align:start position:0%
+think is especially important is that
+ 
+
+ align:start position:0%
+think is especially important is that
+communication requires us focus on
+
+ align:start position:0%
+communication requires us focus on
+ 
+
+ align:start position:0%
+communication requires us focus on
+intentions and this was really the work
+
+ align:start position:0%
+intentions and this was really the work
+ 
+
+ align:start position:0%
+intentions and this was really the work
+of Grice that highlighted this and in
+
+ align:start position:0%
+of Grice that highlighted this and in
+ 
+
+ align:start position:0%
+of Grice that highlighted this and in
+particular a special type of
+
+ align:start position:0%
+particular a special type of
+ 
+
+ align:start position:0%
+particular a special type of
+communicative intention so going back to
+
+ align:start position:0%
+communicative intention so going back to
+ 
+
+ align:start position:0%
+communicative intention so going back to
+the example from the beginning when
+
+ align:start position:0%
+the example from the beginning when
+ 
+
+ align:start position:0%
+the example from the beginning when
+someone asks is there any salt austin
+
+ align:start position:0%
+someone asks is there any salt austin
+ 
+
+ align:start position:0%
+someone asks is there any salt austin
+proposed that there are these three
+
+ align:start position:0%
+proposed that there are these three
+ 
+
+ align:start position:0%
+proposed that there are these three
+levels on which we can think about this
+
+ align:start position:0%
+levels on which we can think about this
+ 
+
+ align:start position:0%
+levels on which we can think about this
+communicative action and grace was the
+
+ align:start position:0%
+communicative action and grace was the
+ 
+
+ align:start position:0%
+communicative action and grace was the
+one who really formalized this by
+
+ align:start position:0%
+one who really formalized this by
+ 
+
+ align:start position:0%
+one who really formalized this by
+talking about this special kind of
+
+ align:start position:0%
+talking about this special kind of
+ 
+
+ align:start position:0%
+talking about this special kind of
+intention that we see in the domain of
+
+ align:start position:0%
+intention that we see in the domain of
+ 
+
+ align:start position:0%
+intention that we see in the domain of
+communication human communication in
+
+ align:start position:0%
+communication human communication in
+ 
+
+ align:start position:0%
+communication human communication in
+particular which is the idea of speaker
+
+ align:start position:0%
+particular which is the idea of speaker
+ 
+
+ align:start position:0%
+particular which is the idea of speaker
+meaning and so his idea is that there
+
+ align:start position:0%
+meaning and so his idea is that there
+ 
+
+ align:start position:0%
+meaning and so his idea is that there
+are the there's this double layered
+
+ align:start position:0%
+are the there's this double layered
+ 
+
+ align:start position:0%
+are the there's this double layered
+intention that comes when we're
+
+ align:start position:0%
+intention that comes when we're
+ 
+
+ align:start position:0%
+intention that comes when we're
+communicating with each other so we have
+
+ align:start position:0%
+communicating with each other so we have
+ 
+
+ align:start position:0%
+communicating with each other so we have
+a communicator who intends the addressee
+
+ align:start position:0%
+a communicator who intends the addressee
+ 
+
+ align:start position:0%
+a communicator who intends the addressee
+to respond in a particular way so here
+
+ align:start position:0%
+to respond in a particular way so here
+ 
+
+ align:start position:0%
+to respond in a particular way so here
+the communicator wants the addressee to
+
+ align:start position:0%
+the communicator wants the addressee to
+ 
+
+ align:start position:0%
+the communicator wants the addressee to
+provide some salt the communicator
+
+ align:start position:0%
+provide some salt the communicator
+ 
+
+ align:start position:0%
+provide some salt the communicator
+intends for the addressee to recognize
+
+ align:start position:0%
+intends for the addressee to recognize
+ 
+
+ align:start position:0%
+intends for the addressee to recognize
+that the communicator intends to have
+
+ align:start position:0%
+that the communicator intends to have
+ 
+
+ align:start position:0%
+that the communicator intends to have
+that response so this person not only
+
+ align:start position:0%
+that response so this person not only
+ 
+
+ align:start position:0%
+that response so this person not only
+wants this person to pass the salt but
+
+ align:start position:0%
+wants this person to pass the salt but
+ 
+
+ align:start position:0%
+wants this person to pass the salt but
+wants her to pass the salt but wants her
+
+ align:start position:0%
+wants her to pass the salt but wants her
+ 
+
+ align:start position:0%
+wants her to pass the salt but wants her
+to recognize that
+
+ align:start position:0%
+to recognize that
+ 
+
+ align:start position:0%
+to recognize that
+what he's asking for that that is the
+
+ align:start position:0%
+what he's asking for that that is the
+ 
+
+ align:start position:0%
+what he's asking for that that is the
+request that he's making and importantly
+
+ align:start position:0%
+request that he's making and importantly
+ 
+
+ align:start position:0%
+request that he's making and importantly
+this third point which is that the
+
+ align:start position:0%
+this third point which is that the
+ 
+
+ align:start position:0%
+this third point which is that the
+communicator intends the addressee to
+
+ align:start position:0%
+communicator intends the addressee to
+ 
+
+ align:start position:0%
+communicator intends the addressee to
+fulfill the to respond that way on the
+
+ align:start position:0%
+fulfill the to respond that way on the
+ 
+
+ align:start position:0%
+fulfill the to respond that way on the
+basis of the recognition of that
+
+ align:start position:0%
+basis of the recognition of that
+ 
+
+ align:start position:0%
+basis of the recognition of that
+intention and so to make this a little
+
+ align:start position:0%
+intention and so to make this a little
+ 
+
+ align:start position:0%
+intention and so to make this a little
+more concrete in this case if he asks
+
+ align:start position:0%
+more concrete in this case if he asks
+ 
+
+ align:start position:0%
+more concrete in this case if he asks
+her for the salt and she passes it
+
+ align:start position:0%
+her for the salt and she passes it
+ 
+
+ align:start position:0%
+her for the salt and she passes it
+because she heard him and understands
+
+ align:start position:0%
+because she heard him and understands
+ 
+
+ align:start position:0%
+because she heard him and understands
+that that those he's asking for it
+
+ align:start position:0%
+that that those he's asking for it
+ 
+
+ align:start position:0%
+that that those he's asking for it
+that's great but the argument is that
+
+ align:start position:0%
+that's great but the argument is that
+ 
+
+ align:start position:0%
+that's great but the argument is that
+communication wouldn't really be
+
+ align:start position:0%
+communication wouldn't really be
+ 
+
+ align:start position:0%
+communication wouldn't really be
+happening if for example she was wearing
+
+ align:start position:0%
+happening if for example she was wearing
+ 
+
+ align:start position:0%
+happening if for example she was wearing
+headphones and listening to music and
+
+ align:start position:0%
+headphones and listening to music and
+ 
+
+ align:start position:0%
+headphones and listening to music and
+she hadn't really been listening to him
+
+ align:start position:0%
+she hadn't really been listening to him
+ 
+
+ align:start position:0%
+she hadn't really been listening to him
+and she just happened to pick up the
+
+ align:start position:0%
+and she just happened to pick up the
+ 
+
+ align:start position:0%
+and she just happened to pick up the
+salt and pass it to him so communication
+
+ align:start position:0%
+salt and pass it to him so communication
+ 
+
+ align:start position:0%
+salt and pass it to him so communication
+I mean it would looks like it would look
+
+ align:start position:0%
+I mean it would looks like it would look
+ 
+
+ align:start position:0%
+I mean it would looks like it would look
+like a communicative interaction the
+
+ align:start position:0%
+like a communicative interaction the
+ 
+
+ align:start position:0%
+like a communicative interaction the
+right kind of outcome is still happening
+
+ align:start position:0%
+right kind of outcome is still happening
+ 
+
+ align:start position:0%
+right kind of outcome is still happening
+in response to what he said but if she
+
+ align:start position:0%
+in response to what he said but if she
+ 
+
+ align:start position:0%
+in response to what he said but if she
+has no access to the actual message if
+
+ align:start position:0%
+has no access to the actual message if
+ 
+
+ align:start position:0%
+has no access to the actual message if
+she doesn't produce the response by
+
+ align:start position:0%
+she doesn't produce the response by
+ 
+
+ align:start position:0%
+she doesn't produce the response by
+virtue of understanding what the
+
+ align:start position:0%
+virtue of understanding what the
+ 
+
+ align:start position:0%
+virtue of understanding what the
+communicators trying to say then
+
+ align:start position:0%
+communicators trying to say then
+ 
+
+ align:start position:0%
+communicators trying to say then
+communication hasn't really occurred
+
+ align:start position:0%
+communication hasn't really occurred
+ 
+
+ align:start position:0%
+communication hasn't really occurred
+it's just sort of a lucky accident
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll skip this part so the question
+
+ align:start position:0%
+so I'll skip this part so the question
+ 
+
+ align:start position:0%
+so I'll skip this part so the question
+is so this is this important kind of
+
+ align:start position:0%
+is so this is this important kind of
+ 
+
+ align:start position:0%
+is so this is this important kind of
+intention that we see in human
+
+ align:start position:0%
+intention that we see in human
+ 
+
+ align:start position:0%
+intention that we see in human
+communication in which I later briefly
+
+ align:start position:0%
+communication in which I later briefly
+ 
+
+ align:start position:0%
+communication in which I later briefly
+mentioned we don't really see an animal
+
+ align:start position:0%
+mentioned we don't really see an animal
+ 
+
+ align:start position:0%
+mentioned we don't really see an animal
+communication in the same sort of way so
+
+ align:start position:0%
+communication in the same sort of way so
+ 
+
+ align:start position:0%
+communication in the same sort of way so
+how do infants start to get this idea
+
+ align:start position:0%
+how do infants start to get this idea
+ 
+
+ align:start position:0%
+how do infants start to get this idea
+about communication that it's not just
+
+ align:start position:0%
+about communication that it's not just
+ 
+
+ align:start position:0%
+about communication that it's not just
+about identifying communicative
+
+ align:start position:0%
+about identifying communicative
+ 
+
+ align:start position:0%
+about identifying communicative
+interactions but also about
+
+ align:start position:0%
+interactions but also about
+ 
+
+ align:start position:0%
+interactions but also about
+understanding these particular kinds of
+
+ align:start position:0%
+understanding these particular kinds of
+ 
+
+ align:start position:0%
+understanding these particular kinds of
+intentions so in the 90s there was this
+
+ align:start position:0%
+intentions so in the 90s there was this
+ 
+
+ align:start position:0%
+intentions so in the 90s there was this
+shift in developmental psychology to
+
+ align:start position:0%
+shift in developmental psychology to
+ 
+
+ align:start position:0%
+shift in developmental psychology to
+looking at word learning not only in
+
+ align:start position:0%
+looking at word learning not only in
+ 
+
+ align:start position:0%
+looking at word learning not only in
+terms of of infants associations of
+
+ align:start position:0%
+terms of of infants associations of
+ 
+
+ align:start position:0%
+terms of of infants associations of
+words in the environment but also with
+
+ align:start position:0%
+words in the environment but also with
+ 
+
+ align:start position:0%
+words in the environment but also with
+the work of Dara Baldwin to thinking
+
+ align:start position:0%
+the work of Dara Baldwin to thinking
+ 
+
+ align:start position:0%
+the work of Dara Baldwin to thinking
+about other people's intentions when
+
+ align:start position:0%
+about other people's intentions when
+ 
+
+ align:start position:0%
+about other people's intentions when
+they're using words and so she had these
+
+ align:start position:0%
+they're using words and so she had these
+ 
+
+ align:start position:0%
+they're using words and so she had these
+really elegant studies where with kind
+
+ align:start position:0%
+really elegant studies where with kind
+ 
+
+ align:start position:0%
+really elegant studies where with kind
+of this funny image where she pointed
+
+ align:start position:0%
+of this funny image where she pointed
+ 
+
+ align:start position:0%
+of this funny image where she pointed
+out that if infants really were learning
+
+ align:start position:0%
+out that if infants really were learning
+ 
+
+ align:start position:0%
+out that if infants really were learning
+words through association then they
+
+ align:start position:0%
+words through association then they
+ 
+
+ align:start position:0%
+words through association then they
+would it wouldn't be very efficient for
+
+ align:start position:0%
+would it wouldn't be very efficient for
+ 
+
+ align:start position:0%
+would it wouldn't be very efficient for
+them because they would make a lot of
+
+ align:start position:0%
+them because they would make a lot of
+ 
+
+ align:start position:0%
+them because they would make a lot of
+mistakes so for example in this kind of
+
+ align:start position:0%
+mistakes so for example in this kind of
+ 
+
+ align:start position:0%
+mistakes so for example in this kind of
+situation here's a dad and his baby the
+
+ align:start position:0%
+situation here's a dad and his baby the
+ 
+
+ align:start position:0%
+situation here's a dad and his baby the
+baby is looking at this lizard the dad
+
+ align:start position:0%
+baby is looking at this lizard the dad
+ 
+
+ align:start position:0%
+baby is looking at this lizard the dad
+is looking at this rooster and the dad
+
+ align:start position:0%
+is looking at this rooster and the dad
+ 
+
+ align:start position:0%
+is looking at this rooster and the dad
+says what a cheeky rooster so if you as
+
+ align:start position:0%
+says what a cheeky rooster so if you as
+ 
+
+ align:start position:0%
+says what a cheeky rooster so if you as
+the infant are only learning words on
+
+ align:start position:0%
+the infant are only learning words on
+ 
+
+ align:start position:0%
+the infant are only learning words on
+the basis of associating what you hear
+
+ align:start position:0%
+the basis of associating what you hear
+ 
+
+ align:start position:0%
+the basis of associating what you hear
+with what you see you're going to learn
+
+ align:start position:0%
+with what you see you're going to learn
+ 
+
+ align:start position:0%
+with what you see you're going to learn
+that the word
+
+ align:start position:0%
+that the word
+ 
+
+ align:start position:0%
+that the word
+rooster refers to this thing rather than
+
+ align:start position:0%
+rooster refers to this thing rather than
+ 
+
+ align:start position:0%
+rooster refers to this thing rather than
+to this thing and you're gonna get it
+
+ align:start position:0%
+to this thing and you're gonna get it
+ 
+
+ align:start position:0%
+to this thing and you're gonna get it
+wrong so Baldwin did these whole host of
+
+ align:start position:0%
+wrong so Baldwin did these whole host of
+ 
+
+ align:start position:0%
+wrong so Baldwin did these whole host of
+studies in the second year of life where
+
+ align:start position:0%
+studies in the second year of life where
+ 
+
+ align:start position:0%
+studies in the second year of life where
+she had infants she set up situations
+
+ align:start position:0%
+she had infants she set up situations
+ 
+
+ align:start position:0%
+she had infants she set up situations
+where infants were looking at particular
+
+ align:start position:0%
+where infants were looking at particular
+ 
+
+ align:start position:0%
+where infants were looking at particular
+objects like here and then she had their
+
+ align:start position:0%
+objects like here and then she had their
+ 
+
+ align:start position:0%
+objects like here and then she had their
+parents or an experimenter look at a
+
+ align:start position:0%
+parents or an experimenter look at a
+ 
+
+ align:start position:0%
+parents or an experimenter look at a
+different object and labeled that one to
+
+ align:start position:0%
+different object and labeled that one to
+ 
+
+ align:start position:0%
+different object and labeled that one to
+see what infants would do and what she
+
+ align:start position:0%
+see what infants would do and what she
+ 
+
+ align:start position:0%
+see what infants would do and what she
+found is that infants actually would
+
+ align:start position:0%
+found is that infants actually would
+ 
+
+ align:start position:0%
+found is that infants actually would
+consult their parent or consult the
+
+ align:start position:0%
+consult their parent or consult the
+ 
+
+ align:start position:0%
+consult their parent or consult the
+other person for cues to reference to
+
+ align:start position:0%
+other person for cues to reference to
+ 
+
+ align:start position:0%
+other person for cues to reference to
+what they're intending to label so if
+
+ align:start position:0%
+what they're intending to label so if
+ 
+
+ align:start position:0%
+what they're intending to label so if
+for example in this situation the infant
+
+ align:start position:0%
+for example in this situation the infant
+ 
+
+ align:start position:0%
+for example in this situation the infant
+went hearing this instead of just
+
+ align:start position:0%
+went hearing this instead of just
+ 
+
+ align:start position:0%
+went hearing this instead of just
+assuming the word refers to what they're
+
+ align:start position:0%
+assuming the word refers to what they're
+ 
+
+ align:start position:0%
+assuming the word refers to what they're
+looking at would actually look up to dad
+
+ align:start position:0%
+looking at would actually look up to dad
+ 
+
+ align:start position:0%
+looking at would actually look up to dad
+to see what he's looking at and then
+
+ align:start position:0%
+to see what he's looking at and then
+ 
+
+ align:start position:0%
+to see what he's looking at and then
+follow his line of gaze to understand
+
+ align:start position:0%
+follow his line of gaze to understand
+ 
+
+ align:start position:0%
+follow his line of gaze to understand
+that this is the object that he's
+
+ align:start position:0%
+that this is the object that he's
+ 
+
+ align:start position:0%
+that this is the object that he's
+actually talking about so hmm yeah at
+
+ align:start position:0%
+actually talking about so hmm yeah at
+ 
+
+ align:start position:0%
+actually talking about so hmm yeah at
+this age yep so the idea is that infants
+
+ align:start position:0%
+this age yep so the idea is that infants
+ 
+
+ align:start position:0%
+this age yep so the idea is that infants
+in the second year of life at least our
+
+ align:start position:0%
+in the second year of life at least our
+ 
+
+ align:start position:0%
+in the second year of life at least our
+understanding that referent that
+
+ align:start position:0%
+understanding that referent that
+ 
+
+ align:start position:0%
+understanding that referent that
+understanding what someone's referring
+
+ align:start position:0%
+understanding what someone's referring
+ 
+
+ align:start position:0%
+understanding what someone's referring
+to involves consulting cues to their
+
+ align:start position:0%
+to involves consulting cues to their
+ 
+
+ align:start position:0%
+to involves consulting cues to their
+attention and intentions rather than
+
+ align:start position:0%
+attention and intentions rather than
+ 
+
+ align:start position:0%
+attention and intentions rather than
+just there at the infant zone and I
+
+ align:start position:0%
+just there at the infant zone and I
+ 
+
+ align:start position:0%
+just there at the infant zone and I
+think I'll skip this one there's just
+
+ align:start position:0%
+think I'll skip this one there's just
+ 
+
+ align:start position:0%
+think I'll skip this one there's just
+there other studies showing this to
+
+ align:start position:0%
+there other studies showing this to
+ 
+
+ align:start position:0%
+there other studies showing this to
+where so in this one there's an
+
+ align:start position:0%
+where so in this one there's an
+ 
+
+ align:start position:0%
+where so in this one there's an
+experimenter who puts these two objects
+
+ align:start position:0%
+experimenter who puts these two objects
+ 
+
+ align:start position:0%
+experimenter who puts these two objects
+in a box the objects which while she's
+
+ align:start position:0%
+in a box the objects which while she's
+ 
+
+ align:start position:0%
+in a box the objects which while she's
+absent and then she looks in one box and
+
+ align:start position:0%
+absent and then she looks in one box and
+ 
+
+ align:start position:0%
+absent and then she looks in one box and
+says she the boxes are closed and she
+
+ align:start position:0%
+says she the boxes are closed and she
+ 
+
+ align:start position:0%
+says she the boxes are closed and she
+says there's a CFO in here so if the
+
+ align:start position:0%
+says there's a CFO in here so if the
+ 
+
+ align:start position:0%
+says there's a CFO in here so if the
+infant understands that they have to pay
+
+ align:start position:0%
+infant understands that they have to pay
+ 
+
+ align:start position:0%
+infant understands that they have to pay
+attention to what the person knows about
+
+ align:start position:0%
+attention to what the person knows about
+ 
+
+ align:start position:0%
+attention to what the person knows about
+or the what the person thinks rather
+
+ align:start position:0%
+or the what the person thinks rather
+ 
+
+ align:start position:0%
+or the what the person thinks rather
+than their own knowledge to figure out
+
+ align:start position:0%
+than their own knowledge to figure out
+ 
+
+ align:start position:0%
+than their own knowledge to figure out
+what she's labeling but now when she
+
+ align:start position:0%
+what she's labeling but now when she
+ 
+
+ align:start position:0%
+what she's labeling but now when she
+says can you get the CFO the infant
+
+ align:start position:0%
+says can you get the CFO the infant
+ 
+
+ align:start position:0%
+says can you get the CFO the infant
+should actually pull the object out of
+
+ align:start position:0%
+should actually pull the object out of
+ 
+
+ align:start position:0%
+should actually pull the object out of
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+assuming that this is the one she's
+
+ align:start position:0%
+assuming that this is the one she's
+ 
+
+ align:start position:0%
+assuming that this is the one she's
+labeling because that's the one that she
+
+ align:start position:0%
+labeling because that's the one that she
+ 
+
+ align:start position:0%
+labeling because that's the one that she
+was attempting to intending label and in
+
+ align:start position:0%
+was attempting to intending label and in
+ 
+
+ align:start position:0%
+was attempting to intending label and in
+fact that's what infants do at 17 months
+
+ align:start position:0%
+fact that's what infants do at 17 months
+ 
+
+ align:start position:0%
+fact that's what infants do at 17 months
+in the case where the experiment had a
+
+ align:start position:0%
+in the case where the experiment had a
+ 
+
+ align:start position:0%
+in the case where the experiment had a
+false belief or about the location of
+
+ align:start position:0%
+false belief or about the location of
+ 
+
+ align:start position:0%
+false belief or about the location of
+the object infants tend to go to the non
+
+ align:start position:0%
+the object infants tend to go to the non
+ 
+
+ align:start position:0%
+the object infants tend to go to the non
+referred box more often because they
+
+ align:start position:0%
+referred box more often because they
+ 
+
+ align:start position:0%
+referred box more often because they
+think that that's the one that she's
+
+ align:start position:0%
+think that that's the one that she's
+ 
+
+ align:start position:0%
+think that that's the one that she's
+labeling but in the case where she saw
+
+ align:start position:0%
+labeling but in the case where she saw
+ 
+
+ align:start position:0%
+labeling but in the case where she saw
+this which happened so now she knows
+
+ align:start position:0%
+this which happened so now she knows
+ 
+
+ align:start position:0%
+this which happened so now she knows
+what every where infants will just go to
+
+ align:start position:0%
+what every where infants will just go to
+ 
+
+ align:start position:0%
+what every where infants will just go to
+the box that she's referring to to
+
+ align:start position:0%
+the box that she's referring to to
+ 
+
+ align:start position:0%
+the box that she's referring to to
+figure out the location of the object
+
+ align:start position:0%
+figure out the location of the object
+ 
+
+ align:start position:0%
+figure out the location of the object
+that she's naming
+
+ align:start position:0%
+that she's naming
+ 
+
+ align:start position:0%
+that she's naming
+so this is all in the second year of
+
+ align:start position:0%
+so this is all in the second year of
+ 
+
+ align:start position:0%
+so this is all in the second year of
+life not those younger sort of core
+
+ align:start position:0%
+life not those younger sort of core
+ 
+
+ align:start position:0%
+life not those younger sort of core
+knowledge ages that Liz was talking
+
+ align:start position:0%
+knowledge ages that Liz was talking
+ 
+
+ align:start position:0%
+knowledge ages that Liz was talking
+about but these so these are this is
+
+ align:start position:0%
+about but these so these are this is
+ 
+
+ align:start position:0%
+about but these so these are this is
+evidence that infants consult speaker
+
+ align:start position:0%
+evidence that infants consult speaker
+ 
+
+ align:start position:0%
+evidence that infants consult speaker
+cues to intentions but not of this
+
+ align:start position:0%
+cues to intentions but not of this
+ 
+
+ align:start position:0%
+cues to intentions but not of this
+special kind of intention that grace was
+
+ align:start position:0%
+special kind of intention that grace was
+ 
+
+ align:start position:0%
+special kind of intention that grace was
+pointing out so I'm just going to tell
+
+ align:start position:0%
+pointing out so I'm just going to tell
+ 
+
+ align:start position:0%
+pointing out so I'm just going to tell
+you about a couple of well one of my
+
+ align:start position:0%
+you about a couple of well one of my
+ 
+
+ align:start position:0%
+you about a couple of well one of my
+favorite studies I just think this is
+
+ align:start position:0%
+favorite studies I just think this is
+ 
+
+ align:start position:0%
+favorite studies I just think this is
+really neat where Ellen Martin's lab and
+
+ align:start position:0%
+really neat where Ellen Martin's lab and
+ 
+
+ align:start position:0%
+really neat where Ellen Martin's lab and
+then later replicated by Thomas Ellis
+
+ align:start position:0%
+then later replicated by Thomas Ellis
+ 
+
+ align:start position:0%
+then later replicated by Thomas Ellis
+lab showed that it seems like children
+
+ align:start position:0%
+lab showed that it seems like children
+ 
+
+ align:start position:0%
+lab showed that it seems like children
+by 30 months and then gotten down to 18
+
+ align:start position:0%
+by 30 months and then gotten down to 18
+ 
+
+ align:start position:0%
+by 30 months and then gotten down to 18
+months by gross at all actually do seem
+
+ align:start position:0%
+months by gross at all actually do seem
+ 
+
+ align:start position:0%
+months by gross at all actually do seem
+to care about not only the effects of
+
+ align:start position:0%
+to care about not only the effects of
+ 
+
+ align:start position:0%
+to care about not only the effects of
+action the effects of communication but
+
+ align:start position:0%
+action the effects of communication but
+ 
+
+ align:start position:0%
+action the effects of communication but
+also that the the effects are produced
+
+ align:start position:0%
+also that the the effects are produced
+ 
+
+ align:start position:0%
+also that the the effects are produced
+by virtue of the message being
+
+ align:start position:0%
+by virtue of the message being
+ 
+
+ align:start position:0%
+by virtue of the message being
+understood so you're probably wondering
+
+ align:start position:0%
+understood so you're probably wondering
+ 
+
+ align:start position:0%
+understood so you're probably wondering
+why there's a dirty sock on the screen
+
+ align:start position:0%
+why there's a dirty sock on the screen
+ 
+
+ align:start position:0%
+why there's a dirty sock on the screen
+so in this study infants where children
+
+ align:start position:0%
+so in this study infants where children
+ 
+
+ align:start position:0%
+so in this study infants where children
+were presented with these with two
+
+ align:start position:0%
+were presented with these with two
+ 
+
+ align:start position:0%
+were presented with these with two
+objects so they saw on a table there
+
+ align:start position:0%
+objects so they saw on a table there
+ 
+
+ align:start position:0%
+objects so they saw on a table there
+were two objects that were out of their
+
+ align:start position:0%
+were two objects that were out of their
+ 
+
+ align:start position:0%
+were two objects that were out of their
+reach a truck and a and a dirty sock and
+
+ align:start position:0%
+reach a truck and a and a dirty sock and
+ 
+
+ align:start position:0%
+reach a truck and a and a dirty sock and
+the idea was to elicit children to
+
+ align:start position:0%
+the idea was to elicit children to
+ 
+
+ align:start position:0%
+the idea was to elicit children to
+request an object now obviously the
+
+ align:start position:0%
+request an object now obviously the
+ 
+
+ align:start position:0%
+request an object now obviously the
+children are going to request this
+
+ align:start position:0%
+children are going to request this
+ 
+
+ align:start position:0%
+children are going to request this
+object which is what the researchers had
+
+ align:start position:0%
+object which is what the researchers had
+ 
+
+ align:start position:0%
+object which is what the researchers had
+intended in this case
+
+ align:start position:0%
+intended in this case
+ 
+
+ align:start position:0%
+intended in this case
+so children tended to point at this
+
+ align:start position:0%
+so children tended to point at this
+ 
+
+ align:start position:0%
+so children tended to point at this
+object so they had children producing
+
+ align:start position:0%
+object so they had children producing
+ 
+
+ align:start position:0%
+object so they had children producing
+their own communication and then the
+
+ align:start position:0%
+their own communication and then the
+ 
+
+ align:start position:0%
+their own communication and then the
+experimenter responded to the
+
+ align:start position:0%
+experimenter responded to the
+ 
+
+ align:start position:0%
+experimenter responded to the
+communication of the infant in one of
+
+ align:start position:0%
+communication of the infant in one of
+ 
+
+ align:start position:0%
+communication of the infant in one of
+four different ways so she either said
+
+ align:start position:0%
+four different ways so she either said
+ 
+
+ align:start position:0%
+four different ways so she either said
+you asked for the truck I'm gonna give
+
+ align:start position:0%
+you asked for the truck I'm gonna give
+ 
+
+ align:start position:0%
+you asked for the truck I'm gonna give
+you the truck so she expressed
+
+ align:start position:0%
+you the truck so she expressed
+ 
+
+ align:start position:0%
+you the truck so she expressed
+understanding of the request and she
+
+ align:start position:0%
+understanding of the request and she
+ 
+
+ align:start position:0%
+understanding of the request and she
+provided the requested object in a
+
+ align:start position:0%
+provided the requested object in a
+ 
+
+ align:start position:0%
+provided the requested object in a
+second case she said you asked for the
+
+ align:start position:0%
+second case she said you asked for the
+ 
+
+ align:start position:0%
+second case she said you asked for the
+truck I'm gonna give you the sock so he
+
+ align:start position:0%
+truck I'm gonna give you the sock so he
+ 
+
+ align:start position:0%
+truck I'm gonna give you the sock so he
+or she expressed understanding but
+
+ align:start position:0%
+or she expressed understanding but
+ 
+
+ align:start position:0%
+or she expressed understanding but
+refused to commit to the request to give
+
+ align:start position:0%
+refused to commit to the request to give
+ 
+
+ align:start position:0%
+refused to commit to the request to give
+alert the same the thing the child had
+
+ align:start position:0%
+alert the same the thing the child had
+ 
+
+ align:start position:0%
+alert the same the thing the child had
+asked for in a third case the
+
+ align:start position:0%
+asked for in a third case the
+ 
+
+ align:start position:0%
+asked for in a third case the
+experimenter said you asked for the sock
+
+ align:start position:0%
+experimenter said you asked for the sock
+ 
+
+ align:start position:0%
+experimenter said you asked for the sock
+I'm going to give you the truck so this
+
+ align:start position:0%
+I'm going to give you the truck so this
+ 
+
+ align:start position:0%
+I'm going to give you the truck so this
+isn't it this is kind of a strange
+
+ align:start position:0%
+isn't it this is kind of a strange
+ 
+
+ align:start position:0%
+isn't it this is kind of a strange
+pragmatic situation where the
+
+ align:start position:0%
+pragmatic situation where the
+ 
+
+ align:start position:0%
+pragmatic situation where the
+experimenter actually gave the child the
+
+ align:start position:0%
+experimenter actually gave the child the
+ 
+
+ align:start position:0%
+experimenter actually gave the child the
+object they wanted but she expressed a
+
+ align:start position:0%
+object they wanted but she expressed a
+ 
+
+ align:start position:0%
+object they wanted but she expressed a
+misunderstanding of the child's request
+
+ align:start position:0%
+misunderstanding of the child's request
+ 
+
+ align:start position:0%
+misunderstanding of the child's request
+and this is the crucial case here so the
+
+ align:start position:0%
+and this is the crucial case here so the
+ 
+
+ align:start position:0%
+and this is the crucial case here so the
+question is obviously in the case where
+
+ align:start position:0%
+question is obviously in the case where
+ 
+
+ align:start position:0%
+question is obviously in the case where
+the experimenter provides the thing and
+
+ align:start position:0%
+the experimenter provides the thing and
+ 
+
+ align:start position:0%
+the experimenter provides the thing and
+expressed as understanding infants
+
+ align:start position:0%
+expressed as understanding infants
+ 
+
+ align:start position:0%
+expressed as understanding infants
+children should be quite happy and in
+
+ align:start position:0%
+children should be quite happy and in
+ 
+
+ align:start position:0%
+children should be quite happy and in
+this situation they probably shouldn't
+
+ align:start position:0%
+this situation they probably shouldn't
+ 
+
+ align:start position:0%
+this situation they probably shouldn't
+be very happy and what the experimenters
+
+ align:start position:0%
+be very happy and what the experimenters
+ 
+
+ align:start position:0%
+be very happy and what the experimenters
+measured was the amount of times that
+
+ align:start position:0%
+measured was the amount of times that
+ 
+
+ align:start position:0%
+measured was the amount of times that
+the child repeated the label of the
+
+ align:start position:0%
+the child repeated the label of the
+ 
+
+ align:start position:0%
+the child repeated the label of the
+object that they had asked for and they
+
+ align:start position:0%
+object that they had asked for and they
+ 
+
+ align:start position:0%
+object that they had asked for and they
+also measured other
+
+ align:start position:0%
+also measured other
+ 
+
+ align:start position:0%
+also measured other
+behaviors as well it's this situation
+
+ align:start position:0%
+behaviors as well it's this situation
+ 
+
+ align:start position:0%
+behaviors as well it's this situation
+that's important for understanding
+
+ align:start position:0%
+that's important for understanding
+ 
+
+ align:start position:0%
+that's important for understanding
+whether what what kids care about in the
+
+ align:start position:0%
+whether what what kids care about in the
+ 
+
+ align:start position:0%
+whether what what kids care about in the
+context of this communicative
+
+ align:start position:0%
+context of this communicative
+ 
+
+ align:start position:0%
+context of this communicative
+interaction so the question is do our
+
+ align:start position:0%
+interaction so the question is do our
+ 
+
+ align:start position:0%
+interaction so the question is do our
+infants perfectly happy here to take the
+
+ align:start position:0%
+infants perfectly happy here to take the
+ 
+
+ align:start position:0%
+infants perfectly happy here to take the
+truck and not complain because they got
+
+ align:start position:0%
+truck and not complain because they got
+ 
+
+ align:start position:0%
+truck and not complain because they got
+what they wanted or do they care about
+
+ align:start position:0%
+what they wanted or do they care about
+ 
+
+ align:start position:0%
+what they wanted or do they care about
+the experiment or giving them what they
+
+ align:start position:0%
+the experiment or giving them what they
+ 
+
+ align:start position:0%
+the experiment or giving them what they
+wanted because they're communicated
+
+ align:start position:0%
+wanted because they're communicated
+ 
+
+ align:start position:0%
+wanted because they're communicated
+message had the proper effect on the
+
+ align:start position:0%
+message had the proper effect on the
+ 
+
+ align:start position:0%
+message had the proper effect on the
+communicator on the on addressing and
+
+ align:start position:0%
+communicator on the on addressing and
+ 
+
+ align:start position:0%
+communicator on the on addressing and
+what they find is that when the correct
+
+ align:start position:0%
+what they find is that when the correct
+ 
+
+ align:start position:0%
+what they find is that when the correct
+object is provided and the experimenter
+
+ align:start position:0%
+object is provided and the experimenter
+ 
+
+ align:start position:0%
+object is provided and the experimenter
+does not express understanding of the
+
+ align:start position:0%
+does not express understanding of the
+ 
+
+ align:start position:0%
+does not express understanding of the
+request infants actually showed the most
+
+ align:start position:0%
+request infants actually showed the most
+ 
+
+ align:start position:0%
+request infants actually showed the most
+repetitions of the name of the requested
+
+ align:start position:0%
+repetitions of the name of the requested
+ 
+
+ align:start position:0%
+repetitions of the name of the requested
+object in this case and so it seems like
+
+ align:start position:0%
+object in this case and so it seems like
+ 
+
+ align:start position:0%
+object in this case and so it seems like
+they the researchers concluded from this
+
+ align:start position:0%
+they the researchers concluded from this
+ 
+
+ align:start position:0%
+they the researchers concluded from this
+the infants don't just care about
+
+ align:start position:0%
+the infants don't just care about
+ 
+
+ align:start position:0%
+the infants don't just care about
+getting what they want or using
+
+ align:start position:0%
+getting what they want or using
+ 
+
+ align:start position:0%
+getting what they want or using
+communication as a means of as a sort of
+
+ align:start position:0%
+communication as a means of as a sort of
+ 
+
+ align:start position:0%
+communication as a means of as a sort of
+instrumental means of getting people to
+
+ align:start position:0%
+instrumental means of getting people to
+ 
+
+ align:start position:0%
+instrumental means of getting people to
+act in certain ways but rather as an
+
+ align:start position:0%
+act in certain ways but rather as an
+ 
+
+ align:start position:0%
+act in certain ways but rather as an
+intention to have their messages
+
+ align:start position:0%
+intention to have their messages
+ 
+
+ align:start position:0%
+intention to have their messages
+understood and delivered to the other
+
+ align:start position:0%
+understood and delivered to the other
+ 
+
+ align:start position:0%
+understood and delivered to the other
+person so they care about the impact of
+
+ align:start position:0%
+person so they care about the impact of
+ 
+
+ align:start position:0%
+person so they care about the impact of
+their communicative signals on the
+
+ align:start position:0%
+their communicative signals on the
+ 
+
+ align:start position:0%
+their communicative signals on the
+understanding of the addressee not just
+
+ align:start position:0%
+understanding of the addressee not just
+ 
+
+ align:start position:0%
+understanding of the addressee not just
+on the response of the addressee which
+
+ align:start position:0%
+on the response of the addressee which
+ 
+
+ align:start position:0%
+on the response of the addressee which
+is sort of like the idea that grace was
+
+ align:start position:0%
+is sort of like the idea that grace was
+ 
+
+ align:start position:0%
+is sort of like the idea that grace was
+talking about with speaker meaning
+
+ align:start position:0%
+talking about with speaker meaning
+ 
+
+ align:start position:0%
+talking about with speaker meaning
+similarly when children are responding
+
+ align:start position:0%
+similarly when children are responding
+ 
+
+ align:start position:0%
+similarly when children are responding
+to other people's requests they also
+
+ align:start position:0%
+to other people's requests they also
+ 
+
+ align:start position:0%
+to other people's requests they also
+care about this so this is a study that
+
+ align:start position:0%
+care about this so this is a study that
+ 
+
+ align:start position:0%
+care about this so this is a study that
+I did in graduate school we had it's
+
+ align:start position:0%
+I did in graduate school we had it's
+ 
+
+ align:start position:0%
+I did in graduate school we had it's
+kind of sort of the opposite of the
+
+ align:start position:0%
+kind of sort of the opposite of the
+ 
+
+ align:start position:0%
+kind of sort of the opposite of the
+previous study or the inverse so we had
+
+ align:start position:0%
+previous study or the inverse so we had
+ 
+
+ align:start position:0%
+previous study or the inverse so we had
+an experiment or asking requesting the
+
+ align:start position:0%
+an experiment or asking requesting the
+ 
+
+ align:start position:0%
+an experiment or asking requesting the
+chat from the child specific object for
+
+ align:start position:0%
+chat from the child specific object for
+ 
+
+ align:start position:0%
+chat from the child specific object for
+doing specific tasks so she would ask
+
+ align:start position:0%
+doing specific tasks so she would ask
+ 
+
+ align:start position:0%
+doing specific tasks so she would ask
+for some this was three-year-olds so she
+
+ align:start position:0%
+for some this was three-year-olds so she
+ 
+
+ align:start position:0%
+for some this was three-year-olds so she
+would request something like a cup to
+
+ align:start position:0%
+would request something like a cup to
+ 
+
+ align:start position:0%
+would request something like a cup to
+pour a cup of water the child had
+
+ align:start position:0%
+pour a cup of water the child had
+ 
+
+ align:start position:0%
+pour a cup of water the child had
+previous information from playing games
+
+ align:start position:0%
+previous information from playing games
+ 
+
+ align:start position:0%
+previous information from playing games
+with the object with another experiment
+
+ align:start position:0%
+with the object with another experiment
+ 
+
+ align:start position:0%
+with the object with another experiment
+or that one of the cups was perfectly
+
+ align:start position:0%
+or that one of the cups was perfectly
+ 
+
+ align:start position:0%
+or that one of the cups was perfectly
+fine and one of the cups was broken and
+
+ align:start position:0%
+fine and one of the cups was broken and
+ 
+
+ align:start position:0%
+fine and one of the cups was broken and
+had a big hole in the bottom and so when
+
+ align:start position:0%
+had a big hole in the bottom and so when
+ 
+
+ align:start position:0%
+had a big hole in the bottom and so when
+the experimenter asked for a cup the
+
+ align:start position:0%
+the experimenter asked for a cup the
+ 
+
+ align:start position:0%
+the experimenter asked for a cup the
+child could either give the cup the
+
+ align:start position:0%
+child could either give the cup the
+ 
+
+ align:start position:0%
+child could either give the cup the
+experimenter asked for which was
+
+ align:start position:0%
+experimenter asked for which was
+ 
+
+ align:start position:0%
+experimenter asked for which was
+sometimes the perfectly good cup or they
+
+ align:start position:0%
+sometimes the perfectly good cup or they
+ 
+
+ align:start position:0%
+sometimes the perfectly good cup or they
+could give the or sometimes the
+
+ align:start position:0%
+could give the or sometimes the
+ 
+
+ align:start position:0%
+could give the or sometimes the
+experiment or requested the broken cup
+
+ align:start position:0%
+experiment or requested the broken cup
+ 
+
+ align:start position:0%
+experiment or requested the broken cup
+and the question was do children pay
+
+ align:start position:0%
+and the question was do children pay
+ 
+
+ align:start position:0%
+and the question was do children pay
+attention to the fit between the task
+
+ align:start position:0%
+attention to the fit between the task
+ 
+
+ align:start position:0%
+attention to the fit between the task
+and what the experimenter wanted when
+
+ align:start position:0%
+and what the experimenter wanted when
+ 
+
+ align:start position:0%
+and what the experimenter wanted when
+they're responding to her request and
+
+ align:start position:0%
+they're responding to her request and
+ 
+
+ align:start position:0%
+they're responding to her request and
+what we found is the infants is that
+
+ align:start position:0%
+what we found is the infants is that
+ 
+
+ align:start position:0%
+what we found is the infants is that
+children were much more likely to give
+
+ align:start position:0%
+children were much more likely to give
+ 
+
+ align:start position:0%
+children were much more likely to give
+the requested object when the experiment
+
+ align:start position:0%
+the requested object when the experiment
+ 
+
+ align:start position:0%
+the requested object when the experiment
+requested a functional object then when
+
+ align:start position:0%
+requested a functional object then when
+ 
+
+ align:start position:0%
+requested a functional object then when
+she'd requested a dysfunctional object
+
+ align:start position:0%
+she'd requested a dysfunctional object
+ 
+
+ align:start position:0%
+she'd requested a dysfunctional object
+so if I say I need to pour a cup of
+
+ align:start position:0%
+so if I say I need to pour a cup of
+ 
+
+ align:start position:0%
+so if I say I need to pour a cup of
+water can you give me that cup and the
+
+ align:start position:0%
+water can you give me that cup and the
+ 
+
+ align:start position:0%
+water can you give me that cup and the
+cup is broken
+
+ align:start position:0%
+cup is broken
+ 
+
+ align:start position:0%
+cup is broken
+children tended to go and get a better
+
+ align:start position:0%
+children tended to go and get a better
+ 
+
+ align:start position:0%
+children tended to go and get a better
+cup instead instead of the one that I
+
+ align:start position:0%
+cup instead instead of the one that I
+ 
+
+ align:start position:0%
+cup instead instead of the one that I
+had requested interestingly though even
+
+ align:start position:0%
+had requested interestingly though even
+ 
+
+ align:start position:0%
+had requested interestingly though even
+though children did this it didn't seem
+
+ align:start position:0%
+though children did this it didn't seem
+ 
+
+ align:start position:0%
+though children did this it didn't seem
+to be enough for them to give the
+
+ align:start position:0%
+to be enough for them to give the
+ 
+
+ align:start position:0%
+to be enough for them to give the
+experiment or something good that she
+
+ align:start position:0%
+experiment or something good that she
+ 
+
+ align:start position:0%
+experiment or something good that she
+wanted this is a graph of the comments
+
+ align:start position:0%
+wanted this is a graph of the comments
+ 
+
+ align:start position:0%
+wanted this is a graph of the comments
+that children made about the function of
+
+ align:start position:0%
+that children made about the function of
+ 
+
+ align:start position:0%
+that children made about the function of
+the object depending on the kind of
+
+ align:start position:0%
+the object depending on the kind of
+ 
+
+ align:start position:0%
+the object depending on the kind of
+request that was made and what you can
+
+ align:start position:0%
+request that was made and what you can
+ 
+
+ align:start position:0%
+request that was made and what you can
+see is that when a dysfunctional object
+
+ align:start position:0%
+see is that when a dysfunctional object
+ 
+
+ align:start position:0%
+see is that when a dysfunctional object
+was requested when children tended to
+
+ align:start position:0%
+was requested when children tended to
+ 
+
+ align:start position:0%
+was requested when children tended to
+provide the functional object instead
+
+ align:start position:0%
+provide the functional object instead
+ 
+
+ align:start position:0%
+provide the functional object instead
+and not respond to the requests they
+
+ align:start position:0%
+and not respond to the requests they
+ 
+
+ align:start position:0%
+and not respond to the requests they
+were much more likely to try to explain
+
+ align:start position:0%
+were much more likely to try to explain
+ 
+
+ align:start position:0%
+were much more likely to try to explain
+their behavior to the experimenter and
+
+ align:start position:0%
+their behavior to the experimenter and
+ 
+
+ align:start position:0%
+their behavior to the experimenter and
+acknowledge what it was the experimenter
+
+ align:start position:0%
+acknowledge what it was the experimenter
+ 
+
+ align:start position:0%
+acknowledge what it was the experimenter
+had originally wanted so it seems like
+
+ align:start position:0%
+had originally wanted so it seems like
+ 
+
+ align:start position:0%
+had originally wanted so it seems like
+children in their own behavior by at
+
+ align:start position:0%
+children in their own behavior by at
+ 
+
+ align:start position:0%
+children in their own behavior by at
+least three which is a little older than
+
+ align:start position:0%
+least three which is a little older than
+ 
+
+ align:start position:0%
+least three which is a little older than
+the other studies acknowledge what the
+
+ align:start position:0%
+the other studies acknowledge what the
+ 
+
+ align:start position:0%
+the other studies acknowledge what the
+speaker meant to ask for and explain
+
+ align:start position:0%
+speaker meant to ask for and explain
+ 
+
+ align:start position:0%
+speaker meant to ask for and explain
+while they're doing something else
+
+ align:start position:0%
+while they're doing something else
+ 
+
+ align:start position:0%
+while they're doing something else
+even when they're not responding to that
+
+ align:start position:0%
+even when they're not responding to that
+ 
+
+ align:start position:0%
+even when they're not responding to that
+thing and so just briefly in the last
+
+ align:start position:0%
+thing and so just briefly in the last
+ 
+
+ align:start position:0%
+thing and so just briefly in the last
+section on I'll talk about a third
+
+ align:start position:0%
+section on I'll talk about a third
+ 
+
+ align:start position:0%
+section on I'll talk about a third
+insight about communication that I think
+
+ align:start position:0%
+insight about communication that I think
+ 
+
+ align:start position:0%
+insight about communication that I think
+is really important which comes from
+
+ align:start position:0%
+is really important which comes from
+ 
+
+ align:start position:0%
+is really important which comes from
+Clarke which is that communication is
+
+ align:start position:0%
+Clarke which is that communication is
+ 
+
+ align:start position:0%
+Clarke which is that communication is
+this joint action of accumulating common
+
+ align:start position:0%
+this joint action of accumulating common
+ 
+
+ align:start position:0%
+this joint action of accumulating common
+ground and so in an example of an adult
+
+ align:start position:0%
+ground and so in an example of an adult
+ 
+
+ align:start position:0%
+ground and so in an example of an adult
+study about this
+
+ align:start position:0%
+study about this
+ 
+
+ align:start position:0%
+study about this
+they showed adults pictures like this
+
+ align:start position:0%
+they showed adults pictures like this
+ 
+
+ align:start position:0%
+they showed adults pictures like this
+one of New York City and they had people
+
+ align:start position:0%
+one of New York City and they had people
+ 
+
+ align:start position:0%
+one of New York City and they had people
+play this game in pairs they had people
+
+ align:start position:0%
+play this game in pairs they had people
+ 
+
+ align:start position:0%
+play this game in pairs they had people
+who knew about New York City who were
+
+ align:start position:0%
+who knew about New York City who were
+ 
+
+ align:start position:0%
+who knew about New York City who were
+experts and who lived there and then
+
+ align:start position:0%
+experts and who lived there and then
+ 
+
+ align:start position:0%
+experts and who lived there and then
+they had other people who didn't know
+
+ align:start position:0%
+they had other people who didn't know
+ 
+
+ align:start position:0%
+they had other people who didn't know
+anything about New York City and they
+
+ align:start position:0%
+anything about New York City and they
+ 
+
+ align:start position:0%
+anything about New York City and they
+gave them a bunch of pictures and they
+
+ align:start position:0%
+gave them a bunch of pictures and they
+ 
+
+ align:start position:0%
+gave them a bunch of pictures and they
+wanted to see they told them that their
+
+ align:start position:0%
+wanted to see they told them that their
+ 
+
+ align:start position:0%
+wanted to see they told them that their
+goal was to had that what the person who
+
+ align:start position:0%
+goal was to had that what the person who
+ 
+
+ align:start position:0%
+goal was to had that what the person who
+was the address he had to sort the
+
+ align:start position:0%
+was the address he had to sort the
+ 
+
+ align:start position:0%
+was the address he had to sort the
+objects in the way that the communicator
+
+ align:start position:0%
+objects in the way that the communicator
+ 
+
+ align:start position:0%
+objects in the way that the communicator
+told them to and so as a communicator
+
+ align:start position:0%
+told them to and so as a communicator
+ 
+
+ align:start position:0%
+told them to and so as a communicator
+the communicator had to indicate because
+
+ align:start position:0%
+the communicator had to indicate because
+ 
+
+ align:start position:0%
+the communicator had to indicate because
+they couldn't see the pictures which
+
+ align:start position:0%
+they couldn't see the pictures which
+ 
+
+ align:start position:0%
+they couldn't see the pictures which
+picture the address he should put where
+
+ align:start position:0%
+picture the address he should put where
+ 
+
+ align:start position:0%
+picture the address he should put where
+and to do this she had to refer that a
+
+ align:start position:0%
+and to do this she had to refer that a
+ 
+
+ align:start position:0%
+and to do this she had to refer that a
+communicator had to refer to things like
+
+ align:start position:0%
+communicator had to refer to things like
+ 
+
+ align:start position:0%
+communicator had to refer to things like
+the picture with the Empire State
+
+ align:start position:0%
+the picture with the Empire State
+ 
+
+ align:start position:0%
+the picture with the Empire State
+Building in it and what they looked at
+
+ align:start position:0%
+Building in it and what they looked at
+ 
+
+ align:start position:0%
+Building in it and what they looked at
+was how people in these interactions
+
+ align:start position:0%
+was how people in these interactions
+ 
+
+ align:start position:0%
+was how people in these interactions
+accumulated shared knowledge or common
+
+ align:start position:0%
+accumulated shared knowledge or common
+ 
+
+ align:start position:0%
+accumulated shared knowledge or common
+ground over time and coordinated so
+
+ align:start position:0%
+ground over time and coordinated so
+ 
+
+ align:start position:0%
+ground over time and coordinated so
+their communication could become more
+
+ align:start position:0%
+their communication could become more
+ 
+
+ align:start position:0%
+their communication could become more
+efficient and what they found is that
+
+ align:start position:0%
+efficient and what they found is that
+ 
+
+ align:start position:0%
+efficient and what they found is that
+when they had two New Yorkers who are
+
+ align:start position:0%
+when they had two New Yorkers who are
+ 
+
+ align:start position:0%
+when they had two New Yorkers who are
+interacting with each other they tended
+
+ align:start position:0%
+interacting with each other they tended
+ 
+
+ align:start position:0%
+interacting with each other they tended
+to very quickly do the tasks because
+
+ align:start position:0%
+to very quickly do the tasks because
+ 
+
+ align:start position:0%
+to very quickly do the tasks because
+they could just they could recognize
+
+ align:start position:0%
+they could just they could recognize
+ 
+
+ align:start position:0%
+they could just they could recognize
+immediately
+
+ align:start position:0%
+immediately
+ 
+
+ align:start position:0%
+immediately
+that person's in New Yorker and would
+
+ align:start position:0%
+that person's in New Yorker and would
+ 
+
+ align:start position:0%
+that person's in New Yorker and would
+just say things like oh it's going with
+
+ align:start position:0%
+just say things like oh it's going with
+ 
+
+ align:start position:0%
+just say things like oh it's going with
+Empire State Building
+
+ align:start position:0%
+Empire State Building
+ 
+
+ align:start position:0%
+Empire State Building
+whereas when they were talking to
+
+ align:start position:0%
+whereas when they were talking to
+ 
+
+ align:start position:0%
+whereas when they were talking to
+someone who wasn't in New Yorker they
+
+ align:start position:0%
+someone who wasn't in New Yorker they
+ 
+
+ align:start position:0%
+someone who wasn't in New Yorker they
+had to sort of ground the conversation
+
+ align:start position:0%
+had to sort of ground the conversation
+ 
+
+ align:start position:0%
+had to sort of ground the conversation
+by establishing these common reference
+
+ align:start position:0%
+by establishing these common reference
+ 
+
+ align:start position:0%
+by establishing these common reference
+before getting to this point and so they
+
+ align:start position:0%
+before getting to this point and so they
+ 
+
+ align:start position:0%
+before getting to this point and so they
+might start out with saying things like
+
+ align:start position:0%
+might start out with saying things like
+ 
+
+ align:start position:0%
+might start out with saying things like
+Oh from the move the one with the
+
+ align:start position:0%
+Oh from the move the one with the
+ 
+
+ align:start position:0%
+Oh from the move the one with the
+building with the pointy top and then
+
+ align:start position:0%
+building with the pointy top and then
+ 
+
+ align:start position:0%
+building with the pointy top and then
+eventually they would coordinate on what
+
+ align:start position:0%
+eventually they would coordinate on what
+ 
+
+ align:start position:0%
+eventually they would coordinate on what
+the actual labels for these up for these
+
+ align:start position:0%
+the actual labels for these up for these
+ 
+
+ align:start position:0%
+the actual labels for these up for these
+things were and so Clark's idea is that
+
+ align:start position:0%
+things were and so Clark's idea is that
+ 
+
+ align:start position:0%
+things were and so Clark's idea is that
+communication is really efficient we're
+
+ align:start position:0%
+communication is really efficient we're
+ 
+
+ align:start position:0%
+communication is really efficient we're
+able to do it in the way we are because
+
+ align:start position:0%
+able to do it in the way we are because
+ 
+
+ align:start position:0%
+able to do it in the way we are because
+we have because we're thinking about the
+
+ align:start position:0%
+we have because we're thinking about the
+ 
+
+ align:start position:0%
+we have because we're thinking about the
+common ground we have with other people
+
+ align:start position:0%
+common ground we have with other people
+ 
+
+ align:start position:0%
+common ground we have with other people
+and we're able to figure out what kind
+
+ align:start position:0%
+and we're able to figure out what kind
+ 
+
+ align:start position:0%
+and we're able to figure out what kind
+of common ground we have with others
+
+ align:start position:0%
+of common ground we have with others
+ 
+
+ align:start position:0%
+of common ground we have with others
+fairly quickly so if I'm interacting
+
+ align:start position:0%
+fairly quickly so if I'm interacting
+ 
+
+ align:start position:0%
+fairly quickly so if I'm interacting
+with one of you I might assume okay we
+
+ align:start position:0%
+with one of you I might assume okay we
+ 
+
+ align:start position:0%
+with one of you I might assume okay we
+both know a lot about cognitive science
+
+ align:start position:0%
+both know a lot about cognitive science
+ 
+
+ align:start position:0%
+both know a lot about cognitive science
+already so I can sort of start at a
+
+ align:start position:0%
+already so I can sort of start at a
+ 
+
+ align:start position:0%
+already so I can sort of start at a
+different level that I might start with
+
+ align:start position:0%
+different level that I might start with
+ 
+
+ align:start position:0%
+different level that I might start with
+say a child or someone who didn't know
+
+ align:start position:0%
+say a child or someone who didn't know
+ 
+
+ align:start position:0%
+say a child or someone who didn't know
+anything about this area and so this is
+
+ align:start position:0%
+anything about this area and so this is
+ 
+
+ align:start position:0%
+anything about this area and so this is
+an important piece of human
+
+ align:start position:0%
+an important piece of human
+ 
+
+ align:start position:0%
+an important piece of human
+communication that it seems like endless
+
+ align:start position:0%
+communication that it seems like endless
+ 
+
+ align:start position:0%
+communication that it seems like endless
+talked a little about this - it seems
+
+ align:start position:0%
+talked a little about this - it seems
+ 
+
+ align:start position:0%
+talked a little about this - it seems
+like infants are starting to show some
+
+ align:start position:0%
+like infants are starting to show some
+ 
+
+ align:start position:0%
+like infants are starting to show some
+signs of understanding the importance of
+
+ align:start position:0%
+signs of understanding the importance of
+ 
+
+ align:start position:0%
+signs of understanding the importance of
+common ground or shared knowledge and
+
+ align:start position:0%
+common ground or shared knowledge and
+ 
+
+ align:start position:0%
+common ground or shared knowledge and
+communication from a really early age
+
+ align:start position:0%
+communication from a really early age
+ 
+
+ align:start position:0%
+communication from a really early age
+but importantly this seems to come in
+
+ align:start position:0%
+but importantly this seems to come in
+ 
+
+ align:start position:0%
+but importantly this seems to come in
+around the same time that they're
+
+ align:start position:0%
+around the same time that they're
+ 
+
+ align:start position:0%
+around the same time that they're
+recognizing the importance of speakers
+
+ align:start position:0%
+recognizing the importance of speakers
+ 
+
+ align:start position:0%
+recognizing the importance of speakers
+facing each other in conversation and
+
+ align:start position:0%
+facing each other in conversation and
+ 
+
+ align:start position:0%
+facing each other in conversation and
+perhaps putting together some of their
+
+ align:start position:0%
+perhaps putting together some of their
+ 
+
+ align:start position:0%
+perhaps putting together some of their
+core knowledge domains which is around
+
+ align:start position:0%
+core knowledge domains which is around
+ 
+
+ align:start position:0%
+core knowledge domains which is around
+nine months to a year so this is really
+
+ align:start position:0%
+nine months to a year so this is really
+ 
+
+ align:start position:0%
+nine months to a year so this is really
+a lot of work on this and this domain
+
+ align:start position:0%
+a lot of work on this and this domain
+ 
+
+ align:start position:0%
+a lot of work on this and this domain
+has been done by Tomasello who showed
+
+ align:start position:0%
+has been done by Tomasello who showed
+ 
+
+ align:start position:0%
+has been done by Tomasello who showed
+that around nine months children were
+
+ align:start position:0%
+that around nine months children were
+ 
+
+ align:start position:0%
+that around nine months children were
+starting to do something different than
+
+ align:start position:0%
+starting to do something different than
+ 
+
+ align:start position:0%
+starting to do something different than
+they've been doing earlier so under nine
+
+ align:start position:0%
+they've been doing earlier so under nine
+ 
+
+ align:start position:0%
+they've been doing earlier so under nine
+months children tend to tend to they
+
+ align:start position:0%
+months children tend to tend to they
+ 
+
+ align:start position:0%
+months children tend to tend to they
+play with objects they interact with
+
+ align:start position:0%
+play with objects they interact with
+ 
+
+ align:start position:0%
+play with objects they interact with
+people but they don't seem to put these
+
+ align:start position:0%
+people but they don't seem to put these
+ 
+
+ align:start position:0%
+people but they don't seem to put these
+two things together whereas at nine
+
+ align:start position:0%
+two things together whereas at nine
+ 
+
+ align:start position:0%
+two things together whereas at nine
+months what they start doing is paying
+
+ align:start position:0%
+months what they start doing is paying
+ 
+
+ align:start position:0%
+months what they start doing is paying
+attention not just objects or to people
+
+ align:start position:0%
+attention not just objects or to people
+ 
+
+ align:start position:0%
+attention not just objects or to people
+but to object and people at the same
+
+ align:start position:0%
+but to object and people at the same
+ 
+
+ align:start position:0%
+but to object and people at the same
+time in the context of a joint
+
+ align:start position:0%
+time in the context of a joint
+ 
+
+ align:start position:0%
+time in the context of a joint
+interaction so they might do things like
+
+ align:start position:0%
+interaction so they might do things like
+ 
+
+ align:start position:0%
+interaction so they might do things like
+look at an object and then look at mom
+
+ align:start position:0%
+look at an object and then look at mom
+ 
+
+ align:start position:0%
+look at an object and then look at mom
+to make sure mom is also looking at it
+
+ align:start position:0%
+to make sure mom is also looking at it
+ 
+
+ align:start position:0%
+to make sure mom is also looking at it
+or they might point at things not just
+
+ align:start position:0%
+or they might point at things not just
+ 
+
+ align:start position:0%
+or they might point at things not just
+because they want the things as a
+
+ align:start position:0%
+because they want the things as a
+ 
+
+ align:start position:0%
+because they want the things as a
+younger child might do but in order only
+
+ align:start position:0%
+younger child might do but in order only
+ 
+
+ align:start position:0%
+younger child might do but in order only
+to share a tension with a parent or with
+
+ align:start position:0%
+to share a tension with a parent or with
+ 
+
+ align:start position:0%
+to share a tension with a parent or with
+someone else to point out that they're
+
+ align:start position:0%
+someone else to point out that they're
+ 
+
+ align:start position:0%
+someone else to point out that they're
+interested in something and to make sure
+
+ align:start position:0%
+interested in something and to make sure
+ 
+
+ align:start position:0%
+interested in something and to make sure
+that the parent is looking and is
+
+ align:start position:0%
+that the parent is looking and is
+ 
+
+ align:start position:0%
+that the parent is looking and is
+interested in it as well so Tomasello
+
+ align:start position:0%
+interested in it as well so Tomasello
+ 
+
+ align:start position:0%
+interested in it as well so Tomasello
+argues that this ability for engaging in
+
+ align:start position:0%
+argues that this ability for engaging in
+ 
+
+ align:start position:0%
+argues that this ability for engaging in
+joint attention sharing attention with
+
+ align:start position:0%
+joint attention sharing attention with
+ 
+
+ align:start position:0%
+joint attention sharing attention with
+someone
+
+ align:start position:0%
+someone
+ 
+
+ align:start position:0%
+someone
+to an object or external referent in the
+
+ align:start position:0%
+to an object or external referent in the
+ 
+
+ align:start position:0%
+to an object or external referent in the
+world is the foundation of linguistic
+
+ align:start position:0%
+world is the foundation of linguistic
+ 
+
+ align:start position:0%
+world is the foundation of linguistic
+communication and also cooperation and
+
+ align:start position:0%
+communication and also cooperation and
+ 
+
+ align:start position:0%
+communication and also cooperation and
+other very important human activities
+
+ align:start position:0%
+other very important human activities
+ 
+
+ align:start position:0%
+other very important human activities
+and it's certainly going to be important
+
+ align:start position:0%
+and it's certainly going to be important
+ 
+
+ align:start position:0%
+and it's certainly going to be important
+for an understanding of common ground
+
+ align:start position:0%
+for an understanding of common ground
+ 
+
+ align:start position:0%
+for an understanding of common ground
+which is important for communication so
+
+ align:start position:0%
+which is important for communication so
+ 
+
+ align:start position:0%
+which is important for communication so
+there's also evidence that around 12
+
+ align:start position:0%
+there's also evidence that around 12
+ 
+
+ align:start position:0%
+there's also evidence that around 12
+months and then start to use prior
+
+ align:start position:0%
+months and then start to use prior
+ 
+
+ align:start position:0%
+months and then start to use prior
+shared experience to interpret
+
+ align:start position:0%
+shared experience to interpret
+ 
+
+ align:start position:0%
+shared experience to interpret
+communication I'm going to skip this I
+
+ align:start position:0%
+communication I'm going to skip this I
+ 
+
+ align:start position:0%
+communication I'm going to skip this I
+think but basically the idea well I'll
+
+ align:start position:0%
+think but basically the idea well I'll
+ 
+
+ align:start position:0%
+think but basically the idea well I'll
+just go through it quickly the idea is
+
+ align:start position:0%
+just go through it quickly the idea is
+ 
+
+ align:start position:0%
+just go through it quickly the idea is
+that infants will use the activities and
+
+ align:start position:0%
+that infants will use the activities and
+ 
+
+ align:start position:0%
+that infants will use the activities and
+objects that they've shared with people
+
+ align:start position:0%
+objects that they've shared with people
+ 
+
+ align:start position:0%
+objects that they've shared with people
+previously to figure out what the person
+
+ align:start position:0%
+previously to figure out what the person
+ 
+
+ align:start position:0%
+previously to figure out what the person
+means in a new case so if the infant
+
+ align:start position:0%
+means in a new case so if the infant
+ 
+
+ align:start position:0%
+means in a new case so if the infant
+interacts with one communicator with one
+
+ align:start position:0%
+interacts with one communicator with one
+ 
+
+ align:start position:0%
+interacts with one communicator with one
+toy and with another communicator with a
+
+ align:start position:0%
+toy and with another communicator with a
+ 
+
+ align:start position:0%
+toy and with another communicator with a
+different toy separately they will
+
+ align:start position:0%
+different toy separately they will
+ 
+
+ align:start position:0%
+different toy separately they will
+figure out the referent of a
+
+ align:start position:0%
+figure out the referent of a
+ 
+
+ align:start position:0%
+figure out the referent of a
+communicators ambiguous request by
+
+ align:start position:0%
+communicators ambiguous request by
+ 
+
+ align:start position:0%
+communicators ambiguous request by
+thinking about what information they've
+
+ align:start position:0%
+thinking about what information they've
+ 
+
+ align:start position:0%
+thinking about what information they've
+shared in the past so it seems like
+
+ align:start position:0%
+shared in the past so it seems like
+ 
+
+ align:start position:0%
+shared in the past so it seems like
+they're starting to track what kinds of
+
+ align:start position:0%
+they're starting to track what kinds of
+ 
+
+ align:start position:0%
+they're starting to track what kinds of
+knowledge is shared and what isn't in
+
+ align:start position:0%
+knowledge is shared and what isn't in
+ 
+
+ align:start position:0%
+knowledge is shared and what isn't in
+order to effectively communicate with
+
+ align:start position:0%
+order to effectively communicate with
+ 
+
+ align:start position:0%
+order to effectively communicate with
+others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's a lot of other important
+
+ align:start position:0%
+okay so there's a lot of other important
+ 
+
+ align:start position:0%
+okay so there's a lot of other important
+questions about common ground but I'm
+
+ align:start position:0%
+questions about common ground but I'm
+ 
+
+ align:start position:0%
+questions about common ground but I'm
+gonna skip those now I just want to come
+
+ align:start position:0%
+gonna skip those now I just want to come
+ 
+
+ align:start position:0%
+gonna skip those now I just want to come
+back to the question of why this why
+
+ align:start position:0%
+back to the question of why this why
+ 
+
+ align:start position:0%
+back to the question of why this why
+infants understanding and children
+
+ align:start position:0%
+infants understanding and children
+ 
+
+ align:start position:0%
+infants understanding and children
+understanding of communication is
+
+ align:start position:0%
+understanding of communication is
+ 
+
+ align:start position:0%
+understanding of communication is
+important for understanding human
+
+ align:start position:0%
+important for understanding human
+ 
+
+ align:start position:0%
+important for understanding human
+intelligence so I think that one reason
+
+ align:start position:0%
+intelligence so I think that one reason
+ 
+
+ align:start position:0%
+intelligence so I think that one reason
+is that when you think about the
+
+ align:start position:0%
+is that when you think about the
+ 
+
+ align:start position:0%
+is that when you think about the
+insights these philosophers had and how
+
+ align:start position:0%
+insights these philosophers had and how
+ 
+
+ align:start position:0%
+insights these philosophers had and how
+we how they seem to be realized in very
+
+ align:start position:0%
+we how they seem to be realized in very
+ 
+
+ align:start position:0%
+we how they seem to be realized in very
+in fairly young infants early and
+
+ align:start position:0%
+in fairly young infants early and
+ 
+
+ align:start position:0%
+in fairly young infants early and
+children infants or early in development
+
+ align:start position:0%
+children infants or early in development
+ 
+
+ align:start position:0%
+children infants or early in development
+when you look at these abilities that
+
+ align:start position:0%
+when you look at these abilities that
+ 
+
+ align:start position:0%
+when you look at these abilities that
+humans have and even that there are
+
+ align:start position:0%
+humans have and even that there are
+ 
+
+ align:start position:0%
+humans have and even that there are
+young humans have and you compare them
+
+ align:start position:0%
+young humans have and you compare them
+ 
+
+ align:start position:0%
+young humans have and you compare them
+to what non-human animals are doing
+
+ align:start position:0%
+to what non-human animals are doing
+ 
+
+ align:start position:0%
+to what non-human animals are doing
+things look really different and so just
+
+ align:start position:0%
+things look really different and so just
+ 
+
+ align:start position:0%
+things look really different and so just
+briefly an animal communication we see
+
+ align:start position:0%
+briefly an animal communication we see
+ 
+
+ align:start position:0%
+briefly an animal communication we see
+some of the same kinds of features that
+
+ align:start position:0%
+some of the same kinds of features that
+ 
+
+ align:start position:0%
+some of the same kinds of features that
+we see in human communication so for one
+
+ align:start position:0%
+we see in human communication so for one
+ 
+
+ align:start position:0%
+we see in human communication so for one
+thing animal communication clearly has a
+
+ align:start position:0%
+thing animal communication clearly has a
+ 
+
+ align:start position:0%
+thing animal communication clearly has a
+social function in the same way that
+
+ align:start position:0%
+social function in the same way that
+ 
+
+ align:start position:0%
+social function in the same way that
+human communication does so it's
+
+ align:start position:0%
+human communication does so it's
+ 
+
+ align:start position:0%
+human communication does so it's
+socially rich in a number of ways I'm
+
+ align:start position:0%
+socially rich in a number of ways I'm
+ 
+
+ align:start position:0%
+socially rich in a number of ways I'm
+not going to go over specific species
+
+ align:start position:0%
+not going to go over specific species
+ 
+
+ align:start position:0%
+not going to go over specific species
+but just to gloss over it most animal
+
+ align:start position:0%
+but just to gloss over it most animal
+ 
+
+ align:start position:0%
+but just to gloss over it most animal
+communication is sensitive to the
+
+ align:start position:0%
+communication is sensitive to the
+ 
+
+ align:start position:0%
+communication is sensitive to the
+presence of an audience so it matters
+
+ align:start position:0%
+presence of an audience so it matters
+ 
+
+ align:start position:0%
+presence of an audience so it matters
+that someone's there to hear your
+
+ align:start position:0%
+that someone's there to hear your
+ 
+
+ align:start position:0%
+that someone's there to hear your
+communication for example species that
+
+ align:start position:0%
+communication for example species that
+ 
+
+ align:start position:0%
+communication for example species that
+produce alarm calls to warn others in
+
+ align:start position:0%
+produce alarm calls to warn others in
+ 
+
+ align:start position:0%
+produce alarm calls to warn others in
+their species in their group of
+
+ align:start position:0%
+their species in their group of
+ 
+
+ align:start position:0%
+their species in their group of
+predators will rarely produce these
+
+ align:start position:0%
+predators will rarely produce these
+ 
+
+ align:start position:0%
+predators will rarely produce these
+calls if there are no other members of
+
+ align:start position:0%
+calls if there are no other members of
+ 
+
+ align:start position:0%
+calls if there are no other members of
+their species present in many cases the
+
+ align:start position:0%
+their species present in many cases the
+ 
+
+ align:start position:0%
+their species present in many cases the
+sensitivity to the audience depends on
+
+ align:start position:0%
+sensitivity to the audience depends on
+ 
+
+ align:start position:0%
+sensitivity to the audience depends on
+the identity of the audience so for
+
+ align:start position:0%
+the identity of the audience so for
+ 
+
+ align:start position:0%
+the identity of the audience so for
+example in some species on such as
+
+ align:start position:0%
+example in some species on such as
+ 
+
+ align:start position:0%
+example in some species on such as
+ground squirrels they call much more in
+
+ align:start position:0%
+ground squirrels they call much more in
+ 
+
+ align:start position:0%
+ground squirrels they call much more in
+the presence of their kin than when
+
+ align:start position:0%
+the presence of their kin than when
+ 
+
+ align:start position:0%
+the presence of their kin than when
+their kin are not around or when there
+
+ align:start position:0%
+their kin are not around or when there
+ 
+
+ align:start position:0%
+their kin are not around or when there
+are other individuals there and in some
+
+ align:start position:0%
+are other individuals there and in some
+ 
+
+ align:start position:0%
+are other individuals there and in some
+cases it seems like there might actually
+
+ align:start position:0%
+cases it seems like there might actually
+ 
+
+ align:start position:0%
+cases it seems like there might actually
+even be a sensitivity to the knowledge
+
+ align:start position:0%
+even be a sensitivity to the knowledge
+ 
+
+ align:start position:0%
+even be a sensitivity to the knowledge
+state of the audience so this is looking
+
+ align:start position:0%
+state of the audience so this is looking
+ 
+
+ align:start position:0%
+state of the audience so this is looking
+a little more like the kind of
+
+ align:start position:0%
+a little more like the kind of
+ 
+
+ align:start position:0%
+a little more like the kind of
+sophisticated communication we see in
+
+ align:start position:0%
+sophisticated communication we see in
+ 
+
+ align:start position:0%
+sophisticated communication we see in
+humans so a wild chimpanzee for example
+
+ align:start position:0%
+humans so a wild chimpanzee for example
+ 
+
+ align:start position:0%
+humans so a wild chimpanzee for example
+will produce an alarm call will start to
+
+ align:start position:0%
+will produce an alarm call will start to
+ 
+
+ align:start position:0%
+will produce an alarm call will start to
+alarm call more if other chimpanzees
+
+ align:start position:0%
+alarm call more if other chimpanzees
+ 
+
+ align:start position:0%
+alarm call more if other chimpanzees
+come over who hadn't heard the original
+
+ align:start position:0%
+come over who hadn't heard the original
+ 
+
+ align:start position:0%
+come over who hadn't heard the original
+alarm call or who hadn't seen the
+
+ align:start position:0%
+alarm call or who hadn't seen the
+ 
+
+ align:start position:0%
+alarm call or who hadn't seen the
+predator but if everyone around has
+
+ align:start position:0%
+predator but if everyone around has
+ 
+
+ align:start position:0%
+predator but if everyone around has
+already seen it they'll reduce their
+
+ align:start position:0%
+already seen it they'll reduce their
+ 
+
+ align:start position:0%
+already seen it they'll reduce their
+alarm calling so it seems like they
+
+ align:start position:0%
+alarm calling so it seems like they
+ 
+
+ align:start position:0%
+alarm calling so it seems like they
+tailor it to how much information others
+
+ align:start position:0%
+tailor it to how much information others
+ 
+
+ align:start position:0%
+tailor it to how much information others
+around them have had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however despite these really interesting
+
+ align:start position:0%
+however despite these really interesting
+ 
+
+ align:start position:0%
+however despite these really interesting
+ways in which animal communication is
+
+ align:start position:0%
+ways in which animal communication is
+ 
+
+ align:start position:0%
+ways in which animal communication is
+social and complex it's also limited in
+
+ align:start position:0%
+social and complex it's also limited in
+ 
+
+ align:start position:0%
+social and complex it's also limited in
+a number of ways that human
+
+ align:start position:0%
+a number of ways that human
+ 
+
+ align:start position:0%
+a number of ways that human
+communication is not so the eliciting
+
+ align:start position:0%
+communication is not so the eliciting
+ 
+
+ align:start position:0%
+communication is not so the eliciting
+stimuli for these communicative signals
+
+ align:start position:0%
+stimuli for these communicative signals
+ 
+
+ align:start position:0%
+stimuli for these communicative signals
+tend to be fairly limited I'll do the
+
+ align:start position:0%
+tend to be fairly limited I'll do the
+ 
+
+ align:start position:0%
+tend to be fairly limited I'll do the
+signals themselves so there tends to be
+
+ align:start position:0%
+signals themselves so there tends to be
+ 
+
+ align:start position:0%
+signals themselves so there tends to be
+sayin vervet monkeys one cry for a hawk
+
+ align:start position:0%
+sayin vervet monkeys one cry for a hawk
+ 
+
+ align:start position:0%
+sayin vervet monkeys one cry for a hawk
+and one cry for snake and they can't
+
+ align:start position:0%
+and one cry for snake and they can't
+ 
+
+ align:start position:0%
+and one cry for snake and they can't
+produce realize new signals for new
+
+ align:start position:0%
+produce realize new signals for new
+ 
+
+ align:start position:0%
+produce realize new signals for new
+kinds of predators and situations as in
+
+ align:start position:0%
+kinds of predators and situations as in
+ 
+
+ align:start position:0%
+kinds of predators and situations as in
+humans the receivers or in humans
+
+ align:start position:0%
+humans the receivers or in humans
+ 
+
+ align:start position:0%
+humans the receivers or in humans
+addressees acquire information from the
+
+ align:start position:0%
+addressees acquire information from the
+ 
+
+ align:start position:0%
+addressees acquire information from the
+signals of others but there's no
+
+ align:start position:0%
+signals of others but there's no
+ 
+
+ align:start position:0%
+signals of others but there's no
+evidence that this information tells the
+
+ align:start position:0%
+evidence that this information tells the
+ 
+
+ align:start position:0%
+evidence that this information tells the
+receivers in animal and animal species
+
+ align:start position:0%
+receivers in animal and animal species
+ 
+
+ align:start position:0%
+receivers in animal and animal species
+anything about the mental states of the
+
+ align:start position:0%
+anything about the mental states of the
+ 
+
+ align:start position:0%
+anything about the mental states of the
+communicator and additionally the
+
+ align:start position:0%
+communicator and additionally the
+ 
+
+ align:start position:0%
+communicator and additionally the
+communicator signals can often cause a
+
+ align:start position:0%
+communicator signals can often cause a
+ 
+
+ align:start position:0%
+communicator signals can often cause a
+response and receivers that's beneficial
+
+ align:start position:0%
+response and receivers that's beneficial
+ 
+
+ align:start position:0%
+response and receivers that's beneficial
+to the communicator for example they get
+
+ align:start position:0%
+to the communicator for example they get
+ 
+
+ align:start position:0%
+to the communicator for example they get
+a bump to indirect Fitness if their can
+
+ align:start position:0%
+a bump to indirect Fitness if their can
+ 
+
+ align:start position:0%
+a bump to indirect Fitness if their can
+run away and survive predators so there
+
+ align:start position:0%
+run away and survive predators so there
+ 
+
+ align:start position:0%
+run away and survive predators so there
+can be benefits of communication but
+
+ align:start position:0%
+can be benefits of communication but
+ 
+
+ align:start position:0%
+can be benefits of communication but
+there's no evidence that the
+
+ align:start position:0%
+there's no evidence that the
+ 
+
+ align:start position:0%
+there's no evidence that the
+communicator has any intention of
+
+ align:start position:0%
+communicator has any intention of
+ 
+
+ align:start position:0%
+communicator has any intention of
+changing the receivers mental state so
+
+ align:start position:0%
+changing the receivers mental state so
+ 
+
+ align:start position:0%
+changing the receivers mental state so
+there's really no evidence of this sort
+
+ align:start position:0%
+there's really no evidence of this sort
+ 
+
+ align:start position:0%
+there's really no evidence of this sort
+of speaker meaning or this special kind
+
+ align:start position:0%
+of speaker meaning or this special kind
+ 
+
+ align:start position:0%
+of speaker meaning or this special kind
+of communication communicative intention
+
+ align:start position:0%
+of communication communicative intention
+ 
+
+ align:start position:0%
+of communication communicative intention
+we see in humans which is that a
+
+ align:start position:0%
+we see in humans which is that a
+ 
+
+ align:start position:0%
+we see in humans which is that a
+communicator doesn't just intend for the
+
+ align:start position:0%
+communicator doesn't just intend for the
+ 
+
+ align:start position:0%
+communicator doesn't just intend for the
+addressee to respond in a particular way
+
+ align:start position:0%
+addressee to respond in a particular way
+ 
+
+ align:start position:0%
+addressee to respond in a particular way
+but intends for the address effort the
+
+ align:start position:0%
+but intends for the address effort the
+ 
+
+ align:start position:0%
+but intends for the address effort the
+audience to respond in a particular way
+
+ align:start position:0%
+audience to respond in a particular way
+ 
+
+ align:start position:0%
+audience to respond in a particular way
+by virtue of having understood the
+
+ align:start position:0%
+by virtue of having understood the
+ 
+
+ align:start position:0%
+by virtue of having understood the
+intention of that communication and so
+
+ align:start position:0%
+intention of that communication and so
+ 
+
+ align:start position:0%
+intention of that communication and so
+this is just a I think particularly well
+
+ align:start position:0%
+this is just a I think particularly well
+ 
+
+ align:start position:0%
+this is just a I think particularly well
+worded quote from Seaforth and Cheney
+
+ align:start position:0%
+worded quote from Seaforth and Cheney
+ 
+
+ align:start position:0%
+worded quote from Seaforth and Cheney
+who say basically that listeners can
+
+ align:start position:0%
+who say basically that listeners can
+ 
+
+ align:start position:0%
+who say basically that listeners can
+acquire information from signalers but
+
+ align:start position:0%
+acquire information from signalers but
+ 
+
+ align:start position:0%
+acquire information from signalers but
+the signalers themselves don't in the
+
+ align:start position:0%
+the signalers themselves don't in the
+ 
+
+ align:start position:0%
+the signalers themselves don't in the
+human sense intend to provide that
+
+ align:start position:0%
+human sense intend to provide that
+ 
+
+ align:start position:0%
+human sense intend to provide that
+information so yeah so the reason really
+
+ align:start position:0%
+information so yeah so the reason really
+ 
+
+ align:start position:0%
+information so yeah so the reason really
+for this contrast between the human and
+
+ align:start position:0%
+for this contrast between the human and
+ 
+
+ align:start position:0%
+for this contrast between the human and
+animal cases that I think if we want to
+
+ align:start position:0%
+animal cases that I think if we want to
+ 
+
+ align:start position:0%
+animal cases that I think if we want to
+build a model of human communication we
+
+ align:start position:0%
+build a model of human communication we
+ 
+
+ align:start position:0%
+build a model of human communication we
+need it to we need to differentiate it
+
+ align:start position:0%
+need it to we need to differentiate it
+ 
+
+ align:start position:0%
+need it to we need to differentiate it
+from other kinds of communicative models
+
+ align:start position:0%
+from other kinds of communicative models
+ 
+
+ align:start position:0%
+from other kinds of communicative models
+we could have and we also needed to
+
+ align:start position:0%
+we could have and we also needed to
+ 
+
+ align:start position:0%
+we could have and we also needed to
+develop the types of abilities that
+
+ align:start position:0%
+develop the types of abilities that
+ 
+
+ align:start position:0%
+develop the types of abilities that
+human infants have taking into account
+
+ align:start position:0%
+human infants have taking into account
+ 
+
+ align:start position:0%
+human infants have taking into account
+the resources that infants start out
+
+ align:start position:0%
+the resources that infants start out
+ 
+
+ align:start position:0%
+the resources that infants start out
+with and the developments that we see in
+
+ align:start position:0%
+with and the developments that we see in
+ 
+
+ align:start position:0%
+with and the developments that we see in
+the first few years of life so if not
+
+ align:start position:0%
+the first few years of life so if not
+ 
+
+ align:start position:0%
+the first few years of life so if not
+going to be enough to have agents that
+
+ align:start position:0%
+going to be enough to have agents that
+ 
+
+ align:start position:0%
+going to be enough to have agents that
+can influence each other's responses or
+
+ align:start position:0%
+can influence each other's responses or
+ 
+
+ align:start position:0%
+can influence each other's responses or
+who can understand language because it
+
+ align:start position:0%
+who can understand language because it
+ 
+
+ align:start position:0%
+who can understand language because it
+seems like the recognition of these more
+
+ align:start position:0%
+seems like the recognition of these more
+ 
+
+ align:start position:0%
+seems like the recognition of these more
+abstract features of communication and
+
+ align:start position:0%
+abstract features of communication and
+ 
+
+ align:start position:0%
+abstract features of communication and
+its causal effects on mental states is
+
+ align:start position:0%
+its causal effects on mental states is
+ 
+
+ align:start position:0%
+its causal effects on mental states is
+actually present fairly
+
+ align:start position:0%
+actually present fairly
+ 
+
+ align:start position:0%
+actually present fairly
+early on as well and I think just
+
+ align:start position:0%
+early on as well and I think just
+ 
+
+ align:start position:0%
+early on as well and I think just
+relating this back to Liz's theory that
+
+ align:start position:0%
+relating this back to Liz's theory that
+ 
+
+ align:start position:0%
+relating this back to Liz's theory that
+we have the infant's might have these
+
+ align:start position:0%
+we have the infant's might have these
+ 
+
+ align:start position:0%
+we have the infant's might have these
+different systems for agents
+
+ align:start position:0%
+different systems for agents
+ 
+
+ align:start position:0%
+different systems for agents
+understanding agents and their actions
+
+ align:start position:0%
+understanding agents and their actions
+ 
+
+ align:start position:0%
+understanding agents and their actions
+on object and then for social being than
+
+ align:start position:0%
+on object and then for social being than
+ 
+
+ align:start position:0%
+on object and then for social being than
+their interactions with each other it
+
+ align:start position:0%
+their interactions with each other it
+ 
+
+ align:start position:0%
+their interactions with each other it
+seems like communication and this type
+
+ align:start position:0%
+seems like communication and this type
+ 
+
+ align:start position:0%
+seems like communication and this type
+of communicative intention that we see
+
+ align:start position:0%
+of communicative intention that we see
+ 
+
+ align:start position:0%
+of communicative intention that we see
+sort of combines these two kinds of
+
+ align:start position:0%
+sort of combines these two kinds of
+ 
+
+ align:start position:0%
+sort of combines these two kinds of
+things where you have an intention to
+
+ align:start position:0%
+things where you have an intention to
+ 
+
+ align:start position:0%
+things where you have an intention to
+produce an effect on someone else but by
+
+ align:start position:0%
+produce an effect on someone else but by
+ 
+
+ align:start position:0%
+produce an effect on someone else but by
+virtue of them understanding the mental
+
+ align:start position:0%
+virtue of them understanding the mental
+ 
+
+ align:start position:0%
+virtue of them understanding the mental
+states that you have toward the world
+
+ align:start position:0%
+states that you have toward the world
+ 
+
+ align:start position:0%
+states that you have toward the world
+and as well as toward them so and maybe
+
+ align:start position:0%
+and as well as toward them so and maybe
+ 
+
+ align:start position:0%
+and as well as toward them so and maybe
+it's the combining of these different
+
+ align:start position:0%
+it's the combining of these different
+ 
+
+ align:start position:0%
+it's the combining of these different
+domains that that helps infants put
+
+ align:start position:0%
+domains that that helps infants put
+ 
+
+ align:start position:0%
+domains that that helps infants put
+together they're possibly human unique
+
+ align:start position:0%
+together they're possibly human unique
+ 
+
+ align:start position:0%
+together they're possibly human unique
+but maybe not communication skills
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/lCKxeRiBdjQ.txt b/lCKxeRiBdjQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4eb5bc69d94c94cb71e327234521c3cb747318c5
--- /dev/null
+++ b/lCKxeRiBdjQ.txt
@@ -0,0 +1,1691 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I'd like us to work on the following
+
+ align:start position:0%
+I'd like us to work on the following
+ 
+
+ align:start position:0%
+I'd like us to work on the following
+problem so given the region R shown
+
+ align:start position:0%
+problem so given the region R shown
+ 
+
+ align:start position:0%
+problem so given the region R shown
+below which I'll mention more of in a
+
+ align:start position:0%
+below which I'll mention more of in a
+ 
+
+ align:start position:0%
+below which I'll mention more of in a
+moment compute the integral double
+
+ align:start position:0%
+moment compute the integral double
+ 
+
+ align:start position:0%
+moment compute the integral double
+integral over R of the quantity 4x^2 -
+
+ align:start position:0%
+integral over R of the quantity 4x^2 -
+ 
+
+ align:start position:0%
+integral over R of the quantity 4x^2 -
+i^ 2 y^2 sorry to the 4th DX Dy and I
+
+ align:start position:0%
+i^ 2 y^2 sorry to the 4th DX Dy and I
+ 
+
+ align:start position:0%
+i^ 2 y^2 sorry to the 4th DX Dy and I
+want you to do it by changing variables
+
+ align:start position:0%
+want you to do it by changing variables
+ 
+
+ align:start position:0%
+want you to do it by changing variables
+to U is equal to 2x - Y and V is Al to
+
+ align:start position:0%
+to U is equal to 2x - Y and V is Al to
+ 
+
+ align:start position:0%
+to U is equal to 2x - Y and V is Al to
+2x + y and the region defined down here
+
+ align:start position:0%
+2x + y and the region defined down here
+ 
+
+ align:start position:0%
+2x + y and the region defined down here
+is just the these three line segments in
+
+ align:start position:0%
+is just the these three line segments in
+ 
+
+ align:start position:0%
+is just the these three line segments in
+their the intersection of the of the
+
+ align:start position:0%
+their the intersection of the of the
+ 
+
+ align:start position:0%
+their the intersection of the of the
+region uh bounded by these three line
+
+ align:start position:0%
+region uh bounded by these three line
+ 
+
+ align:start position:0%
+region uh bounded by these three line
+segments so one of them is a portion of
+
+ align:start position:0%
+segments so one of them is a portion of
+ 
+
+ align:start position:0%
+segments so one of them is a portion of
+the y- axis one of them is a portion of
+
+ align:start position:0%
+the y- axis one of them is a portion of
+ 
+
+ align:start position:0%
+the y- axis one of them is a portion of
+the line defined by 2x - yal 0 and one
+
+ align:start position:0%
+the line defined by 2x - yal 0 and one
+ 
+
+ align:start position:0%
+the line defined by 2x - yal 0 and one
+of them is a portion of the line defined
+
+ align:start position:0%
+of them is a portion of the line defined
+ 
+
+ align:start position:0%
+of them is a portion of the line defined
+by 2x + Y = 2
+
+ align:start position:0%
+by 2x + Y = 2
+ 
+
+ align:start position:0%
+by 2x + Y = 2
+so why don't you do this make make sure
+
+ align:start position:0%
+so why don't you do this make make sure
+ 
+
+ align:start position:0%
+so why don't you do this make make sure
+you use this change of variables and
+
+ align:start position:0%
+you use this change of variables and
+ 
+
+ align:start position:0%
+you use this change of variables and
+then I'll come back and I'll draw uh the
+
+ align:start position:0%
+then I'll come back and I'll draw uh the
+ 
+
+ align:start position:0%
+then I'll come back and I'll draw uh the
+accompanying region in the UV plane and
+
+ align:start position:0%
+accompanying region in the UV plane and
+ 
+
+ align:start position:0%
+accompanying region in the UV plane and
+then we'll see uh how how I set it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up okay welcome back well the first
+
+ align:start position:0%
+up okay welcome back well the first
+ 
+
+ align:start position:0%
+up okay welcome back well the first
+thing I'm going to do is I'm going to
+
+ align:start position:0%
+thing I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+thing I'm going to do is I'm going to
+draw the region in the UV plane that is
+
+ align:start position:0%
+draw the region in the UV plane that is
+ 
+
+ align:start position:0%
+draw the region in the UV plane that is
+determined by this region in the XY
+
+ align:start position:0%
+determined by this region in the XY
+ 
+
+ align:start position:0%
+determined by this region in the XY
+plane and the ch change of variables now
+
+ align:start position:0%
+plane and the ch change of variables now
+ 
+
+ align:start position:0%
+plane and the ch change of variables now
+as was mentioned in the lecture uh all
+
+ align:start position:0%
+as was mentioned in the lecture uh all
+ 
+
+ align:start position:0%
+as was mentioned in the lecture uh all
+of the changes are linear and so I'm
+
+ align:start position:0%
+of the changes are linear and so I'm
+ 
+
+ align:start position:0%
+of the changes are linear and so I'm
+going to be taking lines to lines so
+
+ align:start position:0%
+going to be taking lines to lines so
+ 
+
+ align:start position:0%
+going to be taking lines to lines so
+what I'm going to do is determine uh at
+
+ align:start position:0%
+what I'm going to do is determine uh at
+ 
+
+ align:start position:0%
+what I'm going to do is determine uh at
+each end point here where that end point
+
+ align:start position:0%
+each end point here where that end point
+ 
+
+ align:start position:0%
+each end point here where that end point
+goes under the transformation and then I
+
+ align:start position:0%
+goes under the transformation and then I
+ 
+
+ align:start position:0%
+goes under the transformation and then I
+will connect the dots so what do I get
+
+ align:start position:0%
+will connect the dots so what do I get
+ 
+
+ align:start position:0%
+will connect the dots so what do I get
+well this first one is0 0 for x and y
+
+ align:start position:0%
+well this first one is0 0 for x and y
+ 
+
+ align:start position:0%
+well this first one is0 0 for x and y
+and so that corresponds to X and Y are
+
+ align:start position:0%
+and so that corresponds to X and Y are
+ 
+
+ align:start position:0%
+and so that corresponds to X and Y are
+zero and here so U is zero and X and Y
+
+ align:start position:0%
+zero and here so U is zero and X and Y
+ 
+
+ align:start position:0%
+zero and here so U is zero and X and Y
+are zero here so V is zero so that's the
+
+ align:start position:0%
+are zero here so V is zero so that's the
+ 
+
+ align:start position:0%
+are zero here so V is zero so that's the
+point Z 0 on the UV plane now I want to
+
+ align:start position:0%
+point Z 0 on the UV plane now I want to
+ 
+
+ align:start position:0%
+point Z 0 on the UV plane now I want to
+mention something here is that based on
+
+ align:start position:0%
+mention something here is that based on
+ 
+
+ align:start position:0%
+mention something here is that based on
+how these lines were defined this is
+
+ align:start position:0%
+how these lines were defined this is
+ 
+
+ align:start position:0%
+how these lines were defined this is
+telling you that all along this line 2x
+
+ align:start position:0%
+telling you that all along this line 2x
+ 
+
+ align:start position:0%
+telling you that all along this line 2x
+- y equal 0 that means U is equal to Zer
+
+ align:start position:0%
+- y equal 0 that means U is equal to Zer
+ 
+
+ align:start position:0%
+- y equal 0 that means U is equal to Zer
+all along that segment and if you'll
+
+ align:start position:0%
+all along that segment and if you'll
+ 
+
+ align:start position:0%
+all along that segment and if you'll
+notice also 2x + y is equal to 2 here so
+
+ align:start position:0%
+notice also 2x + y is equal to 2 here so
+ 
+
+ align:start position:0%
+notice also 2x + y is equal to 2 here so
+V is equal to two all along this segment
+
+ align:start position:0%
+V is equal to two all along this segment
+ 
+
+ align:start position:0%
+V is equal to two all along this segment
+so we should expect whatever U is V is
+
+ align:start position:0%
+so we should expect whatever U is V is
+ 
+
+ align:start position:0%
+so we should expect whatever U is V is
+going to be two here and whatever V is
+
+ align:start position:0%
+going to be two here and whatever V is
+ 
+
+ align:start position:0%
+going to be two here and whatever V is
+here U is going to be zero okay
+
+ align:start position:0%
+here U is going to be zero okay
+ 
+
+ align:start position:0%
+here U is going to be zero okay
+so I'm going to have something with u0
+
+ align:start position:0%
+so I'm going to have something with u0
+ 
+
+ align:start position:0%
+so I'm going to have something with u0
+initially and then V2 I can already
+
+ align:start position:0%
+initially and then V2 I can already
+ 
+
+ align:start position:0%
+initially and then V2 I can already
+expect it's going to come up here and
+
+ align:start position:0%
+expect it's going to come up here and
+ 
+
+ align:start position:0%
+expect it's going to come up here and
+move over that way but let's just check
+
+ align:start position:0%
+move over that way but let's just check
+ 
+
+ align:start position:0%
+move over that way but let's just check
+so this is the point
+
+ align:start position:0%
+so this is the point
+ 
+
+ align:start position:0%
+so this is the point
+020 for x and two for y let's see what
+
+ align:start position:0%
+020 for x and two for y let's see what
+ 
+
+ align:start position:0%
+020 for x and two for y let's see what
+it is in the uh UV variables so u in
+
+ align:start position:0%
+it is in the uh UV variables so u in
+ 
+
+ align:start position:0%
+it is in the uh UV variables so u in
+that case is -2 and v in that case is
+
+ align:start position:0%
+that case is -2 and v in that case is
+ 
+
+ align:start position:0%
+that case is -2 and v in that case is
+two and so I'm going to go left two and
+
+ align:start position:0%
+two and so I'm going to go left two and
+ 
+
+ align:start position:0%
+two and so I'm going to go left two and
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+two this might not be drawn to scale but
+
+ align:start position:0%
+two this might not be drawn to scale but
+ 
+
+ align:start position:0%
+two this might not be drawn to scale but
+this is -2
+
+ align:start position:0%
+this is -2
+ 
+
+ align:start position:0%
+this is -2
+and this is up two here and so that's
+
+ align:start position:0%
+and this is up two here and so that's
+ 
+
+ align:start position:0%
+and this is up two here and so that's
+where this point goes under the
+
+ align:start position:0%
+where this point goes under the
+ 
+
+ align:start position:0%
+where this point goes under the
+transformation and this point is2 comma
+
+ align:start position:0%
+transformation and this point is2 comma
+ 
+
+ align:start position:0%
+transformation and this point is2 comma
+2 1 half comma 1 you can actually check
+
+ align:start position:0%
+2 1 half comma 1 you can actually check
+ 
+
+ align:start position:0%
+2 1 half comma 1 you can actually check
+what it is but actually as I mentioned
+
+ align:start position:0%
+what it is but actually as I mentioned
+ 
+
+ align:start position:0%
+what it is but actually as I mentioned
+you already know what has to happen
+
+ align:start position:0%
+you already know what has to happen
+ 
+
+ align:start position:0%
+you already know what has to happen
+because this segment is connected right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then we said all along this
+
+ align:start position:0%
+here and then we said all along this
+ 
+
+ align:start position:0%
+here and then we said all along this
+line V is two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and all along this line U is zero and so
+
+ align:start position:0%
+and all along this line U is zero and so
+ 
+
+ align:start position:0%
+and all along this line U is zero and so
+that actually carves out that rectangle
+
+ align:start position:0%
+that actually carves out that rectangle
+ 
+
+ align:start position:0%
+that actually carves out that rectangle
+so if you were worried and you didn't
+
+ align:start position:0%
+so if you were worried and you didn't
+ 
+
+ align:start position:0%
+so if you were worried and you didn't
+you weren't able to do it that way what
+
+ align:start position:0%
+you weren't able to do it that way what
+ 
+
+ align:start position:0%
+you weren't able to do it that way what
+you could actually do is say well where
+
+ align:start position:0%
+you could actually do is say well where
+ 
+
+ align:start position:0%
+you could actually do is say well where
+does the point one2 one go if I plug in
+
+ align:start position:0%
+does the point one2 one go if I plug in
+ 
+
+ align:start position:0%
+does the point one2 one go if I plug in
+1/2 for x and one for y I notice that I
+
+ align:start position:0%
+1/2 for x and one for y I notice that I
+ 
+
+ align:start position:0%
+1/2 for x and one for y I notice that I
+get U equal 0 and V equals 2 and that's
+
+ align:start position:0%
+get U equal 0 and V equals 2 and that's
+ 
+
+ align:start position:0%
+get U equal 0 and V equals 2 and that's
+this point and so now I'm looking at
+
+ align:start position:0%
+this point and so now I'm looking at
+ 
+
+ align:start position:0%
+this point and so now I'm looking at
+this region now these two things are not
+
+ align:start position:0%
+this region now these two things are not
+ 
+
+ align:start position:0%
+this region now these two things are not
+drawn to scale because what I want to
+
+ align:start position:0%
+drawn to scale because what I want to
+ 
+
+ align:start position:0%
+drawn to scale because what I want to
+point out is they're both triangles it's
+
+ align:start position:0%
+point out is they're both triangles it's
+ 
+
+ align:start position:0%
+point out is they're both triangles it's
+easy to find the area based on how
+
+ align:start position:0%
+easy to find the area based on how
+ 
+
+ align:start position:0%
+easy to find the area based on how
+they're they sitting in two-dimensional
+
+ align:start position:0%
+they're they sitting in two-dimensional
+ 
+
+ align:start position:0%
+they're they sitting in two-dimensional
+space so what we see here is if I wanted
+
+ align:start position:0%
+space so what we see here is if I wanted
+ 
+
+ align:start position:0%
+space so what we see here is if I wanted
+to find the area of this triangle let's
+
+ align:start position:0%
+to find the area of this triangle let's
+ 
+
+ align:start position:0%
+to find the area of this triangle let's
+make this the base that base is two and
+
+ align:start position:0%
+make this the base that base is two and
+ 
+
+ align:start position:0%
+make this the base that base is two and
+the height is 1/2 so 1/2 of Base times
+
+ align:start position:0%
+the height is 1/2 so 1/2 of Base times
+ 
+
+ align:start position:0%
+the height is 1/2 so 1/2 of Base times
+height is that area is equal to 1/2 so
+
+ align:start position:0%
+height is that area is equal to 1/2 so
+ 
+
+ align:start position:0%
+height is that area is equal to 1/2 so
+the area of R is 1/2 and what's the area
+
+ align:start position:0%
+the area of R is 1/2 and what's the area
+ 
+
+ align:start position:0%
+the area of R is 1/2 and what's the area
+of this one the area of this one is well
+
+ align:start position:0%
+of this one the area of this one is well
+ 
+
+ align:start position:0%
+of this one the area of this one is well
+I've got uh base two and height two and
+
+ align:start position:0%
+I've got uh base two and height two and
+ 
+
+ align:start position:0%
+I've got uh base two and height two and
+so it's one2 of 2 * 2 and so that gives
+
+ align:start position:0%
+so it's one2 of 2 * 2 and so that gives
+ 
+
+ align:start position:0%
+so it's one2 of 2 * 2 and so that gives
+me area is two so here the area is 1/2
+
+ align:start position:0%
+me area is two so here the area is 1/2
+ 
+
+ align:start position:0%
+me area is two so here the area is 1/2
+here the area is is two and so notice
+
+ align:start position:0%
+here the area is is two and so notice
+ 
+
+ align:start position:0%
+here the area is is two and so notice
+that I've multiplied by four to get from
+
+ align:start position:0%
+that I've multiplied by four to get from
+ 
+
+ align:start position:0%
+that I've multiplied by four to get from
+here to here so I can anticipate that I
+
+ align:start position:0%
+here to here so I can anticipate that I
+ 
+
+ align:start position:0%
+here to here so I can anticipate that I
+should have based on the the principle
+
+ align:start position:0%
+should have based on the the principle
+ 
+
+ align:start position:0%
+should have based on the the principle
+you saw in lecture I should have
+
+ align:start position:0%
+you saw in lecture I should have
+ 
+
+ align:start position:0%
+you saw in lecture I should have
+something like dudv is going to equal 4
+
+ align:start position:0%
+something like dudv is going to equal 4
+ 
+
+ align:start position:0%
+something like dudv is going to equal 4
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+dxdy that is what I expect to get now
+
+ align:start position:0%
+dxdy that is what I expect to get now
+ 
+
+ align:start position:0%
+dxdy that is what I expect to get now
+let's see if when we do the the Jacobian
+
+ align:start position:0%
+let's see if when we do the the Jacobian
+ 
+
+ align:start position:0%
+let's see if when we do the the Jacobian
+we get the same thing let me double
+
+ align:start position:0%
+we get the same thing let me double
+ 
+
+ align:start position:0%
+we get the same thing let me double
+check right this is this is area two
+
+ align:start position:0%
+check right this is this is area two
+ 
+
+ align:start position:0%
+check right this is this is area two
+this is area 1/2 so I have 1/2 * 4 is
+
+ align:start position:0%
+this is area 1/2 so I have 1/2 * 4 is
+ 
+
+ align:start position:0%
+this is area 1/2 so I have 1/2 * 4 is
+going to give me two yeah that's what I
+
+ align:start position:0%
+going to give me two yeah that's what I
+ 
+
+ align:start position:0%
+going to give me two yeah that's what I
+should get okay
+
+ align:start position:0%
+should get okay
+ 
+
+ align:start position:0%
+should get okay
+okay oops that sticks out a little so
+
+ align:start position:0%
+okay oops that sticks out a little so
+ 
+
+ align:start position:0%
+okay oops that sticks out a little so
+now let's just check our check our
+
+ align:start position:0%
+now let's just check our check our
+ 
+
+ align:start position:0%
+now let's just check our check our
+Jacobian and see if that is indeed what
+
+ align:start position:0%
+Jacobian and see if that is indeed what
+ 
+
+ align:start position:0%
+Jacobian and see if that is indeed what
+we get okay so I'm going to look at uh u
+
+ align:start position:0%
+we get okay so I'm going to look at uh u
+ 
+
+ align:start position:0%
+we get okay so I'm going to look at uh u
+subx u
+
+ align:start position:0%
+subx u
+ 
+
+ align:start position:0%
+subx u
+suby v subx v suby right so U subx is 2
+
+ align:start position:0%
+suby v subx v suby right so U subx is 2
+ 
+
+ align:start position:0%
+suby v subx v suby right so U subx is 2
+U sub y is 1 so I get
+
+ align:start position:0%
+U sub y is 1 so I get
+ 
+
+ align:start position:0%
+U sub y is 1 so I get
+21 V subx is 2 V sub y is 1 so I get 2 1
+
+ align:start position:0%
+21 V subx is 2 V sub y is 1 so I get 2 1
+ 
+
+ align:start position:0%
+21 V subx is 2 V sub y is 1 so I get 2 1
+2 * 1 is 2
+
+ align:start position:0%
+2 * 1 is 2
+ 
+
+ align:start position:0%
+2 * 1 is 2
+minus -2 gives me indeed four so I do
+
+ align:start position:0%
+minus -2 gives me indeed four so I do
+ 
+
+ align:start position:0%
+minus -2 gives me indeed four so I do
+get in fact du DV is equal to 4
+
+ align:start position:0%
+get in fact du DV is equal to 4
+ 
+
+ align:start position:0%
+get in fact du DV is equal to 4
+dxdy so I know that I'm going to have to
+
+ align:start position:0%
+dxdy so I know that I'm going to have to
+ 
+
+ align:start position:0%
+dxdy so I know that I'm going to have to
+because I'm changing variables though
+
+ align:start position:0%
+because I'm changing variables though
+ 
+
+ align:start position:0%
+because I'm changing variables though
+from dxdy to duv I'm going to divide by
+
+ align:start position:0%
+from dxdy to duv I'm going to divide by
+ 
+
+ align:start position:0%
+from dxdy to duv I'm going to divide by
+four obviously when I do the
+
+ align:start position:0%
+four obviously when I do the
+ 
+
+ align:start position:0%
+four obviously when I do the
+substitution the substitution will be
+
+ align:start position:0%
+substitution the substitution will be
+ 
+
+ align:start position:0%
+substitution the substitution will be
+replacing just
+
+ align:start position:0%
+replacing just
+ 
+
+ align:start position:0%
+replacing just
+dxdy so I just mentioned that but notice
+
+ align:start position:0%
+dxdy so I just mentioned that but notice
+ 
+
+ align:start position:0%
+dxdy so I just mentioned that but notice
+again we get what we expect to get we
+
+ align:start position:0%
+again we get what we expect to get we
+ 
+
+ align:start position:0%
+again we get what we expect to get we
+got a four based on the the the picture
+
+ align:start position:0%
+got a four based on the the the picture
+ 
+
+ align:start position:0%
+got a four based on the the the picture
+and we get a four based on the
+
+ align:start position:0%
+and we get a four based on the
+ 
+
+ align:start position:0%
+and we get a four based on the
+Jacobian and so now we we need to finish
+
+ align:start position:0%
+Jacobian and so now we we need to finish
+ 
+
+ align:start position:0%
+Jacobian and so now we we need to finish
+up the process we need to figure out how
+
+ align:start position:0%
+up the process we need to figure out how
+ 
+
+ align:start position:0%
+up the process we need to figure out how
+to write this in terms of u and v and
+
+ align:start position:0%
+to write this in terms of u and v and
+ 
+
+ align:start position:0%
+to write this in terms of u and v and
+then figure out our bounds in terms of u
+
+ align:start position:0%
+then figure out our bounds in terms of u
+ 
+
+ align:start position:0%
+then figure out our bounds in terms of u
+and v and then we're done okay so let me
+
+ align:start position:0%
+and v and then we're done okay so let me
+ 
+
+ align:start position:0%
+and v and then we're done okay so let me
+mention one thing you should notice is
+
+ align:start position:0%
+mention one thing you should notice is
+ 
+
+ align:start position:0%
+mention one thing you should notice is
+that U * V is equal to exactly this is a
+
+ align:start position:0%
+that U * V is equal to exactly this is a
+ 
+
+ align:start position:0%
+that U * V is equal to exactly this is a
+this is going to be a difference of two
+
+ align:start position:0%
+this is going to be a difference of two
+ 
+
+ align:start position:0%
+this is going to be a difference of two
+squares and it is precisely 4x^2 minus
+
+ align:start position:0%
+squares and it is precisely 4x^2 minus
+ 
+
+ align:start position:0%
+squares and it is precisely 4x^2 minus
+y^2 if you need to multiply it out to
+
+ align:start position:0%
+y^2 if you need to multiply it out to
+ 
+
+ align:start position:0%
+y^2 if you need to multiply it out to
+check that's you can check it but that's
+
+ align:start position:0%
+check that's you can check it but that's
+ 
+
+ align:start position:0%
+check that's you can check it but that's
+indeed what it is which is why this
+
+ align:start position:0%
+indeed what it is which is why this
+ 
+
+ align:start position:0%
+indeed what it is which is why this
+particular substitution is quite nice
+
+ align:start position:0%
+particular substitution is quite nice
+ 
+
+ align:start position:0%
+particular substitution is quite nice
+because that means this function I'm
+
+ align:start position:0%
+because that means this function I'm
+ 
+
+ align:start position:0%
+because that means this function I'm
+supposed to be integrating is just UV
+
+ align:start position:0%
+supposed to be integrating is just UV
+ 
+
+ align:start position:0%
+supposed to be integrating is just UV
+raised to 4th so I'm almost done so let
+
+ align:start position:0%
+raised to 4th so I'm almost done so let
+ 
+
+ align:start position:0%
+raised to 4th so I'm almost done so let
+me write in the pieces I know and then
+
+ align:start position:0%
+me write in the pieces I know and then
+ 
+
+ align:start position:0%
+me write in the pieces I know and then
+we'll fill in the last two spots or four
+
+ align:start position:0%
+we'll fill in the last two spots or four
+ 
+
+ align:start position:0%
+we'll fill in the last two spots or four
+spots which will be all the bounds on
+
+ align:start position:0%
+spots which will be all the bounds on
+ 
+
+ align:start position:0%
+spots which will be all the bounds on
+the integral so I'm going to write it
+
+ align:start position:0%
+the integral so I'm going to write it
+ 
+
+ align:start position:0%
+the integral so I'm going to write it
+here give myself some space to write the
+
+ align:start position:0%
+here give myself some space to write the
+ 
+
+ align:start position:0%
+here give myself some space to write the
+bounds and then so I'm replacing the
+
+ align:start position:0%
+bounds and then so I'm replacing the
+ 
+
+ align:start position:0%
+bounds and then so I'm replacing the
+4x^2 minus y^2 by a UV so I'm going to
+
+ align:start position:0%
+4x^2 minus y^2 by a UV so I'm going to
+ 
+
+ align:start position:0%
+4x^2 minus y^2 by a UV so I'm going to
+get U * V and then the function is
+
+ align:start position:0%
+get U * V and then the function is
+ 
+
+ align:start position:0%
+get U * V and then the function is
+raised that is raised to the 4th in the
+
+ align:start position:0%
+raised that is raised to the 4th in the
+ 
+
+ align:start position:0%
+raised that is raised to the 4th in the
+in the initial problem so I raise that
+
+ align:start position:0%
+in the initial problem so I raise that
+ 
+
+ align:start position:0%
+in the initial problem so I raise that
+to the fourth then dxdy as I mentioned
+
+ align:start position:0%
+to the fourth then dxdy as I mentioned
+ 
+
+ align:start position:0%
+to the fourth then dxdy as I mentioned
+will be replaced by a DV / 4 and so I
+
+ align:start position:0%
+will be replaced by a DV / 4 and so I
+ 
+
+ align:start position:0%
+will be replaced by a DV / 4 and so I
+can just put this over four and write uh
+
+ align:start position:0%
+can just put this over four and write uh
+ 
+
+ align:start position:0%
+can just put this over four and write uh
+duv well I should be careful which order
+
+ align:start position:0%
+duv well I should be careful which order
+ 
+
+ align:start position:0%
+duv well I should be careful which order
+I want to do doesn't really matter I can
+
+ align:start position:0%
+I want to do doesn't really matter I can
+ 
+
+ align:start position:0%
+I want to do doesn't really matter I can
+do either
+
+ align:start position:0%
+do either
+ 
+
+ align:start position:0%
+do either
+one du DV okay and so now I want to know
+
+ align:start position:0%
+one du DV okay and so now I want to know
+ 
+
+ align:start position:0%
+one du DV okay and so now I want to know
+what U goes from and to and then what V
+
+ align:start position:0%
+what U goes from and to and then what V
+ 
+
+ align:start position:0%
+what U goes from and to and then what V
+has to go from and to so if I come over
+
+ align:start position:0%
+has to go from and to so if I come over
+ 
+
+ align:start position:0%
+has to go from and to so if I come over
+here you'll see it didn't matter because
+
+ align:start position:0%
+here you'll see it didn't matter because
+ 
+
+ align:start position:0%
+here you'll see it didn't matter because
+I could have picked either direction to
+
+ align:start position:0%
+I could have picked either direction to
+ 
+
+ align:start position:0%
+I could have picked either direction to
+go but if I'm going to go
+
+ align:start position:0%
+go but if I'm going to go
+ 
+
+ align:start position:0%
+go but if I'm going to go
+with u I'm coming from whatever this
+
+ align:start position:0%
+with u I'm coming from whatever this
+ 
+
+ align:start position:0%
+with u I'm coming from whatever this
+function is over to here right and this
+
+ align:start position:0%
+function is over to here right and this
+ 
+
+ align:start position:0%
+function is over to here right and this
+value here is easy that's U equals 0 so
+
+ align:start position:0%
+value here is easy that's U equals 0 so
+ 
+
+ align:start position:0%
+value here is easy that's U equals 0 so
+the top Bound for U is zero and the
+
+ align:start position:0%
+the top Bound for U is zero and the
+ 
+
+ align:start position:0%
+the top Bound for U is zero and the
+bottom Bound for U this is V is equal to
+
+ align:start position:0%
+bottom Bound for U this is V is equal to
+ 
+
+ align:start position:0%
+bottom Bound for U this is V is equal to
+minus U so the bottom Bound for U is
+
+ align:start position:0%
+minus U so the bottom Bound for U is
+ 
+
+ align:start position:0%
+minus U so the bottom Bound for U is
+When U is equal to negative V so I'm
+
+ align:start position:0%
+When U is equal to negative V so I'm
+ 
+
+ align:start position:0%
+When U is equal to negative V so I'm
+running from because I put the DU on the
+
+ align:start position:0%
+running from because I put the DU on the
+ 
+
+ align:start position:0%
+running from because I put the DU on the
+inside my first one is running from
+
+ align:start position:0%
+inside my first one is running from
+ 
+
+ align:start position:0%
+inside my first one is running from
+minus V to what did I say zero and then
+
+ align:start position:0%
+minus V to what did I say zero and then
+ 
+
+ align:start position:0%
+minus V to what did I say zero and then
+the V values from there go between zero
+
+ align:start position:0%
+the V values from there go between zero
+ 
+
+ align:start position:0%
+the V values from there go between zero
+and two you can see this easily from the
+
+ align:start position:0%
+and two you can see this easily from the
+ 
+
+ align:start position:0%
+and two you can see this easily from the
+picture so they go between Z and
+
+ align:start position:0%
+picture so they go between Z and
+ 
+
+ align:start position:0%
+picture so they go between Z and
+two and I am not going to finish it off
+
+ align:start position:0%
+two and I am not going to finish it off
+ 
+
+ align:start position:0%
+two and I am not going to finish it off
+from here because it would require not
+
+ align:start position:0%
+from here because it would require not
+ 
+
+ align:start position:0%
+from here because it would require not
+too much work it's actually quite simple
+
+ align:start position:0%
+too much work it's actually quite simple
+ 
+
+ align:start position:0%
+too much work it's actually quite simple
+because it's just it's just a polinomial
+
+ align:start position:0%
+because it's just it's just a polinomial
+ 
+
+ align:start position:0%
+because it's just it's just a polinomial
+in U and a polinomial in V but there are
+
+ align:start position:0%
+in U and a polinomial in V but there are
+ 
+
+ align:start position:0%
+in U and a polinomial in V but there are
+a lot of powers and there will be big
+
+ align:start position:0%
+a lot of powers and there will be big
+ 
+
+ align:start position:0%
+a lot of powers and there will be big
+powers of two so suffice it to say at
+
+ align:start position:0%
+powers of two so suffice it to say at
+ 
+
+ align:start position:0%
+powers of two so suffice it to say at
+this point we can evaluate this integral
+
+ align:start position:0%
+this point we can evaluate this integral
+ 
+
+ align:start position:0%
+this point we can evaluate this integral
+and it's quite easy to evaluate and the
+
+ align:start position:0%
+and it's quite easy to evaluate and the
+ 
+
+ align:start position:0%
+and it's quite easy to evaluate and the
+main point I think we should make is how
+
+ align:start position:0%
+main point I think we should make is how
+ 
+
+ align:start position:0%
+main point I think we should make is how
+did it make it simpler I mean the the
+
+ align:start position:0%
+did it make it simpler I mean the the
+ 
+
+ align:start position:0%
+did it make it simpler I mean the the
+initial problem if we come over
+
+ align:start position:0%
+initial problem if we come over
+ 
+
+ align:start position:0%
+initial problem if we come over
+here this is annoying to to find an
+
+ align:start position:0%
+here this is annoying to to find an
+ 
+
+ align:start position:0%
+here this is annoying to to find an
+anti-derivative but not impossible but
+
+ align:start position:0%
+anti-derivative but not impossible but
+ 
+
+ align:start position:0%
+anti-derivative but not impossible but
+the really annoying part is kind of I
+
+ align:start position:0%
+the really annoying part is kind of I
+ 
+
+ align:start position:0%
+the really annoying part is kind of I
+would have to take this region and split
+
+ align:start position:0%
+would have to take this region and split
+ 
+
+ align:start position:0%
+would have to take this region and split
+it into a bunch of pieces or at least
+
+ align:start position:0%
+it into a bunch of pieces or at least
+ 
+
+ align:start position:0%
+it into a bunch of pieces or at least
+two pieces to to evaluate the integral
+
+ align:start position:0%
+two pieces to to evaluate the integral
+ 
+
+ align:start position:0%
+two pieces to to evaluate the integral
+in a reasonable way or my yv values
+
+ align:start position:0%
+in a reasonable way or my yv values
+ 
+
+ align:start position:0%
+in a reasonable way or my yv values
+would go from this line here up to this
+
+ align:start position:0%
+would go from this line here up to this
+ 
+
+ align:start position:0%
+would go from this line here up to this
+line here could be complicated so what
+
+ align:start position:0%
+line here could be complicated so what
+ 
+
+ align:start position:0%
+line here could be complicated so what
+we've really done is we've simplified
+
+ align:start position:0%
+we've really done is we've simplified
+ 
+
+ align:start position:0%
+we've really done is we've simplified
+the region that's the the easiest thing
+
+ align:start position:0%
+the region that's the the easiest thing
+ 
+
+ align:start position:0%
+the region that's the the easiest thing
+I mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry we also simplified the function
+
+ align:start position:0%
+sorry we also simplified the function
+ 
+
+ align:start position:0%
+sorry we also simplified the function
+but we've we've really simplified the
+
+ align:start position:0%
+but we've we've really simplified the
+ 
+
+ align:start position:0%
+but we've we've really simplified the
+region we're integrating over and so we
+
+ align:start position:0%
+region we're integrating over and so we
+ 
+
+ align:start position:0%
+region we're integrating over and so we
+only have one is a one is a function and
+
+ align:start position:0%
+only have one is a one is a function and
+ 
+
+ align:start position:0%
+only have one is a one is a function and
+one is a constant and that's quite nice
+
+ align:start position:0%
+one is a constant and that's quite nice
+ 
+
+ align:start position:0%
+one is a constant and that's quite nice
+to have on the inside so I think that's
+
+ align:start position:0%
+to have on the inside so I think that's
+ 
+
+ align:start position:0%
+to have on the inside so I think that's
+where I'll stop
\ No newline at end of file
diff --git a/lU_QT5GSuxI.txt b/lU_QT5GSuxI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f671eee479feedb29ab5e80d9d33c366fe557cdf
--- /dev/null
+++ b/lU_QT5GSuxI.txt
@@ -0,0 +1,1035 @@
+align:start position:0%
+ 
+our method for estimating sums can also
+
+ align:start position:0%
+our method for estimating sums can also
+ 
+
+ align:start position:0%
+our method for estimating sums can also
+be used to estimate products basically
+
+ align:start position:0%
+be used to estimate products basically
+ 
+
+ align:start position:0%
+be used to estimate products basically
+by taking logs to turn a product into a
+
+ align:start position:0%
+by taking logs to turn a product into a
+ 
+
+ align:start position:0%
+by taking logs to turn a product into a
+sum and we're going to use that to come
+
+ align:start position:0%
+sum and we're going to use that to come
+ 
+
+ align:start position:0%
+sum and we're going to use that to come
+up with another important estimate of a
+
+ align:start position:0%
+up with another important estimate of a
+ 
+
+ align:start position:0%
+up with another important estimate of a
+quantity that will come up really very
+
+ align:start position:0%
+quantity that will come up really very
+ 
+
+ align:start position:0%
+quantity that will come up really very
+regularly called n factorial so n
+
+ align:start position:0%
+regularly called n factorial so n
+ 
+
+ align:start position:0%
+regularly called n factorial so n
+factorial is the product of the first n
+
+ align:start position:0%
+factorial is the product of the first n
+ 
+
+ align:start position:0%
+factorial is the product of the first n
+integers 1 times 2 of little n minus 1
+
+ align:start position:0%
+integers 1 times 2 of little n minus 1
+ 
+
+ align:start position:0%
+integers 1 times 2 of little n minus 1
+times n and concise product notation
+
+ align:start position:0%
+times n and concise product notation
+ 
+
+ align:start position:0%
+times n and concise product notation
+it's the product that's PI capital ply
+
+ align:start position:0%
+it's the product that's PI capital ply
+ 
+
+ align:start position:0%
+it's the product that's PI capital ply
+for product from I equals 1 to N of I
+
+ align:start position:0%
+for product from I equals 1 to N of I
+ 
+
+ align:start position:0%
+for product from I equals 1 to N of I
+and it's standard abbreviation is to
+
+ align:start position:0%
+and it's standard abbreviation is to
+ 
+
+ align:start position:0%
+and it's standard abbreviation is to
+write it as n bank pronounced n
+
+ align:start position:0%
+write it as n bank pronounced n
+ 
+
+ align:start position:0%
+write it as n bank pronounced n
+factorial so what I'd like to do is get
+
+ align:start position:0%
+factorial so what I'd like to do is get
+ 
+
+ align:start position:0%
+factorial so what I'd like to do is get
+an asymptotic estimate for n factorial
+
+ align:start position:0%
+an asymptotic estimate for n factorial
+ 
+
+ align:start position:0%
+an asymptotic estimate for n factorial
+again n factorial is one of these
+
+ align:start position:0%
+again n factorial is one of these
+ 
+
+ align:start position:0%
+again n factorial is one of these
+quantities where there isn't any exact
+
+ align:start position:0%
+quantities where there isn't any exact
+ 
+
+ align:start position:0%
+quantities where there isn't any exact
+formula that doesn't have those ellipses
+
+ align:start position:0%
+formula that doesn't have those ellipses
+ 
+
+ align:start position:0%
+formula that doesn't have those ellipses
+in it there's no short formula with
+
+ align:start position:0%
+in it there's no short formula with
+ 
+
+ align:start position:0%
+in it there's no short formula with
+basic operations fixed size up formula
+
+ align:start position:0%
+basic operations fixed size up formula
+ 
+
+ align:start position:0%
+basic operations fixed size up formula
+that expresses n factorial but we get a
+
+ align:start position:0%
+that expresses n factorial but we get a
+ 
+
+ align:start position:0%
+that expresses n factorial but we get a
+nice formula for a tight asymptotic
+
+ align:start position:0%
+nice formula for a tight asymptotic
+ 
+
+ align:start position:0%
+nice formula for a tight asymptotic
+estimate so as I said the first trick is
+
+ align:start position:0%
+estimate so as I said the first trick is
+ 
+
+ align:start position:0%
+estimate so as I said the first trick is
+to turn the product into a sum by taking
+
+ align:start position:0%
+to turn the product into a sum by taking
+ 
+
+ align:start position:0%
+to turn the product into a sum by taking
+logs so log of n factorial is the log of
+
+ align:start position:0%
+logs so log of n factorial is the log of
+ 
+
+ align:start position:0%
+logs so log of n factorial is the log of
+1 the product of 1 through n but a log
+
+ align:start position:0%
+1 the product of 1 through n but a log
+ 
+
+ align:start position:0%
+1 the product of 1 through n but a log
+of a product is the sum of the logs so
+
+ align:start position:0%
+of a product is the sum of the logs so
+ 
+
+ align:start position:0%
+of a product is the sum of the logs so
+it's simply log of 1 plus log of 2 up
+
+ align:start position:0%
+it's simply log of 1 plus log of 2 up
+ 
+
+ align:start position:0%
+it's simply log of 1 plus log of 2 up
+through log of n and expressed in some
+
+ align:start position:0%
+through log of n and expressed in some
+ 
+
+ align:start position:0%
+through log of n and expressed in some
+notation it's the sum from I equals 1 to
+
+ align:start position:0%
+notation it's the sum from I equals 1 to
+ 
+
+ align:start position:0%
+notation it's the sum from I equals 1 to
+N of log of log of a my now the integral
+
+ align:start position:0%
+N of log of log of a my now the integral
+ 
+
+ align:start position:0%
+N of log of log of a my now the integral
+method gives us a way to estimate this
+
+ align:start position:0%
+method gives us a way to estimate this
+ 
+
+ align:start position:0%
+method gives us a way to estimate this
+sum by bracketing it between the values
+
+ align:start position:0%
+sum by bracketing it between the values
+ 
+
+ align:start position:0%
+sum by bracketing it between the values
+of some integrals namely restating the
+
+ align:start position:0%
+of some integrals namely restating the
+ 
+
+ align:start position:0%
+of some integrals namely restating the
+the integral method for some metaphor
+
+ align:start position:0%
+the integral method for some metaphor
+ 
+
+ align:start position:0%
+the integral method for some metaphor
+for bounding integrals by sums this time
+
+ align:start position:0%
+for bounding integrals by sums this time
+ 
+
+ align:start position:0%
+for bounding integrals by sums this time
+we're looking at an increasing function
+
+ align:start position:0%
+we're looking at an increasing function
+ 
+
+ align:start position:0%
+we're looking at an increasing function
+because it's log of X let F be a weakly
+
+ align:start position:0%
+because it's log of X let F be a weakly
+ 
+
+ align:start position:0%
+because it's log of X let F be a weakly
+increasing function from positive reals
+
+ align:start position:0%
+increasing function from positive reals
+ 
+
+ align:start position:0%
+increasing function from positive reals
+to positive reals I'm interested in the
+
+ align:start position:0%
+to positive reals I'm interested in the
+ 
+
+ align:start position:0%
+to positive reals I'm interested in the
+sum from I equals 1 to N of F of I and I
+
+ align:start position:0%
+sum from I equals 1 to N of F of I and I
+ 
+
+ align:start position:0%
+sum from I equals 1 to N of F of I and I
+want to relate it and bound it by the
+
+ align:start position:0%
+want to relate it and bound it by the
+ 
+
+ align:start position:0%
+want to relate it and bound it by the
+integral from 0 from 1 to N of f of X
+
+ align:start position:0%
+integral from 0 from 1 to N of f of X
+ 
+
+ align:start position:0%
+integral from 0 from 1 to N of f of X
+where in this case the particular F that
+
+ align:start position:0%
+where in this case the particular F that
+ 
+
+ align:start position:0%
+where in this case the particular F that
+we're interested in is f of X is log X
+
+ align:start position:0%
+we're interested in is f of X is log X
+ 
+
+ align:start position:0%
+we're interested in is f of X is log X
+and the theorem says that with
+
+ align:start position:0%
+and the theorem says that with
+ 
+
+ align:start position:0%
+and the theorem says that with
+increasing functions S is bracketed
+
+ align:start position:0%
+increasing functions S is bracketed
+ 
+
+ align:start position:0%
+increasing functions S is bracketed
+between the integral plus the
+
+ align:start position:0%
+between the integral plus the
+ 
+
+ align:start position:0%
+between the integral plus the
+term in the sum and the integral plus
+
+ align:start position:0%
+term in the sum and the integral plus
+ 
+
+ align:start position:0%
+term in the sum and the integral plus
+the first term in the sum remember since
+
+ align:start position:0%
+the first term in the sum remember since
+ 
+
+ align:start position:0%
+the first term in the sum remember since
+the functions weakly increasing f of 1
+
+ align:start position:0%
+the functions weakly increasing f of 1
+ 
+
+ align:start position:0%
+the functions weakly increasing f of 1
+is smaller than f of n so that's the way
+
+ align:start position:0%
+is smaller than f of n so that's the way
+ 
+
+ align:start position:0%
+is smaller than f of n so that's the way
+you remember which way the bounds go so
+
+ align:start position:0%
+you remember which way the bounds go so
+ 
+
+ align:start position:0%
+you remember which way the bounds go so
+s is between I plus F of 1 and I plus F
+
+ align:start position:0%
+s is between I plus F of 1 and I plus F
+ 
+
+ align:start position:0%
+s is between I plus F of 1 and I plus F
+of n by our general formula for applying
+
+ align:start position:0%
+of n by our general formula for applying
+ 
+
+ align:start position:0%
+of n by our general formula for applying
+integral balance to sums well what that
+
+ align:start position:0%
+integral balance to sums well what that
+ 
+
+ align:start position:0%
+integral balance to sums well what that
+tells us then is that the sum from 1 to
+
+ align:start position:0%
+tells us then is that the sum from 1 to
+ 
+
+ align:start position:0%
+tells us then is that the sum from 1 to
+N of log of I which is what we're
+
+ align:start position:0%
+N of log of I which is what we're
+ 
+
+ align:start position:0%
+N of log of I which is what we're
+interested in is bracketed between the
+
+ align:start position:0%
+interested in is bracketed between the
+ 
+
+ align:start position:0%
+interested in is bracketed between the
+integral from 1 to N of log X and the
+
+ align:start position:0%
+integral from 1 to N of log X and the
+ 
+
+ align:start position:0%
+integral from 1 to N of log X and the
+integral from 1 to N well it's plus log
+
+ align:start position:0%
+integral from 1 to N well it's plus log
+ 
+
+ align:start position:0%
+integral from 1 to N well it's plus log
+of 0 but a log of 1 rather but that's 0
+
+ align:start position:0%
+of 0 but a log of 1 rather but that's 0
+ 
+
+ align:start position:0%
+of 0 but a log of 1 rather but that's 0
+and the integral from 1 to N of log of X
+
+ align:start position:0%
+and the integral from 1 to N of log of X
+ 
+
+ align:start position:0%
+and the integral from 1 to N of log of X
+plus the last term which is log of n ok
+
+ align:start position:0%
+plus the last term which is log of n ok
+ 
+
+ align:start position:0%
+plus the last term which is log of n ok
+in case you don't remember from first
+
+ align:start position:0%
+in case you don't remember from first
+ 
+
+ align:start position:0%
+in case you don't remember from first
+term calculus the integral from of log
+
+ align:start position:0%
+term calculus the integral from of log
+ 
+
+ align:start position:0%
+term calculus the integral from of log
+of X is in fact has the indefinite
+
+ align:start position:0%
+of X is in fact has the indefinite
+ 
+
+ align:start position:0%
+of X is in fact has the indefinite
+integral is X log of x over E which you
+
+ align:start position:0%
+integral is X log of x over E which you
+ 
+
+ align:start position:0%
+integral is X log of x over E which you
+can easily check by differentiating X
+
+ align:start position:0%
+can easily check by differentiating X
+ 
+
+ align:start position:0%
+can easily check by differentiating X
+log X over e ln means natural log
+
+ align:start position:0%
+log X over e ln means natural log
+ 
+
+ align:start position:0%
+log X over e ln means natural log
+remember in computer science l OG log
+
+ align:start position:0%
+remember in computer science l OG log
+ 
+
+ align:start position:0%
+remember in computer science l OG log
+means log to the base 2 unless you
+
+ align:start position:0%
+means log to the base 2 unless you
+ 
+
+ align:start position:0%
+means log to the base 2 unless you
+explicitly put some base on it like log
+
+ align:start position:0%
+explicitly put some base on it like log
+ 
+
+ align:start position:0%
+explicitly put some base on it like log
+L o G sub 10 so ellen is the natural log
+
+ align:start position:0%
+L o G sub 10 so ellen is the natural log
+ 
+
+ align:start position:0%
+L o G sub 10 so ellen is the natural log
+from calculus and plugging in this value
+
+ align:start position:0%
+from calculus and plugging in this value
+ 
+
+ align:start position:0%
+from calculus and plugging in this value
+for the indefinite integral of log of X
+
+ align:start position:0%
+for the indefinite integral of log of X
+ 
+
+ align:start position:0%
+for the indefinite integral of log of X
+and using the bounds 1/n what we come up
+
+ align:start position:0%
+and using the bounds 1/n what we come up
+ 
+
+ align:start position:0%
+and using the bounds 1/n what we come up
+with is that the sum of the logs is
+
+ align:start position:0%
+with is that the sum of the logs is
+ 
+
+ align:start position:0%
+with is that the sum of the logs is
+bounded between n Times log and over E
+
+ align:start position:0%
+bounded between n Times log and over E
+ 
+
+ align:start position:0%
+bounded between n Times log and over E
+and n Times log and over e plus log of n
+
+ align:start position:0%
+and n Times log and over e plus log of n
+ 
+
+ align:start position:0%
+and n Times log and over e plus log of n
+it's a pretty tight bounds what that
+
+ align:start position:0%
+it's a pretty tight bounds what that
+ 
+
+ align:start position:0%
+it's a pretty tight bounds what that
+means is that informally speaking the
+
+ align:start position:0%
+means is that informally speaking the
+ 
+
+ align:start position:0%
+means is that informally speaking the
+sum of the logs is about this term Plus
+
+ align:start position:0%
+sum of the logs is about this term Plus
+ 
+
+ align:start position:0%
+sum of the logs is about this term Plus
+that term Plus let's take the average
+
+ align:start position:0%
+that term Plus let's take the average
+ 
+
+ align:start position:0%
+that term Plus let's take the average
+value of that term which is half this
+
+ align:start position:0%
+value of that term which is half this
+ 
+
+ align:start position:0%
+value of that term which is half this
+term so we could say that the sum of the
+
+ align:start position:0%
+term so we could say that the sum of the
+ 
+
+ align:start position:0%
+term so we could say that the sum of the
+logs is approximately equal that's a
+
+ align:start position:0%
+logs is approximately equal that's a
+ 
+
+ align:start position:0%
+logs is approximately equal that's a
+little vague but live with it n log n
+
+ align:start position:0%
+little vague but live with it n log n
+ 
+
+ align:start position:0%
+little vague but live with it n log n
+over e plus a lot half of log n well now
+
+ align:start position:0%
+over e plus a lot half of log n well now
+ 
+
+ align:start position:0%
+over e plus a lot half of log n well now
+if I'm interest to remember in an
+
+ align:start position:0%
+if I'm interest to remember in an
+ 
+
+ align:start position:0%
+if I'm interest to remember in an
+estimate for n factorial so let's
+
+ align:start position:0%
+estimate for n factorial so let's
+ 
+
+ align:start position:0%
+estimate for n factorial so let's
+exponentiate both sides so taking eita
+
+ align:start position:0%
+exponentiate both sides so taking eita
+ 
+
+ align:start position:0%
+exponentiate both sides so taking eita
+this sum gives me a product of e to the
+
+ align:start position:0%
+this sum gives me a product of e to the
+ 
+
+ align:start position:0%
+this sum gives me a product of e to the
+e to this times e to that well eat to
+
+ align:start position:0%
+e to this times e to that well eat to
+ 
+
+ align:start position:0%
+e to this times e to that well eat to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is really--it's e to the log of n over e
+
+ align:start position:0%
+is really--it's e to the log of n over e
+ 
+
+ align:start position:0%
+is really--it's e to the log of n over e
+to the nth power which means it's n over
+
+ align:start position:0%
+to the nth power which means it's n over
+ 
+
+ align:start position:0%
+to the nth power which means it's n over
+e to the N and this is e to the log of n
+
+ align:start position:0%
+e to the N and this is e to the log of n
+ 
+
+ align:start position:0%
+e to the N and this is e to the log of n
+to the power half or square root of n so
+
+ align:start position:0%
+to the power half or square root of n so
+ 
+
+ align:start position:0%
+to the power half or square root of n so
+we wind up with n factorial is
+
+ align:start position:0%
+we wind up with n factorial is
+ 
+
+ align:start position:0%
+we wind up with n factorial is
+approximately equal to the square root
+
+ align:start position:0%
+approximately equal to the square root
+ 
+
+ align:start position:0%
+approximately equal to the square root
+of n times n over e to the N now this
+
+ align:start position:0%
+of n times n over e to the N now this
+ 
+
+ align:start position:0%
+of n times n over e to the N now this
+approximately equal is imprecise it's
+
+ align:start position:0%
+approximately equal is imprecise it's
+ 
+
+ align:start position:0%
+approximately equal is imprecise it's
+not asymptotically equal because we were
+
+ align:start position:0%
+not asymptotically equal because we were
+ 
+
+ align:start position:0%
+not asymptotically equal because we were
+doing an arithmetic average of zero and
+
+ align:start position:0%
+doing an arithmetic average of zero and
+ 
+
+ align:start position:0%
+doing an arithmetic average of zero and
+log n over two in addition it's very
+
+ align:start position:0%
+log n over two in addition it's very
+ 
+
+ align:start position:0%
+log n over two in addition it's very
+dangerous when you have two things that
+
+ align:start position:0%
+dangerous when you have two things that
+ 
+
+ align:start position:0%
+dangerous when you have two things that
+are approximately equal to exponentiate
+
+ align:start position:0%
+are approximately equal to exponentiate
+ 
+
+ align:start position:0%
+are approximately equal to exponentiate
+them and expect that they're still
+
+ align:start position:0%
+them and expect that they're still
+ 
+
+ align:start position:0%
+them and expect that they're still
+approximately equal often they aren't
+
+ align:start position:0%
+approximately equal often they aren't
+ 
+
+ align:start position:0%
+approximately equal often they aren't
+but nevertheless this is a kind of a
+
+ align:start position:0%
+but nevertheless this is a kind of a
+ 
+
+ align:start position:0%
+but nevertheless this is a kind of a
+heuristic derivation of some kind of
+
+ align:start position:0%
+heuristic derivation of some kind of
+ 
+
+ align:start position:0%
+heuristic derivation of some kind of
+asymptotic estimate that we would expect
+
+ align:start position:0%
+asymptotic estimate that we would expect
+ 
+
+ align:start position:0%
+asymptotic estimate that we would expect
+that n factorial was roughly like the
+
+ align:start position:0%
+that n factorial was roughly like the
+ 
+
+ align:start position:0%
+that n factorial was roughly like the
+square root of n times n over e to the
+
+ align:start position:0%
+square root of n times n over e to the
+ 
+
+ align:start position:0%
+square root of n times n over e to the
+enth power and it turns out that it's
+
+ align:start position:0%
+enth power and it turns out that it's
+ 
+
+ align:start position:0%
+enth power and it turns out that it's
+that this heuristic gives a pretty
+
+ align:start position:0%
+that this heuristic gives a pretty
+ 
+
+ align:start position:0%
+that this heuristic gives a pretty
+accurate answer a precise approximation
+
+ align:start position:0%
+accurate answer a precise approximation
+ 
+
+ align:start position:0%
+accurate answer a precise approximation
+is that n factorial is actually
+
+ align:start position:0%
+is that n factorial is actually
+ 
+
+ align:start position:0%
+is that n factorial is actually
+asymptotically equal to the square root
+
+ align:start position:0%
+asymptotically equal to the square root
+ 
+
+ align:start position:0%
+asymptotically equal to the square root
+of 2 pi n times n over e to the end and
+
+ align:start position:0%
+of 2 pi n times n over e to the end and
+ 
+
+ align:start position:0%
+of 2 pi n times n over e to the end and
+we're not going to prove that it
+
+ align:start position:0%
+we're not going to prove that it
+ 
+
+ align:start position:0%
+we're not going to prove that it
+requires elementary calculus but more
+
+ align:start position:0%
+requires elementary calculus but more
+ 
+
+ align:start position:0%
+requires elementary calculus but more
+than we want to take time for and this
+
+ align:start position:0%
+than we want to take time for and this
+ 
+
+ align:start position:0%
+than we want to take time for and this
+crucial formula though that we will be
+
+ align:start position:0%
+crucial formula though that we will be
+ 
+
+ align:start position:0%
+crucial formula though that we will be
+using very regularly to estimate the
+
+ align:start position:0%
+using very regularly to estimate the
+ 
+
+ align:start position:0%
+using very regularly to estimate the
+size of n factorial is called Sterling's
+
+ align:start position:0%
+size of n factorial is called Sterling's
+ 
+
+ align:start position:0%
+size of n factorial is called Sterling's
+formula and it's one to have on your
+
+ align:start position:0%
+formula and it's one to have on your
+ 
+
+ align:start position:0%
+formula and it's one to have on your
+crib sheets if you haven't memorized it
\ No newline at end of file
diff --git a/mnkTn0Y6GsU.txt b/mnkTn0Y6GsU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..febcd9320991dc7ed9e54419f39018f10a977954
--- /dev/null
+++ b/mnkTn0Y6GsU.txt
@@ -0,0 +1,3055 @@
+PROFESSOR: So OK, what
+did we do last time?
+
+Thanks for coming
+back by the way.
+
+So last time, we
+did MDS codes.
+
+MDS codes, and we
+looked at this.
+
+And we derived some generic
+properties of these things if
+
+they existed.
+
+And then eventually, we moved
+to Reed-Solomon codes.
+
+And so indeed, they exist.
+
+We talked a little bit about
+existence altogether, the main
+
+conjection, MDS codes,
+I just wrote it down.
+
+And like I said, you
+want to be rich and
+
+famous, solve this.
+
+There's people doing geometry
+in math that would be
+
+deliriously happy if
+you solved it.
+
+So if for nothing else.
+
+So the last thing I wrote down
+last time was something about
+
+a matrix which somebody
+recognized as some Fourier
+
+transform matrix.
+
+And that's where I want to pick
+up here, at least quickly
+
+make that connection.
+
+So let me rewrite the definition
+of Reed-Solomon
+
+codes again.
+
+And so a Reed-Solomon code,
+the way we defined it last
+
+time was all field elements,
+we would evaluate the
+
+polynomial in all
+field elements.
+
+Now we do it slightly
+different.
+
+Let me make it Solomon-Stein
+in order to denote that
+
+difference.
+
+And let's say this is
+beta 0, beta n.
+
+So that's the old definition.
+
+Only the, let's say, the beta 0,
+beta 1, up to beta n, they
+
+are the non-zero elements now.
+
+And just for the heck of it, so
+we talked about punctured
+
+Reed-Solomon codes last
+time that it would
+
+still be MDS codes.
+
+So nothing has changed there.
+
+In particular, all the arguments
+would be the same.
+
+In particular, just to humor me,
+let's say beta i is omega
+
+to the i, where omega
+is primitive in Fq.
+
+So what that means, you remember
+that primitive means
+
+that the powers of omega
+cycle through all
+
+the non-zero elements.
+
+Remember the non-zero elements
+are a multiplicative group.
+
+And it's a cyclic group.
+
+And it's the generator
+of the group.
+
+Good.
+
+So once we write it like this,
+we can actually write down the
+
+whole Reed-Solomon code in some
+sort of transfer domain
+
+description in the Fourier
+transform.
+
+And the way this goes
+is the following.
+
+So from now on, I will make
+implicit identification
+
+without making them.
+
+So this is an identification
+which I
+
+just jump around between.
+
+A vector --
+
+so this one would be a Fqn.
+
+And Fx would be maybe
+0 to MDS 1.
+
+Let's leave it at that.
+
+So I make this --
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, let's make
+this identification free.
+
+It's just a vector of length n
+and a polynomial of length n.
+
+And so whenever I want this
+to have a low degree, the
+
+polynomial, then I just
+write that expression.
+
+So this identification
+we make freely now.
+
+And then how can we write F?
+
+Let F now be code word in
+the Reed-Solomon code.
+
+And then I say Fi.
+
+What is Fi?
+
+The i is element.
+
+Well, we know that this is
+F of omega to the i.
+
+So this is, at the moment,
+counted from 0.
+
+So this is --
+
+you write it out --
+
+Fj omega to the i to the
+j, which is omega i j.
+
+And now, at this point in time,
+
+everybody recognizes this.
+
+This would be the discrete
+Fourier transform of a vector.
+
+This is an element of order n.
+
+Usually, there's e to
+the j and then an
+
+element of order n.
+
+Now it's in the finite field.
+
+But what's the difference?
+
+This would be the Fourier
+transform.
+
+So a code word would be the
+Fourier transform of a vector
+
+F. Let's just make sure it also
+goes the other direction.
+
+So I claim that Fl would be --
+so what would be the Fourier
+
+transform if it, indeed, is
+the Fourier transform?
+
+It is a minus, and then
+it goes n minus 1
+
+Fj omega minus jl.
+
+So the question is
+is that true?
+
+Because that would
+be the inverse.
+
+Is that true?
+
+Well, let's do what we do with
+proofs of this type.
+
+I need that space here.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Sorry?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah.
+
+So let's do what we do with
+proofs of this type.
+
+That means we write it out.
+
+That's another beautiful thing
+about finite fields.
+
+You never have to worry
+about convergence.
+
+So for the F, we just
+plug that in here.
+
+Sum, this would be --
+
+what do we call it --
+
+Fi omega to the ij.
+
+So this would be Fj.
+
+And then I want omega
+minus jl.
+
+So is that true?
+
+Is the identity now true?
+
+Well, we see two sums.
+
+What do we do with two sums?
+
+If we're compelled to exchange
+the order, that's
+
+always what we do.
+
+So Fi goes out.
+
+And then you get
+omega to the --
+
+what do we do --
+
+i minus l times j.
+
+We have this.
+
+And so what is this?
+
+How can we work this out?
+
+Well, you know how to
+express the sum.
+
+So this part of the sum is
+really just omega i minus l to
+
+the n minus 1 minus 1.
+
+Well, that's a standard
+formula for summing
+
+these things up.
+
+But omega is an element
+of order n.
+
+Omega was an element
+of order n.
+
+That's how we chose it.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: It's what?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: You multiplied
+omega --
+
+it's primitive in the
+field, so omega --
+
+we have omega da-da-da-da-da i
+unequal to 1 for all i less
+
+than n and omega n
+is equal to 1.
+
+So OK.
+
+That's fine.
+
+So it's an element of order n.
+
+That means the n-th power.
+
+We can interchange this.
+
+So this is 1 to the some
+power remains 1.
+
+So 1 minus 1 is 0.
+
+The denominator --
+
+well, actually, we get
+two results here.
+
+If i is unequal to l,
+then this is 0.
+
+If i is equal to l, then this
+was just the sum of n once.
+
+So we get n here.
+
+i equal to 0.
+
+But n was q minus 1, the number
+of non-zero field
+
+elements because it was
+primitive in the field.
+
+And this one is just minus
+1 in the field.
+
+Because q, we compute q is the
+power of the prime of p.
+
+So that would be 0.
+
+If we just come out
+as minus 1, that
+
+explains this minus here.
+
+And we can get rid of
+the question mark.
+
+Look correct?
+
+All right.
+
+According to popular
+vote, it is.
+
+So what do we really
+have here?
+
+We have everything we want
+from a Fourier transform.
+
+We have a Fourier
+transform pair.
+
+We have a vector f, which we can
+think of as being in the
+
+frequency domain.
+
+Then we have a vector F,
+which is a Fourier
+
+transform of that.
+
+This one would be in the code
+if the degree of this
+
+polynomial here would
+be less than k.
+
+So now how can we understand
+Reed-Solomon codes now from an
+
+engineering point of view?
+
+Classical --
+
+what about band-limited
+functions?
+
+What do we know about
+band-limited functions?
+
+Because in a sense, the degree
+less than k, this means that
+
+Fi is 0 for all i
+greater than k.
+
+That's what it means.
+
+So in a sense, it's nothing but
+a band-limited function if
+
+this is a frequency domain,
+if you consider this as a
+
+frequency domain.
+
+So what do we know about the
+band-limited function?
+
+Well, if a function
+is band limited,
+
+it cannot be impulsive.
+
+We know that.
+
+It's a part of the frequency,
+and the frequency domain is
+
+inversely relational to the
+support of the function.
+
+So the whole idea of
+Reed-Solomon codes, in a
+
+sense, can actually be
+understood, at least
+
+intuitively, from Fourier
+transform and the duality
+
+between time and frequency.
+
+Yeah.
+
+AUDIENCE: Was q a
+prime number?
+
+PROFESSOR: q is not prime.
+q is a power of a prime.
+
+q to the n.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: There always is.
+
+Oh, sorry.
+
+AUDIENCE: [INAUDIBLE]
+
+or because for any q, there
+would be always a primitive?
+
+PROFESSOR: Why there's always
+a primitive element
+
+in the field --
+
+yeah, sorry.
+
+I thought you had gone
+through that.
+
+It's because the non-zero
+elements in a field always
+
+make up a multiplicative
+group.
+
+And it's always a cyclic
+multiplicative group.
+
+So it's a cyclic multiplicative
+group.
+
+And it's just the generator
+of that group.
+
+AUDIENCE: [INAUDIBLE]
+it was a --
+
+PROFESSOR: It's the same
+statement as saying, a cyclic
+
+group has a generator.
+
+AUDIENCE: If Fq, for example,
+was a z, zq,
+
+then q has to be prime.
+
+PROFESSOR: Yeah.
+
+Yeah, in order for it to be a
+field, q has to be prime.
+
+Right.
+
+That's true.
+
+That's true.
+
+But we are not worried
+about --
+
+There's also a beautiful theory
+[UNINTELLIGIBLE PHRASE]
+
+rings if this would not be a
+prime, very nice theory,
+
+becomes a little bit
+more technical.
+
+You see, more technical,
+then more difficult.
+
+I just wanted to give you this
+correspondence on the Fourier
+
+transform because it's, from an
+engineering point of view,
+
+a very nice insight.
+
+One of the reasons one can
+understand that Reed-Solomon
+
+codes have a good minimum
+distance is because it has a
+
+transform of a band-limited
+function.
+
+So that's what I wanted
+to say about the
+
+Fourier transforms here.
+
+I do not want to spend
+too much time.
+
+I have to get through
+decoding here.
+
+Since we have now this Fourier
+transform correspondence, we
+
+can do another thing.
+
+We can, namely, say, well, F is
+in the code if and only if
+
+the Fourier transform --
+
+so that was the back
+transform here.
+
+Also now, the code word, we can
+interpret the code word as
+
+a polynomial.
+
+And the inverse transform
+is just evaluating
+
+it at an omega again.
+
+F is in the code if and only the
+transform of a code word
+
+is 0 for all i greater than
+k up to n minus 1.
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: So it basically
+just means the support.
+
+If this one is band limited,
+then this one cannot have
+
+arbitrarily small support.
+
+That's what it means.
+
+That's really all
+I wanted to say.
+
+i greater than k and
+less than n.
+
+So we have that F is in the
+code if and only the
+
+polynomial evaluates to 0
+at a bunch of points.
+
+Now that leads to something
+interesting.
+
+Because now we can say, well,
+so what if we've just
+
+construct our set of vectors F
+so that they evaluate to 0
+
+somewhere where we want
+them to zero.
+
+We construct them somewhat
+differently than here.
+
+And in particular, let's define
+g as a product of i
+
+equal k up to n minus 1 of
+x minus omega minus i.
+
+So it's a polynomial.
+
+This is a polynomial which
+satisfies this.
+
+So in particular, we have g of
+omega minus i is equal to 0
+
+for all i less than
+n less than --
+
+I'm sorry --
+
+and greater than k.
+
+So this is a code word, right?
+
+We are agreed this
+is a code word?
+
+Good.
+
+So we found a code word without
+going through this
+
+here, without going through
+the evaluation map.
+
+We found it straight away.
+
+But not only did we find this.
+
+This has degree n minus k.
+
+This has degree n minus k.
+
+So maybe there's another
+interpretation.
+
+Now we can give a whole new
+definition of the Reed-Solomon
+
+code, namely, as a set of
+polynomials, which are sort of
+
+implicitly identified with a set
+of vectors such that times
+
+this g of x and h of x
+is less then k again.
+
+So what we have here, it's
+again, you take a vector space
+
+of functions the h.
+
+It's a k dimensional
+vector space.
+
+And we multiplied with this g.
+
+It's again a linear map, this
+multiplication with a fixed
+
+polynomial.
+
+A linear map of this vector
+space gives us, again, a
+
+vector space of dimension k.
+
+And all elements in this vector
+space evaluate to 0 for
+
+all omega to the minus i.
+
+That's just the same
+again, just the
+
+Reed-Solomon code again.
+
+So it's a very nice
+complementary description to
+
+the same Reed-Solomon code we
+could define up here, we have
+
+found again down here.
+
+What is so nice about this?
+
+Yeah, what do you think
+is so nice about this?
+
+About this description?
+
+So now you have to think
+as engineers.
+
+AUDIENCE: You can still
+evaluate it.
+
+There, we have to evaluate it
+at end points of function.
+
+PROFESSOR: Yeah, exactly.
+
+This is so easy to implement.
+
+So now we think a little
+bit about encoder.
+
+An encoder for a Reed-Solomon
+code.
+
+How would we do that?
+
+You look at this here.
+
+Hey, let's do this.
+
+Let's exactly do this.
+
+Meaning in VLSI, we do
+something like --
+
+and here, you would write
+-- and this is
+
+just a delay element.
+
+This one would be g n minus k.
+
+This one --
+
+so these would be the
+coefficients.
+
+This polynomial, we can evaluate
+once and for all.
+
+We do that once before we
+start our communication.
+
+We evaluate that polynomial
+once and for all.
+
+We know these coefficients.
+
+So these are multipliers which
+multiply with those
+
+corresponding coefficients.
+
+And we feed into here the
+coefficients of this
+
+polynomial.
+
+This is our information symbols,
+which we simply feed
+
+into this circuitry.
+
+And into this circuit, out
+comes F, out comes the
+
+coefficient.
+
+Polynomial multiplication.
+
+If you show that to a
+VLSI designer, they
+
+are deliriously happy.
+
+They say, you know what?
+
+I implement you this thing.
+
+I implement you in 5,000 gates,
+which is close to
+
+nothing nowadays.
+
+Maybe not.
+
+Maybe 10,000.
+
+And there you get to the
+second reason that
+
+Reed-Solomon codes
+are so extremely
+
+important in practice.
+
+On the one hand, they are MDS
+codes, meaning they are about
+
+as good as it gets.
+
+And on the other hand,
+they are algorithms.
+
+They are circuitry for these
+things whose cost is close to
+
+nothing at least today.
+
+When they were invented, that
+was quite different.
+
+In the '60s, that would have
+not been implementable with
+
+transistors on a board or
+something like that.
+
+But today, the cost is
+close to nothing.
+
+So the whole algorithmic
+treatment of Reed-Solomon
+
+codes is very well developed.
+
+The encoder you could
+do like this.
+
+Yeah.
+
+AUDIENCE: Question about why
+do you still require that
+
+degree [INAUDIBLE]?
+
+PROFESSOR: You don't
+need to do that.
+
+But then the mapping is not
+one-to-one anymore.
+
+Then the mapping is not
+one-to-one anymore.
+
+Let's put it other ways.
+
+You want code words
+of length n.
+
+If the degree is larger,
+you run over.
+
+In order to still get a code
+word, then you have to take it
+
+modular x to the n minus 1.
+
+And that would fold the
+coefficients back.
+
+And still, it gives you a valid
+code word then, but this
+
+is not one-to-one anymore.
+
+Anyway, the short answer is if
+you allow more, then they
+
+become longer than n.
+
+So what's the time?
+
+OK.
+
+So this is a nice encoder.
+
+There even is a nicer encoder,
+which I just want to give the
+
+formula for.
+
+The one reason that people still
+have a problem with this
+
+is it's not systematic.
+
+People like to see the symbols
+in the code words themselves.
+
+They want the systematic part.
+
+How could we achieve that?
+
+Well, we go from the same
+description here.
+
+We say, well, let
+h of x be given.
+
+Then compute x to the n minus k
+times h of x modular g of x.
+
+So we divide this polynomial
+by this polynomial g --
+
+it has a name.
+
+It's called the generator
+polynomial.
+
+We divide it by g.
+
+And out comes some polynomial
+r of x of some low degree,
+
+degree less than g.
+
+And degree r of x less than
+n minus k in particular.
+
+So and then we can
+form a code word.
+
+I claim F of x, no, F is --
+
+and here we write r, and
+here we write h.
+
+The coefficient vector
+of h and the
+
+coefficient vector of r.
+
+Why is that a code word?
+
+Why is that a code word?
+
+Maybe minus here.
+
+I'm always thinking
+characteristic 2 anyway.
+
+So why is this a code word?
+
+Anybody, it's clear?
+
+What this is in terms of F of
+x is r of x plus h of x.
+
+Oh, minus r of x.
+
+That's because we wrote
+it like this.
+
+If we now take the F of x
+modular g of x, well, this
+
+part has degree low.
+
+It's not affected by this
+modular operation.
+
+This would be minus r of x plus
+this one, modular g of x,
+
+which is r of x.
+
+So the whole thing is 0.
+
+If this is 0, that means g of
+x is a factor of F. Hence,
+
+it's a code word.
+
+So we have a code word here.
+
+And in the code word, pop up
+our symbols right away, our
+
+encoded information symbols
+right away.
+
+So we get some nice systematic
+encoding going.
+
+This division circuit by
+g is pretty much the
+
+same size as this.
+
+It's not larger at all.
+
+So there, we get beautiful
+algorithms.
+
+This is actually what's
+implemented.
+
+If we go to any disc drive
+[UNINTELLIGIBLE], that is
+
+usually what is implemented
+in there, exactly this.
+
+Algorithms.
+
+Algorithmic treatment of
+Reed-Solomon codes.
+
+Do you have any questions
+about any of this?
+
+Yeah.
+
+AUDIENCE: I have a question
+about do any these
+
+Reed-Solomon codes
+map [INAUDIBLE]?
+
+PROFESSOR: They are
+very costly map.
+
+Usually, it depends a lot
+on the application.
+
+If you think disc drives,
+[UNINTELLIGIBLE] as just being
+
+mapped, you take Reed-Solomon
+codes over a characteristic 2.
+
+Then each field element is
+
+represented as a binary vector.
+
+And that binary vector is mapped
+into on-off keying.
+
+Straight off the bat.
+
+Nothing more fancy.
+
+That is for disc drives.
+
+And as you do this, the
+satellite standard, where it's
+
+mapped onto the 256-QAM field
+elements [UNINTELLIGIBLE].
+
+So it's many different ways.
+
+Many different ways.
+
+AUDIENCE: But to prove some
+performance [UNINTELLIGIBLE]
+
+in the [UNINTELLIGIBLE], we need
+to have mappings, right?
+
+PROFESSOR: In order to prove
+performance mode, we need to
+
+have mappings.
+
+And the Hamming distance bounds
+that we get from here
+
+give you bounds on the minimum
+Euclidean distance.
+
+If these are good bounds or
+not depends a lot on the
+
+modulation scheme.
+
+And to be perfectly honest,
+they usually are not.
+
+They usually are not very
+good, the bounds.
+
+But it's a very difficult
+problem to design a code or to
+
+find a representation of the
+fields that maps nicely onto a
+
+modulation scheme.
+
+Very difficult problem.
+
+AUDIENCE: How do we know
+how to think that
+
+this is a good code?
+
+PROFESSOR: The code itself is
+excellent in terms of MDS, the
+
+MDS property.
+
+AUDIENCE: But why does
+MDS mean good codes?
+
+PROFESSOR: In respect
+to modulation?
+
+AUDIENCE: Yes.
+
+PROFESSOR: It doesn't.
+
+It doesn't.
+
+It's a bit like this.
+
+It's really not easy to define
+codes in Euclidean space.
+
+So all that we do is we find
+ways to do that and guarantee
+
+some performance, some
+sort of performance.
+
+It's not easy to spread out --
+
+I don't know --
+
+2 to the 1,000 points
+in 1,500 dimensions.
+
+These would be typical
+numbers really.
+
+It's not easy.
+
+And since that problem is
+practically daunting, it's a
+
+daunting task, you have to
+develop all sort of crutches
+
+to do that.
+
+And this is really one.
+
+So how to code MDS
+codes playing a
+
+part in this mapping.
+
+If you want to be more fancy
+about that, then you put a
+
+convolutional code or some other
+code also in there and
+
+do a combine scheme.
+
+I think Professor Forney will
+talk about that more.
+
+So here, it's just the
+coding theoretic
+
+groundwork of these things.
+
+Anything else?
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+
+of the [INAUDIBLE] n minus 1.
+
+Close, very close [INAUDIBLE].
+
+PROFESSOR: Yeah, thanks.
+
+So the algorithmic treatment
+of Reed-Solomon codes is
+
+extremely elegant.
+
+And that's the second main
+reason they are so much used.
+
+It doesn't cost so much
+to implement them.
+
+Well, at least we've seen
+that for the encoder.
+
+That's a fairly small circuit.
+
+So what about decoding?
+
+Decoding.
+
+How do we decode these things?
+
+How could we possibly
+decode them?
+
+And I give you --
+
+AUDIENCE: Fourier?
+
+PROFESSOR: Right, that's true.
+
+We could do the Fourier
+transform.
+
+But it doesn't help us so much
+because we receive something.
+
+And we receive a
+vector, say, y.
+
+From now on, let's say
+x is a code word.
+
+rs, right.
+
+So x, it's usually a code
+word from now on.
+
+So this is a code word
+plus an error.
+
+So in particular, if we take the
+Fourier transform, we take
+
+the Fourier transform of the
+code word, which is fine.
+
+But then we get the Fourier
+transform of the error.
+
+So that destroys all the fun.
+
+What else could we do?
+
+Here's typical parameters
+of a code.
+
+255, 239, 256.
+
+And you immediately see
+that, OK, any sort of
+
+group force is out.
+
+How many code words
+do we have here?
+
+We have 8 to the
+239 code words.
+
+Now you don't want
+to search that.
+
+You definitely don't want
+to search that.
+
+So how could we possibly
+decode these things?
+
+Turns out, to decode them in
+some sort of optimal fashion,
+
+maximum likelihood [INAUDIBLE]
+
+actually, it's an
+NP-hard problem.
+
+Maybe last year, actually, it
+has been shown that it's an
+
+NP-hard problem to decode
+Reed-Solomon codes.
+
+It was known that decoding
+in general was NP-hard.
+
+But this is now the constraint
+to Reed-Solomon
+
+codes is still hard.
+
+So what do we do?
+
+Yes, OK, what do we do?
+
+Let's say x is a code word.
+
+We know that.
+
+And set rate e, let's
+just call it t.
+
+So what happens if you
+don't have an error?
+
+Just thought experiment.
+
+Thought experiment, if you don't
+have an error, then yi
+
+in all the positions is
+equal to F of xi for
+
+some F of x of degree.
+
+In particular, since we
+know the x's, we know
+
+the positions --
+
+sorry, oh, sorry.
+
+That's not what I
+wanted to write.
+
+This is definitely not what
+I wanted to write.
+
+Let's keep that as c as a code
+word and position i in c is
+
+associated with xi
+in the fields.
+
+So meaning ci would
+be F of xi.
+
+That's really what I
+wanted to write.
+
+It makes more sense.
+
+So thought experiment.
+
+No errors.
+
+Then yi is F of xi for some F.
+If they ran no errors, then we
+
+could just solve this linear
+system of equations to find
+
+the coefficient of F. And the
+coefficient of F, say, were
+
+our information circuits.
+
+Is it clear that this is a
+linear system of equations?
+
+Yeah?
+
+You could write it out as
+y0, y1, y2 equal to --
+
+and here we have f0,
+f1, up to fk-1.
+
+This is the linear system
+of equations.
+
+We know the xi's.
+
+This is a linear system of
+equation we have to solve.
+
+If there are no errors,
+then life is easy.
+
+That seems to be reasonable.
+
+So what happens if we
+do have errors?
+
+Somehow, we have to make sure
+that the errors that we get do
+
+not cause any problem for us.
+
+And then we do something
+very ingenious.
+
+We define something called an
+error locator which is a
+
+polynomial x such
+that x minus xi.
+
+So it's a polynomial which is
+0 in all error positions.
+
+Well, you might say, we do not
+know the error positions.
+
+Well, OK, that's true.
+
+Basically, this is, in the end,
+what we want to find,
+
+this polynomial.
+
+But nonetheless, this
+polynomial exists.
+
+We can cast, actually,
+the coding problem --
+
+this is form 1 s.
+
+Yes, what?
+
+AUDIENCE: [INAUDIBLE PHRASE].
+
+PROFESSOR: Yeah, it's an
+additive error model.
+
+But you can cast pretty
+much anything in the
+
+[UNINTELLIGIBLE].
+
+If a position is altered, you
+can always model that as if
+
+something was added to it.
+
+Decoding problem one is find
+lambda of x of minimal degree
+
+such that lambda of xi,
+is 0 for all xi and
+
+degree f less than k.
+
+So I claim if you solve this
+problem, namely, this is a
+
+problem I give you.
+
+I give you vector y.
+
+I give you vector y.
+
+Here it is.
+
+Here is vector y.
+
+And I give you vector x which
+corresponds to the field
+
+elements where you evaluated
+that in order to
+
+get the code word.
+
+And then I said, given y and x,
+find two polynomials lambda
+
+and f such that f has maximum
+degree k and lambda has
+
+minimum degree, the smaller
+degree possible so
+
+that this is true.
+
+And I claim this solves
+the decoding problem.
+
+This would solve the decoding
+problem because once we have
+
+found this, then we
+can take lambda to
+
+be the error locator.
+
+And we can basically read
+off the information
+
+symbols from the f.
+
+So this decoding formulation now
+brings it, at least, into
+
+the algebraic ground, brings
+the whole decoding problem,
+
+makes it something
+algebraically.
+
+But now the question becomes,
+is that easy?
+
+Or can we do this?
+
+This problem here.
+
+Do you see any hope for
+solving this problem?
+
+I guess the only
+answer that --
+
+OK, anybody says no?
+
+Anybody does not see any hope?
+
+All right.
+
+This is great.
+
+You all see hope here.
+
+You all see hope here, which
+seems to make you an
+
+opportunistic bunch.
+
+Not opportunistic.
+
+What's the word?
+
+Optimistic.
+
+Optimistic bunch.
+
+Let's put it like this.
+
+What is the problem
+in solving this?
+
+It's not linear.
+
+You get the coefficients
+of lambda.
+
+Multiply the coefficients
+of f.
+
+That whole thing becomes a
+nonlinear problem, where we
+
+say in the end, find the
+solution to a set of
+
+polynomial equations in a field,
+which is a multivariate
+
+polynomial equations, where the
+coefficients of lambda and
+
+f are the variables.
+
+You can do that.
+
+You could use techniques like
+Grobner basis or so, and you
+
+could do that.
+
+But this is very difficult.
+
+This is computationally
+tedious.
+
+So is that clear why this is
+nonlinear, and why this is
+
+hard to solve a nonlinear
+problem here?
+
+If not, then you have to say
+something now, or forever hold
+
+your peace.
+
+So what do we do with
+hard problems?
+
+Once you take the optimization
+classes, there's almost like a
+
+reflex, there is a relax time.
+
+We find the proper relaxation
+of the problem.
+
+Now the proper relaxation of
+this problem is the following.
+
+Decoding problem two.
+
+Find lambda of x of minimal
+degree such that --
+
+it's almost the same,
+almost the same --
+
+lambda fi yi minus h of xi is
+0, where the degree of h is
+
+less than k plus
+degree lambda.
+
+So all that we did from this
+formulation, which would give
+
+us a clean solution to the whole
+thing, right now, we
+
+multiply in this lambda which
+gives here, it keeps the
+
+lambda times y.
+
+And here, we get a new
+polynomial, lambda times f,
+
+which now has degree at most
+k plus degree lambda.
+
+And then we say, let's instead
+solve this problem.
+
+Let's solve this problem.
+
+In particular, the question now
+becomes well, we do not
+
+require this anymore.
+
+In this relaxed formulation,
+we do not require this.
+
+And that makes all
+the difference.
+
+It makes a world of difference
+because this one --
+
+look at it -- it's
+a linear problem.
+
+It's a linear program.
+
+Why is it a linear problem?
+
+Do you see it's a
+linear problem?
+
+Could you write down the
+equation, the matrix equation?
+
+It's pretty straight, right?
+
+It's pretty straight.
+
+You could, for example,
+write it like, here, a
+
+diagonal matrix yn.
+
+Here, you would get something.
+
+I think that seems
+to be all right.
+
+And here, just the evaluation
+of the h.
+
+So up to hk plus
+degree lambda.
+
+That's a linear system
+of equations.
+
+We can certainly solve this.
+
+Well, we do not know really
+what the lambda is, what
+
+degree the lambda has.
+
+But we're just hypothesizing on
+all the possible degrees.
+
+Well, we could say, OK, let's
+assume the degree lambda is 0.
+
+It's a constant, which would
+be the same as saying there
+
+are no errors.
+
+Then we can look at the
+system of equations.
+
+Does it have a solution?
+
+Well, yes, no.
+
+If no, then we say, all right,
+let's assume it's 1.
+
+Well, does it have a solution?
+
+Yes, no.
+
+And so on.
+
+Then we can move on.
+
+So we can solve this
+relaxed problem.
+
+Does that help us?
+
+It's nice to solve a
+relaxed problem.
+
+And in the end, we get two
+vectors out of it, two
+
+polynomials, lambda and h.
+
+Does it really help us?
+
+Well, yes.
+
+Why?
+
+Because --
+
+let's put it like this.
+
+We could easily check
+if this is true.
+
+Once we have our h, we can
+easily check if this is true.
+
+And if it is true, then we
+have solved this problem.
+
+If it is true, we have solved
+this problem, which is the
+
+problem we wanted to solve.
+
+Good.
+
+So is that all we need
+to know about this?
+
+We want to give guarantees.
+
+We want to give guarantees that
+we correct up to so many
+
+errors, t errors, right?
+
+So we have to guarantee that if
+there are not more than t
+
+errors, whatever t will turn
+out to be, we can guarantee
+
+that A, we will find
+a solution, and
+
+B, this will hold.
+
+So two things to prove.
+
+Is that clear?
+
+That we have to prove
+those two things?
+
+So the first one first.
+
+When do we find a solution?
+
+And are we guaranteed
+to find it?
+
+Can we guarantee the existence
+of a solution?
+
+Well, when can we do that?
+
+Let's look at this.
+
+These are n constraints.
+
+This is a system of linear
+equations with n constraints.
+
+If the total number of degrees
+of freedom exceeds n, then we
+
+are left with something
+non-trivial after we solve the
+
+system of equations.
+
+So what's the total number
+of degrees of freedom?
+
+The number of degrees
+of freedom --
+
+so we get the lambda as a degree
+of freedom, so which is
+
+degree lambda plus 1.
+
+And the other one is plus --
+
+what is this one --
+
+plus k plus degree lambda.
+
+This is the total number of
+degrees of freedom here.
+
+And the reason is that this
+one should be minus 1.
+
+Sorry.
+
+So this is total number
+of degrees of freedom.
+
+If this is greater than n,
+then we can guarantee the
+
+existence of a solution,
+a nontrivial solution.
+
+Then this thing will
+have a solution.
+
+It's a homogeneous system
+of equations.
+
+So the 0 is always a solution.
+
+But that's not much
+good to us.
+
+So what do we get here?
+
+Degree lambda.
+
+To a degree lambda greater
+than n minus k plus minus
+
+1 or n minus k.
+
+So the degree lambda greater
+than n minus k over 2 -- does
+
+that remind you of
+anything here?
+
+So this one is d
+minus 1 over 2.
+
+So very interesting, right?
+
+Once upon a time, you learned
+that if you make less than d/2
+
+errors, you can correct that.
+
+Very nice.
+
+It pops up here.
+
+It pops up here out
+of the blue.
+
+The reason that it pops up here
+is, of course, the same
+
+statement, that as long as we
+stay within d/2 errors, we are
+
+guaranteed to be able
+to decode this.
+
+So this is one.
+
+So we know this one was
+the number of errors.
+
+If t is greater or equal
+than this, then --
+
+let's forget about the t.
+
+If you proceed in this algorithm
+hypothesizing the
+
+degrees of lambda, once we've
+reached this number in the
+
+degree, there will
+be a solution.
+
+And we don't have to go
+further than that.
+
+So that's the first one.
+
+So the second thing we have
+to prove is that --
+
+I shouldn't have done this --
+
+that for some t --
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+standard degree of freedom
+or less constraints?
+
+PROFESSOR: You want to
+guarantee a solution.
+
+If you have more constraints
+than degrees of freedom, then,
+
+since it's homogeneous, you
+usually would be stuck with a
+
+zero solution.
+
+Everything's 0, which
+is no good to us.
+
+It solves this problem, but
+it doesn't give us any
+
+information.
+
+Is that all right?
+
+AUDIENCE: Why does it have to be
+the condition that degrees
+
+of freedom has to be greater
+than the constraints?
+
+PROFESSOR: No, no, the
+degrees of freedom --
+
+well, OK, it's true.
+
+We could get lucky.
+
+We could have redundancy in
+this system of equations.
+
+And if we get lucky, that's
+just for the better.
+
+And actually, you can show that
+you do get lucky if very
+
+few errors happen.
+
+Then this would have low rank.
+
+You can show that.
+
+But short of knowing much,
+we want to guarantee --
+
+I just want, at this point in
+time, to guarantee that there
+
+is a solution.
+
+There is a non-zero solution to
+this system of equations,
+
+and the degree of lambda
+is not more than d
+
+minus 1 over 2.
+
+There is a solution with a
+degree of lambda being upper
+
+bounded by this.
+
+AUDIENCE: So [INAUDIBLE]
+
+less constraints?
+
+PROFESSOR: Yeah, no, no.
+
+Once this is satisfied,
+I guarantee
+
+you there is a solution.
+
+That means, the smallest
+solution is guaranteed not to
+
+be larger than that.
+
+But there are, of course, many,
+
+many more larger solutions.
+
+There are many solutions of
+larger degree here, which we
+
+are not interested in since
+we are interested
+
+in the minimal degree.
+
+So this is an upper bound on
+the minimal degree lambda.
+
+So now the other one.
+
+So now we want to make the
+statement about this one here.
+
+When can we guarantee that our
+relaxation didn't matter?
+
+Despite our relaxation, our
+solution that we find that in
+
+the solution that we find
+lambda divides h.
+
+How can we guarantee this?
+
+So how can we guarantee this?
+
+How can we guarantee this?
+
+Let's look at lambda xi
+yi minus h of xi.
+
+And we know this is
+0 for all xi.
+
+We know that.
+
+We know that this guy here can
+actually be written as ci plus
+
+ei minus h of xi.
+
+This is just expanding
+this guy.
+
+We also know that we can write
+lambda xi times ci alone minus
+
+f of xi lambda xi.
+
+This is 0.
+
+We know that this is true too.
+
+AUDIENCE: For some f.
+
+PROFESSOR: For some f.
+
+The text is to f, so that
+this is true too.
+
+Then let's just subtract
+these two guys.
+
+Let's just subtract these
+two things here.
+
+And then we know that lambda
+xi times ei --
+
+so the first two cancel --
+
+minus h of xi minus So we
+know this is true too.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, sorry.
+
+Just in time.
+
+So what can we learn
+from this?
+
+So what is the degree of this?
+
+What is the degree of this?
+
+Well, this guy here --
+
+we'll write it somewhere
+else --
+
+well, this guy had degree h was
+less than n minus k plus
+
+degree lambda less than
+k plus degree lambda.
+
+That's because we set up
+that problem that way.
+
+And we know that this
+guy degree lambda.
+
+We know that.
+
+So this whole thing, let's call
+it S. We know it's 0 for
+
+degree S less than
+degree lambda.
+
+So why does that help us?
+
+Well, let's look
+at the vector.
+
+Now let's look at all
+the positions.
+
+Let's look at the vector where
+we had, in the vector, we have
+
+lambda xi ei.
+
+And now the fundamental
+question.
+
+What is the rate
+of this vector?
+
+At most?
+
+What's the rate of
+this guy at most?
+
+It's 12 seconds,
+[UNINTELLIGIBLE]?
+
+Well, the rate of
+this vector --
+
+it's definitely not more than
+the rate of the error.
+
+Because every time the error
+is 0, the rate drops out.
+
+That's at most t.
+
+What is the rate
+of this vector?
+
+So here we have a vector on
+the other side, S of xi, a
+
+vector on the other side.
+
+What's the rate of this guy?
+
+That's just the polynomial of
+degree at most k plus degree
+
+lambda minus 1.
+
+So we have that the rate of this
+vector is n minus k plus
+
+degree lambda minus 1 plus
+1 because of the minus.
+
+AUDIENCE: Greater than
+or equal to?
+
+PROFESSOR: It's greater
+than or equal, sorry.
+
+Otherwise, I would have been in
+trouble in a second here.
+
+Yeah, so what does that mean?
+
+So actually, this one is nice
+to rewrite is equal to d n
+
+minus t plus 1 d --
+
+I really should have done it
+like this in order not to --
+
+it's d minus degree lambda.
+
+So what can we learn
+from that?
+
+So we know this is true
+for all the positions.
+
+So if this is true for all
+positions, then --
+
+so if d minus degree lambda --
+
+actually, this is t because
+the rate was defined.
+
+t was the number of errors.
+
+And the error locator was just
+defined to have degree t.
+
+Right?
+
+The error locator was just x
+minus xi over all positions
+
+where we had an error, so there
+
+are t of those positions.
+
+The degree of lambda
+is equal to t.
+
+So now we take this.
+
+If d minus t is greater than
+t, so if the rate of this
+
+vector is greater than the rate
+of this vector, then we
+
+have a problem because
+that cannot be.
+
+Of course, by this identity,
+the rate of these
+
+two vectors is equal.
+
+So what is the way out?
+
+What's the way out?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+So if this is true, then S of
+xi I claim has to be 0 and
+
+lambda of xi times ei has
+to be 0 too for all i.
+
+That's the only way
+out of this.
+
+Because, obviously,
+this was allowed.
+
+If we really did find what we
+wanted to find, namely, an
+
+error locator here, then
+this vector --
+
+we said it has to
+be less than t.
+
+It can be less.
+
+In particular, it can
+be 0 if this is,
+
+indeed, an error locator.
+
+And if our relaxation
+didn't matter --
+
+that means the h that we
+find factors as that --
+
+if the relaxation didn't matter,
+then S would be 0 too.
+
+So that is a fair solution.
+
+That's a possibility.
+
+And if d minus t is greater than
+t, then this proves this
+
+is the only solution
+that is feasible.
+
+That's the only solution
+you have.
+
+So what that means is if t
+less than t/2, then the
+
+relaxation doesn't matter and h
+of xi is equal to lambda of
+
+xi times f of xi.
+
+So is that clear?
+
+That's two very simple, yet
+nice ways to prove things.
+
+Here, we guarantee
+the solution.
+
+Here, we guarantee
+the solution.
+
+Here, we guarantee that solution
+is correct, namely,
+
+if not too many errors happen,
+if less than t/2 errors
+
+happens, then relaxing the
+original problem here to this
+
+other form, which we
+could solve, does
+
+not change the solution.
+
+That's what's proved there.
+
+But about one-third
+looks puzzled.
+
+About half looks puzzled,
+I would think.
+
+Half looks puzzled.
+
+Is there any way I can
+explain that better?
+
+Think.
+
+Let's just go through
+the steps quickly.
+
+We had problem number one.
+
+Problem number one, which is a
+nonlinear problem, but you see
+
+that if you could solve
+this, you could solve
+
+the decoding problem.
+
+So you see that.
+
+Anybody who doesn't see that?
+
+All right.
+
+You're smart guys.
+
+If we can solve problem number
+one, we are home free.
+
+We have solved the
+decoding problem.
+
+Fine, we cannot solve it.
+
+It's a nonlinear problem.
+
+Well, we can solve it in
+exponential time, but that's
+
+little fun.
+
+So we relax it.
+
+We relax it into problem
+number two.
+
+All that we do, we multiply
+things out.
+
+And we do not require,
+once we solve the
+
+problem, this anymore.
+
+Now we have solved
+this problem.
+
+We have solved this linear
+system of equations.
+
+And after doing so, we have
+found lambda and h.
+
+They are lying on the table
+and looking at us.
+
+Now what?
+
+Are they any good?
+
+In particular, since a priori we
+cannot guarantee that this
+
+relaxation didn't completely
+destroy everything.
+
+We have solved the system.
+
+Now those two things are lying
+on the table, looking at us,
+
+and asking, what am I?
+
+And in general, if there's an
+arbitrary amount of errors
+
+happening near the channel,
+actually,
+
+they do not mean much.
+
+They do not mean much.
+
+But now I claim that, well, if
+not too many errors happened,
+
+but if the number of errors is
+bounded to be this, less than
+
+half the minimum distance, then,
+actually, I claim it did
+
+not matter if we solved
+the relaxation or
+
+the original problem.
+
+And the argument is
+roughly this.
+
+It goes like this.
+
+Here, we start.
+
+We have solved this.
+
+We have two polynomials lambda
+and h, so that this is true
+
+for all xi.
+
+We know that we can write
+it like this.
+
+That's just by definition
+of yi, just
+
+expanding the yi into this.
+
+We know that this is true by
+the definition of the code.
+
+The ci is the evaluation of
+f, of some polynomial f.
+
+So we can write this just by
+definition of the code.
+
+So once we have these two guys
+here, we can subtract them
+
+[UNINTELLIGIBLE] here.
+
+So we know that we have solved
+the following problem.
+
+We have found lambda and h.
+
+So that there is guaranteed to
+exist the polynomial f, so
+
+that this whole thing, namely,
+S of xi, that S is a
+
+polynomial of degree
+at most --
+
+what did we have --
+
+k plus degree lambda minus 1.
+
+So that's a semi-hairy
+step here.
+
+Is that clear that we can
+guarantee the existence of a
+
+polynomial S of degree at most
+k plus degree lambda minus 1?
+
+So that this equation holds.
+
+Once we have solved this,
+we can guarantee the
+
+existence of this.
+
+That's what we're saying.
+
+We can guarantee the
+existence of this.
+
+So now look at this.
+
+If you write this out for all
+i's and put it in a vector,
+
+what's the rate of
+this vector?
+
+Well, it's at most t because
+all the other e's are 0.
+
+If lambda is an error
+locator, it is 0.
+
+But we do not know that yet.
+
+All we know, it's at most t.
+
+This is on this side, so that
+vector has a rate at most t.
+
+On this side, the rate of this
+vector is at least this.
+
+Just by evaluating a polynomial
+of this degree,
+
+this is the maximum number
+of 0's we can get.
+
+So now we have two equalities,
+this one and this one.
+
+But obviously, the two vectors
+must be the same.
+
+So how can these two vectors be
+the same and still satisfy
+
+these two inequalities?
+
+Good question.
+
+How can they be the same and
+still satisfy this inequality?
+
+If t is less than d/2, then the
+rate of this vector would
+
+have to be larger than
+the rate of this.
+
+If they are non-zero.
+
+If they are non-zero, this would
+have to be larger than
+
+this because then d minus t
+would be greater than t.
+
+If this is true, this
+implies this.
+
+If this is true, this implies
+this which implies that the
+
+rate of this vector would be
+larger than the rate of this
+
+vector if they are non-zero.
+
+But how can that be?
+
+Answer is cannot.
+
+Cannot be, hence,
+they must be 0.
+
+Both vectors must be 0
+completely, which means this
+
+is an error locator.
+
+Because otherwise, this wouldn't
+be 0, and this one --
+
+where did I write it?
+
+Somewhere I wrote it.
+
+Where did I write it?
+
+Oh, here.
+
+So this S has to be 0 too.
+
+If this S is 0, then h of xi is
+exactly this, means factors
+
+in the way you want it to.
+
+So that's all I can say.
+
+I could say it again, but it's
+exactly the same words.
+
+And there's a limited benefit
+to even the repetition code.
+
+So beautiful, right?
+
+We have brought down the entire
+decoding problem for
+
+Reed-Solomon codes to solving a
+linear system of equations,
+
+namely, this one here or this
+one in short form, which,
+
+well, it's no problem at all in
+the grand scheme of things.
+
+And that's the other thing that
+makes Reed-Solomon codes
+
+so beautiful.
+
+They're access encoding, they're
+access decoding,
+
+they're everything
+that we want.
+
+Let me do one more thing about
+the decoding just to bring it
+
+down a little bit, to talk a
+little bit about complexity.
+
+Solving this linear system of
+equations has been subject to
+
+research for 30 years,
+40 years.
+
+So it started out with an
+algorithm which essentially
+
+solved that linear
+system directly.
+
+It was formulated a
+bit different, but
+
+that's what it is.
+
+It's called the
+
+Peterson-Gorenstein-Zierler algorithm.
+
+They realized it was a
+polynomial time decoding
+
+algorithm, a nice decoding
+algorithm.
+
+Then Berlekamp --
+
+I should write down the name.
+
+Berlekamp came up with a fast
+
+algorithm and square algorithm.
+
+Massey had his own formulation
+of that algorithm, which was a
+
+bit more streamlined I think.
+
+Then there was a later version,
+Berlekamp-Welch.
+
+The complexity of these
+algorithms is all roughly the
+
+same, is all n squared roughly,
+
+which solved this here.
+
+And then there's
+roughly nothing
+
+happening for 30 years.
+
+And after 30 years, then Madhu
+Sudan made the next serious
+
+dent in the decoding history
+of Reed-Solomon codes.
+
+So he found a way to solve this
+problem even beyond half
+
+the minimum distance.
+
+And in hindsight, it's a very
+nice and very simple trick
+
+that he used.
+
+So we started with
+the following.
+
+We started that, well, if we
+have no errors, then the pairs
+
+of points xi, yi lie
+on this curve.
+
+That's another way to formulate
+what we said that yi
+
+minus f of xi has to be 0.
+
+We said, well, if there are no
+errors, all the points that we
+
+receive lie on this curve.
+
+Because there are errors, we
+have to multiply this with an
+
+error locator and say this
+is 0 for all xi, yi.
+
+So this was problem
+number one.
+
+The relaxed form was lambda
+xy minus h of x 0 xi, yi.
+
+That's the way we do it.
+
+So what did Madhu do?
+
+Very clever.
+
+He said, all that we have to do
+is annihilate the effect of
+
+the error right in this.
+
+The whole reason for that lambda
+was to annihilate --
+
+so to take out the error
+influence out of this
+
+interpolation formula, to allow
+for a few errors to
+
+happen, which we can
+put in lambda.
+
+Well, Madhu said, well, what
+about we take a polynomial in
+
+two variables?
+
+A polynomial in two variables,
+then same thing.
+
+If no errors happen, then all
+the points xi, yi will lie on
+
+that curve.
+
+If a few errors happen, then
+let's find a lambda xy, two
+
+variables of some minimal
+degree, some very small degree
+
+so that this is still
+satisfied.
+
+And the problem is entirely
+the same.
+
+And this one, you cannot
+solve either.
+
+You cannot solve either.
+
+But again, you can solve
+the relaxation minus --
+
+again, you can solve
+the relaxation.
+
+This is, again, a linear
+system of equations.
+
+And the coefficients of
+lambda and psi now.
+
+Once you solve this linear
+system of equations --
+
+actually, this one you can more
+handily write simply --
+
+now there is no way to
+distinguish the y anymore
+
+since both sides anyway
+depend on y.
+
+Find a polynomial in two
+variables such that this is 0
+
+for all xi, yi.
+
+This is his central problem.
+
+This is his relaxation.
+
+Find a polynomial in two
+variables, which he
+
+evaluates to 0.
+
+And then he has, essentially,
+the same proofs we have here,
+
+a bit more technical,
+but not much.
+
+I'm sure you can come up with
+this if you sit down at home.
+
+Let's put it like this.
+
+There's no heavy machinery
+in it.
+
+There's no heavy math in it.
+
+There's a lot of being clever
+in it, but there's no heavy
+
+math in it.
+
+He can now guarantee that q of
+xy, if t is less than n minus
+
+square root of 2k --
+
+is that right --
+
+2kn, then you can guarantee
+that y minus fx is
+
+a factor q of xy.
+
+The same thing we wanted
+to guarantee.
+
+And like I said, the proof is
+very clever, but no heavy
+
+machinery in it.
+
+It's no heavy algebraic
+geometry or any of
+
+this stuff in that.
+
+It's high school algebra.
+
+Well, freshman college
+algebra.
+
+So that's what happens here.
+
+It took 30 years and a computer
+scientist to solve
+
+that problem.
+
+That was not all I wanted
+to say, but that's
+
+all I have time for.
+
+There's one minute left, so
+there's no point in starting
+
+something now.
+
+Do you have any questions
+about any of this?
+
+I should say that this 2 one can
+get rid of, but that takes
+
+a little bit more machinery.
+
+The 2 one can get rid of, but
+that's a bit more heavy.
+
+All right.
+
+So thanks so much.
+
+That's it.
+
+That's it.
\ No newline at end of file
diff --git a/nDuS5uQ7-lo.txt b/nDuS5uQ7-lo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a0c44d3fc490e07ba6c7a9de1783bbe8f34d8a73
--- /dev/null
+++ b/nDuS5uQ7-lo.txt
@@ -0,0 +1,2315 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about using the
+
+ align:start position:0%
+you've been learning about using the
+ 
+
+ align:start position:0%
+you've been learning about using the
+method of lrange multipliers to optimize
+
+ align:start position:0%
+method of lrange multipliers to optimize
+ 
+
+ align:start position:0%
+method of lrange multipliers to optimize
+functions of several variables given a
+
+ align:start position:0%
+functions of several variables given a
+ 
+
+ align:start position:0%
+functions of several variables given a
+constraint so here's a problem that you
+
+ align:start position:0%
+constraint so here's a problem that you
+ 
+
+ align:start position:0%
+constraint so here's a problem that you
+can use you can practice this method on
+
+ align:start position:0%
+can use you can practice this method on
+ 
+
+ align:start position:0%
+can use you can practice this method on
+so I've got a function f of XYZ = x^2 +
+
+ align:start position:0%
+so I've got a function f of XYZ = x^2 +
+ 
+
+ align:start position:0%
+so I've got a function f of XYZ = x^2 +
+x + 2 y^2 + 3 z^ 2 and what I'd like you
+
+ align:start position:0%
+x + 2 y^2 + 3 z^ 2 and what I'd like you
+ 
+
+ align:start position:0%
+x + 2 y^2 + 3 z^ 2 and what I'd like you
+to do is find the maximum and minimum
+
+ align:start position:0%
+to do is find the maximum and minimum
+ 
+
+ align:start position:0%
+to do is find the maximum and minimum
+values this function takes as the point
+
+ align:start position:0%
+values this function takes as the point
+ 
+
+ align:start position:0%
+values this function takes as the point
+XYZ moves around the unit sphere x^2 +
+
+ align:start position:0%
+XYZ moves around the unit sphere x^2 +
+ 
+
+ align:start position:0%
+XYZ moves around the unit sphere x^2 +
+y^2 + z^2 = 1 so to optimize this
+
+ align:start position:0%
+y^2 + z^2 = 1 so to optimize this
+ 
+
+ align:start position:0%
+y^2 + z^2 = 1 so to optimize this
+function given the constraint x^2 + y^2
+
+ align:start position:0%
+function given the constraint x^2 + y^2
+ 
+
+ align:start position:0%
+function given the constraint x^2 + y^2
++ z^2 equal 1 so why don't you pause the
+
+ align:start position:0%
++ z^2 equal 1 so why don't you pause the
+ 
+
+ align:start position:0%
++ z^2 equal 1 so why don't you pause the
+video take some time to work that out
+
+ align:start position:0%
+video take some time to work that out
+ 
+
+ align:start position:0%
+video take some time to work that out
+come back and we can work it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together hopefully you had some luck
+
+ align:start position:0%
+together hopefully you had some luck
+ 
+
+ align:start position:0%
+together hopefully you had some luck
+working on this problem let's have a go
+
+ align:start position:0%
+working on this problem let's have a go
+ 
+
+ align:start position:0%
+working on this problem let's have a go
+at it so remember that the method of
+
+ align:start position:0%
+at it so remember that the method of
+ 
+
+ align:start position:0%
+at it so remember that the method of
+lrange multipliers in order to apply it
+
+ align:start position:0%
+lrange multipliers in order to apply it
+ 
+
+ align:start position:0%
+lrange multipliers in order to apply it
+what it says is that when you have a a
+
+ align:start position:0%
+what it says is that when you have a a
+ 
+
+ align:start position:0%
+what it says is that when you have a a
+function being being optimized on some
+
+ align:start position:0%
+function being being optimized on some
+ 
+
+ align:start position:0%
+function being being optimized on some
+constraint condition what you what you
+
+ align:start position:0%
+constraint condition what you what you
+ 
+
+ align:start position:0%
+constraint condition what you what you
+do to find the points where the function
+
+ align:start position:0%
+do to find the points where the function
+ 
+
+ align:start position:0%
+do to find the points where the function
+could be maximum or minimum is that that
+
+ align:start position:0%
+could be maximum or minimum is that that
+ 
+
+ align:start position:0%
+could be maximum or minimum is that that
+first you look for points where the
+
+ align:start position:0%
+first you look for points where the
+ 
+
+ align:start position:0%
+first you look for points where the
+gradient of your objective function is
+
+ align:start position:0%
+gradient of your objective function is
+ 
+
+ align:start position:0%
+gradient of your objective function is
+parallel to the gradient of your
+
+ align:start position:0%
+parallel to the gradient of your
+ 
+
+ align:start position:0%
+parallel to the gradient of your
+constraint function so what that means
+
+ align:start position:0%
+constraint function so what that means
+ 
+
+ align:start position:0%
+constraint function so what that means
+is you take the partial derivatives FX
+
+ align:start position:0%
+is you take the partial derivatives FX
+ 
+
+ align:start position:0%
+is you take the partial derivatives FX
+FY FZ and you say FX has to be equal to
+
+ align:start position:0%
+FY FZ and you say FX has to be equal to
+ 
+
+ align:start position:0%
+FY FZ and you say FX has to be equal to
+Lambda * GX FY has to be equal to Lambda
+
+ align:start position:0%
+Lambda * GX FY has to be equal to Lambda
+ 
+
+ align:start position:0%
+Lambda * GX FY has to be equal to Lambda
+* gy and FZ has to be equal to Lambda *
+
+ align:start position:0%
+* gy and FZ has to be equal to Lambda *
+ 
+
+ align:start position:0%
+* gy and FZ has to be equal to Lambda *
+gz for some Lambda and then you solve
+
+ align:start position:0%
+gz for some Lambda and then you solve
+ 
+
+ align:start position:0%
+gz for some Lambda and then you solve
+that system together with the constraint
+
+ align:start position:0%
+that system together with the constraint
+ 
+
+ align:start position:0%
+that system together with the constraint
+equation and so the points that give you
+
+ align:start position:0%
+equation and so the points that give you
+ 
+
+ align:start position:0%
+equation and so the points that give you
+that that are the solutions of of that
+
+ align:start position:0%
+that that are the solutions of of that
+ 
+
+ align:start position:0%
+that that are the solutions of of that
+system of equations those points are
+
+ align:start position:0%
+system of equations those points are
+ 
+
+ align:start position:0%
+system of equations those points are
+your points that you have to check for
+
+ align:start position:0%
+your points that you have to check for
+ 
+
+ align:start position:0%
+your points that you have to check for
+whether they're the maximum or the
+
+ align:start position:0%
+whether they're the maximum or the
+ 
+
+ align:start position:0%
+whether they're the maximum or the
+minimum and also sometimes you have some
+
+ align:start position:0%
+minimum and also sometimes you have some
+ 
+
+ align:start position:0%
+minimum and also sometimes you have some
+some boundary to your region and you
+
+ align:start position:0%
+some boundary to your region and you
+ 
+
+ align:start position:0%
+some boundary to your region and you
+have to check that as well so in this
+
+ align:start position:0%
+have to check that as well so in this
+ 
+
+ align:start position:0%
+have to check that as well so in this
+case the sphere is doesn't have boundary
+
+ align:start position:0%
+case the sphere is doesn't have boundary
+ 
+
+ align:start position:0%
+case the sphere is doesn't have boundary
+right so so we don't have any boundary
+
+ align:start position:0%
+right so so we don't have any boundary
+ 
+
+ align:start position:0%
+right so so we don't have any boundary
+conditions to check so we're going to
+
+ align:start position:0%
+conditions to check so we're going to
+ 
+
+ align:start position:0%
+conditions to check so we're going to
+have a really straightforward problem to
+
+ align:start position:0%
+have a really straightforward problem to
+ 
+
+ align:start position:0%
+have a really straightforward problem to
+solve where we just have to look at the
+
+ align:start position:0%
+solve where we just have to look at the
+ 
+
+ align:start position:0%
+solve where we just have to look at the
+at the partial derivatives so let's
+
+ align:start position:0%
+at the partial derivatives so let's
+ 
+
+ align:start position:0%
+at the partial derivatives so let's
+write down that system of equations that
+
+ align:start position:0%
+write down that system of equations that
+ 
+
+ align:start position:0%
+write down that system of equations that
+we have to solve so the partial
+
+ align:start position:0%
+we have to solve so the partial
+ 
+
+ align:start position:0%
+we have to solve so the partial
+derivative of f with respect to X is
+
+ align:start position:0%
+derivative of f with respect to X is
+ 
+
+ align:start position:0%
+derivative of f with respect to X is
+going to be 2x + 1 so we have to solve
+
+ align:start position:0%
+going to be 2x + 1 so we have to solve
+ 
+
+ align:start position:0%
+going to be 2x + 1 so we have to solve
+the system 2x + 1 equals and the partial
+
+ align:start position:0%
+the system 2x + 1 equals and the partial
+ 
+
+ align:start position:0%
+the system 2x + 1 equals and the partial
+derivative of our constraint is with
+
+ align:start position:0%
+derivative of our constraint is with
+ 
+
+ align:start position:0%
+derivative of our constraint is with
+respect to X is 2x so this has to 2x + 1
+
+ align:start position:0%
+respect to X is 2x so this has to 2x + 1
+ 
+
+ align:start position:0%
+respect to X is 2x so this has to 2x + 1
+has to equal Lambda * 2x that's what we
+
+ align:start position:0%
+has to equal Lambda * 2x that's what we
+ 
+
+ align:start position:0%
+has to equal Lambda * 2x that's what we
+get from the from the X partial
+
+ align:start position:0%
+get from the from the X partial
+ 
+
+ align:start position:0%
+get from the from the X partial
+derivatives how about from the Y partial
+
+ align:start position:0%
+derivatives how about from the Y partial
+ 
+
+ align:start position:0%
+derivatives how about from the Y partial
+derivatives the Y partial derivative of
+
+ align:start position:0%
+derivatives the Y partial derivative of
+ 
+
+ align:start position:0%
+derivatives the Y partial derivative of
+f is going to be 4
+
+ align:start position:0%
+f is going to be 4
+ 
+
+ align:start position:0%
+f is going to be 4
+y so that has to be equal to Lambda and
+
+ align:start position:0%
+y so that has to be equal to Lambda and
+ 
+
+ align:start position:0%
+y so that has to be equal to Lambda and
+the Y partial derivative of the
+
+ align:start position:0%
+the Y partial derivative of the
+ 
+
+ align:start position:0%
+the Y partial derivative of the
+constraint equation is 2
+
+ align:start position:0%
+constraint equation is 2
+ 
+
+ align:start position:0%
+constraint equation is 2
+Y and the Z partial derivative of f is 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z so 6z has to be equal to Lambda time
+
+ align:start position:0%
+Z so 6z has to be equal to Lambda time
+ 
+
+ align:start position:0%
+Z so 6z has to be equal to Lambda time
+well well the Z partial derivative of
+
+ align:start position:0%
+well well the Z partial derivative of
+ 
+
+ align:start position:0%
+well well the Z partial derivative of
+the constraint function is 2 Z Lambda *
+
+ align:start position:0%
+the constraint function is 2 Z Lambda *
+ 
+
+ align:start position:0%
+the constraint function is 2 Z Lambda *
+2 Z and we have the last equation x^2 +
+
+ align:start position:0%
+2 Z and we have the last equation x^2 +
+ 
+
+ align:start position:0%
+2 Z and we have the last equation x^2 +
+y^2 + z^2 = 1 so we get four equations
+
+ align:start position:0%
+y^2 + z^2 = 1 so we get four equations
+ 
+
+ align:start position:0%
+y^2 + z^2 = 1 so we get four equations
+in our variables X Y and Z plus this new
+
+ align:start position:0%
+in our variables X Y and Z plus this new
+ 
+
+ align:start position:0%
+in our variables X Y and Z plus this new
+parameter Lambda that we introduce and
+
+ align:start position:0%
+parameter Lambda that we introduce and
+ 
+
+ align:start position:0%
+parameter Lambda that we introduce and
+we want to solve these to find the
+
+ align:start position:0%
+we want to solve these to find the
+ 
+
+ align:start position:0%
+we want to solve these to find the
+points X Y and Z at which these
+
+ align:start position:0%
+points X Y and Z at which these
+ 
+
+ align:start position:0%
+points X Y and Z at which these
+equations are all satisfied and then
+
+ align:start position:0%
+equations are all satisfied and then
+ 
+
+ align:start position:0%
+equations are all satisfied and then
+once we get those points we have to test
+
+ align:start position:0%
+once we get those points we have to test
+ 
+
+ align:start position:0%
+once we get those points we have to test
+them to see whether they're the maximum
+
+ align:start position:0%
+them to see whether they're the maximum
+ 
+
+ align:start position:0%
+them to see whether they're the maximum
+or the minimum or neither um so so okay
+
+ align:start position:0%
+or the minimum or neither um so so okay
+ 
+
+ align:start position:0%
+or the minimum or neither um so so okay
+so we have this system of equations now
+
+ align:start position:0%
+so we have this system of equations now
+ 
+
+ align:start position:0%
+so we have this system of equations now
+this is a little bit complicated it's
+
+ align:start position:0%
+this is a little bit complicated it's
+ 
+
+ align:start position:0%
+this is a little bit complicated it's
+not a system of linear equations um so
+
+ align:start position:0%
+not a system of linear equations um so
+ 
+
+ align:start position:0%
+not a system of linear equations um so
+we need to think about ways that we can
+
+ align:start position:0%
+we need to think about ways that we can
+ 
+
+ align:start position:0%
+we need to think about ways that we can
+solve it and one thing that I think we
+
+ align:start position:0%
+solve it and one thing that I think we
+ 
+
+ align:start position:0%
+solve it and one thing that I think we
+can do here is if you look at the second
+
+ align:start position:0%
+can do here is if you look at the second
+ 
+
+ align:start position:0%
+can do here is if you look at the second
+and third equations you see that in the
+
+ align:start position:0%
+and third equations you see that in the
+ 
+
+ align:start position:0%
+and third equations you see that in the
+second equation everything has a factor
+
+ align:start position:0%
+second equation everything has a factor
+ 
+
+ align:start position:0%
+second equation everything has a factor
+of Y in it so either Y is equal to zero
+
+ align:start position:0%
+of Y in it so either Y is equal to zero
+ 
+
+ align:start position:0%
+of Y in it so either Y is equal to zero
+or we can divide by it so from the
+
+ align:start position:0%
+or we can divide by it so from the
+ 
+
+ align:start position:0%
+or we can divide by it so from the
+second equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have that either Y is equal to zero
+
+ align:start position:0%
+we have that either Y is equal to zero
+ 
+
+ align:start position:0%
+we have that either Y is equal to zero
+or we can divide by
+
+ align:start position:0%
+or we can divide by
+ 
+
+ align:start position:0%
+or we can divide by
+Y in which case we get Lambda is equal
+
+ align:start position:0%
+Y in which case we get Lambda is equal
+ 
+
+ align:start position:0%
+Y in which case we get Lambda is equal
+to two similarly from the third equation
+
+ align:start position:0%
+to two similarly from the third equation
+ 
+
+ align:start position:0%
+to two similarly from the third equation
+we have that either Z is equal to zero
+
+ align:start position:0%
+we have that either Z is equal to zero
+ 
+
+ align:start position:0%
+we have that either Z is equal to zero
+or we can divide by Z and we get Lambda
+
+ align:start position:0%
+or we can divide by Z and we get Lambda
+ 
+
+ align:start position:0%
+or we can divide by Z and we get Lambda
+is equal to 3 so from the
+
+ align:start position:0%
+is equal to 3 so from the
+ 
+
+ align:start position:0%
+is equal to 3 so from the
+third equation we have Z equal 0
+
+ align:start position:0%
+third equation we have Z equal 0
+ 
+
+ align:start position:0%
+third equation we have Z equal 0
+or Lambda equal 3 so now we have a bunch
+
+ align:start position:0%
+or Lambda equal 3 so now we have a bunch
+ 
+
+ align:start position:0%
+or Lambda equal 3 so now we have a bunch
+of possibilities right so either we have
+
+ align:start position:0%
+of possibilities right so either we have
+ 
+
+ align:start position:0%
+of possibilities right so either we have
+y = zal 0 or we have yal 0 and Lambda
+
+ align:start position:0%
+y = zal 0 or we have yal 0 and Lambda
+ 
+
+ align:start position:0%
+y = zal 0 or we have yal 0 and Lambda
+equal 3 or we have Lambda = 2 and zal 0
+
+ align:start position:0%
+equal 3 or we have Lambda = 2 and zal 0
+ 
+
+ align:start position:0%
+equal 3 or we have Lambda = 2 and zal 0
+or well we the other possibility would
+
+ align:start position:0%
+or well we the other possibility would
+ 
+
+ align:start position:0%
+or well we the other possibility would
+be Lambda equal 2 and Lambda equals 3
+
+ align:start position:0%
+be Lambda equal 2 and Lambda equals 3
+ 
+
+ align:start position:0%
+be Lambda equal 2 and Lambda equals 3
+but that can't happen so we have three
+
+ align:start position:0%
+but that can't happen so we have three
+ 
+
+ align:start position:0%
+but that can't happen so we have three
+possibilities three different ways that
+
+ align:start position:0%
+possibilities three different ways that
+ 
+
+ align:start position:0%
+possibilities three different ways that
+this could be satisfied so let's go over
+
+ align:start position:0%
+this could be satisfied so let's go over
+ 
+
+ align:start position:0%
+this could be satisfied so let's go over
+here and and write down what those U
+
+ align:start position:0%
+here and and write down what those U
+ 
+
+ align:start position:0%
+here and and write down what those U
+possibilities are so case one maybe I'll
+
+ align:start position:0%
+possibilities are so case one maybe I'll
+ 
+
+ align:start position:0%
+possibilities are so case one maybe I'll
+call it case a so the case a is when Y
+
+ align:start position:0%
+call it case a so the case a is when Y
+ 
+
+ align:start position:0%
+call it case a so the case a is when Y
+is equal to Z is equal to
+
+ align:start position:0%
+is equal to Z is equal to
+ 
+
+ align:start position:0%
+is equal to Z is equal to
+zero so when Y is equal to Z is equal 0
+
+ align:start position:0%
+zero so when Y is equal to Z is equal 0
+ 
+
+ align:start position:0%
+zero so when Y is equal to Z is equal 0
+okay well we need to find X still so
+
+ align:start position:0%
+okay well we need to find X still so
+ 
+
+ align:start position:0%
+okay well we need to find X still so
+let's look back at our equations and
+
+ align:start position:0%
+let's look back at our equations and
+ 
+
+ align:start position:0%
+let's look back at our equations and
+when Y is equal to Z is equal to 0 well
+
+ align:start position:0%
+when Y is equal to Z is equal to 0 well
+ 
+
+ align:start position:0%
+when Y is equal to Z is equal to 0 well
+we can solve our constraint equation for
+
+ align:start position:0%
+we can solve our constraint equation for
+ 
+
+ align:start position:0%
+we can solve our constraint equation for
+x when y = zal 0 we have the x^2 = 1 so
+
+ align:start position:0%
+x when y = zal 0 we have the x^2 = 1 so
+ 
+
+ align:start position:0%
+x when y = zal 0 we have the x^2 = 1 so
+there are two possibilities the point uh
+
+ align:start position:0%
+there are two possibilities the point uh
+ 
+
+ align:start position:0%
+there are two possibilities the point uh
+1 0 0 and the point minus one 0 0 so
+
+ align:start position:0%
+1 0 0 and the point minus one 0 0 so
+ 
+
+ align:start position:0%
+1 0 0 and the point minus one 0 0 so
+this gives us in this case we have x = 1
+
+ align:start position:0%
+this gives us in this case we have x = 1
+ 
+
+ align:start position:0%
+this gives us in this case we have x = 1
+or x =
+
+ align:start position:0%
+or x =
+ 
+
+ align:start position:0%
+or x =
+-1 so that gives us the points 1 0 0 and
+
+ align:start position:0%
+-1 so that gives us the points 1 0 0 and
+ 
+
+ align:start position:0%
+-1 so that gives us the points 1 0 0 and
+Min - one 0 0 that we're going to have
+
+ align:start position:0%
+Min - one 0 0 that we're going to have
+ 
+
+ align:start position:0%
+Min - one 0 0 that we're going to have
+to check at the end all right so the
+
+ align:start position:0%
+to check at the end all right so the
+ 
+
+ align:start position:0%
+to check at the end all right so the
+second case is we could have y equal to
+
+ align:start position:0%
+second case is we could have y equal to
+ 
+
+ align:start position:0%
+second case is we could have y equal to
+Z and Lambda equal to 3 so in this case
+
+ align:start position:0%
+Z and Lambda equal to 3 so in this case
+ 
+
+ align:start position:0%
+Z and Lambda equal to 3 so in this case
+let's go back to our equations again so
+
+ align:start position:0%
+let's go back to our equations again so
+ 
+
+ align:start position:0%
+let's go back to our equations again so
+from y from Lambda equals 3
+
+ align:start position:0%
+from y from Lambda equals 3
+ 
+
+ align:start position:0%
+from y from Lambda equals 3
+we have in our first equation that 2x +
+
+ align:start position:0%
+we have in our first equation that 2x +
+ 
+
+ align:start position:0%
+we have in our first equation that 2x +
+1 = 6X so 1 = 4X or X = one4 so this
+
+ align:start position:0%
+1 = 6X so 1 = 4X or X = one4 so this
+ 
+
+ align:start position:0%
+1 = 6X so 1 = 4X or X = one4 so this
+implies over here that x equal one4 and
+
+ align:start position:0%
+implies over here that x equal one4 and
+ 
+
+ align:start position:0%
+implies over here that x equal one4 and
+now let's we still need to find Z so if
+
+ align:start position:0%
+now let's we still need to find Z so if
+ 
+
+ align:start position:0%
+now let's we still need to find Z so if
+we go back to our uh our constraint
+
+ align:start position:0%
+we go back to our uh our constraint
+ 
+
+ align:start position:0%
+we go back to our uh our constraint
+equation here we have that X is a
+
+ align:start position:0%
+equation here we have that X is a
+ 
+
+ align:start position:0%
+equation here we have that X is a
+quarter and Y is Zer so that means 116 +
+
+ align:start position:0%
+quarter and Y is Zer so that means 116 +
+ 
+
+ align:start position:0%
+quarter and Y is Zer so that means 116 +
+z^2 = 1 so has to be the square root of
+
+ align:start position:0%
+z^2 = 1 so has to be the square root of
+ 
+
+ align:start position:0%
+z^2 = 1 so has to be the square root of
+1516 plus or minus um so and Z is equal
+
+ align:start position:0%
+1516 plus or minus um so and Z is equal
+ 
+
+ align:start position:0%
+1516 plus or minus um so and Z is equal
+to plus or minus so that we can also
+
+ align:start position:0%
+to plus or minus so that we can also
+ 
+
+ align:start position:0%
+to plus or minus so that we can also
+write that as the > 15 over 4 so this
+
+ align:start position:0%
+write that as the > 15 over 4 so this
+ 
+
+ align:start position:0%
+write that as the > 15 over 4 so this
+also gives us two points to check the
+
+ align:start position:0%
+also gives us two points to check the
+ 
+
+ align:start position:0%
+also gives us two points to check the
+points are
+
+ align:start position:0%
+points are
+ 
+
+ align:start position:0%
+points are
+one4
+
+ align:start position:0%
+one4
+ 
+
+ align:start position:0%
+one4
+0 < TK 15 over 4 and
+
+ align:start position:0%
+0 < TK 15 over 4 and
+ 
+
+ align:start position:0%
+0 < TK 15 over 4 and
+one4 0 - > 15 over 4 and Fin finally we
+
+ align:start position:0%
+one4 0 - > 15 over 4 and Fin finally we
+ 
+
+ align:start position:0%
+one4 0 - > 15 over 4 and Fin finally we
+have our third case so our third case is
+
+ align:start position:0%
+have our third case so our third case is
+ 
+
+ align:start position:0%
+have our third case so our third case is
+when Lambda is equal to 2 and Z is equal
+
+ align:start position:0%
+when Lambda is equal to 2 and Z is equal
+ 
+
+ align:start position:0%
+when Lambda is equal to 2 and Z is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero so again um let's go back over to
+
+ align:start position:0%
+zero so again um let's go back over to
+ 
+
+ align:start position:0%
+zero so again um let's go back over to
+our equation so when Lambda equals 2 in
+
+ align:start position:0%
+our equation so when Lambda equals 2 in
+ 
+
+ align:start position:0%
+our equation so when Lambda equals 2 in
+the first equation we have 2X + 1 = 4X
+
+ align:start position:0%
+the first equation we have 2X + 1 = 4X
+ 
+
+ align:start position:0%
+the first equation we have 2X + 1 = 4X
+so 2x = 1 or X is a half so this gives
+
+ align:start position:0%
+so 2x = 1 or X is a half so this gives
+ 
+
+ align:start position:0%
+so 2x = 1 or X is a half so this gives
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+xal a half and now if you take zal 0 and
+
+ align:start position:0%
+xal a half and now if you take zal 0 and
+ 
+
+ align:start position:0%
+xal a half and now if you take zal 0 and
+x = 1/2 we can take that down to to our
+
+ align:start position:0%
+x = 1/2 we can take that down to to our
+ 
+
+ align:start position:0%
+x = 1/2 we can take that down to to our
+constraint equation and we get A4 + y^2
+
+ align:start position:0%
+constraint equation and we get A4 + y^2
+ 
+
+ align:start position:0%
+constraint equation and we get A4 + y^2
+= 1 so Y is aare < TK of
+
+ align:start position:0%
+= 1 so Y is aare < TK of
+ 
+
+ align:start position:0%
+= 1 so Y is aare < TK of
+3/4 so y = plus orus < TK 3 / 2 and this
+
+ align:start position:0%
+3/4 so y = plus orus < TK 3 / 2 and this
+ 
+
+ align:start position:0%
+3/4 so y = plus orus < TK 3 / 2 and this
+gives us two
+
+ align:start position:0%
+gives us two
+ 
+
+ align:start position:0%
+gives us two
+points 12 < TK 3 over2
+
+ align:start position:0%
+points 12 < TK 3 over2
+ 
+
+ align:start position:0%
+points 12 < TK 3 over2
+0 and 12 - > 3 over2
+
+ align:start position:0%
+0 and 12 - > 3 over2
+ 
+
+ align:start position:0%
+0 and 12 - > 3 over2
+zero those were our three cases we've
+
+ align:start position:0%
+zero those were our three cases we've
+ 
+
+ align:start position:0%
+zero those were our three cases we've
+solved each of them we' solved each of
+
+ align:start position:0%
+solved each of them we' solved each of
+ 
+
+ align:start position:0%
+solved each of them we' solved each of
+them all the way down to finding the the
+
+ align:start position:0%
+them all the way down to finding the the
+ 
+
+ align:start position:0%
+them all the way down to finding the the
+points that they they lead to now
+
+ align:start position:0%
+points that they they lead to now
+ 
+
+ align:start position:0%
+points that they they lead to now
+remember we said already that there's no
+
+ align:start position:0%
+remember we said already that there's no
+ 
+
+ align:start position:0%
+remember we said already that there's no
+boundry to this region it's just the
+
+ align:start position:0%
+boundry to this region it's just the
+ 
+
+ align:start position:0%
+boundry to this region it's just the
+sphere has it has no edges um so so
+
+ align:start position:0%
+sphere has it has no edges um so so
+ 
+
+ align:start position:0%
+sphere has it has no edges um so so
+these are the only points we have to
+
+ align:start position:0%
+these are the only points we have to
+ 
+
+ align:start position:0%
+these are the only points we have to
+check we have to check these six points
+
+ align:start position:0%
+check we have to check these six points
+ 
+
+ align:start position:0%
+check we have to check these six points
+what do we have to check them for well
+
+ align:start position:0%
+what do we have to check them for well
+ 
+
+ align:start position:0%
+what do we have to check them for well
+we have to look at the value of F at
+
+ align:start position:0%
+we have to look at the value of F at
+ 
+
+ align:start position:0%
+we have to look at the value of F at
+each of these six points to and figure
+
+ align:start position:0%
+each of these six points to and figure
+ 
+
+ align:start position:0%
+each of these six points to and figure
+out we want to figure out where f is
+
+ align:start position:0%
+out we want to figure out where f is
+ 
+
+ align:start position:0%
+out we want to figure out where f is
+maximized and where f is minimized and
+
+ align:start position:0%
+maximized and where f is minimized and
+ 
+
+ align:start position:0%
+maximized and where f is minimized and
+these six points are the the only points
+
+ align:start position:0%
+these six points are the the only points
+ 
+
+ align:start position:0%
+these six points are the the only points
+where that could happen where F could be
+
+ align:start position:0%
+where that could happen where F could be
+ 
+
+ align:start position:0%
+where that could happen where F could be
+maximized or minimized so we just have
+
+ align:start position:0%
+maximized or minimized so we just have
+ 
+
+ align:start position:0%
+maximized or minimized so we just have
+to evaluate our our objective function f
+
+ align:start position:0%
+to evaluate our our objective function f
+ 
+
+ align:start position:0%
+to evaluate our our objective function f
+at these six points and find the largest
+
+ align:start position:0%
+at these six points and find the largest
+ 
+
+ align:start position:0%
+at these six points and find the largest
+value and the smallest value so let's do
+
+ align:start position:0%
+value and the smallest value so let's do
+ 
+
+ align:start position:0%
+value and the smallest value so let's do
+that so our objective function remember
+
+ align:start position:0%
+that so our objective function remember
+ 
+
+ align:start position:0%
+that so our objective function remember
+it's all the way back over here it's
+
+ align:start position:0%
+it's all the way back over here it's
+ 
+
+ align:start position:0%
+it's all the way back over here it's
+this function x^2 + x + 2 y^2 + 3 z^
+
+ align:start position:0%
+this function x^2 + x + 2 y^2 + 3 z^
+ 
+
+ align:start position:0%
+this function x^2 + x + 2 y^2 + 3 z^
+2 Okay so let's let's look at the value
+
+ align:start position:0%
+2 Okay so let's let's look at the value
+ 
+
+ align:start position:0%
+2 Okay so let's let's look at the value
+of that function at these points so x^2
+
+ align:start position:0%
+of that function at these points so x^2
+ 
+
+ align:start position:0%
+of that function at these points so x^2
++ x + 2 y^2 + 3 z^ 2 at the point 1 0
+
+ align:start position:0%
++ x + 2 y^2 + 3 z^ 2 at the point 1 0
+ 
+
+ align:start position:0%
++ x + 2 y^2 + 3 z^ 2 at the point 1 0
+that's just equal to 2 two so I'm just
+
+ align:start position:0%
+that's just equal to 2 two so I'm just
+ 
+
+ align:start position:0%
+that's just equal to 2 two so I'm just
+I'm going to write the function values
+
+ align:start position:0%
+I'm going to write the function values
+ 
+
+ align:start position:0%
+I'm going to write the function values
+just off to the side of the of the
+
+ align:start position:0%
+just off to the side of the of the
+ 
+
+ align:start position:0%
+just off to the side of the of the
+points here so so this gives me the
+
+ align:start position:0%
+points here so so this gives me the
+ 
+
+ align:start position:0%
+points here so so this gives me the
+value two and I'm going to and I'm going
+
+ align:start position:0%
+value two and I'm going to and I'm going
+ 
+
+ align:start position:0%
+value two and I'm going to and I'm going
+to circle them so the point 1 0 0 gives
+
+ align:start position:0%
+to circle them so the point 1 0 0 gives
+ 
+
+ align:start position:0%
+to circle them so the point 1 0 0 gives
+me the value two the point minus one 0 0
+
+ align:start position:0%
+me the value two the point minus one 0 0
+ 
+
+ align:start position:0%
+me the value two the point minus one 0 0
+so that's x^2 is 1 + x is min - one so
+
+ align:start position:0%
+so that's x^2 is 1 + x is min - one so
+ 
+
+ align:start position:0%
+so that's x^2 is 1 + x is min - one so
+that's 1 - 1 is zero and then the Y and
+
+ align:start position:0%
+that's 1 - 1 is zero and then the Y and
+ 
+
+ align:start position:0%
+that's 1 - 1 is zero and then the Y and
+Z terms are both zero so at at the point
+
+ align:start position:0%
+Z terms are both zero so at at the point
+ 
+
+ align:start position:0%
+Z terms are both zero so at at the point
+minus one 0 0 the function value is zero
+
+ align:start position:0%
+minus one 0 0 the function value is zero
+ 
+
+ align:start position:0%
+minus one 0 0 the function value is zero
+I'm going to circle
+
+ align:start position:0%
+I'm going to circle
+ 
+
+ align:start position:0%
+I'm going to circle
+that oh boy okay so at these points at
+
+ align:start position:0%
+that oh boy okay so at these points at
+ 
+
+ align:start position:0%
+that oh boy okay so at these points at
+the point one
+
+ align:start position:0%
+the point one
+ 
+
+ align:start position:0%
+the point one
+qu0 > 15 over4 and 1 qu
+
+ align:start position:0%
+qu0 > 15 over4 and 1 qu
+ 
+
+ align:start position:0%
+qu0 > 15 over4 and 1 qu
+0us 15 over4 uh I'm going to cheat and
+
+ align:start position:0%
+0us 15 over4 uh I'm going to cheat and
+ 
+
+ align:start position:0%
+0us 15 over4 uh I'm going to cheat and
+look at what I wrote down already so you
+
+ align:start position:0%
+look at what I wrote down already so you
+ 
+
+ align:start position:0%
+look at what I wrote down already so you
+could do the arithmetic yourself um but
+
+ align:start position:0%
+could do the arithmetic yourself um but
+ 
+
+ align:start position:0%
+could do the arithmetic yourself um but
+I think it's not that hard to work out
+
+ align:start position:0%
+I think it's not that hard to work out
+ 
+
+ align:start position:0%
+I think it's not that hard to work out
+that in the in both of these cases the
+
+ align:start position:0%
+that in the in both of these cases the
+ 
+
+ align:start position:0%
+that in the in both of these cases the
+function value that you get out is 25
+
+ align:start position:0%
+function value that you get out is 25
+ 
+
+ align:start position:0%
+function value that you get out is 25
+over 8 I'm not going to do the
+
+ align:start position:0%
+over 8 I'm not going to do the
+ 
+
+ align:start position:0%
+over 8 I'm not going to do the
+arithmetic uh right now I don't um so uh
+
+ align:start position:0%
+arithmetic uh right now I don't um so uh
+ 
+
+ align:start position:0%
+arithmetic uh right now I don't um so uh
+but you can you can double check that
+
+ align:start position:0%
+but you can you can double check that
+ 
+
+ align:start position:0%
+but you can you can double check that
+for yourself and at these last two
+
+ align:start position:0%
+for yourself and at these last two
+ 
+
+ align:start position:0%
+for yourself and at these last two
+points the points 12 < tk3 over2 0 and
+
+ align:start position:0%
+points the points 12 < tk3 over2 0 and
+ 
+
+ align:start position:0%
+points the points 12 < tk3 over2 0 and
+12 minus < tk3 over 2 0 um the and and
+
+ align:start position:0%
+12 minus < tk3 over 2 0 um the and and
+ 
+
+ align:start position:0%
+12 minus < tk3 over 2 0 um the and and
+this the the function has the same value
+
+ align:start position:0%
+this the the function has the same value
+ 
+
+ align:start position:0%
+this the the function has the same value
+of both those points that value is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+94s yeah so 25 or8 was the value at both
+
+ align:start position:0%
+94s yeah so 25 or8 was the value at both
+ 
+
+ align:start position:0%
+94s yeah so 25 or8 was the value at both
+of these points and 9/4 was the is the
+
+ align:start position:0%
+of these points and 9/4 was the is the
+ 
+
+ align:start position:0%
+of these points and 9/4 was the is the
+value of both of these points so now to
+
+ align:start position:0%
+value of both of these points so now to
+ 
+
+ align:start position:0%
+value of both of these points so now to
+Maxim to find the maximum value of the
+
+ align:start position:0%
+Maxim to find the maximum value of the
+ 
+
+ align:start position:0%
+Maxim to find the maximum value of the
+function and the minimum value of the
+
+ align:start position:0%
+function and the minimum value of the
+ 
+
+ align:start position:0%
+function and the minimum value of the
+function we just look at the values that
+
+ align:start position:0%
+function we just look at the values that
+ 
+
+ align:start position:0%
+function we just look at the values that
+we got and say which of these is biggest
+
+ align:start position:0%
+we got and say which of these is biggest
+ 
+
+ align:start position:0%
+we got and say which of these is biggest
+and which of these is smallest and in
+
+ align:start position:0%
+and which of these is smallest and in
+ 
+
+ align:start position:0%
+and which of these is smallest and in
+our case it's easy to see that zero is
+
+ align:start position:0%
+our case it's easy to see that zero is
+ 
+
+ align:start position:0%
+our case it's easy to see that zero is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+minimum you know all all the other
+
+ align:start position:0%
+minimum you know all all the other
+ 
+
+ align:start position:0%
+minimum you know all all the other
+values are are positive so zero is the
+
+ align:start position:0%
+values are are positive so zero is the
+ 
+
+ align:start position:0%
+values are are positive so zero is the
+minimum so our minimum
+
+ align:start position:0%
+minimum so our minimum
+ 
+
+ align:start position:0%
+minimum so our minimum
+value the minimum value of f is
+
+ align:start position:0%
+value the minimum value of f is
+ 
+
+ align:start position:0%
+value the minimum value of f is
+zero at the point -1 0 0 and if you just
+
+ align:start position:0%
+zero at the point -1 0 0 and if you just
+ 
+
+ align:start position:0%
+zero at the point -1 0 0 and if you just
+compare the values two and 258 and 9/4
+
+ align:start position:0%
+compare the values two and 258 and 9/4
+ 
+
+ align:start position:0%
+compare the values two and 258 and 9/4
+uh 258 is the is the largest this is
+
+ align:start position:0%
+uh 258 is the is the largest this is
+ 
+
+ align:start position:0%
+uh 258 is the is the largest this is
+bigger than three whereas both of those
+
+ align:start position:0%
+bigger than three whereas both of those
+ 
+
+ align:start position:0%
+bigger than three whereas both of those
+are less than three for example is one
+
+ align:start position:0%
+are less than three for example is one
+ 
+
+ align:start position:0%
+are less than three for example is one
+easy way to see that so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+max of
+
+ align:start position:0%
+max of
+ 
+
+ align:start position:0%
+max of
+f is
+
+ align:start position:0%
+f is
+ 
+
+ align:start position:0%
+f is
+258 and that's achieved at the point
+
+ align:start position:0%
+258 and that's achieved at the point
+ 
+
+ align:start position:0%
+258 and that's achieved at the point
+one4 0 plus orus < TK 15 over
+
+ align:start position:0%
+one4 0 plus orus < TK 15 over
+ 
+
+ align:start position:0%
+one4 0 plus orus < TK 15 over
+4 so there you have it the method of
+
+ align:start position:0%
+4 so there you have it the method of
+ 
+
+ align:start position:0%
+4 so there you have it the method of
+lrange multipliers we just followed
+
+ align:start position:0%
+lrange multipliers we just followed
+ 
+
+ align:start position:0%
+lrange multipliers we just followed
+exactly the the the strategy that that
+
+ align:start position:0%
+exactly the the the strategy that that
+ 
+
+ align:start position:0%
+exactly the the the strategy that that
+that we have so you have you start out
+
+ align:start position:0%
+that we have so you have you start out
+ 
+
+ align:start position:0%
+that we have so you have you start out
+and you have an objective function and a
+
+ align:start position:0%
+and you have an objective function and a
+ 
+
+ align:start position:0%
+and you have an objective function and a
+and a constraint function and so what do
+
+ align:start position:0%
+and a constraint function and so what do
+ 
+
+ align:start position:0%
+and a constraint function and so what do
+you do you write down their partial
+
+ align:start position:0%
+you do you write down their partial
+ 
+
+ align:start position:0%
+you do you write down their partial
+derivatives and you come up with the
+
+ align:start position:0%
+derivatives and you come up with the
+ 
+
+ align:start position:0%
+derivatives and you come up with the
+system of equations so the system of
+
+ align:start position:0%
+system of equations so the system of
+ 
+
+ align:start position:0%
+system of equations so the system of
+equations that you get by setting you
+
+ align:start position:0%
+equations that you get by setting you
+ 
+
+ align:start position:0%
+equations that you get by setting you
+know FX equal Lambda GX FY equal Lambda
+
+ align:start position:0%
+know FX equal Lambda GX FY equal Lambda
+ 
+
+ align:start position:0%
+know FX equal Lambda GX FY equal Lambda
+gy FZ equals Lambda gz and your
+
+ align:start position:0%
+gy FZ equals Lambda gz and your
+ 
+
+ align:start position:0%
+gy FZ equals Lambda gz and your
+constraint equation g equals some
+
+ align:start position:0%
+constraint equation g equals some
+ 
+
+ align:start position:0%
+constraint equation g equals some
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+so then the the one part of this
+
+ align:start position:0%
+so then the the one part of this
+ 
+
+ align:start position:0%
+so then the the one part of this
+procedure that isn't just a a recipe is
+
+ align:start position:0%
+procedure that isn't just a a recipe is
+ 
+
+ align:start position:0%
+procedure that isn't just a a recipe is
+that you need to solve this this system
+
+ align:start position:0%
+that you need to solve this this system
+ 
+
+ align:start position:0%
+that you need to solve this this system
+of equations and sometimes that can be
+
+ align:start position:0%
+of equations and sometimes that can be
+ 
+
+ align:start position:0%
+of equations and sometimes that can be
+hard so in this case there were some a
+
+ align:start position:0%
+hard so in this case there were some a
+ 
+
+ align:start position:0%
+hard so in this case there were some a
+couple of observations that we could
+
+ align:start position:0%
+couple of observations that we could
+ 
+
+ align:start position:0%
+couple of observations that we could
+make from the second and third equations
+
+ align:start position:0%
+make from the second and third equations
+ 
+
+ align:start position:0%
+make from the second and third equations
+that made it relatively straightforward
+
+ align:start position:0%
+that made it relatively straightforward
+ 
+
+ align:start position:0%
+that made it relatively straightforward
+to do um and that gave us some cases and
+
+ align:start position:0%
+to do um and that gave us some cases and
+ 
+
+ align:start position:0%
+to do um and that gave us some cases and
+then in each of those cases we were able
+
+ align:start position:0%
+then in each of those cases we were able
+ 
+
+ align:start position:0%
+then in each of those cases we were able
+to completely solve for the points x y
+
+ align:start position:0%
+to completely solve for the points x y
+ 
+
+ align:start position:0%
+to completely solve for the points x y
+and z now we also could solve for the
+
+ align:start position:0%
+and z now we also could solve for the
+ 
+
+ align:start position:0%
+and z now we also could solve for the
+associated values of Lambda but Lambda
+
+ align:start position:0%
+associated values of Lambda but Lambda
+ 
+
+ align:start position:0%
+associated values of Lambda but Lambda
+isn't important to us it doesn't it
+
+ align:start position:0%
+isn't important to us it doesn't it
+ 
+
+ align:start position:0%
+isn't important to us it doesn't it
+doesn't affect F it's it we can forget
+
+ align:start position:0%
+doesn't affect F it's it we can forget
+ 
+
+ align:start position:0%
+doesn't affect F it's it we can forget
+about it as soon as we' found it once
+
+ align:start position:0%
+about it as soon as we' found it once
+ 
+
+ align:start position:0%
+about it as soon as we' found it once
+we' once we found X Y and Z so we were
+
+ align:start position:0%
+we' once we found X Y and Z so we were
+ 
+
+ align:start position:0%
+we' once we found X Y and Z so we were
+able to solve in this case we got six
+
+ align:start position:0%
+able to solve in this case we got six
+ 
+
+ align:start position:0%
+able to solve in this case we got six
+points of interest and then you just
+
+ align:start position:0%
+points of interest and then you just
+ 
+
+ align:start position:0%
+points of interest and then you just
+look at the value of your objective
+
+ align:start position:0%
+look at the value of your objective
+ 
+
+ align:start position:0%
+look at the value of your objective
+function at those points so that was
+
+ align:start position:0%
+function at those points so that was
+ 
+
+ align:start position:0%
+function at those points so that was
+what I wrote down in these circles so
+
+ align:start position:0%
+what I wrote down in these circles so
+ 
+
+ align:start position:0%
+what I wrote down in these circles so
+you look at the at the value of the
+
+ align:start position:0%
+you look at the at the value of the
+ 
+
+ align:start position:0%
+you look at the at the value of the
+objective function and to find the
+
+ align:start position:0%
+objective function and to find the
+ 
+
+ align:start position:0%
+objective function and to find the
+maximum value of the function you just
+
+ align:start position:0%
+maximum value of the function you just
+ 
+
+ align:start position:0%
+maximum value of the function you just
+look at which of those is largest now
+
+ align:start position:0%
+look at which of those is largest now
+ 
+
+ align:start position:0%
+look at which of those is largest now
+sometimes not in this problem but in
+
+ align:start position:0%
+sometimes not in this problem but in
+ 
+
+ align:start position:0%
+sometimes not in this problem but in
+other problems you'll also have to check
+
+ align:start position:0%
+other problems you'll also have to check
+ 
+
+ align:start position:0%
+other problems you'll also have to check
+if if the region has a boundary you'll
+
+ align:start position:0%
+if if the region has a boundary you'll
+ 
+
+ align:start position:0%
+if if the region has a boundary you'll
+also have to check for possible Maxima
+
+ align:start position:0%
+also have to check for possible Maxima
+ 
+
+ align:start position:0%
+also have to check for possible Maxima
+and Minima on the boundary of the region
+
+ align:start position:0%
+and Minima on the boundary of the region
+ 
+
+ align:start position:0%
+and Minima on the boundary of the region
+but a sphere doesn't have any edges so
+
+ align:start position:0%
+but a sphere doesn't have any edges so
+ 
+
+ align:start position:0%
+but a sphere doesn't have any edges so
+it doesn't have any boundary so we don't
+
+ align:start position:0%
+it doesn't have any boundary so we don't
+ 
+
+ align:start position:0%
+it doesn't have any boundary so we don't
+have to worry about that so that's how
+
+ align:start position:0%
+have to worry about that so that's how
+ 
+
+ align:start position:0%
+have to worry about that so that's how
+we apply the method of lrange
+
+ align:start position:0%
+we apply the method of lrange
+ 
+
+ align:start position:0%
+we apply the method of lrange
+multipliers to this problem and and how
+
+ align:start position:0%
+multipliers to this problem and and how
+ 
+
+ align:start position:0%
+multipliers to this problem and and how
+you can apply it to other problems as
+
+ align:start position:0%
+you can apply it to other problems as
+ 
+
+ align:start position:0%
+you can apply it to other problems as
+well I'll end there
\ No newline at end of file
diff --git a/nyuKHTzr6xA.txt b/nyuKHTzr6xA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..db6dd16ffc3274c235a148644dc7aecc7b07a85b
--- /dev/null
+++ b/nyuKHTzr6xA.txt
@@ -0,0 +1,675 @@
+align:start position:0%
+ 
+now let's talk briefly about
+
+ align:start position:0%
+now let's talk briefly about
+ 
+
+ align:start position:0%
+now let's talk briefly about
+different types of ventilation and
+
+ align:start position:0%
+different types of ventilation and
+ 
+
+ align:start position:0%
+different types of ventilation and
+different ways that they can mix or not
+
+ align:start position:0%
+different ways that they can mix or not
+ 
+
+ align:start position:0%
+different ways that they can mix or not
+mix a
+
+ align:start position:0%
+mix a
+ 
+
+ align:start position:0%
+mix a
+a room the air in a room so the first
+
+ align:start position:0%
+a room the air in a room so the first
+ 
+
+ align:start position:0%
+a room the air in a room so the first
+type which is what we've mainly been
+
+ align:start position:0%
+type which is what we've mainly been
+ 
+
+ align:start position:0%
+type which is what we've mainly been
+talking about is so-called mixing
+
+ align:start position:0%
+talking about is so-called mixing
+ 
+
+ align:start position:0%
+talking about is so-called mixing
+ventilation
+
+ align:start position:0%
+ventilation
+ 
+
+ align:start position:0%
+ventilation
+so this is when uh the cold colder air
+
+ align:start position:0%
+so this is when uh the cold colder air
+ 
+
+ align:start position:0%
+so this is when uh the cold colder air
+is forced from above or in other cases
+
+ align:start position:0%
+is forced from above or in other cases
+ 
+
+ align:start position:0%
+is forced from above or in other cases
+the warmer air is forced from below in
+
+ align:start position:0%
+the warmer air is forced from below in
+ 
+
+ align:start position:0%
+the warmer air is forced from below in
+such a way that there's an
+
+ align:start position:0%
+such a way that there's an
+ 
+
+ align:start position:0%
+such a way that there's an
+unstable thermal gradient so that the
+
+ align:start position:0%
+unstable thermal gradient so that the
+ 
+
+ align:start position:0%
+unstable thermal gradient so that the
+buoyancy
+
+ align:start position:0%
+buoyancy
+ 
+
+ align:start position:0%
+buoyancy
+forces end up contributing towards
+
+ align:start position:0%
+forces end up contributing towards
+ 
+
+ align:start position:0%
+forces end up contributing towards
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+and then you can see that if a person's
+
+ align:start position:0%
+and then you can see that if a person's
+ 
+
+ align:start position:0%
+and then you can see that if a person's
+in the room the natural thermal plume
+
+ align:start position:0%
+in the room the natural thermal plume
+ 
+
+ align:start position:0%
+in the room the natural thermal plume
+rising around
+
+ align:start position:0%
+rising around
+ 
+
+ align:start position:0%
+rising around
+that person of warmer air as well as the
+
+ align:start position:0%
+that person of warmer air as well as the
+ 
+
+ align:start position:0%
+that person of warmer air as well as the
+respiratory plume sketch turn yellow
+
+ align:start position:0%
+respiratory plume sketch turn yellow
+ 
+
+ align:start position:0%
+respiratory plume sketch turn yellow
+from all the breathing
+
+ align:start position:0%
+from all the breathing
+ 
+
+ align:start position:0%
+from all the breathing
+both of them are kind of rising and then
+
+ align:start position:0%
+both of them are kind of rising and then
+ 
+
+ align:start position:0%
+both of them are kind of rising and then
+well mixed in the room before
+
+ align:start position:0%
+well mixed in the room before
+ 
+
+ align:start position:0%
+well mixed in the room before
+they're finally removed by the outlet of
+
+ align:start position:0%
+they're finally removed by the outlet of
+ 
+
+ align:start position:0%
+they're finally removed by the outlet of
+the ventilation
+
+ align:start position:0%
+the ventilation
+ 
+
+ align:start position:0%
+the ventilation
+and so that is the situation we've been
+
+ align:start position:0%
+and so that is the situation we've been
+ 
+
+ align:start position:0%
+and so that is the situation we've been
+mainly talking about of the well-mixed
+
+ align:start position:0%
+mainly talking about of the well-mixed
+ 
+
+ align:start position:0%
+mainly talking about of the well-mixed
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+but it's worth considering that in some
+
+ align:start position:0%
+but it's worth considering that in some
+ 
+
+ align:start position:0%
+but it's worth considering that in some
+other cases the ventilation specifically
+
+ align:start position:0%
+other cases the ventilation specifically
+ 
+
+ align:start position:0%
+other cases the ventilation specifically
+is set up to
+
+ align:start position:0%
+is set up to
+ 
+
+ align:start position:0%
+is set up to
+reduce mixing so especially in rooms
+
+ align:start position:0%
+reduce mixing so especially in rooms
+ 
+
+ align:start position:0%
+reduce mixing so especially in rooms
+that have high
+
+ align:start position:0%
+that have high
+ 
+
+ align:start position:0%
+that have high
+ceilings it can be advantageous to set
+
+ align:start position:0%
+ceilings it can be advantageous to set
+ 
+
+ align:start position:0%
+ceilings it can be advantageous to set
+up a stratified ambient
+
+ align:start position:0%
+up a stratified ambient
+ 
+
+ align:start position:0%
+up a stratified ambient
+where the thermal plume from the body is
+
+ align:start position:0%
+where the thermal plume from the body is
+ 
+
+ align:start position:0%
+where the thermal plume from the body is
+rising
+
+ align:start position:0%
+rising
+ 
+
+ align:start position:0%
+rising
+as well as the respiratory plumes and
+
+ align:start position:0%
+as well as the respiratory plumes and
+ 
+
+ align:start position:0%
+as well as the respiratory plumes and
+are collecting
+
+ align:start position:0%
+are collecting
+ 
+
+ align:start position:0%
+are collecting
+in the upper uh area of the room uh
+
+ align:start position:0%
+in the upper uh area of the room uh
+ 
+
+ align:start position:0%
+in the upper uh area of the room uh
+where they're being uh
+
+ align:start position:0%
+where they're being uh
+ 
+
+ align:start position:0%
+where they're being uh
+gently sucked out as the colder air is
+
+ align:start position:0%
+gently sucked out as the colder air is
+ 
+
+ align:start position:0%
+gently sucked out as the colder air is
+being pumped in now from below so that's
+
+ align:start position:0%
+being pumped in now from below so that's
+ 
+
+ align:start position:0%
+being pumped in now from below so that's
+actually a stable
+
+ align:start position:0%
+actually a stable
+ 
+
+ align:start position:0%
+actually a stable
+thermal gradient uh and so at least the
+
+ align:start position:0%
+thermal gradient uh and so at least the
+ 
+
+ align:start position:0%
+thermal gradient uh and so at least the
+the buoyancy forces are not leading to
+
+ align:start position:0%
+the buoyancy forces are not leading to
+ 
+
+ align:start position:0%
+the buoyancy forces are not leading to
+any uh large-scale convection although
+
+ align:start position:0%
+any uh large-scale convection although
+ 
+
+ align:start position:0%
+any uh large-scale convection although
+there certainly are still boundary layer
+
+ align:start position:0%
+there certainly are still boundary layer
+ 
+
+ align:start position:0%
+there certainly are still boundary layer
+flows and plumes from the people
+
+ align:start position:0%
+flows and plumes from the people
+ 
+
+ align:start position:0%
+flows and plumes from the people
+and from their motion as i have
+
+ align:start position:0%
+and from their motion as i have
+ 
+
+ align:start position:0%
+and from their motion as i have
+described earlier
+
+ align:start position:0%
+described earlier
+ 
+
+ align:start position:0%
+described earlier
+one advantage here is that if a mask is
+
+ align:start position:0%
+one advantage here is that if a mask is
+ 
+
+ align:start position:0%
+one advantage here is that if a mask is
+worn
+
+ align:start position:0%
+worn
+ 
+
+ align:start position:0%
+worn
+then the uh respiratory droplets coming
+
+ align:start position:0%
+then the uh respiratory droplets coming
+ 
+
+ align:start position:0%
+then the uh respiratory droplets coming
+from breathing which are sketcher and
+
+ align:start position:0%
+from breathing which are sketcher and
+ 
+
+ align:start position:0%
+from breathing which are sketcher and
+yellow are kind of brought
+
+ align:start position:0%
+yellow are kind of brought
+ 
+
+ align:start position:0%
+yellow are kind of brought
+closer to the thermal plume and forced
+
+ align:start position:0%
+closer to the thermal plume and forced
+ 
+
+ align:start position:0%
+closer to the thermal plume and forced
+to rise more
+
+ align:start position:0%
+to rise more
+ 
+
+ align:start position:0%
+to rise more
+so it basically causes the uh little
+
+ align:start position:0%
+so it basically causes the uh little
+ 
+
+ align:start position:0%
+so it basically causes the uh little
+droplet let's see the infectious
+
+ align:start position:0%
+droplet let's see the infectious
+ 
+
+ align:start position:0%
+droplet let's see the infectious
+aerosols from the breath
+
+ align:start position:0%
+aerosols from the breath
+ 
+
+ align:start position:0%
+aerosols from the breath
+to be more likely swept to the upper
+
+ align:start position:0%
+to be more likely swept to the upper
+ 
+
+ align:start position:0%
+to be more likely swept to the upper
+reaches where they might sit
+
+ align:start position:0%
+reaches where they might sit
+ 
+
+ align:start position:0%
+reaches where they might sit
+at the higher levels of the room and
+
+ align:start position:0%
+at the higher levels of the room and
+ 
+
+ align:start position:0%
+at the higher levels of the room and
+then be sucked out so that can actually
+
+ align:start position:0%
+then be sucked out so that can actually
+ 
+
+ align:start position:0%
+then be sucked out so that can actually
+be a situation
+
+ align:start position:0%
+be a situation
+ 
+
+ align:start position:0%
+be a situation
+where a less well mixed room can be
+
+ align:start position:0%
+where a less well mixed room can be
+ 
+
+ align:start position:0%
+where a less well mixed room can be
+better on the other hand
+
+ align:start position:0%
+better on the other hand
+ 
+
+ align:start position:0%
+better on the other hand
+the advantage of a well-mixed room is
+
+ align:start position:0%
+the advantage of a well-mixed room is
+ 
+
+ align:start position:0%
+the advantage of a well-mixed room is
+that the pathogen in the droplets is
+
+ align:start position:0%
+that the pathogen in the droplets is
+ 
+
+ align:start position:0%
+that the pathogen in the droplets is
+diluted throughout a larger space and
+
+ align:start position:0%
+diluted throughout a larger space and
+ 
+
+ align:start position:0%
+diluted throughout a larger space and
+that can be
+
+ align:start position:0%
+that can be
+ 
+
+ align:start position:0%
+that can be
+more advantageous in any case this
+
+ align:start position:0%
+more advantageous in any case this
+ 
+
+ align:start position:0%
+more advantageous in any case this
+situation with having uh with high
+
+ align:start position:0%
+situation with having uh with high
+ 
+
+ align:start position:0%
+situation with having uh with high
+ceilings and especially with natural
+
+ align:start position:0%
+ceilings and especially with natural
+ 
+
+ align:start position:0%
+ceilings and especially with natural
+ventilation
+
+ align:start position:0%
+ventilation
+ 
+
+ align:start position:0%
+ventilation
+where you set up a stratified ambient is
+
+ align:start position:0%
+where you set up a stratified ambient is
+ 
+
+ align:start position:0%
+where you set up a stratified ambient is
+a strategy that's been used for a long
+
+ align:start position:0%
+a strategy that's been used for a long
+ 
+
+ align:start position:0%
+a strategy that's been used for a long
+time in fact florence nightingale in the
+
+ align:start position:0%
+time in fact florence nightingale in the
+ 
+
+ align:start position:0%
+time in fact florence nightingale in the
+1800s
+
+ align:start position:0%
+1800s
+ 
+
+ align:start position:0%
+1800s
+recommended that hospitals should have
+
+ align:start position:0%
+recommended that hospitals should have
+ 
+
+ align:start position:0%
+recommended that hospitals should have
+high ceilings and good ventilation
+
+ align:start position:0%
+high ceilings and good ventilation
+ 
+
+ align:start position:0%
+high ceilings and good ventilation
+for protection against airborne
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pathogens
\ No newline at end of file
diff --git a/p8918BiV01c.txt b/p8918BiV01c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d40d43a398014a562363092f6b5f7ccf27281bd
--- /dev/null
+++ b/p8918BiV01c.txt
@@ -0,0 +1,6043 @@
+align:start position:0%
+ 
+I'm Sarah Hansen and today I'm talking
+
+ align:start position:0%
+I'm Sarah Hansen and today I'm talking
+ 
+
+ align:start position:0%
+I'm Sarah Hansen and today I'm talking
+with Anna Bell. She's a super smart
+
+ align:start position:0%
+with Anna Bell. She's a super smart
+ 
+
+ align:start position:0%
+with Anna Bell. She's a super smart
+programmer, author, and senior lecturer
+
+ align:start position:0%
+programmer, author, and senior lecturer
+ 
+
+ align:start position:0%
+programmer, author, and senior lecturer
+at MIT. Her computer science videos on
+
+ align:start position:0%
+at MIT. Her computer science videos on
+ 
+
+ align:start position:0%
+at MIT. Her computer science videos on
+our channel have captivated millions of
+
+ align:start position:0%
+our channel have captivated millions of
+ 
+
+ align:start position:0%
+our channel have captivated millions of
+learners around the world. Today, we
+
+ align:start position:0%
+learners around the world. Today, we
+ 
+
+ align:start position:0%
+learners around the world. Today, we
+talk about Python, growth mindset, and
+
+ align:start position:0%
+talk about Python, growth mindset, and
+ 
+
+ align:start position:0%
+talk about Python, growth mindset, and
+rubber ducks. I have to know what the
+
+ align:start position:0%
+rubber ducks. I have to know what the
+ 
+
+ align:start position:0%
+rubber ducks. I have to know what the
+ducks are now. Like, I I can't continue.
+
+ align:start position:0%
+ducks are now. Like, I I can't continue.
+ 
+
+ align:start position:0%
+ducks are now. Like, I I can't continue.
+Then I ask her, with the emergence of
+
+ align:start position:0%
+Then I ask her, with the emergence of
+ 
+
+ align:start position:0%
+Then I ask her, with the emergence of
+AI, do we even still need to learn how
+
+ align:start position:0%
+AI, do we even still need to learn how
+ 
+
+ align:start position:0%
+AI, do we even still need to learn how
+to code? What's the value proposition of
+
+ align:start position:0%
+to code? What's the value proposition of
+ 
+
+ align:start position:0%
+to code? What's the value proposition of
+learning a language like Python? Do we
+
+ align:start position:0%
+learning a language like Python? Do we
+ 
+
+ align:start position:0%
+learning a language like Python? Do we
+still need to do it? So, not sure if
+
+ align:start position:0%
+still need to do it? So, not sure if
+ 
+
+ align:start position:0%
+still need to do it? So, not sure if
+this exactly answers the question. Oh,
+
+ align:start position:0%
+this exactly answers the question. Oh,
+ 
+
+ align:start position:0%
+this exactly answers the question. Oh,
+tell me more. Find out her answer today
+
+ align:start position:0%
+tell me more. Find out her answer today
+ 
+
+ align:start position:0%
+tell me more. Find out her answer today
+on Chalk Radio. Hi, Anna. Hi. How are
+
+ align:start position:0%
+on Chalk Radio. Hi, Anna. Hi. How are
+ 
+
+ align:start position:0%
+on Chalk Radio. Hi, Anna. Hi. How are
+you? I'm good. You're here. I'm so
+
+ align:start position:0%
+you? I'm good. You're here. I'm so
+ 
+
+ align:start position:0%
+you? I'm good. You're here. I'm so
+excited. Yes, me, too. This is one of
+
+ align:start position:0%
+excited. Yes, me, too. This is one of
+ 
+
+ align:start position:0%
+excited. Yes, me, too. This is one of
+our pilot episodes for something new
+
+ align:start position:0%
+our pilot episodes for something new
+ 
+
+ align:start position:0%
+our pilot episodes for something new
+that we're trying, which is a video
+
+ align:start position:0%
+that we're trying, which is a video
+ 
+
+ align:start position:0%
+that we're trying, which is a video
+version of our Chalk Radio podcast. Many
+
+ align:start position:0%
+version of our Chalk Radio podcast. Many
+ 
+
+ align:start position:0%
+version of our Chalk Radio podcast. Many
+ways, it's an experiment. How do you
+
+ align:start position:0%
+ways, it's an experiment. How do you
+ 
+
+ align:start position:0%
+ways, it's an experiment. How do you
+feel about experiments? Are you an
+
+ align:start position:0%
+feel about experiments? Are you an
+ 
+
+ align:start position:0%
+feel about experiments? Are you an
+adventurous person? No, not at all. Oh,
+
+ align:start position:0%
+adventurous person? No, not at all. Oh,
+ 
+
+ align:start position:0%
+adventurous person? No, not at all. Oh,
+great. We're going to be great. Yeah, I
+
+ align:start position:0%
+great. We're going to be great. Yeah, I
+ 
+
+ align:start position:0%
+great. We're going to be great. Yeah, I
+like stability and I like boring days.
+
+ align:start position:0%
+like stability and I like boring days.
+ 
+
+ align:start position:0%
+like stability and I like boring days.
+Oh, well, I'm not sure we're going to
+
+ align:start position:0%
+Oh, well, I'm not sure we're going to
+ 
+
+ align:start position:0%
+Oh, well, I'm not sure we're going to
+have one of those with these with these
+
+ align:start position:0%
+have one of those with these with these
+ 
+
+ align:start position:0%
+have one of those with these with these
+ducks and so I I actually don't know
+
+ align:start position:0%
+ducks and so I I actually don't know
+ 
+
+ align:start position:0%
+ducks and so I I actually don't know
+what the ducks mean. Um, so I think
+
+ align:start position:0%
+what the ducks mean. Um, so I think
+ 
+
+ align:start position:0%
+what the ducks mean. Um, so I think
+you're going to tell me a little bit
+
+ align:start position:0%
+you're going to tell me a little bit
+ 
+
+ align:start position:0%
+you're going to tell me a little bit
+later, but as we Yeah, I think we're in
+
+ align:start position:0%
+later, but as we Yeah, I think we're in
+ 
+
+ align:start position:0%
+later, but as we Yeah, I think we're in
+for an adventure and a little bit maybe
+
+ align:start position:0%
+for an adventure and a little bit maybe
+ 
+
+ align:start position:0%
+for an adventure and a little bit maybe
+of a choose your own adventure. Mhm. So,
+
+ align:start position:0%
+of a choose your own adventure. Mhm. So,
+ 
+
+ align:start position:0%
+of a choose your own adventure. Mhm. So,
+you're at MIT, you've been here for
+
+ align:start position:0%
+you're at MIT, you've been here for
+ 
+
+ align:start position:0%
+you're at MIT, you've been here for
+about 10 years. Um, and you spend most
+
+ align:start position:0%
+about 10 years. Um, and you spend most
+ 
+
+ align:start position:0%
+about 10 years. Um, and you spend most
+of your time thinking about and teaching
+
+ align:start position:0%
+of your time thinking about and teaching
+ 
+
+ align:start position:0%
+of your time thinking about and teaching
+people who are new to programming,
+
+ align:start position:0%
+people who are new to programming,
+ 
+
+ align:start position:0%
+people who are new to programming,
+introducing them. And I'm wondering what
+
+ align:start position:0%
+introducing them. And I'm wondering what
+ 
+
+ align:start position:0%
+introducing them. And I'm wondering what
+that means to you, why you're interested
+
+ align:start position:0%
+that means to you, why you're interested
+ 
+
+ align:start position:0%
+that means to you, why you're interested
+in teaching in particular, like people
+
+ align:start position:0%
+in teaching in particular, like people
+ 
+
+ align:start position:0%
+in teaching in particular, like people
+like me. What do you get out of that?
+
+ align:start position:0%
+like me. What do you get out of that?
+ 
+
+ align:start position:0%
+like me. What do you get out of that?
+And tell me about that experience. Um,
+
+ align:start position:0%
+And tell me about that experience. Um,
+ 
+
+ align:start position:0%
+And tell me about that experience. Um,
+so I recognize that I well I don't want
+
+ align:start position:0%
+so I recognize that I well I don't want
+ 
+
+ align:start position:0%
+so I recognize that I well I don't want
+everyone to become a computer scientist,
+
+ align:start position:0%
+everyone to become a computer scientist,
+ 
+
+ align:start position:0%
+everyone to become a computer scientist,
+but I do think that everyone should
+
+ align:start position:0%
+but I do think that everyone should
+ 
+
+ align:start position:0%
+but I do think that everyone should
+learn programming as a skill. So
+
+ align:start position:0%
+learn programming as a skill. So
+ 
+
+ align:start position:0%
+learn programming as a skill. So
+programming is should become sort of
+
+ align:start position:0%
+programming is should become sort of
+ 
+
+ align:start position:0%
+programming is should become sort of
+like what math is now where you kind of
+
+ align:start position:0%
+like what math is now where you kind of
+ 
+
+ align:start position:0%
+like what math is now where you kind of
+learn it in um elementary school and you
+
+ align:start position:0%
+learn it in um elementary school and you
+ 
+
+ align:start position:0%
+learn it in um elementary school and you
+obviously use it here and there in your
+
+ align:start position:0%
+obviously use it here and there in your
+ 
+
+ align:start position:0%
+obviously use it here and there in your
+adult life. But I don't know, you know,
+
+ align:start position:0%
+adult life. But I don't know, you know,
+ 
+
+ align:start position:0%
+adult life. But I don't know, you know,
+when you've last used calculus, right?
+
+ align:start position:0%
+when you've last used calculus, right?
+ 
+
+ align:start position:0%
+when you've last used calculus, right?
+like we don't all need to become
+
+ align:start position:0%
+like we don't all need to become
+ 
+
+ align:start position:0%
+like we don't all need to become
+mathematicians after we've learned basic
+
+ align:start position:0%
+mathematicians after we've learned basic
+ 
+
+ align:start position:0%
+mathematicians after we've learned basic
+math. Similarly, I do think people
+
+ align:start position:0%
+math. Similarly, I do think people
+ 
+
+ align:start position:0%
+math. Similarly, I do think people
+should learn basic programming, but they
+
+ align:start position:0%
+should learn basic programming, but they
+ 
+
+ align:start position:0%
+should learn basic programming, but they
+don't have to become computer
+
+ align:start position:0%
+don't have to become computer
+ 
+
+ align:start position:0%
+don't have to become computer
+scientists. So, the reason that I enjoy
+
+ align:start position:0%
+scientists. So, the reason that I enjoy
+ 
+
+ align:start position:0%
+scientists. So, the reason that I enjoy
+teaching students intro programming and
+
+ align:start position:0%
+teaching students intro programming and
+ 
+
+ align:start position:0%
+teaching students intro programming and
+exposing them to intromputer science is
+
+ align:start position:0%
+exposing them to intromputer science is
+ 
+
+ align:start position:0%
+exposing them to intromputer science is
+because it was really hard for me to
+
+ align:start position:0%
+because it was really hard for me to
+ 
+
+ align:start position:0%
+because it was really hard for me to
+understand programming when I first
+
+ align:start position:0%
+understand programming when I first
+ 
+
+ align:start position:0%
+understand programming when I first
+started and I just always remember how
+
+ align:start position:0%
+started and I just always remember how
+ 
+
+ align:start position:0%
+started and I just always remember how
+tough it was.
+
+ align:start position:0%
+tough it was.
+ 
+
+ align:start position:0%
+tough it was.
+And I'm at right I teach at MIT and
+
+ align:start position:0%
+And I'm at right I teach at MIT and
+ 
+
+ align:start position:0%
+And I'm at right I teach at MIT and
+there's obviously a lot of really smart
+
+ align:start position:0%
+there's obviously a lot of really smart
+ 
+
+ align:start position:0%
+there's obviously a lot of really smart
+people here. And I think as you teach
+
+ align:start position:0%
+people here. And I think as you teach
+ 
+
+ align:start position:0%
+people here. And I think as you teach
+more and more it's easy to forget how
+
+ align:start position:0%
+more and more it's easy to forget how
+ 
+
+ align:start position:0%
+more and more it's easy to forget how
+hard it was to start learning. And so
+
+ align:start position:0%
+hard it was to start learning. And so
+ 
+
+ align:start position:0%
+hard it was to start learning. And so
+you know as an intro course you know you
+
+ align:start position:0%
+you know as an intro course you know you
+ 
+
+ align:start position:0%
+you know as an intro course you know you
+might make the problems you give
+
+ align:start position:0%
+might make the problems you give
+ 
+
+ align:start position:0%
+might make the problems you give
+students harder and harder each year
+
+ align:start position:0%
+students harder and harder each year
+ 
+
+ align:start position:0%
+students harder and harder each year
+just because they get maybe boring for
+
+ align:start position:0%
+just because they get maybe boring for
+ 
+
+ align:start position:0%
+just because they get maybe boring for
+you but it's not boring for the
+
+ align:start position:0%
+you but it's not boring for the
+ 
+
+ align:start position:0%
+you but it's not boring for the
+students. And I try to recognize that
+
+ align:start position:0%
+students. And I try to recognize that
+ 
+
+ align:start position:0%
+students. And I try to recognize that
+every like every semester I just
+
+ align:start position:0%
+every like every semester I just
+ 
+
+ align:start position:0%
+every like every semester I just
+remember it was really hard for me.
+
+ align:start position:0%
+remember it was really hard for me.
+ 
+
+ align:start position:0%
+remember it was really hard for me.
+they've never seen this before. So, it's
+
+ align:start position:0%
+they've never seen this before. So, it's
+ 
+
+ align:start position:0%
+they've never seen this before. So, it's
+really important to make sure that they
+
+ align:start position:0%
+really important to make sure that they
+ 
+
+ align:start position:0%
+really important to make sure that they
+have a really good experience. You
+
+ align:start position:0%
+have a really good experience. You
+ 
+
+ align:start position:0%
+have a really good experience. You
+mentioned that when you first started
+
+ align:start position:0%
+mentioned that when you first started
+ 
+
+ align:start position:0%
+mentioned that when you first started
+programming it was difficult. Y I'm
+
+ align:start position:0%
+programming it was difficult. Y I'm
+ 
+
+ align:start position:0%
+programming it was difficult. Y I'm
+wondering like what made it difficult
+
+ align:start position:0%
+wondering like what made it difficult
+ 
+
+ align:start position:0%
+wondering like what made it difficult
+and then what are you doing in your
+
+ align:start position:0%
+and then what are you doing in your
+ 
+
+ align:start position:0%
+and then what are you doing in your
+teaching to make it less difficult? I
+
+ align:start position:0%
+teaching to make it less difficult? I
+ 
+
+ align:start position:0%
+teaching to make it less difficult? I
+honestly don't know what made it
+
+ align:start position:0%
+honestly don't know what made it
+ 
+
+ align:start position:0%
+honestly don't know what made it
+difficult. The the beginning was easy
+
+ align:start position:0%
+difficult. The the beginning was easy
+ 
+
+ align:start position:0%
+difficult. The the beginning was easy
+just kind of understanding the basics of
+
+ align:start position:0%
+just kind of understanding the basics of
+ 
+
+ align:start position:0%
+just kind of understanding the basics of
+just you know writing uh the basics of
+
+ align:start position:0%
+just you know writing uh the basics of
+ 
+
+ align:start position:0%
+just you know writing uh the basics of
+creating an algorithm is basically three
+
+ align:start position:0%
+creating an algorithm is basically three
+ 
+
+ align:start position:0%
+creating an algorithm is basically three
+things. So the first is a sequence of
+
+ align:start position:0%
+things. So the first is a sequence of
+ 
+
+ align:start position:0%
+things. So the first is a sequence of
+steps. So step one, step two, step
+
+ align:start position:0%
+steps. So step one, step two, step
+ 
+
+ align:start position:0%
+steps. So step one, step two, step
+three. Um some sort of way to control
+
+ align:start position:0%
+three. Um some sort of way to control
+ 
+
+ align:start position:0%
+three. Um some sort of way to control
+the flow of those steps. So usually you
+
+ align:start position:0%
+the flow of those steps. So usually you
+ 
+
+ align:start position:0%
+the flow of those steps. So usually you
+go step by step, but at some point you
+
+ align:start position:0%
+go step by step, but at some point you
+ 
+
+ align:start position:0%
+go step by step, but at some point you
+say, well, if this is true, do this,
+
+ align:start position:0%
+say, well, if this is true, do this,
+ 
+
+ align:start position:0%
+say, well, if this is true, do this,
+otherwise do this. So like a branching
+
+ align:start position:0%
+otherwise do this. So like a branching
+ 
+
+ align:start position:0%
+otherwise do this. So like a branching
+kind of idea. And then there's also a
+
+ align:start position:0%
+kind of idea. And then there's also a
+ 
+
+ align:start position:0%
+kind of idea. And then there's also a
+way to control the flow by asking the py
+
+ align:start position:0%
+way to control the flow by asking the py
+ 
+
+ align:start position:0%
+way to control the flow by asking the py
+the program to repeat certain lines. So
+
+ align:start position:0%
+the program to repeat certain lines. So
+ 
+
+ align:start position:0%
+the program to repeat certain lines. So
+it's like, well, if this is true, go
+
+ align:start position:0%
+it's like, well, if this is true, go
+ 
+
+ align:start position:0%
+it's like, well, if this is true, go
+back and repeat this a million times,
+
+ align:start position:0%
+back and repeat this a million times,
+ 
+
+ align:start position:0%
+back and repeat this a million times,
+which is very easy for a computer to do.
+
+ align:start position:0%
+which is very easy for a computer to do.
+ 
+
+ align:start position:0%
+which is very easy for a computer to do.
+So a sequence of steps, a way to control
+
+ align:start position:0%
+So a sequence of steps, a way to control
+ 
+
+ align:start position:0%
+So a sequence of steps, a way to control
+the flow of those steps, and then a way
+
+ align:start position:0%
+the flow of those steps, and then a way
+ 
+
+ align:start position:0%
+the flow of those steps, and then a way
+to stop. Those are the three things that
+
+ align:start position:0%
+to stop. Those are the three things that
+ 
+
+ align:start position:0%
+to stop. Those are the three things that
+make an algorithm. That's that's how you
+
+ align:start position:0%
+make an algorithm. That's that's how you
+ 
+
+ align:start position:0%
+make an algorithm. That's that's how you
+write a program. And the grasping that
+
+ align:start position:0%
+write a program. And the grasping that
+ 
+
+ align:start position:0%
+write a program. And the grasping that
+was not hard. It was just sort of once
+
+ align:start position:0%
+was not hard. It was just sort of once
+ 
+
+ align:start position:0%
+was not hard. It was just sort of once
+you've gotten over that learning curve,
+
+ align:start position:0%
+you've gotten over that learning curve,
+ 
+
+ align:start position:0%
+you've gotten over that learning curve,
+it's learning sort of some of the more
+
+ align:start position:0%
+it's learning sort of some of the more
+ 
+
+ align:start position:0%
+it's learning sort of some of the more
+advanced concepts that were
+
+ align:start position:0%
+advanced concepts that were
+ 
+
+ align:start position:0%
+advanced concepts that were
+um that were harder some of the details
+
+ align:start position:0%
+um that were harder some of the details
+ 
+
+ align:start position:0%
+um that were harder some of the details
+for how that specific language works. So
+
+ align:start position:0%
+for how that specific language works. So
+ 
+
+ align:start position:0%
+for how that specific language works. So
+I started with Java, not Python, which
+
+ align:start position:0%
+I started with Java, not Python, which
+ 
+
+ align:start position:0%
+I started with Java, not Python, which
+was a little which was harder than it's
+
+ align:start position:0%
+was a little which was harder than it's
+ 
+
+ align:start position:0%
+was a little which was harder than it's
+a lot harder than Python. There's a
+
+ align:start position:0%
+a lot harder than Python. There's a
+ 
+
+ align:start position:0%
+a lot harder than Python. There's a
+bunch of details that you need to think
+
+ align:start position:0%
+bunch of details that you need to think
+ 
+
+ align:start position:0%
+bunch of details that you need to think
+about there. So I had the opportunity to
+
+ align:start position:0%
+about there. So I had the opportunity to
+ 
+
+ align:start position:0%
+about there. So I had the opportunity to
+watch some of your lecture videos. Yeah.
+
+ align:start position:0%
+watch some of your lecture videos. Yeah.
+ 
+
+ align:start position:0%
+watch some of your lecture videos. Yeah.
+And I noticed that you make space and
+
+ align:start position:0%
+And I noticed that you make space and
+ 
+
+ align:start position:0%
+And I noticed that you make space and
+time for students to practice like right
+
+ align:start position:0%
+time for students to practice like right
+ 
+
+ align:start position:0%
+time for students to practice like right
+in the class itself. Um definitely
+
+ align:start position:0%
+in the class itself. Um definitely
+ 
+
+ align:start position:0%
+in the class itself. Um definitely
+outside the class as well, but like in
+
+ align:start position:0%
+outside the class as well, but like in
+ 
+
+ align:start position:0%
+outside the class as well, but like in
+the actual space where you're teaching.
+
+ align:start position:0%
+the actual space where you're teaching.
+ 
+
+ align:start position:0%
+the actual space where you're teaching.
+And I'm wondering if you could talk
+
+ align:start position:0%
+And I'm wondering if you could talk
+ 
+
+ align:start position:0%
+And I'm wondering if you could talk
+about that a little bit, why you do
+
+ align:start position:0%
+about that a little bit, why you do
+ 
+
+ align:start position:0%
+about that a little bit, why you do
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+Yeah. So, I think I mentioned this
+
+ align:start position:0%
+Yeah. So, I think I mentioned this
+ 
+
+ align:start position:0%
+Yeah. So, I think I mentioned this
+before. I sort of see programming like
+
+ align:start position:0%
+before. I sort of see programming like
+ 
+
+ align:start position:0%
+before. I sort of see programming like
+math is now, but this will be, you know,
+
+ align:start position:0%
+math is now, but this will be, you know,
+ 
+
+ align:start position:0%
+math is now, but this will be, you know,
+many years from now. Um, it's a skill
+
+ align:start position:0%
+many years from now. Um, it's a skill
+ 
+
+ align:start position:0%
+many years from now. Um, it's a skill
+that people need to get that they don't
+
+ align:start position:0%
+that people need to get that they don't
+ 
+
+ align:start position:0%
+that people need to get that they don't
+have yet. And so, if we think about the
+
+ align:start position:0%
+have yet. And so, if we think about the
+ 
+
+ align:start position:0%
+have yet. And so, if we think about the
+way we learn math in school, it's a lot
+
+ align:start position:0%
+way we learn math in school, it's a lot
+ 
+
+ align:start position:0%
+way we learn math in school, it's a lot
+a lot of practice, right? You just
+
+ align:start position:0%
+a lot of practice, right? You just
+ 
+
+ align:start position:0%
+a lot of practice, right? You just
+always constantly practice adding,
+
+ align:start position:0%
+always constantly practice adding,
+ 
+
+ align:start position:0%
+always constantly practice adding,
+subtracting, multiplying, right? The
+
+ align:start position:0%
+subtracting, multiplying, right? The
+ 
+
+ align:start position:0%
+subtracting, multiplying, right? The
+kids. Yeah. So I think it's very
+
+ align:start position:0%
+kids. Yeah. So I think it's very
+ 
+
+ align:start position:0%
+kids. Yeah. So I think it's very
+important for students to actually get
+
+ align:start position:0%
+important for students to actually get
+ 
+
+ align:start position:0%
+important for students to actually get
+the time to to do to do that practice.
+
+ align:start position:0%
+the time to to do to do that practice.
+ 
+
+ align:start position:0%
+the time to to do to do that practice.
+The way I run the class is a sort of a
+
+ align:start position:0%
+The way I run the class is a sort of a
+ 
+
+ align:start position:0%
+The way I run the class is a sort of a
+flip classroom or a blended learning
+
+ align:start position:0%
+flip classroom or a blended learning
+ 
+
+ align:start position:0%
+flip classroom or a blended learning
+style where students watch sort of the
+
+ align:start position:0%
+style where students watch sort of the
+ 
+
+ align:start position:0%
+style where students watch sort of the
+basics through video first and then in
+
+ align:start position:0%
+basics through video first and then in
+ 
+
+ align:start position:0%
+basics through video first and then in
+the actual classroom we do active
+
+ align:start position:0%
+the actual classroom we do active
+ 
+
+ align:start position:0%
+the actual classroom we do active
+learning. So, uh, I go over maybe
+
+ align:start position:0%
+learning. So, uh, I go over maybe
+ 
+
+ align:start position:0%
+learning. So, uh, I go over maybe
+something that's a little bit more
+
+ align:start position:0%
+something that's a little bit more
+ 
+
+ align:start position:0%
+something that's a little bit more
+confusing and then I give them time to
+
+ align:start position:0%
+confusing and then I give them time to
+ 
+
+ align:start position:0%
+confusing and then I give them time to
+break with the hope that me forcing them
+
+ align:start position:0%
+break with the hope that me forcing them
+ 
+
+ align:start position:0%
+break with the hope that me forcing them
+to have them actually start coding,
+
+ align:start position:0%
+to have them actually start coding,
+ 
+
+ align:start position:0%
+to have them actually start coding,
+they'll be able to see, oh, um, I
+
+ align:start position:0%
+they'll be able to see, oh, um, I
+ 
+
+ align:start position:0%
+they'll be able to see, oh, um, I
+totally understood what she was talking
+
+ align:start position:0%
+totally understood what she was talking
+ 
+
+ align:start position:0%
+totally understood what she was talking
+about in the video and I can totally
+
+ align:start position:0%
+about in the video and I can totally
+ 
+
+ align:start position:0%
+about in the video and I can totally
+code that, but then when they actually
+
+ align:start position:0%
+code that, but then when they actually
+ 
+
+ align:start position:0%
+code that, but then when they actually
+when I'm forcing them to actually do it,
+
+ align:start position:0%
+when I'm forcing them to actually do it,
+ 
+
+ align:start position:0%
+when I'm forcing them to actually do it,
+you know, starting with a blank slate,
+
+ align:start position:0%
+you know, starting with a blank slate,
+ 
+
+ align:start position:0%
+you know, starting with a blank slate,
+it's pretty daunting. And so I want them
+
+ align:start position:0%
+it's pretty daunting. And so I want them
+ 
+
+ align:start position:0%
+it's pretty daunting. And so I want them
+to get over that bump where it's like
+
+ align:start position:0%
+to get over that bump where it's like
+ 
+
+ align:start position:0%
+to get over that bump where it's like
+you have a blank piece of, you know,
+
+ align:start position:0%
+you have a blank piece of, you know,
+ 
+
+ align:start position:0%
+you have a blank piece of, you know,
+blank editor or whatever. And then you
+
+ align:start position:0%
+blank editor or whatever. And then you
+ 
+
+ align:start position:0%
+blank editor or whatever. And then you
+just have to start writing something
+
+ align:start position:0%
+just have to start writing something
+ 
+
+ align:start position:0%
+just have to start writing something
+down once the more you do it, the more
+
+ align:start position:0%
+down once the more you do it, the more
+ 
+
+ align:start position:0%
+down once the more you do it, the more
+you feel comfortable with it. So there's
+
+ align:start position:0%
+you feel comfortable with it. So there's
+ 
+
+ align:start position:0%
+you feel comfortable with it. So there's
+all these breaks for all these
+
+ align:start position:0%
+all these breaks for all these
+ 
+
+ align:start position:0%
+all these breaks for all these
+activities that I that I try to keep the
+
+ align:start position:0%
+activities that I that I try to keep the
+ 
+
+ align:start position:0%
+activities that I that I try to keep the
+class lively, of course, and and kind of
+
+ align:start position:0%
+class lively, of course, and and kind of
+ 
+
+ align:start position:0%
+class lively, of course, and and kind of
+indirectly have them practice these
+
+ align:start position:0%
+indirectly have them practice these
+ 
+
+ align:start position:0%
+indirectly have them practice these
+skills like just just write something
+
+ align:start position:0%
+skills like just just write something
+ 
+
+ align:start position:0%
+skills like just just write something
+just write something down. Yeah. And
+
+ align:start position:0%
+just write something down. Yeah. And
+ 
+
+ align:start position:0%
+just write something down. Yeah. And
+also that does two things I think. Um it
+
+ align:start position:0%
+also that does two things I think. Um it
+ 
+
+ align:start position:0%
+also that does two things I think. Um it
+deemphasizes perfection. You're like
+
+ align:start position:0%
+deemphasizes perfection. You're like
+ 
+
+ align:start position:0%
+deemphasizes perfection. You're like
+this is practice like Yep. I think like
+
+ align:start position:0%
+this is practice like Yep. I think like
+ 
+
+ align:start position:0%
+this is practice like Yep. I think like
+an artist, right? So just like get a
+
+ align:start position:0%
+an artist, right? So just like get a
+ 
+
+ align:start position:0%
+an artist, right? So just like get a
+sketch, write a few lines like just get
+
+ align:start position:0%
+sketch, write a few lines like just get
+ 
+
+ align:start position:0%
+sketch, write a few lines like just get
+something down. Yes. And then we can
+
+ align:start position:0%
+something down. Yes. And then we can
+ 
+
+ align:start position:0%
+something down. Yes. And then we can
+improve it. Yep. Um and then that speaks
+
+ align:start position:0%
+improve it. Yep. Um and then that speaks
+ 
+
+ align:start position:0%
+improve it. Yep. Um and then that speaks
+to something else you've mentioned
+
+ align:start position:0%
+to something else you've mentioned
+ 
+
+ align:start position:0%
+to something else you've mentioned
+before and that's like growth mindset
+
+ align:start position:0%
+before and that's like growth mindset
+ 
+
+ align:start position:0%
+before and that's like growth mindset
+and that programming is not like a gift
+
+ align:start position:0%
+and that programming is not like a gift
+ 
+
+ align:start position:0%
+and that programming is not like a gift
+and you have it or you don't but it's
+
+ align:start position:0%
+and you have it or you don't but it's
+ 
+
+ align:start position:0%
+and you have it or you don't but it's
+really something that can be developed.
+
+ align:start position:0%
+really something that can be developed.
+ 
+
+ align:start position:0%
+really something that can be developed.
+Yeah. A lot of a lot of you know you see
+
+ align:start position:0%
+Yeah. A lot of a lot of you know you see
+ 
+
+ align:start position:0%
+Yeah. A lot of a lot of you know you see
+some people who are really good at
+
+ align:start position:0%
+some people who are really good at
+ 
+
+ align:start position:0%
+some people who are really good at
+programming they didn't get good just
+
+ align:start position:0%
+programming they didn't get good just
+ 
+
+ align:start position:0%
+programming they didn't get good just
+because they had that skill they were
+
+ align:start position:0%
+because they had that skill they were
+ 
+
+ align:start position:0%
+because they had that skill they were
+born with it right there's a lot of
+
+ align:start position:0%
+born with it right there's a lot of
+ 
+
+ align:start position:0%
+born with it right there's a lot of
+growth mindset involved in that and
+
+ align:start position:0%
+growth mindset involved in that and
+ 
+
+ align:start position:0%
+growth mindset involved in that and
+anybody can reach that level of being
+
+ align:start position:0%
+anybody can reach that level of being
+ 
+
+ align:start position:0%
+anybody can reach that level of being
+good at at something programming
+
+ align:start position:0%
+good at at something programming
+ 
+
+ align:start position:0%
+good at at something programming
+included just by lots of practice trying
+
+ align:start position:0%
+included just by lots of practice trying
+ 
+
+ align:start position:0%
+included just by lots of practice trying
+different things challenging themselves
+
+ align:start position:0%
+different things challenging themselves
+ 
+
+ align:start position:0%
+different things challenging themselves
+so not just sticking to things that are
+
+ align:start position:0%
+so not just sticking to things that are
+ 
+
+ align:start position:0%
+so not just sticking to things that are
+obviously way too easy because then
+
+ align:start position:0%
+obviously way too easy because then
+ 
+
+ align:start position:0%
+obviously way too easy because then
+you'll never grow but you kind of like I
+
+ align:start position:0%
+you'll never grow but you kind of like I
+ 
+
+ align:start position:0%
+you'll never grow but you kind of like I
+don't know if you know this um the state
+
+ align:start position:0%
+don't know if you know this um the state
+ 
+
+ align:start position:0%
+don't know if you know this um the state
+of flow. It's like this chart where you
+
+ align:start position:0%
+of flow. It's like this chart where you
+ 
+
+ align:start position:0%
+of flow. It's like this chart where you
+kind of want to be in this like middle
+
+ align:start position:0%
+kind of want to be in this like middle
+ 
+
+ align:start position:0%
+kind of want to be in this like middle
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+um but kind of oscillating between doing
+
+ align:start position:0%
+um but kind of oscillating between doing
+ 
+
+ align:start position:0%
+um but kind of oscillating between doing
+things that are too easy and then
+
+ align:start position:0%
+things that are too easy and then
+ 
+
+ align:start position:0%
+things that are too easy and then
+challenging yourself and doing things
+
+ align:start position:0%
+challenging yourself and doing things
+ 
+
+ align:start position:0%
+challenging yourself and doing things
+that a little bit harder. Um and not you
+
+ align:start position:0%
+that a little bit harder. Um and not you
+ 
+
+ align:start position:0%
+that a little bit harder. Um and not you
+don't want to always do two things too
+
+ align:start position:0%
+don't want to always do two things too
+ 
+
+ align:start position:0%
+don't want to always do two things too
+hard because then that's discouraging
+
+ align:start position:0%
+hard because then that's discouraging
+ 
+
+ align:start position:0%
+hard because then that's discouraging
+and you'll stop. But you don't want to
+
+ align:start position:0%
+and you'll stop. But you don't want to
+ 
+
+ align:start position:0%
+and you'll stop. But you don't want to
+do things that are always too easy
+
+ align:start position:0%
+do things that are always too easy
+ 
+
+ align:start position:0%
+do things that are always too easy
+because then you'll never grow. I wonder
+
+ align:start position:0%
+because then you'll never grow. I wonder
+ 
+
+ align:start position:0%
+because then you'll never grow. I wonder
+if we could write an algorithm for
+
+ align:start position:0%
+if we could write an algorithm for
+ 
+
+ align:start position:0%
+if we could write an algorithm for
+staying in the flow like it tracks like
+
+ align:start position:0%
+staying in the flow like it tracks like
+ 
+
+ align:start position:0%
+staying in the flow like it tracks like
+oh this is too easy for you get in a lot
+
+ align:start position:0%
+oh this is too easy for you get in a lot
+ 
+
+ align:start position:0%
+oh this is too easy for you get in a lot
+of the education platforms right are
+
+ align:start position:0%
+of the education platforms right are
+ 
+
+ align:start position:0%
+of the education platforms right are
+trying to give uh students based on
+
+ align:start position:0%
+trying to give uh students based on
+ 
+
+ align:start position:0%
+trying to give uh students based on
+their responses you know even in math
+
+ align:start position:0%
+their responses you know even in math
+ 
+
+ align:start position:0%
+their responses you know even in math
+questions right and be like oh this
+
+ align:start position:0%
+questions right and be like oh this
+ 
+
+ align:start position:0%
+questions right and be like oh this
+student totally got all these let me
+
+ align:start position:0%
+student totally got all these let me
+ 
+
+ align:start position:0%
+student totally got all these let me
+give them a harder one and it's like oh
+
+ align:start position:0%
+give them a harder one and it's like oh
+ 
+
+ align:start position:0%
+give them a harder one and it's like oh
+that was too hard let me yeah how did
+
+ align:start position:0%
+that was too hard let me yeah how did
+ 
+
+ align:start position:0%
+that was too hard let me yeah how did
+you find your way to programming is this
+
+ align:start position:0%
+you find your way to programming is this
+ 
+
+ align:start position:0%
+you find your way to programming is this
+something that you've always wanted to
+
+ align:start position:0%
+something that you've always wanted to
+ 
+
+ align:start position:0%
+something that you've always wanted to
+do or did it develop along the way um so
+
+ align:start position:0%
+do or did it develop along the way um so
+ 
+
+ align:start position:0%
+do or did it develop along the way um so
+my my parents immigrated from Romania
+
+ align:start position:0%
+my my parents immigrated from Romania
+ 
+
+ align:start position:0%
+my my parents immigrated from Romania
+and we went uh we immigrated to Canada
+
+ align:start position:0%
+and we went uh we immigrated to Canada
+ 
+
+ align:start position:0%
+and we went uh we immigrated to Canada
+and my dad was a electrical engineer and
+
+ align:start position:0%
+and my dad was a electrical engineer and
+ 
+
+ align:start position:0%
+and my dad was a electrical engineer and
+then he went into software engineering
+
+ align:start position:0%
+then he went into software engineering
+ 
+
+ align:start position:0%
+then he went into software engineering
+and uh being an immigrant uh immigrant
+
+ align:start position:0%
+and uh being an immigrant uh immigrant
+ 
+
+ align:start position:0%
+and uh being an immigrant uh immigrant
+parents from Europe uh we were highly
+
+ align:start position:0%
+parents from Europe uh we were highly
+ 
+
+ align:start position:0%
+parents from Europe uh we were highly
+encouraged my sister and I were highly
+
+ align:start position:0%
+encouraged my sister and I were highly
+ 
+
+ align:start position:0%
+encouraged my sister and I were highly
+encouraged to get uh some sort of
+
+ align:start position:0%
+encouraged to get uh some sort of
+ 
+
+ align:start position:0%
+encouraged to get uh some sort of
+engineering job right so it's just what
+
+ align:start position:0%
+engineering job right so it's just what
+ 
+
+ align:start position:0%
+engineering job right so it's just what
+what what is done and so uh computer
+
+ align:start position:0%
+what what is done and so uh computer
+ 
+
+ align:start position:0%
+what what is done and so uh computer
+computer engineering or computer
+
+ align:start position:0%
+computer engineering or computer
+ 
+
+ align:start position:0%
+computer engineering or computer
+science, something along those lines
+
+ align:start position:0%
+science, something along those lines
+ 
+
+ align:start position:0%
+science, something along those lines
+seemed to be the best option uh given
+
+ align:start position:0%
+seemed to be the best option uh given
+ 
+
+ align:start position:0%
+seemed to be the best option uh given
+sort of where things were going in the
+
+ align:start position:0%
+sort of where things were going in the
+ 
+
+ align:start position:0%
+sort of where things were going in the
+future. This was the '9s. Um so just the
+
+ align:start position:0%
+future. This was the '9s. Um so just the
+ 
+
+ align:start position:0%
+future. This was the '9s. Um so just the
+beginning of the internet, the beginning
+
+ align:start position:0%
+beginning of the internet, the beginning
+ 
+
+ align:start position:0%
+beginning of the internet, the beginning
+of all that um right that boom. Uh, so
+
+ align:start position:0%
+of all that um right that boom. Uh, so
+ 
+
+ align:start position:0%
+of all that um right that boom. Uh, so
+my dad recognized that that was sort of
+
+ align:start position:0%
+my dad recognized that that was sort of
+ 
+
+ align:start position:0%
+my dad recognized that that was sort of
+what the what the future would be and he
+
+ align:start position:0%
+what the what the future would be and he
+ 
+
+ align:start position:0%
+what the what the future would be and he
+said, "You should probably learn to
+
+ align:start position:0%
+said, "You should probably learn to
+ 
+
+ align:start position:0%
+said, "You should probably learn to
+program and potentially go, you know,
+
+ align:start position:0%
+program and potentially go, you know,
+ 
+
+ align:start position:0%
+program and potentially go, you know,
+and probably go into that sort of
+
+ align:start position:0%
+and probably go into that sort of
+ 
+
+ align:start position:0%
+and probably go into that sort of
+career." And I wasn't super interested
+
+ align:start position:0%
+career." And I wasn't super interested
+ 
+
+ align:start position:0%
+career." And I wasn't super interested
+in anything else, so I just said,
+
+ align:start position:0%
+in anything else, so I just said,
+ 
+
+ align:start position:0%
+in anything else, so I just said,
+"Sure." Um, and so he taught us Java
+
+ align:start position:0%
+"Sure." Um, and so he taught us Java
+ 
+
+ align:start position:0%
+"Sure." Um, and so he taught us Java
+when I was about 12. Um, I have a a
+
+ align:start position:0%
+when I was about 12. Um, I have a a
+ 
+
+ align:start position:0%
+when I was about 12. Um, I have a a
+picture here. Oh, yeah. Let's see it.
+
+ align:start position:0%
+picture here. Oh, yeah. Let's see it.
+ 
+
+ align:start position:0%
+picture here. Oh, yeah. Let's see it.
+Okay. And it's in this really cool
+
+ align:start position:0%
+Okay. And it's in this really cool
+ 
+
+ align:start position:0%
+Okay. And it's in this really cool
+frame. Oh, I love that frame. Okay. Uh,
+
+ align:start position:0%
+frame. Oh, I love that frame. Okay. Uh,
+ 
+
+ align:start position:0%
+frame. Oh, I love that frame. Okay. Uh,
+very fitting. And so this is this um
+
+ align:start position:0%
+very fitting. And so this is this um
+ 
+
+ align:start position:0%
+very fitting. And so this is this um
+this is very '9s. Like this exudes '90s.
+
+ align:start position:0%
+this is very '9s. Like this exudes '90s.
+ 
+
+ align:start position:0%
+this is very '9s. Like this exudes '90s.
+Peak '9s right there. So we've got the
+
+ align:start position:0%
+Peak '9s right there. So we've got the
+ 
+
+ align:start position:0%
+Peak '9s right there. So we've got the
+room with the computer, right? Like as
+
+ align:start position:0%
+room with the computer, right? Like as
+ 
+
+ align:start position:0%
+room with the computer, right? Like as
+was in the '9s. You all had like the
+
+ align:start position:0%
+was in the '9s. You all had like the
+ 
+
+ align:start position:0%
+was in the '9s. You all had like the
+room with the computer. Yes. And then
+
+ align:start position:0%
+room with the computer. Yes. And then
+ 
+
+ align:start position:0%
+room with the computer. Yes. And then
+like the big chair and the side ponytail
+
+ align:start position:0%
+like the big chair and the side ponytail
+ 
+
+ align:start position:0%
+like the big chair and the side ponytail
+or whatever. That's me on the on the on
+
+ align:start position:0%
+or whatever. That's me on the on the on
+ 
+
+ align:start position:0%
+or whatever. That's me on the on the on
+the left there. That's me. Yep. Yep. And
+
+ align:start position:0%
+the left there. That's me. Yep. Yep. And
+ 
+
+ align:start position:0%
+the left there. That's me. Yep. Yep. And
+that's my sister in the on the chair. Uh
+
+ align:start position:0%
+that's my sister in the on the chair. Uh
+ 
+
+ align:start position:0%
+that's my sister in the on the chair. Uh
+sitting on the chair. Yeah. And that's
+
+ align:start position:0%
+sitting on the chair. Yeah. And that's
+ 
+
+ align:start position:0%
+sitting on the chair. Yeah. And that's
+when we first um or maybe before like
+
+ align:start position:0%
+when we first um or maybe before like
+ 
+
+ align:start position:0%
+when we first um or maybe before like
+very close to the time that we had first
+
+ align:start position:0%
+very close to the time that we had first
+ 
+
+ align:start position:0%
+very close to the time that we had first
+uh started programming. My dad just
+
+ align:start position:0%
+uh started programming. My dad just
+ 
+
+ align:start position:0%
+uh started programming. My dad just
+said, you know, here's you know, here's
+
+ align:start position:0%
+said, you know, here's you know, here's
+ 
+
+ align:start position:0%
+said, you know, here's you know, here's
+some really basic things. And then I
+
+ align:start position:0%
+some really basic things. And then I
+ 
+
+ align:start position:0%
+some really basic things. And then I
+only got to the the if like the the
+
+ align:start position:0%
+only got to the the if like the the
+ 
+
+ align:start position:0%
+only got to the the if like the the
+branching part of the control flow. I
+
+ align:start position:0%
+branching part of the control flow. I
+ 
+
+ align:start position:0%
+branching part of the control flow. I
+didn't really get to the repeating part
+
+ align:start position:0%
+didn't really get to the repeating part
+ 
+
+ align:start position:0%
+didn't really get to the repeating part
+of the control flow. So I made this
+
+ align:start position:0%
+of the control flow. So I made this
+ 
+
+ align:start position:0%
+of the control flow. So I made this
+choose your own adventure program where
+
+ align:start position:0%
+choose your own adventure program where
+ 
+
+ align:start position:0%
+choose your own adventure program where
+it was like I forget what it was like.
+
+ align:start position:0%
+it was like I forget what it was like.
+ 
+
+ align:start position:0%
+it was like I forget what it was like.
+get out and you know exit a castle or
+
+ align:start position:0%
+get out and you know exit a castle or
+ 
+
+ align:start position:0%
+get out and you know exit a castle or
+whatever it was and it was just like a
+
+ align:start position:0%
+whatever it was and it was just like a
+ 
+
+ align:start position:0%
+whatever it was and it was just like a
+bunch of if else if else if else if else
+
+ align:start position:0%
+bunch of if else if else if else if else
+ 
+
+ align:start position:0%
+bunch of if else if else if else if else
+if like something like that. It looked
+
+ align:start position:0%
+if like something like that. It looked
+ 
+
+ align:start position:0%
+if like something like that. It looked
+really ugly but I had a lot of fun doing
+
+ align:start position:0%
+really ugly but I had a lot of fun doing
+ 
+
+ align:start position:0%
+really ugly but I had a lot of fun doing
+it. But in a way you're helping people
+
+ align:start position:0%
+it. But in a way you're helping people
+ 
+
+ align:start position:0%
+it. But in a way you're helping people
+choose their own adventure today through
+
+ align:start position:0%
+choose their own adventure today through
+ 
+
+ align:start position:0%
+choose their own adventure today through
+programming like gaining independence,
+
+ align:start position:0%
+programming like gaining independence,
+ 
+
+ align:start position:0%
+programming like gaining independence,
+critical thinking, uh doing things that
+
+ align:start position:0%
+critical thinking, uh doing things that
+ 
+
+ align:start position:0%
+critical thinking, uh doing things that
+they rely on other people to do like
+
+ align:start position:0%
+they rely on other people to do like
+ 
+
+ align:start position:0%
+they rely on other people to do like
+they can do themselves. Like that's kind
+
+ align:start position:0%
+they can do themselves. Like that's kind
+ 
+
+ align:start position:0%
+they can do themselves. Like that's kind
+of incredible that you do that. It's
+
+ align:start position:0%
+of incredible that you do that. It's
+ 
+
+ align:start position:0%
+of incredible that you do that. It's
+pretty fun. That's that's what I get out
+
+ align:start position:0%
+pretty fun. That's that's what I get out
+ 
+
+ align:start position:0%
+pretty fun. That's that's what I get out
+of it. I like I said, I don't want
+
+ align:start position:0%
+of it. I like I said, I don't want
+ 
+
+ align:start position:0%
+of it. I like I said, I don't want
+people to become computer scientists. I
+
+ align:start position:0%
+people to become computer scientists. I
+ 
+
+ align:start position:0%
+people to become computer scientists. I
+just want to empower them to I don't
+
+ align:start position:0%
+just want to empower them to I don't
+ 
+
+ align:start position:0%
+just want to empower them to I don't
+know like if they want to make their own
+
+ align:start position:0%
+know like if they want to make their own
+ 
+
+ align:start position:0%
+know like if they want to make their own
+app, they can totally do that using
+
+ align:start position:0%
+app, they can totally do that using
+ 
+
+ align:start position:0%
+app, they can totally do that using
+really basic computer science skills or
+
+ align:start position:0%
+really basic computer science skills or
+ 
+
+ align:start position:0%
+really basic computer science skills or
+programming skills, not necessarily
+
+ align:start position:0%
+programming skills, not necessarily
+ 
+
+ align:start position:0%
+programming skills, not necessarily
+computer science skills, but yeah. Yeah.
+
+ align:start position:0%
+computer science skills, but yeah. Yeah.
+ 
+
+ align:start position:0%
+computer science skills, but yeah. Yeah.
+So, uh controversial question. Uh I
+
+ align:start position:0%
+So, uh controversial question. Uh I
+ 
+
+ align:start position:0%
+So, uh controversial question. Uh I
+asked you before the show a question and
+
+ align:start position:0%
+asked you before the show a question and
+ 
+
+ align:start position:0%
+asked you before the show a question and
+I have not seen the answer yet but um
+
+ align:start position:0%
+I have not seen the answer yet but um
+ 
+
+ align:start position:0%
+I have not seen the answer yet but um
+the question was um in an environment
+
+ align:start position:0%
+the question was um in an environment
+ 
+
+ align:start position:0%
+the question was um in an environment
+when there are coding tools out there
+
+ align:start position:0%
+when there are coding tools out there
+ 
+
+ align:start position:0%
+when there are coding tools out there
+that allow people to build things um
+
+ align:start position:0%
+that allow people to build things um
+ 
+
+ align:start position:0%
+that allow people to build things um
+what's the value proposition of learning
+
+ align:start position:0%
+what's the value proposition of learning
+ 
+
+ align:start position:0%
+what's the value proposition of learning
+a language like Python to do that? Like
+
+ align:start position:0%
+a language like Python to do that? Like
+ 
+
+ align:start position:0%
+a language like Python to do that? Like
+do we still need to do it? And what's
+
+ align:start position:0%
+do we still need to do it? And what's
+ 
+
+ align:start position:0%
+do we still need to do it? And what's
+the value proposition of doing it? So
+
+ align:start position:0%
+the value proposition of doing it? So
+ 
+
+ align:start position:0%
+the value proposition of doing it? So
+you're going to reveal your answer. I'll
+
+ align:start position:0%
+you're going to reveal your answer. I'll
+ 
+
+ align:start position:0%
+you're going to reveal your answer. I'll
+reveal my answer.
+
+ align:start position:0%
+reveal my answer.
+ 
+
+ align:start position:0%
+reveal my answer.
+So, not sure if this exactly answers the
+
+ align:start position:0%
+So, not sure if this exactly answers the
+ 
+
+ align:start position:0%
+So, not sure if this exactly answers the
+question, but I said trust, but verify.
+
+ align:start position:0%
+question, but I said trust, but verify.
+ 
+
+ align:start position:0%
+question, but I said trust, but verify.
+Oh, tell me more. Okay. Yeah, I've
+
+ align:start position:0%
+Oh, tell me more. Okay. Yeah, I've
+ 
+
+ align:start position:0%
+Oh, tell me more. Okay. Yeah, I've
+certainly definitely used Genaii tools
+
+ align:start position:0%
+certainly definitely used Genaii tools
+ 
+
+ align:start position:0%
+certainly definitely used Genaii tools
+before. And for even for really simple
+
+ align:start position:0%
+before. And for even for really simple
+ 
+
+ align:start position:0%
+before. And for even for really simple
+things, it can get it wrong, especially
+
+ align:start position:0%
+things, it can get it wrong, especially
+ 
+
+ align:start position:0%
+things, it can get it wrong, especially
+um mathematical things and even
+
+ align:start position:0%
+um mathematical things and even
+ 
+
+ align:start position:0%
+um mathematical things and even
+programming things. And so, I have sort
+
+ align:start position:0%
+programming things. And so, I have sort
+ 
+
+ align:start position:0%
+programming things. And so, I have sort
+of a I would say a basic knowledge of
+
+ align:start position:0%
+of a I would say a basic knowledge of
+ 
+
+ align:start position:0%
+of a I would say a basic knowledge of
+programming. And I Wait, I'm not ready.
+
+ align:start position:0%
+programming. And I Wait, I'm not ready.
+ 
+
+ align:start position:0%
+programming. And I Wait, I'm not ready.
+IoT is a little more than basic for
+
+ align:start position:0%
+IoT is a little more than basic for
+ 
+
+ align:start position:0%
+IoT is a little more than basic for
+everyone out there. More than basic.
+
+ align:start position:0%
+everyone out there. More than basic.
+ 
+
+ align:start position:0%
+everyone out there. More than basic.
+Continue. Um, and so I was able to start
+
+ align:start position:0%
+Continue. Um, and so I was able to start
+ 
+
+ align:start position:0%
+Continue. Um, and so I was able to start
+with what Genai gave me as a as as a
+
+ align:start position:0%
+with what Genai gave me as a as as a
+ 
+
+ align:start position:0%
+with what Genai gave me as a as as a
+program and kind of kind of tell, you
+
+ align:start position:0%
+program and kind of kind of tell, you
+ 
+
+ align:start position:0%
+program and kind of kind of tell, you
+know what, it in this particular test
+
+ align:start position:0%
+know what, it in this particular test
+ 
+
+ align:start position:0%
+know what, it in this particular test
+case, it doesn't really work that well.
+
+ align:start position:0%
+case, it doesn't really work that well.
+ 
+
+ align:start position:0%
+case, it doesn't really work that well.
+And I didn't have to go back and ask it
+
+ align:start position:0%
+And I didn't have to go back and ask it
+ 
+
+ align:start position:0%
+And I didn't have to go back and ask it
+to fix it because that requires a lot
+
+ align:start position:0%
+to fix it because that requires a lot
+ 
+
+ align:start position:0%
+to fix it because that requires a lot
+more sort of back and forth with the
+
+ align:start position:0%
+more sort of back and forth with the
+ 
+
+ align:start position:0%
+more sort of back and forth with the
+with prompting. And I was able, you
+
+ align:start position:0%
+with prompting. And I was able, you
+ 
+
+ align:start position:0%
+with prompting. And I was able, you
+know, to just fix it on my own. It
+
+ align:start position:0%
+know, to just fix it on my own. It
+ 
+
+ align:start position:0%
+know, to just fix it on my own. It
+wasn't that hard of a fix. And, you
+
+ align:start position:0%
+wasn't that hard of a fix. And, you
+ 
+
+ align:start position:0%
+wasn't that hard of a fix. And, you
+know, as soon as you go back and prompt
+
+ align:start position:0%
+know, as soon as you go back and prompt
+ 
+
+ align:start position:0%
+know, as soon as you go back and prompt
+the the genai again and again and again,
+
+ align:start position:0%
+the the genai again and again and again,
+ 
+
+ align:start position:0%
+the the genai again and again and again,
+you start to introduce sort of
+
+ align:start position:0%
+you start to introduce sort of
+ 
+
+ align:start position:0%
+you start to introduce sort of
+variability of English language, right?
+
+ align:start position:0%
+variability of English language, right?
+ 
+
+ align:start position:0%
+variability of English language, right?
+You're like when you're talking to
+
+ align:start position:0%
+You're like when you're talking to
+ 
+
+ align:start position:0%
+You're like when you're talking to
+someone online, it's really hard to tell
+
+ align:start position:0%
+someone online, it's really hard to tell
+ 
+
+ align:start position:0%
+someone online, it's really hard to tell
+what they mean or right, there's all
+
+ align:start position:0%
+what they mean or right, there's all
+ 
+
+ align:start position:0%
+what they mean or right, there's all
+these double meanings. Um, and Genai is
+
+ align:start position:0%
+these double meanings. Um, and Genai is
+ 
+
+ align:start position:0%
+these double meanings. Um, and Genai is
+all probabilistic. So they're basically
+
+ align:start position:0%
+all probabilistic. So they're basically
+ 
+
+ align:start position:0%
+all probabilistic. So they're basically
+going to, you know, pick the highest
+
+ align:start position:0%
+going to, you know, pick the highest
+ 
+
+ align:start position:0%
+going to, you know, pick the highest
+probability of what you mean and then
+
+ align:start position:0%
+probability of what you mean and then
+ 
+
+ align:start position:0%
+probability of what you mean and then
+when they give you answers back again,
+
+ align:start position:0%
+when they give you answers back again,
+ 
+
+ align:start position:0%
+when they give you answers back again,
+they give it to you with whatever the
+
+ align:start position:0%
+they give it to you with whatever the
+ 
+
+ align:start position:0%
+they give it to you with whatever the
+highest probability for the next word to
+
+ align:start position:0%
+highest probability for the next word to
+ 
+
+ align:start position:0%
+highest probability for the next word to
+be, that's what they spit back at you.
+
+ align:start position:0%
+be, that's what they spit back at you.
+ 
+
+ align:start position:0%
+be, that's what they spit back at you.
+So as soon as you introduce sort of that
+
+ align:start position:0%
+So as soon as you introduce sort of that
+ 
+
+ align:start position:0%
+So as soon as you introduce sort of that
+prompting back and forth, it can
+
+ align:start position:0%
+prompting back and forth, it can
+ 
+
+ align:start position:0%
+prompting back and forth, it can
+introduce errors that potentially stack
+
+ align:start position:0%
+introduce errors that potentially stack
+ 
+
+ align:start position:0%
+introduce errors that potentially stack
+on top of errors, misunderstandings, and
+
+ align:start position:0%
+on top of errors, misunderstandings, and
+ 
+
+ align:start position:0%
+on top of errors, misunderstandings, and
+things like that. So having a really
+
+ align:start position:0%
+things like that. So having a really
+ 
+
+ align:start position:0%
+things like that. So having a really
+basic knowledge of programming could
+
+ align:start position:0%
+basic knowledge of programming could
+ 
+
+ align:start position:0%
+basic knowledge of programming could
+allow you to maybe start with a piece of
+
+ align:start position:0%
+allow you to maybe start with a piece of
+ 
+
+ align:start position:0%
+allow you to maybe start with a piece of
+code that the Genai gives you back so
+
+ align:start position:0%
+code that the Genai gives you back so
+ 
+
+ align:start position:0%
+code that the Genai gives you back so
+you're not starting with a blank slate.
+
+ align:start position:0%
+you're not starting with a blank slate.
+ 
+
+ align:start position:0%
+you're not starting with a blank slate.
+It's not super daunting to write it
+
+ align:start position:0%
+It's not super daunting to write it
+ 
+
+ align:start position:0%
+It's not super daunting to write it
+yourself, but you start with something
+
+ align:start position:0%
+yourself, but you start with something
+ 
+
+ align:start position:0%
+yourself, but you start with something
+and then you potentially test it and
+
+ align:start position:0%
+and then you potentially test it and
+ 
+
+ align:start position:0%
+and then you potentially test it and
+then debug it and then, you know, figure
+
+ align:start position:0%
+then debug it and then, you know, figure
+ 
+
+ align:start position:0%
+then debug it and then, you know, figure
+it out. Okay, now I trust that it works
+
+ align:start position:0%
+it out. Okay, now I trust that it works
+ 
+
+ align:start position:0%
+it out. Okay, now I trust that it works
+well. Yeah. I feel like the ability to
+
+ align:start position:0%
+well. Yeah. I feel like the ability to
+ 
+
+ align:start position:0%
+well. Yeah. I feel like the ability to
+verify is the human component. Yes. And
+
+ align:start position:0%
+verify is the human component. Yes. And
+ 
+
+ align:start position:0%
+verify is the human component. Yes. And
+that is sort of what creates the balance
+
+ align:start position:0%
+that is sort of what creates the balance
+ 
+
+ align:start position:0%
+that is sort of what creates the balance
+with AI. Like if you let AI make all the
+
+ align:start position:0%
+with AI. Like if you let AI make all the
+ 
+
+ align:start position:0%
+with AI. Like if you let AI make all the
+decisions, then you've lost your
+
+ align:start position:0%
+decisions, then you've lost your
+ 
+
+ align:start position:0%
+decisions, then you've lost your
+self-reliance. Um, and you can't choose
+
+ align:start position:0%
+self-reliance. Um, and you can't choose
+ 
+
+ align:start position:0%
+self-reliance. Um, and you can't choose
+your own adventure because you're going
+
+ align:start position:0%
+your own adventure because you're going
+ 
+
+ align:start position:0%
+your own adventure because you're going
+to get a bunch of errors and it's going
+
+ align:start position:0%
+to get a bunch of errors and it's going
+ 
+
+ align:start position:0%
+to get a bunch of errors and it's going
+to lead you down the wrong path. So, you
+
+ align:start position:0%
+to lead you down the wrong path. So, you
+ 
+
+ align:start position:0%
+to lead you down the wrong path. So, you
+need the knowledge to be able to choose
+
+ align:start position:0%
+need the knowledge to be able to choose
+ 
+
+ align:start position:0%
+need the knowledge to be able to choose
+um a path that makes sense. Yeah. I have
+
+ align:start position:0%
+um a path that makes sense. Yeah. I have
+ 
+
+ align:start position:0%
+um a path that makes sense. Yeah. I have
+to know what the ducks are now. Like I I
+
+ align:start position:0%
+to know what the ducks are now. Like I I
+ 
+
+ align:start position:0%
+to know what the ducks are now. Like I I
+can't continue. So, okay. And a pig. I'm
+
+ align:start position:0%
+can't continue. So, okay. And a pig. I'm
+ 
+
+ align:start position:0%
+can't continue. So, okay. And a pig. I'm
+Is that like noisy data or just noisy
+
+ align:start position:0%
+Is that like noisy data or just noisy
+ 
+
+ align:start position:0%
+Is that like noisy data or just noisy
+data? Okay. So, okay. Uh every semester
+
+ align:start position:0%
+data? Okay. So, okay. Uh every semester
+ 
+
+ align:start position:0%
+data? Okay. So, okay. Uh every semester
+when we run our classes uh on intro to
+
+ align:start position:0%
+when we run our classes uh on intro to
+ 
+
+ align:start position:0%
+when we run our classes uh on intro to
+programming and computer science, there
+
+ align:start position:0%
+programming and computer science, there
+ 
+
+ align:start position:0%
+programming and computer science, there
+is one particular class that is on
+
+ align:start position:0%
+is one particular class that is on
+ 
+
+ align:start position:0%
+is one particular class that is on
+debugging. Okay. which is the process of
+
+ align:start position:0%
+debugging. Okay. which is the process of
+ 
+
+ align:start position:0%
+debugging. Okay. which is the process of
+okay, you wrote a piece of code and it's
+
+ align:start position:0%
+okay, you wrote a piece of code and it's
+ 
+
+ align:start position:0%
+okay, you wrote a piece of code and it's
+not running as you expect it to. So how
+
+ align:start position:0%
+not running as you expect it to. So how
+ 
+
+ align:start position:0%
+not running as you expect it to. So how
+do you fix it? That is the debugging
+
+ align:start position:0%
+do you fix it? That is the debugging
+ 
+
+ align:start position:0%
+do you fix it? That is the debugging
+process. And so a a lot of times a bunch
+
+ align:start position:0%
+process. And so a a lot of times a bunch
+ 
+
+ align:start position:0%
+process. And so a a lot of times a bunch
+of the errors might be things that you
+
+ align:start position:0%
+of the errors might be things that you
+ 
+
+ align:start position:0%
+of the errors might be things that you
+can easily fix but most of the time uh
+
+ align:start position:0%
+can easily fix but most of the time uh
+ 
+
+ align:start position:0%
+can easily fix but most of the time uh
+your program runs fine and it gives you
+
+ align:start position:0%
+your program runs fine and it gives you
+ 
+
+ align:start position:0%
+your program runs fine and it gives you
+an answer but the answer is not what you
+
+ align:start position:0%
+an answer but the answer is not what you
+ 
+
+ align:start position:0%
+an answer but the answer is not what you
+thought it should be. That's kind of
+
+ align:start position:0%
+thought it should be. That's kind of
+ 
+
+ align:start position:0%
+thought it should be. That's kind of
+where like uh programming is kind of
+
+ align:start position:0%
+where like uh programming is kind of
+ 
+
+ align:start position:0%
+where like uh programming is kind of
+different than like English for example
+
+ align:start position:0%
+different than like English for example
+ 
+
+ align:start position:0%
+different than like English for example
+because in English like if you write a
+
+ align:start position:0%
+because in English like if you write a
+ 
+
+ align:start position:0%
+because in English like if you write a
+sentence somebody else can interpret it
+
+ align:start position:0%
+sentence somebody else can interpret it
+ 
+
+ align:start position:0%
+sentence somebody else can interpret it
+however they'd like. Like one example we
+
+ align:start position:0%
+however they'd like. Like one example we
+ 
+
+ align:start position:0%
+however they'd like. Like one example we
+give to students is the chicken is ready
+
+ align:start position:0%
+give to students is the chicken is ready
+ 
+
+ align:start position:0%
+give to students is the chicken is ready
+to eat. What do you think about when you
+
+ align:start position:0%
+to eat. What do you think about when you
+ 
+
+ align:start position:0%
+to eat. What do you think about when you
+when I say the chicken is ready to eat?
+
+ align:start position:0%
+when I say the chicken is ready to eat?
+ 
+
+ align:start position:0%
+when I say the chicken is ready to eat?
+Well I'm a vegetarian so I don't want to
+
+ align:start position:0%
+Well I'm a vegetarian so I don't want to
+ 
+
+ align:start position:0%
+Well I'm a vegetarian so I don't want to
+actually eat the chicken but I would
+
+ align:start position:0%
+actually eat the chicken but I would
+ 
+
+ align:start position:0%
+actually eat the chicken but I would
+like because I'm a vegetarian I assume
+
+ align:start position:0%
+like because I'm a vegetarian I assume
+ 
+
+ align:start position:0%
+like because I'm a vegetarian I assume
+the chicken wants to eat his food. Okay,
+
+ align:start position:0%
+the chicken wants to eat his food. Okay,
+ 
+
+ align:start position:0%
+the chicken wants to eat his food. Okay,
+there you go. But I would assume I enjoy
+
+ align:start position:0%
+there you go. But I would assume I enjoy
+ 
+
+ align:start position:0%
+there you go. But I would assume I enjoy
+meat.
+
+ align:start position:0%
+meat.
+ 
+
+ align:start position:0%
+meat.
+So, so I my uh my take on that is uh I
+
+ align:start position:0%
+So, so I my uh my take on that is uh I
+ 
+
+ align:start position:0%
+So, so I my uh my take on that is uh I
+have a chicken on the table and I'm
+
+ align:start position:0%
+have a chicken on the table and I'm
+ 
+
+ align:start position:0%
+have a chicken on the table and I'm
+going to eat it. Right. So, there's two
+
+ align:start position:0%
+going to eat it. Right. So, there's two
+ 
+
+ align:start position:0%
+going to eat it. Right. So, there's two
+interpretations to that. But when we
+
+ align:start position:0%
+interpretations to that. But when we
+ 
+
+ align:start position:0%
+interpretations to that. But when we
+write code, there's only one way to
+
+ align:start position:0%
+write code, there's only one way to
+ 
+
+ align:start position:0%
+write code, there's only one way to
+interpret that piece of code that is
+
+ align:start position:0%
+interpret that piece of code that is
+ 
+
+ align:start position:0%
+interpret that piece of code that is
+written, right? So, um, so that's where
+
+ align:start position:0%
+written, right? So, um, so that's where
+ 
+
+ align:start position:0%
+written, right? So, um, so that's where
+things go wrong in our code because
+
+ align:start position:0%
+things go wrong in our code because
+ 
+
+ align:start position:0%
+things go wrong in our code because
+we're like, well, it should work because
+
+ align:start position:0%
+we're like, well, it should work because
+ 
+
+ align:start position:0%
+we're like, well, it should work because
+in my mind, like when I kind of thought
+
+ align:start position:0%
+in my mind, like when I kind of thought
+ 
+
+ align:start position:0%
+in my mind, like when I kind of thought
+about it, it's supposed to give me the
+
+ align:start position:0%
+about it, it's supposed to give me the
+ 
+
+ align:start position:0%
+about it, it's supposed to give me the
+right answer, but it doesn't, right? And
+
+ align:start position:0%
+right answer, but it doesn't, right? And
+ 
+
+ align:start position:0%
+right answer, but it doesn't, right? And
+so, obviously, the program is the one
+
+ align:start position:0%
+so, obviously, the program is the one
+ 
+
+ align:start position:0%
+so, obviously, the program is the one
+who's wrong because the computer is
+
+ align:start position:0%
+who's wrong because the computer is
+ 
+
+ align:start position:0%
+who's wrong because the computer is
+merely following the algorithm, the set
+
+ align:start position:0%
+merely following the algorithm, the set
+ 
+
+ align:start position:0%
+merely following the algorithm, the set
+of instructions, and there's only one
+
+ align:start position:0%
+of instructions, and there's only one
+ 
+
+ align:start position:0%
+of instructions, and there's only one
+way to follow those instructions. That's
+
+ align:start position:0%
+way to follow those instructions. That's
+ 
+
+ align:start position:0%
+way to follow those instructions. That's
+basically what that whole lecture, that
+
+ align:start position:0%
+basically what that whole lecture, that
+ 
+
+ align:start position:0%
+basically what that whole lecture, that
+whole class is about. And then I bring
+
+ align:start position:0%
+whole class is about. And then I bring
+ 
+
+ align:start position:0%
+whole class is about. And then I bring
+out this big box of ducks and I say and
+
+ align:start position:0%
+out this big box of ducks and I say and
+ 
+
+ align:start position:0%
+out this big box of ducks and I say and
+I say, um, well, uh, programming is
+
+ align:start position:0%
+I say, um, well, uh, programming is
+ 
+
+ align:start position:0%
+I say, um, well, uh, programming is
+actually kind of
+
+ align:start position:0%
+actually kind of
+ 
+
+ align:start position:0%
+actually kind of
+creative
+
+ align:start position:0%
+creative
+ 
+
+ align:start position:0%
+creative
+because the solution to a problem, I
+
+ align:start position:0%
+because the solution to a problem, I
+ 
+
+ align:start position:0%
+because the solution to a problem, I
+mean, you could brute force a bunch of
+
+ align:start position:0%
+mean, you could brute force a bunch of
+ 
+
+ align:start position:0%
+mean, you could brute force a bunch of
+things, but often times the solution to
+
+ align:start position:0%
+things, but often times the solution to
+ 
+
+ align:start position:0%
+things, but often times the solution to
+a debugging problem is just to take time
+
+ align:start position:0%
+a debugging problem is just to take time
+ 
+
+ align:start position:0%
+a debugging problem is just to take time
+away from it and then potentially
+
+ align:start position:0%
+away from it and then potentially
+ 
+
+ align:start position:0%
+away from it and then potentially
+explain exactly what your you think the
+
+ align:start position:0%
+explain exactly what your you think the
+ 
+
+ align:start position:0%
+explain exactly what your you think the
+code is doing to someone who knows
+
+ align:start position:0%
+code is doing to someone who knows
+ 
+
+ align:start position:0%
+code is doing to someone who knows
+absolutely nothing about programming. It
+
+ align:start position:0%
+absolutely nothing about programming. It
+ 
+
+ align:start position:0%
+absolutely nothing about programming. It
+could be you. Yes, I'm available. Or it
+
+ align:start position:0%
+could be you. Yes, I'm available. Or it
+ 
+
+ align:start position:0%
+could be you. Yes, I'm available. Or it
+could be a rubber duck. Oh, so this is
+
+ align:start position:0%
+could be a rubber duck. Oh, so this is
+ 
+
+ align:start position:0%
+could be a rubber duck. Oh, so this is
+called rubber ducky debugging. Oh,
+
+ align:start position:0%
+called rubber ducky debugging. Oh,
+ 
+
+ align:start position:0%
+called rubber ducky debugging. Oh,
+because uh it's an inanimate object that
+
+ align:start position:0%
+because uh it's an inanimate object that
+ 
+
+ align:start position:0%
+because uh it's an inanimate object that
+doesn't know anything about programming,
+
+ align:start position:0%
+doesn't know anything about programming,
+ 
+
+ align:start position:0%
+doesn't know anything about programming,
+right? And it forces you to scrutinize
+
+ align:start position:0%
+right? And it forces you to scrutinize
+ 
+
+ align:start position:0%
+right? And it forces you to scrutinize
+every single line of code that you
+
+ align:start position:0%
+every single line of code that you
+ 
+
+ align:start position:0%
+every single line of code that you
+wrote, even ones you think are correct.
+
+ align:start position:0%
+wrote, even ones you think are correct.
+ 
+
+ align:start position:0%
+wrote, even ones you think are correct.
+Um, most often it's the ones that are
+
+ align:start position:0%
+Um, most often it's the ones that are
+ 
+
+ align:start position:0%
+Um, most often it's the ones that are
+that you think are correct that kind of
+
+ align:start position:0%
+that you think are correct that kind of
+ 
+
+ align:start position:0%
+that you think are correct that kind of
+are are the issue. It's kind of like
+
+ align:start position:0%
+are are the issue. It's kind of like
+ 
+
+ align:start position:0%
+are are the issue. It's kind of like
+like where did I put my glasses, right?
+
+ align:start position:0%
+like where did I put my glasses, right?
+ 
+
+ align:start position:0%
+like where did I put my glasses, right?
+And you spend a long time looking for
+
+ align:start position:0%
+And you spend a long time looking for
+ 
+
+ align:start position:0%
+And you spend a long time looking for
+them and they're on top of your head.
+
+ align:start position:0%
+them and they're on top of your head.
+ 
+
+ align:start position:0%
+them and they're on top of your head.
+It's that exact feeling. It's like where
+
+ align:start position:0%
+It's that exact feeling. It's like where
+ 
+
+ align:start position:0%
+It's that exact feeling. It's like where
+is that error coming from? And it's
+
+ align:start position:0%
+is that error coming from? And it's
+ 
+
+ align:start position:0%
+is that error coming from? And it's
+going to be something super simple. So,
+
+ align:start position:0%
+going to be something super simple. So,
+ 
+
+ align:start position:0%
+going to be something super simple. So,
+the rubber duck is what um helps you
+
+ align:start position:0%
+the rubber duck is what um helps you
+ 
+
+ align:start position:0%
+the rubber duck is what um helps you
+figure that that problem out because
+
+ align:start position:0%
+figure that that problem out because
+ 
+
+ align:start position:0%
+figure that that problem out because
+you're explaining it in very grave
+
+ align:start position:0%
+you're explaining it in very grave
+ 
+
+ align:start position:0%
+you're explaining it in very grave
+detail to something that doesn't know.
+
+ align:start position:0%
+detail to something that doesn't know.
+ 
+
+ align:start position:0%
+detail to something that doesn't know.
+And if ducks are not your thing, there
+
+ align:start position:0%
+And if ducks are not your thing, there
+ 
+
+ align:start position:0%
+And if ducks are not your thing, there
+are frogs. Oh, and the pig pigs, of
+
+ align:start position:0%
+are frogs. Oh, and the pig pigs, of
+ 
+
+ align:start position:0%
+are frogs. Oh, and the pig pigs, of
+course. Of course. Or friends, you want
+
+ align:start position:0%
+course. Of course. Or friends, you want
+ 
+
+ align:start position:0%
+course. Of course. Or friends, you want
+to explain it to them. But friends can
+
+ align:start position:0%
+to explain it to them. But friends can
+ 
+
+ align:start position:0%
+to explain it to them. But friends can
+be judgy. Friends can be judgy. Yes. So,
+
+ align:start position:0%
+be judgy. Friends can be judgy. Yes. So,
+ 
+
+ align:start position:0%
+be judgy. Friends can be judgy. Yes. So,
+I used to explain my code to my son when
+
+ align:start position:0%
+I used to explain my code to my son when
+ 
+
+ align:start position:0%
+I used to explain my code to my son when
+he was one. Yeah. Yeah. When I had
+
+ align:start position:0%
+he was one. Yeah. Yeah. When I had
+ 
+
+ align:start position:0%
+he was one. Yeah. Yeah. When I had
+issues cuz he doesn't know anything
+
+ align:start position:0%
+issues cuz he doesn't know anything
+ 
+
+ align:start position:0%
+issues cuz he doesn't know anything
+about programming, right? And so it's
+
+ align:start position:0%
+about programming, right? And so it's
+ 
+
+ align:start position:0%
+about programming, right? And so it's
+the act of talking it through. But you
+
+ align:start position:0%
+the act of talking it through. But you
+ 
+
+ align:start position:0%
+the act of talking it through. But you
+said it has to be in great detail. Yes.
+
+ align:start position:0%
+said it has to be in great detail. Yes.
+ 
+
+ align:start position:0%
+said it has to be in great detail. Yes.
+You can't skip because that's when cuz
+
+ align:start position:0%
+You can't skip because that's when cuz
+ 
+
+ align:start position:0%
+You can't skip because that's when cuz
+you already like clearly your code is
+
+ align:start position:0%
+you already like clearly your code is
+ 
+
+ align:start position:0%
+you already like clearly your code is
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+because of you. And and so don't skip
+
+ align:start position:0%
+because of you. And and so don't skip
+ 
+
+ align:start position:0%
+because of you. And and so don't skip
+any details. Right. That's I feel like
+
+ align:start position:0%
+any details. Right. That's I feel like
+ 
+
+ align:start position:0%
+any details. Right. That's I feel like
+this very much like life outside of
+
+ align:start position:0%
+this very much like life outside of
+ 
+
+ align:start position:0%
+this very much like life outside of
+academia. like you 90% of the time the
+
+ align:start position:0%
+academia. like you 90% of the time the
+ 
+
+ align:start position:0%
+academia. like you 90% of the time the
+problem is probably you you know and
+
+ align:start position:0%
+problem is probably you you know and
+ 
+
+ align:start position:0%
+problem is probably you you know and
+it's like you have to figure out how to
+
+ align:start position:0%
+it's like you have to figure out how to
+ 
+
+ align:start position:0%
+it's like you have to figure out how to
+interact in the world or with others. So
+
+ align:start position:0%
+interact in the world or with others. So
+ 
+
+ align:start position:0%
+interact in the world or with others. So
+I brought all this all these ducks a
+
+ align:start position:0%
+I brought all this all these ducks a
+ 
+
+ align:start position:0%
+I brought all this all these ducks a
+wide variety. So now I have a a question
+
+ align:start position:0%
+wide variety. So now I have a a question
+ 
+
+ align:start position:0%
+wide variety. So now I have a a question
+for you. Which duck would you like to
+
+ align:start position:0%
+for you. Which duck would you like to
+ 
+
+ align:start position:0%
+for you. Which duck would you like to
+keep? This is a hidden personality test.
+
+ align:start position:0%
+keep? This is a hidden personality test.
+ 
+
+ align:start position:0%
+keep? This is a hidden personality test.
+Oh
+
+ align:start position:0%
+Oh
+ 
+
+ align:start position:0%
+Oh
+we'll probably have to cut this because
+
+ align:start position:0%
+we'll probably have to cut this because
+ 
+
+ align:start position:0%
+we'll probably have to cut this because
+it might take a long time. Um I would um
+
+ align:start position:0%
+it might take a long time. Um I would um
+ 
+
+ align:start position:0%
+it might take a long time. Um I would um
+this guy. This guy. Yeah. He's a little
+
+ align:start position:0%
+this guy. This guy. Yeah. He's a little
+ 
+
+ align:start position:0%
+this guy. This guy. Yeah. He's a little
+bit offbeat. Yeah.
+
+ align:start position:0%
+bit offbeat. Yeah.
+ 
+
+ align:start position:0%
+bit offbeat. Yeah.
+Um, you know,
+
+ align:start position:0%
+Um, you know,
+ 
+
+ align:start position:0%
+Um, you know,
+eye-catching and I feel like I could
+
+ align:start position:0%
+eye-catching and I feel like I could
+ 
+
+ align:start position:0%
+eye-catching and I feel like I could
+explain stuff to him. I get to keep him.
+
+ align:start position:0%
+explain stuff to him. I get to keep him.
+ 
+
+ align:start position:0%
+explain stuff to him. I get to keep him.
+Yeah, of course. Thank you. That's so
+
+ align:start position:0%
+Yeah, of course. Thank you. That's so
+ 
+
+ align:start position:0%
+Yeah, of course. Thank you. That's so
+great. You put one for the set as well.
+
+ align:start position:0%
+great. You put one for the set as well.
+ 
+
+ align:start position:0%
+great. You put one for the set as well.
+Really? Oh gosh. Does someone from the
+
+ align:start position:0%
+Really? Oh gosh. Does someone from the
+ 
+
+ align:start position:0%
+Really? Oh gosh. Does someone from the
+crew want to like pick a duck for the
+
+ align:start position:0%
+crew want to like pick a duck for the
+ 
+
+ align:start position:0%
+crew want to like pick a duck for the
+set? You took the one I would have
+
+ align:start position:0%
+set? You took the one I would have
+ 
+
+ align:start position:0%
+set? You took the one I would have
+picked. Oh, no.
+
+ align:start position:0%
+picked. Oh, no.
+ 
+
+ align:start position:0%
+picked. Oh, no.
+All right, then. Um, there's another
+
+ align:start position:0%
+All right, then. Um, there's another
+ 
+
+ align:start position:0%
+All right, then. Um, there's another
+mohawk guy right over there. Yeah. Yeah,
+
+ align:start position:0%
+mohawk guy right over there. Yeah. Yeah,
+ 
+
+ align:start position:0%
+mohawk guy right over there. Yeah. Yeah,
+we'll go two mohawks. There you go.
+
+ align:start position:0%
+we'll go two mohawks. There you go.
+ 
+
+ align:start position:0%
+we'll go two mohawks. There you go.
+Thank you. Yeah, of course. What a gift.
+
+ align:start position:0%
+Thank you. Yeah, of course. What a gift.
+ 
+
+ align:start position:0%
+Thank you. Yeah, of course. What a gift.
+So, you can use it for programming if
+
+ align:start position:0%
+So, you can use it for programming if
+ 
+
+ align:start position:0%
+So, you can use it for programming if
+you decide to start or as you said in
+
+ align:start position:0%
+you decide to start or as you said in
+ 
+
+ align:start position:0%
+you decide to start or as you said in
+even in your day-to-day life, you can if
+
+ align:start position:0%
+even in your day-to-day life, you can if
+ 
+
+ align:start position:0%
+even in your day-to-day life, you can if
+you just explain the problem to Yes. You
+
+ align:start position:0%
+you just explain the problem to Yes. You
+ 
+
+ align:start position:0%
+you just explain the problem to Yes. You
+know, something that doesn't judge or
+
+ align:start position:0%
+know, something that doesn't judge or
+ 
+
+ align:start position:0%
+know, something that doesn't judge or
+Yeah. Um this idea of taking a break
+
+ align:start position:0%
+Yeah. Um this idea of taking a break
+ 
+
+ align:start position:0%
+Yeah. Um this idea of taking a break
+like the process of programming itself
+
+ align:start position:0%
+like the process of programming itself
+ 
+
+ align:start position:0%
+like the process of programming itself
+seems quite intense. There's like an
+
+ align:start position:0%
+seems quite intense. There's like an
+ 
+
+ align:start position:0%
+seems quite intense. There's like an
+image in popular culture of like a
+
+ align:start position:0%
+image in popular culture of like a
+ 
+
+ align:start position:0%
+image in popular culture of like a
+person working alone in the dark like
+
+ align:start position:0%
+person working alone in the dark like
+ 
+
+ align:start position:0%
+person working alone in the dark like
+with a hoodie and like tap tap tap. um
+
+ align:start position:0%
+with a hoodie and like tap tap tap. um
+ 
+
+ align:start position:0%
+with a hoodie and like tap tap tap. um
+for hours on end. Like that sounds
+
+ align:start position:0%
+for hours on end. Like that sounds
+ 
+
+ align:start position:0%
+for hours on end. Like that sounds
+intense. Um so there's two pieces like
+
+ align:start position:0%
+intense. Um so there's two pieces like
+ 
+
+ align:start position:0%
+intense. Um so there's two pieces like
+is that accurate and two like do people
+
+ align:start position:0%
+is that accurate and two like do people
+ 
+
+ align:start position:0%
+is that accurate and two like do people
+work in isolation like that or is it
+
+ align:start position:0%
+work in isolation like that or is it
+ 
+
+ align:start position:0%
+work in isolation like that or is it
+more collaborative? Um so I tend to
+
+ align:start position:0%
+more collaborative? Um so I tend to
+ 
+
+ align:start position:0%
+more collaborative? Um so I tend to
+encourage collaboration. Okay. Uh I have
+
+ align:start position:0%
+encourage collaboration. Okay. Uh I have
+ 
+
+ align:start position:0%
+encourage collaboration. Okay. Uh I have
+certainly put a hoodie on and the hood
+
+ align:start position:0%
+certainly put a hoodie on and the hood
+ 
+
+ align:start position:0%
+certainly put a hoodie on and the hood
+on in the past just like a leave me
+
+ align:start position:0%
+on in the past just like a leave me
+ 
+
+ align:start position:0%
+on in the past just like a leave me
+alone kind of state. Uh mostly for you
+
+ align:start position:0%
+alone kind of state. Uh mostly for you
+ 
+
+ align:start position:0%
+alone kind of state. Uh mostly for you
+know homework and things like that. But
+
+ align:start position:0%
+know homework and things like that. But
+ 
+
+ align:start position:0%
+know homework and things like that. But
+I for for students learning to program I
+
+ align:start position:0%
+I for for students learning to program I
+ 
+
+ align:start position:0%
+I for for students learning to program I
+definitely encourage collaboration
+
+ align:start position:0%
+definitely encourage collaboration
+ 
+
+ align:start position:0%
+definitely encourage collaboration
+because it's when you talk to somebody
+
+ align:start position:0%
+because it's when you talk to somebody
+ 
+
+ align:start position:0%
+because it's when you talk to somebody
+else you kind of see their viewpoint and
+
+ align:start position:0%
+else you kind of see their viewpoint and
+ 
+
+ align:start position:0%
+else you kind of see their viewpoint and
+in programming I know I talked about
+
+ align:start position:0%
+in programming I know I talked about
+ 
+
+ align:start position:0%
+in programming I know I talked about
+like an algorithm but for you know for a
+
+ align:start position:0%
+like an algorithm but for you know for a
+ 
+
+ align:start position:0%
+like an algorithm but for you know for a
+particular algorithm or even just to
+
+ align:start position:0%
+particular algorithm or even just to
+ 
+
+ align:start position:0%
+particular algorithm or even just to
+solve a specific problem there's a ton
+
+ align:start position:0%
+solve a specific problem there's a ton
+ 
+
+ align:start position:0%
+solve a specific problem there's a ton
+of ways to solve it. So I learn from in
+
+ align:start position:0%
+of ways to solve it. So I learn from in
+ 
+
+ align:start position:0%
+of ways to solve it. So I learn from in
+the classroom when students when I ask
+
+ align:start position:0%
+the classroom when students when I ask
+ 
+
+ align:start position:0%
+the classroom when students when I ask
+students for how did they solve a
+
+ align:start position:0%
+students for how did they solve a
+ 
+
+ align:start position:0%
+students for how did they solve a
+particular problem after I give them
+
+ align:start position:0%
+particular problem after I give them
+ 
+
+ align:start position:0%
+particular problem after I give them
+some time to think about it they have so
+
+ align:start position:0%
+some time to think about it they have so
+ 
+
+ align:start position:0%
+some time to think about it they have so
+many different approaches to it that I
+
+ align:start position:0%
+many different approaches to it that I
+ 
+
+ align:start position:0%
+many different approaches to it that I
+would never have thought of and it's
+
+ align:start position:0%
+would never have thought of and it's
+ 
+
+ align:start position:0%
+would never have thought of and it's
+important for students to see all these
+
+ align:start position:0%
+important for students to see all these
+ 
+
+ align:start position:0%
+important for students to see all these
+different approaches because my way
+
+ align:start position:0%
+different approaches because my way
+ 
+
+ align:start position:0%
+different approaches because my way
+might not be the way that they think uh
+
+ align:start position:0%
+might not be the way that they think uh
+ 
+
+ align:start position:0%
+might not be the way that they think uh
+to approach the problem. So I encourage
+
+ align:start position:0%
+to approach the problem. So I encourage
+ 
+
+ align:start position:0%
+to approach the problem. So I encourage
+kind of working together especially as
+
+ align:start position:0%
+kind of working together especially as
+ 
+
+ align:start position:0%
+kind of working together especially as
+you're learning now after you find your
+
+ align:start position:0%
+you're learning now after you find your
+ 
+
+ align:start position:0%
+you're learning now after you find your
+groove maybe it's you know not necessary
+
+ align:start position:0%
+groove maybe it's you know not necessary
+ 
+
+ align:start position:0%
+groove maybe it's you know not necessary
+but yeah as an outsider to this I didn't
+
+ align:start position:0%
+but yeah as an outsider to this I didn't
+ 
+
+ align:start position:0%
+but yeah as an outsider to this I didn't
+realize there was such room for
+
+ align:start position:0%
+realize there was such room for
+ 
+
+ align:start position:0%
+realize there was such room for
+divergent thinking so that's really
+
+ align:start position:0%
+divergent thinking so that's really
+ 
+
+ align:start position:0%
+divergent thinking so that's really
+cool. Yeah, but the taking a break. So,
+
+ align:start position:0%
+cool. Yeah, but the taking a break. So,
+ 
+
+ align:start position:0%
+cool. Yeah, but the taking a break. So,
+especially at a place like MIT, like I
+
+ align:start position:0%
+especially at a place like MIT, like I
+ 
+
+ align:start position:0%
+especially at a place like MIT, like I
+don't I don't know if like taking a
+
+ align:start position:0%
+don't I don't know if like taking a
+ 
+
+ align:start position:0%
+don't I don't know if like taking a
+break is on the menu really. Um, but it
+
+ align:start position:0%
+break is on the menu really. Um, but it
+ 
+
+ align:start position:0%
+break is on the menu really. Um, but it
+should be. I'm guessing it should be.
+
+ align:start position:0%
+should be. I'm guessing it should be.
+ 
+
+ align:start position:0%
+should be. I'm guessing it should be.
+Yeah. And then I'm wondering if you can
+
+ align:start position:0%
+Yeah. And then I'm wondering if you can
+ 
+
+ align:start position:0%
+Yeah. And then I'm wondering if you can
+talk to us about like the thing you
+
+ align:start position:0%
+talk to us about like the thing you
+ 
+
+ align:start position:0%
+talk to us about like the thing you
+created in the world to help people take
+
+ align:start position:0%
+created in the world to help people take
+ 
+
+ align:start position:0%
+created in the world to help people take
+a break and why it's important. Sure.
+
+ align:start position:0%
+a break and why it's important. Sure.
+ 
+
+ align:start position:0%
+a break and why it's important. Sure.
+So, this was a project uh for I don't
+
+ align:start position:0%
+So, this was a project uh for I don't
+ 
+
+ align:start position:0%
+So, this was a project uh for I don't
+know. I just had an idea. I was like,
+
+ align:start position:0%
+know. I just had an idea. I was like,
+ 
+
+ align:start position:0%
+know. I just had an idea. I was like,
+let me just make a coloring book. um
+
+ align:start position:0%
+let me just make a coloring book. um
+ 
+
+ align:start position:0%
+let me just make a coloring book. um
+like you know one of those uh coloring
+
+ align:start position:0%
+like you know one of those uh coloring
+ 
+
+ align:start position:0%
+like you know one of those uh coloring
+books that you just kind of doodle in
+
+ align:start position:0%
+books that you just kind of doodle in
+ 
+
+ align:start position:0%
+books that you just kind of doodle in
+into. And I thought let me just make it
+
+ align:start position:0%
+into. And I thought let me just make it
+ 
+
+ align:start position:0%
+into. And I thought let me just make it
+um computer science themed. And so each
+
+ align:start position:0%
+um computer science themed. And so each
+ 
+
+ align:start position:0%
+um computer science themed. And so each
+one of these is you know like here's a
+
+ align:start position:0%
+one of these is you know like here's a
+ 
+
+ align:start position:0%
+one of these is you know like here's a
+circuit and it's like here's a network
+
+ align:start position:0%
+circuit and it's like here's a network
+ 
+
+ align:start position:0%
+circuit and it's like here's a network
+right of connected people and then
+
+ align:start position:0%
+right of connected people and then
+ 
+
+ align:start position:0%
+right of connected people and then
+here's a like a matrix kind of thing
+
+ align:start position:0%
+here's a like a matrix kind of thing
+ 
+
+ align:start position:0%
+here's a like a matrix kind of thing
+right with bits.
+
+ align:start position:0%
+right with bits.
+ 
+
+ align:start position:0%
+right with bits.
+So uh it was just kind of all these
+
+ align:start position:0%
+So uh it was just kind of all these
+ 
+
+ align:start position:0%
+So uh it was just kind of all these
+ideas from uh computer science and the
+
+ align:start position:0%
+ideas from uh computer science and the
+ 
+
+ align:start position:0%
+ideas from uh computer science and the
+hope is that if you are stuck and you
+
+ align:start position:0%
+hope is that if you are stuck and you
+ 
+
+ align:start position:0%
+hope is that if you are stuck and you
+don't have a duck right then you can
+
+ align:start position:0%
+don't have a duck right then you can
+ 
+
+ align:start position:0%
+don't have a duck right then you can
+take a coloring book doesn't have to be
+
+ align:start position:0%
+take a coloring book doesn't have to be
+ 
+
+ align:start position:0%
+take a coloring book doesn't have to be
+this one but just something that uh
+
+ align:start position:0%
+this one but just something that uh
+ 
+
+ align:start position:0%
+this one but just something that uh
+gives your brain a break but it's this
+
+ align:start position:0%
+gives your brain a break but it's this
+ 
+
+ align:start position:0%
+gives your brain a break but it's this
+idea of mind wandering and this is an
+
+ align:start position:0%
+idea of mind wandering and this is an
+ 
+
+ align:start position:0%
+idea of mind wandering and this is an
+idea from uh psychology where mind
+
+ align:start position:0%
+idea from uh psychology where mind
+ 
+
+ align:start position:0%
+idea from uh psychology where mind
+wandering is not bad like if you're
+
+ align:start position:0%
+wandering is not bad like if you're
+ 
+
+ align:start position:0%
+wandering is not bad like if you're
+folding laundry right you're doing a
+
+ align:start position:0%
+folding laundry right you're doing a
+ 
+
+ align:start position:0%
+folding laundry right you're doing a
+very repetitive task
+
+ align:start position:0%
+very repetitive task
+ 
+
+ align:start position:0%
+very repetitive task
+your brain doesn't have to super focus
+
+ align:start position:0%
+your brain doesn't have to super focus
+ 
+
+ align:start position:0%
+your brain doesn't have to super focus
+on it. And so that's when inspiration
+
+ align:start position:0%
+on it. And so that's when inspiration
+ 
+
+ align:start position:0%
+on it. And so that's when inspiration
+comes because you're kind of
+
+ align:start position:0%
+comes because you're kind of
+ 
+
+ align:start position:0%
+comes because you're kind of
+subconsciously thinking about other
+
+ align:start position:0%
+subconsciously thinking about other
+ 
+
+ align:start position:0%
+subconsciously thinking about other
+things, maybe problems that you have or,
+
+ align:start position:0%
+things, maybe problems that you have or,
+ 
+
+ align:start position:0%
+things, maybe problems that you have or,
+you know, things that you're worried
+
+ align:start position:0%
+you know, things that you're worried
+ 
+
+ align:start position:0%
+you know, things that you're worried
+about. And that's kind of when solutions
+
+ align:start position:0%
+about. And that's kind of when solutions
+ 
+
+ align:start position:0%
+about. And that's kind of when solutions
+come. Just like, you know, when you're
+
+ align:start position:0%
+come. Just like, you know, when you're
+ 
+
+ align:start position:0%
+come. Just like, you know, when you're
+taking a shower, that's mind wandering
+
+ align:start position:0%
+taking a shower, that's mind wandering
+ 
+
+ align:start position:0%
+taking a shower, that's mind wandering
+as well because you're doing a test that
+
+ align:start position:0%
+as well because you're doing a test that
+ 
+
+ align:start position:0%
+as well because you're doing a test that
+you already know how to do. You don't
+
+ align:start position:0%
+you already know how to do. You don't
+ 
+
+ align:start position:0%
+you already know how to do. You don't
+need to dedicate any thought to it. So
+
+ align:start position:0%
+need to dedicate any thought to it. So
+ 
+
+ align:start position:0%
+need to dedicate any thought to it. So
+your brain kind of dedicates thought to
+
+ align:start position:0%
+your brain kind of dedicates thought to
+ 
+
+ align:start position:0%
+your brain kind of dedicates thought to
+other things that um might be worrying
+
+ align:start position:0%
+other things that um might be worrying
+ 
+
+ align:start position:0%
+other things that um might be worrying
+you or on your mind. That's great that
+
+ align:start position:0%
+you or on your mind. That's great that
+ 
+
+ align:start position:0%
+you or on your mind. That's great that
+you've created that. Do you feel like
+
+ align:start position:0%
+you've created that. Do you feel like
+ 
+
+ align:start position:0%
+you've created that. Do you feel like
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+is like what's the percentage of logic
+
+ align:start position:0%
+is like what's the percentage of logic
+ 
+
+ align:start position:0%
+is like what's the percentage of logic
+to creativity when it comes to
+
+ align:start position:0%
+to creativity when it comes to
+ 
+
+ align:start position:0%
+to creativity when it comes to
+programming? Are we like 50/50, 8020?
+
+ align:start position:0%
+programming? Are we like 50/50, 8020?
+ 
+
+ align:start position:0%
+programming? Are we like 50/50, 8020?
+Interesting. 6040
+
+ align:start position:0%
+Interesting. 6040
+ 
+
+ align:start position:0%
+Interesting. 6040
+maybe 50/50 I would say. I think
+
+ align:start position:0%
+maybe 50/50 I would say. I think
+ 
+
+ align:start position:0%
+maybe 50/50 I would say. I think
+creativity comes into the process at all
+
+ align:start position:0%
+creativity comes into the process at all
+ 
+
+ align:start position:0%
+creativity comes into the process at all
+the different levels. So when you're
+
+ align:start position:0%
+the different levels. So when you're
+ 
+
+ align:start position:0%
+the different levels. So when you're
+coming up with a problem or something
+
+ align:start position:0%
+coming up with a problem or something
+ 
+
+ align:start position:0%
+coming up with a problem or something
+that you want to solve using
+
+ align:start position:0%
+that you want to solve using
+ 
+
+ align:start position:0%
+that you want to solve using
+programming, right, you have to be
+
+ align:start position:0%
+programming, right, you have to be
+ 
+
+ align:start position:0%
+programming, right, you have to be
+creative like right. Um so just coming
+
+ align:start position:0%
+creative like right. Um so just coming
+ 
+
+ align:start position:0%
+creative like right. Um so just coming
+up with that is mostly is creativity
+
+ align:start position:0%
+up with that is mostly is creativity
+ 
+
+ align:start position:0%
+up with that is mostly is creativity
+when you're deciding how to solve the
+
+ align:start position:0%
+when you're deciding how to solve the
+ 
+
+ align:start position:0%
+when you're deciding how to solve the
+problem or how to uh how to write the
+
+ align:start position:0%
+problem or how to uh how to write the
+ 
+
+ align:start position:0%
+problem or how to uh how to write the
+code sort of maybe what algorithm to use
+
+ align:start position:0%
+code sort of maybe what algorithm to use
+ 
+
+ align:start position:0%
+code sort of maybe what algorithm to use
+or how to structure it or like what
+
+ align:start position:0%
+or how to structure it or like what
+ 
+
+ align:start position:0%
+or how to structure it or like what
+pieces to use and where. um that
+
+ align:start position:0%
+pieces to use and where. um that
+ 
+
+ align:start position:0%
+pieces to use and where. um that
+requires some creativity potentially,
+
+ align:start position:0%
+requires some creativity potentially,
+ 
+
+ align:start position:0%
+requires some creativity potentially,
+you know, putting things together that
+
+ align:start position:0%
+you know, putting things together that
+ 
+
+ align:start position:0%
+you know, putting things together that
+you might not have put before, you know,
+
+ align:start position:0%
+you might not have put before, you know,
+ 
+
+ align:start position:0%
+you might not have put before, you know,
+pieces of uh uh programming concepts
+
+ align:start position:0%
+pieces of uh uh programming concepts
+ 
+
+ align:start position:0%
+pieces of uh uh programming concepts
+together that you might not have put
+
+ align:start position:0%
+together that you might not have put
+ 
+
+ align:start position:0%
+together that you might not have put
+before. And then you're obviously going
+
+ align:start position:0%
+before. And then you're obviously going
+ 
+
+ align:start position:0%
+before. And then you're obviously going
+to uh run into an error after you write
+
+ align:start position:0%
+to uh run into an error after you write
+ 
+
+ align:start position:0%
+to uh run into an error after you write
+the code the first time. And so then
+
+ align:start position:0%
+the code the first time. And so then
+ 
+
+ align:start position:0%
+the code the first time. And so then
+tons of creativity comes into play
+
+ align:start position:0%
+tons of creativity comes into play
+ 
+
+ align:start position:0%
+tons of creativity comes into play
+there. Uh but you know, drawing or
+
+ align:start position:0%
+there. Uh but you know, drawing or
+ 
+
+ align:start position:0%
+there. Uh but you know, drawing or
+talking to a duck. Um, I'm liking
+
+ align:start position:0%
+talking to a duck. Um, I'm liking
+ 
+
+ align:start position:0%
+talking to a duck. Um, I'm liking
+programming more and more, I have to
+
+ align:start position:0%
+programming more and more, I have to
+ 
+
+ align:start position:0%
+programming more and more, I have to
+say. I know once you're programming,
+
+ align:start position:0%
+say. I know once you're programming,
+ 
+
+ align:start position:0%
+say. I know once you're programming,
+it's kind of like reading a really good
+
+ align:start position:0%
+it's kind of like reading a really good
+ 
+
+ align:start position:0%
+it's kind of like reading a really good
+book. Like, you're in this zen space
+
+ align:start position:0%
+book. Like, you're in this zen space
+ 
+
+ align:start position:0%
+book. Like, you're in this zen space
+where you're just like, "Yeah, this is
+
+ align:start position:0%
+where you're just like, "Yeah, this is
+ 
+
+ align:start position:0%
+where you're just like, "Yeah, this is
+working." Like, I totally see where I'm
+
+ align:start position:0%
+working." Like, I totally see where I'm
+ 
+
+ align:start position:0%
+working." Like, I totally see where I'm
+where this is going. Like, I know what I
+
+ align:start position:0%
+where this is going. Like, I know what I
+ 
+
+ align:start position:0%
+where this is going. Like, I know what I
+want to write next, you know? Like, the
+
+ align:start position:0%
+want to write next, you know? Like, the
+ 
+
+ align:start position:0%
+want to write next, you know? Like, the
+code just kind of fits together. So,
+
+ align:start position:0%
+code just kind of fits together. So,
+ 
+
+ align:start position:0%
+code just kind of fits together. So,
+just like being in a good book is is
+
+ align:start position:0%
+just like being in a good book is is
+ 
+
+ align:start position:0%
+just like being in a good book is is
+awesome. Wow. And then the more you
+
+ align:start position:0%
+awesome. Wow. And then the more you
+ 
+
+ align:start position:0%
+awesome. Wow. And then the more you
+program, the more you want to program
+
+ align:start position:0%
+program, the more you want to program
+ 
+
+ align:start position:0%
+program, the more you want to program
+cuz you're just gaining these skills
+
+ align:start position:0%
+cuz you're just gaining these skills
+ 
+
+ align:start position:0%
+cuz you're just gaining these skills
+along the way. So, it's like you're like
+
+ align:start position:0%
+along the way. So, it's like you're like
+ 
+
+ align:start position:0%
+along the way. So, it's like you're like
+I play video games, so you know, you're
+
+ align:start position:0%
+I play video games, so you know, you're
+ 
+
+ align:start position:0%
+I play video games, so you know, you're
+just constantly like looking for new
+
+ align:start position:0%
+just constantly like looking for new
+ 
+
+ align:start position:0%
+just constantly like looking for new
+ways to level up, but there's no cap.
+
+ align:start position:0%
+ways to level up, but there's no cap.
+ 
+
+ align:start position:0%
+ways to level up, but there's no cap.
+It's uh really fascinating because
+
+ align:start position:0%
+It's uh really fascinating because
+ 
+
+ align:start position:0%
+It's uh really fascinating because
+unlike video games, most of them like
+
+ align:start position:0%
+unlike video games, most of them like
+ 
+
+ align:start position:0%
+unlike video games, most of them like
+you could use open-source
+
+ align:start position:0%
+you could use open-source
+ 
+
+ align:start position:0%
+you could use open-source
+um coding languages and financial
+
+ align:start position:0%
+um coding languages and financial
+ 
+
+ align:start position:0%
+um coding languages and financial
+barriers don't come into play to get
+
+ align:start position:0%
+barriers don't come into play to get
+ 
+
+ align:start position:0%
+barriers don't come into play to get
+that area for growth and that like that
+
+ align:start position:0%
+that area for growth and that like that
+ 
+
+ align:start position:0%
+that area for growth and that like that
+dopamine hit of like leveling up,
+
+ align:start position:0%
+dopamine hit of like leveling up,
+ 
+
+ align:start position:0%
+dopamine hit of like leveling up,
+increasing your skills. It's just Yeah,
+
+ align:start position:0%
+increasing your skills. It's just Yeah,
+ 
+
+ align:start position:0%
+increasing your skills. It's just Yeah,
+it's just kind of a different Like you
+
+ align:start position:0%
+it's just kind of a different Like you
+ 
+
+ align:start position:0%
+it's just kind of a different Like you
+said, it's a growth mindset, right? It's
+
+ align:start position:0%
+said, it's a growth mindset, right? It's
+ 
+
+ align:start position:0%
+said, it's a growth mindset, right? It's
+a different way of of It's a different
+
+ align:start position:0%
+a different way of of It's a different
+ 
+
+ align:start position:0%
+a different way of of It's a different
+fun. It's a different fun. It's a
+
+ align:start position:0%
+fun. It's a different fun. It's a
+ 
+
+ align:start position:0%
+fun. It's a different fun. It's a
+different fun. I I'm like more and more
+
+ align:start position:0%
+different fun. I I'm like more and more
+ 
+
+ align:start position:0%
+different fun. I I'm like more and more
+I'm like maybe I want to try this one.
+
+ align:start position:0%
+I'm like maybe I want to try this one.
+ 
+
+ align:start position:0%
+I'm like maybe I want to try this one.
+Well, oh, there's a book right here.
+
+ align:start position:0%
+Well, oh, there's a book right here.
+ 
+
+ align:start position:0%
+Well, oh, there's a book right here.
+Get programming. Learn to code with
+
+ align:start position:0%
+Get programming. Learn to code with
+ 
+
+ align:start position:0%
+Get programming. Learn to code with
+Python. Yeah. So, this I wrote a while
+
+ align:start position:0%
+Python. Yeah. So, this I wrote a while
+ 
+
+ align:start position:0%
+Python. Yeah. So, this I wrote a while
+ago.
+
+ align:start position:0%
+ago.
+ 
+
+ align:start position:0%
+ago.
+Um, it's a book made lots of books or
+
+ align:start position:0%
+Um, it's a book made lots of books or
+ 
+
+ align:start position:0%
+Um, it's a book made lots of books or
+lots of things claim to be for
+
+ align:start position:0%
+lots of things claim to be for
+ 
+
+ align:start position:0%
+lots of things claim to be for
+beginners, but I wanted to write
+
+ align:start position:0%
+beginners, but I wanted to write
+ 
+
+ align:start position:0%
+beginners, but I wanted to write
+something that is actually for people
+
+ align:start position:0%
+something that is actually for people
+ 
+
+ align:start position:0%
+something that is actually for people
+who have never programmed before. So, I
+
+ align:start position:0%
+who have never programmed before. So, I
+ 
+
+ align:start position:0%
+who have never programmed before. So, I
+think we don't even get into writing
+
+ align:start position:0%
+think we don't even get into writing
+ 
+
+ align:start position:0%
+think we don't even get into writing
+code to like chapter 7 or something like
+
+ align:start position:0%
+code to like chapter 7 or something like
+ 
+
+ align:start position:0%
+code to like chapter 7 or something like
+that. It's mostly kind of just setting
+
+ align:start position:0%
+that. It's mostly kind of just setting
+ 
+
+ align:start position:0%
+that. It's mostly kind of just setting
+up motivation, but not not boring like I
+
+ align:start position:0%
+up motivation, but not not boring like I
+ 
+
+ align:start position:0%
+up motivation, but not not boring like I
+wanted it to re read like a novel,
+
+ align:start position:0%
+wanted it to re read like a novel,
+ 
+
+ align:start position:0%
+wanted it to re read like a novel,
+right? Like you're just like, "Oh, I'm
+
+ align:start position:0%
+right? Like you're just like, "Oh, I'm
+ 
+
+ align:start position:0%
+right? Like you're just like, "Oh, I'm
+just following along." Um, so if you
+
+ align:start position:0%
+just following along." Um, so if you
+ 
+
+ align:start position:0%
+just following along." Um, so if you
+want to start, you could also, you know,
+
+ align:start position:0%
+want to start, you could also, you know,
+ 
+
+ align:start position:0%
+want to start, you could also, you know,
+you could try this book. You can keep
+
+ align:start position:0%
+you could try this book. You can keep
+ 
+
+ align:start position:0%
+you could try this book. You can keep
+this hot. Oh my gosh. I have to tell you
+
+ align:start position:0%
+this hot. Oh my gosh. I have to tell you
+ 
+
+ align:start position:0%
+this hot. Oh my gosh. I have to tell you
+a secret. Yes. So, I requested this
+
+ align:start position:0%
+a secret. Yes. So, I requested this
+ 
+
+ align:start position:0%
+a secret. Yes. So, I requested this
+through interl loan at my home library.
+
+ align:start position:0%
+through interl loan at my home library.
+ 
+
+ align:start position:0%
+through interl loan at my home library.
+So, and I asked um one of my family
+
+ align:start position:0%
+So, and I asked um one of my family
+ 
+
+ align:start position:0%
+So, and I asked um one of my family
+members to pick it up and I was like,
+
+ align:start position:0%
+members to pick it up and I was like,
+ 
+
+ align:start position:0%
+members to pick it up and I was like,
+just so you know, it's really for me.
+
+ align:start position:0%
+just so you know, it's really for me.
+ 
+
+ align:start position:0%
+just so you know, it's really for me.
+Like, cuz they would be like, why is she
+
+ align:start position:0%
+Like, cuz they would be like, why is she
+ 
+
+ align:start position:0%
+Like, cuz they would be like, why is she
+getting this book? This must be the
+
+ align:start position:0%
+getting this book? This must be the
+ 
+
+ align:start position:0%
+getting this book? This must be the
+wrong thing. I was like, it's not a
+
+ align:start position:0%
+wrong thing. I was like, it's not a
+ 
+
+ align:start position:0%
+wrong thing. I was like, it's not a
+mistake. Like, it's actually for me. And
+
+ align:start position:0%
+mistake. Like, it's actually for me. And
+ 
+
+ align:start position:0%
+mistake. Like, it's actually for me. And
+but I didn't really believe that, but
+
+ align:start position:0%
+but I didn't really believe that, but
+ 
+
+ align:start position:0%
+but I didn't really believe that, but
+now I feel like it is for me. Oh, great.
+
+ align:start position:0%
+now I feel like it is for me. Oh, great.
+ 
+
+ align:start position:0%
+now I feel like it is for me. Oh, great.
+Like I do want to read it now, learn.
+
+ align:start position:0%
+Like I do want to read it now, learn.
+ 
+
+ align:start position:0%
+Like I do want to read it now, learn.
+Yeah, anybody can can start for sure.
+
+ align:start position:0%
+Yeah, anybody can can start for sure.
+ 
+
+ align:start position:0%
+Yeah, anybody can can start for sure.
+Yeah, that's just great. Um, do you have
+
+ align:start position:0%
+Yeah, that's just great. Um, do you have
+ 
+
+ align:start position:0%
+Yeah, that's just great. Um, do you have
+any like hot tips for newbies who might
+
+ align:start position:0%
+any like hot tips for newbies who might
+ 
+
+ align:start position:0%
+any like hot tips for newbies who might
+um want to start or even people who are
+
+ align:start position:0%
+um want to start or even people who are
+ 
+
+ align:start position:0%
+um want to start or even people who are
+like deep into programming, deep into
+
+ align:start position:0%
+like deep into programming, deep into
+ 
+
+ align:start position:0%
+like deep into programming, deep into
+the hoodie already? Like things you're
+
+ align:start position:0%
+the hoodie already? Like things you're
+ 
+
+ align:start position:0%
+the hoodie already? Like things you're
+interested in reading or you think other
+
+ align:start position:0%
+interested in reading or you think other
+ 
+
+ align:start position:0%
+interested in reading or you think other
+people should view or listen to um to
+
+ align:start position:0%
+people should view or listen to um to
+ 
+
+ align:start position:0%
+people should view or listen to um to
+start or continue their journey? Mostly
+
+ align:start position:0%
+start or continue their journey? Mostly
+ 
+
+ align:start position:0%
+start or continue their journey? Mostly
+tip for mostly tips for newbies I would
+
+ align:start position:0%
+tip for mostly tips for newbies I would
+ 
+
+ align:start position:0%
+tip for mostly tips for newbies I would
+say. Okay. Um don't get discouraged.
+
+ align:start position:0%
+say. Okay. Um don't get discouraged.
+ 
+
+ align:start position:0%
+say. Okay. Um don't get discouraged.
+Learning curve is steep. Yeah. Okay.
+
+ align:start position:0%
+Learning curve is steep. Yeah. Okay.
+ 
+
+ align:start position:0%
+Learning curve is steep. Yeah. Okay.
+Yeah. It sucks. But can I text you when
+
+ align:start position:0%
+Yeah. It sucks. But can I text you when
+ 
+
+ align:start position:0%
+Yeah. It sucks. But can I text you when
+I Yes, you can text me. Thank you. If
+
+ align:start position:0%
+I Yes, you can text me. Thank you. If
+ 
+
+ align:start position:0%
+I Yes, you can text me. Thank you. If
+the duck doesn't work. If the duck
+
+ align:start position:0%
+the duck doesn't work. If the duck
+ 
+
+ align:start position:0%
+the duck doesn't work. If the duck
+doesn't work. Yeah. No, it's it's I
+
+ align:start position:0%
+doesn't work. Yeah. No, it's it's I
+ 
+
+ align:start position:0%
+doesn't work. Yeah. No, it's it's I
+mean, you're learning a new language.
+
+ align:start position:0%
+mean, you're learning a new language.
+ 
+
+ align:start position:0%
+mean, you're learning a new language.
+Like it's called a programming language,
+
+ align:start position:0%
+Like it's called a programming language,
+ 
+
+ align:start position:0%
+Like it's called a programming language,
+right? And it's basically learning a new
+
+ align:start position:0%
+right? And it's basically learning a new
+ 
+
+ align:start position:0%
+right? And it's basically learning a new
+way to write things that you already
+
+ align:start position:0%
+way to write things that you already
+ 
+
+ align:start position:0%
+way to write things that you already
+know how to do in or how to write in
+
+ align:start position:0%
+know how to do in or how to write in
+ 
+
+ align:start position:0%
+know how to do in or how to write in
+English. Yeah. You're just structuring
+
+ align:start position:0%
+English. Yeah. You're just structuring
+ 
+
+ align:start position:0%
+English. Yeah. You're just structuring
+it structuring it in a completely
+
+ align:start position:0%
+it structuring it in a completely
+ 
+
+ align:start position:0%
+it structuring it in a completely
+different way and a different language.
+
+ align:start position:0%
+different way and a different language.
+ 
+
+ align:start position:0%
+different way and a different language.
+So it the learning curve is steep. But
+
+ align:start position:0%
+So it the learning curve is steep. But
+ 
+
+ align:start position:0%
+So it the learning curve is steep. But
+don't get discouraged with Genai tools.
+
+ align:start position:0%
+don't get discouraged with Genai tools.
+ 
+
+ align:start position:0%
+don't get discouraged with Genai tools.
+Now though it's easy
+
+ align:start position:0%
+Now though it's easy
+ 
+
+ align:start position:0%
+Now though it's easy
+to get started right that's not from
+
+ align:start position:0%
+to get started right that's not from
+ 
+
+ align:start position:0%
+to get started right that's not from
+scratch. So like I mentioned earlier, if
+
+ align:start position:0%
+scratch. So like I mentioned earlier, if
+ 
+
+ align:start position:0%
+scratch. So like I mentioned earlier, if
+you're stuck on a problem, just ask
+
+ align:start position:0%
+you're stuck on a problem, just ask
+ 
+
+ align:start position:0%
+you're stuck on a problem, just ask
+prompt it to give you a solution and
+
+ align:start position:0%
+prompt it to give you a solution and
+ 
+
+ align:start position:0%
+prompt it to give you a solution and
+then work on the trust but verify
+
+ align:start position:0%
+then work on the trust but verify
+ 
+
+ align:start position:0%
+then work on the trust but verify
+uh piece where you'll actually get
+
+ align:start position:0%
+uh piece where you'll actually get
+ 
+
+ align:start position:0%
+uh piece where you'll actually get
+valuable experience debugging, right?
+
+ align:start position:0%
+valuable experience debugging, right?
+ 
+
+ align:start position:0%
+valuable experience debugging, right?
+Because you already start with a piece
+
+ align:start position:0%
+Because you already start with a piece
+ 
+
+ align:start position:0%
+Because you already start with a piece
+of code. So like the confidence level is
+
+ align:start position:0%
+of code. So like the confidence level is
+ 
+
+ align:start position:0%
+of code. So like the confidence level is
+already kind of there. You're like,
+
+ align:start position:0%
+already kind of there. You're like,
+ 
+
+ align:start position:0%
+already kind of there. You're like,
+okay, I'm not starting blank. And then
+
+ align:start position:0%
+okay, I'm not starting blank. And then
+ 
+
+ align:start position:0%
+okay, I'm not starting blank. And then
+you can, you know, try to fix it or
+
+ align:start position:0%
+you can, you know, try to fix it or
+ 
+
+ align:start position:0%
+you can, you know, try to fix it or
+agree that it works. And both are really
+
+ align:start position:0%
+agree that it works. And both are really
+ 
+
+ align:start position:0%
+agree that it works. And both are really
+valuable skills to to practice as
+
+ align:start position:0%
+valuable skills to to practice as
+ 
+
+ align:start position:0%
+valuable skills to to practice as
+beginner programmers. I love the idea of
+
+ align:start position:0%
+beginner programmers. I love the idea of
+ 
+
+ align:start position:0%
+beginner programmers. I love the idea of
+starting with code and practicing
+
+ align:start position:0%
+starting with code and practicing
+ 
+
+ align:start position:0%
+starting with code and practicing
+debugging. That feels like low stakes
+
+ align:start position:0%
+debugging. That feels like low stakes
+ 
+
+ align:start position:0%
+debugging. That feels like low stakes
+and doable. Totally. Yeah. Um, what have
+
+ align:start position:0%
+and doable. Totally. Yeah. Um, what have
+ 
+
+ align:start position:0%
+and doable. Totally. Yeah. Um, what have
+I not asked you that I should have asked
+
+ align:start position:0%
+I not asked you that I should have asked
+ 
+
+ align:start position:0%
+I not asked you that I should have asked
+you? I want to know what games. What
+
+ align:start position:0%
+you? I want to know what games. What
+ 
+
+ align:start position:0%
+you? I want to know what games. What
+games? What games you play? Oh my gosh.
+
+ align:start position:0%
+games? What games you play? Oh my gosh.
+ 
+
+ align:start position:0%
+games? What games you play? Oh my gosh.
+Like video games? Y I like driving a
+
+ align:start position:0%
+Like video games? Y I like driving a
+ 
+
+ align:start position:0%
+Like video games? Y I like driving a
+lot. So I drive in the real I do not.
+
+ align:start position:0%
+lot. So I drive in the real I do not.
+ 
+
+ align:start position:0%
+lot. So I drive in the real I do not.
+You said you don't like being stuck in
+
+ align:start position:0%
+You said you don't like being stuck in
+ 
+
+ align:start position:0%
+You said you don't like being stuck in
+traffic. No, I don't like being stuck.
+
+ align:start position:0%
+traffic. No, I don't like being stuck.
+ 
+
+ align:start position:0%
+traffic. No, I don't like being stuck.
+So, I like to drive. So, I also enjoy
+
+ align:start position:0%
+So, I like to drive. So, I also enjoy
+ 
+
+ align:start position:0%
+So, I like to drive. So, I also enjoy
+driving games. Okay.
+
+ align:start position:0%
+driving games. Okay.
+ 
+
+ align:start position:0%
+driving games. Okay.
+Not just around the track, but like
+
+ align:start position:0%
+Not just around the track, but like
+ 
+
+ align:start position:0%
+Not just around the track, but like
+through random cities and things like
+
+ align:start position:0%
+through random cities and things like
+ 
+
+ align:start position:0%
+through random cities and things like
+that. Escaping the police and you know,
+
+ align:start position:0%
+that. Escaping the police and you know,
+ 
+
+ align:start position:0%
+that. Escaping the police and you know,
+like the You have a whole other side to
+
+ align:start position:0%
+like the You have a whole other side to
+ 
+
+ align:start position:0%
+like the You have a whole other side to
+you. Me for speed.
+
+ align:start position:0%
+you. Me for speed.
+ 
+
+ align:start position:0%
+you. Me for speed.
+GTA played Need for Speed. Yeah. Yeah. I
+
+ align:start position:0%
+GTA played Need for Speed. Yeah. Yeah. I
+ 
+
+ align:start position:0%
+GTA played Need for Speed. Yeah. Yeah. I
+have the setup with the wheel and Yeah.
+
+ align:start position:0%
+have the setup with the wheel and Yeah.
+ 
+
+ align:start position:0%
+have the setup with the wheel and Yeah.
+Yeah. Oh, wow. Well, thank you so much
+
+ align:start position:0%
+Yeah. Oh, wow. Well, thank you so much
+ 
+
+ align:start position:0%
+Yeah. Oh, wow. Well, thank you so much
+for being here. I learned about myself.
+
+ align:start position:0%
+for being here. I learned about myself.
+ 
+
+ align:start position:0%
+for being here. I learned about myself.
+I learned about programming. I have a
+
+ align:start position:0%
+I learned about programming. I have a
+ 
+
+ align:start position:0%
+I learned about programming. I have a
+whole new world view on what is possible
+
+ align:start position:0%
+whole new world view on what is possible
+ 
+
+ align:start position:0%
+whole new world view on what is possible
+with and through programming. And that's
+
+ align:start position:0%
+with and through programming. And that's
+ 
+
+ align:start position:0%
+with and through programming. And that's
+just an incredible gift. And I'm so glad
+
+ align:start position:0%
+just an incredible gift. And I'm so glad
+ 
+
+ align:start position:0%
+just an incredible gift. And I'm so glad
+we get to share that with a lot of
+
+ align:start position:0%
+we get to share that with a lot of
+ 
+
+ align:start position:0%
+we get to share that with a lot of
+people who might also take that gift and
+
+ align:start position:0%
+people who might also take that gift and
+ 
+
+ align:start position:0%
+people who might also take that gift and
+run with it. So, thank you. That's
+
+ align:start position:0%
+run with it. So, thank you. That's
+ 
+
+ align:start position:0%
+run with it. So, thank you. That's
+awesome. Glad to hear. Thank you for the
+
+ align:start position:0%
+awesome. Glad to hear. Thank you for the
+ 
+
+ align:start position:0%
+awesome. Glad to hear. Thank you for the
+chat. This was awesome. And thank you
+
+ align:start position:0%
+chat. This was awesome. And thank you
+ 
+
+ align:start position:0%
+chat. This was awesome. And thank you
+for the duck. Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/peJUDjHJGb4.txt b/peJUDjHJGb4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f7ae9296901d5697757be477aa49cb3b6ab4c144
--- /dev/null
+++ b/peJUDjHJGb4.txt
@@ -0,0 +1,851 @@
+align:start position:0%
+ 
+here I present a spherical distribution
+
+ align:start position:0%
+here I present a spherical distribution
+ 
+
+ align:start position:0%
+here I present a spherical distribution
+problem and how I went about finding an
+
+ align:start position:0%
+problem and how I went about finding an
+ 
+
+ align:start position:0%
+problem and how I went about finding an
+approximate solution in Mathematica
+
+ align:start position:0%
+approximate solution in Mathematica
+ 
+
+ align:start position:0%
+approximate solution in Mathematica
+if you observe light that passes through
+
+ align:start position:0%
+if you observe light that passes through
+ 
+
+ align:start position:0%
+if you observe light that passes through
+a translucent spherical object a
+
+ align:start position:0%
+a translucent spherical object a
+ 
+
+ align:start position:0%
+a translucent spherical object a
+radiation that is transmitted through a
+
+ align:start position:0%
+radiation that is transmitted through a
+ 
+
+ align:start position:0%
+radiation that is transmitted through a
+spherical attenuator the intensity is
+
+ align:start position:0%
+spherical attenuator the intensity is
+ 
+
+ align:start position:0%
+spherical attenuator the intensity is
+not evenly distributed the intensity of
+
+ align:start position:0%
+not evenly distributed the intensity of
+ 
+
+ align:start position:0%
+not evenly distributed the intensity of
+transmitted radiation is described by
+
+ align:start position:0%
+transmitted radiation is described by
+ 
+
+ align:start position:0%
+transmitted radiation is described by
+this exponential function where the
+
+ align:start position:0%
+this exponential function where the
+ 
+
+ align:start position:0%
+this exponential function where the
+intensity distribution is governed by
+
+ align:start position:0%
+intensity distribution is governed by
+ 
+
+ align:start position:0%
+intensity distribution is governed by
+the material thickness X and density
+
+ align:start position:0%
+the material thickness X and density
+ 
+
+ align:start position:0%
+the material thickness X and density
+lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's plot this function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that as the material
+
+ align:start position:0%
+you can see that as the material
+ 
+
+ align:start position:0%
+you can see that as the material
+thickness X increases the intensity of
+
+ align:start position:0%
+thickness X increases the intensity of
+ 
+
+ align:start position:0%
+thickness X increases the intensity of
+the transmitted radiation decreases
+
+ align:start position:0%
+the transmitted radiation decreases
+ 
+
+ align:start position:0%
+the transmitted radiation decreases
+exponentially let's make a function to
+
+ align:start position:0%
+exponentially let's make a function to
+ 
+
+ align:start position:0%
+exponentially let's make a function to
+model the transmitted radiation
+
+ align:start position:0%
+model the transmitted radiation
+ 
+
+ align:start position:0%
+model the transmitted radiation
+intensity in 3d in this module I defined
+
+ align:start position:0%
+intensity in 3d in this module I defined
+ 
+
+ align:start position:0%
+intensity in 3d in this module I defined
+I I naught and lambda to be local
+
+ align:start position:0%
+I I naught and lambda to be local
+ 
+
+ align:start position:0%
+I I naught and lambda to be local
+variables Z is the function for a
+
+ align:start position:0%
+variables Z is the function for a
+ 
+
+ align:start position:0%
+variables Z is the function for a
+hemisphere we want to look at the
+
+ align:start position:0%
+hemisphere we want to look at the
+ 
+
+ align:start position:0%
+hemisphere we want to look at the
+effects on a sphere but it's easier to
+
+ align:start position:0%
+effects on a sphere but it's easier to
+ 
+
+ align:start position:0%
+effects on a sphere but it's easier to
+work with the hemisphere so I multiplied
+
+ align:start position:0%
+work with the hemisphere so I multiplied
+ 
+
+ align:start position:0%
+work with the hemisphere so I multiplied
+the hemisphere by 2 and the function
+
+ align:start position:0%
+the hemisphere by 2 and the function
+ 
+
+ align:start position:0%
+the hemisphere by 2 and the function
+returns intensity as a function of x and
+
+ align:start position:0%
+returns intensity as a function of x and
+ 
+
+ align:start position:0%
+returns intensity as a function of x and
+y position where the xy-plane is the
+
+ align:start position:0%
+y position where the xy-plane is the
+ 
+
+ align:start position:0%
+y position where the xy-plane is the
+projection of the sphere let's have a
+
+ align:start position:0%
+projection of the sphere let's have a
+ 
+
+ align:start position:0%
+projection of the sphere let's have a
+look at the intensity distribution in 3d
+
+ align:start position:0%
+look at the intensity distribution in 3d
+ 
+
+ align:start position:0%
+look at the intensity distribution in 3d
+this plot shows us that the intensity at
+
+ align:start position:0%
+this plot shows us that the intensity at
+ 
+
+ align:start position:0%
+this plot shows us that the intensity at
+the edges of the projection is greater
+
+ align:start position:0%
+the edges of the projection is greater
+ 
+
+ align:start position:0%
+the edges of the projection is greater
+than the intensity in the middle of the
+
+ align:start position:0%
+than the intensity in the middle of the
+ 
+
+ align:start position:0%
+than the intensity in the middle of the
+projection it's a bit hard to visualize
+
+ align:start position:0%
+projection it's a bit hard to visualize
+ 
+
+ align:start position:0%
+projection it's a bit hard to visualize
+so here's another way to look at it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that the intensity is
+
+ align:start position:0%
+you can see that the intensity is
+ 
+
+ align:start position:0%
+you can see that the intensity is
+highest around the edges and lowest in
+
+ align:start position:0%
+highest around the edges and lowest in
+ 
+
+ align:start position:0%
+highest around the edges and lowest in
+the center of the projection I did this
+
+ align:start position:0%
+the center of the projection I did this
+ 
+
+ align:start position:0%
+the center of the projection I did this
+by making the arrow length a function of
+
+ align:start position:0%
+by making the arrow length a function of
+ 
+
+ align:start position:0%
+by making the arrow length a function of
+the intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's see what happens when we
+
+ align:start position:0%
+now let's see what happens when we
+ 
+
+ align:start position:0%
+now let's see what happens when we
+replace lambda which was a constant with
+
+ align:start position:0%
+replace lambda which was a constant with
+ 
+
+ align:start position:0%
+replace lambda which was a constant with
+a function this means that we are
+
+ align:start position:0%
+a function this means that we are
+ 
+
+ align:start position:0%
+a function this means that we are
+changing the materials density as a
+
+ align:start position:0%
+changing the materials density as a
+ 
+
+ align:start position:0%
+changing the materials density as a
+function of the spheres radius I'm going
+
+ align:start position:0%
+function of the spheres radius I'm going
+ 
+
+ align:start position:0%
+function of the spheres radius I'm going
+to alter the intensity function I made
+
+ align:start position:0%
+to alter the intensity function I made
+ 
+
+ align:start position:0%
+to alter the intensity function I made
+before so that we can specify different
+
+ align:start position:0%
+before so that we can specify different
+ 
+
+ align:start position:0%
+before so that we can specify different
+functions for lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I'll show you three functions I
+
+ align:start position:0%
+here I'll show you three functions I
+ 
+
+ align:start position:0%
+here I'll show you three functions I
+tried out earlier for lambda to try and
+
+ align:start position:0%
+tried out earlier for lambda to try and
+ 
+
+ align:start position:0%
+tried out earlier for lambda to try and
+make the intensity constant there's a
+
+ align:start position:0%
+make the intensity constant there's a
+ 
+
+ align:start position:0%
+make the intensity constant there's a
+cosine function a nested sine function
+
+ align:start position:0%
+cosine function a nested sine function
+ 
+
+ align:start position:0%
+cosine function a nested sine function
+as suggested by professor Carter and a
+
+ align:start position:0%
+as suggested by professor Carter and a
+ 
+
+ align:start position:0%
+as suggested by professor Carter and a
+spherical Bessel function let's check
+
+ align:start position:0%
+spherical Bessel function let's check
+ 
+
+ align:start position:0%
+spherical Bessel function let's check
+that our function works on the lambda is
+
+ align:start position:0%
+that our function works on the lambda is
+ 
+
+ align:start position:0%
+that our function works on the lambda is
+a constant case we tried before
+
+ align:start position:0%
+a constant case we tried before
+ 
+
+ align:start position:0%
+a constant case we tried before
+okay good it works
+
+ align:start position:0%
+okay good it works
+ 
+
+ align:start position:0%
+okay good it works
+now let's look at our new density
+
+ align:start position:0%
+now let's look at our new density
+ 
+
+ align:start position:0%
+now let's look at our new density
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one is the cosine function you
+
+ align:start position:0%
+the first one is the cosine function you
+ 
+
+ align:start position:0%
+the first one is the cosine function you
+can see that the shape is not quite a
+
+ align:start position:0%
+can see that the shape is not quite a
+ 
+
+ align:start position:0%
+can see that the shape is not quite a
+hemisphere and now looks a bit closer to
+
+ align:start position:0%
+hemisphere and now looks a bit closer to
+ 
+
+ align:start position:0%
+hemisphere and now looks a bit closer to
+a cylinder next is the sine function it
+
+ align:start position:0%
+a cylinder next is the sine function it
+ 
+
+ align:start position:0%
+a cylinder next is the sine function it
+looks a lot like the cosine function
+
+ align:start position:0%
+looks a lot like the cosine function
+ 
+
+ align:start position:0%
+looks a lot like the cosine function
+more like a cylinder than a hemisphere
+
+ align:start position:0%
+more like a cylinder than a hemisphere
+ 
+
+ align:start position:0%
+more like a cylinder than a hemisphere
+and last is the Bessel function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+it also looks a lot like design and
+
+ align:start position:0%
+it also looks a lot like design and
+ 
+
+ align:start position:0%
+it also looks a lot like design and
+cosine functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the sine cosine and Bessel
+
+ align:start position:0%
+since the sine cosine and Bessel
+ 
+
+ align:start position:0%
+since the sine cosine and Bessel
+functions are very similar I'll plot
+
+ align:start position:0%
+functions are very similar I'll plot
+ 
+
+ align:start position:0%
+functions are very similar I'll plot
+them a different way so you can see them
+
+ align:start position:0%
+them a different way so you can see them
+ 
+
+ align:start position:0%
+them a different way so you can see them
+more clearly here the blue line is the
+
+ align:start position:0%
+more clearly here the blue line is the
+ 
+
+ align:start position:0%
+more clearly here the blue line is the
+Bessel function the red line is the
+
+ align:start position:0%
+Bessel function the red line is the
+ 
+
+ align:start position:0%
+Bessel function the red line is the
+cosine function and the yellow line is
+
+ align:start position:0%
+cosine function and the yellow line is
+ 
+
+ align:start position:0%
+cosine function and the yellow line is
+the nested sine function okay since it's
+
+ align:start position:0%
+the nested sine function okay since it's
+ 
+
+ align:start position:0%
+the nested sine function okay since it's
+hard to see from the 3d plots which of
+
+ align:start position:0%
+hard to see from the 3d plots which of
+ 
+
+ align:start position:0%
+hard to see from the 3d plots which of
+the density functions is closest to
+
+ align:start position:0%
+the density functions is closest to
+ 
+
+ align:start position:0%
+the density functions is closest to
+giving me constant intensity professor
+
+ align:start position:0%
+giving me constant intensity professor
+ 
+
+ align:start position:0%
+giving me constant intensity professor
+Carter suggested that I make a numerical
+
+ align:start position:0%
+Carter suggested that I make a numerical
+ 
+
+ align:start position:0%
+Carter suggested that I make a numerical
+error analysis if the intensity were
+
+ align:start position:0%
+error analysis if the intensity were
+ 
+
+ align:start position:0%
+error analysis if the intensity were
+constant we would get a cylinder in a 3d
+
+ align:start position:0%
+constant we would get a cylinder in a 3d
+ 
+
+ align:start position:0%
+constant we would get a cylinder in a 3d
+plot so I found the height of that
+
+ align:start position:0%
+plot so I found the height of that
+ 
+
+ align:start position:0%
+plot so I found the height of that
+theoretical cylinder by finding the
+
+ align:start position:0%
+theoretical cylinder by finding the
+ 
+
+ align:start position:0%
+theoretical cylinder by finding the
+minimum for each of the intensity
+
+ align:start position:0%
+minimum for each of the intensity
+ 
+
+ align:start position:0%
+minimum for each of the intensity
+functions then I subtracted the volume
+
+ align:start position:0%
+functions then I subtracted the volume
+ 
+
+ align:start position:0%
+functions then I subtracted the volume
+of the intensity from the volume of the
+
+ align:start position:0%
+of the intensity from the volume of the
+ 
+
+ align:start position:0%
+of the intensity from the volume of the
+theoretical cylinder and the square of
+
+ align:start position:0%
+theoretical cylinder and the square of
+ 
+
+ align:start position:0%
+theoretical cylinder and the square of
+this difference is the error here's a
+
+ align:start position:0%
+this difference is the error here's a
+ 
+
+ align:start position:0%
+this difference is the error here's a
+list of the errors but it will be easier
+
+ align:start position:0%
+list of the errors but it will be easier
+ 
+
+ align:start position:0%
+list of the errors but it will be easier
+to compare if I make a bar chart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now you can clearly see which
+
+ align:start position:0%
+okay now you can clearly see which
+ 
+
+ align:start position:0%
+okay now you can clearly see which
+function is the winner when the density
+
+ align:start position:0%
+function is the winner when the density
+ 
+
+ align:start position:0%
+function is the winner when the density
+is constant the intensity is the
+
+ align:start position:0%
+is constant the intensity is the
+ 
+
+ align:start position:0%
+is constant the intensity is the
+furthest from being constant the sine
+
+ align:start position:0%
+furthest from being constant the sine
+ 
+
+ align:start position:0%
+furthest from being constant the sine
+and cosine functions are much closer to
+
+ align:start position:0%
+and cosine functions are much closer to
+ 
+
+ align:start position:0%
+and cosine functions are much closer to
+making the intensity constant but the
+
+ align:start position:0%
+making the intensity constant but the
+ 
+
+ align:start position:0%
+making the intensity constant but the
+spherical Bessel function definitely
+
+ align:start position:0%
+spherical Bessel function definitely
+ 
+
+ align:start position:0%
+spherical Bessel function definitely
+makes the most even intensity
+
+ align:start position:0%
+makes the most even intensity
+ 
+
+ align:start position:0%
+makes the most even intensity
+distribution there is no perfect
+
+ align:start position:0%
+distribution there is no perfect
+ 
+
+ align:start position:0%
+distribution there is no perfect
+solution because at the limit of the
+
+ align:start position:0%
+solution because at the limit of the
+ 
+
+ align:start position:0%
+solution because at the limit of the
+edge of the sphere the material
+
+ align:start position:0%
+edge of the sphere the material
+ 
+
+ align:start position:0%
+edge of the sphere the material
+thickness goes to zero and therefore the
+
+ align:start position:0%
+thickness goes to zero and therefore the
+ 
+
+ align:start position:0%
+thickness goes to zero and therefore the
+density function must go to infinity but
+
+ align:start position:0%
+density function must go to infinity but
+ 
+
+ align:start position:0%
+density function must go to infinity but
+it looks like the Bessel function makes
+
+ align:start position:0%
+it looks like the Bessel function makes
+ 
+
+ align:start position:0%
+it looks like the Bessel function makes
+a good approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/pusPy4EDPC0.txt b/pusPy4EDPC0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce5fbabc383ec90a080235bb6f246777daf84358
--- /dev/null
+++ b/pusPy4EDPC0.txt
@@ -0,0 +1,15515 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit open courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so last time we were talking we talked
+
+ align:start position:0%
+so last time we were talking we talked
+ 
+
+ align:start position:0%
+so last time we were talking we talked
+about factorization in the effective
+
+ align:start position:0%
+about factorization in the effective
+ 
+
+ align:start position:0%
+about factorization in the effective
+theory and
+
+ align:start position:0%
+theory and
+ 
+
+ align:start position:0%
+theory and
+there is one type of factorization which
+
+ align:start position:0%
+there is one type of factorization which
+ 
+
+ align:start position:0%
+there is one type of factorization which
+is this hard clinical factorization that
+
+ align:start position:0%
+is this hard clinical factorization that
+ 
+
+ align:start position:0%
+is this hard clinical factorization that
+happened when the wilson ko which is a
+
+ align:start position:0%
+happened when the wilson ko which is a
+ 
+
+ align:start position:0%
+happened when the wilson ko which is a
+factorization between sort of the low
+
+ align:start position:0%
+factorization between sort of the low
+ 
+
+ align:start position:0%
+factorization between sort of the low
+energy physics described by the operator
+
+ align:start position:0%
+energy physics described by the operator
+ 
+
+ align:start position:0%
+energy physics described by the operator
+and the wilson coefficients
+
+ align:start position:0%
+and the wilson coefficients
+ 
+
+ align:start position:0%
+and the wilson coefficients
+and we decided we wanted to think about
+
+ align:start position:0%
+and we decided we wanted to think about
+ 
+
+ align:start position:0%
+and we decided we wanted to think about
+that in the following ways having
+
+ align:start position:0%
+that in the following ways having
+ 
+
+ align:start position:0%
+that in the following ways having
+convolutions between
+
+ align:start position:0%
+convolutions between
+ 
+
+ align:start position:0%
+convolutions between
+variables that appear in the wilson
+
+ align:start position:0%
+variables that appear in the wilson
+ 
+
+ align:start position:0%
+variables that appear in the wilson
+coefficients and variables that appear
+
+ align:start position:0%
+coefficients and variables that appear
+ 
+
+ align:start position:0%
+coefficients and variables that appear
+in the operator and the way that we can
+
+ align:start position:0%
+in the operator and the way that we can
+ 
+
+ align:start position:0%
+in the operator and the way that we can
+think about that is just what the most
+
+ align:start position:0%
+think about that is just what the most
+ 
+
+ align:start position:0%
+think about that is just what the most
+general possible thing is that we can
+
+ align:start position:0%
+general possible thing is that we can
+ 
+
+ align:start position:0%
+general possible thing is that we can
+write down for the wilson coefficients
+
+ align:start position:0%
+write down for the wilson coefficients
+ 
+
+ align:start position:0%
+write down for the wilson coefficients
+and of course it can depend on large
+
+ align:start position:0%
+and of course it can depend on large
+ 
+
+ align:start position:0%
+and of course it can depend on large
+momenta
+
+ align:start position:0%
+momenta
+ 
+
+ align:start position:0%
+momenta
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+large momenta here includes the label
+
+ align:start position:0%
+large momenta here includes the label
+ 
+
+ align:start position:0%
+large momenta here includes the label
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+ 
+so large momentum always show up in the
+
+ align:start position:0%
+so large momentum always show up in the
+ 
+
+ align:start position:0%
+so large momentum always show up in the
+wilson wilson coefficients
+
+ align:start position:0%
+wilson wilson coefficients
+ 
+
+ align:start position:0%
+wilson wilson coefficients
+and in this case that includes momenta
+
+ align:start position:0%
+and in this case that includes momenta
+ 
+
+ align:start position:0%
+and in this case that includes momenta
+that are the large component the lambda
+
+ align:start position:0%
+that are the large component the lambda
+ 
+
+ align:start position:0%
+that are the large component the lambda
+ordered lambda zero component of linear
+
+ align:start position:0%
+ordered lambda zero component of linear
+ 
+
+ align:start position:0%
+ordered lambda zero component of linear
+fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is hard linear factorization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it just comes out in a kind of
+
+ align:start position:0%
+and it just comes out in a kind of
+ 
+
+ align:start position:0%
+and it just comes out in a kind of
+natural standard way in this effective
+
+ align:start position:0%
+natural standard way in this effective
+ 
+
+ align:start position:0%
+natural standard way in this effective
+theory because
+
+ align:start position:0%
+theory because
+ 
+
+ align:start position:0%
+theory because
+we've set up the effective theory to
+
+ align:start position:0%
+we've set up the effective theory to
+ 
+
+ align:start position:0%
+we've set up the effective theory to
+have the right low energy degrees of
+
+ align:start position:0%
+have the right low energy degrees of
+ 
+
+ align:start position:0%
+have the right low energy degrees of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+so even though it's a little more
+
+ align:start position:0%
+so even though it's a little more
+ 
+
+ align:start position:0%
+so even though it's a little more
+complicated than just a simple product
+
+ align:start position:0%
+complicated than just a simple product
+ 
+
+ align:start position:0%
+complicated than just a simple product
+we see sort of what the variables are
+
+ align:start position:0%
+we see sort of what the variables are
+ 
+
+ align:start position:0%
+we see sort of what the variables are
+that can connect the two things
+
+ align:start position:0%
+that can connect the two things
+ 
+
+ align:start position:0%
+that can connect the two things
+just by power counting essentially
+
+ align:start position:0%
+just by power counting essentially
+ 
+
+ align:start position:0%
+just by power counting essentially
+the large momentum are the
+
+ align:start position:0%
+the large momentum are the
+ 
+
+ align:start position:0%
+the large momentum are the
+ones that are
+
+ align:start position:0%
+ones that are
+ 
+
+ align:start position:0%
+ones that are
+order lambda to zero
+
+ align:start position:0%
+order lambda to zero
+ 
+
+ align:start position:0%
+order lambda to zero
+we can kind of do this generically if we
+
+ align:start position:0%
+we can kind of do this generically if we
+ 
+
+ align:start position:0%
+we can kind of do this generically if we
+recall the definition of our wilson line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see how this would carry over to
+
+ align:start position:0%
+you can see how this would carry over to
+ 
+
+ align:start position:0%
+you can see how this would carry over to
+a generic case in the following way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was
+
+ align:start position:0%
+so that was
+ 
+
+ align:start position:0%
+so that was
+one way of defining the wilson line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as an operator we had relations as
+
+ align:start position:0%
+and as an operator we had relations as
+ 
+
+ align:start position:0%
+and as an operator we had relations as
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this relation and in particular
+
+ align:start position:0%
+this relation and in particular
+ 
+
+ align:start position:0%
+this relation and in particular
+we could take this to any power
+
+ align:start position:0%
+we could take this to any power
+ 
+
+ align:start position:0%
+we could take this to any power
+and that just takes the p bar to any
+
+ align:start position:0%
+and that just takes the p bar to any
+ 
+
+ align:start position:0%
+and that just takes the p bar to any
+power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so you can really think of this as given
+
+ align:start position:0%
+so you can really think of this as given
+ 
+
+ align:start position:0%
+so you can really think of this as given
+any function
+
+ align:start position:0%
+any function
+ 
+
+ align:start position:0%
+any function
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+operator imbar.d
+
+ align:start position:0%
+operator imbar.d
+ 
+
+ align:start position:0%
+operator imbar.d
+you can always write that as a wilson
+
+ align:start position:0%
+you can always write that as a wilson
+ 
+
+ align:start position:0%
+you can always write that as a wilson
+line a function of p bar
+
+ align:start position:0%
+line a function of p bar
+ 
+
+ align:start position:0%
+line a function of p bar
+and a wilson line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you want to do is you want to
+
+ align:start position:0%
+and what you want to do is you want to
+ 
+
+ align:start position:0%
+and what you want to do is you want to
+stick these wilson lines in the operator
+
+ align:start position:0%
+stick these wilson lines in the operator
+ 
+
+ align:start position:0%
+stick these wilson lines in the operator
+and you want to put this function in the
+
+ align:start position:0%
+and you want to put this function in the
+ 
+
+ align:start position:0%
+and you want to put this function in the
+wilson coefficient
+
+ align:start position:0%
+wilson coefficient
+ 
+
+ align:start position:0%
+wilson coefficient
+so you could think let me start with
+
+ align:start position:0%
+so you could think let me start with
+ 
+
+ align:start position:0%
+so you could think let me start with
+operators where i just
+
+ align:start position:0%
+operators where i just
+ 
+
+ align:start position:0%
+operators where i just
+i can throw in i and bar.ds because
+
+ align:start position:0%
+i can throw in i and bar.ds because
+ 
+
+ align:start position:0%
+i can throw in i and bar.ds because
+these guys are ordered lambda 0. these
+
+ align:start position:0%
+these guys are ordered lambda 0. these
+ 
+
+ align:start position:0%
+these guys are ordered lambda 0. these
+are the linear derivatives
+
+ align:start position:0%
+are the linear derivatives
+ 
+
+ align:start position:0%
+are the linear derivatives
+i just allowed to stick as many of those
+
+ align:start position:0%
+i just allowed to stick as many of those
+ 
+
+ align:start position:0%
+i just allowed to stick as many of those
+as i like in my operator
+
+ align:start position:0%
+as i like in my operator
+ 
+
+ align:start position:0%
+as i like in my operator
+but given that i put in any function of
+
+ align:start position:0%
+but given that i put in any function of
+ 
+
+ align:start position:0%
+but given that i put in any function of
+them i could always do this and the
+
+ align:start position:0%
+them i could always do this and the
+ 
+
+ align:start position:0%
+them i could always do this and the
+right way of thinking about it
+
+ align:start position:0%
+right way of thinking about it
+ 
+
+ align:start position:0%
+right way of thinking about it
+is that this should this is
+
+ align:start position:0%
+is that this should this is
+ 
+
+ align:start position:0%
+is that this should this is
+this function here is what your is
+
+ align:start position:0%
+this function here is what your is
+ 
+
+ align:start position:0%
+this function here is what your is
+determined by matching it's your wilson
+
+ align:start position:0%
+determined by matching it's your wilson
+ 
+
+ align:start position:0%
+determined by matching it's your wilson
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what we were effectively
+
+ align:start position:0%
+and that's what we were effectively
+ 
+
+ align:start position:0%
+and that's what we were effectively
+doing up here
+
+ align:start position:0%
+doing up here
+ 
+
+ align:start position:0%
+doing up here
+but this is in some sense a more general
+
+ align:start position:0%
+but this is in some sense a more general
+ 
+
+ align:start position:0%
+but this is in some sense a more general
+discussion you can see that even if you
+
+ align:start position:0%
+discussion you can see that even if you
+ 
+
+ align:start position:0%
+discussion you can see that even if you
+had multiple places in the operator
+
+ align:start position:0%
+had multiple places in the operator
+ 
+
+ align:start position:0%
+had multiple places in the operator
+where you could insert these derivatives
+
+ align:start position:0%
+where you could insert these derivatives
+ 
+
+ align:start position:0%
+where you could insert these derivatives
+then you would just do this and what
+
+ align:start position:0%
+then you would just do this and what
+ 
+
+ align:start position:0%
+then you would just do this and what
+would happen is at the end of the day
+
+ align:start position:0%
+would happen is at the end of the day
+ 
+
+ align:start position:0%
+would happen is at the end of the day
+you get a function of all the possible
+
+ align:start position:0%
+you get a function of all the possible
+ 
+
+ align:start position:0%
+you get a function of all the possible
+large momenta that you
+
+ align:start position:0%
+large momenta that you
+ 
+
+ align:start position:0%
+large momenta that you
+can form from the operator
+
+ align:start position:0%
+can form from the operator
+ 
+
+ align:start position:0%
+can form from the operator
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe one more line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so think of it that you can always
+
+ align:start position:0%
+so think of it that you can always
+ 
+
+ align:start position:0%
+so think of it that you can always
+separate out
+
+ align:start position:0%
+separate out
+ 
+
+ align:start position:0%
+separate out
+you can always separate out that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make a split like we did over there with
+
+ align:start position:0%
+make a split like we did over there with
+ 
+
+ align:start position:0%
+make a split like we did over there with
+the integral over some variable and then
+
+ align:start position:0%
+the integral over some variable and then
+ 
+
+ align:start position:0%
+the integral over some variable and then
+leave something that you can stick in
+
+ align:start position:0%
+leave something that you can stick in
+ 
+
+ align:start position:0%
+leave something that you can stick in
+your operator
+
+ align:start position:0%
+your operator
+ 
+
+ align:start position:0%
+your operator
+if you make it like this so this could
+
+ align:start position:0%
+if you make it like this so this could
+ 
+
+ align:start position:0%
+if you make it like this so this could
+go in the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+that's the coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well here i didn't write it so if i
+
+ align:start position:0%
+well here i didn't write it so if i
+ 
+
+ align:start position:0%
+well here i didn't write it so if i
+wanted to put in i and bar dot d's i'd
+
+ align:start position:0%
+wanted to put in i and bar dot d's i'd
+ 
+
+ align:start position:0%
+wanted to put in i and bar dot d's i'd
+stick them between
+
+ align:start position:0%
+stick them between
+ 
+
+ align:start position:0%
+stick them between
+right if i wanted to have used the
+
+ align:start position:0%
+right if i wanted to have used the
+ 
+
+ align:start position:0%
+right if i wanted to have used the
+formula if i wanted to use this kind of
+
+ align:start position:0%
+formula if i wanted to use this kind of
+ 
+
+ align:start position:0%
+formula if i wanted to use this kind of
+logic i wouldn't have written this
+
+ align:start position:0%
+logic i wouldn't have written this
+ 
+
+ align:start position:0%
+logic i wouldn't have written this
+and i would have said said let me stick
+
+ align:start position:0%
+and i would have said said let me stick
+ 
+
+ align:start position:0%
+and i would have said said let me stick
+an arbitrary function of i and bar.d in
+
+ align:start position:0%
+an arbitrary function of i and bar.d in
+ 
+
+ align:start position:0%
+an arbitrary function of i and bar.d in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+sorry before you even write it has to be
+
+ align:start position:0%
+sorry before you even write it has to be
+ 
+
+ align:start position:0%
+sorry before you even write it has to be
+between them because of the gauging
+
+ align:start position:0%
+between them because of the gauging
+ 
+
+ align:start position:0%
+between them because of the gauging
+you even write variance the wilson line
+
+ align:start position:0%
+you even write variance the wilson line
+ 
+
+ align:start position:0%
+you even write variance the wilson line
+so let's say you started to say okay oh
+
+ align:start position:0%
+so let's say you started to say okay oh
+ 
+
+ align:start position:0%
+so let's say you started to say okay oh
+yeah so there's still right this wilson
+
+ align:start position:0%
+yeah so there's still right this wilson
+ 
+
+ align:start position:0%
+yeah so there's still right this wilson
+line here right right this wilson line
+
+ align:start position:0%
+line here right right this wilson line
+ 
+
+ align:start position:0%
+line here right right this wilson line
+here came from this h
+
+ align:start position:0%
+here came from this h
+ 
+
+ align:start position:0%
+here came from this h
+so that's still going to be true
+
+ align:start position:0%
+so that's still going to be true
+ 
+
+ align:start position:0%
+so that's still going to be true
+and what i'm saying if you think about
+
+ align:start position:0%
+and what i'm saying if you think about
+ 
+
+ align:start position:0%
+and what i'm saying if you think about
+this operator
+
+ align:start position:0%
+this operator
+ 
+
+ align:start position:0%
+this operator
+right i could dress it up by putting any
+
+ align:start position:0%
+right i could dress it up by putting any
+ 
+
+ align:start position:0%
+right i could dress it up by putting any
+function of imbar.ds
+
+ align:start position:0%
+function of imbar.ds
+ 
+
+ align:start position:0%
+function of imbar.ds
+right in here
+
+ align:start position:0%
+right in here
+ 
+
+ align:start position:0%
+right in here
+because that would still be an order
+
+ align:start position:0%
+because that would still be an order
+ 
+
+ align:start position:0%
+because that would still be an order
+walk same order and gauge invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then if i use this right then if i
+
+ align:start position:0%
+but then if i use this right then if i
+ 
+
+ align:start position:0%
+but then if i use this right then if i
+use this formula
+
+ align:start position:0%
+use this formula
+ 
+
+ align:start position:0%
+use this formula
+it would sort of
+
+ align:start position:0%
+it would sort of
+ 
+
+ align:start position:0%
+it would sort of
+push
+
+ align:start position:0%
+push
+ 
+
+ align:start position:0%
+push
+this w
+
+ align:start position:0%
+this w
+ 
+
+ align:start position:0%
+this w
+that would cancel there and then this w
+
+ align:start position:0%
+that would cancel there and then this w
+ 
+
+ align:start position:0%
+that would cancel there and then this w
+comes back then you get the f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in general the right way of thinking
+
+ align:start position:0%
+so in general the right way of thinking
+ 
+
+ align:start position:0%
+so in general the right way of thinking
+about this is as follows we can
+
+ align:start position:0%
+about this is as follows we can
+ 
+
+ align:start position:0%
+about this is as follows we can
+encode this in some notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by just setting up a convenient set of
+
+ align:start position:0%
+by just setting up a convenient set of
+ 
+
+ align:start position:0%
+by just setting up a convenient set of
+building blocks
+
+ align:start position:0%
+building blocks
+ 
+
+ align:start position:0%
+building blocks
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+gauge and variant objects under the
+
+ align:start position:0%
+gauge and variant objects under the
+ 
+
+ align:start position:0%
+gauge and variant objects under the
+linear gauge transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we need to have a fermion
+
+ align:start position:0%
+we need to have a fermion
+ 
+
+ align:start position:0%
+we need to have a fermion
+field but we know that the fermion field
+
+ align:start position:0%
+field but we know that the fermion field
+ 
+
+ align:start position:0%
+field but we know that the fermion field
+generically
+
+ align:start position:0%
+generically
+ 
+
+ align:start position:0%
+generically
+we can make it gage invariant by
+
+ align:start position:0%
+we can make it gage invariant by
+ 
+
+ align:start position:0%
+we can make it gage invariant by
+multiplying by a wilson line like that
+
+ align:start position:0%
+multiplying by a wilson line like that
+ 
+
+ align:start position:0%
+multiplying by a wilson line like that
+and because of this what we were just
+
+ align:start position:0%
+and because of this what we were just
+ 
+
+ align:start position:0%
+and because of this what we were just
+discussing here generically we can be in
+
+ align:start position:0%
+discussing here generically we can be in
+ 
+
+ align:start position:0%
+discussing here generically we can be in
+our wilson coefficients sensitive to the
+
+ align:start position:0%
+our wilson coefficients sensitive to the
+ 
+
+ align:start position:0%
+our wilson coefficients sensitive to the
+momentum of this object
+
+ align:start position:0%
+momentum of this object
+ 
+
+ align:start position:0%
+momentum of this object
+and so we can do that
+
+ align:start position:0%
+and so we can do that
+ 
+
+ align:start position:0%
+and so we can do that
+denote that by
+
+ align:start position:0%
+denote that by
+ 
+
+ align:start position:0%
+denote that by
+defining the following thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is just a chi
+
+ align:start position:0%
+which is just a chi
+ 
+
+ align:start position:0%
+which is just a chi
+field that carries some momentum which
+
+ align:start position:0%
+field that carries some momentum which
+ 
+
+ align:start position:0%
+field that carries some momentum which
+is the overall large momentum of this
+
+ align:start position:0%
+is the overall large momentum of this
+ 
+
+ align:start position:0%
+is the overall large momentum of this
+product of fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sometimes this guy goes by the name
+
+ align:start position:0%
+and sometimes this guy goes by the name
+ 
+
+ align:start position:0%
+and sometimes this guy goes by the name
+of the cork
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jet field
+
+ align:start position:0%
+jet field
+ 
+
+ align:start position:0%
+jet field
+because it's kind of the object if you
+
+ align:start position:0%
+because it's kind of the object if you
+ 
+
+ align:start position:0%
+because it's kind of the object if you
+were to produce a quark in the hard
+
+ align:start position:0%
+were to produce a quark in the hard
+ 
+
+ align:start position:0%
+were to produce a quark in the hard
+scattering process the cork would be
+
+ align:start position:0%
+scattering process the cork would be
+ 
+
+ align:start position:0%
+scattering process the cork would be
+represented in your operator by this w
+
+ align:start position:0%
+represented in your operator by this w
+ 
+
+ align:start position:0%
+represented in your operator by this w
+dagger c
+
+ align:start position:0%
+dagger c
+ 
+
+ align:start position:0%
+dagger c
+the wilson coefficients would talk to
+
+ align:start position:0%
+the wilson coefficients would talk to
+ 
+
+ align:start position:0%
+the wilson coefficients would talk to
+that quark through the large momentum
+
+ align:start position:0%
+that quark through the large momentum
+ 
+
+ align:start position:0%
+that quark through the large momentum
+and that quark in the low energy theory
+
+ align:start position:0%
+and that quark in the low energy theory
+ 
+
+ align:start position:0%
+and that quark in the low energy theory
+would evolve into a jet
+
+ align:start position:0%
+would evolve into a jet
+ 
+
+ align:start position:0%
+would evolve into a jet
+so it goes by that name you could also
+
+ align:start position:0%
+so it goes by that name you could also
+ 
+
+ align:start position:0%
+so it goes by that name you could also
+think of it as a part on field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because as it turns out and as we'll
+
+ align:start position:0%
+because as it turns out and as we'll
+ 
+
+ align:start position:0%
+because as it turns out and as we'll
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+later on if you were to think about the
+
+ align:start position:0%
+later on if you were to think about the
+ 
+
+ align:start position:0%
+later on if you were to think about the
+part-time distribution function
+
+ align:start position:0%
+part-time distribution function
+ 
+
+ align:start position:0%
+part-time distribution function
+and what pulls a quark out of the proton
+
+ align:start position:0%
+and what pulls a quark out of the proton
+ 
+
+ align:start position:0%
+and what pulls a quark out of the proton
+it's exactly this operator
+
+ align:start position:0%
+it's exactly this operator
+ 
+
+ align:start position:0%
+it's exactly this operator
+and then that
+
+ align:start position:0%
+and then that
+ 
+
+ align:start position:0%
+and then that
+park's momentum what momentum that quark
+
+ align:start position:0%
+park's momentum what momentum that quark
+ 
+
+ align:start position:0%
+park's momentum what momentum that quark
+carries is exactly picked up by this
+
+ align:start position:0%
+carries is exactly picked up by this
+ 
+
+ align:start position:0%
+carries is exactly picked up by this
+delta function as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are the objects we'll actually
+
+ align:start position:0%
+so these are the objects we'll actually
+ 
+
+ align:start position:0%
+so these are the objects we'll actually
+usually want to work in terms of
+
+ align:start position:0%
+usually want to work in terms of
+ 
+
+ align:start position:0%
+usually want to work in terms of
+we can do something similar for the
+
+ align:start position:0%
+we can do something similar for the
+ 
+
+ align:start position:0%
+we can do something similar for the
+gluon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a curly bee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to define it
+
+ align:start position:0%
+and i'm going to define it
+ 
+
+ align:start position:0%
+and i'm going to define it
+if we wanted to get a glue on the
+
+ align:start position:0%
+if we wanted to get a glue on the
+ 
+
+ align:start position:0%
+if we wanted to get a glue on the
+natural thing is to use a field strength
+
+ align:start position:0%
+natural thing is to use a field strength
+ 
+
+ align:start position:0%
+natural thing is to use a field strength
+because then you get a glue on without
+
+ align:start position:0%
+because then you get a glue on without
+ 
+
+ align:start position:0%
+because then you get a glue on without
+any derivatives
+
+ align:start position:0%
+any derivatives
+ 
+
+ align:start position:0%
+any derivatives
+but i want my
+
+ align:start position:0%
+but i want my
+ 
+
+ align:start position:0%
+but i want my
+object to be dimension one
+
+ align:start position:0%
+object to be dimension one
+ 
+
+ align:start position:0%
+object to be dimension one
+so i'm going to define it in the
+
+ align:start position:0%
+so i'm going to define it in the
+ 
+
+ align:start position:0%
+so i'm going to define it in the
+following way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's a field strength commutator of
+
+ align:start position:0%
+so here's a field strength commutator of
+ 
+
+ align:start position:0%
+so here's a field strength commutator of
+covariant derivatives
+
+ align:start position:0%
+covariant derivatives
+ 
+
+ align:start position:0%
+covariant derivatives
+these are linear derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i throw wilson lines around it to
+
+ align:start position:0%
+and i throw wilson lines around it to
+ 
+
+ align:start position:0%
+and i throw wilson lines around it to
+make it gauge invariant and then to make
+
+ align:start position:0%
+make it gauge invariant and then to make
+ 
+
+ align:start position:0%
+make it gauge invariant and then to make
+it dimension one i throw in a one over p
+
+ align:start position:0%
+it dimension one i throw in a one over p
+ 
+
+ align:start position:0%
+it dimension one i throw in a one over p
+bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you start expanding this out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the first term will be the a n perp
+
+ align:start position:0%
+then the first term will be the a n perp
+ 
+
+ align:start position:0%
+then the first term will be the a n perp
+gluon and tell you this b just has the a
+
+ align:start position:0%
+gluon and tell you this b just has the a
+ 
+
+ align:start position:0%
+gluon and tell you this b just has the a
+and perp gluon in the same way that the
+
+ align:start position:0%
+and perp gluon in the same way that the
+ 
+
+ align:start position:0%
+and perp gluon in the same way that the
+first kind of border term in this chi is
+
+ align:start position:0%
+first kind of border term in this chi is
+ 
+
+ align:start position:0%
+first kind of border term in this chi is
+just the fermion if i set the wilson
+
+ align:start position:0%
+just the fermion if i set the wilson
+ 
+
+ align:start position:0%
+just the fermion if i set the wilson
+line to one
+
+ align:start position:0%
+line to one
+ 
+
+ align:start position:0%
+line to one
+okay so it's starting out as a
+
+ align:start position:0%
+okay so it's starting out as a
+ 
+
+ align:start position:0%
+okay so it's starting out as a
+perpendicular gluon
+
+ align:start position:0%
+perpendicular gluon
+ 
+
+ align:start position:0%
+perpendicular gluon
+but it's dressed up in a way that makes
+
+ align:start position:0%
+but it's dressed up in a way that makes
+ 
+
+ align:start position:0%
+but it's dressed up in a way that makes
+it gauge invariant in dimension one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then just like we did here we can
+
+ align:start position:0%
+and then just like we did here we can
+ 
+
+ align:start position:0%
+and then just like we did here we can
+put a subscript on it with a mega
+
+ align:start position:0%
+put a subscript on it with a mega
+ 
+
+ align:start position:0%
+put a subscript on it with a mega
+to give it to say that we fixed the
+
+ align:start position:0%
+to give it to say that we fixed the
+ 
+
+ align:start position:0%
+to give it to say that we fixed the
+large momentum of it
+
+ align:start position:0%
+large momentum of it
+ 
+
+ align:start position:0%
+large momentum of it
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes there's a convention that
+
+ align:start position:0%
+sometimes there's a convention that
+ 
+
+ align:start position:0%
+sometimes there's a convention that
+that's done
+
+ align:start position:0%
+that's done
+ 
+
+ align:start position:0%
+that's done
+you have to decide if you want the
+
+ align:start position:0%
+you have to decide if you want the
+ 
+
+ align:start position:0%
+you have to decide if you want the
+wilson line i mean the delt function to
+
+ align:start position:0%
+wilson line i mean the delt function to
+ 
+
+ align:start position:0%
+wilson line i mean the delt function to
+be a w minus p bar w minus p bar dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway it doesn't really matter that
+
+ align:start position:0%
+anyway it doesn't really matter that
+ 
+
+ align:start position:0%
+anyway it doesn't really matter that
+much but it's just not because it's just
+
+ align:start position:0%
+much but it's just not because it's just
+ 
+
+ align:start position:0%
+much but it's just not because it's just
+a sign of what you mean by a w
+
+ align:start position:0%
+a sign of what you mean by a w
+ 
+
+ align:start position:0%
+a sign of what you mean by a w
+if it's an outgoing gluon this is a more
+
+ align:start position:0%
+if it's an outgoing gluon this is a more
+ 
+
+ align:start position:0%
+if it's an outgoing gluon this is a more
+convenient convention
+
+ align:start position:0%
+convenient convention
+ 
+
+ align:start position:0%
+convenient convention
+okay and so this delta function here and
+
+ align:start position:0%
+okay and so this delta function here and
+ 
+
+ align:start position:0%
+okay and so this delta function here and
+this p bar here when i put these square
+
+ align:start position:0%
+this p bar here when i put these square
+ 
+
+ align:start position:0%
+this p bar here when i put these square
+brackets what i mean by that is that
+
+ align:start position:0%
+brackets what i mean by that is that
+ 
+
+ align:start position:0%
+brackets what i mean by that is that
+they do they don't act outside they just
+
+ align:start position:0%
+they do they don't act outside they just
+ 
+
+ align:start position:0%
+they do they don't act outside they just
+act on the operators inside
+
+ align:start position:0%
+act on the operators inside
+ 
+
+ align:start position:0%
+act on the operators inside
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are objects that exist by
+
+ align:start position:0%
+these are objects that exist by
+ 
+
+ align:start position:0%
+these are objects that exist by
+themselves and they don't care about
+
+ align:start position:0%
+themselves and they don't care about
+ 
+
+ align:start position:0%
+themselves and they don't care about
+other things that are multiplying them
+
+ align:start position:0%
+other things that are multiplying them
+ 
+
+ align:start position:0%
+other things that are multiplying them
+later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the gluon analog of the quark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it turns out that we can show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you want to build operators that
+
+ align:start position:0%
+that if you want to build operators that
+ 
+
+ align:start position:0%
+that if you want to build operators that
+are subletting order a complete set of
+
+ align:start position:0%
+are subletting order a complete set of
+ 
+
+ align:start position:0%
+are subletting order a complete set of
+things to do that is as follows it's
+
+ align:start position:0%
+things to do that is as follows it's
+ 
+
+ align:start position:0%
+things to do that is as follows it's
+this cayenne
+
+ align:start position:0%
+this cayenne
+ 
+
+ align:start position:0%
+this cayenne
+the bn perp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+you could also need
+
+ align:start position:0%
+you could also need
+ 
+
+ align:start position:0%
+you could also need
+p perps
+
+ align:start position:0%
+p perps
+ 
+
+ align:start position:0%
+p perps
+and then you could also have ultrasoft
+
+ align:start position:0%
+and then you could also have ultrasoft
+ 
+
+ align:start position:0%
+and then you could also have ultrasoft
+fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where it's really kind of similar to how
+
+ align:start position:0%
+where it's really kind of similar to how
+ 
+
+ align:start position:0%
+where it's really kind of similar to how
+you're used to building operators and
+
+ align:start position:0%
+you're used to building operators and
+ 
+
+ align:start position:0%
+you're used to building operators and
+effective field theories
+
+ align:start position:0%
+effective field theories
+ 
+
+ align:start position:0%
+effective field theories
+but if you just want to talk about the
+
+ align:start position:0%
+but if you just want to talk about the
+ 
+
+ align:start position:0%
+but if you just want to talk about the
+clinical sector the only things you need
+
+ align:start position:0%
+clinical sector the only things you need
+ 
+
+ align:start position:0%
+clinical sector the only things you need
+are this chi in this bn field and then p
+
+ align:start position:0%
+are this chi in this bn field and then p
+ 
+
+ align:start position:0%
+are this chi in this bn field and then p
+perps and no other things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all orders so why aren't there any i'll
+
+ align:start position:0%
+all orders so why aren't there any i'll
+ 
+
+ align:start position:0%
+all orders so why aren't there any i'll
+talk about it
+
+ align:start position:0%
+talk about it
+ 
+
+ align:start position:0%
+talk about it
+yeah we'll show you i'll show you
+
+ align:start position:0%
+yeah we'll show you i'll show you
+ 
+
+ align:start position:0%
+yeah we'll show you i'll show you
+yeah i mean intuitively you would think
+
+ align:start position:0%
+yeah i mean intuitively you would think
+ 
+
+ align:start position:0%
+yeah i mean intuitively you would think
+these are the physical degrees of
+
+ align:start position:0%
+these are the physical degrees of
+ 
+
+ align:start position:0%
+these are the physical degrees of
+freedom right there's two of them
+
+ align:start position:0%
+freedom right there's two of them
+ 
+
+ align:start position:0%
+freedom right there's two of them
+so that's intuitive but i'll show you
+
+ align:start position:0%
+so that's intuitive but i'll show you
+ 
+
+ align:start position:0%
+so that's intuitive but i'll show you
+how you get rid of all the other ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it kind of matches up with what you want
+
+ align:start position:0%
+it kind of matches up with what you want
+ 
+
+ align:start position:0%
+it kind of matches up with what you want
+you could think that you know these are
+
+ align:start position:0%
+you could think that you know these are
+ 
+
+ align:start position:0%
+you could think that you know these are
+the physical gluons that you're
+
+ align:start position:0%
+the physical gluons that you're
+ 
+
+ align:start position:0%
+the physical gluons that you're
+producing and your operators can be set
+
+ align:start position:0%
+producing and your operators can be set
+ 
+
+ align:start position:0%
+producing and your operators can be set
+up so that they only depend
+
+ align:start position:0%
+up so that they only depend
+ 
+
+ align:start position:0%
+up so that they only depend
+that there's not so sort of any spurious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we'll get there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me do let me introduce a bit of
+
+ align:start position:0%
+so let me do let me introduce a bit of
+ 
+
+ align:start position:0%
+so let me do let me introduce a bit of
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider this thing a covalent
+
+ align:start position:0%
+so let's consider this thing a covalent
+ 
+
+ align:start position:0%
+so let's consider this thing a covalent
+derivative sandwiched with wilson lines
+
+ align:start position:0%
+derivative sandwiched with wilson lines
+ 
+
+ align:start position:0%
+derivative sandwiched with wilson lines
+on either side
+
+ align:start position:0%
+on either side
+ 
+
+ align:start position:0%
+on either side
+and this idn here
+
+ align:start position:0%
+and this idn here
+ 
+
+ align:start position:0%
+and this idn here
+is like p bar plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it just involves the linear gluon
+
+ align:start position:0%
+so it just involves the linear gluon
+ 
+
+ align:start position:0%
+so it just involves the linear gluon
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then if i have that operator and i
+
+ align:start position:0%
+so then if i have that operator and i
+ 
+
+ align:start position:0%
+so then if i have that operator and i
+just take n bar
+
+ align:start position:0%
+just take n bar
+ 
+
+ align:start position:0%
+just take n bar
+idn then that's p bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i take
+
+ align:start position:0%
+if i take
+ 
+
+ align:start position:0%
+if i take
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+d n perp mu
+
+ align:start position:0%
+d n perp mu
+ 
+
+ align:start position:0%
+d n perp mu
+then you can show
+
+ align:start position:0%
+then you can show
+ 
+
+ align:start position:0%
+then you can show
+that this guy is p perp u
+
+ align:start position:0%
+that this guy is p perp u
+ 
+
+ align:start position:0%
+that this guy is p perp u
+plus g
+
+ align:start position:0%
+plus g
+ 
+
+ align:start position:0%
+plus g
+b n perp mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this one is just a relation we talked
+
+ align:start position:0%
+so this one is just a relation we talked
+ 
+
+ align:start position:0%
+so this one is just a relation we talked
+about before this one is not as obvious
+
+ align:start position:0%
+about before this one is not as obvious
+ 
+
+ align:start position:0%
+about before this one is not as obvious
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+if you take this guy you can either let
+
+ align:start position:0%
+if you take this guy you can either let
+ 
+
+ align:start position:0%
+if you take this guy you can either let
+the derivative you can let this
+
+ align:start position:0%
+the derivative you can let this
+ 
+
+ align:start position:0%
+the derivative you can let this
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+act on the wilson line or act through if
+
+ align:start position:0%
+act on the wilson line or act through if
+ 
+
+ align:start position:0%
+act on the wilson line or act through if
+it acts through that's this term
+
+ align:start position:0%
+it acts through that's this term
+ 
+
+ align:start position:0%
+it acts through that's this term
+if it acts on then i can manipulate the
+
+ align:start position:0%
+if it acts on then i can manipulate the
+ 
+
+ align:start position:0%
+if it acts on then i can manipulate the
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+so that it is exactly of this form
+
+ align:start position:0%
+so that it is exactly of this form
+ 
+
+ align:start position:0%
+so that it is exactly of this form
+and part of that comes from the fact
+
+ align:start position:0%
+and part of that comes from the fact
+ 
+
+ align:start position:0%
+and part of that comes from the fact
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+i can explain it to you here i have it
+
+ align:start position:0%
+i can explain it to you here i have it
+ 
+
+ align:start position:0%
+i can explain it to you here i have it
+in my notes and you can look at it later
+
+ align:start position:0%
+in my notes and you can look at it later
+ 
+
+ align:start position:0%
+in my notes and you can look at it later
+but let me just explain it in words if
+
+ align:start position:0%
+but let me just explain it in words if
+ 
+
+ align:start position:0%
+but let me just explain it in words if
+you looked at the term in this
+
+ align:start position:0%
+you looked at the term in this
+ 
+
+ align:start position:0%
+you looked at the term in this
+commutator that was the other order
+
+ align:start position:0%
+commutator that was the other order
+ 
+
+ align:start position:0%
+commutator that was the other order
+where the i n bar dot d was acting up
+
+ align:start position:0%
+where the i n bar dot d was acting up
+ 
+
+ align:start position:0%
+where the i n bar dot d was acting up
+was sitting here it would hit the wilson
+
+ align:start position:0%
+was sitting here it would hit the wilson
+ 
+
+ align:start position:0%
+was sitting here it would hit the wilson
+line you get zero so that term was just
+
+ align:start position:0%
+line you get zero so that term was just
+ 
+
+ align:start position:0%
+line you get zero so that term was just
+put in to make it look like a gauge
+
+ align:start position:0%
+put in to make it look like a gauge
+ 
+
+ align:start position:0%
+put in to make it look like a gauge
+field i mean a covariant
+
+ align:start position:0%
+field i mean a covariant
+ 
+
+ align:start position:0%
+field i mean a covariant
+to make it look like a field strength
+
+ align:start position:0%
+to make it look like a field strength
+ 
+
+ align:start position:0%
+to make it look like a field strength
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay so so really you have i am bar.d dn
+
+ align:start position:0%
+okay so so really you have i am bar.d dn
+ 
+
+ align:start position:0%
+okay so so really you have i am bar.d dn
+perp without the
+
+ align:start position:0%
+perp without the
+ 
+
+ align:start position:0%
+perp without the
+without the comma without the brackets
+
+ align:start position:0%
+without the comma without the brackets
+ 
+
+ align:start position:0%
+without the comma without the brackets
+but then this combination here
+
+ align:start position:0%
+but then this combination here
+ 
+
+ align:start position:0%
+but then this combination here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this combination here is just
+
+ align:start position:0%
+this combination here is just
+ 
+
+ align:start position:0%
+this combination here is just
+you can use the identity that we had
+
+ align:start position:0%
+you can use the identity that we had
+ 
+
+ align:start position:0%
+you can use the identity that we had
+with the and basically
+
+ align:start position:0%
+with the and basically
+ 
+
+ align:start position:0%
+with the and basically
+if you push this guy through here you're
+
+ align:start position:0%
+if you push this guy through here you're
+ 
+
+ align:start position:0%
+if you push this guy through here you're
+canceling the p bar
+
+ align:start position:0%
+canceling the p bar
+ 
+
+ align:start position:0%
+canceling the p bar
+so it's just giving you the wilson line
+
+ align:start position:0%
+so it's just giving you the wilson line
+ 
+
+ align:start position:0%
+so it's just giving you the wilson line
+so that's basically
+
+ align:start position:0%
+so that's basically
+ 
+
+ align:start position:0%
+so that's basically
+how you go from here to here
+
+ align:start position:0%
+how you go from here to here
+ 
+
+ align:start position:0%
+how you go from here to here
+okay so this is by way of arguing that i
+
+ align:start position:0%
+okay so this is by way of arguing that i
+ 
+
+ align:start position:0%
+okay so this is by way of arguing that i
+don't really need if i'm considering p
+
+ align:start position:0%
+don't really need if i'm considering p
+ 
+
+ align:start position:0%
+don't really need if i'm considering p
+this is basically what this is saying is
+
+ align:start position:0%
+this is basically what this is saying is
+ 
+
+ align:start position:0%
+this is basically what this is saying is
+i don't need to consider covariant
+
+ align:start position:0%
+i don't need to consider covariant
+ 
+
+ align:start position:0%
+i don't need to consider covariant
+derivatives because i can instead
+
+ align:start position:0%
+derivatives because i can instead
+ 
+
+ align:start position:0%
+derivatives because i can instead
+consider p perps and b perps and that's
+
+ align:start position:0%
+consider p perps and b perps and that's
+ 
+
+ align:start position:0%
+consider p perps and b perps and that's
+equally good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do a similar type of thing
+
+ align:start position:0%
+if you do a similar type of thing
+ 
+
+ align:start position:0%
+if you do a similar type of thing
+in the end component
+
+ align:start position:0%
+in the end component
+ 
+
+ align:start position:0%
+in the end component
+then you can derive a similar type of
+
+ align:start position:0%
+then you can derive a similar type of
+ 
+
+ align:start position:0%
+then you can derive a similar type of
+object so this is the same object as we
+
+ align:start position:0%
+object so this is the same object as we
+ 
+
+ align:start position:0%
+object so this is the same object as we
+have over here but instead of having an
+
+ align:start position:0%
+have over here but instead of having an
+ 
+
+ align:start position:0%
+have over here but instead of having an
+idn perp i'd have an n dot d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so dn replace to
+
+ align:start position:0%
+so dn replace to
+ 
+
+ align:start position:0%
+so dn replace to
+n.d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that looks like it could be
+
+ align:start position:0%
+and that looks like it could be
+ 
+
+ align:start position:0%
+and that looks like it could be
+something that you build operators out
+
+ align:start position:0%
+something that you build operators out
+ 
+
+ align:start position:0%
+something that you build operators out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+so why not and and also furthermore why
+
+ align:start position:0%
+so why not and and also furthermore why
+ 
+
+ align:start position:0%
+so why not and and also furthermore why
+not have operators that depend on this
+
+ align:start position:0%
+not have operators that depend on this
+ 
+
+ align:start position:0%
+not have operators that depend on this
+end up partial
+
+ align:start position:0%
+end up partial
+ 
+
+ align:start position:0%
+end up partial
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for p bar we don't have to worry
+
+ align:start position:0%
+so for p bar we don't have to worry
+ 
+
+ align:start position:0%
+so for p bar we don't have to worry
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+so okay we have you know i said we'll
+
+ align:start position:0%
+so okay we have you know i said we'll
+ 
+
+ align:start position:0%
+so okay we have you know i said we'll
+include this we'll include that
+
+ align:start position:0%
+include this we'll include that
+ 
+
+ align:start position:0%
+include this we'll include that
+i didn't say we include this this and
+
+ align:start position:0%
+i didn't say we include this this and
+ 
+
+ align:start position:0%
+i didn't say we include this this and
+this so there's three things i have to
+
+ align:start position:0%
+this so there's three things i have to
+ 
+
+ align:start position:0%
+this so there's three things i have to
+argue away here
+
+ align:start position:0%
+argue away here
+ 
+
+ align:start position:0%
+argue away here
+the derivatives that are p bars those
+
+ align:start position:0%
+the derivatives that are p bars those
+ 
+
+ align:start position:0%
+the derivatives that are p bars those
+just go into the wilson coefficient so
+
+ align:start position:0%
+just go into the wilson coefficient so
+ 
+
+ align:start position:0%
+just go into the wilson coefficient so
+if we had like p bar
+
+ align:start position:0%
+if we had like p bar
+ 
+
+ align:start position:0%
+if we had like p bar
+chi m comma
+
+ align:start position:0%
+chi m comma
+ 
+
+ align:start position:0%
+chi m comma
+omega for example
+
+ align:start position:0%
+omega for example
+ 
+
+ align:start position:0%
+omega for example
+and that's omega
+
+ align:start position:0%
+and that's omega
+ 
+
+ align:start position:0%
+and that's omega
+k n comma omega and this is in the
+
+ align:start position:0%
+k n comma omega and this is in the
+ 
+
+ align:start position:0%
+k n comma omega and this is in the
+put into the wilson coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's why we don't have to worry
+
+ align:start position:0%
+so that's why we don't have to worry
+ 
+
+ align:start position:0%
+so that's why we don't have to worry
+about having p bars
+
+ align:start position:0%
+about having p bars
+ 
+
+ align:start position:0%
+about having p bars
+in some sense we do have p bars they're
+
+ align:start position:0%
+in some sense we do have p bars they're
+ 
+
+ align:start position:0%
+in some sense we do have p bars they're
+all in the wilson coefficients
+
+ align:start position:0%
+all in the wilson coefficients
+ 
+
+ align:start position:0%
+all in the wilson coefficients
+so it's really these other two that we
+
+ align:start position:0%
+so it's really these other two that we
+ 
+
+ align:start position:0%
+so it's really these other two that we
+have to worry more about
+
+ align:start position:0%
+have to worry more about
+ 
+
+ align:start position:0%
+have to worry more about
+and those actually can be simplified
+
+ align:start position:0%
+and those actually can be simplified
+ 
+
+ align:start position:0%
+and those actually can be simplified
+using the equation of motion so
+
+ align:start position:0%
+using the equation of motion so
+ 
+
+ align:start position:0%
+using the equation of motion so
+if you have i and dot p on i end up
+
+ align:start position:0%
+if you have i and dot p on i end up
+ 
+
+ align:start position:0%
+if you have i and dot p on i end up
+partial on cayenne then the equation of
+
+ align:start position:0%
+partial on cayenne then the equation of
+ 
+
+ align:start position:0%
+partial on cayenne then the equation of
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+when you write it out in terms of these
+
+ align:start position:0%
+when you write it out in terms of these
+ 
+
+ align:start position:0%
+when you write it out in terms of these
+objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has some form
+
+ align:start position:0%
+it has some form
+ 
+
+ align:start position:0%
+it has some form
+and basically you can just get rid of
+
+ align:start position:0%
+and basically you can just get rid of
+ 
+
+ align:start position:0%
+and basically you can just get rid of
+those terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so equation of motion allows us to get
+
+ align:start position:0%
+so equation of motion allows us to get
+ 
+
+ align:start position:0%
+so equation of motion allows us to get
+rid of ion dot
+
+ align:start position:0%
+rid of ion dot
+ 
+
+ align:start position:0%
+rid of ion dot
+partials that are on chi ends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's why we don't have to worry
+
+ align:start position:0%
+so that's why we don't have to worry
+ 
+
+ align:start position:0%
+so that's why we don't have to worry
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those and this is just like
+
+ align:start position:0%
+those and this is just like
+ 
+
+ align:start position:0%
+those and this is just like
+saying that in our leading order action
+
+ align:start position:0%
+saying that in our leading order action
+ 
+
+ align:start position:0%
+saying that in our leading order action
+in our leading order action there wasn't
+
+ align:start position:0%
+in our leading order action there wasn't
+ 
+
+ align:start position:0%
+in our leading order action there wasn't
+i end up partial
+
+ align:start position:0%
+i end up partial
+ 
+
+ align:start position:0%
+i end up partial
+but and that's just like saying there
+
+ align:start position:0%
+but and that's just like saying there
+ 
+
+ align:start position:0%
+but and that's just like saying there
+was time derivatives in our leading
+
+ align:start position:0%
+was time derivatives in our leading
+ 
+
+ align:start position:0%
+was time derivatives in our leading
+order action in some standard effective
+
+ align:start position:0%
+order action in some standard effective
+ 
+
+ align:start position:0%
+order action in some standard effective
+field theory
+
+ align:start position:0%
+field theory
+ 
+
+ align:start position:0%
+field theory
+but then in the low in the higher
+
+ align:start position:0%
+but then in the low in the higher
+ 
+
+ align:start position:0%
+but then in the low in the higher
+dimension operators you can always use
+
+ align:start position:0%
+dimension operators you can always use
+ 
+
+ align:start position:0%
+dimension operators you can always use
+the equations of motion to get rid of
+
+ align:start position:0%
+the equations of motion to get rid of
+ 
+
+ align:start position:0%
+the equations of motion to get rid of
+those time derivatives and here we're
+
+ align:start position:0%
+those time derivatives and here we're
+ 
+
+ align:start position:0%
+those time derivatives and here we're
+using the equation of motion to get rid
+
+ align:start position:0%
+using the equation of motion to get rid
+ 
+
+ align:start position:0%
+using the equation of motion to get rid
+of i end up partial so it appears in the
+
+ align:start position:0%
+of i end up partial so it appears in the
+ 
+
+ align:start position:0%
+of i end up partial so it appears in the
+leading reaction but then we don't have
+
+ align:start position:0%
+leading reaction but then we don't have
+ 
+
+ align:start position:0%
+leading reaction but then we don't have
+to have it in any other
+
+ align:start position:0%
+to have it in any other
+ 
+
+ align:start position:0%
+to have it in any other
+subleading operator and that's why it's
+
+ align:start position:0%
+subleading operator and that's why it's
+ 
+
+ align:start position:0%
+subleading operator and that's why it's
+not one of the ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's included in the list
+
+ align:start position:0%
+that's included in the list
+ 
+
+ align:start position:0%
+that's included in the list
+and if you had i end up partial on curly
+
+ align:start position:0%
+and if you had i end up partial on curly
+ 
+
+ align:start position:0%
+and if you had i end up partial on curly
+b that's also a part of the equations of
+
+ align:start position:0%
+b that's also a part of the equations of
+ 
+
+ align:start position:0%
+b that's also a part of the equations of
+motion of the gluon field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when you do the gluon equations of
+
+ align:start position:0%
+now when you do the gluon equations of
+ 
+
+ align:start position:0%
+now when you do the gluon equations of
+motion there's components because it's a
+
+ align:start position:0%
+motion there's components because it's a
+ 
+
+ align:start position:0%
+motion there's components because it's a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+and one of the other components allows
+
+ align:start position:0%
+and one of the other components allows
+ 
+
+ align:start position:0%
+and one of the other components allows
+you to get rid of the end of n dot b
+
+ align:start position:0%
+you to get rid of the end of n dot b
+ 
+
+ align:start position:0%
+you to get rid of the end of n dot b
+so there's another term that you can
+
+ align:start position:0%
+so there's another term that you can
+ 
+
+ align:start position:0%
+so there's another term that you can
+rearrange
+
+ align:start position:0%
+rearrange
+ 
+
+ align:start position:0%
+rearrange
+and i won't write it out because the
+
+ align:start position:0%
+and i won't write it out because the
+ 
+
+ align:start position:0%
+and i won't write it out because the
+equation is rather messy but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give you some idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's another component that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+where i can get rid of all the n-dot
+
+ align:start position:0%
+where i can get rid of all the n-dot
+ 
+
+ align:start position:0%
+where i can get rid of all the n-dot
+curly b's using the gluon equipped so i
+
+ align:start position:0%
+curly b's using the gluon equipped so i
+ 
+
+ align:start position:0%
+curly b's using the gluon equipped so i
+the glue on equations of motions allows
+
+ align:start position:0%
+the glue on equations of motions allows
+ 
+
+ align:start position:0%
+the glue on equations of motions allows
+me to get rid of both of these things
+
+ align:start position:0%
+me to get rid of both of these things
+ 
+
+ align:start position:0%
+me to get rid of both of these things
+and then i just have the and basically
+
+ align:start position:0%
+and then i just have the and basically
+ 
+
+ align:start position:0%
+and then i just have the and basically
+after i've done that i just have the
+
+ align:start position:0%
+after i've done that i just have the
+ 
+
+ align:start position:0%
+after i've done that i just have the
+objects that i've
+
+ align:start position:0%
+objects that i've
+ 
+
+ align:start position:0%
+objects that i've
+told you we can use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so after using equations of motion we
+
+ align:start position:0%
+so after using equations of motion we
+ 
+
+ align:start position:0%
+so after using equations of motion we
+can get down to those objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and any other thing
+
+ align:start position:0%
+and any other thing
+ 
+
+ align:start position:0%
+and any other thing
+that you might dream up
+
+ align:start position:0%
+that you might dream up
+ 
+
+ align:start position:0%
+that you might dream up
+can be reduced
+
+ align:start position:0%
+can be reduced
+ 
+
+ align:start position:0%
+can be reduced
+to these objects
+
+ align:start position:0%
+to these objects
+ 
+
+ align:start position:0%
+to these objects
+so i'm not
+
+ align:start position:0%
+so i'm not
+ 
+
+ align:start position:0%
+so i'm not
+saying that i went through a complete
+
+ align:start position:0%
+saying that i went through a complete
+ 
+
+ align:start position:0%
+saying that i went through a complete
+list here for example what if you had a
+
+ align:start position:0%
+list here for example what if you had a
+ 
+
+ align:start position:0%
+list here for example what if you had a
+commutator of two
+
+ align:start position:0%
+commutator of two
+ 
+
+ align:start position:0%
+commutator of two
+dn perps
+
+ align:start position:0%
+dn perps
+ 
+
+ align:start position:0%
+dn perps
+right you might say oh that's some new
+
+ align:start position:0%
+right you might say oh that's some new
+ 
+
+ align:start position:0%
+right you might say oh that's some new
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+it's one of these you can also reduce
+
+ align:start position:0%
+it's one of these you can also reduce
+ 
+
+ align:start position:0%
+it's one of these you can also reduce
+that too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me list that one just to give you
+
+ align:start position:0%
+so let me list that one just to give you
+ 
+
+ align:start position:0%
+so let me list that one just to give you
+some idea that there's
+
+ align:start position:0%
+some idea that there's
+ 
+
+ align:start position:0%
+some idea that there's
+others you might think of dreaming up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can reduce all others to this set
+
+ align:start position:0%
+so you can reduce all others to this set
+ 
+
+ align:start position:0%
+so you can reduce all others to this set
+okay so for the linear sector this is
+
+ align:start position:0%
+okay so for the linear sector this is
+ 
+
+ align:start position:0%
+okay so for the linear sector this is
+enough for higher to build higher
+
+ align:start position:0%
+enough for higher to build higher
+ 
+
+ align:start position:0%
+enough for higher to build higher
+dimension operators just these three
+
+ align:start position:0%
+dimension operators just these three
+ 
+
+ align:start position:0%
+dimension operators just these three
+and then for the ultrasoft sector
+
+ align:start position:0%
+and then for the ultrasoft sector
+ 
+
+ align:start position:0%
+and then for the ultrasoft sector
+so i guess
+
+ align:start position:0%
+so i guess
+ 
+
+ align:start position:0%
+so i guess
+this is two
+
+ align:start position:0%
+this is two
+ 
+
+ align:start position:0%
+this is two
+we do need ultra soft cleaner drip
+
+ align:start position:0%
+we do need ultra soft cleaner drip
+ 
+
+ align:start position:0%
+we do need ultra soft cleaner drip
+ultrasoft derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ultrasoft field strengths
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ultrasoft quarks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this part is really just similar to
+
+ align:start position:0%
+so this part is really just similar to
+ 
+
+ align:start position:0%
+so this part is really just similar to
+the story that you'd have
+
+ align:start position:0%
+the story that you'd have
+ 
+
+ align:start position:0%
+the story that you'd have
+for a standard low energy effective
+
+ align:start position:0%
+for a standard low energy effective
+ 
+
+ align:start position:0%
+for a standard low energy effective
+field theory
+
+ align:start position:0%
+field theory
+ 
+
+ align:start position:0%
+field theory
+like integrating out a massive particle
+
+ align:start position:0%
+like integrating out a massive particle
+ 
+
+ align:start position:0%
+like integrating out a massive particle
+you can use the equation of motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one thing that
+
+ align:start position:0%
+one thing that
+ 
+
+ align:start position:0%
+one thing that
+is worth commenting about is the
+
+ align:start position:0%
+is worth commenting about is the
+ 
+
+ align:start position:0%
+is worth commenting about is the
+connection between one and two so one is
+
+ align:start position:0%
+connection between one and two so one is
+ 
+
+ align:start position:0%
+connection between one and two so one is
+collinear and two is ultra soft and a
+
+ align:start position:0%
+collinear and two is ultra soft and a
+ 
+
+ align:start position:0%
+collinear and two is ultra soft and a
+priori you might think well just
+
+ align:start position:0%
+priori you might think well just
+ 
+
+ align:start position:0%
+priori you might think well just
+they're totally independent but we saw
+
+ align:start position:0%
+they're totally independent but we saw
+ 
+
+ align:start position:0%
+they're totally independent but we saw
+last time that re-parametrization and
+
+ align:start position:0%
+last time that re-parametrization and
+ 
+
+ align:start position:0%
+last time that re-parametrization and
+variance connects them
+
+ align:start position:0%
+variance connects them
+ 
+
+ align:start position:0%
+variance connects them
+so if i've decided that this is the type
+
+ align:start position:0%
+so if i've decided that this is the type
+ 
+
+ align:start position:0%
+so if i've decided that this is the type
+of basis i want to use for my operators
+
+ align:start position:0%
+of basis i want to use for my operators
+ 
+
+ align:start position:0%
+of basis i want to use for my operators
+then what is the reparameterization
+
+ align:start position:0%
+then what is the reparameterization
+ 
+
+ align:start position:0%
+then what is the reparameterization
+connection
+
+ align:start position:0%
+connection
+ 
+
+ align:start position:0%
+connection
+you can rewrite what we said last time
+
+ align:start position:0%
+you can rewrite what we said last time
+ 
+
+ align:start position:0%
+you can rewrite what we said last time
+in terms of these curly d's
+
+ align:start position:0%
+in terms of these curly d's
+ 
+
+ align:start position:0%
+in terms of these curly d's
+because it basically just means moving
+
+ align:start position:0%
+because it basically just means moving
+ 
+
+ align:start position:0%
+because it basically just means moving
+the wilson lines that we had in this
+
+ align:start position:0%
+the wilson lines that we had in this
+ 
+
+ align:start position:0%
+the wilson lines that we had in this
+formula last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they were around the ultrasoft
+
+ align:start position:0%
+they were around the ultrasoft
+ 
+
+ align:start position:0%
+they were around the ultrasoft
+operator last time
+
+ align:start position:0%
+operator last time
+ 
+
+ align:start position:0%
+operator last time
+and if i just move them over to the
+
+ align:start position:0%
+and if i just move them over to the
+ 
+
+ align:start position:0%
+and if i just move them over to the
+cliniar operator then i get this curly d
+
+ align:start position:0%
+cliniar operator then i get this curly d
+ 
+
+ align:start position:0%
+cliniar operator then i get this curly d
+right so the rpi
+
+ align:start position:0%
+right so the rpi
+ 
+
+ align:start position:0%
+right so the rpi
+connection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is connecting the curly d to the d ultra
+
+ align:start position:0%
+is connecting the curly d to the d ultra
+ 
+
+ align:start position:0%
+is connecting the curly d to the d ultra
+curly d linear to the d ultra soft and
+
+ align:start position:0%
+curly d linear to the d ultra soft and
+ 
+
+ align:start position:0%
+curly d linear to the d ultra soft and
+then you can write this guy as the p
+
+ align:start position:0%
+then you can write this guy as the p
+ 
+
+ align:start position:0%
+then you can write this guy as the p
+part plus the b perp
+
+ align:start position:0%
+part plus the b perp
+ 
+
+ align:start position:0%
+part plus the b perp
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+and likewise
+
+ align:start position:0%
+and likewise
+ 
+
+ align:start position:0%
+and likewise
+if you do the same for the n bar sector
+
+ align:start position:0%
+if you do the same for the n bar sector
+ 
+
+ align:start position:0%
+if you do the same for the n bar sector
+you move the wilson lines
+
+ align:start position:0%
+you move the wilson lines
+ 
+
+ align:start position:0%
+you move the wilson lines
+from this term to that term then it
+
+ align:start position:0%
+from this term to that term then it
+ 
+
+ align:start position:0%
+from this term to that term then it
+looks like these two combinations so
+
+ align:start position:0%
+looks like these two combinations so
+ 
+
+ align:start position:0%
+looks like these two combinations so
+that's just rewriting what we had before
+
+ align:start position:0%
+that's just rewriting what we had before
+ 
+
+ align:start position:0%
+that's just rewriting what we had before
+but now in terms of these
+
+ align:start position:0%
+but now in terms of these
+ 
+
+ align:start position:0%
+but now in terms of these
+this type of notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's enough to build operators
+
+ align:start position:0%
+okay so that's enough to build operators
+ 
+
+ align:start position:0%
+okay so that's enough to build operators
+at higher order
+
+ align:start position:0%
+at higher order
+ 
+
+ align:start position:0%
+at higher order
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+write down wilson coefficients for those
+
+ align:start position:0%
+write down wilson coefficients for those
+ 
+
+ align:start position:0%
+write down wilson coefficients for those
+operators that are functions of the
+
+ align:start position:0%
+operators that are functions of the
+ 
+
+ align:start position:0%
+operators that are functions of the
+large momentum and then we start doing
+
+ align:start position:0%
+large momentum and then we start doing
+ 
+
+ align:start position:0%
+large momentum and then we start doing
+physics with them
+
+ align:start position:0%
+physics with them
+ 
+
+ align:start position:0%
+physics with them
+so any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the equations of motion yeah
+
+ align:start position:0%
+what are the equations of motion yeah
+ 
+
+ align:start position:0%
+what are the equations of motion yeah
+you always just use the leading order
+
+ align:start position:0%
+you always just use the leading order
+ 
+
+ align:start position:0%
+you always just use the leading order
+equation motion yeah into higher order
+
+ align:start position:0%
+equation motion yeah into higher order
+ 
+
+ align:start position:0%
+equation motion yeah into higher order
+yeah these are the l zero equations of
+
+ align:start position:0%
+yeah these are the l zero equations of
+ 
+
+ align:start position:0%
+yeah these are the l zero equations of
+motion that's what i'm doing here
+
+ align:start position:0%
+motion that's what i'm doing here
+ 
+
+ align:start position:0%
+motion that's what i'm doing here
+writing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's one more actually there's
+
+ align:start position:0%
+yeah there's one more actually there's
+ 
+
+ align:start position:0%
+yeah there's one more actually there's
+three that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's only needed at some very high order
+
+ align:start position:0%
+it's only needed at some very high order
+ 
+
+ align:start position:0%
+it's only needed at some very high order
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+the next thing i want to talk about
+
+ align:start position:0%
+the next thing i want to talk about
+ 
+
+ align:start position:0%
+the next thing i want to talk about
+before we start doing
+
+ align:start position:0%
+before we start doing
+ 
+
+ align:start position:0%
+before we start doing
+explicit examples and going through
+
+ align:start position:0%
+explicit examples and going through
+ 
+
+ align:start position:0%
+explicit examples and going through
+processes is how loops work in this
+
+ align:start position:0%
+processes is how loops work in this
+ 
+
+ align:start position:0%
+processes is how loops work in this
+effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to have to come back and
+
+ align:start position:0%
+and we're going to have to come back and
+ 
+
+ align:start position:0%
+and we're going to have to come back and
+talk about our grid that we had for this
+
+ align:start position:0%
+talk about our grid that we had for this
+ 
+
+ align:start position:0%
+talk about our grid that we had for this
+split up of momentum how should we
+
+ align:start position:0%
+split up of momentum how should we
+ 
+
+ align:start position:0%
+split up of momentum how should we
+actually think about it in
+
+ align:start position:0%
+actually think about it in
+ 
+
+ align:start position:0%
+actually think about it in
+practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll also deal with how
+
+ align:start position:0%
+and then we'll also deal with how
+ 
+
+ align:start position:0%
+and then we'll also deal with how
+matching and running work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to do this in the context
+
+ align:start position:0%
+so i'm going to do this in the context
+ 
+
+ align:start position:0%
+so i'm going to do this in the context
+of an example and again i'm just going
+
+ align:start position:0%
+of an example and again i'm just going
+ 
+
+ align:start position:0%
+of an example and again i'm just going
+to pick the simplest example that has
+
+ align:start position:0%
+to pick the simplest example that has
+ 
+
+ align:start position:0%
+to pick the simplest example that has
+only one jet
+
+ align:start position:0%
+only one jet
+ 
+
+ align:start position:0%
+only one jet
+just to make our lives a little bit
+
+ align:start position:0%
+just to make our lives a little bit
+ 
+
+ align:start position:0%
+just to make our lives a little bit
+simpler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll consider our heavy-duty light
+
+ align:start position:0%
+so we'll consider our heavy-duty light
+ 
+
+ align:start position:0%
+so we'll consider our heavy-duty light
+current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i think actually once you see how it
+
+ align:start position:0%
+and i think actually once you see how it
+ 
+
+ align:start position:0%
+and i think actually once you see how it
+works in this example
+
+ align:start position:0%
+works in this example
+ 
+
+ align:start position:0%
+works in this example
+you'll understand what all the all the
+
+ align:start position:0%
+you'll understand what all the all the
+ 
+
+ align:start position:0%
+you'll understand what all the all the
+general features are of
+
+ align:start position:0%
+general features are of
+ 
+
+ align:start position:0%
+general features are of
+doing loops in sct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators that we constructed lowest
+
+ align:start position:0%
+operators that we constructed lowest
+ 
+
+ align:start position:0%
+operators that we constructed lowest
+order operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me write it in this
+
+ align:start position:0%
+and let me write it in this
+ 
+
+ align:start position:0%
+and let me write it in this
+way which was
+
+ align:start position:0%
+way which was
+ 
+
+ align:start position:0%
+way which was
+prior to making our field redefinition
+
+ align:start position:0%
+prior to making our field redefinition
+ 
+
+ align:start position:0%
+prior to making our field redefinition
+i'll just write it this way if i want
+
+ align:start position:0%
+i'll just write it this way if i want
+ 
+
+ align:start position:0%
+i'll just write it this way if i want
+and gamma
+
+ align:start position:0%
+and gamma
+ 
+
+ align:start position:0%
+and gamma
+for bds gamma
+
+ align:start position:0%
+for bds gamma
+ 
+
+ align:start position:0%
+for bds gamma
+is a tensor operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's
+
+ align:start position:0%
+and there's
+ 
+
+ align:start position:0%
+and there's
+a photon field
+
+ align:start position:0%
+a photon field
+ 
+
+ align:start position:0%
+a photon field
+which is a field strength f menu so
+
+ align:start position:0%
+which is a field strength f menu so
+ 
+
+ align:start position:0%
+which is a field strength f menu so
+let's just think of that as all part of
+
+ align:start position:0%
+let's just think of that as all part of
+ 
+
+ align:start position:0%
+let's just think of that as all part of
+the gamma
+
+ align:start position:0%
+the gamma
+ 
+
+ align:start position:0%
+the gamma
+okay and then that's also appearing here
+
+ align:start position:0%
+okay and then that's also appearing here
+ 
+
+ align:start position:0%
+okay and then that's also appearing here
+and i could use the spin structure
+
+ align:start position:0%
+and i could use the spin structure
+ 
+
+ align:start position:0%
+and i could use the spin structure
+properties of these things to reduce the
+
+ align:start position:0%
+properties of these things to reduce the
+ 
+
+ align:start position:0%
+properties of these things to reduce the
+sigma mu but
+
+ align:start position:0%
+sigma mu but
+ 
+
+ align:start position:0%
+sigma mu but
+that's not really going to be part of
+
+ align:start position:0%
+that's not really going to be part of
+ 
+
+ align:start position:0%
+that's not really going to be part of
+our story so let's not bother with that
+
+ align:start position:0%
+our story so let's not bother with that
+ 
+
+ align:start position:0%
+our story so let's not bother with that
+so what do i do i just compute the qcd
+
+ align:start position:0%
+so what do i do i just compute the qcd
+ 
+
+ align:start position:0%
+so what do i do i just compute the qcd
+loops and the sct loops and i compare
+
+ align:start position:0%
+loops and the sct loops and i compare
+ 
+
+ align:start position:0%
+loops and the sct loops and i compare
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and if sct is the right effective theory
+
+ align:start position:0%
+and if sct is the right effective theory
+ 
+
+ align:start position:0%
+and if sct is the right effective theory
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+limit where i have an energetic photon
+
+ align:start position:0%
+limit where i have an energetic photon
+ 
+
+ align:start position:0%
+limit where i have an energetic photon
+and a back to back with an energetic
+
+ align:start position:0%
+and a back to back with an energetic
+ 
+
+ align:start position:0%
+and a back to back with an energetic
+strange quark
+
+ align:start position:0%
+strange quark
+ 
+
+ align:start position:0%
+strange quark
+then i should match all the infra
+
+ align:start position:0%
+then i should match all the infra
+ 
+
+ align:start position:0%
+then i should match all the infra
+divergences in that qcd computation
+
+ align:start position:0%
+divergences in that qcd computation
+ 
+
+ align:start position:0%
+divergences in that qcd computation
+i should be able to extract the matching
+
+ align:start position:0%
+i should be able to extract the matching
+ 
+
+ align:start position:0%
+i should be able to extract the matching
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+i should be able to determine this what
+
+ align:start position:0%
+i should be able to determine this what
+ 
+
+ align:start position:0%
+i should be able to determine this what
+the c is
+
+ align:start position:0%
+the c is
+ 
+
+ align:start position:0%
+the c is
+from that calculation
+
+ align:start position:0%
+from that calculation
+ 
+
+ align:start position:0%
+from that calculation
+and i should be able to run the operator
+
+ align:start position:0%
+and i should be able to run the operator
+ 
+
+ align:start position:0%
+and i should be able to run the operator
+i should be able to
+
+ align:start position:0%
+i should be able to
+ 
+
+ align:start position:0%
+i should be able to
+make this into ms bar do some more
+
+ align:start position:0%
+make this into ms bar do some more
+ 
+
+ align:start position:0%
+make this into ms bar do some more
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+of this operator and then do some
+
+ align:start position:0%
+of this operator and then do some
+ 
+
+ align:start position:0%
+of this operator and then do some
+normalization group evolution of that of
+
+ align:start position:0%
+normalization group evolution of that of
+ 
+
+ align:start position:0%
+normalization group evolution of that of
+wilson coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's just think about computing
+
+ align:start position:0%
+well let's just think about computing
+ 
+
+ align:start position:0%
+well let's just think about computing
+the graphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have to decide when we compute the
+
+ align:start position:0%
+so we have to decide when we compute the
+ 
+
+ align:start position:0%
+so we have to decide when we compute the
+graphs how to regulate them
+
+ align:start position:0%
+graphs how to regulate them
+ 
+
+ align:start position:0%
+graphs how to regulate them
+right we're going to and we need to use
+
+ align:start position:0%
+right we're going to and we need to use
+ 
+
+ align:start position:0%
+right we're going to and we need to use
+the same infrared regulator in the full
+
+ align:start position:0%
+the same infrared regulator in the full
+ 
+
+ align:start position:0%
+the same infrared regulator in the full
+theory of defective theory
+
+ align:start position:0%
+theory of defective theory
+ 
+
+ align:start position:0%
+theory of defective theory
+so here's how i'm going to regulate them
+
+ align:start position:0%
+so here's how i'm going to regulate them
+ 
+
+ align:start position:0%
+so here's how i'm going to regulate them
+we could do this different ways and it's
+
+ align:start position:0%
+we could do this different ways and it's
+ 
+
+ align:start position:0%
+we could do this different ways and it's
+useful to understand that
+
+ align:start position:0%
+useful to understand that
+ 
+
+ align:start position:0%
+useful to understand that
+various answers that we get are
+
+ align:start position:0%
+various answers that we get are
+ 
+
+ align:start position:0%
+various answers that we get are
+independent of the regulator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to take p squared not equal
+
+ align:start position:0%
+so i'm going to take p squared not equal
+ 
+
+ align:start position:0%
+so i'm going to take p squared not equal
+to zero for the strange quark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's infrared divergences
+
+ align:start position:0%
+so there's infrared divergences
+ 
+
+ align:start position:0%
+so there's infrared divergences
+associated to the strange quark and i'm
+
+ align:start position:0%
+associated to the strange quark and i'm
+ 
+
+ align:start position:0%
+associated to the strange quark and i'm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+take p squared not equal to 0 for them
+
+ align:start position:0%
+take p squared not equal to 0 for them
+ 
+
+ align:start position:0%
+take p squared not equal to 0 for them
+i'm going to use dim rag
+
+ align:start position:0%
+i'm going to use dim rag
+ 
+
+ align:start position:0%
+i'm going to use dim rag
+for the heavy clark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i could take the b quark to also be
+
+ align:start position:0%
+so i could take the b quark to also be
+ 
+
+ align:start position:0%
+so i could take the b quark to also be
+off shell that would make the formulas
+
+ align:start position:0%
+off shell that would make the formulas
+ 
+
+ align:start position:0%
+off shell that would make the formulas
+even more complicated so instead of
+
+ align:start position:0%
+even more complicated so instead of
+ 
+
+ align:start position:0%
+even more complicated so instead of
+doing that i'm just going to allow
+
+ align:start position:0%
+doing that i'm just going to allow
+ 
+
+ align:start position:0%
+doing that i'm just going to allow
+epsilon to regulate the b cork these
+
+ align:start position:0%
+epsilon to regulate the b cork these
+ 
+
+ align:start position:0%
+epsilon to regulate the b cork these
+guys are pretty easy to track so
+
+ align:start position:0%
+guys are pretty easy to track so
+ 
+
+ align:start position:0%
+guys are pretty easy to track so
+that won't
+
+ align:start position:0%
+that won't
+ 
+
+ align:start position:0%
+that won't
+be a problem
+
+ align:start position:0%
+be a problem
+ 
+
+ align:start position:0%
+be a problem
+and i'm going to use feinman gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't have to do that but
+
+ align:start position:0%
+i don't have to do that but
+ 
+
+ align:start position:0%
+i don't have to do that but
+that's a nice gauge for doing
+
+ align:start position:0%
+that's a nice gauge for doing
+ 
+
+ align:start position:0%
+that's a nice gauge for doing
+calculations
+
+ align:start position:0%
+calculations
+ 
+
+ align:start position:0%
+calculations
+so what are the diagrams where i have my
+
+ align:start position:0%
+so what are the diagrams where i have my
+ 
+
+ align:start position:0%
+so what are the diagrams where i have my
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+and i have a vertex
+
+ align:start position:0%
+and i have a vertex
+ 
+
+ align:start position:0%
+and i have a vertex
+diagram like this
+
+ align:start position:0%
+diagram like this
+ 
+
+ align:start position:0%
+diagram like this
+and then i have wave function or
+
+ align:start position:0%
+and then i have wave function or
+ 
+
+ align:start position:0%
+and then i have wave function or
+normalization and so
+
+ align:start position:0%
+normalization and so
+ 
+
+ align:start position:0%
+normalization and so
+let me in the usual kind of cavalier way
+
+ align:start position:0%
+let me in the usual kind of cavalier way
+ 
+
+ align:start position:0%
+let me in the usual kind of cavalier way
+denote the wave function or
+
+ align:start position:0%
+denote the wave function or
+ 
+
+ align:start position:0%
+denote the wave function or
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+which is just the multiplication by the
+
+ align:start position:0%
+which is just the multiplication by the
+ 
+
+ align:start position:0%
+which is just the multiplication by the
+appropriate z factors
+
+ align:start position:0%
+appropriate z factors
+ 
+
+ align:start position:0%
+appropriate z factors
+by diagrams like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a standard qcd calculation
+
+ align:start position:0%
+and this is a standard qcd calculation
+ 
+
+ align:start position:0%
+and this is a standard qcd calculation
+and we can
+
+ align:start position:0%
+and we can
+ 
+
+ align:start position:0%
+and we can
+carry it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what does the answer look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this diagram
+
+ align:start position:0%
+so this diagram
+ 
+
+ align:start position:0%
+so this diagram
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has double logs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and single logs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that involve p squared which is our ir
+
+ align:start position:0%
+that involve p squared which is our ir
+ 
+
+ align:start position:0%
+that involve p squared which is our ir
+regulator
+
+ align:start position:0%
+regulator
+ 
+
+ align:start position:0%
+regulator
+and then it has
+
+ align:start position:0%
+and then it has
+ 
+
+ align:start position:0%
+and then it has
+some terms that are finite
+
+ align:start position:0%
+some terms that are finite
+ 
+
+ align:start position:0%
+some terms that are finite
+which i'll just denote by
+
+ align:start position:0%
+which i'll just denote by
+ 
+
+ align:start position:0%
+which i'll just denote by
+so p here is the momentum of our strange
+
+ align:start position:0%
+so p here is the momentum of our strange
+ 
+
+ align:start position:0%
+so p here is the momentum of our strange
+quark going out
+
+ align:start position:0%
+quark going out
+ 
+
+ align:start position:0%
+quark going out
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+pb is the momentum of our v quark coming
+
+ align:start position:0%
+pb is the momentum of our v quark coming
+ 
+
+ align:start position:0%
+pb is the momentum of our v quark coming
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+and let me not try to
+
+ align:start position:0%
+and let me not try to
+ 
+
+ align:start position:0%
+and let me not try to
+we're not going to talk much about these
+
+ align:start position:0%
+we're not going to talk much about these
+ 
+
+ align:start position:0%
+we're not going to talk much about these
+finite terms but there is some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+what i mean by finite here is terms with
+
+ align:start position:0%
+what i mean by finite here is terms with
+ 
+
+ align:start position:0%
+what i mean by finite here is terms with
+no i are divergences
+
+ align:start position:0%
+no i are divergences
+ 
+
+ align:start position:0%
+no i are divergences
+so the ir divergences are these single
+
+ align:start position:0%
+so the ir divergences are these single
+ 
+
+ align:start position:0%
+so the ir divergences are these single
+logs and double logs and then there's
+
+ align:start position:0%
+logs and double logs and then there's
+ 
+
+ align:start position:0%
+logs and double logs and then there's
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+some remainder that i can write that way
+
+ align:start position:0%
+some remainder that i can write that way
+ 
+
+ align:start position:0%
+some remainder that i can write that way
+i'm expanding for small p squared so p
+
+ align:start position:0%
+i'm expanding for small p squared so p
+ 
+
+ align:start position:0%
+i'm expanding for small p squared so p
+squared is not equal to zero but i take
+
+ align:start position:0%
+squared is not equal to zero but i take
+ 
+
+ align:start position:0%
+squared is not equal to zero but i take
+the limit p squared goes to zero and
+
+ align:start position:0%
+the limit p squared goes to zero and
+ 
+
+ align:start position:0%
+the limit p squared goes to zero and
+then that limit these are the ir
+
+ align:start position:0%
+then that limit these are the ir
+ 
+
+ align:start position:0%
+then that limit these are the ir
+singularities and then there's
+
+ align:start position:0%
+singularities and then there's
+ 
+
+ align:start position:0%
+singularities and then there's
+some function of p dot p
+
+ align:start position:0%
+some function of p dot p
+ 
+
+ align:start position:0%
+some function of p dot p
+b which is just an order one thing and
+
+ align:start position:0%
+b which is just an order one thing and
+ 
+
+ align:start position:0%
+b which is just an order one thing and
+then b squared of course is p b squared
+
+ align:start position:0%
+then b squared of course is p b squared
+ 
+
+ align:start position:0%
+then b squared of course is p b squared
+so that's sort of the remaining
+
+ align:start position:0%
+so that's sort of the remaining
+ 
+
+ align:start position:0%
+so that's sort of the remaining
+kinematic variables this could possibly
+
+ align:start position:0%
+kinematic variables this could possibly
+ 
+
+ align:start position:0%
+kinematic variables this could possibly
+depend on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really finite there's no
+
+ align:start position:0%
+it's really finite there's no
+ 
+
+ align:start position:0%
+it's really finite there's no
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah um
+
+ align:start position:0%
+yeah um
+ 
+
+ align:start position:0%
+yeah um
+yeah so i let's see i uh
+
+ align:start position:0%
+yeah so i let's see i uh
+ 
+
+ align:start position:0%
+yeah so i let's see i uh
+yeah i guess i carried out the so there
+
+ align:start position:0%
+yeah i guess i carried out the so there
+ 
+
+ align:start position:0%
+yeah i guess i carried out the so there
+is a z-10 for the tensor
+
+ align:start position:0%
+is a z-10 for the tensor
+ 
+
+ align:start position:0%
+is a z-10 for the tensor
+and when i write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me do this
+
+ align:start position:0%
+let me do this
+ 
+
+ align:start position:0%
+let me do this
+i think it's better so i added up all
+
+ align:start position:0%
+i think it's better so i added up all
+ 
+
+ align:start position:0%
+i think it's better so i added up all
+these graphs and i want to add one more
+
+ align:start position:0%
+these graphs and i want to add one more
+ 
+
+ align:start position:0%
+these graphs and i want to add one more
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a there's a counter term for
+
+ align:start position:0%
+so there's a there's a counter term for
+ 
+
+ align:start position:0%
+so there's a there's a counter term for
+the tensor field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me add up let me change what i
+
+ align:start position:0%
+so let me add up let me change what i
+ 
+
+ align:start position:0%
+so let me add up let me change what i
+was going to say and do it this way so
+
+ align:start position:0%
+was going to say and do it this way so
+ 
+
+ align:start position:0%
+was going to say and do it this way so
+the sum of these four graphs is this
+
+ align:start position:0%
+the sum of these four graphs is this
+ 
+
+ align:start position:0%
+the sum of these four graphs is this
+okay so then if there's no uv
+
+ align:start position:0%
+okay so then if there's no uv
+ 
+
+ align:start position:0%
+okay so then if there's no uv
+divergences and i'll just tell you what
+
+ align:start position:0%
+divergences and i'll just tell you what
+ 
+
+ align:start position:0%
+divergences and i'll just tell you what
+the z factors for these three are then
+
+ align:start position:0%
+the z factors for these three are then
+ 
+
+ align:start position:0%
+the z factors for these three are then
+you could figure out what this graph is
+
+ align:start position:0%
+you could figure out what this graph is
+ 
+
+ align:start position:0%
+you could figure out what this graph is
+but subtract the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the tensor current in qcd
+
+ align:start position:0%
+so the tensor current in qcd
+ 
+
+ align:start position:0%
+so the tensor current in qcd
+has a
+
+ align:start position:0%
+has a
+ 
+
+ align:start position:0%
+has a
+has a z factor
+
+ align:start position:0%
+has a z factor
+ 
+
+ align:start position:0%
+has a z factor
+it looks like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a z
+
+ align:start position:0%
+there's a z
+ 
+
+ align:start position:0%
+there's a z
+for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heavy cork
+
+ align:start position:0%
+heavy cork
+ 
+
+ align:start position:0%
+heavy cork
+and if i include the finite residue as
+
+ align:start position:0%
+and if i include the finite residue as
+ 
+
+ align:start position:0%
+and if i include the finite residue as
+well as the divergent pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think i'm going to have to make one
+
+ align:start position:0%
+i think i'm going to have to make one
+ 
+
+ align:start position:0%
+i think i'm going to have to make one
+adjustment to my formula here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's fix something here
+
+ align:start position:0%
+let's fix something here
+ 
+
+ align:start position:0%
+let's fix something here
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so if i want it to be the way i say
+
+ align:start position:0%
+so if i want it to be the way i say
+ 
+
+ align:start position:0%
+so if i want it to be the way i say
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+do i have to do so this guy should be
+
+ align:start position:0%
+do i have to do so this guy should be
+ 
+
+ align:start position:0%
+do i have to do so this guy should be
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+halves and
+
+ align:start position:0%
+halves and
+ 
+
+ align:start position:0%
+halves and
+there will be one
+
+ align:start position:0%
+there will be one
+ 
+
+ align:start position:0%
+there will be one
+more divergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think that's right
+
+ align:start position:0%
+i think that's right
+ 
+
+ align:start position:0%
+i think that's right
+so this 2 over epsilon ir here
+
+ align:start position:0%
+so this 2 over epsilon ir here
+ 
+
+ align:start position:0%
+so this 2 over epsilon ir here
+is that one over epsilon i r
+
+ align:start position:0%
+is that one over epsilon i r
+ 
+
+ align:start position:0%
+is that one over epsilon i r
+and the uv renormalization is taken care
+
+ align:start position:0%
+and the uv renormalization is taken care
+ 
+
+ align:start position:0%
+and the uv renormalization is taken care
+of once i have the z tensor that there's
+
+ align:start position:0%
+of once i have the z tensor that there's
+ 
+
+ align:start position:0%
+of once i have the z tensor that there's
+z there's divergences in this diagram
+
+ align:start position:0%
+z there's divergences in this diagram
+ 
+
+ align:start position:0%
+z there's divergences in this diagram
+and these ones but there's one left over
+
+ align:start position:0%
+and these ones but there's one left over
+ 
+
+ align:start position:0%
+and these ones but there's one left over
+and that's taken care of by z tensor so
+
+ align:start position:0%
+and that's taken care of by z tensor so
+ 
+
+ align:start position:0%
+and that's taken care of by z tensor so
+there's no one over epsilon uvs after i
+
+ align:start position:0%
+there's no one over epsilon uvs after i
+ 
+
+ align:start position:0%
+there's no one over epsilon uvs after i
+after i take care of
+
+ align:start position:0%
+after i take care of
+ 
+
+ align:start position:0%
+after i take care of
+this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's just
+
+ align:start position:0%
+okay so that's just
+ 
+
+ align:start position:0%
+okay so that's just
+kind of by the definition of what z
+
+ align:start position:0%
+kind of by the definition of what z
+ 
+
+ align:start position:0%
+kind of by the definition of what z
+tensor should be
+
+ align:start position:0%
+tensor should be
+ 
+
+ align:start position:0%
+tensor should be
+and then everything else is as i wrote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's ir divergences that are
+
+ align:start position:0%
+so there's ir divergences that are
+ 
+
+ align:start position:0%
+so there's ir divergences that are
+associated to the strange quark off
+
+ align:start position:0%
+associated to the strange quark off
+ 
+
+ align:start position:0%
+associated to the strange quark off
+shellness that's these two terms there's
+
+ align:start position:0%
+shellness that's these two terms there's
+ 
+
+ align:start position:0%
+shellness that's these two terms there's
+an iron divergence associated the heavy
+
+ align:start position:0%
+an iron divergence associated the heavy
+ 
+
+ align:start position:0%
+an iron divergence associated the heavy
+quark going on shell that's that term
+
+ align:start position:0%
+quark going on shell that's that term
+ 
+
+ align:start position:0%
+quark going on shell that's that term
+that's the sum of diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what about sct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's going to be an sct linear
+
+ align:start position:0%
+so there's going to be an sct linear
+ 
+
+ align:start position:0%
+so there's going to be an sct linear
+diagrams and
+
+ align:start position:0%
+diagrams and
+ 
+
+ align:start position:0%
+diagrams and
+ultrasoft diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to use fine engage for
+
+ align:start position:0%
+so i'm going to use fine engage for
+ 
+
+ align:start position:0%
+so i'm going to use fine engage for
+everything again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not something i have to do
+
+ align:start position:0%
+this is not something i have to do
+ 
+
+ align:start position:0%
+this is not something i have to do
+this is what i'm going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's start with the ultra soft loops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a vertex graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so using
+
+ align:start position:0%
+so using
+ 
+
+ align:start position:0%
+so using
+the notation that we've adopted
+
+ align:start position:0%
+the notation that we've adopted
+ 
+
+ align:start position:0%
+the notation that we've adopted
+where the linear quarks are
+
+ align:start position:0%
+where the linear quarks are
+ 
+
+ align:start position:0%
+where the linear quarks are
+dashed and the heavy forks are double
+
+ align:start position:0%
+dashed and the heavy forks are double
+ 
+
+ align:start position:0%
+dashed and the heavy forks are double
+lines we have a diagram that looks like
+
+ align:start position:0%
+lines we have a diagram that looks like
+ 
+
+ align:start position:0%
+lines we have a diagram that looks like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there's some pre-factor
+
+ align:start position:0%
+there's some pre-factor
+ 
+
+ align:start position:0%
+there's some pre-factor
+let's focus on what the loop integral
+
+ align:start position:0%
+let's focus on what the loop integral
+ 
+
+ align:start position:0%
+let's focus on what the loop integral
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+so this loop here the k that's going
+
+ align:start position:0%
+so this loop here the k that's going
+ 
+
+ align:start position:0%
+so this loop here the k that's going
+through this loop
+
+ align:start position:0%
+through this loop
+ 
+
+ align:start position:0%
+through this loop
+is just a residual
+
+ align:start position:0%
+is just a residual
+ 
+
+ align:start position:0%
+is just a residual
+k there's no label k for this loop
+
+ align:start position:0%
+k there's no label k for this loop
+ 
+
+ align:start position:0%
+k there's no label k for this loop
+because it's an ultrasoft gluon
+
+ align:start position:0%
+because it's an ultrasoft gluon
+ 
+
+ align:start position:0%
+because it's an ultrasoft gluon
+so when we write down
+
+ align:start position:0%
+so when we write down
+ 
+
+ align:start position:0%
+so when we write down
+all the terms in this loop it's just
+
+ align:start position:0%
+all the terms in this loop it's just
+ 
+
+ align:start position:0%
+all the terms in this loop it's just
+standard field theory there's nothing
+
+ align:start position:0%
+standard field theory there's nothing
+ 
+
+ align:start position:0%
+standard field theory there's nothing
+special about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it since i'm taking
+
+ align:start position:0%
+it since i'm taking
+ 
+
+ align:start position:0%
+it since i'm taking
+the strange quark off shell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the propagator that i get is this
+
+ align:start position:0%
+the propagator that i get is this
+ 
+
+ align:start position:0%
+the propagator that i get is this
+shifted icon propagator where the
+
+ align:start position:0%
+shifted icon propagator where the
+ 
+
+ align:start position:0%
+shifted icon propagator where the
+basically the fact that it's off shell
+
+ align:start position:0%
+basically the fact that it's off shell
+ 
+
+ align:start position:0%
+basically the fact that it's off shell
+gives me this
+
+ align:start position:0%
+gives me this
+ 
+
+ align:start position:0%
+gives me this
+extra term there that's regulating some
+
+ align:start position:0%
+extra term there that's regulating some
+ 
+
+ align:start position:0%
+extra term there that's regulating some
+ir divergences and we want that because
+
+ align:start position:0%
+ir divergences and we want that because
+ 
+
+ align:start position:0%
+ir divergences and we want that because
+we want to regulate the iron divergences
+
+ align:start position:0%
+we want to regulate the iron divergences
+ 
+
+ align:start position:0%
+we want to regulate the iron divergences
+in the same way in the full theory and
+
+ align:start position:0%
+in the same way in the full theory and
+ 
+
+ align:start position:0%
+in the same way in the full theory and
+the effective theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is proportional to that
+
+ align:start position:0%
+this is proportional to that
+ 
+
+ align:start position:0%
+this is proportional to that
+and if i put in all the factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it does have double logs
+
+ align:start position:0%
+so it does have double logs
+ 
+
+ align:start position:0%
+so it does have double logs
+of the p squared
+
+ align:start position:0%
+of the p squared
+ 
+
+ align:start position:0%
+of the p squared
+it doesn't have single logs of the p
+
+ align:start position:0%
+it doesn't have single logs of the p
+ 
+
+ align:start position:0%
+it doesn't have single logs of the p
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+and actually if we look at the double
+
+ align:start position:0%
+and actually if we look at the double
+ 
+
+ align:start position:0%
+and actually if we look at the double
+logs the coefficients also don't match
+
+ align:start position:0%
+logs the coefficients also don't match
+ 
+
+ align:start position:0%
+logs the coefficients also don't match
+with what we had over there and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's going to be some other
+
+ align:start position:0%
+so there's going to be some other
+ 
+
+ align:start position:0%
+so there's going to be some other
+diagrams that are going to involve
+
+ align:start position:0%
+diagrams that are going to involve
+ 
+
+ align:start position:0%
+diagrams that are going to involve
+double logs of p squared as well
+
+ align:start position:0%
+double logs of p squared as well
+ 
+
+ align:start position:0%
+double logs of p squared as well
+one thing that we can note here is that
+
+ align:start position:0%
+one thing that we can note here is that
+ 
+
+ align:start position:0%
+one thing that we can note here is that
+if you think about the scales in the
+
+ align:start position:0%
+if you think about the scales in the
+ 
+
+ align:start position:0%
+if you think about the scales in the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+remember that our loop integral is
+
+ align:start position:0%
+remember that our loop integral is
+ 
+
+ align:start position:0%
+remember that our loop integral is
+totally homogeneous in the power
+
+ align:start position:0%
+totally homogeneous in the power
+ 
+
+ align:start position:0%
+totally homogeneous in the power
+counting lambdas were totally
+
+ align:start position:0%
+counting lambdas were totally
+ 
+
+ align:start position:0%
+counting lambdas were totally
+homogeneous
+
+ align:start position:0%
+homogeneous
+ 
+
+ align:start position:0%
+homogeneous
+and if you think about p squared
+
+ align:start position:0%
+and if you think about p squared
+ 
+
+ align:start position:0%
+and if you think about p squared
+as scaling like lambda squared
+
+ align:start position:0%
+as scaling like lambda squared
+ 
+
+ align:start position:0%
+as scaling like lambda squared
+which is natural size for an external
+
+ align:start position:0%
+which is natural size for an external
+ 
+
+ align:start position:0%
+which is natural size for an external
+linear momentum
+
+ align:start position:0%
+linear momentum
+ 
+
+ align:start position:0%
+linear momentum
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+if p squared squared is like lambda
+
+ align:start position:0%
+if p squared squared is like lambda
+ 
+
+ align:start position:0%
+if p squared squared is like lambda
+squared then
+
+ align:start position:0%
+squared then
+ 
+
+ align:start position:0%
+squared then
+so does
+
+ align:start position:0%
+so does
+ 
+
+ align:start position:0%
+so does
+p squared over m bar dot p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a dimension one thing and
+
+ align:start position:0%
+and this is a dimension one thing and
+ 
+
+ align:start position:0%
+and this is a dimension one thing and
+this is the ultrasoft scale right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+ultrasoft momentum
+
+ align:start position:0%
+ultrasoft momentum
+ 
+
+ align:start position:0%
+ultrasoft momentum
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+if you want to look at these logarithms
+
+ align:start position:0%
+if you want to look at these logarithms
+ 
+
+ align:start position:0%
+if you want to look at these logarithms
+and you ask what scale is this effective
+
+ align:start position:0%
+and you ask what scale is this effective
+ 
+
+ align:start position:0%
+and you ask what scale is this effective
+field of theory diagram
+
+ align:start position:0%
+field of theory diagram
+ 
+
+ align:start position:0%
+field of theory diagram
+sensitive to it's sensitive to the
+
+ align:start position:0%
+sensitive to it's sensitive to the
+ 
+
+ align:start position:0%
+sensitive to it's sensitive to the
+ultrasound scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the logs are not large logs they're
+
+ align:start position:0%
+so the logs are not large logs they're
+ 
+
+ align:start position:0%
+so the logs are not large logs they're
+order one logs
+
+ align:start position:0%
+order one logs
+ 
+
+ align:start position:0%
+order one logs
+as long as mu squared mu is
+
+ align:start position:0%
+as long as mu squared mu is
+ 
+
+ align:start position:0%
+as long as mu squared mu is
+of order lambda squared which is the
+
+ align:start position:0%
+of order lambda squared which is the
+ 
+
+ align:start position:0%
+of order lambda squared which is the
+scale for the for ultrasoft momentum and
+
+ align:start position:0%
+scale for the for ultrasoft momentum and
+ 
+
+ align:start position:0%
+scale for the for ultrasoft momentum and
+that's what we expect from this ultra
+
+ align:start position:0%
+that's what we expect from this ultra
+ 
+
+ align:start position:0%
+that's what we expect from this ultra
+soft diagram that it's telling us about
+
+ align:start position:0%
+soft diagram that it's telling us about
+ 
+
+ align:start position:0%
+soft diagram that it's telling us about
+physics at the ultrasoft scale and
+
+ align:start position:0%
+physics at the ultrasoft scale and
+ 
+
+ align:start position:0%
+physics at the ultrasoft scale and
+that's what we see
+
+ align:start position:0%
+that's what we see
+ 
+
+ align:start position:0%
+that's what we see
+from setting things up
+
+ align:start position:0%
+from setting things up
+ 
+
+ align:start position:0%
+from setting things up
+doing the calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could also think about a wave
+
+ align:start position:0%
+so you could also think about a wave
+ 
+
+ align:start position:0%
+so you could also think about a wave
+function diagram with an ultrasoft gluon
+
+ align:start position:0%
+function diagram with an ultrasoft gluon
+ 
+
+ align:start position:0%
+function diagram with an ultrasoft gluon
+but this guy's zero
+
+ align:start position:0%
+but this guy's zero
+ 
+
+ align:start position:0%
+but this guy's zero
+since in feynman gage
+
+ align:start position:0%
+since in feynman gage
+ 
+
+ align:start position:0%
+since in feynman gage
+you just get n mu n mu which is zero
+
+ align:start position:0%
+you just get n mu n mu which is zero
+ 
+
+ align:start position:0%
+you just get n mu n mu which is zero
+so there's no
+
+ align:start position:0%
+so there's no
+ 
+
+ align:start position:0%
+so there's no
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+z for the
+
+ align:start position:0%
+z for the
+ 
+
+ align:start position:0%
+z for the
+linear quark field from an ultra soft
+
+ align:start position:0%
+linear quark field from an ultra soft
+ 
+
+ align:start position:0%
+linear quark field from an ultra soft
+loop is zero
+
+ align:start position:0%
+loop is zero
+ 
+
+ align:start position:0%
+loop is zero
+that wouldn't necessarily be true in
+
+ align:start position:0%
+that wouldn't necessarily be true in
+ 
+
+ align:start position:0%
+that wouldn't necessarily be true in
+some other gauge and some but in some
+
+ align:start position:0%
+some other gauge and some but in some
+ 
+
+ align:start position:0%
+some other gauge and some but in some
+other gauge this diagram would also
+
+ align:start position:0%
+other gauge this diagram would also
+ 
+
+ align:start position:0%
+other gauge this diagram would also
+change all the diagrams would change and
+
+ align:start position:0%
+change all the diagrams would change and
+ 
+
+ align:start position:0%
+change all the diagrams would change and
+so if there was a non-zero contribution
+
+ align:start position:0%
+so if there was a non-zero contribution
+ 
+
+ align:start position:0%
+so if there was a non-zero contribution
+in this diagram it would just be taken
+
+ align:start position:0%
+in this diagram it would just be taken
+ 
+
+ align:start position:0%
+in this diagram it would just be taken
+care of gauge invariants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then finally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's ultrasoft loop on the heavy
+
+ align:start position:0%
+there's ultrasoft loop on the heavy
+ 
+
+ align:start position:0%
+there's ultrasoft loop on the heavy
+quark
+
+ align:start position:0%
+quark
+ 
+
+ align:start position:0%
+quark
+and that actually just gives us that's
+
+ align:start position:0%
+and that actually just gives us that's
+ 
+
+ align:start position:0%
+and that actually just gives us that's
+an hqt diagram has nothing to do with
+
+ align:start position:0%
+an hqt diagram has nothing to do with
+ 
+
+ align:start position:0%
+an hqt diagram has nothing to do with
+the clinical quark
+
+ align:start position:0%
+the clinical quark
+ 
+
+ align:start position:0%
+the clinical quark
+so from that diagram we would just get
+
+ align:start position:0%
+so from that diagram we would just get
+ 
+
+ align:start position:0%
+so from that diagram we would just get
+the z factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the appropriate z factoring
+
+ align:start position:0%
+which is the appropriate z factoring
+ 
+
+ align:start position:0%
+which is the appropriate z factoring
+hqet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with r regulator
+
+ align:start position:0%
+with r regulator
+ 
+
+ align:start position:0%
+with r regulator
+if i specify ultraviolet and infrared
+
+ align:start position:0%
+if i specify ultraviolet and infrared
+ 
+
+ align:start position:0%
+if i specify ultraviolet and infrared
+divergences that's this
+
+ align:start position:0%
+divergences that's this
+ 
+
+ align:start position:0%
+divergences that's this
+and this infrared divergence here is
+
+ align:start position:0%
+and this infrared divergence here is
+ 
+
+ align:start position:0%
+and this infrared divergence here is
+actually exactly the same as the one
+
+ align:start position:0%
+actually exactly the same as the one
+ 
+
+ align:start position:0%
+actually exactly the same as the one
+that we had
+
+ align:start position:0%
+that we had
+ 
+
+ align:start position:0%
+that we had
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the ultrasoft sector is really
+
+ align:start position:0%
+okay so the ultrasoft sector is really
+ 
+
+ align:start position:0%
+okay so the ultrasoft sector is really
+just there's nothing really tricky about
+
+ align:start position:0%
+just there's nothing really tricky about
+ 
+
+ align:start position:0%
+just there's nothing really tricky about
+it it's just write down the diagrams do
+
+ align:start position:0%
+it it's just write down the diagrams do
+ 
+
+ align:start position:0%
+it it's just write down the diagrams do
+the loops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isn't that like uh higher emergencies of
+
+ align:start position:0%
+isn't that like uh higher emergencies of
+ 
+
+ align:start position:0%
+isn't that like uh higher emergencies of
+those diagrams cancer without we never
+
+ align:start position:0%
+those diagrams cancer without we never
+ 
+
+ align:start position:0%
+those diagrams cancer without we never
+really ever mentioned elevators or for
+
+ align:start position:0%
+really ever mentioned elevators or for
+ 
+
+ align:start position:0%
+really ever mentioned elevators or for
+the initial variable
+
+ align:start position:0%
+the initial variable
+ 
+
+ align:start position:0%
+the initial variable
+um it depends so what are we looking at
+
+ align:start position:0%
+um it depends so what are we looking at
+ 
+
+ align:start position:0%
+um it depends so what are we looking at
+right so it depends on what we're
+
+ align:start position:0%
+right so it depends on what we're
+ 
+
+ align:start position:0%
+right so it depends on what we're
+looking at at here
+
+ align:start position:0%
+looking at at here
+ 
+
+ align:start position:0%
+looking at at here
+and what i'm doing
+
+ align:start position:0%
+and what i'm doing
+ 
+
+ align:start position:0%
+and what i'm doing
+so yes in general that would be true
+
+ align:start position:0%
+so yes in general that would be true
+ 
+
+ align:start position:0%
+so yes in general that would be true
+right if you were calculating some cross
+
+ align:start position:0%
+right if you were calculating some cross
+ 
+
+ align:start position:0%
+right if you were calculating some cross
+section which was ir finite cross
+
+ align:start position:0%
+section which was ir finite cross
+ 
+
+ align:start position:0%
+section which was ir finite cross
+section and
+
+ align:start position:0%
+section and
+ 
+
+ align:start position:0%
+section and
+you that of course would depend on
+
+ align:start position:0%
+you that of course would depend on
+ 
+
+ align:start position:0%
+you that of course would depend on
+defining what you mean by measuring this
+
+ align:start position:0%
+defining what you mean by measuring this
+ 
+
+ align:start position:0%
+defining what you mean by measuring this
+quark
+
+ align:start position:0%
+quark
+ 
+
+ align:start position:0%
+quark
+right so the ir divergence would become
+
+ align:start position:0%
+right so the ir divergence would become
+ 
+
+ align:start position:0%
+right so the ir divergence would become
+some physical scale like you know the
+
+ align:start position:0%
+some physical scale like you know the
+ 
+
+ align:start position:0%
+some physical scale like you know the
+mass of the jet or the
+
+ align:start position:0%
+mass of the jet or the
+ 
+
+ align:start position:0%
+mass of the jet or the
+some some something the ir divergences
+
+ align:start position:0%
+some some something the ir divergences
+ 
+
+ align:start position:0%
+some some something the ir divergences
+would turn into something physical right
+
+ align:start position:0%
+would turn into something physical right
+ 
+
+ align:start position:0%
+would turn into something physical right
+if you put this into a physical cross
+
+ align:start position:0%
+if you put this into a physical cross
+ 
+
+ align:start position:0%
+if you put this into a physical cross
+section
+
+ align:start position:0%
+section
+ 
+
+ align:start position:0%
+section
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that's exactly basically what would
+
+ align:start position:0%
+and that's exactly basically what would
+ 
+
+ align:start position:0%
+and that's exactly basically what would
+happen these p squares would become sort
+
+ align:start position:0%
+happen these p squares would become sort
+ 
+
+ align:start position:0%
+happen these p squares would become sort
+of the mx squareds that we talked about
+
+ align:start position:0%
+of the mx squareds that we talked about
+ 
+
+ align:start position:0%
+of the mx squareds that we talked about
+when we talked about
+
+ align:start position:0%
+when we talked about
+ 
+
+ align:start position:0%
+when we talked about
+bds gamma
+
+ align:start position:0%
+bds gamma
+ 
+
+ align:start position:0%
+bds gamma
+but here what we're interested in doing
+
+ align:start position:0%
+but here what we're interested in doing
+ 
+
+ align:start position:0%
+but here what we're interested in doing
+is a matching calculation so we fix
+
+ align:start position:0%
+is a matching calculation so we fix
+ 
+
+ align:start position:0%
+is a matching calculation so we fix
+the external states to have a particular
+
+ align:start position:0%
+the external states to have a particular
+ 
+
+ align:start position:0%
+the external states to have a particular
+number of protons
+
+ align:start position:0%
+number of protons
+ 
+
+ align:start position:0%
+number of protons
+and we want to compare the full theory
+
+ align:start position:0%
+and we want to compare the full theory
+ 
+
+ align:start position:0%
+and we want to compare the full theory
+calculation of the effective theory the
+
+ align:start position:0%
+calculation of the effective theory the
+ 
+
+ align:start position:0%
+calculation of the effective theory the
+effect of theory should reproduce the
+
+ align:start position:0%
+effect of theory should reproduce the
+ 
+
+ align:start position:0%
+effect of theory should reproduce the
+infrared divergences
+
+ align:start position:0%
+infrared divergences
+ 
+
+ align:start position:0%
+infrared divergences
+so really all we care about is not that
+
+ align:start position:0%
+so really all we care about is not that
+ 
+
+ align:start position:0%
+so really all we care about is not that
+this is infrared finite
+
+ align:start position:0%
+this is infrared finite
+ 
+
+ align:start position:0%
+this is infrared finite
+but rather that it's got the right
+
+ align:start position:0%
+but rather that it's got the right
+ 
+
+ align:start position:0%
+but rather that it's got the right
+infra the effective theory has the same
+
+ align:start position:0%
+infra the effective theory has the same
+ 
+
+ align:start position:0%
+infra the effective theory has the same
+infrared divergences
+
+ align:start position:0%
+infrared divergences
+ 
+
+ align:start position:0%
+infrared divergences
+and we'll see that in the end what you
+
+ align:start position:0%
+and we'll see that in the end what you
+ 
+
+ align:start position:0%
+and we'll see that in the end what you
+can think about is rather than canceling
+
+ align:start position:0%
+can think about is rather than canceling
+ 
+
+ align:start position:0%
+can think about is rather than canceling
+infrared divergences as you're thinking
+
+ align:start position:0%
+infrared divergences as you're thinking
+ 
+
+ align:start position:0%
+infrared divergences as you're thinking
+in the full theory we've matched the
+
+ align:start position:0%
+in the full theory we've matched the
+ 
+
+ align:start position:0%
+in the full theory we've matched the
+full theory onto the effective theory
+
+ align:start position:0%
+full theory onto the effective theory
+ 
+
+ align:start position:0%
+full theory onto the effective theory
+and that matching gives us the wilson
+
+ align:start position:0%
+and that matching gives us the wilson
+ 
+
+ align:start position:0%
+and that matching gives us the wilson
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+and then we take the effect of theory
+
+ align:start position:0%
+and then we take the effect of theory
+ 
+
+ align:start position:0%
+and then we take the effect of theory
+and all the cancellations that you're
+
+ align:start position:0%
+and all the cancellations that you're
+ 
+
+ align:start position:0%
+and all the cancellations that you're
+thinking about between real and virtual
+
+ align:start position:0%
+thinking about between real and virtual
+ 
+
+ align:start position:0%
+thinking about between real and virtual
+graphs will occur in the effective
+
+ align:start position:0%
+graphs will occur in the effective
+ 
+
+ align:start position:0%
+graphs will occur in the effective
+theory too
+
+ align:start position:0%
+theory too
+ 
+
+ align:start position:0%
+theory too
+so you can just think about the
+
+ align:start position:0%
+so you can just think about the
+ 
+
+ align:start position:0%
+so you can just think about the
+effective theory virtual real graphs and
+
+ align:start position:0%
+effective theory virtual real graphs and
+ 
+
+ align:start position:0%
+effective theory virtual real graphs and
+then the cancellation will take place
+
+ align:start position:0%
+then the cancellation will take place
+ 
+
+ align:start position:0%
+then the cancellation will take place
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+but that then you're thinking about that
+
+ align:start position:0%
+but that then you're thinking about that
+ 
+
+ align:start position:0%
+but that then you're thinking about that
+cancellation later at a lower scale
+
+ align:start position:0%
+cancellation later at a lower scale
+ 
+
+ align:start position:0%
+cancellation later at a lower scale
+which is what you actually want to do
+
+ align:start position:0%
+which is what you actually want to do
+ 
+
+ align:start position:0%
+which is what you actually want to do
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+what i just was telling you about ir
+
+ align:start position:0%
+what i just was telling you about ir
+ 
+
+ align:start position:0%
+what i just was telling you about ir
+divergences becoming
+
+ align:start position:0%
+divergences becoming
+ 
+
+ align:start position:0%
+divergences becoming
+different things in the effect in the
+
+ align:start position:0%
+different things in the effect in the
+ 
+
+ align:start position:0%
+different things in the effect in the
+final state becomes very trivial once
+
+ align:start position:0%
+final state becomes very trivial once
+ 
+
+ align:start position:0%
+final state becomes very trivial once
+you're in the effective theory
+
+ align:start position:0%
+you're in the effective theory
+ 
+
+ align:start position:0%
+you're in the effective theory
+and we'll see sort of exactly how that
+
+ align:start position:0%
+and we'll see sort of exactly how that
+ 
+
+ align:start position:0%
+and we'll see sort of exactly how that
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+later on
+
+ align:start position:0%
+later on
+ 
+
+ align:start position:0%
+later on
+but first
+
+ align:start position:0%
+but first
+ 
+
+ align:start position:0%
+but first
+we have to
+
+ align:start position:0%
+we have to
+ 
+
+ align:start position:0%
+we have to
+talk about linear graphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the linear graphs we had graphs
+
+ align:start position:0%
+so in the linear graphs we had graphs
+ 
+
+ align:start position:0%
+so in the linear graphs we had graphs
+like this one where we could take a
+
+ align:start position:0%
+like this one where we could take a
+ 
+
+ align:start position:0%
+like this one where we could take a
+gluon out of the out of the
+
+ align:start position:0%
+gluon out of the out of the
+ 
+
+ align:start position:0%
+gluon out of the out of the
+vertex here that corresponds to taking
+
+ align:start position:0%
+vertex here that corresponds to taking
+ 
+
+ align:start position:0%
+vertex here that corresponds to taking
+it out of the wilson line
+
+ align:start position:0%
+it out of the wilson line
+ 
+
+ align:start position:0%
+it out of the wilson line
+so let's label the graph in the
+
+ align:start position:0%
+so let's label the graph in the
+ 
+
+ align:start position:0%
+so let's label the graph in the
+following way this will be k plus p this
+
+ align:start position:0%
+following way this will be k plus p this
+ 
+
+ align:start position:0%
+following way this will be k plus p this
+will be p
+
+ align:start position:0%
+will be p
+ 
+
+ align:start position:0%
+will be p
+this will be k
+
+ align:start position:0%
+this will be k
+ 
+
+ align:start position:0%
+this will be k
+and if we follow our rules for what this
+
+ align:start position:0%
+and if we follow our rules for what this
+ 
+
+ align:start position:0%
+and if we follow our rules for what this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+we would write a sum
+
+ align:start position:0%
+we would write a sum
+ 
+
+ align:start position:0%
+we would write a sum
+over labels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then an integral over residuals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me put the residual integral in
+
+ align:start position:0%
+and let me put the residual integral in
+ 
+
+ align:start position:0%
+and let me put the residual integral in
+dimensional regulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try to squeeze in everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which won't be possible but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to write out the components
+
+ align:start position:0%
+so i'm going to write out the components
+ 
+
+ align:start position:0%
+so i'm going to write out the components
+to make clear who's the residual and
+
+ align:start position:0%
+to make clear who's the residual and
+ 
+
+ align:start position:0%
+to make clear who's the residual and
+who's label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the denominator there's one more
+
+ align:start position:0%
+so in the denominator there's one more
+ 
+
+ align:start position:0%
+so in the denominator there's one more
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the plus guys are always residual the
+
+ align:start position:0%
+so the plus guys are always residual the
+ 
+
+ align:start position:0%
+so the plus guys are always residual the
+curve and the minuses are always labeled
+
+ align:start position:0%
+curve and the minuses are always labeled
+ 
+
+ align:start position:0%
+curve and the minuses are always labeled
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+the short way of saying what i'm trying
+
+ align:start position:0%
+the short way of saying what i'm trying
+ 
+
+ align:start position:0%
+the short way of saying what i'm trying
+to squeeze in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the denominator has these three
+
+ align:start position:0%
+okay so the denominator has these three
+ 
+
+ align:start position:0%
+okay so the denominator has these three
+terms this guy here this guy here and
+
+ align:start position:0%
+terms this guy here this guy here and
+ 
+
+ align:start position:0%
+terms this guy here this guy here and
+this guy here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when i label the diagram like this
+
+ align:start position:0%
+and when i label the diagram like this
+ 
+
+ align:start position:0%
+and when i label the diagram like this
+you should think
+
+ align:start position:0%
+you should think
+ 
+
+ align:start position:0%
+you should think
+that each of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a label and residual part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so k
+
+ align:start position:0%
+so k
+ 
+
+ align:start position:0%
+so k
+you can think of as a pair k label k
+
+ align:start position:0%
+you can think of as a pair k label k
+ 
+
+ align:start position:0%
+you can think of as a pair k label k
+residual for now
+
+ align:start position:0%
+residual for now
+ 
+
+ align:start position:0%
+residual for now
+and remember the importance of doing
+
+ align:start position:0%
+and remember the importance of doing
+ 
+
+ align:start position:0%
+and remember the importance of doing
+this the importance of doing this was
+
+ align:start position:0%
+this the importance of doing this was
+ 
+
+ align:start position:0%
+this the importance of doing this was
+related to always being able to identify
+
+ align:start position:0%
+related to always being able to identify
+ 
+
+ align:start position:0%
+related to always being able to identify
+what the lowest order term was on the
+
+ align:start position:0%
+what the lowest order term was on the
+ 
+
+ align:start position:0%
+what the lowest order term was on the
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+okay and that actually becomes more
+
+ align:start position:0%
+okay and that actually becomes more
+ 
+
+ align:start position:0%
+okay and that actually becomes more
+important once you start to think about
+
+ align:start position:0%
+important once you start to think about
+ 
+
+ align:start position:0%
+important once you start to think about
+diagrams where
+
+ align:start position:0%
+diagrams where
+ 
+
+ align:start position:0%
+diagrams where
+you would add like an extra ultrasoft
+
+ align:start position:0%
+you would add like an extra ultrasoft
+ 
+
+ align:start position:0%
+you would add like an extra ultrasoft
+gluon somewhere in this picture then
+
+ align:start position:0%
+gluon somewhere in this picture then
+ 
+
+ align:start position:0%
+gluon somewhere in this picture then
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+then of course when that ultra soft glue
+
+ align:start position:0%
+then of course when that ultra soft glue
+ 
+
+ align:start position:0%
+then of course when that ultra soft glue
+on feeds its way through this loop you
+
+ align:start position:0%
+on feeds its way through this loop you
+ 
+
+ align:start position:0%
+on feeds its way through this loop you
+got to make sure that it's only the
+
+ align:start position:0%
+got to make sure that it's only the
+ 
+
+ align:start position:0%
+got to make sure that it's only the
+lowest order piece
+
+ align:start position:0%
+lowest order piece
+ 
+
+ align:start position:0%
+lowest order piece
+that's showing up
+
+ align:start position:0%
+that's showing up
+ 
+
+ align:start position:0%
+that's showing up
+in this case here it's really just we
+
+ align:start position:0%
+in this case here it's really just we
+ 
+
+ align:start position:0%
+in this case here it's really just we
+just have a linear loop
+
+ align:start position:0%
+just have a linear loop
+ 
+
+ align:start position:0%
+just have a linear loop
+and we don't have any sort of
+
+ align:start position:0%
+and we don't have any sort of
+ 
+
+ align:start position:0%
+and we don't have any sort of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+real ultrasoft momentum from ultrasoft
+
+ align:start position:0%
+real ultrasoft momentum from ultrasoft
+ 
+
+ align:start position:0%
+real ultrasoft momentum from ultrasoft
+particles besides the heavy quark
+
+ align:start position:0%
+particles besides the heavy quark
+ 
+
+ align:start position:0%
+particles besides the heavy quark
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which is just an external particle to
+
+ align:start position:0%
+which is just an external particle to
+ 
+
+ align:start position:0%
+which is just an external particle to
+the loop
+
+ align:start position:0%
+the loop
+ 
+
+ align:start position:0%
+the loop
+so what we want to do with this is we
+
+ align:start position:0%
+so what we want to do with this is we
+ 
+
+ align:start position:0%
+so what we want to do with this is we
+want to turn it back into an integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh just let me say it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if it wasn't for these restrictions
+
+ align:start position:0%
+and if it wasn't for these restrictions
+ 
+
+ align:start position:0%
+and if it wasn't for these restrictions
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+then that's very easy actually
+
+ align:start position:0%
+then that's very easy actually
+ 
+
+ align:start position:0%
+then that's very easy actually
+so i claim and then i'll talk about why
+
+ align:start position:0%
+so i claim and then i'll talk about why
+ 
+
+ align:start position:0%
+so i claim and then i'll talk about why
+it's true
+
+ align:start position:0%
+it's true
+ 
+
+ align:start position:0%
+it's true
+i claim that if we ignored the
+
+ align:start position:0%
+i claim that if we ignored the
+ 
+
+ align:start position:0%
+i claim that if we ignored the
+restrictions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those restrictions are ensuring that
+
+ align:start position:0%
+and those restrictions are ensuring that
+ 
+
+ align:start position:0%
+and those restrictions are ensuring that
+we don't double count
+
+ align:start position:0%
+we don't double count
+ 
+
+ align:start position:0%
+we don't double count
+between our linear and our ultrasoft
+
+ align:start position:0%
+between our linear and our ultrasoft
+ 
+
+ align:start position:0%
+between our linear and our ultrasoft
+degrees of freedom so they are important
+
+ align:start position:0%
+degrees of freedom so they are important
+ 
+
+ align:start position:0%
+degrees of freedom so they are important
+but let's ignore them for a minute if we
+
+ align:start position:0%
+but let's ignore them for a minute if we
+ 
+
+ align:start position:0%
+but let's ignore them for a minute if we
+do ignore them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we would just get the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where i just basically stop thinking
+
+ align:start position:0%
+where i just basically stop thinking
+ 
+
+ align:start position:0%
+where i just basically stop thinking
+about residuals and labels write
+
+ align:start position:0%
+about residuals and labels write
+ 
+
+ align:start position:0%
+about residuals and labels write
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+as a full momentum and write down
+
+ align:start position:0%
+as a full momentum and write down
+ 
+
+ align:start position:0%
+as a full momentum and write down
+exactly the same thing i just wrote
+
+ align:start position:0%
+exactly the same thing i just wrote
+ 
+
+ align:start position:0%
+exactly the same thing i just wrote
+so this is a full k squared
+
+ align:start position:0%
+so this is a full k squared
+ 
+
+ align:start position:0%
+so this is a full k squared
+and this is the full k plus p squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i'm going to do is i'm going to
+
+ align:start position:0%
+so what i'm going to do is i'm going to
+ 
+
+ align:start position:0%
+so what i'm going to do is i'm going to
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+ignore these relabel these restrictions
+
+ align:start position:0%
+ignore these relabel these restrictions
+ 
+
+ align:start position:0%
+ignore these relabel these restrictions
+and then i'm going to tell you how it
+
+ align:start position:0%
+and then i'm going to tell you how it
+ 
+
+ align:start position:0%
+and then i'm going to tell you how it
+would work how like this actually does
+
+ align:start position:0%
+would work how like this actually does
+ 
+
+ align:start position:0%
+would work how like this actually does
+turn into this
+
+ align:start position:0%
+turn into this
+ 
+
+ align:start position:0%
+turn into this
+what are the rules for doing that
+
+ align:start position:0%
+what are the rules for doing that
+ 
+
+ align:start position:0%
+what are the rules for doing that
+and then i'll come back and i'll tell
+
+ align:start position:0%
+and then i'll come back and i'll tell
+ 
+
+ align:start position:0%
+and then i'll come back and i'll tell
+you what what these extra
+
+ align:start position:0%
+you what what these extra
+ 
+
+ align:start position:0%
+you what what these extra
+conditions do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so really in order to see
+
+ align:start position:0%
+so really in order to see
+ 
+
+ align:start position:0%
+so really in order to see
+so this is this looks like maybe it's
+
+ align:start position:0%
+so this is this looks like maybe it's
+ 
+
+ align:start position:0%
+so this is this looks like maybe it's
+trivial but
+
+ align:start position:0%
+trivial but
+ 
+
+ align:start position:0%
+trivial but
+we should think about it and
+
+ align:start position:0%
+we should think about it and
+ 
+
+ align:start position:0%
+we should think about it and
+uh it's almost trivial but not quite so
+
+ align:start position:0%
+uh it's almost trivial but not quite so
+ 
+
+ align:start position:0%
+uh it's almost trivial but not quite so
+really what we're doing here is we're
+
+ align:start position:0%
+really what we're doing here is we're
+ 
+
+ align:start position:0%
+really what we're doing here is we're
+combining back together labels in
+
+ align:start position:0%
+combining back together labels in
+ 
+
+ align:start position:0%
+combining back together labels in
+residual momentum right
+
+ align:start position:0%
+residual momentum right
+ 
+
+ align:start position:0%
+residual momentum right
+and the place that we have to worry
+
+ align:start position:0%
+and the place that we have to worry
+ 
+
+ align:start position:0%
+and the place that we have to worry
+about that is in the perp and the minus
+
+ align:start position:0%
+about that is in the perp and the minus
+ 
+
+ align:start position:0%
+about that is in the perp and the minus
+space and recall we have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grid and the grid is sort of our way of
+
+ align:start position:0%
+grid and the grid is sort of our way of
+ 
+
+ align:start position:0%
+grid and the grid is sort of our way of
+got our guiding
+
+ align:start position:0%
+got our guiding
+ 
+
+ align:start position:0%
+got our guiding
+our guidance to sort of see how to put
+
+ align:start position:0%
+our guidance to sort of see how to put
+ 
+
+ align:start position:0%
+our guidance to sort of see how to put
+things back together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we had vectors that lived in this
+
+ align:start position:0%
+so we had vectors that lived in this
+ 
+
+ align:start position:0%
+so we had vectors that lived in this
+space and
+
+ align:start position:0%
+space and
+ 
+
+ align:start position:0%
+space and
+you know this is the label and then
+
+ align:start position:0%
+you know this is the label and then
+ 
+
+ align:start position:0%
+you know this is the label and then
+there's the residual if we want to point
+
+ align:start position:0%
+there's the residual if we want to point
+ 
+
+ align:start position:0%
+there's the residual if we want to point
+to some place in that space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this picture was like a wilsonian
+
+ align:start position:0%
+this picture was like a wilsonian
+ 
+
+ align:start position:0%
+this picture was like a wilsonian
+effective field theory
+
+ align:start position:0%
+effective field theory
+ 
+
+ align:start position:0%
+effective field theory
+because the picture makes you think of
+
+ align:start position:0%
+because the picture makes you think of
+ 
+
+ align:start position:0%
+because the picture makes you think of
+sharp edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the real effective theory that we're
+
+ align:start position:0%
+but the real effective theory that we're
+ 
+
+ align:start position:0%
+but the real effective theory that we're
+doing is a continuum one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you have to expand your brain a
+
+ align:start position:0%
+and so you have to expand your brain a
+ 
+
+ align:start position:0%
+and so you have to expand your brain a
+little bit and think that each of the
+
+ align:start position:0%
+little bit and think that each of the
+ 
+
+ align:start position:0%
+little bit and think that each of the
+boxes in this picture is actually
+
+ align:start position:0%
+boxes in this picture is actually
+ 
+
+ align:start position:0%
+boxes in this picture is actually
+an infinite space as well
+
+ align:start position:0%
+an infinite space as well
+ 
+
+ align:start position:0%
+an infinite space as well
+because the residual space doesn't have
+
+ align:start position:0%
+because the residual space doesn't have
+ 
+
+ align:start position:0%
+because the residual space doesn't have
+restrictions like that that would spoil
+
+ align:start position:0%
+restrictions like that that would spoil
+ 
+
+ align:start position:0%
+restrictions like that that would spoil
+lorenz symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so each grid point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really is specifying an infinite
+
+ align:start position:0%
+really is specifying an infinite
+ 
+
+ align:start position:0%
+really is specifying an infinite
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of residual manta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it's r4 i mean or it's minkowski space
+
+ align:start position:0%
+it's r4 i mean or it's minkowski space
+ 
+
+ align:start position:0%
+it's r4 i mean or it's minkowski space
+so the momenta components are real
+
+ align:start position:0%
+so the momenta components are real
+ 
+
+ align:start position:0%
+so the momenta components are real
+numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's some rules so what are the rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you what the rules are without
+
+ align:start position:0%
+i'll tell you what the rules are without
+ 
+
+ align:start position:0%
+i'll tell you what the rules are without
+restrictions for now
+
+ align:start position:0%
+restrictions for now
+ 
+
+ align:start position:0%
+restrictions for now
+and then we'll come back and i'll tell
+
+ align:start position:0%
+and then we'll come back and i'll tell
+ 
+
+ align:start position:0%
+and then we'll come back and i'll tell
+you what the rules are with restrictions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so rule number one is the simplest and
+
+ align:start position:0%
+so rule number one is the simplest and
+ 
+
+ align:start position:0%
+so rule number one is the simplest and
+it just says that say i had a
+
+ align:start position:0%
+it just says that say i had a
+ 
+
+ align:start position:0%
+it just says that say i had a
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+i'll use kind of a one-dimensional
+
+ align:start position:0%
+i'll use kind of a one-dimensional
+ 
+
+ align:start position:0%
+i'll use kind of a one-dimensional
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+say i had a sum over kl's and an
+
+ align:start position:0%
+say i had a sum over kl's and an
+ 
+
+ align:start position:0%
+say i had a sum over kl's and an
+integral over all kr's
+
+ align:start position:0%
+integral over all kr's
+ 
+
+ align:start position:0%
+integral over all kr's
+well that's just the same as not having
+
+ align:start position:0%
+well that's just the same as not having
+ 
+
+ align:start position:0%
+well that's just the same as not having
+split it up and doing an integral over
+
+ align:start position:0%
+split it up and doing an integral over
+ 
+
+ align:start position:0%
+split it up and doing an integral over
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+because we split this thing into boxes
+
+ align:start position:0%
+because we split this thing into boxes
+ 
+
+ align:start position:0%
+because we split this thing into boxes
+and if we really integrate over all
+
+ align:start position:0%
+and if we really integrate over all
+ 
+
+ align:start position:0%
+and if we really integrate over all
+boxes and
+
+ align:start position:0%
+boxes and
+ 
+
+ align:start position:0%
+boxes and
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+sum over all labels then we should just
+
+ align:start position:0%
+sum over all labels then we should just
+ 
+
+ align:start position:0%
+sum over all labels then we should just
+get back the full integration over all
+
+ align:start position:0%
+get back the full integration over all
+ 
+
+ align:start position:0%
+get back the full integration over all
+the momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's true for each
+
+ align:start position:0%
+so that's true for each
+ 
+
+ align:start position:0%
+so that's true for each
+for minus and momenta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but really what we have to do
+
+ align:start position:0%
+but really what we have to do
+ 
+
+ align:start position:0%
+but really what we have to do
+is we have to do this with some
+
+ align:start position:0%
+is we have to do this with some
+ 
+
+ align:start position:0%
+is we have to do this with some
+integrand right so
+
+ align:start position:0%
+integrand right so
+ 
+
+ align:start position:0%
+integrand right so
+the type of integrand that we have is
+
+ align:start position:0%
+the type of integrand that we have is
+ 
+
+ align:start position:0%
+the type of integrand that we have is
+this following
+
+ align:start position:0%
+this following
+ 
+
+ align:start position:0%
+this following
+if you think about the components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you think about the components that
+
+ align:start position:0%
+if you think about the components that
+ 
+
+ align:start position:0%
+if you think about the components that
+we're talking about here
+
+ align:start position:0%
+we're talking about here
+ 
+
+ align:start position:0%
+we're talking about here
+which are the minus and perp ones
+
+ align:start position:0%
+which are the minus and perp ones
+ 
+
+ align:start position:0%
+which are the minus and perp ones
+then there's in our integrand up there
+
+ align:start position:0%
+then there's in our integrand up there
+ 
+
+ align:start position:0%
+then there's in our integrand up there
+there's no minus or perp
+
+ align:start position:0%
+there's no minus or perp
+ 
+
+ align:start position:0%
+there's no minus or perp
+residuals
+
+ align:start position:0%
+residuals
+ 
+
+ align:start position:0%
+residuals
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's just a function of the labels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so what that says effectively is
+
+ align:start position:0%
+and so what that says effectively is
+ 
+
+ align:start position:0%
+and so what that says effectively is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this is a constant function in in this
+
+ align:start position:0%
+this is a constant function in in this
+ 
+
+ align:start position:0%
+this is a constant function in in this
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+in each of the boxes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and effectively the way that you use
+
+ align:start position:0%
+and effectively the way that you use
+ 
+
+ align:start position:0%
+and effectively the way that you use
+this formula as you do the following
+
+ align:start position:0%
+this formula as you do the following
+ 
+
+ align:start position:0%
+this formula as you do the following
+you say well if it's a constant function
+
+ align:start position:0%
+you say well if it's a constant function
+ 
+
+ align:start position:0%
+you say well if it's a constant function
+in the box
+
+ align:start position:0%
+in the box
+ 
+
+ align:start position:0%
+in the box
+i could evaluate at a different point in
+
+ align:start position:0%
+i could evaluate at a different point in
+ 
+
+ align:start position:0%
+i could evaluate at a different point in
+the box and i'd still get the same value
+
+ align:start position:0%
+the box and i'd still get the same value
+ 
+
+ align:start position:0%
+the box and i'd still get the same value
+so in particular i could evaluate it k
+
+ align:start position:0%
+so in particular i could evaluate it k
+ 
+
+ align:start position:0%
+so in particular i could evaluate it k
+label plus k residual
+
+ align:start position:0%
+label plus k residual
+ 
+
+ align:start position:0%
+label plus k residual
+and then i can use that formula up there
+
+ align:start position:0%
+and then i can use that formula up there
+ 
+
+ align:start position:0%
+and then i can use that formula up there
+to say that this is just an integral
+
+ align:start position:0%
+to say that this is just an integral
+ 
+
+ align:start position:0%
+to say that this is just an integral
+with a continuous k
+
+ align:start position:0%
+with a continuous k
+ 
+
+ align:start position:0%
+with a continuous k
+of the function evaluated at that
+
+ align:start position:0%
+of the function evaluated at that
+ 
+
+ align:start position:0%
+of the function evaluated at that
+continuous k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the way that sort of number
+
+ align:start position:0%
+so that's the way that sort of number
+ 
+
+ align:start position:0%
+so that's the way that sort of number
+one works
+
+ align:start position:0%
+one works
+ 
+
+ align:start position:0%
+one works
+we are integrating functions that are
+
+ align:start position:0%
+we are integrating functions that are
+ 
+
+ align:start position:0%
+we are integrating functions that are
+constant in the boxes and so then it's
+
+ align:start position:0%
+constant in the boxes and so then it's
+ 
+
+ align:start position:0%
+constant in the boxes and so then it's
+kind of trivial that we just how to put
+
+ align:start position:0%
+kind of trivial that we just how to put
+ 
+
+ align:start position:0%
+kind of trivial that we just how to put
+the boxes back together
+
+ align:start position:0%
+the boxes back together
+ 
+
+ align:start position:0%
+the boxes back together
+yeah so this uh
+
+ align:start position:0%
+yeah so this uh
+ 
+
+ align:start position:0%
+yeah so this uh
+dk identification doesn't have k out of
+
+ align:start position:0%
+dk identification doesn't have k out of
+ 
+
+ align:start position:0%
+dk identification doesn't have k out of
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+yeah so what i mean by it is
+
+ align:start position:0%
+yeah so what i mean by it is
+ 
+
+ align:start position:0%
+yeah so what i mean by it is
+yeah so each of so i'm using here
+
+ align:start position:0%
+yeah so each of so i'm using here
+ 
+
+ align:start position:0%
+yeah so each of so i'm using here
+for each minus or perp momenta a
+
+ align:start position:0%
+for each minus or perp momenta a
+ 
+
+ align:start position:0%
+for each minus or perp momenta a
+one-dimensional notation yeah and so i
+
+ align:start position:0%
+one-dimensional notation yeah and so i
+ 
+
+ align:start position:0%
+one-dimensional notation yeah and so i
+have three of these i have to do this
+
+ align:start position:0%
+have three of these i have to do this
+ 
+
+ align:start position:0%
+have three of these i have to do this
+and for each one of them it's true that
+
+ align:start position:0%
+and for each one of them it's true that
+ 
+
+ align:start position:0%
+and for each one of them it's true that
+what i'm saying
+
+ align:start position:0%
+what i'm saying
+ 
+
+ align:start position:0%
+what i'm saying
+but of course if i tried to write that
+
+ align:start position:0%
+but of course if i tried to write that
+ 
+
+ align:start position:0%
+but of course if i tried to write that
+on the board then it would confuse the
+
+ align:start position:0%
+on the board then it would confuse the
+ 
+
+ align:start position:0%
+on the board then it would confuse the
+point i think
+
+ align:start position:0%
+point i think
+ 
+
+ align:start position:0%
+point i think
+which is some sense a simple point
+
+ align:start position:0%
+which is some sense a simple point
+ 
+
+ align:start position:0%
+which is some sense a simple point
+okay so this is in some sense saying
+
+ align:start position:0%
+okay so this is in some sense saying
+ 
+
+ align:start position:0%
+okay so this is in some sense saying
+that this whole split up that we were
+
+ align:start position:0%
+that this whole split up that we were
+ 
+
+ align:start position:0%
+that this whole split up that we were
+doing was not really needed we could
+
+ align:start position:0%
+doing was not really needed we could
+ 
+
+ align:start position:0%
+doing was not really needed we could
+have just written a continuous integral
+
+ align:start position:0%
+have just written a continuous integral
+ 
+
+ align:start position:0%
+have just written a continuous integral
+and that's kind of what this is saying
+
+ align:start position:0%
+and that's kind of what this is saying
+ 
+
+ align:start position:0%
+and that's kind of what this is saying
+right that
+
+ align:start position:0%
+right that
+ 
+
+ align:start position:0%
+right that
+we could have just written a continuous
+
+ align:start position:0%
+we could have just written a continuous
+ 
+
+ align:start position:0%
+we could have just written a continuous
+integral and not worried so much about
+
+ align:start position:0%
+integral and not worried so much about
+ 
+
+ align:start position:0%
+integral and not worried so much about
+all the split up that we were doing
+
+ align:start position:0%
+all the split up that we were doing
+ 
+
+ align:start position:0%
+all the split up that we were doing
+the place that that we have to be
+
+ align:start position:0%
+the place that that we have to be
+ 
+
+ align:start position:0%
+the place that that we have to be
+careful about is these restrictions and
+
+ align:start position:0%
+careful about is these restrictions and
+ 
+
+ align:start position:0%
+careful about is these restrictions and
+we'll come back to that
+
+ align:start position:0%
+we'll come back to that
+ 
+
+ align:start position:0%
+we'll come back to that
+and the other place they have to be
+
+ align:start position:0%
+and the other place they have to be
+ 
+
+ align:start position:0%
+and the other place they have to be
+careful about is when you have the
+
+ align:start position:0%
+careful about is when you have the
+ 
+
+ align:start position:0%
+careful about is when you have the
+multiple expansion but as long as you
+
+ align:start position:0%
+multiple expansion but as long as you
+ 
+
+ align:start position:0%
+multiple expansion but as long as you
+sort of take care of that then basically
+
+ align:start position:0%
+sort of take care of that then basically
+ 
+
+ align:start position:0%
+sort of take care of that then basically
+this is always
+
+ align:start position:0%
+this is always
+ 
+
+ align:start position:0%
+this is always
+is always happening
+
+ align:start position:0%
+is always happening
+ 
+
+ align:start position:0%
+is always happening
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the reason why this works
+
+ align:start position:0%
+the reason why this works
+ 
+
+ align:start position:0%
+the reason why this works
+is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for every label loop momentum that there
+
+ align:start position:0%
+for every label loop momentum that there
+ 
+
+ align:start position:0%
+for every label loop momentum that there
+is in any diagram
+
+ align:start position:0%
+is in any diagram
+ 
+
+ align:start position:0%
+is in any diagram
+there's always going to be some
+
+ align:start position:0%
+there's always going to be some
+ 
+
+ align:start position:0%
+there's always going to be some
+corresponding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+residual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's not specified by delta functions
+
+ align:start position:0%
+that's not specified by delta functions
+ 
+
+ align:start position:0%
+that's not specified by delta functions
+in terms of external momenta
+
+ align:start position:0%
+in terms of external momenta
+ 
+
+ align:start position:0%
+in terms of external momenta
+and effectively therefore we can that we
+
+ align:start position:0%
+and effectively therefore we can that we
+ 
+
+ align:start position:0%
+and effectively therefore we can that we
+can absorb
+
+ align:start position:0%
+can absorb
+ 
+
+ align:start position:0%
+can absorb
+in order to do what we just said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can always go back from
+
+ align:start position:0%
+so we can always go back from
+ 
+
+ align:start position:0%
+so we can always go back from
+this discrete type notation back to a
+
+ align:start position:0%
+this discrete type notation back to a
+ 
+
+ align:start position:0%
+this discrete type notation back to a
+continuous notation the discrete
+
+ align:start position:0%
+continuous notation the discrete
+ 
+
+ align:start position:0%
+continuous notation the discrete
+notation was just helping us to set up
+
+ align:start position:0%
+notation was just helping us to set up
+ 
+
+ align:start position:0%
+notation was just helping us to set up
+the expansion and be careful about it
+
+ align:start position:0%
+the expansion and be careful about it
+ 
+
+ align:start position:0%
+the expansion and be careful about it
+but we can always go back to the
+
+ align:start position:0%
+but we can always go back to the
+ 
+
+ align:start position:0%
+but we can always go back to the
+continuous one because there's always a
+
+ align:start position:0%
+continuous one because there's always a
+ 
+
+ align:start position:0%
+continuous one because there's always a
+kr
+
+ align:start position:0%
+kr
+ 
+
+ align:start position:0%
+kr
+that has this property that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in general though you might have
+
+ align:start position:0%
+now in general though you might have
+ 
+
+ align:start position:0%
+now in general though you might have
+some more complicated thing and if i'm
+
+ align:start position:0%
+some more complicated thing and if i'm
+ 
+
+ align:start position:0%
+some more complicated thing and if i'm
+going to give you some rules i should
+
+ align:start position:0%
+going to give you some rules i should
+ 
+
+ align:start position:0%
+going to give you some rules i should
+sort of give you a complete set
+
+ align:start position:0%
+sort of give you a complete set
+ 
+
+ align:start position:0%
+sort of give you a complete set
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we have to append our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our list of rules by the following one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i thought about doing what i just
+
+ align:start position:0%
+so if i thought about doing what i just
+ 
+
+ align:start position:0%
+so if i thought about doing what i just
+said over here but i went to some higher
+
+ align:start position:0%
+said over here but i went to some higher
+ 
+
+ align:start position:0%
+said over here but i went to some higher
+order then what could happen
+
+ align:start position:0%
+order then what could happen
+ 
+
+ align:start position:0%
+order then what could happen
+well then these kr minus and kr perps
+
+ align:start position:0%
+well then these kr minus and kr perps
+ 
+
+ align:start position:0%
+well then these kr minus and kr perps
+could show up
+
+ align:start position:0%
+could show up
+ 
+
+ align:start position:0%
+could show up
+they'd never show up in the denominator
+
+ align:start position:0%
+they'd never show up in the denominator
+ 
+
+ align:start position:0%
+they'd never show up in the denominator
+of our propagators if they were just
+
+ align:start position:0%
+of our propagators if they were just
+ 
+
+ align:start position:0%
+of our propagators if they were just
+linear propagators but they could show
+
+ align:start position:0%
+linear propagators but they could show
+ 
+
+ align:start position:0%
+linear propagators but they could show
+up at some point in the numerator
+
+ align:start position:0%
+up at some point in the numerator
+ 
+
+ align:start position:0%
+up at some point in the numerator
+and we need actually a rule like this
+
+ align:start position:0%
+and we need actually a rule like this
+ 
+
+ align:start position:0%
+and we need actually a rule like this
+one which is
+
+ align:start position:0%
+one which is
+ 
+
+ align:start position:0%
+one which is
+would be clear if we were regulating dkr
+
+ align:start position:0%
+would be clear if we were regulating dkr
+ 
+
+ align:start position:0%
+would be clear if we were regulating dkr
+in in dimensional organization that the
+
+ align:start position:0%
+in in dimensional organization that the
+ 
+
+ align:start position:0%
+in in dimensional organization that the
+power divergences are getting set to
+
+ align:start position:0%
+power divergences are getting set to
+ 
+
+ align:start position:0%
+power divergences are getting set to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and that is is basically to maintain the
+
+ align:start position:0%
+and that is is basically to maintain the
+ 
+
+ align:start position:0%
+and that is is basically to maintain the
+the rent symmetry in the residual space
+
+ align:start position:0%
+the rent symmetry in the residual space
+ 
+
+ align:start position:0%
+the rent symmetry in the residual space
+we need a rule like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for j greater than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that only comes in doesn't come into
+
+ align:start position:0%
+so that only comes in doesn't come into
+ 
+
+ align:start position:0%
+so that only comes in doesn't come into
+our calculation but
+
+ align:start position:0%
+our calculation but
+ 
+
+ align:start position:0%
+our calculation but
+include it for completeness
+
+ align:start position:0%
+include it for completeness
+ 
+
+ align:start position:0%
+include it for completeness
+so when would these integral over kr
+
+ align:start position:0%
+so when would these integral over kr
+ 
+
+ align:start position:0%
+so when would these integral over kr
+actually do something non-trivial it
+
+ align:start position:0%
+actually do something non-trivial it
+ 
+
+ align:start position:0%
+actually do something non-trivial it
+would do something non-trivial if we had
+
+ align:start position:0%
+would do something non-trivial if we had
+ 
+
+ align:start position:0%
+would do something non-trivial if we had
+ultra soft loops and collinear loops at
+
+ align:start position:0%
+ultra soft loops and collinear loops at
+ 
+
+ align:start position:0%
+ultra soft loops and collinear loops at
+the same time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the case where we just have
+
+ align:start position:0%
+so in the case where we just have
+ 
+
+ align:start position:0%
+so in the case where we just have
+collinear loops it's basically up to
+
+ align:start position:0%
+collinear loops it's basically up to
+ 
+
+ align:start position:0%
+collinear loops it's basically up to
+this issue about the restrictions that
+
+ align:start position:0%
+this issue about the restrictions that
+ 
+
+ align:start position:0%
+this issue about the restrictions that
+we'll talk about it's basically that we
+
+ align:start position:0%
+we'll talk about it's basically that we
+ 
+
+ align:start position:0%
+we'll talk about it's basically that we
+just could have done everything as
+
+ align:start position:0%
+just could have done everything as
+ 
+
+ align:start position:0%
+just could have done everything as
+continuous and ignored this
+
+ align:start position:0%
+continuous and ignored this
+ 
+
+ align:start position:0%
+continuous and ignored this
+this split
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if we have both ultrasoft particles
+
+ align:start position:0%
+but if we have both ultrasoft particles
+ 
+
+ align:start position:0%
+but if we have both ultrasoft particles
+that are sort of participating through
+
+ align:start position:0%
+that are sort of participating through
+ 
+
+ align:start position:0%
+that are sort of participating through
+the loops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+or and and or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then these will give non-trivial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general these will give non-trivial
+
+ align:start position:0%
+in general these will give non-trivial
+ 
+
+ align:start position:0%
+in general these will give non-trivial
+loop momenta
+
+ align:start position:0%
+loop momenta
+ 
+
+ align:start position:0%
+loop momenta
+in the residual momentum
+
+ align:start position:0%
+in the residual momentum
+ 
+
+ align:start position:0%
+in the residual momentum
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+hence there will be some that we can't
+
+ align:start position:0%
+hence there will be some that we can't
+ 
+
+ align:start position:0%
+hence there will be some that we can't
+just absorb in the fashion that we just
+
+ align:start position:0%
+just absorb in the fashion that we just
+ 
+
+ align:start position:0%
+just absorb in the fashion that we just
+said so there will be
+
+ align:start position:0%
+said so there will be
+ 
+
+ align:start position:0%
+said so there will be
+in this situation
+
+ align:start position:0%
+in this situation
+ 
+
+ align:start position:0%
+in this situation
+residual momentum some residual momentum
+
+ align:start position:0%
+residual momentum some residual momentum
+ 
+
+ align:start position:0%
+residual momentum some residual momentum
+will be absorbed in the same way to turn
+
+ align:start position:0%
+will be absorbed in the same way to turn
+ 
+
+ align:start position:0%
+will be absorbed in the same way to turn
+the integrals into continuous ones but
+
+ align:start position:0%
+the integrals into continuous ones but
+ 
+
+ align:start position:0%
+the integrals into continuous ones but
+other ones won't be absorbed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's because the ultrasoft
+
+ align:start position:0%
+and that's because the ultrasoft
+ 
+
+ align:start position:0%
+and that's because the ultrasoft
+propagators rate would involve l r
+
+ align:start position:0%
+propagators rate would involve l r
+ 
+
+ align:start position:0%
+propagators rate would involve l r
+the lr plus the lr minus and the lr perp
+
+ align:start position:0%
+the lr plus the lr minus and the lr perp
+ 
+
+ align:start position:0%
+the lr plus the lr minus and the lr perp
+in the denominator
+
+ align:start position:0%
+in the denominator
+ 
+
+ align:start position:0%
+in the denominator
+so we don't have this rule to apply we
+
+ align:start position:0%
+so we don't have this rule to apply we
+ 
+
+ align:start position:0%
+so we don't have this rule to apply we
+can't do what we said here with the
+
+ align:start position:0%
+can't do what we said here with the
+ 
+
+ align:start position:0%
+can't do what we said here with the
+constant boxes because now the functions
+
+ align:start position:0%
+constant boxes because now the functions
+ 
+
+ align:start position:0%
+constant boxes because now the functions
+are depending on that variable
+
+ align:start position:0%
+are depending on that variable
+ 
+
+ align:start position:0%
+are depending on that variable
+so we just have to do the integral
+
+ align:start position:0%
+so we just have to do the integral
+ 
+
+ align:start position:0%
+so we just have to do the integral
+so you could have something that looks
+
+ align:start position:0%
+so you could have something that looks
+ 
+
+ align:start position:0%
+so you could have something that looks
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just in kind of a schematic formula
+
+ align:start position:0%
+just in kind of a schematic formula
+ 
+
+ align:start position:0%
+just in kind of a schematic formula
+let's have there be two kr and an lr
+
+ align:start position:0%
+let's have there be two kr and an lr
+ 
+
+ align:start position:0%
+let's have there be two kr and an lr
+we're in kind of an obvious notation
+
+ align:start position:0%
+we're in kind of an obvious notation
+ 
+
+ align:start position:0%
+we're in kind of an obvious notation
+i'm saying that the function could
+
+ align:start position:0%
+i'm saying that the function could
+ 
+
+ align:start position:0%
+i'm saying that the function could
+depend on lr residual it doesn't depend
+
+ align:start position:0%
+depend on lr residual it doesn't depend
+ 
+
+ align:start position:0%
+depend on lr residual it doesn't depend
+on kr residuals so we absorb kr back
+
+ align:start position:0%
+on kr residuals so we absorb kr back
+ 
+
+ align:start position:0%
+on kr residuals so we absorb kr back
+into the sum to make it continuous and
+
+ align:start position:0%
+into the sum to make it continuous and
+ 
+
+ align:start position:0%
+into the sum to make it continuous and
+then this integral we just have to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but it's still
+
+ align:start position:0%
+okay but it's still
+ 
+
+ align:start position:0%
+okay but it's still
+we're still in the end just doing an
+
+ align:start position:0%
+we're still in the end just doing an
+ 
+
+ align:start position:0%
+we're still in the end just doing an
+interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come from ultra soft propagators for
+
+ align:start position:0%
+come from ultra soft propagators for
+ 
+
+ align:start position:0%
+come from ultra soft propagators for
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those are the kind of different
+
+ align:start position:0%
+okay so those are the kind of different
+ 
+
+ align:start position:0%
+okay so those are the kind of different
+cases that you can get but nevertheless
+
+ align:start position:0%
+cases that you can get but nevertheless
+ 
+
+ align:start position:0%
+cases that you can get but nevertheless
+even if you have ultrasoft particles and
+
+ align:start position:0%
+even if you have ultrasoft particles and
+ 
+
+ align:start position:0%
+even if you have ultrasoft particles and
+propagators floating around there will
+
+ align:start position:0%
+propagators floating around there will
+ 
+
+ align:start position:0%
+propagators floating around there will
+always be a residual momentum associated
+
+ align:start position:0%
+always be a residual momentum associated
+ 
+
+ align:start position:0%
+always be a residual momentum associated
+to the sort of what we were doing over
+
+ align:start position:0%
+to the sort of what we were doing over
+ 
+
+ align:start position:0%
+to the sort of what we were doing over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+that you can absorb in the same way i
+
+ align:start position:0%
+that you can absorb in the same way i
+ 
+
+ align:start position:0%
+that you can absorb in the same way i
+i stated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's proceed along these lines and
+
+ align:start position:0%
+so let's proceed along these lines and
+ 
+
+ align:start position:0%
+so let's proceed along these lines and
+see where it takes us and then we'll
+
+ align:start position:0%
+see where it takes us and then we'll
+ 
+
+ align:start position:0%
+see where it takes us and then we'll
+come back and put in this
+
+ align:start position:0%
+come back and put in this
+ 
+
+ align:start position:0%
+come back and put in this
+additional restrictions
+
+ align:start position:0%
+additional restrictions
+ 
+
+ align:start position:0%
+additional restrictions
+will you ever have to do a discrete
+
+ align:start position:0%
+will you ever have to do a discrete
+ 
+
+ align:start position:0%
+will you ever have to do a discrete
+sound like is there a cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you never have to do a discrete
+
+ align:start position:0%
+yeah so you never have to do a discrete
+ 
+
+ align:start position:0%
+yeah so you never have to do a discrete
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+the discrete sum is really just a way of
+
+ align:start position:0%
+the discrete sum is really just a way of
+ 
+
+ align:start position:0%
+the discrete sum is really just a way of
+thinking and and i
+
+ align:start position:0%
+thinking and and i
+ 
+
+ align:start position:0%
+thinking and and i
+i'll show you in a minute that you even
+
+ align:start position:0%
+i'll show you in a minute that you even
+ 
+
+ align:start position:0%
+i'll show you in a minute that you even
+can avoid thinking about it once you
+
+ align:start position:0%
+can avoid thinking about it once you
+ 
+
+ align:start position:0%
+can avoid thinking about it once you
+know what to do
+
+ align:start position:0%
+know what to do
+ 
+
+ align:start position:0%
+know what to do
+so it's guiding you towards the right
+
+ align:start position:0%
+so it's guiding you towards the right
+ 
+
+ align:start position:0%
+so it's guiding you towards the right
+answer but it's not really something
+
+ align:start position:0%
+answer but it's not really something
+ 
+
+ align:start position:0%
+answer but it's not really something
+that you have to think about this grid
+
+ align:start position:0%
+that you have to think about this grid
+ 
+
+ align:start position:0%
+that you have to think about this grid
+picture it's really just if you get
+
+ align:start position:0%
+picture it's really just if you get
+ 
+
+ align:start position:0%
+picture it's really just if you get
+confused you can always think about it
+
+ align:start position:0%
+confused you can always think about it
+ 
+
+ align:start position:0%
+confused you can always think about it
+but if you're not confused you don't
+
+ align:start position:0%
+but if you're not confused you don't
+ 
+
+ align:start position:0%
+but if you're not confused you don't
+have to think about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this guy
+
+ align:start position:0%
+okay so this guy
+ 
+
+ align:start position:0%
+okay so this guy
+is what we said
+
+ align:start position:0%
+is what we said
+ 
+
+ align:start position:0%
+is what we said
+proportional to what we said
+
+ align:start position:0%
+proportional to what we said
+ 
+
+ align:start position:0%
+proportional to what we said
+it's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case the reason why it was so
+
+ align:start position:0%
+in this case the reason why it was so
+ 
+
+ align:start position:0%
+in this case the reason why it was so
+simple is because there was only k
+
+ align:start position:0%
+simple is because there was only k
+ 
+
+ align:start position:0%
+simple is because there was only k
+k residual is one component of this guy
+
+ align:start position:0%
+k residual is one component of this guy
+ 
+
+ align:start position:0%
+k residual is one component of this guy
+and then there's these other three right
+
+ align:start position:0%
+and then there's these other three right
+ 
+
+ align:start position:0%
+and then there's these other three right
+and for the other three we just absorb
+
+ align:start position:0%
+and for the other three we just absorb
+ 
+
+ align:start position:0%
+and for the other three we just absorb
+we absorb the sum and the integral back
+
+ align:start position:0%
+we absorb the sum and the integral back
+ 
+
+ align:start position:0%
+we absorb the sum and the integral back
+together and there's
+
+ align:start position:0%
+together and there's
+ 
+
+ align:start position:0%
+together and there's
+nothing further to talk about so that's
+
+ align:start position:0%
+nothing further to talk about so that's
+ 
+
+ align:start position:0%
+nothing further to talk about so that's
+why this isn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some sense very simple
+
+ align:start position:0%
+some sense very simple
+ 
+
+ align:start position:0%
+some sense very simple
+so we just do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what do we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get some one over epsilons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get some logs of p squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm putting an even
+
+ align:start position:0%
+and i'm putting an even
+ 
+
+ align:start position:0%
+and i'm putting an even
+the constant term since it's pretty
+
+ align:start position:0%
+the constant term since it's pretty
+ 
+
+ align:start position:0%
+the constant term since it's pretty
+simple 4 minus pi squared over 6.
+
+ align:start position:0%
+simple 4 minus pi squared over 6.
+ 
+
+ align:start position:0%
+simple 4 minus pi squared over 6.
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+we had a loop we had a if you remember
+
+ align:start position:0%
+we had a loop we had a if you remember
+ 
+
+ align:start position:0%
+we had a loop we had a if you remember
+think about where this came from there
+
+ align:start position:0%
+think about where this came from there
+ 
+
+ align:start position:0%
+think about where this came from there
+was a the place that this wilson line
+
+ align:start position:0%
+was a the place that this wilson line
+ 
+
+ align:start position:0%
+was a the place that this wilson line
+came from was attaching this guy over
+
+ align:start position:0%
+came from was attaching this guy over
+ 
+
+ align:start position:0%
+came from was attaching this guy over
+here and then integrating out that prop
+
+ align:start position:0%
+here and then integrating out that prop
+ 
+
+ align:start position:0%
+here and then integrating out that prop
+that offshore propagator so this is a
+
+ align:start position:0%
+that offshore propagator so this is a
+ 
+
+ align:start position:0%
+that offshore propagator so this is a
+vertex diagram we had a vertex diagram
+
+ align:start position:0%
+vertex diagram we had a vertex diagram
+ 
+
+ align:start position:0%
+vertex diagram we had a vertex diagram
+which is an ultrasoft gluon and now
+
+ align:start position:0%
+which is an ultrasoft gluon and now
+ 
+
+ align:start position:0%
+which is an ultrasoft gluon and now
+we've added an identical type topology
+
+ align:start position:0%
+we've added an identical type topology
+ 
+
+ align:start position:0%
+we've added an identical type topology
+except we drew it different because
+
+ align:start position:0%
+except we drew it different because
+ 
+
+ align:start position:0%
+except we drew it different because
+this line was off shell
+
+ align:start position:0%
+this line was off shell
+ 
+
+ align:start position:0%
+this line was off shell
+so we drew it as a wilson line and
+
+ align:start position:0%
+so we drew it as a wilson line and
+ 
+
+ align:start position:0%
+so we drew it as a wilson line and
+that's the right way of thinking about
+
+ align:start position:0%
+that's the right way of thinking about
+ 
+
+ align:start position:0%
+that's the right way of thinking about
+it but if you think about where it came
+
+ align:start position:0%
+it but if you think about where it came
+ 
+
+ align:start position:0%
+it but if you think about where it came
+from it was the same topology and we've
+
+ align:start position:0%
+from it was the same topology and we've
+ 
+
+ align:start position:0%
+from it was the same topology and we've
+added another vertex diagram so the
+
+ align:start position:0%
+added another vertex diagram so the
+ 
+
+ align:start position:0%
+added another vertex diagram so the
+effective theory has two type of vertex
+
+ align:start position:0%
+effective theory has two type of vertex
+ 
+
+ align:start position:0%
+effective theory has two type of vertex
+diagrams this collinear one and the
+
+ align:start position:0%
+diagrams this collinear one and the
+ 
+
+ align:start position:0%
+diagrams this collinear one and the
+ultrasoft one and we're going to add
+
+ align:start position:0%
+ultrasoft one and we're going to add
+ 
+
+ align:start position:0%
+ultrasoft one and we're going to add
+them together
+
+ align:start position:0%
+them together
+ 
+
+ align:start position:0%
+them together
+and in this one you see the logs are
+
+ align:start position:0%
+and in this one you see the logs are
+ 
+
+ align:start position:0%
+and in this one you see the logs are
+minimized at a different scale mu
+
+ align:start position:0%
+minimized at a different scale mu
+ 
+
+ align:start position:0%
+minimized at a different scale mu
+squared of order p squared which is the
+
+ align:start position:0%
+squared of order p squared which is the
+ 
+
+ align:start position:0%
+squared of order p squared which is the
+right scale for a collinear loop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because remember the linear particles
+
+ align:start position:0%
+because remember the linear particles
+ 
+
+ align:start position:0%
+because remember the linear particles
+lived at a larger p squared than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ultrasoft ones
+
+ align:start position:0%
+the ultrasoft ones
+ 
+
+ align:start position:0%
+the ultrasoft ones
+so this is a larger there's a larger
+
+ align:start position:0%
+so this is a larger there's a larger
+ 
+
+ align:start position:0%
+so this is a larger there's a larger
+scale that would minimize these loops
+
+ align:start position:0%
+scale that would minimize these loops
+ 
+
+ align:start position:0%
+scale that would minimize these loops
+it's the linear scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the effective theory is capturing the
+
+ align:start position:0%
+so the effective theory is capturing the
+ 
+
+ align:start position:0%
+so the effective theory is capturing the
+physics at that scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's squeeze in another diagram here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we do the linear wave function
+
+ align:start position:0%
+if we do the linear wave function
+ 
+
+ align:start position:0%
+if we do the linear wave function
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+then this is non-zero this was zero for
+
+ align:start position:0%
+then this is non-zero this was zero for
+ 
+
+ align:start position:0%
+then this is non-zero this was zero for
+the ultrasoft gluon and but for the
+
+ align:start position:0%
+the ultrasoft gluon and but for the
+ 
+
+ align:start position:0%
+the ultrasoft gluon and but for the
+cleaner glue and it's non-zero
+
+ align:start position:0%
+cleaner glue and it's non-zero
+ 
+
+ align:start position:0%
+cleaner glue and it's non-zero
+and it's exactly actually the same as
+
+ align:start position:0%
+and it's exactly actually the same as
+ 
+
+ align:start position:0%
+and it's exactly actually the same as
+the full theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's same as massless qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can do the diagram using the
+
+ align:start position:0%
+so you can do the diagram using the
+ 
+
+ align:start position:0%
+so you can do the diagram using the
+effective theory fire neurals and that's
+
+ align:start position:0%
+effective theory fire neurals and that's
+ 
+
+ align:start position:0%
+effective theory fire neurals and that's
+what you find
+
+ align:start position:0%
+what you find
+ 
+
+ align:start position:0%
+what you find
+but you could also understand why that's
+
+ align:start position:0%
+but you could also understand why that's
+ 
+
+ align:start position:0%
+but you could also understand why that's
+true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason why it's true is nothing
+
+ align:start position:0%
+and the reason why it's true is nothing
+ 
+
+ align:start position:0%
+and the reason why it's true is nothing
+in this diagram really specifies
+
+ align:start position:0%
+in this diagram really specifies
+ 
+
+ align:start position:0%
+in this diagram really specifies
+a frame
+
+ align:start position:0%
+a frame
+ 
+
+ align:start position:0%
+a frame
+we called all the particles linear but
+
+ align:start position:0%
+we called all the particles linear but
+ 
+
+ align:start position:0%
+we called all the particles linear but
+it's not attached to anything so we
+
+ align:start position:0%
+it's not attached to anything so we
+ 
+
+ align:start position:0%
+it's not attached to anything so we
+could just take the whole diagram and
+
+ align:start position:0%
+could just take the whole diagram and
+ 
+
+ align:start position:0%
+could just take the whole diagram and
+kind of boost back to the
+
+ align:start position:0%
+kind of boost back to the
+ 
+
+ align:start position:0%
+kind of boost back to the
+frame where everything's kind of soft
+
+ align:start position:0%
+frame where everything's kind of soft
+ 
+
+ align:start position:0%
+frame where everything's kind of soft
+and then we would usually be thinking
+
+ align:start position:0%
+and then we would usually be thinking
+ 
+
+ align:start position:0%
+and then we would usually be thinking
+about it in terms of the full theory
+
+ align:start position:0%
+about it in terms of the full theory
+ 
+
+ align:start position:0%
+about it in terms of the full theory
+field so
+
+ align:start position:0%
+field so
+ 
+
+ align:start position:0%
+field so
+there's uh
+
+ align:start position:0%
+there's uh
+ 
+
+ align:start position:0%
+there's uh
+yeah and
+
+ align:start position:0%
+yeah and
+ 
+
+ align:start position:0%
+yeah and
+that's effectively why
+
+ align:start position:0%
+that's effectively why
+ 
+
+ align:start position:0%
+that's effectively why
+this diagram
+
+ align:start position:0%
+this diagram
+ 
+
+ align:start position:0%
+this diagram
+like this that doesn't have any
+
+ align:start position:0%
+like this that doesn't have any
+ 
+
+ align:start position:0%
+like this that doesn't have any
+kind of reference unlike this one which
+
+ align:start position:0%
+kind of reference unlike this one which
+ 
+
+ align:start position:0%
+kind of reference unlike this one which
+has a reference because it's attached to
+
+ align:start position:0%
+has a reference because it's attached to
+ 
+
+ align:start position:0%
+has a reference because it's attached to
+the heavy quark
+
+ align:start position:0%
+the heavy quark
+ 
+
+ align:start position:0%
+the heavy quark
+that's why it's the same as qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you know what yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah for this one um
+
+ align:start position:0%
+yeah for this one um
+ 
+
+ align:start position:0%
+yeah for this one um
+you for this guy
+
+ align:start position:0%
+you for this guy
+ 
+
+ align:start position:0%
+you for this guy
+it actually
+
+ align:start position:0%
+it actually
+ 
+
+ align:start position:0%
+it actually
+doesn't depend on the i epsilon
+
+ align:start position:0%
+doesn't depend on the i epsilon
+ 
+
+ align:start position:0%
+doesn't depend on the i epsilon
+prescription up to uh
+
+ align:start position:0%
+prescription up to uh
+ 
+
+ align:start position:0%
+prescription up to uh
+yeah if i remember correctly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+that's true i believe when i'm being a
+
+ align:start position:0%
+that's true i believe when i'm being a
+ 
+
+ align:start position:0%
+that's true i believe when i'm being a
+little bit cavalier with it but once i
+
+ align:start position:0%
+little bit cavalier with it but once i
+ 
+
+ align:start position:0%
+little bit cavalier with it but once i
+put in the zero bin restrictions i'm not
+
+ align:start position:0%
+put in the zero bin restrictions i'm not
+ 
+
+ align:start position:0%
+put in the zero bin restrictions i'm not
+sure if that's true anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+yeah i mean really what solves that is
+
+ align:start position:0%
+yeah i mean really what solves that is
+ 
+
+ align:start position:0%
+yeah i mean really what solves that is
+that in a minute i'm going to be talking
+
+ align:start position:0%
+that in a minute i'm going to be talking
+ 
+
+ align:start position:0%
+that in a minute i'm going to be talking
+about the fact that there's a
+
+ align:start position:0%
+about the fact that there's a
+ 
+
+ align:start position:0%
+about the fact that there's a
+subtraction term here and once you put
+
+ align:start position:0%
+subtraction term here and once you put
+ 
+
+ align:start position:0%
+subtraction term here and once you put
+the subtraction term in that i zero is
+
+ align:start position:0%
+the subtraction term in that i zero is
+ 
+
+ align:start position:0%
+the subtraction term in that i zero is
+not relevant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i think even if you do this diagram
+
+ align:start position:0%
+but i think even if you do this diagram
+ 
+
+ align:start position:0%
+but i think even if you do this diagram
+with arbitrary i zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because what's happening is that pole is
+
+ align:start position:0%
+because what's happening is that pole is
+ 
+
+ align:start position:0%
+because what's happening is that pole is
+embargo not k going to zero is related
+
+ align:start position:0%
+embargo not k going to zero is related
+ 
+
+ align:start position:0%
+embargo not k going to zero is related
+to some of these one over epsilon so
+
+ align:start position:0%
+to some of these one over epsilon so
+ 
+
+ align:start position:0%
+to some of these one over epsilon so
+we'll talk about that more in a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i'm not 100 sure it could be that
+
+ align:start position:0%
+yeah i'm not 100 sure it could be that
+ 
+
+ align:start position:0%
+yeah i'm not 100 sure it could be that
+there's some sign that might flip
+
+ align:start position:0%
+there's some sign that might flip
+ 
+
+ align:start position:0%
+there's some sign that might flip
+i'm not 100 sure that then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+i i guess i know that
+
+ align:start position:0%
+i i guess i know that
+ 
+
+ align:start position:0%
+i i guess i know that
+if yeah what i know is that
+
+ align:start position:0%
+if yeah what i know is that
+ 
+
+ align:start position:0%
+if yeah what i know is that
+yeah let me let me answer your question
+
+ align:start position:0%
+yeah let me let me answer your question
+ 
+
+ align:start position:0%
+yeah let me let me answer your question
+later it'll be easier because i'm trying
+
+ align:start position:0%
+later it'll be easier because i'm trying
+ 
+
+ align:start position:0%
+later it'll be easier because i'm trying
+to say a bunch of things that depend on
+
+ align:start position:0%
+to say a bunch of things that depend on
+ 
+
+ align:start position:0%
+to say a bunch of things that depend on
+something else that i haven't explained
+
+ align:start position:0%
+something else that i haven't explained
+ 
+
+ align:start position:0%
+something else that i haven't explained
+yet so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are the other possible
+
+ align:start position:0%
+so what are the other possible
+ 
+
+ align:start position:0%
+so what are the other possible
+topologies we could write down so we
+
+ align:start position:0%
+topologies we could write down so we
+ 
+
+ align:start position:0%
+topologies we could write down so we
+could write down this one where we take
+
+ align:start position:0%
+could write down this one where we take
+ 
+
+ align:start position:0%
+could write down this one where we take
+two attachments in the wilson line and
+
+ align:start position:0%
+two attachments in the wilson line and
+ 
+
+ align:start position:0%
+two attachments in the wilson line and
+just loop them back up
+
+ align:start position:0%
+just loop them back up
+ 
+
+ align:start position:0%
+just loop them back up
+but that's proportional n bar squared
+
+ align:start position:0%
+but that's proportional n bar squared
+ 
+
+ align:start position:0%
+but that's proportional n bar squared
+and so that's zero in our final gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and likewise
+
+ align:start position:0%
+and likewise
+ 
+
+ align:start position:0%
+and likewise
+there's kind of a looping back up
+
+ align:start position:0%
+there's kind of a looping back up
+ 
+
+ align:start position:0%
+there's kind of a looping back up
+in the vertex in the wave function
+
+ align:start position:0%
+in the vertex in the wave function
+ 
+
+ align:start position:0%
+in the vertex in the wave function
+normalization but this guy's scaleless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power law divergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we can just set it to zero and
+
+ align:start position:0%
+and so we can just set it to zero and
+ 
+
+ align:start position:0%
+and so we can just set it to zero and
+dim reg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't have to worry about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's all the diagrams let's
+
+ align:start position:0%
+okay so that's all the diagrams let's
+ 
+
+ align:start position:0%
+okay so that's all the diagrams let's
+think about doing matching
+
+ align:start position:0%
+think about doing matching
+ 
+
+ align:start position:0%
+think about doing matching
+right let's think about comparing
+
+ align:start position:0%
+right let's think about comparing
+ 
+
+ align:start position:0%
+right let's think about comparing
+qcd and sct by adding up the diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in qcd we carried out the normalization
+
+ align:start position:0%
+in qcd we carried out the normalization
+ 
+
+ align:start position:0%
+in qcd we carried out the normalization
+we added the z for the tensor current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just write again what the
+
+ align:start position:0%
+let me just write again what the
+ 
+
+ align:start position:0%
+let me just write again what the
+answer kind of looked like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in sat we didn't carry out normalization
+
+ align:start position:0%
+in sat we didn't carry out normalization
+ 
+
+ align:start position:0%
+in sat we didn't carry out normalization
+yet
+
+ align:start position:0%
+yet
+ 
+
+ align:start position:0%
+yet
+so let me call this the bear fct result
+
+ align:start position:0%
+so let me call this the bear fct result
+ 
+
+ align:start position:0%
+so let me call this the bear fct result
+for now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once we add the ultrasoft and linear
+
+ align:start position:0%
+once we add the ultrasoft and linear
+ 
+
+ align:start position:0%
+once we add the ultrasoft and linear
+diagrams together the logs of p squared
+
+ align:start position:0%
+diagrams together the logs of p squared
+ 
+
+ align:start position:0%
+diagrams together the logs of p squared
+match up exactly with the full theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the first sign that we're
+
+ align:start position:0%
+so this is the first sign that we're
+ 
+
+ align:start position:0%
+so this is the first sign that we're
+really that it makes sense to be
+
+ align:start position:0%
+really that it makes sense to be
+ 
+
+ align:start position:0%
+really that it makes sense to be
+thinking about adding these loops even
+
+ align:start position:0%
+thinking about adding these loops even
+ 
+
+ align:start position:0%
+thinking about adding these loops even
+though they were the same topology we
+
+ align:start position:0%
+though they were the same topology we
+ 
+
+ align:start position:0%
+though they were the same topology we
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+correctly reproducing those logs of p
+
+ align:start position:0%
+correctly reproducing those logs of p
+ 
+
+ align:start position:0%
+correctly reproducing those logs of p
+squared in the full theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's some other pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll write out all the other pieces so
+
+ align:start position:0%
+i'll write out all the other pieces so
+ 
+
+ align:start position:0%
+i'll write out all the other pieces so
+you see what they look like
+
+ align:start position:0%
+you see what they look like
+ 
+
+ align:start position:0%
+you see what they look like
+well maybe i won't i won't write the
+
+ align:start position:0%
+well maybe i won't i won't write the
+ 
+
+ align:start position:0%
+well maybe i won't i won't write the
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's all the effective field
+
+ align:start position:0%
+so there's all the effective field
+ 
+
+ align:start position:0%
+so there's all the effective field
+theory terms
+
+ align:start position:0%
+theory terms
+ 
+
+ align:start position:0%
+theory terms
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+these terms here
+
+ align:start position:0%
+these terms here
+ 
+
+ align:start position:0%
+these terms here
+we can match up
+
+ align:start position:0%
+we can match up
+ 
+
+ align:start position:0%
+we can match up
+with these terms here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+good these terms here
+
+ align:start position:0%
+good these terms here
+ 
+
+ align:start position:0%
+good these terms here
+which remember in the full theory were
+
+ align:start position:0%
+which remember in the full theory were
+ 
+
+ align:start position:0%
+which remember in the full theory were
+finite and these terms here which in the
+
+ align:start position:0%
+finite and these terms here which in the
+ 
+
+ align:start position:0%
+finite and these terms here which in the
+effective theory are finite the
+
+ align:start position:0%
+effective theory are finite the
+ 
+
+ align:start position:0%
+effective theory are finite the
+difference of those is going to give the
+
+ align:start position:0%
+difference of those is going to give the
+ 
+
+ align:start position:0%
+difference of those is going to give the
+wilson coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we said that the wilson coefficient
+
+ align:start position:0%
+now we said that the wilson coefficient
+ 
+
+ align:start position:0%
+now we said that the wilson coefficient
+could be a function of p bar
+
+ align:start position:0%
+could be a function of p bar
+ 
+
+ align:start position:0%
+could be a function of p bar
+so what's going on with that
+
+ align:start position:0%
+so what's going on with that
+ 
+
+ align:start position:0%
+so what's going on with that
+well if you look at momentum
+
+ align:start position:0%
+well if you look at momentum
+ 
+
+ align:start position:0%
+well if you look at momentum
+conservation in this process of b s
+
+ align:start position:0%
+conservation in this process of b s
+ 
+
+ align:start position:0%
+conservation in this process of b s
+gamma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i probably should have said this
+
+ align:start position:0%
+so i probably should have said this
+ 
+
+ align:start position:0%
+so i probably should have said this
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+so when you look at b s gamma if you
+
+ align:start position:0%
+so when you look at b s gamma if you
+ 
+
+ align:start position:0%
+so when you look at b s gamma if you
+look at momentum conservation then
+
+ align:start position:0%
+look at momentum conservation then
+ 
+
+ align:start position:0%
+look at momentum conservation then
+the p minus of the strange quark
+
+ align:start position:0%
+the p minus of the strange quark
+ 
+
+ align:start position:0%
+the p minus of the strange quark
+has to be equal to the p minus of the b
+
+ align:start position:0%
+has to be equal to the p minus of the b
+ 
+
+ align:start position:0%
+has to be equal to the p minus of the b
+quark but that's just mb
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+actually p minus is equal to mb by
+
+ align:start position:0%
+actually p minus is equal to mb by
+ 
+
+ align:start position:0%
+actually p minus is equal to mb by
+kinematics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so mb's in this
+
+ align:start position:0%
+so mb's in this
+ 
+
+ align:start position:0%
+so mb's in this
+result here you should think of as p
+
+ align:start position:0%
+result here you should think of as p
+ 
+
+ align:start position:0%
+result here you should think of as p
+minuses and that's
+
+ align:start position:0%
+minuses and that's
+ 
+
+ align:start position:0%
+minuses and that's
+the things that this p-bar that was in
+
+ align:start position:0%
+the things that this p-bar that was in
+ 
+
+ align:start position:0%
+the things that this p-bar that was in
+our wilson coefficient is just getting
+
+ align:start position:0%
+our wilson coefficient is just getting
+ 
+
+ align:start position:0%
+our wilson coefficient is just getting
+set to mb because of some delta
+
+ align:start position:0%
+set to mb because of some delta
+ 
+
+ align:start position:0%
+set to mb because of some delta
+functions that are specifying kinematics
+
+ align:start position:0%
+functions that are specifying kinematics
+ 
+
+ align:start position:0%
+functions that are specifying kinematics
+so that leaves the kind of one over
+
+ align:start position:0%
+so that leaves the kind of one over
+ 
+
+ align:start position:0%
+so that leaves the kind of one over
+epsilon terms
+
+ align:start position:0%
+epsilon terms
+ 
+
+ align:start position:0%
+epsilon terms
+and so what we'd like is that those
+
+ align:start position:0%
+and so what we'd like is that those
+ 
+
+ align:start position:0%
+and so what we'd like is that those
+terms are associated to normalization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the effective theory right i wrote
+
+ align:start position:0%
+of the effective theory right i wrote
+ 
+
+ align:start position:0%
+of the effective theory right i wrote
+that the factor theory was bare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if i want to do that then i have to
+
+ align:start position:0%
+but if i want to do that then i have to
+ 
+
+ align:start position:0%
+but if i want to do that then i have to
+ensure that all these epsilons that are
+
+ align:start position:0%
+ensure that all these epsilons that are
+ 
+
+ align:start position:0%
+ensure that all these epsilons that are
+appearing here
+
+ align:start position:0%
+appearing here
+ 
+
+ align:start position:0%
+appearing here
+are really ultraviolet divergences
+
+ align:start position:0%
+are really ultraviolet divergences
+ 
+
+ align:start position:0%
+are really ultraviolet divergences
+if they're
+
+ align:start position:0%
+if they're
+ 
+
+ align:start position:0%
+if they're
+infrared divergences then doing that
+
+ align:start position:0%
+infrared divergences then doing that
+ 
+
+ align:start position:0%
+infrared divergences then doing that
+doesn't make sense
+
+ align:start position:0%
+doesn't make sense
+ 
+
+ align:start position:0%
+doesn't make sense
+and that's actually
+
+ align:start position:0%
+and that's actually
+ 
+
+ align:start position:0%
+and that's actually
+the remaining issue that we have to deal
+
+ align:start position:0%
+the remaining issue that we have to deal
+ 
+
+ align:start position:0%
+the remaining issue that we have to deal
+with if i
+
+ align:start position:0%
+with if i
+ 
+
+ align:start position:0%
+with if i
+i just wrote epsilon that means i'm
+
+ align:start position:0%
+i just wrote epsilon that means i'm
+ 
+
+ align:start position:0%
+i just wrote epsilon that means i'm
+ignorant to what they are
+
+ align:start position:0%
+ignorant to what they are
+ 
+
+ align:start position:0%
+ignorant to what they are
+and if i i knew this one was epsilon ir
+
+ align:start position:0%
+and if i i knew this one was epsilon ir
+ 
+
+ align:start position:0%
+and if i i knew this one was epsilon ir
+because it came from the wave function
+
+ align:start position:0%
+because it came from the wave function
+ 
+
+ align:start position:0%
+because it came from the wave function
+or normalization of the heavy quark and
+
+ align:start position:0%
+or normalization of the heavy quark and
+ 
+
+ align:start position:0%
+or normalization of the heavy quark and
+that was the same on both sides it was
+
+ align:start position:0%
+that was the same on both sides it was
+ 
+
+ align:start position:0%
+that was the same on both sides it was
+the same diagram as the wave function
+
+ align:start position:0%
+the same diagram as the wave function
+ 
+
+ align:start position:0%
+the same diagram as the wave function
+realization diagram the full and the
+
+ align:start position:0%
+realization diagram the full and the
+ 
+
+ align:start position:0%
+realization diagram the full and the
+effective theory so i could match up
+
+ align:start position:0%
+effective theory so i could match up
+ 
+
+ align:start position:0%
+effective theory so i could match up
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+these ones just came out
+
+ align:start position:0%
+these ones just came out
+ 
+
+ align:start position:0%
+these ones just came out
+but it turns out that so far with what
+
+ align:start position:0%
+but it turns out that so far with what
+ 
+
+ align:start position:0%
+but it turns out that so far with what
+we've done some of these epsilons here
+
+ align:start position:0%
+we've done some of these epsilons here
+ 
+
+ align:start position:0%
+we've done some of these epsilons here
+are ir
+
+ align:start position:0%
+are ir
+ 
+
+ align:start position:0%
+are ir
+and so the ir divergences aren't
+
+ align:start position:0%
+and so the ir divergences aren't
+ 
+
+ align:start position:0%
+and so the ir divergences aren't
+matching up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason is because we didn't put
+
+ align:start position:0%
+and the reason is because we didn't put
+ 
+
+ align:start position:0%
+and the reason is because we didn't put
+in those restrictions
+
+ align:start position:0%
+in those restrictions
+ 
+
+ align:start position:0%
+in those restrictions
+on our sum over labels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that we have these restrictions
+
+ align:start position:0%
+okay so that we have these restrictions
+ 
+
+ align:start position:0%
+okay so that we have these restrictions
+k label not equal to zero
+
+ align:start position:0%
+k label not equal to zero
+ 
+
+ align:start position:0%
+k label not equal to zero
+and k label not equal to minus pl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are the ones those are the
+
+ align:start position:0%
+those are the ones those are the
+ 
+
+ align:start position:0%
+those are the ones those are the
+restrictions that i'm talking about
+
+ align:start position:0%
+restrictions that i'm talking about
+ 
+
+ align:start position:0%
+restrictions that i'm talking about
+the place that those restrictions came
+
+ align:start position:0%
+the place that those restrictions came
+ 
+
+ align:start position:0%
+the place that those restrictions came
+from was kl was the
+
+ align:start position:0%
+from was kl was the
+ 
+
+ align:start position:0%
+from was kl was the
+k was the momentum of the gluon kl not
+
+ align:start position:0%
+k was the momentum of the gluon kl not
+ 
+
+ align:start position:0%
+k was the momentum of the gluon kl not
+equal to zero is saying that the gluon
+
+ align:start position:0%
+equal to zero is saying that the gluon
+ 
+
+ align:start position:0%
+equal to zero is saying that the gluon
+shouldn't be
+
+ align:start position:0%
+shouldn't be
+ 
+
+ align:start position:0%
+shouldn't be
+this is the restriction that the gluon
+
+ align:start position:0%
+this is the restriction that the gluon
+ 
+
+ align:start position:0%
+this is the restriction that the gluon
+is linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because kl equals 0 is the ultrasoft
+
+ align:start position:0%
+because kl equals 0 is the ultrasoft
+ 
+
+ align:start position:0%
+because kl equals 0 is the ultrasoft
+gluon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the restriction that the
+
+ align:start position:0%
+and this is the restriction that the
+ 
+
+ align:start position:0%
+and this is the restriction that the
+fermion is collinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the loop
+
+ align:start position:0%
+in the loop
+ 
+
+ align:start position:0%
+in the loop
+that's why there was two of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are called zero bins
+
+ align:start position:0%
+so these are called zero bins
+ 
+
+ align:start position:0%
+so these are called zero bins
+zero because it's
+
+ align:start position:0%
+zero because it's
+ 
+
+ align:start position:0%
+zero because it's
+the where the ultrasoft momentum lives
+
+ align:start position:0%
+the where the ultrasoft momentum lives
+ 
+
+ align:start position:0%
+the where the ultrasoft momentum lives
+and that's kind of from the point of
+
+ align:start position:0%
+and that's kind of from the point of
+ 
+
+ align:start position:0%
+and that's kind of from the point of
+view of collinear that's zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so composing these restrictions is
+
+ align:start position:0%
+so composing these restrictions is
+ 
+
+ align:start position:0%
+so composing these restrictions is
+removing the zero bin if you like
+
+ align:start position:0%
+removing the zero bin if you like
+ 
+
+ align:start position:0%
+removing the zero bin if you like
+and what these restrictions do is they
+
+ align:start position:0%
+and what these restrictions do is they
+ 
+
+ align:start position:0%
+and what these restrictions do is they
+avoid double double counting
+
+ align:start position:0%
+avoid double double counting
+ 
+
+ align:start position:0%
+avoid double double counting
+and the way i've said it that's i think
+
+ align:start position:0%
+and the way i've said it that's i think
+ 
+
+ align:start position:0%
+and the way i've said it that's i think
+clearer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so far in our calculation we haven't
+
+ align:start position:0%
+so so far in our calculation we haven't
+ 
+
+ align:start position:0%
+so so far in our calculation we haven't
+avoided double counting and that's the
+
+ align:start position:0%
+avoided double counting and that's the
+ 
+
+ align:start position:0%
+avoided double counting and that's the
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have to modify our rule or we
+
+ align:start position:0%
+okay so we have to modify our rule or we
+ 
+
+ align:start position:0%
+okay so we have to modify our rule or we
+extend our rule to avoid to include the
+
+ align:start position:0%
+extend our rule to avoid to include the
+ 
+
+ align:start position:0%
+extend our rule to avoid to include the
+case where we have these restrictions
+
+ align:start position:0%
+case where we have these restrictions
+ 
+
+ align:start position:0%
+case where we have these restrictions
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in an extended version of rule two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has restrictions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so really what we want to do is that
+
+ align:start position:0%
+so really what we want to do is that
+ 
+
+ align:start position:0%
+so really what we want to do is that
+and we want to think about that as an
+
+ align:start position:0%
+and we want to think about that as an
+ 
+
+ align:start position:0%
+and we want to think about that as an
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's how we can manipulate these to
+
+ align:start position:0%
+so here's how we can manipulate these to
+ 
+
+ align:start position:0%
+so here's how we can manipulate these to
+think about it as an integral
+
+ align:start position:0%
+think about it as an integral
+ 
+
+ align:start position:0%
+think about it as an integral
+let's sum over all kls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then we'll
+
+ align:start position:0%
+but then we'll
+ 
+
+ align:start position:0%
+but then we'll
+subtract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll subtract the limit of this f
+
+ align:start position:0%
+we'll subtract the limit of this f
+ 
+
+ align:start position:0%
+we'll subtract the limit of this f
+where we take the f and we we let the kl
+
+ align:start position:0%
+where we take the f and we we let the kl
+ 
+
+ align:start position:0%
+where we take the f and we we let the kl
+go to the the place so we integrate over
+
+ align:start position:0%
+go to the the place so we integrate over
+ 
+
+ align:start position:0%
+go to the the place so we integrate over
+everywhere including the place we don't
+
+ align:start position:0%
+everywhere including the place we don't
+ 
+
+ align:start position:0%
+everywhere including the place we don't
+want to go
+
+ align:start position:0%
+want to go
+ 
+
+ align:start position:0%
+want to go
+and we subtract the and then we subtract
+
+ align:start position:0%
+and we subtract the and then we subtract
+ 
+
+ align:start position:0%
+and we subtract the and then we subtract
+it back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is this fl of k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this f k l goes to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's defined by taking the scaling limit
+
+ align:start position:0%
+it's defined by taking the scaling limit
+ 
+
+ align:start position:0%
+it's defined by taking the scaling limit
+of the collinear momenta towards the
+
+ align:start position:0%
+of the collinear momenta towards the
+ 
+
+ align:start position:0%
+of the collinear momenta towards the
+ultra soft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you take your collinear momentum
+
+ align:start position:0%
+so you take your collinear momentum
+ 
+
+ align:start position:0%
+so you take your collinear momentum
+which are the plot minus and the perp
+
+ align:start position:0%
+which are the plot minus and the perp
+ 
+
+ align:start position:0%
+which are the plot minus and the perp
+here and you scale them towards the an
+
+ align:start position:0%
+here and you scale them towards the an
+ 
+
+ align:start position:0%
+here and you scale them towards the an
+ultrasoft momentum in whatever
+
+ align:start position:0%
+ultrasoft momentum in whatever
+ 
+
+ align:start position:0%
+ultrasoft momentum in whatever
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+i.e you start counting the k ends is
+
+ align:start position:0%
+i.e you start counting the k ends is
+ 
+
+ align:start position:0%
+i.e you start counting the k ends is
+water lambda squared
+
+ align:start position:0%
+water lambda squared
+ 
+
+ align:start position:0%
+water lambda squared
+and you keep the leading order piece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you keep the piece that's the same
+
+ align:start position:0%
+or you keep the piece that's the same
+ 
+
+ align:start position:0%
+or you keep the piece that's the same
+size as this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that defines what this
+
+ align:start position:0%
+and then that defines what this
+ 
+
+ align:start position:0%
+and then that defines what this
+f is it's the once you take that limit
+
+ align:start position:0%
+f is it's the once you take that limit
+ 
+
+ align:start position:0%
+f is it's the once you take that limit
+and you expand then that's what this f
+
+ align:start position:0%
+and you expand then that's what this f
+ 
+
+ align:start position:0%
+and you expand then that's what this f
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what you're doing here by doing this
+
+ align:start position:0%
+so what you're doing here by doing this
+ 
+
+ align:start position:0%
+so what you're doing here by doing this
+procedure
+
+ align:start position:0%
+procedure
+ 
+
+ align:start position:0%
+procedure
+is you're basically setting things up so
+
+ align:start position:0%
+is you're basically setting things up so
+ 
+
+ align:start position:0%
+is you're basically setting things up so
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this guy is integrated over in a way
+
+ align:start position:0%
+this guy is integrated over in a way
+ 
+
+ align:start position:0%
+this guy is integrated over in a way
+that we can combine back into an
+
+ align:start position:0%
+that we can combine back into an
+ 
+
+ align:start position:0%
+that we can combine back into an
+integral but then we have to subtract
+
+ align:start position:0%
+integral but then we have to subtract
+ 
+
+ align:start position:0%
+integral but then we have to subtract
+kind of an overlap
+
+ align:start position:0%
+kind of an overlap
+ 
+
+ align:start position:0%
+kind of an overlap
+of when that integral would go into the
+
+ align:start position:0%
+of when that integral would go into the
+ 
+
+ align:start position:0%
+of when that integral would go into the
+ultrasoft region
+
+ align:start position:0%
+ultrasoft region
+ 
+
+ align:start position:0%
+ultrasoft region
+but the overlap we're subtracting is
+
+ align:start position:0%
+but the overlap we're subtracting is
+ 
+
+ align:start position:0%
+but the overlap we're subtracting is
+also an integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have a difference of integrals
+
+ align:start position:0%
+so we have a difference of integrals
+ 
+
+ align:start position:0%
+so we have a difference of integrals
+and you should think of the second
+
+ align:start position:0%
+and you should think of the second
+ 
+
+ align:start position:0%
+and you should think of the second
+integral as kind of like the square
+
+ align:start position:0%
+integral as kind of like the square
+ 
+
+ align:start position:0%
+integral as kind of like the square
+integrating over the square where the
+
+ align:start position:0%
+integrating over the square where the
+ 
+
+ align:start position:0%
+integrating over the square where the
+zero bin was
+
+ align:start position:0%
+zero bin was
+ 
+
+ align:start position:0%
+zero bin was
+so if you think about our
+
+ align:start position:0%
+so if you think about our
+ 
+
+ align:start position:0%
+so if you think about our
+picture where the cleaners were up here
+
+ align:start position:0%
+picture where the cleaners were up here
+ 
+
+ align:start position:0%
+picture where the cleaners were up here
+the ultrasounds are down here and you
+
+ align:start position:0%
+the ultrasounds are down here and you
+ 
+
+ align:start position:0%
+the ultrasounds are down here and you
+thought about there being some box
+
+ align:start position:0%
+thought about there being some box
+ 
+
+ align:start position:0%
+thought about there being some box
+you're taking the scaling limit when
+
+ align:start position:0%
+you're taking the scaling limit when
+ 
+
+ align:start position:0%
+you're taking the scaling limit when
+this guy goes down into that box
+
+ align:start position:0%
+this guy goes down into that box
+ 
+
+ align:start position:0%
+this guy goes down into that box
+you add up all the boxes that's this
+
+ align:start position:0%
+you add up all the boxes that's this
+ 
+
+ align:start position:0%
+you add up all the boxes that's this
+and then you subtract out that box again
+
+ align:start position:0%
+and then you subtract out that box again
+ 
+
+ align:start position:0%
+and then you subtract out that box again
+and that avoids having a double counting
+
+ align:start position:0%
+and that avoids having a double counting
+ 
+
+ align:start position:0%
+and that avoids having a double counting
+in that region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then this guy here
+
+ align:start position:0%
+okay so then this guy here
+ 
+
+ align:start position:0%
+okay so then this guy here
+you can do the same kind of trick as
+
+ align:start position:0%
+you can do the same kind of trick as
+ 
+
+ align:start position:0%
+you can do the same kind of trick as
+before so
+
+ align:start position:0%
+before so
+ 
+
+ align:start position:0%
+before so
+continuing with the equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if kl is going to zero we can think of
+
+ align:start position:0%
+if kl is going to zero we can think of
+ 
+
+ align:start position:0%
+if kl is going to zero we can think of
+it just as a function of kr's
+
+ align:start position:0%
+it just as a function of kr's
+ 
+
+ align:start position:0%
+it just as a function of kr's
+and so effectively what we get in the
+
+ align:start position:0%
+and so effectively what we get in the
+ 
+
+ align:start position:0%
+and so effectively what we get in the
+end is an integral over all k
+
+ align:start position:0%
+end is an integral over all k
+ 
+
+ align:start position:0%
+end is an integral over all k
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+f of k the full f
+
+ align:start position:0%
+f of k the full f
+ 
+
+ align:start position:0%
+f of k the full f
+evaluated with a continuous momentum
+
+ align:start position:0%
+evaluated with a continuous momentum
+ 
+
+ align:start position:0%
+evaluated with a continuous momentum
+minus some f
+
+ align:start position:0%
+minus some f
+ 
+
+ align:start position:0%
+minus some f
+that's expanded
+
+ align:start position:0%
+that's expanded
+ 
+
+ align:start position:0%
+that's expanded
+and avoids there being overlap in this
+
+ align:start position:0%
+and avoids there being overlap in this
+ 
+
+ align:start position:0%
+and avoids there being overlap in this
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+so rather than having this discrete sum
+
+ align:start position:0%
+so rather than having this discrete sum
+ 
+
+ align:start position:0%
+so rather than having this discrete sum
+with the restriction we have a
+
+ align:start position:0%
+with the restriction we have a
+ 
+
+ align:start position:0%
+with the restriction we have a
+difference of integrals and this
+
+ align:start position:0%
+difference of integrals and this
+ 
+
+ align:start position:0%
+difference of integrals and this
+subtraction term avoids
+
+ align:start position:0%
+subtraction term avoids
+ 
+
+ align:start position:0%
+subtraction term avoids
+the overlap in that region
+
+ align:start position:0%
+the overlap in that region
+ 
+
+ align:start position:0%
+the overlap in that region
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so all the discrete sums are good for is
+
+ align:start position:0%
+so all the discrete sums are good for is
+ 
+
+ align:start position:0%
+so all the discrete sums are good for is
+a means of
+
+ align:start position:0%
+a means of
+ 
+
+ align:start position:0%
+a means of
+figuring out what limits you need to
+
+ align:start position:0%
+figuring out what limits you need to
+ 
+
+ align:start position:0%
+figuring out what limits you need to
+take to generate these subtractions once
+
+ align:start position:0%
+take to generate these subtractions once
+ 
+
+ align:start position:0%
+take to generate these subtractions once
+you've done that everything's a
+
+ align:start position:0%
+you've done that everything's a
+ 
+
+ align:start position:0%
+you've done that everything's a
+continuous integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is called the zero bin
+
+ align:start position:0%
+and this is called the zero bin
+ 
+
+ align:start position:0%
+and this is called the zero bin
+subtraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you like one way of phrasing
+
+ align:start position:0%
+okay so if you like one way of phrasing
+ 
+
+ align:start position:0%
+okay so if you like one way of phrasing
+what's going on is that the linear
+
+ align:start position:0%
+what's going on is that the linear
+ 
+
+ align:start position:0%
+what's going on is that the linear
+propagators are really distributions
+
+ align:start position:0%
+propagators are really distributions
+ 
+
+ align:start position:0%
+propagators are really distributions
+they're distributions that
+
+ align:start position:0%
+they're distributions that
+ 
+
+ align:start position:0%
+they're distributions that
+know that there should be that they
+
+ align:start position:0%
+know that there should be that they
+ 
+
+ align:start position:0%
+know that there should be that they
+should have a subtraction in order to
+
+ align:start position:0%
+should have a subtraction in order to
+ 
+
+ align:start position:0%
+should have a subtraction in order to
+not overlap the other region where we
+
+ align:start position:0%
+not overlap the other region where we
+ 
+
+ align:start position:0%
+not overlap the other region where we
+have another degree of freedom
+
+ align:start position:0%
+have another degree of freedom
+ 
+
+ align:start position:0%
+have another degree of freedom
+so you could think about it that way in
+
+ align:start position:0%
+so you could think about it that way in
+ 
+
+ align:start position:0%
+so you could think about it that way in
+this having this sum
+
+ align:start position:0%
+this having this sum
+ 
+
+ align:start position:0%
+this having this sum
+is just a way of sort of encoding that
+
+ align:start position:0%
+is just a way of sort of encoding that
+ 
+
+ align:start position:0%
+is just a way of sort of encoding that
+but in the end it kind of looks like
+
+ align:start position:0%
+but in the end it kind of looks like
+ 
+
+ align:start position:0%
+but in the end it kind of looks like
+some kind of plus function where you
+
+ align:start position:0%
+some kind of plus function where you
+ 
+
+ align:start position:0%
+some kind of plus function where you
+have a subtraction
+
+ align:start position:0%
+have a subtraction
+ 
+
+ align:start position:0%
+have a subtraction
+so it seems like in the second term
+
+ align:start position:0%
+so it seems like in the second term
+ 
+
+ align:start position:0%
+so it seems like in the second term
+you would have to rewrite the expression
+
+ align:start position:0%
+you would have to rewrite the expression
+ 
+
+ align:start position:0%
+you would have to rewrite the expression
+because initially you know okay you
+
+ align:start position:0%
+because initially you know okay you
+ 
+
+ align:start position:0%
+because initially you know okay you
+ignore yeah
+
+ align:start position:0%
+ignore yeah
+ 
+
+ align:start position:0%
+ignore yeah
+i'll show you how it works in an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's go to our example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's not so what you just said is
+
+ align:start position:0%
+yeah it's not so what you just said is
+ 
+
+ align:start position:0%
+yeah it's not so what you just said is
+not quite the way you should think about
+
+ align:start position:0%
+not quite the way you should think about
+ 
+
+ align:start position:0%
+not quite the way you should think about
+it you should think about it you're
+
+ align:start position:0%
+it you should think about it you're
+ 
+
+ align:start position:0%
+it you should think about it you're
+given the effect of theory f
+
+ align:start position:0%
+given the effect of theory f
+ 
+
+ align:start position:0%
+given the effect of theory f
+and now i'm
+
+ align:start position:0%
+and now i'm
+ 
+
+ align:start position:0%
+and now i'm
+saying that that f as given with its
+
+ align:start position:0%
+saying that that f as given with its
+ 
+
+ align:start position:0%
+saying that that f as given with its
+momentum as given has it still has an
+
+ align:start position:0%
+momentum as given has it still has an
+ 
+
+ align:start position:0%
+momentum as given has it still has an
+overlap with the ultrasoft region that i
+
+ align:start position:0%
+overlap with the ultrasoft region that i
+ 
+
+ align:start position:0%
+overlap with the ultrasoft region that i
+want to subtract
+
+ align:start position:0%
+want to subtract
+ 
+
+ align:start position:0%
+want to subtract
+so i'm taking a limit of that f i'm not
+
+ align:start position:0%
+so i'm taking a limit of that f i'm not
+ 
+
+ align:start position:0%
+so i'm taking a limit of that f i'm not
+adding anything back to it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this guy
+
+ align:start position:0%
+so this guy
+ 
+
+ align:start position:0%
+so this guy
+don't integral dk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what we wrote before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now if i take the ultrasoft limit of
+
+ align:start position:0%
+and now if i take the ultrasoft limit of
+ 
+
+ align:start position:0%
+and now if i take the ultrasoft limit of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+of the k
+
+ align:start position:0%
+of the k
+ 
+
+ align:start position:0%
+of the k
+then i would write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+when i take the scaling limit
+
+ align:start position:0%
+when i take the scaling limit
+ 
+
+ align:start position:0%
+when i take the scaling limit
+if you think about k squared it's k plus
+
+ align:start position:0%
+if you think about k squared it's k plus
+ 
+
+ align:start position:0%
+if you think about k squared it's k plus
+k minus minus k perp squared
+
+ align:start position:0%
+k minus minus k perp squared
+ 
+
+ align:start position:0%
+k minus minus k perp squared
+when i take the scaling limit of all
+
+ align:start position:0%
+when i take the scaling limit of all
+ 
+
+ align:start position:0%
+when i take the scaling limit of all
+momentum being ultrasoft the components
+
+ align:start position:0%
+momentum being ultrasoft the components
+ 
+
+ align:start position:0%
+momentum being ultrasoft the components
+of the k are still homogeneous so
+
+ align:start position:0%
+of the k are still homogeneous so
+ 
+
+ align:start position:0%
+of the k are still homogeneous so
+there's nothing there to expand
+
+ align:start position:0%
+there's nothing there to expand
+ 
+
+ align:start position:0%
+there's nothing there to expand
+some expansion happened in this k plus p
+
+ align:start position:0%
+some expansion happened in this k plus p
+ 
+
+ align:start position:0%
+some expansion happened in this k plus p
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+1 over mbar.k changes its power counting
+
+ align:start position:0%
+1 over mbar.k changes its power counting
+ 
+
+ align:start position:0%
+1 over mbar.k changes its power counting
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh it's still mbar.k and we don't
+
+ align:start position:0%
+uh it's still mbar.k and we don't
+ 
+
+ align:start position:0%
+uh it's still mbar.k and we don't
+there's nothing to expand there so this
+
+ align:start position:0%
+there's nothing to expand there so this
+ 
+
+ align:start position:0%
+there's nothing to expand there so this
+is what the subtraction looks like and
+
+ align:start position:0%
+is what the subtraction looks like and
+ 
+
+ align:start position:0%
+is what the subtraction looks like and
+in the numerator the nbar.k can be
+
+ align:start position:0%
+in the numerator the nbar.k can be
+ 
+
+ align:start position:0%
+in the numerator the nbar.k can be
+dropped relative to the mbar.p which is
+
+ align:start position:0%
+dropped relative to the mbar.p which is
+ 
+
+ align:start position:0%
+dropped relative to the mbar.p which is
+large and external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is taking the ultrasoft
+
+ align:start position:0%
+okay so this is taking the ultrasoft
+ 
+
+ align:start position:0%
+okay so this is taking the ultrasoft
+limit of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so in general i would have to
+
+ align:start position:0%
+yeah so in general i would have to
+ 
+
+ align:start position:0%
+yeah so in general i would have to
+subtract off the ultrasoft limit of the
+
+ align:start position:0%
+subtract off the ultrasoft limit of the
+ 
+
+ align:start position:0%
+subtract off the ultrasoft limit of the
+cork as well
+
+ align:start position:0%
+cork as well
+ 
+
+ align:start position:0%
+cork as well
+and when i do that what i find is a term
+
+ align:start position:0%
+and when i do that what i find is a term
+ 
+
+ align:start position:0%
+and when i do that what i find is a term
+that's power suppressed and i so i drop
+
+ align:start position:0%
+that's power suppressed and i so i drop
+ 
+
+ align:start position:0%
+that's power suppressed and i so i drop
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+but in general i would have to do that
+
+ align:start position:0%
+but in general i would have to do that
+ 
+
+ align:start position:0%
+but in general i would have to do that
+as well that's right
+
+ align:start position:0%
+as well that's right
+ 
+
+ align:start position:0%
+as well that's right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so this is you know it looks kind of
+
+ align:start position:0%
+and so this is you know it looks kind of
+ 
+
+ align:start position:0%
+and so this is you know it looks kind of
+like an ultra soft diagram except it's
+
+ align:start position:0%
+like an ultra soft diagram except it's
+ 
+
+ align:start position:0%
+like an ultra soft diagram except it's
+got this n bar dot k and
+
+ align:start position:0%
+got this n bar dot k and
+ 
+
+ align:start position:0%
+got this n bar dot k and
+instead of the v dot k that we had in
+
+ align:start position:0%
+instead of the v dot k that we had in
+ 
+
+ align:start position:0%
+instead of the v dot k that we had in
+the ultra soft diagram
+
+ align:start position:0%
+the ultra soft diagram
+ 
+
+ align:start position:0%
+the ultra soft diagram
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and if you do a power counting with the
+
+ align:start position:0%
+and if you do a power counting with the
+ 
+
+ align:start position:0%
+and if you do a power counting with the
+loop momentum scaling as ultrasoft then
+
+ align:start position:0%
+loop momentum scaling as ultrasoft then
+ 
+
+ align:start position:0%
+loop momentum scaling as ultrasoft then
+you're this pieces of order the same
+
+ align:start position:0%
+you're this pieces of order the same
+ 
+
+ align:start position:0%
+you're this pieces of order the same
+size as this piece and that's why you
+
+ align:start position:0%
+size as this piece and that's why you
+ 
+
+ align:start position:0%
+size as this piece and that's why you
+keep only that term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+so the prescription we have is that we
+
+ align:start position:0%
+so the prescription we have is that we
+ 
+
+ align:start position:0%
+so the prescription we have is that we
+drop the higher powers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh if you did the higher power lower
+
+ align:start position:0%
+oh if you did the higher power lower
+ 
+
+ align:start position:0%
+oh if you did the higher power lower
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+higher power zero no
+
+ align:start position:0%
+higher power zero no
+ 
+
+ align:start position:0%
+higher power zero no
+so if we did the higher power then this
+
+ align:start position:0%
+so if we did the higher power then this
+ 
+
+ align:start position:0%
+so if we did the higher power then this
+would start out with higher power
+
+ align:start position:0%
+would start out with higher power
+ 
+
+ align:start position:0%
+would start out with higher power
+and then when we took the limit of it it
+
+ align:start position:0%
+and then when we took the limit of it it
+ 
+
+ align:start position:0%
+and then when we took the limit of it it
+would end up you know just starting at
+
+ align:start position:0%
+would end up you know just starting at
+ 
+
+ align:start position:0%
+would end up you know just starting at
+that power or higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you don't have to you don't have to
+
+ align:start position:0%
+yeah you don't have to you don't have to
+ 
+
+ align:start position:0%
+yeah you don't have to you don't have to
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it's kind of really what you
+
+ align:start position:0%
+yeah so it's kind of really what you
+ 
+
+ align:start position:0%
+yeah so it's kind of really what you
+care about subtracting here are the log
+
+ align:start position:0%
+care about subtracting here are the log
+ 
+
+ align:start position:0%
+care about subtracting here are the log
+divergences
+
+ align:start position:0%
+divergences
+ 
+
+ align:start position:0%
+divergences
+and that's what this minimal subtraction
+
+ align:start position:0%
+and that's what this minimal subtraction
+ 
+
+ align:start position:0%
+and that's what this minimal subtraction
+is doing by taking the piece that you're
+
+ align:start position:0%
+is doing by taking the piece that you're
+ 
+
+ align:start position:0%
+is doing by taking the piece that you're
+only keeping the piece that's scaling
+
+ align:start position:0%
+only keeping the piece that's scaling
+ 
+
+ align:start position:0%
+only keeping the piece that's scaling
+the same way you're removing the log
+
+ align:start position:0%
+the same way you're removing the log
+ 
+
+ align:start position:0%
+the same way you're removing the log
+divergent pieces
+
+ align:start position:0%
+divergent pieces
+ 
+
+ align:start position:0%
+divergent pieces
+and it's the log divergent pieces which
+
+ align:start position:0%
+and it's the log divergent pieces which
+ 
+
+ align:start position:0%
+and it's the log divergent pieces which
+are giving our one over epsilons
+
+ align:start position:0%
+are giving our one over epsilons
+ 
+
+ align:start position:0%
+are giving our one over epsilons
+um the pieces that you would get from
+
+ align:start position:0%
+um the pieces that you would get from
+ 
+
+ align:start position:0%
+um the pieces that you would get from
+the higher expansion
+
+ align:start position:0%
+the higher expansion
+ 
+
+ align:start position:0%
+the higher expansion
+you know they would all be kind of like
+
+ align:start position:0%
+you know they would all be kind of like
+ 
+
+ align:start position:0%
+you know they would all be kind of like
+power law divergent terms from the point
+
+ align:start position:0%
+power law divergent terms from the point
+ 
+
+ align:start position:0%
+power law divergent terms from the point
+of view of the power counting and we
+
+ align:start position:0%
+of view of the power counting and we
+ 
+
+ align:start position:0%
+of view of the power counting and we
+just don't have to worry about those
+
+ align:start position:0%
+just don't have to worry about those
+ 
+
+ align:start position:0%
+just don't have to worry about those
+and another way of saying it is you know
+
+ align:start position:0%
+and another way of saying it is you know
+ 
+
+ align:start position:0%
+and another way of saying it is you know
+it's not that i'm removing absolutely
+
+ align:start position:0%
+it's not that i'm removing absolutely
+ 
+
+ align:start position:0%
+it's not that i'm removing absolutely
+this whole integrand in that region
+
+ align:start position:0%
+this whole integrand in that region
+ 
+
+ align:start position:0%
+this whole integrand in that region
+right there could still be a constant
+
+ align:start position:0%
+right there could still be a constant
+ 
+
+ align:start position:0%
+right there could still be a constant
+for example that comes from that region
+
+ align:start position:0%
+for example that comes from that region
+ 
+
+ align:start position:0%
+for example that comes from that region
+but if there's a constant that comes
+
+ align:start position:0%
+but if there's a constant that comes
+ 
+
+ align:start position:0%
+but if there's a constant that comes
+from that region i don't care what i
+
+ align:start position:0%
+from that region i don't care what i
+ 
+
+ align:start position:0%
+from that region i don't care what i
+care about removing is any spurious ir
+
+ align:start position:0%
+care about removing is any spurious ir
+ 
+
+ align:start position:0%
+care about removing is any spurious ir
+singularities
+
+ align:start position:0%
+singularities
+ 
+
+ align:start position:0%
+singularities
+and for those i can make a kind of
+
+ align:start position:0%
+and for those i can make a kind of
+ 
+
+ align:start position:0%
+and for those i can make a kind of
+minimal subtraction which is just the
+
+ align:start position:0%
+minimal subtraction which is just the
+ 
+
+ align:start position:0%
+minimal subtraction which is just the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+term all right so
+
+ align:start position:0%
+term all right so
+ 
+
+ align:start position:0%
+term all right so
+i want to finish this discussion so if
+
+ align:start position:0%
+i want to finish this discussion so if
+ 
+
+ align:start position:0%
+i want to finish this discussion so if
+we do this we get an answer
+
+ align:start position:0%
+we do this we get an answer
+ 
+
+ align:start position:0%
+we do this we get an answer
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i will try
+
+ align:start position:0%
+i will try
+ 
+
+ align:start position:0%
+i will try
+to right on the board for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now i'm going to distinguish all the
+
+ align:start position:0%
+so now i'm going to distinguish all the
+ 
+
+ align:start position:0%
+so now i'm going to distinguish all the
+the epsilons and then we'll see what the
+
+ align:start position:0%
+the epsilons and then we'll see what the
+ 
+
+ align:start position:0%
+the epsilons and then we'll see what the
+subtraction does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i was careful and i distinguished
+
+ align:start position:0%
+so if i was careful and i distinguished
+ 
+
+ align:start position:0%
+so if i was careful and i distinguished
+all the epsilons in our original
+
+ align:start position:0%
+all the epsilons in our original
+ 
+
+ align:start position:0%
+all the epsilons in our original
+calculation
+
+ align:start position:0%
+calculation
+ 
+
+ align:start position:0%
+calculation
+it would actually look like this
+
+ align:start position:0%
+it would actually look like this
+ 
+
+ align:start position:0%
+it would actually look like this
+and then the subtraction piece
+
+ align:start position:0%
+and then the subtraction piece
+ 
+
+ align:start position:0%
+and then the subtraction piece
+gives an extra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contribution and it's actually scaleless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in in the mbar.k here it's so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a scaleless loop in this in this
+
+ align:start position:0%
+there's a scaleless loop in this in this
+ 
+
+ align:start position:0%
+there's a scaleless loop in this in this
+guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it actually vanishes if the epsilon ir
+
+ align:start position:0%
+it actually vanishes if the epsilon ir
+ 
+
+ align:start position:0%
+it actually vanishes if the epsilon ir
+and the epsilon uv are said to be equal
+
+ align:start position:0%
+and the epsilon uv are said to be equal
+ 
+
+ align:start position:0%
+and the epsilon uv are said to be equal
+but what it does is it converts the
+
+ align:start position:0%
+but what it does is it converts the
+ 
+
+ align:start position:0%
+but what it does is it converts the
+epsilon irs that are in the first
+
+ align:start position:0%
+epsilon irs that are in the first
+ 
+
+ align:start position:0%
+epsilon irs that are in the first
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+into epsilon uvs which is what we want
+
+ align:start position:0%
+into epsilon uvs which is what we want
+ 
+
+ align:start position:0%
+into epsilon uvs which is what we want
+so once you add up these two things the
+
+ align:start position:0%
+so once you add up these two things the
+ 
+
+ align:start position:0%
+so once you add up these two things the
+epsilon irs are canceling and the
+
+ align:start position:0%
+epsilon irs are canceling and the
+ 
+
+ align:start position:0%
+epsilon irs are canceling and the
+epsilon irs that were coming in the
+
+ align:start position:0%
+epsilon irs that were coming in the
+ 
+
+ align:start position:0%
+epsilon irs that were coming in the
+original formula
+
+ align:start position:0%
+original formula
+ 
+
+ align:start position:0%
+original formula
+those were coming about because of this
+
+ align:start position:0%
+those were coming about because of this
+ 
+
+ align:start position:0%
+those were coming about because of this
+bad behavior as nbar.k goes kind of into
+
+ align:start position:0%
+bad behavior as nbar.k goes kind of into
+ 
+
+ align:start position:0%
+bad behavior as nbar.k goes kind of into
+the ultrasound into the limit of sort of
+
+ align:start position:0%
+the ultrasound into the limit of sort of
+ 
+
+ align:start position:0%
+the ultrasound into the limit of sort of
+mr.k going small you can think about
+
+ align:start position:0%
+mr.k going small you can think about
+ 
+
+ align:start position:0%
+mr.k going small you can think about
+that roughly is where the ultrasoft is
+
+ align:start position:0%
+that roughly is where the ultrasoft is
+ 
+
+ align:start position:0%
+that roughly is where the ultrasoft is
+this is kind of subtracting off that
+
+ align:start position:0%
+this is kind of subtracting off that
+ 
+
+ align:start position:0%
+this is kind of subtracting off that
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+and the remainder then is coming from
+
+ align:start position:0%
+and the remainder then is coming from
+ 
+
+ align:start position:0%
+and the remainder then is coming from
+you're only having divergences for sort
+
+ align:start position:0%
+you're only having divergences for sort
+ 
+
+ align:start position:0%
+you're only having divergences for sort
+of n bar dot k goes to infinity which is
+
+ align:start position:0%
+of n bar dot k goes to infinity which is
+ 
+
+ align:start position:0%
+of n bar dot k goes to infinity which is
+a sort of proper collinear
+
+ align:start position:0%
+a sort of proper collinear
+ 
+
+ align:start position:0%
+a sort of proper collinear
+ultraviolet divergence not from mbar.k
+
+ align:start position:0%
+ultraviolet divergence not from mbar.k
+ 
+
+ align:start position:0%
+ultraviolet divergence not from mbar.k
+going to zero
+
+ align:start position:0%
+going to zero
+ 
+
+ align:start position:0%
+going to zero
+so once you put the two together the
+
+ align:start position:0%
+so once you put the two together the
+ 
+
+ align:start position:0%
+so once you put the two together the
+epsilon irs cancel and then we get
+
+ align:start position:0%
+epsilon irs cancel and then we get
+ 
+
+ align:start position:0%
+epsilon irs cancel and then we get
+exactly actually the same expression we
+
+ align:start position:0%
+exactly actually the same expression we
+ 
+
+ align:start position:0%
+exactly actually the same expression we
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+before but where all those one over
+
+ align:start position:0%
+before but where all those one over
+ 
+
+ align:start position:0%
+before but where all those one over
+epsilons are one over epsilon uvs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from both terms so they both have
+
+ align:start position:0%
+from both terms so they both have
+ 
+
+ align:start position:0%
+from both terms so they both have
+epsilon irs but they cancel between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and the remainder is just epsilon
+
+ align:start position:0%
+yeah and the remainder is just epsilon
+ 
+
+ align:start position:0%
+yeah and the remainder is just epsilon
+uv so all the epsilons that i wrote my
+
+ align:start position:0%
+uv so all the epsilons that i wrote my
+ 
+
+ align:start position:0%
+uv so all the epsilons that i wrote my
+earlier formula would be now epsilon uvs
+
+ align:start position:0%
+earlier formula would be now epsilon uvs
+ 
+
+ align:start position:0%
+earlier formula would be now epsilon uvs
+once i take into account the subtraction
+
+ align:start position:0%
+once i take into account the subtraction
+ 
+
+ align:start position:0%
+once i take into account the subtraction
+so i could have just ignored the
+
+ align:start position:0%
+so i could have just ignored the
+ 
+
+ align:start position:0%
+so i could have just ignored the
+subtraction and that's a lot often what
+
+ align:start position:0%
+subtraction and that's a lot often what
+ 
+
+ align:start position:0%
+subtraction and that's a lot often what
+people do once if they know that this is
+
+ align:start position:0%
+people do once if they know that this is
+ 
+
+ align:start position:0%
+people do once if they know that this is
+that the zero bins are kind of giving a
+
+ align:start position:0%
+that the zero bins are kind of giving a
+ 
+
+ align:start position:0%
+that the zero bins are kind of giving a
+scalar integral they say well let's
+
+ align:start position:0%
+scalar integral they say well let's
+ 
+
+ align:start position:0%
+scalar integral they say well let's
+ignore the subtraction we'll just say
+
+ align:start position:0%
+ignore the subtraction we'll just say
+ 
+
+ align:start position:0%
+ignore the subtraction we'll just say
+that all the epsilons are uv
+
+ align:start position:0%
+that all the epsilons are uv
+ 
+
+ align:start position:0%
+that all the epsilons are uv
+and the zero bin makes them uv
+
+ align:start position:0%
+and the zero bin makes them uv
+ 
+
+ align:start position:0%
+and the zero bin makes them uv
+but if we really want to look and see
+
+ align:start position:0%
+but if we really want to look and see
+ 
+
+ align:start position:0%
+but if we really want to look and see
+that things are working properly we
+
+ align:start position:0%
+that things are working properly we
+ 
+
+ align:start position:0%
+that things are working properly we
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+take the subtraction and calculate it
+
+ align:start position:0%
+take the subtraction and calculate it
+ 
+
+ align:start position:0%
+take the subtraction and calculate it
+and make sure that that's true
+
+ align:start position:0%
+and make sure that that's true
+ 
+
+ align:start position:0%
+and make sure that that's true
+but we could have just taken the answer
+
+ align:start position:0%
+but we could have just taken the answer
+ 
+
+ align:start position:0%
+but we could have just taken the answer
+that i wrote down earlier and said those
+
+ align:start position:0%
+that i wrote down earlier and said those
+ 
+
+ align:start position:0%
+that i wrote down earlier and said those
+epsilons are ultraviolet and let's throw
+
+ align:start position:0%
+epsilons are ultraviolet and let's throw
+ 
+
+ align:start position:0%
+epsilons are ultraviolet and let's throw
+them in a counter term and calculate an
+
+ align:start position:0%
+them in a counter term and calculate an
+ 
+
+ align:start position:0%
+them in a counter term and calculate an
+almost dimension and that is indeed so
+
+ align:start position:0%
+almost dimension and that is indeed so
+ 
+
+ align:start position:0%
+almost dimension and that is indeed so
+we'll go we'll proceed that way next
+
+ align:start position:0%
+we'll go we'll proceed that way next
+ 
+
+ align:start position:0%
+we'll go we'll proceed that way next
+time but we now know that actually they
+
+ align:start position:0%
+time but we now know that actually they
+ 
+
+ align:start position:0%
+time but we now know that actually they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+ultraviolet divergences
+
+ align:start position:0%
+ultraviolet divergences
+ 
+
+ align:start position:0%
+ultraviolet divergences
+so next time we'll take that that count
+
+ align:start position:0%
+so next time we'll take that that count
+ 
+
+ align:start position:0%
+so next time we'll take that that count
+the ultraviolet divergences and we'll
+
+ align:start position:0%
+the ultraviolet divergences and we'll
+ 
+
+ align:start position:0%
+the ultraviolet divergences and we'll
+define from them a counter term
+
+ align:start position:0%
+define from them a counter term
+ 
+
+ align:start position:0%
+define from them a counter term
+and we'll see how we get an almost
+
+ align:start position:0%
+and we'll see how we get an almost
+ 
+
+ align:start position:0%
+and we'll see how we get an almost
+dimension and what kind of logs
+
+ align:start position:0%
+dimension and what kind of logs
+ 
+
+ align:start position:0%
+dimension and what kind of logs
+we sum by using that in anomalous
+
+ align:start position:0%
+we sum by using that in anomalous
+ 
+
+ align:start position:0%
+we sum by using that in anomalous
+dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the zero bin that that's scalars in
+
+ align:start position:0%
+so the zero bin that that's scalars in
+ 
+
+ align:start position:0%
+so the zero bin that that's scalars in
+this particular example is not always
+
+ align:start position:0%
+this particular example is not always
+ 
+
+ align:start position:0%
+this particular example is not always
+scaleless so sometimes it could give the
+
+ align:start position:0%
+scaleless so sometimes it could give the
+ 
+
+ align:start position:0%
+scaleless so sometimes it could give the
+non depends on the problem you're
+
+ align:start position:0%
+non depends on the problem you're
+ 
+
+ align:start position:0%
+non depends on the problem you're
+dealing with so
+
+ align:start position:0%
+dealing with so
+ 
+
+ align:start position:0%
+dealing with so
+if you're
+
+ align:start position:0%
+if you're
+ 
+
+ align:start position:0%
+if you're
+sometimes you can set things up so
+
+ align:start position:0%
+sometimes you can set things up so
+ 
+
+ align:start position:0%
+sometimes you can set things up so
+that's scalise and then you just
+
+ align:start position:0%
+that's scalise and then you just
+ 
+
+ align:start position:0%
+that's scalise and then you just
+basically can ignore it
+
+ align:start position:0%
+basically can ignore it
+ 
+
+ align:start position:0%
+basically can ignore it
+but that's not always true so you do
+
+ align:start position:0%
+but that's not always true so you do
+ 
+
+ align:start position:0%
+but that's not always true so you do
+have to think about whether it's really
+
+ align:start position:0%
+have to think about whether it's really
+ 
+
+ align:start position:0%
+have to think about whether it's really
+going to be true for what you're doing
+
+ align:start position:0%
+going to be true for what you're doing
+ 
+
+ align:start position:0%
+going to be true for what you're doing
+if it is true then you can ignore then
+
+ align:start position:0%
+if it is true then you can ignore then
+ 
+
+ align:start position:0%
+if it is true then you can ignore then
+you could effectively ignore it because
+
+ align:start position:0%
+you could effectively ignore it because
+ 
+
+ align:start position:0%
+you could effectively ignore it because
+it's sort of just
+
+ align:start position:0%
+it's sort of just
+ 
+
+ align:start position:0%
+it's sort of just
+making the physics come out right making
+
+ align:start position:0%
+making the physics come out right making
+ 
+
+ align:start position:0%
+making the physics come out right making
+sure there's no overlap but if your
+
+ align:start position:0%
+sure there's no overlap but if your
+ 
+
+ align:start position:0%
+sure there's no overlap but if your
+regulator is set up so that it's
+
+ align:start position:0%
+regulator is set up so that it's
+ 
+
+ align:start position:0%
+regulator is set up so that it's
+scaleless you can kind of just
+
+ align:start position:0%
+scaleless you can kind of just
+ 
+
+ align:start position:0%
+scaleless you can kind of just
+get around it but in general that might
+
+ align:start position:0%
+get around it but in general that might
+ 
+
+ align:start position:0%
+get around it but in general that might
+not be true
+
+ align:start position:0%
+not be true
+ 
+
+ align:start position:0%
+not be true
+if you had more scales in the problem if
+
+ align:start position:0%
+if you had more scales in the problem if
+ 
+
+ align:start position:0%
+if you had more scales in the problem if
+you're doing some calculation that had
+
+ align:start position:0%
+you're doing some calculation that had
+ 
+
+ align:start position:0%
+you're doing some calculation that had
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+jets a finite size then
+
+ align:start position:0%
+jets a finite size then
+ 
+
+ align:start position:0%
+jets a finite size then
+that won't be true
+
+ align:start position:0%
+that won't be true
+ 
+
+ align:start position:0%
+that won't be true
+typically
\ No newline at end of file
diff --git a/q2mz6LZVnT8.txt b/q2mz6LZVnT8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..340111353242488f22b3b84d6b19e114d5783a54
--- /dev/null
+++ b/q2mz6LZVnT8.txt
@@ -0,0 +1,1531 @@
+align:start position:0%
+ 
+we're talking today about the role that
+
+ align:start position:0%
+we're talking today about the role that
+ 
+
+ align:start position:0%
+we're talking today about the role that
+shaping the future work
+
+ align:start position:0%
+shaping the future work
+ 
+
+ align:start position:0%
+shaping the future work
+we're talking with Professor Scott's
+
+ align:start position:0%
+we're talking with Professor Scott's
+ 
+
+ align:start position:0%
+we're talking with Professor Scott's
+turn the chair of our Sloan schools
+
+ align:start position:0%
+turn the chair of our Sloan schools
+ 
+
+ align:start position:0%
+turn the chair of our Sloan schools
+technological innovation
+
+ align:start position:0%
+technological innovation
+ 
+
+ align:start position:0%
+technological innovation
+entrepreneurship and strategy group and
+
+ align:start position:0%
+entrepreneurship and strategy group and
+ 
+
+ align:start position:0%
+entrepreneurship and strategy group and
+with Barbara Dyer the president of
+
+ align:start position:0%
+with Barbara Dyer the president of
+ 
+
+ align:start position:0%
+with Barbara Dyer the president of
+Hitachi foundation the foundation works
+
+ align:start position:0%
+Hitachi foundation the foundation works
+ 
+
+ align:start position:0%
+Hitachi foundation the foundation works
+with entrepreneurs to build both good
+
+ align:start position:0%
+with entrepreneurs to build both good
+ 
+
+ align:start position:0%
+with entrepreneurs to build both good
+companies that are financially
+
+ align:start position:0%
+companies that are financially
+ 
+
+ align:start position:0%
+companies that are financially
+successful as well as ones that provide
+
+ align:start position:0%
+successful as well as ones that provide
+ 
+
+ align:start position:0%
+successful as well as ones that provide
+good job opportunities can entrepreneurs
+
+ align:start position:0%
+good job opportunities can entrepreneurs
+ 
+
+ align:start position:0%
+good job opportunities can entrepreneurs
+build a good job strategy creating good
+
+ align:start position:0%
+build a good job strategy creating good
+ 
+
+ align:start position:0%
+build a good job strategy creating good
+opportunities for the full workforce in
+
+ align:start position:0%
+opportunities for the full workforce in
+ 
+
+ align:start position:0%
+opportunities for the full workforce in
+from the beginning so I think one of the
+
+ align:start position:0%
+from the beginning so I think one of the
+ 
+
+ align:start position:0%
+from the beginning so I think one of the
+greatest misconceptions is that being a
+
+ align:start position:0%
+greatest misconceptions is that being a
+ 
+
+ align:start position:0%
+greatest misconceptions is that being a
+good entrepreneur and building a company
+
+ align:start position:0%
+good entrepreneur and building a company
+ 
+
+ align:start position:0%
+good entrepreneur and building a company
+that really scales is actually in
+
+ align:start position:0%
+that really scales is actually in
+ 
+
+ align:start position:0%
+that really scales is actually in
+opposition to building a company that
+
+ align:start position:0%
+opposition to building a company that
+ 
+
+ align:start position:0%
+opposition to building a company that
+creates great jobs in fact I'd claim
+
+ align:start position:0%
+creates great jobs in fact I'd claim
+ 
+
+ align:start position:0%
+creates great jobs in fact I'd claim
+that exactly the reverse is true to
+
+ align:start position:0%
+that exactly the reverse is true to
+ 
+
+ align:start position:0%
+that exactly the reverse is true to
+attract the really best people to really
+
+ align:start position:0%
+attract the really best people to really
+ 
+
+ align:start position:0%
+attract the really best people to really
+create meaningful innovative value for
+
+ align:start position:0%
+create meaningful innovative value for
+ 
+
+ align:start position:0%
+create meaningful innovative value for
+consumers to really be in a situation
+
+ align:start position:0%
+consumers to really be in a situation
+ 
+
+ align:start position:0%
+consumers to really be in a situation
+where ultimately you are able to charge
+
+ align:start position:0%
+where ultimately you are able to charge
+ 
+
+ align:start position:0%
+where ultimately you are able to charge
+a price well above your cost and create
+
+ align:start position:0%
+a price well above your cost and create
+ 
+
+ align:start position:0%
+a price well above your cost and create
+that kind of value means that you need
+
+ align:start position:0%
+that kind of value means that you need
+ 
+
+ align:start position:0%
+that kind of value means that you need
+to be attracting nurturing investing in
+
+ align:start position:0%
+to be attracting nurturing investing in
+ 
+
+ align:start position:0%
+to be attracting nurturing investing in
+employees in meaningful ways if everyone
+
+ align:start position:0%
+employees in meaningful ways if everyone
+ 
+
+ align:start position:0%
+employees in meaningful ways if everyone
+who shows up to your company is simply
+
+ align:start position:0%
+who shows up to your company is simply
+ 
+
+ align:start position:0%
+who shows up to your company is simply
+you all it is about cost well then
+
+ align:start position:0%
+you all it is about cost well then
+ 
+
+ align:start position:0%
+you all it is about cost well then
+there's not much of a company at all
+
+ align:start position:0%
+there's not much of a company at all
+ 
+
+ align:start position:0%
+there's not much of a company at all
+there's not much of an organization
+
+ align:start position:0%
+there's not much of an organization
+ 
+
+ align:start position:0%
+there's not much of an organization
+there what we've observed at the nearly
+
+ align:start position:0%
+there what we've observed at the nearly
+ 
+
+ align:start position:0%
+there what we've observed at the nearly
+100 companies that we've looked at
+
+ align:start position:0%
+100 companies that we've looked at
+ 
+
+ align:start position:0%
+100 companies that we've looked at
+across healthcare and manufacturing is
+
+ align:start position:0%
+across healthcare and manufacturing is
+ 
+
+ align:start position:0%
+across healthcare and manufacturing is
+it the businesses that create great
+
+ align:start position:0%
+it the businesses that create great
+ 
+
+ align:start position:0%
+it the businesses that create great
+quality jobs don't begin with the
+
+ align:start position:0%
+quality jobs don't begin with the
+ 
+
+ align:start position:0%
+quality jobs don't begin with the
+premise that this is a good HR strategy
+
+ align:start position:0%
+premise that this is a good HR strategy
+ 
+
+ align:start position:0%
+premise that this is a good HR strategy
+they start with what is excellence and
+
+ align:start position:0%
+they start with what is excellence and
+ 
+
+ align:start position:0%
+they start with what is excellence and
+they very quickly figure out that the
+
+ align:start position:0%
+they very quickly figure out that the
+ 
+
+ align:start position:0%
+they very quickly figure out that the
+workforce piece of it is a critical part
+
+ align:start position:0%
+workforce piece of it is a critical part
+ 
+
+ align:start position:0%
+workforce piece of it is a critical part
+of operations they have to invest in
+
+ align:start position:0%
+of operations they have to invest in
+ 
+
+ align:start position:0%
+of operations they have to invest in
+their people and they have to create
+
+ align:start position:0%
+their people and they have to create
+ 
+
+ align:start position:0%
+their people and they have to create
+systems to provide ongoing support
+
+ align:start position:0%
+systems to provide ongoing support
+ 
+
+ align:start position:0%
+systems to provide ongoing support
+ongoing learning ongoing incentives so
+
+ align:start position:0%
+ongoing learning ongoing incentives so
+ 
+
+ align:start position:0%
+ongoing learning ongoing incentives so
+that their people are really delivering
+
+ align:start position:0%
+that their people are really delivering
+ 
+
+ align:start position:0%
+that their people are really delivering
+in the best possible way we hear that
+
+ align:start position:0%
+in the best possible way we hear that
+ 
+
+ align:start position:0%
+in the best possible way we hear that
+many investors have a mindset that labor
+
+ align:start position:0%
+many investors have a mindset that labor
+ 
+
+ align:start position:0%
+many investors have a mindset that labor
+is a cost
+
+ align:start position:0%
+is a cost
+ 
+
+ align:start position:0%
+is a cost
+minimized and and put a lot of pressure
+
+ align:start position:0%
+minimized and and put a lot of pressure
+ 
+
+ align:start position:0%
+minimized and and put a lot of pressure
+on entrepreneurs how can we overcome
+
+ align:start position:0%
+on entrepreneurs how can we overcome
+ 
+
+ align:start position:0%
+on entrepreneurs how can we overcome
+that resistance we have to do the hard
+
+ align:start position:0%
+that resistance we have to do the hard
+ 
+
+ align:start position:0%
+that resistance we have to do the hard
+work of persuading investors that it's
+
+ align:start position:0%
+work of persuading investors that it's
+ 
+
+ align:start position:0%
+work of persuading investors that it's
+not a choice between lower profits but a
+
+ align:start position:0%
+not a choice between lower profits but a
+ 
+
+ align:start position:0%
+not a choice between lower profits but a
+better workforce right versus higher
+
+ align:start position:0%
+better workforce right versus higher
+ 
+
+ align:start position:0%
+better workforce right versus higher
+profits and cheaper workforce instead
+
+ align:start position:0%
+profits and cheaper workforce instead
+ 
+
+ align:start position:0%
+profits and cheaper workforce instead
+the choice is for equally viable
+
+ align:start position:0%
+the choice is for equally viable
+ 
+
+ align:start position:0%
+the choice is for equally viable
+businesses we get to choose the kind of
+
+ align:start position:0%
+businesses we get to choose the kind of
+ 
+
+ align:start position:0%
+businesses we get to choose the kind of
+organizations we built successful
+
+ align:start position:0%
+organizations we built successful
+ 
+
+ align:start position:0%
+organizations we built successful
+venture capitalists who have built
+
+ align:start position:0%
+venture capitalists who have built
+ 
+
+ align:start position:0%
+venture capitalists who have built
+successful companies they meaningfully
+
+ align:start position:0%
+successful companies they meaningfully
+ 
+
+ align:start position:0%
+successful companies they meaningfully
+talk about the great organizations
+
+ align:start position:0%
+talk about the great organizations
+ 
+
+ align:start position:0%
+talk about the great organizations
+they've built entrepreneurs are
+
+ align:start position:0%
+they've built entrepreneurs are
+ 
+
+ align:start position:0%
+they've built entrepreneurs are
+uncomfortable talking to investors about
+
+ align:start position:0%
+uncomfortable talking to investors about
+ 
+
+ align:start position:0%
+uncomfortable talking to investors about
+a workforce strategy they are concerned
+
+ align:start position:0%
+a workforce strategy they are concerned
+ 
+
+ align:start position:0%
+a workforce strategy they are concerned
+that investors will view this as excess
+
+ align:start position:0%
+that investors will view this as excess
+ 
+
+ align:start position:0%
+that investors will view this as excess
+as having too high a burn rate they
+
+ align:start position:0%
+as having too high a burn rate they
+ 
+
+ align:start position:0%
+as having too high a burn rate they
+don't have fully at their grasp the
+
+ align:start position:0%
+don't have fully at their grasp the
+ 
+
+ align:start position:0%
+don't have fully at their grasp the
+economics of it they can't really make
+
+ align:start position:0%
+economics of it they can't really make
+ 
+
+ align:start position:0%
+economics of it they can't really make
+the business case as well as they might
+
+ align:start position:0%
+the business case as well as they might
+ 
+
+ align:start position:0%
+the business case as well as they might
+like to as to why it is that building a
+
+ align:start position:0%
+like to as to why it is that building a
+ 
+
+ align:start position:0%
+like to as to why it is that building a
+strategy like this will end up achieving
+
+ align:start position:0%
+strategy like this will end up achieving
+ 
+
+ align:start position:0%
+strategy like this will end up achieving
+the numbers in the next 25 10 years
+
+ align:start position:0%
+the numbers in the next 25 10 years
+ 
+
+ align:start position:0%
+the numbers in the next 25 10 years
+there is a tendency to expect that at
+
+ align:start position:0%
+there is a tendency to expect that at
+ 
+
+ align:start position:0%
+there is a tendency to expect that at
+the startup phase the founders will
+
+ align:start position:0%
+the startup phase the founders will
+ 
+
+ align:start position:0%
+the startup phase the founders will
+certainly work for below market rates
+
+ align:start position:0%
+certainly work for below market rates
+ 
+
+ align:start position:0%
+certainly work for below market rates
+and that the people that are hired will
+
+ align:start position:0%
+and that the people that are hired will
+ 
+
+ align:start position:0%
+and that the people that are hired will
+work for below market rates they'll work
+
+ align:start position:0%
+work for below market rates they'll work
+ 
+
+ align:start position:0%
+work for below market rates they'll work
+around the clock there should be no
+
+ align:start position:0%
+around the clock there should be no
+ 
+
+ align:start position:0%
+around the clock there should be no
+expectation of salary increases or
+
+ align:start position:0%
+expectation of salary increases or
+ 
+
+ align:start position:0%
+expectation of salary increases or
+benefits because the company hasn't
+
+ align:start position:0%
+benefits because the company hasn't
+ 
+
+ align:start position:0%
+benefits because the company hasn't
+started generating a profit now you're a
+
+ align:start position:0%
+started generating a profit now you're a
+ 
+
+ align:start position:0%
+started generating a profit now you're a
+scholar you know that the research tells
+
+ align:start position:0%
+scholar you know that the research tells
+ 
+
+ align:start position:0%
+scholar you know that the research tells
+us that if you build into the DNA of a
+
+ align:start position:0%
+us that if you build into the DNA of a
+ 
+
+ align:start position:0%
+us that if you build into the DNA of a
+company from the very start this kind of
+
+ align:start position:0%
+company from the very start this kind of
+ 
+
+ align:start position:0%
+company from the very start this kind of
+commitment this kind of strategy it'll
+
+ align:start position:0%
+commitment this kind of strategy it'll
+ 
+
+ align:start position:0%
+commitment this kind of strategy it'll
+be the driving framework for the company
+
+ align:start position:0%
+be the driving framework for the company
+ 
+
+ align:start position:0%
+be the driving framework for the company
+over time and so that's where all the
+
+ align:start position:0%
+over time and so that's where all the
+ 
+
+ align:start position:0%
+over time and so that's where all the
+evidence from other organizations plays
+
+ align:start position:0%
+evidence from other organizations plays
+ 
+
+ align:start position:0%
+evidence from other organizations plays
+in if you can help them to make that
+
+ align:start position:0%
+in if you can help them to make that
+ 
+
+ align:start position:0%
+in if you can help them to make that
+business case to understand the
+
+ align:start position:0%
+business case to understand the
+ 
+
+ align:start position:0%
+business case to understand the
+potential then there's some hope and so
+
+ align:start position:0%
+potential then there's some hope and so
+ 
+
+ align:start position:0%
+potential then there's some hope and so
+we have to find ways to deal with that
+
+ align:start position:0%
+we have to find ways to deal with that
+ 
+
+ align:start position:0%
+we have to find ways to deal with that
+could you give us an example of an
+
+ align:start position:0%
+could you give us an example of an
+ 
+
+ align:start position:0%
+could you give us an example of an
+organization or two that has really
+
+ align:start position:0%
+organization or two that has really
+ 
+
+ align:start position:0%
+organization or two that has really
+invested in this way take for example BP
+
+ align:start position:0%
+invested in this way take for example BP
+ 
+
+ align:start position:0%
+invested in this way take for example BP
+BP is an online car marketplace that's
+
+ align:start position:0%
+BP is an online car marketplace that's
+ 
+
+ align:start position:0%
+BP is an online car marketplace that's
+really kind of fixing the lemons problem
+
+ align:start position:0%
+really kind of fixing the lemons problem
+ 
+
+ align:start position:0%
+really kind of fixing the lemons problem
+for used cars basically right now you
+
+ align:start position:0%
+for used cars basically right now you
+ 
+
+ align:start position:0%
+for used cars basically right now you
+can think of the used-car industry is
+
+ align:start position:0%
+can think of the used-car industry is
+ 
+
+ align:start position:0%
+can think of the used-car industry is
+definitely not associated with a good
+
+ align:start position:0%
+definitely not associated with a good
+ 
+
+ align:start position:0%
+definitely not associated with a good
+job strategy not even a good service one
+
+ align:start position:0%
+job strategy not even a good service one
+ 
+
+ align:start position:0%
+job strategy not even a good service one
+of the key choices that alley resident
+
+ align:start position:0%
+of the key choices that alley resident
+ 
+
+ align:start position:0%
+of the key choices that alley resident
+one of the founders of this firm had to
+
+ align:start position:0%
+one of the founders of this firm had to
+ 
+
+ align:start position:0%
+one of the founders of this firm had to
+make was whether or not the technicians
+
+ align:start position:0%
+make was whether or not the technicians
+ 
+
+ align:start position:0%
+make was whether or not the technicians
+the people who'd be inspecting the cars
+
+ align:start position:0%
+the people who'd be inspecting the cars
+ 
+
+ align:start position:0%
+the people who'd be inspecting the cars
+was going to be hiring a series of
+
+ align:start position:0%
+was going to be hiring a series of
+ 
+
+ align:start position:0%
+was going to be hiring a series of
+contractor inspectors or whether or not
+
+ align:start position:0%
+contractor inspectors or whether or not
+ 
+
+ align:start position:0%
+contractor inspectors or whether or not
+he'd be investing in long-term employees
+
+ align:start position:0%
+he'd be investing in long-term employees
+ 
+
+ align:start position:0%
+he'd be investing in long-term employees
+he got different advice from different
+
+ align:start position:0%
+he got different advice from different
+ 
+
+ align:start position:0%
+he got different advice from different
+investors about that choice he
+
+ align:start position:0%
+investors about that choice he
+ 
+
+ align:start position:0%
+investors about that choice he
+ultimately decided that the strength and
+
+ align:start position:0%
+ultimately decided that the strength and
+ 
+
+ align:start position:0%
+ultimately decided that the strength and
+the quality and the innovations of his
+
+ align:start position:0%
+the quality and the innovations of his
+ 
+
+ align:start position:0%
+the quality and the innovations of his
+company could best be made by investing
+
+ align:start position:0%
+company could best be made by investing
+ 
+
+ align:start position:0%
+company could best be made by investing
+in employees they all those employees
+
+ align:start position:0%
+in employees they all those employees
+ 
+
+ align:start position:0%
+in employees they all those employees
+get extensive training they're upping
+
+ align:start position:0%
+get extensive training they're upping
+ 
+
+ align:start position:0%
+get extensive training they're upping
+their skill level they get some equity
+
+ align:start position:0%
+their skill level they get some equity
+ 
+
+ align:start position:0%
+their skill level they get some equity
+in the company and as that company has
+
+ align:start position:0%
+in the company and as that company has
+ 
+
+ align:start position:0%
+in the company and as that company has
+grown all of a sudden they are the
+
+ align:start position:0%
+grown all of a sudden they are the
+ 
+
+ align:start position:0%
+grown all of a sudden they are the
+single most visible and single most
+
+ align:start position:0%
+single most visible and single most
+ 
+
+ align:start position:0%
+single most visible and single most
+memorable and single best advocates for
+
+ align:start position:0%
+memorable and single best advocates for
+ 
+
+ align:start position:0%
+memorable and single best advocates for
+the company as it's scaled across the
+
+ align:start position:0%
+the company as it's scaled across the
+ 
+
+ align:start position:0%
+the company as it's scaled across the
+United States jessamine Rodriguez who is
+
+ align:start position:0%
+United States jessamine Rodriguez who is
+ 
+
+ align:start position:0%
+United States jessamine Rodriguez who is
+the founder of hot bread kitchen started
+
+ align:start position:0%
+the founder of hot bread kitchen started
+ 
+
+ align:start position:0%
+the founder of hot bread kitchen started
+with a long-term vision the idea was to
+
+ align:start position:0%
+with a long-term vision the idea was to
+ 
+
+ align:start position:0%
+with a long-term vision the idea was to
+enable primarily immigrant but other
+
+ align:start position:0%
+enable primarily immigrant but other
+ 
+
+ align:start position:0%
+enable primarily immigrant but other
+women and men who have an ethnic bread
+
+ align:start position:0%
+women and men who have an ethnic bread
+ 
+
+ align:start position:0%
+women and men who have an ethnic bread
+to take that to the market to create
+
+ align:start position:0%
+to take that to the market to create
+ 
+
+ align:start position:0%
+to take that to the market to create
+real economic opportunity through baking
+
+ align:start position:0%
+real economic opportunity through baking
+ 
+
+ align:start position:0%
+real economic opportunity through baking
+bread and to enable them to build their
+
+ align:start position:0%
+bread and to enable them to build their
+ 
+
+ align:start position:0%
+bread and to enable them to build their
+own businesses around their particular
+
+ align:start position:0%
+own businesses around their particular
+ 
+
+ align:start position:0%
+own businesses around their particular
+craft and so hot bread kitchen now very
+
+ align:start position:0%
+craft and so hot bread kitchen now very
+ 
+
+ align:start position:0%
+craft and so hot bread kitchen now very
+successful operation in Harlem is
+
+ align:start position:0%
+successful operation in Harlem is
+ 
+
+ align:start position:0%
+successful operation in Harlem is
+incubating bread businesses throughout
+
+ align:start position:0%
+incubating bread businesses throughout
+ 
+
+ align:start position:0%
+incubating bread businesses throughout
+New York and beyond so it's a bakery yes
+
+ align:start position:0%
+New York and beyond so it's a bakery yes
+ 
+
+ align:start position:0%
+New York and beyond so it's a bakery yes
+but it's far more than that and to help
+
+ align:start position:0%
+but it's far more than that and to help
+ 
+
+ align:start position:0%
+but it's far more than that and to help
+individuals to kind of build math skills
+
+ align:start position:0%
+individuals to kind of build math skills
+ 
+
+ align:start position:0%
+individuals to kind of build math skills
+while they're creating breads to build
+
+ align:start position:0%
+while they're creating breads to build
+ 
+
+ align:start position:0%
+while they're creating breads to build
+business skills while they're creating
+
+ align:start position:0%
+business skills while they're creating
+ 
+
+ align:start position:0%
+business skills while they're creating
+breads to build marketing
+
+ align:start position:0%
+breads to build marketing
+ 
+
+ align:start position:0%
+breads to build marketing
+skills while they're creating bread was
+
+ align:start position:0%
+skills while they're creating bread was
+ 
+
+ align:start position:0%
+skills while they're creating bread was
+a brilliant touch the bakery is a great
+
+ align:start position:0%
+a brilliant touch the bakery is a great
+ 
+
+ align:start position:0%
+a brilliant touch the bakery is a great
+example in one place I should clearly
+
+ align:start position:0%
+example in one place I should clearly
+ 
+
+ align:start position:0%
+example in one place I should clearly
+visit how about other examples recently
+
+ align:start position:0%
+visit how about other examples recently
+ 
+
+ align:start position:0%
+visit how about other examples recently
+we were supporting a sector of energy
+
+ align:start position:0%
+we were supporting a sector of energy
+ 
+
+ align:start position:0%
+we were supporting a sector of energy
+entrepreneurs looking to address issues
+
+ align:start position:0%
+entrepreneurs looking to address issues
+ 
+
+ align:start position:0%
+entrepreneurs looking to address issues
+of climate change and one company
+
+ align:start position:0%
+of climate change and one company
+ 
+
+ align:start position:0%
+of climate change and one company
+rebound is a remarkable refrigeration
+
+ align:start position:0%
+rebound is a remarkable refrigeration
+ 
+
+ align:start position:0%
+rebound is a remarkable refrigeration
+company that has the potential of saving
+
+ align:start position:0%
+company that has the potential of saving
+ 
+
+ align:start position:0%
+company that has the potential of saving
+supermarkets enormous amount of money in
+
+ align:start position:0%
+supermarkets enormous amount of money in
+ 
+
+ align:start position:0%
+supermarkets enormous amount of money in
+refrigeration costs and dramatically
+
+ align:start position:0%
+refrigeration costs and dramatically
+ 
+
+ align:start position:0%
+refrigeration costs and dramatically
+reducing the amount of co2 the founder
+
+ align:start position:0%
+reducing the amount of co2 the founder
+ 
+
+ align:start position:0%
+reducing the amount of co2 the founder
+of that company is eager to build a
+
+ align:start position:0%
+of that company is eager to build a
+ 
+
+ align:start position:0%
+of that company is eager to build a
+business that is focused on good people
+
+ align:start position:0%
+business that is focused on good people
+ 
+
+ align:start position:0%
+business that is focused on good people
+great jobs pathways of upward mobility
+
+ align:start position:0%
+great jobs pathways of upward mobility
+ 
+
+ align:start position:0%
+great jobs pathways of upward mobility
+it's who he is it's where he wants to
+
+ align:start position:0%
+it's who he is it's where he wants to
+ 
+
+ align:start position:0%
+it's who he is it's where he wants to
+take his company entrepreneurship can be
+
+ align:start position:0%
+take his company entrepreneurship can be
+ 
+
+ align:start position:0%
+take his company entrepreneurship can be
+used to provide good jobs how do we get
+
+ align:start position:0%
+used to provide good jobs how do we get
+ 
+
+ align:start position:0%
+used to provide good jobs how do we get
+this to become the norm people need to
+
+ align:start position:0%
+this to become the norm people need to
+ 
+
+ align:start position:0%
+this to become the norm people need to
+vote with their feet right as you when
+
+ align:start position:0%
+vote with their feet right as you when
+ 
+
+ align:start position:0%
+vote with their feet right as you when
+you think about joining a company when
+
+ align:start position:0%
+you think about joining a company when
+ 
+
+ align:start position:0%
+you think about joining a company when
+you think about as say you're in a big
+
+ align:start position:0%
+you think about as say you're in a big
+ 
+
+ align:start position:0%
+you think about as say you're in a big
+company thinking about which kind of
+
+ align:start position:0%
+company thinking about which kind of
+ 
+
+ align:start position:0%
+company thinking about which kind of
+companies to partner with when you think
+
+ align:start position:0%
+companies to partner with when you think
+ 
+
+ align:start position:0%
+companies to partner with when you think
+about I even as an investor make sure
+
+ align:start position:0%
+about I even as an investor make sure
+ 
+
+ align:start position:0%
+about I even as an investor make sure
+you're having that conversation and
+
+ align:start position:0%
+you're having that conversation and
+ 
+
+ align:start position:0%
+you're having that conversation and
+understanding as you're selecting among
+
+ align:start position:0%
+understanding as you're selecting among
+ 
+
+ align:start position:0%
+understanding as you're selecting among
+different groups to work with different
+
+ align:start position:0%
+different groups to work with different
+ 
+
+ align:start position:0%
+different groups to work with different
+firms to work with even different
+
+ align:start position:0%
+firms to work with even different
+ 
+
+ align:start position:0%
+firms to work with even different
+portfolio companies to invest in go one
+
+ align:start position:0%
+portfolio companies to invest in go one
+ 
+
+ align:start position:0%
+portfolio companies to invest in go one
+layer beyond the simple value creation
+
+ align:start position:0%
+layer beyond the simple value creation
+ 
+
+ align:start position:0%
+layer beyond the simple value creation
+value capture logic and get to the
+
+ align:start position:0%
+value capture logic and get to the
+ 
+
+ align:start position:0%
+value capture logic and get to the
+organization and the team you are more
+
+ align:start position:0%
+organization and the team you are more
+ 
+
+ align:start position:0%
+organization and the team you are more
+likely to be investing in a long-term
+
+ align:start position:0%
+likely to be investing in a long-term
+ 
+
+ align:start position:0%
+likely to be investing in a long-term
+play that really delivers fundamental
+
+ align:start position:0%
+play that really delivers fundamental
+ 
+
+ align:start position:0%
+play that really delivers fundamental
+value and really delivers strong returns
+
+ align:start position:0%
+value and really delivers strong returns
+ 
+
+ align:start position:0%
+value and really delivers strong returns
+if you're investing in the kind of
+
+ align:start position:0%
+if you're investing in the kind of
+ 
+
+ align:start position:0%
+if you're investing in the kind of
+company that people are going to be
+
+ align:start position:0%
+company that people are going to be
+ 
+
+ align:start position:0%
+company that people are going to be
+attracted to and allows people to
+
+ align:start position:0%
+attracted to and allows people to
+ 
+
+ align:start position:0%
+attracted to and allows people to
+nurture and grow well Scott I think this
+
+ align:start position:0%
+nurture and grow well Scott I think this
+ 
+
+ align:start position:0%
+nurture and grow well Scott I think this
+is an important message for
+
+ align:start position:0%
+is an important message for
+ 
+
+ align:start position:0%
+is an important message for
+entrepreneurs for investors and for
+
+ align:start position:0%
+entrepreneurs for investors and for
+ 
+
+ align:start position:0%
+entrepreneurs for investors and for
+young people who really do want to build
+
+ align:start position:0%
+young people who really do want to build
+ 
+
+ align:start position:0%
+young people who really do want to build
+great companies that address big
+
+ align:start position:0%
+great companies that address big
+ 
+
+ align:start position:0%
+great companies that address big
+problems in society that are successful
+
+ align:start position:0%
+problems in society that are successful
+ 
+
+ align:start position:0%
+problems in society that are successful
+and that provide good jobs and career
+
+ align:start position:0%
+and that provide good jobs and career
+ 
+
+ align:start position:0%
+and that provide good jobs and career
+opportunities to their peers so thank
+
+ align:start position:0%
+opportunities to their peers so thank
+ 
+
+ align:start position:0%
+opportunities to their peers so thank
+you very much thank you very much as
+
+ align:start position:0%
+you very much thank you very much as
+ 
+
+ align:start position:0%
+you very much thank you very much as
+well thank you so much thank you for
+
+ align:start position:0%
+well thank you so much thank you for
+ 
+
+ align:start position:0%
+well thank you so much thank you for
+your time today you're welcome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/r2NMWEsNcTs.txt b/r2NMWEsNcTs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4bf3f412bb784decb0c49dfca6f3cd2ff0da326e
--- /dev/null
+++ b/r2NMWEsNcTs.txt
@@ -0,0 +1,11323 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mmit.edu. about a theorem that
+
+ align:start position:0%
+ocw.mmit.edu. about a theorem that
+ 
+
+ align:start position:0%
+ocw.mmit.edu. about a theorem that
+was quite powerful and applied to
+
+ align:start position:0%
+was quite powerful and applied to
+ 
+
+ align:start position:0%
+was quite powerful and applied to
+complex vector
+
+ align:start position:0%
+complex vector
+ 
+
+ align:start position:0%
+complex vector
+spaces for all V belonging to
+
+ align:start position:0%
+spaces for all V belonging to
+ 
+
+ align:start position:0%
+spaces for all V belonging to
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+complex vector space.
+
+ align:start position:0%
+complex vector space.
+ 
+
+ align:start position:0%
+complex vector space.
+This implied that the operator was
+
+ align:start position:0%
+This implied that the operator was
+ 
+
+ align:start position:0%
+This implied that the operator was
+zero and uh it's not true for real
+
+ align:start position:0%
+zero and uh it's not true for real
+ 
+
+ align:start position:0%
+zero and uh it's not true for real
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+spaces and uh we gave a proof that made
+
+ align:start position:0%
+spaces and uh we gave a proof that made
+ 
+
+ align:start position:0%
+spaces and uh we gave a proof that made
+it clear that indeed u proof wouldn't
+
+ align:start position:0%
+it clear that indeed u proof wouldn't
+ 
+
+ align:start position:0%
+it clear that indeed u proof wouldn't
+work for a real vector space. I will ask
+
+ align:start position:0%
+work for a real vector space. I will ask
+ 
+
+ align:start position:0%
+work for a real vector space. I will ask
+you in the homework to do something that
+
+ align:start position:0%
+you in the homework to do something that
+ 
+
+ align:start position:0%
+you in the homework to do something that
+uh presumably would be the first thing
+
+ align:start position:0%
+uh presumably would be the first thing
+ 
+
+ align:start position:0%
+uh presumably would be the first thing
+you would do if you had to try to
+
+ align:start position:0%
+you would do if you had to try to
+ 
+
+ align:start position:0%
+you would do if you had to try to
+understand why this is true. take 2x two
+
+ align:start position:0%
+understand why this is true. take 2x two
+ 
+
+ align:start position:0%
+understand why this is true. take 2x two
+matrices and just see why it has to be
+
+ align:start position:0%
+matrices and just see why it has to be
+ 
+
+ align:start position:0%
+matrices and just see why it has to be
+zero in one case and it doesn't have to
+
+ align:start position:0%
+zero in one case and it doesn't have to
+ 
+
+ align:start position:0%
+zero in one case and it doesn't have to
+be zero in the other case and uh I think
+
+ align:start position:0%
+be zero in the other case and uh I think
+ 
+
+ align:start position:0%
+be zero in the other case and uh I think
+that will give you a a better
+
+ align:start position:0%
+that will give you a a better
+ 
+
+ align:start position:0%
+that will give you a a better
+perspective on why this happens and u
+
+ align:start position:0%
+perspective on why this happens and u
+ 
+
+ align:start position:0%
+perspective on why this happens and u
+then once you do it for 2x two and you
+
+ align:start position:0%
+then once you do it for 2x two and you
+ 
+
+ align:start position:0%
+then once you do it for 2x two and you
+see how it works you can do it for n byn
+
+ align:start position:0%
+see how it works you can do it for n byn
+ 
+
+ align:start position:0%
+see how it works you can do it for n byn
+um matrices and it will be clear as well
+
+ align:start position:0%
+um matrices and it will be clear as well
+ 
+
+ align:start position:0%
+um matrices and it will be clear as well
+so we'll use this theorem our immediate
+
+ align:start position:0%
+so we'll use this theorem our immediate
+ 
+
+ align:start position:0%
+so we'll use this theorem our immediate
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+of this theorem
+
+ align:start position:0%
+of this theorem
+ 
+
+ align:start position:0%
+of this theorem
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application. a well-known result that uh
+
+ align:start position:0%
+application. a well-known result that uh
+ 
+
+ align:start position:0%
+application. a well-known result that uh
+you could prove now rigorously that t is
+
+ align:start position:0%
+you could prove now rigorously that t is
+ 
+
+ align:start position:0%
+you could prove now rigorously that t is
+equal to t
+
+ align:start position:0%
+equal to t
+ 
+
+ align:start position:0%
+equal to t
+dagger which is to say the operator is
+
+ align:start position:0%
+dagger which is to say the operator is
+ 
+
+ align:start position:0%
+dagger which is to say the operator is
+equal to the adjint and I still I think
+
+ align:start position:0%
+equal to the adjint and I still I think
+ 
+
+ align:start position:0%
+equal to the adjint and I still I think
+I will call this and in the notes you
+
+ align:start position:0%
+I will call this and in the notes you
+ 
+
+ align:start position:0%
+I will call this and in the notes you
+will see always the adjint as opposed to
+
+ align:start position:0%
+will see always the adjint as opposed to
+ 
+
+ align:start position:0%
+will see always the adjint as opposed to
+her mission conjugate and I will say
+
+ align:start position:0%
+her mission conjugate and I will say
+ 
+
+ align:start position:0%
+her mission conjugate and I will say
+whenever the operator is equal to the
+
+ align:start position:0%
+whenever the operator is equal to the
+ 
+
+ align:start position:0%
+whenever the operator is equal to the
+adjint that it is
+
+ align:start position:0%
+adjint that it is
+ 
+
+ align:start position:0%
+adjint that it is
+hermission. So a hermission operator is
+
+ align:start position:0%
+hermission. So a hermission operator is
+ 
+
+ align:start position:0%
+hermission. So a hermission operator is
+equivalent to saying that V
+
+ align:start position:0%
+equivalent to saying that V
+ 
+
+ align:start position:0%
+equivalent to saying that V
+TV is a real number for all
+
+ align:start position:0%
+TV is a real number for all
+ 
+
+ align:start position:0%
+TV is a real number for all
+V. And we prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that in other words
+
+ align:start position:0%
+that in other words
+ 
+
+ align:start position:0%
+that in other words
+physically her mission operators have
+
+ align:start position:0%
+physically her mission operators have
+ 
+
+ align:start position:0%
+physically her mission operators have
+real expectation values. This is an
+
+ align:start position:0%
+real expectation values. This is an
+ 
+
+ align:start position:0%
+real expectation values. This is an
+expectation value because as as you
+
+ align:start position:0%
+expectation value because as as you
+ 
+
+ align:start position:0%
+expectation value because as as you
+remember in the bracket notation
+
+ align:start position:0%
+remember in the bracket notation
+ 
+
+ align:start position:0%
+remember in the bracket notation
+vtv you could write it v t v it's the
+
+ align:start position:0%
+vtv you could write it v t v it's the
+ 
+
+ align:start position:0%
+vtv you could write it v t v it's the
+same thing. So it is an expectation
+
+ align:start position:0%
+same thing. So it is an expectation
+ 
+
+ align:start position:0%
+same thing. So it is an expectation
+value. So it's an important thing
+
+ align:start position:0%
+value. So it's an important thing
+ 
+
+ align:start position:0%
+value. So it's an important thing
+because we usually deal with hermission
+
+ align:start position:0%
+because we usually deal with hermission
+ 
+
+ align:start position:0%
+because we usually deal with hermission
+operators and we want expectation values
+
+ align:start position:0%
+operators and we want expectation values
+ 
+
+ align:start position:0%
+operators and we want expectation values
+of hermission operators to be real.
+
+ align:start position:0%
+of hermission operators to be real.
+ 
+
+ align:start position:0%
+of hermission operators to be real.
+Now now that we're talking about
+
+ align:start position:0%
+Now now that we're talking about
+ 
+
+ align:start position:0%
+Now now that we're talking about
+hermission operators, I will delay a
+
+ align:start position:0%
+hermission operators, I will delay a
+ 
+
+ align:start position:0%
+hermission operators, I will delay a
+complete discussion of u diagonalization
+
+ align:start position:0%
+complete discussion of u diagonalization
+ 
+
+ align:start position:0%
+complete discussion of u diagonalization
+and diagonalization of several operators
+
+ align:start position:0%
+and diagonalization of several operators
+ 
+
+ align:start position:0%
+and diagonalization of several operators
+simultaneously for the next lecture. Um
+
+ align:start position:0%
+simultaneously for the next lecture. Um
+ 
+
+ align:start position:0%
+simultaneously for the next lecture. Um
+today I want to move forward a bit and
+
+ align:start position:0%
+today I want to move forward a bit and
+ 
+
+ align:start position:0%
+today I want to move forward a bit and
+do some other things and uh this way we
+
+ align:start position:0%
+do some other things and uh this way we
+ 
+
+ align:start position:0%
+do some other things and uh this way we
+spread out a little more the math and uh
+
+ align:start position:0%
+spread out a little more the math and uh
+ 
+
+ align:start position:0%
+spread out a little more the math and uh
+we can begin to look more at u physical
+
+ align:start position:0%
+we can begin to look more at u physical
+ 
+
+ align:start position:0%
+we can begin to look more at u physical
+issues and how they apply here. But at
+
+ align:start position:0%
+issues and how they apply here. But at
+ 
+
+ align:start position:0%
+issues and how they apply here. But at
+any rate, we're just here already and we
+
+ align:start position:0%
+any rate, we're just here already and we
+ 
+
+ align:start position:0%
+any rate, we're just here already and we
+can prove two basic things that uh are
+
+ align:start position:0%
+can prove two basic things that uh are
+ 
+
+ align:start position:0%
+can prove two basic things that uh are
+the kind of things
+
+ align:start position:0%
+the kind of things
+ 
+
+ align:start position:0%
+the kind of things
+that an 805 student should be able to
+
+ align:start position:0%
+that an 805 student should be able to
+ 
+
+ align:start position:0%
+that an 805 student should be able to
+prove at any time. They're really very
+
+ align:start position:0%
+prove at any time. They're really very
+ 
+
+ align:start position:0%
+prove at any time. They're really very
+simple and uh it's a kind of proof that
+
+ align:start position:0%
+simple and uh it's a kind of proof that
+ 
+
+ align:start position:0%
+simple and uh it's a kind of proof that
+is very short couple of lines something
+
+ align:start position:0%
+is very short couple of lines something
+ 
+
+ align:start position:0%
+is very short couple of lines something
+you should be able to reproduce at any
+
+ align:start position:0%
+you should be able to reproduce at any
+ 
+
+ align:start position:0%
+you should be able to reproduce at any
+time. So the first theorem says the igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values of hermission operators.
+
+ align:start position:0%
+values of hermission operators.
+ 
+
+ align:start position:0%
+values of hermission operators.
+H is for her mission are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real and
+
+ align:start position:0%
+real and
+ 
+
+ align:start position:0%
+real and
+of I will do a little bit of a notation
+
+ align:start position:0%
+of I will do a little bit of a notation
+ 
+
+ align:start position:0%
+of I will do a little bit of a notation
+in which I will start with an
+
+ align:start position:0%
+in which I will start with an
+ 
+
+ align:start position:0%
+in which I will start with an
+expression and evaluate it sort of to
+
+ align:start position:0%
+expression and evaluate it sort of to
+ 
+
+ align:start position:0%
+expression and evaluate it sort of to
+the left and to the right. So when you
+
+ align:start position:0%
+the left and to the right. So when you
+ 
+
+ align:start position:0%
+the left and to the right. So when you
+have an equation you start here and you
+
+ align:start position:0%
+have an equation you start here and you
+ 
+
+ align:start position:0%
+have an equation you start here and you
+start evaluating there. So I will start
+
+ align:start position:0%
+start evaluating there. So I will start
+ 
+
+ align:start position:0%
+start evaluating there. So I will start
+with this. consider v
+
+ align:start position:0%
+with this. consider v
+ 
+
+ align:start position:0%
+with this. consider v
+TV and I will box it as being the origin
+
+ align:start position:0%
+TV and I will box it as being the origin
+ 
+
+ align:start position:0%
+TV and I will box it as being the origin
+and I will start evaluating it. Now if V
+
+ align:start position:0%
+and I will start evaluating it. Now if V
+ 
+
+ align:start position:0%
+and I will start evaluating it. Now if V
+is an igon vector. So let V be an igon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector on
+
+ align:start position:0%
+vector on
+ 
+
+ align:start position:0%
+vector on
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+vector. So that um TV is equal to lambda
+
+ align:start position:0%
+vector. So that um TV is equal to lambda
+ 
+
+ align:start position:0%
+vector. So that um TV is equal to lambda
+V and now we say consider that
+
+ align:start position:0%
+V and now we say consider that
+ 
+
+ align:start position:0%
+V and now we say consider that
+expression in the
+
+ align:start position:0%
+expression in the
+ 
+
+ align:start position:0%
+expression in the
+box and you try to evaluate it. So one
+
+ align:start position:0%
+box and you try to evaluate it. So one
+ 
+
+ align:start position:0%
+box and you try to evaluate it. So one
+way to evaluate it, I evaluate to the
+
+ align:start position:0%
+way to evaluate it, I evaluate to the
+ 
+
+ align:start position:0%
+way to evaluate it, I evaluate to the
+left and then evaluate to the right is
+
+ align:start position:0%
+left and then evaluate to the right is
+ 
+
+ align:start position:0%
+left and then evaluate to the right is
+the naive evaluation. T on V is lambda
+
+ align:start position:0%
+the naive evaluation. T on V is lambda
+ 
+
+ align:start position:0%
+the naive evaluation. T on V is lambda
+V. So substitute it there. V lambda V.
+
+ align:start position:0%
+V. So substitute it there. V lambda V.
+ 
+
+ align:start position:0%
+V. So substitute it there. V lambda V.
+We know it. And then by homogenity this
+
+ align:start position:0%
+We know it. And then by homogenity this
+ 
+
+ align:start position:0%
+We know it. And then by homogenity this
+lambda goes out and therefore it's
+
+ align:start position:0%
+lambda goes out and therefore it's
+ 
+
+ align:start position:0%
+lambda goes out and therefore it's
+lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VV. On the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hand, we have that we can go to the
+
+ align:start position:0%
+hand, we have that we can go to the
+ 
+
+ align:start position:0%
+hand, we have that we can go to the
+right. And what is the way you move an
+
+ align:start position:0%
+right. And what is the way you move an
+ 
+
+ align:start position:0%
+right. And what is the way you move an
+operator to the first position? By
+
+ align:start position:0%
+operator to the first position? By
+ 
+
+ align:start position:0%
+operator to the first position? By
+putting a dagger. That's a definition.
+
+ align:start position:0%
+putting a dagger. That's a definition.
+ 
+
+ align:start position:0%
+putting a dagger. That's a definition.
+So this is by
+
+ align:start position:0%
+So this is by
+ 
+
+ align:start position:0%
+So this is by
+definition. By
+
+ align:start position:0%
+definition. By
+ 
+
+ align:start position:0%
+definition. By
+definition. Now we use that the operator
+
+ align:start position:0%
+definition. Now we use that the operator
+ 
+
+ align:start position:0%
+definition. Now we use that the operator
+is hermission. So this is equal
+
+ align:start position:0%
+is hermission. So this is equal
+ 
+
+ align:start position:0%
+is hermission. So this is equal
+to t
+
+ align:start position:0%
+to t
+ 
+
+ align:start position:0%
+to t
+v and this is by t
+
+ align:start position:0%
+v and this is by t
+ 
+
+ align:start position:0%
+v and this is by t
+hermission. Then you can apply again the
+
+ align:start position:0%
+hermission. Then you can apply again the
+ 
+
+ align:start position:0%
+hermission. Then you can apply again the
+equation of the igon value. So this is
+
+ align:start position:0%
+equation of the igon value. So this is
+ 
+
+ align:start position:0%
+equation of the igon value. So this is
+lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v and by conjugate homogeneity of the
+
+ align:start position:0%
+v and by conjugate homogeneity of the
+ 
+
+ align:start position:0%
+v and by conjugate homogeneity of the
+first input this is lambda
+
+ align:start position:0%
+first input this is lambda
+ 
+
+ align:start position:0%
+first input this is lambda
+star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vv. So at the end of the day you have
+
+ align:start position:0%
+vv. So at the end of the day you have
+ 
+
+ align:start position:0%
+vv. So at the end of the day you have
+something on the extreme left something
+
+ align:start position:0%
+something on the extreme left something
+ 
+
+ align:start position:0%
+something on the extreme left something
+on the extreme right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V if it's if there is an igon vector V
+
+ align:start position:0%
+V if it's if there is an igon vector V
+ 
+
+ align:start position:0%
+V if it's if there is an igon vector V
+can be assumed to be non zero. Um the
+
+ align:start position:0%
+can be assumed to be non zero. Um the
+ 
+
+ align:start position:0%
+can be assumed to be non zero. Um the
+way we are saying things in a sense zero
+
+ align:start position:0%
+way we are saying things in a sense zero
+ 
+
+ align:start position:0%
+way we are saying things in a sense zero
+we also think of it as an igon vector
+
+ align:start position:0%
+we also think of it as an igon vector
+ 
+
+ align:start position:0%
+we also think of it as an igon vector
+but it's a trivial one but uh the fact
+
+ align:start position:0%
+but it's a trivial one but uh the fact
+ 
+
+ align:start position:0%
+but it's a trivial one but uh the fact
+that there's an igon value means there's
+
+ align:start position:0%
+that there's an igon value means there's
+ 
+
+ align:start position:0%
+that there's an igon value means there's
+a nonzero v that solves this equation.
+
+ align:start position:0%
+a nonzero v that solves this equation.
+ 
+
+ align:start position:0%
+a nonzero v that solves this equation.
+So we're using that nonzero v and
+
+ align:start position:0%
+So we're using that nonzero v and
+ 
+
+ align:start position:0%
+So we're using that nonzero v and
+therefore this is a
+
+ align:start position:0%
+therefore this is a
+ 
+
+ align:start position:0%
+therefore this is a
+number that is non zero. You
+
+ align:start position:0%
+number that is non zero. You
+ 
+
+ align:start position:0%
+number that is non zero. You
+bring one to the other side and you have
+
+ align:start position:0%
+bring one to the other side and you have
+ 
+
+ align:start position:0%
+bring one to the other side and you have
+lambda minus lambda star time
+
+ align:start position:0%
+lambda minus lambda star time
+ 
+
+ align:start position:0%
+lambda minus lambda star time
+v equals zero. This is different from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero. This is different from zero and
+
+ align:start position:0%
+zero. This is different from zero and
+ 
+
+ align:start position:0%
+zero. This is different from zero and
+therefore lambda is equal to lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star. So it's a classic proof
+
+ align:start position:0%
+star. So it's a classic proof
+ 
+
+ align:start position:0%
+star. So it's a classic proof
+of relatively straightforward.
+
+ align:start position:0%
+of relatively straightforward.
+ 
+
+ align:start position:0%
+of relatively straightforward.
+The second theorem is as simple to prove
+
+ align:start position:0%
+The second theorem is as simple to prove
+ 
+
+ align:start position:0%
+The second theorem is as simple to prove
+and um it's already interesting and it
+
+ align:start position:0%
+and um it's already interesting and it
+ 
+
+ align:start position:0%
+and um it's already interesting and it
+states that different vectors of a
+
+ align:start position:0%
+states that different vectors of a
+ 
+
+ align:start position:0%
+states that different vectors of a
+hermission operator
+
+ align:start position:0%
+hermission operator
+ 
+
+ align:start position:0%
+hermission operator
+um well different values of hermission
+
+ align:start position:0%
+um well different values of hermission
+ 
+
+ align:start position:0%
+um well different values of hermission
+operators correspond to orthogonal
+
+ align:start position:0%
+operators correspond to orthogonal
+ 
+
+ align:start position:0%
+operators correspond to orthogonal
+functions or vectors. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values of hermission
+
+ align:start position:0%
+values of hermission
+ 
+
+ align:start position:0%
+values of hermission
+ops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correspond to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal functions on vectors I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry. So what are we saying here? We're
+
+ align:start position:0%
+sorry. So what are we saying here? We're
+ 
+
+ align:start position:0%
+sorry. So what are we saying here? We're
+saying that suppose you have a v1 that
+
+ align:start position:0%
+saying that suppose you have a v1 that
+ 
+
+ align:start position:0%
+saying that suppose you have a v1 that
+acted on t gives you a lambda 1 v1. It's
+
+ align:start position:0%
+acted on t gives you a lambda 1 v1. It's
+ 
+
+ align:start position:0%
+acted on t gives you a lambda 1 v1. It's
+one value. You have another one v2 is
+
+ align:start position:0%
+one value. You have another one v2 is
+ 
+
+ align:start position:0%
+one value. You have another one v2 is
+equal to lambda 2 v2 and lambda 1 is
+
+ align:start position:0%
+equal to lambda 2 v2 and lambda 1 is
+ 
+
+ align:start position:0%
+equal to lambda 2 v2 and lambda 1 is
+different from lambda 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now just focusing on a fact that is
+
+ align:start position:0%
+Now just focusing on a fact that is
+ 
+
+ align:start position:0%
+Now just focusing on a fact that is
+going to show up later and it's going to
+
+ align:start position:0%
+going to show up later and it's going to
+ 
+
+ align:start position:0%
+going to show up later and it's going to
+cause uh make life interesting is that
+
+ align:start position:0%
+cause uh make life interesting is that
+ 
+
+ align:start position:0%
+cause uh make life interesting is that
+some values may have a multiplicity of
+
+ align:start position:0%
+some values may have a multiplicity of
+ 
+
+ align:start position:0%
+some values may have a multiplicity of
+igon vectors.
+
+ align:start position:0%
+igon vectors.
+ 
+
+ align:start position:0%
+igon vectors.
+In other words, it's not, you know, if a
+
+ align:start position:0%
+In other words, it's not, you know, if a
+ 
+
+ align:start position:0%
+In other words, it's not, you know, if a
+vector V is an igon vector, minus V is
+
+ align:start position:0%
+vector V is an igon vector, minus V is
+ 
+
+ align:start position:0%
+vector V is an igon vector, minus V is
+an igon vector. Square root of 3 V is an
+
+ align:start position:0%
+an igon vector. Square root of 3 V is an
+ 
+
+ align:start position:0%
+an igon vector. Square root of 3 V is an
+igon vector, but that's a onedimensional
+
+ align:start position:0%
+igon vector, but that's a onedimensional
+ 
+
+ align:start position:0%
+igon vector, but that's a onedimensional
+subspace. But sometimes for a given
+
+ align:start position:0%
+subspace. But sometimes for a given
+ 
+
+ align:start position:0%
+subspace. But sometimes for a given
+value, there might be a higher
+
+ align:start position:0%
+value, there might be a higher
+ 
+
+ align:start position:0%
+value, there might be a higher
+dimensional subspace of vectors. That's
+
+ align:start position:0%
+dimensional subspace of vectors. That's
+ 
+
+ align:start position:0%
+dimensional subspace of vectors. That's
+a problem of
+
+ align:start position:0%
+a problem of
+ 
+
+ align:start position:0%
+a problem of
+degeneracy and it's very interesting.
+
+ align:start position:0%
+degeneracy and it's very interesting.
+ 
+
+ align:start position:0%
+degeneracy and it's very interesting.
+Makes life really interesting in quantum
+
+ align:start position:0%
+Makes life really interesting in quantum
+ 
+
+ align:start position:0%
+Makes life really interesting in quantum
+mechanics. So if you have degeneracy in
+
+ align:start position:0%
+mechanics. So if you have degeneracy in
+ 
+
+ align:start position:0%
+mechanics. So if you have degeneracy in
+that set of iggon vectors form a
+
+ align:start position:0%
+that set of iggon vectors form a
+ 
+
+ align:start position:0%
+that set of iggon vectors form a
+subspace and you can choose a basis and
+
+ align:start position:0%
+subspace and you can choose a basis and
+ 
+
+ align:start position:0%
+subspace and you can choose a basis and
+you could have several vectors here. Now
+
+ align:start position:0%
+you could have several vectors here. Now
+ 
+
+ align:start position:0%
+you could have several vectors here. Now
+what do you do in that case? The theorem
+
+ align:start position:0%
+what do you do in that case? The theorem
+ 
+
+ align:start position:0%
+what do you do in that case? The theorem
+doesn't say much. So it means choose
+
+ align:start position:0%
+doesn't say much. So it means choose
+ 
+
+ align:start position:0%
+doesn't say much. So it means choose
+anyone. If you had a basis there choose
+
+ align:start position:0%
+anyone. If you had a basis there choose
+ 
+
+ align:start position:0%
+anyone. If you had a basis there choose
+anyone. The fact remains that if these
+
+ align:start position:0%
+anyone. The fact remains that if these
+ 
+
+ align:start position:0%
+anyone. The fact remains that if these
+two igon values are different then you
+
+ align:start position:0%
+two igon values are different then you
+ 
+
+ align:start position:0%
+two igon values are different then you
+will be able to show that the igon
+
+ align:start position:0%
+will be able to show that the igon
+ 
+
+ align:start position:0%
+will be able to show that the igon
+vectors are
+
+ align:start position:0%
+vectors are
+ 
+
+ align:start position:0%
+vectors are
+orthogonal. So if you have some space of
+
+ align:start position:0%
+orthogonal. So if you have some space of
+ 
+
+ align:start position:0%
+orthogonal. So if you have some space of
+vectors a degenerate higher dimensional
+
+ align:start position:0%
+vectors a degenerate higher dimensional
+ 
+
+ align:start position:0%
+vectors a degenerate higher dimensional
+space of igon vectors one value and
+
+ align:start position:0%
+space of igon vectors one value and
+ 
+
+ align:start position:0%
+space of igon vectors one value and
+another space with another value any
+
+ align:start position:0%
+another space with another value any
+ 
+
+ align:start position:0%
+another space with another value any
+vector here is orthogonal to any vector
+
+ align:start position:0%
+vector here is orthogonal to any vector
+ 
+
+ align:start position:0%
+vector here is orthogonal to any vector
+there. So how do you show
+
+ align:start position:0%
+there. So how do you show
+ 
+
+ align:start position:0%
+there. So how do you show
+this? How do you show this property?
+
+ align:start position:0%
+this? How do you show this property?
+ 
+
+ align:start position:0%
+this? How do you show this property?
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+uh you have to involve V_sub_1 and V2.
+
+ align:start position:0%
+uh you have to involve V_sub_1 and V2.
+ 
+
+ align:start position:0%
+uh you have to involve V_sub_1 and V2.
+So you're never going to be using the
+
+ align:start position:0%
+So you're never going to be using the
+ 
+
+ align:start position:0%
+So you're never going to be using the
+property that T is her mission unless
+
+ align:start position:0%
+property that T is her mission unless
+ 
+
+ align:start position:0%
+property that T is her mission unless
+you have an inner product. So if you
+
+ align:start position:0%
+you have an inner product. So if you
+ 
+
+ align:start position:0%
+you have an inner product. So if you
+didn't have any idea how to prove that
+
+ align:start position:0%
+didn't have any idea how to prove that
+ 
+
+ align:start position:0%
+didn't have any idea how to prove that
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+presumably at some stage realize that
+
+ align:start position:0%
+presumably at some stage realize that
+ 
+
+ align:start position:0%
+presumably at some stage realize that
+you probably have to use an inner
+
+ align:start position:0%
+you probably have to use an inner
+ 
+
+ align:start position:0%
+you probably have to use an inner
+product and we should mix the vector. So
+
+ align:start position:0%
+product and we should mix the vector. So
+ 
+
+ align:start position:0%
+product and we should mix the vector. So
+maybe a V2 inner product with this. So
+
+ align:start position:0%
+maybe a V2 inner product with this. So
+ 
+
+ align:start position:0%
+maybe a V2 inner product with this. So
+we'll take a
+
+ align:start position:0%
+we'll take a
+ 
+
+ align:start position:0%
+we'll take a
+V2 inner product with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TV1. And this is interesting because uh
+
+ align:start position:0%
+TV1. And this is interesting because uh
+ 
+
+ align:start position:0%
+TV1. And this is interesting because uh
+we can use the that TV1 is lambda 1 v1
+
+ align:start position:0%
+we can use the that TV1 is lambda 1 v1
+ 
+
+ align:start position:0%
+we can use the that TV1 is lambda 1 v1
+to show that this is just lambda
+
+ align:start position:0%
+to show that this is just lambda
+ 
+
+ align:start position:0%
+to show that this is just lambda
+1 v2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v1 and that already brings all kinds of
+
+ align:start position:0%
+v1 and that already brings all kinds of
+ 
+
+ align:start position:0%
+v1 and that already brings all kinds of
+good things. You're interested in this
+
+ align:start position:0%
+good things. You're interested in this
+ 
+
+ align:start position:0%
+good things. You're interested in this
+inner product. You want to show it zero
+
+ align:start position:0%
+inner product. You want to show it zero
+ 
+
+ align:start position:0%
+inner product. You want to show it zero
+so it shows up. So it's a good idea. So
+
+ align:start position:0%
+so it shows up. So it's a good idea. So
+ 
+
+ align:start position:0%
+so it shows up. So it's a good idea. So
+we've evaluated this and now you have to
+
+ align:start position:0%
+we've evaluated this and now you have to
+ 
+
+ align:start position:0%
+we've evaluated this and now you have to
+think of evaluating it in a different
+
+ align:start position:0%
+think of evaluating it in a different
+ 
+
+ align:start position:0%
+think of evaluating it in a different
+way. Again the operator is her mission.
+
+ align:start position:0%
+way. Again the operator is her mission.
+ 
+
+ align:start position:0%
+way. Again the operator is her mission.
+So it's asking you to move it to the
+
+ align:start position:0%
+So it's asking you to move it to the
+ 
+
+ align:start position:0%
+So it's asking you to move it to the
+other side and exploit that. So we'll
+
+ align:start position:0%
+other side and exploit that. So we'll
+ 
+
+ align:start position:0%
+other side and exploit that. So we'll
+move it to the other side a little
+
+ align:start position:0%
+move it to the other side a little
+ 
+
+ align:start position:0%
+move it to the other side a little
+quicker this time. Goes as t dagger but
+
+ align:start position:0%
+quicker this time. Goes as t dagger but
+ 
+
+ align:start position:0%
+quicker this time. Goes as t dagger but
+t dagger is equal to t because it's her
+
+ align:start position:0%
+t dagger is equal to t because it's her
+ 
+
+ align:start position:0%
+t dagger is equal to t because it's her
+mission. So this is equal to so this is
+
+ align:start position:0%
+mission. So this is equal to so this is
+ 
+
+ align:start position:0%
+mission. So this is equal to so this is
+the center of the equation. We go one
+
+ align:start position:0%
+the center of the equation. We go one
+ 
+
+ align:start position:0%
+the center of the equation. We go one
+way we go the other way. this time down.
+
+ align:start position:0%
+way we go the other way. this time down.
+ 
+
+ align:start position:0%
+way we go the other way. this time down.
+So we'll put t
+
+ align:start position:0%
+So we'll put t
+ 
+
+ align:start position:0%
+So we'll put t
+v2
+
+ align:start position:0%
+v2
+ 
+
+ align:start position:0%
+v2
+v1 and this is equal to
+
+ align:start position:0%
+v1 and this is equal to
+ 
+
+ align:start position:0%
+v1 and this is equal to
+lambda let let me go a little slow here.
+
+ align:start position:0%
+lambda let let me go a little slow here.
+ 
+
+ align:start position:0%
+lambda let let me go a little slow here.
+uh lambda 2 v2 v1. Uh your impulse
+
+ align:start position:0%
+uh lambda 2 v2 v1. Uh your impulse
+ 
+
+ align:start position:0%
+uh lambda 2 v2 v1. Uh your impulse
+should be oh it goes out as lambda 2
+
+ align:start position:0%
+should be oh it goes out as lambda 2
+ 
+
+ align:start position:0%
+should be oh it goes out as lambda 2
+star but the igon values are already
+
+ align:start position:0%
+star but the igon values are already
+ 
+
+ align:start position:0%
+star but the igon values are already
+real. So it goes out as lambda
+
+ align:start position:0%
+real. So it goes out as lambda
+ 
+
+ align:start position:0%
+real. So it goes out as lambda
+2 v2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v1 because the operator is hermission.
+
+ align:start position:0%
+v1 because the operator is hermission.
+ 
+
+ align:start position:0%
+v1 because the operator is hermission.
+So at this moment you have these two
+
+ align:start position:0%
+So at this moment you have these two
+ 
+
+ align:start position:0%
+So at this moment you have these two
+equations. You bring say this to the
+
+ align:start position:0%
+equations. You bring say this to the
+ 
+
+ align:start position:0%
+equations. You bring say this to the
+right hand side and you get lambda 1
+
+ align:start position:0%
+right hand side and you get lambda 1
+ 
+
+ align:start position:0%
+right hand side and you get lambda 1
+minus lambda
+
+ align:start position:0%
+minus lambda
+ 
+
+ align:start position:0%
+minus lambda
+2 vub1 v2 is equal to
+
+ align:start position:0%
+2 vub1 v2 is equal to
+ 
+
+ align:start position:0%
+2 vub1 v2 is equal to
+zero. And since the igen values are
+
+ align:start position:0%
+zero. And since the igen values are
+ 
+
+ align:start position:0%
+zero. And since the igen values are
+supposed to be different you conclude
+
+ align:start position:0%
+supposed to be different you conclude
+ 
+
+ align:start position:0%
+supposed to be different you conclude
+that v1 inner product with v2 is
+
+ align:start position:0%
+that v1 inner product with v2 is
+ 
+
+ align:start position:0%
+that v1 inner product with v2 is
+zero. So that's the end of the proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and those are the two properties that
+
+ align:start position:0%
+uh and those are the two properties that
+ 
+
+ align:start position:0%
+uh and those are the two properties that
+are very
+
+ align:start position:0%
+are very
+ 
+
+ align:start position:0%
+are very
+quickly proven with rather little
+
+ align:start position:0%
+quickly proven with rather little
+ 
+
+ align:start position:0%
+quickly proven with rather little
+effort.
+
+ align:start position:0%
+effort.
+ 
+
+ align:start position:0%
+effort.
+So what do we go? Where do we go from
+
+ align:start position:0%
+So what do we go? Where do we go from
+ 
+
+ align:start position:0%
+So what do we go? Where do we go from
+now? Well, there's one more class of
+
+ align:start position:0%
+now? Well, there's one more class of
+ 
+
+ align:start position:0%
+now? Well, there's one more class of
+operators that are crucial in the
+
+ align:start position:0%
+operators that are crucial in the
+ 
+
+ align:start position:0%
+operators that are crucial in the
+physics. They're perhaps the as
+
+ align:start position:0%
+physics. They're perhaps the as
+ 
+
+ align:start position:0%
+physics. They're perhaps the as
+important as the hermission operators if
+
+ align:start position:0%
+important as the hermission operators if
+ 
+
+ align:start position:0%
+important as the hermission operators if
+not more. They are some operators that
+
+ align:start position:0%
+not more. They are some operators that
+ 
+
+ align:start position:0%
+not more. They are some operators that
+are called unitary
+
+ align:start position:0%
+are called unitary
+ 
+
+ align:start position:0%
+are called unitary
+operators. And the way I will introduce
+
+ align:start position:0%
+operators. And the way I will introduce
+ 
+
+ align:start position:0%
+operators. And the way I will introduce
+them is as follows.
+
+ align:start position:0%
+them is as follows.
+ 
+
+ align:start position:0%
+them is as follows.
+So I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will say and it's an economical way to
+
+ align:start position:0%
+will say and it's an economical way to
+ 
+
+ align:start position:0%
+will say and it's an economical way to
+introduce them. So we'll talk about
+
+ align:start position:0%
+introduce them. So we'll talk about
+ 
+
+ align:start position:0%
+introduce them. So we'll talk about
+unitary operators.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+See if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unitary and mathematicians call it an
+
+ align:start position:0%
+unitary and mathematicians call it an
+ 
+
+ align:start position:0%
+unitary and mathematicians call it an
+isometry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you find that s acting on any
+
+ align:start position:0%
+If you find that s acting on any
+ 
+
+ align:start position:0%
+If you find that s acting on any
+vector, if you take the
+
+ align:start position:0%
+vector, if you take the
+ 
+
+ align:start position:0%
+vector, if you take the
+norm, it's equal to the norm of the
+
+ align:start position:0%
+norm, it's equal to the norm of the
+ 
+
+ align:start position:0%
+norm, it's equal to the norm of the
+vector for all
+
+ align:start position:0%
+vector for all
+ 
+
+ align:start position:0%
+vector for all
+u in the vector space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and uh make a couple of comments.
+
+ align:start position:0%
+this and uh make a couple of comments.
+ 
+
+ align:start position:0%
+this and uh make a couple of comments.
+An example, a trivial
+
+ align:start position:0%
+An example, a trivial
+ 
+
+ align:start position:0%
+An example, a trivial
+example. This operator lambda times the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identity. Lambda times the identity acts
+
+ align:start position:0%
+identity. Lambda times the identity acts
+ 
+
+ align:start position:0%
+identity. Lambda times the identity acts
+on vectors. What does it do? Lambda
+
+ align:start position:0%
+on vectors. What does it do? Lambda
+ 
+
+ align:start position:0%
+on vectors. What does it do? Lambda
+times the identity. The identity does
+
+ align:start position:0%
+times the identity. The identity does
+ 
+
+ align:start position:0%
+times the identity. The identity does
+nothing on the vector. and lambda
+
+ align:start position:0%
+nothing on the vector. and lambda
+ 
+
+ align:start position:0%
+nothing on the vector. and lambda
+stretches
+
+ align:start position:0%
+stretches
+ 
+
+ align:start position:0%
+stretches
+it. So lambda in order not to change the
+
+ align:start position:0%
+it. So lambda in order not to change the
+ 
+
+ align:start position:0%
+it. So lambda in order not to change the
+length of an iggon ve of any vector
+
+ align:start position:0%
+length of an iggon ve of any vector
+ 
+
+ align:start position:0%
+length of an iggon ve of any vector
+should be kind of one. Well, in fact,
+
+ align:start position:0%
+should be kind of one. Well, in fact,
+ 
+
+ align:start position:0%
+should be kind of one. Well, in fact,
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+suffices is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unitary if the absolute value of lambda
+
+ align:start position:0%
+unitary if the absolute value of lambda
+ 
+
+ align:start position:0%
+unitary if the absolute value of lambda
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+one because then lambda is a phase and
+
+ align:start position:0%
+one because then lambda is a phase and
+ 
+
+ align:start position:0%
+one because then lambda is a phase and
+it just rotates the vector. Or in other
+
+ align:start position:0%
+it just rotates the vector. Or in other
+ 
+
+ align:start position:0%
+it just rotates the vector. Or in other
+words, you know that the norm of
+
+ align:start position:0%
+words, you know that the norm of
+ 
+
+ align:start position:0%
+words, you know that the norm of
+AV is equal to the absolute value of A
+
+ align:start position:0%
+AV is equal to the absolute value of A
+ 
+
+ align:start position:0%
+AV is equal to the absolute value of A
+times the norm of V where this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number. And remember these two norms are
+
+ align:start position:0%
+number. And remember these two norms are
+ 
+
+ align:start position:0%
+number. And remember these two norms are
+different. This is the norm of a vector.
+
+ align:start position:0%
+different. This is the norm of a vector.
+ 
+
+ align:start position:0%
+different. This is the norm of a vector.
+This is the norm of a complex number.
+
+ align:start position:0%
+This is the norm of a complex number.
+ 
+
+ align:start position:0%
+This is the norm of a complex number.
+And therefore if you take lambda
+
+ align:start position:0%
+And therefore if you take lambda
+ 
+
+ align:start position:0%
+And therefore if you take lambda
+I lambda I u norm is lambda u is equal
+
+ align:start position:0%
+I lambda I u norm is lambda u is equal
+ 
+
+ align:start position:0%
+I lambda I u norm is lambda u is equal
+absolute value of lambda u and absolute
+
+ align:start position:0%
+absolute value of lambda u and absolute
+ 
+
+ align:start position:0%
+absolute value of lambda u and absolute
+value of lambda is equal to one is the
+
+ align:start position:0%
+value of lambda is equal to one is the
+ 
+
+ align:start position:0%
+value of lambda is equal to one is the
+answer. So
+
+ align:start position:0%
+answer. So
+ 
+
+ align:start position:0%
+answer. So
+that's a simple unitary operator but a
+
+ align:start position:0%
+that's a simple unitary operator but a
+ 
+
+ align:start position:0%
+that's a simple unitary operator but a
+important one. Another observation
+
+ align:start position:0%
+important one. Another observation
+ 
+
+ align:start position:0%
+important one. Another observation
+um what are the vectors annihilated by
+
+ align:start position:0%
+um what are the vectors annihilated by
+ 
+
+ align:start position:0%
+um what are the vectors annihilated by
+this operator u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero is the only vector because any
+
+ align:start position:0%
+zero is the only vector because any
+ 
+
+ align:start position:0%
+zero is the only vector because any
+other vector is non zero has some length
+
+ align:start position:0%
+other vector is non zero has some length
+ 
+
+ align:start position:0%
+other vector is non zero has some length
+so it's not killed so it kills only zero
+
+ align:start position:0%
+so it's not killed so it kills only zero
+ 
+
+ align:start position:0%
+so it's not killed so it kills only zero
+so um the
+
+ align:start position:0%
+so um the
+ 
+
+ align:start position:0%
+so um the
+null space of S is equal to zero
+
+ align:start position:0%
+null space of S is equal to zero
+ 
+
+ align:start position:0%
+null space of S is equal to zero
+vector. So this
+
+ align:start position:0%
+vector. So this
+ 
+
+ align:start position:0%
+vector. So this
+operator has no kernel. Nothing
+
+ align:start position:0%
+operator has no kernel. Nothing
+ 
+
+ align:start position:0%
+operator has no kernel. Nothing
+non-trivial is put to zero. It's an
+
+ align:start position:0%
+non-trivial is put to zero. It's an
+ 
+
+ align:start position:0%
+non-trivial is put to zero. It's an
+invertible
+
+ align:start position:0%
+invertible
+ 
+
+ align:start position:0%
+invertible
+operator. So s is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invertible.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vertible. So that's a few things that
+
+ align:start position:0%
+Vertible. So that's a few things that
+ 
+
+ align:start position:0%
+Vertible. So that's a few things that
+you get very cheaply. Now from this
+
+ align:start position:0%
+you get very cheaply. Now from this
+ 
+
+ align:start position:0%
+you get very cheaply. Now from this
+equation s u= u. If you square that
+
+ align:start position:0%
+equation s u= u. If you square that
+ 
+
+ align:start position:0%
+equation s u= u. If you square that
+equation you would
+
+ align:start position:0%
+equation you would
+ 
+
+ align:start position:0%
+equation you would
+have s
+
+ align:start position:0%
+have s
+ 
+
+ align:start position:0%
+have s
+u s
+
+ align:start position:0%
+u s
+ 
+
+ align:start position:0%
+u s
+u is equal to u u. Maybe I should call
+
+ align:start position:0%
+u is equal to u u. Maybe I should call
+ 
+
+ align:start position:0%
+u is equal to u u. Maybe I should call
+it v. I don't know why I call it u but
+
+ align:start position:0%
+it v. I don't know why I call it u but
+ 
+
+ align:start position:0%
+it v. I don't know why I call it u but
+let's stick to you.
+
+ align:start position:0%
+let's stick to you.
+ 
+
+ align:start position:0%
+let's stick to you.
+Now remember that we can move operators
+
+ align:start position:0%
+Now remember that we can move operators
+ 
+
+ align:start position:0%
+Now remember that we can move operators
+from one side to the other. So I'll move
+
+ align:start position:0%
+from one side to the other. So I'll move
+ 
+
+ align:start position:0%
+from one side to the other. So I'll move
+this one to that side. If you move an S
+
+ align:start position:0%
+this one to that side. If you move an S
+ 
+
+ align:start position:0%
+this one to that side. If you move an S
+here, you would put an S dagger. But
+
+ align:start position:0%
+here, you would put an S dagger. But
+ 
+
+ align:start position:0%
+here, you would put an S dagger. But
+since the dagger of
+
+ align:start position:0%
+since the dagger of
+ 
+
+ align:start position:0%
+since the dagger of
+uh of an S dagger is S, you can move
+
+ align:start position:0%
+uh of an S dagger is S, you can move
+ 
+
+ align:start position:0%
+uh of an S dagger is S, you can move
+also the S to that side as an S dagger.
+
+ align:start position:0%
+also the S to that side as an S dagger.
+ 
+
+ align:start position:0%
+also the S to that side as an S dagger.
+So U S
+
+ align:start position:0%
+So U S
+ 
+
+ align:start position:0%
+So U S
+dagger S U. You see that if you want to
+
+ align:start position:0%
+dagger S U. You see that if you want to
+ 
+
+ align:start position:0%
+dagger S U. You see that if you want to
+move this one, you can move it by
+
+ align:start position:0%
+move this one, you can move it by
+ 
+
+ align:start position:0%
+move this one, you can move it by
+putting another dagger and you get that
+
+ align:start position:0%
+putting another dagger and you get that
+ 
+
+ align:start position:0%
+putting another dagger and you get that
+one. And this is u
+
+ align:start position:0%
+one. And this is u
+ 
+
+ align:start position:0%
+one. And this is u
+u and therefore you get
+
+ align:start position:0%
+u and therefore you get
+ 
+
+ align:start position:0%
+u and therefore you get
+u s
+
+ align:start position:0%
+u s
+ 
+
+ align:start position:0%
+u s
+dagger s minus the identity acting on u
+
+ align:start position:0%
+dagger s minus the identity acting on u
+ 
+
+ align:start position:0%
+dagger s minus the identity acting on u
+is equal to zero for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u. So for every vector this is true
+
+ align:start position:0%
+u. So for every vector this is true
+ 
+
+ align:start position:0%
+u. So for every vector this is true
+because this is true. We just squared
+
+ align:start position:0%
+because this is true. We just squared
+ 
+
+ align:start position:0%
+because this is true. We just squared
+it. And now you have our favorite
+
+ align:start position:0%
+it. And now you have our favorite
+ 
+
+ align:start position:0%
+it. And now you have our favorite
+theorem that says if this is true in a
+
+ align:start position:0%
+theorem that says if this is true in a
+ 
+
+ align:start position:0%
+theorem that says if this is true in a
+complex vector space this is zero. And
+
+ align:start position:0%
+complex vector space this is zero. And
+ 
+
+ align:start position:0%
+complex vector space this is zero. And
+therefore you've shown that s dagger s
+
+ align:start position:0%
+therefore you've shown that s dagger s
+ 
+
+ align:start position:0%
+therefore you've shown that s dagger s
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. So that's another property of uh
+
+ align:start position:0%
+one. So that's another property of uh
+ 
+
+ align:start position:0%
+one. So that's another property of uh
+unitary operators. In fact that's the
+
+ align:start position:0%
+unitary operators. In fact that's the
+ 
+
+ align:start position:0%
+unitary operators. In fact that's the
+way it's many times defined. Unitary
+
+ align:start position:0%
+way it's many times defined. Unitary
+ 
+
+ align:start position:0%
+way it's many times defined. Unitary
+operators sometimes are said to be
+
+ align:start position:0%
+operators sometimes are said to be
+ 
+
+ align:start position:0%
+operators sometimes are said to be
+operators whose inverse is s
+
+ align:start position:0%
+operators whose inverse is s
+ 
+
+ align:start position:0%
+operators whose inverse is s
+dagger. I will not go into the
+
+ align:start position:0%
+dagger. I will not go into the
+ 
+
+ align:start position:0%
+dagger. I will not go into the
+subtleties of
+
+ align:start position:0%
+subtleties of
+ 
+
+ align:start position:0%
+subtleties of
+whether what steps in all these things
+
+ align:start position:0%
+whether what steps in all these things
+ 
+
+ align:start position:0%
+whether what steps in all these things
+I'm saying are true or not true for
+
+ align:start position:0%
+I'm saying are true or not true for
+ 
+
+ align:start position:0%
+I'm saying are true or not true for
+infinite dimensional operators um
+
+ align:start position:0%
+infinite dimensional operators um
+ 
+
+ align:start position:0%
+infinite dimensional operators um
+infinite dimensional vector spaces. So I
+
+ align:start position:0%
+infinite dimensional vector spaces. So I
+ 
+
+ align:start position:0%
+infinite dimensional vector spaces. So I
+will assume and it will be true in our
+
+ align:start position:0%
+will assume and it will be true in our
+ 
+
+ align:start position:0%
+will assume and it will be true in our
+examples that if s dagger is an inverse
+
+ align:start position:0%
+examples that if s dagger is an inverse
+ 
+
+ align:start position:0%
+examples that if s dagger is an inverse
+from the left it's also an inverse from
+
+ align:start position:0%
+from the left it's also an inverse from
+ 
+
+ align:start position:0%
+from the left it's also an inverse from
+the right and perhaps um everything is
+
+ align:start position:0%
+the right and perhaps um everything is
+ 
+
+ align:start position:0%
+the right and perhaps um everything is
+true for infinite dimensional operator
+
+ align:start position:0%
+true for infinite dimensional operator
+ 
+
+ align:start position:0%
+true for infinite dimensional operator
+vector spaces but I'm not 100%
+
+ align:start position:0%
+vector spaces but I'm not 100%
+ 
+
+ align:start position:0%
+vector spaces but I'm not 100%
+positive.
+
+ align:start position:0%
+positive.
+ 
+
+ align:start position:0%
+positive.
+So s dagger is the
+
+ align:start position:0%
+So s dagger is the
+ 
+
+ align:start position:0%
+So s dagger is the
+inverse dagger is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse of s and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+that's pretty important thing. So one
+
+ align:start position:0%
+that's pretty important thing. So one
+ 
+
+ align:start position:0%
+that's pretty important thing. So one
+last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comment has to do unitary operators has
+
+ align:start position:0%
+comment has to do unitary operators has
+ 
+
+ align:start position:0%
+comment has to do unitary operators has
+to do with bases. So suppose you have an
+
+ align:start position:0%
+to do with bases. So suppose you have an
+ 
+
+ align:start position:0%
+to do with bases. So suppose you have an
+orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis E1 E up to E N.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now you can define another basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+fi equal I'll I'll change to a letter u
+
+ align:start position:0%
+fi equal I'll I'll change to a letter u
+ 
+
+ align:start position:0%
+fi equal I'll I'll change to a letter u
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+ei where u is unitary so it's like the
+
+ align:start position:0%
+ei where u is unitary so it's like the
+ 
+
+ align:start position:0%
+ei where u is unitary so it's like the
+s in fact most books in physics call u
+
+ align:start position:0%
+s in fact most books in physics call u
+ 
+
+ align:start position:0%
+s in fact most books in physics call u
+for unitary So maybe I should have
+
+ align:start position:0%
+for unitary So maybe I should have
+ 
+
+ align:start position:0%
+for unitary So maybe I should have
+changed that letter there too as well.
+
+ align:start position:0%
+changed that letter there too as well.
+ 
+
+ align:start position:0%
+changed that letter there too as well.
+So suppose you change bases, you put
+
+ align:start position:0%
+So suppose you change bases, you put
+ 
+
+ align:start position:0%
+So suppose you change bases, you put
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oh there was something else I wanted to
+
+ align:start position:0%
+oh there was something else I wanted to
+ 
+
+ align:start position:0%
+oh there was something else I wanted to
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+before. Thanks to this equation,
+
+ align:start position:0%
+before. Thanks to this equation,
+ 
+
+ align:start position:0%
+before. Thanks to this equation,
+consider now the following thing. S U SV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S U SV. You can move this S for example
+
+ align:start position:0%
+S U SV. You can move this S for example
+ 
+
+ align:start position:0%
+S U SV. You can move this S for example
+to the other side is S dagger S U V and
+
+ align:start position:0%
+to the other side is S dagger S U V and
+ 
+
+ align:start position:0%
+to the other side is S dagger S U V and
+S dagger S is equal to one and it's
+
+ align:start position:0%
+S dagger S is equal to one and it's
+ 
+
+ align:start position:0%
+S dagger S is equal to one and it's
+UV. So this is a pretty nice property.
+
+ align:start position:0%
+UV. So this is a pretty nice property.
+ 
+
+ align:start position:0%
+UV. So this is a pretty nice property.
+We started from the fact that it
+
+ align:start position:0%
+We started from the fact that it
+ 
+
+ align:start position:0%
+We started from the fact that it
+preserved the norm of a single vector of
+
+ align:start position:0%
+preserved the norm of a single vector of
+ 
+
+ align:start position:0%
+preserved the norm of a single vector of
+all vectors and now you see that in fact
+
+ align:start position:0%
+all vectors and now you see that in fact
+ 
+
+ align:start position:0%
+all vectors and now you see that in fact
+it preserves the inner product. So if
+
+ align:start position:0%
+it preserves the inner product. So if
+ 
+
+ align:start position:0%
+it preserves the inner product. So if
+you have two vectors to compute their
+
+ align:start position:0%
+you have two vectors to compute their
+ 
+
+ align:start position:0%
+you have two vectors to compute their
+inner product compute them after action
+
+ align:start position:0%
+inner product compute them after action
+ 
+
+ align:start position:0%
+inner product compute them after action
+with u or before action with u and it
+
+ align:start position:0%
+with u or before action with u and it
+ 
+
+ align:start position:0%
+with u or before action with u and it
+doesn't make a difference.
+
+ align:start position:0%
+doesn't make a difference.
+ 
+
+ align:start position:0%
+doesn't make a difference.
+So suppose you define a second basis
+
+ align:start position:0%
+So suppose you define a second basis
+ 
+
+ align:start position:0%
+So suppose you define a second basis
+here. You have one orthonormal basis.
+
+ align:start position:0%
+here. You have one orthonormal basis.
+ 
+
+ align:start position:0%
+here. You have one orthonormal basis.
+You define basis vectors like this. Then
+
+ align:start position:0%
+You define basis vectors like this. Then
+ 
+
+ align:start position:0%
+You define basis vectors like this. Then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+claim is that the f_sub_1 up to
+
+ align:start position:0%
+claim is that the f_sub_1 up to
+ 
+
+ align:start position:0%
+claim is that the f_sub_1 up to
+fn is
+
+ align:start position:0%
+fn is
+ 
+
+ align:start position:0%
+fn is
+orthonormal. And for
+
+ align:start position:0%
+orthonormal. And for
+ 
+
+ align:start position:0%
+orthonormal. And for
+that you simply do the following. Just
+
+ align:start position:0%
+that you simply do the following. Just
+ 
+
+ align:start position:0%
+that you simply do the following. Just
+check fi
+
+ align:start position:0%
+check fi
+ 
+
+ align:start position:0%
+check fi
+fj is equal to u
+
+ align:start position:0%
+fj is equal to u
+ 
+
+ align:start position:0%
+fj is equal to u
+ei u
+
+ align:start position:0%
+ei u
+ 
+
+ align:start position:0%
+ei u
+ej by this property you can delete both
+
+ align:start position:0%
+ej by this property you can delete both
+ 
+
+ align:start position:0%
+ej by this property you can delete both
+u's and therefore this is e i
+
+ align:start position:0%
+u's and therefore this is e i
+ 
+
+ align:start position:0%
+u's and therefore this is e i
+ej and that's delta j. So the new basis
+
+ align:start position:0%
+ej and that's delta j. So the new basis
+ 
+
+ align:start position:0%
+ej and that's delta j. So the new basis
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal. If you play with these
+
+ align:start position:0%
+orthonormal. If you play with these
+ 
+
+ align:start position:0%
+orthonormal. If you play with these
+things, it's easy to get uh some extra
+
+ align:start position:0%
+things, it's easy to get uh some extra
+ 
+
+ align:start position:0%
+things, it's easy to get uh some extra
+curious fact
+
+ align:start position:0%
+curious fact
+ 
+
+ align:start position:0%
+curious fact
+here. Let's think of
+
+ align:start position:0%
+here. Let's think of
+ 
+
+ align:start position:0%
+here. Let's think of
+the matrix representation of um of the
+
+ align:start position:0%
+the matrix representation of um of the
+ 
+
+ align:start position:0%
+the matrix representation of um of the
+operator U.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U well we know how these things are and
+
+ align:start position:0%
+U well we know how these things are and
+ 
+
+ align:start position:0%
+U well we know how these things are and
+let's think of this in the basis E basis
+
+ align:start position:0%
+let's think of this in the basis E basis
+ 
+
+ align:start position:0%
+let's think of this in the basis E basis
+so U
+
+ align:start position:0%
+so U
+ 
+
+ align:start position:0%
+so U
+KI is equal to E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K U U E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+EI that's the definition of
+
+ align:start position:0%
+EI that's the definition of
+ 
+
+ align:start position:0%
+EI that's the definition of
+U in the basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E the matrix elements of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U. You can try to figure out what is
+
+ align:start position:0%
+U. You can try to figure out what is
+ 
+
+ align:start position:0%
+U. You can try to figure out what is
+UKI in the F basis. How does the
+
+ align:start position:0%
+UKI in the F basis. How does the
+ 
+
+ align:start position:0%
+UKI in the F basis. How does the
+operator U look in the F
+
+ align:start position:0%
+operator U look in the F
+ 
+
+ align:start position:0%
+operator U look in the F
+basis? Well, let's just do it without
+
+ align:start position:0%
+basis? Well, let's just do it without
+ 
+
+ align:start position:0%
+basis? Well, let's just do it without
+thinking. Um so in the f basis I would
+
+ align:start position:0%
+thinking. Um so in the f basis I would
+ 
+
+ align:start position:0%
+thinking. Um so in the f basis I would
+put f k
+
+ align:start position:0%
+put f k
+ 
+
+ align:start position:0%
+put f k
+u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fi. Well but f k is u e k. So I'll put u
+
+ align:start position:0%
+fi. Well but f k is u e k. So I'll put u
+ 
+
+ align:start position:0%
+fi. Well but f k is u e k. So I'll put u
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+u fi.
+
+ align:start position:0%
+u fi.
+ 
+
+ align:start position:0%
+u fi.
+Now I can delete both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U's and it's E
+
+ align:start position:0%
+U's and it's E
+ 
+
+ align:start position:0%
+U's and it's E
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+FI and I can remember what FI was which
+
+ align:start position:0%
+FI and I can remember what FI was which
+ 
+
+ align:start position:0%
+FI and I can remember what FI was which
+is E
+
+ align:start position:0%
+is E
+ 
+
+ align:start position:0%
+is E
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+EI and it's just the same as the one we
+
+ align:start position:0%
+EI and it's just the same as the one we
+ 
+
+ align:start position:0%
+EI and it's just the same as the one we
+had there. So the operator unitary
+
+ align:start position:0%
+had there. So the operator unitary
+ 
+
+ align:start position:0%
+had there. So the operator unitary
+operator looks the same in both bases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, that might seem strange or a
+
+ align:start position:0%
+Now, that might seem strange or a
+ 
+
+ align:start position:0%
+Now, that might seem strange or a
+coincidence, but it's not. So, I leave
+
+ align:start position:0%
+coincidence, but it's not. So, I leave
+ 
+
+ align:start position:0%
+coincidence, but it's not. So, I leave
+it to you to think about that
+
+ align:start position:0%
+it to you to think about that
+ 
+
+ align:start position:0%
+it to you to think about that
+and visualize why did that
+
+ align:start position:0%
+and visualize why did that
+ 
+
+ align:start position:0%
+and visualize why did that
+happen? What's what's the reason?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the bracket notation we've been using
+
+ align:start position:0%
+So the bracket notation we've been using
+ 
+
+ align:start position:0%
+So the bracket notation we've been using
+it here and
+
+ align:start position:0%
+it here and
+ 
+
+ align:start position:0%
+it here and
+there and uh I will ask you to please
+
+ align:start position:0%
+there and uh I will ask you to please
+ 
+
+ align:start position:0%
+there and uh I will ask you to please
+read the notes. The notes will be posted
+
+ align:start position:0%
+read the notes. The notes will be posted
+ 
+
+ align:start position:0%
+read the notes. The notes will be posted
+this afternoon and they will have not
+
+ align:start position:0%
+this afternoon and they will have not
+ 
+
+ align:start position:0%
+this afternoon and they will have not
+maybe all we've done today but they will
+
+ align:start position:0%
+maybe all we've done today but they will
+ 
+
+ align:start position:0%
+maybe all we've done today but they will
+have some of what we'll do today and all
+
+ align:start position:0%
+have some of what we'll do today and all
+ 
+
+ align:start position:0%
+have some of what we'll do today and all
+of what we've been doing. And the way
+
+ align:start position:0%
+of what we've been doing. And the way
+ 
+
+ align:start position:0%
+of what we've been doing. And the way
+it's done is first done in the sort of
+
+ align:start position:0%
+it's done is first done in the sort of
+ 
+
+ align:start position:0%
+it's done is first done in the sort of
+inner product language and then things
+
+ align:start position:0%
+inner product language and then things
+ 
+
+ align:start position:0%
+inner product language and then things
+are done in the bracket language and
+
+ align:start position:0%
+are done in the bracket language and
+ 
+
+ align:start position:0%
+are done in the bracket language and
+it's a little repetitious and I'm trying
+
+ align:start position:0%
+it's a little repetitious and I'm trying
+ 
+
+ align:start position:0%
+it's a little repetitious and I'm trying
+to take out some things here and there
+
+ align:start position:0%
+to take out some things here and there
+ 
+
+ align:start position:0%
+to take out some things here and there
+so it's less repetitious but um at this
+
+ align:start position:0%
+so it's less repetitious but um at this
+ 
+
+ align:start position:0%
+so it's less repetitious but um at this
+moment it's probably worth reading it
+
+ align:start position:0%
+moment it's probably worth reading it
+ 
+
+ align:start position:0%
+moment it's probably worth reading it
+and reading it again. Yes. Uh is that
+
+ align:start position:0%
+and reading it again. Yes. Uh is that
+ 
+
+ align:start position:0%
+and reading it again. Yes. Uh is that
+true in reverse as well? If you have two
+
+ align:start position:0%
+true in reverse as well? If you have two
+ 
+
+ align:start position:0%
+true in reverse as well? If you have two
+orthonormal bases is the transformation
+
+ align:start position:0%
+orthonormal bases is the transformation
+ 
+
+ align:start position:0%
+orthonormal bases is the transformation
+necessarily unitary.
+
+ align:start position:0%
+necessarily unitary.
+ 
+
+ align:start position:0%
+necessarily unitary.
+Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes. All right. So, so as I was saying,
+
+ align:start position:0%
+Yes. All right. So, so as I was saying,
+ 
+
+ align:start position:0%
+Yes. All right. So, so as I was saying,
+we're going to go into the dra notation
+
+ align:start position:0%
+we're going to go into the dra notation
+ 
+
+ align:start position:0%
+we're going to go into the dra notation
+again. And here is an example of a place
+
+ align:start position:0%
+again. And here is an example of a place
+ 
+
+ align:start position:0%
+again. And here is an example of a place
+where everybody I think tends to use
+
+ align:start position:0%
+where everybody I think tends to use
+ 
+
+ align:start position:0%
+where everybody I think tends to use
+direct notation. And the reason is a a
+
+ align:start position:0%
+direct notation. And the reason is a a
+ 
+
+ align:start position:0%
+direct notation. And the reason is a a
+little curious and uh you will
+
+ align:start position:0%
+little curious and uh you will
+ 
+
+ align:start position:0%
+little curious and uh you will
+appreciate
+
+ align:start position:0%
+appreciate
+ 
+
+ align:start position:0%
+appreciate
+it quite
+
+ align:start position:0%
+it quite
+ 
+
+ align:start position:0%
+it quite
+fast. Um so this will be the case of
+
+ align:start position:0%
+fast. Um so this will be the case of
+ 
+
+ align:start position:0%
+fast. Um so this will be the case of
+where we return to X and P
+
+ align:start position:0%
+where we return to X and P
+ 
+
+ align:start position:0%
+where we return to X and P
+operators and uh nondenuable
+
+ align:start position:0%
+operators and uh nondenuable
+ 
+
+ align:start position:0%
+operators and uh nondenuable
+bases
+
+ align:start position:0%
+bases
+ 
+
+ align:start position:0%
+bases
+non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denuablerable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bases. So
+
+ align:start position:0%
+bases. So
+ 
+
+ align:start position:0%
+bases. So
+uh we're going to try to do X and P. Now
+
+ align:start position:0%
+uh we're going to try to do X and P. Now
+ 
+
+ align:start position:0%
+uh we're going to try to do X and P. Now
+this is the classic of dra notation.
+
+ align:start position:0%
+this is the classic of dra notation.
+ 
+
+ align:start position:0%
+this is the classic of dra notation.
+It's probably as I said the place where
+
+ align:start position:0%
+It's probably as I said the place where
+ 
+
+ align:start position:0%
+It's probably as I said the place where
+everybody likes to use direct notation
+
+ align:start position:0%
+everybody likes to use direct notation
+ 
+
+ align:start position:0%
+everybody likes to use direct notation
+and the reason it's efficient is because
+
+ align:start position:0%
+and the reason it's efficient is because
+ 
+
+ align:start position:0%
+and the reason it's efficient is because
+it prevents you from confusing two
+
+ align:start position:0%
+it prevents you from confusing two
+ 
+
+ align:start position:0%
+it prevents you from confusing two
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+So what was the you know I I've written
+
+ align:start position:0%
+So what was the you know I I've written
+ 
+
+ align:start position:0%
+So what was the you know I I've written
+in the notes that we have all these V's
+
+ align:start position:0%
+in the notes that we have all these V's
+ 
+
+ align:start position:0%
+in the notes that we have all these V's
+that belong to the vector space and then
+
+ align:start position:0%
+that belong to the vector space and then
+ 
+
+ align:start position:0%
+that belong to the vector space and then
+we put this and we still say it belongs
+
+ align:start position:0%
+we put this and we still say it belongs
+ 
+
+ align:start position:0%
+we put this and we still say it belongs
+to the vector space and this is just a
+
+ align:start position:0%
+to the vector space and this is just a
+ 
+
+ align:start position:0%
+to the vector space and this is just a
+decoration that doesn't do
+
+ align:start position:0%
+decoration that doesn't do
+ 
+
+ align:start position:0%
+decoration that doesn't do
+much and we can play with this. Now in
+
+ align:start position:0%
+much and we can play with this. Now in
+ 
+
+ align:start position:0%
+much and we can play with this. Now in
+the non-denuable bases the catch and the
+
+ align:start position:0%
+the non-denuable bases the catch and the
+ 
+
+ align:start position:0%
+the non-denuable bases the catch and the
+possible confusion is that the label is
+
+ align:start position:0%
+possible confusion is that the label is
+ 
+
+ align:start position:0%
+possible confusion is that the label is
+not quite a vector in the vector space.
+
+ align:start position:0%
+not quite a vector in the vector space.
+ 
+
+ align:start position:0%
+not quite a vector in the vector space.
+So that that is the reason why the
+
+ align:start position:0%
+So that that is the reason why the
+ 
+
+ align:start position:0%
+So that that is the reason why the
+notation is helpful because it helps you
+
+ align:start position:0%
+notation is helpful because it helps you
+ 
+
+ align:start position:0%
+notation is helpful because it helps you
+and helps you distinguish two things
+
+ align:start position:0%
+and helps you distinguish two things
+ 
+
+ align:start position:0%
+and helps you distinguish two things
+that you could
+
+ align:start position:0%
+that you could
+ 
+
+ align:start position:0%
+that you could
+confuse. So here here we go. We're going
+
+ align:start position:0%
+confuse. So here here we go. We're going
+ 
+
+ align:start position:0%
+confuse. So here here we go. We're going
+to talk about coordinates X and the X
+
+ align:start position:0%
+to talk about coordinates X and the X
+ 
+
+ align:start position:0%
+to talk about coordinates X and the X
+operator and
+
+ align:start position:0%
+operator and
+ 
+
+ align:start position:0%
+operator and
+the states. Well, this is a state space.
+
+ align:start position:0%
+the states. Well, this is a state space.
+ 
+
+ align:start position:0%
+the states. Well, this is a state space.
+So, what kind of states do we have here?
+
+ align:start position:0%
+So, what kind of states do we have here?
+ 
+
+ align:start position:0%
+So, what kind of states do we have here?
+Well, we've talked about wave functions
+
+ align:start position:0%
+Well, we've talked about wave functions
+ 
+
+ align:start position:0%
+Well, we've talked about wave functions
+as we could give the value of the wave
+
+ align:start position:0%
+as we could give the value of the wave
+ 
+
+ align:start position:0%
+as we could give the value of the wave
+function at different places. We're
+
+ align:start position:0%
+function at different places. We're
+ 
+
+ align:start position:0%
+function at different places. We're
+going to go for a more intrinsic
+
+ align:start position:0%
+going to go for a more intrinsic
+ 
+
+ align:start position:0%
+going to go for a more intrinsic
+definition. We're going to try to
+
+ align:start position:0%
+definition. We're going to try to
+ 
+
+ align:start position:0%
+definition. We're going to try to
+introduce position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states and position states will be
+
+ align:start position:0%
+states and position states will be
+ 
+
+ align:start position:0%
+states and position states will be
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x. Now what is the meaning of this
+
+ align:start position:0%
+x. Now what is the meaning of this
+ 
+
+ align:start position:0%
+x. Now what is the meaning of this
+position state? We should think of this
+
+ align:start position:0%
+position state? We should think of this
+ 
+
+ align:start position:0%
+position state? We should think of this
+intuitively as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X. Now, here is how you can go wrong
+
+ align:start position:0%
+X. Now, here is how you can go wrong
+ 
+
+ align:start position:0%
+X. Now, here is how you can go wrong
+with this thing. If you stop
+
+ align:start position:0%
+with this thing. If you stop
+ 
+
+ align:start position:0%
+with this thing. If you stop
+thinking for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second, what is then ax?
+
+ align:start position:0%
+second, what is then ax?
+ 
+
+ align:start position:0%
+second, what is then ax?
+Is it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x? a being a number. Is it the same
+
+ align:start position:0%
+x? a being a number. Is it the same
+ 
+
+ align:start position:0%
+x? a being a number. Is it the same
+thing? No, not at all. This is a
+
+ align:start position:0%
+thing? No, not at all. This is a
+ 
+
+ align:start position:0%
+thing? No, not at all. This is a
+particle at the coordinate
+
+ align:start position:0%
+particle at the coordinate
+ 
+
+ align:start position:0%
+particle at the coordinate
+ax and this is a particle at x with some
+
+ align:start position:0%
+ax and this is a particle at x with some
+ 
+
+ align:start position:0%
+ax and this is a particle at x with some
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+amplitude. Very different. So this is
+
+ align:start position:0%
+amplitude. Very different. So this is
+ 
+
+ align:start position:0%
+amplitude. Very different. So this is
+not true. Typical mistake. This is not
+
+ align:start position:0%
+not true. Typical mistake. This is not
+ 
+
+ align:start position:0%
+not true. Typical mistake. This is not
+uh minus
+
+ align:start position:0%
+uh minus
+ 
+
+ align:start position:0%
+uh minus
+x. That that's totally different. So
+
+ align:start position:0%
+x. That that's totally different. So
+ 
+
+ align:start position:0%
+x. That that's totally different. So
+there's no such thing as this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either linear. It doesn't mean anything.
+
+ align:start position:0%
+either linear. It doesn't mean anything.
+ 
+
+ align:start position:0%
+either linear. It doesn't mean anything.
+And the reason is that these things are
+
+ align:start position:0%
+And the reason is that these things are
+ 
+
+ align:start position:0%
+And the reason is that these things are
+not our vectors. Our vector is this
+
+ align:start position:0%
+not our vectors. Our vector is this
+ 
+
+ align:start position:0%
+not our vectors. Our vector is this
+whole thing that says a particle at X.
+
+ align:start position:0%
+whole thing that says a particle at X.
+ 
+
+ align:start position:0%
+whole thing that says a particle at X.
+Maybe to make the
+
+ align:start position:0%
+Maybe to make the
+ 
+
+ align:start position:0%
+Maybe to make the
+the a clearer impression, imagine you're
+
+ align:start position:0%
+the a clearer impression, imagine you're
+ 
+
+ align:start position:0%
+the a clearer impression, imagine you're
+in three dimensions and you have an X
+
+ align:start position:0%
+in three dimensions and you have an X
+ 
+
+ align:start position:0%
+in three dimensions and you have an X
+vector. So then you have the K.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This this is the cat particle at
+
+ align:start position:0%
+This this is the cat particle at
+ 
+
+ align:start position:0%
+This this is the cat particle at
+x. X is now a vector but it's a
+
+ align:start position:0%
+x. X is now a vector but it's a
+ 
+
+ align:start position:0%
+x. X is now a vector but it's a
+three-dimensional vector. This is a
+
+ align:start position:0%
+three-dimensional vector. This is a
+ 
+
+ align:start position:0%
+three-dimensional vector. This is a
+vector but it's a vector in an infinite
+
+ align:start position:0%
+vector but it's a vector in an infinite
+ 
+
+ align:start position:0%
+vector but it's a vector in an infinite
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+space because a particle can be
+
+ align:start position:0%
+space because a particle can be
+ 
+
+ align:start position:0%
+space because a particle can be
+anywhere. So this is a vector in quantum
+
+ align:start position:0%
+anywhere. So this is a vector in quantum
+ 
+
+ align:start position:0%
+anywhere. So this is a vector in quantum
+mechanics. This is a complex vector
+
+ align:start position:0%
+mechanics. This is a complex vector
+ 
+
+ align:start position:0%
+mechanics. This is a complex vector
+space. This is a real vector space and
+
+ align:start position:0%
+space. This is a real vector space and
+ 
+
+ align:start position:0%
+space. This is a real vector space and
+it's the label here. So again min - x is
+
+ align:start position:0%
+it's the label here. So again min - x is
+ 
+
+ align:start position:0%
+it's the label here. So again min - x is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+minus x vector. It it's not the vector.
+
+ align:start position:0%
+minus x vector. It it's not the vector.
+ 
+
+ align:start position:0%
+minus x vector. It it's not the vector.
+The addition of the bra has moved you
+
+ align:start position:0%
+The addition of the bra has moved you
+ 
+
+ align:start position:0%
+The addition of the bra has moved you
+from vectors that you're familiar with
+
+ align:start position:0%
+from vectors that you're familiar with
+ 
+
+ align:start position:0%
+from vectors that you're familiar with
+to states that are a little more
+
+ align:start position:0%
+to states that are a little more
+ 
+
+ align:start position:0%
+to states that are a little more
+abstract.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the reason this notation is quite
+
+ align:start position:0%
+So the reason this notation is quite
+ 
+
+ align:start position:0%
+So the reason this notation is quite
+good is because this is a number but
+
+ align:start position:0%
+good is because this is a number but
+ 
+
+ align:start position:0%
+good is because this is a number but
+this is or this is a coordinate and this
+
+ align:start position:0%
+this is or this is a coordinate and this
+ 
+
+ align:start position:0%
+this is or this is a coordinate and this
+is a vector already.
+
+ align:start position:0%
+is a vector already.
+ 
+
+ align:start position:0%
+is a vector already.
+So these are going to be our basis
+
+ align:start position:0%
+So these are going to be our basis
+ 
+
+ align:start position:0%
+So these are going to be our basis
+states and they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-denuable basis
+
+ align:start position:0%
+non-denuable basis
+ 
+
+ align:start position:0%
+non-denuable basis
+states. And here you can have that all x
+
+ align:start position:0%
+states. And here you can have that all x
+ 
+
+ align:start position:0%
+states. And here you can have that all x
+must belong to the real numbers because
+
+ align:start position:0%
+must belong to the real numbers because
+ 
+
+ align:start position:0%
+must belong to the real numbers because
+we have particles in a
+
+ align:start position:0%
+we have particles in a
+ 
+
+ align:start position:0%
+we have particles in a
+line. While this thing can be changed by
+
+ align:start position:0%
+line. While this thing can be changed by
+ 
+
+ align:start position:0%
+line. While this thing can be changed by
+real numbers, the states can be
+
+ align:start position:0%
+real numbers, the states can be
+ 
+
+ align:start position:0%
+real numbers, the states can be
+multiplied by complex numbers because
+
+ align:start position:0%
+multiplied by complex numbers because
+ 
+
+ align:start position:0%
+multiplied by complex numbers because
+we're doing quantum mechanics.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you want to define a vector space
+
+ align:start position:0%
+So if you want to define a vector space
+ 
+
+ align:start position:0%
+So if you want to define a vector space
+now this is all infinite dimensional
+
+ align:start position:0%
+now this is all infinite dimensional
+ 
+
+ align:start position:0%
+now this is all infinite dimensional
+it's a little worse in the sense the
+
+ align:start position:0%
+it's a little worse in the sense the
+ 
+
+ align:start position:0%
+it's a little worse in the sense the
+basis is non-enuable. If I use this
+
+ align:start position:0%
+basis is non-enuable. If I use this
+ 
+
+ align:start position:0%
+basis is non-enuable. If I use this
+basis I cannot make a list of all the
+
+ align:start position:0%
+basis I cannot make a list of all the
+ 
+
+ align:start position:0%
+basis I cannot make a list of all the
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+vectors. So for the inner product we
+
+ align:start position:0%
+vectors. So for the inner product we
+ 
+
+ align:start position:0%
+vectors. So for the inner product we
+will take the following. We will take x
+
+ align:start position:0%
+will take the following. We will take x
+ 
+
+ align:start position:0%
+will take the following. We will take x
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+y to be delta of x -
+
+ align:start position:0%
+y to be delta of x -
+ 
+
+ align:start position:0%
+y to be delta of x -
+y. That will be our inner product. And
+
+ align:start position:0%
+y. That will be our inner product. And
+ 
+
+ align:start position:0%
+y. That will be our inner product. And
+it has all the properties of the inner
+
+ align:start position:0%
+it has all the properties of the inner
+ 
+
+ align:start position:0%
+it has all the properties of the inner
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+um that we may
+
+ align:start position:0%
+um that we may
+ 
+
+ align:start position:0%
+um that we may
+want. And
+
+ align:start position:0%
+want. And
+ 
+
+ align:start position:0%
+want. And
+uh what else? Well, at this moment we
+
+ align:start position:0%
+uh what else? Well, at this moment we
+ 
+
+ align:start position:0%
+uh what else? Well, at this moment we
+can try to this this is physically
+
+ align:start position:0%
+can try to this this is physically
+ 
+
+ align:start position:0%
+can try to this this is physically
+sensible. Let me say because if you have
+
+ align:start position:0%
+sensible. Let me say because if you have
+ 
+
+ align:start position:0%
+sensible. Let me say because if you have
+a particle at one point and a particle
+
+ align:start position:0%
+a particle at one point and a particle
+ 
+
+ align:start position:0%
+a particle at one point and a particle
+at another point, the amplitude that
+
+ align:start position:0%
+at another point, the amplitude that
+ 
+
+ align:start position:0%
+at another point, the amplitude that
+this particle at one point is at this
+
+ align:start position:0%
+this particle at one point is at this
+ 
+
+ align:start position:0%
+this particle at one point is at this
+other point is zero. And these states
+
+ align:start position:0%
+other point is zero. And these states
+ 
+
+ align:start position:0%
+other point is zero. And these states
+are not normalizable. They correspond to
+
+ align:start position:0%
+are not normalizable. They correspond to
+ 
+
+ align:start position:0%
+are not normalizable. They correspond to
+a particle at a point. So once you try
+
+ align:start position:0%
+a particle at a point. So once you try
+ 
+
+ align:start position:0%
+a particle at a point. So once you try
+to normalize them, you get infinity and
+
+ align:start position:0%
+to normalize them, you get infinity and
+ 
+
+ align:start position:0%
+to normalize them, you get infinity and
+you can't do much. But what you can do
+
+ align:start position:0%
+you can't do much. But what you can do
+ 
+
+ align:start position:0%
+you can't do much. But what you can do
+here is uh state more of the properties
+
+ align:start position:0%
+here is uh state more of the properties
+ 
+
+ align:start position:0%
+here is uh state more of the properties
+and learn how to manipulate this. So
+
+ align:start position:0%
+and learn how to manipulate this. So
+ 
+
+ align:start position:0%
+and learn how to manipulate this. So
+remember we had one was the sum
+
+ align:start position:0%
+remember we had one was the sum
+ 
+
+ align:start position:0%
+remember we had one was the sum
+of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ei the unit operator was
+
+ align:start position:0%
+ei the unit operator was
+ 
+
+ align:start position:0%
+ei the unit operator was
+that well let's try to write a similar
+
+ align:start position:0%
+that well let's try to write a similar
+ 
+
+ align:start position:0%
+that well let's try to write a similar
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+The unit operator will be the sum over
+
+ align:start position:0%
+The unit operator will be the sum over
+ 
+
+ align:start position:0%
+The unit operator will be the sum over
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x's. And uh you could say, well, looks
+
+ align:start position:0%
+x's. And uh you could say, well, looks
+ 
+
+ align:start position:0%
+x's. And uh you could say, well, looks
+reasonable, but maybe there's a 1/2 in
+
+ align:start position:0%
+reasonable, but maybe there's a 1/2 in
+ 
+
+ align:start position:0%
+reasonable, but maybe there's a 1/2 in
+here or some factor. Well, no factor is
+
+ align:start position:0%
+here or some factor. Well, no factor is
+ 
+
+ align:start position:0%
+here or some factor. Well, no factor is
+needed. You can check that that you've
+
+ align:start position:0%
+needed. You can check that that you've
+ 
+
+ align:start position:0%
+needed. You can check that that you've
+defined this thing
+
+ align:start position:0%
+defined this thing
+ 
+
+ align:start position:0%
+defined this thing
+properly. So, let me do it.
+
+ align:start position:0%
+properly. So, let me do it.
+ 
+
+ align:start position:0%
+properly. So, let me do it.
+So act on this so-called resolution of
+
+ align:start position:0%
+So act on this so-called resolution of
+ 
+
+ align:start position:0%
+So act on this so-called resolution of
+the identity with the vector y. So one
+
+ align:start position:0%
+the identity with the vector y. So one
+ 
+
+ align:start position:0%
+the identity with the vector y. So one
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+y is equal to y. And now let's act on
+
+ align:start position:0%
+y is equal to y. And now let's act on
+ 
+
+ align:start position:0%
+y is equal to y. And now let's act on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right. x
+
+ align:start position:0%
+right. x
+ 
+
+ align:start position:0%
+right. x
+x y. This is delta of x - y. And then
+
+ align:start position:0%
+x y. This is delta of x - y. And then
+ 
+
+ align:start position:0%
+x y. This is delta of x - y. And then
+when you integrate you get y.
+
+ align:start position:0%
+when you integrate you get y.
+ 
+
+ align:start position:0%
+when you integrate you get y.
+So we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fine. So this looks a little too
+
+ align:start position:0%
+fine. So this looks a little too
+ 
+
+ align:start position:0%
+fine. So this looks a little too
+abstract, but it's not abstract if you
+
+ align:start position:0%
+abstract, but it's not abstract if you
+ 
+
+ align:start position:0%
+abstract, but it's not abstract if you
+now introduce wave functions. So let's
+
+ align:start position:0%
+now introduce wave functions. So let's
+ 
+
+ align:start position:0%
+now introduce wave functions. So let's
+do wave functions. So um you have a
+
+ align:start position:0%
+do wave functions. So um you have a
+ 
+
+ align:start position:0%
+do wave functions. So um you have a
+particle a state of a particle
+
+ align:start position:0%
+particle a state of a particle
+ 
+
+ align:start position:0%
+particle a state of a particle
+pi. Time would be irrelevant. So I will
+
+ align:start position:0%
+pi. Time would be irrelevant. So I will
+ 
+
+ align:start position:0%
+pi. Time would be irrelevant. So I will
+put just this pi like that without the
+
+ align:start position:0%
+put just this pi like that without the
+ 
+
+ align:start position:0%
+put just this pi like that without the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+line. And uh let's look at it. Oh, I
+
+ align:start position:0%
+line. And uh let's look at it. Oh, I
+ 
+
+ align:start position:0%
+line. And uh let's look at it. Oh, I
+want to say one more thing.
+
+ align:start position:0%
+want to say one more thing.
+ 
+
+ align:start position:0%
+want to say one more thing.
+Um the x
+
+ align:start position:0%
+Um the x
+ 
+
+ align:start position:0%
+Um the x
+operator acts on the x states to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x. So these are states of the x
+
+ align:start position:0%
+x. So these are states of the x
+ 
+
+ align:start position:0%
+x. So these are states of the x
+operator. We declare them to be igon
+
+ align:start position:0%
+operator. We declare them to be igon
+ 
+
+ align:start position:0%
+operator. We declare them to be igon
+states of the x operator with iggon
+
+ align:start position:0%
+states of the x operator with iggon
+ 
+
+ align:start position:0%
+states of the x operator with iggon
+value x. That's their physical
+
+ align:start position:0%
+value x. That's their physical
+ 
+
+ align:start position:0%
+value x. That's their physical
+interpretation. I probably should have
+
+ align:start position:0%
+interpretation. I probably should have
+ 
+
+ align:start position:0%
+interpretation. I probably should have
+said that
+
+ align:start position:0%
+said that
+ 
+
+ align:start position:0%
+said that
+before. Now if we have a
+
+ align:start position:0%
+before. Now if we have a
+ 
+
+ align:start position:0%
+before. Now if we have a
+pi as a state or a vector, how do we get
+
+ align:start position:0%
+pi as a state or a vector, how do we get
+ 
+
+ align:start position:0%
+pi as a state or a vector, how do we get
+the wave function? Well, in this
+
+ align:start position:0%
+the wave function? Well, in this
+ 
+
+ align:start position:0%
+the wave function? Well, in this
+language, the wave function which we
+
+ align:start position:0%
+language, the wave function which we
+ 
+
+ align:start position:0%
+language, the wave function which we
+call p of x is defined to be the overlap
+
+ align:start position:0%
+call p of x is defined to be the overlap
+ 
+
+ align:start position:0%
+call p of x is defined to be the overlap
+of x with pi.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that makes sense because this
+
+ align:start position:0%
+And that makes sense because this
+ 
+
+ align:start position:0%
+And that makes sense because this
+overlap is a function of this label here
+
+ align:start position:0%
+overlap is a function of this label here
+ 
+
+ align:start position:0%
+overlap is a function of this label here
+where the particle is and therefore the
+
+ align:start position:0%
+where the particle is and therefore the
+ 
+
+ align:start position:0%
+where the particle is and therefore the
+result is a complex number that is
+
+ align:start position:0%
+result is a complex number that is
+ 
+
+ align:start position:0%
+result is a complex number that is
+dependent on x. So this belongs to the
+
+ align:start position:0%
+dependent on x. So this belongs to the
+ 
+
+ align:start position:0%
+dependent on x. So this belongs to the
+complex numbers because inner products
+
+ align:start position:0%
+complex numbers because inner products
+ 
+
+ align:start position:0%
+complex numbers because inner products
+can have complex numbers. Now I didn't
+
+ align:start position:0%
+can have complex numbers. Now I didn't
+ 
+
+ align:start position:0%
+can have complex numbers. Now I didn't
+put any complex number here but when you
+
+ align:start position:0%
+put any complex number here but when you
+ 
+
+ align:start position:0%
+put any complex number here but when you
+form states you can superpose states
+
+ align:start position:0%
+form states you can superpose states
+ 
+
+ align:start position:0%
+form states you can superpose states
+with complex numbers. So this pi of x
+
+ align:start position:0%
+with complex numbers. So this pi of x
+ 
+
+ align:start position:0%
+with complex numbers. So this pi of x
+will come out this
+
+ align:start position:0%
+will come out this
+ 
+
+ align:start position:0%
+will come out this
+way. And now you can now that you're
+
+ align:start position:0%
+way. And now you can now that you're
+ 
+
+ align:start position:0%
+way. And now you can now that you're
+armed with that you can even think of
+
+ align:start position:0%
+armed with that you can even think of
+ 
+
+ align:start position:0%
+armed with that you can even think of
+this in a nicer way. The state p is
+
+ align:start position:0%
+this in a nicer way. The state p is
+ 
+
+ align:start position:0%
+this in a nicer way. The state p is
+equal to 1 * p and then use the res this
+
+ align:start position:0%
+equal to 1 * p and then use the res this
+ 
+
+ align:start position:0%
+equal to 1 * p and then use the res this
+formula. So this is integral
+
+ align:start position:0%
+formula. So this is integral
+ 
+
+ align:start position:0%
+formula. So this is integral
+dx x x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and again the bracket notation is
+
+ align:start position:0%
+x and again the bracket notation is
+ 
+
+ align:start position:0%
+x and again the bracket notation is
+quite nice because the brow already
+
+ align:start position:0%
+quite nice because the brow already
+ 
+
+ align:start position:0%
+quite nice because the brow already
+meets the k. This is a number and this
+
+ align:start position:0%
+meets the k. This is a number and this
+ 
+
+ align:start position:0%
+meets the k. This is a number and this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+dx x s of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x. This equation has a nice
+
+ align:start position:0%
+x. This equation has a nice
+ 
+
+ align:start position:0%
+x. This equation has a nice
+interpretation. It says that the state
+
+ align:start position:0%
+interpretation. It says that the state
+ 
+
+ align:start position:0%
+interpretation. It says that the state
+is a superposition of the basis states
+
+ align:start position:0%
+is a superposition of the basis states
+ 
+
+ align:start position:0%
+is a superposition of the basis states
+the position states and the component of
+
+ align:start position:0%
+the position states and the component of
+ 
+
+ align:start position:0%
+the position states and the component of
+your original state along the basis
+
+ align:start position:0%
+your original state along the basis
+ 
+
+ align:start position:0%
+your original state along the basis
+state x is precisely the value of the
+
+ align:start position:0%
+state x is precisely the value of the
+ 
+
+ align:start position:0%
+state x is precisely the value of the
+wave function at x. So the wave function
+
+ align:start position:0%
+wave function at x. So the wave function
+ 
+
+ align:start position:0%
+wave function at x. So the wave function
+at x is giving you the weight of the
+
+ align:start position:0%
+at x is giving you the weight of the
+ 
+
+ align:start position:0%
+at x is giving you the weight of the
+state x as it enters into the sum.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So one can compute more things. Uh you
+
+ align:start position:0%
+So one can compute more things. Uh you
+ 
+
+ align:start position:0%
+So one can compute more things. Uh you
+will get practice on this type of
+
+ align:start position:0%
+will get practice on this type of
+ 
+
+ align:start position:0%
+will get practice on this type of
+computations. They're just limited type
+
+ align:start position:0%
+computations. They're just limited type
+ 
+
+ align:start position:0%
+computations. They're just limited type
+of variations that you can do. So uh
+
+ align:start position:0%
+of variations that you can do. So uh
+ 
+
+ align:start position:0%
+of variations that you can do. So uh
+it's not that
+
+ align:start position:0%
+it's not that
+ 
+
+ align:start position:0%
+it's not that
+um complicated. Basically you can
+
+ align:start position:0%
+um complicated. Basically you can
+ 
+
+ align:start position:0%
+um complicated. Basically you can
+introduce resolutions of the identity
+
+ align:start position:0%
+introduce resolutions of the identity
+ 
+
+ align:start position:0%
+introduce resolutions of the identity
+wherever you need them. And uh if you
+
+ align:start position:0%
+wherever you need them. And uh if you
+ 
+
+ align:start position:0%
+wherever you need them. And uh if you
+introduce too many you waste time but um
+
+ align:start position:0%
+introduce too many you waste time but um
+ 
+
+ align:start position:0%
+introduce too many you waste time but um
+you typically get the answer anyway. Um
+
+ align:start position:0%
+you typically get the answer anyway. Um
+ 
+
+ align:start position:0%
+you typically get the answer anyway. Um
+so it's it's not too serious. Um so
+
+ align:start position:0%
+so it's it's not too serious. Um so
+ 
+
+ align:start position:0%
+so it's it's not too serious. Um so
+suppose you want to understand what is
+
+ align:start position:0%
+suppose you want to understand what is
+ 
+
+ align:start position:0%
+suppose you want to understand what is
+the inner product of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states. Put a resolution of the identity
+
+ align:start position:0%
+states. Put a resolution of the identity
+ 
+
+ align:start position:0%
+states. Put a resolution of the identity
+in between. So put five and then put the
+
+ align:start position:0%
+in between. So put five and then put the
+ 
+
+ align:start position:0%
+in between. So put five and then put the
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+dx x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x. Well, the integral goes out and you
+
+ align:start position:0%
+x. Well, the integral goes out and you
+ 
+
+ align:start position:0%
+x. Well, the integral goes out and you
+get five
+
+ align:start position:0%
+get five
+ 
+
+ align:start position:0%
+get five
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+xi and uh remember if x psi is s of
+
+ align:start position:0%
+xi and uh remember if x psi is s of
+ 
+
+ align:start position:0%
+xi and uh remember if x psi is s of
+x 5x is the complex conjugate. So it's
+
+ align:start position:0%
+x 5x is the complex conjugate. So it's
+ 
+
+ align:start position:0%
+x 5x is the complex conjugate. So it's
+phi star of x and that's what you know
+
+ align:start position:0%
+phi star of x and that's what you know
+ 
+
+ align:start position:0%
+phi star of x and that's what you know
+you knew that if you have two wave
+
+ align:start position:0%
+you knew that if you have two wave
+ 
+
+ align:start position:0%
+you knew that if you have two wave
+functions and you want to compute their
+
+ align:start position:0%
+functions and you want to compute their
+ 
+
+ align:start position:0%
+functions and you want to compute their
+overlap you integrate the complex
+
+ align:start position:0%
+overlap you integrate the complex
+ 
+
+ align:start position:0%
+overlap you integrate the complex
+conjugate of one against the
+
+ align:start position:0%
+conjugate of one against the
+ 
+
+ align:start position:0%
+conjugate of one against the
+other. So this notation is doing all
+
+ align:start position:0%
+other. So this notation is doing all
+ 
+
+ align:start position:0%
+other. So this notation is doing all
+what you want from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. You want to compute a matrix
+
+ align:start position:0%
+this. You want to compute a matrix
+ 
+
+ align:start position:0%
+this. You want to compute a matrix
+element of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X. Well, put another resolution of the
+
+ align:start position:0%
+X. Well, put another resolution of the
+ 
+
+ align:start position:0%
+X. Well, put another resolution of the
+identity
+
+ align:start position:0%
+identity
+ 
+
+ align:start position:0%
+identity
+here. So this would be integral
+
+ align:start position:0%
+here. So this would be integral
+ 
+
+ align:start position:0%
+here. So this would be integral
+dx fi the x hat is here and then you put
+
+ align:start position:0%
+dx fi the x hat is here and then you put
+ 
+
+ align:start position:0%
+dx fi the x hat is here and then you put
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x the x hat on x is x that's what this
+
+ align:start position:0%
+x the x hat on x is x that's what this
+ 
+
+ align:start position:0%
+x the x hat on x is x that's what this
+operator does. So you get integral dx of
+
+ align:start position:0%
+operator does. So you get integral dx of
+ 
+
+ align:start position:0%
+operator does. So you get integral dx of
+um I'll put
+
+ align:start position:0%
+um I'll put
+ 
+
+ align:start position:0%
+um I'll put
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+5x x pi which is what you expect it to
+
+ align:start position:0%
+5x x pi which is what you expect it to
+ 
+
+ align:start position:0%
+5x x pi which is what you expect it to
+be integral of x 5 star of x pi of x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now we can do exactly the same thing
+
+ align:start position:0%
+Now we can do exactly the same thing
+ 
+
+ align:start position:0%
+Now we can do exactly the same thing
+with momentum states. So I don't want to
+
+ align:start position:0%
+with momentum states. So I don't want to
+ 
+
+ align:start position:0%
+with momentum states. So I don't want to
+bore you. So I just list the properties.
+
+ align:start position:0%
+bore you. So I just list the properties.
+ 
+
+ align:start position:0%
+bore you. So I just list the properties.
+Basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states are momenta where the momenta is
+
+ align:start position:0%
+states are momenta where the momenta is
+ 
+
+ align:start position:0%
+states are momenta where the momenta is
+real. P prime p is equal delta of p
+
+ align:start position:0%
+real. P prime p is equal delta of p
+ 
+
+ align:start position:0%
+real. P prime p is equal delta of p
+minus p prime.
+
+ align:start position:0%
+minus p prime.
+ 
+
+ align:start position:0%
+minus p prime.
+1 is the integral DP of P
+
+ align:start position:0%
+1 is the integral DP of P
+ 
+
+ align:start position:0%
+1 is the integral DP of P
+P and P hat P is equal to P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P. So these are the momentum basis is
+
+ align:start position:0%
+P. So these are the momentum basis is
+ 
+
+ align:start position:0%
+P. So these are the momentum basis is
+exactly analogous. So all what we've
+
+ align:start position:0%
+exactly analogous. So all what we've
+ 
+
+ align:start position:0%
+exactly analogous. So all what we've
+done for X is true. the completeness and
+
+ align:start position:0%
+done for X is true. the completeness and
+ 
+
+ align:start position:0%
+done for X is true. the completeness and
+normalization are well work well
+
+ align:start position:0%
+normalization are well work well
+ 
+
+ align:start position:0%
+normalization are well work well
+together like we check there and
+
+ align:start position:0%
+together like we check there and
+ 
+
+ align:start position:0%
+together like we check there and
+everything is true. The only thing that
+
+ align:start position:0%
+everything is true. The only thing that
+ 
+
+ align:start position:0%
+everything is true. The only thing that
+you need to make this
+
+ align:start position:0%
+you need to make this
+ 
+
+ align:start position:0%
+you need to make this
+more interesting is a relation between
+
+ align:start position:0%
+more interesting is a relation between
+ 
+
+ align:start position:0%
+more interesting is a relation between
+the x basis and the p basis and that's
+
+ align:start position:0%
+the x basis and the p basis and that's
+ 
+
+ align:start position:0%
+the x basis and the p basis and that's
+where physics comes in. Anybody can
+
+ align:start position:0%
+where physics comes in. Anybody can
+ 
+
+ align:start position:0%
+where physics comes in. Anybody can
+define this too. But then a physical
+
+ align:start position:0%
+define this too. But then a physical
+ 
+
+ align:start position:0%
+define this too. But then a physical
+assumption as to what you really mean by
+
+ align:start position:0%
+assumption as to what you really mean by
+ 
+
+ align:start position:0%
+assumption as to what you really mean by
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+um is necessary. And what we've said is
+
+ align:start position:0%
+um is necessary. And what we've said is
+ 
+
+ align:start position:0%
+um is necessary. And what we've said is
+that the wave function of a particle
+
+ align:start position:0%
+that the wave function of a particle
+ 
+
+ align:start position:0%
+that the wave function of a particle
+with momentum
+
+ align:start position:0%
+with momentum
+ 
+
+ align:start position:0%
+with momentum
+P is e to the
+
+ align:start position:0%
+P is e to the
+ 
+
+ align:start position:0%
+P is e to the
+ip x over h
+
+ align:start position:0%
+ip x over h
+ 
+
+ align:start position:0%
+ip x over h
+bar over square<unk> of 2 pih.
+
+ align:start position:0%
+bar over square<unk> of 2 pih.
+ 
+
+ align:start position:0%
+bar over square<unk> of 2 pih.
+convenient normalization but
+
+ align:start position:0%
+convenient normalization but
+ 
+
+ align:start position:0%
+convenient normalization but
+uh but that was it. That was our
+
+ align:start position:0%
+uh but that was it. That was our
+ 
+
+ align:start position:0%
+uh but that was it. That was our
+physical interpretation of the wave
+
+ align:start position:0%
+physical interpretation of the wave
+ 
+
+ align:start position:0%
+physical interpretation of the wave
+function of a particle with some
+
+ align:start position:0%
+function of a particle with some
+ 
+
+ align:start position:0%
+function of a particle with some
+momentum. And therefore if this is a
+
+ align:start position:0%
+momentum. And therefore if this is a
+ 
+
+ align:start position:0%
+momentum. And therefore if this is a
+wave function that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XP a state of momentum P has this wave
+
+ align:start position:0%
+XP a state of momentum P has this wave
+ 
+
+ align:start position:0%
+XP a state of momentum P has this wave
+function. So we write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh there are checks you can do and
+
+ align:start position:0%
+Okay. Uh there are checks you can do and
+ 
+
+ align:start position:0%
+Okay. Uh there are checks you can do and
+please read the notes but uh let's do a
+
+ align:start position:0%
+please read the notes but uh let's do a
+ 
+
+ align:start position:0%
+please read the notes but uh let's do a
+little computation. Suppose you want to
+
+ align:start position:0%
+little computation. Suppose you want to
+ 
+
+ align:start position:0%
+little computation. Suppose you want to
+compute what is p on
+
+ align:start position:0%
+compute what is p on
+ 
+
+ align:start position:0%
+compute what is p on
+pi and you can say well I don't know why
+
+ align:start position:0%
+pi and you can say well I don't know why
+ 
+
+ align:start position:0%
+pi and you can say well I don't know why
+why would I want to do something with
+
+ align:start position:0%
+why would I want to do something with
+ 
+
+ align:start position:0%
+why would I want to do something with
+that looks simple enough. Well, it's
+
+ align:start position:0%
+that looks simple enough. Well, it's
+ 
+
+ align:start position:0%
+that looks simple enough. Well, it's
+simple enough, but you could say, I want
+
+ align:start position:0%
+simple enough, but you could say, I want
+ 
+
+ align:start position:0%
+simple enough, but you could say, I want
+to see it in terms of wave
+
+ align:start position:0%
+to see it in terms of wave
+ 
+
+ align:start position:0%
+to see it in terms of wave
+functions, coordinate space wave
+
+ align:start position:0%
+functions, coordinate space wave
+ 
+
+ align:start position:0%
+functions, coordinate space wave
+functions. Well, if you want to see them
+
+ align:start position:0%
+functions. Well, if you want to see them
+ 
+
+ align:start position:0%
+functions. Well, if you want to see them
+in terms of coordinate space wave
+
+ align:start position:0%
+in terms of coordinate space wave
+ 
+
+ align:start position:0%
+in terms of coordinate space wave
+functions, you have to introduce a
+
+ align:start position:0%
+functions, you have to introduce a
+ 
+
+ align:start position:0%
+functions, you have to introduce a
+complete set of states. So,
+
+ align:start position:0%
+complete set of states. So,
+ 
+
+ align:start position:0%
+complete set of states. So,
+introduce P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XI. Then you have this wave function and
+
+ align:start position:0%
+XI. Then you have this wave function and
+ 
+
+ align:start position:0%
+XI. Then you have this wave function and
+oh, this is sort of known because it's
+
+ align:start position:0%
+oh, this is sort of known because it's
+ 
+
+ align:start position:0%
+oh, this is sort of known because it's
+the complex conjugate of this. So it's
+
+ align:start position:0%
+the complex conjugate of this. So it's
+ 
+
+ align:start position:0%
+the complex conjugate of this. So it's
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dx px / h bar square<unk> of 2 pi h bar
+
+ align:start position:0%
+dx px / h bar square<unk> of 2 pi h bar
+ 
+
+ align:start position:0%
+dx px / h bar square<unk> of 2 pi h bar
+time p s of
+
+ align:start position:0%
+time p s of
+ 
+
+ align:start position:0%
+time p s of
+x and this was the fia transform what we
+
+ align:start position:0%
+x and this was the fia transform what we
+ 
+
+ align:start position:0%
+x and this was the fia transform what we
+call the fia transform of the wave
+
+ align:start position:0%
+call the fia transform of the wave
+ 
+
+ align:start position:0%
+call the fia transform of the wave
+function. So we can call it sit tilda of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p just to distinguish it. Uh because we
+
+ align:start position:0%
+p just to distinguish it. Uh because we
+ 
+
+ align:start position:0%
+p just to distinguish it. Uh because we
+call pi with x p s p s p s p s p s p s p
+
+ align:start position:0%
+call pi with x p s p s p s p s p s p s p
+ 
+
+ align:start position:0%
+call pi with x p s p s p s p s p s p s p
+s p s p s p s p of x. So if I didn't put
+
+ align:start position:0%
+s p s p s p s p of x. So if I didn't put
+ 
+
+ align:start position:0%
+s p s p s p s p of x. So if I didn't put
+a tilda, you might think it's the same
+
+ align:start position:0%
+a tilda, you might think it's the same
+ 
+
+ align:start position:0%
+a tilda, you might think it's the same
+functional form, but it's the momentum
+
+ align:start position:0%
+functional form, but it's the momentum
+ 
+
+ align:start position:0%
+functional form, but it's the momentum
+space wave
+
+ align:start position:0%
+space wave
+ 
+
+ align:start position:0%
+space wave
+function. So uh here is the wave
+
+ align:start position:0%
+function. So uh here is the wave
+ 
+
+ align:start position:0%
+function. So uh here is the wave
+function in the p basis. It's the FIA
+
+ align:start position:0%
+function in the p basis. It's the FIA
+ 
+
+ align:start position:0%
+function in the p basis. It's the FIA
+transform of the wave function in the x
+
+ align:start position:0%
+transform of the wave function in the x
+ 
+
+ align:start position:0%
+transform of the wave function in the x
+basis.
+
+ align:start position:0%
+basis.
+ 
+
+ align:start position:0%
+basis.
+One last computation and then we change
+
+ align:start position:0%
+One last computation and then we change
+ 
+
+ align:start position:0%
+One last computation and then we change
+subjects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again. It's the classic
+
+ align:start position:0%
+again. It's the classic
+ 
+
+ align:start position:0%
+again. It's the classic
+computation
+
+ align:start position:0%
+computation
+ 
+
+ align:start position:0%
+computation
+that you have now a mixed situation in
+
+ align:start position:0%
+that you have now a mixed situation in
+ 
+
+ align:start position:0%
+that you have now a mixed situation in
+which you have the momentum operator
+
+ align:start position:0%
+which you have the momentum operator
+ 
+
+ align:start position:0%
+which you have the momentum operator
+states and a coordinate um bra. So what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is the following expression
+
+ align:start position:0%
+is is the following expression
+ 
+
+ align:start position:0%
+is is the following expression
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x p
+
+ align:start position:0%
+x p
+ 
+
+ align:start position:0%
+x p
+hat s.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. What is your temptation? Your
+
+ align:start position:0%
+Okay. What is your temptation? Your
+ 
+
+ align:start position:0%
+Okay. What is your temptation? Your
+temptation is to say
+
+ align:start position:0%
+temptation is to say
+ 
+
+ align:start position:0%
+temptation is to say
+look this is like the momentum
+
+ align:start position:0%
+look this is like the momentum
+ 
+
+ align:start position:0%
+look this is like the momentum
+operator acting on the wave function in
+
+ align:start position:0%
+operator acting on the wave function in
+ 
+
+ align:start position:0%
+operator acting on the wave function in
+the x basis. It can only be har over i
+
+ align:start position:0%
+the x basis. It can only be har over i
+ 
+
+ align:start position:0%
+the x basis. It can only be har over i
+dx of s of x. That's probably what it
+
+ align:start position:0%
+dx of s of x. That's probably what it
+ 
+
+ align:start position:0%
+dx of s of x. That's probably what it
+means. Um but the notation is clear
+
+ align:start position:0%
+means. Um but the notation is clear
+ 
+
+ align:start position:0%
+means. Um but the notation is clear
+enough so we can check if that is
+
+ align:start position:0%
+enough so we can check if that is
+ 
+
+ align:start position:0%
+enough so we can check if that is
+exactly what it is. We we can manipulate
+
+ align:start position:0%
+exactly what it is. We we can manipulate
+ 
+
+ align:start position:0%
+exactly what it is. We we can manipulate
+things already. So let's do it. So for
+
+ align:start position:0%
+things already. So let's do it. So for
+ 
+
+ align:start position:0%
+things already. So let's do it. So for
+that I first have to try to get rid of
+
+ align:start position:0%
+that I first have to try to get rid of
+ 
+
+ align:start position:0%
+that I first have to try to get rid of
+this operator. Now the only way I know
+
+ align:start position:0%
+this operator. Now the only way I know
+ 
+
+ align:start position:0%
+this operator. Now the only way I know
+how to get rid of this operator P is
+
+ align:start position:0%
+how to get rid of this operator P is
+ 
+
+ align:start position:0%
+how to get rid of this operator P is
+because it
+
+ align:start position:0%
+because it
+ 
+
+ align:start position:0%
+because it
+has state. So it suggests very strongly
+
+ align:start position:0%
+has state. So it suggests very strongly
+ 
+
+ align:start position:0%
+has state. So it suggests very strongly
+that we should introduce momentum states
+
+ align:start position:0%
+that we should introduce momentum states
+ 
+
+ align:start position:0%
+that we should introduce momentum states
+completeness. So I'll put
+
+ align:start position:0%
+completeness. So I'll put
+ 
+
+ align:start position:0%
+completeness. So I'll put
+DP X P hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P S P S P S P S P S P S P S P S P S P S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P and now I can evaluate a
+
+ align:start position:0%
+P and now I can evaluate a
+ 
+
+ align:start position:0%
+P and now I can evaluate a
+little because P hat and P is little P
+
+ align:start position:0%
+little because P hat and P is little P
+ 
+
+ align:start position:0%
+little because P hat and P is little P
+or P without the hat. So this is
+
+ align:start position:0%
+or P without the hat. So this is
+ 
+
+ align:start position:0%
+or P without the hat. So this is
+P XP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P S P S P S P S P S P S P S P S P S P S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+Now you can uh look at that and and
+
+ align:start position:0%
+Now you can uh look at that and and
+ 
+
+ align:start position:0%
+Now you can uh look at that and and
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+carefully what should you do and there's
+
+ align:start position:0%
+carefully what should you do and there's
+ 
+
+ align:start position:0%
+carefully what should you do and there's
+one thing that you can
+
+ align:start position:0%
+one thing that you can
+ 
+
+ align:start position:0%
+one thing that you can
+do is uh look at the equation on top and
+
+ align:start position:0%
+do is uh look at the equation on top and
+ 
+
+ align:start position:0%
+do is uh look at the equation on top and
+this is a way to avoid working very
+
+ align:start position:0%
+this is a way to avoid working very
+ 
+
+ align:start position:0%
+this is a way to avoid working very
+hard. So look at the equation on top. XP
+
+ align:start position:0%
+hard. So look at the equation on top. XP
+ 
+
+ align:start position:0%
+hard. So look at the equation on top. XP
+is equal to that. How do I get a P to
+
+ align:start position:0%
+is equal to that. How do I get a P to
+ 
+
+ align:start position:0%
+is equal to that. How do I get a P to
+multiply this? I can get a P to multiply
+
+ align:start position:0%
+multiply this? I can get a P to multiply
+ 
+
+ align:start position:0%
+multiply this? I can get a P to multiply
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+XP by doing H bar over
+
+ align:start position:0%
+XP by doing H bar over
+ 
+
+ align:start position:0%
+XP by doing H bar over
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+ddx
+
+ align:start position:0%
+ddx
+ 
+
+ align:start position:0%
+ddx
+of XP.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because if I see it there, I see that
+
+ align:start position:0%
+Because if I see it there, I see that
+ 
+
+ align:start position:0%
+Because if I see it there, I see that
+differentiating by h by ddx brings down
+
+ align:start position:0%
+differentiating by h by ddx brings down
+ 
+
+ align:start position:0%
+differentiating by h by ddx brings down
+an ip over h bar. So if I multiply by h
+
+ align:start position:0%
+an ip over h bar. So if I multiply by h
+ 
+
+ align:start position:0%
+an ip over h bar. So if I multiply by h
+bar over i, I get that. So let's do
+
+ align:start position:0%
+bar over i, I get that. So let's do
+ 
+
+ align:start position:0%
+bar over i, I get that. So let's do
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I claim we can take the h over i dx
+
+ align:start position:0%
+Now I claim we can take the h over i dx
+ 
+
+ align:start position:0%
+Now I claim we can take the h over i dx
+out of this uh
+
+ align:start position:0%
+out of this uh
+ 
+
+ align:start position:0%
+out of this uh
+integral and the reason is that first is
+
+ align:start position:0%
+integral and the reason is that first is
+ 
+
+ align:start position:0%
+integral and the reason is that first is
+not an x integral it's a p integral and
+
+ align:start position:0%
+not an x integral it's a p integral and
+ 
+
+ align:start position:0%
+not an x integral it's a p integral and
+nothing else except this factor depends
+
+ align:start position:0%
+nothing else except this factor depends
+ 
+
+ align:start position:0%
+nothing else except this factor depends
+on x. So if I take it out and they want
+
+ align:start position:0%
+on x. So if I take it out and they want
+ 
+
+ align:start position:0%
+on x. So if I take it out and they want
+to bring it back, it will only act on
+
+ align:start position:0%
+to bring it back, it will only act on
+ 
+
+ align:start position:0%
+to bring it back, it will only act on
+this because this is not X
+
+ align:start position:0%
+this because this is not X
+ 
+
+ align:start position:0%
+this because this is not X
+dependent. So you should think of S. S
+
+ align:start position:0%
+dependent. So you should think of S. S
+ 
+
+ align:start position:0%
+dependent. So you should think of S. S
+doesn't have an X
+
+ align:start position:0%
+doesn't have an X
+ 
+
+ align:start position:0%
+doesn't have an X
+dependence. P S is a state and here is P
+
+ align:start position:0%
+dependence. P S is a state and here is P
+ 
+
+ align:start position:0%
+dependence. P S is a state and here is P
+doesn't have an X dependence. No, it
+
+ align:start position:0%
+doesn't have an X dependence. No, it
+ 
+
+ align:start position:0%
+doesn't have an X dependence. No, it
+does. It looks
+
+ align:start position:0%
+does. It looks
+ 
+
+ align:start position:0%
+does. It looks
+here. No, but it doesn't have it that
+
+ align:start position:0%
+here. No, but it doesn't have it that
+ 
+
+ align:start position:0%
+here. No, but it doesn't have it that
+has been
+
+ align:start position:0%
+has been
+ 
+
+ align:start position:0%
+has been
+integrated. It really doesn't have X
+
+ align:start position:0%
+integrated. It really doesn't have X
+ 
+
+ align:start position:0%
+integrated. It really doesn't have X
+dependence. So we can take this out.
+
+ align:start position:0%
+dependence. So we can take this out.
+ 
+
+ align:start position:0%
+dependence. So we can take this out.
+And we'll have h over i
+
+ align:start position:0%
+And we'll have h over i
+ 
+
+ align:start position:0%
+And we'll have h over i
+dx. And now we have
+
+ align:start position:0%
+dx. And now we have
+ 
+
+ align:start position:0%
+dx. And now we have
+dp x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi. And now by completeness this is just
+
+ align:start position:0%
+pi. And now by completeness this is just
+ 
+
+ align:start position:0%
+pi. And now by completeness this is just
+one. So this becomes xi. So h bar over i
+
+ align:start position:0%
+one. So this becomes xi. So h bar over i
+ 
+
+ align:start position:0%
+one. So this becomes xi. So h bar over i
+dx of
+
+ align:start position:0%
+dx of
+ 
+
+ align:start position:0%
+dx of
+xi which is what we claimed it would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be. So
+
+ align:start position:0%
+be. So
+ 
+
+ align:start position:0%
+be. So
+uh this is rigorous rigorous derivation
+
+ align:start position:0%
+uh this is rigorous rigorous derivation
+ 
+
+ align:start position:0%
+uh this is rigorous rigorous derivation
+as you
+
+ align:start position:0%
+as you
+ 
+
+ align:start position:0%
+as you
+know there's u no guessing uh you can
+
+ align:start position:0%
+know there's u no guessing uh you can
+ 
+
+ align:start position:0%
+know there's u no guessing uh you can
+introduce complete states until you can
+
+ align:start position:0%
+introduce complete states until you can
+ 
+
+ align:start position:0%
+introduce complete states until you can
+see how things act and basically but the
+
+ align:start position:0%
+see how things act and basically but the
+ 
+
+ align:start position:0%
+see how things act and basically but the
+moral is here that you shouldn't have to
+
+ align:start position:0%
+moral is here that you shouldn't have to
+ 
+
+ align:start position:0%
+moral is here that you shouldn't have to
+go through this more than once in your
+
+ align:start position:0%
+go through this more than once in your
+ 
+
+ align:start position:0%
+go through this more than once in your
+life or practice it but once you see
+
+ align:start position:0%
+life or practice it but once you see
+ 
+
+ align:start position:0%
+life or practice it but once you see
+something like that you think you're
+
+ align:start position:0%
+something like that you think you're
+ 
+
+ align:start position:0%
+something like that you think you're
+using x representation and you're
+
+ align:start position:0%
+using x representation and you're
+ 
+
+ align:start position:0%
+using x representation and you're
+talking about the operator P. It cannot
+
+ align:start position:0%
+talking about the operator P. It cannot
+ 
+
+ align:start position:0%
+talking about the operator P. It cannot
+be anything like that. If you want to
+
+ align:start position:0%
+be anything like that. If you want to
+ 
+
+ align:start position:0%
+be anything like that. If you want to
+practice something different, show that
+
+ align:start position:0%
+practice something different, show that
+ 
+
+ align:start position:0%
+practice something different, show that
+the analog P Xhat pi is equal I H bar
+
+ align:start position:0%
+the analog P Xhat pi is equal I H bar
+ 
+
+ align:start position:0%
+the analog P Xhat pi is equal I H bar
+DDP of PI tilda of P. So it's the
+
+ align:start position:0%
+DDP of PI tilda of P. So it's the
+ 
+
+ align:start position:0%
+DDP of PI tilda of P. So it's the
+opposite relation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes. So, how is one supposed to? So,
+
+ align:start position:0%
+Yes. So, how is one supposed to? So,
+ 
+
+ align:start position:0%
+Yes. So, how is one supposed to? So,
+what it appears is happening is you're
+
+ align:start position:0%
+what it appears is happening is you're
+ 
+
+ align:start position:0%
+what it appears is happening is you're
+basically taking some state like S and
+
+ align:start position:0%
+basically taking some state like S and
+ 
+
+ align:start position:0%
+basically taking some state like S and
+you're basically writing in terms of
+
+ align:start position:0%
+you're basically writing in terms of
+ 
+
+ align:start position:0%
+you're basically writing in terms of
+some basis, correct? And then you're
+
+ align:start position:0%
+some basis, correct? And then you're
+ 
+
+ align:start position:0%
+some basis, correct? And then you're
+basically using the L2 norm on the
+
+ align:start position:0%
+basically using the L2 norm on the
+ 
+
+ align:start position:0%
+basically using the L2 norm on the
+coordinates of this thing. But the
+
+ align:start position:0%
+coordinates of this thing. But the
+ 
+
+ align:start position:0%
+coordinates of this thing. But the
+question is what does the this basis
+
+ align:start position:0%
+question is what does the this basis
+ 
+
+ align:start position:0%
+question is what does the this basis
+actually look like? Like what are these
+
+ align:start position:0%
+actually look like? Like what are these
+ 
+
+ align:start position:0%
+actually look like? Like what are these
+vectors? Because if you put them in
+
+ align:start position:0%
+vectors? Because if you put them in
+ 
+
+ align:start position:0%
+vectors? Because if you put them in
+their own coordinates, they're just
+
+ align:start position:0%
+their own coordinates, they're just
+ 
+
+ align:start position:0%
+their own coordinates, they're just
+infinite. Yeah, they're not even delta.
+
+ align:start position:0%
+infinite. Yeah, they're not even delta.
+ 
+
+ align:start position:0%
+infinite. Yeah, they're not even delta.
+I mean, they are delta functions. Uh
+
+ align:start position:0%
+I mean, they are delta functions. Uh
+ 
+
+ align:start position:0%
+I mean, they are delta functions. Uh
+these vectors are delta functions
+
+ align:start position:0%
+these vectors are delta functions
+ 
+
+ align:start position:0%
+these vectors are delta functions
+because if you have a state that has
+
+ align:start position:0%
+because if you have a state that has
+ 
+
+ align:start position:0%
+because if you have a state that has
+this as the position state of a
+
+ align:start position:0%
+this as the position state of a
+ 
+
+ align:start position:0%
+this as the position state of a
+particle, you find the wave function by
+
+ align:start position:0%
+particle, you find the wave function by
+ 
+
+ align:start position:0%
+particle, you find the wave function by
+doing x on it. That's our definition of
+
+ align:start position:0%
+doing x on it. That's our definition of
+ 
+
+ align:start position:0%
+doing x on it. That's our definition of
+a wave function. And it's uh infinite.
+
+ align:start position:0%
+a wave function. And it's uh infinite.
+ 
+
+ align:start position:0%
+a wave function. And it's uh infinite.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+uh you know it's there's not too much
+
+ align:start position:0%
+uh you know it's there's not too much
+ 
+
+ align:start position:0%
+uh you know it's there's not too much
+one can say about this. You know if
+
+ align:start position:0%
+one can say about this. You know if
+ 
+
+ align:start position:0%
+one can say about this. You know if
+people want to work more ma
+
+ align:start position:0%
+people want to work more ma
+ 
+
+ align:start position:0%
+people want to work more ma
+mathematically in a more comfortable way
+
+ align:start position:0%
+mathematically in a more comfortable way
+ 
+
+ align:start position:0%
+mathematically in a more comfortable way
+what you do is instead of taking
+
+ align:start position:0%
+what you do is instead of taking
+ 
+
+ align:start position:0%
+what you do is instead of taking
+infinite things you put everything on a
+
+ align:start position:0%
+infinite things you put everything on a
+ 
+
+ align:start position:0%
+infinite things you put everything on a
+big circle and then you have a furious
+
+ align:start position:0%
+big circle and then you have a furious
+ 
+
+ align:start position:0%
+big circle and then you have a furious
+series and the transform is sums and
+
+ align:start position:0%
+series and the transform is sums and
+ 
+
+ align:start position:0%
+series and the transform is sums and
+everything goes into sums but there's no
+
+ align:start position:0%
+everything goes into sums but there's no
+ 
+
+ align:start position:0%
+everything goes into sums but there's no
+real need. These operations are safe and
+
+ align:start position:0%
+real need. These operations are safe and
+ 
+
+ align:start position:0%
+real need. These operations are safe and
+uh we managed to do them and we're okay
+
+ align:start position:0%
+uh we managed to do them and we're okay
+ 
+
+ align:start position:0%
+uh we managed to do them and we're okay
+with them.
+
+ align:start position:0%
+with them.
+ 
+
+ align:start position:0%
+with them.
+Other
+
+ align:start position:0%
+Other
+ 
+
+ align:start position:0%
+Other
+questions? Yes.
+
+ align:start position:0%
+questions? Yes.
+ 
+
+ align:start position:0%
+questions? Yes.
+So infinite
+
+ align:start position:0%
+So infinite
+ 
+
+ align:start position:0%
+So infinite
+basis are these rules for any
+
+ align:start position:0%
+basis are these rules for any
+ 
+
+ align:start position:0%
+basis are these rules for any
+probably not. You know infinite bases
+
+ align:start position:0%
+probably not. You know infinite bases
+ 
+
+ align:start position:0%
+probably not. You know infinite bases
+are delicate. Um you know Hilbert spaces
+
+ align:start position:0%
+are delicate. Um you know Hilbert spaces
+ 
+
+ align:start position:0%
+are delicate. Um you know Hilbert spaces
+are infinite dimensional vector spaces
+
+ align:start position:0%
+are infinite dimensional vector spaces
+ 
+
+ align:start position:0%
+are infinite dimensional vector spaces
+and uh they not every infinite
+
+ align:start position:0%
+and uh they not every infinite
+ 
+
+ align:start position:0%
+and uh they not every infinite
+dimensional space is a Hilbert space.
+
+ align:start position:0%
+dimensional space is a Hilbert space.
+ 
+
+ align:start position:0%
+dimensional space is a Hilbert space.
+Not you know the most important thing of
+
+ align:start position:0%
+Not you know the most important thing of
+ 
+
+ align:start position:0%
+Not you know the most important thing of
+a Hilbert space is this norm this inner
+
+ align:start position:0%
+a Hilbert space is this norm this inner
+ 
+
+ align:start position:0%
+a Hilbert space is this norm this inner
+product but um the other important thing
+
+ align:start position:0%
+product but um the other important thing
+ 
+
+ align:start position:0%
+product but um the other important thing
+is some convergence facts about
+
+ align:start position:0%
+is some convergence facts about
+ 
+
+ align:start position:0%
+is some convergence facts about
+sequences of vectors that converge to
+
+ align:start position:0%
+sequences of vectors that converge to
+ 
+
+ align:start position:0%
+sequences of vectors that converge to
+points that are on the space. So it's
+
+ align:start position:0%
+points that are on the space. So it's
+ 
+
+ align:start position:0%
+points that are on the space. So it's
+delicate. Infinite dimensional spaces
+
+ align:start position:0%
+delicate. Infinite dimensional spaces
+ 
+
+ align:start position:0%
+delicate. Infinite dimensional spaces
+can be pretty bad. A banana space is not
+
+ align:start position:0%
+can be pretty bad. A banana space is not
+ 
+
+ align:start position:0%
+can be pretty bad. A banana space is not
+a Hilbert space and it's more comp
+
+ align:start position:0%
+a Hilbert space and it's more comp
+ 
+
+ align:start position:0%
+a Hilbert space and it's more comp
+only for Hilbert spaces. and and
+
+ align:start position:0%
+only for Hilbert spaces. and and
+ 
+
+ align:start position:0%
+only for Hilbert spaces. and and
+basically you
+
+ align:start position:0%
+basically you
+ 
+
+ align:start position:0%
+basically you
+know this this problem of a particle on
+
+ align:start position:0%
+know this this problem of a particle on
+ 
+
+ align:start position:0%
+know this this problem of a particle on
+a line or a particle in three space is
+
+ align:start position:0%
+a line or a particle in three space is
+ 
+
+ align:start position:0%
+a line or a particle in three space is
+sufficiently well known that we're
+
+ align:start position:0%
+sufficiently well known that we're
+ 
+
+ align:start position:0%
+sufficiently well known that we're
+totally comfortable with this somewhat
+
+ align:start position:0%
+totally comfortable with this somewhat
+ 
+
+ align:start position:0%
+totally comfortable with this somewhat
+uh singular operations. So the operator
+
+ align:start position:0%
+uh singular operations. So the operator
+ 
+
+ align:start position:0%
+uh singular operations. So the operator
+X or the operator P may not be what
+
+ align:start position:0%
+X or the operator P may not be what
+ 
+
+ align:start position:0%
+X or the operator P may not be what
+mathematicians like them to be bounded
+
+ align:start position:0%
+mathematicians like them to be bounded
+ 
+
+ align:start position:0%
+mathematicians like them to be bounded
+operators and Hbert spaces but but we
+
+ align:start position:0%
+operators and Hbert spaces but but we
+ 
+
+ align:start position:0%
+operators and Hbert spaces but but we
+know how to not to make mistakes with
+
+ align:start position:0%
+know how to not to make mistakes with
+ 
+
+ align:start position:0%
+know how to not to make mistakes with
+them. And uh if you have a very subtle
+
+ align:start position:0%
+them. And uh if you have a very subtle
+ 
+
+ align:start position:0%
+them. And uh if you have a very subtle
+problem one day you probably have to be
+
+ align:start position:0%
+problem one day you probably have to be
+ 
+
+ align:start position:0%
+problem one day you probably have to be
+more careful but for the problems we're
+
+ align:start position:0%
+more careful but for the problems we're
+ 
+
+ align:start position:0%
+more careful but for the problems we're
+interested now we don't.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, our last topic today um is
+
+ align:start position:0%
+So, our last topic today um is
+ 
+
+ align:start position:0%
+So, our last topic today um is
+uncertainties and uncertainty relations.
+
+ align:start position:0%
+uncertainties and uncertainty relations.
+ 
+
+ align:start position:0%
+uncertainties and uncertainty relations.
+Um I probably won't get through all of
+
+ align:start position:0%
+Um I probably won't get through all of
+ 
+
+ align:start position:0%
+Um I probably won't get through all of
+it, but um we'll get
+
+ align:start position:0%
+it, but um we'll get
+ 
+
+ align:start position:0%
+it, but um we'll get
+started and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and so we'll have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainties.
+
+ align:start position:0%
+uncertainties.
+ 
+
+ align:start position:0%
+uncertainties.
+necessarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these and uh we will talk about
+
+ align:start position:0%
+these and uh we will talk about
+ 
+
+ align:start position:0%
+these and uh we will talk about
+operators and uh permission operators.
+
+ align:start position:0%
+operators and uh permission operators.
+ 
+
+ align:start position:0%
+operators and uh permission operators.
+So here is the question basically if you
+
+ align:start position:0%
+So here is the question basically if you
+ 
+
+ align:start position:0%
+So here is the question basically if you
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+state we know the result of a
+
+ align:start position:0%
+state we know the result of a
+ 
+
+ align:start position:0%
+state we know the result of a
+measurement of an observable is the
+
+ align:start position:0%
+measurement of an observable is the
+ 
+
+ align:start position:0%
+measurement of an observable is the
+value of a hermission operator.
+
+ align:start position:0%
+value of a hermission operator.
+ 
+
+ align:start position:0%
+value of a hermission operator.
+Now if the state is an iggon state of
+
+ align:start position:0%
+Now if the state is an iggon state of
+ 
+
+ align:start position:0%
+Now if the state is an iggon state of
+the hermission operator, you measure the
+
+ align:start position:0%
+the hermission operator, you measure the
+ 
+
+ align:start position:0%
+the hermission operator, you measure the
+observable and out comes the iggon
+
+ align:start position:0%
+observable and out comes the iggon
+ 
+
+ align:start position:0%
+observable and out comes the iggon
+value and there's no uncertainty in the
+
+ align:start position:0%
+value and there's no uncertainty in the
+ 
+
+ align:start position:0%
+value and there's no uncertainty in the
+measured observable because the measured
+
+ align:start position:0%
+measured observable because the measured
+ 
+
+ align:start position:0%
+measured observable because the measured
+observable is an igon value and the
+
+ align:start position:0%
+observable is an igon value and the
+ 
+
+ align:start position:0%
+observable is an igon value and the
+state is an iggon state.
+
+ align:start position:0%
+state is an iggon state.
+ 
+
+ align:start position:0%
+state is an iggon state.
+The problem arises when the state that
+
+ align:start position:0%
+The problem arises when the state that
+ 
+
+ align:start position:0%
+The problem arises when the state that
+you're trying to measure this property
+
+ align:start position:0%
+you're trying to measure this property
+ 
+
+ align:start position:0%
+you're trying to measure this property
+is not an iggon state of the
+
+ align:start position:0%
+is not an iggon state of the
+ 
+
+ align:start position:0%
+is not an iggon state of the
+observable. So you know that the
+
+ align:start position:0%
+observable. So you know that the
+ 
+
+ align:start position:0%
+observable. So you know that the
+interpretation of quantum mechanics is
+
+ align:start position:0%
+interpretation of quantum mechanics is
+ 
+
+ align:start position:0%
+interpretation of quantum mechanics is
+there's a probabilistic distribution.
+
+ align:start position:0%
+there's a probabilistic distribution.
+ 
+
+ align:start position:0%
+there's a probabilistic distribution.
+You sometimes get one thing, sometimes
+
+ align:start position:0%
+You sometimes get one thing, sometimes
+ 
+
+ align:start position:0%
+You sometimes get one thing, sometimes
+get another thing depending on the
+
+ align:start position:0%
+get another thing depending on the
+ 
+
+ align:start position:0%
+get another thing depending on the
+amplitudes of the states to be in in
+
+ align:start position:0%
+amplitudes of the states to be in in
+ 
+
+ align:start position:0%
+amplitudes of the states to be in in
+those particular states. But there's an
+
+ align:start position:0%
+those particular states. But there's an
+ 
+
+ align:start position:0%
+those particular states. But there's an
+uncertainty at this time. you don't know
+
+ align:start position:0%
+uncertainty at this time. you don't know
+ 
+
+ align:start position:0%
+uncertainty at this time. you don't know
+what the measured value will
+
+ align:start position:0%
+what the measured value will
+ 
+
+ align:start position:0%
+what the measured value will
+be. So we'll define the uncertainty
+
+ align:start position:0%
+be. So we'll define the uncertainty
+ 
+
+ align:start position:0%
+be. So we'll define the uncertainty
+associated to a hermission
+
+ align:start position:0%
+associated to a hermission
+ 
+
+ align:start position:0%
+associated to a hermission
+operator and uh we want to define this
+
+ align:start position:0%
+operator and uh we want to define this
+ 
+
+ align:start position:0%
+operator and uh we want to define this
+answer. So a will be a hermission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator and you were talking about the
+
+ align:start position:0%
+operator and you were talking about the
+ 
+
+ align:start position:0%
+operator and you were talking about the
+uncertainty. Now the uncertainty of that
+
+ align:start position:0%
+uncertainty. Now the uncertainty of that
+ 
+
+ align:start position:0%
+uncertainty. Now the uncertainty of that
+operator the first thing that you should
+
+ align:start position:0%
+operator the first thing that you should
+ 
+
+ align:start position:0%
+operator the first thing that you should
+remember is you cannot talk about the
+
+ align:start position:0%
+remember is you cannot talk about the
+ 
+
+ align:start position:0%
+remember is you cannot talk about the
+uncertainty of the operator unless you
+
+ align:start position:0%
+uncertainty of the operator unless you
+ 
+
+ align:start position:0%
+uncertainty of the operator unless you
+give me a state. So all the formulas
+
+ align:start position:0%
+give me a state. So all the formulas
+ 
+
+ align:start position:0%
+give me a state. So all the formulas
+we're going to write for uncertainties
+
+ align:start position:0%
+we're going to write for uncertainties
+ 
+
+ align:start position:0%
+we're going to write for uncertainties
+are uncertainties of operators in some
+
+ align:start position:0%
+are uncertainties of operators in some
+ 
+
+ align:start position:0%
+are uncertainties of operators in some
+state. So let's call the
+
+ align:start position:0%
+state. So let's call the
+ 
+
+ align:start position:0%
+state. So let's call the
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s and time will not be relevant. So
+
+ align:start position:0%
+s and time will not be relevant. So
+ 
+
+ align:start position:0%
+s and time will not be relevant. So
+maybe I should delete the the well the
+
+ align:start position:0%
+maybe I should delete the the well the
+ 
+
+ align:start position:0%
+maybe I should delete the the well the
+I'll leave that bar there um just in
+
+ align:start position:0%
+I'll leave that bar there um just in
+ 
+
+ align:start position:0%
+I'll leave that bar there um just in
+case.
+
+ align:start position:0%
+case.
+ 
+
+ align:start position:0%
+case.
+So we're going to try to define
+
+ align:start position:0%
+So we're going to try to define
+ 
+
+ align:start position:0%
+So we're going to try to define
+uncertainty. But uh before we do that,
+
+ align:start position:0%
+uncertainty. But uh before we do that,
+ 
+
+ align:start position:0%
+uncertainty. But uh before we do that,
+let's try to define another thing. The
+
+ align:start position:0%
+let's try to define another thing. The
+ 
+
+ align:start position:0%
+let's try to define another thing. The
+expectation value. Well, the expectation
+
+ align:start position:0%
+expectation value. Well, the expectation
+ 
+
+ align:start position:0%
+expectation value. Well, the expectation
+value, you know it, the expectation
+
+ align:start position:0%
+value, you know it, the expectation
+ 
+
+ align:start position:0%
+value, you know it, the expectation
+value of a. And you could put a pi here
+
+ align:start position:0%
+value of a. And you could put a pi here
+ 
+
+ align:start position:0%
+value of a. And you could put a pi here
+if you wish to remind you that it
+
+ align:start position:0%
+if you wish to remind you that it
+ 
+
+ align:start position:0%
+if you wish to remind you that it
+depends on on the state is well
+
+ align:start position:0%
+depends on on the state is well
+ 
+
+ align:start position:0%
+depends on on the state is well
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+api that's what we call expectation
+
+ align:start position:0%
+api that's what we call expectation
+ 
+
+ align:start position:0%
+api that's what we call expectation
+value in the inner product notation
+
+ align:start position:0%
+value in the inner product notation
+ 
+
+ align:start position:0%
+value in the inner product notation
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apai and one thing you know that this
+
+ align:start position:0%
+apai and one thing you know that this
+ 
+
+ align:start position:0%
+apai and one thing you know that this
+thing is
+
+ align:start position:0%
+thing is
+ 
+
+ align:start position:0%
+thing is
+real because
+
+ align:start position:0%
+real because
+ 
+
+ align:start position:0%
+real because
+the expectation values of permission
+
+ align:start position:0%
+the expectation values of permission
+ 
+
+ align:start position:0%
+the expectation values of permission
+operators is real. That's something we
+
+ align:start position:0%
+operators is real. That's something we
+ 
+
+ align:start position:0%
+operators is real. That's something we
+reviewed at the beginning of the lecture
+
+ align:start position:0%
+reviewed at the beginning of the lecture
+ 
+
+ align:start position:0%
+reviewed at the beginning of the lecture
+today.
+
+ align:start position:0%
+today.
+ 
+
+ align:start position:0%
+today.
+So now comes the question
+
+ align:start position:0%
+So now comes the question
+ 
+
+ align:start position:0%
+So now comes the question
+um what can I do to define an
+
+ align:start position:0%
+um what can I do to define an
+ 
+
+ align:start position:0%
+um what can I do to define an
+uncertainty of an operator and an
+
+ align:start position:0%
+uncertainty of an operator and an
+ 
+
+ align:start position:0%
+uncertainty of an operator and an
+uncertainty now we've said already
+
+ align:start position:0%
+uncertainty now we've said already
+ 
+
+ align:start position:0%
+uncertainty now we've said already
+something I wish to define an
+
+ align:start position:0%
+something I wish to define an
+ 
+
+ align:start position:0%
+something I wish to define an
+uncertainty that is such that the
+
+ align:start position:0%
+uncertainty that is such that the
+ 
+
+ align:start position:0%
+uncertainty that is such that the
+uncertainty is zero if the
+
+ align:start position:0%
+uncertainty is zero if the
+ 
+
+ align:start position:0%
+uncertainty is zero if the
+operator if the state is an iggon state
+
+ align:start position:0%
+operator if the state is an iggon state
+ 
+
+ align:start position:0%
+operator if the state is an iggon state
+and the uncertainty is different from
+
+ align:start position:0%
+and the uncertainty is different from
+ 
+
+ align:start position:0%
+and the uncertainty is different from
+zero if it's not an igen state. In fact,
+
+ align:start position:0%
+zero if it's not an igen state. In fact,
+ 
+
+ align:start position:0%
+zero if it's not an igen state. In fact,
+I wish that the uncertainty is zero if
+
+ align:start position:0%
+I wish that the uncertainty is zero if
+ 
+
+ align:start position:0%
+I wish that the uncertainty is zero if
+and only if the state is an iggon state.
+
+ align:start position:0%
+and only if the state is an iggon state.
+ 
+
+ align:start position:0%
+and only if the state is an iggon state.
+So actually we can achieve that and
+
+ align:start position:0%
+So actually we can achieve that and
+ 
+
+ align:start position:0%
+So actually we can achieve that and
+uh and we sort of in some sense I think
+
+ align:start position:0%
+uh and we sort of in some sense I think
+ 
+
+ align:start position:0%
+uh and we sort of in some sense I think
+the most intuitive
+
+ align:start position:0%
+the most intuitive
+ 
+
+ align:start position:0%
+the most intuitive
+definition is the one
+
+ align:start position:0%
+definition is the one
+ 
+
+ align:start position:0%
+definition is the one
+that I will show here is that we define
+
+ align:start position:0%
+that I will show here is that we define
+ 
+
+ align:start position:0%
+that I will show here is that we define
+the uncertainty delta a and I'll put the
+
+ align:start position:0%
+the uncertainty delta a and I'll put the
+ 
+
+ align:start position:0%
+the uncertainty delta a and I'll put the
+pi here. So this is called the
+
+ align:start position:0%
+pi here. So this is called the
+ 
+
+ align:start position:0%
+pi here. So this is called the
+uncertainty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a in the state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p. So we'll define it a simple way. What
+
+ align:start position:0%
+p. So we'll define it a simple way. What
+ 
+
+ align:start position:0%
+p. So we'll define it a simple way. What
+else do we want? We
+
+ align:start position:0%
+else do we want? We
+ 
+
+ align:start position:0%
+else do we want? We
+said this should be zero if and only if
+
+ align:start position:0%
+said this should be zero if and only if
+ 
+
+ align:start position:0%
+said this should be zero if and only if
+the state is an iggon
+
+ align:start position:0%
+the state is an iggon
+ 
+
+ align:start position:0%
+the state is an iggon
+state. Second I want this thing to be a
+
+ align:start position:0%
+state. Second I want this thing to be a
+ 
+
+ align:start position:0%
+state. Second I want this thing to be a
+real number.
+
+ align:start position:0%
+real number.
+ 
+
+ align:start position:0%
+real number.
+in fact a positive
+
+ align:start position:0%
+in fact a positive
+ 
+
+ align:start position:0%
+in fact a positive
+number. What function do we
+
+ align:start position:0%
+number. What function do we
+ 
+
+ align:start position:0%
+number. What function do we
+know in quantum mechanics that can do
+
+ align:start position:0%
+know in quantum mechanics that can do
+ 
+
+ align:start position:0%
+know in quantum mechanics that can do
+that magic? Well, it's a norm. The norm
+
+ align:start position:0%
+that magic? Well, it's a norm. The norm
+ 
+
+ align:start position:0%
+that magic? Well, it's a norm. The norm
+function is always real and positive. So
+
+ align:start position:0%
+function is always real and positive. So
+ 
+
+ align:start position:0%
+function is always real and positive. So
+this will try to set it equal to a norm.
+
+ align:start position:0%
+this will try to set it equal to a norm.
+ 
+
+ align:start position:0%
+this will try to set it equal to a norm.
+So claim is the norm of the state a
+
+ align:start position:0%
+So claim is the norm of the state a
+ 
+
+ align:start position:0%
+So claim is the norm of the state a
+minus expectation value of a *
+
+ align:start position:0%
+minus expectation value of a *
+ 
+
+ align:start position:0%
+minus expectation value of a *
+1 acting on
+
+ align:start position:0%
+1 acting on
+ 
+
+ align:start position:0%
+1 acting on
+s. This will be our
+
+ align:start position:0%
+s. This will be our
+ 
+
+ align:start position:0%
+s. This will be our
+definition of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty. So it's the norm of this
+
+ align:start position:0%
+uncertainty. So it's the norm of this
+ 
+
+ align:start position:0%
+uncertainty. So it's the norm of this
+vector.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now let's look at this uh suppose the
+
+ align:start position:0%
+Now let's look at this uh suppose the
+ 
+
+ align:start position:0%
+Now let's look at this uh suppose the
+norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and if the uncertainty is zero this
+
+ align:start position:0%
+zero and if the uncertainty is zero this
+ 
+
+ align:start position:0%
+zero and if the uncertainty is zero this
+vector must be zero. So
+
+ align:start position:0%
+vector must be zero. So
+ 
+
+ align:start position:0%
+vector must be zero. So
+a minus expectation value of
+
+ align:start position:0%
+a minus expectation value of
+ 
+
+ align:start position:0%
+a minus expectation value of
+a on
+
+ align:start position:0%
+a on
+ 
+
+ align:start position:0%
+a on
+s is zero
+
+ align:start position:0%
+s is zero
+ 
+
+ align:start position:0%
+s is zero
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+pi is equal to expectation value of a on
+
+ align:start position:0%
+pi is equal to expectation value of a on
+ 
+
+ align:start position:0%
+pi is equal to expectation value of a on
+pi. The one doesn't do much. Many people
+
+ align:start position:0%
+pi. The one doesn't do much. Many people
+ 
+
+ align:start position:0%
+pi. The one doesn't do much. Many people
+don't write the one. I could get tired
+
+ align:start position:0%
+don't write the one. I could get tired
+ 
+
+ align:start position:0%
+don't write the one. I could get tired
+and stop writing it. uh you should um
+
+ align:start position:0%
+and stop writing it. uh you should um
+ 
+
+ align:start position:0%
+and stop writing it. uh you should um
+probably it's good manners to write the
+
+ align:start position:0%
+probably it's good manners to write the
+ 
+
+ align:start position:0%
+probably it's good manners to write the
+I but uh it's not all that necessary.
+
+ align:start position:0%
+I but uh it's not all that necessary.
+ 
+
+ align:start position:0%
+I but uh it's not all that necessary.
+You don't get that confused. If there's
+
+ align:start position:0%
+You don't get that confused. If there's
+ 
+
+ align:start position:0%
+You don't get that confused. If there's
+an operator and uh a number here, there
+
+ align:start position:0%
+an operator and uh a number here, there
+ 
+
+ align:start position:0%
+an operator and uh a number here, there
+must be a identity matrix. So if the
+
+ align:start position:0%
+must be a identity matrix. So if the
+ 
+
+ align:start position:0%
+must be a identity matrix. So if the
+uncertainty is zero, the vector is zero
+
+ align:start position:0%
+uncertainty is zero, the vector is zero
+ 
+
+ align:start position:0%
+uncertainty is zero, the vector is zero
+and this is true. Now you say well this
+
+ align:start position:0%
+and this is true. Now you say well this
+ 
+
+ align:start position:0%
+and this is true. Now you say well this
+equation looks kind of funny but it's it
+
+ align:start position:0%
+equation looks kind of funny but it's it
+ 
+
+ align:start position:0%
+equation looks kind of funny but it's it
+says that pi is an igen state of a
+
+ align:start position:0%
+says that pi is an igen state of a
+ 
+
+ align:start position:0%
+says that pi is an igen state of a
+because this is a
+
+ align:start position:0%
+because this is a
+ 
+
+ align:start position:0%
+because this is a
+number you know it looks a little funny
+
+ align:start position:0%
+number you know it looks a little funny
+ 
+
+ align:start position:0%
+number you know it looks a little funny
+because we're accustom a pi lambda pi
+
+ align:start position:0%
+because we're accustom a pi lambda pi
+ 
+
+ align:start position:0%
+because we're accustom a pi lambda pi
+but this is a number and in fact let me
+
+ align:start position:0%
+but this is a number and in fact let me
+ 
+
+ align:start position:0%
+but this is a number and in fact let me
+show you one thing if you have a pi
+
+ align:start position:0%
+show you one thing if you have a pi
+ 
+
+ align:start position:0%
+show you one thing if you have a pi
+equal lambda
+
+ align:start position:0%
+equal lambda
+ 
+
+ align:start position:0%
+equal lambda
+pi oh I should say here that pi is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normalized. You know if pi would not be
+
+ align:start position:0%
+normalized. You know if pi would not be
+ 
+
+ align:start position:0%
+normalized. You know if pi would not be
+normalize you change the normalization
+
+ align:start position:0%
+normalize you change the normalization
+ 
+
+ align:start position:0%
+normalize you change the normalization
+you change the uh uncertainty. So it
+
+ align:start position:0%
+you change the uh uncertainty. So it
+ 
+
+ align:start position:0%
+you change the uh uncertainty. So it
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+normalized. And look at this. If you
+
+ align:start position:0%
+normalized. And look at this. If you
+ 
+
+ align:start position:0%
+normalized. And look at this. If you
+have a pi equal
+
+ align:start position:0%
+have a pi equal
+ 
+
+ align:start position:0%
+have a pi equal
+lambda, do the inner product with a
+
+ align:start position:0%
+lambda, do the inner product with a
+ 
+
+ align:start position:0%
+lambda, do the inner product with a
+um no do the inner product with pi
+
+ align:start position:0%
+um no do the inner product with pi
+ 
+
+ align:start position:0%
+um no do the inner product with pi
+s, a
+
+ align:start position:0%
+s, a
+ 
+
+ align:start position:0%
+s, a
+pi would be equal to lambda because pi
+
+ align:start position:0%
+pi would be equal to lambda because pi
+ 
+
+ align:start position:0%
+pi would be equal to lambda because pi
+inner product with pi is one. But what
+
+ align:start position:0%
+inner product with pi is one. But what
+ 
+
+ align:start position:0%
+inner product with pi is one. But what
+is this? This is the expectation value
+
+ align:start position:0%
+is this? This is the expectation value
+ 
+
+ align:start position:0%
+is this? This is the expectation value
+of a.
+
+ align:start position:0%
+of a.
+ 
+
+ align:start position:0%
+of a.
+So, so actually given our definition
+
+ align:start position:0%
+So, so actually given our definition
+ 
+
+ align:start position:0%
+So, so actually given our definition
+the value of some operator uh on the
+
+ align:start position:0%
+the value of some operator uh on the
+ 
+
+ align:start position:0%
+the value of some operator uh on the
+state is the expectation value of the
+
+ align:start position:0%
+state is the expectation value of the
+ 
+
+ align:start position:0%
+state is the expectation value of the
+operator in the state. So back to the
+
+ align:start position:0%
+operator in the state. So back to the
+ 
+
+ align:start position:0%
+operator in the state. So back to the
+argument if the uncertainty is
+
+ align:start position:0%
+argument if the uncertainty is
+ 
+
+ align:start position:0%
+argument if the uncertainty is
+zero the state is an
+
+ align:start position:0%
+zero the state is an
+ 
+
+ align:start position:0%
+zero the state is an
+enig value happens to be the expectation
+
+ align:start position:0%
+enig value happens to be the expectation
+ 
+
+ align:start position:0%
+enig value happens to be the expectation
+value that is if the uncertainty is
+
+ align:start position:0%
+value that is if the uncertainty is
+ 
+
+ align:start position:0%
+value that is if the uncertainty is
+zero. On the other hand, if you're in an
+
+ align:start position:0%
+zero. On the other hand, if you're in an
+ 
+
+ align:start position:0%
+zero. On the other hand, if you're in an
+igen state, you're here, then lambda is
+
+ align:start position:0%
+igen state, you're here, then lambda is
+ 
+
+ align:start position:0%
+igen state, you're here, then lambda is
+a and this equation shows that this
+
+ align:start position:0%
+a and this equation shows that this
+ 
+
+ align:start position:0%
+a and this equation shows that this
+vector is zero and therefore you get
+
+ align:start position:0%
+vector is zero and therefore you get
+ 
+
+ align:start position:0%
+vector is zero and therefore you get
+zero. So you've shown that this expecta
+
+ align:start position:0%
+zero. So you've shown that this expecta
+ 
+
+ align:start position:0%
+zero. So you've shown that this expecta
+this norm or this uncertainty is zero if
+
+ align:start position:0%
+this norm or this uncertainty is zero if
+ 
+
+ align:start position:0%
+this norm or this uncertainty is zero if
+and only if the state is an igen state.
+
+ align:start position:0%
+and only if the state is an igen state.
+ 
+
+ align:start position:0%
+and only if the state is an igen state.
+And that's a very powerful statement.
+
+ align:start position:0%
+And that's a very powerful statement.
+ 
+
+ align:start position:0%
+And that's a very powerful statement.
+the the statement that is always known
+
+ align:start position:0%
+the the statement that is always known
+ 
+
+ align:start position:0%
+the the statement that is always known
+by everybody is that um if you have an
+
+ align:start position:0%
+by everybody is that um if you have an
+ 
+
+ align:start position:0%
+by everybody is that um if you have an
+iggon state yes no uncertainty but if
+
+ align:start position:0%
+iggon state yes no uncertainty but if
+ 
+
+ align:start position:0%
+iggon state yes no uncertainty but if
+there's no uncertainty you must have an
+
+ align:start position:0%
+there's no uncertainty you must have an
+ 
+
+ align:start position:0%
+there's no uncertainty you must have an
+iggon state that's the second part and
+
+ align:start position:0%
+iggon state that's the second part and
+ 
+
+ align:start position:0%
+iggon state that's the second part and
+uses the fact that the only vector with
+
+ align:start position:0%
+uses the fact that the only vector with
+ 
+
+ align:start position:0%
+uses the fact that the only vector with
+zero norm is the zero vector a thing
+
+ align:start position:0%
+zero norm is the zero vector a thing
+ 
+
+ align:start position:0%
+zero norm is the zero vector a thing
+that we use over and over again. So let
+
+ align:start position:0%
+that we use over and over again. So let
+ 
+
+ align:start position:0%
+that we use over and over again. So let
+me make
+
+ align:start position:0%
+me make
+ 
+
+ align:start position:0%
+me make
+um couple more comments on how you
+
+ align:start position:0%
+um couple more comments on how you
+ 
+
+ align:start position:0%
+um couple more comments on how you
+compute this.
+
+ align:start position:0%
+compute this.
+ 
+
+ align:start position:0%
+compute this.
+Um so that's the
+
+ align:start position:0%
+Um so that's the
+ 
+
+ align:start position:0%
+Um so that's the
+uncertainty so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far. So the uncertainty vanishes in that
+
+ align:start position:0%
+far. So the uncertainty vanishes in that
+ 
+
+ align:start position:0%
+far. So the uncertainty vanishes in that
+case. Now we can square this equation to
+
+ align:start position:0%
+case. Now we can square this equation to
+ 
+
+ align:start position:0%
+case. Now we can square this equation to
+find a
+
+ align:start position:0%
+find a
+ 
+
+ align:start position:0%
+find a
+formula that is perhaps more familiar
+
+ align:start position:0%
+formula that is perhaps more familiar
+ 
+
+ align:start position:0%
+formula that is perhaps more familiar
+not necessarily more useful but also
+
+ align:start position:0%
+not necessarily more useful but also
+ 
+
+ align:start position:0%
+not necessarily more useful but also
+good for computations is pretty good.
+
+ align:start position:0%
+good for computations is pretty good.
+ 
+
+ align:start position:0%
+good for computations is pretty good.
+Delta a of pi which is real we square
+
+ align:start position:0%
+Delta a of pi which is real we square
+ 
+
+ align:start position:0%
+Delta a of pi which is real we square
+it. Well, the norm square is the inner
+
+ align:start position:0%
+it. Well, the norm square is the inner
+ 
+
+ align:start position:0%
+it. Well, the norm square is the inner
+product of this a
+
+ align:start position:0%
+product of this a
+ 
+
+ align:start position:0%
+product of this a
+-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+s a -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+s norm squared is the inner product of
+
+ align:start position:0%
+s norm squared is the inner product of
+ 
+
+ align:start position:0%
+s norm squared is the inner product of
+these two vectors. Now the thing that we
+
+ align:start position:0%
+these two vectors. Now the thing that we
+ 
+
+ align:start position:0%
+these two vectors. Now the thing that we
+like to do is to move this factor to
+
+ align:start position:0%
+like to do is to move this factor to
+ 
+
+ align:start position:0%
+like to do is to move this factor to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+side. How do you move a factor on the
+
+ align:start position:0%
+side. How do you move a factor on the
+ 
+
+ align:start position:0%
+side. How do you move a factor on the
+first input to the other input? You take
+
+ align:start position:0%
+first input to the other input? You take
+ 
+
+ align:start position:0%
+first input to the other input? You take
+the adjint. So I should move it with an
+
+ align:start position:0%
+the adjint. So I should move it with an
+ 
+
+ align:start position:0%
+the adjint. So I should move it with an
+adjint. So what do I get?
+
+ align:start position:0%
+adjint. So what do I get?
+ 
+
+ align:start position:0%
+adjint. So what do I get?
+S and then I get the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjint and this factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again. Now I should put a dagger
+
+ align:start position:0%
+again. Now I should put a dagger
+ 
+
+ align:start position:0%
+again. Now I should put a dagger
+here but let me not put it because a is
+
+ align:start position:0%
+here but let me not put it because a is
+ 
+
+ align:start position:0%
+here but let me not put it because a is
+her
+
+ align:start position:0%
+her
+ 
+
+ align:start position:0%
+her
+mission and
+
+ align:start position:0%
+mission and
+ 
+
+ align:start position:0%
+mission and
+moreover expectation value of a is
+
+ align:start position:0%
+moreover expectation value of a is
+ 
+
+ align:start position:0%
+moreover expectation value of a is
+real her. So no need for the dagger. So
+
+ align:start position:0%
+real her. So no need for the dagger. So
+ 
+
+ align:start position:0%
+real her. So no need for the dagger. So
+you can put the dagger and then explain
+
+ align:start position:0%
+you can put the dagger and then explain
+ 
+
+ align:start position:0%
+you can put the dagger and then explain
+that this is her mission and this is
+
+ align:start position:0%
+that this is her mission and this is
+ 
+
+ align:start position:0%
+that this is her mission and this is
+real or just not put
+
+ align:start position:0%
+real or just not put
+ 
+
+ align:start position:0%
+real or just not put
+it. And now look at this. This is a
+
+ align:start position:0%
+it. And now look at this. This is a
+ 
+
+ align:start position:0%
+it. And now look at this. This is a
+typical calculation. You'll do it many
+
+ align:start position:0%
+typical calculation. You'll do it many
+ 
+
+ align:start position:0%
+typical calculation. You'll do it many
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+times. You just spread out the things.
+
+ align:start position:0%
+times. You just spread out the things.
+ 
+
+ align:start position:0%
+times. You just spread out the things.
+So let me just do it once. U here you
+
+ align:start position:0%
+So let me just do it once. U here you
+ 
+
+ align:start position:0%
+So let me just do it once. U here you
+get a squared minus a expectation value
+
+ align:start position:0%
+get a squared minus a expectation value
+ 
+
+ align:start position:0%
+get a squared minus a expectation value
+of a minus expectation value of a
+
+ align:start position:0%
+of a minus expectation value of a
+ 
+
+ align:start position:0%
+of a minus expectation value of a
+a plus expectation value of a squared.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigh. So I multiplied everything but you
+
+ align:start position:0%
+Sigh. So I multiplied everything but you
+ 
+
+ align:start position:0%
+Sigh. So I multiplied everything but you
+shouldn't be all that. I should put a
+
+ align:start position:0%
+shouldn't be all that. I should put a
+ 
+
+ align:start position:0%
+shouldn't be all that. I should put a
+one here probably.
+
+ align:start position:0%
+one here probably.
+ 
+
+ align:start position:0%
+one here probably.
+Um shouldn't worry about this much. This
+
+ align:start position:0%
+Um shouldn't worry about this much. This
+ 
+
+ align:start position:0%
+Um shouldn't worry about this much. This
+is a number and an a number and an a.
+
+ align:start position:0%
+is a number and an a number and an a.
+ 
+
+ align:start position:0%
+is a number and an a number and an a.
+The order doesn't matter. These two
+
+ align:start position:0%
+The order doesn't matter. These two
+ 
+
+ align:start position:0%
+The order doesn't matter. These two
+terms are really the
+
+ align:start position:0%
+terms are really the
+ 
+
+ align:start position:0%
+terms are really the
+same. Well let me go slowly on this
+
+ align:start position:0%
+same. Well let me go slowly on this
+ 
+
+ align:start position:0%
+same. Well let me go slowly on this
+once. Um what is the first term? It's pi
+
+ align:start position:0%
+once. Um what is the first term? It's pi
+ 
+
+ align:start position:0%
+once. Um what is the first term? It's pi
+a^2 pi. So it's the expectation value of
+
+ align:start position:0%
+a^2 pi. So it's the expectation value of
+ 
+
+ align:start position:0%
+a^2 pi. So it's the expectation value of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+squared. Now what is this term? Well,
+
+ align:start position:0%
+squared. Now what is this term? Well,
+ 
+
+ align:start position:0%
+squared. Now what is this term? Well,
+you have a number here which is real
+
+ align:start position:0%
+you have a number here which is real
+ 
+
+ align:start position:0%
+you have a number here which is real
+goes out of whatever you're doing and
+
+ align:start position:0%
+goes out of whatever you're doing and
+ 
+
+ align:start position:0%
+goes out of whatever you're doing and
+you have pi api. So this is expectation
+
+ align:start position:0%
+you have pi api. So this is expectation
+ 
+
+ align:start position:0%
+you have pi api. So this is expectation
+value of a and from the leftover pi api
+
+ align:start position:0%
+value of a and from the leftover pi api
+ 
+
+ align:start position:0%
+value of a and from the leftover pi api
+you get another expectation value of a.
+
+ align:start position:0%
+you get another expectation value of a.
+ 
+
+ align:start position:0%
+you get another expectation value of a.
+So this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a here the same thing the number goes
+
+ align:start position:0%
+a here the same thing the number goes
+ 
+
+ align:start position:0%
+a here the same thing the number goes
+out and you're left with a pi a pi which
+
+ align:start position:0%
+out and you're left with a pi a pi which
+ 
+
+ align:start position:0%
+out and you're left with a pi a pi which
+is another expectation value of a so you
+
+ align:start position:0%
+is another expectation value of a so you
+ 
+
+ align:start position:0%
+is another expectation value of a so you
+get minus
+
+ align:start position:0%
+get minus
+ 
+
+ align:start position:0%
+get minus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a and you have a plus expectation value
+
+ align:start position:0%
+a and you have a plus expectation value
+ 
+
+ align:start position:0%
+a and you have a plus expectation value
+of a squared and I don't need the i
+
+ align:start position:0%
+of a squared and I don't need the i
+ 
+
+ align:start position:0%
+of a squared and I don't need the i
+anymore because uh the expectation
+
+ align:start position:0%
+anymore because uh the expectation
+ 
+
+ align:start position:0%
+anymore because uh the expectation
+values have been taken and this always
+
+ align:start position:0%
+values have been taken and this always
+ 
+
+ align:start position:0%
+values have been taken and this always
+happens And there's a minus here, a
+
+ align:start position:0%
+happens And there's a minus here, a
+ 
+
+ align:start position:0%
+happens And there's a minus here, a
+minus here, and a plus here. So there's
+
+ align:start position:0%
+minus here, and a plus here. So there's
+ 
+
+ align:start position:0%
+minus here, and a plus here. So there's
+just one minus at the end of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day. One minus at the end of the day.
+
+ align:start position:0%
+day. One minus at the end of the day.
+ 
+
+ align:start position:0%
+day. One minus at the end of the day.
+And the familiar or famous
+
+ align:start position:0%
+And the familiar or famous
+ 
+
+ align:start position:0%
+And the familiar or famous
+formula comes
+
+ align:start position:0%
+formula comes
+ 
+
+ align:start position:0%
+formula comes
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+that delta of a on
+
+ align:start position:0%
+that delta of a on
+ 
+
+ align:start position:0%
+that delta of a on
+squared is equal to expectation value of
+
+ align:start position:0%
+squared is equal to expectation value of
+ 
+
+ align:start position:0%
+squared is equal to expectation value of
+a^ 2 minus expectation value of a
+
+ align:start position:0%
+a^ 2 minus expectation value of a
+ 
+
+ align:start position:0%
+a^ 2 minus expectation value of a
+squared which shows something uh quite
+
+ align:start position:0%
+squared which shows something uh quite
+ 
+
+ align:start position:0%
+squared which shows something uh quite
+powerful. This is has connections of
+
+ align:start position:0%
+powerful. This is has connections of
+ 
+
+ align:start position:0%
+powerful. This is has connections of
+course with statistical mechanics and
+
+ align:start position:0%
+course with statistical mechanics and
+ 
+
+ align:start position:0%
+course with statistical mechanics and
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+deviations.
+
+ align:start position:0%
+deviations.
+ 
+
+ align:start position:0%
+deviations.
+Um is the probabilistic interpretation
+
+ align:start position:0%
+Um is the probabilistic interpretation
+ 
+
+ align:start position:0%
+Um is the probabilistic interpretation
+of this formula. But one fact that this
+
+ align:start position:0%
+of this formula. But one fact that this
+ 
+
+ align:start position:0%
+of this formula. But one fact that this
+has allowed us to prove is that the
+
+ align:start position:0%
+has allowed us to prove is that the
+ 
+
+ align:start position:0%
+has allowed us to prove is that the
+expectation value of a squared is always
+
+ align:start position:0%
+expectation value of a squared is always
+ 
+
+ align:start position:0%
+expectation value of a squared is always
+greater or equal than that because this
+
+ align:start position:0%
+greater or equal than that because this
+ 
+
+ align:start position:0%
+greater or equal than that because this
+number is positive because it's the
+
+ align:start position:0%
+number is positive because it's the
+ 
+
+ align:start position:0%
+number is positive because it's the
+square of a real positive number. So
+
+ align:start position:0%
+square of a real positive number. So
+ 
+
+ align:start position:0%
+square of a real positive number. So
+that's a slightly non-trivial thing and
+
+ align:start position:0%
+that's a slightly non-trivial thing and
+ 
+
+ align:start position:0%
+that's a slightly non-trivial thing and
+it's good to know
+
+ align:start position:0%
+it's good to know
+ 
+
+ align:start position:0%
+it's good to know
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Now and this formula of course is very
+
+ align:start position:0%
+Now and this formula of course is very
+ 
+
+ align:start position:0%
+Now and this formula of course is very
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+known. Now I'm going to give now a a
+
+ align:start position:0%
+known. Now I'm going to give now a a
+ 
+
+ align:start position:0%
+known. Now I'm going to give now a a
+funny geometrical interpretation of the
+
+ align:start position:0%
+funny geometrical interpretation of the
+ 
+
+ align:start position:0%
+funny geometrical interpretation of the
+uncertainty. Maybe you will find it
+
+ align:start position:0%
+uncertainty. Maybe you will find it
+ 
+
+ align:start position:0%
+uncertainty. Maybe you will find it
+illuminating in some way is turning into
+
+ align:start position:0%
+illuminating in some way is turning into
+ 
+
+ align:start position:0%
+illuminating in some way is turning into
+pictures all the calculations we've
+
+ align:start position:0%
+pictures all the calculations we've
+ 
+
+ align:start position:0%
+pictures all the calculations we've
+done. I think it actually adds value to
+
+ align:start position:0%
+done. I think it actually adds value to
+ 
+
+ align:start position:0%
+done. I think it actually adds value to
+it and uh I don't think it's very well
+
+ align:start position:0%
+it and uh I don't think it's very well
+ 
+
+ align:start position:0%
+it and uh I don't think it's very well
+known. Um or you know it's kind of funny
+
+ align:start position:0%
+known. Um or you know it's kind of funny
+ 
+
+ align:start position:0%
+known. Um or you know it's kind of funny
+because it's nice not be very well known
+
+ align:start position:0%
+because it's nice not be very well known
+ 
+
+ align:start position:0%
+because it's nice not be very well known
+but maybe people don't find it that
+
+ align:start position:0%
+but maybe people don't find it that
+ 
+
+ align:start position:0%
+but maybe people don't find it that
+suggestive but I I kind of find it
+
+ align:start position:0%
+suggestive but I I kind of find it
+ 
+
+ align:start position:0%
+suggestive but I I kind of find it
+suggestive. So here is what I want to
+
+ align:start position:0%
+suggestive. So here is what I want to
+ 
+
+ align:start position:0%
+suggestive. So here is what I want to
+say.
+
+ align:start position:0%
+say.
+ 
+
+ align:start position:0%
+say.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+geometrically you have this vector space
+
+ align:start position:0%
+geometrically you have this vector space
+ 
+
+ align:start position:0%
+geometrically you have this vector space
+and you have a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi. Then you come
+
+ align:start position:0%
+pi. Then you come
+ 
+
+ align:start position:0%
+pi. Then you come
+along and you act with the operator
+
+ align:start position:0%
+along and you act with the operator
+ 
+
+ align:start position:0%
+along and you act with the operator
+a. Now the fact that this thing is
+
+ align:start position:0%
+a. Now the fact that this thing is
+ 
+
+ align:start position:0%
+a. Now the fact that this thing is
+not an igen state means that the after
+
+ align:start position:0%
+not an igen state means that the after
+ 
+
+ align:start position:0%
+not an igen state means that the after
+you act with a you don't keep in the
+
+ align:start position:0%
+you act with a you don't keep in the
+ 
+
+ align:start position:0%
+you act with a you don't keep in the
+same direction. you go in different
+
+ align:start position:0%
+same direction. you go in different
+ 
+
+ align:start position:0%
+same direction. you go in different
+direction. So here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apesai. So what can we say here? Well
+
+ align:start position:0%
+apesai. So what can we say here? Well
+ 
+
+ align:start position:0%
+apesai. So what can we say here? Well
+actually here is this thing. Think of
+
+ align:start position:0%
+actually here is this thing. Think of
+ 
+
+ align:start position:0%
+actually here is this thing. Think of
+this vector
+
+ align:start position:0%
+this vector
+ 
+
+ align:start position:0%
+this vector
+space spanned by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi. Let's call it
+
+ align:start position:0%
+pi. Let's call it
+ 
+
+ align:start position:0%
+pi. Let's call it
+UPI. So it's that line
+
+ align:start position:0%
+UPI. So it's that line
+ 
+
+ align:start position:0%
+UPI. So it's that line
+there. You can
+
+ align:start position:0%
+there. You can
+ 
+
+ align:start position:0%
+there. You can
+project this in
+
+ align:start position:0%
+project this in
+ 
+
+ align:start position:0%
+project this in
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonally. Here is the first claim.
+
+ align:start position:0%
+orthogonally. Here is the first claim.
+ 
+
+ align:start position:0%
+orthogonally. Here is the first claim.
+The vector that you get up to here, this
+
+ align:start position:0%
+The vector that you get up to here, this
+ 
+
+ align:start position:0%
+The vector that you get up to here, this
+vector is nothing else but expectation
+
+ align:start position:0%
+vector is nothing else but expectation
+ 
+
+ align:start position:0%
+vector is nothing else but expectation
+value of a times
+
+ align:start position:0%
+value of a times
+ 
+
+ align:start position:0%
+value of a times
+pi. And that makes sense because it's a
+
+ align:start position:0%
+pi. And that makes sense because it's a
+ 
+
+ align:start position:0%
+pi. And that makes sense because it's a
+number time pi. But precisely the
+
+ align:start position:0%
+number time pi. But precisely the
+ 
+
+ align:start position:0%
+number time pi. But precisely the
+orthogonal projection is this. And here
+
+ align:start position:0%
+orthogonal projection is this. And here
+ 
+
+ align:start position:0%
+orthogonal projection is this. And here
+you get an orthogonal vector that we'll
+
+ align:start position:0%
+you get an orthogonal vector that we'll
+ 
+
+ align:start position:0%
+you get an orthogonal vector that we'll
+call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi. And the funny thing about this piper
+
+ align:start position:0%
+pi. And the funny thing about this piper
+ 
+
+ align:start position:0%
+pi. And the funny thing about this piper
+is that its
+
+ align:start position:0%
+is that its
+ 
+
+ align:start position:0%
+is that its
+length is precisely the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty.
+
+ align:start position:0%
+uncertainty.
+ 
+
+ align:start position:0%
+uncertainty.
+So all these you could trans prove I'm
+
+ align:start position:0%
+So all these you could trans prove I'm
+ 
+
+ align:start position:0%
+So all these you could trans prove I'm
+going to do it. Uh I'm going to show you
+
+ align:start position:0%
+going to do it. Uh I'm going to show you
+ 
+
+ align:start position:0%
+going to do it. Uh I'm going to show you
+all these things are true. But it gives
+
+ align:start position:0%
+all these things are true. But it gives
+ 
+
+ align:start position:0%
+all these things are true. But it gives
+you a bit of an insight. You have a
+
+ align:start position:0%
+you a bit of an insight. You have a
+ 
+
+ align:start position:0%
+you a bit of an insight. You have a
+vector a moves you out. What is the
+
+ align:start position:0%
+vector a moves you out. What is the
+ 
+
+ align:start position:0%
+vector a moves you out. What is the
+uncertainty is the this vertical
+
+ align:start position:0%
+uncertainty is the this vertical
+ 
+
+ align:start position:0%
+uncertainty is the this vertical
+projection vertical thing is the
+
+ align:start position:0%
+projection vertical thing is the
+ 
+
+ align:start position:0%
+projection vertical thing is the
+uncertainty. If you down there you get
+
+ align:start position:0%
+uncertainty. If you down there you get
+ 
+
+ align:start position:0%
+uncertainty. If you down there you get
+nothing. So uh how do we prove
+
+ align:start position:0%
+nothing. So uh how do we prove
+ 
+
+ align:start position:0%
+nothing. So uh how do we prove
+that? Well
+
+ align:start position:0%
+that? Well
+ 
+
+ align:start position:0%
+that? Well
+um let's construct a
+
+ align:start position:0%
+um let's construct a
+ 
+
+ align:start position:0%
+um let's construct a
+projector down to the space up which is
+
+ align:start position:0%
+projector down to the space up which is
+ 
+
+ align:start position:0%
+projector down to the space up which is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+pi s.
+
+ align:start position:0%
+pi s.
+ 
+
+ align:start position:0%
+pi s.
+This is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projector just like any E1. E1 is a
+
+ align:start position:0%
+projector just like any E1. E1 is a
+ 
+
+ align:start position:0%
+projector just like any E1. E1 is a
+projector into the direction of one.
+
+ align:start position:0%
+projector into the direction of one.
+ 
+
+ align:start position:0%
+projector into the direction of one.
+Well, you know, take your first basis
+
+ align:start position:0%
+Well, you know, take your first basis
+ 
+
+ align:start position:0%
+Well, you know, take your first basis
+vector to be pi and that's a projection
+
+ align:start position:0%
+vector to be pi and that's a projection
+ 
+
+ align:start position:0%
+vector to be pi and that's a projection
+to the pi. So let's see what it
+
+ align:start position:0%
+to the pi. So let's see what it
+ 
+
+ align:start position:0%
+to the pi. So let's see what it
+it's a projection to pi. So now let's
+
+ align:start position:0%
+it's a projection to pi. So now let's
+ 
+
+ align:start position:0%
+it's a projection to pi. So now let's
+see what it gives you when it acts on a
+
+ align:start position:0%
+see what it gives you when it acts on a
+ 
+
+ align:start position:0%
+see what it gives you when it acts on a
+pi.
+
+ align:start position:0%
+pi.
+ 
+
+ align:start position:0%
+pi.
+This projector acting on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi is equal to
+
+ align:start position:0%
+pi is equal to
+ 
+
+ align:start position:0%
+pi is equal to
+pi p
+
+ align:start position:0%
+pi p
+ 
+
+ align:start position:0%
+pi p
+si a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi and again the usefulness of bracket
+
+ align:start position:0%
+pi and again the usefulness of bracket
+ 
+
+ align:start position:0%
+pi and again the usefulness of bracket
+notation is kind of nice here. So what
+
+ align:start position:0%
+notation is kind of nice here. So what
+ 
+
+ align:start position:0%
+notation is kind of nice here. So what
+is this the expectation value of a. So
+
+ align:start position:0%
+is this the expectation value of a. So
+ 
+
+ align:start position:0%
+is this the expectation value of a. So
+indeed s expectation value of a is what
+
+ align:start position:0%
+indeed s expectation value of a is what
+ 
+
+ align:start position:0%
+indeed s expectation value of a is what
+you get when you project this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+rest is sort of simple. So if you take
+
+ align:start position:0%
+rest is sort of simple. So if you take
+ 
+
+ align:start position:0%
+rest is sort of simple. So if you take
+pi and
+
+ align:start position:0%
+pi and
+ 
+
+ align:start position:0%
+pi and
+subtract from s
+
+ align:start position:0%
+subtract from s
+ 
+
+ align:start position:0%
+subtract from s
+um well
+
+ align:start position:0%
+um well
+ 
+
+ align:start position:0%
+um well
+I'll subtract from s u s times
+
+ align:start position:0%
+I'll subtract from s u s times
+ 
+
+ align:start position:0%
+I'll subtract from s u s times
+expectation value of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you can I'm sorry I was saying it
+
+ align:start position:0%
+um you can I'm sorry I was saying it
+ 
+
+ align:start position:0%
+um you can I'm sorry I was saying it
+wrong. If you take the original vector a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi and subtract from it what we took
+
+ align:start position:0%
+pi and subtract from it what we took
+ 
+
+ align:start position:0%
+pi and subtract from it what we took
+out which is s time expectation value of
+
+ align:start position:0%
+out which is s time expectation value of
+ 
+
+ align:start position:0%
+out which is s time expectation value of
+a the projected thing. This is some
+
+ align:start position:0%
+a the projected thing. This is some
+ 
+
+ align:start position:0%
+a the projected thing. This is some
+vector but the main thing is that this
+
+ align:start position:0%
+vector but the main thing is that this
+ 
+
+ align:start position:0%
+vector but the main thing is that this
+vector is
+
+ align:start position:0%
+vector is
+ 
+
+ align:start position:0%
+vector is
+orthogonal to
+
+ align:start position:0%
+orthogonal to
+ 
+
+ align:start position:0%
+orthogonal to
+pi. Why? If you take a pi on the left,
+
+ align:start position:0%
+pi. Why? If you take a pi on the left,
+ 
+
+ align:start position:0%
+pi. Why? If you take a pi on the left,
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+orthogonal to pi and how do you see it?
+
+ align:start position:0%
+orthogonal to pi and how do you see it?
+ 
+
+ align:start position:0%
+orthogonal to pi and how do you see it?
+Put up from the
+
+ align:start position:0%
+Put up from the
+ 
+
+ align:start position:0%
+Put up from the
+left and what do you get here? P a pi
+
+ align:start position:0%
+left and what do you get here? P a pi
+ 
+
+ align:start position:0%
+left and what do you get here? P a pi
+which is expectation value of a pi which
+
+ align:start position:0%
+which is expectation value of a pi which
+ 
+
+ align:start position:0%
+which is expectation value of a pi which
+is one and expectation value of a is
+
+ align:start position:0%
+is one and expectation value of a is
+ 
+
+ align:start position:0%
+is one and expectation value of a is
+zero. So this is a vector pip
+
+ align:start position:0%
+zero. So this is a vector pip
+ 
+
+ align:start position:0%
+zero. So this is a vector pip
+per and this is of course a minus
+
+ align:start position:0%
+per and this is of course a minus
+ 
+
+ align:start position:0%
+per and this is of course a minus
+expectation value of a acting on the
+
+ align:start position:0%
+expectation value of a acting on the
+ 
+
+ align:start position:0%
+expectation value of a acting on the
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+pi. Well precisely the norm of piper is
+
+ align:start position:0%
+pi. Well precisely the norm of piper is
+ 
+
+ align:start position:0%
+pi. Well precisely the norm of piper is
+the norm of this but that's what we
+
+ align:start position:0%
+the norm of this but that's what we
+ 
+
+ align:start position:0%
+the norm of this but that's what we
+define to be the uncertainty.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So of indeed the norm of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psy is delta a of
+
+ align:start position:0%
+psy is delta a of
+ 
+
+ align:start position:0%
+psy is delta a of
+pi. So our ideas of projectors and
+
+ align:start position:0%
+pi. So our ideas of projectors and
+ 
+
+ align:start position:0%
+pi. So our ideas of projectors and
+orthogonal projectors allow you to
+
+ align:start position:0%
+orthogonal projectors allow you to
+ 
+
+ align:start position:0%
+orthogonal projectors allow you to
+understand better what is the
+
+ align:start position:0%
+understand better what is the
+ 
+
+ align:start position:0%
+understand better what is the
+uncertainty more pictorially. You have a
+
+ align:start position:0%
+uncertainty more pictorially. You have a
+ 
+
+ align:start position:0%
+uncertainty more pictorially. You have a
+a pictures of vectors and orthogonal
+
+ align:start position:0%
+a pictures of vectors and orthogonal
+ 
+
+ align:start position:0%
+a pictures of vectors and orthogonal
+projections and you want to make the
+
+ align:start position:0%
+projections and you want to make the
+ 
+
+ align:start position:0%
+projections and you want to make the
+uncertainty zero. You have to push the a
+
+ align:start position:0%
+uncertainty zero. You have to push the a
+ 
+
+ align:start position:0%
+uncertainty zero. You have to push the a
+pi into pi. You have to be an ien state
+
+ align:start position:0%
+pi into pi. You have to be an ien state
+ 
+
+ align:start position:0%
+pi into pi. You have to be an ien state
+and you're there. Now the last thing
+
+ align:start position:0%
+and you're there. Now the last thing
+ 
+
+ align:start position:0%
+and you're there. Now the last thing
+I'll use the last five minutes to
+
+ align:start position:0%
+I'll use the last five minutes to
+ 
+
+ align:start position:0%
+I'll use the last five minutes to
+motivate the uncertainty the famous
+
+ align:start position:0%
+motivate the uncertainty the famous
+ 
+
+ align:start position:0%
+motivate the uncertainty the famous
+uncertainty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem. Uncertainty theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And typically the uncertainty theorem is
+
+ align:start position:0%
+And typically the uncertainty theorem is
+ 
+
+ align:start position:0%
+And typically the uncertainty theorem is
+useful for A and
+
+ align:start position:0%
+useful for A and
+ 
+
+ align:start position:0%
+useful for A and
+B to her
+
+ align:start position:0%
+B to her
+ 
+
+ align:start position:0%
+B to her
+mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators. And it relates the
+
+ align:start position:0%
+operators. And it relates the
+ 
+
+ align:start position:0%
+operators. And it relates the
+uncertainty in
+
+ align:start position:0%
+uncertainty in
+ 
+
+ align:start position:0%
+uncertainty in
+A on the state side to the uncertainty
+
+ align:start position:0%
+A on the state side to the uncertainty
+ 
+
+ align:start position:0%
+A on the state side to the uncertainty
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+B of Sing it must be bigger than or
+
+ align:start position:0%
+B of Sing it must be bigger than or
+ 
+
+ align:start position:0%
+B of Sing it must be bigger than or
+equal that some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number. Now, if you look at
+
+ align:start position:0%
+number. Now, if you look at
+ 
+
+ align:start position:0%
+number. Now, if you look at
+that and you think of all the bath we've
+
+ align:start position:0%
+that and you think of all the bath we've
+ 
+
+ align:start position:0%
+that and you think of all the bath we've
+been talking
+
+ align:start position:0%
+been talking
+ 
+
+ align:start position:0%
+been talking
+about, you maybe know
+
+ align:start position:0%
+about, you maybe know
+ 
+
+ align:start position:0%
+about, you maybe know
+exactly how you're supposed to prove the
+
+ align:start position:0%
+exactly how you're supposed to prove the
+ 
+
+ align:start position:0%
+exactly how you're supposed to prove the
+uncertainty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem. Well, what does this remind you
+
+ align:start position:0%
+theorem. Well, what does this remind you
+ 
+
+ align:start position:0%
+theorem. Well, what does this remind you
+of?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ky Schwarz. Uh, Schwarz inequality. I'm
+
+ align:start position:0%
+Ky Schwarz. Uh, Schwarz inequality. I'm
+ 
+
+ align:start position:0%
+Ky Schwarz. Uh, Schwarz inequality. I'm
+sorry, not Ky Schwartz.
+
+ align:start position:0%
+sorry, not Ky Schwartz.
+ 
+
+ align:start position:0%
+sorry, not Ky Schwartz.
+Why? Because and for Schwarz inequality
+
+ align:start position:0%
+Why? Because and for Schwarz inequality
+ 
+
+ align:start position:0%
+Why? Because and for Schwarz inequality
+you have norm of u norm of
+
+ align:start position:0%
+you have norm of u norm of
+ 
+
+ align:start position:0%
+you have norm of u norm of
+v is greater than or equal than the norm
+
+ align:start position:0%
+v is greater than or equal than the norm
+ 
+
+ align:start position:0%
+v is greater than or equal than the norm
+of the inner product of u and
+
+ align:start position:0%
+of the inner product of u and
+ 
+
+ align:start position:0%
+of the inner product of u and
+v absolute value of the inner product of
+
+ align:start position:0%
+v absolute value of the inner product of
+ 
+
+ align:start position:0%
+v absolute value of the inner product of
+u and
+
+ align:start position:0%
+u and
+ 
+
+ align:start position:0%
+u and
+v. Remember in this thing this is norm
+
+ align:start position:0%
+v. Remember in this thing this is norm
+ 
+
+ align:start position:0%
+v. Remember in this thing this is norm
+of a vector norm of a vector and this is
+
+ align:start position:0%
+of a vector norm of a vector and this is
+ 
+
+ align:start position:0%
+of a vector norm of a vector and this is
+value of a scalar and
+
+ align:start position:0%
+value of a scalar and
+ 
+
+ align:start position:0%
+value of a scalar and
+our uncertainties are
+
+ align:start position:0%
+our uncertainties are
+ 
+
+ align:start position:0%
+our uncertainties are
+norms. So it better be that that
+
+ align:start position:0%
+norms. So it better be that that
+ 
+
+ align:start position:0%
+norms. So it better be that that
+inequality is the only inequality that
+
+ align:start position:0%
+inequality is the only inequality that
+ 
+
+ align:start position:0%
+inequality is the only inequality that
+can possibly give you the
+
+ align:start position:0%
+can possibly give you the
+ 
+
+ align:start position:0%
+can possibly give you the
+answer. So
+
+ align:start position:0%
+answer. So
+ 
+
+ align:start position:0%
+answer. So
+uh how would you set this up? You would
+
+ align:start position:0%
+uh how would you set this up? You would
+ 
+
+ align:start position:0%
+uh how would you set this up? You would
+say define as we'll say
+
+ align:start position:0%
+say define as we'll say
+ 
+
+ align:start position:0%
+say define as we'll say
+f equal a min -
+
+ align:start position:0%
+f equal a min -
+ 
+
+ align:start position:0%
+f equal a min -
+a acting on
+
+ align:start position:0%
+a acting on
+ 
+
+ align:start position:0%
+a acting on
+pi and g is equal to b -
+
+ align:start position:0%
+pi and g is equal to b -
+ 
+
+ align:start position:0%
+pi and g is equal to b -
+b acting on pi and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f or ff is delta a squared
+
+ align:start position:0%
+f or ff is delta a squared
+ 
+
+ align:start position:0%
+f or ff is delta a squared
+F G F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G is delta B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared and uh you just need to compute
+
+ align:start position:0%
+squared and uh you just need to compute
+ 
+
+ align:start position:0%
+squared and uh you just need to compute
+the inner product of
+
+ align:start position:0%
+the inner product of
+ 
+
+ align:start position:0%
+the inner product of
+FG because you need the mix one.
+
+ align:start position:0%
+FG because you need the mix one.
+ 
+
+ align:start position:0%
+FG because you need the mix one.
+So if you want to have fun, try it.
+
+ align:start position:0%
+So if you want to have fun, try it.
+ 
+
+ align:start position:0%
+So if you want to have fun, try it.
+We'll do it next time anyway. All right,
+
+ align:start position:0%
+We'll do it next time anyway. All right,
+ 
+
+ align:start position:0%
+We'll do it next time anyway. All right,
+that's it for
\ No newline at end of file
diff --git a/reYwbnuhFU0.txt b/reYwbnuhFU0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7920a8479e096d1506c258aec84f9ba811d58096
--- /dev/null
+++ b/reYwbnuhFU0.txt
@@ -0,0 +1,602 @@
+PROFESSOR: Now having cut
+DNA, we then need to
+
+do something else.
+
+What's the next thing
+we have to do?
+
+AUDIENCE: Paste it.
+
+PROFESSOR: Paste it right.
+
+Oh, I put past.
+
+It should be paste.
+
+There we go.
+
+We should paste it.
+
+So, how are we going
+to paste our DNA?
+
+So let's take some human DNA.
+
+We'll take your human DNA.
+
+We'll add EcoR1 to it.
+
+And your human DNA is going to
+get cut up in lots of little
+
+pieces of length about 4,000.
+
+And I'm writing R1 at the ends
+because these pieces of DNA
+
+have EcoR1 sites.
+
+Now, I can take that human DNA
+and I can combine it with
+
+other pieces of DNA.
+
+Here's a piece of DNA.
+
+Remember it had this
+overhang like that.
+
+T-T-A-A was this piece
+here of human DNA.
+
+And I could take another piece
+of DNA that matched it a
+
+A-A-T-T.
+
+And it doesn't have
+to be human.
+
+It could be something else.
+
+It could be zebra.
+
+Some human DNA, some zebra DNA,
+and by that base pairing
+
+of those four bases, they'll
+sort of stick.
+
+It's not that strong.
+
+It's four bases of base pairing,
+but they'll stick.
+
+Now I'd like to glue
+them together.
+
+What's the word for attaching
+together DNA strands?
+
+We talked about it--
+
+Ligate, we want to ligate
+them together.
+
+So now we go back to our MIT
+engineers and say, please
+
+invent me a protein that's
+able to ligate
+
+together pieces of DNA.
+
+But actually, who invented
+it first?
+
+Bacteria invented it first.
+
+And it's called?
+
+Ligase.
+
+So all we have to do
+is add ligase.
+
+So it was kind of useful
+to know how
+
+DNA replication worked.
+
+We add ligase.
+
+And what does ligase
+do for a living?
+
+For a living, ligase is paid to
+go around and find pieces
+
+of DNA that have nicks and seal
+them back up by repairing
+
+the sugar phosphate
+backbone of DNA.
+
+And again, ancient molecular
+biologists would prove their
+
+mettle by purifying ligase and
+using it in their reactions.
+
+And today, where do
+we get ligase?
+
+It's in the catalog.
+
+Ligase is in the catalog,
+reasonably cheap.
+
+So, when we add ligase we could
+now get a hybrid piece
+
+of DNA that was half human
+and half zebra.
+
+I got to say, this freaks
+some people out.
+
+This doesn't freak me out
+because it's just a sequence
+
+of nucleotides.
+
+If I give you a sequence of
+nucleotides, to my mind,
+
+there's nothing human
+or zebra about it.
+
+It's a chemical.
+
+And you can make bonds between
+chemicals and all that.
+
+So, we now pasted our
+DNA using ligase.
+
+Ligase from the catalog.
+
+Now the question is, what are we
+going to paste our DNA to?
+
+What do we paste our DNA to?
+
+We're going to paste our DNA to
+a fascinating other piece
+
+of DNA like this.
+
+I'll make that a little
+bigger here.
+
+That has an EcoR1 site,
+has an EcoR1 site.
+
+And we're going to take our
+human DNA and paste it in such
+
+a way that it makes a circle.
+
+This piece of DNA is a vector.
+
+Vector means it travels
+around.
+
+It carries things with it.
+
+So I want this vector to be
+able to replicate if I
+
+transfer it to E Coli.
+
+So that's the trick.
+
+I would like to be able to
+attachment my human DNA to
+
+this vector DNA, and when I
+transfer it to E coli, have
+
+this thing be able to grow.
+
+So that means we need to invent
+a piece of DNA, a
+
+vector, that is capable
+of causing E. coli
+
+to replicate itself.
+
+It's got to have all the
+instructions to cause E. coli
+
+to replicate this
+piece of DNA.
+
+So this is another amazing
+bit of engineering.
+
+How do we invent just the right
+sequence of letters that
+
+would allow E. coli to
+replicate this thing?
+
+AUDIENCE: Already
+been invented.
+
+PROFESSOR: Sorry.
+
+AUDIENCE: It's already been
+invented by E. coli.
+
+PROFESSOR: It's already
+been invented by E.
+
+coli, hasn't it?
+
+So you're getting the theme
+here, is that we don't
+
+actually do anything in
+molecular biology.
+
+Now look, in fairness, life's
+had 3.5 billion years.
+
+We've been at this a decade
+or two, on the
+
+whole, maybe three.
+
+On the whole, life's had
+a lot more time to
+
+work this stuff out.
+
+And usually the best solution
+is to look in nature to see
+
+where nature has already
+done it for you.
+
+So E. coli, it turns out,
+replicates its own chromosome.
+
+You could use the machinery
+from its own chromosome.
+
+But it turns out even
+better than that.
+
+E. coli has the following.
+
+Here's its big chromosome, four
+million letters of E.
+
+coli chromosome.
+
+E. Coli also has within
+it little circles
+
+of DNA called plasmids.
+
+These little circles
+of DNA are able to
+
+autonomously replicate.
+
+They can copy themselves.
+
+Or that is to say, E.
+coli copies them.
+
+These little plasmids have the
+full replication instructions
+
+encoded in them.
+
+Now why does E. coli have
+these plasmids?
+
+What's in these plasmids?
+
+What's going on?
+
+Well let's blow up one
+of these plasmids.
+
+It's a big circle.
+
+And it has an instruction here,
+a sequence, called an
+
+origin of replication - or
+amongst friends, just ORI.
+
+It's called ORI.
+
+You'll find on maps, origin
+of replication.
+
+That sequence alone is enough to
+cause E. coli to open it up
+
+and start doing its DNA
+replication from the origin.
+
+But what tells you why this is
+so important is that these
+
+plasmids typically have
+one or two genes.
+
+And the one or two genes that
+they typically have are genes
+
+that encode a protein that gives
+them resistance to an
+
+antibiotic, like say,
+penicillin.
+
+There could be a gene that
+gives you penicillin
+
+resistance.
+
+That's kind of cool.
+
+E. coli, or other bacteria--
+
+not E. coli necessarily
+for penicillin--
+
+carry around often
+little circles.
+
+And these little circles encode
+genes that give them
+
+resistance to streptomycin,
+penicillin, ampicillin, all
+
+sorts of things.
+
+This allows it to grow, even if
+you're taking penicillin.
+
+Now, that's pretty clever.
+
+How did E. Coli come up?
+
+How is it so smart to know to
+have come up with a gene able
+
+to break down penicillin, given
+that we've only been
+
+using penicillin since
+the 1940s?
+
+Pretty fast for E. coli to have
+figured out how to do
+
+that, isn't it?
+
+Oh yeah, who invented
+penicillin?
+
+Nature invented penicillin.
+
+It's produced by fungi.
+
+Fungi have been fighting E.
+Coli with penicillin for
+
+millions of years.
+
+E. coli didn't invent
+it for us.
+
+E. Coli invented it because it's
+in a war down there at
+
+the single cell level
+with fungi.
+
+Fungi make antibi--
+
+You see, we think
+we're so cool.
+
+We make antibiotics.
+
+Well we've been making
+antibiotics
+
+only since the 1940s.
+
+Nature's been making antibiotics
+forever.
+
+Just like the viruses are
+infecting E. coli and E. coli
+
+needs an immune system
+against the viruses.
+
+Well the fungi are throwing
+antibiotics at the bacteria
+
+and it needs a defense
+mechanism.
+
+And the defense mechanism are
+these genes that can break
+
+down those antibiotics.
+
+And as usual, we just
+come along and we
+
+say, oh look at that.
+
+It's already been invented.
+
+Kind of cool.
+
+We'll use that one too.
+
+Now why are these on these
+little circles?
+
+They're on the little circles
+because when this bacteria has
+
+lived a long and happy life and
+it dies and it spews its
+
+guts out, neighboring bacteria
+suck up the DNA.
+
+Sounds a little cannibalistic
+or something.
+
+But that's how it
+is down there at
+
+the single cell level.
+
+The neighboring bacteria
+will suck up DNA.
+
+And why is that cool?
+
+It's cool because they can
+acquire these resistances.
+
+That's pretty impressive.
+
+They can acquire
+the resistance.
+
+And in fact, it even works
+across species.
+
+That's why you don't put it
+on the chromosome here.
+
+Because E. coli could pick it up
+from another species that's
+
+not E. coli, but related
+enough that it
+
+can use that plasmid.
+
+And you can transfer antibiotic
+resistance across
+
+many species of bacteria.
+
+So the bacteria like to suck up
+DNA and see what they find.
+
+Pretty cool.
+
+By the way, this is also why
+indiscriminate use of
+
+antibiotics, for example, in
+animal feed, or when you were
+
+given antibiotics by the MIT
+health service and are told to
+
+take them for two weeks and you
+take them for five days,
+
+you're not doing anything
+very good.
+
+You're just selecting for
+bacteria that can grow in the
+
+presence of antibiotics and
+selecting for multidrug
+
+resistance in the spread
+of antibiotics.
+
+We have to be pretty careful.
+
+Because all these mechanisms
+of swapping antibiotic
+
+resistance are pretty
+impressive tricks.
+
+Anyway, so these things exist.
+
+And originally, molecular
+biologists
+
+discovered these plasmids.
+
+They purified these plasmids.
+
+And the deal was this,
+they cut the
+
+plasmid with EcoR1, ideally.
+
+So I'm going to put this
+up here, vectors.
+
+They cut the plasmid
+with EcoR1.
+
+They ligate human DNA into it.
+
+And they get these circles.
+
+And there you go.
+
+Now today, obviously, if I
+wanted to do this experiment,
+
+would I purify the
+plasmid myself?
+
+No.
+
+Where would I get the
+plasmid from?
+
+AUDIENCE: Catalog.
+
+PROFESSOR: It's in
+the catalog.
+
+There's a whole section
+a plasmids here.
+
+They have vectors
+of all sorts.
+
+So you get it from
+the catalog.
+
+All right.
\ No newline at end of file
diff --git a/sB547f1ogWc.txt b/sB547f1ogWc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..004b3612aaf268d22ae3c0d960c936a368e33e3b
--- /dev/null
+++ b/sB547f1ogWc.txt
@@ -0,0 +1,8922 @@
+align:start position:0%
+ 
+so I wanted to keep talking about uh DC
+
+ align:start position:0%
+so I wanted to keep talking about uh DC
+ 
+
+ align:start position:0%
+so I wanted to keep talking about uh DC
+todc converters today and keep talking
+
+ align:start position:0%
+todc converters today and keep talking
+ 
+
+ align:start position:0%
+todc converters today and keep talking
+about the impact of Ripple and operating
+
+ align:start position:0%
+about the impact of Ripple and operating
+ 
+
+ align:start position:0%
+about the impact of Ripple and operating
+modes of DCd converters right so we said
+
+ align:start position:0%
+modes of DCd converters right so we said
+ 
+
+ align:start position:0%
+modes of DCd converters right so we said
+we we did some analysis last time and
+
+ align:start position:0%
+we we did some analysis last time and
+ 
+
+ align:start position:0%
+we we did some analysis last time and
+what we found is that under reasonable
+
+ align:start position:0%
+what we found is that under reasonable
+ 
+
+ align:start position:0%
+what we found is that under reasonable
+approximations the inductor current wave
+
+ align:start position:0%
+approximations the inductor current wave
+ 
+
+ align:start position:0%
+approximations the inductor current wave
+forms in a pwm dcdc converter tend to
+
+ align:start position:0%
+forms in a pwm dcdc converter tend to
+ 
+
+ align:start position:0%
+forms in a pwm dcdc converter tend to
+look like some DC Value Plus some
+
+ align:start position:0%
+look like some DC Value Plus some
+ 
+
+ align:start position:0%
+look like some DC Value Plus some
+triangular
+
+ align:start position:0%
+triangular
+ 
+
+ align:start position:0%
+triangular
+Ripple and the same thing for the
+
+ align:start position:0%
+Ripple and the same thing for the
+ 
+
+ align:start position:0%
+Ripple and the same thing for the
+capacitor voltage waveforms okay and we
+
+ align:start position:0%
+capacitor voltage waveforms okay and we
+ 
+
+ align:start position:0%
+capacitor voltage waveforms okay and we
+said that we could represent this kind
+
+ align:start position:0%
+said that we could represent this kind
+ 
+
+ align:start position:0%
+said that we could represent this kind
+of waveform sort of a triangle wave with
+
+ align:start position:0%
+of waveform sort of a triangle wave with
+ 
+
+ align:start position:0%
+of waveform sort of a triangle wave with
+an offset as having some DC
+
+ align:start position:0%
+an offset as having some DC
+ 
+
+ align:start position:0%
+an offset as having some DC
+value uh plus triangular Ripple where we
+
+ align:start position:0%
+value uh plus triangular Ripple where we
+ 
+
+ align:start position:0%
+value uh plus triangular Ripple where we
+could find the we could Define
+
+ align:start position:0%
+could find the we could Define
+ 
+
+ align:start position:0%
+could find the we could Define
+the average value and then the peak
+
+ align:start position:0%
+the average value and then the peak
+ 
+
+ align:start position:0%
+the average value and then the peak
+value and because of the properties of a
+
+ align:start position:0%
+value and because of the properties of a
+ 
+
+ align:start position:0%
+value and because of the properties of a
+triangle wave the peak is right in the
+
+ align:start position:0%
+triangle wave the peak is right in the
+ 
+
+ align:start position:0%
+triangle wave the peak is right in the
+average is right in the middle of
+
+ align:start position:0%
+average is right in the middle of
+ 
+
+ align:start position:0%
+average is right in the middle of
+between the two peaks so you sort of
+
+ align:start position:0%
+between the two peaks so you sort of
+ 
+
+ align:start position:0%
+between the two peaks so you sort of
+Swing Delta X Peak to Peak over two
+
+ align:start position:0%
+Swing Delta X Peak to Peak over two
+ 
+
+ align:start position:0%
+Swing Delta X Peak to Peak over two
+above the average and Delta X Peak to
+
+ align:start position:0%
+above the average and Delta X Peak to
+ 
+
+ align:start position:0%
+above the average and Delta X Peak to
+Peak over to below the average okay and
+
+ align:start position:0%
+Peak over to below the average okay and
+ 
+
+ align:start position:0%
+Peak over to below the average okay and
+so we can Define sort of a ripple ratio
+
+ align:start position:0%
+so we can Define sort of a ripple ratio
+ 
+
+ align:start position:0%
+so we can Define sort of a ripple ratio
+for such a wave form sort of a notion of
+
+ align:start position:0%
+for such a wave form sort of a notion of
+ 
+
+ align:start position:0%
+for such a wave form sort of a notion of
+a percentage Ripple which we Define in
+
+ align:start position:0%
+a percentage Ripple which we Define in
+ 
+
+ align:start position:0%
+a percentage Ripple which we Define in
+this class as half half of the peak to
+
+ align:start position:0%
+this class as half half of the peak to
+ 
+
+ align:start position:0%
+this class as half half of the peak to
+Peak swing or the mean to Peak swing
+
+ align:start position:0%
+Peak swing or the mean to Peak swing
+ 
+
+ align:start position:0%
+Peak swing or the mean to Peak swing
+normalized to the average
+
+ align:start position:0%
+normalized to the average
+ 
+
+ align:start position:0%
+normalized to the average
+value okay and one of the nice things
+
+ align:start position:0%
+value okay and one of the nice things
+ 
+
+ align:start position:0%
+value okay and one of the nice things
+about that is we can then if I knew the
+
+ align:start position:0%
+about that is we can then if I knew the
+ 
+
+ align:start position:0%
+about that is we can then if I knew the
+average value from our calculations I
+
+ align:start position:0%
+average value from our calculations I
+ 
+
+ align:start position:0%
+average value from our calculations I
+can actually find the peak value as
+
+ align:start position:0%
+can actually find the peak value as
+ 
+
+ align:start position:0%
+can actually find the peak value as
+being the average time 1 plus the Ripple
+
+ align:start position:0%
+being the average time 1 plus the Ripple
+ 
+
+ align:start position:0%
+being the average time 1 plus the Ripple
+ratio okay um if we apply
+
+ align:start position:0%
+ratio okay um if we apply
+ 
+
+ align:start position:0%
+ratio okay um if we apply
+that we also talked about the device
+
+ align:start position:0%
+that we also talked about the device
+ 
+
+ align:start position:0%
+that we also talked about the device
+stresses in a direct converter such as a
+
+ align:start position:0%
+stresses in a direct converter such as a
+ 
+
+ align:start position:0%
+stresses in a direct converter such as a
+buck or a boost converter and an
+
+ align:start position:0%
+buck or a boost converter and an
+ 
+
+ align:start position:0%
+buck or a boost converter and an
+indirect converter such as the the uh
+
+ align:start position:0%
+indirect converter such as the the uh
+ 
+
+ align:start position:0%
+indirect converter such as the the uh
+inverting buck boost converter and we
+
+ align:start position:0%
+inverting buck boost converter and we
+ 
+
+ align:start position:0%
+inverting buck boost converter and we
+had written it as sort of for a direct
+
+ align:start position:0%
+had written it as sort of for a direct
+ 
+
+ align:start position:0%
+had written it as sort of for a direct
+converter the peak switch voltage the
+
+ align:start position:0%
+converter the peak switch voltage the
+ 
+
+ align:start position:0%
+converter the peak switch voltage the
+peak di voltage which is also the peak
+
+ align:start position:0%
+peak di voltage which is also the peak
+ 
+
+ align:start position:0%
+peak di voltage which is also the peak
+capacitor voltage is this maximum of V1
+
+ align:start position:0%
+capacitor voltage is this maximum of V1
+ 
+
+ align:start position:0%
+capacitor voltage is this maximum of V1
+and V2 times 1 plus the Ripple ratio
+
+ align:start position:0%
+and V2 times 1 plus the Ripple ratio
+ 
+
+ align:start position:0%
+and V2 times 1 plus the Ripple ratio
+that's how we get from this is the
+
+ align:start position:0%
+that's how we get from this is the
+ 
+
+ align:start position:0%
+that's how we get from this is the
+average DC value we see in terms of the
+
+ align:start position:0%
+average DC value we see in terms of the
+ 
+
+ align:start position:0%
+average DC value we see in terms of the
+DC Value Plus the Ripple on the passer
+
+ align:start position:0%
+DC Value Plus the Ripple on the passer
+ 
+
+ align:start position:0%
+DC Value Plus the Ripple on the passer
+voltage increases the peak voltages we
+
+ align:start position:0%
+voltage increases the peak voltages we
+ 
+
+ align:start position:0%
+voltage increases the peak voltages we
+see a little bit and likewise we can
+
+ align:start position:0%
+see a little bit and likewise we can
+ 
+
+ align:start position:0%
+see a little bit and likewise we can
+talk about the uh switch current and the
+
+ align:start position:0%
+talk about the uh switch current and the
+ 
+
+ align:start position:0%
+talk about the uh switch current and the
+diode current Peak values which are
+
+ align:start position:0%
+diode current Peak values which are
+ 
+
+ align:start position:0%
+diode current Peak values which are
+related to the maximum of the average
+
+ align:start position:0%
+related to the maximum of the average
+ 
+
+ align:start position:0%
+related to the maximum of the average
+and input and output currents okay so
+
+ align:start position:0%
+and input and output currents okay so
+ 
+
+ align:start position:0%
+and input and output currents okay so
+for a buck converter the output current
+
+ align:start position:0%
+for a buck converter the output current
+ 
+
+ align:start position:0%
+for a buck converter the output current
+is the bigger one and the input voltage
+
+ align:start position:0%
+is the bigger one and the input voltage
+ 
+
+ align:start position:0%
+is the bigger one and the input voltage
+is the bigger one but we see Peak
+
+ align:start position:0%
+is the bigger one but we see Peak
+ 
+
+ align:start position:0%
+is the bigger one but we see Peak
+stresses and uh and voltage and current
+
+ align:start position:0%
+stresses and uh and voltage and current
+ 
+
+ align:start position:0%
+stresses and uh and voltage and current
+that are related to the maximum of the
+
+ align:start position:0%
+that are related to the maximum of the
+ 
+
+ align:start position:0%
+that are related to the maximum of the
+input and output DC waveforms and the
+
+ align:start position:0%
+input and output DC waveforms and the
+ 
+
+ align:start position:0%
+input and output DC waveforms and the
+Ripple
+
+ align:start position:0%
+Ripple
+ 
+
+ align:start position:0%
+Ripple
+okay then we looked also at this
+
+ align:start position:0%
+okay then we looked also at this
+ 
+
+ align:start position:0%
+okay then we looked also at this
+indirect converter we found the
+
+ align:start position:0%
+indirect converter we found the
+ 
+
+ align:start position:0%
+indirect converter we found the
+difference is instead of seeing the
+
+ align:start position:0%
+difference is instead of seeing the
+ 
+
+ align:start position:0%
+difference is instead of seeing the
+maximum of the input and output we see
+
+ align:start position:0%
+maximum of the input and output we see
+ 
+
+ align:start position:0%
+maximum of the input and output we see
+the sum of the input and output currents
+
+ align:start position:0%
+the sum of the input and output currents
+ 
+
+ align:start position:0%
+the sum of the input and output currents
+and voltages okay so this tells us no
+
+ align:start position:0%
+and voltages okay so this tells us no
+ 
+
+ align:start position:0%
+and voltages okay so this tells us no
+matter what for a given conversion ratio
+
+ align:start position:0%
+matter what for a given conversion ratio
+ 
+
+ align:start position:0%
+matter what for a given conversion ratio
+V1 V2 i1 I2 we're always going to have
+
+ align:start position:0%
+V1 V2 i1 I2 we're always going to have
+ 
+
+ align:start position:0%
+V1 V2 i1 I2 we're always going to have
+higher stresses in an indirect converter
+
+ align:start position:0%
+higher stresses in an indirect converter
+ 
+
+ align:start position:0%
+higher stresses in an indirect converter
+compared to a direct converter and that
+
+ align:start position:0%
+compared to a direct converter and that
+ 
+
+ align:start position:0%
+compared to a direct converter and that
+makes sense because of how we're
+
+ align:start position:0%
+makes sense because of how we're
+ 
+
+ align:start position:0%
+makes sense because of how we're
+processing energy through the converter
+
+ align:start position:0%
+processing energy through the converter
+ 
+
+ align:start position:0%
+processing energy through the converter
+the indirect converter you're basically
+
+ align:start position:0%
+the indirect converter you're basically
+ 
+
+ align:start position:0%
+the indirect converter you're basically
+storing all the energy in the middle of
+
+ align:start position:0%
+storing all the energy in the middle of
+ 
+
+ align:start position:0%
+storing all the energy in the middle of
+the converter and in the direct
+
+ align:start position:0%
+the converter and in the direct
+ 
+
+ align:start position:0%
+the converter and in the direct
+converter you're sort of some of it gets
+
+ align:start position:0%
+converter you're sort of some of it gets
+ 
+
+ align:start position:0%
+converter you're sort of some of it gets
+to flow right through the converter you
+
+ align:start position:0%
+to flow right through the converter you
+ 
+
+ align:start position:0%
+to flow right through the converter you
+can take advantage of that okay so this
+
+ align:start position:0%
+can take advantage of that okay so this
+ 
+
+ align:start position:0%
+can take advantage of that okay so this
+is just a quick review of the
+
+ align:start position:0%
+is just a quick review of the
+ 
+
+ align:start position:0%
+is just a quick review of the
+conclusions we came to last time any
+
+ align:start position:0%
+conclusions we came to last time any
+ 
+
+ align:start position:0%
+conclusions we came to last time any
+questions about this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far the other thing we did was then we
+
+ align:start position:0%
+far the other thing we did was then we
+ 
+
+ align:start position:0%
+far the other thing we did was then we
+took that and we said okay well I know
+
+ align:start position:0%
+took that and we said okay well I know
+ 
+
+ align:start position:0%
+took that and we said okay well I know
+that my inductor current for example has
+
+ align:start position:0%
+that my inductor current for example has
+ 
+
+ align:start position:0%
+that my inductor current for example has
+some triangular Ripple on it right so
+
+ align:start position:0%
+some triangular Ripple on it right so
+ 
+
+ align:start position:0%
+some triangular Ripple on it right so
+this this iil looks like some average
+
+ align:start position:0%
+this this iil looks like some average
+ 
+
+ align:start position:0%
+this this iil looks like some average
+value and some Ripple right and we could
+
+ align:start position:0%
+value and some Ripple right and we could
+ 
+
+ align:start position:0%
+value and some Ripple right and we could
+calculate if I wanted to limit my
+
+ align:start position:0%
+calculate if I wanted to limit my
+ 
+
+ align:start position:0%
+calculate if I wanted to limit my
+peak-to Peak inductor current Ripple
+
+ align:start position:0%
+peak-to Peak inductor current Ripple
+ 
+
+ align:start position:0%
+peak-to Peak inductor current Ripple
+below some value because that's my input
+
+ align:start position:0%
+below some value because that's my input
+ 
+
+ align:start position:0%
+below some value because that's my input
+Ripple current or my Peak to Peak output
+
+ align:start position:0%
+Ripple current or my Peak to Peak output
+ 
+
+ align:start position:0%
+Ripple current or my Peak to Peak output
+voltage Ripple below a certain value I
+
+ align:start position:0%
+voltage Ripple below a certain value I
+ 
+
+ align:start position:0%
+voltage Ripple below a certain value I
+can come up with
+
+ align:start position:0%
+can come up with
+ 
+
+ align:start position:0%
+can come up with
+minimum capacitor and inductor values to
+
+ align:start position:0%
+minimum capacitor and inductor values to
+ 
+
+ align:start position:0%
+minimum capacitor and inductor values to
+do that that are related to you know the
+
+ align:start position:0%
+do that that are related to you know the
+ 
+
+ align:start position:0%
+do that that are related to you know the
+conversion
+
+ align:start position:0%
+conversion
+ 
+
+ align:start position:0%
+conversion
+ratio and I expressed it here in terms
+
+ align:start position:0%
+ratio and I expressed it here in terms
+ 
+
+ align:start position:0%
+ratio and I expressed it here in terms
+of the allowed Ripple ratio of the
+
+ align:start position:0%
+of the allowed Ripple ratio of the
+ 
+
+ align:start position:0%
+of the allowed Ripple ratio of the
+designs okay so now we have a means to
+
+ align:start position:0%
+designs okay so now we have a means to
+ 
+
+ align:start position:0%
+designs okay so now we have a means to
+start sizing inductors and capacitors
+
+ align:start position:0%
+start sizing inductors and capacitors
+ 
+
+ align:start position:0%
+start sizing inductors and capacitors
+right we can't practically use nearly
+
+ align:start position:0%
+right we can't practically use nearly
+ 
+
+ align:start position:0%
+right we can't practically use nearly
+infinite ones because they get too big
+
+ align:start position:0%
+infinite ones because they get too big
+ 
+
+ align:start position:0%
+infinite ones because they get too big
+and expensive if you have too smaller
+
+ align:start position:0%
+and expensive if you have too smaller
+ 
+
+ align:start position:0%
+and expensive if you have too smaller
+one you get too much Ripple and bad
+
+ align:start position:0%
+one you get too much Ripple and bad
+ 
+
+ align:start position:0%
+one you get too much Ripple and bad
+things happen and so the question is how
+
+ align:start position:0%
+things happen and so the question is how
+ 
+
+ align:start position:0%
+things happen and so the question is how
+do you pick those values and one of the
+
+ align:start position:0%
+do you pick those values and one of the
+ 
+
+ align:start position:0%
+do you pick those values and one of the
+things that used to pick those values is
+
+ align:start position:0%
+things that used to pick those values is
+ 
+
+ align:start position:0%
+things that used to pick those values is
+some sort of notion of an an allowable
+
+ align:start position:0%
+some sort of notion of an an allowable
+ 
+
+ align:start position:0%
+some sort of notion of an an allowable
+Ripple which we could express in terms
+
+ align:start position:0%
+Ripple which we could express in terms
+ 
+
+ align:start position:0%
+Ripple which we could express in terms
+of peak to Peak Ripple or we could
+
+ align:start position:0%
+of peak to Peak Ripple or we could
+ 
+
+ align:start position:0%
+of peak to Peak Ripple or we could
+express in terms of Ripple ratios okay
+
+ align:start position:0%
+express in terms of Ripple ratios okay
+ 
+
+ align:start position:0%
+express in terms of Ripple ratios okay
+typically you know in this example
+
+ align:start position:0%
+typically you know in this example
+ 
+
+ align:start position:0%
+typically you know in this example
+you're not usually allowed very much
+
+ align:start position:0%
+you're not usually allowed very much
+ 
+
+ align:start position:0%
+you're not usually allowed very much
+Ripple ratio on the capacitor right
+
+ align:start position:0%
+Ripple ratio on the capacitor right
+ 
+
+ align:start position:0%
+Ripple ratio on the capacitor right
+because um you know if you want a DC
+
+ align:start position:0%
+because um you know if you want a DC
+ 
+
+ align:start position:0%
+because um you know if you want a DC
+output voltage you can't have 10% Ripple
+
+ align:start position:0%
+output voltage you can't have 10% Ripple
+ 
+
+ align:start position:0%
+output voltage you can't have 10% Ripple
+in your up voltage that would usually be
+
+ align:start position:0%
+in your up voltage that would usually be
+ 
+
+ align:start position:0%
+in your up voltage that would usually be
+bad right so maybe that's a percent or
+
+ align:start position:0%
+bad right so maybe that's a percent or
+ 
+
+ align:start position:0%
+bad right so maybe that's a percent or
+something it depends on your
+
+ align:start position:0%
+something it depends on your
+ 
+
+ align:start position:0%
+something it depends on your
+specifications inductor current Ripple
+
+ align:start position:0%
+specifications inductor current Ripple
+ 
+
+ align:start position:0%
+specifications inductor current Ripple
+um you know maybe a bit more is
+
+ align:start position:0%
+um you know maybe a bit more is
+ 
+
+ align:start position:0%
+um you know maybe a bit more is
+acceptable maybe you could have 25%
+
+ align:start position:0%
+acceptable maybe you could have 25%
+ 
+
+ align:start position:0%
+acceptable maybe you could have 25%
+Ripple in that current especially if you
+
+ align:start position:0%
+Ripple in that current especially if you
+ 
+
+ align:start position:0%
+Ripple in that current especially if you
+add on you know another capacitor to
+
+ align:start position:0%
+add on you know another capacitor to
+ 
+
+ align:start position:0%
+add on you know another capacitor to
+help you filter it back here
+
+ align:start position:0%
+help you filter it back here
+ 
+
+ align:start position:0%
+help you filter it back here
+okay so um there's the notion of sizing
+
+ align:start position:0%
+okay so um there's the notion of sizing
+ 
+
+ align:start position:0%
+okay so um there's the notion of sizing
+and we'll talk about this is sort of one
+
+ align:start position:0%
+and we'll talk about this is sort of one
+ 
+
+ align:start position:0%
+and we'll talk about this is sort of one
+way you can start to pick your inductor
+
+ align:start position:0%
+way you can start to pick your inductor
+ 
+
+ align:start position:0%
+way you can start to pick your inductor
+and capacitor values based on Ripple
+
+ align:start position:0%
+and capacitor values based on Ripple
+ 
+
+ align:start position:0%
+and capacitor values based on Ripple
+there are other factors too where we
+
+ align:start position:0%
+there are other factors too where we
+ 
+
+ align:start position:0%
+there are other factors too where we
+said size right so you can kind of
+
+ align:start position:0%
+said size right so you can kind of
+ 
+
+ align:start position:0%
+said size right so you can kind of
+figure the biggest value you can get
+
+ align:start position:0%
+figure the biggest value you can get
+ 
+
+ align:start position:0%
+figure the biggest value you can get
+before it gets too big is probably a
+
+ align:start position:0%
+before it gets too big is probably a
+ 
+
+ align:start position:0%
+before it gets too big is probably a
+good thing but also in terms of
+
+ align:start position:0%
+good thing but also in terms of
+ 
+
+ align:start position:0%
+good thing but also in terms of
+transient performance the dynamic
+
+ align:start position:0%
+transient performance the dynamic
+ 
+
+ align:start position:0%
+transient performance the dynamic
+performance your converter we'll talk
+
+ align:start position:0%
+performance your converter we'll talk
+ 
+
+ align:start position:0%
+performance your converter we'll talk
+about that aspect a little later but
+
+ align:start position:0%
+about that aspect a little later but
+ 
+
+ align:start position:0%
+about that aspect a little later but
+that can also come into to how you pick
+
+ align:start position:0%
+that can also come into to how you pick
+ 
+
+ align:start position:0%
+that can also come into to how you pick
+the values and the reason I mentioned
+
+ align:start position:0%
+the values and the reason I mentioned
+ 
+
+ align:start position:0%
+the values and the reason I mentioned
+that is because you know in your design
+
+ align:start position:0%
+that is because you know in your design
+ 
+
+ align:start position:0%
+that is because you know in your design
+project you're going to have to pick
+
+ align:start position:0%
+project you're going to have to pick
+ 
+
+ align:start position:0%
+project you're going to have to pick
+values and you're going to have to think
+
+ align:start position:0%
+values and you're going to have to think
+ 
+
+ align:start position:0%
+values and you're going to have to think
+about these different aspects okay um
+
+ align:start position:0%
+about these different aspects okay um
+ 
+
+ align:start position:0%
+about these different aspects okay um
+the other thing we said was okay if I
+
+ align:start position:0%
+the other thing we said was okay if I
+ 
+
+ align:start position:0%
+the other thing we said was okay if I
+have some minimum values based on Ripple
+
+ align:start position:0%
+have some minimum values based on Ripple
+ 
+
+ align:start position:0%
+have some minimum values based on Ripple
+what is that say about the energy
+
+ align:start position:0%
+what is that say about the energy
+ 
+
+ align:start position:0%
+what is that say about the energy
+storage requirement of my inductor and
+
+ align:start position:0%
+storage requirement of my inductor and
+ 
+
+ align:start position:0%
+storage requirement of my inductor and
+my capacitor and the reason we talk
+
+ align:start position:0%
+my capacitor and the reason we talk
+ 
+
+ align:start position:0%
+my capacitor and the reason we talk
+about energy storage requirement is
+
+ align:start position:0%
+about energy storage requirement is
+ 
+
+ align:start position:0%
+about energy storage requirement is
+because we ought to you know it's
+
+ align:start position:0%
+because we ought to you know it's
+ 
+
+ align:start position:0%
+because we ought to you know it's
+reasonable to expect that the size of
+
+ align:start position:0%
+reasonable to expect that the size of
+ 
+
+ align:start position:0%
+reasonable to expect that the size of
+your component is probably monotonic
+
+ align:start position:0%
+your component is probably monotonic
+ 
+
+ align:start position:0%
+your component is probably monotonic
+with its energy storage capability right
+
+ align:start position:0%
+with its energy storage capability right
+ 
+
+ align:start position:0%
+with its energy storage capability right
+it's going to get bigger if you have to
+
+ align:start position:0%
+it's going to get bigger if you have to
+ 
+
+ align:start position:0%
+it's going to get bigger if you have to
+store more energy usually right there's
+
+ align:start position:0%
+store more energy usually right there's
+ 
+
+ align:start position:0%
+store more energy usually right there's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+complex tradeoff to design actual
+
+ align:start position:0%
+complex tradeoff to design actual
+ 
+
+ align:start position:0%
+complex tradeoff to design actual
+especially magnetic components but
+
+ align:start position:0%
+especially magnetic components but
+ 
+
+ align:start position:0%
+especially magnetic components but
+nonetheless it's reasonable to expect
+
+ align:start position:0%
+nonetheless it's reasonable to expect
+ 
+
+ align:start position:0%
+nonetheless it's reasonable to expect
+that and what we can see from this
+
+ align:start position:0%
+that and what we can see from this
+ 
+
+ align:start position:0%
+that and what we can see from this
+expression is that if I looked at the
+
+ align:start position:0%
+expression is that if I looked at the
+ 
+
+ align:start position:0%
+expression is that if I looked at the
+energ stored in the capacitor right it
+
+ align:start position:0%
+energ stored in the capacitor right it
+ 
+
+ align:start position:0%
+energ stored in the capacitor right it
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+bigger if I have smaller Ripple ratio
+
+ align:start position:0%
+bigger if I have smaller Ripple ratio
+ 
+
+ align:start position:0%
+bigger if I have smaller Ripple ratio
+this this Factor here tends to get big
+
+ align:start position:0%
+this this Factor here tends to get big
+ 
+
+ align:start position:0%
+this this Factor here tends to get big
+if I make Ripple ratio very
+
+ align:start position:0%
+if I make Ripple ratio very
+ 
+
+ align:start position:0%
+if I make Ripple ratio very
+small okay it gets bigger proportional
+
+ align:start position:0%
+small okay it gets bigger proportional
+ 
+
+ align:start position:0%
+small okay it gets bigger proportional
+to the power my converter needs to
+
+ align:start position:0%
+to the power my converter needs to
+ 
+
+ align:start position:0%
+to the power my converter needs to
+handle okay that's kind of reasonable if
+
+ align:start position:0%
+handle okay that's kind of reasonable if
+ 
+
+ align:start position:0%
+handle okay that's kind of reasonable if
+I want a kilowatt converter it's going
+
+ align:start position:0%
+I want a kilowatt converter it's going
+ 
+
+ align:start position:0%
+I want a kilowatt converter it's going
+to be physically have more energy
+
+ align:start position:0%
+to be physically have more energy
+ 
+
+ align:start position:0%
+to be physically have more energy
+storage than 100 watt
+
+ align:start position:0%
+storage than 100 watt
+ 
+
+ align:start position:0%
+storage than 100 watt
+converter it depends depends on the
+
+ align:start position:0%
+converter it depends depends on the
+ 
+
+ align:start position:0%
+converter it depends depends on the
+conversion ratio and in this case for a
+
+ align:start position:0%
+conversion ratio and in this case for a
+ 
+
+ align:start position:0%
+conversion ratio and in this case for a
+boost converter a bigger conversion
+
+ align:start position:0%
+boost converter a bigger conversion
+ 
+
+ align:start position:0%
+boost converter a bigger conversion
+ratio is a bigger duty cycle so the More
+
+ align:start position:0%
+ratio is a bigger duty cycle so the More
+ 
+
+ align:start position:0%
+ratio is a bigger duty cycle so the More
+Voltage conversion I'm doing the more
+
+ align:start position:0%
+Voltage conversion I'm doing the more
+ 
+
+ align:start position:0%
+Voltage conversion I'm doing the more
+energy storage I'm going to need to do
+
+ align:start position:0%
+energy storage I'm going to need to do
+ 
+
+ align:start position:0%
+energy storage I'm going to need to do
+it okay and the last thing which weighs
+
+ align:start position:0%
+it okay and the last thing which weighs
+ 
+
+ align:start position:0%
+it okay and the last thing which weighs
+heavily on a lot of designers Minds is
+
+ align:start position:0%
+heavily on a lot of designers Minds is
+ 
+
+ align:start position:0%
+heavily on a lot of designers Minds is
+uh we expressed it last time in terms of
+
+ align:start position:0%
+uh we expressed it last time in terms of
+ 
+
+ align:start position:0%
+uh we expressed it last time in terms of
+switching period here I'm expressing it
+
+ align:start position:0%
+switching period here I'm expressing it
+ 
+
+ align:start position:0%
+switching period here I'm expressing it
+in terms of the switching
+
+ align:start position:0%
+in terms of the switching
+ 
+
+ align:start position:0%
+in terms of the switching
+frequency um the energy storage gets
+
+ align:start position:0%
+frequency um the energy storage gets
+ 
+
+ align:start position:0%
+frequency um the energy storage gets
+smaller if I go to a higher switching
+
+ align:start position:0%
+smaller if I go to a higher switching
+ 
+
+ align:start position:0%
+smaller if I go to a higher switching
+frequency so usually I'd like to switch
+
+ align:start position:0%
+frequency so usually I'd like to switch
+ 
+
+ align:start position:0%
+frequency so usually I'd like to switch
+as fast as I can commensurate with other
+
+ align:start position:0%
+as fast as I can commensurate with other
+ 
+
+ align:start position:0%
+as fast as I can commensurate with other
+constraints right because my energy
+
+ align:start position:0%
+constraints right because my energy
+ 
+
+ align:start position:0%
+constraints right because my energy
+storage got smaller my components will
+
+ align:start position:0%
+storage got smaller my components will
+ 
+
+ align:start position:0%
+storage got smaller my components will
+then hopefully get smaller life is good
+
+ align:start position:0%
+then hopefully get smaller life is good
+ 
+
+ align:start position:0%
+then hopefully get smaller life is good
+so there's been always a lot of effort
+
+ align:start position:0%
+so there's been always a lot of effort
+ 
+
+ align:start position:0%
+so there's been always a lot of effort
+to go as high as a frequency you can
+
+ align:start position:0%
+to go as high as a frequency you can
+ 
+
+ align:start position:0%
+to go as high as a frequency you can
+until we run into some other limits and
+
+ align:start position:0%
+until we run into some other limits and
+ 
+
+ align:start position:0%
+until we run into some other limits and
+we'll talk about those limits loss being
+
+ align:start position:0%
+we'll talk about those limits loss being
+ 
+
+ align:start position:0%
+we'll talk about those limits loss being
+one of them okay and I will say that
+
+ align:start position:0%
+one of them okay and I will say that
+ 
+
+ align:start position:0%
+one of them okay and I will say that
+everything we just said about the
+
+ align:start position:0%
+everything we just said about the
+ 
+
+ align:start position:0%
+everything we just said about the
+capacitor we could say in the inductor
+
+ align:start position:0%
+capacitor we could say in the inductor
+ 
+
+ align:start position:0%
+capacitor we could say in the inductor
+and I should note that in this set of
+
+ align:start position:0%
+and I should note that in this set of
+ 
+
+ align:start position:0%
+and I should note that in this set of
+lectures notes I think I wrote 1 minus D
+
+ align:start position:0%
+lectures notes I think I wrote 1 minus D
+ 
+
+ align:start position:0%
+lectures notes I think I wrote 1 minus D
+here and this should be D which is is
+
+ align:start position:0%
+here and this should be D which is is
+ 
+
+ align:start position:0%
+here and this should be D which is is
+correct in the last set of leure notes
+
+ align:start position:0%
+correct in the last set of leure notes
+ 
+
+ align:start position:0%
+correct in the last set of leure notes
+okay but nonetheless the same ideas
+
+ align:start position:0%
+okay but nonetheless the same ideas
+ 
+
+ align:start position:0%
+okay but nonetheless the same ideas
+pertain smaller Ripple means larger
+
+ align:start position:0%
+pertain smaller Ripple means larger
+ 
+
+ align:start position:0%
+pertain smaller Ripple means larger
+energy storage requirement larger
+
+ align:start position:0%
+energy storage requirement larger
+ 
+
+ align:start position:0%
+energy storage requirement larger
+conversion ratio means larger energy
+
+ align:start position:0%
+conversion ratio means larger energy
+ 
+
+ align:start position:0%
+conversion ratio means larger energy
+storage requirement and higher frequency
+
+ align:start position:0%
+storage requirement and higher frequency
+ 
+
+ align:start position:0%
+storage requirement and higher frequency
+means lower energy storage requirements
+
+ align:start position:0%
+means lower energy storage requirements
+ 
+
+ align:start position:0%
+means lower energy storage requirements
+okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay I'd like to keep talking
+
+ align:start position:0%
+that okay I'd like to keep talking
+ 
+
+ align:start position:0%
+that okay I'd like to keep talking
+about this notion of um conversion and
+
+ align:start position:0%
+about this notion of um conversion and
+ 
+
+ align:start position:0%
+about this notion of um conversion and
+the Ripple you see in your converters
+
+ align:start position:0%
+the Ripple you see in your converters
+ 
+
+ align:start position:0%
+the Ripple you see in your converters
+because we haven't actually sort of
+
+ align:start position:0%
+because we haven't actually sort of
+ 
+
+ align:start position:0%
+because we haven't actually sort of
+gotten to all possible cases yet okay
+
+ align:start position:0%
+gotten to all possible cases yet okay
+ 
+
+ align:start position:0%
+gotten to all possible cases yet okay
+and let's just go think about this boost
+
+ align:start position:0%
+and let's just go think about this boost
+ 
+
+ align:start position:0%
+and let's just go think about this boost
+converter okay and what we'll do is
+
+ align:start position:0%
+converter okay and what we'll do is
+ 
+
+ align:start position:0%
+converter okay and what we'll do is
+let's think about the inductor current
+
+ align:start position:0%
+let's think about the inductor current
+ 
+
+ align:start position:0%
+let's think about the inductor current
+and I'll think about the inductor
+
+ align:start position:0%
+and I'll think about the inductor
+ 
+
+ align:start position:0%
+and I'll think about the inductor
+voltage vabel here okay so if I'm
+
+ align:start position:0%
+voltage vabel here okay so if I'm
+ 
+
+ align:start position:0%
+voltage vabel here okay so if I'm
+switching my converter right I'm going
+
+ align:start position:0%
+switching my converter right I'm going
+ 
+
+ align:start position:0%
+switching my converter right I'm going
+to have some switching signal which is
+
+ align:start position:0%
+to have some switching signal which is
+ 
+
+ align:start position:0%
+to have some switching signal which is
+driving you know which is telling when
+
+ align:start position:0%
+driving you know which is telling when
+ 
+
+ align:start position:0%
+driving you know which is telling when
+this gate is turning on and off okay so
+
+ align:start position:0%
+this gate is turning on and off okay so
+ 
+
+ align:start position:0%
+this gate is turning on and off okay so
+I'll have some switching
+
+ align:start position:0%
+I'll have some switching
+ 
+
+ align:start position:0%
+I'll have some switching
+function that's doing this right so it's
+
+ align:start position:0%
+function that's doing this right so it's
+ 
+
+ align:start position:0%
+function that's doing this right so it's
+high for sometime
+
+ align:start position:0%
+high for sometime
+ 
+
+ align:start position:0%
+high for sometime
+DT and then it's low for some time and
+
+ align:start position:0%
+DT and then it's low for some time and
+ 
+
+ align:start position:0%
+DT and then it's low for some time and
+then it's high for some time you know
+
+ align:start position:0%
+then it's high for some time you know
+ 
+
+ align:start position:0%
+then it's high for some time you know
+after a period okay and then I can say
+
+ align:start position:0%
+after a period okay and then I can say
+ 
+
+ align:start position:0%
+after a period okay and then I can say
+okay well what does my inductor voltage
+
+ align:start position:0%
+okay well what does my inductor voltage
+ 
+
+ align:start position:0%
+okay well what does my inductor voltage
+do during that
+
+ align:start position:0%
+do during that
+ 
+
+ align:start position:0%
+do during that
+time okay well my inductor voltage is
+
+ align:start position:0%
+time okay well my inductor voltage is
+ 
+
+ align:start position:0%
+time okay well my inductor voltage is
+positive at V1 when I turn the switch
+
+ align:start position:0%
+positive at V1 when I turn the switch
+ 
+
+ align:start position:0%
+positive at V1 when I turn the switch
+on okay so it looks like
+
+ align:start position:0%
+on okay so it looks like
+ 
+
+ align:start position:0%
+on okay so it looks like
+this at Value
+
+ align:start position:0%
+this at Value
+ 
+
+ align:start position:0%
+this at Value
+V1 and then when I turn the switch off I
+
+ align:start position:0%
+V1 and then when I turn the switch off I
+ 
+
+ align:start position:0%
+V1 and then when I turn the switch off I
+have V1 minus V2 across it and I get
+
+ align:start position:0%
+have V1 minus V2 across it and I get
+ 
+
+ align:start position:0%
+have V1 minus V2 across it and I get
+some negative
+
+ align:start position:0%
+some negative
+ 
+
+ align:start position:0%
+some negative
+voltage okay and what we know is that in
+
+ align:start position:0%
+voltage okay and what we know is that in
+ 
+
+ align:start position:0%
+voltage okay and what we know is that in
+periodic steady state this area
+
+ align:start position:0%
+periodic steady state this area
+ 
+
+ align:start position:0%
+periodic steady state this area
+must equal this
+
+ align:start position:0%
+must equal this
+ 
+
+ align:start position:0%
+must equal this
+area and this ends up being V1 minus
+
+ align:start position:0%
+area and this ends up being V1 minus
+ 
+
+ align:start position:0%
+area and this ends up being V1 minus
+V2 okay and if I were to plot the
+
+ align:start position:0%
+V2 okay and if I were to plot the
+ 
+
+ align:start position:0%
+V2 okay and if I were to plot the
+current okay in the inductor what would
+
+ align:start position:0%
+current okay in the inductor what would
+ 
+
+ align:start position:0%
+current okay in the inductor what would
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+see okay over this same time
+
+ align:start position:0%
+see okay over this same time
+ 
+
+ align:start position:0%
+see okay over this same time
+period right I have some DC
+
+ align:start position:0%
+period right I have some DC
+ 
+
+ align:start position:0%
+period right I have some DC
+value in the inductor current which is
+
+ align:start position:0%
+value in the inductor current which is
+ 
+
+ align:start position:0%
+value in the inductor current which is
+i1 right the DC input current here is
+
+ align:start position:0%
+i1 right the DC input current here is
+ 
+
+ align:start position:0%
+i1 right the DC input current here is
+the DC current coming from the
+
+ align:start position:0%
+the DC current coming from the
+ 
+
+ align:start position:0%
+the DC current coming from the
+source okay
+
+ align:start position:0%
+source okay
+ 
+
+ align:start position:0%
+source okay
+and that's my average value and what
+
+ align:start position:0%
+and that's my average value and what
+ 
+
+ align:start position:0%
+and that's my average value and what
+we'll have is in the first part of the
+
+ align:start position:0%
+we'll have is in the first part of the
+ 
+
+ align:start position:0%
+we'll have is in the first part of the
+cycle I store energy in the inductor and
+
+ align:start position:0%
+cycle I store energy in the inductor and
+ 
+
+ align:start position:0%
+cycle I store energy in the inductor and
+I get this positive triangular Ripple
+
+ align:start position:0%
+I get this positive triangular Ripple
+ 
+
+ align:start position:0%
+I get this positive triangular Ripple
+and in the second part of the cycle I
+
+ align:start position:0%
+and in the second part of the cycle I
+ 
+
+ align:start position:0%
+and in the second part of the cycle I
+get negative slope and I have my
+
+ align:start position:0%
+get negative slope and I have my
+ 
+
+ align:start position:0%
+get negative slope and I have my
+periodic steady state waveform like this
+
+ align:start position:0%
+periodic steady state waveform like this
+ 
+
+ align:start position:0%
+periodic steady state waveform like this
+and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta I Peak to
+
+ align:start position:0%
+Delta I Peak to
+ 
+
+ align:start position:0%
+Delta I Peak to
+Peak okay so that that's what our
+
+ align:start position:0%
+Peak okay so that that's what our
+ 
+
+ align:start position:0%
+Peak okay so that that's what our
+waveforms look
+
+ align:start position:0%
+waveforms look
+ 
+
+ align:start position:0%
+waveforms look
+like okay so let's think about this in
+
+ align:start position:0%
+like okay so let's think about this in
+ 
+
+ align:start position:0%
+like okay so let's think about this in
+terms of Ripple ratio okay so what do I
+
+ align:start position:0%
+terms of Ripple ratio okay so what do I
+ 
+
+ align:start position:0%
+terms of Ripple ratio okay so what do I
+know um Delta i l Peak to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak is you know Delta I is V over L
+
+ align:start position:0%
+Peak is you know Delta I is V over L
+ 
+
+ align:start position:0%
+Peak is you know Delta I is V over L
+delta T right so V is V1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/ L time
+
+ align:start position:0%
+/ L time
+ 
+
+ align:start position:0%
+/ L time
+GT right so this is an expression of how
+
+ align:start position:0%
+GT right so this is an expression of how
+ 
+
+ align:start position:0%
+GT right so this is an expression of how
+much I Rise I'm applying V1 for time DT
+
+ align:start position:0%
+much I Rise I'm applying V1 for time DT
+ 
+
+ align:start position:0%
+much I Rise I'm applying V1 for time DT
+so the Delta is V1 over L
+
+ align:start position:0%
+so the Delta is V1 over L
+ 
+
+ align:start position:0%
+so the Delta is V1 over L
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+okay what is the input current
+
+ align:start position:0%
+okay what is the input current
+ 
+
+ align:start position:0%
+okay what is the input current
+i1 okay what what's i1 going to be well
+
+ align:start position:0%
+i1 okay what what's i1 going to be well
+ 
+
+ align:start position:0%
+i1 okay what what's i1 going to be well
+um the the DC output current is going to
+
+ align:start position:0%
+um the the DC output current is going to
+ 
+
+ align:start position:0%
+um the the DC output current is going to
+be V2 / by whatever this resistor is
+
+ align:start position:0%
+be V2 / by whatever this resistor is
+ 
+
+ align:start position:0%
+be V2 / by whatever this resistor is
+right so if I wanted I2 I would have
+
+ align:start position:0%
+right so if I wanted I2 I would have
+ 
+
+ align:start position:0%
+right so if I wanted I2 I would have
+V2 ID R but this is I2 how does I2
+
+ align:start position:0%
+V2 ID R but this is I2 how does I2
+ 
+
+ align:start position:0%
+V2 ID R but this is I2 how does I2
+relate to i1 I I2 is going to be i1 over
+
+ align:start position:0%
+relate to i1 I I2 is going to be i1 over
+ 
+
+ align:start position:0%
+relate to i1 I I2 is going to be i1 over
+1 minus
+
+ align:start position:0%
+1 minus
+ 
+
+ align:start position:0%
+1 minus
+d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because i1 is bigger than I2 right
+
+ align:start position:0%
+right because i1 is bigger than I2 right
+ 
+
+ align:start position:0%
+right because i1 is bigger than I2 right
+that's just this is
+
+ align:start position:0%
+that's just this is
+ 
+
+ align:start position:0%
+that's just this is
+you know this factor is I2 and then this
+
+ align:start position:0%
+you know this factor is I2 and then this
+ 
+
+ align:start position:0%
+you know this factor is I2 and then this
+gives me 1 over 1 minus D gives me the
+
+ align:start position:0%
+gives me 1 over 1 minus D gives me the
+ 
+
+ align:start position:0%
+gives me 1 over 1 minus D gives me the
+conversion to i1 okay any question about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so then if I were to write the
+
+ align:start position:0%
+that so then if I were to write the
+ 
+
+ align:start position:0%
+that so then if I were to write the
+Ripple
+
+ align:start position:0%
+Ripple
+ 
+
+ align:start position:0%
+Ripple
+ratio right the Ripple ratio in the
+
+ align:start position:0%
+ratio right the Ripple ratio in the
+ 
+
+ align:start position:0%
+ratio right the Ripple ratio in the
+inductor in this example is simply equal
+
+ align:start position:0%
+inductor in this example is simply equal
+ 
+
+ align:start position:0%
+inductor in this example is simply equal
+to Delta I Peak to Peak over two divid
+
+ align:start position:0%
+to Delta I Peak to Peak over two divid
+ 
+
+ align:start position:0%
+to Delta I Peak to Peak over two divid
+by i
+
+ align:start position:0%
+by i
+ 
+
+ align:start position:0%
+by i
+l and this is also equal to I
+
+ align:start position:0%
+l and this is also equal to I
+ 
+
+ align:start position:0%
+l and this is also equal to I
+right and so this is going to give me V1
+
+ align:start position:0%
+right and so this is going to give me V1
+ 
+
+ align:start position:0%
+right and so this is going to give me V1
+DT over
+
+ align:start position:0%
+DT over
+ 
+
+ align:start position:0%
+DT over
+l so this is going to be um 2 l i
+
+ align:start position:0%
+l so this is going to be um 2 l i
+ 
+
+ align:start position:0%
+l so this is going to be um 2 l i
+subel is um
+
+ align:start position:0%
+subel is um
+ 
+
+ align:start position:0%
+subel is um
+V2 R * 1us
+
+ align:start position:0%
+V2 R * 1us
+ 
+
+ align:start position:0%
+V2 R * 1us
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and I can um rewrite this
+
+ align:start position:0%
+and I can um rewrite this
+ 
+
+ align:start position:0%
+and I can um rewrite this
+um in terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of I can get rid of um V1 and V2 here
+
+ align:start position:0%
+of I can get rid of um V1 and V2 here
+ 
+
+ align:start position:0%
+of I can get rid of um V1 and V2 here
+why because V2
+
+ align:start position:0%
+why because V2
+ 
+
+ align:start position:0%
+why because V2
+of V2 is going to be V1 over 1 minus D
+
+ align:start position:0%
+of V2 is going to be V1 over 1 minus D
+ 
+
+ align:start position:0%
+of V2 is going to be V1 over 1 minus D
+so I could rewrite this at V1 over 1
+
+ align:start position:0%
+so I could rewrite this at V1 over 1
+ 
+
+ align:start position:0%
+so I could rewrite this at V1 over 1
+minus D is
+
+ align:start position:0%
+minus D is
+ 
+
+ align:start position:0%
+minus D is
+V2 or V2 * 1 - D is V1 so I could
+
+ align:start position:0%
+V2 or V2 * 1 - D is V1 so I could
+ 
+
+ align:start position:0%
+V2 or V2 * 1 - D is V1 so I could
+rewrite this as d
+
+ align:start position:0%
+rewrite this as d
+ 
+
+ align:start position:0%
+rewrite this as d
+* 1 - d^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 t
+
+ align:start position:0%
+2 t
+ 
+
+ align:start position:0%
+2 t
+r over 2
+
+ align:start position:0%
+r over 2
+ 
+
+ align:start position:0%
+r over 2
+L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and what does this tell
+
+ align:start position:0%
+um and what does this tell
+ 
+
+ align:start position:0%
+um and what does this tell
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+well this says how you know essentially
+
+ align:start position:0%
+well this says how you know essentially
+ 
+
+ align:start position:0%
+well this says how you know essentially
+I'm asking what's this Ripple compared
+
+ align:start position:0%
+I'm asking what's this Ripple compared
+ 
+
+ align:start position:0%
+I'm asking what's this Ripple compared
+to the average value of my current right
+
+ align:start position:0%
+to the average value of my current right
+ 
+
+ align:start position:0%
+to the average value of my current right
+and we can see that the Ripple ratio
+
+ align:start position:0%
+and we can see that the Ripple ratio
+ 
+
+ align:start position:0%
+and we can see that the Ripple ratio
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+up as what it goes up when either R goes
+
+ align:start position:0%
+up as what it goes up when either R goes
+ 
+
+ align:start position:0%
+up as what it goes up when either R goes
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+or L goes
+
+ align:start position:0%
+or L goes
+ 
+
+ align:start position:0%
+or L goes
+down all right those are two things that
+
+ align:start position:0%
+down all right those are two things that
+ 
+
+ align:start position:0%
+down all right those are two things that
+will make the Ripple ratio bigger right
+
+ align:start position:0%
+will make the Ripple ratio bigger right
+ 
+
+ align:start position:0%
+will make the Ripple ratio bigger right
+and that makes sense right
+
+ align:start position:0%
+and that makes sense right
+ 
+
+ align:start position:0%
+and that makes sense right
+it making L smaller is going to make the
+
+ align:start position:0%
+it making L smaller is going to make the
+ 
+
+ align:start position:0%
+it making L smaller is going to make the
+Ripple ratio bigger because I have a
+
+ align:start position:0%
+Ripple ratio bigger because I have a
+ 
+
+ align:start position:0%
+Ripple ratio bigger because I have a
+higher Ripple on the
+
+ align:start position:0%
+higher Ripple on the
+ 
+
+ align:start position:0%
+higher Ripple on the
+inductor okay any questions about
+
+ align:start position:0%
+inductor okay any questions about
+ 
+
+ align:start position:0%
+inductor okay any questions about
+that yeah the DC values of the currents
+
+ align:start position:0%
+that yeah the DC values of the currents
+ 
+
+ align:start position:0%
+that yeah the DC values of the currents
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+L uh the DC vales are ignoring loss yeah
+
+ align:start position:0%
+L uh the DC vales are ignoring loss yeah
+ 
+
+ align:start position:0%
+L uh the DC vales are ignoring loss yeah
+there's no loss this is a perfect
+
+ align:start position:0%
+there's no loss this is a perfect
+ 
+
+ align:start position:0%
+there's no loss this is a perfect
+converter everything's lossless yeah you
+
+ align:start position:0%
+converter everything's lossless yeah you
+ 
+
+ align:start position:0%
+converter everything's lossless yeah you
+throw in loss and things happen right
+
+ align:start position:0%
+throw in loss and things happen right
+ 
+
+ align:start position:0%
+throw in loss and things happen right
+right now I'm treating everything as
+
+ align:start position:0%
+right now I'm treating everything as
+ 
+
+ align:start position:0%
+right now I'm treating everything as
+being perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's start to think about the impact
+
+ align:start position:0%
+so let's start to think about the impact
+ 
+
+ align:start position:0%
+so let's start to think about the impact
+of changing sort of
+
+ align:start position:0%
+of changing sort of
+ 
+
+ align:start position:0%
+of changing sort of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+resistance and inductance so let me
+
+ align:start position:0%
+resistance and inductance so let me
+ 
+
+ align:start position:0%
+resistance and inductance so let me
+replot this so let me plot I again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay and we said okay maybe I have
+
+ align:start position:0%
+right okay and we said okay maybe I have
+ 
+
+ align:start position:0%
+right okay and we said okay maybe I have
+some average
+
+ align:start position:0%
+some average
+ 
+
+ align:start position:0%
+some average
+value and I have some Ripple that does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and so forth okay and this is at
+
+ align:start position:0%
+this and so forth okay and this is at
+ 
+
+ align:start position:0%
+this and so forth okay and this is at
+some resistance value what would happen
+
+ align:start position:0%
+some resistance value what would happen
+ 
+
+ align:start position:0%
+some resistance value what would happen
+if I increase my resistance
+
+ align:start position:0%
+if I increase my resistance
+ 
+
+ align:start position:0%
+if I increase my resistance
+value okay well up here I see if I
+
+ align:start position:0%
+value okay well up here I see if I
+ 
+
+ align:start position:0%
+value okay well up here I see if I
+increase my resistance value I increase
+
+ align:start position:0%
+increase my resistance value I increase
+ 
+
+ align:start position:0%
+increase my resistance value I increase
+the Ripple ratio but how does it change
+
+ align:start position:0%
+the Ripple ratio but how does it change
+ 
+
+ align:start position:0%
+the Ripple ratio but how does it change
+the IL waveforms this is I okay but if I
+
+ align:start position:0%
+the IL waveforms this is I okay but if I
+ 
+
+ align:start position:0%
+the IL waveforms this is I okay but if I
+used a bigger resistance value what
+
+ align:start position:0%
+used a bigger resistance value what
+ 
+
+ align:start position:0%
+used a bigger resistance value what
+might happen happens it might look like
+
+ align:start position:0%
+might happen happens it might look like
+ 
+
+ align:start position:0%
+might happen happens it might look like
+this I will have some lower current
+
+ align:start position:0%
+this I will have some lower current
+ 
+
+ align:start position:0%
+this I will have some lower current
+right to supply the same
+
+ align:start position:0%
+right to supply the same
+ 
+
+ align:start position:0%
+right to supply the same
+voltage at the
+
+ align:start position:0%
+voltage at the
+ 
+
+ align:start position:0%
+voltage at the
+output if I if I doubled my resistance I
+
+ align:start position:0%
+output if I if I doubled my resistance I
+ 
+
+ align:start position:0%
+output if I if I doubled my resistance I
+need have the current half the current
+
+ align:start position:0%
+need have the current half the current
+ 
+
+ align:start position:0%
+need have the current half the current
+to get to the same output voltage if my
+
+ align:start position:0%
+to get to the same output voltage if my
+ 
+
+ align:start position:0%
+to get to the same output voltage if my
+output current halves my input current
+
+ align:start position:0%
+output current halves my input current
+ 
+
+ align:start position:0%
+output current halves my input current
+halves and that means my inductor
+
+ align:start position:0%
+halves and that means my inductor
+ 
+
+ align:start position:0%
+halves and that means my inductor
+current on average halves so okay I get
+
+ align:start position:0%
+current on average halves so okay I get
+ 
+
+ align:start position:0%
+current on average halves so okay I get
+I reduced the average inductor current
+
+ align:start position:0%
+I reduced the average inductor current
+ 
+
+ align:start position:0%
+I reduced the average inductor current
+but V1 and V2 have stayed the same right
+
+ align:start position:0%
+but V1 and V2 have stayed the same right
+ 
+
+ align:start position:0%
+but V1 and V2 have stayed the same right
+and if V1 and V2 have stayed the same
+
+ align:start position:0%
+and if V1 and V2 have stayed the same
+ 
+
+ align:start position:0%
+and if V1 and V2 have stayed the same
+the slope on the Ripple is stayed the
+
+ align:start position:0%
+the slope on the Ripple is stayed the
+ 
+
+ align:start position:0%
+the slope on the Ripple is stayed the
+same right so my inductor current at a
+
+ align:start position:0%
+same right so my inductor current at a
+ 
+
+ align:start position:0%
+same right so my inductor current at a
+higher resistance might look like this
+
+ align:start position:0%
+higher resistance might look like this
+ 
+
+ align:start position:0%
+higher resistance might look like this
+okay this is parallel this is parallel
+
+ align:start position:0%
+okay this is parallel this is parallel
+ 
+
+ align:start position:0%
+okay this is parallel this is parallel
+and so forth and I get this so this is i
+
+ align:start position:0%
+and so forth and I get this so this is i
+ 
+
+ align:start position:0%
+and so forth and I get this so this is i
+l you know this is I at R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small this is I at RL medium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would happen if I kept increasing
+
+ align:start position:0%
+what would happen if I kept increasing
+ 
+
+ align:start position:0%
+what would happen if I kept increasing
+my resistance value well all we saw is
+
+ align:start position:0%
+my resistance value well all we saw is
+ 
+
+ align:start position:0%
+my resistance value well all we saw is
+the waveform doesn't the waveform shape
+
+ align:start position:0%
+the waveform doesn't the waveform shape
+ 
+
+ align:start position:0%
+the waveform doesn't the waveform shape
+just doesn't change the average just
+
+ align:start position:0%
+just doesn't change the average just
+ 
+
+ align:start position:0%
+just doesn't change the average just
+moves down right the Ripple is the same
+
+ align:start position:0%
+moves down right the Ripple is the same
+ 
+
+ align:start position:0%
+moves down right the Ripple is the same
+but the DC value is changing because I
+
+ align:start position:0%
+but the DC value is changing because I
+ 
+
+ align:start position:0%
+but the DC value is changing because I
+need more or less average current to
+
+ align:start position:0%
+need more or less average current to
+ 
+
+ align:start position:0%
+need more or less average current to
+support the output and more or less
+
+ align:start position:0%
+support the output and more or less
+ 
+
+ align:start position:0%
+support the output and more or less
+average power draw to support the
+
+ align:start position:0%
+average power draw to support the
+ 
+
+ align:start position:0%
+average power draw to support the
+output So eventually what's going to
+
+ align:start position:0%
+output So eventually what's going to
+ 
+
+ align:start position:0%
+output So eventually what's going to
+happen is we're going to get something
+
+ align:start position:0%
+happen is we're going to get something
+ 
+
+ align:start position:0%
+happen is we're going to get something
+that we hit another mode of operation
+
+ align:start position:0%
+that we hit another mode of operation
+ 
+
+ align:start position:0%
+that we hit another mode of operation
+we're going to get something where does
+
+ align:start position:0%
+we're going to get something where does
+ 
+
+ align:start position:0%
+we're going to get something where does
+this I'm going to turn my switch
+
+ align:start position:0%
+this I'm going to turn my switch
+ 
+
+ align:start position:0%
+this I'm going to turn my switch
+on and then it's going to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down and then
+
+ align:start position:0%
+down and then
+ 
+
+ align:start position:0%
+down and then
+stop okay so here this is supposed to be
+
+ align:start position:0%
+stop okay so here this is supposed to be
+ 
+
+ align:start position:0%
+stop okay so here this is supposed to be
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+DT okay and here's the same
+
+ align:start position:0%
+DT okay and here's the same
+ 
+
+ align:start position:0%
+DT okay and here's the same
+T okay but I'm going to get this time
+
+ align:start position:0%
+T okay but I'm going to get this time
+ 
+
+ align:start position:0%
+T okay but I'm going to get this time
+period where the current comes down to
+
+ align:start position:0%
+period where the current comes down to
+ 
+
+ align:start position:0%
+period where the current comes down to
+zero now why am I not drawing the
+
+ align:start position:0%
+zero now why am I not drawing the
+ 
+
+ align:start position:0%
+zero now why am I not drawing the
+current is going negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can't really get a negative current
+
+ align:start position:0%
+I can't really get a negative current
+ 
+
+ align:start position:0%
+I can't really get a negative current
+through the diode right so once the
+
+ align:start position:0%
+through the diode right so once the
+ 
+
+ align:start position:0%
+through the diode right so once the
+inductor current ramps down to zero the
+
+ align:start position:0%
+inductor current ramps down to zero the
+ 
+
+ align:start position:0%
+inductor current ramps down to zero the
+diode's going to turn off whereas the
+
+ align:start position:0%
+diode's going to turn off whereas the
+ 
+
+ align:start position:0%
+diode's going to turn off whereas the
+diode was conducting before okay so I
+
+ align:start position:0%
+diode was conducting before okay so I
+ 
+
+ align:start position:0%
+diode was conducting before okay so I
+could build a converter where this was
+
+ align:start position:0%
+could build a converter where this was
+ 
+
+ align:start position:0%
+could build a converter where this was
+an active switch and Allowed by
+
+ align:start position:0%
+an active switch and Allowed by
+ 
+
+ align:start position:0%
+an active switch and Allowed by
+directional current and people do that
+
+ align:start position:0%
+directional current and people do that
+ 
+
+ align:start position:0%
+directional current and people do that
+but if I'm going to build it with a
+
+ align:start position:0%
+but if I'm going to build it with a
+ 
+
+ align:start position:0%
+but if I'm going to build it with a
+diode I'm going to get this alternative
+
+ align:start position:0%
+diode I'm going to get this alternative
+ 
+
+ align:start position:0%
+diode I'm going to get this alternative
+State okay so in this alternative state
+
+ align:start position:0%
+State okay so in this alternative state
+ 
+
+ align:start position:0%
+State okay so in this alternative state
+right what do I have in this Ty here I
+
+ align:start position:0%
+right what do I have in this Ty here I
+ 
+
+ align:start position:0%
+right what do I have in this Ty here I
+have the switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on here I have the diode
+
+ align:start position:0%
+on here I have the diode
+ 
+
+ align:start position:0%
+on here I have the diode
+on okay and in this time period
+
+ align:start position:0%
+on okay and in this time period
+ 
+
+ align:start position:0%
+on okay and in this time period
+everything is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off okay so we haven't considered this
+
+ align:start position:0%
+off okay so we haven't considered this
+ 
+
+ align:start position:0%
+off okay so we haven't considered this
+mode of operation right we always
+
+ align:start position:0%
+mode of operation right we always
+ 
+
+ align:start position:0%
+mode of operation right we always
+assumed it was either the switch or the
+
+ align:start position:0%
+assumed it was either the switch or the
+ 
+
+ align:start position:0%
+assumed it was either the switch or the
+diode that was
+
+ align:start position:0%
+diode that was
+ 
+
+ align:start position:0%
+diode that was
+conducting now I'm telling you hey if I
+
+ align:start position:0%
+conducting now I'm telling you hey if I
+ 
+
+ align:start position:0%
+conducting now I'm telling you hey if I
+make R big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how big is Big we'll get into that
+
+ align:start position:0%
+and how big is Big we'll get into that
+ 
+
+ align:start position:0%
+and how big is Big we'll get into that
+but if I make RL big enough the average
+
+ align:start position:0%
+but if I make RL big enough the average
+ 
+
+ align:start position:0%
+but if I make RL big enough the average
+current goes down to the fact that my
+
+ align:start position:0%
+current goes down to the fact that my
+ 
+
+ align:start position:0%
+current goes down to the fact that my
+current Ripple is going to make me hit
+
+ align:start position:0%
+current Ripple is going to make me hit
+ 
+
+ align:start position:0%
+current Ripple is going to make me hit
+zero current and I'm going to get this
+
+ align:start position:0%
+zero current and I'm going to get this
+ 
+
+ align:start position:0%
+zero current and I'm going to get this
+new kind of funny
+
+ align:start position:0%
+new kind of funny
+ 
+
+ align:start position:0%
+new kind of funny
+state does that make sense to
+
+ align:start position:0%
+state does that make sense to
+ 
+
+ align:start position:0%
+state does that make sense to
+everybody so this is what happens with
+
+ align:start position:0%
+everybody so this is what happens with
+ 
+
+ align:start position:0%
+everybody so this is what happens with
+variations with
+
+ align:start position:0%
+variations with
+ 
+
+ align:start position:0%
+variations with
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+okay what happens with variations in
+
+ align:start position:0%
+okay what happens with variations in
+ 
+
+ align:start position:0%
+okay what happens with variations in
+inductance well slightly
+
+ align:start position:0%
+inductance well slightly
+ 
+
+ align:start position:0%
+inductance well slightly
+different okay maybe what I have is this
+
+ align:start position:0%
+different okay maybe what I have is this
+ 
+
+ align:start position:0%
+different okay maybe what I have is this
+okay I will have again um some value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I maybe this actually maybe maybe make
+
+ align:start position:0%
+I maybe this actually maybe maybe make
+ 
+
+ align:start position:0%
+I maybe this actually maybe maybe make
+it a little smaller I have some average
+
+ align:start position:0%
+it a little smaller I have some average
+ 
+
+ align:start position:0%
+it a little smaller I have some average
+value of I that I'm generating and if I
+
+ align:start position:0%
+value of I that I'm generating and if I
+ 
+
+ align:start position:0%
+value of I that I'm generating and if I
+have some big inductance maybe my ripple
+
+ align:start position:0%
+have some big inductance maybe my ripple
+ 
+
+ align:start position:0%
+have some big inductance maybe my ripple
+is small so it does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is i l l
+
+ align:start position:0%
+right so this is i l l
+ 
+
+ align:start position:0%
+right so this is i l l
+big right have a big inductance in there
+
+ align:start position:0%
+big right have a big inductance in there
+ 
+
+ align:start position:0%
+big right have a big inductance in there
+the Ripple's relatively
+
+ align:start position:0%
+the Ripple's relatively
+ 
+
+ align:start position:0%
+the Ripple's relatively
+small if I got a bit smaller inductor I
+
+ align:start position:0%
+small if I got a bit smaller inductor I
+ 
+
+ align:start position:0%
+small if I got a bit smaller inductor I
+I turn off my converter I pull out one
+
+ align:start position:0%
+I turn off my converter I pull out one
+ 
+
+ align:start position:0%
+I turn off my converter I pull out one
+inductor I put in a new inductor that's
+
+ align:start position:0%
+inductor I put in a new inductor that's
+ 
+
+ align:start position:0%
+inductor I put in a new inductor that's
+half the value what would happen well
+
+ align:start position:0%
+half the value what would happen well
+ 
+
+ align:start position:0%
+half the value what would happen well
+the Ripple would increase right and I
+
+ align:start position:0%
+the Ripple would increase right and I
+ 
+
+ align:start position:0%
+the Ripple would increase right and I
+would get something that did
+
+ align:start position:0%
+would get something that did
+ 
+
+ align:start position:0%
+would get something that did
+this right the Delta I Peak to Peak is
+
+ align:start position:0%
+this right the Delta I Peak to Peak is
+ 
+
+ align:start position:0%
+this right the Delta I Peak to Peak is
+inversely proportional to L so my ripple
+
+ align:start position:0%
+inversely proportional to L so my ripple
+ 
+
+ align:start position:0%
+inversely proportional to L so my ripple
+current would in was a terrible drawing
+
+ align:start position:0%
+current would in was a terrible drawing
+ 
+
+ align:start position:0%
+current would in was a terrible drawing
+my ripple current would
+
+ align:start position:0%
+my ripple current would
+ 
+
+ align:start position:0%
+my ripple current would
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+okay if I turn the converter off and
+
+ align:start position:0%
+okay if I turn the converter off and
+ 
+
+ align:start position:0%
+okay if I turn the converter off and
+then I put in even a smaller inductor
+
+ align:start position:0%
+then I put in even a smaller inductor
+ 
+
+ align:start position:0%
+then I put in even a smaller inductor
+what would happen if I get a really
+
+ align:start position:0%
+what would happen if I get a really
+ 
+
+ align:start position:0%
+what would happen if I get a really
+small inductor I pull a smallest
+
+ align:start position:0%
+small inductor I pull a smallest
+ 
+
+ align:start position:0%
+small inductor I pull a smallest
+inductor I can find in my kit maybe I
+
+ align:start position:0%
+inductor I can find in my kit maybe I
+ 
+
+ align:start position:0%
+inductor I can find in my kit maybe I
+get a waveform that does
+
+ align:start position:0%
+get a waveform that does
+ 
+
+ align:start position:0%
+get a waveform that does
+this starts at zero comes down hits zero
+
+ align:start position:0%
+this starts at zero comes down hits zero
+ 
+
+ align:start position:0%
+this starts at zero comes down hits zero
+and then stays at zero okay so I'm going
+
+ align:start position:0%
+and then stays at zero okay so I'm going
+ 
+
+ align:start position:0%
+and then stays at zero okay so I'm going
+to get a again a case where um I have
+
+ align:start position:0%
+to get a again a case where um I have
+ 
+
+ align:start position:0%
+to get a again a case where um I have
+the diode
+
+ align:start position:0%
+the diode
+ 
+
+ align:start position:0%
+the diode
+on and then I have I'm sorry I have the
+
+ align:start position:0%
+on and then I have I'm sorry I have the
+ 
+
+ align:start position:0%
+on and then I have I'm sorry I have the
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+on in this case and this is only
+
+ align:start position:0%
+on in this case and this is only
+ 
+
+ align:start position:0%
+on in this case and this is only
+pertaining to this bottom picture the
+
+ align:start position:0%
+pertaining to this bottom picture the
+ 
+
+ align:start position:0%
+pertaining to this bottom picture the
+diode's
+
+ align:start position:0%
+diode's
+ 
+
+ align:start position:0%
+diode's
+on and then I get a time period where
+
+ align:start position:0%
+on and then I get a time period where
+ 
+
+ align:start position:0%
+on and then I get a time period where
+both are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off okay and this is a different mode of
+
+ align:start position:0%
+off okay and this is a different mode of
+ 
+
+ align:start position:0%
+off okay and this is a different mode of
+operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is
+
+ align:start position:0%
+that this is
+ 
+
+ align:start position:0%
+that this is
+um this mode of
+
+ align:start position:0%
+um this mode of
+ 
+
+ align:start position:0%
+um this mode of
+operation uh is known as discontinuous
+
+ align:start position:0%
+operation uh is known as discontinuous
+ 
+
+ align:start position:0%
+operation uh is known as discontinuous
+conduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mode it's often abbreviated DCM
+
+ align:start position:0%
+mode it's often abbreviated DCM
+ 
+
+ align:start position:0%
+mode it's often abbreviated DCM
+okay now when we say discontinuous
+
+ align:start position:0%
+okay now when we say discontinuous
+ 
+
+ align:start position:0%
+okay now when we say discontinuous
+there's nothing discontinuous about the
+
+ align:start position:0%
+there's nothing discontinuous about the
+ 
+
+ align:start position:0%
+there's nothing discontinuous about the
+inductor current obviously the inductor
+
+ align:start position:0%
+inductor current obviously the inductor
+ 
+
+ align:start position:0%
+inductor current obviously the inductor
+current is always a continuous waveform
+
+ align:start position:0%
+current is always a continuous waveform
+ 
+
+ align:start position:0%
+current is always a continuous waveform
+but what it's what's meant by that is
+
+ align:start position:0%
+but what it's what's meant by that is
+ 
+
+ align:start position:0%
+but what it's what's meant by that is
+it's not continuously flowing positive
+
+ align:start position:0%
+it's not continuously flowing positive
+ 
+
+ align:start position:0%
+it's not continuously flowing positive
+and negative right it it has this third
+
+ align:start position:0%
+and negative right it it has this third
+ 
+
+ align:start position:0%
+and negative right it it has this third
+state where both devices are off okay
+
+ align:start position:0%
+state where both devices are off okay
+ 
+
+ align:start position:0%
+state where both devices are off okay
+and keep in mind that that's all the
+
+ align:start position:0%
+and keep in mind that that's all the
+ 
+
+ align:start position:0%
+and keep in mind that that's all the
+possible cases because I cannot have a
+
+ align:start position:0%
+possible cases because I cannot have a
+ 
+
+ align:start position:0%
+possible cases because I cannot have a
+case where both the switch and the diode
+
+ align:start position:0%
+case where both the switch and the diode
+ 
+
+ align:start position:0%
+case where both the switch and the diode
+are on the voltage is positive right
+
+ align:start position:0%
+are on the voltage is positive right
+ 
+
+ align:start position:0%
+are on the voltage is positive right
+that can't exist so we sort of exercise
+
+ align:start position:0%
+that can't exist so we sort of exercise
+ 
+
+ align:start position:0%
+that can't exist so we sort of exercise
+all the things that can
+
+ align:start position:0%
+all the things that can
+ 
+
+ align:start position:0%
+all the things that can
+happen right any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so when does this
+
+ align:start position:0%
+that so when does this
+ 
+
+ align:start position:0%
+that so when does this
+happen well right the Ripple ratio like
+
+ align:start position:0%
+happen well right the Ripple ratio like
+ 
+
+ align:start position:0%
+happen well right the Ripple ratio like
+if I were right at the edge of
+
+ align:start position:0%
+if I were right at the edge of
+ 
+
+ align:start position:0%
+if I were right at the edge of
+discontinuous conduction right you could
+
+ align:start position:0%
+discontinuous conduction right you could
+ 
+
+ align:start position:0%
+discontinuous conduction right you could
+imagine a situation where I pick some
+
+ align:start position:0%
+imagine a situation where I pick some
+ 
+
+ align:start position:0%
+imagine a situation where I pick some
+intermediate
+
+ align:start position:0%
+intermediate
+ 
+
+ align:start position:0%
+intermediate
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+of resistance for example in this case
+
+ align:start position:0%
+of resistance for example in this case
+ 
+
+ align:start position:0%
+of resistance for example in this case
+where it go does exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right that oops I didn't draw that
+
+ align:start position:0%
+this right that oops I didn't draw that
+ 
+
+ align:start position:0%
+this right that oops I didn't draw that
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+well right I'm sitting right at the edge
+
+ align:start position:0%
+well right I'm sitting right at the edge
+ 
+
+ align:start position:0%
+well right I'm sitting right at the edge
+right where yes my waveforms are
+
+ align:start position:0%
+right where yes my waveforms are
+ 
+
+ align:start position:0%
+right where yes my waveforms are
+continuous my my diode never turns off
+
+ align:start position:0%
+continuous my my diode never turns off
+ 
+
+ align:start position:0%
+continuous my my diode never turns off
+but only barely so right in that case
+
+ align:start position:0%
+but only barely so right in that case
+ 
+
+ align:start position:0%
+but only barely so right in that case
+the peak to Peak Ripple is exactly twice
+
+ align:start position:0%
+the peak to Peak Ripple is exactly twice
+ 
+
+ align:start position:0%
+the peak to Peak Ripple is exactly twice
+the average current or this case is
+
+ align:start position:0%
+the average current or this case is
+ 
+
+ align:start position:0%
+the average current or this case is
+Ripple ratio equal to
+
+ align:start position:0%
+Ripple ratio equal to
+ 
+
+ align:start position:0%
+Ripple ratio equal to
+one okay it's Rippling up from zero to
+
+ align:start position:0%
+one okay it's Rippling up from zero to
+ 
+
+ align:start position:0%
+one okay it's Rippling up from zero to
+twice the average and back down to zero
+
+ align:start position:0%
+twice the average and back down to zero
+ 
+
+ align:start position:0%
+twice the average and back down to zero
+it's still a triangle wave it's not this
+
+ align:start position:0%
+it's still a triangle wave it's not this
+ 
+
+ align:start position:0%
+it's still a triangle wave it's not this
+funny clipped triangle wave it's still a
+
+ align:start position:0%
+funny clipped triangle wave it's still a
+ 
+
+ align:start position:0%
+funny clipped triangle wave it's still a
+pure triangle wave and that's exactly
+
+ align:start position:0%
+pure triangle wave and that's exactly
+ 
+
+ align:start position:0%
+pure triangle wave and that's exactly
+the Ripple ratio equal to one case does
+
+ align:start position:0%
+the Ripple ratio equal to one case does
+ 
+
+ align:start position:0%
+the Ripple ratio equal to one case does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+everybody so what do I get from
+
+ align:start position:0%
+everybody so what do I get from
+ 
+
+ align:start position:0%
+everybody so what do I get from
+that well
+
+ align:start position:0%
+that well
+ 
+
+ align:start position:0%
+that well
+we can come back and just calculate what
+
+ align:start position:0%
+we can come back and just calculate what
+ 
+
+ align:start position:0%
+we can come back and just calculate what
+happens I have my expression for ripple
+
+ align:start position:0%
+happens I have my expression for ripple
+ 
+
+ align:start position:0%
+happens I have my expression for ripple
+ratio is equal to one so I can write
+
+ align:start position:0%
+ratio is equal to one so I can write
+ 
+
+ align:start position:0%
+ratio is equal to one so I can write
+that again here I get R subel is equal
+
+ align:start position:0%
+that again here I get R subel is equal
+ 
+
+ align:start position:0%
+that again here I get R subel is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+D * 1 - d^ 2 TR r/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2L and that's equal to one at the edge
+
+ align:start position:0%
+2L and that's equal to one at the edge
+ 
+
+ align:start position:0%
+2L and that's equal to one at the edge
+of DCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's where I transition between
+
+ align:start position:0%
+right that's where I transition between
+ 
+
+ align:start position:0%
+right that's where I transition between
+the two
+
+ align:start position:0%
+the two
+ 
+
+ align:start position:0%
+the two
+modes okay so from this we can say the
+
+ align:start position:0%
+modes okay so from this we can say the
+ 
+
+ align:start position:0%
+modes okay so from this we can say the
+DCM happens
+
+ align:start position:0%
+DCM happens
+ 
+
+ align:start position:0%
+DCM happens
+for R is greater
+
+ align:start position:0%
+for R is greater
+ 
+
+ align:start position:0%
+for R is greater
+than uh
+
+ align:start position:0%
+than uh
+ 
+
+ align:start position:0%
+than uh
+2L over D * 1 - d^
+
+ align:start position:0%
+2L over D * 1 - d^
+ 
+
+ align:start position:0%
+2L over D * 1 - d^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh t
+
+ align:start position:0%
+uh t
+ 
+
+ align:start position:0%
+uh t
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+or for L is less
+
+ align:start position:0%
+or for L is less
+ 
+
+ align:start position:0%
+or for L is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+um D * 1 - d^ 2
+
+ align:start position:0%
+um D * 1 - d^ 2
+ 
+
+ align:start position:0%
+um D * 1 - d^ 2
+T r/
+
+ align:start position:0%
+T r/
+ 
+
+ align:start position:0%
+T r/
+2 okay this is sometimes this value of
+
+ align:start position:0%
+2 okay this is sometimes this value of
+ 
+
+ align:start position:0%
+2 okay this is sometimes this value of
+L okay is sometimes called the critical
+
+ align:start position:0%
+L okay is sometimes called the critical
+ 
+
+ align:start position:0%
+L okay is sometimes called the critical
+inductance in the literature there's
+
+ align:start position:0%
+inductance in the literature there's
+ 
+
+ align:start position:0%
+inductance in the literature there's
+nothing very critical about it but all
+
+ align:start position:0%
+nothing very critical about it but all
+ 
+
+ align:start position:0%
+nothing very critical about it but all
+it's saying is if I go out and pick a
+
+ align:start position:0%
+it's saying is if I go out and pick a
+ 
+
+ align:start position:0%
+it's saying is if I go out and pick a
+big inductor bigger than this for the
+
+ align:start position:0%
+big inductor bigger than this for the
+ 
+
+ align:start position:0%
+big inductor bigger than this for the
+specified operating conditions I'm not
+
+ align:start position:0%
+specified operating conditions I'm not
+ 
+
+ align:start position:0%
+specified operating conditions I'm not
+going to run into discontinuous
+
+ align:start position:0%
+going to run into discontinuous
+ 
+
+ align:start position:0%
+going to run into discontinuous
+conduction
+
+ align:start position:0%
+conduction
+ 
+
+ align:start position:0%
+conduction
+okay but understand in a lot of cases
+
+ align:start position:0%
+okay but understand in a lot of cases
+ 
+
+ align:start position:0%
+okay but understand in a lot of cases
+you for some operating mode you're going
+
+ align:start position:0%
+you for some operating mode you're going
+ 
+
+ align:start position:0%
+you for some operating mode you're going
+to have to run into discontinuous
+
+ align:start position:0%
+to have to run into discontinuous
+ 
+
+ align:start position:0%
+to have to run into discontinuous
+conduction why because think about it
+
+ align:start position:0%
+conduction why because think about it
+ 
+
+ align:start position:0%
+conduction why because think about it
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+way I have to run for different load
+
+ align:start position:0%
+way I have to run for different load
+ 
+
+ align:start position:0%
+way I have to run for different load
+resistances right nobody I mean mostly
+
+ align:start position:0%
+resistances right nobody I mean mostly
+ 
+
+ align:start position:0%
+resistances right nobody I mean mostly
+in a power converter right you build a
+
+ align:start position:0%
+in a power converter right you build a
+ 
+
+ align:start position:0%
+in a power converter right you build a
+converter and then people hook loads up
+
+ align:start position:0%
+converter and then people hook loads up
+ 
+
+ align:start position:0%
+converter and then people hook loads up
+up to it you don't know what load they
+
+ align:start position:0%
+up to it you don't know what load they
+ 
+
+ align:start position:0%
+up to it you don't know what load they
+hook up to it right there's some maximum
+
+ align:start position:0%
+hook up to it right there's some maximum
+ 
+
+ align:start position:0%
+hook up to it right there's some maximum
+power rating but maybe they want to put
+
+ align:start position:0%
+power rating but maybe they want to put
+ 
+
+ align:start position:0%
+power rating but maybe they want to put
+very little load on it sometimes right
+
+ align:start position:0%
+very little load on it sometimes right
+ 
+
+ align:start position:0%
+very little load on it sometimes right
+maybe sometimes your microprocessor is
+
+ align:start position:0%
+maybe sometimes your microprocessor is
+ 
+
+ align:start position:0%
+maybe sometimes your microprocessor is
+running maybe sometimes it's not right
+
+ align:start position:0%
+running maybe sometimes it's not right
+ 
+
+ align:start position:0%
+running maybe sometimes it's not right
+and so you might have to deal with a
+
+ align:start position:0%
+and so you might have to deal with a
+ 
+
+ align:start position:0%
+and so you might have to deal with a
+very wide range of load currents up to
+
+ align:start position:0%
+very wide range of load currents up to
+ 
+
+ align:start position:0%
+very wide range of load currents up to
+some Maximum well if you have to deal
+
+ align:start position:0%
+some Maximum well if you have to deal
+ 
+
+ align:start position:0%
+some Maximum well if you have to deal
+with a very high load resistance or a
+
+ align:start position:0%
+with a very high load resistance or a
+ 
+
+ align:start position:0%
+with a very high load resistance or a
+very low load or a light load that means
+
+ align:start position:0%
+very low load or a light load that means
+ 
+
+ align:start position:0%
+very low load or a light load that means
+you're average is going to come down and
+
+ align:start position:0%
+you're average is going to come down and
+ 
+
+ align:start position:0%
+you're average is going to come down and
+down and down and the only way to keep
+
+ align:start position:0%
+down and down and the only way to keep
+ 
+
+ align:start position:0%
+down and down and the only way to keep
+it into CCM would be to use smaller
+
+ align:start position:0%
+it into CCM would be to use smaller
+ 
+
+ align:start position:0%
+it into CCM would be to use smaller
+smaller and smaller Ripple so you never
+
+ align:start position:0%
+smaller and smaller Ripple so you never
+ 
+
+ align:start position:0%
+smaller and smaller Ripple so you never
+hit that mode and the only way to do
+
+ align:start position:0%
+hit that mode and the only way to do
+ 
+
+ align:start position:0%
+hit that mode and the only way to do
+that is to get a bigger and bigger and
+
+ align:start position:0%
+that is to get a bigger and bigger and
+ 
+
+ align:start position:0%
+that is to get a bigger and bigger and
+bigger inductor but guess what you got
+
+ align:start position:0%
+bigger inductor but guess what you got
+ 
+
+ align:start position:0%
+bigger inductor but guess what you got
+to run it high load too and you run into
+
+ align:start position:0%
+to run it high load too and you run into
+ 
+
+ align:start position:0%
+to run it high load too and you run into
+this case where
+
+ align:start position:0%
+this case where
+ 
+
+ align:start position:0%
+this case where
+suddenly right if you've got if you've
+
+ align:start position:0%
+suddenly right if you've got if you've
+ 
+
+ align:start position:0%
+suddenly right if you've got if you've
+done that by a much bigger inductor
+
+ align:start position:0%
+done that by a much bigger inductor
+ 
+
+ align:start position:0%
+done that by a much bigger inductor
+suddenly you've gotten to the point
+
+ align:start position:0%
+suddenly you've gotten to the point
+ 
+
+ align:start position:0%
+suddenly you've gotten to the point
+where you've got a lot of inductor
+
+ align:start position:0%
+where you've got a lot of inductor
+ 
+
+ align:start position:0%
+where you've got a lot of inductor
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+storage right if you're if your Ripple
+
+ align:start position:0%
+storage right if you're if your Ripple
+ 
+
+ align:start position:0%
+storage right if you're if your Ripple
+ratio is small at light load it's really
+
+ align:start position:0%
+ratio is small at light load it's really
+ 
+
+ align:start position:0%
+ratio is small at light load it's really
+tiny at high load and this Factor will
+
+ align:start position:0%
+tiny at high load and this Factor will
+ 
+
+ align:start position:0%
+tiny at high load and this Factor will
+kill you you just have way too big a
+
+ align:start position:0%
+kill you you just have way too big a
+ 
+
+ align:start position:0%
+kill you you just have way too big a
+component so as a practical matter if
+
+ align:start position:0%
+component so as a practical matter if
+ 
+
+ align:start position:0%
+component so as a practical matter if
+you're going to run run over a really
+
+ align:start position:0%
+you're going to run run over a really
+ 
+
+ align:start position:0%
+you're going to run run over a really
+wide power range you might have to deal
+
+ align:start position:0%
+wide power range you might have to deal
+ 
+
+ align:start position:0%
+wide power range you might have to deal
+with DCM okay so we often design our
+
+ align:start position:0%
+with DCM okay so we often design our
+ 
+
+ align:start position:0%
+with DCM okay so we often design our
+converters for continuous conduction
+
+ align:start position:0%
+converters for continuous conduction
+ 
+
+ align:start position:0%
+converters for continuous conduction
+mode at full power but they might go
+
+ align:start position:0%
+mode at full power but they might go
+ 
+
+ align:start position:0%
+mode at full power but they might go
+into DCM if you're at very light load
+
+ align:start position:0%
+into DCM if you're at very light load
+ 
+
+ align:start position:0%
+into DCM if you're at very light load
+power any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay so what can we say about you know
+
+ align:start position:0%
+okay so what can we say about you know
+ 
+
+ align:start position:0%
+okay so what can we say about you know
+operating in this new Switch State okay
+
+ align:start position:0%
+operating in this new Switch State okay
+ 
+
+ align:start position:0%
+operating in this new Switch State okay
+well let's think about that what do our
+
+ align:start position:0%
+well let's think about that what do our
+ 
+
+ align:start position:0%
+well let's think about that what do our
+waveforms look like let's recreate our
+
+ align:start position:0%
+waveforms look like let's recreate our
+ 
+
+ align:start position:0%
+waveforms look like let's recreate our
+switching
+
+ align:start position:0%
+switching
+ 
+
+ align:start position:0%
+switching
+waveforms we said we were going to have
+
+ align:start position:0%
+waveforms we said we were going to have
+ 
+
+ align:start position:0%
+waveforms we said we were going to have
+some Duty ratio right for our switch and
+
+ align:start position:0%
+some Duty ratio right for our switch and
+ 
+
+ align:start position:0%
+some Duty ratio right for our switch and
+we were always focusing on the duty
+
+ align:start position:0%
+we were always focusing on the duty
+ 
+
+ align:start position:0%
+we were always focusing on the duty
+ratio of the switch and that's useful in
+
+ align:start position:0%
+ratio of the switch and that's useful in
+ 
+
+ align:start position:0%
+ratio of the switch and that's useful in
+CCM because you know the diode does
+
+ align:start position:0%
+CCM because you know the diode does
+ 
+
+ align:start position:0%
+CCM because you know the diode does
+exactly the opposite of what the switch
+
+ align:start position:0%
+exactly the opposite of what the switch
+ 
+
+ align:start position:0%
+exactly the opposite of what the switch
+does but now if we're going to talk
+
+ align:start position:0%
+does but now if we're going to talk
+ 
+
+ align:start position:0%
+does but now if we're going to talk
+about DC M we can't talk about that so
+
+ align:start position:0%
+about DC M we can't talk about that so
+ 
+
+ align:start position:0%
+about DC M we can't talk about that so
+here's Q of
+
+ align:start position:0%
+here's Q of
+ 
+
+ align:start position:0%
+here's Q of
+T right and Q of T is doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something so here's T
+
+ align:start position:0%
+something so here's T
+ 
+
+ align:start position:0%
+something so here's T
+DT here's Q of t for the
+
+ align:start position:0%
+DT here's Q of t for the
+ 
+
+ align:start position:0%
+DT here's Q of t for the
+switch but I might have then think okay
+
+ align:start position:0%
+switch but I might have then think okay
+ 
+
+ align:start position:0%
+switch but I might have then think okay
+maybe what I have is some Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subd This is the switching period for
+
+ align:start position:0%
+subd This is the switching period for
+ 
+
+ align:start position:0%
+subd This is the switching period for
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diode Q subd of T right the purple
+
+ align:start position:0%
+diode Q subd of T right the purple
+ 
+
+ align:start position:0%
+diode Q subd of T right the purple
+waveform tells me when the diode's on
+
+ align:start position:0%
+waveform tells me when the diode's on
+ 
+
+ align:start position:0%
+waveform tells me when the diode's on
+because now I have a time where the
+
+ align:start position:0%
+because now I have a time where the
+ 
+
+ align:start position:0%
+because now I have a time where the
+switch is on when the diod on and when
+
+ align:start position:0%
+switch is on when the diod on and when
+ 
+
+ align:start position:0%
+switch is on when the diod on and when
+neither are on all right and maybe this
+
+ align:start position:0%
+neither are on all right and maybe this
+ 
+
+ align:start position:0%
+neither are on all right and maybe this
+happens for some time you know this time
+
+ align:start position:0%
+happens for some time you know this time
+ 
+
+ align:start position:0%
+happens for some time you know this time
+period might might be um D + D2 * T so
+
+ align:start position:0%
+period might might be um D + D2 * T so
+ 
+
+ align:start position:0%
+period might might be um D + D2 * T so
+the diode runs with some Duty ratio
+
+ align:start position:0%
+the diode runs with some Duty ratio
+ 
+
+ align:start position:0%
+the diode runs with some Duty ratio
+D2 okay and you know to be in DCM D2 is
+
+ align:start position:0%
+D2 okay and you know to be in DCM D2 is
+ 
+
+ align:start position:0%
+D2 okay and you know to be in DCM D2 is
+less than 1us d right make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody so okay um we have this
+
+ align:start position:0%
+everybody so okay um we have this
+ 
+
+ align:start position:0%
+everybody so okay um we have this
+additional mode what does the voltage on
+
+ align:start position:0%
+additional mode what does the voltage on
+ 
+
+ align:start position:0%
+additional mode what does the voltage on
+the inductor look like right we were
+
+ align:start position:0%
+the inductor look like right we were
+ 
+
+ align:start position:0%
+the inductor look like right we were
+focusing you know we had the voltage on
+
+ align:start position:0%
+focusing you know we had the voltage on
+ 
+
+ align:start position:0%
+focusing you know we had the voltage on
+the inductor here what does he look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like well in the first part of the cycle
+
+ align:start position:0%
+like well in the first part of the cycle
+ 
+
+ align:start position:0%
+like well in the first part of the cycle
+he's at V1 right
+
+ align:start position:0%
+he's at V1 right
+ 
+
+ align:start position:0%
+he's at V1 right
+here's the voltage on the inductor he
+
+ align:start position:0%
+here's the voltage on the inductor he
+ 
+
+ align:start position:0%
+here's the voltage on the inductor he
+started at V1 in the first part of the
+
+ align:start position:0%
+started at V1 in the first part of the
+ 
+
+ align:start position:0%
+started at V1 in the first part of the
+cycle then when the switch turns off and
+
+ align:start position:0%
+cycle then when the switch turns off and
+ 
+
+ align:start position:0%
+cycle then when the switch turns off and
+the diode turns on he's at V1 minus
+
+ align:start position:0%
+the diode turns on he's at V1 minus
+ 
+
+ align:start position:0%
+the diode turns on he's at V1 minus
+V2
+
+ align:start position:0%
+V2
+ 
+
+ align:start position:0%
+V2
+okay and then he's on for a while until
+
+ align:start position:0%
+okay and then he's on for a while until
+ 
+
+ align:start position:0%
+okay and then he's on for a while until
+this second time period D plus D2 ends
+
+ align:start position:0%
+this second time period D plus D2 ends
+ 
+
+ align:start position:0%
+this second time period D plus D2 ends
+what happens if both the switch and the
+
+ align:start position:0%
+what happens if both the switch and the
+ 
+
+ align:start position:0%
+what happens if both the switch and the
+diode are
+
+ align:start position:0%
+diode are
+ 
+
+ align:start position:0%
+diode are
+off well if both the switch and the
+
+ align:start position:0%
+off well if both the switch and the
+ 
+
+ align:start position:0%
+off well if both the switch and the
+diode are off there's no current in the
+
+ align:start position:0%
+diode are off there's no current in the
+ 
+
+ align:start position:0%
+diode are off there's no current in the
+inductor there's no didt in the inductor
+
+ align:start position:0%
+inductor there's no didt in the inductor
+ 
+
+ align:start position:0%
+inductor there's no didt in the inductor
+if there's no didt in the inductor then
+
+ align:start position:0%
+if there's no didt in the inductor then
+ 
+
+ align:start position:0%
+if there's no didt in the inductor then
+there could be no voltage across the
+
+ align:start position:0%
+there could be no voltage across the
+ 
+
+ align:start position:0%
+there could be no voltage across the
+inductor and ideally this voltage across
+
+ align:start position:0%
+inductor and ideally this voltage across
+ 
+
+ align:start position:0%
+inductor and ideally this voltage across
+the inductor would have to go to zero
+
+ align:start position:0%
+the inductor would have to go to zero
+ 
+
+ align:start position:0%
+the inductor would have to go to zero
+okay so then I'm going to get a time
+
+ align:start position:0%
+okay so then I'm going to get a time
+ 
+
+ align:start position:0%
+okay so then I'm going to get a time
+period where the inductor voltage is
+
+ align:start position:0%
+period where the inductor voltage is
+ 
+
+ align:start position:0%
+period where the inductor voltage is
+zero until the end of the cycle okay so
+
+ align:start position:0%
+zero until the end of the cycle okay so
+ 
+
+ align:start position:0%
+zero until the end of the cycle okay so
+this is the ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waveforms for a discontinuous conduction
+
+ align:start position:0%
+waveforms for a discontinuous conduction
+ 
+
+ align:start position:0%
+waveforms for a discontinuous conduction
+mode where I'm plotting Vel of
+
+ align:start position:0%
+mode where I'm plotting Vel of
+ 
+
+ align:start position:0%
+mode where I'm plotting Vel of
+T okay and what do I have for periodic
+
+ align:start position:0%
+T okay and what do I have for periodic
+ 
+
+ align:start position:0%
+T okay and what do I have for periodic
+steady state requirement the average
+
+ align:start position:0%
+steady state requirement the average
+ 
+
+ align:start position:0%
+steady state requirement the average
+voltage across the inductor still has to
+
+ align:start position:0%
+voltage across the inductor still has to
+ 
+
+ align:start position:0%
+voltage across the inductor still has to
+be zero that means that this
+
+ align:start position:0%
+be zero that means that this
+ 
+
+ align:start position:0%
+be zero that means that this
+area now balances against this area Okay
+
+ align:start position:0%
+area now balances against this area Okay
+ 
+
+ align:start position:0%
+area now balances against this area Okay
+so the average the integral of this over
+
+ align:start position:0%
+so the average the integral of this over
+ 
+
+ align:start position:0%
+so the average the integral of this over
+the cycle still has to be
+
+ align:start position:0%
+the cycle still has to be
+ 
+
+ align:start position:0%
+the cycle still has to be
+zero does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody and if I just plotted the
+
+ align:start position:0%
+everybody and if I just plotted the
+ 
+
+ align:start position:0%
+everybody and if I just plotted the
+current to complete everything right in
+
+ align:start position:0%
+current to complete everything right in
+ 
+
+ align:start position:0%
+current to complete everything right in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case the current starts at zero and
+
+ align:start position:0%
+case the current starts at zero and
+ 
+
+ align:start position:0%
+case the current starts at zero and
+ramps
+
+ align:start position:0%
+ramps
+ 
+
+ align:start position:0%
+ramps
+up in the second part of the cycle it
+
+ align:start position:0%
+up in the second part of the cycle it
+ 
+
+ align:start position:0%
+up in the second part of the cycle it
+ramps down and then it sits at zero for
+
+ align:start position:0%
+ramps down and then it sits at zero for
+ 
+
+ align:start position:0%
+ramps down and then it sits at zero for
+the rest of the cycle until
+
+ align:start position:0%
+the rest of the cycle until
+ 
+
+ align:start position:0%
+the rest of the cycle until
+T okay and so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Isabel all right so this is what we're
+
+ align:start position:0%
+Isabel all right so this is what we're
+ 
+
+ align:start position:0%
+Isabel all right so this is what we're
+going to have in
+
+ align:start position:0%
+going to have in
+ 
+
+ align:start position:0%
+going to have in
+DCM
+
+ align:start position:0%
+DCM
+ 
+
+ align:start position:0%
+DCM
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the conversion ratio in DCM and
+
+ align:start position:0%
+what is the conversion ratio in DCM and
+ 
+
+ align:start position:0%
+what is the conversion ratio in DCM and
+I say well why why do I have to ask that
+
+ align:start position:0%
+I say well why why do I have to ask that
+ 
+
+ align:start position:0%
+I say well why why do I have to ask that
+question because previously how did I
+
+ align:start position:0%
+question because previously how did I
+ 
+
+ align:start position:0%
+question because previously how did I
+find the conversion ratio right the way
+
+ align:start position:0%
+find the conversion ratio right the way
+ 
+
+ align:start position:0%
+find the conversion ratio right the way
+we got that voltage conversion ratio is
+
+ align:start position:0%
+we got that voltage conversion ratio is
+ 
+
+ align:start position:0%
+we got that voltage conversion ratio is
+what we did was we said that V1 DT is
+
+ align:start position:0%
+what we did was we said that V1 DT is
+ 
+
+ align:start position:0%
+what we did was we said that V1 DT is
+actually equal has got to be equal to V2
+
+ align:start position:0%
+actually equal has got to be equal to V2
+ 
+
+ align:start position:0%
+actually equal has got to be equal to V2
+minus V1 * 1 minus DT right the average
+
+ align:start position:0%
+minus V1 * 1 minus DT right the average
+ 
+
+ align:start position:0%
+minus V1 * 1 minus DT right the average
+voltage across the inductor was Zero but
+
+ align:start position:0%
+voltage across the inductor was Zero but
+ 
+
+ align:start position:0%
+voltage across the inductor was Zero but
+that was based on this waveform our
+
+ align:start position:0%
+that was based on this waveform our
+ 
+
+ align:start position:0%
+that was based on this waveform our
+waveforms are now different so now we
+
+ align:start position:0%
+waveforms are now different so now we
+ 
+
+ align:start position:0%
+waveforms are now different so now we
+got to rec
+
+ align:start position:0%
+got to rec
+ 
+
+ align:start position:0%
+got to rec
+calculated okay but we can find the
+
+ align:start position:0%
+calculated okay but we can find the
+ 
+
+ align:start position:0%
+calculated okay but we can find the
+conversion ratio the same way we do it
+
+ align:start position:0%
+conversion ratio the same way we do it
+ 
+
+ align:start position:0%
+conversion ratio the same way we do it
+we know that the average voltage across
+
+ align:start position:0%
+we know that the average voltage across
+ 
+
+ align:start position:0%
+we know that the average voltage across
+the inductor has to be zero so let's
+
+ align:start position:0%
+the inductor has to be zero so let's
+ 
+
+ align:start position:0%
+the inductor has to be zero so let's
+just calculate that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PSS what do I get I get the average
+
+ align:start position:0%
+PSS what do I get I get the average
+ 
+
+ align:start position:0%
+PSS what do I get I get the average
+voltage across the inductor is equal to
+
+ align:start position:0%
+voltage across the inductor is equal to
+ 
+
+ align:start position:0%
+voltage across the inductor is equal to
+zero and that's got to be equal to D *
+
+ align:start position:0%
+zero and that's got to be equal to D *
+ 
+
+ align:start position:0%
+zero and that's got to be equal to D *
+V1
+
+ align:start position:0%
+V1
+ 
+
+ align:start position:0%
+V1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+D2 * V1 -
+
+ align:start position:0%
+D2 * V1 -
+ 
+
+ align:start position:0%
+D2 * V1 -
+V2 that has to equal zero so what I get
+
+ align:start position:0%
+V2 that has to equal zero so what I get
+ 
+
+ align:start position:0%
+V2 that has to equal zero so what I get
+is if I rearrange this equation what I
+
+ align:start position:0%
+is if I rearrange this equation what I
+ 
+
+ align:start position:0%
+is if I rearrange this equation what I
+should get is D plus
+
+ align:start position:0%
+should get is D plus
+ 
+
+ align:start position:0%
+should get is D plus
+D2 * V1 is equal to D2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V2 or
+
+ align:start position:0%
+V2 or
+ 
+
+ align:start position:0%
+V2 or
+V2 over V1 is equal to uh D plus D2 over
+
+ align:start position:0%
+V2 over V1 is equal to uh D plus D2 over
+ 
+
+ align:start position:0%
+V2 over V1 is equal to uh D plus D2 over
+D2
+
+ align:start position:0%
+D2
+ 
+
+ align:start position:0%
+D2
+V1 or D2 plus d over
+
+ align:start position:0%
+V1 or D2 plus d over
+ 
+
+ align:start position:0%
+V1 or D2 plus d over
+D2 okay which is also equal
+
+ align:start position:0%
+D2 okay which is also equal
+ 
+
+ align:start position:0%
+D2 okay which is also equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um 1 + D over
+
+ align:start position:0%
+um 1 + D over
+ 
+
+ align:start position:0%
+um 1 + D over
+D2 okay so that's not exactly an
+
+ align:start position:0%
+D2 okay so that's not exactly an
+ 
+
+ align:start position:0%
+D2 okay so that's not exactly an
+answer okay in terms of it because it
+
+ align:start position:0%
+answer okay in terms of it because it
+ 
+
+ align:start position:0%
+answer okay in terms of it because it
+depends on the duty ratio of the switch
+
+ align:start position:0%
+depends on the duty ratio of the switch
+ 
+
+ align:start position:0%
+depends on the duty ratio of the switch
+but then I got to go figure out what the
+
+ align:start position:0%
+but then I got to go figure out what the
+ 
+
+ align:start position:0%
+but then I got to go figure out what the
+duty ratio of that diode's going to look
+
+ align:start position:0%
+duty ratio of that diode's going to look
+ 
+
+ align:start position:0%
+duty ratio of that diode's going to look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+okay but what I what do I know I know
+
+ align:start position:0%
+okay but what I what do I know I know
+ 
+
+ align:start position:0%
+okay but what I what do I know I know
+that D2 is less than 1 minus D whatever
+
+ align:start position:0%
+that D2 is less than 1 minus D whatever
+ 
+
+ align:start position:0%
+that D2 is less than 1 minus D whatever
+it is is one less than one minus d right
+
+ align:start position:0%
+it is is one less than one minus d right
+ 
+
+ align:start position:0%
+it is is one less than one minus d right
+because this is the duration
+
+ align:start position:0%
+because this is the duration
+ 
+
+ align:start position:0%
+because this is the duration
+D2 or d2t right and that's less than 1
+
+ align:start position:0%
+D2 or d2t right and that's less than 1
+ 
+
+ align:start position:0%
+D2 or d2t right and that's less than 1
+minus DT okay so if I took the
+
+ align:start position:0%
+minus DT okay so if I took the
+ 
+
+ align:start position:0%
+minus DT okay so if I took the
+CCM okay let's what is it this is
+
+ align:start position:0%
+CCM okay let's what is it this is
+ 
+
+ align:start position:0%
+CCM okay let's what is it this is
+DCM okay what is it in
+
+ align:start position:0%
+DCM okay what is it in
+ 
+
+ align:start position:0%
+DCM okay what is it in
+CCM okay in CCM V2 over
+
+ align:start position:0%
+CCM okay in CCM V2 over
+ 
+
+ align:start position:0%
+CCM okay in CCM V2 over
+V1 is equal to 1 over 1us D which is I
+
+ align:start position:0%
+V1 is equal to 1 over 1us D which is I
+ 
+
+ align:start position:0%
+V1 is equal to 1 over 1us D which is I
+could rewrite as 1 - D + D over 1 minus
+
+ align:start position:0%
+could rewrite as 1 - D + D over 1 minus
+ 
+
+ align:start position:0%
+could rewrite as 1 - D + D over 1 minus
+d right all I did was add a minus D and
+
+ align:start position:0%
+d right all I did was add a minus D and
+ 
+
+ align:start position:0%
+d right all I did was add a minus D and
+A plus d in the
+
+ align:start position:0%
+A plus d in the
+ 
+
+ align:start position:0%
+A plus d in the
+numerator and then I could rewrite this
+
+ align:start position:0%
+numerator and then I could rewrite this
+ 
+
+ align:start position:0%
+numerator and then I could rewrite this
+as 1 + D over 1us d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so here we can say that the
+
+ align:start position:0%
+right so here we can say that the
+ 
+
+ align:start position:0%
+right so here we can say that the
+conversion ratio in CCM is can be
+
+ align:start position:0%
+conversion ratio in CCM is can be
+ 
+
+ align:start position:0%
+conversion ratio in CCM is can be
+Rewritten it's less convenient form but
+
+ align:start position:0%
+Rewritten it's less convenient form but
+ 
+
+ align:start position:0%
+Rewritten it's less convenient form but
+it's 1 plus d over 1 minus
+
+ align:start position:0%
+it's 1 plus d over 1 minus
+ 
+
+ align:start position:0%
+it's 1 plus d over 1 minus
+D okay so it's clear for any value of D
+
+ align:start position:0%
+D okay so it's clear for any value of D
+ 
+
+ align:start position:0%
+D okay so it's clear for any value of D
+the conversion ratio is going to be
+
+ align:start position:0%
+the conversion ratio is going to be
+ 
+
+ align:start position:0%
+the conversion ratio is going to be
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+one okay here because D2 is less than 1
+
+ align:start position:0%
+one okay here because D2 is less than 1
+ 
+
+ align:start position:0%
+one okay here because D2 is less than 1
+minus D V2 over V1 is bigger in
+
+ align:start position:0%
+minus D V2 over V1 is bigger in
+ 
+
+ align:start position:0%
+minus D V2 over V1 is bigger in
+discontinuous conduction mode than it
+
+ align:start position:0%
+discontinuous conduction mode than it
+ 
+
+ align:start position:0%
+discontinuous conduction mode than it
+would be in continuous conduction
+
+ align:start position:0%
+would be in continuous conduction
+ 
+
+ align:start position:0%
+would be in continuous conduction
+mode all right so what's going to
+
+ align:start position:0%
+mode all right so what's going to
+ 
+
+ align:start position:0%
+mode all right so what's going to
+happen is for a given Duty ratio
+
+ align:start position:0%
+happen is for a given Duty ratio
+ 
+
+ align:start position:0%
+happen is for a given Duty ratio
+whatever I get for my V2 it's going to
+
+ align:start position:0%
+whatever I get for my V2 it's going to
+ 
+
+ align:start position:0%
+whatever I get for my V2 it's going to
+be bigger than I would get in continuous
+
+ align:start position:0%
+be bigger than I would get in continuous
+ 
+
+ align:start position:0%
+be bigger than I would get in continuous
+conduction mode the output voltage is
+
+ align:start position:0%
+conduction mode the output voltage is
+ 
+
+ align:start position:0%
+conduction mode the output voltage is
+going to get pumped up a
+
+ align:start position:0%
+going to get pumped up a
+ 
+
+ align:start position:0%
+going to get pumped up a
+bit okay so I can tell
+
+ align:start position:0%
+bit okay so I can tell
+ 
+
+ align:start position:0%
+bit okay so I can tell
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um that's
+
+ align:start position:0%
+um that's
+ 
+
+ align:start position:0%
+um that's
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+straightforward okay um it's a little
+
+ align:start position:0%
+straightforward okay um it's a little
+ 
+
+ align:start position:0%
+straightforward okay um it's a little
+little bit messy but we can go figure
+
+ align:start position:0%
+little bit messy but we can go figure
+ 
+
+ align:start position:0%
+little bit messy but we can go figure
+this out because I have the means to
+
+ align:start position:0%
+this out because I have the means to
+ 
+
+ align:start position:0%
+this out because I have the means to
+calculate what D2 is because I know
+
+ align:start position:0%
+calculate what D2 is because I know
+ 
+
+ align:start position:0%
+calculate what D2 is because I know
+exactly what these Ripple waveforms look
+
+ align:start position:0%
+exactly what these Ripple waveforms look
+ 
+
+ align:start position:0%
+exactly what these Ripple waveforms look
+like if I if I write the exact
+
+ align:start position:0%
+like if I if I write the exact
+ 
+
+ align:start position:0%
+like if I if I write the exact
+expression if I basically eliminate D2
+
+ align:start position:0%
+expression if I basically eliminate D2
+ 
+
+ align:start position:0%
+expression if I basically eliminate D2
+from this expression here's what you get
+
+ align:start position:0%
+from this expression here's what you get
+ 
+
+ align:start position:0%
+from this expression here's what you get
+you get V2 over
+
+ align:start position:0%
+you get V2 over
+ 
+
+ align:start position:0%
+you get V2 over
+V1 is equal to a
+
+ align:start position:0%
+V1 is equal to a
+ 
+
+ align:start position:0%
+V1 is equal to a
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+plus uh 12 the square Ro t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of 1
+
+ align:start position:0%
+of 1
+ 
+
+ align:start position:0%
+of 1
++ 2 d^2 RT over 2L or RT over L for DCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boost okay so I'm just writing what this
+
+ align:start position:0%
+boost okay so I'm just writing what this
+ 
+
+ align:start position:0%
+boost okay so I'm just writing what this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um for a boost converter okay it would
+
+ align:start position:0%
+um for a boost converter okay it would
+ 
+
+ align:start position:0%
+um for a boost converter okay it would
+be different for different kind of
+
+ align:start position:0%
+be different for different kind of
+ 
+
+ align:start position:0%
+be different for different kind of
+converters this is just an example but
+
+ align:start position:0%
+converters this is just an example but
+ 
+
+ align:start position:0%
+converters this is just an example but
+what's the difference well we said look
+
+ align:start position:0%
+what's the difference well we said look
+ 
+
+ align:start position:0%
+what's the difference well we said look
+if I'm in
+
+ align:start position:0%
+if I'm in
+ 
+
+ align:start position:0%
+if I'm in
+CCM
+
+ align:start position:0%
+CCM
+ 
+
+ align:start position:0%
+CCM
+right the voltage conversion RTI is just
+
+ align:start position:0%
+right the voltage conversion RTI is just
+ 
+
+ align:start position:0%
+right the voltage conversion RTI is just
+a function of Duty ratio it doesn't
+
+ align:start position:0%
+a function of Duty ratio it doesn't
+ 
+
+ align:start position:0%
+a function of Duty ratio it doesn't
+matter the inductance it doesn't matter
+
+ align:start position:0%
+matter the inductance it doesn't matter
+ 
+
+ align:start position:0%
+matter the inductance it doesn't matter
+the load resistance it's just going to
+
+ align:start position:0%
+the load resistance it's just going to
+ 
+
+ align:start position:0%
+the load resistance it's just going to
+you know very straightforward
+
+ align:start position:0%
+you know very straightforward
+ 
+
+ align:start position:0%
+you know very straightforward
+relationship suddenly when I get into
+
+ align:start position:0%
+relationship suddenly when I get into
+ 
+
+ align:start position:0%
+relationship suddenly when I get into
+DCM it depends on everything it depends
+
+ align:start position:0%
+DCM it depends on everything it depends
+ 
+
+ align:start position:0%
+DCM it depends on everything it depends
+on my load resistor it depends on my
+
+ align:start position:0%
+on my load resistor it depends on my
+ 
+
+ align:start position:0%
+on my load resistor it depends on my
+switching period it depends on my
+
+ align:start position:0%
+switching period it depends on my
+ 
+
+ align:start position:0%
+switching period it depends on my
+inductance it's a mess doesn't mean you
+
+ align:start position:0%
+inductance it's a mess doesn't mean you
+ 
+
+ align:start position:0%
+inductance it's a mess doesn't mean you
+can't do it it's just not a simple
+
+ align:start position:0%
+can't do it it's just not a simple
+ 
+
+ align:start position:0%
+can't do it it's just not a simple
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+anymore okay okay so suddenly it's a lot
+
+ align:start position:0%
+anymore okay okay so suddenly it's a lot
+ 
+
+ align:start position:0%
+anymore okay okay so suddenly it's a lot
+more um complicated than it was in
+
+ align:start position:0%
+more um complicated than it was in
+ 
+
+ align:start position:0%
+more um complicated than it was in
+continuous conduction mode okay and it
+
+ align:start position:0%
+continuous conduction mode okay and it
+ 
+
+ align:start position:0%
+continuous conduction mode okay and it
+also affects the converter's Dynamics as
+
+ align:start position:0%
+also affects the converter's Dynamics as
+ 
+
+ align:start position:0%
+also affects the converter's Dynamics as
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+right any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but that said we can't avoid it
+
+ align:start position:0%
+that but that said we can't avoid it
+ 
+
+ align:start position:0%
+that but that said we can't avoid it
+you how do we know that we stay periodic
+
+ align:start position:0%
+you how do we know that we stay periodic
+ 
+
+ align:start position:0%
+you how do we know that we stay periodic
+St State when we go through these
+
+ align:start position:0%
+St State when we go through these
+ 
+
+ align:start position:0%
+St State when we go through these
+different modes of
+
+ align:start position:0%
+different modes of
+ 
+
+ align:start position:0%
+different modes of
+operation that's a good question um it's
+
+ align:start position:0%
+operation that's a good question um it's
+ 
+
+ align:start position:0%
+operation that's a good question um it's
+a question of will it reach periodic
+
+ align:start position:0%
+a question of will it reach periodic
+ 
+
+ align:start position:0%
+a question of will it reach periodic
+steady
+
+ align:start position:0%
+steady
+ 
+
+ align:start position:0%
+steady
+state um that's the same analysis you go
+
+ align:start position:0%
+state um that's the same analysis you go
+ 
+
+ align:start position:0%
+state um that's the same analysis you go
+do right you can go do this analysis and
+
+ align:start position:0%
+do right you can go do this analysis and
+ 
+
+ align:start position:0%
+do right you can go do this analysis and
+find out whether it'll end up in
+
+ align:start position:0%
+find out whether it'll end up in
+ 
+
+ align:start position:0%
+find out whether it'll end up in
+periodic steady state uh It generally
+
+ align:start position:0%
+periodic steady state uh It generally
+ 
+
+ align:start position:0%
+periodic steady state uh It generally
+will settle I mean because you can solve
+
+ align:start position:0%
+will settle I mean because you can solve
+ 
+
+ align:start position:0%
+will settle I mean because you can solve
+for these things the Boost converter
+
+ align:start position:0%
+for these things the Boost converter
+ 
+
+ align:start position:0%
+for these things the Boost converter
+will end up in periodic steady state
+
+ align:start position:0%
+will end up in periodic steady state
+ 
+
+ align:start position:0%
+will end up in periodic steady state
+unless suppose I disconnected this load
+
+ align:start position:0%
+unless suppose I disconnected this load
+ 
+
+ align:start position:0%
+unless suppose I disconnected this load
+resistor in this case that's equival to
+
+ align:start position:0%
+resistor in this case that's equival to
+ 
+
+ align:start position:0%
+resistor in this case that's equival to
+making r equal to Infinity
+
+ align:start position:0%
+making r equal to Infinity
+ 
+
+ align:start position:0%
+making r equal to Infinity
+right if I come over
+
+ align:start position:0%
+right if I come over
+ 
+
+ align:start position:0%
+right if I come over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um and I make r equal to Infinity V2
+
+ align:start position:0%
+um and I make r equal to Infinity V2
+ 
+
+ align:start position:0%
+um and I make r equal to Infinity V2
+over V1 goes to Infinity right that
+
+ align:start position:0%
+over V1 goes to Infinity right that
+ 
+
+ align:start position:0%
+over V1 goes to Infinity right that
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+the it's just going to wander off to
+
+ align:start position:0%
+the it's just going to wander off to
+ 
+
+ align:start position:0%
+the it's just going to wander off to
+Infinity the output will wander off to
+
+ align:start position:0%
+Infinity the output will wander off to
+ 
+
+ align:start position:0%
+Infinity the output will wander off to
+Infinity why would that happen because
+
+ align:start position:0%
+Infinity why would that happen because
+ 
+
+ align:start position:0%
+Infinity why would that happen because
+look this is iil in DCM right so every
+
+ align:start position:0%
+look this is iil in DCM right so every
+ 
+
+ align:start position:0%
+look this is iil in DCM right so every
+cycle I take energy out of the input put
+
+ align:start position:0%
+cycle I take energy out of the input put
+ 
+
+ align:start position:0%
+cycle I take energy out of the input put
+it in the inductor turn off the switch
+
+ align:start position:0%
+it in the inductor turn off the switch
+ 
+
+ align:start position:0%
+it in the inductor turn off the switch
+and that energy goes to the output and I
+
+ align:start position:0%
+and that energy goes to the output and I
+ 
+
+ align:start position:0%
+and that energy goes to the output and I
+build up some energy on the
+
+ align:start position:0%
+build up some energy on the
+ 
+
+ align:start position:0%
+build up some energy on the
+capacitor and the feedback mechanism
+
+ align:start position:0%
+capacitor and the feedback mechanism
+ 
+
+ align:start position:0%
+capacitor and the feedback mechanism
+that gets you to steady state is the
+
+ align:start position:0%
+that gets you to steady state is the
+ 
+
+ align:start position:0%
+that gets you to steady state is the
+resistor drains some of that energy but
+
+ align:start position:0%
+resistor drains some of that energy but
+ 
+
+ align:start position:0%
+resistor drains some of that energy but
+if you don't ever drain the energy this
+
+ align:start position:0%
+if you don't ever drain the energy this
+ 
+
+ align:start position:0%
+if you don't ever drain the energy this
+just wanders off to Infinity I actually
+
+ align:start position:0%
+just wanders off to Infinity I actually
+ 
+
+ align:start position:0%
+just wanders off to Infinity I actually
+had a converter explode on me once
+
+ align:start position:0%
+had a converter explode on me once
+ 
+
+ align:start position:0%
+had a converter explode on me once
+because of that the the electrolytic
+
+ align:start position:0%
+because of that the the electrolytic
+ 
+
+ align:start position:0%
+because of that the the electrolytic
+capacitor literally blew up in my face
+
+ align:start position:0%
+capacitor literally blew up in my face
+ 
+
+ align:start position:0%
+capacitor literally blew up in my face
+um I what's
+
+ align:start position:0%
+um I what's
+ 
+
+ align:start position:0%
+um I what's
+that you're damn right I I can still
+
+ align:start position:0%
+that you're damn right I I can still
+ 
+
+ align:start position:0%
+that you're damn right I I can still
+see I always wear glasses when working
+
+ align:start position:0%
+see I always wear glasses when working
+ 
+
+ align:start position:0%
+see I always wear glasses when working
+on a higher power thing these days and I
+
+ align:start position:0%
+on a higher power thing these days and I
+ 
+
+ align:start position:0%
+on a higher power thing these days and I
+should on any converter because I
+
+ align:start position:0%
+should on any converter because I
+ 
+
+ align:start position:0%
+should on any converter because I
+literally I was looking down to it and I
+
+ align:start position:0%
+literally I was looking down to it and I
+ 
+
+ align:start position:0%
+literally I was looking down to it and I
+bumped the connection to the load with
+
+ align:start position:0%
+bumped the connection to the load with
+ 
+
+ align:start position:0%
+bumped the connection to the load with
+my elbow and the capacitor just
+
+ align:start position:0%
+my elbow and the capacitor just
+ 
+
+ align:start position:0%
+my elbow and the capacitor just
+literally exploded in my face um they
+
+ align:start position:0%
+literally exploded in my face um they
+ 
+
+ align:start position:0%
+literally exploded in my face um they
+often don't vent so dramatically they're
+
+ align:start position:0%
+often don't vent so dramatically they're
+ 
+
+ align:start position:0%
+often don't vent so dramatically they're
+not supposed to but in this case it
+
+ align:start position:0%
+not supposed to but in this case it
+ 
+
+ align:start position:0%
+not supposed to but in this case it
+exploded um so yes wearing glasses is a
+
+ align:start position:0%
+exploded um so yes wearing glasses is a
+ 
+
+ align:start position:0%
+exploded um so yes wearing glasses is a
+good idea in these kind of things I
+
+ align:start position:0%
+good idea in these kind of things I
+ 
+
+ align:start position:0%
+good idea in these kind of things I
+actually did that this morning on our
+
+ align:start position:0%
+actually did that this morning on our
+ 
+
+ align:start position:0%
+actually did that this morning on our
+demo converter too but that's not what
+
+ align:start position:0%
+demo converter too but that's not what
+ 
+
+ align:start position:0%
+demo converter too but that's not what
+happened uh but what happened was um the
+
+ align:start position:0%
+happened uh but what happened was um the
+ 
+
+ align:start position:0%
+happened uh but what happened was um the
+mosfet started breaking down in other
+
+ align:start position:0%
+mosfet started breaking down in other
+ 
+
+ align:start position:0%
+mosfet started breaking down in other
+words it would just start dumping energy
+
+ align:start position:0%
+words it would just start dumping energy
+ 
+
+ align:start position:0%
+words it would just start dumping energy
+into the mosfet which isn't good for the
+
+ align:start position:0%
+into the mosfet which isn't good for the
+ 
+
+ align:start position:0%
+into the mosfet which isn't good for the
+mosfet so fortunately I didn't kill the
+
+ align:start position:0%
+mosfet so fortunately I didn't kill the
+ 
+
+ align:start position:0%
+mosfet so fortunately I didn't kill the
+demo because I was being stupid by
+
+ align:start position:0%
+demo because I was being stupid by
+ 
+
+ align:start position:0%
+demo because I was being stupid by
+taking off the load okay but the point
+
+ align:start position:0%
+taking off the load okay but the point
+ 
+
+ align:start position:0%
+taking off the load okay but the point
+is you you don't necessarily have to get
+
+ align:start position:0%
+is you you don't necessarily have to get
+ 
+
+ align:start position:0%
+is you you don't necessarily have to get
+to periodic steady state in all
+
+ align:start position:0%
+to periodic steady state in all
+ 
+
+ align:start position:0%
+to periodic steady state in all
+converters and this is an example where
+
+ align:start position:0%
+converters and this is an example where
+ 
+
+ align:start position:0%
+converters and this is an example where
+you can get to really high voltages in
+
+ align:start position:0%
+you can get to really high voltages in
+ 
+
+ align:start position:0%
+you can get to really high voltages in
+fact if you look at like little photo
+
+ align:start position:0%
+fact if you look at like little photo
+ 
+
+ align:start position:0%
+fact if you look at like little photo
+flash chargers for for um you know those
+
+ align:start position:0%
+flash chargers for for um you know those
+ 
+
+ align:start position:0%
+flash chargers for for um you know those
+little cameras that you use you know at
+
+ align:start position:0%
+little cameras that you use you know at
+ 
+
+ align:start position:0%
+little cameras that you use you know at
+weddings that actual film cameras
+
+ align:start position:0%
+weddings that actual film cameras
+ 
+
+ align:start position:0%
+weddings that actual film cameras
+yielding cameras right they they often
+
+ align:start position:0%
+yielding cameras right they they often
+ 
+
+ align:start position:0%
+yielding cameras right they they often
+use a boost or a flyback in DCM to
+
+ align:start position:0%
+use a boost or a flyback in DCM to
+ 
+
+ align:start position:0%
+use a boost or a flyback in DCM to
+charge the output voltage up from like a
+
+ align:start position:0%
+charge the output voltage up from like a
+ 
+
+ align:start position:0%
+charge the output voltage up from like a
+volt and a half up to a few hundred
+
+ align:start position:0%
+volt and a half up to a few hundred
+ 
+
+ align:start position:0%
+volt and a half up to a few hundred
+volts same trick you can get to very
+
+ align:start position:0%
+volts same trick you can get to very
+ 
+
+ align:start position:0%
+volts same trick you can get to very
+large conversion ratios this way all
+
+ align:start position:0%
+large conversion ratios this way all
+ 
+
+ align:start position:0%
+large conversion ratios this way all
+right so your know DCM is harder to
+
+ align:start position:0%
+right so your know DCM is harder to
+ 
+
+ align:start position:0%
+right so your know DCM is harder to
+model how would I think about modeling
+
+ align:start position:0%
+model how would I think about modeling
+ 
+
+ align:start position:0%
+model how would I think about modeling
+it um and I'll let Mony start to set up
+
+ align:start position:0%
+it um and I'll let Mony start to set up
+ 
+
+ align:start position:0%
+it um and I'll let Mony start to set up
+and roll down screens and stuff
+
+ align:start position:0%
+and roll down screens and stuff
+ 
+
+ align:start position:0%
+and roll down screens and stuff
+um one way I could think about this is
+
+ align:start position:0%
+um one way I could think about this is
+ 
+
+ align:start position:0%
+um one way I could think about this is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+following okay maybe I would think about
+
+ align:start position:0%
+following okay maybe I would think about
+ 
+
+ align:start position:0%
+following okay maybe I would think about
+if I if I looked at my converter
+
+ align:start position:0%
+if I if I looked at my converter
+ 
+
+ align:start position:0%
+if I if I looked at my converter
+here this is my inductor current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waveform what does my diode current
+
+ align:start position:0%
+waveform what does my diode current
+ 
+
+ align:start position:0%
+waveform what does my diode current
+waveform look like I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subd okay I subd is zero in the first
+
+ align:start position:0%
+subd okay I subd is zero in the first
+ 
+
+ align:start position:0%
+subd okay I subd is zero in the first
+part of the s
+
+ align:start position:0%
+part of the s
+ 
+
+ align:start position:0%
+part of the s
+cycle then it conducts in this second
+
+ align:start position:0%
+cycle then it conducts in this second
+ 
+
+ align:start position:0%
+cycle then it conducts in this second
+part of the cycle until D plus
+
+ align:start position:0%
+part of the cycle until D plus
+ 
+
+ align:start position:0%
+part of the cycle until D plus
+D2 and then it's zero for the rest of
+
+ align:start position:0%
+D2 and then it's zero for the rest of
+ 
+
+ align:start position:0%
+D2 and then it's zero for the rest of
+the cycle right so this is DT this is D+
+
+ align:start position:0%
+the cycle right so this is DT this is D+
+ 
+
+ align:start position:0%
+the cycle right so this is DT this is D+
+D2 T and so forth right so
+
+ align:start position:0%
+D2 T and so forth right so
+ 
+
+ align:start position:0%
+D2 T and so forth right so
+maybe I could think about modeling my
+
+ align:start position:0%
+maybe I could think about modeling my
+ 
+
+ align:start position:0%
+maybe I could think about modeling my
+converter from a control perspective as
+
+ align:start position:0%
+converter from a control perspective as
+ 
+
+ align:start position:0%
+converter from a control perspective as
+just whatever this current ID is into
+
+ align:start position:0%
+just whatever this current ID is into
+ 
+
+ align:start position:0%
+just whatever this current ID is into
+the output right so maybe I would model
+
+ align:start position:0%
+the output right so maybe I would model
+ 
+
+ align:start position:0%
+the output right so maybe I would model
+it by saying okay let me think of my
+
+ align:start position:0%
+it by saying okay let me think of my
+ 
+
+ align:start position:0%
+it by saying okay let me think of my
+converter is this current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ID which looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this DT D+ D2 T and T and just repeats
+
+ align:start position:0%
+this DT D+ D2 T and T and just repeats
+ 
+
+ align:start position:0%
+this DT D+ D2 T and T and just repeats
+right into my output
+
+ align:start position:0%
+right into my output
+ 
+
+ align:start position:0%
+right into my output
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+resistor so maybe I would s start to
+
+ align:start position:0%
+resistor so maybe I would s start to
+ 
+
+ align:start position:0%
+resistor so maybe I would s start to
+think of my converter as some s sort of
+
+ align:start position:0%
+think of my converter as some s sort of
+ 
+
+ align:start position:0%
+think of my converter as some s sort of
+funny current source and maybe I can
+
+ align:start position:0%
+funny current source and maybe I can
+ 
+
+ align:start position:0%
+funny current source and maybe I can
+relate this current Source back to the
+
+ align:start position:0%
+relate this current Source back to the
+ 
+
+ align:start position:0%
+relate this current Source back to the
+component values and just start thinking
+
+ align:start position:0%
+component values and just start thinking
+ 
+
+ align:start position:0%
+component values and just start thinking
+about my converter as a current Source
+
+ align:start position:0%
+about my converter as a current Source
+ 
+
+ align:start position:0%
+about my converter as a current Source
+because that's really what I've turned
+
+ align:start position:0%
+because that's really what I've turned
+ 
+
+ align:start position:0%
+because that's really what I've turned
+it into right I'm going to be squirting
+
+ align:start position:0%
+it into right I'm going to be squirting
+ 
+
+ align:start position:0%
+it into right I'm going to be squirting
+some current into that output capacitor
+
+ align:start position:0%
+some current into that output capacitor
+ 
+
+ align:start position:0%
+some current into that output capacitor
+every cycle all right well what does
+
+ align:start position:0%
+every cycle all right well what does
+ 
+
+ align:start position:0%
+every cycle all right well what does
+that look like um what I know here is
+
+ align:start position:0%
+that look like um what I know here is
+ 
+
+ align:start position:0%
+that look like um what I know here is
+that this
+
+ align:start position:0%
+that this
+ 
+
+ align:start position:0%
+that this
+current I
+
+ align:start position:0%
+current I
+ 
+
+ align:start position:0%
+current I
+Peak I Peak
+
+ align:start position:0%
+Peak I Peak
+ 
+
+ align:start position:0%
+Peak I Peak
+is equal to V1 DT
+
+ align:start position:0%
+is equal to V1 DT
+ 
+
+ align:start position:0%
+is equal to V1 DT
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+right and this time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+period let me call this time period to
+
+ align:start position:0%
+period let me call this time period to
+ 
+
+ align:start position:0%
+period let me call this time period to
+discharge delta T right which is just
+
+ align:start position:0%
+discharge delta T right which is just
+ 
+
+ align:start position:0%
+discharge delta T right which is just
+d2t right uh what do I know I know that
+
+ align:start position:0%
+d2t right uh what do I know I know that
+ 
+
+ align:start position:0%
+d2t right uh what do I know I know that
+V is equal to LD
+
+ align:start position:0%
+V is equal to LD
+ 
+
+ align:start position:0%
+V is equal to LD
+DT right so delta T is equal to
+
+ align:start position:0%
+DT right so delta T is equal to
+ 
+
+ align:start position:0%
+DT right so delta T is equal to
+d2t is equal to
+
+ align:start position:0%
+d2t is equal to
+ 
+
+ align:start position:0%
+d2t is equal to
+l i
+
+ align:start position:0%
+l i
+ 
+
+ align:start position:0%
+l i
+Peak divided
+
+ align:start position:0%
+Peak divided
+ 
+
+ align:start position:0%
+Peak divided
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+um Li Peak divided V which is V2 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V1
+
+ align:start position:0%
+V1
+ 
+
+ align:start position:0%
+V1
+right and I can put in I Peak here so
+
+ align:start position:0%
+right and I can put in I Peak here so
+ 
+
+ align:start position:0%
+right and I can put in I Peak here so
+that's just going to be uh V1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT V1 DT over L / V2 minus
+
+ align:start position:0%
+DT V1 DT over L / V2 minus
+ 
+
+ align:start position:0%
+DT V1 DT over L / V2 minus
+V1 okay that make sense to
+
+ align:start position:0%
+V1 okay that make sense to
+ 
+
+ align:start position:0%
+V1 okay that make sense to
+everybody and so let me ask what is the
+
+ align:start position:0%
+everybody and so let me ask what is the
+ 
+
+ align:start position:0%
+everybody and so let me ask what is the
+average what's important over the
+
+ align:start position:0%
+average what's important over the
+ 
+
+ align:start position:0%
+average what's important over the
+switching cycle is what's the average
+
+ align:start position:0%
+switching cycle is what's the average
+ 
+
+ align:start position:0%
+switching cycle is what's the average
+current that I'm sticking into the
+
+ align:start position:0%
+current that I'm sticking into the
+ 
+
+ align:start position:0%
+current that I'm sticking into the
+output right I should ask sort of each
+
+ align:start position:0%
+output right I should ask sort of each
+ 
+
+ align:start position:0%
+output right I should ask sort of each
+cycle how much on average am I squirting
+
+ align:start position:0%
+cycle how much on average am I squirting
+ 
+
+ align:start position:0%
+cycle how much on average am I squirting
+into the output well I subd the average
+
+ align:start position:0%
+into the output well I subd the average
+ 
+
+ align:start position:0%
+into the output well I subd the average
+value of I subd is basically the area
+
+ align:start position:0%
+value of I subd is basically the area
+ 
+
+ align:start position:0%
+value of I subd is basically the area
+there which would be 12 the base of that
+
+ align:start position:0%
+there which would be 12 the base of that
+ 
+
+ align:start position:0%
+there which would be 12 the base of that
+which is this delta
+
+ align:start position:0%
+which is this delta
+ 
+
+ align:start position:0%
+which is this delta
+T V1
+
+ align:start position:0%
+T V1
+ 
+
+ align:start position:0%
+T V1
+DT over V2 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V1 okay half the base times the height
+
+ align:start position:0%
+V1 okay half the base times the height
+ 
+
+ align:start position:0%
+V1 okay half the base times the height
+which is I Peak which is V1
+
+ align:start position:0%
+which is I Peak which is V1
+ 
+
+ align:start position:0%
+which is I Peak which is V1
+DT over L okay this is the area under
+
+ align:start position:0%
+DT over L okay this is the area under
+ 
+
+ align:start position:0%
+DT over L okay this is the area under
+that triangle 12 base * height * 1/
+
+ align:start position:0%
+that triangle 12 base * height * 1/
+ 
+
+ align:start position:0%
+that triangle 12 base * height * 1/
+T okay if I rewrite that then what I'm
+
+ align:start position:0%
+T okay if I rewrite that then what I'm
+ 
+
+ align:start position:0%
+T okay if I rewrite that then what I'm
+going to get is 12
+
+ align:start position:0%
+going to get is 12
+ 
+
+ align:start position:0%
+going to get is 12
+V1
+
+ align:start position:0%
+V1
+ 
+
+ align:start position:0%
+V1
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+V1
+
+ align:start position:0%
+V1
+ 
+
+ align:start position:0%
+V1
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+T over 2 V2 - V1 L * D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+^2 okay
+
+ align:start position:0%
+^2 okay
+ 
+
+ align:start position:0%
+^2 okay
+I just see double check to make sure I
+
+ align:start position:0%
+I just see double check to make sure I
+ 
+
+ align:start position:0%
+I just see double check to make sure I
+did my math right here something like
+
+ align:start position:0%
+did my math right here something like
+ 
+
+ align:start position:0%
+did my math right here something like
+this anyways v1^2 T over 2L V2 minus V1
+
+ align:start position:0%
+this anyways v1^2 T over 2L V2 minus V1
+ 
+
+ align:start position:0%
+this anyways v1^2 T over 2L V2 minus V1
+d^2 okay yeah so really what I have is
+
+ align:start position:0%
+d^2 okay yeah so really what I have is
+ 
+
+ align:start position:0%
+d^2 okay yeah so really what I have is
+now I can think of the all the converter
+
+ align:start position:0%
+now I can think of the all the converter
+ 
+
+ align:start position:0%
+now I can think of the all the converter
+leading up to the output cap as just a
+
+ align:start position:0%
+leading up to the output cap as just a
+ 
+
+ align:start position:0%
+leading up to the output cap as just a
+current Source that's a function of the
+
+ align:start position:0%
+current Source that's a function of the
+ 
+
+ align:start position:0%
+current Source that's a function of the
+duty ratio I
+
+ align:start position:0%
+duty ratio I
+ 
+
+ align:start position:0%
+duty ratio I
+control right so I've sort of turned
+
+ align:start position:0%
+control right so I've sort of turned
+ 
+
+ align:start position:0%
+control right so I've sort of turned
+this thing into a current source that
+
+ align:start position:0%
+this thing into a current source that
+ 
+
+ align:start position:0%
+this thing into a current source that
+squirts current into the output and I
+
+ align:start position:0%
+squirts current into the output and I
+ 
+
+ align:start position:0%
+squirts current into the output and I
+think about it that way and control it
+
+ align:start position:0%
+think about it that way and control it
+ 
+
+ align:start position:0%
+think about it that way and control it
+that way and if I know what my load
+
+ align:start position:0%
+that way and if I know what my load
+ 
+
+ align:start position:0%
+that way and if I know what my load
+resistor is and the voltage I want I
+
+ align:start position:0%
+resistor is and the voltage I want I
+ 
+
+ align:start position:0%
+resistor is and the voltage I want I
+know how much average current I want to
+
+ align:start position:0%
+know how much average current I want to
+ 
+
+ align:start position:0%
+know how much average current I want to
+stick into it okay so that's how I might
+
+ align:start position:0%
+stick into it okay so that's how I might
+ 
+
+ align:start position:0%
+stick into it okay so that's how I might
+Model A DCM
+
+ align:start position:0%
+Model A DCM
+ 
+
+ align:start position:0%
+Model A DCM
+converter it's more complicated in some
+
+ align:start position:0%
+converter it's more complicated in some
+ 
+
+ align:start position:0%
+converter it's more complicated in some
+sense than my continuous conduction mode
+
+ align:start position:0%
+sense than my continuous conduction mode
+ 
+
+ align:start position:0%
+sense than my continuous conduction mode
+converter because it's a function of all
+
+ align:start position:0%
+converter because it's a function of all
+ 
+
+ align:start position:0%
+converter because it's a function of all
+this junk it m you know my switching
+
+ align:start position:0%
+this junk it m you know my switching
+ 
+
+ align:start position:0%
+this junk it m you know my switching
+period And my and my inductor value and
+
+ align:start position:0%
+period And my and my inductor value and
+ 
+
+ align:start position:0%
+period And my and my inductor value and
+all that stuff matters where it didn't
+
+ align:start position:0%
+all that stuff matters where it didn't
+ 
+
+ align:start position:0%
+all that stuff matters where it didn't
+before but you know I have to live with
+
+ align:start position:0%
+before but you know I have to live with
+ 
+
+ align:start position:0%
+before but you know I have to live with
+that because it's this more complicated
+
+ align:start position:0%
+that because it's this more complicated
+ 
+
+ align:start position:0%
+that because it's this more complicated
+operating
+
+ align:start position:0%
+operating
+ 
+
+ align:start position:0%
+operating
+mode okay yeah so does that mean when
+
+ align:start position:0%
+mode okay yeah so does that mean when
+ 
+
+ align:start position:0%
+mode okay yeah so does that mean when
+you go from CCM DCM you're probably
+
+ align:start position:0%
+you go from CCM DCM you're probably
+ 
+
+ align:start position:0%
+you go from CCM DCM you're probably
+going to change a duty cycle to maintain
+
+ align:start position:0%
+going to change a duty cycle to maintain
+ 
+
+ align:start position:0%
+going to change a duty cycle to maintain
+a Target voltage that's right you're
+
+ align:start position:0%
+a Target voltage that's right you're
+ 
+
+ align:start position:0%
+a Target voltage that's right you're
+going to use a lower duty cycle than you
+
+ align:start position:0%
+going to use a lower duty cycle than you
+ 
+
+ align:start position:0%
+going to use a lower duty cycle than you
+would otherwise use in the Boost
+
+ align:start position:0%
+would otherwise use in the Boost
+ 
+
+ align:start position:0%
+would otherwise use in the Boost
+converter
+
+ align:start position:0%
+converter
+ 
+
+ align:start position:0%
+converter
+yes that's right because the conversion
+
+ align:start position:0%
+yes that's right because the conversion
+ 
+
+ align:start position:0%
+yes that's right because the conversion
+ratio goes up and so your controller and
+
+ align:start position:0%
+ratio goes up and so your controller and
+ 
+
+ align:start position:0%
+ratio goes up and so your controller and
+we'll talk about this later your
+
+ align:start position:0%
+we'll talk about this later your
+ 
+
+ align:start position:0%
+we'll talk about this later your
+controller usually has to manage that
+
+ align:start position:0%
+controller usually has to manage that
+ 
+
+ align:start position:0%
+controller usually has to manage that
+boundary you know you have to have a
+
+ align:start position:0%
+boundary you know you have to have a
+ 
+
+ align:start position:0%
+boundary you know you have to have a
+controller that works for either case
+
+ align:start position:0%
+controller that works for either case
+ 
+
+ align:start position:0%
+controller that works for either case
+okay let's just take a look at this so
+
+ align:start position:0%
+okay let's just take a look at this so
+ 
+
+ align:start position:0%
+okay let's just take a look at this so
+mon set up a an actual boost converter
+
+ align:start position:0%
+mon set up a an actual boost converter
+ 
+
+ align:start position:0%
+mon set up a an actual boost converter
+that's doing this and let's take take a
+
+ align:start position:0%
+that's doing this and let's take take a
+ 
+
+ align:start position:0%
+that's doing this and let's take take a
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+waveforms in
+
+ align:start position:0%
+waveforms in
+ 
+
+ align:start position:0%
+waveforms in
+yellow you can see the
+
+ align:start position:0%
+yellow you can see the
+ 
+
+ align:start position:0%
+yellow you can see the
+uh you can essentially see the switch
+
+ align:start position:0%
+uh you can essentially see the switch
+ 
+
+ align:start position:0%
+uh you can essentially see the switch
+voltage waveform which is essentially
+
+ align:start position:0%
+voltage waveform which is essentially
+ 
+
+ align:start position:0%
+voltage waveform which is essentially
+this waveform moved up where this is
+
+ align:start position:0%
+this waveform moved up where this is
+ 
+
+ align:start position:0%
+this waveform moved up where this is
+zero right so in the first part of the
+
+ align:start position:0%
+zero right so in the first part of the
+ 
+
+ align:start position:0%
+zero right so in the first part of the
+cycle you get
+
+ align:start position:0%
+cycle you get
+ 
+
+ align:start position:0%
+cycle you get
+zero okay in the yellow away from the
+
+ align:start position:0%
+zero okay in the yellow away from the
+ 
+
+ align:start position:0%
+zero okay in the yellow away from the
+second part of the cycle it's at V2 and
+
+ align:start position:0%
+second part of the cycle it's at V2 and
+ 
+
+ align:start position:0%
+second part of the cycle it's at V2 and
+then you get this time period where you
+
+ align:start position:0%
+then you get this time period where you
+ 
+
+ align:start position:0%
+then you get this time period where you
+see this voltage range
+
+ align:start position:0%
+see this voltage range
+ 
+
+ align:start position:0%
+see this voltage range
+okay what the heck is that well I said
+
+ align:start position:0%
+okay what the heck is that well I said
+ 
+
+ align:start position:0%
+okay what the heck is that well I said
+we had this time period where both the
+
+ align:start position:0%
+we had this time period where both the
+ 
+
+ align:start position:0%
+we had this time period where both the
+switch and the diode were open and so
+
+ align:start position:0%
+switch and the diode were open and so
+ 
+
+ align:start position:0%
+switch and the diode were open and so
+that this voltage here ought to be
+
+ align:start position:0%
+that this voltage here ought to be
+ 
+
+ align:start position:0%
+that this voltage here ought to be
+exactly at B1 right but what really
+
+ align:start position:0%
+exactly at B1 right but what really
+ 
+
+ align:start position:0%
+exactly at B1 right but what really
+happens in the real world is that guess
+
+ align:start position:0%
+happens in the real world is that guess
+ 
+
+ align:start position:0%
+happens in the real world is that guess
+what there's some switch
+
+ align:start position:0%
+what there's some switch
+ 
+
+ align:start position:0%
+what there's some switch
+capacitance and some diode capacitance
+
+ align:start position:0%
+capacitance and some diode capacitance
+ 
+
+ align:start position:0%
+capacitance and some diode capacitance
+and so what happens is this voltage
+
+ align:start position:0%
+and so what happens is this voltage
+ 
+
+ align:start position:0%
+and so what happens is this voltage
+instead of going to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rings with those capacitance the
+
+ align:start position:0%
+rings with those capacitance the
+ 
+
+ align:start position:0%
+rings with those capacitance the
+inductor ringing with the parasitic
+
+ align:start position:0%
+inductor ringing with the parasitic
+ 
+
+ align:start position:0%
+inductor ringing with the parasitic
+capacitances people don't like that
+
+ align:start position:0%
+capacitances people don't like that
+ 
+
+ align:start position:0%
+capacitances people don't like that
+that's unpleasant right it causes noise
+
+ align:start position:0%
+that's unpleasant right it causes noise
+ 
+
+ align:start position:0%
+that's unpleasant right it causes noise
+and stuff but you can't do anything
+
+ align:start position:0%
+and stuff but you can't do anything
+ 
+
+ align:start position:0%
+and stuff but you can't do anything
+about it if you're going to have both
+
+ align:start position:0%
+about it if you're going to have both
+ 
+
+ align:start position:0%
+about it if you're going to have both
+devices off in some cases actually
+
+ align:start position:0%
+devices off in some cases actually
+ 
+
+ align:start position:0%
+devices off in some cases actually
+people actually even put in another
+
+ align:start position:0%
+people actually even put in another
+ 
+
+ align:start position:0%
+people actually even put in another
+switch to short it out but generally you
+
+ align:start position:0%
+switch to short it out but generally you
+ 
+
+ align:start position:0%
+switch to short it out but generally you
+don't generally just let it ring and
+
+ align:start position:0%
+don't generally just let it ring and
+ 
+
+ align:start position:0%
+don't generally just let it ring and
+that's life
+
+ align:start position:0%
+that's life
+ 
+
+ align:start position:0%
+that's life
+okay um but you can now see that you
+
+ align:start position:0%
+okay um but you can now see that you
+ 
+
+ align:start position:0%
+okay um but you can now see that you
+have the rising inductor current the
+
+ align:start position:0%
+have the rising inductor current the
+ 
+
+ align:start position:0%
+have the rising inductor current the
+falling inductor current is zero it's
+
+ align:start position:0%
+falling inductor current is zero it's
+ 
+
+ align:start position:0%
+falling inductor current is zero it's
+exactly doing what this yellow waveform
+
+ align:start position:0%
+exactly doing what this yellow waveform
+ 
+
+ align:start position:0%
+exactly doing what this yellow waveform
+is doing here okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah can you mention the source
+
+ align:start position:0%
+that yeah can you mention the source
+ 
+
+ align:start position:0%
+that yeah can you mention the source
+that cost that range again the it's
+
+ align:start position:0%
+that cost that range again the it's
+ 
+
+ align:start position:0%
+that cost that range again the it's
+basically the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inductor resonating with parasitic
+
+ align:start position:0%
+inductor resonating with parasitic
+ 
+
+ align:start position:0%
+inductor resonating with parasitic
+capacitance at this
+
+ align:start position:0%
+capacitance at this
+ 
+
+ align:start position:0%
+capacitance at this
+node yeah it's it's an unfortunate thing
+
+ align:start position:0%
+node yeah it's it's an unfortunate thing
+ 
+
+ align:start position:0%
+node yeah it's it's an unfortunate thing
+people don't like it it causes noise a
+
+ align:start position:0%
+people don't like it it causes noise a
+ 
+
+ align:start position:0%
+people don't like it it causes noise a
+little bit annoying that's life okay
+
+ align:start position:0%
+little bit annoying that's life okay
+ 
+
+ align:start position:0%
+little bit annoying that's life okay
+um so I said sometimes you have to live
+
+ align:start position:0%
+um so I said sometimes you have to live
+ 
+
+ align:start position:0%
+um so I said sometimes you have to live
+with TCM operation especially if you
+
+ align:start position:0%
+with TCM operation especially if you
+ 
+
+ align:start position:0%
+with TCM operation especially if you
+operate over really wide load ranges
+
+ align:start position:0%
+operate over really wide load ranges
+ 
+
+ align:start position:0%
+operate over really wide load ranges
+right or you want a finite value for
+
+ align:start position:0%
+right or you want a finite value for
+ 
+
+ align:start position:0%
+right or you want a finite value for
+your inductor sizes
+
+ align:start position:0%
+your inductor sizes
+ 
+
+ align:start position:0%
+your inductor sizes
+okay sometimes you actually want DCM
+
+ align:start position:0%
+okay sometimes you actually want DCM
+ 
+
+ align:start position:0%
+okay sometimes you actually want DCM
+operation people often design their
+
+ align:start position:0%
+operation people often design their
+ 
+
+ align:start position:0%
+operation people often design their
+converters for DCM operation why is that
+
+ align:start position:0%
+converters for DCM operation why is that
+ 
+
+ align:start position:0%
+converters for DCM operation why is that
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose I thought of I had a reference
+
+ align:start position:0%
+suppose I thought of I had a reference
+ 
+
+ align:start position:0%
+suppose I thought of I had a reference
+current and in this case since I'm
+
+ align:start position:0%
+current and in this case since I'm
+ 
+
+ align:start position:0%
+current and in this case since I'm
+talking about a boost converter let me
+
+ align:start position:0%
+talking about a boost converter let me
+ 
+
+ align:start position:0%
+talking about a boost converter let me
+think of suppose I had a reference
+
+ align:start position:0%
+think of suppose I had a reference
+ 
+
+ align:start position:0%
+think of suppose I had a reference
+current for current to draw to deliver
+
+ align:start position:0%
+current for current to draw to deliver
+ 
+
+ align:start position:0%
+current for current to draw to deliver
+the power I wanted from the output from
+
+ align:start position:0%
+the power I wanted from the output from
+ 
+
+ align:start position:0%
+the power I wanted from the output from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+input okay if I have a small Ripple
+
+ align:start position:0%
+input okay if I have a small Ripple
+ 
+
+ align:start position:0%
+input okay if I have a small Ripple
+converter and I say okay you know
+
+ align:start position:0%
+converter and I say okay you know
+ 
+
+ align:start position:0%
+converter and I say okay you know
+ideally speaking to support the load I
+
+ align:start position:0%
+ideally speaking to support the load I
+ 
+
+ align:start position:0%
+ideally speaking to support the load I
+had this low current reference and then
+
+ align:start position:0%
+had this low current reference and then
+ 
+
+ align:start position:0%
+had this low current reference and then
+I stepped it up for this higher current
+
+ align:start position:0%
+I stepped it up for this higher current
+ 
+
+ align:start position:0%
+I stepped it up for this higher current
+reference this is sort of I ref for the
+
+ align:start position:0%
+reference this is sort of I ref for the
+ 
+
+ align:start position:0%
+reference this is sort of I ref for the
+reference current for the inductor
+
+ align:start position:0%
+reference current for the inductor
+ 
+
+ align:start position:0%
+reference current for the inductor
+waveform right if I have a small Ripple
+
+ align:start position:0%
+waveform right if I have a small Ripple
+ 
+
+ align:start position:0%
+waveform right if I have a small Ripple
+converter right and it's Rippling like
+
+ align:start position:0%
+converter right and it's Rippling like
+ 
+
+ align:start position:0%
+converter right and it's Rippling like
+this and then I step the reference I
+
+ align:start position:0%
+this and then I step the reference I
+ 
+
+ align:start position:0%
+this and then I step the reference I
+want much more current to deliver more
+
+ align:start position:0%
+want much more current to deliver more
+ 
+
+ align:start position:0%
+want much more current to deliver more
+power what has to happen well the
+
+ align:start position:0%
+power what has to happen well the
+ 
+
+ align:start position:0%
+power what has to happen well the
+inductor current is going to slew
+
+ align:start position:0%
+inductor current is going to slew
+ 
+
+ align:start position:0%
+inductor current is going to slew
+up and eventually it can get there and I
+
+ align:start position:0%
+up and eventually it can get there and I
+ 
+
+ align:start position:0%
+up and eventually it can get there and I
+can deliver this again right but you
+
+ align:start position:0%
+can deliver this again right but you
+ 
+
+ align:start position:0%
+can deliver this again right but you
+notice that there's this time period
+
+ align:start position:0%
+notice that there's this time period
+ 
+
+ align:start position:0%
+notice that there's this time period
+where the inductor current takes a lot
+
+ align:start position:0%
+where the inductor current takes a lot
+ 
+
+ align:start position:0%
+where the inductor current takes a lot
+of time to change if the Ripple is small
+
+ align:start position:0%
+of time to change if the Ripple is small
+ 
+
+ align:start position:0%
+of time to change if the Ripple is small
+the inductor value is Big it takes a lot
+
+ align:start position:0%
+the inductor value is Big it takes a lot
+ 
+
+ align:start position:0%
+the inductor value is Big it takes a lot
+of time to put the voltage across the
+
+ align:start position:0%
+of time to put the voltage across the
+ 
+
+ align:start position:0%
+of time to put the voltage across the
+inductor to slew the current in it right
+
+ align:start position:0%
+inductor to slew the current in it right
+ 
+
+ align:start position:0%
+inductor to slew the current in it right
+and that means for all this time period
+
+ align:start position:0%
+and that means for all this time period
+ 
+
+ align:start position:0%
+and that means for all this time period
+you're not delivering the right output
+
+ align:start position:0%
+you're not delivering the right output
+ 
+
+ align:start position:0%
+you're not delivering the right output
+power or you're at least not drawing the
+
+ align:start position:0%
+power or you're at least not drawing the
+ 
+
+ align:start position:0%
+power or you're at least not drawing the
+right input power right so this
+
+ align:start position:0%
+right input power right so this
+ 
+
+ align:start position:0%
+right input power right so this
+converter its ability to change its
+
+ align:start position:0%
+converter its ability to change its
+ 
+
+ align:start position:0%
+converter its ability to change its
+operating point is limited by the small
+
+ align:start position:0%
+operating point is limited by the small
+ 
+
+ align:start position:0%
+operating point is limited by the small
+Ripple suppose I had a DCM
+
+ align:start position:0%
+Ripple suppose I had a DCM
+ 
+
+ align:start position:0%
+Ripple suppose I had a DCM
+converter well you know maybe I have
+
+ align:start position:0%
+converter well you know maybe I have
+ 
+
+ align:start position:0%
+converter well you know maybe I have
+something like this and I again I step
+
+ align:start position:0%
+something like this and I again I step
+ 
+
+ align:start position:0%
+something like this and I again I step
+my ripple but maybe in a DCM converter
+
+ align:start position:0%
+my ripple but maybe in a DCM converter
+ 
+
+ align:start position:0%
+my ripple but maybe in a DCM converter
+my inductor current looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and the next cycle I want more fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boom right I can deliver that almost
+
+ align:start position:0%
+boom right I can deliver that almost
+ 
+
+ align:start position:0%
+boom right I can deliver that almost
+instantly in other words the high Ripple
+
+ align:start position:0%
+instantly in other words the high Ripple
+ 
+
+ align:start position:0%
+instantly in other words the high Ripple
+means that I can change the average
+
+ align:start position:0%
+means that I can change the average
+ 
+
+ align:start position:0%
+means that I can change the average
+current in the inductor much faster
+
+ align:start position:0%
+current in the inductor much faster
+ 
+
+ align:start position:0%
+current in the inductor much faster
+maybe even within a cycle okay so
+
+ align:start position:0%
+maybe even within a cycle okay so
+ 
+
+ align:start position:0%
+maybe even within a cycle okay so
+there's on the one hand we often want
+
+ align:start position:0%
+there's on the one hand we often want
+ 
+
+ align:start position:0%
+there's on the one hand we often want
+small Ripple because we want nice
+
+ align:start position:0%
+small Ripple because we want nice
+ 
+
+ align:start position:0%
+small Ripple because we want nice
+waveform and not a lot of Ripple and we
+
+ align:start position:0%
+waveform and not a lot of Ripple and we
+ 
+
+ align:start position:0%
+waveform and not a lot of Ripple and we
+got to filter it on the other hand the
+
+ align:start position:0%
+got to filter it on the other hand the
+ 
+
+ align:start position:0%
+got to filter it on the other hand the
+ability to change the energy storage and
+
+ align:start position:0%
+ability to change the energy storage and
+ 
+
+ align:start position:0%
+ability to change the energy storage and
+the energy processing of the converter
+
+ align:start position:0%
+the energy processing of the converter
+ 
+
+ align:start position:0%
+the energy processing of the converter
+quickly might take you towards using DCM
+
+ align:start position:0%
+quickly might take you towards using DCM
+ 
+
+ align:start position:0%
+quickly might take you towards using DCM
+so for a very high transient response
+
+ align:start position:0%
+so for a very high transient response
+ 
+
+ align:start position:0%
+so for a very high transient response
+converter having high Ripple and
+
+ align:start position:0%
+converter having high Ripple and
+ 
+
+ align:start position:0%
+converter having high Ripple and
+possibly DCM operation can be a good
+
+ align:start position:0%
+possibly DCM operation can be a good
+ 
+
+ align:start position:0%
+possibly DCM operation can be a good
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+okay any last questions before we wrap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up okay uh next class we're going to
+
+ align:start position:0%
+up okay uh next class we're going to
+ 
+
+ align:start position:0%
+up okay uh next class we're going to
+start talking about how do I actually do
+
+ align:start position:0%
+start talking about how do I actually do
+ 
+
+ align:start position:0%
+start talking about how do I actually do
+things like design our inductors have a
+
+ align:start position:0%
+things like design our inductors have a
+ 
+
+ align:start position:0%
+things like design our inductors have a
+great day
\ No newline at end of file
diff --git a/t2hNMFoIv8w.txt b/t2hNMFoIv8w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3dbd83d11b1b88b4d8669ffb2bb2703f9567f146
--- /dev/null
+++ b/t2hNMFoIv8w.txt
@@ -0,0 +1,8272 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hello.
+
+ align:start position:0%
+Hello.
+ 
+
+ align:start position:0%
+Hello.
+So, welcome to the last lecture in
+
+ align:start position:0%
+So, welcome to the last lecture in
+ 
+
+ align:start position:0%
+So, welcome to the last lecture in
+003. So, there are more lectures
+
+ align:start position:0%
+003. So, there are more lectures
+ 
+
+ align:start position:0%
+003. So, there are more lectures
+scheduled, but I don't believe in trying
+
+ align:start position:0%
+scheduled, but I don't believe in trying
+ 
+
+ align:start position:0%
+scheduled, but I don't believe in trying
+to cram new material in the last couple
+
+ align:start position:0%
+to cram new material in the last couple
+ 
+
+ align:start position:0%
+to cram new material in the last couple
+of hours before the exam. So, no new
+
+ align:start position:0%
+of hours before the exam. So, no new
+ 
+
+ align:start position:0%
+of hours before the exam. So, no new
+material after today, although it will
+
+ align:start position:0%
+material after today, although it will
+ 
+
+ align:start position:0%
+material after today, although it will
+be helpful if you continue to try to
+
+ align:start position:0%
+be helpful if you continue to try to
+ 
+
+ align:start position:0%
+be helpful if you continue to try to
+work on problems and try to u
+
+ align:start position:0%
+work on problems and try to u
+ 
+
+ align:start position:0%
+work on problems and try to u
+internalize what we did more more
+
+ align:start position:0%
+internalize what we did more more
+ 
+
+ align:start position:0%
+internalize what we did more more
+recently. That's the idea. So, I'm not
+
+ align:start position:0%
+recently. That's the idea. So, I'm not
+ 
+
+ align:start position:0%
+recently. That's the idea. So, I'm not
+trying to pump new information in. That
+
+ align:start position:0%
+trying to pump new information in. That
+ 
+
+ align:start position:0%
+trying to pump new information in. That
+doesn't mean that there are things there
+
+ align:start position:0%
+doesn't mean that there are things there
+ 
+
+ align:start position:0%
+doesn't mean that there are things there
+aren't things that you should be doing.
+
+ align:start position:0%
+aren't things that you should be doing.
+ 
+
+ align:start position:0%
+aren't things that you should be doing.
+Okay. But uh after today, no new
+
+ align:start position:0%
+Okay. But uh after today, no new
+ 
+
+ align:start position:0%
+Okay. But uh after today, no new
+information. In fact, today there's no
+
+ align:start position:0%
+information. In fact, today there's no
+ 
+
+ align:start position:0%
+information. In fact, today there's no
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+information. There will be a session on
+
+ align:start position:0%
+information. There will be a session on
+ 
+
+ align:start position:0%
+information. There will be a session on
+Tuesday, but the idea is primarily to
+
+ align:start position:0%
+Tuesday, but the idea is primarily to
+ 
+
+ align:start position:0%
+Tuesday, but the idea is primarily to
+get feedback from you
+
+ align:start position:0%
+get feedback from you
+ 
+
+ align:start position:0%
+get feedback from you
+people. As I mentioned last time, we've
+
+ align:start position:0%
+people. As I mentioned last time, we've
+ 
+
+ align:start position:0%
+people. As I mentioned last time, we've
+changed a lot of things. We change a lot
+
+ align:start position:0%
+changed a lot of things. We change a lot
+ 
+
+ align:start position:0%
+changed a lot of things. We change a lot
+of things every term. And our primary
+
+ align:start position:0%
+of things every term. And our primary
+ 
+
+ align:start position:0%
+of things every term. And our primary
+source of information is the end of term
+
+ align:start position:0%
+source of information is the end of term
+ 
+
+ align:start position:0%
+source of information is the end of term
+surveys. Tell us what worked. Tell us
+
+ align:start position:0%
+surveys. Tell us what worked. Tell us
+ 
+
+ align:start position:0%
+surveys. Tell us what worked. Tell us
+what didn't work. Tell us what you like.
+
+ align:start position:0%
+what didn't work. Tell us what you like.
+ 
+
+ align:start position:0%
+what didn't work. Tell us what you like.
+Tell us what you didn't like. If you
+
+ align:start position:0%
+Tell us what you didn't like. If you
+ 
+
+ align:start position:0%
+Tell us what you didn't like. If you
+didn't like the electronic submission of
+
+ align:start position:0%
+didn't like the electronic submission of
+ 
+
+ align:start position:0%
+didn't like the electronic submission of
+homework, tell us. If you didn't like
+
+ align:start position:0%
+homework, tell us. If you didn't like
+ 
+
+ align:start position:0%
+homework, tell us. If you didn't like
+the tutor, tell us. If you would rather
+
+ align:start position:0%
+the tutor, tell us. If you would rather
+ 
+
+ align:start position:0%
+the tutor, tell us. If you would rather
+have individual office hours instead of
+
+ align:start position:0%
+have individual office hours instead of
+ 
+
+ align:start position:0%
+have individual office hours instead of
+block office hours, it's a good chance
+
+ align:start position:0%
+block office hours, it's a good chance
+ 
+
+ align:start position:0%
+block office hours, it's a good chance
+for you to tell us um what you think.
+
+ align:start position:0%
+for you to tell us um what you think.
+ 
+
+ align:start position:0%
+for you to tell us um what you think.
+And it's especially important that you
+
+ align:start position:0%
+And it's especially important that you
+ 
+
+ align:start position:0%
+And it's especially important that you
+fill out the uh online subject
+
+ align:start position:0%
+fill out the uh online subject
+ 
+
+ align:start position:0%
+fill out the uh online subject
+evaluation. So, please, if you have a
+
+ align:start position:0%
+evaluation. So, please, if you have a
+ 
+
+ align:start position:0%
+evaluation. So, please, if you have a
+laptop with a certificate on it, feel
+
+ align:start position:0%
+laptop with a certificate on it, feel
+ 
+
+ align:start position:0%
+laptop with a certificate on it, feel
+free to bring it to lecture next time.
+
+ align:start position:0%
+free to bring it to lecture next time.
+ 
+
+ align:start position:0%
+free to bring it to lecture next time.
+Uh that's one of the main ideas, but
+
+ align:start position:0%
+Uh that's one of the main ideas, but
+ 
+
+ align:start position:0%
+Uh that's one of the main ideas, but
+we'll also spend some time just
+
+ align:start position:0%
+we'll also spend some time just
+ 
+
+ align:start position:0%
+we'll also spend some time just
+discussing what uh what you think uh
+
+ align:start position:0%
+discussing what uh what you think uh
+ 
+
+ align:start position:0%
+discussing what uh what you think uh
+what you would suggest for improvements
+
+ align:start position:0%
+what you would suggest for improvements
+ 
+
+ align:start position:0%
+what you would suggest for improvements
+for next
+
+ align:start position:0%
+for next
+ 
+
+ align:start position:0%
+for next
+time. Questions or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comments? Okay. So today is mostly just
+
+ align:start position:0%
+comments? Okay. So today is mostly just
+ 
+
+ align:start position:0%
+comments? Okay. So today is mostly just
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+fun. Today is mostly just to tell you
+
+ align:start position:0%
+fun. Today is mostly just to tell you
+ 
+
+ align:start position:0%
+fun. Today is mostly just to tell you
+about the way 63 plays out in
+
+ align:start position:0%
+about the way 63 plays out in
+ 
+
+ align:start position:0%
+about the way 63 plays out in
+technologies that you might have some uh
+
+ align:start position:0%
+technologies that you might have some uh
+ 
+
+ align:start position:0%
+technologies that you might have some uh
+interest in. And I chose a technology
+
+ align:start position:0%
+interest in. And I chose a technology
+ 
+
+ align:start position:0%
+interest in. And I chose a technology
+that I am particularly interested in
+
+ align:start position:0%
+that I am particularly interested in
+ 
+
+ align:start position:0%
+that I am particularly interested in
+because I've, as I probably have
+
+ align:start position:0%
+because I've, as I probably have
+ 
+
+ align:start position:0%
+because I've, as I probably have
+mentioned in the past, like many of you,
+
+ align:start position:0%
+mentioned in the past, like many of you,
+ 
+
+ align:start position:0%
+mentioned in the past, like many of you,
+I was afflicted with an addiction of
+
+ align:start position:0%
+I was afflicted with an addiction of
+ 
+
+ align:start position:0%
+I was afflicted with an addiction of
+with music at about your age. I
+
+ align:start position:0%
+with music at about your age. I
+ 
+
+ align:start position:0%
+with music at about your age. I
+recovered. You will too.
+
+ align:start position:0%
+recovered. You will too.
+ 
+
+ align:start position:0%
+recovered. You will too.
+Um, but I was very interested in it. It
+
+ align:start position:0%
+Um, but I was very interested in it. It
+ 
+
+ align:start position:0%
+Um, but I was very interested in it. It
+was a very hot topic. And I want to talk
+
+ align:start position:0%
+was a very hot topic. And I want to talk
+ 
+
+ align:start position:0%
+was a very hot topic. And I want to talk
+about some of the things that 003 has
+
+ align:start position:0%
+about some of the things that 003 has
+ 
+
+ align:start position:0%
+about some of the things that 003 has
+done to make that industry very
+
+ align:start position:0%
+done to make that industry very
+ 
+
+ align:start position:0%
+done to make that industry very
+different today from what it was when I
+
+ align:start position:0%
+different today from what it was when I
+ 
+
+ align:start position:0%
+different today from what it was when I
+was an
+
+ align:start position:0%
+was an
+ 
+
+ align:start position:0%
+was an
+undergraduate. It may not surprise
+
+ align:start position:0%
+undergraduate. It may not surprise
+ 
+
+ align:start position:0%
+undergraduate. It may not surprise
+you, but it surprises
+
+ align:start position:0%
+you, but it surprises
+ 
+
+ align:start position:0%
+you, but it surprises
+me that the technology that we used was
+
+ align:start position:0%
+me that the technology that we used was
+ 
+
+ align:start position:0%
+me that the technology that we used was
+really not very different from the
+
+ align:start position:0%
+really not very different from the
+ 
+
+ align:start position:0%
+really not very different from the
+technology that the inventor invented.
+
+ align:start position:0%
+technology that the inventor invented.
+ 
+
+ align:start position:0%
+technology that the inventor invented.
+So who invented the uh photograph?
+
+ align:start position:0%
+So who invented the uh photograph?
+ 
+
+ align:start position:0%
+So who invented the uh photograph?
+You can look at the notes. You're
+
+ align:start position:0%
+You can look at the notes. You're
+ 
+
+ align:start position:0%
+You can look at the notes. You're
+supposed to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that. Just shout, right? Makes me feel
+
+ align:start position:0%
+that. Just shout, right? Makes me feel
+ 
+
+ align:start position:0%
+that. Just shout, right? Makes me feel
+better. Thank you,
+
+ align:start position:0%
+better. Thank you,
+ 
+
+ align:start position:0%
+better. Thank you,
+Edison. So, Edison was, of course, a
+
+ align:start position:0%
+Edison. So, Edison was, of course, a
+ 
+
+ align:start position:0%
+Edison. So, Edison was, of course, a
+genius uh and a prolific inventor. He
+
+ align:start position:0%
+genius uh and a prolific inventor. He
+ 
+
+ align:start position:0%
+genius uh and a prolific inventor. He
+was interested at the time he invented
+
+ align:start position:0%
+was interested at the time he invented
+ 
+
+ align:start position:0%
+was interested at the time he invented
+the photograph, he was interested in two
+
+ align:start position:0%
+the photograph, he was interested in two
+ 
+
+ align:start position:0%
+the photograph, he was interested in two
+things, two things that he was trying to
+
+ align:start position:0%
+things, two things that he was trying to
+ 
+
+ align:start position:0%
+things, two things that he was trying to
+draw, um relations between, telegraphy
+
+ align:start position:0%
+draw, um relations between, telegraphy
+ 
+
+ align:start position:0%
+draw, um relations between, telegraphy
+and telefan. We talked about telegraphy
+
+ align:start position:0%
+and telefan. We talked about telegraphy
+ 
+
+ align:start position:0%
+and telefan. We talked about telegraphy
+before. Telegraphy, telegraph was a way
+
+ align:start position:0%
+before. Telegraphy, telegraph was a way
+ 
+
+ align:start position:0%
+before. Telegraphy, telegraph was a way
+of getting messages
+
+ align:start position:0%
+of getting messages
+ 
+
+ align:start position:0%
+of getting messages
+pointtooint. So person A wanted to get a
+
+ align:start position:0%
+pointtooint. So person A wanted to get a
+ 
+
+ align:start position:0%
+pointtooint. So person A wanted to get a
+message to person B and it would be
+
+ align:start position:0%
+message to person B and it would be
+ 
+
+ align:start position:0%
+message to person B and it would be
+transmitted via the telegraph system.
+
+ align:start position:0%
+transmitted via the telegraph system.
+ 
+
+ align:start position:0%
+transmitted via the telegraph system.
+Now I kind of oversimplified the way the
+
+ align:start position:0%
+Now I kind of oversimplified the way the
+ 
+
+ align:start position:0%
+Now I kind of oversimplified the way the
+telegraph system worked when I talked
+
+ align:start position:0%
+telegraph system worked when I talked
+ 
+
+ align:start position:0%
+telegraph system worked when I talked
+about it the last time. It really worked
+
+ align:start position:0%
+about it the last time. It really worked
+ 
+
+ align:start position:0%
+about it the last time. It really worked
+a lot more like message
+
+ align:start position:0%
+a lot more like message
+ 
+
+ align:start position:0%
+a lot more like message
+passing than you might have thought.
+
+ align:start position:0%
+passing than you might have thought.
+ 
+
+ align:start position:0%
+passing than you might have thought.
+What would happen is that there wouldn't
+
+ align:start position:0%
+What would happen is that there wouldn't
+ 
+
+ align:start position:0%
+What would happen is that there wouldn't
+be a direct connection between person A
+
+ align:start position:0%
+be a direct connection between person A
+ 
+
+ align:start position:0%
+be a direct connection between person A
+and person B. it might have to go
+
+ align:start position:0%
+and person B. it might have to go
+ 
+
+ align:start position:0%
+and person B. it might have to go
+through six
+
+ align:start position:0%
+through six
+ 
+
+ align:start position:0%
+through six
+relays. So in order to get to
+
+ align:start position:0%
+relays. So in order to get to
+ 
+
+ align:start position:0%
+relays. So in order to get to
+California, it might be important that
+
+ align:start position:0%
+California, it might be important that
+ 
+
+ align:start position:0%
+California, it might be important that
+um a message that originated in Boston
+
+ align:start position:0%
+um a message that originated in Boston
+ 
+
+ align:start position:0%
+um a message that originated in Boston
+would go to New York and from New York
+
+ align:start position:0%
+would go to New York and from New York
+ 
+
+ align:start position:0%
+would go to New York and from New York
+to I don't know Pennsylvania, from
+
+ align:start position:0%
+to I don't know Pennsylvania, from
+ 
+
+ align:start position:0%
+to I don't know Pennsylvania, from
+Pennsylvania to Chicago, uh etc. So it
+
+ align:start position:0%
+Pennsylvania to Chicago, uh etc. So it
+ 
+
+ align:start position:0%
+Pennsylvania to Chicago, uh etc. So it
+there may not be a direct route over
+
+ align:start position:0%
+there may not be a direct route over
+ 
+
+ align:start position:0%
+there may not be a direct route over
+long distances. So the way that was
+
+ align:start position:0%
+long distances. So the way that was
+ 
+
+ align:start position:0%
+long distances. So the way that was
+done, you would take your message to
+
+ align:start position:0%
+done, you would take your message to
+ 
+
+ align:start position:0%
+done, you would take your message to
+telegraph office A. The operator would
+
+ align:start position:0%
+telegraph office A. The operator would
+ 
+
+ align:start position:0%
+telegraph office A. The operator would
+uh key it in. It would get written down
+
+ align:start position:0%
+uh key it in. It would get written down
+ 
+
+ align:start position:0%
+uh key it in. It would get written down
+by the receiver, say in New
+
+ align:start position:0%
+by the receiver, say in New
+ 
+
+ align:start position:0%
+by the receiver, say in New
+York, who would listen to the message,
+
+ align:start position:0%
+York, who would listen to the message,
+ 
+
+ align:start position:0%
+York, who would listen to the message,
+write it out, basically reproducing your
+
+ align:start position:0%
+write it out, basically reproducing your
+ 
+
+ align:start position:0%
+write it out, basically reproducing your
+message there, then key it in to the
+
+ align:start position:0%
+message there, then key it in to the
+ 
+
+ align:start position:0%
+message there, then key it in to the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+relay. So it might actually be keyed in
+
+ align:start position:0%
+relay. So it might actually be keyed in
+ 
+
+ align:start position:0%
+relay. So it might actually be keyed in
+uh a dozen times before it hits the
+
+ align:start position:0%
+uh a dozen times before it hits the
+ 
+
+ align:start position:0%
+uh a dozen times before it hits the
+final destination. And that was tedious,
+
+ align:start position:0%
+final destination. And that was tedious,
+ 
+
+ align:start position:0%
+final destination. And that was tedious,
+laborious, hard. And um Edison was
+
+ align:start position:0%
+laborious, hard. And um Edison was
+ 
+
+ align:start position:0%
+laborious, hard. And um Edison was
+interested in uh fixing that. And to do
+
+ align:start position:0%
+interested in uh fixing that. And to do
+ 
+
+ align:start position:0%
+interested in uh fixing that. And to do
+so, he invented a paper tape system so
+
+ align:start position:0%
+so, he invented a paper tape system so
+ 
+
+ align:start position:0%
+so, he invented a paper tape system so
+that the receiver wouldn't need to
+
+ align:start position:0%
+that the receiver wouldn't need to
+ 
+
+ align:start position:0%
+that the receiver wouldn't need to
+listen. It would just punch out paper
+
+ align:start position:0%
+listen. It would just punch out paper
+ 
+
+ align:start position:0%
+listen. It would just punch out paper
+tape as the as the clicks came in. So as
+
+ align:start position:0%
+tape as the as the clicks came in. So as
+ 
+
+ align:start position:0%
+tape as the as the clicks came in. So as
+the dots and dashes came in, it would
+
+ align:start position:0%
+the dots and dashes came in, it would
+ 
+
+ align:start position:0%
+the dots and dashes came in, it would
+make holes in paper. The holes in paper
+
+ align:start position:0%
+make holes in paper. The holes in paper
+ 
+
+ align:start position:0%
+make holes in paper. The holes in paper
+then could be used to transmit to the
+
+ align:start position:0%
+then could be used to transmit to the
+ 
+
+ align:start position:0%
+then could be used to transmit to the
+next station. So Edison did that.
+
+ align:start position:0%
+next station. So Edison did that.
+ 
+
+ align:start position:0%
+next station. So Edison did that.
+He was interested in thinking about
+
+ align:start position:0%
+He was interested in thinking about
+ 
+
+ align:start position:0%
+He was interested in thinking about
+whether you could do the same sort of
+
+ align:start position:0%
+whether you could do the same sort of
+ 
+
+ align:start position:0%
+whether you could do the same sort of
+thing with other kinds of signals
+
+ align:start position:0%
+thing with other kinds of signals
+ 
+
+ align:start position:0%
+thing with other kinds of signals
+besides telegraph signals. And that's
+
+ align:start position:0%
+besides telegraph signals. And that's
+ 
+
+ align:start position:0%
+besides telegraph signals. And that's
+the origin of the photograph. He was
+
+ align:start position:0%
+the origin of the photograph. He was
+ 
+
+ align:start position:0%
+the origin of the photograph. He was
+interested in could you send a voice
+
+ align:start position:0%
+interested in could you send a voice
+ 
+
+ align:start position:0%
+interested in could you send a voice
+message to a relay have it automatically
+
+ align:start position:0%
+message to a relay have it automatically
+ 
+
+ align:start position:0%
+message to a relay have it automatically
+recorded so that it could then be
+
+ align:start position:0%
+recorded so that it could then be
+ 
+
+ align:start position:0%
+recorded so that it could then be
+rebroadcast over the next link. So he
+
+ align:start position:0%
+rebroadcast over the next link. So he
+ 
+
+ align:start position:0%
+rebroadcast over the next link. So he
+was kind of imagining a telephone
+
+ align:start position:0%
+was kind of imagining a telephone
+ 
+
+ align:start position:0%
+was kind of imagining a telephone
+network that was based on the same
+
+ align:start position:0%
+network that was based on the same
+ 
+
+ align:start position:0%
+network that was based on the same
+principle that the telegraph network had
+
+ align:start position:0%
+principle that the telegraph network had
+ 
+
+ align:start position:0%
+principle that the telegraph network had
+been. So the idea was to uh try to
+
+ align:start position:0%
+been. So the idea was to uh try to
+ 
+
+ align:start position:0%
+been. So the idea was to uh try to
+record an audio signal of the type that
+
+ align:start position:0%
+record an audio signal of the type that
+ 
+
+ align:start position:0%
+record an audio signal of the type that
+would come across a um telephone
+
+ align:start position:0%
+would come across a um telephone
+ 
+
+ align:start position:0%
+would come across a um telephone
+wire. So uh he got together with his aid
+
+ align:start position:0%
+wire. So uh he got together with his aid
+ 
+
+ align:start position:0%
+wire. So uh he got together with his aid
+bachelor and made this drawing. This was
+
+ align:start position:0%
+bachelor and made this drawing. This was
+ 
+
+ align:start position:0%
+bachelor and made this drawing. This was
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+1877 and 30 hours later kind of rapid
+
+ align:start position:0%
+1877 and 30 hours later kind of rapid
+ 
+
+ align:start position:0%
+1877 and 30 hours later kind of rapid
+prototyping for the time uh his
+
+ align:start position:0%
+prototyping for the time uh his
+ 
+
+ align:start position:0%
+prototyping for the time uh his
+machinist made this. So that's the first
+
+ align:start position:0%
+machinist made this. So that's the first
+ 
+
+ align:start position:0%
+machinist made this. So that's the first
+photograph. The idea was uh you wrap
+
+ align:start position:0%
+photograph. The idea was uh you wrap
+ 
+
+ align:start position:0%
+photograph. The idea was uh you wrap
+that disc with a piece of wax
+
+ align:start position:0%
+that disc with a piece of wax
+ 
+
+ align:start position:0%
+that disc with a piece of wax
+paper. You turn the
+
+ align:start position:0%
+paper. You turn the
+ 
+
+ align:start position:0%
+paper. You turn the
+crank. As you turn the crank, uh this
+
+ align:start position:0%
+crank. As you turn the crank, uh this
+ 
+
+ align:start position:0%
+crank. As you turn the crank, uh this
+thing is connected to a screw so that
+
+ align:start position:0%
+thing is connected to a screw so that
+ 
+
+ align:start position:0%
+thing is connected to a screw so that
+it's moving this way at the same time
+
+ align:start position:0%
+it's moving this way at the same time
+ 
+
+ align:start position:0%
+it's moving this way at the same time
+this big thing is going around that way.
+
+ align:start position:0%
+this big thing is going around that way.
+ 
+
+ align:start position:0%
+this big thing is going around that way.
+This is a diaphragm so that you shout in
+
+ align:start position:0%
+This is a diaphragm so that you shout in
+ 
+
+ align:start position:0%
+This is a diaphragm so that you shout in
+here and there's a needle connected on
+
+ align:start position:0%
+here and there's a needle connected on
+ 
+
+ align:start position:0%
+here and there's a needle connected on
+the other end so that as you shout the
+
+ align:start position:0%
+the other end so that as you shout the
+ 
+
+ align:start position:0%
+the other end so that as you shout the
+needle gets moved with audio frequencies
+
+ align:start position:0%
+needle gets moved with audio frequencies
+ 
+
+ align:start position:0%
+needle gets moved with audio frequencies
+contained in your voice. Okay. So how do
+
+ align:start position:0%
+contained in your voice. Okay. So how do
+ 
+
+ align:start position:0%
+contained in your voice. Okay. So how do
+you do this then? So you grab the
+
+ align:start position:0%
+you do this then? So you grab the
+ 
+
+ align:start position:0%
+you do this then? So you grab the
+handle, you put a new sheet of wax paper
+
+ align:start position:0%
+handle, you put a new sheet of wax paper
+ 
+
+ align:start position:0%
+handle, you put a new sheet of wax paper
+on it, you grab the handle, you turn at
+
+ align:start position:0%
+on it, you grab the handle, you turn at
+ 
+
+ align:start position:0%
+on it, you grab the handle, you turn at
+a constant speed and shout.
+
+ align:start position:0%
+a constant speed and shout.
+ 
+
+ align:start position:0%
+a constant speed and shout.
+Okay, it took some
+
+ align:start position:0%
+Okay, it took some
+ 
+
+ align:start position:0%
+Okay, it took some
+coordination. Uh, the remarkable thing
+
+ align:start position:0%
+coordination. Uh, the remarkable thing
+ 
+
+ align:start position:0%
+coordination. Uh, the remarkable thing
+is it
+
+ align:start position:0%
+is it
+ 
+
+ align:start position:0%
+is it
+worked. So Edison said, "Mary had a
+
+ align:start position:0%
+worked. So Edison said, "Mary had a
+ 
+
+ align:start position:0%
+worked. So Edison said, "Mary had a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+lamb." And on replaying it, the device
+
+ align:start position:0%
+lamb." And on replaying it, the device
+ 
+
+ align:start position:0%
+lamb." And on replaying it, the device
+said, "Mary had a little lamb." It was a
+
+ align:start position:0%
+said, "Mary had a little lamb." It was a
+ 
+
+ align:start position:0%
+said, "Mary had a little lamb." It was a
+the very first try it worked. Now, it
+
+ align:start position:0%
+the very first try it worked. Now, it
+ 
+
+ align:start position:0%
+the very first try it worked. Now, it
+didn't work all that great. What do you
+
+ align:start position:0%
+didn't work all that great. What do you
+ 
+
+ align:start position:0%
+didn't work all that great. What do you
+suppose happened?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Noise. Of course, there was noise. Yes.
+
+ align:start position:0%
+Noise. Of course, there was noise. Yes.
+ 
+
+ align:start position:0%
+Noise. Of course, there was noise. Yes.
+frequency was
+
+ align:start position:0%
+frequency was
+ 
+
+ align:start position:0%
+frequency was
+terrible. Anything more disastrous?
+
+ align:start position:0%
+terrible. Anything more disastrous?
+ 
+
+ align:start position:0%
+terrible. Anything more disastrous?
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Cranking is not at all constant. So you
+
+ align:start position:0%
+Cranking is not at all constant. So you
+ 
+
+ align:start position:0%
+Cranking is not at all constant. So you
+can make it sound like uh Alvin the
+
+ align:start position:0%
+can make it sound like uh Alvin the
+ 
+
+ align:start position:0%
+can make it sound like uh Alvin the
+Chipmunk if you like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worse. How long do you think the
+
+ align:start position:0%
+worse. How long do you think the
+ 
+
+ align:start position:0%
+worse. How long do you think the
+recording lasted?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, about once.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so the problem was to get the energy
+
+ align:start position:0%
+So, so the problem was to get the energy
+ 
+
+ align:start position:0%
+So, so the problem was to get the energy
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+out, right? You have to, so after
+
+ align:start position:0%
+out, right? You have to, so after
+ 
+
+ align:start position:0%
+out, right? You have to, so after
+recording, right? So, you clean sheet of
+
+ align:start position:0%
+recording, right? So, you clean sheet of
+ 
+
+ align:start position:0%
+recording, right? So, you clean sheet of
+wax paper, crank, crank, crank, yell,
+
+ align:start position:0%
+wax paper, crank, crank, crank, yell,
+ 
+
+ align:start position:0%
+wax paper, crank, crank, crank, yell,
+scream, and now reset the needle to the
+
+ align:start position:0%
+scream, and now reset the needle to the
+ 
+
+ align:start position:0%
+scream, and now reset the needle to the
+beginning and now crank without
+
+ align:start position:0%
+beginning and now crank without
+ 
+
+ align:start position:0%
+beginning and now crank without
+screaming.
+
+ align:start position:0%
+screaming.
+ 
+
+ align:start position:0%
+screaming.
+In order to get the the message back
+
+ align:start position:0%
+In order to get the the message back
+ 
+
+ align:start position:0%
+In order to get the the message back
+out, you had to push on the needle so
+
+ align:start position:0%
+out, you had to push on the needle so
+ 
+
+ align:start position:0%
+out, you had to push on the needle so
+that it would follow the indentations on
+
+ align:start position:0%
+that it would follow the indentations on
+ 
+
+ align:start position:0%
+that it would follow the indentations on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+wax. But if you pushed hard enough for
+
+ align:start position:0%
+wax. But if you pushed hard enough for
+ 
+
+ align:start position:0%
+wax. But if you pushed hard enough for
+it to follow it, what would
+
+ align:start position:0%
+it to follow it, what would
+ 
+
+ align:start position:0%
+it to follow it, what would
+happen? It erased the message, right? So
+
+ align:start position:0%
+happen? It erased the message, right? So
+ 
+
+ align:start position:0%
+happen? It erased the message, right? So
+it was kind of a destructive readout. It
+
+ align:start position:0%
+it was kind of a destructive readout. It
+ 
+
+ align:start position:0%
+it was kind of a destructive readout. It
+was a it didn't last very long because
+
+ align:start position:0%
+was a it didn't last very long because
+ 
+
+ align:start position:0%
+was a it didn't last very long because
+the act of reading it back out tended to
+
+ align:start position:0%
+the act of reading it back out tended to
+ 
+
+ align:start position:0%
+the act of reading it back out tended to
+erase it. So he redid the thing with uh
+
+ align:start position:0%
+erase it. So he redid the thing with uh
+ 
+
+ align:start position:0%
+erase it. So he redid the thing with uh
+tinfoil that worked much better and in
+
+ align:start position:0%
+tinfoil that worked much better and in
+ 
+
+ align:start position:0%
+tinfoil that worked much better and in
+fact it caught on like like
+
+ align:start position:0%
+fact it caught on like like
+ 
+
+ align:start position:0%
+fact it caught on like like
+overnight. So within two years he was
+
+ align:start position:0%
+overnight. So within two years he was
+ 
+
+ align:start position:0%
+overnight. So within two years he was
+invited to the Nationalmies of Sciences
+
+ align:start position:0%
+invited to the Nationalmies of Sciences
+ 
+
+ align:start position:0%
+invited to the Nationalmies of Sciences
+to give a talk on this. That's him
+
+ align:start position:0%
+to give a talk on this. That's him
+ 
+
+ align:start position:0%
+to give a talk on this. That's him
+posing at the National Academy of
+
+ align:start position:0%
+posing at the National Academy of
+ 
+
+ align:start position:0%
+posing at the National Academy of
+Sciences with his then
+
+ align:start position:0%
+Sciences with his then
+ 
+
+ align:start position:0%
+Sciences with his then
+photograph. They loved
+
+ align:start position:0%
+photograph. They loved
+ 
+
+ align:start position:0%
+photograph. They loved
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Now despite the fact they loved it,
+
+ align:start position:0%
+Now despite the fact they loved it,
+ 
+
+ align:start position:0%
+Now despite the fact they loved it,
+nobody knew what to do with it.
+
+ align:start position:0%
+nobody knew what to do with it.
+ 
+
+ align:start position:0%
+nobody knew what to do with it.
+Everybody thought it was just the
+
+ align:start position:0%
+Everybody thought it was just the
+ 
+
+ align:start position:0%
+Everybody thought it was just the
+neatest thing in the world, but they
+
+ align:start position:0%
+neatest thing in the world, but they
+ 
+
+ align:start position:0%
+neatest thing in the world, but they
+didn't have a clue what to do with it.
+
+ align:start position:0%
+didn't have a clue what to do with it.
+ 
+
+ align:start position:0%
+didn't have a clue what to do with it.
+And of course, Edison wanted was a bit
+
+ align:start position:0%
+And of course, Edison wanted was a bit
+ 
+
+ align:start position:0%
+And of course, Edison wanted was a bit
+self-promoting, so he wrote articles
+
+ align:start position:0%
+self-promoting, so he wrote articles
+ 
+
+ align:start position:0%
+self-promoting, so he wrote articles
+about it and tried to explain. He put in
+
+ align:start position:0%
+about it and tried to explain. He put in
+ 
+
+ align:start position:0%
+about it and tried to explain. He put in
+the patent. In the patent, he listed
+
+ align:start position:0%
+the patent. In the patent, he listed
+ 
+
+ align:start position:0%
+the patent. In the patent, he listed
+about seven or eight things you could do
+
+ align:start position:0%
+about seven or eight things you could do
+ 
+
+ align:start position:0%
+about seven or eight things you could do
+with this thing. Today, they sound a
+
+ align:start position:0%
+with this thing. Today, they sound a
+ 
+
+ align:start position:0%
+with this thing. Today, they sound a
+little far-fetched.
+
+ align:start position:0%
+little far-fetched.
+ 
+
+ align:start position:0%
+little far-fetched.
+um recording uh important historical
+
+ align:start position:0%
+um recording uh important historical
+ 
+
+ align:start position:0%
+um recording uh important historical
+addresses, medical
+
+ align:start position:0%
+addresses, medical
+ 
+
+ align:start position:0%
+addresses, medical
+transcription, the one that seems most
+
+ align:start position:0%
+transcription, the one that seems most
+ 
+
+ align:start position:0%
+transcription, the one that seems most
+uh I don't know, sort of gruesome to me,
+
+ align:start position:0%
+uh I don't know, sort of gruesome to me,
+ 
+
+ align:start position:0%
+uh I don't know, sort of gruesome to me,
+recording the last will and testament of
+
+ align:start position:0%
+recording the last will and testament of
+ 
+
+ align:start position:0%
+recording the last will and testament of
+a person as they're
+
+ align:start position:0%
+a person as they're
+ 
+
+ align:start position:0%
+a person as they're
+dying. Now, that sounds gruesome to
+
+ align:start position:0%
+dying. Now, that sounds gruesome to
+ 
+
+ align:start position:0%
+dying. Now, that sounds gruesome to
+me, but imagine what it was like back
+
+ align:start position:0%
+me, but imagine what it was like back
+ 
+
+ align:start position:0%
+me, but imagine what it was like back
+then. Back then, nobody had ever heard
+
+ align:start position:0%
+then. Back then, nobody had ever heard
+ 
+
+ align:start position:0%
+then. Back then, nobody had ever heard
+somebody's voice who was not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alive. I mean, the technology had didn't
+
+ align:start position:0%
+alive. I mean, the technology had didn't
+ 
+
+ align:start position:0%
+alive. I mean, the technology had didn't
+exist. So, all of a sudden, he's
+
+ align:start position:0%
+exist. So, all of a sudden, he's
+ 
+
+ align:start position:0%
+exist. So, all of a sudden, he's
+proposing to record the dying breath of
+
+ align:start position:0%
+proposing to record the dying breath of
+ 
+
+ align:start position:0%
+proposing to record the dying breath of
+it kind of mortified everybody. What
+
+ align:start position:0%
+it kind of mortified everybody. What
+ 
+
+ align:start position:0%
+it kind of mortified everybody. What
+Edison didn't like was the idea that it
+
+ align:start position:0%
+Edison didn't like was the idea that it
+ 
+
+ align:start position:0%
+Edison didn't like was the idea that it
+would be used for music. Okay, that was
+
+ align:start position:0%
+would be used for music. Okay, that was
+ 
+
+ align:start position:0%
+would be used for music. Okay, that was
+trivial. He was doing important
+
+ align:start position:0%
+trivial. He was doing important
+ 
+
+ align:start position:0%
+trivial. He was doing important
+science. So he didn't like the idea that
+
+ align:start position:0%
+science. So he didn't like the idea that
+ 
+
+ align:start position:0%
+science. So he didn't like the idea that
+this would be used for music and so he
+
+ align:start position:0%
+this would be used for music and so he
+ 
+
+ align:start position:0%
+this would be used for music and so he
+downplayed that his entire life.
+
+ align:start position:0%
+downplayed that his entire life.
+ 
+
+ align:start position:0%
+downplayed that his entire life.
+Nevertheless, the commercial
+
+ align:start position:0%
+Nevertheless, the commercial
+ 
+
+ align:start position:0%
+Nevertheless, the commercial
+success was
+
+ align:start position:0%
+success was
+ 
+
+ align:start position:0%
+success was
+music. He was trying to promote this as
+
+ align:start position:0%
+music. He was trying to promote this as
+ 
+
+ align:start position:0%
+music. He was trying to promote this as
+a system for
+
+ align:start position:0%
+a system for
+ 
+
+ align:start position:0%
+a system for
+recording speech, right? Medical
+
+ align:start position:0%
+recording speech, right? Medical
+ 
+
+ align:start position:0%
+recording speech, right? Medical
+transcription, dying breaths, historical
+
+ align:start position:0%
+transcription, dying breaths, historical
+ 
+
+ align:start position:0%
+transcription, dying breaths, historical
+talks. That didn't really catch on. This
+
+ align:start position:0%
+talks. That didn't really catch on. This
+ 
+
+ align:start position:0%
+talks. That didn't really catch on. This
+was a playback device.
+
+ align:start position:0%
+was a playback device.
+ 
+
+ align:start position:0%
+was a playback device.
+This really did catch on. Uh this was
+
+ align:start position:0%
+This really did catch on. Uh this was
+ 
+
+ align:start position:0%
+This really did catch on. Uh this was
+about 60 years later. It's virtually
+
+ align:start position:0%
+about 60 years later. It's virtually
+ 
+
+ align:start position:0%
+about 60 years later. It's virtually
+identical. It became a piece of
+
+ align:start position:0%
+identical. It became a piece of
+ 
+
+ align:start position:0%
+identical. It became a piece of
+furniture that everybody had in their
+
+ align:start position:0%
+furniture that everybody had in their
+ 
+
+ align:start position:0%
+furniture that everybody had in their
+house. Uh the cylinders had gone back to
+
+ align:start position:0%
+house. Uh the cylinders had gone back to
+ 
+
+ align:start position:0%
+house. Uh the cylinders had gone back to
+wax. Alexander Graanbell had worked on
+
+ align:start position:0%
+wax. Alexander Graanbell had worked on
+ 
+
+ align:start position:0%
+wax. Alexander Graanbell had worked on
+the problem. He figured out how to make
+
+ align:start position:0%
+the problem. He figured out how to make
+ 
+
+ align:start position:0%
+the problem. He figured out how to make
+long-lasting
+
+ align:start position:0%
+long-lasting
+ 
+
+ align:start position:0%
+long-lasting
+wax. This crank cranked a
+
+ align:start position:0%
+wax. This crank cranked a
+ 
+
+ align:start position:0%
+wax. This crank cranked a
+spring so you could crank it up, but
+
+ align:start position:0%
+spring so you could crank it up, but
+ 
+
+ align:start position:0%
+spring so you could crank it up, but
+over time it would play. So, you didn't
+
+ align:start position:0%
+over time it would play. So, you didn't
+ 
+
+ align:start position:0%
+over time it would play. So, you didn't
+need to go at exactly the right speed
+
+ align:start position:0%
+need to go at exactly the right speed
+ 
+
+ align:start position:0%
+need to go at exactly the right speed
+anymore. Uh, a number of big
+
+ align:start position:0%
+anymore. Uh, a number of big
+ 
+
+ align:start position:0%
+anymore. Uh, a number of big
+improvements. The cylinders held two
+
+ align:start position:0%
+improvements. The cylinders held two
+ 
+
+ align:start position:0%
+improvements. The cylinders held two
+minutes of recording, so they weren't
+
+ align:start position:0%
+minutes of recording, so they weren't
+ 
+
+ align:start position:0%
+minutes of recording, so they weren't
+exactly long
+
+ align:start position:0%
+exactly long
+ 
+
+ align:start position:0%
+exactly long
+playing. Okay. This was uh the same
+
+ align:start position:0%
+playing. Okay. This was uh the same
+ 
+
+ align:start position:0%
+playing. Okay. This was uh the same
+model of uh photograph I had in college.
+
+ align:start position:0%
+model of uh photograph I had in college.
+ 
+
+ align:start position:0%
+model of uh photograph I had in college.
+Okay. And it's actually remarkably
+
+ align:start position:0%
+Okay. And it's actually remarkably
+ 
+
+ align:start position:0%
+Okay. And it's actually remarkably
+similar. So, uh there's some
+
+ align:start position:0%
+similar. So, uh there's some
+ 
+
+ align:start position:0%
+similar. So, uh there's some
+differences.
+
+ align:start position:0%
+differences.
+ 
+
+ align:start position:0%
+differences.
+There was no
+
+ align:start position:0%
+There was no
+ 
+
+ align:start position:0%
+There was no
+crank. We had
+
+ align:start position:0%
+crank. We had
+ 
+
+ align:start position:0%
+crank. We had
+electricity. It had a motor. So, the
+
+ align:start position:0%
+electricity. It had a motor. So, the
+ 
+
+ align:start position:0%
+electricity. It had a motor. So, the
+motor propelled it. It was no longer a
+
+ align:start position:0%
+motor propelled it. It was no longer a
+ 
+
+ align:start position:0%
+motor propelled it. It was no longer a
+cylinder. Now, it's a disc. There was no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+screw. So, how does the needle track the
+
+ align:start position:0%
+screw. So, how does the needle track the
+ 
+
+ align:start position:0%
+screw. So, how does the needle track the
+the grooves if there's no screw?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There's a there's a spiral. So, the the
+
+ align:start position:0%
+There's a there's a spiral. So, the the
+ 
+
+ align:start position:0%
+There's a there's a spiral. So, the the
+records had a spiral. That's right.
+
+ align:start position:0%
+records had a spiral. That's right.
+ 
+
+ align:start position:0%
+records had a spiral. That's right.
+What held what made the re So this was
+
+ align:start position:0%
+What held what made the re So this was
+ 
+
+ align:start position:0%
+What held what made the re So this was
+the uh thing that read the the grooves.
+
+ align:start position:0%
+the uh thing that read the the grooves.
+ 
+
+ align:start position:0%
+the uh thing that read the the grooves.
+What what held that in the
+
+ align:start position:0%
+What what held that in the
+ 
+
+ align:start position:0%
+What what held that in the
+groove? That was
+
+ align:start position:0%
+groove? That was
+ 
+
+ align:start position:0%
+groove? That was
+gravity, right? So it was the same kind
+
+ align:start position:0%
+gravity, right? So it was the same kind
+ 
+
+ align:start position:0%
+gravity, right? So it was the same kind
+of idea. You had to push on the the
+
+ align:start position:0%
+of idea. You had to push on the the
+ 
+
+ align:start position:0%
+of idea. You had to push on the the
+needle to hold the needle in the groove
+
+ align:start position:0%
+needle to hold the needle in the groove
+ 
+
+ align:start position:0%
+needle to hold the needle in the groove
+so that the needle wouldn't uh so that
+
+ align:start position:0%
+so that the needle wouldn't uh so that
+ 
+
+ align:start position:0%
+so that the needle wouldn't uh so that
+the needle could rec uh report the
+
+ align:start position:0%
+the needle could rec uh report the
+ 
+
+ align:start position:0%
+the needle could rec uh report the
+vibrations that were recorded there.
+
+ align:start position:0%
+vibrations that were recorded there.
+ 
+
+ align:start position:0%
+vibrations that were recorded there.
+Okay, but this was much classier than
+
+ align:start position:0%
+Okay, but this was much classier than
+ 
+
+ align:start position:0%
+Okay, but this was much classier than
+than uh the version in Edison's time. Uh
+
+ align:start position:0%
+than uh the version in Edison's time. Uh
+ 
+
+ align:start position:0%
+than uh the version in Edison's time. Uh
+so in fact, you could tell how serious
+
+ align:start position:0%
+so in fact, you could tell how serious
+ 
+
+ align:start position:0%
+so in fact, you could tell how serious
+the audio file was by how by the
+
+ align:start position:0%
+the audio file was by how by the
+ 
+
+ align:start position:0%
+the audio file was by how by the
+different kinds of uh performance
+
+ align:start position:0%
+different kinds of uh performance
+ 
+
+ align:start position:0%
+different kinds of uh performance
+enhancements of of this sort of thing.
+
+ align:start position:0%
+enhancements of of this sort of thing.
+ 
+
+ align:start position:0%
+enhancements of of this sort of thing.
+So for example,
+
+ align:start position:0%
+So for example,
+ 
+
+ align:start position:0%
+So for example,
+um this little knob, this controls the
+
+ align:start position:0%
+um this little knob, this controls the
+ 
+
+ align:start position:0%
+um this little knob, this controls the
+weight, the force that's placed on the
+
+ align:start position:0%
+weight, the force that's placed on the
+ 
+
+ align:start position:0%
+weight, the force that's placed on the
+needle. If you had a good setup, you
+
+ align:start position:0%
+needle. If you had a good setup, you
+ 
+
+ align:start position:0%
+needle. If you had a good setup, you
+could set it for about 1.2 grams. If you
+
+ align:start position:0%
+could set it for about 1.2 grams. If you
+ 
+
+ align:start position:0%
+could set it for about 1.2 grams. If you
+had a bad setup, it'd go up to two
+
+ align:start position:0%
+had a bad setup, it'd go up to two
+ 
+
+ align:start position:0%
+had a bad setup, it'd go up to two
+grams. So, you could tell by by u
+
+ align:start position:0%
+grams. So, you could tell by by u
+ 
+
+ align:start position:0%
+grams. So, you could tell by by u
+uh you could tell how serious a person
+
+ align:start position:0%
+uh you could tell how serious a person
+ 
+
+ align:start position:0%
+uh you could tell how serious a person
+was by how many uh uh how much force was
+
+ align:start position:0%
+was by how many uh uh how much force was
+ 
+
+ align:start position:0%
+was by how many uh uh how much force was
+required to track. So, uh you could tell
+
+ align:start position:0%
+required to track. So, uh you could tell
+ 
+
+ align:start position:0%
+required to track. So, uh you could tell
+so for example uh the primary thing that
+
+ align:start position:0%
+so for example uh the primary thing that
+ 
+
+ align:start position:0%
+so for example uh the primary thing that
+determined how well the system worked
+
+ align:start position:0%
+determined how well the system worked
+ 
+
+ align:start position:0%
+determined how well the system worked
+was the
+
+ align:start position:0%
+was the
+ 
+
+ align:start position:0%
+was the
+cartridge. So, here's a blow up of a
+
+ align:start position:0%
+cartridge. So, here's a blow up of a
+ 
+
+ align:start position:0%
+cartridge. So, here's a blow up of a
+cartridge.
+
+ align:start position:0%
+cartridge.
+ 
+
+ align:start position:0%
+cartridge.
+cartridge. Anybody who was serious had a
+
+ align:start position:0%
+cartridge. Anybody who was serious had a
+ 
+
+ align:start position:0%
+cartridge. Anybody who was serious had a
+diamond tip needle, right? If they
+
+ align:start position:0%
+diamond tip needle, right? If they
+ 
+
+ align:start position:0%
+diamond tip needle, right? If they
+didn't have a diamond tip tip needle,
+
+ align:start position:0%
+didn't have a diamond tip tip needle,
+ 
+
+ align:start position:0%
+didn't have a diamond tip tip needle,
+you just didn't even think about them.
+
+ align:start position:0%
+you just didn't even think about them.
+ 
+
+ align:start position:0%
+you just didn't even think about them.
+So, everybody I knew had a diamond tip
+
+ align:start position:0%
+So, everybody I knew had a diamond tip
+ 
+
+ align:start position:0%
+So, everybody I knew had a diamond tip
+needle. That was just the way it was.
+
+ align:start position:0%
+needle. That was just the way it was.
+ 
+
+ align:start position:0%
+needle. That was just the way it was.
+Uh, the least expensive kind of
+
+ align:start position:0%
+Uh, the least expensive kind of
+ 
+
+ align:start position:0%
+Uh, the least expensive kind of
+cartridges was a little piece of pre pzo
+
+ align:start position:0%
+cartridges was a little piece of pre pzo
+ 
+
+ align:start position:0%
+cartridges was a little piece of pre pzo
+ceramic. The PZO ceramic was
+
+ align:start position:0%
+ceramic. The PZO ceramic was
+ 
+
+ align:start position:0%
+ceramic. The PZO ceramic was
+stiff so that as you played the records,
+
+ align:start position:0%
+stiff so that as you played the records,
+ 
+
+ align:start position:0%
+stiff so that as you played the records,
+they tended to wear out because you had
+
+ align:start position:0%
+they tended to wear out because you had
+ 
+
+ align:start position:0%
+they tended to wear out because you had
+to put a lot of force on it.
+
+ align:start position:0%
+to put a lot of force on it.
+ 
+
+ align:start position:0%
+to put a lot of force on it.
+mine. I had the V15 type 4. Okay. So,
+
+ align:start position:0%
+mine. I had the V15 type 4. Okay. So,
+ 
+
+ align:start position:0%
+mine. I had the V15 type 4. Okay. So,
+this was a magnetic device. So, there
+
+ align:start position:0%
+this was a magnetic device. So, there
+ 
+
+ align:start position:0%
+this was a magnetic device. So, there
+were tiny little electromagnets so that
+
+ align:start position:0%
+were tiny little electromagnets so that
+ 
+
+ align:start position:0%
+were tiny little electromagnets so that
+the up and down motions would be
+
+ align:start position:0%
+the up and down motions would be
+ 
+
+ align:start position:0%
+the up and down motions would be
+converted into an electrical signal by
+
+ align:start position:0%
+converted into an electrical signal by
+ 
+
+ align:start position:0%
+converted into an electrical signal by
+magnetism, not by paso electric effect.
+
+ align:start position:0%
+magnetism, not by paso electric effect.
+ 
+
+ align:start position:0%
+magnetism, not by paso electric effect.
+And you could track that with a much
+
+ align:start position:0%
+And you could track that with a much
+ 
+
+ align:start position:0%
+And you could track that with a much
+smaller force. And I should just mention
+
+ align:start position:0%
+smaller force. And I should just mention
+ 
+
+ align:start position:0%
+smaller force. And I should just mention
+just, you know, so you know that, you
+
+ align:start position:0%
+just, you know, so you know that, you
+ 
+
+ align:start position:0%
+just, you know, so you know that, you
+know, we were serious back then. So,
+
+ align:start position:0%
+know, we were serious back then. So,
+ 
+
+ align:start position:0%
+know, we were serious back then. So,
+this cost $160 then dollars.
+
+ align:start position:0%
+this cost $160 then dollars.
+ 
+
+ align:start position:0%
+this cost $160 then dollars.
+there's been a factor of six or so
+
+ align:start position:0%
+there's been a factor of six or so
+ 
+
+ align:start position:0%
+there's been a factor of six or so
+inflation. This cost
+
+ align:start position:0%
+inflation. This cost
+ 
+
+ align:start position:0%
+inflation. This cost
+$1,000, right? And if you were serious,
+
+ align:start position:0%
+$1,000, right? And if you were serious,
+ 
+
+ align:start position:0%
+$1,000, right? And if you were serious,
+you had
+
+ align:start position:0%
+you had
+ 
+
+ align:start position:0%
+you had
+these. So,
+
+ align:start position:0%
+these. So,
+ 
+
+ align:start position:0%
+these. So,
+um, that's kind of the technology as it
+
+ align:start position:0%
+um, that's kind of the technology as it
+ 
+
+ align:start position:0%
+um, that's kind of the technology as it
+existed um when I was in undergraduate
+
+ align:start position:0%
+existed um when I was in undergraduate
+ 
+
+ align:start position:0%
+existed um when I was in undergraduate
+and it was good. It had existed for over
+
+ align:start position:0%
+and it was good. It had existed for over
+ 
+
+ align:start position:0%
+and it was good. It had existed for over
+a hundred
+
+ align:start position:0%
+a hundred
+ 
+
+ align:start position:0%
+a hundred
+years, but it was still basically the
+
+ align:start position:0%
+years, but it was still basically the
+ 
+
+ align:start position:0%
+years, but it was still basically the
+same thing Edison had done.
+
+ align:start position:0%
+same thing Edison had done.
+ 
+
+ align:start position:0%
+same thing Edison had done.
+uh the media. Oh, I should show it just
+
+ align:start position:0%
+uh the media. Oh, I should show it just
+ 
+
+ align:start position:0%
+uh the media. Oh, I should show it just
+in case you've never seen a media.
+
+ align:start position:0%
+in case you've never seen a media.
+ 
+
+ align:start position:0%
+in case you've never seen a media.
+Right. So, this is a record. This was my
+
+ align:start position:0%
+Right. So, this is a record. This was my
+ 
+
+ align:start position:0%
+Right. So, this is a record. This was my
+record.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and the problem is of course they
+
+ align:start position:0%
+Um and the problem is of course they
+ 
+
+ align:start position:0%
+Um and the problem is of course they
+scratch, right? So over time these
+
+ align:start position:0%
+scratch, right? So over time these
+ 
+
+ align:start position:0%
+scratch, right? So over time these
+things would scratch. So the
+
+ align:start position:0%
+things would scratch. So the
+ 
+
+ align:start position:0%
+things would scratch. So the
+technologies were things like uh how do
+
+ align:start position:0%
+technologies were things like uh how do
+ 
+
+ align:start position:0%
+technologies were things like uh how do
+you keep them from scratching? How do
+
+ align:start position:0%
+you keep them from scratching? How do
+ 
+
+ align:start position:0%
+you keep them from scratching? How do
+you wear them out? I mean you can also
+
+ align:start position:0%
+you wear them out? I mean you can also
+ 
+
+ align:start position:0%
+you wear them out? I mean you can also
+appreciate sort of where the music
+
+ align:start position:0%
+appreciate sort of where the music
+ 
+
+ align:start position:0%
+appreciate sort of where the music
+industry is coming from. This cost about
+
+ align:start position:0%
+industry is coming from. This cost about
+ 
+
+ align:start position:0%
+industry is coming from. This cost about
+$15. 15 then dollars, right? So with
+
+ align:start position:0%
+$15. 15 then dollars, right? So with
+ 
+
+ align:start position:0%
+$15. 15 then dollars, right? So with
+factor of six is about
+
+ align:start position:0%
+factor of six is about
+ 
+
+ align:start position:0%
+factor of six is about
+$100. So from the point of view of
+
+ align:start position:0%
+$100. So from the point of view of
+ 
+
+ align:start position:0%
+$100. So from the point of view of
+buying music, it was much more expensive
+
+ align:start position:0%
+buying music, it was much more expensive
+ 
+
+ align:start position:0%
+buying music, it was much more expensive
+back then. And from the point of view of
+
+ align:start position:0%
+back then. And from the point of view of
+ 
+
+ align:start position:0%
+back then. And from the point of view of
+the recording industry, think of it, you
+
+ align:start position:0%
+the recording industry, think of it, you
+ 
+
+ align:start position:0%
+the recording industry, think of it, you
+had all these addicted people wanting to
+
+ align:start position:0%
+had all these addicted people wanting to
+ 
+
+ align:start position:0%
+had all these addicted people wanting to
+buy this
+
+ align:start position:0%
+buy this
+ 
+
+ align:start position:0%
+buy this
+stuff and it wears
+
+ align:start position:0%
+stuff and it wears
+ 
+
+ align:start position:0%
+stuff and it wears
+out. So you play it for two or three
+
+ align:start position:0%
+out. So you play it for two or three
+ 
+
+ align:start position:0%
+out. So you play it for two or three
+years, you have to buy a new one. Okay?
+
+ align:start position:0%
+years, you have to buy a new one. Okay?
+ 
+
+ align:start position:0%
+years, you have to buy a new one. Okay?
+So you can sort of appreciate where the
+
+ align:start position:0%
+So you can sort of appreciate where the
+ 
+
+ align:start position:0%
+So you can sort of appreciate where the
+music industry is coming from because
+
+ align:start position:0%
+music industry is coming from because
+ 
+
+ align:start position:0%
+music industry is coming from because
+things have
+
+ align:start position:0%
+things have
+ 
+
+ align:start position:0%
+things have
+changed. Okay. So
+
+ align:start position:0%
+changed. Okay. So
+ 
+
+ align:start position:0%
+changed. Okay. So
+um distortions, expensive, fragile, blah
+
+ align:start position:0%
+um distortions, expensive, fragile, blah
+ 
+
+ align:start position:0%
+um distortions, expensive, fragile, blah
+blah blah. Then in the 1980s, everything
+
+ align:start position:0%
+blah blah. Then in the 1980s, everything
+ 
+
+ align:start position:0%
+blah blah. Then in the 1980s, everything
+changed. In the 1980s there was the
+
+ align:start position:0%
+changed. In the 1980s there was the
+ 
+
+ align:start position:0%
+changed. In the 1980s there was the
+invention of the CD. CD was invented by
+
+ align:start position:0%
+invention of the CD. CD was invented by
+ 
+
+ align:start position:0%
+invention of the CD. CD was invented by
+Philips Corp and Sony Corp working
+
+ align:start position:0%
+Philips Corp and Sony Corp working
+ 
+
+ align:start position:0%
+Philips Corp and Sony Corp working
+together and just everything was
+
+ align:start position:0%
+together and just everything was
+ 
+
+ align:start position:0%
+together and just everything was
+revolutionized.
+
+ align:start position:0%
+revolutionized.
+ 
+
+ align:start position:0%
+revolutionized.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+um we'll talk a little bit about how
+
+ align:start position:0%
+um we'll talk a little bit about how
+ 
+
+ align:start position:0%
+um we'll talk a little bit about how
+this thing how the CD works. The
+
+ align:start position:0%
+this thing how the CD works. The
+ 
+
+ align:start position:0%
+this thing how the CD works. The
+important thing for the discussion is
+
+ align:start position:0%
+important thing for the discussion is
+ 
+
+ align:start position:0%
+important thing for the discussion is
+that unlike records, CDs are virtually
+
+ align:start position:0%
+that unlike records, CDs are virtually
+ 
+
+ align:start position:0%
+that unlike records, CDs are virtually
+indestructible. They have very low
+
+ align:start position:0%
+indestructible. They have very low
+ 
+
+ align:start position:0%
+indestructible. They have very low
+distortion. They're next to
+
+ align:start position:0%
+distortion. They're next to
+ 
+
+ align:start position:0%
+distortion. They're next to
+free and all of that is technology
+
+ align:start position:0%
+free and all of that is technology
+ 
+
+ align:start position:0%
+free and all of that is technology
+that's in large part enabled by 63 and
+
+ align:start position:0%
+that's in large part enabled by 63 and
+ 
+
+ align:start position:0%
+that's in large part enabled by 63 and
+that's what I want to actually talk
+
+ align:start position:0%
+that's what I want to actually talk
+ 
+
+ align:start position:0%
+that's what I want to actually talk
+about. So uh what is a CD? CD is not
+
+ align:start position:0%
+about. So uh what is a CD? CD is not
+ 
+
+ align:start position:0%
+about. So uh what is a CD? CD is not
+very different from a record. So a CD
+
+ align:start position:0%
+very different from a record. So a CD
+ 
+
+ align:start position:0%
+very different from a record. So a CD
+has tracks. The information is written
+
+ align:start position:0%
+has tracks. The information is written
+ 
+
+ align:start position:0%
+has tracks. The information is written
+in tracks. The tracks are written as a
+
+ align:start position:0%
+in tracks. The tracks are written as a
+ 
+
+ align:start position:0%
+in tracks. The tracks are written as a
+spiral. The spiral starts at the inside
+
+ align:start position:0%
+spiral. The spiral starts at the inside
+ 
+
+ align:start position:0%
+spiral. The spiral starts at the inside
+and spirals
+
+ align:start position:0%
+and spirals
+ 
+
+ align:start position:0%
+and spirals
+out. And so the idea is that you read a
+
+ align:start position:0%
+out. And so the idea is that you read a
+ 
+
+ align:start position:0%
+out. And so the idea is that you read a
+spiral of messages. And just like a
+
+ align:start position:0%
+spiral of messages. And just like a
+ 
+
+ align:start position:0%
+spiral of messages. And just like a
+record, the way you make a record is
+
+ align:start position:0%
+record, the way you make a record is
+ 
+
+ align:start position:0%
+record, the way you make a record is
+called embossing. You make a master and
+
+ align:start position:0%
+called embossing. You make a master and
+ 
+
+ align:start position:0%
+called embossing. You make a master and
+then you take um u molten
+
+ align:start position:0%
+then you take um u molten
+ 
+
+ align:start position:0%
+then you take um u molten
+plastic and uh press it and copy the
+
+ align:start position:0%
+plastic and uh press it and copy the
+ 
+
+ align:start position:0%
+plastic and uh press it and copy the
+patterns to make that record. Right? In
+
+ align:start position:0%
+patterns to make that record. Right? In
+ 
+
+ align:start position:0%
+patterns to make that record. Right? In
+fact, there was a big technology on the
+
+ align:start position:0%
+fact, there was a big technology on the
+ 
+
+ align:start position:0%
+fact, there was a big technology on the
+formula that you used for the vinyl.
+
+ align:start position:0%
+formula that you used for the vinyl.
+ 
+
+ align:start position:0%
+formula that you used for the vinyl.
+Right? One of the secrets of RCA at the
+
+ align:start position:0%
+Right? One of the secrets of RCA at the
+ 
+
+ align:start position:0%
+Right? One of the secrets of RCA at the
+time when I was in graduate school, when
+
+ align:start position:0%
+time when I was in graduate school, when
+ 
+
+ align:start position:0%
+time when I was in graduate school, when
+I was in graduate school, they had a
+
+ align:start position:0%
+I was in graduate school, they had a
+ 
+
+ align:start position:0%
+I was in graduate school, they had a
+secret recipe that included dropping
+
+ align:start position:0%
+secret recipe that included dropping
+ 
+
+ align:start position:0%
+secret recipe that included dropping
+four slices of American cheese in their
+
+ align:start position:0%
+four slices of American cheese in their
+ 
+
+ align:start position:0%
+four slices of American cheese in their
+vinyl producing because somebody had
+
+ align:start position:0%
+vinyl producing because somebody had
+ 
+
+ align:start position:0%
+vinyl producing because somebody had
+accidentally once dropped a sandwich and
+
+ align:start position:0%
+accidentally once dropped a sandwich and
+ 
+
+ align:start position:0%
+accidentally once dropped a sandwich and
+those records came out
+
+ align:start position:0%
+those records came out
+ 
+
+ align:start position:0%
+those records came out
+good. So, so there were there were
+
+ align:start position:0%
+good. So, so there were there were
+ 
+
+ align:start position:0%
+good. So, so there were there were
+magical things like that that were trade
+
+ align:start position:0%
+magical things like that that were trade
+ 
+
+ align:start position:0%
+magical things like that that were trade
+secrets at the time. Okay. said that so
+
+ align:start position:0%
+secrets at the time. Okay. said that so
+ 
+
+ align:start position:0%
+secrets at the time. Okay. said that so
+that technology was basically embossing
+
+ align:start position:0%
+that technology was basically embossing
+ 
+
+ align:start position:0%
+that technology was basically embossing
+and that's the same thing you do when
+
+ align:start position:0%
+and that's the same thing you do when
+ 
+
+ align:start position:0%
+and that's the same thing you do when
+you make a CD. CD is
+
+ align:start position:0%
+you make a CD. CD is
+ 
+
+ align:start position:0%
+you make a CD. CD is
+polycarbonate which is u injection
+
+ align:start position:0%
+polycarbonate which is u injection
+ 
+
+ align:start position:0%
+polycarbonate which is u injection
+molded. So um you make a master. The
+
+ align:start position:0%
+molded. So um you make a master. The
+ 
+
+ align:start position:0%
+molded. So um you make a master. The
+master is usually made out of aluminum.
+
+ align:start position:0%
+master is usually made out of aluminum.
+ 
+
+ align:start position:0%
+master is usually made out of aluminum.
+The master is made very similar to the
+
+ align:start position:0%
+The master is made very similar to the
+ 
+
+ align:start position:0%
+The master is made very similar to the
+way that Edison would make a master.
+
+ align:start position:0%
+way that Edison would make a master.
+ 
+
+ align:start position:0%
+way that Edison would make a master.
+There's a big device with an
+
+ align:start position:0%
+There's a big device with an
+ 
+
+ align:start position:0%
+There's a big device with an
+electromagnet with a small stylus and it
+
+ align:start position:0%
+electromagnet with a small stylus and it
+ 
+
+ align:start position:0%
+electromagnet with a small stylus and it
+punches them.
+
+ align:start position:0%
+punches them.
+ 
+
+ align:start position:0%
+punches them.
+But then you copy the CDs uh by
+
+ align:start position:0%
+But then you copy the CDs uh by
+ 
+
+ align:start position:0%
+But then you copy the CDs uh by
+injection molding. So you take that
+
+ align:start position:0%
+injection molding. So you take that
+ 
+
+ align:start position:0%
+injection molding. So you take that
+original and there's actually a
+
+ align:start position:0%
+original and there's actually a
+ 
+
+ align:start position:0%
+original and there's actually a
+complicated process. You use the
+
+ align:start position:0%
+complicated process. You use the
+ 
+
+ align:start position:0%
+complicated process. You use the
+original to make a a half a dozen
+
+ align:start position:0%
+original to make a a half a dozen
+ 
+
+ align:start position:0%
+original to make a a half a dozen
+fathers. The fathers are used to make
+
+ align:start position:0%
+fathers. The fathers are used to make
+ 
+
+ align:start position:0%
+fathers. The fathers are used to make
+mothers. Each father makes 20 mothers.
+
+ align:start position:0%
+mothers. Each father makes 20 mothers.
+ 
+
+ align:start position:0%
+mothers. Each father makes 20 mothers.
+Then each of the mothers make children.
+
+ align:start position:0%
+Then each of the mothers make children.
+ 
+
+ align:start position:0%
+Then each of the mothers make children.
+And so you end up being able to get a
+
+ align:start position:0%
+And so you end up being able to get a
+ 
+
+ align:start position:0%
+And so you end up being able to get a
+lot of copies out of the original
+
+ align:start position:0%
+lot of copies out of the original
+ 
+
+ align:start position:0%
+lot of copies out of the original
+master. The polycarbonate. And there's a
+
+ align:start position:0%
+master. The polycarbonate. And there's a
+ 
+
+ align:start position:0%
+master. The polycarbonate. And there's a
+reflective layer of aluminum that's
+
+ align:start position:0%
+reflective layer of aluminum that's
+ 
+
+ align:start position:0%
+reflective layer of aluminum that's
+evaporated on top of the polycarbonate.
+
+ align:start position:0%
+evaporated on top of the polycarbonate.
+ 
+
+ align:start position:0%
+evaporated on top of the polycarbonate.
+And then there's a thin layer of plastic
+
+ align:start position:0%
+And then there's a thin layer of plastic
+ 
+
+ align:start position:0%
+And then there's a thin layer of plastic
+put over the top. That results in
+
+ align:start position:0%
+put over the top. That results in
+ 
+
+ align:start position:0%
+put over the top. That results in
+something that's extremely um robust.
+
+ align:start position:0%
+something that's extremely um robust.
+ 
+
+ align:start position:0%
+something that's extremely um robust.
+So, and we'll see in a minute how they
+
+ align:start position:0%
+So, and we'll see in a minute how they
+ 
+
+ align:start position:0%
+So, and we'll see in a minute how they
+make it
+
+ align:start position:0%
+make it
+ 
+
+ align:start position:0%
+make it
+robust, but this dimension is like um
+
+ align:start position:0%
+robust, but this dimension is like um
+ 
+
+ align:start position:0%
+robust, but this dimension is like um
+over a millimeter. So when you So um so
+
+ align:start position:0%
+over a millimeter. So when you So um so
+ 
+
+ align:start position:0%
+over a millimeter. So when you So um so
+this is CD version of the same
+
+ align:start position:0%
+this is CD version of the same
+ 
+
+ align:start position:0%
+this is CD version of the same
+album. So this surface is the
+
+ align:start position:0%
+album. So this surface is the
+ 
+
+ align:start position:0%
+album. So this surface is the
+information reading side, right? There's
+
+ align:start position:0%
+information reading side, right? There's
+ 
+
+ align:start position:0%
+information reading side, right? There's
+a millimeter of stuff
+
+ align:start position:0%
+a millimeter of stuff
+ 
+
+ align:start position:0%
+a millimeter of stuff
+here. There's a millimeter of
+
+ align:start position:0%
+here. There's a millimeter of
+ 
+
+ align:start position:0%
+here. There's a millimeter of
+polycarbonate protecting the surface
+
+ align:start position:0%
+polycarbonate protecting the surface
+ 
+
+ align:start position:0%
+polycarbonate protecting the surface
+that has the information from the
+
+ align:start position:0%
+that has the information from the
+ 
+
+ align:start position:0%
+that has the information from the
+environment. So in fact, the way if you
+
+ align:start position:0%
+environment. So in fact, the way if you
+ 
+
+ align:start position:0%
+environment. So in fact, the way if you
+want to destroy somebody's CD, you might
+
+ align:start position:0%
+want to destroy somebody's CD, you might
+ 
+
+ align:start position:0%
+want to destroy somebody's CD, you might
+think the way to do that would be to
+
+ align:start position:0%
+think the way to do that would be to
+ 
+
+ align:start position:0%
+think the way to do that would be to
+write in felt tip on here. No, don't do
+
+ align:start position:0%
+write in felt tip on here. No, don't do
+ 
+
+ align:start position:0%
+write in felt tip on here. No, don't do
+it that way. Use a ballpoint pen on this
+
+ align:start position:0%
+it that way. Use a ballpoint pen on this
+ 
+
+ align:start position:0%
+it that way. Use a ballpoint pen on this
+side because that layer of plastic is
+
+ align:start position:0%
+side because that layer of plastic is
+ 
+
+ align:start position:0%
+side because that layer of plastic is
+very thin. So, use a ballpoint pen here.
+
+ align:start position:0%
+very thin. So, use a ballpoint pen here.
+ 
+
+ align:start position:0%
+very thin. So, use a ballpoint pen here.
+It'll completely screw it up. So, uh
+
+ align:start position:0%
+It'll completely screw it up. So, uh
+ 
+
+ align:start position:0%
+It'll completely screw it up. So, uh
+it's very robust when uh against
+
+ align:start position:0%
+it's very robust when uh against
+ 
+
+ align:start position:0%
+it's very robust when uh against
+imperfections on the read
+
+ align:start position:0%
+imperfections on the read
+ 
+
+ align:start position:0%
+imperfections on the read
+side. Okay. So, uh that's kind of the
+
+ align:start position:0%
+side. Okay. So, uh that's kind of the
+ 
+
+ align:start position:0%
+side. Okay. So, uh that's kind of the
+structure. It's virtually indestructible
+
+ align:start position:0%
+structure. It's virtually indestructible
+ 
+
+ align:start position:0%
+structure. It's virtually indestructible
+is the point.
+
+ align:start position:0%
+is the point.
+ 
+
+ align:start position:0%
+is the point.
+So then uh how do you get the
+
+ align:start position:0%
+So then uh how do you get the
+ 
+
+ align:start position:0%
+So then uh how do you get the
+information on it? Well, the information
+
+ align:start position:0%
+information on it? Well, the information
+ 
+
+ align:start position:0%
+information on it? Well, the information
+is coated in these patterns. The
+
+ align:start position:0%
+is coated in these patterns. The
+ 
+
+ align:start position:0%
+is coated in these patterns. The
+patterns are small. The the pattern
+
+ align:start position:0%
+patterns are small. The the pattern
+ 
+
+ align:start position:0%
+patterns are small. The the pattern
+width is half micron. A human hair is 50
+
+ align:start position:0%
+width is half micron. A human hair is 50
+ 
+
+ align:start position:0%
+width is half micron. A human hair is 50
+to 100 microns
+
+ align:start position:0%
+to 100 microns
+ 
+
+ align:start position:0%
+to 100 microns
+thick. So if you and I have white hair,
+
+ align:start position:0%
+thick. So if you and I have white hair,
+ 
+
+ align:start position:0%
+thick. So if you and I have white hair,
+well I used to have blonde hair. I have
+
+ align:start position:0%
+well I used to have blonde hair. I have
+ 
+
+ align:start position:0%
+well I used to have blonde hair. I have
+gray hair now. Ignoring that for the
+
+ align:start position:0%
+gray hair now. Ignoring that for the
+ 
+
+ align:start position:0%
+gray hair now. Ignoring that for the
+moment. Uh I used to have blonde hair.
+
+ align:start position:0%
+moment. Uh I used to have blonde hair.
+ 
+
+ align:start position:0%
+moment. Uh I used to have blonde hair.
+Blonde hair is about 50 microns um
+
+ align:start position:0%
+Blonde hair is about 50 microns um
+ 
+
+ align:start position:0%
+Blonde hair is about 50 microns um
+diameter. Black hair is about 100
+
+ align:start position:0%
+diameter. Black hair is about 100
+ 
+
+ align:start position:0%
+diameter. Black hair is about 100
+microns diameter. So depending on the
+
+ align:start position:0%
+microns diameter. So depending on the
+ 
+
+ align:start position:0%
+microns diameter. So depending on the
+color of your hair, it would obscure so
+
+ align:start position:0%
+color of your hair, it would obscure so
+ 
+
+ align:start position:0%
+color of your hair, it would obscure so
+30 to 60 tracks if you were to lay a
+
+ align:start position:0%
+30 to 60 tracks if you were to lay a
+ 
+
+ align:start position:0%
+30 to 60 tracks if you were to lay a
+hair across it. So these are very very
+
+ align:start position:0%
+hair across it. So these are very very
+ 
+
+ align:start position:0%
+hair across it. So these are very very
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+patterns. And so the trick
+
+ align:start position:0%
+patterns. And so the trick
+ 
+
+ align:start position:0%
+patterns. And so the trick
+uh for uh uh how you code them is a big
+
+ align:start position:0%
+uh for uh uh how you code them is a big
+ 
+
+ align:start position:0%
+uh for uh uh how you code them is a big
+problem. Before we get there though, the
+
+ align:start position:0%
+problem. Before we get there though, the
+ 
+
+ align:start position:0%
+problem. Before we get there though, the
+how do you code the audio? You won't be
+
+ align:start position:0%
+how do you code the audio? You won't be
+ 
+
+ align:start position:0%
+how do you code the audio? You won't be
+too surprised to find out that it's a
+
+ align:start position:0%
+too surprised to find out that it's a
+ 
+
+ align:start position:0%
+too surprised to find out that it's a
+sample data system. So we do sampling
+
+ align:start position:0%
+sample data system. So we do sampling
+ 
+
+ align:start position:0%
+sample data system. So we do sampling
+just the way we've talked about it
+
+ align:start position:0%
+just the way we've talked about it
+ 
+
+ align:start position:0%
+just the way we've talked about it
+before. Audio, you can hear sounds from
+
+ align:start position:0%
+before. Audio, you can hear sounds from
+ 
+
+ align:start position:0%
+before. Audio, you can hear sounds from
+about 20 hertz to about 20 kHz. This is
+
+ align:start position:0%
+about 20 hertz to about 20 kHz. This is
+ 
+
+ align:start position:0%
+about 20 hertz to about 20 kHz. This is
+an audiogram. Aiograms plot as a
+
+ align:start position:0%
+an audiogram. Aiograms plot as a
+ 
+
+ align:start position:0%
+an audiogram. Aiograms plot as a
+function of frequency. What's the
+
+ align:start position:0%
+function of frequency. What's the
+ 
+
+ align:start position:0%
+function of frequency. What's the
+minimum amplitude required to be able to
+
+ align:start position:0%
+minimum amplitude required to be able to
+ 
+
+ align:start position:0%
+minimum amplitude required to be able to
+hear that frequency? You're most
+
+ align:start position:0%
+hear that frequency? You're most
+ 
+
+ align:start position:0%
+hear that frequency? You're most
+sensitive in the kilhertz
+
+ align:start position:0%
+sensitive in the kilhertz
+ 
+
+ align:start position:0%
+sensitive in the kilhertz
+region. Uh the scale over here is db in
+
+ align:start position:0%
+region. Uh the scale over here is db in
+ 
+
+ align:start position:0%
+region. Uh the scale over here is db in
+something we call sound pressure level.
+
+ align:start position:0%
+something we call sound pressure level.
+ 
+
+ align:start position:0%
+something we call sound pressure level.
+Sound pressure level is the centigrade
+
+ align:start position:0%
+Sound pressure level is the centigrade
+ 
+
+ align:start position:0%
+Sound pressure level is the centigrade
+equivalent for hearing. So zero is just
+
+ align:start position:0%
+equivalent for hearing. So zero is just
+ 
+
+ align:start position:0%
+equivalent for hearing. So zero is just
+audible, 100 is starts to hurt, 120 is
+
+ align:start position:0%
+audible, 100 is starts to hurt, 120 is
+ 
+
+ align:start position:0%
+audible, 100 is starts to hurt, 120 is
+uh permanent damage kind of thing. So
+
+ align:start position:0%
+uh permanent damage kind of thing. So
+ 
+
+ align:start position:0%
+uh permanent damage kind of thing. So
+you can hear about u 100
+
+ align:start position:0%
+you can hear about u 100
+ 
+
+ align:start position:0%
+you can hear about u 100
+dB over a range from 20 to 20
+
+ align:start position:0%
+dB over a range from 20 to 20
+ 
+
+ align:start position:0%
+dB over a range from 20 to 20
+kHz. And so the way they coded it for
+
+ align:start position:0%
+kHz. And so the way they coded it for
+ 
+
+ align:start position:0%
+kHz. And so the way they coded it for
+the CD was uh sampled at 44.1 kHz. They
+
+ align:start position:0%
+the CD was uh sampled at 44.1 kHz. They
+ 
+
+ align:start position:0%
+the CD was uh sampled at 44.1 kHz. They
+chose that funny
+
+ align:start position:0%
+chose that funny
+ 
+
+ align:start position:0%
+chose that funny
+number to be a little bit bigger than
+
+ align:start position:0%
+number to be a little bit bigger than
+ 
+
+ align:start position:0%
+number to be a little bit bigger than
+twice the highest frequency that you can
+
+ align:start position:0%
+twice the highest frequency that you can
+ 
+
+ align:start position:0%
+twice the highest frequency that you can
+hear, but they made it the funny number
+
+ align:start position:0%
+hear, but they made it the funny number
+ 
+
+ align:start position:0%
+hear, but they made it the funny number
+because they wanted it to be an integer
+
+ align:start position:0%
+because they wanted it to be an integer
+ 
+
+ align:start position:0%
+because they wanted it to be an integer
+multip integer multiple of 60. So it was
+
+ align:start position:0%
+multip integer multiple of 60. So it was
+ 
+
+ align:start position:0%
+multip integer multiple of 60. So it was
+easy to synchronize with television
+
+ align:start position:0%
+easy to synchronize with television
+ 
+
+ align:start position:0%
+easy to synchronize with television
+signals. That's where the funny number
+
+ align:start position:0%
+signals. That's where the funny number
+ 
+
+ align:start position:0%
+signals. That's where the funny number
+came from. So 44.1 kHz divided by 60 is
+
+ align:start position:0%
+came from. So 44.1 kHz divided by 60 is
+ 
+
+ align:start position:0%
+came from. So 44.1 kHz divided by 60 is
+some integer.
+
+ align:start position:0%
+some integer.
+ 
+
+ align:start position:0%
+some integer.
+The problem is of course that they
+
+ align:start position:0%
+The problem is of course that they
+ 
+
+ align:start position:0%
+The problem is of course that they
+wanted to be greedy. They wanted all the
+
+ align:start position:0%
+wanted to be greedy. They wanted all the
+ 
+
+ align:start position:0%
+wanted to be greedy. They wanted all the
+bits to code
+
+ align:start position:0%
+bits to code
+ 
+
+ align:start position:0%
+bits to code
+audio. So they only sampled barely over
+
+ align:start position:0%
+audio. So they only sampled barely over
+ 
+
+ align:start position:0%
+audio. So they only sampled barely over
+the frequency that was required. Right?
+
+ align:start position:0%
+the frequency that was required. Right?
+ 
+
+ align:start position:0%
+the frequency that was required. Right?
+So you would according to the sampling
+
+ align:start position:0%
+So you would according to the sampling
+ 
+
+ align:start position:0%
+So you would according to the sampling
+theorem you need
+
+ align:start position:0%
+theorem you need
+ 
+
+ align:start position:0%
+theorem you need
+40 if you get any information that's not
+
+ align:start position:0%
+40 if you get any information that's not
+ 
+
+ align:start position:0%
+40 if you get any information that's not
+that. So if you had um a sample data
+
+ align:start position:0%
+that. So if you had um a sample data
+ 
+
+ align:start position:0%
+that. So if you had um a sample data
+system running at 44, any amount of
+
+ align:start position:0%
+system running at 44, any amount of
+ 
+
+ align:start position:0%
+system running at 44, any amount of
+signal above
+
+ align:start position:0%
+signal above
+ 
+
+ align:start position:0%
+signal above
+22 would alias and sound
+
+ align:start position:0%
+22 would alias and sound
+ 
+
+ align:start position:0%
+22 would alias and sound
+terrible. So you need to put an
+
+ align:start position:0%
+terrible. So you need to put an
+ 
+
+ align:start position:0%
+terrible. So you need to put an
+anti-aliasing filter to prevent
+
+ align:start position:0%
+anti-aliasing filter to prevent
+ 
+
+ align:start position:0%
+anti-aliasing filter to prevent
+that. Uh we've kind of cheated the whole
+
+ align:start position:0%
+that. Uh we've kind of cheated the whole
+ 
+
+ align:start position:0%
+that. Uh we've kind of cheated the whole
+way through. We always said when you
+
+ align:start position:0%
+way through. We always said when you
+ 
+
+ align:start position:0%
+way through. We always said when you
+need a low pass filter, use an ideal
+
+ align:start position:0%
+need a low pass filter, use an ideal
+ 
+
+ align:start position:0%
+need a low pass filter, use an ideal
+one. Well, they don't exist, right? Uh
+
+ align:start position:0%
+one. Well, they don't exist, right? Uh
+ 
+
+ align:start position:0%
+one. Well, they don't exist, right? Uh
+we use ideal filters because they're
+
+ align:start position:0%
+we use ideal filters because they're
+ 
+
+ align:start position:0%
+we use ideal filters because they're
+conceptually simple. There is no such
+
+ align:start position:0%
+conceptually simple. There is no such
+ 
+
+ align:start position:0%
+conceptually simple. There is no such
+thing. If you actually try to make a a
+
+ align:start position:0%
+thing. If you actually try to make a a
+ 
+
+ align:start position:0%
+thing. If you actually try to make a a
+filter using designs like Russ talked
+
+ align:start position:0%
+filter using designs like Russ talked
+ 
+
+ align:start position:0%
+filter using designs like Russ talked
+about in recitation, butterworth
+
+ align:start position:0%
+about in recitation, butterworth
+ 
+
+ align:start position:0%
+about in recitation, butterworth
+filters, things like that, they have
+
+ align:start position:0%
+filters, things like that, they have
+ 
+
+ align:start position:0%
+filters, things like that, they have
+transition bandwidths. So there's a
+
+ align:start position:0%
+transition bandwidths. So there's a
+ 
+
+ align:start position:0%
+transition bandwidths. So there's a
+range of frequencies for which the
+
+ align:start position:0%
+range of frequencies for which the
+ 
+
+ align:start position:0%
+range of frequencies for which the
+filter is neither fully on nor fully off
+
+ align:start position:0%
+filter is neither fully on nor fully off
+ 
+
+ align:start position:0%
+filter is neither fully on nor fully off
+and it's in
+
+ align:start position:0%
+and it's in
+ 
+
+ align:start position:0%
+and it's in
+transition. Uh you would like that range
+
+ align:start position:0%
+transition. Uh you would like that range
+ 
+
+ align:start position:0%
+transition. Uh you would like that range
+of frequencies to be very small so you
+
+ align:start position:0%
+of frequencies to be very small so you
+ 
+
+ align:start position:0%
+of frequencies to be very small so you
+don't waste
+
+ align:start position:0%
+don't waste
+ 
+
+ align:start position:0%
+don't waste
+bandwidth. they allocated. So, so they
+
+ align:start position:0%
+bandwidth. they allocated. So, so they
+ 
+
+ align:start position:0%
+bandwidth. they allocated. So, so they
+would like to reconstruct up to 40 and
+
+ align:start position:0%
+would like to reconstruct up to 40 and
+ 
+
+ align:start position:0%
+would like to reconstruct up to 40 and
+they only allowed four kilhertz in the
+
+ align:start position:0%
+they only allowed four kilhertz in the
+ 
+
+ align:start position:0%
+they only allowed four kilhertz in the
+guard band, right? That was intentional
+
+ align:start position:0%
+guard band, right? That was intentional
+ 
+
+ align:start position:0%
+guard band, right? That was intentional
+because they didn't want to have a lot
+
+ align:start position:0%
+because they didn't want to have a lot
+ 
+
+ align:start position:0%
+because they didn't want to have a lot
+of bits that were not useful for
+
+ align:start position:0%
+of bits that were not useful for
+ 
+
+ align:start position:0%
+of bits that were not useful for
+recording audio. That's the reason they
+
+ align:start position:0%
+recording audio. That's the reason they
+ 
+
+ align:start position:0%
+recording audio. That's the reason they
+only went up to 44 instead of say 80,
+
+ align:start position:0%
+only went up to 44 instead of say 80,
+ 
+
+ align:start position:0%
+only went up to 44 instead of say 80,
+which would have made the anti-aliasing
+
+ align:start position:0%
+which would have made the anti-aliasing
+ 
+
+ align:start position:0%
+which would have made the anti-aliasing
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+simple, but it complicated the the
+
+ align:start position:0%
+simple, but it complicated the the
+ 
+
+ align:start position:0%
+simple, but it complicated the the
+making of the anti-alias filter, right?
+
+ align:start position:0%
+making of the anti-alias filter, right?
+ 
+
+ align:start position:0%
+making of the anti-alias filter, right?
+because there is sounds that come into
+
+ align:start position:0%
+because there is sounds that come into
+ 
+
+ align:start position:0%
+because there is sounds that come into
+microphones above 20 kHz. It's just that
+
+ align:start position:0%
+microphones above 20 kHz. It's just that
+ 
+
+ align:start position:0%
+microphones above 20 kHz. It's just that
+you can't hear
+
+ align:start position:0%
+you can't hear
+ 
+
+ align:start position:0%
+you can't hear
+them. But if you were to record those
+
+ align:start position:0%
+them. But if you were to record those
+ 
+
+ align:start position:0%
+them. But if you were to record those
+sounds and then sample them at at um 40
+
+ align:start position:0%
+sounds and then sample them at at um 40
+ 
+
+ align:start position:0%
+sounds and then sample them at at um 40
+kHz, you would hear the alias and it
+
+ align:start position:0%
+kHz, you would hear the alias and it
+ 
+
+ align:start position:0%
+kHz, you would hear the alias and it
+would be highly objectionable. So you
+
+ align:start position:0%
+would be highly objectionable. So you
+ 
+
+ align:start position:0%
+would be highly objectionable. So you
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+anti-alias. And that's actually hard
+
+ align:start position:0%
+anti-alias. And that's actually hard
+ 
+
+ align:start position:0%
+anti-alias. And that's actually hard
+because if you'd like to hear up to
+
+ align:start position:0%
+because if you'd like to hear up to
+ 
+
+ align:start position:0%
+because if you'd like to hear up to
+20 and if you're sampling at
+
+ align:start position:0%
+20 and if you're sampling at
+ 
+
+ align:start position:0%
+20 and if you're sampling at
+44.1 20
+
+ align:start position:0%
+44.1 20
+ 
+
+ align:start position:0%
+44.1 20
+uh reflects down to
+
+ align:start position:0%
+uh reflects down to
+ 
+
+ align:start position:0%
+uh reflects down to
+24.1 which means that you you want the
+
+ align:start position:0%
+24.1 which means that you you want the
+ 
+
+ align:start position:0%
+24.1 which means that you you want the
+transition band to be u only 4
+
+ align:start position:0%
+transition band to be u only 4
+ 
+
+ align:start position:0%
+transition band to be u only 4
+kHz. Okay.
+
+ align:start position:0%
+kHz. Okay.
+ 
+
+ align:start position:0%
+kHz. Okay.
+And if you think about the design of a
+
+ align:start position:0%
+And if you think about the design of a
+ 
+
+ align:start position:0%
+And if you think about the design of a
+filter like a Butterworth
+
+ align:start position:0%
+filter like a Butterworth
+ 
+
+ align:start position:0%
+filter like a Butterworth
+filter, in order to get a transition
+
+ align:start position:0%
+filter, in order to get a transition
+ 
+
+ align:start position:0%
+filter, in order to get a transition
+that attenuates by 80
+
+ align:start position:0%
+that attenuates by 80
+ 
+
+ align:start position:0%
+that attenuates by 80
+dB, think about the dynamic range of
+
+ align:start position:0%
+dB, think about the dynamic range of
+ 
+
+ align:start position:0%
+dB, think about the dynamic range of
+hearing, you have to make the loudest
+
+ align:start position:0%
+hearing, you have to make the loudest
+ 
+
+ align:start position:0%
+hearing, you have to make the loudest
+sounds small enough so that you can no
+
+ align:start position:0%
+sounds small enough so that you can no
+ 
+
+ align:start position:0%
+sounds small enough so that you can no
+longer hear them. So in general, you
+
+ align:start position:0%
+longer hear them. So in general, you
+ 
+
+ align:start position:0%
+longer hear them. So in general, you
+have to attenuate by about 80
+
+ align:start position:0%
+have to attenuate by about 80
+ 
+
+ align:start position:0%
+have to attenuate by about 80
+dB. Um, you need about 50 poles to get
+
+ align:start position:0%
+dB. Um, you need about 50 poles to get
+ 
+
+ align:start position:0%
+dB. Um, you need about 50 poles to get
+an add attenuation.
+
+ align:start position:0%
+an add attenuation.
+ 
+
+ align:start position:0%
+an add attenuation.
+uh using a Butterworth design in 4 kHz
+
+ align:start position:0%
+uh using a Butterworth design in 4 kHz
+ 
+
+ align:start position:0%
+uh using a Butterworth design in 4 kHz
+at 20 kHz. Everybody sort of know what
+
+ align:start position:0%
+at 20 kHz. Everybody sort of know what
+ 
+
+ align:start position:0%
+at 20 kHz. Everybody sort of know what
+I'm talking
+
+ align:start position:0%
+I'm talking
+ 
+
+ align:start position:0%
+I'm talking
+about. That's
+
+ align:start position:0%
+about. That's
+ 
+
+ align:start position:0%
+about. That's
+impossible. Uh lining up filters there.
+
+ align:start position:0%
+impossible. Uh lining up filters there.
+ 
+
+ align:start position:0%
+impossible. Uh lining up filters there.
+So the way the Butterworth filters work,
+
+ align:start position:0%
+So the way the Butterworth filters work,
+ 
+
+ align:start position:0%
+So the way the Butterworth filters work,
+you remember? So you have
+
+ align:start position:0%
+you remember? So you have
+ 
+
+ align:start position:0%
+you remember? So you have
+um you have a bunch of
+
+ align:start position:0%
+um you have a bunch of
+ 
+
+ align:start position:0%
+um you have a bunch of
+poles like
+
+ align:start position:0%
+poles like
+ 
+
+ align:start position:0%
+poles like
+so. The way you think about that is that
+
+ align:start position:0%
+so. The way you think about that is that
+ 
+
+ align:start position:0%
+so. The way you think about that is that
+you start with a design that looks like
+
+ align:start position:0%
+you start with a design that looks like
+ 
+
+ align:start position:0%
+you start with a design that looks like
+a not so good low pass
+
+ align:start position:0%
+a not so good low pass
+ 
+
+ align:start position:0%
+a not so good low pass
+filter. Then you add these
+
+ align:start position:0%
+filter. Then you add these
+ 
+
+ align:start position:0%
+filter. Then you add these
+poles which give you a peaky
+
+ align:start position:0%
+poles which give you a peaky
+ 
+
+ align:start position:0%
+poles which give you a peaky
+response like that. So that when this is
+
+ align:start position:0%
+response like that. So that when this is
+ 
+
+ align:start position:0%
+response like that. So that when this is
+going down the peakiness here helps to
+
+ align:start position:0%
+going down the peakiness here helps to
+ 
+
+ align:start position:0%
+going down the peakiness here helps to
+cancel
+
+ align:start position:0%
+cancel
+ 
+
+ align:start position:0%
+cancel
+that. Then you do that
+
+ align:start position:0%
+that. Then you do that
+ 
+
+ align:start position:0%
+that. Then you do that
+again. So you do you can think about
+
+ align:start position:0%
+again. So you do you can think about
+ 
+
+ align:start position:0%
+again. So you do you can think about
+these uh successive pole pairs as
+
+ align:start position:0%
+these uh successive pole pairs as
+ 
+
+ align:start position:0%
+these uh successive pole pairs as
+sharpening the transition by pushing
+
+ align:start position:0%
+sharpening the transition by pushing
+ 
+
+ align:start position:0%
+sharpening the transition by pushing
+up on the center frequency and rolling
+
+ align:start position:0%
+up on the center frequency and rolling
+ 
+
+ align:start position:0%
+up on the center frequency and rolling
+off on the edge frequency. But in order
+
+ align:start position:0%
+off on the edge frequency. But in order
+ 
+
+ align:start position:0%
+off on the edge frequency. But in order
+for that to work, they have to all be
+
+ align:start position:0%
+for that to work, they have to all be
+ 
+
+ align:start position:0%
+for that to work, they have to all be
+lined up. So if you've got 50 of them,
+
+ align:start position:0%
+lined up. So if you've got 50 of them,
+ 
+
+ align:start position:0%
+lined up. So if you've got 50 of them,
+you've got to be able to line these up
+
+ align:start position:0%
+you've got to be able to line these up
+ 
+
+ align:start position:0%
+you've got to be able to line these up
+to about a percent or so. Otherwise,
+
+ align:start position:0%
+to about a percent or so. Otherwise,
+ 
+
+ align:start position:0%
+to about a percent or so. Otherwise,
+they don't perform the way they're
+
+ align:start position:0%
+they don't perform the way they're
+ 
+
+ align:start position:0%
+they don't perform the way they're
+supposed to, and they can actually make
+
+ align:start position:0%
+supposed to, and they can actually make
+ 
+
+ align:start position:0%
+supposed to, and they can actually make
+things worse.
+
+ align:start position:0%
+things worse.
+ 
+
+ align:start position:0%
+things worse.
+So making uh an analog filter of that
+
+ align:start position:0%
+So making uh an analog filter of that
+ 
+
+ align:start position:0%
+So making uh an analog filter of that
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+uh was impossible then and is difficult
+
+ align:start position:0%
+uh was impossible then and is difficult
+ 
+
+ align:start position:0%
+uh was impossible then and is difficult
+now. Here's sort of the
+
+ align:start position:0%
+now. Here's sort of the
+ 
+
+ align:start position:0%
+now. Here's sort of the
+state-of-the-art. So this is uh this
+
+ align:start position:0%
+state-of-the-art. So this is uh this
+ 
+
+ align:start position:0%
+state-of-the-art. So this is uh this
+actually does have 80 dB of rolloff
+
+ align:start position:0%
+actually does have 80 dB of rolloff
+ 
+
+ align:start position:0%
+actually does have 80 dB of rolloff
+because it's a fancier design. It's an
+
+ align:start position:0%
+because it's a fancier design. It's an
+ 
+
+ align:start position:0%
+because it's a fancier design. It's an
+elliptic design. The trick here though
+
+ align:start position:0%
+elliptic design. The trick here though
+ 
+
+ align:start position:0%
+elliptic design. The trick here though
+is that all the parts are laser trimmed.
+
+ align:start position:0%
+is that all the parts are laser trimmed.
+ 
+
+ align:start position:0%
+is that all the parts are laser trimmed.
+So they're all done on one substrate.
+
+ align:start position:0%
+So they're all done on one substrate.
+ 
+
+ align:start position:0%
+So they're all done on one substrate.
+All the inductors, all the capacitors
+
+ align:start position:0%
+All the inductors, all the capacitors
+ 
+
+ align:start position:0%
+All the inductors, all the capacitors
+are done on a single substrate. Then
+
+ align:start position:0%
+are done on a single substrate. Then
+ 
+
+ align:start position:0%
+are done on a single substrate. Then
+they're laser trimmed so that they fall
+
+ align:start position:0%
+they're laser trimmed so that they fall
+ 
+
+ align:start position:0%
+they're laser trimmed so that they fall
+in exactly the right
+
+ align:start position:0%
+in exactly the right
+ 
+
+ align:start position:0%
+in exactly the right
+places. Then it's u encased in aluminum
+
+ align:start position:0%
+places. Then it's u encased in aluminum
+ 
+
+ align:start position:0%
+places. Then it's u encased in aluminum
+to help to hold the uh temperature
+
+ align:start position:0%
+to help to hold the uh temperature
+ 
+
+ align:start position:0%
+to help to hold the uh temperature
+constant and to keep the electromagnetic
+
+ align:start position:0%
+constant and to keep the electromagnetic
+ 
+
+ align:start position:0%
+constant and to keep the electromagnetic
+inter interference
+
+ align:start position:0%
+inter interference
+ 
+
+ align:start position:0%
+inter interference
+out. And even so this has just 11 pole
+
+ align:start position:0%
+out. And even so this has just 11 pole
+ 
+
+ align:start position:0%
+out. And even so this has just 11 pole
+pairs. So this is not nearly adequate
+
+ align:start position:0%
+pairs. So this is not nearly adequate
+ 
+
+ align:start position:0%
+pairs. So this is not nearly adequate
+for that kind of a design.
+
+ align:start position:0%
+for that kind of a design.
+ 
+
+ align:start position:0%
+for that kind of a design.
+So what we do instead
+
+ align:start position:0%
+So what we do instead
+ 
+
+ align:start position:0%
+So what we do instead
+uh is we do something called uh
+
+ align:start position:0%
+uh is we do something called uh
+ 
+
+ align:start position:0%
+uh is we do something called uh
+oversampling. So instead of sampling at
+
+ align:start position:0%
+oversampling. So instead of sampling at
+ 
+
+ align:start position:0%
+oversampling. So instead of sampling at
+44.1 which is what you would think would
+
+ align:start position:0%
+44.1 which is what you would think would
+ 
+
+ align:start position:0%
+44.1 which is what you would think would
+happen in a CD, you sample at four times
+
+ align:start position:0%
+happen in a CD, you sample at four times
+ 
+
+ align:start position:0%
+happen in a CD, you sample at four times
+that. By sampling at a very high
+
+ align:start position:0%
+that. By sampling at a very high
+ 
+
+ align:start position:0%
+that. By sampling at a very high
+frequency, you make it easy to make an
+
+ align:start position:0%
+frequency, you make it easy to make an
+ 
+
+ align:start position:0%
+frequency, you make it easy to make an
+anti-aliasing
+
+ align:start position:0%
+anti-aliasing
+ 
+
+ align:start position:0%
+anti-aliasing
+filter because now you only need to
+
+ align:start position:0%
+filter because now you only need to
+ 
+
+ align:start position:0%
+filter because now you only need to
+worry about saving the frequencies up to
+
+ align:start position:0%
+worry about saving the frequencies up to
+ 
+
+ align:start position:0%
+worry about saving the frequencies up to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+kHz, but you've got 170 kHz to drop the
+
+ align:start position:0%
+kHz, but you've got 170 kHz to drop the
+ 
+
+ align:start position:0%
+kHz, but you've got 170 kHz to drop the
+uh transition to do the transition. So
+
+ align:start position:0%
+uh transition to do the transition. So
+ 
+
+ align:start position:0%
+uh transition to do the transition. So
+the filter design becomes very easy. In
+
+ align:start position:0%
+the filter design becomes very easy. In
+ 
+
+ align:start position:0%
+the filter design becomes very easy. In
+fact, a typical design only has five
+
+ align:start position:0%
+fact, a typical design only has five
+ 
+
+ align:start position:0%
+fact, a typical design only has five
+poles. So just a handful of capacitor
+
+ align:start position:0%
+poles. So just a handful of capacitor
+ 
+
+ align:start position:0%
+poles. So just a handful of capacitor
+just uh two capacitors uh uh and two op
+
+ align:start position:0%
+just uh two capacitors uh uh and two op
+ 
+
+ align:start position:0%
+just uh two capacitors uh uh and two op
+amps will do
+
+ align:start position:0%
+amps will do
+ 
+
+ align:start position:0%
+amps will do
+that. So then you've got a system that
+
+ align:start position:0%
+that. So then you've got a system that
+ 
+
+ align:start position:0%
+that. So then you've got a system that
+uh is sampled at 176 kHz. What's the
+
+ align:start position:0%
+uh is sampled at 176 kHz. What's the
+ 
+
+ align:start position:0%
+uh is sampled at 176 kHz. What's the
+problem with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? What's the problem with sampling
+
+ align:start position:0%
+that? What's the problem with sampling
+ 
+
+ align:start position:0%
+that? What's the problem with sampling
+at 176 kHz?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too much information. So what you've
+
+ align:start position:0%
+too much information. So what you've
+ 
+
+ align:start position:0%
+too much information. So what you've
+done by sampling at the higher frequency
+
+ align:start position:0%
+done by sampling at the higher frequency
+ 
+
+ align:start position:0%
+done by sampling at the higher frequency
+is you've increased the amount of
+
+ align:start position:0%
+is you've increased the amount of
+ 
+
+ align:start position:0%
+is you've increased the amount of
+information that needs to be stored by a
+
+ align:start position:0%
+information that needs to be stored by a
+ 
+
+ align:start position:0%
+information that needs to be stored by a
+factor of four. So instead of being able
+
+ align:start position:0%
+factor of four. So instead of being able
+ 
+
+ align:start position:0%
+factor of four. So instead of being able
+to record 74 minutes of
+
+ align:start position:0%
+to record 74 minutes of
+ 
+
+ align:start position:0%
+to record 74 minutes of
+music, you can record 74 divided by
+
+ align:start position:0%
+music, you can record 74 divided by
+ 
+
+ align:start position:0%
+music, you can record 74 divided by
+four, 18 minutes of music. Nobody would
+
+ align:start position:0%
+four, 18 minutes of music. Nobody would
+ 
+
+ align:start position:0%
+four, 18 minutes of music. Nobody would
+like that, right? So how do you fix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? Down sample.
+
+ align:start position:0%
+that? Down sample.
+ 
+
+ align:start position:0%
+that? Down sample.
+Exactly. So what you do is you run that
+
+ align:start position:0%
+Exactly. So what you do is you run that
+ 
+
+ align:start position:0%
+Exactly. So what you do is you run that
+176 this that uh discrete time signal
+
+ align:start position:0%
+176 this that uh discrete time signal
+ 
+
+ align:start position:0%
+176 this that uh discrete time signal
+that was sampled at 176 through a
+
+ align:start position:0%
+that was sampled at 176 through a
+ 
+
+ align:start position:0%
+that was sampled at 176 through a
+discrete lowass
+
+ align:start position:0%
+discrete lowass
+ 
+
+ align:start position:0%
+discrete lowass
+filter which you implement digitally
+
+ align:start position:0%
+filter which you implement digitally
+ 
+
+ align:start position:0%
+filter which you implement digitally
+with arbitrary precision as much as you
+
+ align:start position:0%
+with arbitrary precision as much as you
+ 
+
+ align:start position:0%
+with arbitrary precision as much as you
+want. So here's a design uh based
+
+ align:start position:0%
+want. So here's a design uh based
+ 
+
+ align:start position:0%
+want. So here's a design uh based
+on uh a filter whose length is 200
+
+ align:start position:0%
+on uh a filter whose length is 200
+ 
+
+ align:start position:0%
+on uh a filter whose length is 200
+By making a length 200 discrete time
+
+ align:start position:0%
+By making a length 200 discrete time
+ 
+
+ align:start position:0%
+By making a length 200 discrete time
+filter, you can capture the basic sin t
+
+ align:start position:0%
+filter, you can capture the basic sin t
+ 
+
+ align:start position:0%
+filter, you can capture the basic sin t
+over t shape that you're trying to get
+
+ align:start position:0%
+over t shape that you're trying to get
+ 
+
+ align:start position:0%
+over t shape that you're trying to get
+with an ideal
+
+ align:start position:0%
+with an ideal
+ 
+
+ align:start position:0%
+with an ideal
+filter. You can you so here uh with 200
+
+ align:start position:0%
+filter. You can you so here uh with 200
+ 
+
+ align:start position:0%
+filter. You can you so here uh with 200
+samples, it's easy to reproduce
+
+ align:start position:0%
+samples, it's easy to reproduce
+ 
+
+ align:start position:0%
+samples, it's easy to reproduce
+uh a large number of ripples similar to
+
+ align:start position:0%
+uh a large number of ripples similar to
+ 
+
+ align:start position:0%
+uh a large number of ripples similar to
+the large number of ripples that I
+
+ align:start position:0%
+the large number of ripples that I
+ 
+
+ align:start position:0%
+the large number of ripples that I
+wanted over here, but now with digital
+
+ align:start position:0%
+wanted over here, but now with digital
+ 
+
+ align:start position:0%
+wanted over here, but now with digital
+multiplies, not with uh resistors and
+
+ align:start position:0%
+multiplies, not with uh resistors and
+ 
+
+ align:start position:0%
+multiplies, not with uh resistors and
+capacitors.
+
+ align:start position:0%
+capacitors.
+ 
+
+ align:start position:0%
+capacitors.
+And the um this shows where the poles
+
+ align:start position:0%
+And the um this shows where the poles
+ 
+
+ align:start position:0%
+And the um this shows where the poles
+this is an all zero filter. It's a
+
+ align:start position:0%
+this is an all zero filter. It's a
+ 
+
+ align:start position:0%
+this is an all zero filter. It's a
+finite length filter. We didn't talk
+
+ align:start position:0%
+finite length filter. We didn't talk
+ 
+
+ align:start position:0%
+finite length filter. We didn't talk
+about that. It's an easy way to
+
+ align:start position:0%
+about that. It's an easy way to
+ 
+
+ align:start position:0%
+about that. It's an easy way to
+implement uh filter design. It's an easy
+
+ align:start position:0%
+implement uh filter design. It's an easy
+ 
+
+ align:start position:0%
+implement uh filter design. It's an easy
+way to design filters. Uh it's very
+
+ align:start position:0%
+way to design filters. Uh it's very
+ 
+
+ align:start position:0%
+way to design filters. Uh it's very
+popular way of doing it. So it's an all
+
+ align:start position:0%
+popular way of doing it. So it's an all
+ 
+
+ align:start position:0%
+popular way of doing it. So it's an all
+zero filter and you can sort of figure
+
+ align:start position:0%
+zero filter and you can sort of figure
+ 
+
+ align:start position:0%
+zero filter and you can sort of figure
+out by thinking about the spacing of the
+
+ align:start position:0%
+out by thinking about the spacing of the
+ 
+
+ align:start position:0%
+out by thinking about the spacing of the
+zeros relative to the unit circle how
+
+ align:start position:0%
+zeros relative to the unit circle how
+ 
+
+ align:start position:0%
+zeros relative to the unit circle how
+that implements a low pass filter. That
+
+ align:start position:0%
+that implements a low pass filter. That
+ 
+
+ align:start position:0%
+that implements a low pass filter. That
+was done with an automated u optimizing
+
+ align:start position:0%
+was done with an automated u optimizing
+ 
+
+ align:start position:0%
+was done with an automated u optimizing
+algorithm for finding the best low pass
+
+ align:start position:0%
+algorithm for finding the best low pass
+ 
+
+ align:start position:0%
+algorithm for finding the best low pass
+filter. The method is called the
+
+ align:start position:0%
+filter. The method is called the
+ 
+
+ align:start position:0%
+filter. The method is called the
+parksman
+
+ align:start position:0%
+parksman
+ 
+
+ align:start position:0%
+parksman
+algorithm and it makes a very nice
+
+ align:start position:0%
+algorithm and it makes a very nice
+ 
+
+ align:start position:0%
+algorithm and it makes a very nice
+filter. So this shows a transition of um
+
+ align:start position:0%
+filter. So this shows a transition of um
+ 
+
+ align:start position:0%
+filter. So this shows a transition of um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+80dB passing 20 kHz signals and
+
+ align:start position:0%
+80dB passing 20 kHz signals and
+ 
+
+ align:start position:0%
+80dB passing 20 kHz signals and
+attenuating uh 24 and above. So you can
+
+ align:start position:0%
+attenuating uh 24 and above. So you can
+ 
+
+ align:start position:0%
+attenuating uh 24 and above. So you can
+get a very nice filter by doing that in
+
+ align:start position:0%
+get a very nice filter by doing that in
+ 
+
+ align:start position:0%
+get a very nice filter by doing that in
+discrete time.
+
+ align:start position:0%
+discrete time.
+ 
+
+ align:start position:0%
+discrete time.
+So then uh having done the digital
+
+ align:start position:0%
+So then uh having done the digital
+ 
+
+ align:start position:0%
+So then uh having done the digital
+filter you can throw away the
+
+ align:start position:0%
+filter you can throw away the
+ 
+
+ align:start position:0%
+filter you can throw away the
+frequencies that would alias and then
+
+ align:start position:0%
+frequencies that would alias and then
+ 
+
+ align:start position:0%
+frequencies that would alias and then
+down sample.
+
+ align:start position:0%
+down sample.
+ 
+
+ align:start position:0%
+down sample.
+Yeah. Is the filter in those zero
+
+ align:start position:0%
+Yeah. Is the filter in those zero
+ 
+
+ align:start position:0%
+Yeah. Is the filter in those zero
+locations standardized by anybody or is
+
+ align:start position:0%
+locations standardized by anybody or is
+ 
+
+ align:start position:0%
+locations standardized by anybody or is
+any manufacturer any manufacturer? Yeah.
+
+ align:start position:0%
+any manufacturer any manufacturer? Yeah.
+ 
+
+ align:start position:0%
+any manufacturer any manufacturer? Yeah.
+Every manufacturer is different. What's
+
+ align:start position:0%
+Every manufacturer is different. What's
+ 
+
+ align:start position:0%
+Every manufacturer is different. What's
+happening over time though is that the
+
+ align:start position:0%
+happening over time though is that the
+ 
+
+ align:start position:0%
+happening over time though is that the
+chips are becoming standardized. So if
+
+ align:start position:0%
+chips are becoming standardized. So if
+ 
+
+ align:start position:0%
+chips are becoming standardized. So if
+you buy a particular chip, it has a
+
+ align:start position:0%
+you buy a particular chip, it has a
+ 
+
+ align:start position:0%
+you buy a particular chip, it has a
+particular filter set but it's not
+
+ align:start position:0%
+particular filter set but it's not
+ 
+
+ align:start position:0%
+particular filter set but it's not
+standardized in the code.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's um uh how you generate a
+
+ align:start position:0%
+Okay, so that's um uh how you generate a
+ 
+
+ align:start position:0%
+Okay, so that's um uh how you generate a
+signal that is robust and it's basically
+
+ align:start position:0%
+signal that is robust and it's basically
+ 
+
+ align:start position:0%
+signal that is robust and it's basically
+just 03. Now we have to think about how
+
+ align:start position:0%
+just 03. Now we have to think about how
+ 
+
+ align:start position:0%
+just 03. Now we have to think about how
+would you make the
+
+ align:start position:0%
+would you make the
+ 
+
+ align:start position:0%
+would you make the
+player because what we'd like to do is
+
+ align:start position:0%
+player because what we'd like to do is
+ 
+
+ align:start position:0%
+player because what we'd like to do is
+enable you to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um use a CD in a more portable fashion
+
+ align:start position:0%
+um use a CD in a more portable fashion
+ 
+
+ align:start position:0%
+um use a CD in a more portable fashion
+than you could use this technology.
+
+ align:start position:0%
+than you could use this technology.
+ 
+
+ align:start position:0%
+than you could use this technology.
+Right? So the question is now, how would
+
+ align:start position:0%
+Right? So the question is now, how would
+ 
+
+ align:start position:0%
+Right? So the question is now, how would
+you make a player that can pick up this
+
+ align:start position:0%
+you make a player that can pick up this
+ 
+
+ align:start position:0%
+you make a player that can pick up this
+information off of the
+
+ align:start position:0%
+information off of the
+ 
+
+ align:start position:0%
+information off of the
+CD so that you can reproduce it in a
+
+ align:start position:0%
+CD so that you can reproduce it in a
+ 
+
+ align:start position:0%
+CD so that you can reproduce it in a
+Walkman or in a in a more portable
+
+ align:start position:0%
+Walkman or in a in a more portable
+ 
+
+ align:start position:0%
+Walkman or in a in a more portable
+environment. So I had this brilliant
+
+ align:start position:0%
+environment. So I had this brilliant
+ 
+
+ align:start position:0%
+environment. So I had this brilliant
+idea about two years ago that I would
+
+ align:start position:0%
+idea about two years ago that I would
+ 
+
+ align:start position:0%
+idea about two years ago that I would
+take this
+
+ align:start position:0%
+take this
+ 
+
+ align:start position:0%
+take this
+CD and I would use my microscope. Okay,
+
+ align:start position:0%
+CD and I would use my microscope. Okay,
+ 
+
+ align:start position:0%
+CD and I would use my microscope. Okay,
+I may have mentioned I like microscopy.
+
+ align:start position:0%
+I may have mentioned I like microscopy.
+ 
+
+ align:start position:0%
+I may have mentioned I like microscopy.
+I went into my microscope. I used my
+
+ align:start position:0%
+I went into my microscope. I used my
+ 
+
+ align:start position:0%
+I went into my microscope. I used my
+research quality microscope which cost
+
+ align:start position:0%
+research quality microscope which cost
+ 
+
+ align:start position:0%
+research quality microscope which cost
+$70,000. And I'll take a beautiful
+
+ align:start position:0%
+$70,000. And I'll take a beautiful
+ 
+
+ align:start position:0%
+$70,000. And I'll take a beautiful
+picture of the bits on here and I'll
+
+ align:start position:0%
+picture of the bits on here and I'll
+ 
+
+ align:start position:0%
+picture of the bits on here and I'll
+write a problem set for 003 where you
+
+ align:start position:0%
+write a problem set for 003 where you
+ 
+
+ align:start position:0%
+write a problem set for 003 where you
+have to decode the the bitstream. Okay.
+
+ align:start position:0%
+have to decode the the bitstream. Okay.
+ 
+
+ align:start position:0%
+have to decode the the bitstream. Okay.
+I thought it was brilliant. Uh and you
+
+ align:start position:0%
+I thought it was brilliant. Uh and you
+ 
+
+ align:start position:0%
+I thought it was brilliant. Uh and you
+know it was like a week before the
+
+ align:start position:0%
+know it was like a week before the
+ 
+
+ align:start position:0%
+know it was like a week before the
+homework had to be written. You know the
+
+ align:start position:0%
+homework had to be written. You know the
+ 
+
+ align:start position:0%
+homework had to be written. You know the
+standard thing. And of course I couldn't
+
+ align:start position:0%
+standard thing. And of course I couldn't
+ 
+
+ align:start position:0%
+standard thing. And of course I couldn't
+get it to work in time. The problem was
+
+ align:start position:0%
+get it to work in time. The problem was
+ 
+
+ align:start position:0%
+get it to work in time. The problem was
+that even my $70,000 research microscope
+
+ align:start position:0%
+that even my $70,000 research microscope
+ 
+
+ align:start position:0%
+that even my $70,000 research microscope
+has trouble seeing the the
+
+ align:start position:0%
+has trouble seeing the the
+ 
+
+ align:start position:0%
+has trouble seeing the the
+bits. The bits are really
+
+ align:start position:0%
+bits. The bits are really
+ 
+
+ align:start position:0%
+bits. The bits are really
+small. So when I first tried it, I
+
+ align:start position:0%
+small. So when I first tried it, I
+ 
+
+ align:start position:0%
+small. So when I first tried it, I
+couldn't see
+
+ align:start position:0%
+couldn't see
+ 
+
+ align:start position:0%
+couldn't see
+anything. So I fiddled around with the
+
+ align:start position:0%
+anything. So I fiddled around with the
+ 
+
+ align:start position:0%
+anything. So I fiddled around with the
+microscope. I tried all different kinds
+
+ align:start position:0%
+microscope. I tried all different kinds
+ 
+
+ align:start position:0%
+microscope. I tried all different kinds
+of magnifications. I tried all kinds of
+
+ align:start position:0%
+of magnifications. I tried all kinds of
+ 
+
+ align:start position:0%
+of magnifications. I tried all kinds of
+different optical tricks that I know. I
+
+ align:start position:0%
+different optical tricks that I know. I
+ 
+
+ align:start position:0%
+different optical tricks that I know. I
+couldn't figure out anything. I couldn't
+
+ align:start position:0%
+couldn't figure out anything. I couldn't
+ 
+
+ align:start position:0%
+couldn't figure out anything. I couldn't
+get it to work. So I got my graduate
+
+ align:start position:0%
+get it to work. So I got my graduate
+ 
+
+ align:start position:0%
+get it to work. So I got my graduate
+students. They're always much better at
+
+ align:start position:0%
+students. They're always much better at
+ 
+
+ align:start position:0%
+students. They're always much better at
+this sort of thing. uh and we finally
+
+ align:start position:0%
+this sort of thing. uh and we finally
+ 
+
+ align:start position:0%
+this sort of thing. uh and we finally
+got it to work. We cheated like
+
+ align:start position:0%
+got it to work. We cheated like
+ 
+
+ align:start position:0%
+got it to work. We cheated like
+crazy. So we had to use something called
+
+ align:start position:0%
+crazy. So we had to use something called
+ 
+
+ align:start position:0%
+crazy. So we had to use something called
+water immersion. So uh you put a drop of
+
+ align:start position:0%
+water immersion. So uh you put a drop of
+ 
+
+ align:start position:0%
+water immersion. So uh you put a drop of
+water on the surface so that you can use
+
+ align:start position:0%
+water on the surface so that you can use
+ 
+
+ align:start position:0%
+water on the surface so that you can use
+the so you lose resolution when you go
+
+ align:start position:0%
+the so you lose resolution when you go
+ 
+
+ align:start position:0%
+the so you lose resolution when you go
+through an a um
+
+ align:start position:0%
+through an a um
+ 
+
+ align:start position:0%
+through an a um
+um glass to air
+
+ align:start position:0%
+um glass to air
+ 
+
+ align:start position:0%
+um glass to air
+interface. That's a bunch of microscopy
+
+ align:start position:0%
+interface. That's a bunch of microscopy
+ 
+
+ align:start position:0%
+interface. That's a bunch of microscopy
+that you don't need to know but you do.
+
+ align:start position:0%
+that you don't need to know but you do.
+ 
+
+ align:start position:0%
+that you don't need to know but you do.
+So there are tricks in microscopy where
+
+ align:start position:0%
+So there are tricks in microscopy where
+ 
+
+ align:start position:0%
+So there are tricks in microscopy where
+you can avoid having the air interface
+
+ align:start position:0%
+you can avoid having the air interface
+ 
+
+ align:start position:0%
+you can avoid having the air interface
+by using water. The water is more
+
+ align:start position:0%
+by using water. The water is more
+ 
+
+ align:start position:0%
+by using water. The water is more
+closely optically matched to glass. So
+
+ align:start position:0%
+closely optically matched to glass. So
+ 
+
+ align:start position:0%
+closely optically matched to glass. So
+what we did was we did u immersion
+
+ align:start position:0%
+what we did was we did u immersion
+ 
+
+ align:start position:0%
+what we did was we did u immersion
+microscopy. Put a drop of water on here.
+
+ align:start position:0%
+microscopy. Put a drop of water on here.
+ 
+
+ align:start position:0%
+microscopy. Put a drop of water on here.
+Put the lens in the water and that's the
+
+ align:start position:0%
+Put the lens in the water and that's the
+ 
+
+ align:start position:0%
+Put the lens in the water and that's the
+picture I
+
+ align:start position:0%
+picture I
+ 
+
+ align:start position:0%
+picture I
+got. So the point is that I had to
+
+ align:start position:0%
+got. So the point is that I had to
+ 
+
+ align:start position:0%
+got. So the point is that I had to
+work to get a $70,000
+
+ align:start position:0%
+work to get a $70,000
+ 
+
+ align:start position:0%
+work to get a $70,000
+microscope to read the bits off here.
+
+ align:start position:0%
+microscope to read the bits off here.
+ 
+
+ align:start position:0%
+microscope to read the bits off here.
+And I sort of gave up with the idea that
+
+ align:start position:0%
+And I sort of gave up with the idea that
+ 
+
+ align:start position:0%
+And I sort of gave up with the idea that
+I would record a track because it was
+
+ align:start position:0%
+I would record a track because it was
+ 
+
+ align:start position:0%
+I would record a track because it was
+just too painful to just get this one
+
+ align:start position:0%
+just too painful to just get this one
+ 
+
+ align:start position:0%
+just too painful to just get this one
+image. Now, the trick is they make
+
+ align:start position:0%
+image. Now, the trick is they make
+ 
+
+ align:start position:0%
+image. Now, the trick is they make
+players that cost
+
+ align:start position:0%
+players that cost
+ 
+
+ align:start position:0%
+players that cost
+$10. What do they know that I don't
+
+ align:start position:0%
+$10. What do they know that I don't
+ 
+
+ align:start position:0%
+$10. What do they know that I don't
+know? Right? So, here I am with a
+
+ align:start position:0%
+know? Right? So, here I am with a
+ 
+
+ align:start position:0%
+know? Right? So, here I am with a
+$70,000 research microscope having a
+
+ align:start position:0%
+$70,000 research microscope having a
+ 
+
+ align:start position:0%
+$70,000 research microscope having a
+difficult time getting the bits off. How
+
+ align:start position:0%
+difficult time getting the bits off. How
+ 
+
+ align:start position:0%
+difficult time getting the bits off. How
+do they make a um a CD player for
+
+ align:start position:0%
+do they make a um a CD player for
+ 
+
+ align:start position:0%
+do they make a um a CD player for
+$10? Uh just for fun, I did the same
+
+ align:start position:0%
+$10? Uh just for fun, I did the same
+ 
+
+ align:start position:0%
+$10? Uh just for fun, I did the same
+thing with the DVD. After I figured out
+
+ align:start position:0%
+thing with the DVD. After I figured out
+ 
+
+ align:start position:0%
+thing with the DVD. After I figured out
+how to do the immersion microscopy, I
+
+ align:start position:0%
+how to do the immersion microscopy, I
+ 
+
+ align:start position:0%
+how to do the immersion microscopy, I
+figured I'd at least So, this is a DVD
+
+ align:start position:0%
+figured I'd at least So, this is a DVD
+ 
+
+ align:start position:0%
+figured I'd at least So, this is a DVD
+done with the same sort of
+
+ align:start position:0%
+done with the same sort of
+ 
+
+ align:start position:0%
+done with the same sort of
+thing. So, how do they do it? They do
+
+ align:start position:0%
+thing. So, how do they do it? They do
+ 
+
+ align:start position:0%
+thing. So, how do they do it? They do
+very clever things. The first trick they
+
+ align:start position:0%
+very clever things. The first trick they
+ 
+
+ align:start position:0%
+very clever things. The first trick they
+use is interference. So, I talked about
+
+ align:start position:0%
+use is interference. So, I talked about
+ 
+
+ align:start position:0%
+use is interference. So, I talked about
+interference last time with our uh
+
+ align:start position:0%
+interference last time with our uh
+ 
+
+ align:start position:0%
+interference last time with our uh
+standing wave illumination micros
+
+ align:start position:0%
+standing wave illumination micros
+ 
+
+ align:start position:0%
+standing wave illumination micros
+microscope.
+
+ align:start position:0%
+microscope.
+ 
+
+ align:start position:0%
+microscope.
+they do interference. So I told you that
+
+ align:start position:0%
+they do interference. So I told you that
+ 
+
+ align:start position:0%
+they do interference. So I told you that
+the that this is polycarbonate with an
+
+ align:start position:0%
+the that this is polycarbonate with an
+ 
+
+ align:start position:0%
+the that this is polycarbonate with an
+aluminum coating. The aluminum is
+
+ align:start position:0%
+aluminum coating. The aluminum is
+ 
+
+ align:start position:0%
+aluminum coating. The aluminum is
+actually working like a
+
+ align:start position:0%
+actually working like a
+ 
+
+ align:start position:0%
+actually working like a
+mirror and that's the intent. So they
+
+ align:start position:0%
+mirror and that's the intent. So they
+ 
+
+ align:start position:0%
+mirror and that's the intent. So they
+don't actually um try to code black and
+
+ align:start position:0%
+don't actually um try to code black and
+ 
+
+ align:start position:0%
+don't actually um try to code black and
+white. What they try to code is
+
+ align:start position:0%
+white. What they try to code is
+ 
+
+ align:start position:0%
+white. What they try to code is
+distance. So, the idea is that you take
+
+ align:start position:0%
+distance. So, the idea is that you take
+ 
+
+ align:start position:0%
+distance. So, the idea is that you take
+a laser beam and you you uh reflect it
+
+ align:start position:0%
+a laser beam and you you uh reflect it
+ 
+
+ align:start position:0%
+a laser beam and you you uh reflect it
+off of the CD much like it reflects off
+
+ align:start position:0%
+off of the CD much like it reflects off
+ 
+
+ align:start position:0%
+off of the CD much like it reflects off
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+mirror. And then the features that were
+
+ align:start position:0%
+mirror. And then the features that were
+ 
+
+ align:start position:0%
+mirror. And then the features that were
+embossed are at different depths and the
+
+ align:start position:0%
+embossed are at different depths and the
+ 
+
+ align:start position:0%
+embossed are at different depths and the
+depths chosen very specifically to be
+
+ align:start position:0%
+depths chosen very specifically to be
+ 
+
+ align:start position:0%
+depths chosen very specifically to be
+lambda over four. The wavelength of the
+
+ align:start position:0%
+lambda over four. The wavelength of the
+ 
+
+ align:start position:0%
+lambda over four. The wavelength of the
+light. They use a 700 nanometer
+
+ align:start position:0%
+light. They use a 700 nanometer
+ 
+
+ align:start position:0%
+light. They use a 700 nanometer
+laser and the de the um features are
+
+ align:start position:0%
+laser and the de the um features are
+ 
+
+ align:start position:0%
+laser and the de the um features are
+offset by lambda over
+
+ align:start position:0%
+offset by lambda over
+ 
+
+ align:start position:0%
+offset by lambda over
+four. The idea is that uh so if you have
+
+ align:start position:0%
+four. The idea is that uh so if you have
+ 
+
+ align:start position:0%
+four. The idea is that uh so if you have
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feature and you have
+
+ align:start position:0%
+feature and you have
+ 
+
+ align:start position:0%
+feature and you have
+so you compare what would be the timing
+
+ align:start position:0%
+so you compare what would be the timing
+ 
+
+ align:start position:0%
+so you compare what would be the timing
+for this laser beam if it struck the
+
+ align:start position:0%
+for this laser beam if it struck the
+ 
+
+ align:start position:0%
+for this laser beam if it struck the
+mirror. You compare that to what it
+
+ align:start position:0%
+mirror. You compare that to what it
+ 
+
+ align:start position:0%
+mirror. You compare that to what it
+would be if it struck a feature and you
+
+ align:start position:0%
+would be if it struck a feature and you
+ 
+
+ align:start position:0%
+would be if it struck a feature and you
+rig it so that those two times are
+
+ align:start position:0%
+rig it so that those two times are
+ 
+
+ align:start position:0%
+rig it so that those two times are
+different by lambda over two. lambda
+
+ align:start position:0%
+different by lambda over two. lambda
+ 
+
+ align:start position:0%
+different by lambda over two. lambda
+over four in and lambda over four
+
+ align:start position:0%
+over four in and lambda over four
+ 
+
+ align:start position:0%
+over four in and lambda over four
+out. So then if you rig the
+
+ align:start position:0%
+out. So then if you rig the
+ 
+
+ align:start position:0%
+out. So then if you rig the
+beam to be half of the light falls on
+
+ align:start position:0%
+beam to be half of the light falls on
+ 
+
+ align:start position:0%
+beam to be half of the light falls on
+both, what's the sum of these waveforms
+
+ align:start position:0%
+both, what's the sum of these waveforms
+ 
+
+ align:start position:0%
+both, what's the sum of these waveforms
+going to be? If you have a component
+
+ align:start position:0%
+going to be? If you have a component
+ 
+
+ align:start position:0%
+going to be? If you have a component
+that's at the mirror and a component at
+
+ align:start position:0%
+that's at the mirror and a component at
+ 
+
+ align:start position:0%
+that's at the mirror and a component at
+the indented, if these are different in
+
+ align:start position:0%
+the indented, if these are different in
+ 
+
+ align:start position:0%
+the indented, if these are different in
+timing by lambda over two, when you add
+
+ align:start position:0%
+timing by lambda over two, when you add
+ 
+
+ align:start position:0%
+timing by lambda over two, when you add
+them, the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah, you get complete destructive
+
+ align:start position:0%
+is yeah, you get complete destructive
+ 
+
+ align:start position:0%
+is yeah, you get complete destructive
+interference. You get an answer of zero.
+
+ align:start position:0%
+interference. You get an answer of zero.
+ 
+
+ align:start position:0%
+interference. You get an answer of zero.
+So the idea in the reading of them is to
+
+ align:start position:0%
+So the idea in the reading of them is to
+ 
+
+ align:start position:0%
+So the idea in the reading of them is to
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+interference and rig it so that zeros
+
+ align:start position:0%
+interference and rig it so that zeros
+ 
+
+ align:start position:0%
+interference and rig it so that zeros
+are represented by no
+
+ align:start position:0%
+are represented by no
+ 
+
+ align:start position:0%
+are represented by no
+light and ones are represented by lots
+
+ align:start position:0%
+light and ones are represented by lots
+ 
+
+ align:start position:0%
+light and ones are represented by lots
+of light. Okay, so that's the first uh
+
+ align:start position:0%
+of light. Okay, so that's the first uh
+ 
+
+ align:start position:0%
+of light. Okay, so that's the first uh
+clever trick they
+
+ align:start position:0%
+clever trick they
+ 
+
+ align:start position:0%
+clever trick they
+do. Then the question is how do you
+
+ align:start position:0%
+do. Then the question is how do you
+ 
+
+ align:start position:0%
+do. Then the question is how do you
+focus it? Right? When I was doing my
+
+ align:start position:0%
+focus it? Right? When I was doing my
+ 
+
+ align:start position:0%
+focus it? Right? When I was doing my
+research um microscope, the research
+
+ align:start position:0%
+research um microscope, the research
+ 
+
+ align:start position:0%
+research um microscope, the research
+microscope first off it sits on a half
+
+ align:start position:0%
+microscope first off it sits on a half
+ 
+
+ align:start position:0%
+microscope first off it sits on a half
+ton of granite to make it all very
+
+ align:start position:0%
+ton of granite to make it all very
+ 
+
+ align:start position:0%
+ton of granite to make it all very
+stable because when you're doing the
+
+ align:start position:0%
+stable because when you're doing the
+ 
+
+ align:start position:0%
+stable because when you're doing the
+focusing you you don't want so the
+
+ align:start position:0%
+focusing you you don't want so the
+ 
+
+ align:start position:0%
+focusing you you don't want so the
+vibrations of the floor in my lab are
+
+ align:start position:0%
+vibrations of the floor in my lab are
+ 
+
+ align:start position:0%
+vibrations of the floor in my lab are
+about 100 nanometers about 100
+
+ align:start position:0%
+about 100 nanometers about 100
+ 
+
+ align:start position:0%
+about 100 nanometers about 100
+micrometers
+
+ align:start position:0%
+micrometers
+ 
+
+ align:start position:0%
+micrometers
+sorry it's about 100 micrometers and I
+
+ align:start position:0%
+sorry it's about 100 micrometers and I
+ 
+
+ align:start position:0%
+sorry it's about 100 micrometers and I
+have to have the stability of the system
+
+ align:start position:0%
+have to have the stability of the system
+ 
+
+ align:start position:0%
+have to have the stability of the system
+sub micron so I use a h a table made out
+
+ align:start position:0%
+sub micron so I use a h a table made out
+ 
+
+ align:start position:0%
+sub micron so I use a h a table made out
+of a half ton of granite
+
+ align:start position:0%
+of a half ton of granite
+ 
+
+ align:start position:0%
+of a half ton of granite
+and the microscope sits on top of that
+
+ align:start position:0%
+and the microscope sits on top of that
+ 
+
+ align:start position:0%
+and the microscope sits on top of that
+and that makes everything nice and
+
+ align:start position:0%
+and that makes everything nice and
+ 
+
+ align:start position:0%
+and that makes everything nice and
+stable. They can't do that. So, how do
+
+ align:start position:0%
+stable. They can't do that. So, how do
+ 
+
+ align:start position:0%
+stable. They can't do that. So, how do
+they control the focus without using a
+
+ align:start position:0%
+they control the focus without using a
+ 
+
+ align:start position:0%
+they control the focus without using a
+half I mean it wouldn't work to make a
+
+ align:start position:0%
+half I mean it wouldn't work to make a
+ 
+
+ align:start position:0%
+half I mean it wouldn't work to make a
+walk band, you know, that is uh half ton
+
+ align:start position:0%
+walk band, you know, that is uh half ton
+ 
+
+ align:start position:0%
+walk band, you know, that is uh half ton
+granite, right? So, what do they do to
+
+ align:start position:0%
+granite, right? So, what do they do to
+ 
+
+ align:start position:0%
+granite, right? So, what do they do to
+enable them to um do the same kind of
+
+ align:start position:0%
+enable them to um do the same kind of
+ 
+
+ align:start position:0%
+enable them to um do the same kind of
+focusing that I was doing? They use
+
+ align:start position:0%
+focusing that I was doing? They use
+ 
+
+ align:start position:0%
+focusing that I was doing? They use
+feedback. So the idea is to substitute
+
+ align:start position:0%
+feedback. So the idea is to substitute
+ 
+
+ align:start position:0%
+feedback. So the idea is to substitute
+feedback for precision. So rather than
+
+ align:start position:0%
+feedback for precision. So rather than
+ 
+
+ align:start position:0%
+feedback for precision. So rather than
+trying to make the parts precise, they
+
+ align:start position:0%
+trying to make the parts precise, they
+ 
+
+ align:start position:0%
+trying to make the parts precise, they
+put the imprecise parts in a feedback
+
+ align:start position:0%
+put the imprecise parts in a feedback
+ 
+
+ align:start position:0%
+put the imprecise parts in a feedback
+loop. Very powerful
+
+ align:start position:0%
+loop. Very powerful
+ 
+
+ align:start position:0%
+loop. Very powerful
+method. So here's here's what they do.
+
+ align:start position:0%
+method. So here's here's what they do.
+ 
+
+ align:start position:0%
+method. So here's here's what they do.
+They take the laser, it's trying to
+
+ align:start position:0%
+They take the laser, it's trying to
+ 
+
+ align:start position:0%
+They take the laser, it's trying to
+focus onto the CD that has patterns in
+
+ align:start position:0%
+focus onto the CD that has patterns in
+ 
+
+ align:start position:0%
+focus onto the CD that has patterns in
+it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And uh so there's a beam splitter so
+
+ align:start position:0%
+And uh so there's a beam splitter so
+ 
+
+ align:start position:0%
+And uh so there's a beam splitter so
+that part of the light goes over to the
+
+ align:start position:0%
+that part of the light goes over to the
+ 
+
+ align:start position:0%
+that part of the light goes over to the
+detector. Excuse me, I didn't do that
+
+ align:start position:0%
+detector. Excuse me, I didn't do that
+ 
+
+ align:start position:0%
+detector. Excuse me, I didn't do that
+right. The laser squirts up to here,
+
+ align:start position:0%
+right. The laser squirts up to here,
+ 
+
+ align:start position:0%
+right. The laser squirts up to here,
+goes straight through the beam splitter,
+
+ align:start position:0%
+goes straight through the beam splitter,
+ 
+
+ align:start position:0%
+goes straight through the beam splitter,
+comes back through a focusing lens,
+
+ align:start position:0%
+comes back through a focusing lens,
+ 
+
+ align:start position:0%
+comes back through a focusing lens,
+bounces off the beam splitter through
+
+ align:start position:0%
+bounces off the beam splitter through
+ 
+
+ align:start position:0%
+bounces off the beam splitter through
+another lens, and hits a detector. So
+
+ align:start position:0%
+another lens, and hits a detector. So
+ 
+
+ align:start position:0%
+another lens, and hits a detector. So
+this is So the detector is this way. And
+
+ align:start position:0%
+this is So the detector is this way. And
+ 
+
+ align:start position:0%
+this is So the detector is this way. And
+I'm showing this view then. So the
+
+ align:start position:0%
+I'm showing this view then. So the
+ 
+
+ align:start position:0%
+I'm showing this view then. So the
+detector should be there. I'm showing a
+
+ align:start position:0%
+detector should be there. I'm showing a
+ 
+
+ align:start position:0%
+detector should be there. I'm showing a
+view of it over here. And it's um it's
+
+ align:start position:0%
+view of it over here. And it's um it's
+ 
+
+ align:start position:0%
+view of it over here. And it's um it's
+rigged so that these two lenses, one of
+
+ align:start position:0%
+rigged so that these two lenses, one of
+ 
+
+ align:start position:0%
+rigged so that these two lenses, one of
+the lenses is spherical and one is
+
+ align:start position:0%
+the lenses is spherical and one is
+ 
+
+ align:start position:0%
+the lenses is spherical and one is
+cylindrical. What that means is you
+
+ align:start position:0%
+cylindrical. What that means is you
+ 
+
+ align:start position:0%
+cylindrical. What that means is you
+remember uh I've talked about microscopy
+
+ align:start position:0%
+remember uh I've talked about microscopy
+ 
+
+ align:start position:0%
+remember uh I've talked about microscopy
+in the past out of focus means
+
+ align:start position:0%
+in the past out of focus means
+ 
+
+ align:start position:0%
+in the past out of focus means
+blurred. Blurred for a spot means
+
+ align:start position:0%
+blurred. Blurred for a spot means
+ 
+
+ align:start position:0%
+blurred. Blurred for a spot means
+bigger. As a as a microscope goes out of
+
+ align:start position:0%
+bigger. As a as a microscope goes out of
+ 
+
+ align:start position:0%
+bigger. As a as a microscope goes out of
+focus, the spot gets bigger.
+
+ align:start position:0%
+focus, the spot gets bigger.
+ 
+
+ align:start position:0%
+focus, the spot gets bigger.
+What you do with these two lenses
+
+ align:start position:0%
+What you do with these two lenses
+ 
+
+ align:start position:0%
+What you do with these two lenses
+because one is circularly symmetric and
+
+ align:start position:0%
+because one is circularly symmetric and
+ 
+
+ align:start position:0%
+because one is circularly symmetric and
+the other is cylindrically symmetric.
+
+ align:start position:0%
+the other is cylindrically symmetric.
+ 
+
+ align:start position:0%
+the other is cylindrically symmetric.
+What you do is you make the beam uh in
+
+ align:start position:0%
+What you do is you make the beam uh in
+ 
+
+ align:start position:0%
+What you do is you make the beam uh in
+this direction go out of focus as it's
+
+ align:start position:0%
+this direction go out of focus as it's
+ 
+
+ align:start position:0%
+this direction go out of focus as it's
+going into focus in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction. Okay. So because you get two
+
+ align:start position:0%
+direction. Okay. So because you get two
+ 
+
+ align:start position:0%
+direction. Okay. So because you get two
+lenses, one is symmetric in XY and one
+
+ align:start position:0%
+lenses, one is symmetric in XY and one
+ 
+
+ align:start position:0%
+lenses, one is symmetric in XY and one
+has no magnification in Y but big
+
+ align:start position:0%
+has no magnification in Y but big
+ 
+
+ align:start position:0%
+has no magnification in Y but big
+magnification in X. You can rig it so
+
+ align:start position:0%
+magnification in X. You can rig it so
+ 
+
+ align:start position:0%
+magnification in X. You can rig it so
+that this dot will go out of focus
+
+ align:start position:0%
+that this dot will go out of focus
+ 
+
+ align:start position:0%
+that this dot will go out of focus
+horizontally while it's coming into
+
+ align:start position:0%
+horizontally while it's coming into
+ 
+
+ align:start position:0%
+horizontally while it's coming into
+focus
+
+ align:start position:0%
+focus
+ 
+
+ align:start position:0%
+focus
+vertically. The result is that if you
+
+ align:start position:0%
+vertically. The result is that if you
+ 
+
+ align:start position:0%
+vertically. The result is that if you
+move the CD closer, it becomes fat.
+
+ align:start position:0%
+move the CD closer, it becomes fat.
+ 
+
+ align:start position:0%
+move the CD closer, it becomes fat.
+And if you move the CD further, it
+
+ align:start position:0%
+And if you move the CD further, it
+ 
+
+ align:start position:0%
+And if you move the CD further, it
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+skinny. So all they need to do then is
+
+ align:start position:0%
+skinny. So all they need to do then is
+ 
+
+ align:start position:0%
+skinny. So all they need to do then is
+uh focus up and down until the dot is as
+
+ align:start position:0%
+uh focus up and down until the dot is as
+ 
+
+ align:start position:0%
+uh focus up and down until the dot is as
+close to being circular as they can get
+
+ align:start position:0%
+close to being circular as they can get
+ 
+
+ align:start position:0%
+close to being circular as they can get
+it. That's why they use a quadrant
+
+ align:start position:0%
+it. That's why they use a quadrant
+ 
+
+ align:start position:0%
+it. That's why they use a quadrant
+detector. So the quadrant detector lets
+
+ align:start position:0%
+detector. So the quadrant detector lets
+ 
+
+ align:start position:0%
+detector. So the quadrant detector lets
+them calculate a plus c minus b plus
+
+ align:start position:0%
+them calculate a plus c minus b plus
+ 
+
+ align:start position:0%
+them calculate a plus c minus b plus
+d. And you would like that answer to be
+
+ align:start position:0%
+d. And you would like that answer to be
+ 
+
+ align:start position:0%
+d. And you would like that answer to be
+zero. So now you use that as your error.
+
+ align:start position:0%
+zero. So now you use that as your error.
+ 
+
+ align:start position:0%
+zero. So now you use that as your error.
+You use the light that hits this
+
+ align:start position:0%
+You use the light that hits this
+ 
+
+ align:start position:0%
+You use the light that hits this
+quadrant
+
+ align:start position:0%
+quadrant
+ 
+
+ align:start position:0%
+quadrant
+detector to compute this number. Put
+
+ align:start position:0%
+detector to compute this number. Put
+ 
+
+ align:start position:0%
+detector to compute this number. Put
+that in a feedback loop that drives the
+
+ align:start position:0%
+that in a feedback loop that drives the
+ 
+
+ align:start position:0%
+that in a feedback loop that drives the
+stage up and down the focus. So here's
+
+ align:start position:0%
+stage up and down the focus. So here's
+ 
+
+ align:start position:0%
+stage up and down the focus. So here's
+an ancient CD. The CD would be here.
+
+ align:start position:0%
+an ancient CD. The CD would be here.
+ 
+
+ align:start position:0%
+an ancient CD. The CD would be here.
+Here's the the uh reading
+
+ align:start position:0%
+Here's the the uh reading
+ 
+
+ align:start position:0%
+Here's the the uh reading
+lens. Here's a platform that has an
+
+ align:start position:0%
+lens. Here's a platform that has an
+ 
+
+ align:start position:0%
+lens. Here's a platform that has an
+electromagnet under it that will move it
+
+ align:start position:0%
+electromagnet under it that will move it
+ 
+
+ align:start position:0%
+electromagnet under it that will move it
+up and down 100 microns.
+
+ align:start position:0%
+up and down 100 microns.
+ 
+
+ align:start position:0%
+up and down 100 microns.
+So what you do is
+
+ align:start position:0%
+So what you do is
+ 
+
+ align:start position:0%
+So what you do is
+um so this is this electro u magnet is
+
+ align:start position:0%
+um so this is this electro u magnet is
+ 
+
+ align:start position:0%
+um so this is this electro u magnet is
+under the stage. So this whole thing
+
+ align:start position:0%
+under the stage. So this whole thing
+ 
+
+ align:start position:0%
+under the stage. So this whole thing
+goes up and down to make in a feedback
+
+ align:start position:0%
+goes up and down to make in a feedback
+ 
+
+ align:start position:0%
+goes up and down to make in a feedback
+loop that tries to make this error
+
+ align:start position:0%
+loop that tries to make this error
+ 
+
+ align:start position:0%
+loop that tries to make this error
+signal be
+
+ align:start position:0%
+signal be
+ 
+
+ align:start position:0%
+signal be
+zero. Tries to make the pattern
+
+ align:start position:0%
+zero. Tries to make the pattern
+ 
+
+ align:start position:0%
+zero. Tries to make the pattern
+circularly symmetric. So it's extremely
+
+ align:start position:0%
+circularly symmetric. So it's extremely
+ 
+
+ align:start position:0%
+circularly symmetric. So it's extremely
+clever.
+
+ align:start position:0%
+clever.
+ 
+
+ align:start position:0%
+clever.
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+uh you have this pattern. So the light
+
+ align:start position:0%
+uh you have this pattern. So the light
+ 
+
+ align:start position:0%
+uh you have this pattern. So the light
+is twice as big. Half the photons are
+
+ align:start position:0%
+is twice as big. Half the photons are
+ 
+
+ align:start position:0%
+is twice as big. Half the photons are
+supposed to fit in the pit and half the
+
+ align:start position:0%
+supposed to fit in the pit and half the
+ 
+
+ align:start position:0%
+supposed to fit in the pit and half the
+photons are supposed to hit in the land
+
+ align:start position:0%
+photons are supposed to hit in the land
+ 
+
+ align:start position:0%
+photons are supposed to hit in the land
+that surrounds the pit.
+
+ align:start position:0%
+that surrounds the pit.
+ 
+
+ align:start position:0%
+that surrounds the pit.
+So that as the um CD is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinning, if
+
+ align:start position:0%
+spinning, if
+ 
+
+ align:start position:0%
+spinning, if
+the spot illuminates a place that's
+
+ align:start position:0%
+the spot illuminates a place that's
+ 
+
+ align:start position:0%
+the spot illuminates a place that's
+entirely in the pit, the dot is small
+
+ align:start position:0%
+entirely in the pit, the dot is small
+ 
+
+ align:start position:0%
+entirely in the pit, the dot is small
+because of
+
+ align:start position:0%
+because of
+ 
+
+ align:start position:0%
+because of
+interference. And if it hits a place
+
+ align:start position:0%
+interference. And if it hits a place
+ 
+
+ align:start position:0%
+interference. And if it hits a place
+that doesn't have a pit, the dot is
+
+ align:start position:0%
+that doesn't have a pit, the dot is
+ 
+
+ align:start position:0%
+that doesn't have a pit, the dot is
+large because there's no interference.
+
+ align:start position:0%
+large because there's no interference.
+ 
+
+ align:start position:0%
+large because there's no interference.
+But then you have the problem of how do
+
+ align:start position:0%
+But then you have the problem of how do
+ 
+
+ align:start position:0%
+But then you have the problem of how do
+you keep the dot reading the center of
+
+ align:start position:0%
+you keep the dot reading the center of
+ 
+
+ align:start position:0%
+you keep the dot reading the center of
+the groove. Right? So in this technology
+
+ align:start position:0%
+the groove. Right? So in this technology
+ 
+
+ align:start position:0%
+the groove. Right? So in this technology
+we kept the dot in the center of the
+
+ align:start position:0%
+we kept the dot in the center of the
+ 
+
+ align:start position:0%
+we kept the dot in the center of the
+groove by using
+
+ align:start position:0%
+groove by using
+ 
+
+ align:start position:0%
+groove by using
+gravity. Right? We obviously don't want
+
+ align:start position:0%
+gravity. Right? We obviously don't want
+ 
+
+ align:start position:0%
+gravity. Right? We obviously don't want
+to touch that surface. So that's not the
+
+ align:start position:0%
+to touch that surface. So that's not the
+ 
+
+ align:start position:0%
+to touch that surface. So that's not the
+technology we use. We don't use a
+
+ align:start position:0%
+technology we use. We don't use a
+ 
+
+ align:start position:0%
+technology we use. We don't use a
+screw. We use feedback. Right?
+
+ align:start position:0%
+screw. We use feedback. Right?
+ 
+
+ align:start position:0%
+screw. We use feedback. Right?
+So in order to so here what we
+
+ align:start position:0%
+So in order to so here what we
+ 
+
+ align:start position:0%
+So in order to so here what we
+do instead of projecting a single dot we
+
+ align:start position:0%
+do instead of projecting a single dot we
+ 
+
+ align:start position:0%
+do instead of projecting a single dot we
+use a beam splitter that turns the one
+
+ align:start position:0%
+use a beam splitter that turns the one
+ 
+
+ align:start position:0%
+use a beam splitter that turns the one
+dot into three
+
+ align:start position:0%
+dot into three
+ 
+
+ align:start position:0%
+dot into three
+dots and the three dots are positioned
+
+ align:start position:0%
+dots and the three dots are positioned
+ 
+
+ align:start position:0%
+dots and the three dots are positioned
+so that they hit two more photo sensors
+
+ align:start position:0%
+so that they hit two more photo sensors
+ 
+
+ align:start position:0%
+so that they hit two more photo sensors
+one on each side of the main photo
+
+ align:start position:0%
+one on each side of the main photo
+ 
+
+ align:start position:0%
+one on each side of the main photo
+sensor. And the idea is that if the if
+
+ align:start position:0%
+sensor. And the idea is that if the if
+ 
+
+ align:start position:0%
+sensor. And the idea is that if the if
+the u light is perfectly centered on the
+
+ align:start position:0%
+the u light is perfectly centered on the
+ 
+
+ align:start position:0%
+the u light is perfectly centered on the
+track, these will have equal
+
+ align:start position:0%
+track, these will have equal
+ 
+
+ align:start position:0%
+track, these will have equal
+brightness. But now if the uh beam is
+
+ align:start position:0%
+brightness. But now if the uh beam is
+ 
+
+ align:start position:0%
+brightness. But now if the uh beam is
+off center, one of the dots will be
+
+ align:start position:0%
+off center, one of the dots will be
+ 
+
+ align:start position:0%
+off center, one of the dots will be
+bright because it hit all land compared
+
+ align:start position:0%
+bright because it hit all land compared
+ 
+
+ align:start position:0%
+bright because it hit all land compared
+to the other one which is some of the
+
+ align:start position:0%
+to the other one which is some of the
+ 
+
+ align:start position:0%
+to the other one which is some of the
+light is hitting the
+
+ align:start position:0%
+light is hitting the
+ 
+
+ align:start position:0%
+light is hitting the
+pit. So this is just like the head
+
+ align:start position:0%
+pit. So this is just like the head
+ 
+
+ align:start position:0%
+pit. So this is just like the head
+tracking thing in 601.
+
+ align:start position:0%
+tracking thing in 601.
+ 
+
+ align:start position:0%
+tracking thing in 601.
+So whichever of the two photo sensors
+
+ align:start position:0%
+So whichever of the two photo sensors
+ 
+
+ align:start position:0%
+So whichever of the two photo sensors
+gets more light, you um move the track
+
+ align:start position:0%
+gets more light, you um move the track
+ 
+
+ align:start position:0%
+gets more light, you um move the track
+to compensate for that. So it all works
+
+ align:start position:0%
+to compensate for that. So it all works
+ 
+
+ align:start position:0%
+to compensate for that. So it all works
+in a feedback
+
+ align:start position:0%
+in a feedback
+ 
+
+ align:start position:0%
+in a feedback
+loop. So the idea here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the same sort of deal. You have two
+
+ align:start position:0%
+um the same sort of deal. You have two
+ 
+
+ align:start position:0%
+um the same sort of deal. You have two
+sensors here and you use that the error
+
+ align:start position:0%
+sensors here and you use that the error
+ 
+
+ align:start position:0%
+sensors here and you use that the error
+which is the difference between the two
+
+ align:start position:0%
+which is the difference between the two
+ 
+
+ align:start position:0%
+which is the difference between the two
+to u to move the head to track and the
+
+ align:start position:0%
+to u to move the head to track and the
+ 
+
+ align:start position:0%
+to u to move the head to track and the
+head motion is this thing over here. So
+
+ align:start position:0%
+head motion is this thing over here. So
+ 
+
+ align:start position:0%
+head motion is this thing over here. So
+here's a rack and pinion connected up to
+
+ align:start position:0%
+here's a rack and pinion connected up to
+ 
+
+ align:start position:0%
+here's a rack and pinion connected up to
+a motor and so you have that motor uh
+
+ align:start position:0%
+a motor and so you have that motor uh
+ 
+
+ align:start position:0%
+a motor and so you have that motor uh
+servoed back to some um photo sensors
+
+ align:start position:0%
+servoed back to some um photo sensors
+ 
+
+ align:start position:0%
+servoed back to some um photo sensors
+over here that keep the the beam
+
+ align:start position:0%
+over here that keep the the beam
+ 
+
+ align:start position:0%
+over here that keep the the beam
+centered.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the idea then is that what you get
+
+ align:start position:0%
+So the idea then is that what you get
+ 
+
+ align:start position:0%
+So the idea then is that what you get
+for $10 to read this thing is completely
+
+ align:start position:0%
+for $10 to read this thing is completely
+ 
+
+ align:start position:0%
+for $10 to read this thing is completely
+remarkable. The idea is that it's got
+
+ align:start position:0%
+remarkable. The idea is that it's got
+ 
+
+ align:start position:0%
+remarkable. The idea is that it's got
+very complicated servo mechanisms that
+
+ align:start position:0%
+very complicated servo mechanisms that
+ 
+
+ align:start position:0%
+very complicated servo mechanisms that
+can read very small things that even a
+
+ align:start position:0%
+can read very small things that even a
+ 
+
+ align:start position:0%
+can read very small things that even a
+$70,000 microscope has trouble
+
+ align:start position:0%
+$70,000 microscope has trouble
+ 
+
+ align:start position:0%
+$70,000 microscope has trouble
+reading. And it's stable and you can run
+
+ align:start position:0%
+reading. And it's stable and you can run
+ 
+
+ align:start position:0%
+reading. And it's stable and you can run
+them. You can, you know, jostle them
+
+ align:start position:0%
+them. You can, you know, jostle them
+ 
+
+ align:start position:0%
+them. You can, you know, jostle them
+around and jog with them. And that's all
+
+ align:start position:0%
+around and jog with them. And that's all
+ 
+
+ align:start position:0%
+around and jog with them. And that's all
+because the they use feedback rather
+
+ align:start position:0%
+because the they use feedback rather
+ 
+
+ align:start position:0%
+because the they use feedback rather
+than trying to make precision
+
+ align:start position:0%
+than trying to make precision
+ 
+
+ align:start position:0%
+than trying to make precision
+machining and then they make the signals
+
+ align:start position:0%
+machining and then they make the signals
+ 
+
+ align:start position:0%
+machining and then they make the signals
+robust by using the kind of DT signal
+
+ align:start position:0%
+robust by using the kind of DT signal
+ 
+
+ align:start position:0%
+robust by using the kind of DT signal
+processing that we talked about. So
+
+ align:start position:0%
+processing that we talked about. So
+ 
+
+ align:start position:0%
+processing that we talked about. So
+anyway, the point of today was just to
+
+ align:start position:0%
+anyway, the point of today was just to
+ 
+
+ align:start position:0%
+anyway, the point of today was just to
+give some motivation of the way 603
+
+ align:start position:0%
+give some motivation of the way 603
+ 
+
+ align:start position:0%
+give some motivation of the way 603
+factors into technologies that you might
+
+ align:start position:0%
+factors into technologies that you might
+ 
+
+ align:start position:0%
+factors into technologies that you might
+be interested in. And this is just one
+
+ align:start position:0%
+be interested in. And this is just one
+ 
+
+ align:start position:0%
+be interested in. And this is just one
+example. I could have chosen any number
+
+ align:start position:0%
+example. I could have chosen any number
+ 
+
+ align:start position:0%
+example. I could have chosen any number
+of different devices and they would have
+
+ align:start position:0%
+of different devices and they would have
+ 
+
+ align:start position:0%
+of different devices and they would have
+been similar. So, I hope you enjoyed the
+
+ align:start position:0%
+been similar. So, I hope you enjoyed the
+ 
+
+ align:start position:0%
+been similar. So, I hope you enjoyed the
+course. I hope that you u have fun with
+
+ align:start position:0%
+course. I hope that you u have fun with
+ 
+
+ align:start position:0%
+course. I hope that you u have fun with
+the final. Please come on Tuesday and
+
+ align:start position:0%
+the final. Please come on Tuesday and
+ 
+
+ align:start position:0%
+the final. Please come on Tuesday and
+tell us uh what we should do differently
+
+ align:start position:0%
+tell us uh what we should do differently
+ 
+
+ align:start position:0%
+tell us uh what we should do differently
+next time. Thanks.
\ No newline at end of file
diff --git a/tEMkDHV2uU8.txt b/tEMkDHV2uU8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ad6b1e361d42da83323c2c93153f8e7c9ef8076
--- /dev/null
+++ b/tEMkDHV2uU8.txt
@@ -0,0 +1,5875 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so just to go as an overview today
+
+ align:start position:0%
+and so just to go as an overview today
+ 
+
+ align:start position:0%
+and so just to go as an overview today
+we're going to be talking about
+
+ align:start position:0%
+we're going to be talking about
+ 
+
+ align:start position:0%
+we're going to be talking about
+different techniques to do that are used
+
+ align:start position:0%
+different techniques to do that are used
+ 
+
+ align:start position:0%
+different techniques to do that are used
+to determine protein structure and we
+
+ align:start position:0%
+to determine protein structure and we
+ 
+
+ align:start position:0%
+to determine protein structure and we
+were talking a little bit about the
+
+ align:start position:0%
+were talking a little bit about the
+ 
+
+ align:start position:0%
+were talking a little bit about the
+protein databank or the PDB and then the
+
+ align:start position:0%
+protein databank or the PDB and then the
+ 
+
+ align:start position:0%
+protein databank or the PDB and then the
+latter half of the recitation will be on
+
+ align:start position:0%
+latter half of the recitation will be on
+ 
+
+ align:start position:0%
+latter half of the recitation will be on
+we'll be doing a worksheet to look at
+
+ align:start position:0%
+we'll be doing a worksheet to look at
+ 
+
+ align:start position:0%
+we'll be doing a worksheet to look at
+the structure of ubiquitin and I you
+
+ align:start position:0%
+the structure of ubiquitin and I you
+ 
+
+ align:start position:0%
+the structure of ubiquitin and I you
+acquitted using PI mole so that's just
+
+ align:start position:0%
+acquitted using PI mole so that's just
+ 
+
+ align:start position:0%
+acquitted using PI mole so that's just
+to get you familiar with using PI mole
+
+ align:start position:0%
+to get you familiar with using PI mole
+ 
+
+ align:start position:0%
+to get you familiar with using PI mole
+and so for the first first question that
+
+ align:start position:0%
+and so for the first first question that
+ 
+
+ align:start position:0%
+and so for the first first question that
+I like to pose to you is why should we
+
+ align:start position:0%
+I like to pose to you is why should we
+ 
+
+ align:start position:0%
+I like to pose to you is why should we
+determine protein structure what we can
+
+ align:start position:0%
+determine protein structure what we can
+ 
+
+ align:start position:0%
+determine protein structure what we can
+learn from determining a protein
+
+ align:start position:0%
+learn from determining a protein
+ 
+
+ align:start position:0%
+learn from determining a protein
+structure and so I look to you for
+
+ align:start position:0%
+structure and so I look to you for
+ 
+
+ align:start position:0%
+structure and so I look to you for
+answers a lot of answers but doesn't
+
+ align:start position:0%
+answers a lot of answers but doesn't
+ 
+
+ align:start position:0%
+answers a lot of answers but doesn't
+really have any ideas yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah absolutely yeah you can knowing
+
+ align:start position:0%
+yeah absolutely yeah you can knowing
+ 
+
+ align:start position:0%
+yeah absolutely yeah you can knowing
+protein structures does help you
+
+ align:start position:0%
+protein structures does help you
+ 
+
+ align:start position:0%
+protein structures does help you
+determine enzyme mechanisms anything
+
+ align:start position:0%
+determine enzyme mechanisms anything
+ 
+
+ align:start position:0%
+determine enzyme mechanisms anything
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure what yes absolutely structure
+
+ align:start position:0%
+structure what yes absolutely structure
+ 
+
+ align:start position:0%
+structure what yes absolutely structure
+does indicate function I can you be a
+
+ align:start position:0%
+does indicate function I can you be a
+ 
+
+ align:start position:0%
+does indicate function I can you be a
+bit more specific with respect to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah absolutely yeah you can determine
+
+ align:start position:0%
+yeah absolutely yeah you can determine
+ 
+
+ align:start position:0%
+yeah absolutely yeah you can determine
+active sites of enzymes
+
+ align:start position:0%
+active sites of enzymes
+ 
+
+ align:start position:0%
+active sites of enzymes
+any other ideas it's a lot more to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about can you learn interactions
+
+ align:start position:0%
+what about can you learn interactions
+ 
+
+ align:start position:0%
+what about can you learn interactions
+with other macromolecules say okay well
+
+ align:start position:0%
+with other macromolecules say okay well
+ 
+
+ align:start position:0%
+with other macromolecules say okay well
+let's just go through some of them
+
+ align:start position:0%
+let's just go through some of them
+ 
+
+ align:start position:0%
+let's just go through some of them
+so yeah structure does indeed determine
+
+ align:start position:0%
+so yeah structure does indeed determine
+ 
+
+ align:start position:0%
+so yeah structure does indeed determine
+function and the idea is if you know the
+
+ align:start position:0%
+function and the idea is if you know the
+ 
+
+ align:start position:0%
+function and the idea is if you know the
+structure of a protein you can learn a
+
+ align:start position:0%
+structure of a protein you can learn a
+ 
+
+ align:start position:0%
+structure of a protein you can learn a
+lot about its function in vivo and so
+
+ align:start position:0%
+lot about its function in vivo and so
+ 
+
+ align:start position:0%
+lot about its function in vivo and so
+some of the things that you can study is
+
+ align:start position:0%
+some of the things that you can study is
+ 
+
+ align:start position:0%
+some of the things that you can study is
+you can set the enzyme mechanisms it's
+
+ align:start position:0%
+you can set the enzyme mechanisms it's
+ 
+
+ align:start position:0%
+you can set the enzyme mechanisms it's
+relatively hard to do in extra extra fee
+
+ align:start position:0%
+relatively hard to do in extra extra fee
+ 
+
+ align:start position:0%
+relatively hard to do in extra extra fee
+because every time you solve a crystal
+
+ align:start position:0%
+because every time you solve a crystal
+ 
+
+ align:start position:0%
+because every time you solve a crystal
+structure it's only one snapshot off the
+
+ align:start position:0%
+structure it's only one snapshot off the
+ 
+
+ align:start position:0%
+structure it's only one snapshot off the
+enzyme but you can definitely do it
+
+ align:start position:0%
+enzyme but you can definitely do it
+ 
+
+ align:start position:0%
+enzyme but you can definitely do it
+you can design drugs or substrate that
+
+ align:start position:0%
+you can design drugs or substrate that
+ 
+
+ align:start position:0%
+you can design drugs or substrate that
+bind to the protein if you know what the
+
+ align:start position:0%
+bind to the protein if you know what the
+ 
+
+ align:start position:0%
+bind to the protein if you know what the
+active site looks like you can design a
+
+ align:start position:0%
+active site looks like you can design a
+ 
+
+ align:start position:0%
+active site looks like you can design a
+high affinity inhibitor and this is used
+
+ align:start position:0%
+high affinity inhibitor and this is used
+ 
+
+ align:start position:0%
+high affinity inhibitor and this is used
+in farming this tree a lot you can study
+
+ align:start position:0%
+in farming this tree a lot you can study
+ 
+
+ align:start position:0%
+in farming this tree a lot you can study
+translation and transcription which is
+
+ align:start position:0%
+translation and transcription which is
+ 
+
+ align:start position:0%
+translation and transcription which is
+what we've been learning about in class
+
+ align:start position:0%
+what we've been learning about in class
+ 
+
+ align:start position:0%
+what we've been learning about in class
+this week and we'll be learning next
+
+ align:start position:0%
+this week and we'll be learning next
+ 
+
+ align:start position:0%
+this week and we'll be learning next
+week as well you can also make KO
+
+ align:start position:0%
+week as well you can also make KO
+ 
+
+ align:start position:0%
+week as well you can also make KO
+crystals of proteins with other proteins
+
+ align:start position:0%
+crystals of proteins with other proteins
+ 
+
+ align:start position:0%
+crystals of proteins with other proteins
+and nucleic acids and study interactions
+
+ align:start position:0%
+and nucleic acids and study interactions
+ 
+
+ align:start position:0%
+and nucleic acids and study interactions
+between macromolecules and this is
+
+ align:start position:0%
+between macromolecules and this is
+ 
+
+ align:start position:0%
+between macromolecules and this is
+something that has been emerging it
+
+ align:start position:0%
+something that has been emerging it
+ 
+
+ align:start position:0%
+something that has been emerging it
+makes it harder to solve the crystal
+
+ align:start position:0%
+makes it harder to solve the crystal
+ 
+
+ align:start position:0%
+makes it harder to solve the crystal
+structure but it's very x-ray is very
+
+ align:start position:0%
+structure but it's very x-ray is very
+ 
+
+ align:start position:0%
+structure but it's very x-ray is very
+extra crystallography is a very powerful
+
+ align:start position:0%
+extra crystallography is a very powerful
+ 
+
+ align:start position:0%
+extra crystallography is a very powerful
+tool for this you can also say the
+
+ align:start position:0%
+tool for this you can also say the
+ 
+
+ align:start position:0%
+tool for this you can also say the
+immune system function so this is more
+
+ align:start position:0%
+immune system function so this is more
+ 
+
+ align:start position:0%
+immune system function so this is more
+on the biological side of things you can
+
+ align:start position:0%
+on the biological side of things you can
+ 
+
+ align:start position:0%
+on the biological side of things you can
+study host-pathogen receptors and their
+
+ align:start position:0%
+study host-pathogen receptors and their
+ 
+
+ align:start position:0%
+study host-pathogen receptors and their
+interactions and many many more really
+
+ align:start position:0%
+interactions and many many more really
+ 
+
+ align:start position:0%
+interactions and many many more really
+there's no reason why you shouldn't have
+
+ align:start position:0%
+there's no reason why you shouldn't have
+ 
+
+ align:start position:0%
+there's no reason why you shouldn't have
+a structure for whatever protein you're
+
+ align:start position:0%
+a structure for whatever protein you're
+ 
+
+ align:start position:0%
+a structure for whatever protein you're
+studying right and so the key idea is
+
+ align:start position:0%
+studying right and so the key idea is
+ 
+
+ align:start position:0%
+studying right and so the key idea is
+that protein structures if you know the
+
+ align:start position:0%
+that protein structures if you know the
+ 
+
+ align:start position:0%
+that protein structures if you know the
+protein structure you can that allows
+
+ align:start position:0%
+protein structure you can that allows
+ 
+
+ align:start position:0%
+protein structure you can that allows
+you to carry out biochemical studies but
+
+ align:start position:0%
+you to carry out biochemical studies but
+ 
+
+ align:start position:0%
+you to carry out biochemical studies but
+then also if you if you determine the
+
+ align:start position:0%
+then also if you if you determine the
+ 
+
+ align:start position:0%
+then also if you if you determine the
+structure that can help rationalize
+
+ align:start position:0%
+structure that can help rationalize
+ 
+
+ align:start position:0%
+structure that can help rationalize
+results that you get from a chemical
+
+ align:start position:0%
+results that you get from a chemical
+ 
+
+ align:start position:0%
+results that you get from a chemical
+studies so it goes both ways and final
+
+ align:start position:0%
+studies so it goes both ways and final
+ 
+
+ align:start position:0%
+studies so it goes both ways and final
+point that is
+
+ align:start position:0%
+point that is
+ 
+
+ align:start position:0%
+point that is
+not perhaps not emphasized that much is
+
+ align:start position:0%
+not perhaps not emphasized that much is
+ 
+
+ align:start position:0%
+not perhaps not emphasized that much is
+the structure as a result of sequence
+
+ align:start position:0%
+the structure as a result of sequence
+ 
+
+ align:start position:0%
+the structure as a result of sequence
+and ideally what we would like to know
+
+ align:start position:0%
+and ideally what we would like to know
+ 
+
+ align:start position:0%
+and ideally what we would like to know
+is if we know the primary amino acid
+
+ align:start position:0%
+is if we know the primary amino acid
+ 
+
+ align:start position:0%
+is if we know the primary amino acid
+sequence of a polypeptide we'd like to
+
+ align:start position:0%
+sequence of a polypeptide we'd like to
+ 
+
+ align:start position:0%
+sequence of a polypeptide we'd like to
+be able to predict its complete t
+
+ align:start position:0%
+be able to predict its complete t
+ 
+
+ align:start position:0%
+be able to predict its complete t
+dimensional fold and that's sort of the
+
+ align:start position:0%
+dimensional fold and that's sort of the
+ 
+
+ align:start position:0%
+dimensional fold and that's sort of the
+idea behind protein folding we're not
+
+ align:start position:0%
+idea behind protein folding we're not
+ 
+
+ align:start position:0%
+idea behind protein folding we're not
+quite at that stage yet computationally
+
+ align:start position:0%
+quite at that stage yet computationally
+ 
+
+ align:start position:0%
+quite at that stage yet computationally
+and so that's why we need experiment
+
+ align:start position:0%
+and so that's why we need experiment
+ 
+
+ align:start position:0%
+and so that's why we need experiment
+data but that's something we're moving
+
+ align:start position:0%
+data but that's something we're moving
+ 
+
+ align:start position:0%
+data but that's something we're moving
+forward moving towards as a science and
+
+ align:start position:0%
+forward moving towards as a science and
+ 
+
+ align:start position:0%
+forward moving towards as a science and
+so just to go over I'm gonna cover the
+
+ align:start position:0%
+so just to go over I'm gonna cover the
+ 
+
+ align:start position:0%
+so just to go over I'm gonna cover the
+three main techniques and protein
+
+ align:start position:0%
+three main techniques and protein
+ 
+
+ align:start position:0%
+three main techniques and protein
+structure determination and so the first
+
+ align:start position:0%
+structure determination and so the first
+ 
+
+ align:start position:0%
+structure determination and so the first
+the most common one is extra traction
+
+ align:start position:0%
+the most common one is extra traction
+ 
+
+ align:start position:0%
+the most common one is extra traction
+and the I'll go over some of the details
+
+ align:start position:0%
+and the I'll go over some of the details
+ 
+
+ align:start position:0%
+and the I'll go over some of the details
+of x-ray later I'll be focusing on x-ray
+
+ align:start position:0%
+of x-ray later I'll be focusing on x-ray
+ 
+
+ align:start position:0%
+of x-ray later I'll be focusing on x-ray
+diffraction in this talk some of the
+
+ align:start position:0%
+diffraction in this talk some of the
+ 
+
+ align:start position:0%
+diffraction in this talk some of the
+selling points of x-ray diffraction are
+
+ align:start position:0%
+selling points of x-ray diffraction are
+ 
+
+ align:start position:0%
+selling points of x-ray diffraction are
+that you can study a protein of any size
+
+ align:start position:0%
+that you can study a protein of any size
+ 
+
+ align:start position:0%
+that you can study a protein of any size
+small proteins large proteins you can
+
+ align:start position:0%
+small proteins large proteins you can
+ 
+
+ align:start position:0%
+small proteins large proteins you can
+study complexes or proteins there is a
+
+ align:start position:0%
+study complexes or proteins there is a
+ 
+
+ align:start position:0%
+study complexes or proteins there is a
+need to crystallize your sample which
+
+ align:start position:0%
+need to crystallize your sample which
+ 
+
+ align:start position:0%
+need to crystallize your sample which
+makes a challenging it's very hard to
+
+ align:start position:0%
+makes a challenging it's very hard to
+ 
+
+ align:start position:0%
+makes a challenging it's very hard to
+crystallize proteins in your body no
+
+ align:start position:0%
+crystallize proteins in your body no
+ 
+
+ align:start position:0%
+crystallize proteins in your body no
+protein is crystallized right so you're
+
+ align:start position:0%
+protein is crystallized right so you're
+ 
+
+ align:start position:0%
+protein is crystallized right so you're
+trying to make proteins do something
+
+ align:start position:0%
+trying to make proteins do something
+ 
+
+ align:start position:0%
+trying to make proteins do something
+that they don't really like doing you
+
+ align:start position:0%
+that they don't really like doing you
+ 
+
+ align:start position:0%
+that they don't really like doing you
+can obtain a high resolution high
+
+ align:start position:0%
+can obtain a high resolution high
+ 
+
+ align:start position:0%
+can obtain a high resolution high
+resolution structure so a resolution of
+
+ align:start position:0%
+resolution structure so a resolution of
+ 
+
+ align:start position:0%
+resolution structure so a resolution of
+two angstroms or even less is pretty
+
+ align:start position:0%
+two angstroms or even less is pretty
+ 
+
+ align:start position:0%
+two angstroms or even less is pretty
+common for good protein x-ray structures
+
+ align:start position:0%
+common for good protein x-ray structures
+ 
+
+ align:start position:0%
+common for good protein x-ray structures
+but then also it's difficult to observe
+
+ align:start position:0%
+but then also it's difficult to observe
+ 
+
+ align:start position:0%
+but then also it's difficult to observe
+dynamics so an x-ray structure is just a
+
+ align:start position:0%
+dynamics so an x-ray structure is just a
+ 
+
+ align:start position:0%
+dynamics so an x-ray structure is just a
+snapshot of the protein at a specific
+
+ align:start position:0%
+snapshot of the protein at a specific
+ 
+
+ align:start position:0%
+snapshot of the protein at a specific
+time and so you need often a series of
+
+ align:start position:0%
+time and so you need often a series of
+ 
+
+ align:start position:0%
+time and so you need often a series of
+x-ray structures to really learn
+
+ align:start position:0%
+x-ray structures to really learn
+ 
+
+ align:start position:0%
+x-ray structures to really learn
+something about the mechanism or the
+
+ align:start position:0%
+something about the mechanism or the
+ 
+
+ align:start position:0%
+something about the mechanism or the
+dynamics of these proteins another
+
+ align:start position:0%
+dynamics of these proteins another
+ 
+
+ align:start position:0%
+dynamics of these proteins another
+common the second most popular technique
+
+ align:start position:0%
+common the second most popular technique
+ 
+
+ align:start position:0%
+common the second most popular technique
+is nuclear magnetic resonance or NMR NMR
+
+ align:start position:0%
+is nuclear magnetic resonance or NMR NMR
+ 
+
+ align:start position:0%
+is nuclear magnetic resonance or NMR NMR
+is typically used to study small
+
+ align:start position:0%
+is typically used to study small
+ 
+
+ align:start position:0%
+is typically used to study small
+proteins and the reason for this is that
+
+ align:start position:0%
+proteins and the reason for this is that
+ 
+
+ align:start position:0%
+proteins and the reason for this is that
+if you look at this so this is a 2d NMR
+
+ align:start position:0%
+if you look at this so this is a 2d NMR
+ 
+
+ align:start position:0%
+if you look at this so this is a 2d NMR
+spectra if you look at the 2d NMR
+
+ align:start position:0%
+spectra if you look at the 2d NMR
+ 
+
+ align:start position:0%
+spectra if you look at the 2d NMR
+spectra there's a lot of Peaks right and
+
+ align:start position:0%
+spectra there's a lot of Peaks right and
+ 
+
+ align:start position:0%
+spectra there's a lot of Peaks right and
+the more residues you have the more
+
+ align:start position:0%
+the more residues you have the more
+ 
+
+ align:start position:0%
+the more residues you have the more
+amino acids you have the more Peaks you
+
+ align:start position:0%
+amino acids you have the more Peaks you
+ 
+
+ align:start position:0%
+amino acids you have the more Peaks you
+have and it gets very crowded and so
+
+ align:start position:0%
+have and it gets very crowded and so
+ 
+
+ align:start position:0%
+have and it gets very crowded and so
+that's sort of the limiting factor with
+
+ align:start position:0%
+that's sort of the limiting factor with
+ 
+
+ align:start position:0%
+that's sort of the limiting factor with
+with using NMR to study larger proteins
+
+ align:start position:0%
+with using NMR to study larger proteins
+ 
+
+ align:start position:0%
+with using NMR to study larger proteins
+is that you can't resolve all the
+
+ align:start position:0%
+is that you can't resolve all the
+ 
+
+ align:start position:0%
+is that you can't resolve all the
+chemical shifts the plus point is that
+
+ align:start position:0%
+chemical shifts the plus point is that
+ 
+
+ align:start position:0%
+chemical shifts the plus point is that
+there's no need to crystallize your
+
+ align:start position:0%
+there's no need to crystallize your
+ 
+
+ align:start position:0%
+there's no need to crystallize your
+protein you can study it in solution
+
+ align:start position:0%
+protein you can study it in solution
+ 
+
+ align:start position:0%
+protein you can study it in solution
+state or solid state so let's state NMR
+
+ align:start position:0%
+state or solid state so let's state NMR
+ 
+
+ align:start position:0%
+state or solid state so let's state NMR
+is typically used for membrane proteins
+
+ align:start position:0%
+is typically used for membrane proteins
+ 
+
+ align:start position:0%
+is typically used for membrane proteins
+and solution you can use you can use
+
+ align:start position:0%
+and solution you can use you can use
+ 
+
+ align:start position:0%
+and solution you can use you can use
+Marcus Ellie any soluble proteins you do
+
+ align:start position:0%
+Marcus Ellie any soluble proteins you do
+ 
+
+ align:start position:0%
+Marcus Ellie any soluble proteins you do
+need isotopically labeled samples so
+
+ align:start position:0%
+need isotopically labeled samples so
+ 
+
+ align:start position:0%
+need isotopically labeled samples so
+these are 13 C or 15 n enriched samples
+
+ align:start position:0%
+these are 13 C or 15 n enriched samples
+ 
+
+ align:start position:0%
+these are 13 C or 15 n enriched samples
+which is very hard and expensive to do
+
+ align:start position:0%
+which is very hard and expensive to do
+ 
+
+ align:start position:0%
+which is very hard and expensive to do
+so that's one of the drawbacks with NMR
+
+ align:start position:0%
+so that's one of the drawbacks with NMR
+ 
+
+ align:start position:0%
+so that's one of the drawbacks with NMR
+is that it's a relatively expensive
+
+ align:start position:0%
+is that it's a relatively expensive
+ 
+
+ align:start position:0%
+is that it's a relatively expensive
+technique well x-ray is more is more
+
+ align:start position:0%
+technique well x-ray is more is more
+ 
+
+ align:start position:0%
+technique well x-ray is more is more
+accessible you can obtain a
+
+ align:start position:0%
+accessible you can obtain a
+ 
+
+ align:start position:0%
+accessible you can obtain a
+high-resolution picture with NMR as well
+
+ align:start position:0%
+high-resolution picture with NMR as well
+ 
+
+ align:start position:0%
+high-resolution picture with NMR as well
+but it often requires more work than
+
+ align:start position:0%
+but it often requires more work than
+ 
+
+ align:start position:0%
+but it often requires more work than
+x-ray crystallography in that you need
+
+ align:start position:0%
+x-ray crystallography in that you need
+ 
+
+ align:start position:0%
+x-ray crystallography in that you need
+to do about say 5 experiments NMR
+
+ align:start position:0%
+to do about say 5 experiments NMR
+ 
+
+ align:start position:0%
+to do about say 5 experiments NMR
+experiments that can sometimes take
+
+ align:start position:0%
+experiments that can sometimes take
+ 
+
+ align:start position:0%
+experiments that can sometimes take
+months to determine high resolution
+
+ align:start position:0%
+months to determine high resolution
+ 
+
+ align:start position:0%
+months to determine high resolution
+structure x-ray is more accessible but
+
+ align:start position:0%
+structure x-ray is more accessible but
+ 
+
+ align:start position:0%
+structure x-ray is more accessible but
+really the big upshot of NMR is that you
+
+ align:start position:0%
+really the big upshot of NMR is that you
+ 
+
+ align:start position:0%
+really the big upshot of NMR is that you
+can observe dynamics within proteins so
+
+ align:start position:0%
+can observe dynamics within proteins so
+ 
+
+ align:start position:0%
+can observe dynamics within proteins so
+you can really see proteins are living
+
+ align:start position:0%
+you can really see proteins are living
+ 
+
+ align:start position:0%
+you can really see proteins are living
+breathing machines and you can see that
+
+ align:start position:0%
+breathing machines and you can see that
+ 
+
+ align:start position:0%
+breathing machines and you can see that
+with NMR better than you can with any
+
+ align:start position:0%
+with NMR better than you can with any
+ 
+
+ align:start position:0%
+with NMR better than you can with any
+other technique another quick point
+
+ align:start position:0%
+other technique another quick point
+ 
+
+ align:start position:0%
+other technique another quick point
+which I don't have written up here is
+
+ align:start position:0%
+which I don't have written up here is
+ 
+
+ align:start position:0%
+which I don't have written up here is
+that NMR is sensitive to protons and you
+
+ align:start position:0%
+that NMR is sensitive to protons and you
+ 
+
+ align:start position:0%
+that NMR is sensitive to protons and you
+can study hydrogen's with NMR you cannot
+
+ align:start position:0%
+can study hydrogen's with NMR you cannot
+ 
+
+ align:start position:0%
+can study hydrogen's with NMR you cannot
+study hydrogens with x-ray diffraction
+
+ align:start position:0%
+study hydrogens with x-ray diffraction
+ 
+
+ align:start position:0%
+study hydrogens with x-ray diffraction
+on for reasons that we'll come back to
+
+ align:start position:0%
+on for reasons that we'll come back to
+ 
+
+ align:start position:0%
+on for reasons that we'll come back to
+later in the talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so there are a series of different I
+
+ align:start position:0%
+yes so there are a series of different I
+ 
+
+ align:start position:0%
+yes so there are a series of different I
+don't know how much detail you guys know
+
+ align:start position:0%
+don't know how much detail you guys know
+ 
+
+ align:start position:0%
+don't know how much detail you guys know
+about Emma but basically you can study
+
+ align:start position:0%
+about Emma but basically you can study
+ 
+
+ align:start position:0%
+about Emma but basically you can study
+relaxation of nuclei that's often one
+
+ align:start position:0%
+relaxation of nuclei that's often one
+ 
+
+ align:start position:0%
+relaxation of nuclei that's often one
+that's used so you study t1 and to treat
+
+ align:start position:0%
+that's used so you study t1 and to treat
+ 
+
+ align:start position:0%
+that's used so you study t1 and to treat
+relaxation of nuclei and more mobile
+
+ align:start position:0%
+relaxation of nuclei and more mobile
+ 
+
+ align:start position:0%
+relaxation of nuclei and more mobile
+residues or more mobile atoms relax
+
+ align:start position:0%
+residues or more mobile atoms relax
+ 
+
+ align:start position:0%
+residues or more mobile atoms relax
+faster but really the idea is you can
+
+ align:start position:0%
+faster but really the idea is you can
+ 
+
+ align:start position:0%
+faster but really the idea is you can
+use their whole different their whole
+
+ align:start position:0%
+use their whole different their whole
+ 
+
+ align:start position:0%
+use their whole different their whole
+bunch of different experiments in NMR
+
+ align:start position:0%
+bunch of different experiments in NMR
+ 
+
+ align:start position:0%
+bunch of different experiments in NMR
+and you can access time skills from the
+
+ align:start position:0%
+and you can access time skills from the
+ 
+
+ align:start position:0%
+and you can access time skills from the
+nanosecond up till the milliseconds so
+
+ align:start position:0%
+nanosecond up till the milliseconds so
+ 
+
+ align:start position:0%
+nanosecond up till the milliseconds so
+you know 10 to the negative 9 to about
+
+ align:start position:0%
+you know 10 to the negative 9 to about
+ 
+
+ align:start position:0%
+you know 10 to the negative 9 to about
+10 to the negative 3 seconds of motion
+
+ align:start position:0%
+10 to the negative 3 seconds of motion
+ 
+
+ align:start position:0%
+10 to the negative 3 seconds of motion
+so it's quite and we use different
+
+ align:start position:0%
+so it's quite and we use different
+ 
+
+ align:start position:0%
+so it's quite and we use different
+experiments for different parts of that
+
+ align:start position:0%
+experiments for different parts of that
+ 
+
+ align:start position:0%
+experiments for different parts of that
+time scale and we can talk more about
+
+ align:start position:0%
+time scale and we can talk more about
+ 
+
+ align:start position:0%
+time scale and we can talk more about
+that in in detail the third technique is
+
+ align:start position:0%
+that in in detail the third technique is
+ 
+
+ align:start position:0%
+that in in detail the third technique is
+electron microscopy
+
+ align:start position:0%
+electron microscopy
+ 
+
+ align:start position:0%
+electron microscopy
+so this is restricted so far to large
+
+ align:start position:0%
+so this is restricted so far to large
+ 
+
+ align:start position:0%
+so this is restricted so far to large
+proteins the reason for this is that
+
+ align:start position:0%
+proteins the reason for this is that
+ 
+
+ align:start position:0%
+proteins the reason for this is that
+resolution is not so good again you
+
+ align:start position:0%
+resolution is not so good again you
+ 
+
+ align:start position:0%
+resolution is not so good again you
+don't need to crystallize your proteins
+
+ align:start position:0%
+don't need to crystallize your proteins
+ 
+
+ align:start position:0%
+don't need to crystallize your proteins
+so that's that's not red you don't need
+
+ align:start position:0%
+so that's that's not red you don't need
+ 
+
+ align:start position:0%
+so that's that's not red you don't need
+to use label samples either so the
+
+ align:start position:0%
+to use label samples either so the
+ 
+
+ align:start position:0%
+to use label samples either so the
+sample preparation is probably the
+
+ align:start position:0%
+sample preparation is probably the
+ 
+
+ align:start position:0%
+sample preparation is probably the
+easiest for for electron microscopy the
+
+ align:start position:0%
+easiest for for electron microscopy the
+ 
+
+ align:start position:0%
+easiest for for electron microscopy the
+picture that you get is sometimes low
+
+ align:start position:0%
+picture that you get is sometimes low
+ 
+
+ align:start position:0%
+picture that you get is sometimes low
+resolution because but the but the
+
+ align:start position:0%
+resolution because but the but the
+ 
+
+ align:start position:0%
+resolution because but the but the
+technology is moving forward to the
+
+ align:start position:0%
+technology is moving forward to the
+ 
+
+ align:start position:0%
+technology is moving forward to the
+point where we can get resolution as
+
+ align:start position:0%
+point where we can get resolution as
+ 
+
+ align:start position:0%
+point where we can get resolution as
+good as x-ray structures and I think I
+
+ align:start position:0%
+good as x-ray structures and I think I
+ 
+
+ align:start position:0%
+good as x-ray structures and I think I
+know that there's a 2.2 angstrom
+
+ align:start position:0%
+know that there's a 2.2 angstrom
+ 
+
+ align:start position:0%
+know that there's a 2.2 angstrom
+resolution structure out there
+
+ align:start position:0%
+resolution structure out there
+ 
+
+ align:start position:0%
+resolution structure out there
+definitely and there are others there
+
+ align:start position:0%
+definitely and there are others there
+ 
+
+ align:start position:0%
+definitely and there are others there
+are 3 point 2 angstroms but maybe
+
+ align:start position:0%
+are 3 point 2 angstroms but maybe
+ 
+
+ align:start position:0%
+are 3 point 2 angstroms but maybe
+there's something better than that out
+
+ align:start position:0%
+there's something better than that out
+ 
+
+ align:start position:0%
+there's something better than that out
+there in the literature again it's
+
+ align:start position:0%
+there in the literature again it's
+ 
+
+ align:start position:0%
+there in the literature again it's
+difficult to observe dynamics so similar
+
+ align:start position:0%
+difficult to observe dynamics so similar
+ 
+
+ align:start position:0%
+difficult to observe dynamics so similar
+to x-ray it's just a snapshot of your
+
+ align:start position:0%
+to x-ray it's just a snapshot of your
+ 
+
+ align:start position:0%
+to x-ray it's just a snapshot of your
+enzyme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like yeah yeah absolutely it is very
+
+ align:start position:0%
+like yeah yeah absolutely it is very
+ 
+
+ align:start position:0%
+like yeah yeah absolutely it is very
+similar and you're the only thing is
+
+ align:start position:0%
+similar and you're the only thing is
+ 
+
+ align:start position:0%
+similar and you're the only thing is
+you're you're looking at how electrons
+
+ align:start position:0%
+you're you're looking at how electrons
+ 
+
+ align:start position:0%
+you're you're looking at how electrons
+interact with your métier sample as
+
+ align:start position:0%
+interact with your métier sample as
+ 
+
+ align:start position:0%
+interact with your métier sample as
+compared to light right visible light I
+
+ align:start position:0%
+compared to light right visible light I
+ 
+
+ align:start position:0%
+compared to light right visible light I
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+and yeah you basically each so each of
+
+ align:start position:0%
+and yeah you basically each so each of
+ 
+
+ align:start position:0%
+and yeah you basically each so each of
+these particles here is and is is your
+
+ align:start position:0%
+these particles here is and is is your
+ 
+
+ align:start position:0%
+these particles here is and is is your
+protein is a protein molecule and then
+
+ align:start position:0%
+protein is a protein molecule and then
+ 
+
+ align:start position:0%
+protein is a protein molecule and then
+these are three-dimensional
+
+ align:start position:0%
+these are three-dimensional
+ 
+
+ align:start position:0%
+these are three-dimensional
+reconstruction
+
+ align:start position:0%
+reconstruction
+ 
+
+ align:start position:0%
+reconstruction
+so there's computer software that does
+
+ align:start position:0%
+so there's computer software that does
+ 
+
+ align:start position:0%
+so there's computer software that does
+this so to go from this you basically a
+
+ align:start position:0%
+this so to go from this you basically a
+ 
+
+ align:start position:0%
+this so to go from this you basically a
+signal average over all of these
+
+ align:start position:0%
+signal average over all of these
+ 
+
+ align:start position:0%
+signal average over all of these
+different molecules and then you signal
+
+ align:start position:0%
+different molecules and then you signal
+ 
+
+ align:start position:0%
+different molecules and then you signal
+average all over all of your different
+
+ align:start position:0%
+average all over all of your different
+ 
+
+ align:start position:0%
+average all over all of your different
+orientations of the protein that are
+
+ align:start position:0%
+orientations of the protein that are
+ 
+
+ align:start position:0%
+orientations of the protein that are
+trapped in your static electron
+
+ align:start position:0%
+trapped in your static electron
+ 
+
+ align:start position:0%
+trapped in your static electron
+microscope image and then using some
+
+ align:start position:0%
+microscope image and then using some
+ 
+
+ align:start position:0%
+microscope image and then using some
+image processing you generate a
+
+ align:start position:0%
+image processing you generate a
+ 
+
+ align:start position:0%
+image processing you generate a
+three-dimensional image of your protein
+
+ align:start position:0%
+three-dimensional image of your protein
+ 
+
+ align:start position:0%
+three-dimensional image of your protein
+that has a higher resolution than what
+
+ align:start position:0%
+that has a higher resolution than what
+ 
+
+ align:start position:0%
+that has a higher resolution than what
+you can see just with you know one
+
+ align:start position:0%
+you can see just with you know one
+ 
+
+ align:start position:0%
+you can see just with you know one
+single photo I guess so there's a lot of
+
+ align:start position:0%
+single photo I guess so there's a lot of
+ 
+
+ align:start position:0%
+single photo I guess so there's a lot of
+computer processing that happens behind
+
+ align:start position:0%
+computer processing that happens behind
+ 
+
+ align:start position:0%
+computer processing that happens behind
+the scenes okay yeah sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so fluorescence the difference with
+
+ align:start position:0%
+so fluorescence the difference with
+ 
+
+ align:start position:0%
+so fluorescence the difference with
+fluorescence I mean here electrons can
+
+ align:start position:0%
+fluorescence I mean here electrons can
+ 
+
+ align:start position:0%
+fluorescence I mean here electrons can
+interact with any atoms right any
+
+ align:start position:0%
+interact with any atoms right any
+ 
+
+ align:start position:0%
+interact with any atoms right any
+material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you can because different atoms
+
+ align:start position:0%
+yes you can because different atoms
+ 
+
+ align:start position:0%
+yes you can because different atoms
+interact with different nuclei interact
+
+ align:start position:0%
+interact with different nuclei interact
+ 
+
+ align:start position:0%
+interact with different nuclei interact
+an electron density is interact with
+
+ align:start position:0%
+an electron density is interact with
+ 
+
+ align:start position:0%
+an electron density is interact with
+electrons differently but with
+
+ align:start position:0%
+electrons differently but with
+ 
+
+ align:start position:0%
+electrons differently but with
+fluorescence microscopy you're usually
+
+ align:start position:0%
+fluorescence microscopy you're usually
+ 
+
+ align:start position:0%
+fluorescence microscopy you're usually
+looking at just a single molecule a
+
+ align:start position:0%
+looking at just a single molecule a
+ 
+
+ align:start position:0%
+looking at just a single molecule a
+fluorophore
+
+ align:start position:0%
+fluorophore
+ 
+
+ align:start position:0%
+fluorophore
+right that's reporting on where your
+
+ align:start position:0%
+right that's reporting on where your
+ 
+
+ align:start position:0%
+right that's reporting on where your
+protein is but electron microscopy is a
+
+ align:start position:0%
+protein is but electron microscopy is a
+ 
+
+ align:start position:0%
+protein is but electron microscopy is a
+much higher resolution picture it's
+
+ align:start position:0%
+much higher resolution picture it's
+ 
+
+ align:start position:0%
+much higher resolution picture it's
+actually an Adamek level well maybe a
+
+ align:start position:0%
+actually an Adamek level well maybe a
+ 
+
+ align:start position:0%
+actually an Adamek level well maybe a
+few atoms level picture fluorescence
+
+ align:start position:0%
+few atoms level picture fluorescence
+ 
+
+ align:start position:0%
+few atoms level picture fluorescence
+microscopy is usually just used to study
+
+ align:start position:0%
+microscopy is usually just used to study
+ 
+
+ align:start position:0%
+microscopy is usually just used to study
+where your protein is if proteins are
+
+ align:start position:0%
+where your protein is if proteins are
+ 
+
+ align:start position:0%
+where your protein is if proteins are
+interacting so that's more macro
+
+ align:start position:0%
+interacting so that's more macro
+ 
+
+ align:start position:0%
+interacting so that's more macro
+molecular interactions but you can get
+
+ align:start position:0%
+molecular interactions but you can get
+ 
+
+ align:start position:0%
+molecular interactions but you can get
+single molecule resolution with
+
+ align:start position:0%
+single molecule resolution with
+ 
+
+ align:start position:0%
+single molecule resolution with
+fluorescence microscopy if you use the
+
+ align:start position:0%
+fluorescence microscopy if you use the
+ 
+
+ align:start position:0%
+fluorescence microscopy if you use the
+correct techniques and so just as an
+
+ align:start position:0%
+correct techniques and so just as an
+ 
+
+ align:start position:0%
+correct techniques and so just as an
+introduction to the protein databank
+
+ align:start position:0%
+introduction to the protein databank
+ 
+
+ align:start position:0%
+introduction to the protein databank
+so the first graph tells you the number
+
+ align:start position:0%
+so the first graph tells you the number
+ 
+
+ align:start position:0%
+so the first graph tells you the number
+of PDB structures in the PDB as a
+
+ align:start position:0%
+of PDB structures in the PDB as a
+ 
+
+ align:start position:0%
+of PDB structures in the PDB as a
+function of year going from 1975 all the
+
+ align:start position:0%
+function of year going from 1975 all the
+ 
+
+ align:start position:0%
+function of year going from 1975 all the
+way to 2015 and so you'll see today
+
+ align:start position:0%
+way to 2015 and so you'll see today
+ 
+
+ align:start position:0%
+way to 2015 and so you'll see today
+there are about 110,000 structures of
+
+ align:start position:0%
+there are about 110,000 structures of
+ 
+
+ align:start position:0%
+there are about 110,000 structures of
+which a hundred thousand were deposited
+
+ align:start position:0%
+which a hundred thousand were deposited
+ 
+
+ align:start position:0%
+which a hundred thousand were deposited
+our work determined using x-ray
+
+ align:start position:0%
+our work determined using x-ray
+ 
+
+ align:start position:0%
+our work determined using x-ray
+crystallography and about ten thousand
+
+ align:start position:0%
+crystallography and about ten thousand
+ 
+
+ align:start position:0%
+crystallography and about ten thousand
+using NMR and about a thousand using
+
+ align:start position:0%
+using NMR and about a thousand using
+ 
+
+ align:start position:0%
+using NMR and about a thousand using
+I'll try microscopy it's a really quite
+
+ align:start position:0%
+I'll try microscopy it's a really quite
+ 
+
+ align:start position:0%
+I'll try microscopy it's a really quite
+a nice ratio there and if you see the
+
+ align:start position:0%
+a nice ratio there and if you see the
+ 
+
+ align:start position:0%
+a nice ratio there and if you see the
+yearly increase in the number of PDB
+
+ align:start position:0%
+yearly increase in the number of PDB
+ 
+
+ align:start position:0%
+yearly increase in the number of PDB
+structures you'll see that x-ray is of
+
+ align:start position:0%
+structures you'll see that x-ray is of
+ 
+
+ align:start position:0%
+structures you'll see that x-ray is of
+course really big NMR has been fairly
+
+ align:start position:0%
+course really big NMR has been fairly
+ 
+
+ align:start position:0%
+course really big NMR has been fairly
+consistent over time I think that has to
+
+ align:start position:0%
+consistent over time I think that has to
+ 
+
+ align:start position:0%
+consistent over time I think that has to
+do with the fact that it's expensive and
+
+ align:start position:0%
+do with the fact that it's expensive and
+ 
+
+ align:start position:0%
+do with the fact that it's expensive and
+it takes time to prepare your samples
+
+ align:start position:0%
+it takes time to prepare your samples
+ 
+
+ align:start position:0%
+it takes time to prepare your samples
+but you also see a huge spike in
+
+ align:start position:0%
+but you also see a huge spike in
+ 
+
+ align:start position:0%
+but you also see a huge spike in
+electron microscopy of late and so with
+
+ align:start position:0%
+electron microscopy of late and so with
+ 
+
+ align:start position:0%
+electron microscopy of late and so with
+the advent of cryo am a lot more a lot
+
+ align:start position:0%
+the advent of cryo am a lot more a lot
+ 
+
+ align:start position:0%
+the advent of cryo am a lot more a lot
+more people start using cryo-em to
+
+ align:start position:0%
+more people start using cryo-em to
+ 
+
+ align:start position:0%
+more people start using cryo-em to
+determine protein structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it can be but so for the problem
+
+ align:start position:0%
+yeah it can be but so for the problem
+ 
+
+ align:start position:0%
+yeah it can be but so for the problem
+with that is when you put your sample in
+
+ align:start position:0%
+with that is when you put your sample in
+ 
+
+ align:start position:0%
+with that is when you put your sample in
+the derailleur you can get chemical
+
+ align:start position:0%
+the derailleur you can get chemical
+ 
+
+ align:start position:0%
+the derailleur you can get chemical
+shifts information but chemical shift
+
+ align:start position:0%
+shifts information but chemical shift
+ 
+
+ align:start position:0%
+shifts information but chemical shift
+doesn't tell you anything about protein
+
+ align:start position:0%
+doesn't tell you anything about protein
+ 
+
+ align:start position:0%
+doesn't tell you anything about protein
+structure I mean it tells you a little
+
+ align:start position:0%
+structure I mean it tells you a little
+ 
+
+ align:start position:0%
+structure I mean it tells you a little
+bit about it tells you about what the
+
+ align:start position:0%
+bit about it tells you about what the
+ 
+
+ align:start position:0%
+bit about it tells you about what the
+electron density is at the atoms but
+
+ align:start position:0%
+electron density is at the atoms but
+ 
+
+ align:start position:0%
+electron density is at the atoms but
+what you really need to get from NMR
+
+ align:start position:0%
+what you really need to get from NMR
+ 
+
+ align:start position:0%
+what you really need to get from NMR
+experiments are distance restraints and
+
+ align:start position:0%
+experiments are distance restraints and
+ 
+
+ align:start position:0%
+experiments are distance restraints and
+so this is through space experiments so
+
+ align:start position:0%
+so this is through space experiments so
+ 
+
+ align:start position:0%
+so this is through space experiments so
+you can say that oh you know this carbon
+
+ align:start position:0%
+you can say that oh you know this carbon
+ 
+
+ align:start position:0%
+you can say that oh you know this carbon
+this one carbon nuclei is at a distance
+
+ align:start position:0%
+this one carbon nuclei is at a distance
+ 
+
+ align:start position:0%
+this one carbon nuclei is at a distance
+of six angstroms away from this other
+
+ align:start position:0%
+of six angstroms away from this other
+ 
+
+ align:start position:0%
+of six angstroms away from this other
+carbon nuclei and you typically want to
+
+ align:start position:0%
+carbon nuclei and you typically want to
+ 
+
+ align:start position:0%
+carbon nuclei and you typically want to
+accumulate about five restraints per
+
+ align:start position:0%
+accumulate about five restraints per
+ 
+
+ align:start position:0%
+accumulate about five restraints per
+atom and so to collect you know five
+
+ align:start position:0%
+atom and so to collect you know five
+ 
+
+ align:start position:0%
+atom and so to collect you know five
+times how many other atoms you have in
+
+ align:start position:0%
+times how many other atoms you have in
+ 
+
+ align:start position:0%
+times how many other atoms you have in
+your sample it can take time it's hard
+
+ align:start position:0%
+your sample it can take time it's hard
+ 
+
+ align:start position:0%
+your sample it can take time it's hard
+to do so a chemical shift by itself
+
+ align:start position:0%
+to do so a chemical shift by itself
+ 
+
+ align:start position:0%
+to do so a chemical shift by itself
+doesn't tell you much about protein
+
+ align:start position:0%
+doesn't tell you much about protein
+ 
+
+ align:start position:0%
+doesn't tell you much about protein
+structure any other questions all right
+
+ align:start position:0%
+structure any other questions all right
+ 
+
+ align:start position:0%
+structure any other questions all right
+so so now we will focus the rest of the
+
+ align:start position:0%
+so so now we will focus the rest of the
+ 
+
+ align:start position:0%
+so so now we will focus the rest of the
+talk on well for another part of the
+
+ align:start position:0%
+talk on well for another part of the
+ 
+
+ align:start position:0%
+talk on well for another part of the
+talk on x-axis lovely and so
+
+ align:start position:0%
+talk on x-axis lovely and so
+ 
+
+ align:start position:0%
+talk on x-axis lovely and so
+crystallography is the science of
+
+ align:start position:0%
+crystallography is the science of
+ 
+
+ align:start position:0%
+crystallography is the science of
+determining the three-dimensional
+
+ align:start position:0%
+determining the three-dimensional
+ 
+
+ align:start position:0%
+determining the three-dimensional
+position of atoms in in a crystal and so
+
+ align:start position:0%
+position of atoms in in a crystal and so
+ 
+
+ align:start position:0%
+position of atoms in in a crystal and so
+what a crystal is a crystal is a solid
+
+ align:start position:0%
+what a crystal is a crystal is a solid
+ 
+
+ align:start position:0%
+what a crystal is a crystal is a solid
+material whose constituents are arranged
+
+ align:start position:0%
+material whose constituents are arranged
+ 
+
+ align:start position:0%
+material whose constituents are arranged
+in an ordered pattern expanding and
+
+ align:start position:0%
+in an ordered pattern expanding and
+ 
+
+ align:start position:0%
+in an ordered pattern expanding and
+extending in all three spatial
+
+ align:start position:0%
+extending in all three spatial
+ 
+
+ align:start position:0%
+extending in all three spatial
+dimensions and so the key idea is that
+
+ align:start position:0%
+dimensions and so the key idea is that
+ 
+
+ align:start position:0%
+dimensions and so the key idea is that
+there's translation translational
+
+ align:start position:0%
+there's translation translational
+ 
+
+ align:start position:0%
+there's translation translational
+symmetry to be go in any of the three
+
+ align:start position:0%
+symmetry to be go in any of the three
+ 
+
+ align:start position:0%
+symmetry to be go in any of the three
+directions started for a certain amount
+
+ align:start position:0%
+directions started for a certain amount
+ 
+
+ align:start position:0%
+directions started for a certain amount
+of time or certain amount of length
+
+ align:start position:0%
+of time or certain amount of length
+ 
+
+ align:start position:0%
+of time or certain amount of length
+you'll come back to the same pattern
+
+ align:start position:0%
+you'll come back to the same pattern
+ 
+
+ align:start position:0%
+you'll come back to the same pattern
+that you start off with and so this is
+
+ align:start position:0%
+that you start off with and so this is
+ 
+
+ align:start position:0%
+that you start off with and so this is
+say a crystal off your protein of
+
+ align:start position:0%
+say a crystal off your protein of
+ 
+
+ align:start position:0%
+say a crystal off your protein of
+interest what you want to know is you
+
+ align:start position:0%
+interest what you want to know is you
+ 
+
+ align:start position:0%
+interest what you want to know is you
+want to know how the proteins are packed
+
+ align:start position:0%
+want to know how the proteins are packed
+ 
+
+ align:start position:0%
+want to know how the proteins are packed
+or arranged within this crystal
+
+ align:start position:0%
+or arranged within this crystal
+ 
+
+ align:start position:0%
+or arranged within this crystal
+structure and also as a result how the
+
+ align:start position:0%
+structure and also as a result how the
+ 
+
+ align:start position:0%
+structure and also as a result how the
+atoms are arranged within the crystal
+
+ align:start position:0%
+atoms are arranged within the crystal
+ 
+
+ align:start position:0%
+atoms are arranged within the crystal
+structure and the way this works is by
+
+ align:start position:0%
+structure and the way this works is by
+ 
+
+ align:start position:0%
+structure and the way this works is by
+diffracting x-rays through your sample
+
+ align:start position:0%
+diffracting x-rays through your sample
+ 
+
+ align:start position:0%
+diffracting x-rays through your sample
+of interests and with this slide I just
+
+ align:start position:0%
+of interests and with this slide I just
+ 
+
+ align:start position:0%
+of interests and with this slide I just
+wanted to point out that it's not
+
+ align:start position:0%
+wanted to point out that it's not
+ 
+
+ align:start position:0%
+wanted to point out that it's not
+restricted to proteins you can study
+
+ align:start position:0%
+restricted to proteins you can study
+ 
+
+ align:start position:0%
+restricted to proteins you can study
+salt so you can study your favorite
+
+ align:start position:0%
+salt so you can study your favorite
+ 
+
+ align:start position:0%
+salt so you can study your favorite
+small organic molecule whatever you want
+
+ align:start position:0%
+small organic molecule whatever you want
+ 
+
+ align:start position:0%
+small organic molecule whatever you want
+really and so the general workflow is
+
+ align:start position:0%
+really and so the general workflow is
+ 
+
+ align:start position:0%
+really and so the general workflow is
+that you have a source of x-rays that
+
+ align:start position:0%
+that you have a source of x-rays that
+ 
+
+ align:start position:0%
+that you have a source of x-rays that
+can be a synchrotron or a local source
+
+ align:start position:0%
+can be a synchrotron or a local source
+ 
+
+ align:start position:0%
+can be a synchrotron or a local source
+ink runs are much brighter than local
+
+ align:start position:0%
+ink runs are much brighter than local
+ 
+
+ align:start position:0%
+ink runs are much brighter than local
+sources that you shine on your crystal
+
+ align:start position:0%
+sources that you shine on your crystal
+ 
+
+ align:start position:0%
+sources that you shine on your crystal
+and you obtain what is known as a
+
+ align:start position:0%
+and you obtain what is known as a
+ 
+
+ align:start position:0%
+and you obtain what is known as a
+diffraction pattern and so this tells
+
+ align:start position:0%
+diffraction pattern and so this tells
+ 
+
+ align:start position:0%
+diffraction pattern and so this tells
+you how
+
+ align:start position:0%
+you how
+ 
+
+ align:start position:0%
+you how
+the x-rays are in track this tells you
+
+ align:start position:0%
+the x-rays are in track this tells you
+ 
+
+ align:start position:0%
+the x-rays are in track this tells you
+something about how the x-rays are
+
+ align:start position:0%
+something about how the x-rays are
+ 
+
+ align:start position:0%
+something about how the x-rays are
+interacting with the atoms in the
+
+ align:start position:0%
+interacting with the atoms in the
+ 
+
+ align:start position:0%
+interacting with the atoms in the
+material in the crystal and so this will
+
+ align:start position:0%
+material in the crystal and so this will
+ 
+
+ align:start position:0%
+material in the crystal and so this will
+use to be collected on a photographic
+
+ align:start position:0%
+use to be collected on a photographic
+ 
+
+ align:start position:0%
+use to be collected on a photographic
+plate this particular image is on a
+
+ align:start position:0%
+plate this particular image is on a
+ 
+
+ align:start position:0%
+plate this particular image is on a
+photographic plate but now you use
+
+ align:start position:0%
+photographic plate but now you use
+ 
+
+ align:start position:0%
+photographic plate but now you use
+people your CCD sensors it's a lot
+
+ align:start position:0%
+people your CCD sensors it's a lot
+ 
+
+ align:start position:0%
+people your CCD sensors it's a lot
+easier and knowing the different Ella I
+
+ align:start position:0%
+easier and knowing the different Ella I
+ 
+
+ align:start position:0%
+easier and knowing the different Ella I
+also think each of these dots light and
+
+ align:start position:0%
+also think each of these dots light and
+ 
+
+ align:start position:0%
+also think each of these dots light and
+dark on the diffraction pattern is
+
+ align:start position:0%
+dark on the diffraction pattern is
+ 
+
+ align:start position:0%
+dark on the diffraction pattern is
+called a reflection and that contains
+
+ align:start position:0%
+called a reflection and that contains
+ 
+
+ align:start position:0%
+called a reflection and that contains
+some information about the outer
+
+ align:start position:0%
+some information about the outer
+ 
+
+ align:start position:0%
+some information about the outer
+intensity in the crystal structure and
+
+ align:start position:0%
+intensity in the crystal structure and
+ 
+
+ align:start position:0%
+intensity in the crystal structure and
+from your diffraction pattern you can
+
+ align:start position:0%
+from your diffraction pattern you can
+ 
+
+ align:start position:0%
+from your diffraction pattern you can
+then back calculate the electron density
+
+ align:start position:0%
+then back calculate the electron density
+ 
+
+ align:start position:0%
+then back calculate the electron density
+in your crystal structure that gave rise
+
+ align:start position:0%
+in your crystal structure that gave rise
+ 
+
+ align:start position:0%
+in your crystal structure that gave rise
+to this diffraction pattern and the way
+
+ align:start position:0%
+to this diffraction pattern and the way
+ 
+
+ align:start position:0%
+to this diffraction pattern and the way
+you do that is by looking at the
+
+ align:start position:0%
+you do that is by looking at the
+ 
+
+ align:start position:0%
+you do that is by looking at the
+intensity of these reflections and you
+
+ align:start position:0%
+intensity of these reflections and you
+ 
+
+ align:start position:0%
+intensity of these reflections and you
+also need there's also something called
+
+ align:start position:0%
+also need there's also something called
+ 
+
+ align:start position:0%
+also need there's also something called
+phase we need to determine phase and
+
+ align:start position:0%
+phase we need to determine phase and
+ 
+
+ align:start position:0%
+phase we need to determine phase and
+sometimes you will see if in the paper
+
+ align:start position:0%
+sometimes you will see if in the paper
+ 
+
+ align:start position:0%
+sometimes you will see if in the paper
+in the literature you'll see heavy atoms
+
+ align:start position:0%
+in the literature you'll see heavy atoms
+ 
+
+ align:start position:0%
+in the literature you'll see heavy atoms
+being introduced or mercury being
+
+ align:start position:0%
+being introduced or mercury being
+ 
+
+ align:start position:0%
+being introduced or mercury being
+introduced and that's often to determine
+
+ align:start position:0%
+introduced and that's often to determine
+ 
+
+ align:start position:0%
+introduced and that's often to determine
+the phase which is essential for
+
+ align:start position:0%
+the phase which is essential for
+ 
+
+ align:start position:0%
+the phase which is essential for
+calculating the electron density once
+
+ align:start position:0%
+calculating the electron density once
+ 
+
+ align:start position:0%
+calculating the electron density once
+you determine the outer intensity you
+
+ align:start position:0%
+you determine the outer intensity you
+ 
+
+ align:start position:0%
+you determine the outer intensity you
+know what protein you start off with and
+
+ align:start position:0%
+know what protein you start off with and
+ 
+
+ align:start position:0%
+know what protein you start off with and
+so you know what what your protein looks
+
+ align:start position:0%
+so you know what what your protein looks
+ 
+
+ align:start position:0%
+so you know what what your protein looks
+you know the sequence of your protein
+
+ align:start position:0%
+you know the sequence of your protein
+ 
+
+ align:start position:0%
+you know the sequence of your protein
+right and so then you just take your
+
+ align:start position:0%
+right and so then you just take your
+ 
+
+ align:start position:0%
+right and so then you just take your
+after intensity and fit whatever
+
+ align:start position:0%
+after intensity and fit whatever
+ 
+
+ align:start position:0%
+after intensity and fit whatever
+polypeptide chains you have to that and
+
+ align:start position:0%
+polypeptide chains you have to that and
+ 
+
+ align:start position:0%
+polypeptide chains you have to that and
+then usually this is all automated
+
+ align:start position:0%
+then usually this is all automated
+ 
+
+ align:start position:0%
+then usually this is all automated
+nowadays so you press a few buttons and
+
+ align:start position:0%
+nowadays so you press a few buttons and
+ 
+
+ align:start position:0%
+nowadays so you press a few buttons and
+it goes through sort of software does
+
+ align:start position:0%
+it goes through sort of software does
+ 
+
+ align:start position:0%
+it goes through sort of software does
+everything for you but it was much more
+
+ align:start position:0%
+everything for you but it was much more
+ 
+
+ align:start position:0%
+everything for you but it was much more
+challenging early on and even now the
+
+ align:start position:0%
+challenging early on and even now the
+ 
+
+ align:start position:0%
+challenging early on and even now the
+computers will get you up to a certain
+
+ align:start position:0%
+computers will get you up to a certain
+ 
+
+ align:start position:0%
+computers will get you up to a certain
+point and then in the last last stages
+
+ align:start position:0%
+point and then in the last last stages
+ 
+
+ align:start position:0%
+point and then in the last last stages
+of refinement you always want to use
+
+ align:start position:0%
+of refinement you always want to use
+ 
+
+ align:start position:0%
+of refinement you always want to use
+usually people do that by hand any
+
+ align:start position:0%
+usually people do that by hand any
+ 
+
+ align:start position:0%
+usually people do that by hand any
+questions about x-ray crystallography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead from diffraction pattern but I
+
+ align:start position:0%
+instead from diffraction pattern but I
+ 
+
+ align:start position:0%
+instead from diffraction pattern but I
+mean in organic chemistry in basics one
+
+ align:start position:0%
+mean in organic chemistry in basics one
+ 
+
+ align:start position:0%
+mean in organic chemistry in basics one
+I know that you can from diffraction
+
+ align:start position:0%
+I know that you can from diffraction
+ 
+
+ align:start position:0%
+I know that you can from diffraction
+pattern like you can learn the distance
+
+ align:start position:0%
+pattern like you can learn the distance
+ 
+
+ align:start position:0%
+pattern like you can learn the distance
+between atoms in the the path like in
+
+ align:start position:0%
+between atoms in the the path like in
+ 
+
+ align:start position:0%
+between atoms in the the path like in
+the lattice yes points
+
+ align:start position:0%
+the lattice yes points
+ 
+
+ align:start position:0%
+the lattice yes points
+yes but here in with proteins every
+
+ align:start position:0%
+yes but here in with proteins every
+ 
+
+ align:start position:0%
+yes but here in with proteins every
+point is itself a protein right every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you're looking at every point in
+
+ align:start position:0%
+because you're looking at every point in
+ 
+
+ align:start position:0%
+because you're looking at every point in
+the lattice is still an atom for if
+
+ align:start position:0%
+the lattice is still an atom for if
+ 
+
+ align:start position:0%
+the lattice is still an atom for if
+you're doing proteins it's just that
+
+ align:start position:0%
+you're doing proteins it's just that
+ 
+
+ align:start position:0%
+you're doing proteins it's just that
+there are a lot more atoms and the
+
+ align:start position:0%
+there are a lot more atoms and the
+ 
+
+ align:start position:0%
+there are a lot more atoms and the
+lattice is a lot bigger which is what
+
+ align:start position:0%
+lattice is a lot bigger which is what
+ 
+
+ align:start position:0%
+lattice is a lot bigger which is what
+makes protein crystallography hard
+
+ align:start position:0%
+makes protein crystallography hard
+ 
+
+ align:start position:0%
+makes protein crystallography hard
+compared to small molecule
+
+ align:start position:0%
+compared to small molecule
+ 
+
+ align:start position:0%
+compared to small molecule
+crystallography so it's harder to solve
+
+ align:start position:0%
+crystallography so it's harder to solve
+ 
+
+ align:start position:0%
+crystallography so it's harder to solve
+a protein crystal structure than it is a
+
+ align:start position:0%
+a protein crystal structure than it is a
+ 
+
+ align:start position:0%
+a protein crystal structure than it is a
+small molecule true structure just
+
+ align:start position:0%
+small molecule true structure just
+ 
+
+ align:start position:0%
+small molecule true structure just
+because there's so many more atoms in
+
+ align:start position:0%
+because there's so many more atoms in
+ 
+
+ align:start position:0%
+because there's so many more atoms in
+your lattice but there but the idea is
+
+ align:start position:0%
+your lattice but there but the idea is
+ 
+
+ align:start position:0%
+your lattice but there but the idea is
+exactly the same as small molecule it's
+
+ align:start position:0%
+exactly the same as small molecule it's
+ 
+
+ align:start position:0%
+exactly the same as small molecule it's
+just a lot harder to do and for more
+
+ align:start position:0%
+just a lot harder to do and for more
+ 
+
+ align:start position:0%
+just a lot harder to do and for more
+information I actually have a resource
+
+ align:start position:0%
+information I actually have a resource
+ 
+
+ align:start position:0%
+information I actually have a resource
+at the end that goes sort of in depth
+
+ align:start position:0%
+at the end that goes sort of in depth
+ 
+
+ align:start position:0%
+at the end that goes sort of in depth
+into the mats math off the process but
+
+ align:start position:0%
+into the mats math off the process but
+ 
+
+ align:start position:0%
+into the mats math off the process but
+just soon briefly this diffraction
+
+ align:start position:0%
+just soon briefly this diffraction
+ 
+
+ align:start position:0%
+just soon briefly this diffraction
+pattern is collected and so what's
+
+ align:start position:0%
+pattern is collected and so what's
+ 
+
+ align:start position:0%
+pattern is collected and so what's
+called reciprocal space and to go from
+
+ align:start position:0%
+called reciprocal space and to go from
+ 
+
+ align:start position:0%
+called reciprocal space and to go from
+this to our intensity you need to do a
+
+ align:start position:0%
+this to our intensity you need to do a
+ 
+
+ align:start position:0%
+this to our intensity you need to do a
+Fourier transform into hilbert space
+
+ align:start position:0%
+Fourier transform into hilbert space
+ 
+
+ align:start position:0%
+Fourier transform into hilbert space
+which is what your intensity is based in
+
+ align:start position:0%
+which is what your intensity is based in
+ 
+
+ align:start position:0%
+which is what your intensity is based in
+but I provide a reference for sort of
+
+ align:start position:0%
+but I provide a reference for sort of
+ 
+
+ align:start position:0%
+but I provide a reference for sort of
+more information on that and so the next
+
+ align:start position:0%
+more information on that and so the next
+ 
+
+ align:start position:0%
+more information on that and so the next
+part of the discussion part of this
+
+ align:start position:0%
+part of the discussion part of this
+ 
+
+ align:start position:0%
+part of the discussion part of this
+recitation would be thinking about some
+
+ align:start position:0%
+recitation would be thinking about some
+ 
+
+ align:start position:0%
+recitation would be thinking about some
+of the limitations of x-ray
+
+ align:start position:0%
+of the limitations of x-ray
+ 
+
+ align:start position:0%
+of the limitations of x-ray
+crystallography so they're large them
+
+ align:start position:0%
+crystallography so they're large them
+ 
+
+ align:start position:0%
+crystallography so they're large them
+but I'll turn to all of you for inputs
+
+ align:start position:0%
+but I'll turn to all of you for inputs
+ 
+
+ align:start position:0%
+but I'll turn to all of you for inputs
+yes absolutely it's really hard to
+
+ align:start position:0%
+yes absolutely it's really hard to
+ 
+
+ align:start position:0%
+yes absolutely it's really hard to
+purify and crystallize proteins it's
+
+ align:start position:0%
+purify and crystallize proteins it's
+ 
+
+ align:start position:0%
+purify and crystallize proteins it's
+really not a trivial task it can take
+
+ align:start position:0%
+really not a trivial task it can take
+ 
+
+ align:start position:0%
+really not a trivial task it can take
+months or even years to do so and
+
+ align:start position:0%
+months or even years to do so and
+ 
+
+ align:start position:0%
+months or even years to do so and
+nowadays you have robots that can set up
+
+ align:start position:0%
+nowadays you have robots that can set up
+ 
+
+ align:start position:0%
+nowadays you have robots that can set up
+reactions under hundreds of different
+
+ align:start position:0%
+reactions under hundreds of different
+ 
+
+ align:start position:0%
+reactions under hundreds of different
+crystallization conditions and it's it's
+
+ align:start position:0%
+crystallization conditions and it's it's
+ 
+
+ align:start position:0%
+crystallization conditions and it's it's
+sort of a black magic sort of art like
+
+ align:start position:0%
+sort of a black magic sort of art like
+ 
+
+ align:start position:0%
+sort of a black magic sort of art like
+you can't it's hard to predict what
+
+ align:start position:0%
+you can't it's hard to predict what
+ 
+
+ align:start position:0%
+you can't it's hard to predict what
+crystallization conditions are going to
+
+ align:start position:0%
+crystallization conditions are going to
+ 
+
+ align:start position:0%
+crystallization conditions are going to
+give you a high quality crystal anything
+
+ align:start position:0%
+give you a high quality crystal anything
+ 
+
+ align:start position:0%
+give you a high quality crystal anything
+else yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes absolutely but yeah it's hard to
+
+ align:start position:0%
+yes absolutely but yeah it's hard to
+ 
+
+ align:start position:0%
+yes absolutely but yeah it's hard to
+tell whether the crystal structure that
+
+ align:start position:0%
+tell whether the crystal structure that
+ 
+
+ align:start position:0%
+tell whether the crystal structure that
+you get is depicting what's happening
+
+ align:start position:0%
+you get is depicting what's happening
+ 
+
+ align:start position:0%
+you get is depicting what's happening
+with the protein in vivo and this is
+
+ align:start position:0%
+with the protein in vivo and this is
+ 
+
+ align:start position:0%
+with the protein in vivo and this is
+really this is I mean this is a problem
+
+ align:start position:0%
+really this is I mean this is a problem
+ 
+
+ align:start position:0%
+really this is I mean this is a problem
+that inherent x-ray crystallography rate
+
+ align:start position:0%
+that inherent x-ray crystallography rate
+ 
+
+ align:start position:0%
+that inherent x-ray crystallography rate
+every time you solve it with structure
+
+ align:start position:0%
+every time you solve it with structure
+ 
+
+ align:start position:0%
+every time you solve it with structure
+you don't know whether it's relevant but
+
+ align:start position:0%
+you don't know whether it's relevant but
+ 
+
+ align:start position:0%
+you don't know whether it's relevant but
+I mean usually I think it turned out
+
+ align:start position:0%
+I mean usually I think it turned out
+ 
+
+ align:start position:0%
+I mean usually I think it turned out
+that it's pretty close if not completely
+
+ align:start position:0%
+that it's pretty close if not completely
+ 
+
+ align:start position:0%
+that it's pretty close if not completely
+accurate in solution but sometimes you
+
+ align:start position:0%
+accurate in solution but sometimes you
+ 
+
+ align:start position:0%
+accurate in solution but sometimes you
+do have to be careful about this it's
+
+ align:start position:0%
+do have to be careful about this it's
+ 
+
+ align:start position:0%
+do have to be careful about this it's
+especially challenging for stuff like
+
+ align:start position:0%
+especially challenging for stuff like
+ 
+
+ align:start position:0%
+especially challenging for stuff like
+membrane proteins where you don't really
+
+ align:start position:0%
+membrane proteins where you don't really
+ 
+
+ align:start position:0%
+membrane proteins where you don't really
+know any other ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when proteins are translated do they
+
+ align:start position:0%
+so when proteins are translated do they
+ 
+
+ align:start position:0%
+so when proteins are translated do they
+usually I they usually used just like
+
+ align:start position:0%
+usually I they usually used just like
+ 
+
+ align:start position:0%
+usually I they usually used just like
+that or there's something else happened
+
+ align:start position:0%
+that or there's something else happened
+ 
+
+ align:start position:0%
+that or there's something else happened
+to the proteins in most cells yes
+
+ align:start position:0%
+to the proteins in most cells yes
+ 
+
+ align:start position:0%
+to the proteins in most cells yes
+absolutely posters are made of
+
+ align:start position:0%
+absolutely posters are made of
+ 
+
+ align:start position:0%
+absolutely posters are made of
+modification so most lot of proteins are
+
+ align:start position:0%
+modification so most lot of proteins are
+ 
+
+ align:start position:0%
+modification so most lot of proteins are
+post-translationally modified and so
+
+ align:start position:0%
+post-translationally modified and so
+ 
+
+ align:start position:0%
+post-translationally modified and so
+when you appear when you're making when
+
+ align:start position:0%
+when you appear when you're making when
+ 
+
+ align:start position:0%
+when you appear when you're making when
+you're growing a crystal if your protein
+
+ align:start position:0%
+you're growing a crystal if your protein
+ 
+
+ align:start position:0%
+you're growing a crystal if your protein
+you usually you usually just use a
+
+ align:start position:0%
+you usually you usually just use a
+ 
+
+ align:start position:0%
+you usually you usually just use a
+purified version of your protein so you
+
+ align:start position:0%
+purified version of your protein so you
+ 
+
+ align:start position:0%
+purified version of your protein so you
+can't really calculate and sometimes
+
+ align:start position:0%
+can't really calculate and sometimes
+ 
+
+ align:start position:0%
+can't really calculate and sometimes
+these PTMs are essential for the
+
+ align:start position:0%
+these PTMs are essential for the
+ 
+
+ align:start position:0%
+these PTMs are essential for the
+function of the protein so you're
+
+ align:start position:0%
+function of the protein so you're
+ 
+
+ align:start position:0%
+function of the protein so you're
+missing some part of the picture
+
+ align:start position:0%
+missing some part of the picture
+ 
+
+ align:start position:0%
+missing some part of the picture
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+what about movement can you tell what
+
+ align:start position:0%
+what about movement can you tell what
+ 
+
+ align:start position:0%
+what about movement can you tell what
+proteins are flexible what parts of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes that is true you can can discern
+
+ align:start position:0%
+yes that is true you can can discern
+ 
+
+ align:start position:0%
+yes that is true you can can discern
+anything about dynamics in flexibility
+
+ align:start position:0%
+anything about dynamics in flexibility
+ 
+
+ align:start position:0%
+anything about dynamics in flexibility
+and the answer is you can tell something
+
+ align:start position:0%
+and the answer is you can tell something
+ 
+
+ align:start position:0%
+and the answer is you can tell something
+you can tell about you can tell
+
+ align:start position:0%
+you can tell about you can tell
+ 
+
+ align:start position:0%
+you can tell about you can tell
+something about the relative motion of
+
+ align:start position:0%
+something about the relative motion of
+ 
+
+ align:start position:0%
+something about the relative motion of
+different parts of the protein with
+
+ align:start position:0%
+different parts of the protein with
+ 
+
+ align:start position:0%
+different parts of the protein with
+respect to each other
+
+ align:start position:0%
+respect to each other
+ 
+
+ align:start position:0%
+respect to each other
+but it's hard to tell something about
+
+ align:start position:0%
+but it's hard to tell something about
+ 
+
+ align:start position:0%
+but it's hard to tell something about
+the absolute motion of these proteins so
+
+ align:start position:0%
+the absolute motion of these proteins so
+ 
+
+ align:start position:0%
+the absolute motion of these proteins so
+you can see say a larger scale of
+
+ align:start position:0%
+you can see say a larger scale of
+ 
+
+ align:start position:0%
+you can see say a larger scale of
+motions right most proteins are living
+
+ align:start position:0%
+motions right most proteins are living
+ 
+
+ align:start position:0%
+motions right most proteins are living
+breathing machines and you really it's
+
+ align:start position:0%
+breathing machines and you really it's
+ 
+
+ align:start position:0%
+breathing machines and you really it's
+hard to capture that in an x-ray
+
+ align:start position:0%
+hard to capture that in an x-ray
+ 
+
+ align:start position:0%
+hard to capture that in an x-ray
+structure all right and one more thing
+
+ align:start position:0%
+structure all right and one more thing
+ 
+
+ align:start position:0%
+structure all right and one more thing
+so is there any element that you cannot
+
+ align:start position:0%
+so is there any element that you cannot
+ 
+
+ align:start position:0%
+so is there any element that you cannot
+detect in extra crystallography very
+
+ align:start position:0%
+detect in extra crystallography very
+ 
+
+ align:start position:0%
+detect in extra crystallography very
+well this has to do with the way so in
+
+ align:start position:0%
+well this has to do with the way so in
+ 
+
+ align:start position:0%
+well this has to do with the way so in
+x-ray crystallography you're studying
+
+ align:start position:0%
+x-ray crystallography you're studying
+ 
+
+ align:start position:0%
+x-ray crystallography you're studying
+interactions of x-rays with without
+
+ align:start position:0%
+interactions of x-rays with without
+ 
+
+ align:start position:0%
+interactions of x-rays with without
+Tron's right so does anybody know which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons have one out Tron and so they're
+
+ align:start position:0%
+protons have one out Tron and so they're
+ 
+
+ align:start position:0%
+protons have one out Tron and so they're
+x-ray signal so-called is really weak
+
+ align:start position:0%
+x-ray signal so-called is really weak
+ 
+
+ align:start position:0%
+x-ray signal so-called is really weak
+really really weak and so you can't
+
+ align:start position:0%
+really really weak and so you can't
+ 
+
+ align:start position:0%
+really really weak and so you can't
+really see protons with x-ray
+
+ align:start position:0%
+really see protons with x-ray
+ 
+
+ align:start position:0%
+really see protons with x-ray
+crystallography until you can really
+
+ align:start position:0%
+crystallography until you can really
+ 
+
+ align:start position:0%
+crystallography until you can really
+study hydrogen's or hydrogen bonds and
+
+ align:start position:0%
+study hydrogen's or hydrogen bonds and
+ 
+
+ align:start position:0%
+study hydrogen's or hydrogen bonds and
+if you look at a structure of proteins
+
+ align:start position:0%
+if you look at a structure of proteins
+ 
+
+ align:start position:0%
+if you look at a structure of proteins
+that has hydrogens in it those hydrogens
+
+ align:start position:0%
+that has hydrogens in it those hydrogens
+ 
+
+ align:start position:0%
+that has hydrogens in it those hydrogens
+were put there as a result of an average
+
+ align:start position:0%
+were put there as a result of an average
+ 
+
+ align:start position:0%
+were put there as a result of an average
+bond length their typical bond length
+
+ align:start position:0%
+bond length their typical bond length
+ 
+
+ align:start position:0%
+bond length their typical bond length
+calculation so it's not actually
+
+ align:start position:0%
+calculation so it's not actually
+ 
+
+ align:start position:0%
+calculation so it's not actually
+experimentally determined you can use
+
+ align:start position:0%
+experimentally determined you can use
+ 
+
+ align:start position:0%
+experimentally determined you can use
+Neutron diffraction to get around this
+
+ align:start position:0%
+Neutron diffraction to get around this
+ 
+
+ align:start position:0%
+Neutron diffraction to get around this
+but Neutron diffraction is hard to do
+
+ align:start position:0%
+but Neutron diffraction is hard to do
+ 
+
+ align:start position:0%
+but Neutron diffraction is hard to do
+because you need to grow very large
+
+ align:start position:0%
+because you need to grow very large
+ 
+
+ align:start position:0%
+because you need to grow very large
+crystals to study and I think there are
+
+ align:start position:0%
+crystals to study and I think there are
+ 
+
+ align:start position:0%
+crystals to study and I think there are
+about 80
+
+ align:start position:0%
+about 80
+ 
+
+ align:start position:0%
+about 80
+I think neutron around 100 Neutron
+
+ align:start position:0%
+I think neutron around 100 Neutron
+ 
+
+ align:start position:0%
+I think neutron around 100 Neutron
+structures in the PDB so far but for
+
+ align:start position:0%
+structures in the PDB so far but for
+ 
+
+ align:start position:0%
+structures in the PDB so far but for
+small molecules neutron is much more
+
+ align:start position:0%
+small molecules neutron is much more
+ 
+
+ align:start position:0%
+small molecules neutron is much more
+accessible Neutron diffraction and so
+
+ align:start position:0%
+accessible Neutron diffraction and so
+ 
+
+ align:start position:0%
+accessible Neutron diffraction and so
+the idea is the same as x-ray
+
+ align:start position:0%
+the idea is the same as x-ray
+ 
+
+ align:start position:0%
+the idea is the same as x-ray
+lithography except for you're using
+
+ align:start position:0%
+lithography except for you're using
+ 
+
+ align:start position:0%
+lithography except for you're using
+neutrons all right and the final point
+
+ align:start position:0%
+neutrons all right and the final point
+ 
+
+ align:start position:0%
+neutrons all right and the final point
+is that one structure only tells you
+
+ align:start position:0%
+is that one structure only tells you
+ 
+
+ align:start position:0%
+is that one structure only tells you
+part of the story again and this is
+
+ align:start position:0%
+part of the story again and this is
+ 
+
+ align:start position:0%
+part of the story again and this is
+emphasizing the fact that one structure
+
+ align:start position:0%
+emphasizing the fact that one structure
+ 
+
+ align:start position:0%
+emphasizing the fact that one structure
+is just a snapshot off the protein at a
+
+ align:start position:0%
+is just a snapshot off the protein at a
+ 
+
+ align:start position:0%
+is just a snapshot off the protein at a
+certain time and you want to correctly
+
+ align:start position:0%
+certain time and you want to correctly
+ 
+
+ align:start position:0%
+certain time and you want to correctly
+interpret your data and learn something
+
+ align:start position:0%
+interpret your data and learn something
+ 
+
+ align:start position:0%
+interpret your data and learn something
+more about the protein you often have to
+
+ align:start position:0%
+more about the protein you often have to
+ 
+
+ align:start position:0%
+more about the protein you often have to
+you have to use complementary
+
+ align:start position:0%
+you have to use complementary
+ 
+
+ align:start position:0%
+you have to use complementary
+biophysical biochemical techniques are
+
+ align:start position:0%
+biophysical biochemical techniques are
+ 
+
+ align:start position:0%
+biophysical biochemical techniques are
+there any questions at this point so the
+
+ align:start position:0%
+there any questions at this point so the
+ 
+
+ align:start position:0%
+there any questions at this point so the
+last part of the talk is on how to
+
+ align:start position:0%
+last part of the talk is on how to
+ 
+
+ align:start position:0%
+last part of the talk is on how to
+assess the quality of structures in the
+
+ align:start position:0%
+assess the quality of structures in the
+ 
+
+ align:start position:0%
+assess the quality of structures in the
+PDB there are large structures and you
+
+ align:start position:0%
+PDB there are large structures and you
+ 
+
+ align:start position:0%
+PDB there are large structures and you
+want to be able to know whether the
+
+ align:start position:0%
+want to be able to know whether the
+ 
+
+ align:start position:0%
+want to be able to know whether the
+model is presented to you is act is
+
+ align:start position:0%
+model is presented to you is act is
+ 
+
+ align:start position:0%
+model is presented to you is act is
+actually accurate
+
+ align:start position:0%
+actually accurate
+ 
+
+ align:start position:0%
+actually accurate
+accurately reflects the data that was
+
+ align:start position:0%
+accurately reflects the data that was
+ 
+
+ align:start position:0%
+accurately reflects the data that was
+collected and so the first point is what
+
+ align:start position:0%
+collected and so the first point is what
+ 
+
+ align:start position:0%
+collected and so the first point is what
+is the resolution of a structure and so
+
+ align:start position:0%
+is the resolution of a structure and so
+ 
+
+ align:start position:0%
+is the resolution of a structure and so
+the take-home message at a lower number
+
+ align:start position:0%
+the take-home message at a lower number
+ 
+
+ align:start position:0%
+the take-home message at a lower number
+means a greater resolution and the
+
+ align:start position:0%
+means a greater resolution and the
+ 
+
+ align:start position:0%
+means a greater resolution and the
+resolution actually here is referring to
+
+ align:start position:0%
+resolution actually here is referring to
+ 
+
+ align:start position:0%
+resolution actually here is referring to
+the distances between the atoms in the
+
+ align:start position:0%
+the distances between the atoms in the
+ 
+
+ align:start position:0%
+the distances between the atoms in the
+plane and so that's where the s coming
+
+ align:start position:0%
+plane and so that's where the s coming
+ 
+
+ align:start position:0%
+plane and so that's where the s coming
+from so that's why you if you have a low
+
+ align:start position:0%
+from so that's why you if you have a low
+ 
+
+ align:start position:0%
+from so that's why you if you have a low
+resolution that means you can resolve
+
+ align:start position:0%
+resolution that means you can resolve
+ 
+
+ align:start position:0%
+resolution that means you can resolve
+atoms one angstrom resolution means that
+
+ align:start position:0%
+atoms one angstrom resolution means that
+ 
+
+ align:start position:0%
+atoms one angstrom resolution means that
+you can resolve atoms that are one
+
+ align:start position:0%
+you can resolve atoms that are one
+ 
+
+ align:start position:0%
+you can resolve atoms that are one
+absolute apart on parallel planes but
+
+ align:start position:0%
+absolute apart on parallel planes but
+ 
+
+ align:start position:0%
+absolute apart on parallel planes but
+the take-home message is for at a 1
+
+ align:start position:0%
+the take-home message is for at a 1
+ 
+
+ align:start position:0%
+the take-home message is for at a 1
+angstrom resolution you can see
+
+ align:start position:0%
+angstrom resolution you can see
+ 
+
+ align:start position:0%
+angstrom resolution you can see
+individual atoms and you can discern the
+
+ align:start position:0%
+individual atoms and you can discern the
+ 
+
+ align:start position:0%
+individual atoms and you can discern the
+identities of those atoms by looking at
+
+ align:start position:0%
+identities of those atoms by looking at
+ 
+
+ align:start position:0%
+identities of those atoms by looking at
+their electron density but if you come
+
+ align:start position:0%
+their electron density but if you come
+ 
+
+ align:start position:0%
+their electron density but if you come
+down to a 4 angstrom structure you see
+
+ align:start position:0%
+down to a 4 angstrom structure you see
+ 
+
+ align:start position:0%
+down to a 4 angstrom structure you see
+the benzene ring doesn't really have a
+
+ align:start position:0%
+the benzene ring doesn't really have a
+ 
+
+ align:start position:0%
+the benzene ring doesn't really have a
+clearly defined that tron density and
+
+ align:start position:0%
+clearly defined that tron density and
+ 
+
+ align:start position:0%
+clearly defined that tron density and
+there's no hole in the center but if you
+
+ align:start position:0%
+there's no hole in the center but if you
+ 
+
+ align:start position:0%
+there's no hole in the center but if you
+look at the one angstrom structure you
+
+ align:start position:0%
+look at the one angstrom structure you
+ 
+
+ align:start position:0%
+look at the one angstrom structure you
+can see that there's even a hole in them
+
+ align:start position:0%
+can see that there's even a hole in them
+ 
+
+ align:start position:0%
+can see that there's even a hole in them
+in the benzene ring to account for an
+
+ align:start position:0%
+in the benzene ring to account for an
+ 
+
+ align:start position:0%
+in the benzene ring to account for an
+oil trend entry there and then if you
+
+ align:start position:0%
+oil trend entry there and then if you
+ 
+
+ align:start position:0%
+oil trend entry there and then if you
+look at so this is these are the data
+
+ align:start position:0%
+look at so this is these are the data
+ 
+
+ align:start position:0%
+look at so this is these are the data
+statistics so this is just pulled from
+
+ align:start position:0%
+statistics so this is just pulled from
+ 
+
+ align:start position:0%
+statistics so this is just pulled from
+PDB off to jf5 so this is a PDB ID for
+
+ align:start position:0%
+PDB off to jf5 so this is a PDB ID for
+ 
+
+ align:start position:0%
+PDB off to jf5 so this is a PDB ID for
+Diavik Witten and we'll be looking at
+
+ align:start position:0%
+Diavik Witten and we'll be looking at
+ 
+
+ align:start position:0%
+Diavik Witten and we'll be looking at
+this structure later in the worksheet
+
+ align:start position:0%
+this structure later in the worksheet
+ 
+
+ align:start position:0%
+this structure later in the worksheet
+the resolution tells you of course about
+
+ align:start position:0%
+the resolution tells you of course about
+ 
+
+ align:start position:0%
+the resolution tells you of course about
+the resolution of the crystal structure
+
+ align:start position:0%
+the resolution of the crystal structure
+ 
+
+ align:start position:0%
+the resolution of the crystal structure
+and so this is in this case it's one
+
+ align:start position:0%
+and so this is in this case it's one
+ 
+
+ align:start position:0%
+and so this is in this case it's one
+point nine five angstroms or two
+
+ align:start position:0%
+point nine five angstroms or two
+ 
+
+ align:start position:0%
+point nine five angstroms or two
+angstroms and so that's pretty high
+
+ align:start position:0%
+angstroms and so that's pretty high
+ 
+
+ align:start position:0%
+angstroms and so that's pretty high
+resolution reflections our reflections
+
+ align:start position:0%
+resolution reflections our reflections
+ 
+
+ align:start position:0%
+resolution reflections our reflections
+are each of those points in the
+
+ align:start position:0%
+are each of those points in the
+ 
+
+ align:start position:0%
+are each of those points in the
+diffraction pattern that you collect and
+
+ align:start position:0%
+diffraction pattern that you collect and
+ 
+
+ align:start position:0%
+diffraction pattern that you collect and
+a unique reflection refers to the fact
+
+ align:start position:0%
+a unique reflection refers to the fact
+ 
+
+ align:start position:0%
+a unique reflection refers to the fact
+that you've only collected at once
+
+ align:start position:0%
+that you've only collected at once
+ 
+
+ align:start position:0%
+that you've only collected at once
+so usually when you when you collect
+
+ align:start position:0%
+so usually when you when you collect
+ 
+
+ align:start position:0%
+so usually when you when you collect
+diffraction patterns you collect you put
+
+ align:start position:0%
+diffraction patterns you collect you put
+ 
+
+ align:start position:0%
+diffraction patterns you collect you put
+your protein at a certain certain
+
+ align:start position:0%
+your protein at a certain certain
+ 
+
+ align:start position:0%
+your protein at a certain certain
+orientation respect with respect to the
+
+ align:start position:0%
+orientation respect with respect to the
+ 
+
+ align:start position:0%
+orientation respect with respect to the
+x-ray beam and then you collect
+
+ align:start position:0%
+x-ray beam and then you collect
+ 
+
+ align:start position:0%
+x-ray beam and then you collect
+infraction pattern and then you rotate
+
+ align:start position:0%
+infraction pattern and then you rotate
+ 
+
+ align:start position:0%
+infraction pattern and then you rotate
+to your crystal a whole bunch of times
+
+ align:start position:0%
+to your crystal a whole bunch of times
+ 
+
+ align:start position:0%
+to your crystal a whole bunch of times
+and you collect a whole bunch of
+
+ align:start position:0%
+and you collect a whole bunch of
+ 
+
+ align:start position:0%
+and you collect a whole bunch of
+different diffraction patterns and then
+
+ align:start position:0%
+different diffraction patterns and then
+ 
+
+ align:start position:0%
+different diffraction patterns and then
+you superimpose all of those together to
+
+ align:start position:0%
+you superimpose all of those together to
+ 
+
+ align:start position:0%
+you superimpose all of those together to
+get the master diffraction pattern
+
+ align:start position:0%
+get the master diffraction pattern
+ 
+
+ align:start position:0%
+get the master diffraction pattern
+redundancy refers to the facts of how
+
+ align:start position:0%
+redundancy refers to the facts of how
+ 
+
+ align:start position:0%
+redundancy refers to the facts of how
+often each reflection was observed and
+
+ align:start position:0%
+often each reflection was observed and
+ 
+
+ align:start position:0%
+often each reflection was observed and
+so this is just signal averaging the
+
+ align:start position:0%
+so this is just signal averaging the
+ 
+
+ align:start position:0%
+so this is just signal averaging the
+more redundancy you have the greater
+
+ align:start position:0%
+more redundancy you have the greater
+ 
+
+ align:start position:0%
+more redundancy you have the greater
+number of times you observe that
+
+ align:start position:0%
+number of times you observe that
+ 
+
+ align:start position:0%
+number of times you observe that
+particular reflection completed nough
+
+ align:start position:0%
+particular reflection completed nough
+ 
+
+ align:start position:0%
+particular reflection completed nough
+stuffers - how many of the data points
+
+ align:start position:0%
+stuffers - how many of the data points
+ 
+
+ align:start position:0%
+stuffers - how many of the data points
+were actually measured and so this is
+
+ align:start position:0%
+were actually measured and so this is
+ 
+
+ align:start position:0%
+were actually measured and so this is
+when you created your model you can back
+
+ align:start position:0%
+when you created your model you can back
+ 
+
+ align:start position:0%
+when you created your model you can back
+calculate your diffraction pattern
+
+ align:start position:0%
+calculate your diffraction pattern
+ 
+
+ align:start position:0%
+calculate your diffraction pattern
+and then you see how many of this those
+
+ align:start position:0%
+and then you see how many of this those
+ 
+
+ align:start position:0%
+and then you see how many of this those
+reflections were experimentally observed
+
+ align:start position:0%
+reflections were experimentally observed
+ 
+
+ align:start position:0%
+reflections were experimentally observed
+in your dataset and so for this usually
+
+ align:start position:0%
+in your dataset and so for this usually
+ 
+
+ align:start position:0%
+in your dataset and so for this usually
+one I supposed 100% and anything above
+
+ align:start position:0%
+one I supposed 100% and anything above
+ 
+
+ align:start position:0%
+one I supposed 100% and anything above
+95% is considered fairly good our merge
+
+ align:start position:0%
+95% is considered fairly good our merge
+ 
+
+ align:start position:0%
+95% is considered fairly good our merge
+is is an indicator of how consistent
+
+ align:start position:0%
+is is an indicator of how consistent
+ 
+
+ align:start position:0%
+is is an indicator of how consistent
+measurements are so this is a measure of
+
+ align:start position:0%
+measurements are so this is a measure of
+ 
+
+ align:start position:0%
+measurements are so this is a measure of
+what the DBA what the difference between
+
+ align:start position:0%
+what the DBA what the difference between
+ 
+
+ align:start position:0%
+what the DBA what the difference between
+different measurements for the same
+
+ align:start position:0%
+different measurements for the same
+ 
+
+ align:start position:0%
+different measurements for the same
+reflection are so if you collect the if
+
+ align:start position:0%
+reflection are so if you collect the if
+ 
+
+ align:start position:0%
+reflection are so if you collect the if
+you look at the intensity for for the
+
+ align:start position:0%
+you look at the intensity for for the
+ 
+
+ align:start position:0%
+you look at the intensity for for the
+same reflection a different number of
+
+ align:start position:0%
+same reflection a different number of
+ 
+
+ align:start position:0%
+same reflection a different number of
+times is saying the standard deviation
+
+ align:start position:0%
+times is saying the standard deviation
+ 
+
+ align:start position:0%
+times is saying the standard deviation
+of that and so you want lower as lower
+
+ align:start position:0%
+of that and so you want lower as lower
+ 
+
+ align:start position:0%
+of that and so you want lower as lower
+number as possible so it usually wanted
+
+ align:start position:0%
+number as possible so it usually wanted
+ 
+
+ align:start position:0%
+number as possible so it usually wanted
+to be about point about one tenth of the
+
+ align:start position:0%
+to be about point about one tenth of the
+ 
+
+ align:start position:0%
+to be about point about one tenth of the
+resolution of your crystal structure
+
+ align:start position:0%
+resolution of your crystal structure
+ 
+
+ align:start position:0%
+resolution of your crystal structure
+which is point to act was in this case I
+
+ align:start position:0%
+which is point to act was in this case I
+ 
+
+ align:start position:0%
+which is point to act was in this case I
+forgot to mention this but the values in
+
+ align:start position:0%
+forgot to mention this but the values in
+ 
+
+ align:start position:0%
+forgot to mention this but the values in
+parentheses are for a high resolution
+
+ align:start position:0%
+parentheses are for a high resolution
+ 
+
+ align:start position:0%
+parentheses are for a high resolution
+bin so this is just a certain subset of
+
+ align:start position:0%
+bin so this is just a certain subset of
+ 
+
+ align:start position:0%
+bin so this is just a certain subset of
+this data set that's considered to be
+
+ align:start position:0%
+this data set that's considered to be
+ 
+
+ align:start position:0%
+this data set that's considered to be
+higher quality than the original dataset
+
+ align:start position:0%
+higher quality than the original dataset
+ 
+
+ align:start position:0%
+higher quality than the original dataset
+and that's actually coming from this
+
+ align:start position:0%
+and that's actually coming from this
+ 
+
+ align:start position:0%
+and that's actually coming from this
+value which is signal intense signal or
+
+ align:start position:0%
+value which is signal intense signal or
+ 
+
+ align:start position:0%
+value which is signal intense signal or
+signal intensity over Sigma signal
+
+ align:start position:0%
+signal intensity over Sigma signal
+ 
+
+ align:start position:0%
+signal intensity over Sigma signal
+intensity and that's a measure of the
+
+ align:start position:0%
+intensity and that's a measure of the
+ 
+
+ align:start position:0%
+intensity and that's a measure of the
+signal-to-noise ratio so you want a
+
+ align:start position:0%
+signal-to-noise ratio so you want a
+ 
+
+ align:start position:0%
+signal-to-noise ratio so you want a
+higher signal-to-noise ratio is better
+
+ align:start position:0%
+higher signal-to-noise ratio is better
+ 
+
+ align:start position:0%
+higher signal-to-noise ratio is better
+and this is fairly good and the higher
+
+ align:start position:0%
+and this is fairly good and the higher
+ 
+
+ align:start position:0%
+and this is fairly good and the higher
+the better and cutoff is that two for
+
+ align:start position:0%
+the better and cutoff is that two for
+ 
+
+ align:start position:0%
+the better and cutoff is that two for
+the high resolution bin off your data
+
+ align:start position:0%
+the high resolution bin off your data
+ 
+
+ align:start position:0%
+the high resolution bin off your data
+points all right so this is just the raw
+
+ align:start position:0%
+points all right so this is just the raw
+ 
+
+ align:start position:0%
+points all right so this is just the raw
+data and then the refinement statistics
+
+ align:start position:0%
+data and then the refinement statistics
+ 
+
+ align:start position:0%
+data and then the refinement statistics
+tell you something about your refinement
+
+ align:start position:0%
+tell you something about your refinement
+ 
+
+ align:start position:0%
+tell you something about your refinement
+process that gave you the crystal
+
+ align:start position:0%
+process that gave you the crystal
+ 
+
+ align:start position:0%
+process that gave you the crystal
+structure which you calculated so our
+
+ align:start position:0%
+structure which you calculated so our
+ 
+
+ align:start position:0%
+structure which you calculated so our
+crystallization which is also our crisp
+
+ align:start position:0%
+crystallization which is also our crisp
+ 
+
+ align:start position:0%
+crystallization which is also our crisp
+which is also call our work and also
+
+ align:start position:0%
+which is also call our work and also
+ 
+
+ align:start position:0%
+which is also call our work and also
+Carl called the R factor that tells you
+
+ align:start position:0%
+Carl called the R factor that tells you
+ 
+
+ align:start position:0%
+Carl called the R factor that tells you
+how well your data and your your model
+
+ align:start position:0%
+how well your data and your your model
+ 
+
+ align:start position:0%
+how well your data and your your model
+in your data match and so this is where
+
+ align:start position:0%
+in your data match and so this is where
+ 
+
+ align:start position:0%
+in your data match and so this is where
+you calculate the difference in the
+
+ align:start position:0%
+you calculate the difference in the
+ 
+
+ align:start position:0%
+you calculate the difference in the
+diffraction patterns between what you
+
+ align:start position:0%
+diffraction patterns between what you
+ 
+
+ align:start position:0%
+diffraction patterns between what you
+observed and what with you in what do
+
+ align:start position:0%
+observed and what with you in what do
+ 
+
+ align:start position:0%
+observed and what with you in what do
+you experiment observe and what you
+
+ align:start position:0%
+you experiment observe and what you
+ 
+
+ align:start position:0%
+you experiment observe and what you
+calculated using the model of electron
+
+ align:start position:0%
+calculated using the model of electron
+ 
+
+ align:start position:0%
+calculated using the model of electron
+density our free tells you how well your
+
+ align:start position:0%
+density our free tells you how well your
+ 
+
+ align:start position:0%
+density our free tells you how well your
+model and data match been corrected for
+
+ align:start position:0%
+model and data match been corrected for
+ 
+
+ align:start position:0%
+model and data match been corrected for
+overfitting so the idea behind this is
+
+ align:start position:0%
+overfitting so the idea behind this is
+ 
+
+ align:start position:0%
+overfitting so the idea behind this is
+that when you collect when you collect
+
+ align:start position:0%
+that when you collect when you collect
+ 
+
+ align:start position:0%
+that when you collect when you collect
+your data set you put aside about 5% of
+
+ align:start position:0%
+your data set you put aside about 5% of
+ 
+
+ align:start position:0%
+your data set you put aside about 5% of
+the reflections that you observe in that
+
+ align:start position:0%
+the reflections that you observe in that
+ 
+
+ align:start position:0%
+the reflections that you observe in that
+data set
+
+ align:start position:0%
+data set
+ 
+
+ align:start position:0%
+data set
+to prevent over-fitting and then when
+
+ align:start position:0%
+to prevent over-fitting and then when
+ 
+
+ align:start position:0%
+to prevent over-fitting and then when
+you've created your model you go back
+
+ align:start position:0%
+you've created your model you go back
+ 
+
+ align:start position:0%
+you've created your model you go back
+and see how well those five percent of
+
+ align:start position:0%
+and see how well those five percent of
+ 
+
+ align:start position:0%
+and see how well those five percent of
+data points fit the model that you've
+
+ align:start position:0%
+data points fit the model that you've
+ 
+
+ align:start position:0%
+data points fit the model that you've
+come up with and if they fit well that
+
+ align:start position:0%
+come up with and if they fit well that
+ 
+
+ align:start position:0%
+come up with and if they fit well that
+means you've accurately predicted your
+
+ align:start position:0%
+means you've accurately predicted your
+ 
+
+ align:start position:0%
+means you've accurately predicted your
+crystal structure using the data that
+
+ align:start position:0%
+crystal structure using the data that
+ 
+
+ align:start position:0%
+crystal structure using the data that
+you have but if you don't fit well that
+
+ align:start position:0%
+you have but if you don't fit well that
+ 
+
+ align:start position:0%
+you have but if you don't fit well that
+means you've just fit whatever data
+
+ align:start position:0%
+means you've just fit whatever data
+ 
+
+ align:start position:0%
+means you've just fit whatever data
+points you have to some model right you
+
+ align:start position:0%
+points you have to some model right you
+ 
+
+ align:start position:0%
+points you have to some model right you
+use a bunch of data point and you fit it
+
+ align:start position:0%
+use a bunch of data point and you fit it
+ 
+
+ align:start position:0%
+use a bunch of data point and you fit it
+to some model but that doesn't actually
+
+ align:start position:0%
+to some model but that doesn't actually
+ 
+
+ align:start position:0%
+to some model but that doesn't actually
+that's not actually accurate to the
+
+ align:start position:0%
+that's not actually accurate to the
+ 
+
+ align:start position:0%
+that's not actually accurate to the
+protein structure that you determine and
+
+ align:start position:0%
+protein structure that you determine and
+ 
+
+ align:start position:0%
+protein structure that you determine and
+so for this you want it to be about
+
+ align:start position:0%
+so for this you want it to be about
+ 
+
+ align:start position:0%
+so for this you want it to be about
+one-tenth of a resolution that's also
+
+ align:start position:0%
+one-tenth of a resolution that's also
+ 
+
+ align:start position:0%
+one-tenth of a resolution that's also
+true for our crest but then the other
+
+ align:start position:0%
+true for our crest but then the other
+ 
+
+ align:start position:0%
+true for our crest but then the other
+key point is that it should be very
+
+ align:start position:0%
+key point is that it should be very
+ 
+
+ align:start position:0%
+key point is that it should be very
+close to the R Chris we're just telling
+
+ align:start position:0%
+close to the R Chris we're just telling
+ 
+
+ align:start position:0%
+close to the R Chris we're just telling
+you that it's it's random error or it's
+
+ align:start position:0%
+you that it's it's random error or it's
+ 
+
+ align:start position:0%
+you that it's it's random error or it's
+a quality of a data set that's causing
+
+ align:start position:0%
+a quality of a data set that's causing
+ 
+
+ align:start position:0%
+a quality of a data set that's causing
+this and not some not some over
+
+ align:start position:0%
+this and not some not some over
+ 
+
+ align:start position:0%
+this and not some not some over
+refinement that you've done during the
+
+ align:start position:0%
+refinement that you've done during the
+ 
+
+ align:start position:0%
+refinement that you've done during the
+refinement process B factor tells you
+
+ align:start position:0%
+refinement process B factor tells you
+ 
+
+ align:start position:0%
+refinement process B factor tells you
+about how mobile atoms are in the
+
+ align:start position:0%
+about how mobile atoms are in the
+ 
+
+ align:start position:0%
+about how mobile atoms are in the
+crystal lattice and this is something
+
+ align:start position:0%
+crystal lattice and this is something
+ 
+
+ align:start position:0%
+crystal lattice and this is something
+that's not it's not particularly useful
+
+ align:start position:0%
+that's not it's not particularly useful
+ 
+
+ align:start position:0%
+that's not it's not particularly useful
+if you look at the bulb out statistic
+
+ align:start position:0%
+if you look at the bulb out statistic
+ 
+
+ align:start position:0%
+if you look at the bulb out statistic
+but if you need to it's important to
+
+ align:start position:0%
+but if you need to it's important to
+ 
+
+ align:start position:0%
+but if you need to it's important to
+evaluate this by residue and so if you
+
+ align:start position:0%
+evaluate this by residue and so if you
+ 
+
+ align:start position:0%
+evaluate this by residue and so if you
+look at amino acids in the loops or
+
+ align:start position:0%
+look at amino acids in the loops or
+ 
+
+ align:start position:0%
+look at amino acids in the loops or
+proteins you'll find that they have a
+
+ align:start position:0%
+proteins you'll find that they have a
+ 
+
+ align:start position:0%
+proteins you'll find that they have a
+higher B factor usually meaning that
+
+ align:start position:0%
+higher B factor usually meaning that
+ 
+
+ align:start position:0%
+higher B factor usually meaning that
+they're more mobile and so you can often
+
+ align:start position:0%
+they're more mobile and so you can often
+ 
+
+ align:start position:0%
+they're more mobile and so you can often
+tell what residues are important for
+
+ align:start position:0%
+tell what residues are important for
+ 
+
+ align:start position:0%
+tell what residues are important for
+function by looking at the B factor it
+
+ align:start position:0%
+function by looking at the B factor it
+ 
+
+ align:start position:0%
+function by looking at the B factor it
+also I mean we factors coming from
+
+ align:start position:0%
+also I mean we factors coming from
+ 
+
+ align:start position:0%
+also I mean we factors coming from
+there's inherent vibration vibration
+
+ align:start position:0%
+there's inherent vibration vibration
+ 
+
+ align:start position:0%
+there's inherent vibration vibration
+emotions in all atoms right so there
+
+ align:start position:0%
+emotions in all atoms right so there
+ 
+
+ align:start position:0%
+emotions in all atoms right so there
+will be a B Factory at any temperature
+
+ align:start position:0%
+will be a B Factory at any temperature
+ 
+
+ align:start position:0%
+will be a B Factory at any temperature
+greater than zero but it also does tell
+
+ align:start position:0%
+greater than zero but it also does tell
+ 
+
+ align:start position:0%
+greater than zero but it also does tell
+you a little bit about the disorder in
+
+ align:start position:0%
+you a little bit about the disorder in
+ 
+
+ align:start position:0%
+you a little bit about the disorder in
+protein structures and the B factor of
+
+ align:start position:0%
+protein structures and the B factor of
+ 
+
+ align:start position:0%
+protein structures and the B factor of
+water is often included just so that
+
+ align:start position:0%
+water is often included just so that
+ 
+
+ align:start position:0%
+water is often included just so that
+people who are looking at the crew
+
+ align:start position:0%
+people who are looking at the crew
+ 
+
+ align:start position:0%
+people who are looking at the crew
+structure afterwards can decide whether
+
+ align:start position:0%
+structure afterwards can decide whether
+ 
+
+ align:start position:0%
+structure afterwards can decide whether
+that what is really there or really was
+
+ align:start position:0%
+that what is really there or really was
+ 
+
+ align:start position:0%
+that what is really there or really was
+part of the electron density or whether
+
+ align:start position:0%
+part of the electron density or whether
+ 
+
+ align:start position:0%
+part of the electron density or whether
+it's just an artifact of or refinement
+
+ align:start position:0%
+it's just an artifact of or refinement
+ 
+
+ align:start position:0%
+it's just an artifact of or refinement
+or something like that and then the
+
+ align:start position:0%
+or something like that and then the
+ 
+
+ align:start position:0%
+or something like that and then the
+final statistic that you can look at is
+
+ align:start position:0%
+final statistic that you can look at is
+ 
+
+ align:start position:0%
+final statistic that you can look at is
+at the rmsd from ideal geometry so the
+
+ align:start position:0%
+at the rmsd from ideal geometry so the
+ 
+
+ align:start position:0%
+at the rmsd from ideal geometry so the
+geometries of these bonds and angles are
+
+ align:start position:0%
+geometries of these bonds and angles are
+ 
+
+ align:start position:0%
+geometries of these bonds and angles are
+usually well known and so if you compare
+
+ align:start position:0%
+usually well known and so if you compare
+ 
+
+ align:start position:0%
+usually well known and so if you compare
+the results from your structure to the
+
+ align:start position:0%
+the results from your structure to the
+ 
+
+ align:start position:0%
+the results from your structure to the
+knowns a Stewart chemistry you will find
+
+ align:start position:0%
+knowns a Stewart chemistry you will find
+ 
+
+ align:start position:0%
+knowns a Stewart chemistry you will find
+that this is actually just at the
+
+ align:start position:0%
+that this is actually just at the
+ 
+
+ align:start position:0%
+that this is actually just at the
+threshold of the cutoff for what's
+
+ align:start position:0%
+threshold of the cutoff for what's
+ 
+
+ align:start position:0%
+threshold of the cutoff for what's
+considered good so 0.015 angstroms this
+
+ align:start position:0%
+considered good so 0.015 angstroms this
+ 
+
+ align:start position:0%
+considered good so 0.015 angstroms this
+is a standard deviation of bond lengths
+
+ align:start position:0%
+is a standard deviation of bond lengths
+ 
+
+ align:start position:0%
+is a standard deviation of bond lengths
+your model versus what is well what is
+
+ align:start position:0%
+your model versus what is well what is
+ 
+
+ align:start position:0%
+your model versus what is well what is
+already known and to 0.015 angstroms is
+
+ align:start position:0%
+already known and to 0.015 angstroms is
+ 
+
+ align:start position:0%
+already known and to 0.015 angstroms is
+is just about the cutoff that's
+
+ align:start position:0%
+is just about the cutoff that's
+ 
+
+ align:start position:0%
+is just about the cutoff that's
+considered good for this for extra
+
+ align:start position:0%
+considered good for this for extra
+ 
+
+ align:start position:0%
+considered good for this for extra
+structures and it's same for bond angles
+
+ align:start position:0%
+structures and it's same for bond angles
+ 
+
+ align:start position:0%
+structures and it's same for bond angles
+1.5 degrees is considered sort of the
+
+ align:start position:0%
+1.5 degrees is considered sort of the
+ 
+
+ align:start position:0%
+1.5 degrees is considered sort of the
+threshold of what is conceptual and you
+
+ align:start position:0%
+threshold of what is conceptual and you
+ 
+
+ align:start position:0%
+threshold of what is conceptual and you
+can also look at Ramachandran statistics
+
+ align:start position:0%
+can also look at Ramachandran statistics
+ 
+
+ align:start position:0%
+can also look at Ramachandran statistics
+so this is looking at five side backbone
+
+ align:start position:0%
+so this is looking at five side backbone
+ 
+
+ align:start position:0%
+so this is looking at five side backbone
+angles to tell you if there are any
+
+ align:start position:0%
+angles to tell you if there are any
+ 
+
+ align:start position:0%
+angles to tell you if there are any
+steric clashes say between between four
+
+ align:start position:0%
+steric clashes say between between four
+ 
+
+ align:start position:0%
+steric clashes say between between four
+side chains that should really shouldn't
+
+ align:start position:0%
+side chains that should really shouldn't
+ 
+
+ align:start position:0%
+side chains that should really shouldn't
+be there and you can if you do have
+
+ align:start position:0%
+be there and you can if you do have
+ 
+
+ align:start position:0%
+be there and you can if you do have
+steric clash nowadays you have to report
+
+ align:start position:0%
+steric clash nowadays you have to report
+ 
+
+ align:start position:0%
+steric clash nowadays you have to report
+it to PDB the only exception is for
+
+ align:start position:0%
+it to PDB the only exception is for
+ 
+
+ align:start position:0%
+it to PDB the only exception is for
+glycine which doesn't have a side chain
+
+ align:start position:0%
+glycine which doesn't have a side chain
+ 
+
+ align:start position:0%
+glycine which doesn't have a side chain
+and so it can adopt a strange fire angle
+
+ align:start position:0%
+and so it can adopt a strange fire angle
+ 
+
+ align:start position:0%
+and so it can adopt a strange fire angle
+that's outside the Ramachandran plot any
+
+ align:start position:0%
+that's outside the Ramachandran plot any
+ 
+
+ align:start position:0%
+that's outside the Ramachandran plot any
+questions about on this anything else
+
+ align:start position:0%
+questions about on this anything else
+ 
+
+ align:start position:0%
+questions about on this anything else
+about x-ray crystallography so this
+
+ align:start position:0%
+about x-ray crystallography so this
+ 
+
+ align:start position:0%
+about x-ray crystallography so this
+brings us to the end of the talk and
+
+ align:start position:0%
+brings us to the end of the talk and
+ 
+
+ align:start position:0%
+brings us to the end of the talk and
+this is sort of a nice a resource that I
+
+ align:start position:0%
+this is sort of a nice a resource that I
+ 
+
+ align:start position:0%
+this is sort of a nice a resource that I
+found that has more information about
+
+ align:start position:0%
+found that has more information about
+ 
+
+ align:start position:0%
+found that has more information about
+exa crystallography and the math behind
+
+ align:start position:0%
+exa crystallography and the math behind
+ 
+
+ align:start position:0%
+exa crystallography and the math behind
+x-ray crystallography and more of the
+
+ align:start position:0%
+x-ray crystallography and more of the
+ 
+
+ align:start position:0%
+x-ray crystallography and more of the
+theory behind it but again I want to
+
+ align:start position:0%
+theory behind it but again I want to
+ 
+
+ align:start position:0%
+theory behind it but again I want to
+emphasize that today it's a very
+
+ align:start position:0%
+emphasize that today it's a very
+ 
+
+ align:start position:0%
+emphasize that today it's a very
+automated process is that you click a
+
+ align:start position:0%
+automated process is that you click a
+ 
+
+ align:start position:0%
+automated process is that you click a
+few buttons and anybody can do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/tOsdeaYDCMk.txt b/tOsdeaYDCMk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4c94f9737d6212f54552af249a55634919680172
--- /dev/null
+++ b/tOsdeaYDCMk.txt
@@ -0,0 +1,2219 @@
+align:start position:0%
+ 
+now the standard thing you do with a
+
+ align:start position:0%
+now the standard thing you do with a
+ 
+
+ align:start position:0%
+now the standard thing you do with a
+recursive data type in programming is
+
+ align:start position:0%
+recursive data type in programming is
+ 
+
+ align:start position:0%
+recursive data type in programming is
+you define recursive procedures on them
+
+ align:start position:0%
+you define recursive procedures on them
+ 
+
+ align:start position:0%
+you define recursive procedures on them
+so let's look at how that works I'm
+
+ align:start position:0%
+so let's look at how that works I'm
+ 
+
+ align:start position:0%
+so let's look at how that works I'm
+going to define a function f on a
+
+ align:start position:0%
+going to define a function f on a
+ 
+
+ align:start position:0%
+going to define a function f on a
+recursively defined data type r the way
+
+ align:start position:0%
+recursively defined data type r the way
+ 
+
+ align:start position:0%
+recursively defined data type r the way
+I'm going to do it is I'm going to
+
+ align:start position:0%
+I'm going to do it is I'm going to
+ 
+
+ align:start position:0%
+I'm going to do it is I'm going to
+define f of b explicitly in terms of b
+
+ align:start position:0%
+define f of b explicitly in terms of b
+ 
+
+ align:start position:0%
+define f of b explicitly in terms of b
+and operations that are already
+
+ align:start position:0%
+and operations that are already
+ 
+
+ align:start position:0%
+and operations that are already
+understood for all of the base cases of
+
+ align:start position:0%
+understood for all of the base cases of
+ 
+
+ align:start position:0%
+understood for all of the base cases of
+B in R and then I'm going to define F of
+
+ align:start position:0%
+B in R and then I'm going to define F of
+ 
+
+ align:start position:0%
+B in R and then I'm going to define F of
+a constructor applied to X in terms of X
+
+ align:start position:0%
+a constructor applied to X in terms of X
+ 
+
+ align:start position:0%
+a constructor applied to X in terms of X
+and f of X and if I keep to that
+
+ align:start position:0%
+and f of X and if I keep to that
+ 
+
+ align:start position:0%
+and f of X and if I keep to that
+structure that gives me a recursive
+
+ align:start position:0%
+structure that gives me a recursive
+ 
+
+ align:start position:0%
+structure that gives me a recursive
+definition of the function f on the
+
+ align:start position:0%
+definition of the function f on the
+ 
+
+ align:start position:0%
+definition of the function f on the
+recursively defined data set R let's
+
+ align:start position:0%
+recursively defined data set R let's
+ 
+
+ align:start position:0%
+recursively defined data set R let's
+look at an example to make this recipe
+
+ align:start position:0%
+look at an example to make this recipe
+ 
+
+ align:start position:0%
+look at an example to make this recipe
+explicit and clearer let's think about a
+
+ align:start position:0%
+explicit and clearer let's think about a
+ 
+
+ align:start position:0%
+explicit and clearer let's think about a
+recursive function on the set of matched
+
+ align:start position:0%
+recursive function on the set of matched
+ 
+
+ align:start position:0%
+recursive function on the set of matched
+brackets this is a some one interesting
+
+ align:start position:0%
+brackets this is a some one interesting
+ 
+
+ align:start position:0%
+brackets this is a some one interesting
+one let's define the depth of a string
+
+ align:start position:0%
+one let's define the depth of a string
+ 
+
+ align:start position:0%
+one let's define the depth of a string
+as follows and the ideas that's how
+
+ align:start position:0%
+as follows and the ideas that's how
+ 
+
+ align:start position:0%
+as follows and the ideas that's how
+deeply nested are they successive pairs
+
+ align:start position:0%
+deeply nested are they successive pairs
+ 
+
+ align:start position:0%
+deeply nested are they successive pairs
+of left and right brackets well the
+
+ align:start position:0%
+of left and right brackets well the
+ 
+
+ align:start position:0%
+of left and right brackets well the
+depth of the empty string is 0 got to
+
+ align:start position:0%
+depth of the empty string is 0 got to
+ 
+
+ align:start position:0%
+depth of the empty string is 0 got to
+start somewhere
+
+ align:start position:0%
+start somewhere
+ 
+
+ align:start position:0%
+start somewhere
+and it's got enough no brackets we'll
+
+ align:start position:0%
+and it's got enough no brackets we'll
+ 
+
+ align:start position:0%
+and it's got enough no brackets we'll
+call it f 0 now what about the depth of
+
+ align:start position:0%
+call it f 0 now what about the depth of
+ 
+
+ align:start position:0%
+call it f 0 now what about the depth of
+the constructor putting brackets around
+
+ align:start position:0%
+the constructor putting brackets around
+ 
+
+ align:start position:0%
+the constructor putting brackets around
+s and then following it by Tay well
+
+ align:start position:0%
+s and then following it by Tay well
+ 
+
+ align:start position:0%
+s and then following it by Tay well
+putting brackets around s gives you a
+
+ align:start position:0%
+putting brackets around s gives you a
+ 
+
+ align:start position:0%
+putting brackets around s gives you a
+string that's one deeper than s is and
+
+ align:start position:0%
+string that's one deeper than s is and
+ 
+
+ align:start position:0%
+string that's one deeper than s is and
+then you follow it by Tay and it's as
+
+ align:start position:0%
+then you follow it by Tay and it's as
+ 
+
+ align:start position:0%
+then you follow it by Tay and it's as
+deep as T is so the result is that the
+
+ align:start position:0%
+deep as T is so the result is that the
+ 
+
+ align:start position:0%
+deep as T is so the result is that the
+depth of the constructor is a string
+
+ align:start position:0%
+depth of the constructor is a string
+ 
+
+ align:start position:0%
+depth of the constructor is a string
+whose which is is a number which is
+
+ align:start position:0%
+whose which is is a number which is
+ 
+
+ align:start position:0%
+whose which is is a number which is
+equal to 1 plus the depth of s and the
+
+ align:start position:0%
+equal to 1 plus the depth of s and the
+ 
+
+ align:start position:0%
+equal to 1 plus the depth of s and the
+depth of T whichever is larger the max
+
+ align:start position:0%
+depth of T whichever is larger the max
+ 
+
+ align:start position:0%
+depth of T whichever is larger the max
+of 1 plus depth of s and depth of T and
+
+ align:start position:0%
+of 1 plus depth of s and depth of T and
+ 
+
+ align:start position:0%
+of 1 plus depth of s and depth of T and
+that's our recursive definition of depth
+
+ align:start position:0%
+that's our recursive definition of depth
+ 
+
+ align:start position:0%
+that's our recursive definition of depth
+let's look at maybe another even more
+
+ align:start position:0%
+let's look at maybe another even more
+ 
+
+ align:start position:0%
+let's look at maybe another even more
+familiar example of a recursive
+
+ align:start position:0%
+familiar example of a recursive
+ 
+
+ align:start position:0%
+familiar example of a recursive
+definition let's define the nth power of
+
+ align:start position:0%
+definition let's define the nth power of
+ 
+
+ align:start position:0%
+definition let's define the nth power of
+a an integer or real number
+
+ align:start position:0%
+a an integer or real number
+ 
+
+ align:start position:0%
+a an integer or real number
+kay the zeroth power of K is defined to
+
+ align:start position:0%
+kay the zeroth power of K is defined to
+ 
+
+ align:start position:0%
+kay the zeroth power of K is defined to
+be one and the n plus first power of K
+
+ align:start position:0%
+be one and the n plus first power of K
+ 
+
+ align:start position:0%
+be one and the n plus first power of K
+is defined to be K times the nth power
+
+ align:start position:0%
+is defined to be K times the nth power
+ 
+
+ align:start position:0%
+is defined to be K times the nth power
+of K and this would be an executable
+
+ align:start position:0%
+of K and this would be an executable
+ 
+
+ align:start position:0%
+of K and this would be an executable
+definition of the exponentiation
+
+ align:start position:0%
+definition of the exponentiation
+ 
+
+ align:start position:0%
+definition of the exponentiation
+function in a lot of programming
+
+ align:start position:0%
+function in a lot of programming
+ 
+
+ align:start position:0%
+function in a lot of programming
+languages and my point here is that this
+
+ align:start position:0%
+languages and my point here is that this
+ 
+
+ align:start position:0%
+languages and my point here is that this
+familiar definition a recursive
+
+ align:start position:0%
+familiar definition a recursive
+ 
+
+ align:start position:0%
+familiar definition a recursive
+definition on a non-negative integer n
+
+ align:start position:0%
+definition on a non-negative integer n
+ 
+
+ align:start position:0%
+definition on a non-negative integer n
+is in fact a structural induction using
+
+ align:start position:0%
+is in fact a structural induction using
+ 
+
+ align:start position:0%
+is in fact a structural induction using
+the fact that the natural numbers are
+
+ align:start position:0%
+the fact that the natural numbers are
+ 
+
+ align:start position:0%
+the fact that the natural numbers are
+sorry that the non-negative integers can
+
+ align:start position:0%
+sorry that the non-negative integers can
+ 
+
+ align:start position:0%
+sorry that the non-negative integers can
+be defined recursively as follows zero
+
+ align:start position:0%
+be defined recursively as follows zero
+ 
+
+ align:start position:0%
+be defined recursively as follows zero
+is a non-negative integer and if N is a
+
+ align:start position:0%
+is a non-negative integer and if N is a
+ 
+
+ align:start position:0%
+is a non-negative integer and if N is a
+non-negative integer then n plus 1 is a
+
+ align:start position:0%
+non-negative integer then n plus 1 is a
+ 
+
+ align:start position:0%
+non-negative integer then n plus 1 is a
+non-negative integer so to summarize the
+
+ align:start position:0%
+non-negative integer so to summarize the
+ 
+
+ align:start position:0%
+non-negative integer so to summarize the
+recipe for a recursive function
+
+ align:start position:0%
+recipe for a recursive function
+ 
+
+ align:start position:0%
+recipe for a recursive function
+definition is you define f going from
+
+ align:start position:0%
+definition is you define f going from
+ 
+
+ align:start position:0%
+definition is you define f going from
+the recursive data type to values
+
+ align:start position:0%
+the recursive data type to values
+ 
+
+ align:start position:0%
+the recursive data type to values
+whatever kind of values you want to
+
+ align:start position:0%
+whatever kind of values you want to
+ 
+
+ align:start position:0%
+whatever kind of values you want to
+assign to these recursive data F of B is
+
+ align:start position:0%
+assign to these recursive data F of B is
+ 
+
+ align:start position:0%
+assign to these recursive data F of B is
+defined directly for the base case B of
+
+ align:start position:0%
+defined directly for the base case B of
+ 
+
+ align:start position:0%
+defined directly for the base case B of
+base cases B and F of the constructor of
+
+ align:start position:0%
+base cases B and F of the constructor of
+ 
+
+ align:start position:0%
+base cases B and F of the constructor of
+X is defined using f of X and X now once
+
+ align:start position:0%
+X is defined using f of X and X now once
+ 
+
+ align:start position:0%
+X is defined using f of X and X now once
+you've gotten a function defined
+
+ align:start position:0%
+you've gotten a function defined
+ 
+
+ align:start position:0%
+you've gotten a function defined
+recursively you could start proving
+
+ align:start position:0%
+recursively you could start proving
+ 
+
+ align:start position:0%
+recursively you could start proving
+things about it by structural induction
+
+ align:start position:0%
+things about it by structural induction
+ 
+
+ align:start position:0%
+things about it by structural induction
+or by induction on its own definition or
+
+ align:start position:0%
+or by induction on its own definition or
+ 
+
+ align:start position:0%
+or by induction on its own definition or
+its own recursive definition so let's
+
+ align:start position:0%
+its own recursive definition so let's
+ 
+
+ align:start position:0%
+its own recursive definition so let's
+look at an example of that I want to
+
+ align:start position:0%
+look at an example of that I want to
+ 
+
+ align:start position:0%
+look at an example of that I want to
+prove the following property of the
+
+ align:start position:0%
+prove the following property of the
+ 
+
+ align:start position:0%
+prove the following property of the
+depth of strings in M namely that if I
+
+ align:start position:0%
+depth of strings in M namely that if I
+ 
+
+ align:start position:0%
+depth of strings in M namely that if I
+look at the length of a string R plus 2
+
+ align:start position:0%
+look at the length of a string R plus 2
+ 
+
+ align:start position:0%
+look at the length of a string R plus 2
+so the brackets around R means the the
+
+ align:start position:0%
+so the brackets around R means the the
+ 
+
+ align:start position:0%
+so the brackets around R means the the
+number of of sorry the vertical bars
+
+ align:start position:0%
+number of of sorry the vertical bars
+ 
+
+ align:start position:0%
+number of of sorry the vertical bars
+around our mean the number of brackets
+
+ align:start position:0%
+around our mean the number of brackets
+ 
+
+ align:start position:0%
+around our mean the number of brackets
+in the string R plus 2 is less than or
+
+ align:start position:0%
+in the string R plus 2 is less than or
+ 
+
+ align:start position:0%
+in the string R plus 2 is less than or
+equal to 2 to the power a depth plus 1
+
+ align:start position:0%
+equal to 2 to the power a depth plus 1
+ 
+
+ align:start position:0%
+equal to 2 to the power a depth plus 1
+twice the 2 to the depths of the string
+
+ align:start position:0%
+twice the 2 to the depths of the string
+ 
+
+ align:start position:0%
+twice the 2 to the depths of the string
+and I want to prove that this holds for
+
+ align:start position:0%
+and I want to prove that this holds for
+ 
+
+ align:start position:0%
+and I want to prove that this holds for
+all strings are of matched brackets and
+
+ align:start position:0%
+all strings are of matched brackets and
+ 
+
+ align:start position:0%
+all strings are of matched brackets and
+I'm going to prove it by structural
+
+ align:start position:0%
+I'm going to prove it by structural
+ 
+
+ align:start position:0%
+I'm going to prove it by structural
+induction and just as a walk through
+
+ align:start position:0%
+induction and just as a walk through
+ 
+
+ align:start position:0%
+induction and just as a walk through
+here's how the proof is going to go
+
+ align:start position:0%
+here's how the proof is going to go
+ 
+
+ align:start position:0%
+here's how the proof is going to go
+let's suppose that r is the base case
+
+ align:start position:0%
+let's suppose that r is the base case
+ 
+
+ align:start position:0%
+let's suppose that r is the base case
+is it the case that this inequality
+
+ align:start position:0%
+is it the case that this inequality
+ 
+
+ align:start position:0%
+is it the case that this inequality
+holds for the empty string well the
+
+ align:start position:0%
+holds for the empty string well the
+ 
+
+ align:start position:0%
+holds for the empty string well the
+length of our is zero so length of our
+
+ align:start position:0%
+length of our is zero so length of our
+ 
+
+ align:start position:0%
+length of our is zero so length of our
+plus two is 2 is 0 plus 2 or 2 which is
+
+ align:start position:0%
+plus two is 2 is 0 plus 2 or 2 which is
+ 
+
+ align:start position:0%
+plus two is 2 is 0 plus 2 or 2 which is
+the same as 2 to the 0 plus 1 which is
+
+ align:start position:0%
+the same as 2 to the 0 plus 1 which is
+ 
+
+ align:start position:0%
+the same as 2 to the 0 plus 1 which is
+in fact equal to 2 to the depth of the
+
+ align:start position:0%
+in fact equal to 2 to the depth of the
+ 
+
+ align:start position:0%
+in fact equal to 2 to the depth of the
+empty string plus 1 so this inequality
+
+ align:start position:0%
+empty string plus 1 so this inequality
+ 
+
+ align:start position:0%
+empty string plus 1 so this inequality
+actually holds as an equality in the
+
+ align:start position:0%
+actually holds as an equality in the
+ 
+
+ align:start position:0%
+actually holds as an equality in the
+base case and we're we're good there but
+
+ align:start position:0%
+base case and we're we're good there but
+ 
+
+ align:start position:0%
+base case and we're we're good there but
+we next leave this show is that this
+
+ align:start position:0%
+we next leave this show is that this
+ 
+
+ align:start position:0%
+we next leave this show is that this
+inequality holds in the constructor case
+
+ align:start position:0%
+inequality holds in the constructor case
+ 
+
+ align:start position:0%
+inequality holds in the constructor case
+so we're looking at a an arbitrary
+
+ align:start position:0%
+so we're looking at a an arbitrary
+ 
+
+ align:start position:0%
+so we're looking at a an arbitrary
+string R that's built out of s and T and
+
+ align:start position:0%
+string R that's built out of s and T and
+ 
+
+ align:start position:0%
+string R that's built out of s and T and
+R is left bracket S right bracket P and
+
+ align:start position:0%
+R is left bracket S right bracket P and
+ 
+
+ align:start position:0%
+R is left bracket S right bracket P and
+I want to show that our satisfies this
+
+ align:start position:0%
+I want to show that our satisfies this
+ 
+
+ align:start position:0%
+I want to show that our satisfies this
+inequality well by induction hypothesis
+
+ align:start position:0%
+inequality well by induction hypothesis
+ 
+
+ align:start position:0%
+inequality well by induction hypothesis
+I can assume the S&T satisfy the
+
+ align:start position:0%
+I can assume the S&T satisfy the
+ 
+
+ align:start position:0%
+I can assume the S&T satisfy the
+inequality so I have that the length of
+
+ align:start position:0%
+inequality so I have that the length of
+ 
+
+ align:start position:0%
+inequality so I have that the length of
+s plus 2 is at most 2 to the depth of s
+
+ align:start position:0%
+s plus 2 is at most 2 to the depth of s
+ 
+
+ align:start position:0%
+s plus 2 is at most 2 to the depth of s
+plus 1 and the length of T plus 2 is at
+
+ align:start position:0%
+plus 1 and the length of T plus 2 is at
+ 
+
+ align:start position:0%
+plus 1 and the length of T plus 2 is at
+most 2 to the depth of T plus 1 and
+
+ align:start position:0%
+most 2 to the depth of T plus 1 and
+ 
+
+ align:start position:0%
+most 2 to the depth of T plus 1 and
+let's just walk through the proof you
+
+ align:start position:0%
+let's just walk through the proof you
+ 
+
+ align:start position:0%
+let's just walk through the proof you
+can slow this down and replay it if need
+
+ align:start position:0%
+can slow this down and replay it if need
+ 
+
+ align:start position:0%
+can slow this down and replay it if need
+be some you're just going to go through
+
+ align:start position:0%
+be some you're just going to go through
+ 
+
+ align:start position:0%
+be some you're just going to go through
+it quickly the length of our plus 2r is
+
+ align:start position:0%
+it quickly the length of our plus 2r is
+ 
+
+ align:start position:0%
+it quickly the length of our plus 2r is
+after all brackets s T so it's simply
+
+ align:start position:0%
+after all brackets s T so it's simply
+ 
+
+ align:start position:0%
+after all brackets s T so it's simply
+the length of that string plus 2 by the
+
+ align:start position:0%
+the length of that string plus 2 by the
+ 
+
+ align:start position:0%
+the length of that string plus 2 by the
+definition of our the length of brackets
+
+ align:start position:0%
+definition of our the length of brackets
+ 
+
+ align:start position:0%
+definition of our the length of brackets
+s T is the length of T plus the length
+
+ align:start position:0%
+s T is the length of T plus the length
+ 
+
+ align:start position:0%
+s T is the length of T plus the length
+of s plus the 2 for the two brackets
+
+ align:start position:0%
+of s plus the 2 for the two brackets
+ 
+
+ align:start position:0%
+of s plus the 2 for the two brackets
+that we've added and so we're plugging
+
+ align:start position:0%
+that we've added and so we're plugging
+ 
+
+ align:start position:0%
+that we've added and so we're plugging
+that in to the previous term and getting
+
+ align:start position:0%
+that in to the previous term and getting
+ 
+
+ align:start position:0%
+that in to the previous term and getting
+that plus 2 then just rearrange the
+
+ align:start position:0%
+that plus 2 then just rearrange the
+ 
+
+ align:start position:0%
+that plus 2 then just rearrange the
+terms it's the same as the size of s
+
+ align:start position:0%
+terms it's the same as the size of s
+ 
+
+ align:start position:0%
+terms it's the same as the size of s
+plus 2 plus the size of T plus 2 and I
+
+ align:start position:0%
+plus 2 plus the size of T plus 2 and I
+ 
+
+ align:start position:0%
+plus 2 plus the size of T plus 2 and I
+arranged it that way because by
+
+ align:start position:0%
+arranged it that way because by
+ 
+
+ align:start position:0%
+arranged it that way because by
+induction hypothesis I know that the
+
+ align:start position:0%
+induction hypothesis I know that the
+ 
+
+ align:start position:0%
+induction hypothesis I know that the
+size of s plus 2 is less than or equal
+
+ align:start position:0%
+size of s plus 2 is less than or equal
+ 
+
+ align:start position:0%
+size of s plus 2 is less than or equal
+to 2 to the depth of s plus 1 and
+
+ align:start position:0%
+to 2 to the depth of s plus 1 and
+ 
+
+ align:start position:0%
+to 2 to the depth of s plus 1 and
+likewise for teh now I just play a nice
+
+ align:start position:0%
+likewise for teh now I just play a nice
+ 
+
+ align:start position:0%
+likewise for teh now I just play a nice
+trick to get these two exponents to look
+
+ align:start position:0%
+trick to get these two exponents to look
+ 
+
+ align:start position:0%
+trick to get these two exponents to look
+alike i I say that the depth of s is
+
+ align:start position:0%
+alike i I say that the depth of s is
+ 
+
+ align:start position:0%
+alike i I say that the depth of s is
+less than or equal to the max of the
+
+ align:start position:0%
+less than or equal to the max of the
+ 
+
+ align:start position:0%
+less than or equal to the max of the
+depth of s and the depth of T likewise
+
+ align:start position:0%
+depth of s and the depth of T likewise
+ 
+
+ align:start position:0%
+depth of s and the depth of T likewise
+for the depth of T so in both of those
+
+ align:start position:0%
+for the depth of T so in both of those
+ 
+
+ align:start position:0%
+for the depth of T so in both of those
+terms here I can replace the exponent or
+
+ align:start position:0%
+terms here I can replace the exponent or
+ 
+
+ align:start position:0%
+terms here I can replace the exponent or
+replace the depth of s by the max
+
+ align:start position:0%
+replace the depth of s by the max
+ 
+
+ align:start position:0%
+replace the depth of s by the max
+of depth SNT and likewise here now I've
+
+ align:start position:0%
+of depth SNT and likewise here now I've
+ 
+
+ align:start position:0%
+of depth SNT and likewise here now I've
+got the same term twice so I can say
+
+ align:start position:0%
+got the same term twice so I can say
+ 
+
+ align:start position:0%
+got the same term twice so I can say
+that it's simply twice the max depth and
+
+ align:start position:0%
+that it's simply twice the max depth and
+ 
+
+ align:start position:0%
+that it's simply twice the max depth and
+of course that is equal to by definition
+
+ align:start position:0%
+of course that is equal to by definition
+ 
+
+ align:start position:0%
+of course that is equal to by definition
+of the depth of our twice to to the
+
+ align:start position:0%
+of the depth of our twice to to the
+ 
+
+ align:start position:0%
+of the depth of our twice to to the
+depth of our which is of course two to
+
+ align:start position:0%
+depth of our which is of course two to
+ 
+
+ align:start position:0%
+depth of our which is of course two to
+the depth of our plus 1 and I have by
+
+ align:start position:0%
+the depth of our plus 1 and I have by
+ 
+
+ align:start position:0%
+the depth of our plus 1 and I have by
+more or less automatically plugging into
+
+ align:start position:0%
+more or less automatically plugging into
+ 
+
+ align:start position:0%
+more or less automatically plugging into
+the definitions and a structural
+
+ align:start position:0%
+the definitions and a structural
+ 
+
+ align:start position:0%
+the definitions and a structural
+induction I've proved that this
+
+ align:start position:0%
+induction I've proved that this
+ 
+
+ align:start position:0%
+induction I've proved that this
+inequality holds for the recursively
+
+ align:start position:0%
+inequality holds for the recursively
+ 
+
+ align:start position:0%
+inequality holds for the recursively
+defined depth function and we're done
+
+ align:start position:0%
+defined depth function and we're done
+ 
+
+ align:start position:0%
+defined depth function and we're done
+let's look at one more familiar example
+
+ align:start position:0%
+let's look at one more familiar example
+ 
+
+ align:start position:0%
+let's look at one more familiar example
+I want to give a recursive definition of
+
+ align:start position:0%
+I want to give a recursive definition of
+ 
+
+ align:start position:0%
+I want to give a recursive definition of
+the positive powers of two so the base
+
+ align:start position:0%
+the positive powers of two so the base
+ 
+
+ align:start position:0%
+the positive powers of two so the base
+case is that 2 is a positive power of 2
+
+ align:start position:0%
+case is that 2 is a positive power of 2
+ 
+
+ align:start position:0%
+case is that 2 is a positive power of 2
+and the constructor is just one
+
+ align:start position:0%
+and the constructor is just one
+ 
+
+ align:start position:0%
+and the constructor is just one
+constructor I'm going to use that if x
+
+ align:start position:0%
+constructor I'm going to use that if x
+ 
+
+ align:start position:0%
+constructor I'm going to use that if x
+and y are positive powers of 2 then
+
+ align:start position:0%
+and y are positive powers of 2 then
+ 
+
+ align:start position:0%
+and y are positive powers of 2 then
+their product is a positive power of 2
+
+ align:start position:0%
+their product is a positive power of 2
+ 
+
+ align:start position:0%
+their product is a positive power of 2
+so let's look at some examples I can
+
+ align:start position:0%
+so let's look at some examples I can
+ 
+
+ align:start position:0%
+so let's look at some examples I can
+start with 2 and then the only thing I
+
+ align:start position:0%
+start with 2 and then the only thing I
+ 
+
+ align:start position:0%
+start with 2 and then the only thing I
+can do as a constructor is multiply 2 by
+
+ align:start position:0%
+can do as a constructor is multiply 2 by
+ 
+
+ align:start position:0%
+can do as a constructor is multiply 2 by
+2 to get 4 once I got 4 I can do 4 times
+
+ align:start position:0%
+2 to get 4 once I got 4 I can do 4 times
+ 
+
+ align:start position:0%
+2 to get 4 once I got 4 I can do 4 times
+2 to get 8 and I can do 4 times 4 to get
+
+ align:start position:0%
+2 to get 8 and I can do 4 times 4 to get
+ 
+
+ align:start position:0%
+2 to get 8 and I can do 4 times 4 to get
+16 and I can do 4 times 8 to get 32 and
+
+ align:start position:0%
+16 and I can do 4 times 8 to get 32 and
+ 
+
+ align:start position:0%
+16 and I can do 4 times 8 to get 32 and
+all of these are positive powers of 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's define the log to the base 2
+
+ align:start position:0%
+now let's define the log to the base 2
+ 
+
+ align:start position:0%
+now let's define the log to the base 2
+of a positive power of tow recursively
+
+ align:start position:0%
+of a positive power of tow recursively
+ 
+
+ align:start position:0%
+of a positive power of tow recursively
+well the log to the base 2 of 2 is 1 I'd
+
+ align:start position:0%
+well the log to the base 2 of 2 is 1 I'd
+ 
+
+ align:start position:0%
+well the log to the base 2 of 2 is 1 I'd
+have to define log to the base 2 in the
+
+ align:start position:0%
+have to define log to the base 2 in the
+ 
+
+ align:start position:0%
+have to define log to the base 2 in the
+base case and that's easy to do what
+
+ align:start position:0%
+base case and that's easy to do what
+ 
+
+ align:start position:0%
+base case and that's easy to do what
+about in the constructor case well the
+
+ align:start position:0%
+about in the constructor case well the
+ 
+
+ align:start position:0%
+about in the constructor case well the
+log to the base 2 of X Y is equal to the
+
+ align:start position:0%
+log to the base 2 of X Y is equal to the
+ 
+
+ align:start position:0%
+log to the base 2 of X Y is equal to the
+log to the base 2 of X plus the log to
+
+ align:start position:0%
+log to the base 2 of X plus the log to
+ 
+
+ align:start position:0%
+log to the base 2 of X plus the log to
+the base 2 of Y for all the X why's that
+
+ align:start position:0%
+the base 2 of Y for all the X why's that
+ 
+
+ align:start position:0%
+the base 2 of Y for all the X why's that
+are positive powers of 2 and so I have
+
+ align:start position:0%
+are positive powers of 2 and so I have
+ 
+
+ align:start position:0%
+are positive powers of 2 and so I have
+defined log of the constructor X Y in
+
+ align:start position:0%
+defined log of the constructor X Y in
+ 
+
+ align:start position:0%
+defined log of the constructor X Y in
+terms of the function log of X and the
+
+ align:start position:0%
+terms of the function log of X and the
+ 
+
+ align:start position:0%
+terms of the function log of X and the
+function log applied to Y it conforms to
+
+ align:start position:0%
+function log applied to Y it conforms to
+ 
+
+ align:start position:0%
+function log applied to Y it conforms to
+the standard definition of
+
+ align:start position:0%
+the standard definition of
+ 
+
+ align:start position:0%
+the standard definition of
+a recursive function on a recursively
+
+ align:start position:0%
+a recursive function on a recursively
+ 
+
+ align:start position:0%
+a recursive function on a recursively
+defined data type the positive powers of
+
+ align:start position:0%
+defined data type the positive powers of
+ 
+
+ align:start position:0%
+defined data type the positive powers of
+two this looks okay let's just check it
+
+ align:start position:0%
+two this looks okay let's just check it
+ 
+
+ align:start position:0%
+two this looks okay let's just check it
+out so log of four is log of 2 times two
+
+ align:start position:0%
+out so log of four is log of 2 times two
+ 
+
+ align:start position:0%
+out so log of four is log of 2 times two
+which is by the by that definition of
+
+ align:start position:0%
+which is by the by that definition of
+ 
+
+ align:start position:0%
+which is by the by that definition of
+log the log of 2 plus the log of 2 which
+
+ align:start position:0%
+log the log of 2 plus the log of 2 which
+ 
+
+ align:start position:0%
+log the log of 2 plus the log of 2 which
+is 1 plus 1 which is equal to 2 and
+
+ align:start position:0%
+is 1 plus 1 which is equal to 2 and
+ 
+
+ align:start position:0%
+is 1 plus 1 which is equal to 2 and
+guess what that's correct the log of 8
+
+ align:start position:0%
+guess what that's correct the log of 8
+ 
+
+ align:start position:0%
+guess what that's correct the log of 8
+well 8 is 2 times 4 so by the recursive
+
+ align:start position:0%
+well 8 is 2 times 4 so by the recursive
+ 
+
+ align:start position:0%
+well 8 is 2 times 4 so by the recursive
+definition that's the log of 2 plus the
+
+ align:start position:0%
+definition that's the log of 2 plus the
+ 
+
+ align:start position:0%
+definition that's the log of 2 plus the
+log of 4 which we previously figured out
+
+ align:start position:0%
+log of 4 which we previously figured out
+ 
+
+ align:start position:0%
+log of 4 which we previously figured out
+log of 4 was 2 so we get 3 and the
+
+ align:start position:0%
+log of 4 was 2 so we get 3 and the
+ 
+
+ align:start position:0%
+log of 4 was 2 so we get 3 and the
+answer comes out right now remember
+
+ align:start position:0%
+answer comes out right now remember
+ 
+
+ align:start position:0%
+answer comes out right now remember
+you're not supposed to end this
+
+ align:start position:0%
+you're not supposed to end this
+ 
+
+ align:start position:0%
+you're not supposed to end this
+reasoning use the properties that you
+
+ align:start position:0%
+reasoning use the properties that you
+ 
+
+ align:start position:0%
+reasoning use the properties that you
+know that log to the base 2 has because
+
+ align:start position:0%
+know that log to the base 2 has because
+ 
+
+ align:start position:0%
+know that log to the base 2 has because
+we're defining this function which were
+
+ align:start position:0%
+we're defining this function which were
+ 
+
+ align:start position:0%
+we're defining this function which were
+calling log to the base 2 and implicitly
+
+ align:start position:0%
+calling log to the base 2 and implicitly
+ 
+
+ align:start position:0%
+calling log to the base 2 and implicitly
+claiming that it's right but in order to
+
+ align:start position:0%
+claiming that it's right but in order to
+ 
+
+ align:start position:0%
+claiming that it's right but in order to
+prove that it's right we need to be
+
+ align:start position:0%
+prove that it's right we need to be
+ 
+
+ align:start position:0%
+prove that it's right we need to be
+using just the the structural definition
+
+ align:start position:0%
+using just the the structural definition
+ 
+
+ align:start position:0%
+using just the the structural definition
+of log to the base 2 to prove its
+
+ align:start position:0%
+of log to the base 2 to prove its
+ 
+
+ align:start position:0%
+of log to the base 2 to prove its
+properties so that was what I was
+
+ align:start position:0%
+properties so that was what I was
+ 
+
+ align:start position:0%
+properties so that was what I was
+illustrating with this reasoning that
+
+ align:start position:0%
+illustrating with this reasoning that
+ 
+
+ align:start position:0%
+illustrating with this reasoning that
+just plugging in the the constructor
+
+ align:start position:0%
+just plugging in the the constructor
+ 
+
+ align:start position:0%
+just plugging in the the constructor
+case of log of X Y as log of X plus log
+
+ align:start position:0%
+case of log of X Y as log of X plus log
+ 
+
+ align:start position:0%
+case of log of X Y as log of X plus log
+of Y I can get these numbers out so the
+
+ align:start position:0%
+of Y I can get these numbers out so the
+ 
+
+ align:start position:0%
+of Y I can get these numbers out so the
+point of this is just to make the
+
+ align:start position:0%
+point of this is just to make the
+ 
+
+ align:start position:0%
+point of this is just to make the
+following definition look reasonable I'm
+
+ align:start position:0%
+following definition look reasonable I'm
+ 
+
+ align:start position:0%
+following definition look reasonable I'm
+going to define a new function which I'm
+
+ align:start position:0%
+going to define a new function which I'm
+ 
+
+ align:start position:0%
+going to define a new function which I'm
+going to call the log e function
+
+ align:start position:0%
+going to call the log e function
+ 
+
+ align:start position:0%
+going to call the log e function
+it's another function on the positive
+
+ align:start position:0%
+it's another function on the positive
+ 
+
+ align:start position:0%
+it's another function on the positive
+powers of 2 and here's the definition of
+
+ align:start position:0%
+powers of 2 and here's the definition of
+ 
+
+ align:start position:0%
+powers of 2 and here's the definition of
+the log e function the log e of 2 is
+
+ align:start position:0%
+the log e function the log e of 2 is
+ 
+
+ align:start position:0%
+the log e function the log e of 2 is
+going to be one just as the log is but
+
+ align:start position:0%
+going to be one just as the log is but
+ 
+
+ align:start position:0%
+going to be one just as the log is but
+the log e of XY is gonna be X plus the
+
+ align:start position:0%
+the log e of XY is gonna be X plus the
+ 
+
+ align:start position:0%
+the log e of XY is gonna be X plus the
+log e of Y for all X Y in positive
+
+ align:start position:0%
+log e of Y for all X Y in positive
+ 
+
+ align:start position:0%
+log e of Y for all X Y in positive
+powers of 2 well let's try that
+
+ align:start position:0%
+powers of 2 well let's try that
+ 
+
+ align:start position:0%
+powers of 2 well let's try that
+definition log e of 4 is log you have 2
+
+ align:start position:0%
+definition log e of 4 is log you have 2
+ 
+
+ align:start position:0%
+definition log e of 4 is log you have 2
+times 2 which according to the recursive
+
+ align:start position:0%
+times 2 which according to the recursive
+ 
+
+ align:start position:0%
+times 2 which according to the recursive
+definition is 2 plus the log e of 2
+
+ align:start position:0%
+definition is 2 plus the log e of 2
+ 
+
+ align:start position:0%
+definition is 2 plus the log e of 2
+which is 1 namely it's 3 ok log e of 8
+
+ align:start position:0%
+which is 1 namely it's 3 ok log e of 8
+ 
+
+ align:start position:0%
+which is 1 namely it's 3 ok log e of 8
+well 8 is 2 times 4 so the log e of 8 is
+
+ align:start position:0%
+well 8 is 2 times 4 so the log e of 8 is
+ 
+
+ align:start position:0%
+well 8 is 2 times 4 so the log e of 8 is
+2 plus the log e of 4 we just figured
+
+ align:start position:0%
+2 plus the log e of 4 we just figured
+ 
+
+ align:start position:0%
+2 plus the log e of 4 we just figured
+out that the loggia 4 was 3 so it's 2
+
+ align:start position:0%
+out that the loggia 4 was 3 so it's 2
+ 
+
+ align:start position:0%
+out that the loggia 4 was 3 so it's 2
+plus 3 is 5
+
+ align:start position:0%
+plus 3 is 5
+ 
+
+ align:start position:0%
+plus 3 is 5
+G of 8 is 5 and finally log e of 16 well
+
+ align:start position:0%
+G of 8 is 5 and finally log e of 16 well
+ 
+
+ align:start position:0%
+G of 8 is 5 and finally log e of 16 well
+16 is 8 times 2 so the log e of 8 times
+
+ align:start position:0%
+16 is 8 times 2 so the log e of 8 times
+ 
+
+ align:start position:0%
+16 is 8 times 2 so the log e of 8 times
+2 is 8 plus the log e of 2 which we know
+
+ align:start position:0%
+2 is 8 plus the log e of 2 which we know
+ 
+
+ align:start position:0%
+2 is 8 plus the log e of 2 which we know
+is 1 it's 9 so we've just figured out
+
+ align:start position:0%
+is 1 it's 9 so we've just figured out
+ 
+
+ align:start position:0%
+is 1 it's 9 so we've just figured out
+the log e of 16 is 9 but but now comes
+
+ align:start position:0%
+the log e of 16 is 9 but but now comes
+ 
+
+ align:start position:0%
+the log e of 16 is 9 but but now comes
+the problem 16 of course is not only 8
+
+ align:start position:0%
+the problem 16 of course is not only 8
+ 
+
+ align:start position:0%
+the problem 16 of course is not only 8
+times 2 but it's 2 times 8 and so the
+
+ align:start position:0%
+times 2 but it's 2 times 8 and so the
+ 
+
+ align:start position:0%
+times 2 but it's 2 times 8 and so the
+log e of 2 times 8 is 2 plus the log e
+
+ align:start position:0%
+log e of 2 times 8 is 2 plus the log e
+ 
+
+ align:start position:0%
+log e of 2 times 8 is 2 plus the log e
+of 8 log e of 8 we previously figured
+
+ align:start position:0%
+of 8 log e of 8 we previously figured
+ 
+
+ align:start position:0%
+of 8 log e of 8 we previously figured
+out was 5 so the log e of 16 is 7 and
+
+ align:start position:0%
+out was 5 so the log e of 16 is 7 and
+ 
+
+ align:start position:0%
+out was 5 so the log e of 16 is 7 and
+now I have an inconsistency I have used
+
+ align:start position:0%
+now I have an inconsistency I have used
+ 
+
+ align:start position:0%
+now I have an inconsistency I have used
+this recursive definition of log E to
+
+ align:start position:0%
+this recursive definition of log E to
+ 
+
+ align:start position:0%
+this recursive definition of log E to
+conclude that the log e of 16 is both 9
+
+ align:start position:0%
+conclude that the log e of 16 is both 9
+ 
+
+ align:start position:0%
+conclude that the log e of 16 is both 9
+and 7 and we got a problem it's not a
+
+ align:start position:0%
+and 7 and we got a problem it's not a
+ 
+
+ align:start position:0%
+and 7 and we got a problem it's not a
+good definition of a function the
+
+ align:start position:0%
+good definition of a function the
+ 
+
+ align:start position:0%
+good definition of a function the
+problem is a simple one called ambiguity
+
+ align:start position:0%
+problem is a simple one called ambiguity
+ 
+
+ align:start position:0%
+problem is a simple one called ambiguity
+there's more than one way to construct
+
+ align:start position:0%
+there's more than one way to construct
+ 
+
+ align:start position:0%
+there's more than one way to construct
+the elements of pp2 of positive powers
+
+ align:start position:0%
+the elements of pp2 of positive powers
+ 
+
+ align:start position:0%
+the elements of pp2 of positive powers
+of 2 from the constructor x times y 16
+
+ align:start position:0%
+of 2 from the constructor x times y 16
+ 
+
+ align:start position:0%
+of 2 from the constructor x times y 16
+was 8 times 2 but it's also 2 times 8
+
+ align:start position:0%
+was 8 times 2 but it's also 2 times 8
+ 
+
+ align:start position:0%
+was 8 times 2 but it's also 2 times 8
+and of course it's also 4 times 4 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depending on which constructor you use
+
+ align:start position:0%
+depending on which constructor you use
+ 
+
+ align:start position:0%
+depending on which constructor you use
+to construct 16 you're going to get out
+
+ align:start position:0%
+to construct 16 you're going to get out
+ 
+
+ align:start position:0%
+to construct 16 you're going to get out
+different values assigned to the log e
+
+ align:start position:0%
+different values assigned to the log e
+ 
+
+ align:start position:0%
+different values assigned to the log e
+function so when you have an ambiguously
+
+ align:start position:0%
+function so when you have an ambiguously
+ 
+
+ align:start position:0%
+function so when you have an ambiguously
+defined recursive data structure for
+
+ align:start position:0%
+defined recursive data structure for
+ 
+
+ align:start position:0%
+defined recursive data structure for
+example F 18 is very ambiguous then
+
+ align:start position:0%
+example F 18 is very ambiguous then
+ 
+
+ align:start position:0%
+example F 18 is very ambiguous then
+defining a function defining recursive
+
+ align:start position:0%
+defining a function defining recursive
+ 
+
+ align:start position:0%
+defining a function defining recursive
+functions on that definition is not
+
+ align:start position:0%
+functions on that definition is not
+ 
+
+ align:start position:0%
+functions on that definition is not
+going to work well and you have to very
+
+ align:start position:0%
+going to work well and you have to very
+ 
+
+ align:start position:0%
+going to work well and you have to very
+carefully prove that if a recursive
+
+ align:start position:0%
+carefully prove that if a recursive
+ 
+
+ align:start position:0%
+carefully prove that if a recursive
+definition actually works in his
+
+ align:start position:0%
+definition actually works in his
+ 
+
+ align:start position:0%
+definition actually works in his
+single-valued so for example log to the
+
+ align:start position:0%
+single-valued so for example log to the
+ 
+
+ align:start position:0%
+single-valued so for example log to the
+base 2 does work but that would require
+
+ align:start position:0%
+base 2 does work but that would require
+ 
+
+ align:start position:0%
+base 2 does work but that would require
+proof it doesn't follow on general
+
+ align:start position:0%
+proof it doesn't follow on general
+ 
+
+ align:start position:0%
+proof it doesn't follow on general
+principles when you define a recursive
+
+ align:start position:0%
+principles when you define a recursive
+ 
+
+ align:start position:0%
+principles when you define a recursive
+function on a an ambiguous data type
+
+ align:start position:0%
+function on a an ambiguous data type
+ 
+
+ align:start position:0%
+function on a an ambiguous data type
+I mean only hand the reason why we chose
+
+ align:start position:0%
+I mean only hand the reason why we chose
+ 
+
+ align:start position:0%
+I mean only hand the reason why we chose
+that somewhat unexpected single
+
+ align:start position:0%
+that somewhat unexpected single
+ 
+
+ align:start position:0%
+that somewhat unexpected single
+constructor for the balanced strings am
+
+ align:start position:0%
+constructor for the balanced strings am
+ 
+
+ align:start position:0%
+constructor for the balanced strings am
+ballast the balanced bracket strings was
+
+ align:start position:0%
+ballast the balanced bracket strings was
+ 
+
+ align:start position:0%
+ballast the balanced bracket strings was
+that it turns out
+
+ align:start position:0%
+that it turns out
+ 
+
+ align:start position:0%
+that it turns out
+be unambiguous and so that definition of
+
+ align:start position:0%
+be unambiguous and so that definition of
+ 
+
+ align:start position:0%
+be unambiguous and so that definition of
+depth is a good definition as is any
+
+ align:start position:0%
+depth is a good definition as is any
+ 
+
+ align:start position:0%
+depth is a good definition as is any
+definition based on the recursive
+
+ align:start position:0%
+definition based on the recursive
+ 
+
+ align:start position:0%
+definition based on the recursive
+definition of the set M so the general
+
+ align:start position:0%
+definition of the set M so the general
+ 
+
+ align:start position:0%
+definition of the set M so the general
+problem we have to watch out for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructor created the datum II if
+
+ align:start position:0%
+instructor created the datum II if
+ 
+
+ align:start position:0%
+instructor created the datum II if
+there's more than one way to construct e
+
+ align:start position:0%
+there's more than one way to construct e
+ 
+
+ align:start position:0%
+there's more than one way to construct e
+then you're gonna you're not quite sure
+
+ align:start position:0%
+then you're gonna you're not quite sure
+ 
+
+ align:start position:0%
+then you're gonna you're not quite sure
+which case to use to define the function
+
+ align:start position:0%
+which case to use to define the function
+ 
+
+ align:start position:0%
+which case to use to define the function
+f and that's why this issue of whether
+
+ align:start position:0%
+f and that's why this issue of whether
+ 
+
+ align:start position:0%
+f and that's why this issue of whether
+or not the data structures ambiguous is
+
+ align:start position:0%
+or not the data structures ambiguous is
+ 
+
+ align:start position:0%
+or not the data structures ambiguous is
+critical to getting good definitions of
+
+ align:start position:0%
+critical to getting good definitions of
+ 
+
+ align:start position:0%
+critical to getting good definitions of
+recursive functions
\ No newline at end of file
diff --git a/tYkr4jMSOFg.txt b/tYkr4jMSOFg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1be95bb787baeab6ee39253ee48822dfe74bea61
--- /dev/null
+++ b/tYkr4jMSOFg.txt
@@ -0,0 +1,206 @@
+PHIL: I mean everyone will
+probably eat lunch.
+
+It's just a matter of where they
+eat it and who they eat
+
+it with and if they
+pay for it.
+
+I mean, I'm sure everyone's
+going to eat lunch on a day,
+
+but some are going to have
+to buy their own.
+
+Some are going to be
+dining with me.
+
+[MUSIC PLAYING]
+
+NARRATOR: Yesterday in 5.301,
+the students set up their
+
+crystal growing experiments,
+and some are growing fast.
+
+JULIE: My crystal was
+the first to form.
+
+I think this is the largest
+one I've seen so far.
+
+So I thought I had won.
+
+JOHN DOLHUN: Well, Julie
+did get her crystal.
+
+So I saw it with my own eyes.
+
+NARRATOR: Other crystals are
+growing too, but their owner
+
+isn't looking.
+
+When Jason finally checks up
+on his crystals, they're
+
+looking good.
+
+TENGFEI: In this well, we have
+several a single crystals, and
+
+they are all big.
+
+JASON: She had a crystal first,
+but I haven't been
+
+checking mine daily.
+
+So I might have a
+crystal first.
+
+I don't know.
+
+TENGFEI: Congratulations.
+
+JASON: Thank you.
+
+JULIE: I had a single crystal.
+
+JASON: But I had multiple
+single crystals.
+
+JULIE: What?
+
+JASON: I had multiple
+single crystals.
+
+JULIE: But my crystal
+came first.
+
+JASON:
+
+JULIE: I'm not going
+to bring it up.
+
+I'm still the winner
+as of right now.
+
+JASON: I'm gonna bring it up.
+
+I won.
+
+I had the largest crystal.
+
+I just didn't check it because
+I didn't want to disturb it.
+
+Mine is definitely
+bigger, clearly.
+
+JULIE: OK, but mine crystallized
+like made a
+
+single crystal first.
+
+JASON: And like Julie was like,
+I won, I won, I won.
+
+I've got this tiny
+little crystal.
+
+I just got it first.
+
+No.
+
+The competition was the largest
+
+crystal in one week period.
+
+So I checked after one week.
+
+JULIE: His fault for not talking
+to Dr. Dolhun earlier.
+
+So--
+
+JASON: If I would have just like
+looked at it earlier and
+
+told Dr. Dolhun earlier, I have
+a crystal growing, then I
+
+would have won.
+
+JOHN DOLHUN: But you see
+yeah, Jason, if you
+
+would have came forward--
+
+JASON: I checked mine later.
+
+And then I told Dr. Dolhun.
+
+He was like, yeah,
+but Julie won.
+
+JOHN DOLHUN: We've already
+declared a winner here.
+
+JULIE: Mine.
+
+Fantastic.
+
+JASON: Julie rubs it in
+my face all the time.
+
+JULIE: I mean, I was already
+declared the winner, so he
+
+can't, yeah.
+
+He's honorable mention.
+
+NARRATOR: So Julie wins the
+prize, lunch for her and a
+
+friend or so she thinks.
+
+PHIL: They both grew really
+beautiful single crystals.
+
+So the whole class got to enjoy
+a lunch with the TAs and
+
+the instructor.
+
+PHIL: We ended up going to
+Chinatown for dim sum.
+
+And I have actually never
+tried dim sum before.
+
+So I got to try a lot
+of new foods,
+
+chicken feet, and tripe.
+
+JASON: It's basically
+the lining of a
+
+cow's stomach, I think.
+
+PHIL: It was good.
+
+It was good.
+
+I always enjoy trying new
+food, so everyone had
+
+a really good time.
+
+I've never felt so close to
+dying in my entire life.
+
+[MUSIC PLAYING]
\ No newline at end of file
diff --git a/ttuvXdZNcDM.txt b/ttuvXdZNcDM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a3652ba3fb41c5c1fa0d55f927684d758d95ff65
--- /dev/null
+++ b/ttuvXdZNcDM.txt
@@ -0,0 +1,291 @@
+align:start position:0%
+ 
+basically just a programmable visualizer
+
+ align:start position:0%
+basically just a programmable visualizer
+ 
+
+ align:start position:0%
+basically just a programmable visualizer
+that uses an LED array and ugly no so
+
+ align:start position:0%
+that uses an LED array and ugly no so
+ 
+
+ align:start position:0%
+that uses an LED array and ugly no so
+basically we wanted to be able to have
+
+ align:start position:0%
+basically we wanted to be able to have
+ 
+
+ align:start position:0%
+basically we wanted to be able to have
+cool modern art that's moving with our
+
+ align:start position:0%
+cool modern art that's moving with our
+ 
+
+ align:start position:0%
+cool modern art that's moving with our
+loss and it can display what sorts of
+
+ align:start position:0%
+loss and it can display what sorts of
+ 
+
+ align:start position:0%
+loss and it can display what sorts of
+things basically anything we wanted to
+
+ align:start position:0%
+things basically anything we wanted to
+ 
+
+ align:start position:0%
+things basically anything we wanted to
+but for now we'll just do a little demo
+
+ align:start position:0%
+but for now we'll just do a little demo
+ 
+
+ align:start position:0%
+but for now we'll just do a little demo
+the Lord it looks like we kind of a
+
+ align:start position:0%
+the Lord it looks like we kind of a
+ 
+
+ align:start position:0%
+the Lord it looks like we kind of a
+really colorful pattern and these are of
+
+ align:start position:0%
+really colorful pattern and these are of
+ 
+
+ align:start position:0%
+really colorful pattern and these are of
+course separate ones so they're not
+
+ align:start position:0%
+course separate ones so they're not
+ 
+
+ align:start position:0%
+course separate ones so they're not
+connected to just one are do you know
+
+ align:start position:0%
+connected to just one are do you know
+ 
+
+ align:start position:0%
+connected to just one are do you know
+because we all wanted to take one home
+
+ align:start position:0%
+because we all wanted to take one home
+ 
+
+ align:start position:0%
+because we all wanted to take one home
+they're also four of us in the group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so I mean kind of variations I wanted
+
+ align:start position:0%
+so I mean kind of variations I wanted
+ 
+
+ align:start position:0%
+so I mean kind of variations I wanted
+this is like a standalone this is like
+
+ align:start position:0%
+this is like a standalone this is like
+ 
+
+ align:start position:0%
+this is like a standalone this is like
+one of the bigger versions and then
+
+ align:start position:0%
+one of the bigger versions and then
+ 
+
+ align:start position:0%
+one of the bigger versions and then
+these are my kind of smaller versions
+
+ align:start position:0%
+these are my kind of smaller versions
+ 
+
+ align:start position:0%
+these are my kind of smaller versions
+that can be I guess these three can face
+
+ align:start position:0%
+that can be I guess these three can face
+ 
+
+ align:start position:0%
+that can be I guess these three can face
+up photo frames and you can program on
+
+ align:start position:0%
+up photo frames and you can program on
+ 
+
+ align:start position:0%
+up photo frames and you can program on
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so we're exploring some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I think I'll just put Pryor
+
+ align:start position:0%
+so I think I'll just put Pryor
+ 
+
+ align:start position:0%
+so I think I'll just put Pryor
+you like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not great like resolution just
+
+ align:start position:0%
+it's not great like resolution just
+ 
+
+ align:start position:0%
+it's not great like resolution just
+like one led per square inch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's cool under fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah the original time is activated
+
+ align:start position:0%
+oh yeah the original time is activated
+ 
+
+ align:start position:0%
+oh yeah the original time is activated
+in the frame were thrust of blacks but
+
+ align:start position:0%
+in the frame were thrust of blacks but
+ 
+
+ align:start position:0%
+in the frame were thrust of blacks but
+they were ordered I don't think they can
+
+ align:start position:0%
+they were ordered I don't think they can
+ 
+
+ align:start position:0%
+they were ordered I don't think they can
+even though unfortunately but this will
+
+ align:start position:0%
+even though unfortunately but this will
+ 
+
+ align:start position:0%
+even though unfortunately but this will
+do but it's cool because we'll be able
+
+ align:start position:0%
+do but it's cool because we'll be able
+ 
+
+ align:start position:0%
+do but it's cool because we'll be able
+to use these for you know anything from
+
+ align:start position:0%
+to use these for you know anything from
+ 
+
+ align:start position:0%
+to use these for you know anything from
+danger visualization next arts or
+
+ align:start position:0%
+danger visualization next arts or
+ 
+
+ align:start position:0%
+danger visualization next arts or
+something for just like nice artwork if
+
+ align:start position:0%
+something for just like nice artwork if
+ 
+
+ align:start position:0%
+something for just like nice artwork if
+you draw on the paper as well
+
+ align:start position:0%
+you draw on the paper as well
+ 
+
+ align:start position:0%
+you draw on the paper as well
+and fill it in with
\ No newline at end of file
diff --git a/v90JNWCTupk.txt b/v90JNWCTupk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c65b6bbf7c841612b6fabeb1b74cc8fedfd9bb89
--- /dev/null
+++ b/v90JNWCTupk.txt
@@ -0,0 +1,1563 @@
+align:start position:0%
+ 
+Hi, welcome back to recitation. We've
+
+ align:start position:0%
+Hi, welcome back to recitation. We've
+ 
+
+ align:start position:0%
+Hi, welcome back to recitation. We've
+been talking in lecture about
+
+ align:start position:0%
+been talking in lecture about
+ 
+
+ align:start position:0%
+been talking in lecture about
+anti-derivatives. So I have here a
+
+ align:start position:0%
+anti-derivatives. So I have here a
+ 
+
+ align:start position:0%
+anti-derivatives. So I have here a
+problem for you, just an exercise about
+
+ align:start position:0%
+problem for you, just an exercise about
+ 
+
+ align:start position:0%
+problem for you, just an exercise about
+computing an anti-derivative. So the
+
+ align:start position:0%
+computing an anti-derivative. So the
+ 
+
+ align:start position:0%
+computing an anti-derivative. So the
+question is to compute an
+
+ align:start position:0%
+question is to compute an
+ 
+
+ align:start position:0%
+question is to compute an
+anti-derivative of this big fraction. So
+
+ align:start position:0%
+anti-derivative of this big fraction. So
+ 
+
+ align:start position:0%
+anti-derivative of this big fraction. So
+it on top it's got x 8 + 2x cubed - x
+
+ align:start position:0%
+it on top it's got x 8 + 2x cubed - x
+ 
+
+ align:start position:0%
+it on top it's got x 8 + 2x cubed - x
+2/3 - 3 that whole thing over x^2.
+
+ align:start position:0%
+2/3 - 3 that whole thing over x^2.
+ 
+
+ align:start position:0%
+2/3 - 3 that whole thing over x^2.
+So just a a quick linguistic note about
+
+ align:start position:0%
+So just a a quick linguistic note about
+ 
+
+ align:start position:0%
+So just a a quick linguistic note about
+about why I said an anti-derivatives
+
+ align:start position:0%
+about why I said an anti-derivatives
+ 
+
+ align:start position:0%
+about why I said an anti-derivatives
+instead of the anti-derivative and then
+
+ align:start position:0%
+instead of the anti-derivative and then
+ 
+
+ align:start position:0%
+instead of the anti-derivative and then
+I'll I'll let you work on it a little.
+
+ align:start position:0%
+I'll I'll let you work on it a little.
+ 
+
+ align:start position:0%
+I'll I'll let you work on it a little.
+So an anti-derivative there are many
+
+ align:start position:0%
+So an anti-derivative there are many
+ 
+
+ align:start position:0%
+So an anti-derivative there are many
+functions whose whose derivative is is
+
+ align:start position:0%
+functions whose whose derivative is is
+ 
+
+ align:start position:0%
+functions whose whose derivative is is
+this function right? So, so they all
+
+ align:start position:0%
+this function right? So, so they all
+ 
+
+ align:start position:0%
+this function right? So, so they all
+differ from each other by by constants,
+
+ align:start position:0%
+differ from each other by by constants,
+ 
+
+ align:start position:0%
+differ from each other by by constants,
+but but um so you know I would be happy
+
+ align:start position:0%
+but but um so you know I would be happy
+ 
+
+ align:start position:0%
+but but um so you know I would be happy
+with any one as an answer to this
+
+ align:start position:0%
+with any one as an answer to this
+ 
+
+ align:start position:0%
+with any one as an answer to this
+question. That's why I chose the the
+
+ align:start position:0%
+question. That's why I chose the the
+ 
+
+ align:start position:0%
+question. That's why I chose the the
+word an anti-derivant and
+
+ align:start position:0%
+word an anti-derivant and
+ 
+
+ align:start position:0%
+word an anti-derivant and
+anti-derivative. So I'm looking for a
+
+ align:start position:0%
+anti-derivative. So I'm looking for a
+ 
+
+ align:start position:0%
+anti-derivative. So I'm looking for a
+function whose derivative is equal to
+
+ align:start position:0%
+function whose derivative is equal to
+ 
+
+ align:start position:0%
+function whose derivative is equal to
+this function. So why don't you take a
+
+ align:start position:0%
+this function. So why don't you take a
+ 
+
+ align:start position:0%
+this function. So why don't you take a
+couple minutes work this out come back
+
+ align:start position:0%
+couple minutes work this out come back
+ 
+
+ align:start position:0%
+couple minutes work this out come back
+and you can check your answer against my
+
+ align:start position:0%
+and you can check your answer against my
+ 
+
+ align:start position:0%
+and you can check your answer against my
+work.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, welcome back. So, we were just
+
+ align:start position:0%
+Okay, welcome back. So, we were just
+ 
+
+ align:start position:0%
+Okay, welcome back. So, we were just
+talking about uh this anti-derivative
+
+ align:start position:0%
+talking about uh this anti-derivative
+ 
+
+ align:start position:0%
+talking about uh this anti-derivative
+here. So, one thing you'll you'll notice
+
+ align:start position:0%
+here. So, one thing you'll you'll notice
+ 
+
+ align:start position:0%
+here. So, one thing you'll you'll notice
+about this function is that I've written
+
+ align:start position:0%
+about this function is that I've written
+ 
+
+ align:start position:0%
+about this function is that I've written
+this in a sort of silly form. And it
+
+ align:start position:0%
+this in a sort of silly form. And it
+ 
+
+ align:start position:0%
+this in a sort of silly form. And it
+it's probably a lot easier to get a get
+
+ align:start position:0%
+it's probably a lot easier to get a get
+ 
+
+ align:start position:0%
+it's probably a lot easier to get a get
+a feel for what this function is if you
+
+ align:start position:0%
+a feel for what this function is if you
+ 
+
+ align:start position:0%
+a feel for what this function is if you
+if you break this fraction apart into
+
+ align:start position:0%
+if you break this fraction apart into
+ 
+
+ align:start position:0%
+if you break this fraction apart into
+its several pieces. So, for example, x
+
+ align:start position:0%
+its several pieces. So, for example, x
+ 
+
+ align:start position:0%
+its several pieces. So, for example, x
+to the eth over x^2 is just x. So, well,
+
+ align:start position:0%
+to the eth over x^2 is just x. So, well,
+ 
+
+ align:start position:0%
+to the eth over x^2 is just x. So, well,
+okay. Okay. So let me So this this
+
+ align:start position:0%
+okay. Okay. So let me So this this
+ 
+
+ align:start position:0%
+okay. Okay. So let me So this this
+anti-derivative that I'm interested in
+
+ align:start position:0%
+anti-derivative that I'm interested in
+ 
+
+ align:start position:0%
+anti-derivative that I'm interested in
+anti-derivative of x 8 + 2x cub - x^ 2/3
+
+ align:start position:0%
+anti-derivative of x 8 + 2x cub - x^ 2/3
+ 
+
+ align:start position:0%
+anti-derivative of x 8 + 2x cub - x^ 2/3
+- 3
+
+ align:start position:0%
+- 3
+ 
+
+ align:start position:0%
+- 3
+over x^2
+
+ align:start position:0%
+over x^2
+ 
+
+ align:start position:0%
+over x^2
+dx. So I've written this in the silly
+
+ align:start position:0%
+dx. So I've written this in the silly
+ 
+
+ align:start position:0%
+dx. So I've written this in the silly
+form and you can get it in a nicer form
+
+ align:start position:0%
+form and you can get it in a nicer form
+ 
+
+ align:start position:0%
+form and you can get it in a nicer form
+if you if you just realize that you know
+
+ align:start position:0%
+if you if you just realize that you know
+ 
+
+ align:start position:0%
+if you if you just realize that you know
+this is just a sum of powers of x that
+
+ align:start position:0%
+this is just a sum of powers of x that
+ 
+
+ align:start position:0%
+this is just a sum of powers of x that
+I've I've sort of put over this silly
+
+ align:start position:0%
+I've I've sort of put over this silly
+ 
+
+ align:start position:0%
+I've I've sort of put over this silly
+common denominator here. So okay so so
+
+ align:start position:0%
+common denominator here. So okay so so
+ 
+
+ align:start position:0%
+common denominator here. So okay so so
+our life will be a little simpler if we
+
+ align:start position:0%
+our life will be a little simpler if we
+ 
+
+ align:start position:0%
+our life will be a little simpler if we
+write this out by splitting it up uh
+
+ align:start position:0%
+write this out by splitting it up uh
+ 
+
+ align:start position:0%
+write this out by splitting it up uh
+into the the separate fractions. So if I
+
+ align:start position:0%
+into the the separate fractions. So if I
+ 
+
+ align:start position:0%
+into the the separate fractions. So if I
+do that, this is just equal to the
+
+ align:start position:0%
+do that, this is just equal to the
+ 
+
+ align:start position:0%
+do that, this is just equal to the
+anti-derivative of well x to the eth
+
+ align:start position:0%
+anti-derivative of well x to the eth
+ 
+
+ align:start position:0%
+anti-derivative of well x to the eth
+overx^2 that's x 6 and 2x cubed over x^2
+
+ align:start position:0%
+overx^2 that's x 6 and 2x cubed over x^2
+ 
+
+ align:start position:0%
+overx^2 that's x 6 and 2x cubed over x^2
+is just x. So I have x sorry it's 2x
+
+ align:start position:0%
+is just x. So I have x sorry it's 2x
+ 
+
+ align:start position:0%
+is just x. So I have x sorry it's 2x
++ 2x
+
+ align:start position:0%
++ 2x
+ 
+
+ align:start position:0%
++ 2x
+now okay so x to the 2/3 over x^2. So
+
+ align:start position:0%
+now okay so x to the 2/3 over x^2. So
+ 
+
+ align:start position:0%
+now okay so x to the 2/3 over x^2. So
+that's x to the 2/3 minus 2 which is x
+
+ align:start position:0%
+that's x to the 2/3 minus 2 which is x
+ 
+
+ align:start position:0%
+that's x to the 2/3 minus 2 which is x
+to the - 4/3
+
+ align:start position:0%
+to the - 4/3
+ 
+
+ align:start position:0%
+to the - 4/3
+and - 3x^2. So okay so we could write
+
+ align:start position:0%
+and - 3x^2. So okay so we could write
+ 
+
+ align:start position:0%
+and - 3x^2. So okay so we could write
+that as - 3x^2 or maybe it's a little
+
+ align:start position:0%
+that as - 3x^2 or maybe it's a little
+ 
+
+ align:start position:0%
+that as - 3x^2 or maybe it's a little
+more convenient to write it as -3 x -2
+
+ align:start position:0%
+more convenient to write it as -3 x -2
+ 
+
+ align:start position:0%
+more convenient to write it as -3 x -2
+dx. So, so far I haven't really done
+
+ align:start position:0%
+dx. So, so far I haven't really done
+ 
+
+ align:start position:0%
+dx. So, so far I haven't really done
+anything, you know, a little bit of a
+
+ align:start position:0%
+anything, you know, a little bit of a
+ 
+
+ align:start position:0%
+anything, you know, a little bit of a
+little bit of algebra here. Okay. But
+
+ align:start position:0%
+little bit of algebra here. Okay. But
+ 
+
+ align:start position:0%
+little bit of algebra here. Okay. But
+now we know that we we've we've seen a
+
+ align:start position:0%
+now we know that we we've we've seen a
+ 
+
+ align:start position:0%
+now we know that we we've we've seen a
+formula for anti anti-ifferiating a
+
+ align:start position:0%
+formula for anti anti-ifferiating a
+ 
+
+ align:start position:0%
+formula for anti anti-ifferiating a
+single power of x. I mean, we know how
+
+ align:start position:0%
+single power of x. I mean, we know how
+ 
+
+ align:start position:0%
+single power of x. I mean, we know how
+to differentiate a single power of x.
+
+ align:start position:0%
+to differentiate a single power of x.
+ 
+
+ align:start position:0%
+to differentiate a single power of x.
+And so to do an anti-derivative is just
+
+ align:start position:0%
+And so to do an anti-derivative is just
+ 
+
+ align:start position:0%
+And so to do an anti-derivative is just
+the the inverse process. Um, and
+
+ align:start position:0%
+the the inverse process. Um, and
+ 
+
+ align:start position:0%
+the the inverse process. Um, and
+we also know that when you have the
+
+ align:start position:0%
+we also know that when you have the
+ 
+
+ align:start position:0%
+we also know that when you have the
+derivative of a sum, it's the sum of
+
+ align:start position:0%
+derivative of a sum, it's the sum of
+ 
+
+ align:start position:0%
+derivative of a sum, it's the sum of
+derivatives. And so consequently, if you
+
+ align:start position:0%
+derivatives. And so consequently, if you
+ 
+
+ align:start position:0%
+derivatives. And so consequently, if you
+have the anti-derivative of a sum, it's
+
+ align:start position:0%
+have the anti-derivative of a sum, it's
+ 
+
+ align:start position:0%
+have the anti-derivative of a sum, it's
+just the sum of the anti-derivatives. So
+
+ align:start position:0%
+just the sum of the anti-derivatives. So
+ 
+
+ align:start position:0%
+just the sum of the anti-derivatives. So
+we can write this out into its into its
+
+ align:start position:0%
+we can write this out into its into its
+ 
+
+ align:start position:0%
+we can write this out into its into its
+constituent parts. So it's the
+
+ align:start position:0%
+constituent parts. So it's the
+ 
+
+ align:start position:0%
+constituent parts. So it's the
+anti-derivative of x to the 6 dx
+
+ align:start position:0%
+anti-derivative of x to the 6 dx
+ 
+
+ align:start position:0%
+anti-derivative of x to the 6 dx
+plus the anti. Now, of course, you don't
+
+ align:start position:0%
+plus the anti. Now, of course, you don't
+ 
+
+ align:start position:0%
+plus the anti. Now, of course, you don't
+have to do this. You could probably
+
+ align:start position:0%
+have to do this. You could probably
+ 
+
+ align:start position:0%
+have to do this. You could probably
+proceed just from this step onwards or
+
+ align:start position:0%
+proceed just from this step onwards or
+ 
+
+ align:start position:0%
+proceed just from this step onwards or
+uh but but I don't see any harm in in
+
+ align:start position:0%
+uh but but I don't see any harm in in
+ 
+
+ align:start position:0%
+uh but but I don't see any harm in in
+actually splitting it up myself. So
+
+ align:start position:0%
+actually splitting it up myself. So
+ 
+
+ align:start position:0%
+actually splitting it up myself. So
+anti-derivative of 2x dxus
+
+ align:start position:0%
+anti-derivative of 2x dxus
+ 
+
+ align:start position:0%
+anti-derivative of 2x dxus
+okay x to the - 4/3 dx
+
+ align:start position:0%
+okay x to the - 4/3 dx
+ 
+
+ align:start position:0%
+okay x to the - 4/3 dx
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+- 3x to the - 2 dx. Okay, so I just
+
+ align:start position:0%
+- 3x to the - 2 dx. Okay, so I just
+ 
+
+ align:start position:0%
+- 3x to the - 2 dx. Okay, so I just
+split it up into a bunch of pieces. Oh,
+
+ align:start position:0%
+split it up into a bunch of pieces. Oh,
+ 
+
+ align:start position:0%
+split it up into a bunch of pieces. Oh,
+I guess this one I sort of pulled the
+
+ align:start position:0%
+I guess this one I sort of pulled the
+ 
+
+ align:start position:0%
+I guess this one I sort of pulled the
+minus sign out and this one I didn't.
+
+ align:start position:0%
+minus sign out and this one I didn't.
+ 
+
+ align:start position:0%
+minus sign out and this one I didn't.
+But you know, whatever e either either
+
+ align:start position:0%
+But you know, whatever e either either
+ 
+
+ align:start position:0%
+But you know, whatever e either either
+way. Um, okay. So now, now we just need
+
+ align:start position:0%
+way. Um, okay. So now, now we just need
+ 
+
+ align:start position:0%
+way. Um, okay. So now, now we just need
+to remember our our formulas for for
+
+ align:start position:0%
+to remember our our formulas for for
+ 
+
+ align:start position:0%
+to remember our our formulas for for
+taking the anti-derivative of a power of
+
+ align:start position:0%
+taking the anti-derivative of a power of
+ 
+
+ align:start position:0%
+taking the anti-derivative of a power of
+x. So in order to do that, so when you
+
+ align:start position:0%
+x. So in order to do that, so when you
+ 
+
+ align:start position:0%
+x. So in order to do that, so when you
+take a derivative,
+
+ align:start position:0%
+take a derivative,
+ 
+
+ align:start position:0%
+take a derivative,
+the the power goes down by one. So if
+
+ align:start position:0%
+the the power goes down by one. So if
+ 
+
+ align:start position:0%
+the the power goes down by one. So if
+you take an anti-derivative, the power
+
+ align:start position:0%
+you take an anti-derivative, the power
+ 
+
+ align:start position:0%
+you take an anti-derivative, the power
+will always go up by one. So
+
+ align:start position:0%
+will always go up by one. So
+ 
+
+ align:start position:0%
+will always go up by one. So
+in this case, you get so you're going to
+
+ align:start position:0%
+in this case, you get so you're going to
+ 
+
+ align:start position:0%
+in this case, you get so you're going to
+get x to the 7th. And now when you
+
+ align:start position:0%
+get x to the 7th. And now when you
+ 
+
+ align:start position:0%
+get x to the 7th. And now when you
+differentiate x to the 7th a seven comes
+
+ align:start position:0%
+differentiate x to the 7th a seven comes
+ 
+
+ align:start position:0%
+differentiate x to the 7th a seven comes
+down in front right you get 7 x to the
+
+ align:start position:0%
+down in front right you get 7 x to the
+ 
+
+ align:start position:0%
+down in front right you get 7 x to the
+6th. So in order to get just x to the
+
+ align:start position:0%
+6th. So in order to get just x to the
+ 
+
+ align:start position:0%
+6th. So in order to get just x to the
+6th we have to also divide by that seven
+
+ align:start position:0%
+6th we have to also divide by that seven
+ 
+
+ align:start position:0%
+6th we have to also divide by that seven
+there. So x to the 6 the anti-derivative
+
+ align:start position:0%
+there. So x to the 6 the anti-derivative
+ 
+
+ align:start position:0%
+there. So x to the 6 the anti-derivative
+is x 7th over 7 2x. So that's going to
+
+ align:start position:0%
+is x 7th over 7 2x. So that's going to
+ 
+
+ align:start position:0%
+is x 7th over 7 2x. So that's going to
+give us plus
+
+ align:start position:0%
+give us plus
+ 
+
+ align:start position:0%
+give us plus
+2x^2
+
+ align:start position:0%
+2x^2
+ 
+
+ align:start position:0%
+2x^2
+over 2. Or if you like you could just
+
+ align:start position:0%
+over 2. Or if you like you could just
+ 
+
+ align:start position:0%
+over 2. Or if you like you could just
+recognize right away that 2x is the
+
+ align:start position:0%
+recognize right away that 2x is the
+ 
+
+ align:start position:0%
+recognize right away that 2x is the
+derivative of x^2.
+
+ align:start position:0%
+derivative of x^2.
+ 
+
+ align:start position:0%
+derivative of x^2.
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+minus okay now we've got minus powers
+
+ align:start position:0%
+minus okay now we've got minus powers
+ 
+
+ align:start position:0%
+minus okay now we've got minus powers
+rather negative powers so so that always
+
+ align:start position:0%
+rather negative powers so so that always
+ 
+
+ align:start position:0%
+rather negative powers so so that always
+is a little trickier to to keep track of
+
+ align:start position:0%
+is a little trickier to to keep track of
+ 
+
+ align:start position:0%
+is a little trickier to to keep track of
+so again the same thing is true though
+
+ align:start position:0%
+so again the same thing is true though
+ 
+
+ align:start position:0%
+so again the same thing is true though
+you have to you add one to the to the
+
+ align:start position:0%
+you have to you add one to the to the
+ 
+
+ align:start position:0%
+you have to you add one to the to the
+exponent the exponent goes up by one
+
+ align:start position:0%
+exponent the exponent goes up by one
+ 
+
+ align:start position:0%
+exponent the exponent goes up by one
+when you take an anti-derivative goes
+
+ align:start position:0%
+when you take an anti-derivative goes
+ 
+
+ align:start position:0%
+when you take an anti-derivative goes
+down by one when you take a derivative
+
+ align:start position:0%
+down by one when you take a derivative
+ 
+
+ align:start position:0%
+down by one when you take a derivative
+so okay so when you add one to minus 4/3
+
+ align:start position:0%
+so okay so when you add one to minus 4/3
+ 
+
+ align:start position:0%
+so okay so when you add one to minus 4/3
+you get -3 so we have x to the minus
+
+ align:start position:0%
+you get -3 so we have x to the minus
+ 
+
+ align:start position:0%
+you get -3 so we have x to the minus
+1/3 and then I have to divide divide by
+
+ align:start position:0%
+1/3 and then I have to divide divide by
+ 
+
+ align:start position:0%
+1/3 and then I have to divide divide by
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+1/3 when I take a derivative here we get
+
+ align:start position:0%
+1/3 when I take a derivative here we get
+ 
+
+ align:start position:0%
+1/3 when I take a derivative here we get
+of of x^us 1/3 I get - 1/3 x to the -
+
+ align:start position:0%
+of of x^us 1/3 I get - 1/3 x to the -
+ 
+
+ align:start position:0%
+of of x^us 1/3 I get - 1/3 x to the -
+4/3 so I need to divide by that - 1/3
+
+ align:start position:0%
+4/3 so I need to divide by that - 1/3
+ 
+
+ align:start position:0%
+4/3 so I need to divide by that - 1/3
+okay and finally here so - 3x^us2
+
+ align:start position:0%
+okay and finally here so - 3x^us2
+ 
+
+ align:start position:0%
+okay and finally here so - 3x^us2
+so okay so so just like this first one
+
+ align:start position:0%
+so okay so so just like this first one
+ 
+
+ align:start position:0%
+so okay so so just like this first one
+you you you might recognize that right
+
+ align:start position:0%
+you you you might recognize that right
+ 
+
+ align:start position:0%
+you you you might recognize that right
+off as the derivative of x to the minus
+
+ align:start position:0%
+off as the derivative of x to the minus
+ 
+
+ align:start position:0%
+off as the derivative of x to the minus
+3 so this is plus
+
+ align:start position:0%
+3 so this is plus
+ 
+
+ align:start position:0%
+3 so this is plus
+Oh. Oh. Uh, you could you could do that
+
+ align:start position:0%
+Oh. Oh. Uh, you could you could do that
+ 
+
+ align:start position:0%
+Oh. Oh. Uh, you could you could do that
+if you were completely confused like me.
+
+ align:start position:0%
+if you were completely confused like me.
+ 
+
+ align:start position:0%
+if you were completely confused like me.
+Um, so right. So x to the minus2 it
+
+ align:start position:0%
+Um, so right. So x to the minus2 it
+ 
+
+ align:start position:0%
+Um, so right. So x to the minus2 it
+increase by one increases by one. So
+
+ align:start position:0%
+increase by one increases by one. So
+ 
+
+ align:start position:0%
+increase by one increases by one. So
+when it increases by one you get minus
+
+ align:start position:0%
+when it increases by one you get minus
+ 
+
+ align:start position:0%
+when it increases by one you get minus
+one notus 3. Oh okay good. So this is -3
+
+ align:start position:0%
+one notus 3. Oh okay good. So this is -3
+ 
+
+ align:start position:0%
+one notus 3. Oh okay good. So this is -3
+* x to the minus1 over minus1. Okay
+
+ align:start position:0%
+* x to the minus1 over minus1. Okay
+ 
+
+ align:start position:0%
+* x to the minus1 over minus1. Okay
+that's much better. And if you like
+
+ align:start position:0%
+that's much better. And if you like
+ 
+
+ align:start position:0%
+that's much better. And if you like
+right. So okay. Okay, so we could any
+
+ align:start position:0%
+right. So okay. Okay, so we could any
+ 
+
+ align:start position:0%
+right. So okay. Okay, so we could any
+any constant we add to this, it'll still
+
+ align:start position:0%
+any constant we add to this, it'll still
+ 
+
+ align:start position:0%
+any constant we add to this, it'll still
+be an anti-derivative. Okay, and now we
+
+ align:start position:0%
+be an anti-derivative. Okay, and now we
+ 
+
+ align:start position:0%
+be an anti-derivative. Okay, and now we
+could do a little bit of arithmetic to
+
+ align:start position:0%
+could do a little bit of arithmetic to
+ 
+
+ align:start position:0%
+could do a little bit of arithmetic to
+to rearrange this into nicer forms if
+
+ align:start position:0%
+to rearrange this into nicer forms if
+ 
+
+ align:start position:0%
+to rearrange this into nicer forms if
+you wanted. So you could rewrite this as
+
+ align:start position:0%
+you wanted. So you could rewrite this as
+ 
+
+ align:start position:0%
+you wanted. So you could rewrite this as
+say x to the 7th over 7
+
+ align:start position:0%
+say x to the 7th over 7
+ 
+
+ align:start position:0%
+say x to the 7th over 7
++ x^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
++ 3x^
+
+ align:start position:0%
++ 3x^
+ 
+
+ align:start position:0%
++ 3x^
+- 1/3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
++ 3xus
+
+ align:start position:0%
++ 3xus
+ 
+
+ align:start position:0%
++ 3xus
+1 plus a constant. Now suppose you got
+
+ align:start position:0%
+1 plus a constant. Now suppose you got
+ 
+
+ align:start position:0%
+1 plus a constant. Now suppose you got
+here and suppose that you know you did
+
+ align:start position:0%
+here and suppose that you know you did
+ 
+
+ align:start position:0%
+here and suppose that you know you did
+the same mistake that I just made um and
+
+ align:start position:0%
+the same mistake that I just made um and
+ 
+
+ align:start position:0%
+the same mistake that I just made um and
+you and you had accidentally thought
+
+ align:start position:0%
+you and you had accidentally thought
+ 
+
+ align:start position:0%
+you and you had accidentally thought
+that this was going to be a minus3 power
+
+ align:start position:0%
+that this was going to be a minus3 power
+ 
+
+ align:start position:0%
+that this was going to be a minus3 power
+instead of a minus 1st power. So how
+
+ align:start position:0%
+instead of a minus 1st power. So how
+ 
+
+ align:start position:0%
+instead of a minus 1st power. So how
+would you is there is there any way that
+
+ align:start position:0%
+would you is there is there any way that
+ 
+
+ align:start position:0%
+would you is there is there any way that
+you can prevent yourself making that
+
+ align:start position:0%
+you can prevent yourself making that
+ 
+
+ align:start position:0%
+you can prevent yourself making that
+mistake? Well, there actually is. So one
+
+ align:start position:0%
+mistake? Well, there actually is. So one
+ 
+
+ align:start position:0%
+mistake? Well, there actually is. So one
+nice thing about anti-derivatives is
+
+ align:start position:0%
+nice thing about anti-derivatives is
+ 
+
+ align:start position:0%
+nice thing about anti-derivatives is
+that it's really easy to check your work
+
+ align:start position:0%
+that it's really easy to check your work
+ 
+
+ align:start position:0%
+that it's really easy to check your work
+after you've computed an anti-derivative
+
+ align:start position:0%
+after you've computed an anti-derivative
+ 
+
+ align:start position:0%
+after you've computed an anti-derivative
+or or something that you think is an
+
+ align:start position:0%
+or or something that you think is an
+ 
+
+ align:start position:0%
+or or something that you think is an
+anti-derivative. you can always go back
+
+ align:start position:0%
+anti-derivative. you can always go back
+ 
+
+ align:start position:0%
+anti-derivative. you can always go back
+and take the derivative of the thing
+
+ align:start position:0%
+and take the derivative of the thing
+ 
+
+ align:start position:0%
+and take the derivative of the thing
+that you've computed and check that it's
+
+ align:start position:0%
+that you've computed and check that it's
+ 
+
+ align:start position:0%
+that you've computed and check that it's
+equal to what you started with. So if
+
+ align:start position:0%
+equal to what you started with. So if
+ 
+
+ align:start position:0%
+equal to what you started with. So if
+you if you're if you're ever worried
+
+ align:start position:0%
+you if you're if you're ever worried
+ 
+
+ align:start position:0%
+you if you're if you're ever worried
+that you made a mistake computing an
+
+ align:start position:0%
+that you made a mistake computing an
+ 
+
+ align:start position:0%
+that you made a mistake computing an
+anti-derivative, one thing you can
+
+ align:start position:0%
+anti-derivative, one thing you can
+ 
+
+ align:start position:0%
+anti-derivative, one thing you can
+always do is take a derivative of what
+
+ align:start position:0%
+always do is take a derivative of what
+ 
+
+ align:start position:0%
+always do is take a derivative of what
+you've got at the end. So if we take a
+
+ align:start position:0%
+you've got at the end. So if we take a
+ 
+
+ align:start position:0%
+you've got at the end. So if we take a
+derivative here, we get x 6 + 2x - x -
+
+ align:start position:0%
+derivative here, we get x 6 + 2x - x -
+ 
+
+ align:start position:0%
+derivative here, we get x 6 + 2x - x -
+4/3 - 3xus 2. Okay, so that was just
+
+ align:start position:0%
+4/3 - 3xus 2. Okay, so that was just
+ 
+
+ align:start position:0%
+4/3 - 3xus 2. Okay, so that was just
+using our our rule for powers one by one
+
+ align:start position:0%
+using our our rule for powers one by one
+ 
+
+ align:start position:0%
+using our our rule for powers one by one
+and okay, so you say that out loud or
+
+ align:start position:0%
+and okay, so you say that out loud or
+ 
+
+ align:start position:0%
+and okay, so you say that out loud or
+write it down and then you just check,
+
+ align:start position:0%
+write it down and then you just check,
+ 
+
+ align:start position:0%
+write it down and then you just check,
+right? So, so I said that. So that's
+
+ align:start position:0%
+right? So, so I said that. So that's
+ 
+
+ align:start position:0%
+right? So, so I said that. So that's
+exactly the same thing we've got right
+
+ align:start position:0%
+exactly the same thing we've got right
+ 
+
+ align:start position:0%
+exactly the same thing we've got right
+here. Yeah. So, so x 6 + 2x - x - 4/3 -
+
+ align:start position:0%
+here. Yeah. So, so x 6 + 2x - x - 4/3 -
+ 
+
+ align:start position:0%
+here. Yeah. So, so x 6 + 2x - x - 4/3 -
+3xus 2. So,
+
+ align:start position:0%
+3xus 2. So,
+ 
+
+ align:start position:0%
+3xus 2. So,
+one of the nicest things about
+
+ align:start position:0%
+one of the nicest things about
+ 
+
+ align:start position:0%
+one of the nicest things about
+anti-derivatives, they can be difficult
+
+ align:start position:0%
+anti-derivatives, they can be difficult
+ 
+
+ align:start position:0%
+anti-derivatives, they can be difficult
+to to figure out in the first place, but
+
+ align:start position:0%
+to to figure out in the first place, but
+ 
+
+ align:start position:0%
+to to figure out in the first place, but
+after you've got something that you
+
+ align:start position:0%
+after you've got something that you
+ 
+
+ align:start position:0%
+after you've got something that you
+think is an anti-derivative, it's very
+
+ align:start position:0%
+think is an anti-derivative, it's very
+ 
+
+ align:start position:0%
+think is an anti-derivative, it's very
+easy to go back and check whether you
+
+ align:start position:0%
+easy to go back and check whether you
+ 
+
+ align:start position:0%
+easy to go back and check whether you
+did it correctly by taking the
+
+ align:start position:0%
+did it correctly by taking the
+ 
+
+ align:start position:0%
+did it correctly by taking the
+derivative and making sure that it
+
+ align:start position:0%
+derivative and making sure that it
+ 
+
+ align:start position:0%
+derivative and making sure that it
+matches the the the, you know, the the
+
+ align:start position:0%
+matches the the the, you know, the the
+ 
+
+ align:start position:0%
+matches the the the, you know, the the
+thing that you were trying to
+
+ align:start position:0%
+thing that you were trying to
+ 
+
+ align:start position:0%
+thing that you were trying to
+anti-ifferiate at the beginning. So,
+
+ align:start position:0%
+anti-ifferiate at the beginning. So,
+ 
+
+ align:start position:0%
+anti-ifferiate at the beginning. So,
+that's that.
\ No newline at end of file
diff --git a/w3HgjULieFA.txt b/w3HgjULieFA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0d294bb4c2a26548ae9dbd03fe4a778042dbcf6b
--- /dev/null
+++ b/w3HgjULieFA.txt
@@ -0,0 +1,15587 @@
+align:start position:0%
+ 
+right so today we are going to start a
+
+ align:start position:0%
+right so today we are going to start a
+ 
+
+ align:start position:0%
+right so today we are going to start a
+series of several uh lectures on
+
+ align:start position:0%
+series of several uh lectures on
+ 
+
+ align:start position:0%
+series of several uh lectures on
+refractive index Diagnostics so these
+
+ align:start position:0%
+refractive index Diagnostics so these
+ 
+
+ align:start position:0%
+refractive index Diagnostics so these
+are Diagnostics which use the fact that
+
+ align:start position:0%
+are Diagnostics which use the fact that
+ 
+
+ align:start position:0%
+are Diagnostics which use the fact that
+the refractive index of a plasma is not
+
+ align:start position:0%
+the refractive index of a plasma is not
+ 
+
+ align:start position:0%
+the refractive index of a plasma is not
+one uh in order to make measurements
+
+ align:start position:0%
+one uh in order to make measurements
+ 
+
+ align:start position:0%
+one uh in order to make measurements
+about the plasma so first of all what
+
+ align:start position:0%
+about the plasma so first of all what
+ 
+
+ align:start position:0%
+about the plasma so first of all what
+we're going to do is a very quick recap
+
+ align:start position:0%
+we're going to do is a very quick recap
+ 
+
+ align:start position:0%
+we're going to do is a very quick recap
+of electromagnetic
+
+ align:start position:0%
+of electromagnetic
+ 
+
+ align:start position:0%
+of electromagnetic
+waves in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and you have doubtless seen this
+
+ align:start position:0%
+plasma and you have doubtless seen this
+ 
+
+ align:start position:0%
+plasma and you have doubtless seen this
+before in some courses that you've done
+
+ align:start position:0%
+before in some courses that you've done
+ 
+
+ align:start position:0%
+before in some courses that you've done
+like it's in Chen um there's also a very
+
+ align:start position:0%
+like it's in Chen um there's also a very
+ 
+
+ align:start position:0%
+like it's in Chen um there's also a very
+good expanation of it in Hutchinson um
+
+ align:start position:0%
+good expanation of it in Hutchinson um
+ 
+
+ align:start position:0%
+good expanation of it in Hutchinson um
+and I am going to give like a little
+
+ align:start position:0%
+and I am going to give like a little
+ 
+
+ align:start position:0%
+and I am going to give like a little
+taster of how this derivation goes just
+
+ align:start position:0%
+taster of how this derivation goes just
+ 
+
+ align:start position:0%
+taster of how this derivation goes just
+to sort of remind folks of how this
+
+ align:start position:0%
+to sort of remind folks of how this
+ 
+
+ align:start position:0%
+to sort of remind folks of how this
+actually this result actually comes
+
+ align:start position:0%
+actually this result actually comes
+ 
+
+ align:start position:0%
+actually this result actually comes
+about and I'm going to do it in a rather
+
+ align:start position:0%
+about and I'm going to do it in a rather
+ 
+
+ align:start position:0%
+about and I'm going to do it in a rather
+restrictive way here so that we can make
+
+ align:start position:0%
+restrictive way here so that we can make
+ 
+
+ align:start position:0%
+restrictive way here so that we can make
+some rapid progress and we'll go back
+
+ align:start position:0%
+some rapid progress and we'll go back
+ 
+
+ align:start position:0%
+some rapid progress and we'll go back
+and add in more bits of theory later on
+
+ align:start position:0%
+and add in more bits of theory later on
+ 
+
+ align:start position:0%
+and add in more bits of theory later on
+as we need it okay so for our
+
+ align:start position:0%
+as we need it okay so for our
+ 
+
+ align:start position:0%
+as we need it okay so for our
+electromagnetic waves in a plasma we
+
+ align:start position:0%
+electromagnetic waves in a plasma we
+ 
+
+ align:start position:0%
+electromagnetic waves in a plasma we
+have two fields we have e and B like
+
+ align:start position:0%
+have two fields we have e and B like
+ 
+
+ align:start position:0%
+have two fields we have e and B like
+this and we have Maxell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations so we have that the curl of e
+
+ align:start position:0%
+equations so we have that the curl of e
+ 
+
+ align:start position:0%
+equations so we have that the curl of e
+is equal to minus B Dot and we have c^2
+
+ align:start position:0%
+is equal to minus B Dot and we have c^2
+ 
+
+ align:start position:0%
+is equal to minus B Dot and we have c^2
+* the the curl of b
+
+ align:start position:0%
+* the the curl of b
+ 
+
+ align:start position:0%
+* the the curl of b
+equals e dot plus J over Epsilon KN you
+
+ align:start position:0%
+equals e dot plus J over Epsilon KN you
+ 
+
+ align:start position:0%
+equals e dot plus J over Epsilon KN you
+might be more used to seeing this
+
+ align:start position:0%
+might be more used to seeing this
+ 
+
+ align:start position:0%
+might be more used to seeing this
+equation with a mu I just mov the c s
+
+ align:start position:0%
+equation with a mu I just mov the c s
+ 
+
+ align:start position:0%
+equation with a mu I just mov the c s
+over the other side because it makes the
+
+ align:start position:0%
+over the other side because it makes the
+ 
+
+ align:start position:0%
+over the other side because it makes the
+math a little bit easier on the next
+
+ align:start position:0%
+math a little bit easier on the next
+ 
+
+ align:start position:0%
+math a little bit easier on the next
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+here and so these equations are just
+
+ align:start position:0%
+here and so these equations are just
+ 
+
+ align:start position:0%
+here and so these equations are just
+true they're true in any medium um and
+
+ align:start position:0%
+true they're true in any medium um and
+ 
+
+ align:start position:0%
+true they're true in any medium um and
+so what we want to do is try and reduce
+
+ align:start position:0%
+so what we want to do is try and reduce
+ 
+
+ align:start position:0%
+so what we want to do is try and reduce
+them down a little bit and then put some
+
+ align:start position:0%
+them down a little bit and then put some
+ 
+
+ align:start position:0%
+them down a little bit and then put some
+plasma physics in so the first thing we
+
+ align:start position:0%
+plasma physics in so the first thing we
+ 
+
+ align:start position:0%
+plasma physics in so the first thing we
+normally do when we're D deriving
+
+ align:start position:0%
+normally do when we're D deriving
+ 
+
+ align:start position:0%
+normally do when we're D deriving
+electromagnetic waves is we say what if
+
+ align:start position:0%
+electromagnetic waves is we say what if
+ 
+
+ align:start position:0%
+electromagnetic waves is we say what if
+all of our vectors um had some sort of
+
+ align:start position:0%
+all of our vectors um had some sort of
+ 
+
+ align:start position:0%
+all of our vectors um had some sort of
+time and space variation that looked
+
+ align:start position:0%
+time and space variation that looked
+ 
+
+ align:start position:0%
+time and space variation that looked
+like exponential of I some wave vector k
+
+ align:start position:0%
+like exponential of I some wave vector k
+ 
+
+ align:start position:0%
+like exponential of I some wave vector k
+do some position Vector x minus Omega
+
+ align:start position:0%
+do some position Vector x minus Omega
+ 
+
+ align:start position:0%
+do some position Vector x minus Omega
+the frequency time time like that and so
+
+ align:start position:0%
+the frequency time time like that and so
+ 
+
+ align:start position:0%
+the frequency time time like that and so
+this is a little bit like Foria
+
+ align:start position:0%
+this is a little bit like Foria
+ 
+
+ align:start position:0%
+this is a little bit like Foria
+Transforming Our equations here and we
+
+ align:start position:0%
+Transforming Our equations here and we
+ 
+
+ align:start position:0%
+Transforming Our equations here and we
+end up with oh
+
+ align:start position:0%
+end up with oh
+ 
+
+ align:start position:0%
+end up with oh
+uh K cross E equals I
+
+ align:start position:0%
+uh K cross E equals I
+ 
+
+ align:start position:0%
+uh K cross E equals I
+Omega B and we have c^ 2 K cross B =
+
+ align:start position:0%
+Omega B and we have c^ 2 K cross B =
+ 
+
+ align:start position:0%
+Omega B and we have c^ 2 K cross B =
+minus I
+
+ align:start position:0%
+minus I
+ 
+
+ align:start position:0%
+minus I
+Omega e plus J upon Epsilon and the
+
+ align:start position:0%
+Omega e plus J upon Epsilon and the
+ 
+
+ align:start position:0%
+Omega e plus J upon Epsilon and the
+astute amongst you have noticed I made a
+
+ align:start position:0%
+astute amongst you have noticed I made a
+ 
+
+ align:start position:0%
+astute amongst you have noticed I made a
+sign error in the first equation here so
+
+ align:start position:0%
+sign error in the first equation here so
+ 
+
+ align:start position:0%
+sign error in the first equation here so
+this is plus I Omega B not
+
+ align:start position:0%
+this is plus I Omega B not
+ 
+
+ align:start position:0%
+this is plus I Omega B not
+okay very good and so we could call
+
+ align:start position:0%
+okay very good and so we could call
+ 
+
+ align:start position:0%
+okay very good and so we could call
+these equations one and two and we can
+
+ align:start position:0%
+these equations one and two and we can
+ 
+
+ align:start position:0%
+these equations one and two and we can
+note that if we do K cross with equation
+
+ align:start position:0%
+note that if we do K cross with equation
+ 
+
+ align:start position:0%
+note that if we do K cross with equation
+one that is equal to iega upon c^2 of
+
+ align:start position:0%
+one that is equal to iega upon c^2 of
+ 
+
+ align:start position:0%
+one that is equal to iega upon c^2 of
+equation two so what we're doing here is
+
+ align:start position:0%
+equation two so what we're doing here is
+ 
+
+ align:start position:0%
+equation two so what we're doing here is
+we're just looking at this term and this
+
+ align:start position:0%
+we're just looking at this term and this
+ 
+
+ align:start position:0%
+we're just looking at this term and this
+term and being like hey they've both got
+
+ align:start position:0%
+term and being like hey they've both got
+ 
+
+ align:start position:0%
+term and being like hey they've both got
+B in them we can probably make them look
+
+ align:start position:0%
+B in them we can probably make them look
+ 
+
+ align:start position:0%
+B in them we can probably make them look
+the same so then we can equate we can do
+
+ align:start position:0%
+the same so then we can equate we can do
+ 
+
+ align:start position:0%
+the same so then we can equate we can do
+this calcul we can equate the two sides
+
+ align:start position:0%
+this calcul we can equate the two sides
+ 
+
+ align:start position:0%
+this calcul we can equate the two sides
+of the equation and with a little bit of
+
+ align:start position:0%
+of the equation and with a little bit of
+ 
+
+ align:start position:0%
+of the equation and with a little bit of
+vector magic Vector calculus magic we
+
+ align:start position:0%
+vector magic Vector calculus magic we
+ 
+
+ align:start position:0%
+vector magic Vector calculus magic we
+would end up with something that looks
+
+ align:start position:0%
+would end up with something that looks
+ 
+
+ align:start position:0%
+would end up with something that looks
+like k k dot
+
+ align:start position:0%
+like k k dot
+ 
+
+ align:start position:0%
+like k k dot
+e plus k^
+
+ align:start position:0%
+e plus k^
+ 
+
+ align:start position:0%
+e plus k^
+2 e is equal
+
+ align:start position:0%
+2 e is equal
+ 
+
+ align:start position:0%
+2 e is equal
+to I Omega J over Epsilon c^ 2 plus
+
+ align:start position:0%
+to I Omega J over Epsilon c^ 2 plus
+ 
+
+ align:start position:0%
+to I Omega J over Epsilon c^ 2 plus
+Omega 2 upon c^ 2
+
+ align:start position:0%
+Omega 2 upon c^ 2
+ 
+
+ align:start position:0%
+Omega 2 upon c^ 2
+e like
+
+ align:start position:0%
+e like
+ 
+
+ align:start position:0%
+e like
+that now we are searching for transverse
+
+ align:start position:0%
+that now we are searching for transverse
+ 
+
+ align:start position:0%
+that now we are searching for transverse
+waves here electromagnetic waves that
+
+ align:start position:0%
+waves here electromagnetic waves that
+ 
+
+ align:start position:0%
+waves here electromagnetic waves that
+tend to be transverse and that means
+
+ align:start position:0%
+tend to be transverse and that means
+ 
+
+ align:start position:0%
+tend to be transverse and that means
+that k. e is zero so we're just going to
+
+ align:start position:0%
+that k. e is zero so we're just going to
+ 
+
+ align:start position:0%
+that k. e is zero so we're just going to
+look for transverse wave Solutions
+
+ align:start position:0%
+look for transverse wave Solutions
+ 
+
+ align:start position:0%
+look for transverse wave Solutions
+here we can drop that and that means
+
+ align:start position:0%
+here we can drop that and that means
+ 
+
+ align:start position:0%
+here we can drop that and that means
+that our equation can be Rewritten as
+
+ align:start position:0%
+that our equation can be Rewritten as
+ 
+
+ align:start position:0%
+that our equation can be Rewritten as
+Omega 2 minus c^ 2 k^ 2 *
+
+ align:start position:0%
+Omega 2 minus c^ 2 k^ 2 *
+ 
+
+ align:start position:0%
+Omega 2 minus c^ 2 k^ 2 *
+E equals minus I
+
+ align:start position:0%
+E equals minus I
+ 
+
+ align:start position:0%
+E equals minus I
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+J upon
+
+ align:start position:0%
+J upon
+ 
+
+ align:start position:0%
+J upon
+Epsilon like that and I just want to
+
+ align:start position:0%
+Epsilon like that and I just want to
+ 
+
+ align:start position:0%
+Epsilon like that and I just want to
+point out there's absolutely no plasma
+
+ align:start position:0%
+point out there's absolutely no plasma
+ 
+
+ align:start position:0%
+point out there's absolutely no plasma
+physics in this at the moment right all
+
+ align:start position:0%
+physics in this at the moment right all
+ 
+
+ align:start position:0%
+physics in this at the moment right all
+we've done is manipulate maximal
+
+ align:start position:0%
+we've done is manipulate maximal
+ 
+
+ align:start position:0%
+we've done is manipulate maximal
+equations we haven't said anything about
+
+ align:start position:0%
+equations we haven't said anything about
+ 
+
+ align:start position:0%
+equations we haven't said anything about
+the planting so if I take a standard
+
+ align:start position:0%
+the planting so if I take a standard
+ 
+
+ align:start position:0%
+the planting so if I take a standard
+limit here say I let the current equal
+
+ align:start position:0%
+limit here say I let the current equal
+ 
+
+ align:start position:0%
+limit here say I let the current equal
+zero which is what would be in the
+
+ align:start position:0%
+zero which is what would be in the
+ 
+
+ align:start position:0%
+zero which is what would be in the
+vacuum of space where there's no
+
+ align:start position:0%
+vacuum of space where there's no
+ 
+
+ align:start position:0%
+vacuum of space where there's no
+particles to carry any current then we'
+
+ align:start position:0%
+particles to carry any current then we'
+ 
+
+ align:start position:0%
+particles to carry any current then we'
+simply send up end up with an equation
+
+ align:start position:0%
+simply send up end up with an equation
+ 
+
+ align:start position:0%
+simply send up end up with an equation
+for light INF space and it would have a
+
+ align:start position:0%
+for light INF space and it would have a
+ 
+
+ align:start position:0%
+for light INF space and it would have a
+dispersion relationship Omega s = c^2 k
+
+ align:start position:0%
+dispersion relationship Omega s = c^2 k
+ 
+
+ align:start position:0%
+dispersion relationship Omega s = c^2 k
+s like that so those are light waves so
+
+ align:start position:0%
+s like that so those are light waves so
+ 
+
+ align:start position:0%
+s like that so those are light waves so
+life is
+
+ align:start position:0%
+life is
+ 
+
+ align:start position:0%
+life is
+good any questions on that before we put
+
+ align:start position:0%
+good any questions on that before we put
+ 
+
+ align:start position:0%
+good any questions on that before we put
+some plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics hopefully you're dredging up
+
+ align:start position:0%
+physics hopefully you're dredging up
+ 
+
+ align:start position:0%
+physics hopefully you're dredging up
+your memories of Griffiths and Jackson
+
+ align:start position:0%
+your memories of Griffiths and Jackson
+ 
+
+ align:start position:0%
+your memories of Griffiths and Jackson
+and all sorts of wonderful things like
+
+ align:start position:0%
+and all sorts of wonderful things like
+ 
+
+ align:start position:0%
+and all sorts of wonderful things like
+this this is all making sense so let's
+
+ align:start position:0%
+this this is all making sense so let's
+ 
+
+ align:start position:0%
+this this is all making sense so let's
+keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the next thing we want to do then is
+
+ align:start position:0%
+uh the next thing we want to do then is
+ 
+
+ align:start position:0%
+uh the next thing we want to do then is
+add in some plasma physics and we're
+
+ align:start position:0%
+add in some plasma physics and we're
+ 
+
+ align:start position:0%
+add in some plasma physics and we're
+going to add in some plasma physics with
+
+ align:start position:0%
+going to add in some plasma physics with
+ 
+
+ align:start position:0%
+going to add in some plasma physics with
+some serious assumptions which let us
+
+ align:start position:0%
+some serious assumptions which let us
+ 
+
+ align:start position:0%
+some serious assumptions which let us
+make significant progress quickly uh and
+
+ align:start position:0%
+make significant progress quickly uh and
+ 
+
+ align:start position:0%
+make significant progress quickly uh and
+these assumptions can all be justified
+
+ align:start position:0%
+these assumptions can all be justified
+ 
+
+ align:start position:0%
+these assumptions can all be justified
+uh for most plasmas um and if you can't
+
+ align:start position:0%
+uh for most plasmas um and if you can't
+ 
+
+ align:start position:0%
+uh for most plasmas um and if you can't
+justify it for your plasma you may want
+
+ align:start position:0%
+justify it for your plasma you may want
+ 
+
+ align:start position:0%
+justify it for your plasma you may want
+to revisit these a little bit okay so
+
+ align:start position:0%
+to revisit these a little bit okay so
+ 
+
+ align:start position:0%
+to revisit these a little bit okay so
+the first assumption we're going to make
+
+ align:start position:0%
+the first assumption we're going to make
+ 
+
+ align:start position:0%
+the first assumption we're going to make
+is that we're at using high frequency
+
+ align:start position:0%
+is that we're at using high frequency
+ 
+
+ align:start position:0%
+is that we're at using high frequency
+waves here here and high frequency this
+
+ align:start position:0%
+waves here here and high frequency this
+ 
+
+ align:start position:0%
+waves here here and high frequency this
+is kind of a wishy-washy term uh we want
+
+ align:start position:0%
+is kind of a wishy-washy term uh we want
+ 
+
+ align:start position:0%
+is kind of a wishy-washy term uh we want
+to make that more precise by having a
+
+ align:start position:0%
+to make that more precise by having a
+ 
+
+ align:start position:0%
+to make that more precise by having a
+dimensionless parameter and so we're
+
+ align:start position:0%
+dimensionless parameter and so we're
+ 
+
+ align:start position:0%
+dimensionless parameter and so we're
+going to say that Omega is much much
+
+ align:start position:0%
+going to say that Omega is much much
+ 
+
+ align:start position:0%
+going to say that Omega is much much
+larger larger than Omega Pi here so the
+
+ align:start position:0%
+larger larger than Omega Pi here so the
+ 
+
+ align:start position:0%
+larger larger than Omega Pi here so the
+frequency of our waves is much higher
+
+ align:start position:0%
+frequency of our waves is much higher
+ 
+
+ align:start position:0%
+frequency of our waves is much higher
+than the uh ion plasma frequency what
+
+ align:start position:0%
+than the uh ion plasma frequency what
+ 
+
+ align:start position:0%
+than the uh ion plasma frequency what
+does that condition physically respond
+
+ align:start position:0%
+does that condition physically respond
+ 
+
+ align:start position:0%
+does that condition physically respond
+to what are we saying about the ions and
+
+ align:start position:0%
+to what are we saying about the ions and
+ 
+
+ align:start position:0%
+to what are we saying about the ions and
+their interaction with this Wave by
+
+ align:start position:0%
+their interaction with this Wave by
+ 
+
+ align:start position:0%
+their interaction with this Wave by
+putting this condition in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you're saying you're saying they
+
+ align:start position:0%
+well you're saying you're saying they
+ 
+
+ align:start position:0%
+well you're saying you're saying they
+essentially don't interact at that point
+
+ align:start position:0%
+essentially don't interact at that point
+ 
+
+ align:start position:0%
+essentially don't interact at that point
+yeah so the ions are frozen in
+
+ align:start position:0%
+yeah so the ions are frozen in
+ 
+
+ align:start position:0%
+yeah so the ions are frozen in
+place and they are not going to
+
+ align:start position:0%
+place and they are not going to
+ 
+
+ align:start position:0%
+place and they are not going to
+participate in any of the physics that
+
+ align:start position:0%
+participate in any of the physics that
+ 
+
+ align:start position:0%
+participate in any of the physics that
+we're interested in here and again you
+
+ align:start position:0%
+we're interested in here and again you
+ 
+
+ align:start position:0%
+we're interested in here and again you
+can work out the ion plasma frequency
+
+ align:start position:0%
+can work out the ion plasma frequency
+ 
+
+ align:start position:0%
+can work out the ion plasma frequency
+for um you know some density that you're
+
+ align:start position:0%
+for um you know some density that you're
+ 
+
+ align:start position:0%
+for um you know some density that you're
+interested in and you'll find out it's
+
+ align:start position:0%
+interested in and you'll find out it's
+ 
+
+ align:start position:0%
+interested in and you'll find out it's
+pretty low so this is kind of pretty
+
+ align:start position:0%
+pretty low so this is kind of pretty
+ 
+
+ align:start position:0%
+pretty low so this is kind of pretty
+reasonable but if you start using very
+
+ align:start position:0%
+reasonable but if you start using very
+ 
+
+ align:start position:0%
+reasonable but if you start using very
+low frequency waves it won't be
+
+ align:start position:0%
+low frequency waves it won't be
+ 
+
+ align:start position:0%
+low frequency waves it won't be
+reasonable so another thing that we're
+
+ align:start position:0%
+reasonable so another thing that we're
+ 
+
+ align:start position:0%
+reasonable so another thing that we're
+going to do is make the cold plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation and again we can't just
+
+ align:start position:0%
+approximation and again we can't just
+ 
+
+ align:start position:0%
+approximation and again we can't just
+use the word cold we have to say what we
+
+ align:start position:0%
+use the word cold we have to say what we
+ 
+
+ align:start position:0%
+use the word cold we have to say what we
+mean by cold and we're going to say the
+
+ align:start position:0%
+mean by cold and we're going to say the
+ 
+
+ align:start position:0%
+mean by cold and we're going to say the
+thermal of the electrons is much much
+
+ align:start position:0%
+thermal of the electrons is much much
+ 
+
+ align:start position:0%
+thermal of the electrons is much much
+less than the speed of light here and
+
+ align:start position:0%
+less than the speed of light here and
+ 
+
+ align:start position:0%
+less than the speed of light here and
+this condition is equivalent to us not
+
+ align:start position:0%
+this condition is equivalent to us not
+ 
+
+ align:start position:0%
+this condition is equivalent to us not
+worrying about the maxwan distribution
+
+ align:start position:0%
+worrying about the maxwan distribution
+ 
+
+ align:start position:0%
+worrying about the maxwan distribution
+of the electron so all the electrons are
+
+ align:start position:0%
+of the electron so all the electrons are
+ 
+
+ align:start position:0%
+of the electron so all the electrons are
+just going to sort of be moving with no
+
+ align:start position:0%
+just going to sort of be moving with no
+ 
+
+ align:start position:0%
+just going to sort of be moving with no
+they will be moving unlike the ions
+
+ align:start position:0%
+they will be moving unlike the ions
+ 
+
+ align:start position:0%
+they will be moving unlike the ions
+which are frozen but they will be moving
+
+ align:start position:0%
+which are frozen but they will be moving
+ 
+
+ align:start position:0%
+which are frozen but they will be moving
+uh all at the same speed there's no
+
+ align:start position:0%
+uh all at the same speed there's no
+ 
+
+ align:start position:0%
+uh all at the same speed there's no
+spread of velocities here so um we have
+
+ align:start position:0%
+spread of velocities here so um we have
+ 
+
+ align:start position:0%
+spread of velocities here so um we have
+like a Delta function of velocities and
+
+ align:start position:0%
+like a Delta function of velocities and
+ 
+
+ align:start position:0%
+like a Delta function of velocities and
+we do not
+
+ align:start position:0%
+we do not
+ 
+
+ align:start position:0%
+we do not
+have our maxwan distribution that we
+
+ align:start position:0%
+have our maxwan distribution that we
+ 
+
+ align:start position:0%
+have our maxwan distribution that we
+might normally think
+
+ align:start position:0%
+might normally think
+ 
+
+ align:start position:0%
+might normally think
+about and the final condition we're
+
+ align:start position:0%
+about and the final condition we're
+ 
+
+ align:start position:0%
+about and the final condition we're
+going to write down is
+
+ align:start position:0%
+going to write down is
+ 
+
+ align:start position:0%
+going to write down is
+unmagnetized now this is the one which I
+
+ align:start position:0%
+unmagnetized now this is the one which I
+ 
+
+ align:start position:0%
+unmagnetized now this is the one which I
+think is most complicated because in
+
+ align:start position:0%
+think is most complicated because in
+ 
+
+ align:start position:0%
+think is most complicated because in
+fact there are like a dozen different
+
+ align:start position:0%
+fact there are like a dozen different
+ 
+
+ align:start position:0%
+fact there are like a dozen different
+ways you can write down a dimensionist
+
+ align:start position:0%
+ways you can write down a dimensionist
+ 
+
+ align:start position:0%
+ways you can write down a dimensionist
+parameter for unmagnetized and they all
+
+ align:start position:0%
+parameter for unmagnetized and they all
+ 
+
+ align:start position:0%
+parameter for unmagnetized and they all
+mean subtly different things we could
+
+ align:start position:0%
+mean subtly different things we could
+ 
+
+ align:start position:0%
+mean subtly different things we could
+think about collisionality we could
+
+ align:start position:0%
+think about collisionality we could
+ 
+
+ align:start position:0%
+think about collisionality we could
+think about pressure balance all sorts
+
+ align:start position:0%
+think about pressure balance all sorts
+ 
+
+ align:start position:0%
+think about pressure balance all sorts
+of things like that for the purposes of
+
+ align:start position:0%
+of things like that for the purposes of
+ 
+
+ align:start position:0%
+of things like that for the purposes of
+this derivation unmagnetized means Omega
+
+ align:start position:0%
+this derivation unmagnetized means Omega
+ 
+
+ align:start position:0%
+this derivation unmagnetized means Omega
+is much much larger than Capital Omega I
+
+ align:start position:0%
+is much much larger than Capital Omega I
+ 
+
+ align:start position:0%
+is much much larger than Capital Omega I
+know it's confusing and I'll put a
+
+ align:start position:0%
+know it's confusing and I'll put a
+ 
+
+ align:start position:0%
+know it's confusing and I'll put a
+little subscript e here because we've
+
+ align:start position:0%
+little subscript e here because we've
+ 
+
+ align:start position:0%
+little subscript e here because we've
+Frozen the ions but this is the gyro
+
+ align:start position:0%
+Frozen the ions but this is the gyro
+ 
+
+ align:start position:0%
+Frozen the ions but this is the gyro
+motion of the electrons so the electrons
+
+ align:start position:0%
+motion of the electrons so the electrons
+ 
+
+ align:start position:0%
+motion of the electrons so the electrons
+may be gyrating around field lines there
+
+ align:start position:0%
+may be gyrating around field lines there
+ 
+
+ align:start position:0%
+may be gyrating around field lines there
+may be some magnetic field it doesn't
+
+ align:start position:0%
+may be some magnetic field it doesn't
+ 
+
+ align:start position:0%
+may be some magnetic field it doesn't
+have to be zero but on the time scale
+
+ align:start position:0%
+have to be zero but on the time scale
+ 
+
+ align:start position:0%
+have to be zero but on the time scale
+that the wave goes B and does its stuff
+
+ align:start position:0%
+that the wave goes B and does its stuff
+ 
+
+ align:start position:0%
+that the wave goes B and does its stuff
+the electrons do not move appreciably
+
+ align:start position:0%
+the electrons do not move appreciably
+ 
+
+ align:start position:0%
+the electrons do not move appreciably
+around their gyro orbit so we don't have
+
+ align:start position:0%
+around their gyro orbit so we don't have
+ 
+
+ align:start position:0%
+around their gyro orbit so we don't have
+to care about their gyro motion this is
+
+ align:start position:0%
+to care about their gyro motion this is
+ 
+
+ align:start position:0%
+to care about their gyro motion this is
+one of the places we will definitely
+
+ align:start position:0%
+one of the places we will definitely
+ 
+
+ align:start position:0%
+one of the places we will definitely
+have to relax later on when we want to
+
+ align:start position:0%
+have to relax later on when we want to
+ 
+
+ align:start position:0%
+have to relax later on when we want to
+do Faraday rotation Imaging which relies
+
+ align:start position:0%
+do Faraday rotation Imaging which relies
+ 
+
+ align:start position:0%
+do Faraday rotation Imaging which relies
+on that gyro motion to give us the
+
+ align:start position:0%
+on that gyro motion to give us the
+ 
+
+ align:start position:0%
+on that gyro motion to give us the
+effect okay so this is the final
+
+ align:start position:0%
+effect okay so this is the final
+ 
+
+ align:start position:0%
+effect okay so this is the final
+condition any questions on those three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assumptions okay so then we can write
+
+ align:start position:0%
+assumptions okay so then we can write
+ 
+
+ align:start position:0%
+assumptions okay so then we can write
+down that the current
+
+ align:start position:0%
+down that the current
+ 
+
+ align:start position:0%
+down that the current
+inside our plasma is simply going to be
+
+ align:start position:0%
+inside our plasma is simply going to be
+ 
+
+ align:start position:0%
+inside our plasma is simply going to be
+equal to the charge on the electrons the
+
+ align:start position:0%
+equal to the charge on the electrons the
+ 
+
+ align:start position:0%
+equal to the charge on the electrons the
+number of electrons and how fast they're
+
+ align:start position:0%
+number of electrons and how fast they're
+ 
+
+ align:start position:0%
+number of electrons and how fast they're
+moving and so we've simply transferred
+
+ align:start position:0%
+moving and so we've simply transferred
+ 
+
+ align:start position:0%
+moving and so we've simply transferred
+our lack of knowledge about J into our
+
+ align:start position:0%
+our lack of knowledge about J into our
+ 
+
+ align:start position:0%
+our lack of knowledge about J into our
+lack of knowledge about V so we better
+
+ align:start position:0%
+lack of knowledge about V so we better
+ 
+
+ align:start position:0%
+lack of knowledge about V so we better
+do something about that and we're going
+
+ align:start position:0%
+do something about that and we're going
+ 
+
+ align:start position:0%
+do something about that and we're going
+to do that using the electron equation
+
+ align:start position:0%
+to do that using the electron equation
+ 
+
+ align:start position:0%
+to do that using the electron equation
+of motion and that electron equation of
+
+ align:start position:0%
+of motion and that electron equation of
+ 
+
+ align:start position:0%
+of motion and that electron equation of
+motion looks like M dve DT is equal to
+
+ align:start position:0%
+motion looks like M dve DT is equal to
+ 
+
+ align:start position:0%
+motion looks like M dve DT is equal to
+minus E the charge times capital e the
+
+ align:start position:0%
+minus E the charge times capital e the
+ 
+
+ align:start position:0%
+minus E the charge times capital e the
+vector electric field like
+
+ align:start position:0%
+vector electric field like
+ 
+
+ align:start position:0%
+vector electric field like
+that okay so we could rearrange that so
+
+ align:start position:0%
+that okay so we could rearrange that so
+ 
+
+ align:start position:0%
+that okay so we could rearrange that so
+that we have V is equal to
+
+ align:start position:0%
+that we have V is equal to
+ 
+
+ align:start position:0%
+that we have V is equal to
+e Vector e over I Omega we've done the
+
+ align:start position:0%
+e Vector e over I Omega we've done the
+ 
+
+ align:start position:0%
+e Vector e over I Omega we've done the
+same for transform trick that we did
+
+ align:start position:0%
+same for transform trick that we did
+ 
+
+ align:start position:0%
+same for transform trick that we did
+with all the other quantities we assume
+
+ align:start position:0%
+with all the other quantities we assume
+ 
+
+ align:start position:0%
+with all the other quantities we assume
+it's going to be oscillating in some way
+
+ align:start position:0%
+it's going to be oscillating in some way
+ 
+
+ align:start position:0%
+it's going to be oscillating in some way
+substitute that back into our equation
+
+ align:start position:0%
+substitute that back into our equation
+ 
+
+ align:start position:0%
+substitute that back into our equation
+for e and we'll get Omega s minus c^ 2
+
+ align:start position:0%
+for e and we'll get Omega s minus c^ 2
+ 
+
+ align:start position:0%
+for e and we'll get Omega s minus c^ 2
+k^2 e as we had before is equal to NE
+
+ align:start position:0%
+k^2 e as we had before is equal to NE
+ 
+
+ align:start position:0%
+k^2 e as we had before is equal to NE
+e^2
+
+ align:start position:0%
+e^2
+ 
+
+ align:start position:0%
+e^2
+over Epsilon
+
+ align:start position:0%
+over Epsilon
+ 
+
+ align:start position:0%
+over Epsilon
+me capital E sorry was there a question
+
+ align:start position:0%
+me capital E sorry was there a question
+ 
+
+ align:start position:0%
+me capital E sorry was there a question
+I had someone
+
+ align:start position:0%
+I had someone
+ 
+
+ align:start position:0%
+I had someone
+speak no that was an accident sorry oh
+
+ align:start position:0%
+speak no that was an accident sorry oh
+ 
+
+ align:start position:0%
+speak no that was an accident sorry oh
+no right all good um and just to be
+
+ align:start position:0%
+no right all good um and just to be
+ 
+
+ align:start position:0%
+no right all good um and just to be
+clear here this equation of motion
+
+ align:start position:0%
+clear here this equation of motion
+ 
+
+ align:start position:0%
+clear here this equation of motion
+doesn't have the uh V crossb term in it
+
+ align:start position:0%
+doesn't have the uh V crossb term in it
+ 
+
+ align:start position:0%
+doesn't have the uh V crossb term in it
+which should be like the magnetic field
+
+ align:start position:0%
+which should be like the magnetic field
+ 
+
+ align:start position:0%
+which should be like the magnetic field
+term because we've dropped it because
+
+ align:start position:0%
+term because we've dropped it because
+ 
+
+ align:start position:0%
+term because we've dropped it because
+we're making this uh unmagnetized
+
+ align:start position:0%
+we're making this uh unmagnetized
+ 
+
+ align:start position:0%
+we're making this uh unmagnetized
+approximation but that's where you put
+
+ align:start position:0%
+approximation but that's where you put
+ 
+
+ align:start position:0%
+approximation but that's where you put
+it back in you put in a little term that
+
+ align:start position:0%
+it back in you put in a little term that
+ 
+
+ align:start position:0%
+it back in you put in a little term that
+was like plus b cross B in here and put
+
+ align:start position:0%
+was like plus b cross B in here and put
+ 
+
+ align:start position:0%
+was like plus b cross B in here and put
+little brackets around but for now we're
+
+ align:start position:0%
+little brackets around but for now we're
+ 
+
+ align:start position:0%
+little brackets around but for now we're
+just setting that equal to zero okay
+
+ align:start position:0%
+just setting that equal to zero okay
+ 
+
+ align:start position:0%
+just setting that equal to zero okay
+good and the solution to this equation
+
+ align:start position:0%
+good and the solution to this equation
+ 
+
+ align:start position:0%
+good and the solution to this equation
+that we've got now is Omega s equals
+
+ align:start position:0%
+that we've got now is Omega s equals
+ 
+
+ align:start position:0%
+that we've got now is Omega s equals
+Omega p^ 2 plus c^ 2 K 2 so this looks
+
+ align:start position:0%
+Omega p^ 2 plus c^ 2 K 2 so this looks
+ 
+
+ align:start position:0%
+Omega p^ 2 plus c^ 2 K 2 so this looks
+an awful lot like what we had before
+
+ align:start position:0%
+an awful lot like what we had before
+ 
+
+ align:start position:0%
+an awful lot like what we had before
+which was just these two terms but now
+
+ align:start position:0%
+which was just these two terms but now
+ 
+
+ align:start position:0%
+which was just these two terms but now
+we've got this additional term which
+
+ align:start position:0%
+we've got this additional term which
+ 
+
+ align:start position:0%
+we've got this additional term which
+includes some plasma physics and I could
+
+ align:start position:0%
+includes some plasma physics and I could
+ 
+
+ align:start position:0%
+includes some plasma physics and I could
+write that this is omega PE s um and you
+
+ align:start position:0%
+write that this is omega PE s um and you
+ 
+
+ align:start position:0%
+write that this is omega PE s um and you
+know make it clear it's the electrons
+
+ align:start position:0%
+know make it clear it's the electrons
+ 
+
+ align:start position:0%
+know make it clear it's the electrons
+but remember we've dropped the IR motion
+
+ align:start position:0%
+but remember we've dropped the IR motion
+ 
+
+ align:start position:0%
+but remember we've dropped the IR motion
+already so there's only one uh plasma
+
+ align:start position:0%
+already so there's only one uh plasma
+ 
+
+ align:start position:0%
+already so there's only one uh plasma
+frequency that's very interesting the
+
+ align:start position:0%
+frequency that's very interesting the
+ 
+
+ align:start position:0%
+frequency that's very interesting the
+electron plasma frequency for this
+
+ align:start position:0%
+electron plasma frequency for this
+ 
+
+ align:start position:0%
+electron plasma frequency for this
+derivation
+
+ align:start position:0%
+derivation
+ 
+
+ align:start position:0%
+derivation
+here and then we can go ahead and do all
+
+ align:start position:0%
+here and then we can go ahead and do all
+ 
+
+ align:start position:0%
+here and then we can go ahead and do all
+the standard things we do with a
+
+ align:start position:0%
+the standard things we do with a
+ 
+
+ align:start position:0%
+the standard things we do with a
+um one of these uh functions which is to
+
+ align:start position:0%
+um one of these uh functions which is to
+ 
+
+ align:start position:0%
+um one of these uh functions which is to
+try and write down the phase velocity
+
+ align:start position:0%
+try and write down the phase velocity
+ 
+
+ align:start position:0%
+try and write down the phase velocity
+and the phase velocity squ is just equal
+
+ align:start position:0%
+and the phase velocity squ is just equal
+ 
+
+ align:start position:0%
+and the phase velocity squ is just equal
+to Omega 2 upon k^2 and so that means
+
+ align:start position:0%
+to Omega 2 upon k^2 and so that means
+ 
+
+ align:start position:0%
+to Omega 2 upon k^2 and so that means
+our phase velocity is C
+
+ align:start position:0%
+our phase velocity is C
+ 
+
+ align:start position:0%
+our phase velocity is C
+upon 1 minus Omega p ^ 2 upon Omega s so
+
+ align:start position:0%
+upon 1 minus Omega p ^ 2 upon Omega s so
+ 
+
+ align:start position:0%
+upon 1 minus Omega p ^ 2 upon Omega s so
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+half and then we can write down the
+
+ align:start position:0%
+half and then we can write down the
+ 
+
+ align:start position:0%
+half and then we can write down the
+refractive index because our refractive
+
+ align:start position:0%
+refractive index because our refractive
+ 
+
+ align:start position:0%
+refractive index because our refractive
+index capital N is just equal to C over
+
+ align:start position:0%
+index capital N is just equal to C over
+ 
+
+ align:start position:0%
+index capital N is just equal to C over
+the phase velocity and that is going to
+
+ align:start position:0%
+the phase velocity and that is going to
+ 
+
+ align:start position:0%
+the phase velocity and that is going to
+be equal to 1 - Omega p^ 2 over Omega 2
+
+ align:start position:0%
+be equal to 1 - Omega p^ 2 over Omega 2
+ 
+
+ align:start position:0%
+be equal to 1 - Omega p^ 2 over Omega 2
+and we we often write this not in terms
+
+ align:start position:0%
+and we we often write this not in terms
+ 
+
+ align:start position:0%
+and we we often write this not in terms
+of frequencies but in terms of densities
+
+ align:start position:0%
+of frequencies but in terms of densities
+ 
+
+ align:start position:0%
+of frequencies but in terms of densities
+because the plasma frequency has inside
+
+ align:start position:0%
+because the plasma frequency has inside
+ 
+
+ align:start position:0%
+because the plasma frequency has inside
+it an electron density we write 1 minus
+
+ align:start position:0%
+it an electron density we write 1 minus
+ 
+
+ align:start position:0%
+it an electron density we write 1 minus
+NE Over N critical like this where n
+
+ align:start position:0%
+NE Over N critical like this where n
+ 
+
+ align:start position:0%
+NE Over N critical like this where n
+critical is some critical density and
+
+ align:start position:0%
+critical is some critical density and
+ 
+
+ align:start position:0%
+critical is some critical density and
+we'll get on to why it's so critical in
+
+ align:start position:0%
+we'll get on to why it's so critical in
+ 
+
+ align:start position:0%
+we'll get on to why it's so critical in
+a moment but if you want to approximate
+
+ align:start position:0%
+a moment but if you want to approximate
+ 
+
+ align:start position:0%
+a moment but if you want to approximate
+it then n critical in centimeters to
+
+ align:start position:0%
+it then n critical in centimeters to
+ 
+
+ align:start position:0%
+it then n critical in centimeters to
+minus 3 so particles per cubic
+
+ align:start position:0%
+minus 3 so particles per cubic
+ 
+
+ align:start position:0%
+minus 3 so particles per cubic
+centimeter is roughly 10 21 over Lambda
+
+ align:start position:0%
+centimeter is roughly 10 21 over Lambda
+ 
+
+ align:start position:0%
+centimeter is roughly 10 21 over Lambda
+when Lambda is in microns here so if
+
+ align:start position:0%
+when Lambda is in microns here so if
+ 
+
+ align:start position:0%
+when Lambda is in microns here so if
+you're using like a laser beam at one
+
+ align:start position:0%
+you're using like a laser beam at one
+ 
+
+ align:start position:0%
+you're using like a laser beam at one
+micron that would be a very standard
+
+ align:start position:0%
+micron that would be a very standard
+ 
+
+ align:start position:0%
+micron that would be a very standard
+laser wavelength from a near demium yag
+
+ align:start position:0%
+laser wavelength from a near demium yag
+ 
+
+ align:start position:0%
+laser wavelength from a near demium yag
+or near demium glass laser then you have
+
+ align:start position:0%
+or near demium glass laser then you have
+ 
+
+ align:start position:0%
+or near demium glass laser then you have
+a critical density about 10 to 21 which
+
+ align:start position:0%
+a critical density about 10 to 21 which
+ 
+
+ align:start position:0%
+a critical density about 10 to 21 which
+depending on which your field you're
+
+ align:start position:0%
+depending on which your field you're
+ 
+
+ align:start position:0%
+depending on which your field you're
+working in is either hilariously high
+
+ align:start position:0%
+working in is either hilariously high
+ 
+
+ align:start position:0%
+working in is either hilariously high
+and unreachable or crazy low and happens
+
+ align:start position:0%
+and unreachable or crazy low and happens
+ 
+
+ align:start position:0%
+and unreachable or crazy low and happens
+all the time so again this is one of the
+
+ align:start position:0%
+all the time so again this is one of the
+ 
+
+ align:start position:0%
+all the time so again this is one of the
+exciting things about doing plasma
+
+ align:start position:0%
+exciting things about doing plasma
+ 
+
+ align:start position:0%
+exciting things about doing plasma
+Diagnostics course where we span 60 OD
+
+ align:start position:0%
+Diagnostics course where we span 60 OD
+ 
+
+ align:start position:0%
+Diagnostics course where we span 60 OD
+of magnitude in density
+
+ align:start position:0%
+of magnitude in density
+ 
+
+ align:start position:0%
+of magnitude in density
+um any questions
+
+ align:start position:0%
+um any questions
+ 
+
+ align:start position:0%
+um any questions
+on yeah what's the critical density
+
+ align:start position:0%
+on yeah what's the critical density
+ 
+
+ align:start position:0%
+on yeah what's the critical density
+Point
+
+ align:start position:0%
+Point
+ 
+
+ align:start position:0%
+Point
+again as in what is its physical
+
+ align:start position:0%
+again as in what is its physical
+ 
+
+ align:start position:0%
+again as in what is its physical
+significance yeah like why why do you
+
+ align:start position:0%
+significance yeah like why why do you
+ 
+
+ align:start position:0%
+significance yeah like why why do you
+choose that number we're gonna we're
+
+ align:start position:0%
+choose that number we're gonna we're
+ 
+
+ align:start position:0%
+choose that number we're gonna we're
+gonna look look into that in a moment
+
+ align:start position:0%
+gonna look look into that in a moment
+ 
+
+ align:start position:0%
+gonna look look into that in a moment
+it's a good question it's a solid
+
+ align:start position:0%
+it's a good question it's a solid
+ 
+
+ align:start position:0%
+it's a good question it's a solid
+question but it's just to be clear I can
+
+ align:start position:0%
+question but it's just to be clear I can
+ 
+
+ align:start position:0%
+question but it's just to be clear I can
+the reason I've got there is I've taken
+
+ align:start position:0%
+the reason I've got there is I've taken
+ 
+
+ align:start position:0%
+the reason I've got there is I've taken
+this Omega p squ and this Omega squ and
+
+ align:start position:0%
+this Omega p squ and this Omega squ and
+ 
+
+ align:start position:0%
+this Omega p squ and this Omega squ and
+I've noticed that Omega p^ s has inside
+
+ align:start position:0%
+I've noticed that Omega p^ s has inside
+ 
+
+ align:start position:0%
+I've noticed that Omega p^ s has inside
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+the electron density and I've Rewritten
+
+ align:start position:0%
+the electron density and I've Rewritten
+ 
+
+ align:start position:0%
+the electron density and I've Rewritten
+all the other terms so uh this n
+
+ align:start position:0%
+all the other terms so uh this n
+ 
+
+ align:start position:0%
+all the other terms so uh this n
+critical now has inside it things like
+
+ align:start position:0%
+critical now has inside it things like
+ 
+
+ align:start position:0%
+critical now has inside it things like
+uh Omega squar I made a critical mistake
+
+ align:start position:0%
+uh Omega squar I made a critical mistake
+ 
+
+ align:start position:0%
+uh Omega squar I made a critical mistake
+in my equation up here this is Lambda
+
+ align:start position:0%
+in my equation up here this is Lambda
+ 
+
+ align:start position:0%
+in my equation up here this is Lambda
+squared here for approximating this in
+
+ align:start position:0%
+squared here for approximating this in
+ 
+
+ align:start position:0%
+squared here for approximating this in
+terms of sort of symol quantities so the
+
+ align:start position:0%
+terms of sort of symol quantities so the
+ 
+
+ align:start position:0%
+terms of sort of symol quantities so the
+the N critical now depends on the uh
+
+ align:start position:0%
+the N critical now depends on the uh
+ 
+
+ align:start position:0%
+the N critical now depends on the uh
+laser wavelength or the the frequency of
+
+ align:start position:0%
+laser wavelength or the the frequency of
+ 
+
+ align:start position:0%
+laser wavelength or the the frequency of
+your probing electromagnetic radiation
+
+ align:start position:0%
+your probing electromagnetic radiation
+ 
+
+ align:start position:0%
+your probing electromagnetic radiation
+so it's different for every frequency um
+
+ align:start position:0%
+so it's different for every frequency um
+ 
+
+ align:start position:0%
+so it's different for every frequency um
+but that's the only it depends on the
+
+ align:start position:0%
+but that's the only it depends on the
+ 
+
+ align:start position:0%
+but that's the only it depends on the
+rest of it is all like fundamental
+
+ align:start position:0%
+rest of it is all like fundamental
+ 
+
+ align:start position:0%
+rest of it is all like fundamental
+constants like e and the electron mass
+
+ align:start position:0%
+constants like e and the electron mass
+ 
+
+ align:start position:0%
+constants like e and the electron mass
+that don't change so this is a parameter
+
+ align:start position:0%
+that don't change so this is a parameter
+ 
+
+ align:start position:0%
+that don't change so this is a parameter
+there's a critical density for every
+
+ align:start position:0%
+there's a critical density for every
+ 
+
+ align:start position:0%
+there's a critical density for every
+single uh laser wavelength or
+
+ align:start position:0%
+single uh laser wavelength or
+ 
+
+ align:start position:0%
+single uh laser wavelength or
+electromagnetic wave frequency I'm going
+
+ align:start position:0%
+electromagnetic wave frequency I'm going
+ 
+
+ align:start position:0%
+electromagnetic wave frequency I'm going
+to talk about lasers a lot of course
+
+ align:start position:0%
+to talk about lasers a lot of course
+ 
+
+ align:start position:0%
+to talk about lasers a lot of course
+this also applies like mic waves and
+
+ align:start position:0%
+this also applies like mic waves and
+ 
+
+ align:start position:0%
+this also applies like mic waves and
+things like that as well but some sort
+
+ align:start position:0%
+things like that as well but some sort
+ 
+
+ align:start position:0%
+things like that as well but some sort
+of source of em radiation so I'm going
+
+ align:start position:0%
+of source of em radiation so I'm going
+ 
+
+ align:start position:0%
+of source of em radiation so I'm going
+to get on to what n critical is in in
+
+ align:start position:0%
+to get on to what n critical is in in
+ 
+
+ align:start position:0%
+to get on to what n critical is in in
+just a moment uh but any other questions
+
+ align:start position:0%
+just a moment uh but any other questions
+ 
+
+ align:start position:0%
+just a moment uh but any other questions
+on this before we keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we just said that n is equal to
+
+ align:start position:0%
+okay so we just said that n is equal to
+ 
+
+ align:start position:0%
+okay so we just said that n is equal to
+theare root of 1 minus NE Over N
+
+ align:start position:0%
+theare root of 1 minus NE Over N
+ 
+
+ align:start position:0%
+theare root of 1 minus NE Over N
+critical if we work in a regime where NE
+
+ align:start position:0%
+critical if we work in a regime where NE
+ 
+
+ align:start position:0%
+critical if we work in a regime where NE
+is much much less than n critical so we
+
+ align:start position:0%
+is much much less than n critical so we
+ 
+
+ align:start position:0%
+is much much less than n critical so we
+work far from the critical density we
+
+ align:start position:0%
+work far from the critical density we
+ 
+
+ align:start position:0%
+work far from the critical density we
+can do a tailor expansion and which is
+
+ align:start position:0%
+can do a tailor expansion and which is
+ 
+
+ align:start position:0%
+can do a tailor expansion and which is
+what we often end up doing and we write
+
+ align:start position:0%
+what we often end up doing and we write
+ 
+
+ align:start position:0%
+what we often end up doing and we write
+one minus NE over two and critical like
+
+ align:start position:0%
+one minus NE over two and critical like
+ 
+
+ align:start position:0%
+one minus NE over two and critical like
+this so my questions for you now and we
+
+ align:start position:0%
+this so my questions for you now and we
+ 
+
+ align:start position:0%
+this so my questions for you now and we
+will try and work out what and critical
+
+ align:start position:0%
+will try and work out what and critical
+ 
+
+ align:start position:0%
+will try and work out what and critical
+is doing together for
+
+ align:start position:0%
+is doing together for
+ 
+
+ align:start position:0%
+is doing together for
+n for a density which is greater than
+
+ align:start position:0%
+n for a density which is greater than
+ 
+
+ align:start position:0%
+n for a density which is greater than
+the critical density what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M the refractor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+index the wave becomes
+
+ align:start position:0%
+index the wave becomes
+ 
+
+ align:start position:0%
+index the wave becomes
+right yeah well so that's the result
+
+ align:start position:0%
+right yeah well so that's the result
+ 
+
+ align:start position:0%
+right yeah well so that's the result
+yeah so what happens to n
+
+ align:start position:0%
+yeah so what happens to n
+ 
+
+ align:start position:0%
+yeah so what happens to n
+itself Big N it's
+
+ align:start position:0%
+itself Big N it's
+ 
+
+ align:start position:0%
+itself Big N it's
+imaginary right exactly yeah yeah you
+
+ align:start position:0%
+imaginary right exactly yeah yeah you
+ 
+
+ align:start position:0%
+imaginary right exactly yeah yeah you
+you you you've got the right answer I
+
+ align:start position:0%
+you you you've got the right answer I
+ 
+
+ align:start position:0%
+you you you've got the right answer I
+just wanted to take in a few more steps
+
+ align:start position:0%
+just wanted to take in a few more steps
+ 
+
+ align:start position:0%
+just wanted to take in a few more steps
+so n is
+
+ align:start position:0%
+so n is
+ 
+
+ align:start position:0%
+so n is
+imaginary because it's going to be the
+
+ align:start position:0%
+imaginary because it's going to be the
+ 
+
+ align:start position:0%
+imaginary because it's going to be the
+square root of a negative number which
+
+ align:start position:0%
+square root of a negative number which
+ 
+
+ align:start position:0%
+square root of a negative number which
+we can see
+
+ align:start position:0%
+we can see
+ 
+
+ align:start position:0%
+we can see
+here and so that means our wave becomes
+
+ align:start position:0%
+here and so that means our wave becomes
+ 
+
+ align:start position:0%
+here and so that means our wave becomes
+evanescent so it's going to have
+
+ align:start position:0%
+evanescent so it's going to have
+ 
+
+ align:start position:0%
+evanescent so it's going to have
+properties which decay in time so it's
+
+ align:start position:0%
+properties which decay in time so it's
+ 
+
+ align:start position:0%
+properties which decay in time so it's
+going to look like e minus alpha x e
+
+ align:start position:0%
+going to look like e minus alpha x e
+ 
+
+ align:start position:0%
+going to look like e minus alpha x e
+minus gamma T like this so it dies off
+
+ align:start position:0%
+minus gamma T like this so it dies off
+ 
+
+ align:start position:0%
+minus gamma T like this so it dies off
+okay so that means that we can't
+
+ align:start position:0%
+okay so that means that we can't
+ 
+
+ align:start position:0%
+okay so that means that we can't
+propagate a wave at densities greater
+
+ align:start position:0%
+propagate a wave at densities greater
+ 
+
+ align:start position:0%
+propagate a wave at densities greater
+than the critical density what happens
+
+ align:start position:0%
+than the critical density what happens
+ 
+
+ align:start position:0%
+than the critical density what happens
+to all the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then because this wave is carrying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy abor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no absorption mechanism in our equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually yeah so that I mean from the
+
+ align:start position:0%
+actually yeah so that I mean from the
+ 
+
+ align:start position:0%
+actually yeah so that I mean from the
+math we have it the only option is
+
+ align:start position:0%
+math we have it the only option is
+ 
+
+ align:start position:0%
+math we have it the only option is
+reflection right
+
+ align:start position:0%
+reflection right
+ 
+
+ align:start position:0%
+reflection right
+yeah so reflection is indeed the answer
+
+ align:start position:0%
+yeah so reflection is indeed the answer
+ 
+
+ align:start position:0%
+yeah so reflection is indeed the answer
+so we will get reflection of this wave
+
+ align:start position:0%
+so we will get reflection of this wave
+ 
+
+ align:start position:0%
+so we will get reflection of this wave
+that will bounce off the critical
+
+ align:start position:0%
+that will bounce off the critical
+ 
+
+ align:start position:0%
+that will bounce off the critical
+surface and go somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else um we'd only be able to have
+
+ align:start position:0%
+else um we'd only be able to have
+ 
+
+ align:start position:0%
+else um we'd only be able to have
+absorption if we put for example
+
+ align:start position:0%
+absorption if we put for example
+ 
+
+ align:start position:0%
+absorption if we put for example
+collisions into the equation of motion
+
+ align:start position:0%
+collisions into the equation of motion
+ 
+
+ align:start position:0%
+collisions into the equation of motion
+all the way back there and then we could
+
+ align:start position:0%
+all the way back there and then we could
+ 
+
+ align:start position:0%
+all the way back there and then we could
+have what's called inverse brmr which is
+
+ align:start position:0%
+have what's called inverse brmr which is
+ 
+
+ align:start position:0%
+have what's called inverse brmr which is
+effectively the electrons get oscillated
+
+ align:start position:0%
+effectively the electrons get oscillated
+ 
+
+ align:start position:0%
+effectively the electrons get oscillated
+by the wave and then they collide with
+
+ align:start position:0%
+by the wave and then they collide with
+ 
+
+ align:start position:0%
+by the wave and then they collide with
+some ions and transfer the energy to the
+
+ align:start position:0%
+some ions and transfer the energy to the
+ 
+
+ align:start position:0%
+some ions and transfer the energy to the
+ions and that's a damping mechanism
+
+ align:start position:0%
+ions and that's a damping mechanism
+ 
+
+ align:start position:0%
+ions and that's a damping mechanism
+there could be other damping mechanisms
+
+ align:start position:0%
+there could be other damping mechanisms
+ 
+
+ align:start position:0%
+there could be other damping mechanisms
+like landal but in the equations we've
+
+ align:start position:0%
+like landal but in the equations we've
+ 
+
+ align:start position:0%
+like landal but in the equations we've
+got so far we we don't actually have
+
+ align:start position:0%
+got so far we we don't actually have
+ 
+
+ align:start position:0%
+got so far we we don't actually have
+those so reflection is the only thing
+
+ align:start position:0%
+those so reflection is the only thing
+ 
+
+ align:start position:0%
+those so reflection is the only thing
+that can happen now we also had this
+
+ align:start position:0%
+that can happen now we also had this
+ 
+
+ align:start position:0%
+that can happen now we also had this
+equation for the phase velocity which
+
+ align:start position:0%
+equation for the phase velocity which
+ 
+
+ align:start position:0%
+equation for the phase velocity which
+was that VP is equal to
+
+ align:start position:0%
+was that VP is equal to
+ 
+
+ align:start position:0%
+was that VP is equal to
+C over 1us Omega p^ 2 upon Omega s to
+
+ align:start position:0%
+C over 1us Omega p^ 2 upon Omega s to
+ 
+
+ align:start position:0%
+C over 1us Omega p^ 2 upon Omega s to
+the half does anyone want to comment on
+
+ align:start position:0%
+the half does anyone want to comment on
+ 
+
+ align:start position:0%
+the half does anyone want to comment on
+what happens to the phase velocity as we
+
+ align:start position:0%
+what happens to the phase velocity as we
+ 
+
+ align:start position:0%
+what happens to the phase velocity as we
+go above the critical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density there's a go to
+
+ align:start position:0%
+density there's a go to
+ 
+
+ align:start position:0%
+density there's a go to
+Infinity oh I mean we'll do that
+
+ align:start position:0%
+Infinity oh I mean we'll do that
+ 
+
+ align:start position:0%
+Infinity oh I mean we'll do that
+eventually yes yeah yes I guess right
+
+ align:start position:0%
+eventually yes yeah yes I guess right
+ 
+
+ align:start position:0%
+eventually yes yeah yes I guess right
+there at that point diverges extremely
+
+ align:start position:0%
+there at that point diverges extremely
+ 
+
+ align:start position:0%
+there at that point diverges extremely
+large yeah
+
+ align:start position:0%
+large yeah
+ 
+
+ align:start position:0%
+large yeah
+yes yeah so this is this is going to
+
+ align:start position:0%
+yes yeah so this is this is going to
+ 
+
+ align:start position:0%
+yes yeah so this is this is going to
+start doing very
+
+ align:start position:0%
+start doing very
+ 
+
+ align:start position:0%
+start doing very
+silly things here and those things don't
+
+ align:start position:0%
+silly things here and those things don't
+ 
+
+ align:start position:0%
+silly things here and those things don't
+seem very physical of course because we
+
+ align:start position:0%
+seem very physical of course because we
+ 
+
+ align:start position:0%
+seem very physical of course because we
+don't want things traveling FAS than the
+
+ align:start position:0%
+don't want things traveling FAS than the
+ 
+
+ align:start position:0%
+don't want things traveling FAS than the
+speed of light um fortunately this isn't
+
+ align:start position:0%
+speed of light um fortunately this isn't
+ 
+
+ align:start position:0%
+speed of light um fortunately this isn't
+a big problem um because the phase
+
+ align:start position:0%
+a big problem um because the phase
+ 
+
+ align:start position:0%
+a big problem um because the phase
+velocity doesn't carry any information
+
+ align:start position:0%
+velocity doesn't carry any information
+ 
+
+ align:start position:0%
+velocity doesn't carry any information
+the limitations on things going faster
+
+ align:start position:0%
+the limitations on things going faster
+ 
+
+ align:start position:0%
+the limitations on things going faster
+and the speed of light have to do with
+
+ align:start position:0%
+and the speed of light have to do with
+ 
+
+ align:start position:0%
+and the speed of light have to do with
+information and the information is
+
+ align:start position:0%
+information and the information is
+ 
+
+ align:start position:0%
+information and the information is
+encoded in a quantity called the group
+
+ align:start position:0%
+encoded in a quantity called the group
+ 
+
+ align:start position:0%
+encoded in a quantity called the group
+velocity and the group velocity just
+
+ align:start position:0%
+velocity and the group velocity just
+ 
+
+ align:start position:0%
+velocity and the group velocity just
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+this c times the square root of 1 minus
+
+ align:start position:0%
+this c times the square root of 1 minus
+ 
+
+ align:start position:0%
+this c times the square root of 1 minus
+Omega p^ 2 upon Omega squ and so as we
+
+ align:start position:0%
+Omega p^ 2 upon Omega squ and so as we
+ 
+
+ align:start position:0%
+Omega p^ 2 upon Omega squ and so as we
+get close to the critical density here
+
+ align:start position:0%
+get close to the critical density here
+ 
+
+ align:start position:0%
+get close to the critical density here
+all that happens is the group velocity
+
+ align:start position:0%
+all that happens is the group velocity
+ 
+
+ align:start position:0%
+all that happens is the group velocity
+goes to zero and effectively we transmit
+
+ align:start position:0%
+goes to zero and effectively we transmit
+ 
+
+ align:start position:0%
+goes to zero and effectively we transmit
+no information through that evanescent
+
+ align:start position:0%
+no information through that evanescent
+ 
+
+ align:start position:0%
+no information through that evanescent
+region so we don't have to worry about
+
+ align:start position:0%
+region so we don't have to worry about
+ 
+
+ align:start position:0%
+region so we don't have to worry about
+the fact phase velocity is super luminal
+
+ align:start position:0%
+the fact phase velocity is super luminal
+ 
+
+ align:start position:0%
+the fact phase velocity is super luminal
+because our group velocity is still
+
+ align:start position:0%
+because our group velocity is still
+ 
+
+ align:start position:0%
+because our group velocity is still
+subluminal as you know we'd like
+
+ align:start position:0%
+subluminal as you know we'd like
+ 
+
+ align:start position:0%
+subluminal as you know we'd like
+sh so if the waves being reflected here
+
+ align:start position:0%
+sh so if the waves being reflected here
+ 
+
+ align:start position:0%
+sh so if the waves being reflected here
+and the group velocity is going to zero
+
+ align:start position:0%
+and the group velocity is going to zero
+ 
+
+ align:start position:0%
+and the group velocity is going to zero
+to me that seems like the wave
+
+ align:start position:0%
+to me that seems like the wave
+ 
+
+ align:start position:0%
+to me that seems like the wave
+information is sort of stagnating at the
+
+ align:start position:0%
+information is sort of stagnating at the
+ 
+
+ align:start position:0%
+information is sort of stagnating at the
+Reflection Point how do we see from
+
+ align:start position:0%
+Reflection Point how do we see from
+ 
+
+ align:start position:0%
+Reflection Point how do we see from
+these equations that the wave
+
+ align:start position:0%
+these equations that the wave
+ 
+
+ align:start position:0%
+these equations that the wave
+information is actually being reflected
+
+ align:start position:0%
+information is actually being reflected
+ 
+
+ align:start position:0%
+information is actually being reflected
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+out it's very good
+
+ align:start position:0%
+out it's very good
+ 
+
+ align:start position:0%
+out it's very good
+question I think you um excuse me I
+
+ align:start position:0%
+question I think you um excuse me I
+ 
+
+ align:start position:0%
+question I think you um excuse me I
+think you need to like impose boundary
+
+ align:start position:0%
+think you need to like impose boundary
+ 
+
+ align:start position:0%
+think you need to like impose boundary
+conditions to to do that so because
+
+ align:start position:0%
+conditions to to do that so because
+ 
+
+ align:start position:0%
+conditions to to do that so because
+there' be some sort of discontinuity
+
+ align:start position:0%
+there' be some sort of discontinuity
+ 
+
+ align:start position:0%
+there' be some sort of discontinuity
+right yeah I suspect the model I'm
+
+ align:start position:0%
+right yeah I suspect the model I'm
+ 
+
+ align:start position:0%
+right yeah I suspect the model I'm
+presenting is a little bit too
+
+ align:start position:0%
+presenting is a little bit too
+ 
+
+ align:start position:0%
+presenting is a little bit too
+simplistic to handle this stuff um so we
+
+ align:start position:0%
+simplistic to handle this stuff um so we
+ 
+
+ align:start position:0%
+simplistic to handle this stuff um so we
+would need to bake in some more
+
+ align:start position:0%
+would need to bake in some more
+ 
+
+ align:start position:0%
+would need to bake in some more
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+I think so there certainly as you get
+
+ align:start position:0%
+I think so there certainly as you get
+ 
+
+ align:start position:0%
+I think so there certainly as you get
+very very slow group velocities you're
+
+ align:start position:0%
+very very slow group velocities you're
+ 
+
+ align:start position:0%
+very very slow group velocities you're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+start we've been making some assumptions
+
+ align:start position:0%
+start we've been making some assumptions
+ 
+
+ align:start position:0%
+start we've been making some assumptions
+about the homogeneity here and so we're
+
+ align:start position:0%
+about the homogeneity here and so we're
+ 
+
+ align:start position:0%
+about the homogeneity here and so we're
+effectively there's going to be some
+
+ align:start position:0%
+effectively there's going to be some
+ 
+
+ align:start position:0%
+effectively there's going to be some
+length scale in here which is going to
+
+ align:start position:0%
+length scale in here which is going to
+ 
+
+ align:start position:0%
+length scale in here which is going to
+be like K the size of the wave Vector of
+
+ align:start position:0%
+be like K the size of the wave Vector of
+ 
+
+ align:start position:0%
+be like K the size of the wave Vector of
+the light at a given point and we're
+
+ align:start position:0%
+the light at a given point and we're
+ 
+
+ align:start position:0%
+the light at a given point and we're
+going to be comparing that to the length
+
+ align:start position:0%
+going to be comparing that to the length
+ 
+
+ align:start position:0%
+going to be comparing that to the length
+scale associated with how quickly the
+
+ align:start position:0%
+scale associated with how quickly the
+ 
+
+ align:start position:0%
+scale associated with how quickly the
+electron density changes this gradient
+
+ align:start position:0%
+electron density changes this gradient
+ 
+
+ align:start position:0%
+electron density changes this gradient
+length scale here and as the
+
+ align:start position:0%
+length scale here and as the
+ 
+
+ align:start position:0%
+length scale here and as the
+group velocity gets very very low that K
+
+ align:start position:0%
+group velocity gets very very low that K
+ 
+
+ align:start position:0%
+group velocity gets very very low that K
+is going to get uh very very long and uh
+
+ align:start position:0%
+is going to get uh very very long and uh
+ 
+
+ align:start position:0%
+is going to get uh very very long and uh
+we're going to start violating our our
+
+ align:start position:0%
+we're going to start violating our our
+ 
+
+ align:start position:0%
+we're going to start violating our our
+assumption that K is let's see let me
+
+ align:start position:0%
+assumption that K is let's see let me
+ 
+
+ align:start position:0%
+assumption that K is let's see let me
+maybe I can write this as Lambda that
+
+ align:start position:0%
+maybe I can write this as Lambda that
+ 
+
+ align:start position:0%
+maybe I can write this as Lambda that
+Lambda is going to be much much less
+
+ align:start position:0%
+Lambda is going to be much much less
+ 
+
+ align:start position:0%
+Lambda is going to be much much less
+than this uh change in the gradient so
+
+ align:start position:0%
+than this uh change in the gradient so
+ 
+
+ align:start position:0%
+than this uh change in the gradient so
+for any realistic system our density has
+
+ align:start position:0%
+for any realistic system our density has
+ 
+
+ align:start position:0%
+for any realistic system our density has
+to ramp up right it can't just
+
+ align:start position:0%
+to ramp up right it can't just
+ 
+
+ align:start position:0%
+to ramp up right it can't just
+immediately get up to the critical
+
+ align:start position:0%
+immediately get up to the critical
+ 
+
+ align:start position:0%
+immediately get up to the critical
+density this could be the critical
+
+ align:start position:0%
+density this could be the critical
+ 
+
+ align:start position:0%
+density this could be the critical
+density here and we're going to find out
+
+ align:start position:0%
+density here and we're going to find out
+ 
+
+ align:start position:0%
+density here and we're going to find out
+that there's some region where some of
+
+ align:start position:0%
+that there's some region where some of
+ 
+
+ align:start position:0%
+that there's some region where some of
+the approximations we've implicitly been
+
+ align:start position:0%
+the approximations we've implicitly been
+ 
+
+ align:start position:0%
+the approximations we've implicitly been
+making break down and then you not need
+
+ align:start position:0%
+making break down and then you not need
+ 
+
+ align:start position:0%
+making break down and then you not need
+to start doing like uh wbk and all that
+
+ align:start position:0%
+to start doing like uh wbk and all that
+ 
+
+ align:start position:0%
+to start doing like uh wbk and all that
+sort of stuff and doing everything
+
+ align:start position:0%
+sort of stuff and doing everything
+ 
+
+ align:start position:0%
+sort of stuff and doing everything
+properly so I think effectively this
+
+ align:start position:0%
+properly so I think effectively this
+ 
+
+ align:start position:0%
+properly so I think effectively this
+simple model breaks down but if you do
+
+ align:start position:0%
+simple model breaks down but if you do
+ 
+
+ align:start position:0%
+simple model breaks down but if you do
+it properly and I think Hutchinson does
+
+ align:start position:0%
+it properly and I think Hutchinson does
+ 
+
+ align:start position:0%
+it properly and I think Hutchinson does
+this in the reflectometry section so we
+
+ align:start position:0%
+this in the reflectometry section so we
+ 
+
+ align:start position:0%
+this in the reflectometry section so we
+may end up doing it um you you can get
+
+ align:start position:0%
+may end up doing it um you you can get
+ 
+
+ align:start position:0%
+may end up doing it um you you can get
+the answer about the reflection there
+
+ align:start position:0%
+the answer about the reflection there
+ 
+
+ align:start position:0%
+the answer about the reflection there
+it's a good question this is very
+
+ align:start position:0%
+it's a good question this is very
+ 
+
+ align:start position:0%
+it's a good question this is very
+handwavy at this point I agree thanks
+
+ align:start position:0%
+handwavy at this point I agree thanks
+ 
+
+ align:start position:0%
+handwavy at this point I agree thanks
+cool any other questions on this because
+
+ align:start position:0%
+cool any other questions on this because
+ 
+
+ align:start position:0%
+cool any other questions on this because
+this this equation here we are now going
+
+ align:start position:0%
+this this equation here we are now going
+ 
+
+ align:start position:0%
+this this equation here we are now going
+to use an awful lot so I'd like you to
+
+ align:start position:0%
+to use an awful lot so I'd like you to
+ 
+
+ align:start position:0%
+to use an awful lot so I'd like you to
+agree that it's valid within the
+
+ align:start position:0%
+agree that it's valid within the
+ 
+
+ align:start position:0%
+agree that it's valid within the
+assumptions that we've made and if you
+
+ align:start position:0%
+assumptions that we've made and if you
+ 
+
+ align:start position:0%
+assumptions that we've made and if you
+don't agree we should have talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay good so let's keep going so
+
+ align:start position:0%
+it okay good so let's keep going so
+ 
+
+ align:start position:0%
+it okay good so let's keep going so
+there is a series of different
+
+ align:start position:0%
+there is a series of different
+ 
+
+ align:start position:0%
+there is a series of different
+measurements that we can make and these
+
+ align:start position:0%
+measurements that we can make and these
+ 
+
+ align:start position:0%
+measurements that we can make and these
+are the refractive index Diagnostics so
+
+ align:start position:0%
+are the refractive index Diagnostics so
+ 
+
+ align:start position:0%
+are the refractive index Diagnostics so
+I'm going to just call these n
+
+ align:start position:0%
+I'm going to just call these n
+ 
+
+ align:start position:0%
+I'm going to just call these n
+measurements or n
+
+ align:start position:0%
+measurements or n
+ 
+
+ align:start position:0%
+measurements or n
+Diagnostics because they rely on the
+
+ align:start position:0%
+Diagnostics because they rely on the
+ 
+
+ align:start position:0%
+Diagnostics because they rely on the
+change in the refractive index here so
+
+ align:start position:0%
+change in the refractive index here so
+ 
+
+ align:start position:0%
+change in the refractive index here so
+one type is when the refractive index is
+
+ align:start position:0%
+one type is when the refractive index is
+ 
+
+ align:start position:0%
+one type is when the refractive index is
+not equal to one there's a refractive
+
+ align:start position:0%
+not equal to one there's a refractive
+ 
+
+ align:start position:0%
+not equal to one there's a refractive
+index inside our plasma is not equal to
+
+ align:start position:0%
+index inside our plasma is not equal to
+ 
+
+ align:start position:0%
+index inside our plasma is not equal to
+one which is true anytime there's any
+
+ align:start position:0%
+one which is true anytime there's any
+ 
+
+ align:start position:0%
+one which is true anytime there's any
+density inside the
+
+ align:start position:0%
+density inside the
+ 
+
+ align:start position:0%
+density inside the
+plasma this sort of diagnostic causes a
+
+ align:start position:0%
+plasma this sort of diagnostic causes a
+ 
+
+ align:start position:0%
+plasma this sort of diagnostic causes a
+phase shift so the plasma ends up the
+
+ align:start position:0%
+phase shift so the plasma ends up the
+ 
+
+ align:start position:0%
+phase shift so the plasma ends up the
+the the laser beam going through or the
+
+ align:start position:0%
+the the laser beam going through or the
+ 
+
+ align:start position:0%
+the the laser beam going through or the
+electromagnetic radiation going through
+
+ align:start position:0%
+electromagnetic radiation going through
+ 
+
+ align:start position:0%
+electromagnetic radiation going through
+plas ends up with a different phasee
+
+ align:start position:0%
+plas ends up with a different phasee
+ 
+
+ align:start position:0%
+plas ends up with a different phasee
+than it would have done in the absence
+
+ align:start position:0%
+than it would have done in the absence
+ 
+
+ align:start position:0%
+than it would have done in the absence
+of the plasma and we can measure that
+
+ align:start position:0%
+of the plasma and we can measure that
+ 
+
+ align:start position:0%
+of the plasma and we can measure that
+phase shift using a technique called
+
+ align:start position:0%
+phase shift using a technique called
+ 
+
+ align:start position:0%
+phase shift using a technique called
+interferometry and with interferometry
+
+ align:start position:0%
+interferometry and with interferometry
+ 
+
+ align:start position:0%
+interferometry and with interferometry
+we can therefore say something about the
+
+ align:start position:0%
+we can therefore say something about the
+ 
+
+ align:start position:0%
+we can therefore say something about the
+density inside the
+
+ align:start position:0%
+density inside the
+ 
+
+ align:start position:0%
+density inside the
+plasma another technique is when the
+
+ align:start position:0%
+plasma another technique is when the
+ 
+
+ align:start position:0%
+plasma another technique is when the
+gradient of the refractive index is not
+
+ align:start position:0%
+gradient of the refractive index is not
+ 
+
+ align:start position:0%
+gradient of the refractive index is not
+equal to zero so this is when there is
+
+ align:start position:0%
+equal to zero so this is when there is
+ 
+
+ align:start position:0%
+equal to zero so this is when there is
+any change in the refractive index and
+
+ align:start position:0%
+any change in the refractive index and
+ 
+
+ align:start position:0%
+any change in the refractive index and
+in a plasma that corresponds very
+
+ align:start position:0%
+in a plasma that corresponds very
+ 
+
+ align:start position:0%
+in a plasma that corresponds very
+clearly to just changes in the electron
+
+ align:start position:0%
+clearly to just changes in the electron
+ 
+
+ align:start position:0%
+clearly to just changes in the electron
+density so gradients in the electron
+
+ align:start position:0%
+density so gradients in the electron
+ 
+
+ align:start position:0%
+density so gradients in the electron
+density but of course in general this
+
+ align:start position:0%
+density but of course in general this
+ 
+
+ align:start position:0%
+density but of course in general this
+technique could be used for any medium
+
+ align:start position:0%
+technique could be used for any medium
+ 
+
+ align:start position:0%
+technique could be used for any medium
+weather refractive index changes so air
+
+ align:start position:0%
+weather refractive index changes so air
+ 
+
+ align:start position:0%
+weather refractive index changes so air
+if you heat it up the refracted index
+
+ align:start position:0%
+if you heat it up the refracted index
+ 
+
+ align:start position:0%
+if you heat it up the refracted index
+changes and so you could use these
+
+ align:start position:0%
+changes and so you could use these
+ 
+
+ align:start position:0%
+changes and so you could use these
+techniques these are not specific to
+
+ align:start position:0%
+techniques these are not specific to
+ 
+
+ align:start position:0%
+techniques these are not specific to
+plasma physics and these Diagnostics
+
+ align:start position:0%
+plasma physics and these Diagnostics
+ 
+
+ align:start position:0%
+plasma physics and these Diagnostics
+tend to be called refraction Diagnostics
+
+ align:start position:0%
+tend to be called refraction Diagnostics
+ 
+
+ align:start position:0%
+tend to be called refraction Diagnostics
+because the light refracts and it bends
+
+ align:start position:0%
+because the light refracts and it bends
+ 
+
+ align:start position:0%
+because the light refracts and it bends
+and we end up doing techniques such as
+
+ align:start position:0%
+and we end up doing techniques such as
+ 
+
+ align:start position:0%
+and we end up doing techniques such as
+schen and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ography and then the final type that I'm
+
+ align:start position:0%
+ography and then the final type that I'm
+ 
+
+ align:start position:0%
+ography and then the final type that I'm
+going to talk about are ones where
+
+ align:start position:0%
+going to talk about are ones where
+ 
+
+ align:start position:0%
+going to talk about are ones where
+actually the
+
+ align:start position:0%
+actually the
+ 
+
+ align:start position:0%
+actually the
+polarization uh the the the medium is B
+
+ align:start position:0%
+polarization uh the the the medium is B
+ 
+
+ align:start position:0%
+polarization uh the the the medium is B
+refringent it treats different
+
+ align:start position:0%
+refringent it treats different
+ 
+
+ align:start position:0%
+refringent it treats different
+polarizations differently and so we can
+
+ align:start position:0%
+polarizations differently and so we can
+ 
+
+ align:start position:0%
+polarizations differently and so we can
+have polarizations of Light which are
+
+ align:start position:0%
+have polarizations of Light which are
+ 
+
+ align:start position:0%
+have polarizations of Light which are
+circular we can have the left-handed and
+
+ align:start position:0%
+circular we can have the left-handed and
+ 
+
+ align:start position:0%
+circular we can have the left-handed and
+the right-handed polarizations which we
+
+ align:start position:0%
+the right-handed polarizations which we
+ 
+
+ align:start position:0%
+the right-handed polarizations which we
+sometimes refer to as plus and minus and
+
+ align:start position:0%
+sometimes refer to as plus and minus and
+ 
+
+ align:start position:0%
+sometimes refer to as plus and minus and
+here we would say that the refractive
+
+ align:start position:0%
+here we would say that the refractive
+ 
+
+ align:start position:0%
+here we would say that the refractive
+index for the plus wave is not equal to
+
+ align:start position:0%
+index for the plus wave is not equal to
+ 
+
+ align:start position:0%
+index for the plus wave is not equal to
+the refractive index of the minus wave
+
+ align:start position:0%
+the refractive index of the minus wave
+ 
+
+ align:start position:0%
+the refractive index of the minus wave
+here and so there here we measure the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polarization and this is using a
+
+ align:start position:0%
+polarization and this is using a
+ 
+
+ align:start position:0%
+polarization and this is using a
+technique called
+
+ align:start position:0%
+technique called
+ 
+
+ align:start position:0%
+technique called
+Faraday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or Faraday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation which we briefly discussed in
+
+ align:start position:0%
+rotation which we briefly discussed in
+ 
+
+ align:start position:0%
+rotation which we briefly discussed in
+the context of magnetic field
+
+ align:start position:0%
+the context of magnetic field
+ 
+
+ align:start position:0%
+the context of magnetic field
+measurements using ver glass
+
+ align:start position:0%
+measurements using ver glass
+ 
+
+ align:start position:0%
+measurements using ver glass
+um and in fact it turns out that you
+
+ align:start position:0%
+um and in fact it turns out that you
+ 
+
+ align:start position:0%
+um and in fact it turns out that you
+need to have magnetic fields that are
+
+ align:start position:0%
+need to have magnetic fields that are
+ 
+
+ align:start position:0%
+need to have magnetic fields that are
+nonzero and we also need to relax our
+
+ align:start position:0%
+nonzero and we also need to relax our
+ 
+
+ align:start position:0%
+nonzero and we also need to relax our
+assumption that the plasma is
+
+ align:start position:0%
+assumption that the plasma is
+ 
+
+ align:start position:0%
+assumption that the plasma is
+unmagnetized in the sense that the light
+
+ align:start position:0%
+unmagnetized in the sense that the light
+ 
+
+ align:start position:0%
+unmagnetized in the sense that the light
+frequency is much larger than the
+
+ align:start position:0%
+frequency is much larger than the
+ 
+
+ align:start position:0%
+frequency is much larger than the
+electron cyron frequency so those are
+
+ align:start position:0%
+electron cyron frequency so those are
+ 
+
+ align:start position:0%
+electron cyron frequency so those are
+three different types of refractive
+
+ align:start position:0%
+three different types of refractive
+ 
+
+ align:start position:0%
+three different types of refractive
+index Diagnostic and we're going to
+
+ align:start position:0%
+index Diagnostic and we're going to
+ 
+
+ align:start position:0%
+index Diagnostic and we're going to
+start with what I think is conceptually
+
+ align:start position:0%
+start with what I think is conceptually
+ 
+
+ align:start position:0%
+start with what I think is conceptually
+the simplest but still often causes us
+
+ align:start position:0%
+the simplest but still often causes us
+ 
+
+ align:start position:0%
+the simplest but still often causes us
+lots of problems
+
+ align:start position:0%
+lots of problems
+ 
+
+ align:start position:0%
+lots of problems
+which are the refraction Diagnostics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I see some people rising so I'm
+
+ align:start position:0%
+here I see some people rising so I'm
+ 
+
+ align:start position:0%
+here I see some people rising so I'm
+just going to pause on this slide for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment oky do
+
+ align:start position:0%
+moment oky do
+ 
+
+ align:start position:0%
+moment oky do
+now I just want to have a little aside
+
+ align:start position:0%
+now I just want to have a little aside
+ 
+
+ align:start position:0%
+now I just want to have a little aside
+and this is on conceptual models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+electromagnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagation because I'm going to be
+
+ align:start position:0%
+propagation because I'm going to be
+ 
+
+ align:start position:0%
+propagation because I'm going to be
+switching quite a lot between different
+
+ align:start position:0%
+switching quite a lot between different
+ 
+
+ align:start position:0%
+switching quite a lot between different
+ways of thinking about electromagnetic
+
+ align:start position:0%
+ways of thinking about electromagnetic
+ 
+
+ align:start position:0%
+ways of thinking about electromagnetic
+radiation and how it moves through a
+
+ align:start position:0%
+radiation and how it moves through a
+ 
+
+ align:start position:0%
+radiation and how it moves through a
+plasma because sometimes some models are
+
+ align:start position:0%
+plasma because sometimes some models are
+ 
+
+ align:start position:0%
+plasma because sometimes some models are
+easier to work with than others
+
+ align:start position:0%
+easier to work with than others
+ 
+
+ align:start position:0%
+easier to work with than others
+sometimes models are simplifications and
+
+ align:start position:0%
+sometimes models are simplifications and
+ 
+
+ align:start position:0%
+sometimes models are simplifications and
+they throw away physics um but they make
+
+ align:start position:0%
+they throw away physics um but they make
+ 
+
+ align:start position:0%
+they throw away physics um but they make
+the intuition much simpler so I just
+
+ align:start position:0%
+the intuition much simpler so I just
+ 
+
+ align:start position:0%
+the intuition much simpler so I just
+want to show you two different models
+
+ align:start position:0%
+want to show you two different models
+ 
+
+ align:start position:0%
+want to show you two different models
+that we be going to be using in these
+
+ align:start position:0%
+that we be going to be using in these
+ 
+
+ align:start position:0%
+that we be going to be using in these
+next few lectures so that you have an
+
+ align:start position:0%
+next few lectures so that you have an
+ 
+
+ align:start position:0%
+next few lectures so that you have an
+idea of what's going on one model will
+
+ align:start position:0%
+idea of what's going on one model will
+ 
+
+ align:start position:0%
+idea of what's going on one model will
+be a model of wave
+
+ align:start position:0%
+be a model of wave
+ 
+
+ align:start position:0%
+be a model of wave
+fronts so this is based on the idea that
+
+ align:start position:0%
+fronts so this is based on the idea that
+ 
+
+ align:start position:0%
+fronts so this is based on the idea that
+as we said our electric and magnetic
+
+ align:start position:0%
+as we said our electric and magnetic
+ 
+
+ align:start position:0%
+as we said our electric and magnetic
+fields can be written as just a single
+
+ align:start position:0%
+fields can be written as just a single
+ 
+
+ align:start position:0%
+fields can be written as just a single
+Foria component so there's some strength
+
+ align:start position:0%
+Foria component so there's some strength
+ 
+
+ align:start position:0%
+Foria component so there's some strength
+and polarization of the electric uh
+
+ align:start position:0%
+and polarization of the electric uh
+ 
+
+ align:start position:0%
+and polarization of the electric uh
+field here and this is multiplied by the
+
+ align:start position:0%
+field here and this is multiplied by the
+ 
+
+ align:start position:0%
+field here and this is multiplied by the
+exponential of what we call the phase
+
+ align:start position:0%
+exponential of what we call the phase
+ 
+
+ align:start position:0%
+exponential of what we call the phase
+Factor so i k Dot x minus Omega T like
+
+ align:start position:0%
+Factor so i k Dot x minus Omega T like
+ 
+
+ align:start position:0%
+Factor so i k Dot x minus Omega T like
+this which we could write as e0
+
+ align:start position:0%
+this which we could write as e0
+ 
+
+ align:start position:0%
+this which we could write as e0
+exponential of I times some scalar
+
+ align:start position:0%
+exponential of I times some scalar
+ 
+
+ align:start position:0%
+exponential of I times some scalar
+quantity which is the phase here and so
+
+ align:start position:0%
+quantity which is the phase here and so
+ 
+
+ align:start position:0%
+quantity which is the phase here and so
+if we think of our electromagnetic wave
+
+ align:start position:0%
+if we think of our electromagnetic wave
+ 
+
+ align:start position:0%
+if we think of our electromagnetic wave
+as having a phase and the
+
+ align:start position:0%
+as having a phase and the
+ 
+
+ align:start position:0%
+as having a phase and the
+electromagnetic wave still exists in all
+
+ align:start position:0%
+electromagnetic wave still exists in all
+ 
+
+ align:start position:0%
+electromagnetic wave still exists in all
+places at all points in time blah blah
+
+ align:start position:0%
+places at all points in time blah blah
+ 
+
+ align:start position:0%
+places at all points in time blah blah
+blah blah blah um but that's a very
+
+ align:start position:0%
+blah blah blah um but that's a very
+ 
+
+ align:start position:0%
+blah blah blah um but that's a very
+difficult thing for me to sketch on my
+
+ align:start position:0%
+difficult thing for me to sketch on my
+ 
+
+ align:start position:0%
+difficult thing for me to sketch on my
+iPad here or on the board in front of
+
+ align:start position:0%
+iPad here or on the board in front of
+ 
+
+ align:start position:0%
+iPad here or on the board in front of
+you so what I'll end up sketching are
+
+ align:start position:0%
+you so what I'll end up sketching are
+ 
+
+ align:start position:0%
+you so what I'll end up sketching are
+what we call isophase
+
+ align:start position:0%
+what we call isophase
+ 
+
+ align:start position:0%
+what we call isophase
+Contours so these are
+
+ align:start position:0%
+Contours so these are
+ 
+
+ align:start position:0%
+Contours so these are
+Contours along which the phase
+
+ align:start position:0%
+Contours along which the phase
+ 
+
+ align:start position:0%
+Contours along which the phase
+is constant and so for example it could
+
+ align:start position:0%
+is constant and so for example it could
+ 
+
+ align:start position:0%
+is constant and so for example it could
+be at some integer multiple of Pi right
+
+ align:start position:0%
+be at some integer multiple of Pi right
+ 
+
+ align:start position:0%
+be at some integer multiple of Pi right
+for yes M belonging to Zen so this might
+
+ align:start position:0%
+for yes M belonging to Zen so this might
+ 
+
+ align:start position:0%
+for yes M belonging to Zen so this might
+look like some
+
+ align:start position:0%
+look like some
+ 
+
+ align:start position:0%
+look like some
+waves like this this would be
+
+ align:start position:0%
+waves like this this would be
+ 
+
+ align:start position:0%
+waves like this this would be
+electromagnetic wave which is diverging
+
+ align:start position:0%
+electromagnetic wave which is diverging
+ 
+
+ align:start position:0%
+electromagnetic wave which is diverging
+here actually it could be an
+
+ align:start position:0%
+here actually it could be an
+ 
+
+ align:start position:0%
+here actually it could be an
+electromagnetic wave which is converging
+
+ align:start position:0%
+electromagnetic wave which is converging
+ 
+
+ align:start position:0%
+electromagnetic wave which is converging
+to the left but you know at the moment
+
+ align:start position:0%
+to the left but you know at the moment
+ 
+
+ align:start position:0%
+to the left but you know at the moment
+it looks like it's diverging to the
+
+ align:start position:0%
+it looks like it's diverging to the
+ 
+
+ align:start position:0%
+it looks like it's diverging to the
+right okay so that's one way I could
+
+ align:start position:0%
+right okay so that's one way I could
+ 
+
+ align:start position:0%
+right okay so that's one way I could
+draw a wave
+
+ align:start position:0%
+draw a wave
+ 
+
+ align:start position:0%
+draw a wave
+here another way I could do it is with
+
+ align:start position:0%
+here another way I could do it is with
+ 
+
+ align:start position:0%
+here another way I could do it is with
+array
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and this gets into a topic which
+
+ align:start position:0%
+model and this gets into a topic which
+ 
+
+ align:start position:0%
+model and this gets into a topic which
+is called geometric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optics and it turns out what you can do
+
+ align:start position:0%
+optics and it turns out what you can do
+ 
+
+ align:start position:0%
+optics and it turns out what you can do
+if you have some isophase Contours like
+
+ align:start position:0%
+if you have some isophase Contours like
+ 
+
+ align:start position:0%
+if you have some isophase Contours like
+the ones I just drew say these Contours
+
+ align:start position:0%
+the ones I just drew say these Contours
+ 
+
+ align:start position:0%
+the ones I just drew say these Contours
+here they're doing something slightly
+
+ align:start position:0%
+here they're doing something slightly
+ 
+
+ align:start position:0%
+here they're doing something slightly
+strange because but perhaps there's a
+
+ align:start position:0%
+strange because but perhaps there's a
+ 
+
+ align:start position:0%
+strange because but perhaps there's a
+plasma there which is like you know
+
+ align:start position:0%
+plasma there which is like you know
+ 
+
+ align:start position:0%
+plasma there which is like you know
+moving the phase Contour around right we
+
+ align:start position:0%
+moving the phase Contour around right we
+ 
+
+ align:start position:0%
+moving the phase Contour around right we
+said if there's a change in refractive
+
+ align:start position:0%
+said if there's a change in refractive
+ 
+
+ align:start position:0%
+said if there's a change in refractive
+index that affect the phase the Rays
+
+ align:start position:0%
+index that affect the phase the Rays
+ 
+
+ align:start position:0%
+index that affect the phase the Rays
+that we draw here I can just take these
+
+ align:start position:0%
+that we draw here I can just take these
+ 
+
+ align:start position:0%
+that we draw here I can just take these
+phase contols and I can draw Rays such
+
+ align:start position:0%
+phase contols and I can draw Rays such
+ 
+
+ align:start position:0%
+phase contols and I can draw Rays such
+that they are everywhere normal to the
+
+ align:start position:0%
+that they are everywhere normal to the
+ 
+
+ align:start position:0%
+that they are everywhere normal to the
+isophase Contours so this Ray would look
+
+ align:start position:0%
+isophase Contours so this Ray would look
+ 
+
+ align:start position:0%
+isophase Contours so this Ray would look
+like this this one would look like this
+
+ align:start position:0%
+like this this one would look like this
+ 
+
+ align:start position:0%
+like this this one would look like this
+and this one would look like that so
+
+ align:start position:0%
+and this one would look like that so
+ 
+
+ align:start position:0%
+and this one would look like that so
+they are perpendicular to the wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fronts conveniently they're also
+
+ align:start position:0%
+fronts conveniently they're also
+ 
+
+ align:start position:0%
+fronts conveniently they're also
+parallel to the pointing
+
+ align:start position:0%
+parallel to the pointing
+ 
+
+ align:start position:0%
+parallel to the pointing
+Vector least I'm pretty convinced they
+
+ align:start position:0%
+Vector least I'm pretty convinced they
+ 
+
+ align:start position:0%
+Vector least I'm pretty convinced they
+are If someone knows more about
+
+ align:start position:0%
+are If someone knows more about
+ 
+
+ align:start position:0%
+are If someone knows more about
+geometric optics and thinks I'm wrong
+
+ align:start position:0%
+geometric optics and thinks I'm wrong
+ 
+
+ align:start position:0%
+geometric optics and thinks I'm wrong
+please shout out because this was a very
+
+ align:start position:0%
+please shout out because this was a very
+ 
+
+ align:start position:0%
+please shout out because this was a very
+hard fact to check um in like 10 minutes
+
+ align:start position:0%
+hard fact to check um in like 10 minutes
+ 
+
+ align:start position:0%
+hard fact to check um in like 10 minutes
+before the lecture but I'm pretty
+
+ align:start position:0%
+before the lecture but I'm pretty
+ 
+
+ align:start position:0%
+before the lecture but I'm pretty
+certain they represent the direction of
+
+ align:start position:0%
+certain they represent the direction of
+ 
+
+ align:start position:0%
+certain they represent the direction of
+the energy flux in electromagnetic wav
+
+ align:start position:0%
+the energy flux in electromagnetic wav
+ 
+
+ align:start position:0%
+the energy flux in electromagnetic wav
+so they're quite conceptually useful as
+
+ align:start position:0%
+so they're quite conceptually useful as
+ 
+
+ align:start position:0%
+so they're quite conceptually useful as
+well they tell us where the power is
+
+ align:start position:0%
+well they tell us where the power is
+ 
+
+ align:start position:0%
+well they tell us where the power is
+Flowing now when we think about these
+
+ align:start position:0%
+Flowing now when we think about these
+ 
+
+ align:start position:0%
+Flowing now when we think about these
+Rays here we can start thinking them a
+
+ align:start position:0%
+Rays here we can start thinking them a
+ 
+
+ align:start position:0%
+Rays here we can start thinking them a
+little bit like it's a
+
+ align:start position:0%
+little bit like it's a
+ 
+
+ align:start position:0%
+little bit like it's a
+particle trajectory and I put particle
+
+ align:start position:0%
+particle trajectory and I put particle
+ 
+
+ align:start position:0%
+particle trajectory and I put particle
+here in speech marks so I don't think
+
+ align:start position:0%
+here in speech marks so I don't think
+ 
+
+ align:start position:0%
+here in speech marks so I don't think
+you really need to think about these as
+
+ align:start position:0%
+you really need to think about these as
+ 
+
+ align:start position:0%
+you really need to think about these as
+photons but you can think about them as
+
+ align:start position:0%
+photons but you can think about them as
+ 
+
+ align:start position:0%
+photons but you can think about them as
+little Point particles that move around
+
+ align:start position:0%
+little Point particles that move around
+ 
+
+ align:start position:0%
+little Point particles that move around
+inside a plasma and we'll find out some
+
+ align:start position:0%
+inside a plasma and we'll find out some
+ 
+
+ align:start position:0%
+inside a plasma and we'll find out some
+rules for how they move inside a plasma
+
+ align:start position:0%
+rules for how they move inside a plasma
+ 
+
+ align:start position:0%
+rules for how they move inside a plasma
+in a moment and if you sort of track
+
+ align:start position:0%
+in a moment and if you sort of track
+ 
+
+ align:start position:0%
+in a moment and if you sort of track
+their trajectory that's where the Rays
+
+ align:start position:0%
+their trajectory that's where the Rays
+ 
+
+ align:start position:0%
+their trajectory that's where the Rays
+gone and then you also know some places
+
+ align:start position:0%
+gone and then you also know some places
+ 
+
+ align:start position:0%
+gone and then you also know some places
+where you'll have lines which are normal
+
+ align:start position:0%
+where you'll have lines which are normal
+ 
+
+ align:start position:0%
+where you'll have lines which are normal
+to the wavefront so maybe you can
+
+ align:start position:0%
+to the wavefront so maybe you can
+ 
+
+ align:start position:0%
+to the wavefront so maybe you can
+reconstruct the wavefronts later on um
+
+ align:start position:0%
+reconstruct the wavefronts later on um
+ 
+
+ align:start position:0%
+reconstruct the wavefronts later on um
+but it's important that when we're doing
+
+ align:start position:0%
+but it's important that when we're doing
+ 
+
+ align:start position:0%
+but it's important that when we're doing
+this we ignore the wave
+
+ align:start position:0%
+this we ignore the wave
+ 
+
+ align:start position:0%
+this we ignore the wave
+effects so we no longer track the phase
+
+ align:start position:0%
+effects so we no longer track the phase
+ 
+
+ align:start position:0%
+effects so we no longer track the phase
+of each particle right it's now just a
+
+ align:start position:0%
+of each particle right it's now just a
+ 
+
+ align:start position:0%
+of each particle right it's now just a
+little billiard ball and Billiard balls
+
+ align:start position:0%
+little billiard ball and Billiard balls
+ 
+
+ align:start position:0%
+little billiard ball and Billiard balls
+don't have phase and so we're we're
+
+ align:start position:0%
+don't have phase and so we're we're
+ 
+
+ align:start position:0%
+don't have phase and so we're we're
+gonna get rid of effects like
+
+ align:start position:0%
+gonna get rid of effects like
+ 
+
+ align:start position:0%
+gonna get rid of effects like
+interference and uh defraction
+
+ align:start position:0%
+interference and uh defraction
+ 
+
+ align:start position:0%
+interference and uh defraction
+and we're going to keep effects only
+
+ align:start position:0%
+and we're going to keep effects only
+ 
+
+ align:start position:0%
+and we're going to keep effects only
+like refraction here so no interference
+
+ align:start position:0%
+like refraction here so no interference
+ 
+
+ align:start position:0%
+like refraction here so no interference
+no defraction just refraction so this is
+
+ align:start position:0%
+no defraction just refraction so this is
+ 
+
+ align:start position:0%
+no defraction just refraction so this is
+our Ray model so does anyone have any
+
+ align:start position:0%
+our Ray model so does anyone have any
+ 
+
+ align:start position:0%
+our Ray model so does anyone have any
+questions on these models before we
+
+ align:start position:0%
+questions on these models before we
+ 
+
+ align:start position:0%
+questions on these models before we
+start trying to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them um I was just wondering so if the
+
+ align:start position:0%
+them um I was just wondering so if the
+ 
+
+ align:start position:0%
+them um I was just wondering so if the
+pointing Vector right is e cross B does
+
+ align:start position:0%
+pointing Vector right is e cross B does
+ 
+
+ align:start position:0%
+pointing Vector right is e cross B does
+that mean that if we have any parallel
+
+ align:start position:0%
+that mean that if we have any parallel
+ 
+
+ align:start position:0%
+that mean that if we have any parallel
+electric field to hey like I was
+
+ align:start position:0%
+electric field to hey like I was
+ 
+
+ align:start position:0%
+electric field to hey like I was
+wondering um the your point about the
+
+ align:start position:0%
+wondering um the your point about the
+ 
+
+ align:start position:0%
+wondering um the your point about the
+pointing Vector would that break if
+
+ align:start position:0%
+pointing Vector would that break if
+ 
+
+ align:start position:0%
+pointing Vector would that break if
+there was like a parallel e to the main
+
+ align:start position:0%
+there was like a parallel e to the main
+ 
+
+ align:start position:0%
+there was like a parallel e to the main
+back background magnetic field or is
+
+ align:start position:0%
+back background magnetic field or is
+ 
+
+ align:start position:0%
+back background magnetic field or is
+that just the oscillating D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there that question make sense it does
+
+ align:start position:0%
+there that question make sense it does
+ 
+
+ align:start position:0%
+there that question make sense it does
+actually and I know the answer to it
+
+ align:start position:0%
+actually and I know the answer to it
+ 
+
+ align:start position:0%
+actually and I know the answer to it
+that's good right so if you had some
+
+ align:start position:0%
+that's good right so if you had some
+ 
+
+ align:start position:0%
+that's good right so if you had some
+background magnetic field like in the
+
+ align:start position:0%
+background magnetic field like in the
+ 
+
+ align:start position:0%
+background magnetic field like in the
+toac and then your e was parallel to it
+
+ align:start position:0%
+toac and then your e was parallel to it
+ 
+
+ align:start position:0%
+toac and then your e was parallel to it
+um well let's put it this way the the
+
+ align:start position:0%
+um well let's put it this way the the
+ 
+
+ align:start position:0%
+um well let's put it this way the the
+pointing flux uh oscillates right and so
+
+ align:start position:0%
+pointing flux uh oscillates right and so
+ 
+
+ align:start position:0%
+pointing flux uh oscillates right and so
+you when you're averaging it time
+
+ align:start position:0%
+you when you're averaging it time
+ 
+
+ align:start position:0%
+you when you're averaging it time
+averaging it that's what gives you the
+
+ align:start position:0%
+averaging it that's what gives you the
+ 
+
+ align:start position:0%
+averaging it that's what gives you the
+actual power that's moving if you've got
+
+ align:start position:0%
+actual power that's moving if you've got
+ 
+
+ align:start position:0%
+actual power that's moving if you've got
+a static magnetic field your average
+
+ align:start position:0%
+a static magnetic field your average
+ 
+
+ align:start position:0%
+a static magnetic field your average
+power will go to zero okay y thank you
+
+ align:start position:0%
+power will go to zero okay y thank you
+ 
+
+ align:start position:0%
+power will go to zero okay y thank you
+so you'll only get power flow from
+
+ align:start position:0%
+so you'll only get power flow from
+ 
+
+ align:start position:0%
+so you'll only get power flow from
+oscillating components here because
+
+ align:start position:0%
+oscillating components here because
+ 
+
+ align:start position:0%
+oscillating components here because
+that's what's transporting the
+
+ align:start position:0%
+that's what's transporting the
+ 
+
+ align:start position:0%
+that's what's transporting the
+electromagnetic energy but it's a really
+
+ align:start position:0%
+electromagnetic energy but it's a really
+ 
+
+ align:start position:0%
+electromagnetic energy but it's a really
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+question than like I said I'm not
+
+ align:start position:0%
+question than like I said I'm not
+ 
+
+ align:start position:0%
+question than like I said I'm not
+completely 100% sure that Rays follow
+
+ align:start position:0%
+completely 100% sure that Rays follow
+ 
+
+ align:start position:0%
+completely 100% sure that Rays follow
+the trajectory of the pointing Vector
+
+ align:start position:0%
+the trajectory of the pointing Vector
+ 
+
+ align:start position:0%
+the trajectory of the pointing Vector
+but I I'm pretty certain have to
+
+ align:start position:0%
+but I I'm pretty certain have to
+ 
+
+ align:start position:0%
+but I I'm pretty certain have to
+thinking about it for about 10 minutes
+
+ align:start position:0%
+thinking about it for about 10 minutes
+ 
+
+ align:start position:0%
+thinking about it for about 10 minutes
+that they do so if someone finds out
+
+ align:start position:0%
+that they do so if someone finds out
+ 
+
+ align:start position:0%
+that they do so if someone finds out
+that's wrong please let me know and I'll
+
+ align:start position:0%
+that's wrong please let me know and I'll
+ 
+
+ align:start position:0%
+that's wrong please let me know and I'll
+take it
+
+ align:start position:0%
+take it
+ 
+
+ align:start position:0%
+take it
+out okay so everyone is going to be
+
+ align:start position:0%
+out okay so everyone is going to be
+ 
+
+ align:start position:0%
+out okay so everyone is going to be
+pretty happy if I start drawing Ray
+
+ align:start position:0%
+pretty happy if I start drawing Ray
+ 
+
+ align:start position:0%
+pretty happy if I start drawing Ray
+diagrams and they'll understand that
+
+ align:start position:0%
+diagrams and they'll understand that
+ 
+
+ align:start position:0%
+diagrams and they'll understand that
+these Ray diagrams represent the sort of
+
+ align:start position:0%
+these Ray diagrams represent the sort of
+ 
+
+ align:start position:0%
+these Ray diagrams represent the sort of
+trajectory of little beamlets of light
+
+ align:start position:0%
+trajectory of little beamlets of light
+ 
+
+ align:start position:0%
+trajectory of little beamlets of light
+and you could also reconstruct the fa
+
+ align:start position:0%
+and you could also reconstruct the fa
+ 
+
+ align:start position:0%
+and you could also reconstruct the fa
+wave fronts from them and therefore you
+
+ align:start position:0%
+wave fronts from them and therefore you
+ 
+
+ align:start position:0%
+wave fronts from them and therefore you
+could sort of reconstruct visually what
+
+ align:start position:0%
+could sort of reconstruct visually what
+ 
+
+ align:start position:0%
+could sort of reconstruct visually what
+the entire electromagnetic field looks
+
+ align:start position:0%
+the entire electromagnetic field looks
+ 
+
+ align:start position:0%
+the entire electromagnetic field looks
+like and we're implicitly assuming
+
+ align:start position:0%
+like and we're implicitly assuming
+ 
+
+ align:start position:0%
+like and we're implicitly assuming
+everywhere here that our magnetic field
+
+ align:start position:0%
+everywhere here that our magnetic field
+ 
+
+ align:start position:0%
+everywhere here that our magnetic field
+is perpendicular to our electric field
+
+ align:start position:0%
+is perpendicular to our electric field
+ 
+
+ align:start position:0%
+is perpendicular to our electric field
+which is a pretty good approximation for
+
+ align:start position:0%
+which is a pretty good approximation for
+ 
+
+ align:start position:0%
+which is a pretty good approximation for
+the assumptions we've made so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far okay so now let's try putting
+
+ align:start position:0%
+far okay so now let's try putting
+ 
+
+ align:start position:0%
+far okay so now let's try putting
+electromagnetic wave through a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and it's not going to be any old
+
+ align:start position:0%
+plasma and it's not going to be any old
+ 
+
+ align:start position:0%
+plasma and it's not going to be any old
+plasma here I'm going to choose a slab
+
+ align:start position:0%
+plasma here I'm going to choose a slab
+ 
+
+ align:start position:0%
+plasma here I'm going to choose a slab
+of plasma like this and this slab is
+
+ align:start position:0%
+of plasma like this and this slab is
+ 
+
+ align:start position:0%
+of plasma like this and this slab is
+going to be much
+
+ align:start position:0%
+going to be much
+ 
+
+ align:start position:0%
+going to be much
+denser at the top than it is at the
+
+ align:start position:0%
+denser at the top than it is at the
+ 
+
+ align:start position:0%
+denser at the top than it is at the
+bottom which I've tried to really closly
+
+ align:start position:0%
+bottom which I've tried to really closly
+ 
+
+ align:start position:0%
+bottom which I've tried to really closly
+do is some shading here right so it's
+
+ align:start position:0%
+do is some shading here right so it's
+ 
+
+ align:start position:0%
+do is some shading here right so it's
+going to have a gradient of electron
+
+ align:start position:0%
+going to have a gradient of electron
+ 
+
+ align:start position:0%
+going to have a gradient of electron
+density going up like that and of course
+
+ align:start position:0%
+density going up like that and of course
+ 
+
+ align:start position:0%
+density going up like that and of course
+you remember our Formula 1 minus NE over
+
+ align:start position:0%
+you remember our Formula 1 minus NE over
+ 
+
+ align:start position:0%
+you remember our Formula 1 minus NE over
+2N critical for our refractive index
+
+ align:start position:0%
+2N critical for our refractive index
+ 
+
+ align:start position:0%
+2N critical for our refractive index
+we're going to work in this regime where
+
+ align:start position:0%
+we're going to work in this regime where
+ 
+
+ align:start position:0%
+we're going to work in this regime where
+the density is much less than the
+
+ align:start position:0%
+the density is much less than the
+ 
+
+ align:start position:0%
+the density is much less than the
+critical density so we don't have to
+
+ align:start position:0%
+critical density so we don't have to
+ 
+
+ align:start position:0%
+critical density so we don't have to
+worry about what happens if we get close
+
+ align:start position:0%
+worry about what happens if we get close
+ 
+
+ align:start position:0%
+worry about what happens if we get close
+to the critical
+
+ align:start position:0%
+to the critical
+ 
+
+ align:start position:0%
+to the critical
+density and so you can see then that if
+
+ align:start position:0%
+density and so you can see then that if
+ 
+
+ align:start position:0%
+density and so you can see then that if
+the gradient in the electron density is
+
+ align:start position:0%
+the gradient in the electron density is
+ 
+
+ align:start position:0%
+the gradient in the electron density is
+in this direction then the gradient in
+
+ align:start position:0%
+in this direction then the gradient in
+ 
+
+ align:start position:0%
+in this direction then the gradient in
+the ref active index is in the opposite
+
+ align:start position:0%
+the ref active index is in the opposite
+ 
+
+ align:start position:0%
+the ref active index is in the opposite
+direction like
+
+ align:start position:0%
+direction like
+ 
+
+ align:start position:0%
+direction like
+that and we're going to start by putting
+
+ align:start position:0%
+that and we're going to start by putting
+ 
+
+ align:start position:0%
+that and we're going to start by putting
+through some phase
+
+ align:start position:0%
+through some phase
+ 
+
+ align:start position:0%
+through some phase
+fronts and we're going to start with a
+
+ align:start position:0%
+fronts and we're going to start with a
+ 
+
+ align:start position:0%
+fronts and we're going to start with a
+plain wave right so this is a wave in
+
+ align:start position:0%
+plain wave right so this is a wave in
+ 
+
+ align:start position:0%
+plain wave right so this is a wave in
+which the phase fronts are flat and
+
+ align:start position:0%
+which the phase fronts are flat and
+ 
+
+ align:start position:0%
+which the phase fronts are flat and
+parallel and uh uniformly spaced so
+
+ align:start position:0%
+parallel and uh uniformly spaced so
+ 
+
+ align:start position:0%
+parallel and uh uniformly spaced so
+those are my uh wave
+
+ align:start position:0%
+those are my uh wave
+ 
+
+ align:start position:0%
+those are my uh wave
+fronts I'll put a little coordinate
+
+ align:start position:0%
+fronts I'll put a little coordinate
+ 
+
+ align:start position:0%
+fronts I'll put a little coordinate
+system in here I'm going to tend to put
+
+ align:start position:0%
+system in here I'm going to tend to put
+ 
+
+ align:start position:0%
+system in here I'm going to tend to put
+the Zed coordinate in the direction
+
+ align:start position:0%
+the Zed coordinate in the direction
+ 
+
+ align:start position:0%
+the Zed coordinate in the direction
+waves are going and so there'll be two
+
+ align:start position:0%
+waves are going and so there'll be two
+ 
+
+ align:start position:0%
+waves are going and so there'll be two
+transverse coordinates y and x and I'll
+
+ align:start position:0%
+transverse coordinates y and x and I'll
+ 
+
+ align:start position:0%
+transverse coordinates y and x and I'll
+probably just write y on most of these
+
+ align:start position:0%
+probably just write y on most of these
+ 
+
+ align:start position:0%
+probably just write y on most of these
+I'll try and do things in like a
+
+ align:start position:0%
+I'll try and do things in like a
+ 
+
+ align:start position:0%
+I'll try and do things in like a
+one-dimensional sense but everything I
+
+ align:start position:0%
+one-dimensional sense but everything I
+ 
+
+ align:start position:0%
+one-dimensional sense but everything I
+say you can imagine could be applied to
+
+ align:start position:0%
+say you can imagine could be applied to
+ 
+
+ align:start position:0%
+say you can imagine could be applied to
+a threedimensional picture here I'm
+
+ align:start position:0%
+a threedimensional picture here I'm
+ 
+
+ align:start position:0%
+a threedimensional picture here I'm
+going to say that this plasma slab has
+
+ align:start position:0%
+going to say that this plasma slab has
+ 
+
+ align:start position:0%
+going to say that this plasma slab has
+some length L and it's homogeneous
+
+ align:start position:0%
+some length L and it's homogeneous
+ 
+
+ align:start position:0%
+some length L and it's homogeneous
+within that length apart from the
+
+ align:start position:0%
+within that length apart from the
+ 
+
+ align:start position:0%
+within that length apart from the
+gradient in the uh density
+
+ align:start position:0%
+gradient in the uh density
+ 
+
+ align:start position:0%
+gradient in the uh density
+here so does anyone know what happens to
+
+ align:start position:0%
+here so does anyone know what happens to
+ 
+
+ align:start position:0%
+here so does anyone know what happens to
+the phase fronts as they emerge out from
+
+ align:start position:0%
+the phase fronts as they emerge out from
+ 
+
+ align:start position:0%
+the phase fronts as they emerge out from
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+plasma the wave fronts all the Rays I
+
+ align:start position:0%
+plasma the wave fronts all the Rays I
+ 
+
+ align:start position:0%
+plasma the wave fronts all the Rays I
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mind bent and uh wait Upp down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Daniel oh yeah um they're bent down word
+
+ align:start position:0%
+Daniel oh yeah um they're bent down word
+ 
+
+ align:start position:0%
+Daniel oh yeah um they're bent down word
+right because you've got a lower
+
+ align:start position:0%
+right because you've got a lower
+ 
+
+ align:start position:0%
+right because you've got a lower
+refractive index in the upper
+
+ align:start position:0%
+refractive index in the upper
+ 
+
+ align:start position:0%
+refractive index in the upper
+half yeah you're absolutely right so
+
+ align:start position:0%
+half yeah you're absolutely right so
+ 
+
+ align:start position:0%
+half yeah you're absolutely right so
+these rays will emerge or these wave
+
+ align:start position:0%
+these rays will emerge or these wave
+ 
+
+ align:start position:0%
+these rays will emerge or these wave
+fronts will emerge
+
+ align:start position:0%
+fronts will emerge
+ 
+
+ align:start position:0%
+fronts will emerge
+bent like this and so the rays which I
+
+ align:start position:0%
+bent like this and so the rays which I
+ 
+
+ align:start position:0%
+bent like this and so the rays which I
+didn't draw on before but I meant to so
+
+ align:start position:0%
+didn't draw on before but I meant to so
+ 
+
+ align:start position:0%
+didn't draw on before but I meant to so
+here are some rays for you here you see
+
+ align:start position:0%
+here are some rays for you here you see
+ 
+
+ align:start position:0%
+here are some rays for you here you see
+how they're all normal the wave fronts
+
+ align:start position:0%
+how they're all normal the wave fronts
+ 
+
+ align:start position:0%
+how they're all normal the wave fronts
+here are some rays for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay and they're going to be bent
+
+ align:start position:0%
+here okay and they're going to be bent
+ 
+
+ align:start position:0%
+here okay and they're going to be bent
+by some angle which we'll call Theta
+
+ align:start position:0%
+by some angle which we'll call Theta
+ 
+
+ align:start position:0%
+by some angle which we'll call Theta
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and it turns out if you go and look how
+
+ align:start position:0%
+and it turns out if you go and look how
+ 
+
+ align:start position:0%
+and it turns out if you go and look how
+to do this Theta is going to be equal to
+
+ align:start position:0%
+to do this Theta is going to be equal to
+ 
+
+ align:start position:0%
+to do this Theta is going to be equal to
+D phase
+
+ align:start position:0%
+D phase
+ 
+
+ align:start position:0%
+D phase
+Dy time Lambda over 2 pi and so we can
+
+ align:start position:0%
+Dy time Lambda over 2 pi and so we can
+ 
+
+ align:start position:0%
+Dy time Lambda over 2 pi and so we can
+actually put that all together and we
+
+ align:start position:0%
+actually put that all together and we
+ 
+
+ align:start position:0%
+actually put that all together and we
+can say it's going to be equal to D Dy
+
+ align:start position:0%
+can say it's going to be equal to D Dy
+ 
+
+ align:start position:0%
+can say it's going to be equal to D Dy
+times the integral of capital n d z like
+
+ align:start position:0%
+times the integral of capital n d z like
+ 
+
+ align:start position:0%
+times the integral of capital n d z like
+that which for our plasma is min-1 / 2N
+
+ align:start position:0%
+that which for our plasma is min-1 / 2N
+ 
+
+ align:start position:0%
+that which for our plasma is min-1 / 2N
+critical integral of gradient of the
+
+ align:start position:0%
+critical integral of gradient of the
+ 
+
+ align:start position:0%
+critical integral of gradient of the
+electron density d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z and this DZ here is going to be
+
+ align:start position:0%
+z and this DZ here is going to be
+ 
+
+ align:start position:0%
+z and this DZ here is going to be
+running from zero to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+now I don't know how clear this is to
+
+ align:start position:0%
+now I don't know how clear this is to
+ 
+
+ align:start position:0%
+now I don't know how clear this is to
+everyone that the the Rays should bend
+
+ align:start position:0%
+everyone that the the Rays should bend
+ 
+
+ align:start position:0%
+everyone that the the Rays should bend
+or that they Bend downwards or why they
+
+ align:start position:0%
+or that they Bend downwards or why they
+ 
+
+ align:start position:0%
+or that they Bend downwards or why they
+Bend there's lots of different ways of
+
+ align:start position:0%
+Bend there's lots of different ways of
+ 
+
+ align:start position:0%
+Bend there's lots of different ways of
+thinking about it you can go and just
+
+ align:start position:0%
+thinking about it you can go and just
+ 
+
+ align:start position:0%
+thinking about it you can go and just
+solve a load of equations if you want to
+
+ align:start position:0%
+solve a load of equations if you want to
+ 
+
+ align:start position:0%
+solve a load of equations if you want to
+I like to think of it and you may laugh
+
+ align:start position:0%
+I like to think of it and you may laugh
+ 
+
+ align:start position:0%
+I like to think of it and you may laugh
+at me for this uh as a bunch of soldiers
+
+ align:start position:0%
+at me for this uh as a bunch of soldiers
+ 
+
+ align:start position:0%
+at me for this uh as a bunch of soldiers
+marching arm in-arm through some mixed
+
+ align:start position:0%
+marching arm in-arm through some mixed
+ 
+
+ align:start position:0%
+marching arm in-arm through some mixed
+terrain here so here's my soldiers I'm
+
+ align:start position:0%
+terrain here so here's my soldiers I'm
+ 
+
+ align:start position:0%
+terrain here so here's my soldiers I'm
+looking them from
+
+ align:start position:0%
+looking them from
+ 
+
+ align:start position:0%
+looking them from
+above you can see how I'm lining them up
+
+ align:start position:0%
+above you can see how I'm lining them up
+ 
+
+ align:start position:0%
+above you can see how I'm lining them up
+nicely with the wave fronts very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggestively and maybe some of the
+
+ align:start position:0%
+suggestively and maybe some of the
+ 
+
+ align:start position:0%
+suggestively and maybe some of the
+soldiers over here have got some sort of
+
+ align:start position:0%
+soldiers over here have got some sort of
+ 
+
+ align:start position:0%
+soldiers over here have got some sort of
+marsh they've got to walk through and
+
+ align:start position:0%
+marsh they've got to walk through and
+ 
+
+ align:start position:0%
+marsh they've got to walk through and
+these soldiers are going to fall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behind and because they've all linked
+
+ align:start position:0%
+behind and because they've all linked
+ 
+
+ align:start position:0%
+behind and because they've all linked
+arms they've still got to stay in a
+
+ align:start position:0%
+arms they've still got to stay in a
+ 
+
+ align:start position:0%
+arms they've still got to stay in a
+straight line with each other and so as
+
+ align:start position:0%
+straight line with each other and so as
+ 
+
+ align:start position:0%
+straight line with each other and so as
+they go they turn more and more
+
+ align:start position:0%
+they go they turn more and more
+ 
+
+ align:start position:0%
+they go they turn more and more
+round like this and this is what leads
+
+ align:start position:0%
+round like this and this is what leads
+ 
+
+ align:start position:0%
+round like this and this is what leads
+to our bending here and you can make
+
+ align:start position:0%
+to our bending here and you can make
+ 
+
+ align:start position:0%
+to our bending here and you can make
+this a bit more uh you know rigorous if
+
+ align:start position:0%
+this a bit more uh you know rigorous if
+ 
+
+ align:start position:0%
+this a bit more uh you know rigorous if
+you start thinking about the Rays as
+
+ align:start position:0%
+you start thinking about the Rays as
+ 
+
+ align:start position:0%
+you start thinking about the Rays as
+particles and you think about their
+
+ align:start position:0%
+particles and you think about their
+ 
+
+ align:start position:0%
+particles and you think about their
+velocity and you think about the speed
+
+ align:start position:0%
+velocity and you think about the speed
+ 
+
+ align:start position:0%
+velocity and you think about the speed
+that they're going at inside the plasma
+
+ align:start position:0%
+that they're going at inside the plasma
+ 
+
+ align:start position:0%
+that they're going at inside the plasma
+and you realize that they're actually
+
+ align:start position:0%
+and you realize that they're actually
+ 
+
+ align:start position:0%
+and you realize that they're actually
+going slower in the denser regions and
+
+ align:start position:0%
+going slower in the denser regions and
+ 
+
+ align:start position:0%
+going slower in the denser regions and
+that's going to start giving you uh
+
+ align:start position:0%
+that's going to start giving you uh
+ 
+
+ align:start position:0%
+that's going to start giving you uh
+twist sorry they're going faster in the
+
+ align:start position:0%
+twist sorry they're going faster in the
+ 
+
+ align:start position:0%
+twist sorry they're going faster in the
+denser Regions they're going slower in
+
+ align:start position:0%
+denser Regions they're going slower in
+ 
+
+ align:start position:0%
+denser Regions they're going slower in
+the regions with high refractive index
+
+ align:start position:0%
+the regions with high refractive index
+ 
+
+ align:start position:0%
+the regions with high refractive index
+and that's what gives you the bending
+
+ align:start position:0%
+and that's what gives you the bending
+ 
+
+ align:start position:0%
+and that's what gives you the bending
+here so this is just like a little uh
+
+ align:start position:0%
+here so this is just like a little uh
+ 
+
+ align:start position:0%
+here so this is just like a little uh
+mental model to think about when you're
+
+ align:start position:0%
+mental model to think about when you're
+ 
+
+ align:start position:0%
+mental model to think about when you're
+trying to work out why it is that the
+
+ align:start position:0%
+trying to work out why it is that the
+ 
+
+ align:start position:0%
+trying to work out why it is that the
+the Rays of light are turning but
+
+ align:start position:0%
+the Rays of light are turning but
+ 
+
+ align:start position:0%
+the Rays of light are turning but
+there's many many different ways to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this oh hello hi there is there a
+
+ align:start position:0%
+this oh hello hi there is there a
+ 
+
+ align:start position:0%
+this oh hello hi there is there a
+gradient in density along the uh the Z
+
+ align:start position:0%
+gradient in density along the uh the Z
+ 
+
+ align:start position:0%
+gradient in density along the uh the Z
+axis the way it's drawn it looks like
+
+ align:start position:0%
+axis the way it's drawn it looks like
+ 
+
+ align:start position:0%
+axis the way it's drawn it looks like
+it's only within the y axis it is only
+
+ align:start position:0%
+it's only within the y axis it is only
+ 
+
+ align:start position:0%
+it's only within the y axis it is only
+in the y axis
+
+ align:start position:0%
+in the y axis
+ 
+
+ align:start position:0%
+in the y axis
+yes so then integral of the gradient of
+
+ align:start position:0%
+yes so then integral of the gradient of
+ 
+
+ align:start position:0%
+yes so then integral of the gradient of
+density along Z wouldn't that be
+
+ align:start position:0%
+density along Z wouldn't that be
+ 
+
+ align:start position:0%
+density along Z wouldn't that be
+constant then what is
+
+ align:start position:0%
+constant then what is
+ 
+
+ align:start position:0%
+constant then what is
+it is there no is there a density change
+
+ align:start position:0%
+it is there no is there a density change
+ 
+
+ align:start position:0%
+it is there no is there a density change
+in Z the what I'm asking not in this
+
+ align:start position:0%
+in Z the what I'm asking not in this
+ 
+
+ align:start position:0%
+in Z the what I'm asking not in this
+really simple model I'm proposing of
+
+ align:start position:0%
+really simple model I'm proposing of
+ 
+
+ align:start position:0%
+really simple model I'm proposing of
+course in general there can be a density
+
+ align:start position:0%
+course in general there can be a density
+ 
+
+ align:start position:0%
+course in general there can be a density
+change really this should read
+
+ align:start position:0%
+change really this should read
+ 
+
+ align:start position:0%
+change really this should read
+um radiant of
+
+ align:start position:0%
+um radiant of
+ 
+
+ align:start position:0%
+um radiant of
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+dot DL where L is an
+
+ align:start position:0%
+dot DL where L is an
+ 
+
+ align:start position:0%
+dot DL where L is an
+infimal uh no sorry ignore
+
+ align:start position:0%
+infimal uh no sorry ignore
+ 
+
+ align:start position:0%
+infimal uh no sorry ignore
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um yeah there was there was no gradient
+
+ align:start position:0%
+um yeah there was there was no gradient
+ 
+
+ align:start position:0%
+um yeah there was there was no gradient
+and density in Z and we don't need one
+
+ align:start position:0%
+and density in Z and we don't need one
+ 
+
+ align:start position:0%
+and density in Z and we don't need one
+to get any bending in fact if there was
+
+ align:start position:0%
+to get any bending in fact if there was
+ 
+
+ align:start position:0%
+to get any bending in fact if there was
+a gradient and density in Z it wouldn't
+
+ align:start position:0%
+a gradient and density in Z it wouldn't
+ 
+
+ align:start position:0%
+a gradient and density in Z it wouldn't
+have any effect on the
+
+ align:start position:0%
+have any effect on the
+ 
+
+ align:start position:0%
+have any effect on the
+light it would just forwards at a
+
+ align:start position:0%
+light it would just forwards at a
+ 
+
+ align:start position:0%
+light it would just forwards at a
+different speed but it wouldn't get
+
+ align:start position:0%
+different speed but it wouldn't get
+ 
+
+ align:start position:0%
+different speed but it wouldn't get
+bent all right and then so but then that
+
+ align:start position:0%
+bent all right and then so but then that
+ 
+
+ align:start position:0%
+bent all right and then so but then that
+roll that it's
+
+ align:start position:0%
+roll that it's
+ 
+
+ align:start position:0%
+roll that it's
+just uh grum and
+
+ align:start position:0%
+just uh grum and
+ 
+
+ align:start position:0%
+just uh grum and
+l oh yes for this very simple model
+
+ align:start position:0%
+l oh yes for this very simple model
+ 
+
+ align:start position:0%
+l oh yes for this very simple model
+you're absolutely right I'm just
+
+ align:start position:0%
+you're absolutely right I'm just
+ 
+
+ align:start position:0%
+you're absolutely right I'm just
+introducing generality because we may
+
+ align:start position:0%
+introducing generality because we may
+ 
+
+ align:start position:0%
+introducing generality because we may
+have something different but you're
+
+ align:start position:0%
+have something different but you're
+ 
+
+ align:start position:0%
+have something different but you're
+quite right so we could write this as
+
+ align:start position:0%
+quite right so we could write this as
+ 
+
+ align:start position:0%
+quite right so we could write this as
+minus 2ncr time L and maybe I put a
+
+ align:start position:0%
+minus 2ncr time L and maybe I put a
+ 
+
+ align:start position:0%
+minus 2ncr time L and maybe I put a
+subscript Zed so that I know that it's
+
+ align:start position:0%
+subscript Zed so that I know that it's
+ 
+
+ align:start position:0%
+subscript Zed so that I know that it's
+like my length scale in Zed and Times by
+
+ align:start position:0%
+like my length scale in Zed and Times by
+ 
+
+ align:start position:0%
+like my length scale in Zed and Times by
+the gradient in NE and if this uh is
+
+ align:start position:0%
+the gradient in NE and if this uh is
+ 
+
+ align:start position:0%
+the gradient in NE and if this uh is
+like some
+
+ align:start position:0%
+like some
+ 
+
+ align:start position:0%
+like some
+simple density ramp so I would have any
+
+ align:start position:0%
+simple density ramp so I would have any
+ 
+
+ align:start position:0%
+simple density ramp so I would have any
+0 * 1us X upon ly or something like that
+
+ align:start position:0%
+0 * 1us X upon ly or something like that
+ 
+
+ align:start position:0%
+0 * 1us X upon ly or something like that
+I could simply put this in and say that
+
+ align:start position:0%
+I could simply put this in and say that
+ 
+
+ align:start position:0%
+I could simply put this in and say that
+the entire beam is now Twisted by a nice
+
+ align:start position:0%
+the entire beam is now Twisted by a nice
+ 
+
+ align:start position:0%
+the entire beam is now Twisted by a nice
+linear angle which has an LZ inside it
+
+ align:start position:0%
+linear angle which has an LZ inside it
+ 
+
+ align:start position:0%
+linear angle which has an LZ inside it
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+ne0 and an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh minus one upon ly like this so this
+
+ align:start position:0%
+uh minus one upon ly like this so this
+ 
+
+ align:start position:0%
+uh minus one upon ly like this so this
+is if I give you some analytical result
+
+ align:start position:0%
+is if I give you some analytical result
+ 
+
+ align:start position:0%
+is if I give you some analytical result
+you can then go and work out what the
+
+ align:start position:0%
+you can then go and work out what the
+ 
+
+ align:start position:0%
+you can then go and work out what the
+angle would be and that's a super useful
+
+ align:start position:0%
+angle would be and that's a super useful
+ 
+
+ align:start position:0%
+angle would be and that's a super useful
+thing to be able to do uh as I segue
+
+ align:start position:0%
+thing to be able to do uh as I segue
+ 
+
+ align:start position:0%
+thing to be able to do uh as I segue
+perfectly into my next remark which is
+
+ align:start position:0%
+perfectly into my next remark which is
+ 
+
+ align:start position:0%
+perfectly into my next remark which is
+to do with the first problem that this
+
+ align:start position:0%
+to do with the first problem that this
+ 
+
+ align:start position:0%
+to do with the first problem that this
+causes so this is issues with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection the first issue is if you've
+
+ align:start position:0%
+deflection the first issue is if you've
+ 
+
+ align:start position:0%
+deflection the first issue is if you've
+got some plasma and you're trying to put
+
+ align:start position:0%
+got some plasma and you're trying to put
+ 
+
+ align:start position:0%
+got some plasma and you're trying to put
+some electromagnetic radiation in it you
+
+ align:start position:0%
+some electromagnetic radiation in it you
+ 
+
+ align:start position:0%
+some electromagnetic radiation in it you
+you want to collect that radiation you
+
+ align:start position:0%
+you want to collect that radiation you
+ 
+
+ align:start position:0%
+you want to collect that radiation you
+want to put it onto a detector maybe
+
+ align:start position:0%
+want to put it onto a detector maybe
+ 
+
+ align:start position:0%
+want to put it onto a detector maybe
+that detector is a camera or it might be
+
+ align:start position:0%
+that detector is a camera or it might be
+ 
+
+ align:start position:0%
+that detector is a camera or it might be
+like a wave guide that you're collecting
+
+ align:start position:0%
+like a wave guide that you're collecting
+ 
+
+ align:start position:0%
+like a wave guide that you're collecting
+microwaves with uh and so that camera
+
+ align:start position:0%
+microwaves with uh and so that camera
+ 
+
+ align:start position:0%
+microwaves with uh and so that camera
+has some physical size right and so
+
+ align:start position:0%
+has some physical size right and so
+ 
+
+ align:start position:0%
+has some physical size right and so
+maybe the camera is represented by this
+
+ align:start position:0%
+maybe the camera is represented by this
+ 
+
+ align:start position:0%
+maybe the camera is represented by this
+lens here it's got some physical size d
+
+ align:start position:0%
+lens here it's got some physical size d
+ 
+
+ align:start position:0%
+lens here it's got some physical size d
+and if your rays get
+
+ align:start position:0%
+and if your rays get
+ 
+
+ align:start position:0%
+and if your rays get
+deflected that was a terrible straight
+
+ align:start position:0%
+deflected that was a terrible straight
+ 
+
+ align:start position:0%
+deflected that was a terrible straight
+line okay if your rays get deflected by
+
+ align:start position:0%
+line okay if your rays get deflected by
+ 
+
+ align:start position:0%
+line okay if your rays get deflected by
+an angle greater than Theta Max where
+
+ align:start position:0%
+an angle greater than Theta Max where
+ 
+
+ align:start position:0%
+an angle greater than Theta Max where
+tangent of theta Max is equal to D over
+
+ align:start position:0%
+tangent of theta Max is equal to D over
+ 
+
+ align:start position:0%
+tangent of theta Max is equal to D over
+2 *
+
+ align:start position:0%
+2 *
+ 
+
+ align:start position:0%
+2 *
+L I forgot to put in this L here there
+
+ align:start position:0%
+L I forgot to put in this L here there
+ 
+
+ align:start position:0%
+L I forgot to put in this L here there
+we go then your ray is going to be lost
+
+ align:start position:0%
+we go then your ray is going to be lost
+ 
+
+ align:start position:0%
+we go then your ray is going to be lost
+so for Theta greater than Theta
+
+ align:start position:0%
+so for Theta greater than Theta
+ 
+
+ align:start position:0%
+so for Theta greater than Theta
+Max you lose your
+
+ align:start position:0%
+Max you lose your
+ 
+
+ align:start position:0%
+Max you lose your
+rays so that means you can't collect
+
+ align:start position:0%
+rays so that means you can't collect
+ 
+
+ align:start position:0%
+rays so that means you can't collect
+them you can't detect them anymore so
+
+ align:start position:0%
+them you can't detect them anymore so
+ 
+
+ align:start position:0%
+them you can't detect them anymore so
+this causes big problems because it
+
+ align:start position:0%
+this causes big problems because it
+ 
+
+ align:start position:0%
+this causes big problems because it
+means that we're going to start losing
+
+ align:start position:0%
+means that we're going to start losing
+ 
+
+ align:start position:0%
+means that we're going to start losing
+lights here and just for most situations
+
+ align:start position:0%
+lights here and just for most situations
+ 
+
+ align:start position:0%
+lights here and just for most situations
+we can use the small angle per aular
+
+ align:start position:0%
+we can use the small angle per aular
+ 
+
+ align:start position:0%
+we can use the small angle per aular
+approximation and just replace the tan
+
+ align:start position:0%
+approximation and just replace the tan
+ 
+
+ align:start position:0%
+approximation and just replace the tan
+Theta with Theta here so that means you
+
+ align:start position:0%
+Theta with Theta here so that means you
+ 
+
+ align:start position:0%
+Theta with Theta here so that means you
+want to keep your deflection angle Theta
+
+ align:start position:0%
+want to keep your deflection angle Theta
+ 
+
+ align:start position:0%
+want to keep your deflection angle Theta
+um which is equal to as we said ddy of
+
+ align:start position:0%
+um which is equal to as we said ddy of
+ 
+
+ align:start position:0%
+um which is equal to as we said ddy of
+the integral of ndl that wants to be
+
+ align:start position:0%
+the integral of ndl that wants to be
+ 
+
+ align:start position:0%
+the integral of ndl that wants to be
+less than beta Max so there's a few
+
+ align:start position:0%
+less than beta Max so there's a few
+ 
+
+ align:start position:0%
+less than beta Max so there's a few
+things that you can do to try and do
+
+ align:start position:0%
+things that you can do to try and do
+ 
+
+ align:start position:0%
+things that you can do to try and do
+this you can have a nice big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lens uh you can have a close lens you
+
+ align:start position:0%
+lens uh you can have a close lens you
+ 
+
+ align:start position:0%
+lens uh you can have a close lens you
+can put it nice and close in or you can
+
+ align:start position:0%
+can put it nice and close in or you can
+ 
+
+ align:start position:0%
+can put it nice and close in or you can
+use a
+
+ align:start position:0%
+use a
+ 
+
+ align:start position:0%
+use a
+shorter wavelength because if you go to
+
+ align:start position:0%
+shorter wavelength because if you go to
+ 
+
+ align:start position:0%
+shorter wavelength because if you go to
+a shorter wavelength uh you get a
+
+ align:start position:0%
+a shorter wavelength uh you get a
+ 
+
+ align:start position:0%
+a shorter wavelength uh you get a
+smaller deflection angle uh which you
+
+ align:start position:0%
+smaller deflection angle uh which you
+ 
+
+ align:start position:0%
+smaller deflection angle uh which you
+can see if you go back to maybe this
+
+ align:start position:0%
+can see if you go back to maybe this
+ 
+
+ align:start position:0%
+can see if you go back to maybe this
+formula here a shter wavelength
+
+ align:start position:0%
+formula here a shter wavelength
+ 
+
+ align:start position:0%
+formula here a shter wavelength
+corresponds to a larger and critical and
+
+ align:start position:0%
+corresponds to a larger and critical and
+ 
+
+ align:start position:0%
+corresponds to a larger and critical and
+so you'll get a smaller Angle now not
+
+ align:start position:0%
+so you'll get a smaller Angle now not
+ 
+
+ align:start position:0%
+so you'll get a smaller Angle now not
+all of these things are possible in a
+
+ align:start position:0%
+all of these things are possible in a
+ 
+
+ align:start position:0%
+all of these things are possible in a
+standard experiment if youve got a toat
+
+ align:start position:0%
+standard experiment if youve got a toat
+ 
+
+ align:start position:0%
+standard experiment if youve got a toat
+uh you may have a limit on how big your
+
+ align:start position:0%
+uh you may have a limit on how big your
+ 
+
+ align:start position:0%
+uh you may have a limit on how big your
+detector can be because it's got to fit
+
+ align:start position:0%
+detector can be because it's got to fit
+ 
+
+ align:start position:0%
+detector can be because it's got to fit
+in a gap between some magnets you'll
+
+ align:start position:0%
+in a gap between some magnets you'll
+ 
+
+ align:start position:0%
+in a gap between some magnets you'll
+certainly have a limit on how close you
+
+ align:start position:0%
+certainly have a limit on how close you
+ 
+
+ align:start position:0%
+certainly have a limit on how close you
+can put it to the plasma because you
+
+ align:start position:0%
+can put it to the plasma because you
+ 
+
+ align:start position:0%
+can put it to the plasma because you
+don't want to stick it right inside um
+
+ align:start position:0%
+don't want to stick it right inside um
+ 
+
+ align:start position:0%
+don't want to stick it right inside um
+and you may not be able to choose
+
+ align:start position:0%
+and you may not be able to choose
+ 
+
+ align:start position:0%
+and you may not be able to choose
+whatever wavelength you want perhaps
+
+ align:start position:0%
+whatever wavelength you want perhaps
+ 
+
+ align:start position:0%
+whatever wavelength you want perhaps
+you're doing looking at electron cyron
+
+ align:start position:0%
+you're doing looking at electron cyron
+ 
+
+ align:start position:0%
+you're doing looking at electron cyron
+emission and you've got no choice but to
+
+ align:start position:0%
+emission and you've got no choice but to
+ 
+
+ align:start position:0%
+emission and you've got no choice but to
+use the wavelength that's admitted that
+
+ align:start position:0%
+use the wavelength that's admitted that
+ 
+
+ align:start position:0%
+use the wavelength that's admitted that
+so this can cause big problems and so if
+
+ align:start position:0%
+so this can cause big problems and so if
+ 
+
+ align:start position:0%
+so this can cause big problems and so if
+you're doing some electromagnetic
+
+ align:start position:0%
+you're doing some electromagnetic
+ 
+
+ align:start position:0%
+you're doing some electromagnetic
+probing of your plasma one of the first
+
+ align:start position:0%
+probing of your plasma one of the first
+ 
+
+ align:start position:0%
+probing of your plasma one of the first
+things you should probably do is check
+
+ align:start position:0%
+things you should probably do is check
+ 
+
+ align:start position:0%
+things you should probably do is check
+whether the density gradients are going
+
+ align:start position:0%
+whether the density gradients are going
+ 
+
+ align:start position:0%
+whether the density gradients are going
+to make it hard to actually measure
+
+ align:start position:0%
+to make it hard to actually measure
+ 
+
+ align:start position:0%
+to make it hard to actually measure
+anything any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we're now going to plunge
+
+ align:start position:0%
+all right so we're now going to plunge
+ 
+
+ align:start position:0%
+all right so we're now going to plunge
+in our first
+
+ align:start position:0%
+in our first
+ 
+
+ align:start position:0%
+in our first
+Diagnostic and the point I want to make
+
+ align:start position:0%
+Diagnostic and the point I want to make
+ 
+
+ align:start position:0%
+Diagnostic and the point I want to make
+here is although deflection can be
+
+ align:start position:0%
+here is although deflection can be
+ 
+
+ align:start position:0%
+here is although deflection can be
+frustrating it can also be
+
+ align:start position:0%
+frustrating it can also be
+ 
+
+ align:start position:0%
+frustrating it can also be
+useful because we can use it to measure
+
+ align:start position:0%
+useful because we can use it to measure
+ 
+
+ align:start position:0%
+useful because we can use it to measure
+something about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma the first thing we're going to
+
+ align:start position:0%
+plasma the first thing we're going to
+ 
+
+ align:start position:0%
+plasma the first thing we're going to
+talk about is schen Imaging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this word schen people often assume
+
+ align:start position:0%
+this word schen people often assume
+ 
+
+ align:start position:0%
+this word schen people often assume
+refers to a person it does not um so it
+
+ align:start position:0%
+refers to a person it does not um so it
+ 
+
+ align:start position:0%
+refers to a person it does not um so it
+doesn't have a capital S despite what
+
+ align:start position:0%
+doesn't have a capital S despite what
+ 
+
+ align:start position:0%
+doesn't have a capital S despite what
+Obel will tell you uh and it's actually
+
+ align:start position:0%
+Obel will tell you uh and it's actually
+ 
+
+ align:start position:0%
+Obel will tell you uh and it's actually
+after a German word Scher which is like
+
+ align:start position:0%
+after a German word Scher which is like
+ 
+
+ align:start position:0%
+after a German word Scher which is like
+streaks because this was first used for
+
+ align:start position:0%
+streaks because this was first used for
+ 
+
+ align:start position:0%
+streaks because this was first used for
+looking at small imperfections in Optics
+
+ align:start position:0%
+looking at small imperfections in Optics
+ 
+
+ align:start position:0%
+looking at small imperfections in Optics
+uh and so looking at these little
+
+ align:start position:0%
+uh and so looking at these little
+ 
+
+ align:start position:0%
+uh and so looking at these little
+streaks here so it's a way we of Imaging
+
+ align:start position:0%
+streaks here so it's a way we of Imaging
+ 
+
+ align:start position:0%
+streaks here so it's a way we of Imaging
+things which would otherwise be
+
+ align:start position:0%
+things which would otherwise be
+ 
+
+ align:start position:0%
+things which would otherwise be
+impossible to see uh because they cause
+
+ align:start position:0%
+impossible to see uh because they cause
+ 
+
+ align:start position:0%
+impossible to see uh because they cause
+small gradients in refractive
+
+ align:start position:0%
+small gradients in refractive
+ 
+
+ align:start position:0%
+small gradients in refractive
+index so let's have a little example
+
+ align:start position:0%
+index so let's have a little example
+ 
+
+ align:start position:0%
+index so let's have a little example
+building up towards and imaging this
+
+ align:start position:0%
+building up towards and imaging this
+ 
+
+ align:start position:0%
+building up towards and imaging this
+first thing I'm going to show you is not
+
+ align:start position:0%
+first thing I'm going to show you is not
+ 
+
+ align:start position:0%
+first thing I'm going to show you is not
+SCH and imaging this is just Imaging but
+
+ align:start position:0%
+SCH and imaging this is just Imaging but
+ 
+
+ align:start position:0%
+SCH and imaging this is just Imaging but
+my impression is that some folks need a
+
+ align:start position:0%
+my impression is that some folks need a
+ 
+
+ align:start position:0%
+my impression is that some folks need a
+refresher with some Optics so we're
+
+ align:start position:0%
+refresher with some Optics so we're
+ 
+
+ align:start position:0%
+refresher with some Optics so we're
+going to start with a solid object it's
+
+ align:start position:0%
+going to start with a solid object it's
+ 
+
+ align:start position:0%
+going to start with a solid object it's
+going to be this nice little chalice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and we're going to put in some rays
+
+ align:start position:0%
+here and we're going to put in some rays
+ 
+
+ align:start position:0%
+here and we're going to put in some rays
+of light
+
+ align:start position:0%
+of light
+ 
+
+ align:start position:0%
+of light
+like this now this object is solid and
+
+ align:start position:0%
+like this now this object is solid and
+ 
+
+ align:start position:0%
+like this now this object is solid and
+so it blocks any rays of Light which hit
+
+ align:start position:0%
+so it blocks any rays of Light which hit
+ 
+
+ align:start position:0%
+so it blocks any rays of Light which hit
+it these two Central ones and allows
+
+ align:start position:0%
+it these two Central ones and allows
+ 
+
+ align:start position:0%
+it these two Central ones and allows
+through rays of light going past it
+
+ align:start position:0%
+through rays of light going past it
+ 
+
+ align:start position:0%
+through rays of light going past it
+no allows through rays of light going
+
+ align:start position:0%
+no allows through rays of light going
+ 
+
+ align:start position:0%
+no allows through rays of light going
+past it very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and what we would probably do here
+
+ align:start position:0%
+good and what we would probably do here
+ 
+
+ align:start position:0%
+good and what we would probably do here
+if we're doing a standard Imaging system
+
+ align:start position:0%
+if we're doing a standard Imaging system
+ 
+
+ align:start position:0%
+if we're doing a standard Imaging system
+is we would have a lens right so this is
+
+ align:start position:0%
+is we would have a lens right so this is
+ 
+
+ align:start position:0%
+is we would have a lens right so this is
+how you form an image so we'll put our
+
+ align:start position:0%
+how you form an image so we'll put our
+ 
+
+ align:start position:0%
+how you form an image so we'll put our
+lens here it's going to have a focal
+
+ align:start position:0%
+lens here it's going to have a focal
+ 
+
+ align:start position:0%
+lens here it's going to have a focal
+length F and we're going to place it at
+
+ align:start position:0%
+length F and we're going to place it at
+ 
+
+ align:start position:0%
+length F and we're going to place it at
+a distance which
+
+ align:start position:0%
+a distance which
+ 
+
+ align:start position:0%
+a distance which
+is 2f away from the object we're trying
+
+ align:start position:0%
+is 2f away from the object we're trying
+ 
+
+ align:start position:0%
+is 2f away from the object we're trying
+to image I'll just put that f up
+
+ align:start position:0%
+to image I'll just put that f up
+ 
+
+ align:start position:0%
+to image I'll just put that f up
+there now behind this lens if we're
+
+ align:start position:0%
+there now behind this lens if we're
+ 
+
+ align:start position:0%
+there now behind this lens if we're
+doing a standard 2f Imaging system we're
+
+ align:start position:0%
+doing a standard 2f Imaging system we're
+ 
+
+ align:start position:0%
+doing a standard 2f Imaging system we're
+going to have a focal point and that's
+
+ align:start position:0%
+going to have a focal point and that's
+ 
+
+ align:start position:0%
+going to have a focal point and that's
+going to be at F away and then we're
+
+ align:start position:0%
+going to be at F away and then we're
+ 
+
+ align:start position:0%
+going to be at F away and then we're
+going to have an object
+
+ align:start position:0%
+going to have an object
+ 
+
+ align:start position:0%
+going to have an object
+plane which is also an F away H sorry an
+
+ align:start position:0%
+plane which is also an F away H sorry an
+ 
+
+ align:start position:0%
+plane which is also an F away H sorry an
+image plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play and this is the length with focal
+
+ align:start position:0%
+play and this is the length with focal
+ 
+
+ align:start position:0%
+play and this is the length with focal
+length F so hopefully some of you have
+
+ align:start position:0%
+length F so hopefully some of you have
+ 
+
+ align:start position:0%
+length F so hopefully some of you have
+seen this sort of thing before you know
+
+ align:start position:0%
+seen this sort of thing before you know
+ 
+
+ align:start position:0%
+seen this sort of thing before you know
+that the Rays will pass through the
+
+ align:start position:0%
+that the Rays will pass through the
+ 
+
+ align:start position:0%
+that the Rays will pass through the
+focal point here he says drawing them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carefully and what we'll end up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can't do this on a CH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board is a copy of our image of our
+
+ align:start position:0%
+board is a copy of our image of our
+ 
+
+ align:start position:0%
+board is a copy of our image of our
+object here but it's going to be
+
+ align:start position:0%
+object here but it's going to be
+ 
+
+ align:start position:0%
+object here but it's going to be
+inverted and you can tell that because
+
+ align:start position:0%
+inverted and you can tell that because
+ 
+
+ align:start position:0%
+inverted and you can tell that because
+you can see the Rays have changed place
+
+ align:start position:0%
+you can see the Rays have changed place
+ 
+
+ align:start position:0%
+you can see the Rays have changed place
+so this is a nice one
+
+ align:start position:0%
+so this is a nice one
+ 
+
+ align:start position:0%
+so this is a nice one
+toone
+
+ align:start position:0%
+toone
+ 
+
+ align:start position:0%
+toone
+image it's at
+
+ align:start position:0%
+image it's at
+ 
+
+ align:start position:0%
+image it's at
+magnification one and it is
+
+ align:start position:0%
+magnification one and it is
+ 
+
+ align:start position:0%
+magnification one and it is
+inverted so this is this simplest I
+
+ align:start position:0%
+inverted so this is this simplest I
+ 
+
+ align:start position:0%
+inverted so this is this simplest I
+think the simplest possible Imaging
+
+ align:start position:0%
+think the simplest possible Imaging
+ 
+
+ align:start position:0%
+think the simplest possible Imaging
+system you could possibly develop right
+
+ align:start position:0%
+system you could possibly develop right
+ 
+
+ align:start position:0%
+system you could possibly develop right
+it simply takes whatever is at the
+
+ align:start position:0%
+it simply takes whatever is at the
+ 
+
+ align:start position:0%
+it simply takes whatever is at the
+object plane and puts it at the image FL
+
+ align:start position:0%
+object plane and puts it at the image FL
+ 
+
+ align:start position:0%
+object plane and puts it at the image FL
+some distance
+
+ align:start position:0%
+some distance
+ 
+
+ align:start position:0%
+some distance
+away this could be a microscope this
+
+ align:start position:0%
+away this could be a microscope this
+ 
+
+ align:start position:0%
+away this could be a microscope this
+could be a camera all sorts of things
+
+ align:start position:0%
+could be a camera all sorts of things
+ 
+
+ align:start position:0%
+could be a camera all sorts of things
+like that yes
+
+ align:start position:0%
+like that yes
+ 
+
+ align:start position:0%
+like that yes
+Vincent uh I I think I missed what was F
+
+ align:start position:0%
+Vincent uh I I think I missed what was F
+ 
+
+ align:start position:0%
+Vincent uh I I think I missed what was F
+again I think what what was F like the
+
+ align:start position:0%
+again I think what what was F like the
+ 
+
+ align:start position:0%
+again I think what what was F like the
+focal length of the
+
+ align:start position:0%
+focal length of the
+ 
+
+ align:start position:0%
+focal length of the
+lens thank cool any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's make this more interesting
+
+ align:start position:0%
+okay let's make this more interesting
+ 
+
+ align:start position:0%
+okay let's make this more interesting
+let's put a plasma here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead okay and we're still going to
+
+ align:start position:0%
+instead okay and we're still going to
+ 
+
+ align:start position:0%
+instead okay and we're still going to
+have our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lens there's still going to be a focal
+
+ align:start position:0%
+lens there's still going to be a focal
+ 
+
+ align:start position:0%
+lens there's still going to be a focal
+point and there's still going to be an
+
+ align:start position:0%
+point and there's still going to be an
+ 
+
+ align:start position:0%
+point and there's still going to be an
+image plane here but the
+
+ align:start position:0%
+image plane here but the
+ 
+
+ align:start position:0%
+image plane here but the
+plasma doesn't block the Rays of light
+
+ align:start position:0%
+plasma doesn't block the Rays of light
+ 
+
+ align:start position:0%
+plasma doesn't block the Rays of light
+as long as we've got for example any
+
+ align:start position:0%
+as long as we've got for example any
+ 
+
+ align:start position:0%
+as long as we've got for example any
+much much less than the critical density
+
+ align:start position:0%
+much much less than the critical density
+ 
+
+ align:start position:0%
+much much less than the critical density
+here so that the Rays can pass through
+
+ align:start position:0%
+here so that the Rays can pass through
+ 
+
+ align:start position:0%
+here so that the Rays can pass through
+easily instead what we're going to have
+
+ align:start position:0%
+easily instead what we're going to have
+ 
+
+ align:start position:0%
+easily instead what we're going to have
+is rays that come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in and then they're going to be
+
+ align:start position:0%
+in and then they're going to be
+ 
+
+ align:start position:0%
+in and then they're going to be
+deflected slightly inside this plasma so
+
+ align:start position:0%
+deflected slightly inside this plasma so
+ 
+
+ align:start position:0%
+deflected slightly inside this plasma so
+I haven't draw drawn the density
+
+ align:start position:0%
+I haven't draw drawn the density
+ 
+
+ align:start position:0%
+I haven't draw drawn the density
+gradients we can imagine we've just got
+
+ align:start position:0%
+gradients we can imagine we've just got
+ 
+
+ align:start position:0%
+gradients we can imagine we've just got
+a whole range of exciting density
+
+ align:start position:0%
+a whole range of exciting density
+ 
+
+ align:start position:0%
+a whole range of exciting density
+gradients that cause some deflections so
+
+ align:start position:0%
+gradients that cause some deflections so
+ 
+
+ align:start position:0%
+gradients that cause some deflections so
+they deflect this Ray slightly downwards
+
+ align:start position:0%
+they deflect this Ray slightly downwards
+ 
+
+ align:start position:0%
+they deflect this Ray slightly downwards
+they deflect this Ray slightly upward
+
+ align:start position:0%
+they deflect this Ray slightly upward
+ 
+
+ align:start position:0%
+they deflect this Ray slightly upward
+they deflect this bottom Ray what have I
+
+ align:start position:0%
+they deflect this bottom Ray what have I
+ 
+
+ align:start position:0%
+they deflect this bottom Ray what have I
+done for this one let's how this one go
+
+ align:start position:0%
+done for this one let's how this one go
+ 
+
+ align:start position:0%
+done for this one let's how this one go
+straight for some reason there's no
+
+ align:start position:0%
+straight for some reason there's no
+ 
+
+ align:start position:0%
+straight for some reason there's no
+density gradient exactly there so the r
+
+ align:start position:0%
+density gradient exactly there so the r
+ 
+
+ align:start position:0%
+density gradient exactly there so the r
+just goes through and this bottom one
+
+ align:start position:0%
+just goes through and this bottom one
+ 
+
+ align:start position:0%
+just goes through and this bottom one
+gets deflected downwards as well and
+
+ align:start position:0%
+gets deflected downwards as well and
+ 
+
+ align:start position:0%
+gets deflected downwards as well and
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+say it just about makes it onto the lens
+
+ align:start position:0%
+say it just about makes it onto the lens
+ 
+
+ align:start position:0%
+say it just about makes it onto the lens
+and I'll move the lens downwards to make
+
+ align:start position:0%
+and I'll move the lens downwards to make
+ 
+
+ align:start position:0%
+and I'll move the lens downwards to make
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+true don't do that on the CH board
+
+ align:start position:0%
+true don't do that on the CH board
+ 
+
+ align:start position:0%
+true don't do that on the CH board
+either okay good so what will the lens
+
+ align:start position:0%
+either okay good so what will the lens
+ 
+
+ align:start position:0%
+either okay good so what will the lens
+due to these Rays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now well it's still going to deflect the
+
+ align:start position:0%
+now well it's still going to deflect the
+ 
+
+ align:start position:0%
+now well it's still going to deflect the
+Rays and it's going to deflect them
+
+ align:start position:0%
+Rays and it's going to deflect them
+ 
+
+ align:start position:0%
+Rays and it's going to deflect them
+let's start with this one that actually
+
+ align:start position:0%
+let's start with this one that actually
+ 
+
+ align:start position:0%
+let's start with this one that actually
+didn't get deflected at all so it angle
+
+ align:start position:0%
+didn't get deflected at all so it angle
+ 
+
+ align:start position:0%
+didn't get deflected at all so it angle
+hasn't changed it's going to go straight
+
+ align:start position:0%
+hasn't changed it's going to go straight
+ 
+
+ align:start position:0%
+hasn't changed it's going to go straight
+through the focal point as as you'd
+
+ align:start position:0%
+through the focal point as as you'd
+ 
+
+ align:start position:0%
+through the focal point as as you'd
+expect this one that was deflected
+
+ align:start position:0%
+expect this one that was deflected
+ 
+
+ align:start position:0%
+expect this one that was deflected
+upwards is going to be deflected down
+
+ align:start position:0%
+upwards is going to be deflected down
+ 
+
+ align:start position:0%
+upwards is going to be deflected down
+but it's going to slightly miss the
+
+ align:start position:0%
+but it's going to slightly miss the
+ 
+
+ align:start position:0%
+but it's going to slightly miss the
+focal point it's going to be slightly
+
+ align:start position:0%
+focal point it's going to be slightly
+ 
+
+ align:start position:0%
+focal point it's going to be slightly
+above it like that this one that was
+
+ align:start position:0%
+above it like that this one that was
+ 
+
+ align:start position:0%
+above it like that this one that was
+deflected downwards is going to be the
+
+ align:start position:0%
+deflected downwards is going to be the
+ 
+
+ align:start position:0%
+deflected downwards is going to be the
+opposite way it's going to be slightly
+
+ align:start position:0%
+opposite way it's going to be slightly
+ 
+
+ align:start position:0%
+opposite way it's going to be slightly
+below the focal point and this one was
+
+ align:start position:0%
+below the focal point and this one was
+ 
+
+ align:start position:0%
+below the focal point and this one was
+reflected uh downwards is also going to
+
+ align:start position:0%
+reflected uh downwards is also going to
+ 
+
+ align:start position:0%
+reflected uh downwards is also going to
+be uh slightly below the focal point and
+
+ align:start position:0%
+be uh slightly below the focal point and
+ 
+
+ align:start position:0%
+be uh slightly below the focal point and
+that was a mistake there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go there we go it's not a very good
+
+ align:start position:0%
+go there we go it's not a very good
+ 
+
+ align:start position:0%
+go there we go it's not a very good
+image compared to the one I was hoping
+
+ align:start position:0%
+image compared to the one I was hoping
+ 
+
+ align:start position:0%
+image compared to the one I was hoping
+to draw but there we go nothing quite
+
+ align:start position:0%
+to draw but there we go nothing quite
+ 
+
+ align:start position:0%
+to draw but there we go nothing quite
+works out so we should have an image of
+
+ align:start position:0%
+works out so we should have an image of
+ 
+
+ align:start position:0%
+works out so we should have an image of
+our plasma here this image of the plasma
+
+ align:start position:0%
+our plasma here this image of the plasma
+ 
+
+ align:start position:0%
+our plasma here this image of the plasma
+should still be one:
+
+ align:start position:0%
+should still be one:
+ 
+
+ align:start position:0%
+should still be one:
+one mag one
+
+ align:start position:0%
+one mag one
+ 
+
+ align:start position:0%
+one mag one
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverted the fact that I haven't quite
+
+ align:start position:0%
+inverted the fact that I haven't quite
+ 
+
+ align:start position:0%
+inverted the fact that I haven't quite
+managed to get to work is probably just
+
+ align:start position:0%
+managed to get to work is probably just
+ 
+
+ align:start position:0%
+managed to get to work is probably just
+a flaw is how I managed to draw the Rays
+
+ align:start position:0%
+a flaw is how I managed to draw the Rays
+ 
+
+ align:start position:0%
+a flaw is how I managed to draw the Rays
+this time
+
+ align:start position:0%
+this time
+ 
+
+ align:start position:0%
+this time
+around not quite sure what what went
+
+ align:start position:0%
+around not quite sure what what went
+ 
+
+ align:start position:0%
+around not quite sure what what went
+wrong there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks good on my notes anyway this stuff
+
+ align:start position:0%
+looks good on my notes anyway this stuff
+ 
+
+ align:start position:0%
+looks good on my notes anyway this stuff
+gets a little bit tricky the point is
+
+ align:start position:0%
+gets a little bit tricky the point is
+ 
+
+ align:start position:0%
+gets a little bit tricky the point is
+although the Rays here look like they've
+
+ align:start position:0%
+although the Rays here look like they've
+ 
+
+ align:start position:0%
+although the Rays here look like they've
+all gone upwards slightly they should
+
+ align:start position:0%
+all gone upwards slightly they should
+ 
+
+ align:start position:0%
+all gone upwards slightly they should
+actually still end up in the same places
+
+ align:start position:0%
+actually still end up in the same places
+ 
+
+ align:start position:0%
+actually still end up in the same places
+that they did before and the fact that I
+
+ align:start position:0%
+that they did before and the fact that I
+ 
+
+ align:start position:0%
+that they did before and the fact that I
+can't get it to work right now just
+
+ align:start position:0%
+can't get it to work right now just
+ 
+
+ align:start position:0%
+can't get it to work right now just
+means that I've made a mistake while
+
+ align:start position:0%
+means that I've made a mistake while
+ 
+
+ align:start position:0%
+means that I've made a mistake while
+drawing it live okay good Jack Jack this
+
+ align:start position:0%
+drawing it live okay good Jack Jack this
+ 
+
+ align:start position:0%
+drawing it live okay good Jack Jack this
+said a very basic question but what
+
+ align:start position:0%
+said a very basic question but what
+ 
+
+ align:start position:0%
+said a very basic question but what
+what's the point of having all the Rays
+
+ align:start position:0%
+what's the point of having all the Rays
+ 
+
+ align:start position:0%
+what's the point of having all the Rays
+go through the the trouble of going
+
+ align:start position:0%
+go through the the trouble of going
+ 
+
+ align:start position:0%
+go through the the trouble of going
+through the lens when we could just have
+
+ align:start position:0%
+through the lens when we could just have
+ 
+
+ align:start position:0%
+through the lens when we could just have
+them go straight through and hit our
+
+ align:start position:0%
+them go straight through and hit our
+ 
+
+ align:start position:0%
+them go straight through and hit our
+image plane like I I guess I missed that
+
+ align:start position:0%
+image plane like I I guess I missed that
+ 
+
+ align:start position:0%
+image plane like I I guess I missed that
+up you know what I mean oh yeah
+
+ align:start position:0%
+up you know what I mean oh yeah
+ 
+
+ align:start position:0%
+up you know what I mean oh yeah
+absolutely um so in the top case with
+
+ align:start position:0%
+absolutely um so in the top case with
+ 
+
+ align:start position:0%
+absolutely um so in the top case with
+the solid object the Rays could go if
+
+ align:start position:0%
+the solid object the Rays could go if
+ 
+
+ align:start position:0%
+the solid object the Rays could go if
+the Rays went straight through and hit
+
+ align:start position:0%
+the Rays went straight through and hit
+ 
+
+ align:start position:0%
+the Rays went straight through and hit
+the image plane they will be deflected
+
+ align:start position:0%
+the image plane they will be deflected
+ 
+
+ align:start position:0%
+the image plane they will be deflected
+slightly at the edges and so you'll end
+
+ align:start position:0%
+slightly at the edges and so you'll end
+ 
+
+ align:start position:0%
+slightly at the edges and so you'll end
+up with something fuzzy so it'll be out
+
+ align:start position:0%
+up with something fuzzy so it'll be out
+ 
+
+ align:start position:0%
+up with something fuzzy so it'll be out
+of focus okay so you need a lens to
+
+ align:start position:0%
+of focus okay so you need a lens to
+ 
+
+ align:start position:0%
+of focus okay so you need a lens to
+bring it to focus which effectively is
+
+ align:start position:0%
+bring it to focus which effectively is
+ 
+
+ align:start position:0%
+bring it to focus which effectively is
+mapping the Rays from where they came
+
+ align:start position:0%
+mapping the Rays from where they came
+ 
+
+ align:start position:0%
+mapping the Rays from where they came
+from back to the same place on the
+
+ align:start position:0%
+from back to the same place on the
+ 
+
+ align:start position:0%
+from back to the same place on the
+object plane if you if in the case of
+
+ align:start position:0%
+object plane if you if in the case of
+ 
+
+ align:start position:0%
+object plane if you if in the case of
+the plasma if you don't have the lens
+
+ align:start position:0%
+the plasma if you don't have the lens
+ 
+
+ align:start position:0%
+the plasma if you don't have the lens
+and you just put if you don't have the
+
+ align:start position:0%
+and you just put if you don't have the
+ 
+
+ align:start position:0%
+and you just put if you don't have the
+lens and you just let the Rays propagate
+
+ align:start position:0%
+lens and you just let the Rays propagate
+ 
+
+ align:start position:0%
+lens and you just let the Rays propagate
+to the screen that's a technique called
+
+ align:start position:0%
+to the screen that's a technique called
+ 
+
+ align:start position:0%
+to the screen that's a technique called
+shog graphy which we'll talk about next
+
+ align:start position:0%
+shog graphy which we'll talk about next
+ 
+
+ align:start position:0%
+shog graphy which we'll talk about next
+lecture which I actually think is more
+
+ align:start position:0%
+lecture which I actually think is more
+ 
+
+ align:start position:0%
+lecture which I actually think is more
+difficult even though it's simpler to
+
+ align:start position:0%
+difficult even though it's simpler to
+ 
+
+ align:start position:0%
+difficult even though it's simpler to
+draw and so I want to talk about it
+
+ align:start position:0%
+draw and so I want to talk about it
+ 
+
+ align:start position:0%
+draw and so I want to talk about it
+after this one um
+
+ align:start position:0%
+after this one um
+ 
+
+ align:start position:0%
+after this one um
+so we haven't done anything here at the
+
+ align:start position:0%
+so we haven't done anything here at the
+ 
+
+ align:start position:0%
+so we haven't done anything here at the
+moment and in fact if you do this with a
+
+ align:start position:0%
+moment and in fact if you do this with a
+ 
+
+ align:start position:0%
+moment and in fact if you do this with a
+plasma you won't see anything at all
+
+ align:start position:0%
+plasma you won't see anything at all
+ 
+
+ align:start position:0%
+plasma you won't see anything at all
+because all of the rays are mapped back
+
+ align:start position:0%
+because all of the rays are mapped back
+ 
+
+ align:start position:0%
+because all of the rays are mapped back
+to where they started from and that
+
+ align:start position:0%
+to where they started from and that
+ 
+
+ align:start position:0%
+to where they started from and that
+means that you are going to end up with
+
+ align:start position:0%
+means that you are going to end up with
+ 
+
+ align:start position:0%
+means that you are going to end up with
+uh just the same laser beam that you
+
+ align:start position:0%
+uh just the same laser beam that you
+ 
+
+ align:start position:0%
+uh just the same laser beam that you
+originally started with or the same
+
+ align:start position:0%
+originally started with or the same
+ 
+
+ align:start position:0%
+originally started with or the same
+microwaves you originally started with
+
+ align:start position:0%
+microwaves you originally started with
+ 
+
+ align:start position:0%
+microwaves you originally started with
+so this will be uh invisible so the only
+
+ align:start position:0%
+so this will be uh invisible so the only
+ 
+
+ align:start position:0%
+so this will be uh invisible so the only
+way we can make this visible is to
+
+ align:start position:0%
+way we can make this visible is to
+ 
+
+ align:start position:0%
+way we can make this visible is to
+notice that the Rays do not all pass
+
+ align:start position:0%
+notice that the Rays do not all pass
+ 
+
+ align:start position:0%
+notice that the Rays do not all pass
+through the focal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point now you saw in the case where we
+
+ align:start position:0%
+point now you saw in the case where we
+ 
+
+ align:start position:0%
+point now you saw in the case where we
+did the Imaging that all the Rays did
+
+ align:start position:0%
+did the Imaging that all the Rays did
+ 
+
+ align:start position:0%
+did the Imaging that all the Rays did
+indeed still pass through focal point
+
+ align:start position:0%
+indeed still pass through focal point
+ 
+
+ align:start position:0%
+indeed still pass through focal point
+but here some of them gone above and
+
+ align:start position:0%
+but here some of them gone above and
+ 
+
+ align:start position:0%
+but here some of them gone above and
+some of them gone below and in fact the
+
+ align:start position:0%
+some of them gone below and in fact the
+ 
+
+ align:start position:0%
+some of them gone below and in fact the
+distance they've gone above and the
+
+ align:start position:0%
+distance they've gone above and the
+ 
+
+ align:start position:0%
+distance they've gone above and the
+distance they've gone below is directly
+
+ align:start position:0%
+distance they've gone below is directly
+ 
+
+ align:start position:0%
+distance they've gone below is directly
+proportional to the angle with which
+
+ align:start position:0%
+proportional to the angle with which
+ 
+
+ align:start position:0%
+proportional to the angle with which
+they exited the plasma here and so we
+
+ align:start position:0%
+they exited the plasma here and so we
+ 
+
+ align:start position:0%
+they exited the plasma here and so we
+can learn something about the angle they
+
+ align:start position:0%
+can learn something about the angle they
+ 
+
+ align:start position:0%
+can learn something about the angle they
+can selected uh exited the plasma by
+
+ align:start position:0%
+can selected uh exited the plasma by
+ 
+
+ align:start position:0%
+can selected uh exited the plasma by
+placing a filter at this focal PL and
+
+ align:start position:0%
+placing a filter at this focal PL and
+ 
+
+ align:start position:0%
+placing a filter at this focal PL and
+this filter maybe looks a little bit
+
+ align:start position:0%
+this filter maybe looks a little bit
+ 
+
+ align:start position:0%
+this filter maybe looks a little bit
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this this filter for example here is
+
+ align:start position:0%
+this this filter for example here is
+ 
+
+ align:start position:0%
+this this filter for example here is
+like a little aperture and it lets
+
+ align:start position:0%
+like a little aperture and it lets
+ 
+
+ align:start position:0%
+like a little aperture and it lets
+through these two rays let me color code
+
+ align:start position:0%
+through these two rays let me color code
+ 
+
+ align:start position:0%
+through these two rays let me color code
+them this one and this one and it blocks
+
+ align:start position:0%
+them this one and this one and it blocks
+ 
+
+ align:start position:0%
+them this one and this one and it blocks
+off these two
+
+ align:start position:0%
+off these two
+ 
+
+ align:start position:0%
+off these two
+rays and so lights coming from that bit
+
+ align:start position:0%
+rays and so lights coming from that bit
+ 
+
+ align:start position:0%
+rays and so lights coming from that bit
+of the plasma where the density
+
+ align:start position:0%
+of the plasma where the density
+ 
+
+ align:start position:0%
+of the plasma where the density
+gradients were large will be blocked it
+
+ align:start position:0%
+gradients were large will be blocked it
+ 
+
+ align:start position:0%
+gradients were large will be blocked it
+will no longer appear on our final image
+
+ align:start position:0%
+will no longer appear on our final image
+ 
+
+ align:start position:0%
+will no longer appear on our final image
+and this is what schan Imaging is so we
+
+ align:start position:0%
+and this is what schan Imaging is so we
+ 
+
+ align:start position:0%
+and this is what schan Imaging is so we
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+a a
+
+ align:start position:0%
+a a
+ 
+
+ align:start position:0%
+a a
+stop at the focal play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+filter by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle I'm going to do some exhaustive
+
+ align:start position:0%
+angle I'm going to do some exhaustive
+ 
+
+ align:start position:0%
+angle I'm going to do some exhaustive
+examples of this to try and build some
+
+ align:start position:0%
+examples of this to try and build some
+ 
+
+ align:start position:0%
+examples of this to try and build some
+intuition for what's going on if you're
+
+ align:start position:0%
+intuition for what's going on if you're
+ 
+
+ align:start position:0%
+intuition for what's going on if you're
+a little bit confused right now any
+
+ align:start position:0%
+a little bit confused right now any
+ 
+
+ align:start position:0%
+a little bit confused right now any
+questions on this before we keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have sort of a overall conceptual
+
+ align:start position:0%
+I have sort of a overall conceptual
+ 
+
+ align:start position:0%
+I have sort of a overall conceptual
+question I feel like the highest
+
+ align:start position:0%
+question I feel like the highest
+ 
+
+ align:start position:0%
+question I feel like the highest
+gradients a lot of the time are well
+
+ align:start position:0%
+gradients a lot of the time are well
+ 
+
+ align:start position:0%
+gradients a lot of the time are well
+maybe this isn't quite true but I can
+
+ align:start position:0%
+maybe this isn't quite true but I can
+ 
+
+ align:start position:0%
+maybe this isn't quite true but I can
+imagine a lot of cases it's going to be
+
+ align:start position:0%
+imagine a lot of cases it's going to be
+ 
+
+ align:start position:0%
+imagine a lot of cases it's going to be
+affected most by the edges where it's
+
+ align:start position:0%
+affected most by the edges where it's
+ 
+
+ align:start position:0%
+affected most by the edges where it's
+entering and leaving the plasma because
+
+ align:start position:0%
+entering and leaving the plasma because
+ 
+
+ align:start position:0%
+entering and leaving the plasma because
+you're you know depending on how uniform
+
+ align:start position:0%
+you're you know depending on how uniform
+ 
+
+ align:start position:0%
+you're you know depending on how uniform
+things are so just curious what you
+
+ align:start position:0%
+things are so just curious what you
+ 
+
+ align:start position:0%
+things are so just curious what you
+actually get an image of I mean if you
+
+ align:start position:0%
+actually get an image of I mean if you
+ 
+
+ align:start position:0%
+actually get an image of I mean if you
+especially you don't have a great sense
+
+ align:start position:0%
+especially you don't have a great sense
+ 
+
+ align:start position:0%
+especially you don't have a great sense
+of where the the gradients are or if you
+
+ align:start position:0%
+of where the the gradients are or if you
+ 
+
+ align:start position:0%
+of where the the gradients are or if you
+have the gradients inside don't know
+
+ align:start position:0%
+have the gradients inside don't know
+ 
+
+ align:start position:0%
+have the gradients inside don't know
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+or yeah absolutely um these images are
+
+ align:start position:0%
+or yeah absolutely um these images are
+ 
+
+ align:start position:0%
+or yeah absolutely um these images are
+difficult to interpret so this is not a
+
+ align:start position:0%
+difficult to interpret so this is not a
+ 
+
+ align:start position:0%
+difficult to interpret so this is not a
+generic diagnostic technique that will
+
+ align:start position:0%
+generic diagnostic technique that will
+ 
+
+ align:start position:0%
+generic diagnostic technique that will
+immediately tell you what's going on you
+
+ align:start position:0%
+immediately tell you what's going on you
+ 
+
+ align:start position:0%
+immediately tell you what's going on you
+need to know something about your plasma
+
+ align:start position:0%
+need to know something about your plasma
+ 
+
+ align:start position:0%
+need to know something about your plasma
+maybe you have a simulation and you do a
+
+ align:start position:0%
+maybe you have a simulation and you do a
+ 
+
+ align:start position:0%
+maybe you have a simulation and you do a
+synthetic diagnostic on it or maybe
+
+ align:start position:0%
+synthetic diagnostic on it or maybe
+ 
+
+ align:start position:0%
+synthetic diagnostic on it or maybe
+you've set up your experiment such it's
+
+ align:start position:0%
+you've set up your experiment such it's
+ 
+
+ align:start position:0%
+you've set up your experiment such it's
+particularly simple and we'll talk a
+
+ align:start position:0%
+particularly simple and we'll talk a
+ 
+
+ align:start position:0%
+particularly simple and we'll talk a
+little bit about some simple
+
+ align:start position:0%
+little bit about some simple
+ 
+
+ align:start position:0%
+little bit about some simple
+distributions and what patterns they
+
+ align:start position:0%
+distributions and what patterns they
+ 
+
+ align:start position:0%
+distributions and what patterns they
+make and that will give us an idea for
+
+ align:start position:0%
+make and that will give us an idea for
+ 
+
+ align:start position:0%
+make and that will give us an idea for
+what sorts of things we might be able to
+
+ align:start position:0%
+what sorts of things we might be able to
+ 
+
+ align:start position:0%
+what sorts of things we might be able to
+measure with this but like a a turbul
+
+ align:start position:0%
+measure with this but like a a turbul
+ 
+
+ align:start position:0%
+measure with this but like a a turbul
+like turbulence in the edge of a toac or
+
+ align:start position:0%
+like turbulence in the edge of a toac or
+ 
+
+ align:start position:0%
+like turbulence in the edge of a toac or
+something like that is maybe not the
+
+ align:start position:0%
+something like that is maybe not the
+ 
+
+ align:start position:0%
+something like that is maybe not the
+ideal diagnostic for it fair enough yes
+
+ align:start position:0%
+ideal diagnostic for it fair enough yes
+ 
+
+ align:start position:0%
+ideal diagnostic for it fair enough yes
+and and just I want to make very clear
+
+ align:start position:0%
+and and just I want to make very clear
+ 
+
+ align:start position:0%
+and and just I want to make very clear
+because I I don't know if it came across
+
+ align:start position:0%
+because I I don't know if it came across
+ 
+
+ align:start position:0%
+because I I don't know if it came across
+um when we were talking about it before
+
+ align:start position:0%
+um when we were talking about it before
+ 
+
+ align:start position:0%
+um when we were talking about it before
+but we're we're we only get deflections
+
+ align:start position:0%
+but we're we're we only get deflections
+ 
+
+ align:start position:0%
+but we're we're we only get deflections
+from density gradients which are
+
+ align:start position:0%
+from density gradients which are
+ 
+
+ align:start position:0%
+from density gradients which are
+perpendicular to the direction here so
+
+ align:start position:0%
+perpendicular to the direction here so
+ 
+
+ align:start position:0%
+perpendicular to the direction here so
+if our Ray is going in this direction in
+
+ align:start position:0%
+if our Ray is going in this direction in
+ 
+
+ align:start position:0%
+if our Ray is going in this direction in
+the Z direction we
+
+ align:start position:0%
+the Z direction we
+ 
+
+ align:start position:0%
+the Z direction we
+sense D Dy of NE and D DX of NE but we
+
+ align:start position:0%
+sense D Dy of NE and D DX of NE but we
+ 
+
+ align:start position:0%
+sense D Dy of NE and D DX of NE but we
+do not
+
+ align:start position:0%
+do not
+ 
+
+ align:start position:0%
+do not
+sense d d z of NE so if there's density
+
+ align:start position:0%
+sense d d z of NE so if there's density
+ 
+
+ align:start position:0%
+sense d d z of NE so if there's density
+gradients in the direction the ray is
+
+ align:start position:0%
+gradients in the direction the ray is
+ 
+
+ align:start position:0%
+gradients in the direction the ray is
+propagating the ray will slow down or
+
+ align:start position:0%
+propagating the ray will slow down or
+ 
+
+ align:start position:0%
+propagating the ray will slow down or
+speed up but it won't actually deflect
+
+ align:start position:0%
+speed up but it won't actually deflect
+ 
+
+ align:start position:0%
+speed up but it won't actually deflect
+from that and so that helps you a little
+
+ align:start position:0%
+from that and so that helps you a little
+ 
+
+ align:start position:0%
+from that and so that helps you a little
+bit you're only sensitive to gradients
+
+ align:start position:0%
+bit you're only sensitive to gradients
+ 
+
+ align:start position:0%
+bit you're only sensitive to gradients
+perpendicular to the probing direction
+
+ align:start position:0%
+perpendicular to the probing direction
+ 
+
+ align:start position:0%
+perpendicular to the probing direction
+that might also tell you if you've got a
+
+ align:start position:0%
+that might also tell you if you've got a
+ 
+
+ align:start position:0%
+that might also tell you if you've got a
+plasma which you think has some geometry
+
+ align:start position:0%
+plasma which you think has some geometry
+ 
+
+ align:start position:0%
+plasma which you think has some geometry
+there may be a good direction to send
+
+ align:start position:0%
+there may be a good direction to send
+ 
+
+ align:start position:0%
+there may be a good direction to send
+the probing beam through there may be a
+
+ align:start position:0%
+the probing beam through there may be a
+ 
+
+ align:start position:0%
+the probing beam through there may be a
+bad Direction so you want to think about
+
+ align:start position:0%
+bad Direction so you want to think about
+ 
+
+ align:start position:0%
+bad Direction so you want to think about
+that a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's have a talk about some of these
+
+ align:start position:0%
+so let's have a talk about some of these
+ 
+
+ align:start position:0%
+so let's have a talk about some of these
+uh stops right so I've said that we can
+
+ align:start position:0%
+uh stops right so I've said that we can
+ 
+
+ align:start position:0%
+uh stops right so I've said that we can
+place these stops here let's have a chat
+
+ align:start position:0%
+place these stops here let's have a chat
+ 
+
+ align:start position:0%
+place these stops here let's have a chat
+about what sort of different stops are
+
+ align:start position:0%
+about what sort of different stops are
+ 
+
+ align:start position:0%
+about what sort of different stops are
+available to
+
+ align:start position:0%
+available to
+ 
+
+ align:start position:0%
+available to
+us so types of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stop the first type is to decide whether
+
+ align:start position:0%
+stop the first type is to decide whether
+ 
+
+ align:start position:0%
+stop the first type is to decide whether
+our stop is going to be dark field or
+
+ align:start position:0%
+our stop is going to be dark field or
+ 
+
+ align:start position:0%
+our stop is going to be dark field or
+light field so I'm putting dark in
+
+ align:start position:0%
+light field so I'm putting dark in
+ 
+
+ align:start position:0%
+light field so I'm putting dark in
+Brackets because it will save me writing
+
+ align:start position:0%
+Brackets because it will save me writing
+ 
+
+ align:start position:0%
+Brackets because it will save me writing
+in a moment
+
+ align:start position:0%
+in a moment
+ 
+
+ align:start position:0%
+in a moment
+the difference between dark field and
+
+ align:start position:0%
+the difference between dark field and
+ 
+
+ align:start position:0%
+the difference between dark field and
+light field is that the dark field
+
+ align:start position:0%
+light field is that the dark field
+ 
+
+ align:start position:0%
+light field is that the dark field
+blocks undeflected
+
+ align:start position:0%
+blocks undeflected
+ 
+
+ align:start position:0%
+blocks undeflected
+Rays so ones that do pass through the
+
+ align:start position:0%
+Rays so ones that do pass through the
+ 
+
+ align:start position:0%
+Rays so ones that do pass through the
+focal point and the light field blocks
+
+ align:start position:0%
+focal point and the light field blocks
+ 
+
+ align:start position:0%
+focal point and the light field blocks
+deflected Rays ones which do not pass
+
+ align:start position:0%
+deflected Rays ones which do not pass
+ 
+
+ align:start position:0%
+deflected Rays ones which do not pass
+through the focal point so you can
+
+ align:start position:0%
+through the focal point so you can
+ 
+
+ align:start position:0%
+through the focal point so you can
+either look for Regions where there are
+
+ align:start position:0%
+either look for Regions where there are
+ 
+
+ align:start position:0%
+either look for Regions where there are
+density gradients or where there aren't
+
+ align:start position:0%
+density gradients or where there aren't
+ 
+
+ align:start position:0%
+density gradients or where there aren't
+density gradients we can also choose the
+
+ align:start position:0%
+density gradients we can also choose the
+ 
+
+ align:start position:0%
+density gradients we can also choose the
+shape of our stop because our stop uh is
+
+ align:start position:0%
+shape of our stop because our stop uh is
+ 
+
+ align:start position:0%
+shape of our stop because our stop uh is
+sort of a two diens dimensional plane at
+
+ align:start position:0%
+sort of a two diens dimensional plane at
+ 
+
+ align:start position:0%
+sort of a two diens dimensional plane at
+the focal plane here so we could have a
+
+ align:start position:0%
+the focal plane here so we could have a
+ 
+
+ align:start position:0%
+the focal plane here so we could have a
+circular
+
+ align:start position:0%
+circular
+ 
+
+ align:start position:0%
+circular
+stop and that doesn't care what
+
+ align:start position:0%
+stop and that doesn't care what
+ 
+
+ align:start position:0%
+stop and that doesn't care what
+direction the ray is deflected in it
+
+ align:start position:0%
+direction the ray is deflected in it
+ 
+
+ align:start position:0%
+direction the ray is deflected in it
+only cares on the size of the angle so
+
+ align:start position:0%
+only cares on the size of the angle so
+ 
+
+ align:start position:0%
+only cares on the size of the angle so
+the size of theta so that is basically
+
+ align:start position:0%
+the size of theta so that is basically
+ 
+
+ align:start position:0%
+the size of theta so that is basically
+are there any large density gradients or
+
+ align:start position:0%
+are there any large density gradients or
+ 
+
+ align:start position:0%
+are there any large density gradients or
+we could have what's called a knife
+
+ align:start position:0%
+we could have what's called a knife
+ 
+
+ align:start position:0%
+we could have what's called a knife
+edge which is
+
+ align:start position:0%
+edge which is
+ 
+
+ align:start position:0%
+edge which is
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+uh like this and that is sensitive to
+
+ align:start position:0%
+uh like this and that is sensitive to
+ 
+
+ align:start position:0%
+uh like this and that is sensitive to
+density gradients in Only One Direction
+
+ align:start position:0%
+density gradients in Only One Direction
+ 
+
+ align:start position:0%
+density gradients in Only One Direction
+and it still cares about the size of the
+
+ align:start position:0%
+and it still cares about the size of the
+ 
+
+ align:start position:0%
+and it still cares about the size of the
+density gradient I'll WR that it's like
+
+ align:start position:0%
+density gradient I'll WR that it's like
+ 
+
+ align:start position:0%
+density gradient I'll WR that it's like
+X hat
+
+ align:start position:0%
+X hat
+ 
+
+ align:start position:0%
+X hat
+here so we could for example
+
+ align:start position:0%
+here so we could for example
+ 
+
+ align:start position:0%
+here so we could for example
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+scop at the focal plane no it's not
+
+ align:start position:0%
+scop at the focal plane no it's not
+ 
+
+ align:start position:0%
+scop at the focal plane no it's not
+going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay fine I can't get a nice round
+
+ align:start position:0%
+it okay fine I can't get a nice round
+ 
+
+ align:start position:0%
+it okay fine I can't get a nice round
+circle we could have a stop which is an
+
+ align:start position:0%
+circle we could have a stop which is an
+ 
+
+ align:start position:0%
+circle we could have a stop which is an
+opening inside an opaque sheet of
+
+ align:start position:0%
+opening inside an opaque sheet of
+ 
+
+ align:start position:0%
+opening inside an opaque sheet of
+material here and this opening could be
+
+ align:start position:0%
+material here and this opening could be
+ 
+
+ align:start position:0%
+material here and this opening could be
+positioned such that the focal
+
+ align:start position:0%
+positioned such that the focal
+ 
+
+ align:start position:0%
+positioned such that the focal
+spot in the absence of any plasma sits
+
+ align:start position:0%
+spot in the absence of any plasma sits
+ 
+
+ align:start position:0%
+spot in the absence of any plasma sits
+inside it what sort of stop would this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be light field so this is a light field
+
+ align:start position:0%
+be light field so this is a light field
+ 
+
+ align:start position:0%
+be light field so this is a light field
+stop and what shape is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the best yes okay Circle thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you uh we could also have a stock that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and we can position it such that
+
+ align:start position:0%
+this and we can position it such that
+ 
+
+ align:start position:0%
+this and we can position it such that
+the focal spot is actually within the
+
+ align:start position:0%
+the focal spot is actually within the
+ 
+
+ align:start position:0%
+the focal spot is actually within the
+opaque region and what sort of slot
+
+ align:start position:0%
+opaque region and what sort of slot
+ 
+
+ align:start position:0%
+opaque region and what sort of slot
+would this be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dark field dark field okay dark field
+
+ align:start position:0%
+dark field dark field okay dark field
+ 
+
+ align:start position:0%
+dark field dark field okay dark field
+and what shape is
+
+ align:start position:0%
+and what shape is
+ 
+
+ align:start position:0%
+and what shape is
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+linear so a knife edge here
+
+ align:start position:0%
+linear so a knife edge here
+ 
+
+ align:start position:0%
+linear so a knife edge here
+yeah we call it a knife edge because
+
+ align:start position:0%
+yeah we call it a knife edge because
+ 
+
+ align:start position:0%
+yeah we call it a knife edge because
+actually using a razor blade is a pretty
+
+ align:start position:0%
+actually using a razor blade is a pretty
+ 
+
+ align:start position:0%
+actually using a razor blade is a pretty
+good thing to have because you get a
+
+ align:start position:0%
+good thing to have because you get a
+ 
+
+ align:start position:0%
+good thing to have because you get a
+very nice sharp uniform Edge to it okay
+
+ align:start position:0%
+very nice sharp uniform Edge to it okay
+ 
+
+ align:start position:0%
+very nice sharp uniform Edge to it okay
+and so depending on these stops you can
+
+ align:start position:0%
+and so depending on these stops you can
+ 
+
+ align:start position:0%
+and so depending on these stops you can
+think of as filters in angle space right
+
+ align:start position:0%
+think of as filters in angle space right
+ 
+
+ align:start position:0%
+think of as filters in angle space right
+so they allow through certain angles you
+
+ align:start position:0%
+so they allow through certain angles you
+ 
+
+ align:start position:0%
+so they allow through certain angles you
+can think of arbitrarily complicated
+
+ align:start position:0%
+can think of arbitrarily complicated
+ 
+
+ align:start position:0%
+can think of arbitrarily complicated
+versions of this there's a a technique
+
+ align:start position:0%
+versions of this there's a a technique
+ 
+
+ align:start position:0%
+versions of this there's a a technique
+called um angular not Fringe angular
+
+ align:start position:0%
+called um angular not Fringe angular
+ 
+
+ align:start position:0%
+called um angular not Fringe angular
+filter refractometry which has a set of
+
+ align:start position:0%
+filter refractometry which has a set of
+ 
+
+ align:start position:0%
+filter refractometry which has a set of
+nested anuli which let
+
+ align:start position:0%
+nested anuli which let
+ 
+
+ align:start position:0%
+nested anuli which let
+through uh light which has been
+
+ align:start position:0%
+through uh light which has been
+ 
+
+ align:start position:0%
+through uh light which has been
+deflected by certain specific angles so
+
+ align:start position:0%
+deflected by certain specific angles so
+ 
+
+ align:start position:0%
+deflected by certain specific angles so
+you know the world is your oyster you
+
+ align:start position:0%
+you know the world is your oyster you
+ 
+
+ align:start position:0%
+you know the world is your oyster you
+can come up with all sorts of exciting
+
+ align:start position:0%
+can come up with all sorts of exciting
+ 
+
+ align:start position:0%
+can come up with all sorts of exciting
+different stops if you want to one thing
+
+ align:start position:0%
+different stops if you want to one thing
+ 
+
+ align:start position:0%
+different stops if you want to one thing
+I will note is that the D dynamic range
+
+ align:start position:0%
+I will note is that the D dynamic range
+ 
+
+ align:start position:0%
+I will note is that the D dynamic range
+of your diagnostic which we'll talk
+
+ align:start position:0%
+of your diagnostic which we'll talk
+ 
+
+ align:start position:0%
+of your diagnostic which we'll talk
+about more later depends a great deal on
+
+ align:start position:0%
+about more later depends a great deal on
+ 
+
+ align:start position:0%
+about more later depends a great deal on
+your focal spot
+
+ align:start position:0%
+your focal spot
+ 
+
+ align:start position:0%
+your focal spot
+size so I've shown these focal spots to
+
+ align:start position:0%
+size so I've shown these focal spots to
+ 
+
+ align:start position:0%
+size so I've shown these focal spots to
+be relatively small here uh but that
+
+ align:start position:0%
+be relatively small here uh but that
+ 
+
+ align:start position:0%
+be relatively small here uh but that
+focal spot size at least in a defraction
+
+ align:start position:0%
+focal spot size at least in a defraction
+ 
+
+ align:start position:0%
+focal spot size at least in a defraction
+limited sense it covers an angle which
+
+ align:start position:0%
+limited sense it covers an angle which
+ 
+
+ align:start position:0%
+limited sense it covers an angle which
+is equal to the wavelength of your light
+
+ align:start position:0%
+is equal to the wavelength of your light
+ 
+
+ align:start position:0%
+is equal to the wavelength of your light
+over the size of your lens the diameter
+
+ align:start position:0%
+over the size of your lens the diameter
+ 
+
+ align:start position:0%
+over the size of your lens the diameter
+of your lens here and so you might end
+
+ align:start position:0%
+of your lens here and so you might end
+ 
+
+ align:start position:0%
+of your lens here and so you might end
+up having focal spots which are are not
+
+ align:start position:0%
+up having focal spots which are are not
+ 
+
+ align:start position:0%
+up having focal spots which are are not
+small but actually could be rather large
+
+ align:start position:0%
+small but actually could be rather large
+ 
+
+ align:start position:0%
+small but actually could be rather large
+and then part of the focal spot could be
+
+ align:start position:0%
+and then part of the focal spot could be
+ 
+
+ align:start position:0%
+and then part of the focal spot could be
+obscured and part of the focal spot
+
+ align:start position:0%
+obscured and part of the focal spot
+ 
+
+ align:start position:0%
+obscured and part of the focal spot
+could be clear for some given deflection
+
+ align:start position:0%
+could be clear for some given deflection
+ 
+
+ align:start position:0%
+could be clear for some given deflection
+angle so and in general when we've got a
+
+ align:start position:0%
+angle so and in general when we've got a
+ 
+
+ align:start position:0%
+angle so and in general when we've got a
+plasma
+
+ align:start position:0%
+plasma
+ 
+
+ align:start position:0%
+plasma
+here we have say a small focal spot
+
+ align:start position:0%
+here we have say a small focal spot
+ 
+
+ align:start position:0%
+here we have say a small focal spot
+before we put uh any Plasma in the way
+
+ align:start position:0%
+before we put uh any Plasma in the way
+ 
+
+ align:start position:0%
+before we put uh any Plasma in the way
+when the Plasma's gone in the way
+
+ align:start position:0%
+when the Plasma's gone in the way
+ 
+
+ align:start position:0%
+when the Plasma's gone in the way
+different rays of Light have being
+
+ align:start position:0%
+different rays of Light have being
+ 
+
+ align:start position:0%
+different rays of Light have being
+deflected by different amounts so this
+
+ align:start position:0%
+deflected by different amounts so this
+ 
+
+ align:start position:0%
+deflected by different amounts so this
+thing may take on some complicated
+
+ align:start position:0%
+thing may take on some complicated
+ 
+
+ align:start position:0%
+thing may take on some complicated
+shape here and this is the shape that
+
+ align:start position:0%
+shape here and this is the shape that
+ 
+
+ align:start position:0%
+shape here and this is the shape that
+you're filtering you might be filtering
+
+ align:start position:0%
+you're filtering you might be filtering
+ 
+
+ align:start position:0%
+you're filtering you might be filtering
+it with your knife edge like this or you
+
+ align:start position:0%
+it with your knife edge like this or you
+ 
+
+ align:start position:0%
+it with your knife edge like this or you
+might be filtering it with your circular
+
+ align:start position:0%
+might be filtering it with your circular
+ 
+
+ align:start position:0%
+might be filtering it with your circular
+stop like this so we're basically
+
+ align:start position:0%
+stop like this so we're basically
+ 
+
+ align:start position:0%
+stop like this so we're basically
+filtering the Rays based on how far
+
+ align:start position:0%
+filtering the Rays based on how far
+ 
+
+ align:start position:0%
+filtering the Rays based on how far
+they've been deflected but the focal
+
+ align:start position:0%
+they've been deflected but the focal
+ 
+
+ align:start position:0%
+they've been deflected but the focal
+plane there's no information about where
+
+ align:start position:0%
+plane there's no information about where
+ 
+
+ align:start position:0%
+plane there's no information about where
+the Rays came from inside their plasma
+
+ align:start position:0%
+the Rays came from inside their plasma
+ 
+
+ align:start position:0%
+the Rays came from inside their plasma
+so their spatial information has been
+
+ align:start position:0%
+so their spatial information has been
+ 
+
+ align:start position:0%
+so their spatial information has been
+lost the only thing we know about them
+
+ align:start position:0%
+lost the only thing we know about them
+ 
+
+ align:start position:0%
+lost the only thing we know about them
+is their angular uh position so rays
+
+ align:start position:0%
+is their angular uh position so rays
+ 
+
+ align:start position:0%
+is their angular uh position so rays
+which are deflected by an angle Theta
+
+ align:start position:0%
+which are deflected by an angle Theta
+ 
+
+ align:start position:0%
+which are deflected by an angle Theta
+one from at the top of the plasma and
+
+ align:start position:0%
+one from at the top of the plasma and
+ 
+
+ align:start position:0%
+one from at the top of the plasma and
+rays which are deflected by the same
+
+ align:start position:0%
+rays which are deflected by the same
+ 
+
+ align:start position:0%
+rays which are deflected by the same
+angle from the bottom of plasma end up
+
+ align:start position:0%
+angle from the bottom of plasma end up
+ 
+
+ align:start position:0%
+angle from the bottom of plasma end up
+at the same place in the focal plane um
+
+ align:start position:0%
+at the same place in the focal plane um
+ 
+
+ align:start position:0%
+at the same place in the focal plane um
+even though they came from different
+
+ align:start position:0%
+even though they came from different
+ 
+
+ align:start position:0%
+even though they came from different
+parts of the plas this is the magic of
+
+ align:start position:0%
+parts of the plas this is the magic of
+ 
+
+ align:start position:0%
+parts of the plas this is the magic of
+geometric
+
+ align:start position:0%
+geometric
+ 
+
+ align:start position:0%
+geometric
+optics so any questions on this or
+
+ align:start position:0%
+optics so any questions on this or
+ 
+
+ align:start position:0%
+optics so any questions on this or
+should we do a a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay let's do our
+
+ align:start position:0%
+example okay let's do our
+ 
+
+ align:start position:0%
+example okay let's do our
+example so let us
+
+ align:start position:0%
+example so let us
+ 
+
+ align:start position:0%
+example so let us
+consider a very simple plasma
+
+ align:start position:0%
+consider a very simple plasma
+ 
+
+ align:start position:0%
+consider a very simple plasma
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma will have the coordinate system y
+
+ align:start position:0%
+plasma will have the coordinate system y
+ 
+
+ align:start position:0%
+plasma will have the coordinate system y
+vertically and we'll have Zs in the
+
+ align:start position:0%
+vertically and we'll have Zs in the
+ 
+
+ align:start position:0%
+vertically and we'll have Zs in the
+direction of propagation as we discussed
+
+ align:start position:0%
+direction of propagation as we discussed
+ 
+
+ align:start position:0%
+direction of propagation as we discussed
+before um we'll have Rays oh well I'll
+
+ align:start position:0%
+before um we'll have Rays oh well I'll
+ 
+
+ align:start position:0%
+before um we'll have Rays oh well I'll
+draw the plasma first so the plasma is
+
+ align:start position:0%
+draw the plasma first so the plasma is
+ 
+
+ align:start position:0%
+draw the plasma first so the plasma is
+going to have a density distribution
+
+ align:start position:0%
+going to have a density distribution
+ 
+
+ align:start position:0%
+going to have a density distribution
+that sort of looks gaussian is some sort
+
+ align:start position:0%
+that sort of looks gaussian is some sort
+ 
+
+ align:start position:0%
+that sort of looks gaussian is some sort
+of nice Peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so this is density and
+
+ align:start position:0%
+function so this is density and
+ 
+
+ align:start position:0%
+function so this is density and
+so you can think about this for example
+
+ align:start position:0%
+so you can think about this for example
+ 
+
+ align:start position:0%
+so you can think about this for example
+as like a cylinder so you've got a
+
+ align:start position:0%
+as like a cylinder so you've got a
+ 
+
+ align:start position:0%
+as like a cylinder so you've got a
+cylinder of plasma like a z pinch and
+
+ align:start position:0%
+cylinder of plasma like a z pinch and
+ 
+
+ align:start position:0%
+cylinder of plasma like a z pinch and
+you're probing down the axis of this Z
+
+ align:start position:0%
+you're probing down the axis of this Z
+ 
+
+ align:start position:0%
+you're probing down the axis of this Z
+pinch and it's got a gouon distribution
+
+ align:start position:0%
+pinch and it's got a gouon distribution
+ 
+
+ align:start position:0%
+pinch and it's got a gouon distribution
+of density to it um anything like that
+
+ align:start position:0%
+of density to it um anything like that
+ 
+
+ align:start position:0%
+of density to it um anything like that
+and then we'll have the Rays of light
+
+ align:start position:0%
+and then we'll have the Rays of light
+ 
+
+ align:start position:0%
+and then we'll have the Rays of light
+coming through so we'll have rays of
+
+ align:start position:0%
+coming through so we'll have rays of
+ 
+
+ align:start position:0%
+coming through so we'll have rays of
+Light which are sampling very small
+
+ align:start position:0%
+Light which are sampling very small
+ 
+
+ align:start position:0%
+Light which are sampling very small
+density gradients at the edges here and
+
+ align:start position:0%
+density gradients at the edges here and
+ 
+
+ align:start position:0%
+density gradients at the edges here and
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+rays will just go straight through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's also be a ray that goes through
+
+ align:start position:0%
+there's also be a ray that goes through
+ 
+
+ align:start position:0%
+there's also be a ray that goes through
+the center which also sees a very small
+
+ align:start position:0%
+the center which also sees a very small
+ 
+
+ align:start position:0%
+the center which also sees a very small
+density gradient here right right at the
+
+ align:start position:0%
+density gradient here right right at the
+ 
+
+ align:start position:0%
+density gradient here right right at the
+center of this distribution the density
+
+ align:start position:0%
+center of this distribution the density
+ 
+
+ align:start position:0%
+center of this distribution the density
+gradient is zero but the edges here
+
+ align:start position:0%
+gradient is zero but the edges here
+ 
+
+ align:start position:0%
+gradient is zero but the edges here
+where the density gradient is large will
+
+ align:start position:0%
+where the density gradient is large will
+ 
+
+ align:start position:0%
+where the density gradient is large will
+have some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection and if we place our lens as
+
+ align:start position:0%
+deflection and if we place our lens as
+ 
+
+ align:start position:0%
+deflection and if we place our lens as
+we did
+
+ align:start position:0%
+we did
+ 
+
+ align:start position:0%
+we did
+before some distance away it's going to
+
+ align:start position:0%
+before some distance away it's going to
+ 
+
+ align:start position:0%
+before some distance away it's going to
+focus those Rays onto our focal
+
+ align:start position:0%
+focus those Rays onto our focal
+ 
+
+ align:start position:0%
+focus those Rays onto our focal
+plane and in our focal plane we're going
+
+ align:start position:0%
+plane and in our focal plane we're going
+ 
+
+ align:start position:0%
+plane and in our focal plane we're going
+to put some sort of stop here so the
+
+ align:start position:0%
+to put some sort of stop here so the
+ 
+
+ align:start position:0%
+to put some sort of stop here so the
+undeflected rays are just going to
+
+ align:start position:0%
+undeflected rays are just going to
+ 
+
+ align:start position:0%
+undeflected rays are just going to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+uh straight through the focal point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but the deflected rays are not
+
+ align:start position:0%
+that but the deflected rays are not
+ 
+
+ align:start position:0%
+that but the deflected rays are not
+going to go through the focal point
+
+ align:start position:0%
+going to go through the focal point
+ 
+
+ align:start position:0%
+going to go through the focal point
+right the deflected rays are going to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+above and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+below so now we can put a series of
+
+ align:start position:0%
+below so now we can put a series of
+ 
+
+ align:start position:0%
+below so now we can put a series of
+stops inside here so we could have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stop and that blue dash line that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like a light
+
+ align:start position:0%
+like a light
+ 
+
+ align:start position:0%
+like a light
+field knife
+
+ align:start position:0%
+field knife
+ 
+
+ align:start position:0%
+field knife
+edge we could have a stop that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like dark field life
+
+ align:start position:0%
+like dark field life
+ 
+
+ align:start position:0%
+like dark field life
+Edge we could have a stop that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like a light field Circle
+
+ align:start position:0%
+like a light field Circle
+ 
+
+ align:start position:0%
+like a light field Circle
+and we could have a stop that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like a dark field Circle and what we're
+
+ align:start position:0%
+like a dark field Circle and what we're
+ 
+
+ align:start position:0%
+like a dark field Circle and what we're
+going to do is sketch out what we expect
+
+ align:start position:0%
+going to do is sketch out what we expect
+ 
+
+ align:start position:0%
+going to do is sketch out what we expect
+the intensity to look like from each of
+
+ align:start position:0%
+the intensity to look like from each of
+ 
+
+ align:start position:0%
+the intensity to look like from each of
+these different uh knife edges
+
+ align:start position:0%
+these different uh knife edges
+ 
+
+ align:start position:0%
+these different uh knife edges
+here so if I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plot one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll just draw the density distribution
+
+ align:start position:0%
+I'll just draw the density distribution
+ 
+
+ align:start position:0%
+I'll just draw the density distribution
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+again like that so that's our density
+
+ align:start position:0%
+again like that so that's our density
+ 
+
+ align:start position:0%
+again like that so that's our density
+now we want to know what our intensity
+
+ align:start position:0%
+now we want to know what our intensity
+ 
+
+ align:start position:0%
+now we want to know what our intensity
+distribution looks like so this is now
+
+ align:start position:0%
+distribution looks like so this is now
+ 
+
+ align:start position:0%
+distribution looks like so this is now
+intensity we have our initial intensity
+
+ align:start position:0%
+intensity we have our initial intensity
+ 
+
+ align:start position:0%
+intensity we have our initial intensity
+one and we have zero intensity
+
+ align:start position:0%
+one and we have zero intensity
+ 
+
+ align:start position:0%
+one and we have zero intensity
+corresponding to all the Rays being
+
+ align:start position:0%
+corresponding to all the Rays being
+ 
+
+ align:start position:0%
+corresponding to all the Rays being
+blocked so where for the light field
+
+ align:start position:0%
+blocked so where for the light field
+ 
+
+ align:start position:0%
+blocked so where for the light field
+knife edge do we see no intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry I didn't have that proper can you
+
+ align:start position:0%
+sorry I didn't have that proper can you
+ 
+
+ align:start position:0%
+sorry I didn't have that proper can you
+say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so I think what you said was in
+
+ align:start position:0%
+again so I think what you said was in
+ 
+
+ align:start position:0%
+again so I think what you said was in
+the upper side uh where there's the
+
+ align:start position:0%
+the upper side uh where there's the
+ 
+
+ align:start position:0%
+the upper side uh where there's the
+largest density gradient right so this
+
+ align:start position:0%
+largest density gradient right so this
+ 
+
+ align:start position:0%
+largest density gradient right so this
+this is where the density gradient is
+
+ align:start position:0%
+this is where the density gradient is
+ 
+
+ align:start position:0%
+this is where the density gradient is
+very large so we expect outside of that
+
+ align:start position:0%
+very large so we expect outside of that
+ 
+
+ align:start position:0%
+very large so we expect outside of that
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+our intensity would be pretty much
+
+ align:start position:0%
+our intensity would be pretty much
+ 
+
+ align:start position:0%
+our intensity would be pretty much
+constant but inside that region we'd
+
+ align:start position:0%
+constant but inside that region we'd
+ 
+
+ align:start position:0%
+constant but inside that region we'd
+expect the intensity would drop to zero
+
+ align:start position:0%
+expect the intensity would drop to zero
+ 
+
+ align:start position:0%
+expect the intensity would drop to zero
+because we're blocking the rays which
+
+ align:start position:0%
+because we're blocking the rays which
+ 
+
+ align:start position:0%
+because we're blocking the rays which
+have a large deflection angle uh in One
+
+ align:start position:0%
+have a large deflection angle uh in One
+ 
+
+ align:start position:0%
+have a large deflection angle uh in One
+Direction upwards and the rays which
+
+ align:start position:0%
+Direction upwards and the rays which
+ 
+
+ align:start position:0%
+Direction upwards and the rays which
+have a large deflection angle in One
+
+ align:start position:0%
+have a large deflection angle in One
+ 
+
+ align:start position:0%
+have a large deflection angle in One
+Direction upwards corresponds to that
+
+ align:start position:0%
+Direction upwards corresponds to that
+ 
+
+ align:start position:0%
+Direction upwards corresponds to that
+specific density gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay anyone want to have a go at
+
+ align:start position:0%
+there okay anyone want to have a go at
+ 
+
+ align:start position:0%
+there okay anyone want to have a go at
+telling me what happens with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one what's happening at the edges what's
+
+ align:start position:0%
+one what's happening at the edges what's
+ 
+
+ align:start position:0%
+one what's happening at the edges what's
+happening out in these regions here
+
+ align:start position:0%
+happening out in these regions here
+ 
+
+ align:start position:0%
+happening out in these regions here
+where the density gradients are small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're cropped out because they mostly
+
+ align:start position:0%
+they're cropped out because they mostly
+ 
+
+ align:start position:0%
+they're cropped out because they mostly
+go through the focal fcal spot right
+
+ align:start position:0%
+go through the focal fcal spot right
+ 
+
+ align:start position:0%
+go through the focal fcal spot right
+yeah so these are going to be zero right
+
+ align:start position:0%
+yeah so these are going to be zero right
+ 
+
+ align:start position:0%
+yeah so these are going to be zero right
+so zero zero is there any region where
+
+ align:start position:0%
+so zero zero is there any region where
+ 
+
+ align:start position:0%
+so zero zero is there any region where
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+zero uh I think it's not zero for the
+
+ align:start position:0%
+zero uh I think it's not zero for the
+ 
+
+ align:start position:0%
+zero uh I think it's not zero for the
+uh High gradient region that's lower in
+
+ align:start position:0%
+uh High gradient region that's lower in
+ 
+
+ align:start position:0%
+uh High gradient region that's lower in
+y it's deflected below so you think it's
+
+ align:start position:0%
+y it's deflected below so you think it's
+ 
+
+ align:start position:0%
+y it's deflected below so you think it's
+not zero for this region here yeah yes
+
+ align:start position:0%
+not zero for this region here yeah yes
+ 
+
+ align:start position:0%
+not zero for this region here yeah yes
+does anyone agree with sir or does
+
+ align:start position:0%
+does anyone agree with sir or does
+ 
+
+ align:start position:0%
+does anyone agree with sir or does
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disagree I think that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so we're talking
+
+ align:start position:0%
+right okay so we're talking
+ 
+
+ align:start position:0%
+right okay so we're talking
+about this Ray here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this Ray is indeed passing low
+
+ align:start position:0%
+yeah so this Ray is indeed passing low
+ 
+
+ align:start position:0%
+yeah so this Ray is indeed passing low
+down compared to the knife edge so we'd
+
+ align:start position:0%
+down compared to the knife edge so we'd
+ 
+
+ align:start position:0%
+down compared to the knife edge so we'd
+expect this to show some intensity here
+
+ align:start position:0%
+expect this to show some intensity here
+ 
+
+ align:start position:0%
+expect this to show some intensity here
+not for the upper one which passes
+
+ align:start position:0%
+not for the upper one which passes
+ 
+
+ align:start position:0%
+not for the upper one which passes
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+up okay good we're getting that what
+
+ align:start position:0%
+up okay good we're getting that what
+ 
+
+ align:start position:0%
+up okay good we're getting that what
+about for the circular light
+
+ align:start position:0%
+about for the circular light
+ 
+
+ align:start position:0%
+about for the circular light
+field anyone want to tell me what the
+
+ align:start position:0%
+field anyone want to tell me what the
+ 
+
+ align:start position:0%
+field anyone want to tell me what the
+intensity looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you'd probably get Three Peaks so
+
+ align:start position:0%
+here you'd probably get Three Peaks so
+ 
+
+ align:start position:0%
+here you'd probably get Three Peaks so
+on the edges where the density isn't
+
+ align:start position:0%
+on the edges where the density isn't
+ 
+
+ align:start position:0%
+on the edges where the density isn't
+really where the density is just low and
+
+ align:start position:0%
+really where the density is just low and
+ 
+
+ align:start position:0%
+really where the density is just low and
+then right in the middle where the
+
+ align:start position:0%
+then right in the middle where the
+ 
+
+ align:start position:0%
+then right in the middle where the
+density is high but not really changing
+
+ align:start position:0%
+density is high but not really changing
+ 
+
+ align:start position:0%
+density is high but not really changing
+too much yeah so you say three Peaks I'm
+
+ align:start position:0%
+too much yeah so you say three Peaks I'm
+ 
+
+ align:start position:0%
+too much yeah so you say three Peaks I'm
+going to think about them as two notches
+
+ align:start position:0%
+going to think about them as two notches
+ 
+
+ align:start position:0%
+going to think about them as two notches
+but I agree with what you're saying so
+
+ align:start position:0%
+but I agree with what you're saying so
+ 
+
+ align:start position:0%
+but I agree with what you're saying so
+these notches here correspond to the
+
+ align:start position:0%
+these notches here correspond to the
+ 
+
+ align:start position:0%
+these notches here correspond to the
+points where the density gradient is
+
+ align:start position:0%
+points where the density gradient is
+ 
+
+ align:start position:0%
+points where the density gradient is
+largest here and so those those Rays got
+
+ align:start position:0%
+largest here and so those those Rays got
+ 
+
+ align:start position:0%
+largest here and so those those Rays got
+a big deflection angle they're being
+
+ align:start position:0%
+a big deflection angle they're being
+ 
+
+ align:start position:0%
+a big deflection angle they're being
+blocked out what
+
+ align:start position:0%
+blocked out what
+ 
+
+ align:start position:0%
+blocked out what
+about for the final one here darkfield
+
+ align:start position:0%
+about for the final one here darkfield
+ 
+
+ align:start position:0%
+about for the final one here darkfield
+circular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aperture well there there your basically
+
+ align:start position:0%
+aperture well there there your basically
+ 
+
+ align:start position:0%
+aperture well there there your basically
+notching out all the uh un the minimally
+
+ align:start position:0%
+notching out all the uh un the minimally
+ 
+
+ align:start position:0%
+notching out all the uh un the minimally
+deflected arays so you lose the uh ones
+
+ align:start position:0%
+deflected arays so you lose the uh ones
+ 
+
+ align:start position:0%
+deflected arays so you lose the uh ones
+on the edges and
+
+ align:start position:0%
+on the edges and
+ 
+
+ align:start position:0%
+on the edges and
+Center yeah so we'd have something that
+
+ align:start position:0%
+Center yeah so we'd have something that
+ 
+
+ align:start position:0%
+Center yeah so we'd have something that
+looks like this right so we would just
+
+ align:start position:0%
+looks like this right so we would just
+ 
+
+ align:start position:0%
+looks like this right so we would just
+see light where there was a significant
+
+ align:start position:0%
+see light where there was a significant
+ 
+
+ align:start position:0%
+see light where there was a significant
+deflection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle okay um this may still seem a
+
+ align:start position:0%
+angle okay um this may still seem a
+ 
+
+ align:start position:0%
+angle okay um this may still seem a
+little bit abstract so we're going to
+
+ align:start position:0%
+little bit abstract so we're going to
+ 
+
+ align:start position:0%
+little bit abstract so we're going to
+try try one more thing and I hope that
+
+ align:start position:0%
+try try one more thing and I hope that
+ 
+
+ align:start position:0%
+try try one more thing and I hope that
+you don't hate me for spending so much
+
+ align:start position:0%
+you don't hate me for spending so much
+ 
+
+ align:start position:0%
+you don't hate me for spending so much
+time on Shin but I absolutely love it so
+
+ align:start position:0%
+time on Shin but I absolutely love it so
+ 
+
+ align:start position:0%
+time on Shin but I absolutely love it so
+um that's your loss um which is going to
+
+ align:start position:0%
+um that's your loss um which is going to
+ 
+
+ align:start position:0%
+um that's your loss um which is going to
+be a two-dimensional example here I'll
+
+ align:start position:0%
+be a two-dimensional example here I'll
+ 
+
+ align:start position:0%
+be a two-dimensional example here I'll
+just draw on this uh distribution
+
+ align:start position:0%
+just draw on this uh distribution
+ 
+
+ align:start position:0%
+just draw on this uh distribution
+function there we go density function
+
+ align:start position:0%
+function there we go density function
+ 
+
+ align:start position:0%
+function there we go density function
+down that last one just so you've got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so this actually goes back to
+
+ align:start position:0%
+it so this actually goes back to
+ 
+
+ align:start position:0%
+it so this actually goes back to
+a sketch that I did during the B dot
+
+ align:start position:0%
+a sketch that I did during the B dot
+ 
+
+ align:start position:0%
+a sketch that I did during the B dot
+lecture where we stuck a little B dot
+
+ align:start position:0%
+lecture where we stuck a little B dot
+ 
+
+ align:start position:0%
+lecture where we stuck a little B dot
+inside the plasma and we have plasma
+
+ align:start position:0%
+inside the plasma and we have plasma
+ 
+
+ align:start position:0%
+inside the plasma and we have plasma
+flow coming from left to right and
+
+ align:start position:0%
+flow coming from left to right and
+ 
+
+ align:start position:0%
+flow coming from left to right and
+because it collides with this we get
+
+ align:start position:0%
+because it collides with this we get
+ 
+
+ align:start position:0%
+because it collides with this we get
+some sort of bowel shock like
+
+ align:start position:0%
+some sort of bowel shock like
+ 
+
+ align:start position:0%
+some sort of bowel shock like
+this and we as we all know from our
+
+ align:start position:0%
+this and we as we all know from our
+ 
+
+ align:start position:0%
+this and we as we all know from our
+shock physics at the bow shock we have
+
+ align:start position:0%
+shock physics at the bow shock we have
+ 
+
+ align:start position:0%
+shock physics at the bow shock we have
+strong density
+
+ align:start position:0%
+strong density
+ 
+
+ align:start position:0%
+strong density
+gradients like
+
+ align:start position:0%
+gradients like
+ 
+
+ align:start position:0%
+gradients like
+this where the density jumps across the
+
+ align:start position:0%
+this where the density jumps across the
+ 
+
+ align:start position:0%
+this where the density jumps across the
+shock
+
+ align:start position:0%
+shock
+ 
+
+ align:start position:0%
+shock
+here so if we look at this system when
+
+ align:start position:0%
+here so if we look at this system when
+ 
+
+ align:start position:0%
+here so if we look at this system when
+we have our probing laser coming towards
+
+ align:start position:0%
+we have our probing laser coming towards
+ 
+
+ align:start position:0%
+we have our probing laser coming towards
+us right so our laser is looking towards
+
+ align:start position:0%
+us right so our laser is looking towards
+ 
+
+ align:start position:0%
+us right so our laser is looking towards
+us like this we are the camera what
+
+ align:start position:0%
+us like this we are the camera what
+ 
+
+ align:start position:0%
+us like this we are the camera what
+would we see about this bow shock what
+
+ align:start position:0%
+would we see about this bow shock what
+ 
+
+ align:start position:0%
+would we see about this bow shock what
+could we tell about it so maybe the
+
+ align:start position:0%
+could we tell about it so maybe the
+ 
+
+ align:start position:0%
+could we tell about it so maybe the
+first thing we could do is ask for like
+
+ align:start position:0%
+first thing we could do is ask for like
+ 
+
+ align:start position:0%
+first thing we could do is ask for like
+a light field circular aperture what do
+
+ align:start position:0%
+a light field circular aperture what do
+ 
+
+ align:start position:0%
+a light field circular aperture what do
+we think we would see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and if you're not quite sure at
+
+ align:start position:0%
+here and if you're not quite sure at
+ 
+
+ align:start position:0%
+here and if you're not quite sure at
+each of these places where I've drawn
+
+ align:start position:0%
+each of these places where I've drawn
+ 
+
+ align:start position:0%
+each of these places where I've drawn
+this little arrow you could say that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density maybe as a simple model looks
+
+ align:start position:0%
+density maybe as a simple model looks
+ 
+
+ align:start position:0%
+density maybe as a simple model looks
+like sort of hyperbolic e Tangy type
+
+ align:start position:0%
+like sort of hyperbolic e Tangy type
+ 
+
+ align:start position:0%
+like sort of hyperbolic e Tangy type
+thing like that it's got some region
+
+ align:start position:0%
+thing like that it's got some region
+ 
+
+ align:start position:0%
+thing like that it's got some region
+where the density is NE Z some region
+
+ align:start position:0%
+where the density is NE Z some region
+ 
+
+ align:start position:0%
+where the density is NE Z some region
+where the density is any1 and then some
+
+ align:start position:0%
+where the density is any1 and then some
+ 
+
+ align:start position:0%
+where the density is any1 and then some
+region where the density changes rapidly
+
+ align:start position:0%
+region where the density changes rapidly
+ 
+
+ align:start position:0%
+region where the density changes rapidly
+that's not true for a shock but yeah
+
+ align:start position:0%
+that's not true for a shock but yeah
+ 
+
+ align:start position:0%
+that's not true for a shock but yeah
+it's a model just to get us thinking
+
+ align:start position:0%
+it's a model just to get us thinking
+ 
+
+ align:start position:0%
+it's a model just to get us thinking
+about what this looks like so what would
+
+ align:start position:0%
+about what this looks like so what would
+ 
+
+ align:start position:0%
+about what this looks like so what would
+I see on my image I've got this expanded
+
+ align:start position:0%
+I see on my image I've got this expanded
+ 
+
+ align:start position:0%
+I see on my image I've got this expanded
+laser beam going through this shock and
+
+ align:start position:0%
+laser beam going through this shock and
+ 
+
+ align:start position:0%
+laser beam going through this shock and
+I've decided to use a circular light
+
+ align:start position:0%
+I've decided to use a circular light
+ 
+
+ align:start position:0%
+I've decided to use a circular light
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+stop I might be doing this backwards but
+
+ align:start position:0%
+stop I might be doing this backwards but
+ 
+
+ align:start position:0%
+stop I might be doing this backwards but
+from it looks like what we drew above
+
+ align:start position:0%
+from it looks like what we drew above
+ 
+
+ align:start position:0%
+from it looks like what we drew above
+that would mean that you're not getting
+
+ align:start position:0%
+that would mean that you're not getting
+ 
+
+ align:start position:0%
+that would mean that you're not getting
+your speep gradient sections so it
+
+ align:start position:0%
+your speep gradient sections so it
+ 
+
+ align:start position:0%
+your speep gradient sections so it
+should be dark where the bow shock is
+
+ align:start position:0%
+should be dark where the bow shock is
+ 
+
+ align:start position:0%
+should be dark where the bow shock is
+and yeah so you'd actually have an image
+
+ align:start position:0%
+and yeah so you'd actually have an image
+ 
+
+ align:start position:0%
+and yeah so you'd actually have an image
+yeah you'd have an image which you know
+
+ align:start position:0%
+yeah you'd have an image which you know
+ 
+
+ align:start position:0%
+yeah you'd have an image which you know
+if I was on a chalk board I could do
+
+ align:start position:0%
+if I was on a chalk board I could do
+ 
+
+ align:start position:0%
+if I was on a chalk board I could do
+with an eraser was actually quite hard
+
+ align:start position:0%
+with an eraser was actually quite hard
+ 
+
+ align:start position:0%
+with an eraser was actually quite hard
+here if you imagine this is filled with
+
+ align:start position:0%
+here if you imagine this is filled with
+ 
+
+ align:start position:0%
+here if you imagine this is filled with
+green laser beam beautiful nice laser
+
+ align:start position:0%
+green laser beam beautiful nice laser
+ 
+
+ align:start position:0%
+green laser beam beautiful nice laser
+beam image then you would have a region
+
+ align:start position:0%
+beam image then you would have a region
+ 
+
+ align:start position:0%
+beam image then you would have a region
+where no the Eraser is not very good if
+
+ align:start position:0%
+where no the Eraser is not very good if
+ 
+
+ align:start position:0%
+where no the Eraser is not very good if
+I could make the Eraser smaller that
+
+ align:start position:0%
+I could make the Eraser smaller that
+ 
+
+ align:start position:0%
+I could make the Eraser smaller that
+would work much better you would have a
+
+ align:start position:0%
+would work much better you would have a
+ 
+
+ align:start position:0%
+would work much better you would have a
+region where there was no light
+
+ align:start position:0%
+region where there was no light
+ 
+
+ align:start position:0%
+region where there was no light
+whatsoever and there was just darkness
+
+ align:start position:0%
+whatsoever and there was just darkness
+ 
+
+ align:start position:0%
+whatsoever and there was just darkness
+right so You' just have this dark region
+
+ align:start position:0%
+right so You' just have this dark region
+ 
+
+ align:start position:0%
+right so You' just have this dark region
+here corresponding to the bow shock and
+
+ align:start position:0%
+here corresponding to the bow shock and
+ 
+
+ align:start position:0%
+here corresponding to the bow shock and
+if you did this with a dark field
+
+ align:start position:0%
+if you did this with a dark field
+ 
+
+ align:start position:0%
+if you did this with a dark field
+circular aperture then you'd have the
+
+ align:start position:0%
+circular aperture then you'd have the
+ 
+
+ align:start position:0%
+circular aperture then you'd have the
+opposite you'd have complete darkness
+
+ align:start position:0%
+opposite you'd have complete darkness
+ 
+
+ align:start position:0%
+opposite you'd have complete darkness
+and you would just have a region where
+
+ align:start position:0%
+and you would just have a region where
+ 
+
+ align:start position:0%
+and you would just have a region where
+the bow shock shows up very nicely like
+
+ align:start position:0%
+the bow shock shows up very nicely like
+ 
+
+ align:start position:0%
+the bow shock shows up very nicely like
+this uh and so this is actually
+
+ align:start position:0%
+this uh and so this is actually
+ 
+
+ align:start position:0%
+this uh and so this is actually
+typically what we use for uh shock
+
+ align:start position:0%
+typically what we use for uh shock
+ 
+
+ align:start position:0%
+typically what we use for uh shock
+measurements is dark field circular
+
+ align:start position:0%
+measurements is dark field circular
+ 
+
+ align:start position:0%
+measurements is dark field circular
+aperture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do happen to do something like a
+
+ align:start position:0%
+if you do happen to do something like a
+ 
+
+ align:start position:0%
+if you do happen to do something like a
+dark field with a knife
+
+ align:start position:0%
+dark field with a knife
+ 
+
+ align:start position:0%
+dark field with a knife
+edge and you put your knife
+
+ align:start position:0%
+edge and you put your knife
+ 
+
+ align:start position:0%
+edge and you put your knife
+edge like this so you were measuring
+
+ align:start position:0%
+edge like this so you were measuring
+ 
+
+ align:start position:0%
+edge like this so you were measuring
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+gradients that were in this
+
+ align:start position:0%
+gradients that were in this
+ 
+
+ align:start position:0%
+gradients that were in this
+direction you would end up seeing
+
+ align:start position:0%
+direction you would end up seeing
+ 
+
+ align:start position:0%
+direction you would end up seeing
+something a little bit like just one
+
+ align:start position:0%
+something a little bit like just one
+ 
+
+ align:start position:0%
+something a little bit like just one
+half of the bow shock like that so if
+
+ align:start position:0%
+half of the bow shock like that so if
+ 
+
+ align:start position:0%
+half of the bow shock like that so if
+your set your probe was was sitting here
+
+ align:start position:0%
+your set your probe was was sitting here
+ 
+
+ align:start position:0%
+your set your probe was was sitting here
+you would just see a little bit of the B
+
+ align:start position:0%
+you would just see a little bit of the B
+ 
+
+ align:start position:0%
+you would just see a little bit of the B
+shop you wouldn't see this section
+
+ align:start position:0%
+shop you wouldn't see this section
+ 
+
+ align:start position:0%
+shop you wouldn't see this section
+because the density gradients wouldn't
+
+ align:start position:0%
+because the density gradients wouldn't
+ 
+
+ align:start position:0%
+because the density gradients wouldn't
+be in the correct direction so you
+
+ align:start position:0%
+be in the correct direction so you
+ 
+
+ align:start position:0%
+be in the correct direction so you
+wouldn't be able to observe those but
+
+ align:start position:0%
+wouldn't be able to observe those but
+ 
+
+ align:start position:0%
+wouldn't be able to observe those but
+the knife edge might be a better choice
+
+ align:start position:0%
+the knife edge might be a better choice
+ 
+
+ align:start position:0%
+the knife edge might be a better choice
+for some Shock geometries if you're only
+
+ align:start position:0%
+for some Shock geometries if you're only
+ 
+
+ align:start position:0%
+for some Shock geometries if you're only
+interested in gradients in One Direction
+
+ align:start position:0%
+interested in gradients in One Direction
+ 
+
+ align:start position:0%
+interested in gradients in One Direction
+Aiden I see your
+
+ align:start position:0%
+Aiden I see your
+ 
+
+ align:start position:0%
+Aiden I see your
+hand oh yeah I'm curious how
+
+ align:start position:0%
+hand oh yeah I'm curious how
+ 
+
+ align:start position:0%
+hand oh yeah I'm curious how
+distinct
+
+ align:start position:0%
+distinct
+ 
+
+ align:start position:0%
+distinct
+um the the the actual image gradients
+
+ align:start position:0%
+um the the the actual image gradients
+ 
+
+ align:start position:0%
+um the the the actual image gradients
+would be um given that this is like a
+
+ align:start position:0%
+would be um given that this is like a
+ 
+
+ align:start position:0%
+would be um given that this is like a
+cylindrical phenomenon right the
+
+ align:start position:0%
+cylindrical phenomenon right the
+ 
+
+ align:start position:0%
+cylindrical phenomenon right the
+shock so I assume there's some some
+
+ align:start position:0%
+shock so I assume there's some some
+ 
+
+ align:start position:0%
+shock so I assume there's some some
+density gradients that they slowly
+
+ align:start position:0%
+density gradients that they slowly
+ 
+
+ align:start position:0%
+density gradients that they slowly
+become um parallel to your propagation
+
+ align:start position:0%
+become um parallel to your propagation
+ 
+
+ align:start position:0%
+become um parallel to your propagation
+direction as you rotate to the yeah so
+
+ align:start position:0%
+direction as you rotate to the yeah so
+ 
+
+ align:start position:0%
+direction as you rotate to the yeah so
+you won't see those density gradients
+
+ align:start position:0%
+you won't see those density gradients
+ 
+
+ align:start position:0%
+you won't see those density gradients
+but you will see the ones on the edges
+
+ align:start position:0%
+but you will see the ones on the edges
+ 
+
+ align:start position:0%
+but you will see the ones on the edges
+of the shock yeah it it depends on the
+
+ align:start position:0%
+of the shock yeah it it depends on the
+ 
+
+ align:start position:0%
+of the shock yeah it it depends on the
+exact shock morphology whether it's some
+
+ align:start position:0%
+exact shock morphology whether it's some
+ 
+
+ align:start position:0%
+exact shock morphology whether it's some
+extended like a bow shock that's
+
+ align:start position:0%
+extended like a bow shock that's
+ 
+
+ align:start position:0%
+extended like a bow shock that's
+extended like this or whether it's a bow
+
+ align:start position:0%
+extended like this or whether it's a bow
+ 
+
+ align:start position:0%
+extended like this or whether it's a bow
+shock sort of rotated like the tip of
+
+ align:start position:0%
+shock sort of rotated like the tip of
+ 
+
+ align:start position:0%
+shock sort of rotated like the tip of
+the a nose cone on an aircraft or
+
+ align:start position:0%
+the a nose cone on an aircraft or
+ 
+
+ align:start position:0%
+the a nose cone on an aircraft or
+something like that so it will it will
+
+ align:start position:0%
+something like that so it will it will
+ 
+
+ align:start position:0%
+something like that so it will it will
+make a difference but this is just to
+
+ align:start position:0%
+make a difference but this is just to
+ 
+
+ align:start position:0%
+make a difference but this is just to
+try and get a feel for what this looks
+
+ align:start position:0%
+try and get a feel for what this looks
+ 
+
+ align:start position:0%
+try and get a feel for what this looks
+like in terms of Imaging here I can send
+
+ align:start position:0%
+like in terms of Imaging here I can send
+ 
+
+ align:start position:0%
+like in terms of Imaging here I can send
+around some papers later which have some
+
+ align:start position:0%
+around some papers later which have some
+ 
+
+ align:start position:0%
+around some papers later which have some
+very nice images of schen of shock
+
+ align:start position:0%
+very nice images of schen of shock
+ 
+
+ align:start position:0%
+very nice images of schen of shock
+structures that show you know what sort
+
+ align:start position:0%
+structures that show you know what sort
+ 
+
+ align:start position:0%
+structures that show you know what sort
+of quality of data you can get out from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so any other questions on schen and
+
+ align:start position:0%
+this so any other questions on schen and
+ 
+
+ align:start position:0%
+this so any other questions on schen and
+will then just summarize exactly how to
+
+ align:start position:0%
+will then just summarize exactly how to
+ 
+
+ align:start position:0%
+will then just summarize exactly how to
+use it and when not to use it and things
+
+ align:start position:0%
+use it and when not to use it and things
+ 
+
+ align:start position:0%
+use it and when not to use it and things
+like that but if anyone has any
+
+ align:start position:0%
+like that but if anyone has any
+ 
+
+ align:start position:0%
+like that but if anyone has any
+questions on these sort of worked
+
+ align:start position:0%
+questions on these sort of worked
+ 
+
+ align:start position:0%
+questions on these sort of worked
+examples we've done please go ahead and
+
+ align:start position:0%
+examples we've done please go ahead and
+ 
+
+ align:start position:0%
+examples we've done please go ahead and
+Shout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so schen is good for
+
+ align:start position:0%
+okay so schen is good for
+ 
+
+ align:start position:0%
+okay so schen is good for
+visualizing density
+
+ align:start position:0%
+visualizing density
+ 
+
+ align:start position:0%
+visualizing density
+gradients right and in particular it's
+
+ align:start position:0%
+gradients right and in particular it's
+ 
+
+ align:start position:0%
+gradients right and in particular it's
+good for visualizing strong density
+
+ align:start position:0%
+good for visualizing strong density
+ 
+
+ align:start position:0%
+good for visualizing strong density
+gradients so in particular it's good at
+
+ align:start position:0%
+gradients so in particular it's good at
+ 
+
+ align:start position:0%
+gradients so in particular it's good at
+visualizing shocks so if you're looking
+
+ align:start position:0%
+visualizing shocks so if you're looking
+ 
+
+ align:start position:0%
+visualizing shocks so if you're looking
+at shocks in plasmas this is a nice
+
+ align:start position:0%
+at shocks in plasmas this is a nice
+ 
+
+ align:start position:0%
+at shocks in plasmas this is a nice
+Diagnostic and it's particularly nice
+
+ align:start position:0%
+Diagnostic and it's particularly nice
+ 
+
+ align:start position:0%
+Diagnostic and it's particularly nice
+because it's very simple to set up as I
+
+ align:start position:0%
+because it's very simple to set up as I
+ 
+
+ align:start position:0%
+because it's very simple to set up as I
+showed you it's just got at minimum a
+
+ align:start position:0%
+showed you it's just got at minimum a
+ 
+
+ align:start position:0%
+showed you it's just got at minimum a
+single optic you need to form a focal
+
+ align:start position:0%
+single optic you need to form a focal
+ 
+
+ align:start position:0%
+single optic you need to form a focal
+point so you need to have an optic you
+
+ align:start position:0%
+point so you need to have an optic you
+ 
+
+ align:start position:0%
+point so you need to have an optic you
+need a focal point and you need a stop
+
+ align:start position:0%
+need a focal point and you need a stop
+ 
+
+ align:start position:0%
+need a focal point and you need a stop
+so this is a very simple thing to set up
+
+ align:start position:0%
+so this is a very simple thing to set up
+ 
+
+ align:start position:0%
+so this is a very simple thing to set up
+you can do it very very quickly the
+
+ align:start position:0%
+you can do it very very quickly the
+ 
+
+ align:start position:0%
+you can do it very very quickly the
+trouble is although it's simple it's
+
+ align:start position:0%
+trouble is although it's simple it's
+ 
+
+ align:start position:0%
+trouble is although it's simple it's
+very difficult to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantitative we can say there is some
+
+ align:start position:0%
+quantitative we can say there is some
+ 
+
+ align:start position:0%
+quantitative we can say there is some
+sort of density gradient there we think
+
+ align:start position:0%
+sort of density gradient there we think
+ 
+
+ align:start position:0%
+sort of density gradient there we think
+the density gradient has to be larger
+
+ align:start position:0%
+the density gradient has to be larger
+ 
+
+ align:start position:0%
+the density gradient has to be larger
+than some certain limiting value but
+
+ align:start position:0%
+than some certain limiting value but
+ 
+
+ align:start position:0%
+than some certain limiting value but
+other than that we can't really say much
+
+ align:start position:0%
+other than that we can't really say much
+ 
+
+ align:start position:0%
+other than that we can't really say much
+more than that so it's useful for seeing
+
+ align:start position:0%
+more than that so it's useful for seeing
+ 
+
+ align:start position:0%
+more than that so it's useful for seeing
+where shocks are and their morphology
+
+ align:start position:0%
+where shocks are and their morphology
+ 
+
+ align:start position:0%
+where shocks are and their morphology
+but it's not useful for measuring
+
+ align:start position:0%
+but it's not useful for measuring
+ 
+
+ align:start position:0%
+but it's not useful for measuring
+gradient of NE so we can't measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graad NE e we can
+
+ align:start position:0%
+graad NE e we can
+ 
+
+ align:start position:0%
+graad NE e we can
+measure shape and location of the
+
+ align:start position:0%
+measure shape and location of the
+ 
+
+ align:start position:0%
+measure shape and location of the
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradients now there are some ways where
+
+ align:start position:0%
+gradients now there are some ways where
+ 
+
+ align:start position:0%
+gradients now there are some ways where
+you can make this more quantitative so
+
+ align:start position:0%
+you can make this more quantitative so
+ 
+
+ align:start position:0%
+you can make this more quantitative so
+imagine you've got a little beam of
+
+ align:start position:0%
+imagine you've got a little beam of
+ 
+
+ align:start position:0%
+imagine you've got a little beam of
+light coming
+
+ align:start position:0%
+light coming
+ 
+
+ align:start position:0%
+light coming
+in like this this is going in this
+
+ align:start position:0%
+in like this this is going in this
+ 
+
+ align:start position:0%
+in like this this is going in this
+direction and you have a knife edge that
+
+ align:start position:0%
+direction and you have a knife edge that
+ 
+
+ align:start position:0%
+direction and you have a knife edge that
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+that knife edge is going to be entirely
+
+ align:start position:0%
+that knife edge is going to be entirely
+ 
+
+ align:start position:0%
+that knife edge is going to be entirely
+blocking what's coming through we'll
+
+ align:start position:0%
+blocking what's coming through we'll
+ 
+
+ align:start position:0%
+blocking what's coming through we'll
+have zero light coming through but if we
+
+ align:start position:0%
+have zero light coming through but if we
+ 
+
+ align:start position:0%
+have zero light coming through but if we
+have a beam that comes through and it's
+
+ align:start position:0%
+have a beam that comes through and it's
+ 
+
+ align:start position:0%
+have a beam that comes through and it's
+lined up like
+
+ align:start position:0%
+lined up like
+ 
+
+ align:start position:0%
+lined up like
+this you can see that now about half the
+
+ align:start position:0%
+this you can see that now about half the
+ 
+
+ align:start position:0%
+this you can see that now about half the
+light is going to get through and if we
+
+ align:start position:0%
+light is going to get through and if we
+ 
+
+ align:start position:0%
+light is going to get through and if we
+have a beam come through that's lined up
+
+ align:start position:0%
+have a beam come through that's lined up
+ 
+
+ align:start position:0%
+have a beam come through that's lined up
+above the knife edge we'll have all of
+
+ align:start position:0%
+above the knife edge we'll have all of
+ 
+
+ align:start position:0%
+above the knife edge we'll have all of
+the light coming through and it turns
+
+ align:start position:0%
+the light coming through and it turns
+ 
+
+ align:start position:0%
+the light coming through and it turns
+out that if you have a large enough spot
+
+ align:start position:0%
+out that if you have a large enough spot
+ 
+
+ align:start position:0%
+out that if you have a large enough spot
+that you can actually see this partial
+
+ align:start position:0%
+that you can actually see this partial
+ 
+
+ align:start position:0%
+that you can actually see this partial
+obscuration
+
+ align:start position:0%
+obscuration
+ 
+
+ align:start position:0%
+obscuration
+of the focal point you end up in a
+
+ align:start position:0%
+of the focal point you end up in a
+ 
+
+ align:start position:0%
+of the focal point you end up in a
+regime where the intensity that you see
+
+ align:start position:0%
+regime where the intensity that you see
+ 
+
+ align:start position:0%
+regime where the intensity that you see
+on your detector I is in fact
+
+ align:start position:0%
+on your detector I is in fact
+ 
+
+ align:start position:0%
+on your detector I is in fact
+proportional directly to the gradient of
+
+ align:start position:0%
+proportional directly to the gradient of
+ 
+
+ align:start position:0%
+proportional directly to the gradient of
+the electron
+
+ align:start position:0%
+the electron
+ 
+
+ align:start position:0%
+the electron
+density I'm putting it in Brackets
+
+ align:start position:0%
+density I'm putting it in Brackets
+ 
+
+ align:start position:0%
+density I'm putting it in Brackets
+because you need a large
+
+ align:start position:0%
+because you need a large
+ 
+
+ align:start position:0%
+because you need a large
+uniform focal spot and I'll talk in a
+
+ align:start position:0%
+uniform focal spot and I'll talk in a
+ 
+
+ align:start position:0%
+uniform focal spot and I'll talk in a
+moment about why that's actually
+
+ align:start position:0%
+moment about why that's actually
+ 
+
+ align:start position:0%
+moment about why that's actually
+extremely difficult uh using a laser
+
+ align:start position:0%
+extremely difficult uh using a laser
+ 
+
+ align:start position:0%
+extremely difficult uh using a laser
+which is what we normally use
+
+ align:start position:0%
+which is what we normally use
+ 
+
+ align:start position:0%
+which is what we normally use
+here okay if you can't guarantee that
+
+ align:start position:0%
+here okay if you can't guarantee that
+ 
+
+ align:start position:0%
+here okay if you can't guarantee that
+you have a nice large uniform focal spot
+
+ align:start position:0%
+you have a nice large uniform focal spot
+ 
+
+ align:start position:0%
+you have a nice large uniform focal spot
+you could also use a a graded neutral
+
+ align:start position:0%
+you could also use a a graded neutral
+ 
+
+ align:start position:0%
+you could also use a a graded neutral
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+filter so a neutral density filter is
+
+ align:start position:0%
+filter so a neutral density filter is
+ 
+
+ align:start position:0%
+filter so a neutral density filter is
+sort of smoky glass that blocks light
+
+ align:start position:0%
+sort of smoky glass that blocks light
+ 
+
+ align:start position:0%
+sort of smoky glass that blocks light
+and you can change the amount of
+
+ align:start position:0%
+and you can change the amount of
+ 
+
+ align:start position:0%
+and you can change the amount of
+impurities in it to block more light so
+
+ align:start position:0%
+impurities in it to block more light so
+ 
+
+ align:start position:0%
+impurities in it to block more light so
+we could carefully fabricate for
+
+ align:start position:0%
+we could carefully fabricate for
+ 
+
+ align:start position:0%
+we could carefully fabricate for
+ourselves a neutral density
+
+ align:start position:0%
+ourselves a neutral density
+ 
+
+ align:start position:0%
+ourselves a neutral density
+filter that has a changing absorption so
+
+ align:start position:0%
+filter that has a changing absorption so
+ 
+
+ align:start position:0%
+filter that has a changing absorption so
+we can have a gradient and say we'll
+
+ align:start position:0%
+we can have a gradient and say we'll
+ 
+
+ align:start position:0%
+we can have a gradient and say we'll
+call the absorption Alpha here and then
+
+ align:start position:0%
+call the absorption Alpha here and then
+ 
+
+ align:start position:0%
+call the absorption Alpha here and then
+the idea is that different rays of
+
+ align:start position:0%
+the idea is that different rays of
+ 
+
+ align:start position:0%
+the idea is that different rays of
+Lights at different points of your stop
+
+ align:start position:0%
+Lights at different points of your stop
+ 
+
+ align:start position:0%
+Lights at different points of your stop
+will either come through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh not at all or very attenuated or they
+
+ align:start position:0%
+uh not at all or very attenuated or they
+ 
+
+ align:start position:0%
+uh not at all or very attenuated or they
+will come
+
+ align:start position:0%
+will come
+ 
+
+ align:start position:0%
+will come
+through partially
+
+ align:start position:0%
+through partially
+ 
+
+ align:start position:0%
+through partially
+attenuated or they will come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through basally not attenuated at all
+
+ align:start position:0%
+through basally not attenuated at all
+ 
+
+ align:start position:0%
+through basally not attenuated at all
+and so if you have a really good graded
+
+ align:start position:0%
+and so if you have a really good graded
+ 
+
+ align:start position:0%
+and so if you have a really good graded
+neutral density filter you can again up
+
+ align:start position:0%
+neutral density filter you can again up
+ 
+
+ align:start position:0%
+neutral density filter you can again up
+in this regime where you actually get
+
+ align:start position:0%
+in this regime where you actually get
+ 
+
+ align:start position:0%
+in this regime where you actually get
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sensitivity to uh the position of the
+
+ align:start position:0%
+sensitivity to uh the position of the
+ 
+
+ align:start position:0%
+sensitivity to uh the position of the
+beam and that can get you back into this
+
+ align:start position:0%
+beam and that can get you back into this
+ 
+
+ align:start position:0%
+beam and that can get you back into this
+nice regime up here where the intensity
+
+ align:start position:0%
+nice regime up here where the intensity
+ 
+
+ align:start position:0%
+nice regime up here where the intensity
+of your signal is actually proportional
+
+ align:start position:0%
+of your signal is actually proportional
+ 
+
+ align:start position:0%
+of your signal is actually proportional
+to the gradient of the electron density
+
+ align:start position:0%
+to the gradient of the electron density
+ 
+
+ align:start position:0%
+to the gradient of the electron density
+so that would be a very nice um place to
+
+ align:start position:0%
+so that would be a very nice um place to
+ 
+
+ align:start position:0%
+so that would be a very nice um place to
+be but this is hard to
+
+ align:start position:0%
+be but this is hard to
+ 
+
+ align:start position:0%
+be but this is hard to
+make and you still need a uniform beam
+
+ align:start position:0%
+make and you still need a uniform beam
+ 
+
+ align:start position:0%
+make and you still need a uniform beam
+to start with which is also hard to
+
+ align:start position:0%
+to start with which is also hard to
+ 
+
+ align:start position:0%
+to start with which is also hard to
+make so these techniques a lot of schen
+
+ align:start position:0%
+make so these techniques a lot of schen
+ 
+
+ align:start position:0%
+make so these techniques a lot of schen
+was actually developed um using light
+
+ align:start position:0%
+was actually developed um using light
+ 
+
+ align:start position:0%
+was actually developed um using light
+sources which are very different from
+
+ align:start position:0%
+sources which are very different from
+ 
+
+ align:start position:0%
+sources which are very different from
+the light sources that we have to end up
+
+ align:start position:0%
+the light sources that we have to end up
+ 
+
+ align:start position:0%
+the light sources that we have to end up
+using in um our experiments with plasmas
+
+ align:start position:0%
+using in um our experiments with plasmas
+ 
+
+ align:start position:0%
+using in um our experiments with plasmas
+uh and so you end up yes so I just
+
+ align:start position:0%
+uh and so you end up yes so I just
+ 
+
+ align:start position:0%
+uh and so you end up yes so I just
+looking at the beautiful pictures that
+
+ align:start position:0%
+looking at the beautiful pictures that
+ 
+
+ align:start position:0%
+looking at the beautiful pictures that
+uh Matthew put in the chat here these
+
+ align:start position:0%
+uh Matthew put in the chat here these
+ 
+
+ align:start position:0%
+uh Matthew put in the chat here these
+pictures here are absolutely glorious
+
+ align:start position:0%
+pictures here are absolutely glorious
+ 
+
+ align:start position:0%
+pictures here are absolutely glorious
+and you can see there's a huge amount of
+
+ align:start position:0%
+and you can see there's a huge amount of
+ 
+
+ align:start position:0%
+and you can see there's a huge amount of
+detail on them and this detail uh is due
+
+ align:start position:0%
+detail on them and this detail uh is due
+ 
+
+ align:start position:0%
+detail on them and this detail uh is due
+to the fact that actually I think for
+
+ align:start position:0%
+to the fact that actually I think for
+ 
+
+ align:start position:0%
+to the fact that actually I think for
+these ones they're using the Sun as the
+
+ align:start position:0%
+these ones they're using the Sun as the
+ 
+
+ align:start position:0%
+these ones they're using the Sun as the
+backlighter I may have forgotten this
+
+ align:start position:0%
+backlighter I may have forgotten this
+ 
+
+ align:start position:0%
+backlighter I may have forgotten this
+exactly but the light source is the sun
+
+ align:start position:0%
+exactly but the light source is the sun
+ 
+
+ align:start position:0%
+exactly but the light source is the sun
+and the sun is actually quite large it's
+
+ align:start position:0%
+and the sun is actually quite large it's
+ 
+
+ align:start position:0%
+and the sun is actually quite large it's
+an extended object you may have noticed
+
+ align:start position:0%
+an extended object you may have noticed
+ 
+
+ align:start position:0%
+an extended object you may have noticed
+in the sky um and this gives you really
+
+ align:start position:0%
+in the sky um and this gives you really
+ 
+
+ align:start position:0%
+in the sky um and this gives you really
+nice clearing Imaging but we don't tend
+
+ align:start position:0%
+nice clearing Imaging but we don't tend
+ 
+
+ align:start position:0%
+nice clearing Imaging but we don't tend
+to use nice large objects uh for our
+
+ align:start position:0%
+to use nice large objects uh for our
+ 
+
+ align:start position:0%
+to use nice large objects uh for our
+um our experiments with plasmas we tend
+
+ align:start position:0%
+um our experiments with plasmas we tend
+ 
+
+ align:start position:0%
+um our experiments with plasmas we tend
+to use things like lasers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and lasers are not a good scharen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+source and if you want to read in more
+
+ align:start position:0%
+source and if you want to read in more
+ 
+
+ align:start position:0%
+source and if you want to read in more
+detail why lasers are actually a really
+
+ align:start position:0%
+detail why lasers are actually a really
+ 
+
+ align:start position:0%
+detail why lasers are actually a really
+bad idea you should go read the book
+
+ align:start position:0%
+bad idea you should go read the book
+ 
+
+ align:start position:0%
+bad idea you should go read the book
+that's listed in the bibliography by
+
+ align:start position:0%
+that's listed in the bibliography by
+ 
+
+ align:start position:0%
+that's listed in the bibliography by
+settles which is an absolutely cracking
+
+ align:start position:0%
+settles which is an absolutely cracking
+ 
+
+ align:start position:0%
+settles which is an absolutely cracking
+book has lots of lovely pictures like
+
+ align:start position:0%
+book has lots of lovely pictures like
+ 
+
+ align:start position:0%
+book has lots of lovely pictures like
+the ones which we just posted in the
+
+ align:start position:0%
+the ones which we just posted in the
+ 
+
+ align:start position:0%
+the ones which we just posted in the
+chat and also a very detailed
+
+ align:start position:0%
+chat and also a very detailed
+ 
+
+ align:start position:0%
+chat and also a very detailed
+description of this stuff um but can
+
+ align:start position:0%
+description of this stuff um but can
+ 
+
+ align:start position:0%
+description of this stuff um but can
+anyone tell me why if lasers aren't very
+
+ align:start position:0%
+anyone tell me why if lasers aren't very
+ 
+
+ align:start position:0%
+anyone tell me why if lasers aren't very
+good why do we end up up using lasers as
+
+ align:start position:0%
+good why do we end up up using lasers as
+ 
+
+ align:start position:0%
+good why do we end up up using lasers as
+the light source for schin Imaging in
+
+ align:start position:0%
+the light source for schin Imaging in
+ 
+
+ align:start position:0%
+the light source for schin Imaging in
+plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics what property of a laser is it
+
+ align:start position:0%
+physics what property of a laser is it
+ 
+
+ align:start position:0%
+physics what property of a laser is it
+that we particularly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want monatic time is monocromatic so
+
+ align:start position:0%
+want monatic time is monocromatic so
+ 
+
+ align:start position:0%
+want monatic time is monocromatic so
+monochromatic is somewhat useful
+
+ align:start position:0%
+monochromatic is somewhat useful
+ 
+
+ align:start position:0%
+monochromatic is somewhat useful
+actually it turns out you can do really
+
+ align:start position:0%
+actually it turns out you can do really
+ 
+
+ align:start position:0%
+actually it turns out you can do really
+cool showing techniques with a broad
+
+ align:start position:0%
+cool showing techniques with a broad
+ 
+
+ align:start position:0%
+cool showing techniques with a broad
+band light source as well and filters
+
+ align:start position:0%
+band light source as well and filters
+ 
+
+ align:start position:0%
+band light source as well and filters
+because the different wavelengths will
+
+ align:start position:0%
+because the different wavelengths will
+ 
+
+ align:start position:0%
+because the different wavelengths will
+be deflected by different amounts and so
+
+ align:start position:0%
+be deflected by different amounts and so
+ 
+
+ align:start position:0%
+be deflected by different amounts and so
+if you have like multiple cameras with
+
+ align:start position:0%
+if you have like multiple cameras with
+ 
+
+ align:start position:0%
+if you have like multiple cameras with
+different filters you can really
+
+ align:start position:0%
+different filters you can really
+ 
+
+ align:start position:0%
+different filters you can really
+carefully reconstruct the reflection
+
+ align:start position:0%
+carefully reconstruct the reflection
+ 
+
+ align:start position:0%
+carefully reconstruct the reflection
+angles so monochromatic is a good guess
+
+ align:start position:0%
+angles so monochromatic is a good guess
+ 
+
+ align:start position:0%
+angles so monochromatic is a good guess
+but actually will be okay with Broadband
+
+ align:start position:0%
+but actually will be okay with Broadband
+ 
+
+ align:start position:0%
+but actually will be okay with Broadband
+uh what else when you think laser what
+
+ align:start position:0%
+uh what else when you think laser what
+ 
+
+ align:start position:0%
+uh what else when you think laser what
+do you
+
+ align:start position:0%
+do you
+ 
+
+ align:start position:0%
+do you
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+coherence coherence actually coherence
+
+ align:start position:0%
+coherence coherence actually coherence
+ 
+
+ align:start position:0%
+coherence coherence actually coherence
+isn't good for this and uh we've been
+
+ align:start position:0%
+isn't good for this and uh we've been
+ 
+
+ align:start position:0%
+isn't good for this and uh we've been
+using a ray picture and the coherence
+
+ align:start position:0%
+using a ray picture and the coherence
+ 
+
+ align:start position:0%
+using a ray picture and the coherence
+screws up our nice simple picture it's
+
+ align:start position:0%
+screws up our nice simple picture it's
+ 
+
+ align:start position:0%
+screws up our nice simple picture it's
+going to cause problem so we really want
+
+ align:start position:0%
+going to cause problem so we really want
+ 
+
+ align:start position:0%
+going to cause problem so we really want
+coherence for interferometry and we
+
+ align:start position:0%
+coherence for interferometry and we
+ 
+
+ align:start position:0%
+coherence for interferometry and we
+absolutely hate it for um schen and
+
+ align:start position:0%
+absolutely hate it for um schen and
+ 
+
+ align:start position:0%
+absolutely hate it for um schen and
+that's another that settles has in his
+
+ align:start position:0%
+that's another that settles has in his
+ 
+
+ align:start position:0%
+that's another that settles has in his
+book so coherence is a bad thing so I'm
+
+ align:start position:0%
+book so coherence is a bad thing so I'm
+ 
+
+ align:start position:0%
+book so coherence is a bad thing so I'm
+going to put
+
+ align:start position:0%
+going to put
+ 
+
+ align:start position:0%
+going to put
+coherence no we actually don't want it
+
+ align:start position:0%
+coherence no we actually don't want it
+ 
+
+ align:start position:0%
+coherence no we actually don't want it
+what else do we think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lasers well they tend to produce nice
+
+ align:start position:0%
+lasers well they tend to produce nice
+ 
+
+ align:start position:0%
+lasers well they tend to produce nice
+round spots so it's also easy to deflect
+
+ align:start position:0%
+round spots so it's also easy to deflect
+ 
+
+ align:start position:0%
+round spots so it's also easy to deflect
+them without a changing
+
+ align:start position:0%
+them without a changing
+ 
+
+ align:start position:0%
+them without a changing
+that nice beam yeah you can do that with
+
+ align:start position:0%
+that nice beam yeah you can do that with
+ 
+
+ align:start position:0%
+that nice beam yeah you can do that with
+other light sources but fine it is a
+
+ align:start position:0%
+other light sources but fine it is a
+ 
+
+ align:start position:0%
+other light sources but fine it is a
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+beam anyone ever sha a laser pointer in
+
+ align:start position:0%
+beam anyone ever sha a laser pointer in
+ 
+
+ align:start position:0%
+beam anyone ever sha a laser pointer in
+their eye
+
+ align:start position:0%
+their eye
+ 
+
+ align:start position:0%
+their eye
+if not why
+
+ align:start position:0%
+if not why
+ 
+
+ align:start position:0%
+if not why
+not high energy density they're very
+
+ align:start position:0%
+not high energy density they're very
+ 
+
+ align:start position:0%
+not high energy density they're very
+bright should we put it that way okay so
+
+ align:start position:0%
+bright should we put it that way okay so
+ 
+
+ align:start position:0%
+bright should we put it that way okay so
+lasers are extremely bright why do we
+
+ align:start position:0%
+lasers are extremely bright why do we
+ 
+
+ align:start position:0%
+lasers are extremely bright why do we
+want a bright light source when we're
+
+ align:start position:0%
+want a bright light source when we're
+ 
+
+ align:start position:0%
+want a bright light source when we're
+dealing with
+
+ align:start position:0%
+dealing with
+ 
+
+ align:start position:0%
+dealing with
+plasmas the Plasma's glow yes so we need
+
+ align:start position:0%
+plasmas the Plasma's glow yes so we need
+ 
+
+ align:start position:0%
+plasmas the Plasma's glow yes so we need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+overcome the
+
+ align:start position:0%
+overcome the
+ 
+
+ align:start position:0%
+overcome the
+plasma glow should we call it or should
+
+ align:start position:0%
+plasma glow should we call it or should
+ 
+
+ align:start position:0%
+plasma glow should we call it or should
+I say a mission here so when you're
+
+ align:start position:0%
+I say a mission here so when you're
+ 
+
+ align:start position:0%
+I say a mission here so when you're
+working with like jet planes flying
+
+ align:start position:0%
+working with like jet planes flying
+ 
+
+ align:start position:0%
+working with like jet planes flying
+around and you're taking um schan images
+
+ align:start position:0%
+around and you're taking um schan images
+ 
+
+ align:start position:0%
+around and you're taking um schan images
+of them using the Sun as your background
+
+ align:start position:0%
+of them using the Sun as your background
+ 
+
+ align:start position:0%
+of them using the Sun as your background
+you don't actually have to worry about
+
+ align:start position:0%
+you don't actually have to worry about
+ 
+
+ align:start position:0%
+you don't actually have to worry about
+the the the plasma or the the shock
+
+ align:start position:0%
+the the the plasma or the the shock
+ 
+
+ align:start position:0%
+the the the plasma or the the shock
+shocked air around the plane glowing and
+
+ align:start position:0%
+shocked air around the plane glowing and
+ 
+
+ align:start position:0%
+shocked air around the plane glowing and
+ruining your measurement was a plasma
+
+ align:start position:0%
+ruining your measurement was a plasma
+ 
+
+ align:start position:0%
+ruining your measurement was a plasma
+you really do it makes an awful lot of
+
+ align:start position:0%
+you really do it makes an awful lot of
+ 
+
+ align:start position:0%
+you really do it makes an awful lot of
+light so you need an incredibly bright
+
+ align:start position:0%
+light so you need an incredibly bright
+ 
+
+ align:start position:0%
+light so you need an incredibly bright
+light source and so despite the fact
+
+ align:start position:0%
+light source and so despite the fact
+ 
+
+ align:start position:0%
+light source and so despite the fact
+lasers are terrible for schin it's the
+
+ align:start position:0%
+lasers are terrible for schin it's the
+ 
+
+ align:start position:0%
+lasers are terrible for schin it's the
+brightest light source that we have
+
+ align:start position:0%
+brightest light source that we have
+ 
+
+ align:start position:0%
+brightest light source that we have
+available so we end up using that but
+
+ align:start position:0%
+available so we end up using that but
+ 
+
+ align:start position:0%
+available so we end up using that but
+the trouble with lasers is that they
+
+ align:start position:0%
+the trouble with lasers is that they
+ 
+
+ align:start position:0%
+the trouble with lasers is that they
+have a very small focal spot so they're
+
+ align:start position:0%
+have a very small focal spot so they're
+ 
+
+ align:start position:0%
+have a very small focal spot so they're
+in fact incredibly easy
+
+ align:start position:0%
+in fact incredibly easy
+ 
+
+ align:start position:0%
+in fact incredibly easy
+uh to focus down to a point and we don't
+
+ align:start position:0%
+uh to focus down to a point and we don't
+ 
+
+ align:start position:0%
+uh to focus down to a point and we don't
+want that we want a nice large focal
+
+ align:start position:0%
+want that we want a nice large focal
+ 
+
+ align:start position:0%
+want that we want a nice large focal
+spot and it's actually very difficult to
+
+ align:start position:0%
+spot and it's actually very difficult to
+ 
+
+ align:start position:0%
+spot and it's actually very difficult to
+get a laser to decco here enough to get
+
+ align:start position:0%
+get a laser to decco here enough to get
+ 
+
+ align:start position:0%
+get a laser to decco here enough to get
+a nice big focal spot but maybe there
+
+ align:start position:0%
+a nice big focal spot but maybe there
+ 
+
+ align:start position:0%
+a nice big focal spot but maybe there
+are some t techniques you can do and
+
+ align:start position:0%
+are some t techniques you can do and
+ 
+
+ align:start position:0%
+are some t techniques you can do and
+because we've got a small focal spot
+
+ align:start position:0%
+because we've got a small focal spot
+ 
+
+ align:start position:0%
+because we've got a small focal spot
+laser schen is effectively binary and
+
+ align:start position:0%
+laser schen is effectively binary and
+ 
+
+ align:start position:0%
+laser schen is effectively binary and
+I'll explain what I mean by that when I
+
+ align:start position:0%
+I'll explain what I mean by that when I
+ 
+
+ align:start position:0%
+I'll explain what I mean by that when I
+remember how to spell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+schen what I mean by that is the spot is
+
+ align:start position:0%
+schen what I mean by that is the spot is
+ 
+
+ align:start position:0%
+schen what I mean by that is the spot is
+so small the laser schin it is either
+
+ align:start position:0%
+so small the laser schin it is either
+ 
+
+ align:start position:0%
+so small the laser schin it is either
+completely blocked by the knife
+
+ align:start position:0%
+completely blocked by the knife
+ 
+
+ align:start position:0%
+completely blocked by the knife
+edge or it is completely visible
+
+ align:start position:0%
+edge or it is completely visible
+ 
+
+ align:start position:0%
+edge or it is completely visible
+unblocked by the knife edge and so when
+
+ align:start position:0%
+unblocked by the knife edge and so when
+ 
+
+ align:start position:0%
+unblocked by the knife edge and so when
+you do a laser SCH and image you get an
+
+ align:start position:0%
+you do a laser SCH and image you get an
+ 
+
+ align:start position:0%
+you do a laser SCH and image you get an
+image which is either dark or light zero
+
+ align:start position:0%
+image which is either dark or light zero
+ 
+
+ align:start position:0%
+image which is either dark or light zero
+or one no intensity or full
+
+ align:start position:0%
+or one no intensity or full
+ 
+
+ align:start position:0%
+or one no intensity or full
+intensity and so you don't get those
+
+ align:start position:0%
+intensity and so you don't get those
+ 
+
+ align:start position:0%
+intensity and so you don't get those
+nice images that we were just looking at
+
+ align:start position:0%
+nice images that we were just looking at
+ 
+
+ align:start position:0%
+nice images that we were just looking at
+that were linked and we also um don't
+
+ align:start position:0%
+that were linked and we also um don't
+ 
+
+ align:start position:0%
+that were linked and we also um don't
+have the ability to use the change in
+
+ align:start position:0%
+have the ability to use the change in
+ 
+
+ align:start position:0%
+have the ability to use the change in
+intensity to measure the gradients in
+
+ align:start position:0%
+intensity to measure the gradients in
+ 
+
+ align:start position:0%
+intensity to measure the gradients in
+the electron density because the
+
+ align:start position:0%
+the electron density because the
+ 
+
+ align:start position:0%
+the electron density because the
+intensity is either zero or one so uh we
+
+ align:start position:0%
+intensity is either zero or one so uh we
+ 
+
+ align:start position:0%
+intensity is either zero or one so uh we
+have very very limited dynamic range you
+
+ align:start position:0%
+have very very limited dynamic range you
+ 
+
+ align:start position:0%
+have very very limited dynamic range you
+can think about it that way we have no
+
+ align:start position:0%
+can think about it that way we have no
+ 
+
+ align:start position:0%
+can think about it that way we have no
+dynamic range we even though the density
+
+ align:start position:0%
+dynamic range we even though the density
+ 
+
+ align:start position:0%
+dynamic range we even though the density
+gradient is larger than a number or it's
+
+ align:start position:0%
+gradient is larger than a number or it's
+ 
+
+ align:start position:0%
+gradient is larger than a number or it's
+smaller than a number and that's it so
+
+ align:start position:0%
+smaller than a number and that's it so
+ 
+
+ align:start position:0%
+smaller than a number and that's it so
+it makes very good shock pictures but
+
+ align:start position:0%
+it makes very good shock pictures but
+ 
+
+ align:start position:0%
+it makes very good shock pictures but
+you can't do all the beautiful
+
+ align:start position:0%
+you can't do all the beautiful
+ 
+
+ align:start position:0%
+you can't do all the beautiful
+techniques that people use schen for in
+
+ align:start position:0%
+techniques that people use schen for in
+ 
+
+ align:start position:0%
+techniques that people use schen for in
+standard fluid dynamics where they have
+
+ align:start position:0%
+standard fluid dynamics where they have
+ 
+
+ align:start position:0%
+standard fluid dynamics where they have
+access to different sources so someone
+
+ align:start position:0%
+access to different sources so someone
+ 
+
+ align:start position:0%
+access to different sources so someone
+came up with a nice bright incoherent
+
+ align:start position:0%
+came up with a nice bright incoherent
+ 
+
+ align:start position:0%
+came up with a nice bright incoherent
+large area laser that we could use that
+
+ align:start position:0%
+large area laser that we could use that
+ 
+
+ align:start position:0%
+large area laser that we could use that
+would be absolutely great I have a few
+
+ align:start position:0%
+would be absolutely great I have a few
+ 
+
+ align:start position:0%
+would be absolutely great I have a few
+ideas along this direction um but I
+
+ align:start position:0%
+ideas along this direction um but I
+ 
+
+ align:start position:0%
+ideas along this direction um but I
+haven't had a chance to try them out yet
+
+ align:start position:0%
+haven't had a chance to try them out yet
+ 
+
+ align:start position:0%
+haven't had a chance to try them out yet
+um so yeah they they have some serious
+
+ align:start position:0%
+um so yeah they they have some serious
+ 
+
+ align:start position:0%
+um so yeah they they have some serious
+limitations so schin is a lovely
+
+ align:start position:0%
+limitations so schin is a lovely
+ 
+
+ align:start position:0%
+limitations so schin is a lovely
+technique for plasmas it's very limited
+
+ align:start position:0%
+technique for plasmas it's very limited
+ 
+
+ align:start position:0%
+technique for plasmas it's very limited
+it's obviously useful when you have
+
+ align:start position:0%
+it's obviously useful when you have
+ 
+
+ align:start position:0%
+it's obviously useful when you have
+shocks so you need to be having fast
+
+ align:start position:0%
+shocks so you need to be having fast
+ 
+
+ align:start position:0%
+shocks so you need to be having fast
+moving plasmas and so this is not really
+
+ align:start position:0%
+moving plasmas and so this is not really
+ 
+
+ align:start position:0%
+moving plasmas and so this is not really
+a technique that we normally use inside
+
+ align:start position:0%
+a technique that we normally use inside
+ 
+
+ align:start position:0%
+a technique that we normally use inside
+say a toac or magnetically confirmed
+
+ align:start position:0%
+say a toac or magnetically confirmed
+ 
+
+ align:start position:0%
+say a toac or magnetically confirmed
+device but it is very good when you have
+
+ align:start position:0%
+device but it is very good when you have
+ 
+
+ align:start position:0%
+device but it is very good when you have
+larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+densities all right so any questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this Nigel yeah so did we ever say how
+
+ align:start position:0%
+this Nigel yeah so did we ever say how
+ 
+
+ align:start position:0%
+this Nigel yeah so did we ever say how
+exactly the critical uh density was
+
+ align:start position:0%
+exactly the critical uh density was
+ 
+
+ align:start position:0%
+exactly the critical uh density was
+determined is that for a lecture oh do
+
+ align:start position:0%
+determined is that for a lecture oh do
+ 
+
+ align:start position:0%
+determined is that for a lecture oh do
+you mean like what is a numer what is an
+
+ align:start position:0%
+you mean like what is a numer what is an
+ 
+
+ align:start position:0%
+you mean like what is a numer what is an
+analytical result for the critical
+
+ align:start position:0%
+analytical result for the critical
+ 
+
+ align:start position:0%
+analytical result for the critical
+density yeah when when we had like one
+
+ align:start position:0%
+density yeah when when we had like one
+ 
+
+ align:start position:0%
+density yeah when when we had like one
+minus NE Over N critical like where that
+
+ align:start position:0%
+minus NE Over N critical like where that
+ 
+
+ align:start position:0%
+minus NE Over N critical like where that
+was over determined or is it just like
+
+ align:start position:0%
+was over determined or is it just like
+ 
+
+ align:start position:0%
+was over determined or is it just like
+kind of guess and check when oh no it's
+
+ align:start position:0%
+kind of guess and check when oh no it's
+ 
+
+ align:start position:0%
+kind of guess and check when oh no it's
+absolutely you can you can write it down
+
+ align:start position:0%
+absolutely you can you can write it down
+ 
+
+ align:start position:0%
+absolutely you can you can write it down
+it's a function and I I I neglected to
+
+ align:start position:0%
+it's a function and I I I neglected to
+ 
+
+ align:start position:0%
+it's a function and I I I neglected to
+write it down here and I'm not going to
+
+ align:start position:0%
+write it down here and I'm not going to
+ 
+
+ align:start position:0%
+write it down here and I'm not going to
+try and remember what it is but it is a
+
+ align:start position:0%
+try and remember what it is but it is a
+ 
+
+ align:start position:0%
+try and remember what it is but it is a
+function which has inside it the
+
+ align:start position:0%
+function which has inside it the
+ 
+
+ align:start position:0%
+function which has inside it the
+frequency of the laser light Epsilon not
+
+ align:start position:0%
+frequency of the laser light Epsilon not
+ 
+
+ align:start position:0%
+frequency of the laser light Epsilon not
+e and me and the no not the density
+
+ align:start position:0%
+e and me and the no not the density
+ 
+
+ align:start position:0%
+e and me and the no not the density
+definitely another density inside it so
+
+ align:start position:0%
+definitely another density inside it so
+ 
+
+ align:start position:0%
+definitely another density inside it so
+it is effectively comes from rearranging
+
+ align:start position:0%
+it is effectively comes from rearranging
+ 
+
+ align:start position:0%
+it is effectively comes from rearranging
+the plasma frequency here and you can
+
+ align:start position:0%
+the plasma frequency here and you can
+ 
+
+ align:start position:0%
+the plasma frequency here and you can
+find this in Hutchinson's book and I
+
+ align:start position:0%
+find this in Hutchinson's book and I
+ 
+
+ align:start position:0%
+find this in Hutchinson's book and I
+really should have written in my notes
+
+ align:start position:0%
+really should have written in my notes
+ 
+
+ align:start position:0%
+really should have written in my notes
+but I just didn't okay so um and I'm not
+
+ align:start position:0%
+but I just didn't okay so um and I'm not
+ 
+
+ align:start position:0%
+but I just didn't okay so um and I'm not
+going to try and you and look
+
+ align:start position:0%
+going to try and you and look
+ 
+
+ align:start position:0%
+going to try and you and look
+it up now so yeah the the critical
+
+ align:start position:0%
+it up now so yeah the the critical
+ 
+
+ align:start position:0%
+it up now so yeah the the critical
+density is a number that we can defin it
+
+ align:start position:0%
+density is a number that we can defin it
+ 
+
+ align:start position:0%
+density is a number that we can defin it
+is uniquely defined for every uh
+
+ align:start position:0%
+is uniquely defined for every uh
+ 
+
+ align:start position:0%
+is uniquely defined for every uh
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+wavelength and that is the density which
+
+ align:start position:0%
+wavelength and that is the density which
+ 
+
+ align:start position:0%
+wavelength and that is the density which
+you cannot go above and if you're
+
+ align:start position:0%
+you cannot go above and if you're
+ 
+
+ align:start position:0%
+you cannot go above and if you're
+sensible you'll work well away from the
+
+ align:start position:0%
+sensible you'll work well away from the
+ 
+
+ align:start position:0%
+sensible you'll work well away from the
+critical density because if you get
+
+ align:start position:0%
+critical density because if you get
+ 
+
+ align:start position:0%
+critical density because if you get
+anywhere close to it it really screws up
+
+ align:start position:0%
+anywhere close to it it really screws up
+ 
+
+ align:start position:0%
+anywhere close to it it really screws up
+most of these calculations so most of
+
+ align:start position:0%
+most of these calculations so most of
+ 
+
+ align:start position:0%
+most of these calculations so most of
+the time we relying on this
+
+ align:start position:0%
+the time we relying on this
+ 
+
+ align:start position:0%
+the time we relying on this
+approximation that the density we're
+
+ align:start position:0%
+approximation that the density we're
+ 
+
+ align:start position:0%
+approximation that the density we're
+using is much less than the criticality
+
+ align:start position:0%
+using is much less than the criticality
+ 
+
+ align:start position:0%
+using is much less than the criticality
+and we'll come across that approximation
+
+ align:start position:0%
+and we'll come across that approximation
+ 
+
+ align:start position:0%
+and we'll come across that approximation
+very strongly when we deal with
+
+ align:start position:0%
+very strongly when we deal with
+ 
+
+ align:start position:0%
+very strongly when we deal with
+interferometry in a little
+
+ align:start position:0%
+interferometry in a little
+ 
+
+ align:start position:0%
+interferometry in a little
+bit but we did also use it already when
+
+ align:start position:0%
+bit but we did also use it already when
+ 
+
+ align:start position:0%
+bit but we did also use it already when
+we were ding the schan angle when we got
+
+ align:start position:0%
+we were ding the schan angle when we got
+ 
+
+ align:start position:0%
+we were ding the schan angle when we got
+to this point here we used this linear
+
+ align:start position:0%
+to this point here we used this linear
+ 
+
+ align:start position:0%
+to this point here we used this linear
+approximation where the density is much
+
+ align:start position:0%
+approximation where the density is much
+ 
+
+ align:start position:0%
+approximation where the density is much
+less than the critical
+
+ align:start position:0%
+less than the critical
+ 
+
+ align:start position:0%
+less than the critical
+density any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so uh you were can you hear me I
+
+ align:start position:0%
+yeah so uh you were can you hear me I
+ 
+
+ align:start position:0%
+yeah so uh you were can you hear me I
+can hear you yeah Okay cool so um would
+
+ align:start position:0%
+can hear you yeah Okay cool so um would
+ 
+
+ align:start position:0%
+can hear you yeah Okay cool so um would
+it not be possible to use the quote
+
+ align:start position:0%
+it not be possible to use the quote
+ 
+
+ align:start position:0%
+it not be possible to use the quote
+unquote glow of the plasma itself to use
+
+ align:start position:0%
+unquote glow of the plasma itself to use
+ 
+
+ align:start position:0%
+unquote glow of the plasma itself to use
+lein in some other part of the plasma
+
+ align:start position:0%
+lein in some other part of the plasma
+ 
+
+ align:start position:0%
+lein in some other part of the plasma
+that isn't glowing itself or that it's
+
+ align:start position:0%
+that isn't glowing itself or that it's
+ 
+
+ align:start position:0%
+that isn't glowing itself or that it's
+glowing at some other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency I thought about this I think
+
+ align:start position:0%
+frequency I thought about this I think
+ 
+
+ align:start position:0%
+frequency I thought about this I think
+it's a really cool idea um you
+
+ align:start position:0%
+it's a really cool idea um you
+ 
+
+ align:start position:0%
+it's a really cool idea um you
+definitely have to arrange your plasma
+
+ align:start position:0%
+definitely have to arrange your plasma
+ 
+
+ align:start position:0%
+definitely have to arrange your plasma
+so there's a bit that's glowing and a
+
+ align:start position:0%
+so there's a bit that's glowing and a
+ 
+
+ align:start position:0%
+so there's a bit that's glowing and a
+bit that isn't if the bit you want to
+
+ align:start position:0%
+bit that isn't if the bit you want to
+ 
+
+ align:start position:0%
+bit that isn't if the bit you want to
+measure is also glowing that's going to
+
+ align:start position:0%
+measure is also glowing that's going to
+ 
+
+ align:start position:0%
+measure is also glowing that's going to
+make things very very difficult um so
+
+ align:start position:0%
+make things very very difficult um so
+ 
+
+ align:start position:0%
+make things very very difficult um so
+yeah you could potentially have
+
+ align:start position:0%
+yeah you could potentially have
+ 
+
+ align:start position:0%
+yeah you could potentially have
+something like that like a ICF hotspot
+
+ align:start position:0%
+something like that like a ICF hotspot
+ 
+
+ align:start position:0%
+something like that like a ICF hotspot
+backlighting the whole Ram plasma uh
+
+ align:start position:0%
+backlighting the whole Ram plasma uh
+ 
+
+ align:start position:0%
+backlighting the whole Ram plasma uh
+that sort of thing could could work yeah
+
+ align:start position:0%
+that sort of thing could could work yeah
+ 
+
+ align:start position:0%
+that sort of thing could could work yeah
+but I don't know of anyone who's
+
+ align:start position:0%
+but I don't know of anyone who's
+ 
+
+ align:start position:0%
+but I don't know of anyone who's
+done okay thank
+
+ align:start position:0%
+done okay thank
+ 
+
+ align:start position:0%
+done okay thank
+you all right we're we're past the hour
+
+ align:start position:0%
+you all right we're we're past the hour
+ 
+
+ align:start position:0%
+you all right we're we're past the hour
+now so I think we'll leave it here I
+
+ align:start position:0%
+now so I think we'll leave it here I
+ 
+
+ align:start position:0%
+now so I think we'll leave it here I
+will be back in the classroom next
+
+ align:start position:0%
+will be back in the classroom next
+ 
+
+ align:start position:0%
+will be back in the classroom next
+Tuesday Tuesday I look forward to seeing
+
+ align:start position:0%
+Tuesday Tuesday I look forward to seeing
+ 
+
+ align:start position:0%
+Tuesday Tuesday I look forward to seeing
+all of you there and all the Columbia
+
+ align:start position:0%
+all of you there and all the Columbia
+ 
+
+ align:start position:0%
+all of you there and all the Columbia
+folks online and yeah enjoy your weekend
+
+ align:start position:0%
+folks online and yeah enjoy your weekend
+ 
+
+ align:start position:0%
+folks online and yeah enjoy your weekend
+and bye for now
\ No newline at end of file
diff --git a/wBnlmQR5Vhk.txt b/wBnlmQR5Vhk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a64bf468d1b64fe4ebe644368a82b4194b0b5ff8
--- /dev/null
+++ b/wBnlmQR5Vhk.txt
@@ -0,0 +1,267 @@
+align:start position:0%
+ 
+this lecture consists of two parts that
+
+ align:start position:0%
+this lecture consists of two parts that
+ 
+
+ align:start position:0%
+this lecture consists of two parts that
+deal with two rather different topics in
+
+ align:start position:0%
+deal with two rather different topics in
+ 
+
+ align:start position:0%
+deal with two rather different topics in
+the first part we look into it an
+
+ align:start position:0%
+the first part we look into it an
+ 
+
+ align:start position:0%
+the first part we look into it an
+important special case of a derived
+
+ align:start position:0%
+important special case of a derived
+ 
+
+ align:start position:0%
+important special case of a derived
+distribution problem we start with two
+
+ align:start position:0%
+distribution problem we start with two
+ 
+
+ align:start position:0%
+distribution problem we start with two
+independent random variables with known
+
+ align:start position:0%
+independent random variables with known
+ 
+
+ align:start position:0%
+independent random variables with known
+distributions and wish to find the
+
+ align:start position:0%
+distributions and wish to find the
+ 
+
+ align:start position:0%
+distributions and wish to find the
+distribution of their sum we will see
+
+ align:start position:0%
+distribution of their sum we will see
+ 
+
+ align:start position:0%
+distribution of their sum we will see
+that for either the discrete or the
+
+ align:start position:0%
+that for either the discrete or the
+ 
+
+ align:start position:0%
+that for either the discrete or the
+continuous case there is a nice formula
+
+ align:start position:0%
+continuous case there is a nice formula
+ 
+
+ align:start position:0%
+continuous case there is a nice formula
+gives us the answer we will develop this
+
+ align:start position:0%
+gives us the answer we will develop this
+ 
+
+ align:start position:0%
+gives us the answer we will develop this
+formula and then we will talk a little
+
+ align:start position:0%
+formula and then we will talk a little
+ 
+
+ align:start position:0%
+formula and then we will talk a little
+bit about a graphical way of carrying
+
+ align:start position:0%
+bit about a graphical way of carrying
+ 
+
+ align:start position:0%
+bit about a graphical way of carrying
+out the calculations involved as we will
+
+ align:start position:0%
+out the calculations involved as we will
+ 
+
+ align:start position:0%
+out the calculations involved as we will
+discuss this formula also allows us to
+
+ align:start position:0%
+discuss this formula also allows us to
+ 
+
+ align:start position:0%
+discuss this formula also allows us to
+establish the very important fact that
+
+ align:start position:0%
+establish the very important fact that
+ 
+
+ align:start position:0%
+establish the very important fact that
+the sum of two independent normal random
+
+ align:start position:0%
+the sum of two independent normal random
+ 
+
+ align:start position:0%
+the sum of two independent normal random
+variables is normal in the second part
+
+ align:start position:0%
+variables is normal in the second part
+ 
+
+ align:start position:0%
+variables is normal in the second part
+who introduced the covariance of two
+
+ align:start position:0%
+who introduced the covariance of two
+ 
+
+ align:start position:0%
+who introduced the covariance of two
+random variables and the correlation
+
+ align:start position:0%
+random variables and the correlation
+ 
+
+ align:start position:0%
+random variables and the correlation
+coefficient these are certain quantities
+
+ align:start position:0%
+coefficient these are certain quantities
+ 
+
+ align:start position:0%
+coefficient these are certain quantities
+that allow us to quantify the degree to
+
+ align:start position:0%
+that allow us to quantify the degree to
+ 
+
+ align:start position:0%
+that allow us to quantify the degree to
+which two dependent random variables are
+
+ align:start position:0%
+which two dependent random variables are
+ 
+
+ align:start position:0%
+which two dependent random variables are
+related for example a high value of the
+
+ align:start position:0%
+related for example a high value of the
+ 
+
+ align:start position:0%
+related for example a high value of the
+correlation coefficient will indicate a
+
+ align:start position:0%
+correlation coefficient will indicate a
+ 
+
+ align:start position:0%
+correlation coefficient will indicate a
+strong relation between these random
+
+ align:start position:0%
+strong relation between these random
+ 
+
+ align:start position:0%
+strong relation between these random
+variables we will see the basic
+
+ align:start position:0%
+variables we will see the basic
+ 
+
+ align:start position:0%
+variables we will see the basic
+mathematical properties of these
+
+ align:start position:0%
+mathematical properties of these
+ 
+
+ align:start position:0%
+mathematical properties of these
+quantities and provide some
+
+ align:start position:0%
+quantities and provide some
+ 
+
+ align:start position:0%
+quantities and provide some
+interpretation later on in this class we
+
+ align:start position:0%
+interpretation later on in this class we
+ 
+
+ align:start position:0%
+interpretation later on in this class we
+will see that they play an important
+
+ align:start position:0%
+will see that they play an important
+ 
+
+ align:start position:0%
+will see that they play an important
+role in the problem of estimating one
+
+ align:start position:0%
+role in the problem of estimating one
+ 
+
+ align:start position:0%
+role in the problem of estimating one
+random variable given the value of
+
+ align:start position:0%
+random variable given the value of
+ 
+
+ align:start position:0%
+random variable given the value of
+another
\ No newline at end of file
diff --git a/wOHrNt9ScYs.txt b/wOHrNt9ScYs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a51e4473344eca358978e966b61de40a2cc5514
--- /dev/null
+++ b/wOHrNt9ScYs.txt
@@ -0,0 +1,7731 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Last time we left off with a question
+
+ align:start position:0%
+Last time we left off with a question
+ 
+
+ align:start position:0%
+Last time we left off with a question
+having to do with playing with blocks.
+
+ align:start position:0%
+having to do with playing with blocks.
+ 
+
+ align:start position:0%
+having to do with playing with blocks.
+And this is supposed to get give us a
+
+ align:start position:0%
+And this is supposed to get give us a
+ 
+
+ align:start position:0%
+And this is supposed to get give us a
+visceral feel for for something anyway
+
+ align:start position:0%
+visceral feel for for something anyway
+ 
+
+ align:start position:0%
+visceral feel for for something anyway
+having to do with series. And the
+
+ align:start position:0%
+having to do with series. And the
+ 
+
+ align:start position:0%
+having to do with series. And the
+question was whether I could stack these
+
+ align:start position:0%
+question was whether I could stack these
+ 
+
+ align:start position:0%
+question was whether I could stack these
+blocks build a stack so that I'm going
+
+ align:start position:0%
+blocks build a stack so that I'm going
+ 
+
+ align:start position:0%
+blocks build a stack so that I'm going
+to try it here up. I'm already off
+
+ align:start position:0%
+to try it here up. I'm already off
+ 
+
+ align:start position:0%
+to try it here up. I'm already off
+balance here. See the question is can I
+
+ align:start position:0%
+balance here. See the question is can I
+ 
+
+ align:start position:0%
+balance here. See the question is can I
+build this
+
+ align:start position:0%
+build this
+ 
+
+ align:start position:0%
+build this
+so that the um let's draw a picture of
+
+ align:start position:0%
+so that the um let's draw a picture of
+ 
+
+ align:start position:0%
+so that the um let's draw a picture of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so that the uh first block is like this.
+
+ align:start position:0%
+so that the uh first block is like this.
+ 
+
+ align:start position:0%
+so that the uh first block is like this.
+The next block is like this. And maybe
+
+ align:start position:0%
+The next block is like this. And maybe
+ 
+
+ align:start position:0%
+The next block is like this. And maybe
+the next block is like this. And notice
+
+ align:start position:0%
+the next block is like this. And notice
+ 
+
+ align:start position:0%
+the next block is like this. And notice
+there's no visible means of support for
+
+ align:start position:0%
+there's no visible means of support for
+ 
+
+ align:start position:0%
+there's no visible means of support for
+this block. It's completely to the left
+
+ align:start position:0%
+this block. It's completely to the left
+ 
+
+ align:start position:0%
+this block. It's completely to the left
+of the first block.
+
+ align:start position:0%
+of the first block.
+ 
+
+ align:start position:0%
+of the first block.
+And the question is uh will this fall
+
+ align:start position:0%
+And the question is uh will this fall
+ 
+
+ align:start position:0%
+And the question is uh will this fall
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+or at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or more precisely eventually we'll ask
+
+ align:start position:0%
+or more precisely eventually we'll ask
+ 
+
+ align:start position:0%
+or more precisely eventually we'll ask
+you know how far can we go? Now before
+
+ align:start position:0%
+you know how far can we go? Now before
+ 
+
+ align:start position:0%
+you know how far can we go? Now before
+you answer this question
+
+ align:start position:0%
+you answer this question
+ 
+
+ align:start position:0%
+you answer this question
+um the claim is that that this is a kind
+
+ align:start position:0%
+um the claim is that that this is a kind
+ 
+
+ align:start position:0%
+um the claim is that that this is a kind
+of a natural physical question which
+
+ align:start position:0%
+of a natural physical question which
+ 
+
+ align:start position:0%
+of a natural physical question which
+involves some important
+
+ align:start position:0%
+involves some important
+ 
+
+ align:start position:0%
+involves some important
+answer no matter whether the answer is
+
+ align:start position:0%
+answer no matter whether the answer is
+ 
+
+ align:start position:0%
+answer no matter whether the answer is
+you can do it or you can't. So this is
+
+ align:start position:0%
+you can do it or you can't. So this is
+ 
+
+ align:start position:0%
+you can do it or you can't. So this is
+the good kind of math question where no
+
+ align:start position:0%
+the good kind of math question where no
+ 
+
+ align:start position:0%
+the good kind of math question where no
+matter what the answer is if when you
+
+ align:start position:0%
+matter what the answer is if when you
+ 
+
+ align:start position:0%
+matter what the answer is if when you
+figure out the answer you're going to
+
+ align:start position:0%
+figure out the answer you're going to
+ 
+
+ align:start position:0%
+figure out the answer you're going to
+get something interesting out of it
+
+ align:start position:0%
+get something interesting out of it
+ 
+
+ align:start position:0%
+get something interesting out of it
+because there are two possibilities.
+
+ align:start position:0%
+because there are two possibilities.
+ 
+
+ align:start position:0%
+because there are two possibilities.
+Either there's a limit to how far to the
+
+ align:start position:0%
+Either there's a limit to how far to the
+ 
+
+ align:start position:0%
+Either there's a limit to how far to the
+left we can go in which case that's a
+
+ align:start position:0%
+left we can go in which case that's a
+ 
+
+ align:start position:0%
+left we can go in which case that's a
+very interesting number
+
+ align:start position:0%
+very interesting number
+ 
+
+ align:start position:0%
+very interesting number
+or else there is no limit you can go
+
+ align:start position:0%
+or else there is no limit you can go
+ 
+
+ align:start position:0%
+or else there is no limit you can go
+arbitrarily far and that's also
+
+ align:start position:0%
+arbitrarily far and that's also
+ 
+
+ align:start position:0%
+arbitrarily far and that's also
+interesting and curious and that's the
+
+ align:start position:0%
+interesting and curious and that's the
+ 
+
+ align:start position:0%
+interesting and curious and that's the
+difference between convergence and
+
+ align:start position:0%
+difference between convergence and
+ 
+
+ align:start position:0%
+difference between convergence and
+divergence
+
+ align:start position:0%
+divergence
+ 
+
+ align:start position:0%
+divergence
+the the thing that we were talking about
+
+ align:start position:0%
+the the thing that we were talking about
+ 
+
+ align:start position:0%
+the the thing that we were talking about
+up to now concerning series so my first
+
+ align:start position:0%
+up to now concerning series so my first
+ 
+
+ align:start position:0%
+up to now concerning series so my first
+question is do you think that I can get
+
+ align:start position:0%
+question is do you think that I can get
+ 
+
+ align:start position:0%
+question is do you think that I can get
+it uh get it so that this thing doesn't
+
+ align:start position:0%
+it uh get it so that this thing doesn't
+ 
+
+ align:start position:0%
+it uh get it so that this thing doesn't
+fall down with with well, you see, I
+
+ align:start position:0%
+fall down with with well, you see, I
+ 
+
+ align:start position:0%
+fall down with with well, you see, I
+have about eight blocks here or so. So,
+
+ align:start position:0%
+have about eight blocks here or so. So,
+ 
+
+ align:start position:0%
+have about eight blocks here or so. So,
+you you can vote now. How many in favor
+
+ align:start position:0%
+you you can vote now. How many in favor
+ 
+
+ align:start position:0%
+you you can vote now. How many in favor
+that I can that I can succeed in doing
+
+ align:start position:0%
+that I can that I can succeed in doing
+ 
+
+ align:start position:0%
+that I can that I can succeed in doing
+this sort of thing with maybe more than
+
+ align:start position:0%
+this sort of thing with maybe more than
+ 
+
+ align:start position:0%
+this sort of thing with maybe more than
+three blocks. How many in favor? All
+
+ align:start position:0%
+three blocks. How many in favor? All
+ 
+
+ align:start position:0%
+three blocks. How many in favor? All
+right, somebody's voting twice there.
+
+ align:start position:0%
+right, somebody's voting twice there.
+ 
+
+ align:start position:0%
+right, somebody's voting twice there.
+That's good. I like that. Um, how about
+
+ align:start position:0%
+That's good. I like that. Um, how about
+ 
+
+ align:start position:0%
+That's good. I like that. Um, how about
+how about opposed?
+
+ align:start position:0%
+how about opposed?
+ 
+
+ align:start position:0%
+how about opposed?
+Uh, so I I that was really close to a
+
+ align:start position:0%
+Uh, so I I that was really close to a
+ 
+
+ align:start position:0%
+Uh, so I I that was really close to a
+tie. All right. Uh, but I think that
+
+ align:start position:0%
+tie. All right. Uh, but I think that
+ 
+
+ align:start position:0%
+tie. All right. Uh, but I think that
+there was slightly more opposed.
+
+ align:start position:0%
+there was slightly more opposed.
+ 
+
+ align:start position:0%
+there was slightly more opposed.
+I don't know. You guys who were in the
+
+ align:start position:0%
+I don't know. You guys who were in the
+ 
+
+ align:start position:0%
+I don't know. You guys who were in the
+back maybe could tell. Anyway, it was it
+
+ align:start position:0%
+back maybe could tell. Anyway, it was it
+ 
+
+ align:start position:0%
+back maybe could tell. Anyway, it was it
+was pretty close. All right. So, now I'm
+
+ align:start position:0%
+was pretty close. All right. So, now I'm
+ 
+
+ align:start position:0%
+was pretty close. All right. So, now I'm
+going because this is a real life thing.
+
+ align:start position:0%
+going because this is a real life thing.
+ 
+
+ align:start position:0%
+going because this is a real life thing.
+I'm going to try to do it. All right.
+
+ align:start position:0%
+I'm going to try to do it. All right.
+ 
+
+ align:start position:0%
+I'm going to try to do it. All right.
+All right. So, now I'm going to tell you
+
+ align:start position:0%
+All right. So, now I'm going to tell you
+ 
+
+ align:start position:0%
+All right. So, now I'm going to tell you
+what the trick is.
+
+ align:start position:0%
+what the trick is.
+ 
+
+ align:start position:0%
+what the trick is.
+The trick is to do it backwards. When
+
+ align:start position:0%
+The trick is to do it backwards. When
+ 
+
+ align:start position:0%
+The trick is to do it backwards. When
+most people are playing with blocks,
+
+ align:start position:0%
+most people are playing with blocks,
+ 
+
+ align:start position:0%
+most people are playing with blocks,
+they decide to build it from the bottom
+
+ align:start position:0%
+they decide to build it from the bottom
+ 
+
+ align:start position:0%
+they decide to build it from the bottom
+up, right? But we're going to build it
+
+ align:start position:0%
+up, right? But we're going to build it
+ 
+
+ align:start position:0%
+up, right? But we're going to build it
+from the top down. From the top down.
+
+ align:start position:0%
+from the top down. From the top down.
+ 
+
+ align:start position:0%
+from the top down. From the top down.
+And that's going to make it possible for
+
+ align:start position:0%
+And that's going to make it possible for
+ 
+
+ align:start position:0%
+And that's going to make it possible for
+us to do the optimal thing at each
+
+ align:start position:0%
+us to do the optimal thing at each
+ 
+
+ align:start position:0%
+us to do the optimal thing at each
+stage. So when I build it from the top
+
+ align:start position:0%
+stage. So when I build it from the top
+ 
+
+ align:start position:0%
+stage. So when I build it from the top
+down, the best I can do is well, it'll
+
+ align:start position:0%
+down, the best I can do is well, it'll
+ 
+
+ align:start position:0%
+down, the best I can do is well, it'll
+fall off. I I need to have it less, you
+
+ align:start position:0%
+fall off. I I need to have it less, you
+ 
+
+ align:start position:0%
+fall off. I I need to have it less, you
+know, halfway across. That's the best I
+
+ align:start position:0%
+know, halfway across. That's the best I
+ 
+
+ align:start position:0%
+know, halfway across. That's the best I
+can do. So the top one I'm going to
+
+ align:start position:0%
+can do. So the top one I'm going to
+ 
+
+ align:start position:0%
+can do. So the top one I'm going to
+build like that. I'm going to take it as
+
+ align:start position:0%
+build like that. I'm going to take it as
+ 
+
+ align:start position:0%
+build like that. I'm going to take it as
+far to the left as I can. And then I'm
+
+ align:start position:0%
+far to the left as I can. And then I'm
+ 
+
+ align:start position:0%
+far to the left as I can. And then I'm
+gonna put the next one down as far to
+
+ align:start position:0%
+gonna put the next one down as far to
+ 
+
+ align:start position:0%
+gonna put the next one down as far to
+the left as I can. And then the next one
+
+ align:start position:0%
+the left as I can. And then the next one
+ 
+
+ align:start position:0%
+the left as I can. And then the next one
+as far to the left as I can. Oh, that
+
+ align:start position:0%
+as far to the left as I can. Oh, that
+ 
+
+ align:start position:0%
+as far to the left as I can. Oh, that
+was a little too far. And then I'm going
+
+ align:start position:0%
+was a little too far. And then I'm going
+ 
+
+ align:start position:0%
+was a little too far. And then I'm going
+to do the next one as far to the left as
+
+ align:start position:0%
+to do the next one as far to the left as
+ 
+
+ align:start position:0%
+to do the next one as far to the left as
+I can. And then I'm going to do the next
+
+ align:start position:0%
+I can. And then I'm going to do the next
+ 
+
+ align:start position:0%
+I can. And then I'm going to do the next
+one. Well, let's line it up first.
+
+ align:start position:0%
+one. Well, let's line it up first.
+ 
+
+ align:start position:0%
+one. Well, let's line it up first.
+As far to the left as I can. All right.
+
+ align:start position:0%
+As far to the left as I can. All right.
+ 
+
+ align:start position:0%
+As far to the left as I can. All right.
+And then the next one as far to the left
+
+ align:start position:0%
+And then the next one as far to the left
+ 
+
+ align:start position:0%
+And then the next one as far to the left
+as I can. All right. Now, those of you
+
+ align:start position:0%
+as I can. All right. Now, those of you
+ 
+
+ align:start position:0%
+as I can. All right. Now, those of you
+who are in this line can see.
+
+ align:start position:0%
+who are in this line can see.
+ 
+
+ align:start position:0%
+who are in this line can see.
+All right, I succeeded. All right, this
+
+ align:start position:0%
+All right, I succeeded. All right, this
+ 
+
+ align:start position:0%
+All right, I succeeded. All right, this
+is that's over the edge. All right, so
+
+ align:start position:0%
+is that's over the edge. All right, so
+ 
+
+ align:start position:0%
+is that's over the edge. All right, so
+it can be done. All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So now we know that we can
+
+ align:start position:0%
+All right. So now we know that we can
+ 
+
+ align:start position:0%
+All right. So now we know that we can
+get farther than you know we can we can
+
+ align:start position:0%
+get farther than you know we can we can
+ 
+
+ align:start position:0%
+get farther than you know we can we can
+we can make it overflow. So the question
+
+ align:start position:0%
+we can make it overflow. So the question
+ 
+
+ align:start position:0%
+we can make it overflow. So the question
+now is how far can I get? Okay. Do you
+
+ align:start position:0%
+now is how far can I get? Okay. Do you
+ 
+
+ align:start position:0%
+now is how far can I get? Okay. Do you
+think I can get to here? Can I Can I get
+
+ align:start position:0%
+think I can get to here? Can I Can I get
+ 
+
+ align:start position:0%
+think I can get to here? Can I Can I get
+to the end over here? So, how many how
+
+ align:start position:0%
+to the end over here? So, how many how
+ 
+
+ align:start position:0%
+to the end over here? So, how many how
+many people think I can get this this
+
+ align:start position:0%
+many people think I can get this this
+ 
+
+ align:start position:0%
+many people think I can get this this
+far over to here? How many people think
+
+ align:start position:0%
+far over to here? How many people think
+ 
+
+ align:start position:0%
+far over to here? How many people think
+I can get this far? Well, you know,
+
+ align:start position:0%
+I can get this far? Well, you know,
+ 
+
+ align:start position:0%
+I can get this far? Well, you know,
+remember I'm going to have to use more
+
+ align:start position:0%
+remember I'm going to have to use more
+ 
+
+ align:start position:0%
+remember I'm going to have to use more
+than just this one more block that I've
+
+ align:start position:0%
+than just this one more block that I've
+ 
+
+ align:start position:0%
+than just this one more block that I've
+got. I don't Right. Obviously, I'm
+
+ align:start position:0%
+got. I don't Right. Obviously, I'm
+ 
+
+ align:start position:0%
+got. I don't Right. Obviously, I'm
+thinking actually I do have some more
+
+ align:start position:0%
+thinking actually I do have some more
+ 
+
+ align:start position:0%
+thinking actually I do have some more
+blocks at home, but okay, we're not
+
+ align:start position:0%
+blocks at home, but okay, we're not
+ 
+
+ align:start position:0%
+blocks at home, but okay, we're not
+going to. But anyway, you think I can
+
+ align:start position:0%
+going to. But anyway, you think I can
+ 
+
+ align:start position:0%
+going to. But anyway, you think I can
+get over to here? How many people say
+
+ align:start position:0%
+get over to here? How many people say
+ 
+
+ align:start position:0%
+get over to here? How many people say
+yes?
+
+ align:start position:0%
+yes?
+ 
+
+ align:start position:0%
+yes?
+And how many people say no?
+
+ align:start position:0%
+And how many people say no?
+ 
+
+ align:start position:0%
+And how many people say no?
+More people said no than yes. All right.
+
+ align:start position:0%
+More people said no than yes. All right.
+ 
+
+ align:start position:0%
+More people said no than yes. All right.
+So maybe the the stopping place is some
+
+ align:start position:0%
+So maybe the the stopping place is some
+ 
+
+ align:start position:0%
+So maybe the the stopping place is some
+mysterious number in between here. All
+
+ align:start position:0%
+mysterious number in between here. All
+ 
+
+ align:start position:0%
+mysterious number in between here. All
+right. Well, okay. So now now we're
+
+ align:start position:0%
+right. Well, okay. So now now we're
+ 
+
+ align:start position:0%
+right. Well, okay. So now now we're
+going to do the arithmetic and we're
+
+ align:start position:0%
+going to do the arithmetic and we're
+ 
+
+ align:start position:0%
+going to do the arithmetic and we're
+going to figure out what happens with
+
+ align:start position:0%
+going to figure out what happens with
+ 
+
+ align:start position:0%
+going to figure out what happens with
+this with this problem in in Okay. Let's
+
+ align:start position:0%
+this with this problem in in Okay. Let's
+ 
+
+ align:start position:0%
+this with this problem in in Okay. Let's
+let's do it.
+
+ align:start position:0%
+let's do it.
+ 
+
+ align:start position:0%
+let's do it.
+All right. So now again the idea is the
+
+ align:start position:0%
+All right. So now again the idea is the
+ 
+
+ align:start position:0%
+All right. So now again the idea is the
+idea is we're going to start with the
+
+ align:start position:0%
+idea is we're going to start with the
+ 
+
+ align:start position:0%
+idea is we're going to start with the
+top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the top block.
+
+ align:start position:0%
+the top block.
+ 
+
+ align:start position:0%
+the top block.
+We'll call that block number one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the farthest if you like to the
+
+ align:start position:0%
+And then the farthest if you like to the
+ 
+
+ align:start position:0%
+And then the farthest if you like to the
+right that you can put a block
+
+ align:start position:0%
+right that you can put a block
+ 
+
+ align:start position:0%
+right that you can put a block
+underneath it is exactly halfway.
+
+ align:start position:0%
+underneath it is exactly halfway.
+ 
+
+ align:start position:0%
+underneath it is exactly halfway.
+All right. Well, that's the best job I
+
+ align:start position:0%
+All right. Well, that's the best job I
+ 
+
+ align:start position:0%
+All right. Well, that's the best job I
+can do. Now, in order to make my units
+
+ align:start position:0%
+can do. Now, in order to make my units
+ 
+
+ align:start position:0%
+can do. Now, in order to make my units
+work out easily, I'm going to decide to
+
+ align:start position:0%
+work out easily, I'm going to decide to
+ 
+
+ align:start position:0%
+work out easily, I'm going to decide to
+call the length of the block two. All
+
+ align:start position:0%
+call the length of the block two. All
+ 
+
+ align:start position:0%
+call the length of the block two. All
+right? And that means if I start at
+
+ align:start position:0%
+right? And that means if I start at
+ 
+
+ align:start position:0%
+right? And that means if I start at
+location zero, then the first place
+
+ align:start position:0%
+location zero, then the first place
+ 
+
+ align:start position:0%
+location zero, then the first place
+where I am is supposed to be halfway
+
+ align:start position:0%
+where I am is supposed to be halfway
+ 
+
+ align:start position:0%
+where I am is supposed to be halfway
+and that will be one.
+
+ align:start position:0%
+and that will be one.
+ 
+
+ align:start position:0%
+and that will be one.
+Okay. So, so the first step in the
+
+ align:start position:0%
+Okay. So, so the first step in the
+ 
+
+ align:start position:0%
+Okay. So, so the first step in the
+process is one more to the right or if
+
+ align:start position:0%
+process is one more to the right or if
+ 
+
+ align:start position:0%
+process is one more to the right or if
+you like if I were building up, which is
+
+ align:start position:0%
+you like if I were building up, which is
+ 
+
+ align:start position:0%
+you like if I were building up, which is
+what you would actually have to do in
+
+ align:start position:0%
+what you would actually have to do in
+ 
+
+ align:start position:0%
+what you would actually have to do in
+real life, it would be one to the left.
+
+ align:start position:0%
+real life, it would be one to the left.
+ 
+
+ align:start position:0%
+real life, it would be one to the left.
+Okay. Now, the next one, now here's the
+
+ align:start position:0%
+Okay. Now, the next one, now here's the
+ 
+
+ align:start position:0%
+Okay. Now, the next one, now here's the
+the the the way that you start figuring
+
+ align:start position:0%
+the the the way that you start figuring
+ 
+
+ align:start position:0%
+the the the way that you start figuring
+out the arithmetic. The next one is is
+
+ align:start position:0%
+out the arithmetic. The next one is is
+ 
+
+ align:start position:0%
+out the arithmetic. The next one is is
+based on a physical principle which is
+
+ align:start position:0%
+based on a physical principle which is
+ 
+
+ align:start position:0%
+based on a physical principle which is
+that I the farthest I can stick this
+
+ align:start position:0%
+that I the farthest I can stick this
+ 
+
+ align:start position:0%
+that I the farthest I can stick this
+next block underneath is at what's
+
+ align:start position:0%
+next block underneath is at what's
+ 
+
+ align:start position:0%
+next block underneath is at what's
+called the center of mass of these two
+
+ align:start position:0%
+called the center of mass of these two
+ 
+
+ align:start position:0%
+called the center of mass of these two
+which is exactly halfway here. That is
+
+ align:start position:0%
+which is exactly halfway here. That is
+ 
+
+ align:start position:0%
+which is exactly halfway here. That is
+there's a quarter of this guy and a
+
+ align:start position:0%
+there's a quarter of this guy and a
+ 
+
+ align:start position:0%
+there's a quarter of this guy and a
+quarter of that guy balancing each
+
+ align:start position:0%
+quarter of that guy balancing each
+ 
+
+ align:start position:0%
+quarter of that guy balancing each
+other. All right. So that's as far as I
+
+ align:start position:0%
+other. All right. So that's as far as I
+ 
+
+ align:start position:0%
+other. All right. So that's as far as I
+can go. If I go farther than that it'll
+
+ align:start position:0%
+can go. If I go farther than that it'll
+ 
+
+ align:start position:0%
+can go. If I go farther than that it'll
+fall over. So that's the absolute
+
+ align:start position:0%
+fall over. So that's the absolute
+ 
+
+ align:start position:0%
+fall over. So that's the absolute
+farthest I can do. So the next block
+
+ align:start position:0%
+farthest I can do. So the next block
+ 
+
+ align:start position:0%
+farthest I can do. So the next block
+is going to be over here. And a quarter
+
+ align:start position:0%
+is going to be over here. And a quarter
+ 
+
+ align:start position:0%
+is going to be over here. And a quarter
+of two is a half. So this is three
+
+ align:start position:0%
+of two is a half. So this is three
+ 
+
+ align:start position:0%
+of two is a half. So this is three
+halves here. All right. So we went to
+
+ align:start position:0%
+halves here. All right. So we went to
+ 
+
+ align:start position:0%
+halves here. All right. So we went to
+one, we went to three halves here. And
+
+ align:start position:0%
+one, we went to three halves here. And
+ 
+
+ align:start position:0%
+one, we went to three halves here. And
+then I'm going to keep on going with
+
+ align:start position:0%
+then I'm going to keep on going with
+ 
+
+ align:start position:0%
+then I'm going to keep on going with
+this eventually. All right. So we're
+
+ align:start position:0%
+this eventually. All right. So we're
+ 
+
+ align:start position:0%
+this eventually. All right. So we're
+going to figure out what happens with
+
+ align:start position:0%
+going to figure out what happens with
+ 
+
+ align:start position:0%
+going to figure out what happens with
+this with this stack.
+
+ align:start position:0%
+this with this stack.
+ 
+
+ align:start position:0%
+this with this stack.
+Question. How do you know that this is
+
+ align:start position:0%
+Question. How do you know that this is
+ 
+
+ align:start position:0%
+Question. How do you know that this is
+the best way to optimize
+
+ align:start position:0%
+the best way to optimize
+ 
+
+ align:start position:0%
+the best way to optimize
+your The question is how do I know that
+
+ align:start position:0%
+your The question is how do I know that
+ 
+
+ align:start position:0%
+your The question is how do I know that
+this is the best way to optimize? Um I'm
+
+ align:start position:0%
+this is the best way to optimize? Um I'm
+ 
+
+ align:start position:0%
+this is the best way to optimize? Um I'm
+I can't answer that question, but I can
+
+ align:start position:0%
+I can't answer that question, but I can
+ 
+
+ align:start position:0%
+I can't answer that question, but I can
+tell you that it's the best way if I
+
+ align:start position:0%
+tell you that it's the best way if I
+ 
+
+ align:start position:0%
+tell you that it's the best way if I
+start with the top like this and the
+
+ align:start position:0%
+start with the top like this and the
+ 
+
+ align:start position:0%
+start with the top like this and the
+next one like this, right? Because I'm
+
+ align:start position:0%
+next one like this, right? Because I'm
+ 
+
+ align:start position:0%
+next one like this, right? Because I'm
+doing the farthest possible at each
+
+ align:start position:0%
+doing the farthest possible at each
+ 
+
+ align:start position:0%
+doing the farthest possible at each
+stage. That actually has a name in in
+
+ align:start position:0%
+stage. That actually has a name in in
+ 
+
+ align:start position:0%
+stage. That actually has a name in in
+computer science that's called the
+
+ align:start position:0%
+computer science that's called the
+ 
+
+ align:start position:0%
+computer science that's called the
+greedy algorithm. I'm trying to do the
+
+ align:start position:0%
+greedy algorithm. I'm trying to do the
+ 
+
+ align:start position:0%
+greedy algorithm. I'm trying to do the
+best possible at each stage. The greedy
+
+ align:start position:0%
+best possible at each stage. The greedy
+ 
+
+ align:start position:0%
+best possible at each stage. The greedy
+algorithm starting from the bottom is an
+
+ align:start position:0%
+algorithm starting from the bottom is an
+ 
+
+ align:start position:0%
+algorithm starting from the bottom is an
+extremely bad strategy because when you
+
+ align:start position:0%
+extremely bad strategy because when you
+ 
+
+ align:start position:0%
+extremely bad strategy because when you
+do that you stack it this way and it
+
+ align:start position:0%
+do that you stack it this way and it
+ 
+
+ align:start position:0%
+do that you stack it this way and it
+almost falls over and then the next time
+
+ align:start position:0%
+almost falls over and then the next time
+ 
+
+ align:start position:0%
+almost falls over and then the next time
+you can't do anything. So the greedy
+
+ align:start position:0%
+you can't do anything. So the greedy
+ 
+
+ align:start position:0%
+you can't do anything. So the greedy
+algorithm is terrible from the bottom
+
+ align:start position:0%
+algorithm is terrible from the bottom
+ 
+
+ align:start position:0%
+algorithm is terrible from the bottom
+but it turn this is the greedy algorithm
+
+ align:start position:0%
+but it turn this is the greedy algorithm
+ 
+
+ align:start position:0%
+but it turn this is the greedy algorithm
+starting from the top and it turns out
+
+ align:start position:0%
+starting from the top and it turns out
+ 
+
+ align:start position:0%
+starting from the top and it turns out
+to do much better than the greedy
+
+ align:start position:0%
+to do much better than the greedy
+ 
+
+ align:start position:0%
+to do much better than the greedy
+algorithm starting from the bottom. But
+
+ align:start position:0%
+algorithm starting from the bottom. But
+ 
+
+ align:start position:0%
+algorithm starting from the bottom. But
+of course I'm not addressing whether
+
+ align:start position:0%
+of course I'm not addressing whether
+ 
+
+ align:start position:0%
+of course I'm not addressing whether
+there might not be some other incredibly
+
+ align:start position:0%
+there might not be some other incredibly
+ 
+
+ align:start position:0%
+there might not be some other incredibly
+clever strategy where I wiggle around
+
+ align:start position:0%
+clever strategy where I wiggle around
+ 
+
+ align:start position:0%
+clever strategy where I wiggle around
+and make it go up. That's I'm I'm not an
+
+ align:start position:0%
+and make it go up. That's I'm I'm not an
+ 
+
+ align:start position:0%
+and make it go up. That's I'm I'm not an
+addressing that question. All right. It
+
+ align:start position:0%
+addressing that question. All right. It
+ 
+
+ align:start position:0%
+addressing that question. All right. It
+turns out this is the best you could do,
+
+ align:start position:0%
+turns out this is the best you could do,
+ 
+
+ align:start position:0%
+turns out this is the best you could do,
+but that's not not clear. All right. So
+
+ align:start position:0%
+but that's not not clear. All right. So
+ 
+
+ align:start position:0%
+but that's not not clear. All right. So
+now here here we have this thing and now
+
+ align:start position:0%
+now here here we have this thing and now
+ 
+
+ align:start position:0%
+now here here we have this thing and now
+I have to figure out what the arithmetic
+
+ align:start position:0%
+I have to figure out what the arithmetic
+ 
+
+ align:start position:0%
+I have to figure out what the arithmetic
+pattern is so that I can figure out what
+
+ align:start position:0%
+pattern is so that I can figure out what
+ 
+
+ align:start position:0%
+pattern is so that I can figure out what
+I was doing with those shapes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's let's uh uh figure out the the
+
+ align:start position:0%
+So let's let's uh uh figure out the the
+ 
+
+ align:start position:0%
+So let's let's uh uh figure out the the
+a thought experiment here. All right.
+
+ align:start position:0%
+a thought experiment here. All right.
+ 
+
+ align:start position:0%
+a thought experiment here. All right.
+Now, the thought experiment I want to
+
+ align:start position:0%
+Now, the thought experiment I want to
+ 
+
+ align:start position:0%
+Now, the thought experiment I want to
+imagine to you for you is you've got a
+
+ align:start position:0%
+imagine to you for you is you've got a
+ 
+
+ align:start position:0%
+imagine to you for you is you've got a
+stack of a bunch of blocks.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is the first n blocks.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. And now we're going to put
+
+ align:start position:0%
+All right. And now we're going to put
+ 
+
+ align:start position:0%
+All right. And now we're going to put
+one underneath it.
+
+ align:start position:0%
+one underneath it.
+ 
+
+ align:start position:0%
+one underneath it.
+And what we're going to figure out
+
+ align:start position:0%
+And what we're going to figure out
+ 
+
+ align:start position:0%
+And what we're going to figure out
+is the center of mass
+
+ align:start position:0%
+is the center of mass
+ 
+
+ align:start position:0%
+is the center of mass
+of those n blocks, which I'm going to
+
+ align:start position:0%
+of those n blocks, which I'm going to
+ 
+
+ align:start position:0%
+of those n blocks, which I'm going to
+call C subn.
+
+ align:start position:0%
+call C subn.
+ 
+
+ align:start position:0%
+call C subn.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And that's the place where I'm going to
+
+ align:start position:0%
+And that's the place where I'm going to
+ 
+
+ align:start position:0%
+And that's the place where I'm going to
+put this very next block. I'll put it in
+
+ align:start position:0%
+put this very next block. I'll put it in
+ 
+
+ align:start position:0%
+put this very next block. I'll put it in
+a different color here. Here's the new
+
+ align:start position:0%
+a different color here. Here's the new
+ 
+
+ align:start position:0%
+a different color here. Here's the new
+the next block over. And the next block
+
+ align:start position:0%
+the next block over. And the next block
+ 
+
+ align:start position:0%
+the next block over. And the next block
+over is the n plus first block.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now I want you to think about what's
+
+ align:start position:0%
+And now I want you to think about what's
+ 
+
+ align:start position:0%
+And now I want you to think about what's
+going on here. If the center of mass of
+
+ align:start position:0%
+going on here. If the center of mass of
+ 
+
+ align:start position:0%
+going on here. If the center of mass of
+the first n blocks is this number, this
+
+ align:start position:0%
+the first n blocks is this number, this
+ 
+
+ align:start position:0%
+the first n blocks is this number, this
+new one, it's of length two and its
+
+ align:start position:0%
+new one, it's of length two and its
+ 
+
+ align:start position:0%
+new one, it's of length two and its
+center of mass is one further to the
+
+ align:start position:0%
+center of mass is one further to the
+ 
+
+ align:start position:0%
+center of mass is one further to the
+right than the center of mass that we
+
+ align:start position:0%
+right than the center of mass that we
+ 
+
+ align:start position:0%
+right than the center of mass that we
+had before. So in other words, I've
+
+ align:start position:0%
+had before. So in other words, I've
+ 
+
+ align:start position:0%
+had before. So in other words, I've
+added to this configuration of n blocks
+
+ align:start position:0%
+added to this configuration of n blocks
+ 
+
+ align:start position:0%
+added to this configuration of n blocks
+one more block which is shifted whose
+
+ align:start position:0%
+one more block which is shifted whose
+ 
+
+ align:start position:0%
+one more block which is shifted whose
+center of mass is not lined up with the
+
+ align:start position:0%
+center of mass is not lined up with the
+ 
+
+ align:start position:0%
+center of mass is not lined up with the
+center of mass of this but actually over
+
+ align:start position:0%
+center of mass of this but actually over
+ 
+
+ align:start position:0%
+center of mass of this but actually over
+farther to the to the right. Right? So
+
+ align:start position:0%
+farther to the to the right. Right? So
+ 
+
+ align:start position:0%
+farther to the to the right. Right? So
+the new center of mass of this new block
+
+ align:start position:0%
+the new center of mass of this new block
+ 
+
+ align:start position:0%
+the new center of mass of this new block
+or this is the extra piece of
+
+ align:start position:0%
+or this is the extra piece of
+ 
+
+ align:start position:0%
+or this is the extra piece of
+information that I want to observe is
+
+ align:start position:0%
+information that I want to observe is
+ 
+
+ align:start position:0%
+information that I want to observe is
+that this thing has a center of mass
+
+ align:start position:0%
+that this thing has a center of mass
+ 
+
+ align:start position:0%
+that this thing has a center of mass
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+CN + 1. It's one unit over because this
+
+ align:start position:0%
+CN + 1. It's one unit over because this
+ 
+
+ align:start position:0%
+CN + 1. It's one unit over because this
+total length is two. So right in the
+
+ align:start position:0%
+total length is two. So right in the
+ 
+
+ align:start position:0%
+total length is two. So right in the
+middle there is one over
+
+ align:start position:0%
+middle there is one over
+ 
+
+ align:start position:0%
+middle there is one over
+according to my units.
+
+ align:start position:0%
+according to my units.
+ 
+
+ align:start position:0%
+according to my units.
+All right. Now, this is going to make it
+
+ align:start position:0%
+All right. Now, this is going to make it
+ 
+
+ align:start position:0%
+All right. Now, this is going to make it
+possible for me to figure out what the
+
+ align:start position:0%
+possible for me to figure out what the
+ 
+
+ align:start position:0%
+possible for me to figure out what the
+new center of mass is. So, CN + one is
+
+ align:start position:0%
+new center of mass is. So, CN + one is
+ 
+
+ align:start position:0%
+new center of mass is. So, CN + one is
+the center of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of n +1 blocks.
+
+ align:start position:0%
+of n +1 blocks.
+ 
+
+ align:start position:0%
+of n +1 blocks.
+Now, this is really only in the
+
+ align:start position:0%
+Now, this is really only in the
+ 
+
+ align:start position:0%
+Now, this is really only in the
+horizontal variable, right? I'm not I'm
+
+ align:start position:0%
+horizontal variable, right? I'm not I'm
+ 
+
+ align:start position:0%
+horizontal variable, right? I'm not I'm
+not keeping track of the center of mass.
+
+ align:start position:0%
+not keeping track of the center of mass.
+ 
+
+ align:start position:0%
+not keeping track of the center of mass.
+Actually, this thing is hard to build
+
+ align:start position:0%
+Actually, this thing is hard to build
+ 
+
+ align:start position:0%
+Actually, this thing is hard to build
+because the center of mass is also
+
+ align:start position:0%
+because the center of mass is also
+ 
+
+ align:start position:0%
+because the center of mass is also
+rising. It's getting higher and higher,
+
+ align:start position:0%
+rising. It's getting higher and higher,
+ 
+
+ align:start position:0%
+rising. It's getting higher and higher,
+but I'm only keeping track of its left
+
+ align:start position:0%
+but I'm only keeping track of its left
+ 
+
+ align:start position:0%
+but I'm only keeping track of its left
+right characteristic. So this is the
+
+ align:start position:0%
+right characteristic. So this is the
+ 
+
+ align:start position:0%
+right characteristic. So this is the
+xcoordinate of it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So now here's the idea.
+
+ align:start position:0%
+All right. So now here's the idea.
+ 
+
+ align:start position:0%
+All right. So now here's the idea.
+I'm combining the white ones, the n
+
+ align:start position:0%
+I'm combining the white ones, the n
+ 
+
+ align:start position:0%
+I'm combining the white ones, the n
+blocks, with the pink one, which is the
+
+ align:start position:0%
+blocks, with the pink one, which is the
+ 
+
+ align:start position:0%
+blocks, with the pink one, which is the
+one on the bottom. And there are n of
+
+ align:start position:0%
+one on the bottom. And there are n of
+ 
+
+ align:start position:0%
+one on the bottom. And there are n of
+the white ones, and there's one of the
+
+ align:start position:0%
+the white ones, and there's one of the
+ 
+
+ align:start position:0%
+the white ones, and there's one of the
+pink one. And so in order to get the
+
+ align:start position:0%
+pink one. And so in order to get the
+ 
+
+ align:start position:0%
+pink one. And so in order to get the
+center of mass of the hole, I have to
+
+ align:start position:0%
+center of mass of the hole, I have to
+ 
+
+ align:start position:0%
+center of mass of the hole, I have to
+take the weighted average of the two.
+
+ align:start position:0%
+take the weighted average of the two.
+ 
+
+ align:start position:0%
+take the weighted average of the two.
+That's n * cn plus 1 times the uh center
+
+ align:start position:0%
+That's n * cn plus 1 times the uh center
+ 
+
+ align:start position:0%
+That's n * cn plus 1 times the uh center
+of mass of the pink one, which is cn +
+
+ align:start position:0%
+of mass of the pink one, which is cn +
+ 
+
+ align:start position:0%
+of mass of the pink one, which is cn +
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+And then I have to divide if it's
+
+ align:start position:0%
+And then I have to divide if it's
+ 
+
+ align:start position:0%
+And then I have to divide if it's
+weighted average is a total of n plus1
+
+ align:start position:0%
+weighted average is a total of n plus1
+ 
+
+ align:start position:0%
+weighted average is a total of n plus1
+blocks by n +1.
+
+ align:start position:0%
+blocks by n +1.
+ 
+
+ align:start position:0%
+blocks by n +1.
+Now this is going to give me the new
+
+ align:start position:0%
+Now this is going to give me the new
+ 
+
+ align:start position:0%
+Now this is going to give me the new
+center of mass of my configuration at
+
+ align:start position:0%
+center of mass of my configuration at
+ 
+
+ align:start position:0%
+center of mass of my configuration at
+the n plus1 first stage.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now I can just do the arithmetic and
+
+ align:start position:0%
+And now I can just do the arithmetic and
+ 
+
+ align:start position:0%
+And now I can just do the arithmetic and
+figure out what this is.
+
+ align:start position:0%
+figure out what this is.
+ 
+
+ align:start position:0%
+figure out what this is.
+And the two CN combine I get n +1 * cn +
+
+ align:start position:0%
+And the two CN combine I get n +1 * cn +
+ 
+
+ align:start position:0%
+And the two CN combine I get n +1 * cn +
+1 / n +1.
+
+ align:start position:0%
+1 / n +1.
+ 
+
+ align:start position:0%
+1 / n +1.
+And if I combine these two things and do
+
+ align:start position:0%
+And if I combine these two things and do
+ 
+
+ align:start position:0%
+And if I combine these two things and do
+the cancellation, that gives me this
+
+ align:start position:0%
+the cancellation, that gives me this
+ 
+
+ align:start position:0%
+the cancellation, that gives me this
+recurrence formula. CN + one is equal to
+
+ align:start position:0%
+recurrence formula. CN + one is equal to
+ 
+
+ align:start position:0%
+recurrence formula. CN + one is equal to
+CN plus there's a little extra. These
+
+ align:start position:0%
+CN plus there's a little extra. These
+ 
+
+ align:start position:0%
+CN plus there's a little extra. These
+two cancel. That gives me the CN. But
+
+ align:start position:0%
+two cancel. That gives me the CN. But
+ 
+
+ align:start position:0%
+two cancel. That gives me the CN. But
+then I also have 1 over 1 uh n + one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's how much gain I can get in the
+
+ align:start position:0%
+That's how much gain I can get in the
+ 
+
+ align:start position:0%
+That's how much gain I can get in the
+center of mass by adding one more block.
+
+ align:start position:0%
+center of mass by adding one more block.
+ 
+
+ align:start position:0%
+center of mass by adding one more block.
+That's how much I can shift things over
+
+ align:start position:0%
+That's how much I can shift things over
+ 
+
+ align:start position:0%
+That's how much I can shift things over
+uh depending on how we're thinking of
+
+ align:start position:0%
+uh depending on how we're thinking of
+ 
+
+ align:start position:0%
+uh depending on how we're thinking of
+things to the to the left or the right
+
+ align:start position:0%
+things to the to the left or the right
+ 
+
+ align:start position:0%
+things to the to the left or the right
+depending on which direction we're
+
+ align:start position:0%
+depending on which direction we're
+ 
+
+ align:start position:0%
+depending on which direction we're
+building them.
+
+ align:start position:0%
+building them.
+ 
+
+ align:start position:0%
+building them.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+All right. So now I'm going to work out
+
+ align:start position:0%
+All right. So now I'm going to work out
+ 
+
+ align:start position:0%
+All right. So now I'm going to work out
+the formulas. First of all, C1 that was
+
+ align:start position:0%
+the formulas. First of all, C1 that was
+ 
+
+ align:start position:0%
+the formulas. First of all, C1 that was
+the center of the first block. I put its
+
+ align:start position:0%
+the center of the first block. I put its
+ 
+
+ align:start position:0%
+the center of the first block. I put its
+left end at zero. The center of the
+
+ align:start position:0%
+left end at zero. The center of the
+ 
+
+ align:start position:0%
+left end at zero. The center of the
+first block is at one. That means that
+
+ align:start position:0%
+first block is at one. That means that
+ 
+
+ align:start position:0%
+first block is at one. That means that
+C1 is one.
+
+ align:start position:0%
+C1 is one.
+ 
+
+ align:start position:0%
+C1 is one.
+Okay. C2
+
+ align:start position:0%
+Okay. C2
+ 
+
+ align:start position:0%
+Okay. C2
+according to this formula and actually I
+
+ align:start position:0%
+according to this formula and actually I
+ 
+
+ align:start position:0%
+according to this formula and actually I
+worked it out. We'll check it in a
+
+ align:start position:0%
+worked it out. We'll check it in a
+ 
+
+ align:start position:0%
+worked it out. We'll check it in a
+second. C2 is C1 + 1 /2, right? That's
+
+ align:start position:0%
+second. C2 is C1 + 1 /2, right? That's
+ 
+
+ align:start position:0%
+second. C2 is C1 + 1 /2, right? That's
+the case N= 1. So this is 1 plus a half.
+
+ align:start position:0%
+the case N= 1. So this is 1 plus a half.
+ 
+
+ align:start position:0%
+the case N= 1. So this is 1 plus a half.
+That's what we already did.
+
+ align:start position:0%
+That's what we already did.
+ 
+
+ align:start position:0%
+That's what we already did.
+That's the three halves number. And now
+
+ align:start position:0%
+That's the three halves number. And now
+ 
+
+ align:start position:0%
+That's the three halves number. And now
+the next one is C2 + a3.
+
+ align:start position:0%
+the next one is C2 + a3.
+ 
+
+ align:start position:0%
+the next one is C2 + a3.
+That's the formula again. And so that
+
+ align:start position:0%
+That's the formula again. And so that
+ 
+
+ align:start position:0%
+That's the formula again. And so that
+comes out to be 1 + a half plus a third.
+
+ align:start position:0%
+comes out to be 1 + a half plus a third.
+ 
+
+ align:start position:0%
+comes out to be 1 + a half plus a third.
+And now you can see what the pattern is.
+
+ align:start position:0%
+And now you can see what the pattern is.
+ 
+
+ align:start position:0%
+And now you can see what the pattern is.
+CN,
+
+ align:start position:0%
+CN,
+ 
+
+ align:start position:0%
+CN,
+if you just keep on going here, CN is
+
+ align:start position:0%
+if you just keep on going here, CN is
+ 
+
+ align:start position:0%
+if you just keep on going here, CN is
+going to be 1 + a half plus a third plus
+
+ align:start position:0%
+going to be 1 + a half plus a third plus
+ 
+
+ align:start position:0%
+going to be 1 + a half plus a third plus
+a 4th
+
+ align:start position:0%
+a 4th
+ 
+
+ align:start position:0%
+a 4th
+plus 1 / n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now I would like you to vote again.
+
+ align:start position:0%
+So now I would like you to vote again.
+ 
+
+ align:start position:0%
+So now I would like you to vote again.
+Do you think I can now that we have the
+
+ align:start position:0%
+Do you think I can now that we have the
+ 
+
+ align:start position:0%
+Do you think I can now that we have the
+formula, do you think I can get over to
+
+ align:start position:0%
+formula, do you think I can get over to
+ 
+
+ align:start position:0%
+formula, do you think I can get over to
+here?
+
+ align:start position:0%
+here?
+ 
+
+ align:start position:0%
+here?
+How many people think I can get over to
+
+ align:start position:0%
+How many people think I can get over to
+ 
+
+ align:start position:0%
+How many people think I can get over to
+here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How many people think I can't get over
+
+ align:start position:0%
+How many people think I can't get over
+ 
+
+ align:start position:0%
+How many people think I can't get over
+to here? Oh, there's still a lot of
+
+ align:start position:0%
+to here? Oh, there's still a lot of
+ 
+
+ align:start position:0%
+to here? Oh, there's still a lot of
+people who do. So it's still almost
+
+ align:start position:0%
+people who do. So it's still almost
+ 
+
+ align:start position:0%
+people who do. So it's still almost
+50/50. That's that's amazing. Well, so
+
+ align:start position:0%
+50/50. That's that's amazing. Well, so
+ 
+
+ align:start position:0%
+50/50. That's that's amazing. Well, so
+we'll address that in a in a in a few
+
+ align:start position:0%
+we'll address that in a in a in a few
+ 
+
+ align:start position:0%
+we'll address that in a in a in a few
+minutes. So now let me tell you what's
+
+ align:start position:0%
+minutes. So now let me tell you what's
+ 
+
+ align:start position:0%
+minutes. So now let me tell you what's
+going on.
+
+ align:start position:0%
+going on.
+ 
+
+ align:start position:0%
+going on.
+This CN of course is the same as what we
+
+ align:start position:0%
+This CN of course is the same as what we
+ 
+
+ align:start position:0%
+This CN of course is the same as what we
+called last time Sn.
+
+ align:start position:0%
+called last time Sn.
+ 
+
+ align:start position:0%
+called last time Sn.
+And remember that we actually estimated
+
+ align:start position:0%
+And remember that we actually estimated
+ 
+
+ align:start position:0%
+And remember that we actually estimated
+the size of this guy. This is related to
+
+ align:start position:0%
+the size of this guy. This is related to
+ 
+
+ align:start position:0%
+the size of this guy. This is related to
+what's called the harmonic series. And
+
+ align:start position:0%
+what's called the harmonic series. And
+ 
+
+ align:start position:0%
+what's called the harmonic series. And
+what we showed was that log n is less
+
+ align:start position:0%
+what we showed was that log n is less
+ 
+
+ align:start position:0%
+what we showed was that log n is less
+than sn which is less than s n + one.
+
+ align:start position:0%
+than sn which is less than s n + one.
+ 
+
+ align:start position:0%
+than sn which is less than s n + one.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Now I'm going to call your attention to
+
+ align:start position:0%
+Now I'm going to call your attention to
+ 
+
+ align:start position:0%
+Now I'm going to call your attention to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+red part which is the divergence part of
+
+ align:start position:0%
+red part which is the divergence part of
+ 
+
+ align:start position:0%
+red part which is the divergence part of
+this estimate which is this one for the
+
+ align:start position:0%
+this estimate which is this one for the
+ 
+
+ align:start position:0%
+this estimate which is this one for the
+time being. All right, which is saying
+
+ align:start position:0%
+time being. All right, which is saying
+ 
+
+ align:start position:0%
+time being. All right, which is saying
+that this thing is growing. And what
+
+ align:start position:0%
+that this thing is growing. And what
+ 
+
+ align:start position:0%
+that this thing is growing. And what
+this is saying is that as n goes to
+
+ align:start position:0%
+this is saying is that as n goes to
+ 
+
+ align:start position:0%
+this is saying is that as n goes to
+infinity,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log n goes to infinity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that means
+
+ align:start position:0%
+So that means
+ 
+
+ align:start position:0%
+So that means
+that um sn goes to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of this inequality here. It's
+
+ align:start position:0%
+because of this inequality here. It's
+ 
+
+ align:start position:0%
+because of this inequality here. It's
+bigger than log n. And so if n is big
+
+ align:start position:0%
+bigger than log n. And so if n is big
+ 
+
+ align:start position:0%
+bigger than log n. And so if n is big
+enough, we can get as far as we like.
+
+ align:start position:0%
+enough, we can get as far as we like.
+ 
+
+ align:start position:0%
+enough, we can get as far as we like.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So I can get to here. And at least half
+
+ align:start position:0%
+So I can get to here. And at least half
+ 
+
+ align:start position:0%
+So I can get to here. And at least half
+of you, at least the ones who voted.
+
+ align:start position:0%
+of you, at least the ones who voted.
+ 
+
+ align:start position:0%
+of you, at least the ones who voted.
+That was I don't know. We have a quorum
+
+ align:start position:0%
+That was I don't know. We have a quorum
+ 
+
+ align:start position:0%
+That was I don't know. We have a quorum
+here, but I'm not sure. We certainly
+
+ align:start position:0%
+here, but I'm not sure. We certainly
+ 
+
+ align:start position:0%
+here, but I'm not sure. We certainly
+didn't have a majority on either side.
+
+ align:start position:0%
+didn't have a majority on either side.
+ 
+
+ align:start position:0%
+didn't have a majority on either side.
+Anyway,
+
+ align:start position:0%
+Anyway,
+ 
+
+ align:start position:0%
+Anyway,
+this thing does go to infinity. So in
+
+ align:start position:0%
+this thing does go to infinity. So in
+ 
+
+ align:start position:0%
+this thing does go to infinity. So in
+principle, if I had enough blocks, I
+
+ align:start position:0%
+principle, if I had enough blocks, I
+ 
+
+ align:start position:0%
+principle, if I had enough blocks, I
+could get it over to get it over to
+
+ align:start position:0%
+could get it over to get it over to
+ 
+
+ align:start position:0%
+could get it over to get it over to
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+All right. And that's the meaning of
+
+ align:start position:0%
+All right. And that's the meaning of
+ 
+
+ align:start position:0%
+All right. And that's the meaning of
+divergence in this case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+On the other hand,
+
+ align:start position:0%
+On the other hand,
+ 
+
+ align:start position:0%
+On the other hand,
+I want to discuss with you and the
+
+ align:start position:0%
+I want to discuss with you and the
+ 
+
+ align:start position:0%
+I want to discuss with you and the
+reason why I use this example is I want
+
+ align:start position:0%
+reason why I use this example is I want
+ 
+
+ align:start position:0%
+reason why I use this example is I want
+to discuss with you also what's going on
+
+ align:start position:0%
+to discuss with you also what's going on
+ 
+
+ align:start position:0%
+to discuss with you also what's going on
+with this other inequality here and what
+
+ align:start position:0%
+with this other inequality here and what
+ 
+
+ align:start position:0%
+with this other inequality here and what
+its significance is
+
+ align:start position:0%
+its significance is
+ 
+
+ align:start position:0%
+its significance is
+which is that it's going to take us a
+
+ align:start position:0%
+which is that it's going to take us a
+ 
+
+ align:start position:0%
+which is that it's going to take us a
+lot of numbers n a lot of blocks to get
+
+ align:start position:0%
+lot of numbers n a lot of blocks to get
+ 
+
+ align:start position:0%
+lot of numbers n a lot of blocks to get
+up to a certain level. In other words, I
+
+ align:start position:0%
+up to a certain level. In other words, I
+ 
+
+ align:start position:0%
+up to a certain level. In other words, I
+can't do it with just eight blocks or
+
+ align:start position:0%
+can't do it with just eight blocks or
+ 
+
+ align:start position:0%
+can't do it with just eight blocks or
+nine blocks. In order to get over here,
+
+ align:start position:0%
+nine blocks. In order to get over here,
+ 
+
+ align:start position:0%
+nine blocks. In order to get over here,
+I'd have to use quite a few of them.
+
+ align:start position:0%
+I'd have to use quite a few of them.
+ 
+
+ align:start position:0%
+I'd have to use quite a few of them.
+So, let's just see how many it is.
+
+ align:start position:0%
+So, let's just see how many it is.
+ 
+
+ align:start position:0%
+So, let's just see how many it is.
+So, I I worked this out carefully
+
+ align:start position:0%
+So, I I worked this out carefully
+ 
+
+ align:start position:0%
+So, I I worked this out carefully
+and let's see what I got.
+
+ align:start position:0%
+and let's see what I got.
+ 
+
+ align:start position:0%
+and let's see what I got.
+So to get
+
+ align:start position:0%
+So to get
+ 
+
+ align:start position:0%
+So to get
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+the lab tables.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Um this this distance here I
+
+ align:start position:0%
+All right. Um this this distance here I
+ 
+
+ align:start position:0%
+All right. Um this this distance here I
+I already did this secretly. Uh but I I
+
+ align:start position:0%
+I already did this secretly. Uh but I I
+ 
+
+ align:start position:0%
+I already did this secretly. Uh but I I
+don't actually even have enough of these
+
+ align:start position:0%
+don't actually even have enough of these
+ 
+
+ align:start position:0%
+don't actually even have enough of these
+to show you, but well 1 2 3 4 5 6 and a
+
+ align:start position:0%
+to show you, but well 1 2 3 4 5 6 and a
+ 
+
+ align:start position:0%
+to show you, but well 1 2 3 4 5 6 and a
+half. I guess that's enough. So it's six
+
+ align:start position:0%
+half. I guess that's enough. So it's six
+ 
+
+ align:start position:0%
+half. I guess that's enough. So it's six
+and a half. So it's it's two lab tables
+
+ align:start position:0%
+and a half. So it's it's two lab tables
+ 
+
+ align:start position:0%
+and a half. So it's it's two lab tables
+is 13 of these blocks. All right. So
+
+ align:start position:0%
+is 13 of these blocks. All right. So
+ 
+
+ align:start position:0%
+is 13 of these blocks. All right. So
+there are 13 blocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is equal to 26 units.
+
+ align:start position:0%
+which is equal to 26 units.
+ 
+
+ align:start position:0%
+which is equal to 26 units.
+Okay. That's how far to get across I
+
+ align:start position:0%
+Okay. That's how far to get across I
+ 
+
+ align:start position:0%
+Okay. That's how far to get across I
+need. And uh the first one is already
+
+ align:start position:0%
+need. And uh the first one is already
+ 
+
+ align:start position:0%
+need. And uh the first one is already
+two. So it's really 26 minus 2 which is
+
+ align:start position:0%
+two. So it's really 26 minus 2 which is
+ 
+
+ align:start position:0%
+two. So it's really 26 minus 2 which is
+24 which is that's what I need. Okay.
+
+ align:start position:0%
+24 which is that's what I need. Okay.
+ 
+
+ align:start position:0%
+24 which is that's what I need. Okay.
+So I need log n to be equal to 24
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly speaking in order to get that
+
+ align:start position:0%
+roughly speaking in order to get that
+ 
+
+ align:start position:0%
+roughly speaking in order to get that
+far. So let's just see how how how big
+
+ align:start position:0%
+far. So let's just see how how how big
+ 
+
+ align:start position:0%
+far. So let's just see how how how big
+that is. All right,
+
+ align:start position:0%
+that is. All right,
+ 
+
+ align:start position:0%
+that is. All right,
+I think I worked this out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's see that means that n is equal
+
+ align:start position:0%
+So let's see that means that n is equal
+ 
+
+ align:start position:0%
+So let's see that means that n is equal
+to e to the 24th.
+
+ align:start position:0%
+to e to the 24th.
+ 
+
+ align:start position:0%
+to e to the 24th.
+And if you if you realize that these
+
+ align:start position:0%
+And if you if you realize that these
+ 
+
+ align:start position:0%
+And if you if you realize that these
+blocks
+
+ align:start position:0%
+blocks
+ 
+
+ align:start position:0%
+blocks
+are 3 cm high.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's see how many how many that
+
+ align:start position:0%
+Okay, let's see how many how many that
+ 
+
+ align:start position:0%
+Okay, let's see how many how many that
+we would need here. That's kind of a
+
+ align:start position:0%
+we would need here. That's kind of a
+ 
+
+ align:start position:0%
+we would need here. That's kind of a
+lot. Let's see. It's 3 cm
+
+ align:start position:0%
+lot. Let's see. It's 3 cm
+ 
+
+ align:start position:0%
+lot. Let's see. It's 3 cm
+time um e 24th which is about 8 * 10 the
+
+ align:start position:0%
+time um e 24th which is about 8 * 10 the
+ 
+
+ align:start position:0%
+time um e 24th which is about 8 * 10 the
+8 m.
+
+ align:start position:0%
+8 m.
+ 
+
+ align:start position:0%
+8 m.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And that is twice the distance to the
+
+ align:start position:0%
+And that is twice the distance to the
+ 
+
+ align:start position:0%
+And that is twice the distance to the
+moon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, um, so, okay, I could do
+
+ align:start position:0%
+All right. So, um, so, okay, I could do
+ 
+
+ align:start position:0%
+All right. So, um, so, okay, I could do
+it maybe,
+
+ align:start position:0%
+it maybe,
+ 
+
+ align:start position:0%
+it maybe,
+but, uh, I would need a lot of blocks,
+
+ align:start position:0%
+but, uh, I would need a lot of blocks,
+ 
+
+ align:start position:0%
+but, uh, I would need a lot of blocks,
+right? It's not not very plausible here.
+
+ align:start position:0%
+right? It's not not very plausible here.
+ 
+
+ align:start position:0%
+right? It's not not very plausible here.
+All right, so those of you who voted
+
+ align:start position:0%
+All right, so those of you who voted
+ 
+
+ align:start position:0%
+All right, so those of you who voted
+against this were actually sort of half
+
+ align:start position:0%
+against this were actually sort of half
+ 
+
+ align:start position:0%
+against this were actually sort of half
+right. And in fact, if you wanted to get
+
+ align:start position:0%
+right. And in fact, if you wanted to get
+ 
+
+ align:start position:0%
+right. And in fact, if you wanted to get
+it to the wall over there, which is over
+
+ align:start position:0%
+it to the wall over there, which is over
+ 
+
+ align:start position:0%
+it to the wall over there, which is over
+30 pe feet, the height would be about
+
+ align:start position:0%
+30 pe feet, the height would be about
+ 
+
+ align:start position:0%
+30 pe feet, the height would be about
+the um diameter of the observable
+
+ align:start position:0%
+the um diameter of the observable
+ 
+
+ align:start position:0%
+the um diameter of the observable
+universe. That's kind of kind of a long
+
+ align:start position:0%
+universe. That's kind of kind of a long
+ 
+
+ align:start position:0%
+universe. That's kind of kind of a long
+way. Um there there's there's one other
+
+ align:start position:0%
+way. Um there there's there's one other
+ 
+
+ align:start position:0%
+way. Um there there's there's one other
+thing that that that I wanted to to
+
+ align:start position:0%
+thing that that that I wanted to to
+ 
+
+ align:start position:0%
+thing that that that I wanted to to
+point out to you about this shape here,
+
+ align:start position:0%
+point out to you about this shape here,
+ 
+
+ align:start position:0%
+point out to you about this shape here,
+which is that if you if you lean to the
+
+ align:start position:0%
+which is that if you if you lean to the
+ 
+
+ align:start position:0%
+which is that if you if you lean to the
+left, right, if you if you put your head
+
+ align:start position:0%
+left, right, if you if you put your head
+ 
+
+ align:start position:0%
+left, right, if you if you put your head
+like this, of course, you have to be on
+
+ align:start position:0%
+like this, of course, you have to be on
+ 
+
+ align:start position:0%
+like this, of course, you have to be on
+your side to look at it. This this curve
+
+ align:start position:0%
+your side to look at it. This this curve
+ 
+
+ align:start position:0%
+your side to look at it. This this curve
+um is is the um
+
+ align:start position:0%
+um is is the um
+ 
+
+ align:start position:0%
+um is is the um
+is the shape of a of a of a logarithmic
+
+ align:start position:0%
+is the shape of a of a of a logarithmic
+ 
+
+ align:start position:0%
+is the shape of a of a of a logarithmic
+curve. So in other words, if you think
+
+ align:start position:0%
+curve. So in other words, if you think
+ 
+
+ align:start position:0%
+curve. So in other words, if you think
+of this, the the vertical is the x- axis
+
+ align:start position:0%
+of this, the the vertical is the x- axis
+ 
+
+ align:start position:0%
+of this, the the vertical is the x- axis
+and the the the horizontal that way is
+
+ align:start position:0%
+and the the the horizontal that way is
+ 
+
+ align:start position:0%
+and the the the horizontal that way is
+the vertical is the up direction. Then
+
+ align:start position:0%
+the vertical is the up direction. Then
+ 
+
+ align:start position:0%
+the vertical is the up direction. Then
+this thing is growing very very very
+
+ align:start position:0%
+this thing is growing very very very
+ 
+
+ align:start position:0%
+this thing is growing very very very
+very slowly. If you send the x-axis all
+
+ align:start position:0%
+very slowly. If you send the x-axis all
+ 
+
+ align:start position:0%
+very slowly. If you send the x-axis all
+the way up to the moon, you're still the
+
+ align:start position:0%
+the way up to the moon, you're still the
+ 
+
+ align:start position:0%
+the way up to the moon, you're still the
+graph still hasn't gotten across the lab
+
+ align:start position:0%
+graph still hasn't gotten across the lab
+ 
+
+ align:start position:0%
+graph still hasn't gotten across the lab
+tables here. It's only partway there. If
+
+ align:start position:0%
+tables here. It's only partway there. If
+ 
+
+ align:start position:0%
+tables here. It's only partway there. If
+you go twice the distance to the moon up
+
+ align:start position:0%
+you go twice the distance to the moon up
+ 
+
+ align:start position:0%
+you go twice the distance to the moon up
+that way, it's gotten finally to that
+
+ align:start position:0%
+that way, it's gotten finally to that
+ 
+
+ align:start position:0%
+that way, it's gotten finally to that
+end. All right. So that's how slowly the
+
+ align:start position:0%
+end. All right. So that's how slowly the
+ 
+
+ align:start position:0%
+end. All right. So that's how slowly the
+logarithm grows. It grows very very
+
+ align:start position:0%
+logarithm grows. It grows very very
+ 
+
+ align:start position:0%
+logarithm grows. It grows very very
+slowly. And if you look at it another
+
+ align:start position:0%
+slowly. And if you look at it another
+ 
+
+ align:start position:0%
+slowly. And if you look at it another
+way, if you stand on your head, you can
+
+ align:start position:0%
+way, if you stand on your head, you can
+ 
+
+ align:start position:0%
+way, if you stand on your head, you can
+see a uh an exponential curve and see so
+
+ align:start position:0%
+see a uh an exponential curve and see so
+ 
+
+ align:start position:0%
+see a uh an exponential curve and see so
+you get some sense as to the growth
+
+ align:start position:0%
+you get some sense as to the growth
+ 
+
+ align:start position:0%
+you get some sense as to the growth
+properties of these functions. And
+
+ align:start position:0%
+properties of these functions. And
+ 
+
+ align:start position:0%
+properties of these functions. And
+fortunately,
+
+ align:start position:0%
+fortunately,
+ 
+
+ align:start position:0%
+fortunately,
+these are protecting us from uh from all
+
+ align:start position:0%
+these are protecting us from uh from all
+ 
+
+ align:start position:0%
+these are protecting us from uh from all
+kinds of stuff that would happen if
+
+ align:start position:0%
+kinds of stuff that would happen if
+ 
+
+ align:start position:0%
+kinds of stuff that would happen if
+there weren't exponentially small tails
+
+ align:start position:0%
+there weren't exponentially small tails
+ 
+
+ align:start position:0%
+there weren't exponentially small tails
+in the world. like you know I could walk
+
+ align:start position:0%
+in the world. like you know I could walk
+ 
+
+ align:start position:0%
+in the world. like you know I could walk
+through this wall which I wouldn't like
+
+ align:start position:0%
+through this wall which I wouldn't like
+ 
+
+ align:start position:0%
+through this wall which I wouldn't like
+doing.
+
+ align:start position:0%
+doing.
+ 
+
+ align:start position:0%
+doing.
+Um okay
+
+ align:start position:0%
+Um okay
+ 
+
+ align:start position:0%
+Um okay
+now so this is our last example and and
+
+ align:start position:0%
+now so this is our last example and and
+ 
+
+ align:start position:0%
+now so this is our last example and and
+the important number we for
+
+ align:start position:0%
+the important number we for
+ 
+
+ align:start position:0%
+the important number we for
+unfortunately we didn't discover another
+
+ align:start position:0%
+unfortunately we didn't discover another
+ 
+
+ align:start position:0%
+unfortunately we didn't discover another
+important number there wasn't an amazing
+
+ align:start position:0%
+important number there wasn't an amazing
+ 
+
+ align:start position:0%
+important number there wasn't an amazing
+number place where this stopped all we
+
+ align:start position:0%
+number place where this stopped all we
+ 
+
+ align:start position:0%
+number place where this stopped all we
+discovered again is is some property of
+
+ align:start position:0%
+discovered again is is some property of
+ 
+
+ align:start position:0%
+discovered again is is some property of
+infinity so infinity is still a nice
+
+ align:start position:0%
+infinity so infinity is still a nice
+ 
+
+ align:start position:0%
+infinity so infinity is still a nice
+number and the theme here is just that
+
+ align:start position:0%
+number and the theme here is just that
+ 
+
+ align:start position:0%
+number and the theme here is just that
+infinity isn't just one thing it's a has
+
+ align:start position:0%
+infinity isn't just one thing it's a has
+ 
+
+ align:start position:0%
+infinity isn't just one thing it's a has
+a character which is a rate of growth
+
+ align:start position:0%
+a character which is a rate of growth
+ 
+
+ align:start position:0%
+a character which is a rate of growth
+and you shouldn't just think of there
+
+ align:start position:0%
+and you shouldn't just think of there
+ 
+
+ align:start position:0%
+and you shouldn't just think of there
+being one order of infinity. There are
+
+ align:start position:0%
+being one order of infinity. There are
+ 
+
+ align:start position:0%
+being one order of infinity. There are
+lots of different orders and some of
+
+ align:start position:0%
+lots of different orders and some of
+ 
+
+ align:start position:0%
+lots of different orders and some of
+them have different meaning from others.
+
+ align:start position:0%
+them have different meaning from others.
+ 
+
+ align:start position:0%
+them have different meaning from others.
+All right, so that's the the theme I
+
+ align:start position:0%
+All right, so that's the the theme I
+ 
+
+ align:start position:0%
+All right, so that's the the theme I
+wanted to to do and just have an a
+
+ align:start position:0%
+wanted to to do and just have an a
+ 
+
+ align:start position:0%
+wanted to to do and just have an a
+visceral example of infinity. Now, we're
+
+ align:start position:0%
+visceral example of infinity. Now, we're
+ 
+
+ align:start position:0%
+visceral example of infinity. Now, we're
+going to move on now to some other kinds
+
+ align:start position:0%
+going to move on now to some other kinds
+ 
+
+ align:start position:0%
+going to move on now to some other kinds
+of uh techniques and this is going to be
+
+ align:start position:0%
+of uh techniques and this is going to be
+ 
+
+ align:start position:0%
+of uh techniques and this is going to be
+our last subject.
+
+ align:start position:0%
+our last subject.
+ 
+
+ align:start position:0%
+our last subject.
+What we're going to talk about is what
+
+ align:start position:0%
+What we're going to talk about is what
+ 
+
+ align:start position:0%
+What we're going to talk about is what
+are known as power series.
+
+ align:start position:0%
+are known as power series.
+ 
+
+ align:start position:0%
+are known as power series.
+Now, we've already seen our first power
+
+ align:start position:0%
+Now, we've already seen our first power
+ 
+
+ align:start position:0%
+Now, we've already seen our first power
+series,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to remind you of that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, here we are with power series.
+
+ align:start position:0%
+So, here we are with power series.
+ 
+
+ align:start position:0%
+So, here we are with power series.
+Our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first series was was this one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we mentioned last time that it was
+
+ align:start position:0%
+And we mentioned last time that it was
+ 
+
+ align:start position:0%
+And we mentioned last time that it was
+equal to 1 over 1 - x
+
+ align:start position:0%
+equal to 1 over 1 - x
+ 
+
+ align:start position:0%
+equal to 1 over 1 - x
+for x less than one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This one is known as the geometric
+
+ align:start position:0%
+This one is known as the geometric
+ 
+
+ align:start position:0%
+This one is known as the geometric
+series. I didn't use the letter x last
+
+ align:start position:0%
+series. I didn't use the letter x last
+ 
+
+ align:start position:0%
+series. I didn't use the letter x last
+time. I used the letter a. But this is
+
+ align:start position:0%
+time. I used the letter a. But this is
+ 
+
+ align:start position:0%
+time. I used the letter a. But this is
+known as a geometric series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I'm going to show you one reason why
+
+ align:start position:0%
+Now I'm going to show you one reason why
+ 
+
+ align:start position:0%
+Now I'm going to show you one reason why
+this is true,
+
+ align:start position:0%
+this is true,
+ 
+
+ align:start position:0%
+this is true,
+why the formula holds,
+
+ align:start position:0%
+why the formula holds,
+ 
+
+ align:start position:0%
+why the formula holds,
+and it's just the kind of manipulation
+
+ align:start position:0%
+and it's just the kind of manipulation
+ 
+
+ align:start position:0%
+and it's just the kind of manipulation
+that uh was done when these things were
+
+ align:start position:0%
+that uh was done when these things were
+ 
+
+ align:start position:0%
+that uh was done when these things were
+first introduced. Uh and here's the the
+
+ align:start position:0%
+first introduced. Uh and here's the the
+ 
+
+ align:start position:0%
+first introduced. Uh and here's the the
+idea of a of a proof.
+
+ align:start position:0%
+idea of a of a proof.
+ 
+
+ align:start position:0%
+idea of a of a proof.
+So suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this sum is equal to some number s
+
+ align:start position:0%
+that this sum is equal to some number s
+ 
+
+ align:start position:0%
+that this sum is equal to some number s
+which is the sum of all of the these
+
+ align:start position:0%
+which is the sum of all of the these
+ 
+
+ align:start position:0%
+which is the sum of all of the these
+numbers here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The first thing that I'm going to do is
+
+ align:start position:0%
+The first thing that I'm going to do is
+ 
+
+ align:start position:0%
+The first thing that I'm going to do is
+I'm going to multiply by x.
+
+ align:start position:0%
+I'm going to multiply by x.
+ 
+
+ align:start position:0%
+I'm going to multiply by x.
+Okay. So if I multiply by x,
+
+ align:start position:0%
+Okay. So if I multiply by x,
+ 
+
+ align:start position:0%
+Okay. So if I multiply by x,
+let's think about that. I multiply by x
+
+ align:start position:0%
+let's think about that. I multiply by x
+ 
+
+ align:start position:0%
+let's think about that. I multiply by x
+on both the left and the right hand
+
+ align:start position:0%
+on both the left and the right hand
+ 
+
+ align:start position:0%
+on both the left and the right hand
+side. Then on the left side I get x +
+
+ align:start position:0%
+side. Then on the left side I get x +
+ 
+
+ align:start position:0%
+side. Then on the left side I get x +
+x^2 + x cubed plus and so forth. And on
+
+ align:start position:0%
+x^2 + x cubed plus and so forth. And on
+ 
+
+ align:start position:0%
+x^2 + x cubed plus and so forth. And on
+the right side I get s * x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now I'm going to subtract the two
+
+ align:start position:0%
+And now I'm going to subtract the two
+ 
+
+ align:start position:0%
+And now I'm going to subtract the two
+equations one from the other. And
+
+ align:start position:0%
+equations one from the other. And
+ 
+
+ align:start position:0%
+equations one from the other. And
+there's a very very substantial
+
+ align:start position:0%
+there's a very very substantial
+ 
+
+ align:start position:0%
+there's a very very substantial
+cancellation. This whole tail here gets
+
+ align:start position:0%
+cancellation. This whole tail here gets
+ 
+
+ align:start position:0%
+cancellation. This whole tail here gets
+canceled off. And the only thing that's
+
+ align:start position:0%
+canceled off. And the only thing that's
+ 
+
+ align:start position:0%
+canceled off. And the only thing that's
+left is the one. So when I subtract
+
+ align:start position:0%
+left is the one. So when I subtract
+ 
+
+ align:start position:0%
+left is the one. So when I subtract
+I get one on the left hand side and on
+
+ align:start position:0%
+I get one on the left hand side and on
+ 
+
+ align:start position:0%
+I get one on the left hand side and on
+the right hand side I get s
+
+ align:start position:0%
+the right hand side I get s
+ 
+
+ align:start position:0%
+the right hand side I get s
+time uh minus s * x.
+
+ align:start position:0%
+time uh minus s * x.
+ 
+
+ align:start position:0%
+time uh minus s * x.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now uh that can be rewritten as s *
+
+ align:start position:0%
+And now uh that can be rewritten as s *
+ 
+
+ align:start position:0%
+And now uh that can be rewritten as s *
+1 - x. And so I've got my my formula
+
+ align:start position:0%
+1 - x. And so I've got my my formula
+ 
+
+ align:start position:0%
+1 - x. And so I've got my my formula
+here. This is 1 over 1 - x is equal to
+
+ align:start position:0%
+here. This is 1 over 1 - x is equal to
+ 
+
+ align:start position:0%
+here. This is 1 over 1 - x is equal to
+s.
+
+ align:start position:0%
+s.
+ 
+
+ align:start position:0%
+s.
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+this reasoning
+
+ align:start position:0%
+this reasoning
+ 
+
+ align:start position:0%
+this reasoning
+is has one flaw.
+
+ align:start position:0%
+is has one flaw.
+ 
+
+ align:start position:0%
+is has one flaw.
+It's not complete. And the this
+
+ align:start position:0%
+It's not complete. And the this
+ 
+
+ align:start position:0%
+It's not complete. And the this
+reasoning is is is basically correct
+
+ align:start position:0%
+reasoning is is is basically correct
+ 
+
+ align:start position:0%
+reasoning is is is basically correct
+but it's incomplete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh because
+
+ align:start position:0%
+uh because
+ 
+
+ align:start position:0%
+uh because
+it requires
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that s exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example it doesn't make any sense in
+
+ align:start position:0%
+for example it doesn't make any sense in
+ 
+
+ align:start position:0%
+for example it doesn't make any sense in
+the case x= 1. So for example in the
+
+ align:start position:0%
+the case x= 1. So for example in the
+ 
+
+ align:start position:0%
+the case x= 1. So for example in the
+case s x x= 1 we have 1 + 1 + 1 + etc
+
+ align:start position:0%
+case s x x= 1 we have 1 + 1 + 1 + etc
+ 
+
+ align:start position:0%
+case s x x= 1 we have 1 + 1 + 1 + etc
+equals whatever we call s and then when
+
+ align:start position:0%
+equals whatever we call s and then when
+ 
+
+ align:start position:0%
+equals whatever we call s and then when
+we multiply through by 1 we get 1 + 1 +
+
+ align:start position:0%
+we multiply through by 1 we get 1 + 1 +
+ 
+
+ align:start position:0%
+we multiply through by 1 we get 1 + 1 +
+1 +
+
+ align:start position:0%
+1 +
+ 
+
+ align:start position:0%
+1 +
+= s * 1. And now you see that the
+
+ align:start position:0%
+= s * 1. And now you see that the
+ 
+
+ align:start position:0%
+= s * 1. And now you see that the
+subtraction gives us infinity minus
+
+ align:start position:0%
+subtraction gives us infinity minus
+ 
+
+ align:start position:0%
+subtraction gives us infinity minus
+infinity is equal to infinity minus
+
+ align:start position:0%
+infinity is equal to infinity minus
+ 
+
+ align:start position:0%
+infinity is equal to infinity minus
+infinity. That's what's really going on
+
+ align:start position:0%
+infinity. That's what's really going on
+ 
+
+ align:start position:0%
+infinity. That's what's really going on
+in the argument in this in this context.
+
+ align:start position:0%
+in the argument in this in this context.
+ 
+
+ align:start position:0%
+in the argument in this in this context.
+So it's just nonsense. I mean it doesn't
+
+ align:start position:0%
+So it's just nonsense. I mean it doesn't
+ 
+
+ align:start position:0%
+So it's just nonsense. I mean it doesn't
+give us anything meaningful.
+
+ align:start position:0%
+give us anything meaningful.
+ 
+
+ align:start position:0%
+give us anything meaningful.
+So the the this argument it's great and
+
+ align:start position:0%
+So the the this argument it's great and
+ 
+
+ align:start position:0%
+So the the this argument it's great and
+it gives us the right answer but not
+
+ align:start position:0%
+it gives us the right answer but not
+ 
+
+ align:start position:0%
+it gives us the right answer but not
+always and the times when it gives us
+
+ align:start position:0%
+always and the times when it gives us
+ 
+
+ align:start position:0%
+always and the times when it gives us
+the answer the correct answer is when
+
+ align:start position:0%
+the answer the correct answer is when
+ 
+
+ align:start position:0%
+the answer the correct answer is when
+the series is convergent
+
+ align:start position:0%
+the series is convergent
+ 
+
+ align:start position:0%
+the series is convergent
+and that's why we care about convergence
+
+ align:start position:0%
+and that's why we care about convergence
+ 
+
+ align:start position:0%
+and that's why we care about convergence
+because we want manipulations like this
+
+ align:start position:0%
+because we want manipulations like this
+ 
+
+ align:start position:0%
+because we want manipulations like this
+to be allowed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the good case, this is the red case
+
+ align:start position:0%
+So the good case, this is the red case
+ 
+
+ align:start position:0%
+So the good case, this is the red case
+that we were describing last time and
+
+ align:start position:0%
+that we were describing last time and
+ 
+
+ align:start position:0%
+that we were describing last time and
+it's the bad case. But what we want is
+
+ align:start position:0%
+it's the bad case. But what we want is
+ 
+
+ align:start position:0%
+it's the bad case. But what we want is
+the good case, the convergent case. And
+
+ align:start position:0%
+the good case, the convergent case. And
+ 
+
+ align:start position:0%
+the good case, the convergent case. And
+that is the case when x is less than
+
+ align:start position:0%
+that is the case when x is less than
+ 
+
+ align:start position:0%
+that is the case when x is less than
+one. So this is the convergent case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now. Okay. So there are there are much
+
+ align:start position:0%
+now. Okay. So there are there are much
+ 
+
+ align:start position:0%
+now. Okay. So there are there are much
+more detailed things to check exactly
+
+ align:start position:0%
+more detailed things to check exactly
+ 
+
+ align:start position:0%
+more detailed things to check exactly
+what's going on. But I'm going to just
+
+ align:start position:0%
+what's going on. But I'm going to just
+ 
+
+ align:start position:0%
+what's going on. But I'm going to just
+say general words about how you
+
+ align:start position:0%
+say general words about how you
+ 
+
+ align:start position:0%
+say general words about how you
+recognize convergence. And then we're
+
+ align:start position:0%
+recognize convergence. And then we're
+ 
+
+ align:start position:0%
+recognize convergence. And then we're
+not going to worry about so much about
+
+ align:start position:0%
+not going to worry about so much about
+ 
+
+ align:start position:0%
+not going to worry about so much about
+convergence because it works very very
+
+ align:start position:0%
+convergence because it works very very
+ 
+
+ align:start position:0%
+convergence because it works very very
+well and it's always easy to diagnose
+
+ align:start position:0%
+well and it's always easy to diagnose
+ 
+
+ align:start position:0%
+well and it's always easy to diagnose
+when there's convergence with a power
+
+ align:start position:0%
+when there's convergence with a power
+ 
+
+ align:start position:0%
+when there's convergence with a power
+series.
+
+ align:start position:0%
+series.
+ 
+
+ align:start position:0%
+series.
+All right. So here's the general setup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The general setup is that we have
+
+ align:start position:0%
+The general setup is that we have
+ 
+
+ align:start position:0%
+The general setup is that we have
+not just the coefficients one all the
+
+ align:start position:0%
+not just the coefficients one all the
+ 
+
+ align:start position:0%
+not just the coefficients one all the
+time but any numbers here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot dot dot and we abbreviate that with
+
+ align:start position:0%
+dot dot dot and we abbreviate that with
+ 
+
+ align:start position:0%
+dot dot dot and we abbreviate that with
+this summation notation. This is the sum
+
+ align:start position:0%
+this summation notation. This is the sum
+ 
+
+ align:start position:0%
+this summation notation. This is the sum
+a n x to the n n n n n n n n n n n n n n
+
+ align:start position:0%
+a n x to the n n n n n n n n n n n n n n
+ 
+
+ align:start position:0%
+a n x to the n n n n n n n n n n n n n n
+n n n n n n n= 0 to infinity
+
+ align:start position:0%
+n n n n n n n= 0 to infinity
+ 
+
+ align:start position:0%
+n n n n n n n= 0 to infinity
+and that's what's known as a power
+
+ align:start position:0%
+and that's what's known as a power
+ 
+
+ align:start position:0%
+and that's what's known as a power
+series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fortunately, there's a very simple rule
+
+ align:start position:0%
+Fortunately, there's a very simple rule
+ 
+
+ align:start position:0%
+Fortunately, there's a very simple rule
+about how power series converge and it's
+
+ align:start position:0%
+about how power series converge and it's
+ 
+
+ align:start position:0%
+about how power series converge and it's
+the following.
+
+ align:start position:0%
+the following.
+ 
+
+ align:start position:0%
+the following.
+There's a magic number r which depends
+
+ align:start position:0%
+There's a magic number r which depends
+ 
+
+ align:start position:0%
+There's a magic number r which depends
+on these numbers here such that and this
+
+ align:start position:0%
+on these numbers here such that and this
+ 
+
+ align:start position:0%
+on these numbers here such that and this
+thing is known as a radius of
+
+ align:start position:0%
+thing is known as a radius of
+ 
+
+ align:start position:0%
+thing is known as a radius of
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the problem that we had it's this
+
+ align:start position:0%
+in the problem that we had it's this
+ 
+
+ align:start position:0%
+in the problem that we had it's this
+number one here this thing works for x
+
+ align:start position:0%
+number one here this thing works for x
+ 
+
+ align:start position:0%
+number one here this thing works for x
+less than one in our case it's maybe x
+
+ align:start position:0%
+less than one in our case it's maybe x
+ 
+
+ align:start position:0%
+less than one in our case it's maybe x
+less than r so that's some symmetric
+
+ align:start position:0%
+less than r so that's some symmetric
+ 
+
+ align:start position:0%
+less than r so that's some symmetric
+interval right that's the same as minus
+
+ align:start position:0%
+interval right that's the same as minus
+ 
+
+ align:start position:0%
+interval right that's the same as minus
+r less than x less than are
+
+ align:start position:0%
+r less than x less than are
+ 
+
+ align:start position:0%
+r less than x less than are
+and uh this is the so where there's
+
+ align:start position:0%
+and uh this is the so where there's
+ 
+
+ align:start position:0%
+and uh this is the so where there's
+convergence
+
+ align:start position:0%
+convergence
+ 
+
+ align:start position:0%
+convergence
+okay where the series converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then there's the region where every
+
+ align:start position:0%
+then there's the region where every
+ 
+
+ align:start position:0%
+then there's the region where every
+computation that you give will give you
+
+ align:start position:0%
+computation that you give will give you
+ 
+
+ align:start position:0%
+computation that you give will give you
+nonsense.
+
+ align:start position:0%
+nonsense.
+ 
+
+ align:start position:0%
+nonsense.
+So x greater than r is the um sum a n x
+
+ align:start position:0%
+So x greater than r is the um sum a n x
+ 
+
+ align:start position:0%
+So x greater than r is the um sum a n x
+to the n diverges.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and
+
+ align:start position:0%
+Um and
+ 
+
+ align:start position:0%
+Um and
+x= r is very delicate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+borderline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and will not be used by us.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we're going to stick inside the
+
+ align:start position:0%
+Okay, we're going to stick inside the
+ 
+
+ align:start position:0%
+Okay, we're going to stick inside the
+radius of convergence.
+
+ align:start position:0%
+radius of convergence.
+ 
+
+ align:start position:0%
+radius of convergence.
+Now, the way you'll be able to recognize
+
+ align:start position:0%
+Now, the way you'll be able to recognize
+ 
+
+ align:start position:0%
+Now, the way you'll be able to recognize
+this is the following. What always
+
+ align:start position:0%
+this is the following. What always
+ 
+
+ align:start position:0%
+this is the following. What always
+happens is that these numbers tend to
+
+ align:start position:0%
+happens is that these numbers tend to
+ 
+
+ align:start position:0%
+happens is that these numbers tend to
+zero exponentially fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+for X in R
+
+ align:start position:0%
+for X in R
+ 
+
+ align:start position:0%
+for X in R
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doesn't even tend to zero at all for
+
+ align:start position:0%
+doesn't even tend to zero at all for
+ 
+
+ align:start position:0%
+doesn't even tend to zero at all for
+X greater than R.
+
+ align:start position:0%
+X greater than R.
+ 
+
+ align:start position:0%
+X greater than R.
+All right. So, so you'll just it'll be
+
+ align:start position:0%
+All right. So, so you'll just it'll be
+ 
+
+ align:start position:0%
+All right. So, so you'll just it'll be
+totally obvious when you look at this
+
+ align:start position:0%
+totally obvious when you look at this
+ 
+
+ align:start position:0%
+totally obvious when you look at this
+series here. What's happening when x
+
+ align:start position:0%
+series here. What's happening when x
+ 
+
+ align:start position:0%
+series here. What's happening when x
+less than r is that the numbers are
+
+ align:start position:0%
+less than r is that the numbers are
+ 
+
+ align:start position:0%
+less than r is that the numbers are
+getting smaller and smaller. I'm less
+
+ align:start position:0%
+getting smaller and smaller. I'm less
+ 
+
+ align:start position:0%
+getting smaller and smaller. I'm less
+than one. When x is bigger than one, the
+
+ align:start position:0%
+than one. When x is bigger than one, the
+ 
+
+ align:start position:0%
+than one. When x is bigger than one, the
+numbers are getting bigger and bigger.
+
+ align:start position:0%
+numbers are getting bigger and bigger.
+ 
+
+ align:start position:0%
+numbers are getting bigger and bigger.
+There's no chance that the series
+
+ align:start position:0%
+There's no chance that the series
+ 
+
+ align:start position:0%
+There's no chance that the series
+converges. So that's going to be the
+
+ align:start position:0%
+converges. So that's going to be the
+ 
+
+ align:start position:0%
+converges. So that's going to be the
+case with all power series. there's
+
+ align:start position:0%
+case with all power series. there's
+ 
+
+ align:start position:0%
+case with all power series. there's
+going to be a cutoff and it'll be one
+
+ align:start position:0%
+going to be a cutoff and it'll be one
+ 
+
+ align:start position:0%
+going to be a cutoff and it'll be one
+particular number and below that it'll
+
+ align:start position:0%
+particular number and below that it'll
+ 
+
+ align:start position:0%
+particular number and below that it'll
+be obvious that you have convergence and
+
+ align:start position:0%
+be obvious that you have convergence and
+ 
+
+ align:start position:0%
+be obvious that you have convergence and
+you'll be able to do computations and
+
+ align:start position:0%
+you'll be able to do computations and
+ 
+
+ align:start position:0%
+you'll be able to do computations and
+above that every formula will be wrong
+
+ align:start position:0%
+above that every formula will be wrong
+ 
+
+ align:start position:0%
+above that every formula will be wrong
+and won't make sense. So it's a very
+
+ align:start position:0%
+and won't make sense. So it's a very
+ 
+
+ align:start position:0%
+and won't make sense. So it's a very
+clean thing. There is this very subtle
+
+ align:start position:0%
+clean thing. There is this very subtle
+ 
+
+ align:start position:0%
+clean thing. There is this very subtle
+borderline but we're not going to
+
+ align:start position:0%
+borderline but we're not going to
+ 
+
+ align:start position:0%
+borderline but we're not going to
+discuss that in this in this class and
+
+ align:start position:0%
+discuss that in this in this class and
+ 
+
+ align:start position:0%
+discuss that in this in this class and
+it's actually not used uh uh in direct
+
+ align:start position:0%
+it's actually not used uh uh in direct
+ 
+
+ align:start position:0%
+it's actually not used uh uh in direct
+studies of power series. How do you tell
+
+ align:start position:0%
+studies of power series. How do you tell
+ 
+
+ align:start position:0%
+studies of power series. How do you tell
+when it's when the numbers are declining
+
+ align:start position:0%
+when it's when the numbers are declining
+ 
+
+ align:start position:0%
+when it's when the numbers are declining
+exponentially fast versus it's just
+
+ align:start position:0%
+exponentially fast versus it's just
+ 
+
+ align:start position:0%
+exponentially fast versus it's just
+In other words, 1 /x you zero. The
+
+ align:start position:0%
+In other words, 1 /x you zero. The
+ 
+
+ align:start position:0%
+In other words, 1 /x you zero. The
+question is how could why why was I able
+
+ align:start position:0%
+question is how could why why was I able
+ 
+
+ align:start position:0%
+question is how could why why was I able
+to tell you this word here? Why was I
+
+ align:start position:0%
+to tell you this word here? Why was I
+ 
+
+ align:start position:0%
+to tell you this word here? Why was I
+able to tell you not only is it going to
+
+ align:start position:0%
+able to tell you not only is it going to
+ 
+
+ align:start position:0%
+able to tell you not only is it going to
+zero but it's going exponentially fast?
+
+ align:start position:0%
+zero but it's going exponentially fast?
+ 
+
+ align:start position:0%
+zero but it's going exponentially fast?
+I'm telling you extra information. I'm
+
+ align:start position:0%
+I'm telling you extra information. I'm
+ 
+
+ align:start position:0%
+I'm telling you extra information. I'm
+telling you it always goes exponentially
+
+ align:start position:0%
+telling you it always goes exponentially
+ 
+
+ align:start position:0%
+telling you it always goes exponentially
+fast. You can identify it. In other
+
+ align:start position:0%
+fast. You can identify it. In other
+ 
+
+ align:start position:0%
+fast. You can identify it. In other
+words, in other words, in other words,
+
+ align:start position:0%
+words, in other words, in other words,
+ 
+
+ align:start position:0%
+words, in other words, in other words,
+you'll see it and it will happen every
+
+ align:start position:0%
+you'll see it and it will happen every
+ 
+
+ align:start position:0%
+you'll see it and it will happen every
+single time. I'm just promising you that
+
+ align:start position:0%
+single time. I'm just promising you that
+ 
+
+ align:start position:0%
+single time. I'm just promising you that
+it works that way. And it's really for
+
+ align:start position:0%
+it works that way. And it's really for
+ 
+
+ align:start position:0%
+it works that way. And it's really for
+the same reason that it works that way
+
+ align:start position:0%
+the same reason that it works that way
+ 
+
+ align:start position:0%
+the same reason that it works that way
+here that these are powers. And what's
+
+ align:start position:0%
+here that these are powers. And what's
+ 
+
+ align:start position:0%
+here that these are powers. And what's
+going on over here is there are it's
+
+ align:start position:0%
+going on over here is there are it's
+ 
+
+ align:start position:0%
+going on over here is there are it's
+close to powers with these a
+
+ align:start position:0%
+close to powers with these a
+ 
+
+ align:start position:0%
+close to powers with these a
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+there's a long discussion of radius of
+
+ align:start position:0%
+there's a long discussion of radius of
+ 
+
+ align:start position:0%
+there's a long discussion of radius of
+convergence in many textbooks but really
+
+ align:start position:0%
+convergence in many textbooks but really
+ 
+
+ align:start position:0%
+convergence in many textbooks but really
+it's it's not necessary all right for
+
+ align:start position:0%
+it's it's not necessary all right for
+ 
+
+ align:start position:0%
+it's it's not necessary all right for
+this purpose.
+
+ align:start position:0%
+this purpose.
+ 
+
+ align:start position:0%
+this purpose.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+The question was how do you find r? Yes.
+
+ align:start position:0%
+The question was how do you find r? Yes.
+ 
+
+ align:start position:0%
+The question was how do you find r? Yes.
+So I just said there's a long discussion
+
+ align:start position:0%
+So I just said there's a long discussion
+ 
+
+ align:start position:0%
+So I just said there's a long discussion
+of how you find the radius of
+
+ align:start position:0%
+of how you find the radius of
+ 
+
+ align:start position:0%
+of how you find the radius of
+convergence in textbooks, but we will we
+
+ align:start position:0%
+convergence in textbooks, but we will we
+ 
+
+ align:start position:0%
+convergence in textbooks, but we will we
+will not be discussing that here and it
+
+ align:start position:0%
+will not be discussing that here and it
+ 
+
+ align:start position:0%
+will not be discussing that here and it
+won't be necessary for you because it
+
+ align:start position:0%
+won't be necessary for you because it
+ 
+
+ align:start position:0%
+won't be necessary for you because it
+will be obvious in any given series what
+
+ align:start position:0%
+will be obvious in any given series what
+ 
+
+ align:start position:0%
+will be obvious in any given series what
+what the r is. It will always be either
+
+ align:start position:0%
+what the r is. It will always be either
+ 
+
+ align:start position:0%
+what the r is. It will always be either
+one or infinity. It will always work for
+
+ align:start position:0%
+one or infinity. It will always work for
+ 
+
+ align:start position:0%
+one or infinity. It will always work for
+all x or maybe it'll stop at some point
+
+ align:start position:0%
+all x or maybe it'll stop at some point
+ 
+
+ align:start position:0%
+all x or maybe it'll stop at some point
+but it'll be very clear where it stops
+
+ align:start position:0%
+but it'll be very clear where it stops
+ 
+
+ align:start position:0%
+but it'll be very clear where it stops
+as it is for the for the geometric
+
+ align:start position:0%
+as it is for the for the geometric
+ 
+
+ align:start position:0%
+as it is for the for the geometric
+series.
+
+ align:start position:0%
+series.
+ 
+
+ align:start position:0%
+series.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Okay. So now I need to give you the the
+
+ align:start position:0%
+Okay. So now I need to give you the the
+ 
+
+ align:start position:0%
+Okay. So now I need to give you the the
+basic facts and give you a few examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So why are we looking at these series?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh the answer is we're looking at these
+
+ align:start position:0%
+Uh the answer is we're looking at these
+ 
+
+ align:start position:0%
+Uh the answer is we're looking at these
+series because the role that they play
+
+ align:start position:0%
+series because the role that they play
+ 
+
+ align:start position:0%
+series because the role that they play
+is exactly the reverse of this inequal
+
+ align:start position:0%
+is exactly the reverse of this inequal
+ 
+
+ align:start position:0%
+is exactly the reverse of this inequal
+of this equation here.
+
+ align:start position:0%
+of this equation here.
+ 
+
+ align:start position:0%
+of this equation here.
+That is and this is a theme which I've
+
+ align:start position:0%
+That is and this is a theme which I've
+ 
+
+ align:start position:0%
+That is and this is a theme which I've
+tried to emphasize throughout this
+
+ align:start position:0%
+tried to emphasize throughout this
+ 
+
+ align:start position:0%
+tried to emphasize throughout this
+course. You can read equalities in two
+
+ align:start position:0%
+course. You can read equalities in two
+ 
+
+ align:start position:0%
+course. You can read equalities in two
+directions.
+
+ align:start position:0%
+directions.
+ 
+
+ align:start position:0%
+directions.
+Both are interesting. Typically you can
+
+ align:start position:0%
+Both are interesting. Typically you can
+ 
+
+ align:start position:0%
+Both are interesting. Typically you can
+think I don't know what the value of
+
+ align:start position:0%
+think I don't know what the value of
+ 
+
+ align:start position:0%
+think I don't know what the value of
+this is. Here's a way of evaluating it.
+
+ align:start position:0%
+this is. Here's a way of evaluating it.
+ 
+
+ align:start position:0%
+this is. Here's a way of evaluating it.
+In other words, the left side the the
+
+ align:start position:0%
+In other words, the left side the the
+ 
+
+ align:start position:0%
+In other words, the left side the the
+right side is a formula for the left
+
+ align:start position:0%
+right side is a formula for the left
+ 
+
+ align:start position:0%
+right side is a formula for the left
+side. Or you can think of the left side
+
+ align:start position:0%
+side. Or you can think of the left side
+ 
+
+ align:start position:0%
+side. Or you can think of the left side
+as being a formula for the right side.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the idea of series is that they're
+
+ align:start position:0%
+And the idea of series is that they're
+ 
+
+ align:start position:0%
+And the idea of series is that they're
+flexible enough to represent all of the
+
+ align:start position:0%
+flexible enough to represent all of the
+ 
+
+ align:start position:0%
+flexible enough to represent all of the
+functions that we've encountered in this
+
+ align:start position:0%
+functions that we've encountered in this
+ 
+
+ align:start position:0%
+functions that we've encountered in this
+course.
+
+ align:start position:0%
+course.
+ 
+
+ align:start position:0%
+course.
+Uh this is the tool which is very much
+
+ align:start position:0%
+Uh this is the tool which is very much
+ 
+
+ align:start position:0%
+Uh this is the tool which is very much
+like the decimal expansion which allows
+
+ align:start position:0%
+like the decimal expansion which allows
+ 
+
+ align:start position:0%
+like the decimal expansion which allows
+you to represent numbers like the square
+
+ align:start position:0%
+you to represent numbers like the square
+ 
+
+ align:start position:0%
+you to represent numbers like the square
+root of two. Now we're going to be
+
+ align:start position:0%
+root of two. Now we're going to be
+ 
+
+ align:start position:0%
+root of two. Now we're going to be
+representing all the numbers all the
+
+ align:start position:0%
+representing all the numbers all the
+ 
+
+ align:start position:0%
+representing all the numbers all the
+functions that we know e to the x arc
+
+ align:start position:0%
+functions that we know e to the x arc
+ 
+
+ align:start position:0%
+functions that we know e to the x arc
+tangent s cosine all of those functions
+
+ align:start position:0%
+tangent s cosine all of those functions
+ 
+
+ align:start position:0%
+tangent s cosine all of those functions
+become completely flexible and
+
+ align:start position:0%
+become completely flexible and
+ 
+
+ align:start position:0%
+become completely flexible and
+completely available to us and
+
+ align:start position:0%
+completely available to us and
+ 
+
+ align:start position:0%
+completely available to us and
+computationally available to us
+
+ align:start position:0%
+computationally available to us
+ 
+
+ align:start position:0%
+computationally available to us
+directly. So that's that's what this is
+
+ align:start position:0%
+directly. So that's that's what this is
+ 
+
+ align:start position:0%
+directly. So that's that's what this is
+a tool for and it's just like decimal
+
+ align:start position:0%
+a tool for and it's just like decimal
+ 
+
+ align:start position:0%
+a tool for and it's just like decimal
+expansions giving you a handle on all
+
+ align:start position:0%
+expansions giving you a handle on all
+ 
+
+ align:start position:0%
+expansions giving you a handle on all
+real numbers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here's how it works.
+
+ align:start position:0%
+So here's how it works.
+ 
+
+ align:start position:0%
+So here's how it works.
+the rules
+
+ align:start position:0%
+the rules
+ 
+
+ align:start position:0%
+the rules
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+um convergent power series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um are just like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polomials.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All of the manipulations that you do for
+
+ align:start position:0%
+All of the manipulations that you do for
+ 
+
+ align:start position:0%
+All of the manipulations that you do for
+power serieses are essentially the same
+
+ align:start position:0%
+power serieses are essentially the same
+ 
+
+ align:start position:0%
+power serieses are essentially the same
+as for polomials. So what kinds of
+
+ align:start position:0%
+as for polomials. So what kinds of
+ 
+
+ align:start position:0%
+as for polomials. So what kinds of
+things do we do with polomials?
+
+ align:start position:0%
+things do we do with polomials?
+ 
+
+ align:start position:0%
+things do we do with polomials?
+We add them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We multiply them together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We do substitutions,
+
+ align:start position:0%
+We do substitutions,
+ 
+
+ align:start position:0%
+We do substitutions,
+right? We take one function of another
+
+ align:start position:0%
+right? We take one function of another
+ 
+
+ align:start position:0%
+right? We take one function of another
+function.
+
+ align:start position:0%
+function.
+ 
+
+ align:start position:0%
+function.
+We divide them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And these are all really not very
+
+ align:start position:0%
+Okay. And these are all really not very
+ 
+
+ align:start position:0%
+Okay. And these are all really not very
+surprising operations and we'll be able
+
+ align:start position:0%
+surprising operations and we'll be able
+ 
+
+ align:start position:0%
+surprising operations and we'll be able
+to do them with power series 2. The ones
+
+ align:start position:0%
+to do them with power series 2. The ones
+ 
+
+ align:start position:0%
+to do them with power series 2. The ones
+that are interesting really interesting
+
+ align:start position:0%
+that are interesting really interesting
+ 
+
+ align:start position:0%
+that are interesting really interesting
+for calculus are the last two. We
+
+ align:start position:0%
+for calculus are the last two. We
+ 
+
+ align:start position:0%
+for calculus are the last two. We
+differentiate them
+
+ align:start position:0%
+differentiate them
+ 
+
+ align:start position:0%
+differentiate them
+and we integrate them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And all of these operations we'll be
+
+ align:start position:0%
+And all of these operations we'll be
+ 
+
+ align:start position:0%
+And all of these operations we'll be
+able to do for power series as well.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now let's explain the high points of
+
+ align:start position:0%
+So now let's explain the high points of
+ 
+
+ align:start position:0%
+So now let's explain the high points of
+this which is mainly just the
+
+ align:start position:0%
+this which is mainly just the
+ 
+
+ align:start position:0%
+this which is mainly just the
+differentiation and the integration
+
+ align:start position:0%
+differentiation and the integration
+ 
+
+ align:start position:0%
+differentiation and the integration
+part. So if I take a series like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so forth, the formula for its
+
+ align:start position:0%
+and so forth, the formula for its
+ 
+
+ align:start position:0%
+and so forth, the formula for its
+derivative is just like polomials.
+
+ align:start position:0%
+derivative is just like polomials.
+ 
+
+ align:start position:0%
+derivative is just like polomials.
+That's what I just said. It's just like
+
+ align:start position:0%
+That's what I just said. It's just like
+ 
+
+ align:start position:0%
+That's what I just said. It's just like
+polinomials. So the derivative of the
+
+ align:start position:0%
+polinomials. So the derivative of the
+ 
+
+ align:start position:0%
+polinomials. So the derivative of the
+constant is zero. The derivative of this
+
+ align:start position:0%
+constant is zero. The derivative of this
+ 
+
+ align:start position:0%
+constant is zero. The derivative of this
+term is a1. This one is + 2 a2x.
+
+ align:start position:0%
+term is a1. This one is + 2 a2x.
+ 
+
+ align:start position:0%
+term is a1. This one is + 2 a2x.
+This one is 3 a3 x^2 + etc. That's the
+
+ align:start position:0%
+This one is 3 a3 x^2 + etc. That's the
+ 
+
+ align:start position:0%
+This one is 3 a3 x^2 + etc. That's the
+formula.
+
+ align:start position:0%
+formula.
+ 
+
+ align:start position:0%
+formula.
+Similarly,
+
+ align:start position:0%
+Similarly,
+ 
+
+ align:start position:0%
+Similarly,
+if I integrate,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well, there's an unknown constant which
+
+ align:start position:0%
+well, there's an unknown constant which
+ 
+
+ align:start position:0%
+well, there's an unknown constant which
+I'm going to put first rather than last,
+
+ align:start position:0%
+I'm going to put first rather than last,
+ 
+
+ align:start position:0%
+I'm going to put first rather than last,
+which corresponds sort of to the a z
+
+ align:start position:0%
+which corresponds sort of to the a z
+ 
+
+ align:start position:0%
+which corresponds sort of to the a z
+term which is going to get wiped out.
+
+ align:start position:0%
+term which is going to get wiped out.
+ 
+
+ align:start position:0%
+term which is going to get wiped out.
+That a zero term suddenly becomes a zox
+
+ align:start position:0%
+That a zero term suddenly becomes a zox
+ 
+
+ align:start position:0%
+That a zero term suddenly becomes a zox
+and the anti-derivative of this next
+
+ align:start position:0%
+and the anti-derivative of this next
+ 
+
+ align:start position:0%
+and the anti-derivative of this next
+term is a1x^2 over 2 and the next term
+
+ align:start position:0%
+term is a1x^2 over 2 and the next term
+ 
+
+ align:start position:0%
+term is a1x^2 over 2 and the next term
+is a2x cubed over 3
+
+ align:start position:0%
+is a2x cubed over 3
+ 
+
+ align:start position:0%
+is a2x cubed over 3
+and so forth.
+
+ align:start position:0%
+and so forth.
+ 
+
+ align:start position:0%
+and so forth.
+Yeah. Question is that a series or a
+
+ align:start position:0%
+Yeah. Question is that a series or a
+ 
+
+ align:start position:0%
+Yeah. Question is that a series or a
+polomial? Is this a series or a
+
+ align:start position:0%
+polomial? Is this a series or a
+ 
+
+ align:start position:0%
+polomial? Is this a series or a
+polomial? Good question. It's a polomial
+
+ align:start position:0%
+polomial? Good question. It's a polomial
+ 
+
+ align:start position:0%
+polomial? Good question. It's a polomial
+if it ends. If it goes on infinitely
+
+ align:start position:0%
+if it ends. If it goes on infinitely
+ 
+
+ align:start position:0%
+if it ends. If it goes on infinitely
+far,
+
+ align:start position:0%
+far,
+ 
+
+ align:start position:0%
+far,
+then it's a series. They look
+
+ align:start position:0%
+then it's a series. They look
+ 
+
+ align:start position:0%
+then it's a series. They look
+practically the same. Polinomials and
+
+ align:start position:0%
+practically the same. Polinomials and
+ 
+
+ align:start position:0%
+practically the same. Polinomials and
+series. There's this little dot dot dot
+
+ align:start position:0%
+series. There's this little dot dot dot
+ 
+
+ align:start position:0%
+series. There's this little dot dot dot
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+Is this a series or a polinomial? It's
+
+ align:start position:0%
+Is this a series or a polinomial? It's
+ 
+
+ align:start position:0%
+Is this a series or a polinomial? It's
+the same rule. If it stops at a finite
+
+ align:start position:0%
+the same rule. If it stops at a finite
+ 
+
+ align:start position:0%
+the same rule. If it stops at a finite
+stage, this one stops at a finite stage.
+
+ align:start position:0%
+stage, this one stops at a finite stage.
+ 
+
+ align:start position:0%
+stage, this one stops at a finite stage.
+If it goes on forever, it goes on
+
+ align:start position:0%
+If it goes on forever, it goes on
+ 
+
+ align:start position:0%
+If it goes on forever, it goes on
+forever. So, I thought that series add
+
+ align:start position:0%
+forever. So, I thought that series add
+ 
+
+ align:start position:0%
+forever. So, I thought that series add
+up finite numbers. You can add up terms
+
+ align:start position:0%
+up finite numbers. You can add up terms
+ 
+
+ align:start position:0%
+up finite numbers. You can add up terms
+of x in the series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+so u an interesting question. So the the
+
+ align:start position:0%
+so u an interesting question. So the the
+ 
+
+ align:start position:0%
+so u an interesting question. So the the
+the question that was just asked is I
+
+ align:start position:0%
+the question that was just asked is I
+ 
+
+ align:start position:0%
+the question that was just asked is I
+thought that a series added up finite
+
+ align:start position:0%
+thought that a series added up finite
+ 
+
+ align:start position:0%
+thought that a series added up finite
+numbers. You could add up x. That was
+
+ align:start position:0%
+numbers. You could add up x. That was
+ 
+
+ align:start position:0%
+numbers. You could add up x. That was
+that was what you said, right? Okay. Now
+
+ align:start position:0%
+that was what you said, right? Okay. Now
+ 
+
+ align:start position:0%
+that was what you said, right? Okay. Now
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+that I pulled that off on you by
+
+ align:start position:0%
+that I pulled that off on you by
+ 
+
+ align:start position:0%
+that I pulled that off on you by
+changing the letter a to the letter x at
+
+ align:start position:0%
+changing the letter a to the letter x at
+ 
+
+ align:start position:0%
+changing the letter a to the letter x at
+the very beginning of this
+
+ align:start position:0%
+the very beginning of this
+ 
+
+ align:start position:0%
+the very beginning of this
+commentary here.
+
+ align:start position:0%
+commentary here.
+ 
+
+ align:start position:0%
+commentary here.
+This is a series. For each individual
+
+ align:start position:0%
+This is a series. For each individual
+ 
+
+ align:start position:0%
+This is a series. For each individual
+value of x, it's a number. So in other
+
+ align:start position:0%
+value of x, it's a number. So in other
+ 
+
+ align:start position:0%
+value of x, it's a number. So in other
+words, if I plug in here x equals a
+
+ align:start position:0%
+words, if I plug in here x equals a
+ 
+
+ align:start position:0%
+words, if I plug in here x equals a
+half, I'm going to add one plus a half
+
+ align:start position:0%
+half, I'm going to add one plus a half
+ 
+
+ align:start position:0%
+half, I'm going to add one plus a half
+plus a/4 plus an eighth and I'll get a
+
+ align:start position:0%
+plus a/4 plus an eighth and I'll get a
+ 
+
+ align:start position:0%
+plus a/4 plus an eighth and I'll get a
+number which is two. And I'll plug in a
+
+ align:start position:0%
+number which is two. And I'll plug in a
+ 
+
+ align:start position:0%
+number which is two. And I'll plug in a
+number over here and I get a number. On
+
+ align:start position:0%
+number over here and I get a number. On
+ 
+
+ align:start position:0%
+number over here and I get a number. On
+the other hand, I can do this for each
+
+ align:start position:0%
+the other hand, I can do this for each
+ 
+
+ align:start position:0%
+the other hand, I can do this for each
+value of x. So the interpretation of
+
+ align:start position:0%
+value of x. So the interpretation of
+ 
+
+ align:start position:0%
+value of x. So the interpretation of
+this is that it's a function of x. And
+
+ align:start position:0%
+this is that it's a function of x. And
+ 
+
+ align:start position:0%
+this is that it's a function of x. And
+similarly, this is a function of x. it
+
+ align:start position:0%
+similarly, this is a function of x. it
+ 
+
+ align:start position:0%
+similarly, this is a function of x. it
+works when you plug in the possible
+
+ align:start position:0%
+works when you plug in the possible
+ 
+
+ align:start position:0%
+works when you plug in the possible
+values of x between minus1 and one.
+
+ align:start position:0%
+values of x between minus1 and one.
+ 
+
+ align:start position:0%
+values of x between minus1 and one.
+So there's so there there's there's
+
+ align:start position:0%
+So there's so there there's there's
+ 
+
+ align:start position:0%
+So there's so there there's there's
+really no distinction there. It's just I
+
+ align:start position:0%
+really no distinction there. It's just I
+ 
+
+ align:start position:0%
+really no distinction there. It's just I
+slipped it past you. These are functions
+
+ align:start position:0%
+slipped it past you. These are functions
+ 
+
+ align:start position:0%
+slipped it past you. These are functions
+of x.
+
+ align:start position:0%
+of x.
+ 
+
+ align:start position:0%
+of x.
+And the notion of a power series is this
+
+ align:start position:0%
+And the notion of a power series is this
+ 
+
+ align:start position:0%
+And the notion of a power series is this
+idea that you put coefficients on a
+
+ align:start position:0%
+idea that you put coefficients on a
+ 
+
+ align:start position:0%
+idea that you put coefficients on a
+series, but then you allow yourself the
+
+ align:start position:0%
+series, but then you allow yourself the
+ 
+
+ align:start position:0%
+series, but then you allow yourself the
+flexibility to stick powers here. And
+
+ align:start position:0%
+flexibility to stick powers here. And
+ 
+
+ align:start position:0%
+flexibility to stick powers here. And
+that's exactly what we're what we're
+
+ align:start position:0%
+that's exactly what we're what we're
+ 
+
+ align:start position:0%
+that's exactly what we're what we're
+doing. Okay. There there are other kinds
+
+ align:start position:0%
+doing. Okay. There there are other kinds
+ 
+
+ align:start position:0%
+doing. Okay. There there are other kinds
+of series where you stick other
+
+ align:start position:0%
+of series where you stick other
+ 
+
+ align:start position:0%
+of series where you stick other
+interesting functions in here like ss
+
+ align:start position:0%
+interesting functions in here like ss
+ 
+
+ align:start position:0%
+interesting functions in here like ss
+and cosiness. There are lots of other
+
+ align:start position:0%
+and cosiness. There are lots of other
+ 
+
+ align:start position:0%
+and cosiness. There are lots of other
+series that people study and these are
+
+ align:start position:0%
+series that people study and these are
+ 
+
+ align:start position:0%
+series that people study and these are
+the simplest ones and all of those
+
+ align:start position:0%
+the simplest ones and all of those
+ 
+
+ align:start position:0%
+the simplest ones and all of those
+examples are extremely helpful for
+
+ align:start position:0%
+examples are extremely helpful for
+ 
+
+ align:start position:0%
+examples are extremely helpful for
+representing functions but we're only
+
+ align:start position:0%
+representing functions but we're only
+ 
+
+ align:start position:0%
+representing functions but we're only
+going to do this example here.
+
+ align:start position:0%
+going to do this example here.
+ 
+
+ align:start position:0%
+going to do this example here.
+All right. So here are the the the two
+
+ align:start position:0%
+All right. So here are the the the two
+ 
+
+ align:start position:0%
+All right. So here are the the the two
+rules. And now there's only one other
+
+ align:start position:0%
+rules. And now there's only one other
+ 
+
+ align:start position:0%
+rules. And now there's only one other
+complication here which I have to
+
+ align:start position:0%
+complication here which I have to
+ 
+
+ align:start position:0%
+complication here which I have to
+explain to you
+
+ align:start position:0%
+explain to you
+ 
+
+ align:start position:0%
+explain to you
+before giving you a bunch of examples to
+
+ align:start position:0%
+before giving you a bunch of examples to
+ 
+
+ align:start position:0%
+before giving you a bunch of examples to
+show you that this works extremely well.
+
+ align:start position:0%
+show you that this works extremely well.
+ 
+
+ align:start position:0%
+show you that this works extremely well.
+And the last thing that I have to do for
+
+ align:start position:0%
+And the last thing that I have to do for
+ 
+
+ align:start position:0%
+And the last thing that I have to do for
+you is explain to you something called
+
+ align:start position:0%
+you is explain to you something called
+ 
+
+ align:start position:0%
+you is explain to you something called
+Taylor's formula.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taylor's formula is the way you get from
+
+ align:start position:0%
+Taylor's formula is the way you get from
+ 
+
+ align:start position:0%
+Taylor's formula is the way you get from
+the representation that we're used to of
+
+ align:start position:0%
+the representation that we're used to of
+ 
+
+ align:start position:0%
+the representation that we're used to of
+functions to the representation in the
+
+ align:start position:0%
+functions to the representation in the
+ 
+
+ align:start position:0%
+functions to the representation in the
+form of these coefficients. When I gave
+
+ align:start position:0%
+form of these coefficients. When I gave
+ 
+
+ align:start position:0%
+form of these coefficients. When I gave
+you the function e to the x, it didn't
+
+ align:start position:0%
+you the function e to the x, it didn't
+ 
+
+ align:start position:0%
+you the function e to the x, it didn't
+look like a polomial.
+
+ align:start position:0%
+look like a polomial.
+ 
+
+ align:start position:0%
+look like a polomial.
+And we have to figure out which of these
+
+ align:start position:0%
+And we have to figure out which of these
+ 
+
+ align:start position:0%
+And we have to figure out which of these
+guys it is if it's going to fall into
+
+ align:start position:0%
+guys it is if it's going to fall into
+ 
+
+ align:start position:0%
+guys it is if it's going to fall into
+our category here.
+
+ align:start position:0%
+our category here.
+ 
+
+ align:start position:0%
+our category here.
+And here's the formula. I'll explain to
+
+ align:start position:0%
+And here's the formula. I'll explain to
+ 
+
+ align:start position:0%
+And here's the formula. I'll explain to
+you how it works in a second. So the
+
+ align:start position:0%
+you how it works in a second. So the
+ 
+
+ align:start position:0%
+you how it works in a second. So the
+formula is f ofx turns out there's a
+
+ align:start position:0%
+formula is f ofx turns out there's a
+ 
+
+ align:start position:0%
+formula is f ofx turns out there's a
+formula in terms of the derivatives of
+
+ align:start position:0%
+formula in terms of the derivatives of
+ 
+
+ align:start position:0%
+formula in terms of the derivatives of
+f. Namely, you differentiate n times and
+
+ align:start position:0%
+f. Namely, you differentiate n times and
+ 
+
+ align:start position:0%
+f. Namely, you differentiate n times and
+you evaluate it at zero and you divide
+
+ align:start position:0%
+you evaluate it at zero and you divide
+ 
+
+ align:start position:0%
+you evaluate it at zero and you divide
+by n factorial and multiply by x to the
+
+ align:start position:0%
+by n factorial and multiply by x to the
+ 
+
+ align:start position:0%
+by n factorial and multiply by x to the
+n.
+
+ align:start position:0%
+n.
+ 
+
+ align:start position:0%
+n.
+So here's the here's Taylor's formula.
+
+ align:start position:0%
+So here's the here's Taylor's formula.
+ 
+
+ align:start position:0%
+So here's the here's Taylor's formula.
+This tells you what the uh tailaylor
+
+ align:start position:0%
+This tells you what the uh tailaylor
+ 
+
+ align:start position:0%
+This tells you what the uh tailaylor
+series is.
+
+ align:start position:0%
+series is.
+ 
+
+ align:start position:0%
+series is.
+Now about half of our job for the next
+
+ align:start position:0%
+Now about half of our job for the next
+ 
+
+ align:start position:0%
+Now about half of our job for the next
+few minutes is going to be to give
+
+ align:start position:0%
+few minutes is going to be to give
+ 
+
+ align:start position:0%
+few minutes is going to be to give
+examples of this. But let me just
+
+ align:start position:0%
+examples of this. But let me just
+ 
+
+ align:start position:0%
+examples of this. But let me just
+explain to you why this
+
+ align:start position:0%
+explain to you why this
+ 
+
+ align:start position:0%
+explain to you why this
+has to be. If you pick out this number
+
+ align:start position:0%
+has to be. If you pick out this number
+ 
+
+ align:start position:0%
+has to be. If you pick out this number
+here, this is the a n the magic number a
+
+ align:start position:0%
+here, this is the a n the magic number a
+ 
+
+ align:start position:0%
+here, this is the a n the magic number a
+n here. So let's just illustrate it. If
+
+ align:start position:0%
+n here. So let's just illustrate it. If
+ 
+
+ align:start position:0%
+n here. So let's just illustrate it. If
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+happens to be a 0 + a1 x + a2 x^2 + a3 x
+
+ align:start position:0%
+happens to be a 0 + a1 x + a2 x^2 + a3 x
+ 
+
+ align:start position:0%
+happens to be a 0 + a1 x + a2 x^2 + a3 x
+cubed plus dot dot dot and now I
+
+ align:start position:0%
+cubed plus dot dot dot and now I
+ 
+
+ align:start position:0%
+cubed plus dot dot dot and now I
+differentiate it right I get a1 + 2 a2x
+
+ align:start position:0%
+differentiate it right I get a1 + 2 a2x
+ 
+
+ align:start position:0%
+differentiate it right I get a1 + 2 a2x
++ 3 a3 x^2
+
+ align:start position:0%
++ 3 a3 x^2
+ 
+
+ align:start position:0%
++ 3 a3 x^2
+if I differentiate it another time I get
+
+ align:start position:0%
+if I differentiate it another time I get
+ 
+
+ align:start position:0%
+if I differentiate it another time I get
+2 a2 + 3 sorry 3 * 2 a3 x + dot dot dot
+
+ align:start position:0%
+2 a2 + 3 sorry 3 * 2 a3 x + dot dot dot
+ 
+
+ align:start position:0%
+2 a2 + 3 sorry 3 * 2 a3 x + dot dot dot
+and now a third time
+
+ align:start position:0%
+and now a third time
+ 
+
+ align:start position:0%
+and now a third time
+I get 3 * 2 a3 plus
+
+ align:start position:0%
+I get 3 * 2 a3 plus
+ 
+
+ align:start position:0%
+I get 3 * 2 a3 plus
+etc. So this next term is really in
+
+ align:start position:0%
+etc. So this next term is really in
+ 
+
+ align:start position:0%
+etc. So this next term is really in
+disguise 4 * 3 * 2 x sorry uh a 4x
+
+ align:start position:0%
+disguise 4 * 3 * 2 x sorry uh a 4x
+ 
+
+ align:start position:0%
+disguise 4 * 3 * 2 x sorry uh a 4x
+that's what really comes down if I kept
+
+ align:start position:0%
+that's what really comes down if I kept
+ 
+
+ align:start position:0%
+that's what really comes down if I kept
+track of the fourth term there.
+
+ align:start position:0%
+track of the fourth term there.
+ 
+
+ align:start position:0%
+track of the fourth term there.
+So now here is my function.
+
+ align:start position:0%
+So now here is my function.
+ 
+
+ align:start position:0%
+So now here is my function.
+But now you see if I plug in xals 0 I
+
+ align:start position:0%
+But now you see if I plug in xals 0 I
+ 
+
+ align:start position:0%
+But now you see if I plug in xals 0 I
+can pick off
+
+ align:start position:0%
+can pick off
+ 
+
+ align:start position:0%
+can pick off
+the third term.
+
+ align:start position:0%
+the third term.
+ 
+
+ align:start position:0%
+the third term.
+F triple prime of 0 is equal to 3 * 2 *
+
+ align:start position:0%
+F triple prime of 0 is equal to 3 * 2 *
+ 
+
+ align:start position:0%
+F triple prime of 0 is equal to 3 * 2 *
+a3.
+
+ align:start position:0%
+a3.
+ 
+
+ align:start position:0%
+a3.
+Right? Because all the rest of those
+
+ align:start position:0%
+Right? Because all the rest of those
+ 
+
+ align:start position:0%
+Right? Because all the rest of those
+terms when I plug in zero are just zero.
+
+ align:start position:0%
+terms when I plug in zero are just zero.
+ 
+
+ align:start position:0%
+terms when I plug in zero are just zero.
+Here's the the formula. And so the the
+
+ align:start position:0%
+Here's the the formula. And so the the
+ 
+
+ align:start position:0%
+Here's the the formula. And so the the
+the pattern here is this. And what's
+
+ align:start position:0%
+the pattern here is this. And what's
+ 
+
+ align:start position:0%
+the pattern here is this. And what's
+really going on here is this is really 3
+
+ align:start position:0%
+really going on here is this is really 3
+ 
+
+ align:start position:0%
+really going on here is this is really 3
+* 2 * 1 a3.
+
+ align:start position:0%
+* 2 * 1 a3.
+ 
+
+ align:start position:0%
+* 2 * 1 a3.
+And in general,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a n is equal to f nth derivative / n
+
+ align:start position:0%
+a n is equal to f nth derivative / n
+ 
+
+ align:start position:0%
+a n is equal to f nth derivative / n
+factorial. And of course, n factorial, I
+
+ align:start position:0%
+factorial. And of course, n factorial, I
+ 
+
+ align:start position:0%
+factorial. And of course, n factorial, I
+remind you, is n * n -1
+
+ align:start position:0%
+remind you, is n * n -1
+ 
+
+ align:start position:0%
+remind you, is n * n -1
+* n - 2 all the way down to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now there's one more crazy
+
+ align:start position:0%
+Now there's one more crazy
+ 
+
+ align:start position:0%
+Now there's one more crazy
+convention which is always used which is
+
+ align:start position:0%
+convention which is always used which is
+ 
+
+ align:start position:0%
+convention which is always used which is
+that there's something very strange here
+
+ align:start position:0%
+that there's something very strange here
+ 
+
+ align:start position:0%
+that there's something very strange here
+down at zero which is that zero
+
+ align:start position:0%
+down at zero which is that zero
+ 
+
+ align:start position:0%
+down at zero which is that zero
+factorial turns out has to be set equal
+
+ align:start position:0%
+factorial turns out has to be set equal
+ 
+
+ align:start position:0%
+factorial turns out has to be set equal
+to one. All right. So that's that's what
+
+ align:start position:0%
+to one. All right. So that's that's what
+ 
+
+ align:start position:0%
+to one. All right. So that's that's what
+you do in order to make this formula
+
+ align:start position:0%
+you do in order to make this formula
+ 
+
+ align:start position:0%
+you do in order to make this formula
+work out and that's one of the reasons
+
+ align:start position:0%
+work out and that's one of the reasons
+ 
+
+ align:start position:0%
+work out and that's one of the reasons
+for this convention.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So my my uh next goal is to
+
+ align:start position:0%
+All right. So my my uh next goal is to
+ 
+
+ align:start position:0%
+All right. So my my uh next goal is to
+is to give you some examples
+
+ align:start position:0%
+is to give you some examples
+ 
+
+ align:start position:0%
+is to give you some examples
+and let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do
+
+ align:start position:0%
+let's do
+ 
+
+ align:start position:0%
+let's do
+a couple.
+
+ align:start position:0%
+a couple.
+ 
+
+ align:start position:0%
+a couple.
+So here's well you know
+
+ align:start position:0%
+So here's well you know
+ 
+
+ align:start position:0%
+So here's well you know
+I'm gonna have to let you see a few of
+
+ align:start position:0%
+I'm gonna have to let you see a few of
+ 
+
+ align:start position:0%
+I'm gonna have to let you see a few of
+them next time. But let me just let me
+
+ align:start position:0%
+them next time. But let me just let me
+ 
+
+ align:start position:0%
+them next time. But let me just let me
+just tell you this one which is by far
+
+ align:start position:0%
+just tell you this one which is by far
+ 
+
+ align:start position:0%
+just tell you this one which is by far
+the most impressive.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what happens with e to the x if the
+
+ align:start position:0%
+So what happens with e to the x if the
+ 
+
+ align:start position:0%
+So what happens with e to the x if the
+function is f ofx is e to the x is that
+
+ align:start position:0%
+function is f ofx is e to the x is that
+ 
+
+ align:start position:0%
+function is f ofx is e to the x is that
+its derivative is also e to the x and
+
+ align:start position:0%
+its derivative is also e to the x and
+ 
+
+ align:start position:0%
+its derivative is also e to the x and
+its second derivative is also e to the x
+
+ align:start position:0%
+its second derivative is also e to the x
+ 
+
+ align:start position:0%
+its second derivative is also e to the x
+and it just keeps on going that way.
+
+ align:start position:0%
+and it just keeps on going that way.
+ 
+
+ align:start position:0%
+and it just keeps on going that way.
+They're all the same.
+
+ align:start position:0%
+They're all the same.
+ 
+
+ align:start position:0%
+They're all the same.
+So that means that these numbers in
+
+ align:start position:0%
+So that means that these numbers in
+ 
+
+ align:start position:0%
+So that means that these numbers in
+Taylor's formula in the numerator
+
+ align:start position:0%
+Taylor's formula in the numerator
+ 
+
+ align:start position:0%
+Taylor's formula in the numerator
+the nth derivative is very easy to
+
+ align:start position:0%
+the nth derivative is very easy to
+ 
+
+ align:start position:0%
+the nth derivative is very easy to
+evaluate.
+
+ align:start position:0%
+evaluate.
+ 
+
+ align:start position:0%
+evaluate.
+It's just e to the x. And if I evaluate
+
+ align:start position:0%
+It's just e to the x. And if I evaluate
+ 
+
+ align:start position:0%
+It's just e to the x. And if I evaluate
+it at xals 0 I just get one. So all of
+
+ align:start position:0%
+it at xals 0 I just get one. So all of
+ 
+
+ align:start position:0%
+it at xals 0 I just get one. So all of
+those numerators are one.
+
+ align:start position:0%
+those numerators are one.
+ 
+
+ align:start position:0%
+those numerators are one.
+So the formula here is the sum n= 0 to
+
+ align:start position:0%
+So the formula here is the sum n= 0 to
+ 
+
+ align:start position:0%
+So the formula here is the sum n= 0 to
+infinity of 1 / n factorial x to the n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In particular, we now have an honest
+
+ align:start position:0%
+In particular, we now have an honest
+ 
+
+ align:start position:0%
+In particular, we now have an honest
+formula for e to the first power which
+
+ align:start position:0%
+formula for e to the first power which
+ 
+
+ align:start position:0%
+formula for e to the first power which
+is just e, which if I plug it in x= 1, I
+
+ align:start position:0%
+is just e, which if I plug it in x= 1, I
+ 
+
+ align:start position:0%
+is just e, which if I plug it in x= 1, I
+get 1. This is the n=0 term plus one.
+
+ align:start position:0%
+get 1. This is the n=0 term plus one.
+ 
+
+ align:start position:0%
+get 1. This is the n=0 term plus one.
+This is the n= 1 term plus 1 over2
+
+ align:start position:0%
+This is the n= 1 term plus 1 over2
+ 
+
+ align:start position:0%
+This is the n= 1 term plus 1 over2
+factorial plus 1 over 3 factorial plus 1
+
+ align:start position:0%
+factorial plus 1 over 3 factorial plus 1
+ 
+
+ align:start position:0%
+factorial plus 1 over 3 factorial plus 1
+over 4 factorial.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So this is our first honest
+
+ align:start position:0%
+All right. So this is our first honest
+ 
+
+ align:start position:0%
+All right. So this is our first honest
+formula for e and also this is how you
+
+ align:start position:0%
+formula for e and also this is how you
+ 
+
+ align:start position:0%
+formula for e and also this is how you
+you compute the exponential function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Finally,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you take a function like sinx,
+
+ align:start position:0%
+if you take a function like sinx,
+ 
+
+ align:start position:0%
+if you take a function like sinx,
+what you'll discover is that we can
+
+ align:start position:0%
+what you'll discover is that we can
+ 
+
+ align:start position:0%
+what you'll discover is that we can
+complete the sort of strange business
+
+ align:start position:0%
+complete the sort of strange business
+ 
+
+ align:start position:0%
+complete the sort of strange business
+that we did at the beginning of the
+
+ align:start position:0%
+that we did at the beginning of the
+ 
+
+ align:start position:0%
+that we did at the beginning of the
+course or cossinex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we took the uh linear and
+
+ align:start position:0%
+where we took the uh linear and
+ 
+
+ align:start position:0%
+where we took the uh linear and
+quadratic approximations. Now, we're
+
+ align:start position:0%
+quadratic approximations. Now, we're
+ 
+
+ align:start position:0%
+quadratic approximations. Now, we're
+going to get complete formulas for these
+
+ align:start position:0%
+going to get complete formulas for these
+ 
+
+ align:start position:0%
+going to get complete formulas for these
+functions.
+
+ align:start position:0%
+functions.
+ 
+
+ align:start position:0%
+functions.
+Sin x turns out to be equal to x - x cub
+
+ align:start position:0%
+Sin x turns out to be equal to x - x cub
+ 
+
+ align:start position:0%
+Sin x turns out to be equal to x - x cub
+over 3 factorial + x 5 over 5 factorial
+
+ align:start position:0%
+over 3 factorial + x 5 over 5 factorial
+ 
+
+ align:start position:0%
+over 3 factorial + x 5 over 5 factorial
+- x 7th / 7 factorial
+
+ align:start position:0%
+- x 7th / 7 factorial
+ 
+
+ align:start position:0%
+- x 7th / 7 factorial
+etc.
+
+ align:start position:0%
+etc.
+ 
+
+ align:start position:0%
+etc.
+And cossine x is equal to 1 - x^2 over 2
+
+ align:start position:0%
+And cossine x is equal to 1 - x^2 over 2
+ 
+
+ align:start position:0%
+And cossine x is equal to 1 - x^2 over 2
+factorial. That's the same as this 2
+
+ align:start position:0%
+factorial. That's the same as this 2
+ 
+
+ align:start position:0%
+factorial. That's the same as this 2
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+plus x 4th over 4 factorial - x 6 / 6
+
+ align:start position:0%
+plus x 4th over 4 factorial - x 6 / 6
+ 
+
+ align:start position:0%
+plus x 4th over 4 factorial - x 6 / 6
+factorial plus etc. Now these may feel
+
+ align:start position:0%
+factorial plus etc. Now these may feel
+ 
+
+ align:start position:0%
+factorial plus etc. Now these may feel
+like they're hard to memorize because
+
+ align:start position:0%
+like they're hard to memorize because
+ 
+
+ align:start position:0%
+like they're hard to memorize because
+I've just pulled them out of a hat.
+
+ align:start position:0%
+I've just pulled them out of a hat.
+ 
+
+ align:start position:0%
+I've just pulled them out of a hat.
+Uh, I do expect you to know them.
+
+ align:start position:0%
+Uh, I do expect you to know them.
+ 
+
+ align:start position:0%
+Uh, I do expect you to know them.
+They're actually extremely similar
+
+ align:start position:0%
+They're actually extremely similar
+ 
+
+ align:start position:0%
+They're actually extremely similar
+formulas. The exponential here just has
+
+ align:start position:0%
+formulas. The exponential here just has
+ 
+
+ align:start position:0%
+formulas. The exponential here just has
+this collection of factorials. The sign
+
+ align:start position:0%
+this collection of factorials. The sign
+ 
+
+ align:start position:0%
+this collection of factorials. The sign
+is all the odd powers with alternating
+
+ align:start position:0%
+is all the odd powers with alternating
+ 
+
+ align:start position:0%
+is all the odd powers with alternating
+signs and the cosine is all the even
+
+ align:start position:0%
+signs and the cosine is all the even
+ 
+
+ align:start position:0%
+signs and the cosine is all the even
+powers with alternating signs. So all
+
+ align:start position:0%
+powers with alternating signs. So all
+ 
+
+ align:start position:0%
+powers with alternating signs. So all
+three of them form part of the same
+
+ align:start position:0%
+three of them form part of the same
+ 
+
+ align:start position:0%
+three of them form part of the same
+family. So this will actually make it
+
+ align:start position:0%
+family. So this will actually make it
+ 
+
+ align:start position:0%
+family. So this will actually make it
+easier for you to remember rather than
+
+ align:start position:0%
+easier for you to remember rather than
+ 
+
+ align:start position:0%
+easier for you to remember rather than
+harder.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And and so with that, I'll leave the
+
+ align:start position:0%
+And and so with that, I'll leave the
+ 
+
+ align:start position:0%
+And and so with that, I'll leave the
+practice on differentiation for next
+
+ align:start position:0%
+practice on differentiation for next
+ 
+
+ align:start position:0%
+practice on differentiation for next
+time. And good luck everybody. I'll talk
+
+ align:start position:0%
+time. And good luck everybody. I'll talk
+ 
+
+ align:start position:0%
+time. And good luck everybody. I'll talk
+to you individually.
\ No newline at end of file
diff --git a/wmoKns-IQ-E.txt b/wmoKns-IQ-E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5db1bf41f7325f2d4250cbc2ce23caaa6158249d
--- /dev/null
+++ b/wmoKns-IQ-E.txt
@@ -0,0 +1,8131 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+alright so today's reading comes from a
+
+ align:start position:0%
+alright so today's reading comes from a
+ 
+
+ align:start position:0%
+alright so today's reading comes from a
+game designer who is Pulsifer who
+
+ align:start position:0%
+game designer who is Pulsifer who
+ 
+
+ align:start position:0%
+game designer who is Pulsifer who
+traditionally working war games I
+
+ align:start position:0%
+traditionally working war games I
+ 
+
+ align:start position:0%
+traditionally working war games I
+believe he's telling us on some of the
+
+ align:start position:0%
+believe he's telling us on some of the
+ 
+
+ align:start position:0%
+believe he's telling us on some of the
+board games as well but for the most
+
+ align:start position:0%
+board games as well but for the most
+ 
+
+ align:start position:0%
+board games as well but for the most
+part I think is recognized poised before
+
+ align:start position:0%
+part I think is recognized poised before
+ 
+
+ align:start position:0%
+part I think is recognized poised before
+the wargaming work and that was actually
+
+ align:start position:0%
+the wargaming work and that was actually
+ 
+
+ align:start position:0%
+the wargaming work and that was actually
+there's actually quite a lot of
+
+ align:start position:0%
+there's actually quite a lot of
+ 
+
+ align:start position:0%
+there's actually quite a lot of
+wargaming journals mostly written by
+
+ align:start position:0%
+wargaming journals mostly written by
+ 
+
+ align:start position:0%
+wargaming journals mostly written by
+designers for fan softball fan or for
+
+ align:start position:0%
+designers for fan softball fan or for
+ 
+
+ align:start position:0%
+designers for fan softball fan or for
+pen or by fans for fans things like the
+
+ align:start position:0%
+pen or by fans for fans things like the
+ 
+
+ align:start position:0%
+pen or by fans for fans things like the
+complete strategists used to be quite a
+
+ align:start position:0%
+complete strategists used to be quite a
+ 
+
+ align:start position:0%
+complete strategists used to be quite a
+PC gamer of wargaming right you know
+
+ align:start position:0%
+PC gamer of wargaming right you know
+ 
+
+ align:start position:0%
+PC gamer of wargaming right you know
+it's like this is what's happening and
+
+ align:start position:0%
+it's like this is what's happening and
+ 
+
+ align:start position:0%
+it's like this is what's happening and
+this these are our thoughts these are
+
+ align:start position:0%
+this these are our thoughts these are
+ 
+
+ align:start position:0%
+this these are our thoughts these are
+critiques and that particular reading I
+
+ align:start position:0%
+critiques and that particular reading I
+ 
+
+ align:start position:0%
+critiques and that particular reading I
+feel is very typical of that sort of
+
+ align:start position:0%
+feel is very typical of that sort of
+ 
+
+ align:start position:0%
+feel is very typical of that sort of
+hero of maybe late 80s early to mid 90s
+
+ align:start position:0%
+hero of maybe late 80s early to mid 90s
+ 
+
+ align:start position:0%
+hero of maybe late 80s early to mid 90s
+magazine publications and it's
+
+ align:start position:0%
+magazine publications and it's
+ 
+
+ align:start position:0%
+magazine publications and it's
+interesting because already at that time
+
+ align:start position:0%
+interesting because already at that time
+ 
+
+ align:start position:0%
+interesting because already at that time
+sure there are people who say wrote the
+
+ align:start position:0%
+sure there are people who say wrote the
+ 
+
+ align:start position:0%
+sure there are people who say wrote the
+core rule sets for various games like
+
+ align:start position:0%
+core rule sets for various games like
+ 
+
+ align:start position:0%
+core rule sets for various games like
+you know Axis and Allies of all things
+
+ align:start position:0%
+you know Axis and Allies of all things
+ 
+
+ align:start position:0%
+you know Axis and Allies of all things
+like Dungeons and Dragons but it wasn't
+
+ align:start position:0%
+like Dungeons and Dragons but it wasn't
+ 
+
+ align:start position:0%
+like Dungeons and Dragons but it wasn't
+going to be this assumption that if
+
+ align:start position:0%
+going to be this assumption that if
+ 
+
+ align:start position:0%
+going to be this assumption that if
+you're interested in something like
+
+ align:start position:0%
+you're interested in something like
+ 
+
+ align:start position:0%
+you're interested in something like
+wargaming you're also interested in
+
+ align:start position:0%
+wargaming you're also interested in
+ 
+
+ align:start position:0%
+wargaming you're also interested in
+creating your own scenarios you are
+
+ align:start position:0%
+creating your own scenarios you are
+ 
+
+ align:start position:0%
+creating your own scenarios you are
+already halfway a game designer and so
+
+ align:start position:0%
+already halfway a game designer and so
+ 
+
+ align:start position:0%
+already halfway a game designer and so
+you have to keep all of these things in
+
+ align:start position:0%
+you have to keep all of these things in
+ 
+
+ align:start position:0%
+you have to keep all of these things in
+mind particular game master has everyone
+
+ align:start position:0%
+mind particular game master has everyone
+ 
+
+ align:start position:0%
+mind particular game master has everyone
+been like a dungeon master or game
+
+ align:start position:0%
+been like a dungeon master or game
+ 
+
+ align:start position:0%
+been like a dungeon master or game
+master for role-playing group ok yeah
+
+ align:start position:0%
+master for role-playing group ok yeah
+ 
+
+ align:start position:0%
+master for role-playing group ok yeah
+basically a game designer yeah yeah you
+
+ align:start position:0%
+basically a game designer yeah yeah you
+ 
+
+ align:start position:0%
+basically a game designer yeah yeah you
+know you're taking rule sets that
+
+ align:start position:0%
+know you're taking rule sets that
+ 
+
+ align:start position:0%
+know you're taking rule sets that
+somebody else came and cherry picking
+
+ align:start position:0%
+somebody else came and cherry picking
+ 
+
+ align:start position:0%
+somebody else came and cherry picking
+the stuff that you really want to work
+
+ align:start position:0%
+the stuff that you really want to work
+ 
+
+ align:start position:0%
+the stuff that you really want to work
+with them discarding the stuff that
+
+ align:start position:0%
+with them discarding the stuff that
+ 
+
+ align:start position:0%
+with them discarding the stuff that
+doesn't end in coming up with with your
+
+ align:start position:0%
+doesn't end in coming up with with your
+ 
+
+ align:start position:0%
+doesn't end in coming up with with your
+own rules so so just I said a sample of
+
+ align:start position:0%
+own rules so so just I said a sample of
+ 
+
+ align:start position:0%
+own rules so so just I said a sample of
+reading I felt I believe this the first
+
+ align:start position:0%
+reading I felt I believe this the first
+ 
+
+ align:start position:0%
+reading I felt I believe this the first
+time I've asked you to read anything
+
+ align:start position:0%
+time I've asked you to read anything
+ 
+
+ align:start position:0%
+time I've asked you to read anything
+from the tabletop book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay alright chill ranma's first that's
+
+ align:start position:0%
+okay alright chill ranma's first that's
+ 
+
+ align:start position:0%
+okay alright chill ranma's first that's
+true yeah but this particular piece of
+
+ align:start position:0%
+true yeah but this particular piece of
+ 
+
+ align:start position:0%
+true yeah but this particular piece of
+reading host is also nice little time
+
+ align:start position:0%
+reading host is also nice little time
+ 
+
+ align:start position:0%
+reading host is also nice little time
+capsule of how people used to write
+
+ align:start position:0%
+capsule of how people used to write
+ 
+
+ align:start position:0%
+capsule of how people used to write
+about game design it's a fairly modern
+
+ align:start position:0%
+about game design it's a fairly modern
+ 
+
+ align:start position:0%
+about game design it's a fairly modern
+piece of writing but still it still has
+
+ align:start position:0%
+piece of writing but still it still has
+ 
+
+ align:start position:0%
+piece of writing but still it still has
+that same sort of style so there's a lot
+
+ align:start position:0%
+that same sort of style so there's a lot
+ 
+
+ align:start position:0%
+that same sort of style so there's a lot
+of examples of like this is how this
+
+ align:start position:0%
+of examples of like this is how this
+ 
+
+ align:start position:0%
+of examples of like this is how this
+theoretical game is going to be play and
+
+ align:start position:0%
+theoretical game is going to be play and
+ 
+
+ align:start position:0%
+theoretical game is going to be play and
+I'm going to write it out completely in
+
+ align:start position:0%
+I'm going to write it out completely in
+ 
+
+ align:start position:0%
+I'm going to write it out completely in
+pearls you know it's not going to say
+
+ align:start position:0%
+pearls you know it's not going to say
+ 
+
+ align:start position:0%
+pearls you know it's not going to say
+and II and even when it talks when when
+
+ align:start position:0%
+and II and even when it talks when when
+ 
+
+ align:start position:0%
+and II and even when it talks when when
+they refer to games that already exist
+
+ align:start position:0%
+they refer to games that already exist
+ 
+
+ align:start position:0%
+they refer to games that already exist
+like they do cybg yeah yeah yeah I get
+
+ align:start position:0%
+like they do cybg yeah yeah yeah I get
+ 
+
+ align:start position:0%
+like they do cybg yeah yeah yeah I get
+the explained on they explained that the
+
+ align:start position:0%
+the explained on they explained that the
+ 
+
+ align:start position:0%
+the explained on they explained that the
+mechanic said that discussing about in
+
+ align:start position:0%
+mechanic said that discussing about in
+ 
+
+ align:start position:0%
+mechanic said that discussing about in
+prose it's not like in point form or
+
+ align:start position:0%
+prose it's not like in point form or
+ 
+
+ align:start position:0%
+prose it's not like in point form or
+anything like that it's just free free
+
+ align:start position:0%
+anything like that it's just free free
+ 
+
+ align:start position:0%
+anything like that it's just free free
+prose I don't think there's ever any
+
+ align:start position:0%
+prose I don't think there's ever any
+ 
+
+ align:start position:0%
+prose I don't think there's ever any
+assumption that at all if you
+
+ align:start position:0%
+assumption that at all if you
+ 
+
+ align:start position:0%
+assumption that at all if you
+contributed an essay for something like
+
+ align:start position:0%
+contributed an essay for something like
+ 
+
+ align:start position:0%
+contributed an essay for something like
+the complete strategist that you that
+
+ align:start position:0%
+the complete strategist that you that
+ 
+
+ align:start position:0%
+the complete strategist that you that
+diagrams that you included will be
+
+ align:start position:0%
+diagrams that you included will be
+ 
+
+ align:start position:0%
+diagrams that you included will be
+included into the magazine right because
+
+ align:start position:0%
+included into the magazine right because
+ 
+
+ align:start position:0%
+included into the magazine right because
+a lot of people who actually created
+
+ align:start position:0%
+a lot of people who actually created
+ 
+
+ align:start position:0%
+a lot of people who actually created
+those essays weren't necessarily artists
+
+ align:start position:0%
+those essays weren't necessarily artists
+ 
+
+ align:start position:0%
+those essays weren't necessarily artists
+and that's not to say that you didn't
+
+ align:start position:0%
+and that's not to say that you didn't
+ 
+
+ align:start position:0%
+and that's not to say that you didn't
+have diagrams and magazines like that
+
+ align:start position:0%
+have diagrams and magazines like that
+ 
+
+ align:start position:0%
+have diagrams and magazines like that
+but it was expensive this is before
+
+ align:start position:0%
+but it was expensive this is before
+ 
+
+ align:start position:0%
+but it was expensive this is before
+desktop publishing so people just got
+
+ align:start position:0%
+desktop publishing so people just got
+ 
+
+ align:start position:0%
+desktop publishing so people just got
+really really used to describing things
+
+ align:start position:0%
+really really used to describing things
+ 
+
+ align:start position:0%
+really really used to describing things
+in prose describing core game mechanics
+
+ align:start position:0%
+in prose describing core game mechanics
+ 
+
+ align:start position:0%
+in prose describing core game mechanics
+in prose not even point form more for
+
+ align:start position:0%
+in prose not even point form more for
+ 
+
+ align:start position:0%
+in prose not even point form more for
+the points so so there were basically
+
+ align:start position:0%
+the points so so there were basically
+ 
+
+ align:start position:0%
+the points so so there were basically
+two suggestions that he has on how to
+
+ align:start position:0%
+two suggestions that he has on how to
+ 
+
+ align:start position:0%
+two suggestions that he has on how to
+deal with the whole three player problem
+
+ align:start position:0%
+deal with the whole three player problem
+ 
+
+ align:start position:0%
+deal with the whole three player problem
+you know that like the actually before I
+
+ align:start position:0%
+you know that like the actually before I
+ 
+
+ align:start position:0%
+you know that like the actually before I
+get into this so you guys don't get
+
+ align:start position:0%
+get into this so you guys don't get
+ 
+
+ align:start position:0%
+get into this so you guys don't get
+anyone that I quickly sum up what's the
+
+ align:start position:0%
+anyone that I quickly sum up what's the
+ 
+
+ align:start position:0%
+anyone that I quickly sum up what's the
+main problem with having this design any
+
+ align:start position:0%
+main problem with having this design any
+ 
+
+ align:start position:0%
+main problem with having this design any
+important three players
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean where do eclipse or go I began
+
+ align:start position:0%
+I mean where do eclipse or go I began
+ 
+
+ align:start position:0%
+I mean where do eclipse or go I began
+themselves back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's most of all positive set
+
+ align:start position:0%
+okay so that's most of all positive set
+ 
+
+ align:start position:0%
+okay so that's most of all positive set
+of rules that's one kind of strategy
+
+ align:start position:0%
+of rules that's one kind of strategy
+ 
+
+ align:start position:0%
+of rules that's one kind of strategy
+which encourages you to basically not
+
+ align:start position:0%
+which encourages you to basically not
+ 
+
+ align:start position:0%
+which encourages you to basically not
+interact with anybody else and then when
+
+ align:start position:0%
+interact with anybody else and then when
+ 
+
+ align:start position:0%
+interact with anybody else and then when
+you get it right I was gonna say there
+
+ align:start position:0%
+you get it right I was gonna say there
+ 
+
+ align:start position:0%
+you get it right I was gonna say there
+is this is where it's just one player
+
+ align:start position:0%
+is this is where it's just one player
+ 
+
+ align:start position:0%
+is this is where it's just one player
+chooses what's the other place wins
+
+ align:start position:0%
+chooses what's the other place wins
+ 
+
+ align:start position:0%
+chooses what's the other place wins
+mm-hmm so so I believe keep making what
+
+ align:start position:0%
+mm-hmm so so I believe keep making what
+ 
+
+ align:start position:0%
+mm-hmm so so I believe keep making what
+the name that was given to do that you
+
+ align:start position:0%
+the name that was given to do that you
+ 
+
+ align:start position:0%
+the name that was given to do that you
+may not be in a position to win the game
+
+ align:start position:0%
+may not be in a position to win the game
+ 
+
+ align:start position:0%
+may not be in a position to win the game
+but a game with only three players you
+
+ align:start position:0%
+but a game with only three players you
+ 
+
+ align:start position:0%
+but a game with only three players you
+might have enough influence to basically
+
+ align:start position:0%
+might have enough influence to basically
+ 
+
+ align:start position:0%
+might have enough influence to basically
+say I don't like you that's why you are
+
+ align:start position:0%
+say I don't like you that's why you are
+ 
+
+ align:start position:0%
+say I don't like you that's why you are
+not gonna win that's what the other
+
+ align:start position:0%
+not gonna win that's what the other
+ 
+
+ align:start position:0%
+not gonna win that's what the other
+person's got away even though I right
+
+ align:start position:0%
+person's got away even though I right
+ 
+
+ align:start position:0%
+person's got away even though I right
+now work you more more sort of like
+
+ align:start position:0%
+now work you more more sort of like
+ 
+
+ align:start position:0%
+now work you more more sort of like
+subtle problems that you described
+
+ align:start position:0%
+subtle problems that you described
+ 
+
+ align:start position:0%
+subtle problems that you described
+remember Nia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one with politics of two people the
+
+ align:start position:0%
+one with politics of two people the
+ 
+
+ align:start position:0%
+one with politics of two people the
+other campaign uh Rock yeah he brought
+
+ align:start position:0%
+other campaign uh Rock yeah he brought
+ 
+
+ align:start position:0%
+other campaign uh Rock yeah he brought
+it up this that's come up in a reading
+
+ align:start position:0%
+it up this that's come up in a reading
+ 
+
+ align:start position:0%
+it up this that's come up in a reading
+yeah it's not necessary described as a
+
+ align:start position:0%
+yeah it's not necessary described as a
+ 
+
+ align:start position:0%
+yeah it's not necessary described as a
+problem but something that does happen
+
+ align:start position:0%
+problem but something that does happen
+ 
+
+ align:start position:0%
+problem but something that does happen
+and happens often so you either take
+
+ align:start position:0%
+and happens often so you either take
+ 
+
+ align:start position:0%
+and happens often so you either take
+advantage of it or as a designer or you
+
+ align:start position:0%
+advantage of it or as a designer or you
+ 
+
+ align:start position:0%
+advantage of it or as a designer or you
+or you own all your game separates
+
+ align:start position:0%
+or you own all your game separates
+ 
+
+ align:start position:0%
+or you own all your game separates
+because you hadn't thought about it
+
+ align:start position:0%
+because you hadn't thought about it
+ 
+
+ align:start position:0%
+because you hadn't thought about it
+right this whole idea of somebody's it
+
+ align:start position:0%
+right this whole idea of somebody's it
+ 
+
+ align:start position:0%
+right this whole idea of somebody's it
+elite and two people probably want to do
+
+ align:start position:0%
+elite and two people probably want to do
+ 
+
+ align:start position:0%
+elite and two people probably want to do
+a temporary alliance that very nice try
+
+ align:start position:0%
+a temporary alliance that very nice try
+ 
+
+ align:start position:0%
+a temporary alliance that very nice try
+to take down with that way those are
+
+ align:start position:0%
+to take down with that way those are
+ 
+
+ align:start position:0%
+to take down with that way those are
+called sanitizing and I'm actually
+
+ align:start position:0%
+called sanitizing and I'm actually
+ 
+
+ align:start position:0%
+called sanitizing and I'm actually
+forgetting what that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah pretending that you are light
+
+ align:start position:0%
+oh yeah pretending that you are light
+ 
+
+ align:start position:0%
+oh yeah pretending that you are light
+light like all your trying like
+
+ align:start position:0%
+light like all your trying like
+ 
+
+ align:start position:0%
+light like all your trying like
+bordering on lying right you know honest
+
+ align:start position:0%
+bordering on lying right you know honest
+ 
+
+ align:start position:0%
+bordering on lying right you know honest
+like now I'm not gonna win the game in
+
+ align:start position:0%
+like now I'm not gonna win the game in
+ 
+
+ align:start position:0%
+like now I'm not gonna win the game in
+the next turn
+
+ align:start position:0%
+the next turn
+ 
+
+ align:start position:0%
+the next turn
+don't worry about me new leaf and used
+
+ align:start position:0%
+don't worry about me new leaf and used
+ 
+
+ align:start position:0%
+don't worry about me new leaf and used
+area you know and that that sort of
+
+ align:start position:0%
+area you know and that that sort of
+ 
+
+ align:start position:0%
+area you know and that that sort of
+light Sun of defeat where where you have
+
+ align:start position:0%
+light Sun of defeat where where you have
+ 
+
+ align:start position:0%
+light Sun of defeat where where you have
+to like actively conceal the fact that
+
+ align:start position:0%
+to like actively conceal the fact that
+ 
+
+ align:start position:0%
+to like actively conceal the fact that
+you are not Italy then there are some
+
+ align:start position:0%
+you are not Italy then there are some
+ 
+
+ align:start position:0%
+you are not Italy then there are some
+games that say all right here are some
+
+ align:start position:0%
+games that say all right here are some
+ 
+
+ align:start position:0%
+games that say all right here are some
+ways that you can do that I'm not sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so crunches a game about being
+
+ align:start position:0%
+yeah yeah so crunches a game about being
+ 
+
+ align:start position:0%
+yeah yeah so crunches a game about being
+a banker during I'm trying to fill up
+
+ align:start position:0%
+a banker during I'm trying to fill up
+ 
+
+ align:start position:0%
+a banker during I'm trying to fill up
+your golden parachute before the market
+
+ align:start position:0%
+your golden parachute before the market
+ 
+
+ align:start position:0%
+your golden parachute before the market
+crashes and you are encouraged to play
+
+ align:start position:0%
+crashes and you are encouraged to play
+ 
+
+ align:start position:0%
+crashes and you are encouraged to play
+the game and it's releases so that you
+
+ align:start position:0%
+the game and it's releases so that you
+ 
+
+ align:start position:0%
+the game and it's releases so that you
+can actually actively hide parts and and
+
+ align:start position:0%
+can actually actively hide parts and and
+ 
+
+ align:start position:0%
+can actually actively hide parts and and
+the idea is that at the end of the game
+
+ align:start position:0%
+the idea is that at the end of the game
+ 
+
+ align:start position:0%
+the idea is that at the end of the game
+the amount of money that you've managed
+
+ align:start position:0%
+the amount of money that you've managed
+ 
+
+ align:start position:0%
+the amount of money that you've managed
+to sequester for your own personal use
+
+ align:start position:0%
+to sequester for your own personal use
+ 
+
+ align:start position:0%
+to sequester for your own personal use
+including any cards that you have habit
+
+ align:start position:0%
+including any cards that you have habit
+ 
+
+ align:start position:0%
+including any cards that you have habit
+of hitting on off on yourself will we do
+
+ align:start position:0%
+of hitting on off on yourself will we do
+ 
+
+ align:start position:0%
+of hitting on off on yourself will we do
+the game it's not about keeping your
+
+ align:start position:0%
+the game it's not about keeping your
+ 
+
+ align:start position:0%
+the game it's not about keeping your
+bank system at all it's all about
+
+ align:start position:0%
+bank system at all it's all about
+ 
+
+ align:start position:0%
+bank system at all it's all about
+leaving with the one with with largest
+
+ align:start position:0%
+leaving with the one with with largest
+ 
+
+ align:start position:0%
+leaving with the one with with largest
+personal fortune so it's this rice
+
+ align:start position:0%
+personal fortune so it's this rice
+ 
+
+ align:start position:0%
+personal fortune so it's this rice
+satirical game but that one actively
+
+ align:start position:0%
+satirical game but that one actively
+ 
+
+ align:start position:0%
+satirical game but that one actively
+encourages you to conceal how well
+
+ align:start position:0%
+encourages you to conceal how well
+ 
+
+ align:start position:0%
+encourages you to conceal how well
+they're performing now it's to play a
+
+ align:start position:0%
+they're performing now it's to play a
+ 
+
+ align:start position:0%
+they're performing now it's to play a
+game it's not like a like a trip to
+
+ align:start position:0%
+game it's not like a like a trip to
+ 
+
+ align:start position:0%
+game it's not like a like a trip to
+anything so that you are also well aware
+
+ align:start position:0%
+anything so that you are also well aware
+ 
+
+ align:start position:0%
+anything so that you are also well aware
+that your foot is doing the same sort of
+
+ align:start position:0%
+that your foot is doing the same sort of
+ 
+
+ align:start position:0%
+that your foot is doing the same sort of
+thing you're just trying to do the best
+
+ align:start position:0%
+thing you're just trying to do the best
+ 
+
+ align:start position:0%
+thing you're just trying to do the best
+that you can in accumulating as much
+
+ align:start position:0%
+that you can in accumulating as much
+ 
+
+ align:start position:0%
+that you can in accumulating as much
+cash as possible
+
+ align:start position:0%
+cash as possible
+ 
+
+ align:start position:0%
+cash as possible
+because that that's what's gonna win you
+
+ align:start position:0%
+because that that's what's gonna win you
+ 
+
+ align:start position:0%
+because that that's what's gonna win you
+again but in the situation with three
+
+ align:start position:0%
+again but in the situation with three
+ 
+
+ align:start position:0%
+again but in the situation with three
+players you can imagine a situation
+
+ align:start position:0%
+players you can imagine a situation
+ 
+
+ align:start position:0%
+players you can imagine a situation
+where someone could figure out that
+
+ align:start position:0%
+where someone could figure out that
+ 
+
+ align:start position:0%
+where someone could figure out that
+you're in the lead and that person can
+
+ align:start position:0%
+you're in the lead and that person can
+ 
+
+ align:start position:0%
+you're in the lead and that person can
+catch up and you know what can you do
+
+ align:start position:0%
+catch up and you know what can you do
+ 
+
+ align:start position:0%
+catch up and you know what can you do
+like pass cards to the to the player
+
+ align:start position:0%
+like pass cards to the to the player
+ 
+
+ align:start position:0%
+like pass cards to the to the player
+that you want to win you know for
+
+ align:start position:0%
+that you want to win you know for
+ 
+
+ align:start position:0%
+that you want to win you know for
+instance and that might be tough because
+
+ align:start position:0%
+instance and that might be tough because
+ 
+
+ align:start position:0%
+instance and that might be tough because
+someone might not be able to interfere
+
+ align:start position:0%
+someone might not be able to interfere
+ 
+
+ align:start position:0%
+someone might not be able to interfere
+with the process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's like you're like into your a
+
+ align:start position:0%
+there's like you're like into your a
+ 
+
+ align:start position:0%
+there's like you're like into your a
+like politician in sunlight and some
+
+ align:start position:0%
+like politician in sunlight and some
+ 
+
+ align:start position:0%
+like politician in sunlight and some
+Latin American Banana Republic their
+
+ align:start position:0%
+Latin American Banana Republic their
+ 
+
+ align:start position:0%
+Latin American Banana Republic their
+goal was to embezzle as much warning
+
+ align:start position:0%
+goal was to embezzle as much warning
+ 
+
+ align:start position:0%
+goal was to embezzle as much warning
+money as possible and one of the things
+
+ align:start position:0%
+money as possible and one of the things
+ 
+
+ align:start position:0%
+money as possible and one of the things
+that the the Ghana for daily drama
+
+ align:start position:0%
+that the the Ghana for daily drama
+ 
+
+ align:start position:0%
+that the the Ghana for daily drama
+eacher is variable and like only the
+
+ align:start position:0%
+eacher is variable and like only the
+ 
+
+ align:start position:0%
+eacher is variable and like only the
+president really knows me and so like
+
+ align:start position:0%
+president really knows me and so like
+ 
+
+ align:start position:0%
+president really knows me and so like
+that's other parts lien is that
+
+ align:start position:0%
+that's other parts lien is that
+ 
+
+ align:start position:0%
+that's other parts lien is that
+sometimes like the president will draw
+
+ align:start position:0%
+sometimes like the president will draw
+ 
+
+ align:start position:0%
+sometimes like the president will draw
+very much where's my like cause even
+
+ align:start position:0%
+very much where's my like cause even
+ 
+
+ align:start position:0%
+very much where's my like cause even
+logic cool against it because they think
+
+ align:start position:0%
+logic cool against it because they think
+ 
+
+ align:start position:0%
+logic cool against it because they think
+he's lying and taking a lot for himself
+
+ align:start position:0%
+he's lying and taking a lot for himself
+ 
+
+ align:start position:0%
+he's lying and taking a lot for himself
+and they're scared and waiting for a
+
+ align:start position:0%
+and they're scared and waiting for a
+ 
+
+ align:start position:0%
+and they're scared and waiting for a
+reason like yeah basically there's so
+
+ align:start position:0%
+reason like yeah basically there's so
+ 
+
+ align:start position:0%
+reason like yeah basically there's so
+much uncertainty about how much like
+
+ align:start position:0%
+much uncertainty about how much like
+ 
+
+ align:start position:0%
+much uncertainty about how much like
+it's not computable how much people have
+
+ align:start position:0%
+it's not computable how much people have
+ 
+
+ align:start position:0%
+it's not computable how much people have
+in their head with a J right there yeah
+
+ align:start position:0%
+in their head with a J right there yeah
+ 
+
+ align:start position:0%
+in their head with a J right there yeah
+so because need right it sort of plays
+
+ align:start position:0%
+so because need right it sort of plays
+ 
+
+ align:start position:0%
+so because need right it sort of plays
+around around with this idea that you
+
+ align:start position:0%
+around around with this idea that you
+ 
+
+ align:start position:0%
+around around with this idea that you
+know you have this dictator that's
+
+ align:start position:0%
+know you have this dictator that's
+ 
+
+ align:start position:0%
+know you have this dictator that's
+that's seems to be amassing a large
+
+ align:start position:0%
+that's seems to be amassing a large
+ 
+
+ align:start position:0%
+that's seems to be amassing a large
+personal fortune whether or not the
+
+ align:start position:0%
+personal fortune whether or not the
+ 
+
+ align:start position:0%
+personal fortune whether or not the
+dictator that that is actually being
+
+ align:start position:0%
+dictator that that is actually being
+ 
+
+ align:start position:0%
+dictator that that is actually being
+successful in a process of amassing a
+
+ align:start position:0%
+successful in a process of amassing a
+ 
+
+ align:start position:0%
+successful in a process of amassing a
+bit large personal fortune it is that
+
+ align:start position:0%
+bit large personal fortune it is that
+ 
+
+ align:start position:0%
+bit large personal fortune it is that
+that game is designed to paint a giant
+
+ align:start position:0%
+that game is designed to paint a giant
+ 
+
+ align:start position:0%
+that game is designed to paint a giant
+target may be another game here called
+
+ align:start position:0%
+target may be another game here called
+ 
+
+ align:start position:0%
+target may be another game here called
+king of Tokyo which is basically giant
+
+ align:start position:0%
+king of Tokyo which is basically giant
+ 
+
+ align:start position:0%
+king of Tokyo which is basically giant
+monsters trying to take over the bait
+
+ align:start position:0%
+monsters trying to take over the bait
+ 
+
+ align:start position:0%
+monsters trying to take over the bait
+took away every single generic giant
+
+ align:start position:0%
+took away every single generic giant
+ 
+
+ align:start position:0%
+took away every single generic giant
+robot giant dinosaur octopus singing
+
+ align:start position:0%
+robot giant dinosaur octopus singing
+ 
+
+ align:start position:0%
+robot giant dinosaur octopus singing
+make a dinosaur and and whoever happens
+
+ align:start position:0%
+make a dinosaur and and whoever happens
+ 
+
+ align:start position:0%
+make a dinosaur and and whoever happens
+to be a king of the hill at that point
+
+ align:start position:0%
+to be a king of the hill at that point
+ 
+
+ align:start position:0%
+to be a king of the hill at that point
+has a giant target on not that many game
+
+ align:start position:0%
+has a giant target on not that many game
+ 
+
+ align:start position:0%
+has a giant target on not that many game
+mechanics all support that that's what
+
+ align:start position:0%
+mechanics all support that that's what
+ 
+
+ align:start position:0%
+mechanics all support that that's what
+the games all about so so those are some
+
+ align:start position:0%
+the games all about so so those are some
+ 
+
+ align:start position:0%
+the games all about so so those are some
+of the problems and he and he proposes
+
+ align:start position:0%
+of the problems and he and he proposes
+ 
+
+ align:start position:0%
+of the problems and he and he proposes
+two solutions it's not necessarily in
+
+ align:start position:0%
+two solutions it's not necessarily in
+ 
+
+ align:start position:0%
+two solutions it's not necessarily in
+the only two solutions but these are the
+
+ align:start position:0%
+the only two solutions but these are the
+ 
+
+ align:start position:0%
+the only two solutions but these are the
+ones that now occurs to him and
+
+ align:start position:0%
+ones that now occurs to him and
+ 
+
+ align:start position:0%
+ones that now occurs to him and
+particularly in the wargaming since this
+
+ align:start position:0%
+particularly in the wargaming since this
+ 
+
+ align:start position:0%
+particularly in the wargaming since this
+might work and there are actually kind
+
+ align:start position:0%
+might work and there are actually kind
+ 
+
+ align:start position:0%
+might work and there are actually kind
+of opposite ends of the spectrum
+
+ align:start position:0%
+of opposite ends of the spectrum
+ 
+
+ align:start position:0%
+of opposite ends of the spectrum
+anyone remember one of those two
+
+ align:start position:0%
+anyone remember one of those two
+ 
+
+ align:start position:0%
+anyone remember one of those two
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+equilibrium if one person gets ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they cannot be significant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think equilibrium was the opposite of
+
+ align:start position:0%
+I think equilibrium was the opposite of
+ 
+
+ align:start position:0%
+I think equilibrium was the opposite of
+that yeah so so you've actually just
+
+ align:start position:0%
+that yeah so so you've actually just
+ 
+
+ align:start position:0%
+that yeah so so you've actually just
+completed two answers into one which is
+
+ align:start position:0%
+completed two answers into one which is
+ 
+
+ align:start position:0%
+completed two answers into one which is
+good so so the equilibrium if I recall
+
+ align:start position:0%
+good so so the equilibrium if I recall
+ 
+
+ align:start position:0%
+good so so the equilibrium if I recall
+correctly from the reading the
+
+ align:start position:0%
+correctly from the reading the
+ 
+
+ align:start position:0%
+correctly from the reading the
+equilibria method was or design goal
+
+ align:start position:0%
+equilibria method was or design goal
+ 
+
+ align:start position:0%
+equilibria method was or design goal
+that seems like if you manage to in sign
+
+ align:start position:0%
+that seems like if you manage to in sign
+ 
+
+ align:start position:0%
+that seems like if you manage to in sign
+that is taking advantage of things like
+
+ align:start position:0%
+that is taking advantage of things like
+ 
+
+ align:start position:0%
+that is taking advantage of things like
+the balance of power theory which is if
+
+ align:start position:0%
+the balance of power theory which is if
+ 
+
+ align:start position:0%
+the balance of power theory which is if
+there is a person who's clearly ahead
+
+ align:start position:0%
+there is a person who's clearly ahead
+ 
+
+ align:start position:0%
+there is a person who's clearly ahead
+everybody else who is weaker is probably
+
+ align:start position:0%
+everybody else who is weaker is probably
+ 
+
+ align:start position:0%
+everybody else who is weaker is probably
+going to band up and take you down and
+
+ align:start position:0%
+going to band up and take you down and
+ 
+
+ align:start position:0%
+going to band up and take you down and
+if you balance the game in a certain way
+
+ align:start position:0%
+if you balance the game in a certain way
+ 
+
+ align:start position:0%
+if you balance the game in a certain way
+you give that the tools to do that and
+
+ align:start position:0%
+you give that the tools to do that and
+ 
+
+ align:start position:0%
+you give that the tools to do that and
+does take anyone who seems to be ahead
+
+ align:start position:0%
+does take anyone who seems to be ahead
+ 
+
+ align:start position:0%
+does take anyone who seems to be ahead
+back to a sort of equal power level
+
+ align:start position:0%
+back to a sort of equal power level
+ 
+
+ align:start position:0%
+back to a sort of equal power level
+that's a bad balance of power theory is
+
+ align:start position:0%
+that's a bad balance of power theory is
+ 
+
+ align:start position:0%
+that's a bad balance of power theory is
+something for political science I've
+
+ align:start position:0%
+something for political science I've
+ 
+
+ align:start position:0%
+something for political science I've
+only heard about it in passing if
+
+ align:start position:0%
+only heard about it in passing if
+ 
+
+ align:start position:0%
+only heard about it in passing if
+there's anybody here who's taking
+
+ align:start position:0%
+there's anybody here who's taking
+ 
+
+ align:start position:0%
+there's anybody here who's taking
+political science classes you can tell
+
+ align:start position:0%
+political science classes you can tell
+ 
+
+ align:start position:0%
+political science classes you can tell
+me ever getting this right around the
+
+ align:start position:0%
+me ever getting this right around the
+ 
+
+ align:start position:0%
+me ever getting this right around the
+whole place is not a far-fetched idea
+
+ align:start position:0%
+whole place is not a far-fetched idea
+ 
+
+ align:start position:0%
+whole place is not a far-fetched idea
+right you know you got if you've got a
+
+ align:start position:0%
+right you know you got if you've got a
+ 
+
+ align:start position:0%
+right you know you got if you've got a
+powerful nation other nations were
+
+ align:start position:0%
+powerful nation other nations were
+ 
+
+ align:start position:0%
+powerful nation other nations were
+bothering them that that powerful nation
+
+ align:start position:0%
+bothering them that that powerful nation
+ 
+
+ align:start position:0%
+bothering them that that powerful nation
+are likely to either team up with the
+
+ align:start position:0%
+are likely to either team up with the
+ 
+
+ align:start position:0%
+are likely to either team up with the
+powerful nation are more likely to
+
+ align:start position:0%
+powerful nation are more likely to
+ 
+
+ align:start position:0%
+powerful nation are more likely to
+perish together even though they may not
+
+ align:start position:0%
+perish together even though they may not
+ 
+
+ align:start position:0%
+perish together even though they may not
+be ideologically later ideologically
+
+ align:start position:0%
+be ideologically later ideologically
+ 
+
+ align:start position:0%
+be ideologically later ideologically
+with against that tell powerful nation
+
+ align:start position:0%
+with against that tell powerful nation
+ 
+
+ align:start position:0%
+with against that tell powerful nation
+yeah so in same thing with those four
+
+ align:start position:0%
+yeah so in same thing with those four
+ 
+
+ align:start position:0%
+yeah so in same thing with those four
+players so basically comes down to
+
+ align:start position:0%
+players so basically comes down to
+ 
+
+ align:start position:0%
+players so basically comes down to
+giving everybody the tool to take down
+
+ align:start position:0%
+giving everybody the tool to take down
+ 
+
+ align:start position:0%
+giving everybody the tool to take down
+the leader a notch and man does restore
+
+ align:start position:0%
+the leader a notch and man does restore
+ 
+
+ align:start position:0%
+the leader a notch and man does restore
+everything to a sort of equilibrium
+
+ align:start position:0%
+everything to a sort of equilibrium
+ 
+
+ align:start position:0%
+everything to a sort of equilibrium
+state and then yours your your success
+
+ align:start position:0%
+state and then yours your your success
+ 
+
+ align:start position:0%
+state and then yours your your success
+criteria for the game probably isn't
+
+ align:start position:0%
+criteria for the game probably isn't
+ 
+
+ align:start position:0%
+criteria for the game probably isn't
+who's going to to gain such a massively
+
+ align:start position:0%
+who's going to to gain such a massively
+ 
+
+ align:start position:0%
+who's going to to gain such a massively
+because the game is deliberately
+
+ align:start position:0%
+because the game is deliberately
+ 
+
+ align:start position:0%
+because the game is deliberately
+designed to restore everything to
+
+ align:start position:0%
+designed to restore everything to
+ 
+
+ align:start position:0%
+designed to restore everything to
+equilibria you have you need to have
+
+ align:start position:0%
+equilibria you have you need to have
+ 
+
+ align:start position:0%
+equilibria you have you need to have
+some other kinds of success criteria
+
+ align:start position:0%
+some other kinds of success criteria
+ 
+
+ align:start position:0%
+some other kinds of success criteria
+maybe the game is kind limited for
+
+ align:start position:0%
+maybe the game is kind limited for
+ 
+
+ align:start position:0%
+maybe the game is kind limited for
+instance maybe the game is different
+
+ align:start position:0%
+instance maybe the game is different
+ 
+
+ align:start position:0%
+instance maybe the game is different
+goals for each player or something so
+
+ align:start position:0%
+goals for each player or something so
+ 
+
+ align:start position:0%
+goals for each player or something so
+even though your power levels are about
+
+ align:start position:0%
+even though your power levels are about
+ 
+
+ align:start position:0%
+even though your power levels are about
+the same you might be a
+
+ align:start position:0%
+the same you might be a
+ 
+
+ align:start position:0%
+the same you might be a
+to accomplish of get victory points on
+
+ align:start position:0%
+to accomplish of get victory points on
+ 
+
+ align:start position:0%
+to accomplish of get victory points on
+something faster than others what about
+
+ align:start position:0%
+something faster than others what about
+ 
+
+ align:start position:0%
+something faster than others what about
+the the alternative which you internet
+
+ align:start position:0%
+the the alternative which you internet
+ 
+
+ align:start position:0%
+the the alternative which you internet
+which was basically making it difficult
+
+ align:start position:0%
+which was basically making it difficult
+ 
+
+ align:start position:0%
+which was basically making it difficult
+to take down the person who's in the
+
+ align:start position:0%
+to take down the person who's in the
+ 
+
+ align:start position:0%
+to take down the person who's in the
+lead
+
+ align:start position:0%
+lead
+ 
+
+ align:start position:0%
+lead
+once they already in the lead so that
+
+ align:start position:0%
+once they already in the lead so that
+ 
+
+ align:start position:0%
+once they already in the lead so that
+was like he had one very specific
+
+ align:start position:0%
+was like he had one very specific
+ 
+
+ align:start position:0%
+was like he had one very specific
+implementation of this or one one
+
+ align:start position:0%
+implementation of this or one one
+ 
+
+ align:start position:0%
+implementation of this or one one
+particular rule of thumb on how how how
+
+ align:start position:0%
+particular rule of thumb on how how how
+ 
+
+ align:start position:0%
+particular rule of thumb on how how how
+how effect it must have president he'd
+
+ align:start position:0%
+how effect it must have president he'd
+ 
+
+ align:start position:0%
+how effect it must have president he'd
+be in order to prevent the key making
+
+ align:start position:0%
+be in order to prevent the key making
+ 
+
+ align:start position:0%
+be in order to prevent the key making
+and assign my gaining and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the basic idea is that you must be
+
+ align:start position:0%
+well the basic idea is that you must be
+ 
+
+ align:start position:0%
+well the basic idea is that you must be
+able to do it in a trip and turns in a
+
+ align:start position:0%
+able to do it in a trip and turns in a
+ 
+
+ align:start position:0%
+able to do it in a trip and turns in a
+single turn you should be able to if you
+
+ align:start position:0%
+single turn you should be able to if you
+ 
+
+ align:start position:0%
+single turn you should be able to if you
+are in the lead you should be able to
+
+ align:start position:0%
+are in the lead you should be able to
+ 
+
+ align:start position:0%
+are in the lead you should be able to
+complete the game and win the game as an
+
+ align:start position:0%
+complete the game and win the game as an
+ 
+
+ align:start position:0%
+complete the game and win the game as an
+alternate I'm not so sure whether I
+
+ align:start position:0%
+alternate I'm not so sure whether I
+ 
+
+ align:start position:0%
+alternate I'm not so sure whether I
+agree with that but and I don't think he
+
+ align:start position:0%
+agree with that but and I don't think he
+ 
+
+ align:start position:0%
+agree with that but and I don't think he
+means win it on your turn I think it
+
+ align:start position:0%
+means win it on your turn I think it
+ 
+
+ align:start position:0%
+means win it on your turn I think it
+means like in a round of people like by
+
+ align:start position:0%
+means like in a round of people like by
+ 
+
+ align:start position:0%
+means like in a round of people like by
+the time if you are in the lead in the
+
+ align:start position:0%
+the time if you are in the lead in the
+ 
+
+ align:start position:0%
+the time if you are in the lead in the
+game you should be able to do something
+
+ align:start position:0%
+game you should be able to do something
+ 
+
+ align:start position:0%
+game you should be able to do something
+that to cement that lead so that within
+
+ align:start position:0%
+that to cement that lead so that within
+ 
+
+ align:start position:0%
+that to cement that lead so that within
+that turn no one's gonna be able to do
+
+ align:start position:0%
+that turn no one's gonna be able to do
+ 
+
+ align:start position:0%
+that turn no one's gonna be able to do
+anything about energy before them okay
+
+ align:start position:0%
+anything about energy before them okay
+ 
+
+ align:start position:0%
+anything about energy before them okay
+this is a missus four games where there
+
+ align:start position:0%
+this is a missus four games where there
+ 
+
+ align:start position:0%
+this is a missus four games where there
+is like a clear win condition that's
+
+ align:start position:0%
+is like a clear win condition that's
+ 
+
+ align:start position:0%
+is like a clear win condition that's
+based on overpowering your opponents
+
+ align:start position:0%
+based on overpowering your opponents
+ 
+
+ align:start position:0%
+based on overpowering your opponents
+then you don't want to have the
+
+ align:start position:0%
+then you don't want to have the
+ 
+
+ align:start position:0%
+then you don't want to have the
+situation where yeah I'm in the lead but
+
+ align:start position:0%
+situation where yeah I'm in the lead but
+ 
+
+ align:start position:0%
+situation where yeah I'm in the lead but
+I'm still but everybody else still has
+
+ align:start position:0%
+I'm still but everybody else still has
+ 
+
+ align:start position:0%
+I'm still but everybody else still has
+enough time to to take me down to the
+
+ align:start position:0%
+enough time to to take me down to the
+ 
+
+ align:start position:0%
+enough time to to take me down to the
+point that somebody else can then catch
+
+ align:start position:0%
+point that somebody else can then catch
+ 
+
+ align:start position:0%
+point that somebody else can then catch
+up and be in the lead because that
+
+ align:start position:0%
+up and be in the lead because that
+ 
+
+ align:start position:0%
+up and be in the lead because that
+basically means that you that the first
+
+ align:start position:0%
+basically means that you that the first
+ 
+
+ align:start position:0%
+basically means that you that the first
+person to get in a league will probably
+
+ align:start position:0%
+person to get in a league will probably
+ 
+
+ align:start position:0%
+person to get in a league will probably
+use and that that's that's that sad but
+
+ align:start position:0%
+use and that that's that's that sad but
+ 
+
+ align:start position:0%
+use and that that's that's that sad but
+we've seen that in certain computer
+
+ align:start position:0%
+we've seen that in certain computer
+ 
+
+ align:start position:0%
+we've seen that in certain computer
+games we've seen games where you know
+
+ align:start position:0%
+games we've seen games where you know
+ 
+
+ align:start position:0%
+games we've seen games where you know
+whoever who's in the lead has giant
+
+ align:start position:0%
+whoever who's in the lead has giant
+ 
+
+ align:start position:0%
+whoever who's in the lead has giant
+target painted on their back and you
+
+ align:start position:0%
+target painted on their back and you
+ 
+
+ align:start position:0%
+target painted on their back and you
+know you're expected to be taken down if
+
+ align:start position:0%
+know you're expected to be taken down if
+ 
+
+ align:start position:0%
+know you're expected to be taken down if
+you're the first one in the lead you are
+
+ align:start position:0%
+you're the first one in the lead you are
+ 
+
+ align:start position:0%
+you're the first one in the lead you are
+probably going to get hit but that now
+
+ align:start position:0%
+probably going to get hit but that now
+ 
+
+ align:start position:0%
+probably going to get hit but that now
+gives you enough time to be able to pull
+
+ align:start position:0%
+gives you enough time to be able to pull
+ 
+
+ align:start position:0%
+gives you enough time to be able to pull
+ahead so so that's that's closer to the
+
+ align:start position:0%
+ahead so so that's that's closer to the
+ 
+
+ align:start position:0%
+ahead so so that's that's closer to the
+equilibrium style right so I think I
+
+ align:start position:0%
+equilibrium style right so I think I
+ 
+
+ align:start position:0%
+equilibrium style right so I think I
+heard someone give me Mario Kart in the
+
+ align:start position:0%
+heard someone give me Mario Kart in the
+ 
+
+ align:start position:0%
+heard someone give me Mario Kart in the
+obvious one you get increasingly
+
+ align:start position:0%
+obvious one you get increasingly
+ 
+
+ align:start position:0%
+obvious one you get increasingly
+powerful weapons in support of you and
+
+ align:start position:0%
+powerful weapons in support of you and
+ 
+
+ align:start position:0%
+powerful weapons in support of you and
+you get more useful things that's an
+
+ align:start position:0%
+you get more useful things that's an
+ 
+
+ align:start position:0%
+you get more useful things that's an
+example in this book here the rules of
+
+ align:start position:0%
+example in this book here the rules of
+ 
+
+ align:start position:0%
+example in this book here the rules of
+play this is this is the paperback
+
+ align:start position:0%
+play this is this is the paperback
+ 
+
+ align:start position:0%
+play this is this is the paperback
+version as a perfect Super Monkey Ball
+
+ align:start position:0%
+version as a perfect Super Monkey Ball
+ 
+
+ align:start position:0%
+version as a perfect Super Monkey Ball
+and basically all the weapons say
+
+ align:start position:0%
+and basically all the weapons say
+ 
+
+ align:start position:0%
+and basically all the weapons say
+storage so if you're number one you can
+
+ align:start position:0%
+storage so if you're number one you can
+ 
+
+ align:start position:0%
+storage so if you're number one you can
+only shoot for it that's nothing to
+
+ align:start position:0%
+only shoot for it that's nothing to
+ 
+
+ align:start position:0%
+only shoot for it that's nothing to
+shoot there's nobody ahead of you so
+
+ align:start position:0%
+shoot there's nobody ahead of you so
+ 
+
+ align:start position:0%
+shoot there's nobody ahead of you so
+it's not actually just that it's not a
+
+ align:start position:0%
+it's not actually just that it's not a
+ 
+
+ align:start position:0%
+it's not actually just that it's not a
+technical visit but it's not like a
+
+ align:start position:0%
+technical visit but it's not like a
+ 
+
+ align:start position:0%
+technical visit but it's not like a
+weapon that slows you down but you know
+
+ align:start position:0%
+weapon that slows you down but you know
+ 
+
+ align:start position:0%
+weapon that slows you down but you know
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+it's a useless thing you get these
+
+ align:start position:0%
+it's a useless thing you get these
+ 
+
+ align:start position:0%
+it's a useless thing you get these
+power-ups that are useless so a lot of
+
+ align:start position:0%
+power-ups that are useless so a lot of
+ 
+
+ align:start position:0%
+power-ups that are useless so a lot of
+these feed into a different way of
+
+ align:start position:0%
+these feed into a different way of
+ 
+
+ align:start position:0%
+these feed into a different way of
+looking at games that is very formal
+
+ align:start position:0%
+looking at games that is very formal
+ 
+
+ align:start position:0%
+looking at games that is very formal
+very techie and one that you've probably
+
+ align:start position:0%
+very techie and one that you've probably
+ 
+
+ align:start position:0%
+very techie and one that you've probably
+heard of mentioned multiple times in
+
+ align:start position:0%
+heard of mentioned multiple times in
+ 
+
+ align:start position:0%
+heard of mentioned multiple times in
+this class at another time as well
+
+ align:start position:0%
+this class at another time as well
+ 
+
+ align:start position:0%
+this class at another time as well
+that's just feedback systems I'm not
+
+ align:start position:0%
+that's just feedback systems I'm not
+ 
+
+ align:start position:0%
+that's just feedback systems I'm not
+talking about you IP bag I'm talking
+
+ align:start position:0%
+talking about you IP bag I'm talking
+ 
+
+ align:start position:0%
+talking about you IP bag I'm talking
+about the event from the cybernetics
+
+ align:start position:0%
+about the event from the cybernetics
+ 
+
+ align:start position:0%
+about the event from the cybernetics
+sense anyone tears heard about
+
+ align:start position:0%
+sense anyone tears heard about
+ 
+
+ align:start position:0%
+sense anyone tears heard about
+cybernetics from another class yeah yeah
+
+ align:start position:0%
+cybernetics from another class yeah yeah
+ 
+
+ align:start position:0%
+cybernetics from another class yeah yeah
+yeah yeah I definitely brought it up
+
+ align:start position:0%
+yeah yeah I definitely brought it up
+ 
+
+ align:start position:0%
+yeah yeah I definitely brought it up
+yeah or you had a feedback systems back
+
+ align:start position:0%
+yeah or you had a feedback systems back
+ 
+
+ align:start position:0%
+yeah or you had a feedback systems back
+with you that's it's a positive and
+
+ align:start position:0%
+with you that's it's a positive and
+ 
+
+ align:start position:0%
+with you that's it's a positive and
+negative deal if you win you either will
+
+ align:start position:0%
+negative deal if you win you either will
+ 
+
+ align:start position:0%
+negative deal if you win you either will
+start with even more or you're losing
+
+ align:start position:0%
+start with even more or you're losing
+ 
+
+ align:start position:0%
+start with even more or you're losing
+you start to catch up right so that's
+
+ align:start position:0%
+you start to catch up right so that's
+ 
+
+ align:start position:0%
+you start to catch up right so that's
+the whole basic idea of cybernetics is
+
+ align:start position:0%
+the whole basic idea of cybernetics is
+ 
+
+ align:start position:0%
+the whole basic idea of cybernetics is
+based on sort of automated control you
+
+ align:start position:0%
+based on sort of automated control you
+ 
+
+ align:start position:0%
+based on sort of automated control you
+know you've got you create systems
+
+ align:start position:0%
+know you've got you create systems
+ 
+
+ align:start position:0%
+know you've got you create systems
+mechanical or electronic or with a set
+
+ align:start position:0%
+mechanical or electronic or with a set
+ 
+
+ align:start position:0%
+mechanical or electronic or with a set
+of rules that basically going to either
+
+ align:start position:0%
+of rules that basically going to either
+ 
+
+ align:start position:0%
+of rules that basically going to either
+accelerate or sort of this off slow off
+
+ align:start position:0%
+accelerate or sort of this off slow off
+ 
+
+ align:start position:0%
+accelerate or sort of this off slow off
+slow ball the the performance of the
+
+ align:start position:0%
+slow ball the the performance of the
+ 
+
+ align:start position:0%
+slow ball the the performance of the
+system or bring it back to equilibrium
+
+ align:start position:0%
+system or bring it back to equilibrium
+ 
+
+ align:start position:0%
+system or bring it back to equilibrium
+if this sounds very familiar to
+
+ align:start position:0%
+if this sounds very familiar to
+ 
+
+ align:start position:0%
+if this sounds very familiar to
+something and Mickey or Yee or something
+
+ align:start position:0%
+something and Mickey or Yee or something
+ 
+
+ align:start position:0%
+something and Mickey or Yee or something
+that's that's completely expected thing
+
+ align:start position:0%
+that's that's completely expected thing
+ 
+
+ align:start position:0%
+that's that's completely expected thing
+this all came of that
+
+ align:start position:0%
+this all came of that
+ 
+
+ align:start position:0%
+this all came of that
+so the basic model is then you have some
+
+ align:start position:0%
+so the basic model is then you have some
+ 
+
+ align:start position:0%
+so the basic model is then you have some
+sort of sensor something that detects an
+
+ align:start position:0%
+sort of sensor something that detects an
+ 
+
+ align:start position:0%
+sort of sensor something that detects an
+environmental change it could be
+
+ align:start position:0%
+environmental change it could be
+ 
+
+ align:start position:0%
+environmental change it could be
+something that detects treat the stain
+
+ align:start position:0%
+something that detects treat the stain
+ 
+
+ align:start position:0%
+something that detects treat the stain
+of your game some way of telling you
+
+ align:start position:0%
+of your game some way of telling you
+ 
+
+ align:start position:0%
+of your game some way of telling you
+this is the current state that you're
+
+ align:start position:0%
+this is the current state that you're
+ 
+
+ align:start position:0%
+this is the current state that you're
+looking at that goes to a comparator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a small space because it's longer work
+
+ align:start position:0%
+a small space because it's longer work
+ 
+
+ align:start position:0%
+a small space because it's longer work
+compared read before which performs some
+
+ align:start position:0%
+compared read before which performs some
+ 
+
+ align:start position:0%
+compared read before which performs some
+sort of logical assessment on the state
+
+ align:start position:0%
+sort of logical assessment on the state
+ 
+
+ align:start position:0%
+sort of logical assessment on the state
+of the system that you're looking at
+
+ align:start position:0%
+of the system that you're looking at
+ 
+
+ align:start position:0%
+of the system that you're looking at
+then are you going to an actuator which
+
+ align:start position:0%
+then are you going to an actuator which
+ 
+
+ align:start position:0%
+then are you going to an actuator which
+perform some sort of action and it's
+
+ align:start position:0%
+perform some sort of action and it's
+ 
+
+ align:start position:0%
+perform some sort of action and it's
+called feedback because this thing just
+
+ align:start position:0%
+called feedback because this thing just
+ 
+
+ align:start position:0%
+called feedback because this thing just
+keeps me depend right real life systems
+
+ align:start position:0%
+keeps me depend right real life systems
+ 
+
+ align:start position:0%
+keeps me depend right real life systems
+that do this like what some of the
+
+ align:start position:0%
+that do this like what some of the
+ 
+
+ align:start position:0%
+that do this like what some of the
+simplest real life systems that it is
+
+ align:start position:0%
+simplest real life systems that it is
+ 
+
+ align:start position:0%
+simplest real life systems that it is
+like electronically or mechanically
+
+ align:start position:0%
+like electronically or mechanically
+ 
+
+ align:start position:0%
+like electronically or mechanically
+without human knowledge without
+
+ align:start position:0%
+without human knowledge without
+ 
+
+ align:start position:0%
+without human knowledge without
+intervention washing machine washing
+
+ align:start position:0%
+intervention washing machine washing
+ 
+
+ align:start position:0%
+intervention washing machine washing
+machine never said that was that that's
+
+ align:start position:0%
+machine never said that was that that's
+ 
+
+ align:start position:0%
+machine never said that was that that's
+that way oh yeah yeah yeah that's true
+
+ align:start position:0%
+that way oh yeah yeah yeah that's true
+ 
+
+ align:start position:0%
+that way oh yeah yeah yeah that's true
+so so much that things get too hot
+
+ align:start position:0%
+so so much that things get too hot
+ 
+
+ align:start position:0%
+so so much that things get too hot
+turn on the cooling system you know shut
+
+ align:start position:0%
+turn on the cooling system you know shut
+ 
+
+ align:start position:0%
+turn on the cooling system you know shut
+off the heating system you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sensor is you know whether the water
+
+ align:start position:0%
+the sensor is you know whether the water
+ 
+
+ align:start position:0%
+the sensor is you know whether the water
+is actually hit that hole you know in
+
+ align:start position:0%
+is actually hit that hole you know in
+ 
+
+ align:start position:0%
+is actually hit that hole you know in
+context
+
+ align:start position:0%
+context
+ 
+
+ align:start position:0%
+context
+I guess the sensor is the level of the
+
+ align:start position:0%
+I guess the sensor is the level of the
+ 
+
+ align:start position:0%
+I guess the sensor is the level of the
+water the comparator is at a height of
+
+ align:start position:0%
+water the comparator is at a height of
+ 
+
+ align:start position:0%
+water the comparator is at a height of
+the hole and then the activator is if
+
+ align:start position:0%
+the hole and then the activator is if
+ 
+
+ align:start position:0%
+the hole and then the activator is if
+it's at the right of the hole called a
+
+ align:start position:0%
+it's at the right of the hole called a
+ 
+
+ align:start position:0%
+it's at the right of the hole called a
+hole right so so it's actually just like
+
+ align:start position:0%
+hole right so so it's actually just like
+ 
+
+ align:start position:0%
+hole right so so it's actually just like
+physics is the entire system for you but
+
+ align:start position:0%
+physics is the entire system for you but
+ 
+
+ align:start position:0%
+physics is the entire system for you but
+it's been interior in a way to take a
+
+ align:start position:0%
+it's been interior in a way to take a
+ 
+
+ align:start position:0%
+it's been interior in a way to take a
+bunch of systems like autopilot Amy
+
+ align:start position:0%
+bunch of systems like autopilot Amy
+ 
+
+ align:start position:0%
+bunch of systems like autopilot Amy
+mm-hm this sort of keeping you on the
+
+ align:start position:0%
+mm-hm this sort of keeping you on the
+ 
+
+ align:start position:0%
+mm-hm this sort of keeping you on the
+path that you're supposed to be and it's
+
+ align:start position:0%
+path that you're supposed to be and it's
+ 
+
+ align:start position:0%
+path that you're supposed to be and it's
+always just doing my cute little
+
+ align:start position:0%
+always just doing my cute little
+ 
+
+ align:start position:0%
+always just doing my cute little
+Corrections majority of these things are
+
+ align:start position:0%
+Corrections majority of these things are
+ 
+
+ align:start position:0%
+Corrections majority of these things are
+real world applications of these
+
+ align:start position:0%
+real world applications of these
+ 
+
+ align:start position:0%
+real world applications of these
+negative feedback systems so the idea is
+
+ align:start position:0%
+negative feedback systems so the idea is
+ 
+
+ align:start position:0%
+negative feedback systems so the idea is
+that you know if there is a change in
+
+ align:start position:0%
+that you know if there is a change in
+ 
+
+ align:start position:0%
+that you know if there is a change in
+one direction pull it back you know if
+
+ align:start position:0%
+one direction pull it back you know if
+ 
+
+ align:start position:0%
+one direction pull it back you know if
+it goes if you had a direction pull it
+
+ align:start position:0%
+it goes if you had a direction pull it
+ 
+
+ align:start position:0%
+it goes if you had a direction pull it
+forward so that it so they're always
+
+ align:start position:0%
+forward so that it so they're always
+ 
+
+ align:start position:0%
+forward so that it so they're always
+sort of hovers around let's see these
+
+ align:start position:0%
+sort of hovers around let's see these
+ 
+
+ align:start position:0%
+sort of hovers around let's see these
+are like deliberately designed systems
+
+ align:start position:0%
+are like deliberately designed systems
+ 
+
+ align:start position:0%
+are like deliberately designed systems
+trying to do this all the time but there
+
+ align:start position:0%
+trying to do this all the time but there
+ 
+
+ align:start position:0%
+trying to do this all the time but there
+are a lot of real systems that do the
+
+ align:start position:0%
+are a lot of real systems that do the
+ 
+
+ align:start position:0%
+are a lot of real systems that do the
+opposite right stuff it snowballs for
+
+ align:start position:0%
+opposite right stuff it snowballs for
+ 
+
+ align:start position:0%
+opposite right stuff it snowballs for
+instance a snowball rolling down the
+
+ align:start position:0%
+instance a snowball rolling down the
+ 
+
+ align:start position:0%
+instance a snowball rolling down the
+hill and as it goes down it gets larger
+
+ align:start position:0%
+hill and as it goes down it gets larger
+ 
+
+ align:start position:0%
+hill and as it goes down it gets larger
+and it makes it slightly easier to
+
+ align:start position:0%
+and it makes it slightly easier to
+ 
+
+ align:start position:0%
+and it makes it slightly easier to
+continue whole thing I think surface
+
+ align:start position:0%
+continue whole thing I think surface
+ 
+
+ align:start position:0%
+continue whole thing I think surface
+area in contact to the snow actually
+
+ align:start position:0%
+area in contact to the snow actually
+ 
+
+ align:start position:0%
+area in contact to the snow actually
+decreases from the ratio 522 makes it
+
+ align:start position:0%
+decreases from the ratio 522 makes it
+ 
+
+ align:start position:0%
+decreases from the ratio 522 makes it
+easier to keep only it exact most well I
+
+ align:start position:0%
+easier to keep only it exact most well I
+ 
+
+ align:start position:0%
+easier to keep only it exact most well I
+guess another matter
+
+ align:start position:0%
+guess another matter
+ 
+
+ align:start position:0%
+guess another matter
+at the positive feedback system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's for asteroids because fairly easy
+
+ align:start position:0%
+that's for asteroids because fairly easy
+ 
+
+ align:start position:0%
+that's for asteroids because fairly easy
+other small edits to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are two games that might that
+
+ align:start position:0%
+so there are two games that might that
+ 
+
+ align:start position:0%
+so there are two games that might that
+might be on what is orbital the Nintendo
+
+ align:start position:0%
+might be on what is orbital the Nintendo
+ 
+
+ align:start position:0%
+might be on what is orbital the Nintendo
+game what which can we suspect that
+
+ align:start position:0%
+game what which can we suspect that
+ 
+
+ align:start position:0%
+game what which can we suspect that
+sounds like category policies it's not
+
+ align:start position:0%
+sounds like category policies it's not
+ 
+
+ align:start position:0%
+sounds like category policies it's not
+like oh yeah let's see Osmos yeah I
+
+ align:start position:0%
+like oh yeah let's see Osmos yeah I
+ 
+
+ align:start position:0%
+like oh yeah let's see Osmos yeah I
+think that's a PC and portable device
+
+ align:start position:0%
+think that's a PC and portable device
+ 
+
+ align:start position:0%
+think that's a PC and portable device
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so that I suppose it's an interesting
+
+ align:start position:0%
+so that I suppose it's an interesting
+ 
+
+ align:start position:0%
+so that I suppose it's an interesting
+situation because yes the bigger you get
+
+ align:start position:0%
+situation because yes the bigger you get
+ 
+
+ align:start position:0%
+situation because yes the bigger you get
+the bigger you can get because the idea
+
+ align:start position:0%
+the bigger you can get because the idea
+ 
+
+ align:start position:0%
+the bigger you can get because the idea
+of osmosis by journalists I know people
+
+ align:start position:0%
+of osmosis by journalists I know people
+ 
+
+ align:start position:0%
+of osmosis by journalists I know people
+like long so a story I mean a little
+
+ align:start position:0%
+like long so a story I mean a little
+ 
+
+ align:start position:0%
+like long so a story I mean a little
+like law you can eat anything smaller
+
+ align:start position:0%
+like law you can eat anything smaller
+ 
+
+ align:start position:0%
+like law you can eat anything smaller
+than you and everything that you eat
+
+ align:start position:0%
+than you and everything that you eat
+ 
+
+ align:start position:0%
+than you and everything that you eat
+makes you bigger so you can eat even
+
+ align:start position:0%
+makes you bigger so you can eat even
+ 
+
+ align:start position:0%
+makes you bigger so you can eat even
+bigger things but actually makes it more
+
+ align:start position:0%
+bigger things but actually makes it more
+ 
+
+ align:start position:0%
+bigger things but actually makes it more
+difficult for you to navigate because
+
+ align:start position:0%
+difficult for you to navigate because
+ 
+
+ align:start position:0%
+difficult for you to navigate because
+you're more massive now so you actually
+
+ align:start position:0%
+you're more massive now so you actually
+ 
+
+ align:start position:0%
+you're more massive now so you actually
+had both negative and positive loops
+
+ align:start position:0%
+had both negative and positive loops
+ 
+
+ align:start position:0%
+had both negative and positive loops
+going on at once bumps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it makes other things explode well
+
+ align:start position:0%
+it makes other things explode well
+ 
+
+ align:start position:0%
+it makes other things explode well
+there's that they also know so like like
+
+ align:start position:0%
+there's that they also know so like like
+ 
+
+ align:start position:0%
+there's that they also know so like like
+like that you're using an atomic bomb to
+
+ align:start position:0%
+like that you're using an atomic bomb to
+ 
+
+ align:start position:0%
+like that you're using an atomic bomb to
+set off the hydrogen bomb it's something
+
+ align:start position:0%
+set off the hydrogen bomb it's something
+ 
+
+ align:start position:0%
+set off the hydrogen bomb it's something
+okay yeah yeah you can sort of positive
+
+ align:start position:0%
+okay yeah yeah you can sort of positive
+ 
+
+ align:start position:0%
+okay yeah yeah you can sort of positive
+feedback often happens in military
+
+ align:start position:0%
+feedback often happens in military
+ 
+
+ align:start position:0%
+feedback often happens in military
+conflict right you know if you've got
+
+ align:start position:0%
+conflict right you know if you've got
+ 
+
+ align:start position:0%
+conflict right you know if you've got
+overwhelming if you've got overwhelming
+
+ align:start position:0%
+overwhelming if you've got overwhelming
+ 
+
+ align:start position:0%
+overwhelming if you've got overwhelming
+forces and I'll being every engagement
+
+ align:start position:0%
+forces and I'll being every engagement
+ 
+
+ align:start position:0%
+forces and I'll being every engagement
+just mix though makes the ratio if
+
+ align:start position:0%
+just mix though makes the ratio if
+ 
+
+ align:start position:0%
+just mix though makes the ratio if
+everything goes according to military
+
+ align:start position:0%
+everything goes according to military
+ 
+
+ align:start position:0%
+everything goes according to military
+doctrine every engagement is going to
+
+ align:start position:0%
+doctrine every engagement is going to
+ 
+
+ align:start position:0%
+doctrine every engagement is going to
+give you a yet greater advantage thirty
+
+ align:start position:0%
+give you a yet greater advantage thirty
+ 
+
+ align:start position:0%
+give you a yet greater advantage thirty
+so the way how this has been applied in
+
+ align:start position:0%
+so the way how this has been applied in
+ 
+
+ align:start position:0%
+so the way how this has been applied in
+games is you know just just to make it
+
+ align:start position:0%
+games is you know just just to make it
+ 
+
+ align:start position:0%
+games is you know just just to make it
+literal you have a state some sort of
+
+ align:start position:0%
+literal you have a state some sort of
+ 
+
+ align:start position:0%
+literal you have a state some sort of
+state of the game am I getting this
+
+ align:start position:0%
+state of the game am I getting this
+ 
+
+ align:start position:0%
+state of the game am I getting this
+right yeah you have to stay up the game
+
+ align:start position:0%
+right yeah you have to stay up the game
+ 
+
+ align:start position:0%
+right yeah you have to stay up the game
+you have this let me just make you make
+
+ align:start position:0%
+you have this let me just make you make
+ 
+
+ align:start position:0%
+you have this let me just make you make
+sure I got this perfectly right here we
+
+ align:start position:0%
+sure I got this perfectly right here we
+ 
+
+ align:start position:0%
+sure I got this perfectly right here we
+go you had some sort of scoring function
+
+ align:start position:0%
+go you had some sort of scoring function
+ 
+
+ align:start position:0%
+go you had some sort of scoring function
+it doesn't have to be the literal score
+
+ align:start position:0%
+it doesn't have to be the literal score
+ 
+
+ align:start position:0%
+it doesn't have to be the literal score
+but it has to be some way of assessing
+
+ align:start position:0%
+but it has to be some way of assessing
+ 
+
+ align:start position:0%
+but it has to be some way of assessing
+how close you are to some sort of goal
+
+ align:start position:0%
+how close you are to some sort of goal
+ 
+
+ align:start position:0%
+how close you are to some sort of goal
+so either there's a short-term goal or
+
+ align:start position:0%
+so either there's a short-term goal or
+ 
+
+ align:start position:0%
+so either there's a short-term goal or
+the overall goal of a game some sort of
+
+ align:start position:0%
+the overall goal of a game some sort of
+ 
+
+ align:start position:0%
+the overall goal of a game some sort of
+scoring function and that goes into some
+
+ align:start position:0%
+scoring function and that goes into some
+ 
+
+ align:start position:0%
+scoring function and that goes into some
+sort of player input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are some versions of this diagram
+
+ align:start position:0%
+there are some versions of this diagram
+ 
+
+ align:start position:0%
+there are some versions of this diagram
+that separates this into two things
+
+ align:start position:0%
+that separates this into two things
+ 
+
+ align:start position:0%
+that separates this into two things
+that's kind of like the player decides
+
+ align:start position:0%
+that's kind of like the player decides
+ 
+
+ align:start position:0%
+that's kind of like the player decides
+what they're going to do and then
+
+ align:start position:0%
+what they're going to do and then
+ 
+
+ align:start position:0%
+what they're going to do and then
+actually execute the input and that goes
+
+ align:start position:0%
+actually execute the input and that goes
+ 
+
+ align:start position:0%
+actually execute the input and that goes
+back and actually there is one more
+
+ align:start position:0%
+back and actually there is one more
+ 
+
+ align:start position:0%
+back and actually there is one more
+stage sorry there is one more stage and
+
+ align:start position:0%
+stage sorry there is one more stage and
+ 
+
+ align:start position:0%
+stage sorry there is one more stage and
+that's the kind of the mechanical bias
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the state of the game can be
+
+ align:start position:0%
+so so the state of the game can be
+ 
+
+ align:start position:0%
+so so the state of the game can be
+revealed in some sort of scoring fun
+
+ align:start position:0%
+revealed in some sort of scoring fun
+ 
+
+ align:start position:0%
+revealed in some sort of scoring fun
+part in a player SSS what they want to
+
+ align:start position:0%
+part in a player SSS what they want to
+ 
+
+ align:start position:0%
+part in a player SSS what they want to
+do and then tries to execute it that is
+
+ align:start position:0%
+do and then tries to execute it that is
+ 
+
+ align:start position:0%
+do and then tries to execute it that is
+filtered within the computers or the
+
+ align:start position:0%
+filtered within the computers or the
+ 
+
+ align:start position:0%
+filtered within the computers or the
+board games or the card games
+
+ align:start position:0%
+board games or the card games
+ 
+
+ align:start position:0%
+board games or the card games
+interpretation of what that inputs gonna
+
+ align:start position:0%
+interpretation of what that inputs gonna
+ 
+
+ align:start position:0%
+interpretation of what that inputs gonna
+do and then that feeds back into a game
+
+ align:start position:0%
+do and then that feeds back into a game
+ 
+
+ align:start position:0%
+do and then that feeds back into a game
+state right so for games like Mario Kart
+
+ align:start position:0%
+state right so for games like Mario Kart
+ 
+
+ align:start position:0%
+state right so for games like Mario Kart
+you know you perceive that you are doing
+
+ align:start position:0%
+you know you perceive that you are doing
+ 
+
+ align:start position:0%
+you know you perceive that you are doing
+you perceive you are doing madly because
+
+ align:start position:0%
+you perceive you are doing madly because
+ 
+
+ align:start position:0%
+you perceive you are doing madly because
+you all you know you are the last one at
+
+ align:start position:0%
+you all you know you are the last one at
+ 
+
+ align:start position:0%
+you all you know you are the last one at
+the back of the of the races you drive
+
+ align:start position:0%
+the back of the of the races you drive
+ 
+
+ align:start position:0%
+the back of the of the races you drive
+your your vehicle into one of those
+
+ align:start position:0%
+your your vehicle into one of those
+ 
+
+ align:start position:0%
+your your vehicle into one of those
+rotating boxes because that you're
+
+ align:start position:0%
+rotating boxes because that you're
+ 
+
+ align:start position:0%
+rotating boxes because that you're
+deliberately steering into them because
+
+ align:start position:0%
+deliberately steering into them because
+ 
+
+ align:start position:0%
+deliberately steering into them because
+they're probably your only chance to be
+
+ align:start position:0%
+they're probably your only chance to be
+ 
+
+ align:start position:0%
+they're probably your only chance to be
+able to catch up again you'll get
+
+ align:start position:0%
+able to catch up again you'll get
+ 
+
+ align:start position:0%
+able to catch up again you'll get
+usually something really really sweet
+
+ align:start position:0%
+usually something really really sweet
+ 
+
+ align:start position:0%
+usually something really really sweet
+because you're all the way behind and
+
+ align:start position:0%
+because you're all the way behind and
+ 
+
+ align:start position:0%
+because you're all the way behind and
+the way how the game is designed if
+
+ align:start position:0%
+the way how the game is designed if
+ 
+
+ align:start position:0%
+the way how the game is designed if
+you're all the way behind you get all
+
+ align:start position:0%
+you're all the way behind you get all
+ 
+
+ align:start position:0%
+you're all the way behind you get all
+the best toys you get all the every
+
+ align:start position:0%
+the best toys you get all the every
+ 
+
+ align:start position:0%
+the best toys you get all the every
+single tool that you need to be able to
+
+ align:start position:0%
+single tool that you need to be able to
+ 
+
+ align:start position:0%
+single tool that you need to be able to
+catch up is given to you when you're all
+
+ align:start position:0%
+catch up is given to you when you're all
+ 
+
+ align:start position:0%
+catch up is given to you when you're all
+the way in the back
+
+ align:start position:0%
+the way in the back
+ 
+
+ align:start position:0%
+the way in the back
+that's the mechanic bias all right it
+
+ align:start position:0%
+that's the mechanic bias all right it
+ 
+
+ align:start position:0%
+that's the mechanic bias all right it
+gives you the right tool and that
+
+ align:start position:0%
+gives you the right tool and that
+ 
+
+ align:start position:0%
+gives you the right tool and that
+effects game state because now you have
+
+ align:start position:0%
+effects game state because now you have
+ 
+
+ align:start position:0%
+effects game state because now you have
+this wonderful tool and you use it
+
+ align:start position:0%
+this wonderful tool and you use it
+ 
+
+ align:start position:0%
+this wonderful tool and you use it
+hopefully it works you know and then you
+
+ align:start position:0%
+hopefully it works you know and then you
+ 
+
+ align:start position:0%
+hopefully it works you know and then you
+gain a couple of places up in the race
+
+ align:start position:0%
+gain a couple of places up in the race
+ 
+
+ align:start position:0%
+gain a couple of places up in the race
+so that there are a couple of other
+
+ align:start position:0%
+so that there are a couple of other
+ 
+
+ align:start position:0%
+so that there are a couple of other
+examples that are a little bit you know
+
+ align:start position:0%
+examples that are a little bit you know
+ 
+
+ align:start position:0%
+examples that are a little bit you know
+clearer so say say basketball if you've
+
+ align:start position:0%
+clearer so say say basketball if you've
+ 
+
+ align:start position:0%
+clearer so say say basketball if you've
+got a situation where you've got five
+
+ align:start position:0%
+got a situation where you've got five
+ 
+
+ align:start position:0%
+got a situation where you've got five
+people on your side you could do a game
+
+ align:start position:0%
+people on your side you could do a game
+ 
+
+ align:start position:0%
+people on your side you could do a game
+where if you start to have a lead of
+
+ align:start position:0%
+where if you start to have a lead of
+ 
+
+ align:start position:0%
+where if you start to have a lead of
+five points
+
+ align:start position:0%
+five points
+ 
+
+ align:start position:0%
+five points
+you lose a player you know someone's
+
+ align:start position:0%
+you lose a player you know someone's
+ 
+
+ align:start position:0%
+you lose a player you know someone's
+benched so is that peccadilloes that
+
+ align:start position:0%
+benched so is that peccadilloes that
+ 
+
+ align:start position:0%
+benched so is that peccadilloes that
+positive that's negative right because
+
+ align:start position:0%
+positive that's negative right because
+ 
+
+ align:start position:0%
+positive that's negative right because
+you say all right you were far enough
+
+ align:start position:0%
+you say all right you were far enough
+ 
+
+ align:start position:0%
+you say all right you were far enough
+ahead we're going to take away one of
+
+ align:start position:0%
+ahead we're going to take away one of
+ 
+
+ align:start position:0%
+ahead we're going to take away one of
+the advantages is there another way to
+
+ align:start position:0%
+the advantages is there another way to
+ 
+
+ align:start position:0%
+the advantages is there another way to
+do negative feedback on that example
+
+ align:start position:0%
+do negative feedback on that example
+ 
+
+ align:start position:0%
+do negative feedback on that example
+instead of taking away a player you can
+
+ align:start position:0%
+instead of taking away a player you can
+ 
+
+ align:start position:0%
+instead of taking away a player you can
+add another player to the other side all
+
+ align:start position:0%
+add another player to the other side all
+ 
+
+ align:start position:0%
+add another player to the other side all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's also negative feedback you know
+
+ align:start position:0%
+that's also negative feedback you know
+ 
+
+ align:start position:0%
+that's also negative feedback you know
+that even though you're adding something
+
+ align:start position:0%
+that even though you're adding something
+ 
+
+ align:start position:0%
+that even though you're adding something
+what you're really doing is you're going
+
+ align:start position:0%
+what you're really doing is you're going
+ 
+
+ align:start position:0%
+what you're really doing is you're going
+to give an advantage to someone who is
+
+ align:start position:0%
+to give an advantage to someone who is
+ 
+
+ align:start position:0%
+to give an advantage to someone who is
+not doing so on and does try to bring
+
+ align:start position:0%
+not doing so on and does try to bring
+ 
+
+ align:start position:0%
+not doing so on and does try to bring
+things away forever
+
+ align:start position:0%
+things away forever
+ 
+
+ align:start position:0%
+things away forever
+positive feedback version of this would
+
+ align:start position:0%
+positive feedback version of this would
+ 
+
+ align:start position:0%
+positive feedback version of this would
+be I was thinking something more literal
+
+ align:start position:0%
+be I was thinking something more literal
+ 
+
+ align:start position:0%
+be I was thinking something more literal
+like just giving the person who that the
+
+ align:start position:0%
+like just giving the person who that the
+ 
+
+ align:start position:0%
+like just giving the person who that the
+team that I hit extra players right like
+
+ align:start position:0%
+team that I hit extra players right like
+ 
+
+ align:start position:0%
+team that I hit extra players right like
+you could do it every five points that
+
+ align:start position:0%
+you could do it every five points that
+ 
+
+ align:start position:0%
+you could do it every five points that
+you get one more player and pretty soon
+
+ align:start position:0%
+you get one more player and pretty soon
+ 
+
+ align:start position:0%
+you get one more player and pretty soon
+you've got to buckle yeah and then you
+
+ align:start position:0%
+you've got to buckle yeah and then you
+ 
+
+ align:start position:0%
+you've got to buckle yeah and then you
+just have more more people then anyone
+
+ align:start position:0%
+just have more more people then anyone
+ 
+
+ align:start position:0%
+just have more more people then anyone
+can move on the basketball court and as
+
+ align:start position:0%
+can move on the basketball court and as
+ 
+
+ align:start position:0%
+can move on the basketball court and as
+a result of that you kind of with my
+
+ align:start position:0%
+a result of that you kind of with my
+ 
+
+ align:start position:0%
+a result of that you kind of with my
+default sorry it's like
+
+ align:start position:0%
+default sorry it's like
+ 
+
+ align:start position:0%
+default sorry it's like
+somebody's on fire and make three shots
+
+ align:start position:0%
+somebody's on fire and make three shots
+ 
+
+ align:start position:0%
+somebody's on fire and make three shots
+in a row and a lot of something just
+
+ align:start position:0%
+in a row and a lot of something just
+ 
+
+ align:start position:0%
+in a row and a lot of something just
+like doing it better explain it run
+
+ align:start position:0%
+like doing it better explain it run
+ 
+
+ align:start position:0%
+like doing it better explain it run
+faster they jump a little higher yeah
+
+ align:start position:0%
+faster they jump a little higher yeah
+ 
+
+ align:start position:0%
+faster they jump a little higher yeah
+and the computer game you kissed eclis
+
+ align:start position:0%
+and the computer game you kissed eclis
+ 
+
+ align:start position:0%
+and the computer game you kissed eclis
+if you're if you're throwing a good game
+
+ align:start position:0%
+if you're if you're throwing a good game
+ 
+
+ align:start position:0%
+if you're if you're throwing a good game
+and you're doing better than war a
+
+ align:start position:0%
+and you're doing better than war a
+ 
+
+ align:start position:0%
+and you're doing better than war a
+mortgage is better better pitches more
+
+ align:start position:0%
+mortgage is better better pitches more
+ 
+
+ align:start position:0%
+mortgage is better better pitches more
+playing better but I'm wondering whether
+
+ align:start position:0%
+playing better but I'm wondering whether
+ 
+
+ align:start position:0%
+playing better but I'm wondering whether
+that's correlation of causation
+
+ align:start position:0%
+that's correlation of causation
+ 
+
+ align:start position:0%
+that's correlation of causation
+it's like if the reason why you're doing
+
+ align:start position:0%
+it's like if the reason why you're doing
+ 
+
+ align:start position:0%
+it's like if the reason why you're doing
+better be great effort right now they're
+
+ align:start position:0%
+better be great effort right now they're
+ 
+
+ align:start position:0%
+better be great effort right now they're
+thinking it's causation is causation but
+
+ align:start position:0%
+thinking it's causation is causation but
+ 
+
+ align:start position:0%
+thinking it's causation is causation but
+it definitely comes up in someone
+
+ align:start position:0%
+it definitely comes up in someone
+ 
+
+ align:start position:0%
+it definitely comes up in someone
+psychology right you know is that you
+
+ align:start position:0%
+psychology right you know is that you
+ 
+
+ align:start position:0%
+psychology right you know is that you
+you are sort of building on the mental
+
+ align:start position:0%
+you are sort of building on the mental
+ 
+
+ align:start position:0%
+you are sort of building on the mental
+momentum of doing well and similarly a
+
+ align:start position:0%
+momentum of doing well and similarly a
+ 
+
+ align:start position:0%
+momentum of doing well and similarly a
+team that's not doing well can lose hope
+
+ align:start position:0%
+team that's not doing well can lose hope
+ 
+
+ align:start position:0%
+team that's not doing well can lose hope
+that's that's again that's positive
+
+ align:start position:0%
+that's that's again that's positive
+ 
+
+ align:start position:0%
+that's that's again that's positive
+feedback I just want to be extremely
+
+ align:start position:0%
+feedback I just want to be extremely
+ 
+
+ align:start position:0%
+feedback I just want to be extremely
+clear about that we use the positive is
+
+ align:start position:0%
+clear about that we use the positive is
+ 
+
+ align:start position:0%
+clear about that we use the positive is
+there anything that sort of amplifies
+
+ align:start position:0%
+there anything that sort of amplifies
+ 
+
+ align:start position:0%
+there anything that sort of amplifies
+differences that already exist so now
+
+ align:start position:0%
+differences that already exist so now
+ 
+
+ align:start position:0%
+differences that already exist so now
+let me there are a couple of things to
+
+ align:start position:0%
+let me there are a couple of things to
+ 
+
+ align:start position:0%
+let me there are a couple of things to
+think about when it comes to feedback
+
+ align:start position:0%
+think about when it comes to feedback
+ 
+
+ align:start position:0%
+think about when it comes to feedback
+especially as a problem-solving
+
+ align:start position:0%
+especially as a problem-solving
+ 
+
+ align:start position:0%
+especially as a problem-solving
+technique for design so we've already
+
+ align:start position:0%
+technique for design so we've already
+ 
+
+ align:start position:0%
+technique for design so we've already
+talked about how negative feedback tries
+
+ align:start position:0%
+talked about how negative feedback tries
+ 
+
+ align:start position:0%
+talked about how negative feedback tries
+to bring things down to equilibrium so
+
+ align:start position:0%
+to bring things down to equilibrium so
+ 
+
+ align:start position:0%
+to bring things down to equilibrium so
+it's a stabilizing force if your game is
+
+ align:start position:0%
+it's a stabilizing force if your game is
+ 
+
+ align:start position:0%
+it's a stabilizing force if your game is
+like out of control and unpredictable
+
+ align:start position:0%
+like out of control and unpredictable
+ 
+
+ align:start position:0%
+like out of control and unpredictable
+and chaotic negative feedback and sort
+
+ align:start position:0%
+and chaotic negative feedback and sort
+ 
+
+ align:start position:0%
+and chaotic negative feedback and sort
+of like doing things a little bit I
+
+ align:start position:0%
+of like doing things a little bit I
+ 
+
+ align:start position:0%
+of like doing things a little bit I
+assure me may be unpredictable but it's
+
+ align:start position:0%
+assure me may be unpredictable but it's
+ 
+
+ align:start position:0%
+assure me may be unpredictable but it's
+not going to hurt me so bad or if
+
+ align:start position:0%
+not going to hurt me so bad or if
+ 
+
+ align:start position:0%
+not going to hurt me so bad or if
+somebody gets an advantage it's not
+
+ align:start position:0%
+somebody gets an advantage it's not
+ 
+
+ align:start position:0%
+somebody gets an advantage it's not
+going to be it's not going to be a
+
+ align:start position:0%
+going to be it's not going to be a
+ 
+
+ align:start position:0%
+going to be it's not going to be a
+runaway advantage similar behavior games
+
+ align:start position:0%
+runaway advantage similar behavior games
+ 
+
+ align:start position:0%
+runaway advantage similar behavior games
+just kind of you know actually always
+
+ align:start position:0%
+just kind of you know actually always
+ 
+
+ align:start position:0%
+just kind of you know actually always
+hovering and equilibrium and nobody
+
+ align:start position:0%
+hovering and equilibrium and nobody
+ 
+
+ align:start position:0%
+hovering and equilibrium and nobody
+seems to be getting advantage and
+
+ align:start position:0%
+seems to be getting advantage and
+ 
+
+ align:start position:0%
+seems to be getting advantage and
+positive feedback mechanisms will be
+
+ align:start position:0%
+positive feedback mechanisms will be
+ 
+
+ align:start position:0%
+positive feedback mechanisms will be
+something will destabilize that well it
+
+ align:start position:0%
+something will destabilize that well it
+ 
+
+ align:start position:0%
+something will destabilize that well it
+will make it more likely that somebody
+
+ align:start position:0%
+will make it more likely that somebody
+ 
+
+ align:start position:0%
+will make it more likely that somebody
+who get an advantage will actually get a
+
+ align:start position:0%
+who get an advantage will actually get a
+ 
+
+ align:start position:0%
+who get an advantage will actually get a
+large advantage
+
+ align:start position:0%
+large advantage
+ 
+
+ align:start position:0%
+large advantage
+and that could be a good thing if your
+
+ align:start position:0%
+and that could be a good thing if your
+ 
+
+ align:start position:0%
+and that could be a good thing if your
+games kind of like doll and it's always
+
+ align:start position:0%
+games kind of like doll and it's always
+ 
+
+ align:start position:0%
+games kind of like doll and it's always
+just kind of hovering at the same level
+
+ align:start position:0%
+just kind of hovering at the same level
+ 
+
+ align:start position:0%
+just kind of hovering at the same level
+but that's it but that's a trade-off
+
+ align:start position:0%
+but that's it but that's a trade-off
+ 
+
+ align:start position:0%
+but that's it but that's a trade-off
+with that because any amount of feedback
+
+ align:start position:0%
+with that because any amount of feedback
+ 
+
+ align:start position:0%
+with that because any amount of feedback
+that you're adding into a into your game
+
+ align:start position:0%
+that you're adding into a into your game
+ 
+
+ align:start position:0%
+that you're adding into a into your game
+especially this kind of automated
+
+ align:start position:0%
+especially this kind of automated
+ 
+
+ align:start position:0%
+especially this kind of automated
+feedback this is something that your
+
+ align:start position:0%
+feedback this is something that your
+ 
+
+ align:start position:0%
+feedback this is something that your
+rules are automatically generating can
+
+ align:start position:0%
+rules are automatically generating can
+ 
+
+ align:start position:0%
+rules are automatically generating can
+actually be taking control away from
+
+ align:start position:0%
+actually be taking control away from
+ 
+
+ align:start position:0%
+actually be taking control away from
+players and as a result of that might
+
+ align:start position:0%
+players and as a result of that might
+ 
+
+ align:start position:0%
+players and as a result of that might
+actually make a game less engaging so
+
+ align:start position:0%
+actually make a game less engaging so
+ 
+
+ align:start position:0%
+actually make a game less engaging so
+even a game like with like a party all
+
+ align:start position:0%
+even a game like with like a party all
+ 
+
+ align:start position:0%
+even a game like with like a party all
+right this game is too stable well going
+
+ align:start position:0%
+right this game is too stable well going
+ 
+
+ align:start position:0%
+right this game is too stable well going
+to add some positive feedback mechanisms
+
+ align:start position:0%
+to add some positive feedback mechanisms
+ 
+
+ align:start position:0%
+to add some positive feedback mechanisms
+so that people who have an advantage can
+
+ align:start position:0%
+so that people who have an advantage can
+ 
+
+ align:start position:0%
+so that people who have an advantage can
+sort of capitalize on that advantage but
+
+ align:start position:0%
+sort of capitalize on that advantage but
+ 
+
+ align:start position:0%
+sort of capitalize on that advantage but
+if if that's not done right then you've
+
+ align:start position:0%
+if if that's not done right then you've
+ 
+
+ align:start position:0%
+if if that's not done right then you've
+just got a situation where once once up
+
+ align:start position:0%
+just got a situation where once once up
+ 
+
+ align:start position:0%
+just got a situation where once once up
+someone starts winning everybody else
+
+ align:start position:0%
+someone starts winning everybody else
+ 
+
+ align:start position:0%
+someone starts winning everybody else
+loses interest because there's no way
+
+ align:start position:0%
+loses interest because there's no way
+ 
+
+ align:start position:0%
+loses interest because there's no way
+that they came in sort of catch up so
+
+ align:start position:0%
+that they came in sort of catch up so
+ 
+
+ align:start position:0%
+that they came in sort of catch up so
+these stabilizes it in a point yeah
+
+ align:start position:0%
+these stabilizes it in a point yeah
+ 
+
+ align:start position:0%
+these stabilizes it in a point yeah
+someone's gonna win this game whereas
+
+ align:start position:0%
+someone's gonna win this game whereas
+ 
+
+ align:start position:0%
+someone's gonna win this game whereas
+previously is always stuck in
+
+ align:start position:0%
+previously is always stuck in
+ 
+
+ align:start position:0%
+previously is always stuck in
+equilibrium but it's actually lost it's
+
+ align:start position:0%
+equilibrium but it's actually lost it's
+ 
+
+ align:start position:0%
+equilibrium but it's actually lost it's
+very easy to sort of lose people in a
+
+ align:start position:0%
+very easy to sort of lose people in a
+ 
+
+ align:start position:0%
+very easy to sort of lose people in a
+process because you just create an
+
+ align:start position:0%
+process because you just create an
+ 
+
+ align:start position:0%
+process because you just create an
+automated system to take control away
+
+ align:start position:0%
+automated system to take control away
+ 
+
+ align:start position:0%
+automated system to take control away
+for that so that's one danger of putting
+
+ align:start position:0%
+for that so that's one danger of putting
+ 
+
+ align:start position:0%
+for that so that's one danger of putting
+in a feedback system also we talked
+
+ align:start position:0%
+in a feedback system also we talked
+ 
+
+ align:start position:0%
+in a feedback system also we talked
+about breaking things down so we could
+
+ align:start position:0%
+about breaking things down so we could
+ 
+
+ align:start position:0%
+about breaking things down so we could
+never be able to sort of like make
+
+ align:start position:0%
+never be able to sort of like make
+ 
+
+ align:start position:0%
+never be able to sort of like make
+things a little bit easier for people to
+
+ align:start position:0%
+things a little bit easier for people to
+ 
+
+ align:start position:0%
+things a little bit easier for people to
+catch up on to make advantages a little
+
+ align:start position:0%
+catch up on to make advantages a little
+ 
+
+ align:start position:0%
+catch up on to make advantages a little
+bit less drastic that can also make a
+
+ align:start position:0%
+bit less drastic that can also make a
+ 
+
+ align:start position:0%
+bit less drastic that can also make a
+game much longer right there's nobody
+
+ align:start position:0%
+game much longer right there's nobody
+ 
+
+ align:start position:0%
+game much longer right there's nobody
+get an advantage and depending on your
+
+ align:start position:0%
+get an advantage and depending on your
+ 
+
+ align:start position:0%
+get an advantage and depending on your
+win condition depending on your end of
+
+ align:start position:0%
+win condition depending on your end of
+ 
+
+ align:start position:0%
+win condition depending on your end of
+game conditions could actually just you
+
+ align:start position:0%
+game conditions could actually just you
+ 
+
+ align:start position:0%
+game conditions could actually just you
+know make it interminably long you can
+
+ align:start position:0%
+know make it interminably long you can
+ 
+
+ align:start position:0%
+know make it interminably long you can
+take a half an hour game and make it one
+
+ align:start position:0%
+take a half an hour game and make it one
+ 
+
+ align:start position:0%
+take a half an hour game and make it one
+our game so on the flipside positive
+
+ align:start position:0%
+our game so on the flipside positive
+ 
+
+ align:start position:0%
+our game so on the flipside positive
+feedback game can actually help rein in
+
+ align:start position:0%
+feedback game can actually help rein in
+ 
+
+ align:start position:0%
+feedback game can actually help rein in
+the length of the game so the game is
+
+ align:start position:0%
+the length of the game so the game is
+ 
+
+ align:start position:0%
+the length of the game so the game is
+currently taking you know an hour long
+
+ align:start position:0%
+currently taking you know an hour long
+ 
+
+ align:start position:0%
+currently taking you know an hour long
+with anything like that and and your
+
+ align:start position:0%
+with anything like that and and your
+ 
+
+ align:start position:0%
+with anything like that and and your
+victory conditions happen to be on
+
+ align:start position:0%
+victory conditions happen to be on
+ 
+
+ align:start position:0%
+victory conditions happen to be on
+getting gaining an advantage over your
+
+ align:start position:0%
+getting gaining an advantage over your
+ 
+
+ align:start position:0%
+getting gaining an advantage over your
+the opponents that a positive feedback
+
+ align:start position:0%
+the opponents that a positive feedback
+ 
+
+ align:start position:0%
+the opponents that a positive feedback
+system can help speed that along right
+
+ align:start position:0%
+system can help speed that along right
+ 
+
+ align:start position:0%
+system can help speed that along right
+okay maybe we can cut it down by half by
+
+ align:start position:0%
+okay maybe we can cut it down by half by
+ 
+
+ align:start position:0%
+okay maybe we can cut it down by half by
+just giving some advantages to the
+
+ align:start position:0%
+just giving some advantages to the
+ 
+
+ align:start position:0%
+just giving some advantages to the
+person who's ahead or penalizing the
+
+ align:start position:0%
+person who's ahead or penalizing the
+ 
+
+ align:start position:0%
+person who's ahead or penalizing the
+people who are behind that's a
+
+ align:start position:0%
+people who are behind that's a
+ 
+
+ align:start position:0%
+people who are behind that's a
+interesting little side effect which is
+
+ align:start position:0%
+interesting little side effect which is
+ 
+
+ align:start position:0%
+interesting little side effect which is
+positive because positive feedback
+
+ align:start position:0%
+positive because positive feedback
+ 
+
+ align:start position:0%
+positive because positive feedback
+builds on itself if you have an
+
+ align:start position:0%
+builds on itself if you have an
+ 
+
+ align:start position:0%
+builds on itself if you have an
+advantage early on when you have an
+
+ align:start position:0%
+advantage early on when you have an
+ 
+
+ align:start position:0%
+advantage early on when you have an
+early success then a positive feedback
+
+ align:start position:0%
+early success then a positive feedback
+ 
+
+ align:start position:0%
+early success then a positive feedback
+is going to be the mechanism that's
+
+ align:start position:0%
+is going to be the mechanism that's
+ 
+
+ align:start position:0%
+is going to be the mechanism that's
+going to help you fill in that on the
+
+ align:start position:0%
+going to help you fill in that on the
+ 
+
+ align:start position:0%
+going to help you fill in that on the
+other hand if you have a negative
+
+ align:start position:0%
+other hand if you have a negative
+ 
+
+ align:start position:0%
+other hand if you have a negative
+feedback system in a game which means
+
+ align:start position:0%
+feedback system in a game which means
+ 
+
+ align:start position:0%
+feedback system in a game which means
+everything's kind of being brought down
+
+ align:start position:0%
+everything's kind of being brought down
+ 
+
+ align:start position:0%
+everything's kind of being brought down
+to an equilibrium but everyone's getting
+
+ align:start position:0%
+to an equilibrium but everyone's getting
+ 
+
+ align:start position:0%
+to an equilibrium but everyone's getting
+closer to actually finishing the game
+
+ align:start position:0%
+closer to actually finishing the game
+ 
+
+ align:start position:0%
+closer to actually finishing the game
+but no one really has like a huge lead
+
+ align:start position:0%
+but no one really has like a huge lead
+ 
+
+ align:start position:0%
+but no one really has like a huge lead
+then late successes mean a lot more that
+
+ align:start position:0%
+then late successes mean a lot more that
+ 
+
+ align:start position:0%
+then late successes mean a lot more that
+last boost when you are near the final
+
+ align:start position:0%
+last boost when you are near the final
+ 
+
+ align:start position:0%
+last boost when you are near the final
+the winning line was the finish line the
+
+ align:start position:0%
+the winning line was the finish line the
+ 
+
+ align:start position:0%
+the winning line was the finish line the
+finish line that last boost of the
+
+ align:start position:0%
+finish line that last boost of the
+ 
+
+ align:start position:0%
+finish line that last boost of the
+filler of before you hit the finish line
+
+ align:start position:0%
+filler of before you hit the finish line
+ 
+
+ align:start position:0%
+filler of before you hit the finish line
+and very last Verano mariokart means a
+
+ align:start position:0%
+and very last Verano mariokart means a
+ 
+
+ align:start position:0%
+and very last Verano mariokart means a
+lot because the whole game is designed
+
+ align:start position:0%
+lot because the whole game is designed
+ 
+
+ align:start position:0%
+lot because the whole game is designed
+with and and could make all the
+
+ align:start position:0%
+with and and could make all the
+ 
+
+ align:start position:0%
+with and and could make all the
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+that was pretty much it for not fighting
+
+ align:start position:0%
+that was pretty much it for not fighting
+ 
+
+ align:start position:0%
+that was pretty much it for not fighting
+over it so I'm just saying you know so
+
+ align:start position:0%
+over it so I'm just saying you know so
+ 
+
+ align:start position:0%
+over it so I'm just saying you know so
+negative feedback prioritizes what
+
+ align:start position:0%
+negative feedback prioritizes what
+ 
+
+ align:start position:0%
+negative feedback prioritizes what
+happens they make games but it's
+
+ align:start position:0%
+happens they make games but it's
+ 
+
+ align:start position:0%
+happens they make games but it's
+positive feedback prioritizes what
+
+ align:start position:0%
+positive feedback prioritizes what
+ 
+
+ align:start position:0%
+positive feedback prioritizes what
+happens earlier on strategies that you
+
+ align:start position:0%
+happens earlier on strategies that you
+ 
+
+ align:start position:0%
+happens earlier on strategies that you
+pick the cards that you haven't before
+
+ align:start position:0%
+pick the cards that you haven't before
+ 
+
+ align:start position:0%
+pick the cards that you haven't before
+all employee right in the beginning on
+
+ align:start position:0%
+all employee right in the beginning on
+ 
+
+ align:start position:0%
+all employee right in the beginning on
+the minute something of the people
+
+ align:start position:0%
+the minute something of the people
+ 
+
+ align:start position:0%
+the minute something of the people
+positive feedback stress exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally always keep in mind that any
+
+ align:start position:0%
+and finally always keep in mind that any
+ 
+
+ align:start position:0%
+and finally always keep in mind that any
+interaction of game systems probably
+
+ align:start position:0%
+interaction of game systems probably
+ 
+
+ align:start position:0%
+interaction of game systems probably
+creates version feedback loops even if
+
+ align:start position:0%
+creates version feedback loops even if
+ 
+
+ align:start position:0%
+creates version feedback loops even if
+you have a design of it so what we want
+
+ align:start position:0%
+you have a design of it so what we want
+ 
+
+ align:start position:0%
+you have a design of it so what we want
+to do is you want to try to find that
+
+ align:start position:0%
+to do is you want to try to find that
+ 
+
+ align:start position:0%
+to do is you want to try to find that
+there the tool out there that I've seen
+
+ align:start position:0%
+there the tool out there that I've seen
+ 
+
+ align:start position:0%
+there the tool out there that I've seen
+some student teams use and I don't know
+
+ align:start position:0%
+some student teams use and I don't know
+ 
+
+ align:start position:0%
+some student teams use and I don't know
+whether it be useful for you're just
+
+ align:start position:0%
+whether it be useful for you're just
+ 
+
+ align:start position:0%
+whether it be useful for you're just
+going to do good has anyone heard of
+
+ align:start position:0%
+going to do good has anyone heard of
+ 
+
+ align:start position:0%
+going to do good has anyone heard of
+causal loop diagrams
+
+ align:start position:0%
+causal loop diagrams
+ 
+
+ align:start position:0%
+causal loop diagrams
+that's from economics you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a very simple concept you just
+
+ align:start position:0%
+it's a very simple concept you just
+ 
+
+ align:start position:0%
+it's a very simple concept you just
+basically write it your variables in
+
+ align:start position:0%
+basically write it your variables in
+ 
+
+ align:start position:0%
+basically write it your variables in
+your game and you can add in a few looks
+
+ align:start position:0%
+your game and you can add in a few looks
+ 
+
+ align:start position:0%
+your game and you can add in a few looks
+sort of in between variables if you know
+
+ align:start position:0%
+sort of in between variables if you know
+ 
+
+ align:start position:0%
+sort of in between variables if you know
+how players are thinking about your game
+
+ align:start position:0%
+how players are thinking about your game
+ 
+
+ align:start position:0%
+how players are thinking about your game
+so I could be using Mario Kart too much
+
+ align:start position:0%
+so I could be using Mario Kart too much
+ 
+
+ align:start position:0%
+so I could be using Mario Kart too much
+for example let's pick another game with
+
+ align:start position:0%
+for example let's pick another game with
+ 
+
+ align:start position:0%
+for example let's pick another game with
+obviously just okay so so our pieces in
+
+ align:start position:0%
+obviously just okay so so our pieces in
+ 
+
+ align:start position:0%
+obviously just okay so so our pieces in
+chess sort of influences the number of
+
+ align:start position:0%
+chess sort of influences the number of
+ 
+
+ align:start position:0%
+chess sort of influences the number of
+attack past all right so which means
+
+ align:start position:0%
+attack past all right so which means
+ 
+
+ align:start position:0%
+attack past all right so which means
+number of pieces
+
+ align:start position:0%
+number of pieces
+ 
+
+ align:start position:0%
+number of pieces
+well influence a number of pieces being
+
+ align:start position:0%
+well influence a number of pieces being
+ 
+
+ align:start position:0%
+well influence a number of pieces being
+threatened off of your opponent's pieces
+
+ align:start position:0%
+threatened off of your opponent's pieces
+ 
+
+ align:start position:0%
+threatened off of your opponent's pieces
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Christian until it's just number one end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this taken now if I flick this around a
+
+ align:start position:0%
+this taken now if I flick this around a
+ 
+
+ align:start position:0%
+this taken now if I flick this around a
+little bit I think I could make an
+
+ align:start position:0%
+little bit I think I could make an
+ 
+
+ align:start position:0%
+little bit I think I could make an
+argument that if I switch this to number
+
+ align:start position:0%
+argument that if I switch this to number
+ 
+
+ align:start position:0%
+argument that if I switch this to number
+of my own pieces rather than my opponent
+
+ align:start position:0%
+of my own pieces rather than my opponent
+ 
+
+ align:start position:0%
+of my own pieces rather than my opponent
+pieces then it connects but not
+
+ align:start position:0%
+pieces then it connects but not
+ 
+
+ align:start position:0%
+pieces then it connects but not
+everything is a positive connection
+
+ align:start position:0%
+everything is a positive connection
+ 
+
+ align:start position:0%
+everything is a positive connection
+number of pieces that I have means I if
+
+ align:start position:0%
+number of pieces that I have means I if
+ 
+
+ align:start position:0%
+number of pieces that I have means I if
+I have more pieces I have more attack us
+
+ align:start position:0%
+I have more pieces I have more attack us
+ 
+
+ align:start position:0%
+I have more pieces I have more attack us
+Sarnoff is not exactly linear but it's
+
+ align:start position:0%
+Sarnoff is not exactly linear but it's
+ 
+
+ align:start position:0%
+Sarnoff is not exactly linear but it's
+not ever landed on Chester right I have
+
+ align:start position:0%
+not ever landed on Chester right I have
+ 
+
+ align:start position:0%
+not ever landed on Chester right I have
+more pieces then thank you I am always
+
+ align:start position:0%
+more pieces then thank you I am always
+ 
+
+ align:start position:0%
+more pieces then thank you I am always
+to attack if I have always to attack
+
+ align:start position:0%
+to attack if I have always to attack
+ 
+
+ align:start position:0%
+to attack if I have always to attack
+than you then actually I have few Jesus
+
+ align:start position:0%
+than you then actually I have few Jesus
+ 
+
+ align:start position:0%
+than you then actually I have few Jesus
+read it because I get it's also more
+
+ align:start position:0%
+read it because I get it's also more
+ 
+
+ align:start position:0%
+read it because I get it's also more
+ways to defend so I can say anything
+
+ align:start position:0%
+ways to defend so I can say anything
+ 
+
+ align:start position:0%
+ways to defend so I can say anything
+that I can attack I can prevent from I
+
+ align:start position:0%
+that I can attack I can prevent from I
+ 
+
+ align:start position:0%
+that I can attack I can prevent from I
+say well if you take this piece then I
+
+ align:start position:0%
+say well if you take this piece then I
+ 
+
+ align:start position:0%
+say well if you take this piece then I
+just want to take the piece that we just
+
+ align:start position:0%
+just want to take the piece that we just
+ 
+
+ align:start position:0%
+just want to take the piece that we just
+used and there's good a one-for-one
+
+ align:start position:0%
+used and there's good a one-for-one
+ 
+
+ align:start position:0%
+used and there's good a one-for-one
+trade postal that offices and you and so
+
+ align:start position:0%
+trade postal that offices and you and so
+ 
+
+ align:start position:0%
+trade postal that offices and you and so
+if I can if fewer of my pieces are
+
+ align:start position:0%
+if I can if fewer of my pieces are
+ 
+
+ align:start position:0%
+if I can if fewer of my pieces are
+threatened that means I can see number
+
+ align:start position:0%
+threatened that means I can see number
+ 
+
+ align:start position:0%
+threatened that means I can see number
+of pieces of threatened goes down then a
+
+ align:start position:0%
+of pieces of threatened goes down then a
+ 
+
+ align:start position:0%
+of pieces of threatened goes down then a
+number of pieces that I can kick goes up
+
+ align:start position:0%
+number of pieces that I can kick goes up
+ 
+
+ align:start position:0%
+number of pieces that I can kick goes up
+I think I think I know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the number of Europe then you come
+
+ align:start position:0%
+and the number of Europe then you come
+ 
+
+ align:start position:0%
+and the number of Europe then you come
+you're taking this down as well yeah
+
+ align:start position:0%
+you're taking this down as well yeah
+ 
+
+ align:start position:0%
+you're taking this down as well yeah
+those two are yes yes all right so and
+
+ align:start position:0%
+those two are yes yes all right so and
+ 
+
+ align:start position:0%
+those two are yes yes all right so and
+that should be a series and and and if
+
+ align:start position:0%
+that should be a series and and and if
+ 
+
+ align:start position:0%
+that should be a series and and and if
+the number of pieces taken goes down if
+
+ align:start position:0%
+the number of pieces taken goes down if
+ 
+
+ align:start position:0%
+the number of pieces taken goes down if
+there are pieces of piece of stick and
+
+ align:start position:0%
+there are pieces of piece of stick and
+ 
+
+ align:start position:0%
+there are pieces of piece of stick and
+goes up then I have two pieces if I have
+
+ align:start position:0%
+goes up then I have two pieces if I have
+ 
+
+ align:start position:0%
+goes up then I have two pieces if I have
+fewer pieces taken then I am one four
+
+ align:start position:0%
+fewer pieces taken then I am one four
+ 
+
+ align:start position:0%
+fewer pieces taken then I am one four
+pieces so we have two pluses that we
+
+ align:start position:0%
+pieces so we have two pluses that we
+ 
+
+ align:start position:0%
+pieces so we have two pluses that we
+have to - as relations overall this
+
+ align:start position:0%
+have to - as relations overall this
+ 
+
+ align:start position:0%
+have to - as relations overall this
+entire loop is fully reinforced English
+
+ align:start position:0%
+entire loop is fully reinforced English
+ 
+
+ align:start position:0%
+entire loop is fully reinforced English
+right this is positive feedback you can
+
+ align:start position:0%
+right this is positive feedback you can
+ 
+
+ align:start position:0%
+right this is positive feedback you can
+connect this to other things maybe in
+
+ align:start position:0%
+connect this to other things maybe in
+ 
+
+ align:start position:0%
+connect this to other things maybe in
+chess and I I'm not terribly good at
+
+ align:start position:0%
+chess and I I'm not terribly good at
+ 
+
+ align:start position:0%
+chess and I I'm not terribly good at
+causal loop diagrams to begin with but
+
+ align:start position:0%
+causal loop diagrams to begin with but
+ 
+
+ align:start position:0%
+causal loop diagrams to begin with but
+in chess again you might be able to
+
+ align:start position:0%
+in chess again you might be able to
+ 
+
+ align:start position:0%
+in chess again you might be able to
+connect it to other things like a
+
+ align:start position:0%
+connect it to other things like a
+ 
+
+ align:start position:0%
+connect it to other things like a
+positioning sensor or the valuable
+
+ align:start position:0%
+positioning sensor or the valuable
+ 
+
+ align:start position:0%
+positioning sensor or the valuable
+pieces and so what those might be
+
+ align:start position:0%
+pieces and so what those might be
+ 
+
+ align:start position:0%
+pieces and so what those might be
+reinforcing and reinforcing is basically
+
+ align:start position:0%
+reinforcing and reinforcing is basically
+ 
+
+ align:start position:0%
+reinforcing and reinforcing is basically
+another one I was saying in the positive
+
+ align:start position:0%
+another one I was saying in the positive
+ 
+
+ align:start position:0%
+another one I was saying in the positive
+feedback you another way that you can
+
+ align:start position:0%
+feedback you another way that you can
+ 
+
+ align:start position:0%
+feedback you another way that you can
+say is that the balancing loop which
+
+ align:start position:0%
+say is that the balancing loop which
+ 
+
+ align:start position:0%
+say is that the balancing loop which
+means not a negative image and that's
+
+ align:start position:0%
+means not a negative image and that's
+ 
+
+ align:start position:0%
+means not a negative image and that's
+usually depicted with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the students that I've seen uses for all
+
+ align:start position:0%
+the students that I've seen uses for all
+ 
+
+ align:start position:0%
+the students that I've seen uses for all
+the students from my economics and
+
+ align:start position:0%
+the students from my economics and
+ 
+
+ align:start position:0%
+the students from my economics and
+management who actually learned that
+
+ align:start position:0%
+management who actually learned that
+ 
+
+ align:start position:0%
+management who actually learned that
+because they're trying to study things
+
+ align:start position:0%
+because they're trying to study things
+ 
+
+ align:start position:0%
+because they're trying to study things
+like supply chain power system that's
+
+ align:start position:0%
+like supply chain power system that's
+ 
+
+ align:start position:0%
+like supply chain power system that's
+why before you use this tool and then
+
+ align:start position:0%
+why before you use this tool and then
+ 
+
+ align:start position:0%
+why before you use this tool and then
+decaffeinated and but you know so it
+
+ align:start position:0%
+decaffeinated and but you know so it
+ 
+
+ align:start position:0%
+decaffeinated and but you know so it
+might be was looking up there might be a
+
+ align:start position:0%
+might be was looking up there might be a
+ 
+
+ align:start position:0%
+might be was looking up there might be a
+useful diagnostic tool for your game if
+
+ align:start position:0%
+useful diagnostic tool for your game if
+ 
+
+ align:start position:0%
+useful diagnostic tool for your game if
+you're just trying to figure out what
+
+ align:start position:0%
+you're just trying to figure out what
+ 
+
+ align:start position:0%
+you're just trying to figure out what
+are all the different loops just like
+
+ align:start position:0%
+are all the different loops just like
+ 
+
+ align:start position:0%
+are all the different loops just like
+right just write out all of your
+
+ align:start position:0%
+right just write out all of your
+ 
+
+ align:start position:0%
+right just write out all of your
+variables and figure out whether things
+
+ align:start position:0%
+variables and figure out whether things
+ 
+
+ align:start position:0%
+variables and figure out whether things
+even up to negatives and to positives
+
+ align:start position:0%
+even up to negatives and to positives
+ 
+
+ align:start position:0%
+even up to negatives and to positives
+gives you reinforce in the loop
+
+ align:start position:0%
+gives you reinforce in the loop
+ 
+
+ align:start position:0%
+gives you reinforce in the loop
+positive positive positive positive
+
+ align:start position:0%
+positive positive positive positive
+ 
+
+ align:start position:0%
+positive positive positive positive
+gives you a reinforcing do positive
+
+ align:start position:0%
+gives you a reinforcing do positive
+ 
+
+ align:start position:0%
+gives you a reinforcing do positive
+positive negative and that's a fancy
+
+ align:start position:0%
+positive negative and that's a fancy
+ 
+
+ align:start position:0%
+positive negative and that's a fancy
+blue so the one thing to keep in mind is
+
+ align:start position:0%
+blue so the one thing to keep in mind is
+ 
+
+ align:start position:0%
+blue so the one thing to keep in mind is
+that occasionally what happens is that
+
+ align:start position:0%
+that occasionally what happens is that
+ 
+
+ align:start position:0%
+that occasionally what happens is that
+you have something like you get a
+
+ align:start position:0%
+you have something like you get a
+ 
+
+ align:start position:0%
+you have something like you get a
+benefit in something for instance why we
+
+ align:start position:0%
+benefit in something for instance why we
+ 
+
+ align:start position:0%
+benefit in something for instance why we
+was a box fiber change and you can you
+
+ align:start position:0%
+was a box fiber change and you can you
+ 
+
+ align:start position:0%
+was a box fiber change and you can you
+can put money you can invest money into
+
+ align:start position:0%
+can put money you can invest money into
+ 
+
+ align:start position:0%
+can put money you can invest money into
+research yeah at some point of time in a
+
+ align:start position:0%
+research yeah at some point of time in a
+ 
+
+ align:start position:0%
+research yeah at some point of time in a
+far far future that is off right but
+
+ align:start position:0%
+far far future that is off right but
+ 
+
+ align:start position:0%
+far far future that is off right but
+that doesn't necessarily mean that it's
+
+ align:start position:0%
+that doesn't necessarily mean that it's
+ 
+
+ align:start position:0%
+that doesn't necessarily mean that it's
+going to pay off right away
+
+ align:start position:0%
+going to pay off right away
+ 
+
+ align:start position:0%
+going to pay off right away
+so so it so that may end up in
+
+ align:start position:0%
+so so it so that may end up in
+ 
+
+ align:start position:0%
+so so it so that may end up in
+situations where you start getting
+
+ align:start position:0%
+situations where you start getting
+ 
+
+ align:start position:0%
+situations where you start getting
+things like big fluctuations around is
+
+ align:start position:0%
+things like big fluctuations around is
+ 
+
+ align:start position:0%
+things like big fluctuations around is
+still it's all balancing in terms of
+
+ align:start position:0%
+still it's all balancing in terms of
+ 
+
+ align:start position:0%
+still it's all balancing in terms of
+equilibrium by this but just like a
+
+ align:start position:0%
+equilibrium by this but just like a
+ 
+
+ align:start position:0%
+equilibrium by this but just like a
+thermostat that's you know very slow to
+
+ align:start position:0%
+thermostat that's you know very slow to
+ 
+
+ align:start position:0%
+thermostat that's you know very slow to
+respond you might have something like a
+
+ align:start position:0%
+respond you might have something like a
+ 
+
+ align:start position:0%
+respond you might have something like a
+heater that warms up a room and it makes
+
+ align:start position:0%
+heater that warms up a room and it makes
+ 
+
+ align:start position:0%
+heater that warms up a room and it makes
+a room to warm before the sensor
+
+ align:start position:0%
+a room to warm before the sensor
+ 
+
+ align:start position:0%
+a room to warm before the sensor
+actually realizes that it's warm enough
+
+ align:start position:0%
+actually realizes that it's warm enough
+ 
+
+ align:start position:0%
+actually realizes that it's warm enough
+and then shuts it off and then the room
+
+ align:start position:0%
+and then shuts it off and then the room
+ 
+
+ align:start position:0%
+and then shuts it off and then the room
+becomes really really cold before the
+
+ align:start position:0%
+becomes really really cold before the
+ 
+
+ align:start position:0%
+becomes really really cold before the
+sensor realizes that is too cold and
+
+ align:start position:0%
+sensor realizes that is too cold and
+ 
+
+ align:start position:0%
+sensor realizes that is too cold and
+then turns it back on again
+
+ align:start position:0%
+then turns it back on again
+ 
+
+ align:start position:0%
+then turns it back on again
+and that's again this these oscillations
+
+ align:start position:0%
+and that's again this these oscillations
+ 
+
+ align:start position:0%
+and that's again this these oscillations
+so keep in mind also things like time
+
+ align:start position:0%
+so keep in mind also things like time
+ 
+
+ align:start position:0%
+so keep in mind also things like time
+light when you're drawing out is that
+
+ align:start position:0%
+light when you're drawing out is that
+ 
+
+ align:start position:0%
+light when you're drawing out is that
+right now how long does it take this
+
+ align:start position:0%
+right now how long does it take this
+ 
+
+ align:start position:0%
+right now how long does it take this
+advantage to coming to that advantage of
+
+ align:start position:0%
+advantage to coming to that advantage of
+ 
+
+ align:start position:0%
+advantage to coming to that advantage of
+this increase to 30 to that decrease um
+
+ align:start position:0%
+this increase to 30 to that decrease um
+ 
+
+ align:start position:0%
+this increase to 30 to that decrease um
+and yeah any questions like how much
+
+ align:start position:0%
+and yeah any questions like how much
+ 
+
+ align:start position:0%
+and yeah any questions like how much
+does your point being really near like
+
+ align:start position:0%
+does your point being really near like
+ 
+
+ align:start position:0%
+does your point being really near like
+how much about a one-point lead right
+
+ align:start position:0%
+how much about a one-point lead right
+ 
+
+ align:start position:0%
+how much about a one-point lead right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+positive P that means this is really
+
+ align:start position:0%
+positive P that means this is really
+ 
+
+ align:start position:0%
+positive P that means this is really
+like a cheaper way to provide more for
+
+ align:start position:0%
+like a cheaper way to provide more for
+ 
+
+ align:start position:0%
+like a cheaper way to provide more for
+me later and even though the user system
+
+ align:start position:0%
+me later and even though the user system
+ 
+
+ align:start position:0%
+me later and even though the user system
+o- it's actually more like a half point
+
+ align:start position:0%
+o- it's actually more like a half point
+ 
+
+ align:start position:0%
+o- it's actually more like a half point
+we just was like yeah I that means like
+
+ align:start position:0%
+we just was like yeah I that means like
+ 
+
+ align:start position:0%
+we just was like yeah I that means like
+power grid for instance and I definitely
+
+ align:start position:0%
+power grid for instance and I definitely
+ 
+
+ align:start position:0%
+power grid for instance and I definitely
+have a case where sometimes negative in
+
+ align:start position:0%
+have a case where sometimes negative in
+ 
+
+ align:start position:0%
+have a case where sometimes negative in
+fact to literally be negative in the
+
+ align:start position:0%
+fact to literally be negative in the
+ 
+
+ align:start position:0%
+fact to literally be negative in the
+sense that like taking this leader it
+
+ align:start position:0%
+sense that like taking this leader it
+ 
+
+ align:start position:0%
+sense that like taking this leader it
+now could actually hurt me because the
+
+ align:start position:0%
+now could actually hurt me because the
+ 
+
+ align:start position:0%
+now could actually hurt me because the
+thinking could actually like for me long
+
+ align:start position:0%
+thinking could actually like for me long
+ 
+
+ align:start position:0%
+thinking could actually like for me long
+yeah I didn't positive and negative
+
+ align:start position:0%
+yeah I didn't positive and negative
+ 
+
+ align:start position:0%
+yeah I didn't positive and negative
+since I was originally inherited from
+
+ align:start position:0%
+since I was originally inherited from
+ 
+
+ align:start position:0%
+since I was originally inherited from
+Matt's cybernetics it's actually
+
+ align:start position:0%
+Matt's cybernetics it's actually
+ 
+
+ align:start position:0%
+Matt's cybernetics it's actually
+referring to like a differential yeah
+
+ align:start position:0%
+referring to like a differential yeah
+ 
+
+ align:start position:0%
+referring to like a differential yeah
+rather than B that is it's referring to
+
+ align:start position:0%
+rather than B that is it's referring to
+ 
+
+ align:start position:0%
+rather than B that is it's referring to
+a rate of change right so rather than
+
+ align:start position:0%
+a rate of change right so rather than
+ 
+
+ align:start position:0%
+a rate of change right so rather than
+the actual moment yeah so so that's
+
+ align:start position:0%
+the actual moment yeah so so that's
+ 
+
+ align:start position:0%
+the actual moment yeah so so that's
+that's that's something that we that we
+
+ align:start position:0%
+that's that's something that we that we
+ 
+
+ align:start position:0%
+that's that's something that we that we
+that doesn't package everything up but
+
+ align:start position:0%
+that doesn't package everything up but
+ 
+
+ align:start position:0%
+that doesn't package everything up but
+it's sort of thus it's not because some
+
+ align:start position:0%
+it's sort of thus it's not because some
+ 
+
+ align:start position:0%
+it's sort of thus it's not because some
+people think negative feedback means bad
+
+ align:start position:0%
+people think negative feedback means bad
+ 
+
+ align:start position:0%
+people think negative feedback means bad
+right that's like no we're not gonna sit
+
+ align:start position:0%
+right that's like no we're not gonna sit
+ 
+
+ align:start position:0%
+right that's like no we're not gonna sit
+back put me good and could mean that and
+
+ align:start position:0%
+back put me good and could mean that and
+ 
+
+ align:start position:0%
+back put me good and could mean that and
+negative feedback for someone who's
+
+ align:start position:0%
+negative feedback for someone who's
+ 
+
+ align:start position:0%
+negative feedback for someone who's
+behind could be an advantage so the
+
+ align:start position:0%
+behind could be an advantage so the
+ 
+
+ align:start position:0%
+behind could be an advantage so the
+terminology doesn't quite make it easy
+
+ align:start position:0%
+terminology doesn't quite make it easy
+ 
+
+ align:start position:0%
+terminology doesn't quite make it easy
+for it for everyone to use but it's
+
+ align:start position:0%
+for it for everyone to use but it's
+ 
+
+ align:start position:0%
+for it for everyone to use but it's
+something that is currently in use plus
+
+ align:start position:0%
+something that is currently in use plus
+ 
+
+ align:start position:0%
+something that is currently in use plus
+good to know that game designers between
+
+ align:start position:0%
+good to know that game designers between
+ 
+
+ align:start position:0%
+good to know that game designers between
+using terms the control system where
+
+ align:start position:0%
+using terms the control system where
+ 
+
+ align:start position:0%
+using terms the control system where
+positive feedback would be bad yeah I
+
+ align:start position:0%
+positive feedback would be bad yeah I
+ 
+
+ align:start position:0%
+positive feedback would be bad yeah I
+think that's kind of the opposite of the
+
+ align:start position:0%
+think that's kind of the opposite of the
+ 
+
+ align:start position:0%
+think that's kind of the opposite of the
+word control shake chain reaction might
+
+ align:start position:0%
+word control shake chain reaction might
+ 
+
+ align:start position:0%
+word control shake chain reaction might
+be a great way to describe for you any
+
+ align:start position:0%
+be a great way to describe for you any
+ 
+
+ align:start position:0%
+be a great way to describe for you any
+other questions about these ideas
+
+ align:start position:0%
+other questions about these ideas
+ 
+
+ align:start position:0%
+other questions about these ideas
+a lot of these stuff that I've been
+
+ align:start position:0%
+a lot of these stuff that I've been
+ 
+
+ align:start position:0%
+a lot of these stuff that I've been
+talking about is known as first order
+
+ align:start position:0%
+talking about is known as first order
+ 
+
+ align:start position:0%
+talking about is known as first order
+cybernetics which is basically the
+
+ align:start position:0%
+cybernetics which is basically the
+ 
+
+ align:start position:0%
+cybernetics which is basically the
+system it's doing its own thing happily
+
+ align:start position:0%
+system it's doing its own thing happily
+ 
+
+ align:start position:0%
+system it's doing its own thing happily
+and if I'm taking a look at the system
+
+ align:start position:0%
+and if I'm taking a look at the system
+ 
+
+ align:start position:0%
+and if I'm taking a look at the system
+from the outside you know I don't really
+
+ align:start position:0%
+from the outside you know I don't really
+ 
+
+ align:start position:0%
+from the outside you know I don't really
+have any influence how it's going to
+
+ align:start position:0%
+have any influence how it's going to
+ 
+
+ align:start position:0%
+have any influence how it's going to
+perform but there is a second order
+
+ align:start position:0%
+perform but there is a second order
+ 
+
+ align:start position:0%
+perform but there is a second order
+that's cool whole school of second order
+
+ align:start position:0%
+that's cool whole school of second order
+ 
+
+ align:start position:0%
+that's cool whole school of second order
+cybernetics and I'm totally unfamiliar
+
+ align:start position:0%
+cybernetics and I'm totally unfamiliar
+ 
+
+ align:start position:0%
+cybernetics and I'm totally unfamiliar
+with which actually takes into account
+
+ align:start position:0%
+with which actually takes into account
+ 
+
+ align:start position:0%
+with which actually takes into account
+having a person which you would think
+
+ align:start position:0%
+having a person which you would think
+ 
+
+ align:start position:0%
+having a person which you would think
+would be a lot more of the comfortable
+
+ align:start position:0%
+would be a lot more of the comfortable
+ 
+
+ align:start position:0%
+would be a lot more of the comfortable
+games especially game being played by
+
+ align:start position:0%
+games especially game being played by
+ 
+
+ align:start position:0%
+games especially game being played by
+cable but I think I don't know
+
+ align:start position:0%
+cable but I think I don't know
+ 
+
+ align:start position:0%
+cable but I think I don't know
+southern accent interested in a research
+
+ align:start position:0%
+southern accent interested in a research
+ 
+
+ align:start position:0%
+southern accent interested in a research
+project something like that you know
+
+ align:start position:0%
+project something like that you know
+ 
+
+ align:start position:0%
+project something like that you know
+this is something I never thought I
+
+ align:start position:0%
+this is something I never thought I
+ 
+
+ align:start position:0%
+this is something I never thought I
+would have to be able to find out about
+
+ align:start position:0%
+would have to be able to find out about
+ 
+
+ align:start position:0%
+would have to be able to find out about
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one final word this is a very formal way
+
+ align:start position:0%
+one final word this is a very formal way
+ 
+
+ align:start position:0%
+one final word this is a very formal way
+of looking at game systems just as I
+
+ align:start position:0%
+of looking at game systems just as I
+ 
+
+ align:start position:0%
+of looking at game systems just as I
+have already I just admitted that it
+
+ align:start position:0%
+have already I just admitted that it
+ 
+
+ align:start position:0%
+have already I just admitted that it
+doesn't take people's involvement in the
+
+ align:start position:0%
+doesn't take people's involvement in the
+ 
+
+ align:start position:0%
+doesn't take people's involvement in the
+process very well it is not necessarily
+
+ align:start position:0%
+process very well it is not necessarily
+ 
+
+ align:start position:0%
+process very well it is not necessarily
+the case that the form of ways of
+
+ align:start position:0%
+the case that the form of ways of
+ 
+
+ align:start position:0%
+the case that the form of ways of
+looking at a system just looking at how
+
+ align:start position:0%
+looking at a system just looking at how
+ 
+
+ align:start position:0%
+looking at a system just looking at how
+the rules interact it's necessarily
+
+ align:start position:0%
+the rules interact it's necessarily
+ 
+
+ align:start position:0%
+the rules interact it's necessarily
+always the best way to look at at games
+
+ align:start position:0%
+always the best way to look at at games
+ 
+
+ align:start position:0%
+always the best way to look at at games
+in many ways in many occasions that it's
+
+ align:start position:0%
+in many ways in many occasions that it's
+ 
+
+ align:start position:0%
+in many ways in many occasions that it's
+actually not a useful technique you know
+
+ align:start position:0%
+actually not a useful technique you know
+ 
+
+ align:start position:0%
+actually not a useful technique you know
+I can have all these systems in my rules
+
+ align:start position:0%
+I can have all these systems in my rules
+ 
+
+ align:start position:0%
+I can have all these systems in my rules
+but if you know if people are going to
+
+ align:start position:0%
+but if you know if people are going to
+ 
+
+ align:start position:0%
+but if you know if people are going to
+read my rules and interpret my rules
+
+ align:start position:0%
+read my rules and interpret my rules
+ 
+
+ align:start position:0%
+read my rules and interpret my rules
+that's you've already seen happen in
+
+ align:start position:0%
+that's you've already seen happen in
+ 
+
+ align:start position:0%
+that's you've already seen happen in
+this class differently than dia you know
+
+ align:start position:0%
+this class differently than dia you know
+ 
+
+ align:start position:0%
+this class differently than dia you know
+they may be motivated to do things that
+
+ align:start position:0%
+they may be motivated to do things that
+ 
+
+ align:start position:0%
+they may be motivated to do things that
+operate against my assumptions because
+
+ align:start position:0%
+operate against my assumptions because
+ 
+
+ align:start position:0%
+operate against my assumptions because
+there's something else in my Meredith my
+
+ align:start position:0%
+there's something else in my Meredith my
+ 
+
+ align:start position:0%
+there's something else in my Meredith my
+aesthetic in their own individual
+
+ align:start position:0%
+aesthetic in their own individual
+ 
+
+ align:start position:0%
+aesthetic in their own individual
+motivations like if somebody wants to
+
+ align:start position:0%
+motivations like if somebody wants to
+ 
+
+ align:start position:0%
+motivations like if somebody wants to
+take down somebody else in the game just
+
+ align:start position:0%
+take down somebody else in the game just
+ 
+
+ align:start position:0%
+take down somebody else in the game just
+because they happened to keep that
+
+ align:start position:0%
+because they happened to keep that
+ 
+
+ align:start position:0%
+because they happened to keep that
+person you know and it's outside of the
+
+ align:start position:0%
+person you know and it's outside of the
+ 
+
+ align:start position:0%
+person you know and it's outside of the
+gating rules you know then nothing in
+
+ align:start position:0%
+gating rules you know then nothing in
+ 
+
+ align:start position:0%
+gating rules you know then nothing in
+the rules going to tell me that but it's
+
+ align:start position:0%
+the rules going to tell me that but it's
+ 
+
+ align:start position:0%
+the rules going to tell me that but it's
+still going to affect how that game gets
+
+ align:start position:0%
+still going to affect how that game gets
+ 
+
+ align:start position:0%
+still going to affect how that game gets
+played and I wondered and I wanted to
+
+ align:start position:0%
+played and I wondered and I wanted to
+ 
+
+ align:start position:0%
+played and I wondered and I wanted to
+thank you account the game of the policy
+
+ align:start position:0%
+thank you account the game of the policy
+ 
+
+ align:start position:0%
+thank you account the game of the policy
+for instance you know it has to take
+
+ align:start position:0%
+for instance you know it has to take
+ 
+
+ align:start position:0%
+for instance you know it has to take
+into account the fact that people that
+
+ align:start position:0%
+into account the fact that people that
+ 
+
+ align:start position:0%
+into account the fact that people that
+you're probably playing in with people
+
+ align:start position:0%
+you're probably playing in with people
+ 
+
+ align:start position:0%
+you're probably playing in with people
+that you know and you have some sort of
+
+ align:start position:0%
+that you know and you have some sort of
+ 
+
+ align:start position:0%
+that you know and you have some sort of
+existing relationship I don't think it
+
+ align:start position:0%
+existing relationship I don't think it
+ 
+
+ align:start position:0%
+existing relationship I don't think it
+does a very very good job of insulating
+
+ align:start position:0%
+does a very very good job of insulating
+ 
+
+ align:start position:0%
+does a very very good job of insulating
+you from the fallout of the game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone knows nothing about right okay
+
+ align:start position:0%
+everyone knows nothing about right okay
+ 
+
+ align:start position:0%
+everyone knows nothing about right okay
+just aren't friends and people that you
+
+ align:start position:0%
+just aren't friends and people that you
+ 
+
+ align:start position:0%
+just aren't friends and people that you
+play diplomacy with anymore that's why I
+
+ align:start position:0%
+play diplomacy with anymore that's why I
+ 
+
+ align:start position:0%
+play diplomacy with anymore that's why I
+like talking about it so you know that
+
+ align:start position:0%
+like talking about it so you know that
+ 
+
+ align:start position:0%
+like talking about it so you know that
+that will be going into things like
+
+ align:start position:0%
+that will be going into things like
+ 
+
+ align:start position:0%
+that will be going into things like
+games games for social play in the
+
+ align:start position:0%
+games games for social play in the
+ 
+
+ align:start position:0%
+games games for social play in the
+social function
+
+ align:start position:0%
+social function
+ 
+
+ align:start position:0%
+social function
+you interact with with people some other
+
+ align:start position:0%
+you interact with with people some other
+ 
+
+ align:start position:0%
+you interact with with people some other
+topics are going to be things like games
+
+ align:start position:0%
+topics are going to be things like games
+ 
+
+ align:start position:0%
+topics are going to be things like games
+of simulation games as a and as its
+
+ align:start position:0%
+of simulation games as a and as its
+ 
+
+ align:start position:0%
+of simulation games as a and as its
+might be flow on the road to the real
+
+ align:start position:0%
+might be flow on the road to the real
+ 
+
+ align:start position:0%
+might be flow on the road to the real
+world but an interesting way you know
+
+ align:start position:0%
+world but an interesting way you know
+ 
+
+ align:start position:0%
+world but an interesting way you know
+but it could be a fun house terribly so
+
+ align:start position:0%
+but it could be a fun house terribly so
+ 
+
+ align:start position:0%
+but it could be a fun house terribly so
+so we'll be looking at that in weeks
+
+ align:start position:0%
+so we'll be looking at that in weeks
+ 
+
+ align:start position:0%
+so we'll be looking at that in weeks
+this is probably about exploring this
+
+ align:start position:0%
+this is probably about exploring this
+ 
+
+ align:start position:0%
+this is probably about exploring this
+weekend maybe talking about things like
+
+ align:start position:0%
+weekend maybe talking about things like
+ 
+
+ align:start position:0%
+weekend maybe talking about things like
+information system there's also very
+
+ align:start position:0%
+information system there's also very
+ 
+
+ align:start position:0%
+information system there's also very
+formal just keep in mind that's just
+
+ align:start position:0%
+formal just keep in mind that's just
+ 
+
+ align:start position:0%
+formal just keep in mind that's just
+like one school of paper and writing so
+
+ align:start position:0%
+like one school of paper and writing so
+ 
+
+ align:start position:0%
+like one school of paper and writing so
+weird things that all have an
+
+ align:start position:0%
+weird things that all have an
+ 
+
+ align:start position:0%
+weird things that all have an
+interesting way of dealing with this
+
+ align:start position:0%
+interesting way of dealing with this
+ 
+
+ align:start position:0%
+interesting way of dealing with this
+some of them you are going to see these
+
+ align:start position:0%
+some of them you are going to see these
+ 
+
+ align:start position:0%
+some of them you are going to see these
+problems come up like especially in
+
+ align:start position:0%
+problems come up like especially in
+ 
+
+ align:start position:0%
+problems come up like especially in
+through the game Tommy people we have in
+
+ align:start position:0%
+through the game Tommy people we have in
+ 
+
+ align:start position:0%
+through the game Tommy people we have in
+class today one two three four five six
+
+ align:start position:0%
+class today one two three four five six
+ 
+
+ align:start position:0%
+class today one two three four five six
+seven so 11 that's like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we got a hot to be employed on
+
+ align:start position:0%
+okay so we got a hot to be employed on
+ 
+
+ align:start position:0%
+okay so we got a hot to be employed on
+internet ones are some games like king
+
+ align:start position:0%
+internet ones are some games like king
+ 
+
+ align:start position:0%
+internet ones are some games like king
+of Tokyo is very much a king of the hill
+
+ align:start position:0%
+of Tokyo is very much a king of the hill
+ 
+
+ align:start position:0%
+of Tokyo is very much a king of the hill
+need so it's deliberately trying to ask
+
+ align:start position:0%
+need so it's deliberately trying to ask
+ 
+
+ align:start position:0%
+need so it's deliberately trying to ask
+you to take down the person who's led
+
+ align:start position:0%
+you to take down the person who's led
+ 
+
+ align:start position:0%
+you to take down the person who's led
+and they gave mechanics make you wonder
+
+ align:start position:0%
+and they gave mechanics make you wonder
+ 
+
+ align:start position:0%
+and they gave mechanics make you wonder
+whether being in the lead is really all
+
+ align:start position:0%
+whether being in the lead is really all
+ 
+
+ align:start position:0%
+whether being in the lead is really all
+that great so this playing around is
+
+ align:start position:0%
+that great so this playing around is
+ 
+
+ align:start position:0%
+that great so this playing around is
+like a small world is occupying
+
+ align:start position:0%
+like a small world is occupying
+ 
+
+ align:start position:0%
+like a small world is occupying
+territory with your audience
+
+ align:start position:0%
+territory with your audience
+ 
+
+ align:start position:0%
+territory with your audience
+yeah yeah anybody talk about Vinci small
+
+ align:start position:0%
+yeah yeah anybody talk about Vinci small
+ 
+
+ align:start position:0%
+yeah yeah anybody talk about Vinci small
+roles a updated Vinci yeah no faster to
+
+ align:start position:0%
+roles a updated Vinci yeah no faster to
+ 
+
+ align:start position:0%
+roles a updated Vinci yeah no faster to
+play fix that arrives that we are
+
+ align:start position:0%
+play fix that arrives that we are
+ 
+
+ align:start position:0%
+play fix that arrives that we are
+to if anybody wants to take a look at
+
+ align:start position:0%
+to if anybody wants to take a look at
+ 
+
+ align:start position:0%
+to if anybody wants to take a look at
+that we don't because they think that
+
+ align:start position:0%
+that we don't because they think that
+ 
+
+ align:start position:0%
+that we don't because they think that
+two hours under surface area you know it
+
+ align:start position:0%
+two hours under surface area you know it
+ 
+
+ align:start position:0%
+two hours under surface area you know it
+is lifeboats it's about bunch of sailors
+
+ align:start position:0%
+is lifeboats it's about bunch of sailors
+ 
+
+ align:start position:0%
+is lifeboats it's about bunch of sailors
+trying to get to the trying to get to
+
+ align:start position:0%
+trying to get to the trying to get to
+ 
+
+ align:start position:0%
+trying to get to the trying to get to
+safety
+
+ align:start position:0%
+safety
+ 
+
+ align:start position:0%
+safety
+basically the boat is same boats are
+
+ align:start position:0%
+basically the boat is same boats are
+ 
+
+ align:start position:0%
+basically the boat is same boats are
+sinking and they're all trying to get
+
+ align:start position:0%
+sinking and they're all trying to get
+ 
+
+ align:start position:0%
+sinking and they're all trying to get
+the safety and everyone's jumping on and
+
+ align:start position:0%
+the safety and everyone's jumping on and
+ 
+
+ align:start position:0%
+the safety and everyone's jumping on and
+pushing people out of lifeboats and
+
+ align:start position:0%
+pushing people out of lifeboats and
+ 
+
+ align:start position:0%
+pushing people out of lifeboats and
+slipping to lifeboats and that so so
+
+ align:start position:0%
+slipping to lifeboats and that so so
+ 
+
+ align:start position:0%
+slipping to lifeboats and that so so
+it's all about 2020 yeah I know
+
+ align:start position:0%
+it's all about 2020 yeah I know
+ 
+
+ align:start position:0%
+it's all about 2020 yeah I know
+relatively little about these ones I
+
+ align:start position:0%
+relatively little about these ones I
+ 
+
+ align:start position:0%
+relatively little about these ones I
+forget
+
+ align:start position:0%
+forget
+ 
+
+ align:start position:0%
+forget
+yeah these were recommended by some
+
+ align:start position:0%
+yeah these were recommended by some
+ 
+
+ align:start position:0%
+yeah these were recommended by some
+money scholars when I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+el Grande Spanish shame about the yes
+
+ align:start position:0%
+el Grande Spanish shame about the yes
+ 
+
+ align:start position:0%
+el Grande Spanish shame about the yes
+yeah that's the pocket or anybody but
+
+ align:start position:0%
+yeah that's the pocket or anybody but
+ 
+
+ align:start position:0%
+yeah that's the pocket or anybody but
+I'm pretty sure I look in there against
+
+ align:start position:0%
+I'm pretty sure I look in there against
+ 
+
+ align:start position:0%
+I'm pretty sure I look in there against
+operative prediction of future intrigue
+
+ align:start position:0%
+operative prediction of future intrigue
+ 
+
+ align:start position:0%
+operative prediction of future intrigue
+is again that I like the theme the books
+
+ align:start position:0%
+is again that I like the theme the books
+ 
+
+ align:start position:0%
+is again that I like the theme the books
+it's basically you run a university and
+
+ align:start position:0%
+it's basically you run a university and
+ 
+
+ align:start position:0%
+it's basically you run a university and
+you're trying to put your clothes off in
+
+ align:start position:0%
+you're trying to put your clothes off in
+ 
+
+ align:start position:0%
+you're trying to put your clothes off in
+other universities that's not what the
+
+ align:start position:0%
+other universities that's not what the
+ 
+
+ align:start position:0%
+other universities that's not what the
+game says in the box but I would like
+
+ align:start position:0%
+game says in the box but I would like
+ 
+
+ align:start position:0%
+game says in the box but I would like
+you to try playing the game with that so
+
+ align:start position:0%
+you to try playing the game with that so
+ 
+
+ align:start position:0%
+you to try playing the game with that so
+so yeah you know it's an interesting
+
+ align:start position:0%
+so yeah you know it's an interesting
+ 
+
+ align:start position:0%
+so yeah you know it's an interesting
+game because you are trying you are
+
+ align:start position:0%
+game because you are trying you are
+ 
+
+ align:start position:0%
+game because you are trying you are
+doing exactly the same thing that
+
+ align:start position:0%
+doing exactly the same thing that
+ 
+
+ align:start position:0%
+doing exactly the same thing that
+everybody else is trying to do but in
+
+ align:start position:0%
+everybody else is trying to do but in
+ 
+
+ align:start position:0%
+everybody else is trying to do but in
+order to succeed in the game you have to
+
+ align:start position:0%
+order to succeed in the game you have to
+ 
+
+ align:start position:0%
+order to succeed in the game you have to
+put your troops your your your scholars
+
+ align:start position:0%
+put your troops your your your scholars
+ 
+
+ align:start position:0%
+put your troops your your your scholars
+into other people's territory if you are
+
+ align:start position:0%
+into other people's territory if you are
+ 
+
+ align:start position:0%
+into other people's territory if you are
+trying to put into yours and there's a
+
+ align:start position:0%
+trying to put into yours and there's a
+ 
+
+ align:start position:0%
+trying to put into yours and there's a
+mutual benefit and a whole lot of
+
+ align:start position:0%
+mutual benefit and a whole lot of
+ 
+
+ align:start position:0%
+mutual benefit and a whole lot of
+politicking so a lot of opportunities
+
+ align:start position:0%
+politicking so a lot of opportunities
+ 
+
+ align:start position:0%
+politicking so a lot of opportunities
+for you to sort of it's a pretty good
+
+ align:start position:0%
+for you to sort of it's a pretty good
+ 
+
+ align:start position:0%
+for you to sort of it's a pretty good
+feedback game because it gives you a
+
+ align:start position:0%
+feedback game because it gives you a
+ 
+
+ align:start position:0%
+feedback game because it gives you a
+whole bunch of tools to basically take a
+
+ align:start position:0%
+whole bunch of tools to basically take a
+ 
+
+ align:start position:0%
+whole bunch of tools to basically take a
+look at with which games hi the Wayne
+
+ align:start position:0%
+look at with which games hi the Wayne
+ 
+
+ align:start position:0%
+look at with which games hi the Wayne
+foundation hide the progress or players
+
+ align:start position:0%
+foundation hide the progress or players
+ 
+
+ align:start position:0%
+foundation hide the progress or players
+from you you know something
+
+ align:start position:0%
+from you you know something
+ 
+
+ align:start position:0%
+from you you know something
+some of these games you can easily see
+
+ align:start position:0%
+some of these games you can easily see
+ 
+
+ align:start position:0%
+some of these games you can easily see
+this ahead is up on this game is really
+
+ align:start position:0%
+this ahead is up on this game is really
+ 
+
+ align:start position:0%
+this ahead is up on this game is really
+hard to tell it has a debris so that it
+
+ align:start position:0%
+hard to tell it has a debris so that it
+ 
+
+ align:start position:0%
+hard to tell it has a debris so that it
+was have these situations where someone
+
+ align:start position:0%
+was have these situations where someone
+ 
+
+ align:start position:0%
+was have these situations where someone
+organza on people who
+
+ align:start position:0%
+organza on people who
+ 
+
+ align:start position:0%
+organza on people who
+look at me how they avoid things like
+
+ align:start position:0%
+look at me how they avoid things like
+ 
+
+ align:start position:0%
+look at me how they avoid things like
+totally how they discouraged in place
+
+ align:start position:0%
+totally how they discouraged in place
+ 
+
+ align:start position:0%
+totally how they discouraged in place
+I'm 90 or maybe something to encourage
+
+ align:start position:0%
+I'm 90 or maybe something to encourage
+ 
+
+ align:start position:0%
+I'm 90 or maybe something to encourage
+them and use them to the compound to in
+
+ align:start position:0%
+them and use them to the compound to in
+ 
+
+ align:start position:0%
+them and use them to the compound to in
+favor of them I think we've definitely
+
+ align:start position:0%
+favor of them I think we've definitely
+ 
+
+ align:start position:0%
+favor of them I think we've definitely
+decided all right and then what are
+
+ align:start position:0%
+decided all right and then what are
+ 
+
+ align:start position:0%
+decided all right and then what are
+these boxes up at three o'clock working
+
+ align:start position:0%
+these boxes up at three o'clock working
+ 
+
+ align:start position:0%
+these boxes up at three o'clock working
+our team's it's going to be a lot of
+
+ align:start position:0%
+our team's it's going to be a lot of
+ 
+
+ align:start position:0%
+our team's it's going to be a lot of
+time you're gonna see your team's before
+
+ align:start position:0%
+time you're gonna see your team's before
+ 
+
+ align:start position:0%
+time you're gonna see your team's before
+spring break
+
+ align:start position:0%
+spring break
+ 
+
+ align:start position:0%
+spring break
+so you might want to give each other
+
+ align:start position:0%
+so you might want to give each other
+ 
+
+ align:start position:0%
+so you might want to give each other
+tasks to work on during spring break if
+
+ align:start position:0%
+tasks to work on during spring break if
+ 
+
+ align:start position:0%
+tasks to work on during spring break if
+you can't think of anything test over
+
+ align:start position:0%
+you can't think of anything test over
+ 
+
+ align:start position:0%
+you can't think of anything test over
+spring break Prague a good number of you
+
+ align:start position:0%
+spring break Prague a good number of you
+ 
+
+ align:start position:0%
+spring break Prague a good number of you
+I'm going to see people who who haven't
+
+ align:start position:0%
+I'm going to see people who who haven't
+ 
+
+ align:start position:0%
+I'm going to see people who who haven't
+seen your game yeah and written rules
+
+ align:start position:0%
+seen your game yeah and written rules
+ 
+
+ align:start position:0%
+seen your game yeah and written rules
+the first round here it's great
+
+ align:start position:0%
+the first round here it's great
+ 
+
+ align:start position:0%
+the first round here it's great
+and if you don't have a first chocolate
+
+ align:start position:0%
+and if you don't have a first chocolate
+ 
+
+ align:start position:0%
+and if you don't have a first chocolate
+written rules then this last hour of
+
+ align:start position:0%
+written rules then this last hour of
+ 
+
+ align:start position:0%
+written rules then this last hour of
+class is probably a good time to bring
+
+ align:start position:0%
+class is probably a good time to bring
+ 
+
+ align:start position:0%
+class is probably a good time to bring
+up the laptop and just might start
+
+ align:start position:0%
+up the laptop and just might start
+ 
+
+ align:start position:0%
+up the laptop and just might start
+editing that tanks so that yes you can
+
+ align:start position:0%
+editing that tanks so that yes you can
+ 
+
+ align:start position:0%
+editing that tanks so that yes you can
+go into spring break with something that
+
+ align:start position:0%
+go into spring break with something that
+ 
+
+ align:start position:0%
+go into spring break with something that
+you can test with all right for the game
+
+ align:start position:0%
+you can test with all right for the game
+ 
+
+ align:start position:0%
+you can test with all right for the game
+is probably people to play twice maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah but Brandis probably thank him for
+
+ align:start position:0%
+yeah but Brandis probably thank him for
+ 
+
+ align:start position:0%
+yeah but Brandis probably thank him for
+all the sporty
+
+ align:start position:0%
+all the sporty
+ 
+
+ align:start position:0%
+all the sporty
+[Music]
\ No newline at end of file
diff --git a/wnOOQnW5Un4.txt b/wnOOQnW5Un4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f2539ef5fe4e96fe86c4cc04b53a4c2c2638741
--- /dev/null
+++ b/wnOOQnW5Un4.txt
@@ -0,0 +1,1870 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Please note that this
+is a clicker competition,
+
+perhaps the last of the year,
+before you put in your vote
+
+for this particular
+clicker question.
+
+And the defending champs are
+recitation three, and I
+
+believe that no recitation
+has won more than once.
+
+Is that true?
+
+Is there a recitation that
+has two victories?
+
+So, this might be your last
+chance if your recitation has
+
+not won, or if you want to be
+decisive victors in the
+
+clicker competition to have a
+repeat victory, this is your
+
+chance -- no pressure.
+
+But go ahead and put in
+your clicker response.
+
+OK, let's just take 10 more
+seconds to click in.
+
+OK, the answer here is b, and
+the trick was to recognize
+
+which is the equation for first
+order half life, and
+
+which is the equation for
+second order half life.
+
+Most people got this right.
+
+And we picked this clicker
+question to demonstrate a
+
+point that will, for the final
+exam, which is that you will
+
+have an equation sheet
+of all the equations.
+
+There'll be a few you have to
+memorize, we'll let you know
+
+what they are, but that's
+a lot of equations.
+
+So, so far on each hour exam,
+you've had an equation sheet
+
+that's been related to that
+particular material.
+
+On the final, you of an equation
+sheet that has the
+
+equations from exam 1, exam 2,
+exam 3, and also the fourth
+
+exam material.
+
+And so, it doesn't say on them,
+oh, first order half
+
+life equation, colon, and then
+the equation, it just has all
+
+of the equations.
+
+So one thing that you have to do
+is recognize which equation
+
+can be applied where.
+
+And this is something that
+people, occasionally that's
+
+part of knowing the
+material is to
+
+know/recognize the equations.
+
+You don't have to memorize them,
+but you do have to be
+
+able to recognize them and
+know when to apply them.
+
+So that's something you should
+be thinking about as you're
+
+reviewing the material
+for the exam.
+
+And we're just going to at jump
+right in and talk about
+
+reaction mechanisms. So this is
+the last type of question
+
+that's on problem-set 10.
+
+So, when you're investigating
+reaction mechanisms, you often
+
+will have an experimentally
+determined rate law, and then
+
+you want to try to come up
+with a mechanism that's
+
+consistent with that rate law.
+
+So, for this particular
+reaction, we have 2 n o plus o
+
+2 going to 2 n o 2 gas.
+
+And experimental rate laws
+determined there was a rate
+
+constant called k obs, for k
+observed, the observed rate
+
+constant that was calculated.
+
+And we know that it's the order
+of the reactions here.
+
+Overall, what is the overall
+order at this
+
+particular rate law?
+
+Three.
+
+So we have second order in n
+o and first order in o 2.
+
+So if it's overall order of
+three, is it likely to occur
+
+in one step?
+
+No.
+
+What would it be called if it
+did occur in one step -- if
+
+three things came together
+at the same
+
+time to form a product?
+
+Yeah, thermonuclear.
+
+And we learned last time
+that thermonuclear
+
+reactions are rare.
+
+So it's unlikely that those
+three things, the two n o's
+
+and the one o 2 are going to
+come together at the same time
+
+to form product, so
+it probably has
+
+more than one step.
+
+So, on the board here and on
+your notes, we have a two-step
+
+proposed mechanism, and let's
+talk about these two steps and
+
+come up with a rate law that's
+consistent with this
+
+mechanism, and then see if
+that agrees with the
+
+experimental rate law
+that was determined.
+
+So, in the first step of this
+reaction, we have 2 n o's
+
+coming together.
+
+There's a little rate constant,
+k 1, above the first
+
+arrow, and for the reverse
+direction, we have k minus 1,
+
+so this is written as a
+reversible reaction, and it's
+
+forming an intermediate
+n 2 o 2.
+
+In the second step, we have the
+o 2 coming in, reacting
+
+with that intermediate with a
+rate constant, k 2, and it's
+
+forming two molecules
+of n o 2.
+
+So now we can write the
+rates for each of
+
+these individual steps.
+
+We can write the rate for the
+foward reaction here, and so
+
+that's going to be
+equal to k 1.
+
+And we have n o, two n
+o's, so n o squared.
+
+And again, this is a step or an
+elementary reaction so we
+
+can write the reaction
+exactly as it occurs.
+
+We can write a rate law for
+that step using the
+
+stiochiometry of the reaction.
+
+For an overall reaction, you
+can't do that, it has to be
+
+experimentally determined.
+
+But for an elementary reaction
+or a step in a mechanism, you
+
+can do that.
+
+So we write it exactly
+as it occurs.
+
+So, what would be the order of
+this particular reaction as
+
+written here?
+
+Two.
+
+And what about molecularity?
+
+It would be bimolecular.
+
+So we're just getting you used
+to some of these terms.
+
+All right, so then for the
+reverse direction, the rate of
+
+the reverse direction would be
+equal to what rate constant?
+
+k minus 1.
+
+Times what?
+
+Yeah, n 2 o 2.
+
+So what's the order here?
+
+One.
+
+And what's this called?
+
+Yeah, so that's called
+unimolecular.
+
+All right, what about step 2?
+
+What would be the rate
+here, and that
+
+is a clicker question.
+
+OK, just 10 more seconds.
+
+Yup, so we write it exactly as
+written, so we have a k 2
+
+times the concentration
+of o 2 times the
+
+concentration of n 2 o 2.
+
+All right, so what is the
+overall order here?
+
+Two.
+
+And again, that would
+be the bimolecular.
+
+All right, so we have our two
+steps, and we've written rates
+
+for all of those particular
+steps.
+
+Now we're interested in writing
+the rate of the
+
+overall reaction that
+forms n o 2.
+
+So, let's think about what the
+rate of n o 2 formation is.
+
+So, in the last step, we're
+forming n o 2, and we can just
+
+use that last step to
+write this out.
+
+We're forming two molecules
+of n o 2.
+
+So we're going to put a 2 in
+there, because the rate at
+
+which the concentration of this
+will increase twice as
+
+much as will decrease
+this amount.
+
+And the book is somewhat
+inconsistent in its use of 2's
+
+in these equations.
+
+If you're forming two molecules
+in your last step,
+
+there should be a 2, but 2 is
+not always in the answer key.
+
+So what I've done in the past
+is if you put a 2 and there
+
+should be a 2, great, but if you
+don't put it, that's OK,
+
+too, so I have not taken off for
+this because the book is
+
+not been completely consistent
+in its use of that.
+
+But, if you see a two, and 2
+things are being formed, you
+
+know where that comes from.
+
+So, 2 times k 2, that's the
+rate constant of that last
+
+step, and that we're talking
+about the concentration of o 2
+
+and the concentration
+of n 2 o 2.
+
+So we're writing out just that
+last out there with the 2,
+
+because two molecules of
+n o 2 are being formed.
+
+But we're not done with this, we
+can't use this, because it
+
+has an intermediate
+term in there.
+
+And if we're going to write the
+rate of a reaction, the
+
+rate of product formation, we
+can't have any intermediates
+
+in our equation.
+
+We need to solve it in terms
+of products and reactants.
+
+So, we need to solve
+for n 2 o 2.
+
+So we need to solve for the
+concentration of n 2 o 2, and
+
+substitute that into
+our equation.
+
+So we need to solve
+for it in terms of
+
+products and reactants.
+
+So, we need to think about how
+this intermediate is formed,
+
+and we need to think about
+how the intermediate is
+
+decomposed, and we need to
+think about how this
+
+intermediate is consumed.
+
+So, the net formation of n 2 o
+2 is going to be equal to the
+
+rate at which it's formed.
+
+So the rate at which
+it's formed.
+
+What step is it formed in, the
+intermediate formed in?
+
+It's in step one in the forward
+direction, so the rate
+
+at which its formed is k
+1 times n o squared.
+
+So that's the forward rate
+of the first step.
+
+Then we need to think about
+the rate at which its
+
+decomposed.
+
+What step does the intermediate
+decompose in?
+
+Right, the reverse of
+the first step.
+
+So we're going to put a minus
+sign here, and k minus 1 times
+
+the concentration of
+the intermediate.
+
+And then we also want to
+think about the rate
+
+at which it's consumed.
+
+And it's consumed in the second
+step, so that's k 2
+
+times the concentration of the
+intermediate times the
+
+concentration of o 2.
+
+So that's the net formation.
+
+And now we can use something
+called the steady state
+
+approximation, and the steady
+state approximation is used in
+
+all sorts of kinetics, including
+enzyme kinetics, and
+
+it can be phrased two different
+ways, which are
+
+equivalent.
+
+You can say that the steady
+state approximation is that
+
+the net formation of the
+intermediate equals zero --
+
+i.e. this is the net formation
+of the intermediate, so this
+
+entire equation equals zero.
+
+Another way to say it is that
+the rate of formation of the
+
+intermediate equals
+the rate of decay.
+
+So that's saying the same thing,
+that this term is going
+
+to be equal to those
+two terms. That's
+
+saying the same thing.
+
+So, if we can set this whole
+equation equal to zero, then
+
+we can solve for the
+concentrations of the
+
+intermediates in terms of the
+rate constants and the
+
+concentrations of the reactants
+and the products,
+
+which is what we need to do.
+
+So, let's do that.
+
+So we can rearrange this
+expression now that we have
+
+set equal to zero, and so we can
+bring n 2 o 2 over to one
+
+side, so we have our
+intermediate on one side.
+
+And then we are going to have k
+minus 1, and our little k 2
+
+times the concentration
+of o 2.
+
+And so, that is the rate in
+which the intermediate is
+
+decomposed and consumed, and
+that's going to be equal to
+
+the rate at which it's formed,
+which is another way of
+
+expressing the steady
+state approximation.
+
+So we've just moved the
+decomposed and consumed to one
+
+side, and we have the rate at
+which it's formed on the other
+
+side, and now we can easily
+solve for the concentration of
+
+the n 2 o 2, so we're going
+to do that over here.
+
+So that's now going to be equal
+to our k 1 times n o
+
+squared over k minus 1
+plus k 2 times the
+
+concentration of o 2.
+
+So now we've just solved for n
+2 o 2, our intermediate, in
+
+terms of our rate constants and
+in terms of our reactants.
+
+So that's good.
+
+Now we need to take this and
+substitute it back into here.
+
+And if we substitute it back
+into here, let's do that over
+
+here, so now we'll have
+k, 2 times k 2, we'll
+
+also have a k 1 term.
+
+We're going to have, we
+have n o squared.
+
+We also have an o 2 term from
+over here, and this is all
+
+going to be over k minus
+1 plus k 2 times our
+
+concentration of o 2.
+
+So we've just substituted that
+term in here, and now we have
+
+a new expression for the rate of
+our product formation, and
+
+that's lovely.
+
+Except that it doesn't agree
+with the experiment.
+
+So we have a problem.
+
+In the experiment, there's n o
+squared and o 2, but there is
+
+no o 2 in the bottom, so
+something is going on.
+
+So that means that our reaction
+as written, which
+
+didn't have any fast steps or
+any slow steps is inconsistent
+
+if you write a mechanism for
+this, if you write a rate law
+
+for this, it's inconsistent
+with the experiment.
+
+So we need to do more to
+our proposed mechanism.
+
+We need to add fast steps and
+slow steps until we can write
+
+a mechanism that agrees
+with the experiment.
+
+And so, if we want to do this,
+we're going to assume, now we
+
+can try that the first
+step is fast and the
+
+second step is slow.
+
+So let's talk about this slow
+step and what happens if you
+
+have a slow step.
+
+So I'm going to introduce this
+term of rate determining step.
+
+So the slowest step in an
+elementary reaction is going
+
+to determine the overall rate.
+
+If it's slow compared
+to the other steps.
+
+And so, the overall rate, it
+can't be any faster than that
+
+slow step, and that slow step
+is going to govern how fast
+
+the overall reaction is.
+
+All right, so let me give
+you an example of this.
+
+I know they're you're all
+very anxious to complete
+
+problem-set 10, the last
+problem-set that will be
+
+graded in this course.
+
+And you know, because I told you
+at the beginning of class,
+
+that after today's lecture, you
+will know all the material
+
+that will allow you to complete
+that problem-set.
+
+So some of you are going to get
+really antsy at the end of
+
+class thinking OK, I can go
+and do that problem-set.
+
+So, you're going to be ready,
+you may have already started
+
+packing up your backpack as the
+class is winding down, you
+
+see we're getting close to the
+end of the handouts saying,
+
+all right, I've got to get out
+of here, I've got to get to
+
+the library and finish the
+rest of problem-set 10.
+
+All right, so let's say it takes
+you five seconds to pack
+
+up and be out the door.
+
+Or maybe there's some people
+coming in, OK, maybe ten
+
+seconds to get out the door.
+
+Then you're running down toward
+the library and you're
+
+moving pretty fast, you're
+jumping over people that are
+
+stopping and talking to their
+friends, you're moving very
+
+quickly, you might slide down
+the banisters to get to the
+
+first floor, and you get
+to the library, but
+
+you were too slow.
+
+Even though you did it really
+fast, all the tables are busy,
+
+everyone else is completing
+problem-set 10.
+
+So you go up and down, you're
+looking for a table, there's
+
+no tables, they're all busy,
+everyone has their chemistry
+
+textbooks out and
+they're going.
+
+All right.
+
+So, then you have to leave the
+library, you go to building 2,
+
+that's close by, they're
+classrooms, they're not in
+
+use, the first couple
+you check there's
+
+recitations going on.
+
+Finally you find the
+one that's empty.
+
+When you find it that's empty,
+your backpack is off, your
+
+books are out, your
+calculator's
+
+out and you're going.
+
+Right, maybe another
+ten seconds.
+
+But it took you about
+20 minutes to
+
+find that free table.
+
+So, maybe ten seconds to get
+out of this classroom, ten
+
+seconds to get your books out of
+your backpack, but then 20
+
+minutes overall to find
+that free table.
+
+So that's the rate determining
+step, that 20 minutes to find
+
+that table is going
+to control the
+
+overall rate of the reaction.
+
+And so, many of you have
+probably experienced rate
+
+determining steps in your life,
+some of you may have
+
+friends that are always your
+rate determining step, and so
+
+you know about this.
+
+You know about this.
+
+And so rate determining steps
+allow us to come up with
+
+different kinds of mechanisms
+and simplify different
+
+expressions.
+
+All right, so let's look at what
+this does for us here.
+
+If we make assumptions now about
+a step being fast and a
+
+step being slow.
+
+All right, so we're going to be
+able to -- this expression
+
+here, we're going to be
+able to simplify.
+
+All right, so we're going to ask
+the question then, here,
+
+we're assuming that we're going
+to say, all right, let's
+
+just say the first step
+is fast and the
+
+second step is slow.
+
+We're going to see whether that
+gives us an answer that's
+
+consistent with the
+experimentally
+
+determined rate law.
+
+So here, if we say this is
+fast and this is slow,
+
+basically we're asking the
+question, is the decomposition
+
+of the intermediate or it's
+consumption faster?
+
+So as we wrote this, then, we're
+saying decomposition is
+
+fast. The first step is fast
+and reversible, so the
+
+decomposition is fast. The
+second step is slow, the
+
+consumption of that intermediate
+is slow.
+
+So that allows us to
+change our rate.
+
+So, what we're then saying in
+terms of the here's the words,
+
+here's sort of the equations,
+we're saying that this term
+
+here, this k minus 1 times the
+intermediate term, is a lot
+
+bigger, because this is
+faster than this.
+
+This is slow, the rate of
+consumption is slow.
+
+So k minus 1 is going to
+be a bigger number
+
+than k 2 times o 2.
+
+So, if we say that, if we say
+this is fast, that's a big
+
+number, this is a fast step,
+k 2 is a small number, it's
+
+slow, if this is a lot smaller
+than k minus 1, and these are
+
+both appearing in the bottom
+of the equation here, that
+
+allows you to get rid
+of this term.
+
+So if you have something really
+big and something
+
+pretty small, on the bottom of
+this equation, the really
+
+small thing is kind
+of insignificant.
+
+And so we can get rid
+of that here.
+
+So we can get rid
+of this term.
+
+So that allows us to simplify
+this expression.
+
+Now we have k 1 times n o
+squared over k minus 1.
+
+We can also rearrange that and
+bring our concentration terms
+
+on one side, so we have our
+intermediate over our n o
+
+squared and have that now is
+going to be equal to k 1
+
+over k minus 1.
+
+What is little rate constant
+k 1 over rate
+
+constant k minus 1?
+
+Big k, right.
+
+So that's another way of
+saying the equilibrium
+
+expression.
+
+So it's the equilibrium constant
+for the first step is
+
+equal to k 1 over k minus 1.
+
+So basically what we're saying
+then, if we have the first
+
+step being fast and reversible,
+and the second
+
+step being slow, we're saying
+that the first step is really
+
+an equilibrium.
+
+So what allows us to say that?
+
+Well, if you have a fast
+reversible step followed by a
+
+slow step, that means that not
+much of your intermediate is
+
+being siphoned off by the second
+step, allowing you to
+
+reach equilibrium.
+
+So you can think about that in
+terms of this plot here.
+
+If you have reactants going to
+intermediate, and this is fast
+
+and reversible, so they're going
+back and forth, fast,
+
+reversible, and very little of
+that intermediate is getting
+
+siphoned off, this
+is very slow.
+
+So very, very little
+of this is being
+
+siphoned off to products.
+
+So that allows that first step
+to really reach equilibrium
+
+conditions, because this doesn't
+really factor in, and
+
+so you reach an equilibrium
+here.
+
+And that allows you to simplify
+your expressions.
+
+So now, we can go back with our
+simplified expression, and
+
+we can express it as rate
+constant k 1 over rate
+
+constant k minus 1 times n o
+squared, or we can write it as
+
+the equilibrium constant 1 times
+n o squared, and we can
+
+plug that in solving for
+our intermediate.
+
+And so, if we put that now back
+into this expression, we
+
+have the 2 k 1, k 2, we have our
+oxygen concentration and
+
+our n o squared over k minus 1,
+or we can have equilibrium
+
+constant 1 with our
+k 2 in our 2.
+
+And now, we're consistent.
+
+If we realize that the k
+observed that was given in the
+
+experimental rate law is a
+combination of all of our k
+
+terms. So it's a combination,
+you can't, at least in this
+
+experiment, you weren't able to
+come up with the individual
+
+rate constants, they just came
+up with overall observed rate,
+
+and so that's all of
+our terms in there.
+
+And so if we put that in here,
+we realize that this is
+
+consistent with the
+experiment.
+
+And in doing these problems,
+it's OK to leave your little
+
+rate constants, it's OK to use
+equilibrium constants in
+
+there, you should show all of
+your work, so that if you have
+
+a k obs in your final answer, we
+can look back and see what
+
+that was equal to.
+
+So it's hard not to show all
+your work as you're writing
+
+through all of these on a test,
+but you can end your
+
+answer, it would be correct
+end your answer
+
+here or here or here.
+
+So I don't care which k is
+in your final answer, but
+
+definitely show all your work.
+
+So that agrees with
+the experiment.
+
+All right, so let's look
+at another example now.
+
+And now we have, again, a 2-step
+reaction, and the first
+
+step is fast and reversible, and
+the second step is slow.
+
+So, with those predictions of
+the mechanism, let's just go
+
+right through and try to solve
+for the rate here without
+
+going through all of the steps
+we did the first time and see
+
+if we can do this more
+efficiently.
+
+And again, this is a reaction
+with ozone, and depletion of
+
+ozone is a major problem that
+will be facing us, that has
+
+faced us, and will continue
+to face us in the future.
+
+All right.
+
+So lets first think about the
+rates of the individual steps.
+
+So the rate of the forward
+reaction here
+
+is going to be what?
+
+Just yell it out.
+
+Yup, k 1 times the concentration
+of o 3.
+
+What about for the
+reverse step?
+
+Yup, it's like clear and then
+it gets mumbly. k minus 1
+
+times the concentration of o 2
+times this concentration of o,
+
+which is an intermediate.
+
+All right, so let's look at
+the second step here.
+
+So the rate here is going to be
+k 2 times this intermediate
+
+-- concentration of this
+intermediate, o times the
+
+concentration of o 3.
+
+All right, so now we know that
+this second step is going to
+
+be controlling the rate, it's
+a slow step, at least that's
+
+our prediction that we're
+going to write a rate
+
+expression based on.
+
+And so, that's going to be
+our slow step, our rate
+
+determining step.
+
+And again, we're forming two
+molecules of o 2 in this step.
+
+So we can have a two in there.
+
+And that the rate of formation
+of o 2 in this last step, 2
+
+times k 2 times our intermediate
+o times o 3.
+
+Are we done?
+
+Was it that easy?
+
+Are we done?
+
+No.
+
+Why isn't this finished?
+
+There's an intermediate.
+
+Intermediates will not be your
+friend in doing these
+
+problems.
+
+Yes, we have an intermediate
+so we're not complete.
+
+We need to solve for o in terms
+of products, reactants,
+
+and rate constants.
+
+So we're not done.
+
+So we need to get rid
+of the intermediate.
+
+But now, we can do that more
+simply because we've set this
+
+up that we have a fast
+reversible step
+
+followed by a slow step.
+
+So we can solve for the
+concentration of that
+
+intermediate in terms of
+equilibrium expressions.
+
+So, if you haven't learned how
+to write an equilibrium
+
+expression yet, remember you
+need it for the unit on
+
+chemical equilibrium, the unit
+of acid base, the unit of
+
+oxidation reduction, and here
+you need it again in kinetics,
+
+so definitely want to be able to
+write those for the final.
+
+So we can go ahead
+and write those.
+
+So, for the first step, again,
+it's products over reactants.
+
+You can also express that in
+terms of rate constant k 1
+
+over rate constant k minus 1,
+and that's all equal to our
+
+big k, our equilibrium
+constant, k 1.
+
+And so now we can solve in terms
+of o, our intermediate,
+
+and so here, we pull that out,
+here we've solved for it in
+
+terms of k 1 times o 3 over k
+minus 1 times o 2, so we just
+
+brought those to
+the other side.
+
+You could have also used the
+equilibrium constant here
+
+instead of the rate constants,
+either one is OK.
+
+So, now we've solved for it
+here, and we can put it down
+
+into this expression here.
+
+So we are going back
+to our overall
+
+expression that we wrote.
+
+So the expression that we wrote
+based on this was 2, k 2
+
+times the concentration of our
+intermediate, times the
+
+concentration of o 3.
+
+Now we substitute in for the
+intermediate, so we have 2
+
+times k 2, k 1, we have o 3 and
+an o 3, so that squared,
+
+over k minus 1 times o 2.
+
+And this can also be expressed
+in terms of k observed,
+
+putting those terms together,
+o 3 squared over o 2.
+
+And that would be the answer to
+what the rate is for that
+
+particular proposed mechanism.
+
+So, let's think about if that's
+true, what we should
+
+expect if we do some
+experiments, what we should
+
+expect about the order of the
+reactions, and what would
+
+happen if you double
+concentrations of things and
+
+look for the effect.
+
+So if you're going to
+test this proposal,
+
+what would we get?
+
+So, what is the overall order
+of this rate law here.
+
+Oh, sorry, the order first
+let's do of o 3.
+
+2.
+
+So if we double the
+concentration of o 3, what
+
+would you expect to see
+in terms of the rate?
+
+It will what?
+
+Yup, quadruple.
+
+What is the overall order of o
+2, or order of o 2, and that
+
+is a clicker question,
+actually.
+
+So you know what some
+people think.
+
+And not only tell me the order,
+but tell me the effect
+
+of doubling.
+
+OK, let's just take
+10 more seconds.
+
+Very good.
+
+All right, so the overall minus
+1, that's what it means
+
+if it's on the bottom of
+that equation there.
+
+And so if we double it
+then it should half.
+
+So overall then, what is the
+order of the reaction?
+
+It's 1.
+
+And so, remember you can sum up
+the order of the individual
+
+ones to get the overall order,
+so the overall order is 1.
+
+And what about if you double
+both things, what's going to
+
+happen to the rate?
+
+OK, let's just take
+10 more seconds.
+
+OK, people are doing
+quite well on this.
+
+All right, so you double
+both and you double.
+
+So, everyone's in very good
+shape on these types of
+
+problems, which is excellent
+because this is worth
+
+a lot on the final.
+
+All right, so let's do a final
+example, and in this case
+
+we're given an experimental rate
+law, which is up here, k
+
+observed times the concentration
+of n o and the
+
+concentration of b r 2, and we
+want to figure out from this,
+
+we'll look at if we have one
+step is being fast and the
+
+other step is being fast, and
+see which would be consistent
+
+with this experimentally
+determined rate law.
+
+So these are some of the types
+of problems you have, your
+
+given experimental rate law and
+say tell me which step has
+
+to be fast and which has to be
+slow to have a rate that's
+
+consistent with the
+observed rate.
+
+So, in this reaction we
+have 2 n o plus b r 2
+
+going 2 n o b r.
+
+So if we write this in the first
+step, we have n o plus b
+
+r 2 going to an intermediate,
+n o b r 2 with forward rate
+
+constant, k 1, and reverse
+rate constant, k minus 1.
+
+And in the second step we have
+the intermediate interacting
+
+with another molecule of n o
+forming two molecules of n o b
+
+r, our product.
+
+So let's consider what the rate
+of the forward reaction
+
+is here, and so that would be
+-- you can yell it out. k 1
+
+times -- yes, excellent.
+
+And for the reverse reaction
+then we're going to have our k
+
+minus 1 times our intermediate
+concentration.
+
+Now we can look at step 2 where
+our intermediate is
+
+being consumed, and the rate
+would equal then k 2 times the
+
+concentration of the
+intermediate, n o b r 2 times
+
+the concentration of n o.
+
+All right, so we know nothing
+now about fast or slow steps,
+
+so we can write the formation
+of our product just in terms
+
+of this second step.
+
+And again, there are two
+molecules being formed, so we
+
+have a 2, and 2 times this rate
+for this second step, k 2
+
+times intermediate times n o.
+
+So again, now we have an
+intermediate that we have to
+
+get rid of.
+
+We can't have an intermediate
+in our final expression.
+
+But we can't use the equilibrium
+constant right now
+
+because we don't know anything
+about what are the fast or the
+
+slow steps.
+
+So we're going to write it the
+long way with no assumption
+
+about fast or slow steps.
+
+So to do this, so we have our
+intermediate, and so we're
+
+going to solve for it in terms
+of products and reactants.
+
+So we're going to write about
+the change in the
+
+concentration of that
+intermediate.
+
+So, the intermediate's being
+formed in the first step.
+
+So we first write the rate at
+which it's being formed.
+
+So it's being formed here, so
+that's k 1 times n o times the
+
+concentration of b r 2, so this
+is how it's being formed.
+
+And then we're going to consider
+how it's being
+
+decomposed, and you told me
+before it gets decomposed in
+
+the reverse of the first step.
+
+So we have a minus sign, because
+this is a negative
+
+change in concentration, it's
+being decomposed, and it's
+
+being decomposed with a rate
+constant of k minus 1 times
+
+the concentration of
+that intermediate.
+
+And the intermediate's also
+being consumed, so that's
+
+decreasing the concentration of
+the intermediate, and it's
+
+being consumed in this
+second step.
+
+So it's being consumed here with
+the rate constant of k 2
+
+times the intermediate
+times n o.
+
+So that second step.
+
+So this is how we write it if
+we don't know anything about
+
+the rate at which -- what's slow
+and what's fast. So this
+
+will always, always work to
+write things this way.
+
+So that's the overall change
+in the concentration of the
+
+intermediate, how it's
+being formed,
+
+decomposed, and consumed.
+
+Now we can use the steady state
+approximation, and you
+
+can always use the steady state
+approximation in these
+
+problems, and that says that
+this net change is going to be
+
+equal to zero.
+
+So the steady state
+approximation, then, let's you
+
+set this entire term
+equal to zero.
+
+And sometimes, a question you
+might get is to say what the
+
+steady state approximation is.
+
+So you should be able to
+articulate that in words as
+
+well as use it on a problem.
+
+So now we can set this all
+equal to zero, and we can
+
+solve for our concentration
+of our intermediate.
+
+So, rearranging this then,
+bringing our intermediate
+
+terms on one side of the
+expression, and again, here's
+
+the rate at which it's
+decomposed and consumed being
+
+equal to the rate at which
+it's being formed.
+
+And we can pull out our
+intermediate, so then that's
+
+times k minus 1, k 2 times n
+o, and that's equal to the
+
+rate at which it's
+being formed.
+
+And so now we can take that,
+divide by that term, and we
+
+get an expression for the
+concentration of the
+
+intermediate in terms
+of our reactants
+
+and our rate constants.
+
+So now we need to plug that
+back in to the original
+
+equation that we had.
+
+So this is what we solved for,
+and now we can put it into
+
+here, and if you rearrange that,
+we have the 2, we have
+
+the k 1, we have the k 2, we
+have an n o here, we have an n
+
+o there, so it's squared, b r 2
+here, and then on the bottom
+
+we have k minus 1 plus
+k 2 times n o.
+
+OK, so that's great, but that's
+not consistent with the
+
+experimentally determined rate
+law, so something has to be
+
+fast and something
+has to be slow.
+
+So let's first consider if the
+first step is slow and the
+
+second step is fast, which would
+mean that the second
+
+step is bigger, it's faster,
+that's k 2 times n o would be
+
+bigger than k minus 1.
+
+So the second step then is
+fast, faster than this.
+
+So now why don't you go ahead
+and tell me how this
+
+simplifies if that is true.
+
+All right, let's just take
+10 more seconds.
+
+Yup.
+
+All right, let's look at why.
+
+All right, so that's the answer
+and let's consider why.
+
+So that means if this is much
+bigger than this term, that
+
+cancels out.
+
+If that cancels out, what else
+cancels? k 2 also cancels, and
+
+what else cancels? one n o
+cancels giving you this
+
+expression.
+
+And that is consistent with
+the answer up there.
+
+So you could also see that
+as the k observed.
+
+So that's consistent.
+
+And let's just quick
+-- oh, first tell
+
+me the overall order.
+
+2.
+
+And now let's just look at what
+would have been true if
+
+we had done it the
+other way around.
+
+So if we did it the other way
+around, we'd say that the
+
+first step is fast so that's
+a lot bigger than this.
+
+If this is a lot bigger than
+that, we'd cancel out this
+
+second term here.
+
+Can anything else cancel?
+
+No.
+
+So, we're left with this
+expression, and that is not
+
+consistent with this up
+here, because we have
+
+this squared term.
+
+So even if you write it as
+k observed, that's not
+
+consistent.
+
+And so, the overall order for
+this would have been 3, which
+
+is not consistent with
+the experiment.
+
+All right, so now you know
+everything you need to know to
+
+finish problem-set 10.
+
+Don't let anything be your
+rate determining step.
\ No newline at end of file
diff --git a/x-ijexq_D2U.txt b/x-ijexq_D2U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9fba17833a15808eba4cde7f437c90b3a036b5c4
--- /dev/null
+++ b/x-ijexq_D2U.txt
@@ -0,0 +1,22515 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
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+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
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+offer high quality educational resources
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+for free
+to make a donation or to view additional
+
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+to make a donation or to view additional
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+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
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+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah today's talk is on computational
+
+ align:start position:0%
+so yeah today's talk is on computational
+ 
+
+ align:start position:0%
+so yeah today's talk is on computational
+imaging which as you'll see
+
+ align:start position:0%
+imaging which as you'll see
+ 
+
+ align:start position:0%
+imaging which as you'll see
+there's a lot of inspiration you can
+
+ align:start position:0%
+there's a lot of inspiration you can
+ 
+
+ align:start position:0%
+there's a lot of inspiration you can
+take from this work and i just like to
+
+ align:start position:0%
+take from this work and i just like to
+ 
+
+ align:start position:0%
+take from this work and i just like to
+mention a lot of these slides came from
+
+ align:start position:0%
+mention a lot of these slides came from
+ 
+
+ align:start position:0%
+mention a lot of these slides came from
+our which is graph course so if you want
+
+ align:start position:0%
+our which is graph course so if you want
+ 
+
+ align:start position:0%
+our which is graph course so if you want
+any more detail go to his website and
+
+ align:start position:0%
+any more detail go to his website and
+ 
+
+ align:start position:0%
+any more detail go to his website and
+you can actually see the original uh
+
+ align:start position:0%
+you can actually see the original uh
+ 
+
+ align:start position:0%
+you can actually see the original uh
+course material for this
+
+ align:start position:0%
+course material for this
+ 
+
+ align:start position:0%
+course material for this
+so the basic idea is that
+
+ align:start position:0%
+so the basic idea is that
+ 
+
+ align:start position:0%
+so the basic idea is that
+science is really driven by our
+
+ align:start position:0%
+science is really driven by our
+ 
+
+ align:start position:0%
+science is really driven by our
+technology this is not surprising anyone
+
+ align:start position:0%
+technology this is not surprising anyone
+ 
+
+ align:start position:0%
+technology this is not surprising anyone
+in the room you know the classic example
+
+ align:start position:0%
+in the room you know the classic example
+ 
+
+ align:start position:0%
+in the room you know the classic example
+marco boyd put here is that you know if
+
+ align:start position:0%
+marco boyd put here is that you know if
+ 
+
+ align:start position:0%
+marco boyd put here is that you know if
+you have low end hoof plus microscope
+
+ align:start position:0%
+you have low end hoof plus microscope
+ 
+
+ align:start position:0%
+you have low end hoof plus microscope
+equals microbiology and so really in
+
+ align:start position:0%
+equals microbiology and so really in
+ 
+
+ align:start position:0%
+equals microbiology and so really in
+some sense in the sciences you're
+
+ align:start position:0%
+some sense in the sciences you're
+ 
+
+ align:start position:0%
+some sense in the sciences you're
+waiting around for new technology to
+
+ align:start position:0%
+waiting around for new technology to
+ 
+
+ align:start position:0%
+waiting around for new technology to
+make new discoveries right we're waiting
+
+ align:start position:0%
+make new discoveries right we're waiting
+ 
+
+ align:start position:0%
+make new discoveries right we're waiting
+to put satellites up we're waiting for
+
+ align:start position:0%
+to put satellites up we're waiting for
+ 
+
+ align:start position:0%
+to put satellites up we're waiting for
+birds to stop ruining the large hadron
+
+ align:start position:0%
+birds to stop ruining the large hadron
+ 
+
+ align:start position:0%
+birds to stop ruining the large hadron
+collider right technology is what we're
+
+ align:start position:0%
+collider right technology is what we're
+ 
+
+ align:start position:0%
+collider right technology is what we're
+waiting for
+
+ align:start position:0%
+waiting for
+ 
+
+ align:start position:0%
+waiting for
+and so the question mark avoid ask is
+
+ align:start position:0%
+and so the question mark avoid ask is
+ 
+
+ align:start position:0%
+and so the question mark avoid ask is
+what's the most important instrument in
+
+ align:start position:0%
+what's the most important instrument in
+ 
+
+ align:start position:0%
+what's the most important instrument in
+the last century you know arguably in
+
+ align:start position:0%
+the last century you know arguably in
+ 
+
+ align:start position:0%
+the last century you know arguably in
+terms of science you know what would
+
+ align:start position:0%
+terms of science you know what would
+ 
+
+ align:start position:0%
+terms of science you know what would
+some people put up you could only choose
+
+ align:start position:0%
+some people put up you could only choose
+ 
+
+ align:start position:0%
+some people put up you could only choose
+one thing to take with you on desert
+
+ align:start position:0%
+one thing to take with you on desert
+ 
+
+ align:start position:0%
+one thing to take with you on desert
+desert island where they do science what
+
+ align:start position:0%
+desert island where they do science what
+ 
+
+ align:start position:0%
+desert island where they do science what
+would you take
+
+ align:start position:0%
+would you take
+ 
+
+ align:start position:0%
+would you take
+microwave computers
+
+ align:start position:0%
+microwave computers
+ 
+
+ align:start position:0%
+microwave computers
+exactly you know this is this is not
+
+ align:start position:0%
+exactly you know this is this is not
+ 
+
+ align:start position:0%
+exactly you know this is this is not
+news to anyone that the computer is
+
+ align:start position:0%
+news to anyone that the computer is
+ 
+
+ align:start position:0%
+news to anyone that the computer is
+really arguably the greatest
+
+ align:start position:0%
+really arguably the greatest
+ 
+
+ align:start position:0%
+really arguably the greatest
+scientific device and so what can we
+
+ align:start position:0%
+scientific device and so what can we
+ 
+
+ align:start position:0%
+scientific device and so what can we
+really do with this so you know they
+
+ align:start position:0%
+really do with this so you know they
+ 
+
+ align:start position:0%
+really do with this so you know they
+asked
+
+ align:start position:0%
+asked
+ 
+
+ align:start position:0%
+asked
+just people
+
+ align:start position:0%
+just people
+ 
+
+ align:start position:0%
+just people
+in the general population
+
+ align:start position:0%
+in the general population
+ 
+
+ align:start position:0%
+in the general population
+which of them which is the most
+
+ align:start position:0%
+which of them which is the most
+ 
+
+ align:start position:0%
+which of them which is the most
+important technology that has changed
+
+ align:start position:0%
+important technology that has changed
+ 
+
+ align:start position:0%
+important technology that has changed
+their life
+
+ align:start position:0%
+their life
+ 
+
+ align:start position:0%
+their life
+and they said remote control
+
+ align:start position:0%
+and they said remote control
+ 
+
+ align:start position:0%
+and they said remote control
+and a microwave microwave or remote
+
+ align:start position:0%
+and a microwave microwave or remote
+ 
+
+ align:start position:0%
+and a microwave microwave or remote
+control microwave is the greatest
+
+ align:start position:0%
+control microwave is the greatest
+ 
+
+ align:start position:0%
+control microwave is the greatest
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+so professor horn has said and this is
+
+ align:start position:0%
+so professor horn has said and this is
+ 
+
+ align:start position:0%
+so professor horn has said and this is
+of course very similar to the ideas of
+
+ align:start position:0%
+of course very similar to the ideas of
+ 
+
+ align:start position:0%
+of course very similar to the ideas of
+this class that computational imaging is
+
+ align:start position:0%
+this class that computational imaging is
+ 
+
+ align:start position:0%
+this class that computational imaging is
+simply imaging methods in which
+
+ align:start position:0%
+simply imaging methods in which
+ 
+
+ align:start position:0%
+simply imaging methods in which
+computation is inherent in image
+
+ align:start position:0%
+computation is inherent in image
+ 
+
+ align:start position:0%
+computation is inherent in image
+formation and so when we look at medical
+
+ align:start position:0%
+formation and so when we look at medical
+ 
+
+ align:start position:0%
+formation and so when we look at medical
+imaging and scientific imaging really
+
+ align:start position:0%
+imaging and scientific imaging really
+ 
+
+ align:start position:0%
+imaging and scientific imaging really
+this is the key story in the 20th
+
+ align:start position:0%
+this is the key story in the 20th
+ 
+
+ align:start position:0%
+this is the key story in the 20th
+century and so in some of this talk i'll
+
+ align:start position:0%
+century and so in some of this talk i'll
+ 
+
+ align:start position:0%
+century and so in some of this talk i'll
+show you what the modern way is to take
+
+ align:start position:0%
+show you what the modern way is to take
+ 
+
+ align:start position:0%
+show you what the modern way is to take
+some sort of image say using computer
+
+ align:start position:0%
+some sort of image say using computer
+ 
+
+ align:start position:0%
+some sort of image say using computer
+tomography and i'll show you how they
+
+ align:start position:0%
+tomography and i'll show you how they
+ 
+
+ align:start position:0%
+tomography and i'll show you how they
+did that 100 years ago before they had
+
+ align:start position:0%
+did that 100 years ago before they had
+ 
+
+ align:start position:0%
+did that 100 years ago before they had
+computing power how they did that using
+
+ align:start position:0%
+computing power how they did that using
+ 
+
+ align:start position:0%
+computing power how they did that using
+mechanical computing and so i think
+
+ align:start position:0%
+mechanical computing and so i think
+ 
+
+ align:start position:0%
+mechanical computing and so i think
+that's an interesting process to see how
+
+ align:start position:0%
+that's an interesting process to see how
+ 
+
+ align:start position:0%
+that's an interesting process to see how
+computation is really revolutionized how
+
+ align:start position:0%
+computation is really revolutionized how
+ 
+
+ align:start position:0%
+computation is really revolutionized how
+we take pictures in medicine and science
+
+ align:start position:0%
+we take pictures in medicine and science
+ 
+
+ align:start position:0%
+we take pictures in medicine and science
+and so then if we look out well beyond
+
+ align:start position:0%
+and so then if we look out well beyond
+ 
+
+ align:start position:0%
+and so then if we look out well beyond
+sort of the box we're in which is optics
+
+ align:start position:0%
+sort of the box we're in which is optics
+ 
+
+ align:start position:0%
+sort of the box we're in which is optics
+you know most of what we talk about
+
+ align:start position:0%
+you know most of what we talk about
+ 
+
+ align:start position:0%
+you know most of what we talk about
+coaching photography is this sort of
+
+ align:start position:0%
+coaching photography is this sort of
+ 
+
+ align:start position:0%
+coaching photography is this sort of
+wavefront coding like field photography
+
+ align:start position:0%
+wavefront coding like field photography
+ 
+
+ align:start position:0%
+wavefront coding like field photography
+holography things you've looked at in
+
+ align:start position:0%
+holography things you've looked at in
+ 
+
+ align:start position:0%
+holography things you've looked at in
+your homework if you open the box up a
+
+ align:start position:0%
+your homework if you open the box up a
+ 
+
+ align:start position:0%
+your homework if you open the box up a
+little bit these same ideas really come
+
+ align:start position:0%
+little bit these same ideas really come
+ 
+
+ align:start position:0%
+little bit these same ideas really come
+from a much more broader field and so
+
+ align:start position:0%
+from a much more broader field and so
+ 
+
+ align:start position:0%
+from a much more broader field and so
+the first part i'll talk about is
+
+ align:start position:0%
+the first part i'll talk about is
+ 
+
+ align:start position:0%
+the first part i'll talk about is
+medical imaging i think the key story in
+
+ align:start position:0%
+medical imaging i think the key story in
+ 
+
+ align:start position:0%
+medical imaging i think the key story in
+medical imaging is tomography really
+
+ align:start position:0%
+medical imaging is tomography really
+ 
+
+ align:start position:0%
+medical imaging is tomography really
+that's the central problem how do you
+
+ align:start position:0%
+that's the central problem how do you
+ 
+
+ align:start position:0%
+that's the central problem how do you
+take a cross-sectional image of an
+
+ align:start position:0%
+take a cross-sectional image of an
+ 
+
+ align:start position:0%
+take a cross-sectional image of an
+object non-invasively and you can do
+
+ align:start position:0%
+object non-invasively and you can do
+ 
+
+ align:start position:0%
+object non-invasively and you can do
+that in two ways you can use
+
+ align:start position:0%
+that in two ways you can use
+ 
+
+ align:start position:0%
+that in two ways you can use
+transmission or reflection tomography
+
+ align:start position:0%
+transmission or reflection tomography
+ 
+
+ align:start position:0%
+transmission or reflection tomography
+we'll talk about both and then that
+
+ align:start position:0%
+we'll talk about both and then that
+ 
+
+ align:start position:0%
+we'll talk about both and then that
+story is sort of repeated throughout the
+
+ align:start position:0%
+story is sort of repeated throughout the
+ 
+
+ align:start position:0%
+story is sort of repeated throughout the
+sciences once they understood tomography
+
+ align:start position:0%
+sciences once they understood tomography
+ 
+
+ align:start position:0%
+sciences once they understood tomography
+they said okay we can solve all these
+
+ align:start position:0%
+they said okay we can solve all these
+ 
+
+ align:start position:0%
+they said okay we can solve all these
+problems we can look at geophysics the
+
+ align:start position:0%
+problems we can look at geophysics the
+ 
+
+ align:start position:0%
+problems we can look at geophysics the
+exact same methodologies can be applied
+
+ align:start position:0%
+exact same methodologies can be applied
+ 
+
+ align:start position:0%
+exact same methodologies can be applied
+there which is really what's happening
+
+ align:start position:0%
+there which is really what's happening
+ 
+
+ align:start position:0%
+there which is really what's happening
+in optics now we've you know sort of in
+
+ align:start position:0%
+in optics now we've you know sort of in
+ 
+
+ align:start position:0%
+in optics now we've you know sort of in
+the late 90s they found this link
+
+ align:start position:0%
+the late 90s they found this link
+ 
+
+ align:start position:0%
+the late 90s they found this link
+between tomography and optics and then
+
+ align:start position:0%
+between tomography and optics and then
+ 
+
+ align:start position:0%
+between tomography and optics and then
+all of a sudden you had life build
+
+ align:start position:0%
+all of a sudden you had life build
+ 
+
+ align:start position:0%
+all of a sudden you had life build
+photography geophysics did that about in
+
+ align:start position:0%
+photography geophysics did that about in
+ 
+
+ align:start position:0%
+photography geophysics did that about in
+the 80s they discovered that link and
+
+ align:start position:0%
+the 80s they discovered that link and
+ 
+
+ align:start position:0%
+the 80s they discovered that link and
+they invented all of these methods
+
+ align:start position:0%
+they invented all of these methods
+ 
+
+ align:start position:0%
+they invented all of these methods
+for for unobtrusive measurement
+
+ align:start position:0%
+for for unobtrusive measurement
+ 
+
+ align:start position:0%
+for for unobtrusive measurement
+underground and then in applied physics
+
+ align:start position:0%
+underground and then in applied physics
+ 
+
+ align:start position:0%
+underground and then in applied physics
+we'll sort of talk about when the
+
+ align:start position:0%
+we'll sort of talk about when the
+ 
+
+ align:start position:0%
+we'll sort of talk about when the
+problems become much more difficult
+
+ align:start position:0%
+problems become much more difficult
+ 
+
+ align:start position:0%
+problems become much more difficult
+for light flow photography we look at
+
+ align:start position:0%
+for light flow photography we look at
+ 
+
+ align:start position:0%
+for light flow photography we look at
+ray optics once we start considering uh
+
+ align:start position:0%
+ray optics once we start considering uh
+ 
+
+ align:start position:0%
+ray optics once we start considering uh
+coherent optics or scattering tomography
+
+ align:start position:0%
+coherent optics or scattering tomography
+ 
+
+ align:start position:0%
+coherent optics or scattering tomography
+that's when the problems really get
+
+ align:start position:0%
+that's when the problems really get
+ 
+
+ align:start position:0%
+that's when the problems really get
+interesting i think for those of you
+
+ align:start position:0%
+interesting i think for those of you
+ 
+
+ align:start position:0%
+interesting i think for those of you
+working on final projects really looking
+
+ align:start position:0%
+working on final projects really looking
+ 
+
+ align:start position:0%
+working on final projects really looking
+at scattering tomography and it's linked
+
+ align:start position:0%
+at scattering tomography and it's linked
+ 
+
+ align:start position:0%
+at scattering tomography and it's linked
+to life of photography is where there's
+
+ align:start position:0%
+to life of photography is where there's
+ 
+
+ align:start position:0%
+to life of photography is where there's
+some exciting ideas and hopefully some
+
+ align:start position:0%
+some exciting ideas and hopefully some
+ 
+
+ align:start position:0%
+some exciting ideas and hopefully some
+of you are already thinking about that
+
+ align:start position:0%
+of you are already thinking about that
+ 
+
+ align:start position:0%
+of you are already thinking about that
+for your projects and then we'll we'll
+
+ align:start position:0%
+for your projects and then we'll we'll
+ 
+
+ align:start position:0%
+for your projects and then we'll we'll
+sort of jump away from tomography again
+
+ align:start position:0%
+sort of jump away from tomography again
+ 
+
+ align:start position:0%
+sort of jump away from tomography again
+i'm going to talk about all these things
+
+ align:start position:0%
+i'm going to talk about all these things
+ 
+
+ align:start position:0%
+i'm going to talk about all these things
+but then we'll move to something else
+
+ align:start position:0%
+but then we'll move to something else
+ 
+
+ align:start position:0%
+but then we'll move to something else
+which is really in biology the story
+
+ align:start position:0%
+which is really in biology the story
+ 
+
+ align:start position:0%
+which is really in biology the story
+isn't tomography
+
+ align:start position:0%
+isn't tomography
+ 
+
+ align:start position:0%
+isn't tomography
+necessarily it's again how he took a
+
+ align:start position:0%
+necessarily it's again how he took a
+ 
+
+ align:start position:0%
+necessarily it's again how he took a
+cross-sectional picture but the tricks
+
+ align:start position:0%
+cross-sectional picture but the tricks
+ 
+
+ align:start position:0%
+cross-sectional picture but the tricks
+are very different so we'll talk about
+
+ align:start position:0%
+are very different so we'll talk about
+ 
+
+ align:start position:0%
+are very different so we'll talk about
+confocal microscopy deconvolution uh
+
+ align:start position:0%
+confocal microscopy deconvolution uh
+ 
+
+ align:start position:0%
+confocal microscopy deconvolution uh
+debluring which some of you have
+
+ align:start position:0%
+debluring which some of you have
+ 
+
+ align:start position:0%
+debluring which some of you have
+probably seen already and if the final
+
+ align:start position:0%
+probably seen already and if the final
+ 
+
+ align:start position:0%
+probably seen already and if the final
+area i'll end up on is astronomy which
+
+ align:start position:0%
+area i'll end up on is astronomy which
+ 
+
+ align:start position:0%
+area i'll end up on is astronomy which
+is really where most of my work comes
+
+ align:start position:0%
+is really where most of my work comes
+ 
+
+ align:start position:0%
+is really where most of my work comes
+from is the idea many of these ideas
+
+ align:start position:0%
+from is the idea many of these ideas
+ 
+
+ align:start position:0%
+from is the idea many of these ideas
+especially in biological sciences
+
+ align:start position:0%
+especially in biological sciences
+ 
+
+ align:start position:0%
+especially in biological sciences
+involve refractive optics and then we'll
+
+ align:start position:0%
+involve refractive optics and then we'll
+ 
+
+ align:start position:0%
+involve refractive optics and then we'll
+look at how you can image without
+
+ align:start position:0%
+look at how you can image without
+ 
+
+ align:start position:0%
+look at how you can image without
+refraction and so again for x-rays gamma
+
+ align:start position:0%
+refraction and so again for x-rays gamma
+ 
+
+ align:start position:0%
+refraction and so again for x-rays gamma
+rays you can't build refractive optics
+
+ align:start position:0%
+rays you can't build refractive optics
+ 
+
+ align:start position:0%
+rays you can't build refractive optics
+and so then you get into the ideas of
+
+ align:start position:0%
+and so then you get into the ideas of
+ 
+
+ align:start position:0%
+and so then you get into the ideas of
+coded aperture imaging and
+
+ align:start position:0%
+coded aperture imaging and
+ 
+
+ align:start position:0%
+coded aperture imaging and
+interferometric imaging and then the
+
+ align:start position:0%
+interferometric imaging and then the
+ 
+
+ align:start position:0%
+interferometric imaging and then the
+rest of this is stuff you've already
+
+ align:start position:0%
+rest of this is stuff you've already
+ 
+
+ align:start position:0%
+rest of this is stuff you've already
+seen how do you build panoramas how do
+
+ align:start position:0%
+seen how do you build panoramas how do
+ 
+
+ align:start position:0%
+seen how do you build panoramas how do
+you take light field photographs
+
+ align:start position:0%
+you take light field photographs
+ 
+
+ align:start position:0%
+you take light field photographs
+and so really let's start which i think
+
+ align:start position:0%
+and so really let's start which i think
+ 
+
+ align:start position:0%
+and so really let's start which i think
+this is a great example of medical
+
+ align:start position:0%
+this is a great example of medical
+ 
+
+ align:start position:0%
+this is a great example of medical
+imaging and the idea of tomography and
+
+ align:start position:0%
+imaging and the idea of tomography and
+ 
+
+ align:start position:0%
+imaging and the idea of tomography and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the problem statement is very simple you
+
+ align:start position:0%
+the problem statement is very simple you
+ 
+
+ align:start position:0%
+the problem statement is very simple you
+want to non-invasively image inside of
+
+ align:start position:0%
+want to non-invasively image inside of
+ 
+
+ align:start position:0%
+want to non-invasively image inside of
+of of a living object and so of course
+
+ align:start position:0%
+of of a living object and so of course
+ 
+
+ align:start position:0%
+of of a living object and so of course
+any of you have been to the the ct
+
+ align:start position:0%
+any of you have been to the the ct
+ 
+
+ align:start position:0%
+any of you have been to the the ct
+scanner at the hospital you might have
+
+ align:start position:0%
+scanner at the hospital you might have
+ 
+
+ align:start position:0%
+scanner at the hospital you might have
+had them produce images like this so the
+
+ align:start position:0%
+had them produce images like this so the
+ 
+
+ align:start position:0%
+had them produce images like this so the
+question is how can you do this without
+
+ align:start position:0%
+question is how can you do this without
+ 
+
+ align:start position:0%
+question is how can you do this without
+simply slicing open a person and taking
+
+ align:start position:0%
+simply slicing open a person and taking
+ 
+
+ align:start position:0%
+simply slicing open a person and taking
+a photograph
+
+ align:start position:0%
+a photograph
+ 
+
+ align:start position:0%
+a photograph
+and so in general this involves
+
+ align:start position:0%
+and so in general this involves
+ 
+
+ align:start position:0%
+and so in general this involves
+basically taking the last hundred years
+
+ align:start position:0%
+basically taking the last hundred years
+ 
+
+ align:start position:0%
+basically taking the last hundred years
+of mathematics and solving an inverse
+
+ align:start position:0%
+of mathematics and solving an inverse
+ 
+
+ align:start position:0%
+of mathematics and solving an inverse
+problem we'll talk about what that
+
+ align:start position:0%
+problem we'll talk about what that
+ 
+
+ align:start position:0%
+problem we'll talk about what that
+inverse problem is then there's other
+
+ align:start position:0%
+inverse problem is then there's other
+ 
+
+ align:start position:0%
+inverse problem is then there's other
+ways instead of inverting a system you
+
+ align:start position:0%
+ways instead of inverting a system you
+ 
+
+ align:start position:0%
+ways instead of inverting a system you
+can of course use endoscopes thermal
+
+ align:start position:0%
+can of course use endoscopes thermal
+ 
+
+ align:start position:0%
+can of course use endoscopes thermal
+imaging microscopy to just simply
+
+ align:start position:0%
+imaging microscopy to just simply
+ 
+
+ align:start position:0%
+imaging microscopy to just simply
+directly measure inside the body
+
+ align:start position:0%
+directly measure inside the body
+ 
+
+ align:start position:0%
+directly measure inside the body
+and i think the key thing here is to
+
+ align:start position:0%
+and i think the key thing here is to
+ 
+
+ align:start position:0%
+and i think the key thing here is to
+notice that the mathematics behind
+
+ align:start position:0%
+notice that the mathematics behind
+ 
+
+ align:start position:0%
+notice that the mathematics behind
+tomography all of these devices are
+
+ align:start position:0%
+tomography all of these devices are
+ 
+
+ align:start position:0%
+tomography all of these devices are
+essentially the same ct scanners mri
+
+ align:start position:0%
+essentially the same ct scanners mri
+ 
+
+ align:start position:0%
+essentially the same ct scanners mri
+machines pet scanners ultrasound they
+
+ align:start position:0%
+machines pet scanners ultrasound they
+ 
+
+ align:start position:0%
+machines pet scanners ultrasound they
+all use the same underlying mathematics
+
+ align:start position:0%
+all use the same underlying mathematics
+ 
+
+ align:start position:0%
+all use the same underlying mathematics
+the only difference is the wavelength of
+
+ align:start position:0%
+the only difference is the wavelength of
+ 
+
+ align:start position:0%
+the only difference is the wavelength of
+radiation to zeroth order
+
+ align:start position:0%
+radiation to zeroth order
+ 
+
+ align:start position:0%
+radiation to zeroth order
+and of course the other main areas are
+
+ align:start position:0%
+and of course the other main areas are
+ 
+
+ align:start position:0%
+and of course the other main areas are
+eeg and meg
+
+ align:start position:0%
+eeg and meg
+ 
+
+ align:start position:0%
+eeg and meg
+and so if you think about designing a
+
+ align:start position:0%
+and so if you think about designing a
+ 
+
+ align:start position:0%
+and so if you think about designing a
+non-invasive medical device the first
+
+ align:start position:0%
+non-invasive medical device the first
+ 
+
+ align:start position:0%
+non-invasive medical device the first
+problem you have is ionizing radiation
+
+ align:start position:0%
+problem you have is ionizing radiation
+ 
+
+ align:start position:0%
+problem you have is ionizing radiation
+ct scanners use x-rays whereas mris use
+
+ align:start position:0%
+ct scanners use x-rays whereas mris use
+ 
+
+ align:start position:0%
+ct scanners use x-rays whereas mris use
+radio waves so that's the first major
+
+ align:start position:0%
+radio waves so that's the first major
+ 
+
+ align:start position:0%
+radio waves so that's the first major
+benefit but really the other problems to
+
+ align:start position:0%
+benefit but really the other problems to
+ 
+
+ align:start position:0%
+benefit but really the other problems to
+think about are again minimizing the
+
+ align:start position:0%
+think about are again minimizing the
+ 
+
+ align:start position:0%
+think about are again minimizing the
+invasiveness
+
+ align:start position:0%
+invasiveness
+ 
+
+ align:start position:0%
+invasiveness
+not inserting devices or probes and also
+
+ align:start position:0%
+not inserting devices or probes and also
+ 
+
+ align:start position:0%
+not inserting devices or probes and also
+improving temporal spatial resolution
+
+ align:start position:0%
+improving temporal spatial resolution
+ 
+
+ align:start position:0%
+improving temporal spatial resolution
+and finally making these things very
+
+ align:start position:0%
+and finally making these things very
+ 
+
+ align:start position:0%
+and finally making these things very
+inexpensive for the developing world
+
+ align:start position:0%
+inexpensive for the developing world
+ 
+
+ align:start position:0%
+inexpensive for the developing world
+and so now let's just jump into to what
+
+ align:start position:0%
+and so now let's just jump into to what
+ 
+
+ align:start position:0%
+and so now let's just jump into to what
+tomography is well it's a greek word
+
+ align:start position:0%
+tomography is well it's a greek word
+ 
+
+ align:start position:0%
+tomography is well it's a greek word
+greek origin and it's simply the word
+
+ align:start position:0%
+greek origin and it's simply the word
+ 
+
+ align:start position:0%
+greek origin and it's simply the word
+tomos or a section or cutting plus
+
+ align:start position:0%
+tomos or a section or cutting plus
+ 
+
+ align:start position:0%
+tomos or a section or cutting plus
+photography graphic taking a picture so
+
+ align:start position:0%
+photography graphic taking a picture so
+ 
+
+ align:start position:0%
+photography graphic taking a picture so
+it's a cross-sectional picture of an
+
+ align:start position:0%
+it's a cross-sectional picture of an
+ 
+
+ align:start position:0%
+it's a cross-sectional picture of an
+object so if you have some volumetric
+
+ align:start position:0%
+object so if you have some volumetric
+ 
+
+ align:start position:0%
+object so if you have some volumetric
+function in 3d tomography will take a
+
+ align:start position:0%
+function in 3d tomography will take a
+ 
+
+ align:start position:0%
+function in 3d tomography will take a
+slice of that 3d function and return a
+
+ align:start position:0%
+slice of that 3d function and return a
+ 
+
+ align:start position:0%
+slice of that 3d function and return a
+2d image that's our goal the question is
+
+ align:start position:0%
+2d image that's our goal the question is
+ 
+
+ align:start position:0%
+2d image that's our goal the question is
+how exactly can we do that
+
+ align:start position:0%
+how exactly can we do that
+ 
+
+ align:start position:0%
+how exactly can we do that
+non-invasively and it's a very simple
+
+ align:start position:0%
+non-invasively and it's a very simple
+ 
+
+ align:start position:0%
+non-invasively and it's a very simple
+idea the idea is to this is what i'm
+
+ align:start position:0%
+idea the idea is to this is what i'm
+ 
+
+ align:start position:0%
+idea the idea is to this is what i'm
+describing is known as transmission
+
+ align:start position:0%
+describing is known as transmission
+ 
+
+ align:start position:0%
+describing is known as transmission
+tomography there's also reflection to
+
+ align:start position:0%
+tomography there's also reflection to
+ 
+
+ align:start position:0%
+tomography there's also reflection to
+moderate people we'll get to that later
+
+ align:start position:0%
+moderate people we'll get to that later
+ 
+
+ align:start position:0%
+moderate people we'll get to that later
+so the idea of transmission tomography
+
+ align:start position:0%
+so the idea of transmission tomography
+ 
+
+ align:start position:0%
+so the idea of transmission tomography
+is we have some density function let's
+
+ align:start position:0%
+is we have some density function let's
+ 
+
+ align:start position:0%
+is we have some density function let's
+say our human body and it absorbs
+
+ align:start position:0%
+say our human body and it absorbs
+ 
+
+ align:start position:0%
+say our human body and it absorbs
+electromagnetic radiation and so we're
+
+ align:start position:0%
+electromagnetic radiation and so we're
+ 
+
+ align:start position:0%
+electromagnetic radiation and so we're
+going to put a single point source
+
+ align:start position:0%
+going to put a single point source
+ 
+
+ align:start position:0%
+going to put a single point source
+in the scene say like an x-ray source
+
+ align:start position:0%
+in the scene say like an x-ray source
+ 
+
+ align:start position:0%
+in the scene say like an x-ray source
+have it emit isotropically into the
+
+ align:start position:0%
+have it emit isotropically into the
+ 
+
+ align:start position:0%
+have it emit isotropically into the
+world and put a film plane sensitive to
+
+ align:start position:0%
+world and put a film plane sensitive to
+ 
+
+ align:start position:0%
+world and put a film plane sensitive to
+x-rays on one side of the object and our
+
+ align:start position:0%
+x-rays on one side of the object and our
+ 
+
+ align:start position:0%
+x-rays on one side of the object and our
+hope is that some wavelength of
+
+ align:start position:0%
+hope is that some wavelength of
+ 
+
+ align:start position:0%
+hope is that some wavelength of
+radiation that we can find
+
+ align:start position:0%
+radiation that we can find
+ 
+
+ align:start position:0%
+radiation that we can find
+will transmit ballistically through the
+
+ align:start position:0%
+will transmit ballistically through the
+ 
+
+ align:start position:0%
+will transmit ballistically through the
+object so it'll be little scattering but
+
+ align:start position:0%
+object so it'll be little scattering but
+ 
+
+ align:start position:0%
+object so it'll be little scattering but
+absorption so along a given ray from the
+
+ align:start position:0%
+absorption so along a given ray from the
+ 
+
+ align:start position:0%
+absorption so along a given ray from the
+source to our foam plane
+
+ align:start position:0%
+source to our foam plane
+ 
+
+ align:start position:0%
+source to our foam plane
+the electromagnetic creation the
+
+ align:start position:0%
+the electromagnetic creation the
+ 
+
+ align:start position:0%
+the electromagnetic creation the
+photonics if you will will simply travel
+
+ align:start position:0%
+photonics if you will will simply travel
+ 
+
+ align:start position:0%
+photonics if you will will simply travel
+through the object and the only thing
+
+ align:start position:0%
+through the object and the only thing
+ 
+
+ align:start position:0%
+through the object and the only thing
+that happens is that they're attenuated
+
+ align:start position:0%
+that happens is that they're attenuated
+ 
+
+ align:start position:0%
+that happens is that they're attenuated
+somewhat by the object that's our
+
+ align:start position:0%
+somewhat by the object that's our
+ 
+
+ align:start position:0%
+somewhat by the object that's our
+assumption now of course in the visible
+
+ align:start position:0%
+assumption now of course in the visible
+ 
+
+ align:start position:0%
+assumption now of course in the visible
+wavelength that's not true for human
+
+ align:start position:0%
+wavelength that's not true for human
+ 
+
+ align:start position:0%
+wavelength that's not true for human
+bodies you can't do this and so that's
+
+ align:start position:0%
+bodies you can't do this and so that's
+ 
+
+ align:start position:0%
+bodies you can't do this and so that's
+why they chose x-rays
+
+ align:start position:0%
+why they chose x-rays
+ 
+
+ align:start position:0%
+why they chose x-rays
+because that's easy to generate easy to
+
+ align:start position:0%
+because that's easy to generate easy to
+ 
+
+ align:start position:0%
+because that's easy to generate easy to
+build detectors and for the most part
+
+ align:start position:0%
+build detectors and for the most part
+ 
+
+ align:start position:0%
+build detectors and for the most part
+human bodies
+
+ align:start position:0%
+human bodies
+ 
+
+ align:start position:0%
+human bodies
+satisfy the scattering assumptions and
+
+ align:start position:0%
+satisfy the scattering assumptions and
+ 
+
+ align:start position:0%
+satisfy the scattering assumptions and
+so if you look back at ct scanner
+
+ align:start position:0%
+so if you look back at ct scanner
+ 
+
+ align:start position:0%
+so if you look back at ct scanner
+history if we go back 30 to 40 years
+
+ align:start position:0%
+history if we go back 30 to 40 years
+ 
+
+ align:start position:0%
+history if we go back 30 to 40 years
+really you have two technologies sort of
+
+ align:start position:0%
+really you have two technologies sort of
+ 
+
+ align:start position:0%
+really you have two technologies sort of
+competing against each other but the the
+
+ align:start position:0%
+competing against each other but the the
+ 
+
+ align:start position:0%
+competing against each other but the the
+basic idea is the same we're going to
+
+ align:start position:0%
+basic idea is the same we're going to
+ 
+
+ align:start position:0%
+basic idea is the same we're going to
+have some volumetric function like our
+
+ align:start position:0%
+have some volumetric function like our
+ 
+
+ align:start position:0%
+have some volumetric function like our
+body and we're going to take many
+
+ align:start position:0%
+body and we're going to take many
+ 
+
+ align:start position:0%
+body and we're going to take many
+projections of it right because we're
+
+ align:start position:0%
+projections of it right because we're
+ 
+
+ align:start position:0%
+projections of it right because we're
+trying to estimate a three-dimensional
+
+ align:start position:0%
+trying to estimate a three-dimensional
+ 
+
+ align:start position:0%
+trying to estimate a three-dimensional
+function we need to make a well-posed
+
+ align:start position:0%
+function we need to make a well-posed
+ 
+
+ align:start position:0%
+function we need to make a well-posed
+system to inverse so we need to somehow
+
+ align:start position:0%
+system to inverse so we need to somehow
+ 
+
+ align:start position:0%
+system to inverse so we need to somehow
+sample the variation so a single picture
+
+ align:start position:0%
+sample the variation so a single picture
+ 
+
+ align:start position:0%
+sample the variation so a single picture
+will only take a two-dimensional
+
+ align:start position:0%
+will only take a two-dimensional
+ 
+
+ align:start position:0%
+will only take a two-dimensional
+projection but then if we move the
+
+ align:start position:0%
+projection but then if we move the
+ 
+
+ align:start position:0%
+projection but then if we move the
+source to a new position we'll get a new
+
+ align:start position:0%
+source to a new position we'll get a new
+ 
+
+ align:start position:0%
+source to a new position we'll get a new
+projection if we take a full set of
+
+ align:start position:0%
+projection if we take a full set of
+ 
+
+ align:start position:0%
+projection if we take a full set of
+projections we hope that there's enough
+
+ align:start position:0%
+projections we hope that there's enough
+ 
+
+ align:start position:0%
+projections we hope that there's enough
+data to invert that system and we'll see
+
+ align:start position:0%
+data to invert that system and we'll see
+ 
+
+ align:start position:0%
+data to invert that system and we'll see
+how you do that but really before they
+
+ align:start position:0%
+how you do that but really before they
+ 
+
+ align:start position:0%
+how you do that but really before they
+invented
+
+ align:start position:0%
+invented
+ 
+
+ align:start position:0%
+invented
+the fan simple fan beam tomography there
+
+ align:start position:0%
+the fan simple fan beam tomography there
+ 
+
+ align:start position:0%
+the fan simple fan beam tomography there
+was actually a competing idea that's the
+
+ align:start position:0%
+was actually a competing idea that's the
+ 
+
+ align:start position:0%
+was actually a competing idea that's the
+reason it became popular is the
+
+ align:start position:0%
+reason it became popular is the
+ 
+
+ align:start position:0%
+reason it became popular is the
+mathematical inversion is actually
+
+ align:start position:0%
+mathematical inversion is actually
+ 
+
+ align:start position:0%
+mathematical inversion is actually
+easier and the idea is that
+
+ align:start position:0%
+easier and the idea is that
+ 
+
+ align:start position:0%
+easier and the idea is that
+instead of creating an x-ray point
+
+ align:start position:0%
+instead of creating an x-ray point
+ 
+
+ align:start position:0%
+instead of creating an x-ray point
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+we say have some some cathode 2 that
+
+ align:start position:0%
+we say have some some cathode 2 that
+ 
+
+ align:start position:0%
+we say have some some cathode 2 that
+generates x-rays and then we collimate
+
+ align:start position:0%
+generates x-rays and then we collimate
+ 
+
+ align:start position:0%
+generates x-rays and then we collimate
+them say with a series of lead fans and
+
+ align:start position:0%
+them say with a series of lead fans and
+ 
+
+ align:start position:0%
+them say with a series of lead fans and
+then we get a set of parallel beams so
+
+ align:start position:0%
+then we get a set of parallel beams so
+ 
+
+ align:start position:0%
+then we get a set of parallel beams so
+this is a parallel beam democracy
+
+ align:start position:0%
+this is a parallel beam democracy
+ 
+
+ align:start position:0%
+this is a parallel beam democracy
+problem which is really the easiest one
+
+ align:start position:0%
+problem which is really the easiest one
+ 
+
+ align:start position:0%
+problem which is really the easiest one
+to solve mathematically
+
+ align:start position:0%
+to solve mathematically
+ 
+
+ align:start position:0%
+to solve mathematically
+but now that we have plenty of computing
+
+ align:start position:0%
+but now that we have plenty of computing
+ 
+
+ align:start position:0%
+but now that we have plenty of computing
+power it's very easy to solve this
+
+ align:start position:0%
+power it's very easy to solve this
+ 
+
+ align:start position:0%
+power it's very easy to solve this
+system which is easier to build
+
+ align:start position:0%
+system which is easier to build
+ 
+
+ align:start position:0%
+system which is easier to build
+mechanically which is to simply have
+
+ align:start position:0%
+mechanically which is to simply have
+ 
+
+ align:start position:0%
+mechanically which is to simply have
+point x resources rotating around the
+
+ align:start position:0%
+point x resources rotating around the
+ 
+
+ align:start position:0%
+point x resources rotating around the
+patient so that's our data set simply a
+
+ align:start position:0%
+patient so that's our data set simply a
+ 
+
+ align:start position:0%
+patient so that's our data set simply a
+set of projections so now we have a
+
+ align:start position:0%
+set of projections so now we have a
+ 
+
+ align:start position:0%
+set of projections so now we have a
+mathematical problem it's very simple
+
+ align:start position:0%
+mathematical problem it's very simple
+ 
+
+ align:start position:0%
+mathematical problem it's very simple
+there's some underlying density function
+
+ align:start position:0%
+there's some underlying density function
+ 
+
+ align:start position:0%
+there's some underlying density function
+and so again array is going to pass
+
+ align:start position:0%
+and so again array is going to pass
+ 
+
+ align:start position:0%
+and so again array is going to pass
+through this density function you
+
+ align:start position:0%
+through this density function you
+ 
+
+ align:start position:0%
+through this density function you
+evaluate the line integral and that will
+
+ align:start position:0%
+evaluate the line integral and that will
+ 
+
+ align:start position:0%
+evaluate the line integral and that will
+be the absorption and our task is to
+
+ align:start position:0%
+be the absorption and our task is to
+ 
+
+ align:start position:0%
+be the absorption and our task is to
+invert that those set of line integrals
+
+ align:start position:0%
+invert that those set of line integrals
+ 
+
+ align:start position:0%
+invert that those set of line integrals
+to recover the density function
+
+ align:start position:0%
+to recover the density function
+ 
+
+ align:start position:0%
+to recover the density function
+so if you just take the case of the
+
+ align:start position:0%
+so if you just take the case of the
+ 
+
+ align:start position:0%
+so if you just take the case of the
+simple fan beam projection we have an
+
+ align:start position:0%
+simple fan beam projection we have an
+ 
+
+ align:start position:0%
+simple fan beam projection we have an
+x-ray source that's collimated a foam
+
+ align:start position:0%
+x-ray source that's collimated a foam
+ 
+
+ align:start position:0%
+x-ray source that's collimated a foam
+plane on the opposite side and rotates
+
+ align:start position:0%
+plane on the opposite side and rotates
+ 
+
+ align:start position:0%
+plane on the opposite side and rotates
+180 degrees around the patient and that
+
+ align:start position:0%
+180 degrees around the patient and that
+ 
+
+ align:start position:0%
+180 degrees around the patient and that
+gives you what's known as the radon
+
+ align:start position:0%
+gives you what's known as the radon
+ 
+
+ align:start position:0%
+gives you what's known as the radon
+transform maybe this is sounding
+
+ align:start position:0%
+transform maybe this is sounding
+ 
+
+ align:start position:0%
+transform maybe this is sounding
+familiar to a lot of those in the room
+
+ align:start position:0%
+familiar to a lot of those in the room
+ 
+
+ align:start position:0%
+familiar to a lot of those in the room
+so this radon transform again
+
+ align:start position:0%
+so this radon transform again
+ 
+
+ align:start position:0%
+so this radon transform again
+is simply the crop the projection of the
+
+ align:start position:0%
+is simply the crop the projection of the
+ 
+
+ align:start position:0%
+is simply the crop the projection of the
+density function along a given direction
+
+ align:start position:0%
+density function along a given direction
+ 
+
+ align:start position:0%
+density function along a given direction
+so this is the data set that a ct
+
+ align:start position:0%
+so this is the data set that a ct
+ 
+
+ align:start position:0%
+so this is the data set that a ct
+scanner will give you for the most part
+
+ align:start position:0%
+scanner will give you for the most part
+ 
+
+ align:start position:0%
+scanner will give you for the most part
+and then if you compare that to fan beam
+
+ align:start position:0%
+and then if you compare that to fan beam
+ 
+
+ align:start position:0%
+and then if you compare that to fan beam
+projection where you can imagine i'm
+
+ align:start position:0%
+projection where you can imagine i'm
+ 
+
+ align:start position:0%
+projection where you can imagine i'm
+putting
+
+ align:start position:0%
+putting
+ 
+
+ align:start position:0%
+putting
+a point source say the corner and then
+
+ align:start position:0%
+a point source say the corner and then
+ 
+
+ align:start position:0%
+a point source say the corner and then
+rotating it for the most part it looks
+
+ align:start position:0%
+rotating it for the most part it looks
+ 
+
+ align:start position:0%
+rotating it for the most part it looks
+almost identical it's just this slight
+
+ align:start position:0%
+almost identical it's just this slight
+ 
+
+ align:start position:0%
+almost identical it's just this slight
+nonlinear transformation of the parallel
+
+ align:start position:0%
+nonlinear transformation of the parallel
+ 
+
+ align:start position:0%
+nonlinear transformation of the parallel
+beam projection and so now that we have
+
+ align:start position:0%
+beam projection and so now that we have
+ 
+
+ align:start position:0%
+beam projection and so now that we have
+ample computing power it's very easy to
+
+ align:start position:0%
+ample computing power it's very easy to
+ 
+
+ align:start position:0%
+ample computing power it's very easy to
+re-sample this data set to be equivalent
+
+ align:start position:0%
+re-sample this data set to be equivalent
+ 
+
+ align:start position:0%
+re-sample this data set to be equivalent
+and then use the red inverse radar
+
+ align:start position:0%
+and then use the red inverse radar
+ 
+
+ align:start position:0%
+and then use the red inverse radar
+transform to solve but we still don't
+
+ align:start position:0%
+transform to solve but we still don't
+ 
+
+ align:start position:0%
+transform to solve but we still don't
+know how to invert this problem if i
+
+ align:start position:0%
+know how to invert this problem if i
+ 
+
+ align:start position:0%
+know how to invert this problem if i
+give you this image what algorithm can
+
+ align:start position:0%
+give you this image what algorithm can
+ 
+
+ align:start position:0%
+give you this image what algorithm can
+you apply to recover the original image
+
+ align:start position:0%
+you apply to recover the original image
+ 
+
+ align:start position:0%
+you apply to recover the original image
+so that's really where the insight was
+
+ align:start position:0%
+so that's really where the insight was
+ 
+
+ align:start position:0%
+so that's really where the insight was
+and so i'd recommend make sure
+
+ align:start position:0%
+and so i'd recommend make sure
+ 
+
+ align:start position:0%
+and so i'd recommend make sure
+everybody's up to us with us on the
+
+ align:start position:0%
+everybody's up to us with us on the
+ 
+
+ align:start position:0%
+everybody's up to us with us on the
+forward process
+
+ align:start position:0%
+forward process
+ 
+
+ align:start position:0%
+forward process
+is everybody clear how you go from the
+
+ align:start position:0%
+is everybody clear how you go from the
+ 
+
+ align:start position:0%
+is everybody clear how you go from the
+first image to the second image
+
+ align:start position:0%
+first image to the second image
+ 
+
+ align:start position:0%
+first image to the second image
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now yes first one to second that's the
+
+ align:start position:0%
+now yes first one to second that's the
+ 
+
+ align:start position:0%
+now yes first one to second that's the
+easiest one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that clear i mean just a mechanic is
+
+ align:start position:0%
+is that clear i mean just a mechanic is
+ 
+
+ align:start position:0%
+is that clear i mean just a mechanic is
+very easy to simulate imagine
+
+ align:start position:0%
+very easy to simulate imagine
+ 
+
+ align:start position:0%
+very easy to simulate imagine
+imagine this line is our collimated
+
+ align:start position:0%
+imagine this line is our collimated
+ 
+
+ align:start position:0%
+imagine this line is our collimated
+x-ray source so it's just emitting
+
+ align:start position:0%
+x-ray source so it's just emitting
+ 
+
+ align:start position:0%
+x-ray source so it's just emitting
+parallel rays along the y-axis
+
+ align:start position:0%
+parallel rays along the y-axis
+ 
+
+ align:start position:0%
+parallel rays along the y-axis
+and this is our film plane
+
+ align:start position:0%
+and this is our film plane
+ 
+
+ align:start position:0%
+and this is our film plane
+and so if i just simulate the light
+
+ align:start position:0%
+and so if i just simulate the light
+ 
+
+ align:start position:0%
+and so if i just simulate the light
+going through here along given ray i
+
+ align:start position:0%
+going through here along given ray i
+ 
+
+ align:start position:0%
+going through here along given ray i
+perform the line integral
+
+ align:start position:0%
+perform the line integral
+ 
+
+ align:start position:0%
+perform the line integral
+of this function that gives me the
+
+ align:start position:0%
+of this function that gives me the
+ 
+
+ align:start position:0%
+of this function that gives me the
+absorption along that ray so a given ray
+
+ align:start position:0%
+absorption along that ray so a given ray
+ 
+
+ align:start position:0%
+absorption along that ray so a given ray
+would be some rotation angle and
+
+ align:start position:0%
+would be some rotation angle and
+ 
+
+ align:start position:0%
+would be some rotation angle and
+position so the first column of that
+
+ align:start position:0%
+position so the first column of that
+ 
+
+ align:start position:0%
+position so the first column of that
+middle image is the first parallel beam
+
+ align:start position:0%
+middle image is the first parallel beam
+ 
+
+ align:start position:0%
+middle image is the first parallel beam
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+and then we'd rotate
+
+ align:start position:0%
+and then we'd rotate
+ 
+
+ align:start position:0%
+and then we'd rotate
+both of these slightly
+
+ align:start position:0%
+both of these slightly
+ 
+
+ align:start position:0%
+both of these slightly
+say in 90 degrees that would bring us
+
+ align:start position:0%
+say in 90 degrees that would bring us
+ 
+
+ align:start position:0%
+say in 90 degrees that would bring us
+already here we take another projection
+
+ align:start position:0%
+already here we take another projection
+ 
+
+ align:start position:0%
+already here we take another projection
+and we just get the series of
+
+ align:start position:0%
+and we just get the series of
+ 
+
+ align:start position:0%
+and we just get the series of
+projections as a function of angle do
+
+ align:start position:0%
+projections as a function of angle do
+ 
+
+ align:start position:0%
+projections as a function of angle do
+you have the moving chance uh i don't
+
+ align:start position:0%
+you have the moving chance uh i don't
+ 
+
+ align:start position:0%
+you have the moving chance uh i don't
+have a movie in this one no the the yeah
+
+ align:start position:0%
+have a movie in this one no the the yeah
+ 
+
+ align:start position:0%
+have a movie in this one no the the yeah
+we'll get to it at the end i should put
+
+ align:start position:0%
+we'll get to it at the end i should put
+ 
+
+ align:start position:0%
+we'll get to it at the end i should put
+that earlier
+
+ align:start position:0%
+that earlier
+ 
+
+ align:start position:0%
+that earlier
+um and so then the fan made projection
+
+ align:start position:0%
+um and so then the fan made projection
+ 
+
+ align:start position:0%
+um and so then the fan made projection
+is very simple to simulate as well
+
+ align:start position:0%
+is very simple to simulate as well
+ 
+
+ align:start position:0%
+is very simple to simulate as well
+instead of a line source we have a point
+
+ align:start position:0%
+instead of a line source we have a point
+ 
+
+ align:start position:0%
+instead of a line source we have a point
+source in this corner
+
+ align:start position:0%
+source in this corner
+ 
+
+ align:start position:0%
+source in this corner
+or say in the center here and we we have
+
+ align:start position:0%
+or say in the center here and we we have
+ 
+
+ align:start position:0%
+or say in the center here and we we have
+a set of fan beams going out and then we
+
+ align:start position:0%
+a set of fan beams going out and then we
+ 
+
+ align:start position:0%
+a set of fan beams going out and then we
+rotate those too which is why you get
+
+ align:start position:0%
+rotate those too which is why you get
+ 
+
+ align:start position:0%
+rotate those too which is why you get
+this non-linear transformation so that's
+
+ align:start position:0%
+this non-linear transformation so that's
+ 
+
+ align:start position:0%
+this non-linear transformation so that's
+our input data set now we're trying to
+
+ align:start position:0%
+our input data set now we're trying to
+ 
+
+ align:start position:0%
+our input data set now we're trying to
+invert the system and go from one of the
+
+ align:start position:0%
+invert the system and go from one of the
+ 
+
+ align:start position:0%
+invert the system and go from one of the
+the right images back to the original it
+
+ align:start position:0%
+the right images back to the original it
+ 
+
+ align:start position:0%
+the right images back to the original it
+is a common problem in a lot of
+
+ align:start position:0%
+is a common problem in a lot of
+ 
+
+ align:start position:0%
+is a common problem in a lot of
+conventional imaging situations right
+
+ align:start position:0%
+conventional imaging situations right
+ 
+
+ align:start position:0%
+conventional imaging situations right
+because as uh as duck said you want to
+
+ align:start position:0%
+because as uh as duck said you want to
+ 
+
+ align:start position:0%
+because as uh as duck said you want to
+you don't want to slice the patient
+
+ align:start position:0%
+you don't want to slice the patient
+ 
+
+ align:start position:0%
+you don't want to slice the patient
+so all your observations are from
+
+ align:start position:0%
+so all your observations are from
+ 
+
+ align:start position:0%
+so all your observations are from
+outside
+
+ align:start position:0%
+outside
+ 
+
+ align:start position:0%
+outside
+but you want to infer what's inside
+
+ align:start position:0%
+but you want to infer what's inside
+ 
+
+ align:start position:0%
+but you want to infer what's inside
+so from external observations
+
+ align:start position:0%
+so from external observations
+ 
+
+ align:start position:0%
+so from external observations
+you want to infer what's internal to the
+
+ align:start position:0%
+you want to infer what's internal to the
+ 
+
+ align:start position:0%
+you want to infer what's internal to the
+patient or to an object
+
+ align:start position:0%
+patient or to an object
+ 
+
+ align:start position:0%
+patient or to an object
+or to a oil well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now we'll go into the map which
+
+ align:start position:0%
+right so now we'll go into the map which
+ 
+
+ align:start position:0%
+right so now we'll go into the map which
+there's really one nice result and again
+
+ align:start position:0%
+there's really one nice result and again
+ 
+
+ align:start position:0%
+there's really one nice result and again
+if anyone's working on this you should
+
+ align:start position:0%
+if anyone's working on this you should
+ 
+
+ align:start position:0%
+if anyone's working on this you should
+really look at slanted slanting and cat
+
+ align:start position:0%
+really look at slanted slanting and cat
+ 
+
+ align:start position:0%
+really look at slanted slanting and cat
+they have a really nice book that's
+
+ align:start position:0%
+they have a really nice book that's
+ 
+
+ align:start position:0%
+they have a really nice book that's
+online i think it's out of print now but
+
+ align:start position:0%
+online i think it's out of print now but
+ 
+
+ align:start position:0%
+online i think it's out of print now but
+you can the whole book is online and
+
+ align:start position:0%
+you can the whole book is online and
+ 
+
+ align:start position:0%
+you can the whole book is online and
+these figures are there but really the
+
+ align:start position:0%
+these figures are there but really the
+ 
+
+ align:start position:0%
+these figures are there but really the
+core idea behind this and you've
+
+ align:start position:0%
+core idea behind this and you've
+ 
+
+ align:start position:0%
+core idea behind this and you've
+probably seen this in your own homeworks
+
+ align:start position:0%
+probably seen this in your own homeworks
+ 
+
+ align:start position:0%
+probably seen this in your own homeworks
+on in light field photography i think
+
+ align:start position:0%
+on in light field photography i think
+ 
+
+ align:start position:0%
+on in light field photography i think
+you did refocusing i'm guessing
+
+ align:start position:0%
+you did refocusing i'm guessing
+ 
+
+ align:start position:0%
+you did refocusing i'm guessing
+i don't know if you did foia domain
+
+ align:start position:0%
+i don't know if you did foia domain
+ 
+
+ align:start position:0%
+i don't know if you did foia domain
+refocusing or just
+
+ align:start position:0%
+refocusing or just
+ 
+
+ align:start position:0%
+refocusing or just
+okay so you did the shift and some
+
+ align:start position:0%
+okay so you did the shift and some
+ 
+
+ align:start position:0%
+okay so you did the shift and some
+refocusing and it turns out this is the
+
+ align:start position:0%
+refocusing and it turns out this is the
+ 
+
+ align:start position:0%
+refocusing and it turns out this is the
+first example again mark lavoy
+
+ align:start position:0%
+first example again mark lavoy
+ 
+
+ align:start position:0%
+first example again mark lavoy
+originally
+
+ align:start position:0%
+originally
+ 
+
+ align:start position:0%
+originally
+put these slides together and he had a
+
+ align:start position:0%
+put these slides together and he had a
+ 
+
+ align:start position:0%
+put these slides together and he had a
+very nice paper i think it's 2005 the
+
+ align:start position:0%
+very nice paper i think it's 2005 the
+ 
+
+ align:start position:0%
+very nice paper i think it's 2005 the
+thesis but the idea was that you know
+
+ align:start position:0%
+thesis but the idea was that you know
+ 
+
+ align:start position:0%
+thesis but the idea was that you know
+you for your lifestyle refocusing you
+
+ align:start position:0%
+you for your lifestyle refocusing you
+ 
+
+ align:start position:0%
+you for your lifestyle refocusing you
+did shift and sum which is computational
+
+ align:start position:0%
+did shift and sum which is computational
+ 
+
+ align:start position:0%
+did shift and sum which is computational
+expensive using the foid projection
+
+ align:start position:0%
+expensive using the foid projection
+ 
+
+ align:start position:0%
+expensive using the foid projection
+slice theorem you can actually improve
+
+ align:start position:0%
+slice theorem you can actually improve
+ 
+
+ align:start position:0%
+slice theorem you can actually improve
+uh the running time of that algorithm
+
+ align:start position:0%
+uh the running time of that algorithm
+ 
+
+ align:start position:0%
+uh the running time of that algorithm
+you'll probably see that once we get
+
+ align:start position:0%
+you'll probably see that once we get
+ 
+
+ align:start position:0%
+you'll probably see that once we get
+through this but let's just let's just
+
+ align:start position:0%
+through this but let's just let's just
+ 
+
+ align:start position:0%
+through this but let's just let's just
+consider the tomography problem again we
+
+ align:start position:0%
+consider the tomography problem again we
+ 
+
+ align:start position:0%
+consider the tomography problem again we
+have this density function in 2d let's
+
+ align:start position:0%
+have this density function in 2d let's
+ 
+
+ align:start position:0%
+have this density function in 2d let's
+just analyze this in 2d to begin with so
+
+ align:start position:0%
+just analyze this in 2d to begin with so
+ 
+
+ align:start position:0%
+just analyze this in 2d to begin with so
+we have some density function of x
+
+ align:start position:0%
+we have some density function of x
+ 
+
+ align:start position:0%
+we have some density function of x
+x and y so this is our absorption
+
+ align:start position:0%
+x and y so this is our absorption
+ 
+
+ align:start position:0%
+x and y so this is our absorption
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and then we're going to take a
+
+ align:start position:0%
+and then we're going to take a
+ 
+
+ align:start position:0%
+and then we're going to take a
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+again this is a parallel beam projection
+
+ align:start position:0%
+again this is a parallel beam projection
+ 
+
+ align:start position:0%
+again this is a parallel beam projection
+along some angle and so if we're just
+
+ align:start position:0%
+along some angle and so if we're just
+ 
+
+ align:start position:0%
+along some angle and so if we're just
+projecting along y
+
+ align:start position:0%
+projecting along y
+ 
+
+ align:start position:0%
+projecting along y
+then the projection
+
+ align:start position:0%
+then the projection
+ 
+
+ align:start position:0%
+then the projection
+along y
+
+ align:start position:0%
+along y
+ 
+
+ align:start position:0%
+along y
+is simply the line the integral of this
+
+ align:start position:0%
+is simply the line the integral of this
+ 
+
+ align:start position:0%
+is simply the line the integral of this
+function over y right does that make
+
+ align:start position:0%
+function over y right does that make
+ 
+
+ align:start position:0%
+function over y right does that make
+sense so we're projecting this function
+
+ align:start position:0%
+sense so we're projecting this function
+ 
+
+ align:start position:0%
+sense so we're projecting this function
+onto the x-axis right that's our first
+
+ align:start position:0%
+onto the x-axis right that's our first
+ 
+
+ align:start position:0%
+onto the x-axis right that's our first
+that's that's obvious
+
+ align:start position:0%
+that's that's obvious
+ 
+
+ align:start position:0%
+that's that's obvious
+now the question is let's let's look at
+
+ align:start position:0%
+now the question is let's let's look at
+ 
+
+ align:start position:0%
+now the question is let's let's look at
+a four domain analysis of this problem
+
+ align:start position:0%
+a four domain analysis of this problem
+ 
+
+ align:start position:0%
+a four domain analysis of this problem
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's take the two dimensional fourier
+
+ align:start position:0%
+let's take the two dimensional fourier
+ 
+
+ align:start position:0%
+let's take the two dimensional fourier
+transform of our original density
+
+ align:start position:0%
+transform of our original density
+ 
+
+ align:start position:0%
+transform of our original density
+function and so you can write that it's
+
+ align:start position:0%
+function and so you can write that it's
+ 
+
+ align:start position:0%
+function and so you can write that it's
+very simple everyone remembers this the
+
+ align:start position:0%
+very simple everyone remembers this the
+ 
+
+ align:start position:0%
+very simple everyone remembers this the
+fourier transform function of the two
+
+ align:start position:0%
+fourier transform function of the two
+ 
+
+ align:start position:0%
+fourier transform function of the two
+frequency parameters is simply the
+
+ align:start position:0%
+frequency parameters is simply the
+ 
+
+ align:start position:0%
+frequency parameters is simply the
+original function times this complex
+
+ align:start position:0%
+original function times this complex
+ 
+
+ align:start position:0%
+original function times this complex
+exponential which is the sum of the
+
+ align:start position:0%
+exponential which is the sum of the
+ 
+
+ align:start position:0%
+exponential which is the sum of the
+coefficients in each direction
+
+ align:start position:0%
+coefficients in each direction
+ 
+
+ align:start position:0%
+coefficients in each direction
+and here's the key insight what we'd
+
+ align:start position:0%
+and here's the key insight what we'd
+ 
+
+ align:start position:0%
+and here's the key insight what we'd
+like to do is somehow relate the
+
+ align:start position:0%
+like to do is somehow relate the
+ 
+
+ align:start position:0%
+like to do is somehow relate the
+properties of this fourier transform to
+
+ align:start position:0%
+properties of this fourier transform to
+ 
+
+ align:start position:0%
+properties of this fourier transform to
+a slice in our primary domain and so
+
+ align:start position:0%
+a slice in our primary domain and so
+ 
+
+ align:start position:0%
+a slice in our primary domain and so
+this this is really the neat trick
+
+ align:start position:0%
+this this is really the neat trick
+ 
+
+ align:start position:0%
+this this is really the neat trick
+behind the toy projection slice there is
+
+ align:start position:0%
+behind the toy projection slice there is
+ 
+
+ align:start position:0%
+behind the toy projection slice there is
+let's just look
+
+ align:start position:0%
+let's just look
+ 
+
+ align:start position:0%
+let's just look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+this 1d slice
+
+ align:start position:0%
+this 1d slice
+ 
+
+ align:start position:0%
+this 1d slice
+along the kx
+
+ align:start position:0%
+along the kx
+ 
+
+ align:start position:0%
+along the kx
+the f frequency axis
+
+ align:start position:0%
+the f frequency axis
+ 
+
+ align:start position:0%
+the f frequency axis
+in the foia domain and so that that's
+
+ align:start position:0%
+in the foia domain and so that that's
+ 
+
+ align:start position:0%
+in the foia domain and so that that's
+just given by substituting 0 for the y
+
+ align:start position:0%
+just given by substituting 0 for the y
+ 
+
+ align:start position:0%
+just given by substituting 0 for the y
+into our previous expression right so
+
+ align:start position:0%
+into our previous expression right so
+ 
+
+ align:start position:0%
+into our previous expression right so
+essentially this k x and k y can be
+
+ align:start position:0%
+essentially this k x and k y can be
+ 
+
+ align:start position:0%
+essentially this k x and k y can be
+thought of as a vector and we're just
+
+ align:start position:0%
+thought of as a vector and we're just
+ 
+
+ align:start position:0%
+thought of as a vector and we're just
+selecting the one along x and so here
+
+ align:start position:0%
+selecting the one along x and so here
+ 
+
+ align:start position:0%
+selecting the one along x and so here
+you see that our y term drops out
+
+ align:start position:0%
+you see that our y term drops out
+ 
+
+ align:start position:0%
+you see that our y term drops out
+and what this gives us is the flight
+
+ align:start position:0%
+and what this gives us is the flight
+ 
+
+ align:start position:0%
+and what this gives us is the flight
+transform along the kx axis right just
+
+ align:start position:0%
+transform along the kx axis right just
+ 
+
+ align:start position:0%
+transform along the kx axis right just
+the 1d slice
+
+ align:start position:0%
+the 1d slice
+ 
+
+ align:start position:0%
+the 1d slice
+so the next step is really where all the
+
+ align:start position:0%
+so the next step is really where all the
+ 
+
+ align:start position:0%
+so the next step is really where all the
+magic happens it's just regrouping terms
+
+ align:start position:0%
+magic happens it's just regrouping terms
+ 
+
+ align:start position:0%
+magic happens it's just regrouping terms
+in that integral so if you look at this
+
+ align:start position:0%
+in that integral so if you look at this
+ 
+
+ align:start position:0%
+in that integral so if you look at this
+you can see that it's separable and so
+
+ align:start position:0%
+you can see that it's separable and so
+ 
+
+ align:start position:0%
+you can see that it's separable and so
+we can do the y integration regroup it
+
+ align:start position:0%
+we can do the y integration regroup it
+ 
+
+ align:start position:0%
+we can do the y integration regroup it
+and then do the fourier transform and so
+
+ align:start position:0%
+and then do the fourier transform and so
+ 
+
+ align:start position:0%
+and then do the fourier transform and so
+now you can just substitute the first
+
+ align:start position:0%
+now you can just substitute the first
+ 
+
+ align:start position:0%
+now you can just substitute the first
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+and you get this very nice result so can
+
+ align:start position:0%
+and you get this very nice result so can
+ 
+
+ align:start position:0%
+and you get this very nice result so can
+they do why interpret this you sort of
+
+ align:start position:0%
+they do why interpret this you sort of
+ 
+
+ align:start position:0%
+they do why interpret this you sort of
+you see what this means
+
+ align:start position:0%
+you see what this means
+ 
+
+ align:start position:0%
+you see what this means
+i can explain to you but it'd be nice to
+
+ align:start position:0%
+i can explain to you but it'd be nice to
+ 
+
+ align:start position:0%
+i can explain to you but it'd be nice to
+sort of see if people are following
+
+ align:start position:0%
+sort of see if people are following
+ 
+
+ align:start position:0%
+sort of see if people are following
+so remember we started with
+
+ align:start position:0%
+so remember we started with
+ 
+
+ align:start position:0%
+so remember we started with
+the first row is p of x which means
+
+ align:start position:0%
+the first row is p of x which means
+ 
+
+ align:start position:0%
+the first row is p of x which means
+it's the photo
+
+ align:start position:0%
+it's the photo
+ 
+
+ align:start position:0%
+it's the photo
+taken along the x direction right if you
+
+ align:start position:0%
+taken along the x direction right if you
+ 
+
+ align:start position:0%
+taken along the x direction right if you
+put a sensor
+
+ align:start position:0%
+put a sensor
+ 
+
+ align:start position:0%
+put a sensor
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we get the px photo
+
+ align:start position:0%
+we get the px photo
+ 
+
+ align:start position:0%
+we get the px photo
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+you go through the whole math
+
+ align:start position:0%
+you go through the whole math
+ 
+
+ align:start position:0%
+you go through the whole math
+the second equation is fourier transform
+
+ align:start position:0%
+the second equation is fourier transform
+ 
+
+ align:start position:0%
+the second equation is fourier transform
+third equation is fourier transform
+
+ align:start position:0%
+third equation is fourier transform
+ 
+
+ align:start position:0%
+third equation is fourier transform
+along uh is it along the y axis along
+
+ align:start position:0%
+along uh is it along the y axis along
+ 
+
+ align:start position:0%
+along uh is it along the y axis along
+dropping it just for your transform
+
+ align:start position:0%
+dropping it just for your transform
+ 
+
+ align:start position:0%
+dropping it just for your transform
+along x yeah along x
+
+ align:start position:0%
+along x yeah along x
+ 
+
+ align:start position:0%
+along x yeah along x
+and then but what you get back at the
+
+ align:start position:0%
+and then but what you get back at the
+ 
+
+ align:start position:0%
+and then but what you get back at the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+is the px term which was the original
+
+ align:start position:0%
+is the px term which was the original
+ 
+
+ align:start position:0%
+is the px term which was the original
+photo that you started with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so looking at this expression
+
+ align:start position:0%
+right so so looking at this expression
+ 
+
+ align:start position:0%
+right so so looking at this expression
+there's now this relationship between
+
+ align:start position:0%
+there's now this relationship between
+ 
+
+ align:start position:0%
+there's now this relationship between
+the frequency domain
+
+ align:start position:0%
+the frequency domain
+ 
+
+ align:start position:0%
+the frequency domain
+the fourier transform or density
+
+ align:start position:0%
+the fourier transform or density
+ 
+
+ align:start position:0%
+the fourier transform or density
+function in the original function do you
+
+ align:start position:0%
+function in the original function do you
+ 
+
+ align:start position:0%
+function in the original function do you
+see what that relationship is here
+
+ align:start position:0%
+see what that relationship is here
+ 
+
+ align:start position:0%
+see what that relationship is here
+what is this saying the slice is just
+
+ align:start position:0%
+what is this saying the slice is just
+ 
+
+ align:start position:0%
+what is this saying the slice is just
+the fourier transform of the original
+
+ align:start position:0%
+the fourier transform of the original
+ 
+
+ align:start position:0%
+the fourier transform of the original
+exactly very good so the fourier
+
+ align:start position:0%
+exactly very good so the fourier
+ 
+
+ align:start position:0%
+exactly very good so the fourier
+projection slice theorem this is the key
+
+ align:start position:0%
+projection slice theorem this is the key
+ 
+
+ align:start position:0%
+projection slice theorem this is the key
+insight is that if i take a 1d slice
+
+ align:start position:0%
+insight is that if i take a 1d slice
+ 
+
+ align:start position:0%
+insight is that if i take a 1d slice
+of my density function take its fourier
+
+ align:start position:0%
+of my density function take its fourier
+ 
+
+ align:start position:0%
+of my density function take its fourier
+transform 1d
+
+ align:start position:0%
+transform 1d
+ 
+
+ align:start position:0%
+transform 1d
+1d4 transform that's equal to a slice of
+
+ align:start position:0%
+1d4 transform that's equal to a slice of
+ 
+
+ align:start position:0%
+1d4 transform that's equal to a slice of
+the 2d4 transform
+
+ align:start position:0%
+the 2d4 transform
+ 
+
+ align:start position:0%
+the 2d4 transform
+okay so we have this inside so how could
+
+ align:start position:0%
+okay so we have this inside so how could
+ 
+
+ align:start position:0%
+okay so we have this inside so how could
+you use this to now solve our problem
+
+ align:start position:0%
+you use this to now solve our problem
+ 
+
+ align:start position:0%
+you use this to now solve our problem
+let's go back
+
+ align:start position:0%
+let's go back
+ 
+
+ align:start position:0%
+let's go back
+do you see how you could use this to now
+
+ align:start position:0%
+do you see how you could use this to now
+ 
+
+ align:start position:0%
+do you see how you could use this to now
+go from say this image which is a
+
+ align:start position:0%
+go from say this image which is a
+ 
+
+ align:start position:0%
+go from say this image which is a
+parallel beam projection back to the
+
+ align:start position:0%
+parallel beam projection back to the
+ 
+
+ align:start position:0%
+parallel beam projection back to the
+original density
+
+ align:start position:0%
+original density
+ 
+
+ align:start position:0%
+original density
+can anyone describe the algorithm
+
+ align:start position:0%
+can anyone describe the algorithm
+ 
+
+ align:start position:0%
+can anyone describe the algorithm
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+just take the us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we construct all the
+
+ align:start position:0%
+and then we construct all the
+ 
+
+ align:start position:0%
+and then we construct all the
+slices of okay so
+
+ align:start position:0%
+slices of okay so
+ 
+
+ align:start position:0%
+slices of okay so
+so so okay here's your image what's the
+
+ align:start position:0%
+so so okay here's your image what's the
+ 
+
+ align:start position:0%
+so so okay here's your image what's the
+first step
+
+ align:start position:0%
+first step
+ 
+
+ align:start position:0%
+first step
+um take the line one line say every
+
+ align:start position:0%
+um take the line one line say every
+ 
+
+ align:start position:0%
+um take the line one line say every
+column here is a px okay
+
+ align:start position:0%
+column here is a px okay
+ 
+
+ align:start position:0%
+column here is a px okay
+great um and take all of them uh take
+
+ align:start position:0%
+great um and take all of them uh take
+ 
+
+ align:start position:0%
+great um and take all of them uh take
+their inverses inverse of the x inverse
+
+ align:start position:0%
+their inverses inverse of the x inverse
+ 
+
+ align:start position:0%
+their inverses inverse of the x inverse
+fourier transform the fourier transform
+
+ align:start position:0%
+fourier transform the fourier transform
+ 
+
+ align:start position:0%
+fourier transform the fourier transform
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+and then you will get uh kx
+
+ align:start position:0%
+and then you will get uh kx
+ 
+
+ align:start position:0%
+and then you will get uh kx
+yes and then keep rotating all the cases
+
+ align:start position:0%
+yes and then keep rotating all the cases
+ 
+
+ align:start position:0%
+yes and then keep rotating all the cases
+to generate capital f that's absolutely
+
+ align:start position:0%
+to generate capital f that's absolutely
+ 
+
+ align:start position:0%
+to generate capital f that's absolutely
+correct great and then and then the last
+
+ align:start position:0%
+correct great and then and then the last
+ 
+
+ align:start position:0%
+correct great and then and then the last
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+exactly so let me just summarize that up
+
+ align:start position:0%
+exactly so let me just summarize that up
+ 
+
+ align:start position:0%
+exactly so let me just summarize that up
+that's great that's exactly what they do
+
+ align:start position:0%
+that's great that's exactly what they do
+ 
+
+ align:start position:0%
+that's great that's exactly what they do
+so the algorithm is very simple remember
+
+ align:start position:0%
+so the algorithm is very simple remember
+ 
+
+ align:start position:0%
+so the algorithm is very simple remember
+we're going to get a slice
+
+ align:start position:0%
+we're going to get a slice
+ 
+
+ align:start position:0%
+we're going to get a slice
+for each angle
+
+ align:start position:0%
+for each angle
+ 
+
+ align:start position:0%
+for each angle
+so so you simply take the projection
+
+ align:start position:0%
+so so you simply take the projection
+ 
+
+ align:start position:0%
+so so you simply take the projection
+take its 1d40 transform and assign
+
+ align:start position:0%
+take its 1d40 transform and assign
+ 
+
+ align:start position:0%
+take its 1d40 transform and assign
+initialize an accumulator it's all zeros
+
+ align:start position:0%
+initialize an accumulator it's all zeros
+ 
+
+ align:start position:0%
+initialize an accumulator it's all zeros
+assign the fourier transform then rotate
+
+ align:start position:0%
+assign the fourier transform then rotate
+ 
+
+ align:start position:0%
+assign the fourier transform then rotate
+your source receiver take a new slice
+
+ align:start position:0%
+your source receiver take a new slice
+ 
+
+ align:start position:0%
+your source receiver take a new slice
+one before you transform assign it and
+
+ align:start position:0%
+one before you transform assign it and
+ 
+
+ align:start position:0%
+one before you transform assign it and
+you're going to build up this whole
+
+ align:start position:0%
+you're going to build up this whole
+ 
+
+ align:start position:0%
+you're going to build up this whole
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and after a full 180 degree rotation
+
+ align:start position:0%
+and after a full 180 degree rotation
+ 
+
+ align:start position:0%
+and after a full 180 degree rotation
+you'll have populated
+
+ align:start position:0%
+you'll have populated
+ 
+
+ align:start position:0%
+you'll have populated
+this entire volume
+
+ align:start position:0%
+this entire volume
+ 
+
+ align:start position:0%
+this entire volume
+and then you're gonna inversely
+
+ align:start position:0%
+and then you're gonna inversely
+ 
+
+ align:start position:0%
+and then you're gonna inversely
+transform and get get everything back so
+
+ align:start position:0%
+transform and get get everything back so
+ 
+
+ align:start position:0%
+transform and get get everything back so
+let's i think i have a picture here of
+
+ align:start position:0%
+let's i think i have a picture here of
+ 
+
+ align:start position:0%
+let's i think i have a picture here of
+how that works
+
+ align:start position:0%
+how that works
+ 
+
+ align:start position:0%
+how that works
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so you just described this algorithm
+
+ align:start position:0%
+so you just described this algorithm
+ 
+
+ align:start position:0%
+so you just described this algorithm
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now you can see
+
+ align:start position:0%
+so now you can see
+ 
+
+ align:start position:0%
+so now you can see
+basically that procedure i outlined at
+
+ align:start position:0%
+basically that procedure i outlined at
+ 
+
+ align:start position:0%
+basically that procedure i outlined at
+each step we're going to populate our
+
+ align:start position:0%
+each step we're going to populate our
+ 
+
+ align:start position:0%
+each step we're going to populate our
+accumulator once it's full we can
+
+ align:start position:0%
+accumulator once it's full we can
+ 
+
+ align:start position:0%
+accumulator once it's full we can
+inverse 2d4 transform we get our image
+
+ align:start position:0%
+inverse 2d4 transform we get our image
+ 
+
+ align:start position:0%
+inverse 2d4 transform we get our image
+right so what are some problems you can
+
+ align:start position:0%
+right so what are some problems you can
+ 
+
+ align:start position:0%
+right so what are some problems you can
+see this is this is the textbook and
+
+ align:start position:0%
+see this is this is the textbook and
+ 
+
+ align:start position:0%
+see this is this is the textbook and
+there's the textbook again solution to
+
+ align:start position:0%
+there's the textbook again solution to
+ 
+
+ align:start position:0%
+there's the textbook again solution to
+the inverse radon transform so what are
+
+ align:start position:0%
+the inverse radon transform so what are
+ 
+
+ align:start position:0%
+the inverse radon transform so what are
+some limitations you can already see you
+
+ align:start position:0%
+some limitations you can already see you
+ 
+
+ align:start position:0%
+some limitations you can already see you
+know sort of practically if you built a
+
+ align:start position:0%
+know sort of practically if you built a
+ 
+
+ align:start position:0%
+know sort of practically if you built a
+ct scanner that used this algorithm what
+
+ align:start position:0%
+ct scanner that used this algorithm what
+ 
+
+ align:start position:0%
+ct scanner that used this algorithm what
+would be some of the limitations the
+
+ align:start position:0%
+would be some of the limitations the
+ 
+
+ align:start position:0%
+would be some of the limitations the
+resolution of the angles at which you
+
+ align:start position:0%
+resolution of the angles at which you
+ 
+
+ align:start position:0%
+resolution of the angles at which you
+can take exactly
+
+ align:start position:0%
+can take exactly
+ 
+
+ align:start position:0%
+can take exactly
+so so you see that the problem here is
+
+ align:start position:0%
+so so you see that the problem here is
+ 
+
+ align:start position:0%
+so so you see that the problem here is
+we need to fully populate
+
+ align:start position:0%
+we need to fully populate
+ 
+
+ align:start position:0%
+we need to fully populate
+this transform before we take we need to
+
+ align:start position:0%
+this transform before we take we need to
+ 
+
+ align:start position:0%
+this transform before we take we need to
+fully populate our 2d4 transform before
+
+ align:start position:0%
+fully populate our 2d4 transform before
+ 
+
+ align:start position:0%
+fully populate our 2d4 transform before
+we inverse transform or else we'll have
+
+ align:start position:0%
+we inverse transform or else we'll have
+ 
+
+ align:start position:0%
+we inverse transform or else we'll have
+missing data and artifacts does that
+
+ align:start position:0%
+missing data and artifacts does that
+ 
+
+ align:start position:0%
+missing data and artifacts does that
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+and so this this insight is really at
+
+ align:start position:0%
+and so this this insight is really at
+ 
+
+ align:start position:0%
+and so this this insight is really at
+the core of tomography you can see a lot
+
+ align:start position:0%
+the core of tomography you can see a lot
+ 
+
+ align:start position:0%
+the core of tomography you can see a lot
+of the limitations so the first one you
+
+ align:start position:0%
+of the limitations so the first one you
+ 
+
+ align:start position:0%
+of the limitations so the first one you
+mentioned
+
+ align:start position:0%
+mentioned
+ 
+
+ align:start position:0%
+mentioned
+is resolution
+
+ align:start position:0%
+is resolution
+ 
+
+ align:start position:0%
+is resolution
+right so you mean by angular resolution
+
+ align:start position:0%
+right so you mean by angular resolution
+ 
+
+ align:start position:0%
+right so you mean by angular resolution
+i think so if we built if we built a ct
+
+ align:start position:0%
+i think so if we built if we built a ct
+ 
+
+ align:start position:0%
+i think so if we built if we built a ct
+scanner that took a projection every
+
+ align:start position:0%
+scanner that took a projection every
+ 
+
+ align:start position:0%
+scanner that took a projection every
+five degrees
+
+ align:start position:0%
+five degrees
+ 
+
+ align:start position:0%
+five degrees
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+or every 20 degrees we have lots of
+
+ align:start position:0%
+or every 20 degrees we have lots of
+ 
+
+ align:start position:0%
+or every 20 degrees we have lots of
+zeros left in this data set if we take
+
+ align:start position:0%
+zeros left in this data set if we take
+ 
+
+ align:start position:0%
+zeros left in this data set if we take
+every 20 degrees you're filling up this
+
+ align:start position:0%
+every 20 degrees you're filling up this
+ 
+
+ align:start position:0%
+every 20 degrees you're filling up this
+this image only at every 20 degrees
+
+ align:start position:0%
+this image only at every 20 degrees
+ 
+
+ align:start position:0%
+this image only at every 20 degrees
+right 20 40 60 80 and so right so you
+
+ align:start position:0%
+right 20 40 60 80 and so right so you
+ 
+
+ align:start position:0%
+right 20 40 60 80 and so right so you
+can imagine they'll be huge near the
+
+ align:start position:0%
+can imagine they'll be huge near the
+ 
+
+ align:start position:0%
+can imagine they'll be huge near the
+origin you'll be okay your low frequency
+
+ align:start position:0%
+origin you'll be okay your low frequency
+ 
+
+ align:start position:0%
+origin you'll be okay your low frequency
+reconstruction will be all right but
+
+ align:start position:0%
+reconstruction will be all right but
+ 
+
+ align:start position:0%
+reconstruction will be all right but
+your high frequency detail will be lost
+
+ align:start position:0%
+your high frequency detail will be lost
+ 
+
+ align:start position:0%
+your high frequency detail will be lost
+right or unknown right you'll have many
+
+ align:start position:0%
+right or unknown right you'll have many
+ 
+
+ align:start position:0%
+right or unknown right you'll have many
+zeros out here
+
+ align:start position:0%
+zeros out here
+ 
+
+ align:start position:0%
+zeros out here
+so that already implies that cp scanners
+
+ align:start position:0%
+so that already implies that cp scanners
+ 
+
+ align:start position:0%
+so that already implies that cp scanners
+need to have very dense set of rotations
+
+ align:start position:0%
+need to have very dense set of rotations
+ 
+
+ align:start position:0%
+need to have very dense set of rotations
+or you need to have some prior about the
+
+ align:start position:0%
+or you need to have some prior about the
+ 
+
+ align:start position:0%
+or you need to have some prior about the
+scene but that's that's one problem
+
+ align:start position:0%
+scene but that's that's one problem
+ 
+
+ align:start position:0%
+scene but that's that's one problem
+what's what's another problem you can
+
+ align:start position:0%
+what's what's another problem you can
+ 
+
+ align:start position:0%
+what's what's another problem you can
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+so if i built a ct scanner for instance
+
+ align:start position:0%
+so if i built a ct scanner for instance
+ 
+
+ align:start position:0%
+so if i built a ct scanner for instance
+that could only scan a limited set of
+
+ align:start position:0%
+that could only scan a limited set of
+ 
+
+ align:start position:0%
+that could only scan a limited set of
+angles
+
+ align:start position:0%
+angles
+ 
+
+ align:start position:0%
+angles
+not a full 180 degree rotation
+
+ align:start position:0%
+not a full 180 degree rotation
+ 
+
+ align:start position:0%
+not a full 180 degree rotation
+right then you also have a lot of
+
+ align:start position:0%
+right then you also have a lot of
+ 
+
+ align:start position:0%
+right then you also have a lot of
+missing data here right
+
+ align:start position:0%
+missing data here right
+ 
+
+ align:start position:0%
+missing data here right
+and so that that's the second so having
+
+ align:start position:0%
+and so that that's the second so having
+ 
+
+ align:start position:0%
+and so that that's the second so having
+sufficient angular sampling is one
+
+ align:start position:0%
+sufficient angular sampling is one
+ 
+
+ align:start position:0%
+sufficient angular sampling is one
+problem of ct scanning the other is
+
+ align:start position:0%
+problem of ct scanning the other is
+ 
+
+ align:start position:0%
+problem of ct scanning the other is
+limited baseline if i only rotate over a
+
+ align:start position:0%
+limited baseline if i only rotate over a
+ 
+
+ align:start position:0%
+limited baseline if i only rotate over a
+small set of angles because maybe in
+
+ align:start position:0%
+small set of angles because maybe in
+ 
+
+ align:start position:0%
+small set of angles because maybe in
+whatever system i'm using it's difficult
+
+ align:start position:0%
+whatever system i'm using it's difficult
+ 
+
+ align:start position:0%
+whatever system i'm using it's difficult
+to rotate over a full 100 degree
+
+ align:start position:0%
+to rotate over a full 100 degree
+ 
+
+ align:start position:0%
+to rotate over a full 100 degree
+rotation then i won't be able to get a
+
+ align:start position:0%
+rotation then i won't be able to get a
+ 
+
+ align:start position:0%
+rotation then i won't be able to get a
+complete reconstruction
+
+ align:start position:0%
+complete reconstruction
+ 
+
+ align:start position:0%
+complete reconstruction
+so really keep in tune though keep in
+
+ align:start position:0%
+so really keep in tune though keep in
+ 
+
+ align:start position:0%
+so really keep in tune though keep in
+mind those two limitations of ct
+
+ align:start position:0%
+mind those two limitations of ct
+ 
+
+ align:start position:0%
+mind those two limitations of ct
+scanning you need to have sufficient
+
+ align:start position:0%
+scanning you need to have sufficient
+ 
+
+ align:start position:0%
+scanning you need to have sufficient
+angular density and sufficient baseline
+
+ align:start position:0%
+angular density and sufficient baseline
+ 
+
+ align:start position:0%
+angular density and sufficient baseline
+and they actually map directly to
+
+ align:start position:0%
+and they actually map directly to
+ 
+
+ align:start position:0%
+and they actually map directly to
+problems with lightfield cameras
+
+ align:start position:0%
+problems with lightfield cameras
+ 
+
+ align:start position:0%
+problems with lightfield cameras
+but then let's just look at the step
+
+ align:start position:0%
+but then let's just look at the step
+ 
+
+ align:start position:0%
+but then let's just look at the step
+back again and think about this
+
+ align:start position:0%
+back again and think about this
+ 
+
+ align:start position:0%
+back again and think about this
+so again
+
+ align:start position:0%
+so again
+ 
+
+ align:start position:0%
+so again
+our algorithm is we rotate our source
+
+ align:start position:0%
+our algorithm is we rotate our source
+ 
+
+ align:start position:0%
+our algorithm is we rotate our source
+and receiver around the object if it's
+
+ align:start position:0%
+and receiver around the object if it's
+ 
+
+ align:start position:0%
+and receiver around the object if it's
+fan meme or trello being tomography you
+
+ align:start position:0%
+fan meme or trello being tomography you
+ 
+
+ align:start position:0%
+fan meme or trello being tomography you
+sort of end up with the same thing where
+
+ align:start position:0%
+sort of end up with the same thing where
+ 
+
+ align:start position:0%
+sort of end up with the same thing where
+you take the voice the one these
+
+ align:start position:0%
+you take the voice the one these
+ 
+
+ align:start position:0%
+you take the voice the one these
+transforms and you assign them to the
+
+ align:start position:0%
+transforms and you assign them to the
+ 
+
+ align:start position:0%
+transforms and you assign them to the
+frequency domain and we may have some
+
+ align:start position:0%
+frequency domain and we may have some
+ 
+
+ align:start position:0%
+frequency domain and we may have some
+zeros but there's a third problem which
+
+ align:start position:0%
+zeros but there's a third problem which
+ 
+
+ align:start position:0%
+zeros but there's a third problem which
+i didn't describe and you can sort of
+
+ align:start position:0%
+i didn't describe and you can sort of
+ 
+
+ align:start position:0%
+i didn't describe and you can sort of
+see it here again the algorithm was we
+
+ align:start position:0%
+see it here again the algorithm was we
+ 
+
+ align:start position:0%
+see it here again the algorithm was we
+initialize an accumulator to all zeros
+
+ align:start position:0%
+initialize an accumulator to all zeros
+ 
+
+ align:start position:0%
+initialize an accumulator to all zeros
+we take the 1d40 transform add to the
+
+ align:start position:0%
+we take the 1d40 transform add to the
+ 
+
+ align:start position:0%
+we take the 1d40 transform add to the
+accumulator
+
+ align:start position:0%
+accumulator
+ 
+
+ align:start position:0%
+accumulator
+then rotate add the next one add the
+
+ align:start position:0%
+then rotate add the next one add the
+ 
+
+ align:start position:0%
+then rotate add the next one add the
+next one out of the next one you can see
+
+ align:start position:0%
+next one out of the next one you can see
+ 
+
+ align:start position:0%
+next one out of the next one you can see
+it right here with the opacity i made
+
+ align:start position:0%
+it right here with the opacity i made
+ 
+
+ align:start position:0%
+it right here with the opacity i made
+all of these equal and you can see we're
+
+ align:start position:0%
+all of these equal and you can see we're
+ 
+
+ align:start position:0%
+all of these equal and you can see we're
+building up this really high density in
+
+ align:start position:0%
+building up this really high density in
+ 
+
+ align:start position:0%
+building up this really high density in
+the center
+
+ align:start position:0%
+the center
+ 
+
+ align:start position:0%
+the center
+does that make sense and so when i
+
+ align:start position:0%
+does that make sense and so when i
+ 
+
+ align:start position:0%
+does that make sense and so when i
+inverse square i transform essentially
+
+ align:start position:0%
+inverse square i transform essentially
+ 
+
+ align:start position:0%
+inverse square i transform essentially
+my low frequency terms have been boosted
+
+ align:start position:0%
+my low frequency terms have been boosted
+ 
+
+ align:start position:0%
+my low frequency terms have been boosted
+right and so
+
+ align:start position:0%
+right and so
+ 
+
+ align:start position:0%
+right and so
+we'll lose edge contrast if we don't do
+
+ align:start position:0%
+we'll lose edge contrast if we don't do
+ 
+
+ align:start position:0%
+we'll lose edge contrast if we don't do
+anything here right so the third problem
+
+ align:start position:0%
+anything here right so the third problem
+ 
+
+ align:start position:0%
+anything here right so the third problem
+i identified with the inverse radon
+
+ align:start position:0%
+i identified with the inverse radon
+ 
+
+ align:start position:0%
+i identified with the inverse radon
+transform is that you can't you can't
+
+ align:start position:0%
+transform is that you can't you can't
+ 
+
+ align:start position:0%
+transform is that you can't you can't
+simply evaluate this accumulator in
+
+ align:start position:0%
+simply evaluate this accumulator in
+ 
+
+ align:start position:0%
+simply evaluate this accumulator in
+inverse transform
+
+ align:start position:0%
+inverse transform
+ 
+
+ align:start position:0%
+inverse transform
+right so here's just an example so if
+
+ align:start position:0%
+right so here's just an example so if
+ 
+
+ align:start position:0%
+right so here's just an example so if
+you only take it every 30 degrees you
+
+ align:start position:0%
+you only take it every 30 degrees you
+ 
+
+ align:start position:0%
+you only take it every 30 degrees you
+can see verse 5 versus one degree
+
+ align:start position:0%
+can see verse 5 versus one degree
+ 
+
+ align:start position:0%
+can see verse 5 versus one degree
+there's a there's a huge difference in
+
+ align:start position:0%
+there's a there's a huge difference in
+ 
+
+ align:start position:0%
+there's a there's a huge difference in
+the density of angular sampling but then
+
+ align:start position:0%
+the density of angular sampling but then
+ 
+
+ align:start position:0%
+the density of angular sampling but then
+come back
+
+ align:start position:0%
+come back
+ 
+
+ align:start position:0%
+come back
+we have this problem where we get this
+
+ align:start position:0%
+we have this problem where we get this
+ 
+
+ align:start position:0%
+we have this problem where we get this
+hot spot in the center and so if you
+
+ align:start position:0%
+hot spot in the center and so if you
+ 
+
+ align:start position:0%
+hot spot in the center and so if you
+look at this it sort of goes as the
+
+ align:start position:0%
+look at this it sort of goes as the
+ 
+
+ align:start position:0%
+look at this it sort of goes as the
+inverse of the radial frequency
+
+ align:start position:0%
+inverse of the radial frequency
+ 
+
+ align:start position:0%
+inverse of the radial frequency
+right so as i go up higher in radial
+
+ align:start position:0%
+right so as i go up higher in radial
+ 
+
+ align:start position:0%
+right so as i go up higher in radial
+frequency i don't have this problem as
+
+ align:start position:0%
+frequency i don't have this problem as
+ 
+
+ align:start position:0%
+frequency i don't have this problem as
+much and so the solution it's up here
+
+ align:start position:0%
+much and so the solution it's up here
+ 
+
+ align:start position:0%
+much and so the solution it's up here
+but does anyone want to tell me what the
+
+ align:start position:0%
+but does anyone want to tell me what the
+ 
+
+ align:start position:0%
+but does anyone want to tell me what the
+solution is
+
+ align:start position:0%
+solution is
+ 
+
+ align:start position:0%
+solution is
+to solve the hot spot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiply by the inverse right so that
+
+ align:start position:0%
+multiply by the inverse right so that
+ 
+
+ align:start position:0%
+multiply by the inverse right so that
+inverse is sort of interesting this so
+
+ align:start position:0%
+inverse is sort of interesting this so
+ 
+
+ align:start position:0%
+inverse is sort of interesting this so
+the direct inverse of this function is
+
+ align:start position:0%
+the direct inverse of this function is
+ 
+
+ align:start position:0%
+the direct inverse of this function is
+simply
+
+ align:start position:0%
+simply
+ 
+
+ align:start position:0%
+simply
+omega itself absolute value of omega so
+
+ align:start position:0%
+omega itself absolute value of omega so
+ 
+
+ align:start position:0%
+omega itself absolute value of omega so
+as a frequency domain filter it's simply
+
+ align:start position:0%
+as a frequency domain filter it's simply
+ 
+
+ align:start position:0%
+as a frequency domain filter it's simply
+saying multiply by a gain which is
+
+ align:start position:0%
+saying multiply by a gain which is
+ 
+
+ align:start position:0%
+saying multiply by a gain which is
+proportional to your radius away from
+
+ align:start position:0%
+proportional to your radius away from
+ 
+
+ align:start position:0%
+proportional to your radius away from
+the center of the image
+
+ align:start position:0%
+the center of the image
+ 
+
+ align:start position:0%
+the center of the image
+right so what kind of filter is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high pass filter right so the algorithm
+
+ align:start position:0%
+high pass filter right so the algorithm
+ 
+
+ align:start position:0%
+high pass filter right so the algorithm
+is telling us so we're multiplying by
+
+ align:start position:0%
+is telling us so we're multiplying by
+ 
+
+ align:start position:0%
+is telling us so we're multiplying by
+this high pass filter which means what
+
+ align:start position:0%
+this high pass filter which means what
+ 
+
+ align:start position:0%
+this high pass filter which means what
+we're doing in the primary domain is
+
+ align:start position:0%
+we're doing in the primary domain is
+ 
+
+ align:start position:0%
+we're doing in the primary domain is
+we're sharpening does that make sense
+
+ align:start position:0%
+we're sharpening does that make sense
+ 
+
+ align:start position:0%
+we're sharpening does that make sense
+we're convolving with a sharpening
+
+ align:start position:0%
+we're convolving with a sharpening
+ 
+
+ align:start position:0%
+we're convolving with a sharpening
+filter
+
+ align:start position:0%
+filter
+ 
+
+ align:start position:0%
+filter
+and so that adds some other problems is
+
+ align:start position:0%
+and so that adds some other problems is
+ 
+
+ align:start position:0%
+and so that adds some other problems is
+basically this is this filter amplifies
+
+ align:start position:0%
+basically this is this filter amplifies
+ 
+
+ align:start position:0%
+basically this is this filter amplifies
+high frequency noise
+
+ align:start position:0%
+high frequency noise
+ 
+
+ align:start position:0%
+high frequency noise
+right so in general in ct scanning in
+
+ align:start position:0%
+right so in general in ct scanning in
+ 
+
+ align:start position:0%
+right so in general in ct scanning in
+the 80s and 70s basically they examined
+
+ align:start position:0%
+the 80s and 70s basically they examined
+ 
+
+ align:start position:0%
+the 80s and 70s basically they examined
+you're sort of appetizing this filter
+
+ align:start position:0%
+you're sort of appetizing this filter
+ 
+
+ align:start position:0%
+you're sort of appetizing this filter
+having it trail off
+
+ align:start position:0%
+having it trail off
+ 
+
+ align:start position:0%
+having it trail off
+at some frequency so you don't
+
+ align:start position:0%
+at some frequency so you don't
+ 
+
+ align:start position:0%
+at some frequency so you don't
+arbitrarily amplify high frequencies so
+
+ align:start position:0%
+arbitrarily amplify high frequencies so
+ 
+
+ align:start position:0%
+arbitrarily amplify high frequencies so
+again you can sort of just this is again
+
+ align:start position:0%
+again you can sort of just this is again
+ 
+
+ align:start position:0%
+again you can sort of just this is again
+all this is the textbook solution but it
+
+ align:start position:0%
+all this is the textbook solution but it
+ 
+
+ align:start position:0%
+all this is the textbook solution but it
+sort of contains all of the ideas of ct
+
+ align:start position:0%
+sort of contains all of the ideas of ct
+ 
+
+ align:start position:0%
+sort of contains all of the ideas of ct
+and certainly how they apply to light
+
+ align:start position:0%
+and certainly how they apply to light
+ 
+
+ align:start position:0%
+and certainly how they apply to light
+fields all of these ideas are there as
+
+ align:start position:0%
+fields all of these ideas are there as
+ 
+
+ align:start position:0%
+fields all of these ideas are there as
+well in light field
+
+ align:start position:0%
+well in light field
+ 
+
+ align:start position:0%
+well in light field
+refocusing you need to have these
+
+ align:start position:0%
+refocusing you need to have these
+ 
+
+ align:start position:0%
+refocusing you need to have these
+filters to represent prevent aliasing
+
+ align:start position:0%
+filters to represent prevent aliasing
+ 
+
+ align:start position:0%
+filters to represent prevent aliasing
+right it might feel refocusing you have
+
+ align:start position:0%
+right it might feel refocusing you have
+ 
+
+ align:start position:0%
+right it might feel refocusing you have
+a baseline to sample your light field
+
+ align:start position:0%
+a baseline to sample your light field
+ 
+
+ align:start position:0%
+a baseline to sample your light field
+etc so uh for those of you working on
+
+ align:start position:0%
+etc so uh for those of you working on
+ 
+
+ align:start position:0%
+etc so uh for those of you working on
+final projects you should really try to
+
+ align:start position:0%
+final projects you should really try to
+ 
+
+ align:start position:0%
+final projects you should really try to
+think about the connection to tomography
+
+ align:start position:0%
+think about the connection to tomography
+ 
+
+ align:start position:0%
+think about the connection to tomography
+we're going to talk about the
+
+ align:start position:0%
+we're going to talk about the
+ 
+
+ align:start position:0%
+we're going to talk about the
+teeth oh yeah sorry uh yeah i almost
+
+ align:start position:0%
+teeth oh yeah sorry uh yeah i almost
+ 
+
+ align:start position:0%
+teeth oh yeah sorry uh yeah i almost
+missed that so this is another
+
+ align:start position:0%
+missed that so this is another
+ 
+
+ align:start position:0%
+missed that so this is another
+so the whole assumption that we made at
+
+ align:start position:0%
+so the whole assumption that we made at
+ 
+
+ align:start position:0%
+so the whole assumption that we made at
+the very beginning is that we could find
+
+ align:start position:0%
+the very beginning is that we could find
+ 
+
+ align:start position:0%
+the very beginning is that we could find
+some wavelength of light
+
+ align:start position:0%
+some wavelength of light
+ 
+
+ align:start position:0%
+some wavelength of light
+or electromagnetic radiation that
+
+ align:start position:0%
+or electromagnetic radiation that
+ 
+
+ align:start position:0%
+or electromagnetic radiation that
+travels on a ballistic trajectory
+
+ align:start position:0%
+travels on a ballistic trajectory
+ 
+
+ align:start position:0%
+travels on a ballistic trajectory
+through our object right so our object
+
+ align:start position:0%
+through our object right so our object
+ 
+
+ align:start position:0%
+through our object right so our object
+becomes semi-transparent and simply
+
+ align:start position:0%
+becomes semi-transparent and simply
+ 
+
+ align:start position:0%
+becomes semi-transparent and simply
+absorbs but that's not true for the
+
+ align:start position:0%
+absorbs but that's not true for the
+ 
+
+ align:start position:0%
+absorbs but that's not true for the
+human body for the most part it inside
+
+ align:start position:0%
+human body for the most part it inside
+ 
+
+ align:start position:0%
+human body for the most part it inside
+bone skin
+
+ align:start position:0%
+bone skin
+ 
+
+ align:start position:0%
+bone skin
+and and in various cells that's for the
+
+ align:start position:0%
+and and in various cells that's for the
+ 
+
+ align:start position:0%
+and and in various cells that's for the
+most part true that x-rays travel on a
+
+ align:start position:0%
+most part true that x-rays travel on a
+ 
+
+ align:start position:0%
+most part true that x-rays travel on a
+ballistic trajectory there is some
+
+ align:start position:0%
+ballistic trajectory there is some
+ 
+
+ align:start position:0%
+ballistic trajectory there is some
+scattering for bone you need to handle
+
+ align:start position:0%
+scattering for bone you need to handle
+ 
+
+ align:start position:0%
+scattering for bone you need to handle
+but can anyone guess what these are here
+
+ align:start position:0%
+but can anyone guess what these are here
+ 
+
+ align:start position:0%
+but can anyone guess what these are here
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so the problem with fillings is they're
+
+ align:start position:0%
+so the problem with fillings is they're
+ 
+
+ align:start position:0%
+so the problem with fillings is they're
+metal
+
+ align:start position:0%
+metal
+ 
+
+ align:start position:0%
+metal
+and so they for the most part scatter
+
+ align:start position:0%
+and so they for the most part scatter
+ 
+
+ align:start position:0%
+and so they for the most part scatter
+and absorb x-rays
+
+ align:start position:0%
+and absorb x-rays
+ 
+
+ align:start position:0%
+and absorb x-rays
+and so you'll see we get these artifacts
+
+ align:start position:0%
+and so you'll see we get these artifacts
+ 
+
+ align:start position:0%
+and so you'll see we get these artifacts
+where essentially we have missing data
+
+ align:start position:0%
+where essentially we have missing data
+ 
+
+ align:start position:0%
+where essentially we have missing data
+and so when we reconstruct we get these
+
+ align:start position:0%
+and so when we reconstruct we get these
+ 
+
+ align:start position:0%
+and so when we reconstruct we get these
+halos around the object
+
+ align:start position:0%
+halos around the object
+ 
+
+ align:start position:0%
+halos around the object
+and so yeah i think they're called
+
+ align:start position:0%
+and so yeah i think they're called
+ 
+
+ align:start position:0%
+and so yeah i think they're called
+starbursts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you get these starbursts which
+
+ align:start position:0%
+okay so you get these starbursts which
+ 
+
+ align:start position:0%
+okay so you get these starbursts which
+have to do with your number of samples
+
+ align:start position:0%
+have to do with your number of samples
+ 
+
+ align:start position:0%
+have to do with your number of samples
+you took because you can see the
+
+ align:start position:0%
+you took because you can see the
+ 
+
+ align:start position:0%
+you took because you can see the
+starburst pattern like in the 30 degree
+
+ align:start position:0%
+starburst pattern like in the 30 degree
+ 
+
+ align:start position:0%
+starburst pattern like in the 30 degree
+if you have limited angle you can
+
+ align:start position:0%
+if you have limited angle you can
+ 
+
+ align:start position:0%
+if you have limited angle you can
+actually get starburst patterns you can
+
+ align:start position:0%
+actually get starburst patterns you can
+ 
+
+ align:start position:0%
+actually get starburst patterns you can
+see it also in that one on the left
+
+ align:start position:0%
+see it also in that one on the left
+ 
+
+ align:start position:0%
+see it also in that one on the left
+and so then the question is
+
+ align:start position:0%
+and so then the question is
+ 
+
+ align:start position:0%
+and so then the question is
+how do you handle these occlusion
+
+ align:start position:0%
+how do you handle these occlusion
+ 
+
+ align:start position:0%
+how do you handle these occlusion
+functions and there are some simple and
+
+ align:start position:0%
+functions and there are some simple and
+ 
+
+ align:start position:0%
+functions and there are some simple and
+more complicated methods to handle this
+
+ align:start position:0%
+more complicated methods to handle this
+ 
+
+ align:start position:0%
+more complicated methods to handle this
+but modern ct scanners for the most part
+
+ align:start position:0%
+but modern ct scanners for the most part
+ 
+
+ align:start position:0%
+but modern ct scanners for the most part
+can now scan fillings using
+
+ align:start position:0%
+can now scan fillings using
+ 
+
+ align:start position:0%
+can now scan fillings using
+relatively simple algorithms
+
+ align:start position:0%
+relatively simple algorithms
+ 
+
+ align:start position:0%
+relatively simple algorithms
+and so now
+
+ align:start position:0%
+and so now
+ 
+
+ align:start position:0%
+and so now
+putting all this together we solved the
+
+ align:start position:0%
+putting all this together we solved the
+ 
+
+ align:start position:0%
+putting all this together we solved the
+problem in flatland so now we can build
+
+ align:start position:0%
+problem in flatland so now we can build
+ 
+
+ align:start position:0%
+problem in flatland so now we can build
+a ct scanner to do the volumetric
+
+ align:start position:0%
+a ct scanner to do the volumetric
+ 
+
+ align:start position:0%
+a ct scanner to do the volumetric
+scanning task it's very simple we're
+
+ align:start position:0%
+scanning task it's very simple we're
+ 
+
+ align:start position:0%
+scanning task it's very simple we're
+just going to solve the problem
+
+ align:start position:0%
+just going to solve the problem
+ 
+
+ align:start position:0%
+just going to solve the problem
+repeatedly in two dimensions and so how
+
+ align:start position:0%
+repeatedly in two dimensions and so how
+ 
+
+ align:start position:0%
+repeatedly in two dimensions and so how
+many here have had a ct scan anyone no
+
+ align:start position:0%
+many here have had a ct scan anyone no
+ 
+
+ align:start position:0%
+many here have had a ct scan anyone no
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+right the older ones of us have had cc
+
+ align:start position:0%
+right the older ones of us have had cc
+ 
+
+ align:start position:0%
+right the older ones of us have had cc
+scans i guess
+
+ align:start position:0%
+scans i guess
+ 
+
+ align:start position:0%
+scans i guess
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+so this i think this is great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you go to youtube this is a ct
+
+ align:start position:0%
+so if you go to youtube this is a ct
+ 
+
+ align:start position:0%
+so if you go to youtube this is a ct
+scanner opened up so
+
+ align:start position:0%
+scanner opened up so
+ 
+
+ align:start position:0%
+scanner opened up so
+maybe i should stop it and go back to
+
+ align:start position:0%
+maybe i should stop it and go back to
+ 
+
+ align:start position:0%
+maybe i should stop it and go back to
+the beginning just to explain what
+
+ align:start position:0%
+the beginning just to explain what
+ 
+
+ align:start position:0%
+the beginning just to explain what
+you're seeing
+
+ align:start position:0%
+you're seeing
+ 
+
+ align:start position:0%
+you're seeing
+here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+we'll see
+
+ align:start position:0%
+we'll see
+ 
+
+ align:start position:0%
+we'll see
+yeah the audio is very important so uh
+
+ align:start position:0%
+yeah the audio is very important so uh
+ 
+
+ align:start position:0%
+yeah the audio is very important so uh
+the radiologists at the hospital have to
+
+ align:start position:0%
+the radiologists at the hospital have to
+ 
+
+ align:start position:0%
+the radiologists at the hospital have to
+take apprentice ct scanner periodically
+
+ align:start position:0%
+take apprentice ct scanner periodically
+ 
+
+ align:start position:0%
+take apprentice ct scanner periodically
+and inspect it for damage because it's
+
+ align:start position:0%
+and inspect it for damage because it's
+ 
+
+ align:start position:0%
+and inspect it for damage because it's
+essentially a high quality motor like a
+
+ align:start position:0%
+essentially a high quality motor like a
+ 
+
+ align:start position:0%
+essentially a high quality motor like a
+jet engine so you'll see in a minute why
+
+ align:start position:0%
+jet engine so you'll see in a minute why
+ 
+
+ align:start position:0%
+jet engine so you'll see in a minute why
+why general electric and other
+
+ align:start position:0%
+why general electric and other
+ 
+
+ align:start position:0%
+why general electric and other
+industrial you know jet engine
+
+ align:start position:0%
+industrial you know jet engine
+ 
+
+ align:start position:0%
+industrial you know jet engine
+manufacturers make ct scanners but this
+
+ align:start position:0%
+manufacturers make ct scanners but this
+ 
+
+ align:start position:0%
+manufacturers make ct scanners but this
+this is a ct scanner with the cover
+
+ align:start position:0%
+this is a ct scanner with the cover
+ 
+
+ align:start position:0%
+this is a ct scanner with the cover
+removed and so basically the patient
+
+ align:start position:0%
+removed and so basically the patient
+ 
+
+ align:start position:0%
+removed and so basically the patient
+lays on this gurney and they're slowly
+
+ align:start position:0%
+lays on this gurney and they're slowly
+ 
+
+ align:start position:0%
+lays on this gurney and they're slowly
+translated through this doughnut
+
+ align:start position:0%
+translated through this doughnut
+ 
+
+ align:start position:0%
+translated through this doughnut
+right and so you'll see here this is the
+
+ align:start position:0%
+right and so you'll see here this is the
+ 
+
+ align:start position:0%
+right and so you'll see here this is the
+x it's a little blurry and still but you
+
+ align:start position:0%
+x it's a little blurry and still but you
+ 
+
+ align:start position:0%
+x it's a little blurry and still but you
+can see this is the x-ray source it's a
+
+ align:start position:0%
+can see this is the x-ray source it's a
+ 
+
+ align:start position:0%
+can see this is the x-ray source it's a
+point source this is a fan beam
+
+ align:start position:0%
+point source this is a fan beam
+ 
+
+ align:start position:0%
+point source this is a fan beam
+projection and over here with a bunch of
+
+ align:start position:0%
+projection and over here with a bunch of
+ 
+
+ align:start position:0%
+projection and over here with a bunch of
+fans on top of it are the x-ray
+
+ align:start position:0%
+fans on top of it are the x-ray
+ 
+
+ align:start position:0%
+fans on top of it are the x-ray
+detectors because they generate a lot of
+
+ align:start position:0%
+detectors because they generate a lot of
+ 
+
+ align:start position:0%
+detectors because they generate a lot of
+heat and so basically this thing will
+
+ align:start position:0%
+heat and so basically this thing will
+ 
+
+ align:start position:0%
+heat and so basically this thing will
+rotate around the patient as the patient
+
+ align:start position:0%
+rotate around the patient as the patient
+ 
+
+ align:start position:0%
+rotate around the patient as the patient
+translates slowly so the so in the frame
+
+ align:start position:0%
+translates slowly so the so in the frame
+ 
+
+ align:start position:0%
+translates slowly so the so in the frame
+of the patient the x-ray source will
+
+ align:start position:0%
+of the patient the x-ray source will
+ 
+
+ align:start position:0%
+of the patient the x-ray source will
+move on this helix
+
+ align:start position:0%
+move on this helix
+ 
+
+ align:start position:0%
+move on this helix
+right and at each orientation it will
+
+ align:start position:0%
+right and at each orientation it will
+ 
+
+ align:start position:0%
+right and at each orientation it will
+take a fan beam projection and you can
+
+ align:start position:0%
+take a fan beam projection and you can
+ 
+
+ align:start position:0%
+take a fan beam projection and you can
+re-sample that data
+
+ align:start position:0%
+re-sample that data
+ 
+
+ align:start position:0%
+re-sample that data
+if you have a dense enough helix to be
+
+ align:start position:0%
+if you have a dense enough helix to be
+ 
+
+ align:start position:0%
+if you have a dense enough helix to be
+just a set of pair of parallel beam
+
+ align:start position:0%
+just a set of pair of parallel beam
+ 
+
+ align:start position:0%
+just a set of pair of parallel beam
+projections which you then each of those
+
+ align:start position:0%
+projections which you then each of those
+ 
+
+ align:start position:0%
+projections which you then each of those
+independently apply the inverse radon
+
+ align:start position:0%
+independently apply the inverse radon
+ 
+
+ align:start position:0%
+independently apply the inverse radon
+transform that's not exactly what they
+
+ align:start position:0%
+transform that's not exactly what they
+ 
+
+ align:start position:0%
+transform that's not exactly what they
+do but if you were to implement this in
+
+ align:start position:0%
+do but if you were to implement this in
+ 
+
+ align:start position:0%
+do but if you were to implement this in
+matlab that would be basically good
+
+ align:start position:0%
+matlab that would be basically good
+ 
+
+ align:start position:0%
+matlab that would be basically good
+enough and so then you'll get a series
+
+ align:start position:0%
+enough and so then you'll get a series
+ 
+
+ align:start position:0%
+enough and so then you'll get a series
+of cross-sectional images
+
+ align:start position:0%
+of cross-sectional images
+ 
+
+ align:start position:0%
+of cross-sectional images
+then you can simply do segmentation and
+
+ align:start position:0%
+then you can simply do segmentation and
+ 
+
+ align:start position:0%
+then you can simply do segmentation and
+thresholding for instance high density
+
+ align:start position:0%
+thresholding for instance high density
+ 
+
+ align:start position:0%
+thresholding for instance high density
+regions correspond to bone
+
+ align:start position:0%
+regions correspond to bone
+ 
+
+ align:start position:0%
+regions correspond to bone
+other properties correspond to blood
+
+ align:start position:0%
+other properties correspond to blood
+ 
+
+ align:start position:0%
+other properties correspond to blood
+vessel networks so that's the basics of
+
+ align:start position:0%
+vessel networks so that's the basics of
+ 
+
+ align:start position:0%
+vessel networks so that's the basics of
+the ct scanner but i think it's so the
+
+ align:start position:0%
+the ct scanner but i think it's so the
+ 
+
+ align:start position:0%
+the ct scanner but i think it's so the
+see the the radiologists and the techs
+
+ align:start position:0%
+see the the radiologists and the techs
+ 
+
+ align:start position:0%
+see the the radiologists and the techs
+often have to take this apart to inspect
+
+ align:start position:0%
+often have to take this apart to inspect
+ 
+
+ align:start position:0%
+often have to take this apart to inspect
+it and so you'll notice uh this thing is
+
+ align:start position:0%
+it and so you'll notice uh this thing is
+ 
+
+ align:start position:0%
+it and so you'll notice uh this thing is
+quite scary with the cover off
+
+ align:start position:0%
+quite scary with the cover off
+ 
+
+ align:start position:0%
+quite scary with the cover off
+and you can listen to what the
+
+ align:start position:0%
+and you can listen to what the
+ 
+
+ align:start position:0%
+and you can listen to what the
+radiologists are saying as they're
+
+ align:start position:0%
+radiologists are saying as they're
+ 
+
+ align:start position:0%
+radiologists are saying as they're
+inspecting this
+
+ align:start position:0%
+inspecting this
+ 
+
+ align:start position:0%
+inspecting this
+so again it spins up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you ever get a ct scan that's
+
+ align:start position:0%
+so if you ever get a ct scan that's
+ 
+
+ align:start position:0%
+so if you ever get a ct scan that's
+what's happening but of course the
+
+ align:start position:0%
+what's happening but of course the
+ 
+
+ align:start position:0%
+what's happening but of course the
+safest place to be is inside the donut
+
+ align:start position:0%
+safest place to be is inside the donut
+ 
+
+ align:start position:0%
+safest place to be is inside the donut
+outside is the problem inside the room
+
+ align:start position:0%
+outside is the problem inside the room
+ 
+
+ align:start position:0%
+outside is the problem inside the room
+outside the room is a better place but
+
+ align:start position:0%
+outside the room is a better place but
+ 
+
+ align:start position:0%
+outside the room is a better place but
+you can see that there's a lot of
+
+ align:start position:0%
+you can see that there's a lot of
+ 
+
+ align:start position:0%
+you can see that there's a lot of
+problems i have to solve mechanical so
+
+ align:start position:0%
+problems i have to solve mechanical so
+ 
+
+ align:start position:0%
+problems i have to solve mechanical so
+they have sort of like a hard drive they
+
+ align:start position:0%
+they have sort of like a hard drive they
+ 
+
+ align:start position:0%
+they have sort of like a hard drive they
+have optical encoders here to track
+
+ align:start position:0%
+have optical encoders here to track
+ 
+
+ align:start position:0%
+have optical encoders here to track
+their rotational velocity and then they
+
+ align:start position:0%
+their rotational velocity and then they
+ 
+
+ align:start position:0%
+their rotational velocity and then they
+have what's known as slip rings because
+
+ align:start position:0%
+have what's known as slip rings because
+ 
+
+ align:start position:0%
+have what's known as slip rings because
+basically one of the evolutions believe
+
+ align:start position:0%
+basically one of the evolutions believe
+ 
+
+ align:start position:0%
+basically one of the evolutions believe
+it or not was just getting the data off
+
+ align:start position:0%
+it or not was just getting the data off
+ 
+
+ align:start position:0%
+it or not was just getting the data off
+these detectors and so they actually the
+
+ align:start position:0%
+these detectors and so they actually the
+ 
+
+ align:start position:0%
+these detectors and so they actually the
+bearings are used as a circuit to just
+
+ align:start position:0%
+bearings are used as a circuit to just
+ 
+
+ align:start position:0%
+bearings are used as a circuit to just
+transmit data across the bearings and
+
+ align:start position:0%
+transmit data across the bearings and
+ 
+
+ align:start position:0%
+transmit data across the bearings and
+believe it or not that was a big insight
+
+ align:start position:0%
+believe it or not that was a big insight
+ 
+
+ align:start position:0%
+believe it or not that was a big insight
+and a huge patent and before they they
+
+ align:start position:0%
+and a huge patent and before they they
+ 
+
+ align:start position:0%
+and a huge patent and before they they
+actually could only rotate once and the
+
+ align:start position:0%
+actually could only rotate once and the
+ 
+
+ align:start position:0%
+actually could only rotate once and the
+wires would get tangled up
+
+ align:start position:0%
+wires would get tangled up
+ 
+
+ align:start position:0%
+wires would get tangled up
+so having the slip ring bearing transfer
+
+ align:start position:0%
+so having the slip ring bearing transfer
+ 
+
+ align:start position:0%
+so having the slip ring bearing transfer
+mechanism was the big evolution that
+
+ align:start position:0%
+mechanism was the big evolution that
+ 
+
+ align:start position:0%
+mechanism was the big evolution that
+made million dollar ct scanners possible
+
+ align:start position:0%
+made million dollar ct scanners possible
+ 
+
+ align:start position:0%
+made million dollar ct scanners possible
+and so most of these cost a million
+
+ align:start position:0%
+and so most of these cost a million
+ 
+
+ align:start position:0%
+and so most of these cost a million
+dollars and as you're watching this
+
+ align:start position:0%
+dollars and as you're watching this
+ 
+
+ align:start position:0%
+dollars and as you're watching this
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just point out again that the story i'm
+
+ align:start position:0%
+just point out again that the story i'm
+ 
+
+ align:start position:0%
+just point out again that the story i'm
+trying to give you is that this very
+
+ align:start position:0%
+trying to give you is that this very
+ 
+
+ align:start position:0%
+trying to give you is that this very
+basic idea of tomography and inverse
+
+ align:start position:0%
+basic idea of tomography and inverse
+ 
+
+ align:start position:0%
+basic idea of tomography and inverse
+radon transform gives you almost all the
+
+ align:start position:0%
+radon transform gives you almost all the
+ 
+
+ align:start position:0%
+radon transform gives you almost all the
+medical scanning devices that we're so
+
+ align:start position:0%
+medical scanning devices that we're so
+ 
+
+ align:start position:0%
+medical scanning devices that we're so
+proud of in the 20th century you know of
+
+ align:start position:0%
+proud of in the 20th century you know of
+ 
+
+ align:start position:0%
+proud of in the 20th century you know of
+course x-rays give you ct if you move to
+
+ align:start position:0%
+course x-rays give you ct if you move to
+ 
+
+ align:start position:0%
+course x-rays give you ct if you move to
+gamma rays you get spect
+
+ align:start position:0%
+gamma rays you get spect
+ 
+
+ align:start position:0%
+gamma rays you get spect
+if you look at positron emission
+
+ align:start position:0%
+if you look at positron emission
+ 
+
+ align:start position:0%
+if you look at positron emission
+tomography it's just a different
+
+ align:start position:0%
+tomography it's just a different
+ 
+
+ align:start position:0%
+tomography it's just a different
+wavelength of light and again if we move
+
+ align:start position:0%
+wavelength of light and again if we move
+ 
+
+ align:start position:0%
+wavelength of light and again if we move
+to ultrasound so we become acoustic
+
+ align:start position:0%
+to ultrasound so we become acoustic
+ 
+
+ align:start position:0%
+to ultrasound so we become acoustic
+that's really when you get into
+
+ align:start position:0%
+that's really when you get into
+ 
+
+ align:start position:0%
+that's really when you get into
+ultrasonography which is a reflection
+
+ align:start position:0%
+ultrasonography which is a reflection
+ 
+
+ align:start position:0%
+ultrasonography which is a reflection
+mode version of this you can reformulate
+
+ align:start position:0%
+mode version of this you can reformulate
+ 
+
+ align:start position:0%
+mode version of this you can reformulate
+all of these equations instead of the
+
+ align:start position:0%
+all of these equations instead of the
+ 
+
+ align:start position:0%
+all of these equations instead of the
+transmission through reflection mode and
+
+ align:start position:0%
+transmission through reflection mode and
+ 
+
+ align:start position:0%
+transmission through reflection mode and
+that's in slightly impact but i actually
+
+ align:start position:0%
+that's in slightly impact but i actually
+ 
+
+ align:start position:0%
+that's in slightly impact but i actually
+won't go into it so the takeaway message
+
+ align:start position:0%
+won't go into it so the takeaway message
+ 
+
+ align:start position:0%
+won't go into it so the takeaway message
+is that choose your wavelength apply
+
+ align:start position:0%
+is that choose your wavelength apply
+ 
+
+ align:start position:0%
+is that choose your wavelength apply
+inverse radon transform and you too can
+
+ align:start position:0%
+inverse radon transform and you too can
+ 
+
+ align:start position:0%
+inverse radon transform and you too can
+can image non-invasively so just as a
+
+ align:start position:0%
+can image non-invasively so just as a
+ 
+
+ align:start position:0%
+can image non-invasively so just as a
+thought experiment can you see a
+
+ align:start position:0%
+thought experiment can you see a
+ 
+
+ align:start position:0%
+thought experiment can you see a
+relationship between this crazy jet
+
+ align:start position:0%
+relationship between this crazy jet
+ 
+
+ align:start position:0%
+relationship between this crazy jet
+engine
+
+ align:start position:0%
+engine
+ 
+
+ align:start position:0%
+engine
+and delightful camera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll come back to it but just keep that
+
+ align:start position:0%
+we'll come back to it but just keep that
+ 
+
+ align:start position:0%
+we'll come back to it but just keep that
+in the back of your mind
+
+ align:start position:0%
+in the back of your mind
+ 
+
+ align:start position:0%
+in the back of your mind
+just take the four transformers so
+
+ align:start position:0%
+just take the four transformers so
+ 
+
+ align:start position:0%
+just take the four transformers so
+that's it that's all there is that is
+
+ align:start position:0%
+that's it that's all there is that is
+ 
+
+ align:start position:0%
+that's it that's all there is that is
+this is it and imagine now the
+
+ align:start position:0%
+this is it and imagine now the
+ 
+
+ align:start position:0%
+this is it and imagine now the
+light-filled camera is compact and
+
+ align:start position:0%
+light-filled camera is compact and
+ 
+
+ align:start position:0%
+light-filled camera is compact and
+something you can carry in your pocket
+
+ align:start position:0%
+something you can carry in your pocket
+ 
+
+ align:start position:0%
+something you can carry in your pocket
+question is
+
+ align:start position:0%
+question is
+ 
+
+ align:start position:0%
+question is
+can you carry the cat scan
+
+ align:start position:0%
+can you carry the cat scan
+ 
+
+ align:start position:0%
+can you carry the cat scan
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+in the future
+
+ align:start position:0%
+in the future
+ 
+
+ align:start position:0%
+in the future
+in your pocket
+
+ align:start position:0%
+in your pocket
+ 
+
+ align:start position:0%
+in your pocket
+right so we'll come back to our meshes
+
+ align:start position:0%
+right so we'll come back to our meshes
+ 
+
+ align:start position:0%
+right so we'll come back to our meshes
+puzzle at the end and see if anyone
+
+ align:start position:0%
+puzzle at the end and see if anyone
+ 
+
+ align:start position:0%
+puzzle at the end and see if anyone
+solved it
+
+ align:start position:0%
+solved it
+ 
+
+ align:start position:0%
+solved it
+so before i go on there's a slide later
+
+ align:start position:0%
+so before i go on there's a slide later
+ 
+
+ align:start position:0%
+so before i go on there's a slide later
+that you explain score i only explained
+
+ align:start position:0%
+that you explain score i only explained
+ 
+
+ align:start position:0%
+that you explain score i only explained
+the frequency domain version of this and
+
+ align:start position:0%
+the frequency domain version of this and
+ 
+
+ align:start position:0%
+the frequency domain version of this and
+so for various reasons if you don't have
+
+ align:start position:0%
+so for various reasons if you don't have
+ 
+
+ align:start position:0%
+so for various reasons if you don't have
+a fast fft
+
+ align:start position:0%
+a fast fft
+ 
+
+ align:start position:0%
+a fast fft
+which you do of course now
+
+ align:start position:0%
+which you do of course now
+ 
+
+ align:start position:0%
+which you do of course now
+there's a purely spatial domain
+
+ align:start position:0%
+there's a purely spatial domain
+ 
+
+ align:start position:0%
+there's a purely spatial domain
+algorithm so remember our algorithm was
+
+ align:start position:0%
+algorithm so remember our algorithm was
+ 
+
+ align:start position:0%
+algorithm so remember our algorithm was
+we take all of these projections take
+
+ align:start position:0%
+we take all of these projections take
+ 
+
+ align:start position:0%
+we take all of these projections take
+their one equation transforms and
+
+ align:start position:0%
+their one equation transforms and
+ 
+
+ align:start position:0%
+their one equation transforms and
+populate
+
+ align:start position:0%
+populate
+ 
+
+ align:start position:0%
+populate
+our four transforming inverse but you
+
+ align:start position:0%
+our four transforming inverse but you
+ 
+
+ align:start position:0%
+our four transforming inverse but you
+can actually do this without ever taking
+
+ align:start position:0%
+can actually do this without ever taking
+ 
+
+ align:start position:0%
+can actually do this without ever taking
+a fourier transform
+
+ align:start position:0%
+a fourier transform
+ 
+
+ align:start position:0%
+a fourier transform
+does anyone see how you do that
+
+ align:start position:0%
+does anyone see how you do that
+ 
+
+ align:start position:0%
+does anyone see how you do that
+there's a purely spatial domain
+
+ align:start position:0%
+there's a purely spatial domain
+ 
+
+ align:start position:0%
+there's a purely spatial domain
+algorithm you get the set of projections
+
+ align:start position:0%
+algorithm you get the set of projections
+ 
+
+ align:start position:0%
+algorithm you get the set of projections
+and you directly reconstruct the density
+
+ align:start position:0%
+and you directly reconstruct the density
+ 
+
+ align:start position:0%
+and you directly reconstruct the density
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+you just accumulate the
+
+ align:start position:0%
+you just accumulate the
+ 
+
+ align:start position:0%
+you just accumulate the
+projections
+
+ align:start position:0%
+projections
+ 
+
+ align:start position:0%
+projections
+how so
+
+ align:start position:0%
+how so
+ 
+
+ align:start position:0%
+how so
+let's go back to our image so you can
+
+ align:start position:0%
+let's go back to our image so you can
+ 
+
+ align:start position:0%
+let's go back to our image so you can
+tell i overused the socratic method but
+
+ align:start position:0%
+tell i overused the socratic method but
+ 
+
+ align:start position:0%
+tell i overused the socratic method but
+i like you guys to figure things out
+
+ align:start position:0%
+i like you guys to figure things out
+ 
+
+ align:start position:0%
+i like you guys to figure things out
+because i know the answer
+
+ align:start position:0%
+because i know the answer
+ 
+
+ align:start position:0%
+because i know the answer
+so so you give this data go for it
+
+ align:start position:0%
+so so you give this data go for it
+ 
+
+ align:start position:0%
+so so you give this data go for it
+transfers now how you can get back to
+
+ align:start position:0%
+transfers now how you can get back to
+ 
+
+ align:start position:0%
+transfers now how you can get back to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+without fourier transform this time
+
+ align:start position:0%
+without fourier transform this time
+ 
+
+ align:start position:0%
+without fourier transform this time
+right this is problem b on the home on
+
+ align:start position:0%
+right this is problem b on the home on
+ 
+
+ align:start position:0%
+right this is problem b on the home on
+the on the on the final part a with the
+
+ align:start position:0%
+the on the on the final part a with the
+ 
+
+ align:start position:0%
+the on the on the final part a with the
+support train so now you're not allowed
+
+ align:start position:0%
+support train so now you're not allowed
+ 
+
+ align:start position:0%
+support train so now you're not allowed
+on the mixture
+
+ align:start position:0%
+on the mixture
+ 
+
+ align:start position:0%
+on the mixture
+okay which is next week there will be a
+
+ align:start position:0%
+okay which is next week there will be a
+ 
+
+ align:start position:0%
+okay which is next week there will be a
+question on tomography so yeah okay okay
+
+ align:start position:0%
+question on tomography so yeah okay okay
+ 
+
+ align:start position:0%
+question on tomography so yeah okay okay
+i'm just kind of like shooting the darts
+
+ align:start position:0%
+i'm just kind of like shooting the darts
+ 
+
+ align:start position:0%
+i'm just kind of like shooting the darts
+that's great but uh i guess they take
+
+ align:start position:0%
+that's great but uh i guess they take
+ 
+
+ align:start position:0%
+that's great but uh i guess they take
+the first round and since that yeah oh
+
+ align:start position:0%
+the first round and since that yeah oh
+ 
+
+ align:start position:0%
+the first round and since that yeah oh
+wait actually rotation is this way so
+
+ align:start position:0%
+wait actually rotation is this way so
+ 
+
+ align:start position:0%
+wait actually rotation is this way so
+take the first row like this first let's
+
+ align:start position:0%
+take the first row like this first let's
+ 
+
+ align:start position:0%
+take the first row like this first let's
+follow
+
+ align:start position:0%
+follow
+ 
+
+ align:start position:0%
+follow
+rower kong what do you want first column
+
+ align:start position:0%
+rower kong what do you want first column
+ 
+
+ align:start position:0%
+rower kong what do you want first column
+is the first photo first column is first
+
+ align:start position:0%
+is the first photo first column is first
+ 
+
+ align:start position:0%
+is the first photo first column is first
+projection oh
+
+ align:start position:0%
+projection oh
+ 
+
+ align:start position:0%
+projection oh
+okay first column okay i got first
+
+ align:start position:0%
+okay first column okay i got first
+ 
+
+ align:start position:0%
+okay first column okay i got first
+column and then i'll basically create
+
+ align:start position:0%
+column and then i'll basically create
+ 
+
+ align:start position:0%
+column and then i'll basically create
+rays they're
+
+ align:start position:0%
+rays they're
+ 
+
+ align:start position:0%
+rays they're
+uh representative of those individual
+
+ align:start position:0%
+uh representative of those individual
+ 
+
+ align:start position:0%
+uh representative of those individual
+measured densities and just
+
+ align:start position:0%
+measured densities and just
+ 
+
+ align:start position:0%
+measured densities and just
+uh shoot them back out okay
+
+ align:start position:0%
+uh shoot them back out okay
+ 
+
+ align:start position:0%
+uh shoot them back out okay
+that's the next column and then i guess
+
+ align:start position:0%
+that's the next column and then i guess
+ 
+
+ align:start position:0%
+that's the next column and then i guess
+it's a different slightly different
+
+ align:start position:0%
+it's a different slightly different
+ 
+
+ align:start position:0%
+it's a different slightly different
+angle so i'll do just shoot them back so
+
+ align:start position:0%
+angle so i'll do just shoot them back so
+ 
+
+ align:start position:0%
+angle so i'll do just shoot them back so
+so you're okay so just you're going to
+
+ align:start position:0%
+so you're okay so just you're going to
+ 
+
+ align:start position:0%
+so you're okay so just you're going to
+start with an accumulator again that's
+
+ align:start position:0%
+start with an accumulator again that's
+ 
+
+ align:start position:0%
+start with an accumulator again that's
+all zeros that's your initial estimate
+
+ align:start position:0%
+all zeros that's your initial estimate
+ 
+
+ align:start position:0%
+all zeros that's your initial estimate
+i'm going to take one line of that and
+
+ align:start position:0%
+i'm going to take one line of that and
+ 
+
+ align:start position:0%
+i'm going to take one line of that and
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+uh just fill the entire thing
+
+ align:start position:0%
+uh just fill the entire thing
+ 
+
+ align:start position:0%
+uh just fill the entire thing
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+that so we're gonna take that value and
+
+ align:start position:0%
+that so we're gonna take that value and
+ 
+
+ align:start position:0%
+that so we're gonna take that value and
+just replicate it basically okay and
+
+ align:start position:0%
+just replicate it basically okay and
+ 
+
+ align:start position:0%
+just replicate it basically okay and
+then i'll do that for the second one but
+
+ align:start position:0%
+then i'll do that for the second one but
+ 
+
+ align:start position:0%
+then i'll do that for the second one but
+at an angle okay and i'll normalize it
+
+ align:start position:0%
+at an angle okay and i'll normalize it
+ 
+
+ align:start position:0%
+at an angle okay and i'll normalize it
+yep hopefully i'll get something that
+
+ align:start position:0%
+yep hopefully i'll get something that
+ 
+
+ align:start position:0%
+yep hopefully i'll get something that
+looks like a skull okay that is the
+
+ align:start position:0%
+looks like a skull okay that is the
+ 
+
+ align:start position:0%
+looks like a skull okay that is the
+algorithm it's called filtered back
+
+ align:start position:0%
+algorithm it's called filtered back
+ 
+
+ align:start position:0%
+algorithm it's called filtered back
+projection can you prove why it's
+
+ align:start position:0%
+projection can you prove why it's
+ 
+
+ align:start position:0%
+projection can you prove why it's
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+so so does it does that does everyone
+
+ align:start position:0%
+so so does it does that does everyone
+ 
+
+ align:start position:0%
+so so does it does that does everyone
+understand why that would work even
+
+ align:start position:0%
+understand why that would work even
+ 
+
+ align:start position:0%
+understand why that would work even
+intuitively like imagine
+
+ align:start position:0%
+intuitively like imagine
+ 
+
+ align:start position:0%
+intuitively like imagine
+let's go back to intuition works pretty
+
+ align:start position:0%
+let's go back to intuition works pretty
+ 
+
+ align:start position:0%
+let's go back to intuition works pretty
+well here imagine i just had a big
+
+ align:start position:0%
+well here imagine i just had a big
+ 
+
+ align:start position:0%
+well here imagine i just had a big
+circle here it's it's absorbing 50 it's
+
+ align:start position:0%
+circle here it's it's absorbing 50 it's
+ 
+
+ align:start position:0%
+circle here it's it's absorbing 50 it's
+just a circle right so what about what
+
+ align:start position:0%
+just a circle right so what about what
+ 
+
+ align:start position:0%
+just a circle right so what about what
+i'll see here will just be a big
+
+ align:start position:0%
+i'll see here will just be a big
+ 
+
+ align:start position:0%
+i'll see here will just be a big
+rectangle right
+
+ align:start position:0%
+rectangle right
+ 
+
+ align:start position:0%
+rectangle right
+right i'll just have at some value
+
+ align:start position:0%
+right i'll just have at some value
+ 
+
+ align:start position:0%
+right i'll just have at some value
+it'll be one everywhere in 50 everywhere
+
+ align:start position:0%
+it'll be one everywhere in 50 everywhere
+ 
+
+ align:start position:0%
+it'll be one everywhere in 50 everywhere
+inside and 0 outside right
+
+ align:start position:0%
+inside and 0 outside right
+ 
+
+ align:start position:0%
+inside and 0 outside right
+so if i use kevin's algorithm
+
+ align:start position:0%
+so if i use kevin's algorithm
+ 
+
+ align:start position:0%
+so if i use kevin's algorithm
+first my accumulator will be all
+
+ align:start position:0%
+first my accumulator will be all
+ 
+
+ align:start position:0%
+first my accumulator will be all
+all everything in here will be 50 then
+
+ align:start position:0%
+all everything in here will be 50 then
+ 
+
+ align:start position:0%
+all everything in here will be 50 then
+i'll turn and the center will start
+
+ align:start position:0%
+i'll turn and the center will start
+ 
+
+ align:start position:0%
+i'll turn and the center will start
+getting higher
+
+ align:start position:0%
+getting higher
+ 
+
+ align:start position:0%
+getting higher
+right so i'll get that starburst pattern
+
+ align:start position:0%
+right so i'll get that starburst pattern
+ 
+
+ align:start position:0%
+right so i'll get that starburst pattern
+we saw earlier so intuitively it works
+
+ align:start position:0%
+we saw earlier so intuitively it works
+ 
+
+ align:start position:0%
+we saw earlier so intuitively it works
+but mathematically why does it work and
+
+ align:start position:0%
+but mathematically why does it work and
+ 
+
+ align:start position:0%
+but mathematically why does it work and
+i think again now you can use the foil
+
+ align:start position:0%
+i think again now you can use the foil
+ 
+
+ align:start position:0%
+i think again now you can use the foil
+transform it's easy to see
+
+ align:start position:0%
+transform it's easy to see
+ 
+
+ align:start position:0%
+transform it's easy to see
+for those of you familiar with the foil
+
+ align:start position:0%
+for those of you familiar with the foil
+ 
+
+ align:start position:0%
+for those of you familiar with the foil
+transform it's pretty direct let's go
+
+ align:start position:0%
+transform it's pretty direct let's go
+ 
+
+ align:start position:0%
+transform it's pretty direct let's go
+back to uh
+
+ align:start position:0%
+back to uh
+ 
+
+ align:start position:0%
+back to uh
+okay so anytime you have a foia domain
+
+ align:start position:0%
+okay so anytime you have a foia domain
+ 
+
+ align:start position:0%
+okay so anytime you have a foia domain
+problem you always use the same tricks
+
+ align:start position:0%
+problem you always use the same tricks
+ 
+
+ align:start position:0%
+problem you always use the same tricks
+take slices or or use four transform
+
+ align:start position:0%
+take slices or or use four transform
+ 
+
+ align:start position:0%
+take slices or or use four transform
+pairs right and so
+
+ align:start position:0%
+pairs right and so
+ 
+
+ align:start position:0%
+pairs right and so
+so we know that the slice here
+
+ align:start position:0%
+so we know that the slice here
+ 
+
+ align:start position:0%
+so we know that the slice here
+is equivalent to the projection right
+
+ align:start position:0%
+is equivalent to the projection right
+ 
+
+ align:start position:0%
+is equivalent to the projection right
+so if i had some slice some function
+
+ align:start position:0%
+so if i had some slice some function
+ 
+
+ align:start position:0%
+so if i had some slice some function
+again the slice being this value
+
+ align:start position:0%
+again the slice being this value
+ 
+
+ align:start position:0%
+again the slice being this value
+and i'd take its inverse 2d transform of
+
+ align:start position:0%
+and i'd take its inverse 2d transform of
+ 
+
+ align:start position:0%
+and i'd take its inverse 2d transform of
+just a slice what would i get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the bingo
+
+ align:start position:0%
+the bingo
+ 
+
+ align:start position:0%
+the bingo
+yeah so it's not easy to see but
+
+ align:start position:0%
+yeah so it's not easy to see but
+ 
+
+ align:start position:0%
+yeah so it's not easy to see but
+so give me some yeah so
+
+ align:start position:0%
+so give me some yeah so
+ 
+
+ align:start position:0%
+so give me some yeah so
+so if i just start and i have my
+
+ align:start position:0%
+so if i just start and i have my
+ 
+
+ align:start position:0%
+so if i just start and i have my
+accumulator
+
+ align:start position:0%
+accumulator
+ 
+
+ align:start position:0%
+accumulator
+can everyone hope you can see that i
+
+ align:start position:0%
+can everyone hope you can see that i
+ 
+
+ align:start position:0%
+can everyone hope you can see that i
+have kx i have ky
+
+ align:start position:0%
+have kx i have ky
+ 
+
+ align:start position:0%
+have kx i have ky
+and i have some slice we'll say along x
+
+ align:start position:0%
+and i have some slice we'll say along x
+ 
+
+ align:start position:0%
+and i have some slice we'll say along x
+there's a switch right next to it on the
+
+ align:start position:0%
+there's a switch right next to it on the
+ 
+
+ align:start position:0%
+there's a switch right next to it on the
+right side
+
+ align:start position:0%
+right side
+ 
+
+ align:start position:0%
+right side
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and this function along if i was just
+
+ align:start position:0%
+and this function along if i was just
+ 
+
+ align:start position:0%
+and this function along if i was just
+apply it i'd have kx
+
+ align:start position:0%
+apply it i'd have kx
+ 
+
+ align:start position:0%
+apply it i'd have kx
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+what we call s of
+
+ align:start position:0%
+what we call s of
+ 
+
+ align:start position:0%
+what we call s of
+kx well we'll say it's a continuous
+
+ align:start position:0%
+kx well we'll say it's a continuous
+ 
+
+ align:start position:0%
+kx well we'll say it's a continuous
+function right so i'd have some function
+
+ align:start position:0%
+function right so i'd have some function
+ 
+
+ align:start position:0%
+function right so i'd have some function
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and now what i'm asking is if i take
+
+ align:start position:0%
+and now what i'm asking is if i take
+ 
+
+ align:start position:0%
+and now what i'm asking is if i take
+the inverse
+
+ align:start position:0%
+the inverse
+ 
+
+ align:start position:0%
+the inverse
+y transform
+
+ align:start position:0%
+y transform
+ 
+
+ align:start position:0%
+y transform
+what does this function look like
+
+ align:start position:0%
+what does this function look like
+ 
+
+ align:start position:0%
+what does this function look like
+in the primary domain which is x
+
+ align:start position:0%
+in the primary domain which is x
+ 
+
+ align:start position:0%
+in the primary domain which is x
+and y
+
+ align:start position:0%
+and y
+ 
+
+ align:start position:0%
+and y
+it's constantly one of those little
+
+ align:start position:0%
+it's constantly one of those little
+ 
+
+ align:start position:0%
+it's constantly one of those little
+dimensions of these right because this
+
+ align:start position:0%
+dimensions of these right because this
+ 
+
+ align:start position:0%
+dimensions of these right because this
+guy you can write as some function
+
+ align:start position:0%
+guy you can write as some function
+ 
+
+ align:start position:0%
+guy you can write as some function
+f of kx times a delta function of what
+
+ align:start position:0%
+f of kx times a delta function of what
+ 
+
+ align:start position:0%
+f of kx times a delta function of what
+y right
+
+ align:start position:0%
+y right
+ 
+
+ align:start position:0%
+y right
+and we know that the fourier transform
+
+ align:start position:0%
+and we know that the fourier transform
+ 
+
+ align:start position:0%
+and we know that the fourier transform
+pair of a delta function
+
+ align:start position:0%
+pair of a delta function
+ 
+
+ align:start position:0%
+pair of a delta function
+is this
+
+ align:start position:0%
+is this
+ 
+
+ align:start position:0%
+is this
+is all constant absolutely great
+
+ align:start position:0%
+is all constant absolutely great
+ 
+
+ align:start position:0%
+is all constant absolutely great
+so we get the 1d4 transform
+
+ align:start position:0%
+so we get the 1d4 transform
+ 
+
+ align:start position:0%
+so we get the 1d4 transform
+is this thing and the values are simply
+
+ align:start position:0%
+is this thing and the values are simply
+ 
+
+ align:start position:0%
+is this thing and the values are simply
+the inverse
+
+ align:start position:0%
+the inverse
+ 
+
+ align:start position:0%
+the inverse
+for a transform of the 1d function here
+
+ align:start position:0%
+for a transform of the 1d function here
+ 
+
+ align:start position:0%
+for a transform of the 1d function here
+right so we get you know some different
+
+ align:start position:0%
+right so we get you know some different
+ 
+
+ align:start position:0%
+right so we get you know some different
+values here right
+
+ align:start position:0%
+values here right
+ 
+
+ align:start position:0%
+values here right
+right in the middle and not surprisingly
+
+ align:start position:0%
+right in the middle and not surprisingly
+ 
+
+ align:start position:0%
+right in the middle and not surprisingly
+right so this gets why kevin said
+
+ align:start position:0%
+right so this gets why kevin said
+ 
+
+ align:start position:0%
+right so this gets why kevin said
+he may have already known the algorithm
+
+ align:start position:0%
+he may have already known the algorithm
+ 
+
+ align:start position:0%
+he may have already known the algorithm
+but this is mathematically why we smear
+
+ align:start position:0%
+but this is mathematically why we smear
+ 
+
+ align:start position:0%
+but this is mathematically why we smear
+and now if we rotate
+
+ align:start position:0%
+and now if we rotate
+ 
+
+ align:start position:0%
+and now if we rotate
+we have this one
+
+ align:start position:0%
+we have this one
+ 
+
+ align:start position:0%
+we have this one
+which now comes in as a new smear along
+
+ align:start position:0%
+which now comes in as a new smear along
+ 
+
+ align:start position:0%
+which now comes in as a new smear along
+a new angle
+
+ align:start position:0%
+a new angle
+ 
+
+ align:start position:0%
+a new angle
+i do it the wrong way probably but
+
+ align:start position:0%
+i do it the wrong way probably but
+ 
+
+ align:start position:0%
+i do it the wrong way probably but
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so it's linearity you can write the
+
+ align:start position:0%
+and so it's linearity you can write the
+ 
+
+ align:start position:0%
+and so it's linearity you can write the
+total fourier transform
+
+ align:start position:0%
+total fourier transform
+ 
+
+ align:start position:0%
+total fourier transform
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+of kx ky
+
+ align:start position:0%
+of kx ky
+ 
+
+ align:start position:0%
+of kx ky
+is equal to sum
+
+ align:start position:0%
+is equal to sum
+ 
+
+ align:start position:0%
+is equal to sum
+over all of your angles of this function
+
+ align:start position:0%
+over all of your angles of this function
+ 
+
+ align:start position:0%
+over all of your angles of this function
+f of which we'll just call it the angle
+
+ align:start position:0%
+f of which we'll just call it the angle
+ 
+
+ align:start position:0%
+f of which we'll just call it the angle
+of delta of which is another function of
+
+ align:start position:0%
+of delta of which is another function of
+ 
+
+ align:start position:0%
+of delta of which is another function of
+the angle right
+
+ align:start position:0%
+the angle right
+ 
+
+ align:start position:0%
+the angle right
+and then by linearity of the fourier
+
+ align:start position:0%
+and then by linearity of the fourier
+ 
+
+ align:start position:0%
+and then by linearity of the fourier
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+we come over here we get a sum over
+
+ align:start position:0%
+we come over here we get a sum over
+ 
+
+ align:start position:0%
+we come over here we get a sum over
+angles of the inverse
+
+ align:start position:0%
+angles of the inverse
+ 
+
+ align:start position:0%
+angles of the inverse
+for a transform of that thing right
+
+ align:start position:0%
+for a transform of that thing right
+ 
+
+ align:start position:0%
+for a transform of that thing right
+linearity of fourier transform so that
+
+ align:start position:0%
+linearity of fourier transform so that
+ 
+
+ align:start position:0%
+linearity of fourier transform so that
+gives you
+
+ align:start position:0%
+gives you
+ 
+
+ align:start position:0%
+gives you
+does that roughly make sense to everyone
+
+ align:start position:0%
+does that roughly make sense to everyone
+ 
+
+ align:start position:0%
+does that roughly make sense to everyone
+so just by applying properties you
+
+ align:start position:0%
+so just by applying properties you
+ 
+
+ align:start position:0%
+so just by applying properties you
+already know the fourier transform
+
+ align:start position:0%
+already know the fourier transform
+ 
+
+ align:start position:0%
+already know the fourier transform
+you can argue why it's correct using
+
+ align:start position:0%
+you can argue why it's correct using
+ 
+
+ align:start position:0%
+you can argue why it's correct using
+using the foid projection slice theorem
+
+ align:start position:0%
+using the foid projection slice theorem
+ 
+
+ align:start position:0%
+using the foid projection slice theorem
+but the end result is you don't need to
+
+ align:start position:0%
+but the end result is you don't need to
+ 
+
+ align:start position:0%
+but the end result is you don't need to
+take any fourier transforms you still
+
+ align:start position:0%
+take any fourier transforms you still
+ 
+
+ align:start position:0%
+take any fourier transforms you still
+need to have that sharpening filter
+
+ align:start position:0%
+need to have that sharpening filter
+ 
+
+ align:start position:0%
+need to have that sharpening filter
+though because you can see that you're
+
+ align:start position:0%
+though because you can see that you're
+ 
+
+ align:start position:0%
+though because you can see that you're
+going to build up too much weight in the
+
+ align:start position:0%
+going to build up too much weight in the
+ 
+
+ align:start position:0%
+going to build up too much weight in the
+center
+
+ align:start position:0%
+center
+ 
+
+ align:start position:0%
+center
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but other than that pre-filtering step
+
+ align:start position:0%
+but other than that pre-filtering step
+ 
+
+ align:start position:0%
+but other than that pre-filtering step
+that sharpening step filtered back
+
+ align:start position:0%
+that sharpening step filtered back
+ 
+
+ align:start position:0%
+that sharpening step filtered back
+projection will solve the problem right
+
+ align:start position:0%
+projection will solve the problem right
+ 
+
+ align:start position:0%
+projection will solve the problem right
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+this algorithm i just described rather
+
+ align:start position:0%
+this algorithm i just described rather
+ 
+
+ align:start position:0%
+this algorithm i just described rather
+than using the inverse 2e40 transform
+
+ align:start position:0%
+than using the inverse 2e40 transform
+ 
+
+ align:start position:0%
+than using the inverse 2e40 transform
+it's called filtered back projection
+
+ align:start position:0%
+it's called filtered back projection
+ 
+
+ align:start position:0%
+it's called filtered back projection
+because the first step is you high pass
+
+ align:start position:0%
+because the first step is you high pass
+ 
+
+ align:start position:0%
+because the first step is you high pass
+filter all the projections the second
+
+ align:start position:0%
+filter all the projections the second
+ 
+
+ align:start position:0%
+filter all the projections the second
+step is you back project them you smear
+
+ align:start position:0%
+step is you back project them you smear
+ 
+
+ align:start position:0%
+step is you back project them you smear
+them through as kevin described
+
+ align:start position:0%
+them through as kevin described
+ 
+
+ align:start position:0%
+them through as kevin described
+so there's two ways to solve the inverse
+
+ align:start position:0%
+so there's two ways to solve the inverse
+ 
+
+ align:start position:0%
+so there's two ways to solve the inverse
+radon transform you can take the 2d4
+
+ align:start position:0%
+radon transform you can take the 2d4
+ 
+
+ align:start position:0%
+radon transform you can take the 2d4
+transform or you can use the filter back
+
+ align:start position:0%
+transform or you can use the filter back
+ 
+
+ align:start position:0%
+transform or you can use the filter back
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+okay so now we'll move on to so some of
+
+ align:start position:0%
+okay so now we'll move on to so some of
+ 
+
+ align:start position:0%
+okay so now we'll move on to so some of
+my own work i'm just going to plug so
+
+ align:start position:0%
+my own work i'm just going to plug so
+ 
+
+ align:start position:0%
+my own work i'm just going to plug so
+the idea of really marco boyhead and
+
+ align:start position:0%
+the idea of really marco boyhead and
+ 
+
+ align:start position:0%
+the idea of really marco boyhead and
+presenting this at siggraph is to take
+
+ align:start position:0%
+presenting this at siggraph is to take
+ 
+
+ align:start position:0%
+presenting this at siggraph is to take
+inspiration from medical and scientific
+
+ align:start position:0%
+inspiration from medical and scientific
+ 
+
+ align:start position:0%
+inspiration from medical and scientific
+imaging so we can make better canvas
+
+ align:start position:0%
+imaging so we can make better canvas
+ 
+
+ align:start position:0%
+imaging so we can make better canvas
+right we're competition photographer
+
+ align:start position:0%
+right we're competition photographer
+ 
+
+ align:start position:0%
+right we're competition photographer
+optics people how can we improve this
+
+ align:start position:0%
+optics people how can we improve this
+ 
+
+ align:start position:0%
+optics people how can we improve this
+idea and so
+
+ align:start position:0%
+idea and so
+ 
+
+ align:start position:0%
+idea and so
+one of the limitations ramesh identified
+
+ align:start position:0%
+one of the limitations ramesh identified
+ 
+
+ align:start position:0%
+one of the limitations ramesh identified
+with computer tomography why we can't
+
+ align:start position:0%
+with computer tomography why we can't
+ 
+
+ align:start position:0%
+with computer tomography why we can't
+put it in our pocket is that we have a
+
+ align:start position:0%
+put it in our pocket is that we have a
+ 
+
+ align:start position:0%
+put it in our pocket is that we have a
+lot of moving parts we have these x-ray
+
+ align:start position:0%
+lot of moving parts we have these x-ray
+ 
+
+ align:start position:0%
+lot of moving parts we have these x-ray
+sources moving around the object right
+
+ align:start position:0%
+sources moving around the object right
+ 
+
+ align:start position:0%
+sources moving around the object right
+so the question is how can we remove the
+
+ align:start position:0%
+so the question is how can we remove the
+ 
+
+ align:start position:0%
+so the question is how can we remove the
+moving x-ray sources and so just as a
+
+ align:start position:0%
+moving x-ray sources and so just as a
+ 
+
+ align:start position:0%
+moving x-ray sources and so just as a
+thought experiment i'll quickly explain
+
+ align:start position:0%
+thought experiment i'll quickly explain
+ 
+
+ align:start position:0%
+thought experiment i'll quickly explain
+what we did
+
+ align:start position:0%
+what we did
+ 
+
+ align:start position:0%
+what we did
+basically this is another version of ct
+
+ align:start position:0%
+basically this is another version of ct
+ 
+
+ align:start position:0%
+basically this is another version of ct
+you often find is where instead of
+
+ align:start position:0%
+you often find is where instead of
+ 
+
+ align:start position:0%
+you often find is where instead of
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+a rotating point source we simply have a
+
+ align:start position:0%
+a rotating point source we simply have a
+ 
+
+ align:start position:0%
+a rotating point source we simply have a
+linear array of sources
+
+ align:start position:0%
+linear array of sources
+ 
+
+ align:start position:0%
+linear array of sources
+right and then we have a film plane say
+
+ align:start position:0%
+right and then we have a film plane say
+ 
+
+ align:start position:0%
+right and then we have a film plane say
+our x-ray detector on one side of an
+
+ align:start position:0%
+our x-ray detector on one side of an
+ 
+
+ align:start position:0%
+our x-ray detector on one side of an
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+and then we simply switch these sources
+
+ align:start position:0%
+and then we simply switch these sources
+ 
+
+ align:start position:0%
+and then we simply switch these sources
+at very high speed
+
+ align:start position:0%
+at very high speed
+ 
+
+ align:start position:0%
+at very high speed
+right because only one source can be on
+
+ align:start position:0%
+right because only one source can be on
+ 
+
+ align:start position:0%
+right because only one source can be on
+at a time or else we'll have two
+
+ align:start position:0%
+at a time or else we'll have two
+ 
+
+ align:start position:0%
+at a time or else we'll have two
+projections overlap
+
+ align:start position:0%
+projections overlap
+ 
+
+ align:start position:0%
+projections overlap
+right and so there are
+
+ align:start position:0%
+right and so there are
+ 
+
+ align:start position:0%
+right and so there are
+there's a limitation with this design is
+
+ align:start position:0%
+there's a limitation with this design is
+ 
+
+ align:start position:0%
+there's a limitation with this design is
+you have a limited angle right if you
+
+ align:start position:0%
+you have a limited angle right if you
+ 
+
+ align:start position:0%
+you have a limited angle right if you
+think about this as a ct scanner we've
+
+ align:start position:0%
+think about this as a ct scanner we've
+ 
+
+ align:start position:0%
+think about this as a ct scanner we've
+only gone over some small baseline but
+
+ align:start position:0%
+only gone over some small baseline but
+ 
+
+ align:start position:0%
+only gone over some small baseline but
+using modern tomography that's not such
+
+ align:start position:0%
+using modern tomography that's not such
+ 
+
+ align:start position:0%
+using modern tomography that's not such
+a big deal you can use limited baseline
+
+ align:start position:0%
+a big deal you can use limited baseline
+ 
+
+ align:start position:0%
+a big deal you can use limited baseline
+reconstruction
+
+ align:start position:0%
+reconstruction
+ 
+
+ align:start position:0%
+reconstruction
+uh and so the main limitation with this
+
+ align:start position:0%
+uh and so the main limitation with this
+ 
+
+ align:start position:0%
+uh and so the main limitation with this
+type of device is how fast you can
+
+ align:start position:0%
+type of device is how fast you can
+ 
+
+ align:start position:0%
+type of device is how fast you can
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+the sources on and off it turns out it's
+
+ align:start position:0%
+the sources on and off it turns out it's
+ 
+
+ align:start position:0%
+the sources on and off it turns out it's
+very difficult and expensive to do that
+
+ align:start position:0%
+very difficult and expensive to do that
+ 
+
+ align:start position:0%
+very difficult and expensive to do that
+so what we'd like is to have an
+
+ align:start position:0%
+so what we'd like is to have an
+ 
+
+ align:start position:0%
+so what we'd like is to have an
+algorithm where we simply have
+
+ align:start position:0%
+algorithm where we simply have
+ 
+
+ align:start position:0%
+algorithm where we simply have
+an array of point sources on all the
+
+ align:start position:0%
+an array of point sources on all the
+ 
+
+ align:start position:0%
+an array of point sources on all the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but what you'll have is on the detector
+
+ align:start position:0%
+but what you'll have is on the detector
+ 
+
+ align:start position:0%
+but what you'll have is on the detector
+you have a linear superposition you'll
+
+ align:start position:0%
+you have a linear superposition you'll
+ 
+
+ align:start position:0%
+you have a linear superposition you'll
+have more than one projection
+
+ align:start position:0%
+have more than one projection
+ 
+
+ align:start position:0%
+have more than one projection
+overlapping
+
+ align:start position:0%
+overlapping
+ 
+
+ align:start position:0%
+overlapping
+all right so now you have an interesting
+
+ align:start position:0%
+all right so now you have an interesting
+ 
+
+ align:start position:0%
+all right so now you have an interesting
+mathematical problem which is how do you
+
+ align:start position:0%
+mathematical problem which is how do you
+ 
+
+ align:start position:0%
+mathematical problem which is how do you
+invert
+
+ align:start position:0%
+invert
+ 
+
+ align:start position:0%
+invert
+those series of projections to get back
+
+ align:start position:0%
+those series of projections to get back
+ 
+
+ align:start position:0%
+those series of projections to get back
+to your tomographic data set and as the
+
+ align:start position:0%
+to your tomographic data set and as the
+ 
+
+ align:start position:0%
+to your tomographic data set and as the
+number of point sources increase that
+
+ align:start position:0%
+number of point sources increase that
+ 
+
+ align:start position:0%
+number of point sources increase that
+inversion becomes ill post and so what
+
+ align:start position:0%
+inversion becomes ill post and so what
+ 
+
+ align:start position:0%
+inversion becomes ill post and so what
+we did
+
+ align:start position:0%
+we did
+ 
+
+ align:start position:0%
+we did
+is we inserted
+
+ align:start position:0%
+is we inserted
+ 
+
+ align:start position:0%
+is we inserted
+a mask here
+
+ align:start position:0%
+a mask here
+ 
+
+ align:start position:0%
+a mask here
+and so by putting say some
+
+ align:start position:0%
+and so by putting say some
+ 
+
+ align:start position:0%
+and so by putting say some
+so this is basically a lead panel with
+
+ align:start position:0%
+so this is basically a lead panel with
+ 
+
+ align:start position:0%
+so this is basically a lead panel with
+holes drilled in
+
+ align:start position:0%
+holes drilled in
+ 
+
+ align:start position:0%
+holes drilled in
+and so now you can actually optimize
+
+ align:start position:0%
+and so now you can actually optimize
+ 
+
+ align:start position:0%
+and so now you can actually optimize
+this pattern of holes
+
+ align:start position:0%
+this pattern of holes
+ 
+
+ align:start position:0%
+this pattern of holes
+so that the inverse problem is well
+
+ align:start position:0%
+so that the inverse problem is well
+ 
+
+ align:start position:0%
+so that the inverse problem is well
+poked so again our goal is to get the
+
+ align:start position:0%
+poked so again our goal is to get the
+ 
+
+ align:start position:0%
+poked so again our goal is to get the
+set of projections but they're all
+
+ align:start position:0%
+set of projections but they're all
+ 
+
+ align:start position:0%
+set of projections but they're all
+overlapping so now we're going to design
+
+ align:start position:0%
+overlapping so now we're going to design
+ 
+
+ align:start position:0%
+overlapping so now we're going to design
+a mask to invert that system
+
+ align:start position:0%
+a mask to invert that system
+ 
+
+ align:start position:0%
+a mask to invert that system
+and so if you want to look at this we
+
+ align:start position:0%
+and so if you want to look at this we
+ 
+
+ align:start position:0%
+and so if you want to look at this we
+have a cigarette paper on this called
+
+ align:start position:0%
+have a cigarette paper on this called
+ 
+
+ align:start position:0%
+have a cigarette paper on this called
+shield fields but that's the basic ideas
+
+ align:start position:0%
+shield fields but that's the basic ideas
+ 
+
+ align:start position:0%
+shield fields but that's the basic ideas
+by putting this mask here you can invert
+
+ align:start position:0%
+by putting this mask here you can invert
+ 
+
+ align:start position:0%
+by putting this mask here you can invert
+the system and if you think about it
+
+ align:start position:0%
+the system and if you think about it
+ 
+
+ align:start position:0%
+the system and if you think about it
+very simply it's like a 3d tv you could
+
+ align:start position:0%
+very simply it's like a 3d tv you could
+ 
+
+ align:start position:0%
+very simply it's like a 3d tv you could
+put what's called a parallax barrier
+
+ align:start position:0%
+put what's called a parallax barrier
+ 
+
+ align:start position:0%
+put what's called a parallax barrier
+here so you just have a series of
+
+ align:start position:0%
+here so you just have a series of
+ 
+
+ align:start position:0%
+here so you just have a series of
+pinholes
+
+ align:start position:0%
+pinholes
+ 
+
+ align:start position:0%
+pinholes
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and then if each pinhole was separated
+
+ align:start position:0%
+and then if each pinhole was separated
+ 
+
+ align:start position:0%
+and then if each pinhole was separated
+by the size of this the image of this
+
+ align:start position:0%
+by the size of this the image of this
+ 
+
+ align:start position:0%
+by the size of this the image of this
+array you just get an array of pinhole
+
+ align:start position:0%
+array you just get an array of pinhole
+ 
+
+ align:start position:0%
+array you just get an array of pinhole
+cameras and you could invert that system
+
+ align:start position:0%
+cameras and you could invert that system
+ 
+
+ align:start position:0%
+cameras and you could invert that system
+but of course that doesn't patch them
+
+ align:start position:0%
+but of course that doesn't patch them
+ 
+
+ align:start position:0%
+but of course that doesn't patch them
+with past much light so you can optimize
+
+ align:start position:0%
+with past much light so you can optimize
+ 
+
+ align:start position:0%
+with past much light so you can optimize
+and find better masks so
+
+ align:start position:0%
+and find better masks so
+ 
+
+ align:start position:0%
+and find better masks so
+because we don't like working with
+
+ align:start position:0%
+because we don't like working with
+ 
+
+ align:start position:0%
+because we don't like working with
+x-rays because they didn't want cancer
+
+ align:start position:0%
+x-rays because they didn't want cancer
+ 
+
+ align:start position:0%
+x-rays because they didn't want cancer
+we built this invisible wavelength and
+
+ align:start position:0%
+we built this invisible wavelength and
+ 
+
+ align:start position:0%
+we built this invisible wavelength and
+so what you can see is this is sort of
+
+ align:start position:0%
+so what you can see is this is sort of
+ 
+
+ align:start position:0%
+so what you can see is this is sort of
+like a ct scan scanner built for a
+
+ align:start position:0%
+like a ct scan scanner built for a
+ 
+
+ align:start position:0%
+like a ct scan scanner built for a
+hundred dollars so we have an array of
+
+ align:start position:0%
+hundred dollars so we have an array of
+ 
+
+ align:start position:0%
+hundred dollars so we have an array of
+leds which serves our x-ray sources
+
+ align:start position:0%
+leds which serves our x-ray sources
+ 
+
+ align:start position:0%
+leds which serves our x-ray sources
+we have an opaque object a wooden
+
+ align:start position:0%
+we have an opaque object a wooden
+ 
+
+ align:start position:0%
+we have an opaque object a wooden
+mannequin and then we have what
+
+ align:start position:0%
+mannequin and then we have what
+ 
+
+ align:start position:0%
+mannequin and then we have what
+simulates a large format sensor so this
+
+ align:start position:0%
+simulates a large format sensor so this
+ 
+
+ align:start position:0%
+simulates a large format sensor so this
+is a trick maybe some of you are using
+
+ align:start position:0%
+is a trick maybe some of you are using
+ 
+
+ align:start position:0%
+is a trick maybe some of you are using
+your homework as well to make a really
+
+ align:start position:0%
+your homework as well to make a really
+ 
+
+ align:start position:0%
+your homework as well to make a really
+large detector you can use a camera and
+
+ align:start position:0%
+large detector you can use a camera and
+ 
+
+ align:start position:0%
+large detector you can use a camera and
+just a sheet of paper held between glass
+
+ align:start position:0%
+just a sheet of paper held between glass
+ 
+
+ align:start position:0%
+just a sheet of paper held between glass
+right so we take a photo from behind if
+
+ align:start position:0%
+right so we take a photo from behind if
+ 
+
+ align:start position:0%
+right so we take a photo from behind if
+i was to turn one led one led on it see
+
+ align:start position:0%
+i was to turn one led one led on it see
+ 
+
+ align:start position:0%
+i was to turn one led one led on it see
+a shadow i get the picture of the
+
+ align:start position:0%
+a shadow i get the picture of the
+ 
+
+ align:start position:0%
+a shadow i get the picture of the
+shadows as if i had a giant sensor right
+
+ align:start position:0%
+shadows as if i had a giant sensor right
+ 
+
+ align:start position:0%
+shadows as if i had a giant sensor right
+so that's your cheap way of making huge
+
+ align:start position:0%
+so that's your cheap way of making huge
+ 
+
+ align:start position:0%
+so that's your cheap way of making huge
+sensors and then do we just put a thin
+
+ align:start position:0%
+sensors and then do we just put a thin
+ 
+
+ align:start position:0%
+sensors and then do we just put a thin
+sheet of glass here with our high
+
+ align:start position:0%
+sheet of glass here with our high
+ 
+
+ align:start position:0%
+sheet of glass here with our high
+frequency mask
+
+ align:start position:0%
+frequency mask
+ 
+
+ align:start position:0%
+frequency mask
+and so now we get to the computer vision
+
+ align:start position:0%
+and so now we get to the computer vision
+ 
+
+ align:start position:0%
+and so now we get to the computer vision
+problem so that's what it looks like
+
+ align:start position:0%
+problem so that's what it looks like
+ 
+
+ align:start position:0%
+problem so that's what it looks like
+when the lights are on
+
+ align:start position:0%
+when the lights are on
+ 
+
+ align:start position:0%
+when the lights are on
+so you can sort of see the multiplex
+
+ align:start position:0%
+so you can sort of see the multiplex
+ 
+
+ align:start position:0%
+so you can sort of see the multiplex
+shadows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this is the magic pattern we
+
+ align:start position:0%
+and then this is the magic pattern we
+ 
+
+ align:start position:0%
+and then this is the magic pattern we
+actually used which
+
+ align:start position:0%
+actually used which
+ 
+
+ align:start position:0%
+actually used which
+you can see why if you read the paper
+
+ align:start position:0%
+you can see why if you read the paper
+ 
+
+ align:start position:0%
+you can see why if you read the paper
+but again if you just think about this
+
+ align:start position:0%
+but again if you just think about this
+ 
+
+ align:start position:0%
+but again if you just think about this
+as a mathematical problem we have a set
+
+ align:start position:0%
+as a mathematical problem we have a set
+ 
+
+ align:start position:0%
+as a mathematical problem we have a set
+of projections that are all superimposed
+
+ align:start position:0%
+of projections that are all superimposed
+ 
+
+ align:start position:0%
+of projections that are all superimposed
+we're trying to invert and get the
+
+ align:start position:0%
+we're trying to invert and get the
+ 
+
+ align:start position:0%
+we're trying to invert and get the
+individual shadows
+
+ align:start position:0%
+individual shadows
+ 
+
+ align:start position:0%
+individual shadows
+and it turns out by putting this high
+
+ align:start position:0%
+and it turns out by putting this high
+ 
+
+ align:start position:0%
+and it turns out by putting this high
+frequency pattern in that inversion
+
+ align:start position:0%
+frequency pattern in that inversion
+ 
+
+ align:start position:0%
+frequency pattern in that inversion
+becomes well posed so i'll leave it to
+
+ align:start position:0%
+becomes well posed so i'll leave it to
+ 
+
+ align:start position:0%
+becomes well posed so i'll leave it to
+you to think why that would be you can
+
+ align:start position:0%
+you to think why that would be you can
+ 
+
+ align:start position:0%
+you to think why that would be you can
+also if you go back to the previous
+
+ align:start position:0%
+also if you go back to the previous
+ 
+
+ align:start position:0%
+also if you go back to the previous
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+you can also think of this
+
+ align:start position:0%
+you can also think of this
+ 
+
+ align:start position:0%
+you can also think of this
+as as if you're standing in front of an
+
+ align:start position:0%
+as as if you're standing in front of an
+ 
+
+ align:start position:0%
+as as if you're standing in front of an
+x-ray machine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and every one of those shadows
+
+ align:start position:0%
+and every one of those shadows
+ 
+
+ align:start position:0%
+and every one of those shadows
+would be the shadow you would get in
+
+ align:start position:0%
+would be the shadow you would get in
+ 
+
+ align:start position:0%
+would be the shadow you would get in
+front of the x-ray machine
+
+ align:start position:0%
+front of the x-ray machine
+ 
+
+ align:start position:0%
+front of the x-ray machine
+and as you move the extra source
+
+ align:start position:0%
+and as you move the extra source
+ 
+
+ align:start position:0%
+and as you move the extra source
+you will get
+
+ align:start position:0%
+you will get
+ 
+
+ align:start position:0%
+you will get
+one of the shards they will move
+
+ align:start position:0%
+one of the shards they will move
+ 
+
+ align:start position:0%
+one of the shards they will move
+except here all the sources are on at
+
+ align:start position:0%
+except here all the sources are on at
+ 
+
+ align:start position:0%
+except here all the sources are on at
+the same time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since you're getting this simultaneous
+
+ align:start position:0%
+since you're getting this simultaneous
+ 
+
+ align:start position:0%
+since you're getting this simultaneous
+projection of the x-ray so the question
+
+ align:start position:0%
+projection of the x-ray so the question
+ 
+
+ align:start position:0%
+projection of the x-ray so the question
+is from this one photo
+
+ align:start position:0%
+is from this one photo
+ 
+
+ align:start position:0%
+is from this one photo
+how can i resolve all the original
+
+ align:start position:0%
+how can i resolve all the original
+ 
+
+ align:start position:0%
+how can i resolve all the original
+shadows right
+
+ align:start position:0%
+shadows right
+ 
+
+ align:start position:0%
+shadows right
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+here you can see this is sort of what
+
+ align:start position:0%
+here you can see this is sort of what
+ 
+
+ align:start position:0%
+here you can see this is sort of what
+the data set looks like
+
+ align:start position:0%
+the data set looks like
+ 
+
+ align:start position:0%
+the data set looks like
+so you don't really see anything there
+
+ align:start position:0%
+so you don't really see anything there
+ 
+
+ align:start position:0%
+so you don't really see anything there
+but then just by inverting that system
+
+ align:start position:0%
+but then just by inverting that system
+ 
+
+ align:start position:0%
+but then just by inverting that system
+of equations you can actually pull out
+
+ align:start position:0%
+of equations you can actually pull out
+ 
+
+ align:start position:0%
+of equations you can actually pull out
+from that single image all the
+
+ align:start position:0%
+from that single image all the
+ 
+
+ align:start position:0%
+from that single image all the
+individual shadows so it's as if you had
+
+ align:start position:0%
+individual shadows so it's as if you had
+ 
+
+ align:start position:0%
+individual shadows so it's as if you had
+36 projections all in one image so the
+
+ align:start position:0%
+36 projections all in one image so the
+ 
+
+ align:start position:0%
+36 projections all in one image so the
+key advantage here is we never strobe
+
+ align:start position:0%
+key advantage here is we never strobe
+ 
+
+ align:start position:0%
+key advantage here is we never strobe
+the light so we can record this as fast
+
+ align:start position:0%
+the light so we can record this as fast
+ 
+
+ align:start position:0%
+the light so we can record this as fast
+as the camera can record images right so
+
+ align:start position:0%
+as the camera can record images right so
+ 
+
+ align:start position:0%
+as the camera can record images right so
+for really high speed tomography instead
+
+ align:start position:0%
+for really high speed tomography instead
+ 
+
+ align:start position:0%
+for really high speed tomography instead
+of rotating or strobing the light
+
+ align:start position:0%
+of rotating or strobing the light
+ 
+
+ align:start position:0%
+of rotating or strobing the light
+sources we can just have the light
+
+ align:start position:0%
+sources we can just have the light
+ 
+
+ align:start position:0%
+sources we can just have the light
+sources on all the time we're only
+
+ align:start position:0%
+sources on all the time we're only
+ 
+
+ align:start position:0%
+sources on all the time we're only
+limited by the frame rate of the camera
+
+ align:start position:0%
+limited by the frame rate of the camera
+ 
+
+ align:start position:0%
+limited by the frame rate of the camera
+then of course from these projections
+
+ align:start position:0%
+then of course from these projections
+ 
+
+ align:start position:0%
+then of course from these projections
+you can use the visual hole algorithm
+
+ align:start position:0%
+you can use the visual hole algorithm
+ 
+
+ align:start position:0%
+you can use the visual hole algorithm
+and reconstruct again this isn't exactly
+
+ align:start position:0%
+and reconstruct again this isn't exactly
+ 
+
+ align:start position:0%
+and reconstruct again this isn't exactly
+tomography because it's an opaque object
+
+ align:start position:0%
+tomography because it's an opaque object
+ 
+
+ align:start position:0%
+tomography because it's an opaque object
+but it's essentially the same idea
+
+ align:start position:0%
+but it's essentially the same idea
+ 
+
+ align:start position:0%
+but it's essentially the same idea
+you're doing that filtered back
+
+ align:start position:0%
+you're doing that filtered back
+ 
+
+ align:start position:0%
+you're doing that filtered back
+projection and so you get this
+
+ align:start position:0%
+projection and so you get this
+ 
+
+ align:start position:0%
+projection and so you get this
+reconstruction you can see
+
+ align:start position:0%
+reconstruction you can see
+ 
+
+ align:start position:0%
+reconstruction you can see
+you know looking at the mannequin
+
+ align:start position:0%
+you know looking at the mannequin
+ 
+
+ align:start position:0%
+you know looking at the mannequin
+there's sort of this starburst effect
+
+ align:start position:0%
+there's sort of this starburst effect
+ 
+
+ align:start position:0%
+there's sort of this starburst effect
+you described earlier where you have
+
+ align:start position:0%
+you described earlier where you have
+ 
+
+ align:start position:0%
+you described earlier where you have
+this phantom because of the limited bass
+
+ align:start position:0%
+this phantom because of the limited bass
+ 
+
+ align:start position:0%
+this phantom because of the limited bass
+line and so again that just has to do
+
+ align:start position:0%
+line and so again that just has to do
+ 
+
+ align:start position:0%
+line and so again that just has to do
+with the algorithm used to reconstruct
+
+ align:start position:0%
+with the algorithm used to reconstruct
+ 
+
+ align:start position:0%
+with the algorithm used to reconstruct
+if you had some prior on the smoothness
+
+ align:start position:0%
+if you had some prior on the smoothness
+ 
+
+ align:start position:0%
+if you had some prior on the smoothness
+of the object you could take that out
+
+ align:start position:0%
+of the object you could take that out
+ 
+
+ align:start position:0%
+of the object you could take that out
+but again
+
+ align:start position:0%
+but again
+ 
+
+ align:start position:0%
+but again
+usually you'd have to strobe those
+
+ align:start position:0%
+usually you'd have to strobe those
+ 
+
+ align:start position:0%
+usually you'd have to strobe those
+lights on and off so you'd have to take
+
+ align:start position:0%
+lights on and off so you'd have to take
+ 
+
+ align:start position:0%
+lights on and off so you'd have to take
+36 pictures here we just take one so
+
+ align:start position:0%
+36 pictures here we just take one so
+ 
+
+ align:start position:0%
+36 pictures here we just take one so
+that was the inspiration we took
+
+ align:start position:0%
+that was the inspiration we took
+ 
+
+ align:start position:0%
+that was the inspiration we took
+from the medical imaging world and it
+
+ align:start position:0%
+from the medical imaging world and it
+ 
+
+ align:start position:0%
+from the medical imaging world and it
+turns out all of this can be applied
+
+ align:start position:0%
+turns out all of this can be applied
+ 
+
+ align:start position:0%
+turns out all of this can be applied
+uh to take light field photographs which
+
+ align:start position:0%
+uh to take light field photographs which
+ 
+
+ align:start position:0%
+uh to take light field photographs which
+is what ramesh did in 2007 by putting
+
+ align:start position:0%
+is what ramesh did in 2007 by putting
+ 
+
+ align:start position:0%
+is what ramesh did in 2007 by putting
+that high frequency mask inside the
+
+ align:start position:0%
+that high frequency mask inside the
+ 
+
+ align:start position:0%
+that high frequency mask inside the
+camera so you can see all these ideas
+
+ align:start position:0%
+camera so you can see all these ideas
+ 
+
+ align:start position:0%
+camera so you can see all these ideas
+linked back together
+
+ align:start position:0%
+linked back together
+ 
+
+ align:start position:0%
+linked back together
+and they all start with tomography
+
+ align:start position:0%
+and they all start with tomography
+ 
+
+ align:start position:0%
+and they all start with tomography
+and so now let's take a quick plug uh we
+
+ align:start position:0%
+and so now let's take a quick plug uh we
+ 
+
+ align:start position:0%
+and so now let's take a quick plug uh we
+have a recent paper where we took this
+
+ align:start position:0%
+have a recent paper where we took this
+ 
+
+ align:start position:0%
+have a recent paper where we took this
+idea in yet another direction
+
+ align:start position:0%
+idea in yet another direction
+ 
+
+ align:start position:0%
+idea in yet another direction
+and so the idea is that we're going to
+
+ align:start position:0%
+and so the idea is that we're going to
+ 
+
+ align:start position:0%
+and so the idea is that we're going to
+build this device maybe step back and
+
+ align:start position:0%
+build this device maybe step back and
+ 
+
+ align:start position:0%
+build this device maybe step back and
+did the mat do a presentation have you
+
+ align:start position:0%
+did the mat do a presentation have you
+ 
+
+ align:start position:0%
+did the mat do a presentation have you
+already seen this yeah i think you
+
+ align:start position:0%
+already seen this yeah i think you
+ 
+
+ align:start position:0%
+already seen this yeah i think you
+should so you can go through it quickly
+
+ align:start position:0%
+should so you can go through it quickly
+ 
+
+ align:start position:0%
+should so you can go through it quickly
+okay so the basic idea make sure you can
+
+ align:start position:0%
+okay so the basic idea make sure you can
+ 
+
+ align:start position:0%
+okay so the basic idea make sure you can
+describe the connection between yeah so
+
+ align:start position:0%
+describe the connection between yeah so
+ 
+
+ align:start position:0%
+describe the connection between yeah so
+the basic idea is that we're going to
+
+ align:start position:0%
+the basic idea is that we're going to
+ 
+
+ align:start position:0%
+the basic idea is that we're going to
+take this and build an lcd screen that
+
+ align:start position:0%
+take this and build an lcd screen that
+ 
+
+ align:start position:0%
+take this and build an lcd screen that
+can sense depth and so the trick is
+
+ align:start position:0%
+can sense depth and so the trick is
+ 
+
+ align:start position:0%
+can sense depth and so the trick is
+pretty simple ignore the lcd screen
+
+ align:start position:0%
+pretty simple ignore the lcd screen
+ 
+
+ align:start position:0%
+pretty simple ignore the lcd screen
+we're just going to build the exact
+
+ align:start position:0%
+we're just going to build the exact
+ 
+
+ align:start position:0%
+we're just going to build the exact
+device i just described so we have an
+
+ align:start position:0%
+device i just described so we have an
+ 
+
+ align:start position:0%
+device i just described so we have an
+lcd panel instead of displaying an image
+
+ align:start position:0%
+lcd panel instead of displaying an image
+ 
+
+ align:start position:0%
+lcd panel instead of displaying an image
+we're just going to use it to display
+
+ align:start position:0%
+we're just going to use it to display
+ 
+
+ align:start position:0%
+we're just going to use it to display
+our pieces right no big surprise there
+
+ align:start position:0%
+our pieces right no big surprise there
+ 
+
+ align:start position:0%
+our pieces right no big surprise there
+instead of printing the mask we use the
+
+ align:start position:0%
+instead of printing the mask we use the
+ 
+
+ align:start position:0%
+instead of printing the mask we use the
+lcd to display a mask and then behind
+
+ align:start position:0%
+lcd to display a mask and then behind
+ 
+
+ align:start position:0%
+lcd to display a mask and then behind
+the liquid crystal panel we'll have a
+
+ align:start position:0%
+the liquid crystal panel we'll have a
+ 
+
+ align:start position:0%
+the liquid crystal panel we'll have a
+diffuser which inside lcds you already
+
+ align:start position:0%
+diffuser which inside lcds you already
+ 
+
+ align:start position:0%
+diffuser which inside lcds you already
+have diffusers behind liquid crystal and
+
+ align:start position:0%
+have diffusers behind liquid crystal and
+ 
+
+ align:start position:0%
+have diffusers behind liquid crystal and
+so again we'll have that that giant
+
+ align:start position:0%
+so again we'll have that that giant
+ 
+
+ align:start position:0%
+so again we'll have that that giant
+sensor right we'll have a diffuser our
+
+ align:start position:0%
+sensor right we'll have a diffuser our
+ 
+
+ align:start position:0%
+sensor right we'll have a diffuser our
+lcd panel and some cameras behind it
+
+ align:start position:0%
+lcd panel and some cameras behind it
+ 
+
+ align:start position:0%
+lcd panel and some cameras behind it
+and then we'll be photographing the
+
+ align:start position:0%
+and then we'll be photographing the
+ 
+
+ align:start position:0%
+and then we'll be photographing the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+and so it actually turns out that you
+
+ align:start position:0%
+and so it actually turns out that you
+ 
+
+ align:start position:0%
+and so it actually turns out that you
+can capture the light field with that
+
+ align:start position:0%
+can capture the light field with that
+ 
+
+ align:start position:0%
+can capture the light field with that
+setup
+
+ align:start position:0%
+setup
+ 
+
+ align:start position:0%
+setup
+so by just building that setup
+
+ align:start position:0%
+so by just building that setup
+ 
+
+ align:start position:0%
+so by just building that setup
+using the lcd as a mask
+
+ align:start position:0%
+using the lcd as a mask
+ 
+
+ align:start position:0%
+using the lcd as a mask
+you can capture the light field and then
+
+ align:start position:0%
+you can capture the light field and then
+ 
+
+ align:start position:0%
+you can capture the light field and then
+you can just time multiplex oops let me
+
+ align:start position:0%
+you can just time multiplex oops let me
+ 
+
+ align:start position:0%
+you can just time multiplex oops let me
+go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+on the first frame we turn the back
+
+ align:start position:0%
+on the first frame we turn the back
+ 
+
+ align:start position:0%
+on the first frame we turn the back
+light on and we use the lcd to display a
+
+ align:start position:0%
+light on and we use the lcd to display a
+ 
+
+ align:start position:0%
+light on and we use the lcd to display a
+picture on the next frame we turn the
+
+ align:start position:0%
+picture on the next frame we turn the
+ 
+
+ align:start position:0%
+picture on the next frame we turn the
+back light off and use the lcd to
+
+ align:start position:0%
+back light off and use the lcd to
+ 
+
+ align:start position:0%
+back light off and use the lcd to
+display a mask and get the light filled
+
+ align:start position:0%
+display a mask and get the light filled
+ 
+
+ align:start position:0%
+display a mask and get the light filled
+and repeat at very high frequencies so
+
+ align:start position:0%
+and repeat at very high frequencies so
+ 
+
+ align:start position:0%
+and repeat at very high frequencies so
+that your eye can't perceive it
+
+ align:start position:0%
+that your eye can't perceive it
+ 
+
+ align:start position:0%
+that your eye can't perceive it
+and so now you're getting an lcd panel
+
+ align:start position:0%
+and so now you're getting an lcd panel
+ 
+
+ align:start position:0%
+and so now you're getting an lcd panel
+that can do multi-touch like you
+
+ align:start position:0%
+that can do multi-touch like you
+ 
+
+ align:start position:0%
+that can do multi-touch like you
+normally see and then as the user moves
+
+ align:start position:0%
+normally see and then as the user moves
+ 
+
+ align:start position:0%
+normally see and then as the user moves
+the hand off the table
+
+ align:start position:0%
+the hand off the table
+ 
+
+ align:start position:0%
+the hand off the table
+you can sense depth
+
+ align:start position:0%
+you can sense depth
+ 
+
+ align:start position:0%
+you can sense depth
+and so now instead of having normal
+
+ align:start position:0%
+and so now instead of having normal
+ 
+
+ align:start position:0%
+and so now instead of having normal
+multi-touch you can also have a z-axis
+
+ align:start position:0%
+multi-touch you can also have a z-axis
+ 
+
+ align:start position:0%
+multi-touch you can also have a z-axis
+you can pull things off the table this
+
+ align:start position:0%
+you can pull things off the table this
+ 
+
+ align:start position:0%
+you can pull things off the table this
+is a very simple proof of concept demo
+
+ align:start position:0%
+is a very simple proof of concept demo
+ 
+
+ align:start position:0%
+is a very simple proof of concept demo
+but it shows that just that basic idea
+
+ align:start position:0%
+but it shows that just that basic idea
+ 
+
+ align:start position:0%
+but it shows that just that basic idea
+now we've gone into the hci direction
+
+ align:start position:0%
+now we've gone into the hci direction
+ 
+
+ align:start position:0%
+now we've gone into the hci direction
+here's again matt hirsch did all this
+
+ align:start position:0%
+here's again matt hirsch did all this
+ 
+
+ align:start position:0%
+here's again matt hirsch did all this
+work uh
+
+ align:start position:0%
+work uh
+ 
+
+ align:start position:0%
+work uh
+so you should really talk to him to see
+
+ align:start position:0%
+so you should really talk to him to see
+ 
+
+ align:start position:0%
+so you should really talk to him to see
+the demos and so we're presenting this
+
+ align:start position:0%
+the demos and so we're presenting this
+ 
+
+ align:start position:0%
+the demos and so we're presenting this
+at etec and cigarette asia so if you
+
+ align:start position:0%
+at etec and cigarette asia so if you
+ 
+
+ align:start position:0%
+at etec and cigarette asia so if you
+have any good ideas
+
+ align:start position:0%
+have any good ideas
+ 
+
+ align:start position:0%
+have any good ideas
+on demos you could use with the depth
+
+ align:start position:0%
+on demos you could use with the depth
+ 
+
+ align:start position:0%
+on demos you could use with the depth
+sensing screen please email me or matt
+
+ align:start position:0%
+sensing screen please email me or matt
+ 
+
+ align:start position:0%
+sensing screen please email me or matt
+and if you want to implement them all
+
+ align:start position:0%
+and if you want to implement them all
+ 
+
+ align:start position:0%
+and if you want to implement them all
+the better we'll give you credit when
+
+ align:start position:0%
+the better we'll give you credit when
+ 
+
+ align:start position:0%
+the better we'll give you credit when
+the reporters ask who is the clever guy
+
+ align:start position:0%
+the reporters ask who is the clever guy
+ 
+
+ align:start position:0%
+the reporters ask who is the clever guy
+who programmed that
+
+ align:start position:0%
+who programmed that
+ 
+
+ align:start position:0%
+who programmed that
+so here you can see just a very simple
+
+ align:start position:0%
+so here you can see just a very simple
+ 
+
+ align:start position:0%
+so here you can see just a very simple
+sort of cad explorer you can choose your
+
+ align:start position:0%
+sort of cad explorer you can choose your
+ 
+
+ align:start position:0%
+sort of cad explorer you can choose your
+model which is a touch interaction you
+
+ align:start position:0%
+model which is a touch interaction you
+ 
+
+ align:start position:0%
+model which is a touch interaction you
+can move your hand around it just
+
+ align:start position:0%
+can move your hand around it just
+ 
+
+ align:start position:0%
+can move your hand around it just
+controls the rotation translation and
+
+ align:start position:0%
+controls the rotation translation and
+ 
+
+ align:start position:0%
+controls the rotation translation and
+scale matrix being applied to that model
+
+ align:start position:0%
+scale matrix being applied to that model
+ 
+
+ align:start position:0%
+scale matrix being applied to that model
+right but again so what's neat here is
+
+ align:start position:0%
+right but again so what's neat here is
+ 
+
+ align:start position:0%
+right but again so what's neat here is
+you don't see any cameras there's
+
+ align:start position:0%
+you don't see any cameras there's
+ 
+
+ align:start position:0%
+you don't see any cameras there's
+nothing hidden in the bezel
+
+ align:start position:0%
+nothing hidden in the bezel
+ 
+
+ align:start position:0%
+nothing hidden in the bezel
+so it's so to the user it's sort of
+
+ align:start position:0%
+so it's so to the user it's sort of
+ 
+
+ align:start position:0%
+so it's so to the user it's sort of
+surprising that you're getting the light
+
+ align:start position:0%
+surprising that you're getting the light
+ 
+
+ align:start position:0%
+surprising that you're getting the light
+field and the demo i'm not showing is
+
+ align:start position:0%
+field and the demo i'm not showing is
+ 
+
+ align:start position:0%
+field and the demo i'm not showing is
+that you can do light field transfer
+
+ align:start position:0%
+that you can do light field transfer
+ 
+
+ align:start position:0%
+that you can do light field transfer
+with this if you know what that is
+
+ align:start position:0%
+with this if you know what that is
+ 
+
+ align:start position:0%
+with this if you know what that is
+we done okay on time uh
+
+ align:start position:0%
+we done okay on time uh
+ 
+
+ align:start position:0%
+we done okay on time uh
+can move faster so
+
+ align:start position:0%
+can move faster so
+ 
+
+ align:start position:0%
+can move faster so
+i think ank had already presented this
+
+ align:start position:0%
+i think ank had already presented this
+ 
+
+ align:start position:0%
+i think ank had already presented this
+project right yeah hey project it wasn't
+
+ align:start position:0%
+project right yeah hey project it wasn't
+ 
+
+ align:start position:0%
+project right yeah hey project it wasn't
+pretty slow okay so i'll just go through
+
+ align:start position:0%
+pretty slow okay so i'll just go through
+ 
+
+ align:start position:0%
+pretty slow okay so i'll just go through
+this really fast then so again i
+
+ align:start position:0%
+this really fast then so again i
+ 
+
+ align:start position:0%
+this really fast then so again i
+mentioned that once the computer was
+
+ align:start position:0%
+mentioned that once the computer was
+ 
+
+ align:start position:0%
+mentioned that once the computer was
+invented tomography became easy because
+
+ align:start position:0%
+invented tomography became easy because
+ 
+
+ align:start position:0%
+invented tomography became easy because
+they knew the radon transform and they
+
+ align:start position:0%
+they knew the radon transform and they
+ 
+
+ align:start position:0%
+they knew the radon transform and they
+could invert it but if you don't have a
+
+ align:start position:0%
+could invert it but if you don't have a
+ 
+
+ align:start position:0%
+could invert it but if you don't have a
+computer how can you take a
+
+ align:start position:0%
+computer how can you take a
+ 
+
+ align:start position:0%
+computer how can you take a
+cross-sectional cross-sectional image of
+
+ align:start position:0%
+cross-sectional cross-sectional image of
+ 
+
+ align:start position:0%
+cross-sectional cross-sectional image of
+a patient
+
+ align:start position:0%
+a patient
+ 
+
+ align:start position:0%
+a patient
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+so if i just had an x-ray source and an
+
+ align:start position:0%
+so if i just had an x-ray source and an
+ 
+
+ align:start position:0%
+so if i just had an x-ray source and an
+x-ray film
+
+ align:start position:0%
+x-ray film
+ 
+
+ align:start position:0%
+x-ray film
+film and i had the patient sitting on
+
+ align:start position:0%
+film and i had the patient sitting on
+ 
+
+ align:start position:0%
+film and i had the patient sitting on
+the bernie i could turn the source on i
+
+ align:start position:0%
+the bernie i could turn the source on i
+ 
+
+ align:start position:0%
+the bernie i could turn the source on i
+did a projection
+
+ align:start position:0%
+did a projection
+ 
+
+ align:start position:0%
+did a projection
+but the main problem is every i'm really
+
+ align:start position:0%
+but the main problem is every i'm really
+ 
+
+ align:start position:0%
+but the main problem is every i'm really
+only interested in taking a
+
+ align:start position:0%
+only interested in taking a
+ 
+
+ align:start position:0%
+only interested in taking a
+cross-sectional image so i can identify
+
+ align:start position:0%
+cross-sectional image so i can identify
+ 
+
+ align:start position:0%
+cross-sectional image so i can identify
+a tumor in the brain or something else
+
+ align:start position:0%
+a tumor in the brain or something else
+ 
+
+ align:start position:0%
+a tumor in the brain or something else
+right but everything else out of that
+
+ align:start position:0%
+right but everything else out of that
+ 
+
+ align:start position:0%
+right but everything else out of that
+plane i don't really care about and the
+
+ align:start position:0%
+plane i don't really care about and the
+ 
+
+ align:start position:0%
+plane i don't really care about and the
+problem is if i just have this this
+
+ align:start position:0%
+problem is if i just have this this
+ 
+
+ align:start position:0%
+problem is if i just have this this
+perspective projection everything out of
+
+ align:start position:0%
+perspective projection everything out of
+ 
+
+ align:start position:0%
+perspective projection everything out of
+focus will also be imaged on the sensor
+
+ align:start position:0%
+focus will also be imaged on the sensor
+ 
+
+ align:start position:0%
+focus will also be imaged on the sensor
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so the question is how can i get an
+
+ align:start position:0%
+so the question is how can i get an
+ 
+
+ align:start position:0%
+so the question is how can i get an
+image just through along a slice through
+
+ align:start position:0%
+image just through along a slice through
+ 
+
+ align:start position:0%
+image just through along a slice through
+my volume without using computation
+
+ align:start position:0%
+my volume without using computation
+ 
+
+ align:start position:0%
+my volume without using computation
+and so i think i could explain this but
+
+ align:start position:0%
+and so i think i could explain this but
+ 
+
+ align:start position:0%
+and so i think i could explain this but
+100 years ago this day they did this and
+
+ align:start position:0%
+100 years ago this day they did this and
+ 
+
+ align:start position:0%
+100 years ago this day they did this and
+it's called laminography and it gives
+
+ align:start position:0%
+it's called laminography and it gives
+ 
+
+ align:start position:0%
+it's called laminography and it gives
+you almost identical results purely with
+
+ align:start position:0%
+you almost identical results purely with
+ 
+
+ align:start position:0%
+you almost identical results purely with
+mechanical means so the idea is simple
+
+ align:start position:0%
+mechanical means so the idea is simple
+ 
+
+ align:start position:0%
+mechanical means so the idea is simple
+you simply take the x-ray source and you
+
+ align:start position:0%
+you simply take the x-ray source and you
+ 
+
+ align:start position:0%
+you simply take the x-ray source and you
+mechanically translate it from left to
+
+ align:start position:0%
+mechanically translate it from left to
+ 
+
+ align:start position:0%
+mechanically translate it from left to
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and then at the same time you
+
+ align:start position:0%
+and then at the same time you
+ 
+
+ align:start position:0%
+and then at the same time you
+mechanically translate your film
+
+ align:start position:0%
+mechanically translate your film
+ 
+
+ align:start position:0%
+mechanically translate your film
+from right to left and so pick some
+
+ align:start position:0%
+from right to left and so pick some
+ 
+
+ align:start position:0%
+from right to left and so pick some
+point in the patient and be stationary
+
+ align:start position:0%
+point in the patient and be stationary
+ 
+
+ align:start position:0%
+point in the patient and be stationary
+right you'll have some ray going through
+
+ align:start position:0%
+right you'll have some ray going through
+ 
+
+ align:start position:0%
+right you'll have some ray going through
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+right and then if i turn on the next
+
+ align:start position:0%
+right and then if i turn on the next
+ 
+
+ align:start position:0%
+right and then if i turn on the next
+source you'll have some other ray coming
+
+ align:start position:0%
+source you'll have some other ray coming
+ 
+
+ align:start position:0%
+source you'll have some other ray coming
+in as long as i move the sensor
+
+ align:start position:0%
+in as long as i move the sensor
+ 
+
+ align:start position:0%
+in as long as i move the sensor
+so that that same pixel is illuminated
+
+ align:start position:0%
+so that that same pixel is illuminated
+ 
+
+ align:start position:0%
+so that that same pixel is illuminated
+right then that point will be focused
+
+ align:start position:0%
+right then that point will be focused
+ 
+
+ align:start position:0%
+right then that point will be focused
+but everything else won't
+
+ align:start position:0%
+but everything else won't
+ 
+
+ align:start position:0%
+but everything else won't
+so it's sort of a clever trick to get a
+
+ align:start position:0%
+so it's sort of a clever trick to get a
+ 
+
+ align:start position:0%
+so it's sort of a clever trick to get a
+ct scanner without any computers and so
+
+ align:start position:0%
+ct scanner without any computers and so
+ 
+
+ align:start position:0%
+ct scanner without any computers and so
+we use this uh to publish the paper and
+
+ align:start position:0%
+we use this uh to publish the paper and
+ 
+
+ align:start position:0%
+we use this uh to publish the paper and
+icc actually let's go back to that one
+
+ align:start position:0%
+icc actually let's go back to that one
+ 
+
+ align:start position:0%
+icc actually let's go back to that one
+there's a there's a minor difference
+
+ align:start position:0%
+there's a there's a minor difference
+ 
+
+ align:start position:0%
+there's a there's a minor difference
+though between
+
+ align:start position:0%
+though between
+ 
+
+ align:start position:0%
+though between
+between doing this
+
+ align:start position:0%
+between doing this
+ 
+
+ align:start position:0%
+between doing this
+achieving a cross-section image
+
+ align:start position:0%
+achieving a cross-section image
+ 
+
+ align:start position:0%
+achieving a cross-section image
+through this method versus doing the
+
+ align:start position:0%
+through this method versus doing the
+ 
+
+ align:start position:0%
+through this method versus doing the
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+spinning and multiple projection thing
+
+ align:start position:0%
+spinning and multiple projection thing
+ 
+
+ align:start position:0%
+spinning and multiple projection thing
+what's the difference between the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you don't get as much depth
+
+ align:start position:0%
+so you don't get as much depth
+ 
+
+ align:start position:0%
+so you don't get as much depth
+by what
+
+ align:start position:0%
+by what
+ 
+
+ align:start position:0%
+by what
+the plane of focus but you can control
+
+ align:start position:0%
+the plane of focus but you can control
+ 
+
+ align:start position:0%
+the plane of focus but you can control
+that based on how far how close the
+
+ align:start position:0%
+that based on how far how close the
+ 
+
+ align:start position:0%
+that based on how far how close the
+x-ray source and the sensor is so you
+
+ align:start position:0%
+x-ray source and the sensor is so you
+ 
+
+ align:start position:0%
+x-ray source and the sensor is so you
+can get a pretty narrow depth of field
+
+ align:start position:0%
+can get a pretty narrow depth of field
+ 
+
+ align:start position:0%
+can get a pretty narrow depth of field
+but what happens to stuff that's outside
+
+ align:start position:0%
+but what happens to stuff that's outside
+ 
+
+ align:start position:0%
+but what happens to stuff that's outside
+the depth of field
+
+ align:start position:0%
+the depth of field
+ 
+
+ align:start position:0%
+the depth of field
+it's still going to be blurred yeah and
+
+ align:start position:0%
+it's still going to be blurred yeah and
+ 
+
+ align:start position:0%
+it's still going to be blurred yeah and
+it will be still part of the image so
+
+ align:start position:0%
+it will be still part of the image so
+ 
+
+ align:start position:0%
+it will be still part of the image so
+you don't really eliminate
+
+ align:start position:0%
+you don't really eliminate
+ 
+
+ align:start position:0%
+you don't really eliminate
+what's above and below your plane of
+
+ align:start position:0%
+what's above and below your plane of
+ 
+
+ align:start position:0%
+what's above and below your plane of
+focus it's just
+
+ align:start position:0%
+focus it's just
+ 
+
+ align:start position:0%
+focus it's just
+out of focus but it's still there very
+
+ align:start position:0%
+out of focus but it's still there very
+ 
+
+ align:start position:0%
+out of focus but it's still there very
+fortunate you can make it stronger out
+
+ align:start position:0%
+fortunate you can make it stronger out
+ 
+
+ align:start position:0%
+fortunate you can make it stronger out
+of focus but your contrast will be lower
+
+ align:start position:0%
+of focus but your contrast will be lower
+ 
+
+ align:start position:0%
+of focus but your contrast will be lower
+than ct
+
+ align:start position:0%
+than ct
+ 
+
+ align:start position:0%
+than ct
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+ankit
+
+ align:start position:0%
+ankit
+ 
+
+ align:start position:0%
+ankit
+had a great idea to apply this to uh to
+
+ align:start position:0%
+had a great idea to apply this to uh to
+ 
+
+ align:start position:0%
+had a great idea to apply this to uh to
+photography and so he's going to explain
+
+ align:start position:0%
+photography and so he's going to explain
+ 
+
+ align:start position:0%
+photography and so he's going to explain
+this to you so i'll go quickly through
+
+ align:start position:0%
+this to you so i'll go quickly through
+ 
+
+ align:start position:0%
+this to you so i'll go quickly through
+this but the basic idea is if i have my
+
+ align:start position:0%
+this but the basic idea is if i have my
+ 
+
+ align:start position:0%
+this but the basic idea is if i have my
+normal thin lens equation i have some
+
+ align:start position:0%
+normal thin lens equation i have some
+ 
+
+ align:start position:0%
+normal thin lens equation i have some
+plane in the world on the left and my
+
+ align:start position:0%
+plane in the world on the left and my
+ 
+
+ align:start position:0%
+plane in the world on the left and my
+sensor on the right the lens maps those
+
+ align:start position:0%
+sensor on the right the lens maps those
+ 
+
+ align:start position:0%
+sensor on the right the lens maps those
+and as i make as i stop down the
+
+ align:start position:0%
+and as i make as i stop down the
+ 
+
+ align:start position:0%
+and as i make as i stop down the
+aperture
+
+ align:start position:0%
+aperture
+ 
+
+ align:start position:0%
+aperture
+right the blur circle for the auto focus
+
+ align:start position:0%
+right the blur circle for the auto focus
+ 
+
+ align:start position:0%
+right the blur circle for the auto focus
+point decreases and in the limit if i
+
+ align:start position:0%
+point decreases and in the limit if i
+ 
+
+ align:start position:0%
+point decreases and in the limit if i
+just have a pinhole then i get
+
+ align:start position:0%
+just have a pinhole then i get
+ 
+
+ align:start position:0%
+just have a pinhole then i get
+everything in the world in focus and so
+
+ align:start position:0%
+everything in the world in focus and so
+ 
+
+ align:start position:0%
+everything in the world in focus and so
+if you look at your iphone camera your
+
+ align:start position:0%
+if you look at your iphone camera your
+ 
+
+ align:start position:0%
+if you look at your iphone camera your
+cell phone camera the apertures are so
+
+ align:start position:0%
+cell phone camera the apertures are so
+ 
+
+ align:start position:0%
+cell phone camera the apertures are so
+small that you're essentially taking
+
+ align:start position:0%
+small that you're essentially taking
+ 
+
+ align:start position:0%
+small that you're essentially taking
+pinhole images for everything right and
+
+ align:start position:0%
+pinhole images for everything right and
+ 
+
+ align:start position:0%
+pinhole images for everything right and
+what we'd like to do is take images with
+
+ align:start position:0%
+what we'd like to do is take images with
+ 
+
+ align:start position:0%
+what we'd like to do is take images with
+a cell phone camera that are as if they
+
+ align:start position:0%
+a cell phone camera that are as if they
+ 
+
+ align:start position:0%
+a cell phone camera that are as if they
+have a large lens because really when
+
+ align:start position:0%
+have a large lens because really when
+ 
+
+ align:start position:0%
+have a large lens because really when
+you pay a professional photographer to
+
+ align:start position:0%
+you pay a professional photographer to
+ 
+
+ align:start position:0%
+you pay a professional photographer to
+do your wedding photos it's really the
+
+ align:start position:0%
+do your wedding photos it's really the
+ 
+
+ align:start position:0%
+do your wedding photos it's really the
+blur one of the the blur is one of the
+
+ align:start position:0%
+blur one of the the blur is one of the
+ 
+
+ align:start position:0%
+blur one of the the blur is one of the
+big tricks they have right they take a
+
+ align:start position:0%
+big tricks they have right they take a
+ 
+
+ align:start position:0%
+big tricks they have right they take a
+painful blur you're paying for the blur
+
+ align:start position:0%
+painful blur you're paying for the blur
+ 
+
+ align:start position:0%
+painful blur you're paying for the blur
+in a way you're playing you're paying
+
+ align:start position:0%
+in a way you're playing you're paying
+ 
+
+ align:start position:0%
+in a way you're playing you're paying
+for that big piece of glass and a bit of
+
+ align:start position:0%
+for that big piece of glass and a bit of
+ 
+
+ align:start position:0%
+for that big piece of glass and a bit of
+the talent to focus on the foreground
+
+ align:start position:0%
+the talent to focus on the foreground
+ 
+
+ align:start position:0%
+the talent to focus on the foreground
+object so the background has this really
+
+ align:start position:0%
+object so the background has this really
+ 
+
+ align:start position:0%
+object so the background has this really
+beautiful blur right that's one of the
+
+ align:start position:0%
+beautiful blur right that's one of the
+ 
+
+ align:start position:0%
+beautiful blur right that's one of the
+things that you immediately noticed when
+
+ align:start position:0%
+things that you immediately noticed when
+ 
+
+ align:start position:0%
+things that you immediately noticed when
+you look at a wedding i was like oh gee
+
+ align:start position:0%
+you look at a wedding i was like oh gee
+ 
+
+ align:start position:0%
+you look at a wedding i was like oh gee
+they just blurred the background great
+
+ align:start position:0%
+they just blurred the background great
+ 
+
+ align:start position:0%
+they just blurred the background great
+right so the question is can we get nice
+
+ align:start position:0%
+right so the question is can we get nice
+ 
+
+ align:start position:0%
+right so the question is can we get nice
+defocus
+
+ align:start position:0%
+defocus
+ 
+
+ align:start position:0%
+defocus
+nice blur with a cell phone camera so in
+
+ align:start position:0%
+nice blur with a cell phone camera so in
+ 
+
+ align:start position:0%
+nice blur with a cell phone camera so in
+a way we're going to make our camera
+
+ align:start position:0%
+a way we're going to make our camera
+ 
+
+ align:start position:0%
+a way we're going to make our camera
+worse right a cell phone camera takes
+
+ align:start position:0%
+worse right a cell phone camera takes
+ 
+
+ align:start position:0%
+worse right a cell phone camera takes
+everything in focus which you know maybe
+
+ align:start position:0%
+everything in focus which you know maybe
+ 
+
+ align:start position:0%
+everything in focus which you know maybe
+that's a good thing but it doesn't have
+
+ align:start position:0%
+that's a good thing but it doesn't have
+ 
+
+ align:start position:0%
+that's a good thing but it doesn't have
+that aesthetic feel of having a nice
+
+ align:start position:0%
+that aesthetic feel of having a nice
+ 
+
+ align:start position:0%
+that aesthetic feel of having a nice
+defocused background
+
+ align:start position:0%
+defocused background
+ 
+
+ align:start position:0%
+defocused background
+and so the main trick again i'll credit
+
+ align:start position:0%
+and so the main trick again i'll credit
+ 
+
+ align:start position:0%
+and so the main trick again i'll credit
+with this is a nice insight is uh well
+
+ align:start position:0%
+with this is a nice insight is uh well
+ 
+
+ align:start position:0%
+with this is a nice insight is uh well
+first let's consider moving the pinhole
+
+ align:start position:0%
+first let's consider moving the pinhole
+ 
+
+ align:start position:0%
+first let's consider moving the pinhole
+because we just talked about
+
+ align:start position:0%
+because we just talked about
+ 
+
+ align:start position:0%
+because we just talked about
+laminography and that's like moving the
+
+ align:start position:0%
+laminography and that's like moving the
+ 
+
+ align:start position:0%
+laminography and that's like moving the
+x-ray source so our pinhole here is like
+
+ align:start position:0%
+x-ray source so our pinhole here is like
+ 
+
+ align:start position:0%
+x-ray source so our pinhole here is like
+our x-ray source it's our center of
+
+ align:start position:0%
+our x-ray source it's our center of
+ 
+
+ align:start position:0%
+our x-ray source it's our center of
+projection and so if you translate a
+
+ align:start position:0%
+projection and so if you translate a
+ 
+
+ align:start position:0%
+projection and so if you translate a
+pinhole
+
+ align:start position:0%
+pinhole
+ 
+
+ align:start position:0%
+pinhole
+right and again we have two two points
+
+ align:start position:0%
+right and again we have two two points
+ 
+
+ align:start position:0%
+right and again we have two two points
+in the world they're mapped onto our
+
+ align:start position:0%
+in the world they're mapped onto our
+ 
+
+ align:start position:0%
+in the world they're mapped onto our
+sensor nothing's moving other than the
+
+ align:start position:0%
+sensor nothing's moving other than the
+ 
+
+ align:start position:0%
+sensor nothing's moving other than the
+pinhole
+
+ align:start position:0%
+pinhole
+ 
+
+ align:start position:0%
+pinhole
+then you see that that
+
+ align:start position:0%
+then you see that that
+ 
+
+ align:start position:0%
+then you see that that
+without without moving the sensor you
+
+ align:start position:0%
+without without moving the sensor you
+ 
+
+ align:start position:0%
+without without moving the sensor you
+get these two blur circles
+
+ align:start position:0%
+get these two blur circles
+ 
+
+ align:start position:0%
+get these two blur circles
+but one of them
+
+ align:start position:0%
+but one of them
+ 
+
+ align:start position:0%
+but one of them
+is slightly larger
+
+ align:start position:0%
+is slightly larger
+ 
+
+ align:start position:0%
+is slightly larger
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so again in the interest of saving
+
+ align:start position:0%
+and so again in the interest of saving
+ 
+
+ align:start position:0%
+and so again in the interest of saving
+time you can go through a mathematical
+
+ align:start position:0%
+time you can go through a mathematical
+ 
+
+ align:start position:0%
+time you can go through a mathematical
+analysis but what's really important
+
+ align:start position:0%
+analysis but what's really important
+ 
+
+ align:start position:0%
+analysis but what's really important
+here is it's the same idea
+
+ align:start position:0%
+here is it's the same idea
+ 
+
+ align:start position:0%
+here is it's the same idea
+as laminography applied to c to
+
+ align:start position:0%
+as laminography applied to c to
+ 
+
+ align:start position:0%
+as laminography applied to c to
+to x-rays is basically this is like our
+
+ align:start position:0%
+to x-rays is basically this is like our
+ 
+
+ align:start position:0%
+to x-rays is basically this is like our
+x-ray source this is like our film plane
+
+ align:start position:0%
+x-ray source this is like our film plane
+ 
+
+ align:start position:0%
+x-ray source this is like our film plane
+and if we translate them
+
+ align:start position:0%
+and if we translate them
+ 
+
+ align:start position:0%
+and if we translate them
+at a certain velocity ratio we can
+
+ align:start position:0%
+at a certain velocity ratio we can
+ 
+
+ align:start position:0%
+at a certain velocity ratio we can
+actually put certain planes in the world
+
+ align:start position:0%
+actually put certain planes in the world
+ 
+
+ align:start position:0%
+actually put certain planes in the world
+into focus it's as if our patient has
+
+ align:start position:0%
+into focus it's as if our patient has
+ 
+
+ align:start position:0%
+into focus it's as if our patient has
+moved to the left side instead of the
+
+ align:start position:0%
+moved to the left side instead of the
+ 
+
+ align:start position:0%
+moved to the left side instead of the
+center now we have the x-ray source and
+
+ align:start position:0%
+center now we have the x-ray source and
+ 
+
+ align:start position:0%
+center now we have the x-ray source and
+the film and the velocity now becomes in
+
+ align:start position:0%
+the film and the velocity now becomes in
+ 
+
+ align:start position:0%
+the film and the velocity now becomes in
+the same direction instead of opposite
+
+ align:start position:0%
+the same direction instead of opposite
+ 
+
+ align:start position:0%
+the same direction instead of opposite
+directions but if you think about this
+
+ align:start position:0%
+directions but if you think about this
+ 
+
+ align:start position:0%
+directions but if you think about this
+it's identical
+
+ align:start position:0%
+it's identical
+ 
+
+ align:start position:0%
+it's identical
+right it's identical to the laminography
+
+ align:start position:0%
+right it's identical to the laminography
+ 
+
+ align:start position:0%
+right it's identical to the laminography
+we saw earlier and so then what we can
+
+ align:start position:0%
+we saw earlier and so then what we can
+ 
+
+ align:start position:0%
+we saw earlier and so then what we can
+do is we can just choose this velocity
+
+ align:start position:0%
+do is we can just choose this velocity
+ 
+
+ align:start position:0%
+do is we can just choose this velocity
+ratio
+
+ align:start position:0%
+ratio
+ 
+
+ align:start position:0%
+ratio
+and again if you say look at the blue
+
+ align:start position:0%
+and again if you say look at the blue
+ 
+
+ align:start position:0%
+and again if you say look at the blue
+ray here
+
+ align:start position:0%
+ray here
+ 
+
+ align:start position:0%
+ray here
+it'll always move to the same pixel on
+
+ align:start position:0%
+it'll always move to the same pixel on
+ 
+
+ align:start position:0%
+it'll always move to the same pixel on
+the sensor because we're moving the
+
+ align:start position:0%
+the sensor because we're moving the
+ 
+
+ align:start position:0%
+the sensor because we're moving the
+sensor at just the right speed so that
+
+ align:start position:0%
+sensor at just the right speed so that
+ 
+
+ align:start position:0%
+sensor at just the right speed so that
+that pixel always stays on the blu-ray
+
+ align:start position:0%
+that pixel always stays on the blu-ray
+ 
+
+ align:start position:0%
+that pixel always stays on the blu-ray
+but the blue one is getting the the red
+
+ align:start position:0%
+but the blue one is getting the the red
+ 
+
+ align:start position:0%
+but the blue one is getting the the red
+one is getting blurred right and by
+
+ align:start position:0%
+one is getting blurred right and by
+ 
+
+ align:start position:0%
+one is getting blurred right and by
+changing that velocity ratio we can then
+
+ align:start position:0%
+changing that velocity ratio we can then
+ 
+
+ align:start position:0%
+changing that velocity ratio we can then
+focus at a different point right very
+
+ align:start position:0%
+focus at a different point right very
+ 
+
+ align:start position:0%
+focus at a different point right very
+simple idea
+
+ align:start position:0%
+simple idea
+ 
+
+ align:start position:0%
+simple idea
+and so if you look in the paper what
+
+ align:start position:0%
+and so if you look in the paper what
+ 
+
+ align:start position:0%
+and so if you look in the paper what
+we've done is just recreated what a lens
+
+ align:start position:0%
+we've done is just recreated what a lens
+ 
+
+ align:start position:0%
+we've done is just recreated what a lens
+does but over time and so everyone knows
+
+ align:start position:0%
+does but over time and so everyone knows
+ 
+
+ align:start position:0%
+does but over time and so everyone knows
+this equation the gaussian thin lens
+
+ align:start position:0%
+this equation the gaussian thin lens
+ 
+
+ align:start position:0%
+this equation the gaussian thin lens
+equation right that the distance to the
+
+ align:start position:0%
+equation right that the distance to the
+ 
+
+ align:start position:0%
+equation right that the distance to the
+image plane and the object plane our
+
+ align:start position:0%
+image plane and the object plane our
+ 
+
+ align:start position:0%
+image plane and the object plane our
+inverse reciprocal is equal to the focal
+
+ align:start position:0%
+inverse reciprocal is equal to the focal
+ 
+
+ align:start position:0%
+inverse reciprocal is equal to the focal
+length right hopefully everyone knows
+
+ align:start position:0%
+length right hopefully everyone knows
+ 
+
+ align:start position:0%
+length right hopefully everyone knows
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so normally this focal length is chosen
+
+ align:start position:0%
+so normally this focal length is chosen
+ 
+
+ align:start position:0%
+so normally this focal length is chosen
+by is selected by your chunk of glass
+
+ align:start position:0%
+by is selected by your chunk of glass
+ 
+
+ align:start position:0%
+by is selected by your chunk of glass
+right you choose some refractive index
+
+ align:start position:0%
+right you choose some refractive index
+ 
+
+ align:start position:0%
+right you choose some refractive index
+and some curvatures that gives you the
+
+ align:start position:0%
+and some curvatures that gives you the
+ 
+
+ align:start position:0%
+and some curvatures that gives you the
+focal length here
+
+ align:start position:0%
+focal length here
+ 
+
+ align:start position:0%
+focal length here
+you have a virtual focal length which is
+
+ align:start position:0%
+you have a virtual focal length which is
+ 
+
+ align:start position:0%
+you have a virtual focal length which is
+just simply
+
+ align:start position:0%
+just simply
+ 
+
+ align:start position:0%
+just simply
+it's very simple it's the register
+
+ align:start position:0%
+it's very simple it's the register
+ 
+
+ align:start position:0%
+it's very simple it's the register
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+which is the distance to your pinhole to
+
+ align:start position:0%
+which is the distance to your pinhole to
+ 
+
+ align:start position:0%
+which is the distance to your pinhole to
+the sensor times the velocity ratio so
+
+ align:start position:0%
+the sensor times the velocity ratio so
+ 
+
+ align:start position:0%
+the sensor times the velocity ratio so
+as we change this velocity ratio we can
+
+ align:start position:0%
+as we change this velocity ratio we can
+ 
+
+ align:start position:0%
+as we change this velocity ratio we can
+make arbitrary lenses
+
+ align:start position:0%
+make arbitrary lenses
+ 
+
+ align:start position:0%
+make arbitrary lenses
+and that gives us a virtual f number and
+
+ align:start position:0%
+and that gives us a virtual f number and
+ 
+
+ align:start position:0%
+and that gives us a virtual f number and
+so then just to blow through this this
+
+ align:start position:0%
+so then just to blow through this this
+ 
+
+ align:start position:0%
+so then just to blow through this this
+is the prototype we built so again you
+
+ align:start position:0%
+is the prototype we built so again you
+ 
+
+ align:start position:0%
+is the prototype we built so again you
+can see the story here we knew about
+
+ align:start position:0%
+can see the story here we knew about
+ 
+
+ align:start position:0%
+can see the story here we knew about
+laminography which is a medical imaging
+
+ align:start position:0%
+laminography which is a medical imaging
+ 
+
+ align:start position:0%
+laminography which is a medical imaging
+topic we said we want to publish
+
+ align:start position:0%
+topic we said we want to publish
+ 
+
+ align:start position:0%
+topic we said we want to publish
+something in computational photography
+
+ align:start position:0%
+something in computational photography
+ 
+
+ align:start position:0%
+something in computational photography
+let's build an optical version and here
+
+ align:start position:0%
+let's build an optical version and here
+ 
+
+ align:start position:0%
+let's build an optical version and here
+you go
+
+ align:start position:0%
+you go
+ 
+
+ align:start position:0%
+you go
+so you have two translation stages right
+
+ align:start position:0%
+so you have two translation stages right
+ 
+
+ align:start position:0%
+so you have two translation stages right
+you can see those on the bottom these
+
+ align:start position:0%
+you can see those on the bottom these
+ 
+
+ align:start position:0%
+you can see those on the bottom these
+are from quinn
+
+ align:start position:0%
+are from quinn
+ 
+
+ align:start position:0%
+are from quinn
+and then we have lens and sensor
+
+ align:start position:0%
+and then we have lens and sensor
+ 
+
+ align:start position:0%
+and then we have lens and sensor
+and then you can see this is the type of
+
+ align:start position:0%
+and then you can see this is the type of
+ 
+
+ align:start position:0%
+and then you can see this is the type of
+image if you stop down the lens this is
+
+ align:start position:0%
+image if you stop down the lens this is
+ 
+
+ align:start position:0%
+image if you stop down the lens this is
+what your cell phone would give you
+
+ align:start position:0%
+what your cell phone would give you
+ 
+
+ align:start position:0%
+what your cell phone would give you
+and then by adjusting the velocity ratio
+
+ align:start position:0%
+and then by adjusting the velocity ratio
+ 
+
+ align:start position:0%
+and then by adjusting the velocity ratio
+by making it small we can focus on the
+
+ align:start position:0%
+by making it small we can focus on the
+ 
+
+ align:start position:0%
+by making it small we can focus on the
+foreground
+
+ align:start position:0%
+foreground
+ 
+
+ align:start position:0%
+foreground
+the middle or the background and so that
+
+ align:start position:0%
+the middle or the background and so that
+ 
+
+ align:start position:0%
+the middle or the background and so that
+you know we're only getting blurred 1d
+
+ align:start position:0%
+you know we're only getting blurred 1d
+ 
+
+ align:start position:0%
+you know we're only getting blurred 1d
+here so there's some more complexity but
+
+ align:start position:0%
+here so there's some more complexity but
+ 
+
+ align:start position:0%
+here so there's some more complexity but
+that's the basic idea right so you see
+
+ align:start position:0%
+that's the basic idea right so you see
+ 
+
+ align:start position:0%
+that's the basic idea right so you see
+that path we start with medical imaging
+
+ align:start position:0%
+that path we start with medical imaging
+ 
+
+ align:start position:0%
+that path we start with medical imaging
+we publish a paper in uh and not
+
+ align:start position:0%
+we publish a paper in uh and not
+ 
+
+ align:start position:0%
+we publish a paper in uh and not
+siggraph but a graphics journal it's
+
+ align:start position:0%
+siggraph but a graphics journal it's
+ 
+
+ align:start position:0%
+siggraph but a graphics journal it's
+pretty pretty straightforward algorithm
+
+ align:start position:0%
+pretty pretty straightforward algorithm
+ 
+
+ align:start position:0%
+pretty pretty straightforward algorithm
+and so now just to finish up tomography
+
+ align:start position:0%
+and so now just to finish up tomography
+ 
+
+ align:start position:0%
+and so now just to finish up tomography
+uh you know applying it to optics like
+
+ align:start position:0%
+uh you know applying it to optics like
+ 
+
+ align:start position:0%
+uh you know applying it to optics like
+we did is obvious it's also obvious how
+
+ align:start position:0%
+we did is obvious it's also obvious how
+ 
+
+ align:start position:0%
+we did is obvious it's also obvious how
+you would apply this to other
+
+ align:start position:0%
+you would apply this to other
+ 
+
+ align:start position:0%
+you would apply this to other
+applications so this
+
+ align:start position:0%
+applications so this
+ 
+
+ align:start position:0%
+applications so this
+this is an acoustic version of
+
+ align:start position:0%
+this is an acoustic version of
+ 
+
+ align:start position:0%
+this is an acoustic version of
+tomography because we're just changing
+
+ align:start position:0%
+tomography because we're just changing
+ 
+
+ align:start position:0%
+tomography because we're just changing
+the wavelength in a way
+
+ align:start position:0%
+the wavelength in a way
+ 
+
+ align:start position:0%
+the wavelength in a way
+and so the idea is that say we have some
+
+ align:start position:0%
+and so the idea is that say we have some
+ 
+
+ align:start position:0%
+and so the idea is that say we have some
+underground region we're looking for oil
+
+ align:start position:0%
+underground region we're looking for oil
+ 
+
+ align:start position:0%
+underground region we're looking for oil
+deposits or more noble things like
+
+ align:start position:0%
+deposits or more noble things like
+ 
+
+ align:start position:0%
+deposits or more noble things like
+looking for the skeletons or dinosaurs
+
+ align:start position:0%
+looking for the skeletons or dinosaurs
+ 
+
+ align:start position:0%
+looking for the skeletons or dinosaurs
+and so uh to to find
+
+ align:start position:0%
+and so uh to to find
+ 
+
+ align:start position:0%
+and so uh to to find
+the density function it's very easy you
+
+ align:start position:0%
+the density function it's very easy you
+ 
+
+ align:start position:0%
+the density function it's very easy you
+just set up a set of explosive charges
+
+ align:start position:0%
+just set up a set of explosive charges
+ 
+
+ align:start position:0%
+just set up a set of explosive charges
+right those are going to generate
+
+ align:start position:0%
+right those are going to generate
+ 
+
+ align:start position:0%
+right those are going to generate
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+pressure waves
+
+ align:start position:0%
+pressure waves
+ 
+
+ align:start position:0%
+pressure waves
+and they're going to travel hopefully if
+
+ align:start position:0%
+and they're going to travel hopefully if
+ 
+
+ align:start position:0%
+and they're going to travel hopefully if
+we do things correctly and we model it
+
+ align:start position:0%
+we do things correctly and we model it
+ 
+
+ align:start position:0%
+we do things correctly and we model it
+if we if we select things right then
+
+ align:start position:0%
+if we if we select things right then
+ 
+
+ align:start position:0%
+if we if we select things right then
+they mostly travel on ballistic paths to
+
+ align:start position:0%
+they mostly travel on ballistic paths to
+ 
+
+ align:start position:0%
+they mostly travel on ballistic paths to
+a series of microphones
+
+ align:start position:0%
+a series of microphones
+ 
+
+ align:start position:0%
+a series of microphones
+and then again we can just treat this as
+
+ align:start position:0%
+and then again we can just treat this as
+ 
+
+ align:start position:0%
+and then again we can just treat this as
+a limited baseline tomography and invert
+
+ align:start position:0%
+a limited baseline tomography and invert
+ 
+
+ align:start position:0%
+a limited baseline tomography and invert
+that system and here at each pixel or
+
+ align:start position:0%
+that system and here at each pixel or
+ 
+
+ align:start position:0%
+that system and here at each pixel or
+voxel we're reconstructing the velocity
+
+ align:start position:0%
+voxel we're reconstructing the velocity
+ 
+
+ align:start position:0%
+voxel we're reconstructing the velocity
+right because the velocity is
+
+ align:start position:0%
+right because the velocity is
+ 
+
+ align:start position:0%
+right because the velocity is
+proportional to the density of the
+
+ align:start position:0%
+proportional to the density of the
+ 
+
+ align:start position:0%
+proportional to the density of the
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+and so then we can reconstruct
+
+ align:start position:0%
+and so then we can reconstruct
+ 
+
+ align:start position:0%
+and so then we can reconstruct
+underground objects
+
+ align:start position:0%
+underground objects
+ 
+
+ align:start position:0%
+underground objects
+using tomography using explosives and
+
+ align:start position:0%
+using tomography using explosives and
+ 
+
+ align:start position:0%
+using tomography using explosives and
+microphones sort of cool idea
+
+ align:start position:0%
+microphones sort of cool idea
+ 
+
+ align:start position:0%
+microphones sort of cool idea
+so you can do this for for anything you
+
+ align:start position:0%
+so you can do this for for anything you
+ 
+
+ align:start position:0%
+so you can do this for for anything you
+can do this
+
+ align:start position:0%
+can do this
+ 
+
+ align:start position:0%
+can do this
+not just underground but
+
+ align:start position:0%
+not just underground but
+ 
+
+ align:start position:0%
+not just underground but
+this is how ultrasonic works as well
+
+ align:start position:0%
+this is how ultrasonic works as well
+ 
+
+ align:start position:0%
+this is how ultrasonic works as well
+ultrasound
+
+ align:start position:0%
+ultrasound
+ 
+
+ align:start position:0%
+ultrasound
+ultrasound scanners right
+
+ align:start position:0%
+ultrasound scanners right
+ 
+
+ align:start position:0%
+ultrasound scanners right
+and so then rock avoid proposed this in
+
+ align:start position:0%
+and so then rock avoid proposed this in
+ 
+
+ align:start position:0%
+and so then rock avoid proposed this in
+the course which which i always liked
+
+ align:start position:0%
+the course which which i always liked
+ 
+
+ align:start position:0%
+the course which which i always liked
+which was
+
+ align:start position:0%
+which was
+ 
+
+ align:start position:0%
+which was
+if you could convince the the italians
+
+ align:start position:0%
+if you could convince the the italians
+ 
+
+ align:start position:0%
+if you could convince the the italians
+that you can set up some explosive
+
+ align:start position:0%
+that you can set up some explosive
+ 
+
+ align:start position:0%
+that you can set up some explosive
+charges on their subway which they might
+
+ align:start position:0%
+charges on their subway which they might
+ 
+
+ align:start position:0%
+charges on their subway which they might
+have concerns with and use some
+
+ align:start position:0%
+have concerns with and use some
+ 
+
+ align:start position:0%
+have concerns with and use some
+microphones and you might be able to
+
+ align:start position:0%
+microphones and you might be able to
+ 
+
+ align:start position:0%
+microphones and you might be able to
+reconstruct uh underground rome
+
+ align:start position:0%
+reconstruct uh underground rome
+ 
+
+ align:start position:0%
+reconstruct uh underground rome
+uh just from that algorithm at least a
+
+ align:start position:0%
+uh just from that algorithm at least a
+ 
+
+ align:start position:0%
+uh just from that algorithm at least a
+rough estimate and so it's not bad i
+
+ align:start position:0%
+rough estimate and so it's not bad i
+ 
+
+ align:start position:0%
+rough estimate and so it's not bad i
+mean if you go out to these
+
+ align:start position:0%
+mean if you go out to these
+ 
+
+ align:start position:0%
+mean if you go out to these
+archaeological sites they're huge and
+
+ align:start position:0%
+archaeological sites they're huge and
+ 
+
+ align:start position:0%
+archaeological sites they're huge and
+they all often discover new sites
+
+ align:start position:0%
+they all often discover new sites
+ 
+
+ align:start position:0%
+they all often discover new sites
+underground and so this is another way
+
+ align:start position:0%
+underground and so this is another way
+ 
+
+ align:start position:0%
+underground and so this is another way
+to compete with uh with other scanning
+
+ align:start position:0%
+to compete with uh with other scanning
+ 
+
+ align:start position:0%
+to compete with uh with other scanning
+technologies it's very inexpensive and
+
+ align:start position:0%
+technologies it's very inexpensive and
+ 
+
+ align:start position:0%
+technologies it's very inexpensive and
+so then as long as i'm doing okay on
+
+ align:start position:0%
+so then as long as i'm doing okay on
+ 
+
+ align:start position:0%
+so then as long as i'm doing okay on
+time i'll quickly blow through yeah go
+
+ align:start position:0%
+time i'll quickly blow through yeah go
+ 
+
+ align:start position:0%
+time i'll quickly blow through yeah go
+ahead so
+
+ align:start position:0%
+ahead so
+ 
+
+ align:start position:0%
+ahead so
+we started with tomography which assumes
+
+ align:start position:0%
+we started with tomography which assumes
+ 
+
+ align:start position:0%
+we started with tomography which assumes
+everything travels on a ballistic path
+
+ align:start position:0%
+everything travels on a ballistic path
+ 
+
+ align:start position:0%
+everything travels on a ballistic path
+and so now let's start loosening our
+
+ align:start position:0%
+and so now let's start loosening our
+ 
+
+ align:start position:0%
+and so now let's start loosening our
+assumption on that ballistic path right
+
+ align:start position:0%
+assumption on that ballistic path right
+ 
+
+ align:start position:0%
+assumption on that ballistic path right
+so the first assumption is let's allow
+
+ align:start position:0%
+so the first assumption is let's allow
+ 
+
+ align:start position:0%
+so the first assumption is let's allow
+things to refract so instead of having
+
+ align:start position:0%
+things to refract so instead of having
+ 
+
+ align:start position:0%
+things to refract so instead of having
+an object with just just attenuates rays
+
+ align:start position:0%
+an object with just just attenuates rays
+ 
+
+ align:start position:0%
+an object with just just attenuates rays
+let's assume we have like a lens here
+
+ align:start position:0%
+let's assume we have like a lens here
+ 
+
+ align:start position:0%
+let's assume we have like a lens here
+that's going to bend raise and diffract
+
+ align:start position:0%
+that's going to bend raise and diffract
+ 
+
+ align:start position:0%
+that's going to bend raise and diffract
+them slightly right so we have weakly
+
+ align:start position:0%
+them slightly right so we have weakly
+ 
+
+ align:start position:0%
+them slightly right so we have weakly
+refractive media
+
+ align:start position:0%
+refractive media
+ 
+
+ align:start position:0%
+refractive media
+right so we've made this we've loosened
+
+ align:start position:0%
+right so we've made this we've loosened
+ 
+
+ align:start position:0%
+right so we've made this we've loosened
+it the prior model of the object so if
+
+ align:start position:0%
+it the prior model of the object so if
+ 
+
+ align:start position:0%
+it the prior model of the object so if
+you try applying the the inverse radon
+
+ align:start position:0%
+you try applying the the inverse radon
+ 
+
+ align:start position:0%
+you try applying the the inverse radon
+transform to the data set you gather it
+
+ align:start position:0%
+transform to the data set you gather it
+ 
+
+ align:start position:0%
+transform to the data set you gather it
+turns out we won't be able to
+
+ align:start position:0%
+turns out we won't be able to
+ 
+
+ align:start position:0%
+turns out we won't be able to
+reconstruct this
+
+ align:start position:0%
+reconstruct this
+ 
+
+ align:start position:0%
+reconstruct this
+right that assumption that things will
+
+ align:start position:0%
+right that assumption that things will
+ 
+
+ align:start position:0%
+right that assumption that things will
+move on ballistic paths is essential now
+
+ align:start position:0%
+move on ballistic paths is essential now
+ 
+
+ align:start position:0%
+move on ballistic paths is essential now
+there's some interesting work recently
+
+ align:start position:0%
+there's some interesting work recently
+ 
+
+ align:start position:0%
+there's some interesting work recently
+sigograph on schlieren tomography where
+
+ align:start position:0%
+sigograph on schlieren tomography where
+ 
+
+ align:start position:0%
+sigograph on schlieren tomography where
+they they do manage to do that with
+
+ align:start position:0%
+they they do manage to do that with
+ 
+
+ align:start position:0%
+they they do manage to do that with
+certain assumptions but anyways
+
+ align:start position:0%
+certain assumptions but anyways
+ 
+
+ align:start position:0%
+certain assumptions but anyways
+if we if we loosen this to allow
+
+ align:start position:0%
+if we if we loosen this to allow
+ 
+
+ align:start position:0%
+if we if we loosen this to allow
+refraction then the algorithm changes
+
+ align:start position:0%
+refraction then the algorithm changes
+ 
+
+ align:start position:0%
+refraction then the algorithm changes
+and says this is very clever work again
+
+ align:start position:0%
+and says this is very clever work again
+ 
+
+ align:start position:0%
+and says this is very clever work again
+this is in slandering hack if you're
+
+ align:start position:0%
+this is in slandering hack if you're
+ 
+
+ align:start position:0%
+this is in slandering hack if you're
+interested but the idea is let's
+
+ align:start position:0%
+interested but the idea is let's
+ 
+
+ align:start position:0%
+interested but the idea is let's
+illuminate the object let's make a
+
+ align:start position:0%
+illuminate the object let's make a
+ 
+
+ align:start position:0%
+illuminate the object let's make a
+parallel beam set up again so we'll
+
+ align:start position:0%
+parallel beam set up again so we'll
+ 
+
+ align:start position:0%
+parallel beam set up again so we'll
+start with some monochromatic plane wave
+
+ align:start position:0%
+start with some monochromatic plane wave
+ 
+
+ align:start position:0%
+start with some monochromatic plane wave
+so we have some laser that's generating
+
+ align:start position:0%
+so we have some laser that's generating
+ 
+
+ align:start position:0%
+so we have some laser that's generating
+one wavelength of light it's it's
+
+ align:start position:0%
+one wavelength of light it's it's
+ 
+
+ align:start position:0%
+one wavelength of light it's it's
+coherent traveling towards our object
+
+ align:start position:0%
+coherent traveling towards our object
+ 
+
+ align:start position:0%
+coherent traveling towards our object
+and it arrives on some detector and so
+
+ align:start position:0%
+and it arrives on some detector and so
+ 
+
+ align:start position:0%
+and it arrives on some detector and so
+we get our projection again again this
+
+ align:start position:0%
+we get our projection again again this
+ 
+
+ align:start position:0%
+we get our projection again again this
+what we're trying to reconstruct now is
+
+ align:start position:0%
+what we're trying to reconstruct now is
+ 
+
+ align:start position:0%
+what we're trying to reconstruct now is
+the index of refraction not the
+
+ align:start position:0%
+the index of refraction not the
+ 
+
+ align:start position:0%
+the index of refraction not the
+absorption okay
+
+ align:start position:0%
+absorption okay
+ 
+
+ align:start position:0%
+absorption okay
+so we receive the scattered wave and it
+
+ align:start position:0%
+so we receive the scattered wave and it
+ 
+
+ align:start position:0%
+so we receive the scattered wave and it
+turns out you also need to measure the
+
+ align:start position:0%
+turns out you also need to measure the
+ 
+
+ align:start position:0%
+turns out you also need to measure the
+phase so you'll have a second reference
+
+ align:start position:0%
+phase so you'll have a second reference
+ 
+
+ align:start position:0%
+phase so you'll have a second reference
+beam so essentially taking a hologram of
+
+ align:start position:0%
+beam so essentially taking a hologram of
+ 
+
+ align:start position:0%
+beam so essentially taking a hologram of
+the object for those of you familiar but
+
+ align:start position:0%
+the object for those of you familiar but
+ 
+
+ align:start position:0%
+the object for those of you familiar but
+you can sort of ignore that basically
+
+ align:start position:0%
+you can sort of ignore that basically
+ 
+
+ align:start position:0%
+you can sort of ignore that basically
+you have a plane wave
+
+ align:start position:0%
+you have a plane wave
+ 
+
+ align:start position:0%
+you have a plane wave
+projecting through the object creating
+
+ align:start position:0%
+projecting through the object creating
+ 
+
+ align:start position:0%
+projecting through the object creating
+some scattered field and so if you run
+
+ align:start position:0%
+some scattered field and so if you run
+ 
+
+ align:start position:0%
+some scattered field and so if you run
+through the math you get a new result
+
+ align:start position:0%
+through the math you get a new result
+ 
+
+ align:start position:0%
+through the math you get a new result
+which is very interesting the foid
+
+ align:start position:0%
+which is very interesting the foid
+ 
+
+ align:start position:0%
+which is very interesting the foid
+projection size theorem changes
+
+ align:start position:0%
+projection size theorem changes
+ 
+
+ align:start position:0%
+projection size theorem changes
+it turns out in your frequency domain
+
+ align:start position:0%
+it turns out in your frequency domain
+ 
+
+ align:start position:0%
+it turns out in your frequency domain
+again we take the 2d fourier transform
+
+ align:start position:0%
+again we take the 2d fourier transform
+ 
+
+ align:start position:0%
+again we take the 2d fourier transform
+or index refraction
+
+ align:start position:0%
+or index refraction
+ 
+
+ align:start position:0%
+or index refraction
+and in the transform domain
+
+ align:start position:0%
+and in the transform domain
+ 
+
+ align:start position:0%
+and in the transform domain
+a plane projection a parallel beam
+
+ align:start position:0%
+a plane projection a parallel beam
+ 
+
+ align:start position:0%
+a plane projection a parallel beam
+projection maps to a curve
+
+ align:start position:0%
+projection maps to a curve
+ 
+
+ align:start position:0%
+projection maps to a curve
+an arc in the frequency domain
+
+ align:start position:0%
+an arc in the frequency domain
+ 
+
+ align:start position:0%
+an arc in the frequency domain
+right so now to do tomography we could
+
+ align:start position:0%
+right so now to do tomography we could
+ 
+
+ align:start position:0%
+right so now to do tomography we could
+do what we did before we could rotate
+
+ align:start position:0%
+do what we did before we could rotate
+ 
+
+ align:start position:0%
+do what we did before we could rotate
+the source or the emitter and detector
+
+ align:start position:0%
+the source or the emitter and detector
+ 
+
+ align:start position:0%
+the source or the emitter and detector
+around the object
+
+ align:start position:0%
+around the object
+ 
+
+ align:start position:0%
+around the object
+right and then we just have to know what
+
+ align:start position:0%
+right and then we just have to know what
+ 
+
+ align:start position:0%
+right and then we just have to know what
+this curve trajectory is which is just
+
+ align:start position:0%
+this curve trajectory is which is just
+ 
+
+ align:start position:0%
+this curve trajectory is which is just
+dependent on the wavelength of light
+
+ align:start position:0%
+dependent on the wavelength of light
+ 
+
+ align:start position:0%
+dependent on the wavelength of light
+right and then we'll populate our
+
+ align:start position:0%
+right and then we'll populate our
+ 
+
+ align:start position:0%
+right and then we'll populate our
+accumulator as before inverse transform
+
+ align:start position:0%
+accumulator as before inverse transform
+ 
+
+ align:start position:0%
+accumulator as before inverse transform
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+hopefully to everyone
+
+ align:start position:0%
+hopefully to everyone
+ 
+
+ align:start position:0%
+hopefully to everyone
+but there's a really clever trick again
+
+ align:start position:0%
+but there's a really clever trick again
+ 
+
+ align:start position:0%
+but there's a really clever trick again
+no moving parts is the usual theme in
+
+ align:start position:0%
+no moving parts is the usual theme in
+ 
+
+ align:start position:0%
+no moving parts is the usual theme in
+these things right to reconstruct
+
+ align:start position:0%
+these things right to reconstruct
+ 
+
+ align:start position:0%
+these things right to reconstruct
+tomographically this object we have to
+
+ align:start position:0%
+tomographically this object we have to
+ 
+
+ align:start position:0%
+tomographically this object we have to
+rotate something to populate this
+
+ align:start position:0%
+rotate something to populate this
+ 
+
+ align:start position:0%
+rotate something to populate this
+accumulator it turns out the clever
+
+ align:start position:0%
+accumulator it turns out the clever
+ 
+
+ align:start position:0%
+accumulator it turns out the clever
+trick here is that this arc is dependent
+
+ align:start position:0%
+trick here is that this arc is dependent
+ 
+
+ align:start position:0%
+trick here is that this arc is dependent
+on the frequency
+
+ align:start position:0%
+on the frequency
+ 
+
+ align:start position:0%
+on the frequency
+of illumination does anyone see without
+
+ align:start position:0%
+of illumination does anyone see without
+ 
+
+ align:start position:0%
+of illumination does anyone see without
+looking at the thing on the right what
+
+ align:start position:0%
+looking at the thing on the right what
+ 
+
+ align:start position:0%
+looking at the thing on the right what
+do you do
+
+ align:start position:0%
+do you do
+ 
+
+ align:start position:0%
+do you do
+change the frequency great
+
+ align:start position:0%
+change the frequency great
+ 
+
+ align:start position:0%
+change the frequency great
+that was a great good insight so
+
+ align:start position:0%
+that was a great good insight so
+ 
+
+ align:start position:0%
+that was a great good insight so
+if you just step through the frequency
+
+ align:start position:0%
+if you just step through the frequency
+ 
+
+ align:start position:0%
+if you just step through the frequency
+slowly
+
+ align:start position:0%
+slowly
+ 
+
+ align:start position:0%
+slowly
+right you'll sort of sweep this out
+
+ align:start position:0%
+right you'll sort of sweep this out
+ 
+
+ align:start position:0%
+right you'll sort of sweep this out
+right and you'll get
+
+ align:start position:0%
+right and you'll get
+ 
+
+ align:start position:0%
+right and you'll get
+at least half of the transform
+
+ align:start position:0%
+at least half of the transform
+ 
+
+ align:start position:0%
+at least half of the transform
+but what if i told you that was a real
+
+ align:start position:0%
+but what if i told you that was a real
+ 
+
+ align:start position:0%
+but what if i told you that was a real
+valued function
+
+ align:start position:0%
+valued function
+ 
+
+ align:start position:0%
+valued function
+can you do you know what the property is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what kind of symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conjugate symmetric right right so we
+
+ align:start position:0%
+conjugate symmetric right right so we
+ 
+
+ align:start position:0%
+conjugate symmetric right right so we
+know that this this function is
+
+ align:start position:0%
+know that this this function is
+ 
+
+ align:start position:0%
+know that this this function is
+conjugate symmetric because it's a real
+
+ align:start position:0%
+conjugate symmetric because it's a real
+ 
+
+ align:start position:0%
+conjugate symmetric because it's a real
+value function so getting only half of
+
+ align:start position:0%
+value function so getting only half of
+ 
+
+ align:start position:0%
+value function so getting only half of
+it's enough so we can replicate it right
+
+ align:start position:0%
+it's enough so we can replicate it right
+ 
+
+ align:start position:0%
+it's enough so we can replicate it right
+so again tomography is basically
+
+ align:start position:0%
+so again tomography is basically
+ 
+
+ align:start position:0%
+so again tomography is basically
+remembering signal processing remember
+
+ align:start position:0%
+remembering signal processing remember
+ 
+
+ align:start position:0%
+remembering signal processing remember
+all those transform pairs
+
+ align:start position:0%
+all those transform pairs
+ 
+
+ align:start position:0%
+all those transform pairs
+you'll have good luck in your final
+
+ align:start position:0%
+you'll have good luck in your final
+ 
+
+ align:start position:0%
+you'll have good luck in your final
+project you've decided to use it and so
+
+ align:start position:0%
+project you've decided to use it and so
+ 
+
+ align:start position:0%
+project you've decided to use it and so
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we can take a sequence of images where
+
+ align:start position:0%
+we can take a sequence of images where
+ 
+
+ align:start position:0%
+we can take a sequence of images where
+we just vary the frequency parameter
+
+ align:start position:0%
+we just vary the frequency parameter
+ 
+
+ align:start position:0%
+we just vary the frequency parameter
+we'll populate this guy use conjugate
+
+ align:start position:0%
+we'll populate this guy use conjugate
+ 
+
+ align:start position:0%
+we'll populate this guy use conjugate
+symmetric symmetry and inverse transform
+
+ align:start position:0%
+symmetric symmetry and inverse transform
+ 
+
+ align:start position:0%
+symmetric symmetry and inverse transform
+and so then you get a new result which
+
+ align:start position:0%
+and so then you get a new result which
+ 
+
+ align:start position:0%
+and so then you get a new result which
+is almost as fundamental in this field
+
+ align:start position:0%
+is almost as fundamental in this field
+ 
+
+ align:start position:0%
+is almost as fundamental in this field
+as the foil projection slice theorem
+
+ align:start position:0%
+as the foil projection slice theorem
+ 
+
+ align:start position:0%
+as the foil projection slice theorem
+which is that a white light
+
+ align:start position:0%
+which is that a white light
+ 
+
+ align:start position:0%
+which is that a white light
+hologram
+
+ align:start position:0%
+hologram
+ 
+
+ align:start position:0%
+hologram
+so basically can can reconstruct the
+
+ align:start position:0%
+so basically can can reconstruct the
+ 
+
+ align:start position:0%
+so basically can can reconstruct the
+index refraction of an object because
+
+ align:start position:0%
+index refraction of an object because
+ 
+
+ align:start position:0%
+index refraction of an object because
+right we can use superposition again we
+
+ align:start position:0%
+right we can use superposition again we
+ 
+
+ align:start position:0%
+right we can use superposition again we
+can eliminate with multiple frequencies
+
+ align:start position:0%
+can eliminate with multiple frequencies
+ 
+
+ align:start position:0%
+can eliminate with multiple frequencies
+at the same time as long as we can
+
+ align:start position:0%
+at the same time as long as we can
+ 
+
+ align:start position:0%
+at the same time as long as we can
+resolve them then we'll get all the data
+
+ align:start position:0%
+resolve them then we'll get all the data
+ 
+
+ align:start position:0%
+resolve them then we'll get all the data
+at once
+
+ align:start position:0%
+at once
+ 
+
+ align:start position:0%
+at once
+right so you basically have a broadband
+
+ align:start position:0%
+right so you basically have a broadband
+ 
+
+ align:start position:0%
+right so you basically have a broadband
+plane coherent wave traveling through
+
+ align:start position:0%
+plane coherent wave traveling through
+ 
+
+ align:start position:0%
+plane coherent wave traveling through
+the object and from that you
+
+ align:start position:0%
+the object and from that you
+ 
+
+ align:start position:0%
+the object and from that you
+instantaneously get the index refraction
+
+ align:start position:0%
+instantaneously get the index refraction
+ 
+
+ align:start position:0%
+instantaneously get the index refraction
+so the refraction diffraction is
+
+ align:start position:0%
+so the refraction diffraction is
+ 
+
+ align:start position:0%
+so the refraction diffraction is
+refraction and diffraction
+
+ align:start position:0%
+refraction and diffraction
+ 
+
+ align:start position:0%
+refraction and diffraction
+are being used
+
+ align:start position:0%
+are being used
+ 
+
+ align:start position:0%
+are being used
+interchangeably here yes you know what
+
+ align:start position:0%
+interchangeably here yes you know what
+ 
+
+ align:start position:0%
+interchangeably here yes you know what
+why refraction and diffraction yeah i
+
+ align:start position:0%
+why refraction and diffraction yeah i
+ 
+
+ align:start position:0%
+why refraction and diffraction yeah i
+mean you're trying to reconstruct
+
+ align:start position:0%
+mean you're trying to reconstruct
+ 
+
+ align:start position:0%
+mean you're trying to reconstruct
+something in presence of refraction
+
+ align:start position:0%
+something in presence of refraction
+ 
+
+ align:start position:0%
+something in presence of refraction
+right using a diffraction theorem
+
+ align:start position:0%
+right using a diffraction theorem
+ 
+
+ align:start position:0%
+right using a diffraction theorem
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+do you know what's the length what's
+
+ align:start position:0%
+do you know what's the length what's
+ 
+
+ align:start position:0%
+do you know what's the length what's
+yeah what's the reason for that i know i
+
+ align:start position:0%
+yeah what's the reason for that i know i
+ 
+
+ align:start position:0%
+yeah what's the reason for that i know i
+i don't think i understand this at a
+
+ align:start position:0%
+i don't think i understand this at a
+ 
+
+ align:start position:0%
+i don't think i understand this at a
+deep enough level that i mean
+
+ align:start position:0%
+deep enough level that i mean
+ 
+
+ align:start position:0%
+deep enough level that i mean
+fundamentally i just realized why
+
+ align:start position:0%
+fundamentally i just realized why
+ 
+
+ align:start position:0%
+fundamentally i just realized why
+confronted confusing the two so
+
+ align:start position:0%
+confronted confusing the two so
+ 
+
+ align:start position:0%
+confronted confusing the two so
+yeah i think
+
+ align:start position:0%
+yeah i think
+ 
+
+ align:start position:0%
+yeah i think
+yeah i have to get back to that okay
+
+ align:start position:0%
+yeah i have to get back to that okay
+ 
+
+ align:start position:0%
+yeah i have to get back to that okay
+it's in slam loop but
+
+ align:start position:0%
+it's in slam loop but
+ 
+
+ align:start position:0%
+it's in slam loop but
+this is getting beyond my
+
+ align:start position:0%
+this is getting beyond my
+ 
+
+ align:start position:0%
+this is getting beyond my
+my not so this is what a reconstruction
+
+ align:start position:0%
+my not so this is what a reconstruction
+ 
+
+ align:start position:0%
+my not so this is what a reconstruction
+looks like of a simulated object right
+
+ align:start position:0%
+looks like of a simulated object right
+ 
+
+ align:start position:0%
+looks like of a simulated object right
+so now our artifacts have this arc
+
+ align:start position:0%
+so now our artifacts have this arc
+ 
+
+ align:start position:0%
+so now our artifacts have this arc
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+but again what this is interesting is if
+
+ align:start position:0%
+but again what this is interesting is if
+ 
+
+ align:start position:0%
+but again what this is interesting is if
+you look at schlieren tomography paper
+
+ align:start position:0%
+you look at schlieren tomography paper
+ 
+
+ align:start position:0%
+you look at schlieren tomography paper
+it means you could get real-time
+
+ align:start position:0%
+it means you could get real-time
+ 
+
+ align:start position:0%
+it means you could get real-time
+reconstruction without strobing any
+
+ align:start position:0%
+reconstruction without strobing any
+ 
+
+ align:start position:0%
+reconstruction without strobing any
+lights by just doing a mono by doing
+
+ align:start position:0%
+lights by just doing a mono by doing
+ 
+
+ align:start position:0%
+lights by just doing a mono by doing
+broadband hologram holographic imaging
+
+ align:start position:0%
+broadband hologram holographic imaging
+ 
+
+ align:start position:0%
+broadband hologram holographic imaging
+of your object and then this is why i
+
+ align:start position:0%
+of your object and then this is why i
+ 
+
+ align:start position:0%
+of your object and then this is why i
+mentioned the filtered back projection
+
+ align:start position:0%
+mentioned the filtered back projection
+ 
+
+ align:start position:0%
+mentioned the filtered back projection
+earlier that was the frequency domain
+
+ align:start position:0%
+earlier that was the frequency domain
+ 
+
+ align:start position:0%
+earlier that was the frequency domain
+reconstruction transform so it turns out
+
+ align:start position:0%
+reconstruction transform so it turns out
+ 
+
+ align:start position:0%
+reconstruction transform so it turns out
+there's a purely spatial domain
+
+ align:start position:0%
+there's a purely spatial domain
+ 
+
+ align:start position:0%
+there's a purely spatial domain
+transform for this one as well and so
+
+ align:start position:0%
+transform for this one as well and so
+ 
+
+ align:start position:0%
+transform for this one as well and so
+this one i don't know but the
+
+ align:start position:0%
+this one i don't know but the
+ 
+
+ align:start position:0%
+this one i don't know but the
+2d fourier transform of an arc
+
+ align:start position:0%
+2d fourier transform of an arc
+ 
+
+ align:start position:0%
+2d fourier transform of an arc
+right maps to this strange depth
+
+ align:start position:0%
+right maps to this strange depth
+ 
+
+ align:start position:0%
+right maps to this strange depth
+dependent function you see here
+
+ align:start position:0%
+dependent function you see here
+ 
+
+ align:start position:0%
+dependent function you see here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so that's what filter back projection
+
+ align:start position:0%
+so that's what filter back projection
+ 
+
+ align:start position:0%
+so that's what filter back projection
+becomes is smearing but along
+
+ align:start position:0%
+becomes is smearing but along
+ 
+
+ align:start position:0%
+becomes is smearing but along
+these paths that become wider as you go
+
+ align:start position:0%
+these paths that become wider as you go
+ 
+
+ align:start position:0%
+these paths that become wider as you go
+in depth
+
+ align:start position:0%
+in depth
+ 
+
+ align:start position:0%
+in depth
+right just because that's what the
+
+ align:start position:0%
+right just because that's what the
+ 
+
+ align:start position:0%
+right just because that's what the
+inverse right transform is of
+
+ align:start position:0%
+inverse right transform is of
+ 
+
+ align:start position:0%
+inverse right transform is of
+this arc pattern so you can do filtered
+
+ align:start position:0%
+this arc pattern so you can do filtered
+ 
+
+ align:start position:0%
+this arc pattern so you can do filtered
+back projection but it turns out it's
+
+ align:start position:0%
+back projection but it turns out it's
+ 
+
+ align:start position:0%
+back projection but it turns out it's
+much more computationally expensive so
+
+ align:start position:0%
+much more computationally expensive so
+ 
+
+ align:start position:0%
+much more computationally expensive so
+they generally do this using frequency
+
+ align:start position:0%
+they generally do this using frequency
+ 
+
+ align:start position:0%
+they generally do this using frequency
+domain i think
+
+ align:start position:0%
+domain i think
+ 
+
+ align:start position:0%
+domain i think
+and so then now we move so that was
+
+ align:start position:0%
+and so then now we move so that was
+ 
+
+ align:start position:0%
+and so then now we move so that was
+weakly refracting but now if we move to
+
+ align:start position:0%
+weakly refracting but now if we move to
+ 
+
+ align:start position:0%
+weakly refracting but now if we move to
+say like putting putting leds against
+
+ align:start position:0%
+say like putting putting leds against
+ 
+
+ align:start position:0%
+say like putting putting leds against
+your skin right now we're talking about
+
+ align:start position:0%
+your skin right now we're talking about
+ 
+
+ align:start position:0%
+your skin right now we're talking about
+things that are strongly scattered
+
+ align:start position:0%
+things that are strongly scattered
+ 
+
+ align:start position:0%
+things that are strongly scattered
+right so we've moved from complete just
+
+ align:start position:0%
+right so we've moved from complete just
+ 
+
+ align:start position:0%
+right so we've moved from complete just
+absorbing along a ballistic trajectory
+
+ align:start position:0%
+absorbing along a ballistic trajectory
+ 
+
+ align:start position:0%
+absorbing along a ballistic trajectory
+towards refracting a little bit and now
+
+ align:start position:0%
+towards refracting a little bit and now
+ 
+
+ align:start position:0%
+towards refracting a little bit and now
+we're just scattering completely imagine
+
+ align:start position:0%
+we're just scattering completely imagine
+ 
+
+ align:start position:0%
+we're just scattering completely imagine
+putting an led on your finger and you
+
+ align:start position:0%
+putting an led on your finger and you
+ 
+
+ align:start position:0%
+putting an led on your finger and you
+want to see the bone inside your finger
+
+ align:start position:0%
+want to see the bone inside your finger
+ 
+
+ align:start position:0%
+want to see the bone inside your finger
+right with just visible light so this is
+
+ align:start position:0%
+right with just visible light so this is
+ 
+
+ align:start position:0%
+right with just visible light so this is
+an example you can see like this is sort
+
+ align:start position:0%
+an example you can see like this is sort
+ 
+
+ align:start position:0%
+an example you can see like this is sort
+of like this is this is a cross section
+
+ align:start position:0%
+of like this is this is a cross section
+ 
+
+ align:start position:0%
+of like this is this is a cross section
+through our finger we'll say and we have
+
+ align:start position:0%
+through our finger we'll say and we have
+ 
+
+ align:start position:0%
+through our finger we'll say and we have
+photo diodes all around
+
+ align:start position:0%
+photo diodes all around
+ 
+
+ align:start position:0%
+photo diodes all around
+our finger and then we put this little
+
+ align:start position:0%
+our finger and then we put this little
+ 
+
+ align:start position:0%
+our finger and then we put this little
+like fiber optic
+
+ align:start position:0%
+like fiber optic
+ 
+
+ align:start position:0%
+like fiber optic
+right against our finger and illuminate
+
+ align:start position:0%
+right against our finger and illuminate
+ 
+
+ align:start position:0%
+right against our finger and illuminate
+it and so you'll sort of scatter light
+
+ align:start position:0%
+it and so you'll sort of scatter light
+ 
+
+ align:start position:0%
+it and so you'll sort of scatter light
+all through that volume and you'll
+
+ align:start position:0%
+all through that volume and you'll
+ 
+
+ align:start position:0%
+all through that volume and you'll
+measure its intensity at some points
+
+ align:start position:0%
+measure its intensity at some points
+ 
+
+ align:start position:0%
+measure its intensity at some points
+coming out on the surface right so this
+
+ align:start position:0%
+coming out on the surface right so this
+ 
+
+ align:start position:0%
+coming out on the surface right so this
+is known as diffuse optical tomography
+
+ align:start position:0%
+is known as diffuse optical tomography
+ 
+
+ align:start position:0%
+is known as diffuse optical tomography
+because diffusion is the key process
+
+ align:start position:0%
+because diffusion is the key process
+ 
+
+ align:start position:0%
+because diffusion is the key process
+we're trying to invert
+
+ align:start position:0%
+we're trying to invert
+ 
+
+ align:start position:0%
+we're trying to invert
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+in all of these cases we're just
+
+ align:start position:0%
+in all of these cases we're just
+ 
+
+ align:start position:0%
+in all of these cases we're just
+creating this inverse system right we're
+
+ align:start position:0%
+creating this inverse system right we're
+ 
+
+ align:start position:0%
+creating this inverse system right we're
+creating something that we then apply
+
+ align:start position:0%
+creating something that we then apply
+ 
+
+ align:start position:0%
+creating something that we then apply
+the inverse square transform to invert
+
+ align:start position:0%
+the inverse square transform to invert
+ 
+
+ align:start position:0%
+the inverse square transform to invert
+or what have you so in strongly
+
+ align:start position:0%
+or what have you so in strongly
+ 
+
+ align:start position:0%
+or what have you so in strongly
+refractive or scattering media you end
+
+ align:start position:0%
+refractive or scattering media you end
+ 
+
+ align:start position:0%
+refractive or scattering media you end
+up with a very difficult model to infer
+
+ align:start position:0%
+up with a very difficult model to infer
+ 
+
+ align:start position:0%
+up with a very difficult model to infer
+it's still posed
+
+ align:start position:0%
+it's still posed
+ 
+
+ align:start position:0%
+it's still posed
+but it's ill-posed and non-linear which
+
+ align:start position:0%
+but it's ill-posed and non-linear which
+ 
+
+ align:start position:0%
+but it's ill-posed and non-linear which
+means it's very hard
+
+ align:start position:0%
+means it's very hard
+ 
+
+ align:start position:0%
+means it's very hard
+so what they generally do is they they
+
+ align:start position:0%
+so what they generally do is they they
+ 
+
+ align:start position:0%
+so what they generally do is they they
+use some tricks to get to sort of
+
+ align:start position:0%
+use some tricks to get to sort of
+ 
+
+ align:start position:0%
+use some tricks to get to sort of
+bootstrap the inversion right so if you
+
+ align:start position:0%
+bootstrap the inversion right so if you
+ 
+
+ align:start position:0%
+bootstrap the inversion right so if you
+can start with a good initial guess
+
+ align:start position:0%
+can start with a good initial guess
+ 
+
+ align:start position:0%
+can start with a good initial guess
+of say what the here we're looking maybe
+
+ align:start position:0%
+of say what the here we're looking maybe
+ 
+
+ align:start position:0%
+of say what the here we're looking maybe
+for optical density right we're looking
+
+ align:start position:0%
+for optical density right we're looking
+ 
+
+ align:start position:0%
+for optical density right we're looking
+at how dense the material is that's the
+
+ align:start position:0%
+at how dense the material is that's the
+ 
+
+ align:start position:0%
+at how dense the material is that's the
+2d function we're trying to reconstruct
+
+ align:start position:0%
+2d function we're trying to reconstruct
+ 
+
+ align:start position:0%
+2d function we're trying to reconstruct
+in a cross section
+
+ align:start position:0%
+in a cross section
+ 
+
+ align:start position:0%
+in a cross section
+and if we had a good initial guess for
+
+ align:start position:0%
+and if we had a good initial guess for
+ 
+
+ align:start position:0%
+and if we had a good initial guess for
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+then we could sort of use a forward
+
+ align:start position:0%
+then we could sort of use a forward
+ 
+
+ align:start position:0%
+then we could sort of use a forward
+modeling process where we sort of
+
+ align:start position:0%
+modeling process where we sort of
+ 
+
+ align:start position:0%
+modeling process where we sort of
+perturb that density function and see
+
+ align:start position:0%
+perturb that density function and see
+ 
+
+ align:start position:0%
+perturb that density function and see
+how well it predicts the values we found
+
+ align:start position:0%
+how well it predicts the values we found
+ 
+
+ align:start position:0%
+how well it predicts the values we found
+right and we sort of put that in an
+
+ align:start position:0%
+right and we sort of put that in an
+ 
+
+ align:start position:0%
+right and we sort of put that in an
+optimization framework so we do some
+
+ align:start position:0%
+optimization framework so we do some
+ 
+
+ align:start position:0%
+optimization framework so we do some
+gradient descent and we optimize our
+
+ align:start position:0%
+gradient descent and we optimize our
+ 
+
+ align:start position:0%
+gradient descent and we optimize our
+reconstruction the density function so
+
+ align:start position:0%
+reconstruction the density function so
+ 
+
+ align:start position:0%
+reconstruction the density function so
+that the observations match
+
+ align:start position:0%
+that the observations match
+ 
+
+ align:start position:0%
+that the observations match
+the predicted ops predictions match the
+
+ align:start position:0%
+the predicted ops predictions match the
+ 
+
+ align:start position:0%
+the predicted ops predictions match the
+observations right that's the general
+
+ align:start position:0%
+observations right that's the general
+ 
+
+ align:start position:0%
+observations right that's the general
+sort of inversion framework you have
+
+ align:start position:0%
+sort of inversion framework you have
+ 
+
+ align:start position:0%
+sort of inversion framework you have
+right some sort of non-linear gradient
+
+ align:start position:0%
+right some sort of non-linear gradient
+ 
+
+ align:start position:0%
+right some sort of non-linear gradient
+percent algorithm but the question is
+
+ align:start position:0%
+percent algorithm but the question is
+ 
+
+ align:start position:0%
+percent algorithm but the question is
+how do you get that initial guess
+
+ align:start position:0%
+how do you get that initial guess
+ 
+
+ align:start position:0%
+how do you get that initial guess
+of the density function and so you can
+
+ align:start position:0%
+of the density function and so you can
+ 
+
+ align:start position:0%
+of the density function and so you can
+see it says it right there
+
+ align:start position:0%
+see it says it right there
+ 
+
+ align:start position:0%
+see it says it right there
+you can use some other process that is
+
+ align:start position:0%
+you can use some other process that is
+ 
+
+ align:start position:0%
+you can use some other process that is
+ballistic and so that's correlated with
+
+ align:start position:0%
+ballistic and so that's correlated with
+ 
+
+ align:start position:0%
+ballistic and so that's correlated with
+your with your density function so what
+
+ align:start position:0%
+your with your density function so what
+ 
+
+ align:start position:0%
+your with your density function so what
+they generally do here is they use time
+
+ align:start position:0%
+they generally do here is they use time
+ 
+
+ align:start position:0%
+they generally do here is they use time
+of flight they strobe this record the
+
+ align:start position:0%
+of flight they strobe this record the
+ 
+
+ align:start position:0%
+of flight they strobe this record the
+time it takes to travel through
+
+ align:start position:0%
+time it takes to travel through
+ 
+
+ align:start position:0%
+time it takes to travel through
+it maybe not in this specific example
+
+ align:start position:0%
+it maybe not in this specific example
+ 
+
+ align:start position:0%
+it maybe not in this specific example
+but you can imagine doing this you turn
+
+ align:start position:0%
+but you can imagine doing this you turn
+ 
+
+ align:start position:0%
+but you can imagine doing this you turn
+the light on very quickly and look at
+
+ align:start position:0%
+the light on very quickly and look at
+ 
+
+ align:start position:0%
+the light on very quickly and look at
+the time delay and that will give you an
+
+ align:start position:0%
+the time delay and that will give you an
+ 
+
+ align:start position:0%
+the time delay and that will give you an
+initial rough estimate of your density
+
+ align:start position:0%
+initial rough estimate of your density
+ 
+
+ align:start position:0%
+initial rough estimate of your density
+function so that's generally borehole
+
+ align:start position:0%
+function so that's generally borehole
+ 
+
+ align:start position:0%
+function so that's generally borehole
+tomography also does this it uses time
+
+ align:start position:0%
+tomography also does this it uses time
+ 
+
+ align:start position:0%
+tomography also does this it uses time
+of flight to invert the process but also
+
+ align:start position:0%
+of flight to invert the process but also
+ 
+
+ align:start position:0%
+of flight to invert the process but also
+to get the initial guess
+
+ align:start position:0%
+to get the initial guess
+ 
+
+ align:start position:0%
+to get the initial guess
+and then this is used
+
+ align:start position:0%
+and then this is used
+ 
+
+ align:start position:0%
+and then this is used
+a lot in non-invasive medical imaging so
+
+ align:start position:0%
+a lot in non-invasive medical imaging so
+ 
+
+ align:start position:0%
+a lot in non-invasive medical imaging so
+if you don't want to do a ct scan
+
+ align:start position:0%
+if you don't want to do a ct scan
+ 
+
+ align:start position:0%
+if you don't want to do a ct scan
+because the patient's had too much
+
+ align:start position:0%
+because the patient's had too much
+ 
+
+ align:start position:0%
+because the patient's had too much
+dosage of x-rays
+
+ align:start position:0%
+dosage of x-rays
+ 
+
+ align:start position:0%
+dosage of x-rays
+you can for instance put electrodes
+
+ align:start position:0%
+you can for instance put electrodes
+ 
+
+ align:start position:0%
+you can for instance put electrodes
+on their body like you see here and at
+
+ align:start position:0%
+on their body like you see here and at
+ 
+
+ align:start position:0%
+on their body like you see here and at
+least get a rough something not as high
+
+ align:start position:0%
+least get a rough something not as high
+ 
+
+ align:start position:0%
+least get a rough something not as high
+quality as a ct scan but sufficient to
+
+ align:start position:0%
+quality as a ct scan but sufficient to
+ 
+
+ align:start position:0%
+quality as a ct scan but sufficient to
+make the diagnosis so here's an example
+
+ align:start position:0%
+make the diagnosis so here's an example
+ 
+
+ align:start position:0%
+make the diagnosis so here's an example
+of sort of how you apply diffuse optical
+
+ align:start position:0%
+of sort of how you apply diffuse optical
+ 
+
+ align:start position:0%
+of sort of how you apply diffuse optical
+tomography for diagnostic purposes so
+
+ align:start position:0%
+tomography for diagnostic purposes so
+ 
+
+ align:start position:0%
+tomography for diagnostic purposes so
+here we have two twins two babies
+
+ align:start position:0%
+here we have two twins two babies
+ 
+
+ align:start position:0%
+here we have two twins two babies
+left one versus the right one again the
+
+ align:start position:0%
+left one versus the right one again the
+ 
+
+ align:start position:0%
+left one versus the right one again the
+twins and then one of them uh had a
+
+ align:start position:0%
+twins and then one of them uh had a
+ 
+
+ align:start position:0%
+twins and then one of them uh had a
+says the specific thing left ventricular
+
+ align:start position:0%
+says the specific thing left ventricular
+ 
+
+ align:start position:0%
+says the specific thing left ventricular
+hemorrhage so they have blood vessel
+
+ align:start position:0%
+hemorrhage so they have blood vessel
+ 
+
+ align:start position:0%
+hemorrhage so they have blood vessel
+rupture on the left hemisphere and you
+
+ align:start position:0%
+rupture on the left hemisphere and you
+ 
+
+ align:start position:0%
+rupture on the left hemisphere and you
+can sort of see here you know so they
+
+ align:start position:0%
+can sort of see here you know so they
+ 
+
+ align:start position:0%
+can sort of see here you know so they
+attach all these electrodes
+
+ align:start position:0%
+attach all these electrodes
+ 
+
+ align:start position:0%
+attach all these electrodes
+and they generate these time of flight
+
+ align:start position:0%
+and they generate these time of flight
+ 
+
+ align:start position:0%
+and they generate these time of flight
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+for the initial gas and then i look at
+
+ align:start position:0%
+for the initial gas and then i look at
+ 
+
+ align:start position:0%
+for the initial gas and then i look at
+the absorption the conductivity and they
+
+ align:start position:0%
+the absorption the conductivity and they
+ 
+
+ align:start position:0%
+the absorption the conductivity and they
+reconstruct this density function which
+
+ align:start position:0%
+reconstruct this density function which
+ 
+
+ align:start position:0%
+reconstruct this density function which
+actually they get two density functions
+
+ align:start position:0%
+actually they get two density functions
+ 
+
+ align:start position:0%
+actually they get two density functions
+one is blood volume and oxygen
+
+ align:start position:0%
+one is blood volume and oxygen
+ 
+
+ align:start position:0%
+one is blood volume and oxygen
+saturation and so here you can clearly
+
+ align:start position:0%
+saturation and so here you can clearly
+ 
+
+ align:start position:0%
+saturation and so here you can clearly
+see the hemorrhage because this is the
+
+ align:start position:0%
+see the hemorrhage because this is the
+ 
+
+ align:start position:0%
+see the hemorrhage because this is the
+this is the twin that has the hemorrhage
+
+ align:start position:0%
+this is the twin that has the hemorrhage
+ 
+
+ align:start position:0%
+this is the twin that has the hemorrhage
+this is the one that doesn't you can see
+
+ align:start position:0%
+this is the one that doesn't you can see
+ 
+
+ align:start position:0%
+this is the one that doesn't you can see
+there's a lot of blood volume that's a
+
+ align:start position:0%
+there's a lot of blood volume that's a
+ 
+
+ align:start position:0%
+there's a lot of blood volume that's a
+good indication of a hemorrhage but not
+
+ align:start position:0%
+good indication of a hemorrhage but not
+ 
+
+ align:start position:0%
+good indication of a hemorrhage but not
+a great one because your prefrontal
+
+ align:start position:0%
+a great one because your prefrontal
+ 
+
+ align:start position:0%
+a great one because your prefrontal
+cortex has a lot of leveling to begin
+
+ align:start position:0%
+cortex has a lot of leveling to begin
+ 
+
+ align:start position:0%
+cortex has a lot of leveling to begin
+with but then also you can see low
+
+ align:start position:0%
+with but then also you can see low
+ 
+
+ align:start position:0%
+with but then also you can see low
+oxygenation right
+
+ align:start position:0%
+oxygenation right
+ 
+
+ align:start position:0%
+oxygenation right
+which tells you that that blood hasn't
+
+ align:start position:0%
+which tells you that that blood hasn't
+ 
+
+ align:start position:0%
+which tells you that that blood hasn't
+been refreshed in a while so it's a big
+
+ align:start position:0%
+been refreshed in a while so it's a big
+ 
+
+ align:start position:0%
+been refreshed in a while so it's a big
+big pile of blood that's not oxygenated
+
+ align:start position:0%
+big pile of blood that's not oxygenated
+ 
+
+ align:start position:0%
+big pile of blood that's not oxygenated
+which means hemorrhage
+
+ align:start position:0%
+which means hemorrhage
+ 
+
+ align:start position:0%
+which means hemorrhage
+so this is just an example where a ct
+
+ align:start position:0%
+so this is just an example where a ct
+ 
+
+ align:start position:0%
+so this is just an example where a ct
+scan really wouldn't show this because
+
+ align:start position:0%
+scan really wouldn't show this because
+ 
+
+ align:start position:0%
+scan really wouldn't show this because
+the density would be the same and so by
+
+ align:start position:0%
+the density would be the same and so by
+ 
+
+ align:start position:0%
+the density would be the same and so by
+using the diffuse optic filmography you
+
+ align:start position:0%
+using the diffuse optic filmography you
+ 
+
+ align:start position:0%
+using the diffuse optic filmography you
+can get a good reconstruction but
+
+ align:start position:0%
+can get a good reconstruction but
+ 
+
+ align:start position:0%
+can get a good reconstruction but
+because it's diffuse you're only going
+
+ align:start position:0%
+because it's diffuse you're only going
+ 
+
+ align:start position:0%
+because it's diffuse you're only going
+to get a low frequency detail
+
+ align:start position:0%
+to get a low frequency detail
+ 
+
+ align:start position:0%
+to get a low frequency detail
+and then here's another example where
+
+ align:start position:0%
+and then here's another example where
+ 
+
+ align:start position:0%
+and then here's another example where
+you can see the non-invasive part is
+
+ align:start position:0%
+you can see the non-invasive part is
+ 
+
+ align:start position:0%
+you can see the non-invasive part is
+starting to be weakened this looks
+
+ align:start position:0%
+starting to be weakened this looks
+ 
+
+ align:start position:0%
+starting to be weakened this looks
+pretty invasive to me because i don't
+
+ align:start position:0%
+pretty invasive to me because i don't
+ 
+
+ align:start position:0%
+pretty invasive to me because i don't
+want to take those electrodes off
+
+ align:start position:0%
+want to take those electrodes off
+ 
+
+ align:start position:0%
+want to take those electrodes off
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so here you can see this is off
+
+ align:start position:0%
+so here you can see this is off
+ 
+
+ align:start position:0%
+so here you can see this is off
+wikipedia but this is just an example i
+
+ align:start position:0%
+wikipedia but this is just an example i
+ 
+
+ align:start position:0%
+wikipedia but this is just an example i
+found i found it was interesting where
+
+ align:start position:0%
+found i found it was interesting where
+ 
+
+ align:start position:0%
+found i found it was interesting where
+say we want to take ct like images of
+
+ align:start position:0%
+say we want to take ct like images of
+ 
+
+ align:start position:0%
+say we want to take ct like images of
+the heart to study you know
+
+ align:start position:0%
+the heart to study you know
+ 
+
+ align:start position:0%
+the heart to study you know
+some sort of function then we could just
+
+ align:start position:0%
+some sort of function then we could just
+ 
+
+ align:start position:0%
+some sort of function then we could just
+cope the patient electrodes wire them up
+
+ align:start position:0%
+cope the patient electrodes wire them up
+ 
+
+ align:start position:0%
+cope the patient electrodes wire them up
+strobe these electrodes on and off and
+
+ align:start position:0%
+strobe these electrodes on and off and
+ 
+
+ align:start position:0%
+strobe these electrodes on and off and
+the density of functional reconstructing
+
+ align:start position:0%
+the density of functional reconstructing
+ 
+
+ align:start position:0%
+the density of functional reconstructing
+here is conductivity and versus
+
+ align:start position:0%
+here is conductivity and versus
+ 
+
+ align:start position:0%
+here is conductivity and versus
+resistivity which we can then use to
+
+ align:start position:0%
+resistivity which we can then use to
+ 
+
+ align:start position:0%
+resistivity which we can then use to
+look for various problems you know watch
+
+ align:start position:0%
+look for various problems you know watch
+ 
+
+ align:start position:0%
+look for various problems you know watch
+the heartbeat etc
+
+ align:start position:0%
+the heartbeat etc
+ 
+
+ align:start position:0%
+the heartbeat etc
+and so this problem is actually very
+
+ align:start position:0%
+and so this problem is actually very
+ 
+
+ align:start position:0%
+and so this problem is actually very
+difficult it's called the halogerone
+
+ align:start position:0%
+difficult it's called the halogerone
+ 
+
+ align:start position:0%
+difficult it's called the halogerone
+problem and inverting this system
+
+ align:start position:0%
+problem and inverting this system
+ 
+
+ align:start position:0%
+problem and inverting this system
+is very challenging which is why the
+
+ align:start position:0%
+is very challenging which is why the
+ 
+
+ align:start position:0%
+is very challenging which is why the
+images are so low quality
+
+ align:start position:0%
+images are so low quality
+ 
+
+ align:start position:0%
+images are so low quality
+but again you can see this theme is just
+
+ align:start position:0%
+but again you can see this theme is just
+ 
+
+ align:start position:0%
+but again you can see this theme is just
+being extended and extended we're taking
+
+ align:start position:0%
+being extended and extended we're taking
+ 
+
+ align:start position:0%
+being extended and extended we're taking
+tomographic-like projections of the data
+
+ align:start position:0%
+tomographic-like projections of the data
+ 
+
+ align:start position:0%
+tomographic-like projections of the data
+set but our reconstruction equations are
+
+ align:start position:0%
+set but our reconstruction equations are
+ 
+
+ align:start position:0%
+set but our reconstruction equations are
+not just inverse fourier transform
+
+ align:start position:0%
+not just inverse fourier transform
+ 
+
+ align:start position:0%
+not just inverse fourier transform
+because of the scatter right
+
+ align:start position:0%
+because of the scatter right
+ 
+
+ align:start position:0%
+because of the scatter right
+and so then you might think about well
+
+ align:start position:0%
+and so then you might think about well
+ 
+
+ align:start position:0%
+and so then you might think about well
+if we're now going to make the
+
+ align:start position:0%
+if we're now going to make the
+ 
+
+ align:start position:0%
+if we're now going to make the
+competition photography product project
+
+ align:start position:0%
+competition photography product project
+ 
+
+ align:start position:0%
+competition photography product project
+out of this what if i have scatter
+
+ align:start position:0%
+out of this what if i have scatter
+ 
+
+ align:start position:0%
+out of this what if i have scatter
+scattered light and a light field
+
+ align:start position:0%
+scattered light and a light field
+ 
+
+ align:start position:0%
+scattered light and a light field
+photograph then i end up with this
+
+ align:start position:0%
+photograph then i end up with this
+ 
+
+ align:start position:0%
+photograph then i end up with this
+problem right so there's there's your
+
+ align:start position:0%
+problem right so there's there's your
+ 
+
+ align:start position:0%
+problem right so there's there's your
+final project a plus b equals project
+
+ align:start position:0%
+final project a plus b equals project
+ 
+
+ align:start position:0%
+final project a plus b equals project
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now sort of moving we're almost through
+
+ align:start position:0%
+now sort of moving we're almost through
+ 
+
+ align:start position:0%
+now sort of moving we're almost through
+the talk now but uh we'll take so a lot
+
+ align:start position:0%
+the talk now but uh we'll take so a lot
+ 
+
+ align:start position:0%
+the talk now but uh we'll take so a lot
+of this was on tomography
+
+ align:start position:0%
+of this was on tomography
+ 
+
+ align:start position:0%
+of this was on tomography
+but the general idea of getting a
+
+ align:start position:0%
+but the general idea of getting a
+ 
+
+ align:start position:0%
+but the general idea of getting a
+cross-sectional image reappears
+
+ align:start position:0%
+cross-sectional image reappears
+ 
+
+ align:start position:0%
+cross-sectional image reappears
+throughout the sciences and so in
+
+ align:start position:0%
+throughout the sciences and so in
+ 
+
+ align:start position:0%
+throughout the sciences and so in
+biology
+
+ align:start position:0%
+biology
+ 
+
+ align:start position:0%
+biology
+uh rather than using x-rays they do this
+
+ align:start position:0%
+uh rather than using x-rays they do this
+ 
+
+ align:start position:0%
+uh rather than using x-rays they do this
+optically and they just use 3d
+
+ align:start position:0%
+optically and they just use 3d
+ 
+
+ align:start position:0%
+optically and they just use 3d
+convolution so it's a very simple idea
+
+ align:start position:0%
+convolution so it's a very simple idea
+ 
+
+ align:start position:0%
+convolution so it's a very simple idea
+probably all of you understand it
+
+ align:start position:0%
+probably all of you understand it
+ 
+
+ align:start position:0%
+probably all of you understand it
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+but the idea is say i have some specimen
+
+ align:start position:0%
+but the idea is say i have some specimen
+ 
+
+ align:start position:0%
+but the idea is say i have some specimen
+in a microscope that has some some depth
+
+ align:start position:0%
+in a microscope that has some some depth
+ 
+
+ align:start position:0%
+in a microscope that has some some depth
+to it and i want to reconstruct it in 3d
+
+ align:start position:0%
+to it and i want to reconstruct it in 3d
+ 
+
+ align:start position:0%
+to it and i want to reconstruct it in 3d
+so how do i do that well the simple
+
+ align:start position:0%
+so how do i do that well the simple
+ 
+
+ align:start position:0%
+so how do i do that well the simple
+observation is to model the image
+
+ align:start position:0%
+observation is to model the image
+ 
+
+ align:start position:0%
+observation is to model the image
+formation process
+
+ align:start position:0%
+formation process
+ 
+
+ align:start position:0%
+formation process
+so what if i just had a single beam in
+
+ align:start position:0%
+so what if i just had a single beam in
+ 
+
+ align:start position:0%
+so what if i just had a single beam in
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and i focused on it then i sort of see
+
+ align:start position:0%
+and i focused on it then i sort of see
+ 
+
+ align:start position:0%
+and i focused on it then i sort of see
+this image that would be like the
+
+ align:start position:0%
+this image that would be like the
+ 
+
+ align:start position:0%
+this image that would be like the
+impulse response function for focusing
+
+ align:start position:0%
+impulse response function for focusing
+ 
+
+ align:start position:0%
+impulse response function for focusing
+on this plane
+
+ align:start position:0%
+on this plane
+ 
+
+ align:start position:0%
+on this plane
+and then if i focus slightly below our
+
+ align:start position:0%
+and then if i focus slightly below our
+ 
+
+ align:start position:0%
+and then if i focus slightly below our
+point source i'll see a defocus sort of
+
+ align:start position:0%
+point source i'll see a defocus sort of
+ 
+
+ align:start position:0%
+point source i'll see a defocus sort of
+blur as i defocus more and more i see a
+
+ align:start position:0%
+blur as i defocus more and more i see a
+ 
+
+ align:start position:0%
+blur as i defocus more and more i see a
+larger blur
+
+ align:start position:0%
+larger blur
+ 
+
+ align:start position:0%
+larger blur
+right so this is known as a focal stack
+
+ align:start position:0%
+right so this is known as a focal stack
+ 
+
+ align:start position:0%
+right so this is known as a focal stack
+right i take my microscope i just
+
+ align:start position:0%
+right i take my microscope i just
+ 
+
+ align:start position:0%
+right i take my microscope i just
+translate the specimen slide without
+
+ align:start position:0%
+translate the specimen slide without
+ 
+
+ align:start position:0%
+translate the specimen slide without
+changing the optics any and i create a
+
+ align:start position:0%
+changing the optics any and i create a
+ 
+
+ align:start position:0%
+changing the optics any and i create a
+focal step this three dimensional
+
+ align:start position:0%
+focal step this three dimensional
+ 
+
+ align:start position:0%
+focal step this three dimensional
+impulse response to a point source right
+
+ align:start position:0%
+impulse response to a point source right
+ 
+
+ align:start position:0%
+impulse response to a point source right
+so if i look at this as a function of
+
+ align:start position:0%
+so if i look at this as a function of
+ 
+
+ align:start position:0%
+so if i look at this as a function of
+depth if i just take say this slice
+
+ align:start position:0%
+depth if i just take say this slice
+ 
+
+ align:start position:0%
+depth if i just take say this slice
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+point spread function and then i look as
+
+ align:start position:0%
+point spread function and then i look as
+ 
+
+ align:start position:0%
+point spread function and then i look as
+a function of depth into the object i
+
+ align:start position:0%
+a function of depth into the object i
+ 
+
+ align:start position:0%
+a function of depth into the object i
+have this three-dimensional blur where
+
+ align:start position:0%
+have this three-dimensional blur where
+ 
+
+ align:start position:0%
+have this three-dimensional blur where
+you can see it sort of goes out with
+
+ align:start position:0%
+you can see it sort of goes out with
+ 
+
+ align:start position:0%
+you can see it sort of goes out with
+these two inverted cones
+
+ align:start position:0%
+these two inverted cones
+ 
+
+ align:start position:0%
+these two inverted cones
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so now to model
+
+ align:start position:0%
+and so now to model
+ 
+
+ align:start position:0%
+and so now to model
+right now we can model
+
+ align:start position:0%
+right now we can model
+ 
+
+ align:start position:0%
+right now we can model
+the image formation process if you
+
+ align:start position:0%
+the image formation process if you
+ 
+
+ align:start position:0%
+the image formation process if you
+assume that the specimen you're
+
+ align:start position:0%
+assume that the specimen you're
+ 
+
+ align:start position:0%
+assume that the specimen you're
+observing does not scatter significantly
+
+ align:start position:0%
+observing does not scatter significantly
+ 
+
+ align:start position:0%
+observing does not scatter significantly
+then you can use a linear image
+
+ align:start position:0%
+then you can use a linear image
+ 
+
+ align:start position:0%
+then you can use a linear image
+formation model which is very simple
+
+ align:start position:0%
+formation model which is very simple
+ 
+
+ align:start position:0%
+formation model which is very simple
+you have some three-dimensional
+
+ align:start position:0%
+you have some three-dimensional
+ 
+
+ align:start position:0%
+you have some three-dimensional
+source function which is just
+
+ align:start position:0%
+source function which is just
+ 
+
+ align:start position:0%
+source function which is just
+decomposing your object into a series of
+
+ align:start position:0%
+decomposing your object into a series of
+ 
+
+ align:start position:0%
+decomposing your object into a series of
+point sources
+
+ align:start position:0%
+point sources
+ 
+
+ align:start position:0%
+point sources
+each point source generates a psf
+
+ align:start position:0%
+each point source generates a psf
+ 
+
+ align:start position:0%
+each point source generates a psf
+weighted by whatever the intensity of
+
+ align:start position:0%
+weighted by whatever the intensity of
+ 
+
+ align:start position:0%
+weighted by whatever the intensity of
+that point is that generates the focal
+
+ align:start position:0%
+that point is that generates the focal
+ 
+
+ align:start position:0%
+that point is that generates the focal
+stack i see that make sense to everyone
+
+ align:start position:0%
+stack i see that make sense to everyone
+ 
+
+ align:start position:0%
+stack i see that make sense to everyone
+and again this is only true
+
+ align:start position:0%
+and again this is only true
+ 
+
+ align:start position:0%
+and again this is only true
+under the assumption that scattering is
+
+ align:start position:0%
+under the assumption that scattering is
+ 
+
+ align:start position:0%
+under the assumption that scattering is
+not significant or else this this model
+
+ align:start position:0%
+not significant or else this this model
+ 
+
+ align:start position:0%
+not significant or else this this model
+is not not correct
+
+ align:start position:0%
+is not not correct
+ 
+
+ align:start position:0%
+is not not correct
+so generally what we're doing is we're
+
+ align:start position:0%
+so generally what we're doing is we're
+ 
+
+ align:start position:0%
+so generally what we're doing is we're
+taking a three-dimensional function
+
+ align:start position:0%
+taking a three-dimensional function
+ 
+
+ align:start position:0%
+taking a three-dimensional function
+convolving with another
+
+ align:start position:0%
+convolving with another
+ 
+
+ align:start position:0%
+convolving with another
+three-dimensional function and again you
+
+ align:start position:0%
+three-dimensional function and again you
+ 
+
+ align:start position:0%
+three-dimensional function and again you
+always use the same trick in medical
+
+ align:start position:0%
+always use the same trick in medical
+ 
+
+ align:start position:0%
+always use the same trick in medical
+imaging first thing you do is take the
+
+ align:start position:0%
+imaging first thing you do is take the
+ 
+
+ align:start position:0%
+imaging first thing you do is take the
+fourier transform so if we take the 3d
+
+ align:start position:0%
+fourier transform so if we take the 3d
+ 
+
+ align:start position:0%
+fourier transform so if we take the 3d
+fourier transform of this then everyone
+
+ align:start position:0%
+fourier transform of this then everyone
+ 
+
+ align:start position:0%
+fourier transform of this then everyone
+knows the convolution theorem to
+
+ align:start position:0%
+knows the convolution theorem to
+ 
+
+ align:start position:0%
+knows the convolution theorem to
+simulate this in the frequency domain we
+
+ align:start position:0%
+simulate this in the frequency domain we
+ 
+
+ align:start position:0%
+simulate this in the frequency domain we
+take the 3d40 transform the object 3d4
+
+ align:start position:0%
+take the 3d40 transform the object 3d4
+ 
+
+ align:start position:0%
+take the 3d40 transform the object 3d4
+transform the psf
+
+ align:start position:0%
+transform the psf
+ 
+
+ align:start position:0%
+transform the psf
+multiply the two and that gives us the
+
+ align:start position:0%
+multiply the two and that gives us the
+ 
+
+ align:start position:0%
+multiply the two and that gives us the
+first transform of the focal step
+
+ align:start position:0%
+first transform of the focal step
+ 
+
+ align:start position:0%
+first transform of the focal step
+it won't follow
+
+ align:start position:0%
+it won't follow
+ 
+
+ align:start position:0%
+it won't follow
+okay so now if i want to get rid of the
+
+ align:start position:0%
+okay so now if i want to get rid of the
+ 
+
+ align:start position:0%
+okay so now if i want to get rid of the
+blur because remember we talked about
+
+ align:start position:0%
+blur because remember we talked about
+ 
+
+ align:start position:0%
+blur because remember we talked about
+laminography
+
+ align:start position:0%
+laminography
+ 
+
+ align:start position:0%
+laminography
+things out of the plane will be blurred
+
+ align:start position:0%
+things out of the plane will be blurred
+ 
+
+ align:start position:0%
+things out of the plane will be blurred
+right so i want to take a photograph
+
+ align:start position:0%
+right so i want to take a photograph
+ 
+
+ align:start position:0%
+right so i want to take a photograph
+with a microscope but i want to be like
+
+ align:start position:0%
+with a microscope but i want to be like
+ 
+
+ align:start position:0%
+with a microscope but i want to be like
+a pinhole i want every single thing to
+
+ align:start position:0%
+a pinhole i want every single thing to
+ 
+
+ align:start position:0%
+a pinhole i want every single thing to
+be in focus so i can look at structures
+
+ align:start position:0%
+be in focus so i can look at structures
+ 
+
+ align:start position:0%
+be in focus so i can look at structures
+that have some depth to them right
+
+ align:start position:0%
+that have some depth to them right
+ 
+
+ align:start position:0%
+that have some depth to them right
+but the problem with that is we have the
+
+ align:start position:0%
+but the problem with that is we have the
+ 
+
+ align:start position:0%
+but the problem with that is we have the
+blur and so then we just invert this so
+
+ align:start position:0%
+blur and so then we just invert this so
+ 
+
+ align:start position:0%
+blur and so then we just invert this so
+we take the 3d 40 transform of the focal
+
+ align:start position:0%
+we take the 3d 40 transform of the focal
+ 
+
+ align:start position:0%
+we take the 3d 40 transform of the focal
+stack
+
+ align:start position:0%
+stack
+ 
+
+ align:start position:0%
+stack
+and divide by the three before you
+
+ align:start position:0%
+and divide by the three before you
+ 
+
+ align:start position:0%
+and divide by the three before you
+transform the psf we end up with our
+
+ align:start position:0%
+transform the psf we end up with our
+ 
+
+ align:start position:0%
+transform the psf we end up with our
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+which we then inverse three for our
+
+ align:start position:0%
+which we then inverse three for our
+ 
+
+ align:start position:0%
+which we then inverse three for our
+transform and that gives us the focal
+
+ align:start position:0%
+transform and that gives us the focal
+ 
+
+ align:start position:0%
+transform and that gives us the focal
+stack all in focus
+
+ align:start position:0%
+stack all in focus
+ 
+
+ align:start position:0%
+stack all in focus
+so it probably most of you are you're
+
+ align:start position:0%
+so it probably most of you are you're
+ 
+
+ align:start position:0%
+so it probably most of you are you're
+who's familiar or done decompolation
+
+ align:start position:0%
+who's familiar or done decompolation
+ 
+
+ align:start position:0%
+who's familiar or done decompolation
+before understand it
+
+ align:start position:0%
+before understand it
+ 
+
+ align:start position:0%
+before understand it
+convolution is a new concept to everyone
+
+ align:start position:0%
+convolution is a new concept to everyone
+ 
+
+ align:start position:0%
+convolution is a new concept to everyone
+interesting okay well i probably should
+
+ align:start position:0%
+interesting okay well i probably should
+ 
+
+ align:start position:0%
+interesting okay well i probably should
+have explained this in 2d but hopefully
+
+ align:start position:0%
+have explained this in 2d but hopefully
+ 
+
+ align:start position:0%
+have explained this in 2d but hopefully
+you followed what i was explaining so if
+
+ align:start position:0%
+you followed what i was explaining so if
+ 
+
+ align:start position:0%
+you followed what i was explaining so if
+this was 2d
+
+ align:start position:0%
+this was 2d
+ 
+
+ align:start position:0%
+this was 2d
+right then you can just all these
+
+ align:start position:0%
+right then you can just all these
+ 
+
+ align:start position:0%
+right then you can just all these
+transform become two-dimensional right
+
+ align:start position:0%
+transform become two-dimensional right
+ 
+
+ align:start position:0%
+transform become two-dimensional right
+that's the basic idea but yeah so
+
+ align:start position:0%
+that's the basic idea but yeah so
+ 
+
+ align:start position:0%
+that's the basic idea but yeah so
+deconvolution is it's very similar to
+
+ align:start position:0%
+deconvolution is it's very similar to
+ 
+
+ align:start position:0%
+deconvolution is it's very similar to
+what you did for uh
+
+ align:start position:0%
+what you did for uh
+ 
+
+ align:start position:0%
+what you did for uh
+in the convolution is very similar to
+
+ align:start position:0%
+in the convolution is very similar to
+ 
+
+ align:start position:0%
+in the convolution is very similar to
+what you did for your lightful
+
+ align:start position:0%
+what you did for your lightful
+ 
+
+ align:start position:0%
+what you did for your lightful
+assignment which is
+
+ align:start position:0%
+assignment which is
+ 
+
+ align:start position:0%
+assignment which is
+shift and add shift and add is basically
+
+ align:start position:0%
+shift and add shift and add is basically
+ 
+
+ align:start position:0%
+shift and add shift and add is basically
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+and imagine if you given all those
+
+ align:start position:0%
+and imagine if you given all those
+ 
+
+ align:start position:0%
+and imagine if you given all those
+refocused images you wanted to go back
+
+ align:start position:0%
+refocused images you wanted to go back
+ 
+
+ align:start position:0%
+refocused images you wanted to go back
+and construct the light field
+
+ align:start position:0%
+and construct the light field
+ 
+
+ align:start position:0%
+and construct the light field
+that would be a form of decomposition
+
+ align:start position:0%
+that would be a form of decomposition
+ 
+
+ align:start position:0%
+that would be a form of decomposition
+and instead of doing it in frequency
+
+ align:start position:0%
+and instead of doing it in frequency
+ 
+
+ align:start position:0%
+and instead of doing it in frequency
+domain for the assignment you did it in
+
+ align:start position:0%
+domain for the assignment you did it in
+ 
+
+ align:start position:0%
+domain for the assignment you did it in
+the primal domain you just shifted and
+
+ align:start position:0%
+the primal domain you just shifted and
+ 
+
+ align:start position:0%
+the primal domain you just shifted and
+added the images shifting and adding
+
+ align:start position:0%
+added the images shifting and adding
+ 
+
+ align:start position:0%
+added the images shifting and adding
+in primary domain is same as
+
+ align:start position:0%
+in primary domain is same as
+ 
+
+ align:start position:0%
+in primary domain is same as
+projection or convolution in the sorry
+
+ align:start position:0%
+projection or convolution in the sorry
+ 
+
+ align:start position:0%
+projection or convolution in the sorry
+projection or
+
+ align:start position:0%
+projection or
+ 
+
+ align:start position:0%
+projection or
+convolution basically
+
+ align:start position:0%
+convolution basically
+ 
+
+ align:start position:0%
+convolution basically
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so hopefully everyone understood that to
+
+ align:start position:0%
+so hopefully everyone understood that to
+ 
+
+ align:start position:0%
+so hopefully everyone understood that to
+de-blur to put everything sharply in
+
+ align:start position:0%
+de-blur to put everything sharply in
+ 
+
+ align:start position:0%
+de-blur to put everything sharply in
+focus
+
+ align:start position:0%
+focus
+ 
+
+ align:start position:0%
+focus
+so if i apply this algorithm to the
+
+ align:start position:0%
+so if i apply this algorithm to the
+ 
+
+ align:start position:0%
+so if i apply this algorithm to the
+impulse response itself what would you
+
+ align:start position:0%
+impulse response itself what would you
+ 
+
+ align:start position:0%
+impulse response itself what would you
+expect to see what would these images
+
+ align:start position:0%
+expect to see what would these images
+ 
+
+ align:start position:0%
+expect to see what would these images
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+maybe that's a check to see if you
+
+ align:start position:0%
+maybe that's a check to see if you
+ 
+
+ align:start position:0%
+maybe that's a check to see if you
+understood this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question all become the point source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm trying to remove the blur if i
+
+ align:start position:0%
+so i'm trying to remove the blur if i
+ 
+
+ align:start position:0%
+so i'm trying to remove the blur if i
+had a point source again these images
+
+ align:start position:0%
+had a point source again these images
+ 
+
+ align:start position:0%
+had a point source again these images
+are at different depths right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i apply the decomposition
+
+ align:start position:0%
+so if i apply the decomposition
+ 
+
+ align:start position:0%
+so if i apply the decomposition
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+i expect to see certainly a sharp point
+
+ align:start position:0%
+i expect to see certainly a sharp point
+ 
+
+ align:start position:0%
+i expect to see certainly a sharp point
+right here right
+
+ align:start position:0%
+right here right
+ 
+
+ align:start position:0%
+right here right
+but what about if i move just a little
+
+ align:start position:0%
+but what about if i move just a little
+ 
+
+ align:start position:0%
+but what about if i move just a little
+in depth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember there's a blur here right yeah
+
+ align:start position:0%
+remember there's a blur here right yeah
+ 
+
+ align:start position:0%
+remember there's a blur here right yeah
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+convolution means blur
+
+ align:start position:0%
+convolution means blur
+ 
+
+ align:start position:0%
+convolution means blur
+and in most of the cases deconvolution
+
+ align:start position:0%
+and in most of the cases deconvolution
+ 
+
+ align:start position:0%
+and in most of the cases deconvolution
+means removing the blur
+
+ align:start position:0%
+means removing the blur
+ 
+
+ align:start position:0%
+means removing the blur
+so you wouldn't see anything now you
+
+ align:start position:0%
+so you wouldn't see anything now you
+ 
+
+ align:start position:0%
+so you wouldn't see anything now you
+should see the other image from this one
+
+ align:start position:0%
+should see the other image from this one
+ 
+
+ align:start position:0%
+should see the other image from this one
+which will you see why wouldn't you see
+
+ align:start position:0%
+which will you see why wouldn't you see
+ 
+
+ align:start position:0%
+which will you see why wouldn't you see
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't see anything
+
+ align:start position:0%
+you don't see anything
+ 
+
+ align:start position:0%
+you don't see anything
+all right so you get to go start and so
+
+ align:start position:0%
+all right so you get to go start and so
+ 
+
+ align:start position:0%
+all right so you get to go start and so
+that's that so that checks hopefully if
+
+ align:start position:0%
+that's that so that checks hopefully if
+ 
+
+ align:start position:0%
+that's that so that checks hopefully if
+you understand why all these images were
+
+ align:start position:0%
+you understand why all these images were
+ 
+
+ align:start position:0%
+you understand why all these images were
+completely dark except the center rule
+
+ align:start position:0%
+completely dark except the center rule
+ 
+
+ align:start position:0%
+completely dark except the center rule
+right then that's that's decomposition
+
+ align:start position:0%
+right then that's that's decomposition
+ 
+
+ align:start position:0%
+right then that's that's decomposition
+in general so then just to point out
+
+ align:start position:0%
+in general so then just to point out
+ 
+
+ align:start position:0%
+in general so then just to point out
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+when we're doing this inversion we're
+
+ align:start position:0%
+when we're doing this inversion we're
+ 
+
+ align:start position:0%
+when we're doing this inversion we're
+dividing
+
+ align:start position:0%
+dividing
+ 
+
+ align:start position:0%
+dividing
+by the point transform
+
+ align:start position:0%
+by the point transform
+ 
+
+ align:start position:0%
+by the point transform
+of our blur kernel right
+
+ align:start position:0%
+of our blur kernel right
+ 
+
+ align:start position:0%
+of our blur kernel right
+and so the problem here if you remember
+
+ align:start position:0%
+and so the problem here if you remember
+ 
+
+ align:start position:0%
+and so the problem here if you remember
+earlier when we were doing the inverse
+
+ align:start position:0%
+earlier when we were doing the inverse
+ 
+
+ align:start position:0%
+earlier when we were doing the inverse
+square transform the frequency domain
+
+ align:start position:0%
+square transform the frequency domain
+ 
+
+ align:start position:0%
+square transform the frequency domain
+you really don't want zeros right so if
+
+ align:start position:0%
+you really don't want zeros right so if
+ 
+
+ align:start position:0%
+you really don't want zeros right so if
+i divide by a zero i'm going to have
+
+ align:start position:0%
+i divide by a zero i'm going to have
+ 
+
+ align:start position:0%
+i divide by a zero i'm going to have
+problems right but if you look at our
+
+ align:start position:0%
+problems right but if you look at our
+ 
+
+ align:start position:0%
+problems right but if you look at our
+focal stack and look at the
+
+ align:start position:0%
+focal stack and look at the
+ 
+
+ align:start position:0%
+focal stack and look at the
+the blur kernel
+
+ align:start position:0%
+the blur kernel
+ 
+
+ align:start position:0%
+the blur kernel
+we have lots of zeros right
+
+ align:start position:0%
+we have lots of zeros right
+ 
+
+ align:start position:0%
+we have lots of zeros right
+and these zeros actually come in due to
+
+ align:start position:0%
+and these zeros actually come in due to
+ 
+
+ align:start position:0%
+and these zeros actually come in due to
+the numerical aperture the lens right if
+
+ align:start position:0%
+the numerical aperture the lens right if
+ 
+
+ align:start position:0%
+the numerical aperture the lens right if
+the lens sees at a very sharp angle
+
+ align:start position:0%
+the lens sees at a very sharp angle
+ 
+
+ align:start position:0%
+the lens sees at a very sharp angle
+right we can make this have fewer zeros
+
+ align:start position:0%
+right we can make this have fewer zeros
+ 
+
+ align:start position:0%
+right we can make this have fewer zeros
+so anyways since you haven't seen
+
+ align:start position:0%
+so anyways since you haven't seen
+ 
+
+ align:start position:0%
+so anyways since you haven't seen
+convolution before
+
+ align:start position:0%
+convolution before
+ 
+
+ align:start position:0%
+convolution before
+i think that's probably enough just to
+
+ align:start position:0%
+i think that's probably enough just to
+ 
+
+ align:start position:0%
+i think that's probably enough just to
+observe that when you're de-blurring
+
+ align:start position:0%
+observe that when you're de-blurring
+ 
+
+ align:start position:0%
+observe that when you're de-blurring
+you really need this function to not
+
+ align:start position:0%
+you really need this function to not
+ 
+
+ align:start position:0%
+you really need this function to not
+have zeros right so if you apply the
+
+ align:start position:0%
+have zeros right so if you apply the
+ 
+
+ align:start position:0%
+have zeros right so if you apply the
+concepts we saw earlier in the sort of
+
+ align:start position:0%
+concepts we saw earlier in the sort of
+ 
+
+ align:start position:0%
+concepts we saw earlier in the sort of
+computational photography idea the idea
+
+ align:start position:0%
+computational photography idea the idea
+ 
+
+ align:start position:0%
+computational photography idea the idea
+would be somehow to modify the optics at
+
+ align:start position:0%
+would be somehow to modify the optics at
+ 
+
+ align:start position:0%
+would be somehow to modify the optics at
+apertures codes to make this blur kernel
+
+ align:start position:0%
+apertures codes to make this blur kernel
+ 
+
+ align:start position:0%
+apertures codes to make this blur kernel
+not have zeros so when you do the
+
+ align:start position:0%
+not have zeros so when you do the
+ 
+
+ align:start position:0%
+not have zeros so when you do the
+inversion you don't amplify high
+
+ align:start position:0%
+inversion you don't amplify high
+ 
+
+ align:start position:0%
+inversion you don't amplify high
+frequencies other problems so so
+
+ align:start position:0%
+frequencies other problems so so
+ 
+
+ align:start position:0%
+frequencies other problems so so
+if i understand what you're getting
+
+ align:start position:0%
+if i understand what you're getting
+ 
+
+ align:start position:0%
+if i understand what you're getting
+correctly you're taking multiple images
+
+ align:start position:0%
+correctly you're taking multiple images
+ 
+
+ align:start position:0%
+correctly you're taking multiple images
+and different depth yes
+
+ align:start position:0%
+and different depth yes
+ 
+
+ align:start position:0%
+and different depth yes
+so why can't you focus at different
+
+ align:start position:0%
+so why can't you focus at different
+ 
+
+ align:start position:0%
+so why can't you focus at different
+depths why do you that's what we're
+
+ align:start position:0%
+depths why do you that's what we're
+ 
+
+ align:start position:0%
+depths why do you that's what we're
+doing so
+
+ align:start position:0%
+doing so
+ 
+
+ align:start position:0%
+doing so
+then if you are taking multiple images
+
+ align:start position:0%
+then if you are taking multiple images
+ 
+
+ align:start position:0%
+then if you are taking multiple images
+why don't you shift your focal plane to
+
+ align:start position:0%
+why don't you shift your focal plane to
+ 
+
+ align:start position:0%
+why don't you shift your focal plane to
+different depths that's exactly what
+
+ align:start position:0%
+different depths that's exactly what
+ 
+
+ align:start position:0%
+different depths that's exactly what
+we're doing so
+
+ align:start position:0%
+we're doing so
+ 
+
+ align:start position:0%
+we're doing so
+but it's just like laminography from
+
+ align:start position:0%
+but it's just like laminography from
+ 
+
+ align:start position:0%
+but it's just like laminography from
+before everything
+
+ align:start position:0%
+before everything
+ 
+
+ align:start position:0%
+before everything
+it's a thick specimen
+
+ align:start position:0%
+it's a thick specimen
+ 
+
+ align:start position:0%
+it's a thick specimen
+right so let's go to a picture pictures
+
+ align:start position:0%
+right so let's go to a picture pictures
+ 
+
+ align:start position:0%
+right so let's go to a picture pictures
+are always worth a lot more so we have
+
+ align:start position:0%
+are always worth a lot more so we have
+ 
+
+ align:start position:0%
+are always worth a lot more so we have
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+mandible of some insect right we're
+
+ align:start position:0%
+mandible of some insect right we're
+ 
+
+ align:start position:0%
+mandible of some insect right we're
+trying to get a cross-sectional image
+
+ align:start position:0%
+trying to get a cross-sectional image
+ 
+
+ align:start position:0%
+trying to get a cross-sectional image
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+if we don't do anything if we just focus
+
+ align:start position:0%
+if we don't do anything if we just focus
+ 
+
+ align:start position:0%
+if we don't do anything if we just focus
+at some depth in the specimen it's back
+
+ align:start position:0%
+at some depth in the specimen it's back
+ 
+
+ align:start position:0%
+at some depth in the specimen it's back
+illuminated you get this halo right
+
+ align:start position:0%
+illuminated you get this halo right
+ 
+
+ align:start position:0%
+illuminated you get this halo right
+because everything out of the focal
+
+ align:start position:0%
+because everything out of the focal
+ 
+
+ align:start position:0%
+because everything out of the focal
+plane is blurred yes right yes so now i
+
+ align:start position:0%
+plane is blurred yes right yes so now i
+ 
+
+ align:start position:0%
+plane is blurred yes right yes so now i
+can focus
+
+ align:start position:0%
+can focus
+ 
+
+ align:start position:0%
+can focus
+at another depth and generate a new
+
+ align:start position:0%
+at another depth and generate a new
+ 
+
+ align:start position:0%
+at another depth and generate a new
+image which is exactly what a focal
+
+ align:start position:0%
+image which is exactly what a focal
+ 
+
+ align:start position:0%
+image which is exactly what a focal
+stack is but i'll still have that blur
+
+ align:start position:0%
+stack is but i'll still have that blur
+ 
+
+ align:start position:0%
+stack is but i'll still have that blur
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+so what i'm trying to do is is collect
+
+ align:start position:0%
+so what i'm trying to do is is collect
+ 
+
+ align:start position:0%
+so what i'm trying to do is is collect
+that focal stack and then invert that
+
+ align:start position:0%
+that focal stack and then invert that
+ 
+
+ align:start position:0%
+that focal stack and then invert that
+whole system so i get really what is a
+
+ align:start position:0%
+whole system so i get really what is a
+ 
+
+ align:start position:0%
+whole system so i get really what is a
+cross-sectional image
+
+ align:start position:0%
+cross-sectional image
+ 
+
+ align:start position:0%
+cross-sectional image
+so that nothing
+
+ align:start position:0%
+so that nothing
+ 
+
+ align:start position:0%
+so that nothing
+is blurred in it right which is what
+
+ align:start position:0%
+is blurred in it right which is what
+ 
+
+ align:start position:0%
+is blurred in it right which is what
+laminography does which is what
+
+ align:start position:0%
+laminography does which is what
+ 
+
+ align:start position:0%
+laminography does which is what
+tomography does in general right so you
+
+ align:start position:0%
+tomography does in general right so you
+ 
+
+ align:start position:0%
+tomography does in general right so you
+can see that theme something has to be
+
+ align:start position:0%
+can see that theme something has to be
+ 
+
+ align:start position:0%
+can see that theme something has to be
+done to remove the boiler
+
+ align:start position:0%
+done to remove the boiler
+ 
+
+ align:start position:0%
+done to remove the boiler
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so in this case what's done to
+
+ align:start position:0%
+and so in this case what's done to
+ 
+
+ align:start position:0%
+and so in this case what's done to
+remove the blur is that division
+
+ align:start position:0%
+remove the blur is that division
+ 
+
+ align:start position:0%
+remove the blur is that division
+by our impulse response point transform
+
+ align:start position:0%
+by our impulse response point transform
+ 
+
+ align:start position:0%
+by our impulse response point transform
+right so this d blurring algorithm
+
+ align:start position:0%
+right so this d blurring algorithm
+ 
+
+ align:start position:0%
+right so this d blurring algorithm
+right rather than using a tomographic
+
+ align:start position:0%
+right rather than using a tomographic
+ 
+
+ align:start position:0%
+right rather than using a tomographic
+type typography and so
+
+ align:start position:0%
+type typography and so
+ 
+
+ align:start position:0%
+type typography and so
+just to show you the gist so i think if
+
+ align:start position:0%
+just to show you the gist so i think if
+ 
+
+ align:start position:0%
+just to show you the gist so i think if
+since it seems that decomposition is a
+
+ align:start position:0%
+since it seems that decomposition is a
+ 
+
+ align:start position:0%
+since it seems that decomposition is a
+new concept for everyone definitely go
+
+ align:start position:0%
+new concept for everyone definitely go
+ 
+
+ align:start position:0%
+new concept for everyone definitely go
+and read the wiki entry because i think
+
+ align:start position:0%
+and read the wiki entry because i think
+ 
+
+ align:start position:0%
+and read the wiki entry because i think
+that idea has been beaten to death in
+
+ align:start position:0%
+that idea has been beaten to death in
+ 
+
+ align:start position:0%
+that idea has been beaten to death in
+the competition photography field so you
+
+ align:start position:0%
+the competition photography field so you
+ 
+
+ align:start position:0%
+the competition photography field so you
+can definitely get some final projects
+
+ align:start position:0%
+can definitely get some final projects
+ 
+
+ align:start position:0%
+can definitely get some final projects
+out of it
+
+ align:start position:0%
+out of it
+ 
+
+ align:start position:0%
+out of it
+you can see how you can use that so the
+
+ align:start position:0%
+you can see how you can use that so the
+ 
+
+ align:start position:0%
+you can see how you can use that so the
+base here's some nice results this is
+
+ align:start position:0%
+base here's some nice results this is
+ 
+
+ align:start position:0%
+base here's some nice results this is
+from mark lavoy's work so this is
+
+ align:start position:0%
+from mark lavoy's work so this is
+ 
+
+ align:start position:0%
+from mark lavoy's work so this is
+actually a light field uh microscopy
+
+ align:start position:0%
+actually a light field uh microscopy
+ 
+
+ align:start position:0%
+actually a light field uh microscopy
+image but the ideas are the same you
+
+ align:start position:0%
+image but the ideas are the same you
+ 
+
+ align:start position:0%
+image but the ideas are the same you
+could do deconvolution you can see he
+
+ align:start position:0%
+could do deconvolution you can see he
+ 
+
+ align:start position:0%
+could do deconvolution you can see he
+goes from something that this is what a
+
+ align:start position:0%
+goes from something that this is what a
+ 
+
+ align:start position:0%
+goes from something that this is what a
+typical microscope would produce we have
+
+ align:start position:0%
+typical microscope would produce we have
+ 
+
+ align:start position:0%
+typical microscope would produce we have
+this thick specimen but it's optically
+
+ align:start position:0%
+this thick specimen but it's optically
+ 
+
+ align:start position:0%
+this thick specimen but it's optically
+transparent we produce a nice
+
+ align:start position:0%
+transparent we produce a nice
+ 
+
+ align:start position:0%
+transparent we produce a nice
+tomographic image which we can then
+
+ align:start position:0%
+tomographic image which we can then
+ 
+
+ align:start position:0%
+tomographic image which we can then
+volume render and so if you go to
+
+ align:start position:0%
+volume render and so if you go to
+ 
+
+ align:start position:0%
+volume render and so if you go to
+you know some really expensive
+
+ align:start position:0%
+you know some really expensive
+ 
+
+ align:start position:0%
+you know some really expensive
+commercial packages this is sort of what
+
+ align:start position:0%
+commercial packages this is sort of what
+ 
+
+ align:start position:0%
+commercial packages this is sort of what
+you'll see for a deconvolution so you'll
+
+ align:start position:0%
+you'll see for a deconvolution so you'll
+ 
+
+ align:start position:0%
+you'll see for a deconvolution so you'll
+go from something on the left which has
+
+ align:start position:0%
+go from something on the left which has
+ 
+
+ align:start position:0%
+go from something on the left which has
+all the autofocus blur just some nice
+
+ align:start position:0%
+all the autofocus blur just some nice
+ 
+
+ align:start position:0%
+all the autofocus blur just some nice
+sharp all-in-focus image of an object
+
+ align:start position:0%
+sharp all-in-focus image of an object
+ 
+
+ align:start position:0%
+sharp all-in-focus image of an object
+with a lot of depth to it right so you
+
+ align:start position:0%
+with a lot of depth to it right so you
+ 
+
+ align:start position:0%
+with a lot of depth to it right so you
+can study the fine structure
+
+ align:start position:0%
+can study the fine structure
+ 
+
+ align:start position:0%
+can study the fine structure
+and so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think we have a little time left let's
+
+ align:start position:0%
+i think we have a little time left let's
+ 
+
+ align:start position:0%
+i think we have a little time left let's
+look at some other tricks they use in
+
+ align:start position:0%
+look at some other tricks they use in
+ 
+
+ align:start position:0%
+look at some other tricks they use in
+biology so again the theme in all of
+
+ align:start position:0%
+biology so again the theme in all of
+ 
+
+ align:start position:0%
+biology so again the theme in all of
+these laminography tomography is always
+
+ align:start position:0%
+these laminography tomography is always
+ 
+
+ align:start position:0%
+these laminography tomography is always
+to remove the out-of-focus blur so we
+
+ align:start position:0%
+to remove the out-of-focus blur so we
+ 
+
+ align:start position:0%
+to remove the out-of-focus blur so we
+get a nice cross-sectional image right
+
+ align:start position:0%
+get a nice cross-sectional image right
+ 
+
+ align:start position:0%
+get a nice cross-sectional image right
+so we can see the tumors we can see
+
+ align:start position:0%
+so we can see the tumors we can see
+ 
+
+ align:start position:0%
+so we can see the tumors we can see
+structures clearly
+
+ align:start position:0%
+structures clearly
+ 
+
+ align:start position:0%
+structures clearly
+and so this idea
+
+ align:start position:0%
+and so this idea
+ 
+
+ align:start position:0%
+and so this idea
+is really nice and again i don't have
+
+ align:start position:0%
+is really nice and again i don't have
+ 
+
+ align:start position:0%
+is really nice and again i don't have
+time to show you but there have been two
+
+ align:start position:0%
+time to show you but there have been two
+ 
+
+ align:start position:0%
+time to show you but there have been two
+or three
+
+ align:start position:0%
+or three
+ 
+
+ align:start position:0%
+or three
+computational photography cigarette
+
+ align:start position:0%
+computational photography cigarette
+ 
+
+ align:start position:0%
+computational photography cigarette
+papers again from markleboy using this
+
+ align:start position:0%
+papers again from markleboy using this
+ 
+
+ align:start position:0%
+papers again from markleboy using this
+idea see this theme just keeps coming up
+
+ align:start position:0%
+idea see this theme just keeps coming up
+ 
+
+ align:start position:0%
+idea see this theme just keeps coming up
+you go to the medical literature look
+
+ align:start position:0%
+you go to the medical literature look
+ 
+
+ align:start position:0%
+you go to the medical literature look
+what they were doing in the 60s and 70s
+
+ align:start position:0%
+what they were doing in the 60s and 70s
+ 
+
+ align:start position:0%
+what they were doing in the 60s and 70s
+figure out how exactly it maps onto a
+
+ align:start position:0%
+figure out how exactly it maps onto a
+ 
+
+ align:start position:0%
+figure out how exactly it maps onto a
+camera do it you're published that's
+
+ align:start position:0%
+camera do it you're published that's
+ 
+
+ align:start position:0%
+camera do it you're published that's
+basically the algorithm although
+
+ align:start position:0%
+basically the algorithm although
+ 
+
+ align:start position:0%
+basically the algorithm although
+it's becoming harder to do that because
+
+ align:start position:0%
+it's becoming harder to do that because
+ 
+
+ align:start position:0%
+it's becoming harder to do that because
+too many of us have used that algorithm
+
+ align:start position:0%
+too many of us have used that algorithm
+ 
+
+ align:start position:0%
+too many of us have used that algorithm
+for papers so
+
+ align:start position:0%
+for papers so
+ 
+
+ align:start position:0%
+for papers so
+the idea behind uh confocal microscopy
+
+ align:start position:0%
+the idea behind uh confocal microscopy
+ 
+
+ align:start position:0%
+the idea behind uh confocal microscopy
+which you can be proud of marvin minsky
+
+ align:start position:0%
+which you can be proud of marvin minsky
+ 
+
+ align:start position:0%
+which you can be proud of marvin minsky
+is arguably credited with the invention
+
+ align:start position:0%
+is arguably credited with the invention
+ 
+
+ align:start position:0%
+is arguably credited with the invention
+of it uh here at the media lab and yeah
+
+ align:start position:0%
+of it uh here at the media lab and yeah
+ 
+
+ align:start position:0%
+of it uh here at the media lab and yeah
+live as well so
+
+ align:start position:0%
+live as well so
+ 
+
+ align:start position:0%
+live as well so
+the basic idea is i want i have some
+
+ align:start position:0%
+the basic idea is i want i have some
+ 
+
+ align:start position:0%
+the basic idea is i want i have some
+plane in our my specimen that i want to
+
+ align:start position:0%
+plane in our my specimen that i want to
+ 
+
+ align:start position:0%
+plane in our my specimen that i want to
+get a nice cross-sectional image up and
+
+ align:start position:0%
+get a nice cross-sectional image up and
+ 
+
+ align:start position:0%
+get a nice cross-sectional image up and
+i want everything that's out of focus to
+
+ align:start position:0%
+i want everything that's out of focus to
+ 
+
+ align:start position:0%
+i want everything that's out of focus to
+not contribute anything to the final
+
+ align:start position:0%
+not contribute anything to the final
+ 
+
+ align:start position:0%
+not contribute anything to the final
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+right so i can do that computationally
+
+ align:start position:0%
+right so i can do that computationally
+ 
+
+ align:start position:0%
+right so i can do that computationally
+by doing this deconvolution
+
+ align:start position:0%
+by doing this deconvolution
+ 
+
+ align:start position:0%
+by doing this deconvolution
+and that's sort of like ct scanning or i
+
+ align:start position:0%
+and that's sort of like ct scanning or i
+ 
+
+ align:start position:0%
+and that's sort of like ct scanning or i
+can do it mechanically which is sort of
+
+ align:start position:0%
+can do it mechanically which is sort of
+ 
+
+ align:start position:0%
+can do it mechanically which is sort of
+like laminography there'll be no
+
+ align:start position:0%
+like laminography there'll be no
+ 
+
+ align:start position:0%
+like laminography there'll be no
+computation here at all i'm just going
+
+ align:start position:0%
+computation here at all i'm just going
+ 
+
+ align:start position:0%
+computation here at all i'm just going
+to make sure that the point spread
+
+ align:start position:0%
+to make sure that the point spread
+ 
+
+ align:start position:0%
+to make sure that the point spread
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so if i go back to the point spread
+
+ align:start position:0%
+so if i go back to the point spread
+ 
+
+ align:start position:0%
+so if i go back to the point spread
+function this thing
+
+ align:start position:0%
+function this thing
+ 
+
+ align:start position:0%
+function this thing
+if this was just a point
+
+ align:start position:0%
+if this was just a point
+ 
+
+ align:start position:0%
+if this was just a point
+right then if you look at this math if
+
+ align:start position:0%
+right then if you look at this math if
+ 
+
+ align:start position:0%
+right then if you look at this math if
+you convolve a point with the object you
+
+ align:start position:0%
+you convolve a point with the object you
+ 
+
+ align:start position:0%
+you convolve a point with the object you
+just get the object again right so just
+
+ align:start position:0%
+just get the object again right so just
+ 
+
+ align:start position:0%
+just get the object again right so just
+like laminography sort of solve the
+
+ align:start position:0%
+like laminography sort of solve the
+ 
+
+ align:start position:0%
+like laminography sort of solve the
+problem mechanically if we can make this
+
+ align:start position:0%
+problem mechanically if we can make this
+ 
+
+ align:start position:0%
+problem mechanically if we can make this
+a point our impulse response is a point
+
+ align:start position:0%
+a point our impulse response is a point
+ 
+
+ align:start position:0%
+a point our impulse response is a point
+then we don't need to do deconvolution
+
+ align:start position:0%
+then we don't need to do deconvolution
+ 
+
+ align:start position:0%
+then we don't need to do deconvolution
+that's the main trick
+
+ align:start position:0%
+that's the main trick
+ 
+
+ align:start position:0%
+that's the main trick
+and so confocal microscopy does this in
+
+ align:start position:0%
+and so confocal microscopy does this in
+ 
+
+ align:start position:0%
+and so confocal microscopy does this in
+a very clever way we have some
+
+ align:start position:0%
+a very clever way we have some
+ 
+
+ align:start position:0%
+a very clever way we have some
+area light source put a pinhole in front
+
+ align:start position:0%
+area light source put a pinhole in front
+ 
+
+ align:start position:0%
+area light source put a pinhole in front
+of it okay now it goes through my thin
+
+ align:start position:0%
+of it okay now it goes through my thin
+ 
+
+ align:start position:0%
+of it okay now it goes through my thin
+lens and it goes it's focused based on
+
+ align:start position:0%
+lens and it goes it's focused based on
+ 
+
+ align:start position:0%
+lens and it goes it's focused based on
+the focal length down onto some point in
+
+ align:start position:0%
+the focal length down onto some point in
+ 
+
+ align:start position:0%
+the focal length down onto some point in
+the plane we care about
+
+ align:start position:0%
+the plane we care about
+ 
+
+ align:start position:0%
+the plane we care about
+okay so if i was to now take a picture
+
+ align:start position:0%
+okay so if i was to now take a picture
+ 
+
+ align:start position:0%
+okay so if i was to now take a picture
+somehow of this plane right
+
+ align:start position:0%
+somehow of this plane right
+ 
+
+ align:start position:0%
+somehow of this plane right
+then all i'd see would be things that
+
+ align:start position:0%
+then all i'd see would be things that
+ 
+
+ align:start position:0%
+then all i'd see would be things that
+get illuminated by this beam of light
+
+ align:start position:0%
+get illuminated by this beam of light
+ 
+
+ align:start position:0%
+get illuminated by this beam of light
+right everything else is not eliminated
+
+ align:start position:0%
+right everything else is not eliminated
+ 
+
+ align:start position:0%
+right everything else is not eliminated
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so we're already doing okay because
+
+ align:start position:0%
+so we're already doing okay because
+ 
+
+ align:start position:0%
+so we're already doing okay because
+things way over here
+
+ align:start position:0%
+things way over here
+ 
+
+ align:start position:0%
+things way over here
+aren't going to contribute to the blur
+
+ align:start position:0%
+aren't going to contribute to the blur
+ 
+
+ align:start position:0%
+aren't going to contribute to the blur
+at all
+
+ align:start position:0%
+at all
+ 
+
+ align:start position:0%
+at all
+right so that's the purpose of the
+
+ align:start position:0%
+right so that's the purpose of the
+ 
+
+ align:start position:0%
+right so that's the purpose of the
+pinhole let's make this clear
+
+ align:start position:0%
+pinhole let's make this clear
+ 
+
+ align:start position:0%
+pinhole let's make this clear
+if i look at some point so again let's
+
+ align:start position:0%
+if i look at some point so again let's
+ 
+
+ align:start position:0%
+if i look at some point so again let's
+think about the mandible we saw earlier
+
+ align:start position:0%
+think about the mandible we saw earlier
+ 
+
+ align:start position:0%
+think about the mandible we saw earlier
+if we have some point that's higher in
+
+ align:start position:0%
+if we have some point that's higher in
+ 
+
+ align:start position:0%
+if we have some point that's higher in
+depth than the plane we're trying to
+
+ align:start position:0%
+depth than the plane we're trying to
+ 
+
+ align:start position:0%
+depth than the plane we're trying to
+focus on right then the light will be
+
+ align:start position:0%
+focus on right then the light will be
+ 
+
+ align:start position:0%
+focus on right then the light will be
+spread over a disk
+
+ align:start position:0%
+spread over a disk
+ 
+
+ align:start position:0%
+spread over a disk
+does that make sense we're going to take
+
+ align:start position:0%
+does that make sense we're going to take
+ 
+
+ align:start position:0%
+does that make sense we're going to take
+this cut through our cone of light
+
+ align:start position:0%
+this cut through our cone of light
+ 
+
+ align:start position:0%
+this cut through our cone of light
+right so as a function of radius or
+
+ align:start position:0%
+right so as a function of radius or
+ 
+
+ align:start position:0%
+right so as a function of radius or
+depth away from the plane we care about
+
+ align:start position:0%
+depth away from the plane we care about
+ 
+
+ align:start position:0%
+depth away from the plane we care about
+it's going to fall like what
+
+ align:start position:0%
+it's going to fall like what
+ 
+
+ align:start position:0%
+it's going to fall like what
+the brightness of that point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah 1 over r squared great
+
+ align:start position:0%
+yeah 1 over r squared great
+ 
+
+ align:start position:0%
+yeah 1 over r squared great
+so already if you look think about our
+
+ align:start position:0%
+so already if you look think about our
+ 
+
+ align:start position:0%
+so already if you look think about our
+impulse response we had earlier
+
+ align:start position:0%
+impulse response we had earlier
+ 
+
+ align:start position:0%
+impulse response we had earlier
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so it follows one over r squared now
+
+ align:start position:0%
+so it follows one over r squared now
+ 
+
+ align:start position:0%
+so it follows one over r squared now
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's not bad but can we make it even
+
+ align:start position:0%
+that's not bad but can we make it even
+ 
+
+ align:start position:0%
+that's not bad but can we make it even
+sharper any ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher numerical aperture
+
+ align:start position:0%
+higher numerical aperture
+ 
+
+ align:start position:0%
+higher numerical aperture
+that will spread the energy out it'll
+
+ align:start position:0%
+that will spread the energy out it'll
+ 
+
+ align:start position:0%
+that will spread the energy out it'll
+make it somewhat sharper that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the key trick
+
+ align:start position:0%
+so the key trick
+ 
+
+ align:start position:0%
+so the key trick
+oh you saw it previewed if anyone saw it
+
+ align:start position:0%
+oh you saw it previewed if anyone saw it
+ 
+
+ align:start position:0%
+oh you saw it previewed if anyone saw it
+does anyone think so that we're only
+
+ align:start position:0%
+does anyone think so that we're only
+ 
+
+ align:start position:0%
+does anyone think so that we're only
+doing thing on things on the lighting
+
+ align:start position:0%
+doing thing on things on the lighting
+ 
+
+ align:start position:0%
+doing thing on things on the lighting
+side we haven't considered how we take
+
+ align:start position:0%
+side we haven't considered how we take
+ 
+
+ align:start position:0%
+side we haven't considered how we take
+the picture yet
+
+ align:start position:0%
+the picture yet
+ 
+
+ align:start position:0%
+the picture yet
+it turns out you can use the exact same
+
+ align:start position:0%
+it turns out you can use the exact same
+ 
+
+ align:start position:0%
+it turns out you can use the exact same
+trick
+
+ align:start position:0%
+trick
+ 
+
+ align:start position:0%
+trick
+so to take the picture of this one point
+
+ align:start position:0%
+so to take the picture of this one point
+ 
+
+ align:start position:0%
+so to take the picture of this one point
+on the plane of focus we care about
+
+ align:start position:0%
+on the plane of focus we care about
+ 
+
+ align:start position:0%
+on the plane of focus we care about
+we're just going to put a big photocell
+
+ align:start position:0%
+we're just going to put a big photocell
+ 
+
+ align:start position:0%
+we're just going to put a big photocell
+here we photodiode
+
+ align:start position:0%
+here we photodiode
+ 
+
+ align:start position:0%
+here we photodiode
+right so if i didn't do anything
+
+ align:start position:0%
+right so if i didn't do anything
+ 
+
+ align:start position:0%
+right so if i didn't do anything
+and i put a beam splitter here
+
+ align:start position:0%
+and i put a beam splitter here
+ 
+
+ align:start position:0%
+and i put a beam splitter here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and this light would just fall on the
+
+ align:start position:0%
+and this light would just fall on the
+ 
+
+ align:start position:0%
+and this light would just fall on the
+photocell all over a big region so you
+
+ align:start position:0%
+photocell all over a big region so you
+ 
+
+ align:start position:0%
+photocell all over a big region so you
+have low s and r if you didn't have a
+
+ align:start position:0%
+have low s and r if you didn't have a
+ 
+
+ align:start position:0%
+have low s and r if you didn't have a
+lens here you need the lens of course
+
+ align:start position:0%
+lens here you need the lens of course
+ 
+
+ align:start position:0%
+lens here you need the lens of course
+right so we put a lens
+
+ align:start position:0%
+right so we put a lens
+ 
+
+ align:start position:0%
+right so we put a lens
+that focuses on this plane as well
+
+ align:start position:0%
+that focuses on this plane as well
+ 
+
+ align:start position:0%
+that focuses on this plane as well
+so it collects all the light scattered
+
+ align:start position:0%
+so it collects all the light scattered
+ 
+
+ align:start position:0%
+so it collects all the light scattered
+by this point back onto our photo dial
+
+ align:start position:0%
+by this point back onto our photo dial
+ 
+
+ align:start position:0%
+by this point back onto our photo dial
+right so if we put our photo down at
+
+ align:start position:0%
+right so if we put our photo down at
+ 
+
+ align:start position:0%
+right so if we put our photo down at
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+we get a nice image
+
+ align:start position:0%
+we get a nice image
+ 
+
+ align:start position:0%
+we get a nice image
+but then if we took a focal stack
+
+ align:start position:0%
+but then if we took a focal stack
+ 
+
+ align:start position:0%
+but then if we took a focal stack
+right then the points out of focus would
+
+ align:start position:0%
+right then the points out of focus would
+ 
+
+ align:start position:0%
+right then the points out of focus would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+have intensity one over r squared right
+
+ align:start position:0%
+have intensity one over r squared right
+ 
+
+ align:start position:0%
+have intensity one over r squared right
+but we can do better than that because
+
+ align:start position:0%
+but we can do better than that because
+ 
+
+ align:start position:0%
+but we can do better than that because
+now we can put a pinhole
+
+ align:start position:0%
+now we can put a pinhole
+ 
+
+ align:start position:0%
+now we can put a pinhole
+in front of our photocell
+
+ align:start position:0%
+in front of our photocell
+ 
+
+ align:start position:0%
+in front of our photocell
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so if you think about this
+
+ align:start position:0%
+so if you think about this
+ 
+
+ align:start position:0%
+so if you think about this
+our image say you take this blur disk
+
+ align:start position:0%
+our image say you take this blur disk
+ 
+
+ align:start position:0%
+our image say you take this blur disk
+and you image it it images to a disk
+
+ align:start position:0%
+and you image it it images to a disk
+ 
+
+ align:start position:0%
+and you image it it images to a disk
+but then we're just going to take that
+
+ align:start position:0%
+but then we're just going to take that
+ 
+
+ align:start position:0%
+but then we're just going to take that
+little part in the center of the disk
+
+ align:start position:0%
+little part in the center of the disk
+ 
+
+ align:start position:0%
+little part in the center of the disk
+right so it turns out the imaging side
+
+ align:start position:0%
+right so it turns out the imaging side
+ 
+
+ align:start position:0%
+right so it turns out the imaging side
+by putting a pinhole on your photodiode
+
+ align:start position:0%
+by putting a pinhole on your photodiode
+ 
+
+ align:start position:0%
+by putting a pinhole on your photodiode
+also gives you a function of one over r
+
+ align:start position:0%
+also gives you a function of one over r
+ 
+
+ align:start position:0%
+also gives you a function of one over r
+squared so it actually goes one over r
+
+ align:start position:0%
+squared so it actually goes one over r
+ 
+
+ align:start position:0%
+squared so it actually goes one over r
+to the fourth now which is quite strong
+
+ align:start position:0%
+to the fourth now which is quite strong
+ 
+
+ align:start position:0%
+to the fourth now which is quite strong
+so that deconvolution isn't really
+
+ align:start position:0%
+so that deconvolution isn't really
+ 
+
+ align:start position:0%
+so that deconvolution isn't really
+needed anymore does that make sense and
+
+ align:start position:0%
+needed anymore does that make sense and
+ 
+
+ align:start position:0%
+needed anymore does that make sense and
+so that's why it's called confocal you
+
+ align:start position:0%
+so that's why it's called confocal you
+ 
+
+ align:start position:0%
+so that's why it's called confocal you
+have two pinholes two focal systems and
+
+ align:start position:0%
+have two pinholes two focal systems and
+ 
+
+ align:start position:0%
+have two pinholes two focal systems and
+they're aligned with each item
+
+ align:start position:0%
+they're aligned with each item
+ 
+
+ align:start position:0%
+they're aligned with each item
+but then of course how are you gonna get
+
+ align:start position:0%
+but then of course how are you gonna get
+ 
+
+ align:start position:0%
+but then of course how are you gonna get
+a picture you're gonna have to scan this
+
+ align:start position:0%
+a picture you're gonna have to scan this
+ 
+
+ align:start position:0%
+a picture you're gonna have to scan this
+thing which can take a lot of time right
+
+ align:start position:0%
+thing which can take a lot of time right
+ 
+
+ align:start position:0%
+thing which can take a lot of time right
+so you're going to have to move the
+
+ align:start position:0%
+so you're going to have to move the
+ 
+
+ align:start position:0%
+so you're going to have to move the
+pinholes on the light source
+
+ align:start position:0%
+pinholes on the light source
+ 
+
+ align:start position:0%
+pinholes on the light source
+and the detector in 2d raster scan the
+
+ align:start position:0%
+and the detector in 2d raster scan the
+ 
+
+ align:start position:0%
+and the detector in 2d raster scan the
+whole object right
+
+ align:start position:0%
+whole object right
+ 
+
+ align:start position:0%
+whole object right
+so that's really the limitation of this
+
+ align:start position:0%
+so that's really the limitation of this
+ 
+
+ align:start position:0%
+so that's really the limitation of this
+technique by doing deconvolution by
+
+ align:start position:0%
+technique by doing deconvolution by
+ 
+
+ align:start position:0%
+technique by doing deconvolution by
+doing tricks to make the psf invertible
+
+ align:start position:0%
+doing tricks to make the psf invertible
+ 
+
+ align:start position:0%
+doing tricks to make the psf invertible
+we can do it all in one shot
+
+ align:start position:0%
+we can do it all in one shot
+ 
+
+ align:start position:0%
+we can do it all in one shot
+but with confocal microscopy before we
+
+ align:start position:0%
+but with confocal microscopy before we
+ 
+
+ align:start position:0%
+but with confocal microscopy before we
+had computers
+
+ align:start position:0%
+had computers
+ 
+
+ align:start position:0%
+had computers
+we could do that without needing
+
+ align:start position:0%
+we could do that without needing
+ 
+
+ align:start position:0%
+we could do that without needing
+inversion so you see the trade right it
+
+ align:start position:0%
+inversion so you see the trade right it
+ 
+
+ align:start position:0%
+inversion so you see the trade right it
+should be the same trade as laminography
+
+ align:start position:0%
+should be the same trade as laminography
+ 
+
+ align:start position:0%
+should be the same trade as laminography
+and tomography
+
+ align:start position:0%
+and tomography
+ 
+
+ align:start position:0%
+and tomography
+and so then i should probably finish up
+
+ align:start position:0%
+and so then i should probably finish up
+ 
+
+ align:start position:0%
+and so then i should probably finish up
+right yeah
+
+ align:start position:0%
+right yeah
+ 
+
+ align:start position:0%
+right yeah
+so uh we're getting right near the end
+
+ align:start position:0%
+so uh we're getting right near the end
+ 
+
+ align:start position:0%
+so uh we're getting right near the end
+now so this is used in practice not
+
+ align:start position:0%
+now so this is used in practice not
+ 
+
+ align:start position:0%
+now so this is used in practice not
+quite the way i described it took
+
+ align:start position:0%
+quite the way i described it took
+ 
+
+ align:start position:0%
+quite the way i described it took
+a decade or two to commercialize marvin
+
+ align:start position:0%
+a decade or two to commercialize marvin
+ 
+
+ align:start position:0%
+a decade or two to commercialize marvin
+minsky's idea and this is sort of how
+
+ align:start position:0%
+minsky's idea and this is sort of how
+ 
+
+ align:start position:0%
+minsky's idea and this is sort of how
+it's used in biology and practice now
+
+ align:start position:0%
+it's used in biology and practice now
+ 
+
+ align:start position:0%
+it's used in biology and practice now
+it's called laser scanning confocal
+
+ align:start position:0%
+it's called laser scanning confocal
+ 
+
+ align:start position:0%
+it's called laser scanning confocal
+microscopy the idea is basically the
+
+ align:start position:0%
+microscopy the idea is basically the
+ 
+
+ align:start position:0%
+microscopy the idea is basically the
+same you have a laser source
+
+ align:start position:0%
+same you have a laser source
+ 
+
+ align:start position:0%
+same you have a laser source
+a minimal aperture on both the source
+
+ align:start position:0%
+a minimal aperture on both the source
+ 
+
+ align:start position:0%
+a minimal aperture on both the source
+and the detector and a photodiode and a
+
+ align:start position:0%
+and the detector and a photodiode and a
+ 
+
+ align:start position:0%
+and the detector and a photodiode and a
+special beam splitter we'll get to that
+
+ align:start position:0%
+special beam splitter we'll get to that
+ 
+
+ align:start position:0%
+special beam splitter we'll get to that
+what we do is really it's just like c2
+
+ align:start position:0%
+what we do is really it's just like c2
+ 
+
+ align:start position:0%
+what we do is really it's just like c2
+scans you don't really just care about
+
+ align:start position:0%
+scans you don't really just care about
+ 
+
+ align:start position:0%
+scans you don't really just care about
+the absolute density function often you
+
+ align:start position:0%
+the absolute density function often you
+ 
+
+ align:start position:0%
+the absolute density function often you
+add some contrast agent right so if
+
+ align:start position:0%
+add some contrast agent right so if
+ 
+
+ align:start position:0%
+add some contrast agent right so if
+you're looking for a pulmonary edema you
+
+ align:start position:0%
+you're looking for a pulmonary edema you
+ 
+
+ align:start position:0%
+you're looking for a pulmonary edema you
+inject iodine into the veins
+
+ align:start position:0%
+inject iodine into the veins
+ 
+
+ align:start position:0%
+inject iodine into the veins
+iodine absorbs
+
+ align:start position:0%
+iodine absorbs
+ 
+
+ align:start position:0%
+iodine absorbs
+x-rays and so then you can look at the
+
+ align:start position:0%
+x-rays and so then you can look at the
+ 
+
+ align:start position:0%
+x-rays and so then you can look at the
+vein structures and how they evolve over
+
+ align:start position:0%
+vein structures and how they evolve over
+ 
+
+ align:start position:0%
+vein structures and how they evolve over
+time so they want to look at specific
+
+ align:start position:0%
+time so they want to look at specific
+ 
+
+ align:start position:0%
+time so they want to look at specific
+structures inside cells they don't just
+
+ align:start position:0%
+structures inside cells they don't just
+ 
+
+ align:start position:0%
+structures inside cells they don't just
+want a gross picture of a cell they want
+
+ align:start position:0%
+want a gross picture of a cell they want
+ 
+
+ align:start position:0%
+want a gross picture of a cell they want
+to they want to enhance certain details
+
+ align:start position:0%
+to they want to enhance certain details
+ 
+
+ align:start position:0%
+to they want to enhance certain details
+so what they use is fluorescent beads
+
+ align:start position:0%
+so what they use is fluorescent beads
+ 
+
+ align:start position:0%
+so what they use is fluorescent beads
+usually with some antigen tags for the
+
+ align:start position:0%
+usually with some antigen tags for the
+ 
+
+ align:start position:0%
+usually with some antigen tags for the
+biologists anyways i'll skip that they
+
+ align:start position:0%
+biologists anyways i'll skip that they
+ 
+
+ align:start position:0%
+biologists anyways i'll skip that they
+basically highlight they put fluorescent
+
+ align:start position:0%
+basically highlight they put fluorescent
+ 
+
+ align:start position:0%
+basically highlight they put fluorescent
+dyes
+
+ align:start position:0%
+dyes
+ 
+
+ align:start position:0%
+dyes
+somehow attached to structures they care
+
+ align:start position:0%
+somehow attached to structures they care
+ 
+
+ align:start position:0%
+somehow attached to structures they care
+about right
+
+ align:start position:0%
+about right
+ 
+
+ align:start position:0%
+about right
+so for instance mitochondria cell
+
+ align:start position:0%
+so for instance mitochondria cell
+ 
+
+ align:start position:0%
+so for instance mitochondria cell
+structures dna what have you and that
+
+ align:start position:0%
+structures dna what have you and that
+ 
+
+ align:start position:0%
+structures dna what have you and that
+will enhance the contrast in the final
+
+ align:start position:0%
+will enhance the contrast in the final
+ 
+
+ align:start position:0%
+will enhance the contrast in the final
+image and then what happens is the flexo
+
+ align:start position:0%
+image and then what happens is the flexo
+ 
+
+ align:start position:0%
+image and then what happens is the flexo
+beads are designed to fluoresce at some
+
+ align:start position:0%
+beads are designed to fluoresce at some
+ 
+
+ align:start position:0%
+beads are designed to fluoresce at some
+wavelength which is different than your
+
+ align:start position:0%
+wavelength which is different than your
+ 
+
+ align:start position:0%
+wavelength which is different than your
+source wavelength
+
+ align:start position:0%
+source wavelength
+ 
+
+ align:start position:0%
+source wavelength
+and then you have the beam splitter
+
+ align:start position:0%
+and then you have the beam splitter
+ 
+
+ align:start position:0%
+and then you have the beam splitter
+again but you have a filter on this beam
+
+ align:start position:0%
+again but you have a filter on this beam
+ 
+
+ align:start position:0%
+again but you have a filter on this beam
+splitter that only reflects
+
+ align:start position:0%
+splitter that only reflects
+ 
+
+ align:start position:0%
+splitter that only reflects
+the fluorescent wavelength not the
+
+ align:start position:0%
+the fluorescent wavelength not the
+ 
+
+ align:start position:0%
+the fluorescent wavelength not the
+stimulating wave
+
+ align:start position:0%
+stimulating wave
+ 
+
+ align:start position:0%
+stimulating wave
+right so that improves your contrast
+
+ align:start position:0%
+right so that improves your contrast
+ 
+
+ align:start position:0%
+right so that improves your contrast
+even more so that's the basic trick
+
+ align:start position:0%
+even more so that's the basic trick
+ 
+
+ align:start position:0%
+even more so that's the basic trick
+behind laser scanning focal microscopy
+
+ align:start position:0%
+behind laser scanning focal microscopy
+ 
+
+ align:start position:0%
+behind laser scanning focal microscopy
+but again you have to scan mechanically
+
+ align:start position:0%
+but again you have to scan mechanically
+ 
+
+ align:start position:0%
+but again you have to scan mechanically
+both the light source aperture and the
+
+ align:start position:0%
+both the light source aperture and the
+ 
+
+ align:start position:0%
+both the light source aperture and the
+detector aperture so this is a slow
+
+ align:start position:0%
+detector aperture so this is a slow
+ 
+
+ align:start position:0%
+detector aperture so this is a slow
+process but cellular division also a
+
+ align:start position:0%
+process but cellular division also a
+ 
+
+ align:start position:0%
+process but cellular division also a
+slow process so we can create videos of
+
+ align:start position:0%
+slow process so we can create videos of
+ 
+
+ align:start position:0%
+slow process so we can create videos of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+for instance here you can see
+
+ align:start position:0%
+for instance here you can see
+ 
+
+ align:start position:0%
+for instance here you can see
+typical cellular division process where
+
+ align:start position:0%
+typical cellular division process where
+ 
+
+ align:start position:0%
+typical cellular division process where
+i think they've probably accentuated the
+
+ align:start position:0%
+i think they've probably accentuated the
+ 
+
+ align:start position:0%
+i think they've probably accentuated the
+telomeres so you can see them separate
+
+ align:start position:0%
+telomeres so you can see them separate
+ 
+
+ align:start position:0%
+telomeres so you can see them separate
+i'm guessing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so again cellular division occurs
+
+ align:start position:0%
+right so again cellular division occurs
+ 
+
+ align:start position:0%
+right so again cellular division occurs
+on a long enough time scale that we can
+
+ align:start position:0%
+on a long enough time scale that we can
+ 
+
+ align:start position:0%
+on a long enough time scale that we can
+raster scan that without any
+
+ align:start position:0%
+raster scan that without any
+ 
+
+ align:start position:0%
+raster scan that without any
+difficulties in creating videos
+
+ align:start position:0%
+difficulties in creating videos
+ 
+
+ align:start position:0%
+difficulties in creating videos
+and then just to show you how good the
+
+ align:start position:0%
+and then just to show you how good the
+ 
+
+ align:start position:0%
+and then just to show you how good the
+cross sectional image is i think this is
+
+ align:start position:0%
+cross sectional image is i think this is
+ 
+
+ align:start position:0%
+cross sectional image is i think this is
+a pollen grain
+
+ align:start position:0%
+a pollen grain
+ 
+
+ align:start position:0%
+a pollen grain
+here you can see that
+
+ align:start position:0%
+here you can see that
+ 
+
+ align:start position:0%
+here you can see that
+this is again without any deconvolution
+
+ align:start position:0%
+this is again without any deconvolution
+ 
+
+ align:start position:0%
+this is again without any deconvolution
+no computation you're creating this
+
+ align:start position:0%
+no computation you're creating this
+ 
+
+ align:start position:0%
+no computation you're creating this
+function and then you can take a slice
+
+ align:start position:0%
+function and then you can take a slice
+ 
+
+ align:start position:0%
+function and then you can take a slice
+of the function and you'll see it evolve
+
+ align:start position:0%
+of the function and you'll see it evolve
+ 
+
+ align:start position:0%
+of the function and you'll see it evolve
+on the right here these cross-sectional
+
+ align:start position:0%
+on the right here these cross-sectional
+ 
+
+ align:start position:0%
+on the right here these cross-sectional
+images are very sharp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again by using the fluorescent beads
+
+ align:start position:0%
+and again by using the fluorescent beads
+ 
+
+ align:start position:0%
+and again by using the fluorescent beads
+you can enhance the contrast as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is this idea taken to its
+
+ align:start position:0%
+so this is this idea taken to its
+ 
+
+ align:start position:0%
+so this is this idea taken to its
+natural conclusion this is the
+
+ align:start position:0%
+natural conclusion this is the
+ 
+
+ align:start position:0%
+natural conclusion this is the
+commercial product you get at the end
+
+ align:start position:0%
+commercial product you get at the end
+ 
+
+ align:start position:0%
+commercial product you get at the end
+and so now again to plug some of my own
+
+ align:start position:0%
+and so now again to plug some of my own
+ 
+
+ align:start position:0%
+and so now again to plug some of my own
+work uh well this isn't my own work but
+
+ align:start position:0%
+work uh well this isn't my own work but
+ 
+
+ align:start position:0%
+work uh well this isn't my own work but
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+uh i want to talk just briefly about
+
+ align:start position:0%
+uh i want to talk just briefly about
+ 
+
+ align:start position:0%
+uh i want to talk just briefly about
+coated aperture names coded aperture
+
+ align:start position:0%
+coated aperture names coded aperture
+ 
+
+ align:start position:0%
+coated aperture names coded aperture
+images we talked about biology medical
+
+ align:start position:0%
+images we talked about biology medical
+ 
+
+ align:start position:0%
+images we talked about biology medical
+imaging a little bit about geology so
+
+ align:start position:0%
+imaging a little bit about geology so
+ 
+
+ align:start position:0%
+imaging a little bit about geology so
+now it's not leaving the astronomers out
+
+ align:start position:0%
+now it's not leaving the astronomers out
+ 
+
+ align:start position:0%
+now it's not leaving the astronomers out
+and so what sort of ideas can we mine
+
+ align:start position:0%
+and so what sort of ideas can we mine
+ 
+
+ align:start position:0%
+and so what sort of ideas can we mine
+from the field of astronomical imaging
+
+ align:start position:0%
+from the field of astronomical imaging
+ 
+
+ align:start position:0%
+from the field of astronomical imaging
+and i think
+
+ align:start position:0%
+and i think
+ 
+
+ align:start position:0%
+and i think
+the main takeaway message that's
+
+ align:start position:0%
+the main takeaway message that's
+ 
+
+ align:start position:0%
+the main takeaway message that's
+impacted computational photography is
+
+ align:start position:0%
+impacted computational photography is
+ 
+
+ align:start position:0%
+impacted computational photography is
+idea of coded apertures right so if i'm
+
+ align:start position:0%
+idea of coded apertures right so if i'm
+ 
+
+ align:start position:0%
+idea of coded apertures right so if i'm
+imaging in x-rays i'm looking for
+
+ align:start position:0%
+imaging in x-rays i'm looking for
+ 
+
+ align:start position:0%
+imaging in x-rays i'm looking for
+supernova bursts what have you uh it's
+
+ align:start position:0%
+supernova bursts what have you uh it's
+ 
+
+ align:start position:0%
+supernova bursts what have you uh it's
+impractical to build refractive optics
+
+ align:start position:0%
+impractical to build refractive optics
+ 
+
+ align:start position:0%
+impractical to build refractive optics
+really all you can do is attenuate
+
+ align:start position:0%
+really all you can do is attenuate
+ 
+
+ align:start position:0%
+really all you can do is attenuate
+x-rays you can build lead lead sheets
+
+ align:start position:0%
+x-rays you can build lead lead sheets
+ 
+
+ align:start position:0%
+x-rays you can build lead lead sheets
+like we did in our project
+
+ align:start position:0%
+like we did in our project
+ 
+
+ align:start position:0%
+like we did in our project
+and block them in various ways and so
+
+ align:start position:0%
+and block them in various ways and so
+ 
+
+ align:start position:0%
+and block them in various ways and so
+then the question is how can you image
+
+ align:start position:0%
+then the question is how can you image
+ 
+
+ align:start position:0%
+then the question is how can you image
+a non non-refractive uh wavelengths
+
+ align:start position:0%
+a non non-refractive uh wavelengths
+ 
+
+ align:start position:0%
+a non non-refractive uh wavelengths
+or all with right so any ideas well the
+
+ align:start position:0%
+or all with right so any ideas well the
+ 
+
+ align:start position:0%
+or all with right so any ideas well the
+first idea of course is built pinhole
+
+ align:start position:0%
+first idea of course is built pinhole
+ 
+
+ align:start position:0%
+first idea of course is built pinhole
+apertures right
+
+ align:start position:0%
+apertures right
+ 
+
+ align:start position:0%
+apertures right
+so say i want to take an x-ray image of
+
+ align:start position:0%
+so say i want to take an x-ray image of
+ 
+
+ align:start position:0%
+so say i want to take an x-ray image of
+the world
+
+ align:start position:0%
+the world
+ 
+
+ align:start position:0%
+the world
+but i can't build a thin lens that that
+
+ align:start position:0%
+but i can't build a thin lens that that
+ 
+
+ align:start position:0%
+but i can't build a thin lens that that
+refracts x-rays
+
+ align:start position:0%
+refracts x-rays
+ 
+
+ align:start position:0%
+refracts x-rays
+so i i have this x-ray gumballs
+
+ align:start position:0%
+so i i have this x-ray gumballs
+ 
+
+ align:start position:0%
+so i i have this x-ray gumballs
+and i have i just take a lead sheet
+
+ align:start position:0%
+and i have i just take a lead sheet
+ 
+
+ align:start position:0%
+and i have i just take a lead sheet
+drill a hole in it i have an x-ray film
+
+ align:start position:0%
+drill a hole in it i have an x-ray film
+ 
+
+ align:start position:0%
+drill a hole in it i have an x-ray film
+no problem i get an image
+
+ align:start position:0%
+no problem i get an image
+ 
+
+ align:start position:0%
+no problem i get an image
+but i have exposure issues as always
+
+ align:start position:0%
+but i have exposure issues as always
+ 
+
+ align:start position:0%
+but i have exposure issues as always
+right so any guesses about how to solve
+
+ align:start position:0%
+right so any guesses about how to solve
+ 
+
+ align:start position:0%
+right so any guesses about how to solve
+the exposure issues
+
+ align:start position:0%
+the exposure issues
+ 
+
+ align:start position:0%
+the exposure issues
+as engineers what would be some tricks
+
+ align:start position:0%
+as engineers what would be some tricks
+ 
+
+ align:start position:0%
+as engineers what would be some tricks
+any ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since we're a pinhole you want something
+
+ align:start position:0%
+since we're a pinhole you want something
+ 
+
+ align:start position:0%
+since we're a pinhole you want something
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so if we didn't know about deconvolution
+
+ align:start position:0%
+so if we didn't know about deconvolution
+ 
+
+ align:start position:0%
+so if we didn't know about deconvolution
+yet which it seems the wiki will tell
+
+ align:start position:0%
+yet which it seems the wiki will tell
+ 
+
+ align:start position:0%
+yet which it seems the wiki will tell
+you later um the first step to getting
+
+ align:start position:0%
+you later um the first step to getting
+ 
+
+ align:start position:0%
+you later um the first step to getting
+more light is just make a larger pinhole
+
+ align:start position:0%
+more light is just make a larger pinhole
+ 
+
+ align:start position:0%
+more light is just make a larger pinhole
+right so if you don't really care about
+
+ align:start position:0%
+right so if you don't really care about
+ 
+
+ align:start position:0%
+right so if you don't really care about
+the resolution of your scene you can
+
+ align:start position:0%
+the resolution of your scene you can
+ 
+
+ align:start position:0%
+the resolution of your scene you can
+afford to blur it
+
+ align:start position:0%
+afford to blur it
+ 
+
+ align:start position:0%
+afford to blur it
+right so if we're just looking at stars
+
+ align:start position:0%
+right so if we're just looking at stars
+ 
+
+ align:start position:0%
+right so if we're just looking at stars
+we can blur them we can make bigger
+
+ align:start position:0%
+we can blur them we can make bigger
+ 
+
+ align:start position:0%
+we can blur them we can make bigger
+pinholes and then deconvolve that maybe
+
+ align:start position:0%
+pinholes and then deconvolve that maybe
+ 
+
+ align:start position:0%
+pinholes and then deconvolve that maybe
+even though it's difficult to develop a
+
+ align:start position:0%
+even though it's difficult to develop a
+ 
+
+ align:start position:0%
+even though it's difficult to develop a
+circular aperture right so that's not a
+
+ align:start position:0%
+circular aperture right so that's not a
+ 
+
+ align:start position:0%
+circular aperture right so that's not a
+great solution but we're letting more
+
+ align:start position:0%
+great solution but we're letting more
+ 
+
+ align:start position:0%
+great solution but we're letting more
+light by the function of the radius
+
+ align:start position:0%
+light by the function of the radius
+ 
+
+ align:start position:0%
+light by the function of the radius
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+but the real solution here is again
+
+ align:start position:0%
+but the real solution here is again
+ 
+
+ align:start position:0%
+but the real solution here is again
+called coated aperture and the idea
+
+ align:start position:0%
+called coated aperture and the idea
+ 
+
+ align:start position:0%
+called coated aperture and the idea
+is to drill many holes as kevin said in
+
+ align:start position:0%
+is to drill many holes as kevin said in
+ 
+
+ align:start position:0%
+is to drill many holes as kevin said in
+a way that all the images that overlap
+
+ align:start position:0%
+a way that all the images that overlap
+ 
+
+ align:start position:0%
+a way that all the images that overlap
+are somehow invertible and you saw this
+
+ align:start position:0%
+are somehow invertible and you saw this
+ 
+
+ align:start position:0%
+are somehow invertible and you saw this
+hopefully you remember back to when i
+
+ align:start position:0%
+hopefully you remember back to when i
+ 
+
+ align:start position:0%
+hopefully you remember back to when i
+was talking about the shieldfield
+
+ align:start position:0%
+was talking about the shieldfield
+ 
+
+ align:start position:0%
+was talking about the shieldfield
+project we put all these holes in front
+
+ align:start position:0%
+project we put all these holes in front
+ 
+
+ align:start position:0%
+project we put all these holes in front
+of the plane so that you could invert
+
+ align:start position:0%
+of the plane so that you could invert
+ 
+
+ align:start position:0%
+of the plane so that you could invert
+that system and so we weren't the first
+
+ align:start position:0%
+that system and so we weren't the first
+ 
+
+ align:start position:0%
+that system and so we weren't the first
+to discover this
+
+ align:start position:0%
+to discover this
+ 
+
+ align:start position:0%
+to discover this
+at least for for imaging of point
+
+ align:start position:0%
+at least for for imaging of point
+ 
+
+ align:start position:0%
+at least for for imaging of point
+sources and the basic idea is that as
+
+ align:start position:0%
+sources and the basic idea is that as
+ 
+
+ align:start position:0%
+sources and the basic idea is that as
+long as we design this mask
+
+ align:start position:0%
+long as we design this mask
+ 
+
+ align:start position:0%
+long as we design this mask
+appropriately
+
+ align:start position:0%
+appropriately
+ 
+
+ align:start position:0%
+appropriately
+so that that system of equations is well
+
+ align:start position:0%
+so that that system of equations is well
+ 
+
+ align:start position:0%
+so that that system of equations is well
+posed we can invert it and so here i'll
+
+ align:start position:0%
+posed we can invert it and so here i'll
+ 
+
+ align:start position:0%
+posed we can invert it and so here i'll
+show you something that's not well posed
+
+ align:start position:0%
+show you something that's not well posed
+ 
+
+ align:start position:0%
+show you something that's not well posed
+this is sort of like the the shieldfield
+
+ align:start position:0%
+this is sort of like the the shieldfield
+ 
+
+ align:start position:0%
+this is sort of like the the shieldfield
+side we saw earlier where we had three
+
+ align:start position:0%
+side we saw earlier where we had three
+ 
+
+ align:start position:0%
+side we saw earlier where we had three
+x-ray sources on all the time
+
+ align:start position:0%
+x-ray sources on all the time
+ 
+
+ align:start position:0%
+x-ray sources on all the time
+and those three images were overlapping
+
+ align:start position:0%
+and those three images were overlapping
+ 
+
+ align:start position:0%
+and those three images were overlapping
+on the sensor right so if we do this in
+
+ align:start position:0%
+on the sensor right so if we do this in
+ 
+
+ align:start position:0%
+on the sensor right so if we do this in
+the x-ray domain we have three images
+
+ align:start position:0%
+the x-ray domain we have three images
+ 
+
+ align:start position:0%
+the x-ray domain we have three images
+coming from three centers of projection
+
+ align:start position:0%
+coming from three centers of projection
+ 
+
+ align:start position:0%
+coming from three centers of projection
+they're all just shifts from one another
+
+ align:start position:0%
+they're all just shifts from one another
+ 
+
+ align:start position:0%
+they're all just shifts from one another
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so you can imagine if i just had two pen
+
+ align:start position:0%
+so you can imagine if i just had two pen
+ 
+
+ align:start position:0%
+so you can imagine if i just had two pen
+holes
+
+ align:start position:0%
+holes
+ 
+
+ align:start position:0%
+holes
+and some prior on the scene it wouldn't
+
+ align:start position:0%
+and some prior on the scene it wouldn't
+ 
+
+ align:start position:0%
+and some prior on the scene it wouldn't
+be too difficult to separate two images
+
+ align:start position:0%
+be too difficult to separate two images
+ 
+
+ align:start position:0%
+be too difficult to separate two images
+right so that would double my light
+
+ align:start position:0%
+right so that would double my light
+ 
+
+ align:start position:0%
+right so that would double my light
+and i'd probably be able to invert that
+
+ align:start position:0%
+and i'd probably be able to invert that
+ 
+
+ align:start position:0%
+and i'd probably be able to invert that
+as kevin said that that would be easy
+
+ align:start position:0%
+as kevin said that that would be easy
+ 
+
+ align:start position:0%
+as kevin said that that would be easy
+enough to deconvolve probably
+
+ align:start position:0%
+enough to deconvolve probably
+ 
+
+ align:start position:0%
+enough to deconvolve probably
+although it wouldn't be a linear process
+
+ align:start position:0%
+although it wouldn't be a linear process
+ 
+
+ align:start position:0%
+although it wouldn't be a linear process
+problem so then as we add more and more
+
+ align:start position:0%
+problem so then as we add more and more
+ 
+
+ align:start position:0%
+problem so then as we add more and more
+pinholes we let in more light but that
+
+ align:start position:0%
+pinholes we let in more light but that
+ 
+
+ align:start position:0%
+pinholes we let in more light but that
+inversion that system of equations
+
+ align:start position:0%
+inversion that system of equations
+ 
+
+ align:start position:0%
+inversion that system of equations
+becomes more ill-posed it's condition
+
+ align:start position:0%
+becomes more ill-posed it's condition
+ 
+
+ align:start position:0%
+becomes more ill-posed it's condition
+number uh it's much worse so then that's
+
+ align:start position:0%
+number uh it's much worse so then that's
+ 
+
+ align:start position:0%
+number uh it's much worse so then that's
+where we end up in the sort of field of
+
+ align:start position:0%
+where we end up in the sort of field of
+ 
+
+ align:start position:0%
+where we end up in the sort of field of
+optimizing coded apertures which is what
+
+ align:start position:0%
+optimizing coded apertures which is what
+ 
+
+ align:start position:0%
+optimizing coded apertures which is what
+our work was on and so any of you sort
+
+ align:start position:0%
+our work was on and so any of you sort
+ 
+
+ align:start position:0%
+our work was on and so any of you sort
+of considering
+
+ align:start position:0%
+of considering
+ 
+
+ align:start position:0%
+of considering
+using masks for light field capture or
+
+ align:start position:0%
+using masks for light field capture or
+ 
+
+ align:start position:0%
+using masks for light field capture or
+other things it will very quickly arrive
+
+ align:start position:0%
+other things it will very quickly arrive
+ 
+
+ align:start position:0%
+other things it will very quickly arrive
+at similar results and the idea is to
+
+ align:start position:0%
+at similar results and the idea is to
+ 
+
+ align:start position:0%
+at similar results and the idea is to
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+in this case they generally use
+
+ align:start position:0%
+in this case they generally use
+ 
+
+ align:start position:0%
+in this case they generally use
+something called a mirror code and it's
+
+ align:start position:0%
+something called a mirror code and it's
+ 
+
+ align:start position:0%
+something called a mirror code and it's
+just designed
+
+ align:start position:0%
+just designed
+ 
+
+ align:start position:0%
+just designed
+uh i'll tell you the the main fact about
+
+ align:start position:0%
+uh i'll tell you the the main fact about
+ 
+
+ align:start position:0%
+uh i'll tell you the the main fact about
+the mirror code is that it's our auto
+
+ align:start position:0%
+the mirror code is that it's our auto
+ 
+
+ align:start position:0%
+the mirror code is that it's our auto
+correlation function is equal to a delta
+
+ align:start position:0%
+correlation function is equal to a delta
+ 
+
+ align:start position:0%
+correlation function is equal to a delta
+function and so if you think about
+
+ align:start position:0%
+function and so if you think about
+ 
+
+ align:start position:0%
+function and so if you think about
+deconvolution
+
+ align:start position:0%
+deconvolution
+ 
+
+ align:start position:0%
+deconvolution
+for those of you it seems that you
+
+ align:start position:0%
+for those of you it seems that you
+ 
+
+ align:start position:0%
+for those of you it seems that you
+aren't familiar with it that should tell
+
+ align:start position:0%
+aren't familiar with it that should tell
+ 
+
+ align:start position:0%
+aren't familiar with it that should tell
+you why you can you can do this but the
+
+ align:start position:0%
+you why you can you can do this but the
+ 
+
+ align:start position:0%
+you why you can you can do this but the
+basic idea is that the image formation
+
+ align:start position:0%
+basic idea is that the image formation
+ 
+
+ align:start position:0%
+basic idea is that the image formation
+process we can now model is linear we
+
+ align:start position:0%
+process we can now model is linear we
+ 
+
+ align:start position:0%
+process we can now model is linear we
+have a sequence of pinholes of varying
+
+ align:start position:0%
+have a sequence of pinholes of varying
+ 
+
+ align:start position:0%
+have a sequence of pinholes of varying
+sizes and distributions to image the
+
+ align:start position:0%
+sizes and distributions to image the
+ 
+
+ align:start position:0%
+sizes and distributions to image the
+to simulate the image we receive we can
+
+ align:start position:0%
+to simulate the image we receive we can
+ 
+
+ align:start position:0%
+to simulate the image we receive we can
+involve our aperture
+
+ align:start position:0%
+involve our aperture
+ 
+
+ align:start position:0%
+involve our aperture
+scaled scale the aperture with our
+
+ align:start position:0%
+scaled scale the aperture with our
+ 
+
+ align:start position:0%
+scaled scale the aperture with our
+function this is the image we get on the
+
+ align:start position:0%
+function this is the image we get on the
+ 
+
+ align:start position:0%
+function this is the image we get on the
+sensor
+
+ align:start position:0%
+sensor
+ 
+
+ align:start position:0%
+sensor
+and then believe it or not to deconvolve
+
+ align:start position:0%
+and then believe it or not to deconvolve
+ 
+
+ align:start position:0%
+and then believe it or not to deconvolve
+you simply convolve again
+
+ align:start position:0%
+you simply convolve again
+ 
+
+ align:start position:0%
+you simply convolve again
+to involve this blurred image the
+
+ align:start position:0%
+to involve this blurred image the
+ 
+
+ align:start position:0%
+to involve this blurred image the
+superimposed image with the aperture
+
+ align:start position:0%
+superimposed image with the aperture
+ 
+
+ align:start position:0%
+superimposed image with the aperture
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and you actually get back in the absence
+
+ align:start position:0%
+and you actually get back in the absence
+ 
+
+ align:start position:0%
+and you actually get back in the absence
+of noise you get back exactly the image
+
+ align:start position:0%
+of noise you get back exactly the image
+ 
+
+ align:start position:0%
+of noise you get back exactly the image
+and really this is the key problem of
+
+ align:start position:0%
+and really this is the key problem of
+ 
+
+ align:start position:0%
+and really this is the key problem of
+coded aperture and something you can
+
+ align:start position:0%
+coded aperture and something you can
+ 
+
+ align:start position:0%
+coded aperture and something you can
+investigate there have been a couple
+
+ align:start position:0%
+investigate there have been a couple
+ 
+
+ align:start position:0%
+investigate there have been a couple
+papers from sheen iron others in recent
+
+ align:start position:0%
+papers from sheen iron others in recent
+ 
+
+ align:start position:0%
+papers from sheen iron others in recent
+years where they applied this again it
+
+ align:start position:0%
+years where they applied this again it
+ 
+
+ align:start position:0%
+years where they applied this again it
+took astronomy applied it to
+
+ align:start position:0%
+took astronomy applied it to
+ 
+
+ align:start position:0%
+took astronomy applied it to
+computational photography and they said
+
+ align:start position:0%
+computational photography and they said
+ 
+
+ align:start position:0%
+computational photography and they said
+okay we're going to put coded apertures
+
+ align:start position:0%
+okay we're going to put coded apertures
+ 
+
+ align:start position:0%
+okay we're going to put coded apertures
+and cameras
+
+ align:start position:0%
+and cameras
+ 
+
+ align:start position:0%
+and cameras
+but the key trick is what's that
+
+ align:start position:0%
+but the key trick is what's that
+ 
+
+ align:start position:0%
+but the key trick is what's that
+aperture going to be so that the
+
+ align:start position:0%
+aperture going to be so that the
+ 
+
+ align:start position:0%
+aperture going to be so that the
+inversion is well posed
+
+ align:start position:0%
+inversion is well posed
+ 
+
+ align:start position:0%
+inversion is well posed
+in the presence of noise paper so so
+
+ align:start position:0%
+in the presence of noise paper so so
+ 
+
+ align:start position:0%
+in the presence of noise paper so so
+that should inspire you hopefully for
+
+ align:start position:0%
+that should inspire you hopefully for
+ 
+
+ align:start position:0%
+that should inspire you hopefully for
+your final projects and then
+
+ align:start position:0%
+your final projects and then
+ 
+
+ align:start position:0%
+your final projects and then
+this uh has also been applied for
+
+ align:start position:0%
+this uh has also been applied for
+ 
+
+ align:start position:0%
+this uh has also been applied for
+tomography and so you can do exactly
+
+ align:start position:0%
+tomography and so you can do exactly
+ 
+
+ align:start position:0%
+tomography and so you can do exactly
+what our goal in our project was which
+
+ align:start position:0%
+what our goal in our project was which
+ 
+
+ align:start position:0%
+what our goal in our project was which
+is to have no moving part instantaneous
+
+ align:start position:0%
+is to have no moving part instantaneous
+ 
+
+ align:start position:0%
+is to have no moving part instantaneous
+tomography using some of these concepts
+
+ align:start position:0%
+tomography using some of these concepts
+ 
+
+ align:start position:0%
+tomography using some of these concepts
+the main challenge is doing it when
+
+ align:start position:0%
+the main challenge is doing it when
+ 
+
+ align:start position:0%
+the main challenge is doing it when
+objects are close to the detector and so
+
+ align:start position:0%
+objects are close to the detector and so
+ 
+
+ align:start position:0%
+objects are close to the detector and so
+that's really the problem that we solved
+
+ align:start position:0%
+that's really the problem that we solved
+ 
+
+ align:start position:0%
+that's really the problem that we solved
+in our work
+
+ align:start position:0%
+in our work
+ 
+
+ align:start position:0%
+in our work
+so that concludes my talk so thank you
+
+ align:start position:0%
+so that concludes my talk so thank you
+ 
+
+ align:start position:0%
+so that concludes my talk so thank you
+for your attention if you have any
+
+ align:start position:0%
+for your attention if you have any
+ 
+
+ align:start position:0%
+for your attention if you have any
+questions i'll be i'll take them nice
+
+ align:start position:0%
+questions i'll be i'll take them nice
+ 
+
+ align:start position:0%
+questions i'll be i'll take them nice
+work done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+light films and tomography one the same
+
+ align:start position:0%
+light films and tomography one the same
+ 
+
+ align:start position:0%
+light films and tomography one the same
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that clear to everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's draw on the let's scroll
+
+ align:start position:0%
+all right let's draw on the let's scroll
+ 
+
+ align:start position:0%
+all right let's draw on the let's scroll
+the board
+
+ align:start position:0%
+the board
+ 
+
+ align:start position:0%
+the board
+yeah i think that link is the really the
+
+ align:start position:0%
+yeah i think that link is the really the
+ 
+
+ align:start position:0%
+yeah i think that link is the really the
+one you're next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so your assignment number two which
+
+ align:start position:0%
+and so your assignment number two which
+ 
+
+ align:start position:0%
+and so your assignment number two which
+was all about
+
+ align:start position:0%
+was all about
+ 
+
+ align:start position:0%
+was all about
+shifting and adding but your goal was to
+
+ align:start position:0%
+shifting and adding but your goal was to
+ 
+
+ align:start position:0%
+shifting and adding but your goal was to
+do refocusing over there so you had a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bunch of cameras
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you had some scene out here
+
+ align:start position:0%
+and you had some scene out here
+ 
+
+ align:start position:0%
+and you had some scene out here
+and when you wanted to refocus on a
+
+ align:start position:0%
+and when you wanted to refocus on a
+ 
+
+ align:start position:0%
+and when you wanted to refocus on a
+particular plane if you if you just sum
+
+ align:start position:0%
+particular plane if you if you just sum
+ 
+
+ align:start position:0%
+particular plane if you if you just sum
+up all these images
+
+ align:start position:0%
+up all these images
+ 
+
+ align:start position:0%
+up all these images
+then you're focusing at infinity
+
+ align:start position:0%
+then you're focusing at infinity
+ 
+
+ align:start position:0%
+then you're focusing at infinity
+but if you wanted to focus somewhere
+
+ align:start position:0%
+but if you wanted to focus somewhere
+ 
+
+ align:start position:0%
+but if you wanted to focus somewhere
+closer
+
+ align:start position:0%
+closer
+ 
+
+ align:start position:0%
+closer
+then you would appropriately add
+
+ align:start position:0%
+then you would appropriately add
+ 
+
+ align:start position:0%
+then you would appropriately add
+appropriately shift this image as
+
+ align:start position:0%
+appropriately shift this image as
+ 
+
+ align:start position:0%
+appropriately shift this image as
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+right but what is this particular image
+
+ align:start position:0%
+right but what is this particular image
+ 
+
+ align:start position:0%
+right but what is this particular image
+it's basically
+
+ align:start position:0%
+it's basically
+ 
+
+ align:start position:0%
+it's basically
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+image of a scene
+
+ align:start position:0%
+image of a scene
+ 
+
+ align:start position:0%
+image of a scene
+where all these rays are
+
+ align:start position:0%
+where all these rays are
+ 
+
+ align:start position:0%
+where all these rays are
+you can take a very simplified a bit
+
+ align:start position:0%
+you can take a very simplified a bit
+ 
+
+ align:start position:0%
+you can take a very simplified a bit
+more work and whole model here
+
+ align:start position:0%
+more work and whole model here
+ 
+
+ align:start position:0%
+more work and whole model here
+the projection of the scene
+
+ align:start position:0%
+the projection of the scene
+ 
+
+ align:start position:0%
+the projection of the scene
+onto the sensor
+
+ align:start position:0%
+onto the sensor
+ 
+
+ align:start position:0%
+onto the sensor
+when you move it over here
+
+ align:start position:0%
+when you move it over here
+ 
+
+ align:start position:0%
+when you move it over here
+is the same almost the same word
+
+ align:start position:0%
+is the same almost the same word
+ 
+
+ align:start position:0%
+is the same almost the same word
+being projected from a slightly
+
+ align:start position:0%
+being projected from a slightly
+ 
+
+ align:start position:0%
+being projected from a slightly
+different report
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you're doing tomography it's
+
+ align:start position:0%
+and when you're doing tomography it's
+ 
+
+ align:start position:0%
+and when you're doing tomography it's
+almost the same thing after you have
+
+ align:start position:0%
+almost the same thing after you have
+ 
+
+ align:start position:0%
+almost the same thing after you have
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you have a extra source
+
+ align:start position:0%
+and you have a extra source
+ 
+
+ align:start position:0%
+and you have a extra source
+and you have an object here
+
+ align:start position:0%
+and you have an object here
+ 
+
+ align:start position:0%
+and you have an object here
+and you have
+
+ align:start position:0%
+and you have
+ 
+
+ align:start position:0%
+and you have
+projected
+
+ align:start position:0%
+projected
+ 
+
+ align:start position:0%
+projected
+this object onto the sensor
+
+ align:start position:0%
+this object onto the sensor
+ 
+
+ align:start position:0%
+this object onto the sensor
+and when you shift it around
+
+ align:start position:0%
+and when you shift it around
+ 
+
+ align:start position:0%
+and when you shift it around
+and put the extra source here
+
+ align:start position:0%
+and put the extra source here
+ 
+
+ align:start position:0%
+and put the extra source here
+you're again projecting this
+
+ align:start position:0%
+you're again projecting this
+ 
+
+ align:start position:0%
+you're again projecting this
+from a slightly different viewpoint
+
+ align:start position:0%
+from a slightly different viewpoint
+ 
+
+ align:start position:0%
+from a slightly different viewpoint
+so if as if this object was
+
+ align:start position:0%
+so if as if this object was
+ 
+
+ align:start position:0%
+so if as if this object was
+in this case as if the object was
+
+ align:start position:0%
+in this case as if the object was
+ 
+
+ align:start position:0%
+in this case as if the object was
+outside
+
+ align:start position:0%
+outside
+ 
+
+ align:start position:0%
+outside
+and you're projecting through this
+
+ align:start position:0%
+and you're projecting through this
+ 
+
+ align:start position:0%
+and you're projecting through this
+pinhole and taking an image on this
+
+ align:start position:0%
+pinhole and taking an image on this
+ 
+
+ align:start position:0%
+pinhole and taking an image on this
+detector
+
+ align:start position:0%
+detector
+ 
+
+ align:start position:0%
+detector
+and by by moving this
+
+ align:start position:0%
+and by by moving this
+ 
+
+ align:start position:0%
+and by by moving this
+uh pinhole in this case here
+
+ align:start position:0%
+uh pinhole in this case here
+ 
+
+ align:start position:0%
+uh pinhole in this case here
+you're taking different projections of
+
+ align:start position:0%
+you're taking different projections of
+ 
+
+ align:start position:0%
+you're taking different projections of
+the scene
+
+ align:start position:0%
+the scene
+ 
+
+ align:start position:0%
+the scene
+and over here you're taking different
+
+ align:start position:0%
+and over here you're taking different
+ 
+
+ align:start position:0%
+and over here you're taking different
+projections of what's inside here what's
+
+ align:start position:0%
+projections of what's inside here what's
+ 
+
+ align:start position:0%
+projections of what's inside here what's
+outside and here what's inside but the
+
+ align:start position:0%
+outside and here what's inside but the
+ 
+
+ align:start position:0%
+outside and here what's inside but the
+basic principle is the same which is
+
+ align:start position:0%
+basic principle is the same which is
+ 
+
+ align:start position:0%
+basic principle is the same which is
+you're changing the viewpoint and taking
+
+ align:start position:0%
+you're changing the viewpoint and taking
+ 
+
+ align:start position:0%
+you're changing the viewpoint and taking
+projection of consolidation
+
+ align:start position:0%
+projection of consolidation
+ 
+
+ align:start position:0%
+projection of consolidation
+and as doug explained
+
+ align:start position:0%
+and as doug explained
+ 
+
+ align:start position:0%
+and as doug explained
+this data set is sufficient
+
+ align:start position:0%
+this data set is sufficient
+ 
+
+ align:start position:0%
+this data set is sufficient
+uh you can express it as a radar
+
+ align:start position:0%
+uh you can express it as a radar
+ 
+
+ align:start position:0%
+uh you can express it as a radar
+transform and you can invert that to
+
+ align:start position:0%
+transform and you can invert that to
+ 
+
+ align:start position:0%
+transform and you can invert that to
+figure out what's inside
+
+ align:start position:0%
+figure out what's inside
+ 
+
+ align:start position:0%
+figure out what's inside
+so if this was uh some material that's
+
+ align:start position:0%
+so if this was uh some material that's
+ 
+
+ align:start position:0%
+so if this was uh some material that's
+simply attenuating and not scattering
+
+ align:start position:0%
+simply attenuating and not scattering
+ 
+
+ align:start position:0%
+simply attenuating and not scattering
+then you can figure out the density
+
+ align:start position:0%
+then you can figure out the density
+ 
+
+ align:start position:0%
+then you can figure out the density
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+in case of refocusing
+
+ align:start position:0%
+in case of refocusing
+ 
+
+ align:start position:0%
+in case of refocusing
+what you were doing was you're shifting
+
+ align:start position:0%
+what you were doing was you're shifting
+ 
+
+ align:start position:0%
+what you were doing was you're shifting
+and adding
+
+ align:start position:0%
+and adding
+ 
+
+ align:start position:0%
+and adding
+to focus on a particular play
+
+ align:start position:0%
+to focus on a particular play
+ 
+
+ align:start position:0%
+to focus on a particular play
+and that's the form of a tomography
+
+ align:start position:0%
+and that's the form of a tomography
+ 
+
+ align:start position:0%
+and that's the form of a tomography
+or at least a form of a libenography as
+
+ align:start position:0%
+or at least a form of a libenography as
+ 
+
+ align:start position:0%
+or at least a form of a libenography as
+we were looking at earlier because
+
+ align:start position:0%
+we were looking at earlier because
+ 
+
+ align:start position:0%
+we were looking at earlier because
+you're just looking at a slice which is
+
+ align:start position:0%
+you're just looking at a slice which is
+ 
+
+ align:start position:0%
+you're just looking at a slice which is
+exactly what the word
+
+ align:start position:0%
+exactly what the word
+ 
+
+ align:start position:0%
+exactly what the word
+means recording of the slice
+
+ align:start position:0%
+means recording of the slice
+ 
+
+ align:start position:0%
+means recording of the slice
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the mathematics is identical
+
+ align:start position:0%
+the mathematics is identical
+ 
+
+ align:start position:0%
+the mathematics is identical
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+at least at least to the first order
+
+ align:start position:0%
+at least at least to the first order
+ 
+
+ align:start position:0%
+at least at least to the first order
+because the projections of the 3d world
+
+ align:start position:0%
+because the projections of the 3d world
+ 
+
+ align:start position:0%
+because the projections of the 3d world
+or a 2d sensor
+
+ align:start position:0%
+or a 2d sensor
+ 
+
+ align:start position:0%
+or a 2d sensor
+eventually allow you to compute
+
+ align:start position:0%
+eventually allow you to compute
+ 
+
+ align:start position:0%
+eventually allow you to compute
+something about the 3d mode from a set
+
+ align:start position:0%
+something about the 3d mode from a set
+ 
+
+ align:start position:0%
+something about the 3d mode from a set
+of 2d images you can say something about
+
+ align:start position:0%
+of 2d images you can say something about
+ 
+
+ align:start position:0%
+of 2d images you can say something about
+the 3d world
+
+ align:start position:0%
+the 3d world
+ 
+
+ align:start position:0%
+the 3d world
+uh in in in light photography you mostly
+
+ align:start position:0%
+uh in in in light photography you mostly
+ 
+
+ align:start position:0%
+uh in in in light photography you mostly
+care about creating refocused images one
+
+ align:start position:0%
+care about creating refocused images one
+ 
+
+ align:start position:0%
+care about creating refocused images one
+layer at a time
+
+ align:start position:0%
+layer at a time
+ 
+
+ align:start position:0%
+layer at a time
+but if this was also a
+
+ align:start position:0%
+but if this was also a
+ 
+
+ align:start position:0%
+but if this was also a
+some kind of
+
+ align:start position:0%
+some kind of
+ 
+
+ align:start position:0%
+some kind of
+an object
+
+ align:start position:0%
+an object
+ 
+
+ align:start position:0%
+an object
+which had some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+a pure attenuation then again from all
+
+ align:start position:0%
+a pure attenuation then again from all
+ 
+
+ align:start position:0%
+a pure attenuation then again from all
+these sequence of images you can
+
+ align:start position:0%
+these sequence of images you can
+ 
+
+ align:start position:0%
+these sequence of images you can
+reconstruct
+
+ align:start position:0%
+reconstruct
+ 
+
+ align:start position:0%
+reconstruct
+what the volumetric representation of
+
+ align:start position:0%
+what the volumetric representation of
+ 
+
+ align:start position:0%
+what the volumetric representation of
+this object is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's one major difference though
+
+ align:start position:0%
+okay there's one major difference though
+ 
+
+ align:start position:0%
+okay there's one major difference though
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+uh a cat scan here
+
+ align:start position:0%
+uh a cat scan here
+ 
+
+ align:start position:0%
+uh a cat scan here
+versus a electric camera that's
+
+ align:start position:0%
+versus a electric camera that's
+ 
+
+ align:start position:0%
+versus a electric camera that's
+has an area of uh
+
+ align:start position:0%
+has an area of uh
+ 
+
+ align:start position:0%
+has an area of uh
+a light fluid that's made up of carrier
+
+ align:start position:0%
+a light fluid that's made up of carrier
+ 
+
+ align:start position:0%
+a light fluid that's made up of carrier
+cameras
+
+ align:start position:0%
+cameras
+ 
+
+ align:start position:0%
+cameras
+what's the major difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+a parallel beam that's that's one
+
+ align:start position:0%
+a parallel beam that's that's one
+ 
+
+ align:start position:0%
+a parallel beam that's that's one
+example in fact this if you have an area
+
+ align:start position:0%
+example in fact this if you have an area
+ 
+
+ align:start position:0%
+example in fact this if you have an area
+of pin holes it's very similar to the
+
+ align:start position:0%
+of pin holes it's very similar to the
+ 
+
+ align:start position:0%
+of pin holes it's very similar to the
+cone beam typography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are two or three limitations that
+
+ align:start position:0%
+there are two or three limitations that
+ 
+
+ align:start position:0%
+there are two or three limitations that
+i've mentioned yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angular
+
+ align:start position:0%
+angular
+ 
+
+ align:start position:0%
+angular
+your step size
+
+ align:start position:0%
+your step size
+ 
+
+ align:start position:0%
+your step size
+you're losing a lot of data in terms of
+
+ align:start position:0%
+you're losing a lot of data in terms of
+ 
+
+ align:start position:0%
+you're losing a lot of data in terms of
+angle as well as resolution here you
+
+ align:start position:0%
+angle as well as resolution here you
+ 
+
+ align:start position:0%
+angle as well as resolution here you
+might take thousands of
+
+ align:start position:0%
+might take thousands of
+ 
+
+ align:start position:0%
+might take thousands of
+uh positions of the extra source to
+
+ align:start position:0%
+uh positions of the extra source to
+ 
+
+ align:start position:0%
+uh positions of the extra source to
+construct this volume but here you may
+
+ align:start position:0%
+construct this volume but here you may
+ 
+
+ align:start position:0%
+construct this volume but here you may
+have just a few tons of cameras and also
+
+ align:start position:0%
+have just a few tons of cameras and also
+ 
+
+ align:start position:0%
+have just a few tons of cameras and also
+here you may have a full 180 degree
+
+ align:start position:0%
+here you may have a full 180 degree
+ 
+
+ align:start position:0%
+here you may have a full 180 degree
+rotation of your source and detectors
+
+ align:start position:0%
+rotation of your source and detectors
+ 
+
+ align:start position:0%
+rotation of your source and detectors
+but here you are only within your
+
+ align:start position:0%
+but here you are only within your
+ 
+
+ align:start position:0%
+but here you are only within your
+limited almost by the field of view and
+
+ align:start position:0%
+limited almost by the field of view and
+ 
+
+ align:start position:0%
+limited almost by the field of view and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+arrangement of this camera which is
+
+ align:start position:0%
+arrangement of this camera which is
+ 
+
+ align:start position:0%
+arrangement of this camera which is
+so you might with respect to a given
+
+ align:start position:0%
+so you might with respect to a given
+ 
+
+ align:start position:0%
+so you might with respect to a given
+point you might only span
+
+ align:start position:0%
+point you might only span
+ 
+
+ align:start position:0%
+point you might only span
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+30 degrees or 40 degrees depending on
+
+ align:start position:0%
+30 degrees or 40 degrees depending on
+ 
+
+ align:start position:0%
+30 degrees or 40 degrees depending on
+the frequency
+
+ align:start position:0%
+the frequency
+ 
+
+ align:start position:0%
+the frequency
+and the distance
+
+ align:start position:0%
+and the distance
+ 
+
+ align:start position:0%
+and the distance
+so you could have a missing problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+those are of course just limitations in
+
+ align:start position:0%
+those are of course just limitations in
+ 
+
+ align:start position:0%
+those are of course just limitations in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+the type of reconstruction you can
+
+ align:start position:0%
+the type of reconstruction you can
+ 
+
+ align:start position:0%
+the type of reconstruction you can
+achieve from nitrates but
+
+ align:start position:0%
+achieve from nitrates but
+ 
+
+ align:start position:0%
+achieve from nitrates but
+again in terms of math in terms of how
+
+ align:start position:0%
+again in terms of math in terms of how
+ 
+
+ align:start position:0%
+again in terms of math in terms of how
+you set up the system yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so that's why you can construct a
+
+ align:start position:0%
+so that's why you can construct a
+ 
+
+ align:start position:0%
+so that's why you can construct a
+tomography machine
+
+ align:start position:0%
+tomography machine
+ 
+
+ align:start position:0%
+tomography machine
+using the light field idea which we
+
+ align:start position:0%
+using the light field idea which we
+ 
+
+ align:start position:0%
+using the light field idea which we
+saw as shield field and hopefully we can
+
+ align:start position:0%
+saw as shield field and hopefully we can
+ 
+
+ align:start position:0%
+saw as shield field and hopefully we can
+convert various complex concepts of
+
+ align:start position:0%
+convert various complex concepts of
+ 
+
+ align:start position:0%
+convert various complex concepts of
+tomography and deconvolution
+
+ align:start position:0%
+tomography and deconvolution
+ 
+
+ align:start position:0%
+tomography and deconvolution
+and confocal imaging and all that
+
+ align:start position:0%
+and confocal imaging and all that
+ 
+
+ align:start position:0%
+and confocal imaging and all that
+and achieve them with
+
+ align:start position:0%
+and achieve them with
+ 
+
+ align:start position:0%
+and achieve them with
+principles that we're unfamiliar with in
+
+ align:start position:0%
+principles that we're unfamiliar with in
+ 
+
+ align:start position:0%
+principles that we're unfamiliar with in
+the visible spectrum with optics or
+
+ align:start position:0%
+the visible spectrum with optics or
+ 
+
+ align:start position:0%
+the visible spectrum with optics or
+without optics
+
+ align:start position:0%
+without optics
+ 
+
+ align:start position:0%
+without optics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+make them available on possibly your
+
+ align:start position:0%
+make them available on possibly your
+ 
+
+ align:start position:0%
+make them available on possibly your
+surface cameras
\ No newline at end of file
diff --git a/xDKnMXtZKq8.txt b/xDKnMXtZKq8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a4f0ef3ddb49ebb5522f989825afb9f6441b93d
--- /dev/null
+++ b/xDKnMXtZKq8.txt
@@ -0,0 +1,12595 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we've talked a little bit
+
+ align:start position:0%
+all right so we've talked a little bit
+ 
+
+ align:start position:0%
+all right so we've talked a little bit
+about caching before but today we're
+
+ align:start position:0%
+about caching before but today we're
+ 
+
+ align:start position:0%
+about caching before but today we're
+going to talk in much more detail about
+
+ align:start position:0%
+going to talk in much more detail about
+ 
+
+ align:start position:0%
+going to talk in much more detail about
+caching and how to design cache
+
+ align:start position:0%
+caching and how to design cache
+ 
+
+ align:start position:0%
+caching and how to design cache
+efficient algorithms so first let's look
+
+ align:start position:0%
+efficient algorithms so first let's look
+ 
+
+ align:start position:0%
+efficient algorithms so first let's look
+at the caching Hardware on modern
+
+ align:start position:0%
+at the caching Hardware on modern
+ 
+
+ align:start position:0%
+at the caching Hardware on modern
+machines today so here's what the cache
+
+ align:start position:0%
+machines today so here's what the cache
+ 
+
+ align:start position:0%
+machines today so here's what the cache
+hierarchy looks like for a multi-core
+
+ align:start position:0%
+hierarchy looks like for a multi-core
+ 
+
+ align:start position:0%
+hierarchy looks like for a multi-core
+chip we have a whole bunch of processors
+
+ align:start position:0%
+chip we have a whole bunch of processors
+ 
+
+ align:start position:0%
+chip we have a whole bunch of processors
+they're all they all have their own
+
+ align:start position:0%
+they're all they all have their own
+ 
+
+ align:start position:0%
+they're all they all have their own
+private l1 caches for both the data as
+
+ align:start position:0%
+private l1 caches for both the data as
+ 
+
+ align:start position:0%
+private l1 caches for both the data as
+well as the instruction they also have a
+
+ align:start position:0%
+well as the instruction they also have a
+ 
+
+ align:start position:0%
+well as the instruction they also have a
+private l2 cache and then they share a
+
+ align:start position:0%
+private l2 cache and then they share a
+ 
+
+ align:start position:0%
+private l2 cache and then they share a
+last level cache or l3 cache which is
+
+ align:start position:0%
+last level cache or l3 cache which is
+ 
+
+ align:start position:0%
+last level cache or l3 cache which is
+also called LLC they're all connected to
+
+ align:start position:0%
+also called LLC they're all connected to
+ 
+
+ align:start position:0%
+also called LLC they're all connected to
+a memory controller that can access DRAM
+
+ align:start position:0%
+a memory controller that can access DRAM
+ 
+
+ align:start position:0%
+a memory controller that can access DRAM
+and then oftentimes you'll have multiple
+
+ align:start position:0%
+and then oftentimes you'll have multiple
+ 
+
+ align:start position:0%
+and then oftentimes you'll have multiple
+chips on the same same server and these
+
+ align:start position:0%
+chips on the same same server and these
+ 
+
+ align:start position:0%
+chips on the same same server and these
+chips would be connected through a
+
+ align:start position:0%
+chips would be connected through a
+ 
+
+ align:start position:0%
+chips would be connected through a
+network so here we have a bunch of
+
+ align:start position:0%
+network so here we have a bunch of
+ 
+
+ align:start position:0%
+network so here we have a bunch of
+multi-core chips that are connected
+
+ align:start position:0%
+multi-core chips that are connected
+ 
+
+ align:start position:0%
+multi-core chips that are connected
+together so we can see that there are
+
+ align:start position:0%
+together so we can see that there are
+ 
+
+ align:start position:0%
+together so we can see that there are
+different levels of memory here and the
+
+ align:start position:0%
+different levels of memory here and the
+ 
+
+ align:start position:0%
+different levels of memory here and the
+sizes of each one of these levels of
+
+ align:start position:0%
+sizes of each one of these levels of
+ 
+
+ align:start position:0%
+sizes of each one of these levels of
+memory is different so the sizes tend to
+
+ align:start position:0%
+memory is different so the sizes tend to
+ 
+
+ align:start position:0%
+memory is different so the sizes tend to
+go up as you move up the memory
+
+ align:start position:0%
+go up as you move up the memory
+ 
+
+ align:start position:0%
+go up as you move up the memory
+hierarchy the l1 caches tend to be about
+
+ align:start position:0%
+hierarchy the l1 caches tend to be about
+ 
+
+ align:start position:0%
+hierarchy the l1 caches tend to be about
+32 kilobytes in fact these are the
+
+ align:start position:0%
+32 kilobytes in fact these are the
+ 
+
+ align:start position:0%
+32 kilobytes in fact these are the
+specifications for the machines that
+
+ align:start position:0%
+specifications for the machines that
+ 
+
+ align:start position:0%
+specifications for the machines that
+you're using in this class so 32
+
+ align:start position:0%
+you're using in this class so 32
+ 
+
+ align:start position:0%
+you're using in this class so 32
+kilobytes for both the l1 data cache in
+
+ align:start position:0%
+kilobytes for both the l1 data cache in
+ 
+
+ align:start position:0%
+kilobytes for both the l1 data cache in
+the l1 instruction cache 256 kilobytes
+
+ align:start position:0%
+the l1 instruction cache 256 kilobytes
+ 
+
+ align:start position:0%
+the l1 instruction cache 256 kilobytes
+for the l2 cache so the l2 cache tends
+
+ align:start position:0%
+for the l2 cache so the l2 cache tends
+ 
+
+ align:start position:0%
+for the l2 cache so the l2 cache tends
+to be about 8 to 10 times larger than l1
+
+ align:start position:0%
+to be about 8 to 10 times larger than l1
+ 
+
+ align:start position:0%
+to be about 8 to 10 times larger than l1
+cache and then the last level cache the
+
+ align:start position:0%
+cache and then the last level cache the
+ 
+
+ align:start position:0%
+cache and then the last level cache the
+size is 30 megabytes so this is
+
+ align:start position:0%
+size is 30 megabytes so this is
+ 
+
+ align:start position:0%
+size is 30 megabytes so this is
+typically on the order of tens of
+
+ align:start position:0%
+typically on the order of tens of
+ 
+
+ align:start position:0%
+typically on the order of tens of
+megabytes and then DRAM is on the order
+
+ align:start position:0%
+megabytes and then DRAM is on the order
+ 
+
+ align:start position:0%
+megabytes and then DRAM is on the order
+of Giga bytes so
+
+ align:start position:0%
+of Giga bytes so
+ 
+
+ align:start position:0%
+of Giga bytes so
+we have 128 gigabyte DRAM and nowadays
+
+ align:start position:0%
+we have 128 gigabyte DRAM and nowadays
+ 
+
+ align:start position:0%
+we have 128 gigabyte DRAM and nowadays
+you can actually get machines that have
+
+ align:start position:0%
+you can actually get machines that have
+ 
+
+ align:start position:0%
+you can actually get machines that have
+terabytes of DRAM so the associativity
+
+ align:start position:0%
+terabytes of DRAM so the associativity
+ 
+
+ align:start position:0%
+terabytes of DRAM so the associativity
+tends to go up as you move up the cache
+
+ align:start position:0%
+tends to go up as you move up the cache
+ 
+
+ align:start position:0%
+tends to go up as you move up the cache
+are key and I'll talk more about social
+
+ align:start position:0%
+are key and I'll talk more about social
+ 
+
+ align:start position:0%
+are key and I'll talk more about social
+scientific on the next couple slides the
+
+ align:start position:0%
+scientific on the next couple slides the
+ 
+
+ align:start position:0%
+scientific on the next couple slides the
+time to access the memory also tends to
+
+ align:start position:0%
+time to access the memory also tends to
+ 
+
+ align:start position:0%
+time to access the memory also tends to
+go up so the latency tends to go up as
+
+ align:start position:0%
+go up so the latency tends to go up as
+ 
+
+ align:start position:0%
+go up so the latency tends to go up as
+you move up the memory hierarchies so
+
+ align:start position:0%
+you move up the memory hierarchies so
+ 
+
+ align:start position:0%
+you move up the memory hierarchies so
+the l1 caches are the quickest to access
+
+ align:start position:0%
+the l1 caches are the quickest to access
+ 
+
+ align:start position:0%
+the l1 caches are the quickest to access
+so about 2 nanoseconds you're just rough
+
+ align:start position:0%
+so about 2 nanoseconds you're just rough
+ 
+
+ align:start position:0%
+so about 2 nanoseconds you're just rough
+numbers the l2 cache is a little bit
+
+ align:start position:0%
+numbers the l2 cache is a little bit
+ 
+
+ align:start position:0%
+numbers the l2 cache is a little bit
+slower so say for nanoseconds last level
+
+ align:start position:0%
+slower so say for nanoseconds last level
+ 
+
+ align:start position:0%
+slower so say for nanoseconds last level
+cache maybe 6 nanoseconds and then when
+
+ align:start position:0%
+cache maybe 6 nanoseconds and then when
+ 
+
+ align:start position:0%
+cache maybe 6 nanoseconds and then when
+you have to go to DRAM it's about an
+
+ align:start position:0%
+you have to go to DRAM it's about an
+ 
+
+ align:start position:0%
+you have to go to DRAM it's about an
+order of magnitude slower so 50
+
+ align:start position:0%
+order of magnitude slower so 50
+ 
+
+ align:start position:0%
+order of magnitude slower so 50
+nanoseconds in this example and the
+
+ align:start position:0%
+nanoseconds in this example and the
+ 
+
+ align:start position:0%
+nanoseconds in this example and the
+reason why the memories are further down
+
+ align:start position:0%
+reason why the memories are further down
+ 
+
+ align:start position:0%
+reason why the memories are further down
+in the cache mark you're faster is
+
+ align:start position:0%
+in the cache mark you're faster is
+ 
+
+ align:start position:0%
+in the cache mark you're faster is
+because they're using more expensive
+
+ align:start position:0%
+because they're using more expensive
+ 
+
+ align:start position:0%
+because they're using more expensive
+materials to manufacture these things
+
+ align:start position:0%
+materials to manufacture these things
+ 
+
+ align:start position:0%
+materials to manufacture these things
+but since they tend to be more expensive
+
+ align:start position:0%
+but since they tend to be more expensive
+ 
+
+ align:start position:0%
+but since they tend to be more expensive
+we can't fit as much of that on the
+
+ align:start position:0%
+we can't fit as much of that on the
+ 
+
+ align:start position:0%
+we can't fit as much of that on the
+machines so that's why the faster
+
+ align:start position:0%
+machines so that's why the faster
+ 
+
+ align:start position:0%
+machines so that's why the faster
+memories are smaller than the slower
+
+ align:start position:0%
+memories are smaller than the slower
+ 
+
+ align:start position:0%
+memories are smaller than the slower
+memories but if we're able to take
+
+ align:start position:0%
+memories but if we're able to take
+ 
+
+ align:start position:0%
+memories but if we're able to take
+advantage of locality in our programs
+
+ align:start position:0%
+advantage of locality in our programs
+ 
+
+ align:start position:0%
+advantage of locality in our programs
+and we can make use of the fast memory
+
+ align:start position:0%
+and we can make use of the fast memory
+ 
+
+ align:start position:0%
+and we can make use of the fast memory
+as much as possible we'll talk about
+
+ align:start position:0%
+as much as possible we'll talk about
+ 
+
+ align:start position:0%
+as much as possible we'll talk about
+ways to do that in this lecture today
+
+ align:start position:0%
+ways to do that in this lecture today
+ 
+
+ align:start position:0%
+ways to do that in this lecture today
+there's also the latency across the
+
+ align:start position:0%
+there's also the latency across the
+ 
+
+ align:start position:0%
+there's also the latency across the
+network which tends to be cheaper than
+
+ align:start position:0%
+network which tends to be cheaper than
+ 
+
+ align:start position:0%
+network which tends to be cheaper than
+going to main memory but slower than
+
+ align:start position:0%
+going to main memory but slower than
+ 
+
+ align:start position:0%
+going to main memory but slower than
+doing a last level cache access and
+
+ align:start position:0%
+doing a last level cache access and
+ 
+
+ align:start position:0%
+doing a last level cache access and
+there's a lot of work in trying to get
+
+ align:start position:0%
+there's a lot of work in trying to get
+ 
+
+ align:start position:0%
+there's a lot of work in trying to get
+the cache coherence protocols right as
+
+ align:start position:0%
+the cache coherence protocols right as
+ 
+
+ align:start position:0%
+the cache coherence protocols right as
+we mentioned before so since these
+
+ align:start position:0%
+we mentioned before so since these
+ 
+
+ align:start position:0%
+we mentioned before so since these
+processors all have private caches we
+
+ align:start position:0%
+processors all have private caches we
+ 
+
+ align:start position:0%
+processors all have private caches we
+need to make sure that they all see a
+
+ align:start position:0%
+need to make sure that they all see a
+ 
+
+ align:start position:0%
+need to make sure that they all see a
+consistent view of memory when they're
+
+ align:start position:0%
+consistent view of memory when they're
+ 
+
+ align:start position:0%
+consistent view of memory when they're
+trying to access the same memory
+
+ align:start position:0%
+trying to access the same memory
+ 
+
+ align:start position:0%
+trying to access the same memory
+addresses in parallel so we talked about
+
+ align:start position:0%
+addresses in parallel so we talked about
+ 
+
+ align:start position:0%
+addresses in parallel so we talked about
+the MSI cache protocol before and there
+
+ align:start position:0%
+the MSI cache protocol before and there
+ 
+
+ align:start position:0%
+the MSI cache protocol before and there
+are many other protocols out there and
+
+ align:start position:0%
+are many other protocols out there and
+ 
+
+ align:start position:0%
+are many other protocols out there and
+you can read more about these things
+
+ align:start position:0%
+you can read more about these things
+ 
+
+ align:start position:0%
+you can read more about these things
+online but these are very hard to get
+
+ align:start position:0%
+online but these are very hard to get
+ 
+
+ align:start position:0%
+online but these are very hard to get
+right and there's a lot of verification
+
+ align:start position:0%
+right and there's a lot of verification
+ 
+
+ align:start position:0%
+right and there's a lot of verification
+involved in trying to prove that the
+
+ align:start position:0%
+involved in trying to prove that the
+ 
+
+ align:start position:0%
+involved in trying to prove that the
+cache coherence protocols are correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so any questions so far okay so let's
+
+ align:start position:0%
+so any questions so far okay so let's
+ 
+
+ align:start position:0%
+so any questions so far okay so let's
+talk about the associativity of a cache
+
+ align:start position:0%
+talk about the associativity of a cache
+ 
+
+ align:start position:0%
+talk about the associativity of a cache
+so here I'm showing you a fully
+
+ align:start position:0%
+so here I'm showing you a fully
+ 
+
+ align:start position:0%
+so here I'm showing you a fully
+associative cache and in a fully
+
+ align:start position:0%
+associative cache and in a fully
+ 
+
+ align:start position:0%
+associative cache and in a fully
+associative cache a cache block can
+
+ align:start position:0%
+associative cache a cache block can
+ 
+
+ align:start position:0%
+associative cache a cache block can
+reside anywhere in the cache and the
+
+ align:start position:0%
+reside anywhere in the cache and the
+ 
+
+ align:start position:0%
+reside anywhere in the cache and the
+basic unit of movement here is a cache
+
+ align:start position:0%
+basic unit of movement here is a cache
+ 
+
+ align:start position:0%
+basic unit of movement here is a cache
+block in this example the cache block
+
+ align:start position:0%
+block in this example the cache block
+ 
+
+ align:start position:0%
+block in this example the cache block
+size is 4 bytes but on the on the
+
+ align:start position:0%
+size is 4 bytes but on the on the
+ 
+
+ align:start position:0%
+size is 4 bytes but on the on the
+machines that we're using for this class
+
+ align:start position:0%
+machines that we're using for this class
+ 
+
+ align:start position:0%
+machines that we're using for this class
+the cache block size is 64 bytes but for
+
+ align:start position:0%
+the cache block size is 64 bytes but for
+ 
+
+ align:start position:0%
+the cache block size is 64 bytes but for
+this example I'm going to use a 4 byte
+
+ align:start position:0%
+this example I'm going to use a 4 byte
+ 
+
+ align:start position:0%
+this example I'm going to use a 4 byte
+cache line so each row here corresponds
+
+ align:start position:0%
+cache line so each row here corresponds
+ 
+
+ align:start position:0%
+cache line so each row here corresponds
+to one cache line in a fully associative
+
+ align:start position:0%
+to one cache line in a fully associative
+ 
+
+ align:start position:0%
+to one cache line in a fully associative
+cache means that each line here can go
+
+ align:start position:0%
+cache means that each line here can go
+ 
+
+ align:start position:0%
+cache means that each line here can go
+anywhere in the cache and then here
+
+ align:start position:0%
+anywhere in the cache and then here
+ 
+
+ align:start position:0%
+anywhere in the cache and then here
+we're also assuming a cache size that
+
+ align:start position:0%
+we're also assuming a cache size that
+ 
+
+ align:start position:0%
+we're also assuming a cache size that
+has 32 bytes so in total it can store a
+
+ align:start position:0%
+has 32 bytes so in total it can store a
+ 
+
+ align:start position:0%
+has 32 bytes so in total it can store a
+cache lines since the cache line is 4
+
+ align:start position:0%
+cache lines since the cache line is 4
+ 
+
+ align:start position:0%
+cache lines since the cache line is 4
+bytes so to find a block in a fully
+
+ align:start position:0%
+bytes so to find a block in a fully
+ 
+
+ align:start position:0%
+bytes so to find a block in a fully
+associative cache you have to actually
+
+ align:start position:0%
+associative cache you have to actually
+ 
+
+ align:start position:0%
+associative cache you have to actually
+search the entire cache because a cache
+
+ align:start position:0%
+search the entire cache because a cache
+ 
+
+ align:start position:0%
+search the entire cache because a cache
+line can appear anywhere in the cache
+
+ align:start position:0%
+line can appear anywhere in the cache
+ 
+
+ align:start position:0%
+line can appear anywhere in the cache
+and there's a tag associated with each
+
+ align:start position:0%
+and there's a tag associated with each
+ 
+
+ align:start position:0%
+and there's a tag associated with each
+of these cache lines here that that
+
+ align:start position:0%
+of these cache lines here that that
+ 
+
+ align:start position:0%
+of these cache lines here that that
+basically specify which of the memory
+
+ align:start position:0%
+basically specify which of the memory
+ 
+
+ align:start position:0%
+basically specify which of the memory
+addresses in virtual memory space it
+
+ align:start position:0%
+addresses in virtual memory space it
+ 
+
+ align:start position:0%
+addresses in virtual memory space it
+corresponds to so for the fully
+
+ align:start position:0%
+corresponds to so for the fully
+ 
+
+ align:start position:0%
+corresponds to so for the fully
+associative cache we're actually gonna
+
+ align:start position:0%
+associative cache we're actually gonna
+ 
+
+ align:start position:0%
+associative cache we're actually gonna
+use most of the bits of the address as a
+
+ align:start position:0%
+use most of the bits of the address as a
+ 
+
+ align:start position:0%
+use most of the bits of the address as a
+tag we don't actually need the two lower
+
+ align:start position:0%
+tag we don't actually need the two lower
+ 
+
+ align:start position:0%
+tag we don't actually need the two lower
+order bits because the things are being
+
+ align:start position:0%
+order bits because the things are being
+ 
+
+ align:start position:0%
+order bits because the things are being
+moved that degree and the granularity of
+
+ align:start position:0%
+moved that degree and the granularity of
+ 
+
+ align:start position:0%
+moved that degree and the granularity of
+cache lines which are 4 bytes so the two
+
+ align:start position:0%
+cache lines which are 4 bytes so the two
+ 
+
+ align:start position:0%
+cache lines which are 4 bytes so the two
+lower order bits are always going to be
+
+ align:start position:0%
+lower order bits are always going to be
+ 
+
+ align:start position:0%
+lower order bits are always going to be
+the same but we're just gonna use the
+
+ align:start position:0%
+the same but we're just gonna use the
+ 
+
+ align:start position:0%
+the same but we're just gonna use the
+rest of the bits to store the tag so if
+
+ align:start position:0%
+rest of the bits to store the tag so if
+ 
+
+ align:start position:0%
+rest of the bits to store the tag so if
+our address space is 64 bits then we're
+
+ align:start position:0%
+our address space is 64 bits then we're
+ 
+
+ align:start position:0%
+our address space is 64 bits then we're
+gonna use 62 bits to store the tag in a
+
+ align:start position:0%
+gonna use 62 bits to store the tag in a
+ 
+
+ align:start position:0%
+gonna use 62 bits to store the tag in a
+fully associative cache in scheme and
+
+ align:start position:0%
+fully associative cache in scheme and
+ 
+
+ align:start position:0%
+fully associative cache in scheme and
+when a cache becomes full a block that
+
+ align:start position:0%
+when a cache becomes full a block that
+ 
+
+ align:start position:0%
+when a cache becomes full a block that
+has to be victim a chrome for a new
+
+ align:start position:0%
+has to be victim a chrome for a new
+ 
+
+ align:start position:0%
+has to be victim a chrome for a new
+block and there are various ways that
+
+ align:start position:0%
+block and there are various ways that
+ 
+
+ align:start position:0%
+block and there are various ways that
+you can decide how to evict a block so
+
+ align:start position:0%
+you can decide how to evict a block so
+ 
+
+ align:start position:0%
+you can decide how to evict a block so
+this is known as the replacement policy
+
+ align:start position:0%
+this is known as the replacement policy
+ 
+
+ align:start position:0%
+this is known as the replacement policy
+one common replacement policy is LRU or
+
+ align:start position:0%
+one common replacement policy is LRU or
+ 
+
+ align:start position:0%
+one common replacement policy is LRU or
+least recently used
+
+ align:start position:0%
+least recently used
+ 
+
+ align:start position:0%
+least recently used
+so you basically kick the thing out that
+
+ align:start position:0%
+so you basically kick the thing out that
+ 
+
+ align:start position:0%
+so you basically kick the thing out that
+has been used the farthest in the past
+
+ align:start position:0%
+has been used the farthest in the past
+ 
+
+ align:start position:0%
+has been used the farthest in the past
+dollar schemes such as second chance and
+
+ align:start position:0%
+dollar schemes such as second chance and
+ 
+
+ align:start position:0%
+dollar schemes such as second chance and
+clock replacement we're not going to
+
+ align:start position:0%
+clock replacement we're not going to
+ 
+
+ align:start position:0%
+clock replacement we're not going to
+talk too much about the different
+
+ align:start position:0%
+talk too much about the different
+ 
+
+ align:start position:0%
+talk too much about the different
+replacement schemes today but you can
+
+ align:start position:0%
+replacement schemes today but you can
+ 
+
+ align:start position:0%
+replacement schemes today but you can
+feel free to read about these things
+
+ align:start position:0%
+feel free to read about these things
+ 
+
+ align:start position:0%
+feel free to read about these things
+online so what's a disadvantage of this
+
+ align:start position:0%
+online so what's a disadvantage of this
+ 
+
+ align:start position:0%
+online so what's a disadvantage of this
+scheme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah why is it slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so the disadvantage is that
+
+ align:start position:0%
+yeah so so the disadvantage is that
+ 
+
+ align:start position:0%
+yeah so so the disadvantage is that
+searching for a cache line in the cache
+
+ align:start position:0%
+searching for a cache line in the cache
+ 
+
+ align:start position:0%
+searching for a cache line in the cache
+can be pretty slow because you have to
+
+ align:start position:0%
+can be pretty slow because you have to
+ 
+
+ align:start position:0%
+can be pretty slow because you have to
+search the entire cache in the worst
+
+ align:start position:0%
+search the entire cache in the worst
+ 
+
+ align:start position:0%
+search the entire cache in the worst
+case since a cache block can reside
+
+ align:start position:0%
+case since a cache block can reside
+ 
+
+ align:start position:0%
+case since a cache block can reside
+anywhere in the cache so even though the
+
+ align:start position:0%
+anywhere in the cache so even though the
+ 
+
+ align:start position:0%
+anywhere in the cache so even though the
+search can go on in parallel and
+
+ align:start position:0%
+search can go on in parallel and
+ 
+
+ align:start position:0%
+search can go on in parallel and
+hardware still expensive in terms of
+
+ align:start position:0%
+hardware still expensive in terms of
+ 
+
+ align:start position:0%
+hardware still expensive in terms of
+power and performance to have to search
+
+ align:start position:0%
+power and performance to have to search
+ 
+
+ align:start position:0%
+power and performance to have to search
+most of the cache every time so let's
+
+ align:start position:0%
+most of the cache every time so let's
+ 
+
+ align:start position:0%
+most of the cache every time so let's
+look at another extreme this is a direct
+
+ align:start position:0%
+look at another extreme this is a direct
+ 
+
+ align:start position:0%
+look at another extreme this is a direct
+mapped cache so in a direct mapped cache
+
+ align:start position:0%
+mapped cache so in a direct mapped cache
+ 
+
+ align:start position:0%
+mapped cache so in a direct mapped cache
+each cache block can only go in one
+
+ align:start position:0%
+each cache block can only go in one
+ 
+
+ align:start position:0%
+each cache block can only go in one
+place in the cache so I've color-coded
+
+ align:start position:0%
+place in the cache so I've color-coded
+ 
+
+ align:start position:0%
+place in the cache so I've color-coded
+these cache blocks here so the red
+
+ align:start position:0%
+these cache blocks here so the red
+ 
+
+ align:start position:0%
+these cache blocks here so the red
+blocks can only go in the first row of
+
+ align:start position:0%
+blocks can only go in the first row of
+ 
+
+ align:start position:0%
+blocks can only go in the first row of
+this cache the orange ones can only go
+
+ align:start position:0%
+this cache the orange ones can only go
+ 
+
+ align:start position:0%
+this cache the orange ones can only go
+in the second row and so on and the
+
+ align:start position:0%
+in the second row and so on and the
+ 
+
+ align:start position:0%
+in the second row and so on and the
+position which cache block can go into
+
+ align:start position:0%
+position which cache block can go into
+ 
+
+ align:start position:0%
+position which cache block can go into
+is known as that cache blocks set so the
+
+ align:start position:0%
+is known as that cache blocks set so the
+ 
+
+ align:start position:0%
+is known as that cache blocks set so the
+set determines the location in the cache
+
+ align:start position:0%
+set determines the location in the cache
+ 
+
+ align:start position:0%
+set determines the location in the cache
+for each particular block so let's look
+
+ align:start position:0%
+for each particular block so let's look
+ 
+
+ align:start position:0%
+for each particular block so let's look
+at how the virtual memory address is
+
+ align:start position:0%
+at how the virtual memory address is
+ 
+
+ align:start position:0%
+at how the virtual memory address is
+divided up into and which of the bits
+
+ align:start position:0%
+divided up into and which of the bits
+ 
+
+ align:start position:0%
+divided up into and which of the bits
+we're gonna use to figure out where a
+
+ align:start position:0%
+we're gonna use to figure out where a
+ 
+
+ align:start position:0%
+we're gonna use to figure out where a
+cache block should go in the cache so we
+
+ align:start position:0%
+cache block should go in the cache so we
+ 
+
+ align:start position:0%
+cache block should go in the cache so we
+have the offset we have the set and then
+
+ align:start position:0%
+have the offset we have the set and then
+ 
+
+ align:start position:0%
+have the offset we have the set and then
+the tag fields the offset just tells us
+
+ align:start position:0%
+the tag fields the offset just tells us
+ 
+
+ align:start position:0%
+the tag fields the offset just tells us
+which position we want to access within
+
+ align:start position:0%
+which position we want to access within
+ 
+
+ align:start position:0%
+which position we want to access within
+a cache block so since a cache block has
+
+ align:start position:0%
+a cache block so since a cache block has
+ 
+
+ align:start position:0%
+a cache block so since a cache block has
+B bytes we only need log base two of B
+
+ align:start position:0%
+B bytes we only need log base two of B
+ 
+
+ align:start position:0%
+B bytes we only need log base two of B
+bits that's offset and the reason why we
+
+ align:start position:0%
+bits that's offset and the reason why we
+ 
+
+ align:start position:0%
+bits that's offset and the reason why we
+have to also is because we're not always
+
+ align:start position:0%
+have to also is because we're not always
+ 
+
+ align:start position:0%
+have to also is because we're not always
+accessing something at the beginning of
+
+ align:start position:0%
+accessing something at the beginning of
+ 
+
+ align:start position:0%
+accessing something at the beginning of
+a cache block we might want to access
+
+ align:start position:0%
+a cache block we might want to access
+ 
+
+ align:start position:0%
+a cache block we might want to access
+something in the middle and that's why
+
+ align:start position:0%
+something in the middle and that's why
+ 
+
+ align:start position:0%
+something in the middle and that's why
+we need to offset to specify where in
+
+ align:start position:0%
+we need to offset to specify where in
+ 
+
+ align:start position:0%
+we need to offset to specify where in
+the cache block we want to access then
+
+ align:start position:0%
+the cache block we want to access then
+ 
+
+ align:start position:0%
+the cache block we want to access then
+there's a set field and the set field is
+
+ align:start position:0%
+there's a set field and the set field is
+ 
+
+ align:start position:0%
+there's a set field and the set field is
+going to determine which position in the
+
+ align:start position:0%
+going to determine which position in the
+ 
+
+ align:start position:0%
+going to determine which position in the
+cache that cache block can go into so
+
+ align:start position:0%
+cache that cache block can go into so
+ 
+
+ align:start position:0%
+cache that cache block can go into so
+there are eight possible positions for
+
+ align:start position:0%
+there are eight possible positions for
+ 
+
+ align:start position:0%
+there are eight possible positions for
+each cache block here and therefore we
+
+ align:start position:0%
+each cache block here and therefore we
+ 
+
+ align:start position:0%
+each cache block here and therefore we
+only need log base two of eight bits so
+
+ align:start position:0%
+only need log base two of eight bits so
+ 
+
+ align:start position:0%
+only need log base two of eight bits so
+three bits for the set in this example
+
+ align:start position:0%
+three bits for the set in this example
+ 
+
+ align:start position:0%
+three bits for the set in this example
+and more generally it's going to be log
+
+ align:start position:0%
+and more generally it's going to be log
+ 
+
+ align:start position:0%
+and more generally it's going to be log
+base 2 of M over B and here M over B is
+
+ align:start position:0%
+base 2 of M over B and here M over B is
+ 
+
+ align:start position:0%
+base 2 of M over B and here M over B is
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+and then finally we're gonna use the
+
+ align:start position:0%
+and then finally we're gonna use the
+ 
+
+ align:start position:0%
+and then finally we're gonna use the
+remaining bits as a tag so W minus log
+
+ align:start position:0%
+remaining bits as a tag so W minus log
+ 
+
+ align:start position:0%
+remaining bits as a tag so W minus log
+base 2 of M bits for the tag and that
+
+ align:start position:0%
+base 2 of M bits for the tag and that
+ 
+
+ align:start position:0%
+base 2 of M bits for the tag and that
+gets stored along with the cache block
+
+ align:start position:0%
+gets stored along with the cache block
+ 
+
+ align:start position:0%
+gets stored along with the cache block
+in the cache and that's going to
+
+ align:start position:0%
+in the cache and that's going to
+ 
+
+ align:start position:0%
+in the cache and that's going to
+uniquely identify which of the which of
+
+ align:start position:0%
+uniquely identify which of the which of
+ 
+
+ align:start position:0%
+uniquely identify which of the which of
+the memory blocks the the cache block
+
+ align:start position:0%
+the memory blocks the the cache block
+ 
+
+ align:start position:0%
+the memory blocks the the cache block
+corresponds to in virtual memory and you
+
+ align:start position:0%
+corresponds to in virtual memory and you
+ 
+
+ align:start position:0%
+corresponds to in virtual memory and you
+can verify that the sum of all of these
+
+ align:start position:0%
+can verify that the sum of all of these
+ 
+
+ align:start position:0%
+can verify that the sum of all of these
+quantities here sums to W bits so in
+
+ align:start position:0%
+quantities here sums to W bits so in
+ 
+
+ align:start position:0%
+quantities here sums to W bits so in
+total we have a W bit address space and
+
+ align:start position:0%
+total we have a W bit address space and
+ 
+
+ align:start position:0%
+total we have a W bit address space and
+the sum of those three things is W so
+
+ align:start position:0%
+the sum of those three things is W so
+ 
+
+ align:start position:0%
+the sum of those three things is W so
+what's the advantage and disadvantage of
+
+ align:start position:0%
+what's the advantage and disadvantage of
+ 
+
+ align:start position:0%
+what's the advantage and disadvantage of
+this scheme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first what's the what's a good thing
+
+ align:start position:0%
+so first what's the what's a good thing
+ 
+
+ align:start position:0%
+so first what's the what's a good thing
+about this scheme compared to the
+
+ align:start position:0%
+about this scheme compared to the
+ 
+
+ align:start position:0%
+about this scheme compared to the
+previous scheme that we saw yes yes fast
+
+ align:start position:0%
+previous scheme that we saw yes yes fast
+ 
+
+ align:start position:0%
+previous scheme that we saw yes yes fast
+because you only have to check one place
+
+ align:start position:0%
+because you only have to check one place
+ 
+
+ align:start position:0%
+because you only have to check one place
+because each cache block can only go in
+
+ align:start position:0%
+because each cache block can only go in
+ 
+
+ align:start position:0%
+because each cache block can only go in
+one place in the cache and that's the
+
+ align:start position:0%
+one place in the cache and that's the
+ 
+
+ align:start position:0%
+one place in the cache and that's the
+only place you have to check when you
+
+ align:start position:0%
+only place you have to check when you
+ 
+
+ align:start position:0%
+only place you have to check when you
+try to do a lookup if the cache block is
+
+ align:start position:0%
+try to do a lookup if the cache block is
+ 
+
+ align:start position:0%
+try to do a lookup if the cache block is
+there then you find it if it's not then
+
+ align:start position:0%
+there then you find it if it's not then
+ 
+
+ align:start position:0%
+there then you find it if it's not then
+you know it's not in the cache what's
+
+ align:start position:0%
+you know it's not in the cache what's
+ 
+
+ align:start position:0%
+you know it's not in the cache what's
+the downside to this scheme yeah yeah so
+
+ align:start position:0%
+the downside to this scheme yeah yeah so
+ 
+
+ align:start position:0%
+the downside to this scheme yeah yeah so
+it's a good answer so the downside is
+
+ align:start position:0%
+it's a good answer so the downside is
+ 
+
+ align:start position:0%
+it's a good answer so the downside is
+that you might for example or just be
+
+ align:start position:0%
+that you might for example or just be
+ 
+
+ align:start position:0%
+that you might for example or just be
+accessing the rad cache blocks and then
+
+ align:start position:0%
+accessing the rad cache blocks and then
+ 
+
+ align:start position:0%
+accessing the rad cache blocks and then
+not accessing any of the other cache
+
+ align:start position:0%
+not accessing any of the other cache
+ 
+
+ align:start position:0%
+not accessing any of the other cache
+blocks they'll all get mapped to the
+
+ align:start position:0%
+blocks they'll all get mapped to the
+ 
+
+ align:start position:0%
+blocks they'll all get mapped to the
+same location in the cache and then
+
+ align:start position:0%
+same location in the cache and then
+ 
+
+ align:start position:0%
+same location in the cache and then
+they'll keep keep evicting each other
+
+ align:start position:0%
+they'll keep keep evicting each other
+ 
+
+ align:start position:0%
+they'll keep keep evicting each other
+even though there's a lot of empty space
+
+ align:start position:0%
+even though there's a lot of empty space
+ 
+
+ align:start position:0%
+even though there's a lot of empty space
+in the cache and this is known as a
+
+ align:start position:0%
+in the cache and this is known as a
+ 
+
+ align:start position:0%
+in the cache and this is known as a
+conflict miss and these can be very bad
+
+ align:start position:0%
+conflict miss and these can be very bad
+ 
+
+ align:start position:0%
+conflict miss and these can be very bad
+for performance and very hard to debug
+
+ align:start position:0%
+for performance and very hard to debug
+ 
+
+ align:start position:0%
+for performance and very hard to debug
+so that's one downside of a direct
+
+ align:start position:0%
+so that's one downside of a direct
+ 
+
+ align:start position:0%
+so that's one downside of a direct
+mapped cache is that you can get these
+
+ align:start position:0%
+mapped cache is that you can get these
+ 
+
+ align:start position:0%
+mapped cache is that you can get these
+conflict misses where you have to evict
+
+ align:start position:0%
+conflict misses where you have to evict
+ 
+
+ align:start position:0%
+conflict misses where you have to evict
+things from the cache even though
+
+ align:start position:0%
+things from the cache even though
+ 
+
+ align:start position:0%
+things from the cache even though
+there's empty space in the cache so as
+
+ align:start position:0%
+there's empty space in the cache so as
+ 
+
+ align:start position:0%
+there's empty space in the cache so as
+we said finding a block is very fast
+
+ align:start position:0%
+we said finding a block is very fast
+ 
+
+ align:start position:0%
+we said finding a block is very fast
+only a single location in the cache has
+
+ align:start position:0%
+only a single location in the cache has
+ 
+
+ align:start position:0%
+only a single location in the cache has
+to be searched but you might suffer from
+
+ align:start position:0%
+to be searched but you might suffer from
+ 
+
+ align:start position:0%
+to be searched but you might suffer from
+conflict misses if you keep accessing
+
+ align:start position:0%
+conflict misses if you keep accessing
+ 
+
+ align:start position:0%
+conflict misses if you keep accessing
+things in the same set repeatedly
+
+ align:start position:0%
+things in the same set repeatedly
+ 
+
+ align:start position:0%
+things in the same set repeatedly
+without accessing the things and the
+
+ align:start position:0%
+without accessing the things and the
+ 
+
+ align:start position:0%
+without accessing the things and the
+other sets so any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are sort of the two
+
+ align:start position:0%
+okay so these are sort of the two
+ 
+
+ align:start position:0%
+okay so these are sort of the two
+extremes for cash design there's
+
+ align:start position:0%
+extremes for cash design there's
+ 
+
+ align:start position:0%
+extremes for cash design there's
+actually a hybrid solution called set
+
+ align:start position:0%
+actually a hybrid solution called set
+ 
+
+ align:start position:0%
+actually a hybrid solution called set
+associative cache and in a set
+
+ align:start position:0%
+associative cache and in a set
+ 
+
+ align:start position:0%
+associative cache and in a set
+associative cache you still have sets
+
+ align:start position:0%
+associative cache you still have sets
+ 
+
+ align:start position:0%
+associative cache you still have sets
+but each of the sets contains more than
+
+ align:start position:0%
+but each of the sets contains more than
+ 
+
+ align:start position:0%
+but each of the sets contains more than
+one line now so all the red blocks still
+
+ align:start position:0%
+one line now so all the red blocks still
+ 
+
+ align:start position:0%
+one line now so all the red blocks still
+map to the red set but there's actually
+
+ align:start position:0%
+map to the red set but there's actually
+ 
+
+ align:start position:0%
+map to the red set but there's actually
+two possible locations for the red
+
+ align:start position:0%
+two possible locations for the red
+ 
+
+ align:start position:0%
+two possible locations for the red
+blocks now so in this case this is known
+
+ align:start position:0%
+blocks now so in this case this is known
+ 
+
+ align:start position:0%
+blocks now so in this case this is known
+as a 2-way associative cache since there
+
+ align:start position:0%
+as a 2-way associative cache since there
+ 
+
+ align:start position:0%
+as a 2-way associative cache since there
+are two possible locations inside each
+
+ align:start position:0%
+are two possible locations inside each
+ 
+
+ align:start position:0%
+are two possible locations inside each
+set and again a cache blocks set
+
+ align:start position:0%
+set and again a cache blocks set
+ 
+
+ align:start position:0%
+set and again a cache blocks set
+determines K possible cache locations
+
+ align:start position:0%
+determines K possible cache locations
+ 
+
+ align:start position:0%
+determines K possible cache locations
+for that block so within a set it's
+
+ align:start position:0%
+for that block so within a set it's
+ 
+
+ align:start position:0%
+for that block so within a set it's
+fully associative but each block can
+
+ align:start position:0%
+fully associative but each block can
+ 
+
+ align:start position:0%
+fully associative but each block can
+only go in one of the sets so let's look
+
+ align:start position:0%
+only go in one of the sets so let's look
+ 
+
+ align:start position:0%
+only go in one of the sets so let's look
+again at how the bits are divided into
+
+ align:start position:0%
+again at how the bits are divided into
+ 
+
+ align:start position:0%
+again at how the bits are divided into
+in the address so we still have the tag
+
+ align:start position:0%
+in the address so we still have the tag
+ 
+
+ align:start position:0%
+in the address so we still have the tag
+set and offset fields the offset field
+
+ align:start position:0%
+set and offset fields the offset field
+ 
+
+ align:start position:0%
+set and offset fields the offset field
+is still log base 2 of B the set field
+
+ align:start position:0%
+is still log base 2 of B the set field
+ 
+
+ align:start position:0%
+is still log base 2 of B the set field
+is going to take log base 2 of M over KB
+
+ align:start position:0%
+is going to take log base 2 of M over KB
+ 
+
+ align:start position:0%
+is going to take log base 2 of M over KB
+bits so the number of sets we have is M
+
+ align:start position:0%
+bits so the number of sets we have is M
+ 
+
+ align:start position:0%
+bits so the number of sets we have is M
+over KB so we need log base 2 of that
+
+ align:start position:0%
+over KB so we need log base 2 of that
+ 
+
+ align:start position:0%
+over KB so we need log base 2 of that
+that number to represent the set of a
+
+ align:start position:0%
+that number to represent the set of a
+ 
+
+ align:start position:0%
+that number to represent the set of a
+block and then finally we use the
+
+ align:start position:0%
+block and then finally we use the
+ 
+
+ align:start position:0%
+block and then finally we use the
+remaining bits as a tag so it's going to
+
+ align:start position:0%
+remaining bits as a tag so it's going to
+ 
+
+ align:start position:0%
+remaining bits as a tag so it's going to
+be W minus log base 2 of M over K and
+
+ align:start position:0%
+be W minus log base 2 of M over K and
+ 
+
+ align:start position:0%
+be W minus log base 2 of M over K and
+now to find a block in the cache only K
+
+ align:start position:0%
+now to find a block in the cache only K
+ 
+
+ align:start position:0%
+now to find a block in the cache only K
+locations of the of its set must be
+
+ align:start position:0%
+locations of the of its set must be
+ 
+
+ align:start position:0%
+locations of the of its set must be
+searched
+
+ align:start position:0%
+searched
+ 
+
+ align:start position:0%
+searched
+so you basically find which set the
+
+ align:start position:0%
+so you basically find which set the
+ 
+
+ align:start position:0%
+so you basically find which set the
+cache block maps to and then you check
+
+ align:start position:0%
+cache block maps to and then you check
+ 
+
+ align:start position:0%
+cache block maps to and then you check
+all K locations within that set to see
+
+ align:start position:0%
+all K locations within that set to see
+ 
+
+ align:start position:0%
+all K locations within that set to see
+if that cache block is there and
+
+ align:start position:0%
+if that cache block is there and
+ 
+
+ align:start position:0%
+if that cache block is there and
+whenever you want to whenever you try to
+
+ align:start position:0%
+whenever you want to whenever you try to
+ 
+
+ align:start position:0%
+whenever you want to whenever you try to
+put something in the cache because it's
+
+ align:start position:0%
+put something in the cache because it's
+ 
+
+ align:start position:0%
+put something in the cache because it's
+not there you have to evict something
+
+ align:start position:0%
+not there you have to evict something
+ 
+
+ align:start position:0%
+not there you have to evict something
+and you've X something from the same set
+
+ align:start position:0%
+and you've X something from the same set
+ 
+
+ align:start position:0%
+and you've X something from the same set
+as the block that you're placing into
+
+ align:start position:0%
+as the block that you're placing into
+ 
+
+ align:start position:0%
+as the block that you're placing into
+the cache so for this example I showed a
+
+ align:start position:0%
+the cache so for this example I showed a
+ 
+
+ align:start position:0%
+the cache so for this example I showed a
+2-way associative cache but in practice
+
+ align:start position:0%
+2-way associative cache but in practice
+ 
+
+ align:start position:0%
+2-way associative cache but in practice
+the associativity is usually bigger say
+
+ align:start position:0%
+the associativity is usually bigger say
+ 
+
+ align:start position:0%
+the associativity is usually bigger say
+8 Way 16 way or sometimes 20 way and and
+
+ align:start position:0%
+8 Way 16 way or sometimes 20 way and and
+ 
+
+ align:start position:0%
+8 Way 16 way or sometimes 20 way and and
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+you keep increasing the associativity it
+
+ align:start position:0%
+you keep increasing the associativity it
+ 
+
+ align:start position:0%
+you keep increasing the associativity it
+looks it's gonna look more and more like
+
+ align:start position:0%
+looks it's gonna look more and more like
+ 
+
+ align:start position:0%
+looks it's gonna look more and more like
+a fully associative cache and if you
+
+ align:start position:0%
+a fully associative cache and if you
+ 
+
+ align:start position:0%
+a fully associative cache and if you
+have a one-way associative cache then
+
+ align:start position:0%
+have a one-way associative cache then
+ 
+
+ align:start position:0%
+have a one-way associative cache then
+it's just a direct mapped cache so this
+
+ align:start position:0%
+it's just a direct mapped cache so this
+ 
+
+ align:start position:0%
+it's just a direct mapped cache so this
+is a sort of a hybrid in-between a fully
+
+ align:start position:0%
+is a sort of a hybrid in-between a fully
+ 
+
+ align:start position:0%
+is a sort of a hybrid in-between a fully
+mapped cache and a fully associative
+
+ align:start position:0%
+mapped cache and a fully associative
+ 
+
+ align:start position:0%
+mapped cache and a fully associative
+cache in a direct mapped cache so any
+
+ align:start position:0%
+cache in a direct mapped cache so any
+ 
+
+ align:start position:0%
+cache in a direct mapped cache so any
+questions on set associative caches okay
+
+ align:start position:0%
+questions on set associative caches okay
+ 
+
+ align:start position:0%
+questions on set associative caches okay
+so let's go over a taxonomy of different
+
+ align:start position:0%
+so let's go over a taxonomy of different
+ 
+
+ align:start position:0%
+so let's go over a taxonomy of different
+types of cache misses that you can incur
+
+ align:start position:0%
+types of cache misses that you can incur
+ 
+
+ align:start position:0%
+types of cache misses that you can incur
+so the first type of cache miss is
+
+ align:start position:0%
+so the first type of cache miss is
+ 
+
+ align:start position:0%
+so the first type of cache miss is
+called a cold miss and this is a cache
+
+ align:start position:0%
+called a cold miss and this is a cache
+ 
+
+ align:start position:0%
+called a cold miss and this is a cache
+miss that you have to incur the first
+
+ align:start position:0%
+miss that you have to incur the first
+ 
+
+ align:start position:0%
+miss that you have to incur the first
+time you access a cache block and if you
+
+ align:start position:0%
+time you access a cache block and if you
+ 
+
+ align:start position:0%
+time you access a cache block and if you
+need to access this piece of data
+
+ align:start position:0%
+need to access this piece of data
+ 
+
+ align:start position:0%
+need to access this piece of data
+there's no way to get around getting a
+
+ align:start position:0%
+there's no way to get around getting a
+ 
+
+ align:start position:0%
+there's no way to get around getting a
+cold miss for this because your as cache
+
+ align:start position:0%
+cold miss for this because your as cache
+ 
+
+ align:start position:0%
+cold miss for this because your as cache
+starts out not having this block and the
+
+ align:start position:0%
+starts out not having this block and the
+ 
+
+ align:start position:0%
+starts out not having this block and the
+first time you access it you have to
+
+ align:start position:0%
+first time you access it you have to
+ 
+
+ align:start position:0%
+first time you access it you have to
+bring it into cache
+
+ align:start position:0%
+bring it into cache
+ 
+
+ align:start position:0%
+bring it into cache
+then there are capacity misses so
+
+ align:start position:0%
+then there are capacity misses so
+ 
+
+ align:start position:0%
+then there are capacity misses so
+capacity misses our cache misses you get
+
+ align:start position:0%
+capacity misses our cache misses you get
+ 
+
+ align:start position:0%
+capacity misses our cache misses you get
+because the cache is full and it can't
+
+ align:start position:0%
+because the cache is full and it can't
+ 
+
+ align:start position:0%
+because the cache is full and it can't
+fit all of the cache blocks that you
+
+ align:start position:0%
+fit all of the cache blocks that you
+ 
+
+ align:start position:0%
+fit all of the cache blocks that you
+want to access so you get a capacity
+
+ align:start position:0%
+want to access so you get a capacity
+ 
+
+ align:start position:0%
+want to access so you get a capacity
+miss when the previous cache copy would
+
+ align:start position:0%
+miss when the previous cache copy would
+ 
+
+ align:start position:0%
+miss when the previous cache copy would
+have been you victim 'van with a fully
+
+ align:start position:0%
+have been you victim 'van with a fully
+ 
+
+ align:start position:0%
+have been you victim 'van with a fully
+associative scheme so even if all of the
+
+ align:start position:0%
+associative scheme so even if all of the
+ 
+
+ align:start position:0%
+associative scheme so even if all of the
+possible locations in your cache could
+
+ align:start position:0%
+possible locations in your cache could
+ 
+
+ align:start position:0%
+possible locations in your cache could
+be used for a particular cache line that
+
+ align:start position:0%
+be used for a particular cache line that
+ 
+
+ align:start position:0%
+be used for a particular cache line that
+cache line still has to be evicted
+
+ align:start position:0%
+cache line still has to be evicted
+ 
+
+ align:start position:0%
+cache line still has to be evicted
+because there's not enough space so
+
+ align:start position:0%
+because there's not enough space so
+ 
+
+ align:start position:0%
+because there's not enough space so
+that's what's called a capacity miss and
+
+ align:start position:0%
+that's what's called a capacity miss and
+ 
+
+ align:start position:0%
+that's what's called a capacity miss and
+you can deal with capacity misses by
+
+ align:start position:0%
+you can deal with capacity misses by
+ 
+
+ align:start position:0%
+you can deal with capacity misses by
+introducing more locality into your code
+
+ align:start position:0%
+introducing more locality into your code
+ 
+
+ align:start position:0%
+introducing more locality into your code
+both spatial in temporal locality and
+
+ align:start position:0%
+both spatial in temporal locality and
+ 
+
+ align:start position:0%
+both spatial in temporal locality and
+we'll look at ways to reduce the
+
+ align:start position:0%
+we'll look at ways to reduce the
+ 
+
+ align:start position:0%
+we'll look at ways to reduce the
+capacity misses of algorithms later on
+
+ align:start position:0%
+capacity misses of algorithms later on
+ 
+
+ align:start position:0%
+capacity misses of algorithms later on
+in this lecture then Darr conflict
+
+ align:start position:0%
+in this lecture then Darr conflict
+ 
+
+ align:start position:0%
+in this lecture then Darr conflict
+misses and conflict misses happen in a
+
+ align:start position:0%
+misses and conflict misses happen in a
+ 
+
+ align:start position:0%
+misses and conflict misses happen in a
+set associative caches when you have too
+
+ align:start position:0%
+set associative caches when you have too
+ 
+
+ align:start position:0%
+set associative caches when you have too
+many blocks from the same set mapping to
+
+ align:start position:0%
+many blocks from the same set mapping to
+ 
+
+ align:start position:0%
+many blocks from the same set mapping to
+the wanting to go into the cache and
+
+ align:start position:0%
+the wanting to go into the cache and
+ 
+
+ align:start position:0%
+the wanting to go into the cache and
+some of these have to be evicted because
+
+ align:start position:0%
+some of these have to be evicted because
+ 
+
+ align:start position:0%
+some of these have to be evicted because
+the sack can't fit all of the blocks and
+
+ align:start position:0%
+the sack can't fit all of the blocks and
+ 
+
+ align:start position:0%
+the sack can't fit all of the blocks and
+these blocks wouldn't have been you
+
+ align:start position:0%
+these blocks wouldn't have been you
+ 
+
+ align:start position:0%
+these blocks wouldn't have been you
+Victor do had a fully associative
+
+ align:start position:0%
+Victor do had a fully associative
+ 
+
+ align:start position:0%
+Victor do had a fully associative
+schemes
+
+ align:start position:0%
+schemes
+ 
+
+ align:start position:0%
+schemes
+these are what's called conflict misses
+
+ align:start position:0%
+these are what's called conflict misses
+ 
+
+ align:start position:0%
+these are what's called conflict misses
+you have to for example if you have 16
+
+ align:start position:0%
+you have to for example if you have 16
+ 
+
+ align:start position:0%
+you have to for example if you have 16
+things in a set and you keep accessing
+
+ align:start position:0%
+things in a set and you keep accessing
+ 
+
+ align:start position:0%
+things in a set and you keep accessing
+17 things that all belong in the set
+
+ align:start position:0%
+17 things that all belong in the set
+ 
+
+ align:start position:0%
+17 things that all belong in the set
+something's gonna get kicked out every
+
+ align:start position:0%
+something's gonna get kicked out every
+ 
+
+ align:start position:0%
+something's gonna get kicked out every
+time you want to access something and
+
+ align:start position:0%
+time you want to access something and
+ 
+
+ align:start position:0%
+time you want to access something and
+these cache evictions might not have
+
+ align:start position:0%
+these cache evictions might not have
+ 
+
+ align:start position:0%
+these cache evictions might not have
+happened if you had a fully associative
+
+ align:start position:0%
+happened if you had a fully associative
+ 
+
+ align:start position:0%
+happened if you had a fully associative
+cache and then finally there are sharing
+
+ align:start position:0%
+cache and then finally there are sharing
+ 
+
+ align:start position:0%
+cache and then finally there are sharing
+misses so sharing misses only happened
+
+ align:start position:0%
+misses so sharing misses only happened
+ 
+
+ align:start position:0%
+misses so sharing misses only happened
+in a parallel context and we talked a
+
+ align:start position:0%
+in a parallel context and we talked a
+ 
+
+ align:start position:0%
+in a parallel context and we talked a
+little bit about - sharing a false
+
+ align:start position:0%
+little bit about - sharing a false
+ 
+
+ align:start position:0%
+little bit about - sharing a false
+sharing misses in Prior lectures so
+
+ align:start position:0%
+sharing misses in Prior lectures so
+ 
+
+ align:start position:0%
+sharing misses in Prior lectures so
+let's just review this briefly so
+
+ align:start position:0%
+let's just review this briefly so
+ 
+
+ align:start position:0%
+let's just review this briefly so
+sharing this can happen if multiple
+
+ align:start position:0%
+sharing this can happen if multiple
+ 
+
+ align:start position:0%
+sharing this can happen if multiple
+processors are accessing the same cache
+
+ align:start position:0%
+processors are accessing the same cache
+ 
+
+ align:start position:0%
+processors are accessing the same cache
+line and at least one of them is writing
+
+ align:start position:0%
+line and at least one of them is writing
+ 
+
+ align:start position:0%
+line and at least one of them is writing
+to that cache line if all the processors
+
+ align:start position:0%
+to that cache line if all the processors
+ 
+
+ align:start position:0%
+to that cache line if all the processors
+are just reading from the cache line
+
+ align:start position:0%
+are just reading from the cache line
+ 
+
+ align:start position:0%
+are just reading from the cache line
+then the cache coherence protocol knows
+
+ align:start position:0%
+then the cache coherence protocol knows
+ 
+
+ align:start position:0%
+then the cache coherence protocol knows
+how to make it work so that you don't
+
+ align:start position:0%
+how to make it work so that you don't
+ 
+
+ align:start position:0%
+how to make it work so that you don't
+get cache misses they can all access the
+
+ align:start position:0%
+get cache misses they can all access the
+ 
+
+ align:start position:0%
+get cache misses they can all access the
+same cache line at the same time if
+
+ align:start position:0%
+same cache line at the same time if
+ 
+
+ align:start position:0%
+same cache line at the same time if
+nobody's modifying it but if at least
+
+ align:start position:0%
+nobody's modifying it but if at least
+ 
+
+ align:start position:0%
+nobody's modifying it but if at least
+one processor is modifying it you could
+
+ align:start position:0%
+one processor is modifying it you could
+ 
+
+ align:start position:0%
+one processor is modifying it you could
+get either true sharing misses or false
+
+ align:start position:0%
+get either true sharing misses or false
+ 
+
+ align:start position:0%
+get either true sharing misses or false
+sharing misses so a true sharing miss is
+
+ align:start position:0%
+sharing misses so a true sharing miss is
+ 
+
+ align:start position:0%
+sharing misses so a true sharing miss is
+when two processors are accessing the
+
+ align:start position:0%
+when two processors are accessing the
+ 
+
+ align:start position:0%
+when two processors are accessing the
+same data on the same cache line and as
+
+ align:start position:0%
+same data on the same cache line and as
+ 
+
+ align:start position:0%
+same data on the same cache line and as
+you recall from a previous lecture if
+
+ align:start position:0%
+you recall from a previous lecture if
+ 
+
+ align:start position:0%
+you recall from a previous lecture if
+one of the two processors is writing to
+
+ align:start position:0%
+one of the two processors is writing to
+ 
+
+ align:start position:0%
+one of the two processors is writing to
+this cache line whenever it does a write
+
+ align:start position:0%
+this cache line whenever it does a write
+ 
+
+ align:start position:0%
+this cache line whenever it does a write
+in that it needs to acquire the cache
+
+ align:start position:0%
+in that it needs to acquire the cache
+ 
+
+ align:start position:0%
+in that it needs to acquire the cache
+line in exclusive mode and then
+
+ align:start position:0%
+line in exclusive mode and then
+ 
+
+ align:start position:0%
+line in exclusive mode and then
+invalidate the that cache line in all
+
+ align:start position:0%
+invalidate the that cache line in all
+ 
+
+ align:start position:0%
+invalidate the that cache line in all
+other caches so then when when another
+
+ align:start position:0%
+other caches so then when when another
+ 
+
+ align:start position:0%
+other caches so then when when another
+processor tries to access the same
+
+ align:start position:0%
+processor tries to access the same
+ 
+
+ align:start position:0%
+processor tries to access the same
+memory location has to bring it back
+
+ align:start position:0%
+memory location has to bring it back
+ 
+
+ align:start position:0%
+memory location has to bring it back
+into its own cache and then you get a
+
+ align:start position:0%
+into its own cache and then you get a
+ 
+
+ align:start position:0%
+into its own cache and then you get a
+cache miss there a false sharing miss
+
+ align:start position:0%
+cache miss there a false sharing miss
+ 
+
+ align:start position:0%
+cache miss there a false sharing miss
+happens if two processes are accessing
+
+ align:start position:0%
+happens if two processes are accessing
+ 
+
+ align:start position:0%
+happens if two processes are accessing
+different data that just happened to
+
+ align:start position:0%
+different data that just happened to
+ 
+
+ align:start position:0%
+different data that just happened to
+reside on the same cache line because
+
+ align:start position:0%
+reside on the same cache line because
+ 
+
+ align:start position:0%
+reside on the same cache line because
+the basic unit of movement is a cache
+
+ align:start position:0%
+the basic unit of movement is a cache
+ 
+
+ align:start position:0%
+the basic unit of movement is a cache
+line in the architecture so even if
+
+ align:start position:0%
+line in the architecture so even if
+ 
+
+ align:start position:0%
+line in the architecture so even if
+you're accessing different things if
+
+ align:start position:0%
+you're accessing different things if
+ 
+
+ align:start position:0%
+you're accessing different things if
+they are on the same cache line you're
+
+ align:start position:0%
+they are on the same cache line you're
+ 
+
+ align:start position:0%
+they are on the same cache line you're
+still going to get a sharing miss and
+
+ align:start position:0%
+still going to get a sharing miss and
+ 
+
+ align:start position:0%
+still going to get a sharing miss and
+fall sharing is pretty hard to deal with
+
+ align:start position:0%
+fall sharing is pretty hard to deal with
+ 
+
+ align:start position:0%
+fall sharing is pretty hard to deal with
+because in general you don't know what
+
+ align:start position:0%
+because in general you don't know what
+ 
+
+ align:start position:0%
+because in general you don't know what
+data gets placed on what cache line
+
+ align:start position:0%
+data gets placed on what cache line
+ 
+
+ align:start position:0%
+data gets placed on what cache line
+there's certain heuristics you can use
+
+ align:start position:0%
+there's certain heuristics you can use
+ 
+
+ align:start position:0%
+there's certain heuristics you can use
+for example of your mouth looking a big
+
+ align:start position:0%
+for example of your mouth looking a big
+ 
+
+ align:start position:0%
+for example of your mouth looking a big
+we region you know that that memory
+
+ align:start position:0%
+we region you know that that memory
+ 
+
+ align:start position:0%
+we region you know that that memory
+region is contiguous so you can space
+
+ align:start position:0%
+region is contiguous so you can space
+ 
+
+ align:start position:0%
+region is contiguous so you can space
+your access is far enough apart by
+
+ align:start position:0%
+your access is far enough apart by
+ 
+
+ align:start position:0%
+your access is far enough apart by
+different processors so they don't touch
+
+ align:start position:0%
+different processors so they don't touch
+ 
+
+ align:start position:0%
+different processors so they don't touch
+the same cache line so if you're just
+
+ align:start position:0%
+the same cache line so if you're just
+ 
+
+ align:start position:0%
+the same cache line so if you're just
+declaring local variables on the stack
+
+ align:start position:0%
+declaring local variables on the stack
+ 
+
+ align:start position:0%
+declaring local variables on the stack
+you don't know where the compiler is
+
+ align:start position:0%
+you don't know where the compiler is
+ 
+
+ align:start position:0%
+you don't know where the compiler is
+going to decide to place these variables
+
+ align:start position:0%
+going to decide to place these variables
+ 
+
+ align:start position:0%
+going to decide to place these variables
+in the virtual memory address space so
+
+ align:start position:0%
+in the virtual memory address space so
+ 
+
+ align:start position:0%
+in the virtual memory address space so
+these are for different types of cache
+
+ align:start position:0%
+these are for different types of cache
+ 
+
+ align:start position:0%
+these are for different types of cache
+misses that you should know about
+
+ align:start position:0%
+misses that you should know about
+ 
+
+ align:start position:0%
+misses that you should know about
+and there's many models out there for
+
+ align:start position:0%
+and there's many models out there for
+ 
+
+ align:start position:0%
+and there's many models out there for
+analyzing the cache performance of
+
+ align:start position:0%
+analyzing the cache performance of
+ 
+
+ align:start position:0%
+analyzing the cache performance of
+algorithms and some of the models ignore
+
+ align:start position:0%
+algorithms and some of the models ignore
+ 
+
+ align:start position:0%
+algorithms and some of the models ignore
+some of these different types of cache
+
+ align:start position:0%
+some of these different types of cache
+ 
+
+ align:start position:0%
+some of these different types of cache
+misses so just be aware of this when
+
+ align:start position:0%
+misses so just be aware of this when
+ 
+
+ align:start position:0%
+misses so just be aware of this when
+you're looking at algorithm analysis
+
+ align:start position:0%
+you're looking at algorithm analysis
+ 
+
+ align:start position:0%
+you're looking at algorithm analysis
+because not all the models will capture
+
+ align:start position:0%
+because not all the models will capture
+ 
+
+ align:start position:0%
+because not all the models will capture
+all of these different types of cache
+
+ align:start position:0%
+all of these different types of cache
+ 
+
+ align:start position:0%
+all of these different types of cache
+misses so let's look at a bad case for
+
+ align:start position:0%
+misses so let's look at a bad case for
+ 
+
+ align:start position:0%
+misses so let's look at a bad case for
+conflict misses so here I'm I have a I
+
+ align:start position:0%
+conflict misses so here I'm I have a I
+ 
+
+ align:start position:0%
+conflict misses so here I'm I have a I
+want to access a sub matrix within a
+
+ align:start position:0%
+want to access a sub matrix within a
+ 
+
+ align:start position:0%
+want to access a sub matrix within a
+larger matrix and recall that the
+
+ align:start position:0%
+larger matrix and recall that the
+ 
+
+ align:start position:0%
+larger matrix and recall that the
+matrices are stored in row major order
+
+ align:start position:0%
+matrices are stored in row major order
+ 
+
+ align:start position:0%
+matrices are stored in row major order
+and let's say our matrix is 4096 columns
+
+ align:start position:0%
+and let's say our matrix is 4096 columns
+ 
+
+ align:start position:0%
+and let's say our matrix is 4096 columns
+by 4096 rows and it still stores doubles
+
+ align:start position:0%
+by 4096 rows and it still stores doubles
+ 
+
+ align:start position:0%
+by 4096 rows and it still stores doubles
+so therefore each row here is going to
+
+ align:start position:0%
+so therefore each row here is going to
+ 
+
+ align:start position:0%
+so therefore each row here is going to
+contain two to the fifteenth bytes
+
+ align:start position:0%
+contain two to the fifteenth bytes
+ 
+
+ align:start position:0%
+contain two to the fifteenth bytes
+because 4096 is 2 to the 12 and we have
+
+ align:start position:0%
+because 4096 is 2 to the 12 and we have
+ 
+
+ align:start position:0%
+because 4096 is 2 to the 12 and we have
+doubles each one of which takes 8 bytes
+
+ align:start position:0%
+doubles each one of which takes 8 bytes
+ 
+
+ align:start position:0%
+doubles each one of which takes 8 bytes
+so 2 to 12 times 2 to the third which is
+
+ align:start position:0%
+so 2 to 12 times 2 to the third which is
+ 
+
+ align:start position:0%
+so 2 to 12 times 2 to the third which is
+2 to 15th we're gonna assume the word
+
+ align:start position:0%
+2 to 15th we're gonna assume the word
+ 
+
+ align:start position:0%
+2 to 15th we're gonna assume the word
+width is 64 which is standard we're
+
+ align:start position:0%
+width is 64 which is standard we're
+ 
+
+ align:start position:0%
+width is 64 which is standard we're
+gonna assume that we have a cache size
+
+ align:start position:0%
+gonna assume that we have a cache size
+ 
+
+ align:start position:0%
+gonna assume that we have a cache size
+of 32 K and the cache block size is 64
+
+ align:start position:0%
+of 32 K and the cache block size is 64
+ 
+
+ align:start position:0%
+of 32 K and the cache block size is 64
+which again is standard and let's say we
+
+ align:start position:0%
+which again is standard and let's say we
+ 
+
+ align:start position:0%
+which again is standard and let's say we
+have a four-way associative cache so
+
+ align:start position:0%
+have a four-way associative cache so
+ 
+
+ align:start position:0%
+have a four-way associative cache so
+let's look at how the how the bits are
+
+ align:start position:0%
+let's look at how the how the bits are
+ 
+
+ align:start position:0%
+let's look at how the how the bits are
+divided into so again we have this
+
+ align:start position:0%
+divided into so again we have this
+ 
+
+ align:start position:0%
+divided into so again we have this
+offset which takes log base 2 of B bits
+
+ align:start position:0%
+offset which takes log base 2 of B bits
+ 
+
+ align:start position:0%
+offset which takes log base 2 of B bits
+so how many bits do we have for the
+
+ align:start position:0%
+so how many bits do we have for the
+ 
+
+ align:start position:0%
+so how many bits do we have for the
+offset in this example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we have six bits so it's
+
+ align:start position:0%
+all right so we have six bits so it's
+ 
+
+ align:start position:0%
+all right so we have six bits so it's
+just log base 2 of 64 what about for
+
+ align:start position:0%
+just log base 2 of 64 what about for
+ 
+
+ align:start position:0%
+just log base 2 of 64 what about for
+this set how many bits do we have for
+
+ align:start position:0%
+this set how many bits do we have for
+ 
+
+ align:start position:0%
+this set how many bits do we have for
+that seven who said seven yeah so so it
+
+ align:start position:0%
+that seven who said seven yeah so so it
+ 
+
+ align:start position:0%
+that seven who said seven yeah so so it
+is seven so M is 32 K which is to 215th
+
+ align:start position:0%
+is seven so M is 32 K which is to 215th
+ 
+
+ align:start position:0%
+is seven so M is 32 K which is to 215th
+and then k is 2 to the 2 b is 2 to the 2
+
+ align:start position:0%
+and then k is 2 to the 2 b is 2 to the 2
+ 
+
+ align:start position:0%
+and then k is 2 to the 2 b is 2 to the 2
+to the 6 so it's 2 to 15 divided by 2
+
+ align:start position:0%
+to the 6 so it's 2 to 15 divided by 2
+ 
+
+ align:start position:0%
+to the 6 so it's 2 to 15 divided by 2
+the 8 which is 2 to 7th and log base 2
+
+ align:start position:0%
+the 8 which is 2 to 7th and log base 2
+ 
+
+ align:start position:0%
+the 8 which is 2 to 7th and log base 2
+of that is 7 and finally what about the
+
+ align:start position:0%
+of that is 7 and finally what about the
+ 
+
+ align:start position:0%
+of that is 7 and finally what about the
+tag field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+51 why is that yes it's just 64 minus
+
+ align:start position:0%
+51 why is that yes it's just 64 minus
+ 
+
+ align:start position:0%
+51 why is that yes it's just 64 minus
+seven minus six which is 51 okay so
+
+ align:start position:0%
+seven minus six which is 51 okay so
+ 
+
+ align:start position:0%
+seven minus six which is 51 okay so
+let's say that we want to access a sub
+
+ align:start position:0%
+let's say that we want to access a sub
+ 
+
+ align:start position:0%
+let's say that we want to access a sub
+matrix within this larger matrix let's
+
+ align:start position:0%
+matrix within this larger matrix let's
+ 
+
+ align:start position:0%
+matrix within this larger matrix let's
+say we want to access a 32 by 32 sub
+
+ align:start position:0%
+say we want to access a 32 by 32 sub
+ 
+
+ align:start position:0%
+say we want to access a 32 by 32 sub
+matrix and this is pretty common in
+
+ align:start position:0%
+matrix and this is pretty common in
+ 
+
+ align:start position:0%
+matrix and this is pretty common in
+matrix algorithms where you want to
+
+ align:start position:0%
+matrix algorithms where you want to
+ 
+
+ align:start position:0%
+matrix algorithms where you want to
+access sub matrices especially in
+
+ align:start position:0%
+access sub matrices especially in
+ 
+
+ align:start position:0%
+access sub matrices especially in
+dividing conquer algorithms and let's
+
+ align:start position:0%
+dividing conquer algorithms and let's
+ 
+
+ align:start position:0%
+dividing conquer algorithms and let's
+say we want to access a column of this
+
+ align:start position:0%
+say we want to access a column of this
+ 
+
+ align:start position:0%
+say we want to access a column of this
+sub matrix a so the addresses of the
+
+ align:start position:0%
+sub matrix a so the addresses of the
+ 
+
+ align:start position:0%
+sub matrix a so the addresses of the
+elements that we're going to access are
+
+ align:start position:0%
+elements that we're going to access are
+ 
+
+ align:start position:0%
+elements that we're going to access are
+as follows so let's say we the first
+
+ align:start position:0%
+as follows so let's say we the first
+ 
+
+ align:start position:0%
+as follows so let's say we the first
+element in a column is sort out address
+
+ align:start position:0%
+element in a column is sort out address
+ 
+
+ align:start position:0%
+element in a column is sort out address
+X then the second element in the column
+
+ align:start position:0%
+X then the second element in the column
+ 
+
+ align:start position:0%
+X then the second element in the column
+is going to be stored at address X plus
+
+ align:start position:0%
+is going to be stored at address X plus
+ 
+
+ align:start position:0%
+is going to be stored at address X plus
+two to the fifteenth because each row
+
+ align:start position:0%
+two to the fifteenth because each row
+ 
+
+ align:start position:0%
+two to the fifteenth because each row
+has two to the fifteenth bytes and we're
+
+ align:start position:0%
+has two to the fifteenth bytes and we're
+ 
+
+ align:start position:0%
+has two to the fifteenth bytes and we're
+skipping over an entire row here to get
+
+ align:start position:0%
+skipping over an entire row here to get
+ 
+
+ align:start position:0%
+skipping over an entire row here to get
+to the element in the second in the next
+
+ align:start position:0%
+to the element in the second in the next
+ 
+
+ align:start position:0%
+to the element in the second in the next
+row of the sub matrix so we're gonna add
+
+ align:start position:0%
+row of the sub matrix so we're gonna add
+ 
+
+ align:start position:0%
+row of the sub matrix so we're gonna add
+to the fifteenth and then to get the
+
+ align:start position:0%
+to the fifteenth and then to get the
+ 
+
+ align:start position:0%
+to the fifteenth and then to get the
+third element we're gonna add two times
+
+ align:start position:0%
+third element we're gonna add two times
+ 
+
+ align:start position:0%
+third element we're gonna add two times
+two to the fifteenth and so on until we
+
+ align:start position:0%
+two to the fifteenth and so on until we
+ 
+
+ align:start position:0%
+two to the fifteenth and so on until we
+get to the last element which is X plus
+
+ align:start position:0%
+get to the last element which is X plus
+ 
+
+ align:start position:0%
+get to the last element which is X plus
+31 times two to the fifteenth so which
+
+ align:start position:0%
+31 times two to the fifteenth so which
+ 
+
+ align:start position:0%
+31 times two to the fifteenth so which
+the olds of the address are changing as
+
+ align:start position:0%
+the olds of the address are changing as
+ 
+
+ align:start position:0%
+the olds of the address are changing as
+we go through one column of this sub
+
+ align:start position:0%
+we go through one column of this sub
+ 
+
+ align:start position:0%
+we go through one column of this sub
+matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it's just gonna be the tag
+
+ align:start position:0%
+yeah so it's just gonna be the tag
+ 
+
+ align:start position:0%
+yeah so it's just gonna be the tag
+that's changing the set and the offset
+
+ align:start position:0%
+that's changing the set and the offset
+ 
+
+ align:start position:0%
+that's changing the set and the offset
+are gonna stay the same because we're
+
+ align:start position:0%
+are gonna stay the same because we're
+ 
+
+ align:start position:0%
+are gonna stay the same because we're
+just using the lower 13 bits to store
+
+ align:start position:0%
+just using the lower 13 bits to store
+ 
+
+ align:start position:0%
+just using the lower 13 bits to store
+the setna tag and therefore when we
+
+ align:start position:0%
+the setna tag and therefore when we
+ 
+
+ align:start position:0%
+the setna tag and therefore when we
+increment by to the 15th we're not going
+
+ align:start position:0%
+increment by to the 15th we're not going
+ 
+
+ align:start position:0%
+increment by to the 15th we're not going
+to touch the set in the offset so all of
+
+ align:start position:0%
+to touch the set in the offset so all of
+ 
+
+ align:start position:0%
+to touch the set in the offset so all of
+these addresses fall into the same set
+
+ align:start position:0%
+these addresses fall into the same set
+ 
+
+ align:start position:0%
+these addresses fall into the same set
+and this is a problem because ours us
+
+ align:start position:0%
+and this is a problem because ours us
+ 
+
+ align:start position:0%
+and this is a problem because ours us
+our cache is only 4-way associative so
+
+ align:start position:0%
+our cache is only 4-way associative so
+ 
+
+ align:start position:0%
+our cache is only 4-way associative so
+we can only fit for cash for cache lines
+
+ align:start position:0%
+we can only fit for cash for cache lines
+ 
+
+ align:start position:0%
+we can only fit for cash for cache lines
+in each set and here we're accessing 31
+
+ align:start position:0%
+in each set and here we're accessing 31
+ 
+
+ align:start position:0%
+in each set and here we're accessing 31
+of these things so by the time we get to
+
+ align:start position:0%
+of these things so by the time we get to
+ 
+
+ align:start position:0%
+of these things so by the time we get to
+the next column of a all the things that
+
+ align:start position:0%
+the next column of a all the things that
+ 
+
+ align:start position:0%
+the next column of a all the things that
+we access in the current column of a are
+
+ align:start position:0%
+we access in the current column of a are
+ 
+
+ align:start position:0%
+we access in the current column of a are
+going to be evicted from cache already
+
+ align:start position:0%
+going to be evicted from cache already
+ 
+
+ align:start position:0%
+going to be evicted from cache already
+and this is known as a conflict miss
+
+ align:start position:0%
+and this is known as a conflict miss
+ 
+
+ align:start position:0%
+and this is known as a conflict miss
+because if if you had a fully
+
+ align:start position:0%
+because if if you had a fully
+ 
+
+ align:start position:0%
+because if if you had a fully
+associative cache this might not have
+
+ align:start position:0%
+associative cache this might not have
+ 
+
+ align:start position:0%
+associative cache this might not have
+happened because you could actually use
+
+ align:start position:0%
+happened because you could actually use
+ 
+
+ align:start position:0%
+happened because you could actually use
+any location in the cache to store these
+
+ align:start position:0%
+any location in the cache to store these
+ 
+
+ align:start position:0%
+any location in the cache to store these
+cache blocks so is anybody have any
+
+ align:start position:0%
+cache blocks so is anybody have any
+ 
+
+ align:start position:0%
+cache blocks so is anybody have any
+questions on why we get conflict misses
+
+ align:start position:0%
+questions on why we get conflict misses
+ 
+
+ align:start position:0%
+questions on why we get conflict misses
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so anybody have any ideas on how to fix
+
+ align:start position:0%
+so anybody have any ideas on how to fix
+ 
+
+ align:start position:0%
+so anybody have any ideas on how to fix
+this so what can I do to make it so that
+
+ align:start position:0%
+this so what can I do to make it so that
+ 
+
+ align:start position:0%
+this so what can I do to make it so that
+I'm not incrementing by to the exactly
+
+ align:start position:0%
+I'm not incrementing by to the exactly
+ 
+
+ align:start position:0%
+I'm not incrementing by to the exactly
+to the 15th every time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah yeah so one solution is
+
+ align:start position:0%
+yeah yeah yeah yeah so one solution is
+ 
+
+ align:start position:0%
+yeah yeah yeah yeah so one solution is
+to Pat the matrix you can add some
+
+ align:start position:0%
+to Pat the matrix you can add some
+ 
+
+ align:start position:0%
+to Pat the matrix you can add some
+constant amount of space to the end of
+
+ align:start position:0%
+constant amount of space to the end of
+ 
+
+ align:start position:0%
+constant amount of space to the end of
+the matrix so each row is gonna be
+
+ align:start position:0%
+the matrix so each row is gonna be
+ 
+
+ align:start position:0%
+the matrix so each row is gonna be
+longer than to the 15th bytes so maybe
+
+ align:start position:0%
+longer than to the 15th bytes so maybe
+ 
+
+ align:start position:0%
+longer than to the 15th bytes so maybe
+you add some small constant like 17 so
+
+ align:start position:0%
+you add some small constant like 17 so
+ 
+
+ align:start position:0%
+you add some small constant like 17 so
+add 17 bytes the end of each row and now
+
+ align:start position:0%
+add 17 bytes the end of each row and now
+ 
+
+ align:start position:0%
+add 17 bytes the end of each row and now
+when you act as a column of this sub
+
+ align:start position:0%
+when you act as a column of this sub
+ 
+
+ align:start position:0%
+when you act as a column of this sub
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+you're not just incrementing by to the
+
+ align:start position:0%
+you're not just incrementing by to the
+ 
+
+ align:start position:0%
+you're not just incrementing by to the
+15th you're also adding some small
+
+ align:start position:0%
+15th you're also adding some small
+ 
+
+ align:start position:0%
+15th you're also adding some small
+integer and that's going to cause the
+
+ align:start position:0%
+integer and that's going to cause the
+ 
+
+ align:start position:0%
+integer and that's going to cause the
+set and offset fields to change as well
+
+ align:start position:0%
+set and offset fields to change as well
+ 
+
+ align:start position:0%
+set and offset fields to change as well
+and you're not going to get as many
+
+ align:start position:0%
+and you're not going to get as many
+ 
+
+ align:start position:0%
+and you're not going to get as many
+conflict misses so that's one way to
+
+ align:start position:0%
+conflict misses so that's one way to
+ 
+
+ align:start position:0%
+conflict misses so that's one way to
+solve the problem it turns out that if
+
+ align:start position:0%
+solve the problem it turns out that if
+ 
+
+ align:start position:0%
+solve the problem it turns out that if
+you're doing a matrix multiplication
+
+ align:start position:0%
+you're doing a matrix multiplication
+ 
+
+ align:start position:0%
+you're doing a matrix multiplication
+algorithm that's a cubic work algorithm
+
+ align:start position:0%
+algorithm that's a cubic work algorithm
+ 
+
+ align:start position:0%
+algorithm that's a cubic work algorithm
+and you can basically afford to copy the
+
+ align:start position:0%
+and you can basically afford to copy the
+ 
+
+ align:start position:0%
+and you can basically afford to copy the
+sub matrix into a temporary 32 by 32
+
+ align:start position:0%
+sub matrix into a temporary 32 by 32
+ 
+
+ align:start position:0%
+sub matrix into a temporary 32 by 32
+matrix do all the operations on the
+
+ align:start position:0%
+matrix do all the operations on the
+ 
+
+ align:start position:0%
+matrix do all the operations on the
+temporary matrix and then copy it back
+
+ align:start position:0%
+temporary matrix and then copy it back
+ 
+
+ align:start position:0%
+temporary matrix and then copy it back
+out to the original matrix the copy
+
+ align:start position:0%
+out to the original matrix the copy
+ 
+
+ align:start position:0%
+out to the original matrix the copy
+copying only takes quadratic work to do
+
+ align:start position:0%
+copying only takes quadratic work to do
+ 
+
+ align:start position:0%
+copying only takes quadratic work to do
+across the whole algorithm and since the
+
+ align:start position:0%
+across the whole algorithm and since the
+ 
+
+ align:start position:0%
+across the whole algorithm and since the
+whole algorithm takes cubic work the
+
+ align:start position:0%
+whole algorithm takes cubic work the
+ 
+
+ align:start position:0%
+whole algorithm takes cubic work the
+quadratic work is a lower order term so
+
+ align:start position:0%
+quadratic work is a lower order term so
+ 
+
+ align:start position:0%
+quadratic work is a lower order term so
+you can also you can use temporary space
+
+ align:start position:0%
+you can also you can use temporary space
+ 
+
+ align:start position:0%
+you can also you can use temporary space
+to make sure that you don't get conflict
+
+ align:start position:0%
+to make sure that you don't get conflict
+ 
+
+ align:start position:0%
+to make sure that you don't get conflict
+misses any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this was conflict misses so
+
+ align:start position:0%
+okay so this was conflict misses so
+ 
+
+ align:start position:0%
+okay so this was conflict misses so
+conflict misses are important but
+
+ align:start position:0%
+conflict misses are important but
+ 
+
+ align:start position:0%
+conflict misses are important but
+usually we're going to be first
+
+ align:start position:0%
+usually we're going to be first
+ 
+
+ align:start position:0%
+usually we're going to be first
+concerned about getting good spatial and
+
+ align:start position:0%
+concerned about getting good spatial and
+ 
+
+ align:start position:0%
+concerned about getting good spatial and
+temporal locality because those are
+
+ align:start position:0%
+temporal locality because those are
+ 
+
+ align:start position:0%
+temporal locality because those are
+usually the higher-order factors in the
+
+ align:start position:0%
+usually the higher-order factors in the
+ 
+
+ align:start position:0%
+usually the higher-order factors in the
+performance of a program once we get
+
+ align:start position:0%
+performance of a program once we get
+ 
+
+ align:start position:0%
+performance of a program once we get
+good spatial and temporal locality in
+
+ align:start position:0%
+good spatial and temporal locality in
+ 
+
+ align:start position:0%
+good spatial and temporal locality in
+our program we can then start worrying
+
+ align:start position:0%
+our program we can then start worrying
+ 
+
+ align:start position:0%
+our program we can then start worrying
+about conflict misses for example by
+
+ align:start position:0%
+about conflict misses for example by
+ 
+
+ align:start position:0%
+about conflict misses for example by
+using temporary space or padding or our
+
+ align:start position:0%
+using temporary space or padding or our
+ 
+
+ align:start position:0%
+using temporary space or padding or our
+data by some small constants so that we
+
+ align:start position:0%
+data by some small constants so that we
+ 
+
+ align:start position:0%
+data by some small constants so that we
+don't have as many conflict misses okay
+
+ align:start position:0%
+don't have as many conflict misses okay
+ 
+
+ align:start position:0%
+don't have as many conflict misses okay
+so now I want to talk about a model that
+
+ align:start position:0%
+so now I want to talk about a model that
+ 
+
+ align:start position:0%
+so now I want to talk about a model that
+we can use to analyze the cache
+
+ align:start position:0%
+we can use to analyze the cache
+ 
+
+ align:start position:0%
+we can use to analyze the cache
+performance of algorithms and this is
+
+ align:start position:0%
+performance of algorithms and this is
+ 
+
+ align:start position:0%
+performance of algorithms and this is
+called the ideal cache model so in this
+
+ align:start position:0%
+called the ideal cache model so in this
+ 
+
+ align:start position:0%
+called the ideal cache model so in this
+model we have a two level cache
+
+ align:start position:0%
+model we have a two level cache
+ 
+
+ align:start position:0%
+model we have a two level cache
+hierarchy so we have the cash and then
+
+ align:start position:0%
+hierarchy so we have the cash and then
+ 
+
+ align:start position:0%
+hierarchy so we have the cash and then
+main memory the cache size is of size M
+
+ align:start position:0%
+main memory the cache size is of size M
+ 
+
+ align:start position:0%
+main memory the cache size is of size M
+and the cache line sizes of B bytes and
+
+ align:start position:0%
+and the cache line sizes of B bytes and
+ 
+
+ align:start position:0%
+and the cache line sizes of B bytes and
+therefore we can fit M over B cache
+
+ align:start position:0%
+therefore we can fit M over B cache
+ 
+
+ align:start position:0%
+therefore we can fit M over B cache
+lines inside our cache this model
+
+ align:start position:0%
+lines inside our cache this model
+ 
+
+ align:start position:0%
+lines inside our cache this model
+assumes that the cache is fully
+
+ align:start position:0%
+assumes that the cache is fully
+ 
+
+ align:start position:0%
+assumes that the cache is fully
+associative so any cache block can go
+
+ align:start position:0%
+associative so any cache block can go
+ 
+
+ align:start position:0%
+associative so any cache block can go
+anywhere in the cache and it also
+
+ align:start position:0%
+anywhere in the cache and it also
+ 
+
+ align:start position:0%
+anywhere in the cache and it also
+assumes an optimal Nishant replacement
+
+ align:start position:0%
+assumes an optimal Nishant replacement
+ 
+
+ align:start position:0%
+assumes an optimal Nishant replacement
+policy so this means that what we want
+
+ align:start position:0%
+policy so this means that what we want
+ 
+
+ align:start position:0%
+policy so this means that what we want
+to evict a cache block from the cache
+
+ align:start position:0%
+to evict a cache block from the cache
+ 
+
+ align:start position:0%
+to evict a cache block from the cache
+we're going to pick the thing to evict
+
+ align:start position:0%
+we're going to pick the thing to evict
+ 
+
+ align:start position:0%
+we're going to pick the thing to evict
+that gives us the best performance over
+
+ align:start position:0%
+that gives us the best performance over
+ 
+
+ align:start position:0%
+that gives us the best performance over
+all it gives us the lowest number of
+
+ align:start position:0%
+all it gives us the lowest number of
+ 
+
+ align:start position:0%
+all it gives us the lowest number of
+cache misses throughout our entire
+
+ align:start position:0%
+cache misses throughout our entire
+ 
+
+ align:start position:0%
+cache misses throughout our entire
+algorithm so we're assuming that we know
+
+ align:start position:0%
+algorithm so we're assuming that we know
+ 
+
+ align:start position:0%
+algorithm so we're assuming that we know
+the sequence of memory requests
+
+ align:start position:0%
+the sequence of memory requests
+ 
+
+ align:start position:0%
+the sequence of memory requests
+throughout the entire algorithm and
+
+ align:start position:0%
+throughout the entire algorithm and
+ 
+
+ align:start position:0%
+throughout the entire algorithm and
+that's why it's called the nisshin
+
+ align:start position:0%
+that's why it's called the nisshin
+ 
+
+ align:start position:0%
+that's why it's called the nisshin
+replacement policy and if something is
+
+ align:start position:0%
+replacement policy and if something is
+ 
+
+ align:start position:0%
+replacement policy and if something is
+in cache you can operate on it for free
+
+ align:start position:0%
+in cache you can operate on it for free
+ 
+
+ align:start position:0%
+in cache you can operate on it for free
+and if something is in main memory you
+
+ align:start position:0%
+and if something is in main memory you
+ 
+
+ align:start position:0%
+and if something is in main memory you
+have to bring it into cache and then you
+
+ align:start position:0%
+have to bring it into cache and then you
+ 
+
+ align:start position:0%
+have to bring it into cache and then you
+incur a cache miss so there are two
+
+ align:start position:0%
+incur a cache miss so there are two
+ 
+
+ align:start position:0%
+incur a cache miss so there are two
+performance measures that we care about
+
+ align:start position:0%
+performance measures that we care about
+ 
+
+ align:start position:0%
+performance measures that we care about
+first we care about the order in any
+
+ align:start position:0%
+first we care about the order in any
+ 
+
+ align:start position:0%
+first we care about the order in any
+work which is just the ordinary running
+
+ align:start position:0%
+work which is just the ordinary running
+ 
+
+ align:start position:0%
+work which is just the ordinary running
+time of a program so this this is the
+
+ align:start position:0%
+time of a program so this this is the
+ 
+
+ align:start position:0%
+time of a program so this this is the
+same as before when we were analyzing
+
+ align:start position:0%
+same as before when we were analyzing
+ 
+
+ align:start position:0%
+same as before when we were analyzing
+algorithms it's just a total number of
+
+ align:start position:0%
+algorithms it's just a total number of
+ 
+
+ align:start position:0%
+algorithms it's just a total number of
+operations that the program does and the
+
+ align:start position:0%
+operations that the program does and the
+ 
+
+ align:start position:0%
+operations that the program does and the
+number of cache misses is going to be
+
+ align:start position:0%
+number of cache misses is going to be
+ 
+
+ align:start position:0%
+number of cache misses is going to be
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+we have to transfer between the main
+
+ align:start position:0%
+we have to transfer between the main
+ 
+
+ align:start position:0%
+we have to transfer between the main
+memory and the cache so a number of
+
+ align:start position:0%
+memory and the cache so a number of
+ 
+
+ align:start position:0%
+memory and the cache so a number of
+cache misses just counts the number of
+
+ align:start position:0%
+cache misses just counts the number of
+ 
+
+ align:start position:0%
+cache misses just counts the number of
+cash transfers whereas the work counts
+
+ align:start position:0%
+cash transfers whereas the work counts
+ 
+
+ align:start position:0%
+cash transfers whereas the work counts
+all the operations that you have to do
+
+ align:start position:0%
+all the operations that you have to do
+ 
+
+ align:start position:0%
+all the operations that you have to do
+in the algorithm so ideally we would
+
+ align:start position:0%
+in the algorithm so ideally we would
+ 
+
+ align:start position:0%
+in the algorithm so ideally we would
+like to come up with algorithms that
+
+ align:start position:0%
+like to come up with algorithms that
+ 
+
+ align:start position:0%
+like to come up with algorithms that
+have a low number of cache misses
+
+ align:start position:0%
+have a low number of cache misses
+ 
+
+ align:start position:0%
+have a low number of cache misses
+without increasing the work from the
+
+ align:start position:0%
+without increasing the work from the
+ 
+
+ align:start position:0%
+without increasing the work from the
+traditional standard algorithm sometimes
+
+ align:start position:0%
+traditional standard algorithm sometimes
+ 
+
+ align:start position:0%
+traditional standard algorithm sometimes
+we can do that sometimes we can't do
+
+ align:start position:0%
+we can do that sometimes we can't do
+ 
+
+ align:start position:0%
+we can do that sometimes we can't do
+that and then there's a trade-off
+
+ align:start position:0%
+that and then there's a trade-off
+ 
+
+ align:start position:0%
+that and then there's a trade-off
+between the work and the number of cache
+
+ align:start position:0%
+between the work and the number of cache
+ 
+
+ align:start position:0%
+between the work and the number of cache
+misses and and then you it's a trade-off
+
+ align:start position:0%
+misses and and then you it's a trade-off
+ 
+
+ align:start position:0%
+misses and and then you it's a trade-off
+that you have to decide whether it's
+
+ align:start position:0%
+that you have to decide whether it's
+ 
+
+ align:start position:0%
+that you have to decide whether it's
+worthwhile as a performance engineer
+
+ align:start position:0%
+worthwhile as a performance engineer
+ 
+
+ align:start position:0%
+worthwhile as a performance engineer
+today we're gonna look at an algorithm
+
+ align:start position:0%
+today we're gonna look at an algorithm
+ 
+
+ align:start position:0%
+today we're gonna look at an algorithm
+where you can't actually reduce a number
+
+ align:start position:0%
+where you can't actually reduce a number
+ 
+
+ align:start position:0%
+where you can't actually reduce a number
+of cache misses without increasing the
+
+ align:start position:0%
+of cache misses without increasing the
+ 
+
+ align:start position:0%
+of cache misses without increasing the
+work so you basically get the best of
+
+ align:start position:0%
+work so you basically get the best of
+ 
+
+ align:start position:0%
+work so you basically get the best of
+both worlds so any questions on this
+
+ align:start position:0%
+both worlds so any questions on this
+ 
+
+ align:start position:0%
+both worlds so any questions on this
+ideal cache model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this model is just used for analyzing
+
+ align:start position:0%
+so this model is just used for analyzing
+ 
+
+ align:start position:0%
+so this model is just used for analyzing
+algorithms you can't actually buy one of
+
+ align:start position:0%
+algorithms you can't actually buy one of
+ 
+
+ align:start position:0%
+algorithms you can't actually buy one of
+these caches at the store so this is a
+
+ align:start position:0%
+these caches at the store so this is a
+ 
+
+ align:start position:0%
+these caches at the store so this is a
+very ideal cache and they don't exist
+
+ align:start position:0%
+very ideal cache and they don't exist
+ 
+
+ align:start position:0%
+very ideal cache and they don't exist
+but it turns out that this optimal
+
+ align:start position:0%
+but it turns out that this optimal
+ 
+
+ align:start position:0%
+but it turns out that this optimal
+initial reply sment policy has nice
+
+ align:start position:0%
+initial reply sment policy has nice
+ 
+
+ align:start position:0%
+initial reply sment policy has nice
+theoretical properties and this is a
+
+ align:start position:0%
+theoretical properties and this is a
+ 
+
+ align:start position:0%
+theoretical properties and this is a
+very important lemma that has that was
+
+ align:start position:0%
+very important lemma that has that was
+ 
+
+ align:start position:0%
+very important lemma that has that was
+proved in 1985 it's called the LRU lemma
+
+ align:start position:0%
+proved in 1985 it's called the LRU lemma
+ 
+
+ align:start position:0%
+proved in 1985 it's called the LRU lemma
+it was proof by Slater and targe end and
+
+ align:start position:0%
+it was proof by Slater and targe end and
+ 
+
+ align:start position:0%
+it was proof by Slater and targe end and
+the lemma says suppose that an algorithm
+
+ align:start position:0%
+the lemma says suppose that an algorithm
+ 
+
+ align:start position:0%
+the lemma says suppose that an algorithm
+incurs Q cache misses on an ideal cache
+
+ align:start position:0%
+incurs Q cache misses on an ideal cache
+ 
+
+ align:start position:0%
+incurs Q cache misses on an ideal cache
+of size M then on a fully associative
+
+ align:start position:0%
+of size M then on a fully associative
+ 
+
+ align:start position:0%
+of size M then on a fully associative
+cache of size 2m that uses the LRU or
+
+ align:start position:0%
+cache of size 2m that uses the LRU or
+ 
+
+ align:start position:0%
+cache of size 2m that uses the LRU or
+least recently used replacement policy
+
+ align:start position:0%
+least recently used replacement policy
+ 
+
+ align:start position:0%
+least recently used replacement policy
+it incurs at most 2q cache misses so
+
+ align:start position:0%
+it incurs at most 2q cache misses so
+ 
+
+ align:start position:0%
+it incurs at most 2q cache misses so
+what this says is if I can show the
+
+ align:start position:0%
+what this says is if I can show the
+ 
+
+ align:start position:0%
+what this says is if I can show the
+number of cache misses for an algorithm
+
+ align:start position:0%
+number of cache misses for an algorithm
+ 
+
+ align:start position:0%
+number of cache misses for an algorithm
+on the ideal cache then if I take a
+
+ align:start position:0%
+on the ideal cache then if I take a
+ 
+
+ align:start position:0%
+on the ideal cache then if I take a
+fully associative cache that's twice the
+
+ align:start position:0%
+fully associative cache that's twice the
+ 
+
+ align:start position:0%
+fully associative cache that's twice the
+size and use the LRU replacement policy
+
+ align:start position:0%
+size and use the LRU replacement policy
+ 
+
+ align:start position:0%
+size and use the LRU replacement policy
+which is a pretty practical policy then
+
+ align:start position:0%
+which is a pretty practical policy then
+ 
+
+ align:start position:0%
+which is a pretty practical policy then
+the algorithm is going to incur at most
+
+ align:start position:0%
+the algorithm is going to incur at most
+ 
+
+ align:start position:0%
+the algorithm is going to incur at most
+twice the number of cache misses and the
+
+ align:start position:0%
+twice the number of cache misses and the
+ 
+
+ align:start position:0%
+twice the number of cache misses and the
+implication of this Lama is that for
+
+ align:start position:0%
+implication of this Lama is that for
+ 
+
+ align:start position:0%
+implication of this Lama is that for
+asymptotic analysis you can assume
+
+ align:start position:0%
+asymptotic analysis you can assume
+ 
+
+ align:start position:0%
+asymptotic analysis you can assume
+either the optimal replacement policy or
+
+ align:start position:0%
+either the optimal replacement policy or
+ 
+
+ align:start position:0%
+either the optimal replacement policy or
+the LRU replacement policy as convenient
+
+ align:start position:0%
+the LRU replacement policy as convenient
+ 
+
+ align:start position:0%
+the LRU replacement policy as convenient
+because because the cache number of
+
+ align:start position:0%
+because because the cache number of
+ 
+
+ align:start position:0%
+because because the cache number of
+cache misses is just going to be within
+
+ align:start position:0%
+cache misses is just going to be within
+ 
+
+ align:start position:0%
+cache misses is just going to be within
+a constant factor of each other so this
+
+ align:start position:0%
+a constant factor of each other so this
+ 
+
+ align:start position:0%
+a constant factor of each other so this
+is a very important lemma it says that
+
+ align:start position:0%
+is a very important lemma it says that
+ 
+
+ align:start position:0%
+is a very important lemma it says that
+this basically makes it much easier for
+
+ align:start position:0%
+this basically makes it much easier for
+ 
+
+ align:start position:0%
+this basically makes it much easier for
+us to analyze our cache misses and
+
+ align:start position:0%
+us to analyze our cache misses and
+ 
+
+ align:start position:0%
+us to analyze our cache misses and
+algorithms and here's a software
+
+ align:start position:0%
+algorithms and here's a software
+ 
+
+ align:start position:0%
+algorithms and here's a software
+engineering principle that I want to
+
+ align:start position:0%
+engineering principle that I want to
+ 
+
+ align:start position:0%
+engineering principle that I want to
+point out so first when you're trying to
+
+ align:start position:0%
+point out so first when you're trying to
+ 
+
+ align:start position:0%
+point out so first when you're trying to
+get good performance you should come up
+
+ align:start position:0%
+get good performance you should come up
+ 
+
+ align:start position:0%
+get good performance you should come up
+with a theoretically good algorithm that
+
+ align:start position:0%
+with a theoretically good algorithm that
+ 
+
+ align:start position:0%
+with a theoretically good algorithm that
+has good bounds on the work in the cache
+
+ align:start position:0%
+has good bounds on the work in the cache
+ 
+
+ align:start position:0%
+has good bounds on the work in the cache
+complexity and after you come up with a
+
+ align:start position:0%
+complexity and after you come up with a
+ 
+
+ align:start position:0%
+complexity and after you come up with a
+algorithm that's theoretically good then
+
+ align:start position:0%
+algorithm that's theoretically good then
+ 
+
+ align:start position:0%
+algorithm that's theoretically good then
+you start engineering for detailed
+
+ align:start position:0%
+you start engineering for detailed
+ 
+
+ align:start position:0%
+you start engineering for detailed
+performance you start worrying about the
+
+ align:start position:0%
+performance you start worrying about the
+ 
+
+ align:start position:0%
+performance you start worrying about the
+details such as real world caches not
+
+ align:start position:0%
+details such as real world caches not
+ 
+
+ align:start position:0%
+details such as real world caches not
+being full
+
+ align:start position:0%
+being full
+ 
+
+ align:start position:0%
+being full
+associative and for example loads and
+
+ align:start position:0%
+associative and for example loads and
+ 
+
+ align:start position:0%
+associative and for example loads and
+stores having different costs with
+
+ align:start position:0%
+stores having different costs with
+ 
+
+ align:start position:0%
+stores having different costs with
+respect to bandwidth and latency but
+
+ align:start position:0%
+respect to bandwidth and latency but
+ 
+
+ align:start position:0%
+respect to bandwidth and latency but
+coming up with a theoretically good
+
+ align:start position:0%
+coming up with a theoretically good
+ 
+
+ align:start position:0%
+coming up with a theoretically good
+algorithm is the first-order bit to
+
+ align:start position:0%
+algorithm is the first-order bit to
+ 
+
+ align:start position:0%
+algorithm is the first-order bit to
+getting good performance questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's start analyzing the number
+
+ align:start position:0%
+okay so let's start analyzing the number
+ 
+
+ align:start position:0%
+okay so let's start analyzing the number
+of cache misses in program so here's a
+
+ align:start position:0%
+of cache misses in program so here's a
+ 
+
+ align:start position:0%
+of cache misses in program so here's a
+llama
+
+ align:start position:0%
+llama
+ 
+
+ align:start position:0%
+llama
+so the llama says suppose that a program
+
+ align:start position:0%
+so the llama says suppose that a program
+ 
+
+ align:start position:0%
+so the llama says suppose that a program
+reads a set of our data segments where
+
+ align:start position:0%
+reads a set of our data segments where
+ 
+
+ align:start position:0%
+reads a set of our data segments where
+the ithe segment consists of s sub I
+
+ align:start position:0%
+the ithe segment consists of s sub I
+ 
+
+ align:start position:0%
+the ithe segment consists of s sub I
+bytes and suppose that the sum of the
+
+ align:start position:0%
+bytes and suppose that the sum of the
+ 
+
+ align:start position:0%
+bytes and suppose that the sum of the
+sizes of all the segments is equal to N
+
+ align:start position:0%
+sizes of all the segments is equal to N
+ 
+
+ align:start position:0%
+sizes of all the segments is equal to N
+and we're going to assume that n is less
+
+ align:start position:0%
+and we're going to assume that n is less
+ 
+
+ align:start position:0%
+and we're going to assume that n is less
+than M over 3 so the segments the sum of
+
+ align:start position:0%
+than M over 3 so the segments the sum of
+ 
+
+ align:start position:0%
+than M over 3 so the segments the sum of
+the size of the segments is less than
+
+ align:start position:0%
+the size of the segments is less than
+ 
+
+ align:start position:0%
+the size of the segments is less than
+the cache size divided by 3 we're also
+
+ align:start position:0%
+the cache size divided by 3 we're also
+ 
+
+ align:start position:0%
+the cache size divided by 3 we're also
+going to assume that n over R is greater
+
+ align:start position:0%
+going to assume that n over R is greater
+ 
+
+ align:start position:0%
+going to assume that n over R is greater
+than or equal to B so recall that R is
+
+ align:start position:0%
+than or equal to B so recall that R is
+ 
+
+ align:start position:0%
+than or equal to B so recall that R is
+the number of data segments we have and
+
+ align:start position:0%
+the number of data segments we have and
+ 
+
+ align:start position:0%
+the number of data segments we have and
+n is the total size of the segment so
+
+ align:start position:0%
+n is the total size of the segment so
+ 
+
+ align:start position:0%
+n is the total size of the segment so
+what does n over B mean and over R means
+
+ align:start position:0%
+what does n over B mean and over R means
+ 
+
+ align:start position:0%
+what does n over B mean and over R means
+semantically yes yes oh and over R is
+
+ align:start position:0%
+semantically yes yes oh and over R is
+ 
+
+ align:start position:0%
+semantically yes yes oh and over R is
+just the average size of a segment and
+
+ align:start position:0%
+just the average size of a segment and
+ 
+
+ align:start position:0%
+just the average size of a segment and
+here we're saying that the average size
+
+ align:start position:0%
+here we're saying that the average size
+ 
+
+ align:start position:0%
+here we're saying that the average size
+of a segment is at least B's at least
+
+ align:start position:0%
+of a segment is at least B's at least
+ 
+
+ align:start position:0%
+of a segment is at least B's at least
+the size of a cache line so these two
+
+ align:start position:0%
+the size of a cache line so these two
+ 
+
+ align:start position:0%
+the size of a cache line so these two
+assumptions hold then all of the
+
+ align:start position:0%
+assumptions hold then all of the
+ 
+
+ align:start position:0%
+assumptions hold then all of the
+segments are going to fit into cache and
+
+ align:start position:0%
+segments are going to fit into cache and
+ 
+
+ align:start position:0%
+segments are going to fit into cache and
+the number of cache misses to read them
+
+ align:start position:0%
+the number of cache misses to read them
+ 
+
+ align:start position:0%
+the number of cache misses to read them
+all is at most 3 times n over B so if
+
+ align:start position:0%
+all is at most 3 times n over B so if
+ 
+
+ align:start position:0%
+all is at most 3 times n over B so if
+you if you had just a single array of
+
+ align:start position:0%
+you if you had just a single array of
+ 
+
+ align:start position:0%
+you if you had just a single array of
+size n then the number of cache misses
+
+ align:start position:0%
+size n then the number of cache misses
+ 
+
+ align:start position:0%
+size n then the number of cache misses
+you would need to read that array into
+
+ align:start position:0%
+you would need to read that array into
+ 
+
+ align:start position:0%
+you would need to read that array into
+cache is going to be n over B and this
+
+ align:start position:0%
+cache is going to be n over B and this
+ 
+
+ align:start position:0%
+cache is going to be n over B and this
+is saying that even if our data is
+
+ align:start position:0%
+is saying that even if our data is
+ 
+
+ align:start position:0%
+is saying that even if our data is
+divided into a bunch of segments as long
+
+ align:start position:0%
+divided into a bunch of segments as long
+ 
+
+ align:start position:0%
+divided into a bunch of segments as long
+as an average length of the segments is
+
+ align:start position:0%
+as an average length of the segments is
+ 
+
+ align:start position:0%
+as an average length of the segments is
+large enough then a number of cache
+
+ align:start position:0%
+large enough then a number of cache
+ 
+
+ align:start position:0%
+large enough then a number of cache
+misses is just a constant factor worse
+
+ align:start position:0%
+misses is just a constant factor worse
+ 
+
+ align:start position:0%
+misses is just a constant factor worse
+than reading a single array so let's try
+
+ align:start position:0%
+than reading a single array so let's try
+ 
+
+ align:start position:0%
+than reading a single array so let's try
+to prove this cache miss lemma so here's
+
+ align:start position:0%
+to prove this cache miss lemma so here's
+ 
+
+ align:start position:0%
+to prove this cache miss lemma so here's
+a proof so a single segment S sub I is
+
+ align:start position:0%
+a proof so a single segment S sub I is
+ 
+
+ align:start position:0%
+a proof so a single segment S sub I is
+going to incur at most s sub I over B
+
+ align:start position:0%
+going to incur at most s sub I over B
+ 
+
+ align:start position:0%
+going to incur at most s sub I over B
+plus 2 cache misses says anyone want to
+
+ align:start position:0%
+plus 2 cache misses says anyone want to
+ 
+
+ align:start position:0%
+plus 2 cache misses says anyone want to
+tell me where the S sub I over B plus 2
+
+ align:start position:0%
+tell me where the S sub I over B plus 2
+ 
+
+ align:start position:0%
+tell me where the S sub I over B plus 2
+comes from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the let's say this is a
+
+ align:start position:0%
+so this is the let's say this is a
+ 
+
+ align:start position:0%
+so this is the let's say this is a
+segment that we're analyzing and this is
+
+ align:start position:0%
+segment that we're analyzing and this is
+ 
+
+ align:start position:0%
+segment that we're analyzing and this is
+how it's aligned in virtual memory yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so S sub I over B plus two is the
+
+ align:start position:0%
+yeah so S sub I over B plus two is the
+ 
+
+ align:start position:0%
+yeah so S sub I over B plus two is the
+number of blocks that could overlap with
+
+ align:start position:0%
+number of blocks that could overlap with
+ 
+
+ align:start position:0%
+number of blocks that could overlap with
+in the worst case so you need s mi over
+
+ align:start position:0%
+in the worst case so you need s mi over
+ 
+
+ align:start position:0%
+in the worst case so you need s mi over
+B cache missus just to load those s of I
+
+ align:start position:0%
+B cache missus just to load those s of I
+ 
+
+ align:start position:0%
+B cache missus just to load those s of I
+bytes but then the beginning in the end
+
+ align:start position:0%
+bytes but then the beginning in the end
+ 
+
+ align:start position:0%
+bytes but then the beginning in the end
+of that segment might not be perfectly
+
+ align:start position:0%
+of that segment might not be perfectly
+ 
+
+ align:start position:0%
+of that segment might not be perfectly
+aligned with a cache line boundary and
+
+ align:start position:0%
+aligned with a cache line boundary and
+ 
+
+ align:start position:0%
+aligned with a cache line boundary and
+therefore you could waste at most one
+
+ align:start position:0%
+therefore you could waste at most one
+ 
+
+ align:start position:0%
+therefore you could waste at most one
+block on each side of this segment so
+
+ align:start position:0%
+block on each side of this segment so
+ 
+
+ align:start position:0%
+block on each side of this segment so
+that's where the plus two comes from so
+
+ align:start position:0%
+that's where the plus two comes from so
+ 
+
+ align:start position:0%
+that's where the plus two comes from so
+to get the total number of cache misses
+
+ align:start position:0%
+to get the total number of cache misses
+ 
+
+ align:start position:0%
+to get the total number of cache misses
+we just have to sum this quantity from I
+
+ align:start position:0%
+we just have to sum this quantity from I
+ 
+
+ align:start position:0%
+we just have to sum this quantity from I
+equals 1 to R so if I sum s of I over B
+
+ align:start position:0%
+equals 1 to R so if I sum s of I over B
+ 
+
+ align:start position:0%
+equals 1 to R so if I sum s of I over B
+from I equals 1 to R I just get n over B
+
+ align:start position:0%
+from I equals 1 to R I just get n over B
+ 
+
+ align:start position:0%
+from I equals 1 to R I just get n over B
+by definition and then I sum 2 from
+
+ align:start position:0%
+by definition and then I sum 2 from
+ 
+
+ align:start position:0%
+by definition and then I sum 2 from
+idols 1 to R so that just gives me 2 R
+
+ align:start position:0%
+idols 1 to R so that just gives me 2 R
+ 
+
+ align:start position:0%
+idols 1 to R so that just gives me 2 R
+now I'm going to multiply the top and
+
+ align:start position:0%
+now I'm going to multiply the top and
+ 
+
+ align:start position:0%
+now I'm going to multiply the top and
+the bottom of the second term by B so to
+
+ align:start position:0%
+the bottom of the second term by B so to
+ 
+
+ align:start position:0%
+the bottom of the second term by B so to
+R B over B now and then that's less than
+
+ align:start position:0%
+R B over B now and then that's less than
+ 
+
+ align:start position:0%
+R B over B now and then that's less than
+or equal to n over B plus 2 and over B
+
+ align:start position:0%
+or equal to n over B plus 2 and over B
+ 
+
+ align:start position:0%
+or equal to n over B plus 2 and over B
+so where did I get this inequality here
+
+ align:start position:0%
+so where did I get this inequality here
+ 
+
+ align:start position:0%
+so where did I get this inequality here
+why do I know that to R B is less than
+
+ align:start position:0%
+why do I know that to R B is less than
+ 
+
+ align:start position:0%
+why do I know that to R B is less than
+or equal to 2 n yes
+
+ align:start position:0%
+or equal to 2 n yes
+ 
+
+ align:start position:0%
+or equal to 2 n yes
+yes you know that n is greater than or
+
+ align:start position:0%
+yes you know that n is greater than or
+ 
+
+ align:start position:0%
+yes you know that n is greater than or
+equal to BR by this assumption up here
+
+ align:start position:0%
+equal to BR by this assumption up here
+ 
+
+ align:start position:0%
+equal to BR by this assumption up here
+so therefore RB is less than or equal to
+
+ align:start position:0%
+so therefore RB is less than or equal to
+ 
+
+ align:start position:0%
+so therefore RB is less than or equal to
+N and then NB plus 2n be just sums up to
+
+ align:start position:0%
+N and then NB plus 2n be just sums up to
+ 
+
+ align:start position:0%
+N and then NB plus 2n be just sums up to
+3 and B so in the worst case we're gonna
+
+ align:start position:0%
+3 and B so in the worst case we're gonna
+ 
+
+ align:start position:0%
+3 and B so in the worst case we're gonna
+incur 3 and over B cache misses okay so
+
+ align:start position:0%
+incur 3 and over B cache misses okay so
+ 
+
+ align:start position:0%
+incur 3 and over B cache misses okay so
+any questions on this cache miss lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so important thing to remember here is
+
+ align:start position:0%
+so important thing to remember here is
+ 
+
+ align:start position:0%
+so important thing to remember here is
+that if you're if you have a whole bunch
+
+ align:start position:0%
+that if you're if you have a whole bunch
+ 
+
+ align:start position:0%
+that if you're if you have a whole bunch
+of data segments and the average length
+
+ align:start position:0%
+of data segments and the average length
+ 
+
+ align:start position:0%
+of data segments and the average length
+of your segments is large enough bigger
+
+ align:start position:0%
+of your segments is large enough bigger
+ 
+
+ align:start position:0%
+of your segments is large enough bigger
+than a cache block size that you can
+
+ align:start position:0%
+than a cache block size that you can
+ 
+
+ align:start position:0%
+than a cache block size that you can
+access all of these segments just like
+
+ align:start position:0%
+access all of these segments just like
+ 
+
+ align:start position:0%
+access all of these segments just like
+just like a single array it only
+
+ align:start position:0%
+just like a single array it only
+ 
+
+ align:start position:0%
+just like a single array it only
+increases the number of cache misses by
+
+ align:start position:0%
+increases the number of cache misses by
+ 
+
+ align:start position:0%
+increases the number of cache misses by
+a constant factor and if you're doing an
+
+ align:start position:0%
+a constant factor and if you're doing an
+ 
+
+ align:start position:0%
+a constant factor and if you're doing an
+asymptotic analysis then it doesn't
+
+ align:start position:0%
+asymptotic analysis then it doesn't
+ 
+
+ align:start position:0%
+asymptotic analysis then it doesn't
+matter so we're gonna be using this
+
+ align:start position:0%
+matter so we're gonna be using this
+ 
+
+ align:start position:0%
+matter so we're gonna be using this
+cache miss lemma later on when we
+
+ align:start position:0%
+cache miss lemma later on when we
+ 
+
+ align:start position:0%
+cache miss lemma later on when we
+analyze algorithms ok so another
+
+ align:start position:0%
+analyze algorithms ok so another
+ 
+
+ align:start position:0%
+analyze algorithms ok so another
+assumption that we're gonna need is
+
+ align:start position:0%
+assumption that we're gonna need is
+ 
+
+ align:start position:0%
+assumption that we're gonna need is
+called the tall cache assumption and the
+
+ align:start position:0%
+called the tall cache assumption and the
+ 
+
+ align:start position:0%
+called the tall cache assumption and the
+tall cache assumption basically says
+
+ align:start position:0%
+tall cache assumption basically says
+ 
+
+ align:start position:0%
+tall cache assumption basically says
+that the cache is taller than it is wide
+
+ align:start position:0%
+that the cache is taller than it is wide
+ 
+
+ align:start position:0%
+that the cache is taller than it is wide
+so says that B squared is less than cm
+
+ align:start position:0%
+so says that B squared is less than cm
+ 
+
+ align:start position:0%
+so says that B squared is less than cm
+for some sufficiently small constant C
+
+ align:start position:0%
+for some sufficiently small constant C
+ 
+
+ align:start position:0%
+for some sufficiently small constant C
+less than or equal to 1 so in other
+
+ align:start position:0%
+less than or equal to 1 so in other
+ 
+
+ align:start position:0%
+less than or equal to 1 so in other
+words it says that the number of cache
+
+ align:start position:0%
+words it says that the number of cache
+ 
+
+ align:start position:0%
+words it says that the number of cache
+lines and over B you have is going to be
+
+ align:start position:0%
+lines and over B you have is going to be
+ 
+
+ align:start position:0%
+lines and over B you have is going to be
+bigger than B and this tall cache
+
+ align:start position:0%
+bigger than B and this tall cache
+ 
+
+ align:start position:0%
+bigger than B and this tall cache
+assumption is usually satisfied in
+
+ align:start position:0%
+assumption is usually satisfied in
+ 
+
+ align:start position:0%
+assumption is usually satisfied in
+practice so here the cache line sizes
+
+ align:start position:0%
+practice so here the cache line sizes
+ 
+
+ align:start position:0%
+practice so here the cache line sizes
+and the cache sizes on the machines that
+
+ align:start position:0%
+and the cache sizes on the machines that
+ 
+
+ align:start position:0%
+and the cache sizes on the machines that
+we're using so cache line size is 64
+
+ align:start position:0%
+we're using so cache line size is 64
+ 
+
+ align:start position:0%
+we're using so cache line size is 64
+bytes and the l1 cache size is 32
+
+ align:start position:0%
+bytes and the l1 cache size is 32
+ 
+
+ align:start position:0%
+bytes and the l1 cache size is 32
+kilobytes so 64 bytes squared that's 2
+
+ align:start position:0%
+kilobytes so 64 bytes squared that's 2
+ 
+
+ align:start position:0%
+kilobytes so 64 bytes squared that's 2
+to 12 and 32 kilobytes less to 215th
+
+ align:start position:0%
+to 12 and 32 kilobytes less to 215th
+ 
+
+ align:start position:0%
+to 12 and 32 kilobytes less to 215th
+bytes so 2 to 12 is less than 2 to 15 so
+
+ align:start position:0%
+bytes so 2 to 12 is less than 2 to 15 so
+ 
+
+ align:start position:0%
+bytes so 2 to 12 is less than 2 to 15 so
+it satisfies a tall cache assumption and
+
+ align:start position:0%
+it satisfies a tall cache assumption and
+ 
+
+ align:start position:0%
+it satisfies a tall cache assumption and
+as we go up the memory hierarchy the
+
+ align:start position:0%
+as we go up the memory hierarchy the
+ 
+
+ align:start position:0%
+as we go up the memory hierarchy the
+cache size increases but the cache line
+
+ align:start position:0%
+cache size increases but the cache line
+ 
+
+ align:start position:0%
+cache size increases but the cache line
+length stays the same so
+
+ align:start position:0%
+length stays the same so
+ 
+
+ align:start position:0%
+length stays the same so
+the cash has become even taller as we
+
+ align:start position:0%
+the cash has become even taller as we
+ 
+
+ align:start position:0%
+the cash has become even taller as we
+move up the memory hierarchy so let's
+
+ align:start position:0%
+move up the memory hierarchy so let's
+ 
+
+ align:start position:0%
+move up the memory hierarchy so let's
+see why this tall cache assumption is
+
+ align:start position:0%
+see why this tall cache assumption is
+ 
+
+ align:start position:0%
+see why this tall cache assumption is
+going to be useful to see that we're
+
+ align:start position:0%
+going to be useful to see that we're
+ 
+
+ align:start position:0%
+going to be useful to see that we're
+going to look at what's wrong with a
+
+ align:start position:0%
+going to look at what's wrong with a
+ 
+
+ align:start position:0%
+going to look at what's wrong with a
+short cache
+
+ align:start position:0%
+short cache
+ 
+
+ align:start position:0%
+short cache
+so in the short cache our lines are
+
+ align:start position:0%
+so in the short cache our lines are
+ 
+
+ align:start position:0%
+so in the short cache our lines are
+going to be very wide and they're wider
+
+ align:start position:0%
+going to be very wide and they're wider
+ 
+
+ align:start position:0%
+going to be very wide and they're wider
+than the number of lines that we can
+
+ align:start position:0%
+than the number of lines that we can
+ 
+
+ align:start position:0%
+than the number of lines that we can
+have in our cache and let's say we're
+
+ align:start position:0%
+have in our cache and let's say we're
+ 
+
+ align:start position:0%
+have in our cache and let's say we're
+working with an N by n sub matrix sort
+
+ align:start position:0%
+working with an N by n sub matrix sort
+ 
+
+ align:start position:0%
+working with an N by n sub matrix sort
+and row major order if you have a short
+
+ align:start position:0%
+and row major order if you have a short
+ 
+
+ align:start position:0%
+and row major order if you have a short
+cache then even if n squared is less
+
+ align:start position:0%
+cache then even if n squared is less
+ 
+
+ align:start position:0%
+cache then even if n squared is less
+than cm meaning that you can fit all the
+
+ align:start position:0%
+than cm meaning that you can fit all the
+ 
+
+ align:start position:0%
+than cm meaning that you can fit all the
+bytes of the sub matrix in cache you
+
+ align:start position:0%
+bytes of the sub matrix in cache you
+ 
+
+ align:start position:0%
+bytes of the sub matrix in cache you
+might still not be able to fit it into a
+
+ align:start position:0%
+might still not be able to fit it into a
+ 
+
+ align:start position:0%
+might still not be able to fit it into a
+short cache and this picture sort of
+
+ align:start position:0%
+short cache and this picture sort of
+ 
+
+ align:start position:0%
+short cache and this picture sort of
+illustrates this so we have n rows here
+
+ align:start position:0%
+illustrates this so we have n rows here
+ 
+
+ align:start position:0%
+illustrates this so we have n rows here
+but we can only fit M over B of the rows
+
+ align:start position:0%
+but we can only fit M over B of the rows
+ 
+
+ align:start position:0%
+but we can only fit M over B of the rows
+in the cache because the the cache lines
+
+ align:start position:0%
+in the cache because the the cache lines
+ 
+
+ align:start position:0%
+in the cache because the the cache lines
+are so long and we're actually wasting a
+
+ align:start position:0%
+are so long and we're actually wasting a
+ 
+
+ align:start position:0%
+are so long and we're actually wasting a
+lot of space on each of the cache lines
+
+ align:start position:0%
+lot of space on each of the cache lines
+ 
+
+ align:start position:0%
+lot of space on each of the cache lines
+we're only using a very small fraction
+
+ align:start position:0%
+we're only using a very small fraction
+ 
+
+ align:start position:0%
+we're only using a very small fraction
+of each cache line to store the row of
+
+ align:start position:0%
+of each cache line to store the row of
+ 
+
+ align:start position:0%
+of each cache line to store the row of
+this sub matrix if we if this were the
+
+ align:start position:0%
+this sub matrix if we if this were the
+ 
+
+ align:start position:0%
+this sub matrix if we if this were the
+entire matrix then it would actually be
+
+ align:start position:0%
+entire matrix then it would actually be
+ 
+
+ align:start position:0%
+entire matrix then it would actually be
+okay because consecutive rows are going
+
+ align:start position:0%
+okay because consecutive rows are going
+ 
+
+ align:start position:0%
+okay because consecutive rows are going
+to be placed together consecutively in
+
+ align:start position:0%
+to be placed together consecutively in
+ 
+
+ align:start position:0%
+to be placed together consecutively in
+memory but if this is a sub matrix then
+
+ align:start position:0%
+memory but if this is a sub matrix then
+ 
+
+ align:start position:0%
+memory but if this is a sub matrix then
+we can't be guaranteed that the next row
+
+ align:start position:0%
+we can't be guaranteed that the next row
+ 
+
+ align:start position:0%
+we can't be guaranteed that the next row
+is going to be placed right after the
+
+ align:start position:0%
+is going to be placed right after the
+ 
+
+ align:start position:0%
+is going to be placed right after the
+current row and oftentimes we have to
+
+ align:start position:0%
+current row and oftentimes we have to
+ 
+
+ align:start position:0%
+current row and oftentimes we have to
+deal with sub matrices when we're doing
+
+ align:start position:0%
+deal with sub matrices when we're doing
+ 
+
+ align:start position:0%
+deal with sub matrices when we're doing
+recursive matrix algorithms okay so this
+
+ align:start position:0%
+recursive matrix algorithms okay so this
+ 
+
+ align:start position:0%
+recursive matrix algorithms okay so this
+is what's wrong with short caches and
+
+ align:start position:0%
+is what's wrong with short caches and
+ 
+
+ align:start position:0%
+is what's wrong with short caches and
+that's why we want to assume the tall
+
+ align:start position:0%
+that's why we want to assume the tall
+ 
+
+ align:start position:0%
+that's why we want to assume the tall
+cache assumption and we can assume that
+
+ align:start position:0%
+cache assumption and we can assume that
+ 
+
+ align:start position:0%
+cache assumption and we can assume that
+because it's usually satisfied in
+
+ align:start position:0%
+because it's usually satisfied in
+ 
+
+ align:start position:0%
+because it's usually satisfied in
+practice the TLB actually tends to be
+
+ align:start position:0%
+practice the TLB actually tends to be
+ 
+
+ align:start position:0%
+practice the TLB actually tends to be
+short it only has a couple entries so it
+
+ align:start position:0%
+short it only has a couple entries so it
+ 
+
+ align:start position:0%
+short it only has a couple entries so it
+might not satisfy the tall cache
+
+ align:start position:0%
+might not satisfy the tall cache
+ 
+
+ align:start position:0%
+might not satisfy the tall cache
+assumption but all the other caches will
+
+ align:start position:0%
+assumption but all the other caches will
+ 
+
+ align:start position:0%
+assumption but all the other caches will
+satisfy this assumption any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here's another llama that's going to
+
+ align:start position:0%
+so here's another llama that's going to
+ 
+
+ align:start position:0%
+so here's another llama that's going to
+be useful this is called the sub-matrix
+
+ align:start position:0%
+be useful this is called the sub-matrix
+ 
+
+ align:start position:0%
+be useful this is called the sub-matrix
+caching llama so suppose that we have an
+
+ align:start position:0%
+caching llama so suppose that we have an
+ 
+
+ align:start position:0%
+caching llama so suppose that we have an
+N by n matrix a and it's read into a
+
+ align:start position:0%
+N by n matrix a and it's read into a
+ 
+
+ align:start position:0%
+N by n matrix a and it's read into a
+tall cache that satisfies B squared less
+
+ align:start position:0%
+tall cache that satisfies B squared less
+ 
+
+ align:start position:0%
+tall cache that satisfies B squared less
+than cm for some constant C less than
+
+ align:start position:0%
+than cm for some constant C less than
+ 
+
+ align:start position:0%
+than cm for some constant C less than
+equal to 1 and suppose that N squared is
+
+ align:start position:0%
+equal to 1 and suppose that N squared is
+ 
+
+ align:start position:0%
+equal to 1 and suppose that N squared is
+less than M over 3 but it's greater than
+
+ align:start position:0%
+less than M over 3 but it's greater than
+ 
+
+ align:start position:0%
+less than M over 3 but it's greater than
+or equal to CM then a is going to fit
+
+ align:start position:0%
+or equal to CM then a is going to fit
+ 
+
+ align:start position:0%
+or equal to CM then a is going to fit
+into cache in a number of cache misses
+
+ align:start position:0%
+into cache in a number of cache misses
+ 
+
+ align:start position:0%
+into cache in a number of cache misses
+required to read all of ADEs elements
+
+ align:start position:0%
+required to read all of ADEs elements
+ 
+
+ align:start position:0%
+required to read all of ADEs elements
+into cache is at most 3 n squared over B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so let's see why this is true so
+
+ align:start position:0%
+ok so let's see why this is true so
+ 
+
+ align:start position:0%
+ok so let's see why this is true so
+we're gonna let big n denote the total
+
+ align:start position:0%
+we're gonna let big n denote the total
+ 
+
+ align:start position:0%
+we're gonna let big n denote the total
+number of bytes that we need to access
+
+ align:start position:0%
+number of bytes that we need to access
+ 
+
+ align:start position:0%
+number of bytes that we need to access
+so big n is going to be equal to N
+
+ align:start position:0%
+so big n is going to be equal to N
+ 
+
+ align:start position:0%
+so big n is going to be equal to N
+squared and we're gonna use the cache
+
+ align:start position:0%
+squared and we're gonna use the cache
+ 
+
+ align:start position:0%
+squared and we're gonna use the cache
+miss lemma which says that if the
+
+ align:start position:0%
+miss lemma which says that if the
+ 
+
+ align:start position:0%
+miss lemma which says that if the
+average length of our segments is large
+
+ align:start position:0%
+average length of our segments is large
+ 
+
+ align:start position:0%
+average length of our segments is large
+enough that we can read all the segments
+
+ align:start position:0%
+enough that we can read all the segments
+ 
+
+ align:start position:0%
+enough that we can read all the segments
+in just like it were a single contiguous
+
+ align:start position:0%
+in just like it were a single contiguous
+ 
+
+ align:start position:0%
+in just like it were a single contiguous
+array so the lengths of our segments
+
+ align:start position:0%
+array so the lengths of our segments
+ 
+
+ align:start position:0%
+array so the lengths of our segments
+here are going to be little n so R is
+
+ align:start position:0%
+here are going to be little n so R is
+ 
+
+ align:start position:0%
+here are going to be little n so R is
+gonna be little N and that's also the
+
+ align:start position:0%
+gonna be little N and that's also the
+ 
+
+ align:start position:0%
+gonna be little N and that's also the
+number of segments is going to be little
+
+ align:start position:0%
+number of segments is going to be little
+ 
+
+ align:start position:0%
+number of segments is going to be little
+and and the segment length is also going
+
+ align:start position:0%
+and and the segment length is also going
+ 
+
+ align:start position:0%
+and and the segment length is also going
+to be little ends since we're working
+
+ align:start position:0%
+to be little ends since we're working
+ 
+
+ align:start position:0%
+to be little ends since we're working
+with a square sub-matrix here and then
+
+ align:start position:0%
+with a square sub-matrix here and then
+ 
+
+ align:start position:0%
+with a square sub-matrix here and then
+we also have that the cache block size B
+
+ align:start position:0%
+we also have that the cache block size B
+ 
+
+ align:start position:0%
+we also have that the cache block size B
+is less than or equal to N and that's
+
+ align:start position:0%
+is less than or equal to N and that's
+ 
+
+ align:start position:0%
+is less than or equal to N and that's
+equal to big and over R and where do we
+
+ align:start position:0%
+equal to big and over R and where do we
+ 
+
+ align:start position:0%
+equal to big and over R and where do we
+get this property that B is less than or
+
+ align:start position:0%
+get this property that B is less than or
+ 
+
+ align:start position:0%
+get this property that B is less than or
+equal to n so I made some assumptions up
+
+ align:start position:0%
+equal to n so I made some assumptions up
+ 
+
+ align:start position:0%
+equal to n so I made some assumptions up
+here where I can use to infer that B is
+
+ align:start position:0%
+here where I can use to infer that B is
+ 
+
+ align:start position:0%
+here where I can use to infer that B is
+less than or equal to n does anybody see
+
+ align:start position:0%
+less than or equal to n does anybody see
+ 
+
+ align:start position:0%
+less than or equal to n does anybody see
+where yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I know that B squared is less
+
+ align:start position:0%
+yeah so I know that B squared is less
+ 
+
+ align:start position:0%
+yeah so I know that B squared is less
+than cm cm is less than or equal to n
+
+ align:start position:0%
+than cm cm is less than or equal to n
+ 
+
+ align:start position:0%
+than cm cm is less than or equal to n
+square so therefore B squared is less
+
+ align:start position:0%
+square so therefore B squared is less
+ 
+
+ align:start position:0%
+square so therefore B squared is less
+than N squared in B is less than n so so
+
+ align:start position:0%
+than N squared in B is less than n so so
+ 
+
+ align:start position:0%
+than N squared in B is less than n so so
+now I also have that n is less than M
+
+ align:start position:0%
+now I also have that n is less than M
+ 
+
+ align:start position:0%
+now I also have that n is less than M
+over 3 just by assumption and therefore
+
+ align:start position:0%
+over 3 just by assumption and therefore
+ 
+
+ align:start position:0%
+over 3 just by assumption and therefore
+I can use the cache miss lemma so the
+
+ align:start position:0%
+I can use the cache miss lemma so the
+ 
+
+ align:start position:0%
+I can use the cache miss lemma so the
+cache miss lemma tells me that I only
+
+ align:start position:0%
+cache miss lemma tells me that I only
+ 
+
+ align:start position:0%
+cache miss lemma tells me that I only
+need a total of 3 N squared over B cache
+
+ align:start position:0%
+need a total of 3 N squared over B cache
+ 
+
+ align:start position:0%
+need a total of 3 N squared over B cache
+misses to read this whole thing in any
+
+ align:start position:0%
+misses to read this whole thing in any
+ 
+
+ align:start position:0%
+misses to read this whole thing in any
+questions on the sub-matrix hashing
+
+ align:start position:0%
+questions on the sub-matrix hashing
+ 
+
+ align:start position:0%
+questions on the sub-matrix hashing
+lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's analyze matrix
+
+ align:start position:0%
+okay so now let's analyze matrix
+ 
+
+ align:start position:0%
+okay so now let's analyze matrix
+multiplication so how many of you have
+
+ align:start position:0%
+multiplication so how many of you have
+ 
+
+ align:start position:0%
+multiplication so how many of you have
+seen matrix multiplication before so a
+
+ align:start position:0%
+seen matrix multiplication before so a
+ 
+
+ align:start position:0%
+seen matrix multiplication before so a
+couple of you okay so here's what the
+
+ align:start position:0%
+couple of you okay so here's what the
+ 
+
+ align:start position:0%
+couple of you okay so here's what the
+code looks like for the standard cubic
+
+ align:start position:0%
+code looks like for the standard cubic
+ 
+
+ align:start position:0%
+code looks like for the standard cubic
+work matrix multiplication algorithm so
+
+ align:start position:0%
+work matrix multiplication algorithm so
+ 
+
+ align:start position:0%
+work matrix multiplication algorithm so
+we have two input matrices a and B and
+
+ align:start position:0%
+we have two input matrices a and B and
+ 
+
+ align:start position:0%
+we have two input matrices a and B and
+we're gonna store the result in C and
+
+ align:start position:0%
+we're gonna store the result in C and
+ 
+
+ align:start position:0%
+we're gonna store the result in C and
+the height in the width of our matrix is
+
+ align:start position:0%
+the height in the width of our matrix is
+ 
+
+ align:start position:0%
+the height in the width of our matrix is
+n we're just going to deal with square
+
+ align:start position:0%
+n we're just going to deal with square
+ 
+
+ align:start position:0%
+n we're just going to deal with square
+matrices here but what I'm going to talk
+
+ align:start position:0%
+matrices here but what I'm going to talk
+ 
+
+ align:start position:0%
+matrices here but what I'm going to talk
+about also extends to non square
+
+ align:start position:0%
+about also extends to non square
+ 
+
+ align:start position:0%
+about also extends to non square
+matrices and then we just have three
+
+ align:start position:0%
+matrices and then we just have three
+ 
+
+ align:start position:0%
+matrices and then we just have three
+loops here we're going to loop through I
+
+ align:start position:0%
+loops here we're going to loop through I
+ 
+
+ align:start position:0%
+loops here we're going to loop through I
+from 0 to n minus 1 J from 0 to n minus
+
+ align:start position:0%
+from 0 to n minus 1 J from 0 to n minus
+ 
+
+ align:start position:0%
+from 0 to n minus 1 J from 0 to n minus
+1 and K from 0 to n minus 1 and then
+
+ align:start position:0%
+1 and K from 0 to n minus 1 and then
+ 
+
+ align:start position:0%
+1 and K from 0 to n minus 1 and then
+we're gonna let C of I n plus J be
+
+ align:start position:0%
+we're gonna let C of I n plus J be
+ 
+
+ align:start position:0%
+we're gonna let C of I n plus J be
+incremented by a of I n plus K times B
+
+ align:start position:0%
+incremented by a of I n plus K times B
+ 
+
+ align:start position:0%
+incremented by a of I n plus K times B
+of K n plus J so this is just the
+
+ align:start position:0%
+of K n plus J so this is just the
+ 
+
+ align:start position:0%
+of K n plus J so this is just the
+standard code for matrix multiply so
+
+ align:start position:0%
+standard code for matrix multiply so
+ 
+
+ align:start position:0%
+standard code for matrix multiply so
+what's the work of this algorithm should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be all should be review for all of you
+
+ align:start position:0%
+be all should be review for all of you
+ 
+
+ align:start position:0%
+be all should be review for all of you
+and cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's analyze the number of
+
+ align:start position:0%
+okay so now let's analyze the number of
+ 
+
+ align:start position:0%
+okay so now let's analyze the number of
+cache misses this algorithm is going to
+
+ align:start position:0%
+cache misses this algorithm is going to
+ 
+
+ align:start position:0%
+cache misses this algorithm is going to
+incur and again we're gonna assume that
+
+ align:start position:0%
+incur and again we're gonna assume that
+ 
+
+ align:start position:0%
+incur and again we're gonna assume that
+the matrix is in row major order and we
+
+ align:start position:0%
+the matrix is in row major order and we
+ 
+
+ align:start position:0%
+the matrix is in row major order and we
+satisfy the tall cache assumption we're
+
+ align:start position:0%
+satisfy the tall cache assumption we're
+ 
+
+ align:start position:0%
+satisfy the tall cache assumption we're
+also going to analyze the number of
+
+ align:start position:0%
+also going to analyze the number of
+ 
+
+ align:start position:0%
+also going to analyze the number of
+cache misses in matrix B because it
+
+ align:start position:0%
+cache misses in matrix B because it
+ 
+
+ align:start position:0%
+cache misses in matrix B because it
+turns out that the number of cache
+
+ align:start position:0%
+turns out that the number of cache
+ 
+
+ align:start position:0%
+turns out that the number of cache
+misses incurred by matrix B is going to
+
+ align:start position:0%
+misses incurred by matrix B is going to
+ 
+
+ align:start position:0%
+misses incurred by matrix B is going to
+dominate the number of cache misses
+
+ align:start position:0%
+dominate the number of cache misses
+ 
+
+ align:start position:0%
+dominate the number of cache misses
+overall in there are three cases we need
+
+ align:start position:0%
+overall in there are three cases we need
+ 
+
+ align:start position:0%
+overall in there are three cases we need
+to consider the first case is when n is
+
+ align:start position:0%
+to consider the first case is when n is
+ 
+
+ align:start position:0%
+to consider the first case is when n is
+greater than C M over B for some
+
+ align:start position:0%
+greater than C M over B for some
+ 
+
+ align:start position:0%
+greater than C M over B for some
+constant C and we're gonna analyze
+
+ align:start position:0%
+constant C and we're gonna analyze
+ 
+
+ align:start position:0%
+constant C and we're gonna analyze
+matrix B as I said and we're also going
+
+ align:start position:0%
+matrix B as I said and we're also going
+ 
+
+ align:start position:0%
+matrix B as I said and we're also going
+to assume LRU because we can if you
+
+ align:start position:0%
+to assume LRU because we can if you
+ 
+
+ align:start position:0%
+to assume LRU because we can if you
+recall the LRU lemma it says that
+
+ align:start position:0%
+recall the LRU lemma it says that
+ 
+
+ align:start position:0%
+recall the LRU lemma it says that
+whatever we analyzed using the LRU is
+
+ align:start position:0%
+whatever we analyzed using the LRU is
+ 
+
+ align:start position:0%
+whatever we analyzed using the LRU is
+just going to be a constant factor
+
+ align:start position:0%
+just going to be a constant factor
+ 
+
+ align:start position:0%
+just going to be a constant factor
+within what we analyzed using the ideal
+
+ align:start position:0%
+within what we analyzed using the ideal
+ 
+
+ align:start position:0%
+within what we analyzed using the ideal
+cache so so to do this matrix
+
+ align:start position:0%
+cache so so to do this matrix
+ 
+
+ align:start position:0%
+cache so so to do this matrix
+multiplication I'm going to go through
+
+ align:start position:0%
+multiplication I'm going to go through
+ 
+
+ align:start position:0%
+multiplication I'm going to go through
+one row of a and one column of B and do
+
+ align:start position:0%
+one row of a and one column of B and do
+ 
+
+ align:start position:0%
+one row of a and one column of B and do
+the dot product there this is what
+
+ align:start position:0%
+the dot product there this is what
+ 
+
+ align:start position:0%
+the dot product there this is what
+happens in the innermost loop and how
+
+ align:start position:0%
+happens in the innermost loop and how
+ 
+
+ align:start position:0%
+happens in the innermost loop and how
+many cache misses am I going to incur
+
+ align:start position:0%
+many cache misses am I going to incur
+ 
+
+ align:start position:0%
+many cache misses am I going to incur
+when I go down one column of B here so
+
+ align:start position:0%
+when I go down one column of B here so
+ 
+
+ align:start position:0%
+when I go down one column of B here so
+here I have the case where n is greater
+
+ align:start position:0%
+here I have the case where n is greater
+ 
+
+ align:start position:0%
+here I have the case where n is greater
+than M over B so I can't fit all of I
+
+ align:start position:0%
+than M over B so I can't fit all of I
+ 
+
+ align:start position:0%
+than M over B so I can't fit all of I
+can't fit one block from each row into
+
+ align:start position:0%
+can't fit one block from each row into
+ 
+
+ align:start position:0%
+can't fit one block from each row into
+the cache so how many cache misses do I
+
+ align:start position:0%
+the cache so how many cache misses do I
+ 
+
+ align:start position:0%
+the cache so how many cache misses do I
+have the first time I go down a column
+
+ align:start position:0%
+have the first time I go down a column
+ 
+
+ align:start position:0%
+have the first time I go down a column
+of B so how many rows of B do I have and
+
+ align:start position:0%
+of B so how many rows of B do I have and
+ 
+
+ align:start position:0%
+of B so how many rows of B do I have and
+yeah and how many cache misses do I need
+
+ align:start position:0%
+yeah and how many cache misses do I need
+ 
+
+ align:start position:0%
+yeah and how many cache misses do I need
+for each row one so in total I'm going
+
+ align:start position:0%
+for each row one so in total I'm going
+ 
+
+ align:start position:0%
+for each row one so in total I'm going
+to need n cache misses for the first
+
+ align:start position:0%
+to need n cache misses for the first
+ 
+
+ align:start position:0%
+to need n cache misses for the first
+column of B what about the second column
+
+ align:start position:0%
+column of B what about the second column
+ 
+
+ align:start position:0%
+column of B what about the second column
+of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so recall that I'm assuming the LRU
+
+ align:start position:0%
+so recall that I'm assuming the LRU
+ 
+
+ align:start position:0%
+so recall that I'm assuming the LRU
+replacement policy here so when the
+
+ align:start position:0%
+replacement policy here so when the
+ 
+
+ align:start position:0%
+replacement policy here so when the
+cache is full
+
+ align:start position:0%
+cache is full
+ 
+
+ align:start position:0%
+cache is full
+I'm gonna evict the thing that was least
+
+ align:start position:0%
+I'm gonna evict the thing that was least
+ 
+
+ align:start position:0%
+I'm gonna evict the thing that was least
+recently used used the furthest in the
+
+ align:start position:0%
+recently used used the furthest in the
+ 
+
+ align:start position:0%
+recently used used the furthest in the
+past
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry could you repeat that yes it's
+
+ align:start position:0%
+sorry could you repeat that yes it's
+ 
+
+ align:start position:0%
+sorry could you repeat that yes it's
+still gonna be n why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it's still gonna be n because I
+
+ align:start position:0%
+yeah so it's still gonna be n because I
+ 
+
+ align:start position:0%
+yeah so it's still gonna be n because I
+can't fit one cache block from each row
+
+ align:start position:0%
+can't fit one cache block from each row
+ 
+
+ align:start position:0%
+can't fit one cache block from each row
+into my cache and by the time I get back
+
+ align:start position:0%
+into my cache and by the time I get back
+ 
+
+ align:start position:0%
+into my cache and by the time I get back
+to the top of my matrix B the top block
+
+ align:start position:0%
+to the top of my matrix B the top block
+ 
+
+ align:start position:0%
+to the top of my matrix B the top block
+has already been evicted from the cache
+
+ align:start position:0%
+has already been evicted from the cache
+ 
+
+ align:start position:0%
+has already been evicted from the cache
+and I have to load it back in and this
+
+ align:start position:0%
+and I have to load it back in and this
+ 
+
+ align:start position:0%
+and I have to load it back in and this
+is the same for every other block that I
+
+ align:start position:0%
+is the same for every other block that I
+ 
+
+ align:start position:0%
+is the same for every other block that I
+access I'm again gonna need n cache
+
+ align:start position:0%
+access I'm again gonna need n cache
+ 
+
+ align:start position:0%
+access I'm again gonna need n cache
+misses for the second column of B and
+
+ align:start position:0%
+misses for the second column of B and
+ 
+
+ align:start position:0%
+misses for the second column of B and
+this is going to be the same for all the
+
+ align:start position:0%
+this is going to be the same for all the
+ 
+
+ align:start position:0%
+this is going to be the same for all the
+columns of B and I have to do this again
+
+ align:start position:0%
+columns of B and I have to do this again
+ 
+
+ align:start position:0%
+columns of B and I have to do this again
+for the second row of a so in total I'm
+
+ align:start position:0%
+for the second row of a so in total I'm
+ 
+
+ align:start position:0%
+for the second row of a so in total I'm
+going to need theta of n cubed number of
+
+ align:start position:0%
+going to need theta of n cubed number of
+ 
+
+ align:start position:0%
+going to need theta of n cubed number of
+cache misses and this is one cache miss
+
+ align:start position:0%
+cache misses and this is one cache miss
+ 
+
+ align:start position:0%
+cache misses and this is one cache miss
+per per entry that I access in B and
+
+ align:start position:0%
+per per entry that I access in B and
+ 
+
+ align:start position:0%
+per per entry that I access in B and
+this is not very good because the total
+
+ align:start position:0%
+this is not very good because the total
+ 
+
+ align:start position:0%
+this is not very good because the total
+work was also theta of n cube so I'm not
+
+ align:start position:0%
+work was also theta of n cube so I'm not
+ 
+
+ align:start position:0%
+work was also theta of n cube so I'm not
+gaining anything from having any
+
+ align:start position:0%
+gaining anything from having any
+ 
+
+ align:start position:0%
+gaining anything from having any
+locality in this in this algorithm here
+
+ align:start position:0%
+locality in this in this algorithm here
+ 
+
+ align:start position:0%
+locality in this in this algorithm here
+so any questions on this analysis so
+
+ align:start position:0%
+so any questions on this analysis so
+ 
+
+ align:start position:0%
+so any questions on this analysis so
+this is just a case one let's look at
+
+ align:start position:0%
+this is just a case one let's look at
+ 
+
+ align:start position:0%
+this is just a case one let's look at
+case two so in this case n is less than
+
+ align:start position:0%
+case two so in this case n is less than
+ 
+
+ align:start position:0%
+case two so in this case n is less than
+C M over B so I can fit one block from
+
+ align:start position:0%
+C M over B so I can fit one block from
+ 
+
+ align:start position:0%
+C M over B so I can fit one block from
+each row of B into cache and then n is
+
+ align:start position:0%
+each row of B into cache and then n is
+ 
+
+ align:start position:0%
+each row of B into cache and then n is
+also greater than another constant C
+
+ align:start position:0%
+also greater than another constant C
+ 
+
+ align:start position:0%
+also greater than another constant C
+prime times square root of M so I can't
+
+ align:start position:0%
+prime times square root of M so I can't
+ 
+
+ align:start position:0%
+prime times square root of M so I can't
+fit the whole matrix into cache and
+
+ align:start position:0%
+fit the whole matrix into cache and
+ 
+
+ align:start position:0%
+fit the whole matrix into cache and
+again let's analyze the number of cache
+
+ align:start position:0%
+again let's analyze the number of cache
+ 
+
+ align:start position:0%
+again let's analyze the number of cache
+misses incurred by accessing be assuming
+
+ align:start position:0%
+misses incurred by accessing be assuming
+ 
+
+ align:start position:0%
+misses incurred by accessing be assuming
+LRU so how many cache misses am I going
+
+ align:start position:0%
+LRU so how many cache misses am I going
+ 
+
+ align:start position:0%
+LRU so how many cache misses am I going
+to incur for the first column of B and
+
+ align:start position:0%
+to incur for the first column of B and
+ 
+
+ align:start position:0%
+to incur for the first column of B and
+so the same as before what about the
+
+ align:start position:0%
+so the same as before what about the
+ 
+
+ align:start position:0%
+so the same as before what about the
+second column of B so by the time I get
+
+ align:start position:0%
+second column of B so by the time I get
+ 
+
+ align:start position:0%
+second column of B so by the time I get
+to the beginning of the beginning of the
+
+ align:start position:0%
+to the beginning of the beginning of the
+ 
+
+ align:start position:0%
+to the beginning of the beginning of the
+matrix here is the top block going to be
+
+ align:start position:0%
+matrix here is the top block going to be
+ 
+
+ align:start position:0%
+matrix here is the top block going to be
+in cache so who thinks the block is
+
+ align:start position:0%
+in cache so who thinks the block is
+ 
+
+ align:start position:0%
+in cache so who thinks the block is
+still gonna be in cache when I get back
+
+ align:start position:0%
+still gonna be in cache when I get back
+ 
+
+ align:start position:0%
+still gonna be in cache when I get back
+to the beginning yeah so a couple of
+
+ align:start position:0%
+to the beginning yeah so a couple of
+ 
+
+ align:start position:0%
+to the beginning yeah so a couple of
+people who think is gonna be out of
+
+ align:start position:0%
+people who think is gonna be out of
+ 
+
+ align:start position:0%
+people who think is gonna be out of
+cache okay so turns out it is going to
+
+ align:start position:0%
+cache okay so turns out it is going to
+ 
+
+ align:start position:0%
+cache okay so turns out it is going to
+be in cache because I can fit one block
+
+ align:start position:0%
+be in cache because I can fit one block
+ 
+
+ align:start position:0%
+be in cache because I can fit one block
+for every row of B into my
+
+ align:start position:0%
+for every row of B into my
+ 
+
+ align:start position:0%
+for every row of B into my
+since I have n less than cm over B so
+
+ align:start position:0%
+since I have n less than cm over B so
+ 
+
+ align:start position:0%
+since I have n less than cm over B so
+therefore when I get to the beginning of
+
+ align:start position:0%
+therefore when I get to the beginning of
+ 
+
+ align:start position:0%
+therefore when I get to the beginning of
+the second column that block is still
+
+ align:start position:0%
+the second column that block is still
+ 
+
+ align:start position:0%
+the second column that block is still
+gonna be in cash because I loaded it in
+
+ align:start position:0%
+gonna be in cash because I loaded it in
+ 
+
+ align:start position:0%
+gonna be in cash because I loaded it in
+when I was accessing the first column so
+
+ align:start position:0%
+when I was accessing the first column so
+ 
+
+ align:start position:0%
+when I was accessing the first column so
+I'm not gonna incur any cash misses for
+
+ align:start position:0%
+I'm not gonna incur any cash misses for
+ 
+
+ align:start position:0%
+I'm not gonna incur any cash misses for
+the second column and in general if if
+
+ align:start position:0%
+the second column and in general if if
+ 
+
+ align:start position:0%
+the second column and in general if if
+my if I can fit B columns or some
+
+ align:start position:0%
+my if I can fit B columns or some
+ 
+
+ align:start position:0%
+my if I can fit B columns or some
+constant times B columns in in into cash
+
+ align:start position:0%
+constant times B columns in in into cash
+ 
+
+ align:start position:0%
+constant times B columns in in into cash
+then I can reduce the number of cache
+
+ align:start position:0%
+then I can reduce the number of cache
+ 
+
+ align:start position:0%
+then I can reduce the number of cache
+misses I have by a factor of B so I only
+
+ align:start position:0%
+misses I have by a factor of B so I only
+ 
+
+ align:start position:0%
+misses I have by a factor of B so I only
+need to incur a cache miss the first
+
+ align:start position:0%
+need to incur a cache miss the first
+ 
+
+ align:start position:0%
+need to incur a cache miss the first
+time I access a block and not for all
+
+ align:start position:0%
+time I access a block and not for all
+ 
+
+ align:start position:0%
+time I access a block and not for all
+the subsequent accesses and the same is
+
+ align:start position:0%
+the subsequent accesses and the same is
+ 
+
+ align:start position:0%
+the subsequent accesses and the same is
+true for the second row of a and since I
+
+ align:start position:0%
+true for the second row of a and since I
+ 
+
+ align:start position:0%
+true for the second row of a and since I
+have n rows of a I'm gonna have n times
+
+ align:start position:0%
+have n rows of a I'm gonna have n times
+ 
+
+ align:start position:0%
+have n rows of a I'm gonna have n times
+theta of N squared over B cache misses
+
+ align:start position:0%
+theta of N squared over B cache misses
+ 
+
+ align:start position:0%
+theta of N squared over B cache misses
+for each row of a I'm gonna incur and
+
+ align:start position:0%
+for each row of a I'm gonna incur and
+ 
+
+ align:start position:0%
+for each row of a I'm gonna incur and
+squared over B cache misses
+
+ align:start position:0%
+squared over B cache misses
+ 
+
+ align:start position:0%
+squared over B cache misses
+so the overall number of cache misses is
+
+ align:start position:0%
+so the overall number of cache misses is
+ 
+
+ align:start position:0%
+so the overall number of cache misses is
+and cubed over B and this is because
+
+ align:start position:0%
+and cubed over B and this is because
+ 
+
+ align:start position:0%
+and cubed over B and this is because
+inside matrix B I can exploit spatial
+
+ align:start position:0%
+inside matrix B I can exploit spatial
+ 
+
+ align:start position:0%
+inside matrix B I can exploit spatial
+locality once I load in a block I can
+
+ align:start position:0%
+locality once I load in a block I can
+ 
+
+ align:start position:0%
+locality once I load in a block I can
+reuse it the next time I traverse down a
+
+ align:start position:0%
+reuse it the next time I traverse down a
+ 
+
+ align:start position:0%
+reuse it the next time I traverse down a
+column that's nearby any questions on
+
+ align:start position:0%
+column that's nearby any questions on
+ 
+
+ align:start position:0%
+column that's nearby any questions on
+this analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's look at the third case and
+
+ align:start position:0%
+okay so let's look at the third case and
+ 
+
+ align:start position:0%
+okay so let's look at the third case and
+here n is less than C prime times square
+
+ align:start position:0%
+here n is less than C prime times square
+ 
+
+ align:start position:0%
+here n is less than C prime times square
+root of M so this means that the entire
+
+ align:start position:0%
+root of M so this means that the entire
+ 
+
+ align:start position:0%
+root of M so this means that the entire
+matrix fits into cache so let's analyze
+
+ align:start position:0%
+matrix fits into cache so let's analyze
+ 
+
+ align:start position:0%
+matrix fits into cache so let's analyze
+the number of cache misses for matrix B
+
+ align:start position:0%
+the number of cache misses for matrix B
+ 
+
+ align:start position:0%
+the number of cache misses for matrix B
+again assuming LRU so how many cache
+
+ align:start position:0%
+again assuming LRU so how many cache
+ 
+
+ align:start position:0%
+again assuming LRU so how many cache
+misses do I have now so let's let's
+
+ align:start position:0%
+misses do I have now so let's let's
+ 
+
+ align:start position:0%
+misses do I have now so let's let's
+count the total number of cache misses I
+
+ align:start position:0%
+count the total number of cache misses I
+ 
+
+ align:start position:0%
+count the total number of cache misses I
+have for every time I go through a row
+
+ align:start position:0%
+have for every time I go through a row
+ 
+
+ align:start position:0%
+have for every time I go through a row
+of a yes yeah so the firt for the first
+
+ align:start position:0%
+of a yes yeah so the firt for the first
+ 
+
+ align:start position:0%
+of a yes yeah so the firt for the first
+column is going to be n what about the
+
+ align:start position:0%
+column is going to be n what about the
+ 
+
+ align:start position:0%
+column is going to be n what about the
+second column right so for the so
+
+ align:start position:0%
+second column right so for the so
+ 
+
+ align:start position:0%
+second column right so for the so
+basically for the first row of a the
+
+ align:start position:0%
+basically for the first row of a the
+ 
+
+ align:start position:0%
+basically for the first row of a the
+analysis is going to be the same as
+
+ align:start position:0%
+analysis is going to be the same as
+ 
+
+ align:start position:0%
+analysis is going to be the same as
+before I need n squared over B cache
+
+ align:start position:0%
+before I need n squared over B cache
+ 
+
+ align:start position:0%
+before I need n squared over B cache
+misses to load the cache in what about
+
+ align:start position:0%
+misses to load the cache in what about
+ 
+
+ align:start position:0%
+misses to load the cache in what about
+the second row of a how many cache
+
+ align:start position:0%
+the second row of a how many cache
+ 
+
+ align:start position:0%
+the second row of a how many cache
+misses am I going to incur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so for the second row of a I'm not
+
+ align:start position:0%
+yeah so for the second row of a I'm not
+ 
+
+ align:start position:0%
+yeah so for the second row of a I'm not
+gonna incur any cash misses because once
+
+ align:start position:0%
+gonna incur any cash misses because once
+ 
+
+ align:start position:0%
+gonna incur any cash misses because once
+I load B into cash
+
+ align:start position:0%
+I load B into cash
+ 
+
+ align:start position:0%
+I load B into cash
+it's gonna stay in cash because the
+
+ align:start position:0%
+it's gonna stay in cash because the
+ 
+
+ align:start position:0%
+it's gonna stay in cash because the
+entire matrix can fit in cash I assume
+
+ align:start position:0%
+entire matrix can fit in cash I assume
+ 
+
+ align:start position:0%
+entire matrix can fit in cash I assume
+that n is less than C prime times square
+
+ align:start position:0%
+that n is less than C prime times square
+ 
+
+ align:start position:0%
+that n is less than C prime times square
+root of M so total number of cache
+
+ align:start position:0%
+root of M so total number of cache
+ 
+
+ align:start position:0%
+root of M so total number of cache
+misses I need for matrix B is theta of n
+
+ align:start position:0%
+misses I need for matrix B is theta of n
+ 
+
+ align:start position:0%
+misses I need for matrix B is theta of n
+squared over B since everything fits in
+
+ align:start position:0%
+squared over B since everything fits in
+ 
+
+ align:start position:0%
+squared over B since everything fits in
+cache and I just applied the sub matrix
+
+ align:start position:0%
+cache and I just applied the sub matrix
+ 
+
+ align:start position:0%
+cache and I just applied the sub matrix
+caching lemma from before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overall this is not a very good
+
+ align:start position:0%
+overall this is not a very good
+ 
+
+ align:start position:0%
+overall this is not a very good
+algorithm because as you recall in case
+
+ align:start position:0%
+algorithm because as you recall in case
+ 
+
+ align:start position:0%
+algorithm because as you recall in case
+one I needed a cubic cubic number of
+
+ align:start position:0%
+one I needed a cubic cubic number of
+ 
+
+ align:start position:0%
+one I needed a cubic cubic number of
+cache misses what happens if I swap the
+
+ align:start position:0%
+cache misses what happens if I swap the
+ 
+
+ align:start position:0%
+cache misses what happens if I swap the
+order of the inner two loops so recall
+
+ align:start position:0%
+order of the inner two loops so recall
+ 
+
+ align:start position:0%
+order of the inner two loops so recall
+that this was one of the optimizations
+
+ align:start position:0%
+that this was one of the optimizations
+ 
+
+ align:start position:0%
+that this was one of the optimizations
+in lecture one when Charles was talking
+
+ align:start position:0%
+in lecture one when Charles was talking
+ 
+
+ align:start position:0%
+in lecture one when Charles was talking
+about matrix multiplication and how to
+
+ align:start position:0%
+about matrix multiplication and how to
+ 
+
+ align:start position:0%
+about matrix multiplication and how to
+speed it up so if I swap the order of
+
+ align:start position:0%
+speed it up so if I swap the order of
+ 
+
+ align:start position:0%
+speed it up so if I swap the order of
+the two inner loops then then for every
+
+ align:start position:0%
+the two inner loops then then for every
+ 
+
+ align:start position:0%
+the two inner loops then then for every
+iteration what I'm doing is I'm actually
+
+ align:start position:0%
+iteration what I'm doing is I'm actually
+ 
+
+ align:start position:0%
+iteration what I'm doing is I'm actually
+going over a row of C in a row of B and
+
+ align:start position:0%
+going over a row of C in a row of B and
+ 
+
+ align:start position:0%
+going over a row of C in a row of B and
+a stays fixed inside the innermost
+
+ align:start position:0%
+a stays fixed inside the innermost
+ 
+
+ align:start position:0%
+a stays fixed inside the innermost
+iteration so now when I analyze the
+
+ align:start position:0%
+iteration so now when I analyze the
+ 
+
+ align:start position:0%
+iteration so now when I analyze the
+number of cache misses of matrix B
+
+ align:start position:0%
+number of cache misses of matrix B
+ 
+
+ align:start position:0%
+number of cache misses of matrix B
+assuming LRU I'm gonna benefit from
+
+ align:start position:0%
+assuming LRU I'm gonna benefit from
+ 
+
+ align:start position:0%
+assuming LRU I'm gonna benefit from
+spatial locality since I'm going row by
+
+ align:start position:0%
+spatial locality since I'm going row by
+ 
+
+ align:start position:0%
+spatial locality since I'm going row by
+row and the matrix is stored in row
+
+ align:start position:0%
+row and the matrix is stored in row
+ 
+
+ align:start position:0%
+row and the matrix is stored in row
+major order so across all of the rows
+
+ align:start position:0%
+major order so across all of the rows
+ 
+
+ align:start position:0%
+major order so across all of the rows
+I'm just going to require theta of n
+
+ align:start position:0%
+I'm just going to require theta of n
+ 
+
+ align:start position:0%
+I'm just going to require theta of n
+squared over B cache misses and I have
+
+ align:start position:0%
+squared over B cache misses and I have
+ 
+
+ align:start position:0%
+squared over B cache misses and I have
+to do this end times for the outer loop
+
+ align:start position:0%
+to do this end times for the outer loop
+ 
+
+ align:start position:0%
+to do this end times for the outer loop
+so in total I'm going to get theta of n
+
+ align:start position:0%
+so in total I'm going to get theta of n
+ 
+
+ align:start position:0%
+so in total I'm going to get theta of n
+cubed over B cache misses so if you swap
+
+ align:start position:0%
+cubed over B cache misses so if you swap
+ 
+
+ align:start position:0%
+cubed over B cache misses so if you swap
+the order of the inner two loops this
+
+ align:start position:0%
+the order of the inner two loops this
+ 
+
+ align:start position:0%
+the order of the inner two loops this
+significantly improves the locality of
+
+ align:start position:0%
+significantly improves the locality of
+ 
+
+ align:start position:0%
+significantly improves the locality of
+your algorithm and you can benefit from
+
+ align:start position:0%
+your algorithm and you can benefit from
+ 
+
+ align:start position:0%
+your algorithm and you can benefit from
+spatial locality and that's why we saw a
+
+ align:start position:0%
+spatial locality and that's why we saw a
+ 
+
+ align:start position:0%
+spatial locality and that's why we saw a
+significant performance improvement in
+
+ align:start position:0%
+significant performance improvement in
+ 
+
+ align:start position:0%
+significant performance improvement in
+the first lecture when we swapped the
+
+ align:start position:0%
+the first lecture when we swapped the
+ 
+
+ align:start position:0%
+the first lecture when we swapped the
+order of the loops any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anybody think we can do better than
+
+ align:start position:0%
+does anybody think we can do better than
+ 
+
+ align:start position:0%
+does anybody think we can do better than
+n cubed over B cache misses or you think
+
+ align:start position:0%
+n cubed over B cache misses or you think
+ 
+
+ align:start position:0%
+n cubed over B cache misses or you think
+that it's the best you can do so how
+
+ align:start position:0%
+that it's the best you can do so how
+ 
+
+ align:start position:0%
+that it's the best you can do so how
+many people think you can do better yeah
+
+ align:start position:0%
+many people think you can do better yeah
+ 
+
+ align:start position:0%
+many people think you can do better yeah
+and how many people think this is the
+
+ align:start position:0%
+and how many people think this is the
+ 
+
+ align:start position:0%
+and how many people think this is the
+best you can do okay and how many people
+
+ align:start position:0%
+best you can do okay and how many people
+ 
+
+ align:start position:0%
+best you can do okay and how many people
+don't care so turns out you can do
+
+ align:start position:0%
+don't care so turns out you can do
+ 
+
+ align:start position:0%
+don't care so turns out you can do
+better and we're gonna do better by
+
+ align:start position:0%
+better and we're gonna do better by
+ 
+
+ align:start position:0%
+better and we're gonna do better by
+using an optimization called tiling so
+
+ align:start position:0%
+using an optimization called tiling so
+ 
+
+ align:start position:0%
+using an optimization called tiling so
+how this is gonna work is instead of
+
+ align:start position:0%
+how this is gonna work is instead of
+ 
+
+ align:start position:0%
+how this is gonna work is instead of
+just having three for loops I'm gonna
+
+ align:start position:0%
+just having three for loops I'm gonna
+ 
+
+ align:start position:0%
+just having three for loops I'm gonna
+have six for loops and I'm gonna loop
+
+ align:start position:0%
+have six for loops and I'm gonna loop
+ 
+
+ align:start position:0%
+have six for loops and I'm gonna loop
+over tiles so I've got loop over s by s
+
+ align:start position:0%
+over tiles so I've got loop over s by s
+ 
+
+ align:start position:0%
+over tiles so I've got loop over s by s
+sub matrices and within each sub makes
+
+ align:start position:0%
+sub matrices and within each sub makes
+ 
+
+ align:start position:0%
+sub matrices and within each sub makes
+listing I'm gonna do all the computation
+
+ align:start position:0%
+listing I'm gonna do all the computation
+ 
+
+ align:start position:0%
+listing I'm gonna do all the computation
+I need for that sub matrix before moving
+
+ align:start position:0%
+I need for that sub matrix before moving
+ 
+
+ align:start position:0%
+I need for that sub matrix before moving
+on to the next sub matrix so the three
+
+ align:start position:0%
+on to the next sub matrix so the three
+ 
+
+ align:start position:0%
+on to the next sub matrix so the three
+innermost loops are going to loop inside
+
+ align:start position:0%
+innermost loops are going to loop inside
+ 
+
+ align:start position:0%
+innermost loops are going to loop inside
+a sub matrix and the three outermost
+
+ align:start position:0%
+a sub matrix and the three outermost
+ 
+
+ align:start position:0%
+a sub matrix and the three outermost
+loops are going to loop within the
+
+ align:start position:0%
+loops are going to loop within the
+ 
+
+ align:start position:0%
+loops are going to loop within the
+larger matrix one sub matrix at a time
+
+ align:start position:0%
+larger matrix one sub matrix at a time
+ 
+
+ align:start position:0%
+larger matrix one sub matrix at a time
+so let's analyze the work of this
+
+ align:start position:0%
+so let's analyze the work of this
+ 
+
+ align:start position:0%
+so let's analyze the work of this
+algorithm so the work that we need to do
+
+ align:start position:0%
+algorithm so the work that we need to do
+ 
+
+ align:start position:0%
+algorithm so the work that we need to do
+for a sub matrix of size s by s is going
+
+ align:start position:0%
+for a sub matrix of size s by s is going
+ 
+
+ align:start position:0%
+for a sub matrix of size s by s is going
+to be s cubed since that's just a bound
+
+ align:start position:0%
+to be s cubed since that's just a bound
+ 
+
+ align:start position:0%
+to be s cubed since that's just a bound
+for matrix multiplication and then a
+
+ align:start position:0%
+for matrix multiplication and then a
+ 
+
+ align:start position:0%
+for matrix multiplication and then a
+number of times I have to operate on sub
+
+ align:start position:0%
+number of times I have to operate on sub
+ 
+
+ align:start position:0%
+number of times I have to operate on sub
+matrices is going to be n over s cubed
+
+ align:start position:0%
+matrices is going to be n over s cubed
+ 
+
+ align:start position:0%
+matrices is going to be n over s cubed
+and you can see this if you just
+
+ align:start position:0%
+and you can see this if you just
+ 
+
+ align:start position:0%
+and you can see this if you just
+consider each sub matrix to be a single
+
+ align:start position:0%
+consider each sub matrix to be a single
+ 
+
+ align:start position:0%
+consider each sub matrix to be a single
+element and then using the same cubic
+
+ align:start position:0%
+element and then using the same cubic
+ 
+
+ align:start position:0%
+element and then using the same cubic
+work analysis on the smaller matrix so
+
+ align:start position:0%
+work analysis on the smaller matrix so
+ 
+
+ align:start position:0%
+work analysis on the smaller matrix so
+the work is n over s cubed times s cubed
+
+ align:start position:0%
+the work is n over s cubed times s cubed
+ 
+
+ align:start position:0%
+the work is n over s cubed times s cubed
+which is equal to theta n cube so the
+
+ align:start position:0%
+which is equal to theta n cube so the
+ 
+
+ align:start position:0%
+which is equal to theta n cube so the
+work of this tiled matrix multiplies the
+
+ align:start position:0%
+work of this tiled matrix multiplies the
+ 
+
+ align:start position:0%
+work of this tiled matrix multiplies the
+same as the version that didn't do
+
+ align:start position:0%
+same as the version that didn't do
+ 
+
+ align:start position:0%
+same as the version that didn't do
+tiling and now let's analyze the number
+
+ align:start position:0%
+tiling and now let's analyze the number
+ 
+
+ align:start position:0%
+tiling and now let's analyze the number
+of cache misses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're gonna tune s so that the
+
+ align:start position:0%
+so we're gonna tune s so that the
+ 
+
+ align:start position:0%
+so we're gonna tune s so that the
+sub-matrices
+
+ align:start position:0%
+sub-matrices
+ 
+
+ align:start position:0%
+sub-matrices
+just fit into cash so we're gonna set s
+
+ align:start position:0%
+just fit into cash so we're gonna set s
+ 
+
+ align:start position:0%
+just fit into cash so we're gonna set s
+to be equal to theta of square root of M
+
+ align:start position:0%
+to be equal to theta of square root of M
+ 
+
+ align:start position:0%
+to be equal to theta of square root of M
+who actually need to make this like
+
+ align:start position:0%
+who actually need to make this like
+ 
+
+ align:start position:0%
+who actually need to make this like
+one-third square root of M because we
+
+ align:start position:0%
+one-third square root of M because we
+ 
+
+ align:start position:0%
+one-third square root of M because we
+need to fit three sub matrices in the
+
+ align:start position:0%
+need to fit three sub matrices in the
+ 
+
+ align:start position:0%
+need to fit three sub matrices in the
+cache but it's going to be some constant
+
+ align:start position:0%
+cache but it's going to be some constant
+ 
+
+ align:start position:0%
+cache but it's going to be some constant
+times square root of M the sub-matrix
+
+ align:start position:0%
+times square root of M the sub-matrix
+ 
+
+ align:start position:0%
+times square root of M the sub-matrix
+cashing leva implies that for each sub
+
+ align:start position:0%
+cashing leva implies that for each sub
+ 
+
+ align:start position:0%
+cashing leva implies that for each sub
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+we're gonna need s squared over B misses
+
+ align:start position:0%
+we're gonna need s squared over B misses
+ 
+
+ align:start position:0%
+we're gonna need s squared over B misses
+to load it in and once we load it into
+
+ align:start position:0%
+to load it in and once we load it into
+ 
+
+ align:start position:0%
+to load it in and once we load it into
+cash
+
+ align:start position:0%
+cash
+ 
+
+ align:start position:0%
+cash
+it fits entirely into cache so we can do
+
+ align:start position:0%
+it fits entirely into cache so we can do
+ 
+
+ align:start position:0%
+it fits entirely into cache so we can do
+all of our computations within cash and
+
+ align:start position:0%
+all of our computations within cash and
+ 
+
+ align:start position:0%
+all of our computations within cash and
+not incur any more cache misses so
+
+ align:start position:0%
+not incur any more cache misses so
+ 
+
+ align:start position:0%
+not incur any more cache misses so
+therefore the total number of cache
+
+ align:start position:0%
+therefore the total number of cache
+ 
+
+ align:start position:0%
+therefore the total number of cache
+misses we're going to incur it's going
+
+ align:start position:0%
+misses we're going to incur it's going
+ 
+
+ align:start position:0%
+misses we're going to incur it's going
+to be the number of subproblems which is
+
+ align:start position:0%
+to be the number of subproblems which is
+ 
+
+ align:start position:0%
+to be the number of subproblems which is
+n over s cubed and then the number of
+
+ align:start position:0%
+n over s cubed and then the number of
+ 
+
+ align:start position:0%
+n over s cubed and then the number of
+cache misses per subproblem which is s
+
+ align:start position:0%
+cache misses per subproblem which is s
+ 
+
+ align:start position:0%
+cache misses per subproblem which is s
+squared over B and if you multiply this
+
+ align:start position:0%
+squared over B and if you multiply this
+ 
+
+ align:start position:0%
+squared over B and if you multiply this
+out you're gonna get and cubed over B
+
+ align:start position:0%
+out you're gonna get and cubed over B
+ 
+
+ align:start position:0%
+out you're gonna get and cubed over B
+times square root of M so here I plugged
+
+ align:start position:0%
+times square root of M so here I plugged
+ 
+
+ align:start position:0%
+times square root of M so here I plugged
+in square root of M for s and this is a
+
+ align:start position:0%
+in square root of M for s and this is a
+ 
+
+ align:start position:0%
+in square root of M for s and this is a
+pretty cool result because it says that
+
+ align:start position:0%
+pretty cool result because it says that
+ 
+
+ align:start position:0%
+pretty cool result because it says that
+you can actually do better than the n
+
+ align:start position:0%
+you can actually do better than the n
+ 
+
+ align:start position:0%
+you can actually do better than the n
+cubed over B bound you can improve this
+
+ align:start position:0%
+cubed over B bound you can improve this
+ 
+
+ align:start position:0%
+cubed over B bound you can improve this
+bound by a factor of square root of M
+
+ align:start position:0%
+bound by a factor of square root of M
+ 
+
+ align:start position:0%
+bound by a factor of square root of M
+and in practice square root of M is
+
+ align:start position:0%
+and in practice square root of M is
+ 
+
+ align:start position:0%
+and in practice square root of M is
+actually not insignificant so for
+
+ align:start position:0%
+actually not insignificant so for
+ 
+
+ align:start position:0%
+actually not insignificant so for
+example if you're looking at the last
+
+ align:start position:0%
+example if you're looking at the last
+ 
+
+ align:start position:0%
+example if you're looking at the last
+level cache the size of that is on the
+
+ align:start position:0%
+level cache the size of that is on the
+ 
+
+ align:start position:0%
+level cache the size of that is on the
+order of megabytes so a square root of M
+
+ align:start position:0%
+order of megabytes so a square root of M
+ 
+
+ align:start position:0%
+order of megabytes so a square root of M
+is going to be on the order of thousands
+
+ align:start position:0%
+is going to be on the order of thousands
+ 
+
+ align:start position:0%
+is going to be on the order of thousands
+so this significantly improves the
+
+ align:start position:0%
+so this significantly improves the
+ 
+
+ align:start position:0%
+so this significantly improves the
+performance of the matrix multiplication
+
+ align:start position:0%
+performance of the matrix multiplication
+ 
+
+ align:start position:0%
+performance of the matrix multiplication
+code if you tune s so that the sub
+
+ align:start position:0%
+code if you tune s so that the sub
+ 
+
+ align:start position:0%
+code if you tune s so that the sub
+matrices just fit in the cache it turns
+
+ align:start position:0%
+matrices just fit in the cache it turns
+ 
+
+ align:start position:0%
+matrices just fit in the cache it turns
+out that this bound is off to most so
+
+ align:start position:0%
+out that this bound is off to most so
+ 
+
+ align:start position:0%
+out that this bound is off to most so
+this was shown in 1981
+
+ align:start position:0%
+this was shown in 1981
+ 
+
+ align:start position:0%
+this was shown in 1981
+so for cubic work matrix multiplication
+
+ align:start position:0%
+so for cubic work matrix multiplication
+ 
+
+ align:start position:0%
+so for cubic work matrix multiplication
+this is the best you can do if you use
+
+ align:start position:0%
+this is the best you can do if you use
+ 
+
+ align:start position:0%
+this is the best you can do if you use
+another matrix multiply algorithm like
+
+ align:start position:0%
+another matrix multiply algorithm like
+ 
+
+ align:start position:0%
+another matrix multiply algorithm like
+strassens algorithm you can do better so
+
+ align:start position:0%
+strassens algorithm you can do better so
+ 
+
+ align:start position:0%
+strassens algorithm you can do better so
+I want you to remember this bound it's a
+
+ align:start position:0%
+I want you to remember this bound it's a
+ 
+
+ align:start position:0%
+I want you to remember this bound it's a
+very important bound to know says that
+
+ align:start position:0%
+very important bound to know says that
+ 
+
+ align:start position:0%
+very important bound to know says that
+for matrix multiplication you can you
+
+ align:start position:0%
+for matrix multiplication you can you
+ 
+
+ align:start position:0%
+for matrix multiplication you can you
+can benefit both from spatial locality
+
+ align:start position:0%
+can benefit both from spatial locality
+ 
+
+ align:start position:0%
+can benefit both from spatial locality
+as well as
+
+ align:start position:0%
+as well as
+ 
+
+ align:start position:0%
+as well as
+temporal locality so I get spatial
+
+ align:start position:0%
+temporal locality so I get spatial
+ 
+
+ align:start position:0%
+temporal locality so I get spatial
+locality in the denominator the B term
+
+ align:start position:0%
+locality in the denominator the B term
+ 
+
+ align:start position:0%
+locality in the denominator the B term
+in the denominator and then the square
+
+ align:start position:0%
+in the denominator and then the square
+ 
+
+ align:start position:0%
+in the denominator and then the square
+root of M term comes from temporal
+
+ align:start position:0%
+root of M term comes from temporal
+ 
+
+ align:start position:0%
+root of M term comes from temporal
+locality since I'm doing all of the work
+
+ align:start position:0%
+locality since I'm doing all of the work
+ 
+
+ align:start position:0%
+locality since I'm doing all of the work
+inside the sub-matrix before I evict
+
+ align:start position:0%
+inside the sub-matrix before I evict
+ 
+
+ align:start position:0%
+inside the sub-matrix before I evict
+that sub matrix from cache any questions
+
+ align:start position:0%
+that sub matrix from cache any questions
+ 
+
+ align:start position:0%
+that sub matrix from cache any questions
+on this analysis so what's one issue
+
+ align:start position:0%
+on this analysis so what's one issue
+ 
+
+ align:start position:0%
+on this analysis so what's one issue
+with this algorithm here yes yeah so the
+
+ align:start position:0%
+with this algorithm here yes yeah so the
+ 
+
+ align:start position:0%
+with this algorithm here yes yeah so the
+problem here is I have two two nests for
+
+ align:start position:0%
+problem here is I have two two nests for
+ 
+
+ align:start position:0%
+problem here is I have two two nests for
+my particular machine and I call this a
+
+ align:start position:0%
+my particular machine and I call this a
+ 
+
+ align:start position:0%
+my particular machine and I call this a
+voodoo parameter it's sort of like a
+
+ align:start position:0%
+voodoo parameter it's sort of like a
+ 
+
+ align:start position:0%
+voodoo parameter it's sort of like a
+magic number I I put into my program so
+
+ align:start position:0%
+magic number I I put into my program so
+ 
+
+ align:start position:0%
+magic number I I put into my program so
+that it fits in the cache on the
+
+ align:start position:0%
+that it fits in the cache on the
+ 
+
+ align:start position:0%
+that it fits in the cache on the
+particular machine I'm running on and
+
+ align:start position:0%
+particular machine I'm running on and
+ 
+
+ align:start position:0%
+particular machine I'm running on and
+this makes the code not portable because
+
+ align:start position:0%
+this makes the code not portable because
+ 
+
+ align:start position:0%
+this makes the code not portable because
+when I try if I try to run this code on
+
+ align:start position:0%
+when I try if I try to run this code on
+ 
+
+ align:start position:0%
+when I try if I try to run this code on
+another machine the cache sizes might be
+
+ align:start position:0%
+another machine the cache sizes might be
+ 
+
+ align:start position:0%
+another machine the cache sizes might be
+different there and then I won't get the
+
+ align:start position:0%
+different there and then I won't get the
+ 
+
+ align:start position:0%
+different there and then I won't get the
+same performance as I did on my machine
+
+ align:start position:0%
+same performance as I did on my machine
+ 
+
+ align:start position:0%
+same performance as I did on my machine
+and this is also an issue even if you're
+
+ align:start position:0%
+and this is also an issue even if you're
+ 
+
+ align:start position:0%
+and this is also an issue even if you're
+running it on the same machine because
+
+ align:start position:0%
+running it on the same machine because
+ 
+
+ align:start position:0%
+running it on the same machine because
+you might have other programs running at
+
+ align:start position:0%
+you might have other programs running at
+ 
+
+ align:start position:0%
+you might have other programs running at
+the same time and using a part of the
+
+ align:start position:0%
+the same time and using a part of the
+ 
+
+ align:start position:0%
+the same time and using a part of the
+cache so you don't actually know how
+
+ align:start position:0%
+cache so you don't actually know how
+ 
+
+ align:start position:0%
+cache so you don't actually know how
+much of the cache your program actually
+
+ align:start position:0%
+much of the cache your program actually
+ 
+
+ align:start position:0%
+much of the cache your program actually
+gets to use in a multi programming
+
+ align:start position:0%
+gets to use in a multi programming
+ 
+
+ align:start position:0%
+gets to use in a multi programming
+environment and then this was also just
+
+ align:start position:0%
+environment and then this was also just
+ 
+
+ align:start position:0%
+environment and then this was also just
+for one level of cache if we want to
+
+ align:start position:0%
+for one level of cache if we want to
+ 
+
+ align:start position:0%
+for one level of cache if we want to
+optimize for two levels of caches we're
+
+ align:start position:0%
+optimize for two levels of caches we're
+ 
+
+ align:start position:0%
+optimize for two levels of caches we're
+gonna have to voodoo parameters s and T
+
+ align:start position:0%
+gonna have to voodoo parameters s and T
+ 
+
+ align:start position:0%
+gonna have to voodoo parameters s and T
+we're gonna have sub matrices and sub
+
+ align:start position:0%
+we're gonna have sub matrices and sub
+ 
+
+ align:start position:0%
+we're gonna have sub matrices and sub
+sub matrices and then we have to tune
+
+ align:start position:0%
+sub matrices and then we have to tune
+ 
+
+ align:start position:0%
+sub matrices and then we have to tune
+both of these parameters to get the best
+
+ align:start position:0%
+both of these parameters to get the best
+ 
+
+ align:start position:0%
+both of these parameters to get the best
+performance on our machine and
+
+ align:start position:0%
+performance on our machine and
+ 
+
+ align:start position:0%
+performance on our machine and
+multi-dimensional tuning optimization
+
+ align:start position:0%
+multi-dimensional tuning optimization
+ 
+
+ align:start position:0%
+multi-dimensional tuning optimization
+can't be done simply with binary search
+
+ align:start position:0%
+can't be done simply with binary search
+ 
+
+ align:start position:0%
+can't be done simply with binary search
+so if you're just tuning for one level
+
+ align:start position:0%
+so if you're just tuning for one level
+ 
+
+ align:start position:0%
+so if you're just tuning for one level
+of cache you can do a binary search on
+
+ align:start position:0%
+of cache you can do a binary search on
+ 
+
+ align:start position:0%
+of cache you can do a binary search on
+the parameter s but here you can't do
+
+ align:start position:0%
+the parameter s but here you can't do
+ 
+
+ align:start position:0%
+the parameter s but here you can't do
+binary search so so it's much more
+
+ align:start position:0%
+binary search so so it's much more
+ 
+
+ align:start position:0%
+binary search so so it's much more
+expensive to optimize here and the code
+
+ align:start position:0%
+expensive to optimize here and the code
+ 
+
+ align:start position:0%
+expensive to optimize here and the code
+becomes a little bit Messier you have
+
+ align:start position:0%
+becomes a little bit Messier you have
+ 
+
+ align:start position:0%
+becomes a little bit Messier you have
+nine four loops instead of six and how
+
+ align:start position:0%
+nine four loops instead of six and how
+ 
+
+ align:start position:0%
+nine four loops instead of six and how
+many levels of caches do we have on the
+
+ align:start position:0%
+many levels of caches do we have on the
+ 
+
+ align:start position:0%
+many levels of caches do we have on the
+machines that we're using today three so
+
+ align:start position:0%
+machines that we're using today three so
+ 
+
+ align:start position:0%
+machines that we're using today three so
+four three level cache you have three
+
+ align:start position:0%
+four three level cache you have three
+ 
+
+ align:start position:0%
+four three level cache you have three
+voodoo
+
+ align:start position:0%
+voodoo
+ 
+
+ align:start position:0%
+voodoo
+parameters you have 12 nested for-loops
+
+ align:start position:0%
+parameters you have 12 nested for-loops
+ 
+
+ align:start position:0%
+parameters you have 12 nested for-loops
+this code becomes very ugly and you have
+
+ align:start position:0%
+this code becomes very ugly and you have
+ 
+
+ align:start position:0%
+this code becomes very ugly and you have
+to tune these parameters for your
+
+ align:start position:0%
+to tune these parameters for your
+ 
+
+ align:start position:0%
+to tune these parameters for your
+particular machine and this makes the
+
+ align:start position:0%
+particular machine and this makes the
+ 
+
+ align:start position:0%
+particular machine and this makes the
+code not very portable as one student
+
+ align:start position:0%
+code not very portable as one student
+ 
+
+ align:start position:0%
+code not very portable as one student
+pointed out and in a multi programmed
+
+ align:start position:0%
+pointed out and in a multi programmed
+ 
+
+ align:start position:0%
+pointed out and in a multi programmed
+environment you don't actually know the
+
+ align:start position:0%
+environment you don't actually know the
+ 
+
+ align:start position:0%
+environment you don't actually know the
+effective cache size that your program
+
+ align:start position:0%
+effective cache size that your program
+ 
+
+ align:start position:0%
+effective cache size that your program
+has access to because other jobs are
+
+ align:start position:0%
+has access to because other jobs are
+ 
+
+ align:start position:0%
+has access to because other jobs are
+running at the same time and therefore
+
+ align:start position:0%
+running at the same time and therefore
+ 
+
+ align:start position:0%
+running at the same time and therefore
+it's very easy to miss - in the
+
+ align:start position:0%
+it's very easy to miss - in the
+ 
+
+ align:start position:0%
+it's very easy to miss - in the
+parameters with their question so I need
+
+ align:start position:0%
+parameters with their question so I need
+ 
+
+ align:start position:0%
+parameters with their question so I need
+questions yeah yes so you I mean you can
+
+ align:start position:0%
+questions yeah yes so you I mean you can
+ 
+
+ align:start position:0%
+questions yeah yes so you I mean you can
+auto tune your program so that it's
+
+ align:start position:0%
+auto tune your program so that it's
+ 
+
+ align:start position:0%
+auto tune your program so that it's
+optimized for the cache sizes of your
+
+ align:start position:0%
+optimized for the cache sizes of your
+ 
+
+ align:start position:0%
+optimized for the cache sizes of your
+particular machine instruction to get
+
+ align:start position:0%
+particular machine instruction to get
+ 
+
+ align:start position:0%
+particular machine instruction to get
+the size of your cache I'm not actually
+
+ align:start position:0%
+the size of your cache I'm not actually
+ 
+
+ align:start position:0%
+the size of your cache I'm not actually
+sure do you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah in the rock
+
+ align:start position:0%
+yeah in the rock
+ 
+
+ align:start position:0%
+yeah in the rock
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah proxy pu info yeah yes so you can
+
+ align:start position:0%
+yeah proxy pu info yeah yes so you can
+ 
+
+ align:start position:0%
+yeah proxy pu info yeah yes so you can
+probably get that as well yeah yeah but
+
+ align:start position:0%
+probably get that as well yeah yeah but
+ 
+
+ align:start position:0%
+probably get that as well yeah yeah but
+even if you do that and you're running
+
+ align:start position:0%
+even if you do that and you're running
+ 
+
+ align:start position:0%
+even if you do that and you're running
+this program when other jobs are running
+
+ align:start position:0%
+this program when other jobs are running
+ 
+
+ align:start position:0%
+this program when other jobs are running
+you don't actually know how much cash
+
+ align:start position:0%
+you don't actually know how much cash
+ 
+
+ align:start position:0%
+you don't actually know how much cash
+your program has access to yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's they're actually general-purpose
+
+ align:start position:0%
+no it's they're actually general-purpose
+ 
+
+ align:start position:0%
+no it's they're actually general-purpose
+we're actually
+
+ align:start position:0%
+we're actually
+ 
+
+ align:start position:0%
+we're actually
+I mean today we're just looking at
+
+ align:start position:0%
+I mean today we're just looking at
+ 
+
+ align:start position:0%
+I mean today we're just looking at
+matrix multiply but in on Thursday's
+
+ align:start position:0%
+matrix multiply but in on Thursday's
+ 
+
+ align:start position:0%
+matrix multiply but in on Thursday's
+lecture we'll actually be looking at
+
+ align:start position:0%
+lecture we'll actually be looking at
+ 
+
+ align:start position:0%
+lecture we'll actually be looking at
+many other problems and how to optimize
+
+ align:start position:0%
+many other problems and how to optimize
+ 
+
+ align:start position:0%
+many other problems and how to optimize
+them for the cache hierarchy other
+
+ align:start position:0%
+them for the cache hierarchy other
+ 
+
+ align:start position:0%
+them for the cache hierarchy other
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this was a I mean this was a
+
+ align:start position:0%
+okay so this was a I mean this was a
+ 
+
+ align:start position:0%
+okay so this was a I mean this was a
+good algorithm in terms of cache
+
+ align:start position:0%
+good algorithm in terms of cache
+ 
+
+ align:start position:0%
+good algorithm in terms of cache
+performance but it wasn't very portable
+
+ align:start position:0%
+performance but it wasn't very portable
+ 
+
+ align:start position:0%
+performance but it wasn't very portable
+so let's see if we can do better let's
+
+ align:start position:0%
+so let's see if we can do better let's
+ 
+
+ align:start position:0%
+so let's see if we can do better let's
+see we can come up with a simpler design
+
+ align:start position:0%
+see we can come up with a simpler design
+ 
+
+ align:start position:0%
+see we can come up with a simpler design
+where we still get pretty good cache
+
+ align:start position:0%
+where we still get pretty good cache
+ 
+
+ align:start position:0%
+where we still get pretty good cache
+performance so we're going to turn to
+
+ align:start position:0%
+performance so we're going to turn to
+ 
+
+ align:start position:0%
+performance so we're going to turn to
+dividing conquer we're going to look at
+
+ align:start position:0%
+dividing conquer we're going to look at
+ 
+
+ align:start position:0%
+dividing conquer we're going to look at
+the recursive matrix multiplication
+
+ align:start position:0%
+the recursive matrix multiplication
+ 
+
+ align:start position:0%
+the recursive matrix multiplication
+algorithm that we saw before again we're
+
+ align:start position:0%
+algorithm that we saw before again we're
+ 
+
+ align:start position:0%
+algorithm that we saw before again we're
+going to deal with square matrices but
+
+ align:start position:0%
+going to deal with square matrices but
+ 
+
+ align:start position:0%
+going to deal with square matrices but
+the results generalize to non square
+
+ align:start position:0%
+the results generalize to non square
+ 
+
+ align:start position:0%
+the results generalize to non square
+matrices so how this works is we're
+
+ align:start position:0%
+matrices so how this works is we're
+ 
+
+ align:start position:0%
+matrices so how this works is we're
+going to split our input matrices into
+
+ align:start position:0%
+going to split our input matrices into
+ 
+
+ align:start position:0%
+going to split our input matrices into
+four sub sub matrices or four quadrants
+
+ align:start position:0%
+four sub sub matrices or four quadrants
+ 
+
+ align:start position:0%
+four sub sub matrices or four quadrants
+and then for each quadrant of the output
+
+ align:start position:0%
+and then for each quadrant of the output
+ 
+
+ align:start position:0%
+and then for each quadrant of the output
+matrix it's just going to be the sum of
+
+ align:start position:0%
+matrix it's just going to be the sum of
+ 
+
+ align:start position:0%
+matrix it's just going to be the sum of
+two matrix multiplies on n over two by n
+
+ align:start position:0%
+two matrix multiplies on n over two by n
+ 
+
+ align:start position:0%
+two matrix multiplies on n over two by n
+over two matrices so c1 1 is going to be
+
+ align:start position:0%
+over two matrices so c1 1 is going to be
+ 
+
+ align:start position:0%
+over two matrices so c1 1 is going to be
+a1 1 times b1 1 plus a12 times b1 b2 1
+
+ align:start position:0%
+a1 1 times b1 1 plus a12 times b1 b2 1
+ 
+
+ align:start position:0%
+a1 1 times b1 1 plus a12 times b1 b2 1
+and then we're gonna do this recursively
+
+ align:start position:0%
+and then we're gonna do this recursively
+ 
+
+ align:start position:0%
+and then we're gonna do this recursively
+so every level of recursion we're gonna
+
+ align:start position:0%
+so every level of recursion we're gonna
+ 
+
+ align:start position:0%
+so every level of recursion we're gonna
+get eight multiply adds of n over two by
+
+ align:start position:0%
+get eight multiply adds of n over two by
+ 
+
+ align:start position:0%
+get eight multiply adds of n over two by
+n over two matrices here's what the
+
+ align:start position:0%
+n over two matrices here's what the
+ 
+
+ align:start position:0%
+n over two matrices here's what the
+recursive code looks like you can see
+
+ align:start position:0%
+recursive code looks like you can see
+ 
+
+ align:start position:0%
+recursive code looks like you can see
+that we have eight recursive calls here
+
+ align:start position:0%
+that we have eight recursive calls here
+ 
+
+ align:start position:0%
+that we have eight recursive calls here
+the base case here is of size 1 in
+
+ align:start position:0%
+the base case here is of size 1 in
+ 
+
+ align:start position:0%
+the base case here is of size 1 in
+practice you want a course in the base
+
+ align:start position:0%
+practice you want a course in the base
+ 
+
+ align:start position:0%
+practice you want a course in the base
+case to overcome function call overheads
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's also look at what these values
+
+ align:start position:0%
+let's also look at what these values
+ 
+
+ align:start position:0%
+let's also look at what these values
+here correspond to so I've color-coded
+
+ align:start position:0%
+here correspond to so I've color-coded
+ 
+
+ align:start position:0%
+here correspond to so I've color-coded
+these that they correspond to particular
+
+ align:start position:0%
+these that they correspond to particular
+ 
+
+ align:start position:0%
+these that they correspond to particular
+elements in the sub matrix that I'm
+
+ align:start position:0%
+elements in the sub matrix that I'm
+ 
+
+ align:start position:0%
+elements in the sub matrix that I'm
+looking at on the right so these values
+
+ align:start position:0%
+looking at on the right so these values
+ 
+
+ align:start position:0%
+looking at on the right so these values
+here corresponds to the index of the
+
+ align:start position:0%
+here corresponds to the index of the
+ 
+
+ align:start position:0%
+here corresponds to the index of the
+first element in each of my quadrants so
+
+ align:start position:0%
+first element in each of my quadrants so
+ 
+
+ align:start position:0%
+first element in each of my quadrants so
+the first element in my first quadrant
+
+ align:start position:0%
+the first element in my first quadrant
+ 
+
+ align:start position:0%
+the first element in my first quadrant
+is just gonna have an offset of zero and
+
+ align:start position:0%
+is just gonna have an offset of zero and
+ 
+
+ align:start position:0%
+is just gonna have an offset of zero and
+then the first element of my second
+
+ align:start position:0%
+then the first element of my second
+ 
+
+ align:start position:0%
+then the first element of my second
+quadrant that's gonna be on the same row
+
+ align:start position:0%
+quadrant that's gonna be on the same row
+ 
+
+ align:start position:0%
+quadrant that's gonna be on the same row
+as the first element in my first
+
+ align:start position:0%
+as the first element in my first
+ 
+
+ align:start position:0%
+as the first element in my first
+quadrant so I I just need to add a
+
+ align:start position:0%
+quadrant so I I just need to add a
+ 
+
+ align:start position:0%
+quadrant so I I just need to add a
+difference between the I just need to
+
+ align:start position:0%
+difference between the I just need to
+ 
+
+ align:start position:0%
+difference between the I just need to
+add the width of my quadrant which is n
+
+ align:start position:0%
+add the width of my quadrant which is n
+ 
+
+ align:start position:0%
+add the width of my quadrant which is n
+over 2 and then to get the first element
+
+ align:start position:0%
+over 2 and then to get the first element
+ 
+
+ align:start position:0%
+over 2 and then to get the first element
+in quadrant 2 1 I'm going to jump over
+
+ align:start position:0%
+in quadrant 2 1 I'm going to jump over
+ 
+
+ align:start position:0%
+in quadrant 2 1 I'm going to jump over
+and over to rows and
+
+ align:start position:0%
+and over to rows and
+ 
+
+ align:start position:0%
+and over to rows and
+each row has a length row size so it's
+
+ align:start position:0%
+each row has a length row size so it's
+ 
+
+ align:start position:0%
+each row has a length row size so it's
+just gonna be an over two times row size
+
+ align:start position:0%
+just gonna be an over two times row size
+ 
+
+ align:start position:0%
+just gonna be an over two times row size
+and then to get the first element in
+
+ align:start position:0%
+and then to get the first element in
+ 
+
+ align:start position:0%
+and then to get the first element in
+Quadrant 2 2 it's just the first element
+
+ align:start position:0%
+Quadrant 2 2 it's just the first element
+ 
+
+ align:start position:0%
+Quadrant 2 2 it's just the first element
+in Quadrant 2 1 + + / 2 so that's n over
+
+ align:start position:0%
+in Quadrant 2 1 + + / 2 so that's n over
+ 
+
+ align:start position:0%
+in Quadrant 2 1 + + / 2 so that's n over
+2 times row size plus 1 so let's analyze
+
+ align:start position:0%
+2 times row size plus 1 so let's analyze
+ 
+
+ align:start position:0%
+2 times row size plus 1 so let's analyze
+the work of this algorithm so what's the
+
+ align:start position:0%
+the work of this algorithm so what's the
+ 
+
+ align:start position:0%
+the work of this algorithm so what's the
+recurrence for this algorithm for the
+
+ align:start position:0%
+recurrence for this algorithm for the
+ 
+
+ align:start position:0%
+recurrence for this algorithm for the
+work of this algorithm so how many
+
+ align:start position:0%
+work of this algorithm so how many
+ 
+
+ align:start position:0%
+work of this algorithm so how many
+subproblems do we have 8 and what's the
+
+ align:start position:0%
+subproblems do we have 8 and what's the
+ 
+
+ align:start position:0%
+subproblems do we have 8 and what's the
+size of each subproblem n over 2 and how
+
+ align:start position:0%
+size of each subproblem n over 2 and how
+ 
+
+ align:start position:0%
+size of each subproblem n over 2 and how
+much work are we doing to set up the
+
+ align:start position:0%
+much work are we doing to set up the
+ 
+
+ align:start position:0%
+much work are we doing to set up the
+recursive calls constant amount of work
+
+ align:start position:0%
+recursive calls constant amount of work
+ 
+
+ align:start position:0%
+recursive calls constant amount of work
+so the recurrence is w of n is equal to
+
+ align:start position:0%
+so the recurrence is w of n is equal to
+ 
+
+ align:start position:0%
+so the recurrence is w of n is equal to
+8 w n over 2 plus theta of 1 and what
+
+ align:start position:0%
+8 w n over 2 plus theta of 1 and what
+ 
+
+ align:start position:0%
+8 w n over 2 plus theta of 1 and what
+does that solve to and cubed so it's one
+
+ align:start position:0%
+does that solve to and cubed so it's one
+ 
+
+ align:start position:0%
+does that solve to and cubed so it's one
+of the three cases of the master theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're actually going to analyze this in
+
+ align:start position:0%
+we're actually going to analyze this in
+ 
+
+ align:start position:0%
+we're actually going to analyze this in
+more detail using by drawing out the
+
+ align:start position:0%
+more detail using by drawing out the
+ 
+
+ align:start position:0%
+more detail using by drawing out the
+recursion tree and this is going to give
+
+ align:start position:0%
+recursion tree and this is going to give
+ 
+
+ align:start position:0%
+recursion tree and this is going to give
+us more intuition about why the master
+
+ align:start position:0%
+us more intuition about why the master
+ 
+
+ align:start position:0%
+us more intuition about why the master
+theorem is true so at the top level of
+
+ align:start position:0%
+theorem is true so at the top level of
+ 
+
+ align:start position:0%
+theorem is true so at the top level of
+my recursion tree I'm gonna have a
+
+ align:start position:0%
+my recursion tree I'm gonna have a
+ 
+
+ align:start position:0%
+my recursion tree I'm gonna have a
+problem of size N and then I'm gonna
+
+ align:start position:0%
+problem of size N and then I'm gonna
+ 
+
+ align:start position:0%
+problem of size N and then I'm gonna
+branch into 8 sub problems of size n
+
+ align:start position:0%
+branch into 8 sub problems of size n
+ 
+
+ align:start position:0%
+branch into 8 sub problems of size n
+over 2 and then I'm gonna do a constant
+
+ align:start position:0%
+over 2 and then I'm gonna do a constant
+ 
+
+ align:start position:0%
+over 2 and then I'm gonna do a constant
+amount of work to set up the recursive
+
+ align:start position:0%
+amount of work to set up the recursive
+ 
+
+ align:start position:0%
+amount of work to set up the recursive
+calls here I'm just labeling this with
+
+ align:start position:0%
+calls here I'm just labeling this with
+ 
+
+ align:start position:0%
+calls here I'm just labeling this with
+one so I'm ignoring the constants but
+
+ align:start position:0%
+one so I'm ignoring the constants but
+ 
+
+ align:start position:0%
+one so I'm ignoring the constants but
+it's not gonna matter for asymptotic
+
+ align:start position:0%
+it's not gonna matter for asymptotic
+ 
+
+ align:start position:0%
+it's not gonna matter for asymptotic
+analysis and then I'm gonna branch again
+
+ align:start position:0%
+analysis and then I'm gonna branch again
+ 
+
+ align:start position:0%
+analysis and then I'm gonna branch again
+into 8 sub problems of size and over
+
+ align:start position:0%
+into 8 sub problems of size and over
+ 
+
+ align:start position:0%
+into 8 sub problems of size and over
+four and eventually I'm gonna get down
+
+ align:start position:0%
+four and eventually I'm gonna get down
+ 
+
+ align:start position:0%
+four and eventually I'm gonna get down
+to the leaves and how many levels do I
+
+ align:start position:0%
+to the leaves and how many levels do I
+ 
+
+ align:start position:0%
+to the leaves and how many levels do I
+have until I get to the leaves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes o log n what's the base of the
+
+ align:start position:0%
+yes yes o log n what's the base of the
+ 
+
+ align:start position:0%
+yes yes o log n what's the base of the
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+yes it's log base 2 of n because I'm
+
+ align:start position:0%
+yes it's log base 2 of n because I'm
+ 
+
+ align:start position:0%
+yes it's log base 2 of n because I'm
+dividing my problem size by two every
+
+ align:start position:0%
+dividing my problem size by two every
+ 
+
+ align:start position:0%
+dividing my problem size by two every
+time and therefore the number of leaves
+
+ align:start position:0%
+time and therefore the number of leaves
+ 
+
+ align:start position:0%
+time and therefore the number of leaves
+I have is going to be 8 to the log base
+
+ align:start position:0%
+I have is going to be 8 to the log base
+ 
+
+ align:start position:0%
+I have is going to be 8 to the log base
+2 of n because I'm branching 8 ways
+
+ align:start position:0%
+2 of n because I'm branching 8 ways
+ 
+
+ align:start position:0%
+2 of n because I'm branching 8 ways
+every time 8 to the log base 2 of n is
+
+ align:start position:0%
+every time 8 to the log base 2 of n is
+ 
+
+ align:start position:0%
+every time 8 to the log base 2 of n is
+the same as n to the log base 2 of 8
+
+ align:start position:0%
+the same as n to the log base 2 of 8
+ 
+
+ align:start position:0%
+the same as n to the log base 2 of 8
+which is n cubed the amount of work I'm
+
+ align:start position:0%
+which is n cubed the amount of work I'm
+ 
+
+ align:start position:0%
+which is n cubed the amount of work I'm
+doing at the top level is constant so
+
+ align:start position:0%
+doing at the top level is constant so
+ 
+
+ align:start position:0%
+doing at the top level is constant so
+I'm just gonna say one here the next log
+
+ align:start position:0%
+I'm just gonna say one here the next log
+ 
+
+ align:start position:0%
+I'm just gonna say one here the next log
+was eight times that then 64 and then
+
+ align:start position:0%
+was eight times that then 64 and then
+ 
+
+ align:start position:0%
+was eight times that then 64 and then
+when I get to the leaves it's going to
+
+ align:start position:0%
+when I get to the leaves it's going to
+ 
+
+ align:start position:0%
+when I get to the leaves it's going to
+be theta of n cubed since I have n cubed
+
+ align:start position:0%
+be theta of n cubed since I have n cubed
+ 
+
+ align:start position:0%
+be theta of n cubed since I have n cubed
+leaves and they're all doing constant
+
+ align:start position:0%
+leaves and they're all doing constant
+ 
+
+ align:start position:0%
+leaves and they're all doing constant
+work and the work is geometrically
+
+ align:start position:0%
+work and the work is geometrically
+ 
+
+ align:start position:0%
+work and the work is geometrically
+increasing as I go down the recursion
+
+ align:start position:0%
+increasing as I go down the recursion
+ 
+
+ align:start position:0%
+increasing as I go down the recursion
+tree so the overall work is just
+
+ align:start position:0%
+tree so the overall work is just
+ 
+
+ align:start position:0%
+tree so the overall work is just
+dominated by the work I need to do at
+
+ align:start position:0%
+dominated by the work I need to do at
+ 
+
+ align:start position:0%
+dominated by the work I need to do at
+the leaves so the overall work is just
+
+ align:start position:0%
+the leaves so the overall work is just
+ 
+
+ align:start position:0%
+the leaves so the overall work is just
+gonna be theta n cubed and this is the
+
+ align:start position:0%
+gonna be theta n cubed and this is the
+ 
+
+ align:start position:0%
+gonna be theta n cubed and this is the
+same as the looping versions of matrix
+
+ align:start position:0%
+same as the looping versions of matrix
+ 
+
+ align:start position:0%
+same as the looping versions of matrix
+multiply they're all cubic work now
+
+ align:start position:0%
+multiply they're all cubic work now
+ 
+
+ align:start position:0%
+multiply they're all cubic work now
+let's analyze the number of cache misses
+
+ align:start position:0%
+let's analyze the number of cache misses
+ 
+
+ align:start position:0%
+let's analyze the number of cache misses
+of this dividing conquer algorithm so
+
+ align:start position:0%
+of this dividing conquer algorithm so
+ 
+
+ align:start position:0%
+of this dividing conquer algorithm so
+now a migrant recurrence is gonna be
+
+ align:start position:0%
+now a migrant recurrence is gonna be
+ 
+
+ align:start position:0%
+now a migrant recurrence is gonna be
+different my base case now is when the
+
+ align:start position:0%
+different my base case now is when the
+ 
+
+ align:start position:0%
+different my base case now is when the
+sub matrix fits in the cache so when n
+
+ align:start position:0%
+sub matrix fits in the cache so when n
+ 
+
+ align:start position:0%
+sub matrix fits in the cache so when n
+squared is less than CM and when that's
+
+ align:start position:0%
+squared is less than CM and when that's
+ 
+
+ align:start position:0%
+squared is less than CM and when that's
+true I just need to load that some
+
+ align:start position:0%
+true I just need to load that some
+ 
+
+ align:start position:0%
+true I just need to load that some
+matrix in the cache and then I don't
+
+ align:start position:0%
+matrix in the cache and then I don't
+ 
+
+ align:start position:0%
+matrix in the cache and then I don't
+incur any more cache misses so I need
+
+ align:start position:0%
+incur any more cache misses so I need
+ 
+
+ align:start position:0%
+incur any more cache misses so I need
+theta of N squared over the cache misses
+
+ align:start position:0%
+theta of N squared over the cache misses
+ 
+
+ align:start position:0%
+theta of N squared over the cache misses
+when N squared is less than CM for some
+
+ align:start position:0%
+when N squared is less than CM for some
+ 
+
+ align:start position:0%
+when N squared is less than CM for some
+sophisticated sufficiently small
+
+ align:start position:0%
+sophisticated sufficiently small
+ 
+
+ align:start position:0%
+sophisticated sufficiently small
+constant C less than equal to 1 and then
+
+ align:start position:0%
+constant C less than equal to 1 and then
+ 
+
+ align:start position:0%
+constant C less than equal to 1 and then
+otherwise i recurse into 8 sub problems
+
+ align:start position:0%
+otherwise i recurse into 8 sub problems
+ 
+
+ align:start position:0%
+otherwise i recurse into 8 sub problems
+of size n over 2 and then I add theta of
+
+ align:start position:0%
+of size n over 2 and then I add theta of
+ 
+
+ align:start position:0%
+of size n over 2 and then I add theta of
+1 because I'm doing a constant amount of
+
+ align:start position:0%
+1 because I'm doing a constant amount of
+ 
+
+ align:start position:0%
+1 because I'm doing a constant amount of
+work to set up the recursive calls and I
+
+ align:start position:0%
+work to set up the recursive calls and I
+ 
+
+ align:start position:0%
+work to set up the recursive calls and I
+get this theta of N squared over B term
+
+ align:start position:0%
+get this theta of N squared over B term
+ 
+
+ align:start position:0%
+get this theta of N squared over B term
+from the sub matrix cashing lemma says I
+
+ align:start position:0%
+from the sub matrix cashing lemma says I
+ 
+
+ align:start position:0%
+from the sub matrix cashing lemma says I
+can just load the entire matrix into
+
+ align:start position:0%
+can just load the entire matrix into
+ 
+
+ align:start position:0%
+can just load the entire matrix into
+cache with this many cache misses so so
+
+ align:start position:0%
+cache with this many cache misses so so
+ 
+
+ align:start position:0%
+cache with this many cache misses so so
+the difference between the cache
+
+ align:start position:0%
+the difference between the cache
+ 
+
+ align:start position:0%
+the difference between the cache
+analysis here and the work analysis
+
+ align:start position:0%
+analysis here and the work analysis
+ 
+
+ align:start position:0%
+analysis here and the work analysis
+before is that I have a different base
+
+ align:start position:0%
+before is that I have a different base
+ 
+
+ align:start position:0%
+before is that I have a different base
+case and I think in all of that
+
+ align:start position:0%
+case and I think in all of that
+ 
+
+ align:start position:0%
+case and I think in all of that
+that you've seen before the base case
+
+ align:start position:0%
+that you've seen before the base case
+ 
+
+ align:start position:0%
+that you've seen before the base case
+was always of a constant size but here
+
+ align:start position:0%
+was always of a constant size but here
+ 
+
+ align:start position:0%
+was always of a constant size but here
+we're working with a base case that's
+
+ align:start position:0%
+we're working with a base case that's
+ 
+
+ align:start position:0%
+we're working with a base case that's
+not of a constant size so let's try to
+
+ align:start position:0%
+not of a constant size so let's try to
+ 
+
+ align:start position:0%
+not of a constant size so let's try to
+analyze this using the recursion tree
+
+ align:start position:0%
+analyze this using the recursion tree
+ 
+
+ align:start position:0%
+analyze this using the recursion tree
+approach so at the top level I have a
+
+ align:start position:0%
+approach so at the top level I have a
+ 
+
+ align:start position:0%
+approach so at the top level I have a
+problem of size n then I'm going to
+
+ align:start position:0%
+problem of size n then I'm going to
+ 
+
+ align:start position:0%
+problem of size n then I'm going to
+branch and do eight problems of size n
+
+ align:start position:0%
+branch and do eight problems of size n
+ 
+
+ align:start position:0%
+branch and do eight problems of size n
+over two and then I'm also going to
+
+ align:start position:0%
+over two and then I'm also going to
+ 
+
+ align:start position:0%
+over two and then I'm also going to
+incur constant number of cache misses
+
+ align:start position:0%
+incur constant number of cache misses
+ 
+
+ align:start position:0%
+incur constant number of cache misses
+I'm just gonna say one here then I'm
+
+ align:start position:0%
+I'm just gonna say one here then I'm
+ 
+
+ align:start position:0%
+I'm just gonna say one here then I'm
+gonna branch again and then eventually
+
+ align:start position:0%
+gonna branch again and then eventually
+ 
+
+ align:start position:0%
+gonna branch again and then eventually
+I'm going to get to the base case where
+
+ align:start position:0%
+I'm going to get to the base case where
+ 
+
+ align:start position:0%
+I'm going to get to the base case where
+N squared is less than CM and when N
+
+ align:start position:0%
+N squared is less than CM and when N
+ 
+
+ align:start position:0%
+N squared is less than CM and when N
+squared is less than CM then the number
+
+ align:start position:0%
+squared is less than CM then the number
+ 
+
+ align:start position:0%
+squared is less than CM then the number
+of cache misses that I'm gonna incur is
+
+ align:start position:0%
+of cache misses that I'm gonna incur is
+ 
+
+ align:start position:0%
+of cache misses that I'm gonna incur is
+going to be theta of CM over B so I can
+
+ align:start position:0%
+going to be theta of CM over B so I can
+ 
+
+ align:start position:0%
+going to be theta of CM over B so I can
+just plug in CM here for n squared and
+
+ align:start position:0%
+just plug in CM here for n squared and
+ 
+
+ align:start position:0%
+just plug in CM here for n squared and
+the number of levels of recursion I have
+
+ align:start position:0%
+the number of levels of recursion I have
+ 
+
+ align:start position:0%
+the number of levels of recursion I have
+in this recursion tree is no longer just
+
+ align:start position:0%
+in this recursion tree is no longer just
+ 
+
+ align:start position:0%
+in this recursion tree is no longer just
+log base two of n I'm gonna have log
+
+ align:start position:0%
+log base two of n I'm gonna have log
+ 
+
+ align:start position:0%
+log base two of n I'm gonna have log
+base two of n minus log base two of
+
+ align:start position:0%
+base two of n minus log base two of
+ 
+
+ align:start position:0%
+base two of n minus log base two of
+square root of CM number of levels which
+
+ align:start position:0%
+square root of CM number of levels which
+ 
+
+ align:start position:0%
+square root of CM number of levels which
+is the same as log base two of n minus
+
+ align:start position:0%
+is the same as log base two of n minus
+ 
+
+ align:start position:0%
+is the same as log base two of n minus
+1/2 times log base two of CM and then
+
+ align:start position:0%
+1/2 times log base two of CM and then
+ 
+
+ align:start position:0%
+1/2 times log base two of CM and then
+the number of leaves I get is going to
+
+ align:start position:0%
+the number of leaves I get is going to
+ 
+
+ align:start position:0%
+the number of leaves I get is going to
+be eight to this to this number of
+
+ align:start position:0%
+be eight to this to this number of
+ 
+
+ align:start position:0%
+be eight to this to this number of
+levels here says 8 to log base two of n
+
+ align:start position:0%
+levels here says 8 to log base two of n
+ 
+
+ align:start position:0%
+levels here says 8 to log base two of n
+minus 1/2 of log base two of cm and this
+
+ align:start position:0%
+minus 1/2 of log base two of cm and this
+ 
+
+ align:start position:0%
+minus 1/2 of log base two of cm and this
+is equal to theta of n cubed over m to
+
+ align:start position:0%
+is equal to theta of n cubed over m to
+ 
+
+ align:start position:0%
+is equal to theta of n cubed over m to
+the three halves so the n cubed comes
+
+ align:start position:0%
+the three halves so the n cubed comes
+ 
+
+ align:start position:0%
+the three halves so the n cubed comes
+from the eight to the log base two of n
+
+ align:start position:0%
+from the eight to the log base two of n
+ 
+
+ align:start position:0%
+from the eight to the log base two of n
+term and then if I do eight to the log
+
+ align:start position:0%
+term and then if I do eight to the log
+ 
+
+ align:start position:0%
+term and then if I do eight to the log
+base 8 to the negative one half of log
+
+ align:start position:0%
+base 8 to the negative one half of log
+ 
+
+ align:start position:0%
+base 8 to the negative one half of log
+base two of CM that's just gonna give me
+
+ align:start position:0%
+base two of CM that's just gonna give me
+ 
+
+ align:start position:0%
+base two of CM that's just gonna give me
+m over m to the three halves in the
+
+ align:start position:0%
+m over m to the three halves in the
+ 
+
+ align:start position:0%
+m over m to the three halves in the
+denominator so any questions on how I
+
+ align:start position:0%
+denominator so any questions on how I
+ 
+
+ align:start position:0%
+denominator so any questions on how I
+computed the number of levels of this
+
+ align:start position:0%
+computed the number of levels of this
+ 
+
+ align:start position:0%
+computed the number of levels of this
+recursion tree here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm basically dividing my problem
+
+ align:start position:0%
+so I'm basically dividing my problem
+ 
+
+ align:start position:0%
+so I'm basically dividing my problem
+size by two until I get to a problem
+
+ align:start position:0%
+size by two until I get to a problem
+ 
+
+ align:start position:0%
+size by two until I get to a problem
+size that fits into cash so that means n
+
+ align:start position:0%
+size that fits into cash so that means n
+ 
+
+ align:start position:0%
+size that fits into cash so that means n
+is less than square root of CM so
+
+ align:start position:0%
+is less than square root of CM so
+ 
+
+ align:start position:0%
+is less than square root of CM so
+therefore I can subtract that many
+
+ align:start position:0%
+therefore I can subtract that many
+ 
+
+ align:start position:0%
+therefore I can subtract that many
+levels for my recursion tree and then to
+
+ align:start position:0%
+levels for my recursion tree and then to
+ 
+
+ align:start position:0%
+levels for my recursion tree and then to
+get the number of leaves since I'm
+
+ align:start position:0%
+get the number of leaves since I'm
+ 
+
+ align:start position:0%
+get the number of leaves since I'm
+branching eight ways I just do eight to
+
+ align:start position:0%
+branching eight ways I just do eight to
+ 
+
+ align:start position:0%
+branching eight ways I just do eight to
+the power of the number of levels I have
+
+ align:start position:0%
+the power of the number of levels I have
+ 
+
+ align:start position:0%
+the power of the number of levels I have
+and then that gives me the total number
+
+ align:start position:0%
+and then that gives me the total number
+ 
+
+ align:start position:0%
+and then that gives me the total number
+of leaves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's analyze the number of cache
+
+ align:start position:0%
+so now let's analyze the number of cache
+ 
+
+ align:start position:0%
+so now let's analyze the number of cache
+misses I need at each level of this
+
+ align:start position:0%
+misses I need at each level of this
+ 
+
+ align:start position:0%
+misses I need at each level of this
+recursion tree at the top level I have a
+
+ align:start position:0%
+recursion tree at the top level I have a
+ 
+
+ align:start position:0%
+recursion tree at the top level I have a
+constant number of cache misses let's
+
+ align:start position:0%
+constant number of cache misses let's
+ 
+
+ align:start position:0%
+constant number of cache misses let's
+just say one the next level I have eight
+
+ align:start position:0%
+just say one the next level I have eight
+ 
+
+ align:start position:0%
+just say one the next level I have eight
+sixty-four and then at the leaves I'm
+
+ align:start position:0%
+sixty-four and then at the leaves I'm
+ 
+
+ align:start position:0%
+sixty-four and then at the leaves I'm
+going to have theta of n cubed over B
+
+ align:start position:0%
+going to have theta of n cubed over B
+ 
+
+ align:start position:0%
+going to have theta of n cubed over B
+times square root of M cache misses and
+
+ align:start position:0%
+times square root of M cache misses and
+ 
+
+ align:start position:0%
+times square root of M cache misses and
+I got this quantity just by multiplying
+
+ align:start position:0%
+I got this quantity just by multiplying
+ 
+
+ align:start position:0%
+I got this quantity just by multiplying
+the number of leaves by the number of
+
+ align:start position:0%
+the number of leaves by the number of
+ 
+
+ align:start position:0%
+the number of leaves by the number of
+cache misses per leaf so number of
+
+ align:start position:0%
+cache misses per leaf so number of
+ 
+
+ align:start position:0%
+cache misses per leaf so number of
+leaves is n cubed over m to the three
+
+ align:start position:0%
+leaves is n cubed over m to the three
+ 
+
+ align:start position:0%
+leaves is n cubed over m to the three
+halves the cache misses per leaves is
+
+ align:start position:0%
+halves the cache misses per leaves is
+ 
+
+ align:start position:0%
+halves the cache misses per leaves is
+state of CM over B so I lose one factor
+
+ align:start position:0%
+state of CM over B so I lose one factor
+ 
+
+ align:start position:0%
+state of CM over B so I lose one factor
+of B in the denominator I'm left with
+
+ align:start position:0%
+of B in the denominator I'm left with
+ 
+
+ align:start position:0%
+of B in the denominator I'm left with
+the square root of M at the bottom and
+
+ align:start position:0%
+the square root of M at the bottom and
+ 
+
+ align:start position:0%
+the square root of M at the bottom and
+then I also divide by the block size B
+
+ align:start position:0%
+then I also divide by the block size B
+ 
+
+ align:start position:0%
+then I also divide by the block size B
+so overall I get n cubed over B times
+
+ align:start position:0%
+so overall I get n cubed over B times
+ 
+
+ align:start position:0%
+so overall I get n cubed over B times
+square root of M cache misses and again
+
+ align:start position:0%
+square root of M cache misses and again
+ 
+
+ align:start position:0%
+square root of M cache misses and again
+this is a geometric series and the
+
+ align:start position:0%
+this is a geometric series and the
+ 
+
+ align:start position:0%
+this is a geometric series and the
+number of cache misses at the leaves
+
+ align:start position:0%
+number of cache misses at the leaves
+ 
+
+ align:start position:0%
+number of cache misses at the leaves
+dominates all of the other levels so the
+
+ align:start position:0%
+dominates all of the other levels so the
+ 
+
+ align:start position:0%
+dominates all of the other levels so the
+total number of cache misses I have is
+
+ align:start position:0%
+total number of cache misses I have is
+ 
+
+ align:start position:0%
+total number of cache misses I have is
+going to be theta n cubed over B times
+
+ align:start position:0%
+going to be theta n cubed over B times
+ 
+
+ align:start position:0%
+going to be theta n cubed over B times
+square root of M and notice that I'm
+
+ align:start position:0%
+square root of M and notice that I'm
+ 
+
+ align:start position:0%
+square root of M and notice that I'm
+getting the same number of cache misses
+
+ align:start position:0%
+getting the same number of cache misses
+ 
+
+ align:start position:0%
+getting the same number of cache misses
+as I did with the tiling version of the
+
+ align:start position:0%
+as I did with the tiling version of the
+ 
+
+ align:start position:0%
+as I did with the tiling version of the
+code but here I don't actually have the
+
+ align:start position:0%
+code but here I don't actually have the
+ 
+
+ align:start position:0%
+code but here I don't actually have the
+two in my code for the particular cache
+
+ align:start position:0%
+two in my code for the particular cache
+ 
+
+ align:start position:0%
+two in my code for the particular cache
+size so what cache sizes does this code
+
+ align:start position:0%
+size so what cache sizes does this code
+ 
+
+ align:start position:0%
+size so what cache sizes does this code
+work for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is this code gonna work on your
+
+ align:start position:0%
+so is this code gonna work on your
+ 
+
+ align:start position:0%
+so is this code gonna work on your
+machine it's gonna get good cache
+
+ align:start position:0%
+machine it's gonna get good cache
+ 
+
+ align:start position:0%
+machine it's gonna get good cache
+performance so this code is gonna work
+
+ align:start position:0%
+performance so this code is gonna work
+ 
+
+ align:start position:0%
+performance so this code is gonna work
+for all cache sizes because I didn't
+
+ align:start position:0%
+for all cache sizes because I didn't
+ 
+
+ align:start position:0%
+for all cache sizes because I didn't
+tune it for any particular cache size
+
+ align:start position:0%
+tune it for any particular cache size
+ 
+
+ align:start position:0%
+tune it for any particular cache size
+and this is what's known as a cache
+
+ align:start position:0%
+and this is what's known as a cache
+ 
+
+ align:start position:0%
+and this is what's known as a cache
+oblivious algorithm it doesn't have any
+
+ align:start position:0%
+oblivious algorithm it doesn't have any
+ 
+
+ align:start position:0%
+oblivious algorithm it doesn't have any
+Voodoo tuning parameters has no explicit
+
+ align:start position:0%
+Voodoo tuning parameters has no explicit
+ 
+
+ align:start position:0%
+Voodoo tuning parameters has no explicit
+knowledge of the caches and it's
+
+ align:start position:0%
+knowledge of the caches and it's
+ 
+
+ align:start position:0%
+knowledge of the caches and it's
+essentially passively Auto tuning itself
+
+ align:start position:0%
+essentially passively Auto tuning itself
+ 
+
+ align:start position:0%
+essentially passively Auto tuning itself
+for the particular cache size of your
+
+ align:start position:0%
+for the particular cache size of your
+ 
+
+ align:start position:0%
+for the particular cache size of your
+machine it can also work for multi-level
+
+ align:start position:0%
+machine it can also work for multi-level
+ 
+
+ align:start position:0%
+machine it can also work for multi-level
+caches automatically because I never
+
+ align:start position:0%
+caches automatically because I never
+ 
+
+ align:start position:0%
+caches automatically because I never
+specified what level of cache I'm
+
+ align:start position:0%
+specified what level of cache I'm
+ 
+
+ align:start position:0%
+specified what level of cache I'm
+analyzing this for I can analyze it for
+
+ align:start position:0%
+analyzing this for I can analyze it for
+ 
+
+ align:start position:0%
+analyzing this for I can analyze it for
+any level of cache and it's still gonna
+
+ align:start position:0%
+any level of cache and it's still gonna
+ 
+
+ align:start position:0%
+any level of cache and it's still gonna
+give me good cache complexity and this
+
+ align:start position:0%
+give me good cache complexity and this
+ 
+
+ align:start position:0%
+give me good cache complexity and this
+is also good in multi programmed
+
+ align:start position:0%
+is also good in multi programmed
+ 
+
+ align:start position:0%
+is also good in multi programmed
+environments where you might have other
+
+ align:start position:0%
+environments where you might have other
+ 
+
+ align:start position:0%
+environments where you might have other
+jobs running and you don't know your
+
+ align:start position:0%
+jobs running and you don't know your
+ 
+
+ align:start position:0%
+jobs running and you don't know your
+effective cache size this is just gonna
+
+ align:start position:0%
+effective cache size this is just gonna
+ 
+
+ align:start position:0%
+effective cache size this is just gonna
+pass all the auto-tune for whatever
+
+ align:start position:0%
+pass all the auto-tune for whatever
+ 
+
+ align:start position:0%
+pass all the auto-tune for whatever
+cache size is available turns out that
+
+ align:start position:0%
+cache size is available turns out that
+ 
+
+ align:start position:0%
+cache size is available turns out that
+the best cache oblivious codes today
+
+ align:start position:0%
+the best cache oblivious codes today
+ 
+
+ align:start position:0%
+the best cache oblivious codes today
+work on arbitrary rectangular matrices I
+
+ align:start position:0%
+work on arbitrary rectangular matrices I
+ 
+
+ align:start position:0%
+work on arbitrary rectangular matrices I
+just talked about square matrices but
+
+ align:start position:0%
+just talked about square matrices but
+ 
+
+ align:start position:0%
+just talked about square matrices but
+the best codes work on rectangular
+
+ align:start position:0%
+the best codes work on rectangular
+ 
+
+ align:start position:0%
+the best codes work on rectangular
+matrices and they perform binary
+
+ align:start position:0%
+matrices and they perform binary
+ 
+
+ align:start position:0%
+matrices and they perform binary
+splitting instead of eight-way splitting
+
+ align:start position:0%
+splitting instead of eight-way splitting
+ 
+
+ align:start position:0%
+splitting instead of eight-way splitting
+and you split on the largest of I J and
+
+ align:start position:0%
+and you split on the largest of I J and
+ 
+
+ align:start position:0%
+and you split on the largest of I J and
+K so this is what the best cache
+
+ align:start position:0%
+K so this is what the best cache
+ 
+
+ align:start position:0%
+K so this is what the best cache
+oblivious matrix multiplication
+
+ align:start position:0%
+oblivious matrix multiplication
+ 
+
+ align:start position:0%
+oblivious matrix multiplication
+algorithm does any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I only talked about the serial
+
+ align:start position:0%
+okay so I only talked about the serial
+ 
+
+ align:start position:0%
+okay so I only talked about the serial
+setting so far I was assuming that these
+
+ align:start position:0%
+setting so far I was assuming that these
+ 
+
+ align:start position:0%
+setting so far I was assuming that these
+algorithms ran on just a single thread
+
+ align:start position:0%
+algorithms ran on just a single thread
+ 
+
+ align:start position:0%
+algorithms ran on just a single thread
+what happens if I go to multiple
+
+ align:start position:0%
+what happens if I go to multiple
+ 
+
+ align:start position:0%
+what happens if I go to multiple
+processors turns out that the results do
+
+ align:start position:0%
+processors turns out that the results do
+ 
+
+ align:start position:0%
+processors turns out that the results do
+generalize to a parallel context so this
+
+ align:start position:0%
+generalize to a parallel context so this
+ 
+
+ align:start position:0%
+generalize to a parallel context so this
+is the recursive parallel
+
+ align:start position:0%
+is the recursive parallel
+ 
+
+ align:start position:0%
+is the recursive parallel
+matrix-multiply code that we saw before
+
+ align:start position:0%
+matrix-multiply code that we saw before
+ 
+
+ align:start position:0%
+matrix-multiply code that we saw before
+and notice that we're executing four sub
+
+ align:start position:0%
+and notice that we're executing four sub
+ 
+
+ align:start position:0%
+and notice that we're executing four sub
+calls in parallel doing a sync and then
+
+ align:start position:0%
+calls in parallel doing a sync and then
+ 
+
+ align:start position:0%
+calls in parallel doing a sync and then
+doing four more sub calls in parallel so
+
+ align:start position:0%
+doing four more sub calls in parallel so
+ 
+
+ align:start position:0%
+doing four more sub calls in parallel so
+let's try to analyze the number of cache
+
+ align:start position:0%
+let's try to analyze the number of cache
+ 
+
+ align:start position:0%
+let's try to analyze the number of cache
+misses in this parallel code and to do
+
+ align:start position:0%
+misses in this parallel code and to do
+ 
+
+ align:start position:0%
+misses in this parallel code and to do
+that we're gonna use this theorem which
+
+ align:start position:0%
+that we're gonna use this theorem which
+ 
+
+ align:start position:0%
+that we're gonna use this theorem which
+says that let Q sub P be the number of
+
+ align:start position:0%
+says that let Q sub P be the number of
+ 
+
+ align:start position:0%
+says that let Q sub P be the number of
+cache misses in a deterministic cell
+
+ align:start position:0%
+cache misses in a deterministic cell
+ 
+
+ align:start position:0%
+cache misses in a deterministic cell
+computation won't run on P processors
+
+ align:start position:0%
+computation won't run on P processors
+ 
+
+ align:start position:0%
+computation won't run on P processors
+each with a private cache of size M and
+
+ align:start position:0%
+each with a private cache of size M and
+ 
+
+ align:start position:0%
+each with a private cache of size M and
+let S sub P be the number of successful
+
+ align:start position:0%
+let S sub P be the number of successful
+ 
+
+ align:start position:0%
+let S sub P be the number of successful
+steals during the computation in the
+
+ align:start position:0%
+steals during the computation in the
+ 
+
+ align:start position:0%
+steals during the computation in the
+ideal cache model the number of cache
+
+ align:start position:0%
+ideal cache model the number of cache
+ 
+
+ align:start position:0%
+ideal cache model the number of cache
+misses we're gonna have is Q sub P equal
+
+ align:start position:0%
+misses we're gonna have is Q sub P equal
+ 
+
+ align:start position:0%
+misses we're gonna have is Q sub P equal
+to Q sub 1 plus Big O of number of
+
+ align:start position:0%
+to Q sub 1 plus Big O of number of
+ 
+
+ align:start position:0%
+to Q sub 1 plus Big O of number of
+steals times M over B so a number of
+
+ align:start position:0%
+steals times M over B so a number of
+ 
+
+ align:start position:0%
+steals times M over B so a number of
+cache misses in the parallel context is
+
+ align:start position:0%
+cache misses in the parallel context is
+ 
+
+ align:start position:0%
+cache misses in the parallel context is
+equal to a number of cache misses when
+
+ align:start position:0%
+equal to a number of cache misses when
+ 
+
+ align:start position:0%
+equal to a number of cache misses when
+you run it serially plus this term here
+
+ align:start position:0%
+you run it serially plus this term here
+ 
+
+ align:start position:0%
+you run it serially plus this term here
+which is the number of steals times M
+
+ align:start position:0%
+which is the number of steals times M
+ 
+
+ align:start position:0%
+which is the number of steals times M
+over B and a proof for this goes as fall
+
+ align:start position:0%
+over B and a proof for this goes as fall
+ 
+
+ align:start position:0%
+over B and a proof for this goes as fall
+so every call in the silk runtime system
+
+ align:start position:0%
+so every call in the silk runtime system
+ 
+
+ align:start position:0%
+so every call in the silk runtime system
+we can have workers steal tasks from
+
+ align:start position:0%
+we can have workers steal tasks from
+ 
+
+ align:start position:0%
+we can have workers steal tasks from
+other workers when they don't have work
+
+ align:start position:0%
+other workers when they don't have work
+ 
+
+ align:start position:0%
+other workers when they don't have work
+to do and after workers steals it has
+
+ align:start position:0%
+to do and after workers steals it has
+ 
+
+ align:start position:0%
+to do and after workers steals it has
+from another worker its cache becomes
+
+ align:start position:0%
+from another worker its cache becomes
+ 
+
+ align:start position:0%
+from another worker its cache becomes
+completely cold in the worst case
+
+ align:start position:0%
+completely cold in the worst case
+ 
+
+ align:start position:0%
+completely cold in the worst case
+because it wasn't actually working on
+
+ align:start position:0%
+because it wasn't actually working on
+ 
+
+ align:start position:0%
+because it wasn't actually working on
+that sub problem before but after M over
+
+ align:start position:0%
+that sub problem before but after M over
+ 
+
+ align:start position:0%
+that sub problem before but after M over
+B cold cache misses its cache is going
+
+ align:start position:0%
+B cold cache misses its cache is going
+ 
+
+ align:start position:0%
+B cold cache misses its cache is going
+to become identical to what it would be
+
+ align:start position:0%
+to become identical to what it would be
+ 
+
+ align:start position:0%
+to become identical to what it would be
+in the serial execution so we just need
+
+ align:start position:0%
+in the serial execution so we just need
+ 
+
+ align:start position:0%
+in the serial execution so we just need
+to pay em over B cache misses to make
+
+ align:start position:0%
+to pay em over B cache misses to make
+ 
+
+ align:start position:0%
+to pay em over B cache misses to make
+make it so that the cache looks the same
+
+ align:start position:0%
+make it so that the cache looks the same
+ 
+
+ align:start position:0%
+make it so that the cache looks the same
+as if they were executing serially and
+
+ align:start position:0%
+as if they were executing serially and
+ 
+
+ align:start position:0%
+as if they were executing serially and
+the same is true when a worker resumes a
+
+ align:start position:0%
+the same is true when a worker resumes a
+ 
+
+ align:start position:0%
+the same is true when a worker resumes a
+stolen computation after a silk sync and
+
+ align:start position:0%
+stolen computation after a silk sync and
+ 
+
+ align:start position:0%
+stolen computation after a silk sync and
+the number of times that these two
+
+ align:start position:0%
+the number of times that these two
+ 
+
+ align:start position:0%
+the number of times that these two
+situations can happen is two times SP
+
+ align:start position:0%
+situations can happen is two times SP
+ 
+
+ align:start position:0%
+situations can happen is two times SP
+two times the number of steals and each
+
+ align:start position:0%
+two times the number of steals and each
+ 
+
+ align:start position:0%
+two times the number of steals and each
+time we have to pay
+
+ align:start position:0%
+time we have to pay
+ 
+
+ align:start position:0%
+time we have to pay
+I'm over B cache misses and this is
+
+ align:start position:0%
+I'm over B cache misses and this is
+ 
+
+ align:start position:0%
+I'm over B cache misses and this is
+where this additive term comes from
+
+ align:start position:0%
+where this additive term comes from
+ 
+
+ align:start position:0%
+where this additive term comes from
+order S sub P times M over B we also
+
+ align:start position:0%
+order S sub P times M over B we also
+ 
+
+ align:start position:0%
+order S sub P times M over B we also
+know that the number of steals in a silk
+
+ align:start position:0%
+know that the number of steals in a silk
+ 
+
+ align:start position:0%
+know that the number of steals in a silk
+program is upper bounded by P times T
+
+ align:start position:0%
+program is upper bounded by P times T
+ 
+
+ align:start position:0%
+program is upper bounded by P times T
+infinity an expectation where P is a
+
+ align:start position:0%
+infinity an expectation where P is a
+ 
+
+ align:start position:0%
+infinity an expectation where P is a
+number of processors and T's infinity is
+
+ align:start position:0%
+number of processors and T's infinity is
+ 
+
+ align:start position:0%
+number of processors and T's infinity is
+the span of your computation so if you
+
+ align:start position:0%
+the span of your computation so if you
+ 
+
+ align:start position:0%
+the span of your computation so if you
+can minimize the span of your
+
+ align:start position:0%
+can minimize the span of your
+ 
+
+ align:start position:0%
+can minimize the span of your
+computation then this also gives you
+
+ align:start position:0%
+computation then this also gives you
+ 
+
+ align:start position:0%
+computation then this also gives you
+good cache bounds so moral of the story
+
+ align:start position:0%
+good cache bounds so moral of the story
+ 
+
+ align:start position:0%
+good cache bounds so moral of the story
+here is that minimizing the number of
+
+ align:start position:0%
+here is that minimizing the number of
+ 
+
+ align:start position:0%
+here is that minimizing the number of
+cache misses in the serial illusion
+
+ align:start position:0%
+cache misses in the serial illusion
+ 
+
+ align:start position:0%
+cache misses in the serial illusion
+essentially minimizes them in the
+
+ align:start position:0%
+essentially minimizes them in the
+ 
+
+ align:start position:0%
+essentially minimizes them in the
+parallel execution for a low span
+
+ align:start position:0%
+parallel execution for a low span
+ 
+
+ align:start position:0%
+parallel execution for a low span
+algorithm so in this recursive matrix
+
+ align:start position:0%
+algorithm so in this recursive matrix
+ 
+
+ align:start position:0%
+algorithm so in this recursive matrix
+multiplication algorithm the span of
+
+ align:start position:0%
+multiplication algorithm the span of
+ 
+
+ align:start position:0%
+multiplication algorithm the span of
+this is as follows so T infinity of n is
+
+ align:start position:0%
+this is as follows so T infinity of n is
+ 
+
+ align:start position:0%
+this is as follows so T infinity of n is
+2 T infinity of n over 2 plus theta of 1
+
+ align:start position:0%
+2 T infinity of n over 2 plus theta of 1
+ 
+
+ align:start position:0%
+2 T infinity of n over 2 plus theta of 1
+since we're doing a sync here we have to
+
+ align:start position:0%
+since we're doing a sync here we have to
+ 
+
+ align:start position:0%
+since we're doing a sync here we have to
+pay the critical path length of two sub
+
+ align:start position:0%
+pay the critical path length of two sub
+ 
+
+ align:start position:0%
+pay the critical path length of two sub
+calls this solves two theta of N and
+
+ align:start position:0%
+calls this solves two theta of N and
+ 
+
+ align:start position:0%
+calls this solves two theta of N and
+applying the previous lemma this gives
+
+ align:start position:0%
+applying the previous lemma this gives
+ 
+
+ align:start position:0%
+applying the previous lemma this gives
+us a cache miss bound of theta of n
+
+ align:start position:0%
+us a cache miss bound of theta of n
+ 
+
+ align:start position:0%
+us a cache miss bound of theta of n
+cubed over B square root of M this is
+
+ align:start position:0%
+cubed over B square root of M this is
+ 
+
+ align:start position:0%
+cubed over B square root of M this is
+just the same as the serial execution
+
+ align:start position:0%
+just the same as the serial execution
+ 
+
+ align:start position:0%
+just the same as the serial execution
+and then this additive term is going to
+
+ align:start position:0%
+and then this additive term is going to
+ 
+
+ align:start position:0%
+and then this additive term is going to
+be order P times n and there's a span
+
+ align:start position:0%
+be order P times n and there's a span
+ 
+
+ align:start position:0%
+be order P times n and there's a span
+times M over B so that was a parallel
+
+ align:start position:0%
+times M over B so that was a parallel
+ 
+
+ align:start position:0%
+times M over B so that was a parallel
+that was a parallel algorithm for matrix
+
+ align:start position:0%
+that was a parallel algorithm for matrix
+ 
+
+ align:start position:0%
+that was a parallel algorithm for matrix
+multiply and we saw that we can also get
+
+ align:start position:0%
+multiply and we saw that we can also get
+ 
+
+ align:start position:0%
+multiply and we saw that we can also get
+good cache bounds there so here's a
+
+ align:start position:0%
+good cache bounds there so here's a
+ 
+
+ align:start position:0%
+good cache bounds there so here's a
+summary of what we talked about today we
+
+ align:start position:0%
+summary of what we talked about today we
+ 
+
+ align:start position:0%
+summary of what we talked about today we
+talked about Sousa tivity and caches
+
+ align:start position:0%
+talked about Sousa tivity and caches
+ 
+
+ align:start position:0%
+talked about Sousa tivity and caches
+different different ways you can design
+
+ align:start position:0%
+different different ways you can design
+ 
+
+ align:start position:0%
+different different ways you can design
+a cache talked about the ideal cache
+
+ align:start position:0%
+a cache talked about the ideal cache
+ 
+
+ align:start position:0%
+a cache talked about the ideal cache
+model that's useful for analyzing
+
+ align:start position:0%
+model that's useful for analyzing
+ 
+
+ align:start position:0%
+model that's useful for analyzing
+algorithms we talked about cache aware
+
+ align:start position:0%
+algorithms we talked about cache aware
+ 
+
+ align:start position:0%
+algorithms we talked about cache aware
+algorithm that have explicit knowledge
+
+ align:start position:0%
+algorithm that have explicit knowledge
+ 
+
+ align:start position:0%
+algorithm that have explicit knowledge
+of the cache and the example we use was
+
+ align:start position:0%
+of the cache and the example we use was
+ 
+
+ align:start position:0%
+of the cache and the example we use was
+tiled matrix multiply then we came up
+
+ align:start position:0%
+tiled matrix multiply then we came up
+ 
+
+ align:start position:0%
+tiled matrix multiply then we came up
+with a much simpler algorithm that was
+
+ align:start position:0%
+with a much simpler algorithm that was
+ 
+
+ align:start position:0%
+with a much simpler algorithm that was
+cache oblivious using dividing conquer
+
+ align:start position:0%
+cache oblivious using dividing conquer
+ 
+
+ align:start position:0%
+cache oblivious using dividing conquer
+and then on Thursdays lecture will
+
+ align:start position:0%
+and then on Thursdays lecture will
+ 
+
+ align:start position:0%
+and then on Thursdays lecture will
+actually see much more on cache
+
+ align:start position:0%
+actually see much more on cache
+ 
+
+ align:start position:0%
+actually see much more on cache
+oblivious algorithm designed and then
+
+ align:start position:0%
+oblivious algorithm designed and then
+ 
+
+ align:start position:0%
+oblivious algorithm designed and then
+you'll
+
+ align:start position:0%
+you'll
+ 
+
+ align:start position:0%
+you'll
+an opportunity to analyze the cash
+
+ align:start position:0%
+an opportunity to analyze the cash
+ 
+
+ align:start position:0%
+an opportunity to analyze the cash
+efficiency of some algorithms in the
+
+ align:start position:0%
+efficiency of some algorithms in the
+ 
+
+ align:start position:0%
+efficiency of some algorithms in the
+next homework
\ No newline at end of file
diff --git a/xDN5Onmu0mk.txt b/xDN5Onmu0mk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ebb51ff09db91fc8a5aa3fce4c2ee33d536ba4d7
--- /dev/null
+++ b/xDN5Onmu0mk.txt
@@ -0,0 +1,1907 @@
+align:start position:0%
+ 
+we will now go through a beautiful
+
+ align:start position:0%
+we will now go through a beautiful
+ 
+
+ align:start position:0%
+we will now go through a beautiful
+example in which we approach the same
+
+ align:start position:0%
+example in which we approach the same
+ 
+
+ align:start position:0%
+example in which we approach the same
+question in a number of different ways
+
+ align:start position:0%
+question in a number of different ways
+ 
+
+ align:start position:0%
+question in a number of different ways
+and see that by reasoning based on the
+
+ align:start position:0%
+and see that by reasoning based on the
+ 
+
+ align:start position:0%
+and see that by reasoning based on the
+intuitive properties of a Poisson
+
+ align:start position:0%
+intuitive properties of a Poisson
+ 
+
+ align:start position:0%
+intuitive properties of a Poisson
+process we can arrive quickly to the
+
+ align:start position:0%
+process we can arrive quickly to the
+ 
+
+ align:start position:0%
+process we can arrive quickly to the
+right answer the problem is as follows
+
+ align:start position:0%
+right answer the problem is as follows
+ 
+
+ align:start position:0%
+right answer the problem is as follows
+we have three light bulbs and each light
+
+ align:start position:0%
+we have three light bulbs and each light
+ 
+
+ align:start position:0%
+we have three light bulbs and each light
+bulb is being lit at time 0 it starts
+
+ align:start position:0%
+bulb is being lit at time 0 it starts
+ 
+
+ align:start position:0%
+bulb is being lit at time 0 it starts
+working and the light bulb lasts for a
+
+ align:start position:0%
+working and the light bulb lasts for a
+ 
+
+ align:start position:0%
+working and the light bulb lasts for a
+certain amount of time which is random
+
+ align:start position:0%
+certain amount of time which is random
+ 
+
+ align:start position:0%
+certain amount of time which is random
+so this light bulb at last so long this
+
+ align:start position:0%
+so this light bulb at last so long this
+ 
+
+ align:start position:0%
+so this light bulb at last so long this
+one lasts so long this one lasts that
+
+ align:start position:0%
+one lasts so long this one lasts that
+ 
+
+ align:start position:0%
+one lasts so long this one lasts that
+long the lifetime of a light bulb the
+
+ align:start position:0%
+long the lifetime of a light bulb the
+ 
+
+ align:start position:0%
+long the lifetime of a light bulb the
+time until it burns out will be a random
+
+ align:start position:0%
+time until it burns out will be a random
+ 
+
+ align:start position:0%
+time until it burns out will be a random
+variable and we make the following
+
+ align:start position:0%
+variable and we make the following
+ 
+
+ align:start position:0%
+variable and we make the following
+assumptions the lifetimes of the three
+
+ align:start position:0%
+assumptions the lifetimes of the three
+ 
+
+ align:start position:0%
+assumptions the lifetimes of the three
+light bulbs which we denote by x y and z
+
+ align:start position:0%
+light bulbs which we denote by x y and z
+ 
+
+ align:start position:0%
+light bulbs which we denote by x y and z
+will be independent random variables
+
+ align:start position:0%
+will be independent random variables
+ 
+
+ align:start position:0%
+will be independent random variables
+each of which is an exponential random
+
+ align:start position:0%
+each of which is an exponential random
+ 
+
+ align:start position:0%
+each of which is an exponential random
+variable with the parameter lambda were
+
+ align:start position:0%
+variable with the parameter lambda were
+ 
+
+ align:start position:0%
+variable with the parameter lambda were
+interested in the question of
+
+ align:start position:0%
+interested in the question of
+ 
+
+ align:start position:0%
+interested in the question of
+calculating the expected time until a
+
+ align:start position:0%
+calculating the expected time until a
+ 
+
+ align:start position:0%
+calculating the expected time until a
+light bulb burns out for the first time
+
+ align:start position:0%
+light bulb burns out for the first time
+ 
+
+ align:start position:0%
+light bulb burns out for the first time
+so in this picture the light bulb that
+
+ align:start position:0%
+so in this picture the light bulb that
+ 
+
+ align:start position:0%
+so in this picture the light bulb that
+burned out first is this second light
+
+ align:start position:0%
+burned out first is this second light
+ 
+
+ align:start position:0%
+burned out first is this second light
+bulb and this quantity is the time until
+
+ align:start position:0%
+bulb and this quantity is the time until
+ 
+
+ align:start position:0%
+bulb and this quantity is the time until
+the first burn out how do we calculate
+
+ align:start position:0%
+the first burn out how do we calculate
+ 
+
+ align:start position:0%
+the first burn out how do we calculate
+this quantity the time until the first
+
+ align:start position:0%
+this quantity the time until the first
+ 
+
+ align:start position:0%
+this quantity the time until the first
+light bulb burns out is the minimum of
+
+ align:start position:0%
+light bulb burns out is the minimum of
+ 
+
+ align:start position:0%
+light bulb burns out is the minimum of
+the times at which each one of them
+
+ align:start position:0%
+the times at which each one of them
+ 
+
+ align:start position:0%
+the times at which each one of them
+burns out so we're interested in the
+
+ align:start position:0%
+burns out so we're interested in the
+ 
+
+ align:start position:0%
+burns out so we're interested in the
+expected value of this quantity it's a
+
+ align:start position:0%
+expected value of this quantity it's a
+ 
+
+ align:start position:0%
+expected value of this quantity it's a
+random variable which is a function of
+
+ align:start position:0%
+random variable which is a function of
+ 
+
+ align:start position:0%
+random variable which is a function of
+three random variables how do we
+
+ align:start position:0%
+three random variables how do we
+ 
+
+ align:start position:0%
+three random variables how do we
+calculate the expected value of a
+
+ align:start position:0%
+calculate the expected value of a
+ 
+
+ align:start position:0%
+calculate the expected value of a
+function of random variables we can use
+
+ align:start position:0%
+function of random variables we can use
+ 
+
+ align:start position:0%
+function of random variables we can use
+the expected value rule let us take the
+
+ align:start position:0%
+the expected value rule let us take the
+ 
+
+ align:start position:0%
+the expected value rule let us take the
+function of interest which is the
+
+ align:start position:0%
+function of interest which is the
+ 
+
+ align:start position:0%
+function of interest which is the
+minimum of three numbers then we need to
+
+ align:start position:0%
+minimum of three numbers then we need to
+ 
+
+ align:start position:0%
+minimum of three numbers then we need to
+multiply by the joint PDF of these three
+
+ align:start position:0%
+multiply by the joint PDF of these three
+ 
+
+ align:start position:0%
+multiply by the joint PDF of these three
+random variables XY and Z now because
+
+ align:start position:0%
+random variables XY and Z now because
+ 
+
+ align:start position:0%
+random variables XY and Z now because
+these three random variables are
+
+ align:start position:0%
+these three random variables are
+ 
+
+ align:start position:0%
+these three random variables are
+independent the joint PDF is the product
+
+ align:start position:0%
+independent the joint PDF is the product
+ 
+
+ align:start position:0%
+independent the joint PDF is the product
+of their individual PDFs which are all
+
+ align:start position:0%
+of their individual PDFs which are all
+ 
+
+ align:start position:0%
+of their individual PDFs which are all
+exponential and so we obtained this
+
+ align:start position:0%
+exponential and so we obtained this
+ 
+
+ align:start position:0%
+exponential and so we obtained this
+expression for the joint PDF and we need
+
+ align:start position:0%
+expression for the joint PDF and we need
+ 
+
+ align:start position:0%
+expression for the joint PDF and we need
+to integrate this over all x y&z
+
+ align:start position:0%
+to integrate this over all x y&z
+ 
+
+ align:start position:0%
+to integrate this over all x y&z
+so it's going to be an integral that
+
+ align:start position:0%
+so it's going to be an integral that
+ 
+
+ align:start position:0%
+so it's going to be an integral that
+goes for each one of the three variables
+
+ align:start position:0%
+goes for each one of the three variables
+ 
+
+ align:start position:0%
+goes for each one of the three variables
+from 0 to infinity and here we have DX
+
+ align:start position:0%
+from 0 to infinity and here we have DX
+ 
+
+ align:start position:0%
+from 0 to infinity and here we have DX
+dy DZ so this is one approach that can
+
+ align:start position:0%
+dy DZ so this is one approach that can
+ 
+
+ align:start position:0%
+dy DZ so this is one approach that can
+give us the answer if you're able to
+
+ align:start position:0%
+give us the answer if you're able to
+ 
+
+ align:start position:0%
+give us the answer if you're able to
+manipulate and keep track of everything
+
+ align:start position:0%
+manipulate and keep track of everything
+ 
+
+ align:start position:0%
+manipulate and keep track of everything
+that happens in this three-dimensional
+
+ align:start position:0%
+that happens in this three-dimensional
+ 
+
+ align:start position:0%
+that happens in this three-dimensional
+integral but this is too tedious and
+
+ align:start position:0%
+integral but this is too tedious and
+ 
+
+ align:start position:0%
+integral but this is too tedious and
+this is not a good way to go let us try
+
+ align:start position:0%
+this is not a good way to go let us try
+ 
+
+ align:start position:0%
+this is not a good way to go let us try
+to think of an alternative way can we
+
+ align:start position:0%
+to think of an alternative way can we
+ 
+
+ align:start position:0%
+to think of an alternative way can we
+figure out the distribution of this
+
+ align:start position:0%
+figure out the distribution of this
+ 
+
+ align:start position:0%
+figure out the distribution of this
+random variable it's a function of three
+
+ align:start position:0%
+random variable it's a function of three
+ 
+
+ align:start position:0%
+random variable it's a function of three
+random variables so in some sense it's a
+
+ align:start position:0%
+random variables so in some sense it's a
+ 
+
+ align:start position:0%
+random variables so in some sense it's a
+derived distribution problem so we can
+
+ align:start position:0%
+derived distribution problem so we can
+ 
+
+ align:start position:0%
+derived distribution problem so we can
+try to calculate the cumulative
+
+ align:start position:0%
+try to calculate the cumulative
+ 
+
+ align:start position:0%
+try to calculate the cumulative
+distribution function of the minimum of
+
+ align:start position:0%
+distribution function of the minimum of
+ 
+
+ align:start position:0%
+distribution function of the minimum of
+the three so for the cumulative we would
+
+ align:start position:0%
+the three so for the cumulative we would
+ 
+
+ align:start position:0%
+the three so for the cumulative we would
+be looking at the probability that the
+
+ align:start position:0%
+be looking at the probability that the
+ 
+
+ align:start position:0%
+be looking at the probability that the
+minimum of these three random variables
+
+ align:start position:0%
+minimum of these three random variables
+ 
+
+ align:start position:0%
+minimum of these three random variables
+is less than or equal to a certain
+
+ align:start position:0%
+is less than or equal to a certain
+ 
+
+ align:start position:0%
+is less than or equal to a certain
+number it turns out that the
+
+ align:start position:0%
+number it turns out that the
+ 
+
+ align:start position:0%
+number it turns out that the
+calculations are a little faster if we
+
+ align:start position:0%
+calculations are a little faster if we
+ 
+
+ align:start position:0%
+calculations are a little faster if we
+look at the probability that this is
+
+ align:start position:0%
+look at the probability that this is
+ 
+
+ align:start position:0%
+look at the probability that this is
+larger than or equal to a certain number
+
+ align:start position:0%
+larger than or equal to a certain number
+ 
+
+ align:start position:0%
+larger than or equal to a certain number
+what is this event the minimum is larger
+
+ align:start position:0%
+what is this event the minimum is larger
+ 
+
+ align:start position:0%
+what is this event the minimum is larger
+than or equal to T if and only if all
+
+ align:start position:0%
+than or equal to T if and only if all
+ 
+
+ align:start position:0%
+than or equal to T if and only if all
+three of them are larger than or equal
+
+ align:start position:0%
+three of them are larger than or equal
+ 
+
+ align:start position:0%
+three of them are larger than or equal
+to T so the probability of this event is
+
+ align:start position:0%
+to T so the probability of this event is
+ 
+
+ align:start position:0%
+to T so the probability of this event is
+the same as the probability that X is
+
+ align:start position:0%
+the same as the probability that X is
+ 
+
+ align:start position:0%
+the same as the probability that X is
+larger than or equal to T y larger than
+
+ align:start position:0%
+larger than or equal to T y larger than
+ 
+
+ align:start position:0%
+larger than or equal to T y larger than
+or equal to T and Z larger than or equal
+
+ align:start position:0%
+or equal to T and Z larger than or equal
+ 
+
+ align:start position:0%
+or equal to T and Z larger than or equal
+to T but now x y&z are independent so we
+
+ align:start position:0%
+to T but now x y&z are independent so we
+ 
+
+ align:start position:0%
+to T but now x y&z are independent so we
+need to multiply the probability that X
+
+ align:start position:0%
+need to multiply the probability that X
+ 
+
+ align:start position:0%
+need to multiply the probability that X
+is larger than or equal to T which for
+
+ align:start position:0%
+is larger than or equal to T which for
+ 
+
+ align:start position:0%
+is larger than or equal to T which for
+an exponential random variable is e to
+
+ align:start position:0%
+an exponential random variable is e to
+ 
+
+ align:start position:0%
+an exponential random variable is e to
+the minus lambda t then the probability
+
+ align:start position:0%
+the minus lambda t then the probability
+ 
+
+ align:start position:0%
+the minus lambda t then the probability
+of the second event which is again e to
+
+ align:start position:0%
+of the second event which is again e to
+ 
+
+ align:start position:0%
+of the second event which is again e to
+the minus lambda T and finally the
+
+ align:start position:0%
+the minus lambda T and finally the
+ 
+
+ align:start position:0%
+the minus lambda T and finally the
+probability of the third event which is
+
+ align:start position:0%
+probability of the third event which is
+ 
+
+ align:start position:0%
+probability of the third event which is
+again e to the minus lambda T which is e
+
+ align:start position:0%
+again e to the minus lambda T which is e
+ 
+
+ align:start position:0%
+again e to the minus lambda T which is e
+to the minus 3 lambda T now we look at
+
+ align:start position:0%
+to the minus 3 lambda T now we look at
+ 
+
+ align:start position:0%
+to the minus 3 lambda T now we look at
+this expression for the probability that
+
+ align:start position:0%
+this expression for the probability that
+ 
+
+ align:start position:0%
+this expression for the probability that
+the random variable is larger than or
+
+ align:start position:0%
+the random variable is larger than or
+ 
+
+ align:start position:0%
+the random variable is larger than or
+equal to T and recognize that this is
+
+ align:start position:0%
+equal to T and recognize that this is
+ 
+
+ align:start position:0%
+equal to T and recognize that this is
+the expression that we have when we have
+
+ align:start position:0%
+the expression that we have when we have
+ 
+
+ align:start position:0%
+the expression that we have when we have
+an exponential random variable with
+
+ align:start position:0%
+an exponential random variable with
+ 
+
+ align:start position:0%
+an exponential random variable with
+parameter equal
+
+ align:start position:0%
+parameter equal
+ 
+
+ align:start position:0%
+parameter equal
+two three lambda if you want to do it
+
+ align:start position:0%
+two three lambda if you want to do it
+ 
+
+ align:start position:0%
+two three lambda if you want to do it
+formally subtract this quantity from one
+
+ align:start position:0%
+formally subtract this quantity from one
+ 
+
+ align:start position:0%
+formally subtract this quantity from one
+to find the CDF take the derivative and
+
+ align:start position:0%
+to find the CDF take the derivative and
+ 
+
+ align:start position:0%
+to find the CDF take the derivative and
+you will find an exponential PDF so the
+
+ align:start position:0%
+you will find an exponential PDF so the
+ 
+
+ align:start position:0%
+you will find an exponential PDF so the
+conclusion is that this random variable
+
+ align:start position:0%
+conclusion is that this random variable
+ 
+
+ align:start position:0%
+conclusion is that this random variable
+is exponential with parameter three
+
+ align:start position:0%
+is exponential with parameter three
+ 
+
+ align:start position:0%
+is exponential with parameter three
+lambda and since it's an exponential
+
+ align:start position:0%
+lambda and since it's an exponential
+ 
+
+ align:start position:0%
+lambda and since it's an exponential
+with parameter three lambda then we know
+
+ align:start position:0%
+with parameter three lambda then we know
+ 
+
+ align:start position:0%
+with parameter three lambda then we know
+what the expected value is it is going
+
+ align:start position:0%
+what the expected value is it is going
+ 
+
+ align:start position:0%
+what the expected value is it is going
+to be one over three lambda and this is
+
+ align:start position:0%
+to be one over three lambda and this is
+ 
+
+ align:start position:0%
+to be one over three lambda and this is
+the answer to the question that you were
+
+ align:start position:0%
+the answer to the question that you were
+ 
+
+ align:start position:0%
+the answer to the question that you were
+interested in now the fact that this is
+
+ align:start position:0%
+interested in now the fact that this is
+ 
+
+ align:start position:0%
+interested in now the fact that this is
+an exponential random variable but with
+
+ align:start position:0%
+an exponential random variable but with
+ 
+
+ align:start position:0%
+an exponential random variable but with
+a different parameter is a pretty clean
+
+ align:start position:0%
+a different parameter is a pretty clean
+ 
+
+ align:start position:0%
+a different parameter is a pretty clean
+fact and so it should have a good
+
+ align:start position:0%
+fact and so it should have a good
+ 
+
+ align:start position:0%
+fact and so it should have a good
+explanation let us now try to think
+
+ align:start position:0%
+explanation let us now try to think
+ 
+
+ align:start position:0%
+explanation let us now try to think
+about a good explanation for this fact
+
+ align:start position:0%
+about a good explanation for this fact
+ 
+
+ align:start position:0%
+about a good explanation for this fact
+whenever we deal with an exponential
+
+ align:start position:0%
+whenever we deal with an exponential
+ 
+
+ align:start position:0%
+whenever we deal with an exponential
+random variable one way of thinking
+
+ align:start position:0%
+random variable one way of thinking
+ 
+
+ align:start position:0%
+random variable one way of thinking
+about it is that this exponential random
+
+ align:start position:0%
+about it is that this exponential random
+ 
+
+ align:start position:0%
+about it is that this exponential random
+variable is the first time in a Poisson
+
+ align:start position:0%
+variable is the first time in a Poisson
+ 
+
+ align:start position:0%
+variable is the first time in a Poisson
+process so imagine that there is a
+
+ align:start position:0%
+process so imagine that there is a
+ 
+
+ align:start position:0%
+process so imagine that there is a
+Poisson process that runs forever and X
+
+ align:start position:0%
+Poisson process that runs forever and X
+ 
+
+ align:start position:0%
+Poisson process that runs forever and X
+is the first arrival time for this light
+
+ align:start position:0%
+is the first arrival time for this light
+ 
+
+ align:start position:0%
+is the first arrival time for this light
+bulb we can think the same way and since
+
+ align:start position:0%
+bulb we can think the same way and since
+ 
+
+ align:start position:0%
+bulb we can think the same way and since
+x and y are assumed to be independent we
+
+ align:start position:0%
+x and y are assumed to be independent we
+ 
+
+ align:start position:0%
+x and y are assumed to be independent we
+can assume that here we have an
+
+ align:start position:0%
+can assume that here we have an
+ 
+
+ align:start position:0%
+can assume that here we have an
+independent Poisson process independent
+
+ align:start position:0%
+independent Poisson process independent
+ 
+
+ align:start position:0%
+independent Poisson process independent
+from the first one it has its own
+
+ align:start position:0%
+from the first one it has its own
+ 
+
+ align:start position:0%
+from the first one it has its own
+arrival times and Y is the first arrival
+
+ align:start position:0%
+arrival times and Y is the first arrival
+ 
+
+ align:start position:0%
+arrival times and Y is the first arrival
+time in this Poisson process and finally
+
+ align:start position:0%
+time in this Poisson process and finally
+ 
+
+ align:start position:0%
+time in this Poisson process and finally
+we have a third independent Poisson
+
+ align:start position:0%
+we have a third independent Poisson
+ 
+
+ align:start position:0%
+we have a third independent Poisson
+process and the random variable Z is the
+
+ align:start position:0%
+process and the random variable Z is the
+ 
+
+ align:start position:0%
+process and the random variable Z is the
+first arrival time in that Poisson
+
+ align:start position:0%
+first arrival time in that Poisson
+ 
+
+ align:start position:0%
+first arrival time in that Poisson
+process so XY and z are interpreted as
+
+ align:start position:0%
+process so XY and z are interpreted as
+ 
+
+ align:start position:0%
+process so XY and z are interpreted as
+first arrivals in three independent
+
+ align:start position:0%
+first arrivals in three independent
+ 
+
+ align:start position:0%
+first arrivals in three independent
+Poisson processes now let us take these
+
+ align:start position:0%
+Poisson processes now let us take these
+ 
+
+ align:start position:0%
+Poisson processes now let us take these
+three Poisson processes and merge them
+
+ align:start position:0%
+three Poisson processes and merge them
+ 
+
+ align:start position:0%
+three Poisson processes and merge them
+if we merge these three processes
+
+ align:start position:0%
+if we merge these three processes
+ 
+
+ align:start position:0%
+if we merge these three processes
+what we obtain is a merged process which
+
+ align:start position:0%
+what we obtain is a merged process which
+ 
+
+ align:start position:0%
+what we obtain is a merged process which
+is Poisson with parameter equal to the
+
+ align:start position:0%
+is Poisson with parameter equal to the
+ 
+
+ align:start position:0%
+is Poisson with parameter equal to the
+sum of the rates or parameters of each
+
+ align:start position:0%
+sum of the rates or parameters of each
+ 
+
+ align:start position:0%
+sum of the rates or parameters of each
+one of the processes so it's a Poisson
+
+ align:start position:0%
+one of the processes so it's a Poisson
+ 
+
+ align:start position:0%
+one of the processes so it's a Poisson
+process with parameter 3 lambda now how
+
+ align:start position:0%
+process with parameter 3 lambda now how
+ 
+
+ align:start position:0%
+process with parameter 3 lambda now how
+can we interpret the random variable of
+
+ align:start position:0%
+can we interpret the random variable of
+ 
+
+ align:start position:0%
+can we interpret the random variable of
+interest the first Burnout
+
+ align:start position:0%
+interest the first Burnout
+ 
+
+ align:start position:0%
+interest the first Burnout
+in terms of the merged process so the
+
+ align:start position:0%
+in terms of the merged process so the
+ 
+
+ align:start position:0%
+in terms of the merged process so the
+merged process has an arrival whenever
+
+ align:start position:0%
+merged process has an arrival whenever
+ 
+
+ align:start position:0%
+merged process has an arrival whenever
+one of those three processes has an
+
+ align:start position:0%
+one of those three processes has an
+ 
+
+ align:start position:0%
+one of those three processes has an
+arrival the first arrival in the merged
+
+ align:start position:0%
+arrival the first arrival in the merged
+ 
+
+ align:start position:0%
+arrival the first arrival in the merged
+process will happen the first time that
+
+ align:start position:0%
+process will happen the first time that
+ 
+
+ align:start position:0%
+process will happen the first time that
+one of these three processes is going to
+
+ align:start position:0%
+one of these three processes is going to
+ 
+
+ align:start position:0%
+one of these three processes is going to
+have an arrival therefore we can
+
+ align:start position:0%
+have an arrival therefore we can
+ 
+
+ align:start position:0%
+have an arrival therefore we can
+interpret the random variable of
+
+ align:start position:0%
+interpret the random variable of
+ 
+
+ align:start position:0%
+interpret the random variable of
+interest the first burnout time as the
+
+ align:start position:0%
+interest the first burnout time as the
+ 
+
+ align:start position:0%
+interest the first burnout time as the
+first arrival time in a merged process
+
+ align:start position:0%
+first arrival time in a merged process
+ 
+
+ align:start position:0%
+first arrival time in a merged process
+but now the merged process is Poisson
+
+ align:start position:0%
+but now the merged process is Poisson
+ 
+
+ align:start position:0%
+but now the merged process is Poisson
+with parameter three lambda therefore
+
+ align:start position:0%
+with parameter three lambda therefore
+ 
+
+ align:start position:0%
+with parameter three lambda therefore
+this random variable is going to be an
+
+ align:start position:0%
+this random variable is going to be an
+ 
+
+ align:start position:0%
+this random variable is going to be an
+exponential random variable with
+
+ align:start position:0%
+exponential random variable with
+ 
+
+ align:start position:0%
+exponential random variable with
+parameter three lambda and from this we
+
+ align:start position:0%
+parameter three lambda and from this we
+ 
+
+ align:start position:0%
+parameter three lambda and from this we
+also obtain the expected value of that
+
+ align:start position:0%
+also obtain the expected value of that
+ 
+
+ align:start position:0%
+also obtain the expected value of that
+random variable the beauty of this last
+
+ align:start position:0%
+random variable the beauty of this last
+ 
+
+ align:start position:0%
+random variable the beauty of this last
+approach for coming up with the answer
+
+ align:start position:0%
+approach for coming up with the answer
+ 
+
+ align:start position:0%
+approach for coming up with the answer
+by reasoning in terms of merged Poisson
+
+ align:start position:0%
+by reasoning in terms of merged Poisson
+ 
+
+ align:start position:0%
+by reasoning in terms of merged Poisson
+processes is that we didn't have to do
+
+ align:start position:0%
+processes is that we didn't have to do
+ 
+
+ align:start position:0%
+processes is that we didn't have to do
+any calculations at all just use the
+
+ align:start position:0%
+any calculations at all just use the
+ 
+
+ align:start position:0%
+any calculations at all just use the
+intuitive understanding of Poisson
+
+ align:start position:0%
+intuitive understanding of Poisson
+ 
+
+ align:start position:0%
+intuitive understanding of Poisson
+processes and especially the
+
+ align:start position:0%
+processes and especially the
+ 
+
+ align:start position:0%
+processes and especially the
+interpretation of an exponential random
+
+ align:start position:0%
+interpretation of an exponential random
+ 
+
+ align:start position:0%
+interpretation of an exponential random
+variable as the first arrival time in a
+
+ align:start position:0%
+variable as the first arrival time in a
+ 
+
+ align:start position:0%
+variable as the first arrival time in a
+Poisson process let us now try to solve
+
+ align:start position:0%
+Poisson process let us now try to solve
+ 
+
+ align:start position:0%
+Poisson process let us now try to solve
+a somewhat harder problem let us try to
+
+ align:start position:0%
+a somewhat harder problem let us try to
+ 
+
+ align:start position:0%
+a somewhat harder problem let us try to
+calculate the expected time until all
+
+ align:start position:0%
+calculate the expected time until all
+ 
+
+ align:start position:0%
+calculate the expected time until all
+light bulbs burn out so one light bulb
+
+ align:start position:0%
+light bulbs burn out so one light bulb
+ 
+
+ align:start position:0%
+light bulbs burn out so one light bulb
+will burn out then another one will burn
+
+ align:start position:0%
+will burn out then another one will burn
+ 
+
+ align:start position:0%
+will burn out then another one will burn
+out and finally the third one will burn
+
+ align:start position:0%
+out and finally the third one will burn
+ 
+
+ align:start position:0%
+out and finally the third one will burn
+out we want to find the expected time
+
+ align:start position:0%
+out we want to find the expected time
+ 
+
+ align:start position:0%
+out we want to find the expected time
+until this happens once more we will be
+
+ align:start position:0%
+until this happens once more we will be
+ 
+
+ align:start position:0%
+until this happens once more we will be
+thinking of these burn out times as the
+
+ align:start position:0%
+thinking of these burn out times as the
+ 
+
+ align:start position:0%
+thinking of these burn out times as the
+first arrival times in Poisson processes
+
+ align:start position:0%
+first arrival times in Poisson processes
+ 
+
+ align:start position:0%
+first arrival times in Poisson processes
+the total time until the third burnout
+
+ align:start position:0%
+the total time until the third burnout
+ 
+
+ align:start position:0%
+the total time until the third burnout
+can be split into different periods
+
+ align:start position:0%
+can be split into different periods
+ 
+
+ align:start position:0%
+can be split into different periods
+there is a time until one light bulb
+
+ align:start position:0%
+there is a time until one light bulb
+ 
+
+ align:start position:0%
+there is a time until one light bulb
+burns out and the expected value of this
+
+ align:start position:0%
+burns out and the expected value of this
+ 
+
+ align:start position:0%
+burns out and the expected value of this
+period here is going to be one over
+
+ align:start position:0%
+period here is going to be one over
+ 
+
+ align:start position:0%
+period here is going to be one over
+three lambda what happens at this time
+
+ align:start position:0%
+three lambda what happens at this time
+ 
+
+ align:start position:0%
+three lambda what happens at this time
+the second light bulb has burned out so
+
+ align:start position:0%
+the second light bulb has burned out so
+ 
+
+ align:start position:0%
+the second light bulb has burned out so
+we can forget about it take it out of
+
+ align:start position:0%
+we can forget about it take it out of
+ 
+
+ align:start position:0%
+we can forget about it take it out of
+the picture
+
+ align:start position:0%
+the picture
+ 
+
+ align:start position:0%
+the picture
+we have two light bulbs let us look at
+
+ align:start position:0%
+we have two light bulbs let us look at
+ 
+
+ align:start position:0%
+we have two light bulbs let us look at
+the time it will take until one of these
+
+ align:start position:0%
+the time it will take until one of these
+ 
+
+ align:start position:0%
+the time it will take until one of these
+two light bulbs burns out so we're
+
+ align:start position:0%
+two light bulbs burns out so we're
+ 
+
+ align:start position:0%
+two light bulbs burns out so we're
+interested in this period of time
+
+ align:start position:0%
+interested in this period of time
+ 
+
+ align:start position:0%
+interested in this period of time
+now the Poisson process starts fresh at
+
+ align:start position:0%
+now the Poisson process starts fresh at
+ 
+
+ align:start position:0%
+now the Poisson process starts fresh at
+this time after this time whatever
+
+ align:start position:0%
+this time after this time whatever
+ 
+
+ align:start position:0%
+this time after this time whatever
+happens is just an ordinary Poisson
+
+ align:start position:0%
+happens is just an ordinary Poisson
+ 
+
+ align:start position:0%
+happens is just an ordinary Poisson
+process as if it was starting at this
+
+ align:start position:0%
+process as if it was starting at this
+ 
+
+ align:start position:0%
+process as if it was starting at this
+time so this is going to be an
+
+ align:start position:0%
+time so this is going to be an
+ 
+
+ align:start position:0%
+time so this is going to be an
+exponential random variable starting
+
+ align:start position:0%
+exponential random variable starting
+ 
+
+ align:start position:0%
+exponential random variable starting
+from this time and this is going to be
+
+ align:start position:0%
+from this time and this is going to be
+ 
+
+ align:start position:0%
+from this time and this is going to be
+another exponential random variable so
+
+ align:start position:0%
+another exponential random variable so
+ 
+
+ align:start position:0%
+another exponential random variable so
+the time until the next light bulb burns
+
+ align:start position:0%
+the time until the next light bulb burns
+ 
+
+ align:start position:0%
+the time until the next light bulb burns
+out in this case is going to be the
+
+ align:start position:0%
+out in this case is going to be the
+ 
+
+ align:start position:0%
+out in this case is going to be the
+minimum of two exponential random
+
+ align:start position:0%
+minimum of two exponential random
+ 
+
+ align:start position:0%
+minimum of two exponential random
+variables we can think again about
+
+ align:start position:0%
+variables we can think again about
+ 
+
+ align:start position:0%
+variables we can think again about
+merging these two Poisson processes to
+
+ align:start position:0%
+merging these two Poisson processes to
+ 
+
+ align:start position:0%
+merging these two Poisson processes to
+obtain a Poisson process with total rate
+
+ align:start position:0%
+obtain a Poisson process with total rate
+ 
+
+ align:start position:0%
+obtain a Poisson process with total rate
+two lambda and the time until one of
+
+ align:start position:0%
+two lambda and the time until one of
+ 
+
+ align:start position:0%
+two lambda and the time until one of
+these two burns out is going to be the
+
+ align:start position:0%
+these two burns out is going to be the
+ 
+
+ align:start position:0%
+these two burns out is going to be the
+first arrival time in that merged
+
+ align:start position:0%
+first arrival time in that merged
+ 
+
+ align:start position:0%
+first arrival time in that merged
+process and so the expected time until
+
+ align:start position:0%
+process and so the expected time until
+ 
+
+ align:start position:0%
+process and so the expected time until
+the first arrival of the merged process
+
+ align:start position:0%
+the first arrival of the merged process
+ 
+
+ align:start position:0%
+the first arrival of the merged process
+is going to be one over two lambda and
+
+ align:start position:0%
+is going to be one over two lambda and
+ 
+
+ align:start position:0%
+is going to be one over two lambda and
+finally once this burned out has
+
+ align:start position:0%
+finally once this burned out has
+ 
+
+ align:start position:0%
+finally once this burned out has
+happened we can forget about this light
+
+ align:start position:0%
+happened we can forget about this light
+ 
+
+ align:start position:0%
+happened we can forget about this light
+bulb we're left just with one light bulb
+
+ align:start position:0%
+bulb we're left just with one light bulb
+ 
+
+ align:start position:0%
+bulb we're left just with one light bulb
+and starting from here we wait until
+
+ align:start position:0%
+and starting from here we wait until
+ 
+
+ align:start position:0%
+and starting from here we wait until
+that light bulb burns out once more
+
+ align:start position:0%
+that light bulb burns out once more
+ 
+
+ align:start position:0%
+that light bulb burns out once more
+because of the fresh start property of
+
+ align:start position:0%
+because of the fresh start property of
+ 
+
+ align:start position:0%
+because of the fresh start property of
+the Poisson process starting from here
+
+ align:start position:0%
+the Poisson process starting from here
+ 
+
+ align:start position:0%
+the Poisson process starting from here
+until it burns out is going to be a
+
+ align:start position:0%
+until it burns out is going to be a
+ 
+
+ align:start position:0%
+until it burns out is going to be a
+random variable which is an exponential
+
+ align:start position:0%
+random variable which is an exponential
+ 
+
+ align:start position:0%
+random variable which is an exponential
+random variable and in this case an
+
+ align:start position:0%
+random variable and in this case an
+ 
+
+ align:start position:0%
+random variable and in this case an
+exponential random variable with rate
+
+ align:start position:0%
+exponential random variable with rate
+ 
+
+ align:start position:0%
+exponential random variable with rate
+just lambda and by adding these three
+
+ align:start position:0%
+just lambda and by adding these three
+ 
+
+ align:start position:0%
+just lambda and by adding these three
+quantities we get the expected time
+
+ align:start position:0%
+quantities we get the expected time
+ 
+
+ align:start position:0%
+quantities we get the expected time
+until all three have burned out this is
+
+ align:start position:0%
+until all three have burned out this is
+ 
+
+ align:start position:0%
+until all three have burned out this is
+a problem that would have been quite
+
+ align:start position:0%
+a problem that would have been quite
+ 
+
+ align:start position:0%
+a problem that would have been quite
+hard to solve in a more analytical way
+
+ align:start position:0%
+hard to solve in a more analytical way
+ 
+
+ align:start position:0%
+hard to solve in a more analytical way
+we're dealing with a random variable
+
+ align:start position:0%
+we're dealing with a random variable
+ 
+
+ align:start position:0%
+we're dealing with a random variable
+which is now the maximum of XY and Z and
+
+ align:start position:0%
+which is now the maximum of XY and Z and
+ 
+
+ align:start position:0%
+which is now the maximum of XY and Z and
+the distribution of this random variable
+
+ align:start position:0%
+the distribution of this random variable
+ 
+
+ align:start position:0%
+the distribution of this random variable
+is not so simple to write down so it
+
+ align:start position:0%
+is not so simple to write down so it
+ 
+
+ align:start position:0%
+is not so simple to write down so it
+that would not be a very good approach
+
+ align:start position:0%
+that would not be a very good approach
+ 
+
+ align:start position:0%
+that would not be a very good approach
+for going about this problem but we
+
+ align:start position:0%
+for going about this problem but we
+ 
+
+ align:start position:0%
+for going about this problem but we
+managed to find the expected value
+
+ align:start position:0%
+managed to find the expected value
+ 
+
+ align:start position:0%
+managed to find the expected value
+this random variable without having to
+
+ align:start position:0%
+this random variable without having to
+ 
+
+ align:start position:0%
+this random variable without having to
+write down its distribution by breaking
+
+ align:start position:0%
+write down its distribution by breaking
+ 
+
+ align:start position:0%
+write down its distribution by breaking
+this random variable into a sum of three
+
+ align:start position:0%
+this random variable into a sum of three
+ 
+
+ align:start position:0%
+this random variable into a sum of three
+particular random variables each of
+
+ align:start position:0%
+particular random variables each of
+ 
+
+ align:start position:0%
+particular random variables each of
+which had a nice intuitive
+
+ align:start position:0%
+which had a nice intuitive
+ 
+
+ align:start position:0%
+which had a nice intuitive
+interpretation and that was the key to
+
+ align:start position:0%
+interpretation and that was the key to
+ 
+
+ align:start position:0%
+interpretation and that was the key to
+the solution of this problem
\ No newline at end of file
diff --git a/xVka6z1hu-I.txt b/xVka6z1hu-I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..065245a9bd81cf8cd6b03f6f9a80f68610189bc5
--- /dev/null
+++ b/xVka6z1hu-I.txt
@@ -0,0 +1,13739 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, let's get started.
+
+ align:start position:0%
+All right, let's get started.
+ 
+
+ align:start position:0%
+All right, let's get started.
+Today we have another data structures
+
+ align:start position:0%
+Today we have another data structures
+ 
+
+ align:start position:0%
+Today we have another data structures
+topic which is data structure
+
+ align:start position:0%
+topic which is data structure
+ 
+
+ align:start position:0%
+topic which is data structure
+augmentation.
+
+ align:start position:0%
+augmentation.
+ 
+
+ align:start position:0%
+augmentation.
+Uh the idea here is we're going to take
+
+ align:start position:0%
+Uh the idea here is we're going to take
+ 
+
+ align:start position:0%
+Uh the idea here is we're going to take
+some existing data structure and augment
+
+ align:start position:0%
+some existing data structure and augment
+ 
+
+ align:start position:0%
+some existing data structure and augment
+it to do extra cool things. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take some other data structure that
+
+ align:start position:0%
+take some other data structure that
+ 
+
+ align:start position:0%
+take some other data structure that
+we've covered. Uh typically that'll be a
+
+ align:start position:0%
+we've covered. Uh typically that'll be a
+ 
+
+ align:start position:0%
+we've covered. Uh typically that'll be a
+balanced search tree like an AVL tree or
+
+ align:start position:0%
+balanced search tree like an AVL tree or
+ 
+
+ align:start position:0%
+balanced search tree like an AVL tree or
+a 23 tree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then we'll modify it to store extra
+
+ align:start position:0%
+And then we'll modify it to store extra
+ 
+
+ align:start position:0%
+And then we'll modify it to store extra
+information which will enable additional
+
+ align:start position:0%
+information which will enable additional
+ 
+
+ align:start position:0%
+information which will enable additional
+kinds of searches typically
+
+ align:start position:0%
+kinds of searches typically
+ 
+
+ align:start position:0%
+kinds of searches typically
+and sometimes to do updates better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And in 006 you've seen an example of
+
+ align:start position:0%
+And in 006 you've seen an example of
+ 
+
+ align:start position:0%
+And in 006 you've seen an example of
+this where you took AVL trees and
+
+ align:start position:0%
+this where you took AVL trees and
+ 
+
+ align:start position:0%
+this where you took AVL trees and
+augmented AVL trees so that every node
+
+ align:start position:0%
+augmented AVL trees so that every node
+ 
+
+ align:start position:0%
+augmented AVL trees so that every node
+knew the number of nodes in that rooted
+
+ align:start position:0%
+knew the number of nodes in that rooted
+ 
+
+ align:start position:0%
+knew the number of nodes in that rooted
+subree. Uh today we're going to see that
+
+ align:start position:0%
+subree. Uh today we're going to see that
+ 
+
+ align:start position:0%
+subree. Uh today we're going to see that
+example but also a bunch of other
+
+ align:start position:0%
+example but also a bunch of other
+ 
+
+ align:start position:0%
+example but also a bunch of other
+examples different types of augmentation
+
+ align:start position:0%
+examples different types of augmentation
+ 
+
+ align:start position:0%
+examples different types of augmentation
+you could do. And we'll start out with a
+
+ align:start position:0%
+you could do. And we'll start out with a
+ 
+
+ align:start position:0%
+you could do. And we'll start out with a
+very simple one which I call easy tree
+
+ align:start position:0%
+very simple one which I call easy tree
+ 
+
+ align:start position:0%
+very simple one which I call easy tree
+augmentation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which will include subree size as a
+
+ align:start position:0%
+which will include subree size as a
+ 
+
+ align:start position:0%
+which will include subree size as a
+special case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So with easy tree augmentation
+
+ align:start position:0%
+So with easy tree augmentation
+ 
+
+ align:start position:0%
+So with easy tree augmentation
+uh the idea is you have a tree like an
+
+ align:start position:0%
+uh the idea is you have a tree like an
+ 
+
+ align:start position:0%
+uh the idea is you have a tree like an
+AVL tree or 23 tree or something like
+
+ align:start position:0%
+AVL tree or 23 tree or something like
+ 
+
+ align:start position:0%
+AVL tree or 23 tree or something like
+that and you'd like to store for every
+
+ align:start position:0%
+that and you'd like to store for every
+ 
+
+ align:start position:0%
+that and you'd like to store for every
+node x some function of the subree
+
+ align:start position:0%
+node x some function of the subree
+ 
+
+ align:start position:0%
+node x some function of the subree
+rooted at x such as the number of nodes
+
+ align:start position:0%
+rooted at x such as the number of nodes
+ 
+
+ align:start position:0%
+rooted at x such as the number of nodes
+in there or the sum of the weights of
+
+ align:start position:0%
+in there or the sum of the weights of
+ 
+
+ align:start position:0%
+in there or the sum of the weights of
+the nodes or the sum of the squares of
+
+ align:start position:0%
+the nodes or the sum of the squares of
+ 
+
+ align:start position:0%
+the nodes or the sum of the squares of
+the weights or uh the min or the max or
+
+ align:start position:0%
+the weights or uh the min or the max or
+ 
+
+ align:start position:0%
+the weights or uh the min or the max or
+the median maybe I'm not sure uh any
+
+ align:start position:0%
+the median maybe I'm not sure uh any
+ 
+
+ align:start position:0%
+the median maybe I'm not sure uh any
+some some function f of x which is a
+
+ align:start position:0%
+some some function f of x which is a
+ 
+
+ align:start position:0%
+some some function f of x which is a
+function of that maybe not f ofx but we
+
+ align:start position:0%
+function of that maybe not f ofx but we
+ 
+
+ align:start position:0%
+function of that maybe not f ofx but we
+want to compute store some function of
+
+ align:start position:0%
+want to compute store some function of
+ 
+
+ align:start position:0%
+want to compute store some function of
+that sub tree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say the goal
+
+ align:start position:0%
+Say the goal
+ 
+
+ align:start position:0%
+Say the goal
+is to store
+
+ align:start position:0%
+is to store
+ 
+
+ align:start position:0%
+is to store
+f of the sub tree rooted at x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh at each
+
+ align:start position:0%
+uh at each
+ 
+
+ align:start position:0%
+uh at each
+node x
+
+ align:start position:0%
+node x
+ 
+
+ align:start position:0%
+node x
+in a field which I'll call x.f.
+
+ align:start position:0%
+in a field which I'll call x.f.
+ 
+
+ align:start position:0%
+in a field which I'll call x.f.
+So normally nodes have like a left
+
+ align:start position:0%
+So normally nodes have like a left
+ 
+
+ align:start position:0%
+So normally nodes have like a left
+child, right child, parent, but we're
+
+ align:start position:0%
+child, right child, parent, but we're
+ 
+
+ align:start position:0%
+child, right child, parent, but we're
+going to store an extra field x.f for
+
+ align:start position:0%
+going to store an extra field x.f for
+ 
+
+ align:start position:0%
+going to store an extra field x.f for
+some function that you define. This is
+
+ align:start position:0%
+some function that you define. This is
+ 
+
+ align:start position:0%
+some function that you define. This is
+not always possible.
+
+ align:start position:0%
+not always possible.
+ 
+
+ align:start position:0%
+not always possible.
+But here's a case where it is possible.
+
+ align:start position:0%
+But here's a case where it is possible.
+ 
+
+ align:start position:0%
+But here's a case where it is possible.
+That's going to be the easy case.
+
+ align:start position:0%
+That's going to be the easy case.
+ 
+
+ align:start position:0%
+That's going to be the easy case.
+Suppose X.F F can be computed
+
+ align:start position:0%
+Suppose X.F F can be computed
+ 
+
+ align:start position:0%
+Suppose X.F F can be computed
+uh locally using lower information lower
+
+ align:start position:0%
+uh locally using lower information lower
+ 
+
+ align:start position:0%
+uh locally using lower information lower
+nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll say let's suppose it can be
+
+ align:start position:0%
+and we'll say let's suppose it can be
+ 
+
+ align:start position:0%
+and we'll say let's suppose it can be
+computed in constant time from
+
+ align:start position:0%
+computed in constant time from
+ 
+
+ align:start position:0%
+computed in constant time from
+information in the node X uh from X's
+
+ align:start position:0%
+information in the node X uh from X's
+ 
+
+ align:start position:0%
+information in the node X uh from X's
+children
+
+ align:start position:0%
+children
+ 
+
+ align:start position:0%
+children
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh from
+
+ align:start position:0%
+uh from
+ 
+
+ align:start position:0%
+uh from
+the f value that's stored in the
+
+ align:start position:0%
+the f value that's stored in the
+ 
+
+ align:start position:0%
+the f value that's stored in the
+children. So I'll call that children.f,
+
+ align:start position:0%
+children. So I'll call that children.f,
+ 
+
+ align:start position:0%
+children. So I'll call that children.f,
+but really I mean left child.f, right
+
+ align:start position:0%
+but really I mean left child.f, right
+ 
+
+ align:start position:0%
+but really I mean left child.f, right
+child.f or if you have a two three tree,
+
+ align:start position:0%
+child.f or if you have a two three tree,
+ 
+
+ align:start position:0%
+child.f or if you have a two three tree,
+you have three children potentially and
+
+ align:start position:0%
+you have three children potentially and
+ 
+
+ align:start position:0%
+you have three children potentially and
+the f of each of them. Okay, so suppose
+
+ align:start position:0%
+the f of each of them. Okay, so suppose
+ 
+
+ align:start position:0%
+the f of each of them. Okay, so suppose
+that you can compute x.f uh sort of
+
+ align:start position:0%
+that you can compute x.f uh sort of
+ 
+
+ align:start position:0%
+that you can compute x.f uh sort of
+locally just using one level down in
+
+ align:start position:0%
+locally just using one level down in
+ 
+
+ align:start position:0%
+locally just using one level down in
+constant time. Then as you might expect
+
+ align:start position:0%
+constant time. Then as you might expect
+ 
+
+ align:start position:0%
+constant time. Then as you might expect
+you can update whenever a node needs
+
+ align:start position:0%
+you can update whenever a node needs
+ 
+
+ align:start position:0%
+you can update whenever a node needs
+whenever a node ends up changing.
+
+ align:start position:0%
+whenever a node ends up changing.
+ 
+
+ align:start position:0%
+whenever a node ends up changing.
+Uh so more formally
+
+ align:start position:0%
+Uh so more formally
+ 
+
+ align:start position:0%
+Uh so more formally
+if some set of nodes change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call the set Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so uh I'm stating a very general
+
+ align:start position:0%
+uh so uh I'm stating a very general
+ 
+
+ align:start position:0%
+uh so uh I'm stating a very general
+theorem here. If there are some set
+
+ align:start position:0%
+theorem here. If there are some set
+ 
+
+ align:start position:0%
+theorem here. If there are some set
+of nodes which we change something about
+
+ align:start position:0%
+of nodes which we change something about
+ 
+
+ align:start position:0%
+of nodes which we change something about
+them, we change either their F field, uh
+
+ align:start position:0%
+them, we change either their F field, uh
+ 
+
+ align:start position:0%
+them, we change either their F field, uh
+we change some of the data that's in the
+
+ align:start position:0%
+we change some of the data that's in the
+ 
+
+ align:start position:0%
+we change some of the data that's in the
+node or we change we do rotation, move
+
+ align:start position:0%
+node or we change we do rotation, move
+ 
+
+ align:start position:0%
+node or we change we do rotation, move
+some nodes around, then we count the
+
+ align:start position:0%
+some nodes around, then we count the
+ 
+
+ align:start position:0%
+some nodes around, then we count the
+total number of ancestors of these
+
+ align:start position:0%
+total number of ancestors of these
+ 
+
+ align:start position:0%
+total number of ancestors of these
+nodes. So this uh subree those are the
+
+ align:start position:0%
+nodes. So this uh subree those are the
+ 
+
+ align:start position:0%
+nodes. So this uh subree those are the
+nodes that need to be updated because
+
+ align:start position:0%
+nodes that need to be updated because
+ 
+
+ align:start position:0%
+nodes that need to be updated because
+we're assuming we can compute x.f f just
+
+ align:start position:0%
+we're assuming we can compute x.f f just
+ 
+
+ align:start position:0%
+we're assuming we can compute x.f f just
+given the children data. So if these if
+
+ align:start position:0%
+given the children data. So if these if
+ 
+
+ align:start position:0%
+given the children data. So if these if
+this data is changing, we have to update
+
+ align:start position:0%
+this data is changing, we have to update
+ 
+
+ align:start position:0%
+this data is changing, we have to update
+its parents value of f because it
+
+ align:start position:0%
+its parents value of f because it
+ 
+
+ align:start position:0%
+its parents value of f because it
+depends on this child value. We have to
+
+ align:start position:0%
+depends on this child value. We have to
+ 
+
+ align:start position:0%
+depends on this child value. We have to
+update all those parents all the way up
+
+ align:start position:0%
+update all those parents all the way up
+ 
+
+ align:start position:0%
+update all those parents all the way up
+to the root. Okay, so however many nodes
+
+ align:start position:0%
+to the root. Okay, so however many nodes
+ 
+
+ align:start position:0%
+to the root. Okay, so however many nodes
+there are there, that's the total cost.
+
+ align:start position:0%
+there are there, that's the total cost.
+ 
+
+ align:start position:0%
+there are there, that's the total cost.
+Now luckily
+
+ align:start position:0%
+Now luckily
+ 
+
+ align:start position:0%
+Now luckily
+um in an AVL tree or 23 tree, most uh
+
+ align:start position:0%
+um in an AVL tree or 23 tree, most uh
+ 
+
+ align:start position:0%
+um in an AVL tree or 23 tree, most uh
+balanced search structures, the updates
+
+ align:start position:0%
+balanced search structures, the updates
+ 
+
+ align:start position:0%
+balanced search structures, the updates
+you do are very localized. Like when we
+
+ align:start position:0%
+you do are very localized. Like when we
+ 
+
+ align:start position:0%
+you do are very localized. Like when we
+do splits in a two3 tree, we only do it
+
+ align:start position:0%
+do splits in a two3 tree, we only do it
+ 
+
+ align:start position:0%
+do splits in a two3 tree, we only do it
+up a single path to the root. So the
+
+ align:start position:0%
+up a single path to the root. So the
+ 
+
+ align:start position:0%
+up a single path to the root. So the
+number of ancestors here is just going
+
+ align:start position:0%
+number of ancestors here is just going
+ 
+
+ align:start position:0%
+number of ancestors here is just going
+to be log n. Same thing with an AVL
+
+ align:start position:0%
+to be log n. Same thing with an AVL
+ 
+
+ align:start position:0%
+to be log n. Same thing with an AVL
+tree. If you look at the rotations you
+
+ align:start position:0%
+tree. If you look at the rotations you
+ 
+
+ align:start position:0%
+tree. If you look at the rotations you
+do, they're up a single uh leaftoroot
+
+ align:start position:0%
+do, they're up a single uh leaftoroot
+ 
+
+ align:start position:0%
+do, they're up a single uh leaftoroot
+path.
+
+ align:start position:0%
+path.
+ 
+
+ align:start position:0%
+path.
+And so the number of ancestors is that
+
+ align:start position:0%
+And so the number of ancestors is that
+ 
+
+ align:start position:0%
+And so the number of ancestors is that
+that need to be updated is always order
+
+ align:start position:0%
+that need to be updated is always order
+ 
+
+ align:start position:0%
+that need to be updated is always order
+login. Order login things change and
+
+ align:start position:0%
+login. Order login things change and
+ 
+
+ align:start position:0%
+login. Order login things change and
+there's an order login ancestors of
+
+ align:start position:0%
+there's an order login ancestors of
+ 
+
+ align:start position:0%
+there's an order login ancestors of
+them.
+
+ align:start position:0%
+them.
+ 
+
+ align:start position:0%
+them.
+So this is a little more general than we
+
+ align:start position:0%
+So this is a little more general than we
+ 
+
+ align:start position:0%
+So this is a little more general than we
+need but it's just to point out if we
+
+ align:start position:0%
+need but it's just to point out if we
+ 
+
+ align:start position:0%
+need but it's just to point out if we
+did login rotation spread out somewhere
+
+ align:start position:0%
+did login rotation spread out somewhere
+ 
+
+ align:start position:0%
+did login rotation spread out somewhere
+in the tree that would actually be bad
+
+ align:start position:0%
+in the tree that would actually be bad
+ 
+
+ align:start position:0%
+in the tree that would actually be bad
+because the total number of ancestors
+
+ align:start position:0%
+because the total number of ancestors
+ 
+
+ align:start position:0%
+because the total number of ancestors
+could be like log squared right but
+
+ align:start position:0%
+could be like log squared right but
+ 
+
+ align:start position:0%
+could be like log squared right but
+because in the structures we've seen
+
+ align:start position:0%
+because in the structures we've seen
+ 
+
+ align:start position:0%
+because in the structures we've seen
+we just work on a single path to the
+
+ align:start position:0%
+we just work on a single path to the
+ 
+
+ align:start position:0%
+we just work on a single path to the
+root we get log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, uh, in a little more detail here,
+
+ align:start position:0%
+So, uh, in a little more detail here,
+ 
+
+ align:start position:0%
+So, uh, in a little more detail here,
+whenever we do a rotation in an AVL
+
+ align:start position:0%
+whenever we do a rotation in an AVL
+ 
+
+ align:start position:0%
+whenever we do a rotation in an AVL
+tree,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh let's say a b c x y
+
+ align:start position:0%
+Uh let's say a b c x y
+ 
+
+ align:start position:0%
+Uh let's say a b c x y
+remember rotations. It's been a while
+
+ align:start position:0%
+remember rotations. It's been a while
+ 
+
+ align:start position:0%
+remember rotations. It's been a while
+since we've done rotations. Uh so we've
+
+ align:start position:0%
+since we've done rotations. Uh so we've
+ 
+
+ align:start position:0%
+since we've done rotations. Uh so we've
+we've we haven't changed any of the
+
+ align:start position:0%
+we've we haven't changed any of the
+ 
+
+ align:start position:0%
+we've we haven't changed any of the
+nodes in ABC, but we have changed the
+
+ align:start position:0%
+nodes in ABC, but we have changed the
+ 
+
+ align:start position:0%
+nodes in ABC, but we have changed the
+nodes X and Y. Uh, so we're gonna we
+
+ align:start position:0%
+nodes X and Y. Uh, so we're gonna we
+ 
+
+ align:start position:0%
+nodes X and Y. Uh, so we're gonna we
+would have to trigger an update of Y.
+
+ align:start position:0%
+would have to trigger an update of Y.
+ 
+
+ align:start position:0%
+would have to trigger an update of Y.
+First, we'd want to update Y.F.
+
+ align:start position:0%
+First, we'd want to update Y.F.
+ 
+
+ align:start position:0%
+First, we'd want to update Y.F.
+and then we're going to trigger the
+
+ align:start position:0%
+and then we're going to trigger the
+ 
+
+ align:start position:0%
+and then we're going to trigger the
+update to X.F.
+
+ align:start position:0%
+update to X.F.
+ 
+
+ align:start position:0%
+update to X.F.
+And as long as this one can be computed
+
+ align:start position:0%
+And as long as this one can be computed
+ 
+
+ align:start position:0%
+And as long as this one can be computed
+from its children, then we compute Y.F,
+
+ align:start position:0%
+from its children, then we compute Y.F,
+ 
+
+ align:start position:0%
+from its children, then we compute Y.F,
+then we can compute X from its children.
+
+ align:start position:0%
+then we can compute X from its children.
+ 
+
+ align:start position:0%
+then we can compute X from its children.
+Right? So, a constant number of extra
+
+ align:start position:0%
+Right? So, a constant number of extra
+ 
+
+ align:start position:0%
+Right? So, a constant number of extra
+things we need to do whenever we do a
+
+ align:start position:0%
+things we need to do whenever we do a
+ 
+
+ align:start position:0%
+things we need to do whenever we do a
+rotation. And because the rotations lie
+
+ align:start position:0%
+rotation. And because the rotations lie
+ 
+
+ align:start position:0%
+rotation. And because the rotations lie
+in a single path uh total cost that that
+
+ align:start position:0%
+in a single path uh total cost that that
+ 
+
+ align:start position:0%
+in a single path uh total cost that that
+you know once we stop doing the
+
+ align:start position:0%
+you know once we stop doing the
+ 
+
+ align:start position:0%
+you know once we stop doing the
+rotations uh in AVL insert say then we
+
+ align:start position:0%
+rotations uh in AVL insert say then we
+ 
+
+ align:start position:0%
+rotations uh in AVL insert say then we
+still have to keep updating up to the
+
+ align:start position:0%
+still have to keep updating up to the
+ 
+
+ align:start position:0%
+still have to keep updating up to the
+root but there's only login at most
+
+ align:start position:0%
+root but there's only login at most
+ 
+
+ align:start position:0%
+root but there's only login at most
+login nodes to do that.
+
+ align:start position:0%
+login nodes to do that.
+ 
+
+ align:start position:0%
+login nodes to do that.
+Okay, same thing with uh with two three
+
+ align:start position:0%
+Okay, same thing with uh with two three
+ 
+
+ align:start position:0%
+Okay, same thing with uh with two three
+trees. We have a node split.
+
+ align:start position:0%
+trees. We have a node split.
+ 
+
+ align:start position:0%
+trees. We have a node split.
+So we have I guess three keys, four
+
+ align:start position:0%
+So we have I guess three keys, four
+ 
+
+ align:start position:0%
+So we have I guess three keys, four
+children. That's too many. So we split
+
+ align:start position:0%
+children. That's too many. So we split
+ 
+
+ align:start position:0%
+children. That's too many. So we split
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+two nodes and an extra node up here.
+
+ align:start position:0%
+two nodes and an extra node up here.
+ 
+
+ align:start position:0%
+two nodes and an extra node up here.
+Uh then we just trigger an update of
+
+ align:start position:0%
+Uh then we just trigger an update of
+ 
+
+ align:start position:0%
+Uh then we just trigger an update of
+this f value, an update of this fvalue,
+
+ align:start position:0%
+this f value, an update of this fvalue,
+ 
+
+ align:start position:0%
+this f value, an update of this fvalue,
+and an update of that fal. And because
+
+ align:start position:0%
+and an update of that fal. And because
+ 
+
+ align:start position:0%
+and an update of that fal. And because
+that just follows a single path,
+
+ align:start position:0%
+that just follows a single path,
+ 
+
+ align:start position:0%
+that just follows a single path,
+everything's login.
+
+ align:start position:0%
+everything's login.
+ 
+
+ align:start position:0%
+everything's login.
+Okay, so this is a general theorem about
+
+ align:start position:0%
+Okay, so this is a general theorem about
+ 
+
+ align:start position:0%
+Okay, so this is a general theorem about
+augmentation. Any function that's well
+
+ align:start position:0%
+augmentation. Any function that's well
+ 
+
+ align:start position:0%
+augmentation. Any function that's well
+behaved in this sense, we can maintain
+
+ align:start position:0%
+behaved in this sense, we can maintain
+ 
+
+ align:start position:0%
+behaved in this sense, we can maintain
+in AVL trees and 23 trees.
+
+ align:start position:0%
+in AVL trees and 23 trees.
+ 
+
+ align:start position:0%
+in AVL trees and 23 trees.
+And I'll remind you
+
+ align:start position:0%
+And I'll remind you
+ 
+
+ align:start position:0%
+And I'll remind you
+and state a little more generally what
+
+ align:start position:0%
+and state a little more generally what
+ 
+
+ align:start position:0%
+and state a little more generally what
+you did in 006, which are called order
+
+ align:start position:0%
+you did in 006, which are called order
+ 
+
+ align:start position:0%
+you did in 006, which are called order
+statistic trees in the textbook.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here um we're going to let me first
+
+ align:start position:0%
+So here um we're going to let me first
+ 
+
+ align:start position:0%
+So here um we're going to let me first
+tell you what we're trying to achieve.
+
+ align:start position:0%
+tell you what we're trying to achieve.
+ 
+
+ align:start position:0%
+tell you what we're trying to achieve.
+This is the abstract data type or the
+
+ align:start position:0%
+This is the abstract data type or the
+ 
+
+ align:start position:0%
+This is the abstract data type or the
+interface of the data structure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we want to do insert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh say successor searches.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's the usual thing we want out of a
+
+ align:start position:0%
+It's the usual thing we want out of a
+ 
+
+ align:start position:0%
+It's the usual thing we want out of a
+binary search tree. Predecessor 2. Sure.
+
+ align:start position:0%
+binary search tree. Predecessor 2. Sure.
+ 
+
+ align:start position:0%
+binary search tree. Predecessor 2. Sure.
+Uh we want to do rank
+
+ align:start position:0%
+Uh we want to do rank
+ 
+
+ align:start position:0%
+Uh we want to do rank
+of a of a given key which is uh tell me
+
+ align:start position:0%
+of a of a given key which is uh tell me
+ 
+
+ align:start position:0%
+of a of a given key which is uh tell me
+what is the index
+
+ align:start position:0%
+what is the index
+ 
+
+ align:start position:0%
+what is the index
+of that key
+
+ align:start position:0%
+of that key
+ 
+
+ align:start position:0%
+of that key
+uh in the overall sorted order of the
+
+ align:start position:0%
+uh in the overall sorted order of the
+ 
+
+ align:start position:0%
+uh in the overall sorted order of the
+items of the keys. We've talked about
+
+ align:start position:0%
+items of the keys. We've talked about
+ 
+
+ align:start position:0%
+items of the keys. We've talked about
+rank a few times already in this class.
+
+ align:start position:0%
+rank a few times already in this class.
+ 
+
+ align:start position:0%
+rank a few times already in this class.
+Uh depends whether you start at zero or
+
+ align:start position:0%
+Uh depends whether you start at zero or
+ 
+
+ align:start position:0%
+Uh depends whether you start at zero or
+one. But uh let's say we start at one.
+
+ align:start position:0%
+one. But uh let's say we start at one.
+ 
+
+ align:start position:0%
+one. But uh let's say we start at one.
+Uh so if you say rank of the key that
+
+ align:start position:0%
+Uh so if you say rank of the key that
+ 
+
+ align:start position:0%
+Uh so if you say rank of the key that
+happens to be the minimum, you want to
+
+ align:start position:0%
+happens to be the minimum, you want to
+ 
+
+ align:start position:0%
+happens to be the minimum, you want to
+get one. If you say rank of the key that
+
+ align:start position:0%
+get one. If you say rank of the key that
+ 
+
+ align:start position:0%
+get one. If you say rank of the key that
+happens to be the median, you want to
+
+ align:start position:0%
+happens to be the median, you want to
+ 
+
+ align:start position:0%
+happens to be the median, you want to
+get n over two plus one. Uh and so on.
+
+ align:start position:0%
+get n over two plus one. Uh and so on.
+ 
+
+ align:start position:0%
+get n over two plus one. Uh and so on.
+Okay. So that's a natural thing you
+
+ align:start position:0%
+Okay. So that's a natural thing you
+ 
+
+ align:start position:0%
+Okay. So that's a natural thing you
+might want to find out. uh and the
+
+ align:start position:0%
+might want to find out. uh and the
+ 
+
+ align:start position:0%
+might want to find out. uh and the
+converse operation is select
+
+ align:start position:0%
+converse operation is select
+ 
+
+ align:start position:0%
+converse operation is select
+say of I which is give me the key of
+
+ align:start position:0%
+say of I which is give me the key of
+ 
+
+ align:start position:0%
+say of I which is give me the key of
+rank I.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we've talked about uh select as an
+
+ align:start position:0%
+Okay, we've talked about uh select as an
+ 
+
+ align:start position:0%
+Okay, we've talked about uh select as an
+offline operation given an array uh find
+
+ align:start position:0%
+offline operation given an array uh find
+ 
+
+ align:start position:0%
+offline operation given an array uh find
+me the median or find me the n over 7th
+
+ align:start position:0%
+me the median or find me the n over 7th
+ 
+
+ align:start position:0%
+me the median or find me the n over 7th
+uh rank item and we can do that in
+
+ align:start position:0%
+uh rank item and we can do that in
+ 
+
+ align:start position:0%
+uh rank item and we can do that in
+linear time given no data structure
+
+ align:start position:0%
+linear time given no data structure
+ 
+
+ align:start position:0%
+linear time given no data structure
+here. We want a data structure so that
+
+ align:start position:0%
+here. We want a data structure so that
+ 
+
+ align:start position:0%
+here. We want a data structure so that
+we can find the median or the uh seventh
+
+ align:start position:0%
+we can find the median or the uh seventh
+ 
+
+ align:start position:0%
+we can find the median or the uh seventh
+item or the n over7th key uh whatever in
+
+ align:start position:0%
+item or the n over7th key uh whatever in
+ 
+
+ align:start position:0%
+item or the n over7th key uh whatever in
+login time. We want to do all of these
+
+ align:start position:0%
+login time. We want to do all of these
+ 
+
+ align:start position:0%
+login time. We want to do all of these
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+login per operation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so in particular rank of select of
+
+ align:start position:0%
+Okay, so in particular rank of select of
+ 
+
+ align:start position:0%
+Okay, so in particular rank of select of
+I should equal I, right? We're trying to
+
+ align:start position:0%
+I should equal I, right? We're trying to
+ 
+
+ align:start position:0%
+I should equal I, right? We're trying to
+find the item of that rank.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So far so good. Uh and
+
+ align:start position:0%
+So far so good. Uh and
+ 
+
+ align:start position:0%
+So far so good. Uh and
+just to plug these two parts together,
+
+ align:start position:0%
+just to plug these two parts together,
+ 
+
+ align:start position:0%
+just to plug these two parts together,
+we have this data structure augmentation
+
+ align:start position:0%
+we have this data structure augmentation
+ 
+
+ align:start position:0%
+we have this data structure augmentation
+tool. We have this goal we want to
+
+ align:start position:0%
+tool. We have this goal we want to
+ 
+
+ align:start position:0%
+tool. We have this goal we want to
+achieve. We're going to achieve this
+
+ align:start position:0%
+achieve. We're going to achieve this
+ 
+
+ align:start position:0%
+achieve. We're going to achieve this
+goal by applying this technique where f
+
+ align:start position:0%
+goal by applying this technique where f
+ 
+
+ align:start position:0%
+goal by applying this technique where f
+is just the subree size, the number of
+
+ align:start position:0%
+is just the subree size, the number of
+ 
+
+ align:start position:0%
+is just the subree size, the number of
+nodes in that subree because that will
+
+ align:start position:0%
+nodes in that subree because that will
+ 
+
+ align:start position:0%
+nodes in that subree because that will
+let us compute rank.
+
+ align:start position:0%
+let us compute rank.
+ 
+
+ align:start position:0%
+let us compute rank.
+So, we're going to use
+
+ align:start position:0%
+So, we're going to use
+ 
+
+ align:start position:0%
+So, we're going to use
+uh easy tree augmentation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with f
+
+ align:start position:0%
+with f
+ 
+
+ align:start position:0%
+with f
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+subree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to the number of nodes in the
+
+ align:start position:0%
+equal to the number of nodes in the
+ 
+
+ align:start position:0%
+equal to the number of nodes in the
+subree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in order for this to apply we need to
+
+ align:start position:0%
+So in order for this to apply we need to
+ 
+
+ align:start position:0%
+So in order for this to apply we need to
+check that given a node x uh we can
+
+ align:start position:0%
+check that given a node x uh we can
+ 
+
+ align:start position:0%
+check that given a node x uh we can
+compute x do just using its children.
+
+ align:start position:0%
+compute x do just using its children.
+ 
+
+ align:start position:0%
+compute x do just using its children.
+This is easy. Uh
+
+ align:start position:0%
+This is easy. Uh
+ 
+
+ align:start position:0%
+This is easy. Uh
+we just add everything up. So x do would
+
+ align:start position:0%
+we just add everything up. So x do would
+ 
+
+ align:start position:0%
+we just add everything up. So x do would
+be equal to 1 that's for x plus the sum
+
+ align:start position:0%
+be equal to 1 that's for x plus the sum
+ 
+
+ align:start position:0%
+be equal to 1 that's for x plus the sum
+of cf
+
+ align:start position:0%
+of cf
+ 
+
+ align:start position:0%
+of cf
+for every child c.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll write this as a python
+
+ align:start position:0%
+I'll write this as a python
+ 
+
+ align:start position:0%
+I'll write this as a python
+interpolation
+
+ align:start position:0%
+interpolation
+ 
+
+ align:start position:0%
+interpolation
+so it looks a little more like an
+
+ align:start position:0%
+so it looks a little more like an
+ 
+
+ align:start position:0%
+so it looks a little more like an
+algorithm. Um I'm trying to be generic
+
+ align:start position:0%
+algorithm. Um I'm trying to be generic
+ 
+
+ align:start position:0%
+algorithm. Um I'm trying to be generic
+here. If it's a binary search tree you
+
+ align:start position:0%
+here. If it's a binary search tree you
+ 
+
+ align:start position:0%
+here. If it's a binary search tree you
+just do x.left.f
+
+ align:start position:0%
+just do x.left.f
+ 
+
+ align:start position:0%
+just do x.left.f
+f plus x.right.f. But this will work
+
+ align:start position:0%
+f plus x.right.f. But this will work
+ 
+
+ align:start position:0%
+f plus x.right.f. But this will work
+also for two three trees. Pick your
+
+ align:start position:0%
+also for two three trees. Pick your
+ 
+
+ align:start position:0%
+also for two three trees. Pick your
+favorite uh data structure. As long as
+
+ align:start position:0%
+favorite uh data structure. As long as
+ 
+
+ align:start position:0%
+favorite uh data structure. As long as
+there's a constant number of children,
+
+ align:start position:0%
+there's a constant number of children,
+ 
+
+ align:start position:0%
+there's a constant number of children,
+then uh this will take constant time. So
+
+ align:start position:0%
+then uh this will take constant time. So
+ 
+
+ align:start position:0%
+then uh this will take constant time. So
+we satisfy this condition. So we can do
+
+ align:start position:0%
+we satisfy this condition. So we can do
+ 
+
+ align:start position:0%
+we satisfy this condition. So we can do
+easy tree augmentation. And now we know
+
+ align:start position:0%
+easy tree augmentation. And now we know
+ 
+
+ align:start position:0%
+easy tree augmentation. And now we know
+we have subree sizes. So given any node,
+
+ align:start position:0%
+we have subree sizes. So given any node,
+ 
+
+ align:start position:0%
+we have subree sizes. So given any node,
+we know the number of children sorry the
+
+ align:start position:0%
+we know the number of children sorry the
+ 
+
+ align:start position:0%
+we know the number of children sorry the
+number of descendants below that node.
+
+ align:start position:0%
+number of descendants below that node.
+ 
+
+ align:start position:0%
+number of descendants below that node.
+So that's cool. It lets us compute rank
+
+ align:start position:0%
+So that's cool. It lets us compute rank
+ 
+
+ align:start position:0%
+So that's cool. It lets us compute rank
+and select. I'll just uh give you those
+
+ align:start position:0%
+and select. I'll just uh give you those
+ 
+
+ align:start position:0%
+and select. I'll just uh give you those
+algorithms quickly.
+
+ align:start position:0%
+algorithms quickly.
+ 
+
+ align:start position:0%
+algorithms quickly.
+We can check that they're log end time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah, so the the the idea is pretty
+
+ align:start position:0%
+yeah, so the the the idea is pretty
+ 
+
+ align:start position:0%
+yeah, so the the the idea is pretty
+simple.
+
+ align:start position:0%
+simple.
+ 
+
+ align:start position:0%
+simple.
+You have some key. Let's think about
+
+ align:start position:0%
+You have some key. Let's think about
+ 
+
+ align:start position:0%
+You have some key. Let's think about
+binary trees uh now because it's a
+
+ align:start position:0%
+binary trees uh now because it's a
+ 
+
+ align:start position:0%
+binary trees uh now because it's a
+little bit easier. Um we have some item
+
+ align:start position:0%
+little bit easier. Um we have some item
+ 
+
+ align:start position:0%
+little bit easier. Um we have some item
+X.
+
+ align:start position:0%
+X.
+ 
+
+ align:start position:0%
+X.
+It has a left subree, a right subree.
+
+ align:start position:0%
+It has a left subree, a right subree.
+ 
+
+ align:start position:0%
+It has a left subree, a right subree.
+And now let's uh let's look up from X.
+
+ align:start position:0%
+And now let's uh let's look up from X.
+ 
+
+ align:start position:0%
+And now let's uh let's look up from X.
+Just keep calling uh X.parent.
+
+ align:start position:0%
+Just keep calling uh X.parent.
+ 
+
+ align:start position:0%
+Just keep calling uh X.parent.
+So sometimes the parent is to the right
+
+ align:start position:0%
+So sometimes the parent is to the right
+ 
+
+ align:start position:0%
+So sometimes the parent is to the right
+of us and sometimes the parent is to the
+
+ align:start position:0%
+of us and sometimes the parent is to the
+ 
+
+ align:start position:0%
+of us and sometimes the parent is to the
+left of us.
+
+ align:start position:0%
+left of us.
+ 
+
+ align:start position:0%
+left of us.
+Okay, I'm going to draw this in a kind
+
+ align:start position:0%
+Okay, I'm going to draw this in a kind
+ 
+
+ align:start position:0%
+Okay, I'm going to draw this in a kind
+of funny way,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this funny way has a very special
+
+ align:start position:0%
+but this funny way has a very special
+ 
+
+ align:start position:0%
+but this funny way has a very special
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+which is that the xcoordinate in this
+
+ align:start position:0%
+which is that the xcoordinate in this
+ 
+
+ align:start position:0%
+which is that the xcoordinate in this
+diagram is the key value or is the
+
+ align:start position:0%
+diagram is the key value or is the
+ 
+
+ align:start position:0%
+diagram is the key value or is the
+sorted order of the keys. Right?
+
+ align:start position:0%
+sorted order of the keys. Right?
+ 
+
+ align:start position:0%
+sorted order of the keys. Right?
+Everything in the left subree of X is
+
+ align:start position:0%
+Everything in the left subree of X is
+ 
+
+ align:start position:0%
+Everything in the left subree of X is
+has a value less than X. If we say all
+
+ align:start position:0%
+has a value less than X. If we say all
+ 
+
+ align:start position:0%
+has a value less than X. If we say all
+the keys are different, everything to
+
+ align:start position:0%
+the keys are different, everything to
+ 
+
+ align:start position:0%
+the keys are different, everything to
+the right of X has a value greater than
+
+ align:start position:0%
+the right of X has a value greater than
+ 
+
+ align:start position:0%
+the right of X has a value greater than
+X. If the parent if x was the left child
+
+ align:start position:0%
+X. If the parent if x was the left child
+ 
+
+ align:start position:0%
+X. If the parent if x was the left child
+of its parent that means this thing is
+
+ align:start position:0%
+of its parent that means this thing is
+ 
+
+ align:start position:0%
+of its parent that means this thing is
+also greater than x.
+
+ align:start position:0%
+also greater than x.
+ 
+
+ align:start position:0%
+also greater than x.
+Uh and if we follow a parent and it was
+
+ align:start position:0%
+Uh and if we follow a parent and it was
+ 
+
+ align:start position:0%
+Uh and if we follow a parent and it was
+and this was the right child of that
+
+ align:start position:0%
+and this was the right child of that
+ 
+
+ align:start position:0%
+and this was the right child of that
+parent that means this thing is less
+
+ align:start position:0%
+parent that means this thing is less
+ 
+
+ align:start position:0%
+parent that means this thing is less
+than x. So that's why I drew it all the
+
+ align:start position:0%
+than x. So that's why I drew it all the
+ 
+
+ align:start position:0%
+than x. So that's why I drew it all the
+way over to the left. This thing is also
+
+ align:start position:0%
+way over to the left. This thing is also
+ 
+
+ align:start position:0%
+way over to the left. This thing is also
+less than x because it was a I'll call
+
+ align:start position:0%
+less than x because it was a I'll call
+ 
+
+ align:start position:0%
+less than x because it was a I'll call
+it a left parent. Here we have a right
+
+ align:start position:0%
+it a left parent. Here we have a right
+ 
+
+ align:start position:0%
+it a left parent. Here we have a right
+parent. So that means this is something
+
+ align:start position:0%
+parent. So that means this is something
+ 
+
+ align:start position:0%
+parent. So that means this is something
+greater than x.
+
+ align:start position:0%
+greater than x.
+ 
+
+ align:start position:0%
+greater than x.
+And over here we have a left parent. So
+
+ align:start position:0%
+And over here we have a left parent. So
+ 
+
+ align:start position:0%
+And over here we have a left parent. So
+this is something less than x. Let's say
+
+ align:start position:0%
+this is something less than x. Let's say
+ 
+
+ align:start position:0%
+this is something less than x. Let's say
+that's the root. In general, there's
+
+ align:start position:0%
+that's the root. In general, there's
+ 
+
+ align:start position:0%
+that's the root. In general, there's
+going to be some left edges and some
+
+ align:start position:0%
+going to be some left edges and some
+ 
+
+ align:start position:0%
+going to be some left edges and some
+right edges. As we go up, these arrows
+
+ align:start position:0%
+right edges. As we go up, these arrows
+ 
+
+ align:start position:0%
+right edges. As we go up, these arrows
+will go either left or right in a binary
+
+ align:start position:0%
+will go either left or right in a binary
+ 
+
+ align:start position:0%
+will go either left or right in a binary
+tree. So the rank of x is just uh one
+
+ align:start position:0%
+tree. So the rank of x is just uh one
+ 
+
+ align:start position:0%
+tree. So the rank of x is just uh one
+plus the number of nodes that are less
+
+ align:start position:0%
+plus the number of nodes that are less
+ 
+
+ align:start position:0%
+plus the number of nodes that are less
+than x. Number of keys that are less
+
+ align:start position:0%
+than x. Number of keys that are less
+ 
+
+ align:start position:0%
+than x. Number of keys that are less
+than x. So there's these guys,
+
+ align:start position:0%
+than x. So there's these guys,
+ 
+
+ align:start position:0%
+than x. So there's these guys,
+there's these guys, and there's whatever
+
+ align:start position:0%
+there's these guys, and there's whatever
+ 
+
+ align:start position:0%
+there's these guys, and there's whatever
+is hanging off. Okay, here I've almost
+
+ align:start position:0%
+is hanging off. Okay, here I've almost
+ 
+
+ align:start position:0%
+is hanging off. Okay, here I've almost
+violated my x coordinate rule. If I make
+
+ align:start position:0%
+violated my x coordinate rule. If I make
+ 
+
+ align:start position:0%
+violated my x coordinate rule. If I make
+these really narrow, that's right.
+
+ align:start position:0%
+these really narrow, that's right.
+ 
+
+ align:start position:0%
+these really narrow, that's right.
+So all of these things uh all of these
+
+ align:start position:0%
+So all of these things uh all of these
+ 
+
+ align:start position:0%
+So all of these things uh all of these
+nodes in the left sub trees of these
+
+ align:start position:0%
+nodes in the left sub trees of these
+ 
+
+ align:start position:0%
+nodes in the left sub trees of these
+less than x nodes will also be less than
+
+ align:start position:0%
+less than x nodes will also be less than
+ 
+
+ align:start position:0%
+less than x nodes will also be less than
+x. If you think about these other sub
+
+ align:start position:0%
+x. If you think about these other sub
+ 
+
+ align:start position:0%
+x. If you think about these other sub
+trees, they're going to be bigger than
+
+ align:start position:0%
+trees, they're going to be bigger than
+ 
+
+ align:start position:0%
+trees, they're going to be bigger than
+x. So we don't really care about them.
+
+ align:start position:0%
+x. So we don't really care about them.
+ 
+
+ align:start position:0%
+x. So we don't really care about them.
+So we just want to count up
+
+ align:start position:0%
+So we just want to count up
+ 
+
+ align:start position:0%
+So we just want to count up
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+of these nodes
+
+ align:start position:0%
+of these nodes
+ 
+
+ align:start position:0%
+of these nodes
+and all of these nodes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the algorithm to do that is pretty
+
+ align:start position:0%
+So the algorithm to do that is pretty
+ 
+
+ align:start position:0%
+So the algorithm to do that is pretty
+simple.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh we're just going to
+
+ align:start position:0%
+Uh we're just going to
+ 
+
+ align:start position:0%
+Uh we're just going to
+uh start out with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to switch from this f notation
+
+ align:start position:0%
+I'm going to switch from this f notation
+ 
+
+ align:start position:0%
+I'm going to switch from this f notation
+to size. That's a little more natural.
+
+ align:start position:0%
+to size. That's a little more natural.
+ 
+
+ align:start position:0%
+to size. That's a little more natural.
+In general, you might have many
+
+ align:start position:0%
+In general, you might have many
+ 
+
+ align:start position:0%
+In general, you might have many
+functions. So size is the usual notion
+
+ align:start position:0%
+functions. So size is the usual notion
+ 
+
+ align:start position:0%
+functions. So size is the usual notion
+for usual notation for subree size.
+
+ align:start position:0%
+for usual notation for subree size.
+ 
+
+ align:start position:0%
+for usual notation for subree size.
+Uh so we start out by counting up how
+
+ align:start position:0%
+Uh so we start out by counting up how
+ 
+
+ align:start position:0%
+Uh so we start out by counting up how
+many items are here. And if we want to
+
+ align:start position:0%
+many items are here. And if we want to
+ 
+
+ align:start position:0%
+many items are here. And if we want to
+start at a rank of one, if the min has
+
+ align:start position:0%
+start at a rank of one, if the min has
+ 
+
+ align:start position:0%
+start at a rank of one, if the min has
+rank one, then I should also do plus one
+
+ align:start position:0%
+rank one, then I should also do plus one
+ 
+
+ align:start position:0%
+rank one, then I should also do plus one
+for x itself. If you wanted to start at
+
+ align:start position:0%
+for x itself. If you wanted to start at
+ 
+
+ align:start position:0%
+for x itself. If you wanted to start at
+zero, you just emit that plus one.
+
+ align:start position:0%
+zero, you just emit that plus one.
+ 
+
+ align:start position:0%
+zero, you just emit that plus one.
+And then all I do is walk up from x to
+
+ align:start position:0%
+And then all I do is walk up from x to
+ 
+
+ align:start position:0%
+And then all I do is walk up from x to
+the root of the tree.
+
+ align:start position:0%
+the root of the tree.
+ 
+
+ align:start position:0%
+the root of the tree.
+And uh whenever
+
+ align:start position:0%
+And uh whenever
+ 
+
+ align:start position:0%
+And uh whenever
+we go left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh from say x to x prime. So that means
+
+ align:start position:0%
+uh from say x to x prime. So that means
+ 
+
+ align:start position:0%
+uh from say x to x prime. So that means
+we have an x prime. It's right child is
+
+ align:start position:0%
+we have an x prime. It's right child is
+ 
+
+ align:start position:0%
+we have an x prime. It's right child is
+x. And so when we went from x to its
+
+ align:start position:0%
+x. And so when we went from x to its
+ 
+
+ align:start position:0%
+x. And so when we went from x to its
+parent, we went to the left. Uh then we
+
+ align:start position:0%
+parent, we went to the left. Uh then we
+ 
+
+ align:start position:0%
+parent, we went to the left. Uh then we
+say uh rank
+
+ align:start position:0%
+say uh rank
+ 
+
+ align:start position:0%
+say uh rank
+plus equals
+
+ align:start position:0%
+plus equals
+ 
+
+ align:start position:0%
+plus equals
+uh x prime. left
+
+ align:start position:0%
+uh x prime. left
+ 
+
+ align:start position:0%
+uh x prime. left
+dots size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh plus one for x prime itself.
+
+ align:start position:0%
+uh plus one for x prime itself.
+ 
+
+ align:start position:0%
+uh plus one for x prime itself.
+Okay, maybe there maybe x x xp prime.
+
+ align:start position:0%
+Okay, maybe there maybe x x xp prime.
+ 
+
+ align:start position:0%
+Okay, maybe there maybe x x xp prime.
+size is zero. Maybe there's no nodes
+
+ align:start position:0%
+size is zero. Maybe there's no nodes
+ 
+
+ align:start position:0%
+size is zero. Maybe there's no nodes
+over there. But at the very least, we
+
+ align:start position:0%
+over there. But at the very least, we
+ 
+
+ align:start position:0%
+over there. But at the very least, we
+have to count those nodes that are to
+
+ align:start position:0%
+have to count those nodes that are to
+ 
+
+ align:start position:0%
+have to count those nodes that are to
+the left of us. And if there anything
+
+ align:start position:0%
+the left of us. And if there anything
+ 
+
+ align:start position:0%
+the left of us. And if there anything
+down here, we add up all those things.
+
+ align:start position:0%
+down here, we add up all those things.
+ 
+
+ align:start position:0%
+down here, we add up all those things.
+So that lets us compute rank. How long
+
+ align:start position:0%
+So that lets us compute rank. How long
+ 
+
+ align:start position:0%
+So that lets us compute rank. How long
+does it take? Well, we're just walking
+
+ align:start position:0%
+does it take? Well, we're just walking
+ 
+
+ align:start position:0%
+does it take? Well, we're just walking
+up one path from a leaf to root or not
+
+ align:start position:0%
+up one path from a leaf to root or not
+ 
+
+ align:start position:0%
+up one path from a leaf to root or not
+necessarily leaf but from some node x to
+
+ align:start position:0%
+necessarily leaf but from some node x to
+ 
+
+ align:start position:0%
+necessarily leaf but from some node x to
+the root. And as long as we're using a
+
+ align:start position:0%
+the root. And as long as we're using a
+ 
+
+ align:start position:0%
+the root. And as long as we're using a
+balanced structure like AVL trees, uh I
+
+ align:start position:0%
+balanced structure like AVL trees, uh I
+ 
+
+ align:start position:0%
+balanced structure like AVL trees, uh I
+guess I want binary here. So let's say
+
+ align:start position:0%
+guess I want binary here. So let's say
+ 
+
+ align:start position:0%
+guess I want binary here. So let's say
+AVL trees uh then this will take login
+
+ align:start position:0%
+AVL trees uh then this will take login
+ 
+
+ align:start position:0%
+AVL trees uh then this will take login
+time. So I'm spending constant work per
+
+ align:start position:0%
+time. So I'm spending constant work per
+ 
+
+ align:start position:0%
+time. So I'm spending constant work per
+step and there's login steps.
+
+ align:start position:0%
+step and there's login steps.
+ 
+
+ align:start position:0%
+step and there's login steps.
+Clear?
+
+ align:start position:0%
+Clear?
+ 
+
+ align:start position:0%
+Clear?
+So that's good old rank.
+
+ align:start position:0%
+So that's good old rank.
+ 
+
+ align:start position:0%
+So that's good old rank.
+Easy to do once you have subree size.
+
+ align:start position:0%
+Easy to do once you have subree size.
+ 
+
+ align:start position:0%
+Easy to do once you have subree size.
+Let's do select for fun.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This may seem like review, but I drew
+
+ align:start position:0%
+This may seem like review, but I drew
+ 
+
+ align:start position:0%
+This may seem like review, but I drew
+out this picture explicitly because
+
+ align:start position:0%
+out this picture explicitly because
+ 
+
+ align:start position:0%
+out this picture explicitly because
+we're going to do it a lot today. We'll
+
+ align:start position:0%
+we're going to do it a lot today. We'll
+ 
+
+ align:start position:0%
+we're going to do it a lot today. We'll
+have pictures like this a bunch of
+
+ align:start position:0%
+have pictures like this a bunch of
+ 
+
+ align:start position:0%
+have pictures like this a bunch of
+times. really helps to think about where
+
+ align:start position:0%
+times. really helps to think about where
+ 
+
+ align:start position:0%
+times. really helps to think about where
+the nodes are, which ones are less than
+
+ align:start position:0%
+the nodes are, which ones are less than
+ 
+
+ align:start position:0%
+the nodes are, which ones are less than
+x, which ones are greater than x.
+
+ align:start position:0%
+x, which ones are greater than x.
+ 
+
+ align:start position:0%
+x, which ones are greater than x.
+Okay, let's do select first.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This you may not have seen in 006.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're going to do the reverse. We're
+
+ align:start position:0%
+So, we're going to do the reverse. We're
+ 
+
+ align:start position:0%
+So, we're going to do the reverse. We're
+going to start at the root and we're
+
+ align:start position:0%
+going to start at the root and we're
+ 
+
+ align:start position:0%
+going to start at the root and we're
+going to walk down.
+
+ align:start position:0%
+going to walk down.
+ 
+
+ align:start position:0%
+going to walk down.
+Sounds easy enough. Uh, but now walking
+
+ align:start position:0%
+Sounds easy enough. Uh, but now walking
+ 
+
+ align:start position:0%
+Sounds easy enough. Uh, but now walking
+down is kind of like doing a search, but
+
+ align:start position:0%
+down is kind of like doing a search, but
+ 
+
+ align:start position:0%
+down is kind of like doing a search, but
+we don't have a key we're searching for.
+
+ align:start position:0%
+we don't have a key we're searching for.
+ 
+
+ align:start position:0%
+we don't have a key we're searching for.
+We have a rank we're searching for.
+
+ align:start position:0%
+We have a rank we're searching for.
+ 
+
+ align:start position:0%
+We have a rank we're searching for.
+So, uh what is that rank?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rank is I. Okay. So, uh on the other
+
+ align:start position:0%
+Rank is I. Okay. So, uh on the other
+ 
+
+ align:start position:0%
+Rank is I. Okay. So, uh on the other
+hand, we have the node X. We'd like to
+
+ align:start position:0%
+hand, we have the node X. We'd like to
+ 
+
+ align:start position:0%
+hand, we have the node X. We'd like to
+know the rank of X and compare that to
+
+ align:start position:0%
+know the rank of X and compare that to
+ 
+
+ align:start position:0%
+know the rank of X and compare that to
+I. That will tell us whether we should
+
+ align:start position:0%
+I. That will tell us whether we should
+ 
+
+ align:start position:0%
+I. That will tell us whether we should
+go left or go right or whether we happen
+
+ align:start position:0%
+go left or go right or whether we happen
+ 
+
+ align:start position:0%
+go left or go right or whether we happen
+to find the item. Now, one possibility
+
+ align:start position:0%
+to find the item. Now, one possibility
+ 
+
+ align:start position:0%
+to find the item. Now, one possibility
+is we call rank of X to find the rank of
+
+ align:start position:0%
+is we call rank of X to find the rank of
+ 
+
+ align:start position:0%
+is we call rank of X to find the rank of
+X. But that's dangerous. Uh because I'm
+
+ align:start position:0%
+X. But that's dangerous. Uh because I'm
+ 
+
+ align:start position:0%
+X. But that's dangerous. Uh because I'm
+going to have a a for loop here. And if
+
+ align:start position:0%
+going to have a a for loop here. And if
+ 
+
+ align:start position:0%
+going to have a a for loop here. And if
+and it's going to take log n iterations.
+
+ align:start position:0%
+and it's going to take log n iterations.
+ 
+
+ align:start position:0%
+and it's going to take log n iterations.
+If at every iteration I'm computing rank
+
+ align:start position:0%
+If at every iteration I'm computing rank
+ 
+
+ align:start position:0%
+If at every iteration I'm computing rank
+of x and rank cost log n then overall
+
+ align:start position:0%
+of x and rank cost log n then overall
+ 
+
+ align:start position:0%
+of x and rank cost log n then overall
+cost might be log squared n. So I can't
+
+ align:start position:0%
+cost might be log squared n. So I can't
+ 
+
+ align:start position:0%
+cost might be log squared n. So I can't
+afford to I want to know what the rank
+
+ align:start position:0%
+afford to I want to know what the rank
+ 
+
+ align:start position:0%
+afford to I want to know what the rank
+of x is
+
+ align:start position:0%
+of x is
+ 
+
+ align:start position:0%
+of x is
+but I can't afford to say rank open x
+
+ align:start position:0%
+but I can't afford to say rank open x
+ 
+
+ align:start position:0%
+but I can't afford to say rank open x
+because that recursive call will be too
+
+ align:start position:0%
+because that recursive call will be too
+ 
+
+ align:start position:0%
+because that recursive call will be too
+expensive. So what is the rank of X in
+
+ align:start position:0%
+expensive. So what is the rank of X in
+ 
+
+ align:start position:0%
+expensive. So what is the rank of X in
+this case? This is a little special.
+
+ align:start position:0%
+this case? This is a little special.
+ 
+
+ align:start position:0%
+this case? This is a little special.
+What's that?
+
+ align:start position:0%
+What's that?
+ 
+
+ align:start position:0%
+What's that?
+Number of left children plus one.
+
+ align:start position:0%
+Number of left children plus one.
+ 
+
+ align:start position:0%
+Number of left children plus one.
+Number of left or the size of the left
+
+ align:start position:0%
+Number of left or the size of the left
+ 
+
+ align:start position:0%
+Number of left or the size of the left
+subree plus one. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Plus one if we're counting starting at
+
+ align:start position:0%
+Plus one if we're counting starting at
+ 
+
+ align:start position:0%
+Plus one if we're counting starting at
+one. Very good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm slowly getting better. Um didn't hit
+
+ align:start position:0%
+I'm slowly getting better. Um didn't hit
+ 
+
+ align:start position:0%
+I'm slowly getting better. Um didn't hit
+anyone this time. Okay. So at least for
+
+ align:start position:0%
+anyone this time. Okay. So at least for
+ 
+
+ align:start position:0%
+anyone this time. Okay. So at least for
+the root, this is the rank and that only
+
+ align:start position:0%
+the root, this is the rank and that only
+ 
+
+ align:start position:0%
+the root, this is the rank and that only
+takes us constant time in this special
+
+ align:start position:0%
+takes us constant time in this special
+ 
+
+ align:start position:0%
+takes us constant time in this special
+case. We'll have to check that it still
+
+ align:start position:0%
+case. We'll have to check that it still
+ 
+
+ align:start position:0%
+case. We'll have to check that it still
+holds after I do the loop, but it will.
+
+ align:start position:0%
+holds after I do the loop, but it will.
+ 
+
+ align:start position:0%
+holds after I do the loop, but it will.
+Uh so cool. Now there are three cases. U
+
+ align:start position:0%
+Uh so cool. Now there are three cases. U
+ 
+
+ align:start position:0%
+Uh so cool. Now there are three cases. U
+if I equals rank, if the rank we're
+
+ align:start position:0%
+if I equals rank, if the rank we're
+ 
+
+ align:start position:0%
+if I equals rank, if the rank we're
+searching for is the rank that we happen
+
+ align:start position:0%
+searching for is the rank that we happen
+ 
+
+ align:start position:0%
+searching for is the rank that we happen
+to have, then we're done, right? We just
+
+ align:start position:0%
+to have, then we're done, right? We just
+ 
+
+ align:start position:0%
+to have, then we're done, right? We just
+return x.
+
+ align:start position:0%
+return x.
+ 
+
+ align:start position:0%
+return x.
+Okay, that's the easy case. more more
+
+ align:start position:0%
+Okay, that's the easy case. more more
+ 
+
+ align:start position:0%
+Okay, that's the easy case. more more
+likely is that I will be either less
+
+ align:start position:0%
+likely is that I will be either less
+ 
+
+ align:start position:0%
+likely is that I will be either less
+than or greater than the rank of X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh so if I is less than the rank,
+
+ align:start position:0%
+Okay. Uh so if I is less than the rank,
+ 
+
+ align:start position:0%
+Okay. Uh so if I is less than the rank,
+this is fairly easy. We just say uh X=
+
+ align:start position:0%
+this is fairly easy. We just say uh X=
+ 
+
+ align:start position:0%
+this is fairly easy. We just say uh X=
+X.ft.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh did I get that right? Yeah. Um in
+
+ align:start position:0%
+Uh did I get that right? Yeah. Um in
+ 
+
+ align:start position:0%
+Uh did I get that right? Yeah. Um in
+this case the rank so here we have x
+
+ align:start position:0%
+this case the rank so here we have x
+ 
+
+ align:start position:0%
+this case the rank so here we have x
+it's at rank rank and then we have the
+
+ align:start position:0%
+it's at rank rank and then we have the
+ 
+
+ align:start position:0%
+it's at rank rank and then we have the
+left subree uh and the right subree and
+
+ align:start position:0%
+left subree uh and the right subree and
+ 
+
+ align:start position:0%
+left subree uh and the right subree and
+so if the rank we're searching for is
+
+ align:start position:0%
+so if the rank we're searching for is
+ 
+
+ align:start position:0%
+so if the rank we're searching for is
+less than rank that means we know it's
+
+ align:start position:0%
+less than rank that means we know it's
+ 
+
+ align:start position:0%
+less than rank that means we know it's
+in here so we should go left and if we
+
+ align:start position:0%
+in here so we should go left and if we
+ 
+
+ align:start position:0%
+in here so we should go left and if we
+just set x= x.ft uh you might ask well
+
+ align:start position:0%
+just set x= x.ft uh you might ask well
+ 
+
+ align:start position:0%
+just set x= x.ft uh you might ask well
+what rank are we searching for in here?
+
+ align:start position:0%
+what rank are we searching for in here?
+ 
+
+ align:start position:0%
+what rank are we searching for in here?
+Well exactly the same rank fine that's
+
+ align:start position:0%
+Well exactly the same rank fine that's
+ 
+
+ align:start position:0%
+Well exactly the same rank fine that's
+the easy case. uh in the other situation
+
+ align:start position:0%
+the easy case. uh in the other situation
+ 
+
+ align:start position:0%
+the easy case. uh in the other situation
+if we're searching in here we're
+
+ align:start position:0%
+if we're searching in here we're
+ 
+
+ align:start position:0%
+if we're searching in here we're
+searching for a rank greater than rank
+
+ align:start position:0%
+searching for a rank greater than rank
+ 
+
+ align:start position:0%
+searching for a rank greater than rank
+uh then I want to go right
+
+ align:start position:0%
+uh then I want to go right
+ 
+
+ align:start position:0%
+uh then I want to go right
+but the new rank that I'm searching for
+
+ align:start position:0%
+but the new rank that I'm searching for
+ 
+
+ align:start position:0%
+but the new rank that I'm searching for
+is local to this subree I'm searching
+
+ align:start position:0%
+is local to this subree I'm searching
+ 
+
+ align:start position:0%
+is local to this subree I'm searching
+for uh I minus this stuff this stuff is
+
+ align:start position:0%
+for uh I minus this stuff this stuff is
+ 
+
+ align:start position:0%
+for uh I minus this stuff this stuff is
+rank so I'm going to let I be I minus
+
+ align:start position:0%
+rank so I'm going to let I be I minus
+ 
+
+ align:start position:0%
+rank so I'm going to let I be I minus
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+sure I don't have any off by one errors.
+
+ align:start position:0%
+sure I don't have any off by one errors.
+ 
+
+ align:start position:0%
+sure I don't have any off by one errors.
+Yeah, that's to be right.
+
+ align:start position:0%
+Yeah, that's to be right.
+ 
+
+ align:start position:0%
+Yeah, that's to be right.
+Okay. And then I do a loop. So I'll
+
+ align:start position:0%
+Okay. And then I do a loop. So I'll
+ 
+
+ align:start position:0%
+Okay. And then I do a loop. So I'll
+write repeat.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh so then I'm going to go up here and
+
+ align:start position:0%
+Uh so then I'm going to go up here and
+ 
+
+ align:start position:0%
+Uh so then I'm going to go up here and
+say okay now relative to this thing what
+
+ align:start position:0%
+say okay now relative to this thing what
+ 
+
+ align:start position:0%
+say okay now relative to this thing what
+is the rank of the root of this subree?
+
+ align:start position:0%
+is the rank of the root of this subree?
+ 
+
+ align:start position:0%
+is the rank of the root of this subree?
+Uh well it's again going to be that
+
+ align:start position:0%
+Uh well it's again going to be that
+ 
+
+ align:start position:0%
+Uh well it's again going to be that
+node.left size plus one. And now I have
+
+ align:start position:0%
+node.left size plus one. And now I have
+ 
+
+ align:start position:0%
+node.left size plus one. And now I have
+the new rank I'm searching for I. And I
+
+ align:start position:0%
+the new rank I'm searching for I. And I
+ 
+
+ align:start position:0%
+the new rank I'm searching for I. And I
+just keep going. You could write this
+
+ align:start position:0%
+just keep going. You could write this
+ 
+
+ align:start position:0%
+just keep going. You could write this
+recursively if you like, but here's an
+
+ align:start position:0%
+recursively if you like, but here's an
+ 
+
+ align:start position:0%
+recursively if you like, but here's an
+iterative version.
+
+ align:start position:0%
+iterative version.
+ 
+
+ align:start position:0%
+iterative version.
+So it's actually very familiar to the
+
+ align:start position:0%
+So it's actually very familiar to the
+ 
+
+ align:start position:0%
+So it's actually very familiar to the
+select algorithm that we had uh like
+
+ align:start position:0%
+select algorithm that we had uh like
+ 
+
+ align:start position:0%
+select algorithm that we had uh like
+when we did deterministic linear time
+
+ align:start position:0%
+when we did deterministic linear time
+ 
+
+ align:start position:0%
+when we did deterministic linear time
+median finding or randomized median
+
+ align:start position:0%
+median finding or randomized median
+ 
+
+ align:start position:0%
+median finding or randomized median
+finding. U they had a very similar kind
+
+ align:start position:0%
+finding. U they had a very similar kind
+ 
+
+ align:start position:0%
+finding. U they had a very similar kind
+of recursion but in that case we're
+
+ align:start position:0%
+of recursion but in that case we're
+ 
+
+ align:start position:0%
+of recursion but in that case we're
+spending linear time to do the partition
+
+ align:start position:0%
+spending linear time to do the partition
+ 
+
+ align:start position:0%
+spending linear time to do the partition
+and that was expensive. Here we're just
+
+ align:start position:0%
+and that was expensive. Here we're just
+ 
+
+ align:start position:0%
+and that was expensive. Here we're just
+spending constant time at each node and
+
+ align:start position:0%
+spending constant time at each node and
+ 
+
+ align:start position:0%
+spending constant time at each node and
+so the overall cost is login.
+
+ align:start position:0%
+so the overall cost is login.
+ 
+
+ align:start position:0%
+so the overall cost is login.
+So that's nice. Any questions about
+
+ align:start position:0%
+So that's nice. Any questions about
+ 
+
+ align:start position:0%
+So that's nice. Any questions about
+that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh I have a note here. Subree size
+
+ align:start position:0%
+Okay. Uh I have a note here. Subree size
+ 
+
+ align:start position:0%
+Okay. Uh I have a note here. Subree size
+is obvious once you know that that's
+
+ align:start position:0%
+is obvious once you know that that's
+ 
+
+ align:start position:0%
+is obvious once you know that that's
+what you should do. Another natural
+
+ align:start position:0%
+what you should do. Another natural
+ 
+
+ align:start position:0%
+what you should do. Another natural
+thing to try to do would be to augment
+
+ align:start position:0%
+thing to try to do would be to augment
+ 
+
+ align:start position:0%
+thing to try to do would be to augment
+for each node what is the rank of that
+
+ align:start position:0%
+for each node what is the rank of that
+ 
+
+ align:start position:0%
+for each node what is the rank of that
+node because then rank is really easy to
+
+ align:start position:0%
+node because then rank is really easy to
+ 
+
+ align:start position:0%
+node because then rank is really easy to
+find. And then select would basically be
+
+ align:start position:0%
+find. And then select would basically be
+ 
+
+ align:start position:0%
+find. And then select would basically be
+a regular search. I just look at the
+
+ align:start position:0%
+a regular search. I just look at the
+ 
+
+ align:start position:0%
+a regular search. I just look at the
+rank of the root. I see whether the rank
+
+ align:start position:0%
+rank of the root. I see whether the rank
+ 
+
+ align:start position:0%
+rank of the root. I see whether the rank
+I'm looking for is too big or too small
+
+ align:start position:0%
+I'm looking for is too big or too small
+ 
+
+ align:start position:0%
+I'm looking for is too big or too small
+and I go left or right accordingly. What
+
+ align:start position:0%
+and I go left or right accordingly. What
+ 
+
+ align:start position:0%
+and I go left or right accordingly. What
+would be bad about augmenting with rank
+
+ align:start position:0%
+would be bad about augmenting with rank
+ 
+
+ align:start position:0%
+would be bad about augmenting with rank
+of a node?
+
+ align:start position:0%
+of a node?
+ 
+
+ align:start position:0%
+of a node?
+Updates. Why?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What's a bad example for an update?
+
+ align:start position:0%
+What's a bad example for an update?
+ 
+
+ align:start position:0%
+What's a bad example for an update?
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. Say we insert a new minimum
+
+ align:start position:0%
+Right. Say we insert a new minimum
+ 
+
+ align:start position:0%
+Right. Say we insert a new minimum
+element.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ah, good catch, cameraman.
+
+ align:start position:0%
+Ah, good catch, cameraman.
+ 
+
+ align:start position:0%
+Ah, good catch, cameraman.
+That was for the camera, obviously. Um,
+
+ align:start position:0%
+That was for the camera, obviously. Um,
+ 
+
+ align:start position:0%
+That was for the camera, obviously. Um,
+so, right, if we insert, uh, this is off
+
+ align:start position:0%
+so, right, if we insert, uh, this is off
+ 
+
+ align:start position:0%
+so, right, if we insert, uh, this is off
+to the side, but say we insert, I'll
+
+ align:start position:0%
+to the side, but say we insert, I'll
+ 
+
+ align:start position:0%
+to the side, but say we insert, I'll
+call it minus infinity, a new key that
+
+ align:start position:0%
+call it minus infinity, a new key that
+ 
+
+ align:start position:0%
+call it minus infinity, a new key that
+is smaller than all other keys, then the
+
+ align:start position:0%
+is smaller than all other keys, then the
+ 
+
+ align:start position:0%
+is smaller than all other keys, then the
+rank of every node changes.
+
+ align:start position:0%
+rank of every node changes.
+ 
+
+ align:start position:0%
+rank of every node changes.
+So, uh, that's bad.
+
+ align:start position:0%
+So, uh, that's bad.
+ 
+
+ align:start position:0%
+So, uh, that's bad.
+U, it means that easy tree augmentation
+
+ align:start position:0%
+U, it means that easy tree augmentation
+ 
+
+ align:start position:0%
+U, it means that easy tree augmentation
+in particular isn't going to apply. And
+
+ align:start position:0%
+in particular isn't going to apply. And
+ 
+
+ align:start position:0%
+in particular isn't going to apply. And
+furthermore, it would take linear time
+
+ align:start position:0%
+furthermore, it would take linear time
+ 
+
+ align:start position:0%
+furthermore, it would take linear time
+to do this. And you could keep
+
+ align:start position:0%
+to do this. And you could keep
+ 
+
+ align:start position:0%
+to do this. And you could keep
+inserting. If you insert keys in
+
+ align:start position:0%
+inserting. If you insert keys in
+ 
+
+ align:start position:0%
+inserting. If you insert keys in
+decreasing order from there, every time
+
+ align:start position:0%
+decreasing order from there, every time
+ 
+
+ align:start position:0%
+decreasing order from there, every time
+you do an insert, all the ranks increase
+
+ align:start position:0%
+you do an insert, all the ranks increase
+ 
+
+ align:start position:0%
+you do an insert, all the ranks increase
+by one. Maintaining that's going to cost
+
+ align:start position:0%
+by one. Maintaining that's going to cost
+ 
+
+ align:start position:0%
+by one. Maintaining that's going to cost
+linear time per update. So you have to
+
+ align:start position:0%
+linear time per update. So you have to
+ 
+
+ align:start position:0%
+linear time per update. So you have to
+be really careful that uh the the
+
+ align:start position:0%
+be really careful that uh the the
+ 
+
+ align:start position:0%
+be really careful that uh the the
+function you you want to store actually
+
+ align:start position:0%
+function you you want to store actually
+ 
+
+ align:start position:0%
+function you you want to store actually
+can be maintained. Be very careful about
+
+ align:start position:0%
+can be maintained. Be very careful about
+ 
+
+ align:start position:0%
+can be maintained. Be very careful about
+that. Say on the quiz coming up uh that
+
+ align:start position:0%
+that. Say on the quiz coming up uh that
+ 
+
+ align:start position:0%
+that. Say on the quiz coming up uh that
+when you're augmenting something, you
+
+ align:start position:0%
+when you're augmenting something, you
+ 
+
+ align:start position:0%
+when you're augmenting something, you
+can actually maintain it. For example,
+
+ align:start position:0%
+can actually maintain it. For example,
+ 
+
+ align:start position:0%
+can actually maintain it. For example,
+it's very hard to maintain the depths of
+
+ align:start position:0%
+it's very hard to maintain the depths of
+ 
+
+ align:start position:0%
+it's very hard to maintain the depths of
+nodes because when you do a rotation, a
+
+ align:start position:0%
+nodes because when you do a rotation, a
+ 
+
+ align:start position:0%
+nodes because when you do a rotation, a
+whole lot of depths change. If your
+
+ align:start position:0%
+whole lot of depths change. If your
+ 
+
+ align:start position:0%
+whole lot of depths change. If your
+depth is counting from the root, how
+
+ align:start position:0%
+depth is counting from the root, how
+ 
+
+ align:start position:0%
+depth is counting from the root, how
+deep am I? Uh when I do a rotation, then
+
+ align:start position:0%
+deep am I? Uh when I do a rotation, then
+ 
+
+ align:start position:0%
+deep am I? Uh when I do a rotation, then
+this entire subree went down by one.
+
+ align:start position:0%
+this entire subree went down by one.
+ 
+
+ align:start position:0%
+this entire subree went down by one.
+This entire subree went up by one
+
+ align:start position:0%
+This entire subree went up by one
+ 
+
+ align:start position:0%
+This entire subree went up by one
+in this picture. Uh but it's very easy
+
+ align:start position:0%
+in this picture. Uh but it's very easy
+ 
+
+ align:start position:0%
+in this picture. Uh but it's very easy
+to maintain heights. For example, height
+
+ align:start position:0%
+to maintain heights. For example, height
+ 
+
+ align:start position:0%
+to maintain heights. For example, height
+counting from the bottom is okay because
+
+ align:start position:0%
+counting from the bottom is okay because
+ 
+
+ align:start position:0%
+counting from the bottom is okay because
+I don't affect the height of A, B, and
+
+ align:start position:0%
+I don't affect the height of A, B, and
+ 
+
+ align:start position:0%
+I don't affect the height of A, B, and
+C. I affect it for X and Y but that's
+
+ align:start position:0%
+C. I affect it for X and Y but that's
+ 
+
+ align:start position:0%
+C. I affect it for X and Y but that's
+just two nodes that I can afford. Okay,
+
+ align:start position:0%
+just two nodes that I can afford. Okay,
+ 
+
+ align:start position:0%
+just two nodes that I can afford. Okay,
+so that's what you want to be careful of
+
+ align:start position:0%
+so that's what you want to be careful of
+ 
+
+ align:start position:0%
+so that's what you want to be careful of
+uh in the easy tree augmentation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So most of the time easy tree
+
+ align:start position:0%
+So most of the time easy tree
+ 
+
+ align:start position:0%
+So most of the time easy tree
+augmentation does the job. But uh in the
+
+ align:start position:0%
+augmentation does the job. But uh in the
+ 
+
+ align:start position:0%
+augmentation does the job. But uh in the
+remaining two examples I want to show
+
+ align:start position:0%
+remaining two examples I want to show
+ 
+
+ align:start position:0%
+remaining two examples I want to show
+you cooler examples of augmentation.
+
+ align:start position:0%
+you cooler examples of augmentation.
+ 
+
+ align:start position:0%
+you cooler examples of augmentation.
+These are things you probably wouldn't
+
+ align:start position:0%
+These are things you probably wouldn't
+ 
+
+ align:start position:0%
+These are things you probably wouldn't
+be expected to come up with on your own
+
+ align:start position:0%
+be expected to come up with on your own
+ 
+
+ align:start position:0%
+be expected to come up with on your own
+but they're cool. So and that let us do
+
+ align:start position:0%
+but they're cool. So and that let us do
+ 
+
+ align:start position:0%
+but they're cool. So and that let us do
+more sophisticated operations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So first one is uh called level linking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here we're going to do it in the
+
+ align:start position:0%
+and here we're going to do it in the
+ 
+
+ align:start position:0%
+and here we're going to do it in the
+context of two three trees
+
+ align:start position:0%
+context of two three trees
+ 
+
+ align:start position:0%
+context of two three trees
+partly for variety. Um
+
+ align:start position:0%
+partly for variety. Um
+ 
+
+ align:start position:0%
+partly for variety. Um
+so uh the idea of level linking is very
+
+ align:start position:0%
+so uh the idea of level linking is very
+ 
+
+ align:start position:0%
+so uh the idea of level linking is very
+simple. Let me draw a 23 tree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Not a very impressive 23 tree because I
+
+ align:start position:0%
+Not a very impressive 23 tree because I
+ 
+
+ align:start position:0%
+Not a very impressive 23 tree because I
+don't feel like drawing too much. Uh
+
+ align:start position:0%
+don't feel like drawing too much. Uh
+ 
+
+ align:start position:0%
+don't feel like drawing too much. Uh
+level linking is the idea of in addition
+
+ align:start position:0%
+level linking is the idea of in addition
+ 
+
+ align:start position:0%
+level linking is the idea of in addition
+to these child and parent pointers,
+
+ align:start position:0%
+to these child and parent pointers,
+ 
+
+ align:start position:0%
+to these child and parent pointers,
+we're going to add links on all the
+
+ align:start position:0%
+we're going to add links on all the
+ 
+
+ align:start position:0%
+we're going to add links on all the
+levels.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Horizontal links you might call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's nice. Uh, two questions.
+
+ align:start position:0%
+Okay, so that's nice. Uh, two questions.
+ 
+
+ align:start position:0%
+Okay, so that's nice. Uh, two questions.
+Can we do this? and what's it good for?
+
+ align:start position:0%
+Can we do this? and what's it good for?
+ 
+
+ align:start position:0%
+Can we do this? and what's it good for?
+So let's start with can we do this? Uh
+
+ align:start position:0%
+So let's start with can we do this? Uh
+ 
+
+ align:start position:0%
+So let's start with can we do this? Uh
+remember in two three trees all we have
+
+ align:start position:0%
+remember in two three trees all we have
+ 
+
+ align:start position:0%
+remember in two three trees all we have
+to think about are splits and merges. So
+
+ align:start position:0%
+to think about are splits and merges. So
+ 
+
+ align:start position:0%
+to think about are splits and merges. So
+in a split
+
+ align:start position:0%
+in a split
+ 
+
+ align:start position:0%
+in a split
+we have for a brief period let's say uh
+
+ align:start position:0%
+we have for a brief period let's say uh
+ 
+
+ align:start position:0%
+we have for a brief period let's say uh
+three keys four children that's too
+
+ align:start position:0%
+three keys four children that's too
+ 
+
+ align:start position:0%
+three keys four children that's too
+many.
+
+ align:start position:0%
+many.
+ 
+
+ align:start position:0%
+many.
+So, we change that to uh
+
+ align:start position:0%
+So, we change that to uh
+ 
+
+ align:start position:0%
+So, we change that to uh
+uh yeah,
+
+ align:start position:0%
+uh yeah,
+ 
+
+ align:start position:0%
+uh yeah,
+I'm going to change this in a moment,
+
+ align:start position:0%
+I'm going to change this in a moment,
+ 
+
+ align:start position:0%
+I'm going to change this in a moment,
+but for now, this is the split you know
+
+ align:start position:0%
+but for now, this is the split you know
+ 
+
+ align:start position:0%
+but for now, this is the split you know
+and love maybe at least know. And uh if
+
+ align:start position:0%
+and love maybe at least know. And uh if
+ 
+
+ align:start position:0%
+and love maybe at least know. And uh if
+we think about where the level link
+
+ align:start position:0%
+we think about where the level link
+ 
+
+ align:start position:0%
+we think about where the level link
+pointers are, we have one before. Uh and
+
+ align:start position:0%
+pointers are, we have one before. Uh and
+ 
+
+ align:start position:0%
+pointers are, we have one before. Uh and
+then we just need to distribute those
+
+ align:start position:0%
+then we just need to distribute those
+ 
+
+ align:start position:0%
+then we just need to distribute those
+pointers
+
+ align:start position:0%
+pointers
+ 
+
+ align:start position:0%
+pointers
+uh to the two resulting nodes. And then
+
+ align:start position:0%
+uh to the two resulting nodes. And then
+ 
+
+ align:start position:0%
+uh to the two resulting nodes. And then
+we have to create a new pointer between
+
+ align:start position:0%
+we have to create a new pointer between
+ 
+
+ align:start position:0%
+we have to create a new pointer between
+the nodes that we just created. This is
+
+ align:start position:0%
+the nodes that we just created. This is
+ 
+
+ align:start position:0%
+the nodes that we just created. This is
+of course easy to do. We're here. We're
+
+ align:start position:0%
+of course easy to do. We're here. We're
+ 
+
+ align:start position:0%
+of course easy to do. We're here. We're
+taking this node. We're splitting it in
+
+ align:start position:0%
+taking this node. We're splitting it in
+ 
+
+ align:start position:0%
+taking this node. We're splitting it in
+half. Uh so we have the nodes right in
+
+ align:start position:0%
+half. Uh so we have the nodes right in
+ 
+
+ align:start position:0%
+half. Uh so we have the nodes right in
+our hands. So just add pointers between
+
+ align:start position:0%
+our hands. So just add pointers between
+ 
+
+ align:start position:0%
+our hands. So just add pointers between
+them. And key thing is there's some node
+
+ align:start position:0%
+them. And key thing is there's some node
+ 
+
+ align:start position:0%
+them. And key thing is there's some node
+over here on the left. It used to point
+
+ align:start position:0%
+over here on the left. It used to point
+ 
+
+ align:start position:0%
+over here on the left. It used to point
+to this node. Now we have to change it
+
+ align:start position:0%
+to this node. Now we have to change it
+ 
+
+ align:start position:0%
+to this node. Now we have to change it
+to point to the left version, the left
+
+ align:start position:0%
+to point to the left version, the left
+ 
+
+ align:start position:0%
+to point to the left version, the left
+half of the node. And there's some node
+
+ align:start position:0%
+half of the node. And there's some node
+ 
+
+ align:start position:0%
+half of the node. And there's some node
+over on the right. We have to change it
+
+ align:start position:0%
+over on the right. We have to change it
+ 
+
+ align:start position:0%
+over on the right. We have to change it
+left pointer to point to uh this right
+
+ align:start position:0%
+left pointer to point to uh this right
+ 
+
+ align:start position:0%
+left pointer to point to uh this right
+half of the node. But that's it.
+
+ align:start position:0%
+half of the node. But that's it.
+ 
+
+ align:start position:0%
+half of the node. But that's it.
+Constant time. Okay. So this is this
+
+ align:start position:0%
+Constant time. Okay. So this is this
+ 
+
+ align:start position:0%
+Constant time. Okay. So this is this
+doesn't fall under the category of easy
+
+ align:start position:0%
+doesn't fall under the category of easy
+ 
+
+ align:start position:0%
+doesn't fall under the category of easy
+tree augmentation because this is not
+
+ align:start position:0%
+tree augmentation because this is not
+ 
+
+ align:start position:0%
+tree augmentation because this is not
+isolated to the subree. We're also
+
+ align:start position:0%
+isolated to the subree. We're also
+ 
+
+ align:start position:0%
+isolated to the subree. We're also
+dealing with its left and right sub
+
+ align:start position:0%
+dealing with its left and right sub
+ 
+
+ align:start position:0%
+dealing with its left and right sub
+trees. But still easy to do in constant
+
+ align:start position:0%
+trees. But still easy to do in constant
+ 
+
+ align:start position:0%
+trees. But still easy to do in constant
+time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh merging nodes is going to be similar.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh if we steal a node from our uh parent
+
+ align:start position:0%
+Uh if we steal a node from our uh parent
+ 
+
+ align:start position:0%
+Uh if we steal a node from our uh parent
+then or from our sibling, nothing
+
+ align:start position:0%
+then or from our sibling, nothing
+ 
+
+ align:start position:0%
+then or from our sibling, nothing
+happens in terms of level lengths. But
+
+ align:start position:0%
+happens in terms of level lengths. But
+ 
+
+ align:start position:0%
+happens in terms of level lengths. But
+if we have say an empty node and a node
+
+ align:start position:0%
+if we have say an empty node and a node
+ 
+
+ align:start position:0%
+if we have say an empty node and a node
+that cannot afford any stealing. So we
+
+ align:start position:0%
+that cannot afford any stealing. So we
+ 
+
+ align:start position:0%
+that cannot afford any stealing. So we
+have single child here two children and
+
+ align:start position:0%
+have single child here two children and
+ 
+
+ align:start position:0%
+have single child here two children and
+we merge it into
+
+ align:start position:0%
+we merge it into
+ 
+
+ align:start position:0%
+we merge it into
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're taking something from our parent
+
+ align:start position:0%
+we're taking something from our parent
+ 
+
+ align:start position:0%
+we're taking something from our parent
+bringing it down and we have three
+
+ align:start position:0%
+bringing it down and we have three
+ 
+
+ align:start position:0%
+bringing it down and we have three
+children afterwards. Again we used to
+
+ align:start position:0%
+children afterwards. Again we used to
+ 
+
+ align:start position:0%
+children afterwards. Again we used to
+have these these uh level pointers. Now
+
+ align:start position:0%
+have these these uh level pointers. Now
+ 
+
+ align:start position:0%
+have these these uh level pointers. Now
+we just have these level pointers. It's
+
+ align:start position:0%
+we just have these level pointers. It's
+ 
+
+ align:start position:0%
+we just have these level pointers. It's
+easy to maintain. It's just a constant
+
+ align:start position:0%
+easy to maintain. It's just a constant
+ 
+
+ align:start position:0%
+easy to maintain. It's just a constant
+sized neighborhood. Because we have the
+
+ align:start position:0%
+sized neighborhood. Because we have the
+ 
+
+ align:start position:0%
+sized neighborhood. Because we have the
+level links, we can get to our left and
+
+ align:start position:0%
+level links, we can get to our left and
+ 
+
+ align:start position:0%
+level links, we can get to our left and
+right neighbors and change where the
+
+ align:start position:0%
+right neighbors and change where the
+ 
+
+ align:start position:0%
+right neighbors and change where the
+links point to. So easy to maintain in
+
+ align:start position:0%
+links point to. So easy to maintain in
+ 
+
+ align:start position:0%
+links point to. So easy to maintain in
+constant time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll call it constant overhead. Every
+
+ align:start position:0%
+I'll call it constant overhead. Every
+ 
+
+ align:start position:0%
+I'll call it constant overhead. Every
+time we do a splitter merge, we spend uh
+
+ align:start position:0%
+time we do a splitter merge, we spend uh
+ 
+
+ align:start position:0%
+time we do a splitter merge, we spend uh
+an additional constant time to do it.
+
+ align:start position:0%
+an additional constant time to do it.
+ 
+
+ align:start position:0%
+an additional constant time to do it.
+We're already spending constant time, so
+
+ align:start position:0%
+We're already spending constant time, so
+ 
+
+ align:start position:0%
+We're already spending constant time, so
+just changes everything by a constant
+
+ align:start position:0%
+just changes everything by a constant
+ 
+
+ align:start position:0%
+just changes everything by a constant
+factor.
+
+ align:start position:0%
+factor.
+ 
+
+ align:start position:0%
+factor.
+So far so good. Uh,
+
+ align:start position:0%
+So far so good. Uh,
+ 
+
+ align:start position:0%
+So far so good. Uh,
+now I'm going to have to tweak this data
+
+ align:start position:0%
+now I'm going to have to tweak this data
+ 
+
+ align:start position:0%
+now I'm going to have to tweak this data
+structure a little bit, but let me first
+
+ align:start position:0%
+structure a little bit, but let me first
+ 
+
+ align:start position:0%
+structure a little bit, but let me first
+tell you why. What am I trying to
+
+ align:start position:0%
+tell you why. What am I trying to
+ 
+
+ align:start position:0%
+tell you why. What am I trying to
+achieve with this data structure?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What I'm trying to achieve is something
+
+ align:start position:0%
+What I'm trying to achieve is something
+ 
+
+ align:start position:0%
+What I'm trying to achieve is something
+called uh the finger search property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is uh so let's just think about the
+
+ align:start position:0%
+this is uh so let's just think about the
+ 
+
+ align:start position:0%
+this is uh so let's just think about the
+case where I'm doing uh a successful
+
+ align:start position:0%
+case where I'm doing uh a successful
+ 
+
+ align:start position:0%
+case where I'm doing uh a successful
+search. I'm searching for a key X and I
+
+ align:start position:0%
+search. I'm searching for a key X and I
+ 
+
+ align:start position:0%
+search. I'm searching for a key X and I
+find it in the data structure. I find it
+
+ align:start position:0%
+find it in the data structure. I find it
+ 
+
+ align:start position:0%
+find it in the data structure. I find it
+in the tree. Uh
+
+ align:start position:0%
+in the tree. Uh
+ 
+
+ align:start position:0%
+in the tree. Uh
+suppose I found one. I searched for X. I
+
+ align:start position:0%
+suppose I found one. I searched for X. I
+ 
+
+ align:start position:0%
+suppose I found one. I searched for X. I
+found it. And then I searched for
+
+ align:start position:0%
+found it. And then I searched for
+ 
+
+ align:start position:0%
+found it. And then I searched for
+another key Y. Actually, I think I'll do
+
+ align:start position:0%
+another key Y. Actually, I think I'll do
+ 
+
+ align:start position:0%
+another key Y. Actually, I think I'll do
+the reverse. I first I found Y. Now I'm
+
+ align:start position:0%
+the reverse. I first I found Y. Now I'm
+ 
+
+ align:start position:0%
+the reverse. I first I found Y. Now I'm
+searching for X. If X and Y are nearby
+
+ align:start position:0%
+searching for X. If X and Y are nearby
+ 
+
+ align:start position:0%
+searching for X. If X and Y are nearby
+in the tree, I want this to run
+
+ align:start position:0%
+in the tree, I want this to run
+ 
+
+ align:start position:0%
+in the tree, I want this to run
+especially fast. For example, if X is a
+
+ align:start position:0%
+especially fast. For example, if X is a
+ 
+
+ align:start position:0%
+especially fast. For example, if X is a
+successor of Y, I want this to take
+
+ align:start position:0%
+successor of Y, I want this to take
+ 
+
+ align:start position:0%
+successor of Y, I want this to take
+constant time. That would be nice.
+
+ align:start position:0%
+constant time. That would be nice.
+ 
+
+ align:start position:0%
+constant time. That would be nice.
+uh in the worst case x and y are very
+
+ align:start position:0%
+uh in the worst case x and y are very
+ 
+
+ align:start position:0%
+uh in the worst case x and y are very
+far away from me in the tree then I
+
+ align:start position:0%
+far away from me in the tree then I
+ 
+
+ align:start position:0%
+far away from me in the tree then I
+wanted to take login time. So how could
+
+ align:start position:0%
+wanted to take login time. So how could
+ 
+
+ align:start position:0%
+wanted to take login time. So how could
+I interpolate between uh constant time
+
+ align:start position:0%
+I interpolate between uh constant time
+ 
+
+ align:start position:0%
+I interpolate between uh constant time
+for finding the the successor and login
+
+ align:start position:0%
+for finding the the successor and login
+ 
+
+ align:start position:0%
+for finding the the successor and login
+time for finding the uh worstase search.
+
+ align:start position:0%
+time for finding the uh worstase search.
+ 
+
+ align:start position:0%
+time for finding the uh worstase search.
+So I'm going to call this search
+
+ align:start position:0%
+So I'm going to call this search
+ 
+
+ align:start position:0%
+So I'm going to call this search
+of X from Y. Meaning uh this is a little
+
+ align:start position:0%
+of X from Y. Meaning uh this is a little
+ 
+
+ align:start position:0%
+of X from Y. Meaning uh this is a little
+imprecise, but what I mean is when I
+
+ align:start position:0%
+imprecise, but what I mean is when I
+ 
+
+ align:start position:0%
+imprecise, but what I mean is when I
+call search, I tell it where I've
+
+ align:start position:0%
+call search, I tell it where I've
+ 
+
+ align:start position:0%
+call search, I tell it where I've
+already found Y. And here it is. Here's
+
+ align:start position:0%
+already found Y. And here it is. Here's
+ 
+
+ align:start position:0%
+already found Y. And here it is. Here's
+the node storing Y. And now I want to
+
+ align:start position:0%
+the node storing Y. And now I want to
+ 
+
+ align:start position:0%
+the node storing Y. And now I want to
+I'm given a key X and I want to find
+
+ align:start position:0%
+I'm given a key X and I want to find
+ 
+
+ align:start position:0%
+I'm given a key X and I want to find
+that key X given the node that stores
+
+ align:start position:0%
+that key X given the node that stores
+ 
+
+ align:start position:0%
+that key X given the node that stores
+key Y. So how long should this take?
+
+ align:start position:0%
+key Y. So how long should this take?
+ 
+
+ align:start position:0%
+key Y. So how long should this take?
+What would be a good way to interpolate
+
+ align:start position:0%
+What would be a good way to interpolate
+ 
+
+ align:start position:0%
+What would be a good way to interpolate
+between constant time at one extreme in
+
+ align:start position:0%
+between constant time at one extreme in
+ 
+
+ align:start position:0%
+between constant time at one extreme in
+the good case when x and y are basically
+
+ align:start position:0%
+the good case when x and y are basically
+ 
+
+ align:start position:0%
+the good case when x and y are basically
+neighbors in
+
+ align:start position:0%
+neighbors in
+ 
+
+ align:start position:0%
+neighbors in
+in the sorted order versus uh log n time
+
+ align:start position:0%
+in the sorted order versus uh log n time
+ 
+
+ align:start position:0%
+in the sorted order versus uh log n time
+in the worst case.
+
+ align:start position:0%
+in the worst case.
+ 
+
+ align:start position:0%
+in the worst case.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+the distance along the graph
+
+ align:start position:0%
+the distance along the graph
+ 
+
+ align:start position:0%
+the distance along the graph
+distance along the graph that would be
+
+ align:start position:0%
+distance along the graph that would be
+ 
+
+ align:start position:0%
+distance along the graph that would be
+one reasonable definition. Um, so I me I
+
+ align:start position:0%
+one reasonable definition. Um, so I me I
+ 
+
+ align:start position:0%
+one reasonable definition. Um, so I me I
+have a tree which you can think of as a
+
+ align:start position:0%
+have a tree which you can think of as a
+ 
+
+ align:start position:0%
+have a tree which you can think of as a
+graph. Measure the shortest path length
+
+ align:start position:0%
+graph. Measure the shortest path length
+ 
+
+ align:start position:0%
+graph. Measure the shortest path length
+from X to Y or or we have a more
+
+ align:start position:0%
+from X to Y or or we have a more
+ 
+
+ align:start position:0%
+from X to Y or or we have a more
+sophisticated graph over here. Uh maybe
+
+ align:start position:0%
+sophisticated graph over here. Uh maybe
+ 
+
+ align:start position:0%
+sophisticated graph over here. Uh maybe
+that that length. The trouble with the
+
+ align:start position:0%
+that that length. The trouble with the
+ 
+
+ align:start position:0%
+that that length. The trouble with the
+distance in the graph that's a
+
+ align:start position:0%
+distance in the graph that's a
+ 
+
+ align:start position:0%
+distance in the graph that's a
+reasonable suggestion, but it's very
+
+ align:start position:0%
+reasonable suggestion, but it's very
+ 
+
+ align:start position:0%
+reasonable suggestion, but it's very
+data structure specific. If I use an AVL
+
+ align:start position:0%
+data structure specific. If I use an AVL
+ 
+
+ align:start position:0%
+data structure specific. If I use an AVL
+tree without level links, then the
+
+ align:start position:0%
+tree without level links, then the
+ 
+
+ align:start position:0%
+tree without level links, then the
+distance could be one thing. Whereas if
+
+ align:start position:0%
+distance could be one thing. Whereas if
+ 
+
+ align:start position:0%
+distance could be one thing. Whereas if
+I use a 23 tree, even without level
+
+ align:start position:0%
+I use a 23 tree, even without level
+ 
+
+ align:start position:0%
+I use a 23 tree, even without level
+lengths, it's going to be a different
+
+ align:start position:0%
+lengths, it's going to be a different
+ 
+
+ align:start position:0%
+lengths, it's going to be a different
+distance. If I use a 23 tree with level
+
+ align:start position:0%
+distance. If I use a 23 tree with level
+ 
+
+ align:start position:0%
+distance. If I use a 23 tree with level
+lengths, it's going to be yet another
+
+ align:start position:0%
+lengths, it's going to be yet another
+ 
+
+ align:start position:0%
+lengths, it's going to be yet another
+distance. So that's a little
+
+ align:start position:0%
+distance. So that's a little
+ 
+
+ align:start position:0%
+distance. So that's a little
+unsatisfying. Uh I want this to be an
+
+ align:start position:0%
+unsatisfying. Uh I want this to be an
+ 
+
+ align:start position:0%
+unsatisfying. Uh I want this to be an
+answer to a question. Uh I don't want to
+
+ align:start position:0%
+answer to a question. Uh I don't want to
+ 
+
+ align:start position:0%
+answer to a question. Uh I don't want to
+phrase the question in terms of that
+
+ align:start position:0%
+phrase the question in terms of that
+ 
+
+ align:start position:0%
+phrase the question in terms of that
+data structure. Yeah.
+
+ align:start position:0%
+data structure. Yeah.
+ 
+
+ align:start position:0%
+data structure. Yeah.
+Difference between ranks between X and
+
+ align:start position:0%
+Difference between ranks between X and
+ 
+
+ align:start position:0%
+Difference between ranks between X and
+Y. That's close.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I'm going to look at rank of X and
+
+ align:start position:0%
+So, I'm going to look at rank of X and
+ 
+
+ align:start position:0%
+So, I'm going to look at rank of X and
+rank of Y. Let's say take the absolute
+
+ align:start position:0%
+rank of Y. Let's say take the absolute
+ 
+
+ align:start position:0%
+rank of Y. Let's say take the absolute
+difference. That's kind of how far away
+
+ align:start position:0%
+difference. That's kind of how far away
+ 
+
+ align:start position:0%
+difference. That's kind of how far away
+they are in sorted order. Do you want to
+
+ align:start position:0%
+they are in sorted order. Do you want to
+ 
+
+ align:start position:0%
+they are in sorted order. Do you want to
+add anything?
+
+ align:start position:0%
+add anything?
+ 
+
+ align:start position:0%
+add anything?
+Log. Yeah.
+
+ align:start position:0%
+Log. Yeah.
+ 
+
+ align:start position:0%
+Log. Yeah.
+Because uh in the worst case, the
+
+ align:start position:0%
+Because uh in the worst case, the
+ 
+
+ align:start position:0%
+Because uh in the worst case, the
+difference in ranks could be linear. So,
+
+ align:start position:0%
+difference in ranks could be linear. So,
+ 
+
+ align:start position:0%
+difference in ranks could be linear. So,
+uh I want to add a log out here to get
+
+ align:start position:0%
+uh I want to add a log out here to get
+ 
+
+ align:start position:0%
+uh I want to add a log out here to get
+log N in that worst case.
+
+ align:start position:0%
+log N in that worst case.
+ 
+
+ align:start position:0%
+log N in that worst case.
+add a big O for safety. That's how much
+
+ align:start position:0%
+add a big O for safety. That's how much
+ 
+
+ align:start position:0%
+add a big O for safety. That's how much
+time we want to achieve. So this would
+
+ align:start position:0%
+time we want to achieve. So this would
+ 
+
+ align:start position:0%
+time we want to achieve. So this would
+be the finger search property that you
+
+ align:start position:0%
+be the finger search property that you
+ 
+
+ align:start position:0%
+be the finger search property that you
+can solve this problem in this much
+
+ align:start position:0%
+can solve this problem in this much
+ 
+
+ align:start position:0%
+can solve this problem in this much
+time. So again difference in ranks is at
+
+ align:start position:0%
+time. So again difference in ranks is at
+ 
+
+ align:start position:0%
+time. So again difference in ranks is at
+most n. So this is at most log n. But if
+
+ align:start position:0%
+most n. So this is at most log n. But if
+ 
+
+ align:start position:0%
+most n. So this is at most log n. But if
+y is the successor of x, this will only
+
+ align:start position:0%
+y is the successor of x, this will only
+ 
+
+ align:start position:0%
+y is the successor of x, this will only
+be constant and this will be constant.
+
+ align:start position:0%
+be constant and this will be constant.
+ 
+
+ align:start position:0%
+be constant and this will be constant.
+So this is great if you're doing lots of
+
+ align:start position:0%
+So this is great if you're doing lots of
+ 
+
+ align:start position:0%
+So this is great if you're doing lots of
+searches and you're always you tend to
+
+ align:start position:0%
+searches and you're always you tend to
+ 
+
+ align:start position:0%
+searches and you're always you tend to
+search for things that are nearby but
+
+ align:start position:0%
+search for things that are nearby but
+ 
+
+ align:start position:0%
+search for things that are nearby but
+sometimes you search for things that are
+
+ align:start position:0%
+sometimes you search for things that are
+ 
+
+ align:start position:0%
+sometimes you search for things that are
+far away. This gives you a nice nice
+
+ align:start position:0%
+far away. This gives you a nice nice
+ 
+
+ align:start position:0%
+far away. This gives you a nice nice
+bound. Uh
+
+ align:start position:0%
+bound. Uh
+ 
+
+ align:start position:0%
+bound. Uh
+so um on the one hand we have this is
+
+ align:start position:0%
+so um on the one hand we have this is
+ 
+
+ align:start position:0%
+so um on the one hand we have this is
+our goal log difference of ranks. On the
+
+ align:start position:0%
+our goal log difference of ranks. On the
+ 
+
+ align:start position:0%
+our goal log difference of ranks. On the
+other hand we have the suggestion that
+
+ align:start position:0%
+other hand we have the suggestion that
+ 
+
+ align:start position:0%
+other hand we have the suggestion that
+what we can achieve is something like
+
+ align:start position:0%
+what we can achieve is something like
+ 
+
+ align:start position:0%
+what we can achieve is something like
+the distance in the graph.
+
+ align:start position:0%
+the distance in the graph.
+ 
+
+ align:start position:0%
+the distance in the graph.
+Uh but we have a problem with this. I
+
+ align:start position:0%
+Uh but we have a problem with this. I
+ 
+
+ align:start position:0%
+Uh but we have a problem with this. I
+used to think that data structure solved
+
+ align:start position:0%
+used to think that data structure solved
+ 
+
+ align:start position:0%
+used to think that data structure solved
+this problem but it doesn't. Um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just draw actually I have a tree
+
+ align:start position:0%
+let me just draw actually I have a tree
+ 
+
+ align:start position:0%
+let me just draw actually I have a tree
+right there and I use that one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose uh x is here and y is here.
+
+ align:start position:0%
+Suppose uh x is here and y is here.
+ 
+
+ align:start position:0%
+Suppose uh x is here and y is here.
+Okay, this is a bit of a small tree, but
+
+ align:start position:0%
+Okay, this is a bit of a small tree, but
+ 
+
+ align:start position:0%
+Okay, this is a bit of a small tree, but
+if you think about it long enough, uh
+
+ align:start position:0%
+if you think about it long enough, uh
+ 
+
+ align:start position:0%
+if you think about it long enough, uh
+this node is the predecessor of this
+
+ align:start position:0%
+this node is the predecessor of this
+ 
+
+ align:start position:0%
+this node is the predecessor of this
+node. So their difference in rank should
+
+ align:start position:0%
+node. So their difference in rank should
+ 
+
+ align:start position:0%
+node. So their difference in rank should
+be one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But the the distance in the graph here
+
+ align:start position:0%
+But the the distance in the graph here
+ 
+
+ align:start position:0%
+But the the distance in the graph here
+is two. Okay, not very impressive. But
+
+ align:start position:0%
+is two. Okay, not very impressive. But
+ 
+
+ align:start position:0%
+is two. Okay, not very impressive. But
+in general, you have a tree of height
+
+ align:start position:0%
+in general, you have a tree of height
+ 
+
+ align:start position:0%
+in general, you have a tree of height
+log n. If you look at the root and the
+
+ align:start position:0%
+log n. If you look at the root and the
+ 
+
+ align:start position:0%
+log n. If you look at the root and the
+predecessor of the root,
+
+ align:start position:0%
+predecessor of the root,
+ 
+
+ align:start position:0%
+predecessor of the root,
+they will have a rank difference of one
+
+ align:start position:0%
+they will have a rank difference of one
+ 
+
+ align:start position:0%
+they will have a rank difference of one
+by definition of predecessor, but the
+
+ align:start position:0%
+by definition of predecessor, but the
+ 
+
+ align:start position:0%
+by definition of predecessor, but the
+graph distance will be log n. So that's
+
+ align:start position:0%
+graph distance will be log n. So that's
+ 
+
+ align:start position:0%
+graph distance will be log n. So that's
+bad news because if we're only following
+
+ align:start position:0%
+bad news because if we're only following
+ 
+
+ align:start position:0%
+bad news because if we're only following
+pointers, there's no way to get from
+
+ align:start position:0%
+pointers, there's no way to get from
+ 
+
+ align:start position:0%
+pointers, there's no way to get from
+here to there in constant time. So we're
+
+ align:start position:0%
+here to there in constant time. So we're
+ 
+
+ align:start position:0%
+here to there in constant time. So we're
+not quite there.
+
+ align:start position:0%
+not quite there.
+ 
+
+ align:start position:0%
+not quite there.
+Uh we're going to use a different
+
+ align:start position:0%
+Uh we're going to use a different
+ 
+
+ align:start position:0%
+Uh we're going to use a different
+another tweak on that data structure
+
+ align:start position:0%
+another tweak on that data structure
+ 
+
+ align:start position:0%
+another tweak on that data structure
+which is uh
+
+ align:start position:0%
+which is uh
+ 
+
+ align:start position:0%
+which is uh
+store the data in the leaves.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I tried to find a data structure that
+
+ align:start position:0%
+I tried to find a data structure that
+ 
+
+ align:start position:0%
+I tried to find a data structure that
+didn't require this and still got finger
+
+ align:start position:0%
+didn't require this and still got finger
+ 
+
+ align:start position:0%
+didn't require this and still got finger
+search but as far as I know there is
+
+ align:start position:0%
+search but as far as I know there is
+ 
+
+ align:start position:0%
+search but as far as I know there is
+none no such data structure. So uh if if
+
+ align:start position:0%
+none no such data structure. So uh if if
+ 
+
+ align:start position:0%
+none no such data structure. So uh if if
+you've looked if you look at say
+
+ align:start position:0%
+you've looked if you look at say
+ 
+
+ align:start position:0%
+you've looked if you look at say
+Wikipedia about B trees you'll see
+
+ align:start position:0%
+Wikipedia about B trees you'll see
+ 
+
+ align:start position:0%
+Wikipedia about B trees you'll see
+there's a ton of variations of B trees B
+
+ align:start position:0%
+there's a ton of variations of B trees B
+ 
+
+ align:start position:0%
+there's a ton of variations of B trees B
+plus trees B star trees. This is one of
+
+ align:start position:0%
+plus trees B star trees. This is one of
+ 
+
+ align:start position:0%
+plus trees B star trees. This is one of
+those I think B+ trees. Um
+
+ align:start position:0%
+those I think B+ trees. Um
+ 
+
+ align:start position:0%
+those I think B+ trees. Um
+as you saw B trees are two three trees.
+
+ align:start position:0%
+as you saw B trees are two three trees.
+ 
+
+ align:start position:0%
+as you saw B trees are two three trees.
+Every node stored uh one or two keys
+
+ align:start position:0%
+Every node stored uh one or two keys
+ 
+
+ align:start position:0%
+Every node stored uh one or two keys
+and each key only existed in one spot.
+
+ align:start position:0%
+and each key only existed in one spot.
+ 
+
+ align:start position:0%
+and each key only existed in one spot.
+We're still only going to put each key
+
+ align:start position:0%
+We're still only going to put each key
+ 
+
+ align:start position:0%
+We're still only going to put each key
+in one spot kind of uh but it's only
+
+ align:start position:0%
+in one spot kind of uh but it's only
+ 
+
+ align:start position:0%
+in one spot kind of uh but it's only
+going to be the leaf spots. Okay, good
+
+ align:start position:0%
+going to be the leaf spots. Okay, good
+ 
+
+ align:start position:0%
+going to be the leaf spots. Okay, good
+news is most nodes are leaves, right?
+
+ align:start position:0%
+news is most nodes are leaves, right?
+ 
+
+ align:start position:0%
+news is most nodes are leaves, right?
+Constant fraction of the nodes are going
+
+ align:start position:0%
+Constant fraction of the nodes are going
+ 
+
+ align:start position:0%
+Constant fraction of the nodes are going
+to be leaves. So it doesn't change too
+
+ align:start position:0%
+to be leaves. So it doesn't change too
+ 
+
+ align:start position:0%
+to be leaves. So it doesn't change too
+much from an efficiency space efficiency
+
+ align:start position:0%
+much from an efficiency space efficiency
+ 
+
+ align:start position:0%
+much from an efficiency space efficiency
+standpoint if we just put data down here
+
+ align:start position:0%
+standpoint if we just put data down here
+ 
+
+ align:start position:0%
+standpoint if we just put data down here
+and don't put I'm not going to put any
+
+ align:start position:0%
+and don't put I'm not going to put any
+ 
+
+ align:start position:0%
+and don't put I'm not going to put any
+keys up here for now.
+
+ align:start position:0%
+keys up here for now.
+ 
+
+ align:start position:0%
+keys up here for now.
+Okay. Uh so this is a little weird.
+
+ align:start position:0%
+Okay. Uh so this is a little weird.
+ 
+
+ align:start position:0%
+Okay. Uh so this is a little weird.
+Let me draw an example of such a tree.
+
+ align:start position:0%
+Let me draw an example of such a tree.
+ 
+
+ align:start position:0%
+Let me draw an example of such a tree.
+So maybe we have two and five and seven
+
+ align:start position:0%
+So maybe we have two and five and seven
+ 
+
+ align:start position:0%
+So maybe we have two and five and seven
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+nine. Let's say uh
+
+ align:start position:0%
+nine. Let's say uh
+ 
+
+ align:start position:0%
+nine. Let's say uh
+let's put a one here. So I'm going to
+
+ align:start position:0%
+let's put a one here. So I'm going to
+ 
+
+ align:start position:0%
+let's put a one here. So I'm going to
+have a node here with three children, a
+
+ align:start position:0%
+have a node here with three children, a
+ 
+
+ align:start position:0%
+have a node here with three children, a
+node here with two children, and here's
+
+ align:start position:0%
+node here with two children, and here's
+ 
+
+ align:start position:0%
+node here with two children, and here's
+a node with two children. So I think
+
+ align:start position:0%
+a node with two children. So I think
+ 
+
+ align:start position:0%
+a node with two children. So I think
+this mimics this tree roughly. I got Oh
+
+ align:start position:0%
+this mimics this tree roughly. I got Oh
+ 
+
+ align:start position:0%
+this mimics this tree roughly. I got Oh
+no, I got it exactly right. So here I've
+
+ align:start position:0%
+no, I got it exactly right. So here I've
+ 
+
+ align:start position:0%
+no, I got it exactly right. So here I've
+taken this tree structure. I've redrawn
+
+ align:start position:0%
+taken this tree structure. I've redrawn
+ 
+
+ align:start position:0%
+taken this tree structure. I've redrawn
+it. There's now no keys in these nodes.
+
+ align:start position:0%
+it. There's now no keys in these nodes.
+ 
+
+ align:start position:0%
+it. There's now no keys in these nodes.
+But everything else is going to be the
+
+ align:start position:0%
+But everything else is going to be the
+ 
+
+ align:start position:0%
+But everything else is going to be the
+same. Every node is going to have zero
+
+ align:start position:0%
+same. Every node is going to have zero
+ 
+
+ align:start position:0%
+same. Every node is going to have zero
+children if it's a leaf or two or three
+
+ align:start position:0%
+children if it's a leaf or two or three
+ 
+
+ align:start position:0%
+children if it's a leaf or two or three
+children otherwise. Never have one child
+
+ align:start position:0%
+children otherwise. Never have one child
+ 
+
+ align:start position:0%
+children otherwise. Never have one child
+because then you wouldn't get
+
+ align:start position:0%
+because then you wouldn't get
+ 
+
+ align:start position:0%
+because then you wouldn't get
+logarithmic depth. All the leaves are
+
+ align:start position:0%
+logarithmic depth. All the leaves are
+ 
+
+ align:start position:0%
+logarithmic depth. All the leaves are
+going to be at the same depth.
+
+ align:start position:0%
+going to be at the same depth.
+ 
+
+ align:start position:0%
+going to be at the same depth.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+and that's it.
+
+ align:start position:0%
+and that's it.
+ 
+
+ align:start position:0%
+and that's it.
+Okay, that is uh 23 tree with the data
+
+ align:start position:0%
+Okay, that is uh 23 tree with the data
+ 
+
+ align:start position:0%
+Okay, that is uh 23 tree with the data
+stored in the leaves. It's a useful
+
+ align:start position:0%
+stored in the leaves. It's a useful
+ 
+
+ align:start position:0%
+stored in the leaves. It's a useful
+trick to know. Uh now we're going to do
+
+ align:start position:0%
+trick to know. Uh now we're going to do
+ 
+
+ align:start position:0%
+trick to know. Uh now we're going to do
+a level linked 23 tree. So in addition
+
+ align:start position:0%
+a level linked 23 tree. So in addition
+ 
+
+ align:start position:0%
+a level linked 23 tree. So in addition
+to that picture, we're going to have
+
+ align:start position:0%
+to that picture, we're going to have
+ 
+
+ align:start position:0%
+to that picture, we're going to have
+links like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And I should check that I can
+
+ align:start position:0%
+Okay. And I should check that I can
+ 
+
+ align:start position:0%
+Okay. And I should check that I can
+still do insert and delete into these
+
+ align:start position:0%
+still do insert and delete into these
+ 
+
+ align:start position:0%
+still do insert and delete into these
+structures. It's actually not too hard.
+
+ align:start position:0%
+structures. It's actually not too hard.
+ 
+
+ align:start position:0%
+structures. It's actually not too hard.
+Uh but let's think about it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh I think actually it might be easier.
+
+ align:start position:0%
+Uh I think actually it might be easier.
+ 
+
+ align:start position:0%
+Uh I think actually it might be easier.
+Let's let's see. Uh
+
+ align:start position:0%
+Let's let's see. Uh
+ 
+
+ align:start position:0%
+Let's let's see. Uh
+so if I want to do an insert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay I have to first search for where
+
+ align:start position:0%
+uh okay I have to first search for where
+ 
+
+ align:start position:0%
+uh okay I have to first search for where
+I'm inserting. Uh I haven't told you how
+
+ align:start position:0%
+I'm inserting. Uh I haven't told you how
+ 
+
+ align:start position:0%
+I'm inserting. Uh I haven't told you how
+to do search yet. Um okay so let's first
+
+ align:start position:0%
+to do search yet. Um okay so let's first
+ 
+
+ align:start position:0%
+to do search yet. Um okay so let's first
+think about search.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What we're going to do is
+
+ align:start position:0%
+What we're going to do is
+ 
+
+ align:start position:0%
+What we're going to do is
+uh data structure augmentation. we have
+
+ align:start position:0%
+uh data structure augmentation. we have
+ 
+
+ align:start position:0%
+uh data structure augmentation. we have
+simple tree augmentation. Um, so I'm
+
+ align:start position:0%
+simple tree augmentation. Um, so I'm
+ 
+
+ align:start position:0%
+simple tree augmentation. Um, so I'm
+going to do it and at each node what the
+
+ align:start position:0%
+going to do it and at each node what the
+ 
+
+ align:start position:0%
+going to do it and at each node what the
+functions I'm going to store are the
+
+ align:start position:0%
+functions I'm going to store are the
+ 
+
+ align:start position:0%
+functions I'm going to store are the
+minimum key in the subree and the
+
+ align:start position:0%
+minimum key in the subree and the
+ 
+
+ align:start position:0%
+minimum key in the subree and the
+maximum key in the subree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There are there are many ways to do this
+
+ align:start position:0%
+There are there are many ways to do this
+ 
+
+ align:start position:0%
+There are there are many ways to do this
+but uh here I think this is kind of the
+
+ align:start position:0%
+but uh here I think this is kind of the
+ 
+
+ align:start position:0%
+but uh here I think this is kind of the
+simplest.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what that means is at this node I'm
+
+ align:start position:0%
+So what that means is at this node I'm
+ 
+
+ align:start position:0%
+So what that means is at this node I'm
+going to store one as the min and seven
+
+ align:start position:0%
+going to store one as the min and seven
+ 
+
+ align:start position:0%
+going to store one as the min and seven
+as the max.
+
+ align:start position:0%
+as the max.
+ 
+
+ align:start position:0%
+as the max.
+Uh and at this node it's going to be one
+
+ align:start position:0%
+Uh and at this node it's going to be one
+ 
+
+ align:start position:0%
+Uh and at this node it's going to be one
+at the min and nine at the max. And here
+
+ align:start position:0%
+at the min and nine at the max. And here
+ 
+
+ align:start position:0%
+at the min and nine at the max. And here
+we have eight is the min and nine as the
+
+ align:start position:0%
+we have eight is the min and nine as the
+ 
+
+ align:start position:0%
+we have eight is the min and nine as the
+max. Again, min and max of sub trees are
+
+ align:start position:0%
+max. Again, min and max of sub trees are
+ 
+
+ align:start position:0%
+max. Again, min and max of sub trees are
+easy to store. If I ever change a node,
+
+ align:start position:0%
+easy to store. If I ever change a node,
+ 
+
+ align:start position:0%
+easy to store. If I ever change a node,
+I can update it uh based on its children
+
+ align:start position:0%
+I can update it uh based on its children
+ 
+
+ align:start position:0%
+I can update it uh based on its children
+just by looking at the min of the
+
+ align:start position:0%
+just by looking at the min of the
+ 
+
+ align:start position:0%
+just by looking at the min of the
+leftmost child and the max of the
+
+ align:start position:0%
+leftmost child and the max of the
+ 
+
+ align:start position:0%
+leftmost child and the max of the
+rightmost child. Right? If I had to if I
+
+ align:start position:0%
+rightmost child. Right? If I had to if I
+ 
+
+ align:start position:0%
+rightmost child. Right? If I had to if I
+didn't know one and nine, I could just
+
+ align:start position:0%
+didn't know one and nine, I could just
+ 
+
+ align:start position:0%
+didn't know one and nine, I could just
+look at this min and that max and that's
+
+ align:start position:0%
+look at this min and that max and that's
+ 
+
+ align:start position:0%
+look at this min and that max and that's
+going to be the min and the max of the
+
+ align:start position:0%
+going to be the min and the max of the
+ 
+
+ align:start position:0%
+going to be the min and the max of the
+overall tree. So in constant time I can
+
+ align:start position:0%
+overall tree. So in constant time I can
+ 
+
+ align:start position:0%
+overall tree. So in constant time I can
+update the min and the max of a node
+
+ align:start position:0%
+update the min and the max of a node
+ 
+
+ align:start position:0%
+update the min and the max of a node
+given the min and the max of its
+
+ align:start position:0%
+given the min and the max of its
+ 
+
+ align:start position:0%
+given the min and the max of its
+children. Uh special case is at the
+
+ align:start position:0%
+children. Uh special case is at the
+ 
+
+ align:start position:0%
+children. Uh special case is at the
+leaves. Then you have to actually look
+
+ align:start position:0%
+leaves. Then you have to actually look
+ 
+
+ align:start position:0%
+leaves. Then you have to actually look
+at keys and compare them. But leaves
+
+ align:start position:0%
+at keys and compare them. But leaves
+ 
+
+ align:start position:0%
+at keys and compare them. But leaves
+only have at most two keys. So pretty
+
+ align:start position:0%
+only have at most two keys. So pretty
+ 
+
+ align:start position:0%
+only have at most two keys. So pretty
+easy to compare them. Uh constant time.
+
+ align:start position:0%
+easy to compare them. Uh constant time.
+ 
+
+ align:start position:0%
+easy to compare them. Uh constant time.
+Okay. So that's how I do the
+
+ align:start position:0%
+Okay. So that's how I do the
+ 
+
+ align:start position:0%
+Okay. So that's how I do the
+augmentation. Now how do I do a search?
+
+ align:start position:0%
+augmentation. Now how do I do a search?
+ 
+
+ align:start position:0%
+augmentation. Now how do I do a search?
+Well, if I'm at a node and I'm searching
+
+ align:start position:0%
+Well, if I'm at a node and I'm searching
+ 
+
+ align:start position:0%
+Well, if I'm at a node and I'm searching
+for a key uh well let's say I'm at this
+
+ align:start position:0%
+for a key uh well let's say I'm at this
+ 
+
+ align:start position:0%
+for a key uh well let's say I'm at this
+node. I'm searching for a key like uh
+
+ align:start position:0%
+node. I'm searching for a key like uh
+ 
+
+ align:start position:0%
+node. I'm searching for a key like uh
+eight. What I'm going to do is look at
+
+ align:start position:0%
+eight. What I'm going to do is look at
+ 
+
+ align:start position:0%
+eight. What I'm going to do is look at
+all of the children. In this case,
+
+ align:start position:0%
+all of the children. In this case,
+ 
+
+ align:start position:0%
+all of the children. In this case,
+there's two. In the worst case, there's
+
+ align:start position:0%
+there's two. In the worst case, there's
+ 
+
+ align:start position:0%
+there's two. In the worst case, there's
+three. I look at the min and max and I
+
+ align:start position:0%
+three. I look at the min and max and I
+ 
+
+ align:start position:0%
+three. I look at the min and max and I
+see where does eight fall. Well, it
+
+ align:start position:0%
+see where does eight fall. Well, it
+ 
+
+ align:start position:0%
+see where does eight fall. Well, it
+falls in this interval. If I was
+
+ align:start position:0%
+falls in this interval. If I was
+ 
+
+ align:start position:0%
+falls in this interval. If I was
+searching for seven and a half, I'd know
+
+ align:start position:0%
+searching for seven and a half, I'd know
+ 
+
+ align:start position:0%
+searching for seven and a half, I'd know
+it's not there. It's somewhere. It's
+
+ align:start position:0%
+it's not there. It's somewhere. It's
+ 
+
+ align:start position:0%
+it's not there. It's somewhere. It's
+going to be in between here. If I'm
+
+ align:start position:0%
+going to be in between here. If I'm
+ 
+
+ align:start position:0%
+going to be in between here. If I'm
+doing successor, uh then uh I'll go to
+
+ align:start position:0%
+doing successor, uh then uh I'll go to
+ 
+
+ align:start position:0%
+doing successor, uh then uh I'll go to
+the right. If I'm doing predecessor,
+
+ align:start position:0%
+the right. If I'm doing predecessor,
+ 
+
+ align:start position:0%
+the right. If I'm doing predecessor,
+I'll go to the left and then take the
+
+ align:start position:0%
+I'll go to the left and then take the
+ 
+
+ align:start position:0%
+I'll go to the left and then take the
+either the maximum item or the minimum
+
+ align:start position:0%
+either the maximum item or the minimum
+ 
+
+ align:start position:0%
+either the maximum item or the minimum
+item. If I'm searching for eight, I see,
+
+ align:start position:0%
+item. If I'm searching for eight, I see,
+ 
+
+ align:start position:0%
+item. If I'm searching for eight, I see,
+oh, eight falls in the interval between
+
+ align:start position:0%
+oh, eight falls in the interval between
+ 
+
+ align:start position:0%
+oh, eight falls in the interval between
+eight and nine. So, I should clearly
+
+ align:start position:0%
+eight and nine. So, I should clearly
+ 
+
+ align:start position:0%
+eight and nine. So, I should clearly
+take the right child among those two
+
+ align:start position:0%
+take the right child among those two
+ 
+
+ align:start position:0%
+take the right child among those two
+children. In general, there's three
+
+ align:start position:0%
+children. In general, there's three
+ 
+
+ align:start position:0%
+children. In general, there's three
+children, three intervals, constant
+
+ align:start position:0%
+children, three intervals, constant
+ 
+
+ align:start position:0%
+children, three intervals, constant
+time. I can find where my key falls in
+
+ align:start position:0%
+time. I can find where my key falls in
+ 
+
+ align:start position:0%
+time. I can find where my key falls in
+the interval. Okay, so search is going
+
+ align:start position:0%
+the interval. Okay, so search is going
+ 
+
+ align:start position:0%
+the interval. Okay, so search is going
+to take login time again, provided I
+
+ align:start position:0%
+to take login time again, provided I
+ 
+
+ align:start position:0%
+to take login time again, provided I
+have these mins and maxes.
+
+ align:start position:0%
+have these mins and maxes.
+ 
+
+ align:start position:0%
+have these mins and maxes.
+Okay, so it's it's you think stare at it
+
+ align:start position:0%
+Okay, so it's it's you think stare at it
+ 
+
+ align:start position:0%
+Okay, so it's it's you think stare at it
+long enough, this is pretty much the
+
+ align:start position:0%
+long enough, this is pretty much the
+ 
+
+ align:start position:0%
+long enough, this is pretty much the
+same thing as regular search in a 23
+
+ align:start position:0%
+same thing as regular search in a 23
+ 
+
+ align:start position:0%
+same thing as regular search in a 23
+tree. Uh but I've put the data just one
+
+ align:start position:0%
+tree. Uh but I've put the data just one
+ 
+
+ align:start position:0%
+tree. Uh but I've put the data just one
+level down.
+
+ align:start position:0%
+level down.
+ 
+
+ align:start position:0%
+level down.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good. That was regular search. Uh I
+
+ align:start position:0%
+good. That was regular search. Uh I
+ 
+
+ align:start position:0%
+good. That was regular search. Uh I
+still need to do finger search, but
+
+ align:start position:0%
+still need to do finger search, but
+ 
+
+ align:start position:0%
+still need to do finger search, but
+we'll get there. Uh now, if I want to do
+
+ align:start position:0%
+we'll get there. Uh now, if I want to do
+ 
+
+ align:start position:0%
+we'll get there. Uh now, if I want to do
+an insert into this data structure,
+
+ align:start position:0%
+an insert into this data structure,
+ 
+
+ align:start position:0%
+an insert into this data structure,
+uh what happens? Well, I search for the
+
+ align:start position:0%
+uh what happens? Well, I search for the
+ 
+
+ align:start position:0%
+uh what happens? Well, I search for the
+key. Let's say I'm inserting six. Uh so
+
+ align:start position:0%
+key. Let's say I'm inserting six. Uh so
+ 
+
+ align:start position:0%
+key. Let's say I'm inserting six. Uh so
+maybe I go here. I say oh six because
+
+ align:start position:0%
+maybe I go here. I say oh six because
+ 
+
+ align:start position:0%
+maybe I go here. I say oh six because
+six is in this interval. Uh six is in
+
+ align:start position:0%
+six is in this interval. Uh six is in
+ 
+
+ align:start position:0%
+six is in this interval. Uh six is in
+neither of these intervals. So uh but
+
+ align:start position:0%
+neither of these intervals. So uh but
+ 
+
+ align:start position:0%
+neither of these intervals. So uh but
+it's closest to the interval 25 or the
+
+ align:start position:0%
+it's closest to the interval 25 or the
+ 
+
+ align:start position:0%
+it's closest to the interval 25 or the
+interval 7. Let's say I go down to 25.
+
+ align:start position:0%
+interval 7. Let's say I go down to 25.
+ 
+
+ align:start position:0%
+interval 7. Let's say I go down to 25.
+And well to insert six I'll just add a
+
+ align:start position:0%
+And well to insert six I'll just add a
+ 
+
+ align:start position:0%
+And well to insert six I'll just add a
+six on there. Of course now that note is
+
+ align:start position:0%
+six on there. Of course now that note is
+ 
+
+ align:start position:0%
+six on there. Of course now that note is
+too big. So there's still going to be a
+
+ align:start position:0%
+too big. So there's still going to be a
+ 
+
+ align:start position:0%
+too big. So there's still going to be a
+split case at the leaves where I have uh
+
+ align:start position:0%
+split case at the leaves where I have uh
+ 
+
+ align:start position:0%
+split case at the leaves where I have uh
+let's say A B C too many keys.
+
+ align:start position:0%
+let's say A B C too many keys.
+ 
+
+ align:start position:0%
+let's say A B C too many keys.
+I'm going to split that into
+
+ align:start position:0%
+I'm going to split that into
+ 
+
+ align:start position:0%
+I'm going to split that into
+AB
+
+ align:start position:0%
+AB
+ 
+
+ align:start position:0%
+AB
+and C. This is different from before. It
+
+ align:start position:0%
+and C. This is different from before. It
+ 
+
+ align:start position:0%
+and C. This is different from before. It
+used to be I would promote B to the
+
+ align:start position:0%
+used to be I would promote B to the
+ 
+
+ align:start position:0%
+used to be I would promote B to the
+parent because the parent needed a key
+
+ align:start position:0%
+parent because the parent needed a key
+ 
+
+ align:start position:0%
+parent because the parent needed a key
+there. Now parents don't have keys. So
+
+ align:start position:0%
+there. Now parents don't have keys. So
+ 
+
+ align:start position:0%
+there. Now parents don't have keys. So
+I'm just going to split this thing
+
+ align:start position:0%
+I'm just going to split this thing
+ 
+
+ align:start position:0%
+I'm just going to split this thing
+roughly in half.
+
+ align:start position:0%
+roughly in half.
+ 
+
+ align:start position:0%
+roughly in half.
+It works. Uh it's still the case that
+
+ align:start position:0%
+It works. Uh it's still the case that
+ 
+
+ align:start position:0%
+It works. Uh it's still the case that
+whoever was the parent up here now has
+
+ align:start position:0%
+whoever was the parent up here now has
+ 
+
+ align:start position:0%
+whoever was the parent up here now has
+an additional child. One more child. So
+
+ align:start position:0%
+an additional child. One more child. So
+ 
+
+ align:start position:0%
+an additional child. One more child. So
+maybe that node now has four children,
+
+ align:start position:0%
+maybe that node now has four children,
+ 
+
+ align:start position:0%
+maybe that node now has four children,
+but it's supposed to be two or three. So
+
+ align:start position:0%
+but it's supposed to be two or three. So
+ 
+
+ align:start position:0%
+but it's supposed to be two or three. So
+if I have a node with four children,
+
+ align:start position:0%
+if I have a node with four children,
+ 
+
+ align:start position:0%
+if I have a node with four children,
+what I'm going to do supposed to use
+
+ align:start position:0%
+what I'm going to do supposed to use
+ 
+
+ align:start position:0%
+what I'm going to do supposed to use
+these fancy arrows. Uh what do I do in
+
+ align:start position:0%
+these fancy arrows. Uh what do I do in
+ 
+
+ align:start position:0%
+these fancy arrows. Uh what do I do in
+this case? I'm just going to split that
+
+ align:start position:0%
+this case? I'm just going to split that
+ 
+
+ align:start position:0%
+this case? I'm just going to split that
+into two nodes with two children. Okay.
+
+ align:start position:0%
+into two nodes with two children. Okay.
+ 
+
+ align:start position:0%
+into two nodes with two children. Okay.
+And again, this used to have a parent.
+
+ align:start position:0%
+And again, this used to have a parent.
+ 
+
+ align:start position:0%
+And again, this used to have a parent.
+Now that parent has an additional child,
+
+ align:start position:0%
+Now that parent has an additional child,
+ 
+
+ align:start position:0%
+Now that parent has an additional child,
+and that may cause another split. It's
+
+ align:start position:0%
+and that may cause another split. It's
+ 
+
+ align:start position:0%
+and that may cause another split. It's
+just like before. We'll just potentially
+
+ align:start position:0%
+just like before. We'll just potentially
+ 
+
+ align:start position:0%
+just like before. We'll just potentially
+split all the way up to the root.
+
+ align:start position:0%
+split all the way up to the root.
+ 
+
+ align:start position:0%
+split all the way up to the root.
+If we split the root, then we get an
+
+ align:start position:0%
+If we split the root, then we get an
+ 
+
+ align:start position:0%
+If we split the root, then we get an
+additional level. But uh we can do all
+
+ align:start position:0%
+additional level. But uh we can do all
+ 
+
+ align:start position:0%
+additional level. But uh we can do all
+this and we can still maintain our uh
+
+ align:start position:0%
+this and we can still maintain our uh
+ 
+
+ align:start position:0%
+this and we can still maintain our uh
+level links if we want,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but everything will take login. I won't
+
+ align:start position:0%
+but everything will take login. I won't
+ 
+
+ align:start position:0%
+but everything will take login. I won't
+draw the delete case. It's uh delete is
+
+ align:start position:0%
+draw the delete case. It's uh delete is
+ 
+
+ align:start position:0%
+draw the delete case. It's uh delete is
+slightly more annoying, but I think in
+
+ align:start position:0%
+slightly more annoying, but I think in
+ 
+
+ align:start position:0%
+slightly more annoying, but I think in
+this case, you never have to worry about
+
+ align:start position:0%
+this case, you never have to worry about
+ 
+
+ align:start position:0%
+this case, you never have to worry about
+where's the key coming from. from your
+
+ align:start position:0%
+where's the key coming from. from your
+ 
+
+ align:start position:0%
+where's the key coming from. from your
+child or your your parent. You're just
+
+ align:start position:0%
+child or your your parent. You're just
+ 
+
+ align:start position:0%
+child or your your parent. You're just
+uh you're just merging nodes. So it's a
+
+ align:start position:0%
+uh you're just merging nodes. So it's a
+ 
+
+ align:start position:0%
+uh you're just merging nodes. So it's a
+little bit simpler, but you have to deal
+
+ align:start position:0%
+little bit simpler, but you have to deal
+ 
+
+ align:start position:0%
+little bit simpler, but you have to deal
+with the leaf case separately from the
+
+ align:start position:0%
+with the leaf case separately from the
+ 
+
+ align:start position:0%
+with the leaf case separately from the
+non-leaf case. Okay. So all this was to
+
+ align:start position:0%
+non-leaf case. Okay. So all this was to
+ 
+
+ align:start position:0%
+non-leaf case. Okay. So all this was to
+convince you that we can store data in
+
+ align:start position:0%
+convince you that we can store data in
+ 
+
+ align:start position:0%
+convince you that we can store data in
+the leaves. Two three trees still work
+
+ align:start position:0%
+the leaves. Two three trees still work
+ 
+
+ align:start position:0%
+the leaves. Two three trees still work
+fine.
+
+ align:start position:0%
+fine.
+ 
+
+ align:start position:0%
+fine.
+Now I claim that the graph distance in
+
+ align:start position:0%
+Now I claim that the graph distance in
+ 
+
+ align:start position:0%
+Now I claim that the graph distance in
+level link trees is within a constant
+
+ align:start position:0%
+level link trees is within a constant
+ 
+
+ align:start position:0%
+level link trees is within a constant
+factor of the finger search bound. So I
+
+ align:start position:0%
+factor of the finger search bound. So I
+ 
+
+ align:start position:0%
+factor of the finger search bound. So I
+claim I can get the finger search
+
+ align:start position:0%
+claim I can get the finger search
+ 
+
+ align:start position:0%
+claim I can get the finger search
+property in two three trees with data in
+
+ align:start position:0%
+property in two three trees with data in
+ 
+
+ align:start position:0%
+property in two three trees with data in
+the leaves with level links. Okay. So
+
+ align:start position:0%
+the leaves with level links. Okay. So
+ 
+
+ align:start position:0%
+the leaves with level links. Okay. So
+lots of changes here but in the end
+
+ align:start position:0%
+lots of changes here but in the end
+ 
+
+ align:start position:0%
+lots of changes here but in the end
+we're going to get a finger search
+
+ align:start position:0%
+we're going to get a finger search
+ 
+
+ align:start position:0%
+we're going to get a finger search
+bound.
+
+ align:start position:0%
+bound.
+ 
+
+ align:start position:0%
+bound.
+Let's go here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, here's a finger search operation. Uh
+
+ align:start position:0%
+So, here's a finger search operation. Uh
+ 
+
+ align:start position:0%
+So, here's a finger search operation. Uh
+first thing I want to do is identify uh
+
+ align:start position:0%
+first thing I want to do is identify uh
+ 
+
+ align:start position:0%
+first thing I want to do is identify uh
+a node that I'm working with. I want to
+
+ align:start position:0%
+a node that I'm working with. I want to
+ 
+
+ align:start position:0%
+a node that I'm working with. I want to
+start from y's node. And we're so we're
+
+ align:start position:0%
+start from y's node. And we're so we're
+ 
+
+ align:start position:0%
+start from y's node. And we're so we're
+supposing that we're told the node a
+
+ align:start position:0%
+supposing that we're told the node a
+ 
+
+ align:start position:0%
+supposing that we're told the node a
+leaf uh that contains y. So I'm going to
+
+ align:start position:0%
+leaf uh that contains y. So I'm going to
+ 
+
+ align:start position:0%
+leaf uh that contains y. So I'm going to
+let uh v be that leaf.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? because we're supposing we've
+
+ align:start position:0%
+Okay? because we're supposing we've
+ 
+
+ align:start position:0%
+Okay? because we're supposing we've
+already found y and now all the data is
+
+ align:start position:0%
+already found y and now all the data is
+ 
+
+ align:start position:0%
+already found y and now all the data is
+in the leaf. So give me the leaf that
+
+ align:start position:0%
+in the leaf. So give me the leaf that
+ 
+
+ align:start position:0%
+in the leaf. So give me the leaf that
+contains y.
+
+ align:start position:0%
+contains y.
+ 
+
+ align:start position:0%
+contains y.
+So that should take constant time.
+
+ align:start position:0%
+So that should take constant time.
+ 
+
+ align:start position:0%
+So that should take constant time.
+That's just part of the input.
+
+ align:start position:0%
+That's just part of the input.
+ 
+
+ align:start position:0%
+That's just part of the input.
+Now I'm going to do a combination of
+
+ align:start position:0%
+Now I'm going to do a combination of
+ 
+
+ align:start position:0%
+Now I'm going to do a combination of
+going up and horizontal.
+
+ align:start position:0%
+going up and horizontal.
+ 
+
+ align:start position:0%
+going up and horizontal.
+So I'm starting at a leaf
+
+ align:start position:0%
+So I'm starting at a leaf
+ 
+
+ align:start position:0%
+So I'm starting at a leaf
+and uh the first thing I'm going to do
+
+ align:start position:0%
+and uh the first thing I'm going to do
+ 
+
+ align:start position:0%
+and uh the first thing I'm going to do
+is check does this
+
+ align:start position:0%
+is check does this
+ 
+
+ align:start position:0%
+is check does this
+leaf contain what I want. Does it
+
+ align:start position:0%
+leaf contain what I want. Does it
+ 
+
+ align:start position:0%
+leaf contain what I want. Does it
+contain the key I'm searching for which
+
+ align:start position:0%
+contain the key I'm searching for which
+ 
+
+ align:start position:0%
+contain the key I'm searching for which
+is x. So that's going to be the case at
+
+ align:start position:0%
+is x. So that's going to be the case at
+ 
+
+ align:start position:0%
+is x. So that's going to be the case at
+every node I store the min and the max.
+
+ align:start position:0%
+every node I store the min and the max.
+ 
+
+ align:start position:0%
+every node I store the min and the max.
+So if x happens to fall between the min
+
+ align:start position:0%
+So if x happens to fall between the min
+ 
+
+ align:start position:0%
+So if x happens to fall between the min
+and the max then I'm happy.
+
+ align:start position:0%
+and the max then I'm happy.
+ 
+
+ align:start position:0%
+and the max then I'm happy.
+Then I'm going to do uh a regular search
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in these subree.
+
+ align:start position:0%
+uh in these subree.
+ 
+
+ align:start position:0%
+uh in these subree.
+Okay, this seems weird in the case of a
+
+ align:start position:0%
+Okay, this seems weird in the case of a
+ 
+
+ align:start position:0%
+Okay, this seems weird in the case of a
+leaf. In the case of a leaf, this is
+
+ align:start position:0%
+leaf. In the case of a leaf, this is
+ 
+
+ align:start position:0%
+leaf. In the case of a leaf, this is
+just check the two keys that are there
+
+ align:start position:0%
+just check the two keys that are there
+ 
+
+ align:start position:0%
+just check the two keys that are there
+whe which one is x. Okay. But in
+
+ align:start position:0%
+whe which one is x. Okay. But in
+ 
+
+ align:start position:0%
+whe which one is x. Okay. But in
+general, uh I gave you this search
+
+ align:start position:0%
+general, uh I gave you this search
+ 
+
+ align:start position:0%
+general, uh I gave you this search
+algorithm which was uh if uh I decide
+
+ align:start position:0%
+algorithm which was uh if uh I decide
+ 
+
+ align:start position:0%
+algorithm which was uh if uh I decide
+which child to take according to the
+
+ align:start position:0%
+which child to take according to the
+ 
+
+ align:start position:0%
+which child to take according to the
+ranges, that's a downward search. So
+
+ align:start position:0%
+ranges, that's a downward search. So
+ 
+
+ align:start position:0%
+ranges, that's a downward search. So
+that's what I'm calling regular search
+
+ align:start position:0%
+that's what I'm calling regular search
+ 
+
+ align:start position:0%
+that's what I'm calling regular search
+here. Maybe downward would be a little
+
+ align:start position:0%
+here. Maybe downward would be a little
+ 
+
+ align:start position:0%
+here. Maybe downward would be a little
+better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is the usual login time thing. Uh
+
+ align:start position:0%
+This is the usual login time thing. Uh
+ 
+
+ align:start position:0%
+This is the usual login time thing. Uh
+but we're going to claim a bet a bound
+
+ align:start position:0%
+but we're going to claim a bet a bound
+ 
+
+ align:start position:0%
+but we're going to claim a bet a bound
+better than login. If this is not the
+
+ align:start position:0%
+better than login. If this is not the
+ 
+
+ align:start position:0%
+better than login. If this is not the
+case, then I know X either falls before
+
+ align:start position:0%
+case, then I know X either falls before
+ 
+
+ align:start position:0%
+case, then I know X either falls before
+V do min or after V domax.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if X is less than V dot min,
+
+ align:start position:0%
+So if X is less than V dot min,
+ 
+
+ align:start position:0%
+So if X is less than V dot min,
+then I'm going to uh go left. V equals V
+
+ align:start position:0%
+then I'm going to uh go left. V equals V
+ 
+
+ align:start position:0%
+then I'm going to uh go left. V equals V
+dot uh I'll call it level left to be
+
+ align:start position:0%
+dot uh I'll call it level left to be
+ 
+
+ align:start position:0%
+dot uh I'll call it level left to be
+clear.
+
+ align:start position:0%
+clear.
+ 
+
+ align:start position:0%
+clear.
+You might say left is the left child,
+
+ align:start position:0%
+You might say left is the left child,
+ 
+
+ align:start position:0%
+You might say left is the left child,
+but there's no left child here, of
+
+ align:start position:0%
+but there's no left child here, of
+ 
+
+ align:start position:0%
+but there's no left child here, of
+course, but level left is clear. we take
+
+ align:start position:0%
+course, but level left is clear. we take
+ 
+
+ align:start position:0%
+course, but level left is clear. we take
+the horizontal left pointer uh and
+
+ align:start position:0%
+the horizontal left pointer uh and
+ 
+
+ align:start position:0%
+the horizontal left pointer uh and
+otherwise uh x is greater than v domax
+
+ align:start position:0%
+otherwise uh x is greater than v domax
+ 
+
+ align:start position:0%
+otherwise uh x is greater than v domax
+and in that case uh we'll go right that
+
+ align:start position:0%
+and in that case uh we'll go right that
+ 
+
+ align:start position:0%
+and in that case uh we'll go right that
+seems logical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in both cases we're going to uh go
+
+ align:start position:0%
+and in both cases we're going to uh go
+ 
+
+ align:start position:0%
+and in both cases we're going to uh go
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+x= x dot parent oops v= parent
+
+ align:start position:0%
+x= x dot parent oops v= parent
+ 
+
+ align:start position:0%
+x= x dot parent oops v= parent
+X is not changing here. X is a key we're
+
+ align:start position:0%
+X is not changing here. X is a key we're
+ 
+
+ align:start position:0%
+X is not changing here. X is a key we're
+searching for. V is the node. V for
+
+ align:start position:0%
+searching for. V is the node. V for
+ 
+
+ align:start position:0%
+searching for. V is the node. V for
+vertex.
+
+ align:start position:0%
+vertex.
+ 
+
+ align:start position:0%
+vertex.
+So we're always going to go up and then
+
+ align:start position:0%
+So we're always going to go up and then
+ 
+
+ align:start position:0%
+So we're always going to go up and then
+we're going to go either left or right.
+
+ align:start position:0%
+we're going to go either left or right.
+ 
+
+ align:start position:0%
+we're going to go either left or right.
+And we're going to keep doing that until
+
+ align:start position:0%
+And we're going to keep doing that until
+ 
+
+ align:start position:0%
+And we're going to keep doing that until
+we find a sub tree that contains X in
+
+ align:start position:0%
+we find a sub tree that contains X in
+ 
+
+ align:start position:0%
+we find a sub tree that contains X in
+terms of key range. Then we're going to
+
+ align:start position:0%
+terms of key range. Then we're going to
+ 
+
+ align:start position:0%
+terms of key range. Then we're going to
+stop this part and we're just going to
+
+ align:start position:0%
+stop this part and we're just going to
+ 
+
+ align:start position:0%
+stop this part and we're just going to
+do downward search. I should say uh
+
+ align:start position:0%
+do downward search. I should say uh
+ 
+
+ align:start position:0%
+do downward search. I should say uh
+return here or something.
+
+ align:start position:0%
+return here or something.
+ 
+
+ align:start position:0%
+return here or something.
+uh I'm going to do a downward search
+
+ align:start position:0%
+uh I'm going to do a downward search
+ 
+
+ align:start position:0%
+uh I'm going to do a downward search
+which was this regular algorithm and
+
+ align:start position:0%
+which was this regular algorithm and
+ 
+
+ align:start position:0%
+which was this regular algorithm and
+then whatever it finds that's what I
+
+ align:start position:0%
+then whatever it finds that's what I
+ 
+
+ align:start position:0%
+then whatever it finds that's what I
+return.
+
+ align:start position:0%
+return.
+ 
+
+ align:start position:0%
+return.
+Okay, I claim the algorithm should be
+
+ align:start position:0%
+Okay, I claim the algorithm should be
+ 
+
+ align:start position:0%
+Okay, I claim the algorithm should be
+clear. What's less clear is that it
+
+ align:start position:0%
+clear. What's less clear is that it
+ 
+
+ align:start position:0%
+clear. What's less clear is that it
+achieves the bound that we want. But I
+
+ align:start position:0%
+achieves the bound that we want. But I
+ 
+
+ align:start position:0%
+achieves the bound that we want. But I
+claim this will achieve the finger
+
+ align:start position:0%
+claim this will achieve the finger
+ 
+
+ align:start position:0%
+claim this will achieve the finger
+search property.
+
+ align:start position:0%
+search property.
+ 
+
+ align:start position:0%
+search property.
+Uh let me draw a picture of what this
+
+ align:start position:0%
+Uh let me draw a picture of what this
+ 
+
+ align:start position:0%
+Uh let me draw a picture of what this
+thing looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind of generically.
+
+ align:start position:0%
+kind of generically.
+ 
+
+ align:start position:0%
+kind of generically.
+on small examples, it's hard to see
+
+ align:start position:0%
+on small examples, it's hard to see
+ 
+
+ align:start position:0%
+on small examples, it's hard to see
+what's going on. So, I'm going to draw a
+
+ align:start position:0%
+what's going on. So, I'm going to draw a
+ 
+
+ align:start position:0%
+what's going on. So, I'm going to draw a
+piece of a large example.
+
+ align:start position:0%
+piece of a large example.
+ 
+
+ align:start position:0%
+piece of a large example.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+uh let's say we start here. This is
+
+ align:start position:0%
+uh let's say we start here. This is
+ 
+
+ align:start position:0%
+uh let's say we start here. This is
+where Y was. I'm searching for X. Let's
+
+ align:start position:0%
+where Y was. I'm searching for X. Let's
+ 
+
+ align:start position:0%
+where Y was. I'm searching for X. Let's
+suppose X is to the right just because
+
+ align:start position:0%
+suppose X is to the right just because
+ 
+
+ align:start position:0%
+suppose X is to the right just because
+otherwise I go to the other board. Um so
+
+ align:start position:0%
+otherwise I go to the other board. Um so
+ 
+
+ align:start position:0%
+otherwise I go to the other board. Um so
+X is to the right. I'll discover that
+
+ align:start position:0%
+X is to the right. I'll discover that
+ 
+
+ align:start position:0%
+X is to the right. I'll discover that
+the range, you know, with just this
+
+ align:start position:0%
+the range, you know, with just this
+ 
+
+ align:start position:0%
+the range, you know, with just this
+node, this node maybe contains one other
+
+ align:start position:0%
+node, this node maybe contains one other
+ 
+
+ align:start position:0%
+node, this node maybe contains one other
+key. I'll find that range is too uh
+
+ align:start position:0%
+key. I'll find that range is too uh
+ 
+
+ align:start position:0%
+key. I'll find that range is too uh
+small. So I'm going to go follow the
+
+ align:start position:0%
+small. So I'm going to go follow the
+ 
+
+ align:start position:0%
+small. So I'm going to go follow the
+level right pointer and I get to some
+
+ align:start position:0%
+level right pointer and I get to some
+ 
+
+ align:start position:0%
+level right pointer and I get to some
+other node. Then I'm going to go to the
+
+ align:start position:0%
+other node. Then I'm going to go to the
+ 
+
+ align:start position:0%
+other node. Then I'm going to go to the
+parent. Maybe the parent was the parent
+
+ align:start position:0%
+parent. Maybe the parent was the parent
+ 
+
+ align:start position:0%
+parent. Maybe the parent was the parent
+of those two ch children. So I'm going
+
+ align:start position:0%
+of those two ch children. So I'm going
+ 
+
+ align:start position:0%
+of those two ch children. So I'm going
+to draw it like that. Um maybe I find
+
+ align:start position:0%
+to draw it like that. Um maybe I find
+ 
+
+ align:start position:0%
+to draw it like that. Um maybe I find
+this range is still too too low. I need
+
+ align:start position:0%
+this range is still too too low. I need
+ 
+
+ align:start position:0%
+this range is still too too low. I need
+to go right to get to X. So I'm going to
+
+ align:start position:0%
+to go right to get to X. So I'm going to
+ 
+
+ align:start position:0%
+to go right to get to X. So I'm going to
+follow a level pointer to the right. Uh
+
+ align:start position:0%
+follow a level pointer to the right. Uh
+ 
+
+ align:start position:0%
+follow a level pointer to the right. Uh
+I find a new subree. U I'll go to its
+
+ align:start position:0%
+I find a new subree. U I'll go to its
+ 
+
+ align:start position:0%
+I find a new subree. U I'll go to its
+parent. uh maybe I find that this subree
+
+ align:start position:0%
+parent. uh maybe I find that this subree
+ 
+
+ align:start position:0%
+parent. uh maybe I find that this subree
+still the max is too small so I have to
+
+ align:start position:0%
+still the max is too small so I have to
+ 
+
+ align:start position:0%
+still the max is too small so I have to
+go to the right again and then I take
+
+ align:start position:0%
+go to the right again and then I take
+ 
+
+ align:start position:0%
+go to the right again and then I take
+the parent uh so this was an example of
+
+ align:start position:0%
+the parent uh so this was an example of
+ 
+
+ align:start position:0%
+the parent uh so this was an example of
+a rightward parent here's an example of
+
+ align:start position:0%
+a rightward parent here's an example of
+ 
+
+ align:start position:0%
+a rightward parent here's an example of
+a leftward parent this is maybe the
+
+ align:start position:0%
+a leftward parent this is maybe the
+ 
+
+ align:start position:0%
+a leftward parent this is maybe the
+parent of both of these two children uh
+
+ align:start position:0%
+parent of both of these two children uh
+ 
+
+ align:start position:0%
+parent of both of these two children uh
+then maybe this subree is still too
+
+ align:start position:0%
+then maybe this subree is still too
+ 
+
+ align:start position:0%
+then maybe this subree is still too
+small the max is still smaller than x so
+
+ align:start position:0%
+small the max is still smaller than x so
+ 
+
+ align:start position:0%
+small the max is still smaller than x so
+then I go right one more time
+
+ align:start position:0%
+then I go right one more time
+ 
+
+ align:start position:0%
+then I go right one more time
+uh then I follow the parent always
+
+ align:start position:0%
+uh then I follow the parent always
+ 
+
+ align:start position:0%
+uh then I follow the parent always
+alternating between right and parent
+
+ align:start position:0%
+alternating between right and parent
+ 
+
+ align:start position:0%
+alternating between right and parent
+until I find a node whose subree
+
+ align:start position:0%
+until I find a node whose subree
+ 
+
+ align:start position:0%
+until I find a node whose subree
+contains X. It might have actually X may
+
+ align:start position:0%
+contains X. It might have actually X may
+ 
+
+ align:start position:0%
+contains X. It might have actually X may
+be down here because I immediately went
+
+ align:start position:0%
+be down here because I immediately went
+ 
+
+ align:start position:0%
+be down here because I immediately went
+to the parent without checking whether I
+
+ align:start position:0%
+to the parent without checking whether I
+ 
+
+ align:start position:0%
+to the parent without checking whether I
+found where X is. But if I know that X
+
+ align:start position:0%
+found where X is. But if I know that X
+ 
+
+ align:start position:0%
+found where X is. But if I know that X
+is somewhere in here, then I will do a
+
+ align:start position:0%
+is somewhere in here, then I will do a
+ 
+
+ align:start position:0%
+is somewhere in here, then I will do a
+downward search. Uh it might go left and
+
+ align:start position:0%
+downward search. Uh it might go left and
+ 
+
+ align:start position:0%
+downward search. Uh it might go left and
+then down here or it might go right or
+
+ align:start position:0%
+then down here or it might go right or
+ 
+
+ align:start position:0%
+then down here or it might go right or
+there's actually plus potentially three
+
+ align:start position:0%
+there's actually plus potentially three
+ 
+
+ align:start position:0%
+there's actually plus potentially three
+children. one of these searches will
+
+ align:start position:0%
+children. one of these searches will
+ 
+
+ align:start position:0%
+children. one of these searches will
+find the key X that I'm looking for
+
+ align:start position:0%
+find the key X that I'm looking for
+ 
+
+ align:start position:0%
+find the key X that I'm looking for
+because uh I'm in the case where X is
+
+ align:start position:0%
+because uh I'm in the case where X is
+ 
+
+ align:start position:0%
+because uh I'm in the case where X is
+between V domin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X doesn't exist but it's uh predecessor
+
+ align:start position:0%
+X doesn't exist but it's uh predecessor
+ 
+
+ align:start position:0%
+X doesn't exist but it's uh predecessor
+or successor is in there somewhere. uh
+
+ align:start position:0%
+or successor is in there somewhere. uh
+ 
+
+ align:start position:0%
+or successor is in there somewhere. uh
+and so one of these three sub trees will
+
+ align:start position:0%
+and so one of these three sub trees will
+ 
+
+ align:start position:0%
+and so one of these three sub trees will
+contain the x range and then I go follow
+
+ align:start position:0%
+contain the x range and then I go follow
+ 
+
+ align:start position:0%
+contain the x range and then I go follow
+that path and keep going down uh until I
+
+ align:start position:0%
+that path and keep going down uh until I
+ 
+
+ align:start position:0%
+that path and keep going down uh until I
+find x or its predecessor or successor.
+
+ align:start position:0%
+find x or its predecessor or successor.
+ 
+
+ align:start position:0%
+find x or its predecessor or successor.
+Once I find its predecessor, I can use a
+
+ align:start position:0%
+Once I find its predecessor, I can use a
+ 
+
+ align:start position:0%
+Once I find its predecessor, I can use a
+level right pointer to find its
+
+ align:start position:0%
+level right pointer to find its
+ 
+
+ align:start position:0%
+level right pointer to find its
+successor and so on.
+
+ align:start position:0%
+successor and so on.
+ 
+
+ align:start position:0%
+successor and so on.
+So that's kind of the general picture of
+
+ align:start position:0%
+So that's kind of the general picture of
+ 
+
+ align:start position:0%
+So that's kind of the general picture of
+what's going on. We keep going rightward
+
+ align:start position:0%
+what's going on. We keep going rightward
+ 
+
+ align:start position:0%
+what's going on. We keep going rightward
+and we keep going up. Now
+
+ align:start position:0%
+and we keep going up. Now
+ 
+
+ align:start position:0%
+and we keep going up. Now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+suppose we do k up steps.
+
+ align:start position:0%
+suppose we do k up steps.
+ 
+
+ align:start position:0%
+suppose we do k up steps.
+Let's look at this uh this last step
+
+ align:start position:0%
+Let's look at this uh this last step
+ 
+
+ align:start position:0%
+Let's look at this uh this last step
+here. Uh step k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How high am I in the tree? I started at
+
+ align:start position:0%
+How high am I in the tree? I started at
+ 
+
+ align:start position:0%
+How high am I in the tree? I started at
+the leaf level. Remember in a 23 tree
+
+ align:start position:0%
+the leaf level. Remember in a 23 tree
+ 
+
+ align:start position:0%
+the leaf level. Remember in a 23 tree
+all the leaves have the same level and I
+
+ align:start position:0%
+all the leaves have the same level and I
+ 
+
+ align:start position:0%
+all the leaves have the same level and I
+went up every step. Uh sorry. Uh I don't
+
+ align:start position:0%
+went up every step. Uh sorry. Uh I don't
+ 
+
+ align:start position:0%
+went up every step. Uh sorry. Uh I don't
+know what this is like the two-step
+
+ align:start position:0%
+know what this is like the two-step
+ 
+
+ align:start position:0%
+know what this is like the two-step
+dance uh where when I let's say every
+
+ align:start position:0%
+dance uh where when I let's say every
+ 
+
+ align:start position:0%
+dance uh where when I let's say every
+iteration of this loop I do one left or
+
+ align:start position:0%
+iteration of this loop I do one left or
+ 
+
+ align:start position:0%
+iteration of this loop I do one left or
+right step and then a parent step. So uh
+
+ align:start position:0%
+right step and then a parent step. So uh
+ 
+
+ align:start position:0%
+right step and then a parent step. So uh
+I should call this iteration K. I guess
+
+ align:start position:0%
+I should call this iteration K. I guess
+ 
+
+ align:start position:0%
+I should call this iteration K. I guess
+there's two K steps then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be clear. Uh so in iteration K that
+
+ align:start position:0%
+to be clear. Uh so in iteration K that
+ 
+
+ align:start position:0%
+to be clear. Uh so in iteration K that
+means I've gone up K times and I've gone
+
+ align:start position:0%
+means I've gone up K times and I've gone
+ 
+
+ align:start position:0%
+means I've gone up K times and I've gone
+either right or left K times. You can
+
+ align:start position:0%
+either right or left K times. You can
+ 
+
+ align:start position:0%
+either right or left K times. You can
+show if you start going right you'll
+
+ align:start position:0%
+show if you start going right you'll
+ 
+
+ align:start position:0%
+show if you start going right you'll
+keep going right. If you keep if you
+
+ align:start position:0%
+keep going right. If you keep if you
+ 
+
+ align:start position:0%
+keep going right. If you keep if you
+initially go left you'll keep going
+
+ align:start position:0%
+initially go left you'll keep going
+ 
+
+ align:start position:0%
+initially go left you'll keep going
+left. That doesn't matter too much. Um
+
+ align:start position:0%
+left. That doesn't matter too much. Um
+ 
+
+ align:start position:0%
+left. That doesn't matter too much. Um
+at iteration K I am at height K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or K minus one or however you want to
+
+ align:start position:0%
+or K minus one or however you want to
+ 
+
+ align:start position:0%
+or K minus one or however you want to
+count. Okay but let's call it K. So when
+
+ align:start position:0%
+count. Okay but let's call it K. So when
+ 
+
+ align:start position:0%
+count. Okay but let's call it K. So when
+I do this right pointer here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know that uh for example, I am
+
+ align:start position:0%
+I know that uh for example, I am
+ 
+
+ align:start position:0%
+I know that uh for example, I am
+skipping over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of these keys. All the keys down,
+
+ align:start position:0%
+all of these keys. All the keys down,
+ 
+
+ align:start position:0%
+all of these keys. All the keys down,
+the keys are in the leaves. So all these
+
+ align:start position:0%
+the keys are in the leaves. So all these
+ 
+
+ align:start position:0%
+the keys are in the leaves. So all these
+keys down here, I'm jumping over them.
+
+ align:start position:0%
+keys down here, I'm jumping over them.
+ 
+
+ align:start position:0%
+keys down here, I'm jumping over them.
+How many keys are down there?
+
+ align:start position:0%
+How many keys are down there?
+ 
+
+ align:start position:0%
+How many keys are down there?
+Can you tell me uh roughly how many keys
+
+ align:start position:0%
+Can you tell me uh roughly how many keys
+ 
+
+ align:start position:0%
+Can you tell me uh roughly how many keys
+I'm skipping over when I'm moving right
+
+ align:start position:0%
+I'm skipping over when I'm moving right
+ 
+
+ align:start position:0%
+I'm skipping over when I'm moving right
+at height K?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's not a unique answer, but you can
+
+ align:start position:0%
+It's not a unique answer, but you can
+ 
+
+ align:start position:0%
+It's not a unique answer, but you can
+give me some bounds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say again. It's like the number
+
+ align:start position:0%
+Say again. It's like the number
+ 
+
+ align:start position:0%
+Say again. It's like the number
+number of children to the k power. Yeah,
+
+ align:start position:0%
+number of children to the k power. Yeah,
+ 
+
+ align:start position:0%
+number of children to the k power. Yeah,
+except we don't know the number of
+
+ align:start position:0%
+except we don't know the number of
+ 
+
+ align:start position:0%
+except we don't know the number of
+children, but it's between two and
+
+ align:start position:0%
+children, but it's between two and
+ 
+
+ align:start position:0%
+children, but it's between two and
+three. Sorry, cluster one should be
+
+ align:start position:0%
+three. Sorry, cluster one should be
+ 
+
+ align:start position:0%
+three. Sorry, cluster one should be
+easy, but uh I fail. Um so it's between
+
+ align:start position:0%
+easy, but uh I fail. Um so it's between
+ 
+
+ align:start position:0%
+easy, but uh I fail. Um so it's between
+two and three children. So there's uh
+
+ align:start position:0%
+two and three children. So there's uh
+ 
+
+ align:start position:0%
+two and three children. So there's uh
+the number if you look at a uh a height
+
+ align:start position:0%
+the number if you look at a uh a height
+ 
+
+ align:start position:0%
+the number if you look at a uh a height
+k tree,
+
+ align:start position:0%
+k tree,
+ 
+
+ align:start position:0%
+k tree,
+how many leaves does it have? It's going
+
+ align:start position:0%
+how many leaves does it have? It's going
+ 
+
+ align:start position:0%
+how many leaves does it have? It's going
+to be between 2 to the k and 3 to the k.
+
+ align:start position:0%
+to be between 2 to the k and 3 to the k.
+ 
+
+ align:start position:0%
+to be between 2 to the k and 3 to the k.
+because I have between two and three
+
+ align:start position:0%
+because I have between two and three
+ 
+
+ align:start position:0%
+because I have between two and three
+children at every node. And so it's
+
+ align:start position:0%
+children at every node. And so it's
+ 
+
+ align:start position:0%
+children at every node. And so it's
+exponential in K. That's all I'll need.
+
+ align:start position:0%
+exponential in K. That's all I'll need.
+ 
+
+ align:start position:0%
+exponential in K. That's all I'll need.
+And so, okay, when I'm at height K here,
+
+ align:start position:0%
+And so, okay, when I'm at height K here,
+ 
+
+ align:start position:0%
+And so, okay, when I'm at height K here,
+I'm skipping over a height k minus one
+
+ align:start position:0%
+I'm skipping over a height k minus one
+ 
+
+ align:start position:0%
+I'm skipping over a height k minus one
+tree or something. uh but it's going to
+
+ align:start position:0%
+tree or something. uh but it's going to
+ 
+
+ align:start position:0%
+tree or something. uh but it's going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+so in iteration k I'm I'm skipping uh at
+
+ align:start position:0%
+so in iteration k I'm I'm skipping uh at
+ 
+
+ align:start position:0%
+so in iteration k I'm I'm skipping uh at
+least some constant times 2 to the k
+
+ align:start position:0%
+least some constant times 2 to the k
+ 
+
+ align:start position:0%
+least some constant times 2 to the k
+maybe 2 the k minus one or 2 the k minus
+
+ align:start position:0%
+maybe 2 the k minus one or 2 the k minus
+ 
+
+ align:start position:0%
+maybe 2 the k minus one or 2 the k minus
+2 I don't I'm being very sloppy it
+
+ align:start position:0%
+2 I don't I'm being very sloppy it
+ 
+
+ align:start position:0%
+2 I don't I'm being very sloppy it
+doesn't matter as long as it's
+
+ align:start position:0%
+doesn't matter as long as it's
+ 
+
+ align:start position:0%
+doesn't matter as long as it's
+exponential in k I'm happy because I'm
+
+ align:start position:0%
+exponential in k I'm happy because I'm
+ 
+
+ align:start position:0%
+exponential in k I'm happy because I'm
+supposing
+
+ align:start position:0%
+supposing
+ 
+
+ align:start position:0%
+supposing
+that x and y are somewhat close let's
+
+ align:start position:0%
+that x and y are somewhat close let's
+ 
+
+ align:start position:0%
+that x and y are somewhat close let's
+call this rank difference d
+
+ align:start position:0%
+call this rank difference d
+ 
+
+ align:start position:0%
+call this rank difference d
+then I claim the number of iterations
+
+ align:start position:0%
+then I claim the number of iterations
+ 
+
+ align:start position:0%
+then I claim the number of iterations
+I'll need to do in this loop is at most
+
+ align:start position:0%
+I'll need to do in this loop is at most
+ 
+
+ align:start position:0%
+I'll need to do in this loop is at most
+order log d
+
+ align:start position:0%
+order log d
+ 
+
+ align:start position:0%
+order log d
+because if uh when I get to the kth
+
+ align:start position:0%
+because if uh when I get to the kth
+ 
+
+ align:start position:0%
+because if uh when I get to the kth
+iteration I'm jumping over 2 to the k
+
+ align:start position:0%
+iteration I'm jumping over 2 to the k
+ 
+
+ align:start position:0%
+iteration I'm jumping over 2 to the k
+elements how how large does k have to be
+
+ align:start position:0%
+elements how how large does k have to be
+ 
+
+ align:start position:0%
+elements how how large does k have to be
+before 2 to the k is larger than uh d
+
+ align:start position:0%
+before 2 to the k is larger than uh d
+ 
+
+ align:start position:0%
+before 2 to the k is larger than uh d
+well log d
+
+ align:start position:0%
+well log d
+ 
+
+ align:start position:0%
+well log d
+log base 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So uh the number of iterations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is order log d
+
+ align:start position:0%
+is order log d
+ 
+
+ align:start position:0%
+is order log d
+where d is the rank difference. d is the
+
+ align:start position:0%
+where d is the rank difference. d is the
+ 
+
+ align:start position:0%
+where d is the rank difference. d is the
+absolute value between rank of x and
+
+ align:start position:0%
+absolute value between rank of x and
+ 
+
+ align:start position:0%
+absolute value between rank of x and
+rank of y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I'm being a little uh sloppy here.
+
+ align:start position:0%
+Okay, I'm being a little uh sloppy here.
+ 
+
+ align:start position:0%
+Okay, I'm being a little uh sloppy here.
+You probably want to use an induction.
+
+ align:start position:0%
+You probably want to use an induction.
+ 
+
+ align:start position:0%
+You probably want to use an induction.
+You need to show that they're really
+
+ align:start position:0%
+You need to show that they're really
+ 
+
+ align:start position:0%
+You need to show that they're really
+these items here that you're skipping
+
+ align:start position:0%
+these items here that you're skipping
+ 
+
+ align:start position:0%
+these items here that you're skipping
+over that are strictly between X and Y.
+
+ align:start position:0%
+over that are strictly between X and Y.
+ 
+
+ align:start position:0%
+over that are strictly between X and Y.
+But we know that there's only D items
+
+ align:start position:0%
+But we know that there's only D items
+ 
+
+ align:start position:0%
+But we know that there's only D items
+between X and Y. Actually, D minus one,
+
+ align:start position:0%
+between X and Y. Actually, D minus one,
+ 
+
+ align:start position:0%
+between X and Y. Actually, D minus one,
+I guess. So, uh as soon as we've skipped
+
+ align:start position:0%
+I guess. So, uh as soon as we've skipped
+ 
+
+ align:start position:0%
+I guess. So, uh as soon as we've skipped
+over all the items between X and Y, then
+
+ align:start position:0%
+over all the items between X and Y, then
+ 
+
+ align:start position:0%
+over all the items between X and Y, then
+we'll find a range that contains X and
+
+ align:start position:0%
+we'll find a range that contains X and
+ 
+
+ align:start position:0%
+we'll find a range that contains X and
+then we'll go do the downward search.
+
+ align:start position:0%
+then we'll go do the downward search.
+ 
+
+ align:start position:0%
+then we'll go do the downward search.
+Now, how long does the downward search
+
+ align:start position:0%
+Now, how long does the downward search
+ 
+
+ align:start position:0%
+Now, how long does the downward search
+cost? Whatever the height of the tree
+
+ align:start position:0%
+cost? Whatever the height of the tree
+ 
+
+ align:start position:0%
+cost? Whatever the height of the tree
+is.
+
+ align:start position:0%
+is.
+ 
+
+ align:start position:0%
+is.
+What's the height of the tree? That's
+
+ align:start position:0%
+What's the height of the tree? That's
+ 
+
+ align:start position:0%
+What's the height of the tree? That's
+the number of iterations. So, total
+
+ align:start position:0%
+the number of iterations. So, total
+ 
+
+ align:start position:0%
+the number of iterations. So, total
+cost, the downward search will cost the
+
+ align:start position:0%
+cost, the downward search will cost the
+ 
+
+ align:start position:0%
+cost, the downward search will cost the
+same as the rest of the search.
+
+ align:start position:0%
+same as the rest of the search.
+ 
+
+ align:start position:0%
+same as the rest of the search.
+And so, total cost is going to be order
+
+ align:start position:0%
+And so, total cost is going to be order
+ 
+
+ align:start position:0%
+And so, total cost is going to be order
+log d.
+
+ align:start position:0%
+log d.
+ 
+
+ align:start position:0%
+log d.
+Clear?
+
+ align:start position:0%
+Clear?
+ 
+
+ align:start position:0%
+Clear?
+Any questions about
+
+ align:start position:0%
+Any questions about
+ 
+
+ align:start position:0%
+Any questions about
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+finger searching with level length data
+
+ align:start position:0%
+finger searching with level length data
+ 
+
+ align:start position:0%
+finger searching with level length data
+at the leaves? uh two three trees. Yeah.
+
+ align:start position:0%
+at the leaves? uh two three trees. Yeah.
+ 
+
+ align:start position:0%
+at the leaves? uh two three trees. Yeah.
+So I'm not sure what
+
+ align:start position:0%
+So I'm not sure what
+ 
+
+ align:start position:0%
+So I'm not sure what
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+I'm defining D to be the rank of X minus
+
+ align:start position:0%
+I'm defining D to be the rank of X minus
+ 
+
+ align:start position:0%
+I'm defining D to be the rank of X minus
+rank of Y. So then my goal is to achieve
+
+ align:start position:0%
+rank of Y. So then my goal is to achieve
+ 
+
+ align:start position:0%
+rank of Y. So then my goal is to achieve
+a log D bound and I'm claiming that
+
+ align:start position:0%
+a log D bound and I'm claiming that
+ 
+
+ align:start position:0%
+a log D bound and I'm claiming that
+because uh once I've skipped over D
+
+ align:start position:0%
+because uh once I've skipped over D
+ 
+
+ align:start position:0%
+because uh once I've skipped over D
+items then I'm done. Then I found X and
+
+ align:start position:0%
+items then I'm done. Then I found X and
+ 
+
+ align:start position:0%
+items then I'm done. Then I found X and
+that and in at step K I'm skipping over
+
+ align:start position:0%
+that and in at step K I'm skipping over
+ 
+
+ align:start position:0%
+that and in at step K I'm skipping over
+to the K items. So how big is K going to
+
+ align:start position:0%
+to the K items. So how big is K going to
+ 
+
+ align:start position:0%
+to the K items. So how big is K going to
+be? Log D. That's all.
+
+ align:start position:0%
+be? Log D. That's all.
+ 
+
+ align:start position:0%
+be? Log D. That's all.
+Yeah, that was just not I use D for
+
+ align:start position:0%
+Yeah, that was just not I use D for
+ 
+
+ align:start position:0%
+Yeah, that was just not I use D for
+notation here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So, uh
+
+ align:start position:0%
+Cool. So, uh
+ 
+
+ align:start position:0%
+Cool. So, uh
+finger searching it's nice especially if
+
+ align:start position:0%
+finger searching it's nice especially if
+ 
+
+ align:start position:0%
+finger searching it's nice especially if
+you're doing many consecutive searches
+
+ align:start position:0%
+you're doing many consecutive searches
+ 
+
+ align:start position:0%
+you're doing many consecutive searches
+that are all relatively close to each
+
+ align:start position:0%
+that are all relatively close to each
+ 
+
+ align:start position:0%
+that are all relatively close to each
+other. Uh
+
+ align:start position:0%
+other. Uh
+ 
+
+ align:start position:0%
+other. Uh
+but that was easy. Let's do a more
+
+ align:start position:0%
+but that was easy. Let's do a more
+ 
+
+ align:start position:0%
+but that was easy. Let's do a more
+difficult augmentation. Right.
+
+ align:start position:0%
+difficult augmentation. Right.
+ 
+
+ align:start position:0%
+difficult augmentation. Right.
+Uh so the last topic
+
+ align:start position:0%
+Uh so the last topic
+ 
+
+ align:start position:0%
+Uh so the last topic
+for today is range trees. This is
+
+ align:start position:0%
+for today is range trees. This is
+ 
+
+ align:start position:0%
+for today is range trees. This is
+probably the coolest example of
+
+ align:start position:0%
+probably the coolest example of
+ 
+
+ align:start position:0%
+probably the coolest example of
+augmentation at least that you'll see in
+
+ align:start position:0%
+augmentation at least that you'll see in
+ 
+
+ align:start position:0%
+augmentation at least that you'll see in
+this class. If you want to see more, you
+
+ align:start position:0%
+this class. If you want to see more, you
+ 
+
+ align:start position:0%
+this class. If you want to see more, you
+should take advanced data structure
+
+ align:start position:0%
+should take advanced data structure
+ 
+
+ align:start position:0%
+should take advanced data structure
+6851.
+
+ align:start position:0%
+6851.
+ 
+
+ align:start position:0%
+6851.
+Uh,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and range trees solve a problem called
+
+ align:start position:0%
+and range trees solve a problem called
+ 
+
+ align:start position:0%
+and range trees solve a problem called
+orthogonal range searching.
+
+ align:start position:0%
+orthogonal range searching.
+ 
+
+ align:start position:0%
+orthogonal range searching.
+Not orthogonal search ranging. Uh,
+
+ align:start position:0%
+Not orthogonal search ranging. Uh,
+ 
+
+ align:start position:0%
+Not orthogonal search ranging. Uh,
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+search.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, uh, what's the problem? I'm going to
+
+ align:start position:0%
+So, uh, what's the problem? I'm going to
+ 
+
+ align:start position:0%
+So, uh, what's the problem? I'm going to
+give you a bunch of points.
+
+ align:start position:0%
+give you a bunch of points.
+ 
+
+ align:start position:0%
+give you a bunch of points.
+Draw them as fat dots so you can
+
+ align:start position:0%
+Draw them as fat dots so you can
+ 
+
+ align:start position:0%
+Draw them as fat dots so you can
+actually see them. Uh, in some
+
+ align:start position:0%
+actually see them. Uh, in some
+ 
+
+ align:start position:0%
+actually see them. Uh, in some
+dimension. So, here's this is, for
+
+ align:start position:0%
+dimension. So, here's this is, for
+ 
+
+ align:start position:0%
+dimension. So, here's this is, for
+example, a 2D point set.
+
+ align:start position:0%
+example, a 2D point set.
+ 
+
+ align:start position:0%
+example, a 2D point set.
+Okay. Over here, I will draw a 3D point
+
+ align:start position:0%
+Okay. Over here, I will draw a 3D point
+ 
+
+ align:start position:0%
+Okay. Over here, I will draw a 3D point
+set. You can tell the difference, I'm
+
+ align:start position:0%
+set. You can tell the difference, I'm
+ 
+
+ align:start position:0%
+set. You can tell the difference, I'm
+sure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there. Now it's a 3D point set. Uh, and
+
+ align:start position:0%
+there. Now it's a 3D point set. Uh, and
+ 
+
+ align:start position:0%
+there. Now it's a 3D point set. Uh, and
+this is a static point set. You could
+
+ align:start position:0%
+this is a static point set. You could
+ 
+
+ align:start position:0%
+this is a static point set. You could
+make this dynamic, but let's just think
+
+ align:start position:0%
+make this dynamic, but let's just think
+ 
+
+ align:start position:0%
+make this dynamic, but let's just think
+about the static case.
+
+ align:start position:0%
+about the static case.
+ 
+
+ align:start position:0%
+about the static case.
+Uh, don't want the 2D points and the 3D
+
+ align:start position:0%
+Uh, don't want the 2D points and the 3D
+ 
+
+ align:start position:0%
+Uh, don't want the 2D points and the 3D
+points to mix. So, um, now you get to
+
+ align:start position:0%
+points to mix. So, um, now you get to
+ 
+
+ align:start position:0%
+points to mix. So, um, now you get to
+pre-process this into a data structure.
+
+ align:start position:0%
+pre-process this into a data structure.
+ 
+
+ align:start position:0%
+pre-process this into a data structure.
+So, it's a static data structure
+
+ align:start position:0%
+So, it's a static data structure
+ 
+
+ align:start position:0%
+So, it's a static data structure
+problem. And now I'm going to come along
+
+ align:start position:0%
+problem. And now I'm going to come along
+ 
+
+ align:start position:0%
+problem. And now I'm going to come along
+with a whole bunch of queries. A query
+
+ align:start position:0%
+with a whole bunch of queries. A query
+ 
+
+ align:start position:0%
+with a whole bunch of queries. A query
+will be a box. Okay. In two dimensions,
+
+ align:start position:0%
+will be a box. Okay. In two dimensions,
+ 
+
+ align:start position:0%
+will be a box. Okay. In two dimensions,
+a box is a rectangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like this. Axis aligned. So I
+
+ align:start position:0%
+something like this. Axis aligned. So I
+ 
+
+ align:start position:0%
+something like this. Axis aligned. So I
+give you an x min, an xmaxx, a y min,
+
+ align:start position:0%
+give you an x min, an xmaxx, a y min,
+ 
+
+ align:start position:0%
+give you an x min, an xmaxx, a y min,
+and a yax. I want to know what are the
+
+ align:start position:0%
+and a yax. I want to know what are the
+ 
+
+ align:start position:0%
+and a yax. I want to know what are the
+points inside. Maybe I want you to list
+
+ align:start position:0%
+points inside. Maybe I want you to list
+ 
+
+ align:start position:0%
+points inside. Maybe I want you to list
+them. There's a lot of them. It's going
+
+ align:start position:0%
+them. There's a lot of them. It's going
+ 
+
+ align:start position:0%
+them. There's a lot of them. It's going
+to take a long time to list them. Maybe
+
+ align:start position:0%
+to take a long time to list them. Maybe
+ 
+
+ align:start position:0%
+to take a long time to list them. Maybe
+I just want to know 10 of them as
+
+ align:start position:0%
+I just want to know 10 of them as
+ 
+
+ align:start position:0%
+I just want to know 10 of them as
+examples. You know, maybe this is a
+
+ align:start position:0%
+examples. You know, maybe this is a
+ 
+
+ align:start position:0%
+examples. You know, maybe this is a
+Google search or something. I just get
+
+ align:start position:0%
+Google search or something. I just get
+ 
+
+ align:start position:0%
+Google search or something. I just get
+the first 10 results on the first page.
+
+ align:start position:0%
+the first 10 results on the first page.
+ 
+
+ align:start position:0%
+the first 10 results on the first page.
+I hit next, then I want the next 10.
+
+ align:start position:0%
+I hit next, then I want the next 10.
+ 
+
+ align:start position:0%
+I hit next, then I want the next 10.
+that kind of thing. Uh, or maybe I want
+
+ align:start position:0%
+that kind of thing. Uh, or maybe I want
+ 
+
+ align:start position:0%
+that kind of thing. Uh, or maybe I want
+to know how many search results there
+
+ align:start position:0%
+to know how many search results there
+ 
+
+ align:start position:0%
+to know how many search results there
+are, number of points in the rectangle,
+
+ align:start position:0%
+are, number of points in the rectangle,
+ 
+
+ align:start position:0%
+are, number of points in the rectangle,
+bunch of different problems. In 3D, it's
+
+ align:start position:0%
+bunch of different problems. In 3D, it's
+ 
+
+ align:start position:0%
+bunch of different problems. In 3D, it's
+a a 3D box, which is a little harder to
+
+ align:start position:0%
+a a 3D box, which is a little harder to
+ 
+
+ align:start position:0%
+a a 3D box, which is a little harder to
+draw, but or can't really tell which
+
+ align:start position:0%
+draw, but or can't really tell which
+ 
+
+ align:start position:0%
+draw, but or can't really tell which
+points are inside the box. Let's say
+
+ align:start position:0%
+points are inside the box. Let's say
+ 
+
+ align:start position:0%
+points are inside the box. Let's say
+these three points are all inside the
+
+ align:start position:0%
+these three points are all inside the
+ 
+
+ align:start position:0%
+these three points are all inside the
+box. I give you an interval in X, an
+
+ align:start position:0%
+box. I give you an interval in X, an
+ 
+
+ align:start position:0%
+box. I give you an interval in X, an
+interval in Y, and an interval in Z. And
+
+ align:start position:0%
+interval in Y, and an interval in Z. And
+ 
+
+ align:start position:0%
+interval in Y, and an interval in Z. And
+I want to know what are the points
+
+ align:start position:0%
+I want to know what are the points
+ 
+
+ align:start position:0%
+I want to know what are the points
+inside. Count how many are there? List
+
+ align:start position:0%
+inside. Count how many are there? List
+ 
+
+ align:start position:0%
+inside. Count how many are there? List
+them all. List 10 of them. Whatever.
+
+ align:start position:0%
+them all. List 10 of them. Whatever.
+ 
+
+ align:start position:0%
+them all. List 10 of them. Whatever.
+Okay. Uh
+
+ align:start position:0%
+Okay. Uh
+ 
+
+ align:start position:0%
+Okay. Uh
+I want to do this in poly log time.
+
+ align:start position:0%
+I want to do this in poly log time.
+ 
+
+ align:start position:0%
+I want to do this in poly log time.
+Let's say I'm going to do I'm going to
+
+ align:start position:0%
+Let's say I'm going to do I'm going to
+ 
+
+ align:start position:0%
+Let's say I'm going to do I'm going to
+achieve today log squared for the 2D
+
+ align:start position:0%
+achieve today log squared for the 2D
+ 
+
+ align:start position:0%
+achieve today log squared for the 2D
+problem and log cubed for the 3D problem
+
+ align:start position:0%
+problem and log cubed for the 3D problem
+ 
+
+ align:start position:0%
+problem and log cubed for the 3D problem
+plus whatever the size of the output is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So let me just write that down.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the goal
+
+ align:start position:0%
+So the goal
+ 
+
+ align:start position:0%
+So the goal
+is to pre-process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end points
+
+ align:start position:0%
+end points
+ 
+
+ align:start position:0%
+end points
+in dimensions.
+
+ align:start position:0%
+in dimensions.
+ 
+
+ align:start position:0%
+in dimensions.
+Uh so you get to spend a bunch of time
+
+ align:start position:0%
+Uh so you get to spend a bunch of time
+ 
+
+ align:start position:0%
+Uh so you get to spend a bunch of time
+pre-processing to support a query
+
+ align:start position:0%
+pre-processing to support a query
+ 
+
+ align:start position:0%
+pre-processing to support a query
+which is uh given a box
+
+ align:start position:0%
+which is uh given a box
+ 
+
+ align:start position:0%
+which is uh given a box
+axis aligned box uh find
+
+ align:start position:0%
+axis aligned box uh find
+ 
+
+ align:start position:0%
+axis aligned box uh find
+let's say the number of points
+
+ align:start position:0%
+let's say the number of points
+ 
+
+ align:start position:0%
+let's say the number of points
+in the box
+
+ align:start position:0%
+in the box
+ 
+
+ align:start position:0%
+in the box
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+find k points in the box.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that's good. That includes a
+
+ align:start position:0%
+I think that's good. That includes a
+ 
+
+ align:start position:0%
+I think that's good. That includes a
+special case of find all the points in
+
+ align:start position:0%
+special case of find all the points in
+ 
+
+ align:start position:0%
+special case of find all the points in
+the box. Uh so this of course we have to
+
+ align:start position:0%
+the box. Uh so this of course we have to
+ 
+
+ align:start position:0%
+the box. Uh so this of course we have to
+pay a penalty of order k for the output.
+
+ align:start position:0%
+pay a penalty of order k for the output.
+ 
+
+ align:start position:0%
+pay a penalty of order k for the output.
+Okay, no getting around that. Uh but I
+
+ align:start position:0%
+Okay, no getting around that. Uh but I
+ 
+
+ align:start position:0%
+Okay, no getting around that. Uh but I
+want the the rest of the time to be log
+
+ align:start position:0%
+want the the rest of the time to be log
+ 
+
+ align:start position:0%
+want the the rest of the time to be log
+to the d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're going to achieve log to the dn
+
+ align:start position:0%
+So we're going to achieve log to the dn
+ 
+
+ align:start position:0%
+So we're going to achieve log to the dn
+plus size of the output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you get to control how big you want
+
+ align:start position:0%
+and you get to control how big you want
+ 
+
+ align:start position:0%
+and you get to control how big you want
+the output to be. So it's a pretty
+
+ align:start position:0%
+the output to be. So it's a pretty
+ 
+
+ align:start position:0%
+the output to be. So it's a pretty
+reasonable data structure in a certain
+
+ align:start position:0%
+reasonable data structure in a certain
+ 
+
+ align:start position:0%
+reasonable data structure in a certain
+sense. We will understand what the
+
+ align:start position:0%
+sense. We will understand what the
+ 
+
+ align:start position:0%
+sense. We will understand what the
+output is in log to the d time. If you
+
+ align:start position:0%
+output is in log to the d time. If you
+ 
+
+ align:start position:0%
+output is in log to the d time. If you
+actually want to list points well then
+
+ align:start position:0%
+actually want to list points well then
+ 
+
+ align:start position:0%
+actually want to list points well then
+you have to spend the time to do it.
+
+ align:start position:0%
+you have to spend the time to do it.
+ 
+
+ align:start position:0%
+you have to spend the time to do it.
+All right. So 2D and 3D are great but
+
+ align:start position:0%
+All right. So 2D and 3D are great but
+ 
+
+ align:start position:0%
+All right. So 2D and 3D are great but
+let's start with 1D first. We should
+
+ align:start position:0%
+let's start with 1D first. We should
+ 
+
+ align:start position:0%
+let's start with 1D first. We should
+understand 1D completely. Then we can
+
+ align:start position:0%
+understand 1D completely. Then we can
+ 
+
+ align:start position:0%
+understand 1D completely. Then we can
+generalize.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1D we already know how to do. But
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1D I have a line. I have some points on
+
+ align:start position:0%
+1D I have a line. I have some points on
+ 
+
+ align:start position:0%
+1D I have a line. I have some points on
+the line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm given as a query some interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to know how many points are
+
+ align:start position:0%
+and I want to know how many points are
+ 
+
+ align:start position:0%
+and I want to know how many points are
+in the interval. Give me the points in
+
+ align:start position:0%
+in the interval. Give me the points in
+ 
+
+ align:start position:0%
+in the interval. Give me the points in
+the interval and so on.
+
+ align:start position:0%
+the interval and so on.
+ 
+
+ align:start position:0%
+the interval and so on.
+So how do I do this anyways?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if d is one so I want to achieve log
+
+ align:start position:0%
+uh if d is one so I want to achieve log
+ 
+
+ align:start position:0%
+uh if d is one so I want to achieve log
+d sorry log n plus size of output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I hear whispers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+segment
+
+ align:start position:0%
+segment
+ 
+
+ align:start position:0%
+segment
+segment tree that's fancy we won't cover
+
+ align:start position:0%
+segment tree that's fancy we won't cover
+ 
+
+ align:start position:0%
+segment tree that's fancy we won't cover
+segment trees you probably probably
+
+ align:start position:0%
+segment trees you probably probably
+ 
+
+ align:start position:0%
+segment trees you probably probably
+segment tries do it but yeah we know
+
+ align:start position:0%
+segment tries do it but yeah we know
+ 
+
+ align:start position:0%
+segment tries do it but yeah we know
+lots of ways to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+sorted array is probably the simplest.
+
+ align:start position:0%
+sorted array is probably the simplest.
+ 
+
+ align:start position:0%
+sorted array is probably the simplest.
+If I store the items in a sorted array
+
+ align:start position:0%
+If I store the items in a sorted array
+ 
+
+ align:start position:0%
+If I store the items in a sorted array
+and I have two values here, I'll call
+
+ align:start position:0%
+and I have two values here, I'll call
+ 
+
+ align:start position:0%
+and I have two values here, I'll call
+them uh x1 and x2 because it's the like
+
+ align:start position:0%
+them uh x1 and x2 because it's the like
+ 
+
+ align:start position:0%
+them uh x1 and x2 because it's the like
+the x min and the xmaxx. Uh binary
+
+ align:start position:0%
+the x min and the xmaxx. Uh binary
+ 
+
+ align:start position:0%
+the x min and the xmaxx. Uh binary
+search for x1, binary search for x2,
+
+ align:start position:0%
+search for x1, binary search for x2,
+ 
+
+ align:start position:0%
+search for x1, binary search for x2,
+find the successor of x1 and the
+
+ align:start position:0%
+find the successor of x1 and the
+ 
+
+ align:start position:0%
+find the successor of x1 and the
+predecessor of x2. I'll find these two
+
+ align:start position:0%
+predecessor of x2. I'll find these two
+ 
+
+ align:start position:0%
+predecessor of x2. I'll find these two
+guys and then I know all the ones in
+
+ align:start position:0%
+guys and then I know all the ones in
+ 
+
+ align:start position:0%
+guys and then I know all the ones in
+between. That's the match. Okay, so
+
+ align:start position:0%
+between. That's the match. Okay, so
+ 
+
+ align:start position:0%
+between. That's the match. Okay, so
+that'll take login time to find those
+
+ align:start position:0%
+that'll take login time to find those
+ 
+
+ align:start position:0%
+that'll take login time to find those
+points and then we're good.
+
+ align:start position:0%
+points and then we're good.
+ 
+
+ align:start position:0%
+points and then we're good.
+Okay, so we could do a sorted array. Uh,
+
+ align:start position:0%
+Okay, so we could do a sorted array. Uh,
+ 
+
+ align:start position:0%
+Okay, so we could do a sorted array. Uh,
+of course sorted array is a little hard
+
+ align:start position:0%
+of course sorted array is a little hard
+ 
+
+ align:start position:0%
+of course sorted array is a little hard
+to generalize. Uh, I don't want to do a
+
+ align:start position:0%
+to generalize. Uh, I don't want to do a
+ 
+
+ align:start position:0%
+to generalize. Uh, I don't want to do a
+2D array. That sounds bad. Uh, you could
+
+ align:start position:0%
+2D array. That sounds bad. Uh, you could
+ 
+
+ align:start position:0%
+2D array. That sounds bad. Uh, you could
+of course do a binary search tree like
+
+ align:start position:0%
+of course do a binary search tree like
+ 
+
+ align:start position:0%
+of course do a binary search tree like
+an AVL tree. Same thing because we have
+
+ align:start position:0%
+an AVL tree. Same thing because we have
+ 
+
+ align:start position:0%
+an AVL tree. Same thing because we have
+login search find successor predecessor.
+
+ align:start position:0%
+login search find successor predecessor.
+ 
+
+ align:start position:0%
+login search find successor predecessor.
+I guess you could use van deoas but
+
+ align:start position:0%
+I guess you could use van deoas but
+ 
+
+ align:start position:0%
+I guess you could use van deoas but
+that's hard to generalize to 2D. Um,
+
+ align:start position:0%
+that's hard to generalize to 2D. Um,
+ 
+
+ align:start position:0%
+that's hard to generalize to 2D. Um,
+you could use level linked. Here's a
+
+ align:start position:0%
+you could use level linked. Here's a
+ 
+
+ align:start position:0%
+you could use level linked. Here's a
+fancy version. Uh, we could use level
+
+ align:start position:0%
+fancy version. Uh, we could use level
+ 
+
+ align:start position:0%
+fancy version. Uh, we could use level
+linked uh two three trees with data in
+
+ align:start position:0%
+linked uh two three trees with data in
+ 
+
+ align:start position:0%
+linked uh two three trees with data in
+the leaves. Then once I find xmin, I
+
+ align:start position:0%
+the leaves. Then once I find xmin, I
+ 
+
+ align:start position:0%
+the leaves. Then once I find xmin, I
+find this point I can go to the
+
+ align:start position:0%
+find this point I can go to the
+ 
+
+ align:start position:0%
+find this point I can go to the
+successor in constant time because
+
+ align:start position:0%
+successor in constant time because
+ 
+
+ align:start position:0%
+successor in constant time because
+that's a finger search with a rank
+
+ align:start position:0%
+that's a finger search with a rank
+ 
+
+ align:start position:0%
+that's a finger search with a rank
+difference of one. And I could just keep
+
+ align:start position:0%
+difference of one. And I could just keep
+ 
+
+ align:start position:0%
+difference of one. And I could just keep
+calling successor and in constant time
+
+ align:start position:0%
+calling successor and in constant time
+ 
+
+ align:start position:0%
+calling successor and in constant time
+per item, I will find the next item. So
+
+ align:start position:0%
+per item, I will find the next item. So
+ 
+
+ align:start position:0%
+per item, I will find the next item. So
+we could do that easily with the sorted
+
+ align:start position:0%
+we could do that easily with the sorted
+ 
+
+ align:start position:0%
+we could do that easily with the sorted
+array. BST is not so great if because
+
+ align:start position:0%
+array. BST is not so great if because
+ 
+
+ align:start position:0%
+array. BST is not so great if because
+successor might cost login each time. Uh
+
+ align:start position:0%
+successor might cost login each time. Uh
+ 
+
+ align:start position:0%
+successor might cost login each time. Uh
+but if I have the level lengths then
+
+ align:start position:0%
+but if I have the level lengths then
+ 
+
+ align:start position:0%
+but if I have the level lengths then
+basically I'm just walking down the link
+
+ align:start position:0%
+basically I'm just walking down the link
+ 
+
+ align:start position:0%
+basically I'm just walking down the link
+list at the bottom of the tree. Okay. So
+
+ align:start position:0%
+list at the bottom of the tree. Okay. So
+ 
+
+ align:start position:0%
+list at the bottom of the tree. Okay. So
+actually level
+
+ align:start position:0%
+actually level
+ 
+
+ align:start position:0%
+actually level
+is even better.
+
+ align:start position:0%
+is even better.
+ 
+
+ align:start position:0%
+is even better.
+Uh BST would achieve something like uh
+
+ align:start position:0%
+Uh BST would achieve something like uh
+ 
+
+ align:start position:0%
+Uh BST would achieve something like uh
+log n plus k log n where k is the size
+
+ align:start position:0%
+log n plus k log n where k is the size
+ 
+
+ align:start position:0%
+log n plus k log n where k is the size
+of the output. If there are k or if I
+
+ align:start position:0%
+of the output. If there are k or if I
+ 
+
+ align:start position:0%
+of the output. If there are k or if I
+want k points in the box, I have to pay
+
+ align:start position:0%
+want k points in the box, I have to pay
+ 
+
+ align:start position:0%
+want k points in the box, I have to pay
+log n for each level linked. I'll only
+
+ align:start position:0%
+log n for each level linked. I'll only
+ 
+
+ align:start position:0%
+log n for each level linked. I'll only
+pay log n plus k.
+
+ align:start position:0%
+pay log n plus k.
+ 
+
+ align:start position:0%
+pay log n plus k.
+Here I actually only need the levels at
+
+ align:start position:0%
+Here I actually only need the levels at
+ 
+
+ align:start position:0%
+Here I actually only need the levels at
+at the leaves, but the level lengths.
+
+ align:start position:0%
+at the leaves, but the level lengths.
+ 
+
+ align:start position:0%
+at the leaves, but the level lengths.
+Okay. All all good. But I actually want
+
+ align:start position:0%
+Okay. All all good. But I actually want
+ 
+
+ align:start position:0%
+Okay. All all good. But I actually want
+to tell you a different way to do it uh
+
+ align:start position:0%
+to tell you a different way to do it uh
+ 
+
+ align:start position:0%
+to tell you a different way to do it uh
+that will generalize better.
+
+ align:start position:0%
+that will generalize better.
+ 
+
+ align:start position:0%
+that will generalize better.
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pictures are going to look just like
+
+ align:start position:0%
+the pictures are going to look just like
+ 
+
+ align:start position:0%
+the pictures are going to look just like
+the pictures we've talked about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because I'm uh so this these would
+
+ align:start position:0%
+because I'm uh so this these would
+ 
+
+ align:start position:0%
+because I'm uh so this these would
+actually work dynamically. Uh my goal
+
+ align:start position:0%
+actually work dynamically. Uh my goal
+ 
+
+ align:start position:0%
+actually work dynamically. Uh my goal
+here is just to achieve a static data
+
+ align:start position:0%
+here is just to achieve a static data
+ 
+
+ align:start position:0%
+here is just to achieve a static data
+structure. I'm gonna idealize uh this
+
+ align:start position:0%
+structure. I'm gonna idealize uh this
+ 
+
+ align:start position:0%
+structure. I'm gonna idealize uh this
+solution a little bit
+
+ align:start position:0%
+solution a little bit
+ 
+
+ align:start position:0%
+solution a little bit
+and just say uh suppose I have a perfect
+
+ align:start position:0%
+and just say uh suppose I have a perfect
+ 
+
+ align:start position:0%
+and just say uh suppose I have a perfect
+perfectly balanced binary search tree.
+
+ align:start position:0%
+perfectly balanced binary search tree.
+ 
+
+ align:start position:0%
+perfectly balanced binary search tree.
+That's going to be my data structure.
+
+ align:start position:0%
+That's going to be my data structure.
+ 
+
+ align:start position:0%
+That's going to be my data structure.
+Okay, so the data structure is not hard.
+
+ align:start position:0%
+Okay, so the data structure is not hard.
+ 
+
+ align:start position:0%
+Okay, so the data structure is not hard.
+Uh but what's interesting is how I do a
+
+ align:start position:0%
+Uh but what's interesting is how I do a
+ 
+
+ align:start position:0%
+Uh but what's interesting is how I do a
+range search.
+
+ align:start position:0%
+range search.
+ 
+
+ align:start position:0%
+range search.
+So if I do
+
+ align:start position:0%
+So if I do
+ 
+
+ align:start position:0%
+So if I do
+a range query
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the interval, I'll call it AB.
+
+ align:start position:0%
+of the interval, I'll call it AB.
+ 
+
+ align:start position:0%
+of the interval, I'll call it AB.
+Then what I'm just what I'm going to do
+
+ align:start position:0%
+Then what I'm just what I'm going to do
+ 
+
+ align:start position:0%
+Then what I'm just what I'm going to do
+is do a binary search for A.
+
+ align:start position:0%
+is do a binary search for A.
+ 
+
+ align:start position:0%
+is do a binary search for A.
+Do a binary search for B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh trim the common prefix
+
+ align:start position:0%
+Uh trim the common prefix
+ 
+
+ align:start position:0%
+Uh trim the common prefix
+of those search paths.
+
+ align:start position:0%
+of those search paths.
+ 
+
+ align:start position:0%
+of those search paths.
+That's basically finding the lowest
+
+ align:start position:0%
+That's basically finding the lowest
+ 
+
+ align:start position:0%
+That's basically finding the lowest
+common ancestor
+
+ align:start position:0%
+common ancestor
+ 
+
+ align:start position:0%
+common ancestor
+of those of A and B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'm going to do some stuff. Let
+
+ align:start position:0%
+and then I'm going to do some stuff. Let
+ 
+
+ align:start position:0%
+and then I'm going to do some stuff. Let
+me draw the picture. So here is suppose
+
+ align:start position:0%
+me draw the picture. So here is suppose
+ 
+
+ align:start position:0%
+me draw the picture. So here is suppose
+here's the node that contains A. Here's
+
+ align:start position:0%
+here's the node that contains A. Here's
+ 
+
+ align:start position:0%
+here's the node that contains A. Here's
+the node that contains B. They may not
+
+ align:start position:0%
+the node that contains B. They may not
+ 
+
+ align:start position:0%
+the node that contains B. They may not
+be at the same depth. Who knows? U then
+
+ align:start position:0%
+be at the same depth. Who knows? U then
+ 
+
+ align:start position:0%
+be at the same depth. Who knows? U then
+I'm going to look at the parents of A. I
+
+ align:start position:0%
+I'm going to look at the parents of A. I
+ 
+
+ align:start position:0%
+I'm going to look at the parents of A. I
+mean I just came down from some path
+
+ align:start position:0%
+mean I just came down from some path
+ 
+
+ align:start position:0%
+mean I just came down from some path
+here. and some path down to B. I want to
+
+ align:start position:0%
+here. and some path down to B. I want to
+ 
+
+ align:start position:0%
+here. and some path down to B. I want to
+find this branching point where the
+
+ align:start position:0%
+find this branching point where the
+ 
+
+ align:start position:0%
+find this branching point where the
+paths to A and the paths to B diverge.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, uh let's just look at the parent of
+
+ align:start position:0%
+So, uh let's just look at the parent of
+ 
+
+ align:start position:0%
+So, uh let's just look at the parent of
+A. It could be a right parent.
+
+ align:start position:0%
+A. It could be a right parent.
+ 
+
+ align:start position:0%
+A. It could be a right parent.
+Uh I guess draw that like that in which
+
+ align:start position:0%
+Uh I guess draw that like that in which
+ 
+
+ align:start position:0%
+Uh I guess draw that like that in which
+case there's a sub tree here. It could
+
+ align:start position:0%
+case there's a sub tree here. It could
+ 
+
+ align:start position:0%
+case there's a sub tree here. It could
+be a left parent case sub tree here. Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to follow my convention again
+
+ align:start position:0%
+I'm going to follow my convention again
+ 
+
+ align:start position:0%
+I'm going to follow my convention again
+that X coordinate corresponds roughly to
+
+ align:start position:0%
+that X coordinate corresponds roughly to
+ 
+
+ align:start position:0%
+that X coordinate corresponds roughly to
+key. So maybe
+
+ align:start position:0%
+key. So maybe
+ 
+
+ align:start position:0%
+key. So maybe
+something like this.
+
+ align:start position:0%
+something like this.
+ 
+
+ align:start position:0%
+something like this.
+Left parent here. Maybe right parent
+
+ align:start position:0%
+Left parent here. Maybe right parent
+ 
+
+ align:start position:0%
+Left parent here. Maybe right parent
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. something like that.
+
+ align:start position:0%
+Okay. something like that.
+ 
+
+ align:start position:0%
+Okay. something like that.
+Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay, remember it's a perfect tree. So
+
+ align:start position:0%
+okay, remember it's a perfect tree. So
+ 
+
+ align:start position:0%
+okay, remember it's a perfect tree. So
+actually all the leaves will be at the
+
+ align:start position:0%
+actually all the leaves will be at the
+ 
+
+ align:start position:0%
+actually all the leaves will be at the
+same level.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And roughly here x coordinate
+
+ align:start position:0%
+And roughly here x coordinate
+ 
+
+ align:start position:0%
+And roughly here x coordinate
+corresponds to key.
+
+ align:start position:0%
+corresponds to key.
+ 
+
+ align:start position:0%
+corresponds to key.
+So here was a and I want to return all
+
+ align:start position:0%
+So here was a and I want to return all
+ 
+
+ align:start position:0%
+So here was a and I want to return all
+the keys that are between a and b. So
+
+ align:start position:0%
+the keys that are between a and b. So
+ 
+
+ align:start position:0%
+the keys that are between a and b. So
+that's everything in this sweep line.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. The parents of the LCA don't
+
+ align:start position:0%
+Okay. The parents of the LCA don't
+ 
+
+ align:start position:0%
+Okay. The parents of the LCA don't
+matter because this parent is either
+
+ align:start position:0%
+matter because this parent is either
+ 
+
+ align:start position:0%
+matter because this parent is either
+going to be way over to the right or way
+
+ align:start position:0%
+going to be way over to the right or way
+ 
+
+ align:start position:0%
+going to be way over to the right or way
+over to the left. In both cases, it's
+
+ align:start position:0%
+over to the left. In both cases, it's
+ 
+
+ align:start position:0%
+over to the left. In both cases, it's
+outside the interval A to B. So what
+
+ align:start position:0%
+outside the interval A to B. So what
+ 
+
+ align:start position:0%
+outside the interval A to B. So what
+I've tried to highlight here and I will
+
+ align:start position:0%
+I've tried to highlight here and I will
+ 
+
+ align:start position:0%
+I've tried to highlight here and I will
+color it in blue is
+
+ align:start position:0%
+color it in blue is
+ 
+
+ align:start position:0%
+color it in blue is
+the relevant nodes for the search
+
+ align:start position:0%
+the relevant nodes for the search
+ 
+
+ align:start position:0%
+the relevant nodes for the search
+between A and B. So A is between A and
+
+ align:start position:0%
+between A and B. So A is between A and
+ 
+
+ align:start position:0%
+between A and B. So A is between A and
+B. Uh this subree is greater than A and
+
+ align:start position:0%
+B. Uh this subree is greater than A and
+ 
+
+ align:start position:0%
+B. Uh this subree is greater than A and
+less than B. Uh this node and these
+
+ align:start position:0%
+less than B. Uh this node and these
+ 
+
+ align:start position:0%
+less than B. Uh this node and these
+nodes, this node and these nodes,
+
+ align:start position:0%
+nodes, this node and these nodes,
+ 
+
+ align:start position:0%
+nodes, this node and these nodes,
+this node and these nodes.
+
+ align:start position:0%
+this node and these nodes.
+ 
+
+ align:start position:0%
+this node and these nodes.
+uh the common ancestor and then the
+
+ align:start position:0%
+uh the common ancestor and then the
+ 
+
+ align:start position:0%
+uh the common ancestor and then the
+corresponding thing over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, all the nodes in all these blue
+
+ align:start position:0%
+Okay, all the nodes in all these blue
+ 
+
+ align:start position:0%
+Okay, all the nodes in all these blue
+sub trees plus these individual nodes
+
+ align:start position:0%
+sub trees plus these individual nodes
+ 
+
+ align:start position:0%
+sub trees plus these individual nodes
+fall in the interval between A and B.
+
+ align:start position:0%
+fall in the interval between A and B.
+ 
+
+ align:start position:0%
+fall in the interval between A and B.
+And that's it.
+
+ align:start position:0%
+And that's it.
+ 
+
+ align:start position:0%
+And that's it.
+Okay, this should look super familiar.
+
+ align:start position:0%
+Okay, this should look super familiar.
+ 
+
+ align:start position:0%
+Okay, this should look super familiar.
+It's just like when we were computing
+
+ align:start position:0%
+It's just like when we were computing
+ 
+
+ align:start position:0%
+It's just like when we were computing
+rank. We were trying to figure out how
+
+ align:start position:0%
+rank. We were trying to figure out how
+ 
+
+ align:start position:0%
+rank. We were trying to figure out how
+many guys are to our left or to our
+
+ align:start position:0%
+many guys are to our left or to our
+ 
+
+ align:start position:0%
+many guys are to our left or to our
+right. We're basically doing a rightward
+
+ align:start position:0%
+right. We're basically doing a rightward
+ 
+
+ align:start position:0%
+right. We're basically doing a rightward
+rank from A and a leftward rank from B.
+
+ align:start position:0%
+rank from A and a leftward rank from B.
+ 
+
+ align:start position:0%
+rank from A and a leftward rank from B.
+And that finds all the nodes and and
+
+ align:start position:0%
+And that finds all the nodes and and
+ 
+
+ align:start position:0%
+And that finds all the nodes and and
+stopping when those two searches
+
+ align:start position:0%
+stopping when those two searches
+ 
+
+ align:start position:0%
+stopping when those two searches
+converge. And then we're finding all the
+
+ align:start position:0%
+converge. And then we're finding all the
+ 
+
+ align:start position:0%
+converge. And then we're finding all the
+nodes between A and B. Okay, I'm not
+
+ align:start position:0%
+nodes between A and B. Okay, I'm not
+ 
+
+ align:start position:0%
+nodes between A and B. Okay, I'm not
+going to write down the pseudo code.
+
+ align:start position:0%
+going to write down the pseudo code.
+ 
+
+ align:start position:0%
+going to write down the pseudo code.
+Same kind of thing. You look at right
+
+ align:start position:0%
+Same kind of thing. You look at right
+ 
+
+ align:start position:0%
+Same kind of thing. You look at right
+parents and left parents. Whenever you
+
+ align:start position:0%
+parents and left parents. Whenever you
+ 
+
+ align:start position:0%
+parents and left parents. Whenever you
+you just walk up from A. Whenever you
+
+ align:start position:0%
+you just walk up from A. Whenever you
+ 
+
+ align:start position:0%
+you just walk up from A. Whenever you
+get a right parent, then you want that
+
+ align:start position:0%
+get a right parent, then you want that
+ 
+
+ align:start position:0%
+get a right parent, then you want that
+node and the subtree to its right. And
+
+ align:start position:0%
+node and the subtree to its right. And
+ 
+
+ align:start position:0%
+node and the subtree to its right. And
+so that will highlight these nodes. Same
+
+ align:start position:0%
+so that will highlight these nodes. Same
+ 
+
+ align:start position:0%
+so that will highlight these nodes. Same
+for B, but you look at left parents. And
+
+ align:start position:0%
+for B, but you look at left parents. And
+ 
+
+ align:start position:0%
+for B, but you look at left parents. And
+then you stop when those two searches
+
+ align:start position:0%
+then you stop when those two searches
+ 
+
+ align:start position:0%
+then you stop when those two searches
+converge. So you're going to do them in
+
+ align:start position:0%
+converge. So you're going to do them in
+ 
+
+ align:start position:0%
+converge. So you're going to do them in
+lock step. You do one step for A and B,
+
+ align:start position:0%
+lock step. You do one step for A and B,
+ 
+
+ align:start position:0%
+lock step. You do one step for A and B,
+one step for A and B, and when they
+
+ align:start position:0%
+one step for A and B, and when they
+ 
+
+ align:start position:0%
+one step for A and B, and when they
+happen to hit the same node, then you're
+
+ align:start position:0%
+happen to hit the same node, then you're
+ 
+
+ align:start position:0%
+happen to hit the same node, then you're
+done. You you add that node to your
+
+ align:start position:0%
+done. You you add that node to your
+ 
+
+ align:start position:0%
+done. You you add that node to your
+list.
+
+ align:start position:0%
+list.
+ 
+
+ align:start position:0%
+list.
+And what you end up with
+
+ align:start position:0%
+And what you end up with
+ 
+
+ align:start position:0%
+And what you end up with
+is a bunch of nodes
+
+ align:start position:0%
+is a bunch of nodes
+ 
+
+ align:start position:0%
+is a bunch of nodes
+and rooted sub trees.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The things I circled in blue is going to
+
+ align:start position:0%
+The things I circled in blue is going to
+ 
+
+ align:start position:0%
+The things I circled in blue is going to
+be my return value. So I'm going to
+
+ align:start position:0%
+be my return value. So I'm going to
+ 
+
+ align:start position:0%
+be my return value. So I'm going to
+return all of these nodes explicitly and
+
+ align:start position:0%
+return all of these nodes explicitly and
+ 
+
+ align:start position:0%
+return all of these nodes explicitly and
+I'm also going to return these sub
+
+ align:start position:0%
+I'm also going to return these sub
+ 
+
+ align:start position:0%
+I'm also going to return these sub
+trees. I'm not going to have to write
+
+ align:start position:0%
+trees. I'm not going to have to write
+ 
+
+ align:start position:0%
+trees. I'm not going to have to write
+them down. I'm just going to return the
+
+ align:start position:0%
+them down. I'm just going to return the
+ 
+
+ align:start position:0%
+them down. I'm just going to return the
+root of the sub tree and say hey look
+
+ align:start position:0%
+root of the sub tree and say hey look
+ 
+
+ align:start position:0%
+root of the sub tree and say hey look
+here's an entire subree that contains
+
+ align:start position:0%
+here's an entire subree that contains
+ 
+
+ align:start position:0%
+here's an entire subree that contains
+nodes points that are in the answer.
+
+ align:start position:0%
+nodes points that are in the answer.
+ 
+
+ align:start position:0%
+nodes points that are in the answer.
+I don't have to list them explicitly. I
+
+ align:start position:0%
+I don't have to list them explicitly. I
+ 
+
+ align:start position:0%
+I don't have to list them explicitly. I
+can just give you the tree. Then if I
+
+ align:start position:0%
+can just give you the tree. Then if I
+ 
+
+ align:start position:0%
+can just give you the tree. Then if I
+want to know how many results are in the
+
+ align:start position:0%
+want to know how many results are in the
+ 
+
+ align:start position:0%
+want to know how many results are in the
+answer, well just augment to store
+
+ align:start position:0%
+answer, well just augment to store
+ 
+
+ align:start position:0%
+answer, well just augment to store
+subree size at at the beginning. Then I
+
+ align:start position:0%
+subree size at at the beginning. Then I
+ 
+
+ align:start position:0%
+subree size at at the beginning. Then I
+can count how many nodes are down here,
+
+ align:start position:0%
+can count how many nodes are down here,
+ 
+
+ align:start position:0%
+can count how many nodes are down here,
+how many nodes are down here. Add that
+
+ align:start position:0%
+how many nodes are down here. Add that
+ 
+
+ align:start position:0%
+how many nodes are down here. Add that
+up for all the triangles and then also
+
+ align:start position:0%
+up for all the triangles and then also
+ 
+
+ align:start position:0%
+up for all the triangles and then also
+add one for each of the blue nodes. And
+
+ align:start position:0%
+add one for each of the blue nodes. And
+ 
+
+ align:start position:0%
+add one for each of the blue nodes. And
+then I've counted the number uh the size
+
+ align:start position:0%
+then I've counted the number uh the size
+ 
+
+ align:start position:0%
+then I've counted the number uh the size
+of the answer in how much time how many
+
+ align:start position:0%
+of the answer in how much time how many
+ 
+
+ align:start position:0%
+of the answer in how much time how many
+sub trees and how many nodes am I
+
+ align:start position:0%
+sub trees and how many nodes am I
+ 
+
+ align:start position:0%
+sub trees and how many nodes am I
+returning here
+
+ align:start position:0%
+returning here
+ 
+
+ align:start position:0%
+returning here
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log nodes and log n rooted sub trees
+
+ align:start position:0%
+log nodes and log n rooted sub trees
+ 
+
+ align:start position:0%
+log nodes and log n rooted sub trees
+because at each step I'm going up by one
+
+ align:start position:0%
+because at each step I'm going up by one
+ 
+
+ align:start position:0%
+because at each step I'm going up by one
+for a and up by one for b. So it's like
+
+ align:start position:0%
+for a and up by one for b. So it's like
+ 
+
+ align:start position:0%
+for a and up by one for b. So it's like
+two login.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So I would call this an implicit
+
+ align:start position:0%
+Cool. So I would call this an implicit
+ 
+
+ align:start position:0%
+Cool. So I would call this an implicit
+representation of the answer. From that
+
+ align:start position:0%
+representation of the answer. From that
+ 
+
+ align:start position:0%
+representation of the answer. From that
+implicit representation, you can do uh
+
+ align:start position:0%
+implicit representation, you can do uh
+ 
+
+ align:start position:0%
+implicit representation, you can do uh
+subree size augmentation to count the
+
+ align:start position:0%
+subree size augmentation to count the
+ 
+
+ align:start position:0%
+subree size augmentation to count the
+size of the answer. You can just start
+
+ align:start position:0%
+size of the answer. You can just start
+ 
+
+ align:start position:0%
+size of the answer. You can just start
+walking through one by one. Uh do an in
+
+ align:start position:0%
+walking through one by one. Uh do an in
+ 
+
+ align:start position:0%
+walking through one by one. Uh do an in
+order traversal of the trees and you'll
+
+ align:start position:0%
+order traversal of the trees and you'll
+ 
+
+ align:start position:0%
+order traversal of the trees and you'll
+get the first k points in the answer in
+
+ align:start position:0%
+get the first k points in the answer in
+ 
+
+ align:start position:0%
+get the first k points in the answer in
+order K time question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's right. As I'm walking up the
+
+ align:start position:0%
+That's right. As I'm walking up the
+ 
+
+ align:start position:0%
+That's right. As I'm walking up the
+tree, if it's a right parent, then I
+
+ align:start position:0%
+tree, if it's a right parent, then I
+ 
+
+ align:start position:0%
+tree, if it's a right parent, then I
+take the right sub tree and include that
+
+ align:start position:0%
+take the right sub tree and include that
+ 
+
+ align:start position:0%
+take the right sub tree and include that
+in the answer. If it's a left parent,
+
+ align:start position:0%
+in the answer. If it's a left parent,
+ 
+
+ align:start position:0%
+in the answer. If it's a left parent,
+just forget about it. Don't do anything.
+
+ align:start position:0%
+just forget about it. Don't do anything.
+ 
+
+ align:start position:0%
+just forget about it. Don't do anything.
+Just keep following parents. Whenever I
+
+ align:start position:0%
+Just keep following parents. Whenever I
+ 
+
+ align:start position:0%
+Just keep following parents. Whenever I
+do right parent, then I also add that
+
+ align:start position:0%
+do right parent, then I also add that
+ 
+
+ align:start position:0%
+do right parent, then I also add that
+node and the right sub tree. If it's a
+
+ align:start position:0%
+node and the right sub tree. If it's a
+ 
+
+ align:start position:0%
+node and the right sub tree. If it's a
+left parent, I don't include the node. I
+
+ align:start position:0%
+left parent, I don't include the node. I
+ 
+
+ align:start position:0%
+left parent, I don't include the node. I
+don't include the left subree. I also
+
+ align:start position:0%
+don't include the left subree. I also
+ 
+
+ align:start position:0%
+don't include the left subree. I also
+don't include the right sub tree. That
+
+ align:start position:0%
+don't include the right sub tree. That
+ 
+
+ align:start position:0%
+don't include the right sub tree. That
+would have too much stuff. Yep.
+
+ align:start position:0%
+would have too much stuff. Yep.
+ 
+
+ align:start position:0%
+would have too much stuff. Yep.
+It's easy when you see the picture. If
+
+ align:start position:0%
+It's easy when you see the picture. If
+ 
+
+ align:start position:0%
+It's easy when you see the picture. If
+we write down the algorithm, it's clear.
+
+ align:start position:0%
+we write down the algorithm, it's clear.
+ 
+
+ align:start position:0%
+we write down the algorithm, it's clear.
+It's left versus right uh parents. Yeah,
+
+ align:start position:0%
+It's left versus right uh parents. Yeah,
+ 
+
+ align:start position:0%
+It's left versus right uh parents. Yeah,
+would you include the left subree of B
+
+ align:start position:0%
+would you include the left subree of B
+ 
+
+ align:start position:0%
+would you include the left subree of B
+as well?
+
+ align:start position:0%
+as well?
+ 
+
+ align:start position:0%
+as well?
+I would also think you I should color
+
+ align:start position:0%
+I would also think you I should color
+ 
+
+ align:start position:0%
+I would also think you I should color
+the left subree of B. I didn't apply
+
+ align:start position:0%
+the left subree of B. I didn't apply
+ 
+
+ align:start position:0%
+the left subree of B. I didn't apply
+symmetry perfectly. So we have the right
+
+ align:start position:0%
+symmetry perfectly. So we have the right
+ 
+
+ align:start position:0%
+symmetry perfectly. So we have the right
+subree of A and the left subree of B.
+
+ align:start position:0%
+subree of A and the left subree of B.
+ 
+
+ align:start position:0%
+subree of A and the left subree of B.
+Thanks. Uh I would also include B
+
+ align:start position:0%
+Thanks. Uh I would also include B
+ 
+
+ align:start position:0%
+Thanks. Uh I would also include B
+if it's a closed interval.
+
+ align:start position:0%
+if it's a closed interval.
+ 
+
+ align:start position:0%
+if it's a closed interval.
+Okay, slightly more general. If A and B
+
+ align:start position:0%
+Okay, slightly more general. If A and B
+ 
+
+ align:start position:0%
+Okay, slightly more general. If A and B
+are not in the tree, then this is really
+
+ align:start position:0%
+are not in the tree, then this is really
+ 
+
+ align:start position:0%
+are not in the tree, then this is really
+the successor of A and this is the
+
+ align:start position:0%
+the successor of A and this is the
+ 
+
+ align:start position:0%
+the successor of A and this is the
+predecessor of B. Okay, so then A and B
+
+ align:start position:0%
+predecessor of B. Okay, so then A and B
+ 
+
+ align:start position:0%
+predecessor of B. Okay, so then A and B
+don't have to be in there. This is still
+
+ align:start position:0%
+don't have to be in there. This is still
+ 
+
+ align:start position:0%
+don't have to be in there. This is still
+a well- definfined range search. Okay,
+
+ align:start position:0%
+a well- definfined range search. Okay,
+ 
+
+ align:start position:0%
+a well- definfined range search. Okay,
+now we really understand 1D. I claim
+
+ align:start position:0%
+now we really understand 1D. I claim
+ 
+
+ align:start position:0%
+now we really understand 1D. I claim
+we're we've almost solved all
+
+ align:start position:0%
+we're we've almost solved all
+ 
+
+ align:start position:0%
+we're we've almost solved all
+dimensions.
+
+ align:start position:0%
+dimensions.
+ 
+
+ align:start position:0%
+dimensions.
+All we need is a little bit of
+
+ align:start position:0%
+All we need is a little bit of
+ 
+
+ align:start position:0%
+All we need is a little bit of
+augmentation.
+
+ align:start position:0%
+augmentation.
+ 
+
+ align:start position:0%
+augmentation.
+So, let's do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's start with uh 2D but then 3D and
+
+ align:start position:0%
+Let's start with uh 2D but then 3D and
+ 
+
+ align:start position:0%
+Let's start with uh 2D but then 3D and
+4D and so on will be easy.
+
+ align:start position:0%
+4D and so on will be easy.
+ 
+
+ align:start position:0%
+4D and so on will be easy.
+Uh why do I care about 4D range trees?
+
+ align:start position:0%
+Uh why do I care about 4D range trees?
+ 
+
+ align:start position:0%
+Uh why do I care about 4D range trees?
+Because maybe I have a database. Each of
+
+ align:start position:0%
+Because maybe I have a database. Each of
+ 
+
+ align:start position:0%
+Because maybe I have a database. Each of
+these points is actually just a row in
+
+ align:start position:0%
+these points is actually just a row in
+ 
+
+ align:start position:0%
+these points is actually just a row in
+the database which has four columns,
+
+ align:start position:0%
+the database which has four columns,
+ 
+
+ align:start position:0%
+the database which has four columns,
+four values. And what I'm trying to do
+
+ align:start position:0%
+four values. And what I'm trying to do
+ 
+
+ align:start position:0%
+four values. And what I'm trying to do
+here is like find all the people in my
+
+ align:start position:0%
+here is like find all the people in my
+ 
+
+ align:start position:0%
+here is like find all the people in my
+database that have a salary between this
+
+ align:start position:0%
+database that have a salary between this
+ 
+
+ align:start position:0%
+database that have a salary between this
+and this and have an age between this
+
+ align:start position:0%
+and this and have an age between this
+ 
+
+ align:start position:0%
+and this and have an age between this
+and that and have a profession between
+
+ align:start position:0%
+and that and have a profession between
+ 
+
+ align:start position:0%
+and that and have a profession between
+this and this. I don't know what that
+
+ align:start position:0%
+this and this. I don't know what that
+ 
+
+ align:start position:0%
+this and this. I don't know what that
+means but uh number of degrees between
+
+ align:start position:0%
+means but uh number of degrees between
+ 
+
+ align:start position:0%
+means but uh number of degrees between
+this and this whatever you if you have
+
+ align:start position:0%
+this and this whatever you if you have
+ 
+
+ align:start position:0%
+this and this whatever you if you have
+some numerical data representing a
+
+ align:start position:0%
+some numerical data representing a
+ 
+
+ align:start position:0%
+some numerical data representing a
+person or a thing in your database then
+
+ align:start position:0%
+person or a thing in your database then
+ 
+
+ align:start position:0%
+person or a thing in your database then
+this is a typical kind of search you
+
+ align:start position:0%
+this is a typical kind of search you
+ 
+
+ align:start position:0%
+this is a typical kind of search you
+want to do and you want to know how many
+
+ align:start position:0%
+want to do and you want to know how many
+ 
+
+ align:start position:0%
+want to do and you want to know how many
+answers you've got and then list the
+
+ align:start position:0%
+answers you've got and then list the
+ 
+
+ align:start position:0%
+answers you've got and then list the
+first hundred of them or whatever. So
+
+ align:start position:0%
+first hundred of them or whatever. So
+ 
+
+ align:start position:0%
+first hundred of them or whatever. So
+this is a this is a practical thing in
+
+ align:start position:0%
+this is a this is a practical thing in
+ 
+
+ align:start position:0%
+this is a this is a practical thing in
+databases. It's what you might call an
+
+ align:start position:0%
+databases. It's what you might call an
+ 
+
+ align:start position:0%
+databases. It's what you might call an
+index in the database.
+
+ align:start position:0%
+index in the database.
+ 
+
+ align:start position:0%
+index in the database.
+Okay. But let's start. Suppose your data
+
+ align:start position:0%
+Okay. But let's start. Suppose your data
+ 
+
+ align:start position:0%
+Okay. But let's start. Suppose your data
+is just two dimensional. You have two
+
+ align:start position:0%
+is just two dimensional. You have two
+ 
+
+ align:start position:0%
+is just two dimensional. You have two
+fields for every item.
+
+ align:start position:0%
+fields for every item.
+ 
+
+ align:start position:0%
+fields for every item.
+What I'm going to do is store a 1D range
+
+ align:start position:0%
+What I'm going to do is store a 1D range
+ 
+
+ align:start position:0%
+What I'm going to do is store a 1D range
+tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on all points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by X.
+
+ align:start position:0%
+by X.
+ 
+
+ align:start position:0%
+by X.
+So this this data structure makes sense
+
+ align:start position:0%
+So this this data structure makes sense
+ 
+
+ align:start position:0%
+So this this data structure makes sense
+if you fix a dimension. You say X is all
+
+ align:start position:0%
+if you fix a dimension. You say X is all
+ 
+
+ align:start position:0%
+if you fix a dimension. You say X is all
+I care about. Forget about Y.
+
+ align:start position:0%
+I care about. Forget about Y.
+ 
+
+ align:start position:0%
+I care about. Forget about Y.
+Still have my point set. Yeah. So
+
+ align:start position:0%
+Still have my point set. Yeah. So
+ 
+
+ align:start position:0%
+Still have my point set. Yeah. So
+what that corresponds to is projecting
+
+ align:start position:0%
+what that corresponds to is projecting
+ 
+
+ align:start position:0%
+what that corresponds to is projecting
+each of these points onto the X- axis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And now also projecting my query.
+
+ align:start position:0%
+Okay. And now also projecting my query.
+ 
+
+ align:start position:0%
+Okay. And now also projecting my query.
+So my new query is from here to here in
+
+ align:start position:0%
+So my new query is from here to here in
+ 
+
+ align:start position:0%
+So my new query is from here to here in
+X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so this data structure will let me
+
+ align:start position:0%
+And so this data structure will let me
+ 
+
+ align:start position:0%
+And so this data structure will let me
+find all these points that match in X.
+
+ align:start position:0%
+find all these points that match in X.
+ 
+
+ align:start position:0%
+find all these points that match in X.
+Now that's not good because there's
+
+ align:start position:0%
+Now that's not good because there's
+ 
+
+ align:start position:0%
+Now that's not good because there's
+actually only two points that I want.
+
+ align:start position:0%
+actually only two points that I want.
+ 
+
+ align:start position:0%
+actually only two points that I want.
+But I find four points in this picture.
+
+ align:start position:0%
+But I find four points in this picture.
+ 
+
+ align:start position:0%
+But I find four points in this picture.
+Okay, but it's half of the answer. It's
+
+ align:start position:0%
+Okay, but it's half of the answer. It's
+ 
+
+ align:start position:0%
+Okay, but it's half of the answer. It's
+all the X matches forgetting about Y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, here's the fun part.
+
+ align:start position:0%
+Now, here's the fun part.
+ 
+
+ align:start position:0%
+Now, here's the fun part.
+So, when I do a search here, I get login
+
+ align:start position:0%
+So, when I do a search here, I get login
+ 
+
+ align:start position:0%
+So, when I do a search here, I get login
+nodes.
+
+ align:start position:0%
+nodes.
+ 
+
+ align:start position:0%
+nodes.
+Nodes are good because they have a
+
+ align:start position:0%
+Nodes are good because they have a
+ 
+
+ align:start position:0%
+Nodes are good because they have a
+single key in them. So, I'll just check
+
+ align:start position:0%
+single key in them. So, I'll just check
+ 
+
+ align:start position:0%
+single key in them. So, I'll just check
+for each of those login nodes. Do they
+
+ align:start position:0%
+for each of those login nodes. Do they
+ 
+
+ align:start position:0%
+for each of those login nodes. Do they
+also match in Y? If they do, add it to
+
+ align:start position:0%
+also match in Y? If they do, add it to
+ 
+
+ align:start position:0%
+also match in Y? If they do, add it to
+the answer. If they don't, forget about
+
+ align:start position:0%
+the answer. If they don't, forget about
+ 
+
+ align:start position:0%
+the answer. If they don't, forget about
+it. Okay.
+
+ align:start position:0%
+it. Okay.
+ 
+
+ align:start position:0%
+it. Okay.
+But the tricky part is I also get login
+
+ align:start position:0%
+But the tricky part is I also get login
+ 
+
+ align:start position:0%
+But the tricky part is I also get login
+sub trees representing parts of the
+
+ align:start position:0%
+sub trees representing parts of the
+ 
+
+ align:start position:0%
+sub trees representing parts of the
+answer. So potentially, you know, it
+
+ align:start position:0%
+answer. So potentially, you know, it
+ 
+
+ align:start position:0%
+answer. So potentially, you know, it
+could be that your search, this this
+
+ align:start position:0%
+could be that your search, this this
+ 
+
+ align:start position:0%
+could be that your search, this this
+rectangle only has like five points. But
+
+ align:start position:0%
+rectangle only has like five points. But
+ 
+
+ align:start position:0%
+rectangle only has like five points. But
+if you look at this whole vertical slab,
+
+ align:start position:0%
+if you look at this whole vertical slab,
+ 
+
+ align:start position:0%
+if you look at this whole vertical slab,
+there's a billion points. Now, luckily,
+
+ align:start position:0%
+there's a billion points. Now, luckily,
+ 
+
+ align:start position:0%
+there's a billion points. Now, luckily,
+those billion points are represented
+
+ align:start position:0%
+those billion points are represented
+ 
+
+ align:start position:0%
+those billion points are represented
+succinctly. There's just login subtree
+
+ align:start position:0%
+succinctly. There's just login subtree
+ 
+
+ align:start position:0%
+succinctly. There's just login subtree
+saying, well, there's half a billion
+
+ align:start position:0%
+saying, well, there's half a billion
+ 
+
+ align:start position:0%
+saying, well, there's half a billion
+here and a quarter billion here and an
+
+ align:start position:0%
+here and a quarter billion here and an
+ 
+
+ align:start position:0%
+here and a quarter billion here and an
+eighth of a billion here. Uh
+
+ align:start position:0%
+eighth of a billion here. Uh
+ 
+
+ align:start position:0%
+eighth of a billion here. Uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+can now for each of those that big chunk
+
+ align:start position:0%
+can now for each of those that big chunk
+ 
+
+ align:start position:0%
+can now for each of those that big chunk
+of output I want to very quickly find
+
+ align:start position:0%
+of output I want to very quickly find
+ 
+
+ align:start position:0%
+of output I want to very quickly find
+the ones that match in Y. How would I
+
+ align:start position:0%
+the ones that match in Y. How would I
+ 
+
+ align:start position:0%
+the ones that match in Y. How would I
+find the ones matching in Y?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A range tree. Yeah. Okay. So here's what
+
+ align:start position:0%
+A range tree. Yeah. Okay. So here's what
+ 
+
+ align:start position:0%
+A range tree. Yeah. Okay. So here's what
+we're going to do. For each node
+
+ align:start position:0%
+we're going to do. For each node
+ 
+
+ align:start position:0%
+we're going to do. For each node
+uh let's call it X uh X X is overloaded.
+
+ align:start position:0%
+uh let's call it X uh X X is overloaded.
+ 
+
+ align:start position:0%
+uh let's call it X uh X X is overloaded.
+It's a coordinate so many things. Uh
+
+ align:start position:0%
+It's a coordinate so many things. Uh
+ 
+
+ align:start position:0%
+It's a coordinate so many things. Uh
+let's call it V. Uh in the
+
+ align:start position:0%
+let's call it V. Uh in the
+ 
+
+ align:start position:0%
+let's call it V. Uh in the
+this thing I'm going to call the X tree.
+
+ align:start position:0%
+this thing I'm going to call the X tree.
+ 
+
+ align:start position:0%
+this thing I'm going to call the X tree.
+So for every node in the x tree, I'm
+
+ align:start position:0%
+So for every node in the x tree, I'm
+ 
+
+ align:start position:0%
+So for every node in the x tree, I'm
+going to store another 1D range tree,
+
+ align:start position:0%
+going to store another 1D range tree,
+ 
+
+ align:start position:0%
+going to store another 1D range tree,
+but this time using the y-coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh on
+
+ align:start position:0%
+uh on
+ 
+
+ align:start position:0%
+uh on
+all points
+
+ align:start position:0%
+all points
+ 
+
+ align:start position:0%
+all points
+in these rooted
+
+ align:start position:0%
+in these rooted
+ 
+
+ align:start position:0%
+in these rooted
+subree.
+
+ align:start position:0%
+subree.
+ 
+
+ align:start position:0%
+subree.
+Okay, at this point I really want to
+
+ align:start position:0%
+Okay, at this point I really want to
+ 
+
+ align:start position:0%
+Okay, at this point I really want to
+draw a diagram.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, uh, rough picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+forgive me for not drawing this
+
+ align:start position:0%
+forgive me for not drawing this
+ 
+
+ align:start position:0%
+forgive me for not drawing this
+perfectly. Uh this is roughly what the
+
+ align:start position:0%
+perfectly. Uh this is roughly what the
+ 
+
+ align:start position:0%
+perfectly. Uh this is roughly what the
+answer looks like
+
+ align:start position:0%
+answer looks like
+ 
+
+ align:start position:0%
+answer looks like
+for the 1D range search here. This is
+
+ align:start position:0%
+for the 1D range search here. This is
+ 
+
+ align:start position:0%
+for the 1D range search here. This is
+the X tree and here I've searched
+
+ align:start position:0%
+the X tree and here I've searched
+ 
+
+ align:start position:0%
+the X tree and here I've searched
+between this value and this value in the
+
+ align:start position:0%
+between this value and this value in the
+ 
+
+ align:start position:0%
+between this value and this value in the
+X coordinate. Basically I have login
+
+ align:start position:0%
+X coordinate. Basically I have login
+ 
+
+ align:start position:0%
+X coordinate. Basically I have login
+nodes. I'm going to check those
+
+ align:start position:0%
+nodes. I'm going to check those
+ 
+
+ align:start position:0%
+nodes. I'm going to check those
+separately. Then I also have these login
+
+ align:start position:0%
+separately. Then I also have these login
+ 
+
+ align:start position:0%
+separately. Then I also have these login
+sub trees. For each of those login
+
+ align:start position:0%
+sub trees. For each of those login
+ 
+
+ align:start position:0%
+sub trees. For each of those login
+subrees
+
+ align:start position:0%
+subrees
+ 
+
+ align:start position:0%
+subrees
+I'm going to have a pointer. This is the
+
+ align:start position:0%
+I'm going to have a pointer. This is the
+ 
+
+ align:start position:0%
+I'm going to have a pointer. This is the
+augmentation
+
+ align:start position:0%
+augmentation
+ 
+
+ align:start position:0%
+augmentation
+to uh another tree of exactly the same
+
+ align:start position:0%
+to uh another tree of exactly the same
+ 
+
+ align:start position:0%
+to uh another tree of exactly the same
+size on exactly the same data that's in
+
+ align:start position:0%
+size on exactly the same data that's in
+ 
+
+ align:start position:0%
+size on exactly the same data that's in
+here. It's also over here, but it's
+
+ align:start position:0%
+here. It's also over here, but it's
+ 
+
+ align:start position:0%
+here. It's also over here, but it's
+going to be sorted by Y. And it's a 1D
+
+ align:start position:0%
+going to be sorted by Y. And it's a 1D
+ 
+
+ align:start position:0%
+going to be sorted by Y. And it's a 1D
+range tree by Y. Tons of data
+
+ align:start position:0%
+range tree by Y. Tons of data
+ 
+
+ align:start position:0%
+range tree by Y. Tons of data
+duplication here. I took all these
+
+ align:start position:0%
+duplication here. I took all these
+ 
+
+ align:start position:0%
+duplication here. I took all these
+points and I copied them over here, but
+
+ align:start position:0%
+points and I copied them over here, but
+ 
+
+ align:start position:0%
+points and I copied them over here, but
+then built a 1D range tree in Y. This is
+
+ align:start position:0%
+then built a 1D range tree in Y. This is
+ 
+
+ align:start position:0%
+then built a 1D range tree in Y. This is
+all pre-processing, so I'm not I don't
+
+ align:start position:0%
+all pre-processing, so I'm not I don't
+ 
+
+ align:start position:0%
+all pre-processing, so I'm not I don't
+have to pay for this. It's polinomial
+
+ align:start position:0%
+have to pay for this. It's polinomial
+ 
+
+ align:start position:0%
+have to pay for this. It's polinomial
+time. Don't worry too much. Um, and then
+
+ align:start position:0%
+time. Don't worry too much. Um, and then
+ 
+
+ align:start position:0%
+time. Don't worry too much. Um, and then
+I'm going to search in here. What does
+
+ align:start position:0%
+I'm going to search in here. What does
+ 
+
+ align:start position:0%
+I'm going to search in here. What does
+the search in there look? Well, I'm
+
+ align:start position:0%
+the search in there look? Well, I'm
+ 
+
+ align:start position:0%
+the search in there look? Well, I'm
+going to get, you know, some more trees
+
+ align:start position:0%
+going to get, you know, some more trees
+ 
+
+ align:start position:0%
+going to get, you know, some more trees
+and a couple more nodes.
+
+ align:start position:0%
+and a couple more nodes.
+ 
+
+ align:start position:0%
+and a couple more nodes.
+Okay, but now those items, those points
+
+ align:start position:0%
+Okay, but now those items, those points
+ 
+
+ align:start position:0%
+Okay, but now those items, those points
+match in X and Y because this whole
+
+ align:start position:0%
+match in X and Y because this whole
+ 
+
+ align:start position:0%
+match in X and Y because this whole
+subree matched in X and I just did a Y
+
+ align:start position:0%
+subree matched in X and I just did a Y
+ 
+
+ align:start position:0%
+subree matched in X and I just did a Y
+search. So, I found things that matched
+
+ align:start position:0%
+search. So, I found things that matched
+ 
+
+ align:start position:0%
+search. So, I found things that matched
+in Y. So, I get here another login trees
+
+ align:start position:0%
+in Y. So, I get here another login trees
+ 
+
+ align:start position:0%
+in Y. So, I get here another login trees
+that are actually in my answer. And for
+
+ align:start position:0%
+that are actually in my answer. And for
+ 
+
+ align:start position:0%
+that are actually in my answer. And for
+each of these nodes, I have a
+
+ align:start position:0%
+each of these nodes, I have a
+ 
+
+ align:start position:0%
+each of these nodes, I have a
+corresponding other data structure where
+
+ align:start position:0%
+corresponding other data structure where
+ 
+
+ align:start position:0%
+corresponding other data structure where
+I find I do a little search and I get
+
+ align:start position:0%
+I find I do a little search and I get
+ 
+
+ align:start position:0%
+I find I do a little search and I get
+part of the answer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, you get the idea. Everyone
+
+ align:start position:0%
+Okay, you get the idea. Everyone
+ 
+
+ align:start position:0%
+Okay, you get the idea. Everyone
+sounds huge. State structure sounds
+
+ align:start position:0%
+sounds huge. State structure sounds
+ 
+
+ align:start position:0%
+sounds huge. State structure sounds
+huge, but it's actually small. Uh, but
+
+ align:start position:0%
+huge, but it's actually small. Uh, but
+ 
+
+ align:start position:0%
+huge, but it's actually small. Uh, but
+one thing that's clear is it takes log
+
+ align:start position:0%
+one thing that's clear is it takes log
+ 
+
+ align:start position:0%
+one thing that's clear is it takes log
+squared n time because I have login
+
+ align:start position:0%
+squared n time because I have login
+ 
+
+ align:start position:0%
+squared n time because I have login
+triangles over here. For each of them I
+
+ align:start position:0%
+triangles over here. For each of them I
+ 
+
+ align:start position:0%
+triangles over here. For each of them I
+spend log n to find triangles over here.
+
+ align:start position:0%
+spend log n to find triangles over here.
+ 
+
+ align:start position:0%
+spend log n to find triangles over here.
+The total output is log squared nodes.
+
+ align:start position:0%
+The total output is log squared nodes.
+ 
+
+ align:start position:0%
+The total output is log squared nodes.
+For each of them I have to check
+
+ align:start position:0%
+For each of them I have to check
+ 
+
+ align:start position:0%
+For each of them I have to check
+manually plus uh and so over here I
+
+ align:start position:0%
+manually plus uh and so over here I
+ 
+
+ align:start position:0%
+manually plus uh and so over here I
+there's log n different searches I'm
+
+ align:start position:0%
+there's log n different searches I'm
+ 
+
+ align:start position:0%
+there's log n different searches I'm
+doing. Each one has size log n. So I get
+
+ align:start position:0%
+doing. Each one has size log n. So I get
+ 
+
+ align:start position:0%
+doing. Each one has size log n. So I get
+log squared little triangles that
+
+ align:start position:0%
+log squared little triangles that
+ 
+
+ align:start position:0%
+log squared little triangles that
+contain the results that match in x and
+
+ align:start position:0%
+contain the results that match in x and
+ 
+
+ align:start position:0%
+contain the results that match in x and
+y. How much space in this data
+
+ align:start position:0%
+y. How much space in this data
+ 
+
+ align:start position:0%
+y. How much space in this data
+structure?
+
+ align:start position:0%
+structure?
+ 
+
+ align:start position:0%
+structure?
+That's the remaining challenge.
+
+ align:start position:0%
+That's the remaining challenge.
+ 
+
+ align:start position:0%
+That's the remaining challenge.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+it's it's not that hard because
+
+ align:start position:0%
+it's it's not that hard because
+ 
+
+ align:start position:0%
+it's it's not that hard because
+if you look at a key
+
+ align:start position:0%
+if you look at a key
+ 
+
+ align:start position:0%
+if you look at a key
+so look at some key in this X tree.
+
+ align:start position:0%
+so look at some key in this X tree.
+ 
+
+ align:start position:0%
+so look at some key in this X tree.
+Let's say look at a leaf because that's
+
+ align:start position:0%
+Let's say look at a leaf because that's
+ 
+
+ align:start position:0%
+Let's say look at a leaf because that's
+maybe the most interesting.
+
+ align:start position:0%
+maybe the most interesting.
+ 
+
+ align:start position:0%
+maybe the most interesting.
+I'm going to start start over here.
+
+ align:start position:0%
+I'm going to start start over here.
+ 
+
+ align:start position:0%
+I'm going to start start over here.
+Sorry.
+
+ align:start position:0%
+Sorry.
+ 
+
+ align:start position:0%
+Sorry.
+Here's the X tree. X tree has linear
+
+ align:start position:0%
+Here's the X tree. X tree has linear
+ 
+
+ align:start position:0%
+Here's the X tree. X tree has linear
+size just one tree. If I look at some
+
+ align:start position:0%
+size just one tree. If I look at some
+ 
+
+ align:start position:0%
+size just one tree. If I look at some
+key value, well, uh, you know, it lives
+
+ align:start position:0%
+key value, well, uh, you know, it lives
+ 
+
+ align:start position:0%
+key value, well, uh, you know, it lives
+in this subree. And so there's going to
+
+ align:start position:0%
+in this subree. And so there's going to
+ 
+
+ align:start position:0%
+in this subree. And so there's going to
+be a corresponding blue structure of
+
+ align:start position:0%
+be a corresponding blue structure of
+ 
+
+ align:start position:0%
+be a corresponding blue structure of
+that size that contains that key. And
+
+ align:start position:0%
+that size that contains that key. And
+ 
+
+ align:start position:0%
+that size that contains that key. And
+then there's the parent. So there's a
+
+ align:start position:0%
+then there's the parent. So there's a
+ 
+
+ align:start position:0%
+then there's the parent. So there's a
+structure here that has a corresponding
+
+ align:start position:0%
+structure here that has a corresponding
+ 
+
+ align:start position:0%
+structure here that has a corresponding
+blue triangle. And then its parent,
+
+ align:start position:0%
+blue triangle. And then its parent,
+ 
+
+ align:start position:0%
+blue triangle. And then its parent,
+that's another triangle that contains
+
+ align:start position:0%
+that's another triangle that contains
+ 
+
+ align:start position:0%
+that's another triangle that contains
+I'm looking at a key uh K here. All of
+
+ align:start position:0%
+I'm looking at a key uh K here. All of
+ 
+
+ align:start position:0%
+I'm looking at a key uh K here. All of
+these triangles contain the key K. And
+
+ align:start position:0%
+these triangles contain the key K. And
+ 
+
+ align:start position:0%
+these triangles contain the key K. And
+so key K will be duplicated all this
+
+ align:start position:0%
+so key K will be duplicated all this
+ 
+
+ align:start position:0%
+so key K will be duplicated all this
+many times. But how many how many sub
+
+ align:start position:0%
+many times. But how many how many sub
+ 
+
+ align:start position:0%
+many times. But how many how many sub
+trees is K in log N
+
+ align:start position:0%
+trees is K in log N
+ 
+
+ align:start position:0%
+trees is K in log N
+each key fundamental fact about uh
+
+ align:start position:0%
+each key fundamental fact about uh
+ 
+
+ align:start position:0%
+each key fundamental fact about uh
+binary balanced binary search trees.
+
+ align:start position:0%
+binary balanced binary search trees.
+ 
+
+ align:start position:0%
+binary balanced binary search trees.
+Each key lives in log sub trees namely
+
+ align:start position:0%
+Each key lives in log sub trees namely
+ 
+
+ align:start position:0%
+Each key lives in log sub trees namely
+all of its ancestors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Awesome.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because that means the total space is n
+
+ align:start position:0%
+Because that means the total space is n
+ 
+
+ align:start position:0%
+Because that means the total space is n
+login.
+
+ align:start position:0%
+login.
+ 
+
+ align:start position:0%
+login.
+There's n keys. Each of them is
+
+ align:start position:0%
+There's n keys. Each of them is
+ 
+
+ align:start position:0%
+There's n keys. Each of them is
+duplicated at most log n times.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In general, log to the d minus one. So
+
+ align:start position:0%
+In general, log to the d minus one. So
+ 
+
+ align:start position:0%
+In general, log to the d minus one. So
+if you do it in 3D, each of the blue
+
+ align:start position:0%
+if you do it in 3D, each of the blue
+ 
+
+ align:start position:0%
+if you do it in 3D, each of the blue
+trees, every node in it has a
+
+ align:start position:0%
+trees, every node in it has a
+ 
+
+ align:start position:0%
+trees, every node in it has a
+corresponding pointer to a red tree
+
+ align:start position:0%
+corresponding pointer to a red tree
+ 
+
+ align:start position:0%
+corresponding pointer to a red tree
+that's sorted by Z. And you just keep
+
+ align:start position:0%
+that's sorted by Z. And you just keep
+ 
+
+ align:start position:0%
+that's sorted by Z. And you just keep
+doing this sort of nested searching.
+
+ align:start position:0%
+doing this sort of nested searching.
+ 
+
+ align:start position:0%
+doing this sort of nested searching.
+It's like super augmentation, but you're
+
+ align:start position:0%
+It's like super augmentation, but you're
+ 
+
+ align:start position:0%
+It's like super augmentation, but you're
+only losing a log factor each dimension
+
+ align:start position:0%
+only losing a log factor each dimension
+ 
+
+ align:start position:0%
+only losing a log factor each dimension
+you add.
\ No newline at end of file
diff --git a/xnEZqVz7iy4.txt b/xnEZqVz7iy4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8fdafeba7196db4c55f5eeba2b8a74a1966a0244
--- /dev/null
+++ b/xnEZqVz7iy4.txt
@@ -0,0 +1,515 @@
+align:start position:0%
+ 
+Algorithms is an interesting area
+
+ align:start position:0%
+Algorithms is an interesting area
+ 
+
+ align:start position:0%
+Algorithms is an interesting area
+because it's it's very creative to come
+
+ align:start position:0%
+because it's it's very creative to come
+ 
+
+ align:start position:0%
+because it's it's very creative to come
+up with new algorithms. Um there's often
+
+ align:start position:0%
+up with new algorithms. Um there's often
+ 
+
+ align:start position:0%
+up with new algorithms. Um there's often
+many ways to solve the same problem. Uh
+
+ align:start position:0%
+many ways to solve the same problem. Uh
+ 
+
+ align:start position:0%
+many ways to solve the same problem. Uh
+but unlike art say and algorithms
+
+ align:start position:0%
+but unlike art say and algorithms
+ 
+
+ align:start position:0%
+but unlike art say and algorithms
+they're uh quantifiable measures for how
+
+ align:start position:0%
+they're uh quantifiable measures for how
+ 
+
+ align:start position:0%
+they're uh quantifiable measures for how
+good you did. What is the running time
+
+ align:start position:0%
+good you did. What is the running time
+ 
+
+ align:start position:0%
+good you did. What is the running time
+of the thing you ended up with? How much
+
+ align:start position:0%
+of the thing you ended up with? How much
+ 
+
+ align:start position:0%
+of the thing you ended up with? How much
+space does it use? You is it efficient?
+
+ align:start position:0%
+space does it use? You is it efficient?
+ 
+
+ align:start position:0%
+space does it use? You is it efficient?
+Um so it's nice in that you can act it's
+
+ align:start position:0%
+Um so it's nice in that you can act it's
+ 
+
+ align:start position:0%
+Um so it's nice in that you can act it's
+easy to evaluate whether you kind of
+
+ align:start position:0%
+easy to evaluate whether you kind of
+ 
+
+ align:start position:0%
+easy to evaluate whether you kind of
+succeeded. Did you get the n login and
+
+ align:start position:0%
+succeeded. Did you get the n login and
+ 
+
+ align:start position:0%
+succeeded. Did you get the n login and
+algorithm? Did you get the fastest
+
+ align:start position:0%
+algorithm? Did you get the fastest
+ 
+
+ align:start position:0%
+algorithm? Did you get the fastest
+that's possible? Um but it's hard to
+
+ align:start position:0%
+that's possible? Um but it's hard to
+ 
+
+ align:start position:0%
+that's possible? Um but it's hard to
+measure uh students understanding
+
+ align:start position:0%
+measure uh students understanding
+ 
+
+ align:start position:0%
+measure uh students understanding
+because it's like did you get the
+
+ align:start position:0%
+because it's like did you get the
+ 
+
+ align:start position:0%
+because it's like did you get the
+creative trick that we had in mind or
+
+ align:start position:0%
+creative trick that we had in mind or
+ 
+
+ align:start position:0%
+creative trick that we had in mind or
+find another one that's just as good. U
+
+ align:start position:0%
+find another one that's just as good. U
+ 
+
+ align:start position:0%
+find another one that's just as good. U
+students may find a different creative
+
+ align:start position:0%
+students may find a different creative
+ 
+
+ align:start position:0%
+students may find a different creative
+trick that doesn't end up with as good
+
+ align:start position:0%
+trick that doesn't end up with as good
+ 
+
+ align:start position:0%
+trick that doesn't end up with as good
+an algorithm in the end. So uh we
+
+ align:start position:0%
+an algorithm in the end. So uh we
+ 
+
+ align:start position:0%
+an algorithm in the end. So uh we
+penalize that somewhat but for the most
+
+ align:start position:0%
+penalize that somewhat but for the most
+ 
+
+ align:start position:0%
+penalize that somewhat but for the most
+part we are happy when people get
+
+ align:start position:0%
+part we are happy when people get
+ 
+
+ align:start position:0%
+part we are happy when people get
+correct algorithms when they they
+
+ align:start position:0%
+correct algorithms when they they
+ 
+
+ align:start position:0%
+correct algorithms when they they
+understand the techniques well enough
+
+ align:start position:0%
+understand the techniques well enough
+ 
+
+ align:start position:0%
+understand the techniques well enough
+that they get an algorithm it's pretty
+
+ align:start position:0%
+that they get an algorithm it's pretty
+ 
+
+ align:start position:0%
+that they get an algorithm it's pretty
+good may not be the best uh but we
+
+ align:start position:0%
+good may not be the best uh but we
+ 
+
+ align:start position:0%
+good may not be the best uh but we
+consider that much better than they were
+
+ align:start position:0%
+consider that much better than they were
+ 
+
+ align:start position:0%
+consider that much better than they were
+using the right technique but they ended
+
+ align:start position:0%
+using the right technique but they ended
+ 
+
+ align:start position:0%
+using the right technique but they ended
+up using it wrong and so they end up
+
+ align:start position:0%
+up using it wrong and so they end up
+ 
+
+ align:start position:0%
+up using it wrong and so they end up
+with something that doesn't even work
+
+ align:start position:0%
+with something that doesn't even work
+ 
+
+ align:start position:0%
+with something that doesn't even work
+and that's that's much more uh
+
+ align:start position:0%
+and that's that's much more uh
+ 
+
+ align:start position:0%
+and that's that's much more uh
+discouraging I Yes. Um, but in any case,
+
+ align:start position:0%
+discouraging I Yes. Um, but in any case,
+ 
+
+ align:start position:0%
+discouraging I Yes. Um, but in any case,
+in a timed exam, it's really hard to
+
+ align:start position:0%
+in a timed exam, it's really hard to
+ 
+
+ align:start position:0%
+in a timed exam, it's really hard to
+expect students to be creative. So, in
+
+ align:start position:0%
+expect students to be creative. So, in
+ 
+
+ align:start position:0%
+expect students to be creative. So, in
+that setting, it's hard. We don't expect
+
+ align:start position:0%
+that setting, it's hard. We don't expect
+ 
+
+ align:start position:0%
+that setting, it's hard. We don't expect
+a lot of creativity. We try to keep the
+
+ align:start position:0%
+a lot of creativity. We try to keep the
+ 
+
+ align:start position:0%
+a lot of creativity. We try to keep the
+questions relatively simple. So, you
+
+ align:start position:0%
+questions relatively simple. So, you
+ 
+
+ align:start position:0%
+questions relatively simple. So, you
+need just one simple idea. If you're
+
+ align:start position:0%
+need just one simple idea. If you're
+ 
+
+ align:start position:0%
+need just one simple idea. If you're
+familiar with the material, it should
+
+ align:start position:0%
+familiar with the material, it should
+ 
+
+ align:start position:0%
+familiar with the material, it should
+come quickly. Doesn't always, but um, so
+
+ align:start position:0%
+come quickly. Doesn't always, but um, so
+ 
+
+ align:start position:0%
+come quickly. Doesn't always, but um, so
+problem sets are definitely an easier
+
+ align:start position:0%
+problem sets are definitely an easier
+ 
+
+ align:start position:0%
+problem sets are definitely an easier
+way for students to express creativity.
+
+ align:start position:0%
+way for students to express creativity.
+ 
+
+ align:start position:0%
+way for students to express creativity.
+gives them a little more time to think
+
+ align:start position:0%
+gives them a little more time to think
+ 
+
+ align:start position:0%
+gives them a little more time to think
+about the problem. Uh because some
+
+ align:start position:0%
+about the problem. Uh because some
+ 
+
+ align:start position:0%
+about the problem. Uh because some
+problems are going to come easy to some
+
+ align:start position:0%
+problems are going to come easy to some
+ 
+
+ align:start position:0%
+problems are going to come easy to some
+students and hard to others. It's going
+
+ align:start position:0%
+students and hard to others. It's going
+ 
+
+ align:start position:0%
+students and hard to others. It's going
+to be different each problem set. So
+
+ align:start position:0%
+to be different each problem set. So
+ 
+
+ align:start position:0%
+to be different each problem set. So
+that gives them they have a week to
+
+ align:start position:0%
+that gives them they have a week to
+ 
+
+ align:start position:0%
+that gives them they have a week to
+think about it and also to talk to
+
+ align:start position:0%
+think about it and also to talk to
+ 
+
+ align:start position:0%
+think about it and also to talk to
+others. We allow collaboration in the
+
+ align:start position:0%
+others. We allow collaboration in the
+ 
+
+ align:start position:0%
+others. We allow collaboration in the
+problem sets. So that makes it a lot
+
+ align:start position:0%
+problem sets. So that makes it a lot
+ 
+
+ align:start position:0%
+problem sets. So that makes it a lot
+easier to find solutions but still learn
+
+ align:start position:0%
+easier to find solutions but still learn
+ 
+
+ align:start position:0%
+easier to find solutions but still learn
+learn a lot from it. In the exams it's a
+
+ align:start position:0%
+learn a lot from it. In the exams it's a
+ 
+
+ align:start position:0%
+learn a lot from it. In the exams it's a
+lot harder. Um, in past years, we've
+
+ align:start position:0%
+lot harder. Um, in past years, we've
+ 
+
+ align:start position:0%
+lot harder. Um, in past years, we've
+tried uh take-home exams as a way to
+
+ align:start position:0%
+tried uh take-home exams as a way to
+ 
+
+ align:start position:0%
+tried uh take-home exams as a way to
+more accurately gauge how creative
+
+ align:start position:0%
+more accurately gauge how creative
+ 
+
+ align:start position:0%
+more accurately gauge how creative
+someone is in applying these techniques
+
+ align:start position:0%
+someone is in applying these techniques
+ 
+
+ align:start position:0%
+someone is in applying these techniques
+to design new algorithms. Uh, we didn't
+
+ align:start position:0%
+to design new algorithms. Uh, we didn't
+ 
+
+ align:start position:0%
+to design new algorithms. Uh, we didn't
+do that this year. Um, it's not clear
+
+ align:start position:0%
+do that this year. Um, it's not clear
+ 
+
+ align:start position:0%
+do that this year. Um, it's not clear
+what the right answer is. It's a
+
+ align:start position:0%
+what the right answer is. It's a
+ 
+
+ align:start position:0%
+what the right answer is. It's a
+definitely a challenge in teaching
+
+ align:start position:0%
+definitely a challenge in teaching
+ 
+
+ align:start position:0%
+definitely a challenge in teaching
+algorithms is how to evaluate whether
+
+ align:start position:0%
+algorithms is how to evaluate whether
+ 
+
+ align:start position:0%
+algorithms is how to evaluate whether
+someone can really apply the techniques
+
+ align:start position:0%
+someone can really apply the techniques
+ 
+
+ align:start position:0%
+someone can really apply the techniques
+in new and creative ways.
\ No newline at end of file
diff --git a/y4uc4t5vcdI.txt b/y4uc4t5vcdI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91358beeb5b2bbc1b9f2eeb2899a94e82ad05bfe
--- /dev/null
+++ b/y4uc4t5vcdI.txt
@@ -0,0 +1,14371 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a creative common license. Your support
+
+ align:start position:0%
+a creative common license. Your support
+ 
+
+ align:start position:0%
+a creative common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There were a couple questions on
+
+ align:start position:0%
+There were a couple questions on
+ 
+
+ align:start position:0%
+There were a couple questions on
+estimations. So, one person was as asked
+
+ align:start position:0%
+estimations. So, one person was as asked
+ 
+
+ align:start position:0%
+estimations. So, one person was as asked
+for answers to estimations. I try to
+
+ align:start position:0%
+for answers to estimations. I try to
+ 
+
+ align:start position:0%
+for answers to estimations. I try to
+give you orders of magnitude and give
+
+ align:start position:0%
+give you orders of magnitude and give
+ 
+
+ align:start position:0%
+give you orders of magnitude and give
+you a sense, but if I've missed some,
+
+ align:start position:0%
+you a sense, but if I've missed some,
+ 
+
+ align:start position:0%
+you a sense, but if I've missed some,
+let if you want to like email me and be
+
+ align:start position:0%
+let if you want to like email me and be
+ 
+
+ align:start position:0%
+let if you want to like email me and be
+like, "Hey, I never I never really got
+
+ align:start position:0%
+like, "Hey, I never I never really got
+ 
+
+ align:start position:0%
+like, "Hey, I never I never really got
+this one, let me know and I can review
+
+ align:start position:0%
+this one, let me know and I can review
+ 
+
+ align:start position:0%
+this one, let me know and I can review
+them." Um, and then also the other thing
+
+ align:start position:0%
+them." Um, and then also the other thing
+ 
+
+ align:start position:0%
+them." Um, and then also the other thing
+is I'm never going to give you a like
+
+ align:start position:0%
+is I'm never going to give you a like
+ 
+
+ align:start position:0%
+is I'm never going to give you a like
+6.7 answer because I'm rarely asking you
+
+ align:start position:0%
+6.7 answer because I'm rarely asking you
+ 
+
+ align:start position:0%
+6.7 answer because I'm rarely asking you
+an estimation that has that kind of
+
+ align:start position:0%
+an estimation that has that kind of
+ 
+
+ align:start position:0%
+an estimation that has that kind of
+answer. like some of them do, but
+
+ align:start position:0%
+answer. like some of them do, but
+ 
+
+ align:start position:0%
+answer. like some of them do, but
+usually it's not even that important
+
+ align:start position:0%
+usually it's not even that important
+ 
+
+ align:start position:0%
+usually it's not even that important
+that you get to 6.7. It's important that
+
+ align:start position:0%
+that you get to 6.7. It's important that
+ 
+
+ align:start position:0%
+that you get to 6.7. It's important that
+you get to an order of magnitude of 10.
+
+ align:start position:0%
+you get to an order of magnitude of 10.
+ 
+
+ align:start position:0%
+you get to an order of magnitude of 10.
+And as long as you're there, I'm happy.
+
+ align:start position:0%
+And as long as you're there, I'm happy.
+ 
+
+ align:start position:0%
+And as long as you're there, I'm happy.
+And so that's why I'm not getting to the
+
+ align:start position:0%
+And so that's why I'm not getting to the
+ 
+
+ align:start position:0%
+And so that's why I'm not getting to the
+exact answer, which I know is
+
+ align:start position:0%
+exact answer, which I know is
+ 
+
+ align:start position:0%
+exact answer, which I know is
+uncomfortable and not what you're used
+
+ align:start position:0%
+uncomfortable and not what you're used
+ 
+
+ align:start position:0%
+uncomfortable and not what you're used
+to um educationally, but it's what the
+
+ align:start position:0%
+to um educationally, but it's what the
+ 
+
+ align:start position:0%
+to um educationally, but it's what the
+estimation is there for. Um, another
+
+ align:start position:0%
+estimation is there for. Um, another
+ 
+
+ align:start position:0%
+estimation is there for. Um, another
+person mentioned that uh some people
+
+ align:start position:0%
+person mentioned that uh some people
+ 
+
+ align:start position:0%
+person mentioned that uh some people
+seem like they were taking a really long
+
+ align:start position:0%
+seem like they were taking a really long
+ 
+
+ align:start position:0%
+seem like they were taking a really long
+time and getting sort of lost in the
+
+ align:start position:0%
+time and getting sort of lost in the
+ 
+
+ align:start position:0%
+time and getting sort of lost in the
+estimations. Um so I try to give you the
+
+ align:start position:0%
+estimations. Um so I try to give you the
+ 
+
+ align:start position:0%
+estimations. Um so I try to give you the
+right amount of time for the estimation
+
+ align:start position:0%
+right amount of time for the estimation
+ 
+
+ align:start position:0%
+right amount of time for the estimation
+so that it's reasonable but it is
+
+ align:start position:0%
+so that it's reasonable but it is
+ 
+
+ align:start position:0%
+so that it's reasonable but it is
+something to practice
+
+ align:start position:0%
+something to practice
+ 
+
+ align:start position:0%
+something to practice
+getting more fasile with I guess. All
+
+ align:start position:0%
+getting more fasile with I guess. All
+ 
+
+ align:start position:0%
+getting more fasile with I guess. All
+right so wind energy. So does anyone
+
+ align:start position:0%
+right so wind energy. So does anyone
+ 
+
+ align:start position:0%
+right so wind energy. So does anyone
+know why we have wind on the earth?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah
+
+ align:start position:0%
+Yeah
+ 
+
+ align:start position:0%
+Yeah
+because we have heat.
+
+ align:start position:0%
+because we have heat.
+ 
+
+ align:start position:0%
+because we have heat.
+Yes. From
+
+ align:start position:0%
+Yes. From
+ 
+
+ align:start position:0%
+Yes. From
+sun.
+
+ align:start position:0%
+sun.
+ 
+
+ align:start position:0%
+sun.
+Yes. So, it's kind of funny because wind
+
+ align:start position:0%
+Yes. So, it's kind of funny because wind
+ 
+
+ align:start position:0%
+Yes. So, it's kind of funny because wind
+energy is basically a funky solar
+
+ align:start position:0%
+energy is basically a funky solar
+ 
+
+ align:start position:0%
+energy is basically a funky solar
+energy, which I I find I find pleasing.
+
+ align:start position:0%
+energy, which I I find I find pleasing.
+ 
+
+ align:start position:0%
+energy, which I I find I find pleasing.
+I don't know why, but I do. Um, there's
+
+ align:start position:0%
+I don't know why, but I do. Um, there's
+ 
+
+ align:start position:0%
+I don't know why, but I do. Um, there's
+also some coriololis effect stuff going
+
+ align:start position:0%
+also some coriololis effect stuff going
+ 
+
+ align:start position:0%
+also some coriololis effect stuff going
+around on with the the Earth rotating,
+
+ align:start position:0%
+around on with the the Earth rotating,
+ 
+
+ align:start position:0%
+around on with the the Earth rotating,
+but the um indirect solar energy
+
+ align:start position:0%
+but the um indirect solar energy
+ 
+
+ align:start position:0%
+but the um indirect solar energy
+component is uh more
+
+ align:start position:0%
+component is uh more
+ 
+
+ align:start position:0%
+component is uh more
+more easy to think about and I I think I
+
+ align:start position:0%
+more easy to think about and I I think I
+ 
+
+ align:start position:0%
+more easy to think about and I I think I
+think is the bigger component, though
+
+ align:start position:0%
+think is the bigger component, though
+ 
+
+ align:start position:0%
+think is the bigger component, though
+I'm not sure of that. Um so basically
+
+ align:start position:0%
+I'm not sure of that. Um so basically
+ 
+
+ align:start position:0%
+I'm not sure of that. Um so basically
+you have uneating even heating of the
+
+ align:start position:0%
+you have uneating even heating of the
+ 
+
+ align:start position:0%
+you have uneating even heating of the
+earth. Um hot air rises causes a
+
+ align:start position:0%
+earth. Um hot air rises causes a
+ 
+
+ align:start position:0%
+earth. Um hot air rises causes a
+pressure drop cold air rushes in and
+
+ align:start position:0%
+pressure drop cold air rushes in and
+ 
+
+ align:start position:0%
+pressure drop cold air rushes in and
+that movement is is what we're getting
+
+ align:start position:0%
+that movement is is what we're getting
+ 
+
+ align:start position:0%
+that movement is is what we're getting
+in wind. So that's
+
+ align:start position:0%
+in wind. So that's
+ 
+
+ align:start position:0%
+in wind. So that's
+what's going on there. Um, and then a
+
+ align:start position:0%
+what's going on there. Um, and then a
+ 
+
+ align:start position:0%
+what's going on there. Um, and then a
+lot of confusion sometimes happens like
+
+ align:start position:0%
+lot of confusion sometimes happens like
+ 
+
+ align:start position:0%
+lot of confusion sometimes happens like
+a lot of people see these turbines on or
+
+ align:start position:0%
+a lot of people see these turbines on or
+ 
+
+ align:start position:0%
+a lot of people see these turbines on or
+not turbines but mills on farms and it's
+
+ align:start position:0%
+not turbines but mills on farms and it's
+ 
+
+ align:start position:0%
+not turbines but mills on farms and it's
+confusing like what's this versus this?
+
+ align:start position:0%
+confusing like what's this versus this?
+ 
+
+ align:start position:0%
+confusing like what's this versus this?
+Is this just a junky version of this?
+
+ align:start position:0%
+Is this just a junky version of this?
+ 
+
+ align:start position:0%
+Is this just a junky version of this?
+And so the difference is if it's a mill,
+
+ align:start position:0%
+And so the difference is if it's a mill,
+ 
+
+ align:start position:0%
+And so the difference is if it's a mill,
+it's extracting mechanical power versus
+
+ align:start position:0%
+it's extracting mechanical power versus
+ 
+
+ align:start position:0%
+it's extracting mechanical power versus
+a turbine is extracting electrical
+
+ align:start position:0%
+a turbine is extracting electrical
+ 
+
+ align:start position:0%
+a turbine is extracting electrical
+power. So these mills are um
+
+ align:start position:0%
+power. So these mills are um
+ 
+
+ align:start position:0%
+power. So these mills are um
+very high torque devices that um move
+
+ align:start position:0%
+very high torque devices that um move
+ 
+
+ align:start position:0%
+very high torque devices that um move
+relatively slowly um in terms of their
+
+ align:start position:0%
+relatively slowly um in terms of their
+ 
+
+ align:start position:0%
+relatively slowly um in terms of their
+rotation and are used to do things like
+
+ align:start position:0%
+rotation and are used to do things like
+ 
+
+ align:start position:0%
+rotation and are used to do things like
+pump water or grind grain. They've been
+
+ align:start position:0%
+pump water or grind grain. They've been
+ 
+
+ align:start position:0%
+pump water or grind grain. They've been
+around forever. They're still really
+
+ align:start position:0%
+around forever. They're still really
+ 
+
+ align:start position:0%
+around forever. They're still really
+common in the US and in many places for
+
+ align:start position:0%
+common in the US and in many places for
+ 
+
+ align:start position:0%
+common in the US and in many places for
+pumping water. So if you drive across
+
+ align:start position:0%
+pumping water. So if you drive across
+ 
+
+ align:start position:0%
+pumping water. So if you drive across
+the country, you'll see these
+
+ align:start position:0%
+the country, you'll see these
+ 
+
+ align:start position:0%
+the country, you'll see these
+everywhere. Um, and they're still in use
+
+ align:start position:0%
+everywhere. Um, and they're still in use
+ 
+
+ align:start position:0%
+everywhere. Um, and they're still in use
+and they're really nice and a whole lot
+
+ align:start position:0%
+and they're really nice and a whole lot
+ 
+
+ align:start position:0%
+and they're really nice and a whole lot
+cheaper to build a mill than to build a
+
+ align:start position:0%
+cheaper to build a mill than to build a
+ 
+
+ align:start position:0%
+cheaper to build a mill than to build a
+turbine because you're you're going from
+
+ align:start position:0%
+turbine because you're you're going from
+ 
+
+ align:start position:0%
+turbine because you're you're going from
+mechanical work to mechanical work. So
+
+ align:start position:0%
+mechanical work to mechanical work. So
+ 
+
+ align:start position:0%
+mechanical work to mechanical work. So
+that's very direct and much much cheaper
+
+ align:start position:0%
+that's very direct and much much cheaper
+ 
+
+ align:start position:0%
+that's very direct and much much cheaper
+than doing the extra steps to get from
+
+ align:start position:0%
+than doing the extra steps to get from
+ 
+
+ align:start position:0%
+than doing the extra steps to get from
+um mechanical work to electric power
+
+ align:start position:0%
+um mechanical work to electric power
+ 
+
+ align:start position:0%
+um mechanical work to electric power
+generation. So a wind turbine in
+
+ align:start position:0%
+generation. So a wind turbine in
+ 
+
+ align:start position:0%
+generation. So a wind turbine in
+contrast is electrical power. They have
+
+ align:start position:0%
+contrast is electrical power. They have
+ 
+
+ align:start position:0%
+contrast is electrical power. They have
+been around a long time too, but not not
+
+ align:start position:0%
+been around a long time too, but not not
+ 
+
+ align:start position:0%
+been around a long time too, but not not
+you know basically for most of humanity
+
+ align:start position:0%
+you know basically for most of humanity
+ 
+
+ align:start position:0%
+you know basically for most of humanity
+long time. Um
+
+ align:start position:0%
+long time. Um
+ 
+
+ align:start position:0%
+long time. Um
+and again they're uh they're going to be
+
+ align:start position:0%
+and again they're uh they're going to be
+ 
+
+ align:start position:0%
+and again they're uh they're going to be
+moving very quickly at um much slower
+
+ align:start position:0%
+moving very quickly at um much slower
+ 
+
+ align:start position:0%
+moving very quickly at um much slower
+torque. The the solidity thing to think
+
+ align:start position:0%
+torque. The the solidity thing to think
+ 
+
+ align:start position:0%
+torque. The the solidity thing to think
+about is that when you want high torque,
+
+ align:start position:0%
+about is that when you want high torque,
+ 
+
+ align:start position:0%
+about is that when you want high torque,
+you want to be getting as much of the
+
+ align:start position:0%
+you want to be getting as much of the
+ 
+
+ align:start position:0%
+you want to be getting as much of the
+air hitting your blades as possible. So
+
+ align:start position:0%
+air hitting your blades as possible. So
+ 
+
+ align:start position:0%
+air hitting your blades as possible. So
+that's why there's often many many
+
+ align:start position:0%
+that's why there's often many many
+ 
+
+ align:start position:0%
+that's why there's often many many
+blades or really thick blades on a
+
+ align:start position:0%
+blades or really thick blades on a
+ 
+
+ align:start position:0%
+blades or really thick blades on a
+windmill. Whereas a wind turbine, you
+
+ align:start position:0%
+windmill. Whereas a wind turbine, you
+ 
+
+ align:start position:0%
+windmill. Whereas a wind turbine, you
+want um
+
+ align:start position:0%
+want um
+ 
+
+ align:start position:0%
+want um
+low solidity. So you want a low
+
+ align:start position:0%
+low solidity. So you want a low
+ 
+
+ align:start position:0%
+low solidity. So you want a low
+proportion of your blade to be in that
+
+ align:start position:0%
+proportion of your blade to be in that
+ 
+
+ align:start position:0%
+proportion of your blade to be in that
+swept area. So that's why a turbine is
+
+ align:start position:0%
+swept area. So that's why a turbine is
+ 
+
+ align:start position:0%
+swept area. So that's why a turbine is
+it looks very different.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so wind turbines I'm going to focus
+
+ align:start position:0%
+Um so wind turbines I'm going to focus
+ 
+
+ align:start position:0%
+Um so wind turbines I'm going to focus
+on. Um but I will go back to windmills a
+
+ align:start position:0%
+on. Um but I will go back to windmills a
+ 
+
+ align:start position:0%
+on. Um but I will go back to windmills a
+little bit at the end.
+
+ align:start position:0%
+little bit at the end.
+ 
+
+ align:start position:0%
+little bit at the end.
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have two types, right? The
+
+ align:start position:0%
+you have two types, right? The
+ 
+
+ align:start position:0%
+you have two types, right? The
+horizontal and the vertical axis. The
+
+ align:start position:0%
+horizontal and the vertical axis. The
+ 
+
+ align:start position:0%
+horizontal and the vertical axis. The
+vertical the horizontal axis is what
+
+ align:start position:0%
+vertical the horizontal axis is what
+ 
+
+ align:start position:0%
+vertical the horizontal axis is what
+you're used to seeing around here. Um
+
+ align:start position:0%
+you're used to seeing around here. Um
+ 
+
+ align:start position:0%
+you're used to seeing around here. Um
+and what's in the news a lot um because
+
+ align:start position:0%
+and what's in the news a lot um because
+ 
+
+ align:start position:0%
+and what's in the news a lot um because
+they can go to much higher heights and
+
+ align:start position:0%
+they can go to much higher heights and
+ 
+
+ align:start position:0%
+they can go to much higher heights and
+wind is much better the higher you go
+
+ align:start position:0%
+wind is much better the higher you go
+ 
+
+ align:start position:0%
+wind is much better the higher you go
+basically. Um, and so the horizontal
+
+ align:start position:0%
+basically. Um, and so the horizontal
+ 
+
+ align:start position:0%
+basically. Um, and so the horizontal
+wind axis turbines are um
+
+ align:start position:0%
+wind axis turbines are um
+ 
+
+ align:start position:0%
+wind axis turbines are um
+the more common thing at least in in my
+
+ align:start position:0%
+the more common thing at least in in my
+ 
+
+ align:start position:0%
+the more common thing at least in in my
+knowledge before I started doing any
+
+ align:start position:0%
+knowledge before I started doing any
+ 
+
+ align:start position:0%
+knowledge before I started doing any
+research into them. So there's the rotor
+
+ align:start position:0%
+research into them. So there's the rotor
+ 
+
+ align:start position:0%
+research into them. So there's the rotor
+and the mo the motor are at the top. It
+
+ align:start position:0%
+and the mo the motor are at the top. It
+ 
+
+ align:start position:0%
+and the mo the motor are at the top. It
+has to point into the wind. Um
+
+ align:start position:0%
+has to point into the wind. Um
+ 
+
+ align:start position:0%
+has to point into the wind. Um
+the higher you go the better. Um but you
+
+ align:start position:0%
+the higher you go the better. Um but you
+ 
+
+ align:start position:0%
+the higher you go the better. Um but you
+can imagine the higher you go adds costs
+
+ align:start position:0%
+can imagine the higher you go adds costs
+ 
+
+ align:start position:0%
+can imagine the higher you go adds costs
+and difficulty. Um, you often try to
+
+ align:start position:0%
+and difficulty. Um, you often try to
+ 
+
+ align:start position:0%
+and difficulty. Um, you often try to
+change your blade pitch to maximize the
+
+ align:start position:0%
+change your blade pitch to maximize the
+ 
+
+ align:start position:0%
+change your blade pitch to maximize the
+efficiency because depending on how fast
+
+ align:start position:0%
+efficiency because depending on how fast
+ 
+
+ align:start position:0%
+efficiency because depending on how fast
+the wind is, you want a different blade
+
+ align:start position:0%
+the wind is, you want a different blade
+ 
+
+ align:start position:0%
+the wind is, you want a different blade
+pitch. Um, and they're now really
+
+ align:start position:0%
+pitch. Um, and they're now really
+ 
+
+ align:start position:0%
+pitch. Um, and they're now really
+insanely huge.
+
+ align:start position:0%
+insanely huge.
+ 
+
+ align:start position:0%
+insanely huge.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+this is an insanely huge um se seven
+
+ align:start position:0%
+this is an insanely huge um se seven
+ 
+
+ align:start position:0%
+this is an insanely huge um se seven
+megawatt turbine which um I think you
+
+ align:start position:0%
+megawatt turbine which um I think you
+ 
+
+ align:start position:0%
+megawatt turbine which um I think you
+can sort of see like
+
+ align:start position:0%
+can sort of see like
+ 
+
+ align:start position:0%
+can sort of see like
+is there a truck down there or anything?
+
+ align:start position:0%
+is there a truck down there or anything?
+ 
+
+ align:start position:0%
+is there a truck down there or anything?
+It's it's hard to get scale when it gets
+
+ align:start position:0%
+It's it's hard to get scale when it gets
+ 
+
+ align:start position:0%
+It's it's hard to get scale when it gets
+this big but it's ridiculous. And some
+
+ align:start position:0%
+this big but it's ridiculous. And some
+ 
+
+ align:start position:0%
+this big but it's ridiculous. And some
+of the challenges you can imagine in
+
+ align:start position:0%
+of the challenges you can imagine in
+ 
+
+ align:start position:0%
+of the challenges you can imagine in
+building this thing is just getting all
+
+ align:start position:0%
+building this thing is just getting all
+ 
+
+ align:start position:0%
+building this thing is just getting all
+the materials to the site because you're
+
+ align:start position:0%
+the materials to the site because you're
+ 
+
+ align:start position:0%
+the materials to the site because you're
+probably not going to build your
+
+ align:start position:0%
+probably not going to build your
+ 
+
+ align:start position:0%
+probably not going to build your
+manufacturing plant of how how you build
+
+ align:start position:0%
+manufacturing plant of how how you build
+ 
+
+ align:start position:0%
+manufacturing plant of how how you build
+your your uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm still a little off the long blade
+
+ align:start position:0%
+I'm still a little off the long blade
+ 
+
+ align:start position:0%
+I'm still a little off the long blade
+blade. Thank you.
+
+ align:start position:0%
+blade. Thank you.
+ 
+
+ align:start position:0%
+blade. Thank you.
+You know, you're not going to build your
+
+ align:start position:0%
+You know, you're not going to build your
+ 
+
+ align:start position:0%
+You know, you're not going to build your
+blade right on the site where you're
+
+ align:start position:0%
+blade right on the site where you're
+ 
+
+ align:start position:0%
+blade right on the site where you're
+going to want to install your turbine
+
+ align:start position:0%
+going to want to install your turbine
+ 
+
+ align:start position:0%
+going to want to install your turbine
+probably. So then you have to get your
+
+ align:start position:0%
+probably. So then you have to get your
+ 
+
+ align:start position:0%
+probably. So then you have to get your
+blade there. So then you're actually
+
+ align:start position:0%
+blade there. So then you're actually
+ 
+
+ align:start position:0%
+blade there. So then you're actually
+limited by like the size of a train
+
+ align:start position:0%
+limited by like the size of a train
+ 
+
+ align:start position:0%
+limited by like the size of a train
+railroad car or a large truck or
+
+ align:start position:0%
+railroad car or a large truck or
+ 
+
+ align:start position:0%
+railroad car or a large truck or
+whatever. So there's all these crazy
+
+ align:start position:0%
+whatever. So there's all these crazy
+ 
+
+ align:start position:0%
+whatever. So there's all these crazy
+limits when you're getting up to be this
+
+ align:start position:0%
+limits when you're getting up to be this
+ 
+
+ align:start position:0%
+limits when you're getting up to be this
+enormous. Um
+
+ align:start position:0%
+enormous. Um
+ 
+
+ align:start position:0%
+enormous. Um
+so it's uh kind of remarkable and
+
+ align:start position:0%
+so it's uh kind of remarkable and
+ 
+
+ align:start position:0%
+so it's uh kind of remarkable and
+challenging and this is on of a scale
+
+ align:start position:0%
+challenging and this is on of a scale
+ 
+
+ align:start position:0%
+challenging and this is on of a scale
+that we're not going to be touching of
+
+ align:start position:0%
+that we're not going to be touching of
+ 
+
+ align:start position:0%
+that we're not going to be touching of
+course. Um but it's nice to sort of see
+
+ align:start position:0%
+course. Um but it's nice to sort of see
+ 
+
+ align:start position:0%
+course. Um but it's nice to sort of see
+the extreme of of what is out there. Um,
+
+ align:start position:0%
+the extreme of of what is out there. Um,
+ 
+
+ align:start position:0%
+the extreme of of what is out there. Um,
+so this is a 7 megawatt turbine that's
+
+ align:start position:0%
+so this is a 7 megawatt turbine that's
+ 
+
+ align:start position:0%
+so this is a 7 megawatt turbine that's
+actually running now, I believe, and
+
+ align:start position:0%
+actually running now, I believe, and
+ 
+
+ align:start position:0%
+actually running now, I believe, and
+they're currently building a 10 megawatt
+
+ align:start position:0%
+they're currently building a 10 megawatt
+ 
+
+ align:start position:0%
+they're currently building a 10 megawatt
+that'll be in production in a year or
+
+ align:start position:0%
+that'll be in production in a year or
+ 
+
+ align:start position:0%
+that'll be in production in a year or
+running in a year or two. So, um, which
+
+ align:start position:0%
+running in a year or two. So, um, which
+ 
+
+ align:start position:0%
+running in a year or two. So, um, which
+is a pretty big jump, 7 to 10. So, um,
+
+ align:start position:0%
+is a pretty big jump, 7 to 10. So, um,
+ 
+
+ align:start position:0%
+is a pretty big jump, 7 to 10. So, um,
+yeah, it's it's definitely an area
+
+ align:start position:0%
+yeah, it's it's definitely an area
+ 
+
+ align:start position:0%
+yeah, it's it's definitely an area
+that's taking off. Um, so how
+
+ align:start position:0%
+that's taking off. Um, so how
+ 
+
+ align:start position:0%
+that's taking off. Um, so how
+this is just classic sort of Berni
+
+ align:start position:0%
+this is just classic sort of Berni
+ 
+
+ align:start position:0%
+this is just classic sort of Berni
+drawing um to remind you how they're
+
+ align:start position:0%
+drawing um to remind you how they're
+ 
+
+ align:start position:0%
+drawing um to remind you how they're
+spinning in the wind and that the the
+
+ align:start position:0%
+spinning in the wind and that the the
+ 
+
+ align:start position:0%
+spinning in the wind and that the the
+motion is really dominated by lift not
+
+ align:start position:0%
+motion is really dominated by lift not
+ 
+
+ align:start position:0%
+motion is really dominated by lift not
+drag. Um, one thing to think about is
+
+ align:start position:0%
+drag. Um, one thing to think about is
+ 
+
+ align:start position:0%
+drag. Um, one thing to think about is
+the need to control the spin rate. Um,
+
+ align:start position:0%
+the need to control the spin rate. Um,
+ 
+
+ align:start position:0%
+the need to control the spin rate. Um,
+so you can imagine on days where there's
+
+ align:start position:0%
+so you can imagine on days where there's
+ 
+
+ align:start position:0%
+so you can imagine on days where there's
+not much wind, you might want to change
+
+ align:start position:0%
+not much wind, you might want to change
+ 
+
+ align:start position:0%
+not much wind, you might want to change
+the pitch of the blade to make sure
+
+ align:start position:0%
+the pitch of the blade to make sure
+ 
+
+ align:start position:0%
+the pitch of the blade to make sure
+you're maximizing um the wind you're
+
+ align:start position:0%
+you're maximizing um the wind you're
+ 
+
+ align:start position:0%
+you're maximizing um the wind you're
+capturing. But on hurricane days, you um
+
+ align:start position:0%
+capturing. But on hurricane days, you um
+ 
+
+ align:start position:0%
+capturing. But on hurricane days, you um
+have to make sure that your your wind
+
+ align:start position:0%
+have to make sure that your your wind
+ 
+
+ align:start position:0%
+have to make sure that your your wind
+turbine doesn't completely uh just spin
+
+ align:start position:0%
+turbine doesn't completely uh just spin
+ 
+
+ align:start position:0%
+turbine doesn't completely uh just spin
+out of control. And so this is a really
+
+ align:start position:0%
+out of control. And so this is a really
+ 
+
+ align:start position:0%
+out of control. And so this is a really
+nice relatively simple way to do it. So
+
+ align:start position:0%
+nice relatively simple way to do it. So
+ 
+
+ align:start position:0%
+nice relatively simple way to do it. So
+you can do it mechanically or um
+
+ align:start position:0%
+you can do it mechanically or um
+ 
+
+ align:start position:0%
+you can do it mechanically or um
+electrically or you can do it like
+
+ align:start position:0%
+electrically or you can do it like
+ 
+
+ align:start position:0%
+electrically or you can do it like
+manually. So like old wind turbines from
+
+ align:start position:0%
+manually. So like old wind turbines from
+ 
+
+ align:start position:0%
+manually. So like old wind turbines from
+wind windmills from you know 100 or 200
+
+ align:start position:0%
+wind windmills from you know 100 or 200
+ 
+
+ align:start position:0%
+wind windmills from you know 100 or 200
+years ago there was some poor guy whose
+
+ align:start position:0%
+years ago there was some poor guy whose
+ 
+
+ align:start position:0%
+years ago there was some poor guy whose
+job it was is to turn the turbine into
+
+ align:start position:0%
+job it was is to turn the turbine into
+ 
+
+ align:start position:0%
+job it was is to turn the turbine into
+the wind mill into the wind or not
+
+ align:start position:0%
+the wind mill into the wind or not
+ 
+
+ align:start position:0%
+the wind mill into the wind or not
+depending on how fast it was. So
+
+ align:start position:0%
+depending on how fast it was. So
+ 
+
+ align:start position:0%
+depending on how fast it was. So
+thankfully that there's been ways to
+
+ align:start position:0%
+thankfully that there's been ways to
+ 
+
+ align:start position:0%
+thankfully that there's been ways to
+optimize that either mechanically or
+
+ align:start position:0%
+optimize that either mechanically or
+ 
+
+ align:start position:0%
+optimize that either mechanically or
+um electrically. So this is a method
+
+ align:start position:0%
+um electrically. So this is a method
+ 
+
+ align:start position:0%
+um electrically. So this is a method
+where basically the
+
+ align:start position:0%
+where basically the
+ 
+
+ align:start position:0%
+where basically the
+weight of the tail and the turbine
+
+ align:start position:0%
+weight of the tail and the turbine
+ 
+
+ align:start position:0%
+weight of the tail and the turbine
+allows the tail to um stay connected to
+
+ align:start position:0%
+allows the tail to um stay connected to
+ 
+
+ align:start position:0%
+allows the tail to um stay connected to
+the the turbine so that the tail I'm
+
+ align:start position:0%
+the the turbine so that the tail I'm
+ 
+
+ align:start position:0%
+the the turbine so that the tail I'm
+getting lots of cute faces so I'll go
+
+ align:start position:0%
+getting lots of cute faces so I'll go
+ 
+
+ align:start position:0%
+getting lots of cute faces so I'll go
+slowly. Um so the turbine generally
+
+ align:start position:0%
+slowly. Um so the turbine generally
+ 
+
+ align:start position:0%
+slowly. Um so the turbine generally
+has a tail that's exactly
+
+ align:start position:0%
+has a tail that's exactly
+ 
+
+ align:start position:0%
+has a tail that's exactly
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+perpendicular. So this plane and the
+
+ align:start position:0%
+perpendicular. So this plane and the
+ 
+
+ align:start position:0%
+perpendicular. So this plane and the
+plane of the tail are perpendicular,
+
+ align:start position:0%
+plane of the tail are perpendicular,
+ 
+
+ align:start position:0%
+plane of the tail are perpendicular,
+right? So that the tail make sure it's
+
+ align:start position:0%
+right? So that the tail make sure it's
+ 
+
+ align:start position:0%
+right? So that the tail make sure it's
+always pointing into the wind, which is
+
+ align:start position:0%
+always pointing into the wind, which is
+ 
+
+ align:start position:0%
+always pointing into the wind, which is
+what you want, except when you're going
+
+ align:start position:0%
+what you want, except when you're going
+ 
+
+ align:start position:0%
+what you want, except when you're going
+too fast. Now you need the tail and the
+
+ align:start position:0%
+too fast. Now you need the tail and the
+ 
+
+ align:start position:0%
+too fast. Now you need the tail and the
+front of the turbine to not be
+
+ align:start position:0%
+front of the turbine to not be
+ 
+
+ align:start position:0%
+front of the turbine to not be
+perpendicular, but to start to to if
+
+ align:start position:0%
+perpendicular, but to start to to if
+ 
+
+ align:start position:0%
+perpendicular, but to start to to if
+hypothetically if you're in gales, you
+
+ align:start position:0%
+hypothetically if you're in gales, you
+ 
+
+ align:start position:0%
+hypothetically if you're in gales, you
+need it to be 100, you know, completely
+
+ align:start position:0%
+need it to be 100, you know, completely
+ 
+
+ align:start position:0%
+need it to be 100, you know, completely
+um rotated so that the wind is just
+
+ align:start position:0%
+um rotated so that the wind is just
+ 
+
+ align:start position:0%
+um rotated so that the wind is just
+passing by the turbine. or if you're in
+
+ align:start position:0%
+passing by the turbine. or if you're in
+ 
+
+ align:start position:0%
+passing by the turbine. or if you're in
+a moderate wind where it's too fast for
+
+ align:start position:0%
+a moderate wind where it's too fast for
+ 
+
+ align:start position:0%
+a moderate wind where it's too fast for
+the turbine but still um usable, you
+
+ align:start position:0%
+the turbine but still um usable, you
+ 
+
+ align:start position:0%
+the turbine but still um usable, you
+want it to be off a little bit. And so
+
+ align:start position:0%
+want it to be off a little bit. And so
+ 
+
+ align:start position:0%
+want it to be off a little bit. And so
+the way this works is that when the wind
+
+ align:start position:0%
+the way this works is that when the wind
+ 
+
+ align:start position:0%
+the way this works is that when the wind
+speed gets high enough, you get some
+
+ align:start position:0%
+speed gets high enough, you get some
+ 
+
+ align:start position:0%
+speed gets high enough, you get some
+lift in either the tail or the turbine.
+
+ align:start position:0%
+lift in either the tail or the turbine.
+ 
+
+ align:start position:0%
+lift in either the tail or the turbine.
+I forget how how it operates exactly.
+
+ align:start position:0%
+I forget how how it operates exactly.
+ 
+
+ align:start position:0%
+I forget how how it operates exactly.
+And so that allows this tail stop to be
+
+ align:start position:0%
+And so that allows this tail stop to be
+ 
+
+ align:start position:0%
+And so that allows this tail stop to be
+disengaged. So then the turbine rotates
+
+ align:start position:0%
+disengaged. So then the turbine rotates
+ 
+
+ align:start position:0%
+disengaged. So then the turbine rotates
+a little bit which you can sort of see
+
+ align:start position:0%
+a little bit which you can sort of see
+ 
+
+ align:start position:0%
+a little bit which you can sort of see
+from this top view. These are the front
+
+ align:start position:0%
+from this top view. These are the front
+ 
+
+ align:start position:0%
+from this top view. These are the front
+views and this is the top view. So then
+
+ align:start position:0%
+views and this is the top view. So then
+ 
+
+ align:start position:0%
+views and this is the top view. So then
+the turbine rotates a little bit and
+
+ align:start position:0%
+the turbine rotates a little bit and
+ 
+
+ align:start position:0%
+the turbine rotates a little bit and
+then the weight balances out and so then
+
+ align:start position:0%
+then the weight balances out and so then
+ 
+
+ align:start position:0%
+then the weight balances out and so then
+the top engages again and then it
+
+ align:start position:0%
+the top engages again and then it
+ 
+
+ align:start position:0%
+the top engages again and then it
+maintains this angle of orientation and
+
+ align:start position:0%
+maintains this angle of orientation and
+ 
+
+ align:start position:0%
+maintains this angle of orientation and
+then if the wind speed gets even higher
+
+ align:start position:0%
+then if the wind speed gets even higher
+ 
+
+ align:start position:0%
+then if the wind speed gets even higher
+it will again the weights will get out
+
+ align:start position:0%
+it will again the weights will get out
+ 
+
+ align:start position:0%
+it will again the weights will get out
+of balance, things will lift, the stop
+
+ align:start position:0%
+of balance, things will lift, the stop
+ 
+
+ align:start position:0%
+of balance, things will lift, the stop
+will disengage. So it's a really cool
+
+ align:start position:0%
+will disengage. So it's a really cool
+ 
+
+ align:start position:0%
+will disengage. So it's a really cool
+system um to keep keep your device safe.
+
+ align:start position:0%
+system um to keep keep your device safe.
+ 
+
+ align:start position:0%
+system um to keep keep your device safe.
+Um, and there's a lot of a lot of them
+
+ align:start position:0%
+Um, and there's a lot of a lot of them
+ 
+
+ align:start position:0%
+Um, and there's a lot of a lot of them
+out there. Uh, and so
+
+ align:start position:0%
+out there. Uh, and so
+ 
+
+ align:start position:0%
+out there. Uh, and so
+I just wanted to show an example of what
+
+ align:start position:0%
+I just wanted to show an example of what
+ 
+
+ align:start position:0%
+I just wanted to show an example of what
+happens when you don't remember where's
+
+ align:start position:0%
+happens when you don't remember where's
+ 
+
+ align:start position:0%
+happens when you don't remember where's
+my mouse
+
+ align:start position:0%
+my mouse
+ 
+
+ align:start position:0%
+my mouse
+to include that or don't do it right.
+
+ align:start position:0%
+to include that or don't do it right.
+ 
+
+ align:start position:0%
+to include that or don't do it right.
+Um, so watch carefully.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+that was an expensive day and they're
+
+ align:start position:0%
+that was an expensive day and they're
+ 
+
+ align:start position:0%
+that was an expensive day and they're
+really lucky that no one um was under
+
+ align:start position:0%
+really lucky that no one um was under
+ 
+
+ align:start position:0%
+really lucky that no one um was under
+there. Um so, I'll put it back so you
+
+ align:start position:0%
+there. Um so, I'll put it back so you
+ 
+
+ align:start position:0%
+there. Um so, I'll put it back so you
+can watch it again.
+
+ align:start position:0%
+can watch it again.
+ 
+
+ align:start position:0%
+can watch it again.
+Can you see? Were you saying you
+
+ align:start position:0%
+Can you see? Were you saying you
+ 
+
+ align:start position:0%
+Can you see? Were you saying you
+couldn't see it? Just did you make it
+
+ align:start position:0%
+couldn't see it? Just did you make it
+ 
+
+ align:start position:0%
+couldn't see it? Just did you make it
+work or
+
+ align:start position:0%
+work or
+ 
+
+ align:start position:0%
+work or
+So, what
+
+ align:start position:0%
+So, what
+ 
+
+ align:start position:0%
+So, what
+did the blade just fall off? Like did it
+
+ align:start position:0%
+did the blade just fall off? Like did it
+ 
+
+ align:start position:0%
+did the blade just fall off? Like did it
+just like
+
+ align:start position:0%
+just like
+ 
+
+ align:start position:0%
+just like
+so it rotated so fast that I believe one
+
+ align:start position:0%
+so it rotated so fast that I believe one
+ 
+
+ align:start position:0%
+so it rotated so fast that I believe one
+of the blades broke off and then once
+
+ align:start position:0%
+of the blades broke off and then once
+ 
+
+ align:start position:0%
+of the blades broke off and then once
+one breaks it's totally out of balance
+
+ align:start position:0%
+one breaks it's totally out of balance
+ 
+
+ align:start position:0%
+one breaks it's totally out of balance
+and the whole thing just falls apart and
+
+ align:start position:0%
+and the whole thing just falls apart and
+ 
+
+ align:start position:0%
+and the whole thing just falls apart and
+it's moving at such fast speed that
+
+ align:start position:0%
+it's moving at such fast speed that
+ 
+
+ align:start position:0%
+it's moving at such fast speed that
+really crazy dynamics are going on. Um
+
+ align:start position:0%
+really crazy dynamics are going on. Um
+ 
+
+ align:start position:0%
+really crazy dynamics are going on. Um
+so yeah, so there's really solid reasons
+
+ align:start position:0%
+so yeah, so there's really solid reasons
+ 
+
+ align:start position:0%
+so yeah, so there's really solid reasons
+to design these, right? Um especially
+
+ align:start position:0%
+to design these, right? Um especially
+ 
+
+ align:start position:0%
+to design these, right? Um especially
+when you're talking big scale, but even
+
+ align:start position:0%
+when you're talking big scale, but even
+ 
+
+ align:start position:0%
+when you're talking big scale, but even
+small scale. Um you can imagine in a
+
+ align:start position:0%
+small scale. Um you can imagine in a
+ 
+
+ align:start position:0%
+small scale. Um you can imagine in a
+hurricane it's not going to be a safe
+
+ align:start position:0%
+hurricane it's not going to be a safe
+ 
+
+ align:start position:0%
+hurricane it's not going to be a safe
+thing to be near. Um and the small ones
+
+ align:start position:0%
+thing to be near. Um and the small ones
+ 
+
+ align:start position:0%
+thing to be near. Um and the small ones
+are often
+
+ align:start position:0%
+are often
+ 
+
+ align:start position:0%
+are often
+near people.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So the typical components
+
+ align:start position:0%
+Okay. So the typical components
+ 
+
+ align:start position:0%
+Okay. So the typical components
+of a wind turbine, you have your rotor,
+
+ align:start position:0%
+of a wind turbine, you have your rotor,
+ 
+
+ align:start position:0%
+of a wind turbine, you have your rotor,
+you have your blades,
+
+ align:start position:0%
+you have your blades,
+ 
+
+ align:start position:0%
+you have your blades,
+you have a brake um because you want the
+
+ align:start position:0%
+you have a brake um because you want the
+ 
+
+ align:start position:0%
+you have a brake um because you want the
+turbine to be turning at a certain speed
+
+ align:start position:0%
+turbine to be turning at a certain speed
+ 
+
+ align:start position:0%
+turbine to be turning at a certain speed
+ideally and so you may need to break
+
+ align:start position:0%
+ideally and so you may need to break
+ 
+
+ align:start position:0%
+ideally and so you may need to break
+provide braking before you're providing
+
+ align:start position:0%
+provide braking before you're providing
+ 
+
+ align:start position:0%
+provide braking before you're providing
+rotation out of the wind. That's another
+
+ align:start position:0%
+rotation out of the wind. That's another
+ 
+
+ align:start position:0%
+rotation out of the wind. That's another
+you know smaller step you can take. Um,
+
+ align:start position:0%
+you know smaller step you can take. Um,
+ 
+
+ align:start position:0%
+you know smaller step you can take. Um,
+you have a gear box to get the speed to
+
+ align:start position:0%
+you have a gear box to get the speed to
+ 
+
+ align:start position:0%
+you have a gear box to get the speed to
+the right speed to power your generator.
+
+ align:start position:0%
+the right speed to power your generator.
+ 
+
+ align:start position:0%
+the right speed to power your generator.
+Um, typically on a fancier wind turbine,
+
+ align:start position:0%
+Um, typically on a fancier wind turbine,
+ 
+
+ align:start position:0%
+Um, typically on a fancier wind turbine,
+there's an anometer that provides the
+
+ align:start position:0%
+there's an anometer that provides the
+ 
+
+ align:start position:0%
+there's an anometer that provides the
+electrical control with these yaw drives
+
+ align:start position:0%
+electrical control with these yaw drives
+ 
+
+ align:start position:0%
+electrical control with these yaw drives
+and motors to rotate the um, turbine
+
+ align:start position:0%
+and motors to rotate the um, turbine
+ 
+
+ align:start position:0%
+and motors to rotate the um, turbine
+into the wind or out of the wind to
+
+ align:start position:0%
+into the wind or out of the wind to
+ 
+
+ align:start position:0%
+into the wind or out of the wind to
+maximize uh, the speed of your turbine
+
+ align:start position:0%
+maximize uh, the speed of your turbine
+ 
+
+ align:start position:0%
+maximize uh, the speed of your turbine
+and then your tower. And then so all the
+
+ align:start position:0%
+and then your tower. And then so all the
+ 
+
+ align:start position:0%
+and then your tower. And then so all the
+uh electricity is being generated in
+
+ align:start position:0%
+uh electricity is being generated in
+ 
+
+ align:start position:0%
+uh electricity is being generated in
+this part of the body and then the power
+
+ align:start position:0%
+this part of the body and then the power
+ 
+
+ align:start position:0%
+this part of the body and then the power
+is just going down the um the tower and
+
+ align:start position:0%
+is just going down the um the tower and
+ 
+
+ align:start position:0%
+is just going down the um the tower and
+you can imagine the challenge of when
+
+ align:start position:0%
+you can imagine the challenge of when
+ 
+
+ align:start position:0%
+you can imagine the challenge of when
+you need to do maintenance on this and
+
+ align:start position:0%
+you need to do maintenance on this and
+ 
+
+ align:start position:0%
+you need to do maintenance on this and
+you're talking about something really
+
+ align:start position:0%
+you're talking about something really
+ 
+
+ align:start position:0%
+you're talking about something really
+high up that you have to deal with it.
+
+ align:start position:0%
+high up that you have to deal with it.
+ 
+
+ align:start position:0%
+high up that you have to deal with it.
+So, the smaller turbine or turbines that
+
+ align:start position:0%
+So, the smaller turbine or turbines that
+ 
+
+ align:start position:0%
+So, the smaller turbine or turbines that
+we'll be looking at, they're all on
+
+ align:start position:0%
+we'll be looking at, they're all on
+ 
+
+ align:start position:0%
+we'll be looking at, they're all on
+guide wires and on a pivot so that you
+
+ align:start position:0%
+guide wires and on a pivot so that you
+ 
+
+ align:start position:0%
+guide wires and on a pivot so that you
+can rotate them down so you don't have
+
+ align:start position:0%
+can rotate them down so you don't have
+ 
+
+ align:start position:0%
+can rotate them down so you don't have
+to climb up to do maintenance because
+
+ align:start position:0%
+to climb up to do maintenance because
+ 
+
+ align:start position:0%
+to climb up to do maintenance because
+that requires a much sturdier tower and
+
+ align:start position:0%
+that requires a much sturdier tower and
+ 
+
+ align:start position:0%
+that requires a much sturdier tower and
+is a much more dangerous job.
+
+ align:start position:0%
+is a much more dangerous job.
+ 
+
+ align:start position:0%
+is a much more dangerous job.
+Um, some installation considerations
+
+ align:start position:0%
+Um, some installation considerations
+ 
+
+ align:start position:0%
+Um, some installation considerations
+that one would think would be obvious
+
+ align:start position:0%
+that one would think would be obvious
+ 
+
+ align:start position:0%
+that one would think would be obvious
+but aren't always. So, this is a a wind
+
+ align:start position:0%
+but aren't always. So, this is a a wind
+ 
+
+ align:start position:0%
+but aren't always. So, this is a a wind
+turbine that's been installed basically
+
+ align:start position:0%
+turbine that's been installed basically
+ 
+
+ align:start position:0%
+turbine that's been installed basically
+on a rooftop um by some trees. So, it's
+
+ align:start position:0%
+on a rooftop um by some trees. So, it's
+ 
+
+ align:start position:0%
+on a rooftop um by some trees. So, it's
+got two types of uh
+
+ align:start position:0%
+got two types of uh
+ 
+
+ align:start position:0%
+got two types of uh
+objects that are blocking the wind
+
+ align:start position:0%
+objects that are blocking the wind
+ 
+
+ align:start position:0%
+objects that are blocking the wind
+entirely. So, this, you know, was a many
+
+ align:start position:0%
+entirely. So, this, you know, was a many
+ 
+
+ align:start position:0%
+entirely. So, this, you know, was a many
+thousand installation that's probably
+
+ align:start position:0%
+thousand installation that's probably
+ 
+
+ align:start position:0%
+thousand installation that's probably
+providing zero electricity because it
+
+ align:start position:0%
+providing zero electricity because it
+ 
+
+ align:start position:0%
+providing zero electricity because it
+the wind may be sufficient 30 meters up,
+
+ align:start position:0%
+the wind may be sufficient 30 meters up,
+ 
+
+ align:start position:0%
+the wind may be sufficient 30 meters up,
+but right there is never going to be
+
+ align:start position:0%
+but right there is never going to be
+ 
+
+ align:start position:0%
+but right there is never going to be
+sufficient. Um, so the good 30 meters,
+
+ align:start position:0%
+sufficient. Um, so the good 30 meters,
+ 
+
+ align:start position:0%
+sufficient. Um, so the good 30 meters,
+30 feet. Um, a good rule of thumb is you
+
+ align:start position:0%
+30 feet. Um, a good rule of thumb is you
+ 
+
+ align:start position:0%
+30 feet. Um, a good rule of thumb is you
+want your turbine to be 30 feet above
+
+ align:start position:0%
+want your turbine to be 30 feet above
+ 
+
+ align:start position:0%
+want your turbine to be 30 feet above
+any obstruction within 300 ft. Um, and
+
+ align:start position:0%
+any obstruction within 300 ft. Um, and
+ 
+
+ align:start position:0%
+any obstruction within 300 ft. Um, and
+so obstructions include like houses and
+
+ align:start position:0%
+so obstructions include like houses and
+ 
+
+ align:start position:0%
+so obstructions include like houses and
+plants and anything else that might be
+
+ align:start position:0%
+plants and anything else that might be
+ 
+
+ align:start position:0%
+plants and anything else that might be
+in the way. So, next up is vertical
+
+ align:start position:0%
+in the way. So, next up is vertical
+ 
+
+ align:start position:0%
+in the way. So, next up is vertical
+access wind turbines. And you can see
+
+ align:start position:0%
+access wind turbines. And you can see
+ 
+
+ align:start position:0%
+access wind turbines. And you can see
+there's a huge range of them. Um, and
+
+ align:start position:0%
+there's a huge range of them. Um, and
+ 
+
+ align:start position:0%
+there's a huge range of them. Um, and
+you probably haven't seen most of these
+
+ align:start position:0%
+you probably haven't seen most of these
+ 
+
+ align:start position:0%
+you probably haven't seen most of these
+in production because again, they're
+
+ align:start position:0%
+in production because again, they're
+ 
+
+ align:start position:0%
+in production because again, they're
+they're not um
+
+ align:start position:0%
+they're not um
+ 
+
+ align:start position:0%
+they're not um
+they don't have the same level of
+
+ align:start position:0%
+they don't have the same level of
+ 
+
+ align:start position:0%
+they don't have the same level of
+efficiencies and benefits that um
+
+ align:start position:0%
+efficiencies and benefits that um
+ 
+
+ align:start position:0%
+efficiencies and benefits that um
+horizontal axis wind turbines have, but
+
+ align:start position:0%
+horizontal axis wind turbines have, but
+ 
+
+ align:start position:0%
+horizontal axis wind turbines have, but
+they're a whole lot cheaper and easier
+
+ align:start position:0%
+they're a whole lot cheaper and easier
+ 
+
+ align:start position:0%
+they're a whole lot cheaper and easier
+to build. So, for small scale solutions,
+
+ align:start position:0%
+to build. So, for small scale solutions,
+ 
+
+ align:start position:0%
+to build. So, for small scale solutions,
+they're they can be really ideal.
+
+ align:start position:0%
+they're they can be really ideal.
+ 
+
+ align:start position:0%
+they're they can be really ideal.
+There's a bunch of different names of
+
+ align:start position:0%
+There's a bunch of different names of
+ 
+
+ align:start position:0%
+There's a bunch of different names of
+these different types. So, for example,
+
+ align:start position:0%
+these different types. So, for example,
+ 
+
+ align:start position:0%
+these different types. So, for example,
+this is called a Darius wind turbine.
+
+ align:start position:0%
+this is called a Darius wind turbine.
+ 
+
+ align:start position:0%
+this is called a Darius wind turbine.
+This is a Savonius wind turbine, which
+
+ align:start position:0%
+This is a Savonius wind turbine, which
+ 
+
+ align:start position:0%
+This is a Savonius wind turbine, which
+you'll be building on Friday. Um, and
+
+ align:start position:0%
+you'll be building on Friday. Um, and
+ 
+
+ align:start position:0%
+you'll be building on Friday. Um, and
+this is a cool combo. Savonius, Darius.
+
+ align:start position:0%
+this is a cool combo. Savonius, Darius.
+ 
+
+ align:start position:0%
+this is a cool combo. Savonius, Darius.
+Um, this the Savonius will start up
+
+ align:start position:0%
+Um, this the Savonius will start up
+ 
+
+ align:start position:0%
+Um, this the Savonius will start up
+automatically in wind and the Darius
+
+ align:start position:0%
+automatically in wind and the Darius
+ 
+
+ align:start position:0%
+automatically in wind and the Darius
+won't, but the Darius gets a little bit
+
+ align:start position:0%
+won't, but the Darius gets a little bit
+ 
+
+ align:start position:0%
+won't, but the Darius gets a little bit
+better efficiency. So, the combining
+
+ align:start position:0%
+better efficiency. So, the combining
+ 
+
+ align:start position:0%
+better efficiency. So, the combining
+sort of gets gets you the best of both
+
+ align:start position:0%
+sort of gets gets you the best of both
+ 
+
+ align:start position:0%
+sort of gets gets you the best of both
+worlds with some drawbacks of course
+
+ align:start position:0%
+worlds with some drawbacks of course
+ 
+
+ align:start position:0%
+worlds with some drawbacks of course
+too. Um, and so these power traffic
+
+ align:start position:0%
+too. Um, and so these power traffic
+ 
+
+ align:start position:0%
+too. Um, and so these power traffic
+lights in Taiwan. Um, so there are
+
+ align:start position:0%
+lights in Taiwan. Um, so there are
+ 
+
+ align:start position:0%
+lights in Taiwan. Um, so there are
+places where these are installed
+
+ align:start position:0%
+places where these are installed
+ 
+
+ align:start position:0%
+places where these are installed
+effectively. Um,
+
+ align:start position:0%
+effectively. Um,
+ 
+
+ align:start position:0%
+effectively. Um,
+and they're kind of cool. Um because as
+
+ align:start position:0%
+and they're kind of cool. Um because as
+ 
+
+ align:start position:0%
+and they're kind of cool. Um because as
+you can see here
+
+ align:start position:0%
+you can see here
+ 
+
+ align:start position:0%
+you can see here
+um you can almost build them out of
+
+ align:start position:0%
+um you can almost build them out of
+ 
+
+ align:start position:0%
+um you can almost build them out of
+anything and you will build them out of
+
+ align:start position:0%
+anything and you will build them out of
+ 
+
+ align:start position:0%
+anything and you will build them out of
+anything on Friday. Hey Amit, do we have
+
+ align:start position:0%
+anything on Friday. Hey Amit, do we have
+ 
+
+ align:start position:0%
+anything on Friday. Hey Amit, do we have
+enough plastic bottles? Speaking of
+
+ align:start position:0%
+enough plastic bottles? Speaking of
+ 
+
+ align:start position:0%
+enough plastic bottles? Speaking of
+which, for Friday.
+
+ align:start position:0%
+which, for Friday.
+ 
+
+ align:start position:0%
+which, for Friday.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+added to your homework is on Friday you
+
+ align:start position:0%
+added to your homework is on Friday you
+ 
+
+ align:start position:0%
+added to your homework is on Friday you
+need to bring in a plastic bottle like a
+
+ align:start position:0%
+need to bring in a plastic bottle like a
+ 
+
+ align:start position:0%
+need to bring in a plastic bottle like a
+Gatorade bottle, a 2 liter bottle,
+
+ align:start position:0%
+Gatorade bottle, a 2 liter bottle,
+ 
+
+ align:start position:0%
+Gatorade bottle, a 2 liter bottle,
+whatever. Um it doesn't it doesn't have
+
+ align:start position:0%
+whatever. Um it doesn't it doesn't have
+ 
+
+ align:start position:0%
+whatever. Um it doesn't it doesn't have
+to be two liters. It can be one liter or
+
+ align:start position:0%
+to be two liters. It can be one liter or
+ 
+
+ align:start position:0%
+to be two liters. It can be one liter or
+h you know like a 20 oz can uh bottle.
+
+ align:start position:0%
+h you know like a 20 oz can uh bottle.
+ 
+
+ align:start position:0%
+h you know like a 20 oz can uh bottle.
+But we need plastic bottles. If everyone
+
+ align:start position:0%
+But we need plastic bottles. If everyone
+ 
+
+ align:start position:0%
+But we need plastic bottles. If everyone
+bring brings one, we'll be in good
+
+ align:start position:0%
+bring brings one, we'll be in good
+ 
+
+ align:start position:0%
+bring brings one, we'll be in good
+shape. Is that doable? If you check the
+
+ align:start position:0%
+shape. Is that doable? If you check the
+ 
+
+ align:start position:0%
+shape. Is that doable? If you check the
+recycling bins walking to class, you'll
+
+ align:start position:0%
+recycling bins walking to class, you'll
+ 
+
+ align:start position:0%
+recycling bins walking to class, you'll
+find one. Um, cool. So,
+
+ align:start position:0%
+find one. Um, cool. So,
+ 
+
+ align:start position:0%
+find one. Um, cool. So,
+the some of the advantages, they're
+
+ align:start position:0%
+the some of the advantages, they're
+ 
+
+ align:start position:0%
+the some of the advantages, they're
+close to the ground, so you don't have
+
+ align:start position:0%
+close to the ground, so you don't have
+ 
+
+ align:start position:0%
+close to the ground, so you don't have
+any line losses um associ comparative to
+
+ align:start position:0%
+any line losses um associ comparative to
+ 
+
+ align:start position:0%
+any line losses um associ comparative to
+the horizontal axis wind turbine. Um,
+
+ align:start position:0%
+the horizontal axis wind turbine. Um,
+ 
+
+ align:start position:0%
+the horizontal axis wind turbine. Um,
+you don't need any yaw or pitch control
+
+ align:start position:0%
+you don't need any yaw or pitch control
+ 
+
+ align:start position:0%
+you don't need any yaw or pitch control
+because they're just in the wind.
+
+ align:start position:0%
+because they're just in the wind.
+ 
+
+ align:start position:0%
+because they're just in the wind.
+They're intended to be in the wind and
+
+ align:start position:0%
+They're intended to be in the wind and
+ 
+
+ align:start position:0%
+They're intended to be in the wind and
+that works. Um, so they work for and
+
+ align:start position:0%
+that works. Um, so they work for and
+ 
+
+ align:start position:0%
+that works. Um, so they work for and
+they work generally for lower wind
+
+ align:start position:0%
+they work generally for lower wind
+ 
+
+ align:start position:0%
+they work generally for lower wind
+speeds, which is means lower heights.
+
+ align:start position:0%
+speeds, which is means lower heights.
+ 
+
+ align:start position:0%
+speeds, which is means lower heights.
+They're often much less noisy than wind
+
+ align:start position:0%
+They're often much less noisy than wind
+ 
+
+ align:start position:0%
+They're often much less noisy than wind
+turbines, uh, horizontal axis wind
+
+ align:start position:0%
+turbines, uh, horizontal axis wind
+ 
+
+ align:start position:0%
+turbines, uh, horizontal axis wind
+turbines, and they can often start at
+
+ align:start position:0%
+turbines, and they can often start at
+ 
+
+ align:start position:0%
+turbines, and they can often start at
+lower speeds. Um,
+
+ align:start position:0%
+lower speeds. Um,
+ 
+
+ align:start position:0%
+lower speeds. Um,
+but some of the advantage disadvantages,
+
+ align:start position:0%
+but some of the advantage disadvantages,
+ 
+
+ align:start position:0%
+but some of the advantage disadvantages,
+they're hard to scale up. So you're
+
+ align:start position:0%
+they're hard to scale up. So you're
+ 
+
+ align:start position:0%
+they're hard to scale up. So you're
+never going to get a
+
+ align:start position:0%
+never going to get a
+ 
+
+ align:start position:0%
+never going to get a
+seven megawatt um, vertical axis wind
+
+ align:start position:0%
+seven megawatt um, vertical axis wind
+ 
+
+ align:start position:0%
+seven megawatt um, vertical axis wind
+turbine. that's just not viable. Um
+
+ align:start position:0%
+turbine. that's just not viable. Um
+ 
+
+ align:start position:0%
+turbine. that's just not viable. Um
+they're generally less efficient and
+
+ align:start position:0%
+they're generally less efficient and
+ 
+
+ align:start position:0%
+they're generally less efficient and
+they're more prone to fatigue. So they
+
+ align:start position:0%
+they're more prone to fatigue. So they
+ 
+
+ align:start position:0%
+they're more prone to fatigue. So they
+do wear out um more easily because
+
+ align:start position:0%
+do wear out um more easily because
+ 
+
+ align:start position:0%
+do wear out um more easily because
+they're capturing so much more of of the
+
+ align:start position:0%
+they're capturing so much more of of the
+ 
+
+ align:start position:0%
+they're capturing so much more of of the
+wind typically. Um but they um for our
+
+ align:start position:0%
+wind typically. Um but they um for our
+ 
+
+ align:start position:0%
+wind typically. Um but they um for our
+purposes they're definitely a
+
+ align:start position:0%
+purposes they're definitely a
+ 
+
+ align:start position:0%
+purposes they're definitely a
+possibility to look at um for anything.
+
+ align:start position:0%
+possibility to look at um for anything.
+ 
+
+ align:start position:0%
+possibility to look at um for anything.
+Just a reminder
+
+ align:start position:0%
+Just a reminder
+ 
+
+ align:start position:0%
+Just a reminder
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the equations we're thinking about. So
+
+ align:start position:0%
+the equations we're thinking about. So
+ 
+
+ align:start position:0%
+the equations we're thinking about. So
+the force
+
+ align:start position:0%
+the force
+ 
+
+ align:start position:0%
+the force
+is um that you're receiving is
+
+ align:start position:0%
+is um that you're receiving is
+ 
+
+ align:start position:0%
+is um that you're receiving is
+equivalent to uh 12 * row a v ^ 2. So v
+
+ align:start position:0%
+equivalent to uh 12 * row a v ^ 2. So v
+ 
+
+ align:start position:0%
+equivalent to uh 12 * row a v ^ 2. So v
+is obviously the velocity of the wind,
+
+ align:start position:0%
+is obviously the velocity of the wind,
+ 
+
+ align:start position:0%
+is obviously the velocity of the wind,
+the crosssectional area swept and the
+
+ align:start position:0%
+the crosssectional area swept and the
+ 
+
+ align:start position:0%
+the crosssectional area swept and the
+density of the wind. um
+
+ align:start position:0%
+density of the wind. um
+ 
+
+ align:start position:0%
+density of the wind. um
+the maximum possible
+
+ align:start position:0%
+the maximum possible
+ 
+
+ align:start position:0%
+the maximum possible
+power extraction
+
+ align:start position:0%
+power extraction
+ 
+
+ align:start position:0%
+power extraction
+uh is
+
+ align:start position:0%
+uh is
+ 
+
+ align:start position:0%
+uh is
+uh def dominated by the velocity cubed.
+
+ align:start position:0%
+uh def dominated by the velocity cubed.
+ 
+
+ align:start position:0%
+uh def dominated by the velocity cubed.
+So obviously velocity is going to be you
+
+ align:start position:0%
+So obviously velocity is going to be you
+ 
+
+ align:start position:0%
+So obviously velocity is going to be you
+velocity is really going to be what you
+
+ align:start position:0%
+velocity is really going to be what you
+ 
+
+ align:start position:0%
+velocity is really going to be what you
+worry about when you're designing. Um so
+
+ align:start position:0%
+worry about when you're designing. Um so
+ 
+
+ align:start position:0%
+worry about when you're designing. Um so
+area is important obviously but the cube
+
+ align:start position:0%
+area is important obviously but the cube
+ 
+
+ align:start position:0%
+area is important obviously but the cube
+velocity velocity is cubed so the wind
+
+ align:start position:0%
+velocity velocity is cubed so the wind
+ 
+
+ align:start position:0%
+velocity velocity is cubed so the wind
+speed is huge. Um so whenever you're
+
+ align:start position:0%
+speed is huge. Um so whenever you're
+ 
+
+ align:start position:0%
+speed is huge. Um so whenever you're
+thinking is this a place where the veloc
+
+ align:start position:0%
+thinking is this a place where the veloc
+ 
+
+ align:start position:0%
+thinking is this a place where the veloc
+where is a wind turbine appropriate the
+
+ align:start position:0%
+where is a wind turbine appropriate the
+ 
+
+ align:start position:0%
+where is a wind turbine appropriate the
+first question is well what's the wind
+
+ align:start position:0%
+first question is well what's the wind
+ 
+
+ align:start position:0%
+first question is well what's the wind
+speed? Um and then there's a coefficient
+
+ align:start position:0%
+speed? Um and then there's a coefficient
+ 
+
+ align:start position:0%
+speed? Um and then there's a coefficient
+of performance which just um
+
+ align:start position:0%
+of performance which just um
+ 
+
+ align:start position:0%
+of performance which just um
+is a reality that um wind turbines are
+
+ align:start position:0%
+is a reality that um wind turbines are
+ 
+
+ align:start position:0%
+is a reality that um wind turbines are
+not perfect. Um and so there's a
+
+ align:start position:0%
+not perfect. Um and so there's a
+ 
+
+ align:start position:0%
+not perfect. Um and so there's a
+hypothetical limit and you if you Google
+
+ align:start position:0%
+hypothetical limit and you if you Google
+ 
+
+ align:start position:0%
+hypothetical limit and you if you Google
+the bets limit you can find the proof if
+
+ align:start position:0%
+the bets limit you can find the proof if
+ 
+
+ align:start position:0%
+the bets limit you can find the proof if
+uh that's appealing. It's kind of cool.
+
+ align:start position:0%
+uh that's appealing. It's kind of cool.
+ 
+
+ align:start position:0%
+uh that's appealing. It's kind of cool.
+um of point almost 6 is your
+
+ align:start position:0%
+um of point almost 6 is your
+ 
+
+ align:start position:0%
+um of point almost 6 is your
+hypothetical maximum efficiency. And
+
+ align:start position:0%
+hypothetical maximum efficiency. And
+ 
+
+ align:start position:0%
+hypothetical maximum efficiency. And
+then a typical limit in reality is
+
+ align:start position:0%
+then a typical limit in reality is
+ 
+
+ align:start position:0%
+then a typical limit in reality is
+anywhere from a half for a really sweet
+
+ align:start position:0%
+anywhere from a half for a really sweet
+ 
+
+ align:start position:0%
+anywhere from a half for a really sweet
+horizontal axis wind turbine to less
+
+ align:start position:0%
+horizontal axis wind turbine to less
+ 
+
+ align:start position:0%
+horizontal axis wind turbine to less
+than um a tenth for um a a vertical axis
+
+ align:start position:0%
+than um a tenth for um a a vertical axis
+ 
+
+ align:start position:0%
+than um a tenth for um a a vertical axis
+wind turbine that um I'll show you
+
+ align:start position:0%
+wind turbine that um I'll show you
+ 
+
+ align:start position:0%
+wind turbine that um I'll show you
+later. That's really old school um but
+
+ align:start position:0%
+later. That's really old school um but
+ 
+
+ align:start position:0%
+later. That's really old school um but
+does the job when you need it.
+
+ align:start position:0%
+does the job when you need it.
+ 
+
+ align:start position:0%
+does the job when you need it.
+Um, so the other equation that you want
+
+ align:start position:0%
+Um, so the other equation that you want
+ 
+
+ align:start position:0%
+Um, so the other equation that you want
+to think about is the capacity factor.
+
+ align:start position:0%
+to think about is the capacity factor.
+ 
+
+ align:start position:0%
+to think about is the capacity factor.
+So I've seen some websites that say
+
+ align:start position:0%
+So I've seen some websites that say
+ 
+
+ align:start position:0%
+So I've seen some websites that say
+like, you know, wind is so much better
+
+ align:start position:0%
+like, you know, wind is so much better
+ 
+
+ align:start position:0%
+like, you know, wind is so much better
+than solar because wind is 24/7. Well,
+
+ align:start position:0%
+than solar because wind is 24/7. Well,
+ 
+
+ align:start position:0%
+than solar because wind is 24/7. Well,
+not really. Like unless you're getting
+
+ align:start position:0%
+not really. Like unless you're getting
+ 
+
+ align:start position:0%
+not really. Like unless you're getting
+up way into the atmosphere and even then
+
+ align:start position:0%
+up way into the atmosphere and even then
+ 
+
+ align:start position:0%
+up way into the atmosphere and even then
+there's a lot of variation. You're not
+
+ align:start position:0%
+there's a lot of variation. You're not
+ 
+
+ align:start position:0%
+there's a lot of variation. You're not
+wind is not 247. There's a tremendous
+
+ align:start position:0%
+wind is not 247. There's a tremendous
+ 
+
+ align:start position:0%
+wind is not 247. There's a tremendous
+amount of variation. And so it's
+
+ align:start position:0%
+amount of variation. And so it's
+ 
+
+ align:start position:0%
+amount of variation. And so it's
+generally 20 to 40% of the time is how
+
+ align:start position:0%
+generally 20 to 40% of the time is how
+ 
+
+ align:start position:0%
+generally 20 to 40% of the time is how
+often your turbine is um provide
+
+ align:start position:0%
+often your turbine is um provide
+ 
+
+ align:start position:0%
+often your turbine is um provide
+generating power which is sounding
+
+ align:start position:0%
+generating power which is sounding
+ 
+
+ align:start position:0%
+generating power which is sounding
+starting to sound more like solar
+
+ align:start position:0%
+starting to sound more like solar
+ 
+
+ align:start position:0%
+starting to sound more like solar
+actually. Um so that's one thing to
+
+ align:start position:0%
+actually. Um so that's one thing to
+ 
+
+ align:start position:0%
+actually. Um so that's one thing to
+definitely keep in mind.
+
+ align:start position:0%
+definitely keep in mind.
+ 
+
+ align:start position:0%
+definitely keep in mind.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay. So a typical C power curve. So at
+
+ align:start position:0%
+okay. So a typical C power curve. So at
+ 
+
+ align:start position:0%
+okay. So a typical C power curve. So at
+some point at some given speed um is
+
+ align:start position:0%
+some point at some given speed um is
+ 
+
+ align:start position:0%
+some point at some given speed um is
+when the turbine starts actually turning
+
+ align:start position:0%
+when the turbine starts actually turning
+ 
+
+ align:start position:0%
+when the turbine starts actually turning
+because up until then it can't
+
+ align:start position:0%
+because up until then it can't
+ 
+
+ align:start position:0%
+because up until then it can't
+physically turn because the wind forces
+
+ align:start position:0%
+physically turn because the wind forces
+ 
+
+ align:start position:0%
+physically turn because the wind forces
+aren't high enough. And then your output
+
+ align:start position:0%
+aren't high enough. And then your output
+ 
+
+ align:start position:0%
+aren't high enough. And then your output
+in terms of uh power is very very low.
+
+ align:start position:0%
+in terms of uh power is very very low.
+ 
+
+ align:start position:0%
+in terms of uh power is very very low.
+And then you have an average wind speeds
+
+ align:start position:0%
+And then you have an average wind speeds
+ 
+
+ align:start position:0%
+And then you have an average wind speeds
+generally somewhere around here which is
+
+ align:start position:0%
+generally somewhere around here which is
+ 
+
+ align:start position:0%
+generally somewhere around here which is
+giving you half of the wind power or the
+
+ align:start position:0%
+giving you half of the wind power or the
+ 
+
+ align:start position:0%
+giving you half of the wind power or the
+power that you'd like. And then you have
+
+ align:start position:0%
+power that you'd like. And then you have
+ 
+
+ align:start position:0%
+power that you'd like. And then you have
+a maximum wind speed and then you're
+
+ align:start position:0%
+a maximum wind speed and then you're
+ 
+
+ align:start position:0%
+a maximum wind speed and then you're
+happy happy happy and then at some point
+
+ align:start position:0%
+happy happy happy and then at some point
+ 
+
+ align:start position:0%
+happy happy happy and then at some point
+it gets so high that you have to shut
+
+ align:start position:0%
+it gets so high that you have to shut
+ 
+
+ align:start position:0%
+it gets so high that you have to shut
+the turbine down or else you're in
+
+ align:start position:0%
+the turbine down or else you're in
+ 
+
+ align:start position:0%
+the turbine down or else you're in
+trouble. So, um,
+
+ align:start position:0%
+trouble. So, um,
+ 
+
+ align:start position:0%
+trouble. So, um,
+that's just a a good general way to
+
+ align:start position:0%
+that's just a a good general way to
+ 
+
+ align:start position:0%
+that's just a a good general way to
+think about what's happening over
+
+ align:start position:0%
+think about what's happening over
+ 
+
+ align:start position:0%
+think about what's happening over
+different speeds because you're I'll
+
+ align:start position:0%
+different speeds because you're I'll
+ 
+
+ align:start position:0%
+different speeds because you're I'll
+show you later. We're going to look at
+
+ align:start position:0%
+show you later. We're going to look at
+ 
+
+ align:start position:0%
+show you later. We're going to look at
+data that shows you the different, um,
+
+ align:start position:0%
+data that shows you the different, um,
+ 
+
+ align:start position:0%
+data that shows you the different, um,
+speeds.
+
+ align:start position:0%
+speeds.
+ 
+
+ align:start position:0%
+speeds.
+So, uh,
+
+ align:start position:0%
+So, uh,
+ 
+
+ align:start position:0%
+So, uh,
+these are, uh, maps from NASA that show
+
+ align:start position:0%
+these are, uh, maps from NASA that show
+ 
+
+ align:start position:0%
+these are, uh, maps from NASA that show
+wind speed across the entire globe. Um,
+
+ align:start position:0%
+wind speed across the entire globe. Um,
+ 
+
+ align:start position:0%
+wind speed across the entire globe. Um,
+and you can see if it's um very dark,
+
+ align:start position:0%
+and you can see if it's um very dark,
+ 
+
+ align:start position:0%
+and you can see if it's um very dark,
+it's very low wind speed. And if it's
+
+ align:start position:0%
+it's very low wind speed. And if it's
+ 
+
+ align:start position:0%
+it's very low wind speed. And if it's
+very light, it's higher wind speed. Um,
+
+ align:start position:0%
+very light, it's higher wind speed. Um,
+ 
+
+ align:start position:0%
+very light, it's higher wind speed. Um,
+so if we could just fill this part of
+
+ align:start position:0%
+so if we could just fill this part of
+ 
+
+ align:start position:0%
+so if we could just fill this part of
+the ocean with wind turbines, that would
+
+ align:start position:0%
+the ocean with wind turbines, that would
+ 
+
+ align:start position:0%
+the ocean with wind turbines, that would
+be pretty sweet. But you can actually
+
+ align:start position:0%
+be pretty sweet. But you can actually
+ 
+
+ align:start position:0%
+be pretty sweet. But you can actually
+see um in Nicaragua, which is right over
+
+ align:start position:0%
+see um in Nicaragua, which is right over
+ 
+
+ align:start position:0%
+see um in Nicaragua, which is right over
+here, um you're getting pretty decent
+
+ align:start position:0%
+here, um you're getting pretty decent
+ 
+
+ align:start position:0%
+here, um you're getting pretty decent
+wind um compared to say if we were
+
+ align:start position:0%
+wind um compared to say if we were
+ 
+
+ align:start position:0%
+wind um compared to say if we were
+working in um these parts of Africa or
+
+ align:start position:0%
+working in um these parts of Africa or
+ 
+
+ align:start position:0%
+working in um these parts of Africa or
+up up here in Russia or something. we we
+
+ align:start position:0%
+up up here in Russia or something. we we
+ 
+
+ align:start position:0%
+up up here in Russia or something. we we
+wouldn't be thinking win turbines at
+
+ align:start position:0%
+wouldn't be thinking win turbines at
+ 
+
+ align:start position:0%
+wouldn't be thinking win turbines at
+all. Um, and you can see how much
+
+ align:start position:0%
+all. Um, and you can see how much
+ 
+
+ align:start position:0%
+all. Um, and you can see how much
+variation there is between January and
+
+ align:start position:0%
+variation there is between January and
+ 
+
+ align:start position:0%
+variation there is between January and
+July. And so, of course, there's a lot
+
+ align:start position:0%
+July. And so, of course, there's a lot
+ 
+
+ align:start position:0%
+July. And so, of course, there's a lot
+of seasonal variation no matter what.
+
+ align:start position:0%
+of seasonal variation no matter what.
+ 
+
+ align:start position:0%
+of seasonal variation no matter what.
+Um, and you can see like this blue is 7
+
+ align:start position:0%
+Um, and you can see like this blue is 7
+ 
+
+ align:start position:0%
+Um, and you can see like this blue is 7
+meters/s, which is getting to be useful.
+
+ align:start position:0%
+meters/s, which is getting to be useful.
+ 
+
+ align:start position:0%
+meters/s, which is getting to be useful.
+Um, for horizontal axis wind turbine,
+
+ align:start position:0%
+Um, for horizontal axis wind turbine,
+ 
+
+ align:start position:0%
+Um, for horizontal axis wind turbine,
+you need 5 meters/s. Um, for vertical,
+
+ align:start position:0%
+you need 5 meters/s. Um, for vertical,
+ 
+
+ align:start position:0%
+you need 5 meters/s. Um, for vertical,
+you can go a little bit lower, but five
+
+ align:start position:0%
+you can go a little bit lower, but five
+ 
+
+ align:start position:0%
+you can go a little bit lower, but five
+is a good rule of thumb.
+
+ align:start position:0%
+is a good rule of thumb.
+ 
+
+ align:start position:0%
+is a good rule of thumb.
+Um, and again, why we're looking at
+
+ align:start position:0%
+Um, and again, why we're looking at
+ 
+
+ align:start position:0%
+Um, and again, why we're looking at
+velocity over everything else is because
+
+ align:start position:0%
+velocity over everything else is because
+ 
+
+ align:start position:0%
+velocity over everything else is because
+velocity is cubed for your power
+
+ align:start position:0%
+velocity is cubed for your power
+ 
+
+ align:start position:0%
+velocity is cubed for your power
+equation.
+
+ align:start position:0%
+equation.
+ 
+
+ align:start position:0%
+equation.
+So, great, I've told you wind speeds.
+
+ align:start position:0%
+So, great, I've told you wind speeds.
+ 
+
+ align:start position:0%
+So, great, I've told you wind speeds.
+I've showed you a NASA map of the entire
+
+ align:start position:0%
+I've showed you a NASA map of the entire
+ 
+
+ align:start position:0%
+I've showed you a NASA map of the entire
+Earth, but that doesn't tell you much
+
+ align:start position:0%
+Earth, but that doesn't tell you much
+ 
+
+ align:start position:0%
+Earth, but that doesn't tell you much
+for a given location. So, one way to get
+
+ align:start position:0%
+for a given location. So, one way to get
+ 
+
+ align:start position:0%
+for a given location. So, one way to get
+a really rough estimate of wind speed is
+
+ align:start position:0%
+a really rough estimate of wind speed is
+ 
+
+ align:start position:0%
+a really rough estimate of wind speed is
+this Bowford scale, which was developed
+
+ align:start position:0%
+this Bowford scale, which was developed
+ 
+
+ align:start position:0%
+this Bowford scale, which was developed
+in the 1800s. Um, and it correlates what
+
+ align:start position:0%
+in the 1800s. Um, and it correlates what
+ 
+
+ align:start position:0%
+in the 1800s. Um, and it correlates what
+you can visually see and what kind of
+
+ align:start position:0%
+you can visually see and what kind of
+ 
+
+ align:start position:0%
+you can visually see and what kind of
+damage you're seeing to the speed. Some
+
+ align:start position:0%
+damage you're seeing to the speed. Some
+ 
+
+ align:start position:0%
+damage you're seeing to the speed. Some
+of the caveats on this are number one,
+
+ align:start position:0%
+of the caveats on this are number one,
+ 
+
+ align:start position:0%
+of the caveats on this are number one,
+it's pretty rough. Um, and especially if
+
+ align:start position:0%
+it's pretty rough. Um, and especially if
+ 
+
+ align:start position:0%
+it's pretty rough. Um, and especially if
+you're talking to people in a community
+
+ align:start position:0%
+you're talking to people in a community
+ 
+
+ align:start position:0%
+you're talking to people in a community
+saying like, you know, tell me about
+
+ align:start position:0%
+saying like, you know, tell me about
+ 
+
+ align:start position:0%
+saying like, you know, tell me about
+wind speed and giving them examples.
+
+ align:start position:0%
+wind speed and giving them examples.
+ 
+
+ align:start position:0%
+wind speed and giving them examples.
+It's hard to remember exactly what the
+
+ align:start position:0%
+It's hard to remember exactly what the
+ 
+
+ align:start position:0%
+It's hard to remember exactly what the
+wind is like. Like, can you tell me what
+
+ align:start position:0%
+wind is like. Like, can you tell me what
+ 
+
+ align:start position:0%
+wind is like. Like, can you tell me what
+the Bowford scale was today walking
+
+ align:start position:0%
+the Bowford scale was today walking
+ 
+
+ align:start position:0%
+the Bowford scale was today walking
+here?
+
+ align:start position:0%
+here?
+ 
+
+ align:start position:0%
+here?
+I can't like I don't remember. I don't
+
+ align:start position:0%
+I can't like I don't remember. I don't
+ 
+
+ align:start position:0%
+I can't like I don't remember. I don't
+really pay attention to the wind that
+
+ align:start position:0%
+really pay attention to the wind that
+ 
+
+ align:start position:0%
+really pay attention to the wind that
+much. Um, if you're working with
+
+ align:start position:0%
+much. Um, if you're working with
+ 
+
+ align:start position:0%
+much. Um, if you're working with
+farmers, they're probably a little bit
+
+ align:start position:0%
+farmers, they're probably a little bit
+ 
+
+ align:start position:0%
+farmers, they're probably a little bit
+more aware of it than you and I might
+
+ align:start position:0%
+more aware of it than you and I might
+ 
+
+ align:start position:0%
+more aware of it than you and I might
+be, but still, um, it's challenging. And
+
+ align:start position:0%
+be, but still, um, it's challenging. And
+ 
+
+ align:start position:0%
+be, but still, um, it's challenging. And
+the other thing is that a lot of these
+
+ align:start position:0%
+the other thing is that a lot of these
+ 
+
+ align:start position:0%
+the other thing is that a lot of these
+metrics are on the ground and we're
+
+ align:start position:0%
+metrics are on the ground and we're
+ 
+
+ align:start position:0%
+metrics are on the ground and we're
+probably talking about significantly
+
+ align:start position:0%
+probably talking about significantly
+ 
+
+ align:start position:0%
+probably talking about significantly
+higher than the ground depending on what
+
+ align:start position:0%
+higher than the ground depending on what
+ 
+
+ align:start position:0%
+higher than the ground depending on what
+kind of turbine you're implementing. And
+
+ align:start position:0%
+kind of turbine you're implementing. And
+ 
+
+ align:start position:0%
+kind of turbine you're implementing. And
+so again, that that only helps you. So,
+
+ align:start position:0%
+so again, that that only helps you. So,
+ 
+
+ align:start position:0%
+so again, that that only helps you. So,
+if you're finding out that you're
+
+ align:start position:0%
+if you're finding out that you're
+ 
+
+ align:start position:0%
+if you're finding out that you're
+probably at um 4 m an hour, which is 2
+
+ align:start position:0%
+probably at um 4 m an hour, which is 2
+ 
+
+ align:start position:0%
+probably at um 4 m an hour, which is 2
+m/s and really low, but at the very
+
+ align:start position:0%
+m/s and really low, but at the very
+ 
+
+ align:start position:0%
+m/s and really low, but at the very
+ground level and you're building a
+
+ align:start position:0%
+ground level and you're building a
+ 
+
+ align:start position:0%
+ground level and you're building a
+turbine that's 30 m up, maybe uh 30 ft
+
+ align:start position:0%
+turbine that's 30 m up, maybe uh 30 ft
+ 
+
+ align:start position:0%
+turbine that's 30 m up, maybe uh 30 ft
+up, maybe you have a shot um of getting
+
+ align:start position:0%
+up, maybe you have a shot um of getting
+ 
+
+ align:start position:0%
+up, maybe you have a shot um of getting
+enough wind. Yeah.
+
+ align:start position:0%
+enough wind. Yeah.
+ 
+
+ align:start position:0%
+enough wind. Yeah.
+Is there like a uniform um scale from
+
+ align:start position:0%
+Is there like a uniform um scale from
+ 
+
+ align:start position:0%
+Is there like a uniform um scale from
+like what the wind speed at the ground
+
+ align:start position:0%
+like what the wind speed at the ground
+ 
+
+ align:start position:0%
+like what the wind speed at the ground
+level is and then how how it changes
+
+ align:start position:0%
+level is and then how how it changes
+ 
+
+ align:start position:0%
+level is and then how how it changes
+vertically?
+
+ align:start position:0%
+vertically?
+ 
+
+ align:start position:0%
+vertically?
+So, or is that a regional thing? What's
+
+ align:start position:0%
+So, or is that a regional thing? What's
+ 
+
+ align:start position:0%
+So, or is that a regional thing? What's
+up? Well, so it's both. So, yes, there
+
+ align:start position:0%
+up? Well, so it's both. So, yes, there
+ 
+
+ align:start position:0%
+up? Well, so it's both. So, yes, there
+are some scales that can help you
+
+ align:start position:0%
+are some scales that can help you
+ 
+
+ align:start position:0%
+are some scales that can help you
+estimate if you know what the ground is,
+
+ align:start position:0%
+estimate if you know what the ground is,
+ 
+
+ align:start position:0%
+estimate if you know what the ground is,
+what it is up above, but it also is
+
+ align:start position:0%
+what it is up above, but it also is
+ 
+
+ align:start position:0%
+what it is up above, but it also is
+really dependent on what's around. And
+
+ align:start position:0%
+really dependent on what's around. And
+ 
+
+ align:start position:0%
+really dependent on what's around. And
+so, I'm about to show you a tool that
+
+ align:start position:0%
+so, I'm about to show you a tool that
+ 
+
+ align:start position:0%
+so, I'm about to show you a tool that
+helps a little bit with that, but it's
+
+ align:start position:0%
+helps a little bit with that, but it's
+ 
+
+ align:start position:0%
+helps a little bit with that, but it's
+still very imperfect. Um, ideally you'd
+
+ align:start position:0%
+still very imperfect. Um, ideally you'd
+ 
+
+ align:start position:0%
+still very imperfect. Um, ideally you'd
+have an animometer and you leave it up
+
+ align:start position:0%
+have an animometer and you leave it up
+ 
+
+ align:start position:0%
+have an animometer and you leave it up
+for five years and you'd have it at, you
+
+ align:start position:0%
+for five years and you'd have it at, you
+ 
+
+ align:start position:0%
+for five years and you'd have it at, you
+know, 10 different heights, you know, 10
+
+ align:start position:0%
+know, 10 different heights, you know, 10
+ 
+
+ align:start position:0%
+know, 10 different heights, you know, 10
+different anominers, 10 different
+
+ align:start position:0%
+different anominers, 10 different
+ 
+
+ align:start position:0%
+different anominers, 10 different
+heights and that would get you actual
+
+ align:start position:0%
+heights and that would get you actual
+ 
+
+ align:start position:0%
+heights and that would get you actual
+real data that you'd be psyched for. But
+
+ align:start position:0%
+real data that you'd be psyched for. But
+ 
+
+ align:start position:0%
+real data that you'd be psyched for. But
+that would be a really ridiculously slow
+
+ align:start position:0%
+that would be a really ridiculously slow
+ 
+
+ align:start position:0%
+that would be a really ridiculously slow
+expensive project. And so a lot of this
+
+ align:start position:0%
+expensive project. And so a lot of this
+ 
+
+ align:start position:0%
+expensive project. And so a lot of this
+is just estimations and doing your best
+
+ align:start position:0%
+is just estimations and doing your best
+ 
+
+ align:start position:0%
+is just estimations and doing your best
+guesses. Um, so this I'm sorry for the
+
+ align:start position:0%
+guesses. Um, so this I'm sorry for the
+ 
+
+ align:start position:0%
+guesses. Um, so this I'm sorry for the
+web link. As you'll see, this website is
+
+ align:start position:0%
+web link. As you'll see, this website is
+ 
+
+ align:start position:0%
+web link. As you'll see, this website is
+like web. It's not even web 1.0. It's
+
+ align:start position:0%
+like web. It's not even web 1.0. It's
+ 
+
+ align:start position:0%
+like web. It's not even web 1.0. It's
+like web 0.5, but it has like awesome
+
+ align:start position:0%
+like web 0.5, but it has like awesome
+ 
+
+ align:start position:0%
+like web 0.5, but it has like awesome
+data um from NASA. So,
+
+ align:start position:0%
+data um from NASA. So,
+ 
+
+ align:start position:0%
+data um from NASA. So,
+you go to this website with that awful
+
+ align:start position:0%
+you go to this website with that awful
+ 
+
+ align:start position:0%
+you go to this website with that awful
+link and then there's a bunch of
+
+ align:start position:0%
+link and then there's a bunch of
+ 
+
+ align:start position:0%
+link and then there's a bunch of
+different ways to get this data. And
+
+ align:start position:0%
+different ways to get this data. And
+ 
+
+ align:start position:0%
+different ways to get this data. And
+this is actually for both useful for
+
+ align:start position:0%
+this is actually for both useful for
+ 
+
+ align:start position:0%
+this is actually for both useful for
+solar and wind. So, if you're worrying
+
+ align:start position:0%
+solar and wind. So, if you're worrying
+ 
+
+ align:start position:0%
+solar and wind. So, if you're worrying
+about solar data, too, this is really
+
+ align:start position:0%
+about solar data, too, this is really
+ 
+
+ align:start position:0%
+about solar data, too, this is really
+useful. So, if you don't know where you
+
+ align:start position:0%
+useful. So, if you don't know where you
+ 
+
+ align:start position:0%
+useful. So, if you don't know where you
+want to, you don't know your latitude
+
+ align:start position:0%
+want to, you don't know your latitude
+ 
+
+ align:start position:0%
+want to, you don't know your latitude
+and longitude, you can click use a map
+
+ align:start position:0%
+and longitude, you can click use a map
+ 
+
+ align:start position:0%
+and longitude, you can click use a map
+to click. Um, every time you do this,
+
+ align:start position:0%
+to click. Um, every time you do this,
+ 
+
+ align:start position:0%
+to click. Um, every time you do this,
+you have to log in. Um, but there's it's
+
+ align:start position:0%
+you have to log in. Um, but there's it's
+ 
+
+ align:start position:0%
+you have to log in. Um, but there's it's
+very easy to um join because you just
+
+ align:start position:0%
+very easy to um join because you just
+ 
+
+ align:start position:0%
+very easy to um join because you just
+type your password twice instead of once
+
+ align:start position:0%
+type your password twice instead of once
+ 
+
+ align:start position:0%
+type your password twice instead of once
+once you become a member. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it's slow, but uh it's it looks
+
+ align:start position:0%
+and then it's slow, but uh it's it looks
+ 
+
+ align:start position:0%
+and then it's slow, but uh it's it looks
+so clunky that I was afraid you'd be
+
+ align:start position:0%
+so clunky that I was afraid you'd be
+ 
+
+ align:start position:0%
+so clunky that I was afraid you'd be
+turned off by it. And it has good enough
+
+ align:start position:0%
+turned off by it. And it has good enough
+ 
+
+ align:start position:0%
+turned off by it. And it has good enough
+data that I wanted to go through showing
+
+ align:start position:0%
+data that I wanted to go through showing
+ 
+
+ align:start position:0%
+data that I wanted to go through showing
+you um it. So, you have this map of the
+
+ align:start position:0%
+you um it. So, you have this map of the
+ 
+
+ align:start position:0%
+you um it. So, you have this map of the
+Earth. You click in the part of the
+
+ align:start position:0%
+Earth. You click in the part of the
+ 
+
+ align:start position:0%
+Earth. You click in the part of the
+Earth that you care about to center it.
+
+ align:start position:0%
+Earth that you care about to center it.
+ 
+
+ align:start position:0%
+Earth that you care about to center it.
+You click to zoom.
+
+ align:start position:0%
+You click to zoom.
+ 
+
+ align:start position:0%
+You click to zoom.
+Um, we're in the wrong part of the
+
+ align:start position:0%
+Um, we're in the wrong part of the
+ 
+
+ align:start position:0%
+Um, we're in the wrong part of the
+world, but we're getting there.
+
+ align:start position:0%
+world, but we're getting there.
+ 
+
+ align:start position:0%
+world, but we're getting there.
+Uh, I'm going to zoom in again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. And you can see like this is
+
+ align:start position:0%
+All right. And you can see like this is
+ 
+
+ align:start position:0%
+All right. And you can see like this is
+data for a region, not for a small town.
+
+ align:start position:0%
+data for a region, not for a small town.
+ 
+
+ align:start position:0%
+data for a region, not for a small town.
+So there's all sorts of limits to this
+
+ align:start position:0%
+So there's all sorts of limits to this
+ 
+
+ align:start position:0%
+So there's all sorts of limits to this
+data, but it's useful. And so now you
+
+ align:start position:0%
+data, but it's useful. And so now you
+ 
+
+ align:start position:0%
+data, but it's useful. And so now you
+can finally get your data and now you
+
+ align:start position:0%
+can finally get your data and now you
+ 
+
+ align:start position:0%
+can finally get your data and now you
+can get crazy information. So parameters
+
+ align:start position:0%
+can get crazy information. So parameters
+ 
+
+ align:start position:0%
+can get crazy information. So parameters
+for solar cooking, for solar panels, um
+
+ align:start position:0%
+for solar cooking, for solar panels, um
+ 
+
+ align:start position:0%
+for solar cooking, for solar panels, um
+cloud information, which can be really
+
+ align:start position:0%
+cloud information, which can be really
+ 
+
+ align:start position:0%
+cloud information, which can be really
+useful, temperature, which can be really
+
+ align:start position:0%
+useful, temperature, which can be really
+ 
+
+ align:start position:0%
+useful, temperature, which can be really
+useful. Um and now we're getting to
+
+ align:start position:0%
+useful. Um and now we're getting to
+ 
+
+ align:start position:0%
+useful. Um and now we're getting to
+wind. So you can see the variety. So you
+
+ align:start position:0%
+wind. So you can see the variety. So you
+ 
+
+ align:start position:0%
+wind. So you can see the variety. So you
+can get 50 meter and 10 meter but
+
+ align:start position:0%
+can get 50 meter and 10 meter but
+ 
+
+ align:start position:0%
+can get 50 meter and 10 meter but
+because this is all satellite data or
+
+ align:start position:0%
+because this is all satellite data or
+ 
+
+ align:start position:0%
+because this is all satellite data or
+airport data. Um so 50 m is pretty high
+
+ align:start position:0%
+airport data. Um so 50 m is pretty high
+ 
+
+ align:start position:0%
+airport data. Um so 50 m is pretty high
+for anything we're talking about and
+
+ align:start position:0%
+for anything we're talking about and
+ 
+
+ align:start position:0%
+for anything we're talking about and
+then 10 m for terrain similar to the
+
+ align:start position:0%
+then 10 m for terrain similar to the
+ 
+
+ align:start position:0%
+then 10 m for terrain similar to the
+airport because they're measuring at the
+
+ align:start position:0%
+airport because they're measuring at the
+ 
+
+ align:start position:0%
+airport because they're measuring at the
+airport because that's the place where
+
+ align:start position:0%
+airport because that's the place where
+ 
+
+ align:start position:0%
+airport because that's the place where
+they have an animomer. So all of this
+
+ align:start position:0%
+they have an animomer. So all of this
+ 
+
+ align:start position:0%
+they have an animomer. So all of this
+data you again you have to take with a
+
+ align:start position:0%
+data you again you have to take with a
+ 
+
+ align:start position:0%
+data you again you have to take with a
+grain of salt but it's good to you know
+
+ align:start position:0%
+grain of salt but it's good to you know
+ 
+
+ align:start position:0%
+grain of salt but it's good to you know
+if you use that in conjunction with your
+
+ align:start position:0%
+if you use that in conjunction with your
+ 
+
+ align:start position:0%
+if you use that in conjunction with your
+own visual observations and talking to
+
+ align:start position:0%
+own visual observations and talking to
+ 
+
+ align:start position:0%
+own visual observations and talking to
+people it's it's better than nothing. um
+
+ align:start position:0%
+people it's it's better than nothing. um
+ 
+
+ align:start position:0%
+people it's it's better than nothing. um
+which is the alternative or you know a
+
+ align:start position:0%
+which is the alternative or you know a
+ 
+
+ align:start position:0%
+which is the alternative or you know a
+million-dollar 10-year study which um
+
+ align:start position:0%
+million-dollar 10-year study which um
+ 
+
+ align:start position:0%
+million-dollar 10-year study which um
+isn't viable either. So we're gonna just
+
+ align:start position:0%
+isn't viable either. So we're gonna just
+ 
+
+ align:start position:0%
+isn't viable either. So we're gonna just
+look at wind speed at 50 uh meters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for that area of Nicaragua I just
+
+ align:start position:0%
+for that area of Nicaragua I just
+ 
+
+ align:start position:0%
+for that area of Nicaragua I just
+selected.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you can see the like a 10-year
+
+ align:start position:0%
+And you can see the like a 10-year
+ 
+
+ align:start position:0%
+And you can see the like a 10-year
+average and a minimum and maximum
+
+ align:start position:0%
+average and a minimum and maximum
+ 
+
+ align:start position:0%
+average and a minimum and maximum
+variation. So, it's pretty helpful just
+
+ align:start position:0%
+variation. So, it's pretty helpful just
+ 
+
+ align:start position:0%
+variation. So, it's pretty helpful just
+to get get you into the ballpark of do I
+
+ align:start position:0%
+to get get you into the ballpark of do I
+ 
+
+ align:start position:0%
+to get get you into the ballpark of do I
+have a shot of thinking this might work?
+
+ align:start position:0%
+have a shot of thinking this might work?
+ 
+
+ align:start position:0%
+have a shot of thinking this might work?
+And then some of the other things uh
+
+ align:start position:0%
+And then some of the other things uh
+ 
+
+ align:start position:0%
+And then some of the other things uh
+that you can select for are like, you
+
+ align:start position:0%
+that you can select for are like, you
+ 
+
+ align:start position:0%
+that you can select for are like, you
+know, what how high you are. Um, so
+
+ align:start position:0%
+know, what how high you are. Um, so
+ 
+
+ align:start position:0%
+know, what how high you are. Um, so
+Jessica, this is getting to what you
+
+ align:start position:0%
+Jessica, this is getting to what you
+ 
+
+ align:start position:0%
+Jessica, this is getting to what you
+were interested in. Um, like an an
+
+ align:start position:0%
+were interested in. Um, like an an
+ 
+
+ align:start position:0%
+were interested in. Um, like an an
+estimate of where you are and what your
+
+ align:start position:0%
+estimate of where you are and what your
+ 
+
+ align:start position:0%
+estimate of where you are and what your
+ground cover is and then it sort of
+
+ align:start position:0%
+ground cover is and then it sort of
+ 
+
+ align:start position:0%
+ground cover is and then it sort of
+extrapolates what the what the wind will
+
+ align:start position:0%
+extrapolates what the what the wind will
+ 
+
+ align:start position:0%
+extrapolates what the what the wind will
+be. So, it's pretty useful um and
+
+ align:start position:0%
+be. So, it's pretty useful um and
+ 
+
+ align:start position:0%
+be. So, it's pretty useful um and
+powerful. Is it 100% accurate given that
+
+ align:start position:0%
+powerful. Is it 100% accurate given that
+ 
+
+ align:start position:0%
+powerful. Is it 100% accurate given that
+it's doing really broadbased readings?
+
+ align:start position:0%
+it's doing really broadbased readings?
+ 
+
+ align:start position:0%
+it's doing really broadbased readings?
+Of course not. But it's a start. Um so
+
+ align:start position:0%
+Of course not. But it's a start. Um so
+ 
+
+ align:start position:0%
+Of course not. But it's a start. Um so
+it's nice it's it's a nice uh resource
+
+ align:start position:0%
+it's nice it's it's a nice uh resource
+ 
+
+ align:start position:0%
+it's nice it's it's a nice uh resource
+to know about.
+
+ align:start position:0%
+to know about.
+ 
+
+ align:start position:0%
+to know about.
+Uh so now I want to spend a little time
+
+ align:start position:0%
+Uh so now I want to spend a little time
+ 
+
+ align:start position:0%
+Uh so now I want to spend a little time
+to talk about examples of wind power in
+
+ align:start position:0%
+to talk about examples of wind power in
+ 
+
+ align:start position:0%
+to talk about examples of wind power in
+developing countries.
+
+ align:start position:0%
+developing countries.
+ 
+
+ align:start position:0%
+developing countries.
+So, one is the humdinger wing belt,
+
+ align:start position:0%
+So, one is the humdinger wing belt,
+ 
+
+ align:start position:0%
+So, one is the humdinger wing belt,
+which is totally different from what
+
+ align:start position:0%
+which is totally different from what
+ 
+
+ align:start position:0%
+which is totally different from what
+you're used to seeing and was developed
+
+ align:start position:0%
+you're used to seeing and was developed
+ 
+
+ align:start position:0%
+you're used to seeing and was developed
+by a student who actually took one of
+
+ align:start position:0%
+by a student who actually took one of
+ 
+
+ align:start position:0%
+by a student who actually took one of
+the first DAB classes um when it was
+
+ align:start position:0%
+the first DAB classes um when it was
+ 
+
+ align:start position:0%
+the first DAB classes um when it was
+back when it was the Haiti class. Um,
+
+ align:start position:0%
+back when it was the Haiti class. Um,
+ 
+
+ align:start position:0%
+back when it was the Haiti class. Um,
+and we have a wind belt here, but I
+
+ align:start position:0%
+and we have a wind belt here, but I
+ 
+
+ align:start position:0%
+and we have a wind belt here, but I
+couldn't find it. So, maybe during break
+
+ align:start position:0%
+couldn't find it. So, maybe during break
+ 
+
+ align:start position:0%
+couldn't find it. So, maybe during break
+I'll be able to dig it up or if not,
+
+ align:start position:0%
+I'll be able to dig it up or if not,
+ 
+
+ align:start position:0%
+I'll be able to dig it up or if not,
+maybe we can bring it up by Friday and
+
+ align:start position:0%
+maybe we can bring it up by Friday and
+ 
+
+ align:start position:0%
+maybe we can bring it up by Friday and
+show it in lab on Friday. Um, so the way
+
+ align:start position:0%
+show it in lab on Friday. Um, so the way
+ 
+
+ align:start position:0%
+show it in lab on Friday. Um, so the way
+the wind belt works is that instead of a
+
+ align:start position:0%
+the wind belt works is that instead of a
+ 
+
+ align:start position:0%
+the wind belt works is that instead of a
+rotation, it just uses um the vibration
+
+ align:start position:0%
+rotation, it just uses um the vibration
+ 
+
+ align:start position:0%
+rotation, it just uses um the vibration
+of the belt very similar to I don't know
+
+ align:start position:0%
+of the belt very similar to I don't know
+ 
+
+ align:start position:0%
+of the belt very similar to I don't know
+if you if you guys can remember the um
+
+ align:start position:0%
+if you if you guys can remember the um
+ 
+
+ align:start position:0%
+if you if you guys can remember the um
+the name of the the bridge that um
+
+ align:start position:0%
+the name of the the bridge that um
+ 
+
+ align:start position:0%
+the name of the the bridge that um
+collapsed.
+
+ align:start position:0%
+collapsed.
+ 
+
+ align:start position:0%
+collapsed.
+Yeah. Does everyone know the Tacoma
+
+ align:start position:0%
+Yeah. Does everyone know the Tacoma
+ 
+
+ align:start position:0%
+Yeah. Does everyone know the Tacoma
+Bridge? Yeah. So uh well Google it
+
+ align:start position:0%
+Bridge? Yeah. So uh well Google it
+ 
+
+ align:start position:0%
+Bridge? Yeah. So uh well Google it
+because you can see videos and it's
+
+ align:start position:0%
+because you can see videos and it's
+ 
+
+ align:start position:0%
+because you can see videos and it's
+awesome if you haven't. So,
+
+ align:start position:0%
+awesome if you haven't. So,
+ 
+
+ align:start position:0%
+awesome if you haven't. So,
+um yeah, it is totally scary, especially
+
+ align:start position:0%
+um yeah, it is totally scary, especially
+ 
+
+ align:start position:0%
+um yeah, it is totally scary, especially
+because um
+
+ align:start position:0%
+because um
+ 
+
+ align:start position:0%
+because um
+I have a friend who did some research
+
+ align:start position:0%
+I have a friend who did some research
+ 
+
+ align:start position:0%
+I have a friend who did some research
+into it and so this bridge um was a
+
+ align:start position:0%
+into it and so this bridge um was a
+ 
+
+ align:start position:0%
+into it and so this bridge um was a
+super long bridge and uh it just had
+
+ align:start position:0%
+super long bridge and uh it just had
+ 
+
+ align:start position:0%
+super long bridge and uh it just had
+natural frequencies at the same uh rate
+
+ align:start position:0%
+natural frequencies at the same uh rate
+ 
+
+ align:start position:0%
+natural frequencies at the same uh rate
+as the wind was off and blowing. And so
+
+ align:start position:0%
+as the wind was off and blowing. And so
+ 
+
+ align:start position:0%
+as the wind was off and blowing. And so
+the bridge would just go up and down and
+
+ align:start position:0%
+the bridge would just go up and down and
+ 
+
+ align:start position:0%
+the bridge would just go up and down and
+up and down crazily. And eventually one
+
+ align:start position:0%
+up and down crazily. And eventually one
+ 
+
+ align:start position:0%
+up and down crazily. And eventually one
+day it got so bad that it completely
+
+ align:start position:0%
+day it got so bad that it completely
+ 
+
+ align:start position:0%
+day it got so bad that it completely
+broke apart. And the crazy thing is that
+
+ align:start position:0%
+broke apart. And the crazy thing is that
+ 
+
+ align:start position:0%
+broke apart. And the crazy thing is that
+people used to hang out on the bridge on
+
+ align:start position:0%
+people used to hang out on the bridge on
+ 
+
+ align:start position:0%
+people used to hang out on the bridge on
+the really windy days because it was so
+
+ align:start position:0%
+the really windy days because it was so
+ 
+
+ align:start position:0%
+the really windy days because it was so
+fun like you know it's like a roller
+
+ align:start position:0%
+fun like you know it's like a roller
+ 
+
+ align:start position:0%
+fun like you know it's like a roller
+coaster. So it's extra scary thinking
+
+ align:start position:0%
+coaster. So it's extra scary thinking
+ 
+
+ align:start position:0%
+coaster. So it's extra scary thinking
+about that. So anyway, but this this was
+
+ align:start position:0%
+about that. So anyway, but this this was
+ 
+
+ align:start position:0%
+about that. So anyway, but this this was
+the sort of the inspiration um for the
+
+ align:start position:0%
+the sort of the inspiration um for the
+ 
+
+ align:start position:0%
+the sort of the inspiration um for the
+humdinger which just has a really
+
+ align:start position:0%
+humdinger which just has a really
+ 
+
+ align:start position:0%
+humdinger which just has a really
+tightly pulled belt in the middle um of
+
+ align:start position:0%
+tightly pulled belt in the middle um of
+ 
+
+ align:start position:0%
+tightly pulled belt in the middle um of
+a support structure so that the and you
+
+ align:start position:0%
+a support structure so that the and you
+ 
+
+ align:start position:0%
+a support structure so that the and you
+put this wind so the wind is going
+
+ align:start position:0%
+put this wind so the wind is going
+ 
+
+ align:start position:0%
+put this wind so the wind is going
+perpendicular to the board. And so that
+
+ align:start position:0%
+perpendicular to the board. And so that
+ 
+
+ align:start position:0%
+perpendicular to the board. And so that
+hits the natural frequencies of the belt
+
+ align:start position:0%
+hits the natural frequencies of the belt
+ 
+
+ align:start position:0%
+hits the natural frequencies of the belt
+and causes it to vibrate. And then you
+
+ align:start position:0%
+and causes it to vibrate. And then you
+ 
+
+ align:start position:0%
+and causes it to vibrate. And then you
+just have some magnets next to a coil on
+
+ align:start position:0%
+just have some magnets next to a coil on
+ 
+
+ align:start position:0%
+just have some magnets next to a coil on
+the corner that allow you to generate
+
+ align:start position:0%
+the corner that allow you to generate
+ 
+
+ align:start position:0%
+the corner that allow you to generate
+electricity. So for um certain
+
+ align:start position:0%
+electricity. So for um certain
+ 
+
+ align:start position:0%
+electricity. So for um certain
+applications, this can be a really
+
+ align:start position:0%
+applications, this can be a really
+ 
+
+ align:start position:0%
+applications, this can be a really
+lowcost way to provide electricity and
+
+ align:start position:0%
+lowcost way to provide electricity and
+ 
+
+ align:start position:0%
+lowcost way to provide electricity and
+you can you this is a pretty relatively
+
+ align:start position:0%
+you can you this is a pretty relatively
+ 
+
+ align:start position:0%
+you can you this is a pretty relatively
+fancy way of building it. But you can
+
+ align:start position:0%
+fancy way of building it. But you can
+ 
+
+ align:start position:0%
+fancy way of building it. But you can
+imagine and they have building it out of
+
+ align:start position:0%
+imagine and they have building it out of
+ 
+
+ align:start position:0%
+imagine and they have building it out of
+like a PVC pipe um which you can get
+
+ align:start position:0%
+like a PVC pipe um which you can get
+ 
+
+ align:start position:0%
+like a PVC pipe um which you can get
+anywhere um and build building it really
+
+ align:start position:0%
+anywhere um and build building it really
+ 
+
+ align:start position:0%
+anywhere um and build building it really
+simply and because there's no very few
+
+ align:start position:0%
+simply and because there's no very few
+ 
+
+ align:start position:0%
+simply and because there's no very few
+moving parts and nothing rotating it's
+
+ align:start position:0%
+moving parts and nothing rotating it's
+ 
+
+ align:start position:0%
+moving parts and nothing rotating it's
+much easier to build than even a
+
+ align:start position:0%
+much easier to build than even a
+ 
+
+ align:start position:0%
+much easier to build than even a
+vertical axis wind turbine. Um and so
+
+ align:start position:0%
+vertical axis wind turbine. Um and so
+ 
+
+ align:start position:0%
+vertical axis wind turbine. Um and so
+it's a really neat application and you
+
+ align:start position:0%
+it's a really neat application and you
+ 
+
+ align:start position:0%
+it's a really neat application and you
+know hypothetically you could imagine
+
+ align:start position:0%
+know hypothetically you could imagine
+ 
+
+ align:start position:0%
+know hypothetically you could imagine
+building it into structures like um
+
+ align:start position:0%
+building it into structures like um
+ 
+
+ align:start position:0%
+building it into structures like um
+railings on buildings and stuff um in
+
+ align:start position:0%
+railings on buildings and stuff um in
+ 
+
+ align:start position:0%
+railings on buildings and stuff um in
+order to uh power different things. So
+
+ align:start position:0%
+order to uh power different things. So
+ 
+
+ align:start position:0%
+order to uh power different things. So
+this is one example and we do have at
+
+ align:start position:0%
+this is one example and we do have at
+ 
+
+ align:start position:0%
+this is one example and we do have at
+least a couple at DAB so we'll make sure
+
+ align:start position:0%
+least a couple at DAB so we'll make sure
+ 
+
+ align:start position:0%
+least a couple at DAB so we'll make sure
+to show you them later today or
+
+ align:start position:0%
+to show you them later today or
+ 
+
+ align:start position:0%
+to show you them later today or
+tomorrow.
+
+ align:start position:0%
+tomorrow.
+ 
+
+ align:start position:0%
+tomorrow.
+Um another example is there sort of the
+
+ align:start position:0%
+Um another example is there sort of the
+ 
+
+ align:start position:0%
+Um another example is there sort of the
+classic um wind turbine in developing
+
+ align:start position:0%
+classic um wind turbine in developing
+ 
+
+ align:start position:0%
+classic um wind turbine in developing
+countries was designed by Hugh Pigot. Um
+
+ align:start position:0%
+countries was designed by Hugh Pigot. Um
+ 
+
+ align:start position:0%
+countries was designed by Hugh Pigot. Um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+these are pictures of work being done at
+
+ align:start position:0%
+these are pictures of work being done at
+ 
+
+ align:start position:0%
+these are pictures of work being done at
+Blue Energy on which is in Blue Fields
+
+ align:start position:0%
+Blue Energy on which is in Blue Fields
+ 
+
+ align:start position:0%
+Blue Energy on which is in Blue Fields
+in Nicaragua and we worked with them
+
+ align:start position:0%
+in Nicaragua and we worked with them
+ 
+
+ align:start position:0%
+in Nicaragua and we worked with them
+last year. Um and they build all these
+
+ align:start position:0%
+last year. Um and they build all these
+ 
+
+ align:start position:0%
+last year. Um and they build all these
+turbines. So you can see there's the the
+
+ align:start position:0%
+turbines. So you can see there's the the
+ 
+
+ align:start position:0%
+turbines. So you can see there's the the
+support wires and that you can rotate
+
+ align:start position:0%
+support wires and that you can rotate
+ 
+
+ align:start position:0%
+support wires and that you can rotate
+the uh the turbine down so that you can
+
+ align:start position:0%
+the uh the turbine down so that you can
+ 
+
+ align:start position:0%
+the uh the turbine down so that you can
+um do maintenance on it. Um which is a
+
+ align:start position:0%
+um do maintenance on it. Um which is a
+ 
+
+ align:start position:0%
+um do maintenance on it. Um which is a
+really nice feature. So that's one sort
+
+ align:start position:0%
+really nice feature. So that's one sort
+ 
+
+ align:start position:0%
+really nice feature. So that's one sort
+of classic design that's pretty common
+
+ align:start position:0%
+of classic design that's pretty common
+ 
+
+ align:start position:0%
+of classic design that's pretty common
+in developing countries. Um and then a
+
+ align:start position:0%
+in developing countries. Um and then a
+ 
+
+ align:start position:0%
+in developing countries. Um and then a
+lot of people have heard of William
+
+ align:start position:0%
+lot of people have heard of William
+ 
+
+ align:start position:0%
+lot of people have heard of William
+Kamwamba. Oh, there's the wind belt. So
+
+ align:start position:0%
+Kamwamba. Oh, there's the wind belt. So
+ 
+
+ align:start position:0%
+Kamwamba. Oh, there's the wind belt. So
+let me go back to that. So I'll pass
+
+ align:start position:0%
+let me go back to that. So I'll pass
+ 
+
+ align:start position:0%
+let me go back to that. So I'll pass
+this around but you and the belt is not
+
+ align:start position:0%
+this around but you and the belt is not
+ 
+
+ align:start position:0%
+this around but you and the belt is not
+exactly taught at the moment. Um, but
+
+ align:start position:0%
+exactly taught at the moment. Um, but
+ 
+
+ align:start position:0%
+exactly taught at the moment. Um, but
+you can see just the belt,
+
+ align:start position:0%
+you can see just the belt,
+ 
+
+ align:start position:0%
+you can see just the belt,
+the magnet on the belt that goes against
+
+ align:start position:0%
+the magnet on the belt that goes against
+ 
+
+ align:start position:0%
+the magnet on the belt that goes against
+the coil, and that's really all there is
+
+ align:start position:0%
+the coil, and that's really all there is
+ 
+
+ align:start position:0%
+the coil, and that's really all there is
+to it. And then a little bit of
+
+ align:start position:0%
+to it. And then a little bit of
+ 
+
+ align:start position:0%
+to it. And then a little bit of
+circuitry in order to generate power,
+
+ align:start position:0%
+circuitry in order to generate power,
+ 
+
+ align:start position:0%
+circuitry in order to generate power,
+which is a really simple way to do
+
+ align:start position:0%
+which is a really simple way to do
+ 
+
+ align:start position:0%
+which is a really simple way to do
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+So, what's the idea? The wind goes
+
+ align:start position:0%
+So, what's the idea? The wind goes
+ 
+
+ align:start position:0%
+So, what's the idea? The wind goes
+through the tape there.
+
+ align:start position:0%
+through the tape there.
+ 
+
+ align:start position:0%
+through the tape there.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+And the tape vibrates because it hits
+
+ align:start position:0%
+And the tape vibrates because it hits
+ 
+
+ align:start position:0%
+And the tape vibrates because it hits
+natural frequencies and the vibration
+
+ align:start position:0%
+natural frequencies and the vibration
+ 
+
+ align:start position:0%
+natural frequencies and the vibration
+allows you to generate electricity. It's
+
+ align:start position:0%
+allows you to generate electricity. It's
+ 
+
+ align:start position:0%
+allows you to generate electricity. It's
+movement is all you need.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thanks.
+
+ align:start position:0%
+Thanks.
+ 
+
+ align:start position:0%
+Thanks.
+Um, so William Kamwamba
+
+ align:start position:0%
+Um, so William Kamwamba
+ 
+
+ align:start position:0%
+Um, so William Kamwamba
+um was this guy.
+
+ align:start position:0%
+um was this guy.
+ 
+
+ align:start position:0%
+um was this guy.
+Where did he live? Did I write it down?
+
+ align:start position:0%
+Where did he live? Did I write it down?
+ 
+
+ align:start position:0%
+Where did he live? Did I write it down?
+in Malawi and he just got really
+
+ align:start position:0%
+in Malawi and he just got really
+ 
+
+ align:start position:0%
+in Malawi and he just got really
+interested in how how he could get
+
+ align:start position:0%
+interested in how how he could get
+ 
+
+ align:start position:0%
+interested in how how he could get
+electricity at his house and went to the
+
+ align:start position:0%
+electricity at his house and went to the
+ 
+
+ align:start position:0%
+electricity at his house and went to the
+library and read a bunch of books and
+
+ align:start position:0%
+library and read a bunch of books and
+ 
+
+ align:start position:0%
+library and read a bunch of books and
+got inspired and built his own um wind
+
+ align:start position:0%
+got inspired and built his own um wind
+ 
+
+ align:start position:0%
+got inspired and built his own um wind
+turbine which doesn't look like your
+
+ align:start position:0%
+turbine which doesn't look like your
+ 
+
+ align:start position:0%
+turbine which doesn't look like your
+traditional wind turbine. Um there are a
+
+ align:start position:0%
+traditional wind turbine. Um there are a
+ 
+
+ align:start position:0%
+traditional wind turbine. Um there are a
+few design improvements that could be
+
+ align:start position:0%
+few design improvements that could be
+ 
+
+ align:start position:0%
+few design improvements that could be
+made, especially with better resources.
+
+ align:start position:0%
+made, especially with better resources.
+ 
+
+ align:start position:0%
+made, especially with better resources.
+um but worked well enough for him to
+
+ align:start position:0%
+um but worked well enough for him to
+ 
+
+ align:start position:0%
+um but worked well enough for him to
+power a radio at his house and charge
+
+ align:start position:0%
+power a radio at his house and charge
+ 
+
+ align:start position:0%
+power a radio at his house and charge
+cell phones which got people really
+
+ align:start position:0%
+cell phones which got people really
+ 
+
+ align:start position:0%
+cell phones which got people really
+excited so that then he could they would
+
+ align:start position:0%
+excited so that then he could they would
+ 
+
+ align:start position:0%
+excited so that then he could they would
+start paying him so he could start
+
+ align:start position:0%
+start paying him so he could start
+ 
+
+ align:start position:0%
+start paying him so he could start
+building um more and more um turbines.
+
+ align:start position:0%
+building um more and more um turbines.
+ 
+
+ align:start position:0%
+building um more and more um turbines.
+So it's a really cool
+
+ align:start position:0%
+So it's a really cool
+ 
+
+ align:start position:0%
+So it's a really cool
+story and now he's at Dartmouth um doing
+
+ align:start position:0%
+story and now he's at Dartmouth um doing
+ 
+
+ align:start position:0%
+story and now he's at Dartmouth um doing
+in school which he never could have done
+
+ align:start position:0%
+in school which he never could have done
+ 
+
+ align:start position:0%
+in school which he never could have done
+had he not um built this turbine. So
+
+ align:start position:0%
+had he not um built this turbine. So
+ 
+
+ align:start position:0%
+had he not um built this turbine. So
+he's a cool guy. Um, we may be able to
+
+ align:start position:0%
+he's a cool guy. Um, we may be able to
+ 
+
+ align:start position:0%
+he's a cool guy. Um, we may be able to
+get him to come down to talk to our
+
+ align:start position:0%
+get him to come down to talk to our
+ 
+
+ align:start position:0%
+get him to come down to talk to our
+class this year. We'll see. I'm trying.
+
+ align:start position:0%
+class this year. We'll see. I'm trying.
+ 
+
+ align:start position:0%
+class this year. We'll see. I'm trying.
+Um, but his adviser at Dartmouth is very
+
+ align:start position:0%
+Um, but his adviser at Dartmouth is very
+ 
+
+ align:start position:0%
+Um, but his adviser at Dartmouth is very
+reluctant to let him travel. I'm sorry.
+
+ align:start position:0%
+reluctant to let him travel. I'm sorry.
+ 
+
+ align:start position:0%
+reluctant to let him travel. I'm sorry.
+Yeah. So, but because he didn't grow up
+
+ align:start position:0%
+Yeah. So, but because he didn't grow up
+ 
+
+ align:start position:0%
+Yeah. So, but because he didn't grow up
+here, like he's getting very um parented
+
+ align:start position:0%
+here, like he's getting very um parented
+ 
+
+ align:start position:0%
+here, like he's getting very um parented
+at a different level than um you guys
+
+ align:start position:0%
+at a different level than um you guys
+ 
+
+ align:start position:0%
+at a different level than um you guys
+are.
+
+ align:start position:0%
+are.
+ 
+
+ align:start position:0%
+are.
+So, um by by the professor at Dartmouth.
+
+ align:start position:0%
+So, um by by the professor at Dartmouth.
+ 
+
+ align:start position:0%
+So, um by by the professor at Dartmouth.
+Um so anyway uh so just a cool example
+
+ align:start position:0%
+Um so anyway uh so just a cool example
+ 
+
+ align:start position:0%
+Um so anyway uh so just a cool example
+of something very low tech that worked
+
+ align:start position:0%
+of something very low tech that worked
+ 
+
+ align:start position:0%
+of something very low tech that worked
+really well and u made a remarkable
+
+ align:start position:0%
+really well and u made a remarkable
+ 
+
+ align:start position:0%
+really well and u made a remarkable
+change for this guy and also um his
+
+ align:start position:0%
+change for this guy and also um his
+ 
+
+ align:start position:0%
+change for this guy and also um his
+village. Um and then working all the way
+
+ align:start position:0%
+village. Um and then working all the way
+ 
+
+ align:start position:0%
+village. Um and then working all the way
+down to the really simplest wind
+
+ align:start position:0%
+down to the really simplest wind
+ 
+
+ align:start position:0%
+down to the really simplest wind
+turbine. So, this is a I don't know if
+
+ align:start position:0%
+turbine. So, this is a I don't know if
+ 
+
+ align:start position:0%
+turbine. So, this is a I don't know if
+you say it as Panem or Panamone, but one
+
+ align:start position:0%
+you say it as Panem or Panamone, but one
+ 
+
+ align:start position:0%
+you say it as Panem or Panamone, but one
+of those um wind turbine, which is
+
+ align:start position:0%
+of those um wind turbine, which is
+ 
+
+ align:start position:0%
+of those um wind turbine, which is
+incredibly old technology that was this
+
+ align:start position:0%
+incredibly old technology that was this
+ 
+
+ align:start position:0%
+incredibly old technology that was this
+is the like 10,000 BC technology that
+
+ align:start position:0%
+is the like 10,000 BC technology that
+ 
+
+ align:start position:0%
+is the like 10,000 BC technology that
+we're talking about. And it's just sails
+
+ align:start position:0%
+we're talking about. And it's just sails
+ 
+
+ align:start position:0%
+we're talking about. And it's just sails
+um that rotate. The sails actually each
+
+ align:start position:0%
+um that rotate. The sails actually each
+ 
+
+ align:start position:0%
+um that rotate. The sails actually each
+one rotates 180 degrees. So, they're
+
+ align:start position:0%
+one rotates 180 degrees. So, they're
+ 
+
+ align:start position:0%
+one rotates 180 degrees. So, they're
+always moving in the wind. Um and this
+
+ align:start position:0%
+always moving in the wind. Um and this
+ 
+
+ align:start position:0%
+always moving in the wind. Um and this
+is this is not a turbine. This is a a
+
+ align:start position:0%
+is this is not a turbine. This is a a
+ 
+
+ align:start position:0%
+is this is not a turbine. This is a a
+mill. So, the act of it spinning pulls
+
+ align:start position:0%
+mill. So, the act of it spinning pulls
+ 
+
+ align:start position:0%
+mill. So, the act of it spinning pulls
+this rope pump. Maybe if I turn off the
+
+ align:start position:0%
+this rope pump. Maybe if I turn off the
+ 
+
+ align:start position:0%
+this rope pump. Maybe if I turn off the
+light so it'll be easier to see.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, there's a rope pump here. And the
+
+ align:start position:0%
+So, there's a rope pump here. And the
+ 
+
+ align:start position:0%
+So, there's a rope pump here. And the
+way a rope pump works is incredibly
+
+ align:start position:0%
+way a rope pump works is incredibly
+ 
+
+ align:start position:0%
+way a rope pump works is incredibly
+simple. So, you just have a rope inside
+
+ align:start position:0%
+simple. So, you just have a rope inside
+ 
+
+ align:start position:0%
+simple. So, you just have a rope inside
+a tube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that goes down into the water um
+
+ align:start position:0%
+um that goes down into the water um
+ 
+
+ align:start position:0%
+um that goes down into the water um
+table so that you're you're filling um
+
+ align:start position:0%
+table so that you're you're filling um
+ 
+
+ align:start position:0%
+table so that you're you're filling um
+you're getting water um
+
+ align:start position:0%
+you're getting water um
+ 
+
+ align:start position:0%
+you're getting water um
+through holes in the in the tube. And
+
+ align:start position:0%
+through holes in the in the tube. And
+ 
+
+ align:start position:0%
+through holes in the in the tube. And
+then you either have knots in the rope
+
+ align:start position:0%
+then you either have knots in the rope
+ 
+
+ align:start position:0%
+then you either have knots in the rope
+or if you can find them, rubber washers
+
+ align:start position:0%
+or if you can find them, rubber washers
+ 
+
+ align:start position:0%
+or if you can find them, rubber washers
+like every foot along the tube. And this
+
+ align:start position:0%
+like every foot along the tube. And this
+ 
+
+ align:start position:0%
+like every foot along the tube. And this
+is obviously not to scale in any way.
+
+ align:start position:0%
+is obviously not to scale in any way.
+ 
+
+ align:start position:0%
+is obviously not to scale in any way.
+Um, and so the water gets trapped
+
+ align:start position:0%
+Um, and so the water gets trapped
+ 
+
+ align:start position:0%
+Um, and so the water gets trapped
+between the washers and you pull up the
+
+ align:start position:0%
+between the washers and you pull up the
+ 
+
+ align:start position:0%
+between the washers and you pull up the
+water that way. And so this is really
+
+ align:start position:0%
+water that way. And so this is really
+ 
+
+ align:start position:0%
+water that way. And so this is really
+simple. Again, we're talking about
+
+ align:start position:0%
+simple. Again, we're talking about
+ 
+
+ align:start position:0%
+simple. Again, we're talking about
+ridiculously low efficiencies, but if
+
+ align:start position:0%
+ridiculously low efficiencies, but if
+ 
+
+ align:start position:0%
+ridiculously low efficiencies, but if
+you need to irrigate, this is a way to
+
+ align:start position:0%
+you need to irrigate, this is a way to
+ 
+
+ align:start position:0%
+you need to irrigate, this is a way to
+do it that just uses the wind. Um, it
+
+ align:start position:0%
+do it that just uses the wind. Um, it
+ 
+
+ align:start position:0%
+do it that just uses the wind. Um, it
+works really well. So, and this was
+
+ align:start position:0%
+works really well. So, and this was
+ 
+
+ align:start position:0%
+works really well. So, and this was
+built for $40. So which is ridiculously
+
+ align:start position:0%
+built for $40. So which is ridiculously
+ 
+
+ align:start position:0%
+built for $40. So which is ridiculously
+inexpensive compared to even like a Hugh
+
+ align:start position:0%
+inexpensive compared to even like a Hugh
+ 
+
+ align:start position:0%
+inexpensive compared to even like a Hugh
+Pigot wind turbine which is you know in
+
+ align:start position:0%
+Pigot wind turbine which is you know in
+ 
+
+ align:start position:0%
+Pigot wind turbine which is you know in
+the thousands of dollars. So there are
+
+ align:start position:0%
+the thousands of dollars. So there are
+ 
+
+ align:start position:0%
+the thousands of dollars. So there are
+opportunities for a whole range of
+
+ align:start position:0%
+opportunities for a whole range of
+ 
+
+ align:start position:0%
+opportunities for a whole range of
+possibilities. And then yeah there's
+
+ align:start position:0%
+possibilities. And then yeah there's
+ 
+
+ align:start position:0%
+possibilities. And then yeah there's
+just so many different types out there.
+
+ align:start position:0%
+just so many different types out there.
+ 
+
+ align:start position:0%
+just so many different types out there.
+So if you look into it wind is one of
+
+ align:start position:0%
+So if you look into it wind is one of
+ 
+
+ align:start position:0%
+So if you look into it wind is one of
+the areas where people get really
+
+ align:start position:0%
+the areas where people get really
+ 
+
+ align:start position:0%
+the areas where people get really
+excited and like to build their own
+
+ align:start position:0%
+excited and like to build their own
+ 
+
+ align:start position:0%
+excited and like to build their own
+stuff. And so you can see a huge v
+
+ align:start position:0%
+stuff. And so you can see a huge v
+ 
+
+ align:start position:0%
+stuff. And so you can see a huge v
+variety of designs in the world.
+
+ align:start position:0%
+variety of designs in the world.
+ 
+
+ align:start position:0%
+variety of designs in the world.
+So that's wind in a very fast nutshell.
+
+ align:start position:0%
+So that's wind in a very fast nutshell.
+ 
+
+ align:start position:0%
+So that's wind in a very fast nutshell.
+Are there any questions about that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so uh next is micro hydro. Um and
+
+ align:start position:0%
+Okay, so uh next is micro hydro. Um and
+ 
+
+ align:start position:0%
+Okay, so uh next is micro hydro. Um and
+microhydro is kind of funny because it's
+
+ align:start position:0%
+microhydro is kind of funny because it's
+ 
+
+ align:start position:0%
+microhydro is kind of funny because it's
+harder to find really good examples of
+
+ align:start position:0%
+harder to find really good examples of
+ 
+
+ align:start position:0%
+harder to find really good examples of
+installations in the developing world
+
+ align:start position:0%
+installations in the developing world
+ 
+
+ align:start position:0%
+installations in the developing world
+because they tend to be just built but
+
+ align:start position:0%
+because they tend to be just built but
+ 
+
+ align:start position:0%
+because they tend to be just built but
+not well documented is what I'm finding.
+
+ align:start position:0%
+not well documented is what I'm finding.
+ 
+
+ align:start position:0%
+not well documented is what I'm finding.
+So, um, so I'm going to talk more about
+
+ align:start position:0%
+So, um, so I'm going to talk more about
+ 
+
+ align:start position:0%
+So, um, so I'm going to talk more about
+how you would,
+
+ align:start position:0%
+how you would,
+ 
+
+ align:start position:0%
+how you would,
+uh, determine if a microhydro
+
+ align:start position:0%
+uh, determine if a microhydro
+ 
+
+ align:start position:0%
+uh, determine if a microhydro
+installation would be appropriate, and I
+
+ align:start position:0%
+installation would be appropriate, and I
+ 
+
+ align:start position:0%
+installation would be appropriate, and I
+don't have as many good examples of
+
+ align:start position:0%
+don't have as many good examples of
+ 
+
+ align:start position:0%
+don't have as many good examples of
+installations that are successful, but
+
+ align:start position:0%
+installations that are successful, but
+ 
+
+ align:start position:0%
+installations that are successful, but
+um, they're certainly out there. Uh, so
+
+ align:start position:0%
+um, they're certainly out there. Uh, so
+ 
+
+ align:start position:0%
+um, they're certainly out there. Uh, so
+hydro power is just using the
+
+ align:start position:0%
+hydro power is just using the
+ 
+
+ align:start position:0%
+hydro power is just using the
+gravitational flow of water to generate
+
+ align:start position:0%
+gravitational flow of water to generate
+ 
+
+ align:start position:0%
+gravitational flow of water to generate
+power. Um, considering both the the two
+
+ align:start position:0%
+power. Um, considering both the the two
+ 
+
+ align:start position:0%
+power. Um, considering both the the two
+terms I'm going to use are head and flow
+
+ align:start position:0%
+terms I'm going to use are head and flow
+ 
+
+ align:start position:0%
+terms I'm going to use are head and flow
+rate. So head is the distance that the
+
+ align:start position:0%
+rate. So head is the distance that the
+ 
+
+ align:start position:0%
+rate. So head is the distance that the
+water falls and flow rate is how quickly
+
+ align:start position:0%
+water falls and flow rate is how quickly
+ 
+
+ align:start position:0%
+water falls and flow rate is how quickly
+the water is moving. Um and so hydro
+
+ align:start position:0%
+the water is moving. Um and so hydro
+ 
+
+ align:start position:0%
+the water is moving. Um and so hydro
+power can be at you know two megawws and
+
+ align:start position:0%
+power can be at you know two megawws and
+ 
+
+ align:start position:0%
+power can be at you know two megawws and
+much beyond and can be a sizable um is a
+
+ align:start position:0%
+much beyond and can be a sizable um is a
+ 
+
+ align:start position:0%
+much beyond and can be a sizable um is a
+sizable impact on our nation's
+
+ align:start position:0%
+sizable impact on our nation's
+ 
+
+ align:start position:0%
+sizable impact on our nation's
+electricity supply for example all the
+
+ align:start position:0%
+electricity supply for example all the
+ 
+
+ align:start position:0%
+electricity supply for example all the
+way down to a 200 watt um turbine or
+
+ align:start position:0%
+way down to a 200 watt um turbine or
+ 
+
+ align:start position:0%
+way down to a 200 watt um turbine or
+smaller. Um so I'm saying micro hydro
+
+ align:start position:0%
+smaller. Um so I'm saying micro hydro
+ 
+
+ align:start position:0%
+smaller. Um so I'm saying micro hydro
+for this lecture. probably some of the
+
+ align:start position:0%
+for this lecture. probably some of the
+ 
+
+ align:start position:0%
+for this lecture. probably some of the
+stuff I'm talking about is actually pico
+
+ align:start position:0%
+stuff I'm talking about is actually pico
+ 
+
+ align:start position:0%
+stuff I'm talking about is actually pico
+or mini um ranging um it's and everyone
+
+ align:start position:0%
+or mini um ranging um it's and everyone
+ 
+
+ align:start position:0%
+or mini um ranging um it's and everyone
+defines these differently. So if you
+
+ align:start position:0%
+defines these differently. So if you
+ 
+
+ align:start position:0%
+defines these differently. So if you
+look up what pico hydro is you'll see 10
+
+ align:start position:0%
+look up what pico hydro is you'll see 10
+ 
+
+ align:start position:0%
+look up what pico hydro is you'll see 10
+different definitions. So it's not
+
+ align:start position:0%
+different definitions. So it's not
+ 
+
+ align:start position:0%
+different definitions. So it's not
+critical that you're getting exactly and
+
+ align:start position:0%
+critical that you're getting exactly and
+ 
+
+ align:start position:0%
+critical that you're getting exactly and
+you can even see I
+
+ align:start position:0%
+you can even see I
+ 
+
+ align:start position:0%
+you can even see I
+there's there's uh between pico and
+
+ align:start position:0%
+there's there's uh between pico and
+ 
+
+ align:start position:0%
+there's there's uh between pico and
+micro there's something right.
+
+ align:start position:0%
+micro there's something right.
+ 
+
+ align:start position:0%
+micro there's something right.
+So according to this definition um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so and this is with water power
+
+ align:start position:0%
+yeah so and this is with water power
+ 
+
+ align:start position:0%
+yeah so and this is with water power
+it's the same um as wind in terms of
+
+ align:start position:0%
+it's the same um as wind in terms of
+ 
+
+ align:start position:0%
+it's the same um as wind in terms of
+there's mills and there's turbines so
+
+ align:start position:0%
+there's mills and there's turbines so
+ 
+
+ align:start position:0%
+there's mills and there's turbines so
+you can think of the the o old grist
+
+ align:start position:0%
+you can think of the the o old grist
+ 
+
+ align:start position:0%
+you can think of the the o old grist
+mills and other things that you can see
+
+ align:start position:0%
+mills and other things that you can see
+ 
+
+ align:start position:0%
+mills and other things that you can see
+in parts of New England still um
+
+ align:start position:0%
+in parts of New England still um
+ 
+
+ align:start position:0%
+in parts of New England still um
+they're again they're low velocity high
+
+ align:start position:0%
+they're again they're low velocity high
+ 
+
+ align:start position:0%
+they're again they're low velocity high
+torque delivering mechanical power
+
+ align:start position:0%
+torque delivering mechanical power
+ 
+
+ align:start position:0%
+torque delivering mechanical power
+directly
+
+ align:start position:0%
+directly
+ 
+
+ align:start position:0%
+directly
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as opposed to a turbine which is higher
+
+ align:start position:0%
+as opposed to a turbine which is higher
+ 
+
+ align:start position:0%
+as opposed to a turbine which is higher
+much higher velocity much lower torque
+
+ align:start position:0%
+much higher velocity much lower torque
+ 
+
+ align:start position:0%
+much higher velocity much lower torque
+to allow you to generate electricity. So
+
+ align:start position:0%
+to allow you to generate electricity. So
+ 
+
+ align:start position:0%
+to allow you to generate electricity. So
+those are the two extremes. Um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in terms of micro or hydro power there's
+
+ align:start position:0%
+in terms of micro or hydro power there's
+ 
+
+ align:start position:0%
+in terms of micro or hydro power there's
+two methods. So, one is called run of
+
+ align:start position:0%
+two methods. So, one is called run of
+ 
+
+ align:start position:0%
+two methods. So, one is called run of
+the river, and that means that you're
+
+ align:start position:0%
+the river, and that means that you're
+ 
+
+ align:start position:0%
+the river, and that means that you're
+just taking a chunk of the river um and
+
+ align:start position:0%
+just taking a chunk of the river um and
+ 
+
+ align:start position:0%
+just taking a chunk of the river um and
+siphoning it siphoning it off into a
+
+ align:start position:0%
+siphoning it siphoning it off into a
+ 
+
+ align:start position:0%
+siphoning it siphoning it off into a
+tube that goes directly into your
+
+ align:start position:0%
+tube that goes directly into your
+ 
+
+ align:start position:0%
+tube that goes directly into your
+turbine. Um the as and the other option
+
+ align:start position:0%
+turbine. Um the as and the other option
+ 
+
+ align:start position:0%
+turbine. Um the as and the other option
+is a dam. So, the benefits of this are
+
+ align:start position:0%
+is a dam. So, the benefits of this are
+ 
+
+ align:start position:0%
+is a dam. So, the benefits of this are
+that it's relatively simple. You can
+
+ align:start position:0%
+that it's relatively simple. You can
+ 
+
+ align:start position:0%
+that it's relatively simple. You can
+build it locally um compared to a dam is
+
+ align:start position:0%
+build it locally um compared to a dam is
+ 
+
+ align:start position:0%
+build it locally um compared to a dam is
+much harder harder to build generally.
+
+ align:start position:0%
+much harder harder to build generally.
+ 
+
+ align:start position:0%
+much harder harder to build generally.
+Um it's comparatively lower much lower
+
+ align:start position:0%
+Um it's comparatively lower much lower
+ 
+
+ align:start position:0%
+Um it's comparatively lower much lower
+environmental impact than a dam. um
+
+ align:start position:0%
+environmental impact than a dam. um
+ 
+
+ align:start position:0%
+environmental impact than a dam. um
+they're relatively affordable. Um but
+
+ align:start position:0%
+they're relatively affordable. Um but
+ 
+
+ align:start position:0%
+they're relatively affordable. Um but
+when you have a drought, you don't have
+
+ align:start position:0%
+when you have a drought, you don't have
+ 
+
+ align:start position:0%
+when you have a drought, you don't have
+any storage like you have with a dam. So
+
+ align:start position:0%
+any storage like you have with a dam. So
+ 
+
+ align:start position:0%
+any storage like you have with a dam. So
+that's the drawback. Uh
+
+ align:start position:0%
+that's the drawback. Uh
+ 
+
+ align:start position:0%
+that's the drawback. Uh
+and the dam is, you know, the reverse
+
+ align:start position:0%
+and the dam is, you know, the reverse
+ 
+
+ align:start position:0%
+and the dam is, you know, the reverse
+that you can accumulate your rainfall,
+
+ align:start position:0%
+that you can accumulate your rainfall,
+ 
+
+ align:start position:0%
+that you can accumulate your rainfall,
+which is great, but it's relatively
+
+ align:start position:0%
+which is great, but it's relatively
+ 
+
+ align:start position:0%
+which is great, but it's relatively
+expensive and there's a greater
+
+ align:start position:0%
+expensive and there's a greater
+ 
+
+ align:start position:0%
+expensive and there's a greater
+environmental impact on the negative. Um
+
+ align:start position:0%
+environmental impact on the negative. Um
+ 
+
+ align:start position:0%
+environmental impact on the negative. Um
+because damning up water affects the
+
+ align:start position:0%
+because damning up water affects the
+ 
+
+ align:start position:0%
+because damning up water affects the
+local environment from the fish to just
+
+ align:start position:0%
+local environment from the fish to just
+ 
+
+ align:start position:0%
+local environment from the fish to just
+what the fields look like etc etc. Um
+
+ align:start position:0%
+what the fields look like etc etc. Um
+ 
+
+ align:start position:0%
+what the fields look like etc etc. Um
+I'm sure you've heard of dams in China
+
+ align:start position:0%
+I'm sure you've heard of dams in China
+ 
+
+ align:start position:0%
+I'm sure you've heard of dams in China
+or similar that um you know have
+
+ align:start position:0%
+or similar that um you know have
+ 
+
+ align:start position:0%
+or similar that um you know have
+destroyed entire like many entire
+
+ align:start position:0%
+destroyed entire like many entire
+ 
+
+ align:start position:0%
+destroyed entire like many entire
+communities um for building dams on a
+
+ align:start position:0%
+communities um for building dams on a
+ 
+
+ align:start position:0%
+communities um for building dams on a
+very very large scale. Um and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and there's more maintenance
+
+ align:start position:0%
+yeah and there's more maintenance
+ 
+
+ align:start position:0%
+yeah and there's more maintenance
+associated with the dam too in terms of
+
+ align:start position:0%
+associated with the dam too in terms of
+ 
+
+ align:start position:0%
+associated with the dam too in terms of
+silt silt accumulation. It's it's
+
+ align:start position:0%
+silt silt accumulation. It's it's
+ 
+
+ align:start position:0%
+silt silt accumulation. It's it's
+challenging. Um so we're just going to
+
+ align:start position:0%
+challenging. Um so we're just going to
+ 
+
+ align:start position:0%
+challenging. Um so we're just going to
+talk about the run of the river model.
+
+ align:start position:0%
+talk about the run of the river model.
+ 
+
+ align:start position:0%
+talk about the run of the river model.
+So the components that you have is
+
+ align:start position:0%
+So the components that you have is
+ 
+
+ align:start position:0%
+So the components that you have is
+something called a wear that diverts a
+
+ align:start position:0%
+something called a wear that diverts a
+ 
+
+ align:start position:0%
+something called a wear that diverts a
+chunk of the water into your tube. Um
+
+ align:start position:0%
+chunk of the water into your tube. Um
+ 
+
+ align:start position:0%
+chunk of the water into your tube. Um
+you generally have a settling basin so
+
+ align:start position:0%
+you generally have a settling basin so
+ 
+
+ align:start position:0%
+you generally have a settling basin so
+that any debris um settles out uh
+
+ align:start position:0%
+that any debris um settles out uh
+ 
+
+ align:start position:0%
+that any debris um settles out uh
+because you don't want it going into
+
+ align:start position:0%
+because you don't want it going into
+ 
+
+ align:start position:0%
+because you don't want it going into
+your turbine because you'll destroy your
+
+ align:start position:0%
+your turbine because you'll destroy your
+ 
+
+ align:start position:0%
+your turbine because you'll destroy your
+turbine. Um a for bay which is a small
+
+ align:start position:0%
+turbine. Um a for bay which is a small
+ 
+
+ align:start position:0%
+turbine. Um a for bay which is a small
+holding tank so you're getting reserve
+
+ align:start position:0%
+holding tank so you're getting reserve
+ 
+
+ align:start position:0%
+holding tank so you're getting reserve
+capacity that way but that's talking
+
+ align:start position:0%
+capacity that way but that's talking
+ 
+
+ align:start position:0%
+capacity that way but that's talking
+about like variation on the order of
+
+ align:start position:0%
+about like variation on the order of
+ 
+
+ align:start position:0%
+about like variation on the order of
+seconds or minutes not days or months.
+
+ align:start position:0%
+seconds or minutes not days or months.
+ 
+
+ align:start position:0%
+seconds or minutes not days or months.
+uh pentock, which is a closed pipe
+
+ align:start position:0%
+uh pentock, which is a closed pipe
+ 
+
+ align:start position:0%
+uh pentock, which is a closed pipe
+flowing downhill um that feeds directly
+
+ align:start position:0%
+flowing downhill um that feeds directly
+ 
+
+ align:start position:0%
+flowing downhill um that feeds directly
+into your turbine um that then generates
+
+ align:start position:0%
+into your turbine um that then generates
+ 
+
+ align:start position:0%
+into your turbine um that then generates
+your electricity and then the water is
+
+ align:start position:0%
+your electricity and then the water is
+ 
+
+ align:start position:0%
+your electricity and then the water is
+returned back to the river. There's a
+
+ align:start position:0%
+returned back to the river. There's a
+ 
+
+ align:start position:0%
+returned back to the river. There's a
+lot of different turbine types. Um so
+
+ align:start position:0%
+lot of different turbine types. Um so
+ 
+
+ align:start position:0%
+lot of different turbine types. Um so
+the one of the most efficient, if not
+
+ align:start position:0%
+the one of the most efficient, if not
+ 
+
+ align:start position:0%
+the one of the most efficient, if not
+the most efficient, is called a Pelton
+
+ align:start position:0%
+the most efficient, is called a Pelton
+ 
+
+ align:start position:0%
+the most efficient, is called a Pelton
+wheel. And you can see it's it's got a
+
+ align:start position:0%
+wheel. And you can see it's it's got a
+ 
+
+ align:start position:0%
+wheel. And you can see it's it's got a
+relatively complex geometry. Um and so
+
+ align:start position:0%
+relatively complex geometry. Um and so
+ 
+
+ align:start position:0%
+relatively complex geometry. Um and so
+relatively expensive and challenging to
+
+ align:start position:0%
+relatively expensive and challenging to
+ 
+
+ align:start position:0%
+relatively expensive and challenging to
+build. Um but if you do um it's it's
+
+ align:start position:0%
+build. Um but if you do um it's it's
+ 
+
+ align:start position:0%
+build. Um but if you do um it's it's
+very efficient. Um it works well for a
+
+ align:start position:0%
+very efficient. Um it works well for a
+ 
+
+ align:start position:0%
+very efficient. Um it works well for a
+high head low flow situation. So again
+
+ align:start position:0%
+high head low flow situation. So again
+ 
+
+ align:start position:0%
+high head low flow situation. So again
+head is how far the water is dropping.
+
+ align:start position:0%
+head is how far the water is dropping.
+ 
+
+ align:start position:0%
+head is how far the water is dropping.
+Um Francis wheels which work better for
+
+ align:start position:0%
+Um Francis wheels which work better for
+ 
+
+ align:start position:0%
+Um Francis wheels which work better for
+lower head higher flow. Um which has a
+
+ align:start position:0%
+lower head higher flow. Um which has a
+ 
+
+ align:start position:0%
+lower head higher flow. Um which has a
+high a spiral casing where the water
+
+ align:start position:0%
+high a spiral casing where the water
+ 
+
+ align:start position:0%
+high a spiral casing where the water
+comes in and spins this turbine and then
+
+ align:start position:0%
+comes in and spins this turbine and then
+ 
+
+ align:start position:0%
+comes in and spins this turbine and then
+comes out. uh
+
+ align:start position:0%
+comes out. uh
+ 
+
+ align:start position:0%
+comes out. uh
+cross flow where the water flows over
+
+ align:start position:0%
+cross flow where the water flows over
+ 
+
+ align:start position:0%
+cross flow where the water flows over
+this um cylinder which has a bunch of
+
+ align:start position:0%
+this um cylinder which has a bunch of
+ 
+
+ align:start position:0%
+this um cylinder which has a bunch of
+blades on it and that's what spins the
+
+ align:start position:0%
+blades on it and that's what spins the
+ 
+
+ align:start position:0%
+blades on it and that's what spins the
+spins the ro the shaft to generate
+
+ align:start position:0%
+spins the ro the shaft to generate
+ 
+
+ align:start position:0%
+spins the ro the shaft to generate
+electricity. A propeller which literally
+
+ align:start position:0%
+electricity. A propeller which literally
+ 
+
+ align:start position:0%
+electricity. A propeller which literally
+uses a ship's propeller um and instead
+
+ align:start position:0%
+uses a ship's propeller um and instead
+ 
+
+ align:start position:0%
+uses a ship's propeller um and instead
+of the ship's propeller being powered in
+
+ align:start position:0%
+of the ship's propeller being powered in
+ 
+
+ align:start position:0%
+of the ship's propeller being powered in
+order to move the boat it's it's using
+
+ align:start position:0%
+order to move the boat it's it's using
+ 
+
+ align:start position:0%
+order to move the boat it's it's using
+it in the exact opposite way. Um and you
+
+ align:start position:0%
+it in the exact opposite way. Um and you
+ 
+
+ align:start position:0%
+it in the exact opposite way. Um and you
+can see that these, you know, you need
+
+ align:start position:0%
+can see that these, you know, you need
+ 
+
+ align:start position:0%
+can see that these, you know, you need
+different um types of turbines for
+
+ align:start position:0%
+different um types of turbines for
+ 
+
+ align:start position:0%
+different um types of turbines for
+different flow and head situations. Um
+
+ align:start position:0%
+different flow and head situations. Um
+ 
+
+ align:start position:0%
+different flow and head situations. Um
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+one example is just literally putting
+
+ align:start position:0%
+one example is just literally putting
+ 
+
+ align:start position:0%
+one example is just literally putting
+something in the river, skipping that
+
+ align:start position:0%
+something in the river, skipping that
+ 
+
+ align:start position:0%
+something in the river, skipping that
+all that extra stuff of filtering um of
+
+ align:start position:0%
+all that extra stuff of filtering um of
+ 
+
+ align:start position:0%
+all that extra stuff of filtering um of
+of siphoning off the water and just
+
+ align:start position:0%
+of siphoning off the water and just
+ 
+
+ align:start position:0%
+of siphoning off the water and just
+putting something on top of the water.
+
+ align:start position:0%
+putting something on top of the water.
+ 
+
+ align:start position:0%
+putting something on top of the water.
+Um which seems really simple and great
+
+ align:start position:0%
+Um which seems really simple and great
+ 
+
+ align:start position:0%
+Um which seems really simple and great
+until you think about like all the
+
+ align:start position:0%
+until you think about like all the
+ 
+
+ align:start position:0%
+until you think about like all the
+challenges in terms of flooding and
+
+ align:start position:0%
+challenges in terms of flooding and
+ 
+
+ align:start position:0%
+challenges in terms of flooding and
+debris in the water and etc., etc. This
+
+ align:start position:0%
+debris in the water and etc., etc. This
+ 
+
+ align:start position:0%
+debris in the water and etc., etc. This
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+a device that is really prone to
+
+ align:start position:0%
+a device that is really prone to
+ 
+
+ align:start position:0%
+a device that is really prone to
+failure. Um
+
+ align:start position:0%
+failure. Um
+ 
+
+ align:start position:0%
+failure. Um
+but it works in areas where that's your
+
+ align:start position:0%
+but it works in areas where that's your
+ 
+
+ align:start position:0%
+but it works in areas where that's your
+only option. Um or it can work. Uh yeah.
+
+ align:start position:0%
+only option. Um or it can work. Uh yeah.
+ 
+
+ align:start position:0%
+only option. Um or it can work. Uh yeah.
+So some of the considerations you need
+
+ align:start position:0%
+So some of the considerations you need
+ 
+
+ align:start position:0%
+So some of the considerations you need
+for microhydro
+
+ align:start position:0%
+for microhydro
+ 
+
+ align:start position:0%
+for microhydro
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+uh that
+
+ align:start position:0%
+uh that
+ 
+
+ align:start position:0%
+uh that
+the minimum um head and flow you need is
+
+ align:start position:0%
+the minimum um head and flow you need is
+ 
+
+ align:start position:0%
+the minimum um head and flow you need is
+3 ft of head and 20 gallons per minute
+
+ align:start position:0%
+3 ft of head and 20 gallons per minute
+ 
+
+ align:start position:0%
+3 ft of head and 20 gallons per minute
+of flow. Um so that would be the minimum
+
+ align:start position:0%
+of flow. Um so that would be the minimum
+ 
+
+ align:start position:0%
+of flow. Um so that would be the minimum
+head you need and
+
+ align:start position:0%
+head you need and
+ 
+
+ align:start position:0%
+head you need and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you have more head either bonus you
+
+ align:start position:0%
+if you have more head either bonus you
+ 
+
+ align:start position:0%
+if you have more head either bonus you
+get more power or you can therefore have
+
+ align:start position:0%
+get more power or you can therefore have
+ 
+
+ align:start position:0%
+get more power or you can therefore have
+reduced flow because the the power
+
+ align:start position:0%
+reduced flow because the the power
+ 
+
+ align:start position:0%
+reduced flow because the the power
+equation here is again a coefficient of
+
+ align:start position:0%
+equation here is again a coefficient of
+ 
+
+ align:start position:0%
+equation here is again a coefficient of
+efficiency uh times the water density
+
+ align:start position:0%
+efficiency uh times the water density
+ 
+
+ align:start position:0%
+efficiency uh times the water density
+and gravity times the height which is
+
+ align:start position:0%
+and gravity times the height which is
+ 
+
+ align:start position:0%
+and gravity times the height which is
+your head and Q which is your flow rate.
+
+ align:start position:0%
+your head and Q which is your flow rate.
+ 
+
+ align:start position:0%
+your head and Q which is your flow rate.
+So you can see that HQ you can keep
+
+ align:start position:0%
+So you can see that HQ you can keep
+ 
+
+ align:start position:0%
+So you can see that HQ you can keep
+constant if you you know if you increase
+
+ align:start position:0%
+constant if you you know if you increase
+ 
+
+ align:start position:0%
+constant if you you know if you increase
+your head you can lower your velocity
+
+ align:start position:0%
+your head you can lower your velocity
+ 
+
+ align:start position:0%
+your head you can lower your velocity
+and keep your power constant. Uh
+
+ align:start position:0%
+and keep your power constant. Uh
+ 
+
+ align:start position:0%
+and keep your power constant. Uh
+one nice just rule of thumb is if you
+
+ align:start position:0%
+one nice just rule of thumb is if you
+ 
+
+ align:start position:0%
+one nice just rule of thumb is if you
+stick with SI units row G is about 10.
+
+ align:start position:0%
+stick with SI units row G is about 10.
+ 
+
+ align:start position:0%
+stick with SI units row G is about 10.
+So you can just plug that in rather than
+
+ align:start position:0%
+So you can just plug that in rather than
+ 
+
+ align:start position:0%
+So you can just plug that in rather than
+having to remember the density of water
+
+ align:start position:0%
+having to remember the density of water
+ 
+
+ align:start position:0%
+having to remember the density of water
+and gravity. Though in SI units that's
+
+ align:start position:0%
+and gravity. Though in SI units that's
+ 
+
+ align:start position:0%
+and gravity. Though in SI units that's
+relatively easy but if um
+
+ align:start position:0%
+relatively easy but if um
+ 
+
+ align:start position:0%
+relatively easy but if um
+10 is a nice way to just remember it. Um
+
+ align:start position:0%
+10 is a nice way to just remember it. Um
+ 
+
+ align:start position:0%
+10 is a nice way to just remember it. Um
+and then efficiency is somewhere be
+
+ align:start position:0%
+and then efficiency is somewhere be
+ 
+
+ align:start position:0%
+and then efficiency is somewhere be
+generally between 40 and 70%.
+
+ align:start position:0%
+generally between 40 and 70%.
+ 
+
+ align:start position:0%
+generally between 40 and 70%.
+Uh one other thing to think about is
+
+ align:start position:0%
+Uh one other thing to think about is
+ 
+
+ align:start position:0%
+Uh one other thing to think about is
+just when you have your uh pentock
+
+ align:start position:0%
+just when you have your uh pentock
+ 
+
+ align:start position:0%
+just when you have your uh pentock
+go so that's the water going through the
+
+ align:start position:0%
+go so that's the water going through the
+ 
+
+ align:start position:0%
+go so that's the water going through the
+pipe to get from the top of the river
+
+ align:start position:0%
+pipe to get from the top of the river
+ 
+
+ align:start position:0%
+pipe to get from the top of the river
+down to your generator. Um if your pipe
+
+ align:start position:0%
+down to your generator. Um if your pipe
+ 
+
+ align:start position:0%
+down to your generator. Um if your pipe
+diameter is too small the you're going
+
+ align:start position:0%
+diameter is too small the you're going
+ 
+
+ align:start position:0%
+diameter is too small the you're going
+to have frictional losses in the pipe
+
+ align:start position:0%
+to have frictional losses in the pipe
+ 
+
+ align:start position:0%
+to have frictional losses in the pipe
+that dominate and slow your water down
+
+ align:start position:0%
+that dominate and slow your water down
+ 
+
+ align:start position:0%
+that dominate and slow your water down
+so much that it's problematic. So that's
+
+ align:start position:0%
+so much that it's problematic. So that's
+ 
+
+ align:start position:0%
+so much that it's problematic. So that's
+another thing just to remember. um
+
+ align:start position:0%
+another thing just to remember. um
+ 
+
+ align:start position:0%
+another thing just to remember. um
+because it's tempting to use small
+
+ align:start position:0%
+because it's tempting to use small
+ 
+
+ align:start position:0%
+because it's tempting to use small
+diameter pipe um for a variety of
+
+ align:start position:0%
+diameter pipe um for a variety of
+ 
+
+ align:start position:0%
+diameter pipe um for a variety of
+reasons, but that's dangerous. Um
+
+ align:start position:0%
+reasons, but that's dangerous. Um
+ 
+
+ align:start position:0%
+reasons, but that's dangerous. Um
+so how do you figure out if a air of a
+
+ align:start position:0%
+so how do you figure out if a air of a
+ 
+
+ align:start position:0%
+so how do you figure out if a air of a
+river is appropriate for using um
+
+ align:start position:0%
+river is appropriate for using um
+ 
+
+ align:start position:0%
+river is appropriate for using um
+microhydro? So the two things you need
+
+ align:start position:0%
+microhydro? So the two things you need
+ 
+
+ align:start position:0%
+microhydro? So the two things you need
+to know again are flow and head. So the
+
+ align:start position:0%
+to know again are flow and head. So the
+ 
+
+ align:start position:0%
+to know again are flow and head. So the
+simplest method I can find for measuring
+
+ align:start position:0%
+simplest method I can find for measuring
+ 
+
+ align:start position:0%
+simplest method I can find for measuring
+flow um is called a float method. And
+
+ align:start position:0%
+flow um is called a float method. And
+ 
+
+ align:start position:0%
+flow um is called a float method. And
+you can imagine actually doing this in a
+
+ align:start position:0%
+you can imagine actually doing this in a
+ 
+
+ align:start position:0%
+you can imagine actually doing this in a
+river would be challenging. So it's not
+
+ align:start position:0%
+river would be challenging. So it's not
+ 
+
+ align:start position:0%
+river would be challenging. So it's not
+trivial, but it is possible. Um, so you
+
+ align:start position:0%
+trivial, but it is possible. Um, so you
+ 
+
+ align:start position:0%
+trivial, but it is possible. Um, so you
+mark about a 100 feet along a length
+
+ align:start position:0%
+mark about a 100 feet along a length
+ 
+
+ align:start position:0%
+mark about a 100 feet along a length
+that's ideally straight with uniform
+
+ align:start position:0%
+that's ideally straight with uniform
+ 
+
+ align:start position:0%
+that's ideally straight with uniform
+length and depth or width and depth. Um,
+
+ align:start position:0%
+length and depth or width and depth. Um,
+ 
+
+ align:start position:0%
+length and depth or width and depth. Um,
+which is comical to find in a river,
+
+ align:start position:0%
+which is comical to find in a river,
+ 
+
+ align:start position:0%
+which is comical to find in a river,
+right? Like I've never found a river
+
+ align:start position:0%
+right? Like I've never found a river
+ 
+
+ align:start position:0%
+right? Like I've never found a river
+that has 100 feet of uniform width and
+
+ align:start position:0%
+that has 100 feet of uniform width and
+ 
+
+ align:start position:0%
+that has 100 feet of uniform width and
+depth, but you do your best. Um, and
+
+ align:start position:0%
+depth, but you do your best. Um, and
+ 
+
+ align:start position:0%
+depth, but you do your best. Um, and
+then you calculate your cross-sectional
+
+ align:start position:0%
+then you calculate your cross-sectional
+ 
+
+ align:start position:0%
+then you calculate your cross-sectional
+area. A people usually model it as um a
+
+ align:start position:0%
+area. A people usually model it as um a
+ 
+
+ align:start position:0%
+area. A people usually model it as um a
+semicircle or a trapezoid or even just a
+
+ align:start position:0%
+semicircle or a trapezoid or even just a
+ 
+
+ align:start position:0%
+semicircle or a trapezoid or even just a
+rectangle. Um calculate that
+
+ align:start position:0%
+rectangle. Um calculate that
+ 
+
+ align:start position:0%
+rectangle. Um calculate that
+cross-sectional area. You place a marker
+
+ align:start position:0%
+cross-sectional area. You place a marker
+ 
+
+ align:start position:0%
+cross-sectional area. You place a marker
+at the start and end of your 100 ft and
+
+ align:start position:0%
+at the start and end of your 100 ft and
+ 
+
+ align:start position:0%
+at the start and end of your 100 ft and
+then you put floats in the river at the
+
+ align:start position:0%
+then you put floats in the river at the
+ 
+
+ align:start position:0%
+then you put floats in the river at the
+center of the stream um and time them to
+
+ align:start position:0%
+center of the stream um and time them to
+ 
+
+ align:start position:0%
+center of the stream um and time them to
+find out how long it takes for them to
+
+ align:start position:0%
+find out how long it takes for them to
+ 
+
+ align:start position:0%
+find out how long it takes for them to
+get from one end to the other. If you
+
+ align:start position:0%
+get from one end to the other. If you
+ 
+
+ align:start position:0%
+get from one end to the other. If you
+want to get complicated, you can uh put
+
+ align:start position:0%
+want to get complicated, you can uh put
+ 
+
+ align:start position:0%
+want to get complicated, you can uh put
+them all along a bunch of different
+
+ align:start position:0%
+them all along a bunch of different
+ 
+
+ align:start position:0%
+them all along a bunch of different
+points at different levels to worry
+
+ align:start position:0%
+points at different levels to worry
+ 
+
+ align:start position:0%
+points at different levels to worry
+about friction losses, but you don't
+
+ align:start position:0%
+about friction losses, but you don't
+ 
+
+ align:start position:0%
+about friction losses, but you don't
+actually have to do that to get a a
+
+ align:start position:0%
+actually have to do that to get a a
+ 
+
+ align:start position:0%
+actually have to do that to get a a
+ballpark measurement. You can just do it
+
+ align:start position:0%
+ballpark measurement. You can just do it
+ 
+
+ align:start position:0%
+ballpark measurement. You can just do it
+in the center. Um and so and good floats
+
+ align:start position:0%
+in the center. Um and so and good floats
+ 
+
+ align:start position:0%
+in the center. Um and so and good floats
+could be a tennis ball, could be an
+
+ align:start position:0%
+could be a tennis ball, could be an
+ 
+
+ align:start position:0%
+could be a tennis ball, could be an
+apple or something like that, whatever
+
+ align:start position:0%
+apple or something like that, whatever
+ 
+
+ align:start position:0%
+apple or something like that, whatever
+you can find that floats. Um, and then
+
+ align:start position:0%
+you can find that floats. Um, and then
+ 
+
+ align:start position:0%
+you can find that floats. Um, and then
+you do have to use a conversion factor
+
+ align:start position:0%
+you do have to use a conversion factor
+ 
+
+ align:start position:0%
+you do have to use a conversion factor
+because your water's flowing faster at
+
+ align:start position:0%
+because your water's flowing faster at
+ 
+
+ align:start position:0%
+because your water's flowing faster at
+the top of the water than in the the
+
+ align:start position:0%
+the top of the water than in the the
+ 
+
+ align:start position:0%
+the top of the water than in the the
+river than in the center because um
+
+ align:start position:0%
+river than in the center because um
+ 
+
+ align:start position:0%
+river than in the center because um
+because of the friction associated with
+
+ align:start position:0%
+because of the friction associated with
+ 
+
+ align:start position:0%
+because of the friction associated with
+the the base of the river. Uh, and so
+
+ align:start position:0%
+the the base of the river. Uh, and so
+ 
+
+ align:start position:0%
+the the base of the river. Uh, and so
+you have to um you can use a coefficient
+
+ align:start position:0%
+you have to um you can use a coefficient
+ 
+
+ align:start position:0%
+you have to um you can use a coefficient
+just to correct and then you get your
+
+ align:start position:0%
+just to correct and then you get your
+ 
+
+ align:start position:0%
+just to correct and then you get your
+flow rate. Yay. So that was a lot of
+
+ align:start position:0%
+flow rate. Yay. So that was a lot of
+ 
+
+ align:start position:0%
+flow rate. Yay. So that was a lot of
+work and all you have is a flow rate for
+
+ align:start position:0%
+work and all you have is a flow rate for
+ 
+
+ align:start position:0%
+work and all you have is a flow rate for
+one day and water varies like flow rate
+
+ align:start position:0%
+one day and water varies like flow rate
+ 
+
+ align:start position:0%
+one day and water varies like flow rate
+varies tremendously during the season.
+
+ align:start position:0%
+varies tremendously during the season.
+ 
+
+ align:start position:0%
+varies tremendously during the season.
+So again you can do your 10 10ear study
+
+ align:start position:0%
+So again you can do your 10 10ear study
+ 
+
+ align:start position:0%
+So again you can do your 10 10ear study
+or you can just um get some data on
+
+ align:start position:0%
+or you can just um get some data on
+ 
+
+ align:start position:0%
+or you can just um get some data on
+annual precipitation and when is the
+
+ align:start position:0%
+annual precipitation and when is the
+ 
+
+ align:start position:0%
+annual precipitation and when is the
+rainy season the dry season and do your
+
+ align:start position:0%
+rainy season the dry season and do your
+ 
+
+ align:start position:0%
+rainy season the dry season and do your
+best to estimate. Um but yeah so that's
+
+ align:start position:0%
+best to estimate. Um but yeah so that's
+ 
+
+ align:start position:0%
+best to estimate. Um but yeah so that's
+how you'd get your flow rate.
+
+ align:start position:0%
+how you'd get your flow rate.
+ 
+
+ align:start position:0%
+how you'd get your flow rate.
+And then in terms of head, the simplest
+
+ align:start position:0%
+And then in terms of head, the simplest
+ 
+
+ align:start position:0%
+And then in terms of head, the simplest
+method that again that I found that's
+
+ align:start position:0%
+method that again that I found that's
+ 
+
+ align:start position:0%
+method that again that I found that's
+used is you take a yard stick or a stick
+
+ align:start position:0%
+used is you take a yard stick or a stick
+ 
+
+ align:start position:0%
+used is you take a yard stick or a stick
+of known length. It doesn't need to be a
+
+ align:start position:0%
+of known length. It doesn't need to be a
+ 
+
+ align:start position:0%
+of known length. It doesn't need to be a
+yard stick. And you put on it just a
+
+ align:start position:0%
+yard stick. And you put on it just a
+ 
+
+ align:start position:0%
+yard stick. And you put on it just a
+tube that's clear that has the ends
+
+ align:start position:0%
+tube that's clear that has the ends
+ 
+
+ align:start position:0%
+tube that's clear that has the ends
+capped that's half full of water. And
+
+ align:start position:0%
+capped that's half full of water. And
+ 
+
+ align:start position:0%
+capped that's half full of water. And
+that's a really cheap level. Um,
+
+ align:start position:0%
+that's a really cheap level. Um,
+ 
+
+ align:start position:0%
+that's a really cheap level. Um,
+basically uh or you can get a real level
+
+ align:start position:0%
+basically uh or you can get a real level
+ 
+
+ align:start position:0%
+basically uh or you can get a real level
+if you have a real level. But if you
+
+ align:start position:0%
+if you have a real level. But if you
+ 
+
+ align:start position:0%
+if you have a real level. But if you
+don't have a real level, you can just
+
+ align:start position:0%
+don't have a real level, you can just
+ 
+
+ align:start position:0%
+don't have a real level, you can just
+use a cheap level. And then you
+
+ align:start position:0%
+use a cheap level. And then you
+ 
+
+ align:start position:0%
+use a cheap level. And then you
+hopefully with two people you put the
+
+ align:start position:0%
+hopefully with two people you put the
+ 
+
+ align:start position:0%
+hopefully with two people you put the
+stick at the bottom or the top and then
+
+ align:start position:0%
+stick at the bottom or the top and then
+ 
+
+ align:start position:0%
+stick at the bottom or the top and then
+just keep moving it over and over again
+
+ align:start position:0%
+just keep moving it over and over again
+ 
+
+ align:start position:0%
+just keep moving it over and over again
+until you measure your head which is a
+
+ align:start position:0%
+until you measure your head which is a
+ 
+
+ align:start position:0%
+until you measure your head which is a
+pain but people do it and it works. Um
+
+ align:start position:0%
+pain but people do it and it works. Um
+ 
+
+ align:start position:0%
+pain but people do it and it works. Um
+and actual surveying equipment is really
+
+ align:start position:0%
+and actual surveying equipment is really
+ 
+
+ align:start position:0%
+and actual surveying equipment is really
+expensive and so you're unlikely to have
+
+ align:start position:0%
+expensive and so you're unlikely to have
+ 
+
+ align:start position:0%
+expensive and so you're unlikely to have
+that in the field. So if a community
+
+ align:start position:0%
+that in the field. So if a community
+ 
+
+ align:start position:0%
+that in the field. So if a community
+partner asked about this you have a
+
+ align:start position:0%
+partner asked about this you have a
+ 
+
+ align:start position:0%
+partner asked about this you have a
+method to measure that's plausible.
+
+ align:start position:0%
+method to measure that's plausible.
+ 
+
+ align:start position:0%
+method to measure that's plausible.
+Yeah. Sorry. What the heck was the drop
+
+ align:start position:0%
+Yeah. Sorry. What the heck was the drop
+ 
+
+ align:start position:0%
+Yeah. Sorry. What the heck was the drop
+of the water?
+
+ align:start position:0%
+of the water?
+ 
+
+ align:start position:0%
+of the water?
+Right. So, you're putting this in the
+
+ align:start position:0%
+Right. So, you're putting this in the
+ 
+
+ align:start position:0%
+Right. So, you're putting this in the
+river
+
+ align:start position:0%
+river
+ 
+
+ align:start position:0%
+river
+this way.
+
+ align:start position:0%
+this way.
+ 
+
+ align:start position:0%
+this way.
+So, for the flow measurement, you're
+
+ align:start position:0%
+So, for the flow measurement, you're
+ 
+
+ align:start position:0%
+So, for the flow measurement, you're
+putting the the your floats in the water
+
+ align:start position:0%
+putting the the your floats in the water
+ 
+
+ align:start position:0%
+putting the the your floats in the water
+and watching how long it takes to get
+
+ align:start position:0%
+and watching how long it takes to get
+ 
+
+ align:start position:0%
+and watching how long it takes to get
+from one end to the other. And that'll
+
+ align:start position:0%
+from one end to the other. And that'll
+ 
+
+ align:start position:0%
+from one end to the other. And that'll
+give you a measure of flow. And then
+
+ align:start position:0%
+give you a measure of flow. And then
+ 
+
+ align:start position:0%
+give you a measure of flow. And then
+your river ideally
+
+ align:start position:0%
+your river ideally
+ 
+
+ align:start position:0%
+your river ideally
+is, let me get a picture instead of
+
+ align:start position:0%
+is, let me get a picture instead of
+ 
+
+ align:start position:0%
+is, let me get a picture instead of
+trying to draw a bad picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So your river is hypothetically going
+
+ align:start position:0%
+So your river is hypothetically going
+ 
+
+ align:start position:0%
+So your river is hypothetically going
+down the mountain here and sort of doing
+
+ align:start position:0%
+down the mountain here and sort of doing
+ 
+
+ align:start position:0%
+down the mountain here and sort of doing
+a curve. And so you're saying, okay,
+
+ align:start position:0%
+a curve. And so you're saying, okay,
+ 
+
+ align:start position:0%
+a curve. And so you're saying, okay,
+well, I'm going to put my um weir and
+
+ align:start position:0%
+well, I'm going to put my um weir and
+ 
+
+ align:start position:0%
+well, I'm going to put my um weir and
+everything up here, and I'm going to put
+
+ align:start position:0%
+everything up here, and I'm going to put
+ 
+
+ align:start position:0%
+everything up here, and I'm going to put
+my uh location where I'm going to
+
+ align:start position:0%
+my uh location where I'm going to
+ 
+
+ align:start position:0%
+my uh location where I'm going to
+actually generate the power down here.
+
+ align:start position:0%
+actually generate the power down here.
+ 
+
+ align:start position:0%
+actually generate the power down here.
+So I need to calculate the height from
+
+ align:start position:0%
+So I need to calculate the height from
+ 
+
+ align:start position:0%
+So I need to calculate the height from
+right here to right here to get my head
+
+ align:start position:0%
+right here to right here to get my head
+ 
+
+ align:start position:0%
+right here to right here to get my head
+height. So now I need to, you know, very
+
+ align:start position:0%
+height. So now I need to, you know, very
+ 
+
+ align:start position:0%
+height. So now I need to, you know, very
+painfully go up the mountain in order to
+
+ align:start position:0%
+painfully go up the mountain in order to
+ 
+
+ align:start position:0%
+painfully go up the mountain in order to
+figure out exactly how high this
+
+ align:start position:0%
+figure out exactly how high this
+ 
+
+ align:start position:0%
+figure out exactly how high this
+distance is. Does that clear it up?
+
+ align:start position:0%
+distance is. Does that clear it up?
+ 
+
+ align:start position:0%
+distance is. Does that clear it up?
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, that wraps up microhydro. Are there
+
+ align:start position:0%
+So, that wraps up microhydro. Are there
+ 
+
+ align:start position:0%
+So, that wraps up microhydro. Are there
+any questions
+
+ align:start position:0%
+any questions
+ 
+
+ align:start position:0%
+any questions
+in addition?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, trip. Uh I want to start
+
+ align:start position:0%
+Okay. So, trip. Uh I want to start
+ 
+
+ align:start position:0%
+Okay. So, trip. Uh I want to start
+talking about the trip uh and spend
+
+ align:start position:0%
+talking about the trip uh and spend
+ 
+
+ align:start position:0%
+talking about the trip uh and spend
+actually the rest of the time talking
+
+ align:start position:0%
+actually the rest of the time talking
+ 
+
+ align:start position:0%
+actually the rest of the time talking
+about it. So
+
+ align:start position:0%
+about it. So
+ 
+
+ align:start position:0%
+about it. So
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+uh so let's do that. Um so one um change
+
+ align:start position:0%
+uh so let's do that. Um so one um change
+ 
+
+ align:start position:0%
+uh so let's do that. Um so one um change
+is that one group of students is going
+
+ align:start position:0%
+is that one group of students is going
+ 
+
+ align:start position:0%
+is that one group of students is going
+to go to El Salvador now instead of
+
+ align:start position:0%
+to go to El Salvador now instead of
+ 
+
+ align:start position:0%
+to go to El Salvador now instead of
+Nicaragua. And the reason for that is
+
+ align:start position:0%
+Nicaragua. And the reason for that is
+ 
+
+ align:start position:0%
+Nicaragua. And the reason for that is
+Amy Smith just came back from a trip to
+
+ align:start position:0%
+Amy Smith just came back from a trip to
+ 
+
+ align:start position:0%
+Amy Smith just came back from a trip to
+El Salvador where she found a community
+
+ align:start position:0%
+El Salvador where she found a community
+ 
+
+ align:start position:0%
+El Salvador where she found a community
+partner that's really interested in us
+
+ align:start position:0%
+partner that's really interested in us
+ 
+
+ align:start position:0%
+partner that's really interested in us
+and we think they're doing great work
+
+ align:start position:0%
+and we think they're doing great work
+ 
+
+ align:start position:0%
+and we think they're doing great work
+and are a solid connection and um so we
+
+ align:start position:0%
+and are a solid connection and um so we
+ 
+
+ align:start position:0%
+and are a solid connection and um so we
+decided to see if we could add Necar or
+
+ align:start position:0%
+decided to see if we could add Necar or
+ 
+
+ align:start position:0%
+decided to see if we could add Necar or
+El Salvador and we're able to in about 2
+
+ align:start position:0%
+El Salvador and we're able to in about 2
+ 
+
+ align:start position:0%
+El Salvador and we're able to in about 2
+hours which is remarkably fast compared
+
+ align:start position:0%
+hours which is remarkably fast compared
+ 
+
+ align:start position:0%
+hours which is remarkably fast compared
+to like the months it takes to develop
+
+ align:start position:0%
+to like the months it takes to develop
+ 
+
+ align:start position:0%
+to like the months it takes to develop
+relations with other community partners.
+
+ align:start position:0%
+relations with other community partners.
+ 
+
+ align:start position:0%
+relations with other community partners.
+So hopefully that's a good sign. Um, and
+
+ align:start position:0%
+So hopefully that's a good sign. Um, and
+ 
+
+ align:start position:0%
+So hopefully that's a good sign. Um, and
+they're really interested in charcoal,
+
+ align:start position:0%
+they're really interested in charcoal,
+ 
+
+ align:start position:0%
+they're really interested in charcoal,
+which, um, is something you'll be
+
+ align:start position:0%
+which, um, is something you'll be
+ 
+
+ align:start position:0%
+which, um, is something you'll be
+trained in next week. So, it just seemed
+
+ align:start position:0%
+trained in next week. So, it just seemed
+ 
+
+ align:start position:0%
+trained in next week. So, it just seemed
+like a good fit. So, u, and you've
+
+ align:start position:0%
+like a good fit. So, u, and you've
+ 
+
+ align:start position:0%
+like a good fit. So, u, and you've
+already know about this group, so I'll
+
+ align:start position:0%
+already know about this group, so I'll
+ 
+
+ align:start position:0%
+already know about this group, so I'll
+talk to you offline if you want about
+
+ align:start position:0%
+talk to you offline if you want about
+ 
+
+ align:start position:0%
+talk to you offline if you want about
+it. Um, but yeah, so we're excited to be
+
+ align:start position:0%
+it. Um, but yeah, so we're excited to be
+ 
+
+ align:start position:0%
+it. Um, but yeah, so we're excited to be
+working with them. So, one group of
+
+ align:start position:0%
+working with them. So, one group of
+ 
+
+ align:start position:0%
+working with them. So, one group of
+students is going to be going to El
+
+ align:start position:0%
+students is going to be going to El
+ 
+
+ align:start position:0%
+students is going to be going to El
+Salvador and then two teams will be
+
+ align:start position:0%
+Salvador and then two teams will be
+ 
+
+ align:start position:0%
+Salvador and then two teams will be
+going to Nicaragua. Um, and El Salvador
+
+ align:start position:0%
+going to Nicaragua. Um, and El Salvador
+ 
+
+ align:start position:0%
+going to Nicaragua. Um, and El Salvador
+doesn't border Nicaragua, but it's
+
+ align:start position:0%
+doesn't border Nicaragua, but it's
+ 
+
+ align:start position:0%
+doesn't border Nicaragua, but it's
+pretty close. So, we're not that spread
+
+ align:start position:0%
+pretty close. So, we're not that spread
+ 
+
+ align:start position:0%
+pretty close. So, we're not that spread
+out yet. Uh we're not we're not
+
+ align:start position:0%
+out yet. Uh we're not we're not
+ 
+
+ align:start position:0%
+out yet. Uh we're not we're not
+approaching DAB development quite yet.
+
+ align:start position:0%
+approaching DAB development quite yet.
+ 
+
+ align:start position:0%
+approaching DAB development quite yet.
+So the teams are as follows. So OSO
+
+ align:start position:0%
+So the teams are as follows. So OSO
+ 
+
+ align:start position:0%
+So the teams are as follows. So OSO
+Phoenix will be going to um well Boss
+
+ align:start position:0%
+Phoenix will be going to um well Boss
+ 
+
+ align:start position:0%
+Phoenix will be going to um well Boss
+Roser and Briana will be going to OSO
+
+ align:start position:0%
+Roser and Briana will be going to OSO
+ 
+
+ align:start position:0%
+Roser and Briana will be going to OSO
+Phoenix and um Carter you'll be working
+
+ align:start position:0%
+Phoenix and um Carter you'll be working
+ 
+
+ align:start position:0%
+Phoenix and um Carter you'll be working
+with them um for the start of the term.
+
+ align:start position:0%
+with them um for the start of the term.
+ 
+
+ align:start position:0%
+with them um for the start of the term.
+Just I don't know if I've mentioned
+
+ align:start position:0%
+Just I don't know if I've mentioned
+ 
+
+ align:start position:0%
+Just I don't know if I've mentioned
+this, the teams that you go with to like
+
+ align:start position:0%
+this, the teams that you go with to like
+ 
+
+ align:start position:0%
+this, the teams that you go with to like
+and the projects you work on at for the
+
+ align:start position:0%
+and the projects you work on at for the
+ 
+
+ align:start position:0%
+and the projects you work on at for the
+for the spring break trip may or may not
+
+ align:start position:0%
+for the spring break trip may or may not
+ 
+
+ align:start position:0%
+for the spring break trip may or may not
+be what you end up working on
+
+ align:start position:0%
+be what you end up working on
+ 
+
+ align:start position:0%
+be what you end up working on
+afterwards. So what happens is the week
+
+ align:start position:0%
+afterwards. So what happens is the week
+ 
+
+ align:start position:0%
+afterwards. So what happens is the week
+after you get back from spring break, we
+
+ align:start position:0%
+after you get back from spring break, we
+ 
+
+ align:start position:0%
+after you get back from spring break, we
+sort of figure out what projects are
+
+ align:start position:0%
+sort of figure out what projects are
+ 
+
+ align:start position:0%
+sort of figure out what projects are
+going to happen. You tell me what you
+
+ align:start position:0%
+going to happen. You tell me what you
+ 
+
+ align:start position:0%
+going to happen. You tell me what you
+prefer to work on. And some students are
+
+ align:start position:0%
+prefer to work on. And some students are
+ 
+
+ align:start position:0%
+prefer to work on. And some students are
+really psyched to stay on the project
+
+ align:start position:0%
+really psyched to stay on the project
+ 
+
+ align:start position:0%
+really psyched to stay on the project
+that you went on spring break. And
+
+ align:start position:0%
+that you went on spring break. And
+ 
+
+ align:start position:0%
+that you went on spring break. And
+naturally, I'm going to try to make you
+
+ align:start position:0%
+naturally, I'm going to try to make you
+ 
+
+ align:start position:0%
+naturally, I'm going to try to make you
+or m make it possible for you to stay on
+
+ align:start position:0%
+or m make it possible for you to stay on
+ 
+
+ align:start position:0%
+or m make it possible for you to stay on
+the project you're really psyched about.
+
+ align:start position:0%
+the project you're really psyched about.
+ 
+
+ align:start position:0%
+the project you're really psyched about.
+Um, and especially if you're
+
+ align:start position:0%
+Um, and especially if you're
+ 
+
+ align:start position:0%
+Um, and especially if you're
+knowledgeable about it because you just
+
+ align:start position:0%
+knowledgeable about it because you just
+ 
+
+ align:start position:0%
+knowledgeable about it because you just
+went on a spring break drip, great. Um,
+
+ align:start position:0%
+went on a spring break drip, great. Um,
+ 
+
+ align:start position:0%
+went on a spring break drip, great. Um,
+but if for whatever reason you're like,
+
+ align:start position:0%
+but if for whatever reason you're like,
+ 
+
+ align:start position:0%
+but if for whatever reason you're like,
+you know what, I can't stand Phoenix. I
+
+ align:start position:0%
+you know what, I can't stand Phoenix. I
+ 
+
+ align:start position:0%
+you know what, I can't stand Phoenix. I
+don't want to work with them or any of
+
+ align:start position:0%
+don't want to work with them or any of
+ 
+
+ align:start position:0%
+don't want to work with them or any of
+their projects ever again, I'm not going
+
+ align:start position:0%
+their projects ever again, I'm not going
+ 
+
+ align:start position:0%
+their projects ever again, I'm not going
+to force you. I'm hopefully not going to
+
+ align:start position:0%
+to force you. I'm hopefully not going to
+ 
+
+ align:start position:0%
+to force you. I'm hopefully not going to
+be have to force you to stay on that.
+
+ align:start position:0%
+be have to force you to stay on that.
+ 
+
+ align:start position:0%
+be have to force you to stay on that.
+So, there may be a little shuffling. So,
+
+ align:start position:0%
+So, there may be a little shuffling. So,
+ 
+
+ align:start position:0%
+So, there may be a little shuffling. So,
+especially the people who aren't
+
+ align:start position:0%
+especially the people who aren't
+ 
+
+ align:start position:0%
+especially the people who aren't
+traveling, um, there's variation. And
+
+ align:start position:0%
+traveling, um, there's variation. And
+ 
+
+ align:start position:0%
+traveling, um, there's variation. And
+I'm pretty sure Eric has dropped the
+
+ align:start position:0%
+I'm pretty sure Eric has dropped the
+ 
+
+ align:start position:0%
+I'm pretty sure Eric has dropped the
+class. So, but if he hasn't, um, he, uh,
+
+ align:start position:0%
+class. So, but if he hasn't, um, he, uh,
+ 
+
+ align:start position:0%
+class. So, but if he hasn't, um, he, uh,
+would be on this group. So, the projects
+
+ align:start position:0%
+would be on this group. So, the projects
+ 
+
+ align:start position:0%
+would be on this group. So, the projects
+that you're going to be working on, um,
+
+ align:start position:0%
+that you're going to be working on, um,
+ 
+
+ align:start position:0%
+that you're going to be working on, um,
+one is, uh, last year the students
+
+ align:start position:0%
+one is, uh, last year the students
+ 
+
+ align:start position:0%
+one is, uh, last year the students
+worked on the OJ bag sealer. And so, one
+
+ align:start position:0%
+worked on the OJ bag sealer. And so, one
+ 
+
+ align:start position:0%
+worked on the OJ bag sealer. And so, one
+thing is delivering that bag sealer,
+
+ align:start position:0%
+thing is delivering that bag sealer,
+ 
+
+ align:start position:0%
+thing is delivering that bag sealer,
+which ideally means reading the final
+
+ align:start position:0%
+which ideally means reading the final
+ 
+
+ align:start position:0%
+which ideally means reading the final
+report from last year and learning how
+
+ align:start position:0%
+report from last year and learning how
+ 
+
+ align:start position:0%
+report from last year and learning how
+it works so you can show it to us
+
+ align:start position:0%
+it works so you can show it to us
+ 
+
+ align:start position:0%
+it works so you can show it to us
+Phoenix staff when you get there. Um,
+
+ align:start position:0%
+Phoenix staff when you get there. Um,
+ 
+
+ align:start position:0%
+Phoenix staff when you get there. Um,
+and that's sort of like the side
+
+ align:start position:0%
+and that's sort of like the side
+ 
+
+ align:start position:0%
+and that's sort of like the side
+servicey project as opposed to the
+
+ align:start position:0%
+servicey project as opposed to the
+ 
+
+ align:start position:0%
+servicey project as opposed to the
+investigative parts of the work. And
+
+ align:start position:0%
+investigative parts of the work. And
+ 
+
+ align:start position:0%
+investigative parts of the work. And
+then the one, two, and three are the
+
+ align:start position:0%
+then the one, two, and three are the
+ 
+
+ align:start position:0%
+then the one, two, and three are the
+projects that you're going to be
+
+ align:start position:0%
+projects that you're going to be
+ 
+
+ align:start position:0%
+projects that you're going to be
+investigating. So one is the
+
+ align:start position:0%
+investigating. So one is the
+ 
+
+ align:start position:0%
+investigating. So one is the
+biodigestertor, which is um they have
+
+ align:start position:0%
+biodigestertor, which is um they have
+ 
+
+ align:start position:0%
+biodigestertor, which is um they have
+biodigesttors and they want to be able
+
+ align:start position:0%
+biodigesttors and they want to be able
+ 
+
+ align:start position:0%
+biodigesttors and they want to be able
+to mix internally um so that the slooh
+
+ align:start position:0%
+to mix internally um so that the slooh
+ 
+
+ align:start position:0%
+to mix internally um so that the slooh
+um provides better digestion. Um and
+
+ align:start position:0%
+um provides better digestion. Um and
+ 
+
+ align:start position:0%
+um provides better digestion. Um and
+they're looking at either hand or
+
+ align:start position:0%
+they're looking at either hand or
+ 
+
+ align:start position:0%
+they're looking at either hand or
+bicycle power. Um and they have both
+
+ align:start position:0%
+bicycle power. Um and they have both
+ 
+
+ align:start position:0%
+bicycle power. Um and they have both
+concrete and plastic biodigesttors.
+
+ align:start position:0%
+concrete and plastic biodigesttors.
+ 
+
+ align:start position:0%
+concrete and plastic biodigesttors.
+Uh the second is a feed chopper
+
+ align:start position:0%
+Uh the second is a feed chopper
+ 
+
+ align:start position:0%
+Uh the second is a feed chopper
+mechanism using bicycle power and I can
+
+ align:start position:0%
+mechanism using bicycle power and I can
+ 
+
+ align:start position:0%
+mechanism using bicycle power and I can
+show you video of the feed chopper. And
+
+ align:start position:0%
+show you video of the feed chopper. And
+ 
+
+ align:start position:0%
+show you video of the feed chopper. And
+third is a washing machine. DAB actually
+
+ align:start position:0%
+third is a washing machine. DAB actually
+ 
+
+ align:start position:0%
+third is a washing machine. DAB actually
+has done a lot of work on washing
+
+ align:start position:0%
+has done a lot of work on washing
+ 
+
+ align:start position:0%
+has done a lot of work on washing
+machines and so this is one area where
+
+ align:start position:0%
+machines and so this is one area where
+ 
+
+ align:start position:0%
+machines and so this is one area where
+you can learn about the existing washing
+
+ align:start position:0%
+you can learn about the existing washing
+ 
+
+ align:start position:0%
+you can learn about the existing washing
+machines designs and then potentially
+
+ align:start position:0%
+machines designs and then potentially
+ 
+
+ align:start position:0%
+machines designs and then potentially
+bring them down and even build one while
+
+ align:start position:0%
+bring them down and even build one while
+ 
+
+ align:start position:0%
+bring them down and even build one while
+you're there um is a possibility.
+
+ align:start position:0%
+you're there um is a possibility.
+ 
+
+ align:start position:0%
+you're there um is a possibility.
+Um, and I at the end of going through
+
+ align:start position:0%
+Um, and I at the end of going through
+ 
+
+ align:start position:0%
+Um, and I at the end of going through
+all this, I'm going to
+
+ align:start position:0%
+all this, I'm going to
+ 
+
+ align:start position:0%
+all this, I'm going to
+talk about what you need to do with this
+
+ align:start position:0%
+talk about what you need to do with this
+ 
+
+ align:start position:0%
+talk about what you need to do with this
+information in the next few weeks. And
+
+ align:start position:0%
+information in the next few weeks. And
+ 
+
+ align:start position:0%
+information in the next few weeks. And
+then um, you'll have time to work with
+
+ align:start position:0%
+then um, you'll have time to work with
+ 
+
+ align:start position:0%
+then um, you'll have time to work with
+your teams, talk to me a little bit,
+
+ align:start position:0%
+your teams, talk to me a little bit,
+ 
+
+ align:start position:0%
+your teams, talk to me a little bit,
+your mentor if will show up at two to
+
+ align:start position:0%
+your mentor if will show up at two to
+ 
+
+ align:start position:0%
+your mentor if will show up at two to
+work with you a little bit on all of
+
+ align:start position:0%
+work with you a little bit on all of
+ 
+
+ align:start position:0%
+work with you a little bit on all of
+this. Um,
+
+ align:start position:0%
+this. Um,
+ 
+
+ align:start position:0%
+this. Um,
+the second group of one, Jessica,
+
+ align:start position:0%
+the second group of one, Jessica,
+ 
+
+ align:start position:0%
+the second group of one, Jessica,
+Elizabeth, Vivian,
+
+ align:start position:0%
+Elizabeth, Vivian,
+ 
+
+ align:start position:0%
+Elizabeth, Vivian,
+Sid, and Kurt is going to group of
+
+ align:start position:0%
+Sid, and Kurt is going to group of
+ 
+
+ align:start position:0%
+Sid, and Kurt is going to group of
+Phoenix. Um, Amelia Servey is your trip
+
+ align:start position:0%
+Phoenix. Um, Amelia Servey is your trip
+ 
+
+ align:start position:0%
+Phoenix. Um, Amelia Servey is your trip
+leader. She took the class this class
+
+ align:start position:0%
+leader. She took the class this class
+ 
+
+ align:start position:0%
+leader. She took the class this class
+last year um and did a summers
+
+ align:start position:0%
+last year um and did a summers
+ 
+
+ align:start position:0%
+last year um and did a summers
+fellowship at Group of Phoenix and so
+
+ align:start position:0%
+fellowship at Group of Phoenix and so
+ 
+
+ align:start position:0%
+fellowship at Group of Phoenix and so
+she knows them pretty well. Um
+
+ align:start position:0%
+she knows them pretty well. Um
+ 
+
+ align:start position:0%
+she knows them pretty well. Um
+and she's a grad student now. Um and so
+
+ align:start position:0%
+and she's a grad student now. Um and so
+ 
+
+ align:start position:0%
+and she's a grad student now. Um and so
+the projects are number one they're
+
+ align:start position:0%
+the projects are number one they're
+ 
+
+ align:start position:0%
+the projects are number one they're
+really interested in charcoal both um
+
+ align:start position:0%
+really interested in charcoal both um
+ 
+
+ align:start position:0%
+really interested in charcoal both um
+the stove and a stove project that was
+
+ align:start position:0%
+the stove and a stove project that was
+ 
+
+ align:start position:0%
+the stove and a stove project that was
+worked on last year on making charcoal
+
+ align:start position:0%
+worked on last year on making charcoal
+ 
+
+ align:start position:0%
+worked on last year on making charcoal
+generally. So working with them on
+
+ align:start position:0%
+generally. So working with them on
+ 
+
+ align:start position:0%
+generally. So working with them on
+charcoal. Um two solar cell phone
+
+ align:start position:0%
+charcoal. Um two solar cell phone
+ 
+
+ align:start position:0%
+charcoal. Um two solar cell phone
+chargers um to develop more affordable
+
+ align:start position:0%
+chargers um to develop more affordable
+ 
+
+ align:start position:0%
+chargers um to develop more affordable
+um version for production. Um they
+
+ align:start position:0%
+um version for production. Um they
+ 
+
+ align:start position:0%
+um version for production. Um they
+currently are working on developing a
+
+ align:start position:0%
+currently are working on developing a
+ 
+
+ align:start position:0%
+currently are working on developing a
+cell phone charger. I can show you the
+
+ align:start position:0%
+cell phone charger. I can show you the
+ 
+
+ align:start position:0%
+cell phone charger. I can show you the
+battery charger they have and it's
+
+ align:start position:0%
+battery charger they have and it's
+ 
+
+ align:start position:0%
+battery charger they have and it's
+pretty rudimentary and partly that's a
+
+ align:start position:0%
+pretty rudimentary and partly that's a
+ 
+
+ align:start position:0%
+pretty rudimentary and partly that's a
+function of their poverty and
+
+ align:start position:0%
+function of their poverty and
+ 
+
+ align:start position:0%
+function of their poverty and
+availability of materials but there is
+
+ align:start position:0%
+availability of materials but there is
+ 
+
+ align:start position:0%
+availability of materials but there is
+opportunity to improve it. Um and they
+
+ align:start position:0%
+opportunity to improve it. Um and they
+ 
+
+ align:start position:0%
+opportunity to improve it. Um and they
+would like to have a really good solar
+
+ align:start position:0%
+would like to have a really good solar
+ 
+
+ align:start position:0%
+would like to have a really good solar
+cell phone charger. Um, and then three,
+
+ align:start position:0%
+cell phone charger. Um, and then three,
+ 
+
+ align:start position:0%
+cell phone charger. Um, and then three,
+they have a solar cooker that's really
+
+ align:start position:0%
+they have a solar cooker that's really
+ 
+
+ align:start position:0%
+they have a solar cooker that's really
+expensive. I'll talk about it next week
+
+ align:start position:0%
+expensive. I'll talk about it next week
+ 
+
+ align:start position:0%
+expensive. I'll talk about it next week
+some. Um, and there's a lot of
+
+ align:start position:0%
+some. Um, and there's a lot of
+ 
+
+ align:start position:0%
+some. Um, and there's a lot of
+opportunity for improvement there to
+
+ align:start position:0%
+opportunity for improvement there to
+ 
+
+ align:start position:0%
+opportunity for improvement there to
+make it more affordable to produce and
+
+ align:start position:0%
+make it more affordable to produce and
+ 
+
+ align:start position:0%
+make it more affordable to produce and
+more aesthetically pleasing and um, more
+
+ align:start position:0%
+more aesthetically pleasing and um, more
+ 
+
+ align:start position:0%
+more aesthetically pleasing and um, more
+functional too. Uh, we have some data on
+
+ align:start position:0%
+functional too. Uh, we have some data on
+ 
+
+ align:start position:0%
+functional too. Uh, we have some data on
+there. And then the third group um, in
+
+ align:start position:0%
+there. And then the third group um, in
+ 
+
+ align:start position:0%
+there. And then the third group um, in
+El Salvador is called Asoproar. And so
+
+ align:start position:0%
+El Salvador is called Asoproar. And so
+ 
+
+ align:start position:0%
+El Salvador is called Asoproar. And so
+Benzy, Missy, and Julia will be going
+
+ align:start position:0%
+Benzy, Missy, and Julia will be going
+ 
+
+ align:start position:0%
+Benzy, Missy, and Julia will be going
+there. and Adrian and Benji, you'll be
+
+ align:start position:0%
+there. and Adrian and Benji, you'll be
+ 
+
+ align:start position:0%
+there. and Adrian and Benji, you'll be
+on that team, too. Um, and so the
+
+ align:start position:0%
+on that team, too. Um, and so the
+ 
+
+ align:start position:0%
+on that team, too. Um, and so the
+projects, so they're interested in a
+
+ align:start position:0%
+projects, so they're interested in a
+ 
+
+ align:start position:0%
+projects, so they're interested in a
+charcoal training, and that again, so
+
+ align:start position:0%
+charcoal training, and that again, so
+ 
+
+ align:start position:0%
+charcoal training, and that again, so
+that would be sort of the service part.
+
+ align:start position:0%
+that would be sort of the service part.
+ 
+
+ align:start position:0%
+that would be sort of the service part.
+Um, better ventilation for smoke in the
+
+ align:start position:0%
+Um, better ventilation for smoke in the
+ 
+
+ align:start position:0%
+Um, better ventilation for smoke in the
+home is one area of interest we believe.
+
+ align:start position:0%
+home is one area of interest we believe.
+ 
+
+ align:start position:0%
+home is one area of interest we believe.
+Um, secondly is we think charcoal stoves
+
+ align:start position:0%
+Um, secondly is we think charcoal stoves
+ 
+
+ align:start position:0%
+Um, secondly is we think charcoal stoves
+will be relevant in El Salvador based on
+
+ align:start position:0%
+will be relevant in El Salvador based on
+ 
+
+ align:start position:0%
+will be relevant in El Salvador based on
+what I remember of my trip there. I'm
+
+ align:start position:0%
+what I remember of my trip there. I'm
+ 
+
+ align:start position:0%
+what I remember of my trip there. I'm
+pretty sure they cook with adobe stoves
+
+ align:start position:0%
+pretty sure they cook with adobe stoves
+ 
+
+ align:start position:0%
+pretty sure they cook with adobe stoves
+just like they do in Nicaragua. So,
+
+ align:start position:0%
+just like they do in Nicaragua. So,
+ 
+
+ align:start position:0%
+just like they do in Nicaragua. So,
+it'll be relevant to work on the stove
+
+ align:start position:0%
+it'll be relevant to work on the stove
+ 
+
+ align:start position:0%
+it'll be relevant to work on the stove
+project there. And then potentially
+
+ align:start position:0%
+project there. And then potentially
+ 
+
+ align:start position:0%
+project there. And then potentially
+better lighting um opportunities, too.
+
+ align:start position:0%
+better lighting um opportunities, too.
+ 
+
+ align:start position:0%
+better lighting um opportunities, too.
+Um and a lot of these are sort of have a
+
+ align:start position:0%
+Um and a lot of these are sort of have a
+ 
+
+ align:start position:0%
+Um and a lot of these are sort of have a
+bit of an architectural bent, which we
+
+ align:start position:0%
+bit of an architectural bent, which we
+ 
+
+ align:start position:0%
+bit of an architectural bent, which we
+haven't focused on much in this class,
+
+ align:start position:0%
+haven't focused on much in this class,
+ 
+
+ align:start position:0%
+haven't focused on much in this class,
+but Julia is a grad student
+
+ align:start position:0%
+but Julia is a grad student
+ 
+
+ align:start position:0%
+but Julia is a grad student
+architecture, so she's going to help um
+
+ align:start position:0%
+architecture, so she's going to help um
+ 
+
+ align:start position:0%
+architecture, so she's going to help um
+with that aspect of things. Um guess
+
+ align:start position:0%
+with that aspect of things. Um guess
+ 
+
+ align:start position:0%
+with that aspect of things. Um guess
+what? Uh uh so yeah, so we're excited
+
+ align:start position:0%
+what? Uh uh so yeah, so we're excited
+ 
+
+ align:start position:0%
+what? Uh uh so yeah, so we're excited
+about that project and thanks for the
+
+ align:start position:0%
+about that project and thanks for the
+ 
+
+ align:start position:0%
+about that project and thanks for the
+people who are rolling with just being
+
+ align:start position:0%
+people who are rolling with just being
+ 
+
+ align:start position:0%
+people who are rolling with just being
+sent to a new country with very little
+
+ align:start position:0%
+sent to a new country with very little
+ 
+
+ align:start position:0%
+sent to a new country with very little
+notice. Um so what do you have to do
+
+ align:start position:0%
+notice. Um so what do you have to do
+ 
+
+ align:start position:0%
+notice. Um so what do you have to do
+with all this? Um, so right now and by
+
+ align:start position:0%
+with all this? Um, so right now and by
+ 
+
+ align:start position:0%
+with all this? Um, so right now and by
+right now I mean in the next two hours.
+
+ align:start position:0%
+right now I mean in the next two hours.
+ 
+
+ align:start position:0%
+right now I mean in the next two hours.
+Um, talk to me um, and do some
+
+ align:start position:0%
+Um, talk to me um, and do some
+ 
+
+ align:start position:0%
+Um, talk to me um, and do some
+brainstorming of ideas.
+
+ align:start position:0%
+brainstorming of ideas.
+ 
+
+ align:start position:0%
+brainstorming of ideas.
+Um, and your deliverable for this step
+
+ align:start position:0%
+Um, and your deliverable for this step
+ 
+
+ align:start position:0%
+Um, and your deliverable for this step
+is two annotated pictures from each team
+
+ align:start position:0%
+is two annotated pictures from each team
+ 
+
+ align:start position:0%
+is two annotated pictures from each team
+member. Um, and so there's a lot of
+
+ align:start position:0%
+member. Um, and so there's a lot of
+ 
+
+ align:start position:0%
+member. Um, and so there's a lot of
+different deadlines for all these
+
+ align:start position:0%
+different deadlines for all these
+ 
+
+ align:start position:0%
+different deadlines for all these
+different things. I'm just trying to
+
+ align:start position:0%
+different things. I'm just trying to
+ 
+
+ align:start position:0%
+different things. I'm just trying to
+help you get through the next couple of
+
+ align:start position:0%
+help you get through the next couple of
+ 
+
+ align:start position:0%
+help you get through the next couple of
+weeks in a way that you actually get
+
+ align:start position:0%
+weeks in a way that you actually get
+ 
+
+ align:start position:0%
+weeks in a way that you actually get
+output and don't save it all to the last
+
+ align:start position:0%
+output and don't save it all to the last
+ 
+
+ align:start position:0%
+output and don't save it all to the last
+night, which will lead to really weak
+
+ align:start position:0%
+night, which will lead to really weak
+ 
+
+ align:start position:0%
+night, which will lead to really weak
+both packing and um help for your
+
+ align:start position:0%
+both packing and um help for your
+ 
+
+ align:start position:0%
+both packing and um help for your
+community partner. Um so this is all
+
+ align:start position:0%
+community partner. Um so this is all
+ 
+
+ align:start position:0%
+community partner. Um so this is all
+hopefully in preparation so that you can
+
+ align:start position:0%
+hopefully in preparation so that you can
+ 
+
+ align:start position:0%
+hopefully in preparation so that you can
+maximize the value to you and your
+
+ align:start position:0%
+maximize the value to you and your
+ 
+
+ align:start position:0%
+maximize the value to you and your
+community partner for the spring break
+
+ align:start position:0%
+community partner for the spring break
+ 
+
+ align:start position:0%
+community partner for the spring break
+trip. Um, and for people who aren't
+
+ align:start position:0%
+trip. Um, and for people who aren't
+ 
+
+ align:start position:0%
+trip. Um, and for people who aren't
+traveling, you're helping make sure
+
+ align:start position:0%
+traveling, you're helping make sure
+ 
+
+ align:start position:0%
+traveling, you're helping make sure
+they're maximizing their their work and
+
+ align:start position:0%
+they're maximizing their their work and
+ 
+
+ align:start position:0%
+they're maximizing their their work and
+it's also getting you prepared for doing
+
+ align:start position:0%
+it's also getting you prepared for doing
+ 
+
+ align:start position:0%
+it's also getting you prepared for doing
+the project work after the spring break.
+
+ align:start position:0%
+the project work after the spring break.
+ 
+
+ align:start position:0%
+the project work after the spring break.
+So, I don't think this is busy work for
+
+ align:start position:0%
+So, I don't think this is busy work for
+ 
+
+ align:start position:0%
+So, I don't think this is busy work for
+you in any way. Um,
+
+ align:start position:0%
+you in any way. Um,
+ 
+
+ align:start position:0%
+you in any way. Um,
+so, so that's one is doing a
+
+ align:start position:0%
+so, so that's one is doing a
+ 
+
+ align:start position:0%
+so, so that's one is doing a
+brainstorming effort and I'm going to
+
+ align:start position:0%
+brainstorming effort and I'm going to
+ 
+
+ align:start position:0%
+brainstorming effort and I'm going to
+talk a little bit about brainstorming in
+
+ align:start position:0%
+talk a little bit about brainstorming in
+ 
+
+ align:start position:0%
+talk a little bit about brainstorming in
+a minute. So, you have some guidelines
+
+ align:start position:0%
+a minute. So, you have some guidelines
+ 
+
+ align:start position:0%
+a minute. So, you have some guidelines
+there. Yeah.
+
+ align:start position:0%
+there. Yeah.
+ 
+
+ align:start position:0%
+there. Yeah.
+I pictures you mean find examples of
+
+ align:start position:0%
+I pictures you mean find examples of
+ 
+
+ align:start position:0%
+I pictures you mean find examples of
+existing technology or like do sketches?
+
+ align:start position:0%
+existing technology or like do sketches?
+ 
+
+ align:start position:0%
+existing technology or like do sketches?
+No, just sketches. So, yeah. So,
+
+ align:start position:0%
+No, just sketches. So, yeah. So,
+ 
+
+ align:start position:0%
+No, just sketches. So, yeah. So,
+basically, I'll I'll show you this in a
+
+ align:start position:0%
+basically, I'll I'll show you this in a
+ 
+
+ align:start position:0%
+basically, I'll I'll show you this in a
+minute, but when you do a brainstorm,
+
+ align:start position:0%
+minute, but when you do a brainstorm,
+ 
+
+ align:start position:0%
+minute, but when you do a brainstorm,
+like if I was brainstorming wind
+
+ align:start position:0%
+like if I was brainstorming wind
+ 
+
+ align:start position:0%
+like if I was brainstorming wind
+turbines, I might do a picture that
+
+ align:start position:0%
+turbines, I might do a picture that
+ 
+
+ align:start position:0%
+turbines, I might do a picture that
+looks like that, you know, like takes me
+
+ align:start position:0%
+looks like that, you know, like takes me
+ 
+
+ align:start position:0%
+looks like that, you know, like takes me
+10 seconds to draw tops. Um, and for the
+
+ align:start position:0%
+10 seconds to draw tops. Um, and for the
+ 
+
+ align:start position:0%
+10 seconds to draw tops. Um, and for the
+pictures you and that would be really
+
+ align:start position:0%
+pictures you and that would be really
+ 
+
+ align:start position:0%
+pictures you and that would be really
+appropriate in a brainstorming session
+
+ align:start position:0%
+appropriate in a brainstorming session
+ 
+
+ align:start position:0%
+appropriate in a brainstorming session
+for the pictures you turn in, I'd want
+
+ align:start position:0%
+for the pictures you turn in, I'd want
+ 
+
+ align:start position:0%
+for the pictures you turn in, I'd want
+it to be a little more refined so that
+
+ align:start position:0%
+it to be a little more refined so that
+ 
+
+ align:start position:0%
+it to be a little more refined so that
+um, this is everything is drawn a little
+
+ align:start position:0%
+um, this is everything is drawn a little
+ 
+
+ align:start position:0%
+um, this is everything is drawn a little
+bit more carefully. Um, there's a few
+
+ align:start position:0%
+bit more carefully. Um, there's a few
+ 
+
+ align:start position:0%
+bit more carefully. Um, there's a few
+more elements that actually make this a
+
+ align:start position:0%
+more elements that actually make this a
+ 
+
+ align:start position:0%
+more elements that actually make this a
+real device rather than just something
+
+ align:start position:0%
+real device rather than just something
+ 
+
+ align:start position:0%
+real device rather than just something
+disembodied in air, whatever is
+
+ align:start position:0%
+disembodied in air, whatever is
+ 
+
+ align:start position:0%
+disembodied in air, whatever is
+appropriate. Um,
+
+ align:start position:0%
+appropriate. Um,
+ 
+
+ align:start position:0%
+appropriate. Um,
+not many if any of you are artists,
+
+ align:start position:0%
+not many if any of you are artists,
+ 
+
+ align:start position:0%
+not many if any of you are artists,
+right, or techn graphic designers. And
+
+ align:start position:0%
+right, or techn graphic designers. And
+ 
+
+ align:start position:0%
+right, or techn graphic designers. And
+so I'm not looking for an amazing sketch
+
+ align:start position:0%
+so I'm not looking for an amazing sketch
+ 
+
+ align:start position:0%
+so I'm not looking for an amazing sketch
+that was done by a graphic designer or
+
+ align:start position:0%
+that was done by a graphic designer or
+ 
+
+ align:start position:0%
+that was done by a graphic designer or
+artist. Um, I'm not one either. But um,
+
+ align:start position:0%
+artist. Um, I'm not one either. But um,
+ 
+
+ align:start position:0%
+artist. Um, I'm not one either. But um,
+if you just draw relatively slowly and
+
+ align:start position:0%
+if you just draw relatively slowly and
+ 
+
+ align:start position:0%
+if you just draw relatively slowly and
+carefully, you know, maybe do a couple
+
+ align:start position:0%
+carefully, you know, maybe do a couple
+ 
+
+ align:start position:0%
+carefully, you know, maybe do a couple
+tries, you should be able to get a
+
+ align:start position:0%
+tries, you should be able to get a
+ 
+
+ align:start position:0%
+tries, you should be able to get a
+drawing that looks decent enough that
+
+ align:start position:0%
+drawing that looks decent enough that
+ 
+
+ align:start position:0%
+drawing that looks decent enough that
+it's understandable, which is all I'm
+
+ align:start position:0%
+it's understandable, which is all I'm
+ 
+
+ align:start position:0%
+it's understandable, which is all I'm
+really looking for.
+
+ align:start position:0%
+really looking for.
+ 
+
+ align:start position:0%
+really looking for.
+Um, so then the second thing is a
+
+ align:start position:0%
+Um, so then the second thing is a
+ 
+
+ align:start position:0%
+Um, so then the second thing is a
+literature search on the topic, which
+
+ align:start position:0%
+literature search on the topic, which
+ 
+
+ align:start position:0%
+literature search on the topic, which
+you may have time for as well, but I
+
+ align:start position:0%
+you may have time for as well, but I
+ 
+
+ align:start position:0%
+you may have time for as well, but I
+want you to do a brainstorm initially
+
+ align:start position:0%
+want you to do a brainstorm initially
+ 
+
+ align:start position:0%
+want you to do a brainstorm initially
+just to sort of get creative before you
+
+ align:start position:0%
+just to sort of get creative before you
+ 
+
+ align:start position:0%
+just to sort of get creative before you
+know what's out there necessarily. Um so
+
+ align:start position:0%
+know what's out there necessarily. Um so
+ 
+
+ align:start position:0%
+know what's out there necessarily. Um so
+then so that's why we're doing the
+
+ align:start position:0%
+then so that's why we're doing the
+ 
+
+ align:start position:0%
+then so that's why we're doing the
+brainstorm one brainstorming first but
+
+ align:start position:0%
+brainstorm one brainstorming first but
+ 
+
+ align:start position:0%
+brainstorm one brainstorming first but
+then a second set which you may have
+
+ align:start position:0%
+then a second set which you may have
+ 
+
+ align:start position:0%
+then a second set which you may have
+time to do some today if you brought
+
+ align:start position:0%
+time to do some today if you brought
+ 
+
+ align:start position:0%
+time to do some today if you brought
+laptops or what have you um
+
+ align:start position:0%
+laptops or what have you um
+ 
+
+ align:start position:0%
+laptops or what have you um
+is to get some information on what's out
+
+ align:start position:0%
+is to get some information on what's out
+ 
+
+ align:start position:0%
+is to get some information on what's out
+there um so that you're more informed uh
+
+ align:start position:0%
+there um so that you're more informed uh
+ 
+
+ align:start position:0%
+there um so that you're more informed uh
+about whatever you need to be u whatever
+
+ align:start position:0%
+about whatever you need to be u whatever
+ 
+
+ align:start position:0%
+about whatever you need to be u whatever
+your project is um there's and so the
+
+ align:start position:0%
+your project is um there's and so the
+ 
+
+ align:start position:0%
+your project is um there's and so the
+what I think would be a good deliverable
+
+ align:start position:0%
+what I think would be a good deliverable
+ 
+
+ align:start position:0%
+what I think would be a good deliverable
+for this is an annotated bibliography
+
+ align:start position:0%
+for this is an annotated bibliography
+ 
+
+ align:start position:0%
+for this is an annotated bibliography
+Um, and there's guidelines right there
+
+ align:start position:0%
+Um, and there's guidelines right there
+ 
+
+ align:start position:0%
+Um, and there's guidelines right there
+on how to write an annotated
+
+ align:start position:0%
+on how to write an annotated
+ 
+
+ align:start position:0%
+on how to write an annotated
+bibliography.
+
+ align:start position:0%
+bibliography.
+ 
+
+ align:start position:0%
+bibliography.
+The guidelines for annotated
+
+ align:start position:0%
+The guidelines for annotated
+ 
+
+ align:start position:0%
+The guidelines for annotated
+biblographies are generally on the like
+
+ align:start position:0%
+biblographies are generally on the like
+ 
+
+ align:start position:0%
+biblographies are generally on the like
+liberal arts side of things. And so they
+
+ align:start position:0%
+liberal arts side of things. And so they
+ 
+
+ align:start position:0%
+liberal arts side of things. And so they
+talk about summarizing what was the
+
+ align:start position:0%
+talk about summarizing what was the
+ 
+
+ align:start position:0%
+talk about summarizing what was the
+content, reflecting on whether it was
+
+ align:start position:0%
+content, reflecting on whether it was
+ 
+
+ align:start position:0%
+content, reflecting on whether it was
+useful and assessing the quality of the
+
+ align:start position:0%
+useful and assessing the quality of the
+ 
+
+ align:start position:0%
+useful and assessing the quality of the
+source. And all those things are are
+
+ align:start position:0%
+source. And all those things are are
+ 
+
+ align:start position:0%
+source. And all those things are are
+good things, but basically I want you to
+
+ align:start position:0%
+good things, but basically I want you to
+ 
+
+ align:start position:0%
+good things, but basically I want you to
+focus on summarizing what was there and
+
+ align:start position:0%
+focus on summarizing what was there and
+ 
+
+ align:start position:0%
+focus on summarizing what was there and
+reflecting on how it's relevant to your
+
+ align:start position:0%
+reflecting on how it's relevant to your
+ 
+
+ align:start position:0%
+reflecting on how it's relevant to your
+project for for each annotation and
+
+ align:start position:0%
+project for for each annotation and
+ 
+
+ align:start position:0%
+project for for each annotation and
+assessing the quality of the source. If
+
+ align:start position:0%
+assessing the quality of the source. If
+ 
+
+ align:start position:0%
+assessing the quality of the source. If
+it's a crappy source, just don't include
+
+ align:start position:0%
+it's a crappy source, just don't include
+ 
+
+ align:start position:0%
+it's a crappy source, just don't include
+it in the bibliography. And if it's a
+
+ align:start position:0%
+it in the bibliography. And if it's a
+ 
+
+ align:start position:0%
+it in the bibliography. And if it's a
+great source, include it. Um, and if
+
+ align:start position:0%
+great source, include it. Um, and if
+ 
+
+ align:start position:0%
+great source, include it. Um, and if
+there is something to assess that you
+
+ align:start position:0%
+there is something to assess that you
+ 
+
+ align:start position:0%
+there is something to assess that you
+want to note, don't don't hesitate to,
+
+ align:start position:0%
+want to note, don't don't hesitate to,
+ 
+
+ align:start position:0%
+want to note, don't don't hesitate to,
+but otherwise, you don't really have to
+
+ align:start position:0%
+but otherwise, you don't really have to
+ 
+
+ align:start position:0%
+but otherwise, you don't really have to
+time spend time assessing the source um
+
+ align:start position:0%
+time spend time assessing the source um
+ 
+
+ align:start position:0%
+time spend time assessing the source um
+in a written form. Um, so third is
+
+ align:start position:0%
+in a written form. Um, so third is
+ 
+
+ align:start position:0%
+in a written form. Um, so third is
+developing project specifications. And
+
+ align:start position:0%
+developing project specifications. And
+ 
+
+ align:start position:0%
+developing project specifications. And
+29 does a really nice job of defining
+
+ align:start position:0%
+29 does a really nice job of defining
+ 
+
+ align:start position:0%
+29 does a really nice job of defining
+what a project specification is. So I've
+
+ align:start position:0%
+what a project specification is. So I've
+ 
+
+ align:start position:0%
+what a project specification is. So I've
+provided links to their lecture and
+
+ align:start position:0%
+provided links to their lecture and
+ 
+
+ align:start position:0%
+provided links to their lecture and
+examples. Um, and so you're going to
+
+ align:start position:0%
+examples. Um, and so you're going to
+ 
+
+ align:start position:0%
+examples. Um, and so you're going to
+provide project specifications for each
+
+ align:start position:0%
+provide project specifications for each
+ 
+
+ align:start position:0%
+provide project specifications for each
+project using the 209 format. So that
+
+ align:start position:0%
+project using the 209 format. So that
+ 
+
+ align:start position:0%
+project using the 209 format. So that
+would mean an attribute, a metric, a
+
+ align:start position:0%
+would mean an attribute, a metric, a
+ 
+
+ align:start position:0%
+would mean an attribute, a metric, a
+unit, and a value. And you'll see the
+
+ align:start position:0%
+unit, and a value. And you'll see the
+ 
+
+ align:start position:0%
+unit, and a value. And you'll see the
+definitions there. The value is an
+
+ align:start position:0%
+definitions there. The value is an
+ 
+
+ align:start position:0%
+definitions there. The value is an
+actual number. Like it needs like a
+
+ align:start position:0%
+actual number. Like it needs like a
+ 
+
+ align:start position:0%
+actual number. Like it needs like a
+three or a seven. And a lot of those
+
+ align:start position:0%
+three or a seven. And a lot of those
+ 
+
+ align:start position:0%
+three or a seven. And a lot of those
+numbers you probably won't be able to
+
+ align:start position:0%
+numbers you probably won't be able to
+ 
+
+ align:start position:0%
+numbers you probably won't be able to
+fill in until after your trip. And
+
+ align:start position:0%
+fill in until after your trip. And
+ 
+
+ align:start position:0%
+fill in until after your trip. And
+that's fine. But I would, what I would
+
+ align:start position:0%
+that's fine. But I would, what I would
+ 
+
+ align:start position:0%
+that's fine. But I would, what I would
+like you to do is come up with a best
+
+ align:start position:0%
+like you to do is come up with a best
+ 
+
+ align:start position:0%
+like you to do is come up with a best
+guess. Even if it's a range of a couple
+
+ align:start position:0%
+guess. Even if it's a range of a couple
+ 
+
+ align:start position:0%
+guess. Even if it's a range of a couple
+of orders of magnitude, come with the
+
+ align:start position:0%
+of orders of magnitude, come with the
+ 
+
+ align:start position:0%
+of orders of magnitude, come with the
+best guess so that when you talk to your
+
+ align:start position:0%
+best guess so that when you talk to your
+ 
+
+ align:start position:0%
+best guess so that when you talk to your
+community partner who often don't have a
+
+ align:start position:0%
+community partner who often don't have a
+ 
+
+ align:start position:0%
+community partner who often don't have a
+lot of um comfort with numbers and may
+
+ align:start position:0%
+lot of um comfort with numbers and may
+ 
+
+ align:start position:0%
+lot of um comfort with numbers and may
+give you really wacky numbers, if
+
+ align:start position:0%
+give you really wacky numbers, if
+ 
+
+ align:start position:0%
+give you really wacky numbers, if
+they're giving you numbers that are
+
+ align:start position:0%
+they're giving you numbers that are
+ 
+
+ align:start position:0%
+they're giving you numbers that are
+completely different from what you're
+
+ align:start position:0%
+completely different from what you're
+ 
+
+ align:start position:0%
+completely different from what you're
+expecting, that's a really good
+
+ align:start position:0%
+expecting, that's a really good
+ 
+
+ align:start position:0%
+expecting, that's a really good
+indicator to you that you need to keep
+
+ align:start position:0%
+indicator to you that you need to keep
+ 
+
+ align:start position:0%
+indicator to you that you need to keep
+asking questions so that either you
+
+ align:start position:0%
+asking questions so that either you
+ 
+
+ align:start position:0%
+asking questions so that either you
+learn that your assumptions are totally
+
+ align:start position:0%
+learn that your assumptions are totally
+ 
+
+ align:start position:0%
+learn that your assumptions are totally
+off, um which is a really important
+
+ align:start position:0%
+off, um which is a really important
+ 
+
+ align:start position:0%
+off, um which is a really important
+thing to learn, or that your community
+
+ align:start position:0%
+thing to learn, or that your community
+ 
+
+ align:start position:0%
+thing to learn, or that your community
+partner isn't really understanding the
+
+ align:start position:0%
+partner isn't really understanding the
+ 
+
+ align:start position:0%
+partner isn't really understanding the
+question or doesn't have the um
+
+ align:start position:0%
+question or doesn't have the um
+ 
+
+ align:start position:0%
+question or doesn't have the um
+educational background around to be able
+
+ align:start position:0%
+educational background around to be able
+ 
+
+ align:start position:0%
+educational background around to be able
+to give you a useful number and you have
+
+ align:start position:0%
+to give you a useful number and you have
+ 
+
+ align:start position:0%
+to give you a useful number and you have
+to work in a few different guises to
+
+ align:start position:0%
+to work in a few different guises to
+ 
+
+ align:start position:0%
+to work in a few different guises to
+actually get to that number and we'll
+
+ align:start position:0%
+actually get to that number and we'll
+ 
+
+ align:start position:0%
+actually get to that number and we'll
+talk about that on the trip prep week of
+
+ align:start position:0%
+talk about that on the trip prep week of
+ 
+
+ align:start position:0%
+talk about that on the trip prep week of
+how you actually do that process of
+
+ align:start position:0%
+how you actually do that process of
+ 
+
+ align:start position:0%
+how you actually do that process of
+getting that information.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and then the next aspects are doing
+
+ align:start position:0%
+Um, and then the next aspects are doing
+ 
+
+ align:start position:0%
+Um, and then the next aspects are doing
+a second brainstorm. Um, and it's up to
+
+ align:start position:0%
+a second brainstorm. Um, and it's up to
+ 
+
+ align:start position:0%
+a second brainstorm. Um, and it's up to
+you as a team if you want to do this in
+
+ align:start position:0%
+you as a team if you want to do this in
+ 
+
+ align:start position:0%
+you as a team if you want to do this in
+two stages. So sometimes people like to
+
+ align:start position:0%
+two stages. So sometimes people like to
+ 
+
+ align:start position:0%
+two stages. So sometimes people like to
+brainstorm on their own for a bit and
+
+ align:start position:0%
+brainstorm on their own for a bit and
+ 
+
+ align:start position:0%
+brainstorm on their own for a bit and
+then come together and bring those ideas
+
+ align:start position:0%
+then come together and bring those ideas
+ 
+
+ align:start position:0%
+then come together and bring those ideas
+to a brainstorm and also build on more
+
+ align:start position:0%
+to a brainstorm and also build on more
+ 
+
+ align:start position:0%
+to a brainstorm and also build on more
+in a group brainstorm session. Some
+
+ align:start position:0%
+in a group brainstorm session. Some
+ 
+
+ align:start position:0%
+in a group brainstorm session. Some
+people prefer just to do a group
+
+ align:start position:0%
+people prefer just to do a group
+ 
+
+ align:start position:0%
+people prefer just to do a group
+brainstorming session. So it's up to
+
+ align:start position:0%
+brainstorming session. So it's up to
+ 
+
+ align:start position:0%
+brainstorming session. So it's up to
+you. But the second brainstorm should at
+
+ align:start position:0%
+you. But the second brainstorm should at
+ 
+
+ align:start position:0%
+you. But the second brainstorm should at
+least have a group component. Um and for
+
+ align:start position:0%
+least have a group component. Um and for
+ 
+
+ align:start position:0%
+least have a group component. Um and for
+those it's just two animated annotated
+
+ align:start position:0%
+those it's just two animated annotated
+ 
+
+ align:start position:0%
+those it's just two animated annotated
+pictures for each project. And so it's
+
+ align:start position:0%
+pictures for each project. And so it's
+ 
+
+ align:start position:0%
+pictures for each project. And so it's
+fewer pictures because it's it's not per
+
+ align:start position:0%
+fewer pictures because it's it's not per
+ 
+
+ align:start position:0%
+fewer pictures because it's it's not per
+team member. And so um you guys can just
+
+ align:start position:0%
+team member. And so um you guys can just
+ 
+
+ align:start position:0%
+team member. And so um you guys can just
+figure out how you want to split those
+
+ align:start position:0%
+figure out how you want to split those
+ 
+
+ align:start position:0%
+figure out how you want to split those
+up. Uh, another thing is the big
+
+ align:start position:0%
+up. Uh, another thing is the big
+ 
+
+ align:start position:0%
+up. Uh, another thing is the big
+questions you have that you want to make
+
+ align:start position:0%
+questions you have that you want to make
+ 
+
+ align:start position:0%
+questions you have that you want to make
+sure you get answered that you have
+
+ align:start position:0%
+sure you get answered that you have
+ 
+
+ align:start position:0%
+sure you get answered that you have
+those in mind so that you make sure by
+
+ align:start position:0%
+those in mind so that you make sure by
+ 
+
+ align:start position:0%
+those in mind so that you make sure by
+the end of the trip you've gotten
+
+ align:start position:0%
+the end of the trip you've gotten
+ 
+
+ align:start position:0%
+the end of the trip you've gotten
+answers to those questions. Um, and all
+
+ align:start position:0%
+answers to those questions. Um, and all
+ 
+
+ align:start position:0%
+answers to those questions. Um, and all
+of these questions are related to
+
+ align:start position:0%
+of these questions are related to
+ 
+
+ align:start position:0%
+of these questions are related to
+figuring out can you actually work on
+
+ align:start position:0%
+figuring out can you actually work on
+ 
+
+ align:start position:0%
+figuring out can you actually work on
+this project? Is this a good project?
+
+ align:start position:0%
+this project? Is this a good project?
+ 
+
+ align:start position:0%
+this project? Is this a good project?
+And if you are going to work on it, what
+
+ align:start position:0%
+And if you are going to work on it, what
+ 
+
+ align:start position:0%
+And if you are going to work on it, what
+what is the appropriate deliverable?
+
+ align:start position:0%
+what is the appropriate deliverable?
+ 
+
+ align:start position:0%
+what is the appropriate deliverable?
+That's the type of questions. Um, a
+
+ align:start position:0%
+That's the type of questions. Um, a
+ 
+
+ align:start position:0%
+That's the type of questions. Um, a
+materials list for the trip. So, you may
+
+ align:start position:0%
+materials list for the trip. So, you may
+ 
+
+ align:start position:0%
+materials list for the trip. So, you may
+well need some materials if you're going
+
+ align:start position:0%
+well need some materials if you're going
+ 
+
+ align:start position:0%
+well need some materials if you're going
+to do a charcoal demonstration. If
+
+ align:start position:0%
+to do a charcoal demonstration. If
+ 
+
+ align:start position:0%
+to do a charcoal demonstration. If
+you're going to try to build a washing
+
+ align:start position:0%
+you're going to try to build a washing
+ 
+
+ align:start position:0%
+you're going to try to build a washing
+machine, if you have a great idea for um
+
+ align:start position:0%
+machine, if you have a great idea for um
+ 
+
+ align:start position:0%
+machine, if you have a great idea for um
+a project and you want to try to
+
+ align:start position:0%
+a project and you want to try to
+ 
+
+ align:start position:0%
+a project and you want to try to
+actually implement either a prototype or
+
+ align:start position:0%
+actually implement either a prototype or
+ 
+
+ align:start position:0%
+actually implement either a prototype or
+something in the field, your community
+
+ align:start position:0%
+something in the field, your community
+ 
+
+ align:start position:0%
+something in the field, your community
+partner needs to know so that they can
+
+ align:start position:0%
+partner needs to know so that they can
+ 
+
+ align:start position:0%
+partner needs to know so that they can
+provide the materials andor we need to
+
+ align:start position:0%
+provide the materials andor we need to
+ 
+
+ align:start position:0%
+provide the materials andor we need to
+get them here so that we can bring them
+
+ align:start position:0%
+get them here so that we can bring them
+ 
+
+ align:start position:0%
+get them here so that we can bring them
+down. And so, um
+
+ align:start position:0%
+down. And so, um
+ 
+
+ align:start position:0%
+down. And so, um
+I put that you don't need this until the
+
+ align:start position:0%
+I put that you don't need this until the
+ 
+
+ align:start position:0%
+I put that you don't need this until the
+16th, which is right before the trip.
+
+ align:start position:0%
+16th, which is right before the trip.
+ 
+
+ align:start position:0%
+16th, which is right before the trip.
+And that's only if like that's the last
+
+ align:start position:0%
+And that's only if like that's the last
+ 
+
+ align:start position:0%
+And that's only if like that's the last
+desperate time. If you can define them
+
+ align:start position:0%
+desperate time. If you can define them
+ 
+
+ align:start position:0%
+desperate time. If you can define them
+sooner, that's better so that your
+
+ align:start position:0%
+sooner, that's better so that your
+ 
+
+ align:start position:0%
+sooner, that's better so that your
+community partner has time to get them
+
+ align:start position:0%
+community partner has time to get them
+ 
+
+ align:start position:0%
+community partner has time to get them
+and or we have time to get them if you
+
+ align:start position:0%
+and or we have time to get them if you
+ 
+
+ align:start position:0%
+and or we have time to get them if you
+need help. Um,
+
+ align:start position:0%
+need help. Um,
+ 
+
+ align:start position:0%
+need help. Um,
+oh no, that was questions. Materials is
+
+ align:start position:0%
+oh no, that was questions. Materials is
+ 
+
+ align:start position:0%
+oh no, that was questions. Materials is
+earlier. Okay, good. That makes more
+
+ align:start position:0%
+earlier. Okay, good. That makes more
+ 
+
+ align:start position:0%
+earlier. Okay, good. That makes more
+sense. And then finally on the 16th
+
+ align:start position:0%
+sense. And then finally on the 16th
+ 
+
+ align:start position:0%
+sense. And then finally on the 16th
+you're going to do about a 15inute
+
+ align:start position:0%
+you're going to do about a 15inute
+ 
+
+ align:start position:0%
+you're going to do about a 15inute
+presentation um on your literature
+
+ align:start position:0%
+presentation um on your literature
+ 
+
+ align:start position:0%
+presentation um on your literature
+literature search findings your project
+
+ align:start position:0%
+literature search findings your project
+ 
+
+ align:start position:0%
+literature search findings your project
+specifications the annotated pictures
+
+ align:start position:0%
+specifications the annotated pictures
+ 
+
+ align:start position:0%
+specifications the annotated pictures
+the key questions and your key expected
+
+ align:start position:0%
+the key questions and your key expected
+ 
+
+ align:start position:0%
+the key questions and your key expected
+activities just so that you're well
+
+ align:start position:0%
+activities just so that you're well
+ 
+
+ align:start position:0%
+activities just so that you're well
+prepared for the trip. So that's
+
+ align:start position:0%
+prepared for the trip. So that's
+ 
+
+ align:start position:0%
+prepared for the trip. So that's
+basically the assignments apart from a
+
+ align:start position:0%
+basically the assignments apart from a
+ 
+
+ align:start position:0%
+basically the assignments apart from a
+little bit of reading for the next few
+
+ align:start position:0%
+little bit of reading for the next few
+ 
+
+ align:start position:0%
+little bit of reading for the next few
+weeks um which again violates the
+
+ align:start position:0%
+weeks um which again violates the
+ 
+
+ align:start position:0%
+weeks um which again violates the
+syllabus but um hopefully will work out.
+
+ align:start position:0%
+syllabus but um hopefully will work out.
+ 
+
+ align:start position:0%
+syllabus but um hopefully will work out.
+So, um, or be okay with you guys. Um,
+
+ align:start position:0%
+So, um, or be okay with you guys. Um,
+ 
+
+ align:start position:0%
+So, um, or be okay with you guys. Um,
+but I didn't want to add problem sets on
+
+ align:start position:0%
+but I didn't want to add problem sets on
+ 
+
+ align:start position:0%
+but I didn't want to add problem sets on
+top of this because this is a lot of
+
+ align:start position:0%
+top of this because this is a lot of
+ 
+
+ align:start position:0%
+top of this because this is a lot of
+work. Um, are there any questions about
+
+ align:start position:0%
+work. Um, are there any questions about
+ 
+
+ align:start position:0%
+work. Um, are there any questions about
+all of this? I have it, um, printed out
+
+ align:start position:0%
+all of this? I have it, um, printed out
+ 
+
+ align:start position:0%
+all of this? I have it, um, printed out
+so that when you're working on it today,
+
+ align:start position:0%
+so that when you're working on it today,
+ 
+
+ align:start position:0%
+so that when you're working on it today,
+you have something to refer to. Um,
+
+ align:start position:0%
+you have something to refer to. Um,
+ 
+
+ align:start position:0%
+you have something to refer to. Um,
+yeah.
+
+ align:start position:0%
+yeah.
+ 
+
+ align:start position:0%
+yeah.
+Did you get the dates for the flight?
+
+ align:start position:0%
+Did you get the dates for the flight?
+ 
+
+ align:start position:0%
+Did you get the dates for the flight?
+Yeah. Um, so most people are flying on
+
+ align:start position:0%
+Yeah. Um, so most people are flying on
+ 
+
+ align:start position:0%
+Yeah. Um, so most people are flying on
+Well, are people So people going to
+
+ align:start position:0%
+Well, are people So people going to
+ 
+
+ align:start position:0%
+Well, are people So people going to
+Nicaragua are flying on Sunday and
+
+ align:start position:0%
+Nicaragua are flying on Sunday and
+ 
+
+ align:start position:0%
+Nicaragua are flying on Sunday and
+getting back on the following Sunday.
+
+ align:start position:0%
+getting back on the following Sunday.
+ 
+
+ align:start position:0%
+getting back on the following Sunday.
+Um, what about El Salvador? Unless So,
+
+ align:start position:0%
+Um, what about El Salvador? Unless So,
+ 
+
+ align:start position:0%
+Um, what about El Salvador? Unless So,
+uh, Juan and Jessica have personal
+
+ align:start position:0%
+uh, Juan and Jessica have personal
+ 
+
+ align:start position:0%
+uh, Juan and Jessica have personal
+commitments, so they're flying back on
+
+ align:start position:0%
+commitments, so they're flying back on
+ 
+
+ align:start position:0%
+commitments, so they're flying back on
+Friday.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And do you know what El Salvador is
+
+ align:start position:0%
+And do you know what El Salvador is
+ 
+
+ align:start position:0%
+And do you know what El Salvador is
+doing yet? Am
+
+ align:start position:0%
+doing yet? Am
+ 
+
+ align:start position:0%
+doing yet? Am
+Saturday.
+
+ align:start position:0%
+Saturday.
+ 
+
+ align:start position:0%
+Saturday.
+Okay. So, El Salvador may be traveling a
+
+ align:start position:0%
+Okay. So, El Salvador may be traveling a
+ 
+
+ align:start position:0%
+Okay. So, El Salvador may be traveling a
+day early.
+
+ align:start position:0%
+day early.
+ 
+
+ align:start position:0%
+day early.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+whatever the days are,
+
+ align:start position:0%
+whatever the days are,
+ 
+
+ align:start position:0%
+whatever the days are,
+I think so.
+
+ align:start position:0%
+I think so.
+ 
+
+ align:start position:0%
+I think so.
+Yeah. The 18th is the Friday. So, the
+
+ align:start position:0%
+Yeah. The 18th is the Friday. So, the
+ 
+
+ align:start position:0%
+Yeah. The 18th is the Friday. So, the
+Sunday would be the 20th. Um, and we'll
+
+ align:start position:0%
+Sunday would be the 20th. Um, and we'll
+ 
+
+ align:start position:0%
+Sunday would be the 20th. Um, and we'll
+send out your actual itinerary soon.
+
+ align:start position:0%
+send out your actual itinerary soon.
+ 
+
+ align:start position:0%
+send out your actual itinerary soon.
+Some of the tickets are booked, others
+
+ align:start position:0%
+Some of the tickets are booked, others
+ 
+
+ align:start position:0%
+Some of the tickets are booked, others
+are just reserved and we'll be booking
+
+ align:start position:0%
+are just reserved and we'll be booking
+ 
+
+ align:start position:0%
+are just reserved and we'll be booking
+them today. Um, so there's a couple of
+
+ align:start position:0%
+them today. Um, so there's a couple of
+ 
+
+ align:start position:0%
+them today. Um, so there's a couple of
+reading assignments um that'll be up on
+
+ align:start position:0%
+reading assignments um that'll be up on
+ 
+
+ align:start position:0%
+reading assignments um that'll be up on
+Stellar shortly. Um, this is just a
+
+ align:start position:0%
+Stellar shortly. Um, this is just a
+ 
+
+ align:start position:0%
+Stellar shortly. Um, this is just a
+somewhat different perspective from the
+
+ align:start position:0%
+somewhat different perspective from the
+ 
+
+ align:start position:0%
+somewhat different perspective from the
+Paul Pak reading you did. Um, and then
+
+ align:start position:0%
+Paul Pak reading you did. Um, and then
+ 
+
+ align:start position:0%
+Paul Pak reading you did. Um, and then
+this is directions on on charcoal
+
+ align:start position:0%
+this is directions on on charcoal
+ 
+
+ align:start position:0%
+this is directions on on charcoal
+making. So, both are are quite short.
+
+ align:start position:0%
+making. So, both are are quite short.
+ 
+
+ align:start position:0%
+making. So, both are are quite short.
+So, I know it might be seeming like a
+
+ align:start position:0%
+So, I know it might be seeming like a
+ 
+
+ align:start position:0%
+So, I know it might be seeming like a
+lot, but these are very manageable um to
+
+ align:start position:0%
+lot, but these are very manageable um to
+ 
+
+ align:start position:0%
+lot, but these are very manageable um to
+get done.
+
+ align:start position:0%
+get done.
+ 
+
+ align:start position:0%
+get done.
+So, um, now I just want to go over how
+
+ align:start position:0%
+So, um, now I just want to go over how
+ 
+
+ align:start position:0%
+So, um, now I just want to go over how
+to do brainstorming and then we can take
+
+ align:start position:0%
+to do brainstorming and then we can take
+ 
+
+ align:start position:0%
+to do brainstorming and then we can take
+a break and then you can get into your
+
+ align:start position:0%
+a break and then you can get into your
+ 
+
+ align:start position:0%
+a break and then you can get into your
+project groups and do brainstorming and
+
+ align:start position:0%
+project groups and do brainstorming and
+ 
+
+ align:start position:0%
+project groups and do brainstorming and
+start talking about the trip. Um, and
+
+ align:start position:0%
+start talking about the trip. Um, and
+ 
+
+ align:start position:0%
+start talking about the trip. Um, and
+then at two uh your mentors will show up
+
+ align:start position:0%
+then at two uh your mentors will show up
+ 
+
+ align:start position:0%
+then at two uh your mentors will show up
+unless your mentor is on meet. He's
+
+ align:start position:0%
+unless your mentor is on meet. He's
+ 
+
+ align:start position:0%
+unless your mentor is on meet. He's
+already here. Um, or trip trip leader um
+
+ align:start position:0%
+already here. Um, or trip trip leader um
+ 
+
+ align:start position:0%
+already here. Um, or trip trip leader um
+and uh so you can get support from them
+
+ align:start position:0%
+and uh so you can get support from them
+ 
+
+ align:start position:0%
+and uh so you can get support from them
+as well and and get to know them. So
+
+ align:start position:0%
+as well and and get to know them. So
+ 
+
+ align:start position:0%
+as well and and get to know them. So
+um effective and fun brainstorming you
+
+ align:start position:0%
+um effective and fun brainstorming you
+ 
+
+ align:start position:0%
+um effective and fun brainstorming you
+require a clear problem statement. So
+
+ align:start position:0%
+require a clear problem statement. So
+ 
+
+ align:start position:0%
+require a clear problem statement. So
+for this case um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're it's whatever the project idea is
+
+ align:start position:0%
+you're it's whatever the project idea is
+ 
+
+ align:start position:0%
+you're it's whatever the project idea is
+for your community partner project. Um
+
+ align:start position:0%
+for your community partner project. Um
+ 
+
+ align:start position:0%
+for your community partner project. Um
+after the
+
+ align:start position:0%
+after the
+ 
+
+ align:start position:0%
+after the
+after you get back from spring break,
+
+ align:start position:0%
+after you get back from spring break,
+ 
+
+ align:start position:0%
+after you get back from spring break,
+you have about four weeks of building
+
+ align:start position:0%
+you have about four weeks of building
+ 
+
+ align:start position:0%
+you have about four weeks of building
+and you have about a $500 budget. So,
+
+ align:start position:0%
+and you have about a $500 budget. So,
+ 
+
+ align:start position:0%
+and you have about a $500 budget. So,
+while you'll see I'm going to encourage
+
+ align:start position:0%
+while you'll see I'm going to encourage
+ 
+
+ align:start position:0%
+while you'll see I'm going to encourage
+you to have really wild ideas.
+
+ align:start position:0%
+you to have really wild ideas.
+ 
+
+ align:start position:0%
+you to have really wild ideas.
+And so, if you come up with a idea that
+
+ align:start position:0%
+And so, if you come up with a idea that
+ 
+
+ align:start position:0%
+And so, if you come up with a idea that
+completely violates the four weeks of
+
+ align:start position:0%
+completely violates the four weeks of
+ 
+
+ align:start position:0%
+completely violates the four weeks of
+building in the 500 budgets, still throw
+
+ align:start position:0%
+building in the 500 budgets, still throw
+ 
+
+ align:start position:0%
+building in the 500 budgets, still throw
+it out there. It's nice to have in your
+
+ align:start position:0%
+it out there. It's nice to have in your
+ 
+
+ align:start position:0%
+it out there. It's nice to have in your
+mind a general sense of these sorts of
+
+ align:start position:0%
+mind a general sense of these sorts of
+ 
+
+ align:start position:0%
+mind a general sense of these sorts of
+things so that you're not only
+
+ align:start position:0%
+things so that you're not only
+ 
+
+ align:start position:0%
+things so that you're not only
+brainstorming things that are in the
+
+ align:start position:0%
+brainstorming things that are in the
+ 
+
+ align:start position:0%
+brainstorming things that are in the
+like 7 megawatt wind turbine category.
+
+ align:start position:0%
+like 7 megawatt wind turbine category.
+ 
+
+ align:start position:0%
+like 7 megawatt wind turbine category.
+um if you're thinking about wind power.
+
+ align:start position:0%
+um if you're thinking about wind power.
+ 
+
+ align:start position:0%
+um if you're thinking about wind power.
+Um so for fun and effective
+
+ align:start position:0%
+Um so for fun and effective
+ 
+
+ align:start position:0%
+Um so for fun and effective
+brainstorming um you're trying to
+
+ align:start position:0%
+brainstorming um you're trying to
+ 
+
+ align:start position:0%
+brainstorming um you're trying to
+generate as many ideas as you can in 15
+
+ align:start position:0%
+generate as many ideas as you can in 15
+ 
+
+ align:start position:0%
+generate as many ideas as you can in 15
+minutes. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+15 minutes is a good length of time.
+
+ align:start position:0%
+15 minutes is a good length of time.
+ 
+
+ align:start position:0%
+15 minutes is a good length of time.
+Sometimes you need a little more a
+
+ align:start position:0%
+Sometimes you need a little more a
+ 
+
+ align:start position:0%
+Sometimes you need a little more a
+little le less but around that time for
+
+ align:start position:0%
+little le less but around that time for
+ 
+
+ align:start position:0%
+little le less but around that time for
+any particular project statement. and
+
+ align:start position:0%
+any particular project statement. and
+ 
+
+ align:start position:0%
+any particular project statement. and
+then you can say take a break, take a
+
+ align:start position:0%
+then you can say take a break, take a
+ 
+
+ align:start position:0%
+then you can say take a break, take a
+stretch, and then come back and work on
+
+ align:start position:0%
+stretch, and then come back and work on
+ 
+
+ align:start position:0%
+stretch, and then come back and work on
+the next problem statement. Um, you want
+
+ align:start position:0%
+the next problem statement. Um, you want
+ 
+
+ align:start position:0%
+the next problem statement. Um, you want
+your sketch to really be a picture with
+
+ align:start position:0%
+your sketch to really be a picture with
+ 
+
+ align:start position:0%
+your sketch to really be a picture with
+a few words. So, a lot of people, if you
+
+ align:start position:0%
+a few words. So, a lot of people, if you
+ 
+
+ align:start position:0%
+a few words. So, a lot of people, if you
+know they're brainstorming weapons of
+
+ align:start position:0%
+know they're brainstorming weapons of
+ 
+
+ align:start position:0%
+know they're brainstorming weapons of
+war
+
+ align:start position:0%
+war
+ 
+
+ align:start position:0%
+war
+and you have your eight and a half piece
+
+ align:start position:0%
+and you have your eight and a half piece
+ 
+
+ align:start position:0%
+and you have your eight and a half piece
+of paper, might draw
+
+ align:start position:0%
+of paper, might draw
+ 
+
+ align:start position:0%
+of paper, might draw
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I would say that this picture is a
+
+ align:start position:0%
+And I would say that this picture is a
+ 
+
+ align:start position:0%
+And I would say that this picture is a
+lot more evocative of what your idea is
+
+ align:start position:0%
+lot more evocative of what your idea is
+ 
+
+ align:start position:0%
+lot more evocative of what your idea is
+than using the words big and the, you
+
+ align:start position:0%
+than using the words big and the, you
+ 
+
+ align:start position:0%
+than using the words big and the, you
+know, just a tiny drawing. And those of
+
+ align:start position:0%
+know, just a tiny drawing. And those of
+ 
+
+ align:start position:0%
+know, just a tiny drawing. And those of
+us who are not so good at drawing, and
+
+ align:start position:0%
+us who are not so good at drawing, and
+ 
+
+ align:start position:0%
+us who are not so good at drawing, and
+I'm one of them, are tempted to draw
+
+ align:start position:0%
+I'm one of them, are tempted to draw
+ 
+
+ align:start position:0%
+I'm one of them, are tempted to draw
+really small because you don't want to
+
+ align:start position:0%
+really small because you don't want to
+ 
+
+ align:start position:0%
+really small because you don't want to
+show in really big format just how bad
+
+ align:start position:0%
+show in really big format just how bad
+ 
+
+ align:start position:0%
+show in really big format just how bad
+your drawing is. But even being a weak
+
+ align:start position:0%
+your drawing is. But even being a weak
+ 
+
+ align:start position:0%
+your drawing is. But even being a weak
+drawer, you can still get your idea
+
+ align:start position:0%
+drawer, you can still get your idea
+ 
+
+ align:start position:0%
+drawer, you can still get your idea
+across pretty well. This is like a
+
+ align:start position:0%
+across pretty well. This is like a
+ 
+
+ align:start position:0%
+across pretty well. This is like a
+threeinut sketch for an artist. So none
+
+ align:start position:0%
+threeinut sketch for an artist. So none
+ 
+
+ align:start position:0%
+threeinut sketch for an artist. So none
+of your brainstorm ideas are going to
+
+ align:start position:0%
+of your brainstorm ideas are going to
+ 
+
+ align:start position:0%
+of your brainstorm ideas are going to
+look this crafted. This might be some
+
+ align:start position:0%
+look this crafted. This might be some
+ 
+
+ align:start position:0%
+look this crafted. This might be some
+the actual annotated sketch that you
+
+ align:start position:0%
+the actual annotated sketch that you
+ 
+
+ align:start position:0%
+the actual annotated sketch that you
+turn in that you actually refine and
+
+ align:start position:0%
+turn in that you actually refine and
+ 
+
+ align:start position:0%
+turn in that you actually refine and
+spend some time on. So, you know, the
+
+ align:start position:0%
+spend some time on. So, you know, the
+ 
+
+ align:start position:0%
+spend some time on. So, you know, the
+10-second version is going to be a guy
+
+ align:start position:0%
+10-second version is going to be a guy
+ 
+
+ align:start position:0%
+10-second version is going to be a guy
+and you have a guy and he's shooting
+
+ align:start position:0%
+and you have a guy and he's shooting
+ 
+
+ align:start position:0%
+and you have a guy and he's shooting
+stuff and here's the person who's
+
+ align:start position:0%
+stuff and here's the person who's
+ 
+
+ align:start position:0%
+stuff and here's the person who's
+unhappy getting shot at. And then here's
+
+ align:start position:0%
+unhappy getting shot at. And then here's
+ 
+
+ align:start position:0%
+unhappy getting shot at. And then here's
+the wheel that's moving your wall of
+
+ align:start position:0%
+the wheel that's moving your wall of
+ 
+
+ align:start position:0%
+the wheel that's moving your wall of
+doom. Right? So, this is a really fast
+
+ align:start position:0%
+doom. Right? So, this is a really fast
+ 
+
+ align:start position:0%
+doom. Right? So, this is a really fast
+version of that sketch. And um so that's
+
+ align:start position:0%
+version of that sketch. And um so that's
+ 
+
+ align:start position:0%
+version of that sketch. And um so that's
+what I'm looking for, not that. But I
+
+ align:start position:0%
+what I'm looking for, not that. But I
+ 
+
+ align:start position:0%
+what I'm looking for, not that. But I
+just wanted to emphasize it's most
+
+ align:start position:0%
+just wanted to emphasize it's most
+ 
+
+ align:start position:0%
+just wanted to emphasize it's most
+people start out you doing this and you
+
+ align:start position:0%
+people start out you doing this and you
+ 
+
+ align:start position:0%
+people start out you doing this and you
+really want to force yourself to do that
+
+ align:start position:0%
+really want to force yourself to do that
+ 
+
+ align:start position:0%
+really want to force yourself to do that
+with maybe you know the description at
+
+ align:start position:0%
+with maybe you know the description at
+ 
+
+ align:start position:0%
+with maybe you know the description at
+the top or the bottom but the picture
+
+ align:start position:0%
+the top or the bottom but the picture
+ 
+
+ align:start position:0%
+the top or the bottom but the picture
+should dominate not the words.
+
+ align:start position:0%
+should dominate not the words.
+ 
+
+ align:start position:0%
+should dominate not the words.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+So I'm still a little confused as to how
+
+ align:start position:0%
+So I'm still a little confused as to how
+ 
+
+ align:start position:0%
+So I'm still a little confused as to how
+like the three projects that you listed
+
+ align:start position:0%
+like the three projects that you listed
+ 
+
+ align:start position:0%
+like the three projects that you listed
+on each slide relate to like the
+
+ align:start position:0%
+on each slide relate to like the
+ 
+
+ align:start position:0%
+on each slide relate to like the
+brainstorming and the
+
+ align:start position:0%
+brainstorming and the
+ 
+
+ align:start position:0%
+brainstorming and the
+Yeah. So the three projects, so if one
+
+ align:start position:0%
+Yeah. So the three projects, so if one
+ 
+
+ align:start position:0%
+Yeah. So the three projects, so if one
+of your projects was the feed shopper,
+
+ align:start position:0%
+of your projects was the feed shopper,
+ 
+
+ align:start position:0%
+of your projects was the feed shopper,
+right? Now you know nothing about that
+
+ align:start position:0%
+right? Now you know nothing about that
+ 
+
+ align:start position:0%
+right? Now you know nothing about that
+project, right? So you may not be able
+
+ align:start position:0%
+project, right? So you may not be able
+ 
+
+ align:start position:0%
+project, right? So you may not be able
+to brainstorm that at all until you come
+
+ align:start position:0%
+to brainstorm that at all until you come
+ 
+
+ align:start position:0%
+to brainstorm that at all until you come
+talk to me, which is part of what you
+
+ align:start position:0%
+talk to me, which is part of what you
+ 
+
+ align:start position:0%
+talk to me, which is part of what you
+need to do in the next hour and a half
+
+ align:start position:0%
+need to do in the next hour and a half
+ 
+
+ align:start position:0%
+need to do in the next hour and a half
+um is come talk to me so I can give each
+
+ align:start position:0%
+um is come talk to me so I can give each
+ 
+
+ align:start position:0%
+um is come talk to me so I can give each
+team a little bit more detail about
+
+ align:start position:0%
+team a little bit more detail about
+ 
+
+ align:start position:0%
+team a little bit more detail about
+their three projects. Um but one of them
+
+ align:start position:0%
+their three projects. Um but one of them
+ 
+
+ align:start position:0%
+their three projects. Um but one of them
+like might be something you you can
+
+ align:start position:0%
+like might be something you you can
+ 
+
+ align:start position:0%
+like might be something you you can
+brainstorm on initially um if there's a
+
+ align:start position:0%
+brainstorm on initially um if there's a
+ 
+
+ align:start position:0%
+brainstorm on initially um if there's a
+cue to wait for me. But either way, once
+
+ align:start position:0%
+cue to wait for me. But either way, once
+ 
+
+ align:start position:0%
+cue to wait for me. But either way, once
+you know a little bit about the feed
+
+ align:start position:0%
+you know a little bit about the feed
+ 
+
+ align:start position:0%
+you know a little bit about the feed
+chopper, then that'll be one of your
+
+ align:start position:0%
+chopper, then that'll be one of your
+ 
+
+ align:start position:0%
+chopper, then that'll be one of your
+brainstorming assignments is the the
+
+ align:start position:0%
+brainstorming assignments is the the
+ 
+
+ align:start position:0%
+brainstorming assignments is the the
+project the the community partner needs
+
+ align:start position:0%
+project the the community partner needs
+ 
+
+ align:start position:0%
+project the the community partner needs
+this this um mechanization of the feed
+
+ align:start position:0%
+this this um mechanization of the feed
+ 
+
+ align:start position:0%
+this this um mechanization of the feed
+chopper and let's brainstorm ways to
+
+ align:start position:0%
+chopper and let's brainstorm ways to
+ 
+
+ align:start position:0%
+chopper and let's brainstorm ways to
+mechanize that feed chopper. Um and just
+
+ align:start position:0%
+mechanize that feed chopper. Um and just
+ 
+
+ align:start position:0%
+mechanize that feed chopper. Um and just
+put out as many ideas as you can in 15
+
+ align:start position:0%
+put out as many ideas as you can in 15
+ 
+
+ align:start position:0%
+put out as many ideas as you can in 15
+minutes. Um, and a good goal is to be
+
+ align:start position:0%
+minutes. Um, and a good goal is to be
+ 
+
+ align:start position:0%
+minutes. Um, and a good goal is to be
+generating like at least three ideas per
+
+ align:start position:0%
+generating like at least three ideas per
+ 
+
+ align:start position:0%
+generating like at least three ideas per
+minute, which doesn't sound like that
+
+ align:start position:0%
+minute, which doesn't sound like that
+ 
+
+ align:start position:0%
+minute, which doesn't sound like that
+many, but it's pretty challenging. Um,
+
+ align:start position:0%
+many, but it's pretty challenging. Um,
+ 
+
+ align:start position:0%
+many, but it's pretty challenging. Um,
+but that is sort of something to keep in
+
+ align:start position:0%
+but that is sort of something to keep in
+ 
+
+ align:start position:0%
+but that is sort of something to keep in
+your mind is I should be generating
+
+ align:start position:0%
+your mind is I should be generating
+ 
+
+ align:start position:0%
+your mind is I should be generating
+three ideas per minute. And so, if I'm
+
+ align:start position:0%
+three ideas per minute. And so, if I'm
+ 
+
+ align:start position:0%
+three ideas per minute. And so, if I'm
+not, I need to get crazier probably um,
+
+ align:start position:0%
+not, I need to get crazier probably um,
+ 
+
+ align:start position:0%
+not, I need to get crazier probably um,
+and less inhibited in order to
+
+ align:start position:0%
+and less inhibited in order to
+ 
+
+ align:start position:0%
+and less inhibited in order to
+successfully do it. Um, and so when once
+
+ align:start position:0%
+successfully do it. Um, and so when once
+ 
+
+ align:start position:0%
+successfully do it. Um, and so when once
+you draw this beautiful picture with
+
+ align:start position:0%
+you draw this beautiful picture with
+ 
+
+ align:start position:0%
+you draw this beautiful picture with
+your group, what you do is everyone's
+
+ align:start position:0%
+your group, what you do is everyone's
+ 
+
+ align:start position:0%
+your group, what you do is everyone's
+hopefully drawing and you just say, "Hey
+
+ align:start position:0%
+hopefully drawing and you just say, "Hey
+ 
+
+ align:start position:0%
+hopefully drawing and you just say, "Hey
+guys, my idea is an advancing wall of
+
+ align:start position:0%
+guys, my idea is an advancing wall of
+ 
+
+ align:start position:0%
+guys, my idea is an advancing wall of
+doom." Um, and then you grab a piece of
+
+ align:start position:0%
+doom." Um, and then you grab a piece of
+ 
+
+ align:start position:0%
+doom." Um, and then you grab a piece of
+tape and we're going to use the um the
+
+ align:start position:0%
+tape and we're going to use the um the
+ 
+
+ align:start position:0%
+tape and we're going to use the um the
+three fume hoods as our our boards. So
+
+ align:start position:0%
+three fume hoods as our our boards. So
+ 
+
+ align:start position:0%
+three fume hoods as our our boards. So
+each group will be around a fume hood.
+
+ align:start position:0%
+each group will be around a fume hood.
+ 
+
+ align:start position:0%
+each group will be around a fume hood.
+And so just tape your idea up on the
+
+ align:start position:0%
+And so just tape your idea up on the
+ 
+
+ align:start position:0%
+And so just tape your idea up on the
+wall and then get back on drawing. And
+
+ align:start position:0%
+wall and then get back on drawing. And
+ 
+
+ align:start position:0%
+wall and then get back on drawing. And
+if Kurt, you had said this advancing
+
+ align:start position:0%
+if Kurt, you had said this advancing
+ 
+
+ align:start position:0%
+if Kurt, you had said this advancing
+wall of doom, and I love that idea, I
+
+ align:start position:0%
+wall of doom, and I love that idea, I
+ 
+
+ align:start position:0%
+wall of doom, and I love that idea, I
+can say, yeah, it's going to be an
+
+ align:start position:0%
+can say, yeah, it's going to be an
+ 
+
+ align:start position:0%
+can say, yeah, it's going to be an
+advancing wall of doom, but instead of
+
+ align:start position:0%
+advancing wall of doom, but instead of
+ 
+
+ align:start position:0%
+advancing wall of doom, but instead of
+being wheelpowered, it's going to be um
+
+ align:start position:0%
+being wheelpowered, it's going to be um
+ 
+
+ align:start position:0%
+being wheelpowered, it's going to be um
+on on a big wheelpowered, it's going to
+
+ align:start position:0%
+on on a big wheelpowered, it's going to
+ 
+
+ align:start position:0%
+on on a big wheelpowered, it's going to
+be on a bunch of little wheels. And so
+
+ align:start position:0%
+be on a bunch of little wheels. And so
+ 
+
+ align:start position:0%
+be on a bunch of little wheels. And so
+in other circles, that might be
+
+ align:start position:0%
+in other circles, that might be
+ 
+
+ align:start position:0%
+in other circles, that might be
+considered theft, right? And you'd be
+
+ align:start position:0%
+considered theft, right? And you'd be
+ 
+
+ align:start position:0%
+considered theft, right? And you'd be
+really mad at me for stealing your idea.
+
+ align:start position:0%
+really mad at me for stealing your idea.
+ 
+
+ align:start position:0%
+really mad at me for stealing your idea.
+But in brainstorming, that's really
+
+ align:start position:0%
+But in brainstorming, that's really
+ 
+
+ align:start position:0%
+But in brainstorming, that's really
+encouraged is to quote steal people's
+
+ align:start position:0%
+encouraged is to quote steal people's
+ 
+
+ align:start position:0%
+encouraged is to quote steal people's
+ideas. So have no worry about that. Um
+
+ align:start position:0%
+ideas. So have no worry about that. Um
+ 
+
+ align:start position:0%
+ideas. So have no worry about that. Um
+you guys can work out your patent rights
+
+ align:start position:0%
+you guys can work out your patent rights
+ 
+
+ align:start position:0%
+you guys can work out your patent rights
+if you become millionaires over over
+
+ align:start position:0%
+if you become millionaires over over
+ 
+
+ align:start position:0%
+if you become millionaires over over
+your advancing wall of doom um later.
+
+ align:start position:0%
+your advancing wall of doom um later.
+ 
+
+ align:start position:0%
+your advancing wall of doom um later.
+Um so what are the rules of the game? So
+
+ align:start position:0%
+Um so what are the rules of the game? So
+ 
+
+ align:start position:0%
+Um so what are the rules of the game? So
+one is deferred judgment. So
+
+ align:start position:0%
+one is deferred judgment. So
+ 
+
+ align:start position:0%
+one is deferred judgment. So
+when I propose that I want to make a
+
+ align:start position:0%
+when I propose that I want to make a
+ 
+
+ align:start position:0%
+when I propose that I want to make a
+wind turbine that's just going to float
+
+ align:start position:0%
+wind turbine that's just going to float
+ 
+
+ align:start position:0%
+wind turbine that's just going to float
+in the air magically with helium
+
+ align:start position:0%
+in the air magically with helium
+ 
+
+ align:start position:0%
+in the air magically with helium
+balloons and you see a few flaws in that
+
+ align:start position:0%
+balloons and you see a few flaws in that
+ 
+
+ align:start position:0%
+balloons and you see a few flaws in that
+idea. um you just have to bite your
+
+ align:start position:0%
+idea. um you just have to bite your
+ 
+
+ align:start position:0%
+idea. um you just have to bite your
+tongue, right? Um and the one way you
+
+ align:start position:0%
+tongue, right? Um and the one way you
+ 
+
+ align:start position:0%
+tongue, right? Um and the one way you
+can manage that is by saying, "Okay, I'm
+
+ align:start position:0%
+can manage that is by saying, "Okay, I'm
+ 
+
+ align:start position:0%
+can manage that is by saying, "Okay, I'm
+gonna still take your, you know, I'm
+
+ align:start position:0%
+gonna still take your, you know, I'm
+ 
+
+ align:start position:0%
+gonna still take your, you know, I'm
+gonna build on your idea and instead of
+
+ align:start position:0%
+gonna build on your idea and instead of
+ 
+
+ align:start position:0%
+gonna build on your idea and instead of
+helium balloons, we're going to use a
+
+ align:start position:0%
+helium balloons, we're going to use a
+ 
+
+ align:start position:0%
+helium balloons, we're going to use a
+post that's attached to the ground." Um
+
+ align:start position:0%
+post that's attached to the ground." Um
+ 
+
+ align:start position:0%
+post that's attached to the ground." Um
+so, um but defer judgment even of your
+
+ align:start position:0%
+so, um but defer judgment even of your
+ 
+
+ align:start position:0%
+so, um but defer judgment even of your
+own ideas and of anyone else's. You
+
+ align:start position:0%
+own ideas and of anyone else's. You
+ 
+
+ align:start position:0%
+own ideas and of anyone else's. You
+know, if you're showing your idea, no
+
+ align:start position:0%
+know, if you're showing your idea, no
+ 
+
+ align:start position:0%
+know, if you're showing your idea, no
+saying this is really stupid, but here
+
+ align:start position:0%
+saying this is really stupid, but here
+ 
+
+ align:start position:0%
+saying this is really stupid, but here
+it is. Just say what it is. Um hopefully
+
+ align:start position:0%
+it is. Just say what it is. Um hopefully
+ 
+
+ align:start position:0%
+it is. Just say what it is. Um hopefully
+everyone is coming up with some really
+
+ align:start position:0%
+everyone is coming up with some really
+ 
+
+ align:start position:0%
+everyone is coming up with some really
+terrible ideas as well as really really
+
+ align:start position:0%
+terrible ideas as well as really really
+ 
+
+ align:start position:0%
+terrible ideas as well as really really
+good ones. And some of those really
+
+ align:start position:0%
+good ones. And some of those really
+ 
+
+ align:start position:0%
+good ones. And some of those really
+terrible ones have a kernel of
+
+ align:start position:0%
+terrible ones have a kernel of
+ 
+
+ align:start position:0%
+terrible ones have a kernel of
+awesomeness in them. And so that's why
+
+ align:start position:0%
+awesomeness in them. And so that's why
+ 
+
+ align:start position:0%
+awesomeness in them. And so that's why
+it's worth it to get them out. Um one at
+
+ align:start position:0%
+it's worth it to get them out. Um one at
+ 
+
+ align:start position:0%
+it's worth it to get them out. Um one at
+a time. So if everyone is talking at
+
+ align:start position:0%
+a time. So if everyone is talking at
+ 
+
+ align:start position:0%
+a time. So if everyone is talking at
+once, it's ineffective. So post them up
+
+ align:start position:0%
+once, it's ineffective. So post them up
+ 
+
+ align:start position:0%
+once, it's ineffective. So post them up
+one at a time. And you shouldn't draw
+
+ align:start position:0%
+one at a time. And you shouldn't draw
+ 
+
+ align:start position:0%
+one at a time. And you shouldn't draw
+like three ideas on three pieces of on
+
+ align:start position:0%
+like three ideas on three pieces of on
+ 
+
+ align:start position:0%
+like three ideas on three pieces of on
+one piece of paper. You should have each
+
+ align:start position:0%
+one piece of paper. You should have each
+ 
+
+ align:start position:0%
+one piece of paper. You should have each
+piece of paper for each idea. Um as I
+
+ align:start position:0%
+piece of paper for each idea. Um as I
+ 
+
+ align:start position:0%
+piece of paper for each idea. Um as I
+mentioned, so building on ideas. So
+
+ align:start position:0%
+mentioned, so building on ideas. So
+ 
+
+ align:start position:0%
+mentioned, so building on ideas. So
+theft is encouraged. Um don't be afraid
+
+ align:start position:0%
+theft is encouraged. Um don't be afraid
+ 
+
+ align:start position:0%
+theft is encouraged. Um don't be afraid
+of that. Try to stay focused, which can
+
+ align:start position:0%
+of that. Try to stay focused, which can
+ 
+
+ align:start position:0%
+of that. Try to stay focused, which can
+be hard. Spending 15 minutes trying to
+
+ align:start position:0%
+be hard. Spending 15 minutes trying to
+ 
+
+ align:start position:0%
+be hard. Spending 15 minutes trying to
+generate three ideas per minute. That's
+
+ align:start position:0%
+generate three ideas per minute. That's
+ 
+
+ align:start position:0%
+generate three ideas per minute. That's
+a lot of ideas. Um, but do try to do
+
+ align:start position:0%
+a lot of ideas. Um, but do try to do
+ 
+
+ align:start position:0%
+a lot of ideas. Um, but do try to do
+that. And then, um, as I mentioned, be
+
+ align:start position:0%
+that. And then, um, as I mentioned, be
+ 
+
+ align:start position:0%
+that. And then, um, as I mentioned, be
+visual.
+
+ align:start position:0%
+visual.
+ 
+
+ align:start position:0%
+visual.
+Um, and encourage, use wild ideas. Don't
+
+ align:start position:0%
+Um, and encourage, use wild ideas. Don't
+ 
+
+ align:start position:0%
+Um, and encourage, use wild ideas. Don't
+be afraid to be like, uh, yeah, wall of
+
+ align:start position:0%
+be afraid to be like, uh, yeah, wall of
+ 
+
+ align:start position:0%
+be afraid to be like, uh, yeah, wall of
+doom, but it's going to be made out of
+
+ align:start position:0%
+doom, but it's going to be made out of
+ 
+
+ align:start position:0%
+doom, but it's going to be made out of
+peanut butter. Like something that
+
+ align:start position:0%
+peanut butter. Like something that
+ 
+
+ align:start position:0%
+peanut butter. Like something that
+ridiculous, um, you know, just pops in
+
+ align:start position:0%
+ridiculous, um, you know, just pops in
+ 
+
+ align:start position:0%
+ridiculous, um, you know, just pops in
+your head, throw it out there because it
+
+ align:start position:0%
+your head, throw it out there because it
+ 
+
+ align:start position:0%
+your head, throw it out there because it
+may inspire someone to say, well, not
+
+ align:start position:0%
+may inspire someone to say, well, not
+ 
+
+ align:start position:0%
+may inspire someone to say, well, not
+peanut butter, but what about peanut
+
+ align:start position:0%
+peanut butter, but what about peanut
+ 
+
+ align:start position:0%
+peanut butter, but what about peanut
+shells? That would be a really lowcost
+
+ align:start position:0%
+shells? That would be a really lowcost
+ 
+
+ align:start position:0%
+shells? That would be a really lowcost
+way to make it, right? And all of a
+
+ align:start position:0%
+way to make it, right? And all of a
+ 
+
+ align:start position:0%
+way to make it, right? And all of a
+sudden that's a slightly useful idea for
+
+ align:start position:0%
+sudden that's a slightly useful idea for
+ 
+
+ align:start position:0%
+sudden that's a slightly useful idea for
+this ridiculous wall of doom. Um yeah,
+
+ align:start position:0%
+this ridiculous wall of doom. Um yeah,
+ 
+
+ align:start position:0%
+this ridiculous wall of doom. Um yeah,
+and then once you're done, um you can
+
+ align:start position:0%
+and then once you're done, um you can
+ 
+
+ align:start position:0%
+and then once you're done, um you can
+sort the pile
+
+ align:start position:0%
+sort the pile
+ 
+
+ align:start position:0%
+sort the pile
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um divide
+
+ align:start position:0%
+um divide
+ 
+
+ align:start position:0%
+um divide
+to to get them into themes. So you can
+
+ align:start position:0%
+to to get them into themes. So you can
+ 
+
+ align:start position:0%
+to to get them into themes. So you can
+sort of, you know, just figure out what
+
+ align:start position:0%
+sort of, you know, just figure out what
+ 
+
+ align:start position:0%
+sort of, you know, just figure out what
+are your themes or what are your
+
+ align:start position:0%
+are your themes or what are your
+ 
+
+ align:start position:0%
+are your themes or what are your
+combinations.
+
+ align:start position:0%
+combinations.
+ 
+
+ align:start position:0%
+combinations.
+um figure out do those themes actually
+
+ align:start position:0%
+um figure out do those themes actually
+ 
+
+ align:start position:0%
+um figure out do those themes actually
+make sense and then often refine and
+
+ align:start position:0%
+make sense and then often refine and
+ 
+
+ align:start position:0%
+make sense and then often refine and
+combine the best. So those two ideas
+
+ align:start position:0%
+combine the best. So those two ideas
+ 
+
+ align:start position:0%
+combine the best. So those two ideas
+from each group don't necessarily have
+
+ align:start position:0%
+from each group don't necessarily have
+ 
+
+ align:start position:0%
+from each group don't necessarily have
+to be the ones you came up with but um
+
+ align:start position:0%
+to be the ones you came up with but um
+ 
+
+ align:start position:0%
+to be the ones you came up with but um
+ones that you think are some of the best
+
+ align:start position:0%
+ones that you think are some of the best
+ 
+
+ align:start position:0%
+ones that you think are some of the best
+of the what you came up with. Do you
+
+ align:start position:0%
+of the what you came up with. Do you
+ 
+
+ align:start position:0%
+of the what you came up with. Do you
+guys have questions on that? I went over
+
+ align:start position:0%
+guys have questions on that? I went over
+ 
+
+ align:start position:0%
+guys have questions on that? I went over
+that kind of fast. So
+
+ align:start position:0%
+that kind of fast. So
+ 
+
+ align:start position:0%
+that kind of fast. So
+but yeah. Okay. So then um for the next
+
+ align:start position:0%
+but yeah. Okay. So then um for the next
+ 
+
+ align:start position:0%
+but yeah. Okay. So then um for the next
+hour and a half, you guys can like take
+
+ align:start position:0%
+hour and a half, you guys can like take
+ 
+
+ align:start position:0%
+hour and a half, you guys can like take
+your 10-minute break and then come back
+
+ align:start position:0%
+your 10-minute break and then come back
+ 
+
+ align:start position:0%
+your 10-minute break and then come back
+and do the brainstorming, meet with me.
+
+ align:start position:0%
+and do the brainstorming, meet with me.
+ 
+
+ align:start position:0%
+and do the brainstorming, meet with me.
+Um and then please remember to fill out
+
+ align:start position:0%
+Um and then please remember to fill out
+ 
+
+ align:start position:0%
+Um and then please remember to fill out
+your muddy cards and include the hours
+
+ align:start position:0%
+your muddy cards and include the hours
+ 
+
+ align:start position:0%
+your muddy cards and include the hours
+per week um on them so that uh that you
+
+ align:start position:0%
+per week um on them so that uh that you
+ 
+
+ align:start position:0%
+per week um on them so that uh that you
+think you're spending on the class so
+
+ align:start position:0%
+think you're spending on the class so
+ 
+
+ align:start position:0%
+think you're spending on the class so
+that I I just have a sense of how that's
+
+ align:start position:0%
+that I I just have a sense of how that's
+ 
+
+ align:start position:0%
+that I I just have a sense of how that's
+going.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But it's sort of a big blue box with a
+
+ align:start position:0%
+But it's sort of a big blue box with a
+ 
+
+ align:start position:0%
+But it's sort of a big blue box with a
+lid that you can open and it has like a
+
+ align:start position:0%
+lid that you can open and it has like a
+ 
+
+ align:start position:0%
+lid that you can open and it has like a
+table built in that sits on.
+
+ align:start position:0%
+table built in that sits on.
+ 
+
+ align:start position:0%
+table built in that sits on.
+Wait, so how big is a bunch of
+
+ align:start position:0%
+Wait, so how big is a bunch of
+ 
+
+ align:start position:0%
+Wait, so how big is a bunch of
+um They make them in different size, but
+
+ align:start position:0%
+um They make them in different size, but
+ 
+
+ align:start position:0%
+um They make them in different size, but
+it's basically like this.
+
+ align:start position:0%
+it's basically like this.
+ 
+
+ align:start position:0%
+it's basically like this.
+No, I'm doing a better drawing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Go.
+
+ align:start position:0%
+Go.
+ 
+
+ align:start position:0%
+Go.
+Wait, it doesn't make sense. It's
+
+ align:start position:0%
+Wait, it doesn't make sense. It's
+ 
+
+ align:start position:0%
+Wait, it doesn't make sense. It's
+supposed to be parabola and it's
+
+ align:start position:0%
+supposed to be parabola and it's
+ 
+
+ align:start position:0%
+supposed to be parabola and it's
+supposed to make
+
+ align:start position:0%
+supposed to make
+ 
+
+ align:start position:0%
+supposed to make
+it look like a funnel.
+
+ align:start position:0%
+it look like a funnel.
+ 
+
+ align:start position:0%
+it look like a funnel.
+I like it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Steal your idea. I'm trying to make a
+
+ align:start position:0%
+Steal your idea. I'm trying to make a
+ 
+
+ align:start position:0%
+Steal your idea. I'm trying to make a
+parabola.
+
+ align:start position:0%
+parabola.
+ 
+
+ align:start position:0%
+parabola.
+Well, then make it.
+
+ align:start position:0%
+Well, then make it.
+ 
+
+ align:start position:0%
+Well, then make it.
+Wait, hold on. Let me explain what it
+
+ align:start position:0%
+Wait, hold on. Let me explain what it
+ 
+
+ align:start position:0%
+Wait, hold on. Let me explain what it
+is, though.
+
+ align:start position:0%
+is, though.
+ 
+
+ align:start position:0%
+is, though.
+Oh, yeah.
+
+ align:start position:0%
+Oh, yeah.
+ 
+
+ align:start position:0%
+Oh, yeah.
+Oh, I'm trying to make a parabola. So,
+
+ align:start position:0%
+Oh, I'm trying to make a parabola. So,
+ 
+
+ align:start position:0%
+Oh, I'm trying to make a parabola. So,
+it's a parabolic solar cooker.
+
+ align:start position:0%
+it's a parabolic solar cooker.
+ 
+
+ align:start position:0%
+it's a parabolic solar cooker.
+I had thought of parabola. Let me just
+
+ align:start position:0%
+I had thought of parabola. Let me just
+ 
+
+ align:start position:0%
+I had thought of parabola. Let me just
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+that's why that's why you scratch it out
+
+ align:start position:0%
+that's why that's why you scratch it out
+ 
+
+ align:start position:0%
+that's why that's why you scratch it out
+so I could throw out a parabola with
+
+ align:start position:0%
+so I could throw out a parabola with
+ 
+
+ align:start position:0%
+so I could throw out a parabola with
+basically kind of stealing the idea from
+
+ align:start position:0%
+basically kind of stealing the idea from
+ 
+
+ align:start position:0%
+basically kind of stealing the idea from
+I don't know you guys source. They do
+
+ align:start position:0%
+I don't know you guys source. They do
+ 
+
+ align:start position:0%
+I don't know you guys source. They do
+solar cookers and they're in the
+
+ align:start position:0%
+solar cookers and they're in the
+ 
+
+ align:start position:0%
+solar cookers and they're in the
+Himalayas and they're really they use
+
+ align:start position:0%
+Himalayas and they're really they use
+ 
+
+ align:start position:0%
+Himalayas and they're really they use
+they're really mobile. You can fold them
+
+ align:start position:0%
+they're really mobile. You can fold them
+ 
+
+ align:start position:0%
+they're really mobile. You can fold them
+up and carry them around. So that was
+
+ align:start position:0%
+up and carry them around. So that was
+ 
+
+ align:start position:0%
+up and carry them around. So that was
+the idea.
+
+ align:start position:0%
+the idea.
+ 
+
+ align:start position:0%
+the idea.
+That's a redrawing.
+
+ align:start position:0%
+That's a redrawing.
+ 
+
+ align:start position:0%
+That's a redrawing.
+No, I'm trying to drop.
+
+ align:start position:0%
+No, I'm trying to drop.
+ 
+
+ align:start position:0%
+No, I'm trying to drop.
+You're like fine. Whatever.
+
+ align:start position:0%
+You're like fine. Whatever.
+ 
+
+ align:start position:0%
+You're like fine. Whatever.
+You can like redraw the poster over if
+
+ align:start position:0%
+You can like redraw the poster over if
+ 
+
+ align:start position:0%
+You can like redraw the poster over if
+you really want.
+
+ align:start position:0%
+you really want.
+ 
+
+ align:start position:0%
+you really want.
+Um my plan is to email us
+
+ align:start position:0%
+Um my plan is to email us
+ 
+
+ align:start position:0%
+Um my plan is to email us
+combination box and
+
+ align:start position:0%
+combination box and
+ 
+
+ align:start position:0%
+combination box and
+parabolic solar thing heating some kind
+
+ align:start position:0%
+parabolic solar thing heating some kind
+ 
+
+ align:start position:0%
+parabolic solar thing heating some kind
+of heating element then is
+
+ align:start position:0%
+of heating element then is
+ 
+
+ align:start position:0%
+of heating element then is
+So would that be like a liquid? Yeah,
+
+ align:start position:0%
+So would that be like a liquid? Yeah,
+ 
+
+ align:start position:0%
+So would that be like a liquid? Yeah,
+that's a liquid and Oh. Oh, shoot.
+
+ align:start position:0%
+that's a liquid and Oh. Oh, shoot.
+ 
+
+ align:start position:0%
+that's a liquid and Oh. Oh, shoot.
+Shoot. So, it'll have to cycle back.
\ No newline at end of file
diff --git a/yBgKkYcoPgM.txt b/yBgKkYcoPgM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a1a524cb3b649ca058824d3d56edc739e87658c
--- /dev/null
+++ b/yBgKkYcoPgM.txt
@@ -0,0 +1,627 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Let's boil the 3,000year history of work
+
+ align:start position:0%
+Let's boil the 3,000year history of work
+ 
+
+ align:start position:0%
+Let's boil the 3,000year history of work
+down to 3 minutes. First, there were
+
+ align:start position:0%
+down to 3 minutes. First, there were
+ 
+
+ align:start position:0%
+down to 3 minutes. First, there were
+hunters and gatherers. Everyone
+
+ align:start position:0%
+hunters and gatherers. Everyone
+ 
+
+ align:start position:0%
+hunters and gatherers. Everyone
+contributed, and their business was
+
+ align:start position:0%
+contributed, and their business was
+ 
+
+ align:start position:0%
+contributed, and their business was
+basically to survive. Eventually, people
+
+ align:start position:0%
+basically to survive. Eventually, people
+ 
+
+ align:start position:0%
+basically to survive. Eventually, people
+began to tame plants and animals,
+
+ align:start position:0%
+began to tame plants and animals,
+ 
+
+ align:start position:0%
+began to tame plants and animals,
+allowing for larger and larger
+
+ align:start position:0%
+allowing for larger and larger
+ 
+
+ align:start position:0%
+allowing for larger and larger
+settlements. This opened up new kinds of
+
+ align:start position:0%
+settlements. This opened up new kinds of
+ 
+
+ align:start position:0%
+settlements. This opened up new kinds of
+work, and if you were lucky, leisure. In
+
+ align:start position:0%
+work, and if you were lucky, leisure. In
+ 
+
+ align:start position:0%
+work, and if you were lucky, leisure. In
+these agricultural civilizations,
+
+ align:start position:0%
+these agricultural civilizations,
+ 
+
+ align:start position:0%
+these agricultural civilizations,
+powerful ruling classes emerged for the
+
+ align:start position:0%
+powerful ruling classes emerged for the
+ 
+
+ align:start position:0%
+powerful ruling classes emerged for the
+first time. In some cultures, hard work
+
+ align:start position:0%
+first time. In some cultures, hard work
+ 
+
+ align:start position:0%
+first time. In some cultures, hard work
+was seen as undignified, so it was
+
+ align:start position:0%
+was seen as undignified, so it was
+ 
+
+ align:start position:0%
+was seen as undignified, so it was
+outsourced to slaves, servants, and
+
+ align:start position:0%
+outsourced to slaves, servants, and
+ 
+
+ align:start position:0%
+outsourced to slaves, servants, and
+serfs, even though hard work made those
+
+ align:start position:0%
+serfs, even though hard work made those
+ 
+
+ align:start position:0%
+serfs, even though hard work made those
+rich lifestyles possible.
+
+ align:start position:0%
+rich lifestyles possible.
+ 
+
+ align:start position:0%
+rich lifestyles possible.
+In other places, hard work was seen as a
+
+ align:start position:0%
+In other places, hard work was seen as a
+ 
+
+ align:start position:0%
+In other places, hard work was seen as a
+virtue, one that signified a person's
+
+ align:start position:0%
+virtue, one that signified a person's
+ 
+
+ align:start position:0%
+virtue, one that signified a person's
+contribution to society, promoted group
+
+ align:start position:0%
+contribution to society, promoted group
+ 
+
+ align:start position:0%
+contribution to society, promoted group
+harmony, or pleased the gods. For some,
+
+ align:start position:0%
+harmony, or pleased the gods. For some,
+ 
+
+ align:start position:0%
+harmony, or pleased the gods. For some,
+working hard became synonymous with
+
+ align:start position:0%
+working hard became synonymous with
+ 
+
+ align:start position:0%
+working hard became synonymous with
+doing good and repenting for one's sins.
+
+ align:start position:0%
+doing good and repenting for one's sins.
+ 
+
+ align:start position:0%
+doing good and repenting for one's sins.
+Where land was cheap and plentiful,
+
+ align:start position:0%
+Where land was cheap and plentiful,
+ 
+
+ align:start position:0%
+Where land was cheap and plentiful,
+families could establish their own
+
+ align:start position:0%
+families could establish their own
+ 
+
+ align:start position:0%
+families could establish their own
+farms. Working the land took on a sense
+
+ align:start position:0%
+farms. Working the land took on a sense
+ 
+
+ align:start position:0%
+farms. Working the land took on a sense
+of community. All family members pitched
+
+ align:start position:0%
+of community. All family members pitched
+ 
+
+ align:start position:0%
+of community. All family members pitched
+in, depended on each other, and their
+
+ align:start position:0%
+in, depended on each other, and their
+ 
+
+ align:start position:0%
+in, depended on each other, and their
+work was never done.
+
+ align:start position:0%
+work was never done.
+ 
+
+ align:start position:0%
+work was never done.
+In many parts of the world, agricultural
+
+ align:start position:0%
+In many parts of the world, agricultural
+ 
+
+ align:start position:0%
+In many parts of the world, agricultural
+improvements enabled surplus crops to
+
+ align:start position:0%
+improvements enabled surplus crops to
+ 
+
+ align:start position:0%
+improvements enabled surplus crops to
+feed more and more artisans living in
+
+ align:start position:0%
+feed more and more artisans living in
+ 
+
+ align:start position:0%
+feed more and more artisans living in
+cities and towns. And so came the craft
+
+ align:start position:0%
+cities and towns. And so came the craft
+ 
+
+ align:start position:0%
+cities and towns. And so came the craft
+stage of work like shoemakers and
+
+ align:start position:0%
+stage of work like shoemakers and
+ 
+
+ align:start position:0%
+stage of work like shoemakers and
+carpenters all very skilled and
+
+ align:start position:0%
+carpenters all very skilled and
+ 
+
+ align:start position:0%
+carpenters all very skilled and
+specialized.
+
+ align:start position:0%
+specialized.
+ 
+
+ align:start position:0%
+specialized.
+Then industrial and capitalist
+
+ align:start position:0%
+Then industrial and capitalist
+ 
+
+ align:start position:0%
+Then industrial and capitalist
+revolutions changed everything and
+
+ align:start position:0%
+revolutions changed everything and
+ 
+
+ align:start position:0%
+revolutions changed everything and
+brought with them mass production. New
+
+ align:start position:0%
+brought with them mass production. New
+ 
+
+ align:start position:0%
+brought with them mass production. New
+kinds of factories demanded new kinds of
+
+ align:start position:0%
+kinds of factories demanded new kinds of
+ 
+
+ align:start position:0%
+kinds of factories demanded new kinds of
+workers all eager to earn a living
+
+ align:start position:0%
+workers all eager to earn a living
+ 
+
+ align:start position:0%
+workers all eager to earn a living
+however they could in a rapidly changing
+
+ align:start position:0%
+however they could in a rapidly changing
+ 
+
+ align:start position:0%
+however they could in a rapidly changing
+world.
+
+ align:start position:0%
+world.
+ 
+
+ align:start position:0%
+world.
+Some workers banded together and took
+
+ align:start position:0%
+Some workers banded together and took
+ 
+
+ align:start position:0%
+Some workers banded together and took
+historic stands for humane work
+
+ align:start position:0%
+historic stands for humane work
+ 
+
+ align:start position:0%
+historic stands for humane work
+conditions and demanded all kinds of
+
+ align:start position:0%
+conditions and demanded all kinds of
+ 
+
+ align:start position:0%
+conditions and demanded all kinds of
+fundamental rights, including the
+
+ align:start position:0%
+fundamental rights, including the
+ 
+
+ align:start position:0%
+fundamental rights, including the
+40-hour work week.
+
+ align:start position:0%
+40-hour work week.
+ 
+
+ align:start position:0%
+40-hour work week.
+The development of computers, the
+
+ align:start position:0%
+The development of computers, the
+ 
+
+ align:start position:0%
+The development of computers, the
+worldwide web, and widespread education
+
+ align:start position:0%
+worldwide web, and widespread education
+ 
+
+ align:start position:0%
+worldwide web, and widespread education
+ushered us into the knowledge-based
+
+ align:start position:0%
+ushered us into the knowledge-based
+ 
+
+ align:start position:0%
+ushered us into the knowledge-based
+economy. While new opportunities are
+
+ align:start position:0%
+economy. While new opportunities are
+ 
+
+ align:start position:0%
+economy. While new opportunities are
+available for some, globalization and
+
+ align:start position:0%
+available for some, globalization and
+ 
+
+ align:start position:0%
+available for some, globalization and
+other forces are leaving other workers
+
+ align:start position:0%
+other forces are leaving other workers
+ 
+
+ align:start position:0%
+other forces are leaving other workers
+behind, feeling like they can't get
+
+ align:start position:0%
+behind, feeling like they can't get
+ 
+
+ align:start position:0%
+behind, feeling like they can't get
+ahead, no matter how hard they try.
+
+ align:start position:0%
+ahead, no matter how hard they try.
+ 
+
+ align:start position:0%
+ahead, no matter how hard they try.
+As fewer people and fewer hours are
+
+ align:start position:0%
+As fewer people and fewer hours are
+ 
+
+ align:start position:0%
+As fewer people and fewer hours are
+needed to do the work of yesterday,
+
+ align:start position:0%
+needed to do the work of yesterday,
+ 
+
+ align:start position:0%
+needed to do the work of yesterday,
+people are adapting again. So, here we
+
+ align:start position:0%
+people are adapting again. So, here we
+ 
+
+ align:start position:0%
+people are adapting again. So, here we
+are. Is this the end of work's
+
+ align:start position:0%
+are. Is this the end of work's
+ 
+
+ align:start position:0%
+are. Is this the end of work's
+evolution? No.
+
+ align:start position:0%
+evolution? No.
+ 
+
+ align:start position:0%
+evolution? No.
+How you live and work will invent the
+
+ align:start position:0%
+How you live and work will invent the
+ 
+
+ align:start position:0%
+How you live and work will invent the
+future. You will work in order to eat.
+
+ align:start position:0%
+future. You will work in order to eat.
+ 
+
+ align:start position:0%
+future. You will work in order to eat.
+You'll eat by outsourcing food
+
+ align:start position:0%
+You'll eat by outsourcing food
+ 
+
+ align:start position:0%
+You'll eat by outsourcing food
+production to other workers. You'll tap
+
+ align:start position:0%
+production to other workers. You'll tap
+ 
+
+ align:start position:0%
+production to other workers. You'll tap
+into a deep human drive to work on
+
+ align:start position:0%
+into a deep human drive to work on
+ 
+
+ align:start position:0%
+into a deep human drive to work on
+something and to make a genuine
+
+ align:start position:0%
+something and to make a genuine
+ 
+
+ align:start position:0%
+something and to make a genuine
+difference doing it. You'll rely on your
+
+ align:start position:0%
+difference doing it. You'll rely on your
+ 
+
+ align:start position:0%
+difference doing it. You'll rely on your
+networks and connections to help you
+
+ align:start position:0%
+networks and connections to help you
+ 
+
+ align:start position:0%
+networks and connections to help you
+out. and you'll help others, too. Maybe
+
+ align:start position:0%
+out. and you'll help others, too. Maybe
+ 
+
+ align:start position:0%
+out. and you'll help others, too. Maybe
+you'll specialize in something no one
+
+ align:start position:0%
+you'll specialize in something no one
+ 
+
+ align:start position:0%
+you'll specialize in something no one
+has thought of before using technology
+
+ align:start position:0%
+has thought of before using technology
+ 
+
+ align:start position:0%
+has thought of before using technology
+no one's seen before. Maybe you'll make
+
+ align:start position:0%
+no one's seen before. Maybe you'll make
+ 
+
+ align:start position:0%
+no one's seen before. Maybe you'll make
+your voice heard among those who find
+
+ align:start position:0%
+your voice heard among those who find
+ 
+
+ align:start position:0%
+your voice heard among those who find
+themselves excluded from today's
+
+ align:start position:0%
+themselves excluded from today's
+ 
+
+ align:start position:0%
+themselves excluded from today's
+economy.
+
+ align:start position:0%
+economy.
+ 
+
+ align:start position:0%
+economy.
+So, keep on working, creating, and
+
+ align:start position:0%
+So, keep on working, creating, and
+ 
+
+ align:start position:0%
+So, keep on working, creating, and
+inventing the future of work.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/yG4bJnFT5-o.txt b/yG4bJnFT5-o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b22ce2685c0dd4a1ed2addd1503e729e471872c0
--- /dev/null
+++ b/yG4bJnFT5-o.txt
@@ -0,0 +1,10771 @@
+align:start position:0%
+ 
+last time. One of the things we we did
+
+ align:start position:0%
+last time. One of the things we we did
+ 
+
+ align:start position:0%
+last time. One of the things we we did
+were we proved two mean value
+
+ align:start position:0%
+were we proved two mean value
+ 
+
+ align:start position:0%
+were we proved two mean value
+inequalities.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we proved two mean value inequality
+
+ align:start position:0%
+So we proved two mean value inequality
+ 
+
+ align:start position:0%
+So we proved two mean value inequality
+and let me call those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the first one was that. So if you
+
+ align:start position:0%
+And the first one was that. So if you
+ 
+
+ align:start position:0%
+And the first one was that. So if you
+had a function f on some interval from a
+
+ align:start position:0%
+had a function f on some interval from a
+ 
+
+ align:start position:0%
+had a function f on some interval from a
+to b into r and this function uh f is
+
+ align:start position:0%
+to b into r and this function uh f is
+ 
+
+ align:start position:0%
+to b into r and this function uh f is
+differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then it said that there exist some x0
+
+ align:start position:0%
+Then it said that there exist some x0
+ 
+
+ align:start position:0%
+Then it said that there exist some x0
+with uh x0 between strictly between a
+
+ align:start position:0%
+with uh x0 between strictly between a
+ 
+
+ align:start position:0%
+with uh x0 between strictly between a
+and b. So that the derivative
+
+ align:start position:0%
+and b. So that the derivative
+ 
+
+ align:start position:0%
+and b. So that the derivative
+at x0 is equal to uh the average of the
+
+ align:start position:0%
+at x0 is equal to uh the average of the
+ 
+
+ align:start position:0%
+at x0 is equal to uh the average of the
+function or the average of the function
+
+ align:start position:0%
+function or the average of the function
+ 
+
+ align:start position:0%
+function or the average of the function
+at the end points. So this is the
+
+ align:start position:0%
+at the end points. So this is the
+ 
+
+ align:start position:0%
+at the end points. So this is the
+average on the end points divide. So
+
+ align:start position:0%
+average on the end points divide. So
+ 
+
+ align:start position:0%
+average on the end points divide. So
+it's it's average over the length of the
+
+ align:start position:0%
+it's it's average over the length of the
+ 
+
+ align:start position:0%
+it's it's average over the length of the
+interval. So
+
+ align:start position:0%
+interval. So
+ 
+
+ align:start position:0%
+interval. So
+so this is what the mean value theorem
+
+ align:start position:0%
+so this is what the mean value theorem
+ 
+
+ align:start position:0%
+so this is what the mean value theorem
+said.
+
+ align:start position:0%
+said.
+ 
+
+ align:start position:0%
+said.
+And then there was a second mean value
+
+ align:start position:0%
+And then there was a second mean value
+ 
+
+ align:start position:0%
+And then there was a second mean value
+theorem and that was the cush mean value
+
+ align:start position:0%
+theorem and that was the cush mean value
+ 
+
+ align:start position:0%
+theorem and that was the cush mean value
+theorem.
+
+ align:start position:0%
+theorem.
+ 
+
+ align:start position:0%
+theorem.
+So the cushy bean museum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that was where you had two functions
+
+ align:start position:0%
+and that was where you had two functions
+ 
+
+ align:start position:0%
+and that was where you had two functions
+f and g
+
+ align:start position:0%
+f and g
+ 
+
+ align:start position:0%
+f and g
+on this interval
+
+ align:start position:0%
+on this interval
+ 
+
+ align:start position:0%
+on this interval
+into r and they are both assumed to be
+
+ align:start position:0%
+into r and they are both assumed to be
+ 
+
+ align:start position:0%
+into r and they are both assumed to be
+differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then again it was that there exist
+
+ align:start position:0%
+And then again it was that there exist
+ 
+
+ align:start position:0%
+And then again it was that there exist
+some x0
+
+ align:start position:0%
+some x0
+ 
+
+ align:start position:0%
+some x0
+strictly between
+
+ align:start position:0%
+strictly between
+ 
+
+ align:start position:0%
+strictly between
+uh a and b.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And uh if you take the derivative
+
+ align:start position:0%
+And uh if you take the derivative
+ 
+
+ align:start position:0%
+And uh if you take the derivative
+uh at x0 of f
+
+ align:start position:0%
+uh at x0 of f
+ 
+
+ align:start position:0%
+uh at x0 of f
+times the value
+
+ align:start position:0%
+times the value
+ 
+
+ align:start position:0%
+times the value
+uh the difference in value of G at the
+
+ align:start position:0%
+uh the difference in value of G at the
+ 
+
+ align:start position:0%
+uh the difference in value of G at the
+end points.
+
+ align:start position:0%
+end points.
+ 
+
+ align:start position:0%
+end points.
+Then this is equal to the derivative of
+
+ align:start position:0%
+Then this is equal to the derivative of
+ 
+
+ align:start position:0%
+Then this is equal to the derivative of
+G at X0
+
+ align:start position:0%
+G at X0
+ 
+
+ align:start position:0%
+G at X0
+times the difference in value of F at
+
+ align:start position:0%
+times the difference in value of F at
+ 
+
+ align:start position:0%
+times the difference in value of F at
+the end points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So that was the Kushim man
+
+ align:start position:0%
+Right? So that was the Kushim man
+ 
+
+ align:start position:0%
+Right? So that was the Kushim man
+theorem. So it was a little bit more
+
+ align:start position:0%
+theorem. So it was a little bit more
+ 
+
+ align:start position:0%
+theorem. So it was a little bit more
+complicated than the actual minium
+
+ align:start position:0%
+complicated than the actual minium
+ 
+
+ align:start position:0%
+complicated than the actual minium
+because you had two functions at the
+
+ align:start position:0%
+because you had two functions at the
+ 
+
+ align:start position:0%
+because you had two functions at the
+same time and the point here was that
+
+ align:start position:0%
+same time and the point here was that
+ 
+
+ align:start position:0%
+same time and the point here was that
+you could arrange this x0 to work for
+
+ align:start position:0%
+you could arrange this x0 to work for
+ 
+
+ align:start position:0%
+you could arrange this x0 to work for
+both points for both functions.
+
+ align:start position:0%
+both points for both functions.
+ 
+
+ align:start position:0%
+both points for both functions.
+Let me just make an observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if um so if we're looking at so so
+
+ align:start position:0%
+that if um so if we're looking at so so
+ 
+
+ align:start position:0%
+that if um so if we're looking at so so
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the cushim seems like a more
+
+ align:start position:0%
+right so the cushim seems like a more
+ 
+
+ align:start position:0%
+right so the cushim seems like a more
+elaborate version of the mean value
+
+ align:start position:0%
+elaborate version of the mean value
+ 
+
+ align:start position:0%
+elaborate version of the mean value
+theorem and it really is because if you
+
+ align:start position:0%
+theorem and it really is because if you
+ 
+
+ align:start position:0%
+theorem and it really is because if you
+if you suppose that g here was the
+
+ align:start position:0%
+if you suppose that g here was the
+ 
+
+ align:start position:0%
+if you suppose that g here was the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+uh that is equal to x. So g of x is
+
+ align:start position:0%
+uh that is equal to x. So g of x is
+ 
+
+ align:start position:0%
+uh that is equal to x. So g of x is
+equal to x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have f here on the integral from a to
+
+ align:start position:0%
+I have f here on the integral from a to
+ 
+
+ align:start position:0%
+I have f here on the integral from a to
+b.
+
+ align:start position:0%
+b.
+ 
+
+ align:start position:0%
+b.
+This is again differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, if the other function was just
+
+ align:start position:0%
+Well, if the other function was just
+ 
+
+ align:start position:0%
+Well, if the other function was just
+this sort of rather trivial function G,
+
+ align:start position:0%
+this sort of rather trivial function G,
+ 
+
+ align:start position:0%
+this sort of rather trivial function G,
+of course, G is also differentiable and
+
+ align:start position:0%
+of course, G is also differentiable and
+ 
+
+ align:start position:0%
+of course, G is also differentiable and
+we even know that the derivative of G at
+
+ align:start position:0%
+we even know that the derivative of G at
+ 
+
+ align:start position:0%
+we even know that the derivative of G at
+all points is one, right? So if you are
+
+ align:start position:0%
+all points is one, right? So if you are
+ 
+
+ align:start position:0%
+all points is one, right? So if you are
+now applying the cushy mean then it say
+
+ align:start position:0%
+now applying the cushy mean then it say
+ 
+
+ align:start position:0%
+now applying the cushy mean then it say
+that by the cushy mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? there exist some x0
+
+ align:start position:0%
+right? there exist some x0
+ 
+
+ align:start position:0%
+right? there exist some x0
+with uh x0 strictly between a and b
+
+ align:start position:0%
+with uh x0 strictly between a and b
+ 
+
+ align:start position:0%
+with uh x0 strictly between a and b
+and so that the derivative of f so
+
+ align:start position:0%
+and so that the derivative of f so
+ 
+
+ align:start position:0%
+and so that the derivative of f so
+that's whatever that is that's the
+
+ align:start position:0%
+that's whatever that is that's the
+ 
+
+ align:start position:0%
+that's whatever that is that's the
+derivative of f at x0
+
+ align:start position:0%
+derivative of f at x0
+ 
+
+ align:start position:0%
+derivative of f at x0
+the value of g at these two end points
+
+ align:start position:0%
+the value of g at these two end points
+ 
+
+ align:start position:0%
+the value of g at these two end points
+where g is just a function x so this is
+
+ align:start position:0%
+where g is just a function x so this is
+ 
+
+ align:start position:0%
+where g is just a function x so this is
+just b minus a
+
+ align:start position:0%
+just b minus a
+ 
+
+ align:start position:0%
+just b minus a
+and the derivative of g is one
+
+ align:start position:0%
+and the derivative of g is one
+ 
+
+ align:start position:0%
+and the derivative of g is one
+h and then it's the difference in value
+
+ align:start position:0%
+h and then it's the difference in value
+ 
+
+ align:start position:0%
+h and then it's the difference in value
+of f at the end point
+
+ align:start position:0%
+of f at the end point
+ 
+
+ align:start position:0%
+of f at the end point
+right and so now if you just divide by b
+
+ align:start position:0%
+right and so now if you just divide by b
+ 
+
+ align:start position:0%
+right and so now if you just divide by b
+minus a so this of course imply that
+
+ align:start position:0%
+minus a so this of course imply that
+ 
+
+ align:start position:0%
+minus a so this of course imply that
+frime of x0 is equal to f of b minus f
+
+ align:start position:0%
+frime of x0 is equal to f of b minus f
+ 
+
+ align:start position:0%
+frime of x0 is equal to f of b minus f
+of a divided by b minus a. So in other
+
+ align:start position:0%
+of a divided by b minus a. So in other
+ 
+
+ align:start position:0%
+of a divided by b minus a. So in other
+words and so you see this here gives you
+
+ align:start position:0%
+words and so you see this here gives you
+ 
+
+ align:start position:0%
+words and so you see this here gives you
+uh this here gives you this the more
+
+ align:start position:0%
+uh this here gives you this the more
+ 
+
+ align:start position:0%
+uh this here gives you this the more
+standard mean value inequalities. So in
+
+ align:start position:0%
+standard mean value inequalities. So in
+ 
+
+ align:start position:0%
+standard mean value inequalities. So in
+other words, the cushive mean man
+
+ align:start position:0%
+other words, the cushive mean man
+ 
+
+ align:start position:0%
+other words, the cushive mean man
+theorem is more general than the than
+
+ align:start position:0%
+theorem is more general than the than
+ 
+
+ align:start position:0%
+theorem is more general than the than
+than this mean value inequality, right?
+
+ align:start position:0%
+than this mean value inequality, right?
+ 
+
+ align:start position:0%
+than this mean value inequality, right?
+Because you recover this if you just let
+
+ align:start position:0%
+Because you recover this if you just let
+ 
+
+ align:start position:0%
+Because you recover this if you just let
+one of the two functions be just a
+
+ align:start position:0%
+one of the two functions be just a
+ 
+
+ align:start position:0%
+one of the two functions be just a
+trivial function x, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay, so that was just an observation.
+
+ align:start position:0%
+okay, so that was just an observation.
+ 
+
+ align:start position:0%
+okay, so that was just an observation.
+The second thing I want to talk about uh
+
+ align:start position:0%
+The second thing I want to talk about uh
+ 
+
+ align:start position:0%
+The second thing I want to talk about uh
+is something we didn't get to uh last
+
+ align:start position:0%
+is something we didn't get to uh last
+ 
+
+ align:start position:0%
+is something we didn't get to uh last
+time and this is uh this is this uh
+
+ align:start position:0%
+time and this is uh this is this uh
+ 
+
+ align:start position:0%
+time and this is uh this is this uh
+op uh rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm just going to state one version
+
+ align:start position:0%
+and I'm just going to state one version
+ 
+
+ align:start position:0%
+and I'm just going to state one version
+of it. There are two versions
+
+ align:start position:0%
+of it. There are two versions
+ 
+
+ align:start position:0%
+of it. There are two versions
+and they're both in the notes but I will
+
+ align:start position:0%
+and they're both in the notes but I will
+ 
+
+ align:start position:0%
+and they're both in the notes but I will
+just state one of them. Uh and so this
+
+ align:start position:0%
+just state one of them. Uh and so this
+ 
+
+ align:start position:0%
+just state one of them. Uh and so this
+is so you have so the situation here is
+
+ align:start position:0%
+is so you have so the situation here is
+ 
+
+ align:start position:0%
+is so you have so the situation here is
+that you have two function uh f and g
+
+ align:start position:0%
+that you have two function uh f and g
+ 
+
+ align:start position:0%
+that you have two function uh f and g
+uh and they are defined on some interval
+
+ align:start position:0%
+uh and they are defined on some interval
+ 
+
+ align:start position:0%
+uh and they are defined on some interval
+say from a to b into r
+
+ align:start position:0%
+say from a to b into r
+ 
+
+ align:start position:0%
+say from a to b into r
+uh uh the interval does not include the
+
+ align:start position:0%
+uh uh the interval does not include the
+ 
+
+ align:start position:0%
+uh uh the interval does not include the
+end point. Okay, so these are
+
+ align:start position:0%
+end point. Okay, so these are
+ 
+
+ align:start position:0%
+end point. Okay, so these are
+differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and then we assume that uh the limit
+
+ align:start position:0%
+Uh and then we assume that uh the limit
+ 
+
+ align:start position:0%
+Uh and then we assume that uh the limit
+here we assume that g sorry uh of x is
+
+ align:start position:0%
+here we assume that g sorry uh of x is
+ 
+
+ align:start position:0%
+here we assume that g sorry uh of x is
+uh and not only g of x but also g prime
+
+ align:start position:0%
+uh and not only g of x but also g prime
+ 
+
+ align:start position:0%
+uh and not only g of x but also g prime
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+are not equal to zero for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then we assume that the limit here
+
+ align:start position:0%
+And then we assume that the limit here
+ 
+
+ align:start position:0%
+And then we assume that the limit here
+of g of x as x goes to a
+
+ align:start position:0%
+of g of x as x goes to a
+ 
+
+ align:start position:0%
+of g of x as x goes to a
+that this here is zero. And the same
+
+ align:start position:0%
+that this here is zero. And the same
+ 
+
+ align:start position:0%
+that this here is zero. And the same
+hold for the function
+
+ align:start position:0%
+hold for the function
+ 
+
+ align:start position:0%
+hold for the function
+uh f.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's here
+
+ align:start position:0%
+So let's here
+ 
+
+ align:start position:0%
+So let's here
+and then what you're interested in is
+
+ align:start position:0%
+and then what you're interested in is
+ 
+
+ align:start position:0%
+and then what you're interested in is
+what you're interested in is that you're
+
+ align:start position:0%
+what you're interested in is that you're
+ 
+
+ align:start position:0%
+what you're interested in is that you're
+interested in looking at uh f ofx
+
+ align:start position:0%
+interested in looking at uh f ofx
+ 
+
+ align:start position:0%
+interested in looking at uh f ofx
+divided by g of x. Right? So this here
+
+ align:start position:0%
+divided by g of x. Right? So this here
+ 
+
+ align:start position:0%
+divided by g of x. Right? So this here
+makes sense. g doesn't vanish. So this
+
+ align:start position:0%
+makes sense. g doesn't vanish. So this
+ 
+
+ align:start position:0%
+makes sense. g doesn't vanish. So this
+here makes sense. And you are interested
+
+ align:start position:0%
+here makes sense. And you are interested
+ 
+
+ align:start position:0%
+here makes sense. And you are interested
+in looking at this
+
+ align:start position:0%
+in looking at this
+ 
+
+ align:start position:0%
+in looking at this
+fraction here
+
+ align:start position:0%
+fraction here
+ 
+
+ align:start position:0%
+fraction here
+as x go to a right. If x go to a then
+
+ align:start position:0%
+as x go to a right. If x go to a then
+ 
+
+ align:start position:0%
+as x go to a right. If x go to a then
+the denominator go to zero and the
+
+ align:start position:0%
+the denominator go to zero and the
+ 
+
+ align:start position:0%
+the denominator go to zero and the
+nominator also go to zero right and the
+
+ align:start position:0%
+nominator also go to zero right and the
+ 
+
+ align:start position:0%
+nominator also go to zero right and the
+question is does it has have a limit or
+
+ align:start position:0%
+question is does it has have a limit or
+ 
+
+ align:start position:0%
+question is does it has have a limit or
+not right and so there's one more
+
+ align:start position:0%
+not right and so there's one more
+ 
+
+ align:start position:0%
+not right and so there's one more
+assumption here that you need and that
+
+ align:start position:0%
+assumption here that you need and that
+ 
+
+ align:start position:0%
+assumption here that you need and that
+is that um that if you're looking at the
+
+ align:start position:0%
+is that um that if you're looking at the
+ 
+
+ align:start position:0%
+is that um that if you're looking at the
+Assume also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh that's the limit here uh as x go
+
+ align:start position:0%
+that uh that's the limit here uh as x go
+ 
+
+ align:start position:0%
+that uh that's the limit here uh as x go
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+of frime of x / g prime assume that this
+
+ align:start position:0%
+of frime of x / g prime assume that this
+ 
+
+ align:start position:0%
+of frime of x / g prime assume that this
+here exist
+
+ align:start position:0%
+here exist
+ 
+
+ align:start position:0%
+here exist
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and is equal to some l. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the claim is that then so the
+
+ align:start position:0%
+And then the claim is that then so the
+ 
+
+ align:start position:0%
+And then the claim is that then so the
+claim here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the this fraction here f ofx / g of
+
+ align:start position:0%
+that the this fraction here f ofx / g of
+ 
+
+ align:start position:0%
+that the this fraction here f ofx / g of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+that this does have a limit as x go to a
+
+ align:start position:0%
+that this does have a limit as x go to a
+ 
+
+ align:start position:0%
+that this does have a limit as x go to a
+and that limit is is actually l.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is uh this is one version of of
+
+ align:start position:0%
+So this is uh this is one version of of
+ 
+
+ align:start position:0%
+So this is uh this is one version of of
+of of this rule. Okay. And there's a
+
+ align:start position:0%
+of of this rule. Okay. And there's a
+ 
+
+ align:start position:0%
+of of this rule. Okay. And there's a
+there's another one very similar.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so so we want to prove this. So uh
+
+ align:start position:0%
+And so so we want to prove this. So uh
+ 
+
+ align:start position:0%
+And so so we want to prove this. So uh
+we looking at so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have we want to uh apply the
+
+ align:start position:0%
+so we have we want to uh apply the
+ 
+
+ align:start position:0%
+so we have we want to uh apply the
+Kushim mean value theorem to to prove
+
+ align:start position:0%
+Kushim mean value theorem to to prove
+ 
+
+ align:start position:0%
+Kushim mean value theorem to to prove
+this theorem and so we're looking at a
+
+ align:start position:0%
+this theorem and so we're looking at a
+ 
+
+ align:start position:0%
+this theorem and so we're looking at a
+interval here.
+
+ align:start position:0%
+interval here.
+ 
+
+ align:start position:0%
+interval here.
+Uh so you're looking at at uh say y. So
+
+ align:start position:0%
+Uh so you're looking at at uh say y. So
+ 
+
+ align:start position:0%
+Uh so you're looking at at uh say y. So
+here you have
+
+ align:start position:0%
+here you have
+ 
+
+ align:start position:0%
+here you have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+here you have uh x and then here you
+
+ align:start position:0%
+here you have uh x and then here you
+ 
+
+ align:start position:0%
+here you have uh x and then here you
+have y and here you have b right and I'm
+
+ align:start position:0%
+have y and here you have b right and I'm
+ 
+
+ align:start position:0%
+have y and here you have b right and I'm
+now going to apply so we will apply the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so apply
+
+ align:start position:0%
+so apply
+ 
+
+ align:start position:0%
+so apply
+the kushimi value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But we are applying it on on this
+
+ align:start position:0%
+But we are applying it on on this
+ 
+
+ align:start position:0%
+But we are applying it on on this
+interval here
+
+ align:start position:0%
+interval here
+ 
+
+ align:start position:0%
+interval here
+between uh so so y here is less than x
+
+ align:start position:0%
+between uh so so y here is less than x
+ 
+
+ align:start position:0%
+between uh so so y here is less than x
+but it's strictly bigger than a and this
+
+ align:start position:0%
+but it's strictly bigger than a and this
+ 
+
+ align:start position:0%
+but it's strictly bigger than a and this
+is x is strictly less than than x right
+
+ align:start position:0%
+is x is strictly less than than x right
+ 
+
+ align:start position:0%
+is x is strictly less than than x right
+so the function was differentiable on
+
+ align:start position:0%
+so the function was differentiable on
+ 
+
+ align:start position:0%
+so the function was differentiable on
+this open interval. So of course it's
+
+ align:start position:0%
+this open interval. So of course it's
+ 
+
+ align:start position:0%
+this open interval. So of course it's
+differentiable or both functions are
+
+ align:start position:0%
+differentiable or both functions are
+ 
+
+ align:start position:0%
+differentiable or both functions are
+differentiable on this closed interval.
+
+ align:start position:0%
+differentiable on this closed interval.
+ 
+
+ align:start position:0%
+differentiable on this closed interval.
+So we can apply it and so we get that uh
+
+ align:start position:0%
+So we can apply it and so we get that uh
+ 
+
+ align:start position:0%
+So we can apply it and so we get that uh
+fprime at some intermediate point
+
+ align:start position:0%
+fprime at some intermediate point
+ 
+
+ align:start position:0%
+fprime at some intermediate point
+uh x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh times uh g
+
+ align:start position:0%
+uh times uh g
+ 
+
+ align:start position:0%
+uh times uh g
+of uh uh x minus g of y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is equal to g prime again x0 here
+
+ align:start position:0%
+This is equal to g prime again x0 here
+ 
+
+ align:start position:0%
+This is equal to g prime again x0 here
+is like is some intermediate point in
+
+ align:start position:0%
+is like is some intermediate point in
+ 
+
+ align:start position:0%
+is like is some intermediate point in
+lie between these two
+
+ align:start position:0%
+lie between these two
+ 
+
+ align:start position:0%
+lie between these two
+uh g prime at x0
+
+ align:start position:0%
+uh g prime at x0
+ 
+
+ align:start position:0%
+uh g prime at x0
+times uh f of x minus g of x g of y
+
+ align:start position:0%
+times uh f of x minus g of x g of y
+ 
+
+ align:start position:0%
+times uh f of x minus g of x g of y
+sorry like that
+
+ align:start position:0%
+sorry like that
+ 
+
+ align:start position:0%
+sorry like that
+right this is just uh applying the cushy
+
+ align:start position:0%
+right this is just uh applying the cushy
+ 
+
+ align:start position:0%
+right this is just uh applying the cushy
+mean value
+
+ align:start position:0%
+mean value
+ 
+
+ align:start position:0%
+mean value
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Uh what what did you say? Oh, yeah.
+
+ align:start position:0%
+>> Uh what what did you say? Oh, yeah.
+ 
+
+ align:start position:0%
+>> Uh what what did you say? Oh, yeah.
+Yeah. Yeah. Sorry about that. Thanks.
+
+ align:start position:0%
+Yeah. Yeah. Sorry about that. Thanks.
+ 
+
+ align:start position:0%
+Yeah. Yeah. Sorry about that. Thanks.
+Yeah. Thank you.
+
+ align:start position:0%
+Yeah. Thank you.
+ 
+
+ align:start position:0%
+Yeah. Thank you.
+Right. And so now I just divide. Of
+
+ align:start position:0%
+Right. And so now I just divide. Of
+ 
+
+ align:start position:0%
+Right. And so now I just divide. Of
+course, this here is supposed to be uh
+
+ align:start position:0%
+course, this here is supposed to be uh
+ 
+
+ align:start position:0%
+course, this here is supposed to be uh
+non zero. So I can just divide.
+
+ align:start position:0%
+non zero. So I can just divide.
+ 
+
+ align:start position:0%
+non zero. So I can just divide.
+Um so so we have that
+
+ align:start position:0%
+Um so so we have that
+ 
+
+ align:start position:0%
+Um so so we have that
+uh that fprime of x0
+
+ align:start position:0%
+uh that fprime of x0
+ 
+
+ align:start position:0%
+uh that fprime of x0
+divided by uh
+
+ align:start position:0%
+divided by uh
+ 
+
+ align:start position:0%
+divided by uh
+by g prime of x0
+
+ align:start position:0%
+by g prime of x0
+ 
+
+ align:start position:0%
+by g prime of x0
+and then I will I want to divide by this
+
+ align:start position:0%
+and then I will I want to divide by this
+ 
+
+ align:start position:0%
+and then I will I want to divide by this
+but I just need to make sure that this
+
+ align:start position:0%
+but I just need to make sure that this
+ 
+
+ align:start position:0%
+but I just need to make sure that this
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+um is
+
+ align:start position:0%
+um is
+ 
+
+ align:start position:0%
+um is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that I can divide by right that it's not
+
+ align:start position:0%
+that I can divide by right that it's not
+ 
+
+ align:start position:0%
+that I can divide by right that it's not
+zero this thing here. So I have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now think about X is being fixed and do
+
+ align:start position:0%
+now think about X is being fixed and do
+ 
+
+ align:start position:0%
+now think about X is being fixed and do
+this for all Y. Right? If I do this, if
+
+ align:start position:0%
+this for all Y. Right? If I do this, if
+ 
+
+ align:start position:0%
+this for all Y. Right? If I do this, if
+I do this for y where y is very very
+
+ align:start position:0%
+I do this for y where y is very very
+ 
+
+ align:start position:0%
+I do this for y where y is very very
+close to a, this here becomes really
+
+ align:start position:0%
+close to a, this here becomes really
+ 
+
+ align:start position:0%
+close to a, this here becomes really
+really close to zero. Right? This here
+
+ align:start position:0%
+really close to zero. Right? This here
+ 
+
+ align:start position:0%
+really close to zero. Right? This here
+is fixed and it's it's not equal to
+
+ align:start position:0%
+is fixed and it's it's not equal to
+ 
+
+ align:start position:0%
+is fixed and it's it's not equal to
+zero. Right? So this here is very close
+
+ align:start position:0%
+zero. Right? So this here is very close
+ 
+
+ align:start position:0%
+zero. Right? So this here is very close
+to zero. This is not equal to zero. So
+
+ align:start position:0%
+to zero. This is not equal to zero. So
+ 
+
+ align:start position:0%
+to zero. This is not equal to zero. So
+this here if y is really close if x is
+
+ align:start position:0%
+this here if y is really close if x is
+ 
+
+ align:start position:0%
+this here if y is really close if x is
+fixed y is really close to a. This is
+
+ align:start position:0%
+fixed y is really close to a. This is
+ 
+
+ align:start position:0%
+fixed y is really close to a. This is
+definitely not zero. Right? So I can
+
+ align:start position:0%
+definitely not zero. Right? So I can
+ 
+
+ align:start position:0%
+definitely not zero. Right? So I can
+divide by it right.
+
+ align:start position:0%
+divide by it right.
+ 
+
+ align:start position:0%
+divide by it right.
+So for
+
+ align:start position:0%
+So for
+ 
+
+ align:start position:0%
+So for
+for x fixed
+
+ align:start position:0%
+for x fixed
+ 
+
+ align:start position:0%
+for x fixed
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+y sufficiently close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you have then uh
+
+ align:start position:0%
+then you have then uh
+ 
+
+ align:start position:0%
+then you have then uh
+then g of x minus g of y
+
+ align:start position:0%
+then g of x minus g of y
+ 
+
+ align:start position:0%
+then g of x minus g of y
+is not equal to zero. Right? And so I
+
+ align:start position:0%
+is not equal to zero. Right? And so I
+ 
+
+ align:start position:0%
+is not equal to zero. Right? And so I
+can so I get that uh fprime
+
+ align:start position:0%
+can so I get that uh fprime
+ 
+
+ align:start position:0%
+can so I get that uh fprime
+at this intermediate point divided by g
+
+ align:start position:0%
+at this intermediate point divided by g
+ 
+
+ align:start position:0%
+at this intermediate point divided by g
+prime at the same intermediate point is
+
+ align:start position:0%
+prime at the same intermediate point is
+ 
+
+ align:start position:0%
+prime at the same intermediate point is
+equal to f ofx - f of y / g of x minus g
+
+ align:start position:0%
+equal to f ofx - f of y / g of x minus g
+ 
+
+ align:start position:0%
+equal to f ofx - f of y / g of x minus g
+of y
+
+ align:start position:0%
+of y
+ 
+
+ align:start position:0%
+of y
+and now you see that as y here goes to
+
+ align:start position:0%
+and now you see that as y here goes to
+ 
+
+ align:start position:0%
+and now you see that as y here goes to
+zero right so x is fixed still as y goes
+
+ align:start position:0%
+zero right so x is fixed still as y goes
+ 
+
+ align:start position:0%
+zero right so x is fixed still as y goes
+to sorry not to zero But to a this here
+
+ align:start position:0%
+to sorry not to zero But to a this here
+ 
+
+ align:start position:0%
+to sorry not to zero But to a this here
+goes to zero by assumption. This here
+
+ align:start position:0%
+goes to zero by assumption. This here
+ 
+
+ align:start position:0%
+goes to zero by assumption. This here
+goes to zero. So the whole thing goes to
+
+ align:start position:0%
+goes to zero. So the whole thing goes to
+ 
+
+ align:start position:0%
+goes to zero. So the whole thing goes to
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+divided by g of x.
+
+ align:start position:0%
+divided by g of x.
+ 
+
+ align:start position:0%
+divided by g of x.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+Now the thing is that if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is for all x fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So now if you if you
+
+ align:start position:0%
+Right. So now if you if you
+ 
+
+ align:start position:0%
+Right. So now if you if you
+So now we want to use So now you since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh fprime
+
+ align:start position:0%
+uh fprime
+ 
+
+ align:start position:0%
+uh fprime
+at at say set divided by g prime at set
+
+ align:start position:0%
+at at say set divided by g prime at set
+ 
+
+ align:start position:0%
+at at say set divided by g prime at set
+since this fraction here as set go to a
+
+ align:start position:0%
+since this fraction here as set go to a
+ 
+
+ align:start position:0%
+since this fraction here as set go to a
+this is assumed to go to l right. So
+
+ align:start position:0%
+this is assumed to go to l right. So
+ 
+
+ align:start position:0%
+this is assumed to go to l right. So
+this means that that uh given
+
+ align:start position:0%
+this means that that uh given
+ 
+
+ align:start position:0%
+this means that that uh given
+given epsilon greater than zero there
+
+ align:start position:0%
+given epsilon greater than zero there
+ 
+
+ align:start position:0%
+given epsilon greater than zero there
+exist a delta
+
+ align:start position:0%
+exist a delta
+ 
+
+ align:start position:0%
+exist a delta
+greater than zero. So that if uh if if
+
+ align:start position:0%
+greater than zero. So that if uh if if
+ 
+
+ align:start position:0%
+greater than zero. So that if uh if if
+um set here is uh is less than a plus
+
+ align:start position:0%
+um set here is uh is less than a plus
+ 
+
+ align:start position:0%
+um set here is uh is less than a plus
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+then this fraction here then f prime of
+
+ align:start position:0%
+then this fraction here then f prime of
+ 
+
+ align:start position:0%
+then this fraction here then f prime of
+set minus g prime
+
+ align:start position:0%
+set minus g prime
+ 
+
+ align:start position:0%
+set minus g prime
+of set is minus l
+
+ align:start position:0%
+of set is minus l
+ 
+
+ align:start position:0%
+of set is minus l
+is less than epsilon.
+
+ align:start position:0%
+is less than epsilon.
+ 
+
+ align:start position:0%
+is less than epsilon.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+So now coming back here
+
+ align:start position:0%
+So now coming back here
+ 
+
+ align:start position:0%
+So now coming back here
+if you were starting with so this here
+
+ align:start position:0%
+if you were starting with so this here
+ 
+
+ align:start position:0%
+if you were starting with so this here
+again was for all fixed x
+
+ align:start position:0%
+again was for all fixed x
+ 
+
+ align:start position:0%
+again was for all fixed x
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+uh you had this statement right and
+
+ align:start position:0%
+uh you had this statement right and
+ 
+
+ align:start position:0%
+uh you had this statement right and
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+uh x0 was between y and x right so now
+
+ align:start position:0%
+uh x0 was between y and x right so now
+ 
+
+ align:start position:0%
+uh x0 was between y and x right so now
+if you so if
+
+ align:start position:0%
+if you so if
+ 
+
+ align:start position:0%
+if you so if
+if this x here If x is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is delta close to the left end point of
+
+ align:start position:0%
+is delta close to the left end point of
+ 
+
+ align:start position:0%
+is delta close to the left end point of
+the interval, right?
+
+ align:start position:0%
+the interval, right?
+ 
+
+ align:start position:0%
+the interval, right?
+Then you would have that
+
+ align:start position:0%
+Then you would have that
+ 
+
+ align:start position:0%
+Then you would have that
+x0, right? But x0 remember that x0 is
+
+ align:start position:0%
+x0, right? But x0 remember that x0 is
+ 
+
+ align:start position:0%
+x0, right? But x0 remember that x0 is
+lying here, right? So since
+
+ align:start position:0%
+lying here, right? So since
+ 
+
+ align:start position:0%
+lying here, right? So since
+x0 would lie here, this means that also
+
+ align:start position:0%
+x0 would lie here, this means that also
+ 
+
+ align:start position:0%
+x0 would lie here, this means that also
+x0 here is uh white is is is
+
+ align:start position:0%
+x0 here is uh white is is is
+ 
+
+ align:start position:0%
+x0 here is uh white is is is
+uh in this interval here,
+
+ align:start position:0%
+uh in this interval here,
+ 
+
+ align:start position:0%
+uh in this interval here,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And so this means that this thing this
+
+ align:start position:0%
+And so this means that this thing this
+ 
+
+ align:start position:0%
+And so this means that this thing this
+number here you get is is L with up to
+
+ align:start position:0%
+number here you get is is L with up to
+ 
+
+ align:start position:0%
+number here you get is is L with up to
+some you know it's it's L up to some
+
+ align:start position:0%
+some you know it's it's L up to some
+ 
+
+ align:start position:0%
+some you know it's it's L up to some
+error of like epsilon right
+
+ align:start position:0%
+error of like epsilon right
+ 
+
+ align:start position:0%
+error of like epsilon right
+so this here is almost equal to L and so
+
+ align:start position:0%
+so this here is almost equal to L and so
+ 
+
+ align:start position:0%
+so this here is almost equal to L and so
+this means that this limit here right is
+
+ align:start position:0%
+this means that this limit here right is
+ 
+
+ align:start position:0%
+this means that this limit here right is
+almost equal to L within a error of
+
+ align:start position:0%
+almost equal to L within a error of
+ 
+
+ align:start position:0%
+almost equal to L within a error of
+epsilon right okay so this proof this
+
+ align:start position:0%
+epsilon right okay so this proof this
+ 
+
+ align:start position:0%
+epsilon right okay so this proof this
+version of the
+
+ align:start position:0%
+version of the
+ 
+
+ align:start position:0%
+version of the
+rule and there's a second version and
+
+ align:start position:0%
+rule and there's a second version and
+ 
+
+ align:start position:0%
+rule and there's a second version and
+that's in the notes but uh I'll skip it
+
+ align:start position:0%
+that's in the notes but uh I'll skip it
+ 
+
+ align:start position:0%
+that's in the notes but uh I'll skip it
+actually for now just because you know
+
+ align:start position:0%
+actually for now just because you know
+ 
+
+ align:start position:0%
+actually for now just because you know
+there was sort of from the last lecture
+
+ align:start position:0%
+there was sort of from the last lecture
+ 
+
+ align:start position:0%
+there was sort of from the last lecture
+and it's very similar to this yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> sorry why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Okay. So this is because um
+
+ align:start position:0%
+Yeah. Okay. So this is because um
+ 
+
+ align:start position:0%
+Yeah. Okay. So this is because um
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+of x is for is supposed to be not equal
+
+ align:start position:0%
+of x is for is supposed to be not equal
+ 
+
+ align:start position:0%
+of x is for is supposed to be not equal
+to x for all x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? And now I'm fixing x. Okay? So
+
+ align:start position:0%
+Right? And now I'm fixing x. Okay? So
+ 
+
+ align:start position:0%
+Right? And now I'm fixing x. Okay? So
+this here is non zero. Then I'm letting
+
+ align:start position:0%
+this here is non zero. Then I'm letting
+ 
+
+ align:start position:0%
+this here is non zero. Then I'm letting
+y go to a but then this here goes to
+
+ align:start position:0%
+y go to a but then this here goes to
+ 
+
+ align:start position:0%
+y go to a but then this here goes to
+zero by assumption.
+
+ align:start position:0%
+zero by assumption.
+ 
+
+ align:start position:0%
+zero by assumption.
+Right? So you see that if you're fixing
+
+ align:start position:0%
+Right? So you see that if you're fixing
+ 
+
+ align:start position:0%
+Right? So you see that if you're fixing
+X and you just take a Y sufficiently
+
+ align:start position:0%
+X and you just take a Y sufficiently
+ 
+
+ align:start position:0%
+X and you just take a Y sufficiently
+close to A, then this denominator is
+
+ align:start position:0%
+close to A, then this denominator is
+ 
+
+ align:start position:0%
+close to A, then this denominator is
+definitely not zero. Right? You really
+
+ align:start position:0%
+definitely not zero. Right? You really
+ 
+
+ align:start position:0%
+definitely not zero. Right? You really
+want to let this you want to let Y goes
+
+ align:start position:0%
+want to let this you want to let Y goes
+ 
+
+ align:start position:0%
+want to let this you want to let Y goes
+to A because then this here is
+
+ align:start position:0%
+to A because then this here is
+ 
+
+ align:start position:0%
+to A because then this here is
+eliminated, right? This is not part of
+
+ align:start position:0%
+eliminated, right? This is not part of
+ 
+
+ align:start position:0%
+eliminated, right? This is not part of
+the statement the G of Y, right? Okay.
+
+ align:start position:0%
+the statement the G of Y, right? Okay.
+ 
+
+ align:start position:0%
+the statement the G of Y, right? Okay.
+And so again, as long as we started with
+
+ align:start position:0%
+And so again, as long as we started with
+ 
+
+ align:start position:0%
+And so again, as long as we started with
+a x that was sufficiently close to if x
+
+ align:start position:0%
+a x that was sufficiently close to if x
+ 
+
+ align:start position:0%
+a x that was sufficiently close to if x
+was in this interval, then x0 is even
+
+ align:start position:0%
+was in this interval, then x0 is even
+ 
+
+ align:start position:0%
+was in this interval, then x0 is even
+further to the left. So this is also in
+
+ align:start position:0%
+further to the left. So this is also in
+ 
+
+ align:start position:0%
+further to the left. So this is also in
+this interval. We don't know exactly
+
+ align:start position:0%
+this interval. We don't know exactly
+ 
+
+ align:start position:0%
+this interval. We don't know exactly
+what x0 is, but it is in that interval.
+
+ align:start position:0%
+what x0 is, but it is in that interval.
+ 
+
+ align:start position:0%
+what x0 is, but it is in that interval.
+And so this means that this is strictly
+
+ align:start position:0%
+And so this means that this is strictly
+ 
+
+ align:start position:0%
+And so this means that this is strictly
+smaller than epsilon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+another thing we talked about last time
+
+ align:start position:0%
+another thing we talked about last time
+ 
+
+ align:start position:0%
+another thing we talked about last time
+was this with the tail expansion.
+
+ align:start position:0%
+was this with the tail expansion.
+ 
+
+ align:start position:0%
+was this with the tail expansion.
+Uh,
+
+ align:start position:0%
+Uh,
+ 
+
+ align:start position:0%
+Uh,
+and right and that all of these things
+
+ align:start position:0%
+and right and that all of these things
+ 
+
+ align:start position:0%
+and right and that all of these things
+really came out of this uh bodice
+
+ align:start position:0%
+really came out of this uh bodice
+ 
+
+ align:start position:0%
+really came out of this uh bodice
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+uh and and and that was also the case
+
+ align:start position:0%
+uh and and and that was also the case
+ 
+
+ align:start position:0%
+uh and and and that was also the case
+for the tail expansion.
+
+ align:start position:0%
+for the tail expansion.
+ 
+
+ align:start position:0%
+for the tail expansion.
+So, you have a function f. So this is
+
+ align:start position:0%
+So, you have a function f. So this is
+ 
+
+ align:start position:0%
+So, you have a function f. So this is
+just to remind you about the tail
+
+ align:start position:0%
+just to remind you about the tail
+ 
+
+ align:start position:0%
+just to remind you about the tail
+expansion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have a function
+
+ align:start position:0%
+So you have a function
+ 
+
+ align:start position:0%
+So you have a function
+uh f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say that is defined on some
+
+ align:start position:0%
+and let's say that is defined on some
+ 
+
+ align:start position:0%
+and let's say that is defined on some
+interval here
+
+ align:start position:0%
+interval here
+ 
+
+ align:start position:0%
+interval here
+into r and the function is so f here is
+
+ align:start position:0%
+into r and the function is so f here is
+ 
+
+ align:start position:0%
+into r and the function is so f here is
+uh k times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that that fprime exist
+
+ align:start position:0%
+So this means that that fprime exist
+ 
+
+ align:start position:0%
+So this means that that fprime exist
+fprime up to
+
+ align:start position:0%
+fprime up to
+ 
+
+ align:start position:0%
+fprime up to
+the k derivative right. So they all
+
+ align:start position:0%
+the k derivative right. So they all
+ 
+
+ align:start position:0%
+the k derivative right. So they all
+exist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and then the
+
+ align:start position:0%
+Uh and then the
+ 
+
+ align:start position:0%
+Uh and then the
+statement was so then you looked at the
+
+ align:start position:0%
+statement was so then you looked at the
+ 
+
+ align:start position:0%
+statement was so then you looked at the
+k minus one this is the k minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tail polomium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and it was given by that k minus
+
+ align:start position:0%
+and uh and it was given by that k minus
+ 
+
+ align:start position:0%
+and uh and it was given by that k minus
+one of x is equal to and now you're
+
+ align:start position:0%
+one of x is equal to and now you're
+ 
+
+ align:start position:0%
+one of x is equal to and now you're
+summing here from i =0 to k minus one
+
+ align:start position:0%
+summing here from i =0 to k minus one
+ 
+
+ align:start position:0%
+summing here from i =0 to k minus one
+and you take the i derivative this is
+
+ align:start position:0%
+and you take the i derivative this is
+ 
+
+ align:start position:0%
+and you take the i derivative this is
+sorry this is the i derivative
+
+ align:start position:0%
+sorry this is the i derivative
+ 
+
+ align:start position:0%
+sorry this is the i derivative
+uh of f and you do this in a and you
+
+ align:start position:0%
+uh of f and you do this in a and you
+ 
+
+ align:start position:0%
+uh of f and you do this in a and you
+divide by a factorial and then you're
+
+ align:start position:0%
+divide by a factorial and then you're
+ 
+
+ align:start position:0%
+divide by a factorial and then you're
+looking at uh at x - a to the power i
+
+ align:start position:0%
+looking at uh at x - a to the power i
+ 
+
+ align:start position:0%
+looking at uh at x - a to the power i
+right So this was this was the k minus
+
+ align:start position:0%
+right So this was this was the k minus
+ 
+
+ align:start position:0%
+right So this was this was the k minus
+one tail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then uh the tail expansion
+
+ align:start position:0%
+and then uh the tail expansion
+ 
+
+ align:start position:0%
+and then uh the tail expansion
+tail expansion just told you that uh
+
+ align:start position:0%
+tail expansion just told you that uh
+ 
+
+ align:start position:0%
+tail expansion just told you that uh
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+that uh f here
+
+ align:start position:0%
+that uh f here
+ 
+
+ align:start position:0%
+that uh f here
+at some x was equal to
+
+ align:start position:0%
+at some x was equal to
+ 
+
+ align:start position:0%
+at some x was equal to
+uh p
+
+ align:start position:0%
+uh p
+ 
+
+ align:start position:0%
+uh p
+k minus one it's tail up polinomial plus
+
+ align:start position:0%
+k minus one it's tail up polinomial plus
+ 
+
+ align:start position:0%
+k minus one it's tail up polinomial plus
+and then this is what is usually
+
+ align:start position:0%
+and then this is what is usually
+ 
+
+ align:start position:0%
+and then this is what is usually
+referred to as a remainder term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this was uh the this looked very
+
+ align:start position:0%
+and this was uh the this looked very
+ 
+
+ align:start position:0%
+and this was uh the this looked very
+similar to one of these terms. It was
+
+ align:start position:0%
+similar to one of these terms. It was
+ 
+
+ align:start position:0%
+similar to one of these terms. It was
+the k derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f but then it was evaluated at a
+
+ align:start position:0%
+of f but then it was evaluated at a
+ 
+
+ align:start position:0%
+of f but then it was evaluated at a
+point c
+
+ align:start position:0%
+point c
+ 
+
+ align:start position:0%
+point c
+uh divided by k factorial
+
+ align:start position:0%
+uh divided by k factorial
+ 
+
+ align:start position:0%
+uh divided by k factorial
+time uh time um x minus
+
+ align:start position:0%
+time uh time um x minus
+ 
+
+ align:start position:0%
+time uh time um x minus
+uh a to the power k
+
+ align:start position:0%
+uh a to the power k
+ 
+
+ align:start position:0%
+uh a to the power k
+and c here was supposed to lie between a
+
+ align:start position:0%
+and c here was supposed to lie between a
+ 
+
+ align:start position:0%
+and c here was supposed to lie between a
+and X.
+
+ align:start position:0%
+and X.
+ 
+
+ align:start position:0%
+and X.
+Okay. So that was the this was the this
+
+ align:start position:0%
+Okay. So that was the this was the this
+ 
+
+ align:start position:0%
+Okay. So that was the this was the this
+is the tail expansion theorem right
+
+ align:start position:0%
+is the tail expansion theorem right
+ 
+
+ align:start position:0%
+is the tail expansion theorem right
+and and so the thing is that so why is
+
+ align:start position:0%
+and and so the thing is that so why is
+ 
+
+ align:start position:0%
+and and so the thing is that so why is
+this so useful and it is extremely
+
+ align:start position:0%
+this so useful and it is extremely
+ 
+
+ align:start position:0%
+this so useful and it is extremely
+useful uh in many different settings
+
+ align:start position:0%
+useful uh in many different settings
+ 
+
+ align:start position:0%
+useful uh in many different settings
+also in much more general settings than
+
+ align:start position:0%
+also in much more general settings than
+ 
+
+ align:start position:0%
+also in much more general settings than
+what I'm describing here and that is
+
+ align:start position:0%
+what I'm describing here and that is
+ 
+
+ align:start position:0%
+what I'm describing here and that is
+because that if you take a function here
+
+ align:start position:0%
+because that if you take a function here
+ 
+
+ align:start position:0%
+because that if you take a function here
+then um and it may be a very complicated
+
+ align:start position:0%
+then um and it may be a very complicated
+ 
+
+ align:start position:0%
+then um and it may be a very complicated
+function but this tail expansion theorem
+
+ align:start position:0%
+function but this tail expansion theorem
+ 
+
+ align:start position:0%
+function but this tail expansion theorem
+tells you that it is it is close to if
+
+ align:start position:0%
+tells you that it is it is close to if
+ 
+
+ align:start position:0%
+tells you that it is it is close to if
+you want to evaluate it at some X
+
+ align:start position:0%
+you want to evaluate it at some X
+ 
+
+ align:start position:0%
+you want to evaluate it at some X
+you can evaluate the tail polinom that's
+
+ align:start position:0%
+you can evaluate the tail polinom that's
+ 
+
+ align:start position:0%
+you can evaluate the tail polinom that's
+after all just a polinomial so that's
+
+ align:start position:0%
+after all just a polinomial so that's
+ 
+
+ align:start position:0%
+after all just a polinomial so that's
+easy to evaluate
+
+ align:start position:0%
+easy to evaluate
+ 
+
+ align:start position:0%
+easy to evaluate
+and then you get within this remainder
+
+ align:start position:0%
+and then you get within this remainder
+ 
+
+ align:start position:0%
+and then you get within this remainder
+term of the right answer okay so that's
+
+ align:start position:0%
+term of the right answer okay so that's
+ 
+
+ align:start position:0%
+term of the right answer okay so that's
+how it always is used
+
+ align:start position:0%
+how it always is used
+ 
+
+ align:start position:0%
+how it always is used
+and so the question is now the natural
+
+ align:start position:0%
+and so the question is now the natural
+ 
+
+ align:start position:0%
+and so the question is now the natural
+question is how well does the tail
+
+ align:start position:0%
+question is how well does the tail
+ 
+
+ align:start position:0%
+question is how well does the tail
+polomial
+
+ align:start position:0%
+polomial
+ 
+
+ align:start position:0%
+polomial
+uh approximate
+
+ align:start position:0%
+uh approximate
+ 
+
+ align:start position:0%
+uh approximate
+the value of the given function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So, so how
+
+ align:start position:0%
+Right? So, so how
+ 
+
+ align:start position:0%
+Right? So, so how
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+does the tail upon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh approximate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. and and of course to to um to
+
+ align:start position:0%
+Okay. and and of course to to um to
+ 
+
+ align:start position:0%
+Okay. and and of course to to um to
+understand that you need to estimate the
+
+ align:start position:0%
+understand that you need to estimate the
+ 
+
+ align:start position:0%
+understand that you need to estimate the
+remainder term. Let me write the
+
+ align:start position:0%
+remainder term. Let me write the
+ 
+
+ align:start position:0%
+remainder term. Let me write the
+remainder term here. So this the
+
+ align:start position:0%
+remainder term here. So this the
+ 
+
+ align:start position:0%
+remainder term here. So this the
+remainder term
+
+ align:start position:0%
+remainder term
+ 
+
+ align:start position:0%
+remainder term
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right so the remainder term is
+
+ align:start position:0%
+right so the remainder term is
+ 
+
+ align:start position:0%
+right so the remainder term is
+um so I write this here as uh so it
+
+ align:start position:0%
+um so I write this here as uh so it
+ 
+
+ align:start position:0%
+um so I write this here as uh so it
+really depends on on on x also right but
+
+ align:start position:0%
+really depends on on on x also right but
+ 
+
+ align:start position:0%
+really depends on on on x also right but
+I would just write it like this thing
+
+ align:start position:0%
+I would just write it like this thing
+ 
+
+ align:start position:0%
+I would just write it like this thing
+here so by this I mean the k derivative
+
+ align:start position:0%
+here so by this I mean the k derivative
+ 
+
+ align:start position:0%
+here so by this I mean the k derivative
+of f
+
+ align:start position:0%
+of f
+ 
+
+ align:start position:0%
+of f
+in c divided by k factorial and then x
+
+ align:start position:0%
+in c divided by k factorial and then x
+ 
+
+ align:start position:0%
+in c divided by k factorial and then x
+minus a to the power k.
+
+ align:start position:0%
+minus a to the power k.
+ 
+
+ align:start position:0%
+minus a to the power k.
+So again it depends on really also on
+
+ align:start position:0%
+So again it depends on really also on
+ 
+
+ align:start position:0%
+So again it depends on really also on
+it. Of course it depend on a but it also
+
+ align:start position:0%
+it. Of course it depend on a but it also
+ 
+
+ align:start position:0%
+it. Of course it depend on a but it also
+depends on x right and it's this thing
+
+ align:start position:0%
+depends on x right and it's this thing
+ 
+
+ align:start position:0%
+depends on x right and it's this thing
+here. The thing the the catch here is
+
+ align:start position:0%
+here. The thing the the catch here is
+ 
+
+ align:start position:0%
+here. The thing the the catch here is
+that you don't really know what c is
+
+ align:start position:0%
+that you don't really know what c is
+ 
+
+ align:start position:0%
+that you don't really know what c is
+right the only thing you know about c is
+
+ align:start position:0%
+right the only thing you know about c is
+ 
+
+ align:start position:0%
+right the only thing you know about c is
+that c is lying between uh a and x. So
+
+ align:start position:0%
+that c is lying between uh a and x. So
+ 
+
+ align:start position:0%
+that c is lying between uh a and x. So
+this is essentially all you need, all
+
+ align:start position:0%
+this is essentially all you need, all
+ 
+
+ align:start position:0%
+this is essentially all you need, all
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about C.
+
+ align:start position:0%
+about C.
+ 
+
+ align:start position:0%
+about C.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now let's look at some examples.
+
+ align:start position:0%
+So now let's look at some examples.
+ 
+
+ align:start position:0%
+So now let's look at some examples.
+Let's look at two examples. So the the
+
+ align:start position:0%
+Let's look at two examples. So the the
+ 
+
+ align:start position:0%
+Let's look at two examples. So the the
+first one is like a promising example
+
+ align:start position:0%
+first one is like a promising example
+ 
+
+ align:start position:0%
+first one is like a promising example
+and the second one is much less
+
+ align:start position:0%
+and the second one is much less
+ 
+
+ align:start position:0%
+and the second one is much less
+promising. Uh and so uh but and so the
+
+ align:start position:0%
+promising. Uh and so uh but and so the
+ 
+
+ align:start position:0%
+promising. Uh and so uh but and so the
+thing is that that how well it
+
+ align:start position:0%
+thing is that that how well it
+ 
+
+ align:start position:0%
+thing is that that how well it
+approximate really depends on the
+
+ align:start position:0%
+approximate really depends on the
+ 
+
+ align:start position:0%
+approximate really depends on the
+function. Okay. But the first one is is
+
+ align:start position:0%
+function. Okay. But the first one is is
+ 
+
+ align:start position:0%
+function. Okay. But the first one is is
+quite typical though example.
+
+ align:start position:0%
+quite typical though example.
+ 
+
+ align:start position:0%
+quite typical though example.
+So suppose that the function f ofx is
+
+ align:start position:0%
+So suppose that the function f ofx is
+ 
+
+ align:start position:0%
+So suppose that the function f ofx is
+the exponential function.
+
+ align:start position:0%
+the exponential function.
+ 
+
+ align:start position:0%
+the exponential function.
+Um and then we have that the derivative
+
+ align:start position:0%
+Um and then we have that the derivative
+ 
+
+ align:start position:0%
+Um and then we have that the derivative
+is just the exponential function itself.
+
+ align:start position:0%
+is just the exponential function itself.
+ 
+
+ align:start position:0%
+is just the exponential function itself.
+So this means that if you take the
+
+ align:start position:0%
+So this means that if you take the
+ 
+
+ align:start position:0%
+So this means that if you take the
+derivative k times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you just get the function itself.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that the k minus one
+
+ align:start position:0%
+So this means that the k minus one
+ 
+
+ align:start position:0%
+So this means that the k minus one
+this means that a k minus one tail
+
+ align:start position:0%
+this means that a k minus one tail
+ 
+
+ align:start position:0%
+this means that a k minus one tail
+polinomial
+
+ align:start position:0%
+polinomial
+ 
+
+ align:start position:0%
+polinomial
+right this is just the value of the
+
+ align:start position:0%
+right this is just the value of the
+ 
+
+ align:start position:0%
+right this is just the value of the
+function I'll just write it out here so
+
+ align:start position:0%
+function I'll just write it out here so
+ 
+
+ align:start position:0%
+function I'll just write it out here so
+this is the value and now I do it uh I
+
+ align:start position:0%
+this is the value and now I do it uh I
+ 
+
+ align:start position:0%
+this is the value and now I do it uh I
+do it for a equal to uh zero
+
+ align:start position:0%
+do it for a equal to uh zero
+ 
+
+ align:start position:0%
+do it for a equal to uh zero
+and I'm assuming that b here so I'm
+
+ align:start position:0%
+and I'm assuming that b here so I'm
+ 
+
+ align:start position:0%
+and I'm assuming that b here so I'm
+thinking about I will think about this
+
+ align:start position:0%
+thinking about I will think about this
+ 
+
+ align:start position:0%
+thinking about I will think about this
+function here f ofx
+
+ align:start position:0%
+function here f ofx
+ 
+
+ align:start position:0%
+function here f ofx
+uh on on the this function the
+
+ align:start position:0%
+uh on on the this function the
+ 
+
+ align:start position:0%
+uh on on the this function the
+exponential function I'm going to sing
+
+ align:start position:0%
+exponential function I'm going to sing
+ 
+
+ align:start position:0%
+exponential function I'm going to sing
+about it on the interval say from uh
+
+ align:start position:0%
+about it on the interval say from uh
+ 
+
+ align:start position:0%
+about it on the interval say from uh
+minus1 to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um into r maybe maybe I will maybe I'll
+
+ align:start position:0%
+um into r maybe maybe I will maybe I'll
+ 
+
+ align:start position:0%
+um into r maybe maybe I will maybe I'll
+just take it from zero to one into r
+
+ align:start position:0%
+just take it from zero to one into r
+ 
+
+ align:start position:0%
+just take it from zero to one into r
+Um okay so the and the tail polinomial
+
+ align:start position:0%
+Um okay so the and the tail polinomial
+ 
+
+ align:start position:0%
+Um okay so the and the tail polinomial
+so I'm going to so so so the tailum one
+
+ align:start position:0%
+so I'm going to so so so the tailum one
+ 
+
+ align:start position:0%
+so I'm going to so so so the tailum one
+also talk about that this
+
+ align:start position:0%
+also talk about that this
+ 
+
+ align:start position:0%
+also talk about that this
+tail polinomium is expanded around a
+
+ align:start position:0%
+tail polinomium is expanded around a
+ 
+
+ align:start position:0%
+tail polinomium is expanded around a
+okay so we talk about that the tail
+
+ align:start position:0%
+okay so we talk about that the tail
+ 
+
+ align:start position:0%
+okay so we talk about that the tail
+polom so we talk about tail expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh A. Okay. And this just refer to that
+
+ align:start position:0%
+uh A. Okay. And this just refer to that
+ 
+
+ align:start position:0%
+uh A. Okay. And this just refer to that
+when when you plug in A here, well then
+
+ align:start position:0%
+when when you plug in A here, well then
+ 
+
+ align:start position:0%
+when when you plug in A here, well then
+of course you have exact equality,
+
+ align:start position:0%
+of course you have exact equality,
+ 
+
+ align:start position:0%
+of course you have exact equality,
+right? And that all of the derivative
+
+ align:start position:0%
+right? And that all of the derivative
+ 
+
+ align:start position:0%
+right? And that all of the derivative
+are evaluated at A. Okay? So it's really
+
+ align:start position:0%
+are evaluated at A. Okay? So it's really
+ 
+
+ align:start position:0%
+are evaluated at A. Okay? So it's really
+like the tail polom. It's only a good
+
+ align:start position:0%
+like the tail polom. It's only a good
+ 
+
+ align:start position:0%
+like the tail polom. It's only a good
+approximation near A. Right? So I want
+
+ align:start position:0%
+approximation near A. Right? So I want
+ 
+
+ align:start position:0%
+approximation near A. Right? So I want
+now to tail expand
+
+ align:start position:0%
+now to tail expand
+ 
+
+ align:start position:0%
+now to tail expand
+uh near uh the zero
+
+ align:start position:0%
+uh near uh the zero
+ 
+
+ align:start position:0%
+uh near uh the zero
+and so um so right so the value here of
+
+ align:start position:0%
+and so um so right so the value here of
+ 
+
+ align:start position:0%
+and so um so right so the value here of
+the function is one at zero the
+
+ align:start position:0%
+the function is one at zero the
+ 
+
+ align:start position:0%
+the function is one at zero the
+derivative is right so it's the
+
+ align:start position:0%
+derivative is right so it's the
+ 
+
+ align:start position:0%
+derivative is right so it's the
+derivative is also one because it's just
+
+ align:start position:0%
+derivative is also one because it's just
+ 
+
+ align:start position:0%
+derivative is also one because it's just
+a function itself and so this is so you
+
+ align:start position:0%
+a function itself and so this is so you
+ 
+
+ align:start position:0%
+a function itself and so this is so you
+get x and then you get the next Uh the
+
+ align:start position:0%
+get x and then you get the next Uh the
+ 
+
+ align:start position:0%
+get x and then you get the next Uh the
+next uh element in the tail expansion is
+
+ align:start position:0%
+next uh element in the tail expansion is
+ 
+
+ align:start position:0%
+next uh element in the tail expansion is
+x^2 / 2 + x^2
+
+ align:start position:0%
+x^2 / 2 + x^2
+ 
+
+ align:start position:0%
+x^2 / 2 + x^2
+over 3 factorial
+
+ align:start position:0%
+over 3 factorial
+ 
+
+ align:start position:0%
+over 3 factorial
+and then uh x 4 over 4 factorial etc up
+
+ align:start position:0%
+and then uh x 4 over 4 factorial etc up
+ 
+
+ align:start position:0%
+and then uh x 4 over 4 factorial etc up
+to x ^ k minus one over u uh k minus one
+
+ align:start position:0%
+to x ^ k minus one over u uh k minus one
+ 
+
+ align:start position:0%
+to x ^ k minus one over u uh k minus one
+factorial right so this is the a tail
+
+ align:start position:0%
+factorial right so this is the a tail
+ 
+
+ align:start position:0%
+factorial right so this is the a tail
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+or take k minus one tail polomial
+
+ align:start position:0%
+or take k minus one tail polomial
+ 
+
+ align:start position:0%
+or take k minus one tail polomial
+uh around zero. Okay.
+
+ align:start position:0%
+uh around zero. Okay.
+ 
+
+ align:start position:0%
+uh around zero. Okay.
+And so now if you're interested in
+
+ align:start position:0%
+And so now if you're interested in
+ 
+
+ align:start position:0%
+And so now if you're interested in
+evaluating
+
+ align:start position:0%
+evaluating
+ 
+
+ align:start position:0%
+evaluating
+p you want to say how well does this
+
+ align:start position:0%
+p you want to say how well does this
+ 
+
+ align:start position:0%
+p you want to say how well does this
+here approximate
+
+ align:start position:0%
+here approximate
+ 
+
+ align:start position:0%
+here approximate
+uh the original function the exponential
+
+ align:start position:0%
+uh the original function the exponential
+ 
+
+ align:start position:0%
+uh the original function the exponential
+function. So you want to bound this
+
+ align:start position:0%
+function. So you want to bound this
+ 
+
+ align:start position:0%
+function. So you want to bound this
+thing here right? So you want to have a
+
+ align:start position:0%
+thing here right? So you want to have a
+ 
+
+ align:start position:0%
+thing here right? So you want to have a
+bound for that. Well the thing again is
+
+ align:start position:0%
+bound for that. Well the thing again is
+ 
+
+ align:start position:0%
+bound for that. Well the thing again is
+that f ofx you know that f ofx is equal
+
+ align:start position:0%
+that f ofx you know that f ofx is equal
+ 
+
+ align:start position:0%
+that f ofx you know that f ofx is equal
+to this tail polomial
+
+ align:start position:0%
+to this tail polomial
+ 
+
+ align:start position:0%
+to this tail polomial
+and then plus this remainder term
+
+ align:start position:0%
+and then plus this remainder term
+ 
+
+ align:start position:0%
+and then plus this remainder term
+right in the c right
+
+ align:start position:0%
+right in the c right
+ 
+
+ align:start position:0%
+right in the c right
+now c again has to lie will c will lie
+
+ align:start position:0%
+now c again has to lie will c will lie
+ 
+
+ align:start position:0%
+now c again has to lie will c will lie
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+a and x. In this case a is zero.
+
+ align:start position:0%
+a and x. In this case a is zero.
+ 
+
+ align:start position:0%
+a and x. In this case a is zero.
+So it means that c here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that here here c here is
+
+ align:start position:0%
+So this means that here here c here is
+ 
+
+ align:start position:0%
+So this means that here here c here is
+between zero and x. Right?
+
+ align:start position:0%
+between zero and x. Right?
+ 
+
+ align:start position:0%
+between zero and x. Right?
+And the remainder term here
+
+ align:start position:0%
+And the remainder term here
+ 
+
+ align:start position:0%
+And the remainder term here
+this here was
+
+ align:start position:0%
+this here was
+ 
+
+ align:start position:0%
+this here was
+was equal to that you took the k
+
+ align:start position:0%
+was equal to that you took the k
+ 
+
+ align:start position:0%
+was equal to that you took the k
+derivative of the function. So in this
+
+ align:start position:0%
+derivative of the function. So in this
+ 
+
+ align:start position:0%
+derivative of the function. So in this
+case the k derivative of the function is
+
+ align:start position:0%
+case the k derivative of the function is
+ 
+
+ align:start position:0%
+case the k derivative of the function is
+the function itself. So this here is the
+
+ align:start position:0%
+the function itself. So this here is the
+ 
+
+ align:start position:0%
+the function itself. So this here is the
+value of the k derivative and this is uh
+
+ align:start position:0%
+value of the k derivative and this is uh
+ 
+
+ align:start position:0%
+value of the k derivative and this is uh
+at c this is the k derivative of the
+
+ align:start position:0%
+at c this is the k derivative of the
+ 
+
+ align:start position:0%
+at c this is the k derivative of the
+original function and then you have to
+
+ align:start position:0%
+original function and then you have to
+ 
+
+ align:start position:0%
+original function and then you have to
+divide by a k factorial and then it's x
+
+ align:start position:0%
+divide by a k factorial and then it's x
+ 
+
+ align:start position:0%
+divide by a k factorial and then it's x
+to the power
+
+ align:start position:0%
+to the power
+ 
+
+ align:start position:0%
+to the power
+uh k like that
+
+ align:start position:0%
+uh k like that
+ 
+
+ align:start position:0%
+uh k like that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so you see that if if x here is now
+
+ align:start position:0%
+and so you see that if if x here is now
+ 
+
+ align:start position:0%
+and so you see that if if x here is now
+between zero and one. This means that
+
+ align:start position:0%
+between zero and one. This means that
+ 
+
+ align:start position:0%
+between zero and one. This means that
+this thing here, this
+
+ align:start position:0%
+this thing here, this
+ 
+
+ align:start position:0%
+this thing here, this
+remainder term here, the absolute value
+
+ align:start position:0%
+remainder term here, the absolute value
+ 
+
+ align:start position:0%
+remainder term here, the absolute value
+is so c here is less than one. So this
+
+ align:start position:0%
+is so c here is less than one. So this
+ 
+
+ align:start position:0%
+is so c here is less than one. So this
+means that this thing here is less than
+
+ align:start position:0%
+means that this thing here is less than
+ 
+
+ align:start position:0%
+means that this thing here is less than
+e. So it's less or equal to e divided by
+
+ align:start position:0%
+e. So it's less or equal to e divided by
+ 
+
+ align:start position:0%
+e. So it's less or equal to e divided by
+k factorial. This here is bounded by
+
+ align:start position:0%
+k factorial. This here is bounded by
+ 
+
+ align:start position:0%
+k factorial. This here is bounded by
+since x is bounded by one, this is
+
+ align:start position:0%
+since x is bounded by one, this is
+ 
+
+ align:start position:0%
+since x is bounded by one, this is
+bounded by one. So you're getting this
+
+ align:start position:0%
+bounded by one. So you're getting this
+ 
+
+ align:start position:0%
+bounded by one. So you're getting this
+inequality here, right? And so you see
+
+ align:start position:0%
+inequality here, right? And so you see
+ 
+
+ align:start position:0%
+inequality here, right? And so you see
+that if K is is very large, this is a
+
+ align:start position:0%
+that if K is is very large, this is a
+ 
+
+ align:start position:0%
+that if K is is very large, this is a
+tiny number, right? So it's a really
+
+ align:start position:0%
+tiny number, right? So it's a really
+ 
+
+ align:start position:0%
+tiny number, right? So it's a really
+good approximation. I mean, you don't
+
+ align:start position:0%
+good approximation. I mean, you don't
+ 
+
+ align:start position:0%
+good approximation. I mean, you don't
+even need to make K very large because
+
+ align:start position:0%
+even need to make K very large because
+ 
+
+ align:start position:0%
+even need to make K very large because
+it's exponential, right? Not
+
+ align:start position:0%
+it's exponential, right? Not
+ 
+
+ align:start position:0%
+it's exponential, right? Not
+exponential, it's factorial. Yeah.
+
+ align:start position:0%
+exponential, it's factorial. Yeah.
+ 
+
+ align:start position:0%
+exponential, it's factorial. Yeah.
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's a kind of encouraging
+
+ align:start position:0%
+Okay. So that's a kind of encouraging
+ 
+
+ align:start position:0%
+Okay. So that's a kind of encouraging
+example. Let's say that the the tail
+
+ align:start position:0%
+example. Let's say that the the tail
+ 
+
+ align:start position:0%
+example. Let's say that the the tail
+expansion uh is is a very in this case
+
+ align:start position:0%
+expansion uh is is a very in this case
+ 
+
+ align:start position:0%
+expansion uh is is a very in this case
+is a very good approximation to the
+
+ align:start position:0%
+is a very good approximation to the
+ 
+
+ align:start position:0%
+is a very good approximation to the
+function.
+
+ align:start position:0%
+function.
+ 
+
+ align:start position:0%
+function.
+Uh the another example that is less
+
+ align:start position:0%
+Uh the another example that is less
+ 
+
+ align:start position:0%
+Uh the another example that is less
+encouraging and so again the moral is
+
+ align:start position:0%
+encouraging and so again the moral is
+ 
+
+ align:start position:0%
+encouraging and so again the moral is
+that how well the tail expansion
+
+ align:start position:0%
+that how well the tail expansion
+ 
+
+ align:start position:0%
+that how well the tail expansion
+approximate the function depend on the
+
+ align:start position:0%
+approximate the function depend on the
+ 
+
+ align:start position:0%
+approximate the function depend on the
+function. So suppose that the function
+
+ align:start position:0%
+function. So suppose that the function
+ 
+
+ align:start position:0%
+function. So suppose that the function
+here was
+
+ align:start position:0%
+here was
+ 
+
+ align:start position:0%
+here was
+uh was a function that was zero here.
+
+ align:start position:0%
+uh was a function that was zero here.
+ 
+
+ align:start position:0%
+uh was a function that was zero here.
+When x is less than zero less or equal
+
+ align:start position:0%
+When x is less than zero less or equal
+ 
+
+ align:start position:0%
+When x is less than zero less or equal
+to zero and when x is bigger than zero
+
+ align:start position:0%
+to zero and when x is bigger than zero
+ 
+
+ align:start position:0%
+to zero and when x is bigger than zero
+then it is e to the minus 1 /x^2.
+
+ align:start position:0%
+then it is e to the minus 1 /x^2.
+ 
+
+ align:start position:0%
+then it is e to the minus 1 /x^2.
+Okay. So you see that when x becomes
+
+ align:start position:0%
+Okay. So you see that when x becomes
+ 
+
+ align:start position:0%
+Okay. So you see that when x becomes
+very very small
+
+ align:start position:0%
+very very small
+ 
+
+ align:start position:0%
+very very small
+you are looking at one over this
+
+ align:start position:0%
+you are looking at one over this
+ 
+
+ align:start position:0%
+you are looking at one over this
+squared. So this here is huge
+
+ align:start position:0%
+squared. So this here is huge
+ 
+
+ align:start position:0%
+squared. So this here is huge
+right but now it's with a minus sign. So
+
+ align:start position:0%
+right but now it's with a minus sign. So
+ 
+
+ align:start position:0%
+right but now it's with a minus sign. So
+this means that this thing here is
+
+ align:start position:0%
+this means that this thing here is
+ 
+
+ align:start position:0%
+this means that this thing here is
+incredibly small right and so it's
+
+ align:start position:0%
+incredibly small right and so it's
+ 
+
+ align:start position:0%
+incredibly small right and so it's
+clearly it's clear that this function
+
+ align:start position:0%
+clearly it's clear that this function
+ 
+
+ align:start position:0%
+clearly it's clear that this function
+here is continuous at zero. It's clearly
+
+ align:start position:0%
+here is continuous at zero. It's clearly
+ 
+
+ align:start position:0%
+here is continuous at zero. It's clearly
+continuous everywhere else. But actually
+
+ align:start position:0%
+continuous everywhere else. But actually
+ 
+
+ align:start position:0%
+continuous everywhere else. But actually
+it's you know sort of using in this sort
+
+ align:start position:0%
+it's you know sort of using in this sort
+ 
+
+ align:start position:0%
+it's you know sort of using in this sort
+of argument it's easy to see that this
+
+ align:start position:0%
+of argument it's easy to see that this
+ 
+
+ align:start position:0%
+of argument it's easy to see that this
+function f here is uh infinite
+
+ align:start position:0%
+function f here is uh infinite
+ 
+
+ align:start position:0%
+function f here is uh infinite
+differentiable.
+
+ align:start position:0%
+differentiable.
+ 
+
+ align:start position:0%
+differentiable.
+So it's you can differentiate it
+
+ align:start position:0%
+So it's you can differentiate it
+ 
+
+ align:start position:0%
+So it's you can differentiate it
+infinitely many times and even at zero.
+
+ align:start position:0%
+infinitely many times and even at zero.
+ 
+
+ align:start position:0%
+infinitely many times and even at zero.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and by it and of course the
+
+ align:start position:0%
+and and by it and of course the
+ 
+
+ align:start position:0%
+and and by it and of course the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+uh the derivative is right so it's an
+
+ align:start position:0%
+uh the derivative is right so it's an
+ 
+
+ align:start position:0%
+uh the derivative is right so it's an
+example of a function that looks like
+
+ align:start position:0%
+example of a function that looks like
+ 
+
+ align:start position:0%
+example of a function that looks like
+this is zero until zero and then it goes
+
+ align:start position:0%
+this is zero until zero and then it goes
+ 
+
+ align:start position:0%
+this is zero until zero and then it goes
+up like this right and so the derivative
+
+ align:start position:0%
+up like this right and so the derivative
+ 
+
+ align:start position:0%
+up like this right and so the derivative
+at zero
+
+ align:start position:0%
+at zero
+ 
+
+ align:start position:0%
+at zero
+is zero any derivative however many
+
+ align:start position:0%
+is zero any derivative however many
+ 
+
+ align:start position:0%
+is zero any derivative however many
+times you take the derivative of this
+
+ align:start position:0%
+times you take the derivative of this
+ 
+
+ align:start position:0%
+times you take the derivative of this
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+this thing here
+
+ align:start position:0%
+this thing here
+ 
+
+ align:start position:0%
+this thing here
+if you take any derivative and you
+
+ align:start position:0%
+if you take any derivative and you
+ 
+
+ align:start position:0%
+if you take any derivative and you
+evaluate at zero, you always get zero,
+
+ align:start position:0%
+evaluate at zero, you always get zero,
+ 
+
+ align:start position:0%
+evaluate at zero, you always get zero,
+right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so this means that if you're looking
+
+ align:start position:0%
+So, so this means that if you're looking
+ 
+
+ align:start position:0%
+So, so this means that if you're looking
+at the tail expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at zero, so you're looking at this k
+
+ align:start position:0%
+at zero, so you're looking at this k
+ 
+
+ align:start position:0%
+at zero, so you're looking at this k
+minus one tailor polomial.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This polomial is all of the coefficient
+
+ align:start position:0%
+This polomial is all of the coefficient
+ 
+
+ align:start position:0%
+This polomial is all of the coefficient
+in the polinomial are zero right. So
+
+ align:start position:0%
+in the polinomial are zero right. So
+ 
+
+ align:start position:0%
+in the polinomial are zero right. So
+this polinomial is just zero. So this
+
+ align:start position:0%
+this polinomial is just zero. So this
+ 
+
+ align:start position:0%
+this polinomial is just zero. So this
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+if you're looking at
+
+ align:start position:0%
+if you're looking at
+ 
+
+ align:start position:0%
+if you're looking at
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+well f of x is actually equal to this
+
+ align:start position:0%
+well f of x is actually equal to this
+ 
+
+ align:start position:0%
+well f of x is actually equal to this
+remainder term right. So it's somehow
+
+ align:start position:0%
+remainder term right. So it's somehow
+ 
+
+ align:start position:0%
+remainder term right. So it's somehow
+you know the teleport number is like too
+
+ align:start position:0%
+you know the teleport number is like too
+ 
+
+ align:start position:0%
+you know the teleport number is like too
+trivial. It doesn't really help you all
+
+ align:start position:0%
+trivial. It doesn't really help you all
+ 
+
+ align:start position:0%
+trivial. It doesn't really help you all
+that much. Right? So it's equal to this
+
+ align:start position:0%
+that much. Right? So it's equal to this
+ 
+
+ align:start position:0%
+that much. Right? So it's equal to this
+remainder term.
+
+ align:start position:0%
+remainder term.
+ 
+
+ align:start position:0%
+remainder term.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> Is there a way of um so like the
+
+ align:start position:0%
+>> Is there a way of um so like the
+ 
+
+ align:start position:0%
+>> Is there a way of um so like the
+remainder like bounding this helps us
+
+ align:start position:0%
+remainder like bounding this helps us
+ 
+
+ align:start position:0%
+remainder like bounding this helps us
+figure out how well the expansion
+
+ align:start position:0%
+figure out how well the expansion
+ 
+
+ align:start position:0%
+figure out how well the expansion
+approximates the actual function. Is
+
+ align:start position:0%
+approximates the actual function. Is
+ 
+
+ align:start position:0%
+approximates the actual function. Is
+there a way to determine like how far
+
+ align:start position:0%
+there a way to determine like how far
+ 
+
+ align:start position:0%
+there a way to determine like how far
+from the point you're approximating like
+
+ align:start position:0%
+from the point you're approximating like
+ 
+
+ align:start position:0%
+from the point you're approximating like
+a or zero in this case you can go a
+
+ align:start position:0%
+a or zero in this case you can go a
+ 
+
+ align:start position:0%
+a or zero in this case you can go a
+>> Yeah. by it. That's right. I mean, so
+
+ align:start position:0%
+>> Yeah. by it. That's right. I mean, so
+ 
+
+ align:start position:0%
+>> Yeah. by it. That's right. I mean, so
+you're asking, right? So you're asking
+
+ align:start position:0%
+you're asking, right? So you're asking
+ 
+
+ align:start position:0%
+you're asking, right? So you're asking
+suppose and you definitely could do
+
+ align:start position:0%
+suppose and you definitely could do
+ 
+
+ align:start position:0%
+suppose and you definitely could do
+this, right? You you asking
+
+ align:start position:0%
+this, right? You you asking
+ 
+
+ align:start position:0%
+this, right? You you asking
+you you you're thinking that you have
+
+ align:start position:0%
+you you you're thinking that you have
+ 
+
+ align:start position:0%
+you you you're thinking that you have
+you have a
+
+ align:start position:0%
+you have a
+ 
+
+ align:start position:0%
+you have a
+you you you're thinking a slightly
+
+ align:start position:0%
+you you you're thinking a slightly
+ 
+
+ align:start position:0%
+you you you're thinking a slightly
+different situation than here but
+
+ align:start position:0%
+different situation than here but
+ 
+
+ align:start position:0%
+different situation than here but
+closely related that you have some a
+
+ align:start position:0%
+closely related that you have some a
+ 
+
+ align:start position:0%
+closely related that you have some a
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and you have a function f and and you
+
+ align:start position:0%
+and you have a function f and and you
+ 
+
+ align:start position:0%
+and you have a function f and and you
+want to and you are willing to maybe uh
+
+ align:start position:0%
+want to and you are willing to maybe uh
+ 
+
+ align:start position:0%
+want to and you are willing to maybe uh
+look at you're willing to
+
+ align:start position:0%
+look at you're willing to
+ 
+
+ align:start position:0%
+look at you're willing to
+take some fixed large k and then you're
+
+ align:start position:0%
+take some fixed large k and then you're
+ 
+
+ align:start position:0%
+take some fixed large k and then you're
+asking
+
+ align:start position:0%
+asking
+ 
+
+ align:start position:0%
+asking
+um what I'm interested in how well does
+
+ align:start position:0%
+um what I'm interested in how well does
+ 
+
+ align:start position:0%
+um what I'm interested in how well does
+this how well does this function this
+
+ align:start position:0%
+this how well does this function this
+ 
+
+ align:start position:0%
+this how well does this function this
+polomial approximate this but I want it
+
+ align:start position:0%
+polomial approximate this but I want it
+ 
+
+ align:start position:0%
+polomial approximate this but I want it
+within an error certain area right so
+
+ align:start position:0%
+within an error certain area right so
+ 
+
+ align:start position:0%
+within an error certain area right so
+it's a given epsilon and you're
+
+ align:start position:0%
+it's a given epsilon and you're
+ 
+
+ align:start position:0%
+it's a given epsilon and you're
+interested in how far away can you go
+
+ align:start position:0%
+interested in how far away can you go
+ 
+
+ align:start position:0%
+interested in how far away can you go
+from a so that this here is less than
+
+ align:start position:0%
+from a so that this here is less than
+ 
+
+ align:start position:0%
+from a so that this here is less than
+epsilon and so this is so so this
+
+ align:start position:0%
+epsilon and so this is so so this
+ 
+
+ align:start position:0%
+epsilon and so this is so so this
+becomes a question of this remainder
+
+ align:start position:0%
+becomes a question of this remainder
+ 
+
+ align:start position:0%
+becomes a question of this remainder
+term, right? So this becomes a question
+
+ align:start position:0%
+term, right? So this becomes a question
+ 
+
+ align:start position:0%
+term, right? So this becomes a question
+of this remainder term. When can you
+
+ align:start position:0%
+of this remainder term. When can you
+ 
+
+ align:start position:0%
+of this remainder term. When can you
+always say that this remainder term is
+
+ align:start position:0%
+always say that this remainder term is
+ 
+
+ align:start position:0%
+always say that this remainder term is
+less than epsilon
+
+ align:start position:0%
+less than epsilon
+ 
+
+ align:start position:0%
+less than epsilon
+and so like in this particular you would
+
+ align:start position:0%
+and so like in this particular you would
+ 
+
+ align:start position:0%
+and so like in this particular you would
+have to do it on a casebyase basis. Uh
+
+ align:start position:0%
+have to do it on a casebyase basis. Uh
+ 
+
+ align:start position:0%
+have to do it on a casebyase basis. Uh
+but in this particular case the
+
+ align:start position:0%
+but in this particular case the
+ 
+
+ align:start position:0%
+but in this particular case the
+remainder term is right if this interval
+
+ align:start position:0%
+remainder term is right if this interval
+ 
+
+ align:start position:0%
+remainder term is right if this interval
+here in the in that example over there
+
+ align:start position:0%
+here in the in that example over there
+ 
+
+ align:start position:0%
+here in the in that example over there
+if if you if you have here zero this was
+
+ align:start position:0%
+if if you if you have here zero this was
+ 
+
+ align:start position:0%
+if if you if you have here zero this was
+a in our example and then you want to go
+
+ align:start position:0%
+a in our example and then you want to go
+ 
+
+ align:start position:0%
+a in our example and then you want to go
+out here to some x
+
+ align:start position:0%
+out here to some x
+ 
+
+ align:start position:0%
+out here to some x
+and now you know that c here is between
+
+ align:start position:0%
+and now you know that c here is between
+ 
+
+ align:start position:0%
+and now you know that c here is between
+zero and x but you don't really know
+
+ align:start position:0%
+zero and x but you don't really know
+ 
+
+ align:start position:0%
+zero and x but you don't really know
+anything else right so then it's like
+
+ align:start position:0%
+anything else right so then it's like
+ 
+
+ align:start position:0%
+anything else right so then it's like
+this remainder term you will have this
+
+ align:start position:0%
+this remainder term you will have this
+ 
+
+ align:start position:0%
+this remainder term you will have this
+remainder term in this example
+
+ align:start position:0%
+remainder term in this example
+ 
+
+ align:start position:0%
+remainder term in this example
+uh at this c here this again was equal
+
+ align:start position:0%
+uh at this c here this again was equal
+ 
+
+ align:start position:0%
+uh at this c here this again was equal
+to this thing here over k factorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you would have that you would
+
+ align:start position:0%
+and so you would have that you would
+ 
+
+ align:start position:0%
+and so you would have that you would
+want this thing here
+
+ align:start position:0%
+want this thing here
+ 
+
+ align:start position:0%
+want this thing here
+r k
+
+ align:start position:0%
+r k
+ 
+
+ align:start position:0%
+r k
+you would want this to be less than
+
+ align:start position:0%
+you would want this to be less than
+ 
+
+ align:start position:0%
+you would want this to be less than
+epsilon and so you would have that this
+
+ align:start position:0%
+epsilon and so you would have that this
+ 
+
+ align:start position:0%
+epsilon and so you would have that this
+thing here the the only the only thing
+
+ align:start position:0%
+thing here the the only the only thing
+ 
+
+ align:start position:0%
+thing here the the only the only thing
+you can really do is that you can say
+
+ align:start position:0%
+you can really do is that you can say
+ 
+
+ align:start position:0%
+you can really do is that you can say
+that C is less or equal to to X for C.
+
+ align:start position:0%
+that C is less or equal to to X for C.
+ 
+
+ align:start position:0%
+that C is less or equal to to X for C.
+>> Yeah, that's right. But that no so so
+
+ align:start position:0%
+>> Yeah, that's right. But that no so so
+ 
+
+ align:start position:0%
+>> Yeah, that's right. But that no so so
+you would do so what you would do here
+
+ align:start position:0%
+you would do so what you would do here
+ 
+
+ align:start position:0%
+you would do so what you would do here
+is you would say R K C this here has to
+
+ align:start position:0%
+is you would say R K C this here has to
+ 
+
+ align:start position:0%
+is you would say R K C this here has to
+be bounded by by because XC is less than
+
+ align:start position:0%
+be bounded by by because XC is less than
+ 
+
+ align:start position:0%
+be bounded by by because XC is less than
+X. So this is E to the X you have to
+
+ align:start position:0%
+X. So this is E to the X you have to
+ 
+
+ align:start position:0%
+X. So this is E to the X you have to
+eliminate C. So, so, so you would do
+
+ align:start position:0%
+eliminate C. So, so, so you would do
+ 
+
+ align:start position:0%
+eliminate C. So, so, so you would do
+like this k factorial * x ^ k you have
+
+ align:start position:0%
+like this k factorial * x ^ k you have
+ 
+
+ align:start position:0%
+like this k factorial * x ^ k you have
+to eliminate uh c right because you
+
+ align:start position:0%
+to eliminate uh c right because you
+ 
+
+ align:start position:0%
+to eliminate uh c right because you
+don't know anything really about c and
+
+ align:start position:0%
+don't know anything really about c and
+ 
+
+ align:start position:0%
+don't know anything really about c and
+so this here now has to be less than
+
+ align:start position:0%
+so this here now has to be less than
+ 
+
+ align:start position:0%
+so this here now has to be less than
+epsilon so now you only have you know
+
+ align:start position:0%
+epsilon so now you only have you know
+ 
+
+ align:start position:0%
+epsilon so now you only have you know
+you have fixed your k and so now you
+
+ align:start position:0%
+you have fixed your k and so now you
+ 
+
+ align:start position:0%
+you have fixed your k and so now you
+only have one variable and you can solve
+
+ align:start position:0%
+only have one variable and you can solve
+ 
+
+ align:start position:0%
+only have one variable and you can solve
+that but you you you really have to
+
+ align:start position:0%
+that but you you you really have to
+ 
+
+ align:start position:0%
+that but you you you really have to
+eliminate change yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Okay.
+
+ align:start position:0%
+uh Okay.
+ 
+
+ align:start position:0%
+uh Okay.
+Uh so so so again so so the how well the
+
+ align:start position:0%
+Uh so so so again so so the how well the
+ 
+
+ align:start position:0%
+Uh so so so again so so the how well the
+tail expansion approximate depends on
+
+ align:start position:0%
+tail expansion approximate depends on
+ 
+
+ align:start position:0%
+tail expansion approximate depends on
+the function.
+
+ align:start position:0%
+the function.
+ 
+
+ align:start position:0%
+the function.
+Okay. The next topic is another
+
+ align:start position:0%
+Okay. The next topic is another
+ 
+
+ align:start position:0%
+Okay. The next topic is another
+important topic and so this is uh
+
+ align:start position:0%
+important topic and so this is uh
+ 
+
+ align:start position:0%
+important topic and so this is uh
+integrals
+
+ align:start position:0%
+integrals
+ 
+
+ align:start position:0%
+integrals
+and there are
+
+ align:start position:0%
+and there are
+ 
+
+ align:start position:0%
+and there are
+different ways of
+
+ align:start position:0%
+different ways of
+ 
+
+ align:start position:0%
+different ways of
+of um defining integrals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This here is
+
+ align:start position:0%
+This here is
+ 
+
+ align:start position:0%
+This here is
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here is certainly one of the maybe
+
+ align:start position:0%
+this here is certainly one of the maybe
+ 
+
+ align:start position:0%
+this here is certainly one of the maybe
+the most natural one.
+
+ align:start position:0%
+the most natural one.
+ 
+
+ align:start position:0%
+the most natural one.
+Uh and so this is what's called
+
+ align:start position:0%
+Uh and so this is what's called
+ 
+
+ align:start position:0%
+Uh and so this is what's called
+reman. So it's after German
+
+ align:start position:0%
+reman. So it's after German
+ 
+
+ align:start position:0%
+reman. So it's after German
+mathematicians reman
+
+ align:start position:0%
+mathematicians reman
+ 
+
+ align:start position:0%
+mathematicians reman
+uh integrals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so the thing is that here now you
+
+ align:start position:0%
+And so the thing is that here now you
+ 
+
+ align:start position:0%
+And so the thing is that here now you
+look at a function
+
+ align:start position:0%
+look at a function
+ 
+
+ align:start position:0%
+look at a function
+you have a function on some interval
+
+ align:start position:0%
+you have a function on some interval
+ 
+
+ align:start position:0%
+you have a function on some interval
+from a to b
+
+ align:start position:0%
+from a to b
+ 
+
+ align:start position:0%
+from a to b
+into r and this function f here is um is
+
+ align:start position:0%
+into r and this function f here is um is
+ 
+
+ align:start position:0%
+into r and this function f here is um is
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the idea is so the idea is for
+
+ align:start position:0%
+and the idea is so the idea is for
+ 
+
+ align:start position:0%
+and the idea is so the idea is for
+integrals is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so you have a function function
+
+ align:start position:0%
+that so you have a function function
+ 
+
+ align:start position:0%
+that so you have a function function
+and you want to be able to define. So
+
+ align:start position:0%
+and you want to be able to define. So
+ 
+
+ align:start position:0%
+and you want to be able to define. So
+define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+graph.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So so if this is a function you want to
+
+ align:start position:0%
+So so if this is a function you want to
+ 
+
+ align:start position:0%
+So so if this is a function you want to
+be able to calculate
+
+ align:start position:0%
+be able to calculate
+ 
+
+ align:start position:0%
+be able to calculate
+what is this area. Okay. Now, if the
+
+ align:start position:0%
+what is this area. Okay. Now, if the
+ 
+
+ align:start position:0%
+what is this area. Okay. Now, if the
+function was to if the function was to
+
+ align:start position:0%
+function was to if the function was to
+ 
+
+ align:start position:0%
+function was to if the function was to
+have crossed
+
+ align:start position:0%
+have crossed
+ 
+
+ align:start position:0%
+have crossed
+um the x-axis, then this area here would
+
+ align:start position:0%
+um the x-axis, then this area here would
+ 
+
+ align:start position:0%
+um the x-axis, then this area here would
+count negatively and this area here
+
+ align:start position:0%
+count negatively and this area here
+ 
+
+ align:start position:0%
+count negatively and this area here
+would count positively. Anyway, so this
+
+ align:start position:0%
+would count positively. Anyway, so this
+ 
+
+ align:start position:0%
+would count positively. Anyway, so this
+is this is what you want to do
+
+ align:start position:0%
+is this is what you want to do
+ 
+
+ align:start position:0%
+is this is what you want to do
+and and you always starting with a
+
+ align:start position:0%
+and and you always starting with a
+ 
+
+ align:start position:0%
+and and you always starting with a
+bounded function.
+
+ align:start position:0%
+bounded function.
+ 
+
+ align:start position:0%
+bounded function.
+Now, to do that, right? And so so you
+
+ align:start position:0%
+Now, to do that, right? And so so you
+ 
+
+ align:start position:0%
+Now, to do that, right? And so so you
+want to define that the only thing that
+
+ align:start position:0%
+want to define that the only thing that
+ 
+
+ align:start position:0%
+want to define that the only thing that
+you know for sure is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so there's only like one ingredient
+
+ align:start position:0%
+so so there's only like one ingredient
+ 
+
+ align:start position:0%
+so so there's only like one ingredient
+you have.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so only
+
+ align:start position:0%
+so only
+ 
+
+ align:start position:0%
+so only
+only thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh no you know
+
+ align:start position:0%
+uh no you know
+ 
+
+ align:start position:0%
+uh no you know
+at the outset.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the only thing you know is that if
+
+ align:start position:0%
+So the only thing you know is that if
+ 
+
+ align:start position:0%
+So the only thing you know is that if
+you take a right angle so if this length
+
+ align:start position:0%
+you take a right angle so if this length
+ 
+
+ align:start position:0%
+you take a right angle so if this length
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+um uh is let's call it D and this here
+
+ align:start position:0%
+um uh is let's call it D and this here
+ 
+
+ align:start position:0%
+um uh is let's call it D and this here
+is E right then you know that the area
+
+ align:start position:0%
+is E right then you know that the area
+ 
+
+ align:start position:0%
+is E right then you know that the area
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is D * E right okay that's that's the
+
+ align:start position:0%
+is D * E right okay that's that's the
+ 
+
+ align:start position:0%
+is D * E right okay that's that's the
+only thing we have so Now
+
+ align:start position:0%
+only thing we have so Now
+ 
+
+ align:start position:0%
+only thing we have so Now
+how do we define the the area below the
+
+ align:start position:0%
+how do we define the the area below the
+ 
+
+ align:start position:0%
+how do we define the the area below the
+graph? And to do that we first need to
+
+ align:start position:0%
+graph? And to do that we first need to
+ 
+
+ align:start position:0%
+graph? And to do that we first need to
+talk about partitions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So partition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose I have a
+
+ align:start position:0%
+So suppose I have a
+ 
+
+ align:start position:0%
+So suppose I have a
+interval here. A and b are real numbers.
+
+ align:start position:0%
+interval here. A and b are real numbers.
+ 
+
+ align:start position:0%
+interval here. A and b are real numbers.
+So I have an interval here. Then I talk
+
+ align:start position:0%
+So I have an interval here. Then I talk
+ 
+
+ align:start position:0%
+So I have an interval here. Then I talk
+about a partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and it's useful to have a notation
+
+ align:start position:0%
+and and it's useful to have a notation
+ 
+
+ align:start position:0%
+and and it's useful to have a notation
+for a partition. So I call it P of of
+
+ align:start position:0%
+for a partition. So I call it P of of
+ 
+
+ align:start position:0%
+for a partition. So I call it P of of
+this interval here.
+
+ align:start position:0%
+this interval here.
+ 
+
+ align:start position:0%
+this interval here.
+This is finite is finally many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many dividing points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the dividing points always have to
+
+ align:start position:0%
+and the dividing points always have to
+ 
+
+ align:start position:0%
+and the dividing points always have to
+start at A and end at B. So you have
+
+ align:start position:0%
+start at A and end at B. So you have
+ 
+
+ align:start position:0%
+start at A and end at B. So you have
+finally many let's say k many and you're
+
+ align:start position:0%
+finally many let's say k many and you're
+ 
+
+ align:start position:0%
+finally many let's say k many and you're
+looking at okay take I'll write it k +
+
+ align:start position:0%
+looking at okay take I'll write it k +
+ 
+
+ align:start position:0%
+looking at okay take I'll write it k +
+one many. So uh the first one has to be
+
+ align:start position:0%
+one many. So uh the first one has to be
+ 
+
+ align:start position:0%
+one many. So uh the first one has to be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and then you have uh x1
+
+ align:start position:0%
+and then you have uh x1
+ 
+
+ align:start position:0%
+and then you have uh x1
+up to the last one
+
+ align:start position:0%
+up to the last one
+ 
+
+ align:start position:0%
+up to the last one
+and that has to be b.
+
+ align:start position:0%
+and that has to be b.
+ 
+
+ align:start position:0%
+and that has to be b.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so
+
+ align:start position:0%
+And so
+ 
+
+ align:start position:0%
+And so
+so what you're thinking about is so you
+
+ align:start position:0%
+so what you're thinking about is so you
+ 
+
+ align:start position:0%
+so what you're thinking about is so you
+have this interval here from a to b and
+
+ align:start position:0%
+have this interval here from a to b and
+ 
+
+ align:start position:0%
+have this interval here from a to b and
+you have these dividing points
+
+ align:start position:0%
+you have these dividing points
+ 
+
+ align:start position:0%
+you have these dividing points
+and you are thinking about dividing the
+
+ align:start position:0%
+and you are thinking about dividing the
+ 
+
+ align:start position:0%
+and you are thinking about dividing the
+the original interval into these sub
+
+ align:start position:0%
+the original interval into these sub
+ 
+
+ align:start position:0%
+the original interval into these sub
+intervals. Right? So these are the sub
+
+ align:start position:0%
+intervals. Right? So these are the sub
+ 
+
+ align:start position:0%
+intervals. Right? So these are the sub
+intervals. Right? So you divide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+sub intervals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the sub intervals are I'll do it
+
+ align:start position:0%
+and the sub intervals are I'll do it
+ 
+
+ align:start position:0%
+and the sub intervals are I'll do it
+like this. I will do it the where I take
+
+ align:start position:0%
+like this. I will do it the where I take
+ 
+
+ align:start position:0%
+like this. I will do it the where I take
+from it's always from you know one to
+
+ align:start position:0%
+from it's always from you know one to
+ 
+
+ align:start position:0%
+from it's always from you know one to
+the next and I will write it typically
+
+ align:start position:0%
+the next and I will write it typically
+ 
+
+ align:start position:0%
+the next and I will write it typically
+where I'm starting where I'm ending at I
+
+ align:start position:0%
+where I'm starting where I'm ending at I
+ 
+
+ align:start position:0%
+where I'm starting where I'm ending at I
+and beginning at I minus one.
+
+ align:start position:0%
+and beginning at I minus one.
+ 
+
+ align:start position:0%
+and beginning at I minus one.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+right so I'm dividing it into these sub
+
+ align:start position:0%
+right so I'm dividing it into these sub
+ 
+
+ align:start position:0%
+right so I'm dividing it into these sub
+intervals and so in this case here in
+
+ align:start position:0%
+intervals and so in this case here in
+ 
+
+ align:start position:0%
+intervals and so in this case here in
+this case here where this is x0
+
+ align:start position:0%
+this case here where this is x0
+ 
+
+ align:start position:0%
+this case here where this is x0
+uh there's going to be
+
+ align:start position:0%
+uh there's going to be
+ 
+
+ align:start position:0%
+uh there's going to be
+uh k uh sub intervals okay and it's you
+
+ align:start position:0%
+uh k uh sub intervals okay and it's you
+ 
+
+ align:start position:0%
+uh k uh sub intervals okay and it's you
+know you only
+
+ align:start position:0%
+know you only
+ 
+
+ align:start position:0%
+know you only
+always go from one to the next right so
+
+ align:start position:0%
+always go from one to the next right so
+ 
+
+ align:start position:0%
+always go from one to the next right so
+so that's a partition
+
+ align:start position:0%
+so that's a partition
+ 
+
+ align:start position:0%
+so that's a partition
+and now we need a second notion
+
+ align:start position:0%
+and now we need a second notion
+ 
+
+ align:start position:0%
+and now we need a second notion
+related to this and this is a sub
+
+ align:start position:0%
+related to this and this is a sub
+ 
+
+ align:start position:0%
+related to this and this is a sub
+partition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So subartetition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subartetition this is also sometime
+
+ align:start position:0%
+subartetition this is also sometime
+ 
+
+ align:start position:0%
+subartetition this is also sometime
+called uh sometimes called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+refinement.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a sub partition is so if you have a
+
+ align:start position:0%
+So a sub partition is so if you have a
+ 
+
+ align:start position:0%
+So a sub partition is so if you have a
+partition so P1 is a partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then P2 is a sub partition of
+
+ align:start position:0%
+and then P2 is a sub partition of
+ 
+
+ align:start position:0%
+and then P2 is a sub partition of
+refinement.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If if
+
+ align:start position:0%
+If if
+ 
+
+ align:start position:0%
+If if
+P2
+
+ align:start position:0%
+P2
+ 
+
+ align:start position:0%
+P2
+has all
+
+ align:start position:0%
+has all
+ 
+
+ align:start position:0%
+has all
+the dividing points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of P1 and then some and then some I mean
+
+ align:start position:0%
+of P1 and then some and then some I mean
+ 
+
+ align:start position:0%
+of P1 and then some and then some I mean
+it right right I mean of course it could
+
+ align:start position:0%
+it right right I mean of course it could
+ 
+
+ align:start position:0%
+it right right I mean of course it could
+be a trivial sub partition where P1 and
+
+ align:start position:0%
+be a trivial sub partition where P1 and
+ 
+
+ align:start position:0%
+be a trivial sub partition where P1 and
+P2 are the same. That's okay. But in
+
+ align:start position:0%
+P2 are the same. That's okay. But in
+ 
+
+ align:start position:0%
+P2 are the same. That's okay. But in
+general, it would have some more points
+
+ align:start position:0%
+general, it would have some more points
+ 
+
+ align:start position:0%
+general, it would have some more points
+also, some more dividing points. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+um, right. So, now let me look at uh, so
+
+ align:start position:0%
+um, right. So, now let me look at uh, so
+ 
+
+ align:start position:0%
+um, right. So, now let me look at uh, so
+what is then?
+
+ align:start position:0%
+what is then?
+ 
+
+ align:start position:0%
+what is then?
+So, so now let's try to get closer to
+
+ align:start position:0%
+So, so now let's try to get closer to
+ 
+
+ align:start position:0%
+So, so now let's try to get closer to
+try to define this with the area below
+
+ align:start position:0%
+try to define this with the area below
+ 
+
+ align:start position:0%
+try to define this with the area below
+the graph.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So again we have we have a function f
+
+ align:start position:0%
+So again we have we have a function f
+ 
+
+ align:start position:0%
+So again we have we have a function f
+from a to b
+
+ align:start position:0%
+from a to b
+ 
+
+ align:start position:0%
+from a to b
+into r. We assume that this is so uh
+
+ align:start position:0%
+into r. We assume that this is so uh
+ 
+
+ align:start position:0%
+into r. We assume that this is so uh
+that is bounded.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We have P here is a partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of this interval here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then we defined a upper and a lower sum.
+
+ align:start position:0%
+Then we defined a upper and a lower sum.
+ 
+
+ align:start position:0%
+Then we defined a upper and a lower sum.
+Then we define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upper
+
+ align:start position:0%
+upper
+ 
+
+ align:start position:0%
+upper
+and lower sums.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as follows
+
+ align:start position:0%
+as follows
+ 
+
+ align:start position:0%
+as follows
+right so again you have a given function
+
+ align:start position:0%
+right so again you have a given function
+ 
+
+ align:start position:0%
+right so again you have a given function
+that is bounded and you have a partition
+
+ align:start position:0%
+that is bounded and you have a partition
+ 
+
+ align:start position:0%
+that is bounded and you have a partition
+and so we define upper and lower sums
+
+ align:start position:0%
+and so we define upper and lower sums
+ 
+
+ align:start position:0%
+and so we define upper and lower sums
+and the upper and lower sum I will
+
+ align:start position:0%
+and the upper and lower sum I will
+ 
+
+ align:start position:0%
+and the upper and lower sum I will
+denote like this it depends on the
+
+ align:start position:0%
+denote like this it depends on the
+ 
+
+ align:start position:0%
+denote like this it depends on the
+function of course and then on the
+
+ align:start position:0%
+function of course and then on the
+ 
+
+ align:start position:0%
+function of course and then on the
+partition that's a upper sum and the
+
+ align:start position:0%
+partition that's a upper sum and the
+ 
+
+ align:start position:0%
+partition that's a upper sum and the
+lower sum similar I would denote like
+
+ align:start position:0%
+lower sum similar I would denote like
+ 
+
+ align:start position:0%
+lower sum similar I would denote like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so how are these defined?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So they are defined as follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you have here you have your
+
+ align:start position:0%
+that you have here you have your
+ 
+
+ align:start position:0%
+that you have here you have your
+interval from a to b.
+
+ align:start position:0%
+interval from a to b.
+ 
+
+ align:start position:0%
+interval from a to b.
+Then you have this here is x0 here I
+
+ align:start position:0%
+Then you have this here is x0 here I
+ 
+
+ align:start position:0%
+Then you have this here is x0 here I
+have x1 and here I have maybe x2 and
+
+ align:start position:0%
+have x1 and here I have maybe x2 and
+ 
+
+ align:start position:0%
+have x1 and here I have maybe x2 and
+then this thing here is then x3.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I take uh I look at one of these
+
+ align:start position:0%
+So I take uh I look at one of these
+ 
+
+ align:start position:0%
+So I take uh I look at one of these
+intervals
+
+ align:start position:0%
+intervals
+ 
+
+ align:start position:0%
+intervals
+or it could be this one here. that's
+
+ align:start position:0%
+or it could be this one here. that's
+ 
+
+ align:start position:0%
+or it could be this one here. that's
+between in this case it would be between
+
+ align:start position:0%
+between in this case it would be between
+ 
+
+ align:start position:0%
+between in this case it would be between
+uh x1 and x2
+
+ align:start position:0%
+uh x1 and x2
+ 
+
+ align:start position:0%
+uh x1 and x2
+and I would look at the function in this
+
+ align:start position:0%
+and I would look at the function in this
+ 
+
+ align:start position:0%
+and I would look at the function in this
+interval here and I would so the
+
+ align:start position:0%
+interval here and I would so the
+ 
+
+ align:start position:0%
+interval here and I would so the
+contribution from this here would be
+
+ align:start position:0%
+contribution from this here would be
+ 
+
+ align:start position:0%
+contribution from this here would be
+that I would take so for the upper for
+
+ align:start position:0%
+that I would take so for the upper for
+ 
+
+ align:start position:0%
+that I would take so for the upper for
+the upper
+
+ align:start position:0%
+the upper
+ 
+
+ align:start position:0%
+the upper
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+with respect to this partition the one
+
+ align:start position:0%
+with respect to this partition the one
+ 
+
+ align:start position:0%
+with respect to this partition the one
+that comes from this sub interval here
+
+ align:start position:0%
+that comes from this sub interval here
+ 
+
+ align:start position:0%
+that comes from this sub interval here
+would be um would be
+
+ align:start position:0%
+would be um would be
+ 
+
+ align:start position:0%
+would be um would be
+uh the soup
+
+ align:start position:0%
+uh the soup
+ 
+
+ align:start position:0%
+uh the soup
+of f on this sub interval here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the soup of the function
+
+ align:start position:0%
+So the soup of the function
+ 
+
+ align:start position:0%
+So the soup of the function
+times the length of the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that. So this would be the value
+
+ align:start position:0%
+like that. So this would be the value
+ 
+
+ align:start position:0%
+like that. So this would be the value
+that in the upper that would come uh in
+
+ align:start position:0%
+that in the upper that would come uh in
+ 
+
+ align:start position:0%
+that in the upper that would come uh in
+a minute I'll write it out more more
+
+ align:start position:0%
+a minute I'll write it out more more
+ 
+
+ align:start position:0%
+a minute I'll write it out more more
+clearly but this would be what is coming
+
+ align:start position:0%
+clearly but this would be what is coming
+ 
+
+ align:start position:0%
+clearly but this would be what is coming
+from here and likewise
+
+ align:start position:0%
+from here and likewise
+ 
+
+ align:start position:0%
+from here and likewise
+uh for the lower one
+
+ align:start position:0%
+uh for the lower one
+ 
+
+ align:start position:0%
+uh for the lower one
+um the contribution from this little
+
+ align:start position:0%
+um the contribution from this little
+ 
+
+ align:start position:0%
+um the contribution from this little
+interval here would be the in of f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then times and The idea right is
+
+ align:start position:0%
+and then times and The idea right is
+ 
+
+ align:start position:0%
+and then times and The idea right is
+okay. So that would be the contribution.
+
+ align:start position:0%
+okay. So that would be the contribution.
+ 
+
+ align:start position:0%
+okay. So that would be the contribution.
+Um the idea of course is that you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the only thing we knew was this with
+
+ align:start position:0%
+but the only thing we knew was this with
+ 
+
+ align:start position:0%
+but the only thing we knew was this with
+the area of a right angle.
+
+ align:start position:0%
+the area of a right angle.
+ 
+
+ align:start position:0%
+the area of a right angle.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And so you have this function here and
+
+ align:start position:0%
+And so you have this function here and
+ 
+
+ align:start position:0%
+And so you have this function here and
+you have some little interval here
+
+ align:start position:0%
+you have some little interval here
+ 
+
+ align:start position:0%
+you have some little interval here
+between x i and x i - uh sorry x i - one
+
+ align:start position:0%
+between x i and x i - uh sorry x i - one
+ 
+
+ align:start position:0%
+between x i and x i - uh sorry x i - one
+and x i right
+
+ align:start position:0%
+and x i right
+ 
+
+ align:start position:0%
+and x i right
+and you're focusing on this little
+
+ align:start position:0%
+and you're focusing on this little
+ 
+
+ align:start position:0%
+and you're focusing on this little
+interval here
+
+ align:start position:0%
+interval here
+ 
+
+ align:start position:0%
+interval here
+and you're looking at the function the
+
+ align:start position:0%
+and you're looking at the function the
+ 
+
+ align:start position:0%
+and you're looking at the function the
+function was bounded so there is a soup
+
+ align:start position:0%
+function was bounded so there is a soup
+ 
+
+ align:start position:0%
+function was bounded so there is a soup
+on this and you try to look at the
+
+ align:start position:0%
+on this and you try to look at the
+ 
+
+ align:start position:0%
+on this and you try to look at the
+smallest red angle angle that kind of
+
+ align:start position:0%
+smallest red angle angle that kind of
+ 
+
+ align:start position:0%
+smallest red angle angle that kind of
+have the graph that fits where the graph
+
+ align:start position:0%
+have the graph that fits where the graph
+ 
+
+ align:start position:0%
+have the graph that fits where the graph
+fits inside that right and then you're
+
+ align:start position:0%
+fits inside that right and then you're
+ 
+
+ align:start position:0%
+fits inside that right and then you're
+looking at so this this is the
+
+ align:start position:0%
+looking at so this this is the
+ 
+
+ align:start position:0%
+looking at so this this is the
+contribution
+
+ align:start position:0%
+contribution
+ 
+
+ align:start position:0%
+contribution
+from this little interval
+
+ align:start position:0%
+from this little interval
+ 
+
+ align:start position:0%
+from this little interval
+to P to to the upper sum and then you
+
+ align:start position:0%
+to P to to the upper sum and then you
+ 
+
+ align:start position:0%
+to P to to the upper sum and then you
+have right that you're looking at the
+
+ align:start position:0%
+have right that you're looking at the
+ 
+
+ align:start position:0%
+have right that you're looking at the
+largest right angle like this that fits
+
+ align:start position:0%
+largest right angle like this that fits
+ 
+
+ align:start position:0%
+largest right angle like this that fits
+under the graph and that's then
+
+ align:start position:0%
+under the graph and that's then
+ 
+
+ align:start position:0%
+under the graph and that's then
+contribution to the lower one.
+
+ align:start position:0%
+contribution to the lower one.
+ 
+
+ align:start position:0%
+contribution to the lower one.
+Right? And the idea is that if the
+
+ align:start position:0%
+Right? And the idea is that if the
+ 
+
+ align:start position:0%
+Right? And the idea is that if the
+function is reasonable, if you're
+
+ align:start position:0%
+function is reasonable, if you're
+ 
+
+ align:start position:0%
+function is reasonable, if you're
+looking at finer and finer partition,
+
+ align:start position:0%
+looking at finer and finer partition,
+ 
+
+ align:start position:0%
+looking at finer and finer partition,
+then you should you should certainly get
+
+ align:start position:0%
+then you should you should certainly get
+ 
+
+ align:start position:0%
+then you should you should certainly get
+a better a better approximation to the
+
+ align:start position:0%
+a better a better approximation to the
+ 
+
+ align:start position:0%
+a better a better approximation to the
+area below the graph, right? I mean, and
+
+ align:start position:0%
+area below the graph, right? I mean, and
+ 
+
+ align:start position:0%
+area below the graph, right? I mean, and
+and and if the function is reasonable,
+
+ align:start position:0%
+and and if the function is reasonable,
+ 
+
+ align:start position:0%
+and and if the function is reasonable,
+these two Okay, so now what is then the
+
+ align:start position:0%
+these two Okay, so now what is then the
+ 
+
+ align:start position:0%
+these two Okay, so now what is then the
+uh let me just define this.
+
+ align:start position:0%
+uh let me just define this.
+ 
+
+ align:start position:0%
+uh let me just define this.
+So this thing here
+
+ align:start position:0%
+So this thing here
+ 
+
+ align:start position:0%
+So this thing here
+it would be convenient to to the length
+
+ align:start position:0%
+it would be convenient to to the length
+ 
+
+ align:start position:0%
+it would be convenient to to the length
+of this interval to denote it by by
+
+ align:start position:0%
+of this interval to denote it by by
+ 
+
+ align:start position:0%
+of this interval to denote it by by
+this. So this is x i x i minus one. This
+
+ align:start position:0%
+this. So this is x i x i minus one. This
+ 
+
+ align:start position:0%
+this. So this is x i x i minus one. This
+just the length of that interval.
+
+ align:start position:0%
+just the length of that interval.
+ 
+
+ align:start position:0%
+just the length of that interval.
+Okay. And so now written out this thing
+
+ align:start position:0%
+Okay. And so now written out this thing
+ 
+
+ align:start position:0%
+Okay. And so now written out this thing
+and okay let me make one other notation.
+
+ align:start position:0%
+and okay let me make one other notation.
+ 
+
+ align:start position:0%
+and okay let me make one other notation.
+MI is the soup of f on x i minus one x i
+
+ align:start position:0%
+MI is the soup of f on x i minus one x i
+ 
+
+ align:start position:0%
+MI is the soup of f on x i minus one x i
+that's m capital mi and little mi is
+
+ align:start position:0%
+that's m capital mi and little mi is
+ 
+
+ align:start position:0%
+that's m capital mi and little mi is
+then the in on the same interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that. And so the upper sum
+
+ align:start position:0%
+like that. And so the upper sum
+ 
+
+ align:start position:0%
+like that. And so the upper sum
+for this partition this is the sum from
+
+ align:start position:0%
+for this partition this is the sum from
+ 
+
+ align:start position:0%
+for this partition this is the sum from
+i = uh one to k
+
+ align:start position:0%
+i = uh one to k
+ 
+
+ align:start position:0%
+i = uh one to k
+of m i * delta xi.
+
+ align:start position:0%
+of m i * delta xi.
+ 
+
+ align:start position:0%
+of m i * delta xi.
+That's the upper sum. And the lower sum
+
+ align:start position:0%
+That's the upper sum. And the lower sum
+ 
+
+ align:start position:0%
+That's the upper sum. And the lower sum
+is then the sum
+
+ align:start position:0%
+is then the sum
+ 
+
+ align:start position:0%
+is then the sum
+from i = 1 to k of mi delta xi.
+
+ align:start position:0%
+from i = 1 to k of mi delta xi.
+ 
+
+ align:start position:0%
+from i = 1 to k of mi delta xi.
+Okay. So that's the upper and the lower
+
+ align:start position:0%
+Okay. So that's the upper and the lower
+ 
+
+ align:start position:0%
+Okay. So that's the upper and the lower
+sum. Okay. The first thing you observe
+
+ align:start position:0%
+sum. Okay. The first thing you observe
+ 
+
+ align:start position:0%
+sum. Okay. The first thing you observe
+is the first thing you observe is is a
+
+ align:start position:0%
+is the first thing you observe is is a
+ 
+
+ align:start position:0%
+is the first thing you observe is is a
+trivial fact
+
+ align:start position:0%
+trivial fact
+ 
+
+ align:start position:0%
+trivial fact
+and it's you know that really should be
+
+ align:start position:0%
+and it's you know that really should be
+ 
+
+ align:start position:0%
+and it's you know that really should be
+the case because one is like what fits
+
+ align:start position:0%
+the case because one is like what fits
+ 
+
+ align:start position:0%
+the case because one is like what fits
+inside the graph uh below the graph the
+
+ align:start position:0%
+inside the graph uh below the graph the
+ 
+
+ align:start position:0%
+inside the graph uh below the graph the
+other is you know where the graph fits
+
+ align:start position:0%
+other is you know where the graph fits
+ 
+
+ align:start position:0%
+other is you know where the graph fits
+below the right angle. So you clearly
+
+ align:start position:0%
+below the right angle. So you clearly
+ 
+
+ align:start position:0%
+below the right angle. So you clearly
+have just be and this is just because
+
+ align:start position:0%
+have just be and this is just because
+ 
+
+ align:start position:0%
+have just be and this is just because
+this number here is the in this is the
+
+ align:start position:0%
+this number here is the in this is the
+ 
+
+ align:start position:0%
+this number here is the in this is the
+soup on the same interval. So you
+
+ align:start position:0%
+soup on the same interval. So you
+ 
+
+ align:start position:0%
+soup on the same interval. So you
+clearly have
+
+ align:start position:0%
+clearly have
+ 
+
+ align:start position:0%
+clearly have
+that uh L F
+
+ align:start position:0%
+that uh L F
+ 
+
+ align:start position:0%
+that uh L F
+is less or equal to U FP. Right? So this
+
+ align:start position:0%
+is less or equal to U FP. Right? So this
+ 
+
+ align:start position:0%
+is less or equal to U FP. Right? So this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is clear. Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Let's look at uh
+
+ align:start position:0%
+Let's look at uh
+ 
+
+ align:start position:0%
+Let's look at uh
+let's look at an a couple of examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So just to make sure that this is
+
+ align:start position:0%
+So just to make sure that this is
+ 
+
+ align:start position:0%
+So just to make sure that this is
+totally clear
+
+ align:start position:0%
+totally clear
+ 
+
+ align:start position:0%
+totally clear
+uh let me look at a couple example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So uh
+
+ align:start position:0%
+So uh
+ 
+
+ align:start position:0%
+So uh
+the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first example is so I take a
+
+ align:start position:0%
+the first example is so I take a
+ 
+
+ align:start position:0%
+the first example is so I take a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+f ofx = 2x^2 + 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and my partition and the interval here
+
+ align:start position:0%
+and my partition and the interval here
+ 
+
+ align:start position:0%
+and my partition and the interval here
+I'm going to think about this as a
+
+ align:start position:0%
+I'm going to think about this as a
+ 
+
+ align:start position:0%
+I'm going to think about this as a
+function on minus2 two
+
+ align:start position:0%
+function on minus2 two
+ 
+
+ align:start position:0%
+function on minus2 two
+to two
+
+ align:start position:0%
+to two
+ 
+
+ align:start position:0%
+to two
+into R.
+
+ align:start position:0%
+into R.
+ 
+
+ align:start position:0%
+into R.
+And my partition here
+
+ align:start position:0%
+And my partition here
+ 
+
+ align:start position:0%
+And my partition here
+is going to be min -2 -1 0 1 and two
+
+ align:start position:0%
+is going to be min -2 -1 0 1 and two
+ 
+
+ align:start position:0%
+is going to be min -2 -1 0 1 and two
+um and um right and so you have so let's
+
+ align:start position:0%
+um and um right and so you have so let's
+ 
+
+ align:start position:0%
+um and um right and so you have so let's
+see so this so this here so if I draw
+
+ align:start position:0%
+see so this so this here so if I draw
+ 
+
+ align:start position:0%
+see so this so this here so if I draw
+the function
+
+ align:start position:0%
+the function
+ 
+
+ align:start position:0%
+the function
+then this is looks like if this here is
+
+ align:start position:0%
+then this is looks like if this here is
+ 
+
+ align:start position:0%
+then this is looks like if this here is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh here you have one
+
+ align:start position:0%
+uh here you have one
+ 
+
+ align:start position:0%
+uh here you have one
+then it looks sort of like this. Uh
+
+ align:start position:0%
+then it looks sort of like this. Uh
+ 
+
+ align:start position:0%
+then it looks sort of like this. Uh
+doesn't more or less like this.
+
+ align:start position:0%
+doesn't more or less like this.
+ 
+
+ align:start position:0%
+doesn't more or less like this.
+Okay. And so this means that here and
+
+ align:start position:0%
+Okay. And so this means that here and
+ 
+
+ align:start position:0%
+Okay. And so this means that here and
+here you have two
+
+ align:start position:0%
+here you have two
+ 
+
+ align:start position:0%
+here you have two
+uh and this here is minus one
+
+ align:start position:0%
+uh and this here is minus one
+ 
+
+ align:start position:0%
+uh and this here is minus one
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and here you have uh minus two.
+
+ align:start position:0%
+and uh and here you have uh minus two.
+ 
+
+ align:start position:0%
+and uh and here you have uh minus two.
+So now if you're looking at so that the
+
+ align:start position:0%
+So now if you're looking at so that the
+ 
+
+ align:start position:0%
+So now if you're looking at so that the
+um right so so this means here that so
+
+ align:start position:0%
+um right so so this means here that so
+ 
+
+ align:start position:0%
+um right so so this means here that so
+this is my partition so this means that
+
+ align:start position:0%
+this is my partition so this means that
+ 
+
+ align:start position:0%
+this is my partition so this means that
+x0 is uh equal to minus2
+
+ align:start position:0%
+x0 is uh equal to minus2
+ 
+
+ align:start position:0%
+x0 is uh equal to minus2
+x1 that's the next one is minus one x3
+
+ align:start position:0%
+x1 that's the next one is minus one x3
+ 
+
+ align:start position:0%
+x1 that's the next one is minus one x3
+is the next one
+
+ align:start position:0%
+is the next one
+ 
+
+ align:start position:0%
+is the next one
+that's zero x4
+
+ align:start position:0%
+that's zero x4
+ 
+
+ align:start position:0%
+that's zero x4
+is uh one and x5 y is two, right? And so
+
+ align:start position:0%
+is uh one and x5 y is two, right? And so
+ 
+
+ align:start position:0%
+is uh one and x5 y is two, right? And so
+of course all of these intervals here,
+
+ align:start position:0%
+of course all of these intervals here,
+ 
+
+ align:start position:0%
+of course all of these intervals here,
+right? They all have the same length in
+
+ align:start position:0%
+right? They all have the same length in
+ 
+
+ align:start position:0%
+right? They all have the same length in
+this case. So x i - x i -1. This was
+
+ align:start position:0%
+this case. So x i - x i -1. This was
+ 
+
+ align:start position:0%
+this case. So x i - x i -1. This was
+what we call delta x i. This here is for
+
+ align:start position:0%
+what we call delta x i. This here is for
+ 
+
+ align:start position:0%
+what we call delta x i. This here is for
+each of these is equal to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now we have that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have that the
+
+ align:start position:0%
+and we have that the
+ 
+
+ align:start position:0%
+and we have that the
+when you're looking between minus2 and
+
+ align:start position:0%
+when you're looking between minus2 and
+ 
+
+ align:start position:0%
+when you're looking between minus2 and
+two and sorry minus2 and minus one. So
+
+ align:start position:0%
+two and sorry minus2 and minus one. So
+ 
+
+ align:start position:0%
+two and sorry minus2 and minus one. So
+on this interval here
+
+ align:start position:0%
+on this interval here
+ 
+
+ align:start position:0%
+on this interval here
+um the function is the function on this
+
+ align:start position:0%
+um the function is the function on this
+ 
+
+ align:start position:0%
+um the function is the function on this
+interval here is decreasing. So the
+
+ align:start position:0%
+interval here is decreasing. So the
+ 
+
+ align:start position:0%
+interval here is decreasing. So the
+largest value is achieved at this point
+
+ align:start position:0%
+largest value is achieved at this point
+ 
+
+ align:start position:0%
+largest value is achieved at this point
+here. Right? Uh so uh m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M1 this is the same as a soup of f
+
+ align:start position:0%
+M1 this is the same as a soup of f
+ 
+
+ align:start position:0%
+M1 this is the same as a soup of f
+between uh x0
+
+ align:start position:0%
+between uh x0
+ 
+
+ align:start position:0%
+between uh x0
+and x1. And so this is the same as the
+
+ align:start position:0%
+and x1. And so this is the same as the
+ 
+
+ align:start position:0%
+and x1. And so this is the same as the
+soup of minus2 to minus1 right of f and
+
+ align:start position:0%
+soup of minus2 to minus1 right of f and
+ 
+
+ align:start position:0%
+soup of minus2 to minus1 right of f and
+the function was decreasing so the li on
+
+ align:start position:0%
+the function was decreasing so the li on
+ 
+
+ align:start position:0%
+the function was decreasing so the li on
+this interval so the largest value is
+
+ align:start position:0%
+this interval so the largest value is
+ 
+
+ align:start position:0%
+this interval so the largest value is
+achieved here and that's five
+
+ align:start position:0%
+achieved here and that's five
+ 
+
+ align:start position:0%
+achieved here and that's five
+right so this would be five
+
+ align:start position:0%
+right so this would be five
+ 
+
+ align:start position:0%
+right so this would be five
+and uh on the second interval here
+
+ align:start position:0%
+and uh on the second interval here
+ 
+
+ align:start position:0%
+and uh on the second interval here
+right so this is between minus1 and zero
+
+ align:start position:0%
+right so this is between minus1 and zero
+ 
+
+ align:start position:0%
+right so this is between minus1 and zero
+still decreasing So the value is the
+
+ align:start position:0%
+still decreasing So the value is the
+ 
+
+ align:start position:0%
+still decreasing So the value is the
+largest value is here where it's two. So
+
+ align:start position:0%
+largest value is here where it's two. So
+ 
+
+ align:start position:0%
+largest value is here where it's two. So
+this here is is two and m3
+
+ align:start position:0%
+this here is is two and m3
+ 
+
+ align:start position:0%
+this here is is two and m3
+this is now uh between zero and one. So
+
+ align:start position:0%
+this is now uh between zero and one. So
+ 
+
+ align:start position:0%
+this is now uh between zero and one. So
+now it's increasing. So the large value
+
+ align:start position:0%
+now it's increasing. So the large value
+ 
+
+ align:start position:0%
+now it's increasing. So the large value
+is over here. So that's again two.
+
+ align:start position:0%
+is over here. So that's again two.
+ 
+
+ align:start position:0%
+is over here. So that's again two.
+And then the last one is is is again
+
+ align:start position:0%
+And then the last one is is is again
+ 
+
+ align:start position:0%
+And then the last one is is is again
+five. Right?
+
+ align:start position:0%
+five. Right?
+ 
+
+ align:start position:0%
+five. Right?
+And then likewise for the the the ones
+
+ align:start position:0%
+And then likewise for the the the ones
+ 
+
+ align:start position:0%
+And then likewise for the the the ones
+that are the info. So the first one m1
+
+ align:start position:0%
+that are the info. So the first one m1
+ 
+
+ align:start position:0%
+that are the info. So the first one m1
+well the function was decreasing. So the
+
+ align:start position:0%
+well the function was decreasing. So the
+ 
+
+ align:start position:0%
+well the function was decreasing. So the
+smallest value is over at this end point
+
+ align:start position:0%
+smallest value is over at this end point
+ 
+
+ align:start position:0%
+smallest value is over at this end point
+there. The value is true.
+
+ align:start position:0%
+there. The value is true.
+ 
+
+ align:start position:0%
+there. The value is true.
+So you're getting uh this here is is
+
+ align:start position:0%
+So you're getting uh this here is is
+ 
+
+ align:start position:0%
+So you're getting uh this here is is
+two.
+
+ align:start position:0%
+two.
+ 
+
+ align:start position:0%
+two.
+And then between
+
+ align:start position:0%
+And then between
+ 
+
+ align:start position:0%
+And then between
+between minus1 and zero it's still
+
+ align:start position:0%
+between minus1 and zero it's still
+ 
+
+ align:start position:0%
+between minus1 and zero it's still
+decreasing. So there the smallest is at
+
+ align:start position:0%
+decreasing. So there the smallest is at
+ 
+
+ align:start position:0%
+decreasing. So there the smallest is at
+this point where it's one. So this is m2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then m3
+
+ align:start position:0%
+and then m3
+ 
+
+ align:start position:0%
+and then m3
+this is now here the function is
+
+ align:start position:0%
+this is now here the function is
+ 
+
+ align:start position:0%
+this is now here the function is
+increasing. So it's still the value
+
+ align:start position:0%
+increasing. So it's still the value
+ 
+
+ align:start position:0%
+increasing. So it's still the value
+here. So it's still one. And then the
+
+ align:start position:0%
+here. So it's still one. And then the
+ 
+
+ align:start position:0%
+here. So it's still one. And then the
+last one
+
+ align:start position:0%
+last one
+ 
+
+ align:start position:0%
+last one
+um is between one and two and there it's
+
+ align:start position:0%
+um is between one and two and there it's
+ 
+
+ align:start position:0%
+um is between one and two and there it's
+the infreom is the value here. So that's
+
+ align:start position:0%
+the infreom is the value here. So that's
+ 
+
+ align:start position:0%
+the infreom is the value here. So that's
+two right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you see that in this case the
+
+ align:start position:0%
+and so you see that in this case the
+ 
+
+ align:start position:0%
+and so you see that in this case the
+upper
+
+ align:start position:0%
+upper
+ 
+
+ align:start position:0%
+upper
+for this function
+
+ align:start position:0%
+for this function
+ 
+
+ align:start position:0%
+for this function
+uh for this partition
+
+ align:start position:0%
+uh for this partition
+ 
+
+ align:start position:0%
+uh for this partition
+it's this right all of the intervals
+
+ align:start position:0%
+it's this right all of the intervals
+ 
+
+ align:start position:0%
+it's this right all of the intervals
+have length these small interval have
+
+ align:start position:0%
+have length these small interval have
+ 
+
+ align:start position:0%
+have length these small interval have
+length one so it's just the sum of these
+
+ align:start position:0%
+length one so it's just the sum of these
+ 
+
+ align:start position:0%
+length one so it's just the sum of these
+guys right so this is just equal to five
+
+ align:start position:0%
+guys right so this is just equal to five
+ 
+
+ align:start position:0%
+guys right so this is just equal to five
+if you will it's 5 * 1 that was length
+
+ align:start position:0%
+if you will it's 5 * 1 that was length
+ 
+
+ align:start position:0%
+if you will it's 5 * 1 that was length
+of the interval plus 2 * 1 + uh 2 * 1 +
+
+ align:start position:0%
+of the interval plus 2 * 1 + uh 2 * 1 +
+ 
+
+ align:start position:0%
+of the interval plus 2 * 1 + uh 2 * 1 +
+5 * 1. So in other words, you get here
+
+ align:start position:0%
+5 * 1. So in other words, you get here
+ 
+
+ align:start position:0%
+5 * 1. So in other words, you get here
+14. And for the lower ones,
+
+ align:start position:0%
+14. And for the lower ones,
+ 
+
+ align:start position:0%
+14. And for the lower ones,
+it's again this time I want rise times
+
+ align:start position:0%
+it's again this time I want rise times
+ 
+
+ align:start position:0%
+it's again this time I want rise times
+one. It's a sum of those guys and that's
+
+ align:start position:0%
+one. It's a sum of those guys and that's
+ 
+
+ align:start position:0%
+one. It's a sum of those guys and that's
+actually six, right?
+
+ align:start position:0%
+actually six, right?
+ 
+
+ align:start position:0%
+actually six, right?
+So So that's upper and lower sum. Okay.
+
+ align:start position:0%
+So So that's upper and lower sum. Okay.
+ 
+
+ align:start position:0%
+So So that's upper and lower sum. Okay.
+Now, uh and we had we had one um one
+
+ align:start position:0%
+Now, uh and we had we had one um one
+ 
+
+ align:start position:0%
+Now, uh and we had we had one um one
+observation that was a an immediate
+
+ align:start position:0%
+observation that was a an immediate
+ 
+
+ align:start position:0%
+observation that was a an immediate
+observation and that was uh this thing
+
+ align:start position:0%
+observation and that was uh this thing
+ 
+
+ align:start position:0%
+observation and that was uh this thing
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+Now,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is useful is that you starting with
+
+ align:start position:0%
+what is useful is that you starting with
+ 
+
+ align:start position:0%
+what is useful is that you starting with
+a partition and then you you have a
+
+ align:start position:0%
+a partition and then you you have a
+ 
+
+ align:start position:0%
+a partition and then you you have a
+subartition. So the next one is so I
+
+ align:start position:0%
+subartition. So the next one is so I
+ 
+
+ align:start position:0%
+subartition. So the next one is so I
+take a function f on some interval from
+
+ align:start position:0%
+take a function f on some interval from
+ 
+
+ align:start position:0%
+take a function f on some interval from
+a to b and this function here is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I have p is a partition p1 say
+
+ align:start position:0%
+and then I have p is a partition p1 say
+ 
+
+ align:start position:0%
+and then I have p is a partition p1 say
+is a partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then p2
+
+ align:start position:0%
+and then p2
+ 
+
+ align:start position:0%
+and then p2
+is a sub partition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of P1.
+
+ align:start position:0%
+of P1.
+ 
+
+ align:start position:0%
+of P1.
+And now the thing that is uh useful is
+
+ align:start position:0%
+And now the thing that is uh useful is
+ 
+
+ align:start position:0%
+And now the thing that is uh useful is
+the following.
+
+ align:start position:0%
+the following.
+ 
+
+ align:start position:0%
+the following.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that. So,
+
+ align:start position:0%
+that. So,
+ 
+
+ align:start position:0%
+that. So,
+so the following claim, the following
+
+ align:start position:0%
+so the following claim, the following
+ 
+
+ align:start position:0%
+so the following claim, the following
+leham
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you take a sub partition then I
+
+ align:start position:0%
+that if you take a sub partition then I
+ 
+
+ align:start position:0%
+that if you take a sub partition then I
+claim that the value of the upper sum go
+
+ align:start position:0%
+claim that the value of the upper sum go
+ 
+
+ align:start position:0%
+claim that the value of the upper sum go
+down and the value of the lower go up.
+
+ align:start position:0%
+down and the value of the lower go up.
+ 
+
+ align:start position:0%
+down and the value of the lower go up.
+So this is the following. So uh so lower
+
+ align:start position:0%
+So this is the following. So uh so lower
+ 
+
+ align:start position:0%
+So this is the following. So uh so lower
+of f * p1.
+
+ align:start position:0%
+of f * p1.
+ 
+
+ align:start position:0%
+of f * p1.
+This is less or equal to the lower of f
+
+ align:start position:0%
+This is less or equal to the lower of f
+ 
+
+ align:start position:0%
+This is less or equal to the lower of f
+of p2. We already proved that this thing
+
+ align:start position:0%
+of p2. We already proved that this thing
+ 
+
+ align:start position:0%
+of p2. We already proved that this thing
+here, this one here, this this
+
+ align:start position:0%
+here, this one here, this this
+ 
+
+ align:start position:0%
+here, this one here, this this
+inequality we haven't proved yet. But
+
+ align:start position:0%
+inequality we haven't proved yet. But
+ 
+
+ align:start position:0%
+inequality we haven't proved yet. But
+this one here, we have that this is less
+
+ align:start position:0%
+this one here, we have that this is less
+ 
+
+ align:start position:0%
+this one here, we have that this is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+than the upper one for the same
+
+ align:start position:0%
+than the upper one for the same
+ 
+
+ align:start position:0%
+than the upper one for the same
+partition. And the second claim is that
+
+ align:start position:0%
+partition. And the second claim is that
+ 
+
+ align:start position:0%
+partition. And the second claim is that
+this here is then less than the upper
+
+ align:start position:0%
+this here is then less than the upper
+ 
+
+ align:start position:0%
+this here is then less than the upper
+one for the first.
+
+ align:start position:0%
+one for the first.
+ 
+
+ align:start position:0%
+one for the first.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now why is this the case? This is also
+
+ align:start position:0%
+Now why is this the case? This is also
+ 
+
+ align:start position:0%
+Now why is this the case? This is also
+actually a trivial statement but it's
+
+ align:start position:0%
+actually a trivial statement but it's
+ 
+
+ align:start position:0%
+actually a trivial statement but it's
+very useful statement.
+
+ align:start position:0%
+very useful statement.
+ 
+
+ align:start position:0%
+very useful statement.
+So imagine that you have your partition
+
+ align:start position:0%
+So imagine that you have your partition
+ 
+
+ align:start position:0%
+So imagine that you have your partition
+P1 here and then you have the dividing
+
+ align:start position:0%
+P1 here and then you have the dividing
+ 
+
+ align:start position:0%
+P1 here and then you have the dividing
+points I minus one
+
+ align:start position:0%
+points I minus one
+ 
+
+ align:start position:0%
+points I minus one
+and here you have I
+
+ align:start position:0%
+and here you have I
+ 
+
+ align:start position:0%
+and here you have I
+right and P2 is a sub partition. So
+
+ align:start position:0%
+right and P2 is a sub partition. So
+ 
+
+ align:start position:0%
+right and P2 is a sub partition. So
+there may be intervals like this where
+
+ align:start position:0%
+there may be intervals like this where
+ 
+
+ align:start position:0%
+there may be intervals like this where
+there are no further dividing points
+
+ align:start position:0%
+there are no further dividing points
+ 
+
+ align:start position:0%
+there are no further dividing points
+right but in that case the what you the
+
+ align:start position:0%
+right but in that case the what you the
+ 
+
+ align:start position:0%
+right but in that case the what you the
+contribution that for the lower and
+
+ align:start position:0%
+contribution that for the lower and
+ 
+
+ align:start position:0%
+contribution that for the lower and
+upper is the same for the two partitions
+
+ align:start position:0%
+upper is the same for the two partitions
+ 
+
+ align:start position:0%
+upper is the same for the two partitions
+right but should there be one or more
+
+ align:start position:0%
+right but should there be one or more
+ 
+
+ align:start position:0%
+right but should there be one or more
+let's just say there's one right then
+
+ align:start position:0%
+let's just say there's one right then
+ 
+
+ align:start position:0%
+let's just say there's one right then
+for the upper one you would look at you
+
+ align:start position:0%
+for the upper one you would look at you
+ 
+
+ align:start position:0%
+for the upper one you would look at you
+would then get so you would get a a a
+
+ align:start position:0%
+would then get so you would get a a a
+ 
+
+ align:start position:0%
+would then get so you would get a a a
+new dividing point. Let's call it y.
+
+ align:start position:0%
+new dividing point. Let's call it y.
+ 
+
+ align:start position:0%
+new dividing point. Let's call it y.
+And then you would get for the new one,
+
+ align:start position:0%
+And then you would get for the new one,
+ 
+
+ align:start position:0%
+And then you would get for the new one,
+you would have you would look at the
+
+ align:start position:0%
+you would have you would look at the
+ 
+
+ align:start position:0%
+you would have you would look at the
+soup here on this interval here, right?
+
+ align:start position:0%
+soup here on this interval here, right?
+ 
+
+ align:start position:0%
+soup here on this interval here, right?
+But the soup on this interval here of
+
+ align:start position:0%
+But the soup on this interval here of
+ 
+
+ align:start position:0%
+But the soup on this interval here of
+the function is less than the soup on
+
+ align:start position:0%
+the function is less than the soup on
+ 
+
+ align:start position:0%
+the function is less than the soup on
+the larger interval. So you would get a
+
+ align:start position:0%
+the larger interval. So you would get a
+ 
+
+ align:start position:0%
+the larger interval. So you would get a
+soup of f on the interval from i -1 to y
+
+ align:start position:0%
+soup of f on the interval from i -1 to y
+ 
+
+ align:start position:0%
+soup of f on the interval from i -1 to y
+of f
+
+ align:start position:0%
+of f
+ 
+
+ align:start position:0%
+of f
+you get that and then you would get
+
+ align:start position:0%
+you get that and then you would get
+ 
+
+ align:start position:0%
+you get that and then you would get
+times the length of the interval that's
+
+ align:start position:0%
+times the length of the interval that's
+ 
+
+ align:start position:0%
+times the length of the interval that's
+y - x i -1
+
+ align:start position:0%
+y - x i -1
+ 
+
+ align:start position:0%
+y - x i -1
+and then you would get a second soup but
+
+ align:start position:0%
+and then you would get a second soup but
+ 
+
+ align:start position:0%
+and then you would get a second soup but
+this is now from from y to x I of f and
+
+ align:start position:0%
+this is now from from y to x I of f and
+ 
+
+ align:start position:0%
+this is now from from y to x I of f and
+then you would have multiple by the
+
+ align:start position:0%
+then you would have multiple by the
+ 
+
+ align:start position:0%
+then you would have multiple by the
+length of this interval. So this is this
+
+ align:start position:0%
+length of this interval. So this is this
+ 
+
+ align:start position:0%
+length of this interval. So this is this
+here is then from x i to y. Okay.
+
+ align:start position:0%
+here is then from x i to y. Okay.
+ 
+
+ align:start position:0%
+here is then from x i to y. Okay.
+So this is this is what you get from the
+
+ align:start position:0%
+So this is this is what you get from the
+ 
+
+ align:start position:0%
+So this is this is what you get from the
+new petition. the contribution from the
+
+ align:start position:0%
+new petition. the contribution from the
+ 
+
+ align:start position:0%
+new petition. the contribution from the
+from the second
+
+ align:start position:0%
+from the second
+ 
+
+ align:start position:0%
+from the second
+from the this is what this is the
+
+ align:start position:0%
+from the this is what this is the
+ 
+
+ align:start position:0%
+from the this is what this is the
+contribution that you get from the upper
+
+ align:start position:0%
+contribution that you get from the upper
+ 
+
+ align:start position:0%
+contribution that you get from the upper
+sum for this partition P2 from this part
+
+ align:start position:0%
+sum for this partition P2 from this part
+ 
+
+ align:start position:0%
+sum for this partition P2 from this part
+right but now you see that this thing
+
+ align:start position:0%
+right but now you see that this thing
+ 
+
+ align:start position:0%
+right but now you see that this thing
+here the soup over this little interval
+
+ align:start position:0%
+here the soup over this little interval
+ 
+
+ align:start position:0%
+here the soup over this little interval
+well that of course is less than the
+
+ align:start position:0%
+well that of course is less than the
+ 
+
+ align:start position:0%
+well that of course is less than the
+soup over the larger interval so This is
+
+ align:start position:0%
+soup over the larger interval so This is
+ 
+
+ align:start position:0%
+soup over the larger interval so This is
+less than m i and I just keep this one
+
+ align:start position:0%
+less than m i and I just keep this one
+ 
+
+ align:start position:0%
+less than m i and I just keep this one
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and this one here is also a sub interval
+
+ align:start position:0%
+and this one here is also a sub interval
+ 
+
+ align:start position:0%
+and this one here is also a sub interval
+of this larger interval. So this is less
+
+ align:start position:0%
+of this larger interval. So this is less
+ 
+
+ align:start position:0%
+of this larger interval. So this is less
+than m i again time x i - x y.
+
+ align:start position:0%
+than m i again time x i - x y.
+ 
+
+ align:start position:0%
+than m i again time x i - x y.
+But now you can factor out the mi. So
+
+ align:start position:0%
+But now you can factor out the mi. So
+ 
+
+ align:start position:0%
+But now you can factor out the mi. So
+you're getting MI and you're getting the
+
+ align:start position:0%
+you're getting MI and you're getting the
+ 
+
+ align:start position:0%
+you're getting MI and you're getting the
+sum of these two Y - X I - one +
+
+ align:start position:0%
+sum of these two Y - X I - one +
+ 
+
+ align:start position:0%
+sum of these two Y - X I - one +
+uh X I - Y. And so you see that this
+
+ align:start position:0%
+uh X I - Y. And so you see that this
+ 
+
+ align:start position:0%
+uh X I - Y. And so you see that this
+here is exactly MI * X I - X I - one.
+
+ align:start position:0%
+here is exactly MI * X I - X I - one.
+ 
+
+ align:start position:0%
+here is exactly MI * X I - X I - one.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And so you see that the
+
+ align:start position:0%
+And so you see that the
+ 
+
+ align:start position:0%
+And so you see that the
+contribution that we get here to the
+
+ align:start position:0%
+contribution that we get here to the
+ 
+
+ align:start position:0%
+contribution that we get here to the
+upper sum from this part here
+
+ align:start position:0%
+upper sum from this part here
+ 
+
+ align:start position:0%
+upper sum from this part here
+that was this and this those two things
+
+ align:start position:0%
+that was this and this those two things
+ 
+
+ align:start position:0%
+that was this and this those two things
+this is less than the contribution we
+
+ align:start position:0%
+this is less than the contribution we
+ 
+
+ align:start position:0%
+this is less than the contribution we
+get from the upper sum from the first
+
+ align:start position:0%
+get from the upper sum from the first
+ 
+
+ align:start position:0%
+get from the upper sum from the first
+partition. Right? And so this prove this
+
+ align:start position:0%
+partition. Right? And so this prove this
+ 
+
+ align:start position:0%
+partition. Right? And so this prove this
+proves this inequality here
+
+ align:start position:0%
+proves this inequality here
+ 
+
+ align:start position:0%
+proves this inequality here
+and this inequality is just similar.
+
+ align:start position:0%
+and this inequality is just similar.
+ 
+
+ align:start position:0%
+and this inequality is just similar.
+It's just with the instead of the soups.
+
+ align:start position:0%
+It's just with the instead of the soups.
+ 
+
+ align:start position:0%
+It's just with the instead of the soups.
+Okay. So this is this is a this is like
+
+ align:start position:0%
+Okay. So this is this is a this is like
+ 
+
+ align:start position:0%
+Okay. So this is this is a this is like
+a key point. It's a you know each of
+
+ align:start position:0%
+a key point. It's a you know each of
+ 
+
+ align:start position:0%
+a key point. It's a you know each of
+these steps is like completely trivial.
+
+ align:start position:0%
+these steps is like completely trivial.
+ 
+
+ align:start position:0%
+these steps is like completely trivial.
+Uh but together it it actually means
+
+ align:start position:0%
+Uh but together it it actually means
+ 
+
+ align:start position:0%
+Uh but together it it actually means
+that you can really define something
+
+ align:start position:0%
+that you can really define something
+ 
+
+ align:start position:0%
+that you can really define something
+non-trivial.
+
+ align:start position:0%
+non-trivial.
+ 
+
+ align:start position:0%
+non-trivial.
+Okay. So now um and this may seem
+
+ align:start position:0%
+Okay. So now um and this may seem
+ 
+
+ align:start position:0%
+Okay. So now um and this may seem
+cheating. Now we uh well first of all we
+
+ align:start position:0%
+cheating. Now we uh well first of all we
+ 
+
+ align:start position:0%
+cheating. Now we uh well first of all we
+define the upper and lower integrals.
+
+ align:start position:0%
+define the upper and lower integrals.
+ 
+
+ align:start position:0%
+define the upper and lower integrals.
+So we have upper and lower sum and now
+
+ align:start position:0%
+So we have upper and lower sum and now
+ 
+
+ align:start position:0%
+So we have upper and lower sum and now
+we define the upper and lower intervals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and lower instruments.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um so the upper lower integral so
+
+ align:start position:0%
+Okay. Um so the upper lower integral so
+ 
+
+ align:start position:0%
+Okay. Um so the upper lower integral so
+the upper here is denoted like this.
+
+ align:start position:0%
+the upper here is denoted like this.
+ 
+
+ align:start position:0%
+the upper here is denoted like this.
+We take a bar over this and this is the
+
+ align:start position:0%
+We take a bar over this and this is the
+ 
+
+ align:start position:0%
+We take a bar over this and this is the
+upper lower integral. So this is the
+
+ align:start position:0%
+upper lower integral. So this is the
+ 
+
+ align:start position:0%
+upper lower integral. So this is the
+integral. This is the function. And then
+
+ align:start position:0%
+integral. This is the function. And then
+ 
+
+ align:start position:0%
+integral. This is the function. And then
+you write this.
+
+ align:start position:0%
+you write this.
+ 
+
+ align:start position:0%
+you write this.
+And so this is simply defined to be the
+
+ align:start position:0%
+And so this is simply defined to be the
+ 
+
+ align:start position:0%
+And so this is simply defined to be the
+info
+
+ align:start position:0%
+info
+ 
+
+ align:start position:0%
+info
+over all partitions
+
+ align:start position:0%
+over all partitions
+ 
+
+ align:start position:0%
+over all partitions
+of the upper integral
+
+ align:start position:0%
+of the upper integral
+ 
+
+ align:start position:0%
+of the upper integral
+upper sum. Sorry.
+
+ align:start position:0%
+upper sum. Sorry.
+ 
+
+ align:start position:0%
+upper sum. Sorry.
+Right. And so remember again that if you
+
+ align:start position:0%
+Right. And so remember again that if you
+ 
+
+ align:start position:0%
+Right. And so remember again that if you
+take a partition and you refined it, if
+
+ align:start position:0%
+take a partition and you refined it, if
+ 
+
+ align:start position:0%
+take a partition and you refined it, if
+you're looking at a subartition of the
+
+ align:start position:0%
+you're looking at a subartition of the
+ 
+
+ align:start position:0%
+you're looking at a subartition of the
+given partition, then this number here
+
+ align:start position:0%
+given partition, then this number here
+ 
+
+ align:start position:0%
+given partition, then this number here
+goes down, right? I mean it may stay the
+
+ align:start position:0%
+goes down, right? I mean it may stay the
+ 
+
+ align:start position:0%
+goes down, right? I mean it may stay the
+same, but it's certainly not bigger,
+
+ align:start position:0%
+same, but it's certainly not bigger,
+ 
+
+ align:start position:0%
+same, but it's certainly not bigger,
+right? So so this is so so the idea here
+
+ align:start position:0%
+right? So so this is so so the idea here
+ 
+
+ align:start position:0%
+right? So so this is so so the idea here
+is that essentially this number here you
+
+ align:start position:0%
+is that essentially this number here you
+ 
+
+ align:start position:0%
+is that essentially this number here you
+get by looking at finer and finer
+
+ align:start position:0%
+get by looking at finer and finer
+ 
+
+ align:start position:0%
+get by looking at finer and finer
+partition, right? So idea
+
+ align:start position:0%
+partition, right? So idea
+ 
+
+ align:start position:0%
+partition, right? So idea
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+uh the infirmum uh that this is that
+
+ align:start position:0%
+uh the infirmum uh that this is that
+ 
+
+ align:start position:0%
+uh the infirmum uh that this is that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is a limit
+
+ align:start position:0%
+is a limit
+ 
+
+ align:start position:0%
+is a limit
+over finer and final partition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So that's the idea sort of the
+
+ align:start position:0%
+Right? So that's the idea sort of the
+ 
+
+ align:start position:0%
+Right? So that's the idea sort of the
+the but the precise statement is is is
+
+ align:start position:0%
+the but the precise statement is is is
+ 
+
+ align:start position:0%
+the but the precise statement is is is
+that it's just the info right. So this
+
+ align:start position:0%
+that it's just the info right. So this
+ 
+
+ align:start position:0%
+that it's just the info right. So this
+is the upper integral and then likewise
+
+ align:start position:0%
+is the upper integral and then likewise
+ 
+
+ align:start position:0%
+is the upper integral and then likewise
+we define the lower integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> asset
+
+ align:start position:0%
+>> asset
+ 
+
+ align:start position:0%
+>> asset
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+obviously
+
+ align:start position:0%
+obviously
+ 
+
+ align:start position:0%
+obviously
+>> right there it's it's not you know but
+
+ align:start position:0%
+>> right there it's it's not you know but
+ 
+
+ align:start position:0%
+>> right there it's it's not you know but
+there is a a key assumption is that we
+
+ align:start position:0%
+there is a a key assumption is that we
+ 
+
+ align:start position:0%
+there is a a key assumption is that we
+that for each partitions there are only
+
+ align:start position:0%
+that for each partitions there are only
+ 
+
+ align:start position:0%
+that for each partitions there are only
+finitely many divisions
+
+ align:start position:0%
+finitely many divisions
+ 
+
+ align:start position:0%
+finitely many divisions
+but there's not a but it's but but there
+
+ align:start position:0%
+but there's not a but it's but but there
+ 
+
+ align:start position:0%
+but there's not a but it's but but there
+are infinite many partitions. So it's
+
+ align:start position:0%
+are infinite many partitions. So it's
+ 
+
+ align:start position:0%
+are infinite many partitions. So it's
+really and so so when I say that it's a
+
+ align:start position:0%
+really and so so when I say that it's a
+ 
+
+ align:start position:0%
+really and so so when I say that it's a
+limit over uh finer and finer partitions
+
+ align:start position:0%
+limit over uh finer and finer partitions
+ 
+
+ align:start position:0%
+limit over uh finer and finer partitions
+you should really think about that in
+
+ align:start position:0%
+you should really think about that in
+ 
+
+ align:start position:0%
+you should really think about that in
+sort of quotation mark this not very
+
+ align:start position:0%
+sort of quotation mark this not very
+ 
+
+ align:start position:0%
+sort of quotation mark this not very
+precise statements okay so but the
+
+ align:start position:0%
+precise statements okay so but the
+ 
+
+ align:start position:0%
+precise statements okay so but the
+precise statement is just that it's
+
+ align:start position:0%
+precise statement is just that it's
+ 
+
+ align:start position:0%
+precise statement is just that it's
+infome all partitions
+
+ align:start position:0%
+infome all partitions
+ 
+
+ align:start position:0%
+infome all partitions
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean you can make that precise but
+
+ align:start position:0%
+I mean you can make that precise but
+ 
+
+ align:start position:0%
+I mean you can make that precise but
+then that require a lot of stuff uh that
+
+ align:start position:0%
+then that require a lot of stuff uh that
+ 
+
+ align:start position:0%
+then that require a lot of stuff uh that
+we don't want to do here. Uh and there's
+
+ align:start position:0%
+we don't want to do here. Uh and there's
+ 
+
+ align:start position:0%
+we don't want to do here. Uh and there's
+no reason to it because there's a
+
+ align:start position:0%
+no reason to it because there's a
+ 
+
+ align:start position:0%
+no reason to it because there's a
+perfectly reasonable way of defining it.
+
+ align:start position:0%
+perfectly reasonable way of defining it.
+ 
+
+ align:start position:0%
+perfectly reasonable way of defining it.
+And so that was the upper integral. So
+
+ align:start position:0%
+And so that was the upper integral. So
+ 
+
+ align:start position:0%
+And so that was the upper integral. So
+this is the upper integral.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then similarly the lower integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lower integral. And there I'm just
+
+ align:start position:0%
+the lower integral. And there I'm just
+ 
+
+ align:start position:0%
+the lower integral. And there I'm just
+putting the bar below.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you refine it like this.
+
+ align:start position:0%
+And you refine it like this.
+ 
+
+ align:start position:0%
+And you refine it like this.
+And this is now the soup, right? Because
+
+ align:start position:0%
+And this is now the soup, right? Because
+ 
+
+ align:start position:0%
+And this is now the soup, right? Because
+remember that if you took a partition
+
+ align:start position:0%
+remember that if you took a partition
+ 
+
+ align:start position:0%
+remember that if you took a partition
+and then you take a sub partition, then
+
+ align:start position:0%
+and then you take a sub partition, then
+ 
+
+ align:start position:0%
+and then you take a sub partition, then
+this lower sum actually went up. So it's
+
+ align:start position:0%
+this lower sum actually went up. So it's
+ 
+
+ align:start position:0%
+this lower sum actually went up. So it's
+a soup of all partitions of these lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Right. And so now we say that uh and
+
+ align:start position:0%
+Right. And so now we say that uh and
+ 
+
+ align:start position:0%
+Right. And so now we say that uh and
+then we say that
+
+ align:start position:0%
+then we say that
+ 
+
+ align:start position:0%
+then we say that
+so now here's the the definition. And
+
+ align:start position:0%
+so now here's the the definition. And
+ 
+
+ align:start position:0%
+so now here's the the definition. And
+again this may initially seem like kind
+
+ align:start position:0%
+again this may initially seem like kind
+ 
+
+ align:start position:0%
+again this may initially seem like kind
+of we are uh wimping out uh because but
+
+ align:start position:0%
+of we are uh wimping out uh because but
+ 
+
+ align:start position:0%
+of we are uh wimping out uh because but
+but but it but in a minute we will then
+
+ align:start position:0%
+but but it but in a minute we will then
+ 
+
+ align:start position:0%
+but but it but in a minute we will then
+determine when this is the case. So we
+
+ align:start position:0%
+determine when this is the case. So we
+ 
+
+ align:start position:0%
+determine when this is the case. So we
+define so so f here. So if you have a
+
+ align:start position:0%
+define so so f here. So if you have a
+ 
+
+ align:start position:0%
+define so so f here. So if you have a
+bounded function like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh f is reman integral.
+
+ align:start position:0%
+that uh f is reman integral.
+ 
+
+ align:start position:0%
+that uh f is reman integral.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if uh if the lower sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to the upper sum.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if this has the case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and and uh and and in that case
+
+ align:start position:0%
+um and and uh and and in that case
+ 
+
+ align:start position:0%
+um and and uh and and in that case
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+the reman integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this this common uh so the reman is
+
+ align:start position:0%
+is this this common uh so the reman is
+ 
+
+ align:start position:0%
+is this this common uh so the reman is
+written like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is just
+
+ align:start position:0%
+And this is just
+ 
+
+ align:start position:0%
+And this is just
+this this common value.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now, uh one thing I just want to remark
+
+ align:start position:0%
+Now, uh one thing I just want to remark
+ 
+
+ align:start position:0%
+Now, uh one thing I just want to remark
+um is
+
+ align:start position:0%
+um is
+ 
+
+ align:start position:0%
+um is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that we have you always have
+
+ align:start position:0%
+that we have you always have
+ 
+
+ align:start position:0%
+that we have you always have
+That's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one remark is that so
+
+ align:start position:0%
+so one remark is that so
+ 
+
+ align:start position:0%
+so one remark is that so
+so note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so first of all we had this trivial
+
+ align:start position:0%
+that so first of all we had this trivial
+ 
+
+ align:start position:0%
+that so first of all we had this trivial
+statement that if you take a partition
+
+ align:start position:0%
+statement that if you take a partition
+ 
+
+ align:start position:0%
+statement that if you take a partition
+then the lower sum is less or equal to
+
+ align:start position:0%
+then the lower sum is less or equal to
+ 
+
+ align:start position:0%
+then the lower sum is less or equal to
+the upper sum Fine. Then we had that if
+
+ align:start position:0%
+the upper sum Fine. Then we had that if
+ 
+
+ align:start position:0%
+the upper sum Fine. Then we had that if
+you took a sub partition, if this here
+
+ align:start position:0%
+you took a sub partition, if this here
+ 
+
+ align:start position:0%
+you took a sub partition, if this here
+was a sub partition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of P1. Then this lower sum here
+
+ align:start position:0%
+of P1. Then this lower sum here
+ 
+
+ align:start position:0%
+of P1. Then this lower sum here
+under a sub partition, the lower sum
+
+ align:start position:0%
+under a sub partition, the lower sum
+ 
+
+ align:start position:0%
+under a sub partition, the lower sum
+went up,
+
+ align:start position:0%
+went up,
+ 
+
+ align:start position:0%
+went up,
+but it's still staying below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have this inequality here. Okay.
+
+ align:start position:0%
+So you have this inequality here. Okay.
+ 
+
+ align:start position:0%
+So you have this inequality here. Okay.
+Now what what is this useful form?
+
+ align:start position:0%
+Now what what is this useful form?
+ 
+
+ align:start position:0%
+Now what what is this useful form?
+So as a consequence of this we get that
+
+ align:start position:0%
+So as a consequence of this we get that
+ 
+
+ align:start position:0%
+So as a consequence of this we get that
+the you know whether or not the function
+
+ align:start position:0%
+the you know whether or not the function
+ 
+
+ align:start position:0%
+the you know whether or not the function
+is rem integral you always have that the
+
+ align:start position:0%
+is rem integral you always have that the
+ 
+
+ align:start position:0%
+is rem integral you always have that the
+lower integral here of f dx is less or
+
+ align:start position:0%
+lower integral here of f dx is less or
+ 
+
+ align:start position:0%
+lower integral here of f dx is less or
+equal to the upper integral.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this here is for all functions. And
+
+ align:start position:0%
+So this here is for all functions. And
+ 
+
+ align:start position:0%
+So this here is for all functions. And
+why is this the case? This is because if
+
+ align:start position:0%
+why is this the case? This is because if
+ 
+
+ align:start position:0%
+why is this the case? This is because if
+you take this here is the soup
+
+ align:start position:0%
+you take this here is the soup
+ 
+
+ align:start position:0%
+you take this here is the soup
+of these lower partitions, right?
+
+ align:start position:0%
+of these lower partitions, right?
+ 
+
+ align:start position:0%
+of these lower partitions, right?
+But if you take any given partition,
+
+ align:start position:0%
+But if you take any given partition,
+ 
+
+ align:start position:0%
+But if you take any given partition,
+then this lower thing here is less than
+
+ align:start position:0%
+then this lower thing here is less than
+ 
+
+ align:start position:0%
+then this lower thing here is less than
+than the upper one,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And so now so now imagine that you take
+
+ align:start position:0%
+And so now so now imagine that you take
+ 
+
+ align:start position:0%
+And so now so now imagine that you take
+so if you take a lower partition
+
+ align:start position:0%
+so if you take a lower partition
+ 
+
+ align:start position:0%
+so if you take a lower partition
+right suppose sorry suppose now that you
+
+ align:start position:0%
+right suppose sorry suppose now that you
+ 
+
+ align:start position:0%
+right suppose sorry suppose now that you
+take the soup over all partitions then
+
+ align:start position:0%
+take the soup over all partitions then
+ 
+
+ align:start position:0%
+take the soup over all partitions then
+it means that there is one partition so
+
+ align:start position:0%
+it means that there is one partition so
+ 
+
+ align:start position:0%
+it means that there is one partition so
+that this value here is close to the
+
+ align:start position:0%
+that this value here is close to the
+ 
+
+ align:start position:0%
+that this value here is close to the
+soup.
+
+ align:start position:0%
+soup.
+ 
+
+ align:start position:0%
+soup.
+But uh but for this one here right you
+
+ align:start position:0%
+But uh but for this one here right you
+ 
+
+ align:start position:0%
+But uh but for this one here right you
+have this inequality here right and so
+
+ align:start position:0%
+have this inequality here right and so
+ 
+
+ align:start position:0%
+have this inequality here right and so
+in fact but in fact if you take any so
+
+ align:start position:0%
+in fact but in fact if you take any so
+ 
+
+ align:start position:0%
+in fact but in fact if you take any so
+any other partition you can think about
+
+ align:start position:0%
+any other partition you can think about
+ 
+
+ align:start position:0%
+any other partition you can think about
+maybe I'll explain this more detail next
+
+ align:start position:0%
+maybe I'll explain this more detail next
+ 
+
+ align:start position:0%
+maybe I'll explain this more detail next
+time because I only have a minute but
+
+ align:start position:0%
+time because I only have a minute but
+ 
+
+ align:start position:0%
+time because I only have a minute but
+but it basically come from this
+
+ align:start position:0%
+but it basically come from this
+ 
+
+ align:start position:0%
+but it basically come from this
+inequality here is coming from from from
+
+ align:start position:0%
+inequality here is coming from from from
+ 
+
+ align:start position:0%
+inequality here is coming from from from
+uh from this this inequality here it
+
+ align:start position:0%
+uh from this this inequality here it
+ 
+
+ align:start position:0%
+uh from this this inequality here it
+will take just a few minutes to explain
+
+ align:start position:0%
+will take just a few minutes to explain
+ 
+
+ align:start position:0%
+will take just a few minutes to explain
+it clearly. So maybe I'll just leave it
+
+ align:start position:0%
+it clearly. So maybe I'll just leave it
+ 
+
+ align:start position:0%
+it clearly. So maybe I'll just leave it
+here. But but but a key point here is
+
+ align:start position:0%
+here. But but but a key point here is
+ 
+
+ align:start position:0%
+here. But but but a key point here is
+that you have this inequality here and
+
+ align:start position:0%
+that you have this inequality here and
+ 
+
+ align:start position:0%
+that you have this inequality here and
+it comes from that
+
+ align:start position:0%
+it comes from that
+ 
+
+ align:start position:0%
+it comes from that
+and but but we return to that next time
+
+ align:start position:0%
+and but but we return to that next time
+ 
+
+ align:start position:0%
+and but but we return to that next time
+because it's to make it really clear it
+
+ align:start position:0%
+because it's to make it really clear it
+ 
+
+ align:start position:0%
+because it's to make it really clear it
+it would take a few minutes.
+
+ align:start position:0%
+it would take a few minutes.
+ 
+
+ align:start position:0%
+it would take a few minutes.
+Now the last thing I want to say in the
+
+ align:start position:0%
+Now the last thing I want to say in the
+ 
+
+ align:start position:0%
+Now the last thing I want to say in the
+is that so this so you may think that we
+
+ align:start position:0%
+is that so this so you may think that we
+ 
+
+ align:start position:0%
+is that so this so you may think that we
+sort of whimped out of saying when this
+
+ align:start position:0%
+sort of whimped out of saying when this
+ 
+
+ align:start position:0%
+sort of whimped out of saying when this
+uh right because we just define it we
+
+ align:start position:0%
+uh right because we just define it we
+ 
+
+ align:start position:0%
+uh right because we just define it we
+just say that it's reman integraable if
+
+ align:start position:0%
+just say that it's reman integraable if
+ 
+
+ align:start position:0%
+just say that it's reman integraable if
+if uh those two things are equal right
+
+ align:start position:0%
+if uh those two things are equal right
+ 
+
+ align:start position:0%
+if uh those two things are equal right
+and so but then the question of course
+
+ align:start position:0%
+and so but then the question of course
+ 
+
+ align:start position:0%
+and so but then the question of course
+become when are those two things equal
+
+ align:start position:0%
+become when are those two things equal
+ 
+
+ align:start position:0%
+become when are those two things equal
+right so that's the key question so the
+
+ align:start position:0%
+right so that's the key question so the
+ 
+
+ align:start position:0%
+right so that's the key question so the
+key question is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when are they equal?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And and we'll answer this next time.
+
+ align:start position:0%
+And and we'll answer this next time.
+ 
+
+ align:start position:0%
+And and we'll answer this next time.
+Um where we will show that if f is
+
+ align:start position:0%
+Um where we will show that if f is
+ 
+
+ align:start position:0%
+Um where we will show that if f is
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then they are equal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so uh so anyways I'll return to
+
+ align:start position:0%
+And so uh so anyways I'll return to
+ 
+
+ align:start position:0%
+And so uh so anyways I'll return to
+this. I will first um um you know we
+
+ align:start position:0%
+this. I will first um um you know we
+ 
+
+ align:start position:0%
+this. I will first um um you know we
+need anyway some more information about
+
+ align:start position:0%
+need anyway some more information about
+ 
+
+ align:start position:0%
+need anyway some more information about
+this upper and lower integral and I will
+
+ align:start position:0%
+this upper and lower integral and I will
+ 
+
+ align:start position:0%
+this upper and lower integral and I will
+first show why the lower one is less or
+
+ align:start position:0%
+first show why the lower one is less or
+ 
+
+ align:start position:0%
+first show why the lower one is less or
+equal to the lower one is lesser equal
+
+ align:start position:0%
+equal to the lower one is lesser equal
+ 
+
+ align:start position:0%
+equal to the lower one is lesser equal
+to the upper one always and then we will
+
+ align:start position:0%
+to the upper one always and then we will
+ 
+
+ align:start position:0%
+to the upper one always and then we will
+talk about you know some criteria for
+
+ align:start position:0%
+talk about you know some criteria for
+ 
+
+ align:start position:0%
+talk about you know some criteria for
+when they are equal and then we will
+
+ align:start position:0%
+when they are equal and then we will
+ 
+
+ align:start position:0%
+when they are equal and then we will
+prove this for continuous functions
+
+ align:start position:0%
+prove this for continuous functions
+ 
+
+ align:start position:0%
+prove this for continuous functions
+>> is that only
+
+ align:start position:0%
+>> is that only
+ 
+
+ align:start position:0%
+>> is that only
+>> no no no it's not it's not it's Not it's
+
+ align:start position:0%
+>> no no no it's not it's not it's Not it's
+ 
+
+ align:start position:0%
+>> no no no it's not it's not it's Not it's
+um it's uh yeah it's not a total answer.
+
+ align:start position:0%
+um it's uh yeah it's not a total answer.
+ 
+
+ align:start position:0%
+um it's uh yeah it's not a total answer.
+It's it's a it's a good initial answer
+
+ align:start position:0%
+It's it's a it's a good initial answer
+ 
+
+ align:start position:0%
+It's it's a it's a good initial answer
+but there are many functions that are
+
+ align:start position:0%
+but there are many functions that are
+ 
+
+ align:start position:0%
+but there are many functions that are
+not continuous that are very worth you
+
+ align:start position:0%
+not continuous that are very worth you
+ 
+
+ align:start position:0%
+not continuous that are very worth you
+know that plays in key roles and they're
+
+ align:start position:0%
+know that plays in key roles and they're
+ 
+
+ align:start position:0%
+know that plays in key roles and they're
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+um and we will also look at an example
+
+ align:start position:0%
+um and we will also look at an example
+ 
+
+ align:start position:0%
+um and we will also look at an example
+it's in the notes but I didn't get to
+
+ align:start position:0%
+it's in the notes but I didn't get to
+ 
+
+ align:start position:0%
+it's in the notes but I didn't get to
+it. we look at an example of a function
+
+ align:start position:0%
+it. we look at an example of a function
+ 
+
+ align:start position:0%
+it. we look at an example of a function
+that is u that is not where where you
+
+ align:start position:0%
+that is u that is not where where you
+ 
+
+ align:start position:0%
+that is u that is not where where you
+don't have this equality and this is
+
+ align:start position:0%
+don't have this equality and this is
+ 
+
+ align:start position:0%
+don't have this equality and this is
+like an old
\ No newline at end of file
diff --git a/yI4E3ieyu9o.txt b/yI4E3ieyu9o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b021a9b36670a2009fc42c42fdf3c980899ac35
--- /dev/null
+++ b/yI4E3ieyu9o.txt
@@ -0,0 +1,18739 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a creative common license. Your support
+
+ align:start position:0%
+a creative common license. Your support
+ 
+
+ align:start position:0%
+a creative common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Some content in this audio is not
+
+ align:start position:0%
+Some content in this audio is not
+ 
+
+ align:start position:0%
+Some content in this audio is not
+covered under our creative common
+
+ align:start position:0%
+covered under our creative common
+ 
+
+ align:start position:0%
+covered under our creative common
+license. For more information, see the
+
+ align:start position:0%
+license. For more information, see the
+ 
+
+ align:start position:0%
+license. For more information, see the
+course materials on the MIT Open
+
+ align:start position:0%
+course materials on the MIT Open
+ 
+
+ align:start position:0%
+course materials on the MIT Open
+Courseware website
+
+ align:start position:0%
+Courseware website
+ 
+
+ align:start position:0%
+Courseware website
+>> to a uh who's going to uh uh give us a
+
+ align:start position:0%
+>> to a uh who's going to uh uh give us a
+ 
+
+ align:start position:0%
+>> to a uh who's going to uh uh give us a
+guest lecture on on art games. And uh
+
+ align:start position:0%
+guest lecture on on art games. And uh
+ 
+
+ align:start position:0%
+guest lecture on on art games. And uh
+today's reading uh the the proc reading
+
+ align:start position:0%
+today's reading uh the the proc reading
+ 
+
+ align:start position:0%
+today's reading uh the the proc reading
+is kind of like part two of a lot of
+
+ align:start position:0%
+is kind of like part two of a lot of
+ 
+
+ align:start position:0%
+is kind of like part two of a lot of
+things that uh Jason Begley talked about
+
+ align:start position:0%
+things that uh Jason Begley talked about
+ 
+
+ align:start position:0%
+things that uh Jason Begley talked about
+uh when we did simulations. So um kind
+
+ align:start position:0%
+uh when we did simulations. So um kind
+ 
+
+ align:start position:0%
+uh when we did simulations. So um kind
+if you guys remember his talk while you
+
+ align:start position:0%
+if you guys remember his talk while you
+ 
+
+ align:start position:0%
+if you guys remember his talk while you
+were reading that that that sequest and
+
+ align:start position:0%
+were reading that that that sequest and
+ 
+
+ align:start position:0%
+were reading that that that sequest and
+what that came from. Um, one thing that
+
+ align:start position:0%
+what that came from. Um, one thing that
+ 
+
+ align:start position:0%
+what that came from. Um, one thing that
+I actually forgot to address was that
+
+ align:start position:0%
+I actually forgot to address was that
+ 
+
+ align:start position:0%
+I actually forgot to address was that
+there are actually a couple of uh
+
+ align:start position:0%
+there are actually a couple of uh
+ 
+
+ align:start position:0%
+there are actually a couple of uh
+responses to that uh to that article. If
+
+ align:start position:0%
+responses to that uh to that article. If
+ 
+
+ align:start position:0%
+responses to that uh to that article. If
+you scroll all the way down to the
+
+ align:start position:0%
+you scroll all the way down to the
+ 
+
+ align:start position:0%
+you scroll all the way down to the
+bottom of the article, there's these
+
+ align:start position:0%
+bottom of the article, there's these
+ 
+
+ align:start position:0%
+bottom of the article, there's these
+responses by Arisman and Mizuki and him
+
+ align:start position:0%
+responses by Arisman and Mizuki and him
+ 
+
+ align:start position:0%
+responses by Arisman and Mizuki and him
+back to them. And uh those are kind of
+
+ align:start position:0%
+back to them. And uh those are kind of
+ 
+
+ align:start position:0%
+back to them. And uh those are kind of
+interesting uh you know because it just
+
+ align:start position:0%
+interesting uh you know because it just
+ 
+
+ align:start position:0%
+interesting uh you know because it just
+sort of carries on a conversation and
+
+ align:start position:0%
+sort of carries on a conversation and
+ 
+
+ align:start position:0%
+sort of carries on a conversation and
+people are actually just sort of turning
+
+ align:start position:0%
+people are actually just sort of turning
+ 
+
+ align:start position:0%
+people are actually just sort of turning
+his article into basically a blog post
+
+ align:start position:0%
+his article into basically a blog post
+ 
+
+ align:start position:0%
+his article into basically a blog post
+and then writing comments. um and they
+
+ align:start position:0%
+and then writing comments. um and they
+ 
+
+ align:start position:0%
+and then writing comments. um and they
+were pretty good but a lot of that was
+
+ align:start position:0%
+were pretty good but a lot of that was
+ 
+
+ align:start position:0%
+were pretty good but a lot of that was
+kind of the state of art game discussion
+
+ align:start position:0%
+kind of the state of art game discussion
+ 
+
+ align:start position:0%
+kind of the state of art game discussion
+back in 999 I think I think it's a
+
+ align:start position:0%
+back in 999 I think I think it's a
+ 
+
+ align:start position:0%
+back in 999 I think I think it's a
+pretty old article um where they were
+
+ align:start position:0%
+pretty old article um where they were
+ 
+
+ align:start position:0%
+pretty old article um where they were
+very much thinking about you know games
+
+ align:start position:0%
+very much thinking about you know games
+ 
+
+ align:start position:0%
+very much thinking about you know games
+can games have to be simulations you
+
+ align:start position:0%
+can games have to be simulations you
+ 
+
+ align:start position:0%
+can games have to be simulations you
+know games and narratives uh you know
+
+ align:start position:0%
+know games and narratives uh you know
+ 
+
+ align:start position:0%
+know games and narratives uh you know
+storytelling is like some other mediums
+
+ align:start position:0%
+storytelling is like some other mediums
+ 
+
+ align:start position:0%
+storytelling is like some other mediums
+do uh medium domain it's all about the
+
+ align:start position:0%
+do uh medium domain it's all about the
+ 
+
+ align:start position:0%
+do uh medium domain it's all about the
+simulation um and um and arguably at
+
+ align:start position:0%
+simulation um and um and arguably at
+ 
+
+ align:start position:0%
+simulation um and um and arguably at
+that time there wasn't a big discussion
+
+ align:start position:0%
+that time there wasn't a big discussion
+ 
+
+ align:start position:0%
+that time there wasn't a big discussion
+of an art games movement. There were
+
+ align:start position:0%
+of an art games movement. There were
+ 
+
+ align:start position:0%
+of an art games movement. There were
+other games movements like new games
+
+ align:start position:0%
+other games movements like new games
+ 
+
+ align:start position:0%
+other games movements like new games
+like like like new games which were
+
+ align:start position:0%
+like like like new games which were
+ 
+
+ align:start position:0%
+like like like new games which were
+really more about uh people interacting
+
+ align:start position:0%
+really more about uh people interacting
+ 
+
+ align:start position:0%
+really more about uh people interacting
+with trying to get games to where people
+
+ align:start position:0%
+with trying to get games to where people
+ 
+
+ align:start position:0%
+with trying to get games to where people
+were more cooperative, less competitive
+
+ align:start position:0%
+were more cooperative, less competitive
+ 
+
+ align:start position:0%
+were more cooperative, less competitive
+and less cut through. Um there were
+
+ align:start position:0%
+and less cut through. Um there were
+ 
+
+ align:start position:0%
+and less cut through. Um there were
+other mo there were movements about um
+
+ align:start position:0%
+other mo there were movements about um
+ 
+
+ align:start position:0%
+other mo there were movements about um
+people um there were probably
+
+ align:start position:0%
+people um there were probably
+ 
+
+ align:start position:0%
+people um there were probably
+advertising game movements and there
+
+ align:start position:0%
+advertising game movements and there
+ 
+
+ align:start position:0%
+advertising game movements and there
+were there were a lot there was a lot of
+
+ align:start position:0%
+were there were a lot there was a lot of
+ 
+
+ align:start position:0%
+were there were a lot there was a lot of
+work in people making mods of computer
+
+ align:start position:0%
+work in people making mods of computer
+ 
+
+ align:start position:0%
+work in people making mods of computer
+games that effectively made it
+
+ align:start position:0%
+games that effectively made it
+ 
+
+ align:start position:0%
+games that effectively made it
+unplayable but made really pretty images
+
+ align:start position:0%
+unplayable but made really pretty images
+ 
+
+ align:start position:0%
+unplayable but made really pretty images
+in the process. Um so that there was a
+
+ align:start position:0%
+in the process. Um so that there was a
+ 
+
+ align:start position:0%
+in the process. Um so that there was a
+Doom hack for instance where everything
+
+ align:start position:0%
+Doom hack for instance where everything
+ 
+
+ align:start position:0%
+Doom hack for instance where everything
+becomes black and white and and is
+
+ align:start position:0%
+becomes black and white and and is
+ 
+
+ align:start position:0%
+becomes black and white and and is
+striped including the monsters. It's
+
+ align:start position:0%
+striped including the monsters. It's
+ 
+
+ align:start position:0%
+striped including the monsters. It's
+like there's no way they can see what
+
+ align:start position:0%
+like there's no way they can see what
+ 
+
+ align:start position:0%
+like there's no way they can see what
+the hell's going on but they look pretty
+
+ align:start position:0%
+the hell's going on but they look pretty
+ 
+
+ align:start position:0%
+the hell's going on but they look pretty
+cool. Um,
+
+ align:start position:0%
+cool. Um,
+ 
+
+ align:start position:0%
+cool. Um,
+>> yep.
+
+ align:start position:0%
+>> yep.
+ 
+
+ align:start position:0%
+>> yep.
+>> Have you seen I think it's 96 kilobytes.
+
+ align:start position:0%
+>> Have you seen I think it's 96 kilobytes.
+ 
+
+ align:start position:0%
+>> Have you seen I think it's 96 kilobytes.
+>> There was a competition to make a full
+
+ align:start position:0%
+>> There was a competition to make a full
+ 
+
+ align:start position:0%
+>> There was a competition to make a full
+game in a really really small size. No,
+
+ align:start position:0%
+game in a really really small size. No,
+ 
+
+ align:start position:0%
+game in a really really small size. No,
+it's 4 kilobytes I think and it's a 4
+
+ align:start position:0%
+it's 4 kilobytes I think and it's a 4
+ 
+
+ align:start position:0%
+it's 4 kilobytes I think and it's a 4
+kilob game in full 3D with multiple
+
+ align:start position:0%
+kilob game in full 3D with multiple
+ 
+
+ align:start position:0%
+kilob game in full 3D with multiple
+levels and they have extremely cle
+
+ align:start position:0%
+levels and they have extremely cle
+ 
+
+ align:start position:0%
+levels and they have extremely cle
+including the music and everything
+
+ align:start position:0%
+including the music and everything
+ 
+
+ align:start position:0%
+including the music and everything
+>> like Yeah.
+
+ align:start position:0%
+>> like Yeah.
+ 
+
+ align:start position:0%
+>> like Yeah.
+>> And have you ever heard of this or seen?
+
+ align:start position:0%
+>> And have you ever heard of this or seen?
+ 
+
+ align:start position:0%
+>> And have you ever heard of this or seen?
+>> There are a couple of those u and a lot
+
+ align:start position:0%
+>> There are a couple of those u and a lot
+ 
+
+ align:start position:0%
+>> There are a couple of those u and a lot
+of those come out from the demo scene.
+
+ align:start position:0%
+of those come out from the demo scene.
+ 
+
+ align:start position:0%
+of those come out from the demo scene.
+Uh the demo scene uh which I will put
+
+ align:start position:0%
+Uh the demo scene uh which I will put
+ 
+
+ align:start position:0%
+Uh the demo scene uh which I will put
+off to some other
+
+ align:start position:0%
+off to some other
+ 
+
+ align:start position:0%
+off to some other
+>> very artsy too. It's like very
+
+ align:start position:0%
+>> very artsy too. It's like very
+ 
+
+ align:start position:0%
+>> very artsy too. It's like very
+>> Yeah. It it it's kind of this weird
+
+ align:start position:0%
+>> Yeah. It it it's kind of this weird
+ 
+
+ align:start position:0%
+>> Yeah. It it it's kind of this weird
+thing of like computer hacking, really
+
+ align:start position:0%
+thing of like computer hacking, really
+ 
+
+ align:start position:0%
+thing of like computer hacking, really
+really fast and really really compact
+
+ align:start position:0%
+really fast and really really compact
+ 
+
+ align:start position:0%
+really fast and really really compact
+coding and visual aesthetics and music.
+
+ align:start position:0%
+coding and visual aesthetics and music.
+ 
+
+ align:start position:0%
+coding and visual aesthetics and music.
+Uh which you know it's more of like a
+
+ align:start position:0%
+Uh which you know it's more of like a
+ 
+
+ align:start position:0%
+Uh which you know it's more of like a
+digital music video. Um only there was
+
+ align:start position:0%
+digital music video. Um only there was
+ 
+
+ align:start position:0%
+digital music video. Um only there was
+some people who added a mouse control
+
+ align:start position:0%
+some people who added a mouse control
+ 
+
+ align:start position:0%
+some people who added a mouse control
+and gameplay into it and made these tiny
+
+ align:start position:0%
+and gameplay into it and made these tiny
+ 
+
+ align:start position:0%
+and gameplay into it and made these tiny
+little games. Um but uh that that was
+
+ align:start position:0%
+little games. Um but uh that that was
+ 
+
+ align:start position:0%
+little games. Um but uh that that was
+pretty much art that that's very
+
+ align:start position:0%
+pretty much art that that's very
+ 
+
+ align:start position:0%
+pretty much art that that's very
+different from the art game scene that
+
+ align:start position:0%
+different from the art game scene that
+ 
+
+ align:start position:0%
+different from the art game scene that
+we have today or at least what is
+
+ align:start position:0%
+we have today or at least what is
+ 
+
+ align:start position:0%
+we have today or at least what is
+commonly described as our games. So, uh,
+
+ align:start position:0%
+commonly described as our games. So, uh,
+ 
+
+ align:start position:0%
+commonly described as our games. So, uh,
+I, um, I'd like to aid to talk about
+
+ align:start position:0%
+I, um, I'd like to aid to talk about
+ 
+
+ align:start position:0%
+I, um, I'd like to aid to talk about
+kind of what happened from, um, since
+
+ align:start position:0%
+kind of what happened from, um, since
+ 
+
+ align:start position:0%
+kind of what happened from, um, since
+then, since, uh, since 99.
+
+ align:start position:0%
+then, since, uh, since 99.
+ 
+
+ align:start position:0%
+then, since, uh, since 99.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah. So, hi guys. I'm I'm, uh, Abe. Uh,
+
+ align:start position:0%
+>> Yeah. So, hi guys. I'm I'm, uh, Abe. Uh,
+ 
+
+ align:start position:0%
+>> Yeah. So, hi guys. I'm I'm, uh, Abe. Uh,
+I work here at the lab. I've played a
+
+ align:start position:0%
+I work here at the lab. I've played a
+ 
+
+ align:start position:0%
+I work here at the lab. I've played a
+bunch of your games. I've met a bunch of
+
+ align:start position:0%
+bunch of your games. I've met a bunch of
+ 
+
+ align:start position:0%
+bunch of your games. I've met a bunch of
+you. Um, so it's it's nice to be here.
+
+ align:start position:0%
+you. Um, so it's it's nice to be here.
+ 
+
+ align:start position:0%
+you. Um, so it's it's nice to be here.
+Philip uh, asked me to come in to talk
+
+ align:start position:0%
+Philip uh, asked me to come in to talk
+ 
+
+ align:start position:0%
+Philip uh, asked me to come in to talk
+about, uh, quote unquote art games. Uh I
+
+ align:start position:0%
+about, uh, quote unquote art games. Uh I
+ 
+
+ align:start position:0%
+about, uh, quote unquote art games. Uh I
+think largely because it's a kind of um
+
+ align:start position:0%
+think largely because it's a kind of um
+ 
+
+ align:start position:0%
+think largely because it's a kind of um
+uh I'll say sector of kind of game
+
+ align:start position:0%
+uh I'll say sector of kind of game
+ 
+
+ align:start position:0%
+uh I'll say sector of kind of game
+development that uh my work at Gambit
+
+ align:start position:0%
+development that uh my work at Gambit
+ 
+
+ align:start position:0%
+development that uh my work at Gambit
+tends to intersect with um especially
+
+ align:start position:0%
+tends to intersect with um especially
+ 
+
+ align:start position:0%
+tends to intersect with um especially
+recently. Um and I think too that it's
+
+ align:start position:0%
+recently. Um and I think too that it's
+ 
+
+ align:start position:0%
+recently. Um and I think too that it's
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+>> sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know. I think too that it's um I
+
+ align:start position:0%
+I don't know. I think too that it's um I
+ 
+
+ align:start position:0%
+I don't know. I think too that it's um I
+think too that it's a uh it's kind of a
+
+ align:start position:0%
+think too that it's a uh it's kind of a
+ 
+
+ align:start position:0%
+think too that it's a uh it's kind of a
+sector that's that's a little bit
+
+ align:start position:0%
+sector that's that's a little bit
+ 
+
+ align:start position:0%
+sector that's that's a little bit
+confused and um and possibly confusing
+
+ align:start position:0%
+confused and um and possibly confusing
+ 
+
+ align:start position:0%
+confused and um and possibly confusing
+too. And so um just to give you guys a
+
+ align:start position:0%
+too. And so um just to give you guys a
+ 
+
+ align:start position:0%
+too. And so um just to give you guys a
+sense um you know when he asked me about
+
+ align:start position:0%
+sense um you know when he asked me about
+ 
+
+ align:start position:0%
+sense um you know when he asked me about
+this it actually made me it kind of made
+
+ align:start position:0%
+this it actually made me it kind of made
+ 
+
+ align:start position:0%
+this it actually made me it kind of made
+me think cuz I was like oh yeah cool.
+
+ align:start position:0%
+me think cuz I was like oh yeah cool.
+ 
+
+ align:start position:0%
+me think cuz I was like oh yeah cool.
+I'll talk about like this art games
+
+ align:start position:0%
+I'll talk about like this art games
+ 
+
+ align:start position:0%
+I'll talk about like this art games
+movement or whatever but you know then
+
+ align:start position:0%
+movement or whatever but you know then
+ 
+
+ align:start position:0%
+movement or whatever but you know then
+of course um wait I'm locked into some
+
+ align:start position:0%
+of course um wait I'm locked into some
+ 
+
+ align:start position:0%
+of course um wait I'm locked into some
+kind of weird mode right now.
+
+ align:start position:0%
+kind of weird mode right now.
+ 
+
+ align:start position:0%
+kind of weird mode right now.
+Sorry. Okay. Um that brings up this
+
+ align:start position:0%
+Sorry. Okay. Um that brings up this
+ 
+
+ align:start position:0%
+Sorry. Okay. Um that brings up this
+question which is which is our games
+
+ align:start position:0%
+question which is which is our games
+ 
+
+ align:start position:0%
+question which is which is our games
+art. And just to um just to kind of give
+
+ align:start position:0%
+art. And just to um just to kind of give
+ 
+
+ align:start position:0%
+art. And just to um just to kind of give
+you a a sense for how this this little
+
+ align:start position:0%
+you a a sense for how this this little
+ 
+
+ align:start position:0%
+you a a sense for how this this little
+talk thing whatever is going to go um
+
+ align:start position:0%
+talk thing whatever is going to go um
+ 
+
+ align:start position:0%
+talk thing whatever is going to go um
+I'm going to talk a little bit about
+
+ align:start position:0%
+I'm going to talk a little bit about
+ 
+
+ align:start position:0%
+I'm going to talk a little bit about
+this question um give you kind of
+
+ align:start position:0%
+this question um give you kind of
+ 
+
+ align:start position:0%
+this question um give you kind of
+examples of what people have said about
+
+ align:start position:0%
+examples of what people have said about
+ 
+
+ align:start position:0%
+examples of what people have said about
+this um and opinions that I think are
+
+ align:start position:0%
+this um and opinions that I think are
+ 
+
+ align:start position:0%
+this um and opinions that I think are
+particularly important particularly
+
+ align:start position:0%
+particularly important particularly
+ 
+
+ align:start position:0%
+particularly important particularly
+valid on this subject. Um I also after
+
+ align:start position:0%
+valid on this subject. Um I also after
+ 
+
+ align:start position:0%
+valid on this subject. Um I also after
+that want to show you some examples um
+
+ align:start position:0%
+that want to show you some examples um
+ 
+
+ align:start position:0%
+that want to show you some examples um
+some historical and then kind of moving
+
+ align:start position:0%
+some historical and then kind of moving
+ 
+
+ align:start position:0%
+some historical and then kind of moving
+forward examples. I'm actually going to
+
+ align:start position:0%
+forward examples. I'm actually going to
+ 
+
+ align:start position:0%
+forward examples. I'm actually going to
+get some of you guys to to just come up
+
+ align:start position:0%
+get some of you guys to to just come up
+ 
+
+ align:start position:0%
+get some of you guys to to just come up
+here and maybe even play some of these
+
+ align:start position:0%
+here and maybe even play some of these
+ 
+
+ align:start position:0%
+here and maybe even play some of these
+examples that I think are particularly
+
+ align:start position:0%
+examples that I think are particularly
+ 
+
+ align:start position:0%
+examples that I think are particularly
+important. And and I'd really like it if
+
+ align:start position:0%
+important. And and I'd really like it if
+ 
+
+ align:start position:0%
+important. And and I'd really like it if
+we can kind of keep this less of a uh me
+
+ align:start position:0%
+we can kind of keep this less of a uh me
+ 
+
+ align:start position:0%
+we can kind of keep this less of a uh me
+talking at you and and you engaging me
+
+ align:start position:0%
+talking at you and and you engaging me
+ 
+
+ align:start position:0%
+talking at you and and you engaging me
+as you have questions on this because I
+
+ align:start position:0%
+as you have questions on this because I
+ 
+
+ align:start position:0%
+as you have questions on this because I
+it's really like me you know blabbing at
+
+ align:start position:0%
+it's really like me you know blabbing at
+ 
+
+ align:start position:0%
+it's really like me you know blabbing at
+you as you fall asleep is is um you know
+
+ align:start position:0%
+you as you fall asleep is is um you know
+ 
+
+ align:start position:0%
+you as you fall asleep is is um you know
+maybe good for a nap but less useful for
+
+ align:start position:0%
+maybe good for a nap but less useful for
+ 
+
+ align:start position:0%
+maybe good for a nap but less useful for
+um you know getting anything out of
+
+ align:start position:0%
+um you know getting anything out of
+ 
+
+ align:start position:0%
+um you know getting anything out of
+this. Um, so we'll try to structure this
+
+ align:start position:0%
+this. Um, so we'll try to structure this
+ 
+
+ align:start position:0%
+this. Um, so we'll try to structure this
+as a conversation and and I'll I'll try
+
+ align:start position:0%
+as a conversation and and I'll I'll try
+ 
+
+ align:start position:0%
+as a conversation and and I'll I'll try
+to pull back hearken back to any of my
+
+ align:start position:0%
+to pull back hearken back to any of my
+ 
+
+ align:start position:0%
+to pull back hearken back to any of my
+teacher instincts and see if I can get
+
+ align:start position:0%
+teacher instincts and see if I can get
+ 
+
+ align:start position:0%
+teacher instincts and see if I can get
+you engaged, but we'll see. Um, so our
+
+ align:start position:0%
+you engaged, but we'll see. Um, so our
+ 
+
+ align:start position:0%
+you engaged, but we'll see. Um, so our
+game's art I um I hate this question.
+
+ align:start position:0%
+game's art I um I hate this question.
+ 
+
+ align:start position:0%
+game's art I um I hate this question.
+Uh, I will start off by saying that I
+
+ align:start position:0%
+Uh, I will start off by saying that I
+ 
+
+ align:start position:0%
+Uh, I will start off by saying that I
+fundamentally and I find it abhorent and
+
+ align:start position:0%
+fundamentally and I find it abhorent and
+ 
+
+ align:start position:0%
+fundamentally and I find it abhorent and
+I hear it all the time. Um, and it's
+
+ align:start position:0%
+I hear it all the time. Um, and it's
+ 
+
+ align:start position:0%
+I hear it all the time. Um, and it's
+aggravating to me because I think it's
+
+ align:start position:0%
+aggravating to me because I think it's
+ 
+
+ align:start position:0%
+aggravating to me because I think it's
+it's incontrovertibly yes. Um I think
+
+ align:start position:0%
+it's incontrovertibly yes. Um I think
+ 
+
+ align:start position:0%
+it's incontrovertibly yes. Um I think
+that you can't possibly come up with any
+
+ align:start position:0%
+that you can't possibly come up with any
+ 
+
+ align:start position:0%
+that you can't possibly come up with any
+other answer other than yes, games are
+
+ align:start position:0%
+other answer other than yes, games are
+ 
+
+ align:start position:0%
+other answer other than yes, games are
+art, games have art. Yes. Yes. Yes.
+
+ align:start position:0%
+art, games have art. Yes. Yes. Yes.
+ 
+
+ align:start position:0%
+art, games have art. Yes. Yes. Yes.
+Right. But um it keeps coming up and it
+
+ align:start position:0%
+Right. But um it keeps coming up and it
+ 
+
+ align:start position:0%
+Right. But um it keeps coming up and it
+keeps kind of becoming a question. And I
+
+ align:start position:0%
+keeps kind of becoming a question. And I
+ 
+
+ align:start position:0%
+keeps kind of becoming a question. And I
+should say too that this is a um this is
+
+ align:start position:0%
+should say too that this is a um this is
+ 
+
+ align:start position:0%
+should say too that this is a um this is
+a wholly biased and uh slanted talk.
+
+ align:start position:0%
+a wholly biased and uh slanted talk.
+ 
+
+ align:start position:0%
+a wholly biased and uh slanted talk.
+This is this is my perspective on this
+
+ align:start position:0%
+This is this is my perspective on this
+ 
+
+ align:start position:0%
+This is this is my perspective on this
+and hopefully by the time you're done
+
+ align:start position:0%
+and hopefully by the time you're done
+ 
+
+ align:start position:0%
+and hopefully by the time you're done
+you'll be like wow he is absolutely
+
+ align:start position:0%
+you'll be like wow he is absolutely
+ 
+
+ align:start position:0%
+you'll be like wow he is absolutely
+right. There is no way that games could
+
+ align:start position:0%
+right. There is no way that games could
+ 
+
+ align:start position:0%
+right. There is no way that games could
+be anything but art. Um or at least they
+
+ align:start position:0%
+be anything but art. Um or at least they
+ 
+
+ align:start position:0%
+be anything but art. Um or at least they
+are art and then some. Um, so, um, this
+
+ align:start position:0%
+are art and then some. Um, so, um, this
+ 
+
+ align:start position:0%
+are art and then some. Um, so, um, this
+guy, um, who's a little hard to see
+
+ align:start position:0%
+guy, um, who's a little hard to see
+ 
+
+ align:start position:0%
+guy, um, who's a little hard to see
+right now, but he's totally blown up.
+
+ align:start position:0%
+right now, but he's totally blown up.
+ 
+
+ align:start position:0%
+right now, but he's totally blown up.
+Um, recently brought this into the for
+
+ align:start position:0%
+Um, recently brought this into the for
+ 
+
+ align:start position:0%
+Um, recently brought this into the for
+um, and that's, uh, that's Roger Eert
+
+ align:start position:0%
+um, and that's, uh, that's Roger Eert
+ 
+
+ align:start position:0%
+um, and that's, uh, that's Roger Eert
+of, uh, Eert System Eert fame, or since
+
+ align:start position:0%
+of, uh, Eert System Eert fame, or since
+ 
+
+ align:start position:0%
+of, uh, Eert System Eert fame, or since
+you guys are some of you younger than
+
+ align:start position:0%
+you guys are some of you younger than
+ 
+
+ align:start position:0%
+you guys are some of you younger than
+me, probably Eert and Roer. Um, and he
+
+ align:start position:0%
+me, probably Eert and Roer. Um, and he
+ 
+
+ align:start position:0%
+me, probably Eert and Roer. Um, and he
+had some interesting and controversial
+
+ align:start position:0%
+had some interesting and controversial
+ 
+
+ align:start position:0%
+had some interesting and controversial
+comments recently. Um, and I I pulled
+
+ align:start position:0%
+comments recently. Um, and I I pulled
+ 
+
+ align:start position:0%
+comments recently. Um, and I I pulled
+this quote. Nevertheless, I remain
+
+ align:start position:0%
+this quote. Nevertheless, I remain
+ 
+
+ align:start position:0%
+this quote. Nevertheless, I remain
+convinced that in principle, I love that
+
+ align:start position:0%
+convinced that in principle, I love that
+ 
+
+ align:start position:0%
+convinced that in principle, I love that
+he put that in uh italics. Video games
+
+ align:start position:0%
+he put that in uh italics. Video games
+ 
+
+ align:start position:0%
+he put that in uh italics. Video games
+cannot be art. Perhaps it is foolish of
+
+ align:start position:0%
+cannot be art. Perhaps it is foolish of
+ 
+
+ align:start position:0%
+cannot be art. Perhaps it is foolish of
+me to say never because never, as Rick
+
+ align:start position:0%
+me to say never because never, as Rick
+ 
+
+ align:start position:0%
+me to say never because never, as Rick
+Wakeakeman informs us, is a long, long
+
+ align:start position:0%
+Wakeakeman informs us, is a long, long
+ 
+
+ align:start position:0%
+Wakeakeman informs us, is a long, long
+time. Let me just say that no video
+
+ align:start position:0%
+time. Let me just say that no video
+ 
+
+ align:start position:0%
+time. Let me just say that no video
+gamer now living will survive long
+
+ align:start position:0%
+gamer now living will survive long
+ 
+
+ align:start position:0%
+gamer now living will survive long
+enough to experience the medium as an
+
+ align:start position:0%
+enough to experience the medium as an
+ 
+
+ align:start position:0%
+enough to experience the medium as an
+art form. Um, so apparently we should
+
+ align:start position:0%
+art form. Um, so apparently we should
+ 
+
+ align:start position:0%
+art form. Um, so apparently we should
+all be dead already, um, according to
+
+ align:start position:0%
+all be dead already, um, according to
+ 
+
+ align:start position:0%
+all be dead already, um, according to
+Eert because we wouldn't have lived long
+
+ align:start position:0%
+Eert because we wouldn't have lived long
+ 
+
+ align:start position:0%
+Eert because we wouldn't have lived long
+enough to experience the medium as an
+
+ align:start position:0%
+enough to experience the medium as an
+ 
+
+ align:start position:0%
+enough to experience the medium as an
+art form. But here's a guy who um even
+
+ align:start position:0%
+art form. But here's a guy who um even
+ 
+
+ align:start position:0%
+art form. But here's a guy who um even
+though I don't think he's a particularly
+
+ align:start position:0%
+though I don't think he's a particularly
+ 
+
+ align:start position:0%
+though I don't think he's a particularly
+good film critic, he's a popular film
+
+ align:start position:0%
+good film critic, he's a popular film
+ 
+
+ align:start position:0%
+good film critic, he's a popular film
+critic and he's kind of weighing in on a
+
+ align:start position:0%
+critic and he's kind of weighing in on a
+ 
+
+ align:start position:0%
+critic and he's kind of weighing in on a
+medium that he doesn't particularly
+
+ align:start position:0%
+medium that he doesn't particularly
+ 
+
+ align:start position:0%
+medium that he doesn't particularly
+understand. And I think it's important
+
+ align:start position:0%
+understand. And I think it's important
+ 
+
+ align:start position:0%
+understand. And I think it's important
+to look at what exactly is he doing when
+
+ align:start position:0%
+to look at what exactly is he doing when
+ 
+
+ align:start position:0%
+to look at what exactly is he doing when
+he makes this statement. And so he's in
+
+ align:start position:0%
+he makes this statement. And so he's in
+ 
+
+ align:start position:0%
+he makes this statement. And so he's in
+this kind of business of classification,
+
+ align:start position:0%
+this kind of business of classification,
+ 
+
+ align:start position:0%
+this kind of business of classification,
+right? He's in this business of saying,
+
+ align:start position:0%
+right? He's in this business of saying,
+ 
+
+ align:start position:0%
+right? He's in this business of saying,
+"All right, well, we've got this subject
+
+ align:start position:0%
+"All right, well, we've got this subject
+ 
+
+ align:start position:0%
+"All right, well, we've got this subject
+called art. What can we say falls under
+
+ align:start position:0%
+called art. What can we say falls under
+ 
+
+ align:start position:0%
+called art. What can we say falls under
+that subset and what what what does
+
+ align:start position:0%
+that subset and what what what does
+ 
+
+ align:start position:0%
+that subset and what what what does
+not?" And so, you know, he says things
+
+ align:start position:0%
+not?" And so, you know, he says things
+ 
+
+ align:start position:0%
+not?" And so, you know, he says things
+like painting, sculpture, dance, opera,
+
+ align:start position:0%
+like painting, sculpture, dance, opera,
+ 
+
+ align:start position:0%
+like painting, sculpture, dance, opera,
+literature, film um can all be
+
+ align:start position:0%
+literature, film um can all be
+ 
+
+ align:start position:0%
+literature, film um can all be
+classified as art and and that games um
+
+ align:start position:0%
+classified as art and and that games um
+ 
+
+ align:start position:0%
+classified as art and and that games um
+games are not. Um probably some other
+
+ align:start position:0%
+games are not. Um probably some other
+ 
+
+ align:start position:0%
+games are not. Um probably some other
+things. I don't know where he stands on
+
+ align:start position:0%
+things. I don't know where he stands on
+ 
+
+ align:start position:0%
+things. I don't know where he stands on
+comic books. I don't think he's written
+
+ align:start position:0%
+comic books. I don't think he's written
+ 
+
+ align:start position:0%
+comic books. I don't think he's written
+about it yet, but I'm sure he can
+
+ align:start position:0%
+about it yet, but I'm sure he can
+ 
+
+ align:start position:0%
+about it yet, but I'm sure he can
+probably I don't know where he what he
+
+ align:start position:0%
+probably I don't know where he what he
+ 
+
+ align:start position:0%
+probably I don't know where he what he
+thinks about pornography. Um although
+
+ align:start position:0%
+thinks about pornography. Um although
+ 
+
+ align:start position:0%
+thinks about pornography. Um although
+since it's in film form, maybe he does
+
+ align:start position:0%
+since it's in film form, maybe he does
+ 
+
+ align:start position:0%
+since it's in film form, maybe he does
+think it's art. It's unclear. He hasn't
+
+ align:start position:0%
+think it's art. It's unclear. He hasn't
+ 
+
+ align:start position:0%
+think it's art. It's unclear. He hasn't
+he hasn't weighed in on that yet. Um but
+
+ align:start position:0%
+he hasn't weighed in on that yet. Um but
+ 
+
+ align:start position:0%
+he hasn't weighed in on that yet. Um but
+the interesting thing about this is this
+
+ align:start position:0%
+the interesting thing about this is this
+ 
+
+ align:start position:0%
+the interesting thing about this is this
+is not this is not new, right? This is
+
+ align:start position:0%
+is not this is not new, right? This is
+ 
+
+ align:start position:0%
+is not this is not new, right? This is
+like a high culture, low culture debate
+
+ align:start position:0%
+like a high culture, low culture debate
+ 
+
+ align:start position:0%
+like a high culture, low culture debate
+that's been going on for a really long
+
+ align:start position:0%
+that's been going on for a really long
+ 
+
+ align:start position:0%
+that's been going on for a really long
+time. And I think it's particularly
+
+ align:start position:0%
+time. And I think it's particularly
+ 
+
+ align:start position:0%
+time. And I think it's particularly
+hilarious because he reviews films and
+
+ align:start position:0%
+hilarious because he reviews films and
+ 
+
+ align:start position:0%
+hilarious because he reviews films and
+films had to fight out of the low
+
+ align:start position:0%
+films had to fight out of the low
+ 
+
+ align:start position:0%
+films had to fight out of the low
+culture phenomenon to gain respect as a
+
+ align:start position:0%
+culture phenomenon to gain respect as a
+ 
+
+ align:start position:0%
+culture phenomenon to gain respect as a
+high culture medium, right? And so he's
+
+ align:start position:0%
+high culture medium, right? And so he's
+ 
+
+ align:start position:0%
+high culture medium, right? And so he's
+he's working reviewing a medium that
+
+ align:start position:0%
+he's working reviewing a medium that
+ 
+
+ align:start position:0%
+he's working reviewing a medium that
+that was once conceived as low culture,
+
+ align:start position:0%
+that was once conceived as low culture,
+ 
+
+ align:start position:0%
+that was once conceived as low culture,
+had to work really hard to be considered
+
+ align:start position:0%
+had to work really hard to be considered
+ 
+
+ align:start position:0%
+had to work really hard to be considered
+high culture. And now he's saying,
+
+ align:start position:0%
+high culture. And now he's saying,
+ 
+
+ align:start position:0%
+high culture. And now he's saying,
+"Look, my films are high culture, your
+
+ align:start position:0%
+"Look, my films are high culture, your
+ 
+
+ align:start position:0%
+"Look, my films are high culture, your
+video games are low culture." um which
+
+ align:start position:0%
+video games are low culture." um which
+ 
+
+ align:start position:0%
+video games are low culture." um which
+is totally hilarious because you know in
+
+ align:start position:0%
+is totally hilarious because you know in
+ 
+
+ align:start position:0%
+is totally hilarious because you know in
+the past 50 years um this has been
+
+ align:start position:0%
+the past 50 years um this has been
+ 
+
+ align:start position:0%
+the past 50 years um this has been
+completely collapsed by postmodernism
+
+ align:start position:0%
+completely collapsed by postmodernism
+ 
+
+ align:start position:0%
+completely collapsed by postmodernism
+right but this is a this is that's a
+
+ align:start position:0%
+right but this is a this is that's a
+ 
+
+ align:start position:0%
+right but this is a this is that's a
+whole another talk alto together right
+
+ align:start position:0%
+whole another talk alto together right
+ 
+
+ align:start position:0%
+whole another talk alto together right
+like maybe high culture and low culture
+
+ align:start position:0%
+like maybe high culture and low culture
+ 
+
+ align:start position:0%
+like maybe high culture and low culture
+don't even exist anymore um so Ebert
+
+ align:start position:0%
+don't even exist anymore um so Ebert
+ 
+
+ align:start position:0%
+don't even exist anymore um so Ebert
+brings this all back and he get
+
+ align:start position:0%
+brings this all back and he get
+ 
+
+ align:start position:0%
+brings this all back and he get
+everybody upset and a bunch of trolls
+
+ align:start position:0%
+everybody upset and a bunch of trolls
+ 
+
+ align:start position:0%
+everybody upset and a bunch of trolls
+are on his website saying really
+
+ align:start position:0%
+are on his website saying really
+ 
+
+ align:start position:0%
+are on his website saying really
+terrible things about him and about what
+
+ align:start position:0%
+terrible things about him and about what
+ 
+
+ align:start position:0%
+terrible things about him and about what
+he said but he he kind of reinvigorated
+
+ align:start position:0%
+he said but he he kind of reinvigorated
+ 
+
+ align:start position:0%
+he said but he he kind of reinvigorated
+this talk um and so a new scientist
+
+ align:start position:0%
+this talk um and so a new scientist
+ 
+
+ align:start position:0%
+this talk um and so a new scientist
+inspired by this eert controversy and
+
+ align:start position:0%
+inspired by this eert controversy and
+ 
+
+ align:start position:0%
+inspired by this eert controversy and
+looking for content um on culture lab
+
+ align:start position:0%
+looking for content um on culture lab
+ 
+
+ align:start position:0%
+looking for content um on culture lab
+asked the question can games VR and they
+
+ align:start position:0%
+asked the question can games VR and they
+ 
+
+ align:start position:0%
+asked the question can games VR and they
+sent it out to a bunch of game scholars
+
+ align:start position:0%
+sent it out to a bunch of game scholars
+ 
+
+ align:start position:0%
+sent it out to a bunch of game scholars
+saying what what is your opinion on
+
+ align:start position:0%
+saying what what is your opinion on
+ 
+
+ align:start position:0%
+saying what what is your opinion on
+this? Um and Ian Bogost is is a is a
+
+ align:start position:0%
+this? Um and Ian Bogost is is a is a
+ 
+
+ align:start position:0%
+this? Um and Ian Bogost is is a is a
+very smart guy and and said says you
+
+ align:start position:0%
+very smart guy and and said says you
+ 
+
+ align:start position:0%
+very smart guy and and said says you
+know some really interesting things.
+
+ align:start position:0%
+know some really interesting things.
+ 
+
+ align:start position:0%
+know some really interesting things.
+This is really long. I'm not going to
+
+ align:start position:0%
+This is really long. I'm not going to
+ 
+
+ align:start position:0%
+This is really long. I'm not going to
+read the whole thing but in the first
+
+ align:start position:0%
+read the whole thing but in the first
+ 
+
+ align:start position:0%
+read the whole thing but in the first
+paragraph you know he brings up things
+
+ align:start position:0%
+paragraph you know he brings up things
+ 
+
+ align:start position:0%
+paragraph you know he brings up things
+like fountain uh by Marcel Duchamp which
+
+ align:start position:0%
+like fountain uh by Marcel Duchamp which
+ 
+
+ align:start position:0%
+like fountain uh by Marcel Duchamp which
+is you know a urinal um in a museum for
+
+ align:start position:0%
+is you know a urinal um in a museum for
+ 
+
+ align:start position:0%
+is you know a urinal um in a museum for
+those of you who don't know about it.
+
+ align:start position:0%
+those of you who don't know about it.
+ 
+
+ align:start position:0%
+those of you who don't know about it.
+And that was, you know, that was a
+
+ align:start position:0%
+And that was, you know, that was a
+ 
+
+ align:start position:0%
+And that was, you know, that was a
+statement, a piece of art that he was
+
+ align:start position:0%
+statement, a piece of art that he was
+ 
+
+ align:start position:0%
+statement, a piece of art that he was
+literally trying to confront what what
+
+ align:start position:0%
+literally trying to confront what what
+ 
+
+ align:start position:0%
+literally trying to confront what what
+high culture defines as art by taking
+
+ align:start position:0%
+high culture defines as art by taking
+ 
+
+ align:start position:0%
+high culture defines as art by taking
+literally a urinal, putting it upside
+
+ align:start position:0%
+literally a urinal, putting it upside
+ 
+
+ align:start position:0%
+literally a urinal, putting it upside
+down on art and titling it fountain,
+
+ align:start position:0%
+down on art and titling it fountain,
+ 
+
+ align:start position:0%
+down on art and titling it fountain,
+upside down on a pedal and titling it
+
+ align:start position:0%
+upside down on a pedal and titling it
+ 
+
+ align:start position:0%
+upside down on a pedal and titling it
+fountain and putting it in a museum,
+
+ align:start position:0%
+fountain and putting it in a museum,
+ 
+
+ align:start position:0%
+fountain and putting it in a museum,
+which is the pinnacle of high culture,
+
+ align:start position:0%
+which is the pinnacle of high culture,
+ 
+
+ align:start position:0%
+which is the pinnacle of high culture,
+right? If you can make it in a museum,
+
+ align:start position:0%
+right? If you can make it in a museum,
+ 
+
+ align:start position:0%
+right? If you can make it in a museum,
+your art. Um, and so, you know, this is
+
+ align:start position:0%
+your art. Um, and so, you know, this is
+ 
+
+ align:start position:0%
+your art. Um, and so, you know, this is
+something that, you know, that he did.
+
+ align:start position:0%
+something that, you know, that he did.
+ 
+
+ align:start position:0%
+something that, you know, that he did.
+He he mentions Yoko Ono's performance
+
+ align:start position:0%
+He he mentions Yoko Ono's performance
+ 
+
+ align:start position:0%
+He he mentions Yoko Ono's performance
+art where, um, she's sitting in a chair
+
+ align:start position:0%
+art where, um, she's sitting in a chair
+ 
+
+ align:start position:0%
+art where, um, she's sitting in a chair
+um, and she has scissors next to her and
+
+ align:start position:0%
+um, and she has scissors next to her and
+ 
+
+ align:start position:0%
+um, and she has scissors next to her and
+the audience is invited to come uh, cut
+
+ align:start position:0%
+the audience is invited to come uh, cut
+ 
+
+ align:start position:0%
+the audience is invited to come uh, cut
+her clothes off one piece at a time. um
+
+ align:start position:0%
+her clothes off one piece at a time. um
+ 
+
+ align:start position:0%
+her clothes off one piece at a time. um
+you know a lot of this kind of stuff you
+
+ align:start position:0%
+you know a lot of this kind of stuff you
+ 
+
+ align:start position:0%
+you know a lot of this kind of stuff you
+know uh Andy Warhol pop culture
+
+ align:start position:0%
+know uh Andy Warhol pop culture
+ 
+
+ align:start position:0%
+know uh Andy Warhol pop culture
+paintings um you know Mandrean's uh kind
+
+ align:start position:0%
+paintings um you know Mandrean's uh kind
+ 
+
+ align:start position:0%
+paintings um you know Mandrean's uh kind
+of uh you know abstract paintings and
+
+ align:start position:0%
+of uh you know abstract paintings and
+ 
+
+ align:start position:0%
+of uh you know abstract paintings and
+and um you know he says a lot in that
+
+ align:start position:0%
+and um you know he says a lot in that
+ 
+
+ align:start position:0%
+and um you know he says a lot in that
+first paragraph but I think this this
+
+ align:start position:0%
+first paragraph but I think this this
+ 
+
+ align:start position:0%
+first paragraph but I think this this
+interesting part that I sort of pseudo
+
+ align:start position:0%
+interesting part that I sort of pseudo
+ 
+
+ align:start position:0%
+interesting part that I sort of pseudo
+highlighted down here is interesting um
+
+ align:start position:0%
+highlighted down here is interesting um
+ 
+
+ align:start position:0%
+highlighted down here is interesting um
+starting in the middle he says if the
+
+ align:start position:0%
+starting in the middle he says if the
+ 
+
+ align:start position:0%
+starting in the middle he says if the
+purpose of art is indeed to force us to
+
+ align:start position:0%
+purpose of art is indeed to force us to
+ 
+
+ align:start position:0%
+purpose of art is indeed to force us to
+see something we thought we understood
+
+ align:start position:0%
+see something we thought we understood
+ 
+
+ align:start position:0%
+see something we thought we understood
+in a new light perhaps the most
+
+ align:start position:0%
+in a new light perhaps the most
+ 
+
+ align:start position:0%
+in a new light perhaps the most
+fundamental move video games have made
+
+ align:start position:0%
+fundamental move video games have made
+ 
+
+ align:start position:0%
+fundamental move video games have made
+in the artistic tradition is in the very
+
+ align:start position:0%
+in the artistic tradition is in the very
+ 
+
+ align:start position:0%
+in the artistic tradition is in the very
+eliciting of the question can video
+
+ align:start position:0%
+eliciting of the question can video
+ 
+
+ align:start position:0%
+eliciting of the question can video
+games be art I I think that's really
+
+ align:start position:0%
+games be art I I think that's really
+ 
+
+ align:start position:0%
+games be art I I think that's really
+interesting, right? So, the fact that
+
+ align:start position:0%
+interesting, right? So, the fact that
+ 
+
+ align:start position:0%
+interesting, right? So, the fact that
+people are even asking this question
+
+ align:start position:0%
+people are even asking this question
+ 
+
+ align:start position:0%
+people are even asking this question
+suggests that video games are doing
+
+ align:start position:0%
+suggests that video games are doing
+ 
+
+ align:start position:0%
+suggests that video games are doing
+something that aren't we traditionally
+
+ align:start position:0%
+something that aren't we traditionally
+ 
+
+ align:start position:0%
+something that aren't we traditionally
+conceive of aren't doing. Um, and so
+
+ align:start position:0%
+conceive of aren't doing. Um, and so
+ 
+
+ align:start position:0%
+conceive of aren't doing. Um, and so
+that's, you know, that's I think a
+
+ align:start position:0%
+that's, you know, that's I think a
+ 
+
+ align:start position:0%
+that's, you know, that's I think a
+really kind of powerful statement that
+
+ align:start position:0%
+really kind of powerful statement that
+ 
+
+ align:start position:0%
+really kind of powerful statement that
+that we're even having this discussion.
+
+ align:start position:0%
+that we're even having this discussion.
+ 
+
+ align:start position:0%
+that we're even having this discussion.
+It kind of renders the question question
+
+ align:start position:0%
+It kind of renders the question question
+ 
+
+ align:start position:0%
+It kind of renders the question question
+moot in some senses, which which is, you
+
+ align:start position:0%
+moot in some senses, which which is, you
+ 
+
+ align:start position:0%
+moot in some senses, which which is, you
+know, kind of I would say classic Bosian
+
+ align:start position:0%
+know, kind of I would say classic Bosian
+ 
+
+ align:start position:0%
+know, kind of I would say classic Bosian
+um word play. Um, I think I just made
+
+ align:start position:0%
+um word play. Um, I think I just made
+ 
+
+ align:start position:0%
+um word play. Um, I think I just made
+something up called Bosian.
+
+ align:start position:0%
+something up called Bosian.
+ 
+
+ align:start position:0%
+something up called Bosian.
+tweet him about. Um, so John Sharp from
+
+ align:start position:0%
+tweet him about. Um, so John Sharp from
+ 
+
+ align:start position:0%
+tweet him about. Um, so John Sharp from
+the Savannah College of Art Design um
+
+ align:start position:0%
+the Savannah College of Art Design um
+ 
+
+ align:start position:0%
+the Savannah College of Art Design um
+has had a lot of kind of thoughts on
+
+ align:start position:0%
+has had a lot of kind of thoughts on
+ 
+
+ align:start position:0%
+has had a lot of kind of thoughts on
+this. He's and he's actually a great
+
+ align:start position:0%
+this. He's and he's actually a great
+ 
+
+ align:start position:0%
+this. He's and he's actually a great
+person to talk about this because he
+
+ align:start position:0%
+person to talk about this because he
+ 
+
+ align:start position:0%
+person to talk about this because he
+studies video games, but he does it from
+
+ align:start position:0%
+studies video games, but he does it from
+ 
+
+ align:start position:0%
+studies video games, but he does it from
+an art history background as well,
+
+ align:start position:0%
+an art history background as well,
+ 
+
+ align:start position:0%
+an art history background as well,
+right? And that's particularly useful.
+
+ align:start position:0%
+right? And that's particularly useful.
+ 
+
+ align:start position:0%
+right? And that's particularly useful.
+Um, and uh, you know, he talks about
+
+ align:start position:0%
+Um, and uh, you know, he talks about
+ 
+
+ align:start position:0%
+Um, and uh, you know, he talks about
+some interesting things here. He talks
+
+ align:start position:0%
+some interesting things here. He talks
+ 
+
+ align:start position:0%
+some interesting things here. He talks
+about, you know, similarly similarly to
+
+ align:start position:0%
+about, you know, similarly similarly to
+ 
+
+ align:start position:0%
+about, you know, similarly similarly to
+what Ian was doing. He's talking a bit
+
+ align:start position:0%
+what Ian was doing. He's talking a bit
+ 
+
+ align:start position:0%
+what Ian was doing. He's talking a bit
+about how um you know video games and
+
+ align:start position:0%
+about how um you know video games and
+ 
+
+ align:start position:0%
+about how um you know video games and
+art are are kind of doing some similar
+
+ align:start position:0%
+art are are kind of doing some similar
+ 
+
+ align:start position:0%
+art are are kind of doing some similar
+things at times and yet games you know
+
+ align:start position:0%
+things at times and yet games you know
+ 
+
+ align:start position:0%
+things at times and yet games you know
+have certain affordances that other
+
+ align:start position:0%
+have certain affordances that other
+ 
+
+ align:start position:0%
+have certain affordances that other
+media do not. Um and so uh he says at
+
+ align:start position:0%
+media do not. Um and so uh he says at
+ 
+
+ align:start position:0%
+media do not. Um and so uh he says at
+the end here which I think is
+
+ align:start position:0%
+the end here which I think is
+ 
+
+ align:start position:0%
+the end here which I think is
+interesting all this poses the question
+
+ align:start position:0%
+interesting all this poses the question
+ 
+
+ align:start position:0%
+interesting all this poses the question
+of why are we concerned with giving
+
+ align:start position:0%
+of why are we concerned with giving
+ 
+
+ align:start position:0%
+of why are we concerned with giving
+video games the status of art? This is
+
+ align:start position:0%
+video games the status of art? This is
+ 
+
+ align:start position:0%
+video games the status of art? This is
+one of the reasons why I hate this
+
+ align:start position:0%
+one of the reasons why I hate this
+ 
+
+ align:start position:0%
+one of the reasons why I hate this
+question. Are we simply trying to
+
+ align:start position:0%
+question. Are we simply trying to
+ 
+
+ align:start position:0%
+question. Are we simply trying to
+legitimize them? Does being called quote
+
+ align:start position:0%
+legitimize them? Does being called quote
+ 
+
+ align:start position:0%
+legitimize them? Does being called quote
+unquote art change the qualities of
+
+ align:start position:0%
+unquote art change the qualities of
+ 
+
+ align:start position:0%
+unquote art change the qualities of
+video games? Um only if we can answer
+
+ align:start position:0%
+video games? Um only if we can answer
+ 
+
+ align:start position:0%
+video games? Um only if we can answer
+these questions can we move the
+
+ align:start position:0%
+these questions can we move the
+ 
+
+ align:start position:0%
+these questions can we move the
+conversation forward? And I I think he's
+
+ align:start position:0%
+conversation forward? And I I think he's
+ 
+
+ align:start position:0%
+conversation forward? And I I think he's
+you know he's reacting here to the
+
+ align:start position:0%
+you know he's reacting here to the
+ 
+
+ align:start position:0%
+you know he's reacting here to the
+question itself. Actually he and Ian
+
+ align:start position:0%
+question itself. Actually he and Ian
+ 
+
+ align:start position:0%
+question itself. Actually he and Ian
+both are kind of reacting to the
+
+ align:start position:0%
+both are kind of reacting to the
+ 
+
+ align:start position:0%
+both are kind of reacting to the
+question. Ian saying the question
+
+ align:start position:0%
+question. Ian saying the question
+ 
+
+ align:start position:0%
+question. Ian saying the question
+invalidates itself and John Sharp now
+
+ align:start position:0%
+invalidates itself and John Sharp now
+ 
+
+ align:start position:0%
+invalidates itself and John Sharp now
+saying that we need this question it's
+
+ align:start position:0%
+saying that we need this question it's
+ 
+
+ align:start position:0%
+saying that we need this question it's
+not helping us asking you know how does
+
+ align:start position:0%
+not helping us asking you know how does
+ 
+
+ align:start position:0%
+not helping us asking you know how does
+calling it art what does that do for the
+
+ align:start position:0%
+calling it art what does that do for the
+ 
+
+ align:start position:0%
+calling it art what does that do for the
+medium? That's the important question
+
+ align:start position:0%
+medium? That's the important question
+ 
+
+ align:start position:0%
+medium? That's the important question
+right and so here's some some thoughts
+
+ align:start position:0%
+right and so here's some some thoughts
+ 
+
+ align:start position:0%
+right and so here's some some thoughts
+about the question and and some kind of
+
+ align:start position:0%
+about the question and and some kind of
+ 
+
+ align:start position:0%
+about the question and and some kind of
+more evidence for why I think the
+
+ align:start position:0%
+more evidence for why I think the
+ 
+
+ align:start position:0%
+more evidence for why I think the
+question are video games art is just h
+
+ align:start position:0%
+question are video games art is just h
+ 
+
+ align:start position:0%
+question are video games art is just h
+makes my spine problem. Um, Mary
+
+ align:start position:0%
+makes my spine problem. Um, Mary
+ 
+
+ align:start position:0%
+makes my spine problem. Um, Mary
+Flanigan uh sort of takes it uh takes it
+
+ align:start position:0%
+Flanigan uh sort of takes it uh takes it
+ 
+
+ align:start position:0%
+Flanigan uh sort of takes it uh takes it
+as being assumed that video games are
+
+ align:start position:0%
+as being assumed that video games are
+ 
+
+ align:start position:0%
+as being assumed that video games are
+art, which I think is actually great. In
+
+ align:start position:0%
+art, which I think is actually great. In
+ 
+
+ align:start position:0%
+art, which I think is actually great. In
+Critical Play, she doesn't go to great
+
+ align:start position:0%
+Critical Play, she doesn't go to great
+ 
+
+ align:start position:0%
+Critical Play, she doesn't go to great
+lengths to define video games as art.
+
+ align:start position:0%
+lengths to define video games as art.
+ 
+
+ align:start position:0%
+lengths to define video games as art.
+She just looks at art and she looks at
+
+ align:start position:0%
+She just looks at art and she looks at
+ 
+
+ align:start position:0%
+She just looks at art and she looks at
+games and and compares them. Um, and she
+
+ align:start position:0%
+games and and compares them. Um, and she
+ 
+
+ align:start position:0%
+games and and compares them. Um, and she
+just kind of assumes that this is so and
+
+ align:start position:0%
+just kind of assumes that this is so and
+ 
+
+ align:start position:0%
+just kind of assumes that this is so and
+I think this is a really nice quote from
+
+ align:start position:0%
+I think this is a really nice quote from
+ 
+
+ align:start position:0%
+I think this is a really nice quote from
+from really the beginning of her
+
+ align:start position:0%
+from really the beginning of her
+ 
+
+ align:start position:0%
+from really the beginning of her
+critical playbook. Um, where she says,
+
+ align:start position:0%
+critical playbook. Um, where she says,
+ 
+
+ align:start position:0%
+critical playbook. Um, where she says,
+"Critical play is built on the premise
+
+ align:start position:0%
+"Critical play is built on the premise
+ 
+
+ align:start position:0%
+"Critical play is built on the premise
+that as with other media, games carry
+
+ align:start position:0%
+that as with other media, games carry
+ 
+
+ align:start position:0%
+that as with other media, games carry
+beliefs within their representation
+
+ align:start position:0%
+beliefs within their representation
+ 
+
+ align:start position:0%
+beliefs within their representation
+systems and mechanics." This is really
+
+ align:start position:0%
+systems and mechanics." This is really
+ 
+
+ align:start position:0%
+systems and mechanics." This is really
+important. artists using games as a
+
+ align:start position:0%
+important. artists using games as a
+ 
+
+ align:start position:0%
+important. artists using games as a
+medium of expression. Again, good use of
+
+ align:start position:0%
+medium of expression. Again, good use of
+ 
+
+ align:start position:0%
+medium of expression. Again, good use of
+italics. Um, then manipulate elements
+
+ align:start position:0%
+italics. Um, then manipulate elements
+ 
+
+ align:start position:0%
+italics. Um, then manipulate elements
+common to games, representation, systems
+
+ align:start position:0%
+common to games, representation, systems
+ 
+
+ align:start position:0%
+common to games, representation, systems
+and styles, rules of progress, codes of
+
+ align:start position:0%
+and styles, rules of progress, codes of
+ 
+
+ align:start position:0%
+and styles, rules of progress, codes of
+conduct, context of perception, winning
+
+ align:start position:0%
+conduct, context of perception, winning
+ 
+
+ align:start position:0%
+conduct, context of perception, winning
+and losing paradigms, ways of
+
+ align:start position:0%
+and losing paradigms, ways of
+ 
+
+ align:start position:0%
+and losing paradigms, ways of
+interacting in a game. For they are the
+
+ align:start position:0%
+interacting in a game. For they are the
+ 
+
+ align:start position:0%
+interacting in a game. For they are the
+material properties of game, much like
+
+ align:start position:0%
+material properties of game, much like
+ 
+
+ align:start position:0%
+material properties of game, much like
+marble and chisel or pen and ink bring
+
+ align:start position:0%
+marble and chisel or pen and ink bring
+ 
+
+ align:start position:0%
+marble and chisel or pen and ink bring
+with them their own intended
+
+ align:start position:0%
+with them their own intended
+ 
+
+ align:start position:0%
+with them their own intended
+possibilities, limitations, and
+
+ align:start position:0%
+possibilities, limitations, and
+ 
+
+ align:start position:0%
+possibilities, limitations, and
+conventions. It's a great point. You
+
+ align:start position:0%
+conventions. It's a great point. You
+ 
+
+ align:start position:0%
+conventions. It's a great point. You
+would have a really hard time making a
+
+ align:start position:0%
+would have a really hard time making a
+ 
+
+ align:start position:0%
+would have a really hard time making a
+painting with a chisel um and no paint,
+
+ align:start position:0%
+painting with a chisel um and no paint,
+ 
+
+ align:start position:0%
+painting with a chisel um and no paint,
+right? Like if you were using marble and
+
+ align:start position:0%
+right? Like if you were using marble and
+ 
+
+ align:start position:0%
+right? Like if you were using marble and
+a chisel and you were trying to make a
+
+ align:start position:0%
+a chisel and you were trying to make a
+ 
+
+ align:start position:0%
+a chisel and you were trying to make a
+painting, right? Two different things.
+
+ align:start position:0%
+painting, right? Two different things.
+ 
+
+ align:start position:0%
+painting, right? Two different things.
+Both are art. It's the same thing with
+
+ align:start position:0%
+Both are art. It's the same thing with
+ 
+
+ align:start position:0%
+Both are art. It's the same thing with
+games, right? Games have rule sets.
+
+ align:start position:0%
+games, right? Games have rule sets.
+ 
+
+ align:start position:0%
+games, right? Games have rule sets.
+Games have systems. Uh games have, you
+
+ align:start position:0%
+Games have systems. Uh games have, you
+ 
+
+ align:start position:0%
+Games have systems. Uh games have, you
+know, win loss paradigms. They have all
+
+ align:start position:0%
+know, win loss paradigms. They have all
+ 
+
+ align:start position:0%
+know, win loss paradigms. They have all
+these things that are um kind of
+
+ align:start position:0%
+these things that are um kind of
+ 
+
+ align:start position:0%
+these things that are um kind of
+conventions and and things that we
+
+ align:start position:0%
+conventions and and things that we
+ 
+
+ align:start position:0%
+conventions and and things that we
+associate with with even our definition
+
+ align:start position:0%
+associate with with even our definition
+ 
+
+ align:start position:0%
+associate with with even our definition
+of what a game is, which is at times
+
+ align:start position:0%
+of what a game is, which is at times
+ 
+
+ align:start position:0%
+of what a game is, which is at times
+faulty. Um but but those are our tools.
+
+ align:start position:0%
+faulty. Um but but those are our tools.
+ 
+
+ align:start position:0%
+faulty. Um but but those are our tools.
+Those are how we communicate things. And
+
+ align:start position:0%
+Those are how we communicate things. And
+ 
+
+ align:start position:0%
+Those are how we communicate things. And
+I think her first sentence is really
+
+ align:start position:0%
+I think her first sentence is really
+ 
+
+ align:start position:0%
+I think her first sentence is really
+important. And um I'm guessing with the
+
+ align:start position:0%
+important. And um I'm guessing with the
+ 
+
+ align:start position:0%
+important. And um I'm guessing with the
+with the stuff that you've been talking
+
+ align:start position:0%
+with the stuff that you've been talking
+ 
+
+ align:start position:0%
+with the stuff that you've been talking
+about with them and Gonzalo Frasa um you
+
+ align:start position:0%
+about with them and Gonzalo Frasa um you
+ 
+
+ align:start position:0%
+about with them and Gonzalo Frasa um you
+know that that's kind of coming through
+
+ align:start position:0%
+know that that's kind of coming through
+ 
+
+ align:start position:0%
+know that that's kind of coming through
+and and I actually see that in your
+
+ align:start position:0%
+and and I actually see that in your
+ 
+
+ align:start position:0%
+and and I actually see that in your
+games right you're trying to so for
+
+ align:start position:0%
+games right you're trying to so for
+ 
+
+ align:start position:0%
+games right you're trying to so for
+example I I play tested that FedEx game
+
+ align:start position:0%
+example I I play tested that FedEx game
+ 
+
+ align:start position:0%
+example I I play tested that FedEx game
+and I play tested um the game about
+
+ align:start position:0%
+and I play tested um the game about
+ 
+
+ align:start position:0%
+and I play tested um the game about
+marriage right and there's there's all
+
+ align:start position:0%
+marriage right and there's there's all
+ 
+
+ align:start position:0%
+marriage right and there's there's all
+kinds of meaning in those systems and
+
+ align:start position:0%
+kinds of meaning in those systems and
+ 
+
+ align:start position:0%
+kinds of meaning in those systems and
+meanings in those choices that you get
+
+ align:start position:0%
+meanings in those choices that you get
+ 
+
+ align:start position:0%
+meanings in those choices that you get
+um that that are being communicated and
+
+ align:start position:0%
+um that that are being communicated and
+ 
+
+ align:start position:0%
+um that that are being communicated and
+that's that's very similar to what an
+
+ align:start position:0%
+that's that's very similar to what an
+ 
+
+ align:start position:0%
+that's that's very similar to what an
+artist would do with with any other
+
+ align:start position:0%
+artist would do with with any other
+ 
+
+ align:start position:0%
+artist would do with with any other
+medium right you're you're communicating
+
+ align:start position:0%
+medium right you're you're communicating
+ 
+
+ align:start position:0%
+medium right you're you're communicating
+a message through those and and and
+
+ align:start position:0%
+a message through those and and and
+ 
+
+ align:start position:0%
+a message through those and and and
+sometimes we do it accidentally it's
+
+ align:start position:0%
+sometimes we do it accidentally it's
+ 
+
+ align:start position:0%
+sometimes we do it accidentally it's
+it's not always explicit Right. It's
+
+ align:start position:0%
+it's not always explicit Right. It's
+ 
+
+ align:start position:0%
+it's not always explicit Right. It's
+like we we make something. I I always
+
+ align:start position:0%
+like we we make something. I I always
+ 
+
+ align:start position:0%
+like we we make something. I I always
+say that the the um the graveyard and
+
+ align:start position:0%
+say that the the um the graveyard and
+ 
+
+ align:start position:0%
+say that the the um the graveyard and
+when you get divorced and you put your
+
+ align:start position:0%
+when you get divorced and you put your
+ 
+
+ align:start position:0%
+when you get divorced and you put your
+your divorced person in the graveyard
+
+ align:start position:0%
+your divorced person in the graveyard
+ 
+
+ align:start position:0%
+your divorced person in the graveyard
+was an interesting choice for me because
+
+ align:start position:0%
+was an interesting choice for me because
+ 
+
+ align:start position:0%
+was an interesting choice for me because
+it was creating an equivalence between
+
+ align:start position:0%
+it was creating an equivalence between
+ 
+
+ align:start position:0%
+it was creating an equivalence between
+divorce and death which I think is kind
+
+ align:start position:0%
+divorce and death which I think is kind
+ 
+
+ align:start position:0%
+divorce and death which I think is kind
+of interesting. Um so that's just you
+
+ align:start position:0%
+of interesting. Um so that's just you
+ 
+
+ align:start position:0%
+of interesting. Um so that's just you
+know kind of one interesting example. Um
+
+ align:start position:0%
+know kind of one interesting example. Um
+ 
+
+ align:start position:0%
+know kind of one interesting example. Um
+so Mary Flang in her book talks about
+
+ align:start position:0%
+so Mary Flang in her book talks about
+ 
+
+ align:start position:0%
+so Mary Flang in her book talks about
+this art movement called Plexus. Before
+
+ align:start position:0%
+this art movement called Plexus. Before
+ 
+
+ align:start position:0%
+this art movement called Plexus. Before
+I go on any kind of thoughts or
+
+ align:start position:0%
+I go on any kind of thoughts or
+ 
+
+ align:start position:0%
+I go on any kind of thoughts or
+questions does anybody else think does
+
+ align:start position:0%
+questions does anybody else think does
+ 
+
+ align:start position:0%
+questions does anybody else think does
+anybody think video games aren't art
+
+ align:start position:0%
+anybody think video games aren't art
+ 
+
+ align:start position:0%
+anybody think video games aren't art
+still? It's okay. Oh crap, I'm gonna
+
+ align:start position:0%
+still? It's okay. Oh crap, I'm gonna
+ 
+
+ align:start position:0%
+still? It's okay. Oh crap, I'm gonna
+fight.
+
+ align:start position:0%
+fight.
+ 
+
+ align:start position:0%
+fight.
+>> Totally different. Like when we were
+
+ align:start position:0%
+>> Totally different. Like when we were
+ 
+
+ align:start position:0%
+>> Totally different. Like when we were
+designing our so our project now is you
+
+ align:start position:0%
+designing our so our project now is you
+ 
+
+ align:start position:0%
+designing our so our project now is you
+have to choose a real world
+
+ align:start position:0%
+have to choose a real world
+ 
+
+ align:start position:0%
+have to choose a real world
+>> system and emulate it.
+
+ align:start position:0%
+>> system and emulate it.
+ 
+
+ align:start position:0%
+>> system and emulate it.
+>> That's what we're all working on.
+
+ align:start position:0%
+>> That's what we're all working on.
+ 
+
+ align:start position:0%
+>> That's what we're all working on.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> And one of the big things like that
+
+ align:start position:0%
+>> And one of the big things like that
+ 
+
+ align:start position:0%
+>> And one of the big things like that
+really helped us get started was like
+
+ align:start position:0%
+really helped us get started was like
+ 
+
+ align:start position:0%
+really helped us get started was like
+what is the message we want to get
+
+ align:start position:0%
+what is the message we want to get
+ 
+
+ align:start position:0%
+what is the message we want to get
+across? So we chose evolution was what
+
+ align:start position:0%
+across? So we chose evolution was what
+ 
+
+ align:start position:0%
+across? So we chose evolution was what
+is it about evolution? Do you want to
+
+ align:start position:0%
+is it about evolution? Do you want to
+ 
+
+ align:start position:0%
+is it about evolution? Do you want to
+say that it's random? Do you want to say
+
+ align:start position:0%
+say that it's random? Do you want to say
+ 
+
+ align:start position:0%
+say that it's random? Do you want to say
+that as this? And how do we express
+
+ align:start position:0%
+that as this? And how do we express
+ 
+
+ align:start position:0%
+that as this? And how do we express
+that? How we got into it.
+
+ align:start position:0%
+that? How we got into it.
+ 
+
+ align:start position:0%
+that? How we got into it.
+>> Yeah. No, totally. And it gets even it
+
+ align:start position:0%
+>> Yeah. No, totally. And it gets even it
+ 
+
+ align:start position:0%
+>> Yeah. No, totally. And it gets even it
+gets even crazier when you take when you
+
+ align:start position:0%
+gets even crazier when you take when you
+ 
+
+ align:start position:0%
+gets even crazier when you take when you
+try to look at systems that are not
+
+ align:start position:0%
+try to look at systems that are not
+ 
+
+ align:start position:0%
+try to look at systems that are not
+particularly tangible, right? So, you
+
+ align:start position:0%
+particularly tangible, right? So, you
+ 
+
+ align:start position:0%
+particularly tangible, right? So, you
+know, um maybe you've looked at it, but
+
+ align:start position:0%
+know, um maybe you've looked at it, but
+ 
+
+ align:start position:0%
+know, um maybe you've looked at it, but
+um you know uh Elude is a game about
+
+ align:start position:0%
+um you know uh Elude is a game about
+ 
+
+ align:start position:0%
+um you know uh Elude is a game about
+depression, right? Like there there
+
+ align:start position:0%
+depression, right? Like there there
+ 
+
+ align:start position:0%
+depression, right? Like there there
+there aren't exactly tangible kind of
+
+ align:start position:0%
+there aren't exactly tangible kind of
+ 
+
+ align:start position:0%
+there aren't exactly tangible kind of
+road maps the way there are with like
+
+ align:start position:0%
+road maps the way there are with like
+ 
+
+ align:start position:0%
+road maps the way there are with like
+FedEx systems for for clinical
+
+ align:start position:0%
+FedEx systems for for clinical
+ 
+
+ align:start position:0%
+FedEx systems for for clinical
+depression, right? And yet yet if you're
+
+ align:start position:0%
+depression, right? And yet yet if you're
+ 
+
+ align:start position:0%
+depression, right? And yet yet if you're
+looking at things like emotions,
+
+ align:start position:0%
+looking at things like emotions,
+ 
+
+ align:start position:0%
+looking at things like emotions,
+feelings, um stuff like that that we
+
+ align:start position:0%
+feelings, um stuff like that that we
+ 
+
+ align:start position:0%
+feelings, um stuff like that that we
+might we might call abstract or or um
+
+ align:start position:0%
+might we might call abstract or or um
+ 
+
+ align:start position:0%
+might we might call abstract or or um
+just non- immediate um how do you how do
+
+ align:start position:0%
+just non- immediate um how do you how do
+ 
+
+ align:start position:0%
+just non- immediate um how do you how do
+you uh how do you communicate those in
+
+ align:start position:0%
+you uh how do you communicate those in
+ 
+
+ align:start position:0%
+you uh how do you communicate those in
+systems? Right. It's really tricky.
+
+ align:start position:0%
+systems? Right. It's really tricky.
+ 
+
+ align:start position:0%
+systems? Right. It's really tricky.
+>> I find this is a tougher argument for
+
+ align:start position:0%
+>> I find this is a tougher argument for
+ 
+
+ align:start position:0%
+>> I find this is a tougher argument for
+games which are like more games of
+
+ align:start position:0%
+games which are like more games of
+ 
+
+ align:start position:0%
+games which are like more games of
+chance or more abstract
+
+ align:start position:0%
+chance or more abstract
+ 
+
+ align:start position:0%
+chance or more abstract
+zoker art.
+
+ align:start position:0%
+zoker art.
+ 
+
+ align:start position:0%
+zoker art.
+>> Yeah, I mean it's it's a really good
+
+ align:start position:0%
+>> Yeah, I mean it's it's a really good
+ 
+
+ align:start position:0%
+>> Yeah, I mean it's it's a really good
+question.
+
+ align:start position:0%
+question.
+ 
+
+ align:start position:0%
+question.
+>> What do you what do you say about that?
+
+ align:start position:0%
+>> What do you what do you say about that?
+ 
+
+ align:start position:0%
+>> What do you what do you say about that?
+Yeah. I mean, and I think that falls
+
+ align:start position:0%
+Yeah. I mean, and I think that falls
+ 
+
+ align:start position:0%
+Yeah. I mean, and I think that falls
+along the same lines as like, you know,
+
+ align:start position:0%
+along the same lines as like, you know,
+ 
+
+ align:start position:0%
+along the same lines as like, you know,
+like like I said, I mean, does does
+
+ align:start position:0%
+like like I said, I mean, does does
+ 
+
+ align:start position:0%
+like like I said, I mean, does does
+Ebert consider pornography art? I mean,
+
+ align:start position:0%
+Ebert consider pornography art? I mean,
+ 
+
+ align:start position:0%
+Ebert consider pornography art? I mean,
+it's it's like a really difficult
+
+ align:start position:0%
+it's it's like a really difficult
+ 
+
+ align:start position:0%
+it's it's like a really difficult
+question. And that's that's such a much
+
+ align:start position:0%
+question. And that's that's such a much
+ 
+
+ align:start position:0%
+question. And that's that's such a much
+kind of a much larger kind of art
+
+ align:start position:0%
+kind of a much larger kind of art
+ 
+
+ align:start position:0%
+kind of a much larger kind of art
+history debate, right? About like about
+
+ align:start position:0%
+history debate, right? About like about
+ 
+
+ align:start position:0%
+history debate, right? About like about
+has high culture and low culture
+
+ align:start position:0%
+has high culture and low culture
+ 
+
+ align:start position:0%
+has high culture and low culture
+completely collapsed? Has mass media
+
+ align:start position:0%
+completely collapsed? Has mass media
+ 
+
+ align:start position:0%
+completely collapsed? Has mass media
+proliferation like deteriorated
+
+ align:start position:0%
+proliferation like deteriorated
+ 
+
+ align:start position:0%
+proliferation like deteriorated
+conceptions of, you know, of what, you
+
+ align:start position:0%
+conceptions of, you know, of what, you
+ 
+
+ align:start position:0%
+conceptions of, you know, of what, you
+know, really high culture art are versus
+
+ align:start position:0%
+know, really high culture art are versus
+ 
+
+ align:start position:0%
+know, really high culture art are versus
+low culture? And and and I think that's
+
+ align:start position:0%
+low culture? And and and I think that's
+ 
+
+ align:start position:0%
+low culture? And and and I think that's
+um I I don't have particularly good
+
+ align:start position:0%
+um I I don't have particularly good
+ 
+
+ align:start position:0%
+um I I don't have particularly good
+answers for that. You know, I think just
+
+ align:start position:0%
+answers for that. You know, I think just
+ 
+
+ align:start position:0%
+answers for that. You know, I think just
+as as all of the other media that we
+
+ align:start position:0%
+as as all of the other media that we
+ 
+
+ align:start position:0%
+as as all of the other media that we
+look at, like does a Jerry Brookheimr
+
+ align:start position:0%
+look at, like does a Jerry Brookheimr
+ 
+
+ align:start position:0%
+look at, like does a Jerry Brookheimr
+film count as art, right? Just like we
+
+ align:start position:0%
+film count as art, right? Just like we
+ 
+
+ align:start position:0%
+film count as art, right? Just like we
+would look at that and ask that
+
+ align:start position:0%
+would look at that and ask that
+ 
+
+ align:start position:0%
+would look at that and ask that
+question. Um, we don't then, you know,
+
+ align:start position:0%
+question. Um, we don't then, you know,
+ 
+
+ align:start position:0%
+question. Um, we don't then, you know,
+deny the entire medium of film from from
+
+ align:start position:0%
+deny the entire medium of film from from
+ 
+
+ align:start position:0%
+deny the entire medium of film from from
+the possibility of being artistic. Um
+
+ align:start position:0%
+the possibility of being artistic. Um
+ 
+
+ align:start position:0%
+the possibility of being artistic. Um
+there seems to be this desire because
+
+ align:start position:0%
+there seems to be this desire because
+ 
+
+ align:start position:0%
+there seems to be this desire because
+the majority of games in our sector um
+
+ align:start position:0%
+the majority of games in our sector um
+ 
+
+ align:start position:0%
+the majority of games in our sector um
+which I actually completely disagree
+
+ align:start position:0%
+which I actually completely disagree
+ 
+
+ align:start position:0%
+which I actually completely disagree
+with too because if you go far back
+
+ align:start position:0%
+with too because if you go far back
+ 
+
+ align:start position:0%
+with too because if you go far back
+there they're most I should say video
+
+ align:start position:0%
+there they're most I should say video
+ 
+
+ align:start position:0%
+there they're most I should say video
+games but um because most video games
+
+ align:start position:0%
+games but um because most video games
+ 
+
+ align:start position:0%
+games but um because most video games
+are are kind of commercially intended
+
+ align:start position:0%
+are are kind of commercially intended
+ 
+
+ align:start position:0%
+are are kind of commercially intended
+and involve you know fairly similar
+
+ align:start position:0%
+and involve you know fairly similar
+ 
+
+ align:start position:0%
+and involve you know fairly similar
+themes right does that you know preclude
+
+ align:start position:0%
+themes right does that you know preclude
+ 
+
+ align:start position:0%
+themes right does that you know preclude
+the medium from the possibility of being
+
+ align:start position:0%
+the medium from the possibility of being
+ 
+
+ align:start position:0%
+the medium from the possibility of being
+artistic um you know and I go back to
+
+ align:start position:0%
+artistic um you know and I go back to
+ 
+
+ align:start position:0%
+artistic um you know and I go back to
+that Eber kind of comment about like you
+
+ align:start position:0%
+that Eber kind of comment about like you
+ 
+
+ align:start position:0%
+that Eber kind of comment about like you
+know he he he says they they they can't
+
+ align:start position:0%
+know he he he says they they they can't
+ 
+
+ align:start position:0%
+know he he he says they they they can't
+possibly be or at least you know he says
+
+ align:start position:0%
+possibly be or at least you know he says
+ 
+
+ align:start position:0%
+possibly be or at least you know he says
+never is a long time but not in our
+
+ align:start position:0%
+never is a long time but not in our
+ 
+
+ align:start position:0%
+never is a long time but not in our
+lifetime apparently. Is it possible? So,
+
+ align:start position:0%
+lifetime apparently. Is it possible? So,
+ 
+
+ align:start position:0%
+lifetime apparently. Is it possible? So,
+no, it's a good point. Good question.
+
+ align:start position:0%
+no, it's a good point. Good question.
+ 
+
+ align:start position:0%
+no, it's a good point. Good question.
+>> So, there was actually an interesting uh
+
+ align:start position:0%
+>> So, there was actually an interesting uh
+ 
+
+ align:start position:0%
+>> So, there was actually an interesting uh
+effects with us the game that we're
+
+ align:start position:0%
+effects with us the game that we're
+ 
+
+ align:start position:0%
+effects with us the game that we're
+designing, which is essentially like
+
+ align:start position:0%
+designing, which is essentially like
+ 
+
+ align:start position:0%
+designing, which is essentially like
+city building and city creation in in
+
+ align:start position:0%
+city building and city creation in in
+ 
+
+ align:start position:0%
+city building and city creation in in
+the time of like the Roman Empire.
+
+ align:start position:0%
+the time of like the Roman Empire.
+ 
+
+ align:start position:0%
+the time of like the Roman Empire.
+>> Uh, and we actually didn't intend to
+
+ align:start position:0%
+>> Uh, and we actually didn't intend to
+ 
+
+ align:start position:0%
+>> Uh, and we actually didn't intend to
+like instill any meaning in the game,
+
+ align:start position:0%
+like instill any meaning in the game,
+ 
+
+ align:start position:0%
+like instill any meaning in the game,
+but once we actually designed the
+
+ align:start position:0%
+but once we actually designed the
+ 
+
+ align:start position:0%
+but once we actually designed the
+mechanics and stuff, we realized that it
+
+ align:start position:0%
+mechanics and stuff, we realized that it
+ 
+
+ align:start position:0%
+mechanics and stuff, we realized that it
+was essentially a game about the rich
+
+ align:start position:0%
+was essentially a game about the rich
+ 
+
+ align:start position:0%
+was essentially a game about the rich
+getting richer and trying to control the
+
+ align:start position:0%
+getting richer and trying to control the
+ 
+
+ align:start position:0%
+getting richer and trying to control the
+poor. So, it's like there's almost this
+
+ align:start position:0%
+poor. So, it's like there's almost this
+ 
+
+ align:start position:0%
+poor. So, it's like there's almost this
+like inherent meaning that came out from
+
+ align:start position:0%
+like inherent meaning that came out from
+ 
+
+ align:start position:0%
+like inherent meaning that came out from
+just designing the game.
+
+ align:start position:0%
+just designing the game.
+ 
+
+ align:start position:0%
+just designing the game.
+>> Yeah. Yeah. And you almost can't help,
+
+ align:start position:0%
+>> Yeah. Yeah. And you almost can't help,
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. And you almost can't help,
+right, but but have it happen in some
+
+ align:start position:0%
+right, but but have it happen in some
+ 
+
+ align:start position:0%
+right, but but have it happen in some
+instances. It reminds me of a good thing
+
+ align:start position:0%
+instances. It reminds me of a good thing
+ 
+
+ align:start position:0%
+instances. It reminds me of a good thing
+of um that uh Brenda Brathweight put in
+
+ align:start position:0%
+of um that uh Brenda Brathweight put in
+ 
+
+ align:start position:0%
+of um that uh Brenda Brathweight put in
+one of her talks once which was about
+
+ align:start position:0%
+one of her talks once which was about
+ 
+
+ align:start position:0%
+one of her talks once which was about
+the game uh civilization the the mod
+
+ align:start position:0%
+the game uh civilization the the mod
+ 
+
+ align:start position:0%
+the game uh civilization the the mod
+colonization for Civ 4 which is a great
+
+ align:start position:0%
+colonization for Civ 4 which is a great
+ 
+
+ align:start position:0%
+colonization for Civ 4 which is a great
+mod in which you play one of the
+
+ align:start position:0%
+mod in which you play one of the
+ 
+
+ align:start position:0%
+mod in which you play one of the
+European colonizers and you come over to
+
+ align:start position:0%
+European colonizers and you come over to
+ 
+
+ align:start position:0%
+European colonizers and you come over to
+the new world and um you know there's uh
+
+ align:start position:0%
+the new world and um you know there's uh
+ 
+
+ align:start position:0%
+the new world and um you know there's uh
+there's indigenous peoples there and you
+
+ align:start position:0%
+there's indigenous peoples there and you
+ 
+
+ align:start position:0%
+there's indigenous peoples there and you
+have to kind of negotiate with them at
+
+ align:start position:0%
+have to kind of negotiate with them at
+ 
+
+ align:start position:0%
+have to kind of negotiate with them at
+first but eventually they just kind of
+
+ align:start position:0%
+first but eventually they just kind of
+ 
+
+ align:start position:0%
+first but eventually they just kind of
+um you either beat them up and take
+
+ align:start position:0%
+um you either beat them up and take
+ 
+
+ align:start position:0%
+um you either beat them up and take
+their land or they just give it to you
+
+ align:start position:0%
+their land or they just give it to you
+ 
+
+ align:start position:0%
+their land or they just give it to you
+because you're more powerful than they
+
+ align:start position:0%
+because you're more powerful than they
+ 
+
+ align:start position:0%
+because you're more powerful than they
+are. She was making the point, you know,
+
+ align:start position:0%
+are. She was making the point, you know,
+ 
+
+ align:start position:0%
+are. She was making the point, you know,
+there's this great box art with like the
+
+ align:start position:0%
+there's this great box art with like the
+ 
+
+ align:start position:0%
+there's this great box art with like the
+Native Americans in the corners and like
+
+ align:start position:0%
+Native Americans in the corners and like
+ 
+
+ align:start position:0%
+Native Americans in the corners and like
+the concistador in the middle, you know,
+
+ align:start position:0%
+the concistador in the middle, you know,
+ 
+
+ align:start position:0%
+the concistador in the middle, you know,
+the Spanish and the Dutch. And it's
+
+ align:start position:0%
+the Spanish and the Dutch. And it's
+ 
+
+ align:start position:0%
+the Spanish and the Dutch. And it's
+like, if you were a Native American, how
+
+ align:start position:0%
+like, if you were a Native American, how
+ 
+
+ align:start position:0%
+like, if you were a Native American, how
+would you respond to this game, right? I
+
+ align:start position:0%
+would you respond to this game, right? I
+ 
+
+ align:start position:0%
+would you respond to this game, right? I
+mean, it's like I'm like, "Yeah, I'm I'm
+
+ align:start position:0%
+mean, it's like I'm like, "Yeah, I'm I'm
+ 
+
+ align:start position:0%
+mean, it's like I'm like, "Yeah, I'm I'm
+totally making America again, you know,
+
+ align:start position:0%
+totally making America again, you know,
+ 
+
+ align:start position:0%
+totally making America again, you know,
+and other people would be like, "Oh my
+
+ align:start position:0%
+and other people would be like, "Oh my
+ 
+
+ align:start position:0%
+and other people would be like, "Oh my
+god, you basically just, you know, wiped
+
+ align:start position:0%
+god, you basically just, you know, wiped
+ 
+
+ align:start position:0%
+god, you basically just, you know, wiped
+out my ancestors. Thanks." Um, so it it
+
+ align:start position:0%
+out my ancestors. Thanks." Um, so it it
+ 
+
+ align:start position:0%
+out my ancestors. Thanks." Um, so it it
+it's true. I mean, you kind of sometimes
+
+ align:start position:0%
+it's true. I mean, you kind of sometimes
+ 
+
+ align:start position:0%
+it's true. I mean, you kind of sometimes
+you fall into meaning. It's it's
+
+ align:start position:0%
+you fall into meaning. It's it's
+ 
+
+ align:start position:0%
+you fall into meaning. It's it's
+something that does. And I think, you
+
+ align:start position:0%
+something that does. And I think, you
+ 
+
+ align:start position:0%
+something that does. And I think, you
+know, again, a lot of art does that,
+
+ align:start position:0%
+know, again, a lot of art does that,
+ 
+
+ align:start position:0%
+know, again, a lot of art does that,
+right? And some art did it quite
+
+ align:start position:0%
+right? And some art did it quite
+ 
+
+ align:start position:0%
+right? And some art did it quite
+purposely. um you know where they
+
+ align:start position:0%
+purposely. um you know where they
+ 
+
+ align:start position:0%
+purposely. um you know where they
+weren't divulging the meaning they were
+
+ align:start position:0%
+weren't divulging the meaning they were
+ 
+
+ align:start position:0%
+weren't divulging the meaning they were
+inviting readings of it. Um so Fluxus
+
+ align:start position:0%
+inviting readings of it. Um so Fluxus
+ 
+
+ align:start position:0%
+inviting readings of it. Um so Fluxus
+Fluxus is this um this really
+
+ align:start position:0%
+Fluxus is this um this really
+ 
+
+ align:start position:0%
+Fluxus is this um this really
+interesting uh mid- 20th century art uh
+
+ align:start position:0%
+interesting uh mid- 20th century art uh
+ 
+
+ align:start position:0%
+interesting uh mid- 20th century art uh
+they they rejected the term movement.
+
+ align:start position:0%
+they they rejected the term movement.
+ 
+
+ align:start position:0%
+they they rejected the term movement.
+They called it an attitude. Um that Mary
+
+ align:start position:0%
+They called it an attitude. Um that Mary
+ 
+
+ align:start position:0%
+They called it an attitude. Um that Mary
+Flame talks about a bit in her in her
+
+ align:start position:0%
+Flame talks about a bit in her in her
+ 
+
+ align:start position:0%
+Flame talks about a bit in her in her
+critical playbook and it's actually
+
+ align:start position:0%
+critical playbook and it's actually
+ 
+
+ align:start position:0%
+critical playbook and it's actually
+quite interesting. It's it really starts
+
+ align:start position:0%
+quite interesting. It's it really starts
+ 
+
+ align:start position:0%
+quite interesting. It's it really starts
+out early with with John Cage. Have you
+
+ align:start position:0%
+out early with with John Cage. Have you
+ 
+
+ align:start position:0%
+out early with with John Cage. Have you
+guys heard of him? The composer. Um he's
+
+ align:start position:0%
+guys heard of him? The composer. Um he's
+ 
+
+ align:start position:0%
+guys heard of him? The composer. Um he's
+most famous for this piece of music that
+
+ align:start position:0%
+most famous for this piece of music that
+ 
+
+ align:start position:0%
+most famous for this piece of music that
+he wrote where I forget the duration.
+
+ align:start position:0%
+he wrote where I forget the duration.
+ 
+
+ align:start position:0%
+he wrote where I forget the duration.
+It's like 633.
+
+ align:start position:0%
+It's like 633.
+ 
+
+ align:start position:0%
+It's like 633.
+>> It's four 4 minutes and 33 seconds of
+
+ align:start position:0%
+>> It's four 4 minutes and 33 seconds of
+ 
+
+ align:start position:0%
+>> It's four 4 minutes and 33 seconds of
+not well like not playing. Right. Like
+
+ align:start position:0%
+not well like not playing. Right. Like
+ 
+
+ align:start position:0%
+not well like not playing. Right. Like
+Yeah. He rests. Exactly. So you'd sit
+
+ align:start position:0%
+Yeah. He rests. Exactly. So you'd sit
+ 
+
+ align:start position:0%
+Yeah. He rests. Exactly. So you'd sit
+down at the piano and you'd pull out the
+
+ align:start position:0%
+down at the piano and you'd pull out the
+ 
+
+ align:start position:0%
+down at the piano and you'd pull out the
+music and everyone would hush and then
+
+ align:start position:0%
+music and everyone would hush and then
+ 
+
+ align:start position:0%
+music and everyone would hush and then
+for 4 minutes and 33 seconds you'd sit
+
+ align:start position:0%
+for 4 minutes and 33 seconds you'd sit
+ 
+
+ align:start position:0%
+for 4 minutes and 33 seconds you'd sit
+there possibly with your hands on the
+
+ align:start position:0%
+there possibly with your hands on the
+ 
+
+ align:start position:0%
+there possibly with your hands on the
+keys and then after the time you would
+
+ align:start position:0%
+keys and then after the time you would
+ 
+
+ align:start position:0%
+keys and then after the time you would
+stand up, you'd take your bow and the
+
+ align:start position:0%
+stand up, you'd take your bow and the
+ 
+
+ align:start position:0%
+stand up, you'd take your bow and the
+audience would erupt into you know
+
+ align:start position:0%
+audience would erupt into you know
+ 
+
+ align:start position:0%
+audience would erupt into you know
+incredible applause. Um but he was
+
+ align:start position:0%
+incredible applause. Um but he was
+ 
+
+ align:start position:0%
+incredible applause. Um but he was
+really kind of testing the idea of what
+
+ align:start position:0%
+really kind of testing the idea of what
+ 
+
+ align:start position:0%
+really kind of testing the idea of what
+they what they eventually kind of called
+
+ align:start position:0%
+they what they eventually kind of called
+ 
+
+ align:start position:0%
+they what they eventually kind of called
+scores or event scores, right? This idea
+
+ align:start position:0%
+scores or event scores, right? This idea
+ 
+
+ align:start position:0%
+scores or event scores, right? This idea
+that like music um music is an art form
+
+ align:start position:0%
+that like music um music is an art form
+ 
+
+ align:start position:0%
+that like music um music is an art form
+where you can kind of uh write it down
+
+ align:start position:0%
+where you can kind of uh write it down
+ 
+
+ align:start position:0%
+where you can kind of uh write it down
+and then it becomes performable, right?
+
+ align:start position:0%
+and then it becomes performable, right?
+ 
+
+ align:start position:0%
+and then it becomes performable, right?
+it becomes this kind of thing um that
+
+ align:start position:0%
+it becomes this kind of thing um that
+ 
+
+ align:start position:0%
+it becomes this kind of thing um that
+someone can engage with and and um we
+
+ align:start position:0%
+someone can engage with and and um we
+ 
+
+ align:start position:0%
+someone can engage with and and um we
+don't think of paintings that way. We
+
+ align:start position:0%
+don't think of paintings that way. We
+ 
+
+ align:start position:0%
+don't think of paintings that way. We
+don't think of paintings as having a
+
+ align:start position:0%
+don't think of paintings as having a
+ 
+
+ align:start position:0%
+don't think of paintings as having a
+score, having some kind of you know how
+
+ align:start position:0%
+score, having some kind of you know how
+ 
+
+ align:start position:0%
+score, having some kind of you know how
+do I engage with this, right? It sounds
+
+ align:start position:0%
+do I engage with this, right? It sounds
+ 
+
+ align:start position:0%
+do I engage with this, right? It sounds
+kind of like games. They're they're you
+
+ align:start position:0%
+kind of like games. They're they're you
+ 
+
+ align:start position:0%
+kind of like games. They're they're you
+know figuring out how does interactivity
+
+ align:start position:0%
+know figuring out how does interactivity
+ 
+
+ align:start position:0%
+know figuring out how does interactivity
+work in artistic mediums? Um really
+
+ align:start position:0%
+work in artistic mediums? Um really
+ 
+
+ align:start position:0%
+work in artistic mediums? Um really
+interested in indeterminacy too. Um I
+
+ align:start position:0%
+interested in indeterminacy too. Um I
+ 
+
+ align:start position:0%
+interested in indeterminacy too. Um I
+mean I think you'll see in some of these
+
+ align:start position:0%
+mean I think you'll see in some of these
+ 
+
+ align:start position:0%
+mean I think you'll see in some of these
+examples that they're they're really
+
+ align:start position:0%
+examples that they're they're really
+ 
+
+ align:start position:0%
+examples that they're they're really
+kind of pushing on the boundaries of
+
+ align:start position:0%
+kind of pushing on the boundaries of
+ 
+
+ align:start position:0%
+kind of pushing on the boundaries of
+what um of what what art has been doing
+
+ align:start position:0%
+what um of what what art has been doing
+ 
+
+ align:start position:0%
+what um of what what art has been doing
+to this point. Uh they call it
+
+ align:start position:0%
+to this point. Uh they call it
+ 
+
+ align:start position:0%
+to this point. Uh they call it
+intermedia uh meaning that the more kind
+
+ align:start position:0%
+intermedia uh meaning that the more kind
+ 
+
+ align:start position:0%
+intermedia uh meaning that the more kind
+of um multiple modes that you can use
+
+ align:start position:0%
+of um multiple modes that you can use
+ 
+
+ align:start position:0%
+of um multiple modes that you can use
+for for communicating it. Um was really
+
+ align:start position:0%
+for for communicating it. Um was really
+ 
+
+ align:start position:0%
+for for communicating it. Um was really
+important to the to the attitude. Um
+
+ align:start position:0%
+important to the to the attitude. Um
+ 
+
+ align:start position:0%
+important to the to the attitude. Um
+simplicity was really big right having
+
+ align:start position:0%
+simplicity was really big right having
+ 
+
+ align:start position:0%
+simplicity was really big right having
+you know having kind of basic basic
+
+ align:start position:0%
+you know having kind of basic basic
+ 
+
+ align:start position:0%
+you know having kind of basic basic
+systems and and basic kind of scores.
+
+ align:start position:0%
+systems and and basic kind of scores.
+ 
+
+ align:start position:0%
+systems and and basic kind of scores.
+And then this idea of play um was really
+
+ align:start position:0%
+And then this idea of play um was really
+ 
+
+ align:start position:0%
+And then this idea of play um was really
+kind of important. Um Yoko Ono, it's
+
+ align:start position:0%
+kind of important. Um Yoko Ono, it's
+ 
+
+ align:start position:0%
+kind of important. Um Yoko Ono, it's
+funny, you know, we sort of just
+
+ align:start position:0%
+funny, you know, we sort of just
+ 
+
+ align:start position:0%
+funny, you know, we sort of just
+attached her to John Lennin, but she she
+
+ align:start position:0%
+attached her to John Lennin, but she she
+ 
+
+ align:start position:0%
+attached her to John Lennin, but she she
+was an artist before she was um you
+
+ align:start position:0%
+was an artist before she was um you
+ 
+
+ align:start position:0%
+was an artist before she was um you
+know, just in a relationship with him,
+
+ align:start position:0%
+know, just in a relationship with him,
+ 
+
+ align:start position:0%
+know, just in a relationship with him,
+and she's actually kind of well known as
+
+ align:start position:0%
+and she's actually kind of well known as
+ 
+
+ align:start position:0%
+and she's actually kind of well known as
+one of these kind of Fluxus
+
+ align:start position:0%
+one of these kind of Fluxus
+ 
+
+ align:start position:0%
+one of these kind of Fluxus
+practitioners. Um this is interesting.
+
+ align:start position:0%
+practitioners. Um this is interesting.
+ 
+
+ align:start position:0%
+practitioners. Um this is interesting.
+This is the Fluxus manifesto. Um I kind
+
+ align:start position:0%
+This is the Fluxus manifesto. Um I kind
+ 
+
+ align:start position:0%
+This is the Fluxus manifesto. Um I kind
+of wanted to just put this up because I
+
+ align:start position:0%
+of wanted to just put this up because I
+ 
+
+ align:start position:0%
+of wanted to just put this up because I
+think you can get a little bit of a
+
+ align:start position:0%
+think you can get a little bit of a
+ 
+
+ align:start position:0%
+think you can get a little bit of a
+sense for what they were trying to go
+
+ align:start position:0%
+sense for what they were trying to go
+ 
+
+ align:start position:0%
+sense for what they were trying to go
+for. So um you know they were taking the
+
+ align:start position:0%
+for. So um you know they were taking the
+ 
+
+ align:start position:0%
+for. So um you know they were taking the
+word fluxus and or flux and you know
+
+ align:start position:0%
+word fluxus and or flux and you know
+ 
+
+ align:start position:0%
+word fluxus and or flux and you know
+putting the definition but then they
+
+ align:start position:0%
+putting the definition but then they
+ 
+
+ align:start position:0%
+putting the definition but then they
+were kind of amending it here. So you
+
+ align:start position:0%
+were kind of amending it here. So you
+ 
+
+ align:start position:0%
+were kind of amending it here. So you
+know purge the world of bourgeoa
+
+ align:start position:0%
+know purge the world of bourgeoa
+ 
+
+ align:start position:0%
+know purge the world of bourgeoa
+sickness uh intellectual professional
+
+ align:start position:0%
+sickness uh intellectual professional
+ 
+
+ align:start position:0%
+sickness uh intellectual professional
+and commercialized culture. Purge the
+
+ align:start position:0%
+and commercialized culture. Purge the
+ 
+
+ align:start position:0%
+and commercialized culture. Purge the
+world of dead art, imitation, artificial
+
+ align:start position:0%
+world of dead art, imitation, artificial
+ 
+
+ align:start position:0%
+world of dead art, imitation, artificial
+art, abstract art, illusionistic art,
+
+ align:start position:0%
+art, abstract art, illusionistic art,
+ 
+
+ align:start position:0%
+art, abstract art, illusionistic art,
+mathematical art. I like this. Purge the
+
+ align:start position:0%
+mathematical art. I like this. Purge the
+ 
+
+ align:start position:0%
+mathematical art. I like this. Purge the
+world of Europeanism.
+
+ align:start position:0%
+world of Europeanism.
+ 
+
+ align:start position:0%
+world of Europeanism.
+Don't even know if that's a word. Um
+
+ align:start position:0%
+Don't even know if that's a word. Um
+ 
+
+ align:start position:0%
+Don't even know if that's a word. Um
+>> yeah. Promote a revolutionary flood and
+
+ align:start position:0%
+>> yeah. Promote a revolutionary flood and
+ 
+
+ align:start position:0%
+>> yeah. Promote a revolutionary flood and
+tide in art. um promoting art, anti-art,
+
+ align:start position:0%
+tide in art. um promoting art, anti-art,
+ 
+
+ align:start position:0%
+tide in art. um promoting art, anti-art,
+non-art reality. I mean, these things
+
+ align:start position:0%
+non-art reality. I mean, these things
+ 
+
+ align:start position:0%
+non-art reality. I mean, these things
+these things sound like totally crazy,
+
+ align:start position:0%
+these things sound like totally crazy,
+ 
+
+ align:start position:0%
+these things sound like totally crazy,
+right? I love the I love the to be fully
+
+ align:start position:0%
+right? I love the I love the to be fully
+ 
+
+ align:start position:0%
+right? I love the I love the to be fully
+grasped, but then it crosses out fully,
+
+ align:start position:0%
+grasped, but then it crosses out fully,
+ 
+
+ align:start position:0%
+grasped, but then it crosses out fully,
+right? And and that I don't doubt that
+
+ align:start position:0%
+right? And and that I don't doubt that
+ 
+
+ align:start position:0%
+right? And and that I don't doubt that
+that was completely intentional. Or if
+
+ align:start position:0%
+that was completely intentional. Or if
+ 
+
+ align:start position:0%
+that was completely intentional. Or if
+they wrote fully grass, we're like, "Oh,
+
+ align:start position:0%
+they wrote fully grass, we're like, "Oh,
+ 
+
+ align:start position:0%
+they wrote fully grass, we're like, "Oh,
+this is going to be great, right? I'm
+
+ align:start position:0%
+this is going to be great, right? I'm
+ 
+
+ align:start position:0%
+this is going to be great, right? I'm
+crossing out so you can see that I
+
+ align:start position:0%
+crossing out so you can see that I
+ 
+
+ align:start position:0%
+crossing out so you can see that I
+crossed out fully grasped." We want it
+
+ align:start position:0%
+crossed out fully grasped." We want it
+ 
+
+ align:start position:0%
+crossed out fully grasped." We want it
+to be not fully grasped, you know? We
+
+ align:start position:0%
+to be not fully grasped, you know? We
+ 
+
+ align:start position:0%
+to be not fully grasped, you know? We
+want to be partially grasped by all
+
+ align:start position:0%
+want to be partially grasped by all
+ 
+
+ align:start position:0%
+want to be partially grasped by all
+people. Um not only critics, um talks
+
+ align:start position:0%
+people. Um not only critics, um talks
+ 
+
+ align:start position:0%
+people. Um not only critics, um talks
+and professionals. So, um and it's just
+
+ align:start position:0%
+and professionals. So, um and it's just
+ 
+
+ align:start position:0%
+and professionals. So, um and it's just
+a really interesting thing. And this
+
+ align:start position:0%
+a really interesting thing. And this
+ 
+
+ align:start position:0%
+a really interesting thing. And this
+sort of like screams kind of the avant
+
+ align:start position:0%
+sort of like screams kind of the avant
+ 
+
+ align:start position:0%
+sort of like screams kind of the avant
+guard, right? They were trying to like
+
+ align:start position:0%
+guard, right? They were trying to like
+ 
+
+ align:start position:0%
+guard, right? They were trying to like
+push against boundaries. They're trying
+
+ align:start position:0%
+push against boundaries. They're trying
+ 
+
+ align:start position:0%
+push against boundaries. They're trying
+to figure out what is the edge of the
+
+ align:start position:0%
+to figure out what is the edge of the
+ 
+
+ align:start position:0%
+to figure out what is the edge of the
+medium and then how can we how can we
+
+ align:start position:0%
+medium and then how can we how can we
+ 
+
+ align:start position:0%
+medium and then how can we how can we
+just like, you know, jump way off it.
+
+ align:start position:0%
+just like, you know, jump way off it.
+ 
+
+ align:start position:0%
+just like, you know, jump way off it.
+And um
+
+ align:start position:0%
+And um
+ 
+
+ align:start position:0%
+And um
+some of the classic fluxist works were
+
+ align:start position:0%
+some of the classic fluxist works were
+ 
+
+ align:start position:0%
+some of the classic fluxist works were
+these things called flux boxes or flux
+
+ align:start position:0%
+these things called flux boxes or flux
+ 
+
+ align:start position:0%
+these things called flux boxes or flux
+kits. Um and flux kits tended to have
+
+ align:start position:0%
+kits. Um and flux kits tended to have
+ 
+
+ align:start position:0%
+kits. Um and flux kits tended to have
+event scores. This is one of the most
+
+ align:start position:0%
+event scores. This is one of the most
+ 
+
+ align:start position:0%
+event scores. This is one of the most
+famous called Water Yam by George Breck.
+
+ align:start position:0%
+famous called Water Yam by George Breck.
+ 
+
+ align:start position:0%
+famous called Water Yam by George Breck.
+Um and basically this is a box with 70
+
+ align:start position:0%
+Um and basically this is a box with 70
+ 
+
+ align:start position:0%
+Um and basically this is a box with 70
+event scores. Um, and these are an
+
+ align:start position:0%
+event scores. Um, and these are an
+ 
+
+ align:start position:0%
+event scores. Um, and these are an
+example of kind of event scores. And and
+
+ align:start position:0%
+example of kind of event scores. And and
+ 
+
+ align:start position:0%
+example of kind of event scores. And and
+it's interesting. I mean, event scores
+
+ align:start position:0%
+it's interesting. I mean, event scores
+ 
+
+ align:start position:0%
+it's interesting. I mean, event scores
+really seem like rule systems, right?
+
+ align:start position:0%
+really seem like rule systems, right?
+ 
+
+ align:start position:0%
+really seem like rule systems, right?
+Like they're like the instructions to
+
+ align:start position:0%
+Like they're like the instructions to
+ 
+
+ align:start position:0%
+Like they're like the instructions to
+your board game. Um, except they're
+
+ align:start position:0%
+your board game. Um, except they're
+ 
+
+ align:start position:0%
+your board game. Um, except they're
+they're kind of wacky. I mean, if you
+
+ align:start position:0%
+they're kind of wacky. I mean, if you
+ 
+
+ align:start position:0%
+they're kind of wacky. I mean, if you
+look at you look at air conditioning,
+
+ align:start position:0%
+look at you look at air conditioning,
+ 
+
+ align:start position:0%
+look at you look at air conditioning,
+um, the the rule is move through the
+
+ align:start position:0%
+um, the the rule is move through the
+ 
+
+ align:start position:0%
+um, the the rule is move through the
+place. Um, which is really interesting.
+
+ align:start position:0%
+place. Um, which is really interesting.
+ 
+
+ align:start position:0%
+place. Um, which is really interesting.
+I mean, if you encounter this game and
+
+ align:start position:0%
+I mean, if you encounter this game and
+ 
+
+ align:start position:0%
+I mean, if you encounter this game and
+you're like, "All right, I'm going to
+
+ align:start position:0%
+you're like, "All right, I'm going to
+ 
+
+ align:start position:0%
+you're like, "All right, I'm going to
+play water jam." And then you pull out
+
+ align:start position:0%
+play water jam." And then you pull out
+ 
+
+ align:start position:0%
+play water jam." And then you pull out
+air conditioning, you're like, "Move
+
+ align:start position:0%
+air conditioning, you're like, "Move
+ 
+
+ align:start position:0%
+air conditioning, you're like, "Move
+through the place." Um, and I think
+
+ align:start position:0%
+through the place." Um, and I think
+ 
+
+ align:start position:0%
+through the place." Um, and I think
+that's kind of, you know, pretty
+
+ align:start position:0%
+that's kind of, you know, pretty
+ 
+
+ align:start position:0%
+that's kind of, you know, pretty
+characteristic of the movement, right?
+
+ align:start position:0%
+characteristic of the movement, right?
+ 
+
+ align:start position:0%
+characteristic of the movement, right?
+present you with some sort of objective
+
+ align:start position:0%
+present you with some sort of objective
+ 
+
+ align:start position:0%
+present you with some sort of objective
+or some sort of um some sort of
+
+ align:start position:0%
+or some sort of um some sort of
+ 
+
+ align:start position:0%
+or some sort of um some sort of
+requirement, but one that is kind of uh
+
+ align:start position:0%
+requirement, but one that is kind of uh
+ 
+
+ align:start position:0%
+requirement, but one that is kind of uh
+abstract or nebulous or just, you know,
+
+ align:start position:0%
+abstract or nebulous or just, you know,
+ 
+
+ align:start position:0%
+abstract or nebulous or just, you know,
+kind of strange. This one's even better.
+
+ align:start position:0%
+kind of strange. This one's even better.
+ 
+
+ align:start position:0%
+kind of strange. This one's even better.
+Um on a white chair, a great tape
+
+ align:start position:0%
+Um on a white chair, a great tape
+ 
+
+ align:start position:0%
+Um on a white chair, a great tape
+measure, alphabet, flag, black, and
+
+ align:start position:0%
+measure, alphabet, flag, black, and
+ 
+
+ align:start position:0%
+measure, alphabet, flag, black, and
+spectral colors. Um in this instance,
+
+ align:start position:0%
+spectral colors. Um in this instance,
+ 
+
+ align:start position:0%
+spectral colors. Um in this instance,
+it's not even clear what you're
+
+ align:start position:0%
+it's not even clear what you're
+ 
+
+ align:start position:0%
+it's not even clear what you're
+necessarily supposed to do. Are you
+
+ align:start position:0%
+necessarily supposed to do. Are you
+ 
+
+ align:start position:0%
+necessarily supposed to do. Are you
+supposed to compile these things on a
+
+ align:start position:0%
+supposed to compile these things on a
+ 
+
+ align:start position:0%
+supposed to compile these things on a
+white chair? Um you know, are you
+
+ align:start position:0%
+white chair? Um you know, are you
+ 
+
+ align:start position:0%
+white chair? Um you know, are you
+supposed to sit on a white chair and
+
+ align:start position:0%
+supposed to sit on a white chair and
+ 
+
+ align:start position:0%
+supposed to sit on a white chair and
+hold all of these things? Um it's not
+
+ align:start position:0%
+hold all of these things? Um it's not
+ 
+
+ align:start position:0%
+hold all of these things? Um it's not
+it's not particularly clear. And um and
+
+ align:start position:0%
+it's not particularly clear. And um and
+ 
+
+ align:start position:0%
+it's not particularly clear. And um and
+this is this is you know this is the
+
+ align:start position:0%
+this is this is you know this is the
+ 
+
+ align:start position:0%
+this is this is you know this is the
+playfulness of this movement. This is
+
+ align:start position:0%
+playfulness of this movement. This is
+ 
+
+ align:start position:0%
+playfulness of this movement. This is
+kind of the the energy of this kind of
+
+ align:start position:0%
+kind of the the energy of this kind of
+ 
+
+ align:start position:0%
+kind of the the energy of this kind of
+uh avantgard movement. Um
+
+ align:start position:0%
+uh avantgard movement. Um
+ 
+
+ align:start position:0%
+uh avantgard movement. Um
+you can see kind of the relationship I I
+
+ align:start position:0%
+you can see kind of the relationship I I
+ 
+
+ align:start position:0%
+you can see kind of the relationship I I
+hope between kind of rule systems and
+
+ align:start position:0%
+hope between kind of rule systems and
+ 
+
+ align:start position:0%
+hope between kind of rule systems and
+these the next example is I think
+
+ align:start position:0%
+these the next example is I think
+ 
+
+ align:start position:0%
+these the next example is I think
+another one but but you can see how
+
+ align:start position:0%
+another one but but you can see how
+ 
+
+ align:start position:0%
+another one but but you can see how
+they're kind of playing around with
+
+ align:start position:0%
+they're kind of playing around with
+ 
+
+ align:start position:0%
+they're kind of playing around with
+these ideas. At least they're
+
+ align:start position:0%
+these ideas. At least they're
+ 
+
+ align:start position:0%
+these ideas. At least they're
+incorporating interactivity into these
+
+ align:start position:0%
+incorporating interactivity into these
+ 
+
+ align:start position:0%
+incorporating interactivity into these
+art pieces, right? And keep in mind
+
+ align:start position:0%
+art pieces, right? And keep in mind
+ 
+
+ align:start position:0%
+art pieces, right? And keep in mind
+these are these are being shown in
+
+ align:start position:0%
+these are these are being shown in
+ 
+
+ align:start position:0%
+these are these are being shown in
+galleries. These are being shown in high
+
+ align:start position:0%
+galleries. These are being shown in high
+ 
+
+ align:start position:0%
+galleries. These are being shown in high
+art places, right? These are um being
+
+ align:start position:0%
+art places, right? These are um being
+ 
+
+ align:start position:0%
+art places, right? These are um being
+sent out to their friends as as works of
+
+ align:start position:0%
+sent out to their friends as as works of
+ 
+
+ align:start position:0%
+sent out to their friends as as works of
+of art. Um this one's great. Um this is
+
+ align:start position:0%
+of art. Um this one's great. Um this is
+ 
+
+ align:start position:0%
+of art. Um this one's great. Um this is
+white chess by Yokoono and and it's
+
+ align:start position:0%
+white chess by Yokoono and and it's
+ 
+
+ align:start position:0%
+white chess by Yokoono and and it's
+often kind of depicted on its own and
+
+ align:start position:0%
+often kind of depicted on its own and
+ 
+
+ align:start position:0%
+often kind of depicted on its own and
+you have to imagine what the rules are,
+
+ align:start position:0%
+you have to imagine what the rules are,
+ 
+
+ align:start position:0%
+you have to imagine what the rules are,
+but I actually think her rules as they
+
+ align:start position:0%
+but I actually think her rules as they
+ 
+
+ align:start position:0%
+but I actually think her rules as they
+are written are actually pretty
+
+ align:start position:0%
+are written are actually pretty
+ 
+
+ align:start position:0%
+are written are actually pretty
+important to it. So she says, "Play it
+
+ align:start position:0%
+important to it. So she says, "Play it
+ 
+
+ align:start position:0%
+important to it. So she says, "Play it
+for as long as you can remember who is
+
+ align:start position:0%
+for as long as you can remember who is
+ 
+
+ align:start position:0%
+for as long as you can remember who is
+your opponent and who is your own self."
+
+ align:start position:0%
+your opponent and who is your own self."
+ 
+
+ align:start position:0%
+your opponent and who is your own self."
+Um very interesting wordage, but um so
+
+ align:start position:0%
+Um very interesting wordage, but um so
+ 
+
+ align:start position:0%
+Um very interesting wordage, but um so
+what are the comp what are the
+
+ align:start position:0%
+what are the comp what are the
+ 
+
+ align:start position:0%
+what are the comp what are the
+complications with white chess? Anyone?
+
+ align:start position:0%
+complications with white chess? Anyone?
+ 
+
+ align:start position:0%
+complications with white chess? Anyone?
+Any thoughts based on your perceptions
+
+ align:start position:0%
+Any thoughts based on your perceptions
+ 
+
+ align:start position:0%
+Any thoughts based on your perceptions
+of nonwhite chess or white and black
+
+ align:start position:0%
+of nonwhite chess or white and black
+ 
+
+ align:start position:0%
+of nonwhite chess or white and black
+chess?
+
+ align:start position:0%
+chess?
+ 
+
+ align:start position:0%
+chess?
+>> Yeah. Begin to argue, but that was my
+
+ align:start position:0%
+>> Yeah. Begin to argue, but that was my
+ 
+
+ align:start position:0%
+>> Yeah. Begin to argue, but that was my
+pawn.
+
+ align:start position:0%
+pawn.
+ 
+
+ align:start position:0%
+pawn.
+>> Yes. Yes. You definitely will be hard to
+
+ align:start position:0%
+>> Yes. Yes. You definitely will be hard to
+ 
+
+ align:start position:0%
+>> Yes. Yes. You definitely will be hard to
+keep track of, I would think. Yeah. I
+
+ align:start position:0%
+keep track of, I would think. Yeah. I
+ 
+
+ align:start position:0%
+keep track of, I would think. Yeah. I
+mean, that's why she said as long as you
+
+ align:start position:0%
+mean, that's why she said as long as you
+ 
+
+ align:start position:0%
+mean, that's why she said as long as you
+can remember. Any other um any other
+
+ align:start position:0%
+can remember. Any other um any other
+ 
+
+ align:start position:0%
+can remember. Any other um any other
+kind of weirdness from this?
+
+ align:start position:0%
+kind of weirdness from this?
+ 
+
+ align:start position:0%
+kind of weirdness from this?
+>> Who is friend and who enemy?
+
+ align:start position:0%
+>> Who is friend and who enemy?
+ 
+
+ align:start position:0%
+>> Who is friend and who enemy?
+>> Yeah. I mean, certainly, right? I mean,
+
+ align:start position:0%
+>> Yeah. I mean, certainly, right? I mean,
+ 
+
+ align:start position:0%
+>> Yeah. I mean, certainly, right? I mean,
+this is sort of like, wait, was that my
+
+ align:start position:0%
+this is sort of like, wait, was that my
+ 
+
+ align:start position:0%
+this is sort of like, wait, was that my
+piece? Was that your piece? Not only
+
+ align:start position:0%
+piece? Was that your piece? Not only
+ 
+
+ align:start position:0%
+piece? Was that your piece? Not only
+does that complicate your relationship
+
+ align:start position:0%
+does that complicate your relationship
+ 
+
+ align:start position:0%
+does that complicate your relationship
+to the other player, right? But but now
+
+ align:start position:0%
+to the other player, right? But but now
+ 
+
+ align:start position:0%
+to the other player, right? But but now
+it's like to the game itself, it's like,
+
+ align:start position:0%
+it's like to the game itself, it's like,
+ 
+
+ align:start position:0%
+it's like to the game itself, it's like,
+wait, what was the strategy I was doing?
+
+ align:start position:0%
+wait, what was the strategy I was doing?
+ 
+
+ align:start position:0%
+wait, what was the strategy I was doing?
+>> Friendly fire.
+
+ align:start position:0%
+>> Friendly fire.
+ 
+
+ align:start position:0%
+>> Friendly fire.
+>> Yeah. I mean, it's really hard to keep
+
+ align:start position:0%
+>> Yeah. I mean, it's really hard to keep
+ 
+
+ align:start position:0%
+>> Yeah. I mean, it's really hard to keep
+track of stuff in chess. What about the
+
+ align:start position:0%
+track of stuff in chess. What about the
+ 
+
+ align:start position:0%
+track of stuff in chess. What about the
+board?
+
+ align:start position:0%
+board?
+ 
+
+ align:start position:0%
+board?
+>> You might swap the king and the queen by
+
+ align:start position:0%
+>> You might swap the king and the queen by
+ 
+
+ align:start position:0%
+>> You might swap the king and the queen by
+mistake because you don't have
+
+ align:start position:0%
+mistake because you don't have
+ 
+
+ align:start position:0%
+mistake because you don't have
+>> there's not really any like actual boxes
+
+ align:start position:0%
+>> there's not really any like actual boxes
+ 
+
+ align:start position:0%
+>> there's not really any like actual boxes
+on the board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, they're all they're all white,
+
+ align:start position:0%
+>> Yeah, they're all they're all white,
+ 
+
+ align:start position:0%
+>> Yeah, they're all they're all white,
+right? So, I mean, that sort of
+
+ align:start position:0%
+right? So, I mean, that sort of
+ 
+
+ align:start position:0%
+right? So, I mean, that sort of
+complicates things a little bit too,
+
+ align:start position:0%
+complicates things a little bit too,
+ 
+
+ align:start position:0%
+complicates things a little bit too,
+right? Because you need to kind of
+
+ align:start position:0%
+right? Because you need to kind of
+ 
+
+ align:start position:0%
+right? Because you need to kind of
+remember how you were moving. This one's
+
+ align:start position:0%
+remember how you were moving. This one's
+ 
+
+ align:start position:0%
+remember how you were moving. This one's
+really big. This is like a garden
+
+ align:start position:0%
+really big. This is like a garden
+ 
+
+ align:start position:0%
+really big. This is like a garden
+installment of of white chess. And I
+
+ align:start position:0%
+installment of of white chess. And I
+ 
+
+ align:start position:0%
+installment of of white chess. And I
+think the cool thing too, I mean this is
+
+ align:start position:0%
+think the cool thing too, I mean this is
+ 
+
+ align:start position:0%
+think the cool thing too, I mean this is
+another example of kind of the movement,
+
+ align:start position:0%
+another example of kind of the movement,
+ 
+
+ align:start position:0%
+another example of kind of the movement,
+right? Um, as long as you have the
+
+ align:start position:0%
+right? Um, as long as you have the
+ 
+
+ align:start position:0%
+right? Um, as long as you have the
+components, you could play this game.
+
+ align:start position:0%
+components, you could play this game.
+ 
+
+ align:start position:0%
+components, you could play this game.
+You could create this art piece. I think
+
+ align:start position:0%
+You could create this art piece. I think
+ 
+
+ align:start position:0%
+You could create this art piece. I think
+for Yokoa, the sense is not go play my
+
+ align:start position:0%
+for Yokoa, the sense is not go play my
+ 
+
+ align:start position:0%
+for Yokoa, the sense is not go play my
+installation of white chess. It's that
+
+ align:start position:0%
+installation of white chess. It's that
+ 
+
+ align:start position:0%
+installation of white chess. It's that
+this is the rules. These are the pieces.
+
+ align:start position:0%
+this is the rules. These are the pieces.
+ 
+
+ align:start position:0%
+this is the rules. These are the pieces.
+It can be played. And that screams game,
+
+ align:start position:0%
+It can be played. And that screams game,
+ 
+
+ align:start position:0%
+It can be played. And that screams game,
+right? I mean, that that that screams
+
+ align:start position:0%
+right? I mean, that that that screams
+ 
+
+ align:start position:0%
+right? I mean, that that that screams
+that kind of portability of a game. Um,
+
+ align:start position:0%
+that kind of portability of a game. Um,
+ 
+
+ align:start position:0%
+that kind of portability of a game. Um,
+and but again, you know, this was this
+
+ align:start position:0%
+and but again, you know, this was this
+ 
+
+ align:start position:0%
+and but again, you know, this was this
+wasn't considered anything but art
+
+ align:start position:0%
+wasn't considered anything but art
+ 
+
+ align:start position:0%
+wasn't considered anything but art
+except probably by people who, you know,
+
+ align:start position:0%
+except probably by people who, you know,
+ 
+
+ align:start position:0%
+except probably by people who, you know,
+turned their nose at this sort of thing
+
+ align:start position:0%
+turned their nose at this sort of thing
+ 
+
+ align:start position:0%
+turned their nose at this sort of thing
+anyway. stuff. Um
+
+ align:start position:0%
+anyway. stuff. Um
+ 
+
+ align:start position:0%
+anyway. stuff. Um
+any thoughts on um any thoughts on what
+
+ align:start position:0%
+any thoughts on um any thoughts on what
+ 
+
+ align:start position:0%
+any thoughts on um any thoughts on what
+what white chess could be uh you know
+
+ align:start position:0%
+what white chess could be uh you know
+ 
+
+ align:start position:0%
+what white chess could be uh you know
+kind of about in a in a
+
+ align:start position:0%
+kind of about in a in a
+ 
+
+ align:start position:0%
+kind of about in a in a
+>> two different sides between one and
+
+ align:start position:0%
+>> two different sides between one and
+ 
+
+ align:start position:0%
+>> two different sides between one and
+>> to
+
+ align:start position:0%
+>> to
+ 
+
+ align:start position:0%
+>> to
+eventually get why am I fighting? Why
+
+ align:start position:0%
+eventually get why am I fighting? Why
+ 
+
+ align:start position:0%
+eventually get why am I fighting? Why
+who is my enemy in this situation?
+
+ align:start position:0%
+who is my enemy in this situation?
+ 
+
+ align:start position:0%
+who is my enemy in this situation?
+>> Sure. Sure. Any other thoughts?
+
+ align:start position:0%
+>> Sure. Sure. Any other thoughts?
+ 
+
+ align:start position:0%
+>> Sure. Sure. Any other thoughts?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Racial relations.
+
+ align:start position:0%
+>> Racial relations.
+ 
+
+ align:start position:0%
+>> Racial relations.
+>> Sure. Racial relations. I mean, there's
+
+ align:start position:0%
+>> Sure. Racial relations. I mean, there's
+ 
+
+ align:start position:0%
+>> Sure. Racial relations. I mean, there's
+probably like a whole anti-war thing of
+
+ align:start position:0%
+probably like a whole anti-war thing of
+ 
+
+ align:start position:0%
+probably like a whole anti-war thing of
+like, you know, are we actually
+
+ align:start position:0%
+like, you know, are we actually
+ 
+
+ align:start position:0%
+like, you know, are we actually
+destroying ourselves?
+
+ align:start position:0%
+destroying ourselves?
+ 
+
+ align:start position:0%
+destroying ourselves?
+>> Yeah. And and I mean, that's so that's
+
+ align:start position:0%
+>> Yeah. And and I mean, that's so that's
+ 
+
+ align:start position:0%
+>> Yeah. And and I mean, that's so that's
+an interesting thing. Yokoono was a
+
+ align:start position:0%
+an interesting thing. Yokoono was a
+ 
+
+ align:start position:0%
+an interesting thing. Yokoono was a
+decidedly um a decidedly kind of
+
+ align:start position:0%
+decidedly um a decidedly kind of
+ 
+
+ align:start position:0%
+decidedly um a decidedly kind of
+anti-war activist in the time that she
+
+ align:start position:0%
+anti-war activist in the time that she
+ 
+
+ align:start position:0%
+anti-war activist in the time that she
+was making this in the early 60s. I
+
+ align:start position:0%
+was making this in the early 60s. I
+ 
+
+ align:start position:0%
+was making this in the early 60s. I
+mean, one thing that you can't take
+
+ align:start position:0%
+mean, one thing that you can't take
+ 
+
+ align:start position:0%
+mean, one thing that you can't take
+anything for granted. The pieces aren't
+
+ align:start position:0%
+anything for granted. The pieces aren't
+ 
+
+ align:start position:0%
+anything for granted. The pieces aren't
+all black, right? They're they're all
+
+ align:start position:0%
+all black, right? They're they're all
+ 
+
+ align:start position:0%
+all black, right? They're they're all
+white. So, I think the race thing does
+
+ align:start position:0%
+white. So, I think the race thing does
+ 
+
+ align:start position:0%
+white. So, I think the race thing does
+kind of play a factor. The inability to
+
+ align:start position:0%
+kind of play a factor. The inability to
+ 
+
+ align:start position:0%
+kind of play a factor. The inability to
+remember who you're attacking and and
+
+ align:start position:0%
+remember who you're attacking and and
+ 
+
+ align:start position:0%
+remember who you're attacking and and
+who who you are even. And I think that's
+
+ align:start position:0%
+who who you are even. And I think that's
+ 
+
+ align:start position:0%
+who who you are even. And I think that's
+actually why I really like her words
+
+ align:start position:0%
+actually why I really like her words
+ 
+
+ align:start position:0%
+actually why I really like her words
+because for as long as you can remember
+
+ align:start position:0%
+because for as long as you can remember
+ 
+
+ align:start position:0%
+because for as long as you can remember
+who is your opponent and who is your own
+
+ align:start position:0%
+who is your opponent and who is your own
+ 
+
+ align:start position:0%
+who is your opponent and who is your own
+self. There's something about
+
+ align:start position:0%
+self. There's something about
+ 
+
+ align:start position:0%
+self. There's something about
+incorporating your own self in there.
+
+ align:start position:0%
+incorporating your own self in there.
+ 
+
+ align:start position:0%
+incorporating your own self in there.
+Not just saying who you know what your
+
+ align:start position:0%
+Not just saying who you know what your
+ 
+
+ align:start position:0%
+Not just saying who you know what your
+pieces are, right? She's not saying can
+
+ align:start position:0%
+pieces are, right? She's not saying can
+ 
+
+ align:start position:0%
+pieces are, right? She's not saying can
+you remember what your pieces are. She's
+
+ align:start position:0%
+you remember what your pieces are. She's
+ 
+
+ align:start position:0%
+you remember what your pieces are. She's
+saying you know remember who you're
+
+ align:start position:0%
+saying you know remember who you're
+ 
+
+ align:start position:0%
+saying you know remember who you're
+playing against versus who you are. Um
+
+ align:start position:0%
+playing against versus who you are. Um
+ 
+
+ align:start position:0%
+playing against versus who you are. Um
+that's very different verbiage. Um and
+
+ align:start position:0%
+that's very different verbiage. Um and
+ 
+
+ align:start position:0%
+that's very different verbiage. Um and
+so it's it's it's I I think it's very
+
+ align:start position:0%
+so it's it's it's I I think it's very
+ 
+
+ align:start position:0%
+so it's it's it's I I think it's very
+much a game about about who are you
+
+ align:start position:0%
+much a game about about who are you
+ 
+
+ align:start position:0%
+much a game about about who are you
+fighting anyway? Um you know what is the
+
+ align:start position:0%
+fighting anyway? Um you know what is the
+ 
+
+ align:start position:0%
+fighting anyway? Um you know what is the
+point of war? What is the purpose of
+
+ align:start position:0%
+point of war? What is the purpose of
+ 
+
+ align:start position:0%
+point of war? What is the purpose of
+war? Um and how how does war
+
+ align:start position:0%
+war? Um and how how does war
+ 
+
+ align:start position:0%
+war? Um and how how does war
+particularly function? Um, and in the
+
+ align:start position:0%
+particularly function? Um, and in the
+ 
+
+ align:start position:0%
+particularly function? Um, and in the
+rhetoric of the time it it makes a lot
+
+ align:start position:0%
+rhetoric of the time it it makes a lot
+ 
+
+ align:start position:0%
+rhetoric of the time it it makes a lot
+of sense, right? Um, so that's Yoko's
+
+ align:start position:0%
+of sense, right? Um, so that's Yoko's
+ 
+
+ align:start position:0%
+of sense, right? Um, so that's Yoko's
+white chess, which is which is part of
+
+ align:start position:0%
+white chess, which is which is part of
+ 
+
+ align:start position:0%
+white chess, which is which is part of
+the Flexus movement. Yeah, it's it's
+
+ align:start position:0%
+the Flexus movement. Yeah, it's it's
+ 
+
+ align:start position:0%
+the Flexus movement. Yeah, it's it's
+pretty it's pretty cool. And actually,
+
+ align:start position:0%
+pretty it's pretty cool. And actually,
+ 
+
+ align:start position:0%
+pretty it's pretty cool. And actually,
+Fluxus and and artists in this period
+
+ align:start position:0%
+Fluxus and and artists in this period
+ 
+
+ align:start position:0%
+Fluxus and and artists in this period
+have a really interesting relationship
+
+ align:start position:0%
+have a really interesting relationship
+ 
+
+ align:start position:0%
+have a really interesting relationship
+with chess. There's like some quote, and
+
+ align:start position:0%
+with chess. There's like some quote, and
+ 
+
+ align:start position:0%
+with chess. There's like some quote, and
+I'm going to butcher it, but it was um I
+
+ align:start position:0%
+I'm going to butcher it, but it was um I
+ 
+
+ align:start position:0%
+I'm going to butcher it, but it was um I
+think it was Marcel Duchamp saying that
+
+ align:start position:0%
+think it was Marcel Duchamp saying that
+ 
+
+ align:start position:0%
+think it was Marcel Duchamp saying that
+not um not all chess players are
+
+ align:start position:0%
+not um not all chess players are
+ 
+
+ align:start position:0%
+not um not all chess players are
+artists, but all artists are chess
+
+ align:start position:0%
+artists, but all artists are chess
+ 
+
+ align:start position:0%
+artists, but all artists are chess
+players or something like that. he was
+
+ align:start position:0%
+players or something like that. he was
+ 
+
+ align:start position:0%
+players or something like that. he was
+particularly fascinated with chess and
+
+ align:start position:0%
+particularly fascinated with chess and
+ 
+
+ align:start position:0%
+particularly fascinated with chess and
+and you could see elements of chess in
+
+ align:start position:0%
+and you could see elements of chess in
+ 
+
+ align:start position:0%
+and you could see elements of chess in
+his um in his work, you know, either
+
+ align:start position:0%
+his um in his work, you know, either
+ 
+
+ align:start position:0%
+his um in his work, you know, either
+being, you know, painted or whatever.
+
+ align:start position:0%
+being, you know, painted or whatever.
+ 
+
+ align:start position:0%
+being, you know, painted or whatever.
+And so
+
+ align:start position:0%
+And so
+ 
+
+ align:start position:0%
+And so
+>> he was completely obsessed with chess.
+
+ align:start position:0%
+>> he was completely obsessed with chess.
+ 
+
+ align:start position:0%
+>> he was completely obsessed with chess.
+He he was a he was he played it really
+
+ align:start position:0%
+He he was a he was he played it really
+ 
+
+ align:start position:0%
+He he was a he was he played it really
+hard. He wasn't necessarily a very good
+
+ align:start position:0%
+hard. He wasn't necessarily a very good
+ 
+
+ align:start position:0%
+hard. He wasn't necessarily a very good
+player, but he played it a lot.
+
+ align:start position:0%
+player, but he played it a lot.
+ 
+
+ align:start position:0%
+player, but he played it a lot.
+>> Very into it. Um, so now I'm going to
+
+ align:start position:0%
+>> Very into it. Um, so now I'm going to
+ 
+
+ align:start position:0%
+>> Very into it. Um, so now I'm going to
+kind of move out of this sort of Plexus
+
+ align:start position:0%
+kind of move out of this sort of Plexus
+ 
+
+ align:start position:0%
+kind of move out of this sort of Plexus
+move and I just wanted to show you a
+
+ align:start position:0%
+move and I just wanted to show you a
+ 
+
+ align:start position:0%
+move and I just wanted to show you a
+couple examples, but I think this next
+
+ align:start position:0%
+couple examples, but I think this next
+ 
+
+ align:start position:0%
+couple examples, but I think this next
+one is actually sort of an interesting
+
+ align:start position:0%
+one is actually sort of an interesting
+ 
+
+ align:start position:0%
+one is actually sort of an interesting
+this is a current game that I'm really
+
+ align:start position:0%
+this is a current game that I'm really
+ 
+
+ align:start position:0%
+this is a current game that I'm really
+excited about, which is called um 16
+
+ align:start position:0%
+excited about, which is called um 16
+ 
+
+ align:start position:0%
+excited about, which is called um 16
+Tons. Um, and this is a game I
+
+ align:start position:0%
+Tons. Um, and this is a game I
+ 
+
+ align:start position:0%
+Tons. Um, and this is a game I
+unfortunately have not been able to play
+
+ align:start position:0%
+unfortunately have not been able to play
+ 
+
+ align:start position:0%
+unfortunately have not been able to play
+yet, but I've I've witnessed play
+
+ align:start position:0%
+yet, but I've I've witnessed play
+ 
+
+ align:start position:0%
+yet, but I've I've witnessed play
+because it's it's a game for four
+
+ align:start position:0%
+because it's it's a game for four
+ 
+
+ align:start position:0%
+because it's it's a game for four
+players, but this was created by Eric
+
+ align:start position:0%
+players, but this was created by Eric
+ 
+
+ align:start position:0%
+players, but this was created by Eric
+Zimmerman and Natalie Py. And it's um so
+
+ align:start position:0%
+Zimmerman and Natalie Py. And it's um so
+ 
+
+ align:start position:0%
+Zimmerman and Natalie Py. And it's um so
+it's a really interesting game. It's a
+
+ align:start position:0%
+it's a really interesting game. It's a
+ 
+
+ align:start position:0%
+it's a really interesting game. It's a
+little hard to see from these pictures,
+
+ align:start position:0%
+little hard to see from these pictures,
+ 
+
+ align:start position:0%
+little hard to see from these pictures,
+but it's this giant circle, I would say,
+
+ align:start position:0%
+but it's this giant circle, I would say,
+ 
+
+ align:start position:0%
+but it's this giant circle, I would say,
+almost the size of this room of
+
+ align:start position:0%
+almost the size of this room of
+ 
+
+ align:start position:0%
+almost the size of this room of
+corrugated cardboard. Maybe even bigger,
+
+ align:start position:0%
+corrugated cardboard. Maybe even bigger,
+ 
+
+ align:start position:0%
+corrugated cardboard. Maybe even bigger,
+a little bit bigger than this room. But,
+
+ align:start position:0%
+a little bit bigger than this room. But,
+ 
+
+ align:start position:0%
+a little bit bigger than this room. But,
+um, inside you've got this kind of array
+
+ align:start position:0%
+um, inside you've got this kind of array
+ 
+
+ align:start position:0%
+um, inside you've got this kind of array
+of colored um array of colored circles
+
+ align:start position:0%
+of colored um array of colored circles
+ 
+
+ align:start position:0%
+of colored um array of colored circles
+in these pretty hefty steel uh steel
+
+ align:start position:0%
+in these pretty hefty steel uh steel
+ 
+
+ align:start position:0%
+in these pretty hefty steel uh steel
+tubes that have color. Um, and let's
+
+ align:start position:0%
+tubes that have color. Um, and let's
+ 
+
+ align:start position:0%
+tubes that have color. Um, and let's
+like let's go through the rules. I mean,
+
+ align:start position:0%
+like let's go through the rules. I mean,
+ 
+
+ align:start position:0%
+like let's go through the rules. I mean,
+the first thing to notice is that they
+
+ align:start position:0%
+the first thing to notice is that they
+ 
+
+ align:start position:0%
+the first thing to notice is that they
+they contextualize the title 16 tons
+
+ align:start position:0%
+they contextualize the title 16 tons
+ 
+
+ align:start position:0%
+they contextualize the title 16 tons
+with a quote from the from the song. Um,
+
+ align:start position:0%
+with a quote from the from the song. Um,
+ 
+
+ align:start position:0%
+with a quote from the from the song. Um,
+you load 16 tons and what do you get?
+
+ align:start position:0%
+you load 16 tons and what do you get?
+ 
+
+ align:start position:0%
+you load 16 tons and what do you get?
+another day older and deeper in debt.
+
+ align:start position:0%
+another day older and deeper in debt.
+ 
+
+ align:start position:0%
+another day older and deeper in debt.
+Um, so this is doing an interesting
+
+ align:start position:0%
+Um, so this is doing an interesting
+ 
+
+ align:start position:0%
+Um, so this is doing an interesting
+thing that that actually, you know, John
+
+ align:start position:0%
+thing that that actually, you know, John
+ 
+
+ align:start position:0%
+thing that that actually, you know, John
+Sharp, who you can actually see in the
+
+ align:start position:0%
+Sharp, who you can actually see in the
+ 
+
+ align:start position:0%
+Sharp, who you can actually see in the
+middle, thinks is actually particularly
+
+ align:start position:0%
+middle, thinks is actually particularly
+ 
+
+ align:start position:0%
+middle, thinks is actually particularly
+important for for games and games that
+
+ align:start position:0%
+important for for games and games that
+ 
+
+ align:start position:0%
+important for for games and games that
+are kind of working in this art
+
+ align:start position:0%
+are kind of working in this art
+ 
+
+ align:start position:0%
+are kind of working in this art
+movement, is that they declare their
+
+ align:start position:0%
+movement, is that they declare their
+ 
+
+ align:start position:0%
+movement, is that they declare their
+intentionality. Um, whether they declare
+
+ align:start position:0%
+intentionality. Um, whether they declare
+ 
+
+ align:start position:0%
+intentionality. Um, whether they declare
+what what their meaning is or not is
+
+ align:start position:0%
+what what their meaning is or not is
+ 
+
+ align:start position:0%
+what what their meaning is or not is
+less important, but they to be taken
+
+ align:start position:0%
+less important, but they to be taken
+ 
+
+ align:start position:0%
+less important, but they to be taken
+seriously, you need to take yourself
+
+ align:start position:0%
+seriously, you need to take yourself
+ 
+
+ align:start position:0%
+seriously, you need to take yourself
+seriously, I think, was one of the
+
+ align:start position:0%
+seriously, I think, was one of the
+ 
+
+ align:start position:0%
+seriously, I think, was one of the
+things he said. And and I think um, you
+
+ align:start position:0%
+things he said. And and I think um, you
+ 
+
+ align:start position:0%
+things he said. And and I think um, you
+know, this is another great example. We
+
+ align:start position:0%
+know, this is another great example. We
+ 
+
+ align:start position:0%
+know, this is another great example. We
+can talk about how other games maybe in
+
+ align:start position:0%
+can talk about how other games maybe in
+ 
+
+ align:start position:0%
+can talk about how other games maybe in
+the digital space do this, but right now
+
+ align:start position:0%
+the digital space do this, but right now
+ 
+
+ align:start position:0%
+the digital space do this, but right now
+they're already kind of priming you for
+
+ align:start position:0%
+they're already kind of priming you for
+ 
+
+ align:start position:0%
+they're already kind of priming you for
+reading the rules in a way that is
+
+ align:start position:0%
+reading the rules in a way that is
+ 
+
+ align:start position:0%
+reading the rules in a way that is
+different than just oo let's play,
+
+ align:start position:0%
+different than just oo let's play,
+ 
+
+ align:start position:0%
+different than just oo let's play,
+right? I mean, could you imagine if
+
+ align:start position:0%
+right? I mean, could you imagine if
+ 
+
+ align:start position:0%
+right? I mean, could you imagine if
+Monopoly had some sort of um you know,
+
+ align:start position:0%
+Monopoly had some sort of um you know,
+ 
+
+ align:start position:0%
+Monopoly had some sort of um you know,
+like Marxist quote in the front of it or
+
+ align:start position:0%
+like Marxist quote in the front of it or
+ 
+
+ align:start position:0%
+like Marxist quote in the front of it or
+something like that, right? Your
+
+ align:start position:0%
+something like that, right? Your
+ 
+
+ align:start position:0%
+something like that, right? Your
+experience of it would be completely
+
+ align:start position:0%
+experience of it would be completely
+ 
+
+ align:start position:0%
+experience of it would be completely
+different. So, um you set up, you put
+
+ align:start position:0%
+different. So, um you set up, you put
+ 
+
+ align:start position:0%
+different. So, um you set up, you put
+the pieces kind of in this array. Um you
+
+ align:start position:0%
+the pieces kind of in this array. Um you
+ 
+
+ align:start position:0%
+the pieces kind of in this array. Um you
+stand on a number and that indicates
+
+ align:start position:0%
+stand on a number and that indicates
+ 
+
+ align:start position:0%
+stand on a number and that indicates
+what color you are. And this is great.
+
+ align:start position:0%
+what color you are. And this is great.
+ 
+
+ align:start position:0%
+what color you are. And this is great.
+You take out $3. Although you can see in
+
+ align:start position:0%
+You take out $3. Although you can see in
+ 
+
+ align:start position:0%
+You take out $3. Although you can see in
+uh in this second picture, they're
+
+ align:start position:0%
+uh in this second picture, they're
+ 
+
+ align:start position:0%
+uh in this second picture, they're
+playing um what uh what Eric, the
+
+ align:start position:0%
+playing um what uh what Eric, the
+ 
+
+ align:start position:0%
+playing um what uh what Eric, the
+designer, has deemed high stakes uh 16
+
+ align:start position:0%
+designer, has deemed high stakes uh 16
+ 
+
+ align:start position:0%
+designer, has deemed high stakes uh 16
+times where you pull out three $5 bills.
+
+ align:start position:0%
+times where you pull out three $5 bills.
+ 
+
+ align:start position:0%
+times where you pull out three $5 bills.
+Um and so it says how to win. You win
+
+ align:start position:0%
+Um and so it says how to win. You win
+ 
+
+ align:start position:0%
+Um and so it says how to win. You win
+when the two pieces of your color are
+
+ align:start position:0%
+when the two pieces of your color are
+ 
+
+ align:start position:0%
+when the two pieces of your color are
+directly adjacent to each other. Um so
+
+ align:start position:0%
+directly adjacent to each other. Um so
+ 
+
+ align:start position:0%
+directly adjacent to each other. Um so
+diagonally adjacent does not count for a
+
+ align:start position:0%
+diagonally adjacent does not count for a
+ 
+
+ align:start position:0%
+diagonally adjacent does not count for a
+win. The way you play is players take
+
+ align:start position:0%
+win. The way you play is players take
+ 
+
+ align:start position:0%
+win. The way you play is players take
+turns starting with player one. When
+
+ align:start position:0%
+turns starting with player one. When
+ 
+
+ align:start position:0%
+turns starting with player one. When
+it's your turn, you say, "Put me to
+
+ align:start position:0%
+it's your turn, you say, "Put me to
+ 
+
+ align:start position:0%
+it's your turn, you say, "Put me to
+work." Uh players may then offer to pay
+
+ align:start position:0%
+work." Uh players may then offer to pay
+ 
+
+ align:start position:0%
+work." Uh players may then offer to pay
+you one or more dollars in any order. So
+
+ align:start position:0%
+you one or more dollars in any order. So
+ 
+
+ align:start position:0%
+you one or more dollars in any order. So
+anyone can just say, "I'll give you
+
+ align:start position:0%
+anyone can just say, "I'll give you
+ 
+
+ align:start position:0%
+anyone can just say, "I'll give you
+this." um you have to accept the highest
+
+ align:start position:0%
+this." um you have to accept the highest
+ 
+
+ align:start position:0%
+this." um you have to accept the highest
+payment except if there's a tie, right?
+
+ align:start position:0%
+payment except if there's a tie, right?
+ 
+
+ align:start position:0%
+payment except if there's a tie, right?
+Because with, you know, with specific
+
+ align:start position:0%
+Because with, you know, with specific
+ 
+
+ align:start position:0%
+Because with, you know, with specific
+denominations there's very likely to be
+
+ align:start position:0%
+denominations there's very likely to be
+ 
+
+ align:start position:0%
+denominations there's very likely to be
+a tie. Then you get to choose which of
+
+ align:start position:0%
+a tie. Then you get to choose which of
+ 
+
+ align:start position:0%
+a tie. Then you get to choose which of
+the highest biders um you can take and
+
+ align:start position:0%
+the highest biders um you can take and
+ 
+
+ align:start position:0%
+the highest biders um you can take and
+the the person who pays then tells you
+
+ align:start position:0%
+the the person who pays then tells you
+ 
+
+ align:start position:0%
+the the person who pays then tells you
+what move to make. Um and if no one
+
+ align:start position:0%
+what move to make. Um and if no one
+ 
+
+ align:start position:0%
+what move to make. Um and if no one
+offers to pay you, you get to decide
+
+ align:start position:0%
+offers to pay you, you get to decide
+ 
+
+ align:start position:0%
+offers to pay you, you get to decide
+what to do. Um and then it's the next
+
+ align:start position:0%
+what to do. Um and then it's the next
+ 
+
+ align:start position:0%
+what to do. Um and then it's the next
+player's turn and you continue until one
+
+ align:start position:0%
+player's turn and you continue until one
+ 
+
+ align:start position:0%
+player's turn and you continue until one
+player wins. Um,
+
+ align:start position:0%
+player wins. Um,
+ 
+
+ align:start position:0%
+player wins. Um,
+just off the top of your heads, having
+
+ align:start position:0%
+just off the top of your heads, having
+ 
+
+ align:start position:0%
+just off the top of your heads, having
+not even played it, um, it's tough to
+
+ align:start position:0%
+not even played it, um, it's tough to
+ 
+
+ align:start position:0%
+not even played it, um, it's tough to
+critique games when you haven't played,
+
+ align:start position:0%
+critique games when you haven't played,
+ 
+
+ align:start position:0%
+critique games when you haven't played,
+but just looking at the rules and
+
+ align:start position:0%
+but just looking at the rules and
+ 
+
+ align:start position:0%
+but just looking at the rules and
+hearing about it and even kind of I love
+
+ align:start position:0%
+hearing about it and even kind of I love
+ 
+
+ align:start position:0%
+hearing about it and even kind of I love
+that picture on the left because it it
+
+ align:start position:0%
+that picture on the left because it it
+ 
+
+ align:start position:0%
+that picture on the left because it it
+embodies some of the kind of spirit of
+
+ align:start position:0%
+embodies some of the kind of spirit of
+ 
+
+ align:start position:0%
+embodies some of the kind of spirit of
+the play, too. But, um, what are some
+
+ align:start position:0%
+the play, too. But, um, what are some
+ 
+
+ align:start position:0%
+the play, too. But, um, what are some
+interesting things about this rule set
+
+ align:start position:0%
+interesting things about this rule set
+ 
+
+ align:start position:0%
+interesting things about this rule set
+that you notice?
+
+ align:start position:0%
+that you notice?
+ 
+
+ align:start position:0%
+that you notice?
+>> You play with money, but you don't win
+
+ align:start position:0%
+>> You play with money, but you don't win
+ 
+
+ align:start position:0%
+>> You play with money, but you don't win
+money.
+
+ align:start position:0%
+money.
+ 
+
+ align:start position:0%
+money.
+>> Well, that's an interesting question.
+
+ align:start position:0%
+>> Well, that's an interesting question.
+ 
+
+ align:start position:0%
+>> Well, that's an interesting question.
+Uh, what happens to the money at the end
+
+ align:start position:0%
+Uh, what happens to the money at the end
+ 
+
+ align:start position:0%
+Uh, what happens to the money at the end
+of the game? Who knows? Do you keep it?
+
+ align:start position:0%
+of the game? Who knows? Do you keep it?
+ 
+
+ align:start position:0%
+of the game? Who knows? Do you keep it?
+That's unclear.
+
+ align:start position:0%
+That's unclear.
+ 
+
+ align:start position:0%
+That's unclear.
+>> Very, very unclear. And that's one of
+
+ align:start position:0%
+>> Very, very unclear. And that's one of
+ 
+
+ align:start position:0%
+>> Very, very unclear. And that's one of
+the things that's really great about
+
+ align:start position:0%
+the things that's really great about
+ 
+
+ align:start position:0%
+the things that's really great about
+this game, right? Is that that it puts
+
+ align:start position:0%
+this game, right? Is that that it puts
+ 
+
+ align:start position:0%
+this game, right? Is that that it puts
+you into these social situations where
+
+ align:start position:0%
+you into these social situations where
+ 
+
+ align:start position:0%
+you into these social situations where
+now you're playing with real currency
+
+ align:start position:0%
+now you're playing with real currency
+ 
+
+ align:start position:0%
+now you're playing with real currency
+that was your own. And now it's like,
+
+ align:start position:0%
+that was your own. And now it's like,
+ 
+
+ align:start position:0%
+that was your own. And now it's like,
+well, what what happens to this, right?
+
+ align:start position:0%
+well, what what happens to this, right?
+ 
+
+ align:start position:0%
+well, what what happens to this, right?
+And and so it says you win if your
+
+ align:start position:0%
+And and so it says you win if your
+ 
+
+ align:start position:0%
+And and so it says you win if your
+piece, but maybe you you feel like you
+
+ align:start position:0%
+piece, but maybe you you feel like you
+ 
+
+ align:start position:0%
+piece, but maybe you you feel like you
+win if you move the most pieces and you
+
+ align:start position:0%
+win if you move the most pieces and you
+ 
+
+ align:start position:0%
+win if you move the most pieces and you
+have the most money at the end of the
+
+ align:start position:0%
+have the most money at the end of the
+ 
+
+ align:start position:0%
+have the most money at the end of the
+game, right? I mean, you've got this
+
+ align:start position:0%
+game, right? I mean, you've got this
+ 
+
+ align:start position:0%
+game, right? I mean, you've got this
+kind of weird economy in here. Um, and I
+
+ align:start position:0%
+kind of weird economy in here. Um, and I
+ 
+
+ align:start position:0%
+kind of weird economy in here. Um, and I
+think the fact that it's not explicit um
+
+ align:start position:0%
+think the fact that it's not explicit um
+ 
+
+ align:start position:0%
+think the fact that it's not explicit um
+in this rule set is great, right? Right.
+
+ align:start position:0%
+in this rule set is great, right? Right.
+ 
+
+ align:start position:0%
+in this rule set is great, right? Right.
+I mean, that's that's what creates this
+
+ align:start position:0%
+I mean, that's that's what creates this
+ 
+
+ align:start position:0%
+I mean, that's that's what creates this
+sort of potential for kind of an
+
+ align:start position:0%
+sort of potential for kind of an
+ 
+
+ align:start position:0%
+sort of potential for kind of an
+interesting social dynamic. Other things
+
+ align:start position:0%
+interesting social dynamic. Other things
+ 
+
+ align:start position:0%
+interesting social dynamic. Other things
+that are interesting about this game, if
+
+ align:start position:0%
+that are interesting about this game, if
+ 
+
+ align:start position:0%
+that are interesting about this game, if
+you're the only person who has money,
+
+ align:start position:0%
+you're the only person who has money,
+ 
+
+ align:start position:0%
+you're the only person who has money,
+then you basically you can basically win
+
+ align:start position:0%
+then you basically you can basically win
+ 
+
+ align:start position:0%
+then you basically you can basically win
+if you're the only person who has money.
+
+ align:start position:0%
+if you're the only person who has money.
+ 
+
+ align:start position:0%
+if you're the only person who has money.
+Yeah. So, it does require a little bit
+
+ align:start position:0%
+Yeah. So, it does require a little bit
+ 
+
+ align:start position:0%
+Yeah. So, it does require a little bit
+of strategy, too. Um,
+
+ align:start position:0%
+of strategy, too. Um,
+ 
+
+ align:start position:0%
+of strategy, too. Um,
+>> technically from this that setup, could
+
+ align:start position:0%
+>> technically from this that setup, could
+ 
+
+ align:start position:0%
+>> technically from this that setup, could
+you win on the first turn? Because it
+
+ align:start position:0%
+you win on the first turn? Because it
+ 
+
+ align:start position:0%
+you win on the first turn? Because it
+seems you only have do you have two only
+
+ align:start position:0%
+seems you only have do you have two only
+ 
+
+ align:start position:0%
+seems you only have do you have two only
+two pieces of a certain color?
+
+ align:start position:0%
+two pieces of a certain color?
+ 
+
+ align:start position:0%
+two pieces of a certain color?
+>> Yeah, but up on the right assume the
+
+ align:start position:0%
+>> Yeah, but up on the right assume the
+ 
+
+ align:start position:0%
+>> Yeah, but up on the right assume the
+starting position.
+
+ align:start position:0%
+starting position.
+ 
+
+ align:start position:0%
+starting position.
+>> Yeah, I know. And so you so on your turn
+
+ align:start position:0%
+>> Yeah, I know. And so you so on your turn
+ 
+
+ align:start position:0%
+>> Yeah, I know. And so you so on your turn
+you could take one p your piece and and
+
+ align:start position:0%
+you could take one p your piece and and
+ 
+
+ align:start position:0%
+you could take one p your piece and and
+have it be moved to the square right
+
+ align:start position:0%
+have it be moved to the square right
+ 
+
+ align:start position:0%
+have it be moved to the square right
+next to yours.
+
+ align:start position:0%
+next to yours.
+ 
+
+ align:start position:0%
+next to yours.
+>> No move to any Oh. Oh, you have to move
+
+ align:start position:0%
+>> No move to any Oh. Oh, you have to move
+ 
+
+ align:start position:0%
+>> No move to any Oh. Oh, you have to move
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+>> Read the red.
+
+ align:start position:0%
+>> Read the red.
+ 
+
+ align:start position:0%
+>> Read the red.
+>> Oh, any adjacent note. Okay.
+
+ align:start position:0%
+>> Oh, any adjacent note. Okay.
+ 
+
+ align:start position:0%
+>> Oh, any adjacent note. Okay.
+>> I didn't read the adjacent adjacent
+
+ align:start position:0%
+>> I didn't read the adjacent adjacent
+ 
+
+ align:start position:0%
+>> I didn't read the adjacent adjacent
+empty square. Um
+
+ align:start position:0%
+empty square. Um
+ 
+
+ align:start position:0%
+empty square. Um
+>> that's actually really interesting.
+
+ align:start position:0%
+>> that's actually really interesting.
+ 
+
+ align:start position:0%
+>> that's actually really interesting.
+>> Yeah, it's a really weird I mean there I
+
+ align:start position:0%
+>> Yeah, it's a really weird I mean there I
+ 
+
+ align:start position:0%
+>> Yeah, it's a really weird I mean there I
+think the I also think the the you're
+
+ align:start position:0%
+think the I also think the the you're
+ 
+
+ align:start position:0%
+think the I also think the the you're
+you're not you're the agency you have in
+
+ align:start position:0%
+you're not you're the agency you have in
+ 
+
+ align:start position:0%
+you're not you're the agency you have in
+the game to to win is not by moving your
+
+ align:start position:0%
+the game to to win is not by moving your
+ 
+
+ align:start position:0%
+the game to to win is not by moving your
+own pieces. It's by paying someone to do
+
+ align:start position:0%
+own pieces. It's by paying someone to do
+ 
+
+ align:start position:0%
+own pieces. It's by paying someone to do
+the work for you, right? And so then we
+
+ align:start position:0%
+the work for you, right? And so then we
+ 
+
+ align:start position:0%
+the work for you, right? And so then we
+kind of get back to this quote at the
+
+ align:start position:0%
+kind of get back to this quote at the
+ 
+
+ align:start position:0%
+kind of get back to this quote at the
+beginning of the ego is 16 tons and what
+
+ align:start position:0%
+beginning of the ego is 16 tons and what
+ 
+
+ align:start position:0%
+beginning of the ego is 16 tons and what
+do you get another day in deeper debt?
+
+ align:start position:0%
+do you get another day in deeper debt?
+ 
+
+ align:start position:0%
+do you get another day in deeper debt?
+It's like what what is this game about?
+
+ align:start position:0%
+It's like what what is this game about?
+ 
+
+ align:start position:0%
+It's like what what is this game about?
+I mean, it could be about a lot of
+
+ align:start position:0%
+I mean, it could be about a lot of
+ 
+
+ align:start position:0%
+I mean, it could be about a lot of
+things. And I mean, we we we honestly
+
+ align:start position:0%
+things. And I mean, we we we honestly
+ 
+
+ align:start position:0%
+things. And I mean, we we we honestly
+probably shouldn't dissect it until
+
+ align:start position:0%
+probably shouldn't dissect it until
+ 
+
+ align:start position:0%
+probably shouldn't dissect it until
+we've played it. Um I think too the kind
+
+ align:start position:0%
+we've played it. Um I think too the kind
+ 
+
+ align:start position:0%
+we've played it. Um I think too the kind
+of corrugated cardboard, it gets hot
+
+ align:start position:0%
+of corrugated cardboard, it gets hot
+ 
+
+ align:start position:0%
+of corrugated cardboard, it gets hot
+inside of there if you're not outside.
+
+ align:start position:0%
+inside of there if you're not outside.
+ 
+
+ align:start position:0%
+inside of there if you're not outside.
+And that's a really interesting thing
+
+ align:start position:0%
+And that's a really interesting thing
+ 
+
+ align:start position:0%
+And that's a really interesting thing
+too, right? like you're in there, it's
+
+ align:start position:0%
+too, right? like you're in there, it's
+ 
+
+ align:start position:0%
+too, right? like you're in there, it's
+hot, it's sweaty, you've got dirty money
+
+ align:start position:0%
+hot, it's sweaty, you've got dirty money
+ 
+
+ align:start position:0%
+hot, it's sweaty, you've got dirty money
+in your hands, you're moving around
+
+ align:start position:0%
+in your hands, you're moving around
+ 
+
+ align:start position:0%
+in your hands, you're moving around
+these fair, you know, sizable, they have
+
+ align:start position:0%
+these fair, you know, sizable, they have
+ 
+
+ align:start position:0%
+these fair, you know, sizable, they have
+weight to them. That was really
+
+ align:start position:0%
+weight to them. That was really
+ 
+
+ align:start position:0%
+weight to them. That was really
+important, too, right? I mean, this
+
+ align:start position:0%
+important, too, right? I mean, this
+ 
+
+ align:start position:0%
+important, too, right? I mean, this
+could have been played around a table
+
+ align:start position:0%
+could have been played around a table
+ 
+
+ align:start position:0%
+could have been played around a table
+with, you know, go pieces or something,
+
+ align:start position:0%
+with, you know, go pieces or something,
+ 
+
+ align:start position:0%
+with, you know, go pieces or something,
+you know, painted go pieces, but these
+
+ align:start position:0%
+you know, painted go pieces, but these
+ 
+
+ align:start position:0%
+you know, painted go pieces, but these
+are like, you know, these are
+
+ align:start position:0%
+are like, you know, these are
+ 
+
+ align:start position:0%
+are like, you know, these are
+substantial steel pieces that you've got
+
+ align:start position:0%
+substantial steel pieces that you've got
+ 
+
+ align:start position:0%
+substantial steel pieces that you've got
+to pick up and move. Um, and, you know,
+
+ align:start position:0%
+to pick up and move. Um, and, you know,
+ 
+
+ align:start position:0%
+to pick up and move. Um, and, you know,
+obviously the well, the song was about
+
+ align:start position:0%
+obviously the well, the song was about
+ 
+
+ align:start position:0%
+obviously the well, the song was about
+kind of manual labor. Um,
+
+ align:start position:0%
+kind of manual labor. Um,
+ 
+
+ align:start position:0%
+kind of manual labor. Um,
+so this is a really interesting game.
+
+ align:start position:0%
+so this is a really interesting game.
+ 
+
+ align:start position:0%
+so this is a really interesting game.
+This was this was released at the art
+
+ align:start position:0%
+This was this was released at the art
+ 
+
+ align:start position:0%
+This was this was released at the art
+history of games conference last year
+
+ align:start position:0%
+history of games conference last year
+ 
+
+ align:start position:0%
+history of games conference last year
+and it did well at indicate this year it
+
+ align:start position:0%
+and it did well at indicate this year it
+ 
+
+ align:start position:0%
+and it did well at indicate this year it
+won the uh developers choice award. Um
+
+ align:start position:0%
+won the uh developers choice award. Um
+ 
+
+ align:start position:0%
+won the uh developers choice award. Um
+and it's it's it's really cool. I want
+
+ align:start position:0%
+and it's it's it's really cool. I want
+ 
+
+ align:start position:0%
+and it's it's it's really cool. I want
+to try to get it up to MIT so that we
+
+ align:start position:0%
+to try to get it up to MIT so that we
+ 
+
+ align:start position:0%
+to try to get it up to MIT so that we
+can all play it.
+
+ align:start position:0%
+can all play it.
+ 
+
+ align:start position:0%
+can all play it.
+>> It occurs to me that you could if you
+
+ align:start position:0%
+>> It occurs to me that you could if you
+ 
+
+ align:start position:0%
+>> It occurs to me that you could if you
+play by rules where you keep the money
+
+ align:start position:0%
+play by rules where you keep the money
+ 
+
+ align:start position:0%
+play by rules where you keep the money
+you get at the end of the game. You
+
+ align:start position:0%
+you get at the end of the game. You
+ 
+
+ align:start position:0%
+you get at the end of the game. You
+basically could throw the game to get
+
+ align:start position:0%
+basically could throw the game to get
+ 
+
+ align:start position:0%
+basically could throw the game to get
+all the money.
+
+ align:start position:0%
+all the money.
+ 
+
+ align:start position:0%
+all the money.
+>> Yeah. I mean you could try you could try
+
+ align:start position:0%
+>> Yeah. I mean you could try you could try
+ 
+
+ align:start position:0%
+>> Yeah. I mean you could try you could try
+right but but you know people are going
+
+ align:start position:0%
+right but but you know people are going
+ 
+
+ align:start position:0%
+right but but you know people are going
+to know what you're doing you know and
+
+ align:start position:0%
+to know what you're doing you know and
+ 
+
+ align:start position:0%
+to know what you're doing you know and
+people are going to see your strategy.
+
+ align:start position:0%
+people are going to see your strategy.
+ 
+
+ align:start position:0%
+people are going to see your strategy.
+So it's it's
+
+ align:start position:0%
+So it's it's
+ 
+
+ align:start position:0%
+So it's it's
+>> not going to pay you Jack.
+
+ align:start position:0%
+>> not going to pay you Jack.
+ 
+
+ align:start position:0%
+>> not going to pay you Jack.
+>> Yeah. Yeah, I mean the multiplayer gets
+
+ align:start position:0%
+>> Yeah. Yeah, I mean the multiplayer gets
+ 
+
+ align:start position:0%
+>> Yeah. Yeah, I mean the multiplayer gets
+the multi multiplayer the you know the
+
+ align:start position:0%
+the multi multiplayer the you know the
+ 
+
+ align:start position:0%
+the multi multiplayer the you know the
+game gets in this. Um so I mean again
+
+ align:start position:0%
+game gets in this. Um so I mean again
+ 
+
+ align:start position:0%
+game gets in this. Um so I mean again
+like just kind of cycling back to what
+
+ align:start position:0%
+like just kind of cycling back to what
+ 
+
+ align:start position:0%
+like just kind of cycling back to what
+we're talking about. I mean is this art
+
+ align:start position:0%
+we're talking about. I mean is this art
+ 
+
+ align:start position:0%
+we're talking about. I mean is this art
+you know it would be hard for me to call
+
+ align:start position:0%
+you know it would be hard for me to call
+ 
+
+ align:start position:0%
+you know it would be hard for me to call
+it much of anything else. Um
+
+ align:start position:0%
+it much of anything else. Um
+ 
+
+ align:start position:0%
+it much of anything else. Um
+so this is like one of my one of my
+
+ align:start position:0%
+so this is like one of my one of my
+ 
+
+ align:start position:0%
+so this is like one of my one of my
+favorite games. Uh it's certainly my
+
+ align:start position:0%
+favorite games. Uh it's certainly my
+ 
+
+ align:start position:0%
+favorite games. Uh it's certainly my
+favorite Jason Norade. Who's played
+
+ align:start position:0%
+favorite Jason Norade. Who's played
+ 
+
+ align:start position:0%
+favorite Jason Norade. Who's played
+gravitation here? A couple of you. All
+
+ align:start position:0%
+gravitation here? A couple of you. All
+ 
+
+ align:start position:0%
+gravitation here? A couple of you. All
+right cool. And a bunch of you haven't.
+
+ align:start position:0%
+right cool. And a bunch of you haven't.
+ 
+
+ align:start position:0%
+right cool. And a bunch of you haven't.
+That's awesome. So I'll get one of you
+
+ align:start position:0%
+That's awesome. So I'll get one of you
+ 
+
+ align:start position:0%
+That's awesome. So I'll get one of you
+to play it. Um, one thing I want to
+
+ align:start position:0%
+to play it. Um, one thing I want to
+ 
+
+ align:start position:0%
+to play it. Um, one thing I want to
+point out with this, I mean, we can talk
+
+ align:start position:0%
+point out with this, I mean, we can talk
+ 
+
+ align:start position:0%
+point out with this, I mean, we can talk
+after someone's played Gravitation a
+
+ align:start position:0%
+after someone's played Gravitation a
+ 
+
+ align:start position:0%
+after someone's played Gravitation a
+little bit about um, uh, about, you
+
+ align:start position:0%
+little bit about um, uh, about, you
+ 
+
+ align:start position:0%
+little bit about um, uh, about, you
+know, what we think about the game
+
+ align:start position:0%
+know, what we think about the game
+ 
+
+ align:start position:0%
+know, what we think about the game
+itself, but but I think this quote is
+
+ align:start position:0%
+itself, but but I think this quote is
+ 
+
+ align:start position:0%
+itself, but but I think this quote is
+interesting. You know, he has artist
+
+ align:start position:0%
+interesting. You know, he has artist
+ 
+
+ align:start position:0%
+interesting. You know, he has artist
+statements with all of his games. Um,
+
+ align:start position:0%
+statements with all of his games. Um,
+ 
+
+ align:start position:0%
+statements with all of his games. Um,
+some of them say more, some of them say
+
+ align:start position:0%
+some of them say more, some of them say
+ 
+
+ align:start position:0%
+some of them say more, some of them say
+less. This one responded because this
+
+ align:start position:0%
+less. This one responded because this
+ 
+
+ align:start position:0%
+less. This one responded because this
+was after Passage was released, and I
+
+ align:start position:0%
+was after Passage was released, and I
+ 
+
+ align:start position:0%
+was after Passage was released, and I
+think you guys have all seen Passage,
+
+ align:start position:0%
+think you guys have all seen Passage,
+ 
+
+ align:start position:0%
+think you guys have all seen Passage,
+right? And you can you can immediately
+
+ align:start position:0%
+right? And you can you can immediately
+ 
+
+ align:start position:0%
+right? And you can you can immediately
+identify the aesthetic similarities
+
+ align:start position:0%
+identify the aesthetic similarities
+ 
+
+ align:start position:0%
+identify the aesthetic similarities
+because the character is exactly the
+
+ align:start position:0%
+because the character is exactly the
+ 
+
+ align:start position:0%
+because the character is exactly the
+same. Um, and he was responding to
+
+ align:start position:0%
+same. Um, and he was responding to
+ 
+
+ align:start position:0%
+same. Um, and he was responding to
+criticism from people about his pixel
+
+ align:start position:0%
+criticism from people about his pixel
+ 
+
+ align:start position:0%
+criticism from people about his pixel
+art and why did he go for pixel art? Um,
+
+ align:start position:0%
+art and why did he go for pixel art? Um,
+ 
+
+ align:start position:0%
+art and why did he go for pixel art? Um,
+but he says, "I now see ultra- lowres
+
+ align:start position:0%
+but he says, "I now see ultra- lowres
+ 
+
+ align:start position:0%
+but he says, "I now see ultra- lowres
+pixel art as a kind of digital
+
+ align:start position:0%
+pixel art as a kind of digital
+ 
+
+ align:start position:0%
+pixel art as a kind of digital
+cartooning. It stands right on the line
+
+ align:start position:0%
+cartooning. It stands right on the line
+ 
+
+ align:start position:0%
+cartooning. It stands right on the line
+between the symbolic and the
+
+ align:start position:0%
+between the symbolic and the
+ 
+
+ align:start position:0%
+between the symbolic and the
+representational, leaving plenty of room
+
+ align:start position:0%
+representational, leaving plenty of room
+ 
+
+ align:start position:0%
+representational, leaving plenty of room
+for viewer interpretation. Why draw
+
+ align:start position:0%
+for viewer interpretation. Why draw
+ 
+
+ align:start position:0%
+for viewer interpretation. Why draw
+sideburns when the viewers can imagine
+
+ align:start position:0%
+sideburns when the viewers can imagine
+ 
+
+ align:start position:0%
+sideburns when the viewers can imagine
+sideburns on their own? You just need to
+
+ align:start position:0%
+sideburns on their own? You just need to
+ 
+
+ align:start position:0%
+sideburns on their own? You just need to
+give them something to pin their
+
+ align:start position:0%
+give them something to pin their
+ 
+
+ align:start position:0%
+give them something to pin their
+imagination on, something to guide them
+
+ align:start position:0%
+imagination on, something to guide them
+ 
+
+ align:start position:0%
+imagination on, something to guide them
+a bit. Cartoons are perfect for that."
+
+ align:start position:0%
+a bit. Cartoons are perfect for that."
+ 
+
+ align:start position:0%
+a bit. Cartoons are perfect for that."
+And and I think that's a really
+
+ align:start position:0%
+And and I think that's a really
+ 
+
+ align:start position:0%
+And and I think that's a really
+interesting point. And I think what he's
+
+ align:start position:0%
+interesting point. And I think what he's
+ 
+
+ align:start position:0%
+interesting point. And I think what he's
+what he's also suggesting here, which is
+
+ align:start position:0%
+what he's also suggesting here, which is
+ 
+
+ align:start position:0%
+what he's also suggesting here, which is
+maybe not clear, is that this is doing a
+
+ align:start position:0%
+maybe not clear, is that this is doing a
+ 
+
+ align:start position:0%
+maybe not clear, is that this is doing a
+similar thing to what that quote from
+
+ align:start position:0%
+similar thing to what that quote from
+ 
+
+ align:start position:0%
+similar thing to what that quote from
+the music does. It's priming your
+
+ align:start position:0%
+the music does. It's priming your
+ 
+
+ align:start position:0%
+the music does. It's priming your
+experience of the play. Right? You load
+
+ align:start position:0%
+experience of the play. Right? You load
+ 
+
+ align:start position:0%
+experience of the play. Right? You load
+up this game, you see that it's got this
+
+ align:start position:0%
+up this game, you see that it's got this
+ 
+
+ align:start position:0%
+up this game, you see that it's got this
+low res pixel art that we now associate
+
+ align:start position:0%
+low res pixel art that we now associate
+ 
+
+ align:start position:0%
+low res pixel art that we now associate
+with this kind of art, game movement,
+
+ align:start position:0%
+with this kind of art, game movement,
+ 
+
+ align:start position:0%
+with this kind of art, game movement,
+and you're ready to read this in another
+
+ align:start position:0%
+and you're ready to read this in another
+ 
+
+ align:start position:0%
+and you're ready to read this in another
+way. Um, if I gave you a firsterson
+
+ align:start position:0%
+way. Um, if I gave you a firsterson
+ 
+
+ align:start position:0%
+way. Um, if I gave you a firsterson
+shooter, um, and told you nothing about
+
+ align:start position:0%
+shooter, um, and told you nothing about
+ 
+
+ align:start position:0%
+shooter, um, and told you nothing about
+it except that it was going to be the
+
+ align:start position:0%
+it except that it was going to be the
+ 
+
+ align:start position:0%
+it except that it was going to be the
+fastest, awesomest multiplayer
+
+ align:start position:0%
+fastest, awesomest multiplayer
+ 
+
+ align:start position:0%
+fastest, awesomest multiplayer
+first-person shooter experience, but it
+
+ align:start position:0%
+first-person shooter experience, but it
+ 
+
+ align:start position:0%
+first-person shooter experience, but it
+looked like this. Um,
+
+ align:start position:0%
+looked like this. Um,
+ 
+
+ align:start position:0%
+looked like this. Um,
+you know, would you be inclined to read
+
+ align:start position:0%
+you know, would you be inclined to read
+ 
+
+ align:start position:0%
+you know, would you be inclined to read
+it like an art game? I mean, I I don't
+
+ align:start position:0%
+it like an art game? I mean, I I don't
+ 
+
+ align:start position:0%
+it like an art game? I mean, I I don't
+know. Um, but but certainly in this
+
+ align:start position:0%
+know. Um, but but certainly in this
+ 
+
+ align:start position:0%
+know. Um, but but certainly in this
+instance with these kind of little
+
+ align:start position:0%
+instance with these kind of little
+ 
+
+ align:start position:0%
+instance with these kind of little
+games, right, this this sort of pixel
+
+ align:start position:0%
+games, right, this this sort of pixel
+ 
+
+ align:start position:0%
+games, right, this this sort of pixel
+art aesthetic um that you see being
+
+ align:start position:0%
+art aesthetic um that you see being
+ 
+
+ align:start position:0%
+art aesthetic um that you see being
+duplicated in a lot of places is is sort
+
+ align:start position:0%
+duplicated in a lot of places is is sort
+ 
+
+ align:start position:0%
+duplicated in a lot of places is is sort
+of um I don't know, priming the pump.
+
+ align:start position:0%
+of um I don't know, priming the pump.
+ 
+
+ align:start position:0%
+of um I don't know, priming the pump.
+It's it's establishing some sort of
+
+ align:start position:0%
+It's it's establishing some sort of
+ 
+
+ align:start position:0%
+It's it's establishing some sort of
+context in which you can read this game.
+
+ align:start position:0%
+context in which you can read this game.
+ 
+
+ align:start position:0%
+context in which you can read this game.
+Um, so who wants to play uh gravitation?
+
+ align:start position:0%
+Um, so who wants to play uh gravitation?
+ 
+
+ align:start position:0%
+Um, so who wants to play uh gravitation?
+Actually, let me Oops. No, that's not
+
+ align:start position:0%
+Actually, let me Oops. No, that's not
+ 
+
+ align:start position:0%
+Actually, let me Oops. No, that's not
+supposed to happen. I wanted to click on
+
+ align:start position:0%
+supposed to happen. I wanted to click on
+ 
+
+ align:start position:0%
+supposed to happen. I wanted to click on
+the link. Oh, because I clicked on my
+
+ align:start position:0%
+the link. Oh, because I clicked on my
+ 
+
+ align:start position:0%
+the link. Oh, because I clicked on my
+screen, not this screen. And all it does
+
+ align:start position:0%
+screen, not this screen. And all it does
+ 
+
+ align:start position:0%
+screen, not this screen. And all it does
+is take me out of here.
+
+ align:start position:0%
+is take me out of here.
+ 
+
+ align:start position:0%
+is take me out of here.
+>> Me not being mirrored might be a
+
+ align:start position:0%
+>> Me not being mirrored might be a
+ 
+
+ align:start position:0%
+>> Me not being mirrored might be a
+problem. Let's see.
+
+ align:start position:0%
+problem. Let's see.
+ 
+
+ align:start position:0%
+problem. Let's see.
+Let's see what screen this loads up on.
+
+ align:start position:0%
+Let's see what screen this loads up on.
+ 
+
+ align:start position:0%
+Let's see what screen this loads up on.
+Both one. Crap. Okay, hold on one sec. I
+
+ align:start position:0%
+Both one. Crap. Okay, hold on one sec. I
+ 
+
+ align:start position:0%
+Both one. Crap. Okay, hold on one sec. I
+got to mirror my screen.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, I I should not be choosing who plays
+
+ align:start position:0%
+Um, I I should not be choosing who plays
+ 
+
+ align:start position:0%
+Um, I I should not be choosing who plays
+who wants to. Uh, I can't make a choice.
+
+ align:start position:0%
+who wants to. Uh, I can't make a choice.
+ 
+
+ align:start position:0%
+who wants to. Uh, I can't make a choice.
+Who wants to do it?
+
+ align:start position:0%
+Who wants to do it?
+ 
+
+ align:start position:0%
+Who wants to do it?
+>> Interesting that it's a version zero.
+
+ align:start position:0%
+>> Interesting that it's a version zero.
+ 
+
+ align:start position:0%
+>> Interesting that it's a version zero.
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> I have to explicitly make that the case.
+
+ align:start position:0%
+>> I have to explicitly make that the case.
+ 
+
+ align:start position:0%
+>> I have to explicitly make that the case.
+>> Uh,
+
+ align:start position:0%
+>> Uh,
+ 
+
+ align:start position:0%
+>> Uh,
+>> anybody. It's It's free. It's free to
+
+ align:start position:0%
+>> anybody. It's It's free. It's free to
+ 
+
+ align:start position:0%
+>> anybody. It's It's free. It's free to
+download. So, if you don't play it now,
+
+ align:start position:0%
+download. So, if you don't play it now,
+ 
+
+ align:start position:0%
+download. So, if you don't play it now,
+you can play it on your own.
+
+ align:start position:0%
+you can play it on your own.
+ 
+
+ align:start position:0%
+you can play it on your own.
+>> We have a few games, right? So, what's
+
+ align:start position:0%
+>> We have a few games, right? So, what's
+ 
+
+ align:start position:0%
+>> We have a few games, right? So, what's
+that?
+
+ align:start position:0%
+that?
+ 
+
+ align:start position:0%
+that?
+>> We have a few games, right? So,
+
+ align:start position:0%
+>> We have a few games, right? So,
+ 
+
+ align:start position:0%
+>> We have a few games, right? So,
+>> Oh, yeah. We have a few. So, yeah.
+
+ align:start position:0%
+>> Oh, yeah. We have a few. So, yeah.
+ 
+
+ align:start position:0%
+>> Oh, yeah. We have a few. So, yeah.
+Getting a few different opportunities to
+
+ align:start position:0%
+Getting a few different opportunities to
+ 
+
+ align:start position:0%
+Getting a few different opportunities to
+play. So, anybody jump over and and like
+
+ align:start position:0%
+play. So, anybody jump over and and like
+ 
+
+ align:start position:0%
+play. So, anybody jump over and and like
+>> we'll start with Jason and then we'll do
+
+ align:start position:0%
+>> we'll start with Jason and then we'll do
+ 
+
+ align:start position:0%
+>> we'll start with Jason and then we'll do
+kind of jumping into
+
+ align:start position:0%
+kind of jumping into
+ 
+
+ align:start position:0%
+kind of jumping into
+>> and actually if you wouldn't mind
+
+ align:start position:0%
+>> and actually if you wouldn't mind
+ 
+
+ align:start position:0%
+>> and actually if you wouldn't mind
+talking about your experience of playing
+
+ align:start position:0%
+talking about your experience of playing
+ 
+
+ align:start position:0%
+talking about your experience of playing
+Gravitation as you play it, you know,
+
+ align:start position:0%
+Gravitation as you play it, you know,
+ 
+
+ align:start position:0%
+Gravitation as you play it, you know,
+like like let's play the
+
+ align:start position:0%
+like like let's play the
+ 
+
+ align:start position:0%
+like like let's play the
+>> the live gravitation.
+
+ align:start position:0%
+>> the live gravitation.
+ 
+
+ align:start position:0%
+>> the live gravitation.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> Okay. Oh, I seem to have restricted you
+
+ align:start position:0%
+>> Okay. Oh, I seem to have restricted you
+ 
+
+ align:start position:0%
+>> Okay. Oh, I seem to have restricted you
+and it's falling.
+
+ align:start position:0%
+and it's falling.
+ 
+
+ align:start position:0%
+and it's falling.
+>> Oh, it is falling.
+
+ align:start position:0%
+>> Oh, it is falling.
+ 
+
+ align:start position:0%
+>> Oh, it is falling.
+>> Oh, wait. Oh, I
+
+ align:start position:0%
+>> Oh, wait. Oh, I
+ 
+
+ align:start position:0%
+>> Oh, wait. Oh, I
+>> Oh, I know.
+
+ align:start position:0%
+>> Oh, I know.
+ 
+
+ align:start position:0%
+>> Oh, I know.
+>> Oh, never mind.
+
+ align:start position:0%
+>> Oh, never mind.
+ 
+
+ align:start position:0%
+>> Oh, never mind.
+She stole your ball. Oh, she plays with
+
+ align:start position:0%
+She stole your ball. Oh, she plays with
+ 
+
+ align:start position:0%
+She stole your ball. Oh, she plays with
+you. She stole it.
+
+ align:start position:0%
+you. She stole it.
+ 
+
+ align:start position:0%
+you. She stole it.
+>> I hate her. I stole her ball.
+
+ align:start position:0%
+>> I hate her. I stole her ball.
+ 
+
+ align:start position:0%
+>> I hate her. I stole her ball.
+>> She seemed to like you, but she stole it
+
+ align:start position:0%
+>> She seemed to like you, but she stole it
+ 
+
+ align:start position:0%
+>> She seemed to like you, but she stole it
+for a little bit, but now she seems to
+
+ align:start position:0%
+for a little bit, but now she seems to
+ 
+
+ align:start position:0%
+for a little bit, but now she seems to
+be playing, which is better.
+
+ align:start position:0%
+be playing, which is better.
+ 
+
+ align:start position:0%
+be playing, which is better.
+>> Yes. Hurry up.
+
+ align:start position:0%
+>> Yes. Hurry up.
+ 
+
+ align:start position:0%
+>> Yes. Hurry up.
+>> We seem to be bouncing it back and
+
+ align:start position:0%
+>> We seem to be bouncing it back and
+ 
+
+ align:start position:0%
+>> We seem to be bouncing it back and
+forth. My screen gets bigger whenever I
+
+ align:start position:0%
+forth. My screen gets bigger whenever I
+ 
+
+ align:start position:0%
+forth. My screen gets bigger whenever I
+successfully do so. And it's getting
+
+ align:start position:0%
+successfully do so. And it's getting
+ 
+
+ align:start position:0%
+successfully do so. And it's getting
+brighter than earlier.
+
+ align:start position:0%
+brighter than earlier.
+ 
+
+ align:start position:0%
+brighter than earlier.
+>> A gets bigger when she loves you.
+
+ align:start position:0%
+>> A gets bigger when she loves you.
+ 
+
+ align:start position:0%
+>> A gets bigger when she loves you.
+>> Screaming thing
+
+ align:start position:0%
+>> Screaming thing
+ 
+
+ align:start position:0%
+>> Screaming thing
+more. Yay.
+
+ align:start position:0%
+more. Yay.
+ 
+
+ align:start position:0%
+more. Yay.
+>> Hit it up there.
+
+ align:start position:0%
+>> Hit it up there.
+ 
+
+ align:start position:0%
+>> Hit it up there.
+>> What happens when
+
+ align:start position:0%
+>> What happens when
+ 
+
+ align:start position:0%
+>> What happens when
+>> you're on fire?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> You're on fire. This seems bad.
+
+ align:start position:0%
+>> You're on fire. This seems bad.
+ 
+
+ align:start position:0%
+>> You're on fire. This seems bad.
+>> Really confused.
+
+ align:start position:0%
+>> Really confused.
+ 
+
+ align:start position:0%
+>> Really confused.
+>> You should go to the furnace.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Oh, now you're not on fire. That makes
+
+ align:start position:0%
+>> Oh, now you're not on fire. That makes
+ 
+
+ align:start position:0%
+>> Oh, now you're not on fire. That makes
+sense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Whoa.
+
+ align:start position:0%
+Whoa.
+ 
+
+ align:start position:0%
+Whoa.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Wait, can you bounce the ball up there?
+
+ align:start position:0%
+Wait, can you bounce the ball up there?
+ 
+
+ align:start position:0%
+Wait, can you bounce the ball up there?
+>> I didn't see people jump high. How do I
+
+ align:start position:0%
+>> I didn't see people jump high. How do I
+ 
+
+ align:start position:0%
+>> I didn't see people jump high. How do I
+get up there?
+
+ align:start position:0%
+get up there?
+ 
+
+ align:start position:0%
+get up there?
+>> Oh, there we go.
+
+ align:start position:0%
+>> Oh, there we go.
+ 
+
+ align:start position:0%
+>> Oh, there we go.
+>> Not always the case.
+
+ align:start position:0%
+>> Not always the case.
+ 
+
+ align:start position:0%
+>> Not always the case.
+>> Whoa.
+
+ align:start position:0%
+>> Whoa.
+ 
+
+ align:start position:0%
+>> Whoa.
+>> What's that star?
+
+ align:start position:0%
+>> What's that star?
+ 
+
+ align:start position:0%
+>> What's that star?
+>> Or wall jump.
+
+ align:start position:0%
+>> Or wall jump.
+ 
+
+ align:start position:0%
+>> Or wall jump.
+>> Uh-oh. Well, now you can bounce the
+
+ align:start position:0%
+>> Uh-oh. Well, now you can bounce the
+ 
+
+ align:start position:0%
+>> Uh-oh. Well, now you can bounce the
+ball.
+
+ align:start position:0%
+ball.
+ 
+
+ align:start position:0%
+ball.
+>> Oh, you can jump higher when she size of
+
+ align:start position:0%
+>> Oh, you can jump higher when she size of
+ 
+
+ align:start position:0%
+>> Oh, you can jump higher when she size of
+the screen dictates how high you can
+
+ align:start position:0%
+the screen dictates how high you can
+ 
+
+ align:start position:0%
+the screen dictates how high you can
+jump.
+
+ align:start position:0%
+jump.
+ 
+
+ align:start position:0%
+jump.
+>> Okay, so I guess you'll bounce it more.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh, is gra Oh, there.
+
+ align:start position:0%
+Oh, is gra Oh, there.
+ 
+
+ align:start position:0%
+Oh, is gra Oh, there.
+>> You're just using her.
+
+ align:start position:0%
+>> You're just using her.
+ 
+
+ align:start position:0%
+>> You're just using her.
+>> I'm on fire again.
+
+ align:start position:0%
+>> I'm on fire again.
+ 
+
+ align:start position:0%
+>> I'm on fire again.
+>> How could you?
+
+ align:start position:0%
+>> How could you?
+ 
+
+ align:start position:0%
+>> How could you?
+>> Oh, but you're not on fire.
+
+ align:start position:0%
+>> Oh, but you're not on fire.
+ 
+
+ align:start position:0%
+>> Oh, but you're not on fire.
+>> She's not going to love you very soon.
+
+ align:start position:0%
+>> She's not going to love you very soon.
+ 
+
+ align:start position:0%
+>> She's not going to love you very soon.
+>> Yeah, apparently
+
+ align:start position:0%
+>> Yeah, apparently
+ 
+
+ align:start position:0%
+>> Yeah, apparently
+star is is also good.
+
+ align:start position:0%
+star is is also good.
+ 
+
+ align:start position:0%
+star is is also good.
+>> At least not she presumably loves me.
+
+ align:start position:0%
+>> At least not she presumably loves me.
+ 
+
+ align:start position:0%
+>> At least not she presumably loves me.
+>> Oh, no.
+
+ align:start position:0%
+>> Oh, no.
+ 
+
+ align:start position:0%
+>> Oh, no.
+>> Yeah, but it's faster and faster the
+
+ align:start position:0%
+>> Yeah, but it's faster and faster the
+ 
+
+ align:start position:0%
+>> Yeah, but it's faster and faster the
+higher up you get, I think.
+
+ align:start position:0%
+higher up you get, I think.
+ 
+
+ align:start position:0%
+higher up you get, I think.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Weird. Or maybe the more stars you eat.
+
+ align:start position:0%
+>> Weird. Or maybe the more stars you eat.
+ 
+
+ align:start position:0%
+>> Weird. Or maybe the more stars you eat.
+>> And now it's all ice.
+
+ align:start position:0%
+>> And now it's all ice.
+ 
+
+ align:start position:0%
+>> And now it's all ice.
+>> Oh.
+
+ align:start position:0%
+>> Oh.
+ 
+
+ align:start position:0%
+>> Oh.
+>> Oh, yes. Because she was getting happier
+
+ align:start position:0%
+>> Oh, yes. Because she was getting happier
+ 
+
+ align:start position:0%
+>> Oh, yes. Because she was getting happier
+when I bounced the ball. I guess she
+
+ align:start position:0%
+when I bounced the ball. I guess she
+ 
+
+ align:start position:0%
+when I bounced the ball. I guess she
+doesn't get cold.
+
+ align:start position:0%
+doesn't get cold.
+ 
+
+ align:start position:0%
+doesn't get cold.
+>> Oh my god.
+
+ align:start position:0%
+>> Oh my god.
+ 
+
+ align:start position:0%
+>> Oh my god.
+>> Oh no.
+
+ align:start position:0%
+>> Oh no.
+ 
+
+ align:start position:0%
+>> Oh no.
+>> Oh, it's blocking the um
+
+ align:start position:0%
+>> Oh, it's blocking the um
+ 
+
+ align:start position:0%
+>> Oh, it's blocking the um
+>> There's fire though.
+
+ align:start position:0%
+>> There's fire though.
+ 
+
+ align:start position:0%
+>> There's fire though.
+>> I think it maybe push the stars into the
+
+ align:start position:0%
+>> I think it maybe push the stars into the
+ 
+
+ align:start position:0%
+>> I think it maybe push the stars into the
+fire so that they melt or something.
+
+ align:start position:0%
+fire so that they melt or something.
+ 
+
+ align:start position:0%
+fire so that they melt or something.
+>> Arrow pointing.
+
+ align:start position:0%
+>> Arrow pointing.
+ 
+
+ align:start position:0%
+>> Arrow pointing.
+>> Oh, now it's a star.
+
+ align:start position:0%
+>> Oh, now it's a star.
+ 
+
+ align:start position:0%
+>> Oh, now it's a star.
+>> Interesting.
+
+ align:start position:0%
+>> Interesting.
+ 
+
+ align:start position:0%
+>> Interesting.
+>> Well, there's been a star there the
+
+ align:start position:0%
+>> Well, there's been a star there the
+ 
+
+ align:start position:0%
+>> Well, there's been a star there the
+entire time.
+
+ align:start position:0%
+entire time.
+ 
+
+ align:start position:0%
+entire time.
+>> What?
+
+ align:start position:0%
+>> What?
+ 
+
+ align:start position:0%
+>> What?
+All right, go push. Start with
+
+ align:start position:0%
+All right, go push. Start with
+ 
+
+ align:start position:0%
+All right, go push. Start with
+>> Oh, I see you have a hammer.
+
+ align:start position:0%
+>> Oh, I see you have a hammer.
+ 
+
+ align:start position:0%
+>> Oh, I see you have a hammer.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah, you're dead.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> It's cuz you're on fire.
+
+ align:start position:0%
+>> It's cuz you're on fire.
+ 
+
+ align:start position:0%
+>> It's cuz you're on fire.
+>> The numbers on the stars are all
+
+ align:start position:0%
+>> The numbers on the stars are all
+ 
+
+ align:start position:0%
+>> The numbers on the stars are all
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> the ball can't get to you. It says that.
+
+ align:start position:0%
+>> the ball can't get to you. It says that.
+ 
+
+ align:start position:0%
+>> the ball can't get to you. It says that.
+>> But now I can probably what?
+
+ align:start position:0%
+>> But now I can probably what?
+ 
+
+ align:start position:0%
+>> But now I can probably what?
+>> Push the ice into the fire. And the um
+
+ align:start position:0%
+>> Push the ice into the fire. And the um
+ 
+
+ align:start position:0%
+>> Push the ice into the fire. And the um
+the number on the top goes up every time
+
+ align:start position:0%
+the number on the top goes up every time
+ 
+
+ align:start position:0%
+the number on the top goes up every time
+you Yeah. The numbers on the star
+
+ align:start position:0%
+you Yeah. The numbers on the star
+ 
+
+ align:start position:0%
+you Yeah. The numbers on the star
+correspond to how many like
+
+ align:start position:0%
+correspond to how many like
+ 
+
+ align:start position:0%
+correspond to how many like
+>> you get
+
+ align:start position:0%
+>> you get
+ 
+
+ align:start position:0%
+>> you get
+>> being on fire seems like it would be
+
+ align:start position:0%
+>> being on fire seems like it would be
+ 
+
+ align:start position:0%
+>> being on fire seems like it would be
+bad.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> A
+
+ align:start position:0%
+>> A
+ 
+
+ align:start position:0%
+>> A
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tried to get rid of the ice. Can we put
+
+ align:start position:0%
+tried to get rid of the ice. Can we put
+ 
+
+ align:start position:0%
+tried to get rid of the ice. Can we put
+the lid? Okay.
+
+ align:start position:0%
+the lid? Okay.
+ 
+
+ align:start position:0%
+the lid? Okay.
+Wait, she doesn't want to play.
+
+ align:start position:0%
+Wait, she doesn't want to play.
+ 
+
+ align:start position:0%
+Wait, she doesn't want to play.
+>> That's because I got rid of the ice and
+
+ align:start position:0%
+>> That's because I got rid of the ice and
+ 
+
+ align:start position:0%
+>> That's because I got rid of the ice and
+he was happy, I think.
+
+ align:start position:0%
+he was happy, I think.
+ 
+
+ align:start position:0%
+he was happy, I think.
+>> Oh, it's getting icy, though.
+
+ align:start position:0%
+>> Oh, it's getting icy, though.
+ 
+
+ align:start position:0%
+>> Oh, it's getting icy, though.
+It's getting colder.
+
+ align:start position:0%
+It's getting colder.
+ 
+
+ align:start position:0%
+It's getting colder.
+>> There's no more stars to recharge my
+
+ align:start position:0%
+>> There's no more stars to recharge my
+ 
+
+ align:start position:0%
+>> There's no more stars to recharge my
+thing, though.
+
+ align:start position:0%
+thing, though.
+ 
+
+ align:start position:0%
+thing, though.
+>> I think you just have to go hard. This
+
+ align:start position:0%
+>> I think you just have to go hard. This
+ 
+
+ align:start position:0%
+>> I think you just have to go hard. This
+is where you were last time, I think.
+
+ align:start position:0%
+is where you were last time, I think.
+ 
+
+ align:start position:0%
+is where you were last time, I think.
+Yeah, there.
+
+ align:start position:0%
+Yeah, there.
+ 
+
+ align:start position:0%
+Yeah, there.
+>> Get the star.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh no, no.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get this too fast and your hair is
+
+ align:start position:0%
+you get this too fast and your hair is
+ 
+
+ align:start position:0%
+you get this too fast and your hair is
+burning. That means you're just getting
+
+ align:start position:0%
+burning. That means you're just getting
+ 
+
+ align:start position:0%
+burning. That means you're just getting
+too much love and it like starts falling
+
+ align:start position:0%
+too much love and it like starts falling
+ 
+
+ align:start position:0%
+too much love and it like starts falling
+really fast.
+
+ align:start position:0%
+really fast.
+ 
+
+ align:start position:0%
+really fast.
+>> Oh no.
+
+ align:start position:0%
+>> Oh no.
+ 
+
+ align:start position:0%
+>> Oh no.
+>> Oh no. Oh, no.
+
+ align:start position:0%
+>> Oh no. Oh, no.
+ 
+
+ align:start position:0%
+>> Oh no. Oh, no.
+>> But there's a there's a there's a
+
+ align:start position:0%
+>> But there's a there's a there's a
+ 
+
+ align:start position:0%
+>> But there's a there's a there's a
+counter on the ice blocks of the stars,
+
+ align:start position:0%
+counter on the ice blocks of the stars,
+ 
+
+ align:start position:0%
+counter on the ice blocks of the stars,
+and you get more points if you get them
+
+ align:start position:0%
+and you get more points if you get them
+ 
+
+ align:start position:0%
+and you get more points if you get them
+into the furnace faster.
+
+ align:start position:0%
+into the furnace faster.
+ 
+
+ align:start position:0%
+into the furnace faster.
+>> I think they went down when he started
+
+ align:start position:0%
+>> I think they went down when he started
+ 
+
+ align:start position:0%
+>> I think they went down when he started
+warming up in the furnace. So, the
+
+ align:start position:0%
+warming up in the furnace. So, the
+ 
+
+ align:start position:0%
+warming up in the furnace. So, the
+warmer the world is less points you get
+
+ align:start position:0%
+warmer the world is less points you get
+ 
+
+ align:start position:0%
+warmer the world is less points you get
+for the icing. Is this about global
+
+ align:start position:0%
+for the icing. Is this about global
+ 
+
+ align:start position:0%
+for the icing. Is this about global
+warming?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Okay, so this
+
+ align:start position:0%
+>> Okay, so this
+ 
+
+ align:start position:0%
+>> Okay, so this
+>> I think it's about drugs. He gets love
+
+ align:start position:0%
+>> I think it's about drugs. He gets love
+ 
+
+ align:start position:0%
+>> I think it's about drugs. He gets love
+from this girl and then like I think
+
+ align:start position:0%
+from this girl and then like I think
+ 
+
+ align:start position:0%
+from this girl and then like I think
+make him happy, but only for a little
+
+ align:start position:0%
+make him happy, but only for a little
+ 
+
+ align:start position:0%
+make him happy, but only for a little
+bit.
+
+ align:start position:0%
+bit.
+ 
+
+ align:start position:0%
+bit.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> What?
+
+ align:start position:0%
+>> What?
+ 
+
+ align:start position:0%
+>> What?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> So, if I'm on fire, it seems to reduce
+
+ align:start position:0%
+>> So, if I'm on fire, it seems to reduce
+ 
+
+ align:start position:0%
+>> So, if I'm on fire, it seems to reduce
+at a much faster rate.
+
+ align:start position:0%
+at a much faster rate.
+ 
+
+ align:start position:0%
+at a much faster rate.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should avoid burning by not eating too
+
+ align:start position:0%
+should avoid burning by not eating too
+ 
+
+ align:start position:0%
+should avoid burning by not eating too
+many stars at a time.
+
+ align:start position:0%
+many stars at a time.
+ 
+
+ align:start position:0%
+many stars at a time.
+>> Just hit all
+
+ align:start position:0%
+>> Just hit all
+ 
+
+ align:start position:0%
+>> Just hit all
+>> everything is about drugs.
+
+ align:start position:0%
+>> everything is about drugs.
+ 
+
+ align:start position:0%
+>> everything is about drugs.
+>> I think everything's about drugs.
+
+ align:start position:0%
+>> I think everything's about drugs.
+ 
+
+ align:start position:0%
+>> I think everything's about drugs.
+>> I mean, yeah, obviously I'm crazy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> You can actually catch a triple dragon
+
+ align:start position:0%
+>> You can actually catch a triple dragon
+ 
+
+ align:start position:0%
+>> You can actually catch a triple dragon
+in that case.
+
+ align:start position:0%
+in that case.
+ 
+
+ align:start position:0%
+in that case.
+>> Oh no.
+
+ align:start position:0%
+>> Oh no.
+ 
+
+ align:start position:0%
+>> Oh no.
+Uh two.
+
+ align:start position:0%
+Uh two.
+ 
+
+ align:start position:0%
+Uh two.
+>> Oh no.
+
+ align:start position:0%
+>> Oh no.
+ 
+
+ align:start position:0%
+>> Oh no.
+>> Really stupid design. Go all the way
+
+ align:start position:0%
+>> Really stupid design. Go all the way
+ 
+
+ align:start position:0%
+>> Really stupid design. Go all the way
+back down.
+
+ align:start position:0%
+back down.
+ 
+
+ align:start position:0%
+back down.
+>> There's a column on the right. You can
+
+ align:start position:0%
+>> There's a column on the right. You can
+ 
+
+ align:start position:0%
+>> There's a column on the right. You can
+fall fast.
+
+ align:start position:0%
+fall fast.
+ 
+
+ align:start position:0%
+fall fast.
+>> Oh, really?
+
+ align:start position:0%
+>> Oh, really?
+ 
+
+ align:start position:0%
+>> Oh, really?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> The high you climb the further fall.
+
+ align:start position:0%
+>> The high you climb the further fall.
+ 
+
+ align:start position:0%
+>> The high you climb the further fall.
+>> Poetic.
+
+ align:start position:0%
+>> Poetic.
+ 
+
+ align:start position:0%
+>> Poetic.
+>> Now I probably don't have any stars. So
+
+ align:start position:0%
+>> Now I probably don't have any stars. So
+ 
+
+ align:start position:0%
+>> Now I probably don't have any stars. So
+I think we need to play
+
+ align:start position:0%
+I think we need to play
+ 
+
+ align:start position:0%
+I think we need to play
+>> Oh, she's gone. She's dead.
+
+ align:start position:0%
+>> Oh, she's gone. She's dead.
+ 
+
+ align:start position:0%
+>> Oh, she's gone. She's dead.
+>> You killed her.
+
+ align:start position:0%
+>> You killed her.
+ 
+
+ align:start position:0%
+>> You killed her.
+>> That's too sad. And there's not much
+
+ align:start position:0%
+>> That's too sad. And there's not much
+ 
+
+ align:start position:0%
+>> That's too sad. And there's not much
+fire left.
+
+ align:start position:0%
+fire left.
+ 
+
+ align:start position:0%
+fire left.
+>> Oh no. And the fire isn't bringing
+
+ align:start position:0%
+>> Oh no. And the fire isn't bringing
+ 
+
+ align:start position:0%
+>> Oh no. And the fire isn't bringing
+things back.
+
+ align:start position:0%
+things back.
+ 
+
+ align:start position:0%
+things back.
+>> Oh my god. You didn't get any stars
+
+ align:start position:0%
+>> Oh my god. You didn't get any stars
+ 
+
+ align:start position:0%
+>> Oh my god. You didn't get any stars
+first, so she died.
+
+ align:start position:0%
+first, so she died.
+ 
+
+ align:start position:0%
+first, so she died.
+>> Oh,
+
+ align:start position:0%
+>> Oh,
+ 
+
+ align:start position:0%
+>> Oh,
+>> she eats stars.
+
+ align:start position:0%
+>> she eats stars.
+ 
+
+ align:start position:0%
+>> she eats stars.
+>> Oh, there you go.
+
+ align:start position:0%
+>> Oh, there you go.
+ 
+
+ align:start position:0%
+>> Oh, there you go.
+>> There you go. Oh, is she there now? The
+
+ align:start position:0%
+>> There you go. Oh, is she there now? The
+ 
+
+ align:start position:0%
+>> There you go. Oh, is she there now? The
+fire started warming you again.
+
+ align:start position:0%
+fire started warming you again.
+ 
+
+ align:start position:0%
+fire started warming you again.
+>> Therapy.
+
+ align:start position:0%
+>> Therapy.
+ 
+
+ align:start position:0%
+>> Therapy.
+No.
+
+ align:start position:0%
+No.
+ 
+
+ align:start position:0%
+No.
+>> No, she's gone forever.
+
+ align:start position:0%
+>> No, she's gone forever.
+ 
+
+ align:start position:0%
+>> No, she's gone forever.
+>> You can't play ball alone.
+
+ align:start position:0%
+>> You can't play ball alone.
+ 
+
+ align:start position:0%
+>> You can't play ball alone.
+>> Well, she's going Oh, you're going to
+
+ align:start position:0%
+>> Well, she's going Oh, you're going to
+ 
+
+ align:start position:0%
+>> Well, she's going Oh, you're going to
+go.
+
+ align:start position:0%
+go.
+ 
+
+ align:start position:0%
+go.
+>> Maybe she only comes in the spring.
+
+ align:start position:0%
+>> Maybe she only comes in the spring.
+ 
+
+ align:start position:0%
+>> Maybe she only comes in the spring.
+Maybe winter's too cold. So maybe if I
+
+ align:start position:0%
+Maybe winter's too cold. So maybe if I
+ 
+
+ align:start position:0%
+Maybe winter's too cold. So maybe if I
+wait by the fire.
+
+ align:start position:0%
+wait by the fire.
+ 
+
+ align:start position:0%
+wait by the fire.
+>> Does it go faster?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. What? Why is it getting bigger?
+
+ align:start position:0%
+>> Yeah. What? Why is it getting bigger?
+ 
+
+ align:start position:0%
+>> Yeah. What? Why is it getting bigger?
+>> Cuz he's by the fire. It's getting
+
+ align:start position:0%
+>> Cuz he's by the fire. It's getting
+ 
+
+ align:start position:0%
+>> Cuz he's by the fire. It's getting
+warmer. But that wasn't working earlier.
+
+ align:start position:0%
+warmer. But that wasn't working earlier.
+ 
+
+ align:start position:0%
+warmer. But that wasn't working earlier.
+>> Now it is.
+
+ align:start position:0%
+>> Now it is.
+ 
+
+ align:start position:0%
+>> Now it is.
+>> Go faster.
+
+ align:start position:0%
+>> Go faster.
+ 
+
+ align:start position:0%
+>> Go faster.
+>> He's a rock bottom. It's like spring.
+
+ align:start position:0%
+>> He's a rock bottom. It's like spring.
+ 
+
+ align:start position:0%
+>> He's a rock bottom. It's like spring.
+>> But
+
+ align:start position:0%
+>> But
+ 
+
+ align:start position:0%
+>> But
+she How high can you jump right now?
+
+ align:start position:0%
+she How high can you jump right now?
+ 
+
+ align:start position:0%
+she How high can you jump right now?
+>> Can you hit the ball?
+
+ align:start position:0%
+>> Can you hit the ball?
+ 
+
+ align:start position:0%
+>> Can you hit the ball?
+>> Pretty high. That's a lot of jumps.
+
+ align:start position:0%
+>> Pretty high. That's a lot of jumps.
+ 
+
+ align:start position:0%
+>> Pretty high. That's a lot of jumps.
+>> No, I can't hit the ball.
+
+ align:start position:0%
+>> No, I can't hit the ball.
+ 
+
+ align:start position:0%
+>> No, I can't hit the ball.
+>> Only she can lift the ball.
+
+ align:start position:0%
+>> Only she can lift the ball.
+ 
+
+ align:start position:0%
+>> Only she can lift the ball.
+>> Well, while you're increasing, you
+
+ align:start position:0%
+>> Well, while you're increasing, you
+ 
+
+ align:start position:0%
+>> Well, while you're increasing, you
+should probably go up and get the stars.
+
+ align:start position:0%
+should probably go up and get the stars.
+ 
+
+ align:start position:0%
+should probably go up and get the stars.
+>> Go up. Go up.
+
+ align:start position:0%
+>> Go up. Go up.
+ 
+
+ align:start position:0%
+>> Go up. Go up.
+>> There we go.
+
+ align:start position:0%
+>> There we go.
+ 
+
+ align:start position:0%
+>> There we go.
+>> Stop expanding.
+
+ align:start position:0%
+>> Stop expanding.
+ 
+
+ align:start position:0%
+>> Stop expanding.
+>> Isn't it Is it the stars?
+
+ align:start position:0%
+>> Isn't it Is it the stars?
+ 
+
+ align:start position:0%
+>> Isn't it Is it the stars?
+>> Stop contracting, too.
+
+ align:start position:0%
+>> Stop contracting, too.
+ 
+
+ align:start position:0%
+>> Stop contracting, too.
+>> Oh, you're even on fire now.
+
+ align:start position:0%
+>> Oh, you're even on fire now.
+ 
+
+ align:start position:0%
+>> Oh, you're even on fire now.
+>> He's on fire.
+
+ align:start position:0%
+>> He's on fire.
+ 
+
+ align:start position:0%
+>> He's on fire.
+>> Can you go infinitely high if you're on
+
+ align:start position:0%
+>> Can you go infinitely high if you're on
+ 
+
+ align:start position:0%
+>> Can you go infinitely high if you're on
+fire?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Pretty darn high. That was like pretty.
+
+ align:start position:0%
+>> Pretty darn high. That was like pretty.
+ 
+
+ align:start position:0%
+>> Pretty darn high. That was like pretty.
+Uhoh.
+
+ align:start position:0%
+Uhoh.
+ 
+
+ align:start position:0%
+Uhoh.
+>> Four stars.
+
+ align:start position:0%
+>> Four stars.
+ 
+
+ align:start position:0%
+>> Four stars.
+>> Are you getting all of them? Oh, I Oh,
+
+ align:start position:0%
+>> Are you getting all of them? Oh, I Oh,
+ 
+
+ align:start position:0%
+>> Are you getting all of them? Oh, I Oh,
+>> that might have been a bit of an
+
+ align:start position:0%
+>> that might have been a bit of an
+ 
+
+ align:start position:0%
+>> that might have been a bit of an
+overdose.
+
+ align:start position:0%
+overdose.
+ 
+
+ align:start position:0%
+overdose.
+>> No.
+
+ align:start position:0%
+>> No.
+ 
+
+ align:start position:0%
+>> No.
+>> Yeah, you totally ODed on stars just
+
+ align:start position:0%
+>> Yeah, you totally ODed on stars just
+ 
+
+ align:start position:0%
+>> Yeah, you totally ODed on stars just
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+>> cuz you can always get stars as you go
+
+ align:start position:0%
+>> cuz you can always get stars as you go
+ 
+
+ align:start position:0%
+>> cuz you can always get stars as you go
+back.
+
+ align:start position:0%
+back.
+ 
+
+ align:start position:0%
+back.
+>> Or you can only hold four and then it
+
+ align:start position:0%
+>> Or you can only hold four and then it
+ 
+
+ align:start position:0%
+>> Or you can only hold four and then it
+retracts when you get four and then it
+
+ align:start position:0%
+retracts when you get four and then it
+ 
+
+ align:start position:0%
+retracts when you get four and then it
+turns ice blocks.
+
+ align:start position:0%
+turns ice blocks.
+ 
+
+ align:start position:0%
+turns ice blocks.
+>> What?
+
+ align:start position:0%
+>> What?
+ 
+
+ align:start position:0%
+>> What?
+>> That was intense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> They're worth so much.
+
+ align:start position:0%
+>> They're worth so much.
+ 
+
+ align:start position:0%
+>> They're worth so much.
+Wait,
+
+ align:start position:0%
+Wait,
+ 
+
+ align:start position:0%
+Wait,
+>> and
+
+ align:start position:0%
+>> and
+ 
+
+ align:start position:0%
+>> and
+when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> you won,
+
+ align:start position:0%
+>> you won,
+ 
+
+ align:start position:0%
+>> you won,
+>> y
+
+ align:start position:0%
+>> y
+ 
+
+ align:start position:0%
+>> y
+>> what you want is a good question.
+
+ align:start position:0%
+>> what you want is a good question.
+ 
+
+ align:start position:0%
+>> what you want is a good question.
+>> That's gravitation. And actually, I
+
+ align:start position:0%
+>> That's gravitation. And actually, I
+ 
+
+ align:start position:0%
+>> That's gravitation. And actually, I
+mean, I'm not even kidding. That's
+
+ align:start position:0%
+mean, I'm not even kidding. That's
+ 
+
+ align:start position:0%
+mean, I'm not even kidding. That's
+that's certainly my favorite Jason game.
+
+ align:start position:0%
+that's certainly my favorite Jason game.
+ 
+
+ align:start position:0%
+that's certainly my favorite Jason game.
+It's it's one of
+
+ align:start position:0%
+It's it's one of
+ 
+
+ align:start position:0%
+It's it's one of
+>> it's one of my favorite games. And and I
+
+ align:start position:0%
+>> it's one of my favorite games. And and I
+ 
+
+ align:start position:0%
+>> it's one of my favorite games. And and I
+think even just the example of you guys
+
+ align:start position:0%
+think even just the example of you guys
+ 
+
+ align:start position:0%
+think even just the example of you guys
+playing is great, right? because because
+
+ align:start position:0%
+playing is great, right? because because
+ 
+
+ align:start position:0%
+playing is great, right? because because
+you're just kind of shouting out all
+
+ align:start position:0%
+you're just kind of shouting out all
+ 
+
+ align:start position:0%
+you're just kind of shouting out all
+these different ideas for what it could
+
+ align:start position:0%
+these different ideas for what it could
+ 
+
+ align:start position:0%
+these different ideas for what it could
+be about. Um and um you know there's
+
+ align:start position:0%
+be about. Um and um you know there's
+ 
+
+ align:start position:0%
+be about. Um and um you know there's
+some clear intentionality in in in his
+
+ align:start position:0%
+some clear intentionality in in in his
+ 
+
+ align:start position:0%
+some clear intentionality in in in his
+uh in his design um with this game,
+
+ align:start position:0%
+uh in his design um with this game,
+ 
+
+ align:start position:0%
+uh in his design um with this game,
+right? In terms of the systems trying to
+
+ align:start position:0%
+right? In terms of the systems trying to
+ 
+
+ align:start position:0%
+right? In terms of the systems trying to
+communicate something that's other than
+
+ align:start position:0%
+communicate something that's other than
+ 
+
+ align:start position:0%
+communicate something that's other than
+just, you know, engagement um or or I
+
+ align:start position:0%
+just, you know, engagement um or or I
+ 
+
+ align:start position:0%
+just, you know, engagement um or or I
+don't know, God, fun. Um I was it fun?
+
+ align:start position:0%
+don't know, God, fun. Um I was it fun?
+ 
+
+ align:start position:0%
+don't know, God, fun. Um I was it fun?
+>> Yeah. Oh, all right. Cool. Um yeah,
+
+ align:start position:0%
+>> Yeah. Oh, all right. Cool. Um yeah,
+ 
+
+ align:start position:0%
+>> Yeah. Oh, all right. Cool. Um yeah,
+that's pretty good. Um thoughts on what
+
+ align:start position:0%
+that's pretty good. Um thoughts on what
+ 
+
+ align:start position:0%
+that's pretty good. Um thoughts on what
+it's about? I heard a couple people be
+
+ align:start position:0%
+it's about? I heard a couple people be
+ 
+
+ align:start position:0%
+it's about? I heard a couple people be
+like drugs.
+
+ align:start position:0%
+like drugs.
+ 
+
+ align:start position:0%
+like drugs.
+>> Definitely drugs.
+
+ align:start position:0%
+>> Definitely drugs.
+ 
+
+ align:start position:0%
+>> Definitely drugs.
+>> Definitely drugs.
+
+ align:start position:0%
+>> Definitely drugs.
+ 
+
+ align:start position:0%
+>> Definitely drugs.
+>> Tons of analogies. Yeah.
+
+ align:start position:0%
+>> Tons of analogies. Yeah.
+ 
+
+ align:start position:0%
+>> Tons of analogies. Yeah.
+>> Yeah. It's kind of like drugs.
+
+ align:start position:0%
+>> Yeah. It's kind of like drugs.
+ 
+
+ align:start position:0%
+>> Yeah. It's kind of like drugs.
+>> Well, look,
+
+ align:start position:0%
+>> Well, look,
+ 
+
+ align:start position:0%
+>> Well, look,
+>> love is a relationship versus like
+
+ align:start position:0%
+>> love is a relationship versus like
+ 
+
+ align:start position:0%
+>> love is a relationship versus like
+whatever you're trying to do, your
+
+ align:start position:0%
+whatever you're trying to do, your
+ 
+
+ align:start position:0%
+whatever you're trying to do, your
+career, your
+
+ align:start position:0%
+career, your
+ 
+
+ align:start position:0%
+career, your
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah. I actually I call this like in
+
+ align:start position:0%
+>> Yeah. I actually I call this like in
+ 
+
+ align:start position:0%
+>> Yeah. I actually I call this like in
+life.
+
+ align:start position:0%
+life.
+ 
+
+ align:start position:0%
+life.
+>> I think it's like the ultimate MIT game.
+
+ align:start position:0%
+>> I think it's like the ultimate MIT game.
+ 
+
+ align:start position:0%
+>> I think it's like the ultimate MIT game.
+Um if I uh if I uh told you that this
+
+ align:start position:0%
+Um if I uh if I uh told you that this
+ 
+
+ align:start position:0%
+Um if I uh if I uh told you that this
+was his daughter,
+
+ align:start position:0%
+was his daughter,
+ 
+
+ align:start position:0%
+was his daughter,
+>> um would it change your interpretations
+
+ align:start position:0%
+>> um would it change your interpretations
+ 
+
+ align:start position:0%
+>> um would it change your interpretations
+of of the game and what happened?
+
+ align:start position:0%
+of of the game and what happened?
+ 
+
+ align:start position:0%
+of of the game and what happened?
+>> Yeah. So, so, so now if you know that
+
+ align:start position:0%
+>> Yeah. So, so, so now if you know that
+ 
+
+ align:start position:0%
+>> Yeah. So, so, so now if you know that
+this is his daughter, what do you think
+
+ align:start position:0%
+this is his daughter, what do you think
+ 
+
+ align:start position:0%
+this is his daughter, what do you think
+it's about?
+
+ align:start position:0%
+it's about?
+ 
+
+ align:start position:0%
+it's about?
+>> His job,
+
+ align:start position:0%
+>> His job,
+ 
+
+ align:start position:0%
+>> His job,
+>> neglect,
+
+ align:start position:0%
+>> neglect,
+ 
+
+ align:start position:0%
+>> neglect,
+>> work, neglect, job versus family, right?
+
+ align:start position:0%
+>> work, neglect, job versus family, right?
+ 
+
+ align:start position:0%
+>> work, neglect, job versus family, right?
+You know, he kind of
+
+ align:start position:0%
+You know, he kind of
+ 
+
+ align:start position:0%
+You know, he kind of
+>> um he says he says explicitly like
+
+ align:start position:0%
+>> um he says he says explicitly like
+ 
+
+ align:start position:0%
+>> um he says he says explicitly like
+before you played that this is a game
+
+ align:start position:0%
+before you played that this is a game
+ 
+
+ align:start position:0%
+before you played that this is a game
+about motivation. Um and he doesn't go
+
+ align:start position:0%
+about motivation. Um and he doesn't go
+ 
+
+ align:start position:0%
+about motivation. Um and he doesn't go
+doesn't go too far into telling you what
+
+ align:start position:0%
+doesn't go too far into telling you what
+ 
+
+ align:start position:0%
+doesn't go too far into telling you what
+the game is specifically about. And I
+
+ align:start position:0%
+the game is specifically about. And I
+ 
+
+ align:start position:0%
+the game is specifically about. And I
+think playing through it a couple times,
+
+ align:start position:0%
+think playing through it a couple times,
+ 
+
+ align:start position:0%
+think playing through it a couple times,
+but I mean I will tell you the first
+
+ align:start position:0%
+but I mean I will tell you the first
+ 
+
+ align:start position:0%
+but I mean I will tell you the first
+time I played and I came back out and
+
+ align:start position:0%
+time I played and I came back out and
+ 
+
+ align:start position:0%
+time I played and I came back out and
+she was gone, it was very upsetting for
+
+ align:start position:0%
+she was gone, it was very upsetting for
+ 
+
+ align:start position:0%
+she was gone, it was very upsetting for
+me. I was like, you know, and I don't
+
+ align:start position:0%
+me. I was like, you know, and I don't
+ 
+
+ align:start position:0%
+me. I was like, you know, and I don't
+know if it's just, you know, just, you
+
+ align:start position:0%
+know if it's just, you know, just, you
+ 
+
+ align:start position:0%
+know if it's just, you know, just, you
+know, I was, you know, ready to play it
+
+ align:start position:0%
+know, I was, you know, ready to play it
+ 
+
+ align:start position:0%
+know, I was, you know, ready to play it
+that way or my life stage or something
+
+ align:start position:0%
+that way or my life stage or something
+ 
+
+ align:start position:0%
+that way or my life stage or something
+like that. But the the idea of, you
+
+ align:start position:0%
+like that. But the the idea of, you
+ 
+
+ align:start position:0%
+like that. But the the idea of, you
+know, he's he's playing with his
+
+ align:start position:0%
+know, he's he's playing with his
+ 
+
+ align:start position:0%
+know, he's he's playing with his
+daughter that inspires him. You know, he
+
+ align:start position:0%
+daughter that inspires him. You know, he
+ 
+
+ align:start position:0%
+daughter that inspires him. You know, he
+travels and then, you know, one of these
+
+ align:start position:0%
+travels and then, you know, one of these
+ 
+
+ align:start position:0%
+travels and then, you know, one of these
+days if you're gone too long, she grows
+
+ align:start position:0%
+days if you're gone too long, she grows
+ 
+
+ align:start position:0%
+days if you're gone too long, she grows
+up. I mean, I don't know if she dies,
+
+ align:start position:0%
+up. I mean, I don't know if she dies,
+ 
+
+ align:start position:0%
+up. I mean, I don't know if she dies,
+but but you know,
+
+ align:start position:0%
+but but you know,
+ 
+
+ align:start position:0%
+but but you know,
+>> you didn't bring her any money,
+
+ align:start position:0%
+>> you didn't bring her any money,
+ 
+
+ align:start position:0%
+>> you didn't bring her any money,
+>> right? She cuz she had no money. Yeah,
+
+ align:start position:0%
+>> right? She cuz she had no money. Yeah,
+ 
+
+ align:start position:0%
+>> right? She cuz she had no money. Yeah,
+>> she died.
+
+ align:start position:0%
+>> she died.
+ 
+
+ align:start position:0%
+>> she died.
+>> So, I think this is a really really game
+
+ align:start position:0%
+>> So, I think this is a really really game
+ 
+
+ align:start position:0%
+>> So, I think this is a really really game
+and a game about motivation.
+
+ align:start position:0%
+and a game about motivation.
+ 
+
+ align:start position:0%
+and a game about motivation.
+>> It is. Yeah. or she wish she owed you on
+
+ align:start position:0%
+>> It is. Yeah. or she wish she owed you on
+ 
+
+ align:start position:0%
+>> It is. Yeah. or she wish she owed you on
+drugs.
+
+ align:start position:0%
+drugs.
+ 
+
+ align:start position:0%
+drugs.
+>> So, it's free. If you just Google search
+
+ align:start position:0%
+>> So, it's free. If you just Google search
+ 
+
+ align:start position:0%
+>> So, it's free. If you just Google search
+gravitation Jason, you'll you'll find
+
+ align:start position:0%
+gravitation Jason, you'll you'll find
+ 
+
+ align:start position:0%
+gravitation Jason, you'll you'll find
+the links to it. You'll find his artist
+
+ align:start position:0%
+the links to it. You'll find his artist
+ 
+
+ align:start position:0%
+the links to it. You'll find his artist
+statement, which I think is really kind
+
+ align:start position:0%
+statement, which I think is really kind
+ 
+
+ align:start position:0%
+statement, which I think is really kind
+of good to read. Um, again, with John
+
+ align:start position:0%
+of good to read. Um, again, with John
+ 
+
+ align:start position:0%
+of good to read. Um, again, with John
+Sharp's kind of point about like, you
+
+ align:start position:0%
+Sharp's kind of point about like, you
+ 
+
+ align:start position:0%
+Sharp's kind of point about like, you
+know, declaring your intentionality,
+
+ align:start position:0%
+know, declaring your intentionality,
+ 
+
+ align:start position:0%
+know, declaring your intentionality,
+whether you say what the game's about is
+
+ align:start position:0%
+whether you say what the game's about is
+ 
+
+ align:start position:0%
+whether you say what the game's about is
+important. Um, again, I I think I think
+
+ align:start position:0%
+important. Um, again, I I think I think
+ 
+
+ align:start position:0%
+important. Um, again, I I think I think
+this qualifies, at least for me, as art.
+
+ align:start position:0%
+this qualifies, at least for me, as art.
+ 
+
+ align:start position:0%
+this qualifies, at least for me, as art.
+Um, it's doing things that that I see
+
+ align:start position:0%
+Um, it's doing things that that I see
+ 
+
+ align:start position:0%
+Um, it's doing things that that I see
+other pieces of art doing. Um, okay. So,
+
+ align:start position:0%
+other pieces of art doing. Um, okay. So,
+ 
+
+ align:start position:0%
+other pieces of art doing. Um, okay. So,
+Paulo Percini, how many of your time?
+
+ align:start position:0%
+Paulo Percini, how many of your time?
+ 
+
+ align:start position:0%
+Paulo Percini, how many of your time?
+Um, uh, Paulo Percini is is one of my
+
+ align:start position:0%
+Um, uh, Paulo Percini is is one of my
+ 
+
+ align:start position:0%
+Um, uh, Paulo Percini is is one of my
+favorite game designers right now, and
+
+ align:start position:0%
+favorite game designers right now, and
+ 
+
+ align:start position:0%
+favorite game designers right now, and
+this this game actually is is is one of
+
+ align:start position:0%
+this this game actually is is is one of
+ 
+
+ align:start position:0%
+this this game actually is is is one of
+his newest ones, and I think it's I
+
+ align:start position:0%
+his newest ones, and I think it's I
+ 
+
+ align:start position:0%
+his newest ones, and I think it's I
+think it's hilarious and great. Um, and
+
+ align:start position:0%
+think it's hilarious and great. Um, and
+ 
+
+ align:start position:0%
+think it's hilarious and great. Um, and
+it's called Memory Reloaded: The
+
+ align:start position:0%
+it's called Memory Reloaded: The
+ 
+
+ align:start position:0%
+it's called Memory Reloaded: The
+Downfall. Test your concentration with
+
+ align:start position:0%
+Downfall. Test your concentration with
+ 
+
+ align:start position:0%
+Downfall. Test your concentration with
+Memory Reloaded, a matching game for
+
+ align:start position:0%
+Memory Reloaded, a matching game for
+ 
+
+ align:start position:0%
+Memory Reloaded, a matching game for
+these unstable times. History may be
+
+ align:start position:0%
+these unstable times. History may be
+ 
+
+ align:start position:0%
+these unstable times. History may be
+different from that which you remember.
+
+ align:start position:0%
+different from that which you remember.
+ 
+
+ align:start position:0%
+different from that which you remember.
+And who would like to play Memory
+
+ align:start position:0%
+And who would like to play Memory
+ 
+
+ align:start position:0%
+And who would like to play Memory
+Reloaded? I'm laughing already because
+
+ align:start position:0%
+Reloaded? I'm laughing already because
+ 
+
+ align:start position:0%
+Reloaded? I'm laughing already because
+it's funny. Has anybody played it? I
+
+ align:start position:0%
+it's funny. Has anybody played it? I
+ 
+
+ align:start position:0%
+it's funny. Has anybody played it? I
+need someone who's not played it. Okay,
+
+ align:start position:0%
+need someone who's not played it. Okay,
+ 
+
+ align:start position:0%
+need someone who's not played it. Okay,
+good. Jeremy, you want to do it?
+
+ align:start position:0%
+good. Jeremy, you want to do it?
+ 
+
+ align:start position:0%
+good. Jeremy, you want to do it?
+>> Sure.
+
+ align:start position:0%
+>> Sure.
+ 
+
+ align:start position:0%
+>> Sure.
+>> Awesome.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This presentation is so cool.
+
+ align:start position:0%
+This presentation is so cool.
+ 
+
+ align:start position:0%
+This presentation is so cool.
+>> Okay, you're up.
+
+ align:start position:0%
+>> Okay, you're up.
+ 
+
+ align:start position:0%
+>> Okay, you're up.
+>> I will click.
+
+ align:start position:0%
+>> I will click.
+ 
+
+ align:start position:0%
+>> I will click.
+>> Don't do it.
+
+ align:start position:0%
+>> Don't do it.
+ 
+
+ align:start position:0%
+>> Don't do it.
+>> Oh, you're out.
+
+ align:start position:0%
+>> Oh, you're out.
+ 
+
+ align:start position:0%
+>> Oh, you're out.
+>> You're done. You lost already.
+
+ align:start position:0%
+>> You're done. You lost already.
+ 
+
+ align:start position:0%
+>> You're done. You lost already.
+>> No way. That's kind of scary. All right.
+
+ align:start position:0%
+>> No way. That's kind of scary. All right.
+ 
+
+ align:start position:0%
+>> No way. That's kind of scary. All right.
+Oh, I can already see what they're going
+
+ align:start position:0%
+Oh, I can already see what they're going
+ 
+
+ align:start position:0%
+Oh, I can already see what they're going
+to do. They're You're going to play
+
+ align:start position:0%
+to do. They're You're going to play
+ 
+
+ align:start position:0%
+to do. They're You're going to play
+Switch on me. All right. Afghan freedom
+
+ align:start position:0%
+Switch on me. All right. Afghan freedom
+ 
+
+ align:start position:0%
+Switch on me. All right. Afghan freedom
+fighter. He's going to be a terrorist
+
+ align:start position:0%
+fighter. He's going to be a terrorist
+ 
+
+ align:start position:0%
+fighter. He's going to be a terrorist
+later.
+
+ align:start position:0%
+later.
+ 
+
+ align:start position:0%
+later.
+>> Migrant workforce.
+
+ align:start position:0%
+>> Migrant workforce.
+ 
+
+ align:start position:0%
+>> Migrant workforce.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Life for the workforce. Yay. Nick. Yay.
+
+ align:start position:0%
+Life for the workforce. Yay. Nick. Yay.
+ 
+
+ align:start position:0%
+Life for the workforce. Yay. Nick. Yay.
+>> Iraqi oil. Afghan freedom fighter.
+
+ align:start position:0%
+>> Iraqi oil. Afghan freedom fighter.
+ 
+
+ align:start position:0%
+>> Iraqi oil. Afghan freedom fighter.
+>> I bet if you grab Iraqi oil before
+
+ align:start position:0%
+>> I bet if you grab Iraqi oil before
+ 
+
+ align:start position:0%
+>> I bet if you grab Iraqi oil before
+Afghan freedom fighter, he becomes a
+
+ align:start position:0%
+Afghan freedom fighter, he becomes a
+ 
+
+ align:start position:0%
+Afghan freedom fighter, he becomes a
+terrorist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Global inequality. Peace and
+
+ align:start position:0%
+>> Global inequality. Peace and
+ 
+
+ align:start position:0%
+>> Global inequality. Peace and
+>> global inequality.
+
+ align:start position:0%
+>> global inequality.
+ 
+
+ align:start position:0%
+>> global inequality.
+>> Global inequality.
+
+ align:start position:0%
+>> Global inequality.
+ 
+
+ align:start position:0%
+>> Global inequality.
+>> Global inequality.
+
+ align:start position:0%
+>> Global inequality.
+ 
+
+ align:start position:0%
+>> Global inequality.
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> Yes. Global inequality.
+
+ align:start position:0%
+>> Yes. Global inequality.
+ 
+
+ align:start position:0%
+>> Yes. Global inequality.
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> All right.
+
+ align:start position:0%
+>> All right.
+ 
+
+ align:start position:0%
+>> All right.
+I'm doing well. Ruthless maker
+
+ align:start position:0%
+I'm doing well. Ruthless maker
+ 
+
+ align:start position:0%
+I'm doing well. Ruthless maker
+>> loan chart. Rocky was Rocky here.
+
+ align:start position:0%
+>> loan chart. Rocky was Rocky here.
+ 
+
+ align:start position:0%
+>> loan chart. Rocky was Rocky here.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Awkward. All right. Universal
+
+ align:start position:0%
+>> Awkward. All right. Universal
+ 
+
+ align:start position:0%
+>> Awkward. All right. Universal
+healthcare. Man-made global warming.
+
+ align:start position:0%
+healthcare. Man-made global warming.
+ 
+
+ align:start position:0%
+healthcare. Man-made global warming.
+>> Man-made natural.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Hey, not cool. Universal healthcare.
+
+ align:start position:0%
+>> Hey, not cool. Universal healthcare.
+ 
+
+ align:start position:0%
+>> Hey, not cool. Universal healthcare.
+>> Universal healthcare. Sweet.
+
+ align:start position:0%
+>> Universal healthcare. Sweet.
+ 
+
+ align:start position:0%
+>> Universal healthcare. Sweet.
+>> Oh,
+
+ align:start position:0%
+>> Oh,
+ 
+
+ align:start position:0%
+>> Oh,
+one over there.
+
+ align:start position:0%
+one over there.
+ 
+
+ align:start position:0%
+one over there.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+Nice. Hooray. Right under Valentine.
+
+ align:start position:0%
+Nice. Hooray. Right under Valentine.
+ 
+
+ align:start position:0%
+Nice. Hooray. Right under Valentine.
+>> Well, natural. Come on.
+
+ align:start position:0%
+>> Well, natural. Come on.
+ 
+
+ align:start position:0%
+>> Well, natural. Come on.
+>> Wait. What?
+
+ align:start position:0%
+>> Wait. What?
+ 
+
+ align:start position:0%
+>> Wait. What?
+>> Why? Needy maker. Ruthless maker.
+
+ align:start position:0%
+>> Why? Needy maker. Ruthless maker.
+ 
+
+ align:start position:0%
+>> Why? Needy maker. Ruthless maker.
+>> Oh, that's the order. You click them in.
+
+ align:start position:0%
+>> Oh, that's the order. You click them in.
+ 
+
+ align:start position:0%
+>> Oh, that's the order. You click them in.
+>> Ruthless maker. What?
+
+ align:start position:0%
+>> Ruthless maker. What?
+ 
+
+ align:start position:0%
+>> Ruthless maker. What?
+>> What? What are the other ones now?
+
+ align:start position:0%
+>> What? What are the other ones now?
+ 
+
+ align:start position:0%
+>> What? What are the other ones now?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Oh, there we go.
+
+ align:start position:0%
+>> Oh, there we go.
+ 
+
+ align:start position:0%
+>> Oh, there we go.
+>> Nice.
+
+ align:start position:0%
+>> Nice.
+ 
+
+ align:start position:0%
+>> Nice.
+>> So, that means now let's see.
+
+ align:start position:0%
+>> So, that means now let's see.
+ 
+
+ align:start position:0%
+>> So, that means now let's see.
+Hey. He's never a satisfied baker.
+
+ align:start position:0%
+Hey. He's never a satisfied baker.
+ 
+
+ align:start position:0%
+Hey. He's never a satisfied baker.
+>> Where?
+
+ align:start position:0%
+>> Where?
+ 
+
+ align:start position:0%
+>> Where?
+>> What the hell?
+
+ align:start position:0%
+>> What the hell?
+ 
+
+ align:start position:0%
+>> What the hell?
+>> Oh dear. Did we shoot
+
+ align:start position:0%
+>> Oh dear. Did we shoot
+ 
+
+ align:start position:0%
+>> Oh dear. Did we shoot
+>> better move?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Oh, I get it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's fine. Is it the entire game?
+
+ align:start position:0%
+That's fine. Is it the entire game?
+ 
+
+ align:start position:0%
+That's fine. Is it the entire game?
+>> Yes, that that is the the whole game. Of
+
+ align:start position:0%
+>> Yes, that that is the the whole game. Of
+ 
+
+ align:start position:0%
+>> Yes, that that is the the whole game. Of
+course, you can get different outcomes,
+
+ align:start position:0%
+course, you can get different outcomes,
+ 
+
+ align:start position:0%
+course, you can get different outcomes,
+but uh but yeah, that's the idea. Um
+
+ align:start position:0%
+but uh but yeah, that's the idea. Um
+ 
+
+ align:start position:0%
+but uh but yeah, that's the idea. Um
+>> so I think you guys have seen some of uh
+
+ align:start position:0%
+>> so I think you guys have seen some of uh
+ 
+
+ align:start position:0%
+>> so I think you guys have seen some of uh
+some of Mullet Mysteria's other work
+
+ align:start position:0%
+some of Mullet Mysteria's other work
+ 
+
+ align:start position:0%
+some of Mullet Mysteria's other work
+that you guys saw every day the same
+
+ align:start position:0%
+that you guys saw every day the same
+ 
+
+ align:start position:0%
+that you guys saw every day the same
+dream. I like that
+
+ align:start position:0%
+dream. I like that
+ 
+
+ align:start position:0%
+dream. I like that
+>> which is interesting. Um yeah, that that
+
+ align:start position:0%
+>> which is interesting. Um yeah, that that
+ 
+
+ align:start position:0%
+>> which is interesting. Um yeah, that that
+one's that one's also one of my favorite
+
+ align:start position:0%
+one's that one's also one of my favorite
+ 
+
+ align:start position:0%
+one's that one's also one of my favorite
+games. Um but this is, you know, this is
+
+ align:start position:0%
+games. Um but this is, you know, this is
+ 
+
+ align:start position:0%
+games. Um but this is, you know, this is
+kind of uh this is this is kind of
+
+ align:start position:0%
+kind of uh this is this is kind of
+ 
+
+ align:start position:0%
+kind of uh this is this is kind of
+looking at another kind of sector of
+
+ align:start position:0%
+looking at another kind of sector of
+ 
+
+ align:start position:0%
+looking at another kind of sector of
+art, right? The kind of activist
+
+ align:start position:0%
+art, right? The kind of activist
+ 
+
+ align:start position:0%
+art, right? The kind of activist
+political statement sector of art and
+
+ align:start position:0%
+political statement sector of art and
+ 
+
+ align:start position:0%
+political statement sector of art and
+doing that through games and and it's
+
+ align:start position:0%
+doing that through games and and it's
+ 
+
+ align:start position:0%
+doing that through games and and it's
+something that this music
+
+ align:start position:0%
+something that this music
+ 
+
+ align:start position:0%
+something that this music
+um something that um that he does
+
+ align:start position:0%
+um something that um that he does
+ 
+
+ align:start position:0%
+um something that um that he does
+particularly well with his games and I
+
+ align:start position:0%
+particularly well with his games and I
+ 
+
+ align:start position:0%
+particularly well with his games and I
+think this one's this one's particularly
+
+ align:start position:0%
+think this one's this one's particularly
+ 
+
+ align:start position:0%
+think this one's this one's particularly
+um interesting and kind of funny. I love
+
+ align:start position:0%
+um interesting and kind of funny. I love
+ 
+
+ align:start position:0%
+um interesting and kind of funny. I love
+I love the um
+
+ align:start position:0%
+I love the um
+ 
+
+ align:start position:0%
+I love the um
+the kind of reworking of a really
+
+ align:start position:0%
+the kind of reworking of a really
+ 
+
+ align:start position:0%
+the kind of reworking of a really
+classic game mechanic, right? Like
+
+ align:start position:0%
+classic game mechanic, right? Like
+ 
+
+ align:start position:0%
+classic game mechanic, right? Like
+memory the the entire point of memory is
+
+ align:start position:0%
+memory the the entire point of memory is
+ 
+
+ align:start position:0%
+memory the the entire point of memory is
+your expectation that they would be the
+
+ align:start position:0%
+your expectation that they would be the
+ 
+
+ align:start position:0%
+your expectation that they would be the
+same the second time you turn it over.
+
+ align:start position:0%
+same the second time you turn it over.
+ 
+
+ align:start position:0%
+same the second time you turn it over.
+And when it changes on you, it
+
+ align:start position:0%
+And when it changes on you, it
+ 
+
+ align:start position:0%
+And when it changes on you, it
+reinforces that kind of uh that kind of
+
+ align:start position:0%
+reinforces that kind of uh that kind of
+ 
+
+ align:start position:0%
+reinforces that kind of uh that kind of
+perspective uh I suppose imbalance um
+
+ align:start position:0%
+perspective uh I suppose imbalance um
+ 
+
+ align:start position:0%
+perspective uh I suppose imbalance um
+that can exist when you're not just
+
+ align:start position:0%
+that can exist when you're not just
+ 
+
+ align:start position:0%
+that can exist when you're not just
+turning over, you know, toad stools and
+
+ align:start position:0%
+turning over, you know, toad stools and
+ 
+
+ align:start position:0%
+turning over, you know, toad stools and
+and Bowsers, but you know, actual kind
+
+ align:start position:0%
+and Bowsers, but you know, actual kind
+ 
+
+ align:start position:0%
+and Bowsers, but you know, actual kind
+of interesting things. I really I love
+
+ align:start position:0%
+of interesting things. I really I love
+ 
+
+ align:start position:0%
+of interesting things. I really I love
+the the crying sweating polar bear um
+
+ align:start position:0%
+the the crying sweating polar bear um
+ 
+
+ align:start position:0%
+the the crying sweating polar bear um
+and and the well with like a beach chair
+
+ align:start position:0%
+and and the well with like a beach chair
+ 
+
+ align:start position:0%
+and and the well with like a beach chair
+actually cracks me down. Um and I think
+
+ align:start position:0%
+actually cracks me down. Um and I think
+ 
+
+ align:start position:0%
+actually cracks me down. Um and I think
+humor is actually something that
+
+ align:start position:0%
+humor is actually something that
+ 
+
+ align:start position:0%
+humor is actually something that
+shouldn't be ignored here, right? I
+
+ align:start position:0%
+shouldn't be ignored here, right? I
+ 
+
+ align:start position:0%
+shouldn't be ignored here, right? I
+mean, if we remember that was one of the
+
+ align:start position:0%
+mean, if we remember that was one of the
+ 
+
+ align:start position:0%
+mean, if we remember that was one of the
+kind of the central flux things, this
+
+ align:start position:0%
+kind of the central flux things, this
+ 
+
+ align:start position:0%
+kind of the central flux things, this
+idea of like satire, humor is important.
+
+ align:start position:0%
+idea of like satire, humor is important.
+ 
+
+ align:start position:0%
+idea of like satire, humor is important.
+Um and so, uh I really I I think
+
+ align:start position:0%
+Um and so, uh I really I I think
+ 
+
+ align:start position:0%
+Um and so, uh I really I I think
+Paulini's work is really awesome. And
+
+ align:start position:0%
+Paulini's work is really awesome. And
+ 
+
+ align:start position:0%
+Paulini's work is really awesome. And
+again, I for me it's certainly arc
+
+ align:start position:0%
+again, I for me it's certainly arc
+ 
+
+ align:start position:0%
+again, I for me it's certainly arc
+enough. Um this game is really cool. Uh
+
+ align:start position:0%
+enough. Um this game is really cool. Uh
+ 
+
+ align:start position:0%
+enough. Um this game is really cool. Uh
+who's played love? We have a few people
+
+ align:start position:0%
+who's played love? We have a few people
+ 
+
+ align:start position:0%
+who's played love? We have a few people
+that's played Love. All right, cool. Um
+
+ align:start position:0%
+that's played Love. All right, cool. Um
+ 
+
+ align:start position:0%
+that's played Love. All right, cool. Um
+I'd love someone who has not played Love
+
+ align:start position:0%
+I'd love someone who has not played Love
+ 
+
+ align:start position:0%
+I'd love someone who has not played Love
+to to play it for a little bit. I don't
+
+ align:start position:0%
+to to play it for a little bit. I don't
+ 
+
+ align:start position:0%
+to to play it for a little bit. I don't
+know if we can play the whole game. Um,
+
+ align:start position:0%
+know if we can play the whole game. Um,
+ 
+
+ align:start position:0%
+know if we can play the whole game. Um,
+but uh this is actually a game that I I
+
+ align:start position:0%
+but uh this is actually a game that I I
+ 
+
+ align:start position:0%
+but uh this is actually a game that I I
+really don't like. Um but I like the
+
+ align:start position:0%
+really don't like. Um but I like the
+ 
+
+ align:start position:0%
+really don't like. Um but I like the
+things that it does, if that makes any
+
+ align:start position:0%
+things that it does, if that makes any
+ 
+
+ align:start position:0%
+things that it does, if that makes any
+sense. Like I it bothers me for some
+
+ align:start position:0%
+sense. Like I it bothers me for some
+ 
+
+ align:start position:0%
+sense. Like I it bothers me for some
+reason. Um and yet
+
+ align:start position:0%
+reason. Um and yet
+ 
+
+ align:start position:0%
+reason. Um and yet
+it's such an articulate statement. This
+
+ align:start position:0%
+it's such an articulate statement. This
+ 
+
+ align:start position:0%
+it's such an articulate statement. This
+game bothers me. Um but
+
+ align:start position:0%
+game bothers me. Um but
+ 
+
+ align:start position:0%
+game bothers me. Um but
+>> but I think it's worth looking at
+
+ align:start position:0%
+>> but I think it's worth looking at
+ 
+
+ align:start position:0%
+>> but I think it's worth looking at
+because he's he's doing particularly
+
+ align:start position:0%
+because he's he's doing particularly
+ 
+
+ align:start position:0%
+because he's he's doing particularly
+interesting things.
+
+ align:start position:0%
+interesting things.
+ 
+
+ align:start position:0%
+interesting things.
+Alexander has oius. Aus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+top right.
+
+ align:start position:0%
+top right.
+ 
+
+ align:start position:0%
+top right.
+>> No, you are a girl. Okay. I'm a girl.
+
+ align:start position:0%
+>> No, you are a girl. Okay. I'm a girl.
+ 
+
+ align:start position:0%
+>> No, you are a girl. Okay. I'm a girl.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you say yes, will he like not teach
+
+ align:start position:0%
+If you say yes, will he like not teach
+ 
+
+ align:start position:0%
+If you say yes, will he like not teach
+you how to play?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Don't touch the bones.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's like Sonic.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> What?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> There's two paths.
+
+ align:start position:0%
+>> There's two paths.
+ 
+
+ align:start position:0%
+>> There's two paths.
+I best way of playing like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Can you use that? That's what I was
+
+ align:start position:0%
+>> Can you use that? That's what I was
+ 
+
+ align:start position:0%
+>> Can you use that? That's what I was
+going to do. I make a mistake.
+
+ align:start position:0%
+going to do. I make a mistake.
+ 
+
+ align:start position:0%
+going to do. I make a mistake.
+>> Travel the lower.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Wait, what's appearing?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We need to slow down.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm totally disabled.
+
+ align:start position:0%
+I'm totally disabled.
+ 
+
+ align:start position:0%
+I'm totally disabled.
+>> What? I can't hit the red blocks now.
+
+ align:start position:0%
+>> What? I can't hit the red blocks now.
+ 
+
+ align:start position:0%
+>> What? I can't hit the red blocks now.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> Disgusting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> This game is not only hard, it's also
+
+ align:start position:0%
+>> This game is not only hard, it's also
+ 
+
+ align:start position:0%
+>> This game is not only hard, it's also
+positive.
+
+ align:start position:0%
+positive.
+ 
+
+ align:start position:0%
+positive.
+This is our
+
+ align:start position:0%
+This is our
+ 
+
+ align:start position:0%
+This is our
+>> patience.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yay.
+
+ align:start position:0%
+Yay.
+ 
+
+ align:start position:0%
+Yay.
+>> Those are red.
+
+ align:start position:0%
+>> Those are red.
+ 
+
+ align:start position:0%
+>> Those are red.
+>> I know. That means I can't touch him.
+
+ align:start position:0%
+>> I know. That means I can't touch him.
+ 
+
+ align:start position:0%
+>> I know. That means I can't touch him.
+>> Yay.
+
+ align:start position:0%
+>> Yay.
+ 
+
+ align:start position:0%
+>> Yay.
+>> Don't do it. Don't do it, dude.
+
+ align:start position:0%
+>> Don't do it. Don't do it, dude.
+ 
+
+ align:start position:0%
+>> Don't do it. Don't do it, dude.
+>> Do it.
+
+ align:start position:0%
+>> Do it.
+ 
+
+ align:start position:0%
+>> Do it.
+>> Do it.
+
+ align:start position:0%
+>> Do it.
+ 
+
+ align:start position:0%
+>> Do it.
+>> Do it.
+
+ align:start position:0%
+>> Do it.
+ 
+
+ align:start position:0%
+>> Do it.
+>> Do it.
+
+ align:start position:0%
+>> Do it.
+ 
+
+ align:start position:0%
+>> Do it.
+>> You're just going to have to go back to
+
+ align:start position:0%
+>> You're just going to have to go back to
+ 
+
+ align:start position:0%
+>> You're just going to have to go back to
+the part that was just hard.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+See,
+
+ align:start position:0%
+See,
+ 
+
+ align:start position:0%
+See,
+there's no red blocks. You get red
+
+ align:start position:0%
+there's no red blocks. You get red
+ 
+
+ align:start position:0%
+there's no red blocks. You get red
+blocks when you disobey.
+
+ align:start position:0%
+blocks when you disobey.
+ 
+
+ align:start position:0%
+blocks when you disobey.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+You still can't touch
+
+ align:start position:0%
+You still can't touch
+ 
+
+ align:start position:0%
+You still can't touch
+the yellow card.
+
+ align:start position:0%
+the yellow card.
+ 
+
+ align:start position:0%
+the yellow card.
+>> So, if you disobey, it hides from you
+
+ align:start position:0%
+>> So, if you disobey, it hides from you
+ 
+
+ align:start position:0%
+>> So, if you disobey, it hides from you
+what things actually are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> or or if you obey, they're getting
+
+ align:start position:0%
+>> or or if you obey, they're getting
+ 
+
+ align:start position:0%
+>> or or if you obey, they're getting
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+It's so hard. So little buttons to
+
+ align:start position:0%
+It's so hard. So little buttons to
+ 
+
+ align:start position:0%
+It's so hard. So little buttons to
+press.
+
+ align:start position:0%
+press.
+ 
+
+ align:start position:0%
+press.
+>> Wait, what are the controls?
+
+ align:start position:0%
+>> Wait, what are the controls?
+ 
+
+ align:start position:0%
+>> Wait, what are the controls?
+>> The keys.
+
+ align:start position:0%
+>> The keys.
+ 
+
+ align:start position:0%
+>> The keys.
+>> Right, left.
+
+ align:start position:0%
+>> Right, left.
+ 
+
+ align:start position:0%
+>> Right, left.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> Should this have made
+
+ align:start position:0%
+>> Should this have made
+ 
+
+ align:start position:0%
+>> Should this have made
+>> What? Can you no longer jump?
+
+ align:start position:0%
+>> What? Can you no longer jump?
+ 
+
+ align:start position:0%
+>> What? Can you no longer jump?
+>> I was just screaming out.
+
+ align:start position:0%
+>> I was just screaming out.
+ 
+
+ align:start position:0%
+>> I was just screaming out.
+>> He's doing crouch. Crouch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+risky. Oh, I thought that was bad.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+>> Yeah, but that kind of looks like you.
+
+ align:start position:0%
+>> Yeah, but that kind of looks like you.
+ 
+
+ align:start position:0%
+>> Yeah, but that kind of looks like you.
+>> This game is well aggravatingly tuned
+
+ align:start position:0%
+>> This game is well aggravatingly tuned
+ 
+
+ align:start position:0%
+>> This game is well aggravatingly tuned
+because it's like just build it up.
+
+ align:start position:0%
+because it's like just build it up.
+ 
+
+ align:start position:0%
+because it's like just build it up.
+>> Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+>> crouch crouch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Why you doing that professionally? I
+
+ align:start position:0%
+>> Why you doing that professionally? I
+ 
+
+ align:start position:0%
+>> Why you doing that professionally? I
+just like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So, it's actually a pretty long game. Um
+
+ align:start position:0%
+>> So, it's actually a pretty long game. Um
+ 
+
+ align:start position:0%
+>> So, it's actually a pretty long game. Um
+I I encourage you guys to uh it's pretty
+
+ align:start position:0%
+I I encourage you guys to uh it's pretty
+ 
+
+ align:start position:0%
+I I encourage you guys to uh it's pretty
+it's all flashbased.
+
+ align:start position:0%
+it's all flashbased.
+ 
+
+ align:start position:0%
+it's all flashbased.
+>> What's the message?
+
+ align:start position:0%
+>> What's the message?
+ 
+
+ align:start position:0%
+>> What's the message?
+>> Uh that's a really good question. Let me
+
+ align:start position:0%
+>> Uh that's a really good question. Let me
+ 
+
+ align:start position:0%
+>> Uh that's a really good question. Let me
+uh let me just jump in and go back.
+
+ align:start position:0%
+uh let me just jump in and go back.
+ 
+
+ align:start position:0%
+uh let me just jump in and go back.
+>> Thank you for playing.
+
+ align:start position:0%
+>> Thank you for playing.
+ 
+
+ align:start position:0%
+>> Thank you for playing.
+>> Thank you for playing.
+
+ align:start position:0%
+>> Thank you for playing.
+ 
+
+ align:start position:0%
+>> Thank you for playing.
+>> Disgusting.
+
+ align:start position:0%
+>> Disgusting.
+ 
+
+ align:start position:0%
+>> Disgusting.
+>> You are a changed person because of it.
+
+ align:start position:0%
+>> You are a changed person because of it.
+ 
+
+ align:start position:0%
+>> You are a changed person because of it.
+>> Disgusting.
+
+ align:start position:0%
+>> Disgusting.
+ 
+
+ align:start position:0%
+>> Disgusting.
+>> So yeah. So the question then becomes
+
+ align:start position:0%
+>> So yeah. So the question then becomes
+ 
+
+ align:start position:0%
+>> So yeah. So the question then becomes
+what the point which you know already
+
+ align:start position:0%
+what the point which you know already
+ 
+
+ align:start position:0%
+what the point which you know already
+we're in a position now where we're
+
+ align:start position:0%
+we're in a position now where we're
+ 
+
+ align:start position:0%
+we're in a position now where we're
+asking questions like that which is you
+
+ align:start position:0%
+asking questions like that which is you
+ 
+
+ align:start position:0%
+asking questions like that which is you
+know if you were playing Modern Warfare
+
+ align:start position:0%
+know if you were playing Modern Warfare
+ 
+
+ align:start position:0%
+know if you were playing Modern Warfare
+2 you might say what's the point like
+
+ align:start position:0%
+2 you might say what's the point like
+ 
+
+ align:start position:0%
+2 you might say what's the point like
+would be to blow a lot of stuff up
+
+ align:start position:0%
+would be to blow a lot of stuff up
+ 
+
+ align:start position:0%
+would be to blow a lot of stuff up
+right? So um this is
+
+ align:start position:0%
+right? So um this is
+ 
+
+ align:start position:0%
+right? So um this is
+>> this is a response he had in one of his
+
+ align:start position:0%
+>> this is a response he had in one of his
+ 
+
+ align:start position:0%
+>> this is a response he had in one of his
+interviews he gave after it was
+
+ align:start position:0%
+interviews he gave after it was
+ 
+
+ align:start position:0%
+interviews he gave after it was
+released. He said, "I wanted to get
+
+ align:start position:0%
+released. He said, "I wanted to get
+ 
+
+ align:start position:0%
+released. He said, "I wanted to get
+people to wake up and think about the
+
+ align:start position:0%
+people to wake up and think about the
+ 
+
+ align:start position:0%
+people to wake up and think about the
+games they are playing. Much of the
+
+ align:start position:0%
+games they are playing. Much of the
+ 
+
+ align:start position:0%
+games they are playing. Much of the
+industry appears to be pushing in the
+
+ align:start position:0%
+industry appears to be pushing in the
+ 
+
+ align:start position:0%
+industry appears to be pushing in the
+opposite direction. Essay long
+
+ align:start position:0%
+opposite direction. Essay long
+ 
+
+ align:start position:0%
+opposite direction. Essay long
+tutorials, holding your hand from
+
+ align:start position:0%
+tutorials, holding your hand from
+ 
+
+ align:start position:0%
+tutorials, holding your hand from
+beginning to end in subtext, screamed
+
+ align:start position:0%
+beginning to end in subtext, screamed
+ 
+
+ align:start position:0%
+beginning to end in subtext, screamed
+through pointless exposition. It is
+
+ align:start position:0%
+through pointless exposition. It is
+ 
+
+ align:start position:0%
+through pointless exposition. It is
+treating players like idiots is
+
+ align:start position:0%
+treating players like idiots is
+ 
+
+ align:start position:0%
+treating players like idiots is
+absolutely infuriating." Um, when you
+
+ align:start position:0%
+absolutely infuriating." Um, when you
+ 
+
+ align:start position:0%
+absolutely infuriating." Um, when you
+think about it in terms of a tutorial,
+
+ align:start position:0%
+think about it in terms of a tutorial,
+ 
+
+ align:start position:0%
+think about it in terms of a tutorial,
+right, if this is the tutorial for
+
+ align:start position:0%
+right, if this is the tutorial for
+ 
+
+ align:start position:0%
+right, if this is the tutorial for
+playing the game, it's pretty obnoxious.
+
+ align:start position:0%
+playing the game, it's pretty obnoxious.
+ 
+
+ align:start position:0%
+playing the game, it's pretty obnoxious.
+Um, but it's not that much different
+
+ align:start position:0%
+Um, but it's not that much different
+ 
+
+ align:start position:0%
+Um, but it's not that much different
+than the kind of tutorials that we
+
+ align:start position:0%
+than the kind of tutorials that we
+ 
+
+ align:start position:0%
+than the kind of tutorials that we
+encounter in a lot of games, right? That
+
+ align:start position:0%
+encounter in a lot of games, right? That
+ 
+
+ align:start position:0%
+encounter in a lot of games, right? That
+just basically hold your hand and tell
+
+ align:start position:0%
+just basically hold your hand and tell
+ 
+
+ align:start position:0%
+just basically hold your hand and tell
+you how to do everything. Um, so I think
+
+ align:start position:0%
+you how to do everything. Um, so I think
+ 
+
+ align:start position:0%
+you how to do everything. Um, so I think
+he's really kind of confronting that.
+
+ align:start position:0%
+he's really kind of confronting that.
+ 
+
+ align:start position:0%
+he's really kind of confronting that.
+Um, I guess if I were to say the reasons
+
+ align:start position:0%
+Um, I guess if I were to say the reasons
+ 
+
+ align:start position:0%
+Um, I guess if I were to say the reasons
+that I don't like this game, uh, I think
+
+ align:start position:0%
+that I don't like this game, uh, I think
+ 
+
+ align:start position:0%
+that I don't like this game, uh, I think
+the control scheme is is actually it's a
+
+ align:start position:0%
+the control scheme is is actually it's a
+ 
+
+ align:start position:0%
+the control scheme is is actually it's a
+weakness. The game is so hard that I
+
+ align:start position:0%
+weakness. The game is so hard that I
+ 
+
+ align:start position:0%
+weakness. The game is so hard that I
+mean, you saw like, you know, you
+
+ align:start position:0%
+mean, you saw like, you know, you
+ 
+
+ align:start position:0%
+mean, you saw like, you know, you
+couldn't even get to the things that he
+
+ align:start position:0%
+couldn't even get to the things that he
+ 
+
+ align:start position:0%
+couldn't even get to the things that he
+was trying to communicate. It gets
+
+ align:start position:0%
+was trying to communicate. It gets
+ 
+
+ align:start position:0%
+was trying to communicate. It gets
+weirder the farther along you get. I can
+
+ align:start position:0%
+weirder the farther along you get. I can
+ 
+
+ align:start position:0%
+weirder the farther along you get. I can
+I can promise you it's just it's like
+
+ align:start position:0%
+I can promise you it's just it's like
+ 
+
+ align:start position:0%
+I can promise you it's just it's like
+you have to get really skilled at doing
+
+ align:start position:0%
+you have to get really skilled at doing
+ 
+
+ align:start position:0%
+you have to get really skilled at doing
+it. Um, so there's there's kind of like
+
+ align:start position:0%
+it. Um, so there's there's kind of like
+ 
+
+ align:start position:0%
+it. Um, so there's there's kind of like
+a play barrier for entry on it. Um uh
+
+ align:start position:0%
+a play barrier for entry on it. Um uh
+ 
+
+ align:start position:0%
+a play barrier for entry on it. Um uh
+it's also it also for me I think
+
+ align:start position:0%
+it's also it also for me I think
+ 
+
+ align:start position:0%
+it's also it also for me I think
+dare I say it almost gets like too
+
+ align:start position:0%
+dare I say it almost gets like too
+ 
+
+ align:start position:0%
+dare I say it almost gets like too
+abstract for me at certain points um
+
+ align:start position:0%
+abstract for me at certain points um
+ 
+
+ align:start position:0%
+abstract for me at certain points um
+where I'm I'm it's clear that he's
+
+ align:start position:0%
+where I'm I'm it's clear that he's
+ 
+
+ align:start position:0%
+where I'm I'm it's clear that he's
+trying to say something but there's
+
+ align:start position:0%
+trying to say something but there's
+ 
+
+ align:start position:0%
+trying to say something but there's
+nothing I can latch on to to understand
+
+ align:start position:0%
+nothing I can latch on to to understand
+ 
+
+ align:start position:0%
+nothing I can latch on to to understand
+what it is and it's entirely his
+
+ align:start position:0%
+what it is and it's entirely his
+ 
+
+ align:start position:0%
+what it is and it's entirely his
+prerogative but for me that's I'm just
+
+ align:start position:0%
+prerogative but for me that's I'm just
+ 
+
+ align:start position:0%
+prerogative but for me that's I'm just
+like what like I have no clue what what
+
+ align:start position:0%
+like what like I have no clue what what
+ 
+
+ align:start position:0%
+like what like I have no clue what what
+this is about at all. Um so so that's a
+
+ align:start position:0%
+this is about at all. Um so so that's a
+ 
+
+ align:start position:0%
+this is about at all. Um so so that's a
+little tricky.
+
+ align:start position:0%
+little tricky.
+ 
+
+ align:start position:0%
+little tricky.
+>> He's not you are not fully grasping.
+
+ align:start position:0%
+>> He's not you are not fully grasping.
+ 
+
+ align:start position:0%
+>> He's not you are not fully grasping.
+>> I'm not apparently I'm not. Yeah. I'm
+
+ align:start position:0%
+>> I'm not apparently I'm not. Yeah. I'm
+ 
+
+ align:start position:0%
+>> I'm not apparently I'm not. Yeah. I'm
+partially. So yeah, it's like the
+
+ align:start position:0%
+partially. So yeah, it's like the
+ 
+
+ align:start position:0%
+partially. So yeah, it's like the
+perfect Fluxus piece of art. So um okay,
+
+ align:start position:0%
+perfect Fluxus piece of art. So um okay,
+ 
+
+ align:start position:0%
+perfect Fluxus piece of art. So um okay,
+so I've only got a couple more to talk
+
+ align:start position:0%
+so I've only got a couple more to talk
+ 
+
+ align:start position:0%
+so I've only got a couple more to talk
+about and I got about 15 minutes. This I
+
+ align:start position:0%
+about and I got about 15 minutes. This I
+ 
+
+ align:start position:0%
+about and I got about 15 minutes. This I
+think is actually one of the most
+
+ align:start position:0%
+think is actually one of the most
+ 
+
+ align:start position:0%
+think is actually one of the most
+important games that we can talk about
+
+ align:start position:0%
+important games that we can talk about
+ 
+
+ align:start position:0%
+important games that we can talk about
+today, which is Cow Clicker, who's
+
+ align:start position:0%
+today, which is Cow Clicker, who's
+ 
+
+ align:start position:0%
+today, which is Cow Clicker, who's
+played Cow Clicker. Yay. Um so this is
+
+ align:start position:0%
+played Cow Clicker. Yay. Um so this is
+ 
+
+ align:start position:0%
+played Cow Clicker. Yay. Um so this is
+um by Ian Bogos, the guy we saw earlier.
+
+ align:start position:0%
+um by Ian Bogos, the guy we saw earlier.
+ 
+
+ align:start position:0%
+um by Ian Bogos, the guy we saw earlier.
+Um and he said, "Cow Clicker is a
+
+ align:start position:0%
+Um and he said, "Cow Clicker is a
+ 
+
+ align:start position:0%
+Um and he said, "Cow Clicker is a
+Facebook game about Facebook games. It's
+
+ align:start position:0%
+Facebook game about Facebook games. It's
+ 
+
+ align:start position:0%
+Facebook game about Facebook games. It's
+partly a satire and partly a playable
+
+ align:start position:0%
+partly a satire and partly a playable
+ 
+
+ align:start position:0%
+partly a satire and partly a playable
+theory of today's social games and
+
+ align:start position:0%
+theory of today's social games and
+ 
+
+ align:start position:0%
+theory of today's social games and
+partly an earnest example of that
+
+ align:start position:0%
+partly an earnest example of that
+ 
+
+ align:start position:0%
+partly an earnest example of that
+genre." Um, so this is kind of like a
+
+ align:start position:0%
+genre." Um, so this is kind of like a
+ 
+
+ align:start position:0%
+genre." Um, so this is kind of like a
+classic sort of art thing to do, right?
+
+ align:start position:0%
+classic sort of art thing to do, right?
+ 
+
+ align:start position:0%
+classic sort of art thing to do, right?
+You take something that you're going to
+
+ align:start position:0%
+You take something that you're going to
+ 
+
+ align:start position:0%
+You take something that you're going to
+satire and you make a version of that
+
+ align:start position:0%
+satire and you make a version of that
+ 
+
+ align:start position:0%
+satire and you make a version of that
+that that maybe does some things
+
+ align:start position:0%
+that that maybe does some things
+ 
+
+ align:start position:0%
+that that maybe does some things
+differently, but is fundamentally what
+
+ align:start position:0%
+differently, but is fundamentally what
+ 
+
+ align:start position:0%
+differently, but is fundamentally what
+you are satiring. It's like the Andy
+
+ align:start position:0%
+you are satiring. It's like the Andy
+ 
+
+ align:start position:0%
+you are satiring. It's like the Andy
+Kaufman comedic kind of style, right?
+
+ align:start position:0%
+Kaufman comedic kind of style, right?
+ 
+
+ align:start position:0%
+Kaufman comedic kind of style, right?
+Where you like you just assume that that
+
+ align:start position:0%
+Where you like you just assume that that
+ 
+
+ align:start position:0%
+Where you like you just assume that that
+kind of character or role. And it's it's
+
+ align:start position:0%
+kind of character or role. And it's it's
+ 
+
+ align:start position:0%
+kind of character or role. And it's it's
+it's something that I think is like kind
+
+ align:start position:0%
+it's something that I think is like kind
+ 
+
+ align:start position:0%
+it's something that I think is like kind
+of like joyfully subversive um in in in
+
+ align:start position:0%
+of like joyfully subversive um in in in
+ 
+
+ align:start position:0%
+of like joyfully subversive um in in in
+doing satire. So hopefully I'm logged
+
+ align:start position:0%
+doing satire. So hopefully I'm logged
+ 
+
+ align:start position:0%
+doing satire. So hopefully I'm logged
+into Facebook so you can see and I
+
+ align:start position:0%
+into Facebook so you can see and I
+ 
+
+ align:start position:0%
+into Facebook so you can see and I
+haven't clicked recently so you guys can
+
+ align:start position:0%
+haven't clicked recently so you guys can
+ 
+
+ align:start position:0%
+haven't clicked recently so you guys can
+witness um one of my clicks. Am I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Facebook is down? Facebook is canled
+
+ align:start position:0%
+>> Facebook is down? Facebook is canled
+ 
+
+ align:start position:0%
+>> Facebook is down? Facebook is canled
+forever.
+
+ align:start position:0%
+forever.
+ 
+
+ align:start position:0%
+forever.
+>> Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Has no friends.
+
+ align:start position:0%
+>> Has no friends.
+ 
+
+ align:start position:0%
+>> Has no friends.
+>> It's also possible that the wireless
+
+ align:start position:0%
+>> It's also possible that the wireless
+ 
+
+ align:start position:0%
+>> It's also possible that the wireless
+Yeah, the wireless in this in that
+
+ align:start position:0%
+Yeah, the wireless in this in that
+ 
+
+ align:start position:0%
+Yeah, the wireless in this in that
+corner is kind of bad.
+
+ align:start position:0%
+corner is kind of bad.
+ 
+
+ align:start position:0%
+corner is kind of bad.
+>> Oh, should I switch to Google?
+
+ align:start position:0%
+>> Oh, should I switch to Google?
+ 
+
+ align:start position:0%
+>> Oh, should I switch to Google?
+Oh.
+
+ align:start position:0%
+Oh.
+ 
+
+ align:start position:0%
+Oh.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so I can actually kind of before we even
+
+ align:start position:0%
+so I can actually kind of before we even
+ 
+
+ align:start position:0%
+so I can actually kind of before we even
+see it, I can talk a little bit about
+
+ align:start position:0%
+see it, I can talk a little bit about
+ 
+
+ align:start position:0%
+see it, I can talk a little bit about
+the sort of interesting controversy that
+
+ align:start position:0%
+the sort of interesting controversy that
+ 
+
+ align:start position:0%
+the sort of interesting controversy that
+Cal Clicker is is creating. Um, it's
+
+ align:start position:0%
+Cal Clicker is is creating. Um, it's
+ 
+
+ align:start position:0%
+Cal Clicker is is creating. Um, it's
+it's making money.
+
+ align:start position:0%
+it's making money.
+ 
+
+ align:start position:0%
+it's making money.
+>> MacBook Airs don't have Let me try
+
+ align:start position:0%
+>> MacBook Airs don't have Let me try
+ 
+
+ align:start position:0%
+>> MacBook Airs don't have Let me try
+Google.
+
+ align:start position:0%
+Google.
+ 
+
+ align:start position:0%
+Google.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Um,
+
+ align:start position:0%
+>> Um,
+ 
+
+ align:start position:0%
+>> Um,
+I'm not connected. How about now?
+
+ align:start position:0%
+I'm not connected. How about now?
+ 
+
+ align:start position:0%
+I'm not connected. How about now?
+It seems to be working better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um, so the last part of his statement is
+
+ align:start position:0%
+>> Um, so the last part of his statement is
+ 
+
+ align:start position:0%
+>> Um, so the last part of his statement is
+about an earnest effort in a game. It it
+
+ align:start position:0%
+about an earnest effort in a game. It it
+ 
+
+ align:start position:0%
+about an earnest effort in a game. It it
+it is fundamentally a Facebook game. So
+
+ align:start position:0%
+it is fundamentally a Facebook game. So
+ 
+
+ align:start position:0%
+it is fundamentally a Facebook game. So
+you can see I've got um I've got five
+
+ align:start position:0%
+you can see I've got um I've got five
+ 
+
+ align:start position:0%
+you can see I've got um I've got five
+Mooney. Um my next click is in a minute
+
+ align:start position:0%
+Mooney. Um my next click is in a minute
+ 
+
+ align:start position:0%
+Mooney. Um my next click is in a minute
+and 40. Oh man, I missed one of my
+
+ align:start position:0%
+and 40. Oh man, I missed one of my
+ 
+
+ align:start position:0%
+and 40. Oh man, I missed one of my
+clicks. But maybe if I if we wait while
+
+ align:start position:0%
+clicks. But maybe if I if we wait while
+ 
+
+ align:start position:0%
+clicks. But maybe if I if we wait while
+I talk about it, you can witness one of
+
+ align:start position:0%
+I talk about it, you can witness one of
+ 
+
+ align:start position:0%
+I talk about it, you can witness one of
+my clicks. Um oh wait, I actually have
+
+ align:start position:0%
+my clicks. Um oh wait, I actually have
+ 
+
+ align:start position:0%
+my clicks. Um oh wait, I actually have
+some clicks left. I've got uh I've got,
+
+ align:start position:0%
+some clicks left. I've got uh I've got,
+ 
+
+ align:start position:0%
+some clicks left. I've got uh I've got,
+you know, one this week. But that's in
+
+ align:start position:0%
+you know, one this week. But that's in
+ 
+
+ align:start position:0%
+you know, one this week. But that's in
+two hours.
+
+ align:start position:0%
+two hours.
+ 
+
+ align:start position:0%
+two hours.
+>> Uh,
+
+ align:start position:0%
+>> Uh,
+ 
+
+ align:start position:0%
+>> Uh,
+>> yeah, it looks like that's when I get my
+
+ align:start position:0%
+>> yeah, it looks like that's when I get my
+ 
+
+ align:start position:0%
+>> yeah, it looks like that's when I get my
+next one. So, um, so basically you can
+
+ align:start position:0%
+next one. So, um, so basically you can
+ 
+
+ align:start position:0%
+next one. So, um, so basically you can
+click your cow,
+
+ align:start position:0%
+click your cow,
+ 
+
+ align:start position:0%
+click your cow,
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+why can I not click my cow?
+
+ align:start position:0%
+why can I not click my cow?
+ 
+
+ align:start position:0%
+why can I not click my cow?
+Um, well, you can click your cow and
+
+ align:start position:0%
+Um, well, you can click your cow and
+ 
+
+ align:start position:0%
+Um, well, you can click your cow and
+then you can Oh, it's because I'm on
+
+ align:start position:0%
+then you can Oh, it's because I'm on
+ 
+
+ align:start position:0%
+then you can Oh, it's because I'm on
+scrolling.
+
+ align:start position:0%
+scrolling.
+ 
+
+ align:start position:0%
+scrolling.
+I don't know. Um anyway, you can click
+
+ align:start position:0%
+I don't know. Um anyway, you can click
+ 
+
+ align:start position:0%
+I don't know. Um anyway, you can click
+your cow and then you can use your
+
+ align:start position:0%
+your cow and then you can use your
+ 
+
+ align:start position:0%
+your cow and then you can use your
+mooney uh to buy new cows um that are
+
+ align:start position:0%
+mooney uh to buy new cows um that are
+ 
+
+ align:start position:0%
+mooney uh to buy new cows um that are
+fundamentally the same thing as other
+
+ align:start position:0%
+fundamentally the same thing as other
+ 
+
+ align:start position:0%
+fundamentally the same thing as other
+cows just with aesthetic differences. Um
+
+ align:start position:0%
+cows just with aesthetic differences. Um
+ 
+
+ align:start position:0%
+cows just with aesthetic differences. Um
+so plain cow. Um oh these are the cows I
+
+ align:start position:0%
+so plain cow. Um oh these are the cows I
+ 
+
+ align:start position:0%
+so plain cow. Um oh these are the cows I
+have. I have a plain cow and a steel
+
+ align:start position:0%
+have. I have a plain cow and a steel
+ 
+
+ align:start position:0%
+have. I have a plain cow and a steel
+cow. I haven't been playing a lot of cow
+
+ align:start position:0%
+cow. I haven't been playing a lot of cow
+ 
+
+ align:start position:0%
+cow. I haven't been playing a lot of cow
+clicker. Um if I go to buy a cow, I
+
+ align:start position:0%
+clicker. Um if I go to buy a cow, I
+ 
+
+ align:start position:0%
+clicker. Um if I go to buy a cow, I
+could buy a new cow. Um
+
+ align:start position:0%
+could buy a new cow. Um
+ 
+
+ align:start position:0%
+could buy a new cow. Um
+uh so you can see lots of different cows
+
+ align:start position:0%
+uh so you can see lots of different cows
+ 
+
+ align:start position:0%
+uh so you can see lots of different cows
+um that cost you in-game currency. Um,
+
+ align:start position:0%
+um that cost you in-game currency. Um,
+ 
+
+ align:start position:0%
+um that cost you in-game currency. Um,
+>> paisley cow.
+
+ align:start position:0%
+>> paisley cow.
+ 
+
+ align:start position:0%
+>> paisley cow.
+>> Yeah. Holy cow.
+
+ align:start position:0%
+>> Yeah. Holy cow.
+ 
+
+ align:start position:0%
+>> Yeah. Holy cow.
+Um, oil cow cow retire. Sad. It's got a
+
+ align:start position:0%
+Um, oil cow cow retire. Sad. It's got a
+ 
+
+ align:start position:0%
+Um, oil cow cow retire. Sad. It's got a
+BP logo. It's cute. Um,
+
+ align:start position:0%
+BP logo. It's cute. Um,
+ 
+
+ align:start position:0%
+BP logo. It's cute. Um,
+>> I like BSD cow. Yeah, that's pretty
+
+ align:start position:0%
+>> I like BSD cow. Yeah, that's pretty
+ 
+
+ align:start position:0%
+>> I like BSD cow. Yeah, that's pretty
+good. Um, so there's lots of different
+
+ align:start position:0%
+good. Um, so there's lots of different
+ 
+
+ align:start position:0%
+good. Um, so there's lots of different
+cows and you can buy cows. You can give
+
+ align:start position:0%
+cows and you can buy cows. You can give
+ 
+
+ align:start position:0%
+cows and you can buy cows. You can give
+cows. You can invite a cow. Um, there's
+
+ align:start position:0%
+cows. You can invite a cow. Um, there's
+ 
+
+ align:start position:0%
+cows. You can invite a cow. Um, there's
+cow rankings. Um,
+
+ align:start position:0%
+cow rankings. Um,
+ 
+
+ align:start position:0%
+cow rankings. Um,
+>> invite a cow.
+
+ align:start position:0%
+>> invite a cow.
+ 
+
+ align:start position:0%
+>> invite a cow.
+>> Uh, you can So you can see, you know,
+
+ align:start position:0%
+>> Uh, you can So you can see, you know,
+ 
+
+ align:start position:0%
+>> Uh, you can So you can see, you know,
+Mooney is actually pretty inflated at
+
+ align:start position:0%
+Mooney is actually pretty inflated at
+ 
+
+ align:start position:0%
+Mooney is actually pretty inflated at
+this point. You can get 10 Mooney for 50
+
+ align:start position:0%
+this point. You can get 10 Mooney for 50
+ 
+
+ align:start position:0%
+this point. You can get 10 Mooney for 50
+cents, which is pretty great. Thousand
+
+ align:start position:0%
+cents, which is pretty great. Thousand
+ 
+
+ align:start position:0%
+cents, which is pretty great. Thousand
+for $10, which is kind of awesome. um
+
+ align:start position:0%
+for $10, which is kind of awesome. um
+ 
+
+ align:start position:0%
+for $10, which is kind of awesome. um
+and you know collect a lot of cows and
+
+ align:start position:0%
+and you know collect a lot of cows and
+ 
+
+ align:start position:0%
+and you know collect a lot of cows and
+you can trade cows and you know you can
+
+ align:start position:0%
+you can trade cows and you know you can
+ 
+
+ align:start position:0%
+you can trade cows and you know you can
+go to your friends barns and see how
+
+ align:start position:0%
+go to your friends barns and see how
+ 
+
+ align:start position:0%
+go to your friends barns and see how
+many cows they have and um and you can
+
+ align:start position:0%
+many cows they have and um and you can
+ 
+
+ align:start position:0%
+many cows they have and um and you can
+click on your cows when you make make
+
+ align:start position:0%
+click on your cows when you make make
+ 
+
+ align:start position:0%
+click on your cows when you make make
+your appointment to actually cow. Um so
+
+ align:start position:0%
+your appointment to actually cow. Um so
+ 
+
+ align:start position:0%
+your appointment to actually cow. Um so
+I mean I think you can see how he's
+
+ align:start position:0%
+I mean I think you can see how he's
+ 
+
+ align:start position:0%
+I mean I think you can see how he's
+poking fun at um things like Farmville
+
+ align:start position:0%
+poking fun at um things like Farmville
+ 
+
+ align:start position:0%
+poking fun at um things like Farmville
+uh things like Ravenwood Fair which I'm
+
+ align:start position:0%
+uh things like Ravenwood Fair which I'm
+ 
+
+ align:start position:0%
+uh things like Ravenwood Fair which I'm
+obsessed with now actually. um these
+
+ align:start position:0%
+obsessed with now actually. um these
+ 
+
+ align:start position:0%
+obsessed with now actually. um these
+kind of games where all you're
+
+ align:start position:0%
+kind of games where all you're
+ 
+
+ align:start position:0%
+kind of games where all you're
+fundamentally doing is clicking uh and
+
+ align:start position:0%
+fundamentally doing is clicking uh and
+ 
+
+ align:start position:0%
+fundamentally doing is clicking uh and
+acquiring an in-game currency that you
+
+ align:start position:0%
+acquiring an in-game currency that you
+ 
+
+ align:start position:0%
+acquiring an in-game currency that you
+can then use for in-game goods. Um but
+
+ align:start position:0%
+can then use for in-game goods. Um but
+ 
+
+ align:start position:0%
+can then use for in-game goods. Um but
+then of course you reach this barrier
+
+ align:start position:0%
+then of course you reach this barrier
+ 
+
+ align:start position:0%
+then of course you reach this barrier
+where you don't have enough in-game
+
+ align:start position:0%
+where you don't have enough in-game
+ 
+
+ align:start position:0%
+where you don't have enough in-game
+currency and you need to use real
+
+ align:start position:0%
+currency and you need to use real
+ 
+
+ align:start position:0%
+currency and you need to use real
+currency. Of course, the interesting
+
+ align:start position:0%
+currency. Of course, the interesting
+ 
+
+ align:start position:0%
+currency. Of course, the interesting
+thing is like there are like I don't
+
+ align:start position:0%
+thing is like there are like I don't
+ 
+
+ align:start position:0%
+thing is like there are like I don't
+know 500,000 people playing this or I
+
+ align:start position:0%
+know 500,000 people playing this or I
+ 
+
+ align:start position:0%
+know 500,000 people playing this or I
+don't know if it's that many. It's a
+
+ align:start position:0%
+don't know if it's that many. It's a
+ 
+
+ align:start position:0%
+don't know if it's that many. It's a
+lot. Um here if we go to the cow clicker
+
+ align:start position:0%
+lot. Um here if we go to the cow clicker
+ 
+
+ align:start position:0%
+lot. Um here if we go to the cow clicker
+front page, right, it'll tell us oh Jera
+
+ align:start position:0%
+front page, right, it'll tell us oh Jera
+ 
+
+ align:start position:0%
+front page, right, it'll tell us oh Jera
+was at St. Barthol.
+
+ align:start position:0%
+was at St. Barthol.
+ 
+
+ align:start position:0%
+was at St. Barthol.
+>> Um where does it say how many players
+
+ align:start position:0%
+>> Um where does it say how many players
+ 
+
+ align:start position:0%
+>> Um where does it say how many players
+there are? ranking.
+
+ align:start position:0%
+there are? ranking.
+ 
+
+ align:start position:0%
+there are? ranking.
+>> Ranking. Yeah,
+
+ align:start position:0%
+>> Ranking. Yeah,
+ 
+
+ align:start position:0%
+>> Ranking. Yeah,
+>> I did that on board news.
+
+ align:start position:0%
+>> I did that on board news.
+ 
+
+ align:start position:0%
+>> I did that on board news.
+>> Who's milking the cow clicker?
+
+ align:start position:0%
+>> Who's milking the cow clicker?
+ 
+
+ align:start position:0%
+>> Who's milking the cow clicker?
+>> You can see this person's Monica's
+
+ align:start position:0%
+>> You can see this person's Monica's
+ 
+
+ align:start position:0%
+>> You can see this person's Monica's
+>> no count.
+
+ align:start position:0%
+>> no count.
+ 
+
+ align:start position:0%
+>> no count.
+>> Oh,
+
+ align:start position:0%
+>> Oh,
+ 
+
+ align:start position:0%
+>> Oh,
+>> um
+
+ align:start position:0%
+>> um
+ 
+
+ align:start position:0%
+>> um
+>> yeah, maybe all clicks or this week.
+
+ align:start position:0%
+>> yeah, maybe all clicks or this week.
+ 
+
+ align:start position:0%
+>> yeah, maybe all clicks or this week.
+>> Is there like a Oh,
+
+ align:start position:0%
+>> Is there like a Oh,
+ 
+
+ align:start position:0%
+>> Is there like a Oh,
+>> here we go. Yeah. Yeah.
+
+ align:start position:0%
+>> here we go. Yeah. Yeah.
+ 
+
+ align:start position:0%
+>> here we go. Yeah. Yeah.
+>> Um
+
+ align:start position:0%
+>> Um
+ 
+
+ align:start position:0%
+>> Um
+>> 12,000
+
+ align:start position:0%
+>> 12,000
+ 
+
+ align:start position:0%
+>> 12,000
+>> 12,000 monthly active users. Yes.
+
+ align:start position:0%
+>> 12,000 monthly active users. Yes.
+ 
+
+ align:start position:0%
+>> 12,000 monthly active users. Yes.
+500,000 a bit of a stretch, but um but
+
+ align:start position:0%
+500,000 a bit of a stretch, but um but
+ 
+
+ align:start position:0%
+500,000 a bit of a stretch, but um but
+that's a lot of people and he's making
+
+ align:start position:0%
+that's a lot of people and he's making
+ 
+
+ align:start position:0%
+that's a lot of people and he's making
+some interesting money on it. And I
+
+ align:start position:0%
+some interesting money on it. And I
+ 
+
+ align:start position:0%
+some interesting money on it. And I
+think one of the things that was
+
+ align:start position:0%
+think one of the things that was
+ 
+
+ align:start position:0%
+think one of the things that was
+important that he did is there's kind of
+
+ align:start position:0%
+important that he did is there's kind of
+ 
+
+ align:start position:0%
+important that he did is there's kind of
+an active forum where people can kind of
+
+ align:start position:0%
+an active forum where people can kind of
+ 
+
+ align:start position:0%
+an active forum where people can kind of
+talk about it and so it is a little bit
+
+ align:start position:0%
+talk about it and so it is a little bit
+ 
+
+ align:start position:0%
+talk about it and so it is a little bit
+weirdly controversial, right? Because he
+
+ align:start position:0%
+weirdly controversial, right? Because he
+ 
+
+ align:start position:0%
+weirdly controversial, right? Because he
+made this game that is, you know, poking
+
+ align:start position:0%
+made this game that is, you know, poking
+ 
+
+ align:start position:0%
+made this game that is, you know, poking
+fun at Facebook games and yet it is a
+
+ align:start position:0%
+fun at Facebook games and yet it is a
+ 
+
+ align:start position:0%
+fun at Facebook games and yet it is a
+Facebook game and it's, you know,
+
+ align:start position:0%
+Facebook game and it's, you know,
+ 
+
+ align:start position:0%
+Facebook game and it's, you know,
+presumably making some money, too. So,
+
+ align:start position:0%
+presumably making some money, too. So,
+ 
+
+ align:start position:0%
+presumably making some money, too. So,
+um but I think it's really good. I think
+
+ align:start position:0%
+um but I think it's really good. I think
+ 
+
+ align:start position:0%
+um but I think it's really good. I think
+it's, you know, this is the kind of art
+
+ align:start position:0%
+it's, you know, this is the kind of art
+ 
+
+ align:start position:0%
+it's, you know, this is the kind of art
+that's also important where it's like
+
+ align:start position:0%
+that's also important where it's like
+ 
+
+ align:start position:0%
+that's also important where it's like
+taking what we do and purposely looking
+
+ align:start position:0%
+taking what we do and purposely looking
+ 
+
+ align:start position:0%
+taking what we do and purposely looking
+at at at how is it constructed and how
+
+ align:start position:0%
+at at at how is it constructed and how
+ 
+
+ align:start position:0%
+at at at how is it constructed and how
+is it set up and and satiring it and
+
+ align:start position:0%
+is it set up and and satiring it and
+ 
+
+ align:start position:0%
+is it set up and and satiring it and
+forcing us to kind of be introspective
+
+ align:start position:0%
+forcing us to kind of be introspective
+ 
+
+ align:start position:0%
+forcing us to kind of be introspective
+about the things that we do in the way
+
+ align:start position:0%
+about the things that we do in the way
+ 
+
+ align:start position:0%
+about the things that we do in the way
+that we engage. Um, and so this is a
+
+ align:start position:0%
+that we engage. Um, and so this is a
+ 
+
+ align:start position:0%
+that we engage. Um, and so this is a
+kind of subversive game design that I
+
+ align:start position:0%
+kind of subversive game design that I
+ 
+
+ align:start position:0%
+kind of subversive game design that I
+think you know along the lines of Paulo
+
+ align:start position:0%
+think you know along the lines of Paulo
+ 
+
+ align:start position:0%
+think you know along the lines of Paulo
+Pedroini's work and um and even Galafa
+
+ align:start position:0%
+Pedroini's work and um and even Galafa
+ 
+
+ align:start position:0%
+Pedroini's work and um and even Galafa
+is kind of forcing us to look at how we
+
+ align:start position:0%
+is kind of forcing us to look at how we
+ 
+
+ align:start position:0%
+is kind of forcing us to look at how we
+interact. Um, and cow clicker cow
+
+ align:start position:0%
+interact. Um, and cow clicker cow
+ 
+
+ align:start position:0%
+interact. Um, and cow clicker cow
+clicker is really fun. Um uh so that's
+
+ align:start position:0%
+clicker is really fun. Um uh so that's
+ 
+
+ align:start position:0%
+clicker is really fun. Um uh so that's
+that one and I've got like 15 minutes.
+
+ align:start position:0%
+that one and I've got like 15 minutes.
+ 
+
+ align:start position:0%
+that one and I've got like 15 minutes.
+Philip asked me to talk a little bit
+
+ align:start position:0%
+Philip asked me to talk a little bit
+ 
+
+ align:start position:0%
+Philip asked me to talk a little bit
+about um some work that I'm doing in
+
+ align:start position:0%
+about um some work that I'm doing in
+ 
+
+ align:start position:0%
+about um some work that I'm doing in
+this space. Um so I'm going to talk to
+
+ align:start position:0%
+this space. Um so I'm going to talk to
+ 
+
+ align:start position:0%
+this space. Um so I'm going to talk to
+you about a game uh that I'm it's a work
+
+ align:start position:0%
+you about a game uh that I'm it's a work
+ 
+
+ align:start position:0%
+you about a game uh that I'm it's a work
+in progress. It's tenatively titled
+
+ align:start position:0%
+in progress. It's tenatively titled
+ 
+
+ align:start position:0%
+in progress. It's tenatively titled
+before and ends now. Um and it's by me.
+
+ align:start position:0%
+before and ends now. Um and it's by me.
+ 
+
+ align:start position:0%
+before and ends now. Um and it's by me.
+Um and the idea from it is it's inspired
+
+ align:start position:0%
+Um and the idea from it is it's inspired
+ 
+
+ align:start position:0%
+Um and the idea from it is it's inspired
+a bit by Flexus boxes. Um and those kind
+
+ align:start position:0%
+a bit by Flexus boxes. Um and those kind
+ 
+
+ align:start position:0%
+a bit by Flexus boxes. Um and those kind
+of flux kits. Um, I wanted to I'm really
+
+ align:start position:0%
+of flux kits. Um, I wanted to I'm really
+ 
+
+ align:start position:0%
+of flux kits. Um, I wanted to I'm really
+interested in in like physically
+
+ align:start position:0%
+interested in in like physically
+ 
+
+ align:start position:0%
+interested in in like physically
+tangible games. I don't know why I'm uh
+
+ align:start position:0%
+tangible games. I don't know why I'm uh
+ 
+
+ align:start position:0%
+tangible games. I don't know why I'm uh
+all of a sudden kind of obsessed with
+
+ align:start position:0%
+all of a sudden kind of obsessed with
+ 
+
+ align:start position:0%
+all of a sudden kind of obsessed with
+with holding something, but I was at
+
+ align:start position:0%
+with holding something, but I was at
+ 
+
+ align:start position:0%
+with holding something, but I was at
+indicate and I heard again and it this
+
+ align:start position:0%
+indicate and I heard again and it this
+ 
+
+ align:start position:0%
+indicate and I heard again and it this
+is like the question that drives me more
+
+ align:start position:0%
+is like the question that drives me more
+ 
+
+ align:start position:0%
+is like the question that drives me more
+nuts than than the um than the are video
+
+ align:start position:0%
+nuts than than the um than the are video
+ 
+
+ align:start position:0%
+nuts than than the um than the are video
+games art question, although they're
+
+ align:start position:0%
+games art question, although they're
+ 
+
+ align:start position:0%
+games art question, although they're
+interestingly related, but it's, you
+
+ align:start position:0%
+interestingly related, but it's, you
+ 
+
+ align:start position:0%
+interestingly related, but it's, you
+know, when will we have the citizen cane
+
+ align:start position:0%
+know, when will we have the citizen cane
+ 
+
+ align:start position:0%
+know, when will we have the citizen cane
+in video games? It drives me absolutely
+
+ align:start position:0%
+in video games? It drives me absolutely
+ 
+
+ align:start position:0%
+in video games? It drives me absolutely
+nuts. I think uh 80% of the time the
+
+ align:start position:0%
+nuts. I think uh 80% of the time the
+ 
+
+ align:start position:0%
+nuts. I think uh 80% of the time the
+people who say that have never seen
+
+ align:start position:0%
+people who say that have never seen
+ 
+
+ align:start position:0%
+people who say that have never seen
+citizen cane. Um so I don't really know
+
+ align:start position:0%
+citizen cane. Um so I don't really know
+ 
+
+ align:start position:0%
+citizen cane. Um so I don't really know
+what that means. Um, but I had heard it
+
+ align:start position:0%
+what that means. Um, but I had heard it
+ 
+
+ align:start position:0%
+what that means. Um, but I had heard it
+like for the eenth time in Indie Kane
+
+ align:start position:0%
+like for the eenth time in Indie Kane
+ 
+
+ align:start position:0%
+like for the eenth time in Indie Kane
+and I wanted to throw the television in
+
+ align:start position:0%
+and I wanted to throw the television in
+ 
+
+ align:start position:0%
+and I wanted to throw the television in
+my out of my hotel room window and I was
+
+ align:start position:0%
+my out of my hotel room window and I was
+ 
+
+ align:start position:0%
+my out of my hotel room window and I was
+like I was going nuts and I was like,
+
+ align:start position:0%
+like I was going nuts and I was like,
+ 
+
+ align:start position:0%
+like I was going nuts and I was like,
+"All right, well well what is Citizen
+
+ align:start position:0%
+"All right, well well what is Citizen
+ 
+
+ align:start position:0%
+"All right, well well what is Citizen
+Kane about?" And I don't want to spoil
+
+ align:start position:0%
+Kane about?" And I don't want to spoil
+ 
+
+ align:start position:0%
+Kane about?" And I don't want to spoil
+it. Who's seen Citizen Kane in this
+
+ align:start position:0%
+it. Who's seen Citizen Kane in this
+ 
+
+ align:start position:0%
+it. Who's seen Citizen Kane in this
+room? Actually, a handful of people. All
+
+ align:start position:0%
+room? Actually, a handful of people. All
+ 
+
+ align:start position:0%
+room? Actually, a handful of people. All
+right, good. Um,
+
+ align:start position:0%
+right, good. Um,
+ 
+
+ align:start position:0%
+right, good. Um,
+>> so so I, you know, I see Citizen Kane
+
+ align:start position:0%
+>> so so I, you know, I see Citizen Kane
+ 
+
+ align:start position:0%
+>> so so I, you know, I see Citizen Kane
+and it's about this very kind of, you
+
+ align:start position:0%
+and it's about this very kind of, you
+ 
+
+ align:start position:0%
+and it's about this very kind of, you
+know, interesting
+
+ align:start position:0%
+know, interesting
+ 
+
+ align:start position:0%
+know, interesting
+um idea about, you know, presence and
+
+ align:start position:0%
+um idea about, you know, presence and
+ 
+
+ align:start position:0%
+um idea about, you know, presence and
+and momentos and and happiness uh in a
+
+ align:start position:0%
+and momentos and and happiness uh in a
+ 
+
+ align:start position:0%
+and momentos and and happiness uh in a
+very kind of real way and like the
+
+ align:start position:0%
+very kind of real way and like the
+ 
+
+ align:start position:0%
+very kind of real way and like the
+temporality of happiness, right? Like
+
+ align:start position:0%
+temporality of happiness, right? Like
+ 
+
+ align:start position:0%
+temporality of happiness, right? Like
+are you happy now? Were you happy then?
+
+ align:start position:0%
+are you happy now? Were you happy then?
+ 
+
+ align:start position:0%
+are you happy now? Were you happy then?
+Do you remember being happy? When when
+
+ align:start position:0%
+Do you remember being happy? When when
+ 
+
+ align:start position:0%
+Do you remember being happy? When when
+is happiness? Um, and so I was like,
+
+ align:start position:0%
+is happiness? Um, and so I was like,
+ 
+
+ align:start position:0%
+is happiness? Um, and so I was like,
+well, I'm going to make a Citizen Cane
+
+ align:start position:0%
+well, I'm going to make a Citizen Cane
+ 
+
+ align:start position:0%
+well, I'm going to make a Citizen Cane
+of video games, but it's not going to be
+
+ align:start position:0%
+of video games, but it's not going to be
+ 
+
+ align:start position:0%
+of video games, but it's not going to be
+it's not going to be known for being uh
+
+ align:start position:0%
+it's not going to be known for being uh
+ 
+
+ align:start position:0%
+it's not going to be known for being uh
+uh epically innovative, you know, with
+
+ align:start position:0%
+uh epically innovative, you know, with
+ 
+
+ align:start position:0%
+uh epically innovative, you know, with
+camera movement. Um, it's it's going to
+
+ align:start position:0%
+camera movement. Um, it's it's going to
+ 
+
+ align:start position:0%
+camera movement. Um, it's it's going to
+be about the things I think Citizen Cane
+
+ align:start position:0%
+be about the things I think Citizen Cane
+ 
+
+ align:start position:0%
+be about the things I think Citizen Cane
+are about. Um, so it's it's basically um
+
+ align:start position:0%
+are about. Um, so it's it's basically um
+ 
+
+ align:start position:0%
+are about. Um, so it's it's basically um
+you know in this form uh although I'm
+
+ align:start position:0%
+you know in this form uh although I'm
+ 
+
+ align:start position:0%
+you know in this form uh although I'm
+I'm rethinking what kind of box it's
+
+ align:start position:0%
+I'm rethinking what kind of box it's
+ 
+
+ align:start position:0%
+I'm rethinking what kind of box it's
+going to be in but in this form it's a
+
+ align:start position:0%
+going to be in but in this form it's a
+ 
+
+ align:start position:0%
+going to be in but in this form it's a
+box and inside of it are various objects
+
+ align:start position:0%
+box and inside of it are various objects
+ 
+
+ align:start position:0%
+box and inside of it are various objects
+that start out as uh the starting
+
+ align:start position:0%
+that start out as uh the starting
+ 
+
+ align:start position:0%
+that start out as uh the starting
+objects for the box are things that have
+
+ align:start position:0%
+objects for the box are things that have
+ 
+
+ align:start position:0%
+objects for the box are things that have
+personal significance to me. Um and one
+
+ align:start position:0%
+personal significance to me. Um and one
+ 
+
+ align:start position:0%
+personal significance to me. Um and one
+of the rules of the game in fact I think
+
+ align:start position:0%
+of the rules of the game in fact I think
+ 
+
+ align:start position:0%
+of the rules of the game in fact I think
+the most important rule of the game uh
+
+ align:start position:0%
+the most important rule of the game uh
+ 
+
+ align:start position:0%
+the most important rule of the game uh
+is this one. Rule number one you may
+
+ align:start position:0%
+is this one. Rule number one you may
+ 
+
+ align:start position:0%
+is this one. Rule number one you may
+permanently exchange an object of
+
+ align:start position:0%
+permanently exchange an object of
+ 
+
+ align:start position:0%
+permanently exchange an object of
+personal significance for any object of
+
+ align:start position:0%
+personal significance for any object of
+ 
+
+ align:start position:0%
+personal significance for any object of
+equal value. So when you're playing this
+
+ align:start position:0%
+equal value. So when you're playing this
+ 
+
+ align:start position:0%
+equal value. So when you're playing this
+game, you can take something that
+
+ align:start position:0%
+game, you can take something that
+ 
+
+ align:start position:0%
+game, you can take something that
+belongs to you and you can exchange it
+
+ align:start position:0%
+belongs to you and you can exchange it
+ 
+
+ align:start position:0%
+belongs to you and you can exchange it
+for anything in the box. Um and then of
+
+ align:start position:0%
+for anything in the box. Um and then of
+ 
+
+ align:start position:0%
+for anything in the box. Um and then of
+course the interesting thing is these
+
+ align:start position:0%
+course the interesting thing is these
+ 
+
+ align:start position:0%
+course the interesting thing is these
+these um these objects in the box are of
+
+ align:start position:0%
+these um these objects in the box are of
+ 
+
+ align:start position:0%
+these um these objects in the box are of
+varying uh degrees of interactivity,
+
+ align:start position:0%
+varying uh degrees of interactivity,
+ 
+
+ align:start position:0%
+varying uh degrees of interactivity,
+right? Like you can do them in Etcha
+
+ align:start position:0%
+right? Like you can do them in Etcha
+ 
+
+ align:start position:0%
+right? Like you can do them in Etcha
+Sketch. So you can draw something on the
+
+ align:start position:0%
+Sketch. So you can draw something on the
+ 
+
+ align:start position:0%
+Sketch. So you can draw something on the
+Etcha sketch. Um and um you know the
+
+ align:start position:0%
+Etcha sketch. Um and um you know the
+ 
+
+ align:start position:0%
+Etcha sketch. Um and um you know the
+rules are kind of veiled in this moment
+
+ align:start position:0%
+rules are kind of veiled in this moment
+ 
+
+ align:start position:0%
+rules are kind of veiled in this moment
+now where there's like a couple other
+
+ align:start position:0%
+now where there's like a couple other
+ 
+
+ align:start position:0%
+now where there's like a couple other
+rules that you know are causing you to
+
+ align:start position:0%
+rules that you know are causing you to
+ 
+
+ align:start position:0%
+rules that you know are causing you to
+reflect. This is actually an extension
+
+ align:start position:0%
+reflect. This is actually an extension
+ 
+
+ align:start position:0%
+reflect. This is actually an extension
+of uh Yet One Word, which was a project
+
+ align:start position:0%
+of uh Yet One Word, which was a project
+ 
+
+ align:start position:0%
+of uh Yet One Word, which was a project
+we worked on in the summer, which was a
+
+ align:start position:0%
+we worked on in the summer, which was a
+ 
+
+ align:start position:0%
+we worked on in the summer, which was a
+game that um as you're playing, it's a
+
+ align:start position:0%
+game that um as you're playing, it's a
+ 
+
+ align:start position:0%
+game that um as you're playing, it's a
+platformer, and you're typing, the game
+
+ align:start position:0%
+platformer, and you're typing, the game
+ 
+
+ align:start position:0%
+platformer, and you're typing, the game
+stops and asks you personal questions.
+
+ align:start position:0%
+stops and asks you personal questions.
+ 
+
+ align:start position:0%
+stops and asks you personal questions.
+And what I really liked about that is it
+
+ align:start position:0%
+And what I really liked about that is it
+ 
+
+ align:start position:0%
+And what I really liked about that is it
+was doing something that I was kind of
+
+ align:start position:0%
+was doing something that I was kind of
+ 
+
+ align:start position:0%
+was doing something that I was kind of
+referring to as a um as a mechanic of
+
+ align:start position:0%
+referring to as a um as a mechanic of
+ 
+
+ align:start position:0%
+referring to as a um as a mechanic of
+reflection where where the the the
+
+ align:start position:0%
+reflection where where the the the
+ 
+
+ align:start position:0%
+reflection where where the the the
+activity of play is is reflecting, is
+
+ align:start position:0%
+activity of play is is reflecting, is
+ 
+
+ align:start position:0%
+activity of play is is reflecting, is
+thinking, is you know, just
+
+ align:start position:0%
+thinking, is you know, just
+ 
+
+ align:start position:0%
+thinking, is you know, just
+contemplating. Um it's not interactive
+
+ align:start position:0%
+contemplating. Um it's not interactive
+ 
+
+ align:start position:0%
+contemplating. Um it's not interactive
+in a very kind of, you know, active way
+
+ align:start position:0%
+in a very kind of, you know, active way
+ 
+
+ align:start position:0%
+in a very kind of, you know, active way
+as we think of it. It's more reflective.
+
+ align:start position:0%
+as we think of it. It's more reflective.
+ 
+
+ align:start position:0%
+as we think of it. It's more reflective.
+I I liken it to the moments in chess
+
+ align:start position:0%
+I I liken it to the moments in chess
+ 
+
+ align:start position:0%
+I I liken it to the moments in chess
+where you're planning your move. There's
+
+ align:start position:0%
+where you're planning your move. There's
+ 
+
+ align:start position:0%
+where you're planning your move. There's
+not a lot of action in chess. There's a
+
+ align:start position:0%
+not a lot of action in chess. There's a
+ 
+
+ align:start position:0%
+not a lot of action in chess. There's a
+lot of contemplation in chess. Um so if
+
+ align:start position:0%
+lot of contemplation in chess. Um so if
+ 
+
+ align:start position:0%
+lot of contemplation in chess. Um so if
+it's personal, you know what if that
+
+ align:start position:0%
+it's personal, you know what if that
+ 
+
+ align:start position:0%
+it's personal, you know what if that
+were what if that were personal? And so
+
+ align:start position:0%
+were what if that were personal? And so
+ 
+
+ align:start position:0%
+were what if that were personal? And so
+what I what I don't particularly care
+
+ align:start position:0%
+what I what I don't particularly care
+ 
+
+ align:start position:0%
+what I what I don't particularly care
+about with yet one word is that it
+
+ align:start position:0%
+about with yet one word is that it
+ 
+
+ align:start position:0%
+about with yet one word is that it
+doesn't it it it inspires you to
+
+ align:start position:0%
+doesn't it it it inspires you to
+ 
+
+ align:start position:0%
+doesn't it it it inspires you to
+reflect, but it doesn't do it with with
+
+ align:start position:0%
+reflect, but it doesn't do it with with
+ 
+
+ align:start position:0%
+reflect, but it doesn't do it with with
+tremendous grace. It just asks you a
+
+ align:start position:0%
+tremendous grace. It just asks you a
+ 
+
+ align:start position:0%
+tremendous grace. It just asks you a
+question. It just comes out, you know,
+
+ align:start position:0%
+question. It just comes out, you know,
+ 
+
+ align:start position:0%
+question. It just comes out, you know,
+kind of out of the blue and says, "Hey,
+
+ align:start position:0%
+kind of out of the blue and says, "Hey,
+ 
+
+ align:start position:0%
+kind of out of the blue and says, "Hey,
+you know, when was the last time you
+
+ align:start position:0%
+you know, when was the last time you
+ 
+
+ align:start position:0%
+you know, when was the last time you
+lied?" Um, and if you, you know,
+
+ align:start position:0%
+lied?" Um, and if you, you know,
+ 
+
+ align:start position:0%
+lied?" Um, and if you, you know,
+sometimes you're surprised by that and
+
+ align:start position:0%
+sometimes you're surprised by that and
+ 
+
+ align:start position:0%
+sometimes you're surprised by that and
+that's a good effect, but it's also not,
+
+ align:start position:0%
+that's a good effect, but it's also not,
+ 
+
+ align:start position:0%
+that's a good effect, but it's also not,
+um, subtle. Um, and so I'm trying to
+
+ align:start position:0%
+um, subtle. Um, and so I'm trying to
+ 
+
+ align:start position:0%
+um, subtle. Um, and so I'm trying to
+explore how can we be subtle in in
+
+ align:start position:0%
+explore how can we be subtle in in
+ 
+
+ align:start position:0%
+explore how can we be subtle in in
+causing reflection. And so there are a
+
+ align:start position:0%
+causing reflection. And so there are a
+ 
+
+ align:start position:0%
+causing reflection. And so there are a
+few things here. I mean, the value
+
+ align:start position:0%
+few things here. I mean, the value
+ 
+
+ align:start position:0%
+few things here. I mean, the value
+question is interesting. How do you know
+
+ align:start position:0%
+question is interesting. How do you know
+ 
+
+ align:start position:0%
+question is interesting. How do you know
+what the value of the object is in the
+
+ align:start position:0%
+what the value of the object is in the
+ 
+
+ align:start position:0%
+what the value of the object is in the
+box? Um, do you think of it as a
+
+ align:start position:0%
+box? Um, do you think of it as a
+ 
+
+ align:start position:0%
+box? Um, do you think of it as a
+monetary value? Do you think of it as
+
+ align:start position:0%
+monetary value? Do you think of it as
+ 
+
+ align:start position:0%
+monetary value? Do you think of it as
+value in terms of significance to the
+
+ align:start position:0%
+value in terms of significance to the
+ 
+
+ align:start position:0%
+value in terms of significance to the
+person who put that in there? Um, why is
+
+ align:start position:0%
+person who put that in there? Um, why is
+ 
+
+ align:start position:0%
+person who put that in there? Um, why is
+it significant to the person who put
+
+ align:start position:0%
+it significant to the person who put
+ 
+
+ align:start position:0%
+it significant to the person who put
+that in there? Like what is this thing?
+
+ align:start position:0%
+that in there? Like what is this thing?
+ 
+
+ align:start position:0%
+that in there? Like what is this thing?
+Right? you can look at and reflect and
+
+ align:start position:0%
+Right? you can look at and reflect and
+ 
+
+ align:start position:0%
+Right? you can look at and reflect and
+and then when you leave a trace of
+
+ align:start position:0%
+and then when you leave a trace of
+ 
+
+ align:start position:0%
+and then when you leave a trace of
+yourself in this box, the next person
+
+ align:start position:0%
+yourself in this box, the next person
+ 
+
+ align:start position:0%
+yourself in this box, the next person
+who comes and plays is is going to see
+
+ align:start position:0%
+who comes and plays is is going to see
+ 
+
+ align:start position:0%
+who comes and plays is is going to see
+that and they're going to wonder what
+
+ align:start position:0%
+that and they're going to wonder what
+ 
+
+ align:start position:0%
+that and they're going to wonder what
+was what was that? And so I'm also kind
+
+ align:start position:0%
+was what was that? And so I'm also kind
+ 
+
+ align:start position:0%
+was what was that? And so I'm also kind
+of interested in like um the organicness
+
+ align:start position:0%
+of interested in like um the organicness
+ 
+
+ align:start position:0%
+of interested in like um the organicness
+uh the kind of uh uh the in the the
+
+ align:start position:0%
+uh the kind of uh uh the in the the
+ 
+
+ align:start position:0%
+uh the kind of uh uh the in the the
+never- ending interminable nature of a
+
+ align:start position:0%
+never- ending interminable nature of a
+ 
+
+ align:start position:0%
+never- ending interminable nature of a
+game that that carries the effect of a
+
+ align:start position:0%
+game that that carries the effect of a
+ 
+
+ align:start position:0%
+game that that carries the effect of a
+person who's played it kind of on and on
+
+ align:start position:0%
+person who's played it kind of on and on
+ 
+
+ align:start position:0%
+person who's played it kind of on and on
+and on. Um, the next iteration of this
+
+ align:start position:0%
+and on. Um, the next iteration of this
+ 
+
+ align:start position:0%
+and on. Um, the next iteration of this
+that I want to do, actually, this was an
+
+ align:start position:0%
+that I want to do, actually, this was an
+ 
+
+ align:start position:0%
+that I want to do, actually, this was an
+idea that Jason Bean gave me was to use
+
+ align:start position:0%
+idea that Jason Bean gave me was to use
+ 
+
+ align:start position:0%
+idea that Jason Bean gave me was to use
+um an apothecary chest. Um, because one
+
+ align:start position:0%
+um an apothecary chest. Um, because one
+ 
+
+ align:start position:0%
+um an apothecary chest. Um, because one
+of the things that we play tested it
+
+ align:start position:0%
+of the things that we play tested it
+ 
+
+ align:start position:0%
+of the things that we play tested it
+here with, I left it out for like two
+
+ align:start position:0%
+here with, I left it out for like two
+ 
+
+ align:start position:0%
+here with, I left it out for like two
+weeks and and people, you probably saw
+
+ align:start position:0%
+weeks and and people, you probably saw
+ 
+
+ align:start position:0%
+weeks and and people, you probably saw
+it, it was right there. Um, you know,
+
+ align:start position:0%
+it, it was right there. Um, you know,
+ 
+
+ align:start position:0%
+it, it was right there. Um, you know,
+people were engaging. And this is
+
+ align:start position:0%
+people were engaging. And this is
+ 
+
+ align:start position:0%
+people were engaging. And this is
+actually this is like a photo with
+
+ align:start position:0%
+actually this is like a photo with
+ 
+
+ align:start position:0%
+actually this is like a photo with
+objects that people had left in. So, it
+
+ align:start position:0%
+objects that people had left in. So, it
+ 
+
+ align:start position:0%
+objects that people had left in. So, it
+was really fun for me after two weeks to
+
+ align:start position:0%
+was really fun for me after two weeks to
+ 
+
+ align:start position:0%
+was really fun for me after two weeks to
+kind of go into this box and be like,
+
+ align:start position:0%
+kind of go into this box and be like,
+ 
+
+ align:start position:0%
+kind of go into this box and be like,
+what is all this stuff? You know, like
+
+ align:start position:0%
+what is all this stuff? You know, like
+ 
+
+ align:start position:0%
+what is all this stuff? You know, like
+like what got left? I was actually
+
+ align:start position:0%
+like what got left? I was actually
+ 
+
+ align:start position:0%
+like what got left? I was actually
+surprised the sketch, you know, was left
+
+ align:start position:0%
+surprised the sketch, you know, was left
+ 
+
+ align:start position:0%
+surprised the sketch, you know, was left
+and then but I was like, wow, what is
+
+ align:start position:0%
+and then but I was like, wow, what is
+ 
+
+ align:start position:0%
+and then but I was like, wow, what is
+this stuff? Um, and and to give you one
+
+ align:start position:0%
+this stuff? Um, and and to give you one
+ 
+
+ align:start position:0%
+this stuff? Um, and and to give you one
+really good example, um, one person at
+
+ align:start position:0%
+really good example, um, one person at
+ 
+
+ align:start position:0%
+really good example, um, one person at
+the lab put in a Nintendo DS flash card,
+
+ align:start position:0%
+the lab put in a Nintendo DS flash card,
+ 
+
+ align:start position:0%
+the lab put in a Nintendo DS flash card,
+um, which was really like a wrapped DS
+
+ align:start position:0%
+um, which was really like a wrapped DS
+ 
+
+ align:start position:0%
+um, which was really like a wrapped DS
+flash card. And so now there's this kind
+
+ align:start position:0%
+flash card. And so now there's this kind
+ 
+
+ align:start position:0%
+flash card. And so now there's this kind
+of this kind of next level. The game has
+
+ align:start position:0%
+of this kind of next level. The game has
+ 
+
+ align:start position:0%
+of this kind of next level. The game has
+changed with another level of
+
+ align:start position:0%
+changed with another level of
+ 
+
+ align:start position:0%
+changed with another level of
+interactivity where it's like if I want
+
+ align:start position:0%
+interactivity where it's like if I want
+ 
+
+ align:start position:0%
+interactivity where it's like if I want
+to kind of get at what was the uh, what
+
+ align:start position:0%
+to kind of get at what was the uh, what
+ 
+
+ align:start position:0%
+to kind of get at what was the uh, what
+was the significance of this object to
+
+ align:start position:0%
+was the significance of this object to
+ 
+
+ align:start position:0%
+was the significance of this object to
+this person, I need to I need to get a
+
+ align:start position:0%
+this person, I need to I need to get a
+ 
+
+ align:start position:0%
+this person, I need to I need to get a
+DS and play this, right? Right. So then
+
+ align:start position:0%
+DS and play this, right? Right. So then
+ 
+
+ align:start position:0%
+DS and play this, right? Right. So then
+I open up the and it's got it's got
+
+ align:start position:0%
+I open up the and it's got it's got
+ 
+
+ align:start position:0%
+I open up the and it's got it's got
+folders and it's got um you know a copy
+
+ align:start position:0%
+folders and it's got um you know a copy
+ 
+
+ align:start position:0%
+folders and it's got um you know a copy
+of the game Lemmings. It's got some
+
+ align:start position:0%
+of the game Lemmings. It's got some
+ 
+
+ align:start position:0%
+of the game Lemmings. It's got some
+music in it. Right. And so now it's kind
+
+ align:start position:0%
+music in it. Right. And so now it's kind
+ 
+
+ align:start position:0%
+music in it. Right. And so now it's kind
+of like you've you've like uncovered
+
+ align:start position:0%
+of like you've you've like uncovered
+ 
+
+ align:start position:0%
+of like you've you've like uncovered
+this next layer and it's like you know
+
+ align:start position:0%
+this next layer and it's like you know
+ 
+
+ align:start position:0%
+this next layer and it's like you know
+the interesting traces of the people who
+
+ align:start position:0%
+the interesting traces of the people who
+ 
+
+ align:start position:0%
+the interesting traces of the people who
+have played this game are are now you
+
+ align:start position:0%
+have played this game are are now you
+ 
+
+ align:start position:0%
+have played this game are are now you
+know uh you know marked onto this onto
+
+ align:start position:0%
+know uh you know marked onto this onto
+ 
+
+ align:start position:0%
+know uh you know marked onto this onto
+this box forever. Marley even said to me
+
+ align:start position:0%
+this box forever. Marley even said to me
+ 
+
+ align:start position:0%
+this box forever. Marley even said to me
+I was like talking to her about her play
+
+ align:start position:0%
+I was like talking to her about her play
+ 
+
+ align:start position:0%
+I was like talking to her about her play
+after she had done it and I was like um
+
+ align:start position:0%
+after she had done it and I was like um
+ 
+
+ align:start position:0%
+after she had done it and I was like um
+she told me she wanted to take the
+
+ align:start position:0%
+she told me she wanted to take the
+ 
+
+ align:start position:0%
+she told me she wanted to take the
+instructions. um she wanted to take the
+
+ align:start position:0%
+instructions. um she wanted to take the
+ 
+
+ align:start position:0%
+instructions. um she wanted to take the
+rules as one of the objects that she
+
+ align:start position:0%
+rules as one of the objects that she
+ 
+
+ align:start position:0%
+rules as one of the objects that she
+could take out of that. And I told her I
+
+ align:start position:0%
+could take out of that. And I told her I
+ 
+
+ align:start position:0%
+could take out of that. And I told her I
+had thought about that actually when I
+
+ align:start position:0%
+had thought about that actually when I
+ 
+
+ align:start position:0%
+had thought about that actually when I
+was designing it that someone might be
+
+ align:start position:0%
+was designing it that someone might be
+ 
+
+ align:start position:0%
+was designing it that someone might be
+like, "Ha, I'm going to take the rules."
+
+ align:start position:0%
+like, "Ha, I'm going to take the rules."
+ 
+
+ align:start position:0%
+like, "Ha, I'm going to take the rules."
+And and I was going to put in a rule
+
+ align:start position:0%
+And and I was going to put in a rule
+ 
+
+ align:start position:0%
+And and I was going to put in a rule
+that said, you know, you can turn the
+
+ align:start position:0%
+that said, you know, you can turn the
+ 
+
+ align:start position:0%
+that said, you know, you can turn the
+exchange for an object that's not the
+
+ align:start position:0%
+exchange for an object that's not the
+ 
+
+ align:start position:0%
+exchange for an object that's not the
+rule is so that the game could persist.
+
+ align:start position:0%
+rule is so that the game could persist.
+ 
+
+ align:start position:0%
+rule is so that the game could persist.
+But I but I didn't want I didn't want to
+
+ align:start position:0%
+But I but I didn't want I didn't want to
+ 
+
+ align:start position:0%
+But I but I didn't want I didn't want to
+artificially impose that if someone
+
+ align:start position:0%
+artificially impose that if someone
+ 
+
+ align:start position:0%
+artificially impose that if someone
+takes the rules because that's what they
+
+ align:start position:0%
+takes the rules because that's what they
+ 
+
+ align:start position:0%
+takes the rules because that's what they
+want. That's what and now the game is
+
+ align:start position:0%
+want. That's what and now the game is
+ 
+
+ align:start position:0%
+want. That's what and now the game is
+the game has changed. And maybe someone
+
+ align:start position:0%
+the game has changed. And maybe someone
+ 
+
+ align:start position:0%
+the game has changed. And maybe someone
+comes along later and and modifies it.
+
+ align:start position:0%
+comes along later and and modifies it.
+ 
+
+ align:start position:0%
+comes along later and and modifies it.
+Maybe they put something in that makes
+
+ align:start position:0%
+Maybe they put something in that makes
+ 
+
+ align:start position:0%
+Maybe they put something in that makes
+it a whole new different game. And and I
+
+ align:start position:0%
+it a whole new different game. And and I
+ 
+
+ align:start position:0%
+it a whole new different game. And and I
+really like the idea that you can
+
+ align:start position:0%
+really like the idea that you can
+ 
+
+ align:start position:0%
+really like the idea that you can
+encounter this game and that it's going
+
+ align:start position:0%
+encounter this game and that it's going
+ 
+
+ align:start position:0%
+encounter this game and that it's going
+to be kind of in this state of flux, I
+
+ align:start position:0%
+to be kind of in this state of flux, I
+ 
+
+ align:start position:0%
+to be kind of in this state of flux, I
+guess you could say. Um, and so that's
+
+ align:start position:0%
+guess you could say. Um, and so that's
+ 
+
+ align:start position:0%
+guess you could say. Um, and so that's
+what I'm that's what I'm working on now.
+
+ align:start position:0%
+what I'm that's what I'm working on now.
+ 
+
+ align:start position:0%
+what I'm that's what I'm working on now.
+And like I said, it's going to I think
+
+ align:start position:0%
+And like I said, it's going to I think
+ 
+
+ align:start position:0%
+And like I said, it's going to I think
+one of the things I didn't like is that
+
+ align:start position:0%
+one of the things I didn't like is that
+ 
+
+ align:start position:0%
+one of the things I didn't like is that
+all of the objects are accessible all at
+
+ align:start position:0%
+all of the objects are accessible all at
+ 
+
+ align:start position:0%
+all of the objects are accessible all at
+once. Um, so if it's an apothecary chest
+
+ align:start position:0%
+once. Um, so if it's an apothecary chest
+ 
+
+ align:start position:0%
+once. Um, so if it's an apothecary chest
+with lots of drawers, this was Jason
+
+ align:start position:0%
+with lots of drawers, this was Jason
+ 
+
+ align:start position:0%
+with lots of drawers, this was Jason
+Bean's idea, then you kind of have to do
+
+ align:start position:0%
+Bean's idea, then you kind of have to do
+ 
+
+ align:start position:0%
+Bean's idea, then you kind of have to do
+a little exploring. Um, and maybe the
+
+ align:start position:0%
+a little exploring. Um, and maybe the
+ 
+
+ align:start position:0%
+a little exploring. Um, and maybe the
+rules are in one of those drawers. And
+
+ align:start position:0%
+rules are in one of those drawers. And
+ 
+
+ align:start position:0%
+rules are in one of those drawers. And
+maybe you see the rules first, maybe you
+
+ align:start position:0%
+maybe you see the rules first, maybe you
+ 
+
+ align:start position:0%
+maybe you see the rules first, maybe you
+see the rules way after you've looked at
+
+ align:start position:0%
+see the rules way after you've looked at
+ 
+
+ align:start position:0%
+see the rules way after you've looked at
+a lot of stuff. And then you now you've
+
+ align:start position:0%
+a lot of stuff. And then you now you've
+ 
+
+ align:start position:0%
+a lot of stuff. And then you now you've
+seen all this stuff and played with it
+
+ align:start position:0%
+seen all this stuff and played with it
+ 
+
+ align:start position:0%
+seen all this stuff and played with it
+all and you really like something and
+
+ align:start position:0%
+all and you really like something and
+ 
+
+ align:start position:0%
+all and you really like something and
+now it's like what do I trade? Um
+
+ align:start position:0%
+now it's like what do I trade? Um
+ 
+
+ align:start position:0%
+now it's like what do I trade? Um
+and um and yeah, so I also am trying to
+
+ align:start position:0%
+and um and yeah, so I also am trying to
+ 
+
+ align:start position:0%
+and um and yeah, so I also am trying to
+find a way to give the box a a history
+
+ align:start position:0%
+find a way to give the box a a history
+ 
+
+ align:start position:0%
+find a way to give the box a a history
+as well. I've contemplated some ideas of
+
+ align:start position:0%
+as well. I've contemplated some ideas of
+ 
+
+ align:start position:0%
+as well. I've contemplated some ideas of
+putting in some some kind of clues that
+
+ align:start position:0%
+putting in some some kind of clues that
+ 
+
+ align:start position:0%
+putting in some some kind of clues that
+you could then if you felt if you
+
+ align:start position:0%
+you could then if you felt if you
+ 
+
+ align:start position:0%
+you could then if you felt if you
+thought about it or looked it up, you
+
+ align:start position:0%
+thought about it or looked it up, you
+ 
+
+ align:start position:0%
+thought about it or looked it up, you
+might be able to find a story to this
+
+ align:start position:0%
+might be able to find a story to this
+ 
+
+ align:start position:0%
+might be able to find a story to this
+box. Like if you did an internet search,
+
+ align:start position:0%
+box. Like if you did an internet search,
+ 
+
+ align:start position:0%
+box. Like if you did an internet search,
+you might come upon a fake website. uh
+
+ align:start position:0%
+you might come upon a fake website. uh
+ 
+
+ align:start position:0%
+you might come upon a fake website. uh
+wouldn't be fake. It' just be a website,
+
+ align:start position:0%
+wouldn't be fake. It' just be a website,
+ 
+
+ align:start position:0%
+wouldn't be fake. It' just be a website,
+but a website with a fake story that
+
+ align:start position:0%
+but a website with a fake story that
+ 
+
+ align:start position:0%
+but a website with a fake story that
+kind of tells you a little bit about
+
+ align:start position:0%
+kind of tells you a little bit about
+ 
+
+ align:start position:0%
+kind of tells you a little bit about
+this box and maybe gives you a few more
+
+ align:start position:0%
+this box and maybe gives you a few more
+ 
+
+ align:start position:0%
+this box and maybe gives you a few more
+hooks into what the meaning of this game
+
+ align:start position:0%
+hooks into what the meaning of this game
+ 
+
+ align:start position:0%
+hooks into what the meaning of this game
+or what the inspiration for this game
+
+ align:start position:0%
+or what the inspiration for this game
+ 
+
+ align:start position:0%
+or what the inspiration for this game
+inspiration for this game was. And so
+
+ align:start position:0%
+inspiration for this game was. And so
+ 
+
+ align:start position:0%
+inspiration for this game was. And so
+this is kind of one of my projects that
+
+ align:start position:0%
+this is kind of one of my projects that
+ 
+
+ align:start position:0%
+this is kind of one of my projects that
+I'm working on right now. Like I said,
+
+ align:start position:0%
+I'm working on right now. Like I said,
+ 
+
+ align:start position:0%
+I'm working on right now. Like I said,
+I'm kind of I'm interested in
+
+ align:start position:0%
+I'm kind of I'm interested in
+ 
+
+ align:start position:0%
+I'm kind of I'm interested in
+tangibility, but but you can see where a
+
+ align:start position:0%
+tangibility, but but you can see where a
+ 
+
+ align:start position:0%
+tangibility, but but you can see where a
+lot of the other things that I was
+
+ align:start position:0%
+lot of the other things that I was
+ 
+
+ align:start position:0%
+lot of the other things that I was
+talking about are kind of inspiring
+
+ align:start position:0%
+talking about are kind of inspiring
+ 
+
+ align:start position:0%
+talking about are kind of inspiring
+inspiring this this work. Um and so we
+
+ align:start position:0%
+inspiring this this work. Um and so we
+ 
+
+ align:start position:0%
+inspiring this this work. Um and so we
+kind of come back to that question of
+
+ align:start position:0%
+kind of come back to that question of
+ 
+
+ align:start position:0%
+kind of come back to that question of
+are games art and whether it's even a
+
+ align:start position:0%
+are games art and whether it's even a
+ 
+
+ align:start position:0%
+are games art and whether it's even a
+valid question. We only have five
+
+ align:start position:0%
+valid question. We only have five
+ 
+
+ align:start position:0%
+valid question. We only have five
+minutes. I don't know if you guys have
+
+ align:start position:0%
+minutes. I don't know if you guys have
+ 
+
+ align:start position:0%
+minutes. I don't know if you guys have
+administrative stuff afterwards, but um
+
+ align:start position:0%
+administrative stuff afterwards, but um
+ 
+
+ align:start position:0%
+administrative stuff afterwards, but um
+this is like I said, this is sort of my
+
+ align:start position:0%
+this is like I said, this is sort of my
+ 
+
+ align:start position:0%
+this is like I said, this is sort of my
+viewpoint and I I it's certainly shared
+
+ align:start position:0%
+viewpoint and I I it's certainly shared
+ 
+
+ align:start position:0%
+viewpoint and I I it's certainly shared
+with a lot of other people. Um but it's
+
+ align:start position:0%
+with a lot of other people. Um but it's
+ 
+
+ align:start position:0%
+with a lot of other people. Um but it's
+not um this is not guaranteed truth.
+
+ align:start position:0%
+not um this is not guaranteed truth.
+ 
+
+ align:start position:0%
+not um this is not guaranteed truth.
+It's this is an opinion that I have just
+
+ align:start position:0%
+It's this is an opinion that I have just
+ 
+
+ align:start position:0%
+It's this is an opinion that I have just
+shared. So, um, but any thoughts you
+
+ align:start position:0%
+shared. So, um, but any thoughts you
+ 
+
+ align:start position:0%
+shared. So, um, but any thoughts you
+guys have about this subject or these
+
+ align:start position:0%
+guys have about this subject or these
+ 
+
+ align:start position:0%
+guys have about this subject or these
+ideas of these games or
+
+ align:start position:0%
+ideas of these games or
+ 
+
+ align:start position:0%
+ideas of these games or
+anything at all?
+
+ align:start position:0%
+anything at all?
+ 
+
+ align:start position:0%
+anything at all?
+Yesterday's football game.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Well, cool. Well, I hope this was
+
+ align:start position:0%
+>> Well, cool. Well, I hope this was
+ 
+
+ align:start position:0%
+>> Well, cool. Well, I hope this was
+useful. I hope it was helpful. Um, you
+
+ align:start position:0%
+useful. I hope it was helpful. Um, you
+ 
+
+ align:start position:0%
+useful. I hope it was helpful. Um, you
+know, I think it if if at the very least
+
+ align:start position:0%
+know, I think it if if at the very least
+ 
+
+ align:start position:0%
+know, I think it if if at the very least
+it causes you to continue to think
+
+ align:start position:0%
+it causes you to continue to think
+ 
+
+ align:start position:0%
+it causes you to continue to think
+about, you know, your own games that
+
+ align:start position:0%
+about, you know, your own games that
+ 
+
+ align:start position:0%
+about, you know, your own games that
+you're developing and how meaning can be
+
+ align:start position:0%
+you're developing and how meaning can be
+ 
+
+ align:start position:0%
+you're developing and how meaning can be
+embed in in the play that you might not
+
+ align:start position:0%
+embed in in the play that you might not
+ 
+
+ align:start position:0%
+embed in in the play that you might not
+even realize is there. Um, but also just
+
+ align:start position:0%
+even realize is there. Um, but also just
+ 
+
+ align:start position:0%
+even realize is there. Um, but also just
+kind of the possibility space. I I
+
+ align:start position:0%
+kind of the possibility space. I I
+ 
+
+ align:start position:0%
+kind of the possibility space. I I
+really am excited by I'm discouraged by
+
+ align:start position:0%
+really am excited by I'm discouraged by
+ 
+
+ align:start position:0%
+really am excited by I'm discouraged by
+the safe choices that a lot of
+
+ align:start position:0%
+the safe choices that a lot of
+ 
+
+ align:start position:0%
+the safe choices that a lot of
+independent game developers make and
+
+ align:start position:0%
+independent game developers make and
+ 
+
+ align:start position:0%
+independent game developers make and
+excited when some game developers really
+
+ align:start position:0%
+excited when some game developers really
+ 
+
+ align:start position:0%
+excited when some game developers really
+push on the edge. I don't think we have
+
+ align:start position:0%
+push on the edge. I don't think we have
+ 
+
+ align:start position:0%
+push on the edge. I don't think we have
+a I don't think we have a clear
+
+ align:start position:0%
+a I don't think we have a clear
+ 
+
+ align:start position:0%
+a I don't think we have a clear
+understanding of what the rules are or
+
+ align:start position:0%
+understanding of what the rules are or
+ 
+
+ align:start position:0%
+understanding of what the rules are or
+what even constitutes a game or what
+
+ align:start position:0%
+what even constitutes a game or what
+ 
+
+ align:start position:0%
+what even constitutes a game or what
+what degree of interactivity is
+
+ align:start position:0%
+what degree of interactivity is
+ 
+
+ align:start position:0%
+what degree of interactivity is
+appropriate for a you know quote unquote
+
+ align:start position:0%
+appropriate for a you know quote unquote
+ 
+
+ align:start position:0%
+appropriate for a you know quote unquote
+game. And I think I think some of these
+
+ align:start position:0%
+game. And I think I think some of these
+ 
+
+ align:start position:0%
+game. And I think I think some of these
+designers are really testing the waters
+
+ align:start position:0%
+designers are really testing the waters
+ 
+
+ align:start position:0%
+designers are really testing the waters
+of the medium. You know, what can we
+
+ align:start position:0%
+of the medium. You know, what can we
+ 
+
+ align:start position:0%
+of the medium. You know, what can we
+really do with this? You know, where
+
+ align:start position:0%
+really do with this? You know, where
+ 
+
+ align:start position:0%
+really do with this? You know, where
+where can we go? How edgy and satirical
+
+ align:start position:0%
+where can we go? How edgy and satirical
+ 
+
+ align:start position:0%
+where can we go? How edgy and satirical
+and on guard can we be? Um,
+
+ align:start position:0%
+and on guard can we be? Um,
+ 
+
+ align:start position:0%
+and on guard can we be? Um,
+I think that's always good.
+
+ align:start position:0%
+I think that's always good.
+ 
+
+ align:start position:0%
+I think that's always good.
+So, I'm a revolutionary
+
+ align:start position:0%
+So, I'm a revolutionary
+ 
+
+ align:start position:0%
+So, I'm a revolutionary
+crazy person.
+
+ align:start position:0%
+crazy person.
+ 
+
+ align:start position:0%
+crazy person.
+>> Crazy person.
+
+ align:start position:0%
+>> Crazy person.
+ 
+
+ align:start position:0%
+>> Crazy person.
+That's good to hear.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Folks, um if folks haven't played uh yet
+
+ align:start position:0%
+>> Folks, um if folks haven't played uh yet
+ 
+
+ align:start position:0%
+>> Folks, um if folks haven't played uh yet
+one word this year, which were some of
+
+ align:start position:0%
+one word this year, which were some of
+ 
+
+ align:start position:0%
+one word this year, which were some of
+the games that uh Abe um worked with the
+
+ align:start position:0%
+the games that uh Abe um worked with the
+ 
+
+ align:start position:0%
+the games that uh Abe um worked with the
+team on over the summer, uh those are on
+
+ align:start position:0%
+team on over the summer, uh those are on
+ 
+
+ align:start position:0%
+team on over the summer, uh those are on
+our gamut website uh just opened 2010
+
+ align:start position:0%
+our gamut website uh just opened 2010
+ 
+
+ align:start position:0%
+our gamut website uh just opened 2010
+and and you see yet one more in Sier
+
+ align:start position:0%
+and and you see yet one more in Sier
+ 
+
+ align:start position:0%
+and and you see yet one more in Sier
+which were booked about this summer. We
+
+ align:start position:0%
+which were booked about this summer. We
+ 
+
+ align:start position:0%
+which were booked about this summer. We
+saw us like try to see some of the
+
+ align:start position:0%
+saw us like try to see some of the
+ 
+
+ align:start position:0%
+saw us like try to see some of the
+digital.
+
+ align:start position:0%
+digital.
+ 
+
+ align:start position:0%
+digital.
+>> Yeah. And please play them and give us
+
+ align:start position:0%
+>> Yeah. And please play them and give us
+ 
+
+ align:start position:0%
+>> Yeah. And please play them and give us
+feedback too, right? Because that's the
+
+ align:start position:0%
+feedback too, right? Because that's the
+ 
+
+ align:start position:0%
+feedback too, right? Because that's the
+other thing like these are not perfect
+
+ align:start position:0%
+other thing like these are not perfect
+ 
+
+ align:start position:0%
+other thing like these are not perfect
+articulations of of game is is the pure
+
+ align:start position:0%
+articulations of of game is is the pure
+ 
+
+ align:start position:0%
+articulations of of game is is the pure
+art form, right? Like we're constantly
+
+ align:start position:0%
+art form, right? Like we're constantly
+ 
+
+ align:start position:0%
+art form, right? Like we're constantly
+evolving and trying to improve and so
+
+ align:start position:0%
+evolving and trying to improve and so
+ 
+
+ align:start position:0%
+evolving and trying to improve and so
+any feedback you can give us on this
+
+ align:start position:0%
+any feedback you can give us on this
+ 
+
+ align:start position:0%
+any feedback you can give us on this
+stuff is greatly appreciated.
+
+ align:start position:0%
+stuff is greatly appreciated.
+ 
+
+ align:start position:0%
+stuff is greatly appreciated.
+>> I have one question.
+
+ align:start position:0%
+>> I have one question.
+ 
+
+ align:start position:0%
+>> I have one question.
+>> Do you still have that box like
+
+ align:start position:0%
+>> Do you still have that box like
+ 
+
+ align:start position:0%
+>> Do you still have that box like
+somewhere?
+
+ align:start position:0%
+somewhere?
+ 
+
+ align:start position:0%
+somewhere?
+>> Yeah. Yeah, it's in my office. Yeah.
+
+ align:start position:0%
+>> Yeah. Yeah, it's in my office. Yeah.
+ 
+
+ align:start position:0%
+>> Yeah. Yeah, it's in my office. Yeah.
+Yeah. Yeah. Totally. Yeah. I have a box
+
+ align:start position:0%
+Yeah. Yeah. Totally. Yeah. I have a box
+ 
+
+ align:start position:0%
+Yeah. Yeah. Totally. Yeah. I have a box
+and I need to I'm I'm So the other part
+
+ align:start position:0%
+and I need to I'm I'm So the other part
+ 
+
+ align:start position:0%
+and I need to I'm I'm So the other part
+of it is is when I do the second version
+
+ align:start position:0%
+of it is is when I do the second version
+ 
+
+ align:start position:0%
+of it is is when I do the second version
+of it in the apothecary kind of chest,
+
+ align:start position:0%
+of it in the apothecary kind of chest,
+ 
+
+ align:start position:0%
+of it in the apothecary kind of chest,
+uh, one thing that's important to me is
+
+ align:start position:0%
+uh, one thing that's important to me is
+ 
+
+ align:start position:0%
+uh, one thing that's important to me is
+that each of the I sort of for the
+
+ align:start position:0%
+that each of the I sort of for the
+ 
+
+ align:start position:0%
+that each of the I sort of for the
+prototype, I just sort of threw some
+
+ align:start position:0%
+prototype, I just sort of threw some
+ 
+
+ align:start position:0%
+prototype, I just sort of threw some
+like reasonably meaningful objects in
+
+ align:start position:0%
+like reasonably meaningful objects in
+ 
+
+ align:start position:0%
+like reasonably meaningful objects in
+there, but I I I want it to be populated
+
+ align:start position:0%
+there, but I I I want it to be populated
+ 
+
+ align:start position:0%
+there, but I I I want it to be populated
+with objects that are personally
+
+ align:start position:0%
+with objects that are personally
+ 
+
+ align:start position:0%
+with objects that are personally
+significant to myself or symbolic to
+
+ align:start position:0%
+significant to myself or symbolic to
+ 
+
+ align:start position:0%
+significant to myself or symbolic to
+myself. and um and populating that box
+
+ align:start position:0%
+myself. and um and populating that box
+ 
+
+ align:start position:0%
+myself. and um and populating that box
+at the outset with meaningful objects I
+
+ align:start position:0%
+at the outset with meaningful objects I
+ 
+
+ align:start position:0%
+at the outset with meaningful objects I
+think is important because it it's you
+
+ align:start position:0%
+think is important because it it's you
+ 
+
+ align:start position:0%
+think is important because it it's you
+know sort of once it's once it's quote
+
+ align:start position:0%
+know sort of once it's once it's quote
+ 
+
+ align:start position:0%
+know sort of once it's once it's quote
+unquote released into the world for play
+
+ align:start position:0%
+unquote released into the world for play
+ 
+
+ align:start position:0%
+unquote released into the world for play
+right then it's it's constantly changing
+
+ align:start position:0%
+right then it's it's constantly changing
+ 
+
+ align:start position:0%
+right then it's it's constantly changing
+and so that first that first instant
+
+ align:start position:0%
+and so that first that first instant
+ 
+
+ align:start position:0%
+and so that first that first instant
+instantiation of the game is is the one
+
+ align:start position:0%
+instantiation of the game is is the one
+ 
+
+ align:start position:0%
+instantiation of the game is is the one
+that is is kind of about me in some sort
+
+ align:start position:0%
+that is is kind of about me in some sort
+ 
+
+ align:start position:0%
+that is is kind of about me in some sort
+of sense and about my experiences and
+
+ align:start position:0%
+of sense and about my experiences and
+ 
+
+ align:start position:0%
+of sense and about my experiences and
+then it becomes the world which is play.
+
+ align:start position:0%
+then it becomes the world which is play.
+ 
+
+ align:start position:0%
+then it becomes the world which is play.
+So, the way that your games kind of
+
+ align:start position:0%
+So, the way that your games kind of
+ 
+
+ align:start position:0%
+So, the way that your games kind of
+reminds me of is I'm pretty sure I heard
+
+ align:start position:0%
+reminds me of is I'm pretty sure I heard
+ 
+
+ align:start position:0%
+reminds me of is I'm pretty sure I heard
+this similar that some person uh had a
+
+ align:start position:0%
+this similar that some person uh had a
+ 
+
+ align:start position:0%
+this similar that some person uh had a
+pen and so he just kept he started with
+
+ align:start position:0%
+pen and so he just kept he started with
+ 
+
+ align:start position:0%
+pen and so he just kept he started with
+a pen and he kept trading and made
+
+ align:start position:0%
+a pen and he kept trading and made
+ 
+
+ align:start position:0%
+a pen and he kept trading and made
+>> red paper.
+
+ align:start position:0%
+>> red paper.
+ 
+
+ align:start position:0%
+>> red paper.
+>> Oh, no. Well, no, no, this is a
+
+ align:start position:0%
+>> Oh, no. Well, no, no, this is a
+ 
+
+ align:start position:0%
+>> Oh, no. Well, no, no, this is a
+different one. Not the red paper clip
+
+ align:start position:0%
+different one. Not the red paper clip
+ 
+
+ align:start position:0%
+different one. Not the red paper clip
+for I heard I think it was someone had
+
+ align:start position:0%
+for I heard I think it was someone had
+ 
+
+ align:start position:0%
+for I heard I think it was someone had
+started with a pen or something and kept
+
+ align:start position:0%
+started with a pen or something and kept
+ 
+
+ align:start position:0%
+started with a pen or something and kept
+trading it and over the course of like a
+
+ align:start position:0%
+trading it and over the course of like a
+ 
+
+ align:start position:0%
+trading it and over the course of like a
+year or two he eventually trade got with
+
+ align:start position:0%
+year or two he eventually trade got with
+ 
+
+ align:start position:0%
+year or two he eventually trade got with
+that init from that initial pen he was
+
+ align:start position:0%
+that init from that initial pen he was
+ 
+
+ align:start position:0%
+that init from that initial pen he was
+able to trade for a house or something.
+
+ align:start position:0%
+able to trade for a house or something.
+ 
+
+ align:start position:0%
+able to trade for a house or something.
+It was okay.
+
+ align:start position:0%
+It was okay.
+ 
+
+ align:start position:0%
+It was okay.
+>> Yeah. No, totally. I mean, and that was
+
+ align:start position:0%
+>> Yeah. No, totally. I mean, and that was
+ 
+
+ align:start position:0%
+>> Yeah. No, totally. I mean, and that was
+like sort of an interesting what I like.
+
+ align:start position:0%
+like sort of an interesting what I like.
+ 
+
+ align:start position:0%
+like sort of an interesting what I like.
+I think it was on eBay, too, right? Or
+
+ align:start position:0%
+I think it was on eBay, too, right? Or
+ 
+
+ align:start position:0%
+I think it was on eBay, too, right? Or
+something like that. And that's even
+
+ align:start position:0%
+something like that. And that's even
+ 
+
+ align:start position:0%
+something like that. And that's even
+using a a pretty well-designed game
+
+ align:start position:0%
+using a a pretty well-designed game
+ 
+
+ align:start position:0%
+using a a pretty well-designed game
+system because eBay is totally a game.
+
+ align:start position:0%
+system because eBay is totally a game.
+ 
+
+ align:start position:0%
+system because eBay is totally a game.
+Um, and using a game system to and
+
+ align:start position:0%
+Um, and using a game system to and
+ 
+
+ align:start position:0%
+Um, and using a game system to and
+subverting the system itself to do
+
+ align:start position:0%
+subverting the system itself to do
+ 
+
+ align:start position:0%
+subverting the system itself to do
+something really kind of interesting.
+
+ align:start position:0%
+something really kind of interesting.
+ 
+
+ align:start position:0%
+something really kind of interesting.
+And so, I mean, yeah, that's a that's a
+
+ align:start position:0%
+And so, I mean, yeah, that's a that's a
+ 
+
+ align:start position:0%
+And so, I mean, yeah, that's a that's a
+really kind of great it's like a game
+
+ align:start position:0%
+really kind of great it's like a game
+ 
+
+ align:start position:0%
+really kind of great it's like a game
+inside of a game, right? And I love
+
+ align:start position:0%
+inside of a game, right? And I love
+ 
+
+ align:start position:0%
+inside of a game, right? And I love
+that. That's it's kind of like the cow
+
+ align:start position:0%
+that. That's it's kind of like the cow
+ 
+
+ align:start position:0%
+that. That's it's kind of like the cow
+clickers, right? like making a game
+
+ align:start position:0%
+clickers, right? like making a game
+ 
+
+ align:start position:0%
+clickers, right? like making a game
+inside of the game that subverts the
+
+ align:start position:0%
+inside of the game that subverts the
+ 
+
+ align:start position:0%
+inside of the game that subverts the
+>> Are you familiar with the concept of
+
+ align:start position:0%
+>> Are you familiar with the concept of
+ 
+
+ align:start position:0%
+>> Are you familiar with the concept of
+geocaching?
+
+ align:start position:0%
+geocaching?
+ 
+
+ align:start position:0%
+geocaching?
+>> Uh because what when I first saw what
+
+ align:start position:0%
+>> Uh because what when I first saw what
+ 
+
+ align:start position:0%
+>> Uh because what when I first saw what
+the game you were talking about that you
+
+ align:start position:0%
+the game you were talking about that you
+ 
+
+ align:start position:0%
+the game you were talking about that you
+designed it really reminded me of it. Uh
+
+ align:start position:0%
+designed it really reminded me of it. Uh
+ 
+
+ align:start position:0%
+designed it really reminded me of it. Uh
+so initially what it was is when GPS's
+
+ align:start position:0%
+so initially what it was is when GPS's
+ 
+
+ align:start position:0%
+so initially what it was is when GPS's
+first came out, people were like, "Oh,
+
+ align:start position:0%
+first came out, people were like, "Oh,
+ 
+
+ align:start position:0%
+first came out, people were like, "Oh,
+hey, this is really cool technology. We
+
+ align:start position:0%
+hey, this is really cool technology. We
+ 
+
+ align:start position:0%
+hey, this is really cool technology. We
+should think of something fun to do with
+
+ align:start position:0%
+should think of something fun to do with
+ 
+
+ align:start position:0%
+should think of something fun to do with
+it." So what they did was uh these
+
+ align:start position:0%
+it." So what they did was uh these
+ 
+
+ align:start position:0%
+it." So what they did was uh these
+people hid started hiding um like empty
+
+ align:start position:0%
+people hid started hiding um like empty
+ 
+
+ align:start position:0%
+people hid started hiding um like empty
+tins of like little trinkets and stuff
+
+ align:start position:0%
+tins of like little trinkets and stuff
+ 
+
+ align:start position:0%
+tins of like little trinkets and stuff
+at various like on hiking trails or
+
+ align:start position:0%
+at various like on hiking trails or
+ 
+
+ align:start position:0%
+at various like on hiking trails or
+other And you would look up the
+
+ align:start position:0%
+other And you would look up the
+ 
+
+ align:start position:0%
+other And you would look up the
+coordinates on your GPS finder and you
+
+ align:start position:0%
+coordinates on your GPS finder and you
+ 
+
+ align:start position:0%
+coordinates on your GPS finder and you
+would find this box and what you would
+
+ align:start position:0%
+would find this box and what you would
+ 
+
+ align:start position:0%
+would find this box and what you would
+do is you you trade a trinket and you
+
+ align:start position:0%
+do is you you trade a trinket and you
+ 
+
+ align:start position:0%
+do is you you trade a trinket and you
+get a trinket.
+
+ align:start position:0%
+get a trinket.
+ 
+
+ align:start position:0%
+get a trinket.
+>> And you keep like traveling to these
+
+ align:start position:0%
+>> And you keep like traveling to these
+ 
+
+ align:start position:0%
+>> And you keep like traveling to these
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+>> Yeah. And in that sense like this this
+
+ align:start position:0%
+>> Yeah. And in that sense like this this
+ 
+
+ align:start position:0%
+>> Yeah. And in that sense like this this
+whole worldwide game becomes really kind
+
+ align:start position:0%
+whole worldwide game becomes really kind
+ 
+
+ align:start position:0%
+whole worldwide game becomes really kind
+of changed. Yeah. You know there's
+
+ align:start position:0%
+of changed. Yeah. You know there's
+ 
+
+ align:start position:0%
+of changed. Yeah. You know there's
+there's there's some sh there's some
+
+ align:start position:0%
+there's there's some sh there's some
+ 
+
+ align:start position:0%
+there's there's some sh there's some
+shared ideas with some location based
+
+ align:start position:0%
+shared ideas with some location based
+ 
+
+ align:start position:0%
+shared ideas with some location based
+games that do some really interesting
+
+ align:start position:0%
+games that do some really interesting
+ 
+
+ align:start position:0%
+games that do some really interesting
+things with with that where um you know
+
+ align:start position:0%
+things with with that where um you know
+ 
+
+ align:start position:0%
+things with with that where um you know
+whether it's alternative reality but but
+
+ align:start position:0%
+whether it's alternative reality but but
+ 
+
+ align:start position:0%
+whether it's alternative reality but but
+maybe not even with a with a narrative.
+
+ align:start position:0%
+maybe not even with a with a narrative.
+ 
+
+ align:start position:0%
+maybe not even with a with a narrative.
+There was one I was reading about um
+
+ align:start position:0%
+There was one I was reading about um
+ 
+
+ align:start position:0%
+There was one I was reading about um
+that was at uh it was like come out and
+
+ align:start position:0%
+that was at uh it was like come out and
+ 
+
+ align:start position:0%
+that was at uh it was like come out and
+play I think in New York City at one
+
+ align:start position:0%
+play I think in New York City at one
+ 
+
+ align:start position:0%
+play I think in New York City at one
+point but it was cruel to be kind. uh it
+
+ align:start position:0%
+point but it was cruel to be kind. uh it
+ 
+
+ align:start position:0%
+point but it was cruel to be kind. uh it
+was called. It was a game where um you
+
+ align:start position:0%
+was called. It was a game where um you
+ 
+
+ align:start position:0%
+was called. It was a game where um you
+don't you don't know who's playing, you
+
+ align:start position:0%
+don't you don't know who's playing, you
+ 
+
+ align:start position:0%
+don't you don't know who's playing, you
+know who's on what team, but you use you
+
+ align:start position:0%
+know who's on what team, but you use you
+ 
+
+ align:start position:0%
+know who's on what team, but you use you
+use you get missions and you get a
+
+ align:start position:0%
+use you get missions and you get a
+ 
+
+ align:start position:0%
+use you get missions and you get a
+weapon that's a compliment like um you
+
+ align:start position:0%
+weapon that's a compliment like um you
+ 
+
+ align:start position:0%
+weapon that's a compliment like um you
+know to kill someone who's on the other
+
+ align:start position:0%
+know to kill someone who's on the other
+ 
+
+ align:start position:0%
+know to kill someone who's on the other
+team, mistake them for a celebrity or
+
+ align:start position:0%
+team, mistake them for a celebrity or
+ 
+
+ align:start position:0%
+team, mistake them for a celebrity or
+something like that, right? And so
+
+ align:start position:0%
+something like that, right? And so
+ 
+
+ align:start position:0%
+something like that, right? And so
+you're using these kind of random acts
+
+ align:start position:0%
+you're using these kind of random acts
+ 
+
+ align:start position:0%
+you're using these kind of random acts
+of kindness, you know, helping someone
+
+ align:start position:0%
+of kindness, you know, helping someone
+ 
+
+ align:start position:0%
+of kindness, you know, helping someone
+across the street and you don't know if
+
+ align:start position:0%
+across the street and you don't know if
+ 
+
+ align:start position:0%
+across the street and you don't know if
+it's like in New York City, so you don't
+
+ align:start position:0%
+it's like in New York City, so you don't
+ 
+
+ align:start position:0%
+it's like in New York City, so you don't
+know if someone's playing the game. So
+
+ align:start position:0%
+know if someone's playing the game. So
+ 
+
+ align:start position:0%
+know if someone's playing the game. So
+now all of a sudden you're kind of
+
+ align:start position:0%
+now all of a sudden you're kind of
+ 
+
+ align:start position:0%
+now all of a sudden you're kind of
+wandering around doing really nice
+
+ align:start position:0%
+wandering around doing really nice
+ 
+
+ align:start position:0%
+wandering around doing really nice
+things for people on the chance that you
+
+ align:start position:0%
+things for people on the chance that you
+ 
+
+ align:start position:0%
+things for people on the chance that you
+know on a hunch that you have that maybe
+
+ align:start position:0%
+know on a hunch that you have that maybe
+ 
+
+ align:start position:0%
+know on a hunch that you have that maybe
+they're playing the game and maybe
+
+ align:start position:0%
+they're playing the game and maybe
+ 
+
+ align:start position:0%
+they're playing the game and maybe
+they're not. And so you just help
+
+ align:start position:0%
+they're not. And so you just help
+ 
+
+ align:start position:0%
+they're not. And so you just help
+somebody across the street which is
+
+ align:start position:0%
+somebody across the street which is
+ 
+
+ align:start position:0%
+somebody across the street which is
+totally nice and and it kind of comes to
+
+ align:start position:0%
+totally nice and and it kind of comes to
+ 
+
+ align:start position:0%
+totally nice and and it kind of comes to
+this massive conclusion where you just
+
+ align:start position:0%
+this massive conclusion where you just
+ 
+
+ align:start position:0%
+this massive conclusion where you just
+have these two giant teams who meet up
+
+ align:start position:0%
+have these two giant teams who meet up
+ 
+
+ align:start position:0%
+have these two giant teams who meet up
+at a location to nice each other to
+
+ align:start position:0%
+at a location to nice each other to
+ 
+
+ align:start position:0%
+at a location to nice each other to
+death basically. Um and so you know
+
+ align:start position:0%
+death basically. Um and so you know
+ 
+
+ align:start position:0%
+death basically. Um and so you know
+there there's a lot of really really
+
+ align:start position:0%
+there there's a lot of really really
+ 
+
+ align:start position:0%
+there there's a lot of really really
+kind of interesting stuff especially in
+
+ align:start position:0%
+kind of interesting stuff especially in
+ 
+
+ align:start position:0%
+kind of interesting stuff especially in
+the the kind of location based
+
+ align:start position:0%
+the the kind of location based
+ 
+
+ align:start position:0%
+the the kind of location based
+>> realm. Big big games are really cool.
+
+ align:start position:0%
+>> realm. Big big games are really cool.
+ 
+
+ align:start position:0%
+>> realm. Big big games are really cool.
+There's a lot of people doing really
+
+ align:start position:0%
+There's a lot of people doing really
+ 
+
+ align:start position:0%
+There's a lot of people doing really
+neat stuff with with big games.
+
+ align:start position:0%
+neat stuff with with big games.
+ 
+
+ align:start position:0%
+neat stuff with with big games.
+>> Yeah. So, I I I think like in particular
+
+ align:start position:0%
+>> Yeah. So, I I I think like in particular
+ 
+
+ align:start position:0%
+>> Yeah. So, I I I think like in particular
+with you know, the box and the
+
+ align:start position:0%
+with you know, the box and the
+ 
+
+ align:start position:0%
+with you know, the box and the
+geocaching idea, it's and and you know,
+
+ align:start position:0%
+geocaching idea, it's and and you know,
+ 
+
+ align:start position:0%
+geocaching idea, it's and and you know,
+talking about the paperclip for a house
+
+ align:start position:0%
+talking about the paperclip for a house
+ 
+
+ align:start position:0%
+talking about the paperclip for a house
+thing.
+
+ align:start position:0%
+thing.
+ 
+
+ align:start position:0%
+thing.
+>> It's really interesting like what how
+
+ align:start position:0%
+>> It's really interesting like what how
+ 
+
+ align:start position:0%
+>> It's really interesting like what how
+people value things.
+
+ align:start position:0%
+people value things.
+ 
+
+ align:start position:0%
+people value things.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Like in particular, you know, you have
+
+ align:start position:0%
+>> Like in particular, you know, you have
+ 
+
+ align:start position:0%
+>> Like in particular, you know, you have
+this very vague rule in it that just
+
+ align:start position:0%
+this very vague rule in it that just
+ 
+
+ align:start position:0%
+this very vague rule in it that just
+says, you know, something of of equal
+
+ align:start position:0%
+says, you know, something of of equal
+ 
+
+ align:start position:0%
+says, you know, something of of equal
+value. Like what does it actually mean?
+
+ align:start position:0%
+value. Like what does it actually mean?
+ 
+
+ align:start position:0%
+value. Like what does it actually mean?
+>> Value or
+
+ align:start position:0%
+>> Value or
+ 
+
+ align:start position:0%
+>> Value or
+>> Yeah, exactly. It's kind of interesting
+
+ align:start position:0%
+>> Yeah, exactly. It's kind of interesting
+ 
+
+ align:start position:0%
+>> Yeah, exactly. It's kind of interesting
+like what someone is willing to trade
+
+ align:start position:0%
+like what someone is willing to trade
+ 
+
+ align:start position:0%
+like what someone is willing to trade
+for for something else.
+
+ align:start position:0%
+for for something else.
+ 
+
+ align:start position:0%
+for for something else.
+>> Yeah. And those are those are the kind
+
+ align:start position:0%
+>> Yeah. And those are those are the kind
+ 
+
+ align:start position:0%
+>> Yeah. And those are those are the kind
+of implicit rules like you see in 16
+
+ align:start position:0%
+of implicit rules like you see in 16
+ 
+
+ align:start position:0%
+of implicit rules like you see in 16
+tons, right? Where it's like what
+
+ align:start position:0%
+tons, right? Where it's like what
+ 
+
+ align:start position:0%
+tons, right? Where it's like what
+happens with the money, you know, and
+
+ align:start position:0%
+happens with the money, you know, and
+ 
+
+ align:start position:0%
+happens with the money, you know, and
+and and that's, you know, Jason me
+
+ align:start position:0%
+and and that's, you know, Jason me
+ 
+
+ align:start position:0%
+and and that's, you know, Jason me
+really pointed out because he was
+
+ align:start position:0%
+really pointed out because he was
+ 
+
+ align:start position:0%
+really pointed out because he was
+thinking about value when he was doing
+
+ align:start position:0%
+thinking about value when he was doing
+ 
+
+ align:start position:0%
+thinking about value when he was doing
+the training and it's such a good word,
+
+ align:start position:0%
+the training and it's such a good word,
+ 
+
+ align:start position:0%
+the training and it's such a good word,
+right? Because value is such a different
+
+ align:start position:0%
+right? Because value is such a different
+ 
+
+ align:start position:0%
+right? Because value is such a different
+thing to different people and someone
+
+ align:start position:0%
+thing to different people and someone
+ 
+
+ align:start position:0%
+thing to different people and someone
+might see the like the the flash card
+
+ align:start position:0%
+might see the like the the flash card
+ 
+
+ align:start position:0%
+might see the like the the flash card
+for the DS, right, which has a very
+
+ align:start position:0%
+for the DS, right, which has a very
+ 
+
+ align:start position:0%
+for the DS, right, which has a very
+clear higher monetary value than than an
+
+ align:start position:0%
+clear higher monetary value than than an
+ 
+
+ align:start position:0%
+clear higher monetary value than than an
+etch sketch. Um, and yet maybe you
+
+ align:start position:0%
+etch sketch. Um, and yet maybe you
+ 
+
+ align:start position:0%
+etch sketch. Um, and yet maybe you
+played with an etch sketch when you were
+
+ align:start position:0%
+played with an etch sketch when you were
+ 
+
+ align:start position:0%
+played with an etch sketch when you were
+a kid and all of a sudden it floods back
+
+ align:start position:0%
+a kid and all of a sudden it floods back
+ 
+
+ align:start position:0%
+a kid and all of a sudden it floods back
+these memories that you have. Um,
+
+ align:start position:0%
+these memories that you have. Um,
+ 
+
+ align:start position:0%
+these memories that you have. Um,
+there's also there's another component
+
+ align:start position:0%
+there's also there's another component
+ 
+
+ align:start position:0%
+there's also there's another component
+to it that I didn't really talk about,
+
+ align:start position:0%
+to it that I didn't really talk about,
+ 
+
+ align:start position:0%
+to it that I didn't really talk about,
+which is like the sacrificing of an
+
+ align:start position:0%
+which is like the sacrificing of an
+ 
+
+ align:start position:0%
+which is like the sacrificing of an
+object. And and I think too that it's
+
+ align:start position:0%
+object. And and I think too that it's
+ 
+
+ align:start position:0%
+object. And and I think too that it's
+it's we we tend to be beholden to our
+
+ align:start position:0%
+it's we we tend to be beholden to our
+ 
+
+ align:start position:0%
+it's we we tend to be beholden to our
+material objects um too much um in in in
+
+ align:start position:0%
+material objects um too much um in in in
+ 
+
+ align:start position:0%
+material objects um too much um in in in
+giving it up in in sacrificing it to
+
+ align:start position:0%
+giving it up in in sacrificing it to
+ 
+
+ align:start position:0%
+giving it up in in sacrificing it to
+this game so that you don't have it
+
+ align:start position:0%
+this game so that you don't have it
+ 
+
+ align:start position:0%
+this game so that you don't have it
+anymore. If it's something of personal
+
+ align:start position:0%
+anymore. If it's something of personal
+ 
+
+ align:start position:0%
+anymore. If it's something of personal
+significance, you're you're letting go
+
+ align:start position:0%
+significance, you're you're letting go
+ 
+
+ align:start position:0%
+significance, you're you're letting go
+and and being able to say, "Okay, the
+
+ align:start position:0%
+and and being able to say, "Okay, the
+ 
+
+ align:start position:0%
+and and being able to say, "Okay, the
+memory is one thing. I don't need to."
+
+ align:start position:0%
+memory is one thing. I don't need to."
+ 
+
+ align:start position:0%
+memory is one thing. I don't need to."
+And that's that's how it relates a bit
+
+ align:start position:0%
+And that's that's how it relates a bit
+ 
+
+ align:start position:0%
+And that's that's how it relates a bit
+back to Citizen Kane, which is a movie
+
+ align:start position:0%
+back to Citizen Kane, which is a movie
+ 
+
+ align:start position:0%
+back to Citizen Kane, which is a movie
+you should see because it is good.
+
+ align:start position:0%
+you should see because it is good.
+ 
+
+ align:start position:0%
+you should see because it is good.
+It's everything they said it is,
+
+ align:start position:0%
+It's everything they said it is,
+ 
+
+ align:start position:0%
+It's everything they said it is,
+>> depending on who they are.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Cool. Thanks, guys.
+
+ align:start position:0%
+>> Cool. Thanks, guys.
+ 
+
+ align:start position:0%
+>> Cool. Thanks, guys.
+>> Thanks.
\ No newline at end of file
diff --git a/yP1S37BiEsQ.txt b/yP1S37BiEsQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e2b601afaabe141f10d0d4e41ee4f4d2a63c463c
--- /dev/null
+++ b/yP1S37BiEsQ.txt
@@ -0,0 +1,13131 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
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+to offer highquality educational
+ 
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+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
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+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT
+OpenCourseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's because if I was not, this would be
+
+ align:start position:0%
+It's because if I was not, this would be
+ 
+
+ align:start position:0%
+It's because if I was not, this would be
+basically the last topic we would ever
+
+ align:start position:0%
+basically the last topic we would ever
+ 
+
+ align:start position:0%
+basically the last topic we would ever
+see. And this is arguably probably the
+
+ align:start position:0%
+see. And this is arguably probably the
+ 
+
+ align:start position:0%
+see. And this is arguably probably the
+most important topic in statistics or at
+
+ align:start position:0%
+most important topic in statistics or at
+ 
+
+ align:start position:0%
+most important topic in statistics or at
+least that's probably the reason why
+
+ align:start position:0%
+least that's probably the reason why
+ 
+
+ align:start position:0%
+least that's probably the reason why
+most of you are taking this class
+
+ align:start position:0%
+most of you are taking this class
+ 
+
+ align:start position:0%
+most of you are taking this class
+because regression
+
+ align:start position:0%
+because regression
+ 
+
+ align:start position:0%
+because regression
+implies prediction and prediction is
+
+ align:start position:0%
+implies prediction and prediction is
+ 
+
+ align:start position:0%
+implies prediction and prediction is
+what people are all after now, right?
+
+ align:start position:0%
+what people are all after now, right?
+ 
+
+ align:start position:0%
+what people are all after now, right?
+You don't need to understand what the
+
+ align:start position:0%
+You don't need to understand what the
+ 
+
+ align:start position:0%
+You don't need to understand what the
+model for the financial market is. If
+
+ align:start position:0%
+model for the financial market is. If
+ 
+
+ align:start position:0%
+model for the financial market is. If
+you actually have a formula to predict
+
+ align:start position:0%
+you actually have a formula to predict
+ 
+
+ align:start position:0%
+you actually have a formula to predict
+what uh the stock prices are going to be
+
+ align:start position:0%
+what uh the stock prices are going to be
+ 
+
+ align:start position:0%
+what uh the stock prices are going to be
+tomorrow and regression in a way allows
+
+ align:start position:0%
+tomorrow and regression in a way allows
+ 
+
+ align:start position:0%
+tomorrow and regression in a way allows
+us to do that. And we'll start with a
+
+ align:start position:0%
+us to do that. And we'll start with a
+ 
+
+ align:start position:0%
+us to do that. And we'll start with a
+very simple version of regression which
+
+ align:start position:0%
+very simple version of regression which
+ 
+
+ align:start position:0%
+very simple version of regression which
+is linear regression which is the most
+
+ align:start position:0%
+is linear regression which is the most
+ 
+
+ align:start position:0%
+is linear regression which is the most
+standard one. And then we'll move on to
+
+ align:start position:0%
+standard one. And then we'll move on to
+ 
+
+ align:start position:0%
+standard one. And then we'll move on to
+slightly more advanced notions such as
+
+ align:start position:0%
+slightly more advanced notions such as
+ 
+
+ align:start position:0%
+slightly more advanced notions such as
+nonparametric regression. At least we're
+
+ align:start position:0%
+nonparametric regression. At least we're
+ 
+
+ align:start position:0%
+nonparametric regression. At least we're
+going to see the principles behind it.
+
+ align:start position:0%
+going to see the principles behind it.
+ 
+
+ align:start position:0%
+going to see the principles behind it.
+And uh I'll touch upon a little bit of
+
+ align:start position:0%
+And uh I'll touch upon a little bit of
+ 
+
+ align:start position:0%
+And uh I'll touch upon a little bit of
+high dimensional regression which is
+
+ align:start position:0%
+high dimensional regression which is
+ 
+
+ align:start position:0%
+high dimensional regression which is
+what people are doing today.
+
+ align:start position:0%
+what people are doing today.
+ 
+
+ align:start position:0%
+what people are doing today.
+So the goal of regression is to try to
+
+ align:start position:0%
+So the goal of regression is to try to
+ 
+
+ align:start position:0%
+So the goal of regression is to try to
+predict one variable based on another
+
+ align:start position:0%
+predict one variable based on another
+ 
+
+ align:start position:0%
+predict one variable based on another
+variable. All right. So here the
+
+ align:start position:0%
+variable. All right. So here the
+ 
+
+ align:start position:0%
+variable. All right. So here the
+notation is very important. It's
+
+ align:start position:0%
+notation is very important. It's
+ 
+
+ align:start position:0%
+notation is very important. It's
+extremely standard. It goes from one uh
+
+ align:start position:0%
+extremely standard. It goes from one uh
+ 
+
+ align:start position:0%
+extremely standard. It goes from one uh
+it goes everywhere essentially and
+
+ align:start position:0%
+it goes everywhere essentially and
+ 
+
+ align:start position:0%
+it goes everywhere essentially and
+essentially you have you're trying to
+
+ align:start position:0%
+essentially you have you're trying to
+ 
+
+ align:start position:0%
+essentially you have you're trying to
+explain y as a function of x. Okay,
+
+ align:start position:0%
+explain y as a function of x. Okay,
+ 
+
+ align:start position:0%
+explain y as a function of x. Okay,
+which is the usual yals f ofx question
+
+ align:start position:0%
+which is the usual yals f ofx question
+ 
+
+ align:start position:0%
+which is the usual yals f ofx question
+except that you know if you look at a
+
+ align:start position:0%
+except that you know if you look at a
+ 
+
+ align:start position:0%
+except that you know if you look at a
+calculus class, people tell you yals f
+
+ align:start position:0%
+calculus class, people tell you yals f
+ 
+
+ align:start position:0%
+calculus class, people tell you yals f
+ofx
+
+ align:start position:0%
+ofx
+ 
+
+ align:start position:0%
+ofx
+and they give you a specific form for f
+
+ align:start position:0%
+and they give you a specific form for f
+ 
+
+ align:start position:0%
+and they give you a specific form for f
+and then you do something. Here we're
+
+ align:start position:0%
+and then you do something. Here we're
+ 
+
+ align:start position:0%
+and then you do something. Here we're
+just going to try to estimate what this
+
+ align:start position:0%
+just going to try to estimate what this
+ 
+
+ align:start position:0%
+just going to try to estimate what this
+link function is. And this is why we
+
+ align:start position:0%
+link function is. And this is why we
+ 
+
+ align:start position:0%
+link function is. And this is why we
+often call uh y the explained variable
+
+ align:start position:0%
+often call uh y the explained variable
+ 
+
+ align:start position:0%
+often call uh y the explained variable
+and x the explanatory variable. All
+
+ align:start position:0%
+and x the explanatory variable. All
+ 
+
+ align:start position:0%
+and x the explanatory variable. All
+right. So um we're statisticians. So we
+
+ align:start position:0%
+right. So um we're statisticians. So we
+ 
+
+ align:start position:0%
+right. So um we're statisticians. So we
+start with data. All right. And what
+
+ align:start position:0%
+start with data. All right. And what
+ 
+
+ align:start position:0%
+start with data. All right. And what
+does our data look like? Well, it looks
+
+ align:start position:0%
+does our data look like? Well, it looks
+ 
+
+ align:start position:0%
+does our data look like? Well, it looks
+like a bunch of input output to this
+
+ align:start position:0%
+like a bunch of input output to this
+ 
+
+ align:start position:0%
+like a bunch of input output to this
+relationship. All right. So we have a
+
+ align:start position:0%
+relationship. All right. So we have a
+ 
+
+ align:start position:0%
+relationship. All right. So we have a
+bunch of xi yi. Those are pairs. And I
+
+ align:start position:0%
+bunch of xi yi. Those are pairs. And I
+ 
+
+ align:start position:0%
+bunch of xi yi. Those are pairs. And I
+can do a scatter plot of those guys.
+
+ align:start position:0%
+can do a scatter plot of those guys.
+ 
+
+ align:start position:0%
+can do a scatter plot of those guys.
+Right? So each point here has a x
+
+ align:start position:0%
+Right? So each point here has a x
+ 
+
+ align:start position:0%
+Right? So each point here has a x
+coordinate which is x i and a
+
+ align:start position:0%
+coordinate which is x i and a
+ 
+
+ align:start position:0%
+coordinate which is x i and a
+ycoordinate which is y i. And here I
+
+ align:start position:0%
+ycoordinate which is y i. And here I
+ 
+
+ align:start position:0%
+ycoordinate which is y i. And here I
+have a bunch of end points and I just
+
+ align:start position:0%
+have a bunch of end points and I just
+ 
+
+ align:start position:0%
+have a bunch of end points and I just
+draw them like that. Now if so the
+
+ align:start position:0%
+draw them like that. Now if so the
+ 
+
+ align:start position:0%
+draw them like that. Now if so the
+functions we're going to be interested
+
+ align:start position:0%
+functions we're going to be interested
+ 
+
+ align:start position:0%
+functions we're going to be interested
+in are often function of the form y = a
+
+ align:start position:0%
+in are often function of the form y = a
+ 
+
+ align:start position:0%
+in are often function of the form y = a
++ b * x. Okay. And that means that this
+
+ align:start position:0%
++ b * x. Okay. And that means that this
+ 
+
+ align:start position:0%
++ b * x. Okay. And that means that this
+function looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I do x and y, this function looks
+
+ align:start position:0%
+So if I do x and y, this function looks
+ 
+
+ align:start position:0%
+So if I do x and y, this function looks
+exactly like a line and clearly those
+
+ align:start position:0%
+exactly like a line and clearly those
+ 
+
+ align:start position:0%
+exactly like a line and clearly those
+points are not on a line and it will
+
+ align:start position:0%
+points are not on a line and it will
+ 
+
+ align:start position:0%
+points are not on a line and it will
+basically never happen that those points
+
+ align:start position:0%
+basically never happen that those points
+ 
+
+ align:start position:0%
+basically never happen that those points
+are on a line. There's a famous uh
+
+ align:start position:0%
+are on a line. There's a famous uh
+ 
+
+ align:start position:0%
+are on a line. There's a famous uh
+t-shirt from I think UC Berkeley stats
+
+ align:start position:0%
+t-shirt from I think UC Berkeley stats
+ 
+
+ align:start position:0%
+t-shirt from I think UC Berkeley stats
+department that shows this picture and
+
+ align:start position:0%
+department that shows this picture and
+ 
+
+ align:start position:0%
+department that shows this picture and
+put a line in between them like we're
+
+ align:start position:0%
+put a line in between them like we're
+ 
+
+ align:start position:0%
+put a line in between them like we're
+going to see it and it says uh
+
+ align:start position:0%
+going to see it and it says uh
+ 
+
+ align:start position:0%
+going to see it and it says uh
+statisticians so many points and you
+
+ align:start position:0%
+statisticians so many points and you
+ 
+
+ align:start position:0%
+statisticians so many points and you
+still managed to miss all of them and uh
+
+ align:start position:0%
+still managed to miss all of them and uh
+ 
+
+ align:start position:0%
+still managed to miss all of them and uh
+and so basically essentially we don't
+
+ align:start position:0%
+and so basically essentially we don't
+ 
+
+ align:start position:0%
+and so basically essentially we don't
+believe that this relationship y is
+
+ align:start position:0%
+believe that this relationship y is
+ 
+
+ align:start position:0%
+believe that this relationship y is
+equal to a plus bx is true but maybe up
+
+ align:start position:0%
+equal to a plus bx is true but maybe up
+ 
+
+ align:start position:0%
+equal to a plus bx is true but maybe up
+to some noise and that's where the
+
+ align:start position:0%
+to some noise and that's where the
+ 
+
+ align:start position:0%
+to some noise and that's where the
+statistics is going to come into play.
+
+ align:start position:0%
+statistics is going to come into play.
+ 
+
+ align:start position:0%
+statistics is going to come into play.
+there's going to be some random noise
+
+ align:start position:0%
+there's going to be some random noise
+ 
+
+ align:start position:0%
+there's going to be some random noise
+that's going to play out and hopefully
+
+ align:start position:0%
+that's going to play out and hopefully
+ 
+
+ align:start position:0%
+that's going to play out and hopefully
+the noise is going to be spread out
+
+ align:start position:0%
+the noise is going to be spread out
+ 
+
+ align:start position:0%
+the noise is going to be spread out
+evenly so that we can average it uh if
+
+ align:start position:0%
+evenly so that we can average it uh if
+ 
+
+ align:start position:0%
+evenly so that we can average it uh if
+we have enough points average it out.
+
+ align:start position:0%
+we have enough points average it out.
+ 
+
+ align:start position:0%
+we have enough points average it out.
+Okay. And so this epsilon here is not
+
+ align:start position:0%
+Okay. And so this epsilon here is not
+ 
+
+ align:start position:0%
+Okay. And so this epsilon here is not
+necessarily due to randomness but again
+
+ align:start position:0%
+necessarily due to randomness but again
+ 
+
+ align:start position:0%
+necessarily due to randomness but again
+just like we did modeling in the first
+
+ align:start position:0%
+just like we did modeling in the first
+ 
+
+ align:start position:0%
+just like we did modeling in the first
+place it essentially accounts for
+
+ align:start position:0%
+place it essentially accounts for
+ 
+
+ align:start position:0%
+place it essentially accounts for
+everything we don't understand about
+
+ align:start position:0%
+everything we don't understand about
+ 
+
+ align:start position:0%
+everything we don't understand about
+this relationship. All right. So for
+
+ align:start position:0%
+this relationship. All right. So for
+ 
+
+ align:start position:0%
+this relationship. All right. So for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+uh uh so here I'm not going to be uh so
+
+ align:start position:0%
+uh uh so here I'm not going to be uh so
+ 
+
+ align:start position:0%
+uh uh so here I'm not going to be uh so
+okay give me one second. So uh I'll see
+
+ align:start position:0%
+okay give me one second. So uh I'll see
+ 
+
+ align:start position:0%
+okay give me one second. So uh I'll see
+we'll see an example in a second. But
+
+ align:start position:0%
+we'll see an example in a second. But
+ 
+
+ align:start position:0%
+we'll see an example in a second. But
+the idea here is that if you have data
+
+ align:start position:0%
+the idea here is that if you have data
+ 
+
+ align:start position:0%
+the idea here is that if you have data
+and if you believe that it's of the form
+
+ align:start position:0%
+and if you believe that it's of the form
+ 
+
+ align:start position:0%
+and if you believe that it's of the form
+a plus bx plus some noise, you're trying
+
+ align:start position:0%
+a plus bx plus some noise, you're trying
+ 
+
+ align:start position:0%
+a plus bx plus some noise, you're trying
+to find the line that will explain your
+
+ align:start position:0%
+to find the line that will explain your
+ 
+
+ align:start position:0%
+to find the line that will explain your
+data the best. Right? In the terminology
+
+ align:start position:0%
+data the best. Right? In the terminology
+ 
+
+ align:start position:0%
+data the best. Right? In the terminology
+we've been using before. This would be
+
+ align:start position:0%
+we've been using before. This would be
+ 
+
+ align:start position:0%
+we've been using before. This would be
+the most likely line that explains the
+
+ align:start position:0%
+the most likely line that explains the
+ 
+
+ align:start position:0%
+the most likely line that explains the
+data. So we can see that it's lately
+
+ align:start position:0%
+data. So we can see that it's lately
+ 
+
+ align:start position:0%
+data. So we can see that it's lately
+we've just added another dimension to
+
+ align:start position:0%
+we've just added another dimension to
+ 
+
+ align:start position:0%
+we've just added another dimension to
+our statistical problem. We don't have
+
+ align:start position:0%
+our statistical problem. We don't have
+ 
+
+ align:start position:0%
+our statistical problem. We don't have
+just x's, but we have y's, and we're
+
+ align:start position:0%
+just x's, but we have y's, and we're
+ 
+
+ align:start position:0%
+just x's, but we have y's, and we're
+trying to find the most likely
+
+ align:start position:0%
+trying to find the most likely
+ 
+
+ align:start position:0%
+trying to find the most likely
+explanation of the relationship between
+
+ align:start position:0%
+explanation of the relationship between
+ 
+
+ align:start position:0%
+explanation of the relationship between
+y and x. All right? And so
+
+ align:start position:0%
+y and x. All right? And so
+ 
+
+ align:start position:0%
+y and x. All right? And so
+in practice, the way it's going to look
+
+ align:start position:0%
+in practice, the way it's going to look
+ 
+
+ align:start position:0%
+in practice, the way it's going to look
+like is that we're going to have
+
+ align:start position:0%
+like is that we're going to have
+ 
+
+ align:start position:0%
+like is that we're going to have
+basically two parameters to find the
+
+ align:start position:0%
+basically two parameters to find the
+ 
+
+ align:start position:0%
+basically two parameters to find the
+slope b and the intercept a. And given
+
+ align:start position:0%
+slope b and the intercept a. And given
+ 
+
+ align:start position:0%
+slope b and the intercept a. And given
+data, the goal is going to be to try to
+
+ align:start position:0%
+data, the goal is going to be to try to
+ 
+
+ align:start position:0%
+data, the goal is going to be to try to
+find the best possible line. All right?
+
+ align:start position:0%
+find the best possible line. All right?
+ 
+
+ align:start position:0%
+find the best possible line. All right?
+So what we're going to find is not
+
+ align:start position:0%
+So what we're going to find is not
+ 
+
+ align:start position:0%
+So what we're going to find is not
+exactly A and B the ones that actually
+
+ align:start position:0%
+exactly A and B the ones that actually
+ 
+
+ align:start position:0%
+exactly A and B the ones that actually
+generate the data but some estim est est
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+est est est est est est est est est est
+est est est est est est est est est est
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+est est est est est est est est est est
+est est est est est est est estimators
+
+ align:start position:0%
+est est est est est est est estimators
+ 
+
+ align:start position:0%
+est est est est est est est estimators
+of those parameters a hat and b hat
+
+ align:start position:0%
+of those parameters a hat and b hat
+ 
+
+ align:start position:0%
+of those parameters a hat and b hat
+constructed from the data all right so
+
+ align:start position:0%
+constructed from the data all right so
+ 
+
+ align:start position:0%
+constructed from the data all right so
+we'll see that more generally but we're
+
+ align:start position:0%
+we'll see that more generally but we're
+ 
+
+ align:start position:0%
+we'll see that more generally but we're
+not going to go too much in the details
+
+ align:start position:0%
+not going to go too much in the details
+ 
+
+ align:start position:0%
+not going to go too much in the details
+of this it there's actually quite a bit
+
+ align:start position:0%
+of this it there's actually quite a bit
+ 
+
+ align:start position:0%
+of this it there's actually quite a bit
+that you can understand if you do what's
+
+ align:start position:0%
+that you can understand if you do what's
+ 
+
+ align:start position:0%
+that you can understand if you do what's
+called univariate regression when x is
+
+ align:start position:0%
+called univariate regression when x is
+ 
+
+ align:start position:0%
+called univariate regression when x is
+actually a real valued uh random
+
+ align:start position:0%
+actually a real valued uh random
+ 
+
+ align:start position:0%
+actually a real valued uh random
+variable so when this happens this is
+
+ align:start position:0%
+variable so when this happens this is
+ 
+
+ align:start position:0%
+variable so when this happens this is
+called univariate regression
+
+ align:start position:0%
+called univariate regression
+ 
+
+ align:start position:0%
+called univariate regression
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And when X is in RP
+
+ align:start position:0%
+And when X is in RP
+ 
+
+ align:start position:0%
+And when X is in RP
+for P larger than or equal to two, this
+
+ align:start position:0%
+for P larger than or equal to two, this
+ 
+
+ align:start position:0%
+for P larger than or equal to two, this
+is called multivariate regression.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And so here we're just trying to
+
+ align:start position:0%
+Okay. And so here we're just trying to
+ 
+
+ align:start position:0%
+Okay. And so here we're just trying to
+explain y is a + b x plus epsilon. And
+
+ align:start position:0%
+explain y is a + b x plus epsilon. And
+ 
+
+ align:start position:0%
+explain y is a + b x plus epsilon. And
+here we're going to have something more
+
+ align:start position:0%
+here we're going to have something more
+ 
+
+ align:start position:0%
+here we're going to have something more
+complicated. We're going to have y,
+
+ align:start position:0%
+complicated. We're going to have y,
+ 
+
+ align:start position:0%
+complicated. We're going to have y,
+which is equal to a + b1 x1 + b2
+
+ align:start position:0%
+which is equal to a + b1 x1 + b2
+ 
+
+ align:start position:0%
+which is equal to a + b1 x1 + b2
+x2 + b p xp
+
+ align:start position:0%
+x2 + b p xp
+ 
+
+ align:start position:0%
+x2 + b p xp
+plus epsilon where x is equal to the
+
+ align:start position:0%
+plus epsilon where x is equal to the
+ 
+
+ align:start position:0%
+plus epsilon where x is equal to the
+coordinates of x are given by x1 2xp or
+
+ align:start position:0%
+coordinates of x are given by x1 2xp or
+ 
+
+ align:start position:0%
+coordinates of x are given by x1 2xp or
+p. Okay, so it's still linear, right?
+
+ align:start position:0%
+p. Okay, so it's still linear, right?
+ 
+
+ align:start position:0%
+p. Okay, so it's still linear, right?
+they still add all the coordinates of x
+
+ align:start position:0%
+they still add all the coordinates of x
+ 
+
+ align:start position:0%
+they still add all the coordinates of x
+with a coefficient in front of them but
+
+ align:start position:0%
+with a coefficient in front of them but
+ 
+
+ align:start position:0%
+with a coefficient in front of them but
+it's a bit more complicated than just
+
+ align:start position:0%
+it's a bit more complicated than just
+ 
+
+ align:start position:0%
+it's a bit more complicated than just
+one coefficient for one coordinate of x.
+
+ align:start position:0%
+one coefficient for one coordinate of x.
+ 
+
+ align:start position:0%
+one coefficient for one coordinate of x.
+Okay. So we'll come back to multivate
+
+ align:start position:0%
+Okay. So we'll come back to multivate
+ 
+
+ align:start position:0%
+Okay. So we'll come back to multivate
+regression. Uh there's a of course you
+
+ align:start position:0%
+regression. Uh there's a of course you
+ 
+
+ align:start position:0%
+regression. Uh there's a of course you
+can write this as a uh uh xrpose b
+
+ align:start position:0%
+can write this as a uh uh xrpose b
+ 
+
+ align:start position:0%
+can write this as a uh uh xrpose b
+right. So this entire thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this linear combination is of the form
+
+ align:start position:0%
+this linear combination is of the form
+ 
+
+ align:start position:0%
+this linear combination is of the form
+xrpose b where b is the vector that has
+
+ align:start position:0%
+xrpose b where b is the vector that has
+ 
+
+ align:start position:0%
+xrpose b where b is the vector that has
+coordinates b1 to bp.
+
+ align:start position:0%
+coordinates b1 to bp.
+ 
+
+ align:start position:0%
+coordinates b1 to bp.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Uh sorry here it's in our d
+
+ align:start position:0%
+Uh sorry here it's in our d
+ 
+
+ align:start position:0%
+Uh sorry here it's in our d
+p is the natural notation.
+
+ align:start position:0%
+p is the natural notation.
+ 
+
+ align:start position:0%
+p is the natural notation.
+All right. So our goal here in the
+
+ align:start position:0%
+All right. So our goal here in the
+ 
+
+ align:start position:0%
+All right. So our goal here in the
+univariate one is to try to write a
+
+ align:start position:0%
+univariate one is to try to write a
+ 
+
+ align:start position:0%
+univariate one is to try to write a
+model make sense of this little twiddle
+
+ align:start position:0%
+model make sense of this little twiddle
+ 
+
+ align:start position:0%
+model make sense of this little twiddle
+here essentially from a statistical
+
+ align:start position:0%
+here essentially from a statistical
+ 
+
+ align:start position:0%
+here essentially from a statistical
+modeling question is going to be able to
+
+ align:start position:0%
+modeling question is going to be able to
+ 
+
+ align:start position:0%
+modeling question is going to be able to
+the question is going to be what
+
+ align:start position:0%
+the question is going to be what
+ 
+
+ align:start position:0%
+the question is going to be what
+distributional assumptions do you want
+
+ align:start position:0%
+distributional assumptions do you want
+ 
+
+ align:start position:0%
+distributional assumptions do you want
+to put on epsilon are you going to say
+
+ align:start position:0%
+to put on epsilon are you going to say
+ 
+
+ align:start position:0%
+to put on epsilon are you going to say
+they're Gaussian or you going to say
+
+ align:start position:0%
+they're Gaussian or you going to say
+ 
+
+ align:start position:0%
+they're Gaussian or you going to say
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+binomial uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um are you going to say they're
+
+ align:start position:0%
+okay um are you going to say they're
+ 
+
+ align:start position:0%
+okay um are you going to say they're
+binomial? Are you going to say they're
+
+ align:start position:0%
+binomial? Are you going to say they're
+ 
+
+ align:start position:0%
+binomial? Are you going to say they're
+Bernly? Uh so that's going to be uh what
+
+ align:start position:0%
+Bernly? Uh so that's going to be uh what
+ 
+
+ align:start position:0%
+Bernly? Uh so that's going to be uh what
+we're going to make sense. And then
+
+ align:start position:0%
+we're going to make sense. And then
+ 
+
+ align:start position:0%
+we're going to make sense. And then
+we're going to try to find a method to
+
+ align:start position:0%
+we're going to try to find a method to
+ 
+
+ align:start position:0%
+we're going to try to find a method to
+estimate A and B. And then maybe we're
+
+ align:start position:0%
+estimate A and B. And then maybe we're
+ 
+
+ align:start position:0%
+estimate A and B. And then maybe we're
+going to try to do some inference about
+
+ align:start position:0%
+going to try to do some inference about
+ 
+
+ align:start position:0%
+going to try to do some inference about
+A and B. Maybe test if A and B take
+
+ align:start position:0%
+A and B. Maybe test if A and B take
+ 
+
+ align:start position:0%
+A and B. Maybe test if A and B take
+certain values if they're less than
+
+ align:start position:0%
+certain values if they're less than
+ 
+
+ align:start position:0%
+certain values if they're less than
+something. Maybe find some confidence
+
+ align:start position:0%
+something. Maybe find some confidence
+ 
+
+ align:start position:0%
+something. Maybe find some confidence
+regions for A and B. All right.
+
+ align:start position:0%
+regions for A and B. All right.
+ 
+
+ align:start position:0%
+regions for A and B. All right.
+So why would you want to do this? Well,
+
+ align:start position:0%
+So why would you want to do this? Well,
+ 
+
+ align:start position:0%
+So why would you want to do this? Well,
+I'm sure all of you have an application
+
+ align:start position:0%
+I'm sure all of you have an application
+ 
+
+ align:start position:0%
+I'm sure all of you have an application
+why. If I give you some X, you're trying
+
+ align:start position:0%
+why. If I give you some X, you're trying
+ 
+
+ align:start position:0%
+why. If I give you some X, you're trying
+to predict what Y is. Machine learning
+
+ align:start position:0%
+to predict what Y is. Machine learning
+ 
+
+ align:start position:0%
+to predict what Y is. Machine learning
+is all about doing this, right? Without
+
+ align:start position:0%
+is all about doing this, right? Without
+ 
+
+ align:start position:0%
+is all about doing this, right? Without
+maybe trying to even understand the
+
+ align:start position:0%
+maybe trying to even understand the
+ 
+
+ align:start position:0%
+maybe trying to even understand the
+physics behind this. They're saying,
+
+ align:start position:0%
+physics behind this. They're saying,
+ 
+
+ align:start position:0%
+physics behind this. They're saying,
+well, you give me a bag of words. I want
+
+ align:start position:0%
+well, you give me a bag of words. I want
+ 
+
+ align:start position:0%
+well, you give me a bag of words. I want
+to understand whether it's going to be a
+
+ align:start position:0%
+to understand whether it's going to be a
+ 
+
+ align:start position:0%
+to understand whether it's going to be a
+spam or not. You give me a bunch of
+
+ align:start position:0%
+spam or not. You give me a bunch of
+ 
+
+ align:start position:0%
+spam or not. You give me a bunch of
+indic economic indicators. I want you to
+
+ align:start position:0%
+indic economic indicators. I want you to
+ 
+
+ align:start position:0%
+indic economic indicators. I want you to
+tell me how much I should be selling my
+
+ align:start position:0%
+tell me how much I should be selling my
+ 
+
+ align:start position:0%
+tell me how much I should be selling my
+car for. uh you give me a bunch of uh uh
+
+ align:start position:0%
+car for. uh you give me a bunch of uh uh
+ 
+
+ align:start position:0%
+car for. uh you give me a bunch of uh uh
+uh measurements on some patient. I want
+
+ align:start position:0%
+uh measurements on some patient. I want
+ 
+
+ align:start position:0%
+uh measurements on some patient. I want
+you to predict how this person is going
+
+ align:start position:0%
+you to predict how this person is going
+ 
+
+ align:start position:0%
+you to predict how this person is going
+to respond to my drug and things like
+
+ align:start position:0%
+to respond to my drug and things like
+ 
+
+ align:start position:0%
+to respond to my drug and things like
+this. All right? And so
+
+ align:start position:0%
+this. All right? And so
+ 
+
+ align:start position:0%
+this. All right? And so
+often we actually don't have much
+
+ align:start position:0%
+often we actually don't have much
+ 
+
+ align:start position:0%
+often we actually don't have much
+modeling intuition about what the
+
+ align:start position:0%
+modeling intuition about what the
+ 
+
+ align:start position:0%
+modeling intuition about what the
+relationship between X and Y is. And
+
+ align:start position:0%
+relationship between X and Y is. And
+ 
+
+ align:start position:0%
+relationship between X and Y is. And
+this linear thing is basically the
+
+ align:start position:0%
+this linear thing is basically the
+ 
+
+ align:start position:0%
+this linear thing is basically the
+simplest function we can think of.
+
+ align:start position:0%
+simplest function we can think of.
+ 
+
+ align:start position:0%
+simplest function we can think of.
+Arguably
+
+ align:start position:0%
+Arguably
+ 
+
+ align:start position:0%
+Arguably
+linear functions are the simplest
+
+ align:start position:0%
+linear functions are the simplest
+ 
+
+ align:start position:0%
+linear functions are the simplest
+functions that are not trivial.
+
+ align:start position:0%
+functions that are not trivial.
+ 
+
+ align:start position:0%
+functions that are not trivial.
+Otherwise, we would just say, well,
+
+ align:start position:0%
+Otherwise, we would just say, well,
+ 
+
+ align:start position:0%
+Otherwise, we would just say, well,
+let's just predict X Y to be a constant,
+
+ align:start position:0%
+let's just predict X Y to be a constant,
+ 
+
+ align:start position:0%
+let's just predict X Y to be a constant,
+meaning it does not depend on X. But if
+
+ align:start position:0%
+meaning it does not depend on X. But if
+ 
+
+ align:start position:0%
+meaning it does not depend on X. But if
+you wanted to depend on X, linear
+
+ align:start position:0%
+you wanted to depend on X, linear
+ 
+
+ align:start position:0%
+you wanted to depend on X, linear
+functions are basically as simple as it
+
+ align:start position:0%
+functions are basically as simple as it
+ 
+
+ align:start position:0%
+functions are basically as simple as it
+gets. Turns out, amazingly, this does
+
+ align:start position:0%
+gets. Turns out, amazingly, this does
+ 
+
+ align:start position:0%
+gets. Turns out, amazingly, this does
+the trick quite often. All right, so for
+
+ align:start position:0%
+the trick quite often. All right, so for
+ 
+
+ align:start position:0%
+the trick quite often. All right, so for
+example, if you look at economics, you
+
+ align:start position:0%
+example, if you look at economics, you
+ 
+
+ align:start position:0%
+example, if you look at economics, you
+might want to assume that the demand is
+
+ align:start position:0%
+might want to assume that the demand is
+ 
+
+ align:start position:0%
+might want to assume that the demand is
+a linear function of the price. All
+
+ align:start position:0%
+a linear function of the price. All
+ 
+
+ align:start position:0%
+a linear function of the price. All
+right, so if your price is zero, there's
+
+ align:start position:0%
+right, so if your price is zero, there's
+ 
+
+ align:start position:0%
+right, so if your price is zero, there's
+going to be a certain demand, and as the
+
+ align:start position:0%
+going to be a certain demand, and as the
+ 
+
+ align:start position:0%
+going to be a certain demand, and as the
+price increases, the demand is going to
+
+ align:start position:0%
+price increases, the demand is going to
+ 
+
+ align:start position:0%
+price increases, the demand is going to
+move. Do you think B is going to be
+
+ align:start position:0%
+move. Do you think B is going to be
+ 
+
+ align:start position:0%
+move. Do you think B is going to be
+positive or negative here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What?
+
+ align:start position:0%
+What?
+ 
+
+ align:start position:0%
+What?
+Typically, it's negative. Unless we're
+
+ align:start position:0%
+Typically, it's negative. Unless we're
+ 
+
+ align:start position:0%
+Typically, it's negative. Unless we're
+talking about maybe luxury goods. Uh
+
+ align:start position:0%
+talking about maybe luxury goods. Uh
+ 
+
+ align:start position:0%
+talking about maybe luxury goods. Uh
+where, you know, the more expensive the
+
+ align:start position:0%
+where, you know, the more expensive the
+ 
+
+ align:start position:0%
+where, you know, the more expensive the
+more people actually want it. Uh I mean,
+
+ align:start position:0%
+more people actually want it. Uh I mean,
+ 
+
+ align:start position:0%
+more people actually want it. Uh I mean,
+if we're talking about actual economic
+
+ align:start position:0%
+if we're talking about actual economic
+ 
+
+ align:start position:0%
+if we're talking about actual economic
+demand, it's probably uh definitely
+
+ align:start position:0%
+demand, it's probably uh definitely
+ 
+
+ align:start position:0%
+demand, it's probably uh definitely
+negative. All right. Uh it doesn't have
+
+ align:start position:0%
+negative. All right. Uh it doesn't have
+ 
+
+ align:start position:0%
+negative. All right. Uh it doesn't have
+to be, you know, clearly
+
+ align:start position:0%
+to be, you know, clearly
+ 
+
+ align:start position:0%
+to be, you know, clearly
+uh uh linear so that you can actually
+
+ align:start position:0%
+uh uh linear so that you can actually
+ 
+
+ align:start position:0%
+uh uh linear so that you can actually
+make it linear, transform it into some
+
+ align:start position:0%
+make it linear, transform it into some
+ 
+
+ align:start position:0%
+make it linear, transform it into some
+linear. So for for example you have this
+
+ align:start position:0%
+linear. So for for example you have this
+ 
+
+ align:start position:0%
+linear. So for for example you have this
+like multiplicative relationship right P
+
+ align:start position:0%
+like multiplicative relationship right P
+ 
+
+ align:start position:0%
+like multiplicative relationship right P
+uh you know PV equals NRT which is the
+
+ align:start position:0%
+uh you know PV equals NRT which is the
+ 
+
+ align:start position:0%
+uh you know PV equals NRT which is the
+IDS ga ideal gas law. uh if you want to
+
+ align:start position:0%
+IDS ga ideal gas law. uh if you want to
+ 
+
+ align:start position:0%
+IDS ga ideal gas law. uh if you want to
+actually write this relationship if you
+
+ align:start position:0%
+actually write this relationship if you
+ 
+
+ align:start position:0%
+actually write this relationship if you
+want to predict what the pressure is
+
+ align:start position:0%
+want to predict what the pressure is
+ 
+
+ align:start position:0%
+want to predict what the pressure is
+going to be as a function of the volume
+
+ align:start position:0%
+going to be as a function of the volume
+ 
+
+ align:start position:0%
+going to be as a function of the volume
+and the temperature
+
+ align:start position:0%
+and the temperature
+ 
+
+ align:start position:0%
+and the temperature
+uh and uh well let's assume that the uh
+
+ align:start position:0%
+uh and uh well let's assume that the uh
+ 
+
+ align:start position:0%
+uh and uh well let's assume that the uh
+so n is the avagadra constant and let's
+
+ align:start position:0%
+so n is the avagadra constant and let's
+ 
+
+ align:start position:0%
+so n is the avagadra constant and let's
+assume that the the radius is actually
+
+ align:start position:0%
+assume that the the radius is actually
+ 
+
+ align:start position:0%
+assume that the the radius is actually
+uh fixed then uh you have basically you
+
+ align:start position:0%
+uh fixed then uh you have basically you
+ 
+
+ align:start position:0%
+uh fixed then uh you have basically you
+take the log on each side right so you
+
+ align:start position:0%
+take the log on each side right so you
+ 
+
+ align:start position:0%
+take the log on each side right so you
+get pv equals nrt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what that means is that log PV is
+
+ align:start position:0%
+so what that means is that log PV is
+ 
+
+ align:start position:0%
+so what that means is that log PV is
+equal to log n RT.
+
+ align:start position:0%
+equal to log n RT.
+ 
+
+ align:start position:0%
+equal to log n RT.
+So that means that log P
+
+ align:start position:0%
+So that means that log P
+ 
+
+ align:start position:0%
+So that means that log P
+plus log V is equal to log
+
+ align:start position:0%
+plus log V is equal to log
+ 
+
+ align:start position:0%
+plus log V is equal to log
+N R
+
+ align:start position:0%
+N R
+ 
+
+ align:start position:0%
+N R
+plus log T.
+
+ align:start position:0%
+plus log T.
+ 
+
+ align:start position:0%
+plus log T.
+Okay. So this here we said that R is
+
+ align:start position:0%
+Okay. So this here we said that R is
+ 
+
+ align:start position:0%
+Okay. So this here we said that R is
+constant. So this is actually a
+
+ align:start position:0%
+constant. So this is actually a
+ 
+
+ align:start position:0%
+constant. So this is actually a
+constant. I'm going to call it A.
+
+ align:start position:0%
+constant. I'm going to call it A.
+ 
+
+ align:start position:0%
+constant. I'm going to call it A.
+And then that means that log P
+
+ align:start position:0%
+And then that means that log P
+ 
+
+ align:start position:0%
+And then that means that log P
+is equal to minus log B.
+
+ align:start position:0%
+is equal to minus log B.
+ 
+
+ align:start position:0%
+is equal to minus log B.
+Seriously uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that log p is equal to a
+
+ align:start position:0%
+that log p is equal to a
+ 
+
+ align:start position:0%
+that log p is equal to a
+uh minus log v
+
+ align:start position:0%
+uh minus log v
+ 
+
+ align:start position:0%
+uh minus log v
+plus log t.
+
+ align:start position:0%
+plus log t.
+ 
+
+ align:start position:0%
+plus log t.
+Okay. And so in particular if I write b
+
+ align:start position:0%
+Okay. And so in particular if I write b
+ 
+
+ align:start position:0%
+Okay. And so in particular if I write b
+uh equal to -1 and c equal to + one this
+
+ align:start position:0%
+uh equal to -1 and c equal to + one this
+ 
+
+ align:start position:0%
+uh equal to -1 and c equal to + one this
+gives me the formula that I have here.
+
+ align:start position:0%
+gives me the formula that I have here.
+ 
+
+ align:start position:0%
+gives me the formula that I have here.
+Now again it might be the case that you
+
+ align:start position:0%
+Now again it might be the case that you
+ 
+
+ align:start position:0%
+Now again it might be the case that you
+know this is the ideal gas law. So in
+
+ align:start position:0%
+know this is the ideal gas law. So in
+ 
+
+ align:start position:0%
+know this is the ideal gas law. So in
+practice if I start recording pressure
+
+ align:start position:0%
+practice if I start recording pressure
+ 
+
+ align:start position:0%
+practice if I start recording pressure
+and temperature and volume those things
+
+ align:start position:0%
+and temperature and volume those things
+ 
+
+ align:start position:0%
+and temperature and volume those things
+I might make measurement errors it might
+
+ align:start position:0%
+I might make measurement errors it might
+ 
+
+ align:start position:0%
+I might make measurement errors it might
+be slightly different conditions in such
+
+ align:start position:0%
+be slightly different conditions in such
+ 
+
+ align:start position:0%
+be slightly different conditions in such
+a way that I'm not going to get exactly
+
+ align:start position:0%
+a way that I'm not going to get exactly
+ 
+
+ align:start position:0%
+a way that I'm not going to get exactly
+those and I'm just going to put this
+
+ align:start position:0%
+those and I'm just going to put this
+ 
+
+ align:start position:0%
+those and I'm just going to put this
+little twiddle to account for the fact
+
+ align:start position:0%
+little twiddle to account for the fact
+ 
+
+ align:start position:0%
+little twiddle to account for the fact
+that the points that I'm going to be
+
+ align:start position:0%
+that the points that I'm going to be
+ 
+
+ align:start position:0%
+that the points that I'm going to be
+recording for log pressure log volume
+
+ align:start position:0%
+recording for log pressure log volume
+ 
+
+ align:start position:0%
+recording for log pressure log volume
+and log temperature are not going to be
+
+ align:start position:0%
+and log temperature are not going to be
+ 
+
+ align:start position:0%
+and log temperature are not going to be
+exactly on one line. Okay, they're going
+
+ align:start position:0%
+exactly on one line. Okay, they're going
+ 
+
+ align:start position:0%
+exactly on one line. Okay, they're going
+to be close. Actually, in those physics
+
+ align:start position:0%
+to be close. Actually, in those physics
+ 
+
+ align:start position:0%
+to be close. Actually, in those physics
+experiments, usually they're very close.
+
+ align:start position:0%
+experiments, usually they're very close.
+ 
+
+ align:start position:0%
+experiments, usually they're very close.
+It's actually because the conditions are
+
+ align:start position:0%
+It's actually because the conditions are
+ 
+
+ align:start position:0%
+It's actually because the conditions are
+controlled in under lab experiments. So,
+
+ align:start position:0%
+controlled in under lab experiments. So,
+ 
+
+ align:start position:0%
+controlled in under lab experiments. So,
+it means that the noise is very small.
+
+ align:start position:0%
+it means that the noise is very small.
+ 
+
+ align:start position:0%
+it means that the noise is very small.
+And uh but for other cases like demand
+
+ align:start position:0%
+And uh but for other cases like demand
+ 
+
+ align:start position:0%
+And uh but for other cases like demand
+and price, this is not a law of physics.
+
+ align:start position:0%
+and price, this is not a law of physics.
+ 
+
+ align:start position:0%
+and price, this is not a law of physics.
+And so, this might change. Uh even the
+
+ align:start position:0%
+And so, this might change. Uh even the
+ 
+
+ align:start position:0%
+And so, this might change. Uh even the
+linear structure is probably not clear,
+
+ align:start position:0%
+linear structure is probably not clear,
+ 
+
+ align:start position:0%
+linear structure is probably not clear,
+right? At some point, there's probably
+
+ align:start position:0%
+right? At some point, there's probably
+ 
+
+ align:start position:0%
+right? At some point, there's probably
+going to be some weird curvature
+
+ align:start position:0%
+going to be some weird curvature
+ 
+
+ align:start position:0%
+going to be some weird curvature
+happening. All right. So this slide is
+
+ align:start position:0%
+happening. All right. So this slide is
+ 
+
+ align:start position:0%
+happening. All right. So this slide is
+just to tell you maybe you don't have
+
+ align:start position:0%
+just to tell you maybe you don't have
+ 
+
+ align:start position:0%
+just to tell you maybe you don't have
+obviously a linear relationship but
+
+ align:start position:0%
+obviously a linear relationship but
+ 
+
+ align:start position:0%
+obviously a linear relationship but
+maybe you do if you start taking logs
+
+ align:start position:0%
+maybe you do if you start taking logs
+ 
+
+ align:start position:0%
+maybe you do if you start taking logs
+expect uh exponentials squares you can
+
+ align:start position:0%
+expect uh exponentials squares you can
+ 
+
+ align:start position:0%
+expect uh exponentials squares you can
+sometimes take the product of two
+
+ align:start position:0%
+sometimes take the product of two
+ 
+
+ align:start position:0%
+sometimes take the product of two
+variables things like this right so this
+
+ align:start position:0%
+variables things like this right so this
+ 
+
+ align:start position:0%
+variables things like this right so this
+is variable transformation and it's
+
+ align:start position:0%
+is variable transformation and it's
+ 
+
+ align:start position:0%
+is variable transformation and it's
+mostly domain specific so we're not
+
+ align:start position:0%
+mostly domain specific so we're not
+ 
+
+ align:start position:0%
+mostly domain specific so we're not
+going to go into much details of this
+
+ align:start position:0%
+going to go into much details of this
+ 
+
+ align:start position:0%
+going to go into much details of this
+any questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, um, now I'm going to be
+
+ align:start position:0%
+All right. So, um, now I'm going to be
+ 
+
+ align:start position:0%
+All right. So, um, now I'm going to be
+given, uh, um, so if we start thinking a
+
+ align:start position:0%
+given, uh, um, so if we start thinking a
+ 
+
+ align:start position:0%
+given, uh, um, so if we start thinking a
+little more about what those
+
+ align:start position:0%
+little more about what those
+ 
+
+ align:start position:0%
+little more about what those
+coefficients should be. Well, remember,
+
+ align:start position:0%
+coefficients should be. Well, remember,
+ 
+
+ align:start position:0%
+coefficients should be. Well, remember,
+so just everybody's clear why I don't
+
+ align:start position:0%
+so just everybody's clear why I don't
+ 
+
+ align:start position:0%
+so just everybody's clear why I don't
+put the little i here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+right? I don't put the little i because
+
+ align:start position:0%
+right? I don't put the little i because
+ 
+
+ align:start position:0%
+right? I don't put the little i because
+I'm just talking about a generic x and a
+
+ align:start position:0%
+I'm just talking about a generic x and a
+ 
+
+ align:start position:0%
+I'm just talking about a generic x and a
+generic y, but the observations are x1,
+
+ align:start position:0%
+generic y, but the observations are x1,
+ 
+
+ align:start position:0%
+generic y, but the observations are x1,
+y1, right? So typically on the
+
+ align:start position:0%
+y1, right? So typically on the
+ 
+
+ align:start position:0%
+y1, right? So typically on the
+blackboard I'm often going to write only
+
+ align:start position:0%
+blackboard I'm often going to write only
+ 
+
+ align:start position:0%
+blackboard I'm often going to write only
+XY
+
+ align:start position:0%
+XY
+ 
+
+ align:start position:0%
+XY
+but the data really is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X1 Y1
+
+ align:start position:0%
+X1 Y1
+ 
+
+ align:start position:0%
+X1 Y1
+all the way to XN YN. Right? So those
+
+ align:start position:0%
+all the way to XN YN. Right? So those
+ 
+
+ align:start position:0%
+all the way to XN YN. Right? So those
+are this points in this two-dimensional
+
+ align:start position:0%
+are this points in this two-dimensional
+ 
+
+ align:start position:0%
+are this points in this two-dimensional
+plot. And uh but I think of those as
+
+ align:start position:0%
+plot. And uh but I think of those as
+ 
+
+ align:start position:0%
+plot. And uh but I think of those as
+being copies independent copies of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the pair XY. Okay,
+
+ align:start position:0%
+of the pair XY. Okay,
+ 
+
+ align:start position:0%
+of the pair XY. Okay,
+they have to have the the to contain the
+
+ align:start position:0%
+they have to have the the to contain the
+ 
+
+ align:start position:0%
+they have to have the the to contain the
+relationship. And so when I talk about
+
+ align:start position:0%
+relationship. And so when I talk about
+ 
+
+ align:start position:0%
+relationship. And so when I talk about
+distribution of those random variables,
+
+ align:start position:0%
+distribution of those random variables,
+ 
+
+ align:start position:0%
+distribution of those random variables,
+I can only I talk about the distribution
+
+ align:start position:0%
+I can only I talk about the distribution
+ 
+
+ align:start position:0%
+I can only I talk about the distribution
+of XY and that's the same. Right? So the
+
+ align:start position:0%
+of XY and that's the same. Right? So the
+ 
+
+ align:start position:0%
+of XY and that's the same. Right? So the
+first thing you might want to ask is,
+
+ align:start position:0%
+first thing you might want to ask is,
+ 
+
+ align:start position:0%
+first thing you might want to ask is,
+well, if I have an infinite amount of
+
+ align:start position:0%
+well, if I have an infinite amount of
+ 
+
+ align:start position:0%
+well, if I have an infinite amount of
+data,
+
+ align:start position:0%
+data,
+ 
+
+ align:start position:0%
+data,
+what do I what what can I hope to get
+
+ align:start position:0%
+what do I what what can I hope to get
+ 
+
+ align:start position:0%
+what do I what what can I hope to get
+for A and B, right? If my sample size
+
+ align:start position:0%
+for A and B, right? If my sample size
+ 
+
+ align:start position:0%
+for A and B, right? If my sample size
+goes to infinity, then I should actually
+
+ align:start position:0%
+goes to infinity, then I should actually
+ 
+
+ align:start position:0%
+goes to infinity, then I should actually
+know exactly what the distribution of XY
+
+ align:start position:0%
+know exactly what the distribution of XY
+ 
+
+ align:start position:0%
+know exactly what the distribution of XY
+is. And so there should be an A and a B
+
+ align:start position:0%
+is. And so there should be an A and a B
+ 
+
+ align:start position:0%
+is. And so there should be an A and a B
+that captures this linear relationship
+
+ align:start position:0%
+that captures this linear relationship
+ 
+
+ align:start position:0%
+that captures this linear relationship
+between Y and X. Okay? And so in
+
+ align:start position:0%
+between Y and X. Okay? And so in
+ 
+
+ align:start position:0%
+between Y and X. Okay? And so in
+particular, we're going to try to ask
+
+ align:start position:0%
+particular, we're going to try to ask
+ 
+
+ align:start position:0%
+particular, we're going to try to ask
+the population or theoretic values of A
+
+ align:start position:0%
+the population or theoretic values of A
+ 
+
+ align:start position:0%
+the population or theoretic values of A
+and B. And you can see that you can
+
+ align:start position:0%
+and B. And you can see that you can
+ 
+
+ align:start position:0%
+and B. And you can see that you can
+actually compute them explicitly. So
+
+ align:start position:0%
+actually compute them explicitly. So
+ 
+
+ align:start position:0%
+actually compute them explicitly. So
+let's just try to find how. So as I
+
+ align:start position:0%
+let's just try to find how. So as I
+ 
+
+ align:start position:0%
+let's just try to find how. So as I
+said, we have a bunch of points on this
+
+ align:start position:0%
+said, we have a bunch of points on this
+ 
+
+ align:start position:0%
+said, we have a bunch of points on this
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+close to a line.
+
+ align:start position:0%
+close to a line.
+ 
+
+ align:start position:0%
+close to a line.
+And I'm trying to find the best fit.
+
+ align:start position:0%
+And I'm trying to find the best fit.
+ 
+
+ align:start position:0%
+And I'm trying to find the best fit.
+All right? So this guy is not a good
+
+ align:start position:0%
+All right? So this guy is not a good
+ 
+
+ align:start position:0%
+All right? So this guy is not a good
+fit. This guy is not a good fit. And we
+
+ align:start position:0%
+fit. This guy is not a good fit. And we
+ 
+
+ align:start position:0%
+fit. This guy is not a good fit. And we
+know that this guy is a good fit
+
+ align:start position:0%
+know that this guy is a good fit
+ 
+
+ align:start position:0%
+know that this guy is a good fit
+somehow. So we need to mathematically
+
+ align:start position:0%
+somehow. So we need to mathematically
+ 
+
+ align:start position:0%
+somehow. So we need to mathematically
+formulate the fact that this line here
+
+ align:start position:0%
+formulate the fact that this line here
+ 
+
+ align:start position:0%
+formulate the fact that this line here
+is better than this line here or better
+
+ align:start position:0%
+is better than this line here or better
+ 
+
+ align:start position:0%
+is better than this line here or better
+than this line here. So what we're
+
+ align:start position:0%
+than this line here. So what we're
+ 
+
+ align:start position:0%
+than this line here. So what we're
+trying to do is to create a function
+
+ align:start position:0%
+trying to do is to create a function
+ 
+
+ align:start position:0%
+trying to do is to create a function
+that has values that are smaller for
+
+ align:start position:0%
+that has values that are smaller for
+ 
+
+ align:start position:0%
+that has values that are smaller for
+this curve and larger for these two
+
+ align:start position:0%
+this curve and larger for these two
+ 
+
+ align:start position:0%
+this curve and larger for these two
+curves. And the way we do it is by
+
+ align:start position:0%
+curves. And the way we do it is by
+ 
+
+ align:start position:0%
+curves. And the way we do it is by
+measuring the fit. And the fit is
+
+ align:start position:0%
+measuring the fit. And the fit is
+ 
+
+ align:start position:0%
+measuring the fit. And the fit is
+essentially the aggregate distance of
+
+ align:start position:0%
+essentially the aggregate distance of
+ 
+
+ align:start position:0%
+essentially the aggregate distance of
+all the points to the curve. All right?
+
+ align:start position:0%
+all the points to the curve. All right?
+ 
+
+ align:start position:0%
+all the points to the curve. All right?
+And there's many ways I can measure the
+
+ align:start position:0%
+And there's many ways I can measure the
+ 
+
+ align:start position:0%
+And there's many ways I can measure the
+distance to a curve, right? So if I want
+
+ align:start position:0%
+distance to a curve, right? So if I want
+ 
+
+ align:start position:0%
+distance to a curve, right? So if I want
+to find, so let's just open a
+
+ align:start position:0%
+to find, so let's just open a
+ 
+
+ align:start position:0%
+to find, so let's just open a
+parenthesis. If I have a point here, so
+
+ align:start position:0%
+parenthesis. If I have a point here, so
+ 
+
+ align:start position:0%
+parenthesis. If I have a point here, so
+we're going to do it for one point at a
+
+ align:start position:0%
+we're going to do it for one point at a
+ 
+
+ align:start position:0%
+we're going to do it for one point at a
+time. So if I have a point, there's many
+
+ align:start position:0%
+time. So if I have a point, there's many
+ 
+
+ align:start position:0%
+time. So if I have a point, there's many
+ways I can measure it distance to the
+
+ align:start position:0%
+ways I can measure it distance to the
+ 
+
+ align:start position:0%
+ways I can measure it distance to the
+curve, right? I can measure it like
+
+ align:start position:0%
+curve, right? I can measure it like
+ 
+
+ align:start position:0%
+curve, right? I can measure it like
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+That is one distance to the curve. I can
+
+ align:start position:0%
+That is one distance to the curve. I can
+ 
+
+ align:start position:0%
+That is one distance to the curve. I can
+measure it like that by having a right
+
+ align:start position:0%
+measure it like that by having a right
+ 
+
+ align:start position:0%
+measure it like that by having a right
+angle here. That is one distance to the
+
+ align:start position:0%
+angle here. That is one distance to the
+ 
+
+ align:start position:0%
+angle here. That is one distance to the
+curve. Or I can measure it like that.
+
+ align:start position:0%
+curve. Or I can measure it like that.
+ 
+
+ align:start position:0%
+curve. Or I can measure it like that.
+that is another distance to the curve,
+
+ align:start position:0%
+that is another distance to the curve,
+ 
+
+ align:start position:0%
+that is another distance to the curve,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+There's many ways I can go for it. It
+
+ align:start position:0%
+There's many ways I can go for it. It
+ 
+
+ align:start position:0%
+There's many ways I can go for it. It
+turns out that one is actually going to
+
+ align:start position:0%
+turns out that one is actually going to
+ 
+
+ align:start position:0%
+turns out that one is actually going to
+be fairly convenient for us and that's
+
+ align:start position:0%
+be fairly convenient for us and that's
+ 
+
+ align:start position:0%
+be fairly convenient for us and that's
+the one that says let's look at the
+
+ align:start position:0%
+the one that says let's look at the
+ 
+
+ align:start position:0%
+the one that says let's look at the
+square of the value of x on the curve.
+
+ align:start position:0%
+square of the value of x on the curve.
+ 
+
+ align:start position:0%
+square of the value of x on the curve.
+Right? So if this is the curve
+
+ align:start position:0%
+Right? So if this is the curve
+ 
+
+ align:start position:0%
+Right? So if this is the curve
+y is equal to a + bx.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I'm going to think of this point as
+
+ align:start position:0%
+Now I'm going to think of this point as
+ 
+
+ align:start position:0%
+Now I'm going to think of this point as
+a random point capital X capital Y.
+
+ align:start position:0%
+a random point capital X capital Y.
+ 
+
+ align:start position:0%
+a random point capital X capital Y.
+Okay. And so that means that it's going
+
+ align:start position:0%
+Okay. And so that means that it's going
+ 
+
+ align:start position:0%
+Okay. And so that means that it's going
+to be instant. It's going to be X1 X Y1
+
+ align:start position:0%
+to be instant. It's going to be X1 X Y1
+ 
+
+ align:start position:0%
+to be instant. It's going to be X1 X Y1
+or X2 Y2 etc. Now I want to measure the
+
+ align:start position:0%
+or X2 Y2 etc. Now I want to measure the
+ 
+
+ align:start position:0%
+or X2 Y2 etc. Now I want to measure the
+distance. Can somebody tell me which of
+
+ align:start position:0%
+distance. Can somebody tell me which of
+ 
+
+ align:start position:0%
+distance. Can somebody tell me which of
+the three the first one the second one
+
+ align:start position:0%
+the three the first one the second one
+ 
+
+ align:start position:0%
+the three the first one the second one
+or the third one this formula
+
+ align:start position:0%
+or the third one this formula
+ 
+
+ align:start position:0%
+or the third one this formula
+expectation of y - a minus bx^2 is is is
+
+ align:start position:0%
+expectation of y - a minus bx^2 is is is
+ 
+
+ align:start position:0%
+expectation of y - a minus bx^2 is is is
+which of the three is it representing?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The second one where I have the right
+
+ align:start position:0%
+The second one where I have the right
+ 
+
+ align:start position:0%
+The second one where I have the right
+angle.
+
+ align:start position:0%
+angle.
+ 
+
+ align:start position:0%
+angle.
+Okay. Everybody agrees with this.
+
+ align:start position:0%
+Okay. Everybody agrees with this.
+ 
+
+ align:start position:0%
+Okay. Everybody agrees with this.
+Anybody wants to vote for something
+
+ align:start position:0%
+Anybody wants to vote for something
+ 
+
+ align:start position:0%
+Anybody wants to vote for something
+else? Yeah. The third one. Who?
+
+ align:start position:0%
+else? Yeah. The third one. Who?
+ 
+
+ align:start position:0%
+else? Yeah. The third one. Who?
+Everybody agrees with the third one. So,
+
+ align:start position:0%
+Everybody agrees with the third one. So,
+ 
+
+ align:start position:0%
+Everybody agrees with the third one. So,
+by default, everybody's on the first
+
+ align:start position:0%
+by default, everybody's on the first
+ 
+
+ align:start position:0%
+by default, everybody's on the first
+one. Yeah.
+
+ align:start position:0%
+one. Yeah.
+ 
+
+ align:start position:0%
+one. Yeah.
+Yeah. It is the vertical distance
+
+ align:start position:0%
+Yeah. It is the vertical distance
+ 
+
+ align:start position:0%
+Yeah. It is the vertical distance
+actually. Right. So, and the reason is
+
+ align:start position:0%
+actually. Right. So, and the reason is
+ 
+
+ align:start position:0%
+actually. Right. So, and the reason is
+if it was the one with the straight
+
+ align:start position:0%
+if it was the one with the straight
+ 
+
+ align:start position:0%
+if it was the one with the straight
+angle with the right angle, it would
+
+ align:start position:0%
+angle with the right angle, it would
+ 
+
+ align:start position:0%
+angle with the right angle, it would
+actually be very complicated
+
+ align:start position:0%
+actually be very complicated
+ 
+
+ align:start position:0%
+actually be very complicated
+mathematical formula. So let's just see
+
+ align:start position:0%
+mathematical formula. So let's just see
+ 
+
+ align:start position:0%
+mathematical formula. So let's just see
+why, right? So and by y I mean y okay so
+
+ align:start position:0%
+why, right? So and by y I mean y okay so
+ 
+
+ align:start position:0%
+why, right? So and by y I mean y okay so
+uh this is this means that this is my x
+
+ align:start position:0%
+uh this is this means that this is my x
+ 
+
+ align:start position:0%
+uh this is this means that this is my x
+okay and this is my y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that means that this point is
+
+ align:start position:0%
+right so that means that this point is
+ 
+
+ align:start position:0%
+right so that means that this point is
+xy
+
+ align:start position:0%
+xy
+ 
+
+ align:start position:0%
+xy
+so what I'm measuring is the difference
+
+ align:start position:0%
+so what I'm measuring is the difference
+ 
+
+ align:start position:0%
+so what I'm measuring is the difference
+between y
+
+ align:start position:0%
+between y
+ 
+
+ align:start position:0%
+between y
+minus a + b * x right
+
+ align:start position:0%
+minus a + b * x right
+ 
+
+ align:start position:0%
+minus a + b * x right
+this is the thing I'm going to take the
+
+ align:start position:0%
+this is the thing I'm going to take the
+ 
+
+ align:start position:0%
+this is the thing I'm going to take the
+expectation of the square and then the
+
+ align:start position:0%
+expectation of the square and then the
+ 
+
+ align:start position:0%
+expectation of the square and then the
+expect So a + b * x if this is this line
+
+ align:start position:0%
+expect So a + b * x if this is this line
+ 
+
+ align:start position:0%
+expect So a + b * x if this is this line
+this is this point. So that's this value
+
+ align:start position:0%
+this is this point. So that's this value
+ 
+
+ align:start position:0%
+this is this point. So that's this value
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+This value here is a
+
+ align:start position:0%
+This value here is a
+ 
+
+ align:start position:0%
+This value here is a
+plus bx. Right?
+
+ align:start position:0%
+plus bx. Right?
+ 
+
+ align:start position:0%
+plus bx. Right?
+So what I'm really measuring is the
+
+ align:start position:0%
+So what I'm really measuring is the
+ 
+
+ align:start position:0%
+So what I'm really measuring is the
+difference between y and m plus bx which
+
+ align:start position:0%
+difference between y and m plus bx which
+ 
+
+ align:start position:0%
+difference between y and m plus bx which
+is this distance here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And since I like things like Pythagoras
+
+ align:start position:0%
+And since I like things like Pythagoras
+ 
+
+ align:start position:0%
+And since I like things like Pythagoras
+theorem, uh I'm actually going to put a
+
+ align:start position:0%
+theorem, uh I'm actually going to put a
+ 
+
+ align:start position:0%
+theorem, uh I'm actually going to put a
+square here before I take the
+
+ align:start position:0%
+square here before I take the
+ 
+
+ align:start position:0%
+square here before I take the
+expectation.
+
+ align:start position:0%
+expectation.
+ 
+
+ align:start position:0%
+expectation.
+Okay, so now this is a random variable.
+
+ align:start position:0%
+Okay, so now this is a random variable.
+ 
+
+ align:start position:0%
+Okay, so now this is a random variable.
+This is this random variable. And so I
+
+ align:start position:0%
+This is this random variable. And so I
+ 
+
+ align:start position:0%
+This is this random variable. And so I
+want a number. So I'm going to turn it
+
+ align:start position:0%
+want a number. So I'm going to turn it
+ 
+
+ align:start position:0%
+want a number. So I'm going to turn it
+into a deterministic number. And the way
+
+ align:start position:0%
+into a deterministic number. And the way
+ 
+
+ align:start position:0%
+into a deterministic number. And the way
+I do this is by taking expectation.
+
+ align:start position:0%
+I do this is by taking expectation.
+ 
+
+ align:start position:0%
+I do this is by taking expectation.
+Okay? And doing expectation. If you
+
+ align:start position:0%
+Okay? And doing expectation. If you
+ 
+
+ align:start position:0%
+Okay? And doing expectation. If you
+think expectation should be close to
+
+ align:start position:0%
+think expectation should be close to
+ 
+
+ align:start position:0%
+think expectation should be close to
+average, this is the same thing as
+
+ align:start position:0%
+average, this is the same thing as
+ 
+
+ align:start position:0%
+average, this is the same thing as
+saying I want that in average the y's
+
+ align:start position:0%
+saying I want that in average the y's
+ 
+
+ align:start position:0%
+saying I want that in average the y's
+are close to the a plus bx, right? So
+
+ align:start position:0%
+are close to the a plus bx, right? So
+ 
+
+ align:start position:0%
+are close to the a plus bx, right? So
+we're doing it in expectation, but
+
+ align:start position:0%
+we're doing it in expectation, but
+ 
+
+ align:start position:0%
+we're doing it in expectation, but
+that's going to translate into doing it
+
+ align:start position:0%
+that's going to translate into doing it
+ 
+
+ align:start position:0%
+that's going to translate into doing it
+in average for all the points. All
+
+ align:start position:0%
+in average for all the points. All
+ 
+
+ align:start position:0%
+in average for all the points. All
+right. So this is the thing I want to
+
+ align:start position:0%
+right. So this is the thing I want to
+ 
+
+ align:start position:0%
+right. So this is the thing I want to
+measure. So that's this vertical
+
+ align:start position:0%
+measure. So that's this vertical
+ 
+
+ align:start position:0%
+measure. So that's this vertical
+distance. Yeah.
+
+ align:start position:0%
+distance. Yeah.
+ 
+
+ align:start position:0%
+distance. Yeah.
+Oh, again. Okay. Sorry. I'm just uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is my fault actually. Um
+
+ align:start position:0%
+this is my fault actually. Um
+ 
+
+ align:start position:0%
+this is my fault actually. Um
+maybe we should close those shades.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. I cannot I cannot do just uh one
+
+ align:start position:0%
+Okay. I cannot I cannot do just uh one
+ 
+
+ align:start position:0%
+Okay. I cannot I cannot do just uh one
+at a time. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+the uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So now that I do those uh
+
+ align:start position:0%
+All right. So now that I do those uh
+ 
+
+ align:start position:0%
+All right. So now that I do those uh
+vertical distances, I can I can ask well
+
+ align:start position:0%
+vertical distances, I can I can ask well
+ 
+
+ align:start position:0%
+vertical distances, I can I can ask well
+now I have this function, right? to have
+
+ align:start position:0%
+now I have this function, right? to have
+ 
+
+ align:start position:0%
+now I have this function, right? to have
+a function that takes two parameters a
+
+ align:start position:0%
+a function that takes two parameters a
+ 
+
+ align:start position:0%
+a function that takes two parameters a
+and b maps it to the expectation of y -
+
+ align:start position:0%
+and b maps it to the expectation of y -
+ 
+
+ align:start position:0%
+and b maps it to the expectation of y -
+a + b x^2
+
+ align:start position:0%
+a + b x^2
+ 
+
+ align:start position:0%
+a + b x^2
+sorry the square is here and I can ask
+
+ align:start position:0%
+sorry the square is here and I can ask
+ 
+
+ align:start position:0%
+sorry the square is here and I can ask
+well this is a function that measures
+
+ align:start position:0%
+well this is a function that measures
+ 
+
+ align:start position:0%
+well this is a function that measures
+the fit of the parameters a and b right
+
+ align:start position:0%
+the fit of the parameters a and b right
+ 
+
+ align:start position:0%
+the fit of the parameters a and b right
+this function should be small the value
+
+ align:start position:0%
+this function should be small the value
+ 
+
+ align:start position:0%
+this function should be small the value
+of this function here
+
+ align:start position:0%
+of this function here
+ 
+
+ align:start position:0%
+of this function here
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+of a and E
+
+ align:start position:0%
+of a and E
+ 
+
+ align:start position:0%
+of a and E
+that measures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um point
+
+ align:start position:0%
+um point
+ 
+
+ align:start position:0%
+um point
+xy
+
+ align:start position:0%
+xy
+ 
+
+ align:start position:0%
+xy
+is to the line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a + b * x. Well, y is equal a + b * x.
+
+ align:start position:0%
+a + b * x. Well, y is equal a + b * x.
+ 
+
+ align:start position:0%
+a + b * x. Well, y is equal a + b * x.
+uh in expectation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, agreed? This is what we we just
+
+ align:start position:0%
+Okay, agreed? This is what we we just
+ 
+
+ align:start position:0%
+Okay, agreed? This is what we we just
+said. And you can think if again if
+
+ align:start position:0%
+said. And you can think if again if
+ 
+
+ align:start position:0%
+said. And you can think if again if
+you're not comfortable with the reason
+
+ align:start position:0%
+you're not comfortable with the reason
+ 
+
+ align:start position:0%
+you're not comfortable with the reason
+why to expectations, just think about
+
+ align:start position:0%
+why to expectations, just think about
+ 
+
+ align:start position:0%
+why to expectations, just think about
+having data points and taking the
+
+ align:start position:0%
+having data points and taking the
+ 
+
+ align:start position:0%
+having data points and taking the
+average value for this guy. So it's
+
+ align:start position:0%
+average value for this guy. So it's
+ 
+
+ align:start position:0%
+average value for this guy. So it's
+basically an aggregate distance of the
+
+ align:start position:0%
+basically an aggregate distance of the
+ 
+
+ align:start position:0%
+basically an aggregate distance of the
+points uh to their uh to the uh the the
+
+ align:start position:0%
+points uh to their uh to the uh the the
+ 
+
+ align:start position:0%
+points uh to their uh to the uh the the
+line. Okay, everybody agrees this is a
+
+ align:start position:0%
+line. Okay, everybody agrees this is a
+ 
+
+ align:start position:0%
+line. Okay, everybody agrees this is a
+legitimate measure. If all my points
+
+ align:start position:0%
+legitimate measure. If all my points
+ 
+
+ align:start position:0%
+legitimate measure. If all my points
+were on the line, if my distribution, if
+
+ align:start position:0%
+were on the line, if my distribution, if
+ 
+
+ align:start position:0%
+were on the line, if my distribution, if
+y was actually equal to a plus bx for
+
+ align:start position:0%
+y was actually equal to a plus bx for
+ 
+
+ align:start position:0%
+y was actually equal to a plus bx for
+some a and b, then this function would
+
+ align:start position:0%
+some a and b, then this function would
+ 
+
+ align:start position:0%
+some a and b, then this function would
+be equal to zero for the correct a and
+
+ align:start position:0%
+be equal to zero for the correct a and
+ 
+
+ align:start position:0%
+be equal to zero for the correct a and
+b, right?
+
+ align:start position:0%
+b, right?
+ 
+
+ align:start position:0%
+b, right?
+If they're far, well, it's going to
+
+ align:start position:0%
+If they're far, well, it's going to
+ 
+
+ align:start position:0%
+If they're far, well, it's going to
+depend on how much noise I'm getting.
+
+ align:start position:0%
+depend on how much noise I'm getting.
+ 
+
+ align:start position:0%
+depend on how much noise I'm getting.
+But it's still going to be minimized for
+
+ align:start position:0%
+But it's still going to be minimized for
+ 
+
+ align:start position:0%
+But it's still going to be minimized for
+the best one. So, let's minimize this
+
+ align:start position:0%
+the best one. So, let's minimize this
+ 
+
+ align:start position:0%
+the best one. So, let's minimize this
+thing.
+
+ align:start position:0%
+thing.
+ 
+
+ align:start position:0%
+thing.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+here I don't make any uh again sorry uh
+
+ align:start position:0%
+here I don't make any uh again sorry uh
+ 
+
+ align:start position:0%
+here I don't make any uh again sorry uh
+I don't make any assumption on um on uh
+
+ align:start position:0%
+I don't make any assumption on um on uh
+ 
+
+ align:start position:0%
+I don't make any assumption on um on uh
+uh the distribution of x or y here I
+
+ align:start position:0%
+uh the distribution of x or y here I
+ 
+
+ align:start position:0%
+uh the distribution of x or y here I
+assume somehow that the variance of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not equal to zero. Can somebody tell
+
+ align:start position:0%
+is not equal to zero. Can somebody tell
+ 
+
+ align:start position:0%
+is not equal to zero. Can somebody tell
+me why? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No, here I've actually written the
+
+ align:start position:0%
+No, here I've actually written the
+ 
+
+ align:start position:0%
+No, here I've actually written the
+expectation of the square.
+
+ align:start position:0%
+expectation of the square.
+ 
+
+ align:start position:0%
+expectation of the square.
+If I wanted to write the square of the
+
+ align:start position:0%
+If I wanted to write the square of the
+ 
+
+ align:start position:0%
+If I wanted to write the square of the
+expectation, I would just do this.
+
+ align:start position:0%
+expectation, I would just do this.
+ 
+
+ align:start position:0%
+expectation, I would just do this.
+So, so let's just make it clear,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Do you want me to put an extra
+
+ align:start position:0%
+right? Do you want me to put an extra
+ 
+
+ align:start position:0%
+right? Do you want me to put an extra
+set of parenthesis? That's what you want
+
+ align:start position:0%
+set of parenthesis? That's what you want
+ 
+
+ align:start position:0%
+set of parenthesis? That's what you want
+me to do.
+
+ align:start position:0%
+me to do.
+ 
+
+ align:start position:0%
+me to do.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. That's the one that makes sense.
+
+ align:start position:0%
+Okay. That's the one that makes sense.
+ 
+
+ align:start position:0%
+Okay. That's the one that makes sense.
+So, the square of the expectation.
+
+ align:start position:0%
+So, the square of the expectation.
+ 
+
+ align:start position:0%
+So, the square of the expectation.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+The expectation of the square. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Dyslexia. All right. Uh, any
+
+ align:start position:0%
+Yeah. Dyslexia. All right. Uh, any
+ 
+
+ align:start position:0%
+Yeah. Dyslexia. All right. Uh, any
+question?
+
+ align:start position:0%
+question?
+ 
+
+ align:start position:0%
+question?
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Does this assume that the error is
+
+ align:start position:0%
+Does this assume that the error is
+ 
+
+ align:start position:0%
+Does this assume that the error is
+Gaussian?
+
+ align:start position:0%
+Gaussian?
+ 
+
+ align:start position:0%
+Gaussian?
+No.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean in the sense that like if we knew
+
+ align:start position:0%
+I mean in the sense that like if we knew
+ 
+
+ align:start position:0%
+I mean in the sense that like if we knew
+that the error was like
+
+ align:start position:0%
+that the error was like
+ 
+
+ align:start position:0%
+that the error was like
+follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to minimize the
+
+ align:start position:0%
+we want to minimize the
+ 
+
+ align:start position:0%
+we want to minimize the
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know the answer to your question
+
+ align:start position:0%
+so you know the answer to your question
+ 
+
+ align:start position:0%
+so you know the answer to your question
+so I just want you to use the words that
+
+ align:start position:0%
+so I just want you to use the words that
+ 
+
+ align:start position:0%
+so I just want you to use the words that
+uh right so why would you want to use
+
+ align:start position:0%
+uh right so why would you want to use
+ 
+
+ align:start position:0%
+uh right so why would you want to use
+the fourth power
+
+ align:start position:0%
+the fourth power
+ 
+
+ align:start position:0%
+the fourth power
+because like we want more
+
+ align:start position:0%
+because like we want more
+ 
+
+ align:start position:0%
+because like we want more
+expectations
+
+ align:start position:0%
+expectations
+ 
+
+ align:start position:0%
+expectations
+to be very rare
+
+ align:start position:0%
+to be very rare
+ 
+
+ align:start position:0%
+to be very rare
+or more rare than
+
+ align:start position:0%
+or more rare than
+ 
+
+ align:start position:0%
+or more rare than
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+that would be the maximum likelihood
+
+ align:start position:0%
+that would be the maximum likelihood
+ 
+
+ align:start position:0%
+that would be the maximum likelihood
+estimator that you're describing to me
+
+ align:start position:0%
+estimator that you're describing to me
+ 
+
+ align:start position:0%
+estimator that you're describing to me
+right I can actually write the
+
+ align:start position:0%
+right I can actually write the
+ 
+
+ align:start position:0%
+right I can actually write the
+likelihood of a pair of numbers AB and
+
+ align:start position:0%
+likelihood of a pair of numbers AB and
+ 
+
+ align:start position:0%
+likelihood of a pair of numbers AB and
+if I know this that's actually what's
+
+ align:start position:0%
+if I know this that's actually what's
+ 
+
+ align:start position:0%
+if I know this that's actually what's
+going to come into it because I know
+
+ align:start position:0%
+going to come into it because I know
+ 
+
+ align:start position:0%
+going to come into it because I know
+that the density
+
+ align:start position:0%
+that the density
+ 
+
+ align:start position:0%
+that the density
+is going to come in into play when I
+
+ align:start position:0%
+is going to come in into play when I
+ 
+
+ align:start position:0%
+is going to come in into play when I
+talk about the but here I'm just talking
+
+ align:start position:0%
+talk about the but here I'm just talking
+ 
+
+ align:start position:0%
+talk about the but here I'm just talking
+about a this is a mechanical tool I'm
+
+ align:start position:0%
+about a this is a mechanical tool I'm
+ 
+
+ align:start position:0%
+about a this is a mechanical tool I'm
+just saying let's minimize the distance
+
+ align:start position:0%
+just saying let's minimize the distance
+ 
+
+ align:start position:0%
+just saying let's minimize the distance
+to the curve another thing I could have
+
+ align:start position:0%
+to the curve another thing I could have
+ 
+
+ align:start position:0%
+to the curve another thing I could have
+done is take the absolute value of this
+
+ align:start position:0%
+done is take the absolute value of this
+ 
+
+ align:start position:0%
+done is take the absolute value of this
+thing for example I just decided to take
+
+ align:start position:0%
+thing for example I just decided to take
+ 
+
+ align:start position:0%
+thing for example I just decided to take
+the square before I did it okay so
+
+ align:start position:0%
+the square before I did it okay so
+ 
+
+ align:start position:0%
+the square before I did it okay so
+regardless of what I'm doing I'm just
+
+ align:start position:0%
+regardless of what I'm doing I'm just
+ 
+
+ align:start position:0%
+regardless of what I'm doing I'm just
+taking the squares because that's just
+
+ align:start position:0%
+taking the squares because that's just
+ 
+
+ align:start position:0%
+taking the squares because that's just
+going to be convenient for me to do my
+
+ align:start position:0%
+going to be convenient for me to do my
+ 
+
+ align:start position:0%
+going to be convenient for me to do my
+computations for now but we don't have
+
+ align:start position:0%
+computations for now but we don't have
+ 
+
+ align:start position:0%
+computations for now but we don't have
+any statistical model at this point
+
+ align:start position:0%
+any statistical model at this point
+ 
+
+ align:start position:0%
+any statistical model at this point
+right I didn't say anything that y
+
+ align:start position:0%
+right I didn't say anything that y
+ 
+
+ align:start position:0%
+right I didn't say anything that y
+follows this x follows this. I'm just
+
+ align:start position:0%
+follows this x follows this. I'm just
+ 
+
+ align:start position:0%
+follows this x follows this. I'm just
+doing minimal assumptions as we go. All
+
+ align:start position:0%
+doing minimal assumptions as we go. All
+ 
+
+ align:start position:0%
+doing minimal assumptions as we go. All
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+So, the variance of x is not equal to
+
+ align:start position:0%
+So, the variance of x is not equal to
+ 
+
+ align:start position:0%
+So, the variance of x is not equal to
+zero. Can somebody tell me why?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What would happen in my what would my
+
+ align:start position:0%
+What would happen in my what would my
+ 
+
+ align:start position:0%
+What would happen in my what would my
+point cloud point look like if the
+
+ align:start position:0%
+point cloud point look like if the
+ 
+
+ align:start position:0%
+point cloud point look like if the
+variance of x was equal to zero? Yeah,
+
+ align:start position:0%
+variance of x was equal to zero? Yeah,
+ 
+
+ align:start position:0%
+variance of x was equal to zero? Yeah,
+they would all be at the same point. So,
+
+ align:start position:0%
+they would all be at the same point. So,
+ 
+
+ align:start position:0%
+they would all be at the same point. So,
+it's going to be hard for me to start
+
+ align:start position:0%
+it's going to be hard for me to start
+ 
+
+ align:start position:0%
+it's going to be hard for me to start
+fitting a line, right? I mean, best case
+
+ align:start position:0%
+fitting a line, right? I mean, best case
+ 
+
+ align:start position:0%
+fitting a line, right? I mean, best case
+scenario, I have this x, it has variance
+
+ align:start position:0%
+scenario, I have this x, it has variance
+ 
+
+ align:start position:0%
+scenario, I have this x, it has variance
+zero. So, this is the expectation of x
+
+ align:start position:0%
+zero. So, this is the expectation of x
+ 
+
+ align:start position:0%
+zero. So, this is the expectation of x
+and all my points
+
+ align:start position:0%
+and all my points
+ 
+
+ align:start position:0%
+and all my points
+have the same expectation
+
+ align:start position:0%
+have the same expectation
+ 
+
+ align:start position:0%
+have the same expectation
+then so yes I could probably fit that
+
+ align:start position:0%
+then so yes I could probably fit that
+ 
+
+ align:start position:0%
+then so yes I could probably fit that
+line but uh that wouldn't help very much
+
+ align:start position:0%
+line but uh that wouldn't help very much
+ 
+
+ align:start position:0%
+line but uh that wouldn't help very much
+for other x's right so I need a bit of
+
+ align:start position:0%
+for other x's right so I need a bit of
+ 
+
+ align:start position:0%
+for other x's right so I need a bit of
+variance so that things spread out a
+
+ align:start position:0%
+variance so that things spread out a
+ 
+
+ align:start position:0%
+variance so that things spread out a
+little bit and um and uh
+
+ align:start position:0%
+little bit and um and uh
+ 
+
+ align:start position:0%
+little bit and um and uh
+okay I'm going to have to do this
+
+ align:start position:0%
+okay I'm going to have to do this
+ 
+
+ align:start position:0%
+okay I'm going to have to do this
+I think it's just my um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's hope I'm gonna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, so I'm going to put a little
+
+ align:start position:0%
+All right, so I'm going to put a little
+ 
+
+ align:start position:0%
+All right, so I'm going to put a little
+bit of less variance and the other thing
+
+ align:start position:0%
+bit of less variance and the other thing
+ 
+
+ align:start position:0%
+bit of less variance and the other thing
+is here I don't want to do much more but
+
+ align:start position:0%
+is here I don't want to do much more but
+ 
+
+ align:start position:0%
+is here I don't want to do much more but
+I'm actually going to think of X as
+
+ align:start position:0%
+I'm actually going to think of X as
+ 
+
+ align:start position:0%
+I'm actually going to think of X as
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+uh mean zero and the way I do this is as
+
+ align:start position:0%
+uh mean zero and the way I do this is as
+ 
+
+ align:start position:0%
+uh mean zero and the way I do this is as
+follows. Let's define X tilda which is X
+
+ align:start position:0%
+follows. Let's define X tilda which is X
+ 
+
+ align:start position:0%
+follows. Let's define X tilda which is X
+minus the expectation of X.
+
+ align:start position:0%
+minus the expectation of X.
+ 
+
+ align:start position:0%
+minus the expectation of X.
+Okay. So definitely the expectation of X
+
+ align:start position:0%
+Okay. So definitely the expectation of X
+ 
+
+ align:start position:0%
+Okay. So definitely the expectation of X
+tilda is what?
+
+ align:start position:0%
+tilda is what?
+ 
+
+ align:start position:0%
+tilda is what?
+Zero. Okay. And so now I want to
+
+ align:start position:0%
+Zero. Okay. And so now I want to
+ 
+
+ align:start position:0%
+Zero. Okay. And so now I want to
+minimize
+
+ align:start position:0%
+minimize
+ 
+
+ align:start position:0%
+minimize
+in AB
+
+ align:start position:0%
+in AB
+ 
+
+ align:start position:0%
+in AB
+expectation of Y
+
+ align:start position:0%
+expectation of Y
+ 
+
+ align:start position:0%
+expectation of Y
+minus A + B X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared.
+
+ align:start position:0%
+squared.
+ 
+
+ align:start position:0%
+squared.
+And what I'm going to the way I'm going
+
+ align:start position:0%
+And what I'm going to the way I'm going
+ 
+
+ align:start position:0%
+And what I'm going to the way I'm going
+to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is by turning X into X tilda and
+
+ align:start position:0%
+is by turning X into X tilda and
+ 
+
+ align:start position:0%
+is by turning X into X tilda and
+stuffing the extra
+
+ align:start position:0%
+stuffing the extra
+ 
+
+ align:start position:0%
+stuffing the extra
+um and and putting the extra uh um uh
+
+ align:start position:0%
+um and and putting the extra uh um uh
+ 
+
+ align:start position:0%
+um and and putting the extra uh um uh
+expectation of X into the A. Okay. So
+
+ align:start position:0%
+expectation of X into the A. Okay. So
+ 
+
+ align:start position:0%
+expectation of X into the A. Okay. So
+I'm going to write this as expectation
+
+ align:start position:0%
+I'm going to write this as expectation
+ 
+
+ align:start position:0%
+I'm going to write this as expectation
+of y minus
+
+ align:start position:0%
+of y minus
+ 
+
+ align:start position:0%
+of y minus
+a plus b
+
+ align:start position:0%
+a plus b
+ 
+
+ align:start position:0%
+a plus b
+uh expectation of x
+
+ align:start position:0%
+uh expectation of x
+ 
+
+ align:start position:0%
+uh expectation of x
+which I'm going to call a tilda
+
+ align:start position:0%
+which I'm going to call a tilda
+ 
+
+ align:start position:0%
+which I'm going to call a tilda
+and plus b xtilda.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And uh everybody agrees with this. So
+
+ align:start position:0%
+And uh everybody agrees with this. So
+ 
+
+ align:start position:0%
+And uh everybody agrees with this. So
+now I have two parameters a tilda and b.
+
+ align:start position:0%
+now I have two parameters a tilda and b.
+ 
+
+ align:start position:0%
+now I have two parameters a tilda and b.
+And I'm gonna pretend that now X so now
+
+ align:start position:0%
+And I'm gonna pretend that now X so now
+ 
+
+ align:start position:0%
+And I'm gonna pretend that now X so now
+it's the role of X is played by X tilda
+
+ align:start position:0%
+it's the role of X is played by X tilda
+ 
+
+ align:start position:0%
+it's the role of X is played by X tilda
+which is now a uh which is now a
+
+ align:start position:0%
+which is now a uh which is now a
+ 
+
+ align:start position:0%
+which is now a uh which is now a
+centered random variable. Okay. So I'm
+
+ align:start position:0%
+centered random variable. Okay. So I'm
+ 
+
+ align:start position:0%
+centered random variable. Okay. So I'm
+going to call this guy a tilda. But for
+
+ align:start position:0%
+going to call this guy a tilda. But for
+ 
+
+ align:start position:0%
+going to call this guy a tilda. But for
+for my computations I'm going to call it
+
+ align:start position:0%
+for my computations I'm going to call it
+ 
+
+ align:start position:0%
+for my computations I'm going to call it
+a. So how do I find the minimum of this
+
+ align:start position:0%
+a. So how do I find the minimum of this
+ 
+
+ align:start position:0%
+a. So how do I find the minimum of this
+thing?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Derivative equal to zero. Right? So here
+
+ align:start position:0%
+Derivative equal to zero. Right? So here
+ 
+
+ align:start position:0%
+Derivative equal to zero. Right? So here
+it's a quadratic thing. It's going to be
+
+ align:start position:0%
+it's a quadratic thing. It's going to be
+ 
+
+ align:start position:0%
+it's a quadratic thing. It's going to be
+like that. I take the derivative set it
+
+ align:start position:0%
+like that. I take the derivative set it
+ 
+
+ align:start position:0%
+like that. I take the derivative set it
+to zero. So I'm first going to take the
+
+ align:start position:0%
+to zero. So I'm first going to take the
+ 
+
+ align:start position:0%
+to zero. So I'm first going to take the
+derivative with respect to a and set it
+
+ align:start position:0%
+derivative with respect to a and set it
+ 
+
+ align:start position:0%
+derivative with respect to a and set it
+equal to zero. So that's equivalent to
+
+ align:start position:0%
+equal to zero. So that's equivalent to
+ 
+
+ align:start position:0%
+equal to zero. So that's equivalent to
+saying that the expectation of well here
+
+ align:start position:0%
+saying that the expectation of well here
+ 
+
+ align:start position:0%
+saying that the expectation of well here
+I'm going to pick up a two
+
+ align:start position:0%
+I'm going to pick up a two
+ 
+
+ align:start position:0%
+I'm going to pick up a two
+y minus
+
+ align:start position:0%
+y minus
+ 
+
+ align:start position:0%
+y minus
+um a + b x
+
+ align:start position:0%
+um a + b x
+ 
+
+ align:start position:0%
+um a + b x
+tilda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to zero. And then I also have
+
+ align:start position:0%
+is equal to zero. And then I also have
+ 
+
+ align:start position:0%
+is equal to zero. And then I also have
+that the derivative with respect to b is
+
+ align:start position:0%
+that the derivative with respect to b is
+ 
+
+ align:start position:0%
+that the derivative with respect to b is
+equal to zero which is equivalent to the
+
+ align:start position:0%
+equal to zero which is equivalent to the
+ 
+
+ align:start position:0%
+equal to zero which is equivalent to the
+expectation of well I have a negative
+
+ align:start position:0%
+expectation of well I have a negative
+ 
+
+ align:start position:0%
+expectation of well I have a negative
+sign somewhere so let me put it here -
+
+ align:start position:0%
+sign somewhere so let me put it here -
+ 
+
+ align:start position:0%
+sign somewhere so let me put it here -
+2x tilda y -
+
+ align:start position:0%
+2x tilda y -
+ 
+
+ align:start position:0%
+2x tilda y -
+a + b x tilda.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. See that's why I don't want to put
+
+ align:start position:0%
+Okay. See that's why I don't want to put
+ 
+
+ align:start position:0%
+Okay. See that's why I don't want to put
+too many parenthesis. Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I just took the derivative with
+
+ align:start position:0%
+so I just took the derivative with
+ 
+
+ align:start position:0%
+so I just took the derivative with
+respect to a which is just basically the
+
+ align:start position:0%
+respect to a which is just basically the
+ 
+
+ align:start position:0%
+respect to a which is just basically the
+square and then I have a negative one
+
+ align:start position:0%
+square and then I have a negative one
+ 
+
+ align:start position:0%
+square and then I have a negative one
+that comes out from inside and then I
+
+ align:start position:0%
+that comes out from inside and then I
+ 
+
+ align:start position:0%
+that comes out from inside and then I
+take the derivative with respect to b
+
+ align:start position:0%
+take the derivative with respect to b
+ 
+
+ align:start position:0%
+take the derivative with respect to b
+and I have since b has x tilda in factor
+
+ align:start position:0%
+and I have since b has x tilda in factor
+ 
+
+ align:start position:0%
+and I have since b has x tilda in factor
+it comes out as well right so the
+
+ align:start position:0%
+it comes out as well right so the
+ 
+
+ align:start position:0%
+it comes out as well right so the
+minus2's really won't matter for me
+
+ align:start position:0%
+minus2's really won't matter for me
+ 
+
+ align:start position:0%
+minus2's really won't matter for me
+and so now I have two equations the
+
+ align:start position:0%
+and so now I have two equations the
+ 
+
+ align:start position:0%
+and so now I have two equations the
+first equation well it's pretty simple
+
+ align:start position:0%
+first equation well it's pretty simple
+ 
+
+ align:start position:0%
+first equation well it's pretty simple
+It's just telling me that the
+
+ align:start position:0%
+It's just telling me that the
+ 
+
+ align:start position:0%
+It's just telling me that the
+expectation of y minus a is equal to
+
+ align:start position:0%
+expectation of y minus a is equal to
+ 
+
+ align:start position:0%
+expectation of y minus a is equal to
+zero. So what I know is that a is equal
+
+ align:start position:0%
+zero. So what I know is that a is equal
+ 
+
+ align:start position:0%
+zero. So what I know is that a is equal
+to the expectation
+
+ align:start position:0%
+to the expectation
+ 
+
+ align:start position:0%
+to the expectation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+y. And really that was a tilda which
+
+ align:start position:0%
+y. And really that was a tilda which
+ 
+
+ align:start position:0%
+y. And really that was a tilda which
+implies that the a I want is actually
+
+ align:start position:0%
+implies that the a I want is actually
+ 
+
+ align:start position:0%
+implies that the a I want is actually
+equal to the expectation
+
+ align:start position:0%
+equal to the expectation
+ 
+
+ align:start position:0%
+equal to the expectation
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus b * the expectation
+
+ align:start position:0%
+minus b * the expectation
+ 
+
+ align:start position:0%
+minus b * the expectation
+of x.
+
+ align:start position:0%
+of x.
+ 
+
+ align:start position:0%
+of x.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just because a tilda is a plus b times
+
+ align:start position:0%
+just because a tilda is a plus b times
+ 
+
+ align:start position:0%
+just because a tilda is a plus b times
+the expectation of x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's for my a and then for my b I
+
+ align:start position:0%
+So that's for my a and then for my b I
+ 
+
+ align:start position:0%
+So that's for my a and then for my b I
+use the second one. So the second one
+
+ align:start position:0%
+use the second one. So the second one
+ 
+
+ align:start position:0%
+use the second one. So the second one
+tells me that the expectation of x tilda
+
+ align:start position:0%
+tells me that the expectation of x tilda
+ 
+
+ align:start position:0%
+tells me that the expectation of x tilda
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is equal to a + b * the expectation of x
+
+ align:start position:0%
+is equal to a + b * the expectation of x
+ 
+
+ align:start position:0%
+is equal to a + b * the expectation of x
+tilda which is zero. Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. But this a is actually a tilda in
+
+ align:start position:0%
+Okay. But this a is actually a tilda in
+ 
+
+ align:start position:0%
+Okay. But this a is actually a tilda in
+this problem. So it's actually a plus b
+
+ align:start position:0%
+this problem. So it's actually a plus b
+ 
+
+ align:start position:0%
+this problem. So it's actually a plus b
+expectation of x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now this is the expectation of the
+
+ align:start position:0%
+Now this is the expectation of the
+ 
+
+ align:start position:0%
+Now this is the expectation of the
+product of two random variables but x
+
+ align:start position:0%
+product of two random variables but x
+ 
+
+ align:start position:0%
+product of two random variables but x
+tilda is centered right? It's x minus
+
+ align:start position:0%
+tilda is centered right? It's x minus
+ 
+
+ align:start position:0%
+tilda is centered right? It's x minus
+expectation of x. So this thing is
+
+ align:start position:0%
+expectation of x. So this thing is
+ 
+
+ align:start position:0%
+expectation of x. So this thing is
+actually equal to the coariance between
+
+ align:start position:0%
+actually equal to the coariance between
+ 
+
+ align:start position:0%
+actually equal to the coariance between
+x and y by definition of coariance.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now I have everything I need, right?
+
+ align:start position:0%
+So now I have everything I need, right?
+ 
+
+ align:start position:0%
+So now I have everything I need, right?
+How do I just
+
+ align:start position:0%
+How do I just
+ 
+
+ align:start position:0%
+How do I just
+I'm sorry about that. Uh so I have
+
+ align:start position:0%
+I'm sorry about that. Uh so I have
+ 
+
+ align:start position:0%
+I'm sorry about that. Uh so I have
+everything I need. Now I'm just I have
+
+ align:start position:0%
+everything I need. Now I'm just I have
+ 
+
+ align:start position:0%
+everything I need. Now I'm just I have
+two equations with two unknowns. And uh
+
+ align:start position:0%
+two equations with two unknowns. And uh
+ 
+
+ align:start position:0%
+two equations with two unknowns. And uh
+all I have to do is to basically plug it
+
+ align:start position:0%
+all I have to do is to basically plug it
+ 
+
+ align:start position:0%
+all I have to do is to basically plug it
+in. So it's essentially telling me that
+
+ align:start position:0%
+in. So it's essentially telling me that
+ 
+
+ align:start position:0%
+in. So it's essentially telling me that
+the coariance of XY. So the first
+
+ align:start position:0%
+the coariance of XY. So the first
+ 
+
+ align:start position:0%
+the coariance of XY. So the first
+equation tells me that the coariance of
+
+ align:start position:0%
+equation tells me that the coariance of
+ 
+
+ align:start position:0%
+equation tells me that the coariance of
+XY is equal to A plus B expectation of
+
+ align:start position:0%
+XY is equal to A plus B expectation of
+ 
+
+ align:start position:0%
+XY is equal to A plus B expectation of
+X. But a is expectation of y minus b
+
+ align:start position:0%
+X. But a is expectation of y minus b
+ 
+
+ align:start position:0%
+X. But a is expectation of y minus b
+expectation of x. So uh
+
+ align:start position:0%
+expectation of x. So uh
+ 
+
+ align:start position:0%
+expectation of x. So uh
+it's well actually maybe I should start
+
+ align:start position:0%
+it's well actually maybe I should start
+ 
+
+ align:start position:0%
+it's well actually maybe I should start
+with b.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh sorry sorry sorry. Okay I forgot one
+
+ align:start position:0%
+Oh sorry sorry sorry. Okay I forgot one
+ 
+
+ align:start position:0%
+Oh sorry sorry sorry. Okay I forgot one
+thing. Sorry this is not true. Right? I
+
+ align:start position:0%
+thing. Sorry this is not true. Right? I
+ 
+
+ align:start position:0%
+thing. Sorry this is not true. Right? I
+forgot this term. X tilda multiplies X
+
+ align:start position:0%
+forgot this term. X tilda multiplies X
+ 
+
+ align:start position:0%
+forgot this term. X tilda multiplies X
+tilda here. So what I'm left with is
+
+ align:start position:0%
+tilda here. So what I'm left with is
+ 
+
+ align:start position:0%
+tilda here. So what I'm left with is
+Xtilda. It's minus B times the
+
+ align:start position:0%
+Xtilda. It's minus B times the
+ 
+
+ align:start position:0%
+Xtilda. It's minus B times the
+expectation of X tilda squared. So
+
+ align:start position:0%
+expectation of X tilda squared. So
+ 
+
+ align:start position:0%
+expectation of X tilda squared. So
+that's actually minus B times the
+
+ align:start position:0%
+that's actually minus B times the
+ 
+
+ align:start position:0%
+that's actually minus B times the
+variance of X tilda because XTilda is
+
+ align:start position:0%
+variance of X tilda because XTilda is
+ 
+
+ align:start position:0%
+variance of X tilda because XTilda is
+already centered. Okay, which is
+
+ align:start position:0%
+already centered. Okay, which is
+ 
+
+ align:start position:0%
+already centered. Okay, which is
+actually the variance of X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now I have that this thing is
+
+ align:start position:0%
+Okay. So now I have that this thing is
+ 
+
+ align:start position:0%
+Okay. So now I have that this thing is
+actually a plus b expectation of x minus
+
+ align:start position:0%
+actually a plus b expectation of x minus
+ 
+
+ align:start position:0%
+actually a plus b expectation of x minus
+b variance
+
+ align:start position:0%
+b variance
+ 
+
+ align:start position:0%
+b variance
+of x.
+
+ align:start position:0%
+of x.
+ 
+
+ align:start position:0%
+of x.
+And I also have that a
+
+ align:start position:0%
+And I also have that a
+ 
+
+ align:start position:0%
+And I also have that a
+is equal to expectation of y
+
+ align:start position:0%
+is equal to expectation of y
+ 
+
+ align:start position:0%
+is equal to expectation of y
+minus b expectation of x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So if I sum the two
+
+ align:start position:0%
+Okay. So if I sum the two
+ 
+
+ align:start position:0%
+Okay. So if I sum the two
+Right? So if I sum the two, those guys
+
+ align:start position:0%
+Right? So if I sum the two, those guys
+ 
+
+ align:start position:0%
+Right? So if I sum the two, those guys
+are going to cancel.
+
+ align:start position:0%
+are going to cancel.
+ 
+
+ align:start position:0%
+are going to cancel.
+Those guys are going to cancel.
+
+ align:start position:0%
+Those guys are going to cancel.
+ 
+
+ align:start position:0%
+Those guys are going to cancel.
+And so what I'm going to be left with is
+
+ align:start position:0%
+And so what I'm going to be left with is
+ 
+
+ align:start position:0%
+And so what I'm going to be left with is
+coariance of XY is equal to expectation
+
+ align:start position:0%
+coariance of XY is equal to expectation
+ 
+
+ align:start position:0%
+coariance of XY is equal to expectation
+of X, expectation of Y.
+
+ align:start position:0%
+of X, expectation of Y.
+ 
+
+ align:start position:0%
+of X, expectation of Y.
+And then I'm left with this term here
+
+ align:start position:0%
+And then I'm left with this term here
+ 
+
+ align:start position:0%
+And then I'm left with this term here
+minus B times the variance of X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so that tells me that B,
+
+ align:start position:0%
+And so that tells me that B,
+ 
+
+ align:start position:0%
+And so that tells me that B,
+why do I still have the variance there?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but sex still the center right so you
+
+ align:start position:0%
+but sex still the center right so you
+ 
+
+ align:start position:0%
+but sex still the center right so you
+just you just need to have one that's
+
+ align:start position:0%
+just you just need to have one that's
+ 
+
+ align:start position:0%
+just you just need to have one that's
+centered for this to work
+
+ align:start position:0%
+centered for this to work
+ 
+
+ align:start position:0%
+centered for this to work
+oh I see
+
+ align:start position:0%
+oh I see
+ 
+
+ align:start position:0%
+oh I see
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right I mean you can check it but uh
+
+ align:start position:0%
+right I mean you can check it but uh
+ 
+
+ align:start position:0%
+right I mean you can check it but uh
+basically when you're going to have the
+
+ align:start position:0%
+basically when you're going to have the
+ 
+
+ align:start position:0%
+basically when you're going to have the
+product of the expectations you only
+
+ align:start position:0%
+product of the expectations you only
+ 
+
+ align:start position:0%
+product of the expectations you only
+need one of the two in the product to be
+
+ align:start position:0%
+need one of the two in the product to be
+ 
+
+ align:start position:0%
+need one of the two in the product to be
+zero so the product is zero so um okay
+
+ align:start position:0%
+zero so the product is zero so um okay
+ 
+
+ align:start position:0%
+zero so the product is zero so um okay
+why do kept my uh so I get a a and then
+
+ align:start position:0%
+why do kept my uh so I get a a and then
+ 
+
+ align:start position:0%
+why do kept my uh so I get a a and then
+the b expectation. Okay, so that's
+
+ align:start position:0%
+the b expectation. Okay, so that's
+ 
+
+ align:start position:0%
+the b expectation. Okay, so that's
+probably earlier that I made a mistake.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I get a So this was a tilda
+
+ align:start position:0%
+So I get a So this was a tilda
+ 
+
+ align:start position:0%
+So I get a So this was a tilda
+clear about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that tells me that a tilda maybe it's
+
+ align:start position:0%
+So that tells me that a tilda maybe it's
+ 
+
+ align:start position:0%
+So that tells me that a tilda maybe it's
+not super fair of me to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay I think I know where I made a
+
+ align:start position:0%
+yeah okay I think I know where I made a
+ 
+
+ align:start position:0%
+yeah okay I think I know where I made a
+mistake I should not have centered I
+
+ align:start position:0%
+mistake I should not have centered I
+ 
+
+ align:start position:0%
+mistake I should not have centered I
+wanted to make my life easier and I
+
+ align:start position:0%
+wanted to make my life easier and I
+ 
+
+ align:start position:0%
+wanted to make my life easier and I
+should not have done that and the reason
+
+ align:start position:0%
+should not have done that and the reason
+ 
+
+ align:start position:0%
+should not have done that and the reason
+is a tilda depends on b so when I take
+
+ align:start position:0%
+is a tilda depends on b so when I take
+ 
+
+ align:start position:0%
+is a tilda depends on b so when I take
+the derivative with respect to b what
+
+ align:start position:0%
+the derivative with respect to b what
+ 
+
+ align:start position:0%
+the derivative with respect to b what
+I'm left with here since a tilda depends
+
+ align:start position:0%
+I'm left with here since a tilda depends
+ 
+
+ align:start position:0%
+I'm left with here since a tilda depends
+on b when I take the derivative of this
+
+ align:start position:0%
+on b when I take the derivative of this
+ 
+
+ align:start position:0%
+on b when I take the derivative of this
+guy I actually don't get a tilda here
+
+ align:start position:0%
+guy I actually don't get a tilda here
+ 
+
+ align:start position:0%
+guy I actually don't get a tilda here
+but I really get um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so again this was not uh
+
+ align:start position:0%
+sorry so again this was not uh
+ 
+
+ align:start position:0%
+sorry so again this was not uh
+so that's the first one yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is actually here,
+
+ align:start position:0%
+this is actually here,
+ 
+
+ align:start position:0%
+this is actually here,
+right? When I take the derivative with
+
+ align:start position:0%
+right? When I take the derivative with
+ 
+
+ align:start position:0%
+right? When I take the derivative with
+respect to B.
+
+ align:start position:0%
+respect to B.
+ 
+
+ align:start position:0%
+respect to B.
+And so now what I'm left with is that
+
+ align:start position:0%
+And so now what I'm left with is that
+ 
+
+ align:start position:0%
+And so now what I'm left with is that
+the expectation. So yeah, I'm basically
+
+ align:start position:0%
+the expectation. So yeah, I'm basically
+ 
+
+ align:start position:0%
+the expectation. So yeah, I'm basically
+left with nothing that helps. So um I'm
+
+ align:start position:0%
+left with nothing that helps. So um I'm
+ 
+
+ align:start position:0%
+left with nothing that helps. So um I'm
+sorry about that. Let's start from the
+
+ align:start position:0%
+sorry about that. Let's start from the
+ 
+
+ align:start position:0%
+sorry about that. Let's start from the
+the beginning because this is not
+
+ align:start position:0%
+the beginning because this is not
+ 
+
+ align:start position:0%
+the beginning because this is not
+getting us anywhere and any and a fix is
+
+ align:start position:0%
+getting us anywhere and any and a fix is
+ 
+
+ align:start position:0%
+getting us anywhere and any and a fix is
+not going to help. So let's just do it
+
+ align:start position:0%
+not going to help. So let's just do it
+ 
+
+ align:start position:0%
+not going to help. So let's just do it
+again. Sorry about that. So let's not
+
+ align:start position:0%
+again. Sorry about that. So let's not
+ 
+
+ align:start position:0%
+again. Sorry about that. So let's not
+center anything and just just do it
+
+ align:start position:0%
+center anything and just just do it
+ 
+
+ align:start position:0%
+center anything and just just do it
+brute force because we're gonna b x^
+
+ align:start position:0%
+brute force because we're gonna b x^
+ 
+
+ align:start position:0%
+brute force because we're gonna b x^
+squ. All right,
+
+ align:start position:0%
+squ. All right,
+ 
+
+ align:start position:0%
+squ. All right,
+partial with respect to a is giving
+
+ align:start position:0%
+partial with respect to a is giving
+ 
+
+ align:start position:0%
+partial with respect to a is giving
+equals zero is equivalent. So my minus
+
+ align:start position:0%
+equals zero is equivalent. So my minus
+ 
+
+ align:start position:0%
+equals zero is equivalent. So my minus
+two is going to cancel, right? So I'm
+
+ align:start position:0%
+two is going to cancel, right? So I'm
+ 
+
+ align:start position:0%
+two is going to cancel, right? So I'm
+going to actually forget about this. So
+
+ align:start position:0%
+going to actually forget about this. So
+ 
+
+ align:start position:0%
+going to actually forget about this. So
+it's actually telling me that the
+
+ align:start position:0%
+it's actually telling me that the
+ 
+
+ align:start position:0%
+it's actually telling me that the
+expectation of y
+
+ align:start position:0%
+expectation of y
+ 
+
+ align:start position:0%
+expectation of y
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+a + b x is equal to zero which is
+
+ align:start position:0%
+a + b x is equal to zero which is
+ 
+
+ align:start position:0%
+a + b x is equal to zero which is
+equivalent to a + b expectation of x is
+
+ align:start position:0%
+equivalent to a + b expectation of x is
+ 
+
+ align:start position:0%
+equivalent to a + b expectation of x is
+equal to the expectation of y. Now, if I
+
+ align:start position:0%
+equal to the expectation of y. Now, if I
+ 
+
+ align:start position:0%
+equal to the expectation of y. Now, if I
+take the derivative with respect to B
+
+ align:start position:0%
+take the derivative with respect to B
+ 
+
+ align:start position:0%
+take the derivative with respect to B
+and set it equal to zero, this is
+
+ align:start position:0%
+and set it equal to zero, this is
+ 
+
+ align:start position:0%
+and set it equal to zero, this is
+telling me that the expectation of uh
+
+ align:start position:0%
+telling me that the expectation of uh
+ 
+
+ align:start position:0%
+telling me that the expectation of uh
+well, it's the same thing except that
+
+ align:start position:0%
+well, it's the same thing except that
+ 
+
+ align:start position:0%
+well, it's the same thing except that
+this time I'm going to pull out an x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This guy is equal to zero.
+
+ align:start position:0%
+This guy is equal to zero.
+ 
+
+ align:start position:0%
+This guy is equal to zero.
+This guy is not here. And so that
+
+ align:start position:0%
+This guy is not here. And so that
+ 
+
+ align:start position:0%
+This guy is not here. And so that
+implies that the expectation
+
+ align:start position:0%
+implies that the expectation
+ 
+
+ align:start position:0%
+implies that the expectation
+of XY
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal
+
+ align:start position:0%
+is equal
+ 
+
+ align:start position:0%
+is equal
+to A * the expectation of X plus B times
+
+ align:start position:0%
+to A * the expectation of X plus B times
+ 
+
+ align:start position:0%
+to A * the expectation of X plus B times
+the expectation
+
+ align:start position:0%
+the expectation
+ 
+
+ align:start position:0%
+the expectation
+of X squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So the first one is actually
+
+ align:start position:0%
+All right. So the first one is actually
+ 
+
+ align:start position:0%
+All right. So the first one is actually
+uh not giving me much. So I need to
+
+ align:start position:0%
+uh not giving me much. So I need to
+ 
+
+ align:start position:0%
+uh not giving me much. So I need to
+actually work with the two of those
+
+ align:start position:0%
+actually work with the two of those
+ 
+
+ align:start position:0%
+actually work with the two of those
+guys. So I'm going to take the first. So
+
+ align:start position:0%
+guys. So I'm going to take the first. So
+ 
+
+ align:start position:0%
+guys. So I'm going to take the first. So
+let me rewrite those two equal
+
+ align:start position:0%
+let me rewrite those two equal
+ 
+
+ align:start position:0%
+let me rewrite those two equal
+inequalities that I have. I have a plus
+
+ align:start position:0%
+inequalities that I have. I have a plus
+ 
+
+ align:start position:0%
+inequalities that I have. I have a plus
+b e of x is equal to e of y
+
+ align:start position:0%
+b e of x is equal to e of y
+ 
+
+ align:start position:0%
+b e of x is equal to e of y
+and then I have e of xy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And now the what I do is that I
+
+ align:start position:0%
+Okay. And now the what I do is that I
+ 
+
+ align:start position:0%
+Okay. And now the what I do is that I
+take the I multiply
+
+ align:start position:0%
+take the I multiply
+ 
+
+ align:start position:0%
+take the I multiply
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this guy. So I want to cancel one of
+
+ align:start position:0%
+this guy. So I want to cancel one of
+ 
+
+ align:start position:0%
+this guy. So I want to cancel one of
+these things, right? So what I'm going
+
+ align:start position:0%
+these things, right? So what I'm going
+ 
+
+ align:start position:0%
+these things, right? So what I'm going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah, so I'm going to take this guy and
+
+ align:start position:0%
+yeah, so I'm going to take this guy and
+ 
+
+ align:start position:0%
+yeah, so I'm going to take this guy and
+I'm going to multiply it by E of X and
+
+ align:start position:0%
+I'm going to multiply it by E of X and
+ 
+
+ align:start position:0%
+I'm going to multiply it by E of X and
+take the difference.
+
+ align:start position:0%
+take the difference.
+ 
+
+ align:start position:0%
+take the difference.
+Okay. So I do times E of X and then I
+
+ align:start position:0%
+Okay. So I do times E of X and then I
+ 
+
+ align:start position:0%
+Okay. So I do times E of X and then I
+take the diff I take the I take the sum
+
+ align:start position:0%
+take the diff I take the I take the sum
+ 
+
+ align:start position:0%
+take the diff I take the I take the sum
+of those two and then those two terms
+
+ align:start position:0%
+of those two and then those two terms
+ 
+
+ align:start position:0%
+of those two and then those two terms
+are going to cancel. Okay. So then that
+
+ align:start position:0%
+are going to cancel. Okay. So then that
+ 
+
+ align:start position:0%
+are going to cancel. Okay. So then that
+tells me that B * E of X^
+
+ align:start position:0%
+tells me that B * E of X^
+ 
+
+ align:start position:0%
+tells me that B * E of X^
+squared plus the expectation
+
+ align:start position:0%
+squared plus the expectation
+ 
+
+ align:start position:0%
+squared plus the expectation
+of X Y is equal to.
+
+ align:start position:0%
+of X Y is equal to.
+ 
+
+ align:start position:0%
+of X Y is equal to.
+So this guy uh is the one that
+
+ align:start position:0%
+So this guy uh is the one that
+ 
+
+ align:start position:0%
+So this guy uh is the one that
+cancelled.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then I get this guy here expectation of
+
+ align:start position:0%
+Then I get this guy here expectation of
+ 
+
+ align:start position:0%
+Then I get this guy here expectation of
+X times expectation of Y plus uh the guy
+
+ align:start position:0%
+X times expectation of Y plus uh the guy
+ 
+
+ align:start position:0%
+X times expectation of Y plus uh the guy
+that remains here which is uh B times
+
+ align:start position:0%
+that remains here which is uh B times
+ 
+
+ align:start position:0%
+that remains here which is uh B times
+the expectation of X^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here I have B expectation of X the
+
+ align:start position:0%
+So here I have B expectation of X the
+ 
+
+ align:start position:0%
+So here I have B expectation of X the
+whole thing squared and here I have B
+
+ align:start position:0%
+whole thing squared and here I have B
+ 
+
+ align:start position:0%
+whole thing squared and here I have B
+expectation of X squar. So if I pull
+
+ align:start position:0%
+expectation of X squar. So if I pull
+ 
+
+ align:start position:0%
+expectation of X squar. So if I pull
+this guy here what do I get?
+
+ align:start position:0%
+this guy here what do I get?
+ 
+
+ align:start position:0%
+this guy here what do I get?
+B times the variance of X. Okay so I'm
+
+ align:start position:0%
+B times the variance of X. Okay so I'm
+ 
+
+ align:start position:0%
+B times the variance of X. Okay so I'm
+going to move here and this guy here.
+
+ align:start position:0%
+going to move here and this guy here.
+ 
+
+ align:start position:0%
+going to move here and this guy here.
+When I move this guy here I get
+
+ align:start position:0%
+When I move this guy here I get
+ 
+
+ align:start position:0%
+When I move this guy here I get
+expectation of X time Y minus the
+
+ align:start position:0%
+expectation of X time Y minus the
+ 
+
+ align:start position:0%
+expectation of X time Y minus the
+expectation of X times the expectation
+
+ align:start position:0%
+expectation of X times the expectation
+ 
+
+ align:start position:0%
+expectation of X times the expectation
+of Y. So this is actually telling me
+
+ align:start position:0%
+of Y. So this is actually telling me
+ 
+
+ align:start position:0%
+of Y. So this is actually telling me
+that the covariance of X and Y is equal
+
+ align:start position:0%
+that the covariance of X and Y is equal
+ 
+
+ align:start position:0%
+that the covariance of X and Y is equal
+to B * the variance of X.
+
+ align:start position:0%
+to B * the variance of X.
+ 
+
+ align:start position:0%
+to B * the variance of X.
+And so that then that tells me that B
+
+ align:start position:0%
+And so that then that tells me that B
+ 
+
+ align:start position:0%
+And so that then that tells me that B
+is equal to uh coariance
+
+ align:start position:0%
+is equal to uh coariance
+ 
+
+ align:start position:0%
+is equal to uh coariance
+of XY divided by the variance of X. And
+
+ align:start position:0%
+of XY divided by the variance of X. And
+ 
+
+ align:start position:0%
+of XY divided by the variance of X. And
+that's why I actually need the variance
+
+ align:start position:0%
+that's why I actually need the variance
+ 
+
+ align:start position:0%
+that's why I actually need the variance
+of X to be non zero because I couldn't
+
+ align:start position:0%
+of X to be non zero because I couldn't
+ 
+
+ align:start position:0%
+of X to be non zero because I couldn't
+do that otherwise.
+
+ align:start position:0%
+do that otherwise.
+ 
+
+ align:start position:0%
+do that otherwise.
+And because if it was, it would mean
+
+ align:start position:0%
+And because if it was, it would mean
+ 
+
+ align:start position:0%
+And because if it was, it would mean
+that B should be plus infinity, which is
+
+ align:start position:0%
+that B should be plus infinity, which is
+ 
+
+ align:start position:0%
+that B should be plus infinity, which is
+what the limit of this guy is when the
+
+ align:start position:0%
+what the limit of this guy is when the
+ 
+
+ align:start position:0%
+what the limit of this guy is when the
+variance goes to zero. Okay? Or negative
+
+ align:start position:0%
+variance goes to zero. Okay? Or negative
+ 
+
+ align:start position:0%
+variance goes to zero. Okay? Or negative
+infinity. I cannot sort them out.
+
+ align:start position:0%
+infinity. I cannot sort them out.
+ 
+
+ align:start position:0%
+infinity. I cannot sort them out.
+All right? So I'm sorry about the mess,
+
+ align:start position:0%
+All right? So I'm sorry about the mess,
+ 
+
+ align:start position:0%
+All right? So I'm sorry about the mess,
+but uh that should be uh more clear.
+
+ align:start position:0%
+but uh that should be uh more clear.
+ 
+
+ align:start position:0%
+but uh that should be uh more clear.
+Then a of course you can write it as a
+
+ align:start position:0%
+Then a of course you can write it as a
+ 
+
+ align:start position:0%
+Then a of course you can write it as a
+by plugging in the value of b. So you
+
+ align:start position:0%
+by plugging in the value of b. So you
+ 
+
+ align:start position:0%
+by plugging in the value of b. So you
+know it it's only a function of your
+
+ align:start position:0%
+know it it's only a function of your
+ 
+
+ align:start position:0%
+know it it's only a function of your
+distribution, right? So what are the
+
+ align:start position:0%
+distribution, right? So what are the
+ 
+
+ align:start position:0%
+distribution, right? So what are the
+characteristics of the distri? So
+
+ align:start position:0%
+characteristics of the distri? So
+ 
+
+ align:start position:0%
+characteristics of the distri? So
+distribution can have a bunch of things.
+
+ align:start position:0%
+distribution can have a bunch of things.
+ 
+
+ align:start position:0%
+distribution can have a bunch of things.
+It can have moments of order four of
+
+ align:start position:0%
+It can have moments of order four of
+ 
+
+ align:start position:0%
+It can have moments of order four of
+order 26. It can have heavy tails or
+
+ align:start position:0%
+order 26. It can have heavy tails or
+ 
+
+ align:start position:0%
+order 26. It can have heavy tails or
+light tails. But when you compute le
+
+ align:start position:0%
+light tails. But when you compute le
+ 
+
+ align:start position:0%
+light tails. But when you compute le
+squares, the only thing that matters are
+
+ align:start position:0%
+squares, the only thing that matters are
+ 
+
+ align:start position:0%
+squares, the only thing that matters are
+the variance of x, the expectation of
+
+ align:start position:0%
+the variance of x, the expectation of
+ 
+
+ align:start position:0%
+the variance of x, the expectation of
+the individual ones. And really what
+
+ align:start position:0%
+the individual ones. And really what
+ 
+
+ align:start position:0%
+the individual ones. And really what
+captures how y changes when you change x
+
+ align:start position:0%
+captures how y changes when you change x
+ 
+
+ align:start position:0%
+captures how y changes when you change x
+is is captured in the coariance. The
+
+ align:start position:0%
+is is captured in the coariance. The
+ 
+
+ align:start position:0%
+is is captured in the coariance. The
+rest is really just normalization,
+
+ align:start position:0%
+rest is really just normalization,
+ 
+
+ align:start position:0%
+rest is really just normalization,
+right? It's just telling you I want
+
+ align:start position:0%
+right? It's just telling you I want
+ 
+
+ align:start position:0%
+right? It's just telling you I want
+things to cross the y-axis at the right
+
+ align:start position:0%
+things to cross the y-axis at the right
+ 
+
+ align:start position:0%
+things to cross the y-axis at the right
+place. I want things to cross the x-axis
+
+ align:start position:0%
+place. I want things to cross the x-axis
+ 
+
+ align:start position:0%
+place. I want things to cross the x-axis
+at the right place. But the slope is
+
+ align:start position:0%
+at the right place. But the slope is
+ 
+
+ align:start position:0%
+at the right place. But the slope is
+really captured by how much more
+
+ align:start position:0%
+really captured by how much more
+ 
+
+ align:start position:0%
+really captured by how much more
+coariance you have relative to the
+
+ align:start position:0%
+coariance you have relative to the
+ 
+
+ align:start position:0%
+coariance you have relative to the
+variance of x. Okay. So this is
+
+ align:start position:0%
+variance of x. Okay. So this is
+ 
+
+ align:start position:0%
+variance of x. Okay. So this is
+essentially setting the scale for the
+
+ align:start position:0%
+essentially setting the scale for the
+ 
+
+ align:start position:0%
+essentially setting the scale for the
+x-axis and this is telling you for a
+
+ align:start position:0%
+x-axis and this is telling you for a
+ 
+
+ align:start position:0%
+x-axis and this is telling you for a
+unit scale. This is the uh unit of y
+
+ align:start position:0%
+unit scale. This is the uh unit of y
+ 
+
+ align:start position:0%
+unit scale. This is the uh unit of y
+that you're changing.
+
+ align:start position:0%
+that you're changing.
+ 
+
+ align:start position:0%
+that you're changing.
+Okay. So we have explicit forms and what
+
+ align:start position:0%
+Okay. So we have explicit forms and what
+ 
+
+ align:start position:0%
+Okay. So we have explicit forms and what
+I could do if I wanted to estimate those
+
+ align:start position:0%
+I could do if I wanted to estimate those
+ 
+
+ align:start position:0%
+I could do if I wanted to estimate those
+things is just say well again we have
+
+ align:start position:0%
+things is just say well again we have
+ 
+
+ align:start position:0%
+things is just say well again we have
+expectations right the coariance is the
+
+ align:start position:0%
+expectations right the coariance is the
+ 
+
+ align:start position:0%
+expectations right the coariance is the
+expectation of XY minus the product of
+
+ align:start position:0%
+expectation of XY minus the product of
+ 
+
+ align:start position:0%
+expectation of XY minus the product of
+the expectations I could replace
+
+ align:start position:0%
+the expectations I could replace
+ 
+
+ align:start position:0%
+the expectations I could replace
+expectations by averages and get an
+
+ align:start position:0%
+expectations by averages and get an
+ 
+
+ align:start position:0%
+expectations by averages and get an
+empirical coariance just like we can
+
+ align:start position:0%
+empirical coariance just like we can
+ 
+
+ align:start position:0%
+empirical coariance just like we can
+replace the expectations for the
+
+ align:start position:0%
+replace the expectations for the
+ 
+
+ align:start position:0%
+replace the expectations for the
+variance and get a sample coariance and
+
+ align:start position:0%
+variance and get a sample coariance and
+ 
+
+ align:start position:0%
+variance and get a sample coariance and
+this is basically what we're going to be
+
+ align:start position:0%
+this is basically what we're going to be
+ 
+
+ align:start position:0%
+this is basically what we're going to be
+doing all right this is essentially what
+
+ align:start position:0%
+doing all right this is essentially what
+ 
+
+ align:start position:0%
+doing all right this is essentially what
+you want the problem is that if you view
+
+ align:start position:0%
+you want the problem is that if you view
+ 
+
+ align:start position:0%
+you want the problem is that if you view
+it that way you sort of prevent yourself
+
+ align:start position:0%
+it that way you sort of prevent yourself
+ 
+
+ align:start position:0%
+it that way you sort of prevent yourself
+from being able to solve the multivaried
+
+ align:start position:0%
+from being able to solve the multivaried
+ 
+
+ align:start position:0%
+from being able to solve the multivaried
+problem because it's only in the
+
+ align:start position:0%
+problem because it's only in the
+ 
+
+ align:start position:0%
+problem because it's only in the
+univaried problem that you have closed
+
+ align:start position:0%
+univaried problem that you have closed
+ 
+
+ align:start position:0%
+univaried problem that you have closed
+form solutions for your problem. But if
+
+ align:start position:0%
+form solutions for your problem. But if
+ 
+
+ align:start position:0%
+form solutions for your problem. But if
+you actually go to multivariate, this is
+
+ align:start position:0%
+you actually go to multivariate, this is
+ 
+
+ align:start position:0%
+you actually go to multivariate, this is
+not where you want to replace
+
+ align:start position:0%
+not where you want to replace
+ 
+
+ align:start position:0%
+not where you want to replace
+expectations by averages. You actually
+
+ align:start position:0%
+expectations by averages. You actually
+ 
+
+ align:start position:0%
+expectations by averages. You actually
+want to replace expectation by averages
+
+ align:start position:0%
+want to replace expectation by averages
+ 
+
+ align:start position:0%
+want to replace expectation by averages
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And once you do it here, then you can
+
+ align:start position:0%
+And once you do it here, then you can
+ 
+
+ align:start position:0%
+And once you do it here, then you can
+actually just solve the minimization
+
+ align:start position:0%
+actually just solve the minimization
+ 
+
+ align:start position:0%
+actually just solve the minimization
+problem. All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, um,
+
+ align:start position:0%
+Okay. So, um,
+ 
+
+ align:start position:0%
+Okay. So, um,
+one thing that arises from this guy
+
+ align:start position:0%
+one thing that arises from this guy
+ 
+
+ align:start position:0%
+one thing that arises from this guy
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an interesting formula,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Think about it. If I if I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that y is a + b x plus some noise. Now
+
+ align:start position:0%
+that y is a + b x plus some noise. Now
+ 
+
+ align:start position:0%
+that y is a + b x plus some noise. Now
+not things are no longer on the on
+
+ align:start position:0%
+not things are no longer on the on
+ 
+
+ align:start position:0%
+not things are no longer on the on
+something. I have that y is equal to a +
+
+ align:start position:0%
+something. I have that y is equal to a +
+ 
+
+ align:start position:0%
+something. I have that y is equal to a +
+bx plus some noise which is usually
+
+ align:start position:0%
+bx plus some noise which is usually
+ 
+
+ align:start position:0%
+bx plus some noise which is usually
+denoted by epsilon. So that's the
+
+ align:start position:0%
+denoted by epsilon. So that's the
+ 
+
+ align:start position:0%
+denoted by epsilon. So that's the
+distribution right? If I tell you the
+
+ align:start position:0%
+distribution right? If I tell you the
+ 
+
+ align:start position:0%
+distribution right? If I tell you the
+distribution of X and I say Y is a plus
+
+ align:start position:0%
+distribution of X and I say Y is a plus
+ 
+
+ align:start position:0%
+distribution of X and I say Y is a plus
+bx plus epsilon I tell you the
+
+ align:start position:0%
+bx plus epsilon I tell you the
+ 
+
+ align:start position:0%
+bx plus epsilon I tell you the
+distribution of Y and if maybe that
+
+ align:start position:0%
+distribution of Y and if maybe that
+ 
+
+ align:start position:0%
+distribution of Y and if maybe that
+those two are independent you have a
+
+ align:start position:0%
+those two are independent you have a
+ 
+
+ align:start position:0%
+those two are independent you have a
+distribution on Y.
+
+ align:start position:0%
+distribution on Y.
+ 
+
+ align:start position:0%
+distribution on Y.
+So what happens is that I can actually
+
+ align:start position:0%
+So what happens is that I can actually
+ 
+
+ align:start position:0%
+So what happens is that I can actually
+always say well you know this is
+
+ align:start position:0%
+always say well you know this is
+ 
+
+ align:start position:0%
+always say well you know this is
+equivalent to saying that epsilon is
+
+ align:start position:0%
+equivalent to saying that epsilon is
+ 
+
+ align:start position:0%
+equivalent to saying that epsilon is
+equal to y minus a plus bx right
+
+ align:start position:0%
+equal to y minus a plus bx right
+ 
+
+ align:start position:0%
+equal to y minus a plus bx right
+I can always write this it's just uh I
+
+ align:start position:0%
+I can always write this it's just uh I
+ 
+
+ align:start position:0%
+I can always write this it's just uh I
+mean it's the tology
+
+ align:start position:0%
+mean it's the tology
+ 
+
+ align:start position:0%
+mean it's the tology
+but here for those guys this is not for
+
+ align:start position:0%
+but here for those guys this is not for
+ 
+
+ align:start position:0%
+but here for those guys this is not for
+any guy right this is really for the
+
+ align:start position:0%
+any guy right this is really for the
+ 
+
+ align:start position:0%
+any guy right this is really for the
+best fit a and b those ones that satisfy
+
+ align:start position:0%
+best fit a and b those ones that satisfy
+ 
+
+ align:start position:0%
+best fit a and b those ones that satisfy
+this gradient is equal to zero thing
+
+ align:start position:0%
+this gradient is equal to zero thing
+ 
+
+ align:start position:0%
+this gradient is equal to zero thing
+then what we had is that the expectation
+
+ align:start position:0%
+then what we had is that the expectation
+ 
+
+ align:start position:0%
+then what we had is that the expectation
+of epsilon
+
+ align:start position:0%
+of epsilon
+ 
+
+ align:start position:0%
+of epsilon
+was equal to expectation of y minus a +
+
+ align:start position:0%
+was equal to expectation of y minus a +
+ 
+
+ align:start position:0%
+was equal to expectation of y minus a +
+b expectation of x right by linearity of
+
+ align:start position:0%
+b expectation of x right by linearity of
+ 
+
+ align:start position:0%
+b expectation of x right by linearity of
+the expectation which was equal to zero.
+
+ align:start position:0%
+the expectation which was equal to zero.
+ 
+
+ align:start position:0%
+the expectation which was equal to zero.
+So for this best fit
+
+ align:start position:0%
+So for this best fit
+ 
+
+ align:start position:0%
+So for this best fit
+we have zero.
+
+ align:start position:0%
+we have zero.
+ 
+
+ align:start position:0%
+we have zero.
+Now the coariance between x and y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh between sorry x and epsilon
+
+ align:start position:0%
+uh between sorry x and epsilon
+ 
+
+ align:start position:0%
+uh between sorry x and epsilon
+is what? Well, it's the coariance
+
+ align:start position:0%
+is what? Well, it's the coariance
+ 
+
+ align:start position:0%
+is what? Well, it's the coariance
+between X and well epsilon was Y minus A
+
+ align:start position:0%
+between X and well epsilon was Y minus A
+ 
+
+ align:start position:0%
+between X and well epsilon was Y minus A
++ B X.
+
+ align:start position:0%
++ B X.
+ 
+
+ align:start position:0%
++ B X.
+Okay. Now the coariance is by linear. So
+
+ align:start position:0%
+Okay. Now the coariance is by linear. So
+ 
+
+ align:start position:0%
+Okay. Now the coariance is by linear. So
+what I have is that the coariance of
+
+ align:start position:0%
+what I have is that the coariance of
+ 
+
+ align:start position:0%
+what I have is that the coariance of
+this is the coariance of X and time Y
+
+ align:start position:0%
+this is the coariance of X and time Y
+ 
+
+ align:start position:0%
+this is the coariance of X and time Y
+sorry of X and Y minus the coariance
+
+ align:start position:0%
+sorry of X and Y minus the coariance
+ 
+
+ align:start position:0%
+sorry of X and Y minus the coariance
+well minus A + B coariance
+
+ align:start position:0%
+well minus A + B coariance
+ 
+
+ align:start position:0%
+well minus A + B coariance
+of X and X
+
+ align:start position:0%
+of X and X
+ 
+
+ align:start position:0%
+of X and X
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the variance of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coariance of XY minus A plus be co
+
+ align:start position:0%
+coariance of XY minus A plus be co
+ 
+
+ align:start position:0%
+coariance of XY minus A plus be co
+variance of x
+
+ align:start position:0%
+variance of x
+ 
+
+ align:start position:0%
+variance of x
+and let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coariance of uh okay I didn't write it
+
+ align:start position:0%
+coariance of uh okay I didn't write it
+ 
+
+ align:start position:0%
+coariance of uh okay I didn't write it
+so here I have coariance of xy is equal
+
+ align:start position:0%
+so here I have coariance of xy is equal
+ 
+
+ align:start position:0%
+so here I have coariance of xy is equal
+to b variance of x right
+
+ align:start position:0%
+to b variance of x right
+ 
+
+ align:start position:0%
+to b variance of x right
+uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why uh what did Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Coance of XY. Yeah, that's because I
+
+ align:start position:0%
+Coance of XY. Yeah, that's because I
+ 
+
+ align:start position:0%
+Coance of XY. Yeah, that's because I
+cannot do that with the coariance. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah, I have those averages again. Um,
+
+ align:start position:0%
+yeah, I have those averages again. Um,
+ 
+
+ align:start position:0%
+yeah, I have those averages again. Um,
+no, because this is centered, right?
+
+ align:start position:0%
+no, because this is centered, right?
+ 
+
+ align:start position:0%
+no, because this is centered, right?
+Sorry, this is centered. So this is
+
+ align:start position:0%
+Sorry, this is centered. So this is
+ 
+
+ align:start position:0%
+Sorry, this is centered. So this is
+actually equal to the expectation of x *
+
+ align:start position:0%
+actually equal to the expectation of x *
+ 
+
+ align:start position:0%
+actually equal to the expectation of x *
+y - a + bx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the the coariance is equal to the
+
+ align:start position:0%
+right the the coariance is equal to the
+ 
+
+ align:start position:0%
+right the the coariance is equal to the
+product just because this right hand
+
+ align:start position:0%
+product just because this right hand
+ 
+
+ align:start position:0%
+product just because this right hand
+side is actually centered. So this is
+
+ align:start position:0%
+side is actually centered. So this is
+ 
+
+ align:start position:0%
+side is actually centered. So this is
+the expectation of x * y
+
+ align:start position:0%
+the expectation of x * y
+ 
+
+ align:start position:0%
+the expectation of x * y
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+the expectation of a uh * x
+
+ align:start position:0%
+the expectation of a uh * x
+ 
+
+ align:start position:0%
+the expectation of a uh * x
+a * the expectation of x plus b
+
+ align:start position:0%
+a * the expectation of x plus b
+ 
+
+ align:start position:0%
+a * the expectation of x plus b
+minus b * the expectation of x^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well actually maybe I should not really
+
+ align:start position:0%
+Well actually maybe I should not really
+ 
+
+ align:start position:0%
+Well actually maybe I should not really
+go too far.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is actually the one that I need.
+
+ align:start position:0%
+So this is actually the one that I need.
+ 
+
+ align:start position:0%
+So this is actually the one that I need.
+But if I stop here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is actually equal to zero, right?
+
+ align:start position:0%
+this is actually equal to zero, right?
+ 
+
+ align:start position:0%
+this is actually equal to zero, right?
+Those are the same equations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're just saying that if I actually
+
+ align:start position:0%
+So we're just saying that if I actually
+ 
+
+ align:start position:0%
+So we're just saying that if I actually
+believed that this best fit was the one
+
+ align:start position:0%
+believed that this best fit was the one
+ 
+
+ align:start position:0%
+believed that this best fit was the one
+that gave me the right parameters, what
+
+ align:start position:0%
+that gave me the right parameters, what
+ 
+
+ align:start position:0%
+that gave me the right parameters, what
+would that imply on the noise itself on
+
+ align:start position:0%
+would that imply on the noise itself on
+ 
+
+ align:start position:0%
+would that imply on the noise itself on
+this epsilon? So here we're actually
+
+ align:start position:0%
+this epsilon? So here we're actually
+ 
+
+ align:start position:0%
+this epsilon? So here we're actually
+just trying to find some necessary
+
+ align:start position:0%
+just trying to find some necessary
+ 
+
+ align:start position:0%
+just trying to find some necessary
+condition for the noise to hold for the
+
+ align:start position:0%
+condition for the noise to hold for the
+ 
+
+ align:start position:0%
+condition for the noise to hold for the
+noise. And so those conditions are that
+
+ align:start position:0%
+noise. And so those conditions are that
+ 
+
+ align:start position:0%
+noise. And so those conditions are that
+first the expectation is zero. That's
+
+ align:start position:0%
+first the expectation is zero. That's
+ 
+
+ align:start position:0%
+first the expectation is zero. That's
+what we got here. And then that the
+
+ align:start position:0%
+what we got here. And then that the
+ 
+
+ align:start position:0%
+what we got here. And then that the
+coariance between the noise and x has to
+
+ align:start position:0%
+coariance between the noise and x has to
+ 
+
+ align:start position:0%
+coariance between the noise and x has to
+be zero as well. Okay. So those are
+
+ align:start position:0%
+be zero as well. Okay. So those are
+ 
+
+ align:start position:0%
+be zero as well. Okay. So those are
+actually conditions that the noise must
+
+ align:start position:0%
+actually conditions that the noise must
+ 
+
+ align:start position:0%
+actually conditions that the noise must
+satisfy. But the noise was just not
+
+ align:start position:0%
+satisfy. But the noise was just not
+ 
+
+ align:start position:0%
+satisfy. But the noise was just not
+really defined as noise itself. We were
+
+ align:start position:0%
+really defined as noise itself. We were
+ 
+
+ align:start position:0%
+really defined as noise itself. We were
+just saying okay if we're going to put
+
+ align:start position:0%
+just saying okay if we're going to put
+ 
+
+ align:start position:0%
+just saying okay if we're going to put
+some assumptions on X on the epsilon
+
+ align:start position:0%
+some assumptions on X on the epsilon
+ 
+
+ align:start position:0%
+some assumptions on X on the epsilon
+what do we better have? So the first one
+
+ align:start position:0%
+what do we better have? So the first one
+ 
+
+ align:start position:0%
+what do we better have? So the first one
+is that it's centered which is good
+
+ align:start position:0%
+is that it's centered which is good
+ 
+
+ align:start position:0%
+is that it's centered which is good
+because otherwise the noise would shift
+
+ align:start position:0%
+because otherwise the noise would shift
+ 
+
+ align:start position:0%
+because otherwise the noise would shift
+everything. So now when you look at a a
+
+ align:start position:0%
+everything. So now when you look at a a
+ 
+
+ align:start position:0%
+everything. So now when you look at a a
+a linear regression model typically if
+
+ align:start position:0%
+a linear regression model typically if
+ 
+
+ align:start position:0%
+a linear regression model typically if
+you look if you open a book it doesn't
+
+ align:start position:0%
+you look if you open a book it doesn't
+ 
+
+ align:start position:0%
+you look if you open a book it doesn't
+start by saying let the noise be the
+
+ align:start position:0%
+start by saying let the noise be the
+ 
+
+ align:start position:0%
+start by saying let the noise be the
+difference between y and what I actually
+
+ align:start position:0%
+difference between y and what I actually
+ 
+
+ align:start position:0%
+difference between y and what I actually
+want y to be. It says let y be a plus bx
+
+ align:start position:0%
+want y to be. It says let y be a plus bx
+ 
+
+ align:start position:0%
+want y to be. It says let y be a plus bx
+plus epsilon. So conversely if we assume
+
+ align:start position:0%
+plus epsilon. So conversely if we assume
+ 
+
+ align:start position:0%
+plus epsilon. So conversely if we assume
+that this is the model that we have
+
+ align:start position:0%
+that this is the model that we have
+ 
+
+ align:start position:0%
+that this is the model that we have
+then we're going to have to assume that
+
+ align:start position:0%
+then we're going to have to assume that
+ 
+
+ align:start position:0%
+then we're going to have to assume that
+epsilon we're going to assume that
+
+ align:start position:0%
+epsilon we're going to assume that
+ 
+
+ align:start position:0%
+epsilon we're going to assume that
+epsilon is centered and that the
+
+ align:start position:0%
+epsilon is centered and that the
+ 
+
+ align:start position:0%
+epsilon is centered and that the
+coariance between x and epsilon is zero.
+
+ align:start position:0%
+coariance between x and epsilon is zero.
+ 
+
+ align:start position:0%
+coariance between x and epsilon is zero.
+Actually often we're going to assume
+
+ align:start position:0%
+Actually often we're going to assume
+ 
+
+ align:start position:0%
+Actually often we're going to assume
+much more. And one way to ensure that
+
+ align:start position:0%
+much more. And one way to ensure that
+ 
+
+ align:start position:0%
+much more. And one way to ensure that
+those two things are satisfied is to
+
+ align:start position:0%
+those two things are satisfied is to
+ 
+
+ align:start position:0%
+those two things are satisfied is to
+assume that x is independent of epsilon.
+
+ align:start position:0%
+assume that x is independent of epsilon.
+ 
+
+ align:start position:0%
+assume that x is independent of epsilon.
+For example, if you assume that X is
+
+ align:start position:0%
+For example, if you assume that X is
+ 
+
+ align:start position:0%
+For example, if you assume that X is
+independent of epsilon, of course, the
+
+ align:start position:0%
+independent of epsilon, of course, the
+ 
+
+ align:start position:0%
+independent of epsilon, of course, the
+coariance is going to be zero
+
+ align:start position:0%
+coariance is going to be zero
+ 
+
+ align:start position:0%
+coariance is going to be zero
+or we might assume that the conditional
+
+ align:start position:0%
+or we might assume that the conditional
+ 
+
+ align:start position:0%
+or we might assume that the conditional
+expectation of e of epsilon given x is
+
+ align:start position:0%
+expectation of e of epsilon given x is
+ 
+
+ align:start position:0%
+expectation of e of epsilon given x is
+equal to zero. Then that implies that
+
+ align:start position:0%
+equal to zero. Then that implies that
+ 
+
+ align:start position:0%
+equal to zero. Then that implies that
+okay now the fact that it's centered is
+
+ align:start position:0%
+okay now the fact that it's centered is
+ 
+
+ align:start position:0%
+okay now the fact that it's centered is
+one thing. So if we make this
+
+ align:start position:0%
+one thing. So if we make this
+ 
+
+ align:start position:0%
+one thing. So if we make this
+assumption,
+
+ align:start position:0%
+assumption,
+ 
+
+ align:start position:0%
+assumption,
+what the only thing it's telling us is
+
+ align:start position:0%
+what the only thing it's telling us is
+ 
+
+ align:start position:0%
+what the only thing it's telling us is
+that those abs that come right, we
+
+ align:start position:0%
+that those abs that come right, we
+ 
+
+ align:start position:0%
+that those abs that come right, we
+started from there. Y is equal to A plus
+
+ align:start position:0%
+started from there. Y is equal to A plus
+ 
+
+ align:start position:0%
+started from there. Y is equal to A plus
+B X plus some epsilon for some A and
+
+ align:start position:0%
+B X plus some epsilon for some A and
+ 
+
+ align:start position:0%
+B X plus some epsilon for some A and
+some B. What it turns out is that those
+
+ align:start position:0%
+some B. What it turns out is that those
+ 
+
+ align:start position:0%
+some B. What it turns out is that those
+ep's and B's are actually the ones that
+
+ align:start position:0%
+ep's and B's are actually the ones that
+ 
+
+ align:start position:0%
+ep's and B's are actually the ones that
+you would get by solving this
+
+ align:start position:0%
+you would get by solving this
+ 
+
+ align:start position:0%
+you would get by solving this
+expectation of square thing.
+
+ align:start position:0%
+expectation of square thing.
+ 
+
+ align:start position:0%
+expectation of square thing.
+All right. So when you asked back when
+
+ align:start position:0%
+All right. So when you asked back when
+ 
+
+ align:start position:0%
+All right. So when you asked back when
+you were following Yeah. So uh when you
+
+ align:start position:0%
+you were following Yeah. So uh when you
+ 
+
+ align:start position:0%
+you were following Yeah. So uh when you
+asked uh you know why don't we take the
+
+ align:start position:0%
+asked uh you know why don't we take the
+ 
+
+ align:start position:0%
+asked uh you know why don't we take the
+square for example or the power four or
+
+ align:start position:0%
+square for example or the power four or
+ 
+
+ align:start position:0%
+square for example or the power four or
+something like this then here I'm saying
+
+ align:start position:0%
+something like this then here I'm saying
+ 
+
+ align:start position:0%
+something like this then here I'm saying
+well if I have y is equal to a plus bx I
+
+ align:start position:0%
+well if I have y is equal to a plus bx I
+ 
+
+ align:start position:0%
+well if I have y is equal to a plus bx I
+don't actually need to put too much
+
+ align:start position:0%
+don't actually need to put too much
+ 
+
+ align:start position:0%
+don't actually need to put too much
+assumptions on epsilon if epsilon is
+
+ align:start position:0%
+assumptions on epsilon if epsilon is
+ 
+
+ align:start position:0%
+assumptions on epsilon if epsilon is
+actually satisfying those two things
+
+ align:start position:0%
+actually satisfying those two things
+ 
+
+ align:start position:0%
+actually satisfying those two things
+expectation is equal to zero and
+
+ align:start position:0%
+expectation is equal to zero and
+ 
+
+ align:start position:0%
+expectation is equal to zero and
+coariance with x is equal to zero then
+
+ align:start position:0%
+coariance with x is equal to zero then
+ 
+
+ align:start position:0%
+coariance with x is equal to zero then
+the right a and b that I'm looking for
+
+ align:start position:0%
+the right a and b that I'm looking for
+ 
+
+ align:start position:0%
+the right a and b that I'm looking for
+actually the ones that come with the
+
+ align:start position:0%
+actually the ones that come with the
+ 
+
+ align:start position:0%
+actually the ones that come with the
+square not with power four or power 25.
+
+ align:start position:0%
+square not with power four or power 25.
+ 
+
+ align:start position:0%
+square not with power four or power 25.
+Okay, so those are actually pretty weak
+
+ align:start position:0%
+Okay, so those are actually pretty weak
+ 
+
+ align:start position:0%
+Okay, so those are actually pretty weak
+assumptions. If we want to do inference,
+
+ align:start position:0%
+assumptions. If we want to do inference,
+ 
+
+ align:start position:0%
+assumptions. If we want to do inference,
+we're going to have to assume slightly
+
+ align:start position:0%
+we're going to have to assume slightly
+ 
+
+ align:start position:0%
+we're going to have to assume slightly
+more. If we want to use t distributions
+
+ align:start position:0%
+more. If we want to use t distributions
+ 
+
+ align:start position:0%
+more. If we want to use t distributions
+at some point, for example, and we will,
+
+ align:start position:0%
+at some point, for example, and we will,
+ 
+
+ align:start position:0%
+at some point, for example, and we will,
+we're going to have to assume that
+
+ align:start position:0%
+we're going to have to assume that
+ 
+
+ align:start position:0%
+we're going to have to assume that
+epsilon has a Gaussian distribution. So
+
+ align:start position:0%
+epsilon has a Gaussian distribution. So
+ 
+
+ align:start position:0%
+epsilon has a Gaussian distribution. So
+if you want to start doing more
+
+ align:start position:0%
+if you want to start doing more
+ 
+
+ align:start position:0%
+if you want to start doing more
+statistics beyond just like doing this
+
+ align:start position:0%
+statistics beyond just like doing this
+ 
+
+ align:start position:0%
+statistics beyond just like doing this
+le square thing, which is minimizing the
+
+ align:start position:0%
+le square thing, which is minimizing the
+ 
+
+ align:start position:0%
+le square thing, which is minimizing the
+square criterion, you're actually going
+
+ align:start position:0%
+square criterion, you're actually going
+ 
+
+ align:start position:0%
+square criterion, you're actually going
+to have to put more assumptions. But
+
+ align:start position:0%
+to have to put more assumptions. But
+ 
+
+ align:start position:0%
+to have to put more assumptions. But
+right now, we did not need them. we only
+
+ align:start position:0%
+right now, we did not need them. we only
+ 
+
+ align:start position:0%
+right now, we did not need them. we only
+need that epsilon has mean zero and
+
+ align:start position:0%
+need that epsilon has mean zero and
+ 
+
+ align:start position:0%
+need that epsilon has mean zero and
+coariance zero with x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's start with so that was
+
+ align:start position:0%
+Okay, so let's start with so that was
+ 
+
+ align:start position:0%
+Okay, so let's start with so that was
+basically probabilistic, right? We're
+
+ align:start position:0%
+basically probabilistic, right? We're
+ 
+
+ align:start position:0%
+basically probabilistic, right? We're
+trying to say if I were to do
+
+ align:start position:0%
+trying to say if I were to do
+ 
+
+ align:start position:0%
+trying to say if I were to do
+probability and I were trying to model
+
+ align:start position:0%
+probability and I were trying to model
+ 
+
+ align:start position:0%
+probability and I were trying to model
+the relationship between two random
+
+ align:start position:0%
+the relationship between two random
+ 
+
+ align:start position:0%
+the relationship between two random
+variables x and y in the form y is a
+
+ align:start position:0%
+variables x and y in the form y is a
+ 
+
+ align:start position:0%
+variables x and y in the form y is a
+plus bx plus some noise. This is what
+
+ align:start position:0%
+plus bx plus some noise. This is what
+ 
+
+ align:start position:0%
+plus bx plus some noise. This is what
+would come out. Everything was
+
+ align:start position:0%
+would come out. Everything was
+ 
+
+ align:start position:0%
+would come out. Everything was
+expectations. There was no data
+
+ align:start position:0%
+expectations. There was no data
+ 
+
+ align:start position:0%
+expectations. There was no data
+involved. So now let's go to the data
+
+ align:start position:0%
+involved. So now let's go to the data
+ 
+
+ align:start position:0%
+involved. So now let's go to the data
+problem which is now I do not have I do
+
+ align:start position:0%
+problem which is now I do not have I do
+ 
+
+ align:start position:0%
+problem which is now I do not have I do
+not know what the expectations are in
+
+ align:start position:0%
+not know what the expectations are in
+ 
+
+ align:start position:0%
+not know what the expectations are in
+particular I don't know what the
+
+ align:start position:0%
+particular I don't know what the
+ 
+
+ align:start position:0%
+particular I don't know what the
+coariance of x and y is and I don't know
+
+ align:start position:0%
+coariance of x and y is and I don't know
+ 
+
+ align:start position:0%
+coariance of x and y is and I don't know
+what the expectation of x and the
+
+ align:start position:0%
+what the expectation of x and the
+ 
+
+ align:start position:0%
+what the expectation of x and the
+expectation of y of y are so I have data
+
+ align:start position:0%
+expectation of y of y are so I have data
+ 
+
+ align:start position:0%
+expectation of y of y are so I have data
+to do that so how am I going to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I'm just going to say well if I
+
+ align:start position:0%
+well I'm just going to say well if I
+ 
+
+ align:start position:0%
+well I'm just going to say well if I
+want x1 y1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn and yn and I'm going to assume that
+
+ align:start position:0%
+xn and yn and I'm going to assume that
+ 
+
+ align:start position:0%
+xn and yn and I'm going to assume that
+they're iid
+
+ align:start position:0%
+they're iid
+ 
+
+ align:start position:0%
+they're iid
+and I'm actually going to assume that
+
+ align:start position:0%
+and I'm actually going to assume that
+ 
+
+ align:start position:0%
+and I'm actually going to assume that
+they have some model right so I'm going
+
+ align:start position:0%
+they have some model right so I'm going
+ 
+
+ align:start position:0%
+they have some model right so I'm going
+to assume that I have that a so that yi
+
+ align:start position:0%
+to assume that I have that a so that yi
+ 
+
+ align:start position:0%
+to assume that I have that a so that yi
+follows the same model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so epsilon i and I want say that epsil
+
+ align:start position:0%
+so epsilon i and I want say that epsil
+ 
+
+ align:start position:0%
+so epsilon i and I want say that epsil
+expectation of epsilon i is zero and
+
+ align:start position:0%
+expectation of epsilon i is zero and
+ 
+
+ align:start position:0%
+expectation of epsilon i is zero and
+coariance of x i ep epsilon i is equal
+
+ align:start position:0%
+coariance of x i ep epsilon i is equal
+ 
+
+ align:start position:0%
+coariance of x i ep epsilon i is equal
+to zero so I'm going to put the same
+
+ align:start position:0%
+to zero so I'm going to put the same
+ 
+
+ align:start position:0%
+to zero so I'm going to put the same
+model on all the data. So you can see
+
+ align:start position:0%
+model on all the data. So you can see
+ 
+
+ align:start position:0%
+model on all the data. So you can see
+that A is not AI and B is not BI. It's
+
+ align:start position:0%
+that A is not AI and B is not BI. It's
+ 
+
+ align:start position:0%
+that A is not AI and B is not BI. It's
+the same. So as my data increases, I
+
+ align:start position:0%
+the same. So as my data increases, I
+ 
+
+ align:start position:0%
+the same. So as my data increases, I
+should be able to recover the correct
+
+ align:start position:0%
+should be able to recover the correct
+ 
+
+ align:start position:0%
+should be able to recover the correct
+things as the size of my data increases.
+
+ align:start position:0%
+things as the size of my data increases.
+ 
+
+ align:start position:0%
+things as the size of my data increases.
+Okay, so this is what uh the statistical
+
+ align:start position:0%
+Okay, so this is what uh the statistical
+ 
+
+ align:start position:0%
+Okay, so this is what uh the statistical
+problem look like. You're given the
+
+ align:start position:0%
+problem look like. You're given the
+ 
+
+ align:start position:0%
+problem look like. You're given the
+points.
+
+ align:start position:0%
+points.
+ 
+
+ align:start position:0%
+points.
+There is a true line from which this
+
+ align:start position:0%
+There is a true line from which this
+ 
+
+ align:start position:0%
+There is a true line from which this
+point was generated, right? There was
+
+ align:start position:0%
+point was generated, right? There was
+ 
+
+ align:start position:0%
+point was generated, right? There was
+this line. There was a true AB
+
+ align:start position:0%
+this line. There was a true AB
+ 
+
+ align:start position:0%
+this line. There was a true AB
+that I used to draw this plot and that
+
+ align:start position:0%
+that I used to draw this plot and that
+ 
+
+ align:start position:0%
+that I used to draw this plot and that
+was the line. So first I picked an x say
+
+ align:start position:0%
+was the line. So first I picked an x say
+ 
+
+ align:start position:0%
+was the line. So first I picked an x say
+uniformly at random on this interval 0
+
+ align:start position:0%
+uniformly at random on this interval 0
+ 
+
+ align:start position:0%
+uniformly at random on this interval 0
+to two. Let's say that was this one.
+
+ align:start position:0%
+to two. Let's say that was this one.
+ 
+
+ align:start position:0%
+to two. Let's say that was this one.
+Then I I said well I want y to be a plus
+
+ align:start position:0%
+Then I I said well I want y to be a plus
+ 
+
+ align:start position:0%
+Then I I said well I want y to be a plus
+bx. So it should be here. But then I'm
+
+ align:start position:0%
+bx. So it should be here. But then I'm
+ 
+
+ align:start position:0%
+bx. So it should be here. But then I'm
+going to add some noise epsilon to go
+
+ align:start position:0%
+going to add some noise epsilon to go
+ 
+
+ align:start position:0%
+going to add some noise epsilon to go
+away again back from this line.
+
+ align:start position:0%
+away again back from this line.
+ 
+
+ align:start position:0%
+away again back from this line.
+And actually that's actually mean here.
+
+ align:start position:0%
+And actually that's actually mean here.
+ 
+
+ align:start position:0%
+And actually that's actually mean here.
+We actually got two points correct on
+
+ align:start position:0%
+We actually got two points correct on
+ 
+
+ align:start position:0%
+We actually got two points correct on
+this line. So there's basically two
+
+ align:start position:0%
+this line. So there's basically two
+ 
+
+ align:start position:0%
+this line. So there's basically two
+epsilons that were small enough that the
+
+ align:start position:0%
+epsilons that were small enough that the
+ 
+
+ align:start position:0%
+epsilons that were small enough that the
+dots actually look like they're on the
+
+ align:start position:0%
+dots actually look like they're on the
+ 
+
+ align:start position:0%
+dots actually look like they're on the
+line. Everybody's clear about what I'm
+
+ align:start position:0%
+line. Everybody's clear about what I'm
+ 
+
+ align:start position:0%
+line. Everybody's clear about what I'm
+drawing? So now, of course, if you're a
+
+ align:start position:0%
+drawing? So now, of course, if you're a
+ 
+
+ align:start position:0%
+drawing? So now, of course, if you're a
+statistician, you don't see this. You
+
+ align:start position:0%
+statistician, you don't see this. You
+ 
+
+ align:start position:0%
+statistician, you don't see this. You
+only see this. And you have to recover
+
+ align:start position:0%
+only see this. And you have to recover
+ 
+
+ align:start position:0%
+only see this. And you have to recover
+this guy. And it's going to look like
+
+ align:start position:0%
+this guy. And it's going to look like
+ 
+
+ align:start position:0%
+this guy. And it's going to look like
+this, right? You're going to have an
+
+ align:start position:0%
+this, right? You're going to have an
+ 
+
+ align:start position:0%
+this, right? You're going to have an
+estimated line, which is the red one,
+
+ align:start position:0%
+estimated line, which is the red one,
+ 
+
+ align:start position:0%
+estimated line, which is the red one,
+and the blue line, which is the uh uh uh
+
+ align:start position:0%
+and the blue line, which is the uh uh uh
+ 
+
+ align:start position:0%
+and the blue line, which is the uh uh uh
+the true one, the one that actually
+
+ align:start position:0%
+the true one, the one that actually
+ 
+
+ align:start position:0%
+the true one, the one that actually
+generated the data. And your question
+
+ align:start position:0%
+generated the data. And your question
+ 
+
+ align:start position:0%
+generated the data. And your question
+is, well, this line corresponds to some
+
+ align:start position:0%
+is, well, this line corresponds to some
+ 
+
+ align:start position:0%
+is, well, this line corresponds to some
+parameters a hat and b hat. How can I
+
+ align:start position:0%
+parameters a hat and b hat. How can I
+ 
+
+ align:start position:0%
+parameters a hat and b hat. How can I
+make sure that those two lines, how far
+
+ align:start position:0%
+make sure that those two lines, how far
+ 
+
+ align:start position:0%
+make sure that those two lines, how far
+those two lines are? And one way to
+
+ align:start position:0%
+those two lines are? And one way to
+ 
+
+ align:start position:0%
+those two lines are? And one way to
+address this question is to say how far
+
+ align:start position:0%
+address this question is to say how far
+ 
+
+ align:start position:0%
+address this question is to say how far
+is a from a hat and how far is b from b
+
+ align:start position:0%
+is a from a hat and how far is b from b
+ 
+
+ align:start position:0%
+is a from a hat and how far is b from b
+hat. Okay, another question of course
+
+ align:start position:0%
+hat. Okay, another question of course
+ 
+
+ align:start position:0%
+hat. Okay, another question of course
+that you ask is how do you find a hat
+
+ align:start position:0%
+that you ask is how do you find a hat
+ 
+
+ align:start position:0%
+that you ask is how do you find a hat
+and b hat?
+
+ align:start position:0%
+and b hat?
+ 
+
+ align:start position:0%
+and b hat?
+And as you can see it's basically the
+
+ align:start position:0%
+And as you can see it's basically the
+ 
+
+ align:start position:0%
+And as you can see it's basically the
+same thing. Remember what was a? So b
+
+ align:start position:0%
+same thing. Remember what was a? So b
+ 
+
+ align:start position:0%
+same thing. Remember what was a? So b
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+uh the coariance
+
+ align:start position:0%
+uh the coariance
+ 
+
+ align:start position:0%
+uh the coariance
+between x and y
+
+ align:start position:0%
+between x and y
+ 
+
+ align:start position:0%
+between x and y
+divided by the variance of x right we
+
+ align:start position:0%
+divided by the variance of x right we
+ 
+
+ align:start position:0%
+divided by the variance of x right we
+which I can rewrite as the expectation
+
+ align:start position:0%
+which I can rewrite as the expectation
+ 
+
+ align:start position:0%
+which I can rewrite as the expectation
+of xy minus expectation of x time
+
+ align:start position:0%
+of xy minus expectation of x time
+ 
+
+ align:start position:0%
+of xy minus expectation of x time
+expectation of y
+
+ align:start position:0%
+expectation of y
+ 
+
+ align:start position:0%
+expectation of y
+divided by expectation of x^2
+
+ align:start position:0%
+divided by expectation of x^2
+ 
+
+ align:start position:0%
+divided by expectation of x^2
+minus expectation of x the whole thing
+
+ align:start position:0%
+minus expectation of x the whole thing
+ 
+
+ align:start position:0%
+minus expectation of x the whole thing
+square. Okay,
+
+ align:start position:0%
+square. Okay,
+ 
+
+ align:start position:0%
+square. Okay,
+if you look at the expression for B hat,
+
+ align:start position:0%
+if you look at the expression for B hat,
+ 
+
+ align:start position:0%
+if you look at the expression for B hat,
+I basically replaced all the
+
+ align:start position:0%
+I basically replaced all the
+ 
+
+ align:start position:0%
+I basically replaced all the
+expectations by bars,
+
+ align:start position:0%
+expectations by bars,
+ 
+
+ align:start position:0%
+expectations by bars,
+right? So I said, well, this guy I'm
+
+ align:start position:0%
+right? So I said, well, this guy I'm
+ 
+
+ align:start position:0%
+right? So I said, well, this guy I'm
+going to estimate by an average.
+
+ align:start position:0%
+going to estimate by an average.
+ 
+
+ align:start position:0%
+going to estimate by an average.
+So that's the so xy bar
+
+ align:start position:0%
+So that's the so xy bar
+ 
+
+ align:start position:0%
+So that's the so xy bar
+is 1 / n sum from i= 1 to n of x i * yi.
+
+ align:start position:0%
+is 1 / n sum from i= 1 to n of x i * yi.
+ 
+
+ align:start position:0%
+is 1 / n sum from i= 1 to n of x i * yi.
+XAR of course is just the one that we're
+
+ align:start position:0%
+XAR of course is just the one that we're
+ 
+
+ align:start position:0%
+XAR of course is just the one that we're
+used to.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And same for Y bar. X squar bar, the one
+
+ align:start position:0%
+And same for Y bar. X squar bar, the one
+ 
+
+ align:start position:0%
+And same for Y bar. X squar bar, the one
+that's here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the average of the squares. And XAR
+
+ align:start position:0%
+is the average of the squares. And XAR
+ 
+
+ align:start position:0%
+is the average of the squares. And XAR
+square is the square of the average.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so you just basically replace
+
+ align:start position:0%
+Okay, so you just basically replace
+ 
+
+ align:start position:0%
+Okay, so you just basically replace
+this guy by Xbar, this guy by Y bar,
+
+ align:start position:0%
+this guy by Xbar, this guy by Y bar,
+ 
+
+ align:start position:0%
+this guy by Xbar, this guy by Y bar,
+this guy by X² bar, and this guy by Xar
+
+ align:start position:0%
+this guy by X² bar, and this guy by Xar
+ 
+
+ align:start position:0%
+this guy by X² bar, and this guy by Xar
+in the square. Okay, so that's basically
+
+ align:start position:0%
+in the square. Okay, so that's basically
+ 
+
+ align:start position:0%
+in the square. Okay, so that's basically
+one way to do it. Everywhere you see an
+
+ align:start position:0%
+one way to do it. Everywhere you see an
+ 
+
+ align:start position:0%
+one way to do it. Everywhere you see an
+expectation, you replace it by an
+
+ align:start position:0%
+expectation, you replace it by an
+ 
+
+ align:start position:0%
+expectation, you replace it by an
+average. That's the usual statistical
+
+ align:start position:0%
+average. That's the usual statistical
+ 
+
+ align:start position:0%
+average. That's the usual statistical
+hammer. You can actually be slightly
+
+ align:start position:0%
+hammer. You can actually be slightly
+ 
+
+ align:start position:0%
+hammer. You can actually be slightly
+more subtle about this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And as an exercise, I invite you to just
+
+ align:start position:0%
+And as an exercise, I invite you to just
+ 
+
+ align:start position:0%
+And as an exercise, I invite you to just
+to make sure that you know how to do
+
+ align:start position:0%
+to make sure that you know how to do
+ 
+
+ align:start position:0%
+to make sure that you know how to do
+this computation. It's going to be
+
+ align:start position:0%
+this computation. It's going to be
+ 
+
+ align:start position:0%
+this computation. It's going to be
+exactly the same kind of computations
+
+ align:start position:0%
+exactly the same kind of computations
+ 
+
+ align:start position:0%
+exactly the same kind of computations
+that we've done. But uh as an exercise,
+
+ align:start position:0%
+that we've done. But uh as an exercise,
+ 
+
+ align:start position:0%
+that we've done. But uh as an exercise,
+you can check that if you actually look
+
+ align:start position:0%
+you can check that if you actually look
+ 
+
+ align:start position:0%
+you can check that if you actually look
+at say well what I wanted to minimize
+
+ align:start position:0%
+at say well what I wanted to minimize
+ 
+
+ align:start position:0%
+at say well what I wanted to minimize
+here, I had an expectation, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I said, let's minimize this thing.
+
+ align:start position:0%
+And I said, let's minimize this thing.
+ 
+
+ align:start position:0%
+And I said, let's minimize this thing.
+Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's replace this by an average first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now minimize.
+
+ align:start position:0%
+and now minimize.
+ 
+
+ align:start position:0%
+and now minimize.
+Okay. So if I do this, it turns out I'm
+
+ align:start position:0%
+Okay. So if I do this, it turns out I'm
+ 
+
+ align:start position:0%
+Okay. So if I do this, it turns out I'm
+going to actually get the same result.
+
+ align:start position:0%
+going to actually get the same result.
+ 
+
+ align:start position:0%
+going to actually get the same result.
+The minimum of the average is basically
+
+ align:start position:0%
+The minimum of the average is basically
+ 
+
+ align:start position:0%
+The minimum of the average is basically
+this when I replace the average by the
+
+ align:start position:0%
+this when I replace the average by the
+ 
+
+ align:start position:0%
+this when I replace the average by the
+sorry when I replace the expectation by
+
+ align:start position:0%
+sorry when I replace the expectation by
+ 
+
+ align:start position:0%
+sorry when I replace the expectation by
+the average and then minimize it's the
+
+ align:start position:0%
+the average and then minimize it's the
+ 
+
+ align:start position:0%
+the average and then minimize it's the
+same thing as first minimizing and then
+
+ align:start position:0%
+same thing as first minimizing and then
+ 
+
+ align:start position:0%
+same thing as first minimizing and then
+replacing expectation by averages in
+
+ align:start position:0%
+replacing expectation by averages in
+ 
+
+ align:start position:0%
+replacing expectation by averages in
+this case.
+
+ align:start position:0%
+this case.
+ 
+
+ align:start position:0%
+this case.
+Again, this is a much more general
+
+ align:start position:0%
+Again, this is a much more general
+ 
+
+ align:start position:0%
+Again, this is a much more general
+principle because if you don't have a
+
+ align:start position:0%
+principle because if you don't have a
+ 
+
+ align:start position:0%
+principle because if you don't have a
+closed form for the minimum like for
+
+ align:start position:0%
+closed form for the minimum like for
+ 
+
+ align:start position:0%
+closed form for the minimum like for
+some say likelihood problems, well, you
+
+ align:start position:0%
+some say likelihood problems, well, you
+ 
+
+ align:start position:0%
+some say likelihood problems, well, you
+might not actually have a possibility to
+
+ align:start position:0%
+might not actually have a possibility to
+ 
+
+ align:start position:0%
+might not actually have a possibility to
+just look at what the formula looks
+
+ align:start position:0%
+just look at what the formula looks
+ 
+
+ align:start position:0%
+just look at what the formula looks
+like, see where the expectations show up
+
+ align:start position:0%
+like, see where the expectations show up
+ 
+
+ align:start position:0%
+like, see where the expectations show up
+and then just plug in the averages
+
+ align:start position:0%
+and then just plug in the averages
+ 
+
+ align:start position:0%
+and then just plug in the averages
+instead. So, you might this is the one
+
+ align:start position:0%
+instead. So, you might this is the one
+ 
+
+ align:start position:0%
+instead. So, you might this is the one
+you want to keep in mind. And again as
+
+ align:start position:0%
+you want to keep in mind. And again as
+ 
+
+ align:start position:0%
+you want to keep in mind. And again as
+an exercise.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So here and then you do
+
+ align:start position:0%
+Okay. So here and then you do
+ 
+
+ align:start position:0%
+Okay. So here and then you do
+expectation replace by averages
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that's the same answer and I
+
+ align:start position:0%
+and then that's the same answer and I
+ 
+
+ align:start position:0%
+and then that's the same answer and I
+I encourage you to solve the exercise.
+
+ align:start position:0%
+I encourage you to solve the exercise.
+ 
+
+ align:start position:0%
+I encourage you to solve the exercise.
+Okay, everybody's clear that this is
+
+ align:start position:0%
+Okay, everybody's clear that this is
+ 
+
+ align:start position:0%
+Okay, everybody's clear that this is
+actually the same expression for a hat
+
+ align:start position:0%
+actually the same expression for a hat
+ 
+
+ align:start position:0%
+actually the same expression for a hat
+and b hat that we had before where we
+
+ align:start position:0%
+and b hat that we had before where we
+ 
+
+ align:start position:0%
+and b hat that we had before where we
+that we had for a and b when we replace
+
+ align:start position:0%
+that we had for a and b when we replace
+ 
+
+ align:start position:0%
+that we had for a and b when we replace
+the expectations by averages
+
+ align:start position:0%
+the expectations by averages
+ 
+
+ align:start position:0%
+the expectations by averages
+here. By the way, I minimize the sum
+
+ align:start position:0%
+here. By the way, I minimize the sum
+ 
+
+ align:start position:0%
+here. By the way, I minimize the sum
+rather than the average. It's clear to
+
+ align:start position:0%
+rather than the average. It's clear to
+ 
+
+ align:start position:0%
+rather than the average. It's clear to
+everyone that this is the same thing.
+
+ align:start position:0%
+everyone that this is the same thing.
+ 
+
+ align:start position:0%
+everyone that this is the same thing.
+Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we did switch the derivative and the
+
+ align:start position:0%
+So we did switch the derivative and the
+ 
+
+ align:start position:0%
+So we did switch the derivative and the
+expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before you came I think.
+
+ align:start position:0%
+before you came I think.
+ 
+
+ align:start position:0%
+before you came I think.
+Um all right so indeed the picture was
+
+ align:start position:0%
+Um all right so indeed the picture was
+ 
+
+ align:start position:0%
+Um all right so indeed the picture was
+the one that we said. So visually this
+
+ align:start position:0%
+the one that we said. So visually this
+ 
+
+ align:start position:0%
+the one that we said. So visually this
+is what we're doing. We're looking among
+
+ align:start position:0%
+is what we're doing. We're looking among
+ 
+
+ align:start position:0%
+is what we're doing. We're looking among
+all the lines. For each line, we compute
+
+ align:start position:0%
+all the lines. For each line, we compute
+ 
+
+ align:start position:0%
+all the lines. For each line, we compute
+this distance, right? So, if I gave you
+
+ align:start position:0%
+this distance, right? So, if I gave you
+ 
+
+ align:start position:0%
+this distance, right? So, if I gave you
+another line, there would be another set
+
+ align:start position:0%
+another line, there would be another set
+ 
+
+ align:start position:0%
+another line, there would be another set
+of arrows. You look at their length. You
+
+ align:start position:0%
+of arrows. You look at their length. You
+ 
+
+ align:start position:0%
+of arrows. You look at their length. You
+square it, and then you sum it all, and
+
+ align:start position:0%
+square it, and then you sum it all, and
+ 
+
+ align:start position:0%
+square it, and then you sum it all, and
+you find the line that has the minimum
+
+ align:start position:0%
+you find the line that has the minimum
+ 
+
+ align:start position:0%
+you find the line that has the minimum
+sum of squared length of the arrows. All
+
+ align:start position:0%
+sum of squared length of the arrows. All
+ 
+
+ align:start position:0%
+sum of squared length of the arrows. All
+right? And those are the arrows that
+
+ align:start position:0%
+right? And those are the arrows that
+ 
+
+ align:start position:0%
+right? And those are the arrows that
+we're looking at. But again, you could
+
+ align:start position:0%
+we're looking at. But again, you could
+ 
+
+ align:start position:0%
+we're looking at. But again, you could
+actually think of other distances and
+
+ align:start position:0%
+actually think of other distances and
+ 
+
+ align:start position:0%
+actually think of other distances and
+you would actually get different uh you
+
+ align:start position:0%
+you would actually get different uh you
+ 
+
+ align:start position:0%
+you would actually get different uh you
+could actually get different solutions,
+
+ align:start position:0%
+could actually get different solutions,
+ 
+
+ align:start position:0%
+could actually get different solutions,
+right? So there's something called mean
+
+ align:start position:0%
+right? So there's something called mean
+ 
+
+ align:start position:0%
+right? So there's something called mean
+absolute deviation which rather than
+
+ align:start position:0%
+absolute deviation which rather than
+ 
+
+ align:start position:0%
+absolute deviation which rather than
+minimizing this thing is actually
+
+ align:start position:0%
+minimizing this thing is actually
+ 
+
+ align:start position:0%
+minimizing this thing is actually
+minimizing the sum from i= 1 to n of the
+
+ align:start position:0%
+minimizing the sum from i= 1 to n of the
+ 
+
+ align:start position:0%
+minimizing the sum from i= 1 to n of the
+absolute value of y minus a + bx i
+
+ align:start position:0%
+absolute value of y minus a + bx i
+ 
+
+ align:start position:0%
+absolute value of y minus a + bx i
+and that will that's not something for
+
+ align:start position:0%
+and that will that's not something for
+ 
+
+ align:start position:0%
+and that will that's not something for
+which you're going to have a closed form
+
+ align:start position:0%
+which you're going to have a closed form
+ 
+
+ align:start position:0%
+which you're going to have a closed form
+as you can imagine uh you might have
+
+ align:start position:0%
+as you can imagine uh you might have
+ 
+
+ align:start position:0%
+as you can imagine uh you might have
+something that's sort of implicit uh but
+
+ align:start position:0%
+something that's sort of implicit uh but
+ 
+
+ align:start position:0%
+something that's sort of implicit uh but
+you can actually still solve it
+
+ align:start position:0%
+you can actually still solve it
+ 
+
+ align:start position:0%
+you can actually still solve it
+numerically and this is something that
+
+ align:start position:0%
+numerically and this is something that
+ 
+
+ align:start position:0%
+numerically and this is something that
+people also like to use but way way less
+
+ align:start position:0%
+people also like to use but way way less
+ 
+
+ align:start position:0%
+people also like to use but way way less
+than the le squares
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What did I just what?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The sum of the absolute values of y i
+
+ align:start position:0%
+The sum of the absolute values of y i
+ 
+
+ align:start position:0%
+The sum of the absolute values of y i
+minus a plus bx i.
+
+ align:start position:0%
+minus a plus bx i.
+ 
+
+ align:start position:0%
+minus a plus bx i.
+So it's the same except that I don't
+
+ align:start position:0%
+So it's the same except that I don't
+ 
+
+ align:start position:0%
+So it's the same except that I don't
+have the square here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So arguably, you know, predicting uh
+
+ align:start position:0%
+So arguably, you know, predicting uh
+ 
+
+ align:start position:0%
+So arguably, you know, predicting uh
+price uh a demand based on price is a
+
+ align:start position:0%
+price uh a demand based on price is a
+ 
+
+ align:start position:0%
+price uh a demand based on price is a
+fairly naive problem. Typically, what we
+
+ align:start position:0%
+fairly naive problem. Typically, what we
+ 
+
+ align:start position:0%
+fairly naive problem. Typically, what we
+have is a bunch of data that we've
+
+ align:start position:0%
+have is a bunch of data that we've
+ 
+
+ align:start position:0%
+have is a bunch of data that we've
+collected and we're hoping that together
+
+ align:start position:0%
+collected and we're hoping that together
+ 
+
+ align:start position:0%
+collected and we're hoping that together
+they can help us do a better prediction.
+
+ align:start position:0%
+they can help us do a better prediction.
+ 
+
+ align:start position:0%
+they can help us do a better prediction.
+All right, so maybe I don't have only
+
+ align:start position:0%
+All right, so maybe I don't have only
+ 
+
+ align:start position:0%
+All right, so maybe I don't have only
+the price, but uh maybe I have a bunch
+
+ align:start position:0%
+the price, but uh maybe I have a bunch
+ 
+
+ align:start position:0%
+the price, but uh maybe I have a bunch
+of other social uh indicators. Maybe I
+
+ align:start position:0%
+of other social uh indicators. Maybe I
+ 
+
+ align:start position:0%
+of other social uh indicators. Maybe I
+know the competi competition, the price
+
+ align:start position:0%
+know the competi competition, the price
+ 
+
+ align:start position:0%
+know the competi competition, the price
+of the competition. Maybe I know a bunch
+
+ align:start position:0%
+of the competition. Maybe I know a bunch
+ 
+
+ align:start position:0%
+of the competition. Maybe I know a bunch
+of other things that are actually
+
+ align:start position:0%
+of other things that are actually
+ 
+
+ align:start position:0%
+of other things that are actually
+relevant. And so I'm trying to find a
+
+ align:start position:0%
+relevant. And so I'm trying to find a
+ 
+
+ align:start position:0%
+relevant. And so I'm trying to find a
+way to combine a bunch of points, a
+
+ align:start position:0%
+way to combine a bunch of points, a
+ 
+
+ align:start position:0%
+way to combine a bunch of points, a
+bunch of measures. Let's say for
+
+ align:start position:0%
+bunch of measures. Let's say for
+ 
+
+ align:start position:0%
+bunch of measures. Let's say for
+example, there's a nice example that I
+
+ align:start position:0%
+example, there's a nice example that I
+ 
+
+ align:start position:0%
+example, there's a nice example that I
+like, which is uh uh people were trying
+
+ align:start position:0%
+like, which is uh uh people were trying
+ 
+
+ align:start position:0%
+like, which is uh uh people were trying
+to measure um something related to uh
+
+ align:start position:0%
+to measure um something related to uh
+ 
+
+ align:start position:0%
+to measure um something related to uh
+your body mass index. It's so basically
+
+ align:start position:0%
+your body mass index. It's so basically
+ 
+
+ align:start position:0%
+your body mass index. It's so basically
+the volume of your the density of your
+
+ align:start position:0%
+the volume of your the density of your
+ 
+
+ align:start position:0%
+the volume of your the density of your
+body and the way you can do this is by
+
+ align:start position:0%
+body and the way you can do this is by
+ 
+
+ align:start position:0%
+body and the way you can do this is by
+just you know really weighing someone
+
+ align:start position:0%
+just you know really weighing someone
+ 
+
+ align:start position:0%
+just you know really weighing someone
+and also putting them in some you know
+
+ align:start position:0%
+and also putting them in some you know
+ 
+
+ align:start position:0%
+and also putting them in some you know
+cubic meter of water and see how much
+
+ align:start position:0%
+cubic meter of water and see how much
+ 
+
+ align:start position:0%
+cubic meter of water and see how much
+overflows and then you have both the
+
+ align:start position:0%
+overflows and then you have both the
+ 
+
+ align:start position:0%
+overflows and then you have both the
+volume and the uh and um uh uh and the
+
+ align:start position:0%
+volume and the uh and um uh uh and the
+ 
+
+ align:start position:0%
+volume and the uh and um uh uh and the
+mass of this person and you can you know
+
+ align:start position:0%
+mass of this person and you can you know
+ 
+
+ align:start position:0%
+mass of this person and you can you know
+start computing density but uh as you
+
+ align:start position:0%
+start computing density but uh as you
+ 
+
+ align:start position:0%
+start computing density but uh as you
+can imagine you know I would not
+
+ align:start position:0%
+can imagine you know I would not
+ 
+
+ align:start position:0%
+can imagine you know I would not
+personally like to go to a gym where the
+
+ align:start position:0%
+personally like to go to a gym where the
+ 
+
+ align:start position:0%
+personally like to go to a gym where the
+first thing they ask is to just go in
+
+ align:start position:0%
+first thing they ask is to just go in
+ 
+
+ align:start position:0%
+first thing they ask is to just go in
+some uh uh bucket of water. And so
+
+ align:start position:0%
+some uh uh bucket of water. And so
+ 
+
+ align:start position:0%
+some uh uh bucket of water. And so
+people try to find ways to measure this
+
+ align:start position:0%
+people try to find ways to measure this
+ 
+
+ align:start position:0%
+people try to find ways to measure this
+based on other indicators that are much
+
+ align:start position:0%
+based on other indicators that are much
+ 
+
+ align:start position:0%
+based on other indicators that are much
+easier to measure. For example, I don't
+
+ align:start position:0%
+easier to measure. For example, I don't
+ 
+
+ align:start position:0%
+easier to measure. For example, I don't
+know, the length of my forearm and the
+
+ align:start position:0%
+know, the length of my forearm and the
+ 
+
+ align:start position:0%
+know, the length of my forearm and the
+circumference of my head and maybe from
+
+ align:start position:0%
+circumference of my head and maybe from
+ 
+
+ align:start position:0%
+circumference of my head and maybe from
+maybe my my belly would probably be more
+
+ align:start position:0%
+maybe my my belly would probably be more
+ 
+
+ align:start position:0%
+maybe my my belly would probably be more
+appropriate here. And so, you know, they
+
+ align:start position:0%
+appropriate here. And so, you know, they
+ 
+
+ align:start position:0%
+appropriate here. And so, you know, they
+just try to find something that actually
+
+ align:start position:0%
+just try to find something that actually
+ 
+
+ align:start position:0%
+just try to find something that actually
+makes sense. And so there's actually a
+
+ align:start position:0%
+makes sense. And so there's actually a
+ 
+
+ align:start position:0%
+makes sense. And so there's actually a
+nice example where you can show that if
+
+ align:start position:0%
+nice example where you can show that if
+ 
+
+ align:start position:0%
+nice example where you can show that if
+you measure I think one of the most
+
+ align:start position:0%
+you measure I think one of the most
+ 
+
+ align:start position:0%
+you measure I think one of the most
+significant was with the circumference
+
+ align:start position:0%
+significant was with the circumference
+ 
+
+ align:start position:0%
+significant was with the circumference
+of your wrist. This is actually a very
+
+ align:start position:0%
+of your wrist. This is actually a very
+ 
+
+ align:start position:0%
+of your wrist. This is actually a very
+good indicator of uh your uh your uh
+
+ align:start position:0%
+good indicator of uh your uh your uh
+ 
+
+ align:start position:0%
+good indicator of uh your uh your uh
+body density. And uh it turns out that
+
+ align:start position:0%
+body density. And uh it turns out that
+ 
+
+ align:start position:0%
+body density. And uh it turns out that
+um if you stuff all the bunch of things
+
+ align:start position:0%
+um if you stuff all the bunch of things
+ 
+
+ align:start position:0%
+um if you stuff all the bunch of things
+together, you might actually get a very
+
+ align:start position:0%
+together, you might actually get a very
+ 
+
+ align:start position:0%
+together, you might actually get a very
+good formula that explains things. All
+
+ align:start position:0%
+good formula that explains things. All
+ 
+
+ align:start position:0%
+good formula that explains things. All
+right. So what we're going to do is
+
+ align:start position:0%
+right. So what we're going to do is
+ 
+
+ align:start position:0%
+right. So what we're going to do is
+rather than saying we have only one x to
+
+ align:start position:0%
+rather than saying we have only one x to
+ 
+
+ align:start position:0%
+rather than saying we have only one x to
+explain y's, let's say we have 20 x's
+
+ align:start position:0%
+explain y's, let's say we have 20 x's
+ 
+
+ align:start position:0%
+explain y's, let's say we have 20 x's
+that we're trying to combine to explain
+
+ align:start position:0%
+that we're trying to combine to explain
+ 
+
+ align:start position:0%
+that we're trying to combine to explain
+why. And again, just like assuming
+
+ align:start position:0%
+why. And again, just like assuming
+ 
+
+ align:start position:0%
+why. And again, just like assuming
+something of the form y is a plus b * x
+
+ align:start position:0%
+something of the form y is a plus b * x
+ 
+
+ align:start position:0%
+something of the form y is a plus b * x
+was the simplest thing we could do here.
+
+ align:start position:0%
+was the simplest thing we could do here.
+ 
+
+ align:start position:0%
+was the simplest thing we could do here.
+We're just going to assume that we have
+
+ align:start position:0%
+We're just going to assume that we have
+ 
+
+ align:start position:0%
+We're just going to assume that we have
+y is a + b1 x1 plus b2 x2 plus b3 x3.
+
+ align:start position:0%
+y is a + b1 x1 plus b2 x2 plus b3 x3.
+ 
+
+ align:start position:0%
+y is a + b1 x1 plus b2 x2 plus b3 x3.
+And we can write it in a vector form by
+
+ align:start position:0%
+And we can write it in a vector form by
+ 
+
+ align:start position:0%
+And we can write it in a vector form by
+writing that yi is x i transpose b which
+
+ align:start position:0%
+writing that yi is x i transpose b which
+ 
+
+ align:start position:0%
+writing that yi is x i transpose b which
+is now a vector plus epsilon i. Okay.
+
+ align:start position:0%
+is now a vector plus epsilon i. Okay.
+ 
+
+ align:start position:0%
+is now a vector plus epsilon i. Okay.
+And here on the board I'm going to have
+
+ align:start position:0%
+And here on the board I'm going to have
+ 
+
+ align:start position:0%
+And here on the board I'm going to have
+a right hard time doing boldface but all
+
+ align:start position:0%
+a right hard time doing boldface but all
+ 
+
+ align:start position:0%
+a right hard time doing boldface but all
+these things are vectors right except
+
+ align:start position:0%
+these things are vectors right except
+ 
+
+ align:start position:0%
+these things are vectors right except
+for y
+
+ align:start position:0%
+for y
+ 
+
+ align:start position:0%
+for y
+which is a number right? Yi is a number.
+
+ align:start position:0%
+which is a number right? Yi is a number.
+ 
+
+ align:start position:0%
+which is a number right? Yi is a number.
+it's always the value of my y-axis.
+
+ align:start position:0%
+it's always the value of my y-axis.
+ 
+
+ align:start position:0%
+it's always the value of my y-axis.
+Okay? So even if my x-axis lives on this
+
+ align:start position:0%
+Okay? So even if my x-axis lives on this
+ 
+
+ align:start position:0%
+Okay? So even if my x-axis lives on this
+is x1 and this is x2, y is really just
+
+ align:start position:0%
+is x1 and this is x2, y is really just
+ 
+
+ align:start position:0%
+is x1 and this is x2, y is really just
+the real valued function. And so I'm
+
+ align:start position:0%
+the real valued function. And so I'm
+ 
+
+ align:start position:0%
+the real valued function. And so I'm
+going to get a bunch of points x1 y1 and
+
+ align:start position:0%
+going to get a bunch of points x1 y1 and
+ 
+
+ align:start position:0%
+going to get a bunch of points x1 y1 and
+I'm going to see how much they respond.
+
+ align:start position:0%
+I'm going to see how much they respond.
+ 
+
+ align:start position:0%
+I'm going to see how much they respond.
+Right? So for example, it's the my body
+
+ align:start position:0%
+Right? So for example, it's the my body
+ 
+
+ align:start position:0%
+Right? So for example, it's the my body
+density is y and then all the x's are a
+
+ align:start position:0%
+density is y and then all the x's are a
+ 
+
+ align:start position:0%
+density is y and then all the x's are a
+bunch of other things. Agreed with that?
+
+ align:start position:0%
+bunch of other things. Agreed with that?
+ 
+
+ align:start position:0%
+bunch of other things. Agreed with that?
+So this is an equation that holds on the
+
+ align:start position:0%
+So this is an equation that holds on the
+ 
+
+ align:start position:0%
+So this is an equation that holds on the
+real line. But this guy here is in R
+
+ align:start position:0%
+real line. But this guy here is in R
+ 
+
+ align:start position:0%
+real line. But this guy here is in R
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+and this guy is in RP.
+
+ align:start position:0%
+and this guy is in RP.
+ 
+
+ align:start position:0%
+and this guy is in RP.
+It's actually common to talk to to call
+
+ align:start position:0%
+It's actually common to talk to to call
+ 
+
+ align:start position:0%
+It's actually common to talk to to call
+B beta when it's a vector and that's the
+
+ align:start position:0%
+B beta when it's a vector and that's the
+ 
+
+ align:start position:0%
+B beta when it's a vector and that's the
+usual
+
+ align:start position:0%
+usual
+ 
+
+ align:start position:0%
+usual
+that's the usual linear regression
+
+ align:start position:0%
+that's the usual linear regression
+ 
+
+ align:start position:0%
+that's the usual linear regression
+notation. Y is X beta plus epsilon.
+
+ align:start position:0%
+notation. Y is X beta plus epsilon.
+ 
+
+ align:start position:0%
+notation. Y is X beta plus epsilon.
+So X's are called explanatory variables.
+
+ align:start position:0%
+So X's are called explanatory variables.
+ 
+
+ align:start position:0%
+So X's are called explanatory variables.
+Y is called explain variable or
+
+ align:start position:0%
+Y is called explain variable or
+ 
+
+ align:start position:0%
+Y is called explain variable or
+dependent variable
+
+ align:start position:0%
+dependent variable
+ 
+
+ align:start position:0%
+dependent variable
+uh or response variable. It has a bunch
+
+ align:start position:0%
+uh or response variable. It has a bunch
+ 
+
+ align:start position:0%
+uh or response variable. It has a bunch
+of names. You can use whatever you think
+
+ align:start position:0%
+of names. You can use whatever you think
+ 
+
+ align:start position:0%
+of names. You can use whatever you think
+feel more comfortable with. They should
+
+ align:start position:0%
+feel more comfortable with. They should
+ 
+
+ align:start position:0%
+feel more comfortable with. They should
+it should actually be explicit, right?
+
+ align:start position:0%
+it should actually be explicit, right?
+ 
+
+ align:start position:0%
+it should actually be explicit, right?
+So that's all you care about. Um
+
+ align:start position:0%
+So that's all you care about. Um
+ 
+
+ align:start position:0%
+So that's all you care about. Um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+what we typically do is that rather so
+
+ align:start position:0%
+what we typically do is that rather so
+ 
+
+ align:start position:0%
+what we typically do is that rather so
+you notice here that there's actually no
+
+ align:start position:0%
+you notice here that there's actually no
+ 
+
+ align:start position:0%
+you notice here that there's actually no
+intercept. If I actually fold that back
+
+ align:start position:0%
+intercept. If I actually fold that back
+ 
+
+ align:start position:0%
+intercept. If I actually fold that back
+down to one dimension, there's actually
+
+ align:start position:0%
+down to one dimension, there's actually
+ 
+
+ align:start position:0%
+down to one dimension, there's actually
+a is equal to zero. Right? If I go back
+
+ align:start position:0%
+a is equal to zero. Right? If I go back
+ 
+
+ align:start position:0%
+a is equal to zero. Right? If I go back
+to P is equal to 1,
+
+ align:start position:0%
+to P is equal to 1,
+ 
+
+ align:start position:0%
+to P is equal to 1,
+that would imply that yi is well say
+
+ align:start position:0%
+that would imply that yi is well say
+ 
+
+ align:start position:0%
+that would imply that yi is well say
+beta * x plus epsilon i. And that's not
+
+ align:start position:0%
+beta * x plus epsilon i. And that's not
+ 
+
+ align:start position:0%
+beta * x plus epsilon i. And that's not
+good. I want to have an intercept. And
+
+ align:start position:0%
+good. I want to have an intercept. And
+ 
+
+ align:start position:0%
+good. I want to have an intercept. And
+the way I do this rather than writing a
+
+ align:start position:0%
+the way I do this rather than writing a
+ 
+
+ align:start position:0%
+the way I do this rather than writing a
+plus this and you know just have like a
+
+ align:start position:0%
+plus this and you know just have like a
+ 
+
+ align:start position:0%
+plus this and you know just have like a
+an overload of notation. What I'm
+
+ align:start position:0%
+an overload of notation. What I'm
+ 
+
+ align:start position:0%
+an overload of notation. What I'm
+actually doing is that I fold back I
+
+ align:start position:0%
+actually doing is that I fold back I
+ 
+
+ align:start position:0%
+actually doing is that I fold back I
+fold my intercept back into my x.
+
+ align:start position:0%
+fold my intercept back into my x.
+ 
+
+ align:start position:0%
+fold my intercept back into my x.
+And so if I measure 20 variables, I'm
+
+ align:start position:0%
+And so if I measure 20 variables, I'm
+ 
+
+ align:start position:0%
+And so if I measure 20 variables, I'm
+going to create a 21st variable which is
+
+ align:start position:0%
+going to create a 21st variable which is
+ 
+
+ align:start position:0%
+going to create a 21st variable which is
+always equal to one. Okay? So you should
+
+ align:start position:0%
+always equal to one. Okay? So you should
+ 
+
+ align:start position:0%
+always equal to one. Okay? So you should
+need to think of x as being one and then
+
+ align:start position:0%
+need to think of x as being one and then
+ 
+
+ align:start position:0%
+need to think of x as being one and then
+x1
+
+ align:start position:0%
+x1
+ 
+
+ align:start position:0%
+x1
+x p and now sorry xp minus one I guess.
+
+ align:start position:0%
+x p and now sorry xp minus one I guess.
+ 
+
+ align:start position:0%
+x p and now sorry xp minus one I guess.
+Okay. And now this is in RP.
+
+ align:start position:0%
+Okay. And now this is in RP.
+ 
+
+ align:start position:0%
+Okay. And now this is in RP.
+Okay. So the we I'm always going to
+
+ align:start position:0%
+Okay. So the we I'm always going to
+ 
+
+ align:start position:0%
+Okay. So the we I'm always going to
+assume that the first one is one. I can
+
+ align:start position:0%
+assume that the first one is one. I can
+ 
+
+ align:start position:0%
+assume that the first one is one. I can
+always do that. If I have a table of
+
+ align:start position:0%
+always do that. If I have a table of
+ 
+
+ align:start position:0%
+always do that. If I have a table of
+data, if my data is given to me in an
+
+ align:start position:0%
+data, if my data is given to me in an
+ 
+
+ align:start position:0%
+data, if my data is given to me in an
+Excel spreadsheet
+
+ align:start position:0%
+Excel spreadsheet
+ 
+
+ align:start position:0%
+Excel spreadsheet
+and here I have the density that I
+
+ align:start position:0%
+and here I have the density that I
+ 
+
+ align:start position:0%
+and here I have the density that I
+measured on my data and then maybe here
+
+ align:start position:0%
+measured on my data and then maybe here
+ 
+
+ align:start position:0%
+measured on my data and then maybe here
+I have the height and here I have the
+
+ align:start position:0%
+I have the height and here I have the
+ 
+
+ align:start position:0%
+I have the height and here I have the
+wrists circumference. And I have all
+
+ align:start position:0%
+wrists circumference. And I have all
+ 
+
+ align:start position:0%
+wrists circumference. And I have all
+these things. All I have to do is to
+
+ align:start position:0%
+these things. All I have to do is to
+ 
+
+ align:start position:0%
+these things. All I have to do is to
+create another column here of ones. I
+
+ align:start position:0%
+create another column here of ones. I
+ 
+
+ align:start position:0%
+create another column here of ones. I
+just put one, one, one, one, one, one.
+
+ align:start position:0%
+just put one, one, one, one, one, one.
+ 
+
+ align:start position:0%
+just put one, one, one, one, one, one.
+Okay, that's all I have to do to create
+
+ align:start position:0%
+Okay, that's all I have to do to create
+ 
+
+ align:start position:0%
+Okay, that's all I have to do to create
+this guy. Agreed?
+
+ align:start position:0%
+this guy. Agreed?
+ 
+
+ align:start position:0%
+this guy. Agreed?
+And now my x is going to be just one of
+
+ align:start position:0%
+And now my x is going to be just one of
+ 
+
+ align:start position:0%
+And now my x is going to be just one of
+those rows.
+
+ align:start position:0%
+those rows.
+ 
+
+ align:start position:0%
+those rows.
+Okay, so that's this is x i this entire
+
+ align:start position:0%
+Okay, so that's this is x i this entire
+ 
+
+ align:start position:0%
+Okay, so that's this is x i this entire
+row and this entry here is yi.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now for my noise coefficients, I'm
+
+ align:start position:0%
+So now for my noise coefficients, I'm
+ 
+
+ align:start position:0%
+So now for my noise coefficients, I'm
+still going to assume ask for the same
+
+ align:start position:0%
+still going to assume ask for the same
+ 
+
+ align:start position:0%
+still going to assume ask for the same
+thing except that here the covariance is
+
+ align:start position:0%
+thing except that here the covariance is
+ 
+
+ align:start position:0%
+thing except that here the covariance is
+not between X between one random
+
+ align:start position:0%
+not between X between one random
+ 
+
+ align:start position:0%
+not between X between one random
+variable and and another random variable
+
+ align:start position:0%
+variable and and another random variable
+ 
+
+ align:start position:0%
+variable and and another random variable
+is between a random vector and a random
+
+ align:start position:0%
+is between a random vector and a random
+ 
+
+ align:start position:0%
+is between a random vector and a random
+variable.
+
+ align:start position:0%
+variable.
+ 
+
+ align:start position:0%
+variable.
+Okay, how do I measure the coariance
+
+ align:start position:0%
+Okay, how do I measure the coariance
+ 
+
+ align:start position:0%
+Okay, how do I measure the coariance
+between a vector and a random variable?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. So basically well okay uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so yeah I mean you know coance
+
+ align:start position:0%
+yeah so yeah I mean you know coance
+ 
+
+ align:start position:0%
+yeah so yeah I mean you know coance
+vector is equal to zero is the same
+
+ align:start position:0%
+vector is equal to zero is the same
+ 
+
+ align:start position:0%
+vector is equal to zero is the same
+thing as it norm equal to zero but yeah
+
+ align:start position:0%
+thing as it norm equal to zero but yeah
+ 
+
+ align:start position:0%
+thing as it norm equal to zero but yeah
+this is basically thought of entry-wise
+
+ align:start position:0%
+this is basically thought of entry-wise
+ 
+
+ align:start position:0%
+this is basically thought of entry-wise
+for each coordinate of x I want that the
+
+ align:start position:0%
+for each coordinate of x I want that the
+ 
+
+ align:start position:0%
+for each coordinate of x I want that the
+coariance between epsilon and this co
+
+ align:start position:0%
+coariance between epsilon and this co
+ 
+
+ align:start position:0%
+coariance between epsilon and this co
+this coordinate of x is equal to zero so
+
+ align:start position:0%
+this coordinate of x is equal to zero so
+ 
+
+ align:start position:0%
+this coordinate of x is equal to zero so
+I'm just asking this for all coordinates
+
+ align:start position:0%
+I'm just asking this for all coordinates
+ 
+
+ align:start position:0%
+I'm just asking this for all coordinates
+again in most instances we're going to
+
+ align:start position:0%
+again in most instances we're going to
+ 
+
+ align:start position:0%
+again in most instances we're going to
+think that epsilon is independent of x
+
+ align:start position:0%
+think that epsilon is independent of x
+ 
+
+ align:start position:0%
+think that epsilon is independent of x
+and that's something we can understand
+
+ align:start position:0%
+and that's something we can understand
+ 
+
+ align:start position:0%
+and that's something we can understand
+without thinking about coordinates.
+
+ align:start position:0%
+without thinking about coordinates.
+ 
+
+ align:start position:0%
+without thinking about coordinates.
+All right. So, yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry. Can you repeat the question?
+
+ align:start position:0%
+I'm sorry. Can you repeat the question?
+ 
+
+ align:start position:0%
+I'm sorry. Can you repeat the question?
+I didn't hear.
+
+ align:start position:0%
+I didn't hear.
+ 
+
+ align:start position:0%
+I didn't hear.
+Yeah, beta is the parameter we're
+
+ align:start position:0%
+Yeah, beta is the parameter we're
+ 
+
+ align:start position:0%
+Yeah, beta is the parameter we're
+looking for, right? Just like it was a
+
+ align:start position:0%
+looking for, right? Just like it was a
+ 
+
+ align:start position:0%
+looking for, right? Just like it was a
+and the pair above the whole vector beta
+
+ align:start position:0%
+and the pair above the whole vector beta
+ 
+
+ align:start position:0%
+and the pair above the whole vector beta
+now.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's no well you can you think of
+
+ align:start position:0%
+So there's no well you can you think of
+ 
+
+ align:start position:0%
+So there's no well you can you think of
+an intercept of a function that takes I
+
+ align:start position:0%
+an intercept of a function that takes I
+ 
+
+ align:start position:0%
+an intercept of a function that takes I
+mean there is there is one actually
+
+ align:start position:0%
+mean there is there is one actually
+ 
+
+ align:start position:0%
+mean there is there is one actually
+that's the one for which betas all the
+
+ align:start position:0%
+that's the one for which betas all the
+ 
+
+ align:start position:0%
+that's the one for which betas all the
+betas that don't correspond to the
+
+ align:start position:0%
+betas that don't correspond to the
+ 
+
+ align:start position:0%
+betas that don't correspond to the
+vector of all ones. So the intercept is
+
+ align:start position:0%
+vector of all ones. So the intercept is
+ 
+
+ align:start position:0%
+vector of all ones. So the intercept is
+really the the weight that I put on this
+
+ align:start position:0%
+really the the weight that I put on this
+ 
+
+ align:start position:0%
+really the the weight that I put on this
+guy. That's the beta that's going to
+
+ align:start position:0%
+guy. That's the beta that's going to
+ 
+
+ align:start position:0%
+guy. That's the beta that's going to
+come to this guy. But we don't really
+
+ align:start position:0%
+come to this guy. But we don't really
+ 
+
+ align:start position:0%
+come to this guy. But we don't really
+talk about intercept in two dimensions.
+
+ align:start position:0%
+talk about intercept in two dimensions.
+ 
+
+ align:start position:0%
+talk about intercept in two dimensions.
+If sorry if x lives in two dimensions.
+
+ align:start position:0%
+If sorry if x lives in two dimensions.
+ 
+
+ align:start position:0%
+If sorry if x lives in two dimensions.
+Uh the way you want to think about this
+
+ align:start position:0%
+Uh the way you want to think about this
+ 
+
+ align:start position:0%
+Uh the way you want to think about this
+is uh you take a sheet of paper like
+
+ align:start position:0%
+is uh you take a sheet of paper like
+ 
+
+ align:start position:0%
+is uh you take a sheet of paper like
+that. Right? So I have now I have points
+
+ align:start position:0%
+that. Right? So I have now I have points
+ 
+
+ align:start position:0%
+that. Right? So I have now I have points
+that live in three dimensions. Right? So
+
+ align:start position:0%
+that live in three dimensions. Right? So
+ 
+
+ align:start position:0%
+that live in three dimensions. Right? So
+let's say one direction here is x1. This
+
+ align:start position:0%
+let's say one direction here is x1. This
+ 
+
+ align:start position:0%
+let's say one direction here is x1. This
+direction is x2 and this direction is y.
+
+ align:start position:0%
+direction is x2 and this direction is y.
+ 
+
+ align:start position:0%
+direction is x2 and this direction is y.
+Okay. And so what's going to happen is
+
+ align:start position:0%
+Okay. And so what's going to happen is
+ 
+
+ align:start position:0%
+Okay. And so what's going to happen is
+that I'm going to have like my points
+
+ align:start position:0%
+that I'm going to have like my points
+ 
+
+ align:start position:0%
+that I'm going to have like my points
+that live in this threedimensional
+
+ align:start position:0%
+that live in this threedimensional
+ 
+
+ align:start position:0%
+that live in this threedimensional
+space. And what I'm trying to do when
+
+ align:start position:0%
+space. And what I'm trying to do when
+ 
+
+ align:start position:0%
+space. And what I'm trying to do when
+I'm trying to do a linear model for
+
+ align:start position:0%
+I'm trying to do a linear model for
+ 
+
+ align:start position:0%
+I'm trying to do a linear model for
+those guys when I assume a linear model,
+
+ align:start position:0%
+those guys when I assume a linear model,
+ 
+
+ align:start position:0%
+those guys when I assume a linear model,
+what I assume is that there's a plane in
+
+ align:start position:0%
+what I assume is that there's a plane in
+ 
+
+ align:start position:0%
+what I assume is that there's a plane in
+those three dimensions. So think of this
+
+ align:start position:0%
+those three dimensions. So think of this
+ 
+
+ align:start position:0%
+those three dimensions. So think of this
+guy as being going everywhere and
+
+ align:start position:0%
+guy as being going everywhere and
+ 
+
+ align:start position:0%
+guy as being going everywhere and
+there's a plane al close to which all my
+
+ align:start position:0%
+there's a plane al close to which all my
+ 
+
+ align:start position:0%
+there's a plane al close to which all my
+points should be. Right? That's what's
+
+ align:start position:0%
+points should be. Right? That's what's
+ 
+
+ align:start position:0%
+points should be. Right? That's what's
+happening in two dimensions. If you see
+
+ align:start position:0%
+happening in two dimensions. If you see
+ 
+
+ align:start position:0%
+happening in two dimensions. If you see
+higher dimensions, then congratulations
+
+ align:start position:0%
+higher dimensions, then congratulations
+ 
+
+ align:start position:0%
+higher dimensions, then congratulations
+to you. But uh I can't. All right? So um
+
+ align:start position:0%
+to you. But uh I can't. All right? So um
+ 
+
+ align:start position:0%
+to you. But uh I can't. All right? So um
+uh but you know you can definitely
+
+ align:start position:0%
+uh but you know you can definitely
+ 
+
+ align:start position:0%
+uh but you know you can definitely
+formalize that fairly easily
+
+ align:start position:0%
+formalize that fairly easily
+ 
+
+ align:start position:0%
+formalize that fairly easily
+mathematically and just talk about
+
+ align:start position:0%
+mathematically and just talk about
+ 
+
+ align:start position:0%
+mathematically and just talk about
+vectors right
+
+ align:start position:0%
+vectors right
+ 
+
+ align:start position:0%
+vectors right
+so now here if I talk about the le
+
+ align:start position:0%
+so now here if I talk about the le
+ 
+
+ align:start position:0%
+so now here if I talk about the le
+squared error estimator or just the le
+
+ align:start position:0%
+squared error estimator or just the le
+ 
+
+ align:start position:0%
+squared error estimator or just the le
+squares estimator of beta it's simply
+
+ align:start position:0%
+squares estimator of beta it's simply
+ 
+
+ align:start position:0%
+squares estimator of beta it's simply
+the same thing as before just like we
+
+ align:start position:0%
+the same thing as before just like we
+ 
+
+ align:start position:0%
+the same thing as before just like we
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+so remember you should think of b as
+
+ align:start position:0%
+so remember you should think of b as
+ 
+
+ align:start position:0%
+so remember you should think of b as
+being as beta as being both the pair ab
+
+ align:start position:0%
+being as beta as being both the pair ab
+ 
+
+ align:start position:0%
+being as beta as being both the pair ab
+generalized okay so we said, "Oh, we
+
+ align:start position:0%
+generalized okay so we said, "Oh, we
+ 
+
+ align:start position:0%
+generalized okay so we said, "Oh, we
+wanted to minimize the expectation of y
+
+ align:start position:0%
+wanted to minimize the expectation of y
+ 
+
+ align:start position:0%
+wanted to minimize the expectation of y
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+a + b x^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squar right now. So that's in for p is
+
+ align:start position:0%
+squar right now. So that's in for p is
+ 
+
+ align:start position:0%
+squar right now. So that's in for p is
+equal to 1. Now for p larger than or
+
+ align:start position:0%
+equal to 1. Now for p larger than or
+ 
+
+ align:start position:0%
+equal to 1. Now for p larger than or
+equal to two, we're just going to write
+
+ align:start position:0%
+equal to two, we're just going to write
+ 
+
+ align:start position:0%
+equal to two, we're just going to write
+it as y - x transpose
+
+ align:start position:0%
+it as y - x transpose
+ 
+
+ align:start position:0%
+it as y - x transpose
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+okay. So I'm just trying to minimize
+
+ align:start position:0%
+okay. So I'm just trying to minimize
+ 
+
+ align:start position:0%
+okay. So I'm just trying to minimize
+this quantity. Of course I don't have
+
+ align:start position:0%
+this quantity. Of course I don't have
+ 
+
+ align:start position:0%
+this quantity. Of course I don't have
+access to this. So what I'm going to do
+
+ align:start position:0%
+access to this. So what I'm going to do
+ 
+
+ align:start position:0%
+access to this. So what I'm going to do
+is I'm going to replace my expectation
+
+ align:start position:0%
+is I'm going to replace my expectation
+ 
+
+ align:start position:0%
+is I'm going to replace my expectation
+by an average.
+
+ align:start position:0%
+by an average.
+ 
+
+ align:start position:0%
+by an average.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here I'm using the notation t because
+
+ align:start position:0%
+So here I'm using the notation t because
+ 
+
+ align:start position:0%
+So here I'm using the notation t because
+beta is the true one and I don't want to
+
+ align:start position:0%
+beta is the true one and I don't want to
+ 
+
+ align:start position:0%
+beta is the true one and I don't want to
+to just so here I have a variable t
+
+ align:start position:0%
+to just so here I have a variable t
+ 
+
+ align:start position:0%
+to just so here I have a variable t
+that's just moving around and so now I'm
+
+ align:start position:0%
+that's just moving around and so now I'm
+ 
+
+ align:start position:0%
+that's just moving around and so now I'm
+going to take the square of this thing
+
+ align:start position:0%
+going to take the square of this thing
+ 
+
+ align:start position:0%
+going to take the square of this thing
+and when I minimize this overall t in
+
+ align:start position:0%
+and when I minimize this overall t in
+ 
+
+ align:start position:0%
+and when I minimize this overall t in
+our p the arg min the minimum is
+
+ align:start position:0%
+our p the arg min the minimum is
+ 
+
+ align:start position:0%
+our p the arg min the minimum is
+attained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at beta hat which is my estimator.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I want to actually compute Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh you mean the previous slide?
+
+ align:start position:0%
+Uh you mean the previous slide?
+ 
+
+ align:start position:0%
+Uh you mean the previous slide?
+So again I'm just defining an estimator
+
+ align:start position:0%
+So again I'm just defining an estimator
+ 
+
+ align:start position:0%
+So again I'm just defining an estimator
+just like I would tell you just take the
+
+ align:start position:0%
+just like I would tell you just take the
+ 
+
+ align:start position:0%
+just like I would tell you just take the
+estimator that has coordinates four
+
+ align:start position:0%
+estimator that has coordinates four
+ 
+
+ align:start position:0%
+estimator that has coordinates four
+everywhere.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes. So the answer is yes. I'm I I was
+
+ align:start position:0%
+yes. So the answer is yes. I'm I I was
+ 
+
+ align:start position:0%
+yes. So the answer is yes. I'm I I was
+just trying to think if this was
+
+ align:start position:0%
+just trying to think if this was
+ 
+
+ align:start position:0%
+just trying to think if this was
+captured. So it is not captured in this
+
+ align:start position:0%
+captured. So it is not captured in this
+ 
+
+ align:start position:0%
+captured. So it is not captured in this
+guy because this is just telling me that
+
+ align:start position:0%
+guy because this is just telling me that
+ 
+
+ align:start position:0%
+guy because this is just telling me that
+the expectation of
+
+ align:start position:0%
+the expectation of
+ 
+
+ align:start position:0%
+the expectation of
+epsilon i minus expectation of epsilon i
+
+ align:start position:0%
+epsilon i minus expectation of epsilon i
+ 
+
+ align:start position:0%
+epsilon i minus expectation of epsilon i
+is equal to zero. Okay. Yeah. So yes I
+
+ align:start position:0%
+is equal to zero. Okay. Yeah. So yes I
+ 
+
+ align:start position:0%
+is equal to zero. Okay. Yeah. So yes I
+need to have that epsilon i has mean
+
+ align:start position:0%
+need to have that epsilon i has mean
+ 
+
+ align:start position:0%
+need to have that epsilon i has mean
+zero for let's assume that expectation
+
+ align:start position:0%
+zero for let's assume that expectation
+ 
+
+ align:start position:0%
+zero for let's assume that expectation
+of epsilon i is zero for this problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we also need we're going to need
+
+ align:start position:0%
+and we also need we're going to need
+ 
+
+ align:start position:0%
+and we also need we're going to need
+something about some sort of question
+
+ align:start position:0%
+something about some sort of question
+ 
+
+ align:start position:0%
+something about some sort of question
+about the variance being not equal to
+
+ align:start position:0%
+about the variance being not equal to
+ 
+
+ align:start position:0%
+about the variance being not equal to
+zero, right? But this is going to come
+
+ align:start position:0%
+zero, right? But this is going to come
+ 
+
+ align:start position:0%
+zero, right? But this is going to come
+up later. So let's think for one second
+
+ align:start position:0%
+up later. So let's think for one second
+ 
+
+ align:start position:0%
+up later. So let's think for one second
+about doing the same approach as we did
+
+ align:start position:0%
+about doing the same approach as we did
+ 
+
+ align:start position:0%
+about doing the same approach as we did
+before. Take the partial derivative with
+
+ align:start position:0%
+before. Take the partial derivative with
+ 
+
+ align:start position:0%
+before. Take the partial derivative with
+respect to the first coordinate of t
+
+ align:start position:0%
+respect to the first coordinate of t
+ 
+
+ align:start position:0%
+respect to the first coordinate of t
+with respect to the second coordinate of
+
+ align:start position:0%
+with respect to the second coordinate of
+ 
+
+ align:start position:0%
+with respect to the second coordinate of
+t with respect to the third coordinate
+
+ align:start position:0%
+t with respect to the third coordinate
+ 
+
+ align:start position:0%
+t with respect to the third coordinate
+of t, etc. So that's what we did before.
+
+ align:start position:0%
+of t, etc. So that's what we did before.
+ 
+
+ align:start position:0%
+of t, etc. So that's what we did before.
+We had two equations and we reconciled
+
+ align:start position:0%
+We had two equations and we reconciled
+ 
+
+ align:start position:0%
+We had two equations and we reconciled
+them because it was fairly easy to
+
+ align:start position:0%
+them because it was fairly easy to
+ 
+
+ align:start position:0%
+them because it was fairly easy to
+solve, right?
+
+ align:start position:0%
+solve, right?
+ 
+
+ align:start position:0%
+solve, right?
+But in general, what's going to happen
+
+ align:start position:0%
+But in general, what's going to happen
+ 
+
+ align:start position:0%
+But in general, what's going to happen
+is we're going to have a system of
+
+ align:start position:0%
+is we're going to have a system of
+ 
+
+ align:start position:0%
+is we're going to have a system of
+equations. We're going to have a system
+
+ align:start position:0%
+equations. We're going to have a system
+ 
+
+ align:start position:0%
+equations. We're going to have a system
+of P equations, one for each of the
+
+ align:start position:0%
+of P equations, one for each of the
+ 
+
+ align:start position:0%
+of P equations, one for each of the
+coordinates of T. And we're going to
+
+ align:start position:0%
+coordinates of T. And we're going to
+ 
+
+ align:start position:0%
+coordinates of T. And we're going to
+have P uh unknowns each coordinate of T.
+
+ align:start position:0%
+have P uh unknowns each coordinate of T.
+ 
+
+ align:start position:0%
+have P uh unknowns each coordinate of T.
+And so we're going to have the system to
+
+ align:start position:0%
+And so we're going to have the system to
+ 
+
+ align:start position:0%
+And so we're going to have the system to
+solve. Actually, turns out it's going to
+
+ align:start position:0%
+solve. Actually, turns out it's going to
+ 
+
+ align:start position:0%
+solve. Actually, turns out it's going to
+be a linear system, but it's not going
+
+ align:start position:0%
+be a linear system, but it's not going
+ 
+
+ align:start position:0%
+be a linear system, but it's not going
+to be something that we're going to be
+
+ align:start position:0%
+to be something that we're going to be
+ 
+
+ align:start position:0%
+to be something that we're going to be
+able to solve coordinate by coordinate.
+
+ align:start position:0%
+able to solve coordinate by coordinate.
+ 
+
+ align:start position:0%
+able to solve coordinate by coordinate.
+It's going to be annoying to solve. You
+
+ align:start position:0%
+It's going to be annoying to solve. You
+ 
+
+ align:start position:0%
+It's going to be annoying to solve. You
+know, you can guess that what's going to
+
+ align:start position:0%
+know, you can guess that what's going to
+ 
+
+ align:start position:0%
+know, you can guess that what's going to
+happen, right? We here it involved the
+
+ align:start position:0%
+happen, right? We here it involved the
+ 
+
+ align:start position:0%
+happen, right? We here it involved the
+coariance between X and epsilon right
+
+ align:start position:0%
+coariance between X and epsilon right
+ 
+
+ align:start position:0%
+coariance between X and epsilon right
+that's what it involved to understand um
+
+ align:start position:0%
+that's what it involved to understand um
+ 
+
+ align:start position:0%
+that's what it involved to understand um
+sorry the coordinate the the correlation
+
+ align:start position:0%
+sorry the coordinate the the correlation
+ 
+
+ align:start position:0%
+sorry the coordinate the the correlation
+between X and Y to understand how this
+
+ align:start position:0%
+between X and Y to understand how this
+ 
+
+ align:start position:0%
+between X and Y to understand how this
+the solution of this problem was in this
+
+ align:start position:0%
+the solution of this problem was in this
+ 
+
+ align:start position:0%
+the solution of this problem was in this
+case there's going to be not only the
+
+ align:start position:0%
+case there's going to be not only the
+ 
+
+ align:start position:0%
+case there's going to be not only the
+correlation sorry the coariance between
+
+ align:start position:0%
+correlation sorry the coariance between
+ 
+
+ align:start position:0%
+correlation sorry the coariance between
+X1 and Y X2 and Y X3 etc all the way to
+
+ align:start position:0%
+X1 and Y X2 and Y X3 etc all the way to
+ 
+
+ align:start position:0%
+X1 and Y X2 and Y X3 etc all the way to
+XP and Y but there's also going to be
+
+ align:start position:0%
+XP and Y but there's also going to be
+ 
+
+ align:start position:0%
+XP and Y but there's also going to be
+all the cross coariances between XJ and
+
+ align:start position:0%
+all the cross coariances between XJ and
+ 
+
+ align:start position:0%
+all the cross coariances between XJ and
+X K and so this is going to be a
+
+ align:start position:0%
+X K and so this is going to be a
+ 
+
+ align:start position:0%
+X K and so this is going to be a
+nightmare to solve
+
+ align:start position:0%
+nightmare to solve
+ 
+
+ align:start position:0%
+nightmare to solve
+like in this system and what we do is
+
+ align:start position:0%
+like in this system and what we do is
+ 
+
+ align:start position:0%
+like in this system and what we do is
+that we go on to using a matrix notation
+
+ align:start position:0%
+that we go on to using a matrix notation
+ 
+
+ align:start position:0%
+that we go on to using a matrix notation
+so that when we take derivatives we take
+
+ align:start position:0%
+so that when we take derivatives we take
+ 
+
+ align:start position:0%
+so that when we take derivatives we take
+derivative we we talk about gradients
+
+ align:start position:0%
+derivative we we talk about gradients
+ 
+
+ align:start position:0%
+derivative we we talk about gradients
+and then we can invert matrices and
+
+ align:start position:0%
+and then we can invert matrices and
+ 
+
+ align:start position:0%
+and then we can invert matrices and
+solve linear systems in a somewhat
+
+ align:start position:0%
+solve linear systems in a somewhat
+ 
+
+ align:start position:0%
+solve linear systems in a somewhat
+formal manner by just saying that if I
+
+ align:start position:0%
+formal manner by just saying that if I
+ 
+
+ align:start position:0%
+formal manner by just saying that if I
+want to solve the system ax=
+
+ align:start position:0%
+want to solve the system ax=
+ 
+
+ align:start position:0%
+want to solve the system ax=
+b rather than actually solving this for
+
+ align:start position:0%
+b rather than actually solving this for
+ 
+
+ align:start position:0%
+b rather than actually solving this for
+each coordinate of x individually I just
+
+ align:start position:0%
+each coordinate of x individually I just
+ 
+
+ align:start position:0%
+each coordinate of x individually I just
+say that x is equal to a inverse time b
+
+ align:start position:0%
+say that x is equal to a inverse time b
+ 
+
+ align:start position:0%
+say that x is equal to a inverse time b
+right so that's really what why we're
+
+ align:start position:0%
+right so that's really what why we're
+ 
+
+ align:start position:0%
+right so that's really what why we're
+going to the the equation one because we
+
+ align:start position:0%
+going to the the equation one because we
+ 
+
+ align:start position:0%
+going to the the equation one because we
+have a formalism to write the that X is
+
+ align:start position:0%
+have a formalism to write the that X is
+ 
+
+ align:start position:0%
+have a formalism to write the that X is
+the solution of this system. I'm not
+
+ align:start position:0%
+the solution of this system. I'm not
+ 
+
+ align:start position:0%
+the solution of this system. I'm not
+telling you that this is going to be
+
+ align:start position:0%
+telling you that this is going to be
+ 
+
+ align:start position:0%
+telling you that this is going to be
+easy to solve numerically, but at least
+
+ align:start position:0%
+easy to solve numerically, but at least
+ 
+
+ align:start position:0%
+easy to solve numerically, but at least
+I can write it. Okay? And so here's how
+
+ align:start position:0%
+I can write it. Okay? And so here's how
+ 
+
+ align:start position:0%
+I can write it. Okay? And so here's how
+it goes. I have a bunch of vectors.
+
+ align:start position:0%
+it goes. I have a bunch of vectors.
+ 
+
+ align:start position:0%
+it goes. I have a bunch of vectors.
+I have So what are my vectors? Right? So
+
+ align:start position:0%
+I have So what are my vectors? Right? So
+ 
+
+ align:start position:0%
+I have So what are my vectors? Right? So
+I have X1. Oh, by the way, I didn't
+
+ align:start position:0%
+I have X1. Oh, by the way, I didn't
+ 
+
+ align:start position:0%
+I have X1. Oh, by the way, I didn't
+actually mention that when I put the
+
+ align:start position:0%
+actually mention that when I put the
+ 
+
+ align:start position:0%
+actually mention that when I put the
+lowercase, when I put the subscript, I'm
+
+ align:start position:0%
+lowercase, when I put the subscript, I'm
+ 
+
+ align:start position:0%
+lowercase, when I put the subscript, I'm
+talking about the observation. And when
+
+ align:start position:0%
+talking about the observation. And when
+ 
+
+ align:start position:0%
+talking about the observation. And when
+I put the superscript, I'm talking about
+
+ align:start position:0%
+I put the superscript, I'm talking about
+ 
+
+ align:start position:0%
+I put the superscript, I'm talking about
+the coordinates, right? So I have x1
+
+ align:start position:0%
+the coordinates, right? So I have x1
+ 
+
+ align:start position:0%
+the coordinates, right? So I have x1
+which is equal to one x x11
+
+ align:start position:0%
+which is equal to one x x11
+ 
+
+ align:start position:0%
+which is equal to one x x11
+x uh one p
+
+ align:start position:0%
+x uh one p
+ 
+
+ align:start position:0%
+x uh one p
+x2 which is one x21
+
+ align:start position:0%
+x2 which is one x21
+ 
+
+ align:start position:0%
+x2 which is one x21
+x2 p
+
+ align:start position:0%
+x2 p
+ 
+
+ align:start position:0%
+x2 p
+all the way to xn which is one
+
+ align:start position:0%
+all the way to xn which is one
+ 
+
+ align:start position:0%
+all the way to xn which is one
+x n1
+
+ align:start position:0%
+x n1
+ 
+
+ align:start position:0%
+x n1
+xnp. All right. Right? So those are my n
+
+ align:start position:0%
+xnp. All right. Right? So those are my n
+ 
+
+ align:start position:0%
+xnp. All right. Right? So those are my n
+observed x's and then I have another y1
+
+ align:start position:0%
+observed x's and then I have another y1
+ 
+
+ align:start position:0%
+observed x's and then I have another y1
+y2 yn that comes paired with those guys.
+
+ align:start position:0%
+y2 yn that comes paired with those guys.
+ 
+
+ align:start position:0%
+y2 yn that comes paired with those guys.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So the first thing is that I'm going to
+
+ align:start position:0%
+So the first thing is that I'm going to
+ 
+
+ align:start position:0%
+So the first thing is that I'm going to
+stack those guys into some vector that
+
+ align:start position:0%
+stack those guys into some vector that
+ 
+
+ align:start position:0%
+stack those guys into some vector that
+I'm going to call y. So maybe I should
+
+ align:start position:0%
+I'm going to call y. So maybe I should
+ 
+
+ align:start position:0%
+I'm going to call y. So maybe I should
+put an arrow for the purpose of the
+
+ align:start position:0%
+put an arrow for the purpose of the
+ 
+
+ align:start position:0%
+put an arrow for the purpose of the
+blackboard and it's just y1 to yn. Okay.
+
+ align:start position:0%
+blackboard and it's just y1 to yn. Okay.
+ 
+
+ align:start position:0%
+blackboard and it's just y1 to yn. Okay.
+So this is a vector in rn.
+
+ align:start position:0%
+So this is a vector in rn.
+ 
+
+ align:start position:0%
+So this is a vector in rn.
+Now, if I want to stack those guys
+
+ align:start position:0%
+Now, if I want to stack those guys
+ 
+
+ align:start position:0%
+Now, if I want to stack those guys
+together, I can either create a long
+
+ align:start position:0%
+together, I can either create a long
+ 
+
+ align:start position:0%
+together, I can either create a long
+vector of size n times p, but the
+
+ align:start position:0%
+vector of size n times p, but the
+ 
+
+ align:start position:0%
+vector of size n times p, but the
+problem is that I lose the role of who's
+
+ align:start position:0%
+problem is that I lose the role of who's
+ 
+
+ align:start position:0%
+problem is that I lose the role of who's
+a coordinate and who's uh who's an
+
+ align:start position:0%
+a coordinate and who's uh who's an
+ 
+
+ align:start position:0%
+a coordinate and who's uh who's an
+observation. And so, it's actually nicer
+
+ align:start position:0%
+observation. And so, it's actually nicer
+ 
+
+ align:start position:0%
+observation. And so, it's actually nicer
+for me to just put those guys next to
+
+ align:start position:0%
+for me to just put those guys next to
+ 
+
+ align:start position:0%
+for me to just put those guys next to
+each other and create one new uh
+
+ align:start position:0%
+each other and create one new uh
+ 
+
+ align:start position:0%
+each other and create one new uh
+variable. And so, the way I'm going to
+
+ align:start position:0%
+variable. And so, the way I'm going to
+ 
+
+ align:start position:0%
+variable. And so, the way I'm going to
+do this is rather than actually stacking
+
+ align:start position:0%
+do this is rather than actually stacking
+ 
+
+ align:start position:0%
+do this is rather than actually stacking
+those guys like that, I'm going to take
+
+ align:start position:0%
+those guys like that, I'm going to take
+ 
+
+ align:start position:0%
+those guys like that, I'm going to take
+their transpose and stack them as rows
+
+ align:start position:0%
+their transpose and stack them as rows
+ 
+
+ align:start position:0%
+their transpose and stack them as rows
+of a matrix. Okay? So I'm going to
+
+ align:start position:0%
+of a matrix. Okay? So I'm going to
+ 
+
+ align:start position:0%
+of a matrix. Okay? So I'm going to
+create a matrix which here is denoted
+
+ align:start position:0%
+create a matrix which here is denoted
+ 
+
+ align:start position:0%
+create a matrix which here is denoted
+typically by I'm going to write x
+
+ align:start position:0%
+typically by I'm going to write x
+ 
+
+ align:start position:0%
+typically by I'm going to write x
+doubleb bar
+
+ align:start position:0%
+doubleb bar
+ 
+
+ align:start position:0%
+doubleb bar
+and here I'm going to actually just so
+
+ align:start position:0%
+and here I'm going to actually just so
+ 
+
+ align:start position:0%
+and here I'm going to actually just so
+since I'm taking those guys like this
+
+ align:start position:0%
+since I'm taking those guys like this
+ 
+
+ align:start position:0%
+since I'm taking those guys like this
+the first column is going to be only
+
+ align:start position:0%
+the first column is going to be only
+ 
+
+ align:start position:0%
+the first column is going to be only
+ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'm going to have uh well x11
+
+ align:start position:0%
+and then I'm going to have uh well x11
+ 
+
+ align:start position:0%
+and then I'm going to have uh well x11
+x1 p and here I'm going to have x n1
+
+ align:start position:0%
+x1 p and here I'm going to have x n1
+ 
+
+ align:start position:0%
+x1 p and here I'm going to have x n1
+x np
+
+ align:start position:0%
+x np
+ 
+
+ align:start position:0%
+x np
+okay so here The number of rows is n and
+
+ align:start position:0%
+okay so here The number of rows is n and
+ 
+
+ align:start position:0%
+okay so here The number of rows is n and
+the number of columns is p. One row per
+
+ align:start position:0%
+the number of columns is p. One row per
+ 
+
+ align:start position:0%
+the number of columns is p. One row per
+observation, one column per coordinate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And again, I uh make your life
+
+ align:start position:0%
+And again, I uh make your life
+ 
+
+ align:start position:0%
+And again, I uh make your life
+miserable. Uh because this really should
+
+ align:start position:0%
+miserable. Uh because this really should
+ 
+
+ align:start position:0%
+miserable. Uh because this really should
+be p minus one because I already used
+
+ align:start position:0%
+be p minus one because I already used
+ 
+
+ align:start position:0%
+be p minus one because I already used
+the first one for this guy. I'm sorry
+
+ align:start position:0%
+the first one for this guy. I'm sorry
+ 
+
+ align:start position:0%
+the first one for this guy. I'm sorry
+about that. It's a bit painful. Uh so
+
+ align:start position:0%
+about that. It's a bit painful. Uh so
+ 
+
+ align:start position:0%
+about that. It's a bit painful. Uh so
+usually we don't even write what's in
+
+ align:start position:0%
+usually we don't even write what's in
+ 
+
+ align:start position:0%
+usually we don't even write what's in
+there so we don't have to think about
+
+ align:start position:0%
+there so we don't have to think about
+ 
+
+ align:start position:0%
+there so we don't have to think about
+it. Those are just vectors of size p.
+
+ align:start position:0%
+it. Those are just vectors of size p.
+ 
+
+ align:start position:0%
+it. Those are just vectors of size p.
+Okay, so now that I create this thing, I
+
+ align:start position:0%
+Okay, so now that I create this thing, I
+ 
+
+ align:start position:0%
+Okay, so now that I create this thing, I
+can actually just basically stack up all
+
+ align:start position:0%
+can actually just basically stack up all
+ 
+
+ align:start position:0%
+can actually just basically stack up all
+my models. So y i equals x i transpose
+
+ align:start position:0%
+my models. So y i equals x i transpose
+ 
+
+ align:start position:0%
+my models. So y i equals x i transpose
+beta plus epsilon i for all i = 1 to n.
+
+ align:start position:0%
+beta plus epsilon i for all i = 1 to n.
+ 
+
+ align:start position:0%
+beta plus epsilon i for all i = 1 to n.
+This transforms into this is equivalent
+
+ align:start position:0%
+This transforms into this is equivalent
+ 
+
+ align:start position:0%
+This transforms into this is equivalent
+to saying that the vector Y is equal to
+
+ align:start position:0%
+to saying that the vector Y is equal to
+ 
+
+ align:start position:0%
+to saying that the vector Y is equal to
+the matrix X time beta plus a matrix
+
+ align:start position:0%
+the matrix X time beta plus a matrix
+ 
+
+ align:start position:0%
+the matrix X time beta plus a matrix
+plus a vector epsilon where epsilon is
+
+ align:start position:0%
+plus a vector epsilon where epsilon is
+ 
+
+ align:start position:0%
+plus a vector epsilon where epsilon is
+just epsilon 1 to epsilon N.
+
+ align:start position:0%
+just epsilon 1 to epsilon N.
+ 
+
+ align:start position:0%
+just epsilon 1 to epsilon N.
+Right? So I have just this system which
+
+ align:start position:0%
+Right? So I have just this system which
+ 
+
+ align:start position:0%
+Right? So I have just this system which
+I write as a matrix which really just
+
+ align:start position:0%
+I write as a matrix which really just
+ 
+
+ align:start position:0%
+I write as a matrix which really just
+consists in stacking up all these
+
+ align:start position:0%
+consists in stacking up all these
+ 
+
+ align:start position:0%
+consists in stacking up all these
+equations next to each other.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So now that I have this model, this is
+
+ align:start position:0%
+So now that I have this model, this is
+ 
+
+ align:start position:0%
+So now that I have this model, this is
+the usual le squares model. And here
+
+ align:start position:0%
+the usual le squares model. And here
+ 
+
+ align:start position:0%
+the usual le squares model. And here
+when I want to write my le squares
+
+ align:start position:0%
+when I want to write my le squares
+ 
+
+ align:start position:0%
+when I want to write my le squares
+criterion in terms of matrices, right?
+
+ align:start position:0%
+criterion in terms of matrices, right?
+ 
+
+ align:start position:0%
+criterion in terms of matrices, right?
+My le squares criterion remember was sum
+
+ align:start position:0%
+My le squares criterion remember was sum
+ 
+
+ align:start position:0%
+My le squares criterion remember was sum
+from i= 1 to n of yi minus x i transpose
+
+ align:start position:0%
+from i= 1 to n of yi minus x i transpose
+ 
+
+ align:start position:0%
+from i= 1 to n of yi minus x i transpose
+beta squared. Well, here it's really
+
+ align:start position:0%
+beta squared. Well, here it's really
+ 
+
+ align:start position:0%
+beta squared. Well, here it's really
+just the sum of the square of the
+
+ align:start position:0%
+just the sum of the square of the
+ 
+
+ align:start position:0%
+just the sum of the square of the
+coefficients of the of the vector y - x
+
+ align:start position:0%
+coefficients of the of the vector y - x
+ 
+
+ align:start position:0%
+coefficients of the of the vector y - x
+beta. So this is actually equal to the
+
+ align:start position:0%
+beta. So this is actually equal to the
+ 
+
+ align:start position:0%
+beta. So this is actually equal to the
+norm squar of y - x beta^ 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's just the square norm is by
+
+ align:start position:0%
+That's just the square norm is by
+ 
+
+ align:start position:0%
+That's just the square norm is by
+definition the sum of the square of the
+
+ align:start position:0%
+definition the sum of the square of the
+ 
+
+ align:start position:0%
+definition the sum of the square of the
+coordinates.
+
+ align:start position:0%
+coordinates.
+ 
+
+ align:start position:0%
+coordinates.
+And so now I can actually talk about
+
+ align:start position:0%
+And so now I can actually talk about
+ 
+
+ align:start position:0%
+And so now I can actually talk about
+minimizing a norm squared. And here it's
+
+ align:start position:0%
+minimizing a norm squared. And here it's
+ 
+
+ align:start position:0%
+minimizing a norm squared. And here it's
+going to be easier for me to take
+
+ align:start position:0%
+going to be easier for me to take
+ 
+
+ align:start position:0%
+going to be easier for me to take
+derivatives. All right. So we'll do that
+
+ align:start position:0%
+derivatives. All right. So we'll do that
+ 
+
+ align:start position:0%
+derivatives. All right. So we'll do that
+uh next time.
\ No newline at end of file
diff --git a/zD6tTb74KdU.txt b/zD6tTb74KdU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2c810910c6fadc32ca7afc1a421baeb94af6bfea
--- /dev/null
+++ b/zD6tTb74KdU.txt
@@ -0,0 +1,739 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+in a previous demonstration on two beam
+
+ align:start position:0%
+in a previous demonstration on two beam
+ 
+
+ align:start position:0%
+in a previous demonstration on two beam
+interference we saw that the fringe
+
+ align:start position:0%
+interference we saw that the fringe
+ 
+
+ align:start position:0%
+interference we saw that the fringe
+pattern was a series of vertical lines
+
+ align:start position:0%
+pattern was a series of vertical lines
+ 
+
+ align:start position:0%
+pattern was a series of vertical lines
+the reason was that two the two beams
+
+ align:start position:0%
+the reason was that two the two beams
+ 
+
+ align:start position:0%
+the reason was that two the two beams
+were plane waves and the lines were due
+
+ align:start position:0%
+were plane waves and the lines were due
+ 
+
+ align:start position:0%
+were plane waves and the lines were due
+to the interference of two plane waves
+
+ align:start position:0%
+to the interference of two plane waves
+ 
+
+ align:start position:0%
+to the interference of two plane waves
+with a slight angle between them in this
+
+ align:start position:0%
+with a slight angle between them in this
+ 
+
+ align:start position:0%
+with a slight angle between them in this
+demonstration we're going to show that
+
+ align:start position:0%
+demonstration we're going to show that
+ 
+
+ align:start position:0%
+demonstration we're going to show that
+you can get all kinds of shapes in the
+
+ align:start position:0%
+you can get all kinds of shapes in the
+ 
+
+ align:start position:0%
+you can get all kinds of shapes in the
+fringe pattern by simply placing a lens
+
+ align:start position:0%
+fringe pattern by simply placing a lens
+ 
+
+ align:start position:0%
+fringe pattern by simply placing a lens
+in the setup and here is the setup as
+
+ align:start position:0%
+in the setup and here is the setup as
+ 
+
+ align:start position:0%
+in the setup and here is the setup as
+you may recall here's the laser is the
+
+ align:start position:0%
+you may recall here's the laser is the
+ 
+
+ align:start position:0%
+you may recall here's the laser is the
+beam from the laser being reflected by
+
+ align:start position:0%
+beam from the laser being reflected by
+ 
+
+ align:start position:0%
+beam from the laser being reflected by
+this mirror and here we're going to add
+
+ align:start position:0%
+this mirror and here we're going to add
+ 
+
+ align:start position:0%
+this mirror and here we're going to add
+a lens the light coming out of the lens
+
+ align:start position:0%
+a lens the light coming out of the lens
+ 
+
+ align:start position:0%
+a lens the light coming out of the lens
+and reflected by this mirror here will
+
+ align:start position:0%
+and reflected by this mirror here will
+ 
+
+ align:start position:0%
+and reflected by this mirror here will
+have some curvature now and when it
+
+ align:start position:0%
+have some curvature now and when it
+ 
+
+ align:start position:0%
+have some curvature now and when it
+enters the Michelson interferometer here
+
+ align:start position:0%
+enters the Michelson interferometer here
+ 
+
+ align:start position:0%
+enters the Michelson interferometer here
+the the beam going to this arm being the
+
+ align:start position:0%
+the the beam going to this arm being the
+ 
+
+ align:start position:0%
+the the beam going to this arm being the
+longer arm slightly longer arm will have
+
+ align:start position:0%
+longer arm slightly longer arm will have
+ 
+
+ align:start position:0%
+longer arm slightly longer arm will have
+slightly different curvature when it
+
+ align:start position:0%
+slightly different curvature when it
+ 
+
+ align:start position:0%
+slightly different curvature when it
+interferes with the beam coming from
+
+ align:start position:0%
+interferes with the beam coming from
+ 
+
+ align:start position:0%
+interferes with the beam coming from
+this arm because the path length here is
+
+ align:start position:0%
+this arm because the path length here is
+ 
+
+ align:start position:0%
+this arm because the path length here is
+shorter than this one the two beams will
+
+ align:start position:0%
+shorter than this one the two beams will
+ 
+
+ align:start position:0%
+shorter than this one the two beams will
+interfere and pass along this direction
+
+ align:start position:0%
+interfere and pass along this direction
+ 
+
+ align:start position:0%
+interfere and pass along this direction
+then then they will get reflected at
+
+ align:start position:0%
+then then they will get reflected at
+ 
+
+ align:start position:0%
+then then they will get reflected at
+this mirror through the lens and then
+
+ align:start position:0%
+this mirror through the lens and then
+ 
+
+ align:start position:0%
+this mirror through the lens and then
+onto the screen so now if we take a
+
+ align:start position:0%
+onto the screen so now if we take a
+ 
+
+ align:start position:0%
+onto the screen so now if we take a
+close-up at the at the fringe pattern we
+
+ align:start position:0%
+close-up at the at the fringe pattern we
+ 
+
+ align:start position:0%
+close-up at the at the fringe pattern we
+will see that we have circular fringes
+
+ align:start position:0%
+will see that we have circular fringes
+ 
+
+ align:start position:0%
+will see that we have circular fringes
+and what's interesting about the
+
+ align:start position:0%
+and what's interesting about the
+ 
+
+ align:start position:0%
+and what's interesting about the
+circular fringes is that the spacing
+
+ align:start position:0%
+circular fringes is that the spacing
+ 
+
+ align:start position:0%
+circular fringes is that the spacing
+between the fringes can be changed by
+
+ align:start position:0%
+between the fringes can be changed by
+ 
+
+ align:start position:0%
+between the fringes can be changed by
+disturbing the setup for example if I
+
+ align:start position:0%
+disturbing the setup for example if I
+ 
+
+ align:start position:0%
+disturbing the setup for example if I
+change the length of of the of this arm
+
+ align:start position:0%
+change the length of of the of this arm
+ 
+
+ align:start position:0%
+change the length of of the of this arm
+here I can change the spacing between
+
+ align:start position:0%
+here I can change the spacing between
+ 
+
+ align:start position:0%
+here I can change the spacing between
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+the fringes because I'm getting closer
+
+ align:start position:0%
+the fringes because I'm getting closer
+ 
+
+ align:start position:0%
+the fringes because I'm getting closer
+and closer to the same curvature as in
+
+ align:start position:0%
+and closer to the same curvature as in
+ 
+
+ align:start position:0%
+and closer to the same curvature as in
+the as in the other arm if I go further
+
+ align:start position:0%
+the as in the other arm if I go further
+ 
+
+ align:start position:0%
+the as in the other arm if I go further
+again we can see that I can increase the
+
+ align:start position:0%
+again we can see that I can increase the
+ 
+
+ align:start position:0%
+again we can see that I can increase the
+number of fringes showing that again the
+
+ align:start position:0%
+number of fringes showing that again the
+ 
+
+ align:start position:0%
+number of fringes showing that again the
+curvature has changed relative to this
+
+ align:start position:0%
+curvature has changed relative to this
+ 
+
+ align:start position:0%
+curvature has changed relative to this
+fixed arm over here now I'm going to
+
+ align:start position:0%
+fixed arm over here now I'm going to
+ 
+
+ align:start position:0%
+fixed arm over here now I'm going to
+show the effect of misalignment on the
+
+ align:start position:0%
+show the effect of misalignment on the
+ 
+
+ align:start position:0%
+show the effect of misalignment on the
+on the circular fringes if I adjust this
+
+ align:start position:0%
+on the circular fringes if I adjust this
+ 
+
+ align:start position:0%
+on the circular fringes if I adjust this
+mirror to here and then let's again look
+
+ align:start position:0%
+mirror to here and then let's again look
+ 
+
+ align:start position:0%
+mirror to here and then let's again look
+at the fringes and then you can see that
+
+ align:start position:0%
+at the fringes and then you can see that
+ 
+
+ align:start position:0%
+at the fringes and then you can see that
+by mr. lining this mirror I can get arcs
+
+ align:start position:0%
+by mr. lining this mirror I can get arcs
+ 
+
+ align:start position:0%
+by mr. lining this mirror I can get arcs
+instead of instead of the bull's eye and
+
+ align:start position:0%
+instead of instead of the bull's eye and
+ 
+
+ align:start position:0%
+instead of instead of the bull's eye and
+in fact if I'm if I look closely at the
+
+ align:start position:0%
+in fact if I'm if I look closely at the
+ 
+
+ align:start position:0%
+in fact if I'm if I look closely at the
+arcs I can tell which way the beams are
+
+ align:start position:0%
+arcs I can tell which way the beams are
+ 
+
+ align:start position:0%
+arcs I can tell which way the beams are
+are misaligned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright now what I'll try and do is to
+
+ align:start position:0%
+alright now what I'll try and do is to
+ 
+
+ align:start position:0%
+alright now what I'll try and do is to
+try and make the field go all dark or
+
+ align:start position:0%
+try and make the field go all dark or
+ 
+
+ align:start position:0%
+try and make the field go all dark or
+alright by making the two paths as
+
+ align:start position:0%
+alright by making the two paths as
+ 
+
+ align:start position:0%
+alright by making the two paths as
+identical as possible now you can see I
+
+ align:start position:0%
+identical as possible now you can see I
+ 
+
+ align:start position:0%
+identical as possible now you can see I
+only have about a couple of fringes an
+
+ align:start position:0%
+only have about a couple of fringes an
+ 
+
+ align:start position:0%
+only have about a couple of fringes an
+interference pattern they slightly
+
+ align:start position:0%
+interference pattern they slightly
+ 
+
+ align:start position:0%
+interference pattern they slightly
+misaligned and now I have them look a
+
+ align:start position:0%
+misaligned and now I have them look a
+ 
+
+ align:start position:0%
+misaligned and now I have them look a
+little bit better centered so now let me
+
+ align:start position:0%
+little bit better centered so now let me
+ 
+
+ align:start position:0%
+little bit better centered so now let me
+close in one path and then see if I can
+
+ align:start position:0%
+close in one path and then see if I can
+ 
+
+ align:start position:0%
+close in one path and then see if I can
+get complete darkness or complete
+
+ align:start position:0%
+get complete darkness or complete
+ 
+
+ align:start position:0%
+get complete darkness or complete
+brightness let me just the alignment as
+
+ align:start position:0%
+brightness let me just the alignment as
+ 
+
+ align:start position:0%
+brightness let me just the alignment as
+I move in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you can see I'm getting close to
+
+ align:start position:0%
+here you can see I'm getting close to
+ 
+
+ align:start position:0%
+here you can see I'm getting close to
+equal path a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's almost we're almost we're almost
+
+ align:start position:0%
+that's almost we're almost we're almost
+ 
+
+ align:start position:0%
+that's almost we're almost we're almost
+there you can see if I press on the
+
+ align:start position:0%
+there you can see if I press on the
+ 
+
+ align:start position:0%
+there you can see if I press on the
+table and see screen going bright and
+
+ align:start position:0%
+table and see screen going bright and
+ 
+
+ align:start position:0%
+table and see screen going bright and
+dark and I think I have a little bit to
+
+ align:start position:0%
+dark and I think I have a little bit to
+ 
+
+ align:start position:0%
+dark and I think I have a little bit to
+go and maybe we can get complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extinction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see pre is pretty pretty close to
+
+ align:start position:0%
+see pre is pretty pretty close to
+ 
+
+ align:start position:0%
+see pre is pretty pretty close to
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a complete extinction so in this brief
+
+ align:start position:0%
+a complete extinction so in this brief
+ 
+
+ align:start position:0%
+a complete extinction so in this brief
+demonstration then we've shown that you
+
+ align:start position:0%
+demonstration then we've shown that you
+ 
+
+ align:start position:0%
+demonstration then we've shown that you
+can get circular fringes bullseye arcs
+
+ align:start position:0%
+can get circular fringes bullseye arcs
+ 
+
+ align:start position:0%
+can get circular fringes bullseye arcs
+and what-have-you by simply making the
+
+ align:start position:0%
+and what-have-you by simply making the
+ 
+
+ align:start position:0%
+and what-have-you by simply making the
+input beam to the interferometer have
+
+ align:start position:0%
+input beam to the interferometer have
+ 
+
+ align:start position:0%
+input beam to the interferometer have
+some curvature and by adjusting the path
+
+ align:start position:0%
+some curvature and by adjusting the path
+ 
+
+ align:start position:0%
+some curvature and by adjusting the path
+length difference between the two arms
+
+ align:start position:0%
+length difference between the two arms
+ 
+
+ align:start position:0%
+length difference between the two arms
+you can get a variety of free systems
\ No newline at end of file
diff --git a/zZfr7Zqfqm4.txt b/zZfr7Zqfqm4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f5f5c141afa5c633ebf5339d4907034b3c50dfe7
--- /dev/null
+++ b/zZfr7Zqfqm4.txt
@@ -0,0 +1,1195 @@
+align:start position:0%
+ 
+instead of building all of our logic
+
+ align:start position:0%
+instead of building all of our logic
+ 
+
+ align:start position:0%
+instead of building all of our logic
+functions directly in CMOS it is easier
+
+ align:start position:0%
+functions directly in CMOS it is easier
+ 
+
+ align:start position:0%
+functions directly in CMOS it is easier
+for us to create a higher level of
+
+ align:start position:0%
+for us to create a higher level of
+ 
+
+ align:start position:0%
+for us to create a higher level of
+abstraction known as boolean gates which
+
+ align:start position:0%
+abstraction known as boolean gates which
+ 
+
+ align:start position:0%
+abstraction known as boolean gates which
+represent CMOS gates each gate is
+
+ align:start position:0%
+represent CMOS gates each gate is
+ 
+
+ align:start position:0%
+represent CMOS gates each gate is
+assigned a symbol which can then be used
+
+ align:start position:0%
+assigned a symbol which can then be used
+ 
+
+ align:start position:0%
+assigned a symbol which can then be used
+in schematic diagrams that combine
+
+ align:start position:0%
+in schematic diagrams that combine
+ 
+
+ align:start position:0%
+in schematic diagrams that combine
+multiple logic gates together in order
+
+ align:start position:0%
+multiple logic gates together in order
+ 
+
+ align:start position:0%
+multiple logic gates together in order
+to be able to understand what function
+
+ align:start position:0%
+to be able to understand what function
+ 
+
+ align:start position:0%
+to be able to understand what function
+any combination of logic gates will
+
+ align:start position:0%
+any combination of logic gates will
+ 
+
+ align:start position:0%
+any combination of logic gates will
+produce we will begin by reviewing the
+
+ align:start position:0%
+produce we will begin by reviewing the
+ 
+
+ align:start position:0%
+produce we will begin by reviewing the
+basic gates together with the truth
+
+ align:start position:0%
+basic gates together with the truth
+ 
+
+ align:start position:0%
+basic gates together with the truth
+tables that define their logic we begin
+
+ align:start position:0%
+tables that define their logic we begin
+ 
+
+ align:start position:0%
+tables that define their logic we begin
+with an inverter an inverter is a gate
+
+ align:start position:0%
+with an inverter an inverter is a gate
+ 
+
+ align:start position:0%
+with an inverter an inverter is a gate
+that has a single input and a single
+
+ align:start position:0%
+that has a single input and a single
+ 
+
+ align:start position:0%
+that has a single input and a single
+output the output is simply the inverse
+
+ align:start position:0%
+output the output is simply the inverse
+ 
+
+ align:start position:0%
+output the output is simply the inverse
+of the input when a equals 0 y equals 1
+
+ align:start position:0%
+of the input when a equals 0 y equals 1
+ 
+
+ align:start position:0%
+of the input when a equals 0 y equals 1
+and when a equals 1 y equals 0 next we
+
+ align:start position:0%
+and when a equals 1 y equals 0 next we
+ 
+
+ align:start position:0%
+and when a equals 1 y equals 0 next we
+examine and and or gates the and
+
+ align:start position:0%
+examine and and or gates the and
+ 
+
+ align:start position:0%
+examine and and or gates the and
+function expects all of its inputs to be
+
+ align:start position:0%
+function expects all of its inputs to be
+ 
+
+ align:start position:0%
+function expects all of its inputs to be
+true or 1 in order to produce a 1 as its
+
+ align:start position:0%
+true or 1 in order to produce a 1 as its
+ 
+
+ align:start position:0%
+true or 1 in order to produce a 1 as its
+output so its truth table is for a B
+
+ align:start position:0%
+output so its truth table is for a B
+ 
+
+ align:start position:0%
+output so its truth table is for a B
+equals 0 0 y equals 0 for a B equals 0 1
+
+ align:start position:0%
+equals 0 0 y equals 0 for a B equals 0 1
+ 
+
+ align:start position:0%
+equals 0 0 y equals 0 for a B equals 0 1
+y equals 0 for a B equals 1 0 y equals 0
+
+ align:start position:0%
+y equals 0 for a B equals 1 0 y equals 0
+ 
+
+ align:start position:0%
+y equals 0 for a B equals 1 0 y equals 0
+and for a B equal 1 1 y equals 1 the or
+
+ align:start position:0%
+and for a B equal 1 1 y equals 1 the or
+ 
+
+ align:start position:0%
+and for a B equal 1 1 y equals 1 the or
+function just expects at least one of
+
+ align:start position:0%
+function just expects at least one of
+ 
+
+ align:start position:0%
+function just expects at least one of
+its inputs to be true in order to
+
+ align:start position:0%
+its inputs to be true in order to
+ 
+
+ align:start position:0%
+its inputs to be true in order to
+produce a 1 as its output so for a b
+
+ align:start position:0%
+produce a 1 as its output so for a b
+ 
+
+ align:start position:0%
+produce a 1 as its output so for a b
+equals 0 0 y equals 0 but for the other
+
+ align:start position:0%
+equals 0 0 y equals 0 but for the other
+ 
+
+ align:start position:0%
+equals 0 0 y equals 0 but for the other
+3 combinations y equals 1 NAND and nor
+
+ align:start position:0%
+3 combinations y equals 1 NAND and nor
+ 
+
+ align:start position:0%
+3 combinations y equals 1 NAND and nor
+gates simply produce the inverse of and
+
+ align:start position:0%
+gates simply produce the inverse of and
+ 
+
+ align:start position:0%
+gates simply produce the inverse of and
+and or the reason that we like to work
+
+ align:start position:0%
+and or the reason that we like to work
+ 
+
+ align:start position:0%
+and or the reason that we like to work
+with nand and nor gates is because they
+
+ align:start position:0%
+with nand and nor gates is because they
+ 
+
+ align:start position:0%
+with nand and nor gates is because they
+are inverting gates and they can be
+
+ align:start position:0%
+are inverting gates and they can be
+ 
+
+ align:start position:0%
+are inverting gates and they can be
+implemented as a single CMOS gate
+
+ align:start position:0%
+implemented as a single CMOS gate
+ 
+
+ align:start position:0%
+implemented as a single CMOS gate
+whereas the and and or gates cannot
+
+ align:start position:0%
+whereas the and and or gates cannot
+ 
+
+ align:start position:0%
+whereas the and and or gates cannot
+finally the last basic gate is an
+
+ align:start position:0%
+finally the last basic gate is an
+ 
+
+ align:start position:0%
+finally the last basic gate is an
+exclusive or the exclusive or produces a
+
+ align:start position:0%
+exclusive or the exclusive or produces a
+ 
+
+ align:start position:0%
+exclusive or the exclusive or produces a
+1 output if exactly one of its two
+
+ align:start position:0%
+1 output if exactly one of its two
+ 
+
+ align:start position:0%
+1 output if exactly one of its two
+inputs is a 1 and 0 otherwise so for a B
+
+ align:start position:0%
+inputs is a 1 and 0 otherwise so for a B
+ 
+
+ align:start position:0%
+inputs is a 1 and 0 otherwise so for a B
+equals 0 0 y equals 0 for a B equals 0 1
+
+ align:start position:0%
+equals 0 0 y equals 0 for a B equals 0 1
+ 
+
+ align:start position:0%
+equals 0 0 y equals 0 for a B equals 0 1
+y equals 1
+
+ align:start position:0%
+y equals 1
+ 
+
+ align:start position:0%
+y equals 1
+a B equal to 1 0 y equals 1 and for a be
+
+ align:start position:0%
+a B equal to 1 0 y equals 1 and for a be
+ 
+
+ align:start position:0%
+a B equal to 1 0 y equals 1 and for a be
+equals to 1 1 y equals 0
+
+ align:start position:0%
+equals to 1 1 y equals 0
+ 
+
+ align:start position:0%
+equals to 1 1 y equals 0
+the output of 1 bullion gate can be used
+
+ align:start position:0%
+the output of 1 bullion gate can be used
+ 
+
+ align:start position:0%
+the output of 1 bullion gate can be used
+as an input to another bullion gate so
+
+ align:start position:0%
+as an input to another bullion gate so
+ 
+
+ align:start position:0%
+as an input to another bullion gate so
+multiple gates can be used to generate
+
+ align:start position:0%
+multiple gates can be used to generate
+ 
+
+ align:start position:0%
+multiple gates can be used to generate
+more complex functions for example here
+
+ align:start position:0%
+more complex functions for example here
+ 
+
+ align:start position:0%
+more complex functions for example here
+we have a circuit that consists of 2
+
+ align:start position:0%
+we have a circuit that consists of 2
+ 
+
+ align:start position:0%
+we have a circuit that consists of 2
+inputs and 6 gates which are an inverter
+
+ align:start position:0%
+inputs and 6 gates which are an inverter
+ 
+
+ align:start position:0%
+inputs and 6 gates which are an inverter
+and and gate and or gate 2 nor gates and
+
+ align:start position:0%
+and and gate and or gate 2 nor gates and
+ 
+
+ align:start position:0%
+and and gate and or gate 2 nor gates and
+one NAND gate in order to figure out
+
+ align:start position:0%
+one NAND gate in order to figure out
+ 
+
+ align:start position:0%
+one NAND gate in order to figure out
+what this combination of gates produces
+
+ align:start position:0%
+what this combination of gates produces
+ 
+
+ align:start position:0%
+what this combination of gates produces
+as its output we can work incrementally
+
+ align:start position:0%
+as its output we can work incrementally
+ 
+
+ align:start position:0%
+as its output we can work incrementally
+through the circuit we begin by
+
+ align:start position:0%
+through the circuit we begin by
+ 
+
+ align:start position:0%
+through the circuit we begin by
+enumerated of inputs for a and B we know
+
+ align:start position:0%
+enumerated of inputs for a and B we know
+ 
+
+ align:start position:0%
+enumerated of inputs for a and B we know
+that the output of the inverter is the
+
+ align:start position:0%
+that the output of the inverter is the
+ 
+
+ align:start position:0%
+that the output of the inverter is the
+complement of B the and and or gates use
+
+ align:start position:0%
+complement of B the and and or gates use
+ 
+
+ align:start position:0%
+complement of B the and and or gates use
+the a and B inputs directly so since we
+
+ align:start position:0%
+the a and B inputs directly so since we
+ 
+
+ align:start position:0%
+the a and B inputs directly so since we
+just reviewed what and and or gates
+
+ align:start position:0%
+just reviewed what and and or gates
+ 
+
+ align:start position:0%
+just reviewed what and and or gates
+produce we can fill in these columns as
+
+ align:start position:0%
+produce we can fill in these columns as
+ 
+
+ align:start position:0%
+produce we can fill in these columns as
+well next we want to see what our first
+
+ align:start position:0%
+well next we want to see what our first
+ 
+
+ align:start position:0%
+well next we want to see what our first
+nor gate produces its inputs are a and
+
+ align:start position:0%
+nor gate produces its inputs are a and
+ 
+
+ align:start position:0%
+nor gate produces its inputs are a and
+the complement of B we walk through each
+
+ align:start position:0%
+the complement of B we walk through each
+ 
+
+ align:start position:0%
+the complement of B we walk through each
+of the input combinations and determine
+
+ align:start position:0%
+of the input combinations and determine
+ 
+
+ align:start position:0%
+of the input combinations and determine
+the corresponding output for that gate
+
+ align:start position:0%
+the corresponding output for that gate
+ 
+
+ align:start position:0%
+the corresponding output for that gate
+for input 0 1 the output is 0 for 0 0
+
+ align:start position:0%
+for input 0 1 the output is 0 for 0 0
+ 
+
+ align:start position:0%
+for input 0 1 the output is 0 for 0 0
+the output is 1 for inputs 1 1 the
+
+ align:start position:0%
+the output is 1 for inputs 1 1 the
+ 
+
+ align:start position:0%
+the output is 1 for inputs 1 1 the
+output is 0 and for input 1 0 the output
+
+ align:start position:0%
+output is 0 and for input 1 0 the output
+ 
+
+ align:start position:0%
+output is 0 and for input 1 0 the output
+is 0 in the same manner we evaluate the
+
+ align:start position:0%
+is 0 in the same manner we evaluate the
+ 
+
+ align:start position:0%
+is 0 in the same manner we evaluate the
+outputs for our second nor gate its
+
+ align:start position:0%
+outputs for our second nor gate its
+ 
+
+ align:start position:0%
+outputs for our second nor gate its
+inputs are the outputs of the first nor
+
+ align:start position:0%
+inputs are the outputs of the first nor
+ 
+
+ align:start position:0%
+inputs are the outputs of the first nor
+gate and the and gate again we simply
+
+ align:start position:0%
+gate and the and gate again we simply
+ 
+
+ align:start position:0%
+gate and the and gate again we simply
+walk through each combination of inputs
+
+ align:start position:0%
+walk through each combination of inputs
+ 
+
+ align:start position:0%
+walk through each combination of inputs
+and specify the outputs produced by the
+
+ align:start position:0%
+and specify the outputs produced by the
+ 
+
+ align:start position:0%
+and specify the outputs produced by the
+second or gate when both inputs are 0
+
+ align:start position:0%
+second or gate when both inputs are 0
+ 
+
+ align:start position:0%
+second or gate when both inputs are 0
+the output is 1 when one input is 0 and
+
+ align:start position:0%
+the output is 1 when one input is 0 and
+ 
+
+ align:start position:0%
+the output is 1 when one input is 0 and
+the other is a 1 the output is a 0
+
+ align:start position:0%
+the other is a 1 the output is a 0
+ 
+
+ align:start position:0%
+the other is a 1 the output is a 0
+finally we take those outputs together
+
+ align:start position:0%
+finally we take those outputs together
+ 
+
+ align:start position:0%
+finally we take those outputs together
+with the outputs of the or gate and
+
+ align:start position:0%
+with the outputs of the or gate and
+ 
+
+ align:start position:0%
+with the outputs of the or gate and
+generate the final output of the circuit
+
+ align:start position:0%
+generate the final output of the circuit
+ 
+
+ align:start position:0%
+generate the final output of the circuit
+at the output of the NAND gate here when
+
+ align:start position:0%
+at the output of the NAND gate here when
+ 
+
+ align:start position:0%
+at the output of the NAND gate here when
+both inputs are 1 we get a 0 output
+
+ align:start position:0%
+both inputs are 1 we get a 0 output
+ 
+
+ align:start position:0%
+both inputs are 1 we get a 0 output
+otherwise the output is a 1
+
+ align:start position:0%
+otherwise the output is a 1
+ 
+
+ align:start position:0%
+otherwise the output is a 1
+this nand column of our truth table is
+
+ align:start position:0%
+this nand column of our truth table is
+ 
+
+ align:start position:0%
+this nand column of our truth table is
+the resulting output H now that we have
+
+ align:start position:0%
+the resulting output H now that we have
+ 
+
+ align:start position:0%
+the resulting output H now that we have
+evaluated what our output H is equal to
+
+ align:start position:0%
+evaluated what our output H is equal to
+ 
+
+ align:start position:0%
+evaluated what our output H is equal to
+for each combination of a and B we can
+
+ align:start position:0%
+for each combination of a and B we can
+ 
+
+ align:start position:0%
+for each combination of a and B we can
+represent the circuit as a single truth
+
+ align:start position:0%
+represent the circuit as a single truth
+ 
+
+ align:start position:0%
+represent the circuit as a single truth
+table whose inputs are a and B and whose
+
+ align:start position:0%
+table whose inputs are a and B and whose
+ 
+
+ align:start position:0%
+table whose inputs are a and B and whose
+output is H at this point we can express
+
+ align:start position:0%
+output is H at this point we can express
+ 
+
+ align:start position:0%
+output is H at this point we can express
+the function H as a combination of all
+
+ align:start position:0%
+the function H as a combination of all
+ 
+
+ align:start position:0%
+the function H as a combination of all
+the cases that make H equal to 1 this
+
+ align:start position:0%
+the cases that make H equal to 1 this
+ 
+
+ align:start position:0%
+the cases that make H equal to 1 this
+occurs if a and B are both equal to 0 or
+
+ align:start position:0%
+occurs if a and B are both equal to 0 or
+ 
+
+ align:start position:0%
+occurs if a and B are both equal to 0 or
+if a equals 0 and B equals 1 or if a and
+
+ align:start position:0%
+if a equals 0 and B equals 1 or if a and
+ 
+
+ align:start position:0%
+if a equals 0 and B equals 1 or if a and
+B are both equal to 1 this can be
+
+ align:start position:0%
+B are both equal to 1 this can be
+ 
+
+ align:start position:0%
+B are both equal to 1 this can be
+expressed as a boolean logic expression
+
+ align:start position:0%
+expressed as a boolean logic expression
+ 
+
+ align:start position:0%
+expressed as a boolean logic expression
+as follows H equals not a not B or not a
+
+ align:start position:0%
+as follows H equals not a not B or not a
+ 
+
+ align:start position:0%
+as follows H equals not a not B or not a
+B or a B this notation is called the sum
+
+ align:start position:0%
+B or a B this notation is called the sum
+ 
+
+ align:start position:0%
+B or a B this notation is called the sum
+of products notation any sum of products
+
+ align:start position:0%
+of products notation any sum of products
+ 
+
+ align:start position:0%
+of products notation any sum of products
+can be converted into a simple game or
+
+ align:start position:0%
+can be converted into a simple game or
+ 
+
+ align:start position:0%
+can be converted into a simple game or
+presentation of the function using only
+
+ align:start position:0%
+presentation of the function using only
+ 
+
+ align:start position:0%
+presentation of the function using only
+inverters and and or gates by having one
+
+ align:start position:0%
+inverters and and or gates by having one
+ 
+
+ align:start position:0%
+inverters and and or gates by having one
+large or gate that receives as input one
+
+ align:start position:0%
+large or gate that receives as input one
+ 
+
+ align:start position:0%
+large or gate that receives as input one
+and gate per product term inverters are
+
+ align:start position:0%
+and gate per product term inverters are
+ 
+
+ align:start position:0%
+and gate per product term inverters are
+used as needed to compliment the inputs
+
+ align:start position:0%
+used as needed to compliment the inputs
+ 
+
+ align:start position:0%
+used as needed to compliment the inputs
+to the and gates one thing that's
+
+ align:start position:0%
+to the and gates one thing that's
+ 
+
+ align:start position:0%
+to the and gates one thing that's
+interesting to note about this
+
+ align:start position:0%
+interesting to note about this
+ 
+
+ align:start position:0%
+interesting to note about this
+combination of gates is that it can
+
+ align:start position:0%
+combination of gates is that it can
+ 
+
+ align:start position:0%
+combination of gates is that it can
+easily be converted into a circuit that
+
+ align:start position:0%
+easily be converted into a circuit that
+ 
+
+ align:start position:0%
+easily be converted into a circuit that
+consists purely of NAND gates the way to
+
+ align:start position:0%
+consists purely of NAND gates the way to
+ 
+
+ align:start position:0%
+consists purely of NAND gates the way to
+do this is to realize that if you take
+
+ align:start position:0%
+do this is to realize that if you take
+ 
+
+ align:start position:0%
+do this is to realize that if you take
+the output of a gate and invert it twice
+
+ align:start position:0%
+the output of a gate and invert it twice
+ 
+
+ align:start position:0%
+the output of a gate and invert it twice
+you produce the original output this
+
+ align:start position:0%
+you produce the original output this
+ 
+
+ align:start position:0%
+you produce the original output this
+means that we can add two inverters
+
+ align:start position:0%
+means that we can add two inverters
+ 
+
+ align:start position:0%
+means that we can add two inverters
+between each and output and/or input we
+
+ align:start position:0%
+between each and output and/or input we
+ 
+
+ align:start position:0%
+between each and output and/or input we
+can draw these inverters as bubbles
+
+ align:start position:0%
+can draw these inverters as bubbles
+ 
+
+ align:start position:0%
+can draw these inverters as bubbles
+which represent inversion where replace
+
+ align:start position:0%
+which represent inversion where replace
+ 
+
+ align:start position:0%
+which represent inversion where replace
+one bubble on the output of the and gate
+
+ align:start position:0%
+one bubble on the output of the and gate
+ 
+
+ align:start position:0%
+one bubble on the output of the and gate
+and the other bubble at the inputs of
+
+ align:start position:0%
+and the other bubble at the inputs of
+ 
+
+ align:start position:0%
+and the other bubble at the inputs of
+the or gate we know that an and gate
+
+ align:start position:0%
+the or gate we know that an and gate
+ 
+
+ align:start position:0%
+the or gate we know that an and gate
+followed by an inversion is simply a
+
+ align:start position:0%
+followed by an inversion is simply a
+ 
+
+ align:start position:0%
+followed by an inversion is simply a
+NAND gate we also know that an inverter
+
+ align:start position:0%
+NAND gate we also know that an inverter
+ 
+
+ align:start position:0%
+NAND gate we also know that an inverter
+is equivalent to a NAND gate with both
+
+ align:start position:0%
+is equivalent to a NAND gate with both
+ 
+
+ align:start position:0%
+is equivalent to a NAND gate with both
+of its inputs tied together in addition
+
+ align:start position:0%
+of its inputs tied together in addition
+ 
+
+ align:start position:0%
+of its inputs tied together in addition
+using demorgan's law we know that not a
+
+ align:start position:0%
+using demorgan's law we know that not a
+ 
+
+ align:start position:0%
+using demorgan's law we know that not a
+or not
+
+ align:start position:0%
+or not
+ 
+
+ align:start position:0%
+or not
+B is equivalent to not of a and B this
+
+ align:start position:0%
+B is equivalent to not of a and B this
+ 
+
+ align:start position:0%
+B is equivalent to not of a and B this
+means that the bubbles followed by the
+
+ align:start position:0%
+means that the bubbles followed by the
+ 
+
+ align:start position:0%
+means that the bubbles followed by the
+or gate can also be replaced with a NAND
+
+ align:start position:0%
+or gate can also be replaced with a NAND
+ 
+
+ align:start position:0%
+or gate can also be replaced with a NAND
+gate
+
+ align:start position:0%
+gate
+ 
+
+ align:start position:0%
+gate
+thus arriving at our equivalent circuit
+
+ align:start position:0%
+thus arriving at our equivalent circuit
+ 
+
+ align:start position:0%
+thus arriving at our equivalent circuit
+representation consisting purely of NAND
+
+ align:start position:0%
+representation consisting purely of NAND
+ 
+
+ align:start position:0%
+representation consisting purely of NAND
+gates the advantage of using NAND gates
+
+ align:start position:0%
+gates the advantage of using NAND gates
+ 
+
+ align:start position:0%
+gates the advantage of using NAND gates
+to implement the circuit is that NAND
+
+ align:start position:0%
+to implement the circuit is that NAND
+ 
+
+ align:start position:0%
+to implement the circuit is that NAND
+gates are inverting logic where each
+
+ align:start position:0%
+gates are inverting logic where each
+ 
+
+ align:start position:0%
+gates are inverting logic where each
+gate can be implemented as a single CMOS
+
+ align:start position:0%
+gate can be implemented as a single CMOS
+ 
+
+ align:start position:0%
+gate can be implemented as a single CMOS
+gate all functions can be expressed as a
+
+ align:start position:0%
+gate all functions can be expressed as a
+ 
+
+ align:start position:0%
+gate all functions can be expressed as a
+combination of NAND gates so a NAND gate
+
+ align:start position:0%
+combination of NAND gates so a NAND gate
+ 
+
+ align:start position:0%
+combination of NAND gates so a NAND gate
+is considered a universal gate nor gates
+
+ align:start position:0%
+is considered a universal gate nor gates
+ 
+
+ align:start position:0%
+is considered a universal gate nor gates
+are also universal and can be used to
+
+ align:start position:0%
+are also universal and can be used to
+ 
+
+ align:start position:0%
+are also universal and can be used to
+express any function furthermore any
+
+ align:start position:0%
+express any function furthermore any
+ 
+
+ align:start position:0%
+express any function furthermore any
+circuit that can be used to implement
+
+ align:start position:0%
+circuit that can be used to implement
+ 
+
+ align:start position:0%
+circuit that can be used to implement
+any other function is also considered
+
+ align:start position:0%
+any other function is also considered
+ 
+
+ align:start position:0%
+any other function is also considered
+universal to determine if a gate G is
+
+ align:start position:0%
+universal to determine if a gate G is
+ 
+
+ align:start position:0%
+universal to determine if a gate G is
+universal one needs to check if one can
+
+ align:start position:0%
+universal one needs to check if one can
+ 
+
+ align:start position:0%
+universal one needs to check if one can
+convert G into either a NAND or nor gate
+
+ align:start position:0%
+convert G into either a NAND or nor gate
+ 
+
+ align:start position:0%
+convert G into either a NAND or nor gate
+by simply using one or more copies of G
+
+ align:start position:0%
+by simply using one or more copies of G
+ 
+
+ align:start position:0%
+by simply using one or more copies of G
+together with low and high constant
+
+ align:start position:0%
+together with low and high constant
+ 
+
+ align:start position:0%
+together with low and high constant
+inputs
\ No newline at end of file
diff --git a/zjUDy6a5vx4.txt b/zjUDy6a5vx4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30f7d6d28d5484760bb9e730aee5290f683e5911
--- /dev/null
+++ b/zjUDy6a5vx4.txt
@@ -0,0 +1,3911 @@
+The last lecture of 6.046.
+We are here today to talk more
+
+about cache oblivious
+algorithms.
+
+Last class, we saw several
+cache oblivious algorithms,
+
+although none of them quite too
+difficult.
+
+Today we will see two difficult
+cache oblivious algorithms,
+
+a little bit more advanced.
+I figure we should do something
+
+advanced for the last class just
+to get to some exciting climax.
+
+So without further ado,
+let's get started.
+
+Last time, we looked at the
+binary search problem.
+
+Or, we looked at binary search,
+rather.
+
+And so, the binary search did
+not do so well in the cache
+
+oblivious context.
+And, some people asked me after
+
+class, is it possible to do
+binary search while cache
+
+obliviously?
+And, indeed it is with
+
+something called static search
+trees.
+
+So, this is really binary
+search.
+
+So, I mean, the abstract
+problem is I give you N items,
+
+say presorted,
+build some static data
+
+structure so that you can search
+among those N items quickly.
+
+And quickly,
+I claim, means log base B of N.
+
+We know that with B trees,
+our goal is to get log base B
+
+of N.
+We know that we can achieve
+
+that with B trees when we know
+B.
+
+We'd like to do that when we
+don't know B.
+
+And that's what cache oblivious
+static search trees achieve.
+
+So here's what we're going to
+do.
+
+As you might suspect,
+we're going to use a tree.
+
+So, we're going to store our N
+elements in a complete binary
+
+tree.
+We can't use B trees because we
+
+don't know what B is.
+So, we'll use a binary tree.
+
+And the key is how we lay out a
+binary tree.
+
+The binary tree will have N
+nodes.
+
+Or, you can put the data in the
+leaves.
+
+It doesn't really matter.
+So, here's our tree.
+
+There are the N nodes.
+And we're storing them,
+
+I didn't say,
+in order, you know,
+
+in the usual way,
+in order in a binary tree,
+
+which makes it a binary search
+tree.
+
+So we now had a search in this
+thing.
+
+So, the search will just start
+at the root and a walk down some
+
+root-to-leaf path.
+OK, and each point you know
+
+whether to go left or to go
+right because things are in
+
+order.
+So we're assuming here that we
+
+have an ordered universe of
+keys.
+
+So that's easy.
+We know that that will take log
+
+N time.
+The question is how many memory
+
+transfers?
+We'd like a lot of the nodes
+
+near the root to be somehow
+closer and one block.
+
+But we don't know what the
+block size is.
+
+So are going to do is carve the
+tree in the middle level.
+
+We're going to use divide and
+conquer for our layout of the
+
+tree, how we order the nodes in
+memory.
+
+And the divide and conquer is
+based on cutting in the middle,
+
+which is a bit weird.
+It's not our usual divide and
+
+conquer.
+And we'll see this more than
+
+once today.
+So, when you cut on the middle
+
+level, if the height of your
+original tree is log N,
+
+maybe log N plus one or
+something, it's roughly log N,
+
+then the top half will be log N
+over two.
+
+And at the height of the bottom
+pieces will be log N over two.
+
+How many nodes will there be in
+the top tree?
+
+N over two?
+Not quite.
+
+Two to the log N over two,
+square root of N.
+
+OK, so it would be about root N
+nodes over here.
+
+And therefore,
+there will be about root N
+
+subtrees down here,
+one for each,
+
+or a couple for each leaf.
+OK, so we have these subtrees
+
+of root N, and there are about
+root N of them.
+
+OK, this is how we are carving
+our tree.
+
+Now, we're going to recurse on
+each of the pieces.
+
+I'd like to redraw this
+slightly, sorry,
+
+just to make it a little bit
+clearer.
+
+These triangles are really
+trees, and they are connected by
+
+edges to this tree up here.
+So what we are really doing is
+
+carving in the middle level of
+edges in the tree.
+
+And if N is not exactly a power
+of two, you have to round your
+
+level by taking floors or
+ceilings.
+
+But you cut roughly in the
+middle level of edges.
+
+There is a lot of edges here.
+You conceptually slice there.
+
+That gives you a top tree and
+the bottom tree,
+
+several bottom trees,
+each of size roughly root N.
+
+OK, and then we are going to
+recursively layout these root N
+
+plus one subtrees,
+and then concatenate.
+
+So, this is the idea of the
+recursive layout.
+
+We sought recursive layouts
+with matrices last time.
+
+This is doing the same thing
+for a tree.
+
+So, I want to recursively
+layout the top tree.
+
+So here's the top tree.
+And I imagine it being somehow
+
+squashed down into a linear
+array recursively.
+
+And then I do the same thing
+for each of the bottom trees.
+
+So here are all the bottom
+trees.
+
+And I squashed each of them
+down into some linear order.
+
+And then I concatenate those
+linear orders.
+
+That's the linear order of the
+street.
+
+And you need a base case.
+And the base case,
+
+just a single node,
+is stored in the only order of
+
+a single node there is.
+OK, so that's a recursive
+
+layout of a binary search tree.
+It turns out this works really
+
+well.
+And let's quickly do a little
+
+example just so it's completely
+clear what this layout is
+
+because it's a bit bizarre maybe
+the first time you see it.
+
+So let me draw my favorite
+picture.
+
+So here's a tree of height four
+or three depending on how you
+
+count.
+We divide in the middle level,
+
+and we say, OK,
+that's the top tree.
+
+And then these are the bottom
+trees.
+
+So there's four bottom trees.
+So there are four children
+
+hanging off the root tree.
+They each have the same size in
+
+this case.
+They should all roughly be the
+
+same size.
+And the first we layout the top
+
+thing where we divide on the
+middle level.
+
+We say, OK, this comes first.
+And then, the bottom subtrees
+
+come next, two and three.
+So, I'm writing down the order
+
+in which these nodes are stored
+in an array.
+
+And then, we visit this tree so
+we get four, five,
+
+six.
+And then we visit this one so
+
+we get seven,
+eight, nine.
+
+And then the subtree,
+10, 11, 12, and then the last
+
+subtree.
+So that's the order in which
+
+you store these 15 nodes.
+And you can build that up
+
+recursively.
+OK, so the structure is fairly
+
+simple, just a binary structure
+which we know and love,
+
+but store it in this funny
+order.
+
+This is not depth research
+order or level order,
+
+lots of natural things you
+might try, none of which work in
+
+cache oblivious context.
+This is pretty much the only
+
+thing that works.
+And the intuition as,
+
+well, we are trying to mimic
+all kinds of B trees.
+
+So, if you want a binary tree,
+well, that's the original tree.
+
+It doesn't matter how you store
+things.
+
+If you want a tree where the
+branching factor is four,
+
+well, then here it is.
+These blocks give you a
+
+branching factor of four.
+If we had more leaves down
+
+here, there would be four
+children hanging off of that
+
+node.
+And these are all clustered
+
+together consecutively in
+memory.
+
+So, if your block size happens
+to be three, then this is a
+
+perfect way to store things for
+a block size of three.
+
+If you're block size happens to
+be probably 15,
+
+right, if we count the number
+of, right, the number of nodes
+
+in here is 15,
+if you're block size happens to
+
+be 15, then this recursion will
+give you a perfect blocking in
+
+terms of 15.
+And in general,
+
+it's actually mimicking block
+sizes of 2^K-1.
+
+Think powers of two.
+OK, that's the intuition.
+
+Let me give you the formal
+analysis to make it clearer.
+
+So, we claim that there are
+order, log base B of N memory
+
+transfers.
+That's what we want to prove no
+
+matter what B is.
+So here's what we're going to
+
+do.
+You may recall last time when
+
+we analyzed divide and conquer
+algorithms, we wrote our
+
+recurrence, and that the base
+case was the key.
+
+Here, in fact,
+we are only going to think
+
+about the base case in a certain
+sense.
+
+We don't have,
+really, recursion in the
+
+algorithm.
+The algorithm is just walking
+
+down some root-to-leaf path.
+We only have a recursion in a
+
+definition of the layout.
+So, we can be a little bit more
+
+flexible.
+We don't have to look at our
+
+recurrence.
+We are just going to think
+
+about the base case.
+I want to imagine,
+
+you start with the big
+triangle.
+
+That you cut it in the middle;
+you get smaller triangles.
+
+Imagine the point at which you
+keep recursively cutting.
+
+So imagine this process.
+Big triangles halve in height
+
+each time.
+They're getting smaller and
+
+smaller, stop cutting at the
+point where a triangle fits in a
+
+block.
+OK, and look at that time.
+
+OK, the recursion actually goes
+all the way, but in the analysis
+
+let's think about the point
+where the chunk fits in a block
+
+in one of these triangles,
+one of these boxes fits in a
+
+block.
+So, I'm going to call this a
+
+recursive level.
+So, I'm imagining expanding all
+
+of the recursions in parallel.
+This is some level of detail,
+
+some level of refinement of the
+trees at which the tree you're
+
+looking at, the triangle,
+has size.
+
+In other words,
+there is a number of nodes in
+
+that triangle is less than or
+equal to B.
+
+OK, so let me draw a picture.
+So, I want to draw sort of this
+
+picture but where instead of
+nodes, I have little triangles
+
+of size, at most,
+B.
+
+So, the picture looks something
+like this.
+
+We have a little triangle of
+size, at most,
+
+B.
+It has a bunch of children
+
+which are subtrees of size,
+at most, B, the same size.
+
+And then, these are in a chunk,
+and then we have other chunks
+
+that look like that in recursion
+potentially.
+
+OK, so I haven't drawn
+everything.
+
+There would be a whole bunch
+of, between B and B^2,
+
+in fact, subtrees,
+other squares of this size.
+
+So here, I had to refine the
+entire tree here.
+
+And then I refined each of the
+subtrees here and here at these
+
+levels.
+And then it turned out after
+
+these two recursive levels,
+everything fits in a block.
+
+Everything has the same size,
+so at some point they will all
+
+fit within a block.
+And they might actually be
+
+quite a bit smaller than the
+block.
+
+How small?
+So, what I'm doing is cutting
+
+the number of levels and half at
+each point.
+
+And I stop when the height of
+one of these trees is
+
+essentially at most log B
+because that's when the number
+
+of nodes at there will be B
+roughly.
+
+So, how small can the height
+be?
+
+I keep dividing at half and
+stopping when it's,
+
+at most, log B.
+Log B over two.
+
+So it's, at most,
+log B, it's at least half log
+
+B.
+Therefore, the number of nodes
+
+it here could be between the
+square root of B and B.
+
+So, this could be a lot smaller
+and less than a constant factor
+
+of a block, a claim that doesn't
+matter.
+
+It's OK.
+This could be a small square
+
+root of B.
+I'm not even going to write
+
+that it could be a small square
+root of B because that doesn't
+
+play a role in the analysis.
+It's a worry,
+
+but it's OK essentially because
+our bound only involves log B.
+
+It doesn't involve B.
+So, here's what we do.
+
+We know that each of the height
+of one of these triangles of
+
+size, at most,
+B is at least a half log B.
+
+And therefore,
+if you look at a search path,
+
+so, when we do a search in this
+tree, we're going to start up
+
+here.
+And I'm going to mess up the
+
+diagram now.
+We're going to follow some
+
+path, maybe I should have drawn
+it going down here.
+
+We visit through some of these
+triangles, but it's a
+
+root-to-node path in the tree.
+So, how many of the triangles
+
+could it visit?
+Well, the height of the tree
+
+divided by the height of one of
+the triangles.
+
+So, this visits,
+at most, log N over half log B
+
+triangles, which looks good.
+This is log base B of N,
+
+mind you off factor of two.
+Now, what we worry about is how
+
+many blocks does a triangle
+occupy?
+
+One of these triangles should
+fit in a block.
+
+We know by the recursive
+layout, it is stored in a
+
+consecutive region in memory.
+So, how many blocks could
+
+occupy?
+Two, because of alignment,
+
+it might fall across the
+boundary of a block,
+
+but at most,
+one boundary.
+
+So, it fits in two blocks.
+So, each triangle fits in one
+
+block, but is in,
+at most, two blocks,
+
+memory blocks,
+size B depending on alignment.
+
+So, the number of memory
+transfers, in other words,
+
+a number of blocks we read,
+because all we are doing here
+
+is reading in a search,
+is at most two blocks per
+
+triangle.
+There are this many triangles,
+
+so it's at most,
+4 log base B of N,
+
+OK, which is order log base B
+of N.
+
+And there are papers about
+decreasing this constant 4 with
+
+more sophisticated data
+structures.
+
+You can get it down to a little
+bit less than two I think.
+
+So, there you go.
+So not quite as good as B trees
+
+in terms of the constant,
+but pretty good.
+
+And what's good is that this
+data structure works for all B
+
+at the same time.
+This analysis works for all B.
+
+So, we have a multilevel memory
+hierarchy, no problem.
+
+Any questions about this data
+structure?
+
+This is already pretty
+sophisticated,
+
+but we are going to get even
+more sophisticated.
+
+Next, OK, good,
+no questions.
+
+This is either perfectly clear,
+or a little bit difficult,
+
+or both.
+So, now, I debated with myself
+
+what exactly I would cover next.
+There are two natural things I
+
+could cover, both of which are
+complicated.
+
+My first result in the cache
+oblivious world is making this
+
+data structure dynamic.
+So, there is a dynamic B tree
+
+that's cache oblivious that
+works for all values of B.
+
+And it gets log base B of N,
+insert, delete,
+
+and search.
+So, this just gets search in
+
+log base B of N.
+That data structure,
+
+our first paper was damn
+complicated, and then it got
+
+simplified.
+It's now not too hard,
+
+but it takes a couple of
+lectures in an advanced
+
+algorithms class to teach it.
+So, I'm not going to do that.
+
+But there you go.
+It exists.
+
+Instead, we're going to cover
+our favorite problem sorting in
+
+the cache oblivious context.
+And this is quite complicated,
+
+more than you'd expect,
+OK, much more complicated than
+
+it is in a multithreaded setting
+to get the right answer,
+
+anyway.
+Maybe to get the best answer in
+
+a multithreaded setting is also
+complicated.
+
+The version we got last week
+was pretty easy.
+
+But before we go to cache
+oblivious sorting,
+
+let me talk about cache aware
+sorting because we need to know
+
+what bound we are aiming for.
+And just to warn you,
+
+I may not get to the full
+analysis of the full cache
+
+oblivious sorting.
+But I want to give you an idea
+
+of what goes into it because
+it's pretty cool,
+
+I think, a lot of ideas.
+So, how might you sort?
+
+So, cache aware,
+we assume we can do everything.
+
+Basically, this means we have B
+trees.
+
+That's the only other structure
+we know.
+
+How would you sort N numbers,
+given that that's the only data
+
+structure you have?
+Right, just add them into the B
+
+tree, and then do an in-order
+traversal.
+
+That's one way to sort,
+perfectly reasonable.
+
+We'll call it repeated
+insertion into a B tree.
+
+OK, we know in the usual
+setting, and the BST sort,
+
+where you use a balanced binary
+search tree, like red-black
+
+trees, that takes N log N time,
+log N per operation,
+
+and that's an optimal sorting
+algorithm in the comparison
+
+model, only thinking about
+comparison model here.
+
+So, how many memory transfers
+does this data structure takes?
+
+Sorry, this algorithm for
+sorting?
+
+The number of memory transfers
+is a function of N,
+
+and B_M of N is?
+This is easy.
+
+N insertions,
+OK, you have to think about N
+
+order traversal.
+You have to remember back your
+
+analysis of B trees,
+but this is not too hard.
+
+How long does the insertion
+take, the N insertions?
+
+N log base B of N.
+How long does the traversal
+
+take?
+Less time.
+
+If we think about it,
+you can get away with N over B
+
+memory transfers,
+so quite a bit less than this.
+
+This is bigger than N,
+which is actually pretty bad.
+
+N memory transfers means
+essentially you're doing random
+
+access, visiting every element
+in some random order.
+
+It's even worse.
+There's even a log factor.
+
+Now, the log factor goes down
+by this log B factor.
+
+But, this is actually a really
+bad sorting bound.
+
+So, unlike normal algorithms,
+where using a search tree is a
+
+good way to sort,
+in cache oblivious or cache
+
+aware sorting it's really,
+really bad.
+
+So, what's another natural
+algorithm you might try,
+
+given what we know for sorting?
+And, even cache oblivious,
+
+all the algorithms we've seen
+are cache oblivious.
+
+So, what's a good one to try?
+Merge sort.
+
+OK, we did merge sort in
+multithreaded algorithms.
+
+Let's try a merge sort,
+a good divide and conquer
+
+thing.
+So, I'm going to call it binary
+
+merge sort because it splits the
+array into two pieces,
+
+and it recurses on the two
+pieces.
+
+So, you get a binary recursion
+tree.
+
+So, let's analyze it.
+So the number of memory
+
+transfers on N elements,
+so I mean it has a pretty good
+
+recursive layout,
+right?
+
+The two subarrays that we get
+what we partition our array are
+
+consecutive.
+So, we're recursing on this,
+
+recursing on this.
+So, it's a nice cache oblivious
+
+layout.
+And this is even for cache
+
+aware.
+This is a pretty good
+
+algorithm, a lot better than
+this one, as we'll see.
+
+But, what is the recurrence we
+get?
+
+So, here we have to go back to
+last lecture when we were
+
+thinking about recurrences for
+recursive cache oblivious
+
+algorithms.
+
+I mean, the first part should
+be pretty easy.
+
+There's an O.
+Well, OK, let's put the O at
+
+the end, the divide and the
+conquer part at the end.
+
+The recursion is 2MT of N over
+two, good.
+
+All right, that's just like the
+merge sort recurrence,
+
+and that's the additive term
+that you're thinking about.
+
+OK, so normally,
+we would pay a linear additive
+
+term here, order N because
+merging takes order N time.
+
+Now, we are merging,
+which is three parallel scans,
+
+the two inputs and the output.
+OK, they're not quite parallel
+
+interleaved.
+They're a bit funnily
+
+interleaved, but as long as your
+cache stores at least three
+
+blocks, this is also linear time
+in this setting,
+
+which means you visit each
+block a constant number of
+
+times.
+OK, that's the recurrence.
+
+Now, we also need a base case,
+of course.
+
+We've seen two base cases,
+one MT of B,
+
+and the other,
+MT of whatever fits in cache.
+
+So, let's look at that one
+because it's better.
+
+So, for some constant,
+C, if I have an array of size
+
+M, this fits in cache,
+actually, probably C is one
+
+here, but I'll just be careful.
+For some constant,
+
+this fits in cache.
+A problem of this size fits in
+
+cache, and in that case,
+the number of memory transfers
+
+is, anyone remember?
+We've used this base case more
+
+than once before.
+Do you remember?
+
+Sorry?
+CM over B.
+
+I've got a big O,
+so M over B.
+
+Order M over B because this is
+the size of the data.
+
+So, I mean, just to read it all
+in takes M over B.
+
+Once it's in cache,
+it doesn't really matter what I
+
+do as long as I use linear space
+for the right constant here.
+
+As long as I use linear space
+in that algorithm,
+
+I'll stay in cache,
+and therefore,
+
+not have to write anything out
+until the very end and I spend M
+
+over B to write it out.
+OK, so I can't really spend
+
+more than M over B almost no
+matter what algorithm I have,
+
+so long as it uses linear
+space.
+
+So, this is a base case that's
+useful pretty much in any
+
+algorithm.
+OK, that's a recurrence.
+
+Now we just have to solve it.
+OK, let's see how good binary
+
+merge sort is.
+OK, and again,
+
+I'm going to just give the
+intuition behind the solution to
+
+this recurrence.
+And I won't use the
+
+substitution method to prove it
+formally.
+
+But this one's actually pretty
+simple.
+
+So, we have,
+at the top, actually I'm going
+
+to write it over here.
+Otherwise I won't be able to
+
+see.
+So, at the top of the
+
+recursion, we have N over B
+costs.
+
+I'll ignore the constants.
+There is probably also on
+
+additive one,
+which I'm ignoring here.
+
+Then we split into two problems
+of half the size.
+
+So, we get a half N over B,
+and a half N over B.
+
+OK, usually this was N,
+half N, half N.
+
+You should regard it as from
+lecture one.
+
+So, the total on this level is
+N over B.
+
+The total on this level is N
+over B.
+
+And, you can prove by
+induction, that every level is N
+
+over B.
+The question is how many levels
+
+are there?
+Well, at the bottom,
+
+so, dot, dot,
+dot, at the bottom of this
+
+recursion tree we should get
+something of size M,
+
+and then we're paying M over B.
+Actually here we're paying M
+
+over B.
+So, it's a good thing those
+
+match.
+They should.
+
+So here, we have a bunch of
+leaves, all the size M over B.
+
+You can also compute the number
+of leaves here is N over M.
+
+If you want to be extra sure,
+you should always check the
+
+leaf level.
+It's a good idea.
+
+So we have N over M leaves,
+each costing M over B.
+
+This is an M.
+So, this is N over B also.
+
+So, every level here is N over
+B memory transfers.
+
+And the number of levels is one
+N over B?
+
+Log N over B.
+Yep, that's right.
+
+I just didn't hear it right.
+OK, we are starting at N.
+
+We're getting down to M.
+So, you can think of it as log
+
+N, the whole binary tree minus
+the subtrees log M,
+
+and that's the same as log N
+over M, OK, or however you want
+
+to think about it.
+The point is that this is a log
+
+base two.
+That's where we are not doing
+
+so great.
+So this is actually a pretty
+
+good algorithm.
+So let me write the solution
+
+over here.
+So, the number of memory
+
+transfers on N items is going to
+be the number of levels times
+
+the cost of each level.
+So, this is N over B times log
+
+base two of N over M,
+which is a lot better than
+
+repeated insertion into a B
+tree.
+
+Here, we were getting N times
+log N over log B,
+
+OK, so N log N over log B.
+We're getting a log B savings
+
+over not proving anything,
+and here we are getting a
+
+factor of B savings,
+N log N over B.
+
+In fact, we even made it a
+little bit smaller by dividing
+
+this N by M.
+That doesn't matter too much.
+
+This dividing by B is a big
+one.
+
+OK, so we're almost there.
+This is almost an optimal
+
+algorithm.
+It's even cache oblivious,
+
+which is pretty cool.
+And that extra little step,
+
+which is that you should be
+able to get on other log B
+
+factor improvement,
+I want to combine these two
+
+ideas.
+I want to keep this factor B
+
+improvement over N log N,
+and I want to keep this factor
+
+log B improvement over N log N,
+and get them together.
+
+So, first, before we do that
+cache obliviously,
+
+let's do it cache aware.
+So, this is the third cache
+
+aware algorithm.
+This one was also cache
+
+oblivious.
+So, how should I modify a merge
+
+sort in order to do better?
+I mean, I have this log base
+
+two, and I want a log base B,
+more or less.
+
+So, how would I do that with
+merge sort?
+
+Yeah?
+Split into B subarrays,
+
+yeah.
+Instead of doing binary merge
+
+sort, this is what I was hinting
+at here, instead of splitting it
+
+into two pieces,
+and recursing on the two
+
+pieces, and then merging them,
+I could split potentially into
+
+more pieces.
+OK, and to do that,
+
+I'm going to use my cache.
+So the idea is B pieces.
+
+This is actually not the best
+thing to do, although B pieces
+
+does work.
+And, it's what I was hinting at
+
+because I was saying I want a
+log B.
+
+It's actually not quite log B.
+It's log M over B.
+
+OK, but let's see.
+So, what is the most pieces I
+
+could split into?
+Right, well,
+
+I could split into N pieces.
+That would be good,
+
+wouldn't it,
+at only one recursive level?
+
+I can't split into N pieces.
+Why?
+
+What happens wrong when I split
+into N pieces?
+
+That would be the ultimate.
+You can't merge,
+
+exactly.
+So, if I have N pieces,
+
+you can't merge in cache.
+I mean, so in order to merge in
+
+cache, what I need is to be able
+to store an entire block from
+
+each of the lists that I'm
+merging.
+
+If I can store an entire block
+in cache for each of the lists,
+
+then it's a bunch of parallel
+scans.
+
+So this is like testing the
+limit of parallel scanning
+
+technology.
+If you have K parallel scans,
+
+and you can fit K blocks in
+cache, then all is well because
+
+you can scan through each of
+those K arrays,
+
+and have one block from each of
+the K arrays in cache at the
+
+same time.
+So, that's the idea.
+
+Now, how many blocks can I fit
+in cache?
+
+M over B.
+That's the biggest I could do.
+
+So this will give the best
+running time among these kinds
+
+of merge sort algorithms.
+This is an M over B way merge
+
+sort.
+OK, so now we get somewhat
+
+better recurrence.
+We split into M over B
+
+subproblems now,
+each of size,
+
+well, it's N divided by M over
+B without thinking.
+
+And, the claim is that the
+merge time is still linear
+
+because we have barely enough,
+OK, maybe I should describe
+
+this algorithm.
+So, we divide,
+
+because we've never really done
+non-binary merge sort.
+
+We divide into M over B equal
+size subarrays instead of two.
+
+Here, we are clearly doing a
+cache aware algorithm.
+
+We are assuming we know what M
+over B is.
+
+So, then we recursively sort
+each subarray,
+
+and then we conquer.
+We merge.
+
+And, the reason merge works is
+because we can afford one block
+
+in cache.
+So, let's call it one cache
+
+block per subarray.
+OK, actually,
+
+if you're careful,
+you also need one block for the
+
+output of the merged array
+before you write it out.
+
+So, it should be M over B minus
+one.
+
+But, let's ignore some additive
+constants.
+
+OK, so this is the recurrence
+we get.
+
+The base case is the same.
+And, what improves here?
+
+I mean, the per level cost
+doesn't change,
+
+I claim, because at the top we
+get N over B.
+
+This does before.
+Then we split into M over B
+
+subproblems, each of which costs
+a one over M over B factor times
+
+N over B.
+OK, so you add all those up,
+
+you still get N over B because
+we are not decreasing the number
+
+of elements.
+We're just splitting them.
+
+There's now M over B
+subproblems, each of one over M
+
+over B the size.
+So, just like before,
+
+each level will sum to N over
+B.
+
+What changes is the number of
+levels because now we have
+
+bigger branching factor.
+Instead of log base two,
+
+it's now log base the branching
+factor.
+
+So, the height of this tree is
+log base M over B of N over M,
+
+I believe.
+Let me make sure that agrees
+
+with me.
+Yeah.
+
+OK, and if you're careful,
+this counts not quite the
+
+number of levels,
+but the number of levels minus
+
+one.
+So, I'm going to one plus one
+
+here.
+And the reason why is this is
+
+not quite the bound that I want.
+So, we have log base M over B.
+
+What I really want,
+actually, is N over B.
+
+I claim that these are the same
+because we have minus,
+
+yeah, that's good.
+OK, this should come as rather
+
+mysterious, but it's because I
+know what the sorting bound
+
+should be as I'm doing this
+arithmetic.
+
+So, I'm taking log base M over
+B of N over M.
+
+I'm not changing the base of
+the log.
+
+I'm just saying,
+well, N over M,
+
+that is N over B divided by M
+over B because then the B's
+
+cancel, and the M goes on the
+bottom.
+
+So, if I do that in the logs,
+I get log of N over B minus log
+
+of M over B minus,
+because I'm dividing.
+
+OK, now, log base M over B of M
+over B is one.
+
+So, these cancel,
+and I get log base M over B,
+
+N over B, which is what I was
+aiming for.
+
+Why?
+Because that's the right bound
+
+as it's normally written.
+OK, that's what we will be
+
+trying to get cache obliviously.
+So, that's the height of the
+
+search tree, and at each level
+we are paying N over B memory
+
+transfers.
+So, the overall number of
+
+memory transfers for this M over
+B way merge sort is the sorting
+
+bound.
+
+This is, I'll put it in a box.
+This is the sorting bound,
+
+and it's very special because
+it is the optimal number of
+
+memory transfers for sorting N
+items cache aware.
+
+This has been known since,
+like, 1983.
+
+OK, this is the best thing to
+do.
+
+It's a really weird bound,
+but if you ignore all the
+
+divided by B's,
+it's sort of like N times log
+
+base M of N.
+So, that's little bit more
+
+reasonable.
+But, there's lots of divided by
+
+B's.
+So, the number of the blocks in
+
+the input times log base the
+number of blocks in the cache of
+
+the number of blocks in the
+input.
+
+That's a little bit more
+intuitive.
+
+That is the bound.
+And that's what we are aiming
+
+for.
+So, this algorithm,
+
+crucially, assume that we knew
+what M over B was.
+
+Now, we are going to try and do
+it without knowing M over B,
+
+do it cache obliviously.
+And that is the result of only
+
+a few years ago.
+Are you ready?
+
+Everything clear so far?
+It's a pretty natural
+
+algorithm.
+We were going to try to mimic
+
+it essentially and do a merge
+sort, but not M over B way merge
+
+sort because we don't know how.
+We're going to try and do it
+
+essentially a square root of N
+way merge sort.
+
+If you play around,
+that's the natural thing to do.
+
+The tricky part is that it's
+hard to merge square root of N
+
+lists at the same time,
+in a cache efficient way.
+
+We know that if the square root
+of N is bigger than M over B,
+
+you're hosed if you just do a
+straightforward merge.
+
+So, we need a fancy merge.
+We are going to do a divide and
+
+conquer merge.
+It's a lot like the
+
+multithreaded algorithms of last
+week, try and do a divide and
+
+conquer merge so that no matter
+how many lists are merging,
+
+as long as it's less than the
+square root of N,
+
+or actually cubed root of N,
+we can do it cache efficiently,
+
+OK?
+So, we'll do this,
+
+we need a bit of setup.
+But that's where we're going,
+
+cache oblivious sorting.
+So, we want to get the sorting
+
+bound, and, yeah.
+It turns out,
+
+to do cache oblivious sorting,
+you need an assumption about
+
+the cache size.
+This is kind of annoying,
+
+because we said,
+well, cache oblivious
+
+algorithms should work for all
+values of B and all values of M.
+
+But, you can actually prove you
+need an additional assumption in
+
+order to get this bound cache
+obliviously.
+
+That's the result of,
+like, last year by Garrett
+
+Brodel.
+So, and the assumption is,
+
+well, the assumption is fairly
+weak.
+
+That's the good news.
+OK, we've actually made an
+
+assumption several times.
+We said, well,
+
+assuming the cache can store at
+least three blocks,
+
+or assuming the cache can store
+at least four blocks,
+
+yeah, it's reasonable to say
+the cache can store at least
+
+four blocks, or at least any
+constant number of blocks.
+
+This is that the number of
+blocks that your cache can store
+
+is at least B to the epsilon
+blocks.
+
+This is saying your cache
+isn't, like, really narrow.
+
+It's about as tall as it is
+wide.
+
+This actually gives you a lot
+of sloth.
+
+And, we're going to use a
+simple version of this
+
+assumption that M is at least
+B^2.
+
+OK, this is pretty natural.
+It's saying that your cache is
+
+at least as tall as it is wide
+where these are the blocks.
+
+OK, the number of blocks is it
+least the size of a block.
+
+That's a pretty reasonable
+assumption, and if you look at
+
+caches these days,
+they all satisfy this,
+
+at least for some epsilon.
+Pretty much universally,
+
+M is at least B^2 or so.
+OK, and in fact,
+
+if you think from our speed of
+light arguments from last time,
+
+B^2 or B^3 is actually the
+right thing to do.
+
+As you go out,
+I guess in 3-D,
+
+B^2 would be the surface area
+of the sphere out there.
+
+OK, so this is actually the
+natural thing of how much space
+
+you should have at a particular
+distance.
+
+Assuming we live in a constant
+dimensional space,
+
+that assumption would be true.
+This even allows going up to 42
+
+dimensions or whatever,
+OK, so a pretty reasonable
+
+assumption.
+Good.
+
+Now, we are going to achieve
+this bound.
+
+And what we are going to try to
+do is use an N to the epsilon
+
+way merge sort for some epsilon.
+And, if we assume that M is at
+
+least B^2, the epsilon will be
+one third, it turns out.
+
+So, we are going to do the
+cubed root of N way merge sort.
+
+I'll start by giving you and
+analyzing the sorting
+
+algorithms, assuming that we
+know how to do merge in a
+
+particular bound.
+OK, then we'll do the merge.
+
+The merge is the hard part.
+OK, so the merge,
+
+I'm going to give you the black
+box first of all.
+
+First of all,
+what does merge do?
+
+The K way merger is called the
+K funnel just because it looks
+
+like a funnel,
+which you'll see.
+
+So, a K funnel is a data
+structure, or is an algorithm,
+
+let's say, that looks like a
+data structure.
+
+And it merges K sorted lists.
+So, supposing you already have
+
+K lists, and they're sorted,
+and assuming that the lists are
+
+relatively long,
+so we need some additional
+
+assumptions for this black box
+to work, and we'll be able to
+
+get them as we sort.
+We want the total size of those
+
+lists.
+You add up all the elements,
+
+and all the lists should have
+size at least K^3 is the
+
+assumption.
+Then, it merges these lists
+
+using essentially the sorting
+bound.
+
+Actually, I should really say
+theta K^3.
+
+I also don't want to be too
+much bigger than K^3.
+
+Sorry about that.
+So, the number of memory
+
+transfers that this funnel
+merger uses is the sorting bound
+
+on K^3, so K^3 over B,
+log base M over B of K^3 over
+
+B, plus another K memory
+transfers.
+
+Now, K memory transfers is
+pretty reasonable.
+
+You've got to at least start
+reading each list,
+
+so you got to pay one memory
+transfer per list.
+
+OK, but our challenge in some
+sense will be getting rid of
+
+this plus K.
+This is how fast we can merge.
+
+We'll do that after.
+Now, assuming we have this,
+
+let me tell you how to sort.
+This is, eventually enough,
+
+called funnel sort.
+But in a certain sense,
+
+it's really cubed root of N way
+merge sort.
+
+OK, but we'll analyze it using
+this.
+
+OK, so funnel sort,
+we are going to define K to be
+
+N to the one third,
+and apply this merger.
+
+So, what do we do?
+It's just like here.
+
+We're going to divide our array
+into N to the one third.
+
+I mean, it they should be
+consecutive subarrays.
+
+I'll call them segments of the
+array.
+
+OK, for cache oblivious,
+it's really crucial how these
+
+things are laid out.
+We're going to cut and get
+
+consecutive chunks of the array,
+N to the one third of them.
+
+Then I'm going to recursively
+sort them, and then I'm going to
+
+merge.
+OK, and I'm going to merge
+
+using the K funnel,
+the N to the one third funnel
+
+because, now,
+why do I use one third?
+
+Well, because of this three.
+OK, in order to use the N to
+
+the one third funnel,
+I need to guarantee that the
+
+total number of elements that
+I'm merging is at least the cube
+
+of this number,
+K^3.
+
+The cube of this number is N.
+That's exactly how many
+
+elements I have in total.
+OK, so this is exactly what I
+
+can apply the funnel.
+It's going to require that I
+
+have it least K^3 elements,
+so that I can only use an N to
+
+the one third funnel.
+I mean, if it didn't have this
+
+requirement, I could just say,
+well, I have N lists each of
+
+size one.
+OK, that's clearly not going to
+
+work very well for our merger,
+I mean, intuitively because
+
+this plus K will kill you.
+That will be a plus M which is
+
+way too big.
+But we can use an N to the one
+
+third funnel,
+and this is how we would sort.
+
+So, let's analyze this
+algorithm.
+
+Hopefully, it will give the
+sorting bound if I did
+
+everything correctly.
+OK, this is pretty easy.
+
+The only thing that makes this
+messy as I have to write the
+
+sorting bound over and over.
+OK, this is the cost of the
+
+merge.
+So that's at the root.
+
+But K^3 in this case is N.
+So at the root of the
+
+recursion, let me write the
+recurrence first.
+
+Sorry.
+So, we have memory transfers on
+
+N elements is N to the one
+third.
+
+Let me get this right.
+Yeah, N to the one third
+
+recursions, each of size N to
+the two thirds,
+
+OK, plus this time,
+except K^3 is N.
+
+So, this is plus N over B,
+log base M over B of N over B
+
+plus cubed root of M.
+This is additive plus K term.
+
+OK, so that's my recurrence.
+The base case will be the
+
+usual.
+MT is some constant times M is
+
+order M over B.
+So, we sort of know what we
+
+should get here.
+Well, not really.
+
+So, in all the previous
+recurrence is,
+
+we have the same costs at every
+level, and that's where we got
+
+our log factor.
+Now, we already have a log
+
+factor, so we better not get
+another one.
+
+Right, this is the bound we
+want to prove.
+
+So, let me cheat here for a
+second.
+
+All right, indeed.
+You may already be wondering,
+
+this N to the one third seems
+rather large.
+
+If it's bigger than this,
+we are already in trouble at
+
+the very top level of the
+recursion.
+
+So, I claim that that's OK.
+Let's look at N to the one
+
+third.
+OK, there is a base case here
+
+which covers all values of N
+that are, at most,
+
+some constant times N.
+So, if I'm in this case,
+
+I know that N is at least as
+big as the cache up to some
+
+constant.
+OK, now the cache is it least
+
+B^2, we've assumed.
+And you can do this with B to
+
+the one plus epsilon if you're
+more careful.
+
+So, N is at least B^2,
+OK?
+
+And then, I always have trouble
+with these.
+
+So this means that N divided by
+B is omega root N.
+
+OK, there's many things you
+could say here,
+
+and only one of them is right.
+So, why?
+
+So this says that the square
+root of N is at least B,
+
+and so N divided by B is at
+most N divided by square root of
+
+N.
+So that's at least the square
+
+root of N if you check that all
+out.
+
+I'm going to go through this
+arithmetic relatively quickly
+
+because it's tedious but
+necessary.
+
+OK, the square root of N is
+strictly bigger than cubed root
+
+of N.
+OK, so that means that N over B
+
+is strictly bigger than N to the
+one third.
+
+Here we have N over B times
+something that's bigger than
+
+one.
+So this term definitely
+
+dominates this term in this
+case.
+
+As long as I'm not in the base
+case, I know N is at least order
+
+M.
+This term disappears from my
+
+recurrence.
+OK, so, good.
+
+That was a bit close.
+Now, what we want to get is
+
+this running time overall.
+So, the recursive cost better
+
+be small, better be less than
+the constant factor increase
+
+over this.
+So, let's write the recurrence.
+
+So, we get N over B,
+log base M over B,
+
+N over B at the root.
+Then, we split into a lot of
+
+subproblems, N to the one third
+subproblems here,
+
+and each one costs essentially
+this but with N replaced by N to
+
+the two thirds.
+OK, so N to the two thirds log
+
+base M over B,
+oops I forgot to divide it by B
+
+out here, of N to the two thirds
+divided by B.
+
+That's the cost of one of these
+nodes, N to the one third of
+
+them.
+What should they add up to?
+
+Well, there is N to the one
+third, and there's an N to the
+
+two thirds here that multiplies
+out to N.
+
+So, we get N over B.
+This looks bad.
+
+This looks the same.
+And we don't want to lose
+
+another log factor.
+But the good news is we have
+
+two thirds in here.
+OK, this is what we get in
+
+total at this level.
+It looks like the sorting
+
+bound, but in the log there's
+still a two thirds.
+
+Now, a power of two thirds and
+a log comes out as a multiple of
+
+two thirds.
+So, this is in fact two thirds
+
+times N over B,
+log base M over B of N over B,
+
+the sorting bound.
+So, this is two thirds of the
+
+sorting bound.
+And this is the sorting bound,
+
+one times the sorting bound.
+So, it's going down
+
+geometrically,
+yea!
+
+OK, I'm not going to prove it,
+but it's true.
+
+This went down by a factor of
+two thirds.
+
+The next one will also go down
+by a factor of two thirds by
+
+induction.
+OK, if you prove it at one
+
+level, it should be true at all
+of them.
+
+And I'm going to skip the
+details there.
+
+So, we could check the leaf
+level just to make sure.
+
+That's always a good sanity
+check.
+
+At the leaves,
+we know our cost is M over B.
+
+OK, and how many leaves are
+there?
+
+Just like before,
+in some sense,
+
+we have N/M leaves.
+OK, so in fact the total cost
+
+at the bottom is N over B.
+And it turns out that that's
+
+what you get.
+So, you essentially,
+
+it looks funny,
+because you'd think that this
+
+would actually be smaller than
+this at some intuitive level.
+
+It's not.
+In fact, what's happening is
+
+you have this N over B times
+this log thing,
+
+whatever the log thing is.
+We don't care too much.
+
+Let's just call it log.
+What you are taking at the next
+
+level is two thirds times that
+log.
+
+And at the next level,
+it's four ninths times that log
+
+and so on.
+So, it's geometrically
+
+decreasing until the log gets
+down to one.
+
+And then you stop the
+recursion.
+
+And that's what you get N over
+B here with no log.
+
+So, what you're doing is
+decreasing the log,
+
+not the N over B stuff.
+The two thirds should really be
+
+over here.
+In fact, the number of levels
+
+here is log, log N.
+It's the number of times you
+
+have to divide a log by three
+halves before you get down to
+
+one, OK?
+So, we don't actually need
+
+that.
+We don't care how many levels
+
+are because it's geometrically
+decreasing.
+
+It could be infinitely many
+levels.
+
+It's geometrically decreasing,
+and we get this as our running
+
+time.
+MT of N is the sorting bound
+
+for funnel sort.
+So, this is great.
+
+As long as we can get a funnel
+that merges this quickly,
+
+we get a sorting algorithm that
+sorts as fast as it possibly
+
+can.
+I didn't write that on the
+
+board that this is
+asymptotically optimal.
+
+Even if you knew what B and M
+were, this is the best that you
+
+could hope to do.
+And here, we are doing it no
+
+matter what, B and M are.
+Good.
+
+Get ready for the funnel.
+The funnel will be another
+
+recursion.
+So, this is a recursive
+
+algorithm in a recursive
+algorithm.
+
+It's another divide and
+conquer, kind of like the static
+
+search trees we saw at the
+beginning of this lecture.
+
+So, these all tie together.
+
+All right, the K funnel,
+so, I'm calling it K funnel
+
+because I want to think of it at
+some recursive level,
+
+not just N to the one third.
+OK, we're going to recursively
+
+use, in fact,
+the square root of K funnel.
+
+So, here's, and I need to
+achieve that bound.
+
+So, the recursion is like the
+static search tree,
+
+and a little bit hard to draw
+on one board,
+
+but here we go.
+So, we have a square root of K
+
+funnel.
+Recursively,
+
+we have a buffer up here.
+This is called the output
+
+buffer, and it has size K^3,
+and just for kicks,
+
+let's suppose it that filled up
+a little bit.
+
+And, we have some more buffers.
+And, let's suppose they've been
+
+filled up by different amounts.
+And each of these has size K to
+
+the three halves,
+of course.
+
+Halves, these are called
+buffers, let's say,
+
+with the intermediate buffers.
+And, then hanging off of them,
+
+we have more funnels,
+the square root of K funnel
+
+here, and a square root of K
+funnel here, one for each
+
+buffer, one for each child of
+this funnel.
+
+OK, and then hanging off of
+these funnels are the input
+
+arrays.
+
+OK, I'm not going to draw all K
+of them, but there are K input
+
+arrays, input lists let's call
+them down at the bottom.
+
+OK, so the idea is we are going
+to merge bottom-up in this
+
+picture.
+We start with our K input
+
+arrays of total size at least
+K^3.
+
+That's what we're assuming we
+have up here.
+
+We are clustering them into
+groups of size square root of K,
+
+so, the square root of K
+groups, throw each of them into
+
+a square root of K funnel that
+recursively merges those square
+
+root of K lists.
+The output of those funnels we
+
+are putting into a buffer to
+sort of accumulate what the
+
+answer should be.
+These buffers have besides
+
+exactly K to the three halves,
+which might not be perfect
+
+because we know that on average,
+there should be K to the three
+
+halves elements in each of these
+because there's K^3 total,
+
+and the square root of K
+groups.
+
+So, it should be K^3 divided by
+the square root of K,
+
+which is K to the three halves
+on average.
+
+But some of these will be
+bigger.
+
+Some of them will be smaller.
+I've drawn it here.
+
+Some of them had emptied a bit
+more depending on how you merge
+
+things.
+But on average,
+
+these will all fill at the same
+time.
+
+And then, we plug them into a
+square root of K funnel,
+
+and that we get the output of
+size K^3.
+
+So, that is roughly what we
+should have happen.
+
+OK, but in fact,
+some of these might fill first,
+
+and we have to do some merging
+in order to empty a buffer,
+
+make room for more stuff coming
+up.
+
+That's the picture.
+Now, before I actually tell you
+
+what the algorithm is,
+or analyze the algorithm,
+
+let's first just think about
+space, a very simple warm-up
+
+analysis.
+So, let's look at the space
+
+excluding the inputs and
+outputs, those buffers.
+
+OK, why do I want to exclude
+input and output buffers?
+
+Well, because I want to only
+count each buffer once,
+
+and this buffer is actually the
+input to this one and the output
+
+to this one.
+So, in order to recursively
+
+count all the buffers exactly
+once, I'm only going to count
+
+these middle buffers.
+And then separately,
+
+I'm going to have to think of
+the overall output and input
+
+buffers.
+But those are sort of given.
+
+I mean, I need K^3 for the
+output.
+
+I need K^3 for the input.
+So ignore those overall.
+
+And that if I count the middle
+buffers recursively,
+
+I'll get all the buffers.
+So, then we get a very simple
+
+recurrence for space.
+S of K is roughly square root
+
+of K plus one times S of square
+root of K plus order K^2,
+
+K^2 because we have the square
+root of K of these buffers,
+
+each of size K to the three
+halves.
+
+Work that out,
+does that sound right?
+
+That sounds an awful lot like
+K^3, but maybe,
+
+all right.
+Oh, no, that's right.
+
+It's K to the three halves
+times the square root of K,
+
+which is K to the three halves
+plus a half, which is K to the
+
+four halves, which is K^2.
+Phew, OK, good.
+
+I'm just bad with my arithmetic
+here.
+
+OK, so K^2 total buffering
+here.
+
+You add them up for each level,
+each recursion,
+
+and the plus one here is to
+take into account the top guy,
+
+the square root of K bottom
+guys, so the square root of K
+
+plus one.
+If this were,
+
+well, let me just draw the
+recurrence tree.
+
+There's many ways you could
+solve this recurrence.
+
+A natural one is instead of
+looking at K,
+
+you look at log K,
+because here at log K is
+
+getting divided by two.
+I just going to draw the
+
+recursion trees,
+so you can see the intuition.
+
+But if you are going to solve
+it, you should probably take the
+
+logs, substitute by log.
+So, we have the square root of
+
+K.
+plus one branching factor.
+
+And then, the problem is size
+square root of K,
+
+so this is going to be K,
+I believe, for each of these.
+
+This is square root of K
+squared is the cost of these
+
+levels.
+And, you keep going.
+
+I don't particularly care what
+the bottom looks like because at
+
+the top we have K^2.
+That we have K times root K
+
+plus one cost at the next level.
+This is K to the three halves
+
+plus K.
+OK, so we go from K^2 to K to
+
+the three halves plus K.
+This is a super-geometric.
+
+It's like an exponential
+geometric decrease.
+
+This is decreasing really fast.
+So, it's order K^2.
+
+That's my hand-waving argument.
+OK, so the cost is basically
+
+the size of the buffers at the
+top level, the total space.
+
+We're going to need this.
+It's actually theta K^2 because
+
+I have a theta K^2 here.
+We are going to be this in
+
+order to analyze the time.
+That's why it mentioned it.
+
+It's not just a good feeling
+that the space is not too big.
+
+In fact, the funnel is a lot
+smaller than a total input size.
+
+The input size is K^3.
+But that's not so crucial.
+
+What's crucial is that it's
+K^2, and we'll use that in the
+
+analysis.
+OK, naturally,
+
+this thing is laid out
+recursively.
+
+You recursively store the
+funnel, top funnel.
+
+Then, for example,
+you write out each buffer as a
+
+consecutive array,
+in this case.
+
+There's no recursion there.
+So just write them all out one
+
+by one.
+Don't interleave them or
+
+anything.
+Store them in order.
+
+And that, you write out
+recursively these funnels,
+
+the bottom funnels.
+OK, any way you do it
+
+recursively, as long as each
+funnel remains a consecutive
+
+chunk of memory,
+each buffer remains a
+
+consecutive chuck of memory,
+the time analysis that we are
+
+about to do will work.
+
+OK, let me actually give you
+the algorithm that we're
+
+analyzing.
+In order to make the funnel go,
+
+what we do is say,
+initially, all the buffers are
+
+empty.
+Everything is at the bottom.
+
+And what we are going to do is,
+say, fill the root buffer.
+
+Fill this one.
+And, that's a recursive
+
+algorithm, which I'll define in
+a second, how to fill a buffer.
+
+Once it's filled,
+that means everything has been
+
+pulled up, and then it's merged.
+OK, so that's how we get
+
+started.
+So, merge means to merge
+
+algorithm is fill the topmost
+buffer, the topmost output
+
+buffer.
+OK, and now,
+
+here's how you fill a buffer.
+So, in general,
+
+if you expand out this
+recursion all the way,
+
+in the base case,
+I didn't mention you sort of
+
+get a little node there.
+So, if you look at an arbitrary
+
+buffer in this picture that you
+want to fill,
+
+so this one's empty and you
+want to fill it,
+
+then immediately below it will
+be a vertex who has two
+
+children, two other buffers.
+OK, maybe they look like this.
+
+You have no idea how big they
+are, except they are the same
+
+size.
+It could be a lot smaller than
+
+this one, a lot bigger,
+we don't know.
+
+But in the end,
+you do get a binary structure
+
+out of this just like we did
+with the binary search tree at
+
+the beginning.
+So, how do we fill this buffer?
+
+Well, we just merge these two
+child buffers as long as we can.
+
+So, we merge the two children
+buffers as long as they are both
+
+non-empty.
+So, in general,
+
+the invariant will be that this
+buffer, let me write down a
+
+sentence.
+As long as a buffer is
+
+non-empty, or whatever is in
+that buffer, and hasn't been
+
+used already,
+it's a prefix of the merged
+
+output of the entire subtree
+beneath it.
+
+OK, so this is a partially
+merged subsequence of everything
+
+down here.
+This is a partially merged
+
+subsequence of everything down
+here.
+
+I can just merge element by
+element off the top,
+
+and that will give me outputs
+to put there until one of them
+
+gets emptied.
+And, we have no idea which one
+
+will empty first just because it
+depends on the order.
+
+OK, whenever one of them
+empties, we recursively fill it,
+
+and that's it.
+That's the algorithm.
+
+Whenever one empties --
+
+-- we recursively fill it.
+And at the base case at the
+
+leaves, there's sort of nothing
+to do.
+
+I believe you just sort of
+directly read from an input
+
+list.
+So, at the very bottom,
+
+if you have some note here
+that's trying to merge between
+
+these two, that's just a
+straightforward merge between
+
+two lists.
+We know how to do that with two
+
+parallel scans.
+So, in fact,
+
+we can merge the entire thing
+here and just spit it out to the
+
+buffer.
+Well, it depends how big the
+
+buffer is.
+We can only merge it until the
+
+buffer fills.
+Whenever a buffer is full,
+
+we stop and we pop up the
+recursive layers.
+
+OK, so we keep doing this merge
+until the buffer we are trying
+
+to fill fills,
+and that we stop,
+
+pop up.
+OK, that's the algorithm for
+
+merging.
+Now, we just have to analyze
+
+the algorithm.
+It's actually not too hard,
+
+but it's a pretty clever
+analysis.
+
+And, to top it off,
+it's an amortization,
+
+your favorite.
+OK, so we get one last practice
+
+at amortized analysis in the
+context of cache oblivious
+
+algorithms.
+So, this is going to be a bit
+
+sophisticated.
+We are going to combine all the
+
+ideas we've seen.
+The main analysis idea we've
+
+seen is that we are doing this
+recursion in the construction,
+
+and if we imagine,
+we take our K funnel,
+
+we split it in the middle
+level, make a whole bunch of
+
+square root of K funnels,
+and so on, and then we cut
+
+those in the middle level,
+get fourth root of K funnels,
+
+and so on, and so on,
+at some point the funnel we
+
+look at fits in cache.
+OK, before we said if it's in a
+
+block.
+Now, we're going to say that at
+
+some point, one of these funnels
+will fit in cache.
+
+Each of the funnels at that
+recursive level of detail will
+
+fit in cache.
+We are going to analyze that
+
+level.
+We'll call that level J.
+
+So, consider the first
+recursive level of detail,
+
+and I'll call it J,
+at which every J funnel we have
+
+fits, let's say,
+not only does it fit in cache,
+
+but four of them fit in cache.
+It fits in one quarter of the
+
+cache.
+OK, but we need to leave some
+
+cache extra for doing other
+things.
+
+But I want to make sure that
+the J funnel fits.
+
+OK, now what does that mean?
+Well, we've analyzed space.
+
+We know that the space of a J
+funnel is about J^2,
+
+some constant times J^2.
+We'll call it C times J^2.
+
+OK, so this is saying that C
+times J^2 is at most,
+
+M over 4, one quarter of the
+cache.
+
+OK, that means a J funnel that
+happens at the size sits in the
+
+quarter of the cache.
+OK, at some point in the
+
+recursion, we'll have this big
+tree of J funnels,
+
+with all sorts of buffers in
+between them,
+
+and each of the J funnels will
+fit.
+
+So, let's think about one of
+those J funnels.
+
+Suppose J is like the square
+root of K.
+
+So, this is the picture because
+otherwise I have to draw a
+
+bigger one.
+So, suppose this is a J funnel.
+
+It has a bunch of input
+buffers, has one output buffer.
+
+So, we just want to think about
+how the J funnel executes.
+
+And, for a long time,
+as long as these buffers are
+
+all full, this is just a merger.
+It's doing something
+
+recursively, but we don't really
+care.
+
+As soon as this whole thing
+swaps in, and actually,
+
+I should be drawing this,
+as soon as the funnel,
+
+the output buffer,
+and the input buffer swap in,
+
+in other words,
+you bring all those blocks in,
+
+you can just merge,
+and you can go on your merry
+
+way merging until something
+empties or you fill the output.
+
+So, let's analyze that.
+Suppose everything is in
+
+memory, because we know it fits.
+OK, well I have to be a little
+
+bit careful.
+The input buffers are actually
+
+pretty big in total size because
+the total size is K to the three
+
+halves here versus K to the one
+half.
+
+Actually, this is of size K.
+Let me draw a general picture.
+
+We have a J funnel,
+because otherwise the
+
+arithmetic is going to get
+messy.
+
+We have a J funnel.
+Its size is C times J^2,
+
+we're supposing.
+The number of inputs is J,
+
+and the size of them is pretty
+big.
+
+Where did we define that?
+We have a K funnel.
+
+The total input size is K^3.
+So, the total input size here
+
+would be J^3.
+We can't afford to put all that
+
+in cache.
+That's an extra factor of J.
+
+But, we can afford to one block
+per input.
+
+And for merging,
+that's all we need.
+
+I claim that I can fit the
+first block of each of these
+
+input arrays in cash at the same
+time along with the J funnel.
+
+And so, for that duration,
+as long as all of that is in
+
+cache, this thing can merge at
+full speed just like we were
+
+doing parallel scans.
+You use up all the blocks down
+
+here, and one of them empties.
+You go to the next block in the
+
+input buffer and so on,
+just like the normal merge
+
+analysis of parallel arrays,
+at this point we assume that
+
+everything here is fitting in
+cache.
+
+So, it's just like before.
+Of course, in fact,
+
+it's recursive but we are
+analyzing it at this level.
+
+OK, I need to prove that you
+can fit one block per input.
+
+It's not hard.
+It's just computation.
+
+And, it's basically the way
+that these funnels were designed
+
+was so that you could fit one
+block per input buffer.
+
+And, here's the argument.
+So, the claim is you can also
+
+fit one memory block in the
+cache per input buffer.
+
+So, this is in addition to one
+J funnel.
+
+You could also fit one block
+for each of its input buffers.
+
+OK, this is of the J funnel.
+It's not any funnel because
+
+bigger funnels are way too big.
+OK, so here's how we prove
+
+that.
+J^2 is at most a quarter M.
+
+That's what we assumed here,
+actually CJ2.
+
+I'm not going to bother with
+the C because that's going to
+
+make my life even harder.
+OK, I think this is even a
+
+weaker constraint.
+So, the size of our funnel
+
+proves about J^2.
+That's at most a quarter of the
+
+cache.
+That implies that J,
+
+if we take square roots of both
+sides, is at most a half square
+
+root of M.
+OK, also, we know that B is at
+
+most square root of M because M
+is at least B squared.
+
+So, we put these together,
+and we get J times B is at most
+
+a half M.
+OK, now I claim that what we
+
+are asking for here is J times B
+because in a J funnel,
+
+there are J input arrays.
+And so, if you want one block
+
+each, that costs a space of B
+each.
+
+So, for each input buffer we
+have one block of size B,
+
+and the claim is that that
+whole thing fits in half the
+
+cache.
+And, we've only used a quarter
+
+of the cache.
+So in total,
+
+we use three quarters of the
+cache and that's all we'll use.
+
+OK, so that's good news.
+We can also fit one more block
+
+to the output.
+Not too big a deal.
+
+So now, as long as this J
+funnel is running,
+
+if it's all in cache,
+all is well.
+
+What does that mean?
+Let me first analyze how long
+
+it takes for us to swap in this
+funnel.
+
+OK, so how long does it take
+for us to read all the stuff in
+
+a J funnel and one block per
+input buffer?
+
+That's what it would take to
+get started.
+
+So, this is swapping in a J
+funnel, which means reading the
+
+J funnel in its entirety,
+and reading one block per input
+
+buffer.
+OK, the cost of the swap in is
+
+pretty natural.
+The size of the buffer divided
+
+by B, because that's just sort
+of a linear scan to read it in,
+
+and we need to read one block
+per buffer.
+
+These buffers could be all over
+the place because they're pretty
+
+big.
+So, let's say we pay one memory
+
+transfer for each input buffer
+just to get started to read the
+
+first block.
+OK, the claim is,
+
+and here we need to do some
+more arithmetic.
+
+This is, at most,
+J^3 over B.
+
+OK, why is it,
+at most, J^3 over B?
+
+Well, this was the first level
+at which things fit in cache.
+
+That means the next level
+bigger, which is J^2,
+
+which has size J^4,
+should be bigger than cache.
+
+Otherwise we would have stopped
+then.
+
+OK, so this is just more
+arithmetic.
+
+You can either believe me or
+follow the arithmetic.
+
+We know that J^4 is at least M.
+So, this means that,
+
+and we know that M is at least
+B^2.
+
+Therefore, J^2,
+instead of J^4,
+
+we take the square root of both
+sides, J^2 is at least B.
+
+OK, so certainly J^2 over B is
+at most J^3 over B.
+
+But also J is at most J^3 over
+B because J^2 is at least B.
+
+Hopefully that should be clear.
+That's just algebra.
+
+OK, so we're not going to use
+this bound because that's kind
+
+of complicated.
+We're just going to say,
+
+well, it causes J^3 over B to
+get swapped in.
+
+Now, why is J^3 over B a good
+thing?
+
+Because we know the total size
+of inputs to the J funnel is
+
+J^3.
+So, to read all of the inputs
+
+to the J funnel takes J^3 over
+B.
+
+So, this is really just a
+linear extra cost to get the
+
+whole thing swapped in.
+It sounds good.
+
+To do the merging would also
+cost J^3 over B.
+
+So, the swap-in causes J^3 over
+B to merge all these J^3
+
+elements.
+If they were all there in the
+
+inputs, it would take J^3 over B
+because once everything is
+
+there, you're merging at full
+speed, one per B items per
+
+memory transfer on average.
+OK, the problem is you're going
+
+to swap out, which you may have
+imagined.
+
+As soon as one of your input
+buffers empties,
+
+let's say this one's almost
+gone, as soon as it empties,
+
+you're going to totally
+obliterate that funnel and swap
+
+in this one in order to merge
+all the stuff there,
+
+and fill this buffer back up.
+This is where the amortization
+
+comes in.
+And this is where the log
+
+factor comes in because so far
+it we've basically paid a linear
+
+cost.
+We are almost done.
+
+So, we charge,
+sorry, I'm jumping ahead of
+
+myself.
+So, when an input buffer
+
+empties, we swap out.
+And we recursively fill that
+
+buffer.
+OK, I'm going to assume that
+
+there is absolutely no reuse,
+that is recursive filling
+
+completely swapped everything
+out and I have to start from
+
+scratch for this funnel.
+So, when that happens,
+
+I feel this buffer,
+and then I come back and I say,
+
+well, I go swap it back in.
+So when the recursive call
+
+finishes, I swap back in.
+OK, so I recursively fill,
+
+and then I swap back in.
+And, at the swapping back in
+
+costs J^3 over B.
+I'm going to charge that cost
+
+to the elements that just got
+filled.
+
+So this is an amortized
+charging argument.
+
+How many are there?
+It's the only question.
+
+It turns out,
+things are really good,
+
+like here, for the square root
+of K funnel, we have each buffer
+
+has size K to the three halves.
+OK, so this is a bit
+
+complicated.
+But I claim that the number of
+
+elements here that fill the
+buffer is J^3.
+
+So, if you have a J funnel,
+each of the input buffers has
+
+size J^3.
+It should be correct if you
+
+work it out.
+So, we're charging this J^3
+
+over B cost to J^3 elements,
+which sounds like you're
+
+charging, essentially,
+one over B to each element.
+
+Sounds great.
+That means that,
+
+so you're thinking overall,
+I mean, there are N elements,
+
+and to each one you charge a
+one over B cost.
+
+That sounds like the total
+running time is N over B.
+
+It's a bit too fast for
+sorting.
+
+We lost the log factor.
+So, what's going on is that
+
+we're actually charging to one
+element more than once.
+
+And, this is something that we
+don't normally do,
+
+never done it in this class,
+but you can do it as long as
+
+you bound that the number of
+times you charge.
+
+OK, and wherever you do a
+charging argument,
+
+you say, well,
+this doesn't happen too many
+
+times because whenever this
+happens, this happens.
+
+You should say,
+you should prove that the thing
+
+that you're charging to,
+Ito charged to that think very
+
+many times.
+So here, I have a quantifiable
+
+thing that I'm charging to:
+elements.
+
+So, I'm saying that for each
+element that happened to come
+
+into this buffer,
+I'm going to charge it a one
+
+over B cost.
+How many times does one element
+
+get charged?
+Well, each time it gets charged
+
+to, it's moved into a new
+buffer.
+
+How many buffers could it move
+through?
+
+Well, it's just going up all
+the time.
+
+Merging always goes up.
+So, we start here and you go to
+
+the next buffer,
+and you go to the next buffer.
+
+The number of buffers you visit
+is the right log,
+
+it turns out.
+I don't know which log that is.
+
+So, the number of charges of a
+one over B cost to each element
+
+is the number of buffers it
+visits, and that's a log factor.
+
+That's where we get an extra
+log factor on the running time.
+
+It is, this is the number of
+levels of J funnels that you can
+
+visit.
+So, it's log K divided by log
+
+J, if I got it right.
+OK, and we're almost done.
+
+Let's wrap up a bit.
+Just a little bit more
+
+arithmetic, unfortunately.
+So, log K over log J.
+
+Now, J^2 is like M,
+roughly.
+
+It might be square root of M.
+But, log J is basically log M.
+
+There's some constants there.
+So, the number of charges here
+
+is theta, log K over log M.
+So, now this is a bit,
+
+we haven't seen this in
+amortization necessarily,
+
+but we just need to count up
+total amount of charging.
+
+All work gets charged to
+somebody, except we didn't
+
+charge the very initial swapping
+in to everybody.
+
+But, every time we do some
+swapping in, we charge it to
+
+someone.
+So, how many times does
+
+everything it charged?
+Well, there are N elements.
+
+Each gets charged to a one over
+B cost, and the number of times
+
+it gets charged is its log K
+over log M.
+
+So therefore,
+the total cost is number of
+
+elements times a one over B
+times this log thing.
+
+OK, it's actually plus K.
+We forgot about a plus K,
+
+but that's just to get started
+in the very beginning,
+
+and start on all of the input
+lists.
+
+OK, this is an amortization
+analysis to prove this bound.
+
+Sorry, what was N here?
+I assumed that I started out
+
+with K cubed elements at the
+bottom.
+
+The total number of elements in
+the bottom was K^3 theta.
+
+OK, so I should have written
+K^3 not M.
+
+This should be almost the same
+as this, OK, but not quite.
+
+This is log based M of K,
+and if you do a little bit of
+
+arithmetic, this should be K^3
+over B times log base M over B
+
+of K over B plus K.
+That's what I want to prove.
+
+Actually there's a K^3 here
+instead of a K,
+
+but that's just a factor of
+three.
+
+And this follows because we
+assume we are not in the base
+
+case.
+So, K is at least M,
+
+which is at least B^2,
+and therefore K over B is omega
+
+square root of K.
+OK, so K over B is basically
+
+the same as K when you put it in
+a log.
+
+So here we have log base M.
+I turned it into log base M
+
+over B.
+That's even worse.
+
+It doesn't matter.
+And, I have log of K.
+
+I replaced it with K over B,
+but K over B is basically
+
+square root of K.
+So in a log,
+
+that's just a factor of a half.
+So that concludes the analysis
+
+of the funnel.
+We get this crazy running time,
+
+which is basically sorting
+bound plus a little bit.
+
+We plug that into our funnel
+sort, and we get,
+
+magically, optimal cache
+oblivious sorting just in time.
+
+Tuesday is the final.
+The final is more in the style
+
+of quiz one, so not too much
+creativity, mostly mastery of
+
+material.
+It covers everything.
+
+You don't have to worry about
+the details of funnel sort,
+
+but everything else.
+So it's like quiz one but for
+
+the entire class.
+It's three hours long,
+
+and good luck.
+It's been a pleasure having
+
+you, all the students.
+I'm sure Charles agrees,
+
+so thanks everyone.
+It was a lot of fun.
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